{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "首先说明一下,这一节其实与EM没多大关系,只是想对GMM的分类作一个实现并推导它与LogisticRegression之间的关系\n", "### 一.分类原理\n", "分类实现的原理非常简单,对每一个类训练一个高斯模型模型(如果你喜欢,多个也是可以的,这里你就可以使用用EM算法了,将前面的GMMCluster简单封装一下就可以)即可,然后每个类的权重由其样本所占比例确定" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os\n", "os.chdir('../')\n", "import numpy as np\n", "%matplotlib inline\n", "from ml_models.em import GMMCluster\n", "\n", "\"\"\"\n", "利用GMMCluster实现分类,代码封装到ml_models.em\n", "\"\"\"\n", "\n", "class GMMClassifier(object):\n", " def __init__(self, cluster_each_class=1, n_iter=100, tol=1e-3, shr_cov=False):\n", " \"\"\"\n", " :param cluster_each_class:每个类需要几个高斯模型去拟合,默认1个\n", " :param n_iter:迭代次数\n", " :param tol: -log likehold增益" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#训练模型并可视化\n", "gmm = GMMClassifier(n_iter=100)\n", "gmm.fit(X, y)\n", "utils.plot_decision_function(X, y, gmm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "代码里面添加了一个`shr_cov`的超参,如果`shr_cov=True`表示所有的模型都会共享同一个协方差矩阵,我们接下来看看会发生什么" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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4DKqwYQQOn0F3Zxsv/+8p3D4JXVAYLns3XpcDkBBEJX5RRXtbCyaz5UfjKC7Mx+5XMvbi23pLMV1JI/ls6euMmzJjwOr700aM4gPhRaw+O9CznuDxe2gVGxiVcepKUfsLkzGAP/z6QUori2ltbyY6Iq5POmnj1nWEE4tGcWjtJFIXR05bJZW15cRHJw5G2IPOQVGX69VPDFnY+xlJknjwd3dQ09BIUNI4EAXy9uTyt3tv57H/vYHBaPrB65cteYcuQcu0G/6Ezy/hsHVRsOpDHO1NQBqu7g7aqovxKfW8+dKz2CU1erebrqYaQpMyERUKdn3+Gm3l+VhTJ6DSB4Ag4GxvxNbWiCUoGOhpzrEvL4eujjbiklKIjusrIHtycwiITe8VdQCVzgBqA1989DazzrlwQNwfzYFWEjJmULhtFZ3dUQiSSKvYwNQZM4iPSer3+50KBEEgKS6ZpLjD/W6cDgcqQXXY+QpBidvtOlUhnlYcXCyVRf3EkYX9BKkqL6Fwby4arY6ssZMIsAQCkLdjK9U1NaRcdDtqfY+IB6eMY/+yF1n95adccOkvjjqmJElsXLeKyOmX0NLSgtvlQhAErOmTqNu7AbXOSOn2bzBGDsOr0lNSvBONORhVaAJdVaVU5W5i5Lm/QBAkWgq3ozJYCIhOwW1rpzF3LQZLMPvz84iOS+DZf/0dr8qI0mDBvuQDRowYyTW33NVb8aLX6/G2tPTG5uhoYffKd/B5fewsrmLb3//EuPETufy6X/6o0djxMix9ElfNm0N23la8Xg9ZGdeSEJM0KDtfB5pRWWP5ZN/HhEsxvTuOG7tqqXfUsG7DKvx+P2nDBs6v6HREXiw9eWRhP04kSeKjt15m8+bNGKNT8LudfPLhu9xw291kZI1l59YNBMQN7xV1AJXehDk+gz252T8o7H6/n+7OTjq6ulEZzGgtJnweD4LdhqOjmdLt3xA7+wo0Rgv2tkbMCSOp3bIMU3g8wSljaSrYRunWlei0OpTWaOxNVTTv24xCqSFyxCQ0SgVV5aWsWrEMbfxowlN7NiT5fV72rf6ALeu/YersntzvhKmz+PaRB3DED0dntlKw/hNMsSMIiEwkMiYWv9fLrtXvk7RxLROnz+n39xwRFsX58y5ma84G3nz3ZdraW0hISGbheZcQF53Q7/cbKBxOO1tzNlJeUUpYWDhTxs3AHBDY++8TRk9la/Ymcks2ESSF0dzZSK23gjhjMs157fwv7ynOPmcB5827aBCf4tRxMAUjL5aeHPLi6XFSuGcXW7OzSTvveuLGziFh8nnETLuY1194GrfLhcUajN/r4ftOL36vmyBr8A+OrVAoEETorC1FqdYiCCJKtQZXewNuWycKYxAep4Pu5lp8Xg/G4EhM0Sm0VRbgddrQWaNoLNlN6vCRqP0ufN2t6AKsqLRaWkt309VQgUaroa6unrCUQz7tokJJaPoEtmz8tvdYVGw8l1x+DWWr36FgxRt0NlRhikwgJCwcAQGFUkVI2gQ2b1zXn6+XvLyqXm+YVRuW8947bxPYFk6mYgqO/R6eeOYhqusq+/WeA0V7ZxsP/uuPfP3xChp2tLD5y8387Z9/oKq2ovcclVLFXTffx2XXXI0Y76dN2ciM8HMZGTSOWEMSWdrJfLni0zN6k9axIufV+w9Z2I+THds2YUnIRKE6VIdsColCabJSXLiXmfMX4Gooo7uhEr/Pi9/vx9ZcS1dlPuf//Oiz9Y72Vp57/CG6urppzFtH/sdP0Zi/hfrctbTv3waCgFKjQxcYgtYcjKhU4bJ3IYoK2opyKPziZWq2foHf6yFleAYdzQ2EZM4mcf7VJJ59PQGJWT2in5F1IG/eN60hiAp8Pm+fY5NnzuUfT7zAhQsWYAm0Ehkdi/o79deiUoXH7e6fF3uA2tJGADxeD8u+Wspw7RismjA0Ci0xhkTCfLF89fVn/XrPgWLZio/RtBsYbhhLtKFn92mYO453P1rc5zylUsm4zIlEhEaSbBhJgPrQ4rZGocUsBFFcvv9Uh39KySuoA2RR7y/kVMxxIghiH4vbXqQeqQy0hnD9LXfw5qvPowjqqUN2N1dy5TU3ERUbf8Qx/X4/zz3+EC5DBGkX3IpfqaGrtpi67cuJzpiIITAUY1Qy3XWluG2dKHUmVHoztuYqmvdnY4qIJ3ryRfg9LgRXF198+hFhqWMxh0bgaO8RSktEPCRl0NXRTmBAAM1le1Fp9AgKBaaQKJqLcpg/fcphsen0eqbOPptvli+jo6aUwOhhPY8r+Wku3sW8qRP747X2ITMtgubWRiQPGPR9F5ut6lAqKs8MkduVt4NU7eg+xyJ1sWyqWIHT5TzMCMxoNOGWDv824saFTqcf0FgHG+WCxYQFyt45/cWQEnZJksjN3szG9WtwOR2MHjuBKbPPOq5t+D/GmAmTyXnxOUKHZaI8MHvtbKzGZ2tlWFqPOdH0eecyYvR49u7ajgSMGDWOQGvIUccsLy6ktdNG6tTpuJwOmpoascQNx9PVCgJ0NVSRPHcqgaGRlK96m4DYdBAVtOzbgs/lxDp8Ol5HFyqlgpDYJJpDY/GJakJCw3uaZUg91gWOiiDs3d1MmjaDN15+Dk1gBCDh7mgiNS2daXOO3B9VFEWuuel2/vfUP+moKUZlDMRWW0yo2cC0uT/cU/V4+G4axmQ0I4k+nD4HWoWu95x2TxthYWfG7lONRoPH1rf23id5EUXxiLYMk8fPYO26bwjzRGFSmZEkiTpnJQqjSGpi+qkK+5RzMAVzQcx5gxzJ0GFICfvS9xazeetWrGkTUVo0rFy/iZztm7nr9w/221b41IwspkyazIavXsUQOQzJ48LRUM7Nt/+mz3b9QGsw0+aee0xjtrU2ozEHIwgCWp0ea3AI7W2tICppLc4mOTkZn60Nc0wasXorzpYavC4HKpUabUAgSpUKg15PoDUEAQiKHkZV7gYk/zk9FSsC+DwuuutKCQpZyIfvvcnon92OqDXh83lxNNfQWbAR6bCVgUMkpQ7nzw89Qfam9bS1tzFs+mWMHD0BhbL/foVqSxt7hV2j1jBrxnw2r95IijYTncJAi7uRGkq4c+5v++2eA8m0KbNZ+8UqMlTjUQiKnv629n2MHTsRlfLw38eI0EiuvvJG3n7/VdQOHV486C167rrx3h57giHIw+71LEROwfQ3Q+a3paWpgW/XriLt/JtRqntm6JaoRIpWv0de9mbGTp7xIyMcG4IgsOjK65k0fTaFe/PQaLVkjv0tRtMPf42027rZnbMVu82GwWhCpVITFZdAaHgkMfFJ2Bor8Xk9KJQq9HoDOr0Be9FWLrvlLuKGpfD4Q3/B7fOhsESiC4mmPmc1oenjaKsoxGNrRx0U1Js197udBBq0FK35gKCkLPxeL61F2UyZNp3iwny8Ci1NxbvRB4YQmjQSS2Am9ppC8nN3MHrC1KM+gznQytwFA7sL8Lve6xedewlqlZpv1i7HZXMSHBzKjRfdRnJi2g+McPowf8Z5VFdXsD1vDWYxCJvUSUR8FJdffHTzr/GjJpORksnuwl0EBgQyLCGt38tJTyfkvqUDw5AR9vKS/RjC4npFHXpE2BSVQmHB3n4T9oNExsQfc8Pp4oK9vPD0YygCQmmsKsHv92MOjUZ0dTJ6zDiuuvF2xo2fRO6aDwnLmIxSraWpeBcGwc2YydPRaLTcfe+f+PCd18hZ9hkqUxCBiVkYEzJxOlxUrv8I3cyF+IPCaK8uwl1XxL0PPEpJYT47tm9GqVRx3i+uISI6jr/edweSORKfxkhDZTHVuzeRdd61KDQGnHZ7v76j4yEv7/Cm4QpRwflnLeK8eQtxe9xo1JoBqWVvaWumqKwAvc5AevKII86mTwSlUsnN19xJXWMttfVVWINCiItK+MFn2LB1LR9//h4+lx+/4GXKpBn8/MKrDovJ4bRTWVOOUW8kMjzmjKvxzyuoQ7lgsdy3dIAYMm/VZDLj6T7cB8Vta8ccM3h1zz6vl1ee+w/h48+jdt92zIlZhI6YhqurlSCzhb3bv2TDqq+44vpbiV+7km/XrcbmcjJh7ATmnntR7/pAbGIy9/zpYe7/9U1U19bj6WqlcddqnK11mMyB+Kr34GwpZWRqOrNuvBa9wcjE6XOY/J2erS88+ShB6ZNRhsSjDbBiTR5D456NlGxbib+jgWHpvxys19QnDfN9RFEckI5DkiTx+colrPzmSyxY8eDGr/dw5y33ERsV32/3iQiNPCZXyrx9O/nww3dIV4/BpDfj9rnYtXEXgiD2meWv3rCCpZ9/gB4jLr+DkMgwbrv+1wRZrP0W80BzcLFUzqsPDENG2Ielj0CvhLp92YSnjUEQRDrqK7FV7WPSTTcMWlzlJfuRVDqMwRG01ZSSfH7PTk2lRo/D5SQsYyob1q1m5lnnM3XOOUz93gJmS1MDq5d/TknxfswWC21tbUy68h466spAEAmKTqK7pR5XyTZ+99d/surLpTz2tz/gcrsICDBz0c8uZ9yUmfj9fvbk5jDiZ3fR3taKs6sVhVqPKSaV4s+f59Krrjtl7fiOxqlugbeveA+rv/6asdoZqBU9C+H1jmr+9+qTPHT/E6c8BbJy1TJixWRMqh4fHrVCQ6oui41b1nHxgsvQqDUUluTz6SdLyNJMRqc0IEkS5TWFvLj4aX5/999Oabwnyj9qcliUJC+WDiRDRthFUeRX99zPq//7D/mfbUep1qDEx023/RpraNigxSVJfhAE/D4fCCLC9xbBlBotLpfziNc21tfy+D/uRxc9HPOwSTQ119LVbaOjvpyQxEPtwQRRgd/n4+svlrJq7TpiZ16Kzmylq6mGd95+A41Ox4hR4xEEaGmoxeMHv+RHcNlQ+FxYQ0K44JKj19gPNEdKw5wKtmzbQBgxvaIOEK6LprarjLKqkiN6uwwkrW2txCn7rh9oFFoEl4DdYUOj1rB+42oiiEWn7Ok9KwgC8fpUtlWvoa6x9rT3q/9HTQ6LZqyU8+oDzJARdoCQsAjue+CfNDXU4Xa5iIiO7dduP16vh63rV7F18wYAJk6exsQZc1H+QE42LikVnN04OprRmQLprC4iIDoFr8uB2Wqlce8mRo0Zd8Rrl3/2Efq4TKIzexY0A0KjcfkE9n+7jOD49N6a+saC7cwcP4lVyz8ndtbl6AKCgJ6NUxGjZrPs4/fJ2bqZ5sYGmj97kcCkLMJGTscv+WjZvYXZc84e1BztD6VhBhK324VCOPy/gAIlHm//brw6FpISh1GXU4dRdWghvsPdikavIcDUM4vv6u5C853yT+gRd42oxe6wndJ4T4RFM1bK9eqngCG33C4IAqHhkUTHJfSrqEuSxCvPPs5ny1fiCx+OL3w4ny1fyav/fQJJOnqZoEql4rpb76Jm8+fo9AZqNi+jcuOnOBtKqcteibKrjrPO/9kRr91fkI/1QDclr9eL2+0iMnkEXmc3RWuXULlzPftXvkWYUcW4KTPo6Oigy+GiqbEeu92G1+fFI6rZvSubnOJqks67mcSzrwOg6IuXqN7wMd21JYwYdeQPllPJqU7DAIwZNZ5Gqbqn1v8AnZ523EoniTHDBvz+Hq+HotICyiqL8fv9nDf/Ypo1tZR1F9Dl6aDWXkmhZxc/u/CK3o5KmSOzaPLW9vmd6/Z04hGdxETEDnjMJ8PBvqVyCmbgOekZuyAIMcAbQDjgB16UJOmpkx33dKN0/z6Ky8pIOee63ibPlsgECr96jbKiAhJTjr6BJG3EKP762DPs2r6JlsYsbHY7fr9EYlIm46bMRKPVHfE6syUQe0cL3S4PTocDQaHA6+hGIYrQ3UJHczXpIzK59JqbeePFZ3A4ndg629BaQmlubkLy+Wgu3I42MIKAlHGISg1agwm9JQSvrZ2w+DQkt42WxnoYPnJA3tvpzNjMiWzL2cKufZsI8Fpx+x20q5u58drb+lgnfJfW9mZ2F+xCFEQy00f3MfQ6HnLzd/D62y+i9Kjx40NtUnPbDXfz+9/8la+++YyS0iKCrSH8cu5dDE8+9LOZNmE2m7duYG99NsFiBE6/g0ahissuu/qoMZ8OHMyry31LTw39kYrxAvdIkpQjCIIJ2CEIwteSJOX3w9inDWXFBejCEnpFHUAUFegoC1fAAAAgAElEQVTDEykt2veDwg5gCjAz/QgbljxuN9+u+oqc7G2o1WqmTJ9N5tiJCILAnLPO44X/PUvohAVoTEH4PG4a927C45MIyJiBMSCQquJcHvnzPfjVRlJnXER5zjeEZc0CpQZbcw2d5XsJTp+AWmvA43bh8/lQqdQYwxNAAFd7I8FhhyxSJUli24bVfLPiS5rqazAHBJCUkk7WuEkMzxrX7z1Pv7vb9IeQJIniskL2lxZgMBgZnTGOto4WvD4vcdGJJ1SiqFAouebSm3jsvw9SUrEXjUKLQhKpqqlk9Ijxh6Wn1m76mo+WvkugFIIkSHwgvM1Vl13HpLHTj+u+za1NvLz4OdLFMZh1PWmz+q5qnn7hXzzy5ye5/opbj3qtVqPj3jv/wubs9ezJzyM4IJwrJ19JQuzAf8M4UQ7m1WUr3lPHSQu7JEl1QN2BP3cJgrAPiAKGlLCbAiz47J2HHffZOwgwn9iszef18tzj/6Cuw4E1KQu7x8Wbby5mSlEBi664jtjEZBztjZQsfw1NgBWPoxufy86wBb9ENBgxBkdgDI4g94vFKBVqwlPHoNToqN69hZbKQgzh8cSMmUF7XQVKjRa3oxuP045SGYC9uRpJoyYswEBSao/ftyRJfLn0PVavXUO3zY4PNW5MlK9bz6pVKwkPC+eu+x44qufN8VJVXsK7Lz2No7MWg97EvElzOWvmeYc1cvb5fbzy1nPs270Xsy8Yp9/GC91PYTEGYVSb8Km9XP+LXzIybfRR7nR03vrwVRRNauaHLEIURNw+J2u/WUVkRBTjsyb3ntfYXM+Spe8xSj0VnbLHt8Xm7eLt918nLXkEloBA8ot2s27DKmy2bjJHjGL6pDnotId7vGzbuYkgbyhmY1DvsXBdNE2OGvbuz2NUxg+nxrQaLbOnnsXs7/RNPZ05mFeXrXhPHf26eCoIQjwwGtjan+OeDmSOncTS99+iqXQvwQnDAWguy8fX3kDm2BMzwtq9cxu1LR0kz7sCQehZ7giKSebbZS8RHhnFu6+9gNcPCfOvRVAocHc00V1fjiCKeDyHPEgCopJo3p8DQHB8OsHx6Wz/6L8Epk4gMiGFjppSGvPWE5g0CkdHE82719FdU8T4+edxydU3Ifn9LFv6Hmu+/oq6mipUOhOmuHSisub0ODjau2je8y12t42Xn/03f3706ZMuBWysr+Xpx/6OOnYsGbMX4bR1sCJnNe3d7VxxwdV9zt2Ru4X9eQWM1k9DRKSmrgqNz0hVdzFTIifT6Wnnpdf+ywO/fxRr4A9bI3+XLlsX+fvymKCfg3jg/asVWmLFYaxZ93UfYd+5N5tAf2ivqAMYlCbMLiu79+3E5XLx+WcfE0kCGoWetWVr2LxtA7+7+wG0mr6pNpu9G6Wk5vsoJTV2x+BtEhsI8pMeRRBFOa9+ium3xVNBEIzAEuDXkiQdNrUVBOEWQRCyBUHI7ug487yldXo9t//2fjyVueR/9jz5n72ApzKXO+79E9qjOO/tztnKfx7+Cw/cdwdvv/IcTQ11ff49f3cuktpAU8keXLaeV6ZUa9GFxvLmi89iTh6DITwenTUcXVAEKmMg7u42BJUGUfxOmsBtx2drp7Oxp2xQkiT0lmCa925ApVKSec4vUEk+ipY9T9PWT5iQFs/Tr7zHDbffgynAzEdvv8qG7TnEzLyUlItuxy9JGKNSQZIQAIVagyVpFLa2RrqcHqorSk/6fa5ZsQxVZDrWhJEoVGoMlhASpl7Itzs20mXr6nPutuzNhAuxKAQFTpcDwS8QrAxH6VfS4WnFog7C4g1h285NxxWDy+VARIlC7Du/0Si02GzdfY5JfglBOrxySEDA4XLw6RcfMVI7iWhDAiHaCIYbxuJscLNp+/rDrklPzqBNbOqzaOvxu2mXmkk5Q+wSjoWD5l43jrh0kCP56dEvM3ZBEFT0iPrbkiR9fKRzJEl6EXgRYFhqxtHLSE5jmhrq8HjcOLraUSqUZM6YeVRbgXVff8Fnn31C2MjpBCdaKa4sIO/v93PfA49gDQmjvGQ/G9asxKu14HC5KNq8nNisqcRkTsXW2oguJAa9ORi1rg53dztKrQF1QDAg0FqwjZjMyUiSRFt1Ma37dxBgtpD94TMoVVr0BiMREZFkjBnFnmUvoQsMxdPezMw587n65jv7uF12d3WyZdN60hbcgqBU0d5ViahQotIa8bodKFRq/F4vokKJ5PcjKpV4PZ4jPvPxUF1dicacgua7PVU1OjSmQJpbGjAZDtn1igoFfnq84v1+H8IBVxxJkHr/rJLUdH/vA+HHCLIEozfpaeyuo9PTSqO9rkfkFTBt0jRWb1jBpi3r8fq8pKSk0yzWEeNNwuGzARIaUU+b0ITFZEGPEZ3i0Ae8IAgEKyLYu283c6ad3ee+w1MyGZY+jNx9mwkTovFJPhqoYs7sswgOCj2uZzhdeW7vHmbJfUsHjf6oihGAV4B9kiQ9cfIhnZ7szd3BW4tfxZwwEl9rBx4Jlnz0Hps3rOW+v/6ToOBD/yE9bjfLln5AwqzL0Zl7tnnrA0Oo8vtZ9dVnLLryOl546jFip12MU9SgNljwe92Ur34Xr8sBjk704SMJjE6mZMtKFAJIPg8+t4vo0bOoWPchVc2l1Gt0KAU/glqHIiSeIFM4Pp8PW10JQUFBXHvr3ZQW7qO8pJDk4ZkkDEs97LnaWppQGywoD4i93mBAHxpLe8UeLAkj8Hlc+Fw2umv2ExAajeC2E5Nw8gt1UdEx7CyrQRd/aBOQ1+3E1dV2mLhNHDeFd/IXE+6PQqPW4qOFFn8DkihhVgXhl/y0iU2kJx8yKOvoaqe7u5NgaxiiIKBSHZ76EEWRyxf9gn8+9SAWTwhhYjRuyUWtWM6m7G9R2bXEqJIQBZHd3+7Gr/Cysm4Jer8JQRCwCV0svODnRIXH4PI7kCSpz4Kr02cnxHz4hiFRFPnldXeRnbeVHTnbUKtVnD9+ARmpWSf9Xk8XZl24jLOSRvz4iTIDQn/M2KcCVwO7BUHYdeDYHyVJ+rIfxj5tWP75xwQmj6F853qiJp6PITSmp0olbz3/ffwh7n/oP7155+bGegSVrlfUD2KJHkZx4UaKC/YiaQyExKfhcNhpaW4ERAwRibQX53DzHb9l8asvII6aQeLE+ZSuX4I+PAGf14PUVs2iy65i7jkX4na7eOqRv9LSWYfU1Y3OGom9pRZBoWbr1k0U33o1okaPNsDKV198xpRpM1h4+XV9KlusIWF4bB14HDZUOgNB1hC8WdPI/+p1bLXF6ENicXc24e5owmwycs0d9/RLZUxE7BjWfv0vGgKthMSl4+xupzpnFVNHTcZk7LuBZfSI8eRP2M32beuxSMG0a1pocNaQYhhJnaOKRqmaxLREhqdk4nDaeeP9l8jbvQu73Y7N2YVeZ2BYYiqXLbqa5IS+H25Ot4tIYyxx3jR8Pi9arZY4ZSJrqpcxO2IBxgPb+w0KEytqPmK0aQoWpRUQcCnsbN22iQvm/4zQyHDKagpJ0KciCAJdng4axGqumtJ3veAgCoWSiaOnMnH00d00z1QOpmBiDbKwDxb9URWzge/3WRuCNDbUIQaqCIjLwBAaA4BCpSYgYSSd+WspLy7sLXkMMFvwOLrxul29zTgA7G1NBIeE4vG4EZU9x3U6PVExcT0t5jrDSEwKJ2vcJKbuz2fTyjfRRw7D63HSXrEXndmKwWRm355c5p23kEBrCBVlxQRmziIweSyiqCCIsTTu2UjjrtW0dHQx8dLrENQ6mhtq+XLFx3z95ackDUtBpdUTGGRl5txzmDn3LDZ8u5SoMXPQmgKRbK2EWYOYc/YCaqvKcdhVJKXOZ/KMuX2+mZwMjg6RK8+5mdzCNeRlr8CgNzJv8lzOnXn+YeeKosjVl97ErGnzKSrbh15rQKVSsWPXdtxuNz8bcxnjsyYhiiJvvv8yVXk16J0mBKeSdGEsPocPqn08+/y/+d3/PUBkWHTv2PuL9hGiiMAacGjRtdvWhQUrnZ529EoTNm8XDc5aAqVQAsRAAkwHW9eZabbVsWtvNr+68Te88PrTbKtag1pU41V4uPCCRdQ31tLR2cbwlMx+c408nZH7lp4eDClLgYEkJi6BgrJqjLHDe4/5vB6UCgVqUyCd31kQNpgCGDN+Ivu2Lid2wlmoNDq6mmtp3reZS+/6LVGx8TjbnsHR0YLObEVAQKlQYKsuJOuqnhneoiuuZ2TWOF557glCUsaQMG5Oz0YmSaJ863K+XPo+i668Hp/PR0B0Wp8UgDl+OI25awgIT6C9oYqWhlr8fj+BiZm0V+yjrMWOWuHAbozi2Scf49LLruL8s89i9dfL6epoIzktg2v/+Hei4wbWFfOsGRM5a8bEw1IYRyMmMo6YyLjev4/NnNTn37u6O8nbs4uRmklsavua0eI0FIISt9+N6IYQRRSr16/gF5fc2HuNxRJIiVTWZxxRFHFgo9PdQV7Ldrw+Dy7JiZWwA/1iD6Hwq7A7bFgCAvndXQ/Q2FyPzd5N7p4cPvn8QywE4xHc+LRu7rzlXuKiB89pdKDJK6hDKefVTwtkYT9Gzrvo5+z52+9prwBzXAZ+nxePvROT0UBrUxVxiX0Noy675hY+fPsVNn30FF6fD71Ox5U33MawtJ6a8cuuuoH333mdgNgMRLWWrqp9pA1LYsTo8UDP4ltiajpOp5OMifNAEGku7ameMYREs3XTemLjE1CqlLht7QhKFQq1Fr/Xg7uzDYVGh721nqINVejDE9AGBNNRU4Szo4mkeVdRuvJ1gmKSMYfFsuSDt3j4yZeYedbhs+WB4PumX/3lU9Nt60ItaPBILrSCvtcHRiGIeL0eTEoLtXU1fa6ZMn4mq1Yvp9nVgFUdioREg78Gt8pFQdsudBiIEhLw4qWWMko68hljmoLX66Hb0U29p4rI8ENVH6HB4RQU72Xt6m/6uEY2OGr43yv/4aE//+ewOv2hgty39PRBFvZjJDE5nf/7w9954uE/U7HuA4ISM9GqVdTnr2XGrHmH9TSVJD8tjY1ozcFog6PwdrawYtlSUoaPxGwJYuL02cQlJbN90zqcDgcZ828mbcQofF4vH7z9Mjt3bMdus9FUXw3rPqe7oRytJQx1QBBd+dnYGipZ+sVy1OYQ2op2EJg6AVFUICiUdJbvRqFQ4nV0Ez7+HMzxGQiCiCkunfrslbSW5KI2BeHsasccHouo1lNfU0lMfNKpe5/f221aXVfJ+5+8QWHxPgJMZi4+/zKmjpt5XGMGW0NBJYFPwinZ8UhuVIIaj+RBp9XS4qknPa5vOWFwUAi33fwbXn/nRcq68vFJPmLi4hjpz2Lvjt1kMB4lKgRRwEoYeZ7NqOrV+Nw+mqlDVIu8+OrT3HDNbYwe0fOhvGX7BkKlQ66Rkt9PgBBIWVsBRWUFpCVlnMSbOz2R+5aeXsjCfhykZGTy5Mvv8u3q5ezcsR2tX8uCy65gzMRpfc5rbqznxScfpbSymrDU0UQNn4DGaKZq51o+fPMVbrrzXgDMliDmnnsRekOPyDXW1/LAb2/Dow5AHxpHe8MujNFpNJfkYU0djzV1PBqDCVPsCOqyv0ITGM6oyQvYu+Jdajd9gj4oHFtjFaLfzdhxE9i2dSv6sFi8bieS14Pk9WBNn0RT7hr8Ljt6sxW/z4vb0Y3B2FNeWFddSXVFKZYgK0mpGT+6EamlsYEtG1bT3NSI1+WiraMdhVLJpCkzmDBt9hGN2GpLG1k45tA3nMqacv700D3gEAgjGk+rh2f++y9Kzi3kmktvOeafj0qp4mcLr+CDD94iQGNhnzOHSCEBlajCpeimXdvEnOl397nG4/XQZeskPXUECoWC8aMnk5qUzm//djthYnQfe1wLVoI8oRR79hKjS2SEcSxh2mi6vB289tbzpD4wHL3OgNvj7q2Nt9m7aW1rRpQU2PzdPP3CY/zmtj8etoh7JvOm5QPGIqdgTidkYT9OtDo98xcsYv6CRb3HqitK+eCNlygt2Y9SqcLhdKKOSCZ0zDzsrfXkfPYymedeTeSIyexe+l+a6uv48O1XKSzYCxLEJyZxxXW/5OVn/oXdC0nzfkbJyjeInXkpCp2R8q/fICh1PG57F363A7/XQ3jWLBr3rCcmaxpZF1xPzZ4tOMt3ce9D/yIuKYXuzg6Kim5Dr1LS3d2JqNKgNQXS2d2Bs72JuKypKDRaqneuZdiwZMyWIBY//xS7cndiDIvD1dGExaDl9nvuxxx45M48+/PzeOGZxzHEpNFQshdJoSYoKZPAwCCWfv45hfm7ue623/zoO337o1fBITBaMR3lgfRJuD+GL1d8zkXnXIo5wPIjIxxi6viZWIOCWbVmOfvLCqh3lKFSqRieOpIbFtxEcNChb1Yut4snn3+EpopmDC4zNl83a9d/za03/prIiEjKyir7pIkkyY9P8hKpi2Fc8CF/mACVBaPdwt79eYzPmszorHG8n/cWoZ4IWlub0QkGHNjxi36GCZk89/ITPPKXpwakK9Sp5mH3ehZaS2VRP82Qhf0k+eLj93jntedRBQQhCgq8ti5CRk5HHxqL3hKCOSYVld5EefZq0uf8HL8k8ezjf0cMTSZj4e0IokhjUS7/fvAP2Gw2TBGJdDdWorNGoQuOwmPrRBDEnhy6RodC8iGoVPi9Xjhg3SoIAkZrODpbGAnJPamGAEsg8QlJOFqqiRqWSUdbG46uNlr3bULpd+PtqCf/0+dJTEzk2l/+hg2rl5NfWsHwC27p2YwkSdTkbuDtV5/nV/fcf9hz+/1+3nr1eSLHn4vf76Oxopj4uVfisXWh0utInnMZu798harykj4pniM11SgqKSCcGJSCEgkJj9+DUlJh9JvZtTebmZPnHXbND5GWlHFM6Y6N29bSUtZKSHcMgl/ARBB6l4nHn/kHv73rz2RvfYgOXxQG0Ywk+WmXWrCru4hQxuCTfIiI3xP+np/HmJET2D58C1t3rMHgtyAI0CzUkRE0ljBtZI8nTGEuYzNPzIridOGTnCIWXrJJNvc6DRlyfuynktVffsI7i19CExyN2hiEHwm3vQtjxDCQwO2wIQGWuOG011VQX5hDeHgELtREZ05FoVQhigrCU8cgGIPxAa7OZiSfF1HZs6FGqTOi1BvpqixAEERUKhUKhZKm/C2ExPeUV0p+P02F2UyY1DcldPVNt+OqzKVyw6fYKnfTvXc1Y4an8N83lnLbbXdy/4P/5M77HsBoCmDj+jWEZUxGPNDhSRAEIkZMYn/BXuzf214PPS37bE4X5sgEOhsqMUT2bORRanTY7TZEhRJDWALlxYV9rjtSUw293oAPLz7JR7enA7fXic/nxef3snrDSrxe72H3lySJ9s42HM6je6t0dXdSUlFER+eRLSxydm1H7zCj8CvQiQY0opYQRQQan45v1n3JDdfeSoluD/vZRbFiN/XmMkZmjmZ/525WVi1hQ/1Kmpx1dHs66RLbe+11FaKCW6+7m5HjRmLXdGAIMDIlfB6R+h6/dKWkxHmUrllnEimXLGF4RLhs7nUaIs/YTxC3y8Xbi18kcvKFmOOGIwgi9tZ6Spe/ir25uqfW3efG1dWGx9aBz+3AWZHHlBmz2bq35LDx9KEx2Jsqe8S9tRFbfSluWyeiQok1dSKNuatpL80lNC4FZ1MFzroK3EYdFTvW4GgsJyE6iqlz+m5dDw2P5C//fJa9u7bT3tZCbPzFJCT3lEYaTH2rF9weNwZVXz9vUaEAUXFECwG1Wo3f40aS/Kh0Rjx1B31q/IgHZrFeewfGAPNh136/qcb55yxi8esvYfIEYcCEUlDR6W/HI7rprrOxYdsaZk2Z33t+zu5tvPzGf+ls70RQCIzOGset192NXteTD/f7/Xzw6Vts2LQWvWjE7u9m/NhJXPnz6/vUkms0GhpdrQQpDtXmHyy9LC4p5N7b/8KE0VPIL9qNKIoUlRSya9NOxptm4en2YPN0s61hPUaLkZuu+RVGgwm/309pZRGdXR2MHz2F4vxiknTpKISetQaXz0kbzaQnn9kLqA+717MQZFE/TZGF/QTJz9uByhyKOTrlgBiAPiicwKQsGnatIW7WJURGx+Gy2yjZsZzJk6dw3W3/R211BWvWrkGS/L2OjpIk4WyqZMFFP+PrFV9gayrH1d1G0WfPYknIQlQq8bnsRFnNTB+ZREzC2SQmp7E7Zxud7W3EJZ3HsLQRRywbVKlUjBo/5UefZ/TYCWzfl4Mh6NzecZrL9hEeFobJfHiO2xxoJSExido9WwhNHkXlrg10VBehMgUSZLHQUJyL4OhgxKjxvdccrbfpObMuYO++XDZv7ulB6pO82MROxoZOQRQUbN76ba+w7y/dx7+e/DtJ/hEME0bh8bkp3rafRzoe4NZr72JPYS4FxXsp3VPGONNMVKIar99D/vYcPjctYdGCQ7ngaZNn8Z/N/yRMikYtHChL9FehVmpRqnrSLAEmM5PGTMPpcvDmOy8zWjcdjVGLx+jG4bSjcAsEppuYMGYKre0tPPPiv+ho7kCHgXZfC0aLiV0dGwmWIvHjo1Go4bxzLiLI0teF0u6w0dhcT6DFitl07GsKg8HD7vUsTN8k59VPY2RhP0EcdjtaUyBueyd+f49Ln0KtQ2204Oxoombte/jiU3G0NzJ50hQuu/pmFEolCcPSSIiNoWT9J4RlTEIUlTQUbCdQp+SsCy9h6uyzWf/Nl3z52RKEgHA8js6embHfT3NrKwgiGVljAZgwbXa/Pc/8BRezJ/fPlKz7CENYPK7OFlwNpdxxz/1HrTO/5uY7ee6Jhyhdux9LcChV6z9Abwqky2gk2BrEHb/9Eyr1IY+WH+pteu1lt1BSVEykFI1SoSJMF4VKVNPsaujTBu7ND14h3BdLmKpn96gKNcn+kWwtWMXfH7ufMCGG5vZGOmmjQVlDtCEBpagiWTuCdRtWcfF5l/U+z6iMcSSkJZKdv5ZgKQIXDiSFnyB9MCMnjOzz3B2d7ShRo1H0LHiqVOoe/xm3RENbOQCvvvUcikYNY/TTEQQBj99Dbvtmpsyeit1mR6VUcfnYKxgWf6gixu/38+nyD1m9diVaQYfDb2fcmIlcdckNp+1O1YXpm2QfmNMcWdhPkLikFNoqHseYPB61safRhsfeRUthNiMzR3Pzr39PV0c7oeGRfapKBEHglrt+x+qvPmXzplX4fT4mTJjM/AUXo1SqMAda8Xp9BCWPRRWegibAiqhQ4Gitp3rTp6xYvozMMeOP6ip5ougNRu79y6PkZm+mtHg/wckjGT/1TgIsgZTu38fqFV/Q0tJE0rAU5pxzAUHBoViCrPz+wX9TXlxIZ0cbMfFJeDweFAoFwaHhR/xAOFpvU2tgCGHh4aibtL25aEmSqPWUM3/8oRRTbW01kWJin2sFQUDj1xIvpBNjSkDXUY4giOS3ZROqjUCt0KJR6HDaHfj9PhTfWUf4w90P8sT/HqKstASTaEFS+rHGBbLo/L6z0UBzEH7Ri8Nr6y2BBGh1NxEbm0BrezMVFeVM0M/pfW6VqCJGkURlRQU3XXM7uXt3UFFdhskQQFhIz3vYsG0NG1atZ7RuGhqFFq/fw77snSw1vM+lF/7ieH+MA05+0qMY9RrZB+Y0Rxb2E6SuugKtIYDG7BWYk0aBoKCjLBeF5OXSa28hPDKG8MiYI16rUqs5+6JLOPuiS/B5vdTXVuOw23rr2fP35GGIHYNXpenJcwO6oHAEhRJNcCy7c7b3u7ADqDUaxk+dxfips3qP7dy2kTdffwlr2iT0iQnsri4h+2+/594/P4I1NAxRFH+0LSAcPQ1zEEEQuP6qW3nyf4/Sbm9C7dPSoWglJjmmT1WMxRJIW1czoUT1HrP7bDhxYNX2lDJqtTp8Tj9mgmhy1ROlj6fBUU1CXBI19VUsW7GU8opSQoLDOHf+Bfzh7gcpqyqhvrGW0OCw/2fvvAOrqLI//pl5vScvvTcIEFpCCb2IVCkiiGDvdXVtK+rPVXftde1iQbEiKh2UIoj0TiCEUBJI7+0leb3N748nwRhAFFjL5vNf5t25c2de3rl3zj3ne0hJSG0zKSmVKsaNnsTqb1YQL0/F4bVS46rEoWrmuhE3YLNbcbs81DtqEUURvd6AUqFCISopqSnkn0/ej8kfgiiJLBa/ZuzoCYwfdQlr1q0kSdG55U1ALiqIVSSxdv1KJoycjPYMygb+tzjuV5/R4ZJfbNvO70u7Yf+NVJQWE5mWid4cQdXR/Uh+P0k9BmCvr6C6ooxOXX9ZgnXfrq3M++QDfKIcj8tBQlwC199+NwajkTpbIzKlHolA1IvX7cLzYwTIOcrABwLl6bZvDmS/duuZQfde/VqSivx+P/O/+IS4AZMwhgdcH8aIOEpEGauWLeCKG+/4Vdf6pdqm8TGJPPXIf8jK2YGl0UJSQgqdU1onSU2ZOIM3Zr2IyqsiXBaDW3KR789BJzOgVQT6DzIFU+mqwOVz0eS24JIOUSsvY9rAq3jp9aeJ9iXSUZVOU0kD781+i6uuvJ7MjIEk/0Ld0DEXTMTtcTN3/kfgEpAEEOwS737yGkqZmmarhXqpDoNowmarIDg4hHJ/EVXWSgYYR2L4USnS7XOyavU3dE9Lx2ptJuHHqkxuv4t9dduxOOvwST5m/uvvTJ44jZFD2tbK/W9z3K/e7oL5c9Bu2H8jYRFReLL2Y04fgjk+FQi4DvIKsgkJ/+W43vKSQj7+4B3iB1+CITQaye+nbP8WXvzXQ/gkiaKCH1AYzJhT+xKU3IPanM0ojaGU5e5EOTjznNzDlh9WM//LuZiSeyJXacieN4/EDeu49e4HkcnlNDbU4XC5Woz6cULiO3N4969TZf55tump0Gq0DOo7/JSfD+wzlKqp5Sz65msqXMUgSEQlxuBqduHyOVHJ1IFi3WY9LpsNfbKG+NgEbhpyKwuWfkG0L5E4XSCuXivXoXZrmL/kC4wGE3kSaxwAACAASURBVC63i5SEjuh/UuTjpzRbm/jmu0X43D5ixGQiZXF48ZB/IAevwk3f0OHsq9tGqBSFCjV5dfsxxRqJFGJbjDoEyu+F+qPYvW8HnTp2oTKnjERdR7LrdiA65XSnP5LSh0kRzPIli4kMi6Jb5/Rf9bzPNe2bpX8u2g37byS97wCWL/qKsv1biOzcJ2CYc7ZgUsvPaLW+ef1aTMnpGEIDhRgEUUQXGkX2jjV0GXkZfQZNpbIwj6p966nc/R1KQxAyAeJ6DGLFsoUMGjH2rHTR7TYr8+d9SsrIq1AbAnsEER3TObJmLtl7tpOROQiNVofk9eBxOVD8pG6no6keU9CZF/D+JTfMr0EQBKaMv5yxIy6moqoUkzGIUHM4365ZwopVSwn2h+EX/DTK6rjr1n+0SgIqLDpKZ1XvVv3JBDlFJcd47523UMvUNEsWLpk0vU3VI0tTA0+88DCOGicRxBEtJeLxutHK9XQigyzPBozKIAZGjqTUWoDT50AhyhjYfyhZ6/ec4m4kJl00jRfynsDRZKXGUUkPYQAewUVYcARquYYYdzJr16+mW+d06i21bNr+A9XVlSQldWBA7yEtIZ7nk9yU51Ao203Fn4n2BKXfiEqt4Z6H/02E3EnOwjfIXfI28UY50668/qQJPT/H0lCPSt86xrskeyvhPYdjiEzEFBRCUGQ8sQMnodBoSek1jN6X3EZK/zGg0lNSmH9W4y/IO4Q6OKrFqENgcjEldiU7azcQkE/o028gxTtW4/O4AHA2W6jav5ELx4xv1Z/X62H7xrW8/Z9neP/1F8jevb1VNMsvuWHOeNzF+Xz29Qd8/MW7VNaUt4QGXjTyYh598BmGX3IBCRlx6HQ6Pvj0bZ599XEO5R8AICQkjGaPpaUvSZLYUb2eBCmV3trBdFX3padyEEuWzOdo4ZFW11297hu0ViNqdAQThgIlKtTYvTZkyNBIeqyeRnRyA52CetDDnIlapaV753SahAasnhNlgN1+F7VCJRnd+xIVHs0j9z9JQu845HIZap2KyIjolgLYGpmWpiYLx4ryeOyZmexYtYP6bCvfL17Lky89guUUyVfniuPiXtd2vvS8Xqedc0u7YT8LQsIiuPWeh/jPe58xaerlHDqQzfvvvsVj//gbn77/Bm6X65Tndk7rRlNpXqtj9oZqVAYzSlUgploUZWhMoShUWsI69EBtCEKSJHweJ0rl2emMKFUqfG5Hm+M+txON5sTq/NKrbqRTXDgHl73HkZVzKFj7GRPGT6BnnwEtbfx+P++//gILly6jWRtNrczMJ598xIK5c4CAG+ZcsGHbWl554zmKtpViPehm6ZeL+M+sZ/B43ACEh0YAAgf2HCDW3pGusr7U5NXy7CuPsXX3RsaNmkih7xBN7oAxrHSU4vV5SDR1bNm40Mi0hPtj2bxjfatr5x7MJlqTgErUYJOakZAQkSFI4JKc2GnG7gvsgUiSRLH9KObwYFKTu3D1jBvJ8e7gkHUvh5uzyXJs4sKRY0iMC7iEQs1hXD/jdkIiQlEYFK3K+FV7yoiMiubfzz+EpaaBYssxKmwlpKjTUNRrWPTNl+fk2Z6Mtw/kAO3iXn9G2t+vzgE5WTv5dsU3JF94JWpDMD6Pi4PbVrJg7hwuv/62k56TOWg4G9d9x7HNyzAndcPjsOF1NCO4rbitjTSUHsXr8+GUfgyd+3EFV5OfTZBOR0x84lmNOTk1DaXkprYgl9CkQPEQl7URy9G9ZE5+uKWdSqXm2lvvZkpTI82NDYSER7Yqhg1wcH8WBSXlpI6+uqUQhTm+E5u/eZ/w6B6AcMowxzPF4bTz9aK59FD2RysPrP6jpDj2F29nx94tDOo7HJ/fxzcrF9FFlUGVo4xjjYcJIZJgfySz3n2Fq668kctmXMXi5V/htDlx+Z0YdSZMxtZuJYWoxOFoPenp9Qac9Q5SQ7qxrXotGklHMKG4cVFJMRqZngPWXTTKanH7nRjCDPzt+vsRBIHMjIF0TO5MVs5OvF4v3Tr3bFXFCUAulzN96tV8PncOke54NDI9dd5KnHorWft2EeVIIlqWiB8/JY6jbClfQ7wsibXrl2J1ljBl7K3ERMWf1TP+Oe11S/+8tBv2c8D3q78lssfQFreGTKEivu8odnzzPlMuvzZQ+ehnqNQa7v2/J9m0diX79u7GpNMz48prmT/vU0qzfsAU3wWvy4GlYD9KmYzCLcvwOppRSh7uOE3S0Jkik8m49e6HeOfVZ2nI3xMozFFTxuRpl5OYktqmvcFownASeQCAvIM56KI7tqouJFeq0EcmU16ST6/IjLMaK0BByVG0GFqMOgT87aFCNPv2ZzGo73DsdhsupwuUcKzxEN3F/igFFX7RT6g/kqXLF/DYg8/y/ONvYLU1gyDwzyfvxeZtRicPbJhKkkSNVM7Q7tNbXX/EsDF88tEHdBJ7EkdHyikgj2z8+IkS4wkjBndEE1ddcR06jY7EuJRW31GwycyIQa399j8nM2MgIeYwftj0HQ319WR2ysThdHBgfS5q0QACyJARLSVgESrQh9nJiNFx9bRGXp/9JP+49TW0Gu1ZP2tor1v6Z6fdsJ8DGi0NhHb42apPrUWQKbDbbCc17AAarY5RE6cyauJUAIqP5aFetoTYvhfhF2TIZXJi0vpQs2sFE0aPICg4hI5durfROPf5fFRXlKHR6ggyn1xi92TEJiTx7xff5ujhXJxOBympXdpoyJwJeoMRn7PtBqnX2YzN4obTBAl5vB52Z2/nUPEhgnQmBmYM/dGl0hqtWotHcrUpo+eWXETozYE2Gi1KlZIS2zHMRLTIBPgkL1qVDrMUTs7hLEYMGovREJikLptyNV/N/4wwZzRKQU0tFUR3iG6jvJjRrS9VF1Xw9eK5uPEgAcFCKKnynihFFWXeAhRKBd06ndg4r62vxtLUQHRE7BlvcqYkdCQl4UT00Iefv41WNKDWaHE5HChRI4qgE/UUOou4b3IY4y4MY/ueEnZnb2VIvwvP6Dqno71u6Z+fdsN+DujYOY2jxYfRBp3Q+m6qLkWrUWEKNp9xP3t2bCEktTexia3DAq2F+9FotHTu1jbkLXv3duZ9MhuPJOB1OUjp0JFrbg5kjJ4MSZIoLTpGdUUZYZHRxCWmkNq1xxmP8WT07j+EFcsW0VTVBWNEHJIkUVuQC/ZGIqNTT+mGcbqc/OeT56jVuTCkJ+CpL2LNnMe5beJtbcL74mOSMJgNlNYWEKtNQhAE7F4bVUIxl/e/AgCZTM7Y0RP58qtP0UuB+/f6PbhxEmaMoMFbhSi0nhQH9xtOfGwCW3ZuxG6zMqLbBWR07YsoihzMy6HeUktcdALxMUmMu/BivH4PC7+aj8KrpKOsBwqUNPkbKOUoF6VNAgJuow8+e5vDhw6ikemwS1bGXDieCaOn/Oo3reSkVPKyVpAW3IsaXxU2ZzPgo8ZfyWWjgrns4sCs2SFJJPdQ3a/q+2Qs3pNHanvd0j897Yb9HDBmwhReevIRSrxeTLEdsFuqqTu4jauvu/kXKxD9FL/fd9L2giji9/nbHC8vKeSj2W8TN/BijOGx+H1eyrI38f4bL3LfP59uY0RcTgez33iJY0WFaEOisdeVkxgfzy1/n3nKt4ozITgklJvuuIdPZr9NpVyF3+dFr1IwauINuG2nDsncsON76kL8pF5/UctYG7sm8NGcOTyf+h8Acg7t5eCRAxj0Bi6/9Dq+mP8Re+o3okSFTWjm0ksub5VYNGroRbhcTj7/8iOCvKEYlEZCg8LxybxY/LX0SOvVagw+vw+3x01G9z4kx3dAoVBiaWrg1Xeew1pjReXXUuUoQ6lTMHzwSNI690Bn1GL0mMmxBSJ/5KIcpV7JmOETAfh8/hyqDtaQqbsAUZDh8jlZ990aIiKiyEz/ZUG2n9K/9yDW/rCCvNr9RAUn4LE7OWLdz4xLzTz3eGABIEkSm3d46NE5+Rd6Oz1Ple1hyrTV7frqfwHaDfs5ICwiipmPP8v3K5dxNH8b4aFhXH7Pg2eUav9TevTqx5atrxLRqTdyZcCNYLfU4qgpOemqetO67zAlp7ckEIkyObHpQzm4/H0qSouIjkvE7/djqa9FrdGycsnXlDW56DLhZgRBRJL8FGz5hmXz53LpVTee1TPo0qMXT/3nHUoKjyKTy4mJT2L10qzThjlm5e8hdFynVhOQKSmKMg2UlBWxZMXXFB8pJlgKx4OTlbLl3HTtHZiMQdiddpLiUtCoW/uUBUFg1LDxNDTWsW7DGsIUkVj81TR66rhi+vWYgwKuqrKKYj75ajZ7s3ejQYdea0BhlHPdlbeyaes6xGoV3VRdqaoqx+gPo8CRy4ZVP7Bl20b6DRjIzm3biJen4PP7aJTXcsnFlxESHIrdYSdr3y4ytRe0vB2oZGriZB35fv3qVoa9rqE2UOyjrpYOKan0TR/YpqqSWqVh5t8fZ+W6Zezdtxu1WUOcEI2PBvYfbEKhEJm/rB5LYzTdzzKJacrQ1YxO6dbuV/8L0G7YzxEhYRFMu/qms+ojpVMaAwYMYMvKOehiOyP5PNhKD3HFtTe31CT9KQ0N9agNrf3RgiCi0gfR1GihpmobX30+B4fLjc/jwtbcSM8pd7XIBQuCSEz6MLau/visDTuATC4nsUPrWp6ni4ZRKdU0O1qHhEp+Pz6nh9y8bMqOlJGhHdRi+C3uej7+4n2e/9cbp1Q+LCjO5433XkLl0hKtTKDKXUaXjmn848r/I+jH6Jfq2iqef/0J6qrq6EJvgsQQXHYnEj7e/+hNXG4X6eIgKqvKkflkqGUa4qWOFHkPE+/tQGVFOQ/e/xh7c/cgCgLp3QLx6ABOlwOZJEMmtP5pqWUa6ppLW/7OO3aIN997mWBPGBpBz+E9y1jzw0pm3vUYup9Nhga9kWkTr2TaxCspLD3Glws/ZfHSYhYurics3MiIwZO45cpJLeJmv4X2zdK/Fu2G/Q+EIAhMveIG+vYfwoF9e1AolWTcehMhYW03EwFSO6Xx3eZtLeGKEKja5KivwufzMevV5xB0ZlzWRty2JrxuF9U1VcToDC2GUa5U4XG722xKni1nkm06tMdQPl7zBcGd4lFo1UiSRMXG/UTrIzian0eEGNtqTEFKM54mD599PZuI8Ch69cgkMiy65XOf38esD18l3pNKmDYwoXT0d2Pf0a2UVhRj1Js4dPQAX8z/CF+9RBBmQmSBZ6tBi91uxSAGU2HZj1VmxevzoECJW/IgyER8ko8oTTybClYQGR7N+JOEFwYZg9Gb9DTYajCrThTwqHKV0rVP4K1LkiQ+mTebRKkL4frAOGNJ4mD1Xr5b/y2Tx1120udVXVvJK289S4w3heGmidQ0VXOs/ADrN6+nd89BbUIof46lqYEN21ZSUX0Qoz6SQX3HER+T1F6M+i9Ie4LSH5DYxBRS07oTERWN8jQFj/sPvRCNp5ljW7+lsbKYmoJcjn4/j9EXTeTT99/EpzKhjeuCufsw9DGpKPQmGsuOUlVe1qIhX3k4i649e51To36cX8o2zejWlyHx/ch98iuOzlnDoZcX499YzC1Tb0epVOL1ty6Jl9uQRZ2ljmPbCtn+zQ6efuFR1m9d2/J5QXE+fjuEqU+8JShEJRHEsm3nJt7/9A1mv/s2pUdLEV1yBJ+s5TkIgoiAiMfhRS4osGJBFERAAD9UeIuI1Mbi8jtRKdWIYutN2OOIosgV064jz7+fQtthapwVHLbtw25oZOyFgc3VeksdjfUWwlStfdnRyniy9u465fP6fuNqQjxRhMoiqK6uROaUkyr1pLy4nKdf+ieFpcdOeW5tfQ1vzHmQ2Jh13HWzlSEDcvh0wePMWrqc3u3FqP9ytK/Y/2BUV5Yz6z/PYPP4UWgN2GvLGD/pUkaOn9ymrUar5b5/Ps2GNd+yL2sHer2BcddcT0hYBF9/OZeE0dfj9bhQGUMJSkjj2KqPaMjPwtNUi6e+A9gt+BsrmPLwE+f8Pk5XVOM4giBw6ZgZjOg3koLioxh7mkhJTEUURQb0G8qcnHeJ8AcKbjS4ayltLqC7PJP4oCQA7N5k5i+aS3q33pgMQfh8gQLTba8jo6q6gvryBjK0g8hx7cZj9VLjL8fptaNV6pGQ8EpeqjyldA5Kp9iaj8avRyVpsNOMEwfd9X3Jd+QwZNgFp5wIfX4f0ZFx3H3HTDbvWE9tTQ19O/Zl2ICRLSGWSoUSHz78+JFxYoJw+92o1aeeyMvKSzDKgmiw1KNEjUIMZKiaCCbYE8HCZfO47/b/O+m5azct4rJJItfNCEx6vXuY6JisYeYbH9A5YtJpv6d2/ny0G/Y/EJIk8d7rLyCP7UanToHoDbe9mRUr5hKflExqWtsNVJ3ewLjJ0xk3eToet5vs3dtY/MUcVEYzXrcLUa5EABBETIlpuCw1qEQJoeowF46ZSN9Bw07qvz8bVixbw7qlX7LKWoM5KJSxoyYyOHP4KY2hOSi0Tam47p3TGTx8GOvWf0cQIVTYSwkWwogKO6HDrpXrMLrN5B7JZkDvoSTHd8CjcNHorsekDISZ+iQf1f4SgoXgHzXcA5WNin1HMRFMrrSbKE88kiBhUdUgkwtEaGKI0sRxpHk/1Y5yPF43GkHLPtdmeqb3YvK4aSe9jx17tvD1ks9x2V34BT8DM4dw160PtNkPMOiNdErtQuHhwyTruiAIAl6/hxJvPlMGn7xvgPi4RHILDqJwazHIApOEV/Jgl6xkaAew99iWU55bWJrNvbe1LrmX2ssGbg+dxF6nOKudPyvthv0PRGnRMSxWG51TT2RqKrUGgjv2YcuG709q2I/T2FDHK88+jkumAW0wXp+f0k0LiegzGsWPK2dXUwPGkAhEZxPjRo1n4PDR5/wejh05yLefvEOyryMxhnSabY0s/OpLnE4Ho4ZddMb9CILA1AmXM2zgheQXHmHfgd1UZFW30lEBkPAj+9EtolAoue7KW5n98VsEW8OQSwoaZDV06dkVhVxBRWkNhxr3UW4tQo0GO1ac2Gn016PT6lCpVOCFTdWrkPnlBImhGKQgLGINCWmJ3HXjA4Saw042XA7m5fDZ3Dl0VqRj0ppx+5xkb81G4lOuvPSGNu2vnXEzb7z/EnsqN6IRdDRK9QwYMJgBvYe2tHE47bjcLkyGIARB4ILBo9mybT0yNKj8ajy4KZKOEK2Lxyt5MBlOnhkMoNeaqKyxkxAXCGutkzXgs/pRoUenOzvdoXb+eLQb9j8QLqcTuUrbZmWrUGlwOCynOCvAwnmfgDmRDhlDkSQJTVRHavOysOTvQaEx4G6qw1F1DHNQEKLTQu/+Q87LPaxa8DVR7gTCtDHIRDlByhC6CL34dvUSMjMGsHn3RvKLjxFuDmNYvwtaoklORag5nFBzOPExiTyb/ThxvmTUskCIY5O7AaussSWZafuezSz9dgF2pw2Pwk2Xzl2ZPuJyUpO7cPhoLrP2vEZlYxnhxJIkdEEAXJKLvWwi2BlO79CBuDwusq07sdJEnJCCX/ATJo+iyVKLydi2yLTf7+fw0Vw+/HwWIa4oDJof3S0yNZ216WzdsZ5Lxs9ok+pvMgbzyH1PUVByFEtjPfExiYSaA5utdoeNz+fPYe++XYiIBIWYuXLa9XTu0JV/3PVPXn/vRbYXrkUvM5Bg7EisNpFc5x4uumjiKZ9j354XMeuj90hJ1KLTCMg0Dj76yMXQ4b3QalVn/P3+Fux2F2tW76OwsIL4+EhGjenZPpmcZ9oN+x+IuKQUvNYG7A01aIMDK0NJ8tNQmMPgMaNOeZ4kSezdtZ20iwMVjQRBIDwyCr/XRd6KD6G5FkdTPQajkdRII5PuvP2sEpJOR0VxEWZlMhr1CfeDTmHAZXXyxJuPI4bGY4hKoqKxhk3vPMWlo6ZQWlpEY6OFrmk96N97SJtYboDoiFguufgyFi75kiBCkQQ/zUIDN1xzO1qNjh1ZW5g792M6yrvTxdSHals5WTu2c+hILt069+SiURczeNhwvvh6DtEkIQkSkgB2WTMGbxARUhxKmRpbs40kWRfy2Y/X4CJKG4dSmUC2YxuH8w+0yoj1er3MmvMKBUeOUVtfg14KpcxRSnhYBCplwAeuQIHV1nxSDRdBEE5atem9T96g7oiFTO0IZIKcWksls95/lYfu/zcxUfE88+irLFw+jw2bvqdJqGOvt5wLLxzDBYNO/QbWN30g9Y2VXHHbEiISm6iq9jEosy8zZ178a7/iX0VlpYX77nqLLiluenZVsn9XFvM+X80rb95JVNSZa/q38+toN+x/IFQqNTOuvpG5n36IKakHCq2BpuJDRJi0ZA664LTnimIg4eg4CoWSsPBILGERzPzXc0RGx/2qLNjfwtzSbBwhehqr65F7tMi9AmEaDXavFavHji6yN+a4VORKNSFxnajQBTPrs7fopuqBRq5j1aEVbNyyjgfuerRFj/ynjBg8hozufck9ko1MJqd75/SWmO/lKxfRQd6VYFUodocNt8VDkpRGcUMepfsqeHz3TEYMG4NcrkCUBOSiHFEUcfpsGAhqeUs6HvZpkILwyjwof0wUkyHH/aM8MIDP5+X7zSspOlhMhn4wOdpd2G1WjFIwtXU1xETFYfU0ISgEgoPOXFaisqacY/n59NVd8GNUTiDKp8lmYcOWNUyffA0CAgnxSSQmJONw2BjQbwhDB4w87fcrCAJjh08lfMZB6ivs/GfwdMLDT+26OVe8P2s5Ey70c/M1sdjtLoYNsDJ3QT33/X0W735wL0bj+Vlg/K/Tbtj/YPQZOIzouAS2bvye5uZmRl08ifTMQaetliQIAr0yB5KXs4X43hciCEIgJjxnC/2HDCc6NuG8jXdHRRn5voBGSXxEEOn33MQH9z+F3q9FkgVz1F5BtesQglxGxb7tNOzLwSu5UJiDMXbrj1ymJUoTj8NnwyyFU1VayqYd6xg55OT++GCT+aSl86prK+mgCwhwNVjqUQlatIKeHM8OhGaRcOLZu3YfokykzFNAAqnIJDlySUkNlcRqA5E2Go0Wm9VKk9SA2qqhzFoCCgmLupZOKWlIksSqdctZtWYZNTU1CD6RYvJJ1ndmm/17kEDt1VHWXEiZWMCUqdNbbZ5KksTu/TvYvHU9Xo+b3r36MajvsJa9g3pLHVrR0GLUj6MTDVTXBHTtP5v/Afu2ZxEtS0RHCKsWryTnYDZ33fTAaY37M+4NTNbJeWzKLWf47Z49Wzbn8PBnCTQ02GiotxBilnHtZXrmzD3Gnbe9xpvv3N1u3M8D7Yb9v0R1ZTkVpUWEhEUQE5902rjx6LhEpl7RdsPtdFwy4xreeOHfHPnuM9TmKJx15YQatUy69L6zHfopmVuaDcCUvj/NVozlmmdm8s07n1B4NBtZkAEhMQXHui300A5Grw5BkiTK645Svv07JJ+XHY5NeENEVJFBNOXVsGj1fAb2Gf6rJGijImJoqKslRBWGz+dFI+qo81YiIqO7rB8CYPfbSDCnsLV2LV65G63XgF3ZjFOy0qCqJthnRlSIlAmF1HurMUkhVItlVLiL0So0OJwOtu3exOpvVtBF3Yd4hQ27z0aB5SAys5z+ESPIb8rliCOLtOge3HDRbfT8mTbNvEWfsHPLdqKFBGSihhUFy9m9dwf33PogMpmcmMg4rP5GPH53SzgjgMVfw8CUwZRVlrBr53b6aIchEwM/31Apkr1HNpObt7+VuuTP+T3qliqVcuwOH7YmC4lxCpRKkdo6LxHhCrp1sLN08Tauuub0b6Pt/HraDft5xuv18NnsN9m3NwtdWCyOhiriY2O55e8z0WjPXb1KvcHIg/9+kUM5e6muLCMyahypXXuec/fLT1fo8HOjHqBTnww6zc7A7/cjiiILXn2HnM0dEFwSboUPuSASpUymrOEIktyHZmRXIob1xOd041mymaqtR/jbA9fRObUr48dMJjm+wy/K3k666FLmfPQOkisNPxL1vmry/DlECnGIgojX70GukBOuiSY+JJnMof0QEImOjCE1OY1lqxawa+96kCSalI30NPXD4bUhE1QM1o2m2lXO6h++IWvfTlJVPQL67ToBt8tNIp0paDpMXFQyRmUwocZwJo67hLTU7q3GWF1byZYtG+ijGYZcDKziw6Qo9hVsYf+hvaR37YPJEMTwoRey5YfNJMhTUcvUlLtK8BidDO53AXtzdmKSQluMOoAoiJj8oeQdPXhKw/571S0dMaoPsz7cyQ3T5SiVIpIk8f5nFkZfEMLQgUY+W3Ko3bCfB9oN+3lm3YqlHCwoI23SbYgyOZLkp3D7KhbM/YirbvrbOb2WKIqk9ehFWo/zE5d8fIUeHxFEn/jTp68fHw9Ac52FqJBI1C4dTQ21eGRyJJ8PpU+GVesifHDAAB77dA26IgV9zCMRLG7q91XzxN7/wxwUQnqP3lx92Y1tdFSOk9GtD+INt7P0mwUctR7B4/SiVxnRe034JB8unIQYftSqFyR6dc+kQ+IJXZsbrridG664nbKKYl5+5VmSNZ2RJAm/5EMmyvFJXvLzD9PU1Ij+R816nVaP0+nAa/NgcdezrnoZNlczCaaOfPHxZ/g1c/j7rTOJiw64wg7l5+Bz+tlr34ZSpiJen0KQMgSTP4xDebmkd+0DwJTxlxMVEcMPG9dQZbPSvW8G4y6chEFnQK8z4BGcbe7fI7owGtpG7cDvW7f0plvGcu9dBVxz1yHGjdCz/6ALnU7Ff56OYfU6C0FBv17/v51fpt2wn2c2bvie6IzRiD8KNAmCSGz6MHYtf48Z192C/BRiVn8kfq1B/zmd+qWzbutCuoZkYgwOwu1yU2trxOmSkPQK7IIdd1kD3tJmkoxDkFxenC4bkbJ43Lgx+A1U7K/kHftr3H/HI6e8Ts+03vRM643f7+fbtUtYtmI+hQ2H0aInNDgMrVZPhb0Er9KDXndyg2I0BuPyOznYkEWprRCf5EWnMGJWhxDfKR6/Gcd5XgAAIABJREFU30ddQzWh6oDGTIg5DLuimRBFCDgEBoVMRSkLbLhWOEp4Z85rPPnwS7g9LpatXITX5iNcDMElOdll20Qnc3fcgpMg04kIEVEUGZQ5nEGZw9uMr1unnnyh+5hyexFR6ngEQaDWWUWTop4+6f3btH+qbA9Tfkd9dZ1Ozbsf3MM1V7xEcUUN9/0tmd7pekrKXHz8ZRMPPvrLMsbl5fWs/HY3jY1W0jM6MGRoGnL5ySUd2glwTgy7IAhjgdcAGTBbkqTnzkW/fwVcDjvyn0V4yJQq/D4fPp/vD2vYf74p+lsM+nF6jxzO9mXfkXt0F+HyGFw+JxWqImbcdQsL5i/CXt2M3+PHpDAjl8mxWSwoBRVyUYHeZ8TptdPDmMnOgnWUV5X+otiVKIpMGHUJo4ePZ8HyL9i48XvsWGhsqKfWVk24KZJnnn+U2Pg4brrmzhYpXyCwKjbqqSooJ03si1rUUO+p4pB7LxelTWBA5hA+mPM2HrsLkzKEencN5bICEmKSoFjZYtQBItWxFNYe5plXH6W4tBCFVU2S2AUlKkJkKoKkUHLqt2MKCyIz48x02hUKJXffOpN35rxOXkUOHpcHQQVXzrge00lW7FOGrv7ddWAEQeDVN27jyX99yuMvlhAW0kBphZ8bb5lMekbSKc+rqGhg6eKdLFu0hovH6ukQIWPxvN0sWxzLcy/dhFIpx2p1IpOJaDTKU/bzv8hZG3ZBEGTAW8AooBTYKQjCUkmScs+2778C3dN7k5e3l/iM4S3Hao7mkJjSsU1R6D8KJ98U/e0o1Wpuf/UpdqxcS+7GHRiCghk18TI6ZvQkIa0Ts597DleMAZutksjmOESPH7kYeDaN1BGujEYQBLSiAUtjfSvD3tTcyKK1X7P78C5EUaR/1wFcPGIqGrWW3fu3s6cwC1+ojApnBW6HncGhYwhWh+KX/BQVH+Gt2S/zz/tPFCWxO2xYm62k6XvhtLuwS81o5QY6q3ty8NABbr7mTu649V6+Xb2EI1V7iY2P4+9jHmDFd8twCb5W921paqChoR5rsxVJ8hHqiwUZeGUePD43AiAKMi6ZcFmryeWXCDGHo1Ao0MuMBOvDkAkylixagFyUM2zAyJZ2uSnPtapD+3sSEmrg1TfvoKSklsZGOykpkac0xl6vj5dfmM+WjXuoqW7g2UdC6NFNQVS0mcsmC9z7zxI+eP87DuUeJf9IMRICfTPTuPu+KZhDzq08xp+Vc7FizwTyJUk6BiAIwjzgYqDdsAPjL5nBy08/QsEWK9qwOJyWapyV+fz9gUd/76G14kw2Rc8GlUbDkEsmMOSSCa2OJ3Xtwj9efomda79n89FmCo8dJkqdhNfeRJNUj11mJVaXhMfvptlvIeYnUrkej5sXPnoaX88wOjw0GcnrZ8/q3RR+/hKj+43l881fknjjBXSIj6DyWCHHPlpHbUU1wYQiCiKJ2k7srtpAUVkBibGB6kMNjfWoRA3h5iikYD9+v4RMJsPirqO0vJjtWZtRyBXcceN9rRKp+vSqZuGhr4iQYnG5nNTUVtHkseDFQ4wniQaphiKO0E3KBBEiI6LwS35M3iDSOv260oRbd23AUeWil3Fwy4QU5o1iwZJ59Os1GLVK3eJXv7HbySWAf08O5paSd6SCoUPTCAlta4i//GIj9RX7ef7RCF57x874UQYqq93UVDcSGRnM5HF67nlkOU88FMf4Zzvgdvv5cG4RD/7jfd794J7znq/xZ+BcGPYY4Kfi26VAv583EgThFuAWgNCIUxdf+KsRHBLK/z35Mts3rqO46BiR3VPp/7fbMAWf+QrtfHIuXS6/leDwMEZfPp0Rl05hw4KlLJkzH5uzHK1opJc5E4u7jmJvHsOHX9jK3ZB1YBeOcAWpkwa0HEueMZyDLy7kq9XziJ7RH0N8wBcuN2mJnjqQIy+vRFWnQa3WEGQKRi1qsVqbWs4PCQ7Diwunz45apuV43fDy5mKKLHks/WIxfnw45LO57Ya76dyhKwCZ6QPYtWcbu3LXI1oUOH0OGqmnk5CODgNGzBRymCqplBB3BJbGBqyaBqLjYn5RVuHn7M/ZS5gY3SpkVivXo/FqKS4rwDtqCXBqv7rX6+P7tfvZuT0XjVbN6LF96Natrbb8uWbuZz/w9RcrGTFYg8sl8dHsJdx93wxGjAxMbI2NdgoLqlmycD0vPhaKXC5gtweS7sJCFRwtsBMREURNrYOIUIGLLwr8huRyGX+7MZJtdxSTtaeA3n1Szvu9/NE5F4b9ZAHZUpsDkvQe8B5Ah05d23z+V0ar03PB2FPrePw3cbmcZO/axu78QzgjTIR26UxidMjvYtB/jlyhYMSMqYyYMZXm+gbefPkd9uzaj0ytYVTaaKZOaJ3+XlZdirpDeKtjgiCgTYmg6vtsomNOKEb6/X4EkxJJDipRg98lUVpdTIOphoTYE7VC1So1o0dO4PuV35Gs6IJWrqfcWkS+7QADw0e1bJo2uGqZ9eGrPP/4G6hVamQyOX+78X7e+uhl9m7LwinZ6SZlokGLJIEXL+FEc4R9NFCD1+4mKSaF+649uczu6TAYjVT4q1sdkyQJp9/Jx01FXMnpjfojD83B1VzIxNE6Gpt9PPnoTi67YgJTpw361WM5U/KOVLB4/iq+eDeeEHNgX+looYNb7p9Hrz4pfP3lRpYtXk9yvILS4kpmfdjMc4+loFDKWb7ayoTReiRJoqnZy0fzGujft/XmtyAIdOqgoLKi4bzdw5+Jc2HYS4G4n/wdC5Sfg37bOcfUVlfy1BMP4dMGoQqKQDx4EPvu3Vz03GO/99DaYDAH8/DTDwOwq7iUbbuO8XR5Fv+MCYRyHszLYf/hvVTpmzEP6IROo2vJuHUU1hAflUDDkRIi+3YJGD2XE0dFPT6PB6u/CS9uivx5xIfHYdC3NhLjR07GoDfy9dLPqHM2IigFjJpgTMoTkSvBqlC0Dj25R7Lp1T0TCGzaqmRqEvUdOGY5gkbS4ff7EAQRERGv5EGOghhTAl7RxegLx/8q3/pxhgy4gNf3vESoNxKd3IAkSRTajxAeE8HkKVnc1OPyU567/ocDOJsKeffleGSywJps5DAXV92xnJGjMzCZzjwp7Nfww7psJozStBh1gJREDf0ylLzx2jdUFO1j/gdxBAcpKCrWMOuDSl5+q4Sn/5nCfY/kMW9RE3q9nPxiFwnJaTTbSlv17/VK7NrrZPy0/x1vwOk4F86onUBHQRCSBEFQAjOApeeg33bOIXNLs3nunRdQxXejx9gr6NT/QjqMugKbpGftFwt+7+Gdlj7xsdw5JSBn+1TZHu5a/CZvr3oX99BoHNUN5K/aQkVFKR6bk8IlWzC7NVw14XpqFu+mcnsutjoLtiOV1H+5mxgpmmplKc3qBlLMnZELbaOSBEEgvzwPRddwes6cRsrd42FAGNtsG/BJgQ1SSZLwOD2s37qWDdvWYnfYAUjt2Bm7aEWn1FMpFCEIAj7Jh12yUkI+CaYOpAVlgBKCTb9NBKtDYiemTb2cHN8O9jm3stPxA0KMjwv/JUOUnT4McMe2A0wYrWsx6gBRESp6pqnYt7fgN43nTJD8EoqTDE0QYV9WLn+73kxwUOC7iI4K5vIpQSxaXsOBwzaGDQ7lSKGa1IyLeHv2TJ5/6XpKqw289FY5RSVOcg/beOiJEpJTU+nUOabtRf4HOesVuyRJXkEQ7gRWEQh3/FCSpANnPbJ2zgnHfeg+txtXWTndLj2RpCIIAuFpmexZv4iJN1/7O47yzLhzylCa6uuZ+dGrdHh4KnKDhsxuyeQv2ciBf32BQaVnSMYwpl1zBwadgfun/4MlGxZTtGwfleXlZIiZxIYktvRXbMsnNCq8zXXKq0rZU7SPbo9OR1TI0bqc+I0qqi1bqSwuIUodT3FVAaWeIrS5RlblrWDZtwu5785H6N97MOs2rEbn01Pvq6ZSKkFCwik46GbuTZKhE8X2fBRBMtI6dm9z7TNlSP8R9M0YSElZIVqtDsvAzxAE4Rc3S7U6DRaLt81xS6PvvMr3DhnejSceWc+0yV5MxoDZKS51sm23C61WTXjYiQgZhUJGWloUGq2F1ZtDSe4Qx+df92ulBvnK63fwycdruOuRbJRKBSNGDefyK4edt/H/2TgnceySJH0LfHsu+mrn3PDzTdEeEWHsACS/H366cvL7f3GV90eiMPcwsRnJRMeFU9tko8EoJ3bGSII7xZN0RM71l9zc0jYpvgP3XPUPAL5a8hk7N+wg2BuCVqan2llOhVjEFSOuwuNxU1tfg0FvRK8zUFRagKFzDKIi8PNQqdTo9Tos3cM4lneEWmsVZe5Cupv7kGhIBaDEdpTPv/qQf9z5T2b+/XHWblzJ3n27QRCIjYuj4NhRaurLqLaXkpCYxL1XPIxMdnY/P7VKTcfkzrx9IIfhgnBG8epjxvXlsYe2M+oCFzFRAUP+3Q/11FpUZPRKbtO+0WJj/teb2bs7F4NJz/iJgxg0uEubdg31Vr5bvQ9LQzM9M5Lpm9mhVXRKly6xXDh2GJfe+D3hwV4aLB5KKuCuey+lvLSa1T8c4pZrTtSAzcq2ERMXxbMv3nRSXaVgs567753M3fe2LRnZTnvm6V+O00W5dOndk8oD24lJDxTZkCQ/lTlb6XvBb9s027t+E98tWkh9VTUxSUmMmzGdlB7nNkzy52gNetyWgNsj1KjDYnfgwEttvQV5w6ljmKdOvBytRsva9auwW23ERidwx+R7OVqYxytvPYPok+OWXPTt3Z+Mnn1xVbYubGIODqXGJhHSMZaCY/mk6wbg9NvZWLEKv+QnXBtF7dFyHE47Oq2eSWMuZdKYE29HkiRRb6lDLpNhMp5bHfLhk5YzOuXMnnvnzjFcdd1krrlzMV07KWlq9lPfqOLJZ29EJmvtmW1qcnDX7W/Qu5uTO681Ul1bx3tvfkpx4Wguv2p4S7t9ewv51z9nM7SfnJhIkQ9nbWTh/CSefOY6lD/Rpxkzrg9LFm4kKUHk0okmCkokFsxbw70PXsHrL+fS1FzOoEwdecdczF1o44H/u+68FFn/X0CQpP9+gEqHTl2lF9774r9+3b8yPzXop4pBb6yt4+2H/o3TK0dpCsdRW0JUdAg3PfEwKs2vk07dsXoNi7/+gtjpA9HFhdN4qISK+du4eeaDJHfv+pvvw+/301zfgFqnPemY/D4fz9x+J7qRnQgfkIYgCNhKazj42nKiR1yKOiQUs0XJHV1P/gwkSfox41fO3gO7+GjOe6Sp+qCTG/D6PRyy7yOtXxeOVOdB/2iih6cjiAK1+49R89UOnrjtGV547d80l9nwurzECMmIyKiUiqkUi5n92jwMuv9OkkyzrZnV1scRZQL/vvKWX+VKaWpysD+7EI1GRc/0xDZGHeDzT3+gPH8d/3rwxOKgusbN5beV8tmXj2E0avD7/Vw1/RkeulPNgL4BfXefT+Lu/yum//AJXDL1hMzBE499StekIiaPM2JpaMbr9bFpu4tVm0N45oWbWLRwK0cOHSMiMoyM3ql8t2oH+/bkYTRpGT9pMFdefcFJx/m/RLDh6t2SJPX5pXbtK/Y/OcezROGXk4pMoSE8MOtlDu/Kor6qmqik8SR37/qrEzr8fj8rvvyKxBtHoI8P+KhDe3fE7/Oz6uuvuT4lmbL8o2h0OqKSE8941ZW9cQtLPvkYu9uJ5PLSd+hQJt10PQrlCf+rKJNxy6OPMOe5Fzi49gByrQpvTTPX3H4H6UMHA/Dmwg08VbanJYLmpwiCgFwe+Lf/7vsVxIupAaVGQC4qSNV2Z/uuDTxy/xPMXfk5+9d+jiATCdOFcM/0+zAZgujcpRsr85eRKR+BKATcWLG+FFwyOwePZJOZcf7CBo+zeccPfLz0VYx+M0a1jnHvP8MLr19Jv/6pZ3S+0ag5qUvlp+RkH+HSMa1F18LDlHRMUpKfV0Gv3skcza9CKXcwoG9ESxuZTGD6ZBNzl2W1Muy7dx3i1ulB1NXWExEmR6mUMU6n5ImXc2losHLzrWOAgDbMnbe8wi1Xa3l2ZhJVNW5embWOV2ss3P/A1DN9RP/TtBv2PylnskI/GXKFgq4DMs/q2k67HbvN2mLUjxPUKZbsOWt54qZbUEUH4260EaIP5vqHZhIc0XaT8qcU5OQy74P3iL9hBMbkKDxWBwfmbcDzzvvM+HtrFUxzZATT77yDuopKTKGhJHRObWX875wylA9Xb+epsj0AJzXwABZLA/Hy1sWplaIKmSRDpVJz/7UP0mxtwuN1E2wKaZmgEmOTMKvCcXjtyCQ5fnyICpEYbRLHCo+ed8NeVVPBx3Pn0D24L/GmQBRIvaOemXd9zjfrHkavPzdSFcHmIErLa1od8/slSivcmM0Bgy+TiXi9UkvlqeN4vVIboS6tVsWxwgaGD9ChVIot55uMIl9/uZ7/ezQQprlowWYuHqtk6sRAHoJep+G5R2MYMWUzOp2exKRwhg3v+qv1YfLzKli1chfWZhu9+6Yx/IKuf1kxsf/t95o/IesO5vDGugVkV+cRHxF0zlP/zwS1VotKpcZeUd/qeOXG/TgFHx0euJiO90wk7bHp+HqGMef5F/mpy6+2vIIVn3zOF6+9wa416/C43fywfDmhY3tiTA7EISv0GhKvHM7ebVuxNTW3nHto1x6evOk2Pnz7NRZ9+Tlfz3qH2rKKNmO8YXQ/7pwyFK1exVNle1qMPATcMfsPZWGXOdnh2EKprQD/j2UFLe56VFoVQcZAOTuD3og5KLSV0Qo1h6MyKggPj8QYbCQ0NIzoyFjcMgehoaGcb5asXk2oWo9Jc8LlY9aY0XpNbNl86KTnVFVZePftb3n4gfd48/WllJTU/uJ1Jlw8gM8WWDmcH9jT8Hj8zJpTRVRMHIlJgYk6KTkchTqI1etO7Ek4nX4+m9/IsBGtPQb9Bvbkw7mN+H+s4Oj1Srw+u55Rw80czStuaVdUUEpG9xNuOLfbzyNPHcOksyPaN7F17WKuveJZCo5VBdoXVrNq5V527zqK3+/nZHz7zW4evO91ghV7yehYwPL5X/HwAx/g8bSNEPor0L5i/5PwefFeDi5dTOWhHMI7RGMvq8PfI50ed9+JUnV+q8z/HFEUGXnJZFZ//A0JVw9HGx1CU14ZxYu3ETdtIOqwgK9VEASiR6STu+krKgqKiE5O5PCuLD5+9RWM/VJQRhg5vHYJG1eswOPxYBrUemUt16hQGDU0NzSgMxpoqKrmk1deIf6WURhTopAkidpdR3jvyad55J23kCvbxqTfMDqgbnHcPWO2KAkv2c+Gwm0ETe6O39ZI7qZ8iooLiBcTKRcLuHr6jad1T3VKSUMXqqOs5hgJ2lRERMrtxdhUjfTLGHwOn/TJkTpuQZatwqT8WfalJMPl9LRpX1hQzf13v8nY4XKmjdWQc6iKu2/fwZPP30rXrnFt2kNgIti0Pgejycz0mwpIjNfgcEp0SE3m8SeuOHFNQeCRx67moQfeZcVaGzGRIhu2OUnvk86Ysemt+rzuhgsZ/ekqJlxVSnKCgu177Oh1chLjJeTKE28ZsfHRZOdmt/js5y2sRi5z89Zz4SSlRKOQy1jybR0vPvcFCYlR7NyWRd8MDQVFHtx+E8+9dEureq52u4t331rI7P9EkxgfuM7F40L424MlrPkum3EXnZ/6Bb8n7Yb9D85xH3rhxg14PLX0e/5aZGolfo+XY598z4pP53LxTdf/18c15OKJCKKM799dTHNjIyGRESSldkQV3rpwsyCKKIN0OKxW/D4f895+m7gbLsCUGtiQixjUlaNzvkNXA5acQgxJJ0LeHDUW/FY3IVGBY1nrN6Lvk4QxJbCqFwSBsL6dsGzN4/DurNO6mI4nOL384WI27l1F5wenERlsIsLnpbFXJw6+vAiv3Madk+8nNfn0vmdRFLnntof49MvZbD+yBhCIjorhnhkPtsliPdd8GvQVyb3NFHxbhdfvRf5jJSWHx0EjtfQb0NbH/uH733LtNBWXTw2ssocMgMS4et57ewmvvXVnm/b5eRU8eP/bjB2u4NYr1ezNCWbpaiePPnEj/fp1BALSBKtX7mXThj2IMhk33jIJuVyGxWLj4THR7NxxhJuvfxGFXM6IUf2YcukAgoL0XHnNaA5kbSHncBPXTDOR2UvNziwnS1aXsHnTIQYN7swlUwdx9+07iY2qY/QFwXy7ppbrp2sxGHUofnSdTBxr5oU3c8FTxaKPklCrA9WZ5syt5sVn5/HiK7e23M/+7CJSk+UtRh1AFAUmjdGzbuv+dsPezn+PuaXZeF0uyvfswexupmzTZjrePwmZOuBXFBVy4qYMZNszC5h4w7X/dUU7QRAYMmk8gydehM/jRaaQs2X5StbsXENIekqL68JRbcFVYeH/2TvLMKnK/o9/pntnZ7Z72WCX7u7ulFAE0UfEwG5FUR8VRcRCEFExaFAQkW4F6V5gly22O2Z3us7/xcjiCigij/X384Lr2sOJ+5yZ+Z77/mVkYjylefk4RG5qsosp/P40qkA9Yd2aEdg5GeuGs1gOZJEnkxDQPA5bWTXF3xxh4LhxdfZzc20tUv9LKe+2kipMGYU47DZqq6uvOM6f0z1Sh6NDQwStjCKXFQTwU6sJ7NwIdRr16sb8Ega9kQenPonFasbtcV+xFvqN5lRqEW2GZHFnz6koU9exYfUPBHjCEPBSLink3sf61ZupXuTY0fM8/0D9mXm/ngZennMel8tNbY2NzZuOUVRUTnJyDDu2H2bqRDWjh/rMSr26GYgML+Prr/bQoUMiXq+XF59fjM2UwbjhfrjcAsu+/Iq45FY8+PBIHrh3LolR1cx42IDD4eWTpZs5dyabF16exH33D2XSLWcZ2NPNsAFaxGIJ/5kUQtfObl57fw2dOj9NVFQgr7xxNx998A2vvJ1OjcmBTB5ASGj9MFGb1c4to0KRy0WYTFY8Hi9jhvmzbE02VZVmDD/6AdRqBTW19UsqA5hqPKjU/8xG2v8K+1+MizN0l9VGzpdLsRul0Dwa83YL5cUlyAJ1qHU+26rMT4XL4cDr8fxppUpFIlGdCaRt354c2r2LjIWbMbRLwFltoXJnCsMnTkShUmGzWCnLzMUTo0ObHIE5r5yjM5cS3LkxKo+XaS//l11r15H56ffoDQZuvm0Kzbp0pLywCJvZQmxSEkdWHcTbqyXZa/dSfPAc2kbhWCqr2LBsGbGNkgiNjfnF8aq0GlzVVoL9dThqzJxbu4eswkpcpTVU2uGF+c/w5O3PYvS/Nlv51Vr13WhOpRYhHfI5WrUCkUjEk9NH0G9Qc3bvPINcLqXfgKFXTaf381NRWu7EX3/p515R6UKpkpOeXsTzT39E9w5iooI8bFqzl117TUy/r37v1CH9jLy78DwAR49kUZKfzhfzYpBKfS/w7p30jJ1ylOXBAfipKpnxRFTdy/2tZA033XGW9PNFJDYMQyL2MmF8LNERCiRSMSKgTUuB2ppSKivMBAb50bhxFG/PnYbX62XZku/YuGMHPbtRV3Jww9ZKPF4pwcESsrOKUClBJoOqSi/mWjNWmwMDvs+mSdMorA4Nm3dUMrCPb0VZVu5kxde1PDG93Y36iP5S/CvsfxF+HuWyZckK0sNVxE/sRd7mwwgeL3mL91Ag20fcsM5E9GlF+ZHzxCYnIZX9NbowKVQqpr36X45s383Zk8cJ1vkx5qlniW3k6y16eOcugvo2J3BYa+R+avRtGiAL8SPnsz0Yw0N576lnGTB+HANuHochJJiaykrmPTuD/IILyHQavCYrapWWky8txe510uDRIQhuLzEjO+PMKOOz2XN46v13fzG8Mqlta7wLP6L4h7Nkrd+HKj6YwD5NsWaXYjqURXWgiFVbl3PPuAf+qMd2TUiHfI5MLuXmhFGA74Xauk0crdv8+gpj8LCuvLdwB2+8EIlaLcHh8PL2ghIGDunE+29/xbQ7lDRJcKNWiRg7zMiM1928NS+TmTOSUKt9q6XyShdanc+UceJ4Jn26KutEHUClktCjo5K9351haE9Fvc9ALhfTqa2K1HP5JDYMQ++vJS/PSoC/gEwmRaWWU2v24HSBWuPzF1mtDhZ9vIVtmw9hszoRgJtuz6R/TzXZuV5SzosZOrIHny3dx8xnjfjpfL+Bs2lm7HYXp0/lEhHhK7AmFot58ZU7eO7pj1m1LpcAo4Sjp+zcOmnQL3Zw+jvzr7D/yVwtbDHl+FEChzelYMdxSo6fp+GLY/F4PbhNVvJWH6TqZBbicjt3P/fcnzX0KyJXKuk8dCCdhw687P/OHD1Kgwf6UWu1YjNX4kVAGWVELBEjClRTmVfKqrVLWDJvLmqFGo1Oh65bIk3vvhWRRIy1sILMeZvQCnK0XeNRiGWoA3SoNBoEYwDntpyiKOsC4fGXfqyCIJCXlk5NVRUR8XEYgoO467lnefvRJ5HG6wns3xzB48UvKRJDh4Zkv7ORnbWFTB0z7S/TsGGm8ztGcv3NqG+5tQclJZUMn3SYhvEKMrIdtG7blDHjurFlw17aNDMil7oJDvSJ+ISb9Nz9eBH5BZUkJobidHh5b2EpA4f4wjj9/DQUZV5u2igq9RISaiQzp5zaWhs1JgserxeNRkV6tpMOvfXYbE7Ky628+lYu77wcgt3pZef3VjZsM5NTIPD8M4u4697hfPrxJozqPBbPC8VPK2Xtxgo+XmrGKu5Iux5BPPFiE1LPFXDvndt5flYF3Tqoyc51sW2PjXvvDOe7XUcYOKhV3djiE0JZsvJZjh/Lwmy289DTsXWmGgCPx8vBA+mUlFTTMCmcxo0j/9ZZr/8K+5/EryUWqdRqXLU28nccI2pqH1ThRrxuD1a3l/Bh7ahYdohn5r1X51j8O6BQKfHa3ITGRlFeWIQTNzKtyhcDbVASe9MgRFIJUpWc3IU7KD6XT1Cr3oh+zDZUhwcQ0KcpFRtOEBYWQkDopXsXiUQdkah0AAAgAElEQVSI5VLcrktRIaaKShbNfJ0KSxWKYD2WjCI69e7LsP9MJqZxEpXJShR+GqRqBYhESNUKlEYtlqpKXi08jkgkumoM/B/F18fSGTn2h9/Vt1QiEfPYEzdx2+19yc0pJzzCSFiYAbPZjscL1dU2EuMurfoUCjFyuYQxd+TSvauL85lO2nZozuQ7fG33+vZrwZ1LNjHgeC1tW/nKBu/eW83ZdHh/wUBuGXOIBhFWhg/QIggiPl9ZwOFjdl5/J5rPPtlGq8Z2oiPCuP3BQmrNLnp0VtG7q5Kjp1zYTek8eO87+PuJeHdJQl0Vyoljg7mQ68Jfr2LwEN9notYoaNQokN7ddZxJNRMcqOKLDxpwJtVCSublGfUSiZi27RIu215SUs0TjyzAoLWQGCdlzQoHUQ0SePHl2+qVRPg78fcc9d+Ya80U7dy3L6tXLcZZaUYZ7rMLus12VBotxuhYqlYe+VuJOkCnPv3Y/e1OEqYOQiyVIJaIKNtwDMHjJWhgKzweNzKDBolESsjQNlgyinELHhw2W115AUWADq2/PxV7zxHQIq6up2dNZhEis6vebH3l3Hk4G+ppNLgvIpEIt83BkbnfErmrATq9Pya3HY/dhVTjMzF43R5sRVV06dOD22/qcU1JTv9rGo79CtkNEpegID1BQZecq1qtklZtkvnq2xQev88fhVyM0ymwaJmJ/0yMYNFyM4NHj+OhhuGEh1+KdgoI1PH8S//hhVeXYPCrwuX24vJoePWNqcjlMiQyCRu2O1jypRmPRyApUUO3Dnq2bz3Jjm2HWPhmECFBclatLeH5R/UM6KX58cxSpjxaTESIQKBRWq+0MEDzxgqOpF1q9dCwYRhOt4rAAClPPxyD1eqhpMzJsjUm+g3tfc3P5a3ZqxnSy81/bvV1kXK7BZ76bzarVnzPxNt6XceT/vP5V9j/IH5L6j9Ai+5dyc++wPpzX1C5Pw11g2BkEinGsFCqTmYTGX9t0Rt/JbqPHEpxfi6nXliGNExPWeoF/BqEIvdTg0SEWCpDEATEYjFyoxaPw4XH5sTlcNQJe/WxLLr06UP6mRTS5nyNtmUsbpMV8+EsJj38cJ2/obayiqzzqTSdPLFuSS1VKQge2Ir9O7bTf8wYPn3/HRQRRuxON8jElG44jsorZey0e4HLY+CH14bRPPmPa+RwNv51tGpFnV39Irk5ZeTnV9IgLrheKdvr4ZHHxnD7pCz2Hiygc1s1R085aNpYR0WlQM9eLenR88rf1TZt41n+5fOkphYgkYhp2DAMsVjM3u/P0bmtjjn/Daes3IVUKsJokLFpeyV7jp7H6XSjVkk4cdpMRJiEFk0UKBUi7A4BpVLM2GFaVqyzcTLFgscjIJaIqK6yYDKZ2bqzjKIqOUVFVYSFGRCLxTw1fSLPT/8IpSSf4lIrMqkIq11G5162a7r/mhobZ05l8NZzl35PUqmI228O4JV3D/4r7P9yZa439V8kEjH09kmERUWxbOEHaEZ1wC8pmvKD5yldf5QpTzz5vxry/4TCzGx2fv01hbm5NIhrSGKTJqRwhFJ7FValAtOxbLSNI1D4qUEE1Ycz8G8YyYW5mxBGdcEVGkjlkXQUJQ46PTKAnjeN4Nyho6SnpKAN9aPNW9PqlS1w2O2IFXJEP0sZl2lUmG02GrZuyeCRY9m0ZAX4KbCVmQgLCeeexZ+h0dePRb9/dHeO5ObzzZEsvikoommJjpGtE/+nz+tiM+qfirrV6uCVl5aSnppOYpyCs2l2OndrzaNP3HTdqfEBgTrWrn+Bp574jK+3nKZlcz1nzkNYZCgvvDz6F4+VSMSXJTj5GzQUFPvMYT+tsZ5f6MIQoKdj56Z8uT6d1s00SCUinE4Bp0uo82d4veBwCkiVBl6YlcfYYSpkEhsHjthJz3IxqH8tD933Hgs+fhRjgI4WLWPp1bstF9J+4J1X4wkP01BWKfDEC5swBujp2++XG4ULXi9iMZetDhQKEW73FUIkqy2kphZgNOpISAz9y9rh/xX2/xG/dYZ+Ndr06Yl/UCDbv1pD/o5thEVFM+qZZ4ltnHwjhvmHcOFcGgtnvoqxXzP8O7elNquYbd+u445HHsNpt7N/61ZOrTuMI6ccdcNQ7DnlWNOKCGmbjK0WQgpEWM7n0CwygXJPGa9Nux+dwUCPQYMZMeWOK/64jKEhaOQqTGl5+CdHIwheRCIR5ftTadfGF+LWbfgQ2vfrTVF2Dlp/PYHhV5+Nt42OrCuB/P6a70gpOPY/E/iLztKf29U/mPctRlUO3yxugFQqwmbz8MSLp1i5PJhbJ/W87utJpVLmvD2F4uJqMjOKCQnRk5B4fSuTJk2ikMiNfPh5MU2SVGi1UiRi+GqDlTff7YBGq+Thae+TmW3iXLqDs+ddSKQiIsMUWCweFi2vJiXNi0Lh4fNlFr5YLiASgUwqZvTwIO6ZHIbTWczXaw/wnyn9cDrd7Nx+mOULYuteJOEyD3eMVzJr9nIUCimduyRftSqk3l9DTGwEa78tJzJcgVotpkmymlVfV9KlW4e6/QRBYMkXO1m9YjuNEuUUFLnQG0N56ZXbCQz63yalXQ//lu29wdwoQf9fUV1WjtNuJzAi/HdFfVjNZkpy8vAzGn7V1j9v+gxcrYMI7nDpZVR+PAPvdzk8PNs3M60sKWXHqi85/N13WKprUPlpSGrRktFTp1BdWkZ+ehabVq8kaGhLjC0TsJdWU7DmAD269qXfzWOveN30E6dYOHMmkibBSIwazCl5KMqcPP/xh+iMv8+EseZwCoV5vlo5N9r+fjb+9ctE3e32MGLwc6z5NAqj4ZKj89x5K9NfN7N4xfQbOobfw5LFu5j71ioSG4ioNXvJLxJ48plJjJ/gK7dgsdjZtuUke78/zdFDZ+jQWopa4WLbHgs1FgldO6gpLbNxzyQtPbuqSD3vYuZ7VWjVEuLj/ejbw8iXW/TMfGMqpmoLt93yX7Z96UuKM5vtFBdVYLN5ueepEhITgtDoY3jl9Tuu6gj95ONtzH9nFc2byLHZvOQVeomJi2XBxw/j5+czAX7/3VkWLVjC/FmRBAbI8HoFPllSypGzAbz13r1/2LP9t2zvH8xFQf95c4u/CqbyCpa+/S65OdlIVXIUyBh/7z00bN3y1w/+CYIgsGPVV+xY9zWKUH8c5TXExSdx62MPodZeOVkn5/x5mt3Rod62gOZxHPtkB16vF7FYjDEkmLEP3MfYB+7DbrUhEkFtVTULX3oFm8yDQ+Km2lKNpqyGUL0Ghb8W5dQB7Hp9Ld1HDL1i7XatXo8IENu8iKschLZKwn6hjE1LlzPugft+033/nNHtmkI7briD9Wz861d0lrrdHjzuS23lLhJgkGKx2H/3da+EIAgUFFTi9XiJig68JrNDWmoBa1du5vO5EfhpXQgCHD7pYdmXOxkzvjMSiRiNRsnI0R0YOboDNTU29uxKwWJx0L6vhmWfrsbptPDQXXo6tlGg14lp21LCc48YmD3PxP5DJowGJSFhvpWSzk+FVqfj1FkLzRtrKCmuJDJcyvotZrp1NDDz+WgefCaXzRuPMXzk5SUnzqcVsumbnWxc3RSDnxen0813+20sXutFq71Ug2nThh+4c4KewADfS1UsFnHHhGC+ujWrzub/V+JfYf+d/NVn6OD7gX78ykw8TQNpOvVWxBIJpvP5fPb2Wzw6a9YvmiB+zum9+9m1azMNn70Jhb8Wr8dD7pf7WD1vAZOfevyKx/gZDFhLqtDFXKrZbSupQmfwRywWU5qXz+6vvyE3K5PgsHDa9exJWX4BG5YuRdEsgoaTB1NWUkyA00nuwu1owgMI7dIEhVEHahkn9+wlqW1r9IEB9a67Z/23BA1qRUS/S4LrsTs5NmM5gyfditb/8vT738pFB+uX+08wbfkcqo+fRC+IaJLcnNHDbiEsOPyaz3XRrn6leHWlUk5iwyi27a6qy54E2LitkjZtr90s53Z72Lc3lcyMYsIjjPTs1QSl8vLyt9lZJbz+6lKqK8uQiEXIlX48/swEmjaN/sXzb1h/kN5dPERHeAgwKBAQ8Ne7WbK6lGPHMmnXrr7pys9PxbARPtPYzh2naRinYM/eChLj/FDIxYAIRALNGynIK3QRFiJj9TdmPlzUGfAlH025ewTTZy5jygQNBq2Dg0c9fLG6lvdmJSEWi7hpqI41205cUdg3bzrM2GEa4mIulaoYO9KfDTtyOXH8Ql0CWG2NhQBD/URAqVSEv16KudYOf5xP/Zr4V9ivk7+DoF8kJ/U81Y5akgcMqJt16RtGYuqQwKFtOxg8eeI1n+v7LZsJGdIGhb9vdi6WSIga2YmU55ZiqalF43d596AeQ4eyddW3xE3pj8KgxWmykLtyLz2HDKEw6wLzX3gRv55J6G9qRe7hNL576knCujdH0ikKS0E1J2avBJ0Sc0YhEq2Ssx9vwFZWja3cRFl2Hhu3rWPNF5/TsmMnxtw7tS4yprSwAG3/+kIiUcpRBPlRVVp23cKeduQ4m1etpCgnl8CwUPqNvgnrzn1oThcSRltkEjmFJwp4M/tlZjz12jXVkZl/JoWe8Zfb1X/KvQ+O4rknPyQ9y0njhgqOnLSx5wC8M2/QNY27psbGYw99gFZRRfuWMvZt9/DFoo3Mee++ejNOh8PFU499yN0T5Qwd0ACRCPbsMzHjmY/4dPHT6P01V71G+vkCerYREVLnOBURGizD6A9HDl0u7D8lITGMee/YiIlUkpntQq8To1ZL8Lrh2Ck7Br2Y1HQPd97Tl9mvLSMnpwS93o9GTRPp3b8na7amcvJYHiOHGHnonhiqqtxYLB7sDgG5/Mq12821FhpHXu54DjBIMJsvRda0adeUjdu/o22rS9/vs2kWTLUSYhsE4XK5EQT+MnHvf41R/I34Own6RcxVvgSdny+lFcF+VBdUXuWoK2OprUVvvFRBUBAERDIxEqUMu8VyRWHvMnQQVrOZPa+vQaxR4DU76DpwAD1Hj+Cz19/AMLAZYT2aIwgC5xdvJfrufmiiAvGKQBnqT/YHW7DllhL//GjEUgmOwmoKFn+Hx+qg2cyJBEaE43G4SF20je0rv2TgRF/Dhui4eNLS8usqSQI4a6w4y2oICP/1HIDctHS2rV5NbmYWASHB9Bk5Cplcxmdz3yZ8XGcaN+yGOaeYpQs/wHvBTJegwUjEPpGQiGXkmM08t+UL5o558FevdS19Sxs3jmLeR4/xzdr9bNpbQoP4aBYu6lAvg/KX+PSTLTRPrOGphy7Vcfl8RQlz31nD/Q+N4uCBdBQKGV6vl/hoD8MHXVoB9ezqz+59FrZvO8VNYztd9RpanR/b9lgICpRyMsWOv15ExzYqUjMctO5y6ft39Egmu3Ycw+Vy07V7C7p0TSY6OpDW7Vpw7tQR3lpgYuokHR3bKMi44GLmuybsThUDhrZl59ZdPHaPkXWb3GRk5eKtLeZcvorKCjUBQSHsP1TB+fRa/PUSzmc68aLkielDrzjetu0bs2ndOYYNFBCLfeMrLXNy4oyDR6fH1u03ekxnHpp2jGdfyadPNw35RU6Wr7Uw8Y4RvPrSMg78kAJA63ZJ3P/QqHpx/38G/wr7NfJ3FPSLRCYmYH6/CLfVjlStxONx4/V4qTmVQ+euQ37xWKfdzul9BygvKiYsNobExk1IPZKONjoYU0UFltparHnlVOYVUZqXf0VHqlgsZsCE8fQcNRxTeSX6QGOdTTw7NY244cOxFlZgzi/DUWPF0D4BW34FYrEYr8OFrlUMrkozCq0GW2k1YpmEgF5NqNp9loAfzUgShYyo0Z344b3NdcLebdgQjj71NIUaBYFtGmIvr6FgzX66DRx4VX/ARXLT0lnwyssEDmlF7PDBmPNKWfrRfOQuMWFjOxHQIh4A/+RojN0bUX7mCJKQSzO/YH8tXkk4GSVldXXgr9aH9aIJJlrz69+rsDADd983+Ff3uxL79pxgweyAei/48SODeKPPcc6dTqdHZxVmi8CGbdWMG+57PoIANTVWzLVW9FobBw6kMnpMx6va27t2b8SMp/cAAsMHaMgvdHP7g0UIgohtWw5x2+09WbZkNzs27WBwbylisYd5cw6wfl0zZr15J089O45VK8JY+sU2nn2tHLvDjUopIzomjAcfH8Hq5dt5/pEgsnJs4HXyzRdROBxeSirgWIqEGa8Vc9/tGob11yCTiTif6eTZ12oJCNCyeuVe1qzeRVmZiUaNorl9yhB69W7K5g0HeODpXIYN0GGq8bB8bS0TJg7C33BpZeLnp+L9BQ+wYf1RNnyXhiHAn1dmtWPWzOX06ezgpVVxiMUiVn9TzGMPzmfR4id/c4enG8m/wv4r/NWdoteCf1AgXfr2Y/8736DqEItXAqYjmdhSClEPHn/V4ypLSpn/3Ay8IWrk0QHs/+YHFLVenA4HKWXrUSaH4LG6qNx1hqiRnVk89z3um/ECkYnxVzyfQqUiOKp+BUKVRs3JOavxuD1IVHJsJVVYCysRPB60fn6Yy2rw2t2IpBKc5TUoxDIC4iLJrbWDu347NrlBi63WXPd3QFgo017+L5uXryBj61q0/v4MGjSCjoP6/+oz27pqNYFDWxPaxdeYW2HUIddrOfLcZ8QmDK+3b0CreLLd2/F43UjEl35SNUIV/fp3xdA2jgNHsq6Y5HTRWXq9dWB+CyKRiJ83GDp91oxS7mTZwigCjT4h6thGwcy3LvDY/RFUVpjwuu3o/cTsP2zGZEnh7TlrefTxK8e415gsdO+sZcajfshkIiRiEa2aK3hoejnNkxws+mgbmzfs5q0XVMREyVCrxIwYoGbMlMN89WVjxoztzISJPQkK8ufD+WvRaTxUVbtJahRFhw6JvDFzCW1aNuSjLwq4Z7IeqVSERCLGWehgQC9/XpntYsSwaPw04PF46NhBwd23V/DG66vRKauYPSOYuJhg9h4wMfOlj3nptXt5/c0pbN96ku37T6PWqHhievsrFgfTaJSMu7kL42721czZ+/05DNpa7rn9kt9h0rhgTqbks2tnSl3pgz+Df4X9KvydZ+hXYsjtkzi+53vKNh9HbtAR1CwObf8OLP9gPiFRkQRHXf7SWvvRJyg6xxLRrw3gM7vkrPqOBi4Dh3btwGtzogzwo9m0kehiQyjUa9jzzXpufezhaxqTIAg4rDaUjUIJG9UBR3E1qS+upHJ/GkF9mmG1WxEjomr3WTRRQfjrjai0GkQiEfbMMmSa+r09yw6lkdC8/mcVGhPN7U//9mSuvKwsYkfUnxnrYkMQy6VUp+UR3Dbp0n24PciNas7VHCNe0xiZRElR7QVqNdV0GNwXP6ORttGR9ZKcnotoXWdX/yNEHaBH7zZ8sfIwzz0WUfdCfPuDfG4dY6gTdYARgwOZM6+QKQ9mMGqQlOhIOe9+VE1IsIpFM+IZP/UwWaO6EBcfctk1jh5OYdL4MOwOKy6XgIBAk4ZKGicpaddKxYLFh2nRyEtCA3ldhI9aJeGWUTo+WbiRMWM7c/p0Dgvnr+Sdl0NJSlDjdHqZtyifV/+7lIiIAM6k+bJSL+Zk2exeZHIpHo8XqVSECBE63aWIFr1OQkZaNptXNyIsxLe9VzcD1TUeVi7dwcuv3cHgoW0YPLTNb3qe+fkVNGp4eWXVxg0lFBZU/KZz3Wj+Ffaf8NMsUfhnCPpFirIv4JALdHj5rrr6KgDWvHL2b93OiDtvr7e/2+ki7cQJmk2YXLdNJBIR2rsl5974GmNiNMmP1O8Yr4kKouz0uWseU/GFXFxSgdhBHagpqSb3812Eje9E1b7z2LNKUUUEUH04g0CVAU9ODdWHM3BFBVGTmofrYC4yr5fcdfvRxoVizirGfCCLYY88gtNuR678fQ2dA0KCMeeX+SJvfsReZkKn9aPkmyMo/DT4JUZgzi0ld8kexj92L9XFFRz8ZisOi52k9i25795X8TNesrVeTHK6WKJg9PCtNP4D6/1M/k9fnn48m8n359K2hZxz6W7SssQM6HO5M7RdGyNnM1V8siyPqAgFPboEMnZEEHK5mB6dlBw7lnVFYVeplNgdZmQyMTGREgSvACIBi8VNSUk1UqmO4hIHOm19h6XdIVBcVIUgCKz/+gcmj9ORlOCLVJHLxTwwJZRhE7MYMWYgr769lZZNNKz4upakBBnFpR6MAQb2HbJSYxYBl3JzBEHg6001BAUq6kT9Ii2aaFi69vJ+uddKfHwoH2924vVess8LgsDhky4Gj/5z6zj9K+w/8k8wufwSNZVVKIP09UQdQBmsp+p82eUHiHz/CJ76CWxerxe5QoGr0oKjyozCcMlWbTqbS1L85dXzroa11ozCoMMvwIhcLCXH7CC0b0sCOzfCeioPpURBSHIcjt0ZTHz4Ib5bv4HSlFQSYuMIGt+C4tw8Si8UIirKJ0imxCGT8cmc2eDx0rprN0ZOueO6Bb7PyFE+m7qfBl1sCPYyExcW72LAuDEEhYezacVKMoo24B8YwNDRY+g4sL+vDMTUyT6H8i/EfF9s0+fxHKBzUM/rGt/1oNEoeXfeNA4fyiArs4ThrYyMnSTjg3c/Y+xwD2q1T2wv5No5ccbF6LE9qCl28MzD9UM2S8q8JLRQ4nZ7Litl0G9gR5Z8voIn7pFSbXITFCBhxdcWgoOk7N5rQSozcjzFxf7DVrp08L1Q0rMcfLvVSlSkz/5fWVFFdPf69mmpVER4iJwWLWLx149k8WebSD9v4fhpB0MHGCgur+ToKYHbpwzjnsf3MWG0jgCjhA3bLHjEYQiiYopKHPXE/eQZC9Ex1x+n2KZtHF+oQ3hlTgGTbw5EKhWx7KsKqsx6unX/5faK/2v+3wv7P13QLxIZH4flQikusw2Z9lIyT82pHNq2urzQkVQmo0m7thRuO0r0cF8UhOD1UrT5KG27d0epVrHnw82Ej2yPMlBPxfFMLAey6P7G1GseU0R8AxyFVdjLTUgUMhBA8Ap47U6CWiWiVKspO51JTWUVCqWKCY88iMVUw7znZpCSexZVUigOnQt7ai5Ot4sGU/ujT4rEbbGT9uU+Vr3/ARMff+S6nleTju0YbZnMxs+Wk201IxVL6TF0CH3GjUEsFtOye1c8bjdiieQyEf+r1A+x251s3XyCk8dT0el1DBrcnqTkCDp0bEiHjr7IJkEQ+KFtOybcc4jBfVRUVbtZu7GG7n060a17Yx57aAcDeteSnCDHYraz77CZbbsqOHh0OXNeX0brdklMe3AkUVGBCIJATEwQ4TGNmDTtO1o1lVJS5qbK5EWjkdK/VwBb91QxbFQP7npsNx3bqlApxZw970CnUzNwhO972KRZQ3bt3VvXzBqgqMTBhXw38QmhNG8Ry9Dh7bDbnRw7msW5s/k0buPH/U82x89PRfceTdm88SCWs1Y69mxC/4GtWLFsD8+8sounHwwmPlbJ3gMmPvyihpdeu/W6n69YLOb1N+/i80Xbmfb0UTxeL117tOKtd/shk/250vr/sqTAT00u/3RB/ykbPl/C/kPfEzywJXI/DWX7zuI5V8qdzz9LVMPLZ9o1lZUseOG/WGRulNEBWDOKCdEGMmXGcyhUSo7u2M2eDRuoNVWT0LgJ/cePu8w5+mvs+3YTG9asIqBvU/J3nkCVHEpQl0Yo1Wqqy8opWLYXb5kZjVrHkJtvprqsnLO12cSO71F3jvPrvqPqwHk6vDalbpvH6eLMc0t5Zu5c9AHXH3rm9XqxWywoVCok0hv7Y/V43mBY1PVFuPwaNpuTxx76AKO2gv49NZSWuVixzsJd945jwE8aUIBP3FNO5zLnjTWkn89maH8/xBIpPxx2MmxUbz77eD2B/g4UchFFJS4cToHHpoUxfGAQW3eb+eIrF8+9OJkFc7+m1lSGv17Cvv0lDBvgT8umOoxGKS2aaokIU9B/bCafLJ7Oki928vVX3xFgkGB3ihkwuDPTHhiGRCKmqtLMtLvfpWtbF/176ykucfLREhODhg/k5gndr+t5CILAl6v2sfbLXZSWXoqKadP2yo7+vyrXWlLg/52wX5yh/5Ps59eKIAic/G4vP2zfTmFmNrU1JvRx4bhrbYQGhzP5yccvE0Gvx0Pa0eNUFJUQGhtNXLMmN7yzUOapM+zfto3K0lIyT6Zgx4nH68Hr9qCOCULfJAbToQyUggylXEGDR4eiCrmUUFOck0vaa2vo+s59dc2+AdJmr+XO+x4hOimR/IxMtn+5hoKcCwSHhdNn1EjimjW5offxW/lfCvvqlfs4c2QLb7x4qRNQ1gUb9zxZxoqvZqBQ1Hf6HT2SyXtvfsKn70Wh0/peYCnnLNzxUD5x0TIevy8Qt9uJ0c+MVCzirsdLmftaKHKZmFlzy9m4w8ozDwbyn0nRaDQKDh4u5eHpOXw6rzHJiT6Ty+YdlSxbJ+eDj32rqKoqM1mZJTSIC8Fo1HI+rZCPFqzn+LF0EMQ4nC5sVitqtYIBg7vyzHNj/jJdrf4s/q0V8xP+yU7R34JIJKJlj27oAwP56M1ZNH/pVlQhBgSvl4LNR/n8jTd5cNbMeseIJRIatb/0PTJXm3C7XHXp+7XVJk7u2cvxAz8gCAKtOnWm8+CBdQ2uf42qklJK8/JIbNwEU1g4JVUl6NtHIQvTY8suo2pvKsbuyciMGiq3n0GoMeO02pC7dXUzaLlMjtflhp/86B3VZpxlNQRHRpCTmsaHr75KwMAWhPTpTu2FYj5+8w0mTXug3r39kzhyKIWRfdU/Ror47OBxsSoiQn31XJq3iK23/+5dJxg9WFMn6gDxsTLw1NK5tZaQADtWqxOdVkJwoITGSTKOnLDQp6uabh2UnD7n4PabtRQVlhMdE0Lb1oGMGlLNfU9kcffkEDKy3Xx/yMOrb/iynNevO8TizzZht1mRyRX0HdCRrRv3Me0OLY/eGcU9j6YyZYKGrh1j8Ahq3vrgJB8t0HD3fb+cdwG+VdbhQxkUFlaRkBBK02bRfwZATp4AACAASURBVBnz2B/FP17Y/7/Y0H8L+7duI6Bv07pZr0gsJmJgG868sJyS3DxCoqMuO8ZUXsHK9+eTlZaKSCpGJVMBAgUXcpDHGIkY1BadwZ8dO7dz9uhRpr4041dnV+s/+ZxdG7/F0CYeweMld/sRWr5yG2a3FUW4AV2jCECgbPtpQoe1pWD5Ppx2L2krdxI+tjMKpRJjaDA1BzNRIKVw2zEC2iZiLzdR/M0Reg8fjlKjZtOyFQSNaEtIR59DSx1mRK7XsH7JUpLbtUEkEuG02zm6YzdnThxHq9XRsV/fP6Q0cq4l5ZoSk34Lu3eeZu93Z2jWQE5suA2VSklomBGRSERVtQe1WnHZMT6H76W/bTYnBfllKOUCKqWIAIMXi8VNrRnCgiV4vaCQiQgOknDwuI2QYCl6PxkOp4vqagvBwXqaNg7geJqcjJIGhDYI4OP7WmMwatm25QRfLv+aOS+GkJwYTk6enUembyMyTMKIwbHMejeHCaN1/GeCPxnZDuIaGJn9YgRj7tzLLRN711VcvBKVFbU8+dhC5OIqjP4Cny60E5cQz2uzp1wxYchud2IxOzAYNf+o1cA/505+wqGiApbln2JZ/imiQ/wZ3a7pv6L+E2prTMgN9VP/RWIxcn8t1pray/b3er18+NLLVEdIaDpzIskvjsfdMZSC0gJk4XoSnx6FOERLzo4jlKVd4Mje73nzwUcpzsm98vWrq/nvbVNYt3wJQVO7o+wWh7ptDOoGwdhw+jJO3R4QQNckEltuOY4yE26bg4b3D0WlVpP/2W7yvz3E4WcWIUs38cQ7bxHr8KdowU7c2zMYNfoW+o73lfPNzcjA2Kx+wol/o2hKCwrwuNw47XbmP/cCW/dvxdpMT77RzsLZr7N/05Yb9MSvTKbjkilIEIQrNnb4raSmFvD+O8t44oFgtu224aeTIJe5KCwoZ9XX5Wj1gcQnXB6K171HC9ZusmC1+sZQUVGDqcaD2yNiww4bTidEhEnxeGDbHivnzjtJiJPx8VITGVkuzGaB8go3KqUIl8uFIAhs3W1lxKiuPPzoKG6+tXtd6YPVK7fz5LQAkhN94YwxUUoev09PVpYFQRDIzLbSurkSsViEUiHG6XRj8JcRESqlsPCXS2DMfedrkmOrsVlqKCmuITHGzeEDx3n2qS/q7edwuHh7zhrGjnyBu25/lUk3v8aeXSm/+/n/VfhHzdivt1vR/zcaNW/B7iPfE9D8UjswW1k1ztKaej1DL5KdchYzdpIGtkUkEmEqq8K/fQL2gkrsRVWIZBIKV+9HHuZP4kvj8NgdmA9l8+q90+jcty+dBg0ktpEvoae8sIhXpt6LxWPH0D0ZkVqGSCnF43LjqrUhIKBQKnHWOhCJRdhyKxAppOR+tgttmK+qY0jnxtRmFWHOLaU4vZKx995DTKMkYholXTZ2AH1AANaC8no1Y2yl1ai1WsRSCYc37cCkdJFw98C6JbuhaQzr31xCqx6+CKD/FYIgsPar/axcto3y8hoiIwO57Y7B9O77y51/rsY3a/cxcYyWW8cE43EL3HpvEU2S5Bw/bcc/KJrZb99+RbNEu/YJ7G/XnpunHqRfDyXn0ys5k+Zk5vPxZOfYufnuItq3kpKe5SQ9y4VCIWLCPcWMH6njv08HkXJext2PlzBsgAqjUcu7H+VTaQ6gR69mnD6dg1IhJz4hhDMpeZxPKyAyPAaBH6NqgfgGGqpMblwugehIFWdSHbRsqsTu8CKXSzFbPBQUuwgN8cfr9VJjsqHRKupFnzidbvbvO0WA3s5dE3UM7a9FJBKRmm5n3F2HyUgfUtdA5N231uIwpfDlJ1EY/KWcPGPh2VeXYjDefZmZ6u/IP0bY/65OUUEQOLFnLwd27sDpcNCsXXu6DBl4xfriN4r2/ftycNcuMhZtxdA2AWe1mYrtKQy9dcIVr5ublo5LJaa8qAiZXI7L4UTsJ0cZbqD2bD7W7FLcVgfRN3VAIpXhqKxB3TIaS1EFxzJO8P0jW1DIFQSEhmIz1aLsHo9GKcfr9aAMM+Aoq0Hqr0GTGEbRlwdInNAbsUxK5fEcilfsR+YVYQgIJGCcL0VbJBLhFx+OX3w4trRiLKaaX7zf3sOHs+7L5cjv7IcqxICjykzu0j30GDIEsVjMmRPHMbRPqCd4qiB/FGEG8tMzSGjR7MZ+AD9hy7pzHNlygtkzQkhKCOXEaTMvvLEcmVxKt+6Nf/P5KiuqiOngM7XcdnMowwcFcvqsmfySCh5+6mYiIq4cISQSiXjokZEMGNSOQwfSSUnfxSP3KOnVzUCvbjCwr5HFKy5wIqWWdV9EYTRIeHN+JcWlbqqqBYYMCORCjpM5C2rp0DGGzt1a0Vmv4Y6JrxESKFBr9pCdYyEsRIFO7WTnnkK6dNARFRWEVCohp0CE0yVm/ZYKhg8M5NHnziOXC3TpYKSsws0bc0vo0bsdx45m8snCbzDX1oJIyuChXbhz6gCkUglerxez2UlCNAwbcGlFGhcrZ9xwDZs3Heb+xOGYqi3s/e4Y33wRi0bj8z+0bKrlrol2vlq1519h/7P5JzhF1328iKOnDhPUvwUylYK9+37g1IED3D/zlWt2QF7E6/WSdz4dm9lCdHLDqxa6UmrUPPDaqxzcso1zh05i0Pkx6pHHiWvWBIfNRuapM4hEEN+8KaX5BWxatZIal4VgRSfsXhcumw2JVMCaUYJgdVLx/TlUUYEAOKvNIBahCjOgigqg+MhhQke2QxUdiJ/Gj5LPtyIrqyF0cBsuLNxKQI8mSP1UeEw2DB0bUjh/Oxfe3IDL48JWY0arUNO2b09CIiPZd/oHgjs2rhNgl9mGJauEqIa/HLLWtm8vrBYz295Zg1cKIqeXboMG0WuMr5+oVudHtcla7xhBEHDVWFFpr16i9vcieL1sXHWM+a+Gkxjne6G2aq7jyfu9fLJ023UJe6MmCez54Xu6dvTFgPvrpSQnqqmqqSQ+4deTcZKTI0hOjiC2QRAfzl1CXKyKpo00eDwCZ85LUGu05BUrCAhUMXG8hoen5/HqXDdabSmt2zZj9boBSKVisjKLmfXKZ7z7aiiNkzSUlprYtM3N2o027r3XyLsLShCLvBSXOLA4tLy70MTDj9/CrsPpvL0gHUR65i+W8NZH5SgUNQQFB3A69Sgrlmxh5GAj0x+NxWzx8spb+1n4gYf7HhiGUiknOjYcuTyPvQetZOc4iYmSkRArJSJCTXqRBYDy8lqCAqR1on6RhAYq1m75c0sB3Cj+lsL+T4lDrygu4cCeXTR+4RakPzp29EmRpL//Laf2/kDr3j1+5QyXKCsoZNHM1zELDmR+Kmy55Qy9dSJdhgy84v5KjZoeo0fQY/SIum1n9h9i2fvvo4g2IngFXO9Vo9P7Eza2I8q0PPI/3U3QwJZ43G6Kvj6EI6eCpLsGk7FsJ44aMwE9GiOWiJH7++q5VHx3Dv+OiQQPaImjrAaZWkvkpO5kzd2I3VSLrnkMGa+txa9VLB6TDWdKERMfeZi8jAxOpB4n8b4hyP015OxPJWNLCgqViqzFOwjsmIzLbKN0y0m6DRhYL23/SohEInqMHE6XwYOorapCa/BH9pP63B379mHh7NcxNI1BFeSPIAgU7TqJQa0nPO5y09Sv4fV6OXfwCKcPHUImk9G6ezcaNL1cpN0ONyaTpU7UL9K0kYa8vPzffF2AkaM6cu9dB3hzXiEDeukpLXPy0ZJqxt7c9xedjj+ne48m2KzjmP76t9TWFCGVyRk1ph/DxxpZuHwb+bmF+OnVjLt1BBMm9kQsFlNWZuK1l5dxISsHt8uO1WKn2uR74ZvNVm4ZrWfXPgtysZvZL4Tw0ZIqZrxRgVqtZubse+jVuxnQs9447HYnD98/n6SYKnp3kaNVh7B2o4VHpmew4K0kXnwyjHF37eeOKQNQqeQ88PAIpkyehdnioV1LJTu+r6W6RkCn0zPyFp/zPDzCSHmlQGGxg/DQS47k/UdqSUz+c0NgbxS/S9hFItFsYBjgBDKBOwRBqL4RA7sS/xRBv0he2nm0DSPqRB18IqRrEUvG2TPXLOxer5dFr81C1rUByV2b+IpklZvY8O4KIhrEXlN0R01lJUvfn0vstIFoo4N927KKOPzsIno80o/gDo0o3HOS4vXHcNRaqE0twC86lLPvfo3O35+QsFis29Pw756ESzBTufsszgozoaOi8LjduJ0u3HI3YqkERZgB3F5Cb+qAvlMCOe9uxplbyYzFn2AICmTd4s9p8t8JSJRyPE4X2rgQCtLyaN26LUq1itObjqJSqxl382Sadb16bfCfI5XLMIQEX7Y9tnEyw8bdwvrZS1CEG3DVWDGo9dzxzFO/OUxOEASWv/0eqRdS8e/UEK/LytG3Z9Or3yD63Tyu3r6NjSPZqV/AmVQLTZIvrQyOnaylQdy1d176KXp/De8veJBVK75n1gdn8fPzY9KUwfTo+dsFa8CgVvQb0AKz2cGF7BLmv7eWosJi3B7o1KUpjzw+ps4hKggCzz75MX0725j3Shzl5dWcT6/m5dlZLHirEYIggOAlNEiMIBLRpoWaZo1U9BmTS/NmRhwO9xXHcORwJnJRBdMfjeJCdjGRYTKaP67itvuLOHi0hk7t9KhVUF1tQaWSs29vCreND2bSGDkBBgliiYg586vYuV9Ao1Gwc8dpWrVqwC239ufR57fwwBQjUREKdu8zsWaji3fnX/tk6q/M752xbwOeEQTBLRKJZgHPAE/9/mHV55/qFNUZDDjLL7cPO8tM6IOuPYMzPz0Ts8dWJ+oAykA9xl5NOLRj5zUJ++l9B1E3j6oTdQC/uDAkGiWmglIC4qOI6N0KRaNQLJUmCr/4nk6z7sLjdJE+fyO9uw/CUmtm77LNFOflEtzZ5+S0ZJegahiK4PFgtVtx251YzxdR66/FVWmh9lQO6mADfjINQeFh5KVnoGkQgkQppzo1l3OfbEIRbsArE9i4cgX/efIJHvmxAfaNpNOgAbTq0Z389AxUWg3hcQ2uK/Y581QK5zLOkPzkaMQ/OvaC2yex45XVtO3Vs96LRSQS0Wl0EjNmZfP0A4E0TtJw5EQtb35QxRPPjrruezEG6Lhn2mDg2pOfBEHg8KEMdm4/isftoXO35vTo6UtGs9kcvDD9Y56c5kfvbvHY7V4WfpHLjOmf8t78+xGJRKSk5OJ1VXLHhBhEIhFqtZIG0XJGDNLwzaZyxo3QciGvhsMnHDx6r+8ZrNtcQ/PGWpolSVm/7iDvvfUl5WUViERiGjWJ4c6pw8jMKKZDaxkikQiFUo7F6sRokNGhtYL0TBshQXJcbimBgTpfJM6mQ3w8x4BWK8Hq8EX4jBsZwOLV2Xz43kKiI7S8PdvFhEkDuXnyeD5ZuZuKimqaNEvg7bl9iYwM+KXH9Lfhdwm7IAhbf/LnAeCG1h/9p5XO/TkNmjZG7ZZRsOM44T1bIJKIqU7Nw3w4m3Zzpl3zeRxWK1Kt8jIhkulUWArNVzmqPk67DbH68jhfv5hgCtbsx/+BEERyCRZTLeXbThHe1edQlMhlhA5sxaFNu3l0zmwG3DqeQ9t2sHbRp9QINmwlVYgVMoydkhBLJJRs2IvCX0tAbAROk5UGfdsT0DKesy+txG61YggKxFZYSfW5XI7NWoG+dQMCejdFHuyHuMrJV599SkxyEkER1zejvYjX66UwKxuv20N4fAOkMhlKtep3O0rPHT2GX5sGdaIOINOp0TWJIuPkadr171Nv/1a9I+kU2p63P9lGQX4O8fFhPP7MHbTvcPUWcv8LPvpwM/t2f8/4EVoUchFfLj3H3j2NeO7FCWz89ggDesrp28OX96BWS3jo7lDG3nmBs2fzadIkiqpKM1HhsrrvoE6nxFQtR6WwcORELdGRCt6aX4bDIbBtdy2pGS5OpLh49/WGTL4vHa22Eo3Cxcw3A4mJlLL/SBXvzfmcTl07U1XsE2ij0Y/8vFJEIhcpaU6SE9089XIxEyf7ShG88dpqyksrkUtVSCViLBYvgiDCYXcSYBDx4Rv+VJsEJDIDDz+/hadn3M3cBQ/9oc/5j+JG2tj/A6y8USf7u0a5/BbEYjF3v/Aci996h9PblyBVylGKZNz+2GMYr2AyuBpRSQ1xFFRhK61GFezrryl4vVQdTKdTr2HXdI7EVi3Y9uo3uAe2qzMNua12pDaB5NhEzsxYjjzYj6LT54no24aowe3qjpWoFDgdjrq/2/frg6m0ghUL5uPXIobqgxkUrz2ESAC/5EjEIhHRgy41Fjadz0ctU2AMDUEsFiN3iznxzlcY+zZFbtCQv2IfqjADze4ahr19PCe+20u/W+qbNX4LhZnZfP7mHCxeB2KZBLHFzS33309Sm5bXfc6LKFVqPKWOy7Z7zHYUavUVjoB+A1rSb8Dvv/b1kpdXzuZv97D6kxj8dD5JGNjHyG33n+XY0SyKi8ro0Lj+S18kEpHYQEFJcTVNmkSR3CiSOa/bqal146eTIhKJCI8M4MCxaooqA9h7IoLHpw9j7jtrWflNJQN665k11sCipaWYal1EhCl4/L5A2rfy+QEUCjFancBnX6Vhs8pYsrqUcSMCCQwK5JMleeza68Di8ue2KX3p3acZ+/amknHuJONHB7F5p4UHpgSg07jIznWweaeFwX11BAfK0Wo8FBSbGT9Cy9YtR/4RETBX4leFXSQSbQeuVFx4uiAI637cZzrgBpb+wnmmAlMBAkOu7J3/p9nQrwVDSDAPzppJZUkpLoeDoMiI35wBp1SrGDF5MuveW4KhRzIyPzXVhzIJFOto3evabIaRCfG079SNI2+uxb9LQwRBoHrfebr27sfQO26jprKS8sJiVr4/D03TWMT/1959xzdVto8f/9xJmjZN94LullJaVil7yhBkKijK4xZR8RE3Krj1h4840C/ORxFRQVQeURFlgwxF9oayNxRK90ibtGmS+/dHaqFSoEtCy/1+vXzZnCbnXCekV865zn2uW3t2REHWmr207Xg2UTscDv5YvJCoMf0J7OocW2632kj99g90Zjvmk/kc+Xo5Pq2jsZzJJWvpDm68Z6TzzsiMTMylFmLGXIc2wIhbgBd+nZty9P8WUHQsA43BjRJLcbXen3OVWq1MfX0i/sPaEtU+HiEEBYdPM2PyZJ794L3yVgk11bZXD1aM/xVz1+Z4hjnXlbv3BKWpeSR2aHuJV7vG1i1HuKazoTypg7MH+sDeHmzasJ9mCTGs27yPG865Dl9S4mBbioWRDzv/lkNCfBk4pAePPLuO+273xc9Xx6+L88k1hzD9m8fK73bt3CWer79azqIVm1m0Mp/ouDi6dRbs2JlB+6Sz/d2NBkHzpjpOHs9k+nfP8+F7P/H5zINICcntE5i/dHiFCbjX/rmLGwd50renPw8/s599h87QurmOlX+a2Z5Swup5zovgngYtGmHDw11Dsbnmn6Mr3SUTu5Sy38V+L4QYCVwP9JUX6SgmpZwKTAVnE7Bzf3c1JvS/q84RemU6D+hHWGwMG39bTmGmiR7X3Uhyzx7VGjI5bPR9tOzUkR1r1iKEhuRHx5Y3yspJz2TNokVIITj48Xxye7TAq2kohbtTMeQ76D3m7OiazNRTSIMOn9jGlJosuHkb0Op1BHRpxvEPF/Pwy6+Qcyadrcv/5MyRw3iE+LHwl59Ys3QJbTp1wS02ELdAH+ylVoRWg87bE98OTTi1NgVO5NP80WEX2oVL2r95K6KxF8Edzk7I7RMXhle7aLau+qN8CGRNBYWFcuvofzP7/c/wiArEYbUhcyzc9+z4C/aG/yfaClSH0ehBTp7jvOXZeQ6MwQYGDGrL3J9W8d6U09w4yJ+CQjtTZ2TTsUsykWXDXAEeemQIy5ZGMHvROsxFFjp17cn7T3er0MLAaPRgzKNDGPOos+fL6dM5PPrgJCLC3Nm113lTEoClWHL4eCmRUUGEhwfw9rujMZtLEEJU2hpAq9NiLYXAADdmTmnBqjV5bNmWSVa2A6OnluJiZ8qRUmK1Opi/zMzQf/1z9ye4Wm1HxQzEebG0l5TSfKnn/11Dr6FfbpHNmlbafreqhBDEJycRn1zxrsdda9cz67NPCRyQhH/HjrAriMxlO4jWBXPNNYNJ7tWjQtLSu7tjt5QQEBxCdkY6xYXFCJ0GS2o2jUPDSereFVNOLst+nkP849fjlxiFlJKsTfv5bcYcSht70CjQC5u5hJIzeei8PCgtsJC7YjfX3TScJq2rP777L2ZTITq/88ema309KaqknUJNJPfqQWLH9hxN2Y1Wp6NJq5YX/II9XNKSNtTNdmuqW/cEPvlQsm5TPl07+lJcXMrGzRl8MfMU8c3W4Otr5P2PH+GbmSsY+2oKBk93+g8cyM0julVYjxCC/gOS6X9OWclqtZGamk1AgFelPWrCwgJISm5B6pGdTHg3iwnjA4mO0LF+i4Wp39m5d/TZL/HKXv+Xvv3aMen1TQy5zh9/Pzf69wnA4OFg5ux8Xngqin+PS+OmwV7otJKfF5UQ1bQNfa5tuDmntjX2jwF3YFnZRZP1UsqHLvWi7FLLVVFDbwgcDge/TJ9O1H3X4hPnvGDp2zQMnYceg8VIpwHnn9D5NwohPCKajNUphPVrR2FeHgUZOeSu2ENyYluKCkxsW7UaffPG6MMDKC0pwc3dneBOieSs2c/JDSmYT2ThFdcYrYeeouMZ5K87iLvGjRGPjqlVp77Yli0wfTMDm8Vafi1B2h0Ubj9G03sH1Hi9f+fhaag3nSM9Pd2ZMPF+XntlOoF+OeTl5JGRbeeNl2KJjjLw/me/kJOTzxNjb4SxN1ZpnVJKvv/uD/733TKMBgcFhZLB13fnwTGD0Worlhqfe+k2PvvUh9mzVjF8VBpCCGJiG/PAQ7fQf2DVrj20SY6h36BruXX0cnp28aDAJNm2286gob346vsUIkL9+OxrEzq9gUefvJMbhnY8L46GxCX92P2bNJH/XTznsm9Xqb787BzeevIJWr95T4Xl5jM5nJn2Oy9N+YQju3bzx4KF5OVkE5eYSM+hN+Cw25k28U3S8zKweWooTsslsFUsHt5eaI/kU5ibj6N9I4L7tsZhtZW1HGjE8f+tpnDDUbKL8zAmhIJWUHQgDUN0MNpjJh5/eyJRCc1qldznfv4lm7etJ/DaVmjddGSv3kOkbxj3vfjcZe/wd8C8gOGhJpeWYv5is9kZ99SXhHgf46Wno/DwcL4XGZlW7hhzilk/vnrRo+ZzLVywhTmzfuKd/xdGRJg72TmlvPr2aZol9eT+0f0rfY3D4aC01I5Wqzlvyr2qOnUqh00bD+Lp6U73HokYjR5kZ5nYt+8UgUHeJCSE1esWvlXtx+6Sryx/z9pNNKxcPh6eBmSpg9JCS4Xllow8fPz82bZqNdP+bxI5MTrcByWSUniM98Y9C0Iw5vUJyPxiIrq3odNro4i9qQeGiEBOnjpOsZ+G4mOZ6P2M6EN8KLZbSTt8nLztR7l97GN4SC22ohJ0XgaMieEUHUyDBH8++s8EFsz4plb7NOyBUdx29/34HyrBc2ce1w8Yzr3PjWtQbVtrQqfTUmw2cetNweVJHSAkWE9wgIbTpy7eWfFcP/+4gqfHBBER5vwiCAxw44WxjZk39w+Ki6388ftuFs7fUqFbo0ajwd3drcZJHSA8PIAbb+pM/wHJGI3OPBMY5E33HokkJobX66ReHfWypYBy+bgbDLS/pgd7Z68m9o7eaD30FGcXcObXTdxy6z38MmMGMf/uj1ek8+Kvb3w4JzRr+X3ur7Tu0gWf+HBCeydx5KfVpG/Yi3dSFNrG3piz8vAM9ufwxwsJ6NkcR6mdMz9tRJtvRe/hgYenEV1QAOmr9xDYqyWJE25F6+mOPdPE2hnLSe7RjYimFXvE5KRnsGDmt+zZsgV3Dw86X3st19064rz6thCCVl0706pr58v2PtYXYeEh7Dt4gtYtzl6HKDDZyMi2E9LIr8rryc4qIPZvE0WHNtJTVGjm9hGv0yxWEOivYeonFgYP7cXoczprKrWnErtyScMeuA/bp5+x45VZ6P29sOeZue7mmwmPj6NU6yhP6n/xbxvHgdlb6DZoACVZ+eTsOkrWrsPEvzQcrcEd0/Ez2AuKOf3dn/gnJZK39iBSSuz5Flo+eTM/Tv0Modfi3ywCh6eG8Nt7AOCw2bG5afHuEMu+TVsrJPaiAhMfPf8iuvYRxIy7Ho1dsnHeZtInp3Lvc+Mv6/tVHXZHM3bk/HxFlGIAmjWP4T/vrGXOvHQG9gukR2dfPpqWRZ9+HavVayaheTSr12dy4+Czo2Y2bTNRUGDhP881om8vZ3+fApON+59cTVKbOLp0bXah1SnVpBK7ckl6d3duf/JxbsjLpyA7h8CwxrgbDJhNJuxFJdiLrRXmGi3OzMfHz5+QyAjCw6I59P3vBFzbHK2nOw5rKQKBZ3QwOj9PjDGNCB3SgYwl2zF6+xDQOoZT3/2BXqenJK8Qxzk9ROwWK+7u7litNnR/mwV+6XffU+ArCW0XgclqRpbaCL21G/sn/VrprFA56RnsXL0Gi9lMYvt2xLRIdMkRY3OveOy1n1/jgnZsP8by37bisNvpfk0SXbpe+PrEtzNXsnTBMl5+pjEailmwNIM3Jp9i1ANDyloUVN3I+wbx/DOfYLE46NjOm737zXwwNZuwUGN5Ugfw8dZxx3Bvli/dpBJ7Hbq6i4pKtXj5+RIWF1ves93T25vWHTpy/Mc/sZeUAs7ae8aCLfQc7EwEI8c/jbtFUppvpjgtF2umCf/gYByFVuwWK3lbj3Jy+iry1xygyY3dneO+bQ4GjBhBwZYj5G8/RtGxDEpNFmz5ZtxKBabNx2jd4+xQO5u1lBVz5+LdJgqPxn54NPLFPcSX/JxsPCIDSD9RsVPiztVreeepp1l7chs7LEeZ9sG7zP7oExyO88dy12dffbGMSa9/RmzwXppHHuCLT77mnbd+3X8fDwAAFyhJREFUpLIBE/l5Rfzv2yV8OimcEcNCGT4sls8/bM0NgxoRERlSYUKLqkhMDOed9x5l15EYXnzLzPKNwdx291CiIs6/+9bgocFqLa3xfirnU0fsSq3c8vC/mf3xp+x++Tv0fkbs+RYG/GsEDoedOVM+x+jtzfV33cWiJb8QOKALek8DQggcuWZIL8Kcf4yI6zsRekd/dAY9J+aspXlyMt2vH4R/cDBzPp/G4dd+wqdVNF6+PuQcyeTm++8nsPHZuxT3b9mGm7+RkrSzjUU1eh0ag57c/ScJuu9srbfYbOH7KVNo8sQQjGV3htqva8eud+eStGUbzTu2v3xv3j8oNTWbX+csZ/a0aPx8nX/mQwc6uOvhbezc0ZE2yTEVnr9nTyotm3kQHOQ88xKAVqthQB8jS9bs48bhnVm/7gC/LdlIidVK125t6D8w+aIJv2l8KC++emf545KSUmbPWsqe/UUEBbjh7aVFr9fw80IT/YdWPlJGqRmV2Bu4rNNpbPv9D8xFZhKTk4lv16ZOR3+4GwzcPe4p8jKyOLh9J17+vvw+bz6nC9LxbheDLec0+QsPERYazuHJ8/BqF42jsITCrcd56NVXOZySwvqVKyk9no0lLZfwRhGMeG4MAC06d6BF5w6YCws5sGUbDruDZs8k4+XnWyGGEosF36bhZO08QXaYP/5dE7CbS0j7aT1ebp6ENYkpf+6RXbtxjwooT+rgbGTm160Zu9ZvaDCJfdPGQ/TqaihP6gAeHs42ARvW7z8vsfv5G0nLKC2b1PpsqSbtTCm+/j588flS/lz5O3fe7I3RU8PPC3/h95XbePOd+6s8Htzd3Y1rendg+D0LCPIXWEslbnp32nZsQ7/rajYVoFI5ldgbsJ2r1zLrs0/x6RSH1suDzV9Noelv8dw9bmyFXi+1dTRlD19Pfg+Hl47C9BxKPTUkjRuBsNjQeRkIaBfHySm/MfKpsRxO2Y0hyEibe57ELziI1t0602f4jZw+egzfwEBCY6PPqwF7enmR3OuaC26/SeuWWKZ9TovRQzixeBN7f9qIcNOitUlGjn+uwnO1Wi3Sdn7JRdrsaLUN58/BYNBTYDq/5JJnkng3On8semJiOHpDIDNnZ3LXiGA0GsHBIxZmzS1i7PjmTJo4g5++isbXx/ke9e3pzwNPHmfNn3vp2atqvd43bjjIxjXr+f6LBMIbQ1aOlY+n5RMaGlCrIY7K+RrOJ1mpoMRSVnJ4fDDGcOfIBMe1yRx47xdS1m0kqRoTVFyMubCQL956m9CRPfFvHkXKJ7+gdYPNr8zAzdMDh8VKUHJThK87Or2egXffcd46fIMCa9V8yy84iL5Dh7Lqu8X4dm2KT/MITJuPEh/elJZ/G9LYJKkl9o8KyT+QWj65dWmhhdzV+2g3dlyNY6iNwyUt67xfTI9rmjPl45/YttNE2yTn/J+Hj1lYsrKYT6ZVPDq2Wm18PX056Weymfh/Wbz7cSpxsb6YS9x46JFbMZmK6dzeUJ7UATQawYA+BjZv2l/lxD7nh5U8cp8fbVr5ABAUBK+/6MfwUZsY/dDg8nHnSu2pxN5AHd+7H324f3lSB9DotPh3T2DnhvV1lth3r92Ae7NG+DePAqC0wIwpPZvoR/pjjAxGWu2c+n4N5mOncXM/v3lTXek+ZBCbV6zi5Jx16Lw80BTbEeHxOGx2NPqzpQI3vZ6RTz/FV5PeISsuGI2nHtOuE/QZfEOl09ddDnZHM1LNS4iqw+lVvbw8eHnCKJ6bMIO46Hzc3AQp+6w88dRthIVVnErw3bd/oDh/D1990JiggEjmLc7k06+LmDLtCSKjgljz5z6yss8fupORZcfHp/J5dSuTkZ5DXGzFi6d+vjp8vAQ5OYXliX3fvlMcOpBGaJg/bdvFXvU3jtWESuwNlFbnhr34/JEG9pJS3PSV9wWvCbOpEK3v2fHNDpudwD4tcQ/1R0rQGvQ0ur49+/88gF9w0EXWdGkOu50jKXswmwqJbp6Ab+DZBDX38y+RiYF0e/lG58VZm51D05awas5c+t02osJ64pJa8dJnn7J30xZKzBbi70kiMLSyztT1W/sOccz68WU2bzqM3W7nxQ5x5x0Vp6Xlsmn9DuZ9E4u7uzOB3jq8MWcy01i0YBMPjhlEp85N+XCyjiUrcunfxw8hBPsOmpm31MKHU9pVOZ5miTGs23iowhyvR45ZKLbqaNzYD6vVxoRXZnLs0AHat/Fg/pxS7MLZ2TEg0Ltu3pSrhErsDVRMiwS0hTaydx4hMKkJAKUmM7m/7+Wmx5+qs+3EJbViycK52G8oRat3AwSGiEBKTufi5mWg1CERdklgVCjmgkK8fH0vuc7KZJw8xbSJb1Csd6AP8KLwkzSuvWEo1902AnupjR3r19Py9TvK6/ManZawIR3YMGPVeYkdnJN5t+194bp9Q+Hu7kb3HheeGvHE8UwS4jzKk/pfklsZmLv8FABubjomvj2aCa9M58vvjmM0akhNgyeevqNC295Luf3Oaxn7aApCk07Prr4cPV7MR1/kcve9N+DmpmP6l8vR2Y7w45ex6HQCKSWffJnOB5PnMGHiyJq9AVcpldgbKK1Ox6hnxzHtjTfJ+WMPOm8Dpt2pXHvDUOKSztZyzSYTaxcsZu/OHXj7+NJ9QH/i27ap8nbCmzYhObkjuyb/QkCvFmj1Okw7TxAxoAMGLyMarRZ7rpl8h6bGPeellEyf9A6GPvHEdHfWc0tNZn6f/CvR8fHEtEzE4XCgca/YOkBncMda3HAnU6gLUdHB7D9cTEmJo0Jy355iITLqbO38yOF0HHY7h04UYfA0MPK+AfTqU71rAtExIUz+6HG+/XoZcxYdJSjYjwceHlxeo1+xbAMTnwtCp3N+OQshGHV7MINu24PFYq20D7tSOZXYG7CohHhe/nwK+7dso7jITNzoVviHBJf/3lxYyIfjX8AW5UXAtU3JzTHx1cfvM+SmEXS//tJ3Gu5ev4nVixZRkJtLhE9jNHtMxPlFcnj7HoqCjuHepglF6Xmkz9vMsNvvqNakH+dKO3KMgpJCmnc7WwN38/YksG8rNqxcQUKHtsQ0a0bmhn006nY2GaWvTqFVx/rROje7uNrTGdSJ0FB/OnRqzYsT9/HkQ40ICnBj0fIcFq4o5ZPPnTeB/b5qNzOmfc9rz4bQukUIR44XM+GdZeh0Wv51W/XOemJiQyqMbT+X1WrD4KHBZpN8O/sM85dlYTbbych0cOZMHrGxtZuM5mqiEnsD56bXX7DZ1fpFS7FFGmly97Xly3zjI1jw7v/o0LdP+R2mlVn96wIWz5tDyJB2+AY1IWfbIazbjvPkO29jt9lY+dNcDs3ahF9AAPeMeYzEDlWvxf6dtaQErUF/3jBIndGDkmJnd8Dhox/g0/83AcvxLNwjAjAfSENzuoj+bzxe4+1eLv90W4FLGff8rUz/Yhn3j11HQYGF9h2bMWny9TRu7Gz69f23yxj3SCBJLZ0XSuNiDLw6rhGPvbCcW/7Vvc4ubnbtkcQPv+6g0FRMXp6Z/4wPQAjJD/OKeGHcVD778ulq9au5mqnEfhXbv2snft0qdkj0CPZFH+JN2tHjxLSovDZrLS5m8fffE/fMUDyCnTVz75hGHLf/yZ/zFjDk3ru5+eEH6yzOiKZxOHLMFJ7MxCvSecYhHQ5y1u5nYE/nmUVobDTjP3iPTb+tJPPMaSI79KVtn154eKpEcCl6vY4HxwziwTGDzrtBCeDUqUxaJIRXWNYk2oNCUxHFxaVV7tF+KfeM7MeD9+8i60w2874NQzoERWbBuMeb8Ob7GSycv5nb7mj410XqgkrsVzFfP3/SsvMrLJN2ByU5hRh9fS74uozUU2j9PcuT+l/8kmI4tGRPncep07sx4sEHmfXJFHy7NsXN34uCLUdp5O5P+769y5/n5edLn1uqNsOPUrnKGoQ1iQtj83YT1/U+OwopZa+ZgEDfOq17+wd48eCYG1j26/cgjOg9dAQ38kSr1dC5vYHV20/U2bYaOpXYr2LdBg5g6qQ38Y2PwDMsEIfdTur8jURGRBMcHnbB13n7+2PNMWG32tDqz36ELOm5BAfVbkjjhSRd043GMVFsWr6SwqwCEm74F626dUHnVrO6vVJ1d40cyBsTpgHQsa0Pew8UMenjbO4eNaLOO2JGR4dw6owgONgXjebsuvceLCE0TNXYq8olU+M1adVCvj7nu8u+XeV8m5evZO70GWh8PbDmFxET25S7nnryvH4sfzfjrXc4SS7Rt3RH66Gn8EQGx6YuY8S995OVlobFbCahTZs6703TUNntk7ghsnqtcS+nLZsPM3P6Yo4eOU1YWBC33nkdvas5KqYqpJQ8/cQUmoSlM2ZUI4yeWpauzOX9qYVM+fIZQkJqNly2oajq1HgqsSuUWq2kHz+JwdurQtfEiyk2W/jxkyns2rIZndEdN7uGpA6d2LTuT3w6NUHr5UHuugOEeAYybPQoYlokqgR/EXb7JAI9POkW3NvVobicyWThvx/+wh+rtoN0EBcfySNPDCcxMfzSL27gVGJXLouiAhNmkwkvXx9e//fDRD86EK/IYE4s3MjJZZvR+XnibtMSaPTngRefb5B3eNaFvYUH6eq/RCX2c1itNkpLbaqHzDmqmthVjV2pFaOPN0Yfbw5s3Y4+zA+vyGByUo5xen0KTV8aDhqBtkRSuj+D6ZPe5anJ71y0LmstKWHt/EVsW78OrVZLx5696NS/L1qd+qhebfR6HXq9+nevCXVurNQJrc4Nh9U5jd2ZtbsJ6tsaNx9PkBKNRkPja1qRU5BN+vELj2xw2O1Me20iv29fjcegRLR9mrB45Xy+m/zB5doNRWkQ1NehUidiWiSgNTl709hLrGi9PJB2BzZTMX4hjRAaDTovA8WWC9/iv3/LNs4UZpHw9DBEWT3et1k4e16fTeqhw0Q0jSuf1k3NaK8oF6YSu1IntDod95b1prHaLWQu24mbvxEfPz/cDQaKUjOx55iJiGtywXUc27cfY6uI8qQOoHHT4dU8nJR1G1j2w4/s2bwFnZsbHXv3ZvDdd+JhrLtOlYrSUKhSjFJn/upNc9foh/Ev1FE4fxeW/Wc4uXATR/67mFtGP3DRfjE+/gGUZhaUPy42mzlz8iSntu7lh88+54TRRNLb99DspVvYk3uEL998q9KJmesrV/WLURoedcSu1Ck3vZ62va6hVdfO7PhjDft27MDbN5ROr91JaGz0BV9nt9lwN7iTsWYP2mh/gts1Iycjg8JDp7HlWwjs0wJj5yaYCk34BQURe2dv9rw+m5P7DxKV2KzCulIPHebwjhQMXkZade+Cp1fVJ4NwFVf3i1EaFpXYlX+Em15Ph3596NCvzyWfW2q1Mu21iaQVZRHUuxUnZ6/h8IzlaPU6fGJCCW4Xj1vTINwDvSlKy8UnIACNRoNnbAiZp06XJ3aHw8GP/53C9m2b8GoThaOgmF9nzuS+Z8fTpHXVpm9TlIZAJXbF5TYuWU66I5+EsUMRGg1xt/XmwII/yVyyneRx/+L07zvIOnSCwJ4tEFoNDpsNodNhPpxOyM0R5evZs34ju/bvoPlLI8om/YC8fSeYOfl9Xvr8UzVkUrlqqBq74nI7Nm0gqEeL8oumQgiCOyUgPPUUnsykUZfmFB/NJH3hVmyFxZQWmDkycwWRYdFExJ/tTrl1zRoCerYoT+oAfolROLx1nNh/8LLvl6K4ikrsisvp9XrsJdYKy7z9fLHnmcnedgiHzUHsTT3IWbSTU+8t4ei780lqlMio58dXGPYopYTKRkHWo6GRJ4pSXB2C0gCoc1PF5Tr17sPsWdPxbxWLrqwNbM7mQ0SGRxOSp+fQG3Pw8fdn5GNP0LF/3wuOYW/brTs/fD+DoPbNyrtO5u0/iSiwEpUQf9n2p6YOWG4i0LyEKKOrI1HqO5XYFZdr3b0LR/ftY92E/+HdPJzSnCJ0BaU8+MpLhERGXHoFZVp168yeLVvYNfEHjMnOi6eWvae5b/x4VV9Xrirq0664nBCCYQ+MovvggRzbsw+jrw/N2rapdjLWaDTc+vgjdDtwiMM7d2GI86L1Y10x+nj/Q5ErypVJJXblihEUFkpQWGit1iGEICohvl6UXhTln6IuniqKojQwKrEryhVEtRVQ6kKdJHYhxDNCCCmE+GcmvFSUq0BzL1U+UupGrRO7ECISuA5QU4griqJcAeriiP09YDzQcNrsKYqi1GO1SuxCiKHAKSnljio890EhxGYhxGZTbl5tNqsoiqJcxCWHOwohfgMqm4H4ReAFoH9VNiSlnApMBedk1tWIUVEURamGSyZ2KWW/ypYLIVoDscCOslu8I4CtQohOUsozdRqlolxF1mauoltwb1eHodRjNS7FSCl3SSlDpJQxUsoYIBVop5K6otTcActNrg5BaQDUOHZFUZQGps5aCpQdtSuKoigupo7YFUVRGhiV2BXlCqPaCii1pRK7olxBVFsBpS6oxK4oitLAqMSuKIrSwKjEriiK0sCoxK4oitLACCkvf9sWIUQmcLwaLwkCsv6hcC4ntR9XnoayL2o/rjz/xL5ESymDL/UklyT26hJCbJZSdnB1HLWl9uPK01D2Re3HlceV+6JKMYqiKA2MSuyKoigNTH1J7FNdHUAdUftx5Wko+6L248rjsn2pFzV2RVEUperqyxG7oiiKUkX1IrELId4RQuwTQuwUQvwshPBzdUzVIYQYKITYL4Q4JIR4ztXx1JQQIlIIsVIIsVcIsVsI8YSrY6oNIYRWCLFNCDHf1bHUlBDCTwjxY9nfx14hRFdXx1RTQoixZZ+rFCHELCGEh6tjqgohxJdCiAwhRMo5ywKEEMuEEAfL/u9/OWOqF4kdWAa0klImAQeA510cT5UJIbTAf4FBQAvgdiFEC9dGVWM24GkpZXOgC/BIPd4XgCeAva4OopY+ABZLKROBNtTT/RFChAOPAx2klK0ALXCba6OqsunAwL8tew5YLqWMB5aXPb5s6kVil1IulVLayh6uxzm/an3RCTgkpTwipbQC/wOGuTimGpFSpkkpt5b9bMKZRMJdG1XNCCEigCHANFfHUlNCCB+gJ/AFgJTSKqXMc21UtaIDDEIIHeAJnHZxPFUipfwDyPnb4mHAjLKfZwA3Xs6Y6kVi/5v7gEWuDqIawoGT5zxOpZ4mw3MJIWKAtsAG10ZSY+8D4wGHqwOphSZAJvBVWUlpmhDC6OqgakJKeQp4FzgBpAH5Usqlro2qVhpJKdPAeUAEhFzOjV8xiV0I8VtZbe3v/w075zkv4iwHfOu6SKtNVLKsXg9FEkJ4AT8BT0opC1wdT3UJIa4HMqSUW1wdSy3pgHbAp1LKtkARl/mUv66U1aCHAbFAGGAUQtzl2qjqrzqb87S2pJT9LvZ7IcRI4Hqgr6xfYzRTgchzHkdQT04xKyOEcMOZ1L+VUs5xdTw11B0YKoQYDHgAPkKIb6SU9S2RpAKpUsq/zpp+pJ4mdqAfcFRKmQkghJgDdAO+cWlUNZcuhAiVUqYJIUKBjMu58SvmiP1ihBADgWeBoVLK+jZv2CYgXggRK4TQ47wg9KuLY6oRIYTAWc/dK6Wc7Op4akpK+byUMqJsAvbbgBX1MKkjpTwDnBRCJJQt6gvscWFItXEC6CKE8Cz7nPWlnl4ILvMrMLLs55HAL5dz41fMEfslfAy4A8uc/+asl1I+5NqQqkZKaRNCPAoswXml/0sp5W4Xh1VT3YG7gV1CiO1ly16QUi50YUxXu8eAb8sOGo4Ao1wcT41IKTcIIX4EtuIst26jntyFKoSYBfQGgoQQqcCrwFvAbCHE/Ti/tEZc1pjqV1VDURRFuZR6UYpRFEVRqk4ldkVRlAZGJXZFUZQGRiV2RVGUBkYldkVRlAZGJXZFUZQGRiV2RVGUBkYldkVRlAbm/wNiwlDLqHjVNQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gmm = GMMClassifier(n_iter=100,shr_cov=True)\n", "gmm.fit(X, y)\n", "utils.plot_decision_function(X, y, gmm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可以发现类与类的边界都变成了**直线**,这时的GMM模型似乎退化成了一个线性模型,这是为什么呢?它这时其实是一个带有一定约束的LogisticRegression模型,接下来我们推推看它们之间的关系" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 二.协方差矩阵共享的GMM模型与LogisticRegression的关系\n", "以二分类为例进行推导,假如我们训练好了两个分类模型,分别为$C_1,C_2$,那么有: \n", "\n", "$$\n", "p(x\\mid C_1)=N(x\\mid u_1,\\Sigma)\\\\\n", "p(x\\mid C_2)=N(x\\mid u_2,\\Sigma)\\\\\n", "p(C_1)+p(C_2)=1\n", "$$ \n", "所以,高斯混合模型: \n", "\n", "$$\n", "p(x)=p(C_1)p(x\\mid C_1)+p(C_2)p(x\\mid C_2)\n", "$$ \n", "\n", "接下来,我们转换为判断模型的形式: \n", "\n", "$$\n", "p(C_1\\mid x)=\\frac{p(C_1)p(x\\mid C_1)}{p(x)}\\\\\n", "=\\frac{p(C_1)p(x\\mid C_1)}{p(C_1)p(x\\mid C_1)+p(C_2)p(x\\mid C_2)}\\\\\n", "=\\frac{1}{1+exp(-Z)}\n", "$$ \n", "\n", "这里$Z=log\\frac{p(C_1)p(x\\mid C_1)}{p(C_2)p(x\\mid C_2)}$,这里已经看到了LogisticRegression的雏形了,接着,我们将$Z$化简看看: \n", "\n", "$$\n", "Z=log\\frac{p(C_1)p(x\\mid C_1)}{p(C_2)p(x\\mid C_2)}\\\\\n", "=log\\frac{p(x\\mid C_1)}{p(x\\mid C_2)}+log\\frac{p(C_1)}{p(C_2)}\\\\\n", "=....省略....\\\\\n", "=(u_1-u_2)^T\\Sigma^{-1}x-\\frac{1}{2}u_1^T\\Sigma^{-1}u_1+\\frac{1}{2}u_2^T\\Sigma^{-1}u_2+log\\frac{N_1}{N_2}(N_1,N_2表示1,2类的样本量\\frac{p(C_1)}{p(C_2)}=\\frac{N_1}{N_2})\n", "$$ \n", "\n", "所以,如果令: \n", "$$\n", "w^T=(u_1-u_2)^T\\Sigma^{-1}\\\\\n", "b=-\\frac{1}{2}u_1^T\\Sigma^{-1}u_1+\\frac{1}{2}u_2^T\\Sigma^{-1}u_2+log\\frac{N_1}{N_2}\n", "$$ \n", "\n", "那么: \n", "\n", "$$\n", "Z=w^Tx+b\n", "$$ \n", "\n", "那么: \n", "\n", "$$\n", "p(C_1\\mid x)=\\frac{1}{1+exp(-w^Tx-b)}\n", "$$ \n", "\n", "所以,如果数据量大没必要去训练一个复杂的GMM分类器,就训练一个LR就好啦..." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }