{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# k-Means" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "根据训练样本中是否包含标签信息,机器学习可以分为 **监督学习** 和 **无监督学习**。`聚类算法`是典型的无监督学习,其训练的样本中值包含`样本的特征`,**不包含样本的标签信息**。在聚类算法中,利用样本的特征,将具有相似特征空间分布的样本划分到同一类别中。\n", "\n", "\n", "![cluster illustration](images/kmeans-illustration.jpeg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. 方法\n", "\n", "由于具有出色的速度和良好的可扩展性,K-Means聚类算法最经典的聚类方法。***k-Means算法是一个重复移动类中心点(重心,centroids)的过程***:\n", "* 移动中心点到其包含成员的平均位置;\n", "* 然后重新划分其内部成员。\n", "\n", "`k`是算法中的超参数,表示类的数量;k-Means可以自动分配样本到不同的类,但是不能决定究竟要分几个类。`k`必须是一个比训练集样本数小的正整数。有时,类的数量是由问题内容指定的。例如,一个鞋厂有三种新款式,它想知道每种新款式都有哪些潜在客户,于是它调研客户,然后从数据里找出三类。也有一些问题没有指定聚类的数量,最优的聚类数量是不确定的。\n", "\n", "k-Means的参数是类的重心位置和其内部观测值的位置。与广义线性模型和决策树类似,k-Means参数的最优解也是以代价函数最小化为目标。k-Means代价函数公式如下:\n", "$$\n", "J = \\sum_{k=1}^{K} \\sum_{i \\in C_k} | x_i - u_k|^2\n", "$$\n", "\n", "$u_k$是第$k$个类的重心位置,定义为:\n", "$$\n", "u_k = \\frac{1}{|C_k|} \\sum_{i \\in C_k} x_i\n", "$$\n", "\n", "\n", "成本函数是各个类畸变程度(distortions)之和。每个类的畸变程度等于该类重心与其内部成员位置距离的平方和。若类内部的成员彼此间越紧凑则类的畸变程度越小,反之,若类内部的成员彼此间越分散则类的畸变程度越大。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. 算法\n", "求解成本函数最小化的参数就是一个重复配置每个类包含的观测值,并不断移动类重心的过程。\n", "\n", "输入:$T=\\{ x_1, x_2, ..., x_N\\}$,其中$x_i \\in R_n$,i=1,2...N\n", "\n", "输出:聚类集合$C_k$, 聚类中心$u_k$, 其中k=1,2,...K\n", "\n", "1. 初始化类的重心$u_k$,可以随机选择样本作为聚类中心\n", "2. 每次迭代的时候,把所有样本分配到离它们最近的类,即更新聚类集合$C_k$\n", "3. 然后把重心移动到该类全部成员位置的平均值那里,即更新$u_k$\n", "4. 若达到最大迭代步数,或两次迭代差小于设定的阈值则算法结束,否则重复步骤2\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. 计算过程演示" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "X0 = np.array([7, 5, 7, 3, 4, 1, 0, 2, 8, 6, 5, 3])\n", "X1 = np.array([5, 7, 7, 3, 6, 4, 0, 2, 7, 8, 5, 7])\n", "plt.figure()\n", "plt.axis([-1, 9, -1, 9])\n", "plt.grid(True)\n", "plt.plot(X0, X1, 'k.');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "假设K-Means初始化时,将第一个类的重心设置在第5个样本,第二个类的重心设置在第11个样本.那么我们可以把每个实例与两个重心的距离都计算出来,将其分配到最近的类里面。计算结果如下表所示:\n", "![data_0](images/data_0.png)\n", "\n", "新的重心位置和初始聚类结果如下图所示。第一类用X表示,第二类用点表示。重心位置用稍大的点突出显示。\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "C1 = [1, 4, 5, 9, 11]\n", "C2 = list(set(range(12)) - set(C1))\n", "X0C1, X1C1 = X0[C1], X1[C1]\n", "X0C2, X1C2 = X0[C2], X1[C2]\n", "plt.figure()\n", "plt.title('1st iteration results')\n", "plt.axis([-1, 9, -1, 9])\n", "plt.grid(True)\n", "plt.plot(X0C1, X1C1, 'rx')\n", "plt.plot(X0C2, X1C2, 'g.')\n", "plt.plot(4,6,'rx',ms=12.0)\n", "plt.plot(5,5,'g.',ms=12.0);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "现在我们重新计算两个类的重心,把重心移动到新位置,并重新计算各个样本与新重心的距离,并根据距离远近为样本重新归类。结果如下表所示:\n", "\n", "![data_1](images/data_1.png)\n", "\n", "画图结果如下:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAEICAYAAAB25L6yAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAUz0lEQVR4nO3dfZBddX3H8feXDQmEKKjBpULCpg+KjI61CeLCaHcbxpFC1Zm2FMWgpk5aWiw6WitSFLXUqe1YdVQciqEFtmYyaFtEWtGwa32IlASYIgRba0ICgsQHHjbobh6+/eOe9S7hZvcu2Zvz2933a2Zn99577jnf8927nz33d+69v8hMJEnlOqzuAiRJEzOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1Br2kTEmyPiGwe4bWlEDEdE16Gua1wN50XEzXVt/2BFRE9EZETMq7sWHVoG9RwWEQsi4rMRcV9EPB4Rd0bEmZ3YVmZuz8xFmbm32vZQRLy1E9uq1v+UUMvMgcx8Vae2eah1uocqh0E9t80DdgC/CRwN/CWwPiJ66iyqHXUemU/GI15NN4N6DsvMXZl5WWZuy8x9mXkjsBVYDhARfRFxf0S8MyIejogHI+ItY/ePiOdExA0R8VhE/BfwKwfa1vgj3Ii4HHgF8MlqOOST1TInRcRXIuInEfHdiDhn3P3/MSKuiIibImIX0B8RZ0XEHdX2d0TEZeM2+Z/V90eqbfTuPzQTEadFxG0R8Wj1/bRxtw1FxIci4pvVs42bI2LxAfZtrE9/EREPAVdHxGER8Z6I+L+I+HFErI+IZ1fLHxER11XXP1Jtu7u6bVtEnDFu3ZdFxHUttvmUHkbD31e/q8ci4q6IeNGBfieaOQxq/UIVFs8H7h539XE0jraPB/4Q+FREPKu67VPAz4FfAlZXX5PKzEuArwMXVsMhF0bEUcBXgH8GngucC3w6Ik4ed9c3AJcDzwC+AewCzgeOAc4CLoiI11XLvrL6fky1jY377euzgS8BnwCeA3wU+FJEPGe/7b2lqmc+8K4Jdus44NnAicAa4G3A62g8W3ke8FMa/QJ4E42eLqm2/cfAzyZY91O06iHwqmq/n1+t/xzgx1NZr8pkUAuAiDgcGAD+KTPvHXfTbuCDmbk7M28ChoEXVEMPvwu8rzoy/w7wTwdRwtnAtsy8OjP3ZOYdwOeB3x+3zL9l5jero/+fZ+ZQZt5VXf5v4HM0grEdZwH/m5nXVtv7HHAv8Dvjlrk6M/8nM38GrAd+fYL17QPen5kj1fJ/DFySmfdn5ghwGfB71bDIbhoB/auZuTczN2fmY23WPZHdNP6JnQREZm7JzAenYb2qmUEtIuIw4FpgFLhwv5t/nJl7xl1+AlgEHEtzjHvMfQdRxonAqdVQwCMR8QhwHo0j1THjt0VEnBoRgxGxMyIepRGOLYcnWnhei3rvo/HMYcxD434e2+8D2ZmZPx93+UTgX8btyxZgL9BNo9dfBtZFxA8i4iPVP8qDkpm3AJ+kceT+cERcGRHPPNj1qn4G9RwXEQF8lkaA/G5m7m7zrjuBPTSevo9ZOoVN7/+xjTuAr2XmMeO+FmXmBRPc55+BG4AlmXk08BkgDrDs/n5AI0zHWwo80PYePFmr/Tlzv/05IjMfqJ6dfCAzTwZOo/Fs4vzqfruAhePWcxwH9pR9zMxPZOZy4GQaQyB//jT3RwUxqHUF8ELgd6qn7G2pXmb3BeCyiFhYjSW/aQrb/SHwy+Mu3wg8PyJWRcTh1dcpEfHCCdbxDOAnmfnziHgZjTHlMTtpDEf8cst7wk3V9t5QneD8AxrhduMU9mEinwEuj4gTASLi2Ih4bfVzf0S8uBo+eozGkMW+6n53AudW+78C+L0JtvGkHlb9OrU6Ot9F4/zBvgPdWTOHQT2HVSHyRzTGXh+qXj0wHBHntbmKC2kMBzwE/CNw9RQ2/3EaY7Y/jYhPZObjNE6GnUvjaPch4G+ABROs40+AD0bE48D7aIwjA5CZT9A48fjNavjh5ePvmJk/pnEk+04aJ9zeDZydmT+awj5Mtn83ADdX9X0bOLW67TjgehohvQX4Go3hEIBLabx65qfAB2g8a5hoG7/oIfBM4B+q+95X7dffTtP+qEbhxAGSVDaPqCWpcAa1JBXOoJakwhnUklS4jnx4zOLFi7Onp6cTq27brl27OOqoo2qtoRT2osleNNmLphJ6sXnz5h9l5rGtbutIUPf09LBp06ZOrLptQ0ND9PX11VpDKexFk71oshdNJfQiIg74zl6HPiSpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwbQV1RLwjIu6OiO9ExOci4ohOFyapAz7yERgcfPJ1g4ON61WsSYM6Io4H/gxYkZkvArqAcztdmKQOOOUUOOecZlgPDjYun3JKvXVpQu3OmTgPODIidgMLgR90riRJHdPfD+vXwznn0HPmmfDv/9643N9fd2WaQGTm5AtFXARcDvwMuDkzz2uxzBpgDUB3d/fydevWTXOpUzM8PMyiRYtqraEU9qLJXjT0rF1Lz7XXsm3VKratXl13ObUr4XHR39+/OTNXtLwxMyf8Ap4F3AIcCxwO/Cvwxonus3z58qzb4OBg3SUUw1402YvMvOWWzMWLc+uqVZmLFzcuz3ElPC6ATXmATG3nZOIZwNbM3JmZu4EvAKcd/P8PSYfc2Jj0+vWNI+lqGOQpJxhVlHaCejvw8ohYGBEBrAS2dLYsSR1x221PHpMeG7O+7bZ669KEJj2ZmJm3RsT1wO3AHuAO4MpOFyapA9797qde19/vycTCtfWqj8x8P/D+DtciSWrBdyZKUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqBW5zjjdZO9aCqlF6XU0QaDWp3jjNdN9qKplF6UUkcb2p2FXJq6cTNec8EFcMUVc3fGa3vRVEovZtCM7B5Rq7P6+xt/jB/6UON7gX8Eh4y9aCqlF1UdPddeW/TvxKBWZw0ONo6YLr208X0uT6JqL5pK6UVVx7ZVq4r+nRjU6pxxM17zwQ/O7Rmv7UVTKb2YQTOyG9TqHGe8brIXTaX0opQ62uDJRHWOM1432YumUnpRSh1t8IhakgpnUEtS4QxqzVyt3ll2IIW+40xqh0GtmWv/d5YdSMHvOJPaYVBr5hr/DrcDhfX4l4IVeJJIaodBrZltorA2pDVLGNSa+VqFtSGtWcTXUWt2KOWDfqQO8Ihas0cpH/QjTTODWrNHKR/0I00zg1qzQykf9CN1gEGtma/VicN2XronzRAGtWa2iV7dYVhrlmgrqCPimIi4PiLujYgtEdHb6cKkSbXzEjzDWrNAu0fUHwf+IzNPAl4CbOlcSVKb9v884YmWu/jiJ3/OsJ/9oRlk0tdRR8TRwCuBNwNk5igw2tmypDa0+jzhVsY+E2T9+sbl8Ufi0gzQzhtelgE7gasj4iXAZuCizNzV0cqk6TKDZpuWWonMnHiBiBXAt4HTM/PWiPg48FhmXrrfcmuANQDd3d3L161b16GS2zM8PMyiRYtqraEU9qKhZ+1aeq69lm2rVjXmyJvjfFw0ldCL/v7+zZm5ouWNmTnhF3AcsG3c5VcAX5roPsuXL8+6DQ4O1l1CMexFZt5yS+bixbl11arMxYsbl+c4HxdNJfQC2JQHyNRJTyZm5kPAjoh4QXXVSuCeafgHIh0aM2i2aamVdl/18TZgICL+G/h14K87VpE03WbQbNNSK219el5m3gm0HjuRSjeDZpuWWvGdiZJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1dAht3LGRD3/9w2zcsbHuUmpnL9rX1udRSzp4G3dsZOU1KxndO8r8rvlsOH8DvUt66y6rFvZiajyilg6RoW1DjO4dZW/uZXTvKEPbhuouqTb2YmoMaukQ6evpY37XfLqii/ld8+nr6au7pNrYi6lx6EM6RHqX9LLh/A0MbRuir6dvTj/VtxdTY1BLh1Dvkl5DqWIv2ufQhyQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUzRw1wA9H+vhsA8cRs/Hehi4a6DukjTL+el50hQM3DXAmi+u4YndTwBw36P3seaLawA478Xn1VmaZjGPqKUpuGTDJb8I6TFP7H6CSzZcUlNFmgvaDuqI6IqIOyLixk4WJJVs+6Pbp3S9NB2mckR9EbClU4XMRs6yPPssPXrplK6XpkNbQR0RJwBnAVd1tpzZY2yW5UsHL2XlNSsN61ni8pWXs/DwhU+6buHhC7l85eU1VaS5IDJz8oUirgc+DDwDeFdmnt1imTXAGoDu7u7l69atm+ZSp2Z4eJhFixbVtv2B7QOs3bqWfezjMA5j9bLVnLe0npNNdfeiJNPRi6/+8KtctfUqHh55mOcueC5vXfZWzug+Y5oqPHR8XDSV0Iv+/v7Nmbmi5Y2ZOeEXcDbw6ernPuDGye6zfPnyrNvg4GCt2//W9m/lkX91ZHZ9oCuP/Ksj81vbv1VbLXX3oiT2osleNJXQC2BTHiBT23l53unAayLit4EjgGdGxHWZ+cZp+CcyaznLsqTpMmlQZ+bFwMUAEdFHY+jDkG6DsyxLmg6+jlqSCjeldyZm5hAw1JFKJEkteUQtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUKvjnI1dOjhT+jxqaarGZmMf3TvK/K75bDh/g7PeSFPkEbU6amjbEKN7R9mbexndO8rQtqG6S5JmHINaHdXX08f8rvl0RRfzu+bT19NXd0nSjOPQhzrK2dilg2dQq+OcjV06OA59SFLhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCTRrUEbEkIgYj4p6IuDsiLjoUhUmSGtr5POo9wDsz8/aIeAawOSK+kpn3dLg2SRJtHFFn5oOZeXv18+PAFuD4Them6bFxx0YGtg84A7g0g01pjDoieoCXArd2pBpNq7EZwNduXcvKa1Ya1tIM1fZUXBGxCPg88PbMfKzF7WuANQDd3d0MDQ1NV41Py/DwcO011G1g+wAje0bYxz5G9oywdnAtI0tH6i6rVj4umuxFU+m9iMycfKGIw4EbgS9n5kcnW37FihW5adOmaSjv6RsaGqKvr6/WGuo2dkQ9smeEBfMWsOH8DXN+7kIfF032oqmEXkTE5sxc0eq2dl71EcBngS3thLTKMTYD+Oplqw1paQZrZ+jjdGAVcFdE3Fld997MvKljVWna9C7pZWTpiCEtzWCTBnVmfgOIQ1CLJKkF35koSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVrq2gjohXR8R3I+J7EfGeThclSWqaNKgjogv4FHAmcDLw+og4udOFHYyNOzYysH2AjTs21l2KJB20do6oXwZ8LzO/n5mjwDrgtZ0t6+nbuGMjK69Zydqta1l5zUrDWtKMN6+NZY4Hdoy7fD9w6v4LRcQaYA1Ad3c3Q0ND01HflA1sH2Bkzwj72MfInhHWDq5lZOlILbWUYnh4uLbfR2nsRZO9aCq9F+0EdVsy80rgSoAVK1ZkX1/fdK16ShbsWMDAjkZYL5i3gNX9q+ld0ltLLaUYGhqirt9HaexFk71oKr0X7Qx9PAAsGXf5hOq6IvUu6WXD+RtYvWw1G87fMOdDWtLM184R9W3Ar0XEMhoBfS7who5WdZB6l/QysnTEkJY0K0wa1Jm5JyIuBL4MdAFrM/PujlcmSQLaHKPOzJuAmzpciySpBd+ZKEmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqXGTm9K80Yidw37SveGoWAz+quYZS2Isme9FkL5pK6MWJmXlsqxs6EtQliIhNmbmi7jpKYC+a7EWTvWgqvRcOfUhS4QxqSSrcbA7qK+suoCD2osleNNmLpqJ7MWvHqCVptpjNR9SSNCsY1JJUuFkZ1BHx6oj4bkR8LyLeU3c9dYmIJRExGBH3RMTdEXFR3TXVKSK6IuKOiLix7lrqFBHHRMT1EXFvRGyJiN66a6pLRLyj+tv4TkR8LiKOqLumVmZdUEdEF/Ap4EzgZOD1EXFyvVXVZg/wzsw8GXg58KdzuBcAFwFb6i6iAB8H/iMzTwJewhztSUQcD/wZsCIzXwR0AefWW1Vrsy6ogZcB38vM72fmKLAOeG3NNdUiMx/MzNurnx+n8Qd5fL1V1SMiTgDOAq6qu5Y6RcTRwCuBzwJk5mhmPlJrUfWaBxwZEfOAhcAPaq6npdkY1McDO8Zdvp85Gk7jRUQP8FLg1ppLqcvHgHcD+2quo27LgJ3A1dUw0FURcVTdRdUhMx8A/g7YDjwIPJqZN9dbVWuzMai1n4hYBHweeHtmPlZ3PYdaRJwNPJyZm+uupQDzgN8ArsjMlwK7gDl5HicinkXj2fYy4HnAURHxxnqram02BvUDwJJxl0+orpuTIuJwGiE9kJlfqLuempwOvCYittEYCvutiLiu3pJqcz9wf2aOPbO6nkZwz0VnAFszc2dm7ga+AJxWc00tzcagvg34tYhYFhHzaZwcuKHmmmoREUFjLHJLZn607nrqkpkXZ+YJmdlD4/FwS2YWeeTUaZn5ELAjIl5QXbUSuKfGkuq0HXh5RCys/lZWUuiJ1Xl1FzDdMnNPRFwIfJnGWdy1mXl3zWXV5XRgFXBXRNxZXffezLypvpJUgLcBA9WBzPeBt9RcTy0y89aIuB64ncYrpO6g0LeS+xZySSrcbBz6kKRZxaCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1Jhft/uEEZ1c5o3CIAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "C1 = [1, 2, 4, 8, 9, 11]\n", "C2 = list(set(range(12)) - set(C1))\n", "X0C1, X1C1 = X0[C1], X1[C1]\n", "X0C2, X1C2 = X0[C2], X1[C2]\n", "plt.figure()\n", "plt.title('2nd iteration results')\n", "plt.axis([-1, 9, -1, 9])\n", "plt.grid(True)\n", "plt.plot(X0C1, X1C1, 'rx')\n", "plt.plot(X0C2, X1C2, 'g.')\n", "plt.plot(3.8,6.4,'rx',ms=12.0)\n", "plt.plot(4.57,4.14,'g.',ms=12.0);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们再重复一次上面的做法,把重心移动到新位置,并重新计算各个样本与新重心的距离,并根据距离远近为样本重新归类。结果如下表所示:\n", "![data_2](images/data_2.png)\n", "\n", "画图结果如下:\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "C1 = [0, 1, 2, 4, 8, 9, 10, 11]\n", "C2 = list(set(range(12)) - set(C1))\n", "X0C1, X1C1 = X0[C1], X1[C1]\n", "X0C2, X1C2 = X0[C2], X1[C2]\n", "plt.figure()\n", "plt.title('3rd iteration results')\n", "plt.axis([-1, 9, -1, 9])\n", "plt.grid(True)\n", "plt.plot(X0C1, X1C1, 'rx')\n", "plt.plot(X0C2, X1C2, 'g.')\n", "plt.plot(5.5,7.0,'rx',ms=12.0)\n", "plt.plot(2.2,2.8,'g.',ms=12.0);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "再重复上面的方法就会发现类的重心不变了,k-Means会在条件满足的时候停止重复聚类过程。通常,条件是前后两次迭代的成本函数值的差达到了限定值,或者是前后两次迭代的重心位置变化达到了限定值。如果这些停止条件足够小,k-Means就能找到最优解。不过这个最优解不一定是全局最优解。\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Program" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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aLCporg7ixhhjumIzIcYYY0xnQlsBmY7HJYxEdit4OMaYoUcVMoOgRG9/Gl6v1hhjTAvN/Ig234I234Smpxc7nA40Mxd30Zm4cybjzt0ct/HfaK5Git0Zy21C4y+hiTdQzdc1PjdxaqHqT3jllwN4vzrDENkfCW7Qq3iMMWa4s5kQY4wZhtzmu6HxIlrqCTdeilb8Bqfi2KLGtZi6TeiCvcGtAzKgDdB8PZr+CKm5vkdjudFHoOGPIH681xuAmuuQ4LrdHsMp2xcNbgjxp1BNIOHtkMCkHsVhjDH5CW5B27cWnyUhxhgzzGhmdjYBaVftqekyr9qTf6XixKUZtPl6iN4O7kK8vRit92PEIfE2mvoKCazavTHT33kJCPE2/Vt04bEw5nVEwt2OT/zjoOL4YfY2wRhjBoYtxzLGmOEm/lyeExk01mWT2wGjDX+EpqvAnQekybkhXBxIf979MWMPZMdqz4XEK72M1Bhj+pfi7QkZyEepsZkQY4wxWUq7du+Fu3NmPsQeBbqx58M3rvsDuw3kTULcxu6PY4wxpl+VXlpkjDFmYIW3y3MigER2KmgoLdLfQpdd5f3gWw4C63V7WAltC1LW8YS6ENq0ZzH2M9UYGn8BjT+Huk1FjcUYU3wZnAF9lJrSi8gYY8yAEt9YqDyDJdWe/N6fK05EitVk0T8O8la+EiAAoS2R2tt61oE+tBUENmiXiESg/GjEt2wfAu4bTbyMzt0ErT8Drf8dOncz3CIuhTPGmEKz5VjGGDMMOeVHoKGtIf4MkIHwDoh/5aLFI75l0dDmkPgfbTbMSwRqbkcCq/ZoE3nL5eJAzbUQfxqNP5Ht7XEAEtqk5TneLISDODlmTAaAunXowl8D8bYn6s9Eg+sivqULEocxpnQogqvDq+yFJSHGGDNMiX88VBxX7DBaSPWlaMNFEHsISIFvJWTEn5Hg2n0bV/wQ2R2J7N7muKa+ROt/D+kvva+DmyAjLkZ8o/p0vy7Fn4WcNbZciD8B5Z2XSVY3ikZvh/iTIGVI2aEQ3q1nM0TGGFNkloQYY4wpCSJhZMRf0KrzgFSvZj66S906tO4Q0Fab05NvesdGPe3NoAzYzZvJvVk+jbrRTksAqybQugMg/QOLZ4y0/jNITkVGnDcAwRpjCqUU920MpOH1ao0xxpQ8Ed+AJiAAGn0IOnROT3vlgZNvDui9CW5J7l+/ISS0ZefXxp+AzEza9niJQey/aHpm/8VojDEDzJIQY4wxRaGaKF5VqPQ3dNiTAaCZ7Jv8gSOBCVB2kLffpUUEIrtAoPOlZ5p4DTSaa1BIvde/gRpjCkYBV50BfZQaW45ljDGmoNStR+v/AImXAEX9KyEjLkK6eAPeX9zYM5B4PvdJEQhMGvAYpPJsCG2Lxh4GMkhkTwhu3vW+DmdpvF/dOZZzOSMBULcRMjPAtxziVPVz5MYY0z8sCTHGGFMwqorWHQXpr4Dscqj0V2jdETDqKcS3TKfXkngRjd7hNRoM74yUHdKjqlaa+B/Un0HOWRBCEFgHCazVk5fUKyICoU3aVOnq1nVlB6HRO2mbhAhIJRr4GdpwPkTv82ZGNIVG9kWq/oiIr1/jN8b0NyHT6Y6woaf05maMMcYMXelPIP0dLQnIYppGo3d1eqk2XoIu+i0kX4f0R9B0OVq3P6q5Eoo8YzRdTu4EBCg7Aqm5vttjFYP4l0eqLwcZAVIORLwqYrW3Q/QmiN4PJECbvP+PPYg2/afIURtjTEc2E2KMMaZw0jNAfN4C6DaSXtf0PDQzD6I3e89rkYD0TIg9CmUH5L9WFeJPoM3XZmdgcgkj5YcjXXZt7xvVOMSfg8wsCKwJwU17XIlLwttA6E2vtLBEEP9K3tjNNwOxds+OQ/RWqPx1/7wAY8yAWLwnZDixJMQYM2R5y3deRqP3gMa8PhGRvRAJFju04SuwWo6qVABhCKyX/7rUeyDBHF3VY2jiJaSzJKT5ami+FrT9G/RWxN+yp2KguKlvoO6g7OtPgoTAtzLU3t7jRokifgis0fagNuR+sjahqtZHxJgSZ8uxjDFmiNDGi9FFv4HkS5B6C228EK07CtVcPRpMT6iql+T1kPhXgtCWQOsSvD5wyjtNJHBqyTF9kr12qfxxus3QdE3nCQg+KD8JEs/jNvwVt/kO1M3zhr6X3NhjsGD3bKIQAzJelav0V16S1B/8q+c5PtESEGNMybEkxBgzJGl6JkTvpM3yFI1B+jNIvFC0uAYTTbyNO38P3J9Ww52zEW7Ttbjp2bgLT0LnTELnTMJdeDKamdujcaX6Mqg4wUsepMrr9j3yIZCQd4+5O+PO3RJ3/v64jVd64wc28PZBdPi1FUDKDs5/s8w0b5ajK7EH0UVneUu+Gv+BztsGTX3Ro9eVj6Y+g/qzATfH2QTEHu6X+0jVOUCEJd8jAcJI1R/7ZXxjzMBRFSvRa4wxQ0Lyndx7DzSKJl5GwjsVJazBQlMfoQuPo2UTty6Epv9A8zWgcSDjHU+8hC74DEY/2+1lbiIBpOKXUPHLJffTDFp3EKS+oKURn/sTpD9GozcgNTcjtbehC4+HzGzvvy0KVRcggYn5b+aMybGEq70MZKazZLN8DBS0/gxk1GPdek2d8apZdRZDz2eUcpHg+jDyXrTpKkh/4c2AVJyEFKDkMHh9X0h9DFIG/tVt9sUY0ylLQowxQ5MzAnKur/Vnl/aYzmjjlbTtyg0Qz/F+OQNaD4kXIbxz72+YeBVSX+e4p+sljvWnI6OeR0Y95TUa1CYIrNFl4iO+0WhoK2/8DmMv5qNDtS6A9PdoZgHi6+Nekcwc8icafojs2bfxW5HAakjNFf02Xne5sSeg4Ry8f3Out7+m5jrEv3LBYzFmsMqU4GzFQOqXVysi1SJyv4h8ISKfi0jPCp8bY0x/C20BBHKc8COR/QodzeCT/opuf0KvsWzZ3d7T1FQgRyfwxTLzwJ2NiCCBCUhwve7PvFT/E8I70PHvgwOEwanJF1V2xiX7VeJt3LrDvaViC09GU5936/6EtqbtHpjWwdVCcLNe7a8pFZr6GurPAm32kkONQmYmWnckqplih2eMKVH9lXJdDjytqqsB6wDd/MlsjDEDQySI1N7iLceRcpAKb5nIiIsR/4rFDq/0+Vcl90xSDhIB/yp9up04S5H3jTrg7afoXVUzkQhO9SXImLeh5i4IHwj+SRD+OTLyAYgcDLQvzetAYE3EqfbuHnvWW56WfNtbJpZ4AV1wEJr6uOv7R/YB3zI57uEDbYRFJ6ELDkDdpl69vmLT6D10XG6mXlKSfLsYIRkz6CjgIgP6KDV9Xo4lIiOALYGjAFQ1SeeLX40xpiAkMAlGvwqpj0ATEFx3wPtADBVS+St0wVu0bewXznbijrGkY3e2tG1o277dMLIHNF2SZ/LFgcAkxDeqT7cQpwIJTYbQ5LYn/OPR5NteI0VNe69RKpAR/wKypZ4bL6Dt90KBGNr4d69RYKf3LYORD3id3uPPgDsP3Dq876G3/4T0Z2jjRciIi/r0GovCnUfuTfeAu6iQkRhjBpH+mAlZEZgH3Cwi74vIDSJS3v5JInK8iEwRkSnz5s3rh9saY0zXRBwkuC4S2sgSkB6QwNpe93D/aoCA1HgbyUc9A+Fd8WYtwtnKVvd5fSv6cj+nGqm5BWRZ2lZ3ioCzNFJ9aZ/G7/TeEkJqb0dqbkQqT0dG/B0Z/SLiX857gjaDOz/3xalPuncPpwKn4kScUQ+B28CSJK5lIIg93uvXUEwS3tqbZWxPUxDcoODxGDM4CRl1BvRRavpjY7ofWB84RVXfFpHLgd8DbWoCqup1wHUAkydPHryLX40xZpiQ0EZI6NGOJ6r/OTD3C64DY16CzA9oehrizgPf0tmu4r6uB+jLvUW8N8y53jRLGG8/SY7+Mr1qcJivT02uJo6lQzUN7lyQ6rbNFcO7Q/Nt2X1Bi2eLIlB2BOLL38PFGDO89UcSMhOYqaqLF37ej5eEGGOMKUGanIo2/tPbfO4bi1ScioS3K3ZYQDYZ8K+A+FcodigtRPxo2cEQvYUOy45kdM8HDG4CydfbjeV4x0uUG/0vNP7dW9aIopE9kapzvb1XEoSR96DR+yD+JEglUnYIEt6m2GEbM2go4Grp7dsYSH2em1HVn4AZIrK4UPt2wGd9HdcYY0z/0+S7aN3RkJrqbYpOf4EuOg03+nCxQyttoR3JuVE//YnXjLAHpOo8r0ljy0b8MEgVUvWnPgY5MDT+EjSc75ViJo7XYPFRtOFPLc8RCeOUH4Ez8h6c2ustATHGdKm/+oScAtwpXr3E74Cj+2lcY4wx/Ugb/0HbDdZ4Xzf93ft02xrM5SSpN9Gcu+YzkHgdetAQUPzjYfTzaOwBSH3mNfYr2xdxRvRfwP1Im68i59+Z2GNo5R8Qp8M2UGNML2T6rWjt4NAvSYiqfgBM7up5xhhjiiz9Ve7j7iJvA7ZUFDScQUMq8PaFtG94GACn598zcaqQ8kHyeV1mdp4TDrgLwZIQY0wvDK+Uyxhjhjtn6dzHJeT1+zC5hXcl53IsoW+d4geDwLrkfu1+sI3nxvQLRXB1YB+lxpIQY4wZZFQzuM234M7bFnfOxriLzkQzP3V+TWYebvwlCO9Fx6aAESg/ZsArUA1m4huNVF/ulaKVipaHVP8HydtxfWiQilOzCWrrNzERqPgtIu270BtjTPf0154QY4wxBaINZ0PsKVrW6ccfQxOvwuinOrwhVk2j9Wd4VYta9jQEgXIg5TXmKzsKKf9l4V7AICXhbSD0FiTfBQSCG3qVoYY4CUyA2v+iTZdC6gOvb0vFyUh4+2KHZsyQ4g6zuQFLQowxZhDRzI8QewJItjqaAW1Go3cjFSe3fX7Tte0SELLXujDyQUAgehO6YE/UvxpSfrz3prP9fTUNiZe8zuLO0khkrw4dzFVdyHwH+MC3wpDY5K5uHRp9CDLfIoH1ILI7Etqi2GEVnAQmIDVXFTsMY8wQYkmIMcYMJqnPvf0bmmx3IgHJKR2f33wT5KzqlIbmWyHxZHasDKS/RuPPQu3NSHD9lmeqxtEFh0LmW9AoEEKbr4SaG5CgV5NEk++hi04FbQBVb69A9X+QwKr99ML7h6qiqfcgPQMJrJEz4Wp5buoLtO5Qr/M3cTT2BDRdCSMfRHy9aVJojDG5qUKmBPdtDKThNe9jjDGDnW8saK6O237wr5jjeCz/WIkXQGNAJnvABWJow5/bPE2bb4X019kEBCABGkUXnea9qXfr0IXHgDsnO17c63pedxiq7Uu7Fo+b/ASdsx7UHQwNZ6IL9sBdcDjaIaHzaP3vvV4qLeVpY+DOQ5suKVjMxhgzVFkSYowxg4gEVoPAqnjlYtucQMqO6HhBYI18I2Wbz+WQ/txbWrVY7DE69onAm/XIfItGHwF1O54nBfEX8tw/x3BuI5r6CnWbun1N98dugroDgWiroy6k3kYbL8sZS+5yxmmIP9fv8ZUKTbyFu+BA3Dkb4i44EE281fcxNYnGHsdt+Dsa/S/qNvdDpMYMPVYdyxhjTEmTmhsgtBVeIhIE3zik5nrEv3zH51ZdAOSoeuXUAnma40k5It6vB0195iUbuah6MbhzyZ2kpMCd1+XrUU3j1p+Hzt0ErTsQnbuJ94Y1Z2LTOxq9H0jlPhm9J8fBTiqF5diMrppEU1+jmfm9iq8UaOIVdOHxkHofdBGk3kcXHu8VPejtmG4dOn8XtOEciN6ANlyIztsOTU/vv8CNGQK8Er3OgD5KTelFZIwxplPijMCpuQpG/At8y0LmR3TRmbjRBzo+NzARRj4F/vXwqmKFIbQ7MuoJqDiSjuV6wxA51EsMFp6MLjgI3FxvrMW7t288EvyZV7q2Ax8EN+jy9Wjj5RB7CEh6DRNJQPRONHprl9d2h7oN0PzvTp7RvgEhiFMGwU3ouHUyBJH92hxxow+gczdG6w5A522NW3esd89BRhv+Sq7O6N7xXo7Z+A+v2WHLUr4o6CK0/uxej2mMGRpsY7oxxgxCmngV6s+k5U2j+yM0/AVX4zjlh7Z5rhNYAUbd23GQ8hO9/iKxh71P9zUB4V2RylPR6J2Q+B8d35RKNuEIITVXIiJoaCvwrwqpL1o9PwKhzZDAWp2/DlWI3p7jPjFovgH6oau4Nl+f3auSR2DdnIdlxN+8jenuPNAMiEBgXaTipCVjJ96Ghj+3jT/5FrroVKT25j7HXlCZ73t2vDvizwDt9zC5kJqKanJYlDg2prsyuZqCDmGWhBhjzCCkjf8i5xv3pivQsoNbllN1RsSHjDgfrTwN0jPAPw5xar3xo/fmGB/AB5W/RyJ7t7yBFPFB7e1o8x0QfxjwQ+QApGz/rl+HO5e2+zRacfPsWempnG+EF3NgxMU5z4hvNIx6GpJvQWYmBFbvkFRp8/V0/D6lIDkFzcxGfMv0NfrCcWrBXZD7eO8H7cO1xpihzJIQY4wZjDLTch/XRm/pi1R0eyhxaiHY/o1m7opR4EeCm3T4BFskhFQcCxXHdvu+ADTmTgCATjbV91DOpWIAAjX34viXy3+pOBDaNP/Ybp5O9RLwlrENpiSk/ARovJS2FdUiUH5Sviu6Fv45xO6l7X4cHwQ3t1kQY1pRKMnN4wPJPqIwxpjByDcu93Ep7+RNdw+Ed8fbQ9KOMzL/vXsj/mz+cxVn9c89yg4FIu0OOuBfEye0Tt/GzrlvBG/5lm/lvo0NaOpL3MZLcBv/gaY+7vN4nZGyI6HiRO/vECHv/ytORsoO6/2Ylb8F/4Ts38mAN6ZvGWTEhf0WtzFmcLKZEGOMGYSk4rfoot/QdilQxHvT2I2lWF2OX/4LNPE8pGfiLZcKgfiQ6ksK1wnd/QlV7fP9JLIvmnrfKzUs2V97Ti1Sk3+zumYWoE2XeeV4JQRlByDlx3WcASr/BRp7NNtPJL34hlBxqre5vQ/cpuu85oikAEWbb0fLDsOpOjN/3H34fokIUnESWv4LcBeBU41IoMvrOh3TqYCRD0LyTUh/Cb7lIbQVIvb2w5i2pCQrWA0k+ylgjDGDkIS3RUdcDE1/h8wsb4aivG+fWrcZf/Gbx/jzaPId8I319oH4RuW9RtVFm2+E6K3efo7gukjl2Uhg9fw3Cm0LiefJuWej4XdoaipS9Ye+vRZxkBEXoeUnQepD8I2BwOS8yZq6UXTBPtnywmlvnUTTtWjqQ6TmunaDl0PVOd6+k/QX4IxByn+BhLftU8yangFN/6Zt5a44RG9HI7sjgUltn594GW24CDLTUKmFihORsiN7lZCIBMA3uk/xtx3PgdBm3sMYY7IsCTHGmEHKiewCkV1Qdftl9qM9kSBEdkUiu3br+dpwPsQepGVPQfJttO5gGPkw4l8h9z2q/ogu+ChbBrjdPhSNQfQetPxoxLdsr19Hy73848Df9VIyjT3izQS0SYzikHgLTX3hNYwE3Oa7oPFv2dkVBRmBjDgf8edehqWxx9DmayAzD4LrIRX/hwRW9c6lv0ebb4LU595eGKfGG7ODBBr9LzLivCXjJt5EF/6allkxrYPGS1GNIhUnd/l6jTGlwR1m1bGG17yPMcYMQQORgPSUugsh9l/abmoGNIE2X5fzGvAqUMnoZ/NvQhc/JKf2X6DdkXqPDq8DQBxIfwaAJj/0EhDioE1efxN3Nlp3dM4mi27T9Wj9OZD+2msEmHjZ6yuS/hZNfogu2Ati90P6I+/72HwteYsDxJ/0ShtnadNl5C5xfD2qeRo0GmNMkdlMiDHGmL5LT8/2Gmn/xjkDXWyoFgmi/rUg9QE5P/3vU4nYXvCviLcpP0cS4PMqaWn0Ljo2OVRvb0jqPQhOXnJUE9D8H9omNgoaR5v+A+lp7fqY5CsnvPjSqNe7w79S9ul5+nhoGtyF3vIzY0xJU4WMVccyxhgznGniZdx5u+L+tAbuvG1xo490fZFvbI4EBLwqVBM6vdR1E5B4lpwJiJRDcONuxd1fJLK/V2K3DT84S0HgZ96Xbh25l0sJtO+WnpnhHe/AhcT7kP60hwH6vMaSLaGtlOd5/uyyLmOM6ZqI3CQic0XkkzzntxaRehH5IPs4t9W5nUXkSxH5RkR+3537WRJijDGmhSZe9fYXZL4BUl6TvoY/4kZzdFxvRXyjILwTEG53JoSUH9/5TRednL/fRvW/vWaIXcWd/h638R+49b9D4091axmSagZN/A+N3oOmliQC4huN1N4OvglAwHsEN0Zq72zZ6C3hHehY9hcvEQuu3/aYMwbyxeMf51XT6gkJex3qF39ZcRodv+9ef4++VrcyxhSOq86APrrhFmDnLp7zmqqum338BUC8H9L/AXYBJgEHi8ikzgYBW45ljDGmFW38Jx33F8Sh6TI0ckCn1ZZkxF9Rpxai9wJJ8K2IVP2pZSN3zvtlZkPy9TxnQ4g7r8uY3djTUH8m3jKmNBp/Bvw3Q+0deRviaeYntO4Qb7mSZgBBg5ORmqsRCSKBNZHRT3h7XQh41cLIVs6K3gTRRwEXL0lJ4c10hKHi14hT3fb74lSh4d0g/hTtSypLxclo4iWI3k3uDvVtRgLCyIh/tUnMJLQR1PwnWx3r+2yltJOQskO7/N4ZY8xiqvqqiKzQi0s3BL5R1e8AROQeYE/gs84usiTEGGPMEulpuY+7i7x9C500QhQJIlV/QCvPAtLd64idnII3Kd9xMzekod0b+vZUE9BwFm3ewGsUUl+i0QeR8oNyX7foDMjMBjKtYnkXbb4eqfjlktfUajmTatpLXNLfsmQ/iB+kxpspKT8MCf4s5/1kxPmoBCH2sHfAqYTKPyChjSG4PurOgfgL2X01zdmrWn9PHIjsh1T8EsnRhV1CWyCjn8p5b2NM6VOkEB3TR4nIlFZfX6eq+SuH5LaJiHwI/AicrqqfAmOBGa2eMxPYqKuBLAkxxhizhG8sZL7teFwqur1syKvW1Y0EBLJJRoDcm7FDEJic43grqY/Ivd8iBvHHIJuEaHqGt/fCtyzqrJCtgJVpd00cov+FVklIG4kXIDONthvS06BxpOI4JLBm3jBFgl4iUvUHcJu8ZonZqmYiQaT6MjTzE6R/QH3LQNN/IP6Ed7FT680o9bH3iDFm2Juvql38UO3Ue8DyqtokIrsCDwOdb/rrhCUhxhhjWkjlaeii08ndiX0APqULbgJOObjtS+IKVF/WdflhCZF7FgWQMm/fR/3vIf50drO5C05nPUfylMUFNDnFm2XpIAPJ96GTJKQlJAmDr/3+jew539LgW9pLqaovRvXP4DZnE5bhVTXHmOGo1PuEqGpDqz8/KSJXicgoYBbQugnTctljnbKN6cYYY1pIeEcYcRE4ywDiLTWqPB0pO2pg7id+pPY2cMZmZ1oiQBiqLsUJb931AP41QapynIggZQej0Tu8buYksv08otlN97lmXgIQ6mRPprMMEMrxIgIDUgZXJIz4RloCYowpCSKytGR/IInIhnh5xALgXWCCiKwo3jrcg4BHuxrPZkKMMca04UR2h8juqKYRGfhfE+JfBUa/iKY+85YgxV+CpgtxU68iFafm3AOhmoL4M2j8Ka/RYaIZxMXrv5GBsoMgtA3M35HcG77bldeVMm/GofKU/HGW7YU2/7tteVzEq1YV2mbJyO4ib8mVb9mSaCRpjCl9CoXYE9IpEbkb2Bpv78hM4Dy89bKo6jXAfsBJIpLGa3x0kHqdU9Mi8ivgGcAH3JTdK9IpS0KMMcbkVIgEZMm9BI0/DLH7ljTuiz2Mxp5FI/uAbykksgfiWzq7QfzobBPEGN6ekBCEdkNCG0JwQ8Q3FgDNuXyqvTKk8lyI7Ootl8oXo1MLNTeji04DdwGg4BuP1Pzba7jo1ntL2ZJvAD5wKtCq85DAOtklVUv2yWjmJ6/XiH+V7m3gLwLVpNedPf4COCORsoM6rXRmjBncVPXgLs5fCVyZ59yTwJM9uZ8lIcYYY4pO3bpsmdrWezJcoAlitwFBtOnf6Ih/ISQhvTgBAe8zxDjEH4eqM7xkYbHQthB7gM67kMchtHGnCchiElwXRr8Imekg/pZkB0AXnpjdKJ/yHm4cFp2CEgQJoOW/hMg+sOhUrzt8NsnTyj/glO3X5b0LSTWBLjjYK1KgMcBBYw+iVX/BKdur2OEZMyR1s5fHkDG8Xq0xxpjSlPo8u8k8nyQQh4YzvCVY2n4jO96b+uTbgJfUaPRBr1t7SwWufBxv+RSgmR9xG6/Erf8TGn8B1fYVtLxZG/Ev3zYBSX8PqU/xEpAcsWszNP8b6g6E1FS8PSrN3qPhfDT5bifxFZ5GH/BKEbd8n10gDo3nobm+98YY00M2E2KMMaaoVBV1m0C7atYH4GSfl6e3iFTgRh+Ahj+B+LJbPzIQ3BmST9KxLC9AGfhXRhMve93iyQApb3mYfxLU3tL1kqnMbG+DemevQWOQ+SHHiRjafGPeHiNFEX+KJTNNrfkg+QGENilwQMYMcVqQPiElxWZCjDHGFI1mfkLn7woNvyN3gpBDaGty9yEJos44LwEhkS2nG/X+nHwWqq/G2zPZmh+p/jvgtipNnJ3N0CikPvFmBboSWA00f3nfLmV+6v21A8GpzHPC9UoqG2P6leKV6B3IR6mxJMQYY0zR6MKTvAaAGqXtzEb7ZGEJKTsAKs8EQtkmiuUgNUjtTUjyefL1DZHMDBj9LpQdD4H1IXwwMupRrwlg6pM818Uh3mWlSW8fStlheCWGO31mjmNBCG3e5T0KScoOoeNrEZBq8K9VhIiMMUONLccyxhhTFJqe7u07yDUD4l/LK70bewAvOfCDKFL9H6/DePlhaGQPSL7jldcNboSIH028Qu5kwgWSOL4KqDq94+nFjQxz6Wb1Kqk8EwKros03ezMb2tjutYUhsjfEHmbJUqcAOFVI2dHdukehSGhztOIX0HRt9vUrSBlSe4P1LTFmgAy35ViWhBhjjCkObST/hHwMZ8R5aPmhkPgfSCWEd0CcJY0JxRkB4R3aDhncEriajomN41XKah+CupCZhkqN1/SwQ0lfP6Q+wZ2zAYS2QirP9Dqb5yAiENkbieztjZ14HW36t7cPxD8RqfgNElwXDW2NNt/olfkNbYmUH4f4Rub9NhWLU3EKGjkIUlO8GZDghojkn6EyxpiesCTEGGNMwWnqE7T+PLw9G+0FIbQjkG1k6F+l6/E0gTb8NTtzkmTJsifxxis/FvGv2PaaxFto/engNgIu+MZ6yQ6u1/CQJF7zw0bvgviTaPJNGPVMm2QoHwlthoQ263g8vA0S3ibHFaVHfKPBt0uxwzBmyCuFZoWFZkmIMcaYgtL0DLTusByzDgBh8I1Gyo/s2ZiLTofEy0DrbuZ+CO+OlB+OBNruY9DMj+jCE2hTASozDWQMVJ0F6a+h+To69C1xm9Ho/UjFMT2KzxhjTFuWhBhjjCkojd6Sp5KUQPkxSPkvEKei++Nl5uRIQMDb46EdEhAvhvvo2MDQBRq9WQ7/SqgEcsQZ9xoNGmNMP7OZEGOMMaYTmp6GNt8C6a8gsA5SfmTefRI5pT4nZwdzqUCCkztNQFRTkHwPcCG4gde/IzPT2zytOZKQ9Ne5B8r8SO7GggruHPCtTO6N6sFuLQ8zxhjTOUtCjDHGdJsm30frjsJ7A5+G1Ido7D4Y+V/Ev1L3BgmsmZ1NaJeIaBI6GUOT76ALT6ZNclB9mTdehwQEwA+BdXKOJaGN0cSzHZeEaQYC64JvRe+R/po2yYoEkLID88Y4HGh6Jtr4T0i+7u2hKT8CKTsCEav6b0xvKdas0BhjjMlLG87F20exOIFIgTahDX/r9hhSfhRIqN3RMIS2RXzL5r6v24AuPA60AbSp5aELf+UlDpF96dDXQkJI+bG5gwjvBs7SQOs4IhDeGfGvhIggtbdkK2r58HpkjIKq8xDfUt1+rZ1Rdb0KWtF70dQn/TLmQNPMPHTB3pB4GrQe3JnQeCna8Mdih9YrmvkJt+k63IaL0cSbqGqxQzJm2LCZEGOMMd2imsizvEkh+Xa3xxHfslB7D9p4ASSnen0+yg5GKk7Jf1H8aXI3+lOIP4FUnYv6loPoreA2eEu1Ks9C/ONzxyAhGHm/Vyo3/iRIGCKHImX7LXmOU42Gd8/uN1HQOqg/Dzf5NlJ1UZ/6ZWhmLlp3KLjzvSRKBA2sh9Rc5y0xK1EavQM0RtulajGIPYJW/LrfErRC0PgL6KLTWNxDRmN3Q3ATqL7SShGboijFruYDyZIQY4wx3eQHAnTcAA445T0aSQITkdrbu3+BNoLm2sORRN1FOOJDKo6DiuO6H4NTgVSeCpWn5r6l2wz1Z9L29cYg9iSEd4HQlt2Pv/3Y9b/z9rIs7meiQHIq2nQNUvnrXo874JJTaFsxLEuCXoI6SJIQ1YRXnpl4q4NRSL7pJbyR3YoWmzHDhS3HMsYY0y0iPoj8nLZLmADCUHbYwN48uAnesqj2QYWR0OYDc8/km5Bzn0MMjT3a62HVbc7OHLVvqJiA2H97PW5B+Fci538HTXt9VgaL5BRyzqxpFI09UvBwjEG96lgD+Sg1loQYY4zpNqk6B4IbAaFsY78QhHdCyo8f2PsGJkFkV2/pVsvBCAS3hMAGA3JPzczMU0oYci8N6672yUfrm+a7X6unZObgNl2DW/9nNP4sqjkqjQ0QKT8KaL9cLOhVSWvXDLK0dbIQRAKFC8OYYcyWYxljjOk2kQhSewOang6Z6eBfpWflefty76q/QmhbNPoA4CKRvb2N5H3Ym5GP23wzNF5CzjK+EkEie/V6bHGqUP8qkP6i3Rk/hHfs9FpNvIUuOqGlo7vGHwLfeLTiDCS4FuJU9zqu7hD/ylBzHdrwB8jMBgTC2yNVFwzofftdcH1yz6yVIZH9Oh43ZoBZx3RjjDGmG8Q/HvJs+h6we4pAeEekizfqfaWZ+dkEJFfZ3wBE9oPgpn26h4y42NuYrmm8fQll4FQjlaflj0szaP1p2Y3hiw9GvWRm0UkooOXHIBWnDUhi1hJ7aCMY9RzoIi8hk/CA3WugiASg5ip04fGgilftzYHwnhDausjRGTM8WBJijDFmQGlmFtp0PaTeA9/ySMXxObuYl4zkG+T8lBwgtBVOVd/L0UpgdRj9PBp9EDLfI4H1ILIbIpH8F6W/apuAtJFdxhW9FfyrQmT3PsfYGREBqRnQeww0Cf4MRr8GiefAbYTQpog1ojRFZDMhxhhjTB7qNnifvDujutWcUNPfowv2BY0DaUh/iSZegerLkfA23bunKmS+A20G/2oDX8JWQt6G9A4tIxzI08ekV7dxapGKX/TggkD2U/tOaAxtvhEZ4CRkqBCnAiJ7FzsMY4YlS0KMMcZ0i9t0JTRd65Vj1RQamIjUXIs4tXmv0cZ/ZbuSL+4roUAcbfgThLbuctmQpqejC0+EzAwQP+CgVRfiRHbunxeVS2hLcmQgQBCJ7DNw9+2Kb2Xwjfb24nTGXVSQcIwx/cc6phtjjDE5aPxZaLoeSHg9O4hD6lN0Ye4eGy2S79C2sV2WuwDcuk4vdd0MOn9fyHyTvW+zd+/6M9FUrqaJ/UMkglRfA1LuPSgDQlD5W69KVx+4sSdw522H+9NquPO2wY12v9SviCDVV3vLoCRfXxY/hLbqU4zGGFMINhNijDGmS9p8E9B+P0IaUh+gmTn5O2U71ZBZlOdcFw0OGy8C6nOcSKDRu5AR53V+fR9IaCMY8wYkXvWWkgU3R3wj+zSmG3sC6s+ipUFeZhY0nIOL4pTt2b24AhNgzGuQeAmNvwrxR/A2VbtAEKQCqTipT3EaY4pDh9lMiCUhxhhjuuYuzH1c/ODW5++UXf4LaLiQtglMCMK7dFpVSdWF+AP5zkL6WzT1Gfgnek0UweuXoXGQ8n6pDiUSgfBOfR6nReMltOnQDd7XTZdAN5MQL66g15slvBOaOhhtvtlbrhbcFCk/otPlcUOVqkLyHTT+JOBDInsiwXWKHZYxPeL2qf/Q4GNJiDHGmK6FtoLoTDr2zfBBJ03qJLI/mv4BordlN1anILQFMuLPqCYg/ixkZkJgDW+2YXGHco123rgvNdUrcUsIHfE3SLwIsYeAtLd5vOovSGizPr7o7lFVSH/jxRxYPf/GeXdGnuOzUdVeJU4SWBOp/lePrxtqtOE8b1ZI44CgsfvR8mNxKrtYLmiMKRpLQowxxnRJyk9A44+D24BXDlbw9kmc6/VcyHedCFJ1BlpxAqS/B99SiG9pb8N53YFeyVmNg4TBtwLU3ok45V5ndCkHzbUcCyDlJTQ0w6KT8ErqZpOWzAx04Ukw8p4+7+HoiqanoQtPgMxPXkUtHLTqrziRtr1MNPVZ/kGkZkD7egx1mvwQYo+wZLbNK35A8w1oZG+vp40xJU51+JXotY3pxhhjuiS+kciox6H8OAisA6Gdkdrbccp+3r3rnSokuE5Ld3WtP8Nb4rW4cpZGIf0N2nyV93xxoOLXQCd9M1p43cPbSqCNl3f35fWKagatOwIy04BYq43zp6Ppb9s+OfkOeXuP+Eu4Z8ogoIkX6bjMLSvxciFDMcb0gCUhxhhjukWcWpzKU3FG/hen5vJer7lXtxFSn9CxalYy+4l29n5lh0HVH8BZGnBARgLd7RGikHwZd95uPaqkpW6DN0uj7Zed5ZB8O1sprH053xQavbftIWekN9vTgQ8KtGxsyJIQORM8cfJ8z40pTaoyoI9SY0mIMcaYAuus4d6ScyKCU3YAzphXcZb+Ahl5Oz37taWQ+QatOxTN22k8+0yN4S46DZ27KTp/D3TuJrjR+5ecT3+DRu9B4y+gi/equHV5XkoG3LltD4W3zx27BJHIHj14TaY9Ce9OziREFcI7FDweY0z32J4QY4wxBSVOFRqYBKmPaPsuPgjh/G/Ixb8KGt4ZEs94e0kACGf3jjSTe0mOAklvA3wkfwUqXfR7b3P74mVdGoOG83GdMRB/1LseQHzep+u1d0BwA7zyuO2FQarQxP8guDEifq/SVu1t6MKTs/tcBCSEjLgc8Y3KG5fpmvjHo1V/goY/AT4QAc3AiEsQp6a4wRnTbcOvWaElIcYYYwpORvwDnX8gXuIQ8zai+8YhFb/q4rq/QXwTNHoPaMJLWsoOhtj90HQZaFPHizQBmTl5x1R3ISReoOO+khg0XuhtOl+c4CigUXThyciop6HsEIjd0yop8gEJiD2Kxh/zXlftbYh/ZSSwBox+GdJfAhnwr9ZSXrgnVDMQfwSNeiWMJbIvRPbs1Vi9pepC8k1Ifwv+lSG4yZLKZkXglO2LhreFxGt4S9y2QpyKTq9RzXjL6aSyoN87Y4zHkhBjjDEFpe5CtPEfQCPggjMKyk5Ayg/r8s2giAORvZHI3m1PlB+B+pdHF52a3eze+qKQt5k+H3dBtnxwjpLAmVxliRUysyEzDan8PQTXR5vvBPdHyPzonSfaKmE5AUY951UKE4HAap2+xs6oKrroFEi8zuJqUJr6BBLPQfVVBamypW49WneI12xR016vGN9YqL0LcUYM+P3zEacGIl0XSlBVNHobNP3bSx4ljJafjJQfY1XKTFGV4r6NgWR7QowxxhSMqqJ1R0HiJVo6fbvzoeliNDOrb4MHtwD/BCDU6mAY/GtCcMP81/nylXB1QDqpzqUJL7EI74Qz8jbwLUfH5VkK7rzs7EcnQ6W/xa3/C+7CE3Cbb0XdHDM6AKkP2iQgnhgk34DUe53eo6c0PQ1NvIJmZrc93nAhpKdlk71ktrLZNLThgn69/0DR2H1eg0htwCv13AhNV6DR24sdmjHDiiUhxhhjCif1ofcGtsOb9TTUHdGnoUUcpPZ2qDjJ6zniWxEqfonU3tTpJ9wiQag4jbblgB1vKVXkACBXhaU4mvqq7aH2MzAtfK2Wa3WkiZfR+XtD7G4vOWu8BF2wh7dMrL3kW0Ai1yBeta5+oG4Ut+4Yb4P+ot+i83bEXXS615EeIP4UHWeHUtnjg0DTf3L894hB89VFCccY8CZOXZUBfZQaS0KMMcYUTmYGuTdzA+6czpv6dYNIGKfiZJzRz+KMfgan4oT8HcxbccqPQKov8ZZtOUtDeDdk5ENI5Sleed1cGv/YtupWeFdyJyx4HeFzUM2g9Wfh7TnJZI/GIDMPbb4hR6A12ZK07YW8c/1AG/+S7WuSyJYg9jrba/N12Wdk8lyZ8brHlzp3Xp7jCwZH/MYMEZaEGGOMKRz/auR/E+tAuvs9PfqbhLfzeqCMeRWn+l+If3mvqpVvpTxX+CA5Zcn1ZQd5m7RbZlT8QBiq/po/EcpMyzODklxSkau18C7kLvUr2SSob1TTEHucjpv04xC90/tjaKscMTjeZvDBsKfCt0Ke4+MGR/xmaFKvqvRAPkqNbUw3xhhTMBKYgPqWh8z3Oc76wb9iwWPqklOW54S2aYYnEoaR90L8KTTxMjhLIWUHIP58SQzZ8sJ5kjLxqjtpcioaewg0hUR2g+rrof4U0MUliUNIzb/7aVN4irxJYrbymFSdiy74CNxmIAqUgVOGVJ3bD/cfeFL1O3Thr2lb0jkMFb8vVkjGDEuWhBhjjCms2lth3va0/bQ9AIGJ4F+rV0OqG4XUFG+c4GREAr0OT91Gb6M3AQhtipQdiCZfzbGPIASB9dscEQl65XI76UnS5vm+pdHAGtmeKa3f/EeQ8iNwGy+F5lvw3jArGn8awjvCqNeQzGfex5uBNfutxKxIBPWvDOmv2p+B4CbZmJeBUc9B/Ek0/QXin+gtX8ubrJUWCW0NNVejjZd4ybBveaTyN0hoq2KHZoY5l+E1E2dJiDHGDGKqaa+qT/Qu701yaHuk4hTEl2cfQwlwfEujox5B68/LJg5+iOyOVJ7Tq+UwbuwpaPg9Xo8O9caruRYJrt/FlTnGij4CDeewpImiA9VXQeQwiN7mfS0O4CC11/XLm3+pvsKrGObO9sbXJET2Qf3rQ/25tN2IHoPEs0j6QCQ4uVvja3qGV1XLGQ3BDbvs5yFV56MLjwJN4e3fCXqNFSuXzBSIUwZl+w3at0wS2gwJbVbsMIwZ1iwJMcaYQUzrz4T487QsLYndhyZehFFPtjRrU016vTCcWiTnpubCE//KyMg7vKZ3SK/X4mt6OtT/jvbd0nXhsTD69R59Oq/p6dBwNh0qPy06Dka/hZQd7FWnciohtHW3v5eanulVBfONgcAGHZIA8S0Fo570ZkPcORBY25shid5JzmXcGkfjL3SZhKgq2vBHiD3i9fIAkGqovR3xL5f3OgmuByMfQ5tv9UoLB9dDyg7z4jTGDAhl+PUJsSTEGGMGKU1Pg/hztP2kPA1uPRp7EMoOR6M3QdOV2X0HgpYdhlT+X1G7W7fW1zg09hB5q20lXoTI7j0Y62E6lp4FyEDTZciI88C/X/fHa0kCHvaaIQI4tV4S4Fu2zXNFBILtGypG8GZ32vN5e0m6En8Y4o/hVbnK/h3RGLrol8ioRzq9VPzjkRF/7PoexhjTS6XxW8gYY0zPpT4h92dJMUi+i8YegMYrQJvxZgpiEL0DbbqyV7dTddHEq2jT9Wj8GW+GZQD0qEyq20DOJEQzLRupuy39bf5zsTtxF/4GdRd1f7z4Q9kkIOn9N9BmyMxCF57SvevD20POuRAf0p3O4M135NjH4kL6O292xhhTQga2R4j1CTHGGNN/fMuC5HqTGgDfMtBwAW07a+N9Hb05uwyq+9RtQhfshS76Ndp0KVr/e3Te9mjmp95G32F8t/4s3J/WQudMwq071lse1QUJb+01Few4IuqfiGqumY08Aut2fj7xHFp3aLeTpPxJwFdo5scurxenCqm50nt9Up6d/QhB1V8Qf74u760DyNM8UTpvnmiMMYVgSYgxxgxWgfW8RKTDbIgfEm/hlU/NQWPk7LrdCW28xJsp0CiQ9j7Vd+ei9Wf3PO72Y6uidUdALLt0iAwkX0cX7I+6DZ1fHNwMghu2S0T83hh1R6BzN8Rtuq57iUPZIeRe/rRYCjKzut+ZXJtzHxdfJ93V2z01tAUy5k1kxN+RERchY17HKdu7e/cP7wLk2rfiQ201tjElZ7j1CbEkxBhjBikRQWpu896EEwCC4BsHlWeB+0P+C52lyNvZO5/4Y3TcL+FC8s2+L8tKvQeZ72hbstf19i/EHur0UhEHqb4aqboAQtuAfyLer7Y03l6IZmj6Dxq9q8swHCfk9eCgkw7r6ubpcZJDeOfcY0lZJw0QczxdIkh4ByS8C+JUdf+68mOySeri5onZ5RiahgU/x607CnV7uGTNGDNgVGVAH6XGkhBjjBnExDcKp/YWZMwbyOgXkFHPI04Y8hZPdaDy7F5Uo+rsY7Q+fsSW/i7Px3RxSH/e5eUiPiSyO07NtZCZS8du3zFovqZboTjhzZExr0Fod3LutxEH/BO6NZaUH+sti2vXQV1GXFyQwgDiVCCjHkGq/gj+SSz5lZ+dCUtOQRsGR4NBY8zQY0mIMcYMAeKMQHxLecmFf0KeN/UC4f1xIjv1/Abhnen4ptzJlpztY9lf/8qQMymKZN88d4+qgi7MfdKd3+1xxKlBRpwPTg1tf00GwbcyBDbo5jhVyKhHvZmp0E5QdgQy6jEktEW3Y+krkTBSth9oAx07oSch/gyq8VyXGmMKyFsyZTMhxhhjBjEJrAGBtWi7FMgBqUaqTu/dmJWng2+5VnsvysCpQUZc1Ndws3tbVsZbUraYAxJGIt3c/0C2zK0vz4Ztf/eXPwGIU46MfABCOwAhkAqI7IvU3tqjWSSRCE75QTg1/8ap+j3iX75HcfQbtzHPiRTadJXXcd4YYwrIdqYZY8wQJLXXo43/9HpUaAICa4MzAl14IhrcFCk/DHFquj+eUw2jnoDEC2jqc+/NdHgXRCJdXtvl2CJQeyva+Nfs5vQ0BDdDqs5FnMqejVX5B3TRqbRtXhhGKs/qeVy+pZGaf/f4upIU3BQSzwA5qqI134QmXoGR/0Wkk/0wxpgBVYpldAeSJSHGGDMEiUS8vQBVf8SNPZXtKp4EXEh9gsbugZGPIr6RPRgzAOGdkfDO/R+vU4GMuBBGXNi3ccLbQM01aNPlkP4e/CsjlachwQ37KdLBSSr/D02+nq2M1r7AQBLSP0D82R41dzTGmL6w5VjGGDOEqaah4Vy8mYHFn4InwF2EdnOz9mAjoU1xRt6Ls9Q7OCPv7nMCouqiGu9ZE8USI/7xyKgnIbgRuX/1R9Hkm4UOyxjTipXoNcYYM3RkptHxk2+8Y4mXCxvLIKPq4jZdic6djM5ZF523DW7suWKH1WviG4OUHQ45l9AFwVmm22NpZg6amd1/wRljik5EbhKRuSLySZ7zh4rIRyLysYi8ISLrtDo3LXv8AxGZ0p379VsSIiI+EXlfRB7vrzGNMcb0kVR5fSFycaoLGspgo42XQNP1oE2AC+6PUP9/aOL1YofWe6HNs0lI+7XnPq+KVhc0/R3u/J+j87ZD5+2IO28XNNV1GWVjTNdKoDrWLUBn622/B7ZS1bWA84Hr2p3fRlXXVdXJ3blZf86EnArYTyJjjCkh4hvjVZ9qvwVQIkjZ0UWJaTBQTUD0dryeGq3F0aYrihFSt2hmHm79H3DnboI7d5tst/glM2EiAaT2zmw1srBX7cwZjdRcg/iW7nxsjaMLDoH0l3j7ixKQ+RatOwzNW33LGDNYqOqrQF0n599QbamD/hawXF/u1y8b00VkOWA34ELgt/0xpjHGmP4hNZejdcdD+msQH2gKyo6C8C7FDq10uQvJ24Qx00k3+iJStwldsA+4C/A6xgNNV6Kpj9tU+RL/isjoJ9H0D17lNP8q3WueGH8eSNDx+5KG+BNQdlA/vRJjhh+lIL08RrVbKnWdqrafzeiuY4GnWn2twLMiosC13Rm3v6pjXQacCeStpSgixwPHA4wfn6eOuzHGmH4nTi0y6n40/Y3XUTyweo/K8w5LzshswpbjnH9iwcPpDo09AG49LQkIAHFIvIymv0Pa9Urpcc8Sd46XtHS8MZr5scMCrw5Pc5u8JW7xxwAXwjsilWcgTm3P4jDG9Nb87i6V6oyIbIOXhGze6vDmqjpLRMYAz4nIF9mZlbz6vBxLRHYH5qrq1M6ep6rXqepkVZ08evTovt7WGGNMD4l/FSS0qSUg3SASgPJf5djEHUYqTitKTF1KTqFtf5Qs8UPqs76PH1gbcvURkTIksG6nl6q6aN2hELsXtB60EWKPoAv2RzXZ99iMGQJ0gB/9QUTWBm4A9lTVBS2xq87K/v9c4CGgy7KE/bEnZDPg5yIyDbgH2FZE7uiHcY0xxpiikfJjoPIc8I0FQhBYG6m9EQmuOyD3U02hibfRxJu9e2PuXwnI1WxQs6+hjwKTwb8mEG51MAS+FSG0VefXJt+EzHTaVmpLe0vH4s/2PTZjzIATkfHAg8DhqvpVq+PlIlK5+M/AjkDOClut9Xk5lqqeBZyVvfHWwOmqelhfxzXGGGOKSUSQsv2hbP8Bv5cm30EXnkybjubVlyGhLbs9hpQdjEZvhTYJjB98y0EXMxXdGl8Eam9Cm2+G2P1erOE9kfJfIOLr/OL0F+3iytIomvocKXCTxOlfzOLtx6cSCAfYYt+NGbmMzQ6aIlMKsSekUyJyN7A13t6RmcB5QABAVa8BzgVGAleJCEA6u7xrKeCh7DE/cJeqPt3V/axjujHGmGFFNY02Xe1Vv9JGCKyFVJ2DBNYuTjxuA7rwuGw381bHF/4KRr+A+Lq3hFl8S0PNLWj97yEzwzsY3ASp/jvZNwd9JhJEKk6AihN6dqFveW8pl7bvWVOG+Ffsl9i66+Y/3s39lzyOm3FxfA7Xn3kH/3fTSWx70OZdX2zMEKaqB3dx/hfAL3Ic/w5Yp+MVnevXJERVXwZe7s8xjTHGmP6kDedB7DFa9k+kPkAXHA6jHkT8Kxc+oPgzeU64XtWp8qO6PZQE10VGP426dUAQcSr6I8K+C20NMgI0DmSyBx2QMIR3LVgYX7zzNQ9c+jjJWNtZmX8dczWTd1yHqtq89XWMGXgl2NV8IFnHdGOMMcOGunUQe4SOG7iTaFNvK1X2kTbkaSiZQt1FvRpSnNrSSUAAET8y8l4Ibgb4vEdgMjLyPsQpK1gcL93zOslY+9kY8Pkd3n7ivYLFYYyx5VjGGGOGk/SM7LKg9vsTMpDuhwpSvRHcBO+Nebs3xxJGQkNniZD4lkJqb8huuldEQgWPQV31msXn+sR5mH0KbUpPsfeEFJrNhBhjjBk+/ONyb5DGAf9q3R5GNY7bdBXuvB1x5+2U7Uzeu1KzEpgEkV297uUtB8sguCUENujVmKVMJFiUBARg6wM3JRjuWEEsk86w4a7rFSEiY4Yvmwkxxpgi0/R0NPYoaCMS2hqCG/fbRmLTlji1aGR3iD1J2yVZIaT8+C6v1+SHaPQOSLyQ3Uie3d/QdCWaeBVqb+/Vfzup+iuEtvMaDqqLlO0NoZ3s70E/m7TJRPY4aUceu/oZUok0Pp+DOMKvrz6OEaOqih2eGeZ0mM3GWRJijDFF5MYeh/qz8bpcp9HYPd4n4NWXI2KT1QNBqi5AnTEQvQO0GfyrI1XnIoEJnV7nNt8DjRcBCTqu3YlD+hNIvQvBLnt0dYxJBMI7IOEdenyt6ZkT/nEEOxy+FW8+NoVgOMhW+2/MmPHWRNkUlzL8lmNZEmKMMUWiblM2AWn1ibzGIPEaJF6E8PZFi20oE/Ejlb+Fyt+iqp3ONqi6Xi8L1WwCkqMjecuTE5D8oFdJiCmsldZenpXWXr7YYRgzrFkSYowxxZJ8G8SfY0NsFI09igyCJEQzsyH1MThLeR3FB9nyoXzxqirafCM0X51ddhWmy53LEgLfUv0eozFmGFDAZkKMMcYUhHTyI1g6bp4tJaqa7bfxEEgAcMG3LNTcgvjGFDu8PtPoTdD0b2BxA8GmLq4QIAjhHQc2MGOMGSJswbExxhRLcJM8JyJIZN+ChtJTGrsf4o8ACdAm0Cikv0cX/abYofWZqkLTNSxJQLoSAN8qyMi7EIkMZGjGmCFMdWAfpcZmQowxpkhEglB9NbrohOxKHxdQKDsECeVLUEpE9PbsMqXWMpD6CM3MR3yj2pxRtw5tvgHiL4NTi5QfCxJGm66AzDTwT0QqfoME1y3QC+hMCrQx/2kpBwQ0BeVHIWUHI75lCxadMcYMBZaEGGNMEUloIxj9v2zJ1yYIbo74B8GGWW3Oc8KXPbckCVF3ITr/5+AuBFKQAV30Pl7mle0UnnwDrXsPam9Egj8buLCTH6LN10B6GgTXRspPQvwrtHtWAJzR4M7pOIBvIjLifNBFEFgPcUYMWKzGmGGmBGcrBpItxzLGmCITpwKJ7ImUHTo4EhCA0HZAoONxpwJ849oc0ubbwV1E247gKVoSkBZxtOGv/RpmmzjiL6F1h3uVxzLfQuwRdMHeaOqrNs8TEag4A28zemthpOp3SHBdJLS1JSDGGNMHloQYY4zpMak4EZxRLHmj7gPCyIi/dexvkngV6GY38fRXXT+nF7yN9H/GK7G7+OPGbPndxn90eL5T9nOk+l/gWwUkAv41kJqrkdDmAxJff9DMPDT+DJp81ystbIwZRATVgX2UGluOZYwxpsfEqYVRT3gb1JNvgG8cUnYY4l+x45N9S0P6Y7q11sAZ1fVzekMbwJ2X6wSkpua8RAZJ80BVRRsvgejN2apqClINtbci/vHFDs8YY3KyJMQYY0yviFOBlB8F5Ud1/rzyY9DEq7Rt9Lf4U7nWiUkEyk/s1xiX3C5C3sl/pybvZZr6GG24AFIfgVRA2eFIxclIZ+WVCy3xIkRvA5Kg2RknjaELj4dRTyEiXsWv5Oto7CFAkcjPIbjVoOvrYsyQZntCjDHGmP4jwfWh6jyvqpSUAyHwrweRw4GI95ByqPglUnbgwMQgQYjsTcd9HhEoOy7nNZr+Dq07DFLv4+2mr4fmG9CGcwckxt7S6B10LCfsQmY2pL/xntPwZ3TRLyH+GMQfRxf9Bm04q+CxGmPMYiX0UY4xxpihyinbF43s4b0pdqpbStpq1Rng1oEz0ksUBpBUnYNqE8Sf9ZYtaQrKjsib+GjzdUtmFlrEIfYoWnm6tyStlzT1GRp/BnCQ8K5IYEKvx8JtyH1cvEplmvoCYg/SZiZKoxB7Ci07BAms3ft7G2P6h1KS+zYGkiUhxhhjCkIkCIFJ7Y6FwLdMwe4v1Zegbh1kfgLfeMSpyH9B6jMgk2OgEKR/gGDvkhC34Z9Llk8haPONaMWvcSp+0avxCO8CTV8BiY7nApOy92pfiQzv+YlXwZIQY0wR2HIsY4wxw4o4tUhgUucJCIB/dXL+mtREhzLE3aWpz7NJQRyvOWXG+3PT5Wh6Zq/GlLKDwT8eb2kbLK5URtX5XuIn5eT+zDHg7XMxxpQGHeBHibEkxBhjjMlBKo4DQu2OhiG8a4eO8N2l8efIW6448WKvxhSnHBn5AFJ1tte/JXIgMvK/OJHdsiHvlO9KCO/aq3saY0xf2XIsY4wxw4Kmv4HEK0AQwjsjvtGdPl/8q0DtrV5/kfRn3oxC5BCk8tQ+ROHH+/yvfR8PgT5U3BIJQ9mBOfe3iFMLNf9GF53Kks8eM8iIfyK+Mb2+pzGmv9meEGOMMWZIcRv+AdHb8ZY/+aDx7+iIv+NEdun0Ogmui4x6CFXtl3K2EtkFbb6Gjns0FEID15NEQlvBmLcg8aZ3r+DGiFM2YPczxpiuWBJijDFmSNPk+xC9gyXVoVLe/9WfiYY2Q5yqLsdon4CoZiD1IZCGwLqIBL2KV9H7QRuR8I4Q2hYRX9tx/CuiladD4z/wPvUUwPX2b3QxM9NXImEIbzOg9zDG9EEJ7tsYSJaEGGOMGdI09ihtGyVmid+rDhXZvWfjJT9AF56IV43KS040vAfEHsLb7+F6ez+Ck6Hm2g6JiFN+BBreMbsHxIHQ9r3eY2KMMYOVJSHGGGOGuDwfL2on5/KN5DajC48BbWp7InZ3u2dGITUFEs/n3BguvqWh7JAe3dsYM8QNs5kQq45ljDFmSJPI7nTslA6QhtCWPRss8QIdN5XnoVE0/nTPxjfGmGHCkhBjjDFDW2ADKDsALxHxAUEgBFUXIs6Ino3lLgLN1fgvF8f6cBhjukcBlYF9lBhbjmWMMWZIExGk6g9oZB9IvOx1PA/vgvSmU3twE7r/+V0QiezX83sYY4YlHWbLsSwJMcYYMyxIYHUIrN7HMSagkT0g/gRoNHs0Av6JkP7G26euCqSh4lQkuE5fwzbGmCHJkhBjjDGmB6TqAght6ZXjJYVE9oLw7oALif95yUlwY6t4ZYzpGZsJMcYYY0qDagJSn3rdyv2r9kvDwL4SEQjvhOSoekV428IHZIwxg5AlIcYYY0qSG3sMGs7FW+OUAWdpqLkO8S9f7NCMMab/leDm8YFk1bGMMcaUHE19CfV/AG32enJoDDLT0LojUO1miVxjjDEly5IQY4wxJUejd+F1H29zFLQBUlOLEZIxxgwo0YF9lBpLQowxxpQedx65mwIKuHWFjsYYY0w/syTEGGNMyZHQ1kCk4wlNQmD9QodjjDEDSwvwKDGWhBhjjCk9kZ+Dfxxel/MsiUD5MYhvdNHCMsYY0z+sOpYxxpiSIxKG2vvQ6D2QeAqkCik7DAlvU/BYNDMfEi8CCqFtEN+YgsdgjBnqZNhVx7IkxBhjTEkSpwypOAYqjilaDG70QWg4D8TJLme4AK06B6fswKLF1F9UXURsQYQxpjjsp48xxhiTg2Z+8hIQEl6JYGLenxsuQNMzixxd77mx53HnbYfOWQ13zoa4TTeiWoILxo0ZbmxPiDHGGGOIP5vnhAuJpwsaSn/RxOtQ/1vIzMgeWATNV6DNVxc1LmPM8GNJiDHGGJNTitxlgl3QVKGD6RfadBkQb3cwBs3Xo4P0NRkzZNhMiDHGGGMIbUvuX5N+CG1f6Gj6R3pa7uOaBre+oKEYY4Y3S0KMMcaYHMS/IlScgFcm2Mk+wlB+NBKYUNzgesu/cu7jEgSnuqChGGPaGWYzIVYdyxhjhhh1GyHxCpCE4JaIb1SxQxq0nIpfoaHt0PiTgCLhXZDAGsUOq9ek8rdo3S9ouyQrAuUnI2JvCYwxhWM/cYwxZgjR+EvoolNBfICCZtDK3+GUH1bs0AYtCayOBFYvdhj9QoIbQs3VaOPfIP0tOKO8BGQIlBw2ZlBTrE+IMcaYwUndBi8BId526r3xYjS0MeJfpVihmRIioc2Q0GPFDsMYM8zZnhBjjBkqEi+Q+8d6Go09WuhojDHG9IDowD5Kjc2EGGPMUKEJcu8+dEHjOY4bMzC+eOdr7vnbQ8z6+icmbTqRg36/F8usuFSxwzKmtJVgojCQLAkxxpihIrQ1cGGOE2EkvGOBgzHD1ZuPTeHCgy8lGUuiCjO+nMXL977OlW//lXETxxY7PGNMibDlWMYYM0SIb2moOIUlJWUFJAKR3SCwQZGjM8OBqnLFydeTiHoJCEAm7RJrjHPj2XcVNzhjTEmxJMQYY4YQp+J4ZOQ9UHYkRA5Bqq9Dqi5EZHhVXTHFsWheA/XzGzocV1U+evWzIkRkjOkuEblJROaKyCd5zouIXCEi34jIRyKyfqtzR4rI19nHkd25ny3HMsaYIUYCk5DApGKHYYahssowkDvhHTGqqrDBGDPIlMDm8VuAK4Hb8pzfBZiQfWwEXA1sJCK1wHnAZLydLVNF5FFVXdjZzWwmxBhjjDH9IhQJsfVBmxIMB9ocD5eHOPCMPYsUlTGmO1T1VaCuk6fsCdymnreAahFZBtgJeE5V67KJx3PAzl3dz2ZCjDHGlCxNfwfpb8C3IhKYUOxwTDf8+j/HEWuI8/aT7xEI+Ukn0+z9613Z6ehtih2aMaVt4JsVjhKRKa2+vk5Vr+vB9WOBGa2+npk9lu94pywJMcYYU3JUk+iiUyDxBkgANI0G1kFqrkWcsmKHZzoRLgtx3gOnU/fTQubNrGO5CUtTPqK82GEZY2C+qk4udhCL2XIsY4wxJUcbL4PEm0ACtAmIQ+p9tDFXCWJTimqXrmHi5JUtATGmO7QAj76bBYxr9fVy2WP5jnfKkhBjjDGlJ3Yf0L7BYhJij6Ba/N2bxhgzDD0KHJGtkrUxUK+qs4FngB1FpEZEaoAds8c6ZcuxjDHGlJ68Hd5TQAb79WWMGXKK/PmKiNwNbI23d2QmXsWrAICqXgM8CewKfANEgaOz5+pE5Hzg3exQf1HVzja4A/ZT3BhjTCkKbgzJ1+jwWzmwDiL2q2s4SMQSfPH2N4TLQ6w6eWXrdWPMAFPVg7s4r8Av85y7CbipJ/ezn+TGGGNKjlSdgy7YLzsjkgSCIAGk6s/FDs0UwAt3vcZlJ16H4wjqKpUjK7noibNYftK4ri82ZpAqgT4hBWV7QowxxpQc8a+AjHoayk+A4FZQfjQy6ikksHqxQzMDbNqnM7j0uGuIN8WJNsSINcWZ+8M8ztj+L2TSmWKHZ4zpJzYTYowxpiSJbxRSeUqxwzAF9sS1z5FKpjscTzQn+OClT9hgh3WKEJUxBWAzIcYYY4wxxbFwbj1uxu1wXFEaFjQVISJjzECwJMQYY4wxJWPj3TcgXB7qcDydzLDWlrYczwxhpd8npF9ZEmKMMcaYkrHVAZswfvXlCJUFW46Fy0Psf/oejFq2toiRGWP6k+0JMcYYY0zJCAQDXPrqX3jm5pd4+d43KBsRYY8Td2LDXdYrdmjGDBjR4Vcdy5IQY4wxxpSUYDjIHiftxB4n7VTsUIwxA8SSEGNKwHuzf+SeTz6iKZlktwkT2WmVCfgdWy1pjDHGDBs6vBpyWhJiTJFdO+UdLn/nTRLpNAq8On0a9376MTfvuQ8+S0SMMcaY4WGYLceydzjGFNG8aDOXvf0G8WwCAhBNpXjvpx95/vtvixqbMcYYY8xAsSTEmCJ6c8b0nMuuoqkUT3/9VREiMsaY4UdViTbGcN2O/UmMKZTFm9MH6lFqLAkxpojKg0GEjmtAHYSqcLgIERljzPDy1I0vsP/Sv2CfkUezz8ijuffvD6Nagu/YjBlibE+IMUW0+bjl8Tkdk5Cg38eBa6xVhIiMMWb4eOme1/nPqTeTiCYAaK6Pcvtf7gcRDjxjzyJHZ4adYZb72kyIMUUU8vu5Za/9qA6HqQgGqQgGCfl8/GGLrZk0ekyxwzPGmCHt1vPubUlAFktEE9zz14dsNsSYAWYzIcYU2TpLLc3bx57IWzNnEE2n2GS5cVSFbCmWMcYMtHkzFuQ8Hm2MkYglCZeFChyRGbZKdN/GQLIkxJgSEPD52GL5FYodhjFmiJrx5SwevvJpfvpuDutssya7Hbcd5SPKix1W0Y1ffSzfvP99h+PVY0YQigSLEJExw4clIcb0wXcL6/jb66/yzqyZjAiFOXa9DTh87XURGV4Nh4wxpWvKsx/yp33+TjqZJpN2+fDlT3noiie4eurfqR49otjhFdVxFx/GuXteTCKWbDkWKgvyi78daj/HTeENs5kQ2xNiTC/Namxgr3vv5IXvvqUhkWBGQz0Xv/4qF7z2crFDM8YYAFzX5Z/H/IdENEkm7ZWfTcSSLJpTz10XPljk6Ipv/e3X5i+P/p4JG6xEuDzE8pOW43e3/ZodDt+q2KEZM+TZTIgxvXT91HfbNBkEiKXT3PXxh/zqZxtTE4kULTZjjAGYM20eTYuaOxxPpzK88ci7nHzZ0UWIqrSsv91aXPXuxcUOwxibCTHGdM/U2T+SztHYKujz8+3CuiJEZIwxbYUrwriZ3O9syqrsgxJjTPH0OQkRkXEi8pKIfCYin4rIqf0RmDGlbuWaWpwca4aTmTRjK6uKEJExxrRVM2YEkzZZFZ/f1+Z4qCzE3r/etUhRGWNysY7pPZcG/k9VJwEbA78UkUn9MK4xJe2EDX5G0NfuF3u2ytUylZVFisoYY9r6w92/YfzqYwmXhyirihAIBdjh8C3Z+Zhtix2aMWYY6/OeEFWdDczO/rlRRD4HxgKf9XVsY0rZ6qPHcO1ue3LOS8/zU1Mjjgi7r7oaf9l6u2KHZowxLWqWqubaD/7JV1O/Y8GsOiZssBKjlxtZ7LCMMcNcv25MF5EVgPWAt3OcOx44HmD8+PH9eVtjimaL5Vfg5SOPpSGRIOz3E/IXvtbDzIZ6nv32G0SEHVdahbFVthTMGNOWiDBx8soweeVih2KMMUA/JiEiUgE8APxGVRvan1fV64DrACZPnlyCK9OM6R0RYUQ4d4dzVW15zkC45YP3uPj1V1u+/vvrr/L7zbfkyHXWH5D7GWPMcPf2k+9x8zl3M/u7OYxbbSzHXnQI6227VrHDMkPBMHt33C9JiIgE8BKQO1XVCo+bYUdVueXD97l6ytvUxWIsP6KamnCYD+f8BMBWy6/IBdtuz9IV/bdXZHr9Ii5+/VUSmUyb43/736tsu8LKjBsxvJuQGWNMf3v1/jf5+1FXkoh6zQ2/fOcb/vjzv/GnB89k8o7rFDk6YwaX/qiOJcCNwOeqeknfQzJm8PnPu2/xzzdeY340iqvK94sW8t5Ps8moklHllR++Z5/77iKRTvfbPZ/59mtc7fixiap3zhhjekpVeeL65zhilV+xZ/UR/G7H8/nmg++LHVbJuPaM21oSkMUS0STXnXlbkSIyQ8YAV8YaqtWxNgMOB7YVkQ+yD6v7V+JiqRR/evlF1rr6Cla98lIOf+i/fGe9LXolmclwzdR3iXWSYGRUaUwkePa7b/rtvjnyD+949n/GGNNTt/35v1x92q3M/m4O0YYY7z3/EadtcS4/fD6z2KEVXSadYd70+TnPzfjixwJHY8zg1+ckRFX/p6qiqmur6rrZx5P9EZwZOMc//jD3fvoRzakUadfljRnT2ee+u5gfjRY7tEGnLhbNOSPRXnMqxbd1/Zfo7bDyKjjS8Z+wIw47rjSh3+5jjBkeYs1x/vvPR0lEE22OJ2MJ7jz//iJFVTocn0NlbUXOcyOXqSlwNGZI0gF+lBjrmD4MfblgPlNn/9hmL4ECiXSauz7+sHiBDVK1kbKcTQvbKw8EWHVk/5XFXLG6ht9stAkhnx+/4+B3HMI+P7/ZeBOWr67ut/sYY4aHn76fi8/X8W2B6ypfvtt/s7iDlYhw0Fl7Ey4PtTkeKgtx+Hn7FykqM6QMsySk8PVETdF9s2AB/hyfoCcyGT6ZN6cIEQ1uQZ+P49efzLWdLMnyOw61kTK2X2mVfr33CZM3ZIeVV+Hpb75GBHZaeQIr1dT26z1KQWMiwcNffMbn8+cxafQY9py4OpWhUNcXGmO6bdTYWtKp3D/Dxk5YpsDRlKb9TtuDTCrDPX97mGQsSbgizBF/2p+djtqm2KEZM+hYEjIMrVxbS1rdDsdDPh9rjl6qCBENfqdsuAllgSDXTH2HhdnqWMtWVvH+Tz+iwI4rrcI5W27TocN6f1ipppaTf7ZRv49bKmY21LPXvXcSS6WIpdNE/H4uf/sNHj7wMOuJYkw/qqypYJtDNuflu18nEVuy+TpUFuTQc/YrYmSlQ0Q46Hd7s//pP6e5Pkr5iDJ8A/Bz3Qw/QmluHh9IloQMQ6uNGs26Sy/De7N/JJldkiVA0Ofn4LXWLm5wg5SI8Iv1J/OL9SejqgPWF2Q4OvelF1gUj7fsu4ml0yQyGc57+QVu+PneRY7OmKHl1KuOI1Ie5qkbXiCdzjBymRp+9e9jWWPTicUOraT4fD6qavuv5Loxw5ElIcPUDXvszUWvvcyDX3xGMpNhw2XH8uett2d0WXmxQyuqxUlZX2YsLAHpP6rKa9Onddj476ry6vRpxQnKmCEsEAzwy8uP4YR/HkEimqCsqsx+phlTKDYTYoaDskCAC7bdgQu23WFQf3Kvqjz1zdfc9+nHZNRl79Um8fOJq+N3elZzYVZjA2e98CxvzpgOwGbjluei7XZg2Upb7lNsPsch064hI9Dj/8bGmO7zB/z4R9hbBGPMwLGfMGbQJiAAv3v+GZ78+iui6RQA783+kce//pIb99i7268rkU6zX7Y8cSb7ifv/ZvzAvvfdzctHHkvIb/9MikVE2GPViTz65Zek3CWJSNDnY49VVytiZMYYY0w/KtGGggPJPko0g9bn8+fx+NdftiQg4O0XeGfWTN6YOb3b4zz97dc0JZMtCQh4y32akgme/+7bfo3Z9Nwft9yGCbW1lAUChP1+ygIBJtSO5A9bbF3s0IwxxhjTS/YRrxm03pwxHdft+LFBNJXifz/8wGbjlu/WOD8sWkRzKtXheCyVZlr9wj7HafqmKhTmsYMP590fZ/FN3QJWqR3Jz5YdO6hn8IwxxpgOhtlMiCUhZtCqDofx+xySbtv9AiGfj5pIpNvjTBw1ivJAoEMiEgn4mThyVL/EavpGRNhw7HJsOHa5YodijBkgi3uU+AP21sSY4cCWY5lBa8eVJ+TsVC4i7Dlx9W6Ps92KKzOmvIJAq43OAcdhmYpKtllhpX6J1RhjCiWVTPHW41N57rZXmDt9XrHD6dLcGfM5a+cL2K38UHYrP5Szd72IeTMXFDssYwrPOqabUtacTPLMt18zPxpl8rJjWW/pZYbtspSKYJBb9tyX4x9/mEQ64zX6EeGKnXdjqYqKbo/jdxweOOBgLn79NZ78+ksAdpswkd9ttiW+fq7A9FNTI/d++jHfL1zIz8Yux96rTaIsEOjXexhjhq9vP5zGmdv/hXQqjbpKJp1hr1N24Rd/O6wkf1ck40l+vcnZLJxTj5vxmuhOfe5Dfr3p2dz2zZUEgj3/+ZjJZHj0qmd47KpniEcTbLHvxhx6zr7d7uuRiCWY/d1capeupmqk9QIxZqCIauFTo8mTJ+uUKVMKft/B7tO5czj0of+Sdl2SmQwBx8fGyy3HtbvvNazLlWZclw/mzCbjKusuvQyOCO/MmkksleJnY8dSFQoXO0QAPvhpNoe1+u8X8QeoiYR55MDDGFlWVuzwjDGDnOu6HDL+JBb8WNfmeLg8xDn3/paNdl2/SJHl9+Ld/+OyE64l1hRvczxSGeb/rj+JrQ7YtMdjXnTIZbzx6BQS0QQA/qCfUcvWct3H/yJS3vnvg//+61Fu+9N9iOOQTqbZdK+fccZNJxOKhHochykdIjJVVScXO47ORJYZpysd9dsBvcdnf/ttSX0fbCakhP3Y2MD5r77Ey9O+b0kyWu9bSLsub82cwb2ffsyha61TrDCLzuc4bLDMWAA+mTuHox95gES2r0Qq43LOllt3+f2pj8f5csF8lq6oYPyI6l7FkUin8TtOztkTVeX/nn2KaKp1Ja8UqeYMl7/9Bn/ZZvte3dMYYxb74p1viDZGOxyPNyd44trnSjIJmfX1bGLN8Q7HE80JZn49u8fjzfhyFq8/8i7JWLLlWDqZZtG8el644zV2P2GHvNe+ev+b3HrefS3JC8Cbj7zLZSdcx+9uO6XHsRhjOjd8Pz4vcc3JJHvfexfPffctiUyG5lQqdwWndJr7Pv24CBGWnlQmwxEP38+CWIymZJKmZJJEJs2Fr73Mp3Pn5LxGVbnkzdfZ+MZrOO6xh9jpjls5+IF7aUh0/KWYz0dzfmL3u29njauvYI2rr+CM556mOZls85z5sSizGhs6XJt2XZ759psevU5jjMklGUvmXXKV641+KVhhzfE5ZyeCZSFWWHNcj8f74p1v8Pk6vrWJNyf46JVPO7327r8+2CYBAUjGU7xy/5tEG2M9jsWYHhtme0IsCSlRj3z5OU3JJG43lst15znDwRszppPOriluLZXJcE+eRO2xr77gxvenkMhkaMwmLe/N/pHTnnmyW/ec1dDAIQ/ex2fz5uKqksxkeOyrLzju8YfbPC/k85Fv6WPYmiEaY/rB6htPQHOULQ+Xh9j24M2LEFHXNtljA2qXqcEf8LU5Hm+K869jr+LRq5/p0XhjxuWuaBgI+ll2laU7vbbup/qcxx1HaFrY1KM4jDFdsySkRH0ydw6xdMeZj/bCfj/7rr5GASIqfU3JZM5EP6NKfTz3p4DXvzeFWDrd5ljKdXl9xnQWxrr+5OuWD98jlWlbIjiZyfDBT7P5pm5JdZeqUJjJy44l12eUa4we0+V9jDGmK6FIiP+74SRCkSA+v/emPlweZuV1V2T7w7cscnS5+QN+rnjjQrY/fEsCobab0BvrmrnujNt59raXuz3eWluuTu0yNTjtZkN8AR+7Htf5stc1N18NcTr+lA5FQowcW9vtGIzplYGeBSnBz6stCSlRq40aTSTPJ+SLS8mWBQKss9TSHDKM94O0tuFyy5Fq1zMEvO/TTitPyHnNwnjuRMMnDg2JRM5zrX05fz4pt+PsS8BxmLaobaPDo9bJvR77xe+/ZUG04zpuY4zpqa0O2JSr3/s7+/xmN3Y4civOuPlk/vXSn3pVZapQqkZW8tvrTyJS0XHzdyKa4PY/3dftsRzH4Z8vnsekTVYlEPITjARZaoXRXPTkH/LOkix29PkHESkPt0lgQmUhTrrsKHw+XydXGmN6w9aBlKi9VpvE5W+/SSKTaVluFXAclq+u5rC11mV+tJmfLbscm41fPmevjLnNTdTFYqxUU0twmPzwHF1Wzm822pR/v/Mm8XQaxUtA1hqzFDutkjsJ2WL8Cjzw2Sek2y2Vivj9LFdV1eU91116Gd75cSbJHLMhq7ZrdPj6jB9yfhDh9/l4+Yfv2WnlCXwydw7V4TATR44qyXKaxpjSN27iWI7/++HFDqNHMukMjXW5lzzN/3FhzuP5jBo7kktfPZ9F8+pJxpKMHte9n6fLrbosV029mDsveIBPX/+CpVYYw8Fn7c16267Vo/sb01tSgrMVA8mSkBJVFQrx4AGH8IeXnuOtmTNwRNhi/PKMH1HDx3N+YqsVVmTj5cZ1SEDq43FOeepx3vlxJgHHhwics8XWHLDG8PgheuLkDZm87Fju+eQjGpMJdp0wkV1XWTVvCeNfb7gJz377NU3JJCnXRfCWuJ2/zXbd6hFy+DrrcvtH75N23ZZkMezzs/UKK3aosuVzHByg/byJAG9Mn84fX3qegOOQdpVxVVXctOc+LFuZOxF6c8Z07vrkI5qSCXZfdTX2WHW1QZ1szmtuZmZDPSvW1FAd7n63e2PM0OAP+Bm93Cjmzpjf4dy4icv2aszq0SN6fM3YVZbhzFt+lfd8JpPhlfve5NlbX0ZE2Omordly/01whnGZfGN6y/qEDAKuKs99+zWnPfsUadcl7bqUBQJMqB3JPfseSKjVsq1DH7yPKT/OarNEKOL3c9PP92Gj5XpeaWQ4mBdt5sb3pvLmzOmMHzGCX6z/M9ZZqvMNjK1NW7SQC197hTdm/EBZIMAha63Dr362MYF2ScHHc+dw4P33EG+3ByWQLevb+rhPhJVrannq0CM7fIJ3xdtvcO3Ud1v2skT8AdYYM4a79jlg0PWLSaTTnP7cUzz/3bcEfT6SmQwHrbk2f9xym5wzfMaYoeuV+97gH8f8h0R0SXXBUCTIeQ+ewc92Wrd4gWWpKn/e759MffZD4s3ect1weYhNfj6Zs+/8TXGDM50aFH1Clh6nKx8+sH1CPv2n9QkxPZR2Xc54/pk2b1KjqRRfLpjPfZ9+zOHrrAfArMYG3pv9Y4c9CrF0muvee9eSkDxGl5Xz+817v2lzheoart9jry6ft9aYpThxg59x9ZR3AcURQYGJtaP4cO5PbZ6bUWVGQz1f1S1gYqtlXXObm7hqyjttln/F0ik+mzeXZ775mt1Wndjr11EMF772Ms9/9x2JTKalt8t9n37MuKoRHLPeBsUNzhhTUFsdsCnBSJCbz7mbn76fy7iJy3LsXw9l/e3Xzvn85vpmXrnvTebNWsDqG63K5J3WGdAZiU/f+LJNAgJe6d83HpnCl1O+ZeLklQfs3sYMRZaEDAIft3uDulg8nebRr75oSULmNzcT8Pla3sy1NruxcUBjNN3z6402Zc+Jk3hp2neE/H52XGkVTnjikZzP9TkOi9pV6Hpr5gwCjtNhD0o0leK5774ZVElI2nX572efksi0nRmKpdPc+P5US0KMGYY22WMym+zR9Qe13344jf/b+jwy6Qzx5gSRijDLrzGOf7543oB1N3//hY/bzNIslk6mef+Fjy0JMX1W7D0hIrIzcDngA25Q1b+1O38psE32yzJgjKpWZ89lgMX9EKar6s+7up8lIYNA2OfP2wskElhS8WSZyso2HbkXCzgOm41ffsDiMz2zfHU1R627pFLW9iuuzGdz5xJv92Y87bqsOWapNseqQuGcGywdEaojg2svRTKTIZ2jmhmQt6SyMcaoKhccdCnN9UuqCsaa4nz30TQeuPRxDjl73wG5b2VtBYFwoE03dvB6kFTVVgzIPc0wU8QkRER8wH+AHYCZwLsi8qiqfrb4Oap6WqvnnwKs12qImKqu25N7Dq4F5MPUpNFjqMmxWTfiD3Boq/K8Z7/wXM4+FCG/n+PX/9kARjh4JNJpnv32a+7+5CO+W1hX7HAAOHStdViqooKwb8lnAhG/n99ttgXlwWCb5242bjwBp+MG9KDPx0GDrPhAWSDAuBG5N45usOzYAkdjjBks5s2Yz9wf5nU4noylePbWVwbsvlsfuClOjj4iOMKW+28yYPc1pkA2BL5R1e9UNQncA+zZyfMPBu7uyw0tCRkERIQbfr43IyMRygNByvwBQj4fB66xFjuutAoA86NR/jfjBzI5ZkxWqRnJ6PLyQoddcr6YP49Nb7qO0599mgtefYnd776ds55/Nm8n80KpDIV49KDDOHWjTdhgmWXZaeVVuHnPfTkyR1+RgM/H7Xvvx+iyMioCQSqCQcJ+P3/ealtWGzW6CNH3zfnbbE/E72/ZhO4ToTwQ4OwttipyZMaYktVJ0YqBLG1ePXoEf374d1TUlFNWFaGsMkJlbQUXPPZ7Kqrtd6zpo8I0KxwlIlNaPY5vFcFYYEarr2dmj3UgIssDKwIvtjoczo75lojs1Z2XbMuxBomJI0fxxjEn8Nr0H1gYj7Hhssu1+RS5LhbNuVcA8jfkG05UleMee7jD9+LRrz5n0/Hj2WPV1YoUmacyFOKEyRtywuQNu3zupNFjeOOYE5g6+0diqRSTlx3bYcZksNhs3PLcv//BXDP1Hb6uq2OdpZbmxA02ZPnq6mKHZowpUWPGjWKZlZZi+uczaf0ZUigSZKejt8l/YT9Yf7u1+O9PN/D5W18jAqtvvGpLd3pjBoH5/VQd6yDgflVt/aZzeVWdJSIrAS+KyMeq+m1ng1gSMogEfD62XXGlnOeWH1ENORZj+UXYdNz4gQ1sEPhi/rycyVgsneaujz8sehLSUz7HYcOxyxU7jH6x+ugxXL7z7sUOwxgziPzxvt/y263OJZVIk4wnCYQCrDp5Zfb5zW4Dfm9/wM9aW6w+4Pcxw4uQ611cQc0CWpdRXS57LJeDgF+2PqCqs7L//52IvIy3X8SSkOEg5Pdz1uZbcuFrL7f0j/A7DhF/gJ1XnkDGdbvVfG+oSmYyOHn+eeeqJmaMMaZ0LT9pHHf+cA3/e/Bt5s+qY/WNJrD2VpMGdDmWMUPcu8AEEVkRL/k4CDik/ZNEZDWgBniz1bEaIKqqCREZBWwG/L2rG1oSMoQcstY6jBsxguumvsv0+noaE3Fi6TQnPfkoEb+ff+6wC1utsGKxwyyKSaPH5EzCwn4/e060T7SK5Zu6Bbw5cwa14QjbrbQSYX+g64uGiPp4nJTrMqqsrNihGDMohctCbH9Y73s8AcybuYA7zr+fqc9+SPWYKvY/fU+2sk3mpliKuEVVVdMi8ivgGbwSvTep6qci8hdgiqo+mn3qQcA92nZD7erAtSLi4u03/1vrqlr5WMf0ISjjumx1yw381NzUprRvxO/nyUOOHLbr7V+Z9j0nPfkorirJTIayQICJI0dx1z4HtOk6bwaeqnLWC8/y6FdfoKr4s13j79h7/w5liYean5oaOe2ZJ3lv9o+ICOOrRvCvnXZlrSH+us3wlU6lmfnVbCqqyxg1dmSxw2mxYPZCjl/7/2iuj5JJezPi4fIQB/5uLw47Z78iR2f602DomF621Dhd5ZCB7Zj+8WXWMd0MsLdmzaA+Ee/QWyTlutz9yUd96g4+mG21woo8d/jR3P/ZJ8xtbmbL5VdguxVXxt9qhmRGfT1/euUF/jf9BwI+H/usNonfb74VZYHh8wl9ITz59Vc89tWXxLNLBxcviTvusYd5/ZjjW6plDTUZ1+XA++9lVmNDy7/PbxbWccgD9/HSkcfarIgpacl4kieuf56X7v4f4bIQe5y0E5vvs1GnS6Bevvd1Lj/pejLpDOlUhtU2msAf7/stNWNyl+cupPsveYxoY6wlAQGvA/rdf32IvX+9K+VV9u/RFFaxmxUWmiUhQ9C85mjO42nXZXZTQ4GjKS1jK6s4daNNc56rj8fZ6947WxK4lOty32ef8Pn8edy330G21rgf3fPpR8TSHRtrNiUTfDJ3DmsvtXQRohp4b8yYTl0s1uEDgrSb4f7PPuHEblRHM6YY0qk0v93qXKZ9OqOla/inb37JLi9vx6/+fWzOa76c8i3/PPaqNl3GP3vzS87Z/a/8552/5bymkD548RPSyXSH4/6An2mfzGCNTSf26/1SyRQ/fjuH6tFVjBhV1a9jGzMYDd+dykPY+sssQ9p1Oxwv8wfYfPwKhQ9okPjvZ58QS6favEFMZjJ8Nm8eH82dU8TIhp5cpaTBq/GfytNFfSjwZkA6/ttMZDJ8v2hhESIypntef+gdpn06s01CkYylePTqZ5j++cyc1zx42eMkY20/bMikMvzw2Ux++GxGzmsKaakVRudsOZJOphi5bE2/3uupG19g/6V+wSkbn8XB407kvL3/TrRx8JfPnz9rAV+++82QeC0lYeD7hJQUS0KGoPEjqtln9UlEWu1zCPl8LFtZyc8HWSnaQvp03pyW5UGtiXgbqE3/2Wvi6m3+fi7miLD2mKE5CwKw1pilcv4eKAsE+Jl1iTcl7N2n3ycRTXQ4rq5y3Rm357xm7vT5OZvB+gM+Fsxe1N8h9tgBp/+cYKRtj6VA0M+kTSey9Apj+u0+7z3/Ef859Saa66PEGuOkEineffp9Ljr08n67R6HFmmKcs8dfOXLCKZy5w184YOlfcOcF9xe9+a8ZXCwJGaIu2GYHLthmB9ZZamkm1I7k5Mkb8eCBh9oG7E6sPmoM4Tzfn5VragsczdC236Q1WWepZVr22gR9PsJ+P5fttBsB39Bt/LXGmKXYeOy4Nn/PAo7DqLIydl+1f5d+GNOfqpeqznvuo9dyF8HZYIe1CYQ77qdLJVKsst4KpFNp7rjgfg4aezx71RzJBQddytzp8/or5C5N2mQi/3fjyVSNrCBcHiIQCrD+DmvzpwdO79f73HPxw21mkABSiTTvPfcRC+cs6td7Fco/jrmK957/mGQ8RbQhRiKW5J6LH+aV+94odmiD2zCbCbF3pEOUiLD36pPYe/VJxQ6l4BLpNM999w0/1C9itZGj2XqFFbvVI2X/SWty9ZS3SaTTLf9Wgz4fE2pHss4Q3aNQLAGfj9v33o9XfpjG/6ZPY1RZGXutNollK4f+Oulrdt+TG96bwj2ffkQyk2HnVVblNxttMqzKE5vBZ6ejtubeix/OeS6Tyr2E8ue/3JnHr32O+vmNLXsvwuUh9vvtHlTVVvKX/f/JO0++TyLmvUF/7f43+eDFj7np88upGlnZMs7c6fP45PUvqR4zgnW2noSvkw8qGuoaefza5/jktc8Zv/pY9vzlLiyzUv7Kc9scuBlb7rsxs7+fS2VN+YDs1Zg3I/dMeiDoZ+Gcemo6SfBKUXN9M289NoVUou3KgXhzgnv//jBbH7hZkSIzg40lIWZI+bGxgX3vu5umZIJYKk0k4GeZyiru3/8gqkLhlufFUinu/uQjHv3qC8oCAQ5bax12WWVVHjjgEP740vO8PWsmfsdhj1Uncu6W29qmdOCdWTP56/9e4csF81mqvIJfb7gxe6++Rq/H8zkO2664EtuuuFI/Rln6gj4fJ/9sI07+2UbFDsWYbhs3cSxjJyzDrK9ntzkuIqy77Zo5r6mqreTq9/7BvRc/zNtPTKVqZCX7nrY7W+y7MTO/ns3bT7xHMr5kz4jrKrHmBE9e/zwH/X5vVJWrT7uFJ657Dl/AhyCUV5fxjxfOY+wqy3S437yZCzh5gzOJNsZIxlO8/8LHPHHd8/z16XNYc7P8S5F9fh/LTeg4Xn9ZZ+s1mP3dnDZVuABcVcZOGHwfcDUubMbx+YCOy5cXzhnexW/6RK06ljGD2u9feJb50WYy2XWpzakUPyxayMWvv8aF2+4AeJuiD7j/Hr5dWNeyB+Sjn37inVkz+dPW23HnPge0rGu15MMzdfYsjnrkgZbv1w/1izjnpedpSCY4cp31ixydMUNLc30zjt9HpDzc9ZML6Jx7T+O3W55LMpEik8oQDAcIhoOcdMlRea+pGTOCE/91JCf+68g2x7//6Af8QX+bJAQgGUvy6ZtfAvDq/W/x1I0veM/JPi/WFOfcPS/mhk8u7fDz+caz76Khrgk34xV/SKe8ssD/OvYqbv7iir6+/B5TVd556v2WJWbiCOp6v1tCZSGOufBgQpFQwePqq9HjRhIqC3bYI+Q4+RNSY3KxPSFmyEhmMrw5Y3pLArJYynV54usvW75+6puv+H7hwjab0KPpFPd++jEz6usBL/mwBGSJf7z+vw6b9mPpNJe+9UbOSmzGmJ777qMfOHH9M9h3zLHsXXsU/8/eWYdHcXVx+J31jQsJBAIEd3d3L+5taSmFuhv19itV6hSoUYfi7u7uENwhIUCIJ6szO98fgS3LbpJNSEgC8z5Pn6eZnblzZ0l277nnnN/vre4fk3il6KimVa5fgSlHvmXQyw/QuFt9hrzRl9+PfUdk1dK5HiuiYkkk0f2zQ6PTUL5mJACLJi3HkuG60JVlmasX4rl04rLbtbuX73cGILdy5Xw8qQlpuZ7jnTLpxd/5eOg37F5xAEmUUKkE9EYdtVpW490ZL9P/+Z53fU75gVqt5vkfHkfv819Tv1qrxhhg5NH/DSnEmd0DKD0hCgrFk+xUOW59aeOFc5g8eFSoVSr2XI6lbGDhm2gVNU4kXPd43CqKJFnMhPn4ur3mkGW2XrzA8YR4ygUG0TGq4j3ddK6gcCekXE/llXbvk5Hyn8/T/nXRvNLuA34/9h0qL/ra7gbhZUsw+vOH73icyg0qULFOOU7tP+fi1aHVaejzdDcATOkWj9eq1GrMHl4z+hmyDDY8NcgXJJdOxLL8t3XYzP81pEuiA61BxSP/G0rDTnXu6nzym/ZDW1EiMpRZ4xcSd+4qddvWZOjYfoSXLVHYU1MoRihBiMI9g16joVlkWXbGXHLJhmhVKnpVqer8uaSvHxqVym0HX0AgxGi8a/MtTpQNDCTlmvuXvlqlIlDvXjKSZrUyfO5MzqckY5Mk9GoNgXo9c4YMp5Sfv9v5Cgr3Oyv/3ID9NuM8SZRIvJLEgXXRNOxct8DnkJqQRmpiOhEVwlFr1EiShCAIbgGQJEkc2ngUU6qZOm1quDSR54ZPl7/Dt0/+zLaFu5EdMuVqRvLKL08SXi4MgHaDW3LxWKzLQh5ArVFRqV55t/H6PNudvz+c6aJEpdFpaNazoUtp2+n955g5fgExJ+Oo2bIaQ1/v47xnfrFvzWHX3a8bWNIt7Fq+r9gHIQC1W1Wn9kJF9j8/UXpCFBSKMV906sbAWf+SYbdhstvx0Wop6efH2FZtnecMrVWHvw7udwlCBDK9GlqVc/9iU4CXm7fk2WWLXUqyjBoNo+o3Quchu/H19i2cTkzAduM9Fh02LKKdN9eu4s++A+/avBUUiguXjrsvtgEcksyVc9cK9N4ZqSa+eOQH9qw8gFqjRq1RExYZysXjsQiCQIs+jXnxxzEEhQVy7vAFxnb7GGuGFYRMqdnHPh7G4Ff75Pq+fkG+vDfzFWxWO6JNxMffdROo77PdWDttE1fOXcOSYUWtUaPRqnn9j2fRaN2XL/1e6MGZA+fYMm8nGp0GSXRQoXZZXv3taec5u1fs53+DvsJmsSM7ZM5HX2Tt1E1M3PV5vjan+wX5otaoAdesu1anwT/EL9/uo6BQnFGCEIV7ijIBAWwcOZoVZ05xITmZ6iVK0LFCJTS37ORFBQXzQ/cHeHX1chwOGUmWCff1ZUrvfi7nKfxHh6iKfNG5G59u3sh1UwZGrZYxDRvzbJPmHs9feOK4MwC5iSTLbL14EasoKn41CkiixLIpa1n+21okUaLzw23p+2x3dAZdzhffg9RqWY0NM7e69UAAVGpQoUDvPW7w1xzadBS7VXTKrt5aFrZ98R7OR1/kl8Nf82b3T0i6kuxy/V8fzKJG86rZKlBlh06vRad3L5cy+hmZtOtz1s/Yyq7l+wmLDKXXE50pW83V2PPMwfN8//QvHN95Go1OQ4s+jWnVrynlapShcv3/3jtZlvnu6V9cMiWiXUJKM/P729N4f7b3/iCn95/j+K7ThJUNpXHXejcCjv9o2bcx3z/zi9t1glpF54fauh1XUACKZN9GQaKsBBTuOfQaDX2r1cj2nE4VK7F79NMcjb+GQaulakio0oieA72rVueBKtWw3AgiVNm8X44s+3Pus09YhSz5aPDX7F19yKmw89fJmWyZv4tvNv4vWx+Ie5X2w1rxz7jZ2G2i03dDZ9BSo3kVqjWu5NUY1y8ncu1CPGWrl8E/2Lvd9muXrnN48zE3z4dbkewSCXFJzP9+ORYPvRg2s5UlP63KcxCSHTqDjm4jO9BtZAePr1+PTeCVtu9jSjMDmUaI2xftIeV6Kl+t/dDl3JTrqW4BFGS6vh9Yf8Sr+Yh2kQ8HfJl5viyj0qjxC/Lh203jKFn+v5Iuo5+RT5e9w/t9v3BK88oOmdf/fI6S5cNwOBwcWBfNxWOxlK1emgad6hSZvh+FwkMpx1JQuE/QqtXUK5W39Pu55CRWnTmFLEO3ylWoEBScz7MrmgiCgFGbc4Nnj8pVmHf8qEvJm0oQaFK6jJIFUeDE7tMuAQiA1Wzj3KEL7FlxgGa9GhXi7AoHg4+eiTs/5493p7N1/i60Og3dR3XgwXdyLl+0mq18/vAP7Fq+D61ei91qp/cz3Xjyy0dy3FxJjEvyKJV7O6JN4vKpuMza1duQ5UzviMJg5viFbk3qdqud4ztPcf7IJaJqlQXgXPRF5n+/FDELY0VvS6TmfbeUA+uinQaLAFaTlU+Gf8uEbZ+6nFu7VXVmxf3Kka0nsNtE6rSpjt6oJy0pnVfavc/V8/GIdgmNVk3JqDC+2fiR18FjVqRcT+XghiMY/Y006FjbY9magkJRQfntVChSJFvM/Lx3N6vOnMZfp2Nk/Yb0rVajULIU++MuM/toNGbRTq8q1ehYoRIqQeDXvbv5Zsc2HHLmAvv7ndt5pXlLxjRqkut7SA4Hv+3fy9+H9pNhs9O2fBRvtGxDmYDi7Rw+tlVbdsbGEG/KcPbmGDUaPu/crbCnplAEOLL1BA7JfTFoTrdwcOPR+zIIgUxPjVd+eYpXfnkqV9dNfP53di3PNP67GUws+Wk1pSuVcipNZUW5GpFZLsxvRaNV0+yBRqz+Z5PbawZfPW0HNSfm5GUmvfgHB9ZHozfq6DG6E4+NG1ZgJXY2q51lv67xqIyoUqu4dOIyUbXKsnXBLj576HvsNtHp03Ereh89g1/t7dU9l01Z4xKAADgkB6f3nyPpWgrB4a7qihqthnrtXU1df3juNy4ei3XKCdutdmJOxjH5pT8Y+9fzXs3DE3O+Wcwf707PDDyEzKb8z5a/Q9VG3mXSFAqZIiqjW5AouT+FIkO6zUbv6VP548A+ziUncejaVd5Zt4aPNq3P1TgW0U5cWtod+VdM2r2Dh+bNYsaRwyw8cZznli/hycULOJeUxDc7tmGVROwOB3aHA6sk8s2ObZxPzr2e/+trVvDdzm1cTksjxWph6ckT9JnxDwkmU84XF2GCjUZWPjySLzp14+lGTfmgXUc2jhxDucCgwp6aQhEgqGQgGp37HpjOoKVEmZBCmFHxxWa1s3baZrdMhtVkZc7Xi3K83sffyEPvDMDgm7VpnkanoXTlUjR/oBFPfjUCvY8OQZW5MWTw1VOhTjkadqrD883fZu+qg4g2kYwUE4smreB/g76+swfMhq3zd+HwEFRAZsN8VK1IJFHi69E/YjXb3DxEtHoNWr2WB57qQq8nunh1z6zK1gRBcJEazgpTmpn1M7a4zUW0iWyctd2rOXji6I6T/Pn+DGwWO6Y0M6ZUM6nX03irxyeI9pznpaBQGCiZEIUiw5yj0SSYTdhu2SE1i3ZmRB/iyUZNcpR2FR0OPt+ykX+jDwGgEVQ8Vr8BzzRpnqsSoLi0NH7Yud2lsdomSaw9fxaDVu3MgNyKQ3aw6sxpnshFNiQ2NZXlp05iveV5HciY7HamHT7IC81aeD1WUUSnVtOrajV6Va1W2FNRKGK06teEic//5nZcpVHT8cHWhTCj4ovVZPW4uw+QmpDu1RgPvj2QyKqlmfXlIpKuJlOzVTUs6Rb2r41GrVbRYXhrxox/GEEQ6PNMd6o1qcySX1aTmpBG6/7NaD+0JdM/m4/NYnPJStgsdvatOcTDFZ8hMS6JUhVKMvrzh2jZJ/dZY09cOHopy4V/RIVwylYrw7noi1meE1IqiMl7xxMQ4r3EcLshLVnwwzK3YCSsbKhXAfSCH5ZludvtyWjRW5b9ugab2b2kTrSKHNp49K5IPCvkA/dZJkQJQhTumC0XLzDt8AFSrFZ6Va7KoJq181T3v/nieTdXbgCtSs2hq1dyDELGb93Ev9GHXMb4YfdOftm3lzdbt+HReg29mseWSxeybKzecP58ltfltmLs+PV4tGq1SxACYJUk9sTF5m4wBYVihN6o5+v1H/LhgK9IiEtCEDIlTd+Z8TJBYYpZaG7wC/IltHQwVy/EuxwXBIG6bWtme60syxzZdoJzhy5QunIpJmz/xKvm6GpNKlOtSWWXYyd2nfbYVyLaRK6ez5zbpeOxfPrgd7w19UVa9Wua431yolyNSIx+BreeEI1WzaPjhgHgG2B0NobfTkhEcK4CEICH3hnA9sV7uB6biCXdgs6gRa1R89bUF70qG940Z0eWr9VsUTXL13IiIyXDs2GvgEdjRwWFooAShNzHXE1PZ9ym9aw9dxa1SqBXlWq806YdAR7M57Ji4q7t/LhnF+YbC/+DV+KYeTSa2YOG5ToQKeMfgFoQXIwGITM7EO6bfbOeTZKYdvigxyDGKomM37qZCD9/ulaqkuM8fDRatzncxGS3o/XwJa0SBLp5MfatRAYGInkoGdOoVFQKVkpSFO5tKtQpz58nJxBz8jKS6KB8zUhFoe42ZFkmestxYk9foXL9KCp7kOoVBIEXf3qC/w380ul9odao0fvoGP1F1s7m5gwLb3b7mLMHLyA7HKg0KkIjgvlm0zi3vgZvqFQ/iv3rDmersgVgNdn49c2puQpC0pLSWf7bOo7tOElU7bI88GRXQiOCaT2gGb+9NQ2bxYYkZn6WqrVqwsuF0frG+OHlwqhQtzyn9p51yTQYfPX0f6FXrp/TN9CXnw98xeY5Ozi8+RgRlcLp+mgHl/cs6WoylgwrJaPC3II630CfLMd+9H9Dcj2fm7QZ2II9Kw+6STyLNpG67bIPRhWKBgL3nzqW0hNyn2IR7fSfNY2VZ05hlURMdjsLjh9l6JyZ2cirunLdZGLi7p3OAATALIqcSUxkyakTuZ7TI/UaoL1NmlMtCET4+VOvZKlsr023WbMMHG7Oa/KeXV7No0OFilm+plapeLF5S/RqNTq1Gp1KjV6t5o1WbXPd71AttAQ1w8LRqlyfWadWM9LLrI2CQnFGEATKVitDVK2ySgByGynXU3my/mu80+tTJr3wGy+1eY83unyEzeJuaNikW32+2/wxbQe3oGK98vQc3YmfD3xFueplPIycyV/vz+DU3rNYMixYzTbMaRbizl7j2yd+ytN8+zzTDa0uZ+U8gLgzV70e99rFeEZVf5G/P5jJlnk7mfnFAkZVf5HT+8+h02uZsP1TWvRpgkanQaPT0GZAM77f9rGLb8eHc18jsmoEBj8DPgFGtHotvZ7sQvuhLd3uZzVbuXbpOnZb1mphWp2GGs2rMPi13gx5ra8zAEmIS+Lldu/zUNTTjKn7Cg+We5p9aw65XNvv+Z5u/TeCAOVrRVKvfW2v35fbaTe4BdUaV3KOrVIJ6H10jBk/4o4Vt7JDlmWO7TzF6n82cnr/uQK7j8K9ieAxfVfANG7cWN6zZ89dv6/Cf8w7doT3N6zFZHf9oPXVapncqw9tykXlOMaK06d4Y/UK0u3uX4pdKlbm5wf65npea8+d4c01KzGLIpLDQc2wcCb17E1JXz9mH43m1317SLZYaFm2HK+2aOVc+DtkmaZTfiTRbM5y7JK+fmx//Emv5vHcssUsO33S5ZgA1CtZinlDH+JSSgorz5wCoFulKpQNzFsJSarVyttrV7H67GkAygUG8VmnrjQunfXiQUFB4d7nw4FfsnPJXhflKp1BS/8XejL686wzHN4yMGwUqQlpbsdVahWL0/9Bp8+9otXZQxeY8MyvHN1xEq1Og6ASXIwBb1KyfBhTz032asxxQ79hy9wdbg3oVRpVZPLuL7yemyzLnNxzhoS4JKo1qUxohKusuiRJ/PbWNBZNWgkCqNVqHn5/EINe6Y0gCFy/nMjJPWcwp5n5+3+zSbicCEBoRDDvzXqVSvWjGF3nFWJvZPZuovfR8/OBLylTOcI5jylvTmX+hOVodRpkWSYoPJDxa96nVFS418/jCUmU2DJvJ5vn7sAv2I8eozt57TGTF9KTMxjb9SMuHotFEAQcDpnqzSrzyZK30BuzFjooDARB2CvLcuPCnkd2+IaVlav3e6VA77FvyitF6n1QgpD7lE82b+C3/XvdjuvUat5o2YZRDXKWyNx+6SJPLFlIxm1BiEoQGFKzNp926pqnuUkOB+eSk/DT6Zx9IJ9t2cjUQwecWRe1IOCr07H8wUeJ8M88Z96xI7y7bjUWD9KfKkGgR+Uq/NDDOxnGdJuNwbOncz45CaskYdRoMWo1zBo0jIoFUCplEe1YRYlAg/elcAoKCvcmdpudPv4jPErnBoYFMOeqe1N/bukb9AimVM+bNtWbVeaLVe/j42/M09iSJKFSqVg2ZQ0/vvyXix+M3kdHn2e7U7tldeq1r4lvoG+2Y/UJGOGxp0GlVrEw5W8MPvmz2P3jvenM/Xapy1wNPnqem/g4Zw6cZ+kvq1Fr1ZjT3OfiG+jD+3Ne5YP+X7qZOaq1avo9152nvh7pcvz65USO7ThFcMlAarWsViwzgZ89PIFNc7a7NP5rDVr6PN3V7XkLGyUIyaSoBSFKT8h9RmxqKmk2K5WCQ/DRat0yIVqV2utFdtMykfjptJjsNhdBB51azUN16nk1htluZ+mpE5xMuE6NEuH0rFIVvUZD5ZBQ5znJFjN/H9zv0sAtyTJmu50p+/fwXttMJ90BNWoRbDTywfq1xKSlOs9VCwIGjZaXm7fyak4AfjodS4aPYMP5cxyJv0ZkQAA9Klf1yqgvLxg0WgyaghlbQUGheCGJjmykZ7M3FfSWFn2asGHGVo9N22cOnOenV//KtV/JTW463vca0wXZIfPXB7NIiU/FP8QXm8XG0p9Ws/Tn1Yh2iWe/f4yeozt7HMecbnbz5LiJSq1Crcm+ojwtKR2VWoVvQNZ9GJAZNM3/fplLAAJgMVmZ8uY0LBmWzKb7LAwdJVFiy9ydqDwEEpJd4rKH8rMSpUNoM6BZtvMqyjgcDjbN3u4m/2u32Fn554YiF4QUF4RCSAwUJkoQUkw5lZDA+eQkqoSGEuWFW/eV9DSeXrqI49fj0ahUqAUVGkHl0giuUakI9/WlTbnyXs1BrVLxT//BPLZwHskWM4IgIDkcfNiuI7XCS+Z4fWxaKgNm/kuG3eY0tPtq+xbmD33QpRH9VGICOg8qUnaHg92xMS7HOkRVpMNjFdl04TyTd+8kNi2VRhGlebF5y1y7mqtVKjpVrESniorRU1ak22yk26yE+/p5/AJWUFDIPQYfPVUaVuTE7tMux1VqFc0fyB8jxyfGP8yhjUeIv5Tg9prdKrJu2maPQYhoFzm24xSyLFOjeZUc+0AeeLIrvZ7ogindwsPln8aS4RpUTH7xD2o0q0KFOu7fOwsnrshSdbBFn8ZZ3vtc9EXGPzqR80cuAZmqU2P/fp7wsiU8nm8z2zz22gCkxKd6Vp26BavJhs6ow+5BCljvo6NBpzrZXl8ckR0ykoeqA8gMRBQUvEEJQooZGTYbY5Ys4MCVODQqFXZJol35Ckzo8QC625q6byLLMo8smMO5pCQkWXYu5vVqNfVLRXDgShyCINC1YmX+174Tai8kGm9SOSSUTSNHc+jqFdJsNhpGlMbHy2zBe+vWkGg2OYMgk92OVRQZt2m9S9lUab8AF++Qm6gEIcsArG35KNqWj/L6ObJDlmUcspyr9+VeJ91m4801K1l99gwqAQINBj7p2IVOFZSATUEhP3h1ylO83PZ97DYRm9mGwUePT6APY8aPyJfxQ0oF8/ux7+kbMMJj1sVuE5Fl2aVM6ODGI/xv4FfO7IlKpeLdmS/TqEv2mW9BEDi4PtqjD4bdJrL893U88+1jbq9tnL3Npb/COZ5KyNIJPj05g1favk96cobzWPSW47zU+l3+OTPJpWH9JgZfA8Glgrgek+j2mlav8Sg97Hq9nma9GmJKzTQivKlQpdFpCCwRQLeRHbK9vjii1qip2bwqR7ef4NYYTaUSaNy9fqHNq1hzHzqmK0FIMeOjTevYF3fZZVG+6eJ5Juzcxmst23i85tC1q1xOS3NTjxIdDqqEhDJz0LBMabg87GSfTUpkwfGjWESRzhUrY7why+uQ5Wx3xh2yzOaL593mJMkya86ecTlWJiCAZpFl2RlzySUbolOrc2UO6A3HrsdzPSODWuHh6NUaPtq0noUnjmGXJBqUiuDjjl2oXiIsX+9ZHHlu2WJ2xF7C7sj897iWkcHzy5cwc9Aw6niRBVNQUMiemxLGK35fz4Ujl6jevApdRrTLc5+GJww+ehp2qcfe1QddDA8FlUCDjrURBIHEK0n8+PKfbFu42+Ni/MP+X/L32Uk5yvqa0yweMwoOyUF6UoaHK8Do5/lZdQZtlsaAa6dtcstIOCQHGckmdi3fT4vejbly/ho/PDeFvasOodaq6TC0JaM+Hs73z/zq0kiv99HTql8TNs/Z4THLAaA36qjSsCL1O9SmXvtaVG9amQUTl2NKM9O6fzOGv9U/X//NihIv//IkL7Z6F7vVjs1iR++jw+Br4OlvRhb21BSKCUoQUoyQHA4WnjjulhWwiCLTow9nGYRcz8jwXKsqy8Smpea5jGZ69CHGbVqPKElIssy0w4eoHRZOTFoqcelphPn48mKzFjx4oz8k1ZrZsBegN/wX9Hj4UlIJ7hmHiT168/baVaw6exoBCDYYGdexM7XzacEbn5HBYwvnci45CY1KhU2SCDEauW4yYb/h5bHvShxDZs9gzSOP5ehbci8Tm5rKztgYt99DmyTx697dTOjxQCHNTEHh3iIoLJBhY/u5HTelmVn9z0b2rz1M2aqlGfRaHwJDc2e6d5PnJz7Oc83ewma2YTXb0Bt16Iw6nps4GpvFxvPN3ybhclKWhn8OWWbjzG30e75Htvep16GWx0Z7g68+S8+Qvs9259S+sy7eF4JKoFSFkkRWLe3xmtjTV9x6OyAz43L1fDwZqSaea/YWaQlpOBwykiixbvoWzhy6wIfz3mDqR7OJPX2FSvWjeGzcMCIqliR6y3FS4lOxmm0IKgGVWiC0dCg+fga6jmxP3+d6IAgCgiDQc0xneo7x3ONS1Em8kkTC5SQiq0ZkGQDeSvmaZTMD5d/WcfbQBao2rkT3UR3xC8pebEAha+43nxAlCClGSLKM6MHcDsAsZp0urluylMdyJoNGQ7vy7uZX3pBoNvHRxnUumQmzaGf3LU7f8aYMPtm8gQSTifUXznHkWmZzXq3wknzTtQddKlZm9dnTLs+kVanoVcXdNdZPp2NCjwfIsNnIsNsI8/HNVzWRp5ct4kTCdZfMTFx6utt5dofE1EMHeaWF903u9xqxaano1Cqst/1KOWSZ88lJhTMpBYX7hPiYBJ5q8BqpienO0o2ZXy7koXcGcPFYLDarnU4PtqHNoObOBvHsKF2plDPjcubAOSrVr0D3UR0ICPFn7bTNpCWmZxmAQGb9f2qiu9Tv7ZQoHcJD7w5k+mfzsZmtyHJmAFKzZTWa9/bc59J2cAuObDvBkp9Xo9FlPot/sB8fLXgjy/tUb1rFo4u6WqOmcsMKrPlnI9YMq0sJmt0qEnMyDoOPju+2fOw25i+HvmbFb2vZu/oQpSqE0/fZ7pSvWTbHZy4umDMsfP7wBHavOIBWr0GySzz4zgAefHtgjtcGhQUy7M3+d2GWCvciShBSjNCp1dQKC+fwNVelDZUg0DKyXJbXhfn68mi9Bkw9dNAZrOjUakr4+DCkVt4a5jZdOI9GpXJrFr8dsyjy3c5tmRriNxb4h65eYdDs6Swa9hDHrl8jPiMDm+RAp1ZR2j+Ad9q0z3I8X50OX13u9euz43JaKkeuXc3W7PAmVkni2PX4fL1/caNaaAmPQa1WpaJZ5L3zxaygUBT54bkppCa4bpDIDpmp4+Y6fz6wLpo1Uzfx0cKxbo7dnggI8WfIa33cjp87fMGjPO6t6H10NOxc16u5P/TOQOq1q8myKWsxpZppP7QlbQZmHSwJgsAz3z3GoFd7c3TbCYJLBlGnbY1sn6nNwGb8/eEsrl6Id0rH6gxaqjSsQK2W1Vj15wYsHjIlskPmwtEYareu4faab4APA1/uzcCXvZN4L258M+Yn9qw8gN1qd6qvTf90PhEVS9Fh2P274VYoKJkQhaLMJx27MGzuTOySA7tDQq9WY9BoeKdt+2yve7NVW+qGl+KPg/tItVroVrEKoxs2xi+PC3qNSkWmfV/OyOBSC+yQZayiyK7YWFY//BibLp7nTGIiVUNL0Lpc+buuspRqtXoVUEFmM3/dkvd3z0OgwcDI+g35++B+p2+LCgEfrZbHvfCXUVBQyDu7VxzI8RxLhpWDG46yf+3hHJvGs6Ns9TIY/PRY0t0X7ZCZyWjUtR61WlbzesyaLatRrkYkPgFGNFrvliDhZUsQPtSzstXtaHVaftjxKX9/MIuNs7eh1qjpNrI9w98egCAIVKxXHoOP3i0QEVQC5WpEev0cWSHLMgfWR3Ni9xlKlg+jVb8m6Az5u3GWH5jSzGSkmDD46dk6f5eb9LPFZGXm+AVKEKJQoChBSDGjdnhJVj08kr8PHuD49XjqlSrFw3XrE+aTfQ2mIAj0qlqNXlW9/7LIjvZRFXHInkvDvMFktxOTmopapcqU1Y2qmC/zyok1Z0/z+ZZNXEhJppSfPy81b0mfqtU9Kl8JN/5z3PKzQaPhwdp5/1K/V3ijZRsqBgUzZf9ekixmWkaW49UWrZ3mkgoKCgWDt2WolgwLO5ftu6MgpN2Qlvz+9r/YzHanspVKpUKr11C7TQ26jexA28HNvZ7Tuhlb+Onlv0hLSketUfPAU10Y8/nDHhWrsiM1IY2Lx2IILx/mUXbXP9iPZyeM4tkJo9xe6/JIO6Z+NAebxeYsydLqNERWjaB26+q5msftWM1WxnYdx9mDF7BZ7OiMWia/+DvfbvmYyCoRdzR2fmHOsPDNmJ/YOn8XgkrA4KNHzqLMO+lqyl2enYLSE6JQ5CntH8CbrdsW6hz8dDom9uzNc8sWO0utbvZ23N7jIQiCW/mOj1ZLrfDwXN1zz+VYvt6+hZMJ1ykfGMTLzVvRJhcyvOvOneWFFUux3Ni9j01L5f31a7BLEp906MLra1ZgkyQcsoxBrSHQYKBrxUosPHkciyjSqmw53mvbgVCf7I2v7gcEQWBwrToMzmM5n4KCgvec2HOGqR/N5sLRGPxDfEmMS87xGo1OjX/wnQloGHz0/LDjU757+lf2rjqIIAi07NuY5yeNyVEN63Z2rzzAN6N/dKpPiTaRJT+tQrJLPPu9e7DgCYfDwU+v/MXSX1aj1WuxW+006lKPt6e/5LVzum+ADz/s/JSJz//G3lUHUWs1dBjakqe/HXnHfYYzxy/k1N6zThUxc5qEJd3KZw9+x6TdX9zR2PnFZw9+z97VB52ZD1tWZpAqgXrta97NqSnchwg5mfAUBI0bN5b37Nlz1++rkP+kWi2sPnsGiyjSvnwFjsRf5Yutm7mYkkxp/wBeat6S3/bt4XRSojMQ0anVVA4OYeGwh7323tgZc4nHFs1zBhAARo2Gr7v0oLuHRnZPdJ/6JycT3Y25Qo0+7Br9FEfir/HngX3EpqXSrnwFHqxTlwC9wauxFRQUFAqC/esO816fz7GZbchy5gaAN9/beqOOX6O/IaJC/pSPOhwOpwJUbojeepwfX/6Dk3vOenxda9AybuFY/IJ8qdKoYrb9HgsmLmfKm9Nc1K+0eg01WlSlfrvalKtRhpb9muRooFhQPFzxGa6ed+8Z1Oo1TLvwU64Dt/wmIS6JRyo961FqWaVS4bixgajWqDH46pm85wtKVyp1t6dZIAiCsFeW5caFPY/s8C1RVq7V6+UCvcfuv18tUu+DkglRuCMC9AYG1qjl/LlMQABdK1VxOadLxcpM3LWdBSeOAdCvWg2ea9oiV+Z/n27Z6BKAQGbT+ydbNtKtchWvvhgvpHhOLSdZzFglkdrhJfmqa/Yyk3lBlmVmHjnMj3t2kWA2USe8JG+1bkfdkvfGh7uCgkLBMemF3128K24GIEHhgWi0anRGHc16NWTVXxtwSJmBgkNy8Pofz+ZbAAJ41eB+O6f3n+PNbh97lMy9id1i538DvwLAN9CHj5e8RaV6UR7PnfvtErex7FaRQxuOcmjDUYx+Bn4Z+w8/bP+UkFKejWwLioMbj5CcZfmSZzn6u831mAQ0Os/mi+HlS1C+ZiRxZ69Rp00Nhr/Vn5LlFU+su4qslGMpKOQ7fjodb7Zux5ut2+V5jJMJ1z0ej0tPwyZJ6DU5/ypHBgRwJsndETdQb0CvLrg/hR927eDnvbucTdw7Y2MYPncmj9ZtwOJTJ0i2mGkYUYa327SjWqh3zZcKCgr3Pg6HgwtHYzy+lpaUznLLdOZ9v5Sp4+ZgSbei99HReUQ7xnzxsNflSQXJPx/NxmbOOgC5yU0FLnO6hTc6f8T0mJ/R6d2zGWlJ7rLpt49js9iZ+PxvvD/7tWzPlWWZMwfOkxyfSrUmle6odO2n1/5i/vfLPDrCCwKUrVaa4JJBeR4/vyhbvQySB68WtVZNk+71eWHSmEKYlcL9TO63NhQUCoGsGu99tTp0XmjhA7zWsjWG24IVo0bDC828b6zMLRbRzs97dzsDkJuYRZFf9u8hNi2VDLudzRfPM3DWv4rPhoKCghNBEPAJ8Gwa5x/ix8JJK/jj3RmkJ2UgiRKmVDMr/1jPxlnb7vJMPXP20IVcJwDsNpE9WSiA1WtXK8fPakmU2L54b7Yla/ExCYyp8wovt32Pj4d+w7AyT/Dvp3OzPD87Ns3ZztxvlngMQDRaNb5Bvrw17cU8jZ3f+PgbGfJGX/S3BKiqG83pnkwxFQoBuYD/K2IoQYhCseD5Zi0wegggxjRs5HUA0a1SFcZ37kZp/0wFpxI+PrzVuh2P1G3g9TzMdjvxGRle1WQDXE5LQ5XF9By3jWEVRX7cs8vrueQVuySx/vxZ5h07Qkyqon6ioFBUEQSBAS/2Qu/jKvGq99Ez+NXeTPt4rlt5ktVk5e8PZ93NaWZJ+VplvVVydyI7HKQmeDY/HPPFwxj9DWi02W88SaLEkW0nsnz9vd6fc+nEZSwZVjJSTNgsdv79dD67lu/P3VxlmQnPTsny9YhKpZh2/keiahUd/6QR7w/m5Z+fpELdcgSXDKTdkJZM3vMF4eWU0iuFu49SjqVQoCw/fZLvd27jSno6NUuEM7ZVG+qVyr1UYe+q1dgTG8Pik8eRAbWgYlSDRjzTpHmuxnmganUeqFodhyznyo/EbLfz7vo1LD11AgEIMhgY16EznStWzva6MB/fLF3ub0eSZQ5eveL1nPLCyYTrPDRvFhZRQkZGcjgYXrse77VtX2DZIAUFhbzz8PuDMkuvpqxFo9UgihJ9nunKgJd68esbUz1ek3DZvew0OyRJ4sC6aOJjEqnetHK+LZpHvDeIvSsPItpFt9cEIbMBWrytPMghOajXvpbb+QCRVUvz66GvmfXVIo5uP0lKfCoJsYlIt2UhZIfMm90+ZtSnwxnwQi+X1y6diCXm1GW3zIXVZGX+90tp2sP7TamU66mkJ2dk+XrlBhXw8fecySosBEGg00Nt6PRQm8KeisJtCCg9IQrFEIcsk2AyEaDXe9Ubcbf49/BBPtm8wVmKtCP2EsPnzWL6wKFUDy3B0lMn2BcXR4XgYAZUr0mw0fOH9eFrV3l0/hxEhwOVSoXocPBo/Qa80iLvJkq5NUR8eeUyNl4451T4upqRwQsrljJ9wJBsgyp/vZ6BNWox+2g09hyCEQGoFFxwzZSyLDN60XwSzGaX47OOHKZ5ZKSboICCgkLho1areW7C4zw2bhjXLiVQsnyYc2FbKiqMKx7UmMp44UlhNVtZ/fcm1v27mVP7zt5Q3gKHQ6ZZr4a88+9LufbvuJ1qTSrT7/nuzP12qcfscVB4IGlJGc5sjsFXT/dRHYmomHVDfXi5MJ6b8DgASddSeLHlO1y/nIj9tmZrq8nKb29Oo+sj7fEL+q+cNy0pI8vnSr6emqvnM/oZyPKrRIC+z3bP1XgKCvcbRWfFqpAnFhw/ysebN5BhsyEgMLhWbd5t0x6tl30SBYXkcPDlts1uvRAWUeTzLRu5nJZGgtmEyW7HoNEwYed2ZgwaSo0SYW7jjFo4j2SrxeX4nwf20bJsOVqVLV/gz3ItI52NF865OapbRZEf9+7ip159s70+KijIrfQKMj1Ubg1MDBoNTzdu5vW84tLSSLKYqRQc4lXweTT+GokWs9txk2hn6uGDShCicN8giRIHNx4lI8VE3bY1CCwRkC/jxp6O43psIhXqlCMgxDvjztP7zzH14zmcO3yRCnXK8fC7g6jcoILbeb6BvlQIdO2NGzN+BONHTnRRz9IbdTwxfkS297SarbzQ8h1iT13xqFy1a9k+Fv24kv7P9/TqGbJjyOt9WTR5pZsik86o44N5r3Fm/3nW/rsZg4+eB57sSos+3quHBocH8vux73i++duc3n/O7XWNTsORrcdp1quR81jl+lHIDvfPY51BS+v+TXPxZKA36mk3uCWbZm/HbnP9rms/tFWunOQVFIAioaJ2N1GCkGLM5gvneXvdahfp2tlHohEdDj7p2KUQZwaJZjMW0V2FA2D/lTgXc0OLKGJB5PXVy1ky/BGXc/fGXcYquqfyzaLIjOhDdyUIiUtLQ6tWuwUhMnA+OTnbax2yzKTdO5E8fLD4anWYRRHRIVHGP4BxHTpTOzxnSc0ks5nnli9mX9xlNCo1IPNOm/YMq1032+vMophlBshsd5dsVFC4Fzl76AJju47LNGkTMk3zHv1oGENe65PnMdOS0vmg33hO7jmDRqfBbrUz4KVejPrkwWzLHA9vPsZbPT654QEiE3fmKntWHuTzFe9Qu3WNHO/bdlALtHotf7w7nbizVylTJYLHP32QJt2zLyla+ccGYk/FuQQvt2I12Vjy46p8CUKCSwbx3MTHmfjcb8iyjEOSUWvVDHq1N9WbVKF6kyr0eiLv31carYbyNSM5c+Cc2/pNlmV8A13NZXUGHc9OGMUPz03BZrYjyzI6o47QiGD6PedZov30/nMs+nElSVeSaf5AIzqPaIvemNnc/eJPT5CRYmLv6kzjQ9Fqp9dTXXn2u8fy/EyFxeHNx/j307lcPn2FGi2q8fC7A4msWrqwp6VwD6MEIcWYCbu2u3lnWCSReceO8FbrdvjpdFlcWfAE6PVZpqlvd0+/yamEBFIsFgIN/xkEmu32LBsbM2x3Z+FcMTgEu4c5awSBxhHZf0Cb7HYysljgWyWRw08/j0UU8dVqve7JeHrZIvbHXcbucDgDo3Gb1hMVFEzzyKxruetkEeAYNBr6VK3u1b0VFIozkiTxZvePSb7mKsjw94ezqNmiKrVb5e3v4PMREzi28xSiTcR6w4F6wQ/LqVC7HB0fzLr2ftKLv7tkImRZxmqyMunF3/lx75de3btF78a06O2ePbCYrMz4bB6r/t6ILMt0eqgND70zEKOfkS3zd2YZgNzEasn+9dzQY1QnGnWuy6Y5OxDtEi37NqFc9TL5Nn6fZ7qxZf4ul/dSEDJ9R2p6yEZ0G9mB8jUjmT9hOQmXE2nWqyE9x3TGN8DH7dzV/2zk+6d+wW6143DIHFgXzcJJK/h+2ycYfQ0YfQ2MW/Qm1y5d59rF65SrUcbrLFhRYvPcHXzx6A/O34sr5+PZtmAXE7Z/WqQa6+917reeEEUdqxgTk+q5flUtqEg0m+7ybFzRazSMqFPfTdEqO2RwMzBsXLoMkodeCqNGQ++7tHD21+t5vEFjl2dRCQIGrZanGmefvvfRavHXedbrrxAUjEalwk+n8zoAiUlN4dDVK279JWZR5Nd9u7O9Vq/R8GXn7hg0GjQ33mcfrZZqoSUYUquOV/f3hFUUOZ2YQJLZvdSrKGKXJKYdOkDfGVPpO2Mq/xzc7zHIVLj3iN5yHEuGe/mRzWxlyU+r8jRmakIa+9ceRrytHMeSYWX214uzvfbsoQsej5856Pm4tzgcDl7v9D9mf72Y+EsJXI9JZN53y3i57ftIkkRAqF/WvQxkOny3HdQiy9eP7TzFWz0+ZnjZJxnbbRxHt2etRHWT8HJhDHqlN8PG9ssyADFnWIjeepyYk5dzHO9WaraoxujPHkRn0OITYMTobyC0TAifr3wvS5PF6k2r8NbUF/hq3YcMfrWPxwDEYrIy4ZlfsZptOG6UcFlMVi6fvsLyKWtdn69sCWq3ql4sAxCHw8HE539zCUwdkgNLhoXf3v63EGemcK+jZEKKMfVKlmL12dNu0s8qlUApv8L/IHyjVRtUKoG/Dx7AKoo4shGpVgFNy0S6ZW98dTrGdejMu+vXYJckJFnGR6ulbngpHqh69+ptX23RivJBQfyydzeJZhPNypTltZatiQwIzPY6lSDwSvOWfLplo0t/jEGj4Y1WbXM9j+smkzOAuJ0r6dkbeQF0q1yFZSUeYeaRw1zLyKBDVAW6VaqS5x6iqYcO8MXWzYCM3eGgY1RFvuraAx+tu9FYUUCWZZ5YspBdsZec/x6nExNYffYMf/UbqCiE3eOY0yweF9+yTLYqR9mRkWJCrVFjt7qXjWYlNXsTvyBf0hLd/279gz37InnLgXXRnD9yyaUPw261c/n0FXYt20+fZ7qzY8lej9kQg6+B0NLBPPj2ACRRYtonc1k0eSXmNDO1W9egw/BWTHzuN2fG53psIke2HOejhWNp2Dn7ktDsWDhpOb+OnYZao0KyS5SrGcm4RW8SGuGdWEe/53vSeUQ7jmw97syA5MXl/VZO7jmDSu0+htVsY+Ps7Qx4sZeHq4ofKdfTPBpByjIc2Xq8EGZ0n1JEvTwKEiUIKca83KIVWy5dwGy3O39vjRoNLzdv5bWBX0GiVqkY26otLzdvReNfJ5Nuyzq9b9Bo+aqLZyWRATVqUSe8FLOOHibZbKZTxcp0rlgpy8V4QSAIAoNr1mZwzdq5vvahuvUxaLR8u3MrV9PTiQoK5q3W7WhbPirXY5X298fmoUdGq1J5PV5UUDBjW7XFIcuZkoB5WHg7ZJnf9u/h621bsN2SlVl//iyvr17OpJ55r68vSPbExbL7coxLQGgWRfZduczO2Jhsy9kUij912lRHtLlnvQy+mQ3GeSG8fAn0Pnq3DItKraJBp+w/Lwa81IsZn893bSz30THgpQfyNJebnNxzBruHcipzuoWTe87w6P+GMnLcMP54ZzoanQaH5ECtUVO/Q21a9GlMh2Gt0Bl0fD5iAlvm7XQGHPvWHmLfmkNu41rNNia/9AdTor/N03wPrI/m17HTXMqpzh48z3t9Pmfy7i+8HscvyNelCf1O8QkwejQhhDsPFIsSvgHGLL8Hgktmv9GmoHAnKEFIMaZaaAn+7T+Yz7Zs4nhCPKX8/HmuSXN63cUMgTfo1GqCDIZsgxBJdnAxJSXLDE6V0FDeadO+gGaYiVUUSbfZCDYacy3hmxMDa9ZiYE3P2vfe8ueBfYzfutnty0KrUhGgN/B4A+9UZY5dj+f99WvYF3cZvVrDgBo1eadNe4xeZi/OJiXyyPw5XMlIdzdclCTWnjtLssVMkKFo6eMD7IqNdeujgszeo12xMVQKDmHa4YMcvx5PnZIlGV67LiFG9zINheKJb6AvT379CL+8/jc2ix3ZIWPw1VOpXhTth+UtCFGr1bz44xN88cgE55iCSsAhOVj99yaO7TjFSz89SZ027o3mw9/qT0p8Kst+XZPpAWIX6Tm6M8Pf6n9HzxlePgydQYc53VVV0OCrp2T5TAXCQS/3ptvIDhzddgK/YD9qNK/ikjm4HpvApjk7sFtv6WnLZpf2wrEYZFnO06bG3O+WuKl0SaKDi8diuHQilrLV8q9/JDdUqhdFaOlgLp++6iIxbPDV0zeLJvbiiM6go/OIdqyZuilTsOEGeh89w8be2e+iQu4QvLMVu2dQgpBiiizL/LJvNxN37UAGJIdMk9Jl6Fa5aMqsPlavIV9t3+Im2XsTqyTx0LxZVC8Rxjdde1IlNPSuzc0qiozbtJ65x44gA4F6PR+060jPKkUnmNsVG8OX2zZjkVzfP61KxcN16vNU46aU8Ml5sRyXlsaQ2TPIsGd+0VgkkbnHjnAhJZl/+g/O8XqHLPPIgjnEpadluR7RqFQkmvMehFhFkeWnT7H3cizlgoIYUL0moV48mzeU8PHBoNZgEl3FAgwaDQ5ZpvM/v2OTJKySxMYL55iyby/zhz5IVFDB+bco3F36PN2Nak0qs/SX1aQlpNF6QHPaDWmBRpv3r8M2A5pRsvxHzP56MbuX78ecbkFGxiE5uHgslrd6fMLkPV+49UKo1Wqe/X4UIz8ayrWL1wkvVwLfwDvfYW/dvyk/vvwHFpPVKUcrCKDVa2k35L9eD/9gvywzBxePxaIzaF2DkGwICPHLczljYlyyx+NqjYaU62mULaSPYkEQ+GTp27zR+SPSktIRBAHRJjLk9b406Va/cCZVQDw7YRRWk5XNc3eg1mZmx4a/2Y/OI3JfNqyg4C1KEFJMmX/8KBN2bndZ1M85dgS9WsM7bdsX3sSy4NH6DTmbnMT06EMePTMg0zH8aPw1hs6ZwabHxtw1da93169h6ckTTqWpeJOJ11avIMTo47E8J9VqYeHxY5xLTqJuyVL0qFy1wE0i/ziw12MAp1WrGVSzFmG+3i1cph4+gN1xm9+JJLE37jKnExOoHJJ98HfwShwpFku2ZasqQcixVyYrUq0W+s/8l6sZ6U4PmR92bmfawCFZqnvlhp6Vq/LJ5g1ux9WCik0Xz5N2S7bOKknYHQ7GbVrPb30G3PG9FYoO1RpXolrjSvk6ZtVGlRj18XC2LdjlVsJjt9qZ881iXvnlKY/X+gb6UqFO/pX36Aw6vtvyMZ89PIEzB84jAOVrleXNqS9g9PNuc6B05VJeByB6Hz2DXs17CWbzBxpxLvqim+GgJEpUqh+V53HzgzKVI/jn7CSObjtByvU0arasRnB4/pQonTl4noMbjhBYIoCW/Zpg9M1UhkxNSOPXN6eyZe5OBJVAh+GtGfXJcI/N8/mFTq/lzX9e4JnvHyPhchIRFUti8PEsqqJQgCg9IblHEITuwPeAGpgiy/Ln+TGuQtZM2r3ToxHgv9EHeaNVm0I3K7wdlSAwrkNnhtWuw8BZ07OU6ZXJXPwtPXmcoTn4XuQHqVYLi08ed5uPRRSZtHuHWxByOjGBwbMz528WRXy0Wr7buY35Qx7K0vE9P7jd5fwmakEgyWLx+JonjsZf8/jea1UqziYl5hiEpNls2ZaqGTUa3mzVNs89ST/s2kFsWqpzjjdLp15ZuYzVI+5cd99fr2dq/8E8s3SR0wAzQK9nYvcHGDxnhtv5Dllm66WLd3xfhfuDuHPX0Oq1bsZ8mRmRmLs6lzKVI5i44zNSrqciyzJBYblbOJeKCqdRl3rsXX3Q7XluRaUS6Pd8D4a+kb1pa3b0e74HK35fR9K1FGcgovfRM/rzh5wL88JEpVJ55dviLQ6Hgy8encjW+TtxSDIarZofnpvCF6veo2K98jzf4m2uXYhHtGd+Di6fsoboLcf4ce/4O262z4mAEP9iqfClUDy54yBEEAQ1MAnoAsQAuwVBWCTL8tE7HVsha+JNnpVcRIcDs2gvckHITWqFlWRK7/68uGIJ6Tabm9QsgFm0E5PmWX44v7mWkYFWpfK4ML+Qkux27PXVK0i1Wp2bFSa7nctpaXy1fYvTINIqiqw8c4oT169TKSSEnlWqYtDcmVpU14qVib521a2fwe5wULdkKa/HqRNeku0xl9ye1+5w5BiAANQvFYHNQ6OmAJQLDOKDdh1pH+Xu9uwtS0+d8PhvcSk1hfiMDK8zPtlRt2QpNj82hpOJCciyTLXQEkBmVsnTvfVqJWF8P3DhWAzTxs3hxJ4zRFYtzUPvDKBmi9zVAZWvGelxwa7RqanerHBKZe/EDf6dGS/x82t/s/LPDS69AjfRGXW8P+uVO24G9w/246f9X7Lgh+XsWLKXkFJBDHipFw065l06vCizYeY2ti3Y5RQkuJlx+qDfeJ76ZiRJV5KdAUjm6yJxZ66yb81hGnetVyhzVrg73G8+Ifnx7doUOC3L8lkAQRBmAH2BIhOEJFvMzD9+lAvJyTSIKE33SlUKvHymIJBlmV2xMeyMjSHMx9djo3eI0ZilL0VRoXW58uwa/TTTow/x6ZaNbgtr3xsSvHeDyIAAj27mkFmicyvpNhtH4q+5ZUtFh4PZR6PpWaUqVUNLMGDmvyRbzGTY7fhotXyxdTPzhj5IGf/sFwOJZhNLTp4gxWqhZdlyNCxV2lljPbx2XaZHHyIuLc3ZF2LUaHijVZtcla2NqNuAvw4ewC5JzufQqzW0jCxHxeCQHK8P0Ot5q3Vbvti6CYsoIt+YR4WgYOYMGX7HwZZW5Tl4lmU5X9XQBEFwBh836VutOguPH8d2S7maXq1m8B0KCigUfU4fOMfLbd7HZrbicMhcPn2FgxuieW9m7hbYoRHBdHqoDetnbHU2WguCgN6oZ+AdKl7lhrSkdA5vOoZPgJE6bWugzuOmlN6o54VJY3h+4mjORV/i7Z6fYEo1OXsjHnx7QL6pUfkH+zHi/cGMeD/n3rTizvIpaz361ZjSzexeud9NUAAyA5WzB88rQYjCPUV+rMTLAJdu+TkGaJYP4+YLx67HM2zOTOyShEUSmXPsCBN2bmfekAddnLnvBnlVDoHMhe6YxfPZHRuLWbR7LHcxaDS817ZDsfA6UKtUPFSnHvOPH+Vo/DVnP4ZOraZsQCAdKlS8K/MwaLTUCgtnb5y7OdbltFSum0zOhu/sypBEh4MnFi+gQnAwV9PTEG8ENia7Haso8t66NfzeN+u+gu2XLjJ68QJkWcYmify0ZzftykfxQ48HUKtU+Op0LBr2MNOjD7H67GlCjT6MrN+QpmUic/W8Yb6+zBsynP9tWs/OmEsYNFqG1qrNqy1aez3GI/UaUCe8JP8cPkCiyUz3ylXoX71mvgT2Q2vVYeKuHS4N+GpBoE7JUgVa7gbwXtuOnEtK4kj8NdSCClF20DiiDK+19P69USie/PL6P1gyXBd+VpONH577jaY9G+bqM/Wln58gsmoEC35YTkaKiXodavPE+IcJi7w7YhvzJizltzenodFpQM6U/P185XtUrFs+z2MKgkDFOuWYdn4y0VuOk5aYTu3W1XNd4lUQSKLExtnb2TR7Gz6BPvQa04VaHlzSAUxpZpb8tIqtC3YRWCKAfi/0pGGnu59tEe2eBVoEQSC0dAgGX3fJZ61BS+nKd2dzTqGQkMk0ZylEcmqvEARhJPAlEHvj0ERZlqfceO1R4N0bxz+WZfmvHO8n3+EDC4IwCOguy/LoGz+PAJrJsvzcbec9ATwBUK5cuUYXLtyZI6y39Jj2FycSrrsc06rUPFynHu+161Dg9xcdDibs3M7fB/eTZrNSIyycD9t1pHHp3EkOTj98kI83b3DrA9Gp1AQbjZQPDOKFZi1oWbZcPs6+4DHb7fy4Zyfzjh1FkmX6VqvBc02b37WmdID+M6dx8OoVt+P+Oj0/P9DXpS9kxPzZ7Ii5lGX2JCvUgsCJ5172GMiIDgdNfv2RFKvrIsio0fJZpy70qZZ/tchFHZsk8cTiBey+HIPjRvYjUG9g5qBhlAnIe1lJbjgaf42zSYlUCS3hli1RuDfpEzDC4+6zWqNm7vXfC7QhOD85tvMUr3f60M2EMLhkINNjfs5zRqSoIokSY7uO48Tu01gyrAiCgM6oY8QHgxn6umuPijndzDONx3LtUoKztEzvo+eRD4cw5LW762u0/Le1TH7pD7dAwz/Ej7/PTOSxqi+QmpDmdGlXqVWUKBPCX6d+uCMVt/sZQRD2yrLsnY59IeEXXFau1+nFAr3HtrmvZ/k+3GivOMkt7RXA8FvbK24EIY09rPFDgD1AYzLDqb1AI1mWk7KbT37UN8QCt3bvRvJfhOREluVfZFluLMty47CwsHy4bc4kmk2cTXJ/frtDYsmpE3dlDu+vX8OU/XtItWX2ERyNv8ajC+Zw/Hp8rsaZc+yIR3UkjVrFlN79mDFoaKEEIMkWM8tOnWDN2dNYRO+UVG7FqNXySovWbBn1BNsff5I3W7e9qwEIQJWQUNQeggObJBF528L3yy7difD3z7WPSHY7qfuvXEaSPffGzD4anav7FHd0ajV/9hvI9IFDebdtB77v/gAbRo6+awEIQM2wcB6oWl0JQO4jAsM8/35ptOpipRC09OdV2Mzun8NWk43Dm45x4VgMHw3+iqFlnuC5Zm+xffGeQphl/rFl/i5O7D7jXMzLsozVZOWv92dydPsJJPG/0splU9YSf0sAAtw4dwbpyZ57LAuKLo+0o2aLahj8MqsxdAYteh897854Gb9AX77f9gm129RArVGh1qhp2LkO32/9WAlA7gMEuWD/ywFne4UsyzbgZnuFN3QDVsuynHgj8FgNeHagvoX8+I3eDVQRBKECmcHHMODBfBj3jsms6ff8rmvvgtt2kjmzF8UquUui/rhnF9937+X1WNktYu9W+ZUsy2y5dIElJ0+gUanw1+n56+A+NCo1AoAAvzzQr9i5To9u2Jilp064BHl6tZrmkWXdzBPtkoOhNesw7fBBrmSku42lFoTMeulbGu41KhWdK1TKMnARyObfNpvXbudmz9DZ5CSqhITSKKJ0sSjN80TdkqVy1XCvoHAnDH2jLz+9+reLYZ7eqKPnmM6oNcUne5CWlIHH6gYBzh+9xPt9v3B6hyTGJfHJ8O948qsR9H6q292fbD6wZd5OtzI6yOyfeK3j/zD46nnxxydoN7gF2xftcTq/34osy0RvPUHzXg3vxpQB0Gg1fLbiHfatOcz+tYcICg+k00NtCCmV6UdUulIpvl7/P2wWGwgCOv2d9dopFCMKvhqrhCAIt+4+/CLL8i83/t/b9oqBgiC0JTNr8rIsy5eyuDbHkp87DkJkWRYFQXgOWElmDdnvsiwfudNx84NAg4H6pSLYF3fZpXxGr1YzpFbB14FeSk1Bq1a7BSEOWebY9Wu5Gmtwzdoci7/mlg3x1+moXqLgM0uyLDN2zUqWnTqJSbQj8N/fyq3PN2bxfHaOfhofL923iwJVQ0vwa+/+vLNuNbFpqQhAtRJhHLp6haoTvyXCz583W7XFKom8t34tDtnhEmTcRC0IVAwOQQbi0lKxShJ6tZpQHx/+16FTlvevXyrCY1Dso9EyuFZtt+PR167y/c5tHIuPp3JIKC82a0HF4BCGz53JxdQUHLKMShCoEhLKP/0H3/XMkoJCcaPXE12Ij0lg7jdLUGvU2G0i7Ye1Ysz4hwt7armi9YBm7FtzyK3MR7SJ7F110MW8EDIzAb+99S89Hu9ULHfZ/UN8UakEZ9nSrditduxWO18+NpFSUWEElwryOIbdKvLvJ3No1rPBXd20UalUNO5aL9tGc51B+exWyHeu32FZ2mJguizLVkEQngT+AjrmdbB8+dSRZXkZsCw/xspvvunWkyGzZ5BqtSI6JFSCinolS/FkoyYFfu9ygYHYPUh+qgSBmiXCczXWwBq1WH3mNDtiL2EVRfRqDSpB4MdefXNdGpQX9l25zNJTJzHfKLnKLlhff+4svaoWHbdxb2hZthzrHhlFms3KrOjDfLtzmzPgi0tPY+yalYhZBB/GGw3ZFYKCmdKnP2E+vmy+eIFTidepGBRCu6gK2So7aVQqfuzVl1GL5t1oTJfQqdV0qFCRXre5tu++HMPIBXOdylSX09PYdTmG+iUjOJOU6CJ5fCw+ns+3bOTjG9LBCgoKnhEEgcfGDWfY2H5cOXeNEpGh+Af7Ffa0ck37oS1Z8tMqzh66cEuPhJZRnwxn1peLXQKQm0iiRHxMAhEVcjYDTYhLYuGk5ZzYfYZK9aLo91x3wsvdnfJqT/R4vBOr/tzgMcNxE5vZzuxvFjPghZ5snb/LowHjucMXid5ynDpt7p/+O4Wih0ChS/Tm2F4hy3LCLT9OAcbfcm37267dkNMNi9/WRy4p4x/AxpGj2XjhHLGpqdQJL0n9UhF3ZccjyGBkYI1azDt+1EWGVq9W80yT3AmIaVQqfu3dj31XLrMzJoZQHx96Vq6Kv/7u1CuvO3fWq54PhyxjyuE8WZY5ePUKh65eoZSfH+2jKubZ3C4vWEWRVJuVUKOPSwAnCAL+Oj2T9+5yN4KURI+FUQLQplwUr7dsTZmAAC6kpKBXa2gfVSFbvwxZlplz7Ag/7dlFgtlEo4jS/NV3ICcTE0gym2lVthz1SkW4XffxJndxAososiP2ktu5NofEwhPHlCBEQcFLjH5GKtTJu4pUYaPVaflq/YdsmLmNzXN34B/sR68nu1CzeVU2zNhGwuVEt2skyeGVl8jF47G80OJtbJbMDMOhjUdY8vMqvtn4EZXr590b6E6o0rAiT379CD+98heCSuVSTncTWZa5ej6emi2q0bBLHXYu2ed2jiXDykeDvuLFn56gdf8iI+6poHC3ybG9QhCECFmW42782Ac4duP/VwKfCoIQfOPnrsBbOd3wng9CIHMB36lCpUK59//adyLc15c/D+wn1Wal1g11rKp5aHoVBIFGEWVoFJE7Za38wKjRolGpPJoL3opDlmldNusvcZsk8cSSBeyO/U/9yEerY9agYZQPCsrnWbtilyQ+27KRGUcOI8syvlodb7dpx4Aa//lAWESRNKv7Fxl4zv4IgkCEvz9rzp1hws4dqAQBu0OiS8XKfNmlW5a+Gd/v3M6v+3Y7A4oN58+xMzaGRcMeztavI7eCBjn9eykoKNxbaHVauoxoR5cR7VyOP/TuQMYN/dZloa7RaegwtBU+/jnLX09+8XdMqSangqhokxBtEhOe+ZUJ2z7N8rrzRy6xbeFuNFo1bQY1zzHjEh+TwOY5OxDtIs17N6Zc9ey/73o/1Y0Ow1qzc+levho12cXkD0Cr1zpleJv1bMSBddFu6mEAyfGpfD5iAi//8hSdHmyT7T0LG5vVzqzxC1j+2zrsNpE2A5rx6P+GEhCqOJ0Xa2S5UCV6s2qvEAThI2CPLMuLgBcEQegDiEAiMPLGtYmCIIwjM5AB+EiWZfddj9u4Y4nevNC4cWN5z57ircpxv3ExJZnuU/9y8W+4HaNGwzNNmvFsk+ZZnvPz3t18v3ObS2YoszwtjEXDR+TrnG/ngw1rmX002uXeRo2GiT170yEq05dElmWaTvmJBLPJ7fpb+2Buvf7ZJs2YtHunW2N7ryrV+KprD7dxMmw2mkz50c2kUS0I9KlWg689XHOTZlN+It7kruSiFgRkMoPAm6gEgc4VKvHTA96KW+QP2y9dZMKu7VxISaZ2eElebtaSGmG5Kz9UUFDIf5b8vIqJL/yOdGOhrtaoKFEmlG82fUR42ew3xnoah2O3un/+C4LActt0j/K/f7w3nbnfLEG0SwgqAZVK4JnvH6PXGM/Z2ZV/rWfC078C4JAcqDRqBr/Wm5H/G+bV8/314UzmfL3Y2ROj1qjxD/Hj18NfExQWSHpyBg9FPY0p1ZzlGCUiQ5h+8Wev7ldYvNn9Y6I3H3OWoWl0GsLKhPBr9DfojcVHze1uUhwkev2DIuX67QtWonfLwjeK1PtQ8BJRCvcE5QKDGJdNc7UATO0/ONsABGDWkcNui2+HLHMyMYH4jPyRSbyYksxba1fRdeofPLF4AfvjLmO225l1JNrt3mZR5IedO7CKIhk2G4Ig8GqLVs4+j5sYNBqeadwUg0aDUaNBr1ajV6tvKGuddCuRskoSS0+dIMODq/3F1BQ0gvufniTLHLgS53b8Vp5o2NhtbkaNhhF16xOg1ztf89FoCTEaef8ueOHcyopTJ3l88Xx2xsZwJT2dtWfPMGj2dA558GFRUFC4u1jNNtSa/z57JNFBfEwCnz74XY7X6rOQKtbqNag89Lyd3n+Oud8swWq2IYkSok3EZrEz+cU/SIhzl85PupbChKd/xWaxY7PYEe0SNrONOV8v5vT+c1493yMfDOG1356hWpNKlKoQTs8xnfhp/5dOU0W/IF/Gr/mAkuWz7mNJiE3Cbsu93Pzd4uTeM0RvOe7SByPaRJLiU9k4a3shzkwhPyhkid67zn1RjqWQPwysWZulp06w8cJ5l4yAWhDoWqkKDSJK5ziG3eHeqA+ZQUxWr+WGs0mJ9Js5DbPdjiTLnElMZOulC7zXpgOqLNqAjsZfpc5PPyDLMtVLhPFF52580rEL3+7YRlx6GlFBQYxt1ZZOFSoxsn4jVp45hVWS6BBVgaigYKZHH/L8TIJAitWC723qVKV8/bBl8axROZSkjWrQiCSLhT8O7EUlCEiyzPDadXmrdTteat6KeceOcCLhOrXDwulbveZdVcaSZZn/bVrvEujJZAZ6X2zdxLQBQ+7aXBQUFFxJS0pnwQ/L3XxEHJKDk3vOkByfQlBYILIss/rvjUz7eC6JV5KoVC+KJ74cQc8xnW9c/9/iV2fQ0uXR9h57LDfN2e6xCVxQCexYvIdaraqzbeFu1Bo1bQc35+D6I6jU7sGMzWLnu6d/pnyNsjTt2ZDW/ZtmKZssCALthrSk3ZCWWb4P1RpX4p+zk3go6mniLyW4ve4f6udUCrNZbKQnZxAYFlBkjB5P7T2Lp+JgS7qF6K3H6fpo+7s+JwWFvKIEIQq54rNO3eg/axppVisZdju+Wi0BegMfZLHjfi45iVlHDpNgMtE+qiIPVKnG7wf2YbtNNay0fwARfndezzp+62YybDbnR/TNRfB3O7dmqVBldzic5x+Jv8awOTNZ++go+lWv6XZuqI8PD9ZxlVRsUjqSlWdOuZRCQWY2oqSvu8JOsNFIj8pVWXnmlMuC3aDR8HTj7JsiBUHgtZatGd2gEYtOHkclCLSPqoBapSJAr2dk/bundX87aTabxzI2gENXr97l2Sgo3BvcLJnOq5iKKc3MlyMnsXPZvqx3+GXYvmgPLfo0ZvXfG/nrg1nO3pEj207wRpeP+GLV+8ScuMyelQfQ6LVINpHabWrw1NePeh5TEDL/u23BLCCwffEeJr/8J5JNRFAJ/P3hTNoM9JxFlx0yJ3af4cSuM2yau4P53y/ly3UfoNXlXQZeEARGf/YQ3zzxs0uPjMFXz0PvDEQSJX55/R+W/boGWZYx+hkY8+UIuj16dzPLnggvH+YxWNMZdURWdRczUShmFMFsRUGiBCFFjNOJCSSazdQKC3fbQS8KlPTzY/0jj7P89CnOJCVQOSSU7pWqoNe4/yotP3WCV1evQHRkStsuO32SqiGhlA8MIjYtFZPdjkGjQSOo+LZbz3xRLNt9Ocbj33Cy1coLzZozaddOt9Kp28+3OyRmRh/iuaYtvLrnqy1asfnieUx2uzMQMWo0vN+uA+osAp/PO3XFR6tl3rEjyECIwcgH7TrSuHTOogPR164yYv5sJIeMA5lPNm9gRN0GvNW6baGaE/potWhVKo8yxmE+PoUwIwWF4kt8TAITnvmV3Sv2AwLNezfihUmjnYZ23vLJ8G/Zv/awx36Om9htIj++8ic/PDcF5Myfb8VqsvHPR7P5fMW7XD5zhQtHY4isGkHZall/XrUf0pJ53y5xk88VRYn9aw9js9wIiCTALrFpzg6yXIHdOGxJt3D6wHlW/bmBXk/cmepfxwfbYDXb+P2d6aQlpuET4MOD7wyg/ws9mfjCb6z8Y71z7jaLnR+enUJQWCDNehbeRg9Aw851CCwRgNVkwyHdYoqrUStZEIVih9KYXkS4mp7O44vmcS45yalC9XrLNjxWiDvbd4JVFGn862Qy7K47b0aNhjdbtSXUx5e9l2MpExBA/+o1CTbmrM7iDV3++YMzSe6CDDq1mgNPPsu6c+f4Ydd2rmakE+7rx8WUZLc+EYA+VavzXS4c7c8nJzFx1w72xl2mbEAATzduRouy5XK8ziqKZNhtBBuMXgUQksNBy99/Jt7kmnEwarRM6tk7W1ngu8EnmzYwLfqgW/P/R+07M7BmrWyuVFBQuInNYuPRKs+TeCXZudBUa9SElQ3lj+Pfe20seD02gUeqPI/dcuc9DkHhgcy+MiVX10z7eA7/fprpf3Tz861B5zrsXrbfzWBQ76OnzcBmbJq9HVmWkUSHyyL7Vuq1r8VX6z7M03PcjizLWExWDD56BEHAYrIyMGyUS9nZTao3rcwPOz7Ll/veCddjE/jikR+I3noCgMiqEYz963kqNyjcz/+iTHFpTG/YpmAb0zctKVqN6UompIgwevF8TiRcd3F2/2rbZqqGhtIqG8nbosrCE8ewiu59D2ZRZNnpk0wfOJSeVarm+32faNSEDzesvU2pSsMDVath0GjpWaWq877HrsczcNa/bmMYNRrqe/DoyI6ooGCPSlg5oddoPGaRHLKMLMtumZQDV+Mw2d2DJrNoZ3r0oUIPQsa2znSWn3002jn355o0Z0AN99I2BQUFz2yZt5OMFJPLIlwSJVKup7Jz6T5a9Wvq1TgJcclodZp8CUJKV87ZzPB2Hnp3EO2GtmL7oj2ZEr0Dm7Hkp9XsXn4A96yHTK2W1Xls3DA2zdnB5bNXWfH7Oo9zN/oZsrzn3tUHmfvdUlKupdDsgUb0f6FntsaTgiBg9P1vvNTrqVluCF29kDuJ9IKiRJlQvlz7IRkpGYh2ySufFwWFoogShBQBziYlciYp0SUAgcwF+x/79xW7IGT7pYt8sGEtoux5F8tHm/da3pwYVKMWMakp/LJ3D1q1Crsk0bFCBY/KXjVKhNG0TCQ7Yy5hvdGjohYE/HR6BtbI/a792cREJuzaTpLFzIDqtWgeGYlDhlJ+fl6XScWbMnh33WrWnTsLQMuy5fm0YxfKBGR+yVhFiayGMtu9X2jYJYkFJ44x/9gRtGo1w2rXpXulKndczqVRqfioQ2fGtmrLdZOJUn5+HoMsBYX7meuxCditIqUqhHv8m7t4PBZzusXtuM1s49LxWLfjWVGuemmnHG9uEFSCi7u63qjj0Q+H5nocgMgqEQx+tbfz53ZDWzLnm8VuZVqyQ6Zl38aElApm0Cu92TR7O4snr3QbT++jy7IUa863S/jzvRnOPo9zRy6x6s8N/LT/S/yCfL2ab0hEMBqtmtvdogQBqjap7NUYdwvfQO+eSaGYkKmzX9izuKsoq4MiQJLFjFalwv0rB6578IQo6ry/Ya1zUX87PhotD9au5/G1rIhNTWV69EEupqTQLLIs/avXzDKQEQSBl5u3YkzDJpxPTqKknx8BOj2T9+xk7tEjiLKDXlWq8WKzFgToDfzcqy+Tdu9g5pHDWESJjhUqMrZVm1w70f+0Zxfjt212/rz54gUAdCoVkQGBfNe9F7XDs99JFB0OBs+ezuXUVGdAuu3SBfrPmsbGR0dj1GppGBHh1gAPmeVYfapV92quDllm1KJ57IuLw3zD3X7v5ctsqnaezzp19WqMnPDV6YpkT5OCQmESd/YqHw35mgtHY1AJAsElA3lr2ovUbFHN5bwKtcth9DO4BSI6o47ytcp6fT+jn5EH3xnAv5/Nx5rh2YT1dnRGLbVbVefYjlPYLDaCSwXz1NeP0rBzXa/vmx0VapfjwXcGMO3juS5lWi9MHuPsd5EkiQnPeS79iqhUima93MuUTWlm/nx3uktwY7fYSbqawqIfV/LgWwO8mp9Gq2HUJ8P55Y2pLk3reqOex8Z551eioKDgHUoQUgSoUSLcYzOvXq2mYyE5vecVqyhyLtldA/4mw2rXoWOFil6Ptys2hscWzkN0OLA7JNaeO8vPe3exaNjDBBmy7iPx0+moHV4SWZYZPm8WB69cwXrDaHHa4YNsunCepQ8+gl6j4ZUWrXmlRWvvH/I20m02lwDkVmwOB2eTk3hw3iw2jRyd7Zw3nj9HgsmEeEuQIckyJrudZadPMrBGLQwaLeM7d+O1Wxr+fbRa6oSXpG+1Gl7Nd9OF8+y/8l8AAmAS7Sw8cYzHGzSickiol0+uoKDgLaJd5OW275F4JdmZZbhyPp43u33MX6d+ILhkkPPclv2aMOXNadgsdqQbZa0arZrQiBCa9myQq/s++PZAylQpzawvF3D1fDzpyRlo9VpkOXNOyDKyQ8bhkNH76ImoWJIP57+BzqDFZrZh8DW4ZWsyUk2kJqQRXrZElnK5Oc2p3ZCWbF+0B7Ums0yrRJn/PneuXbjuEgC43Ds5w2P26NTes2h0GrcMi81iY+eSvV4HIQB9nulOcMkg/hk3h+uxCVRrXJnHP32QSvWivB5DQSFP3F+JECUIKQr4aLW81bodn23Z6Oxl0KvVlPDx5dF6ufvCKWy0ajV6tcZlgXuTUKORd9t6lji8lJKCTRKpGBzi/IKRZZlXVi1zGcss2rmaLjFp907eadM+x/nsiYsl+tpVZwACYJMkrqSnsfrMaXpVreZ2jVUUWXLqBNsuXaSMvz9Da9V1lkN5Ynr0wRznITocLDx+jEezERo4l5zkJl0MYLLbOZ34n559zyrVqBEWzuwj0SSaTXSsUJFOFSplqcR1O4tPHsfkoXRLlmW2x1xSghAFhXwiLSmdo9tO4BvoQ2piOuY0i0uZE2T2eqz8awPD3ujnPKbVaZmw/RN+fPlPti3cDYJAm4HNePqbkXnyq2g3uAXtBmeq/WWkmtixeC9Wk5XG3euTEp/Koh9XknQlmRa9G9N5RFun67bRz3XTxGq28s2Yn9g8dydqjQqNTsOTXz1C98c65npOZSpHMOiV3h5f8w3ycQZftxNYwrOUe1B4AKKH0jNByCyxyi1tBjbPUjZYQUEhf1CCkCLCw3XrUyUklN8P7CPelEHHqAo8Uq8BAfqsG/CKIipBYFjtOkyPPuSmkPREoyZu559LTuKZpYu4kJKMgECAXs/33XvRtEwkl9PSSDSb3a6xOxysOH3KqyAk+to1j1mmDLud/Vfi3IKQNKuVgbP+5XJ6Gia7Ha1KzW/79/Jr7/60vE3t6nxyEueSk0gyuc/xdiyiSExaarbnVAkJRadWY79tvr5aLTVKuDr8VggK5o1WbbIdzyqKxKalUsLHx/l7FJ+RwbJTJzyer1GpCDLk/fdNlmUSzGaMGo1SiqVw3zPv+yX89ta/aHSaTJEJtRq7B1EJm8XOlbPX3I4Hlwzi7X9fyrf5yLLM0e0n2bV8H36BvrQf1oqwyFDCy5bg1V+f9mqML0dNZvvC3ditduxWIMPKxOd/JywylEZdPJfZOhwOFk5awdxvlpCWlE6dNjUYM34E5WtEZnmfgBB/GnWpx95VB13kgjU6DQ885blktHzNskRWjeDc4YsuDf06o56BL3mvdKigUJgURVfzgkQJQgoIuySx4fw5LqQkUzMsnBaRZXNs+m0WWZZmkd7X+xZVxrZqS5LFzLJTJ9Gr1dgkiSG16vB4A1dVOLskMXzOTOJNGc4MpFm0M2rhPNY+Mgq9RuOx/wEygxpvKOPvj1aldsswGDUaygUGup3/2/69XEpNcfa02B0Sdge8snIZ2x5/EpUgYBHtPLtsMdsuXUKnVnnMXtyOr1ZLo4jsPUDalI+iTEAg55ISnYFIZmBgpFulKl49703+PrifL7dtQUZGdDjoUbkqn3fqytTDB8hKllsGOuex/G/7pYuMXbuSaxkZyLJMxwoV+aJzt2IXRCso5AfRW4/z+zvTsVns//lhAHj4CjD6GajbrmDV42RZ5vMRE9i2cDcWkxWtTsOfH8zkzX9eoM2A7A1Sb5KamMa2BbvdXNCtJivTP5ufZRDy06t/sfzXtVhulFftWraPw5uO8dOBL4mokHWf3Ni/n+fDAV9yePMxZ1AhyzI/vvwX4eXCaNKtvts1Hy95i/f7fM7F47GoNWockoMnv36U2q29K1UtTiTEJTHj8/nsW3OI0NIhDHm9L4275q7fUkGhsFGCkAIgLi2NwbOnk2K1YJMc6NQqKgaH8O+AIffFDrFOreabrj15u3V7YtNSiQoMItDDDvumi+fJsNs9mgW+vmYFLSPLUTW0BMfir7kohxk1Gh6uW9+ruXSIqoifTodFtLuMoVWr6Ve9BpdSUvj70H7OJiXSpHQki04c89hUn263cS4pkUohoXy6eSPbLl3EKklYb5yqEVRZqoHp1GrKBgTSuWL2C3yVIDBr0FA+3byRpadO4JChS8VKvNO2fa4UpladOcUXWze5yBSvPH0SlSCQZDZj85AZAniuaXOMeVAuO5uUyOjF813ut+7cWUYvms+swcNzPZ6CQnFn8Y8rPfpMqFQq1Fq1U3ZWq9cSXj6MNgO9CwTyyvbFezIDkBvN6TeNC8c/+gONu9VzkajNiqSrKWi0arcgBLKWrk1NTGPpz6tdAjFZBqvZxuwvF/HC5DFZ3s8vyJcRHwzmnZ6fOvs8JLuEZJcYN/hrZl2ZgsHHVUCkROkQJu8ZT8zJy6QmpFGxXpTbOfcCCXFJPFnvVTJSTIh2iYvHYjm6/SRPjH+YPs90L+zpKdwJheDdV5goQUgB8MaaFVzJSHfu4tsdEicSrvPtjq1Z9kTci5Tw8aFENk7Z8RkZODws3O0OB1svXmBnzCUgU2lJurFwFh0OulaqzEN1vNvx0arVzBk8nJdWLuXQ1SsAVA4J5euuPTiZkMCjC+YiOiTsDgfbYy5hzyKrITlkDBotsiwz5+gRt0BFlB346XQ0KxNJgslEqNGHA1fjSLPZCDEaebBOPU+boG4E6A183rkbn3fu5tXz3cp1k4lUq4VJu91d4S2SxLJTJ3i0XgO2xVx0y94YNBo6ReUtC/L7/r1u49kdDqLjr3EqIYEqoUqPicK9w8ENR5j2yVzizl6lRvMqjHh/sJtzeGpiuse1hN5HR8fhbYjecgy7VaTD8FYMeb0vWt2dyZZnpJpY+cd6Dm8+RmTV0vR+qgvh5f4r4Vzyy2pnAHIrKrWKg+uP0PyBRjneI6Ki56yFSq2iThaZhpgTl9Hqta7ZIDL7YI7uOJnjPVf/tQGbxT2YE1QC+9YcomUf9xJfgMiqpXMcuzgz4/P5zgDkJlaTlV/fnEb3UR3RGe79zU6FewMlCMlnLKKdnbExbmVEthu+DAUVhCSaTaRYrZQNCETjZYPy3cBkt3MlPY1Sfv5usroNIkpnKQQhg7MkyW61YlRrGFq7DiPqNaBCUO6aDMsEBDB78HBSLBYk2UGI0QdZlun8zx8uTe8WUUQg0yvk1qyJShCoFBxMmYAAJIfDpcn9VqyiyK+9+yPfkMA12e03muDT+WzLJjZfPM9PvfresRfH7SSZzbywYgm7L8feKBfzPD+VINC9clX+jT6EXZKc771eraZRROk8Bwtnk5PcPG4AtCoVsWmpShCicM+wYdZWvho1Gaspc2F87UI8OxbvZcL2T4m6RTq3db+mHN50zE3hSbI7GPPFQ/nq75B4JYlnGo8lPdmE1WRFo9OwYOJyvlj5LjVbVCPpajL71xzO8nqV2rvvC51ey8iPh/HH29OdpVUqlYDBV89D7w30eE14+TCPmRNBJVCuevblqQCS6MhyY1gSHSReSUKr12ZrRljckESJ7Yv3cPbgBUpXLkWbgc2cQgE32bfmkMcmfJVK4OKxWMU5vRhzv/WEFJ3V6j1Cdj4zWfU33AmpVguPL5pHy99/ofe//9B0yo8sOXk83++TWxyyzBdbN9H418n0mTGVxr9O5rPNG13eg2qhJehUoaJX/R1mSWTGkcNYs1hge0OgwUCIMTMzk2yxEJOa4naODKhVKvRqDT5aLb5aLSV9/fixV1+48Vqd8FJu1wlA0zKRxKamMmzuDDZeOO+SjTCLdrZcvMj+K3F5nn9WjFk8n12xMdgkKcsABDLLwmqHl2TO4OE0LROJShAwajQMrlmbXx7ol+f7NyldBr0HxR6bJFG9RIk8j6ugUJRwOBxMfvEPZwCSeUzGkmHht7f/dTm3yyPtKFe9NAbfzMWjIAjofXSMGf9wvhvM/fHeDJKvpToDHtEmYkm38OVjk5BlmQU/LM+yD8whydTv4L0x64AXevHm1Beo1qQSoaVDaDu4BZN2f0GZyhEezy9ROoSmPRuiM7huQOkMWoa80TfH+3UY3tr5Ht6K3Sry25tTebjCMwyJGMOrHT7gemwCqYlpJMe7f64XF1IT0xhd5xXGPzqRfz6azYRnfuWRSs9x5byrcEFo6RCP14s2kaBwxT1dofigZELyGR+tlnolS7Ev7rLLLr9GpaJH5ar5fr+nly5iz+VY7A4HNiRMop2xa1ZSxj+ABhGFl5L+dd8e/j6432VRPPXwAQINBp5p8l/983fdejHryGGmRR/kSno6yWYznjsWMhvZ/zl0gE86enbLzQ3Z9ViE+fjyV7+B7L8SR7iPLy3LlnORv/24Y2eGzZ2JXcos49Kp1ejUal5u3oq+M6eS5EHRC8AmieyMvUTDfPx3OZuUyNHr8W6KWrejVal4q3U7NCoVVUNLMH3gUBejsDvhkboNmHboIHaHxRlkGjUa+lSrQSk/z3KaCgrFjZT4VNJTTG7HZRmObnPd+NEZdHy35WPWTtvM5nk7CSzhT++nu1Gzef5/B+xYvMejnO3VC/GkXE/lyLYTWbqmD3+rf65Ld1r1a0qrfk29Pv/Nf55n8ot/sGbqJiTJQclyJXhh8hgq1895t75J9/q06t+MrfN3YjFZ0Wg1CCoBZJnY01ec5x3efIxHKj+f+ZkGlK1ehjf/eZ7wciWwWUWCwgLyPQNdEEx5cxpXzl1DvKEIZk63YDVZ+Xr0j3y55gPneUNe78vR7SddMm0anYbabWq4+K0oFDNkFJ8QhTvni87dGDx7BhZRxCza8dVqKeHjy2t3YIjniZjUFPbFxbktQC2iyC/7djt37wuDX/fudutLMIsiv+3f4xKEqFUqhtepx/A69TifnESPaX9nWe4kyTKXc5C59RYfrZZ2URXYeP6cy/tn0GgYUbc+FYNDqBjsebepdnhJVjz0KH8c2Mex6/HUDS/Fo/UasPTUCUweGu1voldrnJmY/OJKejpalQpLDud1KF+RIbXquBzLry/lUB8fFg5/mG+2b2Xj+XP46/U8Wq8BjxQzjxsFhezwCTBm2dcVXCrI7ZjOoKPH453o8XinAp1XVo3XspzZ+F6+ZiTRW44hia7fEzqjLtcN8amJaSz4YTk7l+2jROkQBrzYi3rts8+k6I16Xv7lKZ6fNBqryYpPgE+Onz0Oh4PlU9ayaPJKLCYrbQY2xz/En8ASfqQlpbNo0krXZ3XILmVfZw9d4OlGbyAIAoJKILxcGG/8+aybM31RY/OcHc4A5CYOh8yhjUexWe3o9JkZpcZd6/HElyOYMnYqgkpAtInUaVODd2a8XBjTVsgnBEBQGtMV7pSKwSFsGjmaJSePcy45mdrh4XStVAVdHkymsuNqRjo6tcqp0HQTGYhJzZ/Fel5JtnpeFidbLFnuwEcFBfNai1Z8uX2LR9lbo0ZD+yjv3dZzYnznboxcMJfTiYmoVAJ2SaJrxcqMapBzk2ZkQCDv3dbfc/BqXLblUCpBoGc+Z8NqlAjLUSLYR6ulX42ClQAt4x/A1117FOg9FBQKE71RT+cR7VgzdZOL8pXeR58rN+78pvfT3fj7f7NcysQ0WjUNOtXBN8CH/i/2YtWfG5DE/3bNtXoNNZpXcWuoz47UxDSeavA6yfGp2C12TnKGvasP8eRXI+j9VM5CGhqtBk2gd0uOLx+bxJZ5O53N9HFnr+Ljb+TrDR8y97ulbo3unrg16Io9FcfYbh/z25FvCS9bhEtEc7Ev1OfpbnR/rAMXj8USFB6gZEAUiiVKT0gB4avTMbR2Xd5s3ZYHqlbP9wAEoGpICY8LUK1KRcvIch6uuHtUDfX8QV81tES2u2CPN2zM6ocfo0VkWbS3lEDp1WrCff0YVMP7+uWcCDIYWTDsYWYOGsqXXbqz6uHH+K57rzw39lcLLeGxNwIg2GDk7/6D8Nfnr1xksNHI4w0aZdlXo1eriQoMylEeWEFBIWeenTCKtoOao9VrMfobMPjqefi9gXR8MHvj0IJk4MsP0KxXI3RGXeac/AyUrV6GN/58FoDIKhF8uvwdylYrjVqrRqvT0HpAcz5aMDZX95n3/TKSr6U45YUhU5Hp59f+cTaq5wcxJy+zafZ2FzUv2SGTkWLiuWZvExDi77FPJCdEm8jSn1fn2zwLgvZDW6LRun6HqNQqGnSs7cyC3IrOoKNygwpKAHIv4Sjg/4oYSiakGOOv1/N046b8fEvpk1oQ8NPpGN2wcQ5XFyzvt+3AqEXzXDIDBo3GLXvgibKBgUztP5gVZ07x54F9pFmtdK9clZH1GxaIz0qt8JLUCs/aNMtbhtauy6/79rjI92oEFVFBQSx/6FGXvpL85NUWralWIowp+/aQZDZTys+PhBt9KX2r1WB0w8ZFSjFNQaG4otNrGfvX8zzz3WMkXkmmVFSYm3LR7VhMVhZNXsmGmVsx+Orp83Q32g1pmW/lkGqNmvdmvkLMycuc2neOklFh1GhWxWX8Om1q8Pux70lPzkBn0OZJwnXX0n1OfxHX+6s4e+hCvvW7HNt5CrVGDbhnO0SbyPoZWwkMC0C0J7mVLmWHaBO5dOJyvsyxoGjctT5Lf1njcswvyIdXpnjnaK+gUNxQgpBizvNNW1ApOJRf9u0m0WyiTbkonm/agjDf/FVgyS3NI8syfeBQvt+xjZMJ16kSWoKXmrWgXinPKiq3IwgCPSpXLZBm/oIixWJhSK06rDx9iti0VKcYwUcdOhVYAAKZ71XvqtXpXbV6gd1DQUHhP/yD/byShbVZ7bzY6h1iT8Y5DfdO7T3Loc3HeGHi6HydU2TV0jn6Y/gF5f17IahkoMfjkl0iIDRrAYor568RfymBqNplvXrPQkuHZFuWlJGSwbebxrHqzw1snrcDrV6L3WInIS4px7HDyhXdjEFqQhqfPTwB+TaJTavJhlanLNXuF5SeEIVihSAI9KpajV5Vi17DXb2Spfi9b+HVSt8pqVYrmy6cQwbalY8iQJ+1q/D4rZv448B+HLIDtUqFTq3mi87d6FPNs4mXwp1z5NpVZhw5TLLFTNdKVeheqQraAih7VFDIK5tmb+fy6SvOAATAkmFl5e/rGPxqbyIq3HkG9m4x6OUHOLTxqIsik1qjonytskRWcd9cykg1MW7w1xzefCwzULDa6fdCT0Z/9lC2WaB67WsSEOKPOc1zX6FDchBergTPThjFsxNGATC267icgxABSkUV3fd705wdHmMvWZZZP2MrA17sddfnpKBQ0ChBiAeSLWb2xl0mQK+nUUQZVMVA2u9eJMFkYtnpk6RarbQuV556Jd39OQqK5adO8OrqFagFARCQHA6+6NyN3tXcsw374y7z18H9TlWvm2pbb65ZRfuoCtkGLwp5Y3r0IcZtWo9dkpBkmfXnzzH10AH+6T+4QPqvFBTywp6VBzw7lWvURG85XqyCkIad6zLq0+H8/ta/qHUaJJtI+VplGbfov94SSZQwpZnxDfTh69E/cmjTUexW0dlIvmjSCspVK0O3x7Iuy1Wr1Xy94X+82v4Drl6Id31Nq6ZWq+oElnD1wog5mXOZlcGop3L9qFw88d0lI8WE3e5eXma3iWR4kIZWuAdRJHoVpuzbw9fbt6BVq5FlmQC9gb/7DaRSSNFN496LbL5wnqeWLkSWweaQmLx7B90rV+WrLt0LXO89PiODV1etwHKbVPDYNStpXLoMEf6upQcLTxxz6QO5iVolsP78Ofoq2ZB8JdVqZdzG9S7/Pia7nT2XY3l11XK+6tI9Wx8YBYW7RYkyIWi0ajd3a5UgEBTuubwpv5BlmRO7T3N40zGCwgNpPaApRj/jHY054IVe9BjVkTMHzhMYFuBU15JlmX8/ncesLxdis9gx+hkwpZrcZIEtGVZmf7Mo2yAEoGT5MP4+M5Hxj05k46ztaA0aZIdMmcoRvDP9Jbfzo2qXI/7S9Szd1TU6DWWqRlC7ddEqWU28kkTMyThKVy5Foy51+eejWW6eLnqjjsbd6hfOBBUUChjlm/oWdsXG8O2OrVglybmoNNntPLpwLptGjlEyIncJqyjy7PLFtzmOi6w8c4pulSrTtVKVArv3iYTrvL5qhUevEgcyy06f5PHbJHxlyNKROKvjCnlnz+VYNGoVeJCmXn76JJfTUpk1aFiB9uEoKHhDj9GdWDBxuUsQIggCBj8DDTvVyebKO0OSJMYN+Ya9qw5it4lo9Vomvfg749e8T9VGd6aUZ/QzUru168bKjM/nM/2z+c5SrbTE9CyvT72e5tV9VCoVb/7zAo9/9hCn9p0lLDKUyg0qeNyEeuTDIRzcEO0iUyyoBGSHjEanoe2gFjz3w6giY1goiRLfPvkz66dvcZaqtejbhLYDm7P5Fmlig6+eFn0aU71p5UKescLdQSbLSPoeRQlCbuGfQwfcfB5kMhuOD16JK1QH8vsFmyTx58F9SB4cwE12O88sW0yI0cgjdRvwVOOm+ar6dOBKHA/Nm4VFFD1mRCWHA4vortiiVak8nm+TJNpH5ewKnBv2XI5levQh0m1WelSuRq8qVe+7PghfrTbLz2mHLHMi4TqbLp6nQz56yigo5IUylSN4d8YrjH/0ByTRgcPhoESZUMYtGntDAapgWP3XRvauOuhczN7cXf9wwJdMO/9jvi7GHQ4HM8cvdOkVyQqVSqBh57q5Gj8sMpSwyOwrEao1rsSny97hx1f+5NyhCwSE+jP4tT4MeKkXKpXK6+dNS0pnxe/rOLX3LJXqR9Hj8U7ZNt3nlWmfzGXDzK3YLHZnqdr2RXvo9URn3pr2Iqv+3IAsy3R5pB0t+zYpMsGTgkJ+owQht5BssXhcTAqCQJrN5uEVhfxkR8wlnlq6EJsouZVC3cQhy1w3mZi8Zyfnk5P4Kh8N8j7auM7N5f1WtGo1HW9b2EoOB3OPHfF4foSfH0GGOyt/uJWf9+xiwq7tziBp68WLzDhyiKn9B99XEryNS5fBqNWQYff8N2my29kdG6sEIQpFguYPNGL21d84feA8Bl895aqXKfBF5bIpaz32oqQlpXPu8EUq1i2fb/eymm0e73UTQRCQ5cyMhMFXz8hxw/Lt3rdSt21NftwzPs/Xx529ynPN3sJqsmI129i6cDczvljAhG2f5MrU0RsWTVrhkrUBsJltLJ+ylqe/GUnLPk3y9X4KxQfh/kqEKGaFt9K9chWPpm+iw0EDL6VlFfJGqtXK6MXzSbVaswxAbsUiiiw9dYIr6Z5T+6lWK8tPn2T1mdOY7Tm76wJEx1/L9vU+VatTIyzc+XOi2cSv+/ZkGaAmWTyru+SF6yYT3+3chvmWLI1JtBN97SorT5/Kt/sUB9QqFX/2HYiv1rPXgUGtoZRfzlKgCgp3C7VGTbXGlShfI/Ku7GrLHjLJAAICDil/HcsMPnoCS3jOFpSrEUm7oS2p0qgifZ/rzq+Hv6FUVLjHc2VZZs3UTTzTZCyPVH6OH1/5k+T4lHyda3ZMfOE30pLSnUpmNrONjGQT3z/zq8t5NouNgxuOcHTHSRxZvM85kZFq9njcarLmeUwFheKIkgm5hUE1ajEj+hBnkxIxiyICoNdoeLt1u3x3ulZwZeWZ3C+kdWo1pxMTKeXn+gW44PhR3l67OjM7IGRmTyb37EPb8lHZjheg15No9vzloFWpqVEizPnz9ksXGb14AQ6HA0cWtUGRAXfeeHo2KZHf9+9lZ2wMksP9Pia7nRVnThZJieaCpGZYONtGjaHl77+QcVuQqVYJ9PGgYqagUNS42TOW34FJl0facy76ottuu8HXQMV6+ZcFgcy5j/lyBN89+bPL/fRGHc9PfJz6HWp7Nc5Pr/zpksFZNHklm+Zs59dD39yRv4m37Ftz2M2jQ5ZlDm08iizLCILApjnb+WrU5Mx+E1nGx9/Ix0veonL93JXd1mxelUObjrodr1gvCvV9Vl6rcBv3WU+Ikgm5Bb1Gw5zBw3m/XUfalY+if/Wa/DtgCA/XrV/YU7vnSbNaEbPYAQrz8fH4i2qTHJQPDHI5diklhbfXrsYiiaTbbaTbbJjsdp5eupBUq4VUq5VDV68Qb8pwG29U/UZZljUJ/Ce9KzocPLNsMWbRjtXhrop1kySLmYXH3b9ovGVXbAy9p09l5pHDnElKRJTd3x+1IORryVdxwl9vYM6QB6kQFIxBo8Go0VLGP4B/+g++b98TheJBQlwSHw74kh764fQ0DOejwV+RdDU538bvOaYTNZtXxeCXKQ+uM+ow+Bl4f/YrqAqgdLPzQ215a+qLVKhTDqO/kRrNq/DJsre9DkAS4pJY/NNql7Iu0SaSlpDO0l9W5/t8PaHVe96T1Wgzg4LY03GMf3Qi5nQLplQz5jQLCZeTGNvlI+w277LtN3n6u5EY/QzOviCVWoXBR88Lk/LXwFJBoaijZEJuQ6/RMLRWHYbWKjjlEgV3Wpcrz1fbt7gd99Fqebt1O95et9qlX0OvVtOybFnKBrpmGxaeOIbkYbEuCAIvrljKjphL6NRqrJJEl4qVXeRcn2rclBMJ11l88riH66FzxUxVmf1XLnu8x+1cSU/n7XWriTeZGN2wMZAp/xuTmkKF4OAcF8pvr12F2UMj/K1o1WqG3ce/q9VCS7BmxGNcTElBkh1UCApWmjgVijQ2q50XWrxNwuVEp4TttoV7OLX3HH+c+B6N9s6/ljVaDZ+veo8D66I5uOEIwaWC6DCslZu/Rn7Sql9TWvVrmqdrT+87i1avwW51/byzmm3sW3uYoW/0y4cZZk+XEe1Y/ts6lzlodBo6Dm+NIAis+G0doui+6STaJHavOJCrPo7K9Svw84GvmPXlQk7uOUPFelEMeb1PvveeKBQzZBDus2o8JQhRKBJUDS3BwOq1mHf8qHPh7aPR0q58FH2q1SAyMJB3163hVGICWpWK/tVr8l5bV615qyiy6ORxZ8biVmyiyLZLF7E7HE755TVnzzBu03o+7tiFVKsVuyTxffdelDAamRZ9CLskIQgCOrWapxs3JSooGMisq/YWsyjy/c7tDKtdh7fXrmb12dPo1GpsksTQWnV4v11Hj9LPaVYrF1Ozrof20+qwOxy806Y9tcKLj+FZQSAIAuWDggp7GgoKXrFtwS7SktJdPDQkUSIlIZXti/fSZkCzfLmPSqWiYee6uVajKgxCS4d47FVRqVVZ9pDkN6O/eJizhy9wet85ZzN9VO1yPP3dYwAkx6e4eXhApjpYakLWksRZEVGxJC/++MQdz1tBoTijBCF3ictpqXy3YxubLp4nyGDg8fqNGFSztrJrewsfdehEhwoVmXM0GtHhoF/1mnSvXAVBEGgUUYblDz2KVRTRqFQePSA+2LCWC8nJHscWZXf9baskMudoNGeSEtkXdxkQiAoK4quuPehXoxbLTp1AQKB31WouDen1S0WgzUVJg0N28L8N61hz7oyLB83so9FEBgQ6syS3olOrUWUR7IQYjXzRqRtNypRR3NgV7hi7zU5iXDJB4QHojUrvW0Fz6fhlzGnuohXWDCsXj8UA+ROEFCcq1Y+idKVSXDgag3RLtkGr19Dv+fxTQMwOo6+BbzeO4+TeM1w4EkPZ6qWp1qSy8zu6Wa9GbJi1HUu667+dQ3JQv0OtuzJHhfuA+6wnRAlC7gLxpgx6T/+HVKsVSZa5lpHBhxvXcSoxgbfbtC/s6RUZBEGgY4WKdKyQtbRqVk7YZrudBSeOYffQoyEAGpXKc4bE4WDP5VikG3/4pxITeHDuLNY/+jhjW7X1eC+NSsWPvfoyatE8ZFnGJkno1GoMGo1HRSzJIbP01Ek31S+zKPL7/r0egxC9RkOPKlVZfvoktlvc2I0aDU80bEKnindmOKagIMsyM8cv4N9P5iE7ZGRZps+z3Xn8sweV5tgCpFzNSIz+BrdARO+rJ6pW2UKaVeEiCAKfr3yXcUO/5fjOU6g1mT0Sr0x5mgq1y93VuVRtVMmjoWOL3o2p0qACp/aexWL6z0yw15Nd7lq2RkHhXkMJQu4Cfx7YR4bN7lzoQuYC9O9DB3iqcVNCjD6FOLuiTfS1qyw+cRwZmV5VqlEvC6nkNJs1yyIpP52OhhFl2HjhnMfXpdt2HkSHxJyj0TzVOOv65qZlItn62BMsO32SZIuZlpHlSLVZeXLJQhfDS6NGw4AatZgefcjjOMnWrGV8P+7QmeumDPbGXUarUmGTJHpVqebm2K6gkBeW/7aWqePmupjMLZq8Er2Pnkc/HFKIM7u3adm3MVPGBmAz2527/mqtmuDwQJo/cP/+bQeXDGLMFw+z4IdlpCeb6PpIO5r2bFDY03Ki1qj5YvV7rPlnE+umb8Hgo6fXE11o1qthYU9N4V7i/kqEKEHI3WBHzCVsHnbo9Wo1J65fp0XZu7vTU9S4mp7O3GNHuJKeTouyZelSsTIalYrvd2zj5327sYkSMjLTDh9kRN0GvNnaPUNRwscXP50eq9nkclwAWkSW4+UWrdh68XxmWVYOWCWJc8mJOZ4XaDAwvLZrvfUXnbvx8aYNJFvMaFQqHqpTnzdatWH7pYucTU5yG6NRROksx/fV6fin/2DOJScRk5JCldBQNzliBYW88u+n89xcrq0mK/O+XcKI9wcViIqSAmh1WiZs/4TJL/3B1gW7EYTMpu5nvn+sQF3UizqzvlrE3x/OxGaxIztkDm6I5t/P5uEf7Idol+j0UBu6j+qAVqcttDlqdVp6PN6JHo93KrQ5KCjcSyhByF2gfGAQB69ecfOTsDsclPK/vxeVO2Iu8fiieUg3yprmHT9CxeAQvujUlZ/27sZ6SwlTZvZoP32r13Dx7ABQCQLvt+3A2DUrsNwoX1KRWdb0aovWVAkNJcho5LrJNUjxhI9GS+PSkXl6nt5Vq/NAlWqkWq34aLVob5S1jOvQmdGL52OVJByyjFoQMj1ovCjHqxAUTIUbTfEKCvlF0pVkj8ctJiuiTURn8GwGqXDnBJcM4p3pLxf2NIoMSVeT+ev9Gdgs/ylTWU02zh684Pz59P5zbJixlfFr31fKBRXuWYT7rCdE2eq6C4xu2Bj9bR+aWpWKuiVL3deLS4cs8+KKpZhF0dn3YLLbOZ2QwFfbtziNvG7FLkmsPXvG43hNy0Tip9c71aYEQSAyIJCIG4FegC7nplutSkWIj5HeXpr/XUhOZvzWzby+ajlLTh53KmoFGgzOAASgRdlyzBnyIL2qVKV6aAkG1azNkuEj3IKpm+yPu8yba1by/PIlLD99EulGP4vkcLD5wnmmHT7IgStxHt8jBQVvqFgvyuPxsMhQtPrC221WuP/Yvy4atTb7wMJqsnJy31n2rDhwdyaloFAY3BTRKaj/ihhKJuQuUDMsnB969ObttatItVlxyDJty0fxVZfuhT21QuVUYgIZdpvbcYskcjQ+3qNymOqGZK4nxq5ZSZLZ7Mw4SbLMhZRkvtm+lffbdeDhuvX5cttmF78RNVA6IBCHLGOTRLpVqsJLzVti0OS8CFtz9jQvrFiK6HAgOhwsP3OKKfv3MnPgUI8N9DVKhPF99wdyHPfnvbv4fud2rKKIDKw/f5ZZpcvwaccuPDhvNtdNJiSHA5UgULdkKf7oOyDLhn0Fhax48qtHeLPbOFeXax8dT387UlHtU7irGP0MXkmfW9It7Fl9iGa97t/eGQWFewll5XKX6FihItsef5K49DT8dTpFWpXMrENWO/khBgPJFrPbcbWgomeVqm7HraLItpiLbk3mNkli4YmjvN+uAyPq1ufg1SusOH0SrUqNA5ky/gFMHTCYMB/fXM3dJkm8umqFSxO6yW7nZMJ1pkcfYmT9vDUrxpsy+HbHNhdFLJPdzu7LsYxZvICY1BSXZ9x/5TITd+3g1Zat83Q/hfuX2q2q8/X6//HHezM4e+gCZaqU4tEPh3rtcq2gkF807FLXme3NDpVaILhkYI7nKSgUS2RAMStUKChUgkAZ/4JzrC1uVAgKJsLfn3NJSS6CEEaNhqG163I+OZlphw+gVWVmPiTZwYftOxIZ4P4lECNNwAAAJZhJREFUJCNnGdDcXLSrVSq+7daTl5q1JPraVSL8/WlQKiJPu75Hrl1F9iBjYRFFFp88nucgZPuli04lrFsx2e0cux7vdkerJDHraLQShCjkiWpNKvP5incLexoKueDc4Qsc3HCUoPAAWvRpfE94u/z25jRkD2aFt+OQ5Fw5kysoKBRtlCBEodAQBIGfevVl+NyZWEQRySGDADVLhPPF1k2oBRU6lRqbI9Nd/IVmLSnh41nO2KDR0jCiNHvjLrsIAGhVKrpXquJybvmgIHx0Wn7Zu5t31q2mpJ8fYxo2plXZ8l7P3aDRuAkN3MRHm/d6el+tznMZGlkr94kelNcUFBTuLRwOB+NHTmLL3B3Isoxaq0b9jJrPV7zLlXPX2DJ/F/4hvvQc05nK9SsU9nS95uLxWJb+stqlKT0r9D56UhPS7sKscub8kUtcOh5LuRplKF/z/vR3UchfBOT7rjFdCUIU7hpmu51DV6/gq9NRKywcQRCoHBLK1lFPsuH8WeJNJioEBTN60Xw3Y7/ZR4/wfNMW2Y7/ReduDJw1HYsoYhbt+Gq1hPr48EarNi7nxWdk0PPfv0i1WrE7HJxIuM7u2Bjeat2Oh+vW9+pZqpcII8RoxGR3/eL00Wp5sE49r8bwROty5T06pes0Gsr4+3MmyVXmV6tS0fW2IEtBQeHeY/30rWydvxOr+UYPz41F+8tt3kOtVWPJsKJSq1j11wae/nYkvcZ0KcTZ/kfStRSQZYJLBnl8fd9qzx5KHpFlQiL+E3Mxp5u5eCyWkIhgwiJD73Cm3pF8PZXnmr7J1QvxAKjVKmq3qcEnS94qElmpy2eusPrvDaQlptO0ZyMad6unyG0rFFmUIEThrjD/+FHeW7cGlUrAIcuEGn34o+8AKgaHoFOrnQvpvw7uy2LHX2bpqRPZljlFBQWzceRolp48ztnkJGqHl6RrxcpuTds/793lDEBuYhZFPt+6icE1a3vV5C0IAlN69+ehebMyZXcdMpLsYFCNWm6Zl9yg12j4o+8ARt2QLUYGu0PirVZtaVImkmFzZmJzSFhEER+tlmCDkddaKKVYCgr3Okt/XY0lw+p23G4TsdsyN20ckgOrycbkl/6k/ZCW+AbmrtctP7l0IpZPH/yeC0cvAVCueiRvTXvBLWvgE2C84Y+SfSZEo1NTuWFFIqtkGtZO/2we0z6ei1qrRrSJ1G1Xk3dnvoJvQMGZ/8qyzBN1XiHpaorzmCQ6OLjhCL+88Q/P/zC6wO7tDRtnbWP8Y5OQRAnJLrHyr43UaVODcYvGKrLGxQUlE6JwP+KQZae0bX5zLP4a76xb7dLEbban8NC82Wx5bAzqW3ZpTHa7x/Ii0eFwyzp4wk+nY+htBoK3s/niBZcA5CYqQeBUYgK1w0vmeB+AqqEl2DbqSTZfvECSxUyT0mUoFxjk1bXZ0SCiNDtHP822Sxcxi3ZaRJYlyGAEYMPIx5l37ChnkhJpUCqCB6pW80rJS0FBoXgj2sScT7qBRqvm8ObjhebAbjFZeanNe6QlpDt79c4eOs/Lbd9n2vnJGP2MznNb9W/KxOd/cxtDo9OgN+qQJAeSXaJu2xq8Pf0lADbN2c60T+ZlZoVu6Jcc3HCU8Y9O5H/z3yiw5zq08ahLAOJEhhW/rSvUIMScYeGrUZOxmf9Tu7OkWzi86SgbZ22n43Bls0qh6KEEIfc5O2Iu8eGGtZxMTCBAp2dk/YY837S5S2Bwp0w7fAj7bY3WMpBus7H7cizNI//bGWtfvgI/7NqBJLp+4WrVatpH5U+dc7ivL6cSE9yO2yWJUGPudtG0ajUdK1TMl3ndii6L5w0yGBnVQJGnVFC43+j8cDvOHrrgIqmcJTIYfAuvNGjLvJ3YLXYXsRBZBrvVzsbZO+j+WAfncd8AH8YtepMP+o93nu8QHbzx13O07NuE2NNX8A/2dSnnmvXlQqwm16yQ3Wpn94oDpCamERBSMCbAJ/Z49qjKvL/3QWJBEL3lOCqN+/e2JcPKun83K0FIcUHJhCjcLxy+dpVRi+Y5MxSpNiu/7ttNssXMh+075dt9EswZbtK5AIIASbfJ8NYIC2dIzdrMPnoEs5iZ+fDRaBlQoyY1w8LzZT5jGjZhX9xlF78QrUpFw4jSTmNDBQUFhcJAEiXmfreUJT+twmqy0qp/Ux75cAg9Rndkw6xtnN53FnO6xcVQ0m51zRLrDFrqtKlxt6fu5NrF6//1rtyCJcNK/KXrbsfrta/F7KtTOLTxKKJdom67mhh9M2Xsy1Uv43a+x2wEoNaoSE1IL7AgJKJCeGZJscP9+yyyWkSB3NNbtLqsl3M6g+4uzkRBwXuUIOQ+ZuKuTEO8WzGLIjOPHOaVFq0J0OfPTlrHCpXYdOG8y6IfMjMPjUu7f8F80K4jXStVYcHxowD0rV6DlpHl8mUuAG3LR/FGqzaM37oFtSBgd0g0KFWaST1759s9FBQUFPLCx8O+ZfeK/c6Mx/Ipa9m5dB9Tor/hq3UfsHvFAfatOURIqSA6j2jHqr82MPWj2Wi0GhAyy5g+Xf7OjT6LwqFak0rojDos6RaX40Y/A1UbV/J4jVanpVEX70Q9Gnauw+q/NyKJrmW1OoOWiAr5s1nliea9G+Ef4k/K9VS318b+/XyB3dcbareujub/7d15fFTV/f/x15k9IYSETSAgICISRbYAIlqwgCwKgoqggigu1ap16a+K2qrV6hf3atVWtLbuWFfUiggK2lpBQEBlUzbZArJvWWY7vz9mjIkZJJDlTjLv5+MxDzJ3Zu79hJtM5nPPOZ9Pgq7zgXp+hl42wIGI5JCpT4ikkhXbtyVcBO51u9m0dw+Z/iaHvW9rLbuLi0j3+hh+zLE8u/gL1uzcWZKIpHm8XNYtL2GTQGMMJ7U6kpNaVV3i8VPjO3fj3NxOfLtjO43S09W/pQrtCwZZu2snzTLqH7CksoiU993S9Xw+bWGZef3hUIQ92/cy8/lPGHblIHoN7UavoT8W6Dhv4kgGT/gli2d9Tb0G6XTt3ymWkDioa/9OtDmuFasXry0pvesNeGnZoQU9Bnep9P7H3TaKT9+aR+HeQsKh2FRff7qPXz8yoVqTL6/Py1/m3sOfxjzMtwtWg4XsIxpw65Tr6JB3dLUdtyI8Xg93vT2RW4bcQ9RGiUYsNhrljCtOo/vAn18nKeIUJSEprGPjJqzfvbtcIhKKRCr1oXz6ym/548cfsb2wAJcxnJN7PC+dNYo3ly/nvW9XkOkPMLZTZ/pW0RqPw5Xm9XLCEc0cjaEusdby0JxPefqLBXjdsYaLA49qxwMDh1So4phIqvtmwWrc7sTz+r/6zzKGXTko4euymzag3+g+1R1ehblcLu7/8HZeue8tZjz7MdZaBo77BaMnjqyScrFNj2zC5MUP8Mp9U1k8ewlHtG7C6BvP5PiTq38KWvO2R/D43Ens27WfaDRabVO/EomEI6xctBZfwEub41qV6ymV27sDUzZNZu67C9i3az/dBpxA86MqVmhFkoP6hEidMm/TBu76ZDbLt20lyx/g0m55XNotD5cxXNOzd7lpUmkeD+cd35n6hzkVa96mDVz/wXtlKmG9vnQJhaEQD5w2hNPbd2DR5k1k+v1Yaw+rW7kkp1eXfs0zCxdQHAlTHK9D8OHqVdw++0MmDUj84UlEfnRE68Sjz16/l5xjKr7mYN+u/bz56Hv8b+rnZDbK5Kxrh9Lr9JotaBFI9zP+jtGMv2N0pfbz/bqt7Nmxj9a5LfH6flwH0zinEVc9MqGyYR62jKyaLX/8+bSFTBr7KJFwhGg0SnazLO6aelO5kseBdD99zz2pRmMTOVxKQuqwr7/fwkVvvV6SZGwrLOCRuf9jR2EhE0/+BblNmvLsiHP40yezWbJ1C1mBNC7p2p3Lu/c47GM+/vncMgkIQFEkzDvfLCc7EOD5rxbjc7ux1tKkXj2eHzGKnExNhaoLnlwwr9y6n6JIhKkrlvHHfv01GiJyEJ1O6UijnIbkr9pcZr2Dx+vm9ArO69+/p4Aru9/IjvydJVOhln62gjETR3LBrWdXS9zVYeeWXfzx7Af49ovVJetdrv7LJQwc19fp0Grc5rXfc+eoB8pURstftYUru93IHW/+jp5DyvfPmvPuAp666QU2rdxMkyMbcfFd53HqmOQZLZMDcHgkxBgzGHgEcANPW2sn/eTxG4BLgTCwFZhgrf0u/lgE+Cr+1HXW2uEHO57aaNZhj879rFxCUBgO89yXC9kfjL2Z5bXI4a0xF/DtNTcw77IruSKvZ6X6hazdvTPhdrdx8eJXXxKMRNgXDLI/FGLd7t1c9s6bh30sSS47CgsTbo9ay/5QBcqKiqQ4YwwPzrqDE/oeh8fnwev30vKY5kz64A80zqlYR/B/T57Jzs27ShIQiE3neunu19mzY2+Vx7xp1Wbe+PO/mfr4+2zPT/z+fzh+P2wSyz9fSbAoRMHeQgr2FPLIlZNZOuebKjtGbfH+Mx8RCZfvnxUKhrnjrAd4/s5Xy2yf8+4C/jT6IdYt20A4FCZ/1RYevPQJpj87q6ZCllrIGOMGHgeGALnAecaY3J88bSGQZ609AXgNuK/UY4XW2i7x20ETEFASUqct37414cJztzHk76v6P0YAXY5onjCJCUbCFEXKJkRRa1m7exerd+6ollikZuW1yCFR+tooPZ3sQFqCR0Tkpxo2y+a+Gbfx6uaneWHN4/xj+aPknnhMhV8/998LEpbH9fq9rJh34D4Xh+Ole17nsk438PTNL/LUjc9zYburmPniJ5Xe73fLNvDd0vXlPngHC4O88ed3K73/2mb7xh2Eg+WTEIiVZ3550pvs3LKrZNvTE18o9zNQXBDkmVters4wpdJsbCSkOm8/ryew0lq72lobBKYAZ5aJ0NpZ1tqC+N05QMvKfMdKQuqw9g0TXzkLR6M0y6iexXTX9DyRwE+m3aR5PDRKUAULwONysTdYdVfJQ5EIbyxbwkVvvc4V/57K7LVryjTMkupz40mnkO714o4noQYIeDzc2a+/1v6IHKKMrHo0bJZ9yK9rnNMo4e9bOBiu0vfC1V9+x0t3v0GwKESoOERxYZBgUYiHL/sbu7Ym7uNRUbu27MadYPqmtbB1fflGs3Vd3qAuBOJ9UxLxej18+cmykvubVm1O+LydW3YRCoYSPiYC5ADrS93fEN92IJcA00rdDxhj5htj5hhjRlTkgEpC6rDf9OydMCE4v1NnMnzV07yoXcNGvDbqPPq2bkOmz0/brGzu6NefsZ0643eXL51oiFXpqgqRaJSLpr7OH2bN5JN1a/lg1Uqueu8dJn1a+StzcnDtGzXi3fMu5KyOx3F0dkP6t23HiyNHMeAoZ0tXiqSSs64dii/NW257sCjEHSPv49d5N5K/ZkuljzNryn8JBct3CXe5XXz29vxK7btdlzaEE3xY9ga85A3qUql910Z9RvbkyI45uBJUTvtB/YYZJV83PTLx39TMhhmOl2+Wn2GpiZGQxvFE4Yfb5YcTqjFmLJAH3F9qc2trbR5wPvBnY0zipkClKAmpwzo3a85Tw0aUjIhk+v1c0b0nt5xcvQv7jm3chH+ceTaLrriaDy+cwKjc47moSzea169fkhS5jSHg8XD3LwfiS5CcHI5Za1ezeMvmMoujC8Mhnlu8kA17KndlTiqmdVYW9w4YxAfjLmbysBF0bd7C6ZBEUkqHHkdz7V8vJ61+gLSMH6+eW2sJFYdZtWgtv+13O5FI4uk9FRWN2oQjK9aCTdBR/FBkZNXjgt+fTaDej1UavT4PmY3qc+bVgyu179rI4/Xw0Md/5KzrTse4yo9yBer56dzvx6n7F981Bn962QuNgXQ/424fpVFp2WatzSt1m1zqsY1A6XJrLePbyjDGDABuBYZba4t/2G6t3Rj/dzUwG+h6sGCUEtdxfVq1ZvrYi4haW6kF55VV3+/n3fMu5NWlXzN77WqaZdTnwhO60LFJ1XW3/WjNagpC5a+euYyL/61fx7nHdaqyY4mIJKuB4/rSd1RvHvvNM8x4dnZJQz+IJQ/7dhXwxcyv6FGJUYW+o3oz9bFpZSo2AdholF5nVL4c8Pm3nE3bTq15/eF32fX9bk4c1p1Rvx1eo305kok/zc+v7r+QNse34i9X/R23x4WNWjKy6/F/027FXepiXt9zTyIUDPH3m19i+6YdZDbO5MLbRx2wz4wkEWc7ps8D2htj2hJLPsYQG9UoYYzpCjwJDLbWfl9qezZQYK0tNsY0BvpQdtF6QkpCUoSTCcgP0r1exnfuyvjOB02OD0t2Whoel4twtOxvscsYGgQOPJ9WRKSu8QV8REKRMgnID2w0yvZNlatkdUz3dpx59RCm/mUaoWAYl8vgcru44qHxNGp+6GtZEuk9LI/ew/KqZF91xaDxp/KLc3qzbM63pNcPcExeu4QNIAeM7cuAsX0Jh8KaglWLONms0FobNsZcDUwnVqL3GWvtEmPMncB8a+3bxKZfZQCvxkfVfijF2xF40hgTJTbLapK1dunBjqmfTKkzzsk9nn8s+qJcEuJ2Gfq1drY7u4hITety6vF88tpnFO0vLrM9GrV0PLF9pfd/2aSx9D//FD6d+jler4dfjOpNi3bNKr3fZLDh23xevucNls35hpYdWjBm4shDqlJWndLqBejWv2Ij+0pA5FBYa98D3vvJtttKfZ2wYZG19n/AIU830U+n1Blts7K5f8Bgbpo5HZfLYK0l4PHy9+Ej1ShPRFJO33N7M+XeN8lf8z2heN8Qf7qfk4bn0bpjpSprljjqhNYcdULrKtlXsli7ZD2/6X0LxYVBopEoG77ZxBczv+T3U27gxCqYaiZyQClWzVOfzOSwrN21k/s+/Q+fbVhPpt/PhC7dGNe5q+PTvk4/pgO/bHsU8/M3EvB46NasBe4EQ9XJZltBAa8u/Ypvd2ynW7MWjDw2l3rVVMFMRFKDL+Dj0c/u4dUH32H2lE/xp/kYduUghlz6S6dDS2pPT3yBov1FJZ8HrY312Xj0qqfodXo3Le4WqSLGiR4KeXl5dv78ypXwE+ds3reXwS8+y75gkGj85yfN4+Hsjsdx56kJR+rkZyzbtpXRr00hFIlQHImQ5vGS6fcxdcxYmtbLOPgORESkyoxoOJ79uwrKbff4PLyyaXLKLo6vzYwxC+LlY5NWg0Bze1Lr8dV6jPe/uTep/h+S/xKxJJ1nFn5BYShckoAAFIbDvLr0a7YVlH/jlp9304z32RcMUhwvmVkYDrGtoIB7P/2Pw5GJiKSerMaZCbe7XOZnmwaKyKFREiKHbEH+RkLR8hVXfG43K3ekXjfbytgfDLJ827Zy2yPW8uGaVQ5EJCKS2kb9bniZHiUAvjQvA8f3xecv3whSpGpUc6PCJFxvoiREDtlR2dm4E8yJDUai5NRPfAVJEvO4XLG28Qkk6jB/qPYUF/P5xg2s2VW5cpwiIrVJOBSmcH/RYb126KUDOOu60/EFfKRnpuH1e+kzohe/fvjiKo5SJLVpYbocsku79eC9b78p05nc53bTK6clrRo0cDCy2sfv8dC3dVs+/m5NmdLCfrebc3Mr11zxr/Pm8ujnc/C5XYSiUTo2bsLkM0bQKD29smGLiCSlooJiHrvm73z00n+JRiLktG/OdX/7FZ1O6VjhfRhjuPiu8xh94wg2rdpM45yGZDXR3zapAUk4WlGdNBIih6xDo8ZMHjaCVpkN8Lpc+Nxuhhx9DI8PHXbQ1+4oLGDZtq0UJuhsnqom9T+NtlnZpHu9pHu9pHk89GjRkqt7nnjY+5y5eiWPzZtDcSTM3mCQonCYr77fwtXT3qnCyEVEksudox5k1sv/JVQcIhKOsm7ZRm4ecjfrV2w85H2l10/j6C5tlYCIVBONhMhh6dOqNbPHX8Lu4iLSPN6D9uEoCof43YzpzFi9Ep/LTcRGuarHify6R68aijh5NUpP5/0LxjNv00bW7d5FbpOm5DZpWql9PvXF/DIjVQDhaJRFm/PJ37uX5vVV3UVE6pb8NVtYPOtrgkVlL3KFikO89tA7XP/kFQ5FJlJBKTYSoiREDpsxhqxAWoWe+/uPZjJz9UqCkQjBeBWox+fNoWVmJsM7VHyYvK4yxtAzpyU9c6qmgdiOwsKE2z0uN7uKi5SEiEidk7/6e7x+b7kkJBqJsnbJBoeiEpED0XQsqXYFoRDvfruipATtDwrDYf46/3OHoqrb+rVpizdBk0aXgXbZDR2ISESkerXObUmouPxUX4/PTccT2zsQkQAU7i/i41c/Y8ZzH7M9X0VSDsgCUVu9tySjkRCpdnuKizAHKAGlviLV41fde/L2iuXsLi4iGIlggIDHw+19f4mvCqpuiYgkm0bNszn1/JOZPeVTiguCQGyU2Z/m5+zrznA4utS0aNbX3HbmvWBiM40i4QgT/nQe59xw8DWkUvcpCZFq17ReBhk+H8WFZdcouIyhR4sch6Kq2xqnpzPtggv556KF/GfdWppn1OeSbt3p3lz/3yJSdwSLQyye9TXhUITO/Y7j+id/Rcv2LXjrsWkU7C6gc7/juPz+cTRp2cjpUFNOUUExt424l8J9ZUsl//MPU+jc7zjadzvKociSlQUbPfjT6hAlIVLtXMZwW99TmThzesliaZcxpHm8/LZ3H4ejq7sapqVzQ+8+3KD/YxGpg778ZCm3nXkvNr6YNxKKcP1TVzDmphGMuWmEs8EJ86YtTDgLIlQc4oNnZysJESUhUjOGHXMsTdPr8cT8z1m3exd5LVpwVY8TaZOV7XRoIiJSyxTuK+TW0++haH9xme0PX/Y3OvZqT4t2zRyKLHVYa1n44Vf85/U5eANeThvfj6O7tC15PFgUKkkQS4tGLUWH2UiyzlN1LJHq0atlK3q1bOV0GCIiUstYazEmdlW9cF8h1/b5fbkEBGJrDmY8/zHj7xhd0yGmFGstk8Y9yv+mzqNofzEul+G9p2Yy/o+jGfXb4QB0G3gCkXCk3GsD9fyccnbvmg5ZkpCqY4mIiEhS+vdTMxidczmnuc9lbNtfM/uVT3no8if5blnikrvhUIR9O/fXcJSpZ+FHX5ckIBAb3SguCPKPP0wpqYCV3bQBl903Fn+aD5c79nEzUM9PzyHd6DG4i1OhJy9Vxzo0xpj7gWFAEFgFXGyt3VUFcYmIiEgKe+dv03ny/z1PcUHsg+6W77bywIQnCIfCRMOJF/AGMgL0HpZXk2GmpP++OTfhSJTb7WL+9EUMuuhUAEZcPZROp+Qy47mPKdpfRJ+Rvcg7rXPJqJaktspOx5oB3GytDRtj7gVuBm6qfFjiJGstn3y3lpeXfElRKMzwDscy7Jhj8aq0q4iI1ABrLc/e/q+SBOQHxYVBDlDxHYDuAzrRtX+nao5OfhjdiEbKJoPGZfAFfGW2tevchnYPtqnB6GoxrQmpOGvtB6XuzgHOqVw4kgwmffoJL3y5mMJwrOnTvE0beGPZUp4dcTbuBA3wREREqlIoGGbP9r2JHzzA57Tckzpw22v/T1fZa8BpF/blnSemx5LCUmzU0uv0bg5FVQekWBJSlZ8oJwDTDvSgMeZyY8x8Y8z8rVu3VuFhpSqt372b5xYvLElAINbZfNGWfGavXeNgZCIikiq8Pg9ZTTITPtakVWP86T5crliy4fF5yMiqx8TnrsGlC2U1om2n1kz4v/Px+r2kZQRIqx8gUM/P7a//jvT6aU6HJ7XEQUdCjDEzgUS17m611k6NP+dWIAy8eKD9WGsnA5MB8vLyUivVq0U+27AOl3EBZStaFIRCfLhmFf2PaudMYCIikjKMMVx01xieuO6fZaZk+dN9XP2XCTRr05RXH3ybDSs2cdzJx3LO9WfQOEcNCWvSWb85nVNH92H+9MX4Al56Du1KWoYSkMNnU24k5KBJiLV2wM89boy5CDgD6G8TFYSWWiXTH8CVYCjb43KRnaY3FxERqRlDLx2A1+/ln3+YwraNO2h+1BFcdu9YThreA4Cbnr3G4Qgl+4gsBl7Y1+kwpJaqbHWswcCNQF9rbUHVhCROOrVNW9yuxEnIObnHOxCRiIikqoHj+jJwnD7kSgqwQDRx1be6qrKTJx8D6gMzjDGLjDF/q4KYxEF+j4fnRpxDo7R0Mrw+Mnw+0j1e7hswiLbqbi4iIiIiVaCy1bGOrqpAJHmccEQz5lzyKxbkb6I4EiaveQ5pXq/TYYmIiIjUXSm2qqGyfUKkjnK7XPTMael0GFLKnuJi/vTJLN75ZjnhaJQ+R7bmrn4DaNWggdOhiYiIiBwS1bITqQWstYx981WmrlhOcSRCxFr+u+47Rv7rRfYUl+9aKyIiIrWMtdV7SzJKQkRqgfn5G1m9cweh6I+lk6PWUhgK8cayJQ5GJiIiInLoNB1LpBZYtWMHiSpgF4bDLNum5p8iIiK1m4Vo8o1WVCclIVJnFIfDPDL3M/619CuKwxFObdOWm0/uS/P69Z0OrdKObtgIk6B/S5rHQ26Tpg5EJCIiInL4lIRInXHZO28xb9MGiiOxKUvTVn7DnI3rmTluApl+v8PRVU735i1ol92QFdu3EYx/fy5jSPN6OevYXIejExERkUqxYK36hIjUOsu2fs+C/I0lCQhAxFr2B4N1Ys2EMYYXRo5iRIeOBDwePC4XfVu34c1zL6B+LU+wREREJPVoJETqhGXbtuJKMF2pMBxm4eZ8Lqr5kKpcfb+fSQMGMWnAIKdDERERkaqWYmtCNBIidULrrCwS/er63W6OadioxuMRERERkQNTEiJ1QrdmLWjTIAuvq+yPtNft5tzjOzkUlYiIiEgFqU+ISO1jjOGFs0Yx4Kh2eF0u3MZwQtNmvHLOGJqk13M6PBEREREpRWtCpM7ICqTx+NDhBCMRojZKwON1OiQRERGRg7MWoqlVHUtJiNQ5PrcbcDsdhoiIiIgcgJIQERERERGnJeG6jeqkNSEiIiIiIlKjNBIiIiIiIuIwqzUhIiIiIiJSc5KzjG510nQsERERERGpURoJERERERFxkgWiGgkRERERERGpNhoJERERERFxmk2thekaCRERERERkRqlkRAREREREQdZwGpNiIiIiIiISPXRSIiIiIiIiJOs1ZoQERERERGR6qQkRERERETEYTZqq/V2MMaYwcaYFcaYlcaYiQke9xtjXok/PtcY06bUYzfHt68wxgyqyPerJEREREREJIUZY9zA48AQIBc4zxiT+5OnXQLstNYeDTwM3Bt/bS4wBjgOGAw8Ed/fz1ISIiIiIiLiNBut3tvP6wmstNauttYGgSnAmT95zpnAs/GvXwP6G2NMfPsUa22xtXYNsDK+v5+lJEREREREJLXlAOtL3d8Q35bwOdbaMLAbaFTB15bjSHWsBQsWbDPGfOfEsZNMY2Cb00FIGTonyUfnJDnpvCQfnZPko3OSHFo7HcDB7GXn9Jn2tcbVfJiAMWZ+qfuTrbWTq/mYB+RIEmKtbeLEcZONMWa+tTbP6TjkRzonyUfnJDnpvCQfnZPko3MiFWWtHexwCBuBVqXut4xvS/ScDcYYD9AA2F7B15aj6VgiIiIiIqltHtDeGNPWGOMjttD87Z88521gfPzrc4CPrLU2vn1MvHpWW6A98PnBDqhmhSIiIiIiKcxaGzbGXA1MB9zAM9baJcaYO4H51tq3gb8DzxtjVgI7iCUqxJ/3L2ApEAaustZGDnZMJSHOcmwenhyQzkny0TlJTjovyUfnJPnonEitYa19D3jvJ9tuK/V1ETDqAK+9G7j7UI5nYqMoIiIiIiIiNUNrQkREREREpEYpCXGQMeZ+Y8xyY8yXxpg3jTFZTseUyowxg40xK4wxK40xE52OJ9UZY1oZY2YZY5YaY5YYY651OiaJMca4jTELjTHvOh2LxBhjsowxr8X/piwzxvR2OqZUZ4y5Pv7e9bUx5mVjTMDpmESSiZIQZ80AjrfWngB8A9zscDwpyxjjBh4HhgC5wHnGmFxno0p5YeC31tpc4ETgKp2TpHEtsMzpIKSMR4D3rbXHAp3R+XGUMSYH+A2QZ609nthC3zHORiWSXJSEOMha+0G84yTAHGJ1lcUZPYGV1trV1togMAU40+GYUpq1Nt9a+0X8673EPlQdtAOrVC9jTEvgdOBpp2ORGGNMA+AXxCrXYK0NWmt3ORqUQKz4T1q8n0I6sMnheESSipKQ5DEBmOZ0ECksB1hf6v4G9IE3aRhj2gBdgbkOhyLwZ+BGIOpwHPKjtsBW4B/xaXJPG2PqOR1UKrPWbgQeANYB+cBua+0HzkYlklyUhFQzY8zM+HzQn97OLPWcW4lNPXnRuUhFkpMxJgN4HbjOWrvH6XhSmTHmDOB7a+0Cp2ORMjxAN+Cv1tquwH5A69ocZIzJJjaa3hZoAdQzxox1NiqR5KI+IdXMWjvg5x43xlwEnAH0t6qX7KSNQKtS91vGt4mDjDFeYgnIi9baN5yOR+gDDDfGDAUCQKYx5gVrrT5cOWsDsMFa+8NI4WsoCXHaAGCNtXYrgDHmDeAk4AVHoxJJIhoJcZAxZjCxaQ3DrbUFTseT4uYB7Y0xbY0xPmILCN92OKaUZowxxOa4L7PWPuR0PALW2puttS2ttW2I/Y58pATEedbazcB6Y0yH+Kb+xDoXi3PWAScaY9Lj72X9UbEAkTI0EuKsxwA/MCP2HsUca+0VzoaUmqy1YWPM1cB0YlVMnrHWLnE4rFTXBxgHfGWMWRTfdku8o6uIlHUN8GL8Ispq4GKH40lp1tq5xpjXgC+ITbdeiLqni5ShjukiIiIiIlKjNB1LRERERERqlJIQERERERGpUUpCRERERESkRikJERERERGRGqUkREREREREapSSEBERERERqVFKQkREREREpEYpCRERERERkRr1/wFch42u9Wt3pgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# This line configures matplotlib to show figures embedded in the notebook, \n", "# instead of opening a new window for each figure. More about that later. \n", "# If you are using an old version of IPython, try using '%pylab inline' instead.\n", "%matplotlib inline\n", "\n", "# import librarys\n", "import numpy as np\n", "from sklearn.datasets import make_blobs\n", "import matplotlib.pyplot as plt\n", "import random\n", "\n", "# 生成数据\n", "centers = [(7, 0), (0, 0), (5, 5)]\n", "n_samples = 500\n", "\n", "X, y = make_blobs(n_samples=n_samples, n_features=2, \n", " cluster_std=1.0, centers=centers, \n", " shuffle=True, random_state=42)\n", "\n", "# 画出数据\n", "plt.figure(figsize=(15, 9))\n", "plt.scatter(X[:, 0], X[:, 1], c=y)\n", "plt.colorbar()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# k-means\n", "\n", "def calc_distance(v1, v2):\n", " \"\"\"\n", " 计算两个向量的距离\n", " \n", " v1 - 特征1\n", " v2 - 特征2\n", " \"\"\"\n", " return np.sum(np.square(v1-v2))\n", "\n", "def rand_cluster_cents(X, k):\n", " \"\"\"\n", " 初始化聚类中心:通过在区间范围随机产生的值作为新的中心点\n", " \n", " X - 数据样本\n", " k - 聚类个数\n", " \"\"\"\n", "\n", " # 样本数\n", " n=np.shape(X)[0]\n", " \n", " # 生成随机下标列表\n", " dataIndex=list(range(n))\n", " random.shuffle(dataIndex)\n", " centroidsIndex = dataIndex[:k]\n", " \n", " # 返回随机的聚类中心\n", " return X[centroidsIndex, :]\n", "\n", "def kmeans(X, k):\n", " \"\"\"\n", " kMeans算法\n", " \n", " X - 数据样本\n", " k - 聚类个数\n", " \"\"\"\n", " # 样本总数\n", " n = np.shape(X)[0]\n", " \n", " # 分配样本到最近的簇:存[簇序号,距离的平方] (n行 x 2列)\n", " clusterAssment = np.zeros((n, 2))\n", "\n", " # step1: 通过随机产生的样本点初始化聚类中心\n", " centroids = rand_cluster_cents(X, k)\n", " print('最初的中心=', centroids)\n", "\n", " iterN = 0\n", " \n", " while True: \n", " clusterChanged = False\n", " \n", " # step2:分配到最近的聚类中心对应的簇中\n", " for i in range(n):\n", " minDist = np.inf;\n", " minIndex = -1\n", " for j in range(k):\n", " # 计算第i个样本到第j个中心点的距离\n", " distJI = calc_distance(centroids[j, :], X[i, :])\n", " if distJI < minDist:\n", " minDist = distJI\n", " minIndex = j\n", " \n", " # 样本上次分配结果跟本次不一样,标志位clusterChanged置True\n", " if clusterAssment[i, 0] != minIndex:\n", " clusterChanged = True\n", " clusterAssment[i, :] = minIndex, minDist ** 2 # 分配样本到最近的簇\n", " \n", " iterN += 1\n", " sse = sum(clusterAssment[:, 1])\n", " print('the SSE of %d' % iterN + 'th iteration is %f' % sse)\n", " \n", " # step3:更新聚类中心\n", " for cent in range(k): # 样本分配结束后,重新计算聚类中心\n", " ptsInClust = X[clusterAssment[:, 0] == cent, :]\n", " centroids[cent, :] = np.mean(ptsInClust, axis=0)\n", " \n", " # 如果聚类重心没有发生改变,则退出迭代\n", " if not clusterChanged:\n", " break\n", " \n", " return centroids, clusterAssment\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "最初的中心= [[ 4.55381657 3.11045927]\n", " [ 2.5733598 0.05921843]\n", " [-0.1580079 -0.42688107]]\n", "the SSE of 1th iteration is 63997.694980\n", "the SSE of 2th iteration is 20276.698293\n", "the SSE of 3th iteration is 4446.593824\n", "the SSE of 4th iteration is 3500.485900\n", "the SSE of 5th iteration is 3502.239035\n" ] } ], "source": [ "# 进行k-means聚类\n", "k = 3 # 用户定义聚类数\n", "mycentroids, clusterAssment = kmeans(X, k)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def datashow(dataSet, k, centroids, clusterAssment): # 二维空间显示聚类结果\n", " from matplotlib import pyplot as plt\n", " num, dim = np.shape(dataSet) # 样本数num ,维数dim\n", "\n", " if dim != 2:\n", " print('sorry,the dimension of your dataset is not 2!')\n", " return 1\n", " marksamples = ['or', 'ob', 'og', 'ok', '^r', '^b', ' len(marksamples):\n", " print('sorry,your k is too large,please add length of the marksample!')\n", " return 1\n", " # 绘所有样本\n", " for i in range(num):\n", " markindex = int(clusterAssment[i, 0]) # 矩阵形式转为int值, 簇序号\n", " # 特征维对应坐标轴x,y;样本图形标记及大小\n", " plt.plot(dataSet[i, 0], dataSet[i, 1], marksamples[markindex], markersize=6)\n", "\n", " # 绘中心点\n", " markcentroids = ['o', '*', '^'] # 聚类中心图形标记\n", " label = ['0', '1', '2']\n", " c = ['yellow', 'pink', 'red']\n", " for i in range(k):\n", " plt.plot(centroids[i, 0], centroids[i, 1], markcentroids[i], markersize=15, label=label[i], c=c[i])\n", " plt.legend(loc='upper left') #图例\n", " plt.xlabel('feature 1')\n", " plt.ylabel('feature 2')\n", "\n", " plt.title('k-means cluster result') # 标题\n", " plt.show()\n", " \n", " \n", "# 画出实际图像\n", "def trgartshow(dataSet, k, labels):\n", " from matplotlib import pyplot as plt\n", "\n", " num, dim = np.shape(dataSet)\n", " label = ['0', '1', '2']\n", " marksamples = ['ob', 'or', 'og', 'ok', '^r', '^b', '" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import load_digits\n", "import matplotlib.pyplot as plt \n", "from sklearn.cluster import KMeans\n", "\n", "# load digital data\n", "digits, dig_label = load_digits(return_X_y=True)\n", "\n", "# draw one digital\n", "plt.gray() \n", "plt.matshow(digits[0].reshape([8, 8])) \n", "plt.show() \n", "\n", "# calculate train/test data number\n", "N = len(digits)\n", "N_train = int(N*0.8)\n", "N_test = N - N_train\n", "\n", "# split train/test data\n", "x_train = digits[:N_train, :]\n", "y_train = dig_label[:N_train]\n", "x_test = digits[N_train:, :]\n", "y_test = dig_label[N_train:]\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# do kmeans\n", "kmeans = KMeans(n_clusters=10, random_state=0).fit(x_train)\n", "\n", "# kmeans.labels_ - output label\n", "# kmeans.cluster_centers_ - cluster centers\n", "\n", "# draw cluster centers\n", "fig, axes = plt.subplots(nrows=1, ncols=10)\n", "for i in range(10):\n", " img = kmeans.cluster_centers_[i].reshape(8, 8)\n", " axes[i].imshow(img)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6. 深入思考\n", "\n", "1. 如何计算聚类的精度?\n", "2. 如何匹配聚类的类别和真实类别?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7. 评估聚类性能\n", "\n", "### 7.1 方法1 - ARI\n", "\n", "如果被用来评估的数据本身带有正确的类别信息,则利用Adjusted Rand Index(ARI)对聚类结果进行评估,ARI与分类问题中计算准确性的方法类似,兼顾了类簇无法和分类标记一一对应的问题。\n", "\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ari_train = 0.687021\n" ] } ], "source": [ "from sklearn.metrics import adjusted_rand_score\n", "\n", "ari_train = adjusted_rand_score(y_train, kmeans.labels_)\n", "print(\"ari_train = %f\" % ari_train)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "contingency表的定义:\n", "\n", "![ARI_ct](images/ARI_ct.png)\n", "其中$X$为真实类别,$Y$为聚类的簇\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 7.1.1 RI\n", "为了方便理解ARI,先讨论一下RI,也就是rand index,是ARI的基础方法。\n", "\n", "假如有两类,那么针对这两类的的RI评价指标为:\n", "\n", "$$\n", "R = \\frac{a + b}{a+b+c+d}\n", "$$\n", "\n", "a,b,c,d分别代表的含义为:\n", "* a : 应该在一类,最后聚类到一类的数量,\n", "* b : 不应该在一类,最后聚类结果也没把他们聚类在一起的数量。\n", "* c和d那么就是应该在一起而被分开的和不应该在一起而被迫在一起的。毕竟强扭的瓜不甜,c和d固然是错误的。\n", "\n", "所以从R的表达式中可以看出,a和b是对的,这样能够保证R在0到1之间,而且,聚类越准确,指标越接近于1.\n", "\n", "这里有一个关键性的问题,就是什么叫数量?怎么去计算?准确的说,是配对的数量。比如说a是应该在一起而真的幸福的在一起了的数量,这显然就应该像人类一样按照小夫妻数量计算,但是我们的样本可不管一夫一妻制,任意选两个就是一个配对,所以,就是 $n(n-1)/2$ 这样来计算,也就是组合数,n个当中选两个的选法。同时我们看到,分母其实是所有配对的总和,所以,我们最后可以写成这样:\n", "\n", "$$\n", "R = \\frac{a + b}{a+b+c+d} = \\frac{a + b}{\\binom{n}{2}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 7.1.2 ARI\n", "\n", "有了先前RI的感性理解之后,接下来解释一下ARI。\n", "\n", "RI有一个缺点,就是惩罚力度不够,换句话说,大家普遍得分比较高,没什么区分度,遍地80分。这样的话,往往是考试的制度不合适,于是就诞生出了ARI,这个指标相对于RI就很有区分度了。\n", "\n", "$$\n", "ARI = \\frac{Index - ExpctedIndex}{MaxIndex - ExpectedIndex}\n", "$$\n", "\n", "具体的公式是:\n", "$$\n", "ARI = \\frac{ \\sum_{ij} \\binom{n_{ij}}{2} - \\left[ \\sum_i \\binom{a_i}{2} \\sum_j \\binom{b_j}{2} \\right] / \\binom{n}{2} }{ \\frac{1}{2} \\left[ \\sum_i \\binom{a_i}{2} + \\sum_j \\binom{b_j}{2} \\right] - \\left[ \\sum_i \\binom{a_i}{2} \\sum_j \\binom{b_j}{2} \\right] / \\binom{n}{2} }\n", "$$\n", "\n", "ARI取值范围为[-1,1],值越大越好,反映两种划分的重叠程度,使用该度量指标需要数据本身有类别标记。\n", "\n", "* $ \\sum_{ij} \\binom{n_{ij}}{2}$ : $n_{ij}$代表的是聚类之后在$i$类,应该在$j$类的样本数量,很显然,这一求和,就是RI中的a,应该在一起而真的在一起的数量。\n", "\n", "* $\\frac{1}{2} \\left[ \\sum_i \\binom{a_i}{2} + \\sum_j \\binom{b_j}{2} \\right]$ : 是如果聚类是完全对的,那么就应该是$a$, $b$的所有组合可能之和,所以在表达式里面叫做MaxIndex。\n", "\n", "* $\\left[ \\sum_i \\binom{a_i}{2} \\sum_j \\binom{b_j}{2} \\right] / \\binom{n}{2}$ 是a的期望\n", "$$\n", "E(\\sum_{ij} \\binom{n_{ij}}{2}) = \\sum_i \\binom{n_i}{2} \\sum_j \\binom{n_j}{2} / \\binom{n}{2}\n", "$$\n", "\n", "假设配对矩阵是这样的,共有n(n-1)/2个配对方法。在行方向计算出可能取到的配对数,在列方向计算可能取到的配对数,相乘以后,除以总的配对数,这就是a的期望了。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "* [ARI聚类效果评价指标](https://blog.csdn.net/qtlyx/article/details/52678895)\n", "* [ARI reference](https://davetang.org/muse/2017/09/21/adjusted-rand-index/)\n", "* [聚类性能评估-ARI(调兰德指数)](https://zhuanlan.zhihu.com/p/145856959)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### 7.2 方法2 - 轮廓系数\n", "如果被用来评估的数据没有所属类别,则使用轮廓系数(Silhouette Coefficient)来度量聚类结果的质量,评估聚类的效果。**轮廓系数同时兼顾了聚类的凝聚度和分离度,取值范围是[-1,1],轮廓系数越大,表示聚类效果越好。** \n", "\n", "轮廓系数的具体计算步骤: \n", "1. 对于已聚类数据中第i个样本$x_i$,计算$x_i$与其同一类簇内的所有其他样本距离的平均值,记作$a_i$,用于量化簇内的凝聚度 \n", "2. 选取$x_i$外的一个簇$b$,计算$x_i$与簇$b$中所有样本的平均距离,遍历所有其他簇,找到最近的这个平均距离,记作$b_i$,用于量化簇之间分离度 \n", "3. 对于样本$x_i$,轮廓系数为$sc_i = \\frac{b_i−a_i}{max(b_i,a_i)}$ \n", "4. 最后,对所有样本集合$\\mathbf{X}$求出平均值,即为当前聚类结果的整体轮廓系数。" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from sklearn.cluster import KMeans\n", "from sklearn.metrics import silhouette_score\n", "import matplotlib.pyplot as plt\n", "\n", "plt.rcParams['figure.figsize']=(10,10)\n", "plt.subplot(3,2,1)\n", "\n", "x1=np.array([1,2,3,1,5,6,5,5,6,7,8,9,7,9]) #初始化原始数据\n", "x2=np.array([1,3,2,2,8,6,7,6,7,1,2,1,1,3])\n", "X=np.array(list(zip(x1,x2))).reshape(len(x1),2)\n", "\n", "plt.xlim([0,10])\n", "plt.ylim([0,10])\n", "plt.title('Instances')\n", "plt.scatter(x1,x2)\n", "\n", "colors=['b','g','r','c','m','y','k','b']\n", "markers=['o','s','D','v','^','p','*','+']\n", "\n", "clusters=[2,3,4,5,8]\n", "subplot_counter=1\n", "sc_scores=[]\n", "for t in clusters:\n", " subplot_counter +=1\n", " plt.subplot(3,2,subplot_counter)\n", " kmeans_model=KMeans(n_clusters=t).fit(X) #KMeans建模\n", "\n", " for i,l in enumerate(kmeans_model.labels_):\n", " plt.plot(x1[i],x2[i],color=colors[l],marker=markers[l],ls='None')\n", "\n", " plt.xlim([0,10])\n", " plt.ylim([0,10])\n", "\n", " sc_score=silhouette_score(X,kmeans_model.labels_,metric='euclidean') #计算轮廓系数\n", " sc_scores.append(sc_score)\n", "\n", " plt.title('k=%s,silhouette coefficient=%0.03f'%(t,sc_score))\n", "\n", "plt.figure()\n", "plt.plot(clusters,sc_scores,'*-') #绘制类簇数量与对应轮廓系数关系\n", "plt.xlabel('Number of Clusters')\n", "plt.ylabel('Silhouette Coefficient Score')\n", "\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8. 如何确定K\n", "\n", "利用“肘部观察法”可以粗略地估计相对合理的聚类个数。K-means模型最终期望*所有数据点到其所属的类簇距离的平方和趋于稳定,所以可以通过观察这个值随着K的走势来找出最佳的类簇数量。理想条件下,这个折线在不断下降并且趋于平缓的过程中会有斜率的拐点,这表示从这个拐点对应的K值开始,类簇中心的增加不会过于破坏数据聚类的结构*。\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from sklearn.cluster import KMeans\n", "from scipy.spatial.distance import cdist\n", "import matplotlib.pyplot as plt\n", "\n", "cluster1=np.random.uniform(0.5,1.5,(2,10))\n", "cluster2=np.random.uniform(5.5,6.5,(2,10))\n", "cluster3=np.random.uniform(3,4,(2,10))\n", "\n", "X=np.hstack((cluster1,cluster2,cluster3)).T\n", "plt.scatter(X[:,0],X[:,1])\n", "plt.xlabel('x1')\n", "plt.ylabel('x2')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "K=range(1,10)\n", "meandistortions=[]\n", "\n", "for k in K:\n", " kmeans=KMeans(n_clusters=k)\n", " kmeans.fit(X)\n", " meandistortions.append(\\\n", " sum(np.min(cdist(X,kmeans.cluster_centers_,'euclidean'),axis=1))/X.shape[0])\n", "\n", "plt.plot(K,meandistortions,'bx-')\n", "plt.xlabel('k')\n", "plt.ylabel('Average Dispersion')\n", "plt.title('Selecting k with the Elbow Method')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "从上图可见,类簇数量从1降到2再降到3的过程,更改K值让整体聚类结构有很大改变,这意味着新的聚类数量让算法有更大的收敛空间,这样的K值不能反映真实的类簇数量。而当K=3以后再增大K,平均距离的下降速度显著变缓慢,这意味着进一步增加K值不再会有利于算法的收敛,同时也暗示着K=3是相对最佳的类簇数量。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考资料\n", "* [机器学习聚类算法之K-Means](https://www.biaodianfu.com/k-means.html)" ] } ], "metadata": { "jupytext_formats": "ipynb,py", "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 }