{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "path_data = '../../data/'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "from scipy import stats\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "plt.style.use('fivethirtyeight')\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# HIDDEN \n", "\n", "galton = pd.read_csv(path_data + 'galton.csv')\n", "heights = galton[['midparentHeight', 'childHeight']]\n", "\n", "heights = heights.rename(columns={'midparentHeight':'MidParent', 'childHeight':'Child'})\n", "\n", "hybrid = pd.read_csv(path_data + 'hybrid.csv')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "def standard_units(x):\n", " return (x - np.mean(x))/np.std(x)\n", "\n", "def correlation(table, x, y):\n", " x_in_standard_units = standard_units(table[x])\n", " y_in_standard_units = standard_units(table[y])\n", " return np.mean(x_in_standard_units * y_in_standard_units)\n", "\n", "def slope(table, x, y):\n", " r = correlation(table, x, y)\n", " return r * np.std(table[y])/np.std(table[x])\n", "\n", "def intercept(table, x, y):\n", " a = slope(table, x, y)\n", " return np.mean(table[y]) - a * np.mean(table[x])\n", "\n", "def fit(table, x, y):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * table[x] + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Visual Diagnostics\n", "Suppose a data scientist has decided to use linear regression to estimate values of one variable (called the response variable) based on another variable (called the predictor). To see how well this method of estimation performs, the data scientist must measure how far off the estimates are from the actual values. These differences are called *residuals*.\n", "\n", "$$\n", "\\mbox{residual} ~=~ \\mbox{observed value} ~-~ \\mbox{regression estimate}\n", "$$\n", "\n", "A residual is what's left over – the residue – after estimation. \n", "\n", "Residuals are the vertical distances of the points from the regression line. There is one residual for each point in the scatter plot. The residual is the difference between the observed value of $y$ and the fitted value of $y$, so for the point $(x, y)$,\n", "\n", "$$\n", "\\mbox{residual} ~~ = ~~ y ~-~\n", "\\mbox{fitted value of }y\n", "~~ = ~~ y ~-~\n", "\\mbox{height of regression line at }x\n", "$$\n", "\n", "The function `residual` calculates the residuals. The calculation assumes all the relevant functions we have already defined: `standard_units`, `correlation`, `slope`, `intercept`, and `fit`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def residual(table, x, y):\n", " return table[y] - fit(table, x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Continuing our example of using Galton's data to estimate the heights of adult children (the response) based on the midparent height (the predictor), let us calculate the fitted values and the residuals." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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MidParentChildFitted VlaueResidual
075.4373.270.7123732.487627
175.4369.270.712373-1.512373
275.4369.070.712373-1.712373
375.4369.070.712373-1.712373
473.6673.569.5842443.915756
...............
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934 rows × 4 columns

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" ], "text/plain": [ " MidParent Child Fitted Vlaue Residual\n", "0 75.43 73.2 70.712373 2.487627\n", "1 75.43 69.2 70.712373 -1.512373\n", "2 75.43 69.0 70.712373 -1.712373\n", "3 75.43 69.0 70.712373 -1.712373\n", "4 73.66 73.5 69.584244 3.915756\n", ".. ... ... ... ...\n", "929 66.64 64.0 65.109971 -1.109971\n", "930 66.64 62.0 65.109971 -3.109971\n", "931 66.64 61.0 65.109971 -4.109971\n", "932 65.27 66.5 64.236786 2.263214\n", "933 65.27 57.0 64.236786 -7.236786\n", "\n", "[934 rows x 4 columns]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "heights['Fitted Vlaue'] = fit(heights, 'MidParent', 'Child')\n", "\n", "heights['Residual'] = residual(heights, 'MidParent', 'Child')\n", "\n", "heights" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When there are so many variables to work with, it is always helpful to start with visualization. The function `scatter_fit` draws the scatter plot of the data, as well as the regression line. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def scatter_fit(table, x, y):\n", " \n", " fig, ax = plt.subplots(figsize=(7,6))\n", "\n", " ax.scatter(table[x], \n", " table[y], \n", "\n", " color='darkblue')\n", "\n", " ax.plot(table[x], fit(table, x, y), lw=4, color='gold')\n", "\n", " x_label = x\n", "\n", " y_label = y\n", "\n", " y_vals = ax.get_yticks()\n", "\n", " plt.ylabel(y_label)\n", "\n", "\n", " plt.xlabel(x_label)\n", "\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter_fit(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A *residual plot* can be drawn by plotting the residuals against the predictor variable. The function `residual_plot` does just that. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def residual_plot(table, x, y):\n", " \n", " fig, ax = plt.subplots(figsize=(7,6))\n", " \n", " x_array = table[x]\n", " \n", " t = pd.DataFrame({x:x_array, 'residuals':residual(table, x, y)})\n", "\n", " ax.scatter(t[x], t['residuals'], color='r')\n", " \n", " xlims = np.array([min(x_array), max(x_array)])\n", " \n", " ax.plot(xlims, np.array([0, 0]), color='darkblue', lw=4)\n", "\n", " x_label = x\n", "\n", " y_label = y\n", "\n", " y_vals = ax.get_yticks()\n", "\n", " plt.ylabel(y_label)\n", "\n", "\n", " plt.xlabel(x_label)\n", " \n", " plt.title('Residual Plot')\n", "\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "residual_plot(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The midparent heights are on the horizontal axis, as in the original scatter plot. But now the vertical axis shows the residuals. Notice that the plot appears to be centered around the horizontal line at the level 0 (shown in dark blue). Notice also that the plot shows no upward or downward trend. We will observe later that this is true of all regressions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regression Diagnostics\n", "Residual plots help us make visual assessments of the quality of a linear regression analysis. Such assessments are called *diagnostics*. The function ``regression_diagnostic_plots`` draws the original scatter plot as well as the residual plot for ease of comparison." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def regression_diagnostic_plots(table, x, y):\n", " scatter_fit(table, x, y)\n", " residual_plot(table, x, y)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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+QpucdEbY1uCrqpoxdepOGgM+htbACaKDkJ7O/KJkOy4Xq1efJSWqTgrXGjyNAd9DDpwgOggWC3MwkdXKHWTkLVVVzClCpETV8bFHX+t04Yy/0xjwLeTACaKDoNRmEjodc4oQKVF1DpKTYzF2bG/G32gM+BZy4ATRQVBqM4k5c1JJba2TQ4p7ykBBbATRQVBK9ax37whSW+vkkOKeMpADJwShpOqVEghRI8vPv4CcnH2orW1xqC4lJkZ79BMAzmNtbVb8+GMVzGYrwsK0WLEiC9On92O0x17G0KE6LF5ciJYWM7RaNW64QYeQELXLvWG6Z2VlJg+bmdTCxKirPfhgD6Smtv9WU9OMo0ersHOnAd26sauRsdkZGxsCm82G+nqzy/+722Pv+8rKBlb1MzFtEjIWAn3sK22nfSMTwn9QHngnR0j/MCkepabGdtgUESHtzc+/gLvv3gGz+erjo1YD8fGRLoE7iYlRAICysgbOY+6sW3erw4kz2cNFamos3n47C088sd/lmoSESFRWNsJqvXquVqtiVQtjusdMtiQkhEGr1TK2h698Jju52rV58wSUlZk8+t69vlGjeskybuUowx/voGB+RukdLR1aAyd4UVL1SgmEtDcnZ5+HA7FaPaNuy8oaPBwb0zF35s7dz2kPF2fPGpGTs8/jmvJyV+cNcKuFCVVXKy9vYW0PX/lMdnK1Ky+vkLHv3etjs1XsuA2WsR8sdhLyQg6c4EVJ1SslENLe2lrfqiu1tFzdElWM8pcdMepPXGphQtXVpJYvVqWqvLyRt+/tZcoxboNl7AeLnYS8kAMneFEqPUkphLQ3Ls636kphYVfDU8Qof9kRo/7EpRYmVF1NavliVaoSEiJ5+95ephzjNljGfrDYScgLOXCCl86WIiKkvatWjfFQYVKrPV+YiYlRjjVvrmPurFiRxWkPF4mJUVcC6rjrALjVwoSqqyUkhHHWtXDhMNbyV60aI7htdnuY+t69PWy2ih23wTL2g8VOQl4oiK2TI7R/fKmoFYgIUSOzR0LX1bU4VJfsUejO/QSA81hrq/AodHsZQ4fqsGBBASwWz8d3woQ++PTT8Xjgga+wc+c5j9/ZlKKkqqu1R6GnYPLk7SgtNXmcP2NGX6xdextr+c7HY2LaI89NJrPL/7vbY+/7qqoGVvUzMW3iwtsy/PUOCtZnlN7R0iEH3smRq3/cJQ11ugikpcWySjgGekqOnUBW2uJSgurfvytOnbqMqqpmj9/DwtQIC9N4pJFJxT6G2OzJyuqJrVsneVWHL/DXWKR3EDfUP9KhPHDCa5hSWEpLTTh6tMpFlYrpvEBXrQpkpS0uJaiqKk9HaqelxYqWFiuMxjbcffcOR9qVt8TEML9OoqMD7zUTjGORINyhNXDCa7jSnJxTWYIx1SWQlbbEro0z4Zx25S0qFfO6NNtxJQnGsUgQ7pADJ7yGL7XInsoSjKkugay0Zd++csaMvsjK6smqCMWH2FQuNpi0yAGgvp75uJIE41gkCHcCb26LCDr4UovskdnBkOrivi4aFcX8iEixmWnrVW+nrp23r8zO3o0NG86ILkNsKhcbwXB/7QSTrQTBBn2BE17DNZXrnMoS6Kku9nXRDRvO4MCBi9iw4QxOnar3SJGSYrN969XSUhOMxjaUlrZvB5qff0E2+5n6ly3dyvl3e9qVt8ycmeFRn1arwsyZGbKULyeBPhYJQgj0BU54jbMSUUlJPSoqGhEfH+F4IdqDggJdsYhpXbSiohUTJuhx880JXtnMtP2nff352LEHvLYdYO7fmTMzsH79Sce/x49PwqJFR1xS3+QIYAOA9etPMrZx/fqTstUhF4E+FglCCJRG1snxV//4YvrYW9yny4uLjTh6tMrjPJUKGDOmF958M8vjBe9eht1huqcmJSWtZ1wj7tIlBAbDTM4y2RTN2BTH3M91t8muZNbUZIZarUK/fl0waFB3jzKLi42oqmpi/GPMGXuq3R13bGFMW3NPI8vPv4CHHvoGNTXta+9hYWr8859jMH16P1ZlMvc0L6EpYFLGndzpZXv3HsPHH1cz3iO2PhZqd7ClZTJB72jpkAPv5Pijf5iUu5xVo5SAKY0oKkqLhgYz6zUJCZHYtWuyixNxL0OrVbm0064INWHCVly44Bkg1atXJH799UFOu5jUy9iUvJjOdbeJDT51MDZ1q717j+EvfznBmolg31gGaB8LkyZth43BnGXLRmDNml9Zy7HXD0CQ8paUcSe3qpfBYMTEiVtQVnb1DxsuNbp2Jz4Ujz++l9fuYFYgc4be0dKhNXDC53BNHysF03R5Q4OZNWgNaI9Qdk4zYirDvZ321KT0dOYXqvtxpjKZ1MvYlLyYzhXivLnKdG+LO0ypds44p5Hl5OxjdN4AsGBBAWc59vqFpoBJGXdyp5fl5RW6OG+AW43u7Fkj5s7dL8huSoUjyIETPodNPUqu9CUpsKURXXddN87AL+c0I6HKXOXljbBYmMu0Wl2Pi1H78kX/8ZXJlGbFlmpnxzmNjEtJjGlbWKb6haaASRl3cqeXSVFvc1aic8bdbkqFI8iBEz6HTT1KrvQlKbClEZWUGBEaqmG9zjnNSKgyV0JCpE/UviIjQwSfKxS+e8KUZqXTCb+GS0lMo+Hf8EVMX0oZd3Knl0lRb3NWonPG3W5KhQtA2KaXfAQ5cMLnMKlHyZm+JAW21LeqqmY0NjJ/ATkLkbCV4d5Oe2CSN2pfiYlR0Os9N2lpbTV7OD2NRsV4rhC0WhUWLhwmKCXQmTlzUgVfs2rVGLBtzLZkyXDOneXE9qWUcSd3ellubiYSE13vB5caXWpqLFasyBJkN6XCBQDWWmibv0K48QVEVd+OiLo5fq2egtg6Of6OQvdF+pJU7BG8e/eeZ4yeDg/XwGy2QqNR4eabEzij0NnStpgip8WqfeXmZuK55w5hx45SQe26664kREWFsLZr8ODu+PnnGsYp6xkz+iI3N9NFmEavj0RKSgxvFLrQa4REobsrk0ntSynjTm5VL3sUOpMaHVt/CbU7WBXInAmmd7TKUg1N60FoW/OhbT0ItflnqHD1ObKqE1AffwKsf6XKDOWBE7LAl84yalQvj3xnpVNg7LuYTZq0jVH8Y+DA7ujeHTCZNNDpIjjLcIbNQTCd6wxX6tCZM+zBXe6UltbjwIF7cPvtmxkdeGxsKG6+OYFROay8vJHXTjsbN57G3Ln70dxsRkiIGjfcoEN4uBbDh+t576VWq3a842JjQxzTvs51O/eHwRCGsjKTy54CfDYaDEasX38SSUkx6NlT7/jjaunS7znHm3vZBoMR2dm7vR6nzrOrfPYnJkZj+HC9o87ExGjG8/jKUeIZU/q5lhOV5SK0rQehueKwNeaTnOerreVQW87Cqk3zi33kwAmvkaLsFEhqUGxrib/+WuOSVuZL+9xTnpyVwsrLG3HqVK3gsn755TI2bjyNkycvM/7OtUYqdP1048bTeOyxPY5/t7RYUVBQ4fg3W1/l51/AlCk7XL7+q6paMHHidmzfPtHxBwtXfwiZuWEaX198UewS3S3kfno7Tg0GI5544ieXSHR/PRtKPGOB9FyLxmaDylLq+LrWtOZDYzkruhhN249+c+C0Bk54jZR0lkBKgWFaS2TKCfelfVwpT3Pn7me9jinwy2YD5s7dz5jTHhWlFbWOzAaXTQB7X+Xk7GONNndOk/I29VBMip/YcsSMA6Y0Mn89G0o8Y4H0XPNis0FtPo2QxvcRUTsbMZUDEVs1GJF1f0Jo00eCnbdFex1aIrPRELcexvjf0BYxzceGX4W+wAmvkZLOEkgpMEzbarLtyuYr+7hSntjSilQqICJCA5PJ83e2a667rpvjS8ibrUTZyneGqa+40sic06S8TT0Uk+InpRyh40DJZ0OJZyyQnmsPbFaozSdcpsTV1kpxRUANS8ggWEJHwRw6EpbQkbCpu/rIYH7IgRNeIyWdJRBSYLjW6rKzdzM6cF/ZFxcXxrLVahja2myMkfEREVp06xYOk8nk8VtYmJbxmpSUGMf/C13rZoKtfGfc+8pgMHJuKuOcJsXVH0IQk+InpRyh40DJZ0OJZywQnmsHNjPU5p+hbcmHtjUfmtZDUNuYl5VYi0AILCFDrjjrUTCH3gSoA2cpgKbQCa+RMh2rdAoMk/LY1Kk7YTAYFbGPK+VpxYosxmtWrMhivW7Fiiyf2s9mE1td9v7mcvrOaVLeph6KSfHjYvz4JFHHmexwTyPz17OhxDOm6HNta4Wm9TuEmV5HZM0MxFakIqZ6LCLqFyCkZYcg521DOMyht6A5+u8wddsCY4IBDT12oSV2IczhdwSU8wYUTCMbOHAgzp0753F83Lhx+Pe//w2bzYZly5bh/fffR21tLYYOHYrly5fj2muvFVVPMKUoKIFc/SMlnUXJFBg27ewZM/o6vkoNBiOefXYPGho0frGPK3XIHvHd0mJGWJgWK1ZkYfr0fpzX+bp/maLQQ0PVjHVxaZXrdGFYv/4Oj+A0b1MPxaT4sTFo0KcoLfWc4UhKihasIseURuavZ0OJZ0xsnZLfQbYmaFqPOgWdfQcVmsQVoYqCOWQ4LGFXpsRDhgAq5TaYEotiDry6uhoWi8Xx7/LycowdOxYrV67E73//e7zxxhtYvnw5Vq5cifT0dLzyyis4fPgwjhw5gpiYGI6SXSEHzg1b/4hJBZEjbcRgMOK55w7hyJH2NanMTB2WLRvpUo639Thff+rUZV7lrI0bT+PPf96HlhYrq2rXk0/uw+HDlbBYbIiPj8DatbciMTHaxc7x45OQm3sYVVXNjDnlTO0qKzO5pJT96U/X4803f/IoA4BHXYsWHXFJRXO2JzY2BGVlRvz8cy2sVte29+0bi2uu6YLz5xtw+rQRKpUN3btHeDhOu732HOaYGKBHj2gUFRlRU9OElhYb1GoVtNqrdv75z98ypq0NGxaPlJQYXjU3qeTnX8CsWbtZ+54J5/tx+HA547Q/k4ocG1zvoEBU6ROLt8+l4He01QRt23ftedgt+dC0HYUKraJstaliYQ69GebQW2AJHQlLyGBAFbwryQGzkcvy5cvx1ltv4eTJk4iIiEBGRgays7Mxb948AEBTUxPS09Px0ksv4dFHHxVcLjlwbpj6R4zKkRyKSO2KTds8BB4SE6Owffskh7P0ph6m65mwf4G7p0k5Y1ft+uMf/4uKCtc/AlQqQK+P5A3asSubAZ7KWnp9OKqrW3j3Bu/RIwzh4VpWYQygPUq9R48wDzvF4KyEJbQfnUlIiMSNN3bHzp2eM27u0f5sam5SnHh+/gVMnrzd4w8Vd1U5Z4S2T8wXONs7KBBV+sQix/PP+o621kLbevhqSlfbj1DB4nkeB1Z1D1hCR8IcOhLm0FGwaq8DVOxbJQcbAbEGbrPZ8OGHH+K+++5DZGQkDAYDKioqcNttVwNsIiIiMHLkSBQUFChoaedATCqIHGkj7ak2nk6orKzBUY4c6Tx8L2XntTquNCm7aheTU7TZhEXc2pXNmOyqqGgWJOxRXd3C6byBdoEQb5w34Jq+JaQf3Skvb4RKpRKUqicl1YuNnJx9Hs7bbg9bmULaJ9c2wIGo0icWOdPGVJZqaJu+RHjds4iuykJsRSqiLt+PsIa3oG07Ksh5W9U90Rp+D5pi/4H6HgWojy9CY9cP0Bo1B9aQgR3KeQMBEoW+Z88eGAwGPPTQQwCAior2DSF0Op3LeTqdDhcvek7DOVNUVCToGHEV9/4pLq5mPK+4+JJX57LBVoZzOd7Ww3Z9t24hSE2Ngk4XijlzUtHaWoGiogo0N3NHWNfUiFtrY7bpEoCAmADjpaamifM+8FFRYcTrr1+L1avPoqqqFTpdKM6da8Qvv3iuL7sjZiw5w3WP2Mpka19IiAphYWrExGixcGEG4uMbRNnEdC6bffa+Dga8eS5DVFWI1vyApLDvEVr2PSI04jdNabH2Qr3lRtRbhsBkGYIWW28AzsGKp0WXGUjwzR4HhAN///33MWTIEAwaNMjluMptP1mbzeZxzB33BtMUOjdM/ZOWdg5Hj9Z5nJuW1t2rc9lgK8O5HG/rYbv+9tuTGFOpwsMPcEZMd+sWwZi+JYaqKjMGDOgKgLntgUS3bhGc94GPtLTuGDt2EMaOvfqMZ2fvFuTAxYwlZ7p1K2S9R2xlsrVv6tQ0ySl3bO8gNvvsfR0MCH4uPXY5OwiNpVh0fRZNevuU+JWgM5smESEAul35r7Oh+BR6VVUVduzYgUceecRxTK/XAwAqK12T7Kurqz2+ygn5EZMKIkfaSHuqjac6U2JilKMcb+sRez1XmlRqaixWrRrDqPqlUgnPeS0tNeH48RqPtuv14YKkNYXU5Y06mR3nKWM2FTcu3FXc7MiV6sXGqlVjoGZ4w7HZw2aTr9KgAlGlTyzs/TWUZ5czYc7bdZezUzDFH0FT3Jtoi7gXNk2iL5oUVCgexPbmm2/i1VdfxYkTJxzR5TabDRkZGZg9ezb+9re/AQCam5uRnp6OxYsXUxCbjPBFoQtJBZEjVUVMFLrUesRe7x6Fnp7eBQMHCo9Ct9djj0IvL29ilAu2q4c522WPQrenUHXtGoKffvLMY50woQ+io0Nd6lq06IhL6pWzPTEx7FHoduLiQtHaaoVabUO3buxR6CUl9aioaERMjAo9ekShqMiIy5eb0NzsGYUudOxISfXiwh6FXl3dDLVaXBS6XDYIiUIPJJU+sRgMRixZ8h0i1EXIGlqM6RMuIjbkCNTWCv6LnQi0Xc6CAUUduM1mQ2ZmJkaNGoW33nrL5bc33ngDr732GlauXIl+/fph+fLlOHjwIKWRyUyg949zikpMjBYqlQpGY5vXaWRCr5czT/6OO7Ywpq4NGtQNtbWtnKlEkyZtY0zDck57E8sdd2xGYaHnbnPOZQrps0AdQ4GiihWo/eMVNgvU5uOy7HJW1ZCBWP0kmEOHB9xGKYGOomvg+/fvx5kzZ/DOO+94/PbUU0+hqakJzzzzjGMjl02bNoly3kRww5fSI1YVSimVJHvdTM4bAI4fr3F8mbOpbsm9RaXBYMSJE9xqZcGsLBXMtgcktlZo2n500sIugMomLhvBhnBYQjMdKV2W0GGAKhLnLxchMryD/YHjJxRdAx89erTDObujUqnw3HPP4dSpU6ioqMCOHTtw3XXXKWAloRR8KT3eppH5SyWJqx1arcpjWp0plUjutdm8vEJOtTI2uwNWWcqNYLY9ILA1Q9NyAGH1LyPq0t2IrUhB9KVxiKh/ESEtXwty3qaGUOw6cA0WvDEez7+7pH1b0u7b0BLz/2AJGwOoFNgfvYMREFHoBMGEEEUpX6pCyQVb3TpdOBob22A2e+a3uqtuMSmmeTMlzGbTtdd2dZQZ0MpSPASz7YpgNUHbduSKSlc+NK3Sdjk7+GNffLGrF74tTMMPJ3rDbG7Pu87K6ol5QbRFabBADpwIWIQoSvFNIdvXQU+dYp4uNhjqMWnSNp+ukbK1Y+zY3igoqEBDg2cqEZfqFlMgHBNca8BsNjl/5QeUshQLbG2U0/ZAWUuXFVl2Oet+ZZez9qAzq3YA3ty4j3HP+0AaM75CiXFCDpwIWHJzM1FYWMU6/cw3hcy3hq7VqlBaanKIVfhqjZSpHXbby8pMjNtpuqcSiV3T5TufyyYhdgcCXG2Uy/aOspauslRfWb9uX8NWm3+GSuQmQlZ1zytr1/ZtSa9pz2V0ItDHjK9QapwonkbmazpkBKiMBHr/OKf0REe3R6HX17cJmkJmU8DS6cIREaFlVJlyViMD/KPWJiSVSIh6mtjzhaRLCTlHqTHE10Y50sHE9jsTSvSPynLR8XWtbT0Ijfmk6DKsmiTH17Ul9BZYNSkeDpsJv6mRBRByjBMp0Bc4AcD30z/uClY6XQTi48N508KSk2M9HI7R2Caorl27Shl/b21lnyq0r5HayygurkZa2jlW5zZ//kFHKtawYfFYuvRmAK4KYfbc5l9/rcHZs/VQq4GCggqHox41qpeLMIbBYMTvf7/LJSe+uJh597OdO0swaNCniI+PQGpqrKMutraXlNQjO3u3S1qekCl5pnPsf3jU1DQhJCQfjY1WtLS09639Pa/TReC9925zkTeVY4wZDEbs3Xue8Tf7PbTPNMyffxB7957H3r3nHfdIaL1sa+l7956HwWD0+hmRS41MZTY4vq693uUsdCTMYSNh0/QRdB3TffWl0wpElIq5oC/wTk5RURFCQ/VeKwpxIVThiatOoapHUtSynJkxoy9yczN562JTUNPrwxESonE57q6w5XzcPV2MrVyhsNVlh0lAxA5TG9n6gWnqnw2NRoV33hmLvLyjsowxvnvs/AXOp3LHB5eOuVD7ZVcjs9mgtpxxBJxpWw9CbSnjbYs7Fu11V76wR8ESejNsGr3oMnyqRhZE3H33VuzbV+5xfMyYBGzZMtln9Sq+lSqhPL5OuRGqYMVVp1Abpahl2bGv1Qmpi01BraKi2eM4m5NjShdjK1coUp03wNxGtn5gUtJiw2KxYe7c/bKNMa577LzeKkTljg+urWO9fUYEq5HZrFC3/YrQhrWIuPwoYiozEFOVici6pxDa9G9BztsGNcwhN6Al6k9o6PoxjPpimHQH0dzlVZgjpkpy3gCl69kpKmIej2zH5YKm0AmfT/8ISQfjq1OojWLqAtrXwzMyurqs1QmpS2w9bLini8lVrjNduoRg3LgkFBcbcfSo585rzghpY3l5I2prWxh/Y6OlhfkPByljjCstz/nLj6svhdZrT99j20XPm2eErQ/r65ugbvvRy13OtLCEDHEKOvPNLmeUrteOycS8rNfQwL3c5y3kwAmfpwsJSQfjq1OojWLqAtpTudzX64TUJbYeNtzTxeQq15nQ0PZc3Ph4flETIW2MiQkR/PVtJyxMy6juJmWMcaXlOU/bcvWl2HojIphfld48I3FxYTAa26DVWpB5/TmMzjyLMcOKccvQEsRUi9NwtyHsyi5nV6bEQzIBtadAkNwEQ6qhP7DfS3e40kHlgNbAOzmdeQ2crT4hdYlZqw6UNXC76hlb2ULWwPnKYGPZshFYs+ZXn62Bs40Fb9fAucaT5DVwWzM0rYX47cetqDn/X9w82ICoSHFfajZVFMwhw69Ia46EJWQooMBGKbQG3o7keAYv4XTgXbt25dXfZqKmpsYro+SkIwwOX2LvH7kVmNxxV7CKj4+AThcuKi1MqI3O56nVNhQVGdHQ0IaoqBCkp8fCalUJVlgrLr6EtLTuvFHoRmMrWlo85b2SkqKxatUYrF9/EidO1KC4uB4ajQpdu7JHHDMps91zTz8XlbGFC4fhq69KHVH9en0kUlJiHFHoe/eeZ5zydVY+E5KW597nJlMrdu4851FuaKgKKpXaEYXujj04UK4xJmYsMGUKCK2XLYgtKSkaW7dOFFTOmaKf0D+pxutdzsyhN1+ZEh8FS8ggQBUiqgxf4e27o6O8o5VQluOcQv/73//u4cC3b9+OEydO4Pbbb0e/fv1gs9lw+vRp7N69G9dddx3uuusunxpMCEdM2o5zupYvYCvf2ca8vEJBDz9f2hNfW+x1/vGPu1FV1eRIwXKu214G18slOTkWn346HgC7WlhycowjVcz9fiQmRrOW+8knd3ocnz69H+e/7W0DwOpI6+vbHGXbndvJk5dx8uRlNDS0eTg3976cNGkbY7nDhydg69ZJrApnzmuiNhtgMrXiuecOwWhsQ2xsCGw2G+rrzYLSy8Smo0VHh6J//66SUtfY1niTk2PYy3HZ5ewgboj6Aeoaqbuc2TdNGQCoNIznBspOcUJ3COyouKeD+gNOB/7cc8+5/PvDDz9EZWUlDh065PFSO3XqFCZPnozERBJZDwSCYQcpMTbK1R6mckpLTSgsrPKqf2JimB+l6GitrPZzIWT5wNke9+nlHTtKcezYJc7pZa41T4PBiGPHmIPkWlvNgpc2vNlhTuq5bAhZ41VZL0HTks++y5mAScwLlbHYdyQN+46kIaL7GLy45GHBm6Yo+ZwrXX9nR1Qa2VtvvYXs7GzGL5L+/ftj1qxZePPNN2UzjpBOMKR3iLFRrvZwpSB50z9sS0324/64H0JS6JztkZJixZRWlZgY7pgeb2WZGf7ppxrB6X1ypBOKPZcNpvYOH2rFqy9cQHjd3xBdNQKxFX0RVfswwhpXQ2M+LmiL0srL8aixTMezrz+Mfnc+i95jcvH7eQ/iP9/diUcf/50g5y1XG71B6fo7O6Ki0M+dO4ewMPZAiYiICJw757k+RvifYEjvEGOjXO3hS9OS2j9su8PV17dx1ivn/RCSgsZnD59NTKpoDz7YgzP9DgDa2sRNIXubTij2XDaSk2OxffP1+O/Wz5CqP4Yh1/6Gnt2vLJWIuHWnzuqw70gavi1MxbeFaUjpdx22bp2EB/9sxNnLheiVLG39WOnnXOn6OzuiHHjfvn3x0Ucf4eGHH0aXLl1cfqutrcWHH36Ifv081+UI/xMM6R1ibJSrPXxpWlL7h88+til2Oe+HGPU2b1Ks3NfFi4qKeMtkSyMTa4PPx4xjl7OD0LYegLb1IK4NLcO10/ltdsa+y9k/34vFy29HoqLa1SmPuKXdBm9jT5R+zpWuv7Mjagr9hRdewJkzZ5CZmYkXXngBH3zwAT744AM8//zzGDZsGIqLi/H888/7ylZCBExTf4GmCiTGRrnaw7Wzljf9w2WfwWDE8eOemRmJiVGy3g+utjnbYz/XnhIml025uZnQ6z1zzTUaFVasyOK0jc1OpjpkHTOsu5w9KcsuZ7f/7imEhMcLbp9YlH7Ola6/syM6D3zfvn144YUXcOzYMZfjgwYNwqJFizB27Fg57fMaJVIUhEaFChUykBpl6p66pdNFIC3NNdparv6RIspgMBjx5JP7cPhwJdrarAgL0yA9vQv69+8qWhnLuf6oKC369+8Ks9mG1tY2HD9+Ga2tFoSFabFiRRYyM+ORl1fImdZlMBiRnf1fFBZWw2oFIiI0ePvt0YyR33z2saUide8ejmuv7So4Ctt5HGi1wKlTdTAaW2CzqdCvXyz69+/qSCNzT6Gzp7UkJkY7yjAam3DsWK2j/K5dQ/HRR//jct82bjyNuXP3o6XF7Og/9z7461934r33yhxRyGo1YHXKqHvmmRuwYMEwlzSbyMj2e9TQYEZZmQnNzWZotWqkpXVBaakRDQ1m1nEkJm3J89wbkdrLcGWXs4NXdjkTl/Z6dZezkbCEjoI59CZA3YX1/M8++w7/+79nGNOLvI0gd36GLBYb4uMjsHbtrbKVLwRv06c6ShqZEkjeyKWyshKlpaWw2WxITk5GfHw8/0UK4O/BIXRjA6GJ/95ulMB3vRz9I2UTA74NS8S0kal+LtatuxWZmfGs/QIAt932BS5d8ozIWrfuVk4nzgRbihkb3mxQ49wGKZuw6HQR+OabKUhOjsXGjafx2GN7PM5x7oMlS47g1Vd/5G0T00YuQuzxejMMWxs0bT9cmRLPh7a1ACqbuP2pvdnlrH2cb0FZ2dWcfK57JPbZ5tqoxtvyhUAbuSgL7cQmM0J1YQcN+pRRjzopKdoll9BbnVm+6+XoH6FtEWIXk41S62cjMlKLiROTWfsFAKttkZFaXLjwqOC6AGFtZbLDue1iyuBrg9C6e/V6j3Hd2rkPunZdKyj/V6NRwWKR9qrhGkceXNnlzCGt2XYEKpu4gKr2Xc5uav+69nKXM67nD2C+R94+23KVL4Rg1UvvKHAGseXn50sqdNSoUZKu6wgIjcpkEzIQKm4hNMrTH1GiQtvijJCIaaE2ShHW4OoXLofkLMohdHoyNzcTn39+RtRGF96ItPC1QWjdbAIkzseF1iPVeQPc4whWE7RtR2Tc5WwkLCGDZdvlTMo48/bZlqt8b2ygKHT/wOnAJ02aJGorVZvNBpVKFVBbqfoboVGZQje/9zbK0x9RolI28hcTMS21fjbCwrSS+yUsTPzGLMnJsUhIiMDFi02CbfRGpMXbe2u/ni1y3N4HQHu6sq+/wF3GkbUW2taCK876IDRtP0IF4dHtgLhdzrxFyjjz9tmWq3xvbKAodP/A6cC3bt3qLzs6DLm5mSgsrPJYE3KPyly1agzjuvGqVWMkleetPd4gtC3udh06VM65Bi7URqb6ubAHsrn3S1SUFjNnZiAxMRq7d59jXANfsSILAPcGFkxTh+++e5tgG1NTYzFzZgays3c7vu5nzszwsJftWnu/ufevXh+OkBAN7xq4/foVK7IY18DtfQAA8+bdIGgNfMmS4ZLWwPU9GrHp/VCE182HtvUg1AI3SnHGqk5wktUcBau2v+CNUrylfZyf91gDt/ext8820zPknEng62ffH+8Xgh1aA/cBQqNkhUZveisWwHW93FHoYiJRnYUmzGYrIiK06N07GikpMaLbyBThbDK14fjxSy4iI85BWvn5F3DvvbvQ0HD1C845wIgrCp0tMC0rqye2bp0k2EaLxYaYmPYodJPJjISEdmf9xBP7PV6Kb7+d5Ygw12jao9Dr61tgtV6NQrf3G1OAU2JiFNasGesoo6WlDT/9dAmtrTaoVMCwYXq8885Yl36XEoWekBCOyspmj35jGocAXI79bnIE8r/egBv6n8LozGJckyw8+M+OVZPk+Lq2hI6CVZPqN4fNxN69x/Dxx9WMz58czzaXWIuvRYrkqIPWwKVDDryTI6V/AkU8gc+mvLxCzgAbIQE4bP0jJnjH2baYmHYFMKOxjbXvhJTNdQ/y8y9gxoxdjNPfdjUy5+sAeHU/7Q5KzPV2+60tpRh70xnc/T8XoG07eHWXMxGcOqtD2aXBuPn2GTCHjYRN04exLqXGK72DuKH+kQ7nFPrLL78MlUqFefPmQa1W4+WXX+YtUKVS4e9//7tsBhKBRSCKF7DZ1L078xq8PcDGmwAcoVOHfOlfTH3HZxfXPSgrM3FO1e/efR7NzVe3NT10qByA6zS2mPtpMBjxxBM/uUwRs15/ZZezuov/xZkDm/DqnFNI7lXLW4c7x39LuLItafvWpBXVse0zH5M9Zz4CcbwShFxwOvBly5ZBpVLh6aefRmhoKJYtW8ZbIDnwjo3YtV8lbbJYmOU6+bYTFRKAw7QnONOXHZ/ACFPf8dnFdQ8KCio419mdnTfAvP4s5n62i6K46o47rn9nLNTmk46AM23rQaitFYjRAokCh4rFosKPJ3s5HPbZ8utx7BfP89juWSCOV4KQC04HfvnyZc5/E52PQEwbYbMpPj4CGo2a9SvZ2wAcIftYS0mX47OL6x5wpdSFh2s8HLhQm9hwtkWttmJwxgWMGVaM3935GWIqZone5aytTY0jP/fBt4Xt0poHf0iG0RTh+H3YsHikpjYLvmeBOF4JQi5EiZkQhNJpI0zrmWw2pabGYt26TNavZKFf0d4gJV2Ozy5uTW7mlLrISC3GjOmJnTuFqQUKup+2Noy+6RxGZuzH6Mxi3DKkBF1inL7GBUTXNLdocfinJIfDPvxTMhqbQlnPT0mJwbvv3urom+jo9piCP//5W8b1baXHK0H4Egpi6+SI7R85tk6UClvdb7+dxRi1LYdN3o4fvjVwKXZy3QOmNXD7dqSJidGCtldltUmmXc5MliFY82E3bPm6F44c74OWVs9NU9RqID4+0uVL2d0uIWNRyfFqh95B3FD/SEe0A//ggw/w/vvvo6SkhHFKXaVS4dKlS7IZ6C00OLjxJgrdl6kpTHBFZ9ujzuW2SY7x49xf9i/G+vo2r+wUIuzCJZ7BlcrlKMuHu5w522Ew1DNuhTthQh9ER4ey3lOhmQBKjVc79A7ihvpHOqKm0BcvXow33ngDAwYMwIwZMxAXF+cjs4KbQFEj8yUmUytOnryMkycvo6GhDX/+80CsX39SFhvZ+oVtPbOkpN4rtTa2lKrW1jb89FMNWlr2QqVqX0OOiwt1KJ0x1WUwGPHcc4dw5EglACAzU4dly0Zi7drbPBTTNBrXqV/nutnKZvo9P/8CJk/ejtraFkRHhyA9PRZJSTHo2VPvKNd5Uxjn68aP/xJVVc3QaFS447YYvPx8G3rFLYem+iA0rT9CpRK3y1lVTRTyf+iLhLT/wYBhU2DVXs+4y1lZmQkFBRW4dKnZJQ/fpayqZkRHh7Lu9CZkfZspj13quJT6HJ4/34RXXtkta+oek01CUhSJjoWoL/BrrrkGN910Ez766CNf2iQrnV2NjA8pU+hMCkjuW2VKtZGrX95++xjjGm54uBrNzVc3axFSN1O/CtkZzB3nurjUoRYtugmPP76XNUKcbyqbbRzk5g6VVG5u7lDMf2YbRg0pxphhxRideRY3ZFyAWi1uRe1CZeyVCPFU7DvSFyeLdbDZ1ADYlduEqsdFRWkZN9mx31e+L3AhampCkfocMqmRiVq2EGmTM/5eKpAKfYFLR5QD7927N5YsWYKZM2f60CR56exqZHyI7R+xqlhibeTql+uv74YdO0plqVuKQhhfXVxlRkYy7yvubdliyk3QGa8462KMvakY1/WtEG1P5WUd4nrdjtwlWmza1RtnSrsDYN7ljE25TYh6nLvztuO+mQ2XUxWipiYUqc+hL58XORX9lIQcuHRETaGPGDECv/zCkIRJOAg0NTK5EauKJRaufhEjWMJXt5h2CK2Lq0w2ZS9vy+YqN6nXZYwZdgajM89izLBipCdXi67/1Fndla/rNOw/mobkvtdh69ZJWPOv9bz3g802PvW4kBAVrr22q2N7UGec7ytftL4QNTWhSH0Offm8yKnoRwQnohz4q6++iqlTp2Lw4MF48MEHRSmVdRYCTY1MbnytisXVL3LWLaYsoXVxlcmm7OVt2VfLtSE9pRqjM4sdX9lSdzm7cPkG/FoyAK+sjER5lev06/BR7XYIUYBzVi1zhu/akBAN4uMjGH9jSrlj+8IUoqYmFKnPodQxK2S9XU5FPyI44ZxCHz58uMexuro6VFZWIjw8HL169YJG4xqgolKpcPjwYfktlQitgXMj1xq4O4mJUdi+fZKsa+Bep0G5tSOY18BVKivGjWnAC8+0oOy3r5A1tBg9dfWC7Qau7nJmz8E+cDQV6pAe+OabKQDAOe6ErGN7swYuxzpxsK6BC62L1sAJTgc+ceJESV/Z27Zt88ooOSE1Mm6kppHZFZCMxlYXtS87Eyb0waefjpdkk2xpUALawVVWu1pXDVparB5R6BaLjbEutih0u9NjUiMT1A6bBZXnDuPgN58jNeEYbrjmN8RGiXPYZosGxRf6Iq7X7Vj3STcseyvMZZczwPW+8Y07e3tqapoQEqJGY6MVZrOFVbXMGfu1ly41o7HRzBhpzpdGJgQhampCkfocMqmRAez3WopQjpwpiv6GHLh0aCMXH+BN2pe/U8a8VSM7deoyqqqaPc7hktVUGjF9LKZ/xJTLJwMJWxs0bT9eycE+CG3rYahs3Frg7tgQhgbrDfjq2yQc+L4vLjUMwjPP3oLk5FhJcqju7Tx71ojKyiYAbaiutkCtBmJiQjjT7Jj6qbjYiKNHPde7hdjCl4rJdU+E3i9vn0mxz5g39yYYIQcuHdpKVWa8UT8KBuUkvmk7O4G69uarPhZTLtNU+3+/OYPFtsN4+xU1ukcehbbtO9G7nDU0huD7k/2QPmgiovW34ezFfrh76h4nm84j/9BObN48QfKaLt/9N5nMuHixyfFv9z5guj4qivk1xGeL+1S80diGu+/e4ViG4rongOcSAdP9UuKZDLS4FyJwUfOdUFFRgWHDhuGll17iPO+ll17CTTfdhOpq8ZGuHQku9SNfXusv+NS1AHGCIP7GV30spty8vELUXLqMO0b+hsVPfoV9H/4TdUeex+f/eB0J2tcQ0rpXkPOuqw/Htr3X4u/L78Lw++YibvhLGP3gH/Hk4pGwhI7ES3k/s9qUm5uJ1FRXByTkvgm5/0z1cV3f0GD2cOJCbMnJ2eexjm4225CTs4+1Lrs9Qu+XEs+k1HtDdD54v8BXr16NmpoaPP3005znPfXUU1i/fj3WrFmDBQsWyGVf0OFN2legpYwxwWajTheOjIyuAb/25qs+5i3XWgdt62FoWw9i4cxt+Pj5swgJ8Ywd4KL6cqQj4OzbwjQcO9UTVqvn3+BC9M6lCrlISb9z7lu266+7rhtSUmJE2cKXisnVfrbd3dzHgRLPpD9EdoiOAa8D/89//oNp06YhJiaG87zY2FhMnz4dO3fu7NQO3Jvpr2CYOmOzcezY3gG/YQTguz52L7d7XAOyMosx6/d7EV31CtTm41BdkecakCasTKtaf2UP8VFYsESDN1a1OHY540Ko3rkQOVR3pKTfRUdffc2wXZ+SEiPaFr5UTCn32v03pZ5JKfeG6Hzwvg3Onj2L66+/XlBhAwYMQHFxsddGBTPeTH8Fw9RZMNjIha/sfzG3D5545BRWvrAJx79cjupDL+KLFR9g4s3boTEfczhvLs6Vd0ONZToau7yFet1R1MefRFPX/0Nr1GOY+fg0pKTE8Zbhrncud1uZyuTj+PEaGAxG2W1atWoMtFrXLBmtVoVVq8bw1iXUjmAf70THhjcKvXfv3sjLy8Ojj/JvPfjee+8hNzcX58+fl81AbwnkNDK5r5VCMKmRyYUY+9n6R2UuhfZKhLim9SA0FvHbsp6vTMDuglQc/qkfGjAcf/37FN6cYrvdMTEhsNlsqKpqRmVlE/T6SKSkxLAKoMh5r+xllpTUo6KiEfYodI1GhbY2K5qbLR7XuG+BKpdNfKmYXHUJtcNbeynKmhvqH+nwTqEnJSXh6NGjghz4999/j6SkJFkMUwo507jY1tm4CNSpM650HWc1LC5VNXfE9rVc90ZIH+fnX8C99+5AQ4MNwB6kp1Tjfxe04fabDTDXfwtdnPhgzZNne2H3oWTsK2xfw65vjENjY/s6uE4HjL6tUnDK0/jxSVi06Ahqa1sQFqaGwVCPU6cuo6CgwtH/+fkXkJ29B5WVTdBoVBgxIt7FHrb+tB8vLjaiqqoJ8fERjq/O5ORYj/6z5znb0wqZHLj7FqgzZ2YgJ2cffvihCtu3G5CaGoOkpGg0NZnxyy/tMsUeqXUMtv/6aw2qq5uhVnv+VlxsRHFxLS5fbp9mV6mA0lIT3nlnLGM77DCNdV89k75MG+Xak0BOAlEtsbPA+wX+4osvYs2aNdi3bx+uueYa1vN+++03jBkzBnPmzMHChQtlN1QqYvN4vd31zNc7p8mNkP7h2h0NgKAd5dwR20/+7Nf8/DL8/en3XLYllbrL2Q8n++PwsX7Y/J9euFQbJaoMe/sAz5QnLrRaFfLyhmPBggIXhTgA0OvD8Z//3M1YZmpqLN5+OwtPPLGfsS623cDcdxpjwvkLXKgaGcC8ox9XKptGo0KPHmGoqGC3R6eLwDffMM92CN0hUQxsz5gvxzTXroBSdkjkqsfbNtAXuHR4HXh1dTVGjBgBjUaDJUuWYOrUqdBqr364m81mbN68Gbm5ubBarTh06BC6d+/uc8OFImZwyKH85Wv1MLkR0j9cCmEABKmquSO2n3zarzYL1Obj7RumtOSjvnIvunURvp0qANigRdG5NGz6qje+LUxF/vcpHrucSWHGjL4AIFo5zV3eVWiZSUnRnEph7v0tRBHL/YUuRI3M2zrFlmlHqEqgGNieMV+Oaa4+kvNdJEcbyIFLh3cKvUePHtiwYQMefPBBzJ49G08++ST69euH6OhomEwmnD59Gs3NzejZsyc+++yzgHLeYpEjZSQYUsHEwpWuw7ZM4K6q5o7YfpK1X3l2OevWhb+I5hYtCo4lYd+RNFxuycSLy+bisew9jDtoeQNXyhMXbM6br0y++yY0zYorrZBPjUxqnd6UaUeoSqAc+PJdwdVHcr6LOuL7LpgQtBPbjTfeiEOHDuG9997DV199hVOnTqG+vh4xMTEYNGgQJkyYgJkzZ6JLFwFvvgBGjpSRYEgFEwtfuo4QVTV3xPaTV/1qa4am9Si0rfnQtB6UvMtZ/g8p+PbK+vV3x/qgpTUEwJUvWnWUrApndmJiQvDzzzWir+P6Aufqsy5dwlBXx64UJjTNKjNTx7oXvhAlMyl1ioGtD4SqBMqBL98VXH0k57uoI77vggnaC90JOdZzfLGG5ks65Bq4tQHatu+ufGHnQ9N6FCq0crbRnbr6cOw/mnpFC7svvv+1N8zmdjGT2tqrZfGpSElROPP2Wn+vgY8b9wUqKlz7l2utldbA2dtBa+CEGMiBu+FtykhHXAMHuNN1hKqquSO2r1nPd9rlTNOaD03bj1BBnPa2VdUNltCRMIeNhDl0FPZ/1w333rvrShR6O888cwP+8If+nDZzKZx99105SksbHNPXUVFqpyj0CCxdOgJffVXquNZkasXOnec8bE1KisbChcOwaNER1NW1IDRUDZVKjZYWs0v/M0Whv/XWGN40KnexErYUNTtTpmzCt99e8jjONebtY+by5RZYLDakpcWgTx/xUegnTtSguLgeGo0KXbu2tz0xMdph/5kzrlHoN92kd0ShsyF1PLPB9Yz5MiXT31HolGbnf8iBy0ywKQnJ1T/+TCVRWS+1T4W3tK9hO+9yJhSrWg9j203YsKMnvi1MQ40pCYAGRmObw34AePbZPTCZNKLaxNQXAPDcc4dw6FA5GhvNCAtTIzo6FL16RblsDGK/TqOx4dChSrS2em636jyWuNLL4uLCsHDhMGzceIbxJS7knrG1xfnYjz9eRFGR55KEWg2sXeupve2vsSJX+7y1z1eKdoEGnzIcG+TApUNqZDITE8Pcpc7bSXY0fK3YpLKUO76uta0HoTGfEF2GVdMH5tCRjq1Jz57vgalTv3JR6nLm0KFyAK7T10LaxNQXhw6Vo63N4jKt29JihdFoxoULjSgsrGKsjw37+iJTXc6zP0ZjGx57bI/LtTt3nsPx49uwZs1Yj6lyIcphYuy0WuGo3+7E/aXuJaQeoe3zlyJgMKgRssGnDEf4Bv6NlQlRqFQqUcc7AnIrNqnMpQhp/AwRtXMRXTkUsZUZiKz9I8Ia1wl23hZNX7RGPIzGLqth1B1DffxxNMWtQVvkw7Bq+yIv7yhnXnVZWYOHkxLSJqa+KCtr4FyTZauPCfevdTHKYM515eTs471nbG0RuyY/d+5+zjJ9oe4lpB6h7fOXImAwqBGywacMR/iGjvtZqBBs0bX19cKjboMNr1JJbDaoLcWOgDNtaz7UljLRNli01175uh4Jc+hI2DQJkmzmg69NcqQ4saHVqly+xrypiy0tSohymFhaWq7GI/gr7UhIPWLa54+0qGBOyfJn+h1xFXLgMtMZ0ypEtdlmhdp86mpKV+tBqK3louqzQQ2rduCVgLN27WubWtz+A1JTkZzbxLRe6YtUMjvx8REu9cXGhkguiy1dTIhymFjCwvjLlPv5EFKPmPb54/kN5neHP9PviKvQFLrMdEb1Is422yxQt/2I0IZ/IrLmQcRU9ENM9c2IMM5DaPMmQc7bBi3MIcPQEvUUGrr+G0b9WZh0+9AcuxTm8MminTebzc4kJkY50rg82oSr65UbNpzBgQMXsWHDGUyduhMzZ2Z4lJuYGAW9PpzTHqb6nGnP67a61Hfs2CXOa9jQ68OvRGt7XsunHMZkp0bDXd+KFVmO//fX8zFzZgajUtnMmRmctvDdd18SzO8OPmU4wjcoGoVeXl6OF198EV9//TVMJhNSUlLw2muv4ZZbbgEA5OTk4NNPP3W5JjMzE998843gOoJNjczfyB2FXlVlxMgbL+KJPxrRI+qoxy5nQrAhDJbQoVeCzm6BJWQYoBbvqITaXF7eiOhoLVQqFerr21zSv559dg8aGjQe95ErXTA3N5Mxlcw1Cl2D6OgQ9O4d7UjRAuC4Tq22oajIiIaGNnTpEobU1Gjs2+f5x86ECX0QHR3qqMsehV5X14K2NhsaGz3T6e66KwmffHInfv/7Xdixo5SxDVzKYc52JiRE4vbbo/Hf/5pQXt6IlpY2HD9+Ga2tFoSFabFiRRZrFLovnw+h6ZxC2qdEFHowvDvckZp+R1Ho0lFsCr22thZ33nknRowYgX//+9/o3r07DAYDdDqdy3ljx47FmjVrHP8ODQ31t6miKSszoaCgArW1LTAYwlBWZvLqIZSanmFn48bTmDt3P1pazKwvVT5Y01uu7HIWr96N3Ee+RnriKUSEXVn3Erj8ZVNFwhxyEyyho65MiQ8FVMxfrExtAcDaPq6+41Mls3+JOm87ai/v/HnmvbztQUdMaUCjR/dyOMz2KPQ2VFQ04aefqrFv33nodBGor29zqH8552xPmrSNsb6qqmY0Nrbhu+8qYbHYkJ9/EWvX3opRo3qxpjSWlZkwaNCnOHeOuQ2nTl3GoEGf4tKlJpjNNkREaBESokZMjOuUfWOjGQUFFfjxx4s4d64Rzdxxeh5j6O23R0t+LvjSrYSuJzONgfz8C7I+v2IIVDVCIYwa1UvyfvGENBT7Al+8eDHy8/Oxa9cu1nNycnJQU1ODf/3rX5Lr8fdfd3Lv5ORteRs3nvZIJQKAdeva83OF9I9zektkRCtuvqEEd//PeTx63yVEqX+ESqinvoJNFQtz6AhH0Jkl5AZAxb+ey9YWJtatuxUJCZGS+44ppUevD0d1dQvnPuNRUVo0NFz96rXvSrVzpwHz5x8WZLv7tcnJsaxflKGhQKvbJnMajQpffnkX1q8/yXiNSiVN6hZoX4/ValWiItHXrbsVmZnxsu06JmT3r6lTt2Pv3gse144d2wubN09kLdufO7ER7VD/SEcxBz58+HDcfvvtuHjxIvbv34+EhAQ8/PDDyM7OdqRc5eTkYPv27QgNDUWXLl0watQoPP/88x5f6Vz4e3DIrWbkbXm9er3HOI0aGanFhQuP8vePtQ7/fG0N1M0HMTqzGJkDyhAS4rm5CBfuu5xZtdcDKp6FUwbY2sJEZKQWPXqES+47KYpX7s7bzowZfbFpUzGn42fDPuXL5LTY6gPa27h160SPa7RalaAtTOUkMlKLiROTZduhUMj0+LXXfoSLF5s8zunZMwInTvyBtWx/qpER7VD/SEexKfSSkhKsW7cOf/rTn/D000/j+PHjePbZZwEAs2fPBgDccccdmDx5MpKTk1FaWoq8vDxMmTIFe/fuRVgYc3RjUVGRoGO+oqbG86VhPy7FDm/La25mfsE3N5sd1zuXo0UtojU/IEbzA6I13yNSXYTn/iDOYV+sisG+I2koqRyASfdOQbM1Fa7xksWiynO2Wcy53vRdcXG14LrUamDcuHiUlTXh5589dcOLiy9Jct72a+22vv76tVi9+iyqqlqh04Wy1ge0t7G1tcLjmn37qmAWt8us1zQ3m1n707l9QhFSVn0989739fWtnPXJ/fza8ec7KBih/mGG7w8bxRy41WrFjTfeiIULFwIABg8ejOLiYrz77rsOBz59+nTH+QMGDMANN9yAgQMHYteuXZgyZQpjue4N9vdfd926FcJk8vwLvlu3CEl2eFteePgBxq/W8HAt0tPTUXL6ENJ7X/Rql7PKyzp89W0f7DvSF98WpuK0oQcAFWbM6IucvvKt57G1hflcLbp1C5fcd2lp53D0aJ2gutrXh2OQlBTO6FDT0rrjxx/rJDnxtLTuDlvT04GxYwc5fsvO3s3qwO1tdL9GrBa3HISHa5GW1oOxP53bJxS2e+NcltTnRu7nF6AvTD6of6SjWBqZXq9H//79XY5dc801KCtj38SjZ8+e6NWrF4qLpX3B+QO50ym8Le+FF1xTUJJ6XcYfphzFwU3fILpyKAZHTRC9y9lvJT3wr12jUGp+HUbdMZRHHcWLax7H/228CacNOgAqn6S/OKcjCTnXm75jSunR68Oh0XjuqNfSYmVN67L3w5IlwwXb7n4tl41M6WkaDXsbmfrEmbi4UKg53go6XQTn70ysWJEla4qUkLKk3ntKhyKCCcXWwGfNmoXz589j586djmN5eXnYunUrCgoKGK+5dOkSMjIy8NZbb+GBB4StRynx153cakaSy7PZ8Pz8j9F4aS9GZxZjzLBiJPeqFV2/RXstLrcMw4cbe+DbI6kIiegtSIXLF5G7UqPQpdwLg8HokUZWVmZCTs4+XLjQwLiW7J7W5dwPq1cf9whk02hU0GhUiIsLRXx8BIzGNl71L3cbn3xyHw4fbo9Cj4+PcEShs2Hvk4oKE1quxB+q1cCwYe1KXfY21tQ0oa3tahT6sGHxsNlsjAppanX73ufOREa63gs5x4iQsqTee3+qkRHUP96gmAP//vvvMW7cOMyfPx/Tpk3DsWPH8OSTT+L5559HdnY2TCYTli1bhilTpkCv16O0tBSLFy/G+fPnUVBQgJiYGEH1dKrBIcsuZ6oru5yNkrTLmT/UlNzrmDkzA+vXn2Ss0xt77A6cSY2MLUVLpwtHcnIMKiuboNNFIC0tVhZ7hKYCii1frOQkW7sHDeqG2tpWQamOXDY6p/1FRWnRv39XmM02yWpwMTHt+f3OKnNSot69GdN79x7Dxx9XB6XCmD/oVO9omVF0I5ddu3Zh8eLFOH36NBITE5GdnY3HH38cKpUKTU1NePDBB3Hs2DHU1dVBr9cjKysLCxYsQGJiouA6OvTgsFmgNh+HtvUgtC0HoWk9CLWtRlQRbW1qFP6SiG8L0/DbuevxlwWPo09yH0nmCEnv8RamOtwjq+11ApBsD19bHnjgK8YvUSa8tYcvFVCozUxtnDhxm0dKWGJiFLZvn8R4jdB2s6VecdlYVmbySOFyRkhfMZUvtgyh9gr9Y2LixC0oK7uaJC/3MxHsdOh3tI8hPfBgwtYGTduPV76u8yXtctbcosVPv6WiuHwg1n3aHYd/SkZD49WIfilpPXaE7n7lDULTu2bM6AsAku3hawvbLma+sIcvFVCoze5w9SXbNWLazZR6xWVjQUEFb4AdX18JGR9ixqO3Y9ofz0Sw06He0X6GxEwCmSu7nDm0sNu+g8omTpnIpoqEyTIEO/Yk4sD3/VDTdD2enT8S/3zrWxw45DkV6o3ykT/UlIQqSJWXN7JuViLEHr62sKnO+cIeZzUvruNi+5+rL9muEdNuJiUqLhvZFK2E2MVXvpgyhJQntIxgVhgjAh9y4AGEylKF0IaV0Jh/g8pWC03rURl2ORsMqEIx/g/AeKf9K3yhfOQPNSWhClJcdQqxh68tYpW6vLEnLEzL+AXurPLFZRNb+VxtkHKNO0xKVFw2GgzMilZcdrmvT8fE8L/SxIxHb8d0MCuMEYEPTaEriMpyDmGmtxDWuFZyGVZV1yu7nLUHnVm1AwXtcuaL9erOtAYuxA657AmkNXCmOnr0CEVNTatLFLo/1sCZyrKn8bFt9Upr4IFHIL+jAx1y4H5EbS5CmOk1hDZ9JrkMq1rv+Lpud9gZgEpaOj9TmpS3LxV/pJO512GPQmeq0xt7+PqHzY6SknpUVDQ6REnksEdsFLrQ8sVGoTPV8eCDPRAS0kNw6hWXjc4pXJGR7VHoFouNsS1s68t33ZWEqKgQVpU5qVHoUse0PQo9GBXG/EEgvaODDXLgPsD+wEdrf8Xj07dh+ABxIhbOWDWJMIeOuuK0R8GqSWtXoxABlyKXlP5hSqspLKx0OBitVo0bbtAhJETNmzbDVJY9D1mM+pov0tfy8y9g1qxv0NBglaQC527br7/W4OzZeqjVQLdu4Y7y3G23S4I6tz8xMRrz5x9EYWEVAGDYsHgsXXozkpNjXe6vRqPC5cvt24iqVEBGRldUV7dvD5qZqcMTTwzCK68cxeHDlWhpsUKlAtRqFbRaFW6+OQFvvpklut+cx5Cc94FPhY8tpW3YsHikpMQISjOUUq9YuJ4xf6Rd+huxbSIHLh1y4DKiaT0IW9VSxKj3e11Wc3QuWiPuhU2b5FU5fOpKYvuHaUqxe/dQXLrEvPc0wD5lKFTxi08NyhdT93KpUnGlNWm1KqxZMxZ5eUdZ054AXNnoJcSjjxMTo7Bo0U14/PG9ggVK+JTIEhIisWvXZFH9Zh9Dct4HIf3P9gXuLvLCtsTCZJM/1cj8seTkb6S0iRy4dBTbSjXosdmgbf4aUdXj0OViHLpcjEP0pbskO++2sEmo77EXdT1rUdezFi0x87x23gCQk7PP4+VuNtuQk7NPUnl5eYUezobLeQNXNbKFlFVR0eyxZzifvUzlsNUpFLn6jck25/Lmzt3P6bwBwGKxMfZxWVkD5s7dL0pdjE9GtLy8UXK/yXkfhPQ/05aqTApt7uVw2ST388KFL8at0nTENgUyFIUuFJsFIc1fIsz0KjTmX70urjXiPrRE/w1W7TUyGMcOW2oOU4qPEISmcbnDlDYjpiwue32RqiNXv/G1kS1FTCjeXs+E1H6T8z4I6f/k5PYvO+f16eJiI44ereItn80muZ8XLjpiillHbFMgQw6cDVsbQpo+Q7jpVagtwjfsYGNXwXjcPOkVWb6qxRAXx5yaw5TiIwSx6VN2mNJmvE1J4ivHm1QdufqNr41sKWJC8fZ6JqT2m5z3QWz/22cW4uM9xV3E2CT388JFR0wx64htCmRoCt0dWxPC6/6OLuU6RNbNley8X353LPS3vADVta8i7a416HnjO3533oD86kpM05bdu4dyXsOmOiVU8YvPXjmVruzI1W9MtjmXt2JFFuvvdjQaFbp08fxbW6NR4YUXMjnVxcSi0agwc2aGpGvlvA9C+t++3rphwxkcOHARGzacwfHjNR6KcO7lcNnkTzUyX4xbpemIbQpkKIjNjdCGdxFhnCeqDhtC0RL9DFqisgF1nN+UuYTCpa7kTRS6c/uYotBDQ9W87Wcqyx6FLkYNyhd9bo9Cb2y0eqVKZbftxIkaFBfXQ6NRoWvXMJco9MmTtzNuIxoZqcWGDXdi5crjjFuYzpjRFzNnZjj6S612jUKPiQlh/KJkUg9zLlPMNp9MUehy3Ac+VTAhaWR8aYZS6hWLkCj0QHlXyIHYNlEQm3RoCt0NlfUS7zlWVVe0xDyD1ohHAHWUx+/JybEBsc+xczrH8OF62V4OTO1LTo5lzEtmsoUptaSx0YyCggo89thupKbGYuvWiZJs5QvSEmNTYmI0Bg/u4lAjS0yMdrm+3cHvRlVVMzQa/jSsuLhwjBkT7VDHWr/+JBITo5GcHIukpBhGBz50qA6jRvXC0qXfM5Z59qwR69efRFJSDHr21GP8+CTk5hagqqoJarUKjY3MO5up1Sqo1Z4BXsDV9UopKU5ixz5XHaNG9fLYS90ZtvXW+vo2fPLJnS7HxDhg93oNBiOys3f7JNUrUN4VctIR2xSokAN3ozXyQYQ0fwGN+aTjmFXTB83Rz6At4n5AxT1dHCgwpXMUFlYpkqLCZsvbb2fhiSdco7BLS00oLKwSZauUtvJdw/d7fv4FTJ683fEVazbbsHfvBdx551aXNCw+dSx7mXxrh2xbhP7yS40jNxxwF0th/2uGK3I9JibEL+PH2zr8sd4aSM8RQbhDa+Bu2DSJMPU4hDp9CeoSLqGuZy3q44+jLfLhoHHeQGClc7DZkpOzj9WxibFVSlv5ruH7PSdnH+MUtHsaFlcamXOZfGuHKpbNe5qaLKxlS8Vms/ll/Hhbhz/WWwPpOSIId+gLnAmVClDFKW2FVwRSOgebLXypOb5UfOK7hu93LuUs53qFqmMxpUQ5T9WKVT/zBpPJjPp65sh2fyjLCa2Dr88CwUaC8CXkwDsogZTOwWZLly5hqKtjd0y+VHySqjZm/50t3ci9XiGpcvbzudYOpabvScFbJTeha+dyjFFfr7cG0nNEEO7QFHoHJZDSOdhsWbVqDGsKlRhbpbSV7xq+31etGgM1w9Nj/wrkqkeMnXZmzszwSG9Sq+V3JHZ7pI4fptSuqVN3wmDwXEYIpDHKRjDYSHReKI2sAyMkncNf/cNmi/342bNGVFY2Qa+PREpKjOipUCnpOHzX8KmR2aPQq6uboVazR6E71yNVHYstZWrChD6Ijg51tME9Ch2wobXV8xEPC1MjNjYUAwZ0RWRkCKM9QvvUeQyx2cmWmhYMaVTe2tiZ30FCoP6RDjlwHxBoCkNc9gjtH64ynNWboqNDkJ4eC4tFJajtYvuK6XwAePLJfTh8uBIWiw1du4ZiwIDuMJttLmWKqctgMGL+/IMoKCiHRqNxqH8557tzyXoysXr1cSxYUACLxQaNRoW//nUwSkrqHX+8hIaqceFCI5qazC7pcFFRKqSkxOGXXy57lJmV1RNbt05ibcMdd2xBVVWzx29hYWqEhWm8UtuyS5w2N5uh0QCxseG4fLmZMbjP3U77mKmpaT8/NTUGSUlXU+zkem4C4Vm0y4kGyvsg0CAHLh1y4DITaApDfPYI6R+uMsrKTB7qTc5wtV1sXzGdn5gYhaamNl41NKaUNS6VtIkTt6GsrMHleJcuWtTVeQZ3rVt3K68TX736OObPly4rywbXly1X+pozUtS2Nm48jcce2yPJTibFLya8fW4C4VlsH0tbUFZ29Y+oYFcckxty4NKhNXCZCbS0Ezns4SqDSb1JaF1ibWM6v6ysQZAaGlPKGpdKmrvzBsDovAFg7lx+BboFCwp4z+HDfYtZrrVYvvQ1Z6SobQlps52oKK2LnXxjxo63z00gPIvtY8l1BoTS0Ai5oCh0mQm0tBM57OEqgyudiq8usbZJVUID2FPWvFVJA4QpgrlLpEohMlKL8eOTBK3Fim2DWLUtMSpo117b1cVOIWPGjjfPTSA8i4FgA9FxIQcuM4GWdiKHPVxlGAzs6VR8dYm1zZtUKraUNW9V0oB2RTA+NBqV1068a9cwwSlTbG2IjGRWLxOrtiVGBc09ipsrBc8dg6EeBoNR0nRzIDyLgWAD0XGhKXSZCbS0Ezns4SqDSb1JaF1ibWM6PzExSpAaGlPKGpdKmruiFQBGRTAAWLEii7N+AFiyZDjvOXyIUcRi69sVK7JkUdsS0mZ72e7qZnxjxpnSUhNrGhofgfAsto8lV4lTSkMj5IKC2HxAoKXGcNkjNgqdqQxn9aaoqPYodKtVJUiJbP78gygsrEJ9fTNaWtrFSFQqYPDg7oiODvWI2mWyA2COQrdYbIwpa0Lui5Ao9NBQDZKSIlFS0gCLxQa1GoiICEFoqNpxvnP5S5YcwfLlPzraOGvWtaitbUVJST0qKhoRFqbG+fONHl+24eHAypW34quvSh2RzOPHJ2HRoiOorW1xiSR3jrqOiWlPWauqakZFRSN0ugikpcU6rnVX2xIbse0chW6zsQvJMAXa2cfM5cstsFhsSEuLQZ8+0fjpp0u4cMFzelmsQpodrnvurwh1exR6oLwPAg0KYpMOOfBOjlL9IyZKWsmoXbb+MRiMGDduCyoqPFO07CQmRmH79kms4ihM7WKLtAfAGFhnR6tVYc2ascjLO8p7rdB6hfb7Z599hyeeOMYamHb99V1x4MA9nGXYmTRpGw4cuOhxnCtdTgr+jFCndxA31D/SoSl0QhHEREkHYtRuXl4hp/MG2p2mUHEU53KZIu25nDfQHkk+d+5+QdcKrVdovy9adJIzqry4uJ63DDv+WjMOhAh1gvAWcuCEIoiNkg60qF2h9gsVRxFbLhNiIsOF1iuk39mET+y4p79x4a91a4oOJzoCFIVOKILYSO9Ai9oVar9QcRSx5TIhJjJcaL1C+j0mRguTiV3WtGtX4RHu/lAYA9j11aOj6ZVIBA/0BU4oAp/IhzOBGLWbm5sJvT6c85zExCjB4ijO5TJF2jNFxTuj1aqwYkUW47XudjrbxVWv0H5fuNBTaMXZLrER7naFsa1bJ2Ht2tt8EvvApq/OdpwgAhH6c5NQBPcvrbq6JvzySx0sFpsjCj0mJjRgo3aTk2Pxn//c7RL9zhWFLvTLku08AC7H2CLJMzPjXc6bOTMDjz++V1B7pH75Dh3aFVu23IWcnH2oqmpAaysQHq5B9+7hkvdZ9zVseej19f7TXScIbyEH7gOEpqf4K43FH/U4C5pERWnRv39XDzERd6RqOTO1p6zM5KjfOa3KG6GVjRtP489//hZtbXtZhUsiI0MQG9ueh+7stJnSuQyGevz222WYze0pV19+WYL+/bugf/+uDic9f/5BHD5cgcZGM6KiQhATE+Loq5kzM5CTsw8//VSNgoIKrFo1BomJ0cjO/i8mT94OqxWIiNDg7bdHY/r0fjAYjJg8ebtHEJs9uC43N9OjH73V1g4J0UKnYxZIETIOne+XN0IrfATKBivePpuBINZCKAelkcmMN+lCvkhjkUPMhA8+cQo528XUnoSESFRWNrqoYGm1KuTlDUduboEku9jEOuzCJWyCJ4mJUVizZqyHcAofiYlRaGuzMEa2JyZGYdGim/D443td2qJWA1FRGtTXe64/L1s2AmvW/Mpqw7Bh8aiubpZl/DGlkbkLpAgZ70zjSIrQihACIY3MWxsCQaxFDiiNTDq0Bi4z3qQL+SKNxR/1eCNoIham9pSXN3pIWJrNNixYwO68+exiE+uwH2cTPCkra2AUTuGjrKyBNS2trKwBc+fu92iL1QpG5w20i6dw2VBR0SjbuGBKI3MXSBEyDpnGkRShFSHYlwxmzOiLrKyemDGjr98dn7fPJqXCETSFLjPepgvJncbij3q8ETQRi5g0KyF7j7PZxZaSZT/OZYdYYRAhiEkRA7jbnpoai27dwlBaavL4Tcp9Yksjc+4HIeOQbRz5oj8B6Us4cuHts0mpcAR9gcuMt+lCcq/B+aOeuDj+NCG56hOTZiUk/5jNLjaBEvtxLjvECoMIQYhgijNsbU9KisbmzROQlsb8pSnlPrGlZDn3g5BxyDaOfNGfgYC3z2agrOMTykEOXGa8SRfyRbqUP+qRKmhiMBiRnb0bkyZtQ3b2bkGCFUztSUiIhNptJGu1KixZMpzXrpkzMxhtYBPrsB9nEzxJTIxiFE7hgyndy/k3JhEStRqIidEwXrNkyXDG+75160QkJ8fKOi6Y0sjc08eE1Mc0jqSkoQULXH0i5NkIBLEWQlkoiM0HCBXN8JfoiRxiJnw4C5pERrZHobuLibjbJDUAh6k99ih097QqLqGVmTMzPILNnG1oj0Lfh7Y2K2MUurMYC8AchV5e3ojo6PYo9NLSepw6dTUKPSxMwxuFPmKE3lGmc1vsbbRHoRcWVjNGoXONL7nGX1FRESoroxj7n+++sUWhc5UTbHA9Y2ziPEKfjUATTpICBbFJhxx4J0ep/snO3o0NG854HJeqOuULGwwGI559dg9MJg1jio4/U3i46mL7zWAw4rnnDuHIkUoAQGamDsuWjVRMrKOzpjyJfcYC4dnwJ/SOlg4FsRGKEAgBOFw2MM0QFBZWOb6C+H6XE666AM+vtcLCKrz9dhYef3yvS6T8zp3ncPz4NodCmj/xZ38FO4HwbBDBAa2BE4oQCAE4XDbwpej4M4WHqy6233Jy9rGmuSmRZkQpT8IJhGeDCA7IgROKEAgBOFw28H0F+fMriasutt+4Uq+U+JKjr0rhBMKzQQQHNIVOKIK/VKek2sD3FeTPryQpdXXpEoa6OuZ9vdmu8+UaNX1VCicQng0iOKAgtk4O9Q8zfFHy/tzGkqsugDlimWkNHGhPSWNaA/emPULGUEfZ9lMK9IxxQ/0jHXLgnRzqH3bsUegNDRqfpmEJtYWtLrbfxEShexP5LDYKvbN9VdIzxg31j3RoCt0HBFq6jNz2MClGJSZGe6hvGY1tirdfjrbbnP7E9aY8JoUy5z4CwFq2ffMV++92NbHk5FjOLUGjokKQnByDysomVFY2u1znbNOuXaWM18u5Rl1WZkJBQQVqa1tw+rQWTz21n1exjiAIdsiBy0ygpcvIbY+7YpTR2IbJk7cjPj6S9WWvVPu9aTvTtYcOlQOAy7S0N+U5w1e22LYwnV9aasLRo1WcKWjuyLVGzTRuLl5sEtQWgiCYoSh0mQm0dBm57WFSjLJaub/UlGq/N21nurasrMFjTdmb8sSULbYtXPVxpaA5I2fksz8V6wiis0Bf4DITaOkyctsjRHlMzvq8wZu2i1E9k7s8prLFtoWvvvLyRpelAWe6dAnBuHFJsk5r+1OxjiA6C+TAZSbQ0mXkticuLgxGI3N6EhdKtN+btotRPZO7PKayxbaFrz4um8eNS5J9y04h44ZSyghCHDSFLjOBtgmD3PYwKUap1dwvX6Xa703bma5NTIzyUCDzpjwxZYttC1d99uv8OValKtYRBMEOpZH5gEBLl5FbjYxNFctdfau+vk3x9ntzL5jSyAB4VR5XH/GVLbYt9vNLSupRUdGI+PgIh6PkS0ETg9AxJFaxrqNAaVLcUP9Ihxx4J0fJ/uFS0ZIr7c3bssT0D1N6XbBLYQqBnjFuqH+4of6RDq2BE4rAlhb19ttZHhrdUlOM/JnSx5QmdffdO7Bly12dwokTBOF/aA2cUAQuFS250t78mdLHlCZlNtuQk7NP9roIgiAAcuCEQohV0ZKSYuTPlD62NCkuVTCCIAhvIAdOKAJbmlOXLmGMx6WkGPkzpS8ujtlutvYQBEF4CzlwQhHYUphWrRojW2qT0mlSWq0Kq1aNkb0ugiAIQGEHXl5ejjlz5qBv377Q6/UYPnw4Dhw44PjdZrNh6dKlyMjIQEJCAiZOnIgTJ04oaDEhF3bN4xkz+iIrqydmzOiLzZsnYNSoXozHpQSdsdXhi3SlUaN6YcuWu5CUFI0uXUKQlBQddAFsBoMR2dm7MWnSNmRn74bBwL7NKkEQyqNYGlltbS3GjBmDESNGYPbs2ejevTsMBgMSEhLQv39/AMAbb7yB5cuXY+XKlUhPT8crr7yCw4cP48iRI4iJiRFUj9gUBTlSmORW//KlupmUFI7Vq49jwYICWCw2aDQqLFkyHBMmJAeUAptcuPePL+4FU5mAqzLZzJkZWL/+JGO9bOlrQmy1X1tT04ymJgsslquvAzF64KGh+oC9/0qrA1KaFDfUP9JRzIEvXrwY+fn52LVrF+PvNpsNGRkZyM7Oxrx58wAATU1NSE9Px0svvYRHH31UUD1iBgdT2pHQl5icZfiyPHfEPjyrVx/H/PmHPY536xaGmpqrAVty2qgkzv3ji3vBVKZ9RzZncROtVuUS5W6vt6zM5JK+Zj93zZqxyMs7ymmre+obE0L0wPfuPYa//OWEz8aoN/j6+RECOShuqH+ko9gU+vbt2zF06FA8+uij6NevH2655Ra88847sF1RWDAYDKioqMBtt119eURERGDkyJEoKCjwiU1ypB3JnboUaOpmCxYw972z8wY6prqUL+6FUNUzdydrr5ctfW3u3P28tvIphAHCIvZXrz4bUGPUmUB7fghCThTbyKWkpATr1q3Dn/70Jzz99NM4fvw4nn32WQDA7NmzUVFRAQDQ6XQu1+l0Oly8eJG13KKiIkHHmCgurmY5fsmvZfiyPCbElOM8xcqHnDYqib0NvrgXbGUKu/YSamqaGH9rbjazXmO3le1aZ6KiLLxtq6piTpULhPvvj+dHCEr3Q6BD/cMM38yEYg7carXixhtvxMKFCwEAgwcPRnFxMd59913Mnj3bcZ5K5RrZa7PZPI45495gMdMzaWnncPRoHcPx7n4tw5fluSN2+kqj2SfYictlo5I4948v7gVbmcKu7Y6qKjNMJpPHb+HhWjQ2ejpxZ1u7dStkvNZOamosXn75Vt6pZp3uV1b7lL7/vn5+hEBTxNxQ/0hHsSl0vV7vCFazc80116CsrMzxOwBUVla6nFNdXe3xVS4XcqQdyZ26FGjqZkuWDGc83q2ba75zR1SX8sW9EKp65p6iZq+XLX1txYosXluZrlWpgOuv7yoqYn/OnNSAGqPOBNrzQxByotgX+IgRI3D69GmXY6dPn0afPn0AAMnJydDr9dizZw+GDBkCAGhubsahQ4ewePFin9hkTzvyRp1JjjJ8WZ63zJkzEABYo9ADwUZf4Yt7wVYm4KpMZo9Cd683OTkWW7bc5aEON2pUL2RmxnPaak99Y7pWDL17RwTUGHUm0J4fgpATxaLQv//+e4wbNw7z58/HtGnTcOzYMTz55JN4/vnnkZ2dDaA9jey1117DypUr0a9fPyxfvhwHDx70aRpZZ4P6hxvqH36oj7ih/uGG+kc6in2BDxkyBB9//DEWL16MV199FYmJifh//+//YdasWY5znnrqKTQ1NeGZZ55BbW0thg4dik2bNgl23gRBEATRUVFUTvTOO+/EnXfeyfq7SqXCc889h+eee86PVhEEQRBE4EN7oRMEQRBEEEIOnCAIgiCCEHLgBEEQBBGEkAMnCIIgiCBE0SA2gvA1SitREQRB+Apy4ESHhUmJqrCwKiBUsgiCILyFptCJDgspUREE0ZEhB050WC5eZJbCFCKRSRAEEeiQAyc6LD17RjIeT0hgPk4QBBFMkAMnOiykREUQREeGgtiIDgspUREE0ZEhB050aJKTY7F27W1Km0EQBCE7NIVOEARBEEEIOXCCIAiCCELIgRMEQRBEEEIOnCAIgiCCEHLgBEEQBBGEkAMnCIIgiCCE0sh8AClgEQRBEL6GHLjMkAIWQRAE4Q9oCl1mSAGLIAiC8AfkwGWGFLAIgiAIf0AOXGZIAYsgCILwB+TAZYYUsAiCIAh/QEFsMkMKWARBEIQ/IAfuA0gBq3NC6YMEQfgTcuAEIQOUPkgQhL+hNXCCkAFKHyQIwt+QAycIGaD0QYIg/A05cIKQAUofJAjC35ADJwgZoPRBgiD8DQWxEYQMUPogQRD+hhy4D/AmnYhSkYIXSh8kCMKfkAOXGW/SiSgViSAIghAKrYHLjDfpRJSKRBAEQQiFHLjMeJNORKlIBEEQhFDIgcuMN+lElIpEEARBCIUcuMx4k05EqUgEQRCEUCiITWa8SSeiVCSCIAhCKOTAfYA36USUikQQBEEIgabQCYIgCCIIIQdOEARBEEEIOXCCIAiCCELIgRMEQRBEEEIOnCAIgiCCEIpCJ0RDgisEQRDKQw6cEAUJrhAEQQQGNIVOiIIEVwiCIAIDcuCEKEhwhSAIIjAgB06IggRXCIIgAgNy4IQoSHCFIAgiMKAgNkIUJLhCEAQRGJADJ0RDgisEQRDKQ1PoBEEQBBGEkAMnCIIgiCCEHDhBEARBBCHkwAmCIAgiCCEHThAEQRBBiGIOfOnSpYiLi3P575prrnH8npOT4/H7HXfcoZS5BEEQBBFQKJpGlp6ejm3btjn+rdFoXH4fO3Ys1qxZ4/h3aGio32wjCIIgiEBGUQeu1Wqh1+tZfw8LC+P8nSAIgiA6K4qugZeUlODaa6/FoEGD8Mc//hElJSUuvx86dAj9+vXD0KFD8eSTT6KqqkoZQwmCIAgiwFDV1tbalKj466+/hslkQnp6Oqqrq/Hqq6+iqKgIhw8fRrdu3bBx40ZEREQgOTkZpaWlyMvLg9Vqxd69exEWFsZablFRkR9bQRAEQRC+IT09nfN3xRy4OyaTCTfccAOefvppPPHEEx6/X7x4EQMHDsT//d//YcqUKQpYSBAEQRCBQ8CkkUVHRyMjIwPFxcWMv/fs2RO9evVi/Z0gCIIgOhMB48Cbm5tRVFTEGrR26dIlXLx4kYLaCIIgCAIKOvDc3FwcOHAAJSUlKCwsxCOPPILGxkY88MADMJlMyM3NxXfffQeDwYD9+/fj/vvvh06nw6RJk5QymSAIgiACBsXSyC5cuIBZs2bh0qVL6NGjBzIzM/H1118jKSkJTU1N+PXXX/HZZ5+hrq4Oer0eWVlZeO+99xATE6OUyQRBEAQRMARMEBtBEARBEMIJmDVwbygvL8ecOXPQt29f6PV6DB8+HAcOHGA896mnnkJcXBxWrFjhZyuVQ0j/nD59Gn/4wx+QlJSEnj17YvTo0Th16pRCFvsfvj4ymUx45plncN111yEhIQGZmZlYuXKlghb7j4EDB3psaxwXF4d7770XAGCz2bB06VJkZGQgISEBEydOxIkTJxS22n9w9U9bWxsWLlyIkSNHolevXujfvz9mzZqFc+fOKW22X+EbQ850xne0VBTdiU0Oamtrceedd2LEiBH497//je7du8NgMECn03mcu2XLFnz//ffo2bOnApYqg5D+KSkpwZ133on7778fX375JeLi4vDbb78hKipKQcv9h5A+WrBgAfbu3YvVq1cjOTkZBw8exFNPPYXu3bvj/vvvV9B637Nnzx5YLBbHv8vLyzF27FhMnToVAPDmm29i5cqVWLlyJdLT0/HKK6/gd7/7HY4cOdIplry4+qexsRE//fQT5s2bh4EDB8JoNCI3Nxf33HMP8vPzodUG/StYEHxjyE5nfEd7Q9CPnrfeegsJCQkue6anpKR4nFdaWor58+dj8+bNuOeee/xoobII6Z+8vDzcdtttWLJkCes5HRkhffTdd9/hvvvuw+jRowEAycnJ+PDDD3H06NEO78B79Ojh8u8PP/wQMTExmDp1Kmw2G1atWoWnn34ad999NwBg1apVSE9Px+eff45HH31UCZP9Clf/REZGYvPmzS6/v/766xgxYgROnTqFAQMG+NFS5eDqIzud9R3tDUE/hb59+3YMHToUjz76KPr164dbbrkF77zzDmy2q0v7ZrMZs2bNwrx589C/f38FrfU/fP1jtVrx1VdfoX///pg+fTr69u2LW2+9FZs2bVLYcv8hZAyNGDECX331FcrKygAABQUF+Pnnn3H77bcrZbYi2Gw2fPjhh7jvvvsQGRkJg8GAiooK3HbbbY5zIiIiMHLkSBQUFChoqTK49w8T9fX1AIC4uDg/WhY4MPVRZ35He0PQO/CSkhKsW7cOKSkp2LhxI+bMmYNFixZh7dq1jnOWLl2Krl274rHHHlPQUmXg65+qqiqYTCb84x//wK233oovvvgC06dPR3Z2Nr766iuFrfcPQsbQyy+/jIEDB+L6669Hjx49MHHiRLz44osYP368gpb7nz179sBgMOChhx4CAFRUVACAx5KVTqdDZWWl3+1TGvf+cae1tRW5ubkYP348evfu7WfrAgOmPurM72hvCPopdKvVihtvvBELFy4EAAwePBjFxcV49913MXv2bBw4cACffPIJ9u/fr7ClysDXP1arFQBw1113ObawHTRoEH788Ue8++67ncJB8fURAKxZswYFBQX49NNP0adPHxw8eBDPP/88kpKSOpVO/fvvv48hQ4Zg0KBBLsdVKpXLv202m8exzgBb/wDtX5mzZ89GXV0dPv30UwWsCwzc+6izv6O9Iei/wPV6vceUyzXXXOOY6ty/fz/Ky8vRv39/dO/eHd27d8e5c+ewcOFCXHfddUqY7Ff4+qd79+7QarWc53R0+PqoqakJixcvxqJFizBhwgRcf/31mD17NqZNm9apImWrqqqwY8cOPPLII45j9p0R3b+2q6urGQNJOzJM/WPHbDbjsccewy+//IItW7agW7duClioPEx91Nnf0d4Q9F/gI0aMwOnTp12OnT59Gn369AEAzJo1yxFcY2f69OmYPn0644PW0eDrn9DQUAwZMsRDxc35nI4OXx+1tbWhra0NGo3G5RyNRuOYwegMfPLJJwgLC8O0adMcx5KTk6HX67Fnzx4MGTIEQPu2yIcOHcLixYuVMlURmPoHaB8/f/zjH3HixAls27atU28HzdRHnf0d7Q1B78D/9Kc/Ydy4cVi+fDmmTZuGY8eO4Z133sHzzz8PoH0tzv1LQKvVQq/X80q1dQT4+gcAnnzySTz66KMYOXIkRo8ejf3792PTpk34+OOPFbTcf/D1UWxsLEaNGoVFixYhKioKffr0QX5+Pj777DMsWrRIYev9g81mwwcffIBp06a5pIapVCrk5OTgtddeQ3p6Ovr164fly5cjKiqqU0USs/WP2WzGI488gh9++AGffvopVCqVI24gNjYWERERSpnsd9j6qLO/o72hQ+zEtmvXLixevBinT59GYmIisrOz8fjjj7OuwQ0cOBCzZ8/G3Llz/WypMgjpn48//hj/+Mc/cP78eaSlpeGvf/1rp3oB8/VRRUUFFi1ahD179uDy5cvo06cPHn74YTzxxBOdYq3322+/xZQpU/Df//4XQ4cOdfnNZrNh2bJlWL9+PWprazF06FAsX768U01/svWPwWDA4MGDGa9ZuXIlHnzwQX+ZqDhcY8idzvaOlkqHcOAEQRAE0dkI+iA2giAIguiMkAMnCIIgiCCEHDhBEARBBCHkwAmCIAgiCCEHThAEQRBBCDlwgiAIgghCyIETRAdh4MCByMnJ4T3PYDAgLi6u02zUQxAdFXLgBBFgfPzxx4iLi0NcXBy+/fZbxnNuu+02xMXFYdiwYbLUuXTpUkedcXFx0Ol0GDRoEJ577jnU1dXJUoev+PXXX7F06VIYDAalTSEIvxL0W6kSREclPDwcGzZswOjRo12OnzlzBt9//z3Cw8NdjhcWFkKt9u5v8ldffRWxsbFoaGjA7t27sWrVKvzwww/YuXNnwO44d+LECbz88su45ZZbkJycrLQ5BOE36AucIAKUcePGYcuWLWhpaXE5/q9//Qvx8fG48cYbXY6HhYUhJCTEqzqnTJmC++67D3/84x/x0UcfYfLkyTh8+DAKCwu9Ktdms6G5udmrMgiCcIUcOEEEKNOnT4fJZMJXX33lcvzzzz/HtGnTPL62mdbAy8vL8cgjjyAxMREpKSl44oknUF9fL9gG+9d/SUkJWltbsWTJEowdOxbJyclISEjA7bffjh07dnhcFxcXh7/85S/YvHkzRo4cifj4eGzcuBEAYDQakZubi4EDByI+Ph7XX389XnzxRY8/VOxlfP3118jKyoJer8eQIUPw+eefO875+OOP8dhjjwEAJk+e7FgCoPV9ojNAU+gEEaD06tULo0aNwoYNGxxyi4WFhSguLsa9996L48ePc17f3NyMu+++G8XFxcjOzkZycjK2bt2KOXPmCLbh7NmzAIBu3bqhvr4e7733Hn73u9/hD3/4A5qamrBhwwY8+OCD+Pzzz3H77be7XHvo0CFs2bIF2dnZ0Ov1uOaaa9DU1IRJkybBYDBg5syZSE1NxfHjx/H222/jt99+wyeffOJSxpEjR7B9+3Y8+uijeOihh/DBBx9g9uzZGDhwIPr3749Ro0YhOzsba9euxd/+9jdcc801AIDhw4cLbiNBBCvkwAkigJkxYwbmzZuH2tpaxMXF4V//+hf69u3r0N7m4v3338epU6ewevVq3H///QDatZcnTZrEes3ly5eh1Woda+D/93//B71ej5tvvhlhYWH45ZdfEBYW5jj/8ccfR1ZWFlasWOHhwE+dOoV9+/Zh0KBBjmOvvfYaioqKsHfvXvTv399x/Nprr8W8efNw8OBBjBw50nH85MmTyM/Pd5w7depUXH/99fjoo4/w0ksvISUlBSNGjMDatWsxduxYZGVl8fYLQXQUaAqdIAKYu+++GyqVClu2bIHZbMbmzZsxY8YMQdfu2rULOp3O5XyNRoPHH3+c9ZoRI0agb9++GDRoEJ5++mkMHjwYn3/+OSIjI6HRaBzOu7W1FZcvX0Z9fT1GjRqFH3/80aOs4cOHuzhvAPjiiy8wfPhw9OjRA5cuXXL8N3bsWADwiLrPyspycfTx8fFIT09HSUmJoD4giI4MfYETRADTpUsXjBs3Dv/+97/Rq1cvVFVVCXbg586dQ2pqKjQajcvxfv36sV6zfv16xMXFITIyEn369EHPnj1dfv/ggw/wz3/+E6dOnYLNdlWJmClCPSUlxePYmTNn8PPPP6Nv376M9VdXV7v8u0+fPh7nxMXF4fLly6xtIIjOAjlwgghwZsyYgUceeQQAMHToUFbn547NZmN0rM6O152bb74Zer2e8bfPP/8cTz75JCZMmICnnnoKOp0OWq0WH3/8MTZs2OBxfkREhMcxq9WK0aNH469//StjHb169XL5t/sfH0LaQBCdBXLgBBHg3HnnnYiNjUV+fj6WLVsm+LqkpCQcP34cFovFxRGeOXNGkh2bNm1CSkoKPvnkE5c/DMREfKempsJkMjmmzOUgUPPTCcLX0Bo4QQQ4YWFheO211/Dss8/innvuEXzduHHjUFVV5fJ1bLFYsGbNGkl22P8IcP76LSkpwbZt2wSXMW3aNHz//feMqWdNTU0wmUyi7YqMjAQA1NbWir6WIIIZ+gIniCBAjOO288gjj2DdunWYO3cujh07hpSUFHz55Zei8sCdmTBhArZu3YoHHngAEyZMwIULF7Bu3Tr07dsXP//8s6Ay5s6di//85z946KGHcO+992Lo0KFoaWnB6dOn8cUXX2DDhg2it4cdPHgw1Go1Xn/9ddTV1SEiIgJDhw5lXIMniI4EOXCC6KBERERgy5YtmD9/Pt5//32EhIRg0qRJmDNnDm655RbR5f3+979HdXU11q1bh7179yItLQ3/+7//i+LiYsEOPCIiAl9++SXefPNNbNq0CRs3bkRUVBRSUlKQk5OD9PR00Xb17NkTb7zxBt544w089dRTsFgsWLlyJTlwosOjqq2tpWgQgiAIgggyaA2cIAiCIIIQcuAEQRAEEYSQAycIgiCIIIQcOEEQBEEEIeTACYIgCCIIIQdOEARBEEEIOXCCIAiCCELIgRMEQRBEEEIOnCAIgiCCEHLgBEEQBBGE/H9ZbcKNuu0ZCgAAAABJRU5ErkJggg==\n", 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fX4//+Z//wdmzZ9G/f3+8//77yMzMjGGvCYIgCCL2mEaYDx48GGfPnpX9O8dxmD59OqZPnx69ThEEQRCEBbCEzZwgCIIgCHlImBMEQRCExSFhThAEQRAWh4Q5QRAEQVgcEuYEQRAEYXFImBMEQcQRnNOJtIkT4Rg5EmkTJ4JzOmPdJSIKmCY0jSAIgggPzumEY/Ro8JWV/mv8jh1wrVwJIT8/hj0jIg2dzAmCIOKE1JkzRYIcAPjKSqTOnBmjHhHRgoQ5QRBEnGCTKQltO3Eiyj0hog0Jc4IgiDjB07kz+3qnTlHuCRFtSJgTBEHECQ1lZXAXFIiuuQsK0FBWFqMeEdGCHOAIgiDiBCE/H66VK5E6cyZsJ07A06kTGsrKyPktASBhThAEEUcI+fmoX7Qo1t0gogyp2QmCIAjC4pAwJwiCIAiLQ8KcIAiCICwOCXOCIAiCsDgkzAmCIAjC4pAwJwiCIAiLQ8KcIAiCICwOCXOCIBICKg1KxDOUNIYgiLiHSoMS8Q6dzAmCiHuoNCgR75AwJwgi7qHSoES8Q8KcIIi4h0qDEvEOCXOCIAzFjI5mVBqUiHfIAY4gCMNIPnYMjsceM52jGZUGJeIdEuYEQRhG1wULZB3NYl2Wk0qDEvEMqdkJgjCMpKoq5nVyNCOIyELCnCAIw2jOzmZe1+poZkZ7O0FYAVKzEwRhGMdKS5G1f79I1a7V0YwSuxBE6NDJnCAIw2jq2hWulSvRNHYsWgYPRtPYsZqFMSV2IYjQoZM5QRCGEqqjGSV2IYjQoZM5QUQZsguzocQuBBE6dDIndMM5nd543R9/hKdzZ4rX1YGZ7MJme44NZWXgd+wIyd5OEIkOCXNCF2YSRtHCJ/R6HDqE1O7dwxJ6SnbhaMZAm/E5UmIXgggdEuaELswijKJFoNBLBoCdO8MSemaxC5v1OVJiF4IIDbKZE7owizCKFlo9rLXawc1iFw7lOZKtn9ALvTPRg07mhC7MIoyihRahp0dlbRa7sN7naEa1PGFu6J2JLnQyJ3SRaNWntAg9PfHRPrtwKHHYRqL3OSZiDDidKsMjEd+ZWEInc0IXieakpOUkrUdlbRYPcr3PMdHMK3SqDJ9Ee2diDQlzQjeJ5KQUKPQaZLzZtaqszSYg9DzHRDOvaHUQNMvmzIwk2jsTa0iYE4QKPqF34MABFBYWSv6u1Q5uVg9yLZjF1h8tjPaVSEQS7Z2JNWQzJ4gw0WoHt7La0Sy2/mhhtK9EIpJo70ysoZM5YTic04nU6dNh374dANAyYAAa5syJ6x+xFpW11dWOkTavcE4nUqdNg33HDgBAy5VXomH27Ji8N0b7SiQqiWSSizUkzAlD4ZxOOEpKwB896r+WvG4d+N274VqzJq4FuhqkdpSH+d6sXQt+166YvDdaHAStvjkj4gtSsxOGkjpzpmhB9sEfPZrw6sdIqx2tHEplxvfGd6p0lZejftEiZs6ARArTJMwNncwJQ5FTPQJS9WMiegJHSu1odWcsPe+NXiL1niVamCZhbkiYE4Yip3oExOpHqwsfs2FlT3lA+3ujl0i/Z2QTJswCqdkJQ2koK4M7N1dy3Z2bK1I/kiewsVjdGUvre6MXes+IRIGEOWEoQn4+XGvWoGnECHiys+HJzkbT8OESJyYrCR+fLbpHaalpbdFWd8byvzfDh59/b0aMCNv5zUrvGUGEA6nZCcMR8vNRv3Sp4mesInyMLoEaKeLBU17Iz0f9O+8Yek+rvGcEES50MidiglU8ga2ippV4yg8ZAjQ0IGPwYGQUFcFWURHrLsYEre+ZlSMBCAKgkzkRI6ziCaxVTWurqED65Mngzp6FkJWFuvnz4SkujkYX/ficsWwVFcgYNQpcS4v3D9XVyBg1CrWrVkW9T7FGy3tGzphEPEDCnIg6ZhB8WtGippUTnq6FC5G8fn3UQ+/SJ08+35dWuJYWpE+ejNpduyLevtlQ8zi3eiQAQQAkzIkoY7VToxZbtJzwdDzwgOh6tE573Nmz7OtnzkSuzdZY7h4yleXMDDnJEfEACXMiqljt1KilBKqs8AwaJ19ZidTp0wGHI6KndSErC6iulv6hrg6c02l4eywnQfv77wN2O9DSAqSmQujQwbQaGHKSI+IBEuZEVJEVfOfORbcjOlArgSorPBkkffopuIYG/7/5rVvhLiqCrbraMOFeN38+MkaOBCcIous2tzsiqmOWmtrmdgNut/cfLhfgcplWAxMPkQAEQd7sRFQRsrLY19u2jW5HDKRu/nwIdvG+WOA45mcDBTngzT2evHYt7Js3I3nZMmTcdBMyc3LQpkMHZHbpAn7FCt398RQXw92nD/NvkVAdK6ViDcSngQHM5T1OpTqJeICEORFVmILPbkfd/Pkx6pE+WELIU1yM2lWr4M7Lg6dtW7jz8uB65RVJSJSQmqp6f1tVFWyNjeDcbtjq6uC4//7QBLqMMI+E6lgpFWsw3LlzfrV88rJl/k1M5hVXILN7d6TdfXdMBLtaURWCMDvc2bNnBfWPxQdyalLCi1Hzo1bYwu/Nfu4chLZtTWtLDca5YQMueewxiTpW7hTnn4fWkCjU1iJ53Trd7XrS01Fz/Lj0vgp2d1a4lVJfw4HVlhzuvDy4Bw5E8rJl8p/JzY3bcrm0BilD8xM6JMwJP0bMTzSFSLRp+dWv0GH9esn1prFjNdmh9Qi9QASeR/Xp07L3cHfoAM7lAtfcDCElBXVz58I9ZoxkMxFJD3NfW01ffw3Hf/4jsdcDXg1M7apVSJs9G/bNmxXvp3VOrQatQcrQ/IQOOcARhhJPMbvBJ+AmRr1tQLsdWpLAJCMD/O7dzDreou+lpPj/P3N+WwU9AHCtqnn3n/4ET1FR1ELEAp0Ee5465dW8VFUBTU0Sb3YtankKCyMIfZAwJwwl1Jhds9U2Z52AbWlpzM/qsUMHJzAJPD0LTU2wb9uGQNc5AUDd3Lnn+6DB2YwDYN+/H9i/PyaZzITcXLgHDpR9lizv8WAoLIwg9EHCnFBFj6ANJWbXDOk0g8eI2lqJsLHX10NwOMC5XP5r4YYwBQt3fsUKpD/0ELjGRpHK3IceZzPgvFakoawsKpul5GPH4AjyKwh+ln4NxbRpSPq//wPX1CS6R6hlT822ISSIaEI2c8IPa3702sBDsZmnTZzIdIiKlt2U1WchNVUSRgYALQMGwFNQELN88qHY3VuuvBLcTz9Jnkl9WRnSZswwNK2uXr8CzulE6rRpsO/Y4e9rw+zZuufUKr4atAYpQ/MTOpYJTZs9ezaysrJE//Xo0SPW3Yp79FYNCyVmN9bpNFljZAlyAOC/+gqoqkLdvHkxCWGSzO/AgVDbjXMnTzKfoWPCBPBHjsBWXQ3+yBFkjBoVdnW1pKoq5nW5Z+kre1pz4ABqDhxA/dKlIc2p2ntqprj2SJNIYyXOYyk1e2FhIT744AP/v3mej2FvEgO9gjYUVWes02nKjZF1Ouc8HiRv2AD+5pvh+vDDmJz6glXzTT7VfF2dt48Bn3UXFEBo3x44ckRyn2CP88C0uqGqrJuzs5nXI/0sld5TM5hxokUijZUQY5mTOQDY7Xbk5OT4/7vgggti3aW4R4+gZSUDcYwerXoyiHVtc7kxNt94Izzp6cy/8SdOiLQTek9DtooKZBQVITMvL+x64+4xY1C7dSs8BQUiQe5xOFA3bx483btrvpdcUhctzxEAjpWWxuRZKr2nWrRLep+fWU+/ejVpRPxgqZP54cOH0bt3byQlJWHAgAH4wx/+gG7dusl+/sCBA5quEecJnp/kcePQY+tWpAaETzXk5uL7cePQFPTZgqeeYi4kzU88gcpnn1VsN/kvf0HXBQuQVFWF5uxsHCstRVNTExCF58UaY0taGpqOHIE9yDkrkIZDh3DgwAEkHzuGHlOnIjng+56tW/H9vHlo6tpV8j3Hzp3oOWWKN385AFRXw3Hbbdj/8stw9e8f0hhYc29zudA0dy4qS0sl4xMgPsH7aEpPR/MTT4T8HNG1K/bG4Fkqvafdnn3WWwAmiFCfn97PBxPJNajHoUOKY7UCVulntFHzJbCMA9zHH3+M2tpaFBYW4qeffsLzzz+PAwcO4IsvvkD79u013YOcK5SRmx+tyUccI0cyk4G0DB4MV3l5RPpsFP4xVlaC37dP5LEuh8+pS9aBb/hwICNDoqrOKCoCz1B7u/PyQq4cJzf3nrZt0TJsGJpuuQXpDz8MW8C4ggW6WlKX4OfIUsV/39QUs9+Y3Huq5mCp1wEzHIfNSK9BsXYmDRdao0PHMifz//qv/xL9e8CAAbj88suxdOlSTJ06NUa9SgyCbbRyxNr2HQ6+MaZNnOj3rFbC3SosAHl7bdJnn4krpLXaLiNROU5u7m3nziF52TIkrV0r2aBw8KaKRVKSKK2ulucoZ5tN/stfwCUnxyRETO49VauKptcvJNYOm0pQBbjExVI280AyMjLQq1cvHDp0KNZdIVoxyvbNOZ1Iu/tuZBYWIrOwEGl33RU1m6SsM1xSEjx2O4SUFDQNGSJyfpMTfpIKaa22SyEjg92GwxFyv1lzL+qLjKbB078/apxO1O7a5Q9L0/Ic5WyzF/75z9IiKpdfjow+fcL2lA8VtQgLvZtQT2Ym+7rMc40mVAEucbHMyTyYhoYGHDhwAIMHD451V4hWJOlKQ4jD5pxOOEpKRClOk9etA797d1SKb8g6w40ejV2//z1TBcg6DQkpKeAaGyWftZ04AXdhIfiAwik+3GGoFwPn3v7RR7BpPOXbvvwSmXl5ojhzLc9RbtOTsWcP+J9/Fl3jBAH88eMxrWeupF3SfZqVKW8rez3KaNWkEfGFZYR5WVkZbrnlFuTm5vpt5nV1dbjrrrti3TUigHAXktSZM5m5yvmjR0X53SOV7UtuYW8cPx4FTz0FR22tpD2W8IPLheS1ayX393TqJK+m9Xgk1/SMM9BUoFSVTNRmYyPQ2AhUV4uErdpzlNv0KDngGBH6Fgn0bkJt1dXs6zU1kewmQShiGWF+/PhxTJgwAadPn8YFF1yAAQMG4OOPP0ZeXl6su0YYiFLucZ9NMpKxtKyFvXH8eKRPnYpMlRSlwTnX+X37mKc9uTChYLVuqONkagpkMtqJ2gsQtmrIbXpcF16I5E2b5NsICH1jjQuAqeztLKzsG0LEL5YR5q+99lqsu0BEAaXc477FMhKV2ZROimkTJ+puT+m0p1WtKzvO6dMBh0NW4DE1BRprqWt1wpMb3w+VlWjzww+y6WaFtm3lxzVtGvjvvhP9LWntWrh79YKne3fT5Fo30snMTBqKSBDv4zMTlhHmRGLQUFYGfutWiao9sPiG0d7EaifgUNuTO+1pVevKesl/+inTSx6QP9VyTqdEUDL73Lat4t/VxtfU1OQd28SJSPryS0kFuPqnn0bq668z72ffsQO2oHSwnMsF+86dwM6dphHsRviGAPGfrS3ex2c2SJgTEmK5mxby8+Faswap06fDvn07AG9xk4Y5c0L2PmYROEbuyBFJ3HfgyTsSalUtal1dXvKMU23gwikRQDyPpE2bwAXY6QW7HXXz54c8Jv998vOB/HxwX34p7jeA5PXrdVd+838/QLDHWigY4WQWCQ2TmYj38ZkNEuaECDPspoX8fNQvXSr793DVnForj/lO3rGK3dVj+2adatVU8o0VFUifPBncuXOiOHMjUNJm1M2bx5xPd+/eTKdBFoFCweYbx6lTQHMzkJoKoUMHQ8cTCcwcr24E8T4+s0HCnBBhhd10uGpO1hhZ+E7evvaan3gCbV2uqJU+1WX79qWGDUKikt+6Fe6iItiqq+Hp3Bmu8vKIjEMpFlvu+QGQOA0qYTtxwpvjftQocC0t5//gcgEuV0xD4bQQ74508T4+s0HCPMJYzQHEzLtp0VxmZnrjeoMqf2lByWPeR/DJW8jPR+Wzz0Yt1aT/tBlUa5xzOsHv3i0N36uvZ95HopI/elT0XfuGDUB1NbimJgg2GzwXXwxPUVH476lKLLacmtov5A8fhu3f/xalnw3G06mTd44CBXlgU0He+Wb7LUZC42OmMVI2uuhCwjyCmEFlrRez7qbVVON65lVujO68PAj5+cyTN79iBS6fMgV8Y6OxQo+B5LQZFAPuLiqSCHNbfb1EBS8kJ4NTKBQDQKSa59xu2PbvB/bvD/s9DTUWO1DI+wUTQ7D7hEKGStIon3e+GX+LRjnS+WCN0b52LVzvvRezRD1Gjo9QxrLpXK2AWcoR6inXGOtypHKoqcb1zKvcGF3l5XCVl6N+0SKJIHfcfz/sDQ3gBAE2txv2/ft1lQbVA+u06TtlAoDtP/9hfzFYS8HzIffBN5+hlvo0YlPoE+yujz9G7ZYtzBSlQlaW8j1avfPN8lsMxj9GxnunF9YYbS4XMu68M+olWn3vTfqUKQCAunnzwh4foQydzCOIHpW1nFo1XPSeSMy6m9aiGtdqCtA7xvSHHmKWCwXOC4SmW27xfq6xEUJKCurmzoV7zBhN/QlGqRALv2IF+P372X8PSh/L1dfD43AoqqqVsB0+LHl3klavRvPQoWiYPVs9cU1QiGFgeKFe5NTydfPnS23mvu8EeOeb2XxkFHJj5FyuqPq8mFELkgiQMI8gWk8namrVcAjFoS3SuZ0Dy41yp05ByM5WjR3WEs4UyqlPU38ZOdYDse3eDceyZX6Bz9XVwXH//airqkLSzp267ZdCVhbAUFMLbdvKbizk6pN7unZFy2WXeUu77tmjmgUuEO7kSUnIHtfYiOS1a8Hv22eKxdlTXIzaVau8G+GqKqCpienNblbzkZEo/UaiuWmxghNtPEJq9giiVWWtplYNB7OdSHy79uRly2DfsQP8kSOw79yJ5GXLkHHNNXDcdBNTnatWFUyvKUCP+lhISVG8l+3AAYkg5QCkT58uqh7mGD0a/IoVyCgqQmZeHjKKipiVxOrmz4dgF++zfadMtY1FMPyBA2gcPx6eggKmIJdzH3Tn5kLIzpa/r4qKmpVj35df32g8xcWo3bULNT/+iJrTp1Fz7JioChxgjPkoVJNDtGgoK4NHpvJeNDctZltzEgU6mUcQrepcrfWtQ/FUNduJRMn2bXO5YNuxA9ixg5n7XDSXGRkAx8FWU6PbFKBXDVg3dy4c99/PPPm6CwpgO3yY3U6QDZuvrIRjwoTz16urkTFyJFyvvCJSyYtOm0Ex4EJKCri6OklbQkoKhJYW2IJC1DhBQPrkybKC2d2rl1dD0tgoGZ+nY0fmd3zILc6c0+n1ktfxnUgTrvnICqpjIT8frvfe89rIGc6C0YBzOsEFaXN8xJMWxIyQMI8wWtS5SmpVH0YW3YilQ5sW2zfAVssZpf7XqwZ0jxkDF4DUQG/2wkJ4+vb1elRffTVTwLIIFvCcIMDxwAOoGTBA9Bx9p81gWBsLAUDd3/+O9EceAWprpW2eOQPb6dPM/nj69oWnb19JlTX+6FG4i4rgLiiQ3XyxFufkY8fgeOwxSQIb/3diWPM7nPfHKqpjT3ExarZsiYnPi3+NYghzMzjRxjukZjcBSmpVH6F64/pOJCxP4FigJ5Wn0ikuHJVnKGpA95gx+Obzz1F95gxqTp+G64sv/N65dXPnStTVeqLfuZYW/3NUG5d7zBi4Xn0VnvR0CDwPT3o6XK++CveYMRDat5fpvFt0UvPhcTjQUFYmPx81Nd53Z/hwCKmp4lvKLM5dFyxQTvoSFH9uq6hQNTuYASupjo30kNeDnNbNnZdnKg1GvEIncxOgpFb1Ec5iEmmHNj2wNAVyyKnlQtVS+M0UMt7goaoBfSf3QG/2+j/8AakLF4pTsdrtsglObCdOyI6rvqwMaTNmiCIdao4fl9yD5dkt2O3wFBTAtnevdLx9+njj6hVMMUJ+PurfeQcNvrlTOe0lyZzI/eMMiDO3VVQg47bbwPlMAzJmBzNgNnOVGZFbo3y1AYjIQsLcJMipVf1/N2gxiXWGKJHt8vBhcCdPQmjTBnxlpWY7XygqT7WkM+GqAd1jxqAmSAC5hg8XCcCmW24R28wD8HTqJDsuiZ39ttvgadMGXE0NOJ5H89VXo+Gll2Q3hSmLFwMsYd6tGwBtphitG8JmBac53zh9pN9333lB3gonCHBMnIiaAQMARK+2udrvwmzmKjMil8LX9uWXyMzLMzTklpBCwtwiGLGYmMWJhyUYOI0nP0CflsJ3X/uGDUw7ric7Gy1DhqBx/HjDBQdrnC4AjgceEJ+eU1IAlwu2kyeZ95HY2d1u8GfOeP/R0oLkDRvA33wzXB9+yNwUNuTmKr47RuYWOFZaiqz9+9nq1qD3Vc6uznk8SJ0+XZKnPVIlULX8Lsyaf8FUyKTwtTU2Ao2NhobcElK4s2fP6k9ubVEOHDgQtdzakUCPwGORNnGixNEJAJrGjkX9okWWmR+1cfjQUh2tZfBg1M2bJ/mcu6BAsskxan44pxOp06Yh6bPPxOlXHQ6mbVsrTcOHAxkZsvXMIymI+BUrkP7QQ0BDA5CUBPfll4Nzu715BHJy4OnWTdJmZrt2sMnk1vdkZ8sKe4D9fEJF6/tkBFb5jYWCY+RI2DdvVv2cOy9PVgsZz/MTaehkbiHCtX2b3YlHqwlAq5ZCS3U027ffwnHrrYr1zCMBv3evJO6bc7kkGds8PC8JN5MjeHPAf/45wHHgXK6Iqjh96W7957LGRnDbtsHdsyfcAwfKPkfhggsAFRu7bJsBzydc05HZfxdWQatza3DILWEMJMwTCDM78egxAWhVeWpKAVtdzQwLBCKzmCuF7wBep7SWbt3EdvYgtbzsvYMrpAX2v1XF6Vq4EMnr1xtqTmBlpeMA2FWKttQtXoyMkhLJd92dOsF9xRXsUq8BKDkN6jm1m/l3YSVYKXxZBIbcEsZBoWkJhFmLqAD6Q++0hN/oCYNjEYnFXE1b4HE4wG/bBtu334Lftg1Cp06oXbUK7rw8eNq2hbtjR2bYW3BoIwuupQWOSZNEWekyr7oKmVlZaJOVhczOncGvWKF7TGpZ6eSeo6e4GLVr1sDduTM8SUkQUlLQNGQIXB9+iIY5cxQz/gHKToN6Ms2Z+XdhdSQhm0Eht4RxkDCPMGZKAWm2mPNA9Ko6tcyrWgpYJQIXc19bPUpLw36GStoCd6dOSNq0CfyRI7BVV4M/cgQZo0YBgDddqdOJ2u+/h+vVVyEEVUQTkpI0tS/xHm9shA3ek7Stvh6O++9Hm6wspF99teZxqqW7BeSfo233bnCnToFrbobQ0oLmW27xhzL539Urr5SkKfU9H73FjFgx7Wb+XYRCrNYcVgpfDoAnPd27Ec3LI+e3CEJq9ghiFu/xQKIRcx5KBTg9qk6t8ypSx+/b57VTyzhcAex65oFtJQPAzp1hPUOlWupobgbn8YjH2pqjP9BhKHn9eolQttXXh+1AB5wv1pK0bx/sAwbA3b07bD/8AHCcpHiJD6V0tz5Yz9G+YAHSp007X6DG7Ub6tGmoA9BSWsqubR5kVjGqmJGZcjGEQyzXHNmNqsOB2k8+sezmyCrQyTyCmLWGciTxLZrBp0u1zF56VJ165tWvjt+8GbUffOBVV2dmwhN0spWrZ661La2ZzJRqqcsJ4mCHIblF09279/nT5ZAhEGzin7cgEzokB9fcDPv+/bDV1cHmcsk+y8CsdB5GO3LPMe3JJ5m29rQnn5R8Vs6sYoZiRmYilmuO3MbKVlUFx+jRpitME2+QMI8gRqgArUaoi6YeVWeo3sf+6lo//IDar74yrC09GxilcQpZWcy2gh2GZE+jBQXnBd7KlagtLz9va8/L82ZWC9Hs4CPwWQaqc5PXr0ft1q34avt21Hzzjaa5DdYuyF3nnE6k3X03MgsLkVlYiLS77vILBq3vjdZiRpJ2TWIi00osPfOVzFrxfogxA6RmjyBmqGcebUJZNAF9memM8D7WqlbV0pbsBmbCBLivvVYyJrm25dKxBjsMaQ3NYyWQcQ0Y4M++Z/v2W9iamlRmQAp37hxTnZu0di16duuGlD59VL3kOacTAscxzR6B/gCc0wlHSYnIFpu8bh343bvhWrNGcT5F99RQzCi4f2YzkWkhlp75vo1Vxk03MXMEUKhfZKGTeQQxWgVohZOC1tNlIKIa561e1hn9+sFx3XWaa5uH6n3sn9OhQ5FRVCSpp66lLbkNjO3ECUk9c1tFhbe94mJkdumCzNxcvybGl4418DTN2tCF47DlV1d//DFqt29H01VXeVXjOuZMaNuWqc7lXC5k7t3rf36ZOTnI7NABmV27irRNvufNShgjAKifNcv/b5ZTFaC/NrqWYkaBWNVEFmvPfCE/Hy1DhjD/RqF+kYUywEUYLZm3MvPyvPHOQXjatkVNq1BhnRSMzIIFGDM/Ei0DvIumkpZBLgOXD9Y4jchoppQhLrBNX1sNhw4hlZFKNKOoSDZuPJjgpDA+1OYokqjNfyC+fqbNnq0p25fouzYbasvLkbJ4MbM9D8ehfvZstJSW+q8pZRVrGTwYrvJyze37HTNlihkFIteu3jaDicYaFOlsf1raD3WtogxwoUNq9mih4EWtRQVo1nrKLPW4WgW4YNSSu0SqtrlSzHdgm7625BYapnocYHp3swQ5wPZaV8LIgjly8+/Jzoanc2fYDh4EbDYI7dv7n2UoMfycx4P0CRMgXHQRu71rrxUJckA5V4DWk17gXCllpNPSrhVOl7H2zKc89rGBhHkE0Wp302IrNWPKSaXxaRVKgLbkLpEYp9omQmubrGpl7s6dkbxtm67+sPwKOKcTqdOnw759OwCgZcAANE6divSpUw2z53ratGFeb7nyStQvXcr8m55StoFwP/0E97XXsvvBEJRyWcXcubmaVMdy72jdvHlIWbyYqqRFiFhvKGJNLKpTks08gmi1u2mxlZrxpGCUXbGhrEySFCSYSIxTbROhp02/p7zTCVd5OfhjxySfEVJTFe8R7Ffgc/5KXrsWtqoq2KqqkLxuHTJuv91Ye66c1khJm6SS1EUOzmaTtes2jh8v8QkR8vPhWrMGTSNGeDUF2dloGj7c7/ymhtw7mnHnnRJ/hkDfjEglkkk+dsz0fi9EeLB8gKIRmkcn8wii5zStVs/cjCcFo7QFQn4+XO+9h4w772TGWusdpyhpjcMBd8+esLW0SHbISqfLcOZWzmmredAg8E4nsz2WM5bcfTgZD3T7Rx8hbeJE5ilA6aRgq6lh3s9WW6t6j+CkLk1ffw3Hf/4jm5yn+eqrmWrYxvHjpdqGrVvhLiqCrboans6dQ0o8IveOBr9nkTLliNp0OtFj6lQkBzzT4DGSOtr6xMokqijM27VrB05nogkA+Pnnn0PukJkIV1US7mk6uH2/atAkdigjtQWe4mLUbNniHW9lpWLpTCVYYX58wIJuX74cHMdBSE1F3dy554VKGG1K+iC3yXG7RRnpbIcOATwPoV07pl+BlkIxos+fO4fkZcuQtHo1mocORcPs2ZIsdj4C1fJanqPaPQL9CnqeOoX0CRNg+/FHkd+Au1MnNLz0EgCpoEybOFG6AB49KtrMhGJK0GPbj7TJKnXmTJEgB6RjtK9dC0/v3vC0biZJsFuPWJlEFYX573//e4kwX7NmDfbt24ehQ4fi4osvhiAIOHjwID799FP06dMHI0aMiGiHo4URcabhnKatEOdqtLbAiJMQK8wvEJsgAIIArq4Ojvvvh+vVVw3fLXsyM9nXMzJ0jTHUQjFcYyOS164Fv2sX3H37wr5jhyTuN/CkoOU56jlteIqLUbtvny6vai0bl1BON6yxyUUUqG1CI1VqVfQZlwu2HTuAHTv8v3fu6FHd6ZGJ2BErk6iiMJ8+fbro32+99RZOnTqFrVu3Srx69+/fj1tvvRW5ubnG9zIGGKEqCcer06ze64GY0WtVLuab+Vl4y3fWjBljrMOKnDYr4LqW9rSWlJQj+NQXjO+koOU5hnLaiMTGJSQTjgaVvtomNJKlVuXgKyuR+sgjSNq8OS4SSiUKsTKJ6rKZ/+1vf8PEiROZ4Tk9e/bEhAkT8NJLL+Gee+4xrIOxwkh7cCjC14ze6yzM5rUqF+YnB9fYaLgWhJUzADhvm9ZVKGbNGrE3e/fuSNq+XVKQJRQ8mZlImzgxaln3lNDqHR9Ke6x3VO8m1IjNdUNZGTxbtyJVx+bMvnWrbEIpPREjRPSI1SFHlzD/4YcfkKJQ7jAtLQ0//PBD2J0yA0YtXqGe+Mzovc6CczqROm0a7Dt2APCGM/lstbGAFeanhJCSorpQc04nUidORL8dO8B5PBDS0lA3bx7cY8Yw76n27PQIBiE/XxIe1hiY/MThANxu8CdPahqvD3duLvhduzTbayN92pAsgBkZ4HfvFvUv3PZCqebn/64Bm2shPx/fz5uHXkuWyI4xGNn89UFhjLEIhSLkicUhR5cwv+iii/D222/jN7/5DdoGhdGcPXsWb731Fi6++GJDOxgrjFi8wjnxmdF7PRhm3uy1a8Hv3Al3//4x8dCVxHynp3u92Y8dA3/ggMghS4C3fGfq668z72U7ccI7xhtvBH/6tP8611r32wUwBbraswtXMARHPvg2VEmffQauoUH5u9nZ3nSbtbVIXrdO3D7DXut7btE4bQQvgEZmMmPWPxg50lt8RmZTFohRm+umrl3ZY6ysBL9vn8jL3l1QADQ0iBw4fQSGMVrBv4aIPLrSuX744YcYN24c2rVrh7vuussvuA8cOIB3330XZ86cwZIlS3DzzTdHrMPhoDdVYLiLiVyazKaxYzXt2qKdllHv/GhNA2p02lk1WKcUAJICEJ7sbNR+8onXy1jmOQGQHaMnPR01x48r94Hx7NLuuksiSH3thbObF7WZmSk5eQc+B6U0qeH0x6zpOOVS7gp2O2p27lR9NzmnE45hw0QaEHdODlwffaTrvXZu2OA9mTNO0Kx3hjt6VDU9crjrjJkw6/tjBXSdzG+++WasWLECf/jDHzB37lzR34qKirBo0SIMkUmyb0XCVZWEewIzmz06GK2hU9F03JM7pbh795Z4dNuqqrw51xknacHh8CYxmT1bvq3GRtm/yT07zukEv3u35LrWjGZKKJ5sMzIAjkP6lCnwdO4s63EfSPB7amVVrmw1v5YWTe8md/QobD/9JLpm++kncEePap4DZpw5I7wvECE/XzU9slX8a4jIojtpzPXXX4+NGzfi1KlTOHLkCARBQH5+Pjp27BiJ/lkaq9i9Q8VMMbw+5OzRXFACFB+2Eycg5Oejbt48OO680x+yxLlcSJ86Fe5evWTbEhT8RxT7x7CRuouKDBeMPuHALHyRm+u1myvYa/XEmZsdJcdIuXczcPNi++oraZ11t1uXIxozzlzDRlctoVS8rzOENkJO59qxY0cMGDAAV155JQlyGRrKyuAOCtUz4gRmFljjkyMSCwurJKzeRCu+fqUsXiyJPeYrKwGOg7tDB8n3fPZ2vcieomSysIWDb34ybrqJmZDFXVTkTVc6YIDXkS4APXHmQKtNuqgIl99wAzIKCpCZk4M2HTogs0sX8CtWGD42vdTNnw9BJmSQ9W4Gp+S01dUxv8vKpy9HqCdotdLHsS57SpgDxZN5RWv9Yb0UU/xjQuAPnfJ5s7vdEHgetnPnRClHQ11YlLyPZdXpMifplgEDwH/3nX6ntJoauD79FKkTJ8Ku4M2uVQUtd4qy7dolm4o1FJTKu4rG1uopr+afoSSIWGVv/f1oTc4jTJyI+v/9X0lVtGjhKS6G65VX4HjgAVE/5d5NpYp6gQTn01fsQwgnaC0aETPmeyCij6IwHzlypK50roIggOO4uEnnGi4slSp/9KipEr+Ei5Cfj/p33mEuOkJqKppvvDGkUDWm93FAsgy5k6K7d2+4CwqkQnvOHACQXfCUFlohPx/1H30k65yjRwXdUFYG/vPPwQedxnypWPmtW+Hu2xe2mpqw7NJahJEnI8P//9X8M5TmRy3rHofW8qfTpqEOiJlAd48Zg5oBAzQJPS0aHlY+fSVYceZqG12tYYxm968hIo+iMC8vL49WP+KSRHBM8Z3o7Bs2SBzMuIYGwOEISRixBERgsgzFk7TCKUVuwQsnFFBv3LhshjgYk48c0OicGJyRTiFfAHN+cnOB2lrYGBXimM0BSHvySdSUlkbVmS6UtmQ3L+npQFIS0xFNDUmcuYYTdCKsIYQxKArza2XqDhPaUMrRHQ9oUuWGuOjIeh+32iiNyn/uIxxVpd4Fl1UZTo5QIwE01YgPzEjHyhewa5e/1KhkflpD31ghdkpwbndUnelCbUtucxduH4PjzNUg5zZCK1TPPJJoyNFtZTSpckNcdISsLPZ1n41Sbg7r60OuF+3bBLjKy1G/aFHYObflxi43NjlYm4JQnKLk+ifnYe8zCfn7HTA/cDhCyhkv8LyqM12osOYk1LYiVc9cL0Y6t6m9M4S1UTyZP/fcc+A4Do8//jhsNhuee+451RtyHIff//73hnXQyqjl6LY6aqrccDxqWWlZA22UcnOb9MUXoixo0Qif0qui15tyNnhTwDptJr3/PoTkZIDj4Ln4Ynh69jxfMlcmu5ia8x8gr12Q+47HZoPQti24M2e8tvKAvwkA6mfNQsoHH+hqSwtyJ3ChffuQ24q2HVrO4dMI5zarhxYS6igK8zlz5oDjODz66KNITk7GnFYnIiVImJ8n3lVksuNrTRkajh1UkpY1yEYp13ZwOtNoJKzRq6IXje3nnwGPxyuAGfnSWZsC1mmTc7vB1dcD8HrGY9cu0WKt5K2upJKXe1flvnNm2DDY330XnNOJjBtu8I7PN0/t28M9fDg8O3fqaksLsg6RMrnNzfYbVHP4DPf9tUIVRiI8FIX5mTNnFP9NKGOF/OrhECm7og+lZBnMrG2pqczc5NFwFtJ6igt0xnIPHCgR+iyhC0BU3cx26JCmPjEXa0GavVmu1KpSTgS5Z3+stBT5aI0aCIpqsf38s2zGvXB+F5zTCfuGDcy/CTk5cPO86X+Dag6f4UKOdPGP7gxwhHbiNf5TpA50ONA0ZAhsbndUx8eaW1bxEEDbKSwa3tUsVSerUllwSlZJyF9Qghcl/MViFFSsknwBUK9+J/duN7XmF7DJ+FLYDh829HfhG1twJIUPT7duaHjlFdP/BtUcPsMl3rWEhM5CK1aHkvgro2V+WAlCggs/xApm2lINmgK57/ltzq0C/rtx45AfRu0BtcI0rL7KfcfjcEgy1rFQKhbTNGIE4HAYuoHxvUMZhYXgGQLWnZ2N2gMHwmojEKU5jXaBHy3I/cbkCsG48/IMOZmH+tuINrRGh45ub/Y333wTQ4cOxUUXXYT27dtL/uvASH2ZyPjSXGbm5SGjqAi2ELPqmQUldSAQ2/GG6oEsZ0903HmnP51n8rJluPT229EmKwuZ7dohs3Nn3eNTcxhkeVnLOpr16eMdZ9++smlKfepkuXskffqpaHwZl13mHV+HDrAvWKBhRPLInSh91/2e1UOHIqOoCI6bbgrJw1p2frKzJc+eczqRdtddyCwsRGZhIdLuvts0Ht118+dDsIsVpXqT0ihhFu98InLoUrM/88wz+Otf/4pLLrkEY8eORZbOEJtEQ82pxYooqQPNMN5QPJBl7YlBJ19bq72ZEwSgvh44cgQZJSVoHjIEDS+9FHIiElEbQTZMWfVot27+cfrNHoHOdD17+k/aWp0FfTt7zu0OO1sb5/HIXmfmJzhyxFtHXWcGPLmxtQwZIhHkarH0qmOKoClGzeHTCChLXHyjS83eo0cPXHXVVXj77bcj2aeIEW0VTqRVZ0ajZX6UxgTAUuP1obUuuxKhqvODCa5BbYR6lCXIhORkUf58Fh6eR83p0/5/8ytWIP2hh8A1NkJISUHd3Lmi/PRAgJq9Tx/wjFrv7i5d4C4u1jzfamPVOj9Kz1hL3W+j1NSJpkbWuwFKtPkxEl1qdpfLhZtuuilSfYk7Iu3UEguU1IFWHS8rMYceJzNARkUeZHLgjh49r+rUUKkM0KYeDSkZCM+rfiSw5Ce/YgUc998PW10dOLcbttYCKnIV0eoWLYIQ1IbA86hbtEhXZTu1BC9a1cehxNIHEqlEN/FMcOW55GXL4Bg92jSmjXhDl5p90KBB2Lt3b6T6EnfI1VDWU2nJbCipA8MZbzRzdQfD8q5uHD8e6VOnaqqc5SNQKCiZHHynQLVKZYH9kzs5akkGwsrwxtXXqzrRBQrj9IceQrBlnmu9XhNwOs+ZPx+Zr78OThAgAPC0aQOO40TviRZzQyBKwjbcanWANo9uCu3SD8W2RxddJ/Pnn38eH374Id5++20IjHhVQozRTi1mcabzxX/XOJ2o3bXLb9cLdbyx3MH7TrXpU6YAAOrmzUP9okX+zFtNY8eipbAQWt72QKGgxVHQceutsH/4ITinE43jxxtWHS24znjS6tXs/vqc6PLzJePzZWvz972xkXmPwOtJs2Yh97XXYBMEcPAuLrbqanDnzoE7dgy23bsBaEs1K+qnjLDV8940lJV5C8MEoRRLL+qDXOna776j1Kgy0AYouijazAcOHCi5du7cOZw6dQqpqano0qUL+CBVGsdx+OKLL4zvqQHEwh7jd04K06klGiFhRsxPKOOVs2dqsWWGgx47KL9iBVKnTAHf0AABkKQqDf5eZl4eM+Wsp21buJYulT5LQLMjXSCOkSNh37xZcr1l8GDUT5ummDZWFJpWXQ373r3gWmvS18+aJXJ+y+zSBba6Oul40tNR02obz2zXzu8kyEIAUDdnDloCq6ZVVoI7dQpCTg482dnMDHhydmm9741aZTgl1PwdtNrPE8kmHMrvOpHmx2gU1ewXXHCBpJ55dnY2Lr744oh2Kp5QymKmh0hniDKKUMYbyg7eCLW8HjWge8wYfFNU5F9o1FTkSiYH5rMEkLxhA/jRo+FaudLfv1DVx2p1xt0yqWNrZQRS3dy5cNx/vyTXet3cuefHoKKtCyyB6ic1VZQJT6vpAQjx5JeRAU/PnrrfmUBTDKvcL6mPpcR7BkyzoSjM16xZE61+ECpY1blMC3qzUxlVNCIcNaBamI9SoRjHXXfJfo+vrETq9Ong9+3TND6lBTNj8GBmG56kJLj79pVky+MrK5E6bRqQkSHZRLjHjIELUPRmFzhOXaBrKIGqVSDqeW+MeGd8fXOMHMnMOEfqY+km2594ycTZ9+IFSudqEYxyptMSXhQuek/NenfwRjnWRDLFZSiOgj7s27drPvkppUaVfWc6d5at3Jf02WeyVefcY8aInN2CaXj8caQ9/7zEUU7UtlIJ1OnTdWWk0/PeGPHO+N/r/fuZf0/01KhUmS22qArzkydPYuTIkbjtttvw1FNPyX7u2WefRXl5OdauXYsLLrjA0E4S6iVBteALL/IttlxreJELMEygh/KD1pur2yjHmkirAeVMDnpLoPoIHJ+WDZPSO5OyeDGzjXCqzjU/+SROnz6Nrq3e7IC+EqhJn34q3khs2gTwPLjaWlFJUP/9dLw34b4zWmzmia4+Ju/12KLqzb5gwQL8/PPPePTRRxU/98gjj+D06dNYuHChUX0jAvCd9Nx5efC0betNxKLT+U0pvMgoQo3H9akwXeXlqF+0KKSsX3pPRpFMcakU++1/lp07S1KxugsK0DJgAPOevvEpeXEHRjykT56Mupkzme8MM7Y+JYXZrp5N0snJk1Fz5gyqz55F3Zw58PC8N0SN5/3Ob5rL1548Cf74cdiqq8EfOYKMUaMkERxa35tw3xnWew1408Ya9d6YJVolVMh7Pbaonsw/+ugj3HHHHcjMzFT8XJs2bTBmzBisW7cOTz75pGEdJM4TrjOdlvCicInGD9rIE3UkUlxq0U54iotRu2+fbMlT/rvvZMcnu2F6+GEkVVSIYtvTp0+Hu08fSblVZtU5lwvJa9dKxqNnk5R87BjS/vQnv8ag9quvNNn55crXBhKOw2e474xsDvhevQx5f8yQCjlcqDJbbFEV5pWVlZg0aZKmm11yySWWTfWaCAgpKeAY4UVyJ7JQiMYP2uylZfWoG+U2E0rjkxMs9i++kHrJCwLse/cCe/eC37FDUgku8L6c0ylxvNMj8DinEz2mTkVygIc8y8Sip3ytpI0QHT7DfWci/V5bJVpFCfJejy2qwpzjOHhkiiYE4/F4JKFshHnQEl6kBSV7bbR+0GYuGqFHO+Gfy0OHwFVVQejY0V/bXG58smrqgPSrLHyV4AKzvknqmoch8FJnzhQJcl+bWjYxnNMp0UawCCd7YjjvTKTf63iIVjH7JjveUbWZ5+XlYefOnZpu9tVXXyGvteBGpHjllVdQVFSEnJwcXH/99diyZUtE2wuXkPJmRwjPgAHwBJWo9XToAI+MjZaFWtateCy1aKuoQEbXruh35ZXeEqFZWUgKyI4WjNZTnGgud+4Ef+QI7Dt2qGbAY9m73QUF8HTsqD6WoPStPmFrq6hARu/eyOjfH0mrV8PD87oX4nBD/UTvzfXXS3O7G1gSVC+Rfq8FmQqUVkv9rMf3hTAW1appf/zjH7Fw4UJs3LgRPXr0kP3c999/j+uvvx6lpaV4+umnDe8oALz//vuYNGkSXnzxRQwaNAivvPIKli5dii+++AIXXnih6vdDzS6UlWXOEyBBEARhXs6enRi1tlRP5lOnToXD4cCtt96K5cuXoyXIrtPS0oLly5fjtttuQ2ZmJqZOnRqxzr788su4++67ce+996Jnz554/vnnkZOTg9deey1ibRIEQRCE2VG1mV9wwQVYtmwZxo0bh0mTJuHhhx/GxRdfjIyMDNTW1uLgwYNoaGhA586d8e6776JDkBrXKJqamvDNN9/goaAwqhtvvBHbtm1jfufAgQOarhEEQRCE0Rgpb9S0ypoywF1xxRXYunUrXn/9daxfvx779+9HTU0NMjMzUVRUhOHDh2P8+PFoG0H7zunTp+F2u5GdnS26np2djVOnTjG/Ezz40JP4bwjhOwRBEEQiE82iMZrTubZt2xaPPvqoavKYSBPsLS8IQsQ96EO1e+ipyhUt5OKa9fRTqRhGrCqgRQpbRQUySkoUU5T6CByj3LMPDg1rHD/e++/A6mHduik6n8lVSgtG67smN0Z3p05wffgh0qdMka3M5iovZ1f0AwCbDUJqqmzKYLl3RQtNY8fC9uOPiv0yG0q/jYayMtOtFeGiVNFP7vlQ1bTQsUxu9g4dOoDneckp/KeffpKc1s2CGUM1WOE5aRMn6krDqBTiY9VYU1G4XWYmwHGwVVfD07kzXK++irSHHwbncoFDq6DKyoItIJwoeIxysebBoWFJy5Z5S6qmpsLTsSPq//hH1SQhct7ywQQ/Q7mQQiE3F55OncAHeJ17UlNR9+qrEPLzVb3z5arAweNRTBnMTB7jcIAL8rhnYTtxwnJJShrKyuDZuhWpQZXqfM/BbGtFuFjt+Vgdywjz5ORkXH755fjss88wevRo//XPPvsMt912W+w6poKZ46F9GJm1zYqLklrebX7HDri2bMH3TU2aS6DKzmmQoPLXRW9o8KYsLSmBp2NH1L3+uqxQZwlBOXzPUCkrXerMmSJBDgC2hgakLF6M+tbUr0obNLkY6cAxpj/0kKRIC+tdabrlFjgeeEA1b71vzq20cRTy8/H9vHnotWQJ872xwlqhB6s9H6tjGWEOAFOmTMEDDzyA/v37Y+DAgXjttddw4sQJ3HfffbHumqUxegcdrUXJqApwcnm3/e20VvQq8HjgqK31n2qVxqj19BwMB4A/dQoZt92G5muvhc3tliTmEQnBw4dh+/e/JZsEfz9an6FSVjq1zZzaBk2tChygkjK4tha2776D7bvvwG/erCrIwznN6q3oZzRNXbtG9LcR6/EFYsWNvZWxlDC/44478PPPP+P555/HyZMn0bt3b7z33nsRT1QT70RiBx3pRcXICnBywiyQpE8/RQeZ0qAswlEhA95sbskbN8q2F7hh4pxOpE6bJilfGvgMlQS2ls2c0gZNSxU4VspgzumEo6QEfFDWOGZfsrPh6dUrrNOsGUp0BueuN/J3YYbxsX738aRtMDOqSWPiCXKu8Do7pU+eDO7sWVFZSc7pRPMTT6CtyxX2Djoajn+ZXbrAxsgz70lOBux2Xaf1UB2x1Jz6glXxjePHI33qVE3qcaX25DZKoTomGuF85XuvhB9/BN/cLEkZ7Hr1Vclz0DPvWhwo1TaQsXbO5JxOJJeUSGzmRv0uzDC+cN8jWqNDx1IncyI81CozVT77rCE/pGjUNZatANfUBK6pyfv/g07rchsZNRu0XEUvNZ8C1qnRtXIlUn/9ayTt2qXJQz64PebpS6XuN6CsfQlVHRosPF3l5fi+qQm9du3SZP7QohHx9bNx/HikTZwoK6i1nEpjXaJTLXd9uNosM4yP6pnHDhLmCUS0KjNFY1GRqwAnV6/d1amT4kZGJMwyMrze7DU1ihW91HwK5Bbn+k2b0LxgAdKefBKc2+31Zmf0ndUec8E8efL8P6qrkVFSAsHhgNChg1+wq9q9dfo5sIRn0tq16NmtG5L79EHt1q2qgkiLX4EnKQl18+ZJNBrBglqLIIm1d7XS78IIFbmZx0dEHhLmCUS0KjNFY1GRqwDHEohcY6PqRkZJmLEqeqn5FCgtzgCQtGkT0L49BAAtAwag6Re/QNqMGeDOnYPgcABut0hI+9pLnzJFtk1/24DXNu9y+TcsAJA+cSJsp05B4Hl4Bg1SvY8SLOHJuVzIbC23mrR8OTwXXAD3JZfA1tLCPGk2lJWB37pV0WYudO6MlMWLVQW1FkESa+9qpd+FEadaM4+PiDyqudmJ+CFalZnkqnoZuai4x4yB69VX4UlP9wqn1v9lIaSkhLWR8Z1qT99yi+aKWbKL8/TpcJSUIHntWtiqqmCrqkLyunVwTJgAd/fuqN20CbX//jdcH30kqdAFANyRI6r9FY2vpQXp992HjNtuA3/8OLiWFtgaG5G8cSMcw4aFXMVPTUXOCQL4qiokb9jArK4HtM7rmjVoGj4cnqwsBDvvCADc3bvDJmP+CBTUWp34YlnRr6GsDA25uaJrvt+FEadaM4wv0r97Qh4S5hHGTCVQ6+bPh2AXK2PCLSvJGl+0FhX3mDGoOX4c1adPo+b4cdT94x9MgVA3d27YGxkhPx+Vzz4rW9oxeB7kBJB9+3bmSZQTBCRv2ABHSYn4HRG8I+KOHvWe9HUKcwCwVVUxa53zJ08ideZMZv/V3tNQQu98J81AhPx81L/zDmoOH0btmjVwd+4MoTWjIwcgecMG2PbtY/chQFBrEST8ihXIuPpqJL3/Pmw7d6LplluiGiblizNn/S7CPdX6np9Pc1M3b17US5DGejOR6JA3ewQxYzpXvxPYuXMQ2rYVOUvpnR8zjC/YLt3cvz/SnnlG4nzFTDlqt/tt5lraaX7iCbQNiDP3jZE1Dx6Hgxn77cnOhq2qSrGtphEjwO/bJw5r4zhwgvSn6s7Ohu3nn5nC2t8mx8HG+C7gTa1ZN2+e7ueolmhHjuBUnsHPT84/ITisj9U/JW/+4FBGQN7LPpLI/cbC+S2xviukpKB56FA0zJ5tKWFK3uyhQ8I8gsQ6VMSHVi9ZvfMjO76rroJ9zx6vQLXb4b78cnBJSVGJq3Xn5sLdt6/XeS2oPaWNjO52cnL8HuRoaWGGybEEkLtXL6awCkSLwPfRMngw6qdN846rqgpcfb1YYNnt8LRrB17mfk1jxwKAYtia3Lvjf69UEtcE31Mpf71c5EDLgAHwFBSEnHxENpQxPR01x49rvk+4KP3G1LIKyqEU4he4IYhGQplw2yBhHjrkABdBzODdGclEEnLjS/ryy/PJXNxu2AJK1BqZxIJplz56VKTGDmzPU1wckte+qge5DO7evSUCCAD43bs1JUrRgqdTJ9G4WBsWAMi47TbJ6d2dk6PoVGc7fFjqsb56tejEJ0pc8/DDSNq4UdYr352bq5q/niXIAcBTUBDWBlg2lFEpM12UCTVzopL/gs+0wcolYHRCGTMkrUlkyGYeQczg3ankJRsucuNTCrEyqm1AW5xyYHuh+i9ojYcOxuMrABSg4vY7fQ0ZIrHvA16B1zJggKb7B9uEOacTKYsXQ8jLQ8uwYXCVl8NTXOwV9qtXw92li/eknpKCpuuvh+ujjxTttdzJk1Jh29iI5LVrmc5s9atW4bsFC+DOy4MnI0PWIdGH3LwKqamK4wwFVgY6petWQs1/wXbiRETXAR/RaIOQh07mESTWoSJAZLUDzJSlUI+Xlmtbr4pOqxNWuHG8oTh7uXNzJSfwwPbqV65EQ2saVvuOHQCAliuvRMPs2d7PBoXCSfqUni7qOzPu+4MPvILRbkfLgAFwrVvHHKvceyq0bw/IONzJhU01d+oE98CBsG/Y4DVBBH7n6FFNcd/NN94IOByG5vOWC2Wsmzs3rPuaAbWkR55OnaKiJTSDJjKRoZN5BDGDd2cktQOs8Qlpaep9YrTtE0bJy5bJhjIFw/JglmsvnFOD5nbS0/3z4C4qkqjSA9uzL1iAjMsuQ9K6deCqqiC0tKBxyhRvSdLAeb30Ur93tw/Bbodr2TLRe8RUWdfXw3bmzPnwt2HDkDZ6NDILC5FZWIi0u+5SjD7wdO+uON7gRZpzOtFj6lQkL1sma/MPjvtmeqDPno36RYtkIwdk+1NRgYyiImTm5SGjqAi2iorz92WEMobj/GamKBX/8xs+XFarEQ0toRk0kYkMOcDFOXq8ZI2YH5bXcCBybcs58XjS0wG7XTZNqchpKDMT/K5dIiHqay99yhTYN2+W3D/Yu1oOUe56mw1JmzeLbNACz4uqnNkqK/0n7uD2GktKkD5tmmSOBACe7t3h7t9f1XFPyM0VaTHk2lPDnZsL15o1TIGp5rEe7MipJdd68HdCdfoKJtxoBT2E43ke6TVIbj6jEXlCudljC6nZ45xolyF0jxkDF3A+N7fPmz05WbFtWRWdzwM5KP2qj2CnIbnFzLBTgyAAHTvC9Y9/SDK2BVY58zgcsu2lPfkkO1MdAP7QIfCHDiFp1Sp4OnSA0LUrPAUFcJWXq4bChYJP9S3nte5auVK1IpsPNd8C1neMKperJVWxUd7cZs5BLjef0VgHqORpbCFhngBEq764D/eYMajRqb7UYpfWkkdebqzh+C/I2ttbBSzrRGpzuZihaQ1lZcjUUCmMa2oC/+OPwI8/Ajt2iOztLGHCak8rLK91kX3/nXe89n2VRVp2w5SdjZYhQ5jfERW/yciAu7CQWcNdDbUMf0Z6WodjG45kCVQ1oroOyOQ1SBRiUVeehHmCEYuXTAtqTjw+tKRflRtjqKcGtZOY3OLOCk0T8vMh8LxikhcWuto7fBi2PXtgq6/XdG/u5ElJZrngk6aQny86vftO88G51j1bt4pKfHocDrgWL2aqullV/PiAmG97eTmQng7wvN85UO55CVlZQHW19Hprhj+1Z6jndxGqlsfvUyDjFGl1KDTNS6zmgYR5AmGWH5sWYWvbuZOdiEUl/araGI2M4/WdxDyZmcy/e7Kzme3Vz5rFtJmr9sPXnpwwCYjF5pxOpE6fDvv27QCAlj59wO/dC/6nn0TfcefmQsjOZnqtB540tbw7Qn4+KsvK0Ot3v/NrCGwuF9KnTmW+YyzVuKj9hgagVbWfvHYt+F27ZO37dfPnM23mvjh7IyuWharlkSuB6rj1Vgh5eabaXIeCmc0P0SRW80De7AmEGeJAlbzWfcLWVV7u9dYOIY98JMaoehLj2GKZ37lT4jkOAC2lpaibMwcegBlrLtuP1vbkvMAbx49H2qhRyMzJQWb//uC/+QauxYtRc+AAGv72NyDI01lIS0PdwoWyXuuBJ025eXXceqvIo7vjypUSVb/c/MupxuXw2feZfS0uRu2qVd4Y97Zt4c7LE/lXhFqxjEWoUSpyGwr+yBHNERxmhkLTvMRqHuhknkCY4cemtHAGO2G5Fi4872SmMf1qJMaodhKzMdS7AMCfOuX//8nr1oHfvdt/smwpLUVNael5m/HPPwNuN7iWFnDNzZJ7BbbHMhk0jh+P9N/+VpSZjj9+HBm33Yba1au9ZUSDToVcfT1SFi9mliINztamJIh8p3p+xw402NlLCmv+5VTjSrDuE6jpcQ8cyDzdKj1D2Qx4jNC7cExUWvxCrHySpdA0Lx6ZZEkeW2TPziTMEwgz/Nhkha2G1KFaiMQYfcLTH5oWZG/XmlQmOGlKYMY2nxACvBseW2UluFOnIOTkwNOtm0RwBJsM0iZOZKaY5dxupE+eDCEvj9knrZscrYIoTWYhs23ZAn7FClFcN0s1rtqPoOfITJazfDk8nTujbtEi/+ZPyWdCyztjhImK5VPAwqonWTMkyTID/IEDuq4bBQnzBMKoH1s4JxTF1KFBdltf6lB+3z7Ni2akFhRfCVRWDKxW5z3g/EKtJByMzs/NnTsHt5zA4nlkXH21xD8heOOhdYw2Gcc+m9sNx/33wwX4BbpPNe6PoXc4vN7sLhf4PXskedqDtQWATLIcQfBqJUaNgmvhQiQvXy7Kslc3b57EcU/tnTHCDuorgdpryRK/rZ5V0taqJ1kKTfMSnPnQfz2ESBM9kDCPMGbyHjfixxbuCcXI1KEsIrWg2CoqcOmECUh2uSQJbILblFukgfMLtdFOMkonZ6FtW/a8d+qEpE2bwHk8zO/ZDh8+fw8dY5SDgzf/QGDYopCbC/fAgZLfByeT6lYS2qa0iWlpQfqkSaINRvLatUhauxbgOLRcdRXq//EPTe+MUeabpq5dFavGhbrxFK0zmZkAx8FWXR3f4W8mRS2yIlKQMI8gZvEeDyTcH5tqmFagDdjjgaegAJ4+fc6HZcksnKkzZwI7d8q2q2fRNHpBYYVQBSewCa4g5igpkdioA0+WRtv2G8rKwG/aJFG1CzzvzRjHmHd+82ZZQQ4Atl27wK9Y4fVbOHtWtIlhli/VEOceWKVMNfLgnXdUx61aZIShKeAAQBCQtG0b+JtuQu0nn6i+M5E034S78VTL1BfrNSfRUIusiBTkzR5BzOA9bjRKQsgn9PgjR2CrrYWtrg72vXslXrqBXuu+3Ntq+c/1LJpG581Wyi7Gwl8ZbcQIeLKz4cnORtPw4aKwqnCEA79iBTK7dEGbDh2Q2aUL+BUrvG1+9BGarr8enpQUb+a9Ll1Qu3q1ZMPhm3c1wWtrbIRjwgTv86yuBn/kCDJKSpCZn4/U6dNRN2+eyKO79r330JCbq3jPwCplRvw+tObNl8NWVRVyfn6jzDdqeejV3mfWPAZi9TXHaqhFVkQKOplHED2nLzOp45VQEkJKccNqKmS9qUPliIQ2RC27GAshPx/1S5fK/j1U235w7nuurk5ki65ftUrx+6I+avAm54IyeXHwjjt57VrwX30F9xVX+LN9Cbm5523C33wD/sABxSplRmgn/O8No5a6wHGS/utpT5SdLisL9U8/jeT166NqD9byPmsp0WtVpzqr4ikuVsxUGQnoZB5BtJ6+QqkYFiuUTihqccNqC4pPtVqzbVvIleYioQ0RsrLY18OwgYUaq5z+0EOSZDM+W7Re6ubPl8Ty64E/cQLJ69b539mMa65B99bNSN3y5apVyoxSXQv53lrqtWvWiE5DrldegVtFUyDXnkjL1KqVcDzwABrHj9ddzS0ctLzPWiINrOpUR2iHhHkE0aqas5I6XkkIyQk9H1rSXaZNnOiP+62bN0/3ohnqaU9JlckSeqHawPztFBcj4+qrYV+3DpzTicbx4zWNM9DmrHZdTT3rVwe2a8dMXiPojIu1uVzI2LMHycuWIfOyy+C4/36grg6Q8XA3WnXtOw3VOJ2o3bXLW/RnzRo0DR8Oj8PBHKMnO5vZnl7TSqTQ8j6rmRoSMTwsESE1ewTR6uBihmQuepBzFlKKG1ZbUIxSj4dy2lNr2yf0kiZMQHJdneYENlraAQDU1jIrwrEQUlLAsdLcBtiitYzJh6e4GLWVleBXrED6gw+Ca2ryenpfeSUaJ02C44EHdMWB+9sP/t8gcwAQvUpePkc61hh93uyS/odgWokEWt5nyTxmZHi92WtqEjY8LBGheuYmQK4OdHDt50hjxPz47YxnzgBuNzzdu8PTu7fqgmLUHIRSU1lr2+HOj1q9b3deHlzl5Yq+E6x68QIgUWEbNZ+2igqkT5gA248/6s4lz8KTno6a48ej6iMSSlsZRUXM0Dt3Xl5YtlC971A06pCbCbOu0VaATuYmIJ4yJ4Xq+BGKdsKo6mha2uacThQ89RQctbUhCx81RyXuzBnpaXrTJoDnwdXW+kPDXK++er5efEoK6ubOFQlyrWMSte2bS1/muexseLp3R0NZGWr37ZPGfV9yCfh9+5hZ5xTH2NgY1ZDNUNuKVXhRMJSIhdAKCXMTQD9Y/epxuUW6bt48pCxerOsUptZ2pE0Aftxuqe9EoLBsjW93LVyIlpIS/xg9AwZobos1n0z1/5EjwM6dsnHfvlh6vQgpKVGtKhVqW5LsdCGaVoyAErEQWiAHOJOgJd7UCIyOwTYKvc5QslW87rxTFBWQ0a8f+BUrwmpbi4MiK/ZbSzs+BLsdHg3x0r6sZqIxXnMNbBUVusYUiFKcspwjZurMmZKkOAAgn4LmfGhaNH1E9IaHBv42hNxckUNdLAQ5QWiFTuYJhBkz0vnQq52QXaSDEqH4coK7X3oJnp49mfdUa1tNIKjFfjPb2bcPtkOHAJ6H0K4d6ubPR8rixcDevSozJc1qZnO5kHHnnajZsgXc0aPnY6MzMtB0/fWweTyK86mm/mcJPrnv1PXti+TaWtgrK8HBK8A5AEJ6ut8c4Fm/nvndSIRP6Q0PFf02tm6Fu6goamlRrZJrgjAnJMwTiGiqN/WidyHTWqkM8AoT+65dwK5d/s0LAEl7cnOgJhCUYr9rgmzZSirThtxczQVbguFcLm/ilIoKUdpZ2/HjAAAbz4Pv3x8tpaXScajMJUvIejIzmZ9tbtcO7s8/V7xfNH1EWG15HA40jh8v+hzzt3H0qEj7EMmNr5k32oQ1IDV7AmHWEDhW0pyMyy5Dm6wsZHboAPuCBZLvsNTIgsOh2hZfWYnU6dN1JelRU1mHHPt9111Iu/tuv1oXgDeGf/hwCKmpzHsKnLxPuf2LL6Sx0a3/2dxupE+bhsyuXZFZWIi0u+7yj1dJ/S8rZBX6YauoQEZRETLz8pBRVCQxAYSaMEcOJdORkJ/vrZIW8G7YXC6kT50q+pyWLGqRzP1gpVwThDmhk3kCYYZ65ixYC5lvl8m1CqGWd99F/Rtv+Bd8lmq8cfx4OG67TbYMpw/79u2wVVWJrilpKNTqmYcT+y3qg09rkJEhKf8JeMO66ubORfrDD0vMCYB3rpTg0FqG0eVC8rp13nSs/frBVlMDd69ecPfuDVtVFbiTJyF07AhPqyBnquZl0sAmnziBdJWiNIBxTl1aTrQpixdL8tAHP2+tmp5IbXzNutEmrAMJ8whjJjuYWUPgVEO2ACR98w1so0eLFmmWQKj7xz/gmDBBU05uST+UwramTUPql1/CxvMSFXPd3LnM2O/APOSA9oIYcvPh6d8f7jFjUAdIxijY7fC0bw/+1CnFMYraO3kS/Lp15+8PAGlpELKzUT9jhqLDl5zwSzlyRDZzWiRyVWsxHdn272d+NziLmhYTR6Q2vmbdaBPWgdTsEcRsOdeNVm8ahdZTkRa1o3vMGNR+8IE3R3dGhiQNq7ugAC2MUC5AIWyrpATJ69Yh+eefYauqQvLatXCUlPifo3vMGNU85ID2ghhqC3vy+vXSAigtLXD37h1WrnUbAFt9vbc62siRilEAcqYHOfW7XOa0cKMr1E60tooK8Lt3Mz/DyqLm/20MHy7J6x7JjW+kqrIRiQOdzCOIGR3OohGzKqo25XDA3bMnbC0tspoJraciQJvaMTBxjV8zEuClDgD8d99p0lDIhWDxR48io18/r6d2a+KWmlZnM9l+aSyIoaZBkRVgHo8/Ntp26hTQ0BBy1jZOEOB44AHUDBjA3OzJRQAk33IL7PX10s8zitKoqciDq5ax4rxVnRMnT2ZqaQS7XfK8g38brHcnUhvfSOea4JxOpE6fDvv27QCAlgED0DBnTsw38oRxUDrXCOIYORL2zZsl11sGD4arvDxq/dCKUelc5fKzA/KpKP0L55dfgnc6ZYWQUSlutS7Ucs8wGFZKVVabSjbzwLlR6l/aXXchOUA97qNp+HBRYhf7ggVIe/JJvy09FMGud76Pv/suek2dKsmcxso7r5RytnH8eGkGNgDNQ4ag4aWX/HOhlu40My+Pad/3ZGSghrFJizSxSFfq0y4Fb0rdublwrVljKoFO6VxDh9TsESQR7WBKNc0BeVW5P2nOt9+ibs4ceDhOUuXKSLWj1iQ9Wk0AWsqQslS5TSNGME0eiv2T8ySvrxeprN3Dh6Pm9GlUnz2Lmm+/RdOQIforoel0wHL17++txBZQilSugIySipxZtQxA8oYNIlOVmulItnxt+/aqY1HzyrcKStol8paPH0jNHkHM6nAWSdRqmgPqAqKltBQ1paVRVXPK0VBWBn7rVuZiGIxciFogRpg55DzJk774QuQFb//gAyA5GWhoANLTIaSmgvMo5WiTEsrGU2t+fqXNrv3bb2W/F2yqUprTUHOsSzRMMl75kcQo51klXw3ylo8f6GQeQczqcBZJ1GqaA9oFRLRS3Kr1wVcTu6l9e3iys+HhefZng0LRlLAvWIDMDh0UY+nlkBOCweFstvp62M6dg62xEbYzZ8DLLOpCUhKz1rc7Nzesjaeac5uS05fae6RVCPlrtmvQFAQS63rmRjrPKmmX4llLmGjQyTzCJFqRBKWa5oA1NRO+IiM+e55cGdLgUDQ57AsWIH3atPPpXwNi6Tm7XVK1jOkwGKQtEJKTvXW6Qxmf283c1buLisJK5KIW/63k9KX2HmkVQpzTiZTFiyHk5cGt43Qb63rmRjrPymmXwt2sEeaChDlhKJJqU+npXm92tztuqsG5x4yBC1AtQypH2pNPMtO/Jn3zzfkLrVXLkpYvh6dzZ9QtWqR4mhR4PmTPdZuM6j04sY4etAojuc2u/z2aMAG2EydEHulaN4SsDYV97Vp4evdWTIgDtGqYGOYMlld+JDAyiYxPu0Te7PENCXPCcEKpaR6qfTBWSXncY8ZI8q5rRS1Tm+izggD++HFklJRAgDdlrXvAAMkpy1ZfD8HhkGQ6Cwfbv/8Nzuk01E6rRxh5iovP11IPwXeCmVnQ5YJtxw5gxw7F3OexrmdutPOskJ+P+qVLw+mSJsyUJCvRIGGeYJjxxxZqkQm579WXlSFtxgzF+GSj4Ves0HxSF3hel0AHzudYh8sF28aNzM+4W0+ctspK8Hv3gmPEe+vB5nL5T9JGFcIJRRhpNVUF99F26JDi55XU1rGuZ25F51kqFhNbSJgrYEbBFw5m/bGFah+UrWkemOo0Cl7IciVQhUceAdLS0HLllWiYPds/x/WzZols5nqR+56noMA/X/4kIV98AdTWgmtqEtv4bTZNnu22EydCem+MFEZaEp6w+qil8I6SpiAUDZNRRDqJTCQwY5KsRIK82WUwWypWIzBrZaZQVbJy32OlOk2fPDliccNyJVBttbXM9K8tpaXeWHqehwDAw3HwaIh7DiS4elqwoPSpVWsOHULNqVPeOPMRI/zV2LSGqHk6dQrpvTEqksOfTnftWtiqqrzzuW6daD4B9rvNuVzwqAh0PZqCcFPP6sUM0Rx6oGIxsYVO5jLE4y7TrD+2UFWyumqaV1VJ44ZHjoS7Tx94+vQJ69SjJb7cl6DD9+64hw9Hy86dfq1P4/jxSFm8GLbDh8E5nbCdOqV4cvd07gx3cbGuUxu/Zw+7GltKCpCeDq6hQaSa920Q0qdMYd5P7b0xIpJDLeGJv5iKXHGaPn3Q0q2b1/Swb5/Ip0CPpsCsWi0zkYhJsswECXMZzCr4wsGsP7ZQVbKs7wl2OzucqalJYqfmBAH2vXuBvXvDWpjlSqAG43t3tAgGW0UF0u+8EzaXSyLUBUDVuz0Qf3tHjjD/7rnqKrjKy2UdzWL53mhNeCLbx27dxKaHENXW8bi5Nxor2vnjCVKzy2BWwRcOkajMZITqOlSVLPN7CxdKKocJdjvQql6WIxxzQ93cucykK8H43h0tamtPcTFqjx1D/f/8DzzwCnAPALfDgdo1a3TZ/9VKr9p27kRmXh4ct96KxvHjJWrdWFb00prwRK6PjePH+1XjqTNnoqGsLCS1dTxu7o0mEZNkmQk6mctg1C7TTE50RjvVGJnyMlSVLOt7tZ06SbyQ0ydPBlTCtpQWZn7FClw+ZQr45maJt7oo7ryhAYLHI9klBybo0CMYWu65By2HD4f1/iidbgUANp9WQeb5xdIZS2vCE1YfG8ePR/rUqWINyNatcBcVwVZdrWs+43FzHwkSLUmWmaCqaQqEmxtcraKT2dA7PxlFRUzVrbtzZ7ivvdYUGxgfatXcAPkKYXIZ3+SqpHFOJ1KnTYN9xw4AkHizK1ULCy7BacT7I9eeh+dhY4TIufPyQvbiDqfqldzGN9TynXLjDkTrfBr1LJwbNqDXkiWm+m1EAi3la1lQ1bTQIWEeQbQu2mZB7/zIlZcUOE7kUe5xODRl3Yo0/gXmzBmgrk4kyJQW5swuXc6fXgPwpKf7a5jrWby0CgbZ92fECMDh0CwQ5NrjTp2CjaGt8LRti5oQPbUD3yE9WikjhCUrzty+c6fq97T+Ho3Y3CeXlCA1QMtg5s19qLA2znJlcIMhYR46pGaPIPFuZ5NLeRkcGqY161akCYwbZi3MgFeASk6GMt7qvut6zQ1a1dZy70/Sp5+KvNL5zz8HOA6cy8XcSMi157j1VqbpwYiUpXq9v8N1MAs1zhyQ/z2yNmjhbMJTZ85EcpC5IB6d6JSK1MQqbj8RIGEeQeLdzsZMeQn5pCaAeRavYNueovCR8Vb3VUlTW7zkTqhqc6C1OhofKIwCNhJCbq7iydjIlKW+DHj9GhqA1FS4+/bVJZzD3fgqxZmztA+BsH6PkSiBGu+bex+xLlKTqJAwjyBGh2qYyZkOYKe8dHfvjuQNGxS/Z8bFS+lkWDd3rmKVNKXFS7bYR5cusB07BthsENq3Z6rlmaF3qanMWHFRuy0tSJ8wAUhNVTwZG5WyVOJTUFcHbts25mflnn24G1/VOPMTJ+DJyAC/e7fImU7u9xiJ02W8b+59xLpITaJCwjyCGOkFbNakFcEpLzmnE3xQPyXfMeHipXRq8nmrp8p4systXrLFPg4cOH+hthYZJSVoufxy1L/xhmKJUNTWInndOtXxcD/9BFtzs+gaX1mJ1GnTgIwM0YYwXNWnXAY8Fp7MTOb1cDe+WuLMAe1270icLhvKyuDZulViM4+3OOxYF6lJVEiYRxijQjWskrRCJIDCzLoVTdROTe4xY/BNURHTOUdp8UqbPVtT+74SqLabb4brww8BQKSFqZs3z+/ZzX/3neJmCQA4GzuFRNJnn4nt7QZsCLVkwPMT5E/hvxzmxlfrZkDr7zESp0shPx/fz5vn9Wa3SL71UIh1kZpEhYS5RbCSvS1wwQzXAzhaqAkDzulEwVNPwVFbKzFxKC1eelLOAl77d+r06eD37RP1JWnFCjRfdx0aXnpJLPR4HkmbNolyrQt2O5qvvppp7pDY22U2hHpMOloz4AHefPWif4cYwiTpg8Gx8JE6XTZ17WqqzXekiGWRmkSFhLlFsKq9zSpJJJSEgRYTh9zixdokqGHfvh22qirRNc7jQfKGDeBLSuBas0Y0p40+gRiwkRBycyXmDiElhXmKDt4Q6jXpsHwK5Ah8X5lOZr58+Xl5AMfpSu5i5LtGp0vCalCcuUWIRgIaK89PJNGSL0DpJOv/G8PswMKTnS0R5sHtNo4fr3qiDdaKwOVC8tq1iuPQOt5gfN7sqKs7X3s9CHduLlxr1vjnRS7pEIt4icem35gyND+hQ7nZLQLlPQ6fUEtYqpk41Mrl+ktZfvIJarZs8T7D/HxmPnd3p05oGTBAuT/79yNj1CjwR47AVl0N/sgR779XrEDasGHIbN8ebbKykDFoEJpuucWfi7xxyhRm3vrG8eN1jZeFe8wY1Bw/jq+2b0ftmjVwd+6smq9ezsmMhRlK9UaaaJdYJeILUrNbCKuorEMh0mF34UQDqJk49DgnBj5DW0UF0idMAPfTT+BsNjRffTUaXnoJAGDftEk2Ptp28CAzbCpY1c3V18Nx//1wwStsUxYvZn4vZfFi1Aec6sM16XiKi+G+9lrwQaf74LKlck5mcsTaPySS76hZo1UI60AncyLmqJ1sjUBLpTI51KqGheqc6CkuRu2+faipqkL1yZOob124hfx8uN57DwKj0ps7Nxfg2NZp1lUOraFjTifsMvH/wf0Mt0qaraICSatXq7ZVN3++RFOgRCz9QyL9jobzfhIEQMKcMAGyC9m0aYapHcOJBvCZOE7fcgvTxBEJ50RPcTFqtm1D0/Dh8GRnw5OdjaYRI7w25w4ddN2La2iAY/RoWTt8cD/DMek4du70OrXJhKt5AkLmfE5m7rw8eDIz4eF52fvGOqQx0sLWStEqhDmxjJq9pKQEFUG1su+44w689tprMeoRAQD2BQuQ9uST4NxuCDyP+lmz0FJaqusesjnIDYyJNkzgMuKkjc70528qPx/177wjuc4MmwoqbiO6D8fJetP7+slSIYdi0imYMUOxMh0fmCwHCvnyMzK83uxVVeBOnoTQvr2/Hnmoaudw1OSRFrZWjVYhzINlhDkAjBs3Dn/4wx/8/05lqCGJ6GFfsADp06b51buc2430adNQf/o07DpqcGvOQR5GkpxwBC7TnhlUF7tu3jykLF4clXh6VthU/dNPI+33vwd/+rToswIAT0EBbAcPSu+TnQ3XypUAYJi91l5To/h3JU9+2Xz5R44AR44AO3eG3K9wbdKRFraR2hASiYOlhHl6ejpycnJi3Q2ilbQnn2Sm8Ux7/nnRdbVFk5mDXGNMtFbCSSrCVLEePSrK8R1NZyXO6UTK4sUQ8vLgDtgsuQYMQOrEibDv2AHO44GQloa6efOQvH49wBDmLUOGQMjPR9rEiYZlF2zJzIQ9KDFMIHoyqBmZ9TDce0Va2Bqd9IZIPCwTZ15SUoJ9+/YBADp27IibbroJTzzxBDJlcj0D3phFInL0v/JKTYlCAOD0Lbeg8tlnZf+efOwYui5YgKSqKjRnZ8NWV4d2mzbpvk8k6FFaijYa6mJHo2/Jx46hx9SpovzeDbm5+H7ePDR17RrSd+TGV92/P75fsEBX/xw7d6LnlCmiWvE+PDyP/S+/DFf//pruZWS/jLhX8Dt6rLRUds4JwmjU4u8tczIfO3YsLrzwQnTq1AnfffcdZsyYgT179mBlq5qQRfDgKSGBMnrnR+B5cIxFm0Vbl0v53oWFwJAhEOB9KTmnE25Gkpyk555DYZRtpqnduwMahLnqGA0g7U9/ktTETj16FL2WLEH9okXsMQ4ZgqY1a2ALOPU1lZUhv3XscuNL7d5d93gOAHCtXu01AVRVAU1NQGoqhA4dUDd/PrroyKBmZL8MuVfQOxrKW0hrkDI0P6ETU2E+c+ZMvPDCC4qfKS8vx+DBgzE+ILHFJZdcgm7dumHo0KH45ptvcPnll0e2owST+lmzRDZzQL6euV7botFqx3BsplpTskbDWUnJEUttjHLq5IipkJOSIGRnh5wG1ch+kU2aiHdiqmY/ffo0Tgc57ASTm5uL9PR0yXWPx4Ps7GwsWrQId9xxh6b2aNenTCjzE+zN3vDf/42U5csjmnY2FEJJURoI53Si+Ykn0Nblkq2LrWeM/hP0oUPgqqogdOwIT6twUbqH0jgAyP6toawMqdOnw759OwCgZcAANMyZI005G+bG6fi776LX1KmSAiW1q1aFJNCNLNRjhqI/tAYpQ/MTOpaxmQeze/duDB48GGvWrEGxxkWCXhRljJofMyyawThGjoR982bJ9ZbBg+EqL9d0j8D5CWeMrBO0D7VNgVKO/vQpU9hjvPJKcD/+KNp8ANJc6UaQ0rs3UhnaA3deHlXRAq1BatD8hI4lbOaVlZV47733MGzYMLRv3x779+9HWVkZioqKMGjQoFh3jwjCjGlnjQ4tCmeMLM9qHz4P64ayMqZ9X8n8IBvid/KkRJAD0vSqRiAXmsadOyf+d4TT9xJEomEJYZ6UlISNGzdiwYIFcLlc6Nq1K4YNG4Zp06aBV8gaRRA+zGQzlbN7+/9++LCi7VtuIyE3RqF9e2+cNqstgzOMyYWmBYakJXIe8uRjx5D2pz/RJoYwHEukc83NzcXatWtRWVmJU6dO4euvv8Zzzz2Hdu3axbprhEUwU9U5uRO0D+7kSdXUoawKW3Jj9HTvLt8Xg532Kp9+mlmZrW7+fP+/taZGtVVUIKOoCJl5ecgoKoItKAOkkUSjYhnndKLH1KkRrUFgNqgSXPSwxMmcIIwgmup/W0WFbL1xJe94pZN0cMlVrV7rDWVl4LduZdrMjdZMuPr3l2SnC/Zm15Ia1VZRIU5ZW12NjFGjQnakUyJamoLUmTMlYYXhZDU0O4msgYkFljiZE4SV8Ami4HrjvpOl6AQ9YADceXloufJK1ZO0lpKrLIT8fLjWrEHTiBHni7YMH26485u/n6351mucTtTu2iURvlr8F9InT2aWa02fPNnw/karYlmiFVOhSnDRhU7mBGEwSoLI59EdTtx3yELB4YCnZ09NttpIOqhp8V/gzp5l9yvIkc4IoiVkE62YSqJtXmINCXOCMJhwBZFawhy9QoGl7kwqL0fzDTeIYs2VPm+kelRLQiAhKwuorpZ+V0dud614ZFJCezIyDG2noawMnq1bRWl14zlxTaJtXmINqdkjDDmAJB5CVhb7ug5B5Du5u8rLUb9okUjQNZSVwV1QIPq8klBgqTu5hgYkr1vHdMCKqnpUpmxr3fz5qo50hsHJVBiQux4iQn6+Nx++CZwwo4He95QIDzqZRxByAElMmPXGDRREelPdKoXCBTpg+VTr9g8/ZN/HIPWolt8Fq8xrqGlh1bAxNAAAYFMp5xoKTV27xqWzGwuqBBddSJhHECNLOBLmQsmmHA1BpMczXy0UTi6vu+Q+BqlHtf4ufI50kYbUwZHDjAmk4hUS5hGEHEDiE80nS5OkL1UrFOPp1EkxKx1grHrUbL8LMyUUIohQIZt5BKEdf3xitZAbfyjciBEQUlNFf/MJLTkB62nb1nDbrtl+F2ZKKEQQoUIn8whCO/74xGwnSy0I+fmoX7oUDTIFYuQEbMuwYYarSc34uyB1MGF1SJhHEHIAiU/MdrLUg9687pEQsPS7IAjjIWEeYWjHH3+Y8WQZLtEWsPS7IAhjIWFOEDqJpOCLZWlQs+SuJwhCPyTMCSIEIiH45Lzk6+bNQ8rixXFTNpNZRKWkBM1DhqDhpZcsPTaCiBUkzAnCJMh5yWfceSc4l+v8ta1b4e7bF7aaGksKd2buegDJGzaAHz2aPMkJIgRImBOESZDzkg8U5ADAHz0qKmdqtayCcrnrgcROqhRLEwthfSjOnEgYzJ4nXy1TmxyBMe62igpkFBUhMy8PGUVF/rKrZkIud70PM4f4RQqfiSV52TLYN29G8rJlzLz5BCEHCXMiIbDCYskqTOFxODR913bihGoddbPAKqISiBVC/IzGaomICPNBwpxICKywWDIzkb33nkTAs/B06qRYR91MWglf7np3584QgiqTWT3EL1SsmIiIMBdkMycSAqssliwveVEYXGYm+F27RDZznwDMGDyYeU/uzBnd1fsibb/1FBejdt++8+0kePIYKyciIswBCfMIQ04t5sDKi2WwgJcTgEJWFsAq5+l2q1YpE8V9Z2R4v3Py5PnPR8jJjpLHeAk3ERGtMwQJ8whC9czNQzxlbZMTgHJ11D0FBbDt3Sv5vE8rwYr7DiaRvcyjQTiJiGidIQCymUcUK9hpE4VEqIzlt0Xn5cHTti3ceXmoXbUKnj592J9v1UqwbO0szGaSiDd8mzRXeTnqFy3yv5tq/g60zhAAncwjilXstIlCIqh0WXXUG3JzFbUSSnHfontbwCQRb2g5ddM6QwB0Mo8o4dppzeSBTFgXNa2EWtw3YF2ThNXRcuq2sj8IYRx0Mo8g4dhpyQ5GGImSVoJpa+d5NF97LWwej24vc3LGMg4tp+548gchQoeEeQQJx6lFaUce76piIrr4bO3pkyeDO3cOQtu2IVcxSz52DI7HHqNNqEFoOXVTfXgCIGEecUK105IdjIgmLFt7KHRdsIA2oQai9dSdCP4ghDIkzE0K2cEIK5JUVcW8TpvQ0KBTN6EVEuYmhexghBVpzs5mXqdNaOjQqZvQAnmzm5REiIsm4o9jpaWSXPK0CSWIyEMncxNDO3LCajR17UpqYYKIASTMCYIwFNqEEkT0ITU7QRAEQVgcEuYEQRAEYXFImBMEQRCExSFhThBEwkD1Doh4hRzgCIJICKjeARHP0MmcIIiEgOp+E/EMCXOCIBICqndAxDMkzAmCSAio3gERz5AwJwgiIWgoK6NUs0TcQg5wBEEkBFSBjIhnSJgTBJEwUKpZIl4hNTtBEARBWBwS5gRBEARhcUiYE0QEoExjBEFEE7KZE4TBUKYxgiCiDZ3MCcJgKNMYQRDRhoQ5QRgMZRojCCLakDAnwoJsw1Io0xhBENGGbOZEyJBtmE1DWRn4HTtE80KZxgiCiCR0MidChmzDbHyZxprGjkXL4MFoGjs24Tc4BEFEFjqZEyFDtmF5KNMYQRDRhE7mRMiQbZggCMIckDAnQoaqUBEEQZgDUrMTIUNVqAiCIMwBCXMiLMg2TBAEEXtIzU4QBEEQFoeEOUEQBEFYHBLmBEEQBGFxSJgTBEEQhMUhYU4QBEEQFoeEOUEQBEFYHBLmBEEQBGFxSJgTBEEQhMUhYU4QBEEQFoeEOUEQBEFYHO7s2bNCrDtBEARBEETo0MmcIAiCICwOCXOCIAiCsDgkzAmCIAjC4pAwJwiCIAiLQ8KcIAiCICwOCXOCIAiCsDhxJ8xPnDiB0tJSXHTRRcjJycHAgQOxefNm5mcfeeQRZGVlYe7cuVHuZezQMj8HDx7EPffcg7y8PHTu3BnXXXcd9u/fH6MeRxe1+amtrcX//M//oE+fPujUqRMGDBiAl19+OYY9ji59+/ZFVlaW5L8777wTACAIAmbPno1evXqhU6dOKCkpwb59+2Lc6+ihND/Nzc14+umncc0116BLly7o2bMnJkyYgB9++CHW3Y4aau9PIIm4PoeDPdYdMJKzZ8/i5ptvxqBBg/Dee++hQ4cOcDqdyM7Olnx21apV+Oqrr9C5c+cY9DQ2aJmfw4cP4+abb8avfvUrrF69GllZWfj+++/hcDhi2PPooGV+nnzySWzYsAELFixAfn4+tmzZgkceeQQdOnTAr371qxj2Pjp89tlncLvd/n+fOHECQ4YMwejRowEAL730El5++WW8/PLLKCwsxJ/+9Cfcfvvt2L59OzIzM2PU6+ihND91dXX49ttv8fjjj6Nv376orq5GWVkZfvGLX6CiogJ2e1wtx0zU3h8fibg+h0tcvT1/+9vf0KlTJyxcuNB/rVu3bpLPHTlyBNOmTcPKlSvxi1/8Ioo9jC1a5mfmzJm48cYbMWvWLNnPxCta5ufLL7/EL3/5S1x33XUAgPz8fLz11lvYuXNnQgjzCy64QPTvt956C5mZmRg9ejQEQcD8+fPx6KOPYtSoUQCA+fPno7CwEMuXL8d9990Xiy5HFaX5SU9Px8qVK0V//8tf/oJBgwZh//79uOSSS6LY09igND8+EnV9Dpe4UrOvWbMG/fv3x3333YeLL74Y1157Lf7xj39AEM4nuWtpacGECRPw+OOPo2fPnjHsbfRRmx+Px4P169ejZ8+eGDNmDC666CLccMMNeP/992Pc8+ig5f0ZNGgQ1q9fj6NHjwIAtm3bhj179mDo0KGx6nbMEAQBb731Fn75y18iPT0dTqcTJ0+exI033uj/TFpaGq655hps27Ythj2NDcHzw6KmpgYAkJWVFcWemQPW/CTy+hwucSXMDx8+jFdffRXdunXDihUrUFpaihkzZmDRokX+z8yePRvt2rXD/fffH8Oexga1+amqqkJtbS3+/Oc/44YbbsC//vUvjBkzBhMnTsT69etj3PvIo+X9ee6559C3b19ceumluOCCC1BSUoI//vGPuOWWW2LY89jw2Wefwel04te//jUA4OTJkwAgMWtlZ2fj1KlTUe9frAmen2CamppQVlaGW265BV27do1y72IPa34SeX0Ol7hSs3s8HlxxxRV4+umnAQCXXXYZDh06hFdeeQWTJk3C5s2bsXTpUnz++ecx7mlsUJsfj8cDABgxYgSmTp0KACgqKsI333yDV155Je4Fltr8AMDChQuxbds2vPPOO7jwwguxZcsWPPXUU8jLy8NNN90Uy+5HnTfeeAP9+vVDUVGR6DrHcaJ/C4IguZYIyM0P4D2BTpo0CefOncM777wTg97FnuD5SfT1OVzi6mSek5MjUc306NHDrxL9/PPPceLECfTs2RMdOnRAhw4d8MMPP+Dpp59Gnz59YtHlqKI2Px06dIDdblf8TDyjNj/19fV45plnMGPGDAwfPhyXXnopJk2ahDvuuCPhPG6rqqqwdu1a3Hvvvf5rOTk5ACA5hf/0009MJ9R4hjU/PlpaWnD//fdj7969WLVqFdq3bx+DHsYW1vwk+vocLnF1Mh80aBAOHjwounbw4EFceOGFAIAJEyb4HXN8jBkzBmPGjGH+6OINtflJTk5Gv379cODAAdnPxDNq89Pc3Izm5mbwPC/6DM/zfq1GorB06VKkpKTgjjvu8F/Lz89HTk4OPvvsM/Tr1w8A0NDQgK1bt+KZZ56JVVdjAmt+AO879Nvf/hb79u3DBx984N8AJRqs+Un09Tlc4kqYP/jggxg2bBheeOEF3HHHHdi1axf+8Y9/4KmnngLgtd0FnxDsdjtycnJQWFgYiy5HFbX5AYCHH34Y9913H6655hpcd911+Pzzz/H+++9jyZIlMex5dFCbnzZt2qC4uBgzZsyAw+HAhRdeiIqKCrz77ruYMWNGjHsfPQRBwJtvvok77rhDFG7GcRwmT56MF198EYWFhbj44ovxwgsvwOFwJJRXstz8tLS04N5778XXX3+Nd955BxzH+f0M2rRpg7S0tFh1OarIzU+ir8/hEnf1zD/88EM888wzOHjwIHJzczFx4kQ88MADsja7vn37YtKkSXjooYei3NPYoGV+lixZgj//+c84duwYunfvjv/+7/9OmMVYbX5OnjyJGTNm4LPPPsOZM2dw4YUX4je/+Q2mTp2aMHbhTZs24bbbbsP//d//oX///qK/CYKAOXPmYPHixTh79iz69++PF154IaHUpHLz43Q6cdlllzG/8/LLL2PcuHHR6mJMUXp/gkm09Tkc4k6YEwRBEESiEVcOcARBEASRiJAwJwiCIAiLQ8KcIAiCICwOCXOCIAiCsDgkzAmCIAjC4pAwJwiCIAiLQ8KcIOKQvn37YvLkyaqfczqdyMrKSoikQAQRz5AwJwgTs2TJEmRlZSErKwubNm1ifubGG29EVlYWrrzySkPanD17tr/NrKwsZGdno6ioCNOnT8e5c+cMaSNS/Pvf/8bs2bPhdDpj3RWCiCpxlc6VIOKV1NRULFu2DNddd53o+n/+8x989dVXSE1NFV3fsWMHbLbw9urPP/882rRpA5fLhU8//RTz58/H119/jXXr1pk2292+ffvw3HPP4dprr0V+fn6su0MQUYNO5gRhAYYNG4ZVq1ahsbFRdP2f//wnOnbsiCuuuEJ0PSUlBUlJSWG1edttt+GXv/wlfvvb3+Ltt9/Grbfeii+++AI7duwI676CIKChoSGsexAEIYaEOUFYgDFjxqC2thbr168XXV++fDnuuOMOySmcZTM/ceIE7r33XuTm5qJbt26YOnUqampqNPfBpxU4fPgwmpqaMGvWLAwZMgT5+fno1KkThg4dirVr10q+l5WVhcceewwrV67ENddcg44dO2LFihU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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This residual plot indicates that linear regression was a reasonable method of estimation. Notice how the residuals are distributed fairly symmetrically above and below the horizontal line at 0, corresponding to the original scatter plot being roughly symmetrical above and below. Notice also that the vertical spread of the plot is fairly even across the most common values of the children's heights. In other words, apart from a few outlying points, the plot isn't narrower in some places and wider in others.\n", "\n", "In other words, the accuracy of the regression appears to be about the same across the observed range of the predictor variable. \n", "\n", "**The residual plot of a good regression shows no pattern. The residuals look about the same, above and below the horizontal line at 0, across the range of the predictor variable.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Detecting Nonlinearity\n", "Drawing the scatter plot of the data usually gives an indication of whether the relation between the two variables is non-linear. Often, however, it is easier to spot non-linearity in a residual plot than in the original scatter plot. This is usually because of the scales of the two plots: the residual plot allows us to zoom in on the errors and hence makes it easier to spot patterns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Dugong-dugon_wikipedia](../../images/Dugong_dugon.jpg)\n", "\n", "Our data are a [dataset](http://www.statsci.org/data/oz/dugongs.html) on the age and length of dugongs, which are marine mammals related to manatees and sea cows (image from [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Dugong_dugon.jpg)). The data are in a table called `dugong`. Age is measured in years and length in meters. Because dugongs tend not to keep track of their birthdays, ages are estimated based on variables such as the condition of their teeth." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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LengthAge
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" ], "text/plain": [ " Length Age\n", "0 1.80 1.0\n", "1 1.85 1.5\n", "2 1.87 1.5\n", "3 1.77 1.5\n", "4 2.02 2.5\n", "5 2.27 4.0\n", "6 2.15 5.0\n", "7 2.26 5.0\n", "8 2.35 7.0\n", "9 2.47 8.0" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dugong = pd.read_csv('http://www.statsci.org/data/oz/dugongs.txt')\n", "\n", "dugong[['Age','Length']] = dugong['Age\\tLength'].str.split('\\t',expand=True)\n", "\n", "dugong = dugong.drop(columns=['Age\\tLength'])\n", "\n", "length = dugong.pop('Length')\n", "\n", "dugong.insert(0, 'Length', length)\n", "\n", "dugong['Length'] = dugong['Length'].astype(float)\n", "\n", "dugong['Age'] = dugong['Age'].astype(float)\n", "\n", "dugong.head(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we could measure the length of a dugong, what could we say about its age? Let's examine what our data say. Here is a regression of age (the response) on length (the predictor). The correlation between the two variables is substantial, at 0.83." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.8296474554905715" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(dugong, 'Length', 'Age')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "High correlation notwithstanding, the plot shows a curved pattern that is much more visible in the residual plot." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(dugong, 'Length', 'Age')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While you can spot the non-linearity in the original scatter, it is more clearly evident in the residual plot.\n", "\n", "At the low end of the lengths, the residuals are almost all positive; then they are almost all negative; then positive again at the high end of lengths. In other words the regression estimates have a pattern of being too high, then too low, then too high. That means it would have been better to use a curve instead of a straight line to estimate the ages.\n", "\n", "**When a residual plot shows a pattern, there may be a non-linear relation between the variables.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Detecting Heteroscedasticity\n", "\n", "*Heteroscedasticity* is a word that will surely be of interest to those who are preparing for Spelling Bees. For data scientists, its interest lies in its meaning, which is \"uneven spread\". \n", "\n", "Recall the table `hybrid` that contains data on hybrid cars in the U.S. Here is a regression of fuel efficiency on the rate of acceleration. The association is negative: cars that accelearate quickly tend to be less efficient." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(hybrid, 'acceleration', 'mpg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how the residual plot flares out towards the low end of the accelerations. In other words, the variability in the size of the errors is greater for low values of acceleration than for high values. Uneven variation is often more easily noticed in a residual plot than in the original scatter plot.\n", "\n", "**If the residual plot shows uneven variation about the horizontal line at 0, the regression estimates are not equally accurate across the range of the predictor variable.**" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.12" } }, "nbformat": 4, "nbformat_minor": 1 }