aula02IAC.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Redes Bayesianas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Introdução\n",
    "\n",
    "Rede bayesiana é um modelo probabilistco representado por grafos direcionados acíclicos, os quais representam um conjunto de variáveis e suas dependências condicionais. As redes bayesianas são comumente usadas quando se deseja representar relação causal entre variáveis aleatórias.  Tais redes são parametrizadas usando a Distribuição de Probabilidade Condicional (Condicional Probability Distributions - CPD). Cada nó na rede é parametrizado usando $P(n| Pai(n))$, com $Pai(n)$ representando o pai do nó na rede.\n",
    "\n",
    "Considere que a grama do jardim de uma casa, com sistema de irrigação, esteja molhada. Qual o probabilidade de ter chovido?\n",
    "Abaixo temos um desenho de uma rede bayesiana para esse caso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WmuqKioqio6O5V6Fyurm5qXgvtDDr8sKWpzfV1pXrqHLo3V2+fFnXyRgAjBhiHwDoyvHjx+nWxcXlqUtyw5QcPHjQ399f6yU5evQoxSaWw8rLy9OlKJWqyGQMLRYSEkJRj57I5lD28vHxUdo7OC0tLTg4WCINcPSO6IXc3d1zc3OVrvmTTz4JCwuTXZiVKicnZ8yYMYrLjxw5kl66oKAAsQ8ANIbYBwC6wtqxBg4cqM7CrMFv5syZb7/9tnaHKcnLy6OgJtsKePLkSS8vL8pkT548UT2a4FtvvVVbWyt7XHXt2rVz585NTk7OzMyUTah1dXUs8ym+kOJqa2pqWOaTXbioqIgiMhX1559/Vrycyeuvv063R44cweh9AKAxxD4A0Inm5mY28Yc//EGd5XXa4JeRkSF75NfT0zM6Ojo2NvapYyArHgg2NTXdtGkTxb7w8HDZctIcpS8UFxcXFRUltxI2hLXcwkOHDmULz5kzZ8+ePXJPYfGUdZEBANAMYh8A6ERLSwubUH+MYt01+NEK5ea8//77FPu2bt2qQeOZmZkZ62DR2trKneHHsp3iC1GGk4t9VDOsHVRx4Q8++IAWpkdTU1PlaqBz587tLScAgBzEPgDQCXb5DcWDlSrorsFPMUT26NGDbuWim1KNjY3Jyck5OTmso4asX375hfXtbWpqauuFunTpIjeHqxnFhbmewrSMXK9hLj03NzdrdrUPAAD8dwCADg0ePLhdy+/cuZM1+I0fP15b4cbDw0NxJjdgyj//+U8VL8TOt5NIryPCenX4+fnR7YwZMygycgeyWZJT+kKK2e6nn36StF0z7IIctIxc7MNl2QCg4xD7AECHLl++3K7lzc3N2flt69at01bfhZs3byrO5I5Bq4hTjY2NlPksLS0vXbqkerQXFhyVvpAidrj20aNHSh+trq6WKDukyxUYAEBjiH0AoBMsuNTX17f3iR9++GGUFE0oPsqOGl+4cEHxoZqaGqUrrKqqUpzJ2uckKmPf1atX6XblypVyma+1tVVunc8991xbL8Qd/+Www77cQICyKNuxGlM8NMy1LOIILwBoDH8fAKATGp+LxjX4bdy4UfFRFvsUO7RSYDp69Ghb66ysrJQbw/nrr7+m25CQEBUlYbFP8aoYiq16JiYm7OCs4gspjttnZmZG74LineLC7PJ09KjiRTs0OFcSAEAOYh8A6ATXivbrr7+qeU0zDtfgp5hyKEGyzFRaWuro6MjN37Rpk4qWRVrh4cOHua4blESXL18ukbbkqSgGG3Fw3rx5QUFB3EzKlxMmTFBceNeuXS4uLoovtHjxYsWFd+7cGRAQoLjwjBkzJNKBXRSf0tjYKGn/uZIAALIQ+wBAV1i33IqKiqFDh7briVyDn9IkxzLT8OHDacLT0/POnTvbt2+nqOTh4aF0WDtbW9tHjx5RdIuNjbWysqLlZ8+eXVJSEhIS0taV0JhBgwaxiLl06dKFCxdKpFcZpmTm4OAgUThKS++RCpCdnS33QrSw4vHct99+m0olu/DVq1enTJlSVVVFK1F6HY7vvvuObseNG6ey5gAAVEHsAwBd8fPzo9hHUay9sU/ye4NfW6tlgy1T+GNzKEKVlZUtWbJEaezr06dPbm6ul5eXvb09NzM8PHzDhg2qy2BmZnb+/Plhw4bFSrGZlGXT0tJGjBihuDy9ytSpU9k11mQX5u5yOnXqVF5ePn/+/OTkZNlHqVTr169XWpgjR45IpOM/qy4zAIAKiH0AoCsUmOg2JycnNDRU6QLTpk2bNGmS0oGIzc3NHz9+zPoxyPVvMDExiYmJWbhwYXFxMd19+eWXe/ToQTNXrVq1fPly2YVfeumln3/+2VTq9OnTDx48YD2LnZ2dFQ8fs4WfeeYZ2Zl2dnb37t379ttvafrZZ58dOHAge+JXX31FZevatavswvQqFPI+/fRTuVeh1UoUumJQpty+ffvatWvZu5BduVL79u2TqH2lOwAApRD7AEBXWAfY7OzslpYWpR1mzaTaerrqMwIpIck1fZlLyc6hF+WCFOVCKysrFa1lsgvLFVLxWW2VTemrqAhziu9CqYaGhvr6elpYLmgCALQLYh8A6AoFJl9fX4p9586dc3Nz47s4BuzQoUMS6aXbVF9QBABANcQ+oTh27FhKSkppaSlN9+7de+LEiX5+fir27IuLi9saeyIsLOzdd9/VVUENBOpTIBYtWkSxLzExcc+ePXyXxYCtXr2abqdPn853QQDAsCH2CcLmzZt37NjRpUuXyZMn0y1FlqSkpK+//vrzzz9X/UQKNH369JGbyS42KmaoT+F444036DY9PX3nzp1yR2BBTTU1NSUlJZaWlv379+e7LABg2BD7+FdcXEwZhQLH7t27WXPUvHnzlixZQmGFYorqdqaJEyeiIUoO6lNQzMzM2DAuGzdu1NbF1sRmwYIFdBsREYEjvADQQYh9/MvJyZFIo4nsIcj58+dTTDlw4EBbKUTplZ1AgvoUnoSEBIp97GJraPBrr5qaGjbCi9JL1QEAtAtiH/8KCgro9vXXX5ed2atXL0dHx9LS0tu3b9N0W89t78UPxAD1KTTW1taswW/JkiUUAfkujoFhp5zGxcUhMQNAxyH28e/WrVtdunRR7G3A5tTW1qqIKYQ2pRR0Hj16RCsZPXr0tGnTVC9v9FCfArR161aKfYmJiQsWLGCjuoA6ioqKsrOzLS0tP/roI77LAgDGALGPZw8fPpRIrwGl+NCwYcPy8/N/+eUXFU9ftWpV7969J0+eLJH2Xd23bx/d0iZ2wIABOiqwwKE+hYmCC7vY2ogRI65du6Z0DD+Q09zcPGrUKIn0YnQqRjcEAFAfYh/Prl+/rnqBH3/8cfjw4YrzGxoa3N3dvby8Jk6cyObMmzdv9erVlFQWL16cmZmp9aIaBNSnYFE1pqWllZSULF++PCYmhu/iGIBFixbV19f7+vr6+/vzXRYAMBKIfTzr169fWw9REKHbtoZsoFCiODMyMrKgoODWrVvl5eXibKBCfQpWp06dTpw40a1bt9jYWMrWGlylV1SKiooSExMtLS0Vr+cLAKAxxD6esRPO8vPzFR8qKyuj2+eee65dK+zTpw/FlCdPnmileAYH9SlkVlZWGRkZAQEBo0aNqqiooLt8l0igampqXFxcaIKqC92MAECLEPv417t3bwoWDx8+lOuFcPPmTbrt1q0bT+UyVKhPIfP39w8PD09MTHR1daUgjt6pihoaGhwdHWkiOjpancv1AgCoD7GPf25ubvv27fvuu+9Gjx7Nzbx9+zZlF/r3b6sbaWhoKN1+8sknsjMp61y5ckUi7nCD+hS4DRs2XLhwIS8vjz6g3NxcU1P8C/2f5ubm4cOH19fXBwYG4gxIANA6/OHyb9q0aRRTNm/e/Prrr7MGKkob7BKcU6dOVfHE/Px8Wkz2ygdbtmx59OiRu7u7mMccQX0KnImJCaU9Ozs7Sn5eXl5IfpympiZvb++SkhIPD4+UlBS+iwMARgj/tvyjSBEWFpaUlBQQEDB69Gh2Ddlbt25NnjxZtr3K1dWVbi9cuMDuhoaGXrlyhfJNQUEBW4w9q3fv3rGxsby8EYFAfQof5byysjIHBwckP05jYyNVSFVVla2tLX33UCEAoAv4ZxGEd999t3///tu2baPYQXcdHR0puKi+OOyAAQO+kKKYsmPHDu5Zfn5+iiMViw3qU/jMzc1lk9+JEyfEPDRdQ0PD4MGDKfN5eHiIvCoAQKcQ+4RiuJSKBbh2KU6vXr1wbfu2oD6FTzb5de/e/fz583Z2dnwXige0p+Hu7k4TlPnQ8AkAOoX/FwDgDUt+kydPzs7Otre3T01NDQoK4rtQ+tPa2hofHx8VFSWRXnt3y5YtyHwAoFP4iwEAPlHyO3z48IIFCzZu3BgcHJyVlbVz504xDOxSX18/YcKEvLw8iXR8PlyKAwD0ALEPAHj2j3/8g13+rnPnzulSqampgYGBxnrp3ubm5nXr1rFGPltb2/z8fGtra74LBQCigNgHAHxqbW0NCAioqqry9fXdu3dvdHR0YmJicHAwpaI9e/a4ubnxXUBtojd77NixKVOm1NfX0924uLjFixf/9ttvfJcLAMQCsQ8A+LRs2bLs7GxbW9uMjAwzM7OEhARKQj4+PiUlJe7u7pQFd+/ebRyXcauurp4wYQK9L5oODAzcunWrpaXl3/72t48//hiXqgMA/UDsAwDeZGZmsmERL1y4wI1aYm1tfenSpZMnTwYEBFAi7NatW3R09NKlSw13WJOGhoYFCxYkJydLpEd1KeAOHTpUIr32bkhICE3Y29vTW7axseG5oABg7BD7AIAfpaWlFOxoorCwULGty9PT88GDB5s2bQoLC4uVSkpKCgoKMqxWserq6u3bt3MjflPg8/PzMzExYXcp4F65cmXQoEH19fUUBysqKsQ5hA0A6A1iHwDwgIIOG1gxNTWVNX0p6tSpU2ho6MyZM1lTWZiUk5PTmjVrvL29hTzWSVNT0/79+6OioqqqqticthosHR0dKe3Z29tLpG1++fn5RnY6IwAIinD/NwHAWDU3Nzs7O1PyCw8Pf+pAfRYWFtu3b1+5cuW+ffso9pWUlPj4+EikA91FRET079+fazzjXUtLy9WrVxctWpSdnc3mWFparlu3LjAwkN5FW8+ys7O7c+cO5T+qEHd399zcXE9PTz2VGABEBrEPAPSqtbXVz8+PXYhsw4YNaj7L2to6NDT0gw8+KCsrY7kqWYrlKlohjwd/6R3dvXuXpVJuJiXa+fPnq3nQlt4da/Oj5Ofl5SW2YasBQG8Q+wBAr+Lj4ym0UVw7ceJEexvqaHlHR8cjR47IHkUNkZJIu8dS/hsyZEi/fv10PeBzQ0MDBbW8vLycnByubU8ivcBadHS0BsegKbbeuXPHwcGB3lFwcPCTJ09mzZql7VIDgNgh9gGA/hw9epQNU1xaWtqRnrn03CCp6urq1NRUtk421DNbgGLljBkzKAUOHjz4hRde6PiB4JaWlnv37pWUlFDOS0xMlHvU1tZ26dKlHWx0ZJeqc3Nzo1ehIHvjxo2YmJgOFRoA4D8h9gGAnlBEY6flafG6FDY2NpFSXPPb3r176ba+vj5Rii1GsYz1GqZkRreUBVW3xj169OjatWu0klOnTtFdxZwn+b1xcdiwYVQGbQ0uQ8nv4sWLXl5e9BZY/9+VK1cK5+RFADB0iH0AoA8Uy4YMGUITSUlJuuisamFhMVQqNDRUsWWuqqqKTSgNcGqi7Dht2jRvb29nZ2dLS0utFFsR5dHc3FwKlNnZ2ZT8KMumpaUh+QGAViD2AYDONTc3Dx8+vL6+PiQkhGKZrl+uU6dO1lJjxoxJSEigxEkFuHr16q+//vr9999fu3aNLaY0AnLtguS1116jlbz44os9e/bs3Lmz3saLpuR3+PDhoKAg7rB1amqqsV6hGAD0CbEPAHRu6tSpJSUlHh4e27Zt0/+rs8FTWBOj7NgolAj1Xxg1mZiYpKWlUeikbErJ7/bt27m5uUIeqhAADAL+RABAt1avXk3BxdLS8tixY2iyUh8lPwqmlFljY2Pz8vK8vLyoAnXdQxkAjBtiHwDo0MmTJ1k320uXLiGyaCAmJqZv374hISGU/BwcHMrKylCNAKAxxD4A0JWamhovLy+ayMnJsbGx4bs4hooN4EfJr6qqipJfcXGx7jqUAIBxQ+wDAJ1obGx0dHSkibi4uDFjxvBdHMNGya93794+Pj6U/Pr161dRUcHjVUkAwHAh9gGA9rW0tIwePbq+vj4wMDAyMpLv4hgDis65ubleXl5Uq/b29ufPn1fzym8AABzEPgDQvtmzZ+fl5Tk5OaWkpPBdFuPh6enJXbqXbmkayQ8A2gWxDwC07JNPPklOTra0tDx79izGHNEuynks+dE03ebn5+ti7GsAMFb4R1bu1Vdf5bsIRgX1KR4FBQVhYWE0cf78eTZgHmgXJb/a2lrW5ufu7p6bmys7GCEAgAqIfQCgNTU1NRREaCIjIwPHH3XHysqqoqLC1dW1qqrKy8srOTmZ9fYFAFANsQ8AtKOpqYllvujoaH9/f76LY+Qo+ZWVlTk4OFDyCwkJkfw+zgsAgAqIfQCgBa2trd7e3hRBfH19V65cyXdxRMHc3JyS3+jRo/Py8ij53bhxIyYmhu9CAYCgIfYBgBZ89NFHFD5sbW2zsrJMTEz4Lo5YUPJjo7pQ5cfGxtIcytyofwBoC2IfAHRUWlpaYmKipaVlcXExuu7qGVU4Jb+pU6emp6dT8quoqKCPA8kPAJTCHzQAdEhRUVFwcDBNnD17FhcN4wUlP4p6NJEuRRMpKSnI3wCgCP8LAKC5uro6FxcXmkhNTWWXYgNemJiYUPKzt7ePjY2l5Hf79u3c3FwkPwCQgz8FANBQU1OTq6srTYSHhwcFBfFdHLGj5Me6dFDyy8vL8/LyOnbsmLm5Od/lAgABQewDAE20trYGBARUVVV5eHhs2LCB7+LAv1Hy69u3b0hICCU/BweHsrIyJD8A4CD2AYAmli1blp2dbWtre+LECXQgEBQ2gB8lPwrllPwuXLhgZWXFd6EAQBAQ+wCg3TIzM9lwIRQpzMzM+C4OyKPk179/fy8vL0p+9vb2FRUVSH4AIEHsA4D2Ki0tDQgIoInCwkKECcHy9PTMz893d3evr6/v1q0bJT9cLg8AEPsAoB0oQwwfPpwmkpOThw4dyndxQBU3NzdKe/b29jTN2vyQ/ABEDrEPANTV3Nzs7OxMyS8kJARXgDUIlPOqqqqGDBlCnxolv9zcXE9PT74LBQC8QewDALW0trb6+fmxrrvbtm3juzigLhsbG9bmR8nPy8srJydnzJgxfBcKAPiB2AcAaomPj8/Ozra0tDx27FinTp34Lg60g5WV1fXr152dnSm1+/j4JCcno7EWQJwQ+wDg6Y4ePRoVFSWR9ufAOHCGiPJ6WVmZg4MDJb+QkBDJ7+O8AICoIPYBwFNUV1f7+PjQRH5+vrW1Nd/FAQ1RXi8vL/f29s7Ly6Pkd+PGDXZVDwAQD8Q+AFCloaFhyJAhNJGUlOTm5sZ3caBDzMzMcnNzvby8KPnFxsbSh7thwwaMtg0gHoh9ANCm5ubm4cOH19fXBwYGhoaG8l0c0AJTU9PTp08HBQWlp6cnJibW1NSkpaUh+QGIBGIfALRp6tSpJSUlTk5OKSkpfJcFtIZCHkU9mkiXogn6fCkO8l0uANA5/M4BQLnVq1dTJrC0tDx79iwygZGh5Ldnzx57e/vY2Fj6lG/fvp2bm4tPGcDo4UcOAEoUFBSwrruXLl2ysLDguzigEzExMc899xx90Hl5ea+++ip96OimDWDcEPsAQF5NTY27uztN5OTk2NjY8F0c0KHIyMhu3bqFhISUlJQ4ODiUlZUh+QEYMcQ+APgPjY2Njo6ONBEXF4fLOYjBrFmzXnjhhYCAgKqqqp49e1ZUVFhZWfFdKADQCcQ+APg/LS0to0ePrq+v9/X1jYyM5Ls4oCf+/v5sYBd26V4kPwBjhdgHICKVlZX9+/dXMVrH7Nmz8/LybG1ts7Ky9Fkw4J2np2dhYaGLiwslv27dulHys7Oz47tQAKBliH0AYtHS0jJkyBBKfm1daeOTTz5JTk62tLQsLi5Gp04RGjp0KKU9e3t7mqbbK1eusMP9AGA08M8OIBbffvvtkydPfvnlF6WPFhQUhIWF0cTZs2cp+em1ZCAYdnZ2d+7cobRXX18/aNCg3NxcT09PvgsFAFqD2AcgFjNmzKDbW7duKR68q6urY113MzIy0MAjctbW1qzNj5Kfl5dXTk6OOj17duzY4erq6uTkpIcSAoDGEPsARKGyspK18929e1fuoaamJtpg00R0dLS/v7/+ywZCY2VldefOHQcHh6qqKh8fn+Tk5FmzZql+CmXEkSNHPnjwoFOnTvopJABoALEPQBRos80CH23OZee3trZ6e3vT1t3X13flypU8lQ4Ex9zcvKysjCW/kJCQJ0+ePPWizA0NDevWrVu8eLF+SggAGkDsAzB+9fX1tPFm0+fOnZN96KOPPmJddzMyMlT08AURouRXWVnp5eVF35CwsLD79+/HxMS0tbCNjU1zc/PmzZvnzZuHy7oACBZiH4Dxo601F/tqamq4+WlpaYmJiTRx4cIFMzMzXsoGQmZqapqbm+vn55ednR0bG9vQ0LBhwwaluwdsnD/6mo0bN+7UqVN6LykAqAWxD8DINTc3p6amcnfv3bvHJoqKioKDg2misLAQY/NCWyj5HT58OCgoKD09nXYSaLeB9hZUNAxfvXr1/Pnzw4YN02chAUBNiH0ARo420vX19dzdH374QSLtuuvi4kITlAiHDh3KV9nAIFDIo2+RtbU1xT4Kf48fP87KypIb2bFr164vvvjifak///nPFP7QtwNAgBD7AIxZa2vrxx9//Ouvv3JzunTpQndZ193w8PCgoCD+SgcGg5JfQkKChYVFbGxsdna2l5dXbm6ubPJ7/vnnuZx3+/Zt9O0AECbEPgBjduHCBbk5zz777Lhx46qqqjw8PDZs2MBLqcBAxcTEvPjii2FhYXl5eXZ2dmVlZebm5oqLPXnyBH07AIQJsQ/AmE2cOPH+/fuycxoaGr755htLS8sjR448fPhQIh3ShS3z5ZdfPpbKzs4+fvz4n/70J34KDQIWGhrauXPnkJAQ2nNwcHDgkt9zUtxi6NsBIEyIfQBGq6amRvH8qidPnkikQ7r079+fbad/+eWXuro6bgELC4t9+/Yh80FbZs2a1bt3bx8fH8p2PXv2rKiosLKyovDX3Nwsuxj6dgAIEGIfgNEKCQmprq5u69E6Kdk5nTt3trW1/fbbb3FNXlBtzJgxubm5Xl5etP9gb29fWlqqeLQXfTsABAixD8A4NTY2Xr58Wf3lKfDNmzdv0aJFGLQZ1OHp6cldurdnz56nTp1SjHfo2wEgNIh9AMYpOjpaRVOfHCcnpxMnTmD0PmgXOzs7lvxoeuTIkV26dJFbAH07AIQGsQ/ACLW0tOzdu1edJW1sbEaPHr1t2zYciQMNUPKrra1lbX6PHj1SXAB9OwAEBbEPwAh9+eWXcuftKUVb64MHDw4cOFAPRQJDVFlZyRrzOgJ9OwCEA7EPwAitWLFCdohmRS+++KKXl1dqaioa+UAFOzu79PT0+fPnq7MX0Rb07QAQDsQ+AGNz/vz5x48fq1igf//+ycnJnp6e+ioRGLB33nnnf/7nf7Zu3bp48eKGhgbNVnL79u1ly5bFxsZqt2wA0F6IfQDG5uOPP5YbopnTo0cPFxeXjIwMMzMzPZcKDJeJicncuXPnzJmzbt26lStXahD+njx5kpKSQt9MjA0EwC/EPgCjUlNTc+PGDaUP2drafvLJJxMmTNBvicBIUPhbtGjRwoULV61atX79+vr6+nY9vaqq6p133jl27JhuSgcAakHsAzAqy5YtUxy3xdLS0sHBgba4GEcDOqhTp07R0dGRkZEffvjhjh07VJ9CKufSpUvo2wHAL8Q+AOPR2Nio2Jpia2u7fv36SZMm8VIkMEqmpqabNm3auHHjjBkzsrKy1Dzse//+/YkTJ1ZVVaFvBwBfEPsAjEdKSopsUx8utgY6ReGPvnK0s0HhLzs7W53w99NPP6FvBwCPEPsAjERLS8uSJUu4u7jYGuiHubl5enr6gwcPAgMDv/vuO9XhD307APiF2AdgJP7+979zg6vhYmugZy+88MLXX39N4c/Hx6eyslJFhw/07QDgEWIfgP6wbeH169cfPnz4448/Xr58WfXyI0eOtLS07N27NwW4Z555xtzcvK0l//nPf06dOlUiPe725z//eceOHTh9CvSPwt/58+dv3bo1bty4a9eutdXyh74dAHxB7APQIcp5V69ePXnyZFpaWklJSXufnpiYKDfHw8PjnXfeoVt7e3vZbrmjR49ubm6mqHfmzBk3N7cOFhugI2hHhYId7dWMHz/+559/VrxWL/p2APAFsQ9Amyh73blzp7Cw8MiRI8nJyUqXCQ8Pl/zekqd6bTU1NefOnWtoaOBWlScluyofHx8bG5tvv/3W1NSUtqM9e/bUyhsB6KDBgwffuHGDfguU8BTDHyU/9O0A0D/EPgAtqKys3L1798GDBxWb9EJCQkaNGjVs2LBevXqpOErblqCgILrdvn073VL+q66uzs/PP3DgQHZ2tkTaHMi1CA4aNGj//v20PE7pA+FwcXGh8HfmzJmZM2fevn2bG+evqalpy5Yt6NsBoGeIfQCaoxyWnp4eExNTVVXFzXRycqLs5enpOXDgQO1u0iwsLBylZs2a1dra+uDBg8uXL584ceKLL76gAly5ciVMigqwZs0ab29vU1P8wEEQ3nzzzYqKisOHD8+bN+/+/fuU+STSwVxcXV1pl4nv0qmFCs93EeSNHz9egKXiESpEHdgqALRbS0vLuXPnKO2xJjeJdLSUpUuXvvXWWz179tRP2DIxMbGysvKUopLQdrS6uvqrr76i2FdSUuLj4yORNjRGRETY2dnpoTwAqtE3dsKECWzD/N5777Fe5z/++GNoaOgnn3zCd+kAxAKxD6AdKFqlpqZGRUVxc6Kjo6dPn857tDIzM6My0BZ0/vz5V69eXbRoEUXSZCkWSQMDA3FlNuAdC3/37t2Lj4+n3w7tQX366af29va0u8J30QBEAbEPQC0U+GhzxZ265+HhERMTQ7dCO5DaqVMnR0fHI0eONDY2ZmZmUkKtqqoK+V1CQgLCH/COvqX0zaRdFAp89+/fX7hw4fvvv6/Bma8A0F7C2mIBCBDlp7CwMNaX1tLSct26dX5+fsLvNkEb0SApCqzbt2+PjY1ljX9JSUm0ucXAGaA3Sodu7ty5c5cuXW7fvj1mzJjJkycj8wHoB2IfQJtaWlrS09ODg4PZ3YyMDAp8BnetMxsbm5iYmKVLl9IthT+KsMuWLfvqq68wvB9oEWW74uJimsjKypJIfyyy/ZxU69atW3l5+eDBg/v379+7d2/6xpqZmemuqABihtgHoFxBQcGUKVPYpis8PHzVqlUG3SBB21GKfR9++GFAQEBeXp67u7uHh8fevXutra35LhoYJNaL6Pz585TzaO+oI6tSfLqtre20adO8vb2dnZ0xwguAFiH2Acirq6ubPn0666Xr5OSUk5NjNNnIysrqzJkzLNFS+OvZs6cRJFrQG9akx40ZJPdoSEgI/V5eeeWVZ599duDAgRLpSRGqV0jZ8cmTJ48ePbp27dpvv/1Gv7ULFy7QN5NWHivFFgsMDPTz8xs2bBgaAnXt+vXrS5YsGTBgwIoVK3gsBn0TNm3atGjRohEjRvBYDFkCqRlJhysHsQ/gP6SlpbGjurTFysjI8PT05LtE2ufm5kZbWXb8OjExcdeuXd98883QoUP5LhcIFO0I0e9i2bJlcmfpeXh4jBs3riNDVJpJ0XMpz9HdMWPGSKQnV9y7d6+kpIQ2b2w08nQp9hRfX9+lS5e+9tprwj8/tbS0NCIigiZmzJgxadIkxQWWL19eWFh46NAhXRdAjoWFBf3ex48f7+joKDv/8ePHbDCdjz/+WO4pd+/ePX78eFFRUUVFBZtjb29PK3nrrbd69OihlVJxWHXRF2Dt2rV9+vTp169fu9bfkTLwWDNr1qyhffL58+ez4beUYl8YCnxvvvmmxpXzr9gnwOENMeiiHFSIOqiWOvL05ubmuXPnsq4bcXFxixcvFv52RWP01oKCgiZMmLBgwQJ6yy4uLklJSR988IHBnbkIukO/iBMnTsTGxipeD9DJyal79+46+oHQaq2lKAUmJCQ0NDTQBpW2duziNIxEOnbS+++/z/KiwNGe1fDhw9sbj7SFosyAAQNk59TU1JyRkmsxyszMpKqmmc8//7zs8qdPn6aQwVZF/xVsZnl5OS28d+9ezZqdFEvF6datG92+++67lKXor/izzz5r78o1LgOPNTNq1Ch6XfqStxX7KF/Sr4AFUyq2xpWD1j6Af6mrq3N1da2qqrK0tLx06ZJBbEs6jv5Btm/f/uc//9nLyyssLCwnJ2ffvn044AvsYoOyF8ylvQI/Pz9efhdsO0dmzZrFRkqnrSklUXYU2NbWljZ+/v7+gv3e2tvbUwjYsmULXwcHlR6XZHmFSkWPsjxKqYKd7CuXVLhko9gQRf8Y9D2hRzt37kz/nx0vlSwq1eTJkykxUwF0dKhXUDVDi9FLUO4sLS2Va2tkjh8/LpG2dj8vpXHlIPYB/GsjR3/NEukvSoS5x9PT886dO+7u7tnZ2Q4ODsXFxTiJXpyampr279/Pxnpkc+gXQdFqyJAhAmn5pmK4ubmdOXNG9rqI7KwMKiptZZVuL/nF2vmozBQFVBy/0zPKCgUFBVQq+r2zUrFUMXXqVNnFHj9+TAGIJpQ2XNETraysUlNT6VNob+xTB1UdJZuUlBR9nuHHY81MnDhx06ZNp06dUvo1Zo3cb731FrurceUg9oHY0S+cEo9Eesxo5cqV4jzKSXuZlH3pf402pf369auoqBD+wISgRa2trceOHZsyZQo7e481oU2YMEGwg3tTwWZJ0feWtpSJiYns4K8w+6ez45W7d++mTbXcUUIe9e/fn8LNL7/8wu6yVCF3ju/Zs2cpYbu4uLSVLVyldFRCistvvvkmFfL69eu6OMOvLXzVDH096MtML0d/xYpHk9nLcacKaFw5iH0gakePHmX7c8nJybQJ4bs4fDI1NU1LS5NIT5/v1q0bJT/erzgH+lFaWhoUFMSuQBMYGBgbG2tAHz0VNSEhYe3atSdOnJg9ezbXPz0+Pl44fX5pCz19+nTaom/ZsmXx4sV8F+ffnjx5wk1TdGCpQi5t5Ofn0623t7c6K6T9BBWP0so1OMzt5OREyaawsFCfsY+vmqGX8PX1pdhHmVKuYZi+3oovp1nlIPaBeBUUFLCfVmpqKm32+C4O/0xMTPbs2WNvb08bfrqtra1Fm59xq6+vnzNnDuskS5sQyv0CPEiqDtppGTNmzLVr13bu3BkSEpIoJajx1emvhoICbaRHjRqlu+axdqHCSKQtu3T7ww8/SKQZWm6Zx48fS6QDP6mzwhkzZqh4lHXUaC92OintkyjtCq0jPNYMfU8o9sl17GCdORRPLtSschD7QKRqamrYsV3aNvj7+/NdHAGJiYmhvVvaalLyu3PnjtjOdBSJlpaWTZs2hYWFsbs5OTmjR48WSELSWKdOnWbNmhUYGMj6pwcEBNCWmzaiAsmytO2njfdnn3328ssv83uo9/r163//+9/pP5B+4yyDsgOanTt3lluSG5REHe0KH1QVbbWBxcfHcx9Znz59JL9nLD3gvWb69evH+gDJduxgJxey4Y1kaVY5Iop9AhlrEaNQqqC3yqFYw35R0dHRyHyKNmzYUF5eTttLigKnTp0SyOn8oC0FBQVjx45lp/HRT2Dp0qXCOR7acax/ekREBBv7bdCgQRQEd+7cyfsODG3RKfnt2rUrMzNz2rRpenvdtgKWi4sLNwodO6zp4OCguAw9XRelUjGAi+wnxfJxuzKW+oRZM7RJWrt2rWzHDnZy4fDhw+WW1KxyNIx9RjAKpYoRI62trWkltKcozlEotV4zehuFUk0tLS30+6FtHm0MYmJidPQqBs3ExCQrK+vVV1/Ny8ubPXs2bUT5LhFoR2tr60cffcTGQPb19d29e7exHse3s7MrLi5m/VTS09OPHj169uxZ3pv96P+fSrJ37176cemtMHIBi2qmc+fOtra2sseaKysrlT73ueeeo9vq6mqtl1YIDQ3CrBnayFLBuI4dFy5caGhooC2jtsZ97Ghrn6GPQql0h4NWQjV++vTphQsXanAShnGMQqnFmtHbKJRqohhKydvDwyM1NVVHL2EETE1NCwoKevbsmZyc/Oc//9kor1YiNrTxoL9r1nUjPz/fzc2N7xLpFu29jBkzpra2lg3DPmjQICH03AoPD6f9akreuvuLk6NOwKLEo7TtinUaUPHvLUsXXTp0Spg1wzp20L4B69jxzTffSDp8MQJZHYp9hj4KZVtrIPv376dESz9LDWKfEYxC2dYaJBrVjN5GoVQH7bpFRUXRxKFDh3DsUjVzc/OvvvrK3d09ICAAJ/kZOvrmDxs2rL6+njZXtDkR7MgsWkc7MNu3bx83bhx9jUNCQujfJiUlhWbyVR76D3znnXfoj5f+S/kqgyJ27lpZWZncXzTtJ+zevZv+vdsadPD69eu0l/7mm29OmzZNF1062IlrbFxVXvBSM2+99RZ9Q44dO0avQuGSNqBKN52aVU6HvvoGPQqlaqwpXkVS6SAhj0KpmmY1o59RKJ+qubmZtnwSadddjEisDjc3N9pSJicnz5w5c8+ePXwXBzRUVFTErhxFn+a2bdtEuMPj7+9fVVVFfynp6em3b9/Ozc3lMflRYehPj/7lhDO+IDtkKTtwCUP74XPnzl27di39gdfW1lLJZY8L0c75li1bGhoaWHDRRWfbmzdvSn4/iY0XvNQMJSt27iAlP4l0A6p0Mc0qp6Pfe8MdhfKpWAOV9gsnJeRRKJ9Kg5rRzyiUT7Vu3br6+noPDw8M16I++uD27dtHG8uIiIj2flVACE6ePOnl5SWR9t4Q88msNjY2ZWVlDg4OeXl5VCG0QeWrAZv+AxcuXLhixQrdbWLa6+WXX5a0cR4b2/2mELNXSvbKs/TXLVF2aTItqq6ulkiPqOpo/U/FV814e3tT7KP/XomyzhyMZpXT0dhnuKNQqsbONpP83kFaVKNQqqZZzehnFErVGhsb2eFd+n1qa51iYGZmtnPnzoCAgBkzZly6dInv4kD7cJlPCKe18Y5yHpf86Jam+Up+rq6uuusKqgH6p7WwsKDyPH78WHGLQPlmwIAB9O9dUlLClZnKb2dn99Zbb+n05H52KiqXqPSPr5qhNaekpNCOATv9SekymlWOFlq5DXQUShUuXLjATvZ/5513WHWLahRKFTpSM3oYhVK1jRs3SqQXIRDOgRVD8fbbb1taWtLHUVBQYPT9AIxJUVERMp8cynmVlZVULZT8dD0+kaOjo4rhLPRwTrzqAshh3QjoO6P07BpKMJOk9FkqSlrszDatN44Is2bkqO70o3HlaOfkBkMchZJRMWIkJRtuRDdRjULJaL1m9DAKpQpcU19CQoK21iketF3cs2cP5fWxY8f+9NNPhj6or0jQj501AyDzyTE1Nc3NzaU9XoxPJIt1I9DzGeeqsTPb2nX2uS4IsGYkHagc7cQ+QxyFkpEbpoRyBuUSis8rV67UuHnW0EehZHRRM7oehVIF+mZK0NTXARTNbW1tq6qqfvzxRwO6YKtocQOSh4eHI/MpouR3+fJl2r2kTNy/f//IyEi+S8Q/+mNnXYx1N8REu9y9e3ffvn1KB5rQM6HVjKRjlaO1rkwGNwolIzdMCYWbhQsX0l7yTz/9pHG4MfRRKBld1IyuR6FUYfXq1XS7bNkyXb+QEVu6dGlISMimTZvQYip87CIcvr6+GzZs4LssAkX/RZcuXaJ/xaioKNqrQXcliXTPvKioaMuWLVQbvPfR/Pzzz2kDsWrVKn6LwQiqZiQdqxxt9mA3rFEolaKPk3sX69ev5z5dUY1CqZRWakbXo1C2pa6urqSkxNLScuDAgbLzm5qa5LrlUzg2xKtU0Qb+v//7v+kD0mkgo107dpF7+gKIcAQQA/K3v/0tLy+PAk1WVhaOyKtgY2OTm5vr5eU1atQojEwpkf5Fh4aGLlmyZN26dbxfxZRdXECfXR5VEE7NSDpcOdqMfYY1CmVbaDE2eojsAWtRjULZFq3UjE5HoWwLbfzoljKrXFj54osvKMcoLk/5afny5RjYTw5ViIeHB+WJq1ev8n6RK2gL7eSwb/XXX3/N49B0hsLT05ONTDl58uQjR47wXRz+UZJIS0vjuxT/6gIonMGAGYHUjKTDlaPlPwUDGoVSBTYYoewBa1GNQqlCx2tGp6NQtuXAgQMSaXdUpY86OTnRvj6bLi8vpy9wolRVVRXrUAychQsXUuw7ceIEYp9gsbGQoqOjcQqmmtjIlPTDpx1arrMagLHScuwzrFEo28INRih3QFO7hDwKZVu0UjO6G4VSqdbWVtZxpK328LCwMNlz3hsbG2m/n54yYcIEDFMnZ/DgwRLpwIehoaF8lwWUoL0ydj4D78ehDIiZmdk333xDu6MzZ86knUOcwADGTfuHAAxrFMq2+Pj4HDt2rKKigm51NK6ewEehbEvHa0Z3o1Aq9eDBA4n0AKWaJ+7QYsnJyT179qQyNDQ0iOfSpXIoLiueFtarVy+6zcvLU/oo8I6ddLFz505kl3YZOnQo7WTST/7gwYNo8APjpmHsM4JRKJ+6Bg16wBnHKJS6qBk5OhqFUinWnDl58mT1n8L1LL57967ckbKWlpZNmzbl5OSwFkQPD4/o6GjFcQcl0lbDVatWffrpp6xD5dSpU4OCggoKCtLT0+fPny+72tLSUtrYxMfH05JsTnh4+OLFi9s6UyIzM3P9+vXsnP05c+Z88MEHKt7L0aNHKQTQi7LSjhs3jtYslwlkS5WWlpaVlUV3aWE2uLcsysQUoKmcVDPCOZEDGPpisKa+ts5nABV27dqFBj8QA1Gc8CvAsRYxCqUK2q0cCih0265rS/zzn/9kE1ZWVrLzq6urqaKqqqoob1EyozmJiYk+Pj4hISFyI77W1dW5urrSkk5OTqwBZt68eRTvXnzxRXqKn5+fbOwbNGiQRHpEmy1ZXl7OTi5UHGW3tbX1L3/5C82naXpRCwuLeKmMjAzFd0EJdfbs2WxhNmAhrZPC4tatWy9fvizbinnlyhX2Rnbv3h0bG0u5gd4dFUNp5bzxxhsUebnLOoNwUGSh22+++QapRQNcg9/x48eV7sgBGAdRxD6hjbWIUShV0HrlsIO8L7zwgvpP+f777yXS48KynXkpRQ0ZMqS+vj4/P58LkevXrw8ODqZoNW7cONljQ97e3pT5kpKSuHPg1q5dy64HpfhyqampkyZNkh04hvIlvRYFO1q57LHprKwsei0Kndy1RDds2BAUFMQuwCVn586dcgsnJCQsXbqUgh2lQMVOi1OmTLGxsfn5559Vd2EeMGAAxT7KtegxICj0naEvJ312zs7OfJfFUG3bts3d3X3x4sWIfWDERBH7JAIbaxGjUKqg9cq5fPmyRJrh1FmYXvrChQsBAQE0vXnzZtmHNm3aRJtVimiyDYedOnWiAh89enTmzJm+vr4surHT6p2cnGT7PZiamh46dOi///u/FV+UcpvcHIpfGRkZFOYyMzO5Ryl3suYcyp1cFjQxMaEiUQG4A8RMY2MjG8VDdmESExNz8OBBym1USLnxaWkNpaWlT62ol156iW5//fVX1YuBnrGLZa9cuRLnXGrstddek0hPLGYBmu/iAOiEWGKfcMZaxCiUKuiucnr37t3WQyFSsnPoH//KlStyY5SEhYVJpClZ7ukU9T744IPY2NgHDx6w091Yk96aNWvklqTVUjRkJwU+Fesze+7cOS723bt3j50mKHdSHUVPSqjBwcGyM1kfZMWFycaNGylQHjhwQC72KV1YERvu8ccff/T09FTnjYAetLa2xsfHS5TtQoD66KcUHR1Nv+WvvvoKNQnGSiyxTyKYsRYxCqUKuqscNv6zmt544w25I5hNTU1s4rvvvlNcnl07uKqqisUm1g25f//+iku++eabSmNfTU3N7t27KUuxU/E4Fy5c4KZp/RJpFSk+fciQIXJzrl+/3tbCrLlOsa89lU1x4ba066A56Nrdu3dpl8DW1lbubFRor+nTp1Pso/0oxD4wViKKfSBO3bt3p9uHDx+2tYBsz4m6ujq6GxUVRc+6d+8ed74dO0GQKD2LjuGOe547d06i0B2EUXpBF3a+nUTa3sZ6ikikQZB1v+WwJCd7qWXOiy++KDentLS0rYW7dOlCt99++63cfLkr17Xlxo0bErUPmoN+sL2ROXPm8F0Qg9e3b1+JtMG+ubkZ1zgBo4SvNRg5lrTUHD+cslpkZCQFvsTExIiICO4St3/4wx/o1tbWtri4uK3ncn1jHRwcSkpKHj16pJiNFK+JUllZSZnPw8Pjq6++ku1dW19fLxf7/vjHP9LtTz/9pPjSiqtlQVDpwrQ9k0hPH5Sbr/7pjxJlQRN4dOrUKUk7u6uDUhT16GdeVVVVW1uLIYrAKCH2gZFjZ/XV1dWp/5T4+Phdu3ZR8uMGz2ORiDYGXbt2feop887OzpTYrl27phit2PFfWexqJV9++aXcuNCUGuWW7NOnj+T3Zjw5d+7ckZvD2vmULnz//n3J72eva4Add5btdwy8o6+r5PfzQaGDpk2bRnti3333HcZtBqOE2AdGjp1j167riVGm2blzZ0BAwIIFC/bs2SORtgGwYYqLi4vlekIoGjNmTFRU1NKlS+WGO25sbJQ7dY+w5kN24FUW65gpi4XITz/9dMWKFXIDs1FClVuYvWulC7MmTM1ahlpbW1mHFXa5DhCC5uZm1o9bWydcNjQ03L1799atW7QD07lzZ8WIz/Z8/vGPfxjlYVAPDw+6vXjxImIfGCUj/NECyNLsemK+vr50m56eTiGJNfixq3ZSFiwvL1fcEDY1NXEz2biv9IqyV3anV2fDr8hhTYNffPGFbCqlrTgFR7klLSwsAgMD06Vkzzevrq6WOxxM7Ozs2NizcguzkxdpQq7nr5rae6U70AN22F3yexrTWEtLy8KFCxV3ISgG0V6QeIZpZM3qbJh3AOOD2AdGjgIKO1mnXdcTowwXFxdH2Ytr8KMwx1JX9+7dac7rr7/OliwuLv7yyy8pS1Gw455+6NAhelHKiPSUKVOmUFpih+HCw8PlNquTJ0+mV1m2bFnnzp0pa1JpaYXsiYph7tNPP6WZLLGNHTtWIu3nMWrUKKULs4tN0cL03kNCQkxNTdma6aGkpCTNchu70h27mggIBDtZk7VRaYw+2T/96U/sujL0jfLx8XnmmWcKCgqOHDlCOzD29vapqaki6dzK9t+uXr3Kd0EAdAKxD4wfZR0KWz/88EO7ztH+8MMPKZDJNvilpaVRhqO1KQ6MwloHOTY2Nnfu3HF0dGSNcxLp6IBbtmzZvXu35D/7Q9jZ2VFklBs7kOZMmjRJMclZWVnRhnnIkCGybXVtLUw5taKiYtiwYVFS3PyObL9PnjxJtyNHjtTs6aAL7Aiv4nkC6qupqaFgJ5Hulqxfv547K8DT0zMyMrKhoYF2fhS7DRkr1gf/5s2bfBcEQCcQ+8D4BQYGUuxbu3at3AjD06ZNo8DExh9WZG5u/vjx4+bmZm4BExMTf3//3377rbKykrYKRUVFbm5uXbt2HTRokOJhX0qKP//8c2NjIy3PdQRhlwyRu1bHrFmz/Pz86KHvv/+eUtrAgQMtLS1bW1vp6YrnTlGgvHfv3pUrVwoLC/v37+/s7Mwt/Mwzz8gtTJmytra2XOrBgwdUToqMiu18rB7k+pQo4sYExkDNgsIGlVQ6WI+a3nnnHbqNjo6OiYlRfJS+GNu3b29XpygjwIbJBDA+iH1g/FxdXek2Ozu7oaFBNtyYSal4otIkRE9xlFLnwp3mUmy6paWFHepVPPXeysrKU4qbQzGxrRFVqABDpdRZmIIjK62KQj61Hpgff/yxvr7eyckJg/YJCvvsZEf2bhfae2HddJYsWaJiMaXjUNJezcaNG7du3cqODq9Zs0buR0EL0GpfeuklxQ5VBQUF6enp8+fPZ2cNVldXJyQkvPbaa0qbomlHa9OmTT4+Ptz6S0tLDx48SPshrLGTvpMzZsz43//9X20NWE1vRyvrARAaxD4wfhR92El1X3/9tX5657HTrWTb6lpbW2mjSJuouLg4Ax39hLa7dBsZGcl3QeA/sKCjOOKPmg4cOCCRNvW193TP2tpad3d3CnyBgYF9+vSh7EixjL7est+Q3377jX53Hh4eirHvypUr9JCfnx+LfT179mSnvdLa5PqeS6RjKiUnJ7///vvsLv2+Bg0aJJEOpcnONM3IyEiUys3N7WBrNGvX7MhBcwAhQ+wDUaANBm0SZs6c+fbbbytuVLTuxo0b9vb2ISEhkydPfuaZZ2pqalavXl1SUkJbqQ8//FDXr64LjY2NbKvMupKAcLC9C8UhIdXEztf09vZu7xMdHR3XrVv33nvvsRMY6EtOc6KiougbrkGHIXoX9HuhbHfu3Dm50YWamppovqWlpYODA5tDP+HU1NRJkyZxe1AJCQmlpaWUBQMCAh48eNCR3zi7kCM7RABgfBD7QBRog8QGNDl48KAeGvxoE+Xr65ssxc1kvToMdKizVatWSaQtMTjCKzTcuaeaXU+MHeFlo5q3y5gxY7irGkqkJ7OuXLkyLCzs6NGjmv3EFixYQL+XmJiYI0eOyM7Pzc2lW1o5N0INpTrFY8H0G2e9o06fPt2RBj92Vh+7qCOA8THILRCABtiAJvpp8LOysqJNF22GuTHVDDot1dTUsKsGf/rpp3yXBeTRl1nj64mxsxEkbZy6p9qyZcvk5rBBZDQe+sTBwYF+JtnZ2Y2NjbLthYsXL6Zbdbqfu7u70+3333/fkdjHQieudAfGCrEPxIKNoqw4grHusGt76OGFdG3BggV0GxcXp63z5UG75syZExUVpcH1xP7rv/6LTdTV1bX3u9qzZ0+5Oc8//zzd3rt3r13r4ZiYmCi2F1LB6DdLv1zF7x7tjWzevJn2rGiPjnXsYK5du6ZZARh2vURc6Q6MFWIfiAg3gvHYsWONI5DpAetxKZEOZMh3WUA51jR16tSp9sY+SlpsX+jWrVvtvQ7HU0f80QDtj1HsW758OfdG0tLS6HbFihVyS9KuCDvZ1NfXlxs/vLy8PDs7uyMFaGxs1O6V7gCEBrEPRGTo0KHstPEJEyacPn26gxezEoOmpibWhyMnJwcXZBMsZ2dniXSvZsOGDe39Vo8aNYpiXwcPjGqLlZUVi6F1dXWseY8dSpYbF+bkyZOU+SjwZWRkyPaLr6ys7GDsu3TpkkR6Div+HMBYIfaBuGzZsuX48eN5eXk7duyQPSEdlJo/f359fT1tBdUZpBD4YmlpyU7v+/HHH9vbaOfj40MRitIVfdZaP+eVDSGudHCZ2tpapU9Zs2YNFSktLS00NJRiHH392EULZZfZunUr3X755ZdyYyF1fExp1oI4Z86cDq4HQLAQ+0BcTE1Nv/76aza6iru7u+pxjEWONr1s4IzPP/+c77LAU8TFxQUHB2/atCkhIaFdTxw9erQ6ndybmpo0GG/y2WeflbQxuAw7eqvIy8tLIm3ko9jHhopcunSp3DIFBQUSZUeZ5S543V6NjY3sfIY33nijI+sBEDLEPhAdOzu71NRU2kYOGjSotrYW3RSUoi0ru/Lv2bNnDXR8aVFhx+LZRQjbNYyLiYkJO+c1ICAgIyNDMfm1tLQsX768b9++GrSOc+cOlpaWyu5inTx5sq2BBunLxs7EYEdyac5rr70mt4ybm1tVVdWJEydkG6ErKysVr0zdLkePHpVIj/Aq/cKPHz++IyvXEWGWikeokKdC7AMxCgoKou1QbGysvb39nTt3cNaanOrqajYWBuUANIgaBEtLSxawdu/e3d58NnToUDbiHSU/X1/fRYsW9e7dm1Z4+fJlilZffPEFZSzZESjbhWXK4cOH03fJ2dm5ubk5LS1t2bJl9EJtnYc3b948ejnW7BcdHa146HnmzJmU8GbPnh0XF/fWW29RzKWMSIWnxKZx8qN0S6uliYiICKULXLx4UbM1686rr74qwFLxCBWiDsQ+EKmVK1cWFhbShsfBwaGsrAzJj1NXVzdkyBCJdIurn2vZgVYcOnTI1taW0ltwcHB7v8+UFP38/Ly9vbOlZB+i/EeJ7e2339asVJQpKZxFRUWxGMdWWFFRkZWV1Vbso68fLcN61E6fPl1xgTFjxrAWQdYgzeTm5lJa1Tj2HTx4kF1yWvZq1wDGB7EPRMrExIQ2PLR3WFJSguTHqaystLe3l0gPdcXExPBdHGgHGxsb1ty1ceNGDS6dbGVldenSJYo+d+7cuXnzZnl5+SuvvPLyyy93795drr3t559/lvznJaeZl156iR5i3ThkUWEoqN2/f//WrVvu7u52dnZmZmbTpk2bNGmS0lFg6OWoAGwo6bYGWtq+ffvSpUuvXbv2/fffe3h40JeWVtXS0qK0AE/FNfXt2rWrvc8FMCyIfSBetN26ePGil5dXXl5ez549KyoqRH6eH5f5QkJCPvvsM76LA+2WkJBAsS8qKmrOnDmajUxpKeXo6Kii73Zba6a41tZDik1oZlJtvYQ6gwLaSMmOO6OiAKrt3LkTTX0gEoh9IGqU/HJzc/38/LKzsynxfPPNN6L938/MzAwICJBIj+2inc9AWVtb08cXGxs7YcKEM2fO8F0cw1BTU0P7ORLpUXK+ywKgc4h9IHaU/A4fPhwUFJSenu7i4pKUlPTBBx+IarDW5ubmuXPnsnP24+LiNDg+CMKxYsWKL774Ii8vLy0tTT8XITRoLS0tPj4+NEHffxsbG76LA6BziH0A/zrPb8+ePX5+fsHBwWFhYTk5ORQBdXHtKQGqqalxd3evqqqytLQUc2On0ejUqVN2dvagQYPoy/zWW2+J/LyFp1qzZg275u97773Hd1kA9AGxD+DfgoKChg8fPmLECNpqPv/88xkZGRQEjbjZr7m5ecWKFbGxsTTt4eHx1VdfiSTpGj1HR8fw8PDExERXV1f0VVIhMzMzKipKIr2csRH/0gFk/Sv2CXN4Q2GWikeoED2wsbEpLy+fP39+cnJyQECAra0thT/jawBrbW09duzYlClT2BgZIjyubfTWr19/4cKFvLy80aNHU6bR+lXXjEBpaSk7mTU/P1+zjiDqKC4uZicOtiUsLOzdd9/V0atrBf1XpKSkUHXRdO/evSdOnEj7w127dlXxlIcPH2ZlZX399dfcs9zc3KZNm9arVy89FVovNKgZxWfpv2b+FfsEOLwhBl2UgwpRB9VSx1diZmbGxoaYMGFCSUmJi4tLYGDg1q1bdbdh0DP6uwkKCmLXSDCytwYcynknTpwYMGAAJb/g4OA9e/bwXSJhqaurGzRoEE2kpqbSdlfXL9elSxf2cop69Oih61fviM2bN+/YsYPKP3nyZLqlyEJ7iZTnVFywkTJfaGgo/c+4u7tTqKU5d+7c2bdvHz2X/m3oO6nH4uuQBjVDVq9eTVVBy9P+GGU+eharmS+++EJvyQ8HeQGUsLGxod101iSWLhUXF7d48WKDbjVpaGhYsGAB67rh5OSUlpaGK3AYMdqBoe9wv3796NtrbW29YcMGNOgylPnYQEXh4eH66fVCme+TTz7RwwtpF31/KNlQOtm9ezdrxJo3b96SJUvoj5HCTVuNlFlZWZT5KAzJdg6jtLdq1apdu3bRrZ5Kr0ua1QwLefSvS18G7lksCFLs01tfOsQ+AOVoGzlmzJja2tp169ZFScXHx+/Zs8fb27td1zwVAgp8O3fuZHveEukl14z7tEVg2PUwKOIkJibW1NRQ0MeHXllZOWzYsPr6+sDAQIrCfBdH0HJyciTSaCJ74HL+/PkUXw4cONBWuDl//jzdsv7RHPrbpMBHTzSO2KdZzbARgmbPni37rGnTplHsKygo0HGR/4+Bbb0A9IwSHu2EhYSETJ8+PTs7m/2X0d2IiAg7Ozu+S/cULS0t586di4mJ4a6CFR0dvXTpUhXD5IKRsbKyouTn6uqanp5++/btEydOiPnTLy0tZQdbMTilOlgWef3112Vn9urVy9HRkWqSvk5Kj0s6ODjk5+ffv39fdua9e/ck0s5Guiyv/mhWM6zF9+HDh7Iz9d+RDrEP4Olo23nkyBH6PS9atIgiVLKUpaXlunXrAgMDBdgBtrq6OjU1lfVSZGg79+GHH2I4DxGiD72srIw2xnl5eQMGDKBNsrW1Nd+F4gFtdFmDd1JSUmhoKN/FMQC3bt3q0qWLYh8FNqe2tlZpuPHz89u3b9/q1aufe+654cOH05zy8nI2YsBHH32k+1Lrg2Y1I7sM57vvvqNbPZxgykHsA1AX7clR+GtsbGTjPlRVVYVIeXh4rF271tXVlfeDv01NTfv376c/XNZjQyIdmUUgZQMemZub06Y3ICCAdlp69uyZk5Oj4tprxod+F+y9S6RnOPj7+/NdIgPAGqWU9kQZNmwY7Tz88ssvSp9IieeLL76gfyHaz+Rm0p8n7So7OzvrprB6pXHNKKJfJVUUJchp06Zps4gqYUsA0D60BQ2Sqq6u3r59O+3F5uXlubu700O+vr4TJ06k6X79+ultsLSGhoaKigoqw969e+mWzWQtkbTbjeY9YMzMzA4fPvzpp5+GhYX5+PjQ7kpSUpIYhvQrKiqizEc7aba2tny1dNLr0q6X0ocEG4auX7+ueoEff/yRNeYpysrKordM/4QUgyS/9+TdsGFDdHS0EfTk7UjNyKLMN2fOHJrYunWrvgdwAQAN2NjYxMTELF++/MKFC4sWLaLIlS3FHqXgNWPGDApegwcP/uMf/6jFLsDNzc30N1pYWHjkyBHWLVcWbc4XLFjg4OCAk/dBDn0lQkNDvb29aZvETlRITU0NDAw06P7pKtTV1bFTciXSsYo+//xzvs5rVDGAS+fOnfVcGDXRvmtbD9GuJt32799f6aNUzzt27JDrycv2NGgnWfX4JgZB45qRdezYsdWrV0ukmU/PUVjz2Gfoo1C2d6BFFe9X4O9UA6gc9Zmamrq5uZ05c4Z+8NXV1bSPe+DAAdrS1NfXJ0qxxTw8PMaNG8dO4GA791SfT01mLS0tjx49opx3+fJlunvixImDBw9yB3A59AHRnyztWFMSFfMJ+6AOR0dH2m1YsmQJfTmDg4OjoqJkxySnr9zx48cN/RAw/WRYB3yJdAeM3qCnpyeP5THEAVzYHz79oSk+VFZWRrfPPfec0ifu2rWLbufOnSs7k/70WHeH8vJyQ2/w07hmOGzMP6qQuLg4/Q9h3dHWPgMdhVKzgRYl0gzUp08fuZlCfqcaQOVoxsLCwlFq1qxZra2tDx48oKyWlZVFf4IUAfOktPVatra206ZN8/b2piBIO9B/+MMfpkyZguY9UJO5uXlCQsKCBQu4Mcl9fX13795tZWW1cOFCioOPHz8WYEclNR09epS7Ag1tVj/++GOc2KoZ+ku/devWw4cP5fb5b968SbfdunVT+izaU5UodFzg5jx58kQnZdUvzWqGYQP1jR49OiIi4qmX9NCFjv4YDHEnRrOBFpmJEycad9sVKkcrKIHRFtRTiravjY2N169fv3//PqVAifSk8qqqKvXX5uHh4erq2r17dzc3N/poZJv0WBsGJT9ra2t6IR28FTBa9EW6dOnSyZMnWXcH2lbRN412TnJzcw0081VXV7MgK5GeaPvll1/iCjQdQX84FFC+++47yijczNu3b1Piof1b1c1UipFIbuASg6ZxzWzevJmeKHcEXM/EuA+k2UCLikfWjBIqRxfMzc1ZQyBLaSyfNTc3sxNBVFDnQDAbfoySH22qMRQZtBd9Jx88eLBp06awsDDWIP3999+//PLLBjTIS0tLy9WrV9ngShJpW7hRXkpb/9hIwpRUXn/9dbZFoOjGzkibOnVqW8+iTEPP2rJli2yyKS4uLi0tpb1WYfZfaS/Naoa1qri7u/OY+STijH2aDbTIGOhOsPpQOXpjamqqraYILvlx0wDq69Sp0+zZs1etWtUgFSbl5OS0Zs0agV+Tpqamhra+3OVnJNJr7OKEB22hf3uq26SkpICAgNGjR7Nzfm7dukXBTraVi3VSvnDhArtLkYhdhYy2F7I9eWmCojkf70P7NKuZv/71r5Lfr1msuE6aqZ+zHoX7e9adjgy0SJYsWULZ6NGjR+xqyvQV1/8pmbqDyjFQK1eurKiooOT34osvYihaaC/aev3666/379//5Zdf0tLSaJNWUlIi2GvSNDU1ZWdnL1++XHZ8yujoaIGHVEP07rvv9u/ff9u2bSy30f7/U3vp0X9+RkZGVlbW119/TcFIIj0TjvLQxIkTDb0zhywNaoY2rxLppWKUPjpr1ixdlFOR6H4hHRxokXaI2TdY8vtllelW/x2wdQSVY7hMTExoay2Rdp3u3Lmz3v5BwAj87W9/oxRFuw3mUrTb8MEHH5SVlSlek8bPz++FF17gqy2NnSObkJDAjVsk/PEpnZ2ducYeAzVcSsUCim+wa9eu70rpslz8a2/NCOSb0NHYZ3CjUGo80GJDQ4O7u7uXlxftsrA58+bNY11yFi9enJmZqfWi6h8qx6Cx5Pf48WM2mA6SH6ijqKiIvjD0dy3bnkffJXZNGnbdF9lr0kh+H5bcxcXF3t5ep6d2KPaI5x7C+JQAmtHhAC7CHIVS44EWKccozoyMjCwoKLh165YRjEUkQeUYPtoE0gaS8jdtFOnD4nesMhA++l2PGjWKvi1t7SSYmZlx16RJTU2Nj4+n7CU7LDkJDw/38fFxcnLq3r17x0d+ZledKSwsZONfyj1KiTMsLIy+4RifEkAzohvApeMDLcrp06cPJRvjGIsIlWMETE1Nc3NzvaRoAskP2tLS0jJ27Fj61W/ZsuWpC9vY2ERKsSOt3LDk9JDssOQS6fUwrK2tBw8ezO0lKj3s8+jRo2vXrrHpEydOUNr75ptvFMcEkL3aDY/HlwGMhujO7ZN0bKBFo4fKMQIs+dnZ2VHyo80zuzQIgJyFCxfm5eXV1ta2qxsENxqR0mHJaYH09PQOFoyXa1sDiIQYY59mAy2y3pFyTZsUj65cuSIxojyEyjEOtCEvKytzcHCgbWdFRYWgumGCEBw9ejQxMZF2DzrSGUJxWPLffvutrq6O/i4oAp46dYpbsqamhouDtra2AQEB3ENsHHJJey5aCAAaE2Ps02ygRYn06CctJjvQ4pYtWx49ekRbVqMZpgSVYzTMzc1Z8rO3t0fyA1kUwnx8fKKjo7V7DgDrCGxpacm+bP7+/rKP7tmzR4uvBQCaEWPs02ygxdDQ0CtXrlAkKigoYIuxZ/Xu3ZsNk2scUDnGhLbBxcXF/fr1o+RXVVVlY2PDd4mAf83NzbQz5uHhsXLlSr7LAgD6JsbYJ9FooMUBAwZ8IUXJZseOHdyz/Pz8eLmasu6gcoyJpaVlRUUFxb4hQ4bQhGCHNwO9mTp16sOHDy9fvoxjqQAipHnsM/RRKDUYgrJXr178XkpPb1A5xoSiHkt+7Ggvkp+Y/e1vf0tPT79y5QoupQggTiJt7QMQFYp658+fZ8nv5s2b2OSLU2lpKRuZ2dHRke+yAAA/EPsARMHOzo61+Q0ePLisrAzjYohNQ0PD8OHDAwMDcfkWADFD7AMQC0p+V65cGTRokIODA5KfqLS2trKRmVNSUvguCwDwCbEPQEQcHR3ZNTzc3NwuXrzYrnF6wXAtW7YsLy/vzp07+MQBRA5/AQDi4unpKXv1NuQAo3fy5MnY2NicnBxra2u+ywIAPMM/PoDoUPLLyMgICAhA8jN6dXV19CmHh4ePGTOG77IAAP/wdw8gRv7+/snJySEhIX5+focPH8YQbkapubnZ1dXVw8Nj/fr1fJcFAAQBsQ9ApFiPTkp+QUFBaWlpSH7GZ+7cuWxk5k6dOvFdFgAQBMQ+APGi5Hfjxg12AT0kPyNDH2hycnJhYSGGaQQADmIfgKjFxMTQLSU/e3t7Ng1GoLKyMjg4OCkpaejQoXyXxUi8+uqrfBdBCWGWikeokKdC7AMQOy75cdNg0BobG4cNG+br6xsaGsp3WYxHTU0N30WQZ21tLcBS8QgVog7EPgCQrFy5sqKiAsnPCLS2to4ePbpr164ZGRl8lwUABAexDwAkJiYmaWlpEmmbX9++fXH9LsMVHx/PRmY2MzPjuywAIDiIfQDwLyz5PX78OCQkRPJ7P18wLCdPnoyKisrIyMDIzACgFGIfAPwbJb+srCwvLy9Kfi+88IK/vz/fJYJ2qK+vZyMz44MDgLYg9gHA/zE1NWWXbgsICKAJT09PvksEamlubh45cqSTkxNGZgYAFRD7AOA/sORnZ2fHLt2G5GcQ5s6dW11dff36dYzMDAAqIPYBgDxKfmVlZQ4ODpT8CgsLMfabwGVmZrKRmS0tLfkuCwAI2r9inzCHNxRmqXiECgF9Mjc3Z8nPxcWloqLCzs6O7xKBcpWVlQEBAXFxcUjnQjNnzpyDBw/Gx8dPmzatrWWCg4NPnjy5ZcsWPz8/fZZNfVlZWVu3br106RJN9+3bd+rUqUFBQf/93//drmeNHDmSasPW1lYfJdYXDWrm559/TktLO3ToEI8186/YJ8DhDTHoohxUiDrQe1G7KPkVFxf369fP3t4eyU+Ympqa2MjMkZGRfJcF5P3P//wPxT6KdG3FvqqqKsp8Xbt2HTFihJ7LpqbVq1cnJSVRCadPn0639HZiY2MptXz11VcqnhUVFbV7925a/u2336ZkQ8+iu5mZmTk5OUaT/DSoGcp8lPIp8Hl6ekZHR9OcmzdvsprZv3+/o6OjfkqOg7wA0CZLS0sKfPZStbW1VlZWSherr6/H4UX9a21tDQgIoAmMzCxM3t7eFHpu3Lhx7ty51157TXEBNlgm5YanNp7xgopNyYbewpEjR1gJae+CNWFu3rx53rx5Sp+VlZVFUWbIkCGpqancs1gQ3Lp1a1xcnF7fg25oVjP0cVPmo49bthIo7UVERNDaqHL0U3jEPgBQhaIel/xoQmnyoz8+2m3t3bu3/osnBnV1dUqrPT4+Pjs7u6qqCiMzC9bcuXNpo065XGnsoyREt0FBQXovl1rY7gSVXzaVUoCjcJOSktJWuElPT6fbjz/+WPZZFInozZ46dUrHRdYTzWomLy+PbtmuGmf8+PG0HnoiYh8ACAVljvPnz6tOflOmTGF/aqB1gwYNKi4uljuHoaioiI3MbGNjw1fB4KnYRp0Sz+LFi+Wa9LKysh4+fOjp6SnY454spckdgKbSDhky5NKlS7S/obTkqampEukBTdmZXbp00WVJ9U2zmnFycjp58qTc+VrsLj1Rl+X9D4h9APB0dnZ2rM3P1dW1rKzM3NxcboGLFy+eOXPmzTff5KV4RqyysvL+/fu0EZWNffX19S4uLiEhIRiZWeAo6k2fPp1i3+HDh+XO8GOtYoGBgTwV7elu3LjRtWtXxQPQbM69e/dUBFa5Z50+fZpuR44cqYNi8kCzmgkKCqJvQmRkpIWFhbe3N80pLS1duHAhTaxYsUL3pf43xD4AUAslvytXrgwaNMjBwUEx+f3666/BwcE3b97kq3jGil0l79q1a9wZ3y0tLWxk5m3btvFaNFALpT3a2Mt17GCdOfr27SvYDrysuU5p93APDw8q/OPHj9VcFYUbyjqUk+bMmaPNIvJE45qhLJiTkxMVFSX7TRgyZEhmZqbScwB0BLEPANRFyYNdw0Np8qurq0ODn3Y1NjbeuHGDJsrLy7mZs2fPLikpoW0PRmY2CPSrYcf+ZDt2sM4cU6dO5bVoqlRUVKhe4IcffmBNVqpR5ps0aRJN7N+/X7CHs9ulIzVDnzvlQk9PTwqIkt978i5fvnz9+vXoyQsAQkR/WCz5jR49miZMTf/vP+TXX3+dOXMmBRTEEW1JSUmprq6WSHsOsjkYmdkQzZkzZ+7cubIdO1hnjnHjxvFaLlXs7e3beujRo0d0+/LLLz91JVlZWWxoIX0OUKJrGtfM5s2bk5KS5HryBgQE+Pv7L1y4UPWYOFqkYewzglEoNRuCkj42bqBF2oGjehDmu+sgzSpHIt04hYeH37hxIzo6uq3eTGDoKPnRBoz+rdjV22ST3+3bt7dt20ZbOB6LZ0wWL17MJlgDQ01NDUZmNkQjRozo2rUr17HjxIkTDx8+fPvtt4Xc+sX+8GkjrvhQSUkJ3T7//POq18BGtqMNJW1NhPxO20vjmvnkk08kMj9qhvYEWGNwaWmpfpKxhrHP0Eeh1GwIyrFjx9JnQzEoLCxMIt1do81bQUGBcQxExNGscugTp3qghfVWTuAR7Z4mJyeHhIRQ8pMdlOHXX39dtmzZ7Nmz0eDXcefPn+dGZqFNQlNTE20VPDw8IiIi+C0YtBfr2EH/q6xjx9///nea+d577/Fdrqdggw7+/PPPcvv87MSD7t27q3guG6iPoi1tF4Q5KmFHaFYzlPUlCp1duDkNDQ26KKoiDWOfQY9CqdlAi1988QVlPtkhKGnbFhwcTN/sP/3pT+qc4mAQNKsc4uPjQ99pNvI4xUT9lRh4wroaUPKjX4Hs/Lq6usTExI8++oinchmPjz/++P79+2ya8t/48eNp4sSJEyYmJtwyjY2Nv/32Gw74Cl9QUBD9tdLmgz5H+jul/1h9nsWvmZEjR9JW/vTp07IHtWgPn2bSplBFA97q1atpyyh3NNOYaFwzEmmPELlcJDfYja5pfm6f4Y5CqdlAi2wsohUrVnDPogm66+/vT7tuRhP7NKscibRbE/3C6etO6VAfBQUBoORHf3OKKX/jxo30/6A4yAuoj3b9aSvC3W1qajp+/PiqVau+/fZbNqxrVlbWr7/+ShPOzs4XL15E86rA0X+jp6fnyZMnWZuIQZwIwcZYjo+PHzFiBNsiUEChzQF7qK1nsbYDerPGmvkkmtYMG8pnzZo1sjVD1cWOIuptN0Dz2Ge4o1BqNtAiO9FN7oNhd/U5vrauaVY5kt9jMRil1tZWGxubW7duqbl8dXX1xx9/vGnTJp2Wyrh99tlnsrGPEl6XLl2WLFkiu0zv3r0DAgIoZMu2/4FgBQYGUuxjJ3ixtluBo3/76Oho2q974403/P392Tk/tKdH8UW2latnz550e+fOHXY3PDxc8vv1ZxXXSSs0gr4dmtUMJcLMzExKTfTTlu3JSxMxMTF6K7zmsc9wR6HsyBCUbVGRhwyLLioHDB2liqKiIkoYv/322/nz59V5yp49e9atW4cGP820tLQkJCTIzWSdBDn29vb09+vu7q7HckGHUCCIj49n4UCApz8pNW/evJdffpl+yyyd0P7/U7vrsfPbWEOJIhYKjYAGNUNbz2+//TYtLe3QoUPsIEnfvn3py0AJSp9RuEMDuBjiKJQaD7SoOPCSROaQvHHkIS2OzwlGxsrK6syZMxT+6MdO3xNu/7UtP/3005///OcDBw7op3hG5uLFi01NTW092rlzZ/o7OnHiBFK1waGtPt9FaDdvKRULyP0bPPXPwWi0t2Yk0gaUeVK6LNdTdCj2GeIolBoPtDhhwgR6p8uXL+e6dJA1a9Zov4j80db4nGCsaJfg+++/379/P+3X3r59W3XXM8ouNTU1cleSBXXMmTOH68whx8bGZv78+XJjQAAAqKmjwzUb3CiUGg+0GBQUxEbso7f29ttvS6Sn9HXt2pUFXwsLCx0VWJ+0Mj4nGDcTE5PJkyfTTyAqKurYsWOXL19ua8nq6upJkyYZYvMGv+rr6x88eKD0ocGDB//9738fOHCgnosEAEajo7HP4Eah1HigRXpiamrqtm3b6M1yw9qxMVwk0oZPHRZaXzo+PieIhJmZ2fr16+vq6qZMmXLv3r22wl9ZWdmtW7d69+6t5+IZtJiYGNnOHMwf//jHkSNH7tmzhxvJDwBAAx2NfYY4CqXGQ1DS8pFS3BxaCet6rauy6l1HxucEsbGysvr6668LCgpCQkJqamp++uknuQXq6+s9PT0rKyt5KZ4hamlp2bt3r9xM2ov+61//OmPGDD5KBABGRQvX5DW4USg1G2ixtLSUNmx2dnayC9BK6JYd8zUOHRmFEsTJzc2tpKRk165da9as+eGHH+Qeffz48fnz54cNG8ZL2QzOt99+q9hjl2ZSwuarSABgTLQQ+wxuFErNBlq8ePFiREQEJTxuiD4KgpGRkV27dhXmqNSa0axyQOQ6der03nvv0Q+BviTfffedbPi7f/9+YGDgtWvXeCyeAQkJCeFiX48ePWg3jPaoMRQzAGiLFmKfxNBGodRsoEV6X/T/S0tWVVVNmDDh5s2bmZmZDx8+3LJlizG1gWlWOZSAuUs1sMPBKSkpeXl5bI5xjM8JT2Vubk77DDU1NfRjuXXrFtcXlX4shw4dol+NTl+9vr6emy4uLuams7KyNF5n9+7d3dzc2DT9Fvr168emTU1NddGLi6ru3r17bJp+ifSPqutKAwCx0U7sM7hRKDUYaJF16VizZs2pU6dYxHn77bffe+89gR/R1oAGldPQ0CDXEeSGFJs2mvE5QR3W1tYXL16k0D916lQKMb/++mtzc/OMGTNqa2s70mrFUl1dXR27WAgLc+Xl5dnZ2VoquIZCQkIoAnIB8aWXXurSpQtNaHCd3MWLF9PbpFqiH+C5c+eMY3wAABAU7cQ+iQGOQqnZQItGfJFBWe2tHMq+4hmiE9Th4eFx7dq1VatWbdmyhb4bP/3000cffZSYmPjUJ1JGpL0Iesr9+/dPnDhx9+7d5ORk3ZdXc6qLR/s8LBH27t3bysqqa9eubV1IjfIxO55LEZnWieutAYAuaC32AQDIogQTHR1NuWf06NH5+fkbN25csGCB3BkRFPLq6+svX75cUFBQXFzMruuoAdbkxqZ9fHyeeeYZNj148GBT0w79yz169Ig7MbGmpubcuXNsWs2GRqVJl+rkpZdeeuWVV5ydnbt06cIaQf39/VtaWijwzZo1qyMFBgBQAbEPAHSI0ti33367f//+yZMnjxgx4tKlS3fu3KHMdOrUqV27dsmekKeCk5PTqFGjJL9HOu40OxWNZ9piaWlpY2PD3VXsv8WaJ2ni6tWrv/76K70jemt0NyMjQ3H4PUYuC1IUDggI6N69+8qVKwV7KXMAMA6IfQCgW3V1dS+88MLEiRMPHDjw1HN/PTw8XF1dR44cSXlr8ODBzz77rMBPcTM1NWWn8XGdP/z9/ek2ISFBIj0lsbGx8Ycffvjxxx8vX76sNAvSHC4ILlu2jNb2wQcfjBs3jt6+wN87ABgcxD4A0D6KehcvXty3b5/qU99YM56fn99LL73UrVs3c3NzvZVQPyylrK2tPT09JTJZkOqHgmBOTo5iEKRHY6XY3fDwcKofZ2dnDfqIAADIQewDAO1obGy8dOnS3/72NxVRLyQkhKLesGHDBg4cqIdDtMLEsqCdnd2YMWMoCKo+wTFRij2LDR06YMCADp6wCACihf8OANBca2vrzZs3jx8/npSUxC7crAjtVapRhrOysvKUortpaWkPHjxQbCulaBglJZEeCp83bx4tb21tzVexAcAQIfYBQLtR2isrK9u+fXtbY7JER0fj7DTNmJiYUAocI0U1TGmvuLj4yy+/lI2AeVJsOi4ubvLkyXZ2djyVFwAMCWIfALRDZWXlvn37WJuTHDRB6YKlpSVrCPzss8+UNqyyJkBabOXKlX5+frL9jgEA5CD2AcDT1dTUUNpbtmyZ4pAr0dHREydOHDRokJmZGR9FEwsTExOKdLOkFE+jpM8lTMrW1nbp0qWTJk3CIXUAUITYBwBtam1tLS4upjDBHVLkhIeHz58/v3///uLslsEvc3NzN6lt27ZdvXp15cqVXEeQqqqqEClfX9+NGzfi4K+2CLMNW5il4hEq5KkQ+wBAiaampv3798+bN0+ueS8wMDAiImLIkCEducAuaAt9Co6Ojnv27ElJSaFovnbtWu7aIdlStra2FA29vb3R+RcAJIh9ACCHct769eu5ceMYJyenjRs3vvHGGziSK0yU6tgpgI2NjZmZmVFRUWw4QLr18fGhiaSkpJCQEOMbGREA2gWxDwD+jQLfihUr5DrnUlZYunQpOgoYCgp2QVKlpaWLFi3iGv/YmX9xcXEffvghwh+AaCH2AcC/RlreuHGjbP9cS0vLdevWBQcHIyIYKEdHxyNHjtTV1SUnJ3OfLOv2S3OmT5+Ow74AIoSfPYCoNTU1bdiwQTbw2dra7tq1a8SIETh7zwhYWVlFRkZ+/PHHhw8fnjlzJjtTk/X5SE1NDQwMxKcMICqIfQDiVVBQMHbsWK7ThqWl5c6dO/38/NA518iYmpr6+/u//fbb9PlS4GMzg4ODKe5//fXX6O0LIB6IfQBi1NDQEBgYyJ34xQIfxQK0/Rgx+nBnzZo1ffr03bt3s/BXVVVlb29P05s2bUJnHQAxQOwDEJfW1tY9e/YEBwdzc6Kjo1esWIHAJxKmpqYU/qZNmzZ//nw22jPd7tu3j74VY8aM4bt0AKBb/4p9whzeUJil4hEqBDquqakpICCAa+RzcnI6dOgQeumKkJmZ2fbt2+fNm0ffh6qqqvr6eh8fn5CQkG3btmEHAMCIobUPQCxqamrc3d3ZcG4SaRvPe++9h9P4tKu1tfXUqVM04enpyc2srKy8devW66+/rrdu0UVFRQ8fPvTw8FDdXXfo0KHXrl1bvnw5G6aRvhLnzp07e/ashYWFfsoJAHqG2AcgCidPnvTy8mLTtra2xcXFstdsraury8rKunz5MjdoX2BgoLOzc0hIiJWVld4LqxMFBQXcFcwSEhI0Xka1f/7zn6yeKf9xMzdt2kQVW1FRobfOE+x6ej///PNTr8zbqVOnmJiY999/f8iQIfX19SUlJX369KHk5+joqJeSAoBeIfYBGL/Vq1dzQ7RQnktJSeEagSid7Nixg+vdSXx9fbOzs9Ol6Fl0d9++fUYwet+VK1e4ULtgwQKlh7Znz55NuYdNaxb7DBTVxp07d0aPHk1hkcLfoEGDUlNTg4KC+C4XAGgZYh+Akfvkk0+4zBcXFxcZGck9RJlvxIgRtKWn6YyMjD/96U/c0b2Ghobq6mqKQRQBb9++bTRjfNja2lZVVW3fvj0mJkbuobq6Osp8bAFeysYvSvanT5/+y1/+wvp5BAcH//GPf0QnDwAjg9gHYMzS0tLCwsLYdE5OjtxWPCsrizKfpaVlRUWF3MFcyn+Ojo5nzpwpKCjQX3F1b+HChevXr//0008VOy9TXUmkyVi2m7OomJiYUCB2c3Njrb8+Pj75+fl0l+9yAYDWIPYBGK2TJ09yCSYjI0Mu8zU2NgYEBNDEN998o+IEPrmtvmyXBZp+8ODB5cuXKT7+7//+L7eSmpqaH374gW7r6upeeeUVZ2dnxTPMFNdz8eLFn376ie7KdlqnQl69erWwsLB///5tdVBoaGigMjx8+JAirLe390svvaSib3Lnzp1ZsLt06dLQoUNly7Ns2TJbW9u33nqrredyb42iMFXLyy+/rEH/evaOjh49Smtoq6jNzc03bty4desWvdDAgQN79Ojh6uqqonMGleq7776jCRcXl549e6pekn00T548oSql1Sr23pg1a1ZtbS1rIXZ3d9fnKYkAoGuIfQDGqbKykuvDkZyc7O/vL7dAZmYm3VKWkk0/T8V1WWhpaQkKCuI6QMyfP59iH2UaylWKz1IcGrCt9bAinTlzhpWQBVOGsmNpaalc0urbt6/sMVnWI5XWcOjQobZ6M0yYMIFuN2/evH37dm7mjz/+WF9fv27durYyU1NT07vvvitbTon0PEjK0+oPdEwfir29veycpKSk0NBQ2Tly75qj2FgrkdYeRVjZUlFyLS8vV3y6+h8NiYyM/OWXX1hlUoEfP36Mvr0AxgGxD8AIURr405/+xKZpuz5r1izFZc6dO0e3M2bM0OwlKKuVlZUVFhb269ePIgXLWL/99puTk9PGjRudnZ3ZYo8ePfrzn/9MAeK5556TPa1Qdj2UKthRZlrPO++8k5eXl5aWNnDgwJkzZ+bn59MELbZ169aoqCgfH59Lly7JPv3hw4cUaidNmsTuNjc3/7//9/8SExNHjhxZXFysdHgaSjAU1+hZspemoGm65dYjh+qze/fulAsDAwMTEhLMzc2pqAsWLKC8NWDAgGvXrqkz1h3rz5uamjp27Fi6e/XqVXd397CwsMmTJ8tm2QcPHoSEhCxdurRLly5sznfffTdlyhR67xRw5VoH6W1SdVHM3bt3b7du3Wpra6lU3t7eN2/elHt1+mhosbVr17L6lEjPZaQabuujiYmJoQ+FBUp610eOHHnqGwQA4UPsAzBCy5cvZ21gtMFW7LvAfPPNN3Tbv39/zV6CMt/FixdZ2xjXrta1a1e5WEYPnTp1aujQoRTaPvzwQ6U9grlIQQsfO3asc+fO7Ni0bCMT5RLKgiUlJaWlpbJji/z0009y2Y5iGUU0ejlaVVs9EihUZWdnf/vtt2x0PQqLFMgoFVEBuCsUyzp48CDNp7BIZWAvR0vu2bOHJigY0aOKjamK6CVkc5ubm1tGRkZAQMCyZctk2x3fe+89uZhO74Ledc+ePSdMmCBbvUVFRZT5KGefPn2alYriI5WKMiLrpiOLCszaUGXn0Efz0ksvtfXRUEKlT5nqnOrq6NGj6N4BYAQQ+wCMDUUEdniOXWlX6TKtra1spJLevXvLPUQZSC400DKKZ3ft2rVL8Xio0ta1Tp06rVixgvLN1atXFQ8or1mzRvYuhQ/KMVS26OhouQOLlPwoDt68eVM29il9xZCQEIoy9C7aSiqurq4SafhjSYi937byMZk5cybdrl27VjFiUuyjR9WJfVQqubY6ypGS35tdVb8jynOsWujT4aqdddahD0LuKVSlcgej20IfzcKFC2k9169fVxyojx49dOiQra2tRNq9A4d6AYwAYh+AsRk+fDibyMjI0GC8vYaGBu6kQCY8PFxxELtBgwapWEl9fT2FvF9//ZXdZb03qqqqFGNft27d5Oa89tprlG+8vb3l5rMjobdu3VJa5urq6vv373OvTreFhYVtFY+SE72pxMREWpLCMeU5mvnGG28oXbilpYWt0MHBQWmR6NHGxsanVvW4cePk5rBDw9xIgbIo3tXW1v7www/cHHbMl16L6zrD0uorr7wi99w+ffq0VQaK+w8fPiwuLubmXLt2jW7lwjSHcmpSUhLLlxRbWQMnABguxD4Ao1JaWsoySmBgoOz1weSYmJiw1iNKUXIteRYWFrm5uWw6KyuLG+JYTlv9GE6ePDljxgylQ989ePBAcaZiWmJNSorNkErV1dUFBAQoHtOUSE8rVPHE+fPn01v76quvJkyYkJ2dTZmmrXf0008/SaRNp0rb4Vg1UkR76qWNBwwYoHoBhpLZp59+yg27I4eLfU1NTWyO0jZXpUerjx49Onv2bKUfjdIwzVBFJScn03tMT0+nCTT4ARg0xD4Ao7Jy5Uo2wY7zqjBq1Cjalv/4449y6ZBihOyctmKfUkVFRV5eXpQ5MjIy2Eq6dOnSqVMn2UvDaVFDQ4O9vT3lm6SkpMmTJ1OCfOaZZ+i2ubn5D3/4g+rnUtilckZFRT158kQivW5HW0v+4x//kEjbvZQ+yhrhuBCmgpodfj/66CN2ouG2bdt69uwp+f3USSqh7Geh+hWptHKxr6CgwMfHx9bWNicn5/XXX5eo/dHQMhs3bmTLUPJT2j0IAAwFYh+A8WhsbGQnddHW/aljrb322msS6ZlhWtyQs5FHFIdZUdpPouMOHTpEa6aIKXdqnZovt27duhApylVc/1ZFLHUpPRRLLl++TLc9evRQt9AqUZClbCfbS4Nz4cIF2bvPPfccm2hpaVHsR6xY2ilTprDSyjXXUe5/aqlGjBjBJj7++OP33ntPaasnABgExD4A48GG4pOo10THolJeXl5RUVG7hu5rS3NzMzuAqDiI8cWLFzu+fkVZWVkS6Sh9cvMrKyvVefqkSZPY5SgiIiJUjMDCHYamTCaXmShns4ipdEg8DVRUVEikg9rIRSvKdnIHsmkBdh25e/fuyVU4lVNuteyjoeUVD9EeOHDgqaWiyomLi4uKiqI3SzERozcDGC7EPgDjwZ22xY7iqUZphg0gMmrUKMWLs2ngv/7rv9iEXDyibPTUI86aef755yXSFiy549SzZ89W5+mWlpY///yz5PezCVVgoefTTz+VG99u48aNEmlfB3XG7VPHM888I5FeJk7uhQ4ePKi4MIV7+vh2794tt7BiN1720dDXQ67rSU1NTXZ2tjoFGzNmDLtuB2IfgEFD7AMwHlwPzbYuUCHHz8/Pw8MjLy+vW7du7Gw82SdWV1dv3bpV/Vc3MTFha5ONRxQBhw8f3tZ4eB00bty45OTkDz/8sKioiAWvlpYWynxUcjXXoGZF0UtESbm5uXER8+TJkywJJSUlaVB4pfr16yeRHqKtrKzk0hW9EMU7xTp8++232emJAwcO5A5zU1WwJkxZ3EdDOZX7aGht7u7uan403FHs8vJyDOAHYLgQ+wCMR1lZGZt49tln1Vme0sDp06d37NhBQUHpBcEk0h7B//u//6tmAb788ktbW1sKIkeOHHF1df3mm2/YCHyUOXx8fNRcifoo99DL0Uu89NJLVH5KJNnZ2fRabHBjLb6Qubl5YWGhi4sL67AyY8aMXbt2sbSUn5+vwSg5Kl6IDZhib29PH4qFhQU7Xk+v/vnnn8sdu6eke/78eVqSfXbh4eGsVLm5uUuXLpU7KCz30VDKr6qqUv+j4fJxW+c4AoBBQOwDMB5sk0xbd/VPuqclZ82a5efnl5WVdfnyZS5YUObo0aPHvHnz5M4bo6hB8aKttdnY2NTW1lK2SE5OpthBkXHNmjVjxoyprKykZ8kO9adiPSNHjpQoa4fr3bu34koo6m3bto1yEpWcXXJt+vTpbOWUBWWfTk+Ue7pSzzzzjNKCDR069PHjxxSnKDDRa1ElU/hbvny5XDmVvq+23pHShUNDQ1955ZUPP/yQ3gs9hZIZ+xTYEXy5ldjZ2VGFs+vREVrb/PnzaeY777xD2Y4dMmbYR0OVQ8mYPhr6fCdPnqz0o1GK25G4evWq6iUBQMgQ+wCMBztg9/Dhw/Y+0crKivXnVRyWWQ4lFdXL0Kq2S8nOpCAi9ywV6/GXUpyvuBKJdFSUUCm5+YpLukmpKDljbm7eVsEsLCwSpFQ8Xen7ausdtVUJnp6ecte4U7ESqnDFUilWCFtS8dK6SmtV0T//+U82wV0pGAAMEWIfgPEYPHhwXl4eJT+lg3oAaIzrHezi4sJvSQCgIxD7AIyHq6srO6PryZMnuJoCaFFdXR2bUHoNNwAwFIh9AMZj8ODBbOLu3bsYZQO0iBvVmfU1BgADhdgHYDy4A3CbNm1S54QtADVxIy9yuxYAYIgQ+wCMh7OzM+vVkZiYGB8fr+ZFYAFUq6urYycPBAYG4uQBAIOG2AdgPExMTNh1Zmk6OztbacdPgPZKTk5mExEREfyWBAA6CLEPwKgEBgay2Ddz5kxfX180+EEH1dXVsYuRWFpaOjs7810cAOgQxD4Ao2JhYUGxLzk5ub6+fv78+XLj5wG0S2trq7e3N5veuXOn+sOAA4AwIfYBGJtNmzbt27ePYh+Fv1mzZqkzRjGAUjt27GCXfvHw8MA5AwBGALEPwNiYmZmdPXuWXW5r7Nixd+7c0eJFY0E8ampq2AkD5NChQ/wWBgC0ArEPwAg5OjqGh4cnJibW19c7ODiUlZUh+UG71NXVcSMzp6amKl5QGAAMEWIfgHFau3bthQsX8vLyqqqq3NzcLl68aGqK3zuopbGx0d7envYZJNJOQkFBQXyXCAC0A5sBAONEIe/YsWMODg4U+0pKSry8vHJzc5H84Kko89HXhmU+Dw+PlJQUvksEAFqDbQCA0TI3N798+XKfPn1oE56Xl+fn55eRkYEhXUCFhoaG4cOH064CTdva2mJXAcDI4PcMYMwsLCwqKirYAbvs7OwBAwbk5+dbW1vzXS4QotLSUsp8rJ2PMl9ZWRkyH4CRwU8awMhZWVnR5tzd3b1KqmfPnrm5uZ6ennyXC4QlLS0tODiYTTs5ORUUFKAbEIDxQewDMH7W1tbl5eUBAQHZ2dl018vLKzo6esWKFZ06deK7aMC/pqam+fPnc1dgCwkJ2bZtG74bAEYJsQ9AFMzMzA4fPhwfH88utBUbG/vFF19QCuQG6QBxKigoGDt2LDuwK5GO1YJ+uwBGDLEPQCxMTEwiIyPd3Ny8vLzoblVV1aBBg0JCQjZt2oR+HiLU0NAQGBjIGoAl0kvunj17FrsBAMYNsQ9AXDw9PX/77TfuoF6yVE5OzujRo3HFVZFoaWnZuXMndwUOgoP+ACKB2AcgOmZmZtu3b1+wYIGvry8bqsPHx8fW1nbXrl0jR45E+DNiFPgOHjw4c+ZM7qiuk5MThX507gYQCcQ+AJFydHS8du3apk2bwsLCJNJjvl5eXhT+MjIyhg4dynfpQMtaW1uPHTs2ZcoULvAR+qz9/PwQ9AHEA7EPQLw6deoUGho6bdq0FStWJCYmSqThz8XFxcnJaePGjSNGjMBRPyPQ3Nx8+PDh8PBw1rLLxMXFffjhhxiiBUBsEPsAxM7S0jIhIWH58uVz5sxJT0+nOexibhLpmX+BgYEWFhZ8lxE0UVdXR58g67vNofy3atUqBD4AcULsA4B/ofC3Z88eyn8LFixg4U8iHcKNiYiIsLOz47eEoL7S0tJFixZxvXQZCnwU7umD5qlQAMA/xD4A+D/W1tYU/j799NONGzfGxsaymay3r5OTU2Rk5NixY5EbBKumpoaiXkxMjOzxXJKUlDRz5ky02gIAYh8AyLOysqLosHz5ctlzwkpKStjFuzw8PBYuXOjr64vR/gSioaHh0KFDq1evps9Idj7O0QQAOYh9AKCcqampv1RlZeWHH37IHTHMk6IJSn5Lly51cXFB/uNFY2Pj6dOnY2Nj2cchKyQkhD4aGxsbXgoGAIKF2AcAT2FnZ3fkyJGmpqbc3FzZkJEtJZG2/82bN8/T0xPDv+laa2vrzZs3jx8/npSUJNe2J/k9iLu6ulJk56V4ACBw+GsAALWYmZmNkaqvr//qq6+ioqK4E8i49j+J9HoPEydOtLe3x5lkWkR1fvXq1b/97W/s2ipynJycVqxYQR8N+ucCgGqIfQDQPpaWlkFS1dXVZ8+e3bx5s+xBxlgpttiMGTP8/PwGDx5sZWXFX3kNUmtr6927d0tKSnJyctiQiop8fX3ff/99T09PdLIBADUh9gGAhmykKP81NTVduXLlwIEDXOdfibSBKlGK3Q0MDJwyZYqLi0vPnj1xCFIpqkZK0ufPn09JSZEbe4VDCS8iIuLtt98eMGAAqhEA2gv/GgDQUWZmZkOlYmJiampqTp48qRhc0qXYNGsI9PHx6d+/f69evUR7aLKhoYFyXnl5+alTp9pq0mNYaPbw8EC7KQB0BGIfAGiTtbU1OwTMDlN+9913R44ckTsjTa4hUCLteTpu3DiKg4MHD3722WeN8rxAeteNjY0//PDDjz/+ePz4cS4EtyU8PByHyAFAuxD7AEAnTExMKAKyIWC2b99Ooae4uDgrK+ubb75R7ILKRoSWnePk5DRq1KjXXnuNVkLRx9TUlLKgQRzWbGpqevLkCZfwLl++nJGRITd+slIeHh6enp4UfwcOHIjT9QBAFwzgPxQAjADlGE8pmm5paXn06BGlwIKCgjNnzig9j61ESumqwsPD6fall1565ZVXaIKFQu5VdFL637GSs2mauHbtGk3Qu7h3715NTc1TG/DkBAYGDh8+fNiwYZTzunbtSkFZ+yUGAJCB2AcA+tapUycuBUZGRkqkB0Dv3Llz//79EydO3L17V+kwJRzVp8FxQkJC2jpY7OfnJzeHCnDq1CmlC5eXl7fVwaJdKK12797dzc2td+/ePXr0MMoD2QAgcIh9AMA/SylHR0fWHLh9+3bWrlZXV3fr1i3WnNbQ0KA6DspRsbCawVEzso2RdNulSxccsQUAgUDsAwAhYi2CxM7OjmVBiTQOSn4/eY4miouL2fysrCzuibqLdLa2tgEBAWzawsLC29ubJp599tmBAwfSBMU7XPoWAAQOsQ8ADIyZFE1wcZCbIAkJCdx0fX19B1/rmWeeEe34MgBgfBD7AMBo4egqAIAsxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AvTp8+DDfRRCu8ePHo37agspRDfWjAlUO30UAoUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAxCRLVu2ZGdnK85ftGjRiBEj9F8eYbp79+77778vO8ew6kfpp+zi4rJixQrZOaWlpRERETNmzJg0aRI3c8KECbLL+Pr6zp07V27NcjOZ06dPr127VvFV1C8hKyTdFhYWHjp06Kkr0YzAK2f58uVtvX22/kGDBl25ckV39QNGD7EPQHTkthlsm1RbWyu7hROt/fv379q1S3Z7zxJASkrKZ599xm/Z2kXuU6bI8pe//EX2LdCbko2zim+cxV+KGnKrojmKyebEiRMdLCFnuZQ68VFjgq0cb29vin30k1TczaA1s+Coh/oBI4bYByB2tIG5cuUKbdUQ+2hzS/Ug17bn6OgYHx9POYC2/YZbRewtcHliy5Yt1tbW3NtU+sZ79Oixfft2Cje0MBdlKHnU1NTI5RLKQBRWWFtdx9Fr0YsqjT46IpzKoSfSDgbFRLn3Tuuk28DAQAkf9QPGBLEPACQvvvgi30UQBNrcym7vOZT8DP2w2h//+Ee6ra2tlUiDSHZ2NuUY7tG23jiFG8U3PnToULlccvbsWXo6LUxr7nhRaT0Ukij96C3WCKpyxowZQymTFqanyJWBvocSPuoHjAliHwBISkpKaKPCdyn4V1hY6Ovry3cpdOKnn36i227dukmkQUQibVjiHlX/jdfU1AQGBkZERMjmkqNHj1JYuX//PrureHIkZ/v27bJppi3e3t5r166Viz66I6jKGT58OMU+KobsAWUqw4wZM7gl9Vw/YEwQ+wDE7vTp03IbFXFijTHG2vBJWYRrsqKUL3vMsb1v3NHRkVbF5ZLS0lKKOxRWMjIy2AJKm8HaZcCAAXRbXl6un1gjqMphjXkUFrnYx5IorYRbRs/1A8YEsQ9AdOQ6JEqk5zax40dgNOQ+ZdlupBREhg4d2q6nyyWVMWPGcLnk1KlTtHIN8ofi95DrM8HWxo666oLAK4c15lFkZL9KWpvcSnRdP2DEEPsAREd2K0UbMF9fX2Q+ye+bUu5gnKFTv71N6Rvnns46sco9hR2IZLlE7kw4bZXQ2tpad5+FwCuHdeygyEhrYO2F4eHhcsvotH7AiCH2AYgabZPWrl07cuRIJD+JtNWnqKiI71LwoL1vnB2IpFxSV1cn+c8z4STaOLdPUHipHNaxY+7cubQerjMHQMch9gGIGmtXSExMNKxB6XSEnY+vdKAW1iyqOCSbcVDxxtvCDkRKpKMWyz3U8XP7JNKDrRR9OrgSreClcliT4enTpylxKq0H4dQPGBbEPgCxCw8PN/RB6bTF0dFxxowZtLm9f/8+l/BY84y1tbXRZD56L3KDiSh94+Qvf/kLxQul3X1oh4GSTXZ2dnx8vNZLyIrHutbqmUAqhxulhfUIkXuUx/oBQ4fYByB2tFXz9fWlrRptRTAS2CSpCRMmyF7Cy7AuzvZUTk5OimeksTdOUUa2vwJ9MVQ0A9OjRUVFujj+WF5eLvm9v6qeCadyWJOh0h4hPNYPGDrEPgARmSul/nzRMujBmZ/6aXIHEBWzrOpj/XKrVX23IyW8cuWKZr2DO/7SvFcOZ4SU0od0Vz9g9BD7AADEheKCr6+vYC/zoHidDH0SeOVI+K4fMHSIfQAAojN37twJEyYI87quW7ZscXFx4bFgQq4ciQDqBwwaYh8AgBjFx8dHRETU1tYKqivP8uXLCwsLeT/ILszKkQimfsBwIfYBAIiRo6OjANMDd7UMfgmzciSCqR8wXIh9AAAAAKKA2AcAAAAgCoh9AAAAAKKA2AcAAAAgCoh9AAAAAKKA2AcAAAAgCoh9AAAAAKKA2AcAAAAgCoh9AAAAAKKA2AcAAAAgCoh9AHo1fvx4vosgaKgfFVA5qqF+AJ4KsQ9Ary5evMh3EYTr1VdfRf20BZWjGupHBaocvosAQoHYBwAAACAKiH0AAAAAooDYBwAAACAKiH0AAAAAooDYBwAAACAKiH0AAAAAooDYByAuq1ev3rdvn+J8d3f3Tz75RP/lERRUjjo+//zzpKQk1IlSx44dW7JkCZtGFYEAIfYBiNGFCxf4LoJwoXLaUlxcHBISQhO9e/fmuyxCxDJfcnKys7Mz3fX39w8NDUXyA0FB7AMAALXcv38/LCzs3XffpTTDd1mEaPPmzZMnT2aZj/z1r3+llExZmZsDwDvEPgAAUMvo0aP5LoJw3b59+9atWy4uLtwcSnu9e/cuKSlB7APhQOwDAADoqNraWrp98cUXZWf26dPn/Pnz7777Lk+FApCH2AcAANBR9+/fp9tu3brxXRAAVRD7AMTI1dVVbg47Z4uXwggNKgcAjBViH4AYobOqCqgc0AA7vFtbW9urVy9u5s2bN/v06cNfoQDkIfYBAAB0FDu8yw71cm7dujVx4kSeSgSgBGIfAABAR/Xq1at3796FhYVcf+fi4mK6dXJy4rNYAP8JsQ8AAEAL2EB9Pj4+bMQWuuvu7o7RW0BQEPsAAEAtoaGh+fn53F3W92Xy5MmRkZH8FUpAKOElJyezC5lIUDMgSIh9AOISKcV3KQQKlaMarjP2VJT80CUIhAyxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsA9OrVV1/luwiChvpRAZWjGuoH4KkQ+wD0qqamhu8iCJe1tTXqpy2oHNVQPypQ5fBdBBAKxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AEQkODj558uSdO3cUH4qKitq9e3d+fr6tra3+CyYQrBIU53t6eqampuq/PPzKysqaO3cum35qDWzevDk2NlZUFaV+/bDKYdPTp0+Pi4vTR/kAlEHsAxCRwMBAin20ufLz85N7iOIObbrEnPk4SmOx2LBMk5mZ+dprr9HdN954g/YZlCabc+fO+fv700Tfvn31W0Y+qV8/LPNxS/bs2ZNukfyAL4h9ACJCaS8+Pj49PV0u9tE2jG7Dw8P5KRYID31Ppk+fzpIKSUxMpGxHCY+bw6mpqYmOjp43bx7lHr0Xkzfq1w9lPqofbv6WLVsoL86ZMwe7WMALxD4AcZk6dSpth6qqqmS3OhQE+/btq7jFAnGir8eNGzciIiK4OfTdoG/IhQsXFL8kii3HRk/9+qEl6bZXr17cHGdnZ7o9cuQIBWU9FRdABmIfgLiMGzeOYp/sVoe2TCdPnoyOjua3YCAc9+7dkyhc0YtiTV5eHsKKpGP1w3a3bt68qbviAaiA2AcgLrTV8fT0TElJ4bZPFAEl0jjIa7lAQNjFbbt37853QQRK/fphIe/27dvcnHPnzumuYABPhdgHIDqBgYFz587lzkOiCIjOHLLYSfey2LlrvBQGDB19eWJjY11dXdnPDWfQAr8Q+wBEh3XsyMjIoO0Qhb8bN24kJibyXSgBQU9edvjy3r17sjsD9D0RVV9dFdpVP7TDcPPmTdbZmWRmZlLy69Onjz4KCqAAsQ9AjFjHjri4OAp/6MwBctjhS3Yok0Oxhr42PJVIWNpbP3FSskvKdvIA0CfEPgAxYh07srKyTp06hW05yLG1taWdgYKCAq6XLjsjzdXVlddyCUW76ueNN96gnxh3kgAbLEmE3Z9BIBD7AMSIdeyIj4+/ceMGOnOAIjYQXUBAAHdGGn1h2LTc+MPipH79jBw5ku7Sr4x+dFVVVXPnzkWveeARYh+ASLGOHejMAUpRZKHgwp2RpuKSYuyKf9xd1iHG6C9Bpn79sPnu7u7s7pYtW9DUBzxC7AMQKT8pvkshLHLnYIkcJRulvVvmSXF3xXMRXjlq1o8E3ysQEsQ+AAAAAFFA7AMAAAAQBcQ+AAAAAFFA7AMAAAAQBcQ+AAAAAFFA7AMAAAAQBcQ+AAAAAFFA7AMAAAAQBcQ+AAAAAFFA7AMAAAAQBcQ+AAAAAFFA7AMAAAAQBcQ+AAAAAFFA7AMAAAAQBcQ+AL2ytrbmuwiChvpRAZWjGuoH4KkQ+wD06uLFi3wXQbheffVV1E9bUDmqoX5UoMrhuwggFIh9AAAAAKKA2AcAAAAgCoh9AAAAAKKA2AcAAAAgCoh9AAAAAKKA2AcAAAAgCoh9AOKyevXqffv2Kc53d3f/5JNP9F8e4QgNDc3Pz79w4YLiQ6zSsrKyevXqpf+C8eXYsWNLlixh00/9enz++edJSUmi+hapXz+sctj05MmTIyMj9VE+AGUQ+wDESGm4EbkJEyZQ7KNt+ejRo+UeosxH23URZr7k5GRnZ2e66+/vT7FYabIpLi4OCQmhid69e+u5kDxSv35Y5uOWdHV1pVskP+ALYh8AwL9Q2tu8efOhQ4fkYh9t4Ol21qxZPJWLH1QVkydPZkmF/PWvf6VsRwmPm8O5f/9+WFjYu+++S7lHz4Xkkfr1Q5mP6oebv2rVKsqL06ZNE9VeBAgHYh8AwL9NnDiRNtK3b9+W3SRTEOzdu7fi5tyIUQ3cunXLxcWFm0NvnyqhpKREsR4UG0eNnvr1Q0vSbY8ePbg5gwYNotsTJ05QUNZTcQFkIPYBAPybt7c3xT7ZTTJttvPz88PCwvgtmJ7V1tbS7Ysvvig7s0+fPufPn0dYkXSsftgexZ07d3RXPAAVEPsAAP6NNsnu7u4HDhzgNt4UASXSOMhrufTt/v37dNutWze+CyJQ6tcPC3l3797l5hQXF+usXABPh9gHIEbsvHJZ7PQsXgojKBMmTFiyZAl3khZFQLF15gDtol9WUlKSk5MT+0b99a9/5blAIG6IfQBihJ68bWEdO3JycmgjTeHv1q1bItxOs8OXtbW1snn35s2bffr04a9QAtKu+qG9qTt37rDOziQ5OZm+UT179tRPUQHkIPYBAPwH1rEjMjKSwp/YOnMw7PAlO5TJoQRMNcNTiYSlvfUTKSW7pGwnDwB9QuwDAPgPrGPHsWPHCgoKxBl0evXqRXm3sLCQ66XLzkhzcnLis1iC0a768ff3p28RdwYFGw9IhN2fQSAQ+wAA/gPr2LF58+Zbt26JrTMHhw1E5+Pjw52RRnXCpuXGHxYn9evHzc2N7tIXib5Xt2/fXrJkidg6hoOgIPYBAMhjHTvE3JmDIgsFF+6MNBWXFGMXtePust5CRn8JMvXrh8338/Njd1etWoWmPuARYh+AuMidZgRKjZbiuxQ8o2SjtOvPu1LcXfFchFeOmvUjwY8OhASxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsAAAAARAGxDwAAAEAUEPsA9OrVV1/luwiChvpRAZWjGuoH4KkQ+wD0qqamhu8iCJe1tTXqpy2oHNVQPypQ5fBdBBAKxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAwAAABAFxD4AAAAAUUDsAxCR4ODgkydP3rlzR/GhqKio3bt35+fn29ra6r9gQoDKIVlZWXPnzmXTnp6eqampGi+5efPm2NhY1SsxLOpXDnvvbHr69OlxcXHqPwqgU4h9ACISGBhIyYa2Xn5+fnIPUayhLZnRxxoVUDks1mRmZr722mt094033qAorDTcqF7y3Llz/v7+NNG3b1+9FV7X1K8cluq4JXv27Em3XLZT/SiAriH2AYgIBZr4+Pj09HS5ZEObNLoNDw/np1jCgMqhtz99+nQWR0hiYiKlN8pw3Bw1l6ypqYmOjp43bx4FI32WX6fUrxxKdfT2uflbtmyhvDhnzhy226D6UQBdQ+wDEJepU6fShqeqqkp2M0NZp2/fvoobMLERc+XQu75x40ZERAQ3h94yvfELFy7IvfenLqnYXGro2lU5dNurVy9ujrOzM90eOXKEcrDqR3X6FgAYxD4AcRk3bhwlG9nNDG2KTp48GR0dzW/BhEDMlXPv3j2JwuUcKNnk5eXJJRL1lzQaHXnLbBfi5s2bGjwKoHWIfQDiQpsZT0/PlJQUbnNFKUciTTy8lksQxFw57Mpm3bt31+KSRkP9t8xi3O3bt7k5586dU/NRAD1A7AMQncDAwLlz53KnJVHKEUN/BTWhcqCDoqOjY2NjXV1d2VdI7qxQ1Y8C6BpiH4DosL4LGRkZtOGhfHPjxo3ExES+CyUUoq0cdgTz3r17shmX3r5ib1z1lzQa7XrL8+bNu3nzJuvLTDIzMynb9enTR51HAXQNsQ9AjFjfhbi4OMo3Yuiv0C7irBx2BJMdzeRQsqHa0HhJo9HetxwnJbukbDcO1Y8C6BRiH4AYsb4LWVlZp06dMuKttWbEWTm2traUcQsKCrh+uOy0M1dXV42XNBrtestvvPEGfW2400PZAEDcE1U/CqBriH0AYsT6LsTHx9+4cUMM/RXaRbSVw8aiCwgI4E47o3pg03KDDKtY0lipXzkjR46ku/TNoS9SVVXV3LlzZXuCq34UQNcQ+wBEivVdQH8FpcRZOZRaKLtwp52puG6Y6iXZZe64u+xCFIZ+FTL1K4fNd3d3Z3e3bNki25in+lEAXUPsAxApPym+SyFQoq0cCjdKr0o8T0qdJYnRXIRXjvqVI3f2nhzVjwLoFGIfAAAAgCgg9gEAAACIAmIfAAAAgCgg9gEAAACIAmIfAAAAgCgg9gEAAACIAmIfAAAAgCgg9gEAAACIAmIfAAAAgCgg9gEAAACIAmIfAAAAgCgg9gEAAACIAmIfAAAAgCgg9gEAAACIAmIfAAAAgCj8f/eSf1LPGhDPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./imagens/gramamolhada.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Na figura anterior temos que estar Nublado é causa Pai. Em dia limpo, a pessoa pode ou não ligar o regador, mas em dia nublado teremos uma maior chance do regador não ser acionado. O mesmo ocorre para chuva, em dia limpo temos menos chance de chuva do que em dia seco. Assim, a combinação de fatores possíveis para termos grama molhada vai depender de se choveu ou não e se a pessoa ligou ou não o sistema de irrigação. Note que temos duas causas possíveis para a grama molhada, veja que a tabela final será o resultado da combinação de todos os estamos possíveis para Chuva e Regador. Como são duas causas, o número de combinações possíveis para a tabela de efeito, chuva molhada é de $2^2=4$. De modo geral, a tabela efeito terá o número de linhas dado por $2^{n}$, sendo $n$ o número de causas possíveis associadas a um dado efeito."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Redes Bayesianas em Python\n",
    "\n",
    "Usaremos o pgmpy para definir a estrutura de rede e criar as tabelas de Distribuição de Probabilidade Condicional.\n",
    "O primeiro passo será o de importar as bibliotecas necessárias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from pgmpy.models import BayesianModel\n",
    "from pgmpy.factors.discrete import TabularCPD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Em seguida iremos escrever o nosso modelo de rede bayesiana, a partir das relações contidas nos nós do grafo acíclico. Vamos considerar N como o nó Nublado, R para o nó regador, C para o nó Chuva e G para o Nó GamaMolhada. Veja que esse grafo pode ser representado pela seguinte tupla de nós: ((N,R),(N,C),(R,G),(C,G)).\n",
    "\n",
    "O modelo desse grafo será escrito em Python como:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "#Definicao da estrutura do modelo. Isso sera realizado passando apenas os pares de nos.\n",
    "model = BayesianModel([('N', 'R'), ('N', 'C'), ('R', 'G'), ('C', 'G')])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Vamos transcrever a Tabela de Probabilidade Condicional para cada um do nós da nossa rede:\n",
    "\n",
    "I. Tabela para Nublado:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "#definicao das tabelas individuais\n",
    "\n",
    "cpd_n = TabularCPD(variable='N', variable_card=2, values=[[0.5, 0.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "II. Tabela para Regador ligado:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "cpd_r = TabularCPD(variable='R', variable_card=2, values=[[0.5, 0.9],[0.5, 0.1]],\n",
    "                   evidence=['N'], evidence_card=[2]\n",
    "                  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "III. Tabela para Chuva:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "cpd_c = TabularCPD(variable='C', variable_card=2, values=[[0.8, 0.2], [0.2, 0.8]],\n",
    "                   evidence=['N'], evidence_card=[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "IV. Tabela para Grama Molhada:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "cpd_g = TabularCPD(variable='G', variable_card=2, values=[[1,0.1,0.1,0.001],[0,0.9,0.9,0.99]], \n",
    "                    evidence=['R','C'], evidence_card=[2,2])\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Com as tabelas definidas, precisamos adicioná-las ao nosso modelo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "#Associando CPD ao modelo\n",
    "model.add_cpds(cpd_n, cpd_r, cpd_c, cpd_g)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Para finalizar, precisamos verificar se o modelo foi construído corretamente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.check_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Podemos agora obter as relações das Distribuições de Probabilidade Condicional:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<TabularCPD representing P(N:2) at 0x1e8ebc09908>,\n",
       " <TabularCPD representing P(R:2 | N:2) at 0x1e8ebc09860>,\n",
       " <TabularCPD representing P(C:2 | N:2) at 0x1e8ebc09f98>,\n",
       " <TabularCPD representing P(G:2 | R:2, C:2) at 0x1e8ebc09fd0>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.get_cpds()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['N', 'R', 'C', 'G']\n"
     ]
    }
   ],
   "source": [
    "print(model.nodes())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Passando o nome do nó, podemos ter a distribuição de probabilidade condicional para o nó específico:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═════╤═════╤═════╤═════╤═══════╕\n",
      "│ R   │ R_0 │ R_0 │ R_1 │ R_1   │\n",
      "├─────┼─────┼─────┼─────┼───────┤\n",
      "│ C   │ C_0 │ C_1 │ C_0 │ C_1   │\n",
      "├─────┼─────┼─────┼─────┼───────┤\n",
      "│ G_0 │ 1.0 │ 0.1 │ 0.1 │ 0.001 │\n",
      "├─────┼─────┼─────┼─────┼───────┤\n",
      "│ G_1 │ 0.0 │ 0.9 │ 0.9 │ 0.99  │\n",
      "╘═════╧═════╧═════╧═════╧═══════╛\n"
     ]
    }
   ],
   "source": [
    "print(model.get_cpds('G'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═════╤═════╤═════╕\n",
      "│ N   │ N_0 │ N_1 │\n",
      "├─────┼─────┼─────┤\n",
      "│ R_0 │ 0.5 │ 0.9 │\n",
      "├─────┼─────┼─────┤\n",
      "│ R_1 │ 0.5 │ 0.1 │\n",
      "╘═════╧═════╧═════╛\n"
     ]
    }
   ],
   "source": [
    "print(model.get_cpds('R'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═════╤═════╤═════╕\n",
      "│ N   │ N_0 │ N_1 │\n",
      "├─────┼─────┼─────┤\n",
      "│ C_0 │ 0.8 │ 0.2 │\n",
      "├─────┼─────┼─────┤\n",
      "│ C_1 │ 0.2 │ 0.8 │\n",
      "╘═════╧═════╧═════╛\n"
     ]
    }
   ],
   "source": [
    "print(model.get_cpds('C'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═════╤═════╕\n",
      "│ N_0 │ 0.5 │\n",
      "├─────┼─────┤\n",
      "│ N_1 │ 0.5 │\n",
      "╘═════╧═════╛\n"
     ]
    }
   ],
   "source": [
    "print(model.get_cpds('N'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Também podemos avaliar a cardinalidade de um dado nó:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.get_cardinality('G')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Inferência\n",
    "\n",
    "Vamos considerar uma rede bayesiana para a relação entre Fumar, Câncer e Bronquite:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./imagens/fumarCancer.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "A partir da rede anterior, qual a probabilidade de alguém ter câncer, sabendo que ela fuma? Qual a probabilidade de algúem ter bronquite, se ela fuma? Qual a porcentagem das pessoas que fuma?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$P(C|F) = 0.7$, $P(B|F) = 0.8$, $P(F) = 0.4$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Vamos mudar a pergunta. Sabendo que a pessoa teve cancer, qual a probabilidade dessa pessoa ter fumado?\n",
    "Ou seja, queremos encontrar:\n",
    "\n",
    "$P(F=V|C=V)=\\frac{P(F=V \\land C=V)}{P(C=V)}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Primeiramente precisamos resolver a relação $P(F=V \\land C=V)$.\n",
    "\n",
    "Lembrando o Teorema de Bayes: \n",
    "\n",
    "$P(a\\land b) = P(a|b)P(b)$, \n",
    "\n",
    "$P(b\\land a) = P(b|a)P(a)$\n",
    "\n",
    "$P(b|a) = \\frac{P(a|b)P(b)}{P(a)}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Podemos então calcular:\n",
    "\n",
    "$P(F=V \\land C=V) = P(C=V|F=V)P(F=V) = 0,7\\times0,4=0,28$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Já a relação $P(C=V)$ é dada por:\n",
    "\n",
    "$P(C=V) = \\sum_{i} P(C=V|F=i)P(F=i)$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Já a relação $P(C=V)$ é dada por:\n",
    "\n",
    "$P(C=V) = \\sum_{i} P(C=V|F=i)P(F=i)$\n",
    "\n",
    "$P(C=V) = P(C=V|F=V)P(F=V) + P(C=V|F=F)P(F=F)$\n",
    "\n",
    "$P(C=V) = (0,7 \\times 0,4) + (0,1 \\times 0,6) = 0,34$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Dessa forma, tempos que:\n",
    "\n",
    "$P(F=V|C=V)=\\frac{P(F=V \\land C=V)}{P(C=V)} = 0,28 / 0,34 = 0,82$\n",
    "\n",
    "Ou seja, podemos dizer, com 82% de certeza,  que uma pessoa com câncer fumava. Lembre que isso é válido para a rede bayesiana apresentada anteriormente.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exercícios\n",
    "\n",
    "1. Calcule a probabilidade de ter chovido, sabendo que a grama está molhada.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Dica: \n",
    "\n",
    "$P(C=1|G=1) = \\frac{P(C=1 \\land G=1)}{P(G=1)}$\n",
    "\n",
    "$P(C=1 \\land G=1) = \\sum_{i} P(N=i,R=i,C=1,G=1)$\n",
    "\n",
    "$P(G=1) = \\sum_{ijk}P(N=i,R=j,C=k,G=1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "2. A partir da rede bayesiana da relação Fumar x Câncer, escreva um programa em python para esse modelo de rede, usando pgmpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./imagens/fumarCancer.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═════╤══════════╕\n",
      "│ C   │   phi(C) │\n",
      "╞═════╪══════════╡\n",
      "│ C_0 │   0.2921 │\n",
      "├─────┼──────────┤\n",
      "│ C_1 │   0.7079 │\n",
      "╘═════╧══════════╛\n"
     ]
    }
   ],
   "source": [
    "from pgmpy.inference import VariableElimination\n",
    "gramaMolhada_inferencia = VariableElimination(model)\n",
    "prob_c = gramaMolhada_inferencia.query(variables=['C'], evidence={'G': 1})\n",
    "print(prob_c['C'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}