index.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algoritmos de Inteligencia Artificial con Redes Neuronales Artificiales #\n",
    "<img align=\"left\" src=\"home.jpg\" style=\"width: 400px\"/>\n",
    "<br/><br/>\n",
    "<br/><br/>\n",
    "<br/><br/>\n",
    "<br/><br/>\n",
    "<br/><br/>\n",
    "<br/><br/>\n",
    "\n",
    "\"Estructura de los centros nerviosos de las aves\" dibujo de Ramón y Cajal, obtenido de [wikipedia](https://en.wikipedia.org/wiki/Santiago_Ram%C3%B3n_y_Cajal#/media/File:CajalCerebellum.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Taller impartido en el Instituto Tecnológico Superior del sur de Guanajuato en el 2018 ###\n",
    "\n",
    "Únete a la conversación en el subredit [r/algoritmica](https://reddit.com/r/algoritmica)\n",
    "\n",
    "---\n",
    "### Cómo obtener los materiales del curso ###\n",
    "1. Crea una cuenta en [github](https://github.com) \n",
    "2. Inicia sesión en [juliabox](https://v1.juliabox.com) usando tu cuenta de github\n",
    "3. En la consola de juliabox escribe el siguiente comando:\n",
    "```\n",
    "git clone https://github.com/iranroman/algoritmica_ejercicios.git\n",
    "```\n",
    "4. (opcional) crea una cuenta en [reddit](https://reddit.com/r/algoritmica) y continúa la discusión fuera del aula\n",
    "\n",
    "Así obtendrás una versión en linea del lenguaje de programación Julia y los ejercicios que estudiaremos en este taller. \n",
    "\n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 1.1: Características de Datos #\n",
    "\n",
    "Los objetos del mundo real pueden ser descritos por sus características. Existen un número infinito de características asociadas con un objeto específico. Sin embargo, unas de estas características resultan ser más importantes al diferenciar un objeto de otro. \n",
    "\n",
    "Por ejemplo, supongamos que nos interesa diferenciar tres tipos de flores por especie. Esto le interesó a [Ronald Fisher](https://en.wikipedia.org/wiki/Ronald_Fisher) en 1993. En un estudio científico, Fisher se propuso identificar las características más importantes que podrían diferenciar tres especies distintas de flores.\n",
    "<a href=\"https://i.ytimg.com/vi/RSKhj2BZQBg/maxresdefault.jpg\">\n",
    "<img src=\"https://i.ytimg.com/vi/RSKhj2BZQBg/maxresdefault.jpg\" style=\"width: 400px\"/>\n",
    "</a>    \n",
    "Para diferenciar estas flores, Fisher usó la longitud y anchura de los pétalos y sépalos de estás tres especies.\n",
    "\n",
    "Los datos que Fisher colectó se han convertido en una base de datos clásica para estudiar algoritmos de inteligencia artificial. Se encuentra disponible de forma gratuita en internet. \n",
    "\n",
    "El siguiente programa prepara los datos de Fisher para poder trabajar con ellos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34mINFO: Nothing to be done\n",
      "\u001b[0m\u001b[1m\u001b[34mINFO: METADATA is out-of-date — you may not have the latest version of MAT\n",
      "\u001b[0m\u001b[1m\u001b[34mINFO: Use `Pkg.update()` to get the latest versions of your packages\n",
      "\u001b[0m"
     ]
    }
   ],
   "source": [
    "# instalamos un paquete de Julia para poder obtener los datos\n",
    "Pkg.add(\"MAT\") \n",
    "using MAT\n",
    "\n",
    "# obtenemos los datos que necesitamos\n",
    "iris = matread(\"iris.mat\")\n",
    "caracteristicas = iris[\"meas\"]\n",
    "especies = iris[\"species\"];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aquí obtenemos los datos de 150 flores que Fisher midió. La variable `caracteristicas` es una matriz 150x4, cuyas ileras corresponden a las características (longitud de pétalo, anchura de pétalo, longitud de sépalo, y anchura de sépalo) de cada flor. Las primeras 50 ileras, corresponden a la especie setosa, las ileras 51 a 100 corresponden a la especie versicolor, y las ileras 101 a 150 corresponden a la especie virginica. La variable `especies` es un vector 150x1 que contiene los nombres de especies que corresponden a las ileras de la matriz `características`.\n",
    "\n",
    "El siguiente código muestra como podemos visualizar la primera de las cuatro características. En la figura, cada color representa un tipo de flor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a015e2b90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34mINFO: Nothing to be done\n",
      "\u001b[0m\u001b[1m\u001b[34mINFO: METADATA is out-of-date — you may not have the latest version of PyPlot\n",
      "\u001b[0m\u001b[1m\u001b[34mINFO: Use `Pkg.update()` to get the latest versions of your packages\n",
      "\u001b[0m"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x7f6a01526e50>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# instalamos un paquete de Julia para poder visualizar los datos\n",
    "Pkg.add(\"PyPlot\")\n",
    "using PyPlot\n",
    "\n",
    "# graficamos la longitud de pétalo para el primer tipo de flores\n",
    "scatter(0.1*randn(50,1),caracteristicas[1:50,1])\n",
    "# agregamos la longitud de pétalo para el segundo tipo de flores\n",
    "scatter(1+0.1*randn(50,1),caracteristicas[51:100,1])\n",
    "# agregamos la longitud de pétalo para el tercer tipo de flores\n",
    "scatter(2+0.1*randn(50,1),caracteristicas[101:150,1])\n",
    "ylabel(\"Longitud del Pétalo (cm)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el siguiente espacio, trabaja con la persona junto a tí y grafiquen las cuatro características en cuatro figuras distintas. Determinen cuales son las dos características que mejor sirven para diferenciar las tres especies de flores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VuHz66adatWqV+vTp43Q8AAA0eZHrB+08tNPUPk4vDbDz0E79/cu/p2XLczy2EpchQ4Zoy5YtJC4AAFhkZv2gSFY7fsJLCFQeqIw5OTfDl6F7V95b+9pu95IbbCUuf/zjH3X99ddr69at6t+/f4NuowEDBjgSHAAATUm4e6h+QhEvaZGsdfyElxCYtnSafPJFTV6irVc0bek0TxTp+gzDSLyQQT3Lly/XpZdeqk2bNn1/IJ/PleLcQCAgv9+vqqoq5ebmNtp5AQCwoiZYo3ELxsUtnK1/56VbTjfdNvQ2W8mE3Ts7i36yqFEeG9n9/W3rjstVV12lQYMG6YUXXqA4FwAAE8x0+wSNoH4z5DfqlN0p6dqT+ksI7Dy0s87jofqsdi+5xVbisnnzZi1cuFC9e/d2Oh4AXhKskTZ/KO37RmqbJ/UYIXmkwA/NQ2QRbLREIN7nifa1GsdH2z4ytW2n7E46t+e5ts5TX+T4/r9/+XdT+9hd56ix2EpczjzzTH366ackLkBztm6htOg2KbDt+/dyu0tnz5aKJ7gXF3BUohH68T6X5Nj4/dLNpbrrw7tUddjcJFu76wwl8lXgK1fP7xRbNS5PPvmkfve73+mqq67SiSee2KA4d8KExvtLixoXwAXrFkp/vkJqUPR39LHxRc+SvMBVsYpgw8WuV/a7UvM+mxf181idOOF9rRSwlm4u1S1LbzG1bSprTMzE4ZUaF1uJS0ZG7JUCKM4FmrhgjfRA/7p3Wurwhe683LyGx0ZwRaIiWJ988vl8MYtU47Hyy70mWKOxr4xV5cFK08dORVePmaLgVJ4/Fru/v22tVRQMBmP+MO4faOI2fxgnaZEkQwpsDW0HuMDMCH07SUt433ABq5k4zCYtkvTLk36ZkqTB7BIAqTq/05JeZBFAM7Mv8V+AlrYDHNYYxaVmzmE1juPaHWc3HEfiSNX5nWarOPfGG29U7969deONN9Z5/5FHHtG///1vPfDAA44EB8AFiTqF2uaZO47Z7QCHNUZxabRz1O9C6tS6U9LHTMRM51PH7I4pO78bbCUuCxYs0MKFCxu8P2LECM2aNct04nLXXXdp5syZdd7r06ePPv/8czthAUiWmU6hHiNC7wUq1LA4V6qtcekxojEiBhpINPLeiRqX+uP3Y3Uo5bbMVeBIIOFx81qbH+mf6JyRnU+lm0tV8s+SuMexuqSA22w9Ktq5c6f8fn+D93Nzc/Xtt99aOla/fv1UUVFR+/P+++/bCQlAssKdQvXrVwIVoffXHf2flYzMUCIjqbaLqNbR12fPojAXrgmPvJe+7wQKC7+eXDw5lMDE+DzevvXH74c7mOrXkVQeqDSVtEjS9GHTLXXyxDvntKXTVLq5tHabeHU2dpYUcJutxKV3795atGhRg/fffPNN9ezZ09KxWrRooW7dutX+dO7c2U5IAJIRrAndaYl6B+Xoe4umh7aTQndfLnpWys2vu2lud1qhkRZG9xituSPnqmtO1zrv5+Xkae7IuZp28rSYn98/8n7dP/L+mPtGFrDWBGs0a8WsqHd2DBnyyaf2We2V2yp610z7Vu11/8j7LRXFJjqnFJpBU/LPkpit3WFdc7p6Yn2iSLYeFU2bNk1Tp07Vjh07dOaZZ0qS3n77bc2ZM8dyfcu//vUvde/eXdnZ2Ro+fLhKSkp03HGxC4Sqq6tVXV1d+zoQMJfNAojDSqdQ0Wmht4onSCeMZ3Iu0lb9kff1a0ASfR7vszAzHUx7qvfoqTFPyefz6Z/b/qmKAxXKz8nXsO7DdHLeyZbvdJg5p5kuIkm650f3aFj+MEvnd5vttYqqq6t1zz336O6775YkFRYW6rHHHtMVV1xh+jjDhg3TvHnz1KdPH1VUVGjmzJk67bTTtHbtWrVr1y7qPiUlJQ3qYgAkyW6nUEbm94kMkIYiR95b/TzRvpL5jp1dh3bp3J7nOpIkONk1tfPgTseO1VhsJS6SdMMNN+iGG27Qjh071Lp1a7Vt29byMc4555zafx8wYICGDRumHj166M9//rOuvvrqqPvMmDFD06ZNq30dCARUUFBg/QsA+F66dQql4xpI6RgTXGe2EyfRdtG6gyRFvePjZPdP/WM5uT5TqthOXMK6dHHuArZv317HH3+8/v3vf8fcJisrS1lZWY6dE4DSq1MoHddASseYkBbMdDAl6tiJ1h3kz/JLhuqsbxTuGBpVMCrhObvmdJVhGNpxcIfpuMx0KaUD08W5Z599tpYvX55wu71792r27Nl69NFHLQezb98+bdy4Ufn5+Yk3BuCcdOkUMtvZ1JjSMSakDTMdTPE6dmJ1B1VVVzVYlDHcMbRky5KE55w+dLpmDJthOi4zXUrpwnTicuGFF+onP/mJiouLddttt+nll1/WBx98oFWrVqm0tFQPPfSQLrroIuXn56usrEznn39+wmPeeuutWrZsmTZt2qQPP/xQP/7xj5WZmalLLrkkqS8FwAa3O4WsdjY1hnSMCWknUQdTrLsV8bqDoglvN3vFbI0qGJXwnGbjMtOlNHvFbNWkyZ9z04+Krr76ak2aNEkvv/yyXnrpJT355JOqqgplgz6fT8XFxRo3bpxWrlypvn37mjrm119/rUsuuUQ7d+5Uly5d9KMf/UjLly939PETAAvc7BSy09nUHGNCWkrUoRSN2TWEIkWulWTmnGa2MdOlFD5nomLlxmCpxiUrK0uTJk3SpEmTJElVVVU6ePCgOnXqpJYtW1o++Ysvvmh5HwAp5lankNnOpr0VUvl7jZNYsS4TLDDThRQpme6gHQd2JCykrf/5uMJxURMps3E0xhpQZiRVnOv3+6NO0AUAy8x2LC2aIR2ImNCdyiLZdOu2QpOSTHfQV3u/0rgF42IW0loptHWqM6qx+AzDMPdwLU0FAgH5/X5VVVUpNzf6ZEIAHhCskR7on+DRTDRHCw9TUYdTG1OCbqub19AaDctqgjUat2BczO6gaHzyyd/Kr6rDVQ32CRfdXtnvSs37bF7Mz6NN/40XR7gDadFPFjnaGm3397etkf8A4LiMTGlc/MXgokthkWy6dFuhSYrXkRSNTz4ZMmT4jLiFtPPXzbdUaJtsZ1RjI3EBkD5yOtncMaJI1mlud1uhSYvV+dM+q738reqWYuTl5GnKwCmqqq7bJh3JkBF31evIQlszcSTqjHJD0gPoAMAxyRa5pqpIlnWZkEKxOn+khpNzF29a7Mg5oxXa2umMckNSicuqVau0fv16SVJxcbEGD449GRBAM2VlVH6yRa5OFcnGipmWZ6RIrI6k+u85VSAb6zhWO6PcYCtxqays1MUXX6ylS5eqffv2kqQ9e/Zo1KhRevHFF5nDAiDE6qj8/TslX4YU51Z3TLnHOLMkAeP9kcbMLDHg8/liPi4yswRBurNV4/KrX/1Ke/fu1WeffaZdu3Zp165dWrt2rQKBgG688UanYwTgRVZH5a9bKL1ypb2kRZLyByb/6Ibx/khzZgppJxdPDiUwHii0tcNWO7Tf71dpaamGDKl7O2nFihUaO3as9uzZ41iAidAODaShhK3N9dqIbbdCRx4yU/qv7VKLVvb2txoz4KJoc1q65XTTbUNviznHJfLzdGD397etR0XBYDDqpNyWLVsqGLT5f0sAmg6ro/ITbm+CUSOtfEoaPsXe/oz3h4ckKqT1SqGtHbYSlzPPPFM33XSTXnjhBXXv3l2StHXrVt1yyy0666yzHA0QgAdZHZXvVDfQ7k3292W8PzwmUSGtFwpt7bBV4/LII48oEAiosLBQvXr1Uq9evVRUVKRAIKCHH37Y6RgBeEmwxvwv93AXkFPdQB0Ko78frAmtb7TmldA/ow2qY7w/4Am27rgUFBSorKxMpaWl+vzzzyVJffv21ejR6fHcDIBLonXkxNK64/ddQD1GhOpHYo7WN8GXKQ251lxM0bqEEsZwtMbFic4lALaxVhEAZ4Q7cqwkHhc9933yULu/6h3jaGdEn3OkDX+PfawRN0pj7zYZU4z1jRLFwKRcwDF2f3+bTlweeugh0wdtzJZoEhcgDdjqCorSpRP17sgxofWAiidI/7hd+uiRui3TvsxQQW79pMVul1CiGAA4IuWJS1FRkbkD+nz68ssvTQeQLBIXIA2UvyfNP8/evpPfqNulk2jS7neHQ91DuzeFalqGXBu9BdpsTPXPbyYGAElLeTt0eXm5rcAANAN7K+zvW7+QNzxaP5w8fPZa3eShRavQHZbw5+sXSm26fP/aJ6nHj6T9lebOX76sYWLCeH/PqgnWNMkWYHyPRRYBJGfdQmnRdPv7R+vSSVRQm7AI+D6pVVtz53/3Pmn1/89I/yYg2tC1vJw8TR86PW2GriF5totzv/76ay1cuFBfffWVDh8+XOezuXPnOhKcGTwqAlxkpyC3vgvnS/0mmjjm0QLZEb+SPnw4uXM2QPGt15VuLtW0pdMarN8THnM/d+Rckpc0k/Ial0hvv/22JkyYoJ49e+rzzz9X//79tWnTJhmGocGDB+udd96xekjbSFwAlzgxpl8KFb6aHv3vk3w+G+sZ+ZQ40WGkv1fVBGs0bsG4OndaIoUXFlz0k0U8Nkojdn9/2xpAN2PGDN16661as2aNsrOztWDBAm3ZskVnnHGGLrzwQjuHBOA1Tozpl74fo2/qmIa9RRhzOpnYyKgbCzyjrLIsZtIiSYYMbT+wXWWVZY0YFVLFVuKyfv16XXFFaNZBixYtdPDgQbVt21a//e1vNXv2bEcDBJCmnBx97/To//rOLpFO+7W1WOAZOw7scHQ7pDdbiUubNm1q61ry8/O1cePG2s++/fZbZyIDkH4iR+c7+Qve6dH/9bXLl3qeYS2WWMwsH4BG1SWni6PbIb3Z6io65ZRT9P7776tv374699xz9Z//+Z9as2aNXn31VZ1yyilOxwggHUTr5PFlxHl0c7RmxAhKe7fL1Bj9HiNCSwEc3BX7mFZrXNpFHD/RsgKRyxBEY3b5ADSqwV0HKy8nT5UHKhsU50rf17gM7jrYhejgNFt3XObOnathw4ZJkmbOnKmzzjpLL730kgoLC/WnP/3J0QABpIFwp0/9+pN4SYsUmjZ7zr1134u2Tbhg8vO/xUlaJMmQhk89um/948VwzuzQ8TMyQwlGvCLdg7tCMUQT6xoEKkLvr1toLh44LjMjU9OHhlryffX+XIRf3zb0NgpzmwjWKgIQn5nuofp3XuqPyDczRt/MeVp3lH7971BykWgxx9YdpfMfrHsnJFgj3ddLOrg71heJ3llkd/kANKpoc1y65XTTbUNvoxU6DaV8cm6knj17auXKlerUqW6l/p49ezR48OBGHfkPIMXMdA8ZQWnc70P1IdFG5BdPkE4YH3+MvpnzHNwV2q7+8aJNzi06rWESsfnDOEmLVKezKHJyrplup2j7oVGN7jFaowpGMTm3ibOVuGzatEk1NQ0L0qqrq7V169akgwKQRswW4bbNk078aezPE43RN3ue8HbRjtf7THP7mj1Hsvuh0WVmZGpItyFuh4EUspS4LFz4/TPcxYsXy+/3176uqanR22+/rcLCQseCA5AGzHb6WOkIiraIYSrOU/+cVpIwO+dMVVcUgFqWEpeJE0NjuX0+nyZPnlzns5YtW6qwsFBz5sxxLjoA7usxIkE3Tr3OoERideaMK3H2PInOGVWMczh9DQDYZqmrKBgMKhgM6rjjjlNlZWXt62AwqOrqam3YsEHnnWdzaXsA6am2G0cy1RkUT7zOnJevlPqHHzUleR4z52wgzjmcvAYAkmKrHbq8vFydO3eWJB06dMjRgACkoeIJoQUIc/Prvp/b3fzChMGa0F2PqHcsjr63doH003nJncf0OetJdA4nrgGApNkqzg0Gg7rnnnv0+OOP65tvvtEXX3yhnj176vbbb1dhYaGuvvpqp+ME4DYznUHxmO3MadNJunmt/fNYOudR434vDbs+8TmSvQYAkmYqcXnppZc0fPhwHXfccZKk3/3ud5o/f77uvfdeXXvttbXb9e/fXw888ACJC9BUJeoMisdsYez6o02g/J6bAAAgAElEQVQAdhOC7w5LK5+Sdm+SDlaZ26dNF/PnSuYaAEiaqUdF2dnZOv300/Xpp59KkubPn68nn3xSl112mTIzv/+PfeDAgfr8889TEykAbzPbcbPiSWn+eaGBb1an0f7jdumePGnx/xc6zpqXzO23aAaTbwGPMJW4XHDBBXrxxRc1adIkSdK2bdvUu3fvBtsFg0EdOXLE2QgBNA3hzhyzo/qtjtL/x+3Shw9ZW8co7MBOxvYDHmG6OPeUU07RsmXLJEnFxcV67733GmzzyiuvaNCgQc5FB6DpiNuZE83RgtpF0xOvwPzdYemjR5IIzsK5ALjKUnFux44dJUl33HGHJk+erK1btyoYDOrVV1/Vhg0b9Oyzz+qNN95ISaAAmoBwZ46pmSqS6VH6K5+yd6fFzrkAuMpWO/QFF1yg119/XaWlpWrTpo3uuOMOrV+/Xq+//rrGjBnjdIwAmpLiCaGuoclvSEOvM7dPosLe3ZuSDsv0uQC4ylY7tCSddtppeuutt5yMBUBzEdmZs+LJxNvndJbK34vdgtyh0LnY2nRx7lgAHOczDMPEZKbvvfTSS1q4cKEOHz6ss846S9dff32qYjPF7rLYANJAsEa6r3do1eeofFLrDlLL7IZLBJw9+/uhb98dDnUTxXtc5MsIJT17tyvuQLp2+dI59zJQDkgxu7+/LT0qeuyxx3TJJZfo448/1r/+9S9NmTJFv/71ry0HCwCSpM//FidpkSQj9Hm0JQIiu4BatJKGT41/ruFTQwmJpLjFwXu302EEpDFLicsjjzyiO++8Uxs2bNDq1as1f/58/eEPf0hVbACastpx/PHESjCidAGNvVsacWPozkqdQ2SG3h97d+yx/YmODSBtWHpU1Lp1a61fv16FhYWSQnNbWrdurU2bNik/P95fBKnDoyLAo8rfCw2aS9bkN+p2AUVOzu1QKA25NnRHJtLGpdJzF1g/NgDH2P39bak4t7q6Wm3atKl9nZGRoVatWungwYNWDgOguQjWxF7Xx6nunS+X1D1ui1bS8Cnx9znwrblj02EEpB3LXUW33367cnJyal8fPnxY99xzj/x+f+17c+fOdSY6AN61bmHDeS2RRbVmlwBI5L050sfPSOc/aL6g1uy5nYoRgGMs1bicfvrp2rBhgz755JPanxEjRujLL7+sfb169WrbwcyaNUs+n08333yz7WMASAPrFoYKXOMV1fYYIbXu6Mz5Du6S/ny5+YLahMsP+KTcY0LbAUgrlu64LF26NEVhSCtXrtQTTzyhAQMGpOwcABpBbdFttPI5Q5IvVPh6/NkWpt36YhyvnkXTpRPGJ17pObz8wJ+viHLso8nM2bPsrU4NIKVsTc512r59+3TZZZfpqaeeUocOHeJuW11drUAgUOcHQBrZ/GGCcf5HR+uvfEo6tMfcMbPamdsuPLLfjFgdRrndQ+8zxwVIS2mRuEyZMkXjx4/X6NGjE25bUlIiv99f+1NQUNAIEQIwzWxBq5Ux/QMucv78Ut3lB37yp9A/b15D0gKkMdsj/53y4osvqqysTCtXrjS1/YwZMzRt2rTa14FAgOQFiBSvk6cxmC1otTKmv2NP588fFrn8gNvXDkBCriYuW7Zs0U033aS33npL2dnZpvbJyspSVlZWiiMDPCpRJ09jCBe+BioUvS7FF/p8yLXShw9LeyviHy/3GPPbtu5ov6A2Ha4dgIRcfVS0atUqVVZWavDgwWrRooVatGihZcuW6aGHHlKLFi1UU8PUSsA0M508jSFc+CqpYddOROFri1YRI/jjsLLtwV2hZQSsSpdrByAh05Nz/+///s/0Qc12Bu3du1ebN2+u897Pf/5znXDCCbrtttvUv3//hMdgci6g0COOB/rHKYo9epfj5jWN9+gj6h2MY0KJSOQdjHULpddvlA7urrt/644NZ7N89hfp5SsVu8PIxvdMx2sHNAMpn5x70kknyefzKVaeE/7M5/OZvlPSrl27BslJmzZt1KlTJ1NJC4CjzHbybP6w8UbYF08ItSYnqhkJb1f+nrT5/VBOUnSaVPijhtvmdFL8tmgb3zMdrx2AmEwnLuXl5amMA0AyzHbSNPYI+8jC10Tb9RoZ+oknFd8zXa8dgKhMJy49evRIZRy1UjnkDmiymssIe6vf00yXUHO5dkATYbs497nnntOpp56q7t2719apPPDAA/rrX//qWHAATGouI+ytfM91C0O1K/PPkxZcHfrnA/0bFto2l2sHNBG2EpfHHntM06ZN07nnnqs9e/bU1rS0b99eDzzwgKMBAjDBbCeP14tLzX7Pz/9mvkuouVw7oImwlbg8/PDDeuqpp/Rf//Vfysz8/j/mk08+WWvWrHEsOAAWNJcR9om+5wnjE6yVpNCaRsGIJoLmcu2AJsDWALry8nINGjSowftZWVnav39/0kEBsMlsJ4/Xxfue5e/Z6xJqLtcO8DhbiUtRUZFWr17doGB30aJF6tu3ryOBAbDJbCeP18X6nsl0CTWXawd4mK3EZdq0aZoyZYoOHTokwzC0YsUKvfDCCyopKdEf//hHp2MEAPPoEgKaNFuJyzXXXKPWrVvrv//7v3XgwAFdeuml6t69ux588EFdfPHFTscIAOYd2Jl4G7qEAM8yPfI/lgMHDmjfvn3q2rWrUzFZwsh/ALUSju8/6qfzpf4TGycmAFGlfOR/LDk5OcrJyUn2MACQvITj+49q0yn1sQBICdOJy6BBg+TzxRrQVFdZWZntgADANsb3A02e6cRl4sTvb6seOnRIf/jDH1RcXKzhw4dLkpYvX67PPvtMv/zlL52PEkD6MTNOv7FRmAs0eaYTlzvvvLP236+55hrdeOONuvvuuxtss2XLFueiA5Ce1i0MDXmLfCyT2z00gdbNYW3h8f2BCkUfQOcLfU5hLuBZtibnvvzyy7riiisavD9p0iQtWLAg6aAApLF1C82P029sjO8HmjxbiUvr1q31wQcfNHj/gw8+UHZ2dtJBAUhTwRrr4/QbG+P7gSbNVlfRzTffrBtuuEFlZWUaOnSoJOmf//ynnn76ad1+++2OBgggjSTs2okxTr+xMb4faLJsJS7Tp09Xz5499eCDD+r555+XJPXt21fPPPOMLrroIkcDBJBGvNS1w/h+oEmyPcfloosuIkkBmhsvdu2kY/cTANuSHkAHoBlJ2LUjyZch7Tcxdr8xpGv3EwDbbBXnAmim6nTtxGAEpVeudLe7SErv7icAtpG4ALCmeIJ04bzQnZV43Owu8kL3EwBbSFwAWJfTKXRnJaaI7iI3WOl+AuApJC4ArEv37qJ0jw+AbaaLc6dNm2b6oHPnzrUVDACPSPfuonSPD4BtphOXTz75pM7rsrIyfffdd+rTp48k6YsvvlBmZqZ++MMfOhshgPST7msCpXt8AGwznbgsWbKk9t/nzp2rdu3aaf78+erQoYMkaffu3fr5z3+u005j4BPQ5IW7i/58hUJrAEUmB2mwJlC6xwfANp9hGDGGMcR2zDHH6B//+If69etX5/21a9dq7Nix2rYtXlGcswKBgPx+v6qqqpSbm9to5wWgGHNSjgklBekwJyXd4wOaMbu/v20NoAsEAtqxY0eD93fs2KG9e/faOSQAL0r3NYHSPT4AltlKXH784x/r5z//uebMmVNnkcVf//rX+o//+A9HAwSAuBKN9GfNIqBJsZW4PP7447r11lt16aWX6siRI6EDtWihq6++Wvfdd5+jAQJIY26P1Hf7/AAana0al7D9+/dr48aNkqRevXqpTZs2jgVmFjUugEvCI/UbdO0cLX696NnUJg9unx9AUuz+/k5qAF2bNm00YMAADRgwwJWkBYBL3B6p7/b5AbjG1qOiUaNGyefzxfz8nXfesR0QAA+wMlI/FfUlbp8fgGtsJS4nnXRSnddHjhzR6tWrtXbtWk2ePNmRwACkMbdH6rt9fgCusZW43H///VHfv+uuu7Rv376kAgLgAW6P1Hf7/ABc4+gii5MmTdLTTz/t5CEBpKPwSH3FemTsCw16S9VIfbfPD8A1jiYuH330kbKzs508JIB0FB6pL6lh8tAII/XdPj8A19h6VFR/yJxhGKqoqNDHH3+s22+/3ZHAAKS54gmhluOoc1QaYaS+2+cH4Apbc1yuvPLKOl1FGRkZ6tKli84880yNHTvW0QATYY4L4LJEk2ub+vkB2GL393dSA+jSAYkLAADe06gD6Hr27KmdO3c2eH/Pnj3q2bOnnUMCAAAkZCtx2bRpk2pqGk6krK6u1tatW5MOCgAAIBpLxbkLFy6s/ffFixfL7/fXvq6pqdHbb7+twsJCx4IDAACIZClxmThxoiTJ5/M1mJDbsmVLFRYWas6cOc5FBwAAEMFS4hIMBiVJRUVFWrlypTp37pySoAAAAKKxNcelvLzc6TgAwBraoIFmyXTi8tBDD+m6665Tdna2Hnroobjb3njjjaaO+dhjj+mxxx7Tpk2bJEn9+vXTHXfcoXPOOcdsWACao3ULYwyem83gOaCJMz3HpaioSB9//LE6deqkoqKi2Af0+fTll1+aOvnrr7+uzMxM/eAHP5BhGJo/f77uu+8+ffLJJ+rXr5+pYzDHBWhm1i2U/nyFpPp/dR0dinnRsyQvgAc0mQF0HTt21H333aerr77a1PYkLkAzEqyRHuhf905LHb7QnZeb1/DYCEhzdn9/26pxSYWamhq9/PLL2r9/v4YPHx5zu+rqalVXV9e+DgQCjREegHSw+cM4SYskGVJga2i7otMaLSwAjcdW4jJt2rSo7/t8PmVnZ6t379664IIL1LFjx4THWrNmjYYPH65Dhw6pbdu2eu2111RcXBxz+5KSEs2cOdNO2AC8bt83zm4HwHNsPSoaNWqUysrKVFNToz59+kiSvvjiC2VmZuqEE07Qhg0b5PP59P7778dNQiTp8OHD+uqrr1RVVaVXXnlFf/zjH7Vs2bKY+0W741JQUMCjIqA5KH9Pmn9e4u0mv8EdFyDNNepaRRdccIFGjx6tbdu2adWqVVq1apW+/vprjRkzRpdccom2bt2q008/XbfcckvCY7Vq1Uq9e/fWD3/4Q5WUlGjgwIF68MEHY26flZWl3NzcOj8AmokeI0I1LPLF2MAn5R4T2g5Ak2Qrcbnvvvt0991310ka/H6/7rrrLt17773KycnRHXfcoVWrVlk+djAYrHNHBQBqZWSGWp4lNUxejr4+exaFuUATZitxqaqqUmVlZYP3d+zYUVss2759ex0+fDjucWbMmKF3331XmzZt0po1azRjxgwtXbpUl112mZ2wADQHxRNCLc+5+XXfz+1OKzTQDNgqzr3gggt01VVXac6cORoyZIgkaeXKlbr11ltr1zNasWKFjj/++LjHqays1BVXXKGKigr5/X4NGDBAixcv1pgxY+yEBaC5KJ4gnTCeyblAM2SrOHffvn265ZZb9Oyzz+q7776TJLVo0UKTJ0/W/fffrzZt2mj16tWSpJNOOsnZiOthjgsAAN7jygC6ffv21U7J7dmzp9q2bWv3ULaRuAAA4D2uDKBr27atBgwYkMwhAAAATLOVuOzfv1+zZs3S22+/rcrKSgWDwTqfm12rCAAAwApbics111yjZcuW6fLLL1d+fr58vlgzFQAAAJxjK3F588039be//U2nnnqq0/EAAADEZGuOS4cOHUytQwQAAOAkW4nL3XffrTvuuEMHDhxwOh4AAICYbD0qmjNnjjZu3Ki8vDwVFhaqZcuWdT4vKytzJDgAAIBIthKX8HRcAACAxpTUALp0wAA6AAC8x5UBdKtWrdL69eslSf369dOgQYOSORwAAEBcthKXyspKXXzxxVq6dKnat28vSdqzZ49GjRqlF198UV26dHE0SAAAAMlmV9GvfvUr7d27V5999pl27dqlXbt2ae3atQoEArrxxhudjhEAAECSzRoXv9+v0tJSDRkypM77K1as0NixY7Vnzx7HAkyEGhcAALzH7u9vW3dcgsFggxZoSWrZsmWDdYsAAACcYitxOfPMM3XTTTdp27Ztte9t3bpVt9xyi8466yzHggMAAIhkK3F55JFHFAgEVFhYqF69eqlXr14qKipSIBDQww8/7HSMAAAAkmx2FRUUFKisrEylpaX6/PPPJUl9+/bV6NGjHQ0OAAAgkqMD6L7++mv99re/1ZNPPunUIROiOBcAAO9p1OLcWHbu3Kk//elPTh4SAACglqOJCwAAQCqRuAAAAM8gcQEAAJ5hqavoP/7jP+J+3pgTcwEAQPNjKXHx+/0JP7/iiiuSCggAACAWS4nLM888k6o4AAAAEqLGBQAAeAaJCwAA8AwSFwAA4BkkLgAAwDNIXAAAgGeQuAAAAM8gcQEAAJ5B4gIAADyDxAUAAHgGiQsAAPAMEhcAAOAZJC4AAMAzSFwAAIBnkLgAAADPIHEBAACeQeICAAA8g8QFAAB4BokLAADwDBIXAADgGSQuAADAM1xNXEpKSjRkyBC1a9dOXbt21cSJE7VhwwY3QwIAAGnM1cRl2bJlmjJlipYvX6633npLR44c0dixY7V//343wwIAAGnKZxiG4XYQYTt27FDXrl21bNkynX766VG3qa6uVnV1de3rQCCggoICVVVVKTc3t7FCBQAASQgEAvL7/ZZ/f6dVjUtVVZUkqWPHjjG3KSkpkd/vr/0pKChorPAAAIDL0uaOSzAY1IQJE7Rnzx69//77Mbfzyh2XmqChFeW7VLn3kLq2y9bQoo7KzPC5dhwAANKJ3TsuLVIYkyVTpkzR2rVr4yYtkpSVlaWsrKxGisqeRWsrNPP1daqoOlT7Xr4/W3eeX6yz++c3+nEAAGgq0uJR0dSpU/XGG29oyZIlOvbYY90OJymL1lbohufL6iQbkrS96pBueL5Mi9ZWNOpxAABoSlxNXAzD0NSpU/Xaa6/pnXfeUVFRkZvhJK0maGjm6+sU7dlb+L2Zr69TTTD+0zmnjgMAQFPjauIyZcoUPf/88/rf//1ftWvXTtu3b9f27dt18OBBN8OybUX5rgZ3SCIZkiqqDmlF+a5GOQ4AAE2Nq4nLY489pqqqKo0cOVL5+fm1Py+99JKbYdlWuTd2smFlO6eOAwBAU+NqcW6aNDQ5pmu7bEe2c+o4AAA0NWlRnNtUDC3qqHx/tmI1K/sU6goaWhR7To2TxwEAoKkhcXFQZoZPd55fLEkNko7w6zvPL044h8Wp4wAA0NSQuDjs7P75emzSYHXz132M082frccmDTY9f8Wp4wAA0JSkzeRcu+xO3ks1JucCABCb5yfnelms5GJ4r05JH9vMcSLP37lNluSTvt1XnXSiQ9IEAEg3JC5Jcnssf7TzR7Ibi9vfCwCAaKhxSYLbY/ljnT/ZWNz+XgAAxELiYpPbY/njnT+ZWNz+XgAAxEPiYpPbY/kTnd9uLG5/LwAA4iFxscntsfx2jmtmH7e/FwAA8VCcG0OdTp22WZIhfbv/+06dVIzlj9XFE+19O+P+Y+0Tefxv91abPla0uCTRiQQASBkSlyjMdOrcPr6v8v3Z2l51KGo9iE+hYXFmx/LH6uKZMDBfCz+taPD+7eOL457fbCzRzpvhk2KVsISPtXv/Yf1o9jt19muf01KStOfAkTqx0okEAHAKA+jqCXfUxLso4fsH151epCffLZekOtuHPzc74dbMOa2cP9q20WJJ9rxm9rN6LQAAzYPd39/UuESw2qmz8NMKPXppcmP5zZ4z9vkHNTi/mVjMnLf+E55u/mw9eukgLfy0wnS8dCIBAJzEo6IIdjp1OrRppfdvO9N2XYeVc0Y/f1ad85udnGvmvEFDun18X3Vul1V7LDvxRnYiOTFNGADQfJG4RLDbqZPMeP9ku3Psnt/seTu3y9IFJx1jeb9kzgkAQCwkLhGc6NSx0hlUEzT08abk5qFEdvdsDxzSrn3V6timlbr5W+uHPTpo1ebdUe/EdG6TZer4HXNa6U/vfanNuw6ooENrJVMRZef6AgAQicQlwtCijkl16ljpDMpplamDR2psJwLxunvC4nUHdcvNVvuclqo6cCRuYe/lT6+wF2CUWM12WAEAEAvFuREyM3y68/xiSd93w0QT/uzO84tr60dire9TUXVIT7xb3uD9A4eTS1okacLAfE3539hrFcWrhf0mcEh74iQtUuxOJSuiXSsAAOwicann7P75emxSw06hSPU7dex0BpmR78/WL04vUn6UriWr3T31GQolFR1yWsZN0pJlpcMKAIBEeFQUxdn98zWmuFvcybmRdw/sdgbFc/kpx+muCf2VmeHTb87u26A+xolzGpJ2RwyLc9LUUb11au/OTM4FADiKxCUGK506qeiWqag6pDf+b1ttolI/lu2B9O7Q+UFe29qYYxUsAwBgFYmLA1LRLVO6vlKl6yslNRybv2hthe5+4zPHz+mk8DWJVbDMMgAAADuocXHA0KKOtev0pML2qkO64fkyLVpbUVsEvGt/8o94fFJK4s4/2kEUq2A58vsAAGAFd1w8IFxIO/P1dTIMw7Fun1QN4L99fKgzK1bBcuT3GVPcjcdGAADTuOPigBXlu+qsiJwK4bH52wPVjhyvmz9bt4z+QUri7tCmVcLi4chlAAAAMIs7Lg4wW5w7dVRv/SCvrf71zV49smRjiqOKF0cv3TKmj974v20pOb6VYmWWAQAAWMEdFwtqgoY+2rhTf129VR9t3Fm72rHZ4txTe3fWBScdo1N7d0llmAkNK+qk5Rt3asnnlSk5ftd22aavCcsAAACs4I6LSfG6Y8YUd4u7VED9kffhpQWszmGJN8LfiiueXpGS+pb639PKNQEAwAzuuJiQqDvmrXXbYy4VEG3kfXhpAaslqU4kLVJqinLrf894yyewDAAAwC4SlwTijfMPvxfujom2VECskffhpQXqj/OPxs3f7b4o526TldmgjTra94y1fALLAAAA7PIZht2l/tJDIBCQ3+9XVVWVcnNzHT/+Rxt36pKnlifc7oVrT9HwXp0sT4kNb7+96qB27T+sjm2z1LVtluSTvt1XrW/3Vuvuv6138isldPkpx2nwcR3Uzd9aP+zRQSvLd+mjL7+VFJomfErP0ERcs9+TybkAgPrs/v6mxiUBs10v4e2sLBVgZvu/rt5q+lhOObmwoy446Zja16f+oLNO/UHnBtuZ/Z5WrwkAALHwqCgBs10v3+6tbtBt1JjndxKdPgCAdMUdlwTCHUCxumOkUA1K5OMcJ9fiMXN+J+XT6QMASGPccUkgXndMWP0bLE6uxWPm/E6i0wcAkM5IXEyI1R0T6/d7ZLeRE4+NYp2/fU5LtWmV2WB7O2lHh5yWepxOHwBAmqOryILI7hiz3T7hbiOnzx/uzpGk5V/u1Ecbd0oy5G/dUvf8/fOEx/qvc09Q1cEjiuwU4k4LAKCx0FXUCCK7Y8x2+zi5Fk+s7pxTe3fWqb07W4qra262rj29l2OxuYl2awBoPkhcbErXtXjSNa5UibcUA4+9AKDpocbFpnC3T6z/r/fJnQ6ddI0rFRItxeBEcTQAIL2QuNiUrmvxpGtcTjO7FIOTM3UAAO4jcUlCuq7Fk65xOWlF+a64q2sbkiqqDmlF+a7GCwoAkHLUuCTp7P75GlPcLe2KQ9M1LqdYXYoBANA0kLg4IDPDp6FFHWuThBXlu9IiSWjKawQ1tyJkAECI64nLu+++q/vuu0+rVq1SRUWFXnvtNU2cONHtsCyhs6XxJVoKwafQo7GmUIQMAPie6zUu+/fv18CBA/Xoo4+6HYotdLa4o7kUIQMA6nL9jss555yjc845x+0wbEnU2eJTqLNlTHE3foGmQLgIuf7drm7c7QKAJsv1xMWq6upqVVdX174OBAKuxWKls6Wp1pq4rakXIQMA6vJc4lJSUqKZM2e6HYYkOlvSRVMuQgYA1OV6jYtVM2bMUFVVVe3Pli1bXIuFzhYAABqX5+64ZGVlKSsry+0wJNHZAgBAY/PcHZd0QmcLAACNy/XEZd++fVq9erVWr14tSSovL9fq1av11VdfuRyZOc1hvD4AAOnCZxiGq6vQLV26VKNGjWrw/uTJkzVv3ryE+wcCAfn9flVVVSk3NzcFEZpTEzTobAEAwCS7v79dr3EZOXKkXM6dHEFnCwAAqef6oyIAAACzSFwAAIBnkLgAAADPIHEBAACeQeICAAA8g8QFAAB4BokLAADwDBIXAADgGSQuAADAM1yfnJus8NTdQCDgciQAAMCs8O9tq9PzPZ+47N27V5JUUFDgciQAAMCqvXv3yu/3m97e9UUWkxUMBrVt2za1a9dOPl/zXNQwEAiooKBAW7ZscXWhyeaG6+4Ornvj45q7o6lfd8MwtHfvXnXv3l0ZGeYrVzx/xyUjI0PHHnus22Gkhdzc3Cb5hzvdcd3dwXVvfFxzdzTl627lTksYxbkAAMAzSFwAAIBnZN511113uR0EkpeZmamRI0eqRQvPP/3zFK67O7jujY9r7g6ue0OeL84FAADNB4+KAACAZ5C4AAAAzyBxAQAAnkHiAgAAPIPEBQAAeAaJi0c8+uijKiwsVHZ2toYNG6YVK1bE3f7ll1/WCSecoOzsbJ144on6+9//3kiRNi1Wrvu8efPk8/nq/GRnZzditN737rvv6vzzz1f37t3l8/n0l7/8JeE+S5cu1eDBg5WVlaXevXtr3rx5qQ+0ibF63ZcuXdrgz7rP59P27dsbKWLvKykp0ZAhQ9SuXTt17dpVEydO1IYNGxLux9/tJC6e8NJLL2natGm68847VVZWpoEDB2rcuHGqrKyMuv2HH36oSy65RFdffbU++eQTTZw4URMnTtTatWsbOXJvs3rdpdBo7oqKitqfzZs3N2LE3rd//34NHDhQjz76qKnty8vLNX78eI0aNUqrV6/WzTffrGuuuUaLFy9OcaRNi9XrHrZhw4Y6f967du2aogibnmXLlmnKlClavny53nrrLR02/7oAAASHSURBVB05ckRjx47V/v37Y+7D3+1HGUh7Q4cONaZMmVL7uqamxujevbtRUlISdfuLLrrIGD9+fJ33hg0bZvziF79IaZxNjdXr/swzzxh+v7+xwmvyJBmvvfZa3G1+85vfGP369avz3s9+9jNj3LhxqQytSTNz3ZcsWWJIMnbv3t1IUTV9lZWVhiRj2bJlMbfh7/YQ7rikucOHD2vVqlUaPXp07XsZGRkaPXq0Pvroo6j7fPTRR3W2l6Rx48bF3B4N2bnukrRv3z716NFDBQUFuuCCC/TZZ581RrjNFn/W3XXSSScpPz9fY8aM0QcffOB2OJ5WVVUlSerYsWPMbfjzHkLikua+/fZb1dTUKC8vr877eXl5MZ8nb9++3dL2aMjOde/Tp4+efvpp/fWvf9Xzzz+vYDCoESNG6Ouvv26MkJulWH/WA4GADh486FJUTV9+fr4ef/xxLViwQAsWLFBBQYFGjhypsrIyt0PzpGAwqJtvvlmnnnqq+vfvH3M7/m4PYfEDwCHDhw/X8OHDa1+PGDFCffv21RNPPKG7777bxcgAZ/Xp00d9+vSpfT1ixAht3LhR999/v5577jkXI/OmKVOmaO3atXr//ffdDsUTuOOS5jp37qzMzEx98803dd7/5ptv1K1bt6j7dOvWzdL2aMjOda+vZcuWGjRokP7973+nIkQo9p/13NxctW7d2qWomqehQ4fyZ92GqVOn6o033tCSJUt07LHHxt2Wv9tDSFzSXKtWrfTDH/5Qb7/9du17wWBQb7/9dp3/u480fPjwOttL0ltvvRVzezRk57rXV1NTozVr1ig/Pz9VYTZ7/FlPH6tXr+bPugWGYWjq1Kl67bXX9M4776ioqCjhPvx5P8rt6mAk9uKLLxpZWVnGvHnzjHXr1hnXXXed0b59e2P79u2GYRjG5ZdfbkyfPr12+w8++MBo0aKF8T//8z/G+vXrjTvvvNNo2bKlsWbNGre+gidZve4zZ840Fi9ebGzcuNFYtWqVcfHFFxvZ2dnGZ5995tZX8Jy9e/can3zyifHJJ58Ykoy5c+can3zyibF582bDMAxj+vTpxuWXX167/Zdffmnk5OQYv/71r43169cbjz76qJGZmWksWrTIra/gSVav+/3332/85S9/Mf71r38Za9asMW666SYjIyPDKC0tdesreM4NN9xg+P1+Y+nSpUZFRUXtz4EDB2q34e/26EhcPOLhhx82jjvuOKNVq1bG0KFDjeXLl9d+dsYZZxiTJ0+us/2f//xn4/jjjzdatWpl9OvXz/jb3/7WyBE3DVau+80331y7bV5ennHuuecaZWVlLkTtXeE22/o/4es8efJk44wzzmiwz0knnWS0atXK6Nmzp/HMM880etxeZ/W6z5492+jVq5eRnZ1tdOzY0Rg5cqTxzjvvuBO8R0W73pLq/Pnl7/bofIZhGI19lwcAAMAOalwAAIBnkLgAAADPIHEBAACeQeICAAA8g8QFAAB4BokLAADwDBIXAADgGSQuAADAM0hcAACAZ5C4AAAAzyBxAQAAnvH/APhvx8Dr8fcoAAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a014c9810>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a013f8410>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a013942d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a0131ef90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x7f6a012ccc50>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# graficamos la longitud de pétalo para el primer tipo de flores\n",
    "figure(1)\n",
    "scatter(0.1*randn(50,1),caracteristicas[1:50,1])\n",
    "scatter(1+0.1*randn(50,1),caracteristicas[51:100,1])\n",
    "scatter(2+0.1*randn(50,1),caracteristicas[101:150,1])\n",
    "ylabel(\"Longitud del Pétalo (cm)\")\n",
    "\n",
    "# graficamos la anchura del pétalo\n",
    "figure(2)\n",
    "\n",
    "# graficamos la longitud del sépalo\n",
    "figure(3)\n",
    "\n",
    "# graficamos la anchura del sépalo\n",
    "figure(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Al parecer, las dos características que mejor separan los tres tipos de flores fueron la _______ de _______ y la _______ de _______. La siguiente figura muestra como estas dos características diferencian los tres tipos de flores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a011c9d10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x7f6a0118b610>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(caracteristicas[1:50,1],caracteristicas[1:50,2])\n",
    "scatter(caracteristicas[51:100,1],caracteristicas[51:100,2])\n",
    "scatter(caracteristicas[101:150,1],caracteristicas[101:150,2])\n",
    "xlabel(\"Longitud del Pétalo (cm)\")\n",
    "ylabel(\"Anchura del Pétalo (cm)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Experimenta generando otras figuras donde grafiques otras características en los ejes x, y. Determina si alguna otra pareja de características sirve para diferenciar las tres especies de flores. Después procede a responder las siguientes preguntas con la persona sentada junto a tí.\n",
    "\n",
    "Preguntas para reflexionar:\n",
    "\n",
    "1. ¿Serán estas en realidad las mejores características para diferenciar estas especies de flores?\n",
    "2. ¿Cuales son las mayores desventajas de usar estas características para diferenciar especies de flores?\n",
    "3. ¿Qué otras características de flores podríamos utilizar para diferenciar distintas especies?\n",
    "4. ¿Por qué dijimos al inicio que un objeto, en este caso un tipo de flor, tiene un número infinito de características?\n",
    "5. Si salimos al campo y obtenemos medidas nuevas de una flor de cada especie que Fisher estudió, ¿serán nuestras medidas similares a las de Fisher? ¿Podrías estimar donde quedarían las medidas de flores nuevas en la última figura que generaste?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 1.2: Clasificación de Datos #\n",
    "\n",
    "Usando una base de datos como la de Fisher podemos diseñar un método para determinar si las características de una flor pertenecen a uno de los tres grupos. Un método capáz de hacer esto es llamado un Algoritmo de Clasificación. \n",
    "\n",
    "Usando los datos de Fisher, ¿cómo podríamos diseñar un método para determinar si las características de una flor pertenecen a una especie específica?\n",
    "\n",
    "Muchos algoritmos actuales para la clasificación de datos se enfocan en maximizar el producto interno entre dos vectores de la misma clase, donde uno de los vectores son las características de un objeto, y el otro vector son las características \"promedio\" de una clase específica.\n",
    "\n",
    "Estudiemos esto con las dos características de las flores que midió Fisher que determinamos mejor sirven para separar distintas especies de flores. En la siguiente figura se observan estas dos características."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fecac0e9bd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x7fecac2b7550>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# graficamos las dos características que más sirven para diferenciar las especies de flores.\n",
    "scatter(caracteristicas[1:50,1],caracteristicas[1:50,2], color=\"b\")\n",
    "scatter(caracteristicas[51:100,1],caracteristicas[51:100,2], color=\"r\")\n",
    "scatter(caracteristicas[101:150,1],caracteristicas[101:150,2], color=\"g\")\n",
    "xlabel(\"Longitud del Pétalo (cm)\")\n",
    "ylabel(\"Anchura del Pétalo (cm)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Al trabajar con datos como estos, el primer paso es hacer que los datos estén centrados al rededor de cero. Esto se logra extrayendo las características promedio de todos los datos (globales). El siguiente bloque muestra como hacer esto."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZBdv5+hMWRkRE5JXczuqeLN29FNVXqlXPrbYjvBkF2/n6GxZGRETklbfO6t5Y7VbkfJmjam4tHeHNKNjO19+wMCIiIq/UdGNvqOh8kaa5fRGDGQTb+fobVQ9fFxcX45dffkFlZSViY2Nx4403Ijw83NexERGRSajpxt5Q+xbtNc3tixjMINjO19/IvmL0888/46mnnkKbNm3Qrl073HXXXbj33nvRq1cvxMTEYMiQIfjwww9hswXGypdERHSVt87q3lgEC6b1mqZqbi0d4c0o2M7X38gqjJ544gl0794dx44dw/z58/HDDz+grKwM1dXVKC0txaeffoo777wTc+bMwc0334z9+/frHTcRETUiuZ3VPUlPSfe4npGeHeHNKNjO19/IKoyuvfZa/PTTT1i3bh0mTJiATp06oWnTprjmmmsQFxeHQYMG4YUXXsChQ4ewZMkSHD9+XO+4iYiokUl1Vl8/bj0y+mbAIjj/Y24RLMjom+F1HSM9O8KbUbCdrz+R9YzRggULZE94zz33qA6GiIjMTapre2qXVMwfOF/1ytd6doQ3o2A7X3/Bla+JiEgRqa7tYdeEIe32NF3mDkTBdr7+QHFhdO7cOcyZMwdbt27Fr7/+6vKw9fnz530WHBEREVFjUlwYTZgwAUePHsXkyZPRsmVLCIK6NxSIiIiIzEZxYVRYWIidO3eie/fuesRDRESNoLrqMnI+zEDR2SNof31HTBu7GGHhkeK+K9WqnxMyslu8VNxa49IyXs+cGJnvQKW4MOrcuTMuX76sRyxERNQI5rw1HotP58LqeC+5bDNmvbQc6XEjgT/8AUt3L3VqBjtr8yykp6R7fbPMyG7xmQWZHuO+Pel2TXF9fPhjzChQN17PnBiZ70CmuCVITk4Onn32WWzfvh3nzp1DeXm50xcREZnbsrOfwNrgKQirACw+sxGLdy12Ki4Asc/Z4l2LkVmQ6XFOI7vFZxZkSsY9et1oTXFN2DBB1Xg9c2JkvgOd4sKoWbNmKC8vx6BBgxAXF4fmzZujefPmaNasGZo3b65HjERE5APV1b9f/aHh46GOn10bvtdZunspqq9Uu2w3slt89ZVqLN29VPE4OXE5tqs5Lz1zYmS+g4HiwujBBx9EaGgo1qxZgy1btuDzzz/H559/jq1bt+Lzzz/XI0YiIvKBtzc8J/7C0zszgsQ+iFdgcr7McdluZLf4nC9zXK4UyeUtrt0ndqser2dOjMx3MFD8jNF3332Hr7/+Gp06ddIjHiIi0smxc0Vo23SQpjmKzhe5bDOyW7y7eJTyFFfppVJEIUrVeD1zYmS+g4HiK0a9evViyw8iIj/U7jr33e2VaN/CdQ4ju8W7i0cpT3HFN4lXPV7PnBiZ72CguDD629/+hhkzZmDVqlU4cOAAvvnmG6cvIiIyp0fvny/+wtNzRHaJfRD7nk3rNc1lu5Hd4qf1mubSn00ub3GlJKXUHad0vJ45MTLfwUBxYfSnP/0Jhw4dwqRJk3DbbbehR48euOWWW+q+ExGROYWFRVz9oWEB5PhZ4hmj9JR0t+sZGdktPuyaMKSnpHs9Tk1c9bcrHa9nTozMdzBQXBgdO3bM5eunn36q+05EROY24/rhsDQojCx2ICN2JDL6ZrhcgbEIFmT0zZBcx8jIbvFZQ7Ik414/br2muFbfv1rVeD1zYmS+A53ih6/btGmjRxxERNRI/j5lDebZ/uVx5ev5A+erWvnayG7xWUOyJOPWEteITiMwsqu68XrmxMh8BzLFhdGCBQvQsmVLTJo0yWn7ypUrcebMGTz11FM+C46IiPQRFh6JtP/vNff7rglD2u1pquY1slu8VNxa49IyXs+cGJnvQKX4Vtobb7yBzp07u2y/8cYbsWLFCp8ERURERGQExVeMSktLkZDg+gpgbGwsSkq4ZgIRka+YtkGo1QoUFgIlJUBCAtCvH2AxQVxEPqC4MEpOTsYXX3yBdu3aOW3/4osvkJiY6LPAiIiCmWkbhOblATNmACfqrbyclAQsWwak8oFf8n+Kb6VNmTIFaWlpePfdd/HLL7/gl19+wcqVK/Hkk09iypQpesToZPny5Wjbti0iIiLQp08f7Nu3z+Oxq1atgiAITl8REREejyciMgPTNgjNywPGjHEuigDg5Elxex4bl5L/U3zFKCMjA+fOncO0adNQXS02E4yIiMBTTz2F2bNn+zzA+tauXYv09HSsWLECffr0QXZ2NoYNG4bDhw8jLi7O7Zjo6GgcPny47mdBkFikg4jIYN4ahAoQkLYpDSM7jWzc22pWq3ilyO5mBUi7HRAEIC0NGDmSt9XIrym+YiQIAhYtWoQzZ85gz549+L//+z+cP38ec+bM0SM+J0uXLsWUKVPwyCOPoGvXrlixYgWioqKwcuVKyXjj4+Prvlq2bKl7nEREapm2QWhhoeuVovrsduD4cfE4Ij+m+IqRQ5MmTXDbbbf5MhZJ1dXVOHDggNNVqZCQEAwePBi7d3vugHzp0iW0adMGNpsNt956K1566SXceOONHo+vqqpCVVVV3c/l5eUAgJqaGtTU1NT9uv53ksZ8KcN8KRNo+SopK0FkSKSs45Ses6ZclZQAkd7jQkkJECC/F4H2Z0tvZsuX2jgEu93ddVFnjz32GJ577jkkJSV5nXDt2rW4cuUKHnzwQVUBeXLq1Cm0atUKu3btQkpKSt32zMxMbN++HXv37nUZs3v3bhw5cgQ333wzysrKsGTJEuzYsQPff/+9x3OZO3cu5s2b57J9zZo1iIry3mWZiIiIjFdZWYnx48ejrKwM0dHRssfJumIUGxuLG2+8EXfccQdGjBiBXr16ITExEREREfjtt9/www8/YOfOnfjggw+QmJiIN998U/WJ+FJKSopTEdW3b1906dIFb7zxBv7xj3+4HTN79mykp1/tu1NeXo7k5GQMHTq0LrE1NTUoKCjAkCFDEBoaqu9JBADmSxnmS5lAy5fVZkW317vh1MVTbp8zEiCgVdNW+GbqN4qfMdKUK6sV6NYNOHXK/XNGggC0agV8803APGMUaH+29Ga2fDnu+CglqzD6xz/+genTp+Ptt99GTk4OfvjhB6f9TZs2xeDBg/Hmm2/innvuURWIN9dffz0sFgtOnz7ttP306dOIj4+XNUdoaChuueUWHD161OMx4eHhCA8Pdzu24W+0u23kGfOlDPOlTKDkKxShWDRsEcasGwMATsWRo0HowmELERGu/g1bVbkKDQUWLRLfPgOciyPHSy0LFwIB+OZvoPzZaixmyZfaGGQ/fN2yZUs8++yz+Pbbb3H27Fl89dVX+OKLL3D48GH89ttvyM3N1a0oAoCwsDD07NkTW7Zsqdtms9mwZcsWp6tCUqxWK7799lu3C1QSEZmFaRuEpqYCubnilSGnwJLE7VzHiAKAqoevmzdvjubNm/s6Fq/S09MxceJE9OrVC71790Z2djYqKirwyCOPAAAeeughtGrVCgsWLAAA/P3vf8ftt9+ODh064MKFC1i8eDF++eUXPProo40eOxGREqZtEJqaKr6Sz5WvKUCpfivNCH/6059w5swZzJkzB6WlpejRowc2bdpU9wp+cXExQkKuXgT77bffMGXKFJSWlqJ58+bo2bMndu3aha5duxp1CkREspm2QajFAgwYYHQURLrwq8IIAKZPn47p06e73bdt2zann1955RW88sorjRAVERERBQLFCzwSERERBSq/u2JERBQ0tHSxdze2MWiJ2cSsNqv5nvciXagujM6cOVPXg6xTp06IjY31WVBEREFPSxd7qbF6FilaYjaxjw9/jBkFM5xatSRFJ2HZPcuMe0OQdKP4VlpFRQUmTZqExMRE9O/fH/3790diYiImT56MyspKPWIkIgouWrrYS42dMMH3scr5XG8xm9yEDRNc+tedLD+JMevGIO+Q/54Xuae4MEpPT8f27dvx0Ucf4cKFC7hw4QI2btyI7du3Y+bMmXrESEQUPLx1sQfELvZWq7qxjuN8SUvMJma1ifG6W4HcsS1tU1rdcRQYFBdG69evxzvvvIN7770X0dHRiI6Oxn333Ye33noLubm5esRIRBQ8tHSxlzMWACQab6uiJWYT231COk922HG8/DgKi/3rvEia4sKosrKybt2g+uLi4ngrjYhIq5IS9cfJHVtaKj8etbFoOc4kSi/Jy1PJRf86L5KmuDBKSUnBCy+8gN9//71u2+XLlzFv3jzZrTmIiMgDuS2L3B0nd6zM/pKyaYnZxOKbyMtTQlP/Oi+SpvittGXLlmHYsGFISkpC9+7dAQD/93//h4iICHz22Wc+D5CIKKj06ye+yXXypOcu9klJ7l+/lzMWAHz9H7FaYjaxlKQUfPbdZ3XNexsSICApOgn9WvvXeZE0xVeMbrrpJhw5cgQLFixAjx490KNHDyxcuBBHjhzBjTfeqEeMRETBw2IRX28HrhYyDo6fs7Pdv3YvZ6zjOF/SErOJ1V+nqGFx5Pg5+55srmcUYFStfB0VFYUpU6bg5Zdfxssvv4xHH30UkZGRvo6NiCg4aeliLzV29Wrfxyrnc73FbHKr71+NVtHO55UUnYTccblcxygAybqV9tFHH8me8I9//KPqYIiIqJaWLvaextpswKefmjNmExvRaQRGdh3Jla+DhKzCaNSoUbImEwQBVj9bp4KIyLS0dLF3N9Zm0xqRus8NAJYQCwa0HWB0GNQIZBVGtsb4y0RERERkMFXPGBEREREFIlVNZCsqKrB9+3YUFxejurraad8TTzzhk8CIiPyCnt3ky8qA4cOB4mKgdWvgk0+AmBh5n+tuv1zV1UBODlBUBLRvD0ybBoSFXZ1aotM8u9CTv1NcGH399de47777UFlZiYqKCrRo0QJnz55FVFQU4uLiWBgRUfDQs5t8hw5iYeJw/DjQrJlYqGRlSX+uVFzeirbMTGDpUue+ZrNmAenpQFYW8g7lYcYm953mAXjcx7e3yF8ovpX25JNPYsSIEfjtt98QGRmJPXv24JdffkHPnj2xZMkSPWIkIjIfPbvJNyyK6isqAkaP9vy5mZme45owQfpzMzOBxYtdm71arcDixcibPQpj1o1x22l+9LrRGL1uNLvQk99TXBgdPHgQM2fOREhICCwWC6qqqpCcnIysrCw888wzesRIRGQuenaTLyvzXBRJsdvFr6VLpeMC3MdVXS2O9cAqADOqNkp2mncbFrvQk59RXBiFhoYiJEQcFhcXh+LiYgBATEwMjh8/7tvoiIjMSM9u8sOHq48LkC7GHMXRbjdd43NyJMcWtgFOxKgLiV3oyZ8ofsbolltuwf79+9GxY0fcddddmDNnDs6ePYvVq1fjpptu0iNGIiJz0bObfO1/bOqq1E3XeC9XqUqaaP9YdqEnf6D4itFLL72EhNoOyS+++CKaN2+OqVOn4syZM3jjjTd8HiARkeno2U2+dWvlY5SKd9M1vn17ySEJl7R/LLvQkz9QfMWoV69edb+Oi4vDpk2bfBoQEZHp6dlN/pNPxLfP1LJYxBWuPcUFACkprvumTRPfPvNwO63fL0BSGXAyRpB8psgddqEnf6L4itGgQYNw4cIFl+3l5eUYNGiQT4IiIjI1PbvJx8R4vXrj8XMFQXytXiouwH1cYWFXx7phsQPLwkeKU3noNC+1j13oyV8oLoy2bdvmsqgjAPz+++8oVPOgIRGRP9Kzm/zRo56Lo/btgfXrPX9uVpbnuFavlv7crCwgI8O1cLJYgIwMpC7IR+64XLed5tePW4/149azCz35Pdm30r755pu6X//www8orffwntVqxaZNm9Cq4V9EIqJApmc3+aNHpVe+lvpcT3HZbMCnn0p/blYWMH++x5WvU7ukYmQnz53mpfYR+QPZhVGPHj0gCAIEQXB7yywyMhKvvvqqT4MjIjI9PbvJx8QAO3eq+1x3++U2BA8LE9dh8jS1RKd5dqEnfye7MDp27BjsdjtuuOEG7Nu3D7GxsXX7wsLCEBcXB4uv+gMRERERGUB2YdSmTRsAgE3uf3EQERER+RnFr+sDwOpDJ0olAAAgAElEQVTVq7FixQocO3YMu3fvRps2bfDKK6/ghhtuwMiRI30dIxGRNt460RvFSxd7Sd7Oyd3c9d9MM2tOdGK1WfnsE8ni9a20zz77DGVlZXU/v/7660hPT8d9992HCxcuwFq75kXz5s2RnZ2tX6RERGrk5QFt2wIDBwLjx4vf27bV1uTVFzIzgago4MkngddeE79HRYnbvfF2Tp7mnjNH3P/xx+bMiU7yDuWh7bK2GPjeQIzPG4+B7w1E22Vt2diW3PJaGJWWluKOO+7Aidq+QK+++ireeustPPvss07PFPXq1QvffvutfpESESmVl+e50/yYMcYVAl662EsWR97OadQoz3M71l6aMMF8OdFJ3qE8jFk3BifKnc/3ZPlJjFk3hsURufBaGE2cOBHz5s3DsGHDAIgPYd9yyy0ux4WHh6OiosL3ERIRqWG1AjNmSHeaT0uTbrqqBy9d7AGI+92sFyfrnDZu9B6D2XKiE6vNihmbZrhdqduxLW1TGqy2wDhf8g1ZCzyOHj0aH330EQCgXbt2OHjwoMsxmzZtQpcuXXwbHRGRWoWFrldF6rPbgePHxeMak5cu9gDE/Tk5rtvlnJMWRuVEJ4XFhS5Xiuqzw47j5cdRWBwY50u+Ifvh6/a1q7Cmp6fj8ccfx++//w673Y59+/bh/fffx4IFC/D222/rFigRkSJyO9vLPc5XvHSxlzyusWJt7JzopOSivPOQexwFB8VvpT366KOIjIzEc889h8rKSowfPx6JiYlYtmwZHnjgAT1iJCJSTm5ne7nH+YqcPmiejmusWBs7JzpJaCrvPOQeR8FBca80AHjwwQdx5MgRXLp0CaWlpThx4gQmT57s69iIiNTr10/sD9awmaqDIADJyeJxjWnaNO+vxVss4nENyTknOcyWE530a90PSdFJLo1tHQQISI5ORr/WgXG+5BuKCqM9e/bg2WefRUZGBjZt2oSoqCjExcXpFRsRkXoWy9W3sDx1ms/Obvy1e7x0sQcg7ne3npGcc5K7lpyZcqITS4gFy+4R89WwOHL8nH1PNtczIieyC6Pc3FzccccdWLZsGd5++20MHz4cS5Ys0TM2IiJtUlM9d5rPzRX3G8FLF3tkZXke6+2c8vM9zz1jhvjr1avNlxOdpHZJRe64XLSKdj7fpOgk5I7LRWqXwDpf0k72M0YLFizAlClTsHz5clgsFixYsAAvvfQSZs2apWd8RETaeOo0b/RVES9d7CV5OydPcwsC8OmnwIgR5syJTlK7pGJkp5Fc+ZpkkV0YHT58GGvXrq1b1HHmzJmYM2cOfv31V95OIyJz89aJ3iheuthL8nZO7uauqZE/PsBYQiwY0HaA0WGQH5B9K62yshLR0dF1P4eFhSEiIgKXLl3SJTAiIiKixqbodf23334bTZo0qfv5ypUrWLVqFa6//vq6bU888YTvoiMiIiJqRLILo9atW+Ott95y2hYfH4/Vq1fX/SwIAgsjIlLHyG7vly+LDywfOQJ07Cj2GouMFPe561Jf/zkgLfu9nbPUfiPzRRTAZBdGP//8s45hEFFQy8sT35iq3+4iKUl8NV3vt6RGjXLuL7Z5M7B8ufhw8h/+IPYtq9/CY9Ys8XX6rCyx2ava/bffLn3OUjkBjMsXUYBTvPI1EZFPObrFN+zz5ej2rucr5A2Lovo8bbdaxStK27YB+/er3++O45xnzQKWLHGfk9GjpccG4Cv3RI1J1crXREQ+IadbvF7d3i9flteJ3hN3RY+S/e44znnpUumcSI3VK19EQYKFEREZR063eL26vWdk+H5OX7Db1Rc2euaLKEiwMCIi48jt4q5Ht/cjR3w/p1nokS+iIMHCiIiMI7eLux7d3jt29P2cZqFHvoiChKyHr8vLy2VPWH8RSCIiSY5u8SdPun9+RhDE/Xp0e1+8WHz7zGwEAQgJUXc7Tc98EQUJWVeMmjVrhubNm0t+OY4hIpJNTrd4vbq9R0bK70Tvzm23adsPeD7n9HTx1572S43VK19EQULWFaOtW7fqHQcRBStHt3h36/JkZ+v76nl+vudX9j2tY2SxSK9TJHe/p3WMHOcstR8wJl9EQUBWYXTXXXfpHQcRBTNv3eL1lJ8vvfK1uy71jpWrPXWxl7tf6py95cSofBEFOFULPBYWFuKNN97ATz/9hA8//BCtWrXC6tWr0a5dO9x5552+jpGIgoGR3d4jI4HXXnO/z12Xel/t93bOUvuNzBdRAFP8Vtr69esxbNgwREZG4quvvkJVVRUAoKysDC+99JLPAyQiIiJqLIoLo/nz52PFihV46623EBoaWrf9jjvuwFdffeXT4IiIiIgak+JbaYcPH0b//v1dtsfExODChQs+CYqIyKe0dLHXOrdeY9XMTUReKb5iFB8fj6NHj7ps37lzJ2644QafBCVl+fLlaNu2LSIiItCnTx/s27dP8vgPP/wQnTt3RkREBLp164ZPP/1U9xiJyETy8oC2bYGBA4Hx48XvbduK2+Xs1zK3XmPVzv3xx9rnJgpwigujKVOmYMaMGdi7dy8EQcCpU6fw73//G7NmzcLUqVP1iLHO2rVrkZ6ejhdeeAFfffUVunfvjmHDhuHXX391e/yuXbvw5z//GZMnT8bXX3+NUaNGYdSoUfjuu+90jZOITCIvT+w437Afm6MTfWam9H6pIsXb3HqN9UZq7gkT1M9LFCzsCtlsNvv8+fPt1157rV0QBLsgCPaIiAj7c889p3QqxXr37m1//PHH6362Wq32xMRE+4IFC9weP27cOPvw4cOdtvXp08f+17/+VfZnlpWV2QHYy8rK6rZVV1fb8/Pz7dXV1QrPIDgxX8owX8p4zNeVK3Z7UpLdLq6p7f7LYvG8TxDs9uRkcZ6GvM2t11hvvMxdHRUl5uryZeVzByH+XVTGbPly9++3HIqfMRIEAc8++ywyMjJw9OhRXLp0CV27dkWTJk18X7XVU11djQMHDmD27Nl120JCQjB48GDs3r3b7Zjdu3cjPT3daduwYcOQn5/v8XOqqqrq3rQDrrZDqampQU1NTd2v638nacyXMsyXMh7ztXMncO7c1fWI1Dh7FtixA2i4DImcufUY642XuWsiIsTvu3bxmSMZ+HdRGbPlS20cgt3urkGR+Zw6dQqtWrXCrl27kJKSUrc9MzMT27dvx969e13GhIWF4b333sOf//znum05OTmYN28eTp8+7fZz5s6di3nz5rlsX7NmDaKionxwJkRERKS3yspKjB8/HmVlZYr6uMq6YpSqYIn5PF88OGig2bNnO11lKi8vR3JyMoYOHVqX2JqaGhQUFGDIkCFOSxaQe8yXMsyXMh7ztXMnMHy49g/45BP3V33kzO3rsd54mbsmMhIFK1diSNOmCOUVI6/4d1EZs+XLccdHKVmFUUxMTN2v7XY7NmzYgJiYGPTq1QsAcODAAVy4cEFRAaXU9ddfD4vF4nKl5/Tp04iPj3c7Jj4+XtHxABAeHo7w8HCX7aGhoS6/0e62kWfMlzLMlzIu+erfH7juOvGhY08Xxi0WwGZzv9/Rqb5/f9dX6L3NrddYb+TMDSC0b1/+2VKAfxeVMUu+1MYg6620d999t+6rZcuWGDduHI4dO4a8vDzk5eXhp59+wgMPPIDrr79eVRByhIWFoWfPntiyZUvdNpvNhi1btjjdWqsvJSXF6XgAKCgo8Hg8EQUQiwVYtkz8tbtO9IIgNnP1tB/w3Kne29x6jfVGztyO44jILcWv669cuRKzZs2Cpd5fLIvFgvT0dKxcudKnwTWUnp6Ot956C++99x4OHTqEqVOnoqKiAo888ggA4KGHHnJ6OHvGjBnYtGkTXn75Zfz444+YO3cuvvzyS0yfPl3XOInIJFJTgdxcoFUr5+1JSeL2rCzp/VJXwb3NrddYb6TmXr1a/bxEQULxW2lXrlzBjz/+iE6dOjlt//HHH2Gz2XwWmDt/+tOfcObMGcyZMwelpaXo0aMHNm3ahJYtWwIAiouLERJytdbr27cv1qxZg+eeew7PPPMMOnbsiPz8fNx00026xklEJuKtS723/Vrm1mus2rltNoCL3BJJUlwYPfLII5g8eTKKiorQu3dvAMDevXuxcOHCuis3epo+fbrHKz7btm1z2TZ27FiMHTtW56iIyNS0dLHXOrdeY9XMrfN/vBIFAsWF0ZIlSxAfH4+XX34ZJSUlAICEhARkZGRg5syZPg+QiIiIqLEoLoxCQkKQmZmJzMzMulfhlKwPQERERGRWiguj+lgQEZmUnl3bzcpqBb74wv05B2M+iEgVTYUREZlQXh4wY4ZzE9GkJPE1bh3XGjNct27A0aNXf3acMxCc+SAiVRS/rk9EJqZn13az+vhj8fvJk87bT54ERo8Wv4IpH0SkCQsjokBhtYpXRtyteOzYlpYmHhcorFbgqafc75NqAxmo+SAizVgYEQWKwkLXKyP12e3A8ePicYGisND1SpFcgZgPItJM1TNGFRUV2L59O4qLi1FdXe2074knnvBJYESkUO3yGT47zh/44lwCKR9EpJniwujrr7/Gfffdh8rKSlRUVKBFixY4e/YsoqKiEBcXx8KIyCgJCb49zh/44lwCKR9EpJniW2lPPvkkRowYgd9++w2RkZHYs2cPfvnlF/Ts2RNLlizRI0YikqNfP/Ftq4bNQx0EAUhOFo8LFP36ufYEkysQ80FEmikujA4ePIiZM2ciJCQEFosFVVVVSE5ORlZWFp555hk9YiQiOfTs2m5WFguwaJH4a6lu8sGSDyLSTHFhFBoaWteoNS4uDsXFxQCAmJgYHD9+3LfREZEyenZtN6sRI8TviYnO25OSgPXrxa9gygcRaaL4GaNbbrkF+/fvR8eOHXHXXXdhzpw5OHv2LFavXs2u9URmoGfXdjP79ltgzx735xyM+SAiVRQXRi+99BIuXrwIAHjxxRfx0EMPYerUqejYsSNWrlzp8wCJSAU9u7abldQ5B2M+iEgVRYWR3W5HXFxc3ZWhuLg4bNq0SZfAiIiIiBqbomeM7HY7OnTowGeJiIiIKCApumIUEhKCjh074ty5c+jYsaNeMRGRmVVXAzk5QFER0L49MG0aEBam/1irVb/nhKTm1vNzich0FD9jtHDhQmRkZOD111/nw9ZEwSYzE1i61Lm/2KxZQHo6kJWl39i8PLEPXP2WJ0lJ4vIEjrfS1JKaG/C8j2+0EQUkxYXRQw89hMrKSnTv3h1hYWGIjIx02n/+/HmfBUdEJpKZCSxe7Lrdar263VOBo2VsXh4wZoxrU9iTJ8Xtubnqr+BIzT16tPsx9T+XxRFRwFFcGGVnZ+sRBxGZWXW1eLVHytKlwPz5rrfGtIy1WsUrNg0LF0DcJgjA00+7L7q88Ta3J47PTUsTlwHgbTWigKK4MJo4caIecRCRmeXkON8Cc8dqFY9LS/Pd2MJC59tYDdnt0vuleJtbit0OHD8uzsFlAIgCiuLCyLHStSetW7dWHQwRmVRRkfrjtIwtKZE3Vg1fzK1nfERkCMWFUdu2bSF4alIJwOrtvwyJyP+0b6/+OC1jExLkjVXDF3PrGR8RGUJxr7Svv/4aX331Vd3X3r17sWLFCvzhD3/Ahx9+qEeMRGS0adO8P0tjsYjH+XJsv37iW2Ce/mNMEMT9anibW4ogAMnJ4hxEFFAUF0bdu3d3+urVqxemTJmCJUuW4J///KceMRKR0cLCxNfqpaSnu1+TSMtYi+Xqa/MNCxjHzwsXSs/tiZy5pfZlZ/PBa6IApLgw8qRTp07Yv3+/r6YjIrPJygIyMlyLAYtF3C61FpGWsamp4qvxrVo5b09KErdrWcdIau7168UvT5/LV/WJApLiZ4zKy8udfrbb7SgpKcHcuXO5GjZRoMvKEl+rV7N6tZaxqaniq/HuVqCuqdF2TlJzA9L7iCjgKC6MmjVr5vLwtd1uR3JyMj744AOfBUZEJhUW5vpafWOMtVj0ezVeam49P5eITEdxYbR161ann0NCQhAbG4sOHTrgmmsUT0dERERkGoormbvuukuPOIiIiIgMp+oSz5EjR7B161b8+uuvsNlsTvvmzJnjk8CIiIiIGpviwuitt97C1KlTcf311yM+Pt7peSNBEFgYERERkd9SXBjNnz8fL774Ip566ik94iEiIiIyjOJ1jH777TeMHTtWj1iIiIiIDKW4MBo7diw2b96sRyxEREREhpJ1K61+q48OHTrg+eefx549e9CtWzeEhoY6HfvEE0/4NkIiIiKiRiKrMHrllVecfm7SpAm2b9+O7du3O20XBIGFEREREfktWYXRsWPH9I6DiIiIyHA+ayJLRERE5O8UF0ajR4/GokWLXLZnZWXxbTUiIiLya4oLox07duC+++5z2X7vvfdix44dPgmKiIiIyAiKC6NLly4hLCzMZXtoaCjKy8t9EhQRERGRERQXRt26dcPatWtdtn/wwQfo2rWrT4IiIiIiMoLiliDPP/88UlNTUVRUhEGDBgEAtmzZgvfffx8ffvihzwMkIiIiaiyKC6MRI0YgPz8fL730EnJzcxEZGYmbb74Z//vf/3DXXXfpESMRERFRo1BcGAHA8OHDMXz4cF/HQkRERGQoVYURAFRXV+PXX3+FzWZz2t66dWvNQREREREZQXFhdOTIEUyaNAm7du1y2m632yEIAqxWq8+CIyIiImpMigujhx9+GNdccw3+85//ICEhAYIg6BEXERERUaNTXBgdPHgQBw4cQOfOnfWIh4iIiMgwitcx6tq1K86ePatHLERERESGUlwYLVq0CJmZmdi2bRvOnTuH8vJypy8iIiIif6X4VtrgwYMBAHfffbfTdj58TURERP5OcWG0detWPeIgIiIiMpziwkhqdevvvvtOUzBERERERlL8jFFDFy9exJtvvonevXuje/fuvoiJiIiIyBCqC6MdO3Zg4sSJSEhIwJIlSzBo0CDs2bPHl7ERERERNSpFt9JKS0uxatUqvPPOOygvL8e4ceNQVVWF/Px8dO3aVa8YiYiIiBqF7CtGI0aMQKdOnfDNN98gOzsbp06dwquvvqpnbERERESNSnZh9N///heTJ0/GvHnzMHz4cFgsFj3jcnH+/Hk8+OCDiI6ORrNmzTB58mRcunRJcsyAAQMgCILT12OPPdZIERMREZG/kV0Y7dy5ExcvXkTPnj3Rp08fvPbaa426AvaDDz6I77//HgUFBfjPf/6DHTt24C9/+YvXcVOmTEFJSUndV1ZWViNES0RERP5I9jNGt99+O26//XZkZ2dj7dq1WLlyJdLT02Gz2VBQUIDk5GQ0bdpUlyAPHTqETZs2Yf/+/ejVqxcA4NVXX8V9992HJUuWIDEx0ePYqKgoxMfHy/6sqqoqVFVV1f3sWM27pqYGNTU1db+u/52kMV/KMF/KMF/yMVfKMF/KmC1fauMQ7Ha7Xe2HHj58GO+88w5Wr16NCxcuYMiQIfjoo4/UTufRypUrMXPmTPz22291265cuYKIiAh8+OGHuP/++92OGzBgAL7//nvY7XbEx8djxIgReP755xEVFeXxs+bOnYt58+a5bF+zZo3kOCIiIjKPyspKjB8/HmVlZYiOjpY9TvECj/V16tQJWVlZWLBgAT7++GOsXLlSy3QelZaWIi4uzmnbNddcgxYtWqC0tNTjuPHjx6NNmzZITEzEN998g6eeegqHDx9GXl6exzGzZ89Genp63c/l5eVITk7G0KFD6xJbU1ODgoICDBkyBKGhoRrPLvAxX8owX8owX/IxV8owX8qYLV9q+7dqKowcLBYLRo0ahVGjRika9/TTT2PRokWSxxw6dEh1XPWfQerWrRsSEhJw9913o6ioCO3bt3c7Jjw8HOHh4S7bQ0NDXX6j3W0jz5gvZZgvZZgv+ZgrZZgvZcySL7Ux+KQwUmvmzJl4+OGHJY+54YYbEB8fj19//dVp+5UrV3D+/HlFzw/16dMHAHD06FGPhREREREFL0MLo9jYWMTGxno9LiUlBRcuXMCBAwfQs2dPAMDnn38Om81WV+zIcfDgQQBAQkKCuoCJiIgooGnuldYYunTpgnvuuQdTpkzBvn378MUXX2D69Ol44IEH6t5IO3nyJDp37ox9+/YBAIqKivCPf/wDBw4cwM8//4yPPvoIDz30EPr374+bb77ZyNMhIiIik/KLwggA/v3vf6Nz5864++67cd999+HOO+/Em2++Wbe/pqYGhw8fRmVlJQAgLCwM//vf/zB06FB07twZM2fOxOjRo/Hxxx8bdQpERERkcobeSlOiRYsWWLNmjcf9bdu2Rf2VB5KTk7F9+/bGCI2IiIgChN9cMSIiIiLSm99cMSJzsFqBwkKgpARISAD69QMauW0eERGRblgYkWx5ecCMGcCJE1e3JSUBy5YBqanGxUVEROQrvJVGsuTlAWPGOBdFAHDypLhdYjFxIiIiv8HCiLyyWsUrRe666jm2paWJxxEREfkzFkbkVWGh65Wi+ux24Phx8TgiIiJ/xsKIvCop8e1xREREZsXCiLyS20GFnVaIiMjfsTAir/r1E98+EwT3+wUBSE4WjyMiIvJnLIzIK4tFfCUfcC2OHD9nZ3M9IyIi8n8sjEiW1FQgNxdo1cp5e1KSuJ3rGBERUSDgAo8kW2oqMHIkV74mIqLAxcKIFLFYgAEDjI6CiIhIH7yVRkRERFSLhRERERFRLd5KI5+xWvn8ERER+TcWRuQTeXliP7X6rUOSksTX/EeMMC4uIiIiJVgYkWZ5ecCYMa5NZk+eFLfn5vLKERER+Qc+Y0SaWK3ilaKGRRFwddvTTzduTERERGqxMCJNCgudb581ZLdL7yciIjITFkakSUmJ0REQERH5Dgsj0iQhwegIiIiIfIeFEWnSr5/49lnD5rIOgiDuJyIi8gcsjEgTi0V8JR9wLY4cPy9c2LgxERERqcXCiDRLTRVfyW/Vynl7UpK4nesYERGRv+A6RuQTqanAyJHuV76uqTE6OiIiInlYGJHPWCzAgAFGR0FERKQeb6URERER1WJhRERERFSLt9ICkJYu95cvAxkZwJEjQMeOwOLFQGSkvLm1fK6WsURERL7CwijASHW5T02VHjtqFLBx49WfN28Gli8XH6rOz5eeG/C8z9tbaVpiJiIi8iUWRgFETpd7T4VGw6Kovo0bgd69gS+/dD/36NHux9X/XE9Xf7TETERE5Gt8xihAyOlyn5YmHtfQ5cueiyKH/ful53bHse/pp30fMxERkR5YGAUIOV3ujx8Xj2soI0O/uOx2z3FpiZmIiEgPLIwChNwu9+6OO3LEt7HIpSVmIiIiPbAwChByu9y7O65jR9/GIpeWmImIiPTAwihAyOlyn5wsHtfQ4sX6xSUIYlzuaImZiIhIDyyMAoScLvfZ2e7fDouMFF/Jl3LbbeI8nuaW+tyFC30fMxERkR5YGAUQb13upV57z8/3XByNHAns2+d57vXrxS9Pnyu1jpGWmImIiHyN6xgFGKku997k50uvfO1tbk/7amr0i5mIiMiXWBgFIC1d7iMjgddeUze3ls/VMpaIiMhXeCuNiIiIqBYLIyIiIqJavJUWgKqrgZwcoKgIaN8emDYNCAsT90k9QwRo63KvZSwREZEZsDAKMJmZwNKlzv3FZs0C0tOB//f/nHuibd4MLF8uPvicn6+ty73UWKm30oiIiMyEhVEAycx0v1ij1Sq9iOPGjUDv3sCXX6rrcp+XJx4jNZZXjoiIyB/wGaMAUV0tXilSa/9+dV3urVbxSpHU2KefVh8XERFRY2JhFCByctwXLr4g1eW+sND59pm7sVL7iYiIzISFUYAoKtL/M9x1uXe3jYiIyF+xMAoQ7dvr/xnuuty720ZEROSvWBgFiGnT9HvAWarLfb9+4ttnDZvA1h+blKRPXERERL7GwihAhIWJr+SrddttYhGjtMu9xSK+kl//2IZjFy5UHxcREVFjYmEUQLKyxMUbGxYwFou4feRI9+NGjgT27VPf5T41VXos1zEiIiJ/wXWMAkxWFjB/vrqVr7V0uZcaW1Oj3/kSERH5EgujABQWJq475E5kJPDaa57Haulyr2UsERGRGfBWGhEREVEtFkYGsVqBbduA998XvytZnLG6WnwY+m9/E79XVzvvv3QJuP9+4Oabxe+XLl3dV1oKxMcDERHi99JS57FnzgDt2gFNmojfz5xx3l9WBtx5J9C6tfi9rMw356RlLBERka/wVpoBtDRrlWoSm5Ul9jzbv//qvm+/BZo2Fd86+/57oLLy6r7Tp8VngaKigIoKoFkz50KnogKIiwNiYoALF4AOHZwXkjx+XBzTvr342WqbyGrJBxERkS/5zRWjF198EX379kVUVBSaNWsma4zdbsecOXOQkJCAyMhIDB48GEeOHNE5UmmOhqsN22Q4Gq7m5Xke62gS2/BqiqNJbHy8c1FU3/79zkVRfZWV4qv19Yui+srKgJAQz6trFxUBo0d7PqePP/Z8TlryQURE5Gt+UxhVV1dj7NixmDp1quwxWVlZ+Oc//4kVK1Zg7969uPbaazFs2DD8/vvvOkbqmZyGq56atcppEnv6tPYYPXEXs9wxnprIaskHERGRHvymMJo3bx6efPJJdOvWTdbxdrsd2dnZeO655zBy5EjcfPPN+Ne//oVTp04hPz9f52jdk9Nw1VOzVj2bxOpJqomslnwQERHpIWCfMTp27BhKS0sxePDgum0xMTHo06cPdu/ejQceeMDtuKqqKlRVVdX9XF5eDgCoqalBTe2CPA2/y1VScnXNIG/HNZz655/ljTWjyEj3+dKSj0Cm9s9XsGK+5GOulGG+lDFbvtTGIdjtam6SGGfVqlVIS0vDhQsXJI/btWsX7rjjDpw6dQoJ9Tqdjhs3DoIgYO3atW7HzZ07F/PmzXPZvmbNGkRFRWkLnoiIiBpFZWUlxo8fj7KyMkRHR8seZ+gVo6effhqLFi2SPAd36VYAABU7SURBVObQoUPo3LlzI0UEzJ49G+n1mo6Vl5cjOTkZQ4cOrUtsTU0NCgoKMGTIEISGhsqe22oFunUDTp1y/1yNIIhtNb75xnW16epq8eFqf7udJgjADTfUYP5813xpyUcgU/vnK1gxX/IxV8owX8qYLV+OOz5KGVoYzZw5Ew8//LDkMTfccIOquePj4wEAp0+fdrpidPr0afTo0cPjuPDwcISHh7tsDw0NdfmNdrdNSmgosGiR+LYV4FwM1G+4GhHhfuzUqeLbZ560bKnfA9iC4P0B7IbHOM7JcQGuYb605CMYKP3zFeyYL/mYK2WYL2XMki+1MRj68HVsbCw6d+4s+RXmaPKlULt27RAfH48tW7bUbSsvL8fevXuRkpLiq1NQzFvDVal1e7w1iS0tFdcrcue228T1ityJihKLkpgY9/tjYgCbTVyvyJ327YH169U1kdWSDyIiIl/zm4evi4uLcf78eRQXF8NqteLgwYMAgA4dOqBJkyYAgM6dO2PBggW4//77IQgC0tLSMH/+fHTs2BHt2rXD888/j8TERIwaNcrIU9HUrNVbk9h9+8SVridMuLp/9WpxJWtALJ569BAXbGzWDDh4ULxFB4jbzpwRF4k8cwaIjRXni40V9x89Kq5pNHw4UFwsrn79ySdXCyq1TWS15IOIiMiX/KYwmjNnDt577726n2+55RYAwNatWzGgtnPp4cOHUVZvlcLMzExUVFTgL3/5Cy5cuIA777wTmzZtQoQJ7s1oabgq1SQWEIugDRvc73PXBqS+2Fjg2DHP+2NigJ073e9jA1oiIvJ3flMYrVq1CqtWrZI8puELdoIg4O9//zv+/ve/6xgZERERBQq/WeCRiIiISG9+c8Uo2Fit+jxzU13t+fkkOfuJiIgCGQsjE9Kr23xmpthvrf5aSLNmAenp4kPd3vYTEREFOhZGJuPoNt9wzSBHt3m1r7BnZrpfA8lqFbdv2wbs3+95P8DiiIiIAh+fMTIRvbrNV1eLV4KkuCuK6lu6VJyHiIgokLEwMhG9us3n5GhvJWK1ivMQEREFMhZGJlJS4tvjHIqKlMei5zxERERmxcLIROq1dPPJcQ6eWnko5at5iIiIzIqFkYn06ye+feZooNqQIADJyeJxSkybpv1Vf4tFnIeIiCiQsTAyEYtFfCUfcC2OHD9nZysvcsLCxFfupXhqPuuQns71jIiIKPCxMDIZvbrNZ2UBGRmuRZXFIm7ft096P1/VJyKiYMB1jExIr27zWVnA/PmeV7b2tp+IiCjQsTAyKb26zYeFiWshqd1PREQUyHgrjYiIiKgWCyMiIiKiWiyMiIiIiGqxMCIiIiKqxcKIiIiIqBYLIyIiIqJaLIyIiIiIarEwIiIiIqrFwoiIiIioFgsjIiIiolpsCeKF3W4HAJSXl9dtq6mpQWVlJcrLyxEaGmpUaH6D+VKG+VKG+ZKPuVKG+VLGbPly/Lvt+HdcLhZGXly8eBEAkJycbHAkREREpNTFixcRExMj+3jBrrSUCjI2mw2nTp1C06ZNIQgCALEKTU5OxvHjxxEdHW1whObHfCnDfCnDfMnHXCnDfCljtnzZ7XZcvHgRiYmJCAmR/+QQrxh5ERISgqSkJLf7oqOjTfGb7y+YL2WYL2WYL/mYK2WYL2XMlC8lV4oc+PA1ERERUS0WRkRERES1LHPnzp1rdBD+yGKxYMCAAbjmGt6NlIP5Uob5Uob5ko+5Uob5UiYQ8sWHr4mIiIhq8VYaERERUS0WRkRERES1WBgRERER1WJhRERERFSLhRERERFRLRZGGv3xj39E69atERERgYSEBEyYMAGnTp0yOixT+vnnnzF58mS0a9cOkZGRaN++PV544QVUV1cbHZppvfjii+jbty+ioqLQrFkzo8MxneXLl6Nt27aIiIhAnz59sG/fPqNDMq0dO3ZgxIgRSExMhCAIyM/PNzok01qwYAFuu+02NG3aFHFxcRg1ahQOHz5sdFim9frrr+Pmm2+uW/E6JSUF//3vf40OSzUWRhoNHDgQ69atw+HDh7F+/XoUFRVhzJgxRodlSj/++CNsNhveeOMNfP/993jllVewYsUKPPPMM0aHZlrV1dUYO3Yspk6danQoprN27Vqkp6fjhRdewFdffYXu3btj2LBh+PXXX40OzZQqKirQvXt3LF++3OhQTG/79u14/PHHsWfPHhQUFKCmpgZDhw5FRUWF0aGZUlJSEhYuXIgDBw7gyy+/xKBBgzBy5Eh8//33RoemCtcx8rGPPvoIo0aNQlVVFUJDQ40Ox/QWL16M119/HT/99JPRoZjaqlWrkJaWhgsXLhgdimn06dMHt912G1577TUAYsPn5ORk/O1vf8PTTz9tcHTmJggCNmzYgFGjRhkdil84c+YM4uLisH37dvTv39/ocPxCixYtsHjxYkyePNnoUBTjFSMfOn/+PP7973+jb9++LIpkKisrQ4sWLYwOg/xMdXU1Dhw4gMGDB9dtCwkJweDBg7F7924DI6NAVFZWBgD8/yoZrFYrPvjgA1RUVCAlJcXocFRhYeQDTz31FK699lpcd911KC4uxsaNG40OyS8cPXoUr776Kv76178aHQr5mbNnz8JqtaJly5ZO21u2bInS0lKDoqJAZLPZkJaWhjvuuAM33XST0eGY1rfffosmTZogPDwcjz32GDZs2ICuXbsaHZYqLIzcePrppyEIguTXjz/+WHd8RkYGvv76a2zevBkWiwUPPfQQgukOpdJ8AcDJkydxzz33YOzYsZgyZYpBkRtDTb6IyBiPP/44vvvuO3zwwQdGh2JqnTp1wsGDB7F3715MnToVEydOxA8//GB0WKrwGSM3zpw5g3Pnzkkec8MNNyAsLMxl+4kTJ5CcnIxdu3b57WVEpZTm69SpUxgwYABuv/12rFq1CiEhwVWfq/nzxWeMnFVXVyMqKgq5ublOz8lMnDgRFy5c4FVbL/iMkTzTp0/Hxo0bsWPHDrRr187ocPzK4MGD0b59e7zxxhtGh6KY/7a/1VFsbCxiY2NVjbXZbACAqqoqX4ZkakrydfLkSQwcOBA9e/bEu+++G3RFEaDtzxeJwsLC0LNnT2zZsqXuH3ebzYYtW7Zg+vTpBkdH/s5ut+Nvf/sbNmzYgG3btrEoUsFms/ntv4MsjDTYu3cv9u/fjzvvvBPNmzdHUVERnn/+ebRv3z5orhYpcfLkSQwYMABt2rTBkiVLcObMmbp98fHxBkZmXsXFxTh//jyKi4thtVpx8OBBAECHDh3QpEkTg6MzVnp6OiZOnIhevXqhd+/eyM7ORkVFBR555BGjQzOlS5cu4ejRo3U/Hzt2DAcPHkSLFi3QunVrAyMzn8cffxxr1qzBxo0b0bRp07rn1mJiYhAZGWlwdOYze/Zs3HvvvWjdujUuXryINWvWYNu2bfjss8+MDk0dO6n2zTff2AcOHGhv0aKFPTw83N62bVv7Y489Zj9x4oTRoZnSu+++awfg9ovcmzhxott8bd261ejQTOHVV1+1t27d2h4WFmbv3bu3fc+ePUaHZFpbt251+2dp4sSJRodmOp7+f+rdd981OjRTmjRpkr1Nmzb2sLAwe2xsrP3uu++2b9682eiwVOMzRkRERES1gu8BDyIiIiIPWBgRERER1WJhRERERFSLhRERERFRLRZGRERERLVYGBERERHVYmFEREREVIuFERGRj+Tn5+P99983Ogwi0oCFERGp0rZtW2RnZ+sy94ABA5CWlqZozNy5c9GjRw/Zx//8888QBKGuzYpWe/bswRNPPOGzdkC+yu8777yDoUOH+iAiz1asWIERI0bo+hlEjYWFEZGfefjhh03RFX3//v34y1/+UvezIAjIz883MCLfGzBgAARBgCAIiIiIQNeuXZGTk+Ny3Llz5zB58mTk5+ejbdu2TvuMzMvvv/+O559/Hi+88IKunzNp0iR89dVXKCws1PVziBoDCyMiUiU2NhZRUVFGh6G7KVOmoKSkBD/88APGjRuHxx9/3OV22XXXXYfvv/8et956q0FRupebm4vo6Gjccccdun5OWFgYxo8fj3/+85+6fg5RY2BhRBRgiouLMXLkSDRp0gTR0dEYN+7/b+feY5o6+wCOf4tvkWJJRSJYDZOVmlkIW+QyhrhhlARdaIiLe11GAibVedtEjSwxDAUvxIQBJltczLwwUfGSuEHI/oCZyJC4C5GZCY3O4qaJRBNFKGxMmc/7D57XQ7lONy/5fZImPL/z3M5zmvTHc077X27cuKEdf3DLqaKigoiICCwWC++88w5er1er4/V6yczMZMKECVitVsrKynxubz18q+fBLsmiRYswGAxaebDdrXXr1jF37lyt3NPTQ1ZWFmazGavVSklJyajOc+fOnYSFhREUFITL5aK3t9enzt69e3E4HAQEBDBz5sxBd3tGEhgYyJQpU7DZbBQUFDBjxgyqq6u141VVVcTGxhIQEIDNZqOwsJC+vj5g6HXxeDxkZGQQFhaG2WwmISGBb775Zth5jHRdB3P06NFBb3Ht37+f6Ohoxo8fj9Vq5f3339eOGQwG9uzZQ3p6OoGBgTgcDs6ePcvly5eZO3cuEyZMYPbs2Xg8Hl2fTqeT6upq/vjjj2HnJMTTThIjIZ4j9+/fJyMjg9u3b1NfX09dXR1tbW0sWbJEV8/j8fDVV19RU1NDTU0N9fX17Ny5Uzu+YcMGGhsbqa6upq6ujoaGBs6dOzfkuD/++CMABw4coL29XSuPRm5uLvX19VRVVVFbW8vp06eHHQvg+PHjFBQUUFRURFNTE1ar1SfpOXz4MJs3b2bHjh243W6KiorIz8/niy++GPXcBmMymbh79y4ADQ0NZGVlkZOTQ2trK3v27KG8vJwdO3YAQ69Ld3c3b775JqdOnaK5uZkFCxbgdDq5evXqoGOO9roOdObMGeLj43Wxzz77jDVr1vDee+/x888/U11djd1u19XZtm0bWVlZ/PTTT8ycOZN3332XFStWsGnTJpqamlBK6ZIpgPj4ePr6+vj+++9HuZJCPKWUEOKZkp2drTIyMgY9Vltbq8aNG6euXr2qxVpaWhSgfvjhB6WUUlu2bFGBgYGqq6tLq5Obm6sSExOVUkp1dXUpo9GoTpw4oR2/c+eOCgwMVDk5OVps+vTpqqysTCsD6ssvvxxxrjk5OSolJUUppZTX61X+/v7q+PHj2vFbt24pk8mkG2ugpKQktXr1al0sMTFRvfLKK1o5MjJSHTlyRFdn27ZtKikpSSml1JUrVxSgmpubhxwnJSVFm0dfX5+qqKhQgPr000+VUkrNnz9fFRUV6dpUVFQoq9WqlQdbl8FER0erTz75RCs/vL6jua4DdXR0KEB9++23uvjUqVNVXl7ekPMA1EcffaSVz549qwC1b98+LVZZWakCAgJ82gYHB6vy8vIRzlSIp5vsGAnxHHG73YSHhxMeHq7FoqKimDhxIm63W4tFREQQFBSkla1WKzdv3gSgra2Ne/fu8eqrr2rHLRYLL7300mOfr8fj4e7duyQmJmqxSZMmjTiW2+3WtQF03wbr6enB4/Hgcrkwm83aa/v27T63gEaye/duzGYzJpOJ5cuXs379elatWgXA+fPn2bp1q26MB88k/f7770P22d3dzcaNG3E4HEycOBGz2Yzb7R5yx2i01/VhD25pBQQEaLGbN29y/fp15s+fP+w5v/zyy9rfYWFhAMTExOhivb29dHV16dqZTKZhz1uIZ8F/nvQEhBD/PqPRqCsbDAbu37//2Mfx8/NDKaWL3bt377GPM1B3dzcAn3/+uU8CNW7cuDH1lZmZSV5eHiaTCavVip/f//+f7O7uprCwkLfeesun3cMJyUAbN26krq6Ojz/+GLvdjslkYvHixdotuschJCQEg8FAR0eHFjOZTKNq+/D7w2AwDBkb+J65ffs2kydP/ttzFuJpIDtGQjxHHA4H165d49q1a1qstbWVO3fuEBUVNao+bDYbRqNR95xQZ2cnly5dGrad0Wjkr7/+0sUmT55Me3u7Lvbw7wZFRkZiNBp1z6V0dHSMOJbD4fB5luW7777T/g4LC2Pq1Km0tbVht9t1rxdffHHYvgeyWCzY7XamTZumS4oAYmNjuXjxos8YdrtdqzvYujQ2NrJ06VIWLVpETEwMU6ZM4ddffx32fMd6Xf39/YmKiqK1tVWLBQUFERERwalTp8a0BqPh8Xjo7e1l1qxZj71vIf5NsmMkxDOos7PT54cJQ0JCSE1NJSYmhszMTHbt2kVfXx+rV68mJSXF5yHcoQQFBZGdnU1ubi6TJk0iNDSULVu24Ofnp+0UDObBB25ycjLjx48nODiYefPmUVxczMGDB0lKSuLQoUNcuHBB+/A0m824XC5yc3MJCQkhNDSUvLw8nwRkoJycHJYuXUp8fDzJyckcPnyYlpYWbDabVqewsJC1a9disVhYsGABf/75J01NTXR0dLBhw4ZRrcVINm/eTHp6Oi+88AKLFy/Gz8+P8+fPc+HCBbZv3z7kusyYMYOTJ0/idDoxGAzk5+cPu2P3d69rWloaZ86c0X2bsKCggJUrVxIaGsrChQvxer00NjbywQcfPNJaNDQ0YLPZiIyMfKR+hHjSZMdIiGfQ6dOnmTVrlu5VWFiIwWCgqqqK4OBg3njjDVJTU7HZbBw7dmxM/ZeWlpKUlER6ejqpqakkJydrX3sfSklJCXV1dYSHh2uJT1paGvn5+Xz44YckJCTg9XrJysrStSsuLub111/H6XSSmprKnDlziIuLG3Z+S5Ys0fqNi4vjt99+0577eWDZsmXs3buXAwcOEBMTQ0pKCuXl5WPeMRpOWloaNTU11NbWkpCQwGuvvUZZWRnTp0/X6gy2LqWlpQQHBzN79mycTidpaWnD/gbS372uLpeLr7/+ms7OTi2WnZ3Nrl272L17N9HR0aSnp/PLL7884kpAZWUly5cvf+R+hHjSDGrgAwBCCDFAT08P06ZNo6SkBJfL9aSnI8bg7bffJjY2lk2bNv1jY7S0tDBv3jwuXbqExWL5x8YR4t8gO0ZCCB/Nzc1UVlbi8Xg4d+4cmZmZAGRkZDzhmYmxKi4uxmw2/6NjtLe3c/DgQUmKxHNBdoyEED6am5tZtmwZFy9exN/fn7i4OEpLS3Vf2RZCiOeRJEZCCCGEEP3kVpoQQgghRD9JjIQQQggh+kliJIQQQgjRTxIjIYQQQoh+khgJIYQQQvSTxEgIIYQQop8kRkIIIYQQ/SQxEkIIIYTo9z9L5ttljxmkBwAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a0159add0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generamos una variable con las dos características que nos interesan\n",
    "x = [caracteristicas[:,1] caracteristicas[:,2]]\n",
    "\n",
    "# obtenemos las características globales promedio\n",
    "x_prom = mean(x,1)\n",
    "\n",
    "# extraemos las caracteristicas globales promedio de nuestros datos\n",
    "x = x - x_prom.*ones(150,2)\n",
    "\n",
    "# graficamos nuevamente\n",
    "scatter(x[1:50,1],x[1:50,2], color=\"b\")\n",
    "scatter(x[51:100,1],x[51:100,2], color=\"r\")\n",
    "scatter(x[101:150,1],x[101:150,2], color=\"g\")\n",
    "xlabel(\"Longitud del Pétalo (cm)\")\n",
    "ylabel(\"Anchura del Pétalo (cm)\")\n",
    "grid(\"on\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El siguiente paso consiste en encontrar el vector promedio para cada una de las expecies de plantas. El siguiente bloque muestra como se logra esto y también grafica los vectores con los datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6a01202e50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.quiver.Quiver object at 0x7f69fd8a4890>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# graficamos los datos nuevamente\n",
    "scatter(x[1:50,1],x[1:50,2],alpha=0.25, color=\"b\")\n",
    "scatter(x[51:100,1],x[51:100,2],alpha=0.25, color=\"r\")\n",
    "scatter(x[101:150,1],x[101:150,2],alpha=0.25, color=\"g\")\n",
    "xlabel(\"Longitud del Pétalo (cm)\")\n",
    "ylabel(\"Anchura del Pétalo (cm)\")\n",
    "grid(\"on\")\n",
    "\n",
    "# obtenemos los vectores con las características promedio para cada una de las clases de flores\n",
    "prom_1 = mean(x[1:50,:],1)\n",
    "prom_2 = mean(x[51:100,:],1)\n",
    "prom_3 = mean(x[101:150,:],1)\n",
    "\n",
    "# graficamos los vectores\n",
    "quiver(prom_1[1,1],prom_1[1,2],angles=\"xy\", scale_units=\"xy\", scale=1, color=\"b\")\n",
    "quiver(prom_2[1,1],prom_2[1,2],angles=\"xy\", scale_units=\"xy\", scale=1, color=\"r\")\n",
    "quiver(prom_3[1,1],prom_3[1,2],angles=\"xy\", scale_units=\"xy\", scale=1, color=\"g\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como podemos ver, estos \"vectores promedio\" están máximamente alineados con los datos de las clases de flores que les corresponden. El siguiente bloque de código toma una hilera de datos aleatoriamente, y calcula el producto interno de estos datos con los tres vectores promedio. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "el producto interno del vector muestra con de los vectores promedio correspondientes a las especies de plantas son: \n",
      "\n",
      " setosa [6.13707]\n",
      " versicolor [-1.2601]\n",
      " virginica [-4.87697]\n",
      "\n",
      "y la especie correcta del vector muestra es: \n",
      "\n",
      " Any[\"setosa\"]"
     ]
    }
   ],
   "source": [
    "# escogemos aleatoriamente una ilera en los datos\n",
    "ilera_al = rand(1:150,1)\n",
    "\n",
    "# extraemos los datos de esta ilera en una variable nueva\n",
    "x_muestra = x[ilera_al,:]\n",
    "\n",
    "# calculamos el producto interno de esta muestra con cada uno de los vectores promedio\n",
    "prod_1 = x_muestra*prom_1'\n",
    "prod_2 = x_muestra*prom_2'\n",
    "prod_3 = x_muestra*prom_3'\n",
    "\n",
    "# imprimimos los resultados\n",
    "print(\"el producto interno del vector muestra con de los vectores promedio correspondientes a las especies de plantas son: \\n\")\n",
    "print(\"\\n setosa \", prod_1)\n",
    "print(\"\\n versicolor \", prod_2)\n",
    "print(\"\\n virginica \", prod_3)\n",
    "print(\"\\n\\ny la especie correcta del vector muestra es: \\n\")\n",
    "print(\"\\n \", especies[ilera_al])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como podemos ver, el producto interno máximo es el que corresponde a la clase correcta de la especie de flor.\n",
    "\n",
    "Preguntas para reflexionar en grupo:\n",
    "\n",
    "1. ¿Cual sería el algoritmo a seguir si medimos una flor nueva y queremos determinar a que clase pertenece usando nuestro método?\n",
    "2. ¿Son las características promedio de cada clase de flor el mejor método para clasificar los datos de Fisher?\n",
    "3. ¿Qué problemas podríamos encontrar con nuestro método?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 1.3: Desarrollando un Algoritmo de Clasificación y Midiendo su Eficacia #"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supongamos que el método descrito en 1.2, clasificación  con las características promedio, es un algoritmo idoneo para la clasificación de datos. En esta sección desarrollaremos el algoritmo formalmente y mediremos su eficiencia.\n",
    "\n",
    "Empezaremos por usar otra base de datos. Ahora la meta es clasificar tres tipos distintos de vinos en base a su contenido de alcohol, su contenido de Flavonoides, y su Densidad Optica relativa. El siguiente bloque prepara los datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# obtenemos los datos que necesitamos y los ponemos en una matriz de Julia\n",
    "vinos = matread(\"wine.mat\")\n",
    "datos = vinos[\"data\"]\n",
    "\n",
    "# separamos las caracteristicas y los tipos de vino\n",
    "caracteristicas = datos[:,2:end]\n",
    "tipo_de_vino = datos[:,1];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este punto tenemos una matriz `caracteristicas` con tamaño 135x3, cuyas ileras tienen las características de vinos distintos, y las columnas contienen las tres características. Hay tres tipos distintos de vinos, 45 ejemplos (o muestras) por cada clase. Las ileras 1 a 45 corresponden al tipo de vino No. 1, las ileras 46 a 90 corresponden al vino No. 2, y las ileras 91 a 135 corresponden al vino No. 3. El vector `tipo_de_vino` tiene los números 1, 2, y 3, los cuales indican el tipo de vino que corresponde a las ileras de la matriz `caracteristicas`.\n",
    "\n",
    "Una vez que tenemos los datos listos, el siguiente paso es separar los datos aleatoriamente en dos grupos, uno para entrenar el algoritmo, y otro para probarlo. Normalmente guardamos cerca del 15% de los datos para probar el algoritmo después de entrenarlo. El siguiente bloque muestra como hacer esta separación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Tenemos 45 datos por cada clase, entonces seleccionaremos aleatoriamente 6 ileras de características (~15%) para  probar el algoritmo al final.\n",
    "\n",
    "using StatsBase\n",
    "# aleatorizamos los números en el rango del 1 al 45\n",
    "vino_1_aleat = sample(1:45, 45, replace = false)\n",
    "# aleatorizamos los números en el rango del 46 al 90\n",
    "vino_2_aleat = sample(46:90, 45, replace = false)\n",
    "# aleatorizamos los números en el rango del 91 al 135\n",
    "vino_3_aleat = sample(91:135, 45, replace = false)\n",
    "\n",
    "# separamos los datos que nos servirán para entrenar\n",
    "x_entren = [caracteristicas[vino_1_aleat[1:39],:]; caracteristicas[vino_2_aleat[1:39],:]; caracteristicas[vino_3_aleat[1:39],:]]\n",
    "y_entren = [tipo_de_vino[vino_1_aleat[1:39]]; tipo_de_vino[vino_2_aleat[1:39]]; tipo_de_vino[vino_3_aleat[1:39]]]\n",
    "\n",
    "# separamos los datos que nos servirán para probar el algoritmo\n",
    "x_prueba = [caracteristicas[vino_1_aleat[40:end],:]; caracteristicas[vino_2_aleat[40:end],:]; caracteristicas[vino_3_aleat[40:end],:]]\n",
    "y_prueba = [tipo_de_vino[vino_1_aleat[40:end]]; tipo_de_vino[vino_2_aleat[40:end]]; tipo_de_vino[vino_3_aleat[40:end]]];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De aquí en adelante solo trabajaremos con las variables `x_entren` e `y_entren`, y dejaremos las variables `x_prueba` e `y_prueba` para el final.\n",
    "\n",
    "Empezemos por visualizar los datos que tenemos disponibles para entrenar nuestro algoritmo. El siguiente bloque muestra esta visualización con las tres características que tenemos disponibles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f69fb6f95d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x7f69fb7ecb10>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter3D(x_entren[1:39,1],x_entren[1:39,2],x_entren[1:39,3], color=\"b\")\n",
    "scatter3D(x_entren[40:78,1],x_entren[40:78,2],x_entren[40:78,3], color=\"r\")\n",
    "scatter3D(x_entren[79:end,1],x_entren[79:end,2],x_entren[79:end,3], color=\"g\")\n",
    "xlabel(\"Contenido de Alcohol\")\n",
    "ylabel(\"Contenido de Flavonoides\")\n",
    "zlabel(\"Densidad Optica relativa\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora si podemos empezar a trabajar:\n",
    "\n",
    "1. Recuerda que el primer paso es substraer el promedio global para hacer que los datos estén centrados en cero.\n",
    "\n",
    "2. Después procederemos a encontrar las características promedio para cada uno de los tipos de vino. \n",
    "\n",
    "Recuerda que calcularemos el producto interno entre las características promedio de cada clase de vino con las ileras de `x_entren`.\n",
    "\n",
    "En el siguiente bloque, trabaja en equipo para llevar a cabo estos pasos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ggLGxMUQiEezatQudnZ1IpVJpF8REIoFQKLSusM1kMsFisYAQgpWVFeWO8EaiFjbqaqYhZEo9pw0GA5qamtDU1KQ8JghCWhrD7XYjHA4DgBLxUgsJtZ2z2HVs5MZQpzEym09l6wlBqT5ULFDKRi5elO8egPwOB/mO4/z582hubs7qcCgGtVjQgnLSELFYDBMTE1hcXMTAwAAOHz6c1n1PjTxuObOwLRQKwe/3w+/3Y2JiAtFoFAaDQYlAyBfzcirjKRuz3QQLx3Gw2+2w2+1px1dP5/T5fHC5XEilUrBYLIp4SCQSZQto6sbY2lCxQCmZQgc9yYiiiPn5eUxMTAAADh06lLZRlor8fFqJhVLSEGqLZ1tbG06ePAmz2Zx1nfnQ6/VoamqCxWLB7Owsbr311rQGP6FQCD6fD5FIBBzHpQkIOaSsVSqmmtTKRl3tNZQz+bIQGIaB1WpNG7gmb9qygAgGg4jH4xgbG8PU1NS6CES551wxaQy/3w+dTofm5maaxthkqFiglESxMxyWl5cxPj4OQghGRkZw5cqVtIY15aCuWdDqeIUeixCiCCCz2Vz2ECsZ+b0khECn06GhoSHtuOqQcigUUjoEMgyjXMjlf+VMSryRqfRGXegaNvtvxzDMuqjXq6++iuHhYeh0OkVEqO2cmQ2l6urqKmLn9Pl8sFgsqK+vp2mMTYaKBUpR5HI45GJtbQ3j4+OIRCLYsWMHent7AQBXrlyBIAjQ6/WarEvLXguFRhZWVlYwNjYGnuexZ88etLe3a3Zh2ug42ULKcodAWUDI1jpCSFEthmuBWrirr5U11ILQkz+r9fX1aaJVfc6Fw2EsLCwgHA5DEASleFd97pXzeWcYRlmHugA6M42hhqYxtIOKBUpBqB0O6qrmXBfTaDQKh8OB5eXltNy9jNa9DLQWC/kiC+FwGOPj41hdXcWOHTvQ399fsYtPMdESdYfAzs5O5ffVF3O5xbAgCOtsnOWOWt5u1IJYEEWxJkRdrghHrq6U8XhcSZ2tra1hbm5OsXNmCtdi7JyCIKxbRyFpDFlEUDdG6dArAyUv6pyhWiDk+lAlk0lMTk5ibm4OXV1dOR0Olei6WOkCx2QyCafTCbfbjZ6eHuzbtw8Gg0GT58xEnYYo9zjZctJqb7561LJ8NygLw1QqpVn0pxhqYaOuhTWIoliV9z/bOgoVLWo7Z2trq/K4XLwri4ilpSVEo1FwHLdOQORKnQmCUJCgzefGkKOjNI1RHFQsULKitkFOTEwgkUhg7969OT84giBgenoaLpcLjY2NOHHiRFrzmExqefhT5rFEUcTMzAwmJyfR2NhYtnuj0DVU8tjZvPlqK+fS0hJisRj+/Oc/K8191P8qJZJkaqHHRK2IhWqHzOVC5nLXIRfv5rNzqlNn2YZrZYssFIr8t8wUPcWkMSKRSNnplK0KFQuUNLI5HDZqzywX+JlMJhw6dChtVG8uanmeg7oj5OLiIhwOB1iWxcGDBzVxbxTDZm6a6qI2juMQDAYxMjKiCIhQKISFhYWsVs5iw8lbgVoQC7VQsyB/Tiuxjlx2zlgslmbnlCNfDMNgdnYW4XA4rStlORSTxjh79iz+/u//Hh//+MfLes5aIhgMwuFwKFEsi8UCu90Oo9GIhoYG5e9OxQIFwPUPRzaHQ7b2zHJl8vj4OARBwO7du9HR0VHwxVVuzKQVWtcsJJNJvPHGG4hEIhgeHlYG6GwWWqUhyoEQkvVukOf5NCvn8vIyotEodDrdOidGqbY6ulFL1IojA1h/R14pGIaBxWKBxWJBe3u78ngikcBrr70Gq9WqFFPKwjUzAmGxWCpi55RFynbB5/Phm9/8Jn77298qlnY1//7v/457771XSv9UYX2UGmMjh0Pmxh4IBDA+Po5QKIQdO3agr6+v6ItqrdYsxONxzM3NIRwOY2hoaF1h5mZR7Q0iH4VaOcPh8LopiVvJylkLgqUW0hCVjCwUg9FoBCEEPT09Sg0Oz/M5LcSZXSm1cACFQiHNLN/VRJ718dRTT+HFF1/EM888gyeeeAL79+/HBz7wAXz1q1/FLbfcgg9+8IMApD2AioUbGDmSwPM8gPRCHzUsy0IQBESj0bTuhIcOHSo5d1drYkHdVMlut6Ourg67du3SbH1AaW2kayF3Xwi5rJyRSESJQuSzcmbz5Vd7o6ZiQUIQhJpwCsgpUvWGr9PpUF9fn7aBy3ZOdSGl7ABSd6VUz2IplFAotK0iCy+88AI+85nP4OTJk0gkEhgcHMSZM2fwb//2b/jHf/xHzM7Oorm5Wer3Uu3FUjafbDMc8l0MCCGIRCJ45ZVX0NnZiTvuuKOkGQ5qaqXAMVtTpWQyCYfDodnaSqEW0hDlop6SWKyVMx6PV/2114JYqIU11Ip9U45ubrQWtZ2zo6MDgPQ+ygW84XAYa2tryiwWo9G4Trhma6VOCNk2kQWZSCSiRAhZllUcIgcOHMDVq1cRiUSUn6Vi4Qai0EFPMoIgKC4AABs6HIqhFgocczVV8vl8Vd+oqr1BVOr5N7JyhkIhrKysYG1tDYIg4LXXXls3E2OzKtFrZaOudmShFtYAFC4WssEwDEwmE0wm0zo7ZzgcVqIQ6lbq6voHt9uNnTt3QhCEbSEW5L/noUOH4PV6AUjX9//5n//Bhz70IVy4cAGJREJxSzEMQ8XCjUA2h8NG7Zk9Hg8mJiZgMBiwc+dOzM3NaRp+q2aBY2ZTpb6+vrQLkNYNo0qllLTFViSblXN+fh5LS0vo7e3N2thnM6yctVJcWO2Nuhy7otbryBxCVS56vR6NjY1obGxMex519Ovy5cu47777kEqlYLfb8fDDD+PIkSM4dOgQDhw4kJZ6K5Tz58/je9/7Hi5evAiv14tf//rX+NCHPpTz519++WXcdddd6x73er1K9KQY5PP6gQcewNTUFOLxOD73uc/h7Nmz2LVrF0RRxCOPPIL+/n7ld6hY2MYUO+hJdjg4HA6kUilltHIgEMD09LSma6tGzUKhTZW0tGGWS62soxqwLIuWlpasUznlf16vF7FYrCJWzlqILNSKI6NW0hCbsQ71gDYA2LVrFzweD1588UV85jOfQU9PD373u9/hO9/5DrxeL1ZXV4uONkQiERw4cAD33XcfPvzhDxf8e+Pj42niRN0npRSOHz+O48ePAwC6u7vxxhtv4PXXX0dbWxt2796ddv5TsbBNKWbQEyB5bcfHxxEMBjE0NJTWwljrKACwuWJBFEXMzs7C6XSioaFhw6ZKtXJHX+2Nqprk2qg308pZC2KhFqIbtRRZqJZo4TgOLS0t0Ol0+OY3v6n8TXw+X0lpibNnz+Ls2bNF/15bW5smg+pknnjiCZw5c0aJkJhMJtx5551Zf5aKhW1GsYOeYrEYJiYmsLCwgP7+fhw8eHBdTljrjb0Sx8yWOiCEYGlpCePj42BZFgcOHEjLVxZzrGpQK6Kl1inFyllIa+FaEQvV3qhrYQ1AdcUCkN0JsdlN2g4ePKh0033iiSdw++23l3wsnufx3HPP4Te/+Q2OHTuGj3zkI9i3bx+ampqy/r2pWNgmyDbIQCCA0dFRHDlyJG80IZVKYXJyErOzs+jo6MCpU6dgNpuz/qzclEnLi6dsx9SKTPERCAQwNjamNFXq7u4u+IJH0xDVp9xzLZ+VM1tr4cwIhNVqrQmxUCtpiGqvAagdsVCNc6KzsxM/+tGPcOTIESQSCTz99NM4ffo0Xn/9ddxyyy0lHVOn0+HixYt49tlnce7cOXz4wx/G0aNH8dGPfhQf+chH1kVfqVjY4mQ6HAghCAQCOT/cgiBgdnYWU1NTsNvtOH78+IYFOvKxCh3iUgiVckPE43E4HA4sLCxknXZZCJWMLBSzAVV7o9puqKMKMmorZygUwuLiIpxOpxKZm56eRmNjoxKJ2OzNqlbSEDdSzUIugsFgScWMWjAyMoKRkRHl69tuuw2Tk5P4wQ9+gP/4j/8o+bgmkwmf+tSn8KlPfQoOhwNPP/00vvKVr+CLX/wiHnzwQXz7299WfpaKhS2KXLyYSqWUu0+WZaHX69PGSKt/3uv1wuFwQK/X48CBAwWH0OQPqJYbKMdxiqdXK1ZWVjAzM4O2tra8kZKNoJGF2njuzdgk1VZOtSc/Ho/jtddeg16vx8rKClwuF1KplDKVc7OsnLVwV18LawCqLxbC4XDFB8gVw7Fjx/DKK69odrzOzk585StfwYkTJ3D//ffjv/7rv/Dtb39bed+pWNhibORwUG/s8v/LDodkMonh4WF0dXUVdSFWRxa0QqvIgtxUyePxgOM4HD16tOwCILlWoNphaFqzUB1kKycA9Pf3w2w2KxMJ5QjEZlg55XOw2ht1rbghqr2OUChUtchCNi5duqQ0OysFdeH36OgoXn75ZbzyyitIJBI4e/YsPvaxjwG4fv2nYmELUYjDQf4wyQVeDocDa2trWfsJFIrsba41saBuqtTc3Ay9Xq9JpbC6e2K1xcKNSrXf+0yxyDBM2lROmWQymebEkK2cmV0BS7FyqiOG1aRW3BA8z28bsRAOh+F0OpWvXS4XLl26hKamJvT19eGRRx7B/Pw8fvrTnwIAnnzySQwODuLmm29GPB7H008/jZdeegm///3vi35uOVJ06dIlPPjggwgGg0ilUrjrrrvw7LPP4u677077efmcpWJhC1CMw0F+/OrVq1heXkZfXx/2799f9p1OtsmT5VCOWIhEIhgfH4ff71dsni6XC9FoVLO1AbVRXFgLa6gG1X7d8vNvtLkbDIasVk65iFK2ckYiEej1+nVOjHxWTnXksJrUShqi2pGFYDCoWffGCxcupDVZeuihhwAAn/zkJ3Hu3Dl4vV7Mzs4q308mk/jSl76E+fl5WCwW7N+/Hy+++GLWRk0bIf8teZ7H/v378cADD+Dw4cMb/h4VCzWMemR0Ie2ZU6kUpqamAEgfrJMnT8JisWiylkp0XCz2eMlkEpOTk5ibm0N3dzdOnTqlzLLXss5Afn+rfXGqZhqi2htUtSlULGRDp9Nl7QqobitciJWzVqY9iqJYkQ6ZxaJlgXUphEIh9Pb2anKs06dP5/1snzt3Lu3rL3/5y/jyl7+syXMD0vl97NgxHDt2rODfoWKhBil2hoOce5qcnITNZoNOp8POnTs1EwqA9u6FYiIV6tdXX1+fdUaFluurlcjCjVyzUAtpCEA70cRxXNbpiJlWzlAoBADKTAJAiqRlm8qpJhoF5ucZBAIMLBags1OESquURa2kIQRBUG4OqoH8d9jKPPXUU/D7/fja176G559/Hr/85S+xY8cO2O12NDQ0wG63KzU3w8PDaG9vV36XioUaIpfDIV97Zq/Xi4mJCXAch/3796OlpQXnz59Xxk5rRTVmOWQ2Vdq/f3/OpkpaigV1ZEEramHEL6VwtBYL2djIyrm6ugpAKmTLnMqptnKurQGvvcZhcZGBXg/wPAObjcXRowJ6esoXm7WShqi2G6Ka1kmtaGlpUSYGe71e/OlPf8Kbb76JQCCAaDSKRCKhnIPf/OY38cgjj1A3RC1R7AwHQCruGx8fRyKRUJoOqR0RlWjPvJliQd1UaefOnejp6cl7waqEWNDyrj4ajcLpdIJhGEW95+ocqF7HjRpZAKqbCtkMsZANtZXTZrNhcXERp06dSpvK6fP5FCun1WrF1FQHFhYaMTysg9Vqhk6ng9fL4PJlFm1tAsrNIFQ7HSdTbbGwHcZT33PPPcr/f/rTn8anP/1p5WtBEJBMJpWiXVkYye85FQtVptgZDqFQCA6HA6urq0pxX+YHqBJiYbMKHNVNlfr7+wtuqqRlIyVZqGmxUfM8j6mpKUxPT6OtrQ06nW5d50BZPGQKiBtZLFT7dVdLLKiR7+izTeWUrZzLy2FcugQYDAHMzYWRTCZhNBphMJjh9dZjxw5gaMhSVs1BLaUhqiUWCCEIh8OaTt6tFqlUCnq9Hk899RRuuukmnDlzRjnXTCYTzGYzHA6HEvmSoWKhSoiiqBQ7NTY2bjjDIR6PY2JiAl6vF729vTknJgKVEwsfcDXzAAAgAElEQVRaHjPzeDzPw+VyYXp6Gq2trUUXZ2rdSKlc8SGniMbHx2E2m3HrrbfCYrEoF97MzoHZBATP84jFYjUTBt5sbsTIQuYacv3dZStnc7MRbW06GAwEdru0EcRiMYTDMSwtJTA56YbHEyjLylkr5x+NLJQPIURpIvbUU0/h85//PM6cObPu7/uJT3wCjz/+OO655x7l70/FwiYjOxx4noff74fL5cKJEyfyOhxcLhdmZmYK3kS3UhqCEAKPxwOHwwGTyYQjR46kVZEXezwt11eq+JDnc8RiMYyMjKCzsxMMw6TVkeTqHKgWEDzPw+l0wul05o1AbEdqocCx2nUmhbR6NpulYkaHg0VdnbQR6PV6RCL12LeP4P/8n3aw7MZWTllIZLNy0jSERLZBUlsJ+Zz+3e9+B7PZDEEQ4Pf7MTExAYZhYLFYYLFYlGi3XB9G+yxsMtkcDjqdDjzPZ70giKKIubk5ZaM4duxYwap2q6QheJ7Hq6++imQyid27d6Ojo6Pki/NmTLHciEQiAYfDAa/Xi8HBQQwODqalUDYSH5kCYnV1FQMDA7BarXkjEJUSENVOBRQKIYAoAlruI9UWK0D2O3qfj8HiIoNUCmhoIOjqIhgZEbG6ymB6moHBAKRSQF0dsH+/eK1eIbeVUz6vZmZmEA6HwXHcuqFaNA0hPXc0Gt3SBY7yOX3u3DlMTk7C5XLhZz/7mdLYieM4GI1GOJ1O1NfXY3h4GAAVC5uGWiRkOhzkOQ6ZP7+4uKjkjPbt24fW1taiLlw6na6mIwuRSARjY2MQBAEdHR1Z6y5KWV+1IguiKGJ6ehqTk5MlpVById/ZbhSB2EwBsVkUslkLAuByMZiaYpFIMGhtFbFjB0FrqzYOgGqLhcw0hNPJ4O23OcRiAMtKIqmvT8SxYyLuuEOAx8NgdVWyTnZ1iVD1iVrHRlbOUCgEt9uNcDgMURQxMTGBhoaGtKmcm31eVVMsBINBANjSaQj573X//fcjHo/jkUcewQc/+EG0trYiFAohHo8jlUrhzJkzuOeee9DX15f2+1QsVIhCHA6ZEQC/34/x8XHE43FlhkMpH8harVlQN1WS/btDQ0NaLE/zSZGFHI8QguXlZYyNjYHjOBw+fDitk58WZBMsN6qAUEMIcOUKi3feYWE2A0YjwcQEC68XOHlSKFsw1EpkQV7Dygrw8sscEgmgpQVoaiLgOMDlYtHaCtx0k4jhYQKg9Nedy8r55z//Ge3t7UilUlhYWFCmcuayclYC+aarWudtKBQCwzBbvs8CAKXro9lsxunTpwv+PSoWNEbuKS87HIDcNkg5DSE7HNTti8vpVFaJiY7lHFPdVMlut+PEiRMwGAzwer2aFU9VosAx3/HC4TBGR0cRDAYxPDyM3t5ezTeXYtwQ201AbLRZr60BExMsWloI5L2tsZFgZoaB08lsG7HAsiyiUeDFFzlcvMiiqQnweoH6eoKREem1z8ww2LMHqMRyZdHc2toKq9UK4PpUzlxWzsw0hhZdF2XhXq0OjqFQaMPGWFsF+Ub29OnTCIfDcLlc0Ov1MBqNqKurg9VqhclkWvdaqVjQkGJtkHLB26uvvoqenh7ccccdmnQo4zgO8Xi87OOoKSUNka+pkiw8tBQLm2HtTKVScDqdmJubQ29vLw4ePFixEcXlblblCIhkMlnTNQuhEIN4HLj2shTq6wmWl1mkUiLK+bPUklhwOFi43SwaGoDOTulvsrzMwOkEenoIKvlnkjcW9Wc0n5Uz21ROs9m8zolRrJVTvvZUa7MOBoOw2WxVPye0gGEYcBwHp9OJb33rW5iamoLD4YDZbFaKWa1WKy5dupT2e1QsaAAhBKlUal0kIdeJpbYJAsDRo0dLcgDkohYKHIPBIMbGxhAOh7M2VZL/X8sWzVqnIdSbpSiKcLvdmJiYQH19PW677baiQ5KlXGi03rALFRDBYBCEEFy4cKEqEYiNRjPrdNKdNM9L/y+TTDKwWEjZxY61IBakCCWLhQUW3d0i4nEO4TBgswHNzQTLywx0OuDuu8WKRBXkNQDYML2QbyqnfF6Fw+F1UznVKYx8Vk5BEJS299VA7rFQ7XNCK5LJJB577DGMjY3h/vvvx0MPPYTHH38cly9fxh//+Efce++9636HioUyyOZwyCcS5A3H6XTCarXi6NGjeP311zXvd17NmgV1P4j+/n4cOnQo6513rYsFdVpjZWUFo6OjEEWxpILTUtmspkzZBITb7cbi4iK6u7trMoXR2ioVMno8DLq7JXEQjQLhMLB3L0G5y6kFsSCdzywEQRIIAwMinE4pLcEwgM8H7NsnYnBQu/M+k3Lv6A0GA5qbm9Hc3Kw8JqdeZQGxtLS0oZVTrleo1t9kq9smM1lZWcELL7yAd999Fw0NDXjsscfw8MMPw2Aw4Ktf/apS0KmGioUSKHbQk9rhwDAM9u7dq2w4ct2CllSqz0K+zZjneUxPT8PlchXkCJBFlVbrlDdWrS7yDMMgFovh7bffhs/nw86dO9Hf37+pm2I1Nyv53Ozo6CivBiIeB+PxgIlEQEwmkM5Oyde3ARuJJL0eOHxYxMWLLNxuBqIIGI1Sod/QUPmb50aRjc1AFEWYTAza2kRMTbHo6yOoqxOwssLA52Nw8CDwvvcJuFZKULE1ANqG//NN5cxl5ZTTFpFIBBaLZdM/G3IaYrsQCASg1+vR2dmJsbExWK1WLC0tKenwv/u7v8N3vvOdtBQUFQtFkM3hsJHaXV1dxfj4OKLRqDLDQf3Bq1XnQqHHLKepkpa9G9STIsu9kPA8j0QigfHxcXR3d2tWS1ILaYhyKLYGoh5Ax/Q07KEQTGYzDDod0NIC8dgxkGu57o2eLx8tLQR33SVgeZlBMgnY7ZJLQIt9pFYiCxzHYmSEYGVFKmS0WgGTCejtJTh8WMhrj9RqDZsR/t/Iyunz+UAIwZtvvgkA64ooK23lDIVCW7rHQiaiKKK9vR2XL19Gc3MzOjo68Pzzz+Oee+7Bq6++qrxW9fWHioUCKGXQUzgcxsTEBHw+HwYHBzEwMJC1knerRBayHdPv92NsbAzJZDKtU2GhVGKsdDkFk+oWzYIgYGhoSGlMUg20TkPwvFQYFw5Ld+Ht7QTlaqB8AiL18ssQfD4s1NcjFo+DiCIaPB7ofD7gfe+DraEhZwqj0NdtMADd3doLqkqKBZ6XmkhtVOMnr6GlheDUKR4zMyxWVhhYrQR9fUQpdqwk1bQrqq2cer0e8XgcR48eTROnCwsLmJiYgCiKqKurSxMRWlo5t1saor29Hffffz+WlpZw4MABfPCDH8QjjzyCH//4x/B4PHj00UcBpAt2KhY2QBYJ7733Hvr6+jYMgSUSCTidTszPzxd0V7pVIgvqjT0SicDhcMDn82FoaAgDAwMlfSgrJRZKYW1tDaOjo0gkEhgZGYHb7VZGuWpJMZu/lptVNApcuCBV1fO8lPNuayM4elT7u1OGYWAFoEskQG66CW02GwghSCQSiK6tIeV2wzM+DodOlzOFUe07+0o8fzwu2T1nZqQ6hLY2Ebt2ETQ3Zz8n1MK3sRFobKxcbUIuam0uRC5xKs3DCGe1cmY6MUqxX26XIVIyzc3N+OxnP6t8/eijj2L37t0YHR3F6dOnceeddwJITz9RsZCDTBuk1+vNe+esztm3tLQUXC2/lSILPM9jdHQUc3Nz6OrqKjs8XwtiQS7IXFhYwMDAgNKi2ev1ap4CKOV4Wq1hbIyFy8Wip4fAYJC6H87NSR0BT58WsroHynpuuQfztc8LwzAwmUwwtbSASaXQun8/xJaWnCkMjuOUCXjVKKLUWiwIgiTWnE7JAqnTETidLJaXgZMn+ayCrRY26q0wF0I910Bt5UwkEkoRZblWzlAohM7OTs1fV63AcRw+8pGP5P0ZKhYyUDdUUufrcm3qaoeDxWIpehBSJTd2rRBFEYuLi0gkEgiHwzhx4oQmKlvLFtLyhb1QsZCtRbPZbE47npbuilLQKg0RjwNzcyyamogS+uY4ybO/tCS1CG5p0TikbbVCbGsDOzsLYrVeFw3LyyD19SD19XlTGGNjY0o9TDVcGFq3e15aYjA7K4k1WV/b7QTT09LjTU3rz7VaKLLcqnMhFHFqMim9XYDCrZyygJDPgVAohJGREc1f12byi1/8At/61rewa9cuWK1W2O12pU6kvr4eNpsNdrsdRqMRIyMj6OnpSft9KhYykHsmZDocMsWC3HDI4XCAEIKbbroJ7e3tRV9gKhVZyNZMpVjU7YzlC9eRI0c0u4hWYjjVRpurulFUvhbNWneELAWt3mdBkPLkmVXzOt3172kOw4Ds2QOsrYGdngYxmYBEAjCbIe7blzNhLwsIuenP4OCgpp0oRRHw+xkkEoDFQtDQkL3zodaRhXBYeq/VgTiGkYwhi4u5rdbVvquvhegGoN1ciI2snKFQKM3K+atf/QqEEASDQaVRWTnnxfnz5/G9730PFy9ehNfrxa9//Wt86EMfyvs7L7/8Mh566CFcvXoVvb29eOyxx7L2QdiI1tZW3HzzzWBZFktLS3A6nQgGgwiFQojFYojH4xBFEeFwGI8++ii+8Y1vgOd5JW1DxUIGLMtmdTioN/W1tTWMj48jEolkbThUDJWKLADlfdDlpkqhUAjDw8Nobm7Gn//8Zy2XuWldF2VCoRDGxsYQDAaxa9cu9PT05Pzg10JkAdAmDWE2A83NIjweFlbr9eOtrjKw26Wuh5WAtLaCv+MOsG631J+5rg6kpwdE1bQHAIJBIBplYDSmb96MKoVRbCdK+S5JLSAiEeCtt1jMz7NIpaSNe2BAxMGD4jrtorVY0OmuZ2bUH8lEAjlbU9fCRp0pWDLXv1lUcohUPivnu+++i//93//Fe++9h5dffhlPPvkkbrnlFhw6dAj33nsv9u3bV9RzRSIRHDhwAPfddx8+/OEPb/jzLpcLH/jAB/DAAw/g5z//Of7whz/g05/+NDo7O/H+97+/qOc+c+YMzpw5k/P7iUQCgiAgEokoUVZ1fQcVC1nIdlep0+kQjUYV3/3AwAAOHz5cdq/ySkUWAKSpwkLJ1VQpkUgA0PYiulliIZlMwul0wu12F9yiebMaIm3GGlgWGBkh8Puv2+/kbuCHDwtQZV/SnlsTGhogNjRk/VYqBbz7LoupKanRkNEI9PaKOHBALHqcN5BfQFitdXA6O7C83IiBAT3q642IRlmMjrIwGoEDB9LPG63FQnu7VMg4P8+gs1NqIrW2JgmI/v7sr7WW0hDz8wymphgEAizsdhFDQwTd3drYVAtdx2ZGWWQr54MPPogHH3wQx48fx5NPPonh4WG89dZbeOutt7I2LtqIs2fP4uzZswX//I9+9CMMDg7in/7pnwAAe/bswSuvvIIf/OAHRYsFGfnclgv319bWsGfPHrS2tiKZTKKpqSnre03FQgHIufrl5WV0d3fj1KlTmlXKcxyHZDKpybFk5MhIMRELQRDgcrlyNlWSTx4tc5iVFgvltGiuRBqi2M1HS8HS2Ulw6pSAqSkGKytSjcLAAEFPj3T8cBjwehlEo8y16EPld4HxcWlqZEsLQWsrEIsBDod0btlspb1fuQSE2x3B8jILjlvC7GwEhBCYzWakUja8/bYZ3d0smpqupzC0FgsWC3DkiIi335Y2XkKkFMShQyJ6e2s7srCwYMb4OAdRBKxWgvl5FvPzwK23Chga2hxBLQhC0fMktIIQgnA4jJaWFhw6dAiHDh3C3/7t327Kc7/66qt43/vel/bY+9//fnzhC18o+Zhyw7nvf//7+OMf/4iXXnoJ3/3ud/Hwww/j+eefx9TUFD7xiU+k1XoAVCzkhed5zMzMYGpqCgaDAV1dXdi7d6+mz6F1MaL6uIWIhUKbKskXLUEQNBucpHUKRp06KLdFc62kIbREbpGcic/H4PXXWWXWgCAAOp0ZPT2VuzwkEsDUFIuGBgK5143FIt2Bu90senpY2O3adOK0Wq1obKxDczOH7u52sOw1G2c0Cr8/hqWlAN58cxZmc0pJYcg9VbTcsNvbCe6+W+rAKAhS+idfnbDWRZalkEiImJ2tQ1PT9X4WTU1SYezoKIueHmHDfhFasNmRhUyq1WdhYWEB7e3taY+1t7cjGAwiFoulFWUXgnw+//jHP8azzz6Lxx57DAsLC8pE0f7+fnz/+9/HyZMn0dramiaaqVjIAiEEc3NzcDqdMJlMOHz4MHw+n+ZjnwEpDaF1zQJQ2EZcTFMlOVqxmTUGpRxPbtG8srKCHTt2lNyiuVYKHCu9BlEE3nmHxdoag6EhKawsPaZDMmnFHXdUZvRxMin9y7z+ms3SzINkUts7aquVwGKR6iMaG69XyieTDLq6CO6+uwfJ5PUURiAQQCKRwPnz53PWQJSCwYCCmykVIlQEQRJ7sZjU2bG1tfwhWmrCYSAS0a+LIDQ2EiwuMgiFAFWtYMWoZrEnIQShUCitu+RWRb6enDt3Dp///Ofx0Y9+FN/+9rcVsXDTTTdhfn4+6w0sFQtZeOuttxAOh7Fnzx7F4bC2toZYLKb5c1UjslBqUyWtIwFaigWe55FKpXD16lUlVVROD4hKRBaqmYbIxdqa1NWxre16/pllgaYmHh6PDqEQUIkut2aztIGHw9KUSJlQSIowmEy8pnfVViswPCylAVIpwGyWnlsQgF27ROj1DPT66ykMvV6PcDiMwcHBooootWSjVEgkgmuzMaQmTxwHdHeLOHxYLGT8RkEwjAC9XqovUWdek0lpPkeZJVsFw/N81cRCLBYDz/NVEQsdHR1YXFxMe2xxcRF2u73oqAJw/RoUCASUnhSBQAAN1+qKeJ5HIBBQoii0g+MG7NmzB0ajMb17VQUKEeXjViKykO24qVQKk5OTmJ2dLamp0ma7FwpBnUYRBAHDw8MYGhoqe20bbtShkNQW0WQCiriIVDusnAkh0r/MZUlfS7n1SqDTSZv0669zWFxkYLMRRKMMgkGp2JDjtE8B7dkjwmiUmiHF4wyamgh27hSzFhjKxYWluDBkEVGugNgosvDuuyxcLg7d3SKMRmkDn57mYDAAx49rM7babObR2SnA52NhNEqukVRK6huxc6dYESGZjWpGFkKhEABUJQ1x4sQJ/Pa3v0177IUXXsCJEydKOp58Pv3VX/0VfvGLX+Cv//qvwfO8Usv1k5/8BL29vcr5roaKhSzU1dWt22grJRY2I7IgiqKSVrHb7SU3VapEZKGc46lbNO/evRszMzOaFZ7mTEOkUmCuXAGmpsDEYiAGA9DfD3LwYPqtlwZsRmShvl7KQft8jJKTJgTw+znU1yfz5tTLRQptC5iYYBEKMTCbCY4dIxgeFvHee1nuqqNRMD4fIIogTU2A3Y5kUupTEI0yMJkI2ttJzj8DxwHDwwRDQwKSScl9kWsvlu/qEwnA42GwvMzAYAA6Ogja2/MLCK/Xi4mJibIFRD6xEA4DbjeL1lZR6d1gMEgtpOfnWYRC2mzkgiBgZCQBv1/A/LwUwWBZaZDVvn3aCJJC11EtsRAOh2EwGDS5toTDYTidTuVrl8uFS5cuoampCX19fXjkkUcwPz+Pn/70pwCABx54AP/yL/+CL3/5y7jvvvvw0ksv4T//8z/x/PPPl7WOL33pS7jvvvvwhS98AfPz8/jv//5v/OY3v8HTTz+NH/7wh+uKGwEqFgpmq0UWZBEiNyACUFKhX+YxtVxrqUIpHo/D4XBgcXERAwMDGBoaAsdxmJub0yzykSsNwYyNgbl8GaS5WdqwYjEwo6NSE6Jbb9XkudVrqLRY0OmAvXulO3yXi4HRCCQSDOrqCHp7oxX11DMMsGMHQX+/gHhc2uxyFcsxMzPgLl8GAgFJzVitWOvfh9fXdsPjvb7IQuZdcByy2kXVEEKQTLJ47TVploNOJ9VyjI4C+/eLuOmm6xtlITbOUgREPutkKiU108p8v4xGKbWkVXmVNKBJGv29vEwQjUrvXWsr2bQUBFBdsSCPp9YiKnjhwgXcddddytcPPfQQAOCTn/wkzp07B6/Xi9nZWeX7g4ODeP755/HFL34R//zP/4yenh48/fTTJdsmZXbt2oVnnnkG3/jGN3D8+HE899xzaG5uxjPPPJOz7TMVCwWy1SILcjvjVCqFnTt3ore3t+ycarXTEIIgYGZmJmeLZq1nTazbqBMJwOkEqa+/nnqoqwOJRKRdZNcuaeKPRmxWyqKri+DOO3nMz7MIBqWXptNFEYtpX9CbDZ0O63Lsae/96iq4ixeliEJfn6QyVlfx3m/dcDd0o2+fXXFxuN0M3nmHxR13iGUJHWkejAmLiyx6ewlkA1AgALz3HovOTjGnICEE8PlYLC3ZIAg2NDURDA4ScFxxAiKfG6KuDrDZCNbWGLS3Zzbayu+yKAY5/M9xUlSlWlRTLGjphDh9+nTeG4Bz585l/Z23335bk+dXMzIygp/97GfrHs9VK0PFQhayvlEVjCyIoqiZrzsej8PpdMLv96OhoQEnTpyoWatjoZu73KJ5bGwMOp1uU1o0Z40sJBLSP1kQBAJgXC5gZQXw+4H6epCTJ4EsITz5dRRrxdssR0ZTE9LmE3g8IipQz1sU8ueBXVoCwmGQwUHle2FzKzx+Bm0NS9DppHg7x0mRhcVFFmtruTfzQiCEYGHBAKsVUH986uulP/XKilTzsP73pKFd77zDIpGQdA3DADt3SoWHxUQgCCGYn59HPB5fF4HQ64Hdu6WI0Py81BsjEpFqTA4cWN+RslRqYTYEIWTbRBZqhVAoBL1eD5PJpOw94XAYHo8Hzz33nDKiWg0VCwUiiwXt28BKfwKe58va1AVBwPT0NKamptDS0oLOzk6YzWbNhAKg7eAn+XgbiYViWjRrGVnImgKQSvgl/x0hYK5eBRMKgej1QH09mOVl4NVXQU6fXmchCAQCuHr1KkKhUFolfb4w9Ha6OBVL2nufSq2rwBREBgKnh05IpD0upwtEkQFQutCSUgDZ3/9s+o0QKeqwsMDgwgUWjY0EXV3S9+TR1G1tZJ0FMV8K48KFC2AYJmcEorXVjttus8Ll4hAMsujokDor5mryVAq10BhKFk7bIbJQbVwuF5588km4XC4MDw/jU5/6FPbu3YtXXnkFP/nJT/Dzn/8cu3fvxqOPPrrub0/FQhZyRRbkO0MtT1p1Z8RSNnZ5fLbD4YDBYFCaKo2NjVVk5oTWaYhcayylRXPF0xB6PTAyAua11wCPR5qg2NgIJhoF2bkTZMcOKdIwPw9yTSwkk0k4HA54PB4MDAxgZGQE0WgUwWAQCwsLyiagDkHLVrxqNoaqtlBRi3L5vUQqpdzm1+kTaOKiWCR96Fb93soKg/p6Aru9vA2TEIKurhTc7rSnxdqapBebm68fPxoFLl+WLIwzMwzm5lgcPizAZiNgWanuVa8H5ueZgjoeygKCYRgMDAygrq4ubwTCaq1Da6sNDQ021NfbQYgFDKPNBl8Lw6zka0Q1Cxy3g1jw+/14/PHH8fvf/x779u3DD3/4Q7zwwgv43Oc+hyeeeALHjh3Db3/7W5w+fRoA1olEKhYKRB0B0PKkladblpLiWF1dxdjYGBKJBHbt2pXWVInjOGWeg1ZUosAxczNUOzeKbdGs5eaa61hk507p+88/D5JMAjodyMiIkksnej0QDCqNvSYmJtDQ0ICTJ09eawKUhM1mU7qyyZuAPP3N7XYjHA6DYRjodDro9XosLS3BZrPBZDJVfROvBqSzE2J/P9ipKSkPwDDQBwK46eAA/GjCzAwDi0XatA0GqRiv3DA8IQTd3SkYDCJmZliwrBSxMBikAkc5xUEI8PbbLCYnpchBWxvg8RBMTLDQ6a63cpZ/vxjUNQuFFFEuLHjhdJbvwlBTC2kI+ZpTrXWEQiHYN8sjWkEcDgdeeeUV/OpXv8Ltt9+Or3/96/j617+OP/zhD7h48WJWu6QaKhYKRO5gyPN8Wc1+slGsIyIajWJ8fDxvU6VKTLOsdBpC3aJ5//79We07xRyv3LVlrRdgWZBdu4B4HIzRKIkH1fnApFIIiCLe+ctfIAgC9u3bpzQ/yequUG0CnZ2dys9FIhFMTk4iHo9jenoakUgEOp0uLfogz57frijCSK+HePQo0NwMZnoaDCEQDhxA+9AQ7kjoMTMjwu+XrJ/d3dLd/NgYC44jaGsjxbTBUCCEwGRicPy4tOHPzTHQ6yW7Z1vb9fPC75csjB0dBGYz0NAgPR/PS5GEri4CUZTmXnR1FRft2CgFUCkXRjFr2AzkeoVqCeWtLhbkKJ3b7UZdXR1uv/12AMCRI0fQ19eHZ555BlardcO6ECoWspDrpKy2IyKzqVK+gVaVGn1dCTeELH5qqUXzRlEKMjAATE0Bi4tAWxvAMODn5+EJBOBcWEDf/v0Fd8bMhGVZ5YJuMpmwe/duZWRuKBRCMBjE8vIyIpEIDAZDmniw2WxVG7ijJdnqRcSbbwb27JG+vnZ+tOL6vItEQupo6HKx1+oWpNKRW24Rck52zPf8UudWBi4XC5+PAcsCqZQInY4oLY4TCQbJ5HUrZn29NDlzfJyF18tiZkbqjDk4KKKvr/A1yK9f/TkoZDy01gKiVtIQ1VxDMBjc0mJBZnV1Nc095vf70d3drbR63ug9pmKhCKrVa0EdmrfZbDh+/PiGJ2+lxIKWxySEIB6P45VXXlHETzl3ylpGPjYUHnY7yPHjYN55B1hehs/nw1w8Dt0tt+B4hqWzHOQ1yCNz1S1neZ5XNgC5BiIWi8FkMq0TEKWMUi9HeInidSdAqWQV7Xl2S5eLxcQEi+5uAqNRShEsLTG4fJlDSwuPa9fEghBFEaEQh3fe4RAOX69RmJ1lEQ4zuPNOAVar1DbaZJKaJNXVScvbsYMgmSTgeRE7d4ro6JCmexZzal8XqixcLkmwRKMMmptF7NiRHt3YiHIEBM9r23a7FKqdCgmHw+iSq1W3MPxRJ+AAACAASURBVGtra7hw4QLuvfdeNDQ04I033sDU1BT+9V//FVarFfX19TAYDNi9ezcGVc4jGSoWiqDSDZQyIYRgeXm5pKZKlejfwLKsJsO05BbNY2Nj4Hkex48f16TvetHrIwRYXgazsgIQIjVZamsDrqWcNtwsOzrgY1lMvPkm0NCAnUeOoCVjQlw5bLQGnU6HxsbGtCmhqVRKEQ/BYBButxt8MAizyQRrayvs9fWw2+2oq6uryN3a4iJzbQw2C4uFYHBQaqdc7LW+WKFCCDAzw6Cu7npWiGGk5kEzM1IHRmn0duHPv7BgwNoaMDBwfW5Gby/B9DQDj4fB8DBBQwMwMCDi6lUWqZQkHIJBqdfBiRMCBgdLE1yyWBgflwSLwQAYjQSTkyy8XuC224Sy+h4UKiB4nsdbb72liAetWlkXgyAIJYldrdjqbgh5vzh58iQ+9rGPIRKJYHZ2FkajEf39/fjWt76FWCwGQRCwtraGhx9+GN/97nfB83za+07FQhY2Ow2RTYSoLYOlNFWq1ciCukXzwMAApqenNRvQwjCMVHS4siKZ7q8VwwGA0qdW/poQMO++C7z7Lph4XPp9gwFkzx6Qgwc3TEPE43GMjY1heXkZO2+6qeTUyUavp1j0ej2ampqkPhSBANjRUQihEGKLiwgtL8PX1obpa0LSarWmRR/q6urKeg0eD4O//IVDIgHU1REsLzPwejnEYlLHw2Ip9vXz/PrAA8tKQqLY7BkhBOEwB6MxPTrCspI9MxKRrJkMc72vwfQ0i0BAeu2HDokYGCjPuhmLcZiY0MFuJ0prj6YmgtlZBg6H1IyJYaSBUnNzLBYWJOdFTw9BV1fxAi2bgHjppZdw4MABJJNJTVtZF0O1IwtbvWZB5sSJEzlnSgiCgGQyiVgspkR3MwUaFQs5yHZXtxk1C4lEAhMTE/B4POjr6yvIMpjrmFrb7soJ82dr0RyNRuFyuTRbn9HrBXf5MtixMRCWBbq6QHp6wCwuAktLUin7jh0gQ0OAzwfmyhUQmw1EDjFGImCuXgVpbQVrNme9u5U7Y05OTqK9vT1v3YgWlJwKiMfBvf46mPl5MHo97IEA6mdn0ZVKgf/AB5AwmRQHxtLSEiYnJyEIAurq6mC32yGKIgRBKLiviCgC4+MMUimocvMEfj8wPs6iv18sKg1QbD8ThgG6uwkuX2bR1HR9owwEpCmWjY3F1yzYbAQej/w1EAoxiEaBtbX0SZkGgyQYRkZEJJPS85V7IyzV8ugRizEYGEj/XmMjwcoKi3hcBM8Dr77KweORHCE8L5XS7NsnYu/e8mY3yNcPq9WKpqamis/CyEW1axbC4fC2GE+dD47jYDab86ZPqVgogkpGFuTiRbmp0smTJ2GxWEo+Zq0UOKqbRWW2aNa0fbTXC8vly4hEIiAjI9LAp3feAfOHPwB9fVKKIRgE85e/SE2VDAapIq5b5dK3WiURsbAAZmho3dqWl5cxOjoKjuNydpHUknJmQzAejyQUVlfBXbkCJhgERBHs228DPA/m4x+Hqa1NcWpId7IxRUD4/X7EYjH86U9/WufAMJvN6zbyeBxYXWXR0JC+3sZGYGZGCs0XkwYohaEhEQsLDKanpY0zlZI2+f37RVybwFswhBB0dvJYXATOndPh/HkdFhevb3o/+pGIBx9M4v/+35RybJNJu1lioihCpwN0OgY8T9K6SKZSuPY9qdmT18tiYECEvJ8GApIbpKdHLKv7uHz+Z272m+HCUFNNsUAI2fJpCK2gYqEIKiEW5CK/hYUFWK1WzTahStQsFCNA1C2a9Xp91tcliwUtumIyLhdYnkeiqSltIhHj8UDcuxeyMZ5EIsDEBNDZmbVYjjAMwPNpBY7RaBRjY2Pw+/0YHh7WZM5GQa9po/ckFgMTCEh2zqamtNtZJhIBs7AA9upVAADp6QEYBozLBe6FFyAePy6JKtVzWSwWWCwWdHR0oK6uDh6PByMjI0oNhNvtRigUAsdxaRd/u90OjjNCp5PGJKu51ooCxQbHSjkn7Hbg5EkBs7NSSN5slkLy3d2k6DtsQgjefdeMhx4yZW17PTvL4JFHjPjGN4z4j/+I4X3v01aYi6KI+voU7HYCj0eyhep0sihjcPiwJCbcbqk+Qr2Xyi2pV1eZoiMqmWsACmuGVEkBUe3IwnZxQ5QLFQs52Iw0hNxUSQ5zHT16VLPKY3lj17I99bo0RDgMxusFYjEQq1W6SzeZlHqLUCiE4eHhnC2a5QuAJmtcWwNRpw5EUWqOZLFIEQQZqxXM0hJEvR4My0pXX/l2MJkEIwgQ29uVmgWn0wmXy4WOjo6y3RqlkDWyQAgYpxPc6Kh0G8lxIK2tEA8eBLnWm4IYDGDm5qTb0M5OyLsJaWgAw/NgL12CsGtXXrsCwzCoq6tDXV3duh4QcgGlugdEItGBmZlWDAzo0dRkBsPosbAg9RooZ9MqBnlC4k03lXec119vwFe+0nPtq/XvESHSY7EYwd/8jRnPPaetYCCEQK9ncfPNAgRBmv9AiCS8RkZE7NolpRg4bn09hnzKlKtn5c96qZ9NrQREtcVCOBzelmJBfW0p5G9MxUIRSBfE8rsiRqNROBwOLC8vY3BwEC0tLYhGo5palOQPl5Y+6bQ0xOIimNdfB+PzARwHhhCkWlow0dqK2UCgoHoL+U5CkwKmpibonE6Ico8BlpXWxfMg6g1eEOQENwjLghkfl7ouMgyYZBJkxw6Q7m6sejxIJpNYWlrC0aNH0VBsHFsDcqUhGK8X3IULgMkkdY4UBCmK8MYbEO6+GzCbQdraAJ0OTCQiTUgQRcnfZzQCFguYcFh6LMe5kW/+hnxB776WwpF7QHR2hpBKBTE6KiIWS0Gv16GnR4eWFoJAQNoICq2/2awBWtlYWwMef/xmEHJdFORCFBmwLMHHP27G6Gi46HRH7uNK3RubmoDTpwUsLzPXCkeBlpbrNRn9/QSvvcagvv66C2R5mYHdLv1cuWuQm9FpRSkCQhAEGAwGhMPhTXVhANK5HYlEtpVYkG/Oiv27UrFQBOVGFlKpFKampjAzM4POzk6lOG5mZgahUEjDlabPnNBKLCiRBZ4Hc+kSEAiADA2BAFhaWID//Hmwe/bgtr/5m4JaNMsfei3qFsjAAHD5MvRLS8DgoFTpRQjSxgYKAuDxgLS0AJ2dIN3dIO3tYObnAUIgdncj0tSE0StXsLa2BpZlceLECc0vluX+LDM7K1k9W1qkB1gWpLsbzMwMmIUFaTpjYyOE224DOzMjxaR1OklENDSAiUQgdnfnFArFou4BIdWOMggEBKRSYRgMq4jHQxgbcyMej8NsNqfVQOTrAVEtf///+396JBLshkJBRhQZRKMEzz6rx4MPajPWW9050WCQijezMTgoYmUFSiMqQgCbDTh4UFg39ruUNeS7dhAiCatEQqpHKTWtv5GAmJmZQTQaxcWLFzfVhQFAuS5vpwJHhmEQi8UwNjYGADAYDIobSq/X56zPoGIhB1qOqRZFEW63GxMTE1mbKlWqGBGApsdVIgurq2B8PpCODgSvfZgJIRg4eBB2g0HK+xeA/B5rUuTY0YHk0aNI/elP0ubIcSAnTkh31V4vmOlpAABpaQE5evT6bdjQEMjQEHiex9TUFKbffBPd3d3YsWMH3nzzTc03LPmOudDjZo0shEJY1+Hnmi2USSaVWYvimTMQZmbAjI5KiWyDAUwgAHFwEOTgwXJeRk5YFtdmJLAA7Nf+SaRSKaWAcm1tDXNzc0gkElktnNWKLBAC/PjHhqyTJTfiRz8y4IEHUmU5EGQKbbNsNAK33irZNAMBBjod0NZWfEFnsWuQh2fNzUmjuC0WqcB0716x6PqUbKgFhM/ng81mQ19f36a6MIDrYmE7FTjOzc3hiSeewPT0NK5evQqr1YpUKqW8X5cuXcoaSaVioQiKFQuEEPh8PoyNjYEQkrOpUiUKJxmGqcjgJ0EQAEKQiMcx63IhEA6ju7sb7e3tYCIRyfRd4JVWHqKl1RpJby9WbrkFZP9+6a5Z/oD7/SDBIK5dSdM2WkIIFhcXMTY2BpPJhFtvvRX19fWIRqNVDYUDudMQpKVFqhVRc22MM1H5E0lrK1If/zi48+el+gaOA3/wIMSTJ0E2GBpTCfR6PZqbm9Es90qGZBWWBYTP54PL5VK6BrrdbiQSCdjtdlit1k0JP/v9UrfEYiGEgcvFwO8HVC+vZKQR2YWtQ6eDMhdDS3KlBwmRhILDcX0mRigEvPMOC4MBuPlmbS3b6tkQm+nCAKCMlK/2fAwt+drXvoaLFy/iH/7hH3D//ffjs5/9LBYXF/HLX/4Sn/jEJ2hkoVjKjSwU01SpEpGFShxXno45sbyMiMeDVpMJ/YcOSXloQqRoQ38/ijHUa9kPgmVZCAyDdX6x5uasV/BwOIz33nsP4XAYIyMj6OrqSpvyRwjRtEC0WHKJBbGvD+zsLJjZWZDGRkAQwPr9EPr7QTI7SHZ1QfjoRyEkk1JqxmwuuAfzZoglo9GI1tZWZWiY7A66ePEiOI7D4uIinE6ncvFXWzjlMd5aEg6X+/tM2vjqUlFPnKwWudIQa2vS8Kz2dgLZ3W23S3p1aorF8HD5Uz/V5EulVlpABINB2Gy2qv8ttOTXv/41zv9/9r48SrKqvv9zX+1LL9X7vi/TPfvOLDAYQBA1IsYDSgQxQn5BiIoxYqJEwQQRZMlIHI2aHBWiMYm7QTkYZIBhYIaBGXrfq7fqru6urn197/7+uP1eV1XXXq+6esb+nDNHqa6679Wr9+793O/y+bz4IrZv34577rkHH//4x1FdXY3W1lapNTwWNslCGkiFLGQiqpQr/QZZd+0r0tMAsORyYeuNN6KgpwdkagpUowHx+UBNJtDu7rQMAdLSWvB4WORCo2GzU4ZjhUIhDA8Pw2w2o76+HrtFwhMGcXLIJ1mIi9JS8IcOgfT3g1spMOW3b4fQ2Rm/RzGsnXQjgxACnU4HpVKJ2tpalJSUREz+DocDMzMzGBgYACEkYuIvKCiIqQGRDrLN8xuN8hCsjeL2GOscAgFWbLki0SFBp6NwOtnf1ossxIKcBMLlcl1SKQi32w0AaGhogNPphFarxcLCAqqrq3HdddfhgQcewLe//e2Yn90kC2kgkXZBuPhQWVkZjhw5Irl5pTJuLiILcnlZiBLNvhVZ5D179kClUrGK+8lJwOkELSkBra9HusnSlBZ4ngfp6QGGh1l1v0YDNDaC7twZoYKTTMSIUorZ2VkMDAzAYDDg0KFDcScCcbKQc3ed7iKW6PvQigrWLun1spTLJWZVHd3WFT35i26lYgrDbDbD5XJJGhCi/kNBQQE0Gk3K176khPlZjI+TlAsc2TlSNDVRyKXTlU4aIleIR1j0ehZRcDoRYf/tcrFCR5k81CTIUaSdLoEwm8144YUXUFJSAr1ej1AolJGSbjieeuopPPLII7BYLNi5cyeOHz+OAwcOxHzvv//7v+P222+PeE2j0UhzcKbw+/1oaGjAK6+8gmPHjqGjowM/+clPUF5ejmeffVaqpYu1SdokC3EQLw0hCELEQyQuQIODg1Cr1RmJKuVSRjobshAu0dzc3IyGhgb8/ve/X53Iy8ulvv5MkQpZIIODIG+8AVpczKSZvV6Q3l5AEEAvu0yKZCQay+FwoK+vDx6PB1u2bEFVVdXqb+xygYyOAlNTbOFtbgZZaQuU26JXjm6IsDcAWah8bnQk+v4cx0kaECIEQYDL5ZIIxOjoqGTjHa1CGc/GmxDgL/8ygM9/Pn3y9f/+X0CW4kZgY0QW4t37BQWsmPGttzgEg4w8iBGFXbuErKWuo5ErnYVEBIIQAo1Gg5MnT2JoaAiFhYXYuXMn9u7di6uvvhrvf//70zrWj3/8Y9x77704ceIEDh48iCeeeALXXnstBgYGJBXVaBQWFkomguL5Zgu9Xo+/+Zu/Ac/z0Ov1+OhHP4rPfvaz+M1vfoPx8XF85jOfifvZTbKQBsQWr1AoBLVaLYkq+Xw+dHR0ROS804FCoQClVPYJIlOyEE+iWSQJctdBJCQLwSAwNARqNK7WIhQUsI4Lsxno6pKiGbHGCgaDGBoawtTUFBobG7F3797IVj23G+Tll0Gmp0ELCgBBAHnpJSjb2kBWRK1yhlCIOV4Gg+zYMdqz8l1kmS9k8r05jpMiCiJ4no+w8Z6bm4PH44FGo1lj4y3uHD/84SC+9CUlAgEFBCH588xxbDf9oQ/J0zYJbIyahUT6J9u2CdBogJERAqeTSOZZLS3y36/rKcokEohjx47h2LFjOH78OE6dOoVHHnkEZ8+exdmzZ9HT05M2WXjsscdwxx13SNGCEydO4Ne//jW+973v4b777ot7LlUyFyJrtVp85CMfkf779ttvR11dHc6dO4cDBw7gyiuvlI4djU2ykAbEilyn04nJyUlJVKmpqSkrC9VoEiIX0iULySSac9FhkbSuwu8HvN61NQoGAyuo9HpjkgVKKaanpzEwMIDCwkIcPnw4pvYDMZsZUWhqWlU59PtBxsagyYEZl4SlJSjOngWZn2fiSDodhLY2CNu3S+eRjTfExQBKmU1HKERQUEDX5LnlWCwVCgWKi4sjWsFEG+/wGghRA0IkDp//vAsPPHAAHEcTEgaOY1LSP/yhVzZBJmBjpyEA1oHR1SWgtZVJemu12ZtnJTqPfCk4Op1OFBUVYcuWLdiyZQtuueWWtMcIBAI4e/YsPv/5z0uvcRyHq6++GqdOnYr7OZfLhcbGRgiCgD179uCf/umfsHXr1oy+hwifz4fR0VGYTCZJlfWaa67BNddcg2AwmPg3z+rIlzBiTVRiS9fZs2cjRJWyhfjj5JMspCrRLKv5E1LohtBqWdWZyxUZcnc6QXW6iM4L0c8h3AZ727ZtqKioiL/wzM0xSejwyUijAaEUKrc7N4t1MAjFmTMg8/MsraJUAg4HuAsXQI1G0LY2APkTJVoPOJ3AhQscZmZYKLuwkGLLFrYzJSRxYWkwyP5ptZlJGkfYeK9AtGB2OBxYXl7Gzp0L+MIXTuHhhw/A7xdlyVfPhxB2X+h0jChcdZX83hAbgSwkW6RzXTcrpn3zSRayVW9cWFgAz/OojOpUqqyslISRotHZ2Ynvfe972LFjB+x2Ox599FEcPnwYPT09qKuri/mZRBCfpwsXLuCpp57CXXfdherqauk+s1gs+I//+A9s2bIF73rXu2KOsUkWUkC4qBIAdHV1ob6+XrbxCSGyFSOGIxWyEAgEMDw8jKmpqZS6N3IRWUhIFpRKoL0d5NVXQefnWYTB6wWx2ZieQmGk6A8AvPbaa2hubkZLS0vySUatZitPFMiKEH8uIgvEamVEobZ2dTtWVAR4veBGR8G3tjKBpTxGFnJJVEIh4MwZBSYnCSoqWETBZiN4/XUOarWA+vrY3zkUYi6Lo6MEfj8zUOroYO/P9nTVanWEBsQLL7yAj32sDjfcMIVnnlHi6adLMTOzWrlXW+vHrbfaceutFFVVOgDyLuwbPQ2xXkjHzCoXcLlcaxb59cChQ4dw6NAh6b8PHz6Mrq4ufOtb38KDDz6Y9ngi4Tp79iz6+/uxe/duAKsb1crKSkxNTeH8+fN417veFTP1s0kWksBqtWJgYACCIGD79u0YGBjIiZlQrlQc440pCAImJycxPDyM4uLiuGH6aMjZjimOl2xBpm1tLGY9OMjUGbVa0N27WZsmGGuenJzE4OAgAKxRyEw4dl0duJERJtpUWMiOY7WCGo0IrNSSyI5AAJIrUPi5aLUgPh+TpV7526WYhrBaCWZnCerqmPUyz7MIwfw8h9dfB2pqYhugXbjA4cIFDgUFrE1vcZHg5ZcVOHKER0OD/NdJo9GgtVWPL34R+MIXQlhacmJhwQ9KHVAo7HA6HRgacmJwkK5p4cxWA+JiiSzkGuJck8/IQnt7e1ZjlJWVSZoh4Zibm0u5JkGlUmH37t0YHh7O6lxsNhuKioqkDWG44FUgEJC6LWLNO5tkIQ54nseZM2dgt9vR2tqKhoYGcByH0dHRnHQu5KIjIh5ZCFeV3LFjhySIk+qYcu62U0prcByzU25uZloLWq3UMmmz2dDb2wue57Ft2za8+eab6aWG6upYhKKvjxUbUgpaWAi6axf4sbHcLNYFBSyi4fFEpFaIwwGhqUkiCvneWeYKIh9Sqdgl6O/nsLhI4HYDk5MKmEwUPB+5ONjtwMgIh9JSKgWTjEZm3zw4yKGujs/aZTEc0WSFEFHbSwOgfOXfavW82IExNTUFl8slaUCEt3Bqtdq0ZL7lJgs8v3rdUzkNQRBkTYtmgtCKXXy+ngWxZiEbiF1yzz//PG644QYA7No+//zzuPvuu1Mag+d5XLhwAddff31G5yBev7q6OlitVjz//PO46qqrJBI2PDyMvr4+HDlyJOL94dgkC3GgVCpRWVmJHTt2RDwwG7XNMd6Y4S6ZHo8H/f39WFpaQltbm0SA0oHckYW0vndYgtTv92NgYABzc3NoaWlBc3NzZl4THMfIQn09k4UmhKnNFBSAjI/nJA1BS0ogNDeD6+sDCguZnfTyMouYrNQrAPkvcMzVsXU6ViLi9wPDwxysVoLycrY4FxcLMJsVCAQMOHhwdcJyuwm83rVCQIWFFA4Hgc8nXxdpOsqd4e130TbeYg3ExMQEXC4XlErlmhbOeFFKOXf1PA+MjhKMjHDw+QhKSgS0tVHU1CT+fTdKGiKf0Q1R7jlb3Hvvvbjtttuwb98+HDhwAE888QTcbrfUHXHrrbeitrYWDz30EADggQcewGWXXYa2tjYsLy/jkUcewcTEBD7+8Y9ndHzxd3zPe96DX/7yl/j0pz+Nv/qrv0JnZyfcbjeeeOIJ+Hw+qcsj1u++SRYSoKGhYc2EmYvaAnHcXEQWBEFAKBTCyMgIJiYmUFNTg8svvzzjVMq61yxEQRAEmM1mDA8Po6ysTGrrFEEISX+BJwQoKQGN0scQCyblBFlaApmaAvx+5hrp9YIEgxAaGkDb29fINV+KaYjycoraWgG9vQpMTxNpwec4oLER0GgEvPWWDh4Pkew9NBq2I/b7I3S44PMRaDRUFvMi5pFG4PNReL2KjHez4TbeNTU1AFZtvEUCYbVaJQ2I6BZOtVoNQRCyFgESIaZv9HpAo6GYmuIwNwccPswn9JPYCKmQUCiUd7Ighz31TTfdBKvVivvvvx8WiwW7du3Cs88+K9VDmM3miGtts9lwxx13wGKxwGQyYe/evXjllVfQvZJ6TQfhxNdkMuFLX/oSvvKVr+DLX/4y/H4/gsEgjhw5gm9+85vYsWMHgM3Igiy4mCILHMfB7Xbj5MmT0Ov1aeXy4yEvaYgVLC4uoq+vD5RS7N69O8KQSERGZCEO5ByLUoq5M2fgePZZaAUB2sJC6AmBuroaOHgQqKpaExu+VNMQCgWwb58Anw8YGlJBpQIKCigaGynKyyl8PlbMGP6YmUwUNTUCxsc5VFdTaDSso8LhAA4cyJ4sOBzAuXMcZmfZ7ttsrkB1tRI7d8rj5B1u4y0iFApFiEhZLBZ4vV5otVpQSmEwGGCz2RLaeCeD3c6iNyYTlWQ8iooopqYIhoYIamriF4fme1ef73OglMLlcslmT3333XfHTTu88MILEf/9+OOP4/HHH5fluNHzSHd3N5555hksLy9jYWEBtbW1ERuueNgkCwkQKwycS7Ig57jLy8sYHx+H3+/H9u3bIxULs0AuChyTjefz+dDf3w+r1Yq2tjY0NjbG3fHIGQ2QKw3gcrnQ99Zb0L34IqqKi+EvKYHd48Gs2w3lmTMQFhbAHz6MwqIiFBYWSi53+U5D5BIGA3DllQKczhA8HoKGBiotyjYbgcEQjPAj4zhg925G3MR2S50O2LFDQHt7doSO54GzZ1l3RnU1hVIpYHqa4vx5JQoLgba23PwGSqUyrgbE0NAQ/H4/ent74ff7odfrI2ogjEZjSouoyxU7fVNURGGzcfD5hLjyzBshDbGegkyx4HQ6L3pviGeffRZdXV1obGzE22+/LZljif9cLhd8Ph80Gg30CXJ5m2QhTSiVSni93pyMK8ciHC7RXF5eDrfbLeVS5UAuIguBQCDm3wRBwPj4OEZGRlBZWZmSroWcOhDZjhWe/mnW6dBaXQ1aUwMaVrAVqq2F12bDHFjh6ejoKARBgNFohEajQSgUgsfjydogaSNCo2HywK+/roDFQqDTUbjdBAoF0NDgWiPyU1AAHD0qwGaj8PsBg4HGEr1MGwsLrDujtpa1cYZCFEZjEDodK6psaZG3eDIRRA0InU4Hk8mE+vp6BAIBOBwOOBwOLC0tYXx8HKFQCAaDISJ9EctKWa1m9bLBYKQegt9PoFYnjshshDREPskCpVSWAsd84/jx4/jrv/5rNDY24pFHHsGFCxdgMpnAcRzUajW0Wi30ej3cbjcef/xxNDY2xhxnkywkQLY21ekg28hCuERzRUUFjh49CpfLFVf0I1PInS6JRz6sVqtkl5qO34acZCGbnf3c3Bz6+vqg1WpZ+sfrBRkfR0gQIpSElEolCouKoG9uBvR6UErh9XqlvHYoFMJrr70m5cHFnWWi4riLCa2tFBoNj7ExAoeDQ329gNZWiqEhbxxRMMhiAR0Ov59FF8TFlFKKUIiD3w/MzzPPg3TMkbxeYHycw+Qkq8NoaKBobBTS8voKX6jVajXKyspQVlYmnZ/f75fSF/Pz8xgZGQHP82tsvE0mA6qqOExNMTKkUjF9M7sdOHiQJlRd3AhpiHySBZ/Ph2AwKEvNQj7x93//9+jo6AAA3Hzzzdi9e7dUgOt2u+F2uyVCmuhab5KFNJErsqBUKiM6F1JFtETzvn37YFrxUPB6vTmpg8hlgWN4x0Z7ezvq6+vT2t3IHVlIlyx4PB709fVheXkZnZ2dqK2tZYueTgdaWsrEmKqrWX0Cz4MsLkLo6JBK+Qkh0Ov10Ov152fHvQAAIABJREFU0Ol0cDgcOHTokJTbdjgckkGS6G8Q3p6Xjex4ONYrikEIUF9PUV8veqOw1wcH1y/9YjBQqZNVp8NKO6YJY2NqlJRQvPyyArt3CymRFL8fOH2aw/g404OgFJiaIrBYgEOHhJRrKxK1ThJCoNVqodVqJROicJIZ7aDIccUAqtDfXwC1WoeCAhW2bhXQ1pb4OfljT0M4nU4AuOjJwuHDh6X/X1dXF1ehMRk2yUKayCVZEL3GU4XT6URfXx9cLhc6OjpWF6YV5KodMxhD8TBTiIs7z/MYGxvD2NiYJKWdyc45XwWOgiBgbGwMo6Oj0vlH9KirVKxF89QpcOPjLDYcCoFWVUHYsiXuuOKiEW2QFAqFpMp6h8OBqakp+P3+iNB0eP3DxYDo01wvwlJSAjQ1Cejv5yAIQF+fAsvLKmzZIqC7m2JujuD0aQ7veAefNMIwNUVgNnNobFzdtZeUABMT7LXGxtRIULoKjuEkM9xBUdxBlpfbMTU1j+VlDwwGCoVCi4mJgogoVfTxNkpkgedZ10wwyFJRJSXZK3amApfLBZVKJYukfz5BKQXP81AqlXj/+9+PX/3qV2hvb19zj33wgx/ED3/4QxjCi4XCsEkWEmC90xCpLuzREs27d++O2WaVK7KQrad6OAgh8Pl8eOmll6BSqbB///6Igq90IWeBY6pjLS4uore3FxzHRUR21qC2FqErrwSZmQHx+5kPRE1NXIGARGkQpVIJk8kUcSwxNC2mMMLrH8IjEBu1/sHpBKamOCwuAoODhWhu5hAnfZo1bDa2gC8tMeHOmhoKvV7Ab3/LweulqKjwY8cOiooKCp4HzGaCuTmCpqbE98PCAoFKFSnOKYog2WwkLbKQLckjhEg23tXV1ejuXtWAEO+T8fFxuN1ulg6LauHcCDULCwtAT48JKpUClLJUUUuLgF27Uo/SZAqxEDDf1yBbiHYCADA6Ooq6ujooFIoIImiz2fDzn/88YbvuJllIE7mMLCQbN1qi+ciRI3FZoDimIAgpC8ykAjnD/G63G2azGS6XC93d3ZHmVSuyy2R5mQknlZfHtHDO5fkliyz4fD4MDAxgfn4e7e3tqYlcFRVBKCxMWfAnHWg0GpSXl0uKnOGhaTH64HK5NmT9g80GnDqlgNVKoNUCExMFOHlSjVCIoLU1coEVBGBxkUhFjsXFqSkSipifJ3j1VQWWlxlPm5kBRkeB/ft5dHdTlJaG4HDYUVHBjqtQsPH9fgIg8WKvVrP6h2gIQnotmLlynQzXgKitrQWwqgERXgPh8XgAAENDQzCZTGtsvNcDwSDw9ttaLC+rsHs3i9S43UBvL0vxbNmSI0fYFVwKnRAAi0K+733vg8lkgkajwZe//GVUV1dLmw2DwYCXXnoJLS0tCRU7N8lCmshXZCETiWZxshFDUDk/T0FgDeuEsO1anBk8FAphdHQU4+PjUuFihDEXz4O8+SbIwADzUQAAoxF0926gtTXh+a1HgaNI2oaGhlBWVpa2+2g65C2bKEms0LQgCCnVP+RCeCwRBgY4LCywnTvHARaLB0olRU+PAjU1ISn873QCb7zB3CpDISbQ1NSU+k6TUqC/n8DpBJqaVsPZ8/MEvb1MTnpmhkKhWP19xKybwZD8t6iqoujvZwWEIrddWmKdH1VVqf+W67mrj6UBEQwGcfLkSRQVFcHlckXYeIdHH+Ssk4nGwgKB1apAQwMvRWoMBpaKGBsjaG+XRwMjHhwOB4xG44aMwqWDYDAIvV4Pq9UKv9+P5557Dm63Gx6PB16vVyriTGZQtUkWEiBeGoLnYxvdZIN4JCQbiWbxIZaTLMQtcLRYQHp6AKuVkYTKStDt25mg/goopbBYLBgYGJC6BETZ5giYzSA9PUzh0GBYjTKcOwdaWgokSFPkusBxeXkZvb29CIVC2LVrl1ShngvkQmchnfoHjuPQ19cnvd9gMCS990IhNskHAmxxLSlJvuv3+wGLhUNJCY2oWygtBSwWFr7X6SgEgQknTUxwqKlhwkwuF9tp6vXA1q3Jf3e3G7BauTV579JSiulpgtZWAQYDxcSEDi4XixIsLnJoaBBQWZkaWdixQ0BvL0txUMpu4V27BJSVxf683Q6YzRysVhbpqK+n4Pn8uk6Kv3N9fb0UTQgGg1L0YXl5GZOTk2vqZMQWTjlqHYJBgOcp1OrodlCKQICA53NLFuRSb8w3dDodfvKTn2Bubg4PPPAAHnroIajVaqmrhud5lJSUJL3fNslCmhAX3VAoJGtILnrHHi3RfMUVV6Rt6kJWbI5z3uq4vAxy6hSbucvLAUEAmZgA3G7QK68EDAa4XC709vbC5XKhs7MTNTU1IIRgcXFxzXhkagpUoYCkyrPi10BGR5kjZAKykKsCx0AggMHBQczOzkpeFLne+a3XYhGr/mF6ehpmsxlqtVpqzUtW/7C8zMSN5uaI1IqYSn6ZEFbcKP5sqwSJgJBVsmGzEczMrCo4AoDRyMjG2BhBRweSRhc4jv2LfiRE58uyMmD/fj8WFvzweJjmw9atPLZsSS1yQQjQ3S2gulrA0hI78bIyGpffLi2x9MviIge9nsJiAcbHKXheh23b8pcrF+eM8HtcpVJF2HgDrE5GJJqLi4sYGxuTNCDCayBSIZrRKCigUKlC8Hgiq0rtdoKmJgG59ri6VNIQIiorK/HUU08BACYmJuDz+WA0GlFWVpbSXLNJFtKEyJhzQRZCoRAopZiZmcHg4GDWEs2EkJzoIkSPRyYnQZaXQVtapNeoTsd0BSYnMQSmfV5fX7+mGDNmJCAQWGPfLCHJd8mFKNPU1BQGBgZQVFSEI0eOJFQ5kxv5UnBUqVRQKpVoXUn7xKp/cDqdUCgUK4tBIXp6KrC4aERzswIq1Wp+2WBgC2g8qNVAXZ2At99WoLCQtU9SyiyrTSaKkhJ2DQIBttuMLq/QaCg8HhbNSPZI6vVAbS3rfDAYWB5cEIC5OWZmZTJRqFQ8du1awp49IXBcehoLgGQ1Ip13IgwPM8fNpiZBIkVLS0BPjxFer0IW0alMID5DyRZ4jUYDjUYToQHh8/kkAjE/P4/h4WFQStdoQCSz8TaZgJoaF5aWSmCxMA8Qh4PAYADa23P/XLhcrksishCOwcFBfPOb38Qbb7wBjuMk6+u77rorrhiTiE2ykACxbmRxAZa7bkFMb5w6dQqBQABdXV2orKzMeneZC+OnNePZ7aDRMzjHweZwYOjkSQg7d+LQoUMxWXrM8aqrQSYmQMPjjF4vaz9MMnvK2Q0RCoVgNpsBANu2bUNFRcW6hoY3ktxzsvqH8XEP3n57EVrtKAIBFfR6PQwGAxQKI4aHtWhvT7yQd3QIsNkIJicJKAUsFgPq6ih27RLCoggUBgMriwm/DRwOgtJSmvKi3tUlwOkkmJoSXUrZ7n/XLgEKhVhcSJCgdlgWBIMs/WIyRaZETCbA4+GwvMxh5VKvO8SaiXTvd0IIdDoddDpdXA2ImZkZDAwMSDbe4SmM6E6d5mY7OjoCK6qdLE3U1sY8RHKNSyUNIabMzWYzPv3pT+PChQv48Ic/jNLSUszOzuI///M/8Ytf/AI///nPJfGmWNgkCxlA7iJH0fsAAMrKytDa2ipbf/O6KC4WFrJWwJX/9Hg8GB8bg2JmBo1/+qco278/7qQTazza2AhMToKMj4Majazg0e8H7eoColwZoyFHZCEUCmF4eBgLCwsoLi7Gvn37clPExfMgCwtAIMC+Z1TL5UYvrAqvfyCEYGxMgbq6ELxeDzweD9xuNxYWljA6yqO42IXycmPc+gejETh6lMfsLIHdTgEs4corG1FWtsowCgpYWuPCBW5FVZHtNAFGNlKNcjPZaB4WC4HHw2SPq6qoRA7krkeKBzH9EgpFdlkIAkCpAKUyv2kIudJs8Yimx+ORCITYFaVQKCI6dSgNobVVgMnEp91Rki3E1smLHeL9fPLkSbz99tt44YUX0BIWBf6Hf/gHvO9978PXvvY1fOc734krhLVJFhIg3oQhF1kIl2gWuxsaGxtlFUJZjzQErasDhoYgTExgKhDAgtWKGoUC5ZddBm7nzoQVbjEXd4MB9OhRYHwcmJ4GlEoIjY3MvzjJBJYNWaCUSjLNer0elZWVMBqNuSEKy8tQnD0LMjfHUitaLYTWVgg7dkSkYDZKZCEZCgoo9HrA7VagqKhAmmTVaoKyMj86O5fgcjmS1j80NbHnYnHRhcLCtd99+3YBej3FyAhzh6yooGhvF1BXl9510miwonmw9nO5aluMhlIJNDQIeOMNDoWFLPJCKTA7CxQUBJBCw1POkOtuDI7jJA2I8GOGt3COjo7C7/ejp6cnQqW0sLAw7fqtTOByuSRycynAZrOhvb1dIgoiKSgqKsKBAwcwPDwMIP6cs0kWMkC2pk/iojQwMBAh0fzb3/4WoVBI1p73XKQh1kQCTCbMNDbC+vzzKAqFsK22Fur6eqZYGDYZxBuPUrp2N2cwgG7dCmzdmtb5ZVrg6Ha70dfXB4fDIRVg9vb2rh2LUmBxkRVzGo2sZD/FXahYcAqeZ0RhZga0tpatEk4nuAsXAIMBQmen9H52yPXZ6Uafazpg7owCzp/n4PMBWi3b9atUQHe3EpWV5aisXNV/8Hg8Ul47uv5BXECCweCaRUGhADo6KFpbeckcSe41bT2vd3u7gOVl1g3BIgpAUZGA1lY7dLr8RRbyod4Yq1Pn//7v/9De3i51YszNzcHj8UitvuEpDLk1IC6VyIJI+q688kq89dZbePrpp3HTTTdJm6ALFy7AarXiyiuvBJBgk7wuZ3sRQ26b6kQSzXI5T4YjV5EFcUK12+3o7e1FIBDAlo98BBVqNQjHsY6FFGZx8UaWa3JKN7IgykyPjo6itrYWO3fulCadiPqH5WUofvhDcP/yL+BGR6XPCy0tEO66C/yf/3nCls5wkIUFkLm5VaIAsNi4z8c6PtraAIViw6chorFtG9v1j46yXX9dHcsv19REPj+EEBgMBhgMhpj1D3a7HQBw+vTpuP4XCkXuQtLrSRZ0OuYZ0dJC4XIRKJUUpaVBnDvny+vvn20aIhRi2hVeL/uOFRWJTatiQdxEFBcXR+iYhEIhKfrgcDgiNCCiCUQ2c8qlUuAoRhB6enrwgx/8AE8//TR+97vfobm5GX6/Hz/+8Y/R0dGBj3zkIzhz5gyUSiWamprWKOlukoUMkAlZCAQCGBoawvT0NBoaGrBnz5414e1cFE7KPab48Pl8PoyMjGBmZgbNzc1oaWnJ6MEUPyOXYUw6Rleis6VSqcTBgwfXWNGKUQry3HNQ3XwzcxqKAhkbg+Kzn4XiH/4BwR/9CPSaa5IfOBBgs2nUTohqNCB+P/tbGFnIR2QhEygUrEq9tZWXvl6qpx2+q6yqqsLc3BwOHz4s5bWj/S/CCUQmbXmJkK4vQ7ZQqbCSRhG7PlLrREgGt5tJWk9NEahUzKyrsTGxLbWIbNIQTifw+usKzMwQiCarNTUU+/fzSGejLj7H0fOCUqlESUlJhBNtIBCQyMPy8jLMZjMCgcCaFs50vFIuBXtqYPU+8vl8uOaaa6BWq9Hb24vTp09Leiqvv/46rrvuOigUCvj9fjz55JO45557IsbZJAtJkG1kQRAEmM1mDA8Pw2QyJZRovhgiCyJefvlllJSU4OjRo1m1EoZHFuQAx3FJja58Ph/6+vqwuLgoyTTH63wxvvwyVJ/6FEApSIxcnvga9XqhuuEGBH/2s6SEgRYUsB4+pxPhsyex2yHU1SG6gfxiqVsIBtkCpVbHtbtICeL3jbUohPtfpKr/kMnx80nOxO+fDVlwu4FXXmELNqsRJpicBBYWBOzfLySNymQa6aMUePttRlDq6hgxCQaZwZZGw+HwYSFlAhmPLMSCWq2OqQEh3isLCwsYHR2NaeOt1+vXXGtKKZxOZ0RNxcUKcdNz22234bbbblvz90AggGAwiGAwCJ/PB7vdjsoYheSbZCEDpEoWwiWad+7cmVSiOVeRBbkWYpvNht7eXgBAV1eXpC2fDcQ8ftJzFARgfh5kcREAmJJjRcWaVEeiNIQgCJiYmMDw8DAqKyuTOlsqXS60/O3fMqKQ5PyIIIByHFQ334zAyEjclAQhBCguhtDSwmoUvF5QrRbEbgfUatC2Nmk7fjFEEwC2QIyOEgwMcHA6CdRqoLFRQHe3gGwM+2J9/1j+F+FV9dH1D+H/Ui2KyzdZECMb2ZyD2cxheprJZ4trrc8HjI4y98vq6sQENNM0hNMJTE9zKC9fjWCoVCwNMTvLweEQUtaO4HkehJCMSVOse8Xn80n3isVikWy8w1s4HQ4HWlpaLpnIghi1DQQCOHv2LObm5qDRaFBVVYXm5mYUFxdHPBvxijo3yUIGUCqV8Pv9cf/udrsxMDCQtkRzriIL2RIQn8+HwcFBzM3NSQ9RNs6Q0UhaZyAIzCuir0/yiiBqNWh3N+jOnRGEIR7xsNls6OnpAaUUe/bsidiBxIPpF78A5/PFjCjEAhEEUI8HiqefBv+JT8R8j7hrFHbsAAwGkNFREL8fQl0daFsbc6EM+y7hn1lvpHpcs5ngtdcUUKuZEJHfD6m98bLLUt9JpntcILL+obq6GsBa/wvRGEmr1UbUPsTzNdgoZCEbzM4yAdTwTblWyzJcdjtJShYyTUOEQjEzbFCp2OvpTG9ypSZFhGtAiDvnaLI5OTmJG2+8EYFAAIWFhfjud7+L2dlZ7N+/H01NTRn/Lk899RQeeeQRWCwW7Ny5E8ePH8eBAwfivv8nP/kJvvjFL2J8fBzt7e14+OGHcf3116d9XDFC9Nprr+GRRx7Bq6++Cq/XC0op9Ho9jh07hs9+9rPYuXNn0rE2yUISxPOHcLvda14Pl2iura1NW6I5V5GFgGjGlCbCd+Ll5eU4evQodDodxsbGZItWACnUGczOgvT2gppMq90VLhfzj6ioAMIiHNGiTIFAAAMDA7BYLGhtbUVTU1NqkyClKH3mmcy+z1NPgb/rrsQJe6WSdT20tbFZVK2O+/6NnIYQBKZCyHGQXBq1WkClojCbOXR0UJSWZnb+mU7M8fwvRPJgt9sjfA2i6x8yIQuUMuVFr5e5Zkb7XKQ3Vvatm2o1u61inadCkfz3yDQNUVAAFBVR2GwkwjjLZiMoLKRp1yzkuiMjFtkcHh7G2bNn8eEPfxiBQAAPP/wwzp8/j6KiIvT09MQM0SfCj3/8Y9x77704ceIEDh48iCeeeALXXnstBgYGJOGqcLzyyiv40Ic+hIceegjvec978Mwzz+CGG27AG2+8gW3btqV1bI7jMDw8jI997GNQqVT46Ec/ivr6eoRCIfT39+MXv/gFXnzxRfzv//4vtibpPNskCxkgOg1BKcX09DSGhoaykmjeSDULi4uL6OvrA4A1O/F1EXoKg6RFEJ4/NBqB8K6CFYhRCkoppqamMDg4CJPJJBGdlLG4CPXkZNrfhVDKOhqWliJMtOIiQVk/4XloFxfBjYyAFBYyYpQjh79MEQwCTieB0Ri5AOn1wPw8qwlN5TKEIxfkKJX6B1GWWDTZsVgsKdU/+HzAm28ygytRqby+XsDu3UJGKpByaBzU11OMj692+FLKDL4KCpCS+mGmaQiViilknj6twOQkgcFA4XYzj42urtT8NcLPYb3bNwGWvuju7sbS0hK+8Y1voKSkBD6fD+fPn4+5uCfDY489hjvuuAO33347AODEiRP49a9/je9973u477771rz/ySefxHXXXYfPfvazAIAHH3wQzz33HL7xjW/gxIkTKR9XJL0PPfQQamtrcfz48TUKjV/60pfwzne+E1//+tdx/PjxuPV0wCZZyAjhZMFms6Gvr08WieZcRRbSWdi9Xi8GBgZgtVrR1taGxsbGNZNGOh0HqSBpGoJS0HjXNGph4TgOgUAAr776KgKBALZv357RAw6XK/3PhMPpTH+VjPq88rXXUP7mm1C6XFCoVKA1NeD370da27McQ6UC9HoKu51EiCj5fGzRlLtmQU7Eq3+YmJjA8vJyyvUPvb0c+vuZwZVez777yIgCCkVmaRg50hB1dRRbtwoYHGRulpQyLYydO/mUOnyzaWVuaqJQq3mMjREsL3NobBTQ3Ly2hTYZ8kUWANYJAUDSWdBqtQnTBvEg1gl8/vOfl17jOA5XX301Tp06FfMzp06dwr333hvx2rXXXouf/exnaR8fAH7zm9/g+9//Pjo6OqSNlJiuLSkpwfHjx3HLLbfA6/VukoVsEC8NEQgEcP78eSmP39TUlPWNnc/IgiAIkt6AWPynjTPTy1k0CSQnC7SsDByloH7/qovQSs0IDbOIDgaDmJ2dhd1uR0tLS3ay2dlWQWezoFMK7u23QSYn4S0pAd/YCA7MjZPTaiEcOpR6T6LMCAQkwUlJrritTVhxTiQoKqLw+ZgJVHMzn1EKIl9pFzEkXVBQAJ7nsX379qT1DypVEXp7y2Ey6aDXM1Kt1QIVFQKmp9Mr6BMhR2RBoWC22PX1FDYb+53KyylSDXhmew41NYwcUJo+WRKRb7LAvE2yO/7CwgJ4nl+TuqisrJQk/qNhsVhivt9isaR1bHHtcrlcaGxsXPObivNud3c3ZmZm4s73IjbJQprgeV5SESsqKkq4qKYLscdVTqRCFkS9AYVCIalJJsK6RxZqa0Hb20EGB0FXwvAkFALt6GB/oxSzs7OSIqbRaExoiJISSksRaGiAanIy5QJHAKCEgDY3M9vBGEhpx+h0gpuehlBRAboiUASVCrS8HNzMDASnEynP+jLB6wUGBjiYzRx4HigtFdDZSVFZSdHURBEIsF3s7Czrhujo4LFjR+p+DbGQryLD8JqFZPUP09MOjI0FoNV6UFSkkQy01Go9/H49gsFI34dUjy+HbgQhzCArjE+nDJ7nZZE5z+YnzCdZENUbL5aOpERoaGjAqVOnpDlRJONip0lfXx+MRmPCqAKwSRaSIrwiXZRo5jgOCoUipQrSdJCLyEKiMT0eD/r7+7G0tIT29nbU19enNEnlIrKQ8HsrlaD794NWVYHMzgIAhOpqoL4erhXNBJfLhc7OTnAch9EwhcWMQQgct96K0n/8x7Q/KnziE9nNklEl5dJOWywplzlVFQvhkyTPA2fOcBgZYQ6JGg0wOclhcRG4/HIeZWUUW7YIaGoS4HIxAaDCwswvwUbvRgivf6itBex2BRyOEAwGFzweD2w2GyyWeQAUg4Ne2GxGqS0vFf2H9RaFincO6+GPkewc8kUWXC6XLFLPZWVlUCgUmJubi3h9bm4ubouiKEqW6vsTgVKKv/iLv8B9992H2tpaXHXVVRH31ujoKO6//35cf/31Se+5TbKQAqIlmk0mE06ePCn7pLZeNQs8z2N0dBTj4+Oorq7OqGtjPQscAbCFsqUFNMwEZWRkBOPj46ivr8euXbugUqlgtVplIzLuP/szmB59FFwgkFRnAQAoxwE6Hfhbbon7Hp7nkxePFRSAFhWBW15m44o7AZsNtLBw3WsW5ucJJic51NVRKQtUUEAxPk4wNkZQVrbaBaHVbtzOjVSRznOtUgGdnQJOn1bB6zWhoKAYHMcI07ZtblRV2eBwODA5OSm5KibTf/hjX6hFhEKhvKYh5IgsqNVq7N27F88//zxuuOEGAOzaPv/887j77rtjfubQoUN4/vnn8alPfUp67bnnnsOhQ4fSPj4hBH/+53+O3/72t/izP/szfOADH0B3dzeMRiMmJyfxzErH17e//e2kY22ShSRYWlrCqVOn0NjYKEk0i62IcoXqROQishC+a6eUYn5+Hv39/VCpVNi/f39GegnrnoaIwvz8PPr6+qBWq9d0nshhUS2huBhvf/nL2PF3fwfKcQkJA+U4gBAEf/SjmIJMlFLMzMygv78foVAoQnGwqKgocsepUkHo6oLi9GnoFxaAxUUQngcUCgjd3Wub2HMMl4sFM6L1q4xGwGqVfwec78hCusdvaaFQKHgMDzNRqsJCij17BDQ3a8Fx1WnpPxQWFiIUCuWdLMhpUZ0p8klY5DSRuvfee3Hbbbdh3759OHDgAJ544gm43W6pO+LWW29FbW0tHnroIQDAJz/5SRw7dgxf//rX8e53vxs/+tGPcObMmZQW9FioqKjAd7/7XTzxxBP43e9+h5/+9KfSHHTZZZfhq1/9KpqampKOs0kWkiCWpLFIEEKhkKxkIReRBZGAiK6KdrsdHR0dqKury6prYz0LHEV4vV709fXBZrPF/Q5ZkQWeB8xmELMZ8PuhVqth37oVwZ/9DKqbbwZd8YYIr2GQujR0urjeEG63Gz09PXC73ejq6oJOp5MWjenpaSm1FU4eCmtrob78cnitVqbJUFcH2twcIdq0XtBoWEphha9I8PkgRRXgcIAsLACCAFpSAphMeSvCzBbpkgVCWAdAQwOPQCC+E2as+odgMBjT00ChUKCvry9n/hfJsBGiG3JvxtKBGFmQAzfddBOsVivuv/9+WCwW7Nq1C88++6xUxGg2myOu9eHDh/HMM8/gC1/4Av7u7/4O7e3t+NnPfpa2xkI46urq8Oijj8JsNmNmZgaCIKC5uVkisqlgkywkASFkjfcBx3HgOC5nC7vcCIVCePnll1FXV4cdO3Zk7QWfVhoiFAIsFhCnkxXpVVUxaTmHgyn6FBYmXeAFQcD4+DhGRkZQVVWFyy+/PO53yJgsUAry1lsgFy6wIkqVCurZWRQGg6B33onAyAgUTz8N7qmnmI6C+LHmZgif+ARznYwqexcEAaOjoxgbG0NdXR327NkDQgiCwSAMBoM0WUQ7Ls7NzcHr9UKn08Hb3Y2JhgaUV1QwE5z0v1nWqKigKC+nmJ5myn8KBbC8zNrxGhspyMgIFOfPs3ZRANBqIXR1Qdi6NSP/6HyLUGUa2eC49FtFVSrVGv2HsbExWK1WqNXqCP0Hse5B/KfVanMWgdkIaQie5xPKsecSTqdW+c0bAAAgAElEQVRTVsfJu+++O27a4YUXXljz2gc/+EF88IMflO344j3d0NCAhoYG6fV0SOEmWcgQG1WaWYQoKiO25xw4cEA2ieaUF2SvF+S110AmJlZ1XpVKptgTCjGyUFoKrVIJPo7z0OLiInp7e0EISalTI5bxV0pYXAQGBpjnxMqOQlCroTp9GmRsDHTnTvCf+ARTZlxaWjWBKimJuYNeWlpCT08POI7DgQMHJI35UCi05vzCd5x1dXUA2I7T4XDg/PnzWLbbMb2yGzAajSzysA4LhnieWi2wf7+AN97gYLEQ8Dz76nv2CKg3LELxf+cAhQK0qYldC4cD3IULoCYT6Mr3SRcXUxpCbigUCuh0OrS2tkrnE+6+aTab4XK5oFQqIwyR0vG/SIaNkIbId+vkpWBPLSKWdHy6vhubZCEJ4k0amdhUJ4NcBCS8ILO9vR09PT1J22LSQaqRBTI0BDIyAlpfz2KzPh/I738PBAKg73gHi2/Pz6NgcRGeqPPz+/0YGBjA3NxcXHGoWMg0skCWl0H8/khvBoUCQZ0OmJoCxM4XQpjYUhzBpXB56XTOOxoqlQqlpaVQKBTo7OyEwWCA1+uF3W5fs2CEk4fCwsKchG5LSyne8Q4eS0sEoRCT9DUYAG7ACuJ2Q1gpPAXA2jrtdpDp6YzIwsUaWZDz+OH3TKb+FyKRyGTB3ShpiHx2QyQz/rsYkc19vUkWUkC2NtWpQqwFyPRBDQaDGB4exuTkJBoaGrBnzx4oFAr09PSA53moZCqME1USE4LngfFx0KKiVcvlpSUQANBoQAMBFravr4dichKK6WkAbKI0m80YGhpCaWlp2joWmZIFynGsFoFSKVLAcRz7Hilct/ACxuLi4vTlpZOMLabD9Hq9tGDwPA+XyyURiJmZGfh8vph+B3JM/Erlqv+DhFCIFXdGQ6FgWtAZYiMt1uuNVFon06l/MBqNEdGHVO6HjZKGyGdkQYzsXMyIngvD76t0n7FNspAhchVZANIPAYoL1cDAAIxGIw4dOhRRnCN390JKBY6CwBbasF0uCQTYosxOevW9Oh04ux12ux09PT0IhUIpWXrHgmgklfbusKICtLgYmJsDKisZYfB6ofD7gebmhB8NL2DcunVrVpLf0UiUVlEoFCgqKoqw0Y3ndxBOHoqKimTLBdOiInatwtU1eZ5Zb6dpuCONuQEiC/kmC5lGo1L1v0hW/7CZhrg00hBy/oabZCFD5CqyACCtKIDD4UBvby98Ph+6urpQVVW1ZqHKhS5C0vFUKqCmhrlFriwoVK0G53IxiebwSmO/H4s8j4HTp9HS0oLm5uaMJwnx4Uh7Z2Q0gu7ZA3L2LMjYGEAIFIEAnLW1LBcfA+EFjLW1tVJrrZxIl3TE8jtwu93SgjE+Pg6XywWNRrOm3z+Ta06rqiA0N4MbHmaFq4QATidoXV2EwVe6yHdkId/Hl2uSj+d/kaz+YZMsyNcNkS88+uij+M53voP29nbo9XrU1dWhrKwMarUahYWFKCkpQUVFBZRKJTo7OyNIZixskoUUsF5pCEJIykWOgUAAw8PDmJqaQlNTE1paWuIuVHKThVQjFbS9HZifZwWCej3TDNZqWVqCUsDvh21oCFa3G+6ODhw5ciTr2opYhTwpo7ERtKQEdH4eJBRCSKGAbXQ0ZhoivIAxU72KVJHNTpsQAqPRCKMgoG5hAWRpCSGlEi6DAUt6vSQYJHZoiMRBNJxJCqUSwr59oBUV4MbGWOvkli0QmppYIWsGyHdkId8KirmsF4hV/yCms8QUxvz8PCilePPNNyPqYTKtf8gU+SYLF3tkoaWlBQcPHgSlFMFgEN/4xjcQDAZRuyKRv7S0BJ/PBwD4zne+g4997GMJr/kmWcgQuSALQPKFPdx6uaioKKUFVm79hpR1FkpKQK+4ApiYYOH9+nrw+/aBLC7CNzGB6clJuDUaqK64AnqTSZYizPDIQkYoKGAKigDgckGIko4OBAIYHBzE7OxsRgWM6S5CsixadjsUr7wCzmoFNRqhCgZhmp1FUXc3hD17QBEZrp6dnYXD4QClFOfOnVvVfohXba/RgLa3g29vz/5cV5DvnX2+ycJ6LpLR6Sye5/GHP/wB7e3t8Hg8Uv2DSCjTrX/IFPkiC5RSuFyuiPTexYgbb7wR733ve6FSqfCLX/wCHMfh2LFjuPbaa6FSqWA2m/HQQw+hoaFBUpdMdL03yUKGUCqVCGZRwJVo3HgL+/LysmSHvW3bNlRUVKQ0qcktopRWpKKoCHTHDuk/Q6EQRoaHMW2zof6d70TXzp2YtVrhitJCzxRZk4WoscRdrmhW1d/fj6KiIlkLGBMh41bQMHBjY+Dm59luX5zY3W5ww8OgjY1AWRm0Wi20Wq1k572wsIDBwUFUVFTAbrdjeHg4otpeJA9Go1H2CT3fkYWNQBbyXTMBQApTA+yahBPKubm5nOo/UErzmgq5FCILwGod3D//8z/jPe95D+68807pbzU1Nfj2t7+NG2+8ERcuXMCxY8cS3vubZCEFxLOp9nq9sh8r1kIcvpttbm5OO6efizREuouxKDXd19cHrVaL/ddcI+UE5ZRoJoRIXu1yjCXuMsRW1O7u7qwKGDP5XLaLJ5mZYZ4S4ROvwQDMzzN1pRi2hGJKrLa2FrUrtQditb3dbsfS0hLGx8cl2djwcHUqZklJz/mPOLKwEQosgchdJiFkDaFMVv8Qnr5IV/9BPIdLQcExnxBVMK1WK5ZXvGbCUVBQgJGRkZTmmE2ykCFylYYIH1cQBExOTmJoaAglJSU4cuTIGjXJVJCLNEQ65MPj8aCvrw/Ly8vo7OxEbW1txGScb6+JmAgGgakp6C0WnPn1r1GxdSt279697pOXHJEFaLXM4CEc4phpkM7oantKKXw+n9S6OTU1BafTuWaxKCwsTKttdzOykN/IAs/zEulOhET1D+ERiEz0H8T5IB/Xwe/3IxAIXPRpCGCV8H3sYx/Do48+CqPRiD/5kz+BVquFSqXCY489huLiYjQ2NgJITNI3yUKGyGXNQigUgs1mQ29vL3iez7iNMHzMde+GAJv0xsbGMDo6iurq6rgyzXKnSbJeYG02uH7/e8y+8QZKfT40d3TAYLeDRrWCZnN+uXhvPAgNDVBMTQEeDys6pBTEYgGKi0FXdomZgBACnU4HnU4n2ecKgiAVyjkcDlgsFni9Xuj1+ojFwmg0JlwI8r2zzzdZyPfxM00txWrnjaX/EF1QW1hYCL1eL90TImHJB1lwOBwAcEmkIcT76I477sDs7Cz+7d/+DT/96U+h1+sxOTkJh8OBEydOoDlJeziwSRZSQrw0RC7IAiEEU1NTcLvdaG1tRVNTU9YPTD7SEAsLC+jt7YVCoUjaLSCrU2SW4wW8Xsz+93/DMziIom3bsDw3B219PcjAAGuvFJUc1wlyRBZoUxMEm421N4q1IcXF4HfvZumIeJ/L4Lgcx61ZLAKBgEQerFYrRkdHIQhCRK5b1H6QJZKSJTYCWch3GkLO48eKSIXXP1gsFgwNDUXUP6jV6rz9BmIqZT1qktYLer0eX/3qV/Hud78bb775JpxOJ2pqavChD30oZc2VTbKQIeQO7QuCgImJCSwsLECv18taQLeekQWfz4f+/n4sLCygvb0d9fX1SSeejUAWxALG0VdfRb3FgrZjx6DU6zE9Nweq0TDBprExoKtrVZFynZD14qlUQti7lxUz2u3Mx6GignlMrwPUajXKyspQtlIbEZ3rnpiYgNvthkqlklIWgiDI7uqaKvJNFvJ9/FwXFqZS/zA7OwtBEPDSSy9lXf+QLkR76nzrTMgJ8Z66/PLLcfnll2c0xiZZSAG5jiyEmyWVl5dDr9fLympzEVmglEbsQARBkGSaKyoqcPTo0ZRlmnNCFgIB5qEs+isngNvtRm9vL1wuF7a1tqLC4QAMBohLtCAIkrcFQqF1JQuyLRocxwhCFmkHuRAv1y2Gqq1WK4LBIF588UUpVC0WUBoMhpwvpPlerDdCZGG9Wxaj74mlpSX09/dj69atWdc/pAuHwwHjOhHp9QIhBP/1X/+FN998E1qtFjzPw2QyoaKiAhqNBu9///uTjrFJFjKEHGTB6/ViYGAACwsLaGtrQ0NDA4aHh2VvyVQoFLKOKT6Y4qQm1lcIgoA9e/agNI7JUjzIShb8fhSMjUE9MQGi1wM6HVBczFo4CwqA6mpJZCm8pqK2tha7du2Cyu8HhoeB5WWQcIdLmw2oq2PjrSM2Qlh+PaBQKFBcXIzi4mIYjUYMDg5i9+7dkm23GKoGWAV3ePeF3DbGG6Eb4Y/5+MBqFb8c9Q/pQuyEyCdhlBM8z+PEiRN47LHHUFJSgrNnz6K5uRlWqxUulwvV1dWbZCGXUCqVa3bXqSJ8kaqsrMTll18uTXi5aMmU205bJAs+nw/j4+OYnZ2VZJozeUBl64YQBJCzZ1E0MAC0t7MF/w9/AKEUtKMDpLAQtKkJ9OBBLHk8sRUYVSqgsxPk3DlQjwdql4uJShUWgnZ0JI1S5AJ/DGQhHOL3jSddLXZfjI6Owu12Q6PRyKo0mO/IQr7JykaWes6k/iFd/YdLRWNBxMLCAh5//HF87nOfw5/+6Z9i+/bteP3113Hu3Dl89atfxYMPPpjSOJtkIQXES0MATGQonRya1WpFX18fFAoF9u3bB1P47hXypwwA+VsTRbz66qswmUw4sncv9ILA2vMyeMjEboi4k3QoxFIAanXiFIDVCjI2hmBFBXi9HmR4mKlIBgKASgVaUwN+YACjNhvGDIa4Coy0uxtUrwcZHQWGhsA3NYFu2wasVPyvJy6V3U26iPW9Jelqo1HSfgiFQtJCEb7TNBqNa3aaqV7LjdCNkO/jb1SyEI149Q9ut1uKQMTTf4jX0nupkYX5+Xm43W7ceeed6O3thUqlglqtxlVXXYXZ2Vn87d/+LV588cWkv/smWcgQHMeBEJIyWfB4POjv78fS0hI6OjpQX18fc0KQu3BSHFMusuB0OtHT0wMAaG9tRZPfD5w8CeJygapUQH096xhIQw9CvEHXkAVBYAv24CDgdLIUQFsb2+HHKnxzuYBgEFSrBbHb2TlVVQEOB2CzYdHhgGVmBlqvF0f+4i+gj5eX5DigpQW0uRlWQUDLwYPQ5lGgJR+RhXzvrFOFUqmMqf0gEgjRjTXc0ln8F++5zXdkId+L9cVuTx1OKuPpP4gtveH1D5RSlJSUXDKCTOJ97Ha7YTQaEQqFEAgEUFhYiOHhYezatQsejwcWi0V6fyJskoUMQQhJqW6B53nJmbCmpgZXXHFFQnIhd8pArjFDoRCGhoYwOTmJxsZGuFwulDocIOfPg+r1zI7Y7wfp7wdCIdAjRyIVAxMgvEgyfJIkw8Mgp0+DajQsYuHxgLz2GhAIgO7atXYglQogBBylEHheShkEPR5Y/H4s6PVoqq9HcVkZM7ZKBkJAZNaASBd/LDUL0chGIVPUfqhcscgWBCFioZifn4fH44FOp4to3RS1H/JNFjbTEPL7QsTTfwiPSv3rv/4rfvCDH6C+vh46nQ7f/e53ceDAAXR3d8t2LktLS7jnnnvwy1/+EhzH4QMf+ACefPLJhAWVV155Jf7whz9EvPaXf/mXOHHiRMJjifdwSUkJjh49ijNnzmDLli3o7OzEF77wBdxwww341re+hSuuuCKlc98kCykgrlZ2ArIgyhv39/dDrVbjwIEDKTkTbrTIAqUUFosF/f39MBgMOHz4MIxGI2anp0GGh1k0QZQLVqlAlUqQyUnQxUUgRSGp8IJJCcEgMDAAqtWuVvDr9aBKJTAywmoSojUCKitBy8uhPXsWfE0NqFoNW38/7A4HlHv3YvvWrVCazaD19WkRmXwu1n+MZEHu7xseVRARvlAsLS1hbGwMPM+joKAAgUAANpsNOp1OFp+DdLERIguXGlmIBZVKhdLSUqkg+8knn8QnP/lJ/OM//iPGxsbwgx/8AJ/61KdAKcXXvvY13HXXXVkf85ZbbsHs7Cyee+45BINB3H777bjzzjvxzDPPJPzcHXfcgQceeED671SUfMXfsb6+Hp/61Keg1WpRXFyMe+65B5/5zGdw33334R3veAe++MUvAkhsIgVskoWUkY5NtdvtRl9fH+x2e0x540TIRWQhU7IgthQ6nU5s2bIF1dXV0vdQUgrqdALRnQ9aLRAIMDvqFCGOGXGOXi/gdgNRNR0oKACZngZ1u9eSBY0G9MABBMfGEFpYwMTsLNTLy6jq6ICmshLEbAatqgJta0vr3OSOLPA8L+1e8z0pb1TkeoGOXigopfB6vXA4HOjv74fVaoXZbI7Ic4tFlLnWftgINQsXcxoiU3Ach7a2NqjValx//fV48MEHwfM8+vv7M5LZj0ZfXx+effZZvP7669i3bx8A4Pjx47j++uvx6KOPoqamJu5n9Xq9pJKaKsS5RafTYWeYmNzVV1+Nt956K+1rvEkWskA0WQiFQhgZGcHExATq6uqwc+fOtDTxY40pB9IlC+Gpk7q6OtZSGPU9iFoN3mBYW9To9bIixDQeLnHRjFiU1WqmkeDxMAISNj4V/xYDgcJCTHd1QZibQ+vRoygvKYHC4WCfq6gAbWhIS4xIrp09pVTqnhEd9cKPEU4cIlIxl1pkweUCmZ8HeB4wmUBLS9d0mOSrRkOv10Ov12N4eBjd3d0wGAxS+sJut2N2dhY+n0+Srg7XfpCT9G2mIdg55Fp8KR7CaxYUCgW2bt0qy7inTp1CcXGxRBQAtnBzHIfTp08nbF98+umn8cMf/hBVVVV473vfiy9+8YsJCcz58+fx6quvory8HCqVChqNBsXFxdDpdOA4DgaDATqdDpRSFBcXp9R+vEkWsoC4sIeH6nU6HS677LKMq2nFhV3OvGk6ZMFqtaK3txdqtRoHDx6Ma6aiUKkQaGwEGRwEnZsDiopYzcLCAmhn59qIQxKsIQtaLdDaCnLmDEs9FBSwmoW5OdCuLna8MIRbSBNCUL17N+q3bGF/S+tMkpxXBhBJgjiORqOJIA7RfxePm+9OCLkXbWI2Q3HuHFORBAC1GkJ7O4SdO9cUrOa7ZkB03RTz3PX19QBWpavtdjvm5+cjbJrD2zdTFSSLdex8kwVBENLe5MiNfEQWRLhcrpx0Q1gsFqljQ4RYoCsWGcbChz/8YTQ2NqKmpgbnz5/H5z73OQwMDOB//ud/4n7m5MmTePjhh1FZWQm1Wg1BEGC1WqHT6VBWViZ1DFFKcdddd+F973tf0jVnkyykiHhpCLfbjddffx1utxudnZ0RofpMEK7fINfDkgoB8Xq96O/vx+LiYsJujfAx/VVVEEpLWVHj0hKrWdixA3Tr1rT1CGItyrSri9UujI6CLC2BarWgXV1rihvDFRi7u7thtVplu3bZ7OzDSYC4AIRf0/BzFN8XTiB8Ph98Ph9CoRCCwWDc6MNFAaeTEYVAALSpid0fbje43l5Qkwm0pUV6a74jKYmek3jS1aL2w/j4OFwuF9Rq9Rrth1TSF+IzkG+ykO80RD7PId3Wyfvuuw8PP/xwwvf09fVlfD533nmn9P+3b9+O6upqXHXVVRgZGUFra2vMz9x4443Yvn07AGBgYAAnTpxAdXU1jhw5AgAYHx/HCy+8AI1GI0UVNslCjiAqibndbjQ2NmLPnj2y5DLFB0ROZh1eQBg9puhJMTw8vEYgKhE4joNAKdDaykL7LhdLHSQwJko23proh0oFuncv0N4OKqYjiookIhJTgVGlwtLSkmx1BpkUOIrv53leyj8nixRwHBfRQjo9PY2hoSGYTKaIqv5Y0YeLofaBWK3A8jJoc/MqkTQYALud1ZKEkQVgY0QWUkG4TLGYcw6FQhHOm5OTkwgEAmu0H2JJV4u/76XsDZEKQqFQXslCOq2Tn/nMZ/DRj3404XtaWlpQVVWF+fn5iNdDoRCWlpbSqkc4ePAgAGB4eDguWaiurpbaRs+fP4+DBw/i/vvvjzjOf//3f+NXv/qV5DiZ7DffJAtpglIa0btdVVWFLSvhbjmQrn5DKohHQJaWltDb2wsA2Lt3r9SrnuqY0uKuUq0tRMzgHOMu8IWFa8SebDYbenp6QAhZ42opZ1FiumOJ9Qjh4eR0Jn6v14ve3l643W5s3bo1ImwZK/oQfm6Jah/yDrGVNfpaKJUgfn/ESxs5spAKlEolTCZThOBauPaDxWLB4OAgCCER5CE85ZfvyEK+7518RRYopXA6nXHTr7EQrjKaCIcOHcLy8jLOnj2LvXv3AgB+//vfQxAEiQCkgjfffBMAJDIQD36/HxqNBt///vdx0003oaqqCjzPS1LaH/jAB/CVr3wF586dQ2dn56Yok1wghMDhcKC3txc+nw/d3d1wuVzweDyyHycXxk/Aqtqk3+/HwMAA5ubmVlUM3W6Q3l7AamUtinV1TLEwzqQptypkqrUBgUAAg4ODmJ2djavAKOe5pRpZiK49EH/HVEEphdlsxsjICKqqqrBjx441eePw6AMAiTSE/++GjT4UFTFS6fGsFr8KAojLBaGjY83bL5bIQqqIVhkUBAFut1uqfxgZGYHH45GielNTU5L2w3ovmhshDZHPmoVcKTh2dXXhuuuuwx133IETJ04gGAzi7rvvxs033yxFpaanp3HVVVfh+9//Pg4cOICRkRE888wzuP7661FaWorz58/j05/+NK644grs2LEj4fHE+aOrqws//elP8c53vvP/s/fmwY3c55n/p3EDBAiA931zhpxbo2MOjSTbsqLE2S0n5Up2t7w/X7uR7dhbcZxd25uy7Ng57XgTl5Jdq7JRre2s7U3iTbk2m7J2LdleSdFYmZFnNMMDvMH7AEncZwPdvz+gbjVIkARIgKBkPlUslYZko9Fs9Pf5vu/zPg9nz55Vr+uPf/xjVldX1Xtyr3v+mCwUiOnpacbGxujq6qKnpweDwYDX6y355AKU3mtBS0Dm5uYYHx+ntrb2jRjsQADh5ZcRVlaQrVYEUUSYmEC+776sW+IO53iYsdJaAaPT6eTBBx/cUQ2s0+lKFpxVSGVBW01QXr+YxSYcDjMyMkI6nebChQsFV3iUxX+r9mFrdSNf9eGwCYRcV4fU14fO48lOshgMCOEwUmMjUldX7s9WsLKgXLNykxWdTofD4cDhcORYVyt28H6/n9nZWdLpdE77wul0YrVay3p+R6ENUSmyoJC4ctk9f+tb3+LjH/84jz76qGrK9NRTT6nfF0WRsbExdRNqMpl47rnn+OpXv0o0GqW9vZ33vOc9fPazn93ztZS/4Wc+8xk+8pGP8KEPfYiHH36Y5uZm/H4/3/nOd3jkkUdUbcMxWSgR6uvrqauro0rTky/HmKNy3FJ7LQiCoM7Wnj9/PqdsJoyPZ6cMuruzUcYA6+swNAStrXl1CIdZWYi9HvqkCBgbGxv37P+Xsg2x0+K1tZpQLEmQJInp6WlmZ2fp6Oigp6fnwA/IrQRCuQ4KedBWIRRoNRXK75d8MdLpkO65B7mmBt3sLKRSSH19WaKQpz9cqcqC8reuxOsbDAY1BOv8+fOqyFURTy4uLuLxeNDr9du8H0o5vfCzXFmIRCLIslw2slBTU7OrAVNXV1fO86a9vX2be2Mh0LYUBgcH+dM//VOeeeYZXnzxRcLhMHq9nn/1r/4V//E//seC47iPyUKBqK6u3kYMykUWSllZEEWRiYkJ0uk01dXVnD59OvdDKIqwuIjsdue6GtbWIni9WSfGPGRBr9eTSqVKco6Qn3zsJGAs5FjlFjhuHXcsligEAgFGRkbU1MtyPZzy6Re2ti3y+T5oyUXJdpkGA3JvL5kdRFkKKl1ZgMqSFS1hU6yrFWGaYl2tEIjV1VXi8bhqXa2QB8W6ej+otGZBuR8rQRbC4TDAmz5Iauvf7+LFi1y8ePFAxzwmCwfAUa4saMv2DodDdQDb9gEUhCxJ2Pp6kvTG9/Kg1G2IrcfbTcC4F8opcNy6Oy+WJKTTaSYnJ1lcXKS3t5eOjo5DfzDvVX1IJpMsLi7m3N/5qg/lxM9iZQH2dm/MZ12teD+EQiHW19eZnp5GkiTsdvs274dC3lel2xBKxa5SZMFms5XdpbPc+PznP88nP/lJnE4n3/zmN9Hr9VRVVak6GJPJhM1my5ni2Qtv7ityiNgpproc0c8HrSxEIhFVUT84OEhTUxM/+clP8p+rwQAdHQi3biFXV2dFaLIMq6vZaoOS+7AF5WpDKD273QSMhRyrVLtT7bGUHU+h45BbofSjbTYbV65cKYmFbCmg3cmurq6qupDz589jMBh2dZ0sh/bhZ7mysJ9d/U7eDwqBUCKajUbjtuTNfItipdsQyn1WiXMIhUI4HI6KG6IdFC+99BK/+Zu/CcDTTz+tfoYVKEGIOp2OF154oaBjHpOFA+CoVRYymQxTU1N4vV7a29tzvB92m7CQT54Evx9hbi77D5KE7HIh33NPrtWyBqWuLAiCQDAYZGZmhurq6l0FjHuh1JoFSZJUp879jEOmUinGxsZYX1+nv7+/qKyQw0IymcTj8eD3+xkYGNimC9lafdhJPFmq6kOlKwuV2lmXwr1R6/2gjWjWej8sLi6STCapqqrK0T9UVVVVvA2hPKcqcQ5vlXjqv/iLv8DpdCLLMr/7u7+LKIrEYjGi0SixWAxJkggGgyS3jC3vhmOycAAoi3qpP1z7qSysra0xMjKCxWLJaze96zimzYZ87Rry0hJCOAwmE3JT0zZL5YKPVyRisRibm5uk02nOnj27p4BxL5SKLGjz4BOJBGazuSiioNiAj42N4Xa7uXLlyr5tgMsF7TnW1NRw9erVvP4ee2kflP9uvSf2M7p5XFko/SKp1+txuVw57bxkMqmSh9XVVSYnJ4HsYj0/P09tbS3V1dUFmbSVEopeoRJ/g0gk8paoLGjNmh599NFt39+PJuSYLBSIndoQQEkNlJTjFroQx2IxRkdHCQQCuzKdiRMAACAASURBVCZc7rm4m0zQ1VVwjkIp2hBaAaPVaqWhoaHoZLWdzq0UeQ6ZTAa3283MzAwvvfQSNptNzQpwuVzY7fZd7bNHR0cJh8MMDg6qLoxHCYlEgtHRUUKh0L7OcafRzVIYR1Vysa4kDjNx0mw25xgKKYZEN2/eVMPkotEoZrM5RzypTGyUC5X0WFDaEG92KBudYDDIX/7lX3L16lWuXLlCMBjk6aef5pVXXuEd73gHH/7whwuepDkmCweAckOXmizo9XoSicSuP6NdaJubm3nooYd2PYdSGz0dtA2hCBgB7rvvPtbW1kp2fgcROG4dh2xubqalpQVRFAkEAmqA0MTEBEAOeXA6nRgMBubn51X77LNnz1Y8lGcrFBfS8fFx6uvruXLlSsnu372Mo3YLzVJIRKUrC8q5VAKVbAEoyZsAJ0+eVNus4XCYYDBIIBBgbm4OURRVsZzSwrDZbCW7ZpUUWL5V2hAKZmdn+epXv8rDDz8MwP/+3/+bJ598kp//+Z/nS1/6EjabjQ996EMFeYsck4UDQBGJlFrkuNcxNzY21LG7++67L8dWdieUgyzs53haAWNvby9dXV3odDrW19dLZqS03wVnt3FIo9G4bRcWiURUAuHxeIjH4+rvtLW10dLScuRU1UrFIxKJcObMmYJsag+C/VQflPuqEqFKh2HItNfrHyW9wFbramVaRnGe1Frfb03e3C8BVeyIK4FyuTdWCqurq1gsFu6//34WFhZ49tln+a3f+i3+8A//kD/+4z/mv//3/86HPvShgkStR+tJdoSx0wOkHCLHnTQLightbW2N/v7+osbuSu0KWWypXzvKmU/AWGpvhGLPrVhzJUEQchz4ZmZmmJmZoba2FpvNpgYI6XS6nOpDqQ10CoUsyywsLDAxMVHxisdu1Qefz8f8/DxNTU059+th2VZXmixUWlyonfTJB0EQdrSuVrwf1tbWiMViWCyWbcmbhby3SlcW3gpkQbmPY7GYei0XFhbweDxqiqXZbFYr2IVsro7JQhHYKaa61GRha2VByQ2YmJigrq6Ohx56qGihnMFgKEr5uheKqSxoHRiVUc6tD+RS5zkUShYOOg4Z2NhgxONB0Ol44IEHch40WgOdQCDA8vIy8XicqqoqtW3hcrlKWsLNh1gsxsjICPF4nPPnz1NbW1u219oPFHvusbExfD4fAwMDNDQ05G1fKChXaNZRIAuVfv39jCorxFmBKIqqeHJzc1O1xnc4HDmjm/msqyudC1G3w7j4mwnK33BgYIDW1lYee+wxJEmitraWhx56iFgshsfjoet1q/VC7rljsnBAlKuyoCycitOfkhuw3xu5HOFUex1Pq6toaWnZ1YGxlKOYhZCFrQ6GRZsr+Xws/r//R3hsjP6WFuouXULYQuC0Bjrt7e1AtjoUDAbVEq7H41GrDwqBULQPB4Usy6p+orm5mQsXLhy5tghk/SdGRkaorq7ecWLksEKzKk0WjkIbohSvbzQaqa2tVYmpLMvE43GVQCwsLBAOhzEYDNu8HypJFiKRCD1b4tLfzDh58iSf/vSn+ZM/+RPq6ur4d//u3wHZeOt4PM473/lO4JgsHArKVVkQRZHh4WGWlpbo6emhu7v7QB/icgkcd3q4bhUw7qWrKIc3Qj7kS4cslihsTE/j++53qYrFODk4iFmvR/inf0L2+5EuX4ZdHnRms5mGhoacEq5WQLa4uEgikcBut+eQh2KrD9FolJGREZLJZFHhVIcJURQZHx9nbW2NEydO0NLSsuN7PKzQrEqThaPQhijH6yviScVJFrLEJBKJqARieXmZRCKB0WhEr9eryZtVVVWHdk3eKm0ILR5//HEef/zxnH87d+4cX/7yl9VR2kKu7zFZKAKH0YaQZZmNjQ3i8TiJROJA5kRalIMswHa3t50EjHvhsPIcDpIOqcRjJ37yE04YDDjf9jaE19+bXF2N4PUi9PQg75Ezv/VcFULQ0dEBoIYHBQIBFhYWGBkZwWAwbKs+5Nt9SZKkRl23tbXR19dX8VCgfNjY2GB4eBi73b5v/4lShWZpcRTIQqVf/7DuF71er97LChQDs3g8js/nY2pqClmW1faFooEwm81luU5vpWkI5V5eWVnh5Zdfxu/3Y7Vacbvd1NTUYLFYMJvNx6OTh4VSkgUlqjgajaLT6bh48WLJPhDlaEPAG/3FvQSMhRyvXG2Ig6ZDao2LXC4XF5qaMLlcubkZFguk0xAKQRFkIR8UAZnieyBJkqo+DwQCzM/Pk0qltlUfMpmM2rK69957i8rTOCyk02nGx8dZWVnhxIkTJXWz3G9olvbrKJCFt0IbYr8wmUyYzWYsFgv9/f051tXBYBCv10s0Gs2xrnY6nTgcjpK02N4qlQXlPn7ttdf4/Oc/z9jYGDabjXg8rgYAer1evvGNb/De9763oNbPMVkoAjuZHR2ULCjhQnNzc3R2dnL69GleeumlAx1zK8pZWVAEdIq5Tz4B414otcBRIQjAgaoJWuMixQZZHw4jhEK5BlaynP0qw4SBTqdT3fc629tBFElkMgRef4DOzc0RCoUAsNlsNDc3VzS5bydsbm4yPDyM1WrlypUrWK3Wsr9msdWHZDKppm4eVmiWFpXWLFSarED2b6O4Ru5mXa2N7tZaVyvVh6qqqqI3BZFIJKfS8WaFUiH6sz/7M3w+H1/4whc4efIkyWSSZDKJKIr4/X4uXboEFJbDcUwWDgiDwbCngdJOkGVZDe5RHqAOh0P1GyjlvHGpyYKyE/N6vczPz9PS0sL58+f3PY5XaoEjZEmYdrdY7INDO2qoNS6SOzoQvF4IBrOW2JkMwuvBW/LrWoSSQ5KybY7JSYRoFJvdjrW/n6rmZvx+Pzabjc7OTtLpNMFgkPn5eURRVGfflQpEocmDpUQmk2FiYoKlpSX6+vpob2+v2O59t+qDYrZVX19/aKFZW1HpEKdKvz7sPQ2xk3W1Qh5WVlZU07St3g97WVe/VdoQyubo9u3bPPHEE/zqr/7qgY95TBYOiP22IbS78ZMnT+aIu7TOkEeVLPj9fvUBW6gx1G4otcARsu5lbre74PluBYo4MJFI5B01lNvbkS5cQOfxwOZm9t9qapDvvRfs9pK8h60QxsfR3bgBZjOyzQYbG/ju3mWyro66q1fp6enJeY+yLJNIJFTTKK/XSyQSwWQy5fg+lNu6VxG6ms1mLl++fGSSNrWQJImxsTHW1tbUsU2lunAYoVlbz6WSjp+VbkMo51DsPZlPOByNRlXxpNa6eqv3g/a13iptCOU9/fqv/zozMzMlWUuOyUIR2CkfohiykMlkVAOfnXbjimnNUXBc3ApFwb60tIRer+fMmTMHJgpQujwHZZfY19eH3+/H6/UiSRLV1dXqbsTpdOZ1l5MkCa/Xy8zMDG1tbVy8eDH/Q0unQz57lkxbG0IwCHo9cl0dlKusnkggjI0hV1VBXR3RaBSv348xkeCCxYKloyNXP0H2XrVarVit1pzybSgUIhAIEAgE1Nl3pXSrrT4cFJlMhsnJSRYWFujr66Ojo+NIhvMorRElNlz73g8jNGsrjkIb4qhXFgqB1vuhtbUVyG6+FPIQCASYnZ0lnU5TVVXF17/+dQYHB7FarWWpLPz+7/8+//AP/8Dt27cxmUwEAoE9f0eWZT7/+c/zX//rfyUQCPDggw/yta99jf7+/oJfd2lpiWeeeYa1tTUeeuihnBFVi8XCyZMnC77Wx2ThgCiGLKyvr6vK9gceeGDX3lipHRf3GnXcC4rIb3R0VBUw3rx5s2Q+/gchC/nGIbu6uuju7kaWZdVdLhAIMDExQTQaxWaz5RgjpdNpRkdHgeyoZ0F9S7cbuQREaU9EIgjRKJn6epYWFlhbW6O5uZmm3l50m5tkotFsENge0Ov126x74/G4Wn2YmZkhHA6rznva6kMxC1gwGGRoaAij0cjly5epqqra91svFxQys7i4SH9/P21tbbt+LsoZmqVFpTUDb9bKQiEwGAzU1NSoY8RK9c3n8yHLMt/61rcIhUKcO3eOBx54gEuXLnHp0iXe9a53HZjoplIpfuVXfoUrV67wzDPPFPQ7X/7yl3nqqaf4xje+QXd3N08++SSPP/64mi5cCDweD52dnfzgBz/ghRdewGAwqPfoxsYGt2/fLji875gsHBCFkIVEIoHH42F9fV21ad4ztKPEmRPKh28/OoidBIylnmDYz/vdaxxSEATsdjt2u13dYaRSKdUYSZngkGVZ3YWn0+mStoAODJOJqCgye+cO2O0MDAxky/nBYJYk7NODXzv73tLSAryx+woEAmxubjIzM0Mmk1GrDwqByNf7lSSJqakp5ubm6OnpobOzs+ILTz6EQiGGhobQ6/VcunRp32SmFKFZW3EURicr/Tc7LGGuUn3r6Ojga1/7GtPT01y8eJFnn32Wmzdv8sorr/CP//iP/OIv/uKBX+sLX/gCAF//+tcL+nlZlvnqV7/KZz/7Wd797ncD8M1vfpPGxka+973v8S//5b/c9feVe+hzn/uc2n5JJpP4/X6i0SjpdJpAIFCU/8oReRq+OVBsG0KZeVdEcg899FDB2fDlqCxAcToIpSw/NTWVt2VSSh2EMn5ZaOXjIOOQJpOJ+vp6dDodKysrVFdX09HRQSqVIhAIsLS0RCKRyBEHulyugsSBkiyxFl3Dn/AjCAJ11jpqrbX7XgAymQyTy8tEwmF6ZJmari4EqxXicYSNDaQzZ6CEO/d8u69YLKZWZqanp4lEIlgslpzKjCRJarjZpUuXsJdJu3EQaNtM3d3dBXuAFIpSVB+O2xCVs3tWxI1KVeFjH/vYoZ+DgpmZGVZWVlSHRcgm3F66dInr16/vSRYUnDhxAshWEYLBIPfcc8++z+mYLBwQO5EFv9/PyMgIkiRx8eLFov34S11ZUBbTQo9ZiANjqccdobCH1UHNlRTdxerq6rYSdD5jpLm5OYaHhzEajTkLZHV1dc6DPSNluL16m7HNMcSMmK1WGK2cazjHQO1A0YRhc3OTkZERTCYTp//Fv8Dh8SDMz4MoZoWO/f3Ip08XdcxioR1dU6oPiu9/IBBgfX2diYkJJEnCYrFQV1dHLBbDZDKVNLb9oIhGowwPD5NOpwtvM5UAe1UftpIJURTV+7sSo5uSJFW8olYpshAKhY7MJMTKygqA6rWioLGxUf1eIfD7/Tz55JMMDQ2RTCb57ne/S3NzM9/73vdob2/n/vvvL/hYx2ShCOxUWVAWLkEQVAeylZWVohwMt6LU0wuFHlMrYNzr/Msx7rgbWSiFudLa2ppqHLXbrP9WY6R84kBted7lchESQoysj1BnraPKlN3tBxIB7qzeoc5WR72tsDhoxXdD+RsobSupthY2NhASCWSrFWproQIla8X332Qysba2htVqpbe3Vy1tTk5OEo1GsVqtOeTqMG17FWhHYFtbWyvuaLlT9SGZTDI2NqZWtPKNbpY6NCsfMplMxUlepaobyiREoc+Uz3zmM3zpS1/a9WdGR0cZGBgoxekVDVEU+d3f/V1efPFF3v3ud/MHf/AHGAwGZFnm5s2bfPOb3+R73/tewcc7JgsHhMLC0+k0KysrjI+P43a7uXbt2oFMZ8odULUV+QSMe425lZLQaB0h842Obe3/FkoUwqkwa9E1YokYvjkfxGBwoHjjqHziQG15fmpqipsrN/HJPqRaiaqqKux2O06rk83EJr6YryCysLGxoQqYto0a6nRQX09pJKX7h7ac39nZmTO2qehCRFFUdSGKfwGgTqUo+odyLkyJREJ1RD2q+RjwRhVPIbDKA73coVn5UOk2hPI+K9mGKBS/9Vu/xQc+8IFdf2a/oVSK6HB1dVWdZlL+/8KFCwUdw+fz8e1vf5sf/ehHDAwM8Od//udYLBb0ej2PPvoof/3Xfw0UbnF+TBYOCIUs3LhxA1EUOXv2rDrrexAcZmVhvw6Me7UhfDEfq5FVUpkUbqubVkcrJn3+xUF5+G2tVBwkHXIuOMery6/iXfWytrqGu9rNtcFr1DfWH1hElq88n/KmGFsZw4xZDYUCCApBGsVGGmjA6XTmJUOiKDIxMcHKykpB6vxKIRKJMDQ0hCRJu5bzjUYjdXV1akqq4o6nEIjx8XFisRg2my1nbNNut5fkfSvEt76+nrNnz1bUu2AnaCcy8llflzs0Kx8qLXBU3lMlKwuFor6+nvr6wqqFxaK7u5umpiaef/55lRyEQiFeeeUVPvrRjxZ0jM3NTWRZZnBwkJs3b2IwGNTrmkqliMfjwDFZKAu2XtB0Oq3umJxOJwMDAyW7yQ+jsrCXgLGQ4+3UhpjcnOTV5VeJpWPoBT2SLNHp7ORy62WsxvwVF+10hdaqeT/pkJFUhOuz15mencaOnauDVzHajEwEJ2isbqTX3Vvw+ywUrc5WZkIz1DvqaWlpQZZl/GE/sxuzmGUzHo+HeDyerThohJPRaJTR0VGqqqoOzQa5WMiyjNfrZXp6mo6ODnp6eoq61wVBUOfe29ragNyplNXVVcbHxwG2BWYVc0+KoojH42FjY4NTp05t6/keFUQiEe7evasKQveayChHaFY+VHp0Unk+VYoslEuYOzc3x+bmJnNzc2QyGW7fvg1AX1+f+poDAwP84R/+Ib/8y7+MIAh84hOf4Pd+7/fo7+9XRydbWlr4pV/6pYJe02AwUFdXx4svvkhXVxc2mw273U4ikeDZZ5/l3LlzwBvP2j2Pt4/3/TMPpWTv8XioqqrCaDTS2tpa0hu83JWFYiOk82GnykIoGeL26m0MOgM9rmwZTsyIzARmaLA1cLohvyhPIQtbd1DFahMkSeLVsVf56ehPOdNyhra2NvVvYzaYmQ3OloUstDva6XJ24Q16sRgsSLKEKIlc6rvE/c33o9fpSSaTqq/B/Py8+jew2+3U1NSQSCQwmUwVV6RroYgDRVEsaUCVMpWi7M4U1z3l+iwvLxOPx6mqqsohEDt5/itJlg6HgytXrhQ8eXSYkGWZ+fl5JiYmtrVwikEpQrN2Gt2sNFko9vNeKpTTvfFzn/sc3/jGN9T/V6YSfvSjH/G2t70NgLGxMYLBoPozn/rUp4hGozzxxBMEAgGuXbvGs88+W7DHQl9fHx/60If4D//hP3DixAlCoRDf/e53+dGPfsRzzz3HV7/6VaBwDcwxWSgSihVwJBLh5MmTNDc389JLL5W8CmAwGEgmkyU9pl6vJ5VKMTw8XJCAsZDj5SML6/F1IqkIXc4u9d+MeiMOkwNvyMup+lN5HwY6nY50Op1TTSh20QyFQoyMjLAaXaWrs4vOls6c7xt1RpKZ0l5XBWaDmcutl2l1tLIYXsQgGGitbqW9uh297nWyYjbT2NiIIAgsLy9TW1tLW1ubqn+Ym5tDFMWyuCoWC1mWmZubY3Jy8lDirrWue+3t7QDqOGswGGRpaQmPx5MT6+1yubDb7czMzLC0tFTyJMtSIplMMjw8TDQa5eLFiyVxPtWiFNWHSmsWKhl+Vs5ciK9//et7eixs3eELgsAXv/hFvvjFL+7rNQ0GA//23/5bYrEY3//+9+no6OCTn/wkNTU1fO5zn+MXfuEXiiKHx2ShCMiyzE9/+lPq6uq4cOGCWh49bDHifiDLsto2cblcRUdI54NCPvK+Xh4ZniAI7KTOUyoIS0tLpNNpnE5nUQ+NTCbD1NQU8/PzWffGM908P/s84WQYuynbB5dkiVAyRH9N4XapxcJisNBf07/ja6RSKbVMrpBN7cKmuCru5Wtgt9vLugOMxWIMDw+TTCbLsrAVCpPJtM3zPxKJqARiYWGBVCqFTqdTvTMULcRRIgxra2uMjIxQV1d3aBqKYqsPR2F0s9JkoaurqyKvXQ7IsozT6eTJJ5/ks5/9rDrirExnFFtFOiYLRUAQBK5du7btIVQOslDKYyoCxnA4TENDA+fPny/Jg3SnNkStpRa70Y4/4afGmlWgZ6QMwWSQk7Unty2OysOrp7WV0Ogo8y++yJQkYezsxNbdjcvt3tE1EHL9CJT+71xwjnAizI2lG1SbqmlxtGDSm2iyN9Ht6j7wey8W2oRRl8vF1atX874frauiooJWkiQVX4OpqSkkScqpPLhcrpIsQEqZfHJykpaWlp3zMSoEnU5HdXU1drudVCpFOp2mu7sbh8NBMBhkcXGR0dFR9Hp9TvWhurq6Iv4B6XRaDalSxMOVxE7Vh3g8rjqZVlVVbWtflCM0Kx8qTRbeCiFSCgmQJInnn3+eqakprFYrbW1tqkkTFD+Ce0wWikQ+UV+5KgsHPaZWwNjc3ExzczNms7lkO66dBI5Oi5Mz9We4tXoLb8CLXqdHlEQ6qjtUDQNsGYdMJGj1emlfW0O2WhGTSWJeL+uZDNO1tUQikW1z+2azmYmJCVZXV3Oijyc2J7ixdAO72c6pulPMBefwBr083PEw19qv4TAdrvFKMpnE4/Hg9/sZGBhQ2xCFwmAwUFtbqxp7KXkXiufD6uoqsVgsp7fvcrmK3l3H43GGh4eJx+NHetRQmciQZZkHHnhALR0rYkZJkgiHwyrBWlxczHHkVK6R1Wota/UhGAxy9+5dLBbLtpCqowKdTsfGxgZDQ0O4XC6uXLmiuqmWOzQrHypJFiKRyJExZdovFKJw9+5dfvu3f5vr169jMpkQBAFRFGlqauLjH/84H/zgB4veXByThRKg1NbMcHAHx3wCxtHR0UNLshyoG8BtdbMUXiKZSVJvq6etug2LwbLtQaTT6dDNzqKbnUVubwejESPg9PtxxeN0Dwwg2u3qw39tbY3x8XE1zre1tRW73Y4kSaTlNJ4ND2aDGafZSSAZwGl2EhWjyLKMRX94D2xFCDs2NkZNTQ1Xr14tia+ANu8iZ7JgZYXY5CSBoSHm0mnE+noc9fU5kwX5HsSyLLO4uMj4+DhNTU1cuHCh4i5++aDVUHR0dNDb25t3odJqGvI5ci4sLKiBbtprU2zraydofSh6e3vp7Ow8Ui0RBUqWx/z8fEGjm6UOzcqHSlcWDsvZs1zQ6XQEAgE+9alPMTs7y+/8zu/Q1dWFJEksLS3x/e9/n0984hMAPPHEE0UFCx69J8IRRyliqgvBfjULWgfGnp4euru71Q9uqUWTuwVJCYJAk72JJntu2VXph24dhxTm57MRzFq263bD9DTCxgZGt5u6ujocDgfRaBSdTkdXVxcGg0FNOUylUmTMGcYSYzjtTjxpD/FMHBkZHTrWoms80PIAdba6kl2DnZBIJBgdHSUUCnHq1KmSeG/sBlMkQuPQEILPB4AsSUTDYdabmvCHw8zPz5NKpbDb7TlR3ZB1mYtEIpw/f75oW/LDglL1SCQS+9JQ5HPkDIfDOZMp2uujVB8KyQPZep5DQ0OIosj9999/ZMvasViMu3fvIkkSDzzwwJ4jg+UIzcqHSpOFN3NlQVn4/8f/+B/EYjH+7M/+jEcffTTnZz7ykY/wxBNP8Ld/+7f8/M//vEqmC8ExWSgBDAbDjkK/gxyzGAKiHee02+15BYylFk0Wc7xCxiEFdtQ/qrvfiYkJ6urqePDBB7ft0uPxOPNr89wZu8MN7w0SyQQ1lhpsNhtRIcq6sM5KZKWsZEGWZZaWlhgfH6e+vp4rV66U3z5XktDduYOwvo7c2Zl1esxksM/NURUM0n7tGjK5u2uv10s4HAayC2lbW5saX1vp1EEtZFlmeXmZsbExGhsbS1b10Ov1KmlSXmevPBCn00l1dfWO1RnlPJuamjhx4sSR0nposby8zOjoKC0tLfT39+/rPMsV2V0psiDL8pu+sqCQheeee45r166pI5npdFrVlxmNRn7jN36DD3/4w0xMTNDR0XFsynSYMBgMxGKxkh6zmIVY68A4MDCwTWG/n2MWgkKCpLbuOnYyV5Lb2xGWlrIhSUp1we8Hu52Yzcbwq68Si8U4c+bMjq5pVquV/o5+emI9jKfHOes+i5SSCEVDBMNBhJTAD17+Acn2ZM7uulQl93g8ru7SdzvPkiMYRFhdRW5szBIFAL0euaEBYWUFwmGE6mqsVquq+xgdHSWRSKi5E4FAgNnZWSRJyrFkdrlcFcsKSKVSjI6OEggEyn49lbhiq9WqihCVPBCFQMzOziKKIg6HI+f66PV6RkdH8fv9h/t3LxLpdBqPx8P6+jpnz54t+XkWE5ql/R0tiaikKdSbvbKgYHJykscff1x93muJXSaT4cSJE2xsbBS9FhyThSJxmG0IbWBSPmwVMO7lwFiOysJuQVLFpEPK3d3Iq6sIs7Og10Mmg2Q0stDQoO6CCtlVCoJAX00fdct1hFNhMnIGfZWeC/UXqLXWYpJNNLgacqKotaX5/ZSetWFFjY2Nh28vLMsgSW8QBQV6ffbfNa6YSvWpvr6eBx98MOc8lbwLRTipBEJpLZmVQKhy9+DX1tYYHR1VRXeVICz58kASiYTautBWZ0wmE21tbRiNxiNXnYE3xJZWq5XLly8fithyP9UHZQxWmwFzGFDsyI9q26gYbG5u0tubNZ3LV6XR6/WEQqGiR+ePyUIJUK7RSdjZfjUQCDA0NAQU7sBYaiHmTuRjX+mQFgvS1asInZ2wvk4snWbU7ydusXDx9GncZjOEQmCzwR4PuiZ7E6cbTqNHj06nw6w3U22qZi48x2DDIO1N7arpT77Ss8lkyqk8OByOHR9aSlUnHo9XrudfXY1cU4OwsYH8ek4FkG1L1NeDw6FOZAQCAU6fPp1XQ6HNu9AGQimLoyLW3GqKVMrqjHbUcGBgoOjAr3JCW31obGxUyVRraysmk0nVPqTT6SNhqgXZz+Ls7CxTU1P09PTQ1dVV0eu5U/Uhk8mwsrKixsZrn1OHMboZiURUX4I3OxKJBN/85jcZHx/HaDRit9vVz7XNZsPhcLC+vq6uGccCxzLhMCsLkH14and/uwkYCzlmqSKlIX8bYr/pkACYTKQ7OphOp5mbm6PzxAnOt7ZiGBtDhJDiJwAAIABJREFUNzMDr0czyydOIJ88md0550G9rZ4+dx+edQ92fVa4NR+ep8ZSQ5erK+dn8wnfdvI0qDGZcDocVLe0YDCZVD+C5ubmyk4QGAzIp08j/OQnCF4vWK0Qj4Pdjnz6NCs+Hx6Ph5qamqJ36UajcZsls9YUKV91xul07mss0e/3MzQ0hM1mO7KjhvDG6CbA5cuXc3IdtGmkwWAwx1RLSx52I6ClQjKZZGhoiHg8vmvoVyWhuLaOj4+zsbHB+fPncbvd2zROxdpWFwulQvRmriwon7f777+fsbExpqenSafT6jVUoKxXSshboTgmCyVAOciCYnWsdVfbS8C4F8rZhthXNWEL/H6/OtKmzM8Lr76K7u5d5JoaqK+HSATdjRtIgoA8OJj3ODpBx8Wmi7jMLmaCM4gZkVN1p+h19+K27F6B0ev11NTUqB4DsiwTW1khduMG4vR0drLAYiHS2Umqro729vaS54LsB3JbG5lHHkGYn0cIBpFdLlJNTYz6fGxubqq79INCMUXSPlS11Rkl70IrDHS5XDgcjh2vkdZ9s7+/X/XLOGrQtpva29vzjm7mSyNVTLWCwSAbGxsqAd0a113KLAufz8fw8DB1dXWcP3/+SI7CQnaRvnPnjhrJrr0G5Q7N2noeVqv1SKaTFgrlM/Nf/st/IRwOk0gkiMVi6lc8Hlf/+653vatoH5WjeQe9yXBQT4TdjptOpwsWMO6FcggctTuA/aRDQm48c29vryq6IxxGNzODXFcHyuJUU4MsSQgTE8i9vbDDLtmkNzFQN8DJ2pNIsqRmMxQLQRRxDA9T7fcj9fWxtrFBemyMGp2OZHs7fr+f2dnZbYtjdXX14fet6+uR6+uReaPn73Q6yx6qlK86oxUGer1etTS/1VQrHA4zNDSEIAhcunSpbKl/B0UymVQzYYo1rMpnqqVoQ4LBIFNTU6rp2Na47mLvIUmSmJiYYHFxkYGBAZWwHDUoxGt8fJyuri56enp2fGaUKzRLi1AolN2cHEGSWiw6Ozv3/qF94JgsFInd2hDFGFwUAp1Ox8LCAsvLywUJGPfCQTQLkiyhE3I/cMoH0O/3qzvHYt//2tqamt55+fLl3GpJPJ792qoDsNsR/P7s9/YoqQuCgF7Y/65fWFlBWFoiVleHd2GBTCZD17VrONbXkUwm5HvvVRfHQCCA3+/H6/WSyWTUxVF5+B+GSE+JaF5fX69Yzz+fMDAej6vCSaU0r3xuamtr6e3t3TOmuVJQduk1NTVcvnz5wLvPnbQhyj3k8/mYnJxU219aArHbPRSNRrlz5w46nW77Z+kIQRRFdXrknnvu2ZdTaKkju98qkxDlxDFZKAEMBoN6Y5aqHB0IBEgmk6yvr+87QnorlMpCMaRmIbTAtH+aQDJAtbmaHlcPbY6sa6AgCNTV1XHr1i0EQchRzO/lhpdMJhkbG9sxUAnI9t6tVohG36gsAEQiyMr3ygwpEmFjbY25zU0aGhpoaWnJVlRiMYTNTWTyL47aqYLx8fED2zHLskwoFULMiDhMDsyG7ZUC75KXW8O3cFW7uHT5Ejbr0VgstHkXLS0tqiFQMpmkoaGBRCLBq6++CrBtcaxkWTiTyTA2Nsbq6mrZiZfRaNzR0jsYDDIxMUE0Gt1mea5UYhQHzp3aI0cFylSGokspFYHeT/VB+XlBEAiHw9jt9rdEZaFcOCYLJYDSD0yn0wcmC1oBo8lkoq+vr2SJf1oWXsh5egNeri9eJy2lsRvtLIYWWQwtcl/TfWrGw4ULF9SxI2VxVJIAtTtrZV5fa15TW1u7Y6ASAA4HUnd3VrMgSdlJiEgEIRRCunRpz6rCQREOh5nyeHAGg5y8dIkqDWEREgmkHcp9+XaO+aKWtcZAu/X1I6kId9busBheRJRE7EY7A7UD9Nf0IwgCiWSCZ3/6LHeW7uCsdxKvivNPa//EPU334DQfHVGb1lZ6qyGQ9h4KBoN4PB7i8ThVVVU5BPSw0iRDoRB3797FZDJx+fJlrIdATLXIZ+ktimKO5fnExATwRsWwu7ub9vb2I0kUlICyiYmJQ5vK2Kv6oNVZvfDCC2xsbJT1fN7sOCYLRSLfDa6MA6XT6X33hpVUwtHRUex2O1evXsXj8ZR0ekH50BTikpaW0oysjyAg0FGdtQR1W9yshFcY8Y3Q5mjDYsyq1QVBUEVviiOYMo/u9/vVnqzFYlFZfl9fH21tbXs+MOSzZ5EEAZ3XC6+HTEn334+sSU8rNSRJYnp6mtnZWbpOnKDbYkG/vo5sMoFej7C5CUZjNseiQOSLWlbKzvn6+sqX3qDn5vJNvAEvjVWNGPVGgskgN5ZvYDaYsaft/ODVHzCZmuTUwCnq7fUkM0lmg7NIssQjHY/sW69RSiSTSYaHh3e0lRYEAYfDgcPhUMdak8lkThiUNk1SuT47OSruF7Is4/V6mZ6ePhKjhloYjUbq6upUFbvf7+fOnTsYjUbcbjfLy8tMTU1hs9lyqg+H4YuxG0RRZHh4mHA4zL333qu6Zh428lUfEokETz75JN/5znf4yEc+UpHzerPgmCzsA4Ig5IyiwMEmImKxGKOjowSDwRwBYzmmF4CCjhlJRQgmg9RYanJ+x21xsxpbJSJGVLKwFdp59ObmZmRZZmZmhpmZGWw2G3q9nvHxcaampnIWxryiQJMJ+eJFMidPQiKRrS6UcZcXDAYZGRkBeMPbv7kZ+bXXEFZXQZKQnU7kM2fgANMFOp1um92wtq+vzPDH9XFGU6N01HSgs+iyo4y2euaD8/zw9g9pE9uQXBL9Vf00OLJExGKw0OpoZTmyjC/m25bPcdhQSHBdXR1XrlwpuLVgNpvzEiytL0Y+R0Vl5DKRTrAZ30RGpsZSg9W4+32j5DqkUqkjO2oI2Xtlenoar9e7bXoklUqpkxf5fDGUr8Nq7wQCAe7evYvD4SiJ3qOUmJub4/3vfz/xeJxXX32VkydPVvqUjjSOyUKJsB+yIEkSs7Oz6qz+tWvXcnp4pTZR0lqq7gWDzoBBMJBKpzAKGp8HWcSoM2LQFXbrhMNhRkZGSKfTOWKmfDtrRRTodrvVB7/6cKmqyn7tE2kpzUpkhY34BjpBR0NVAw22BvUhm8lkmJ6eZm5uju7ubrq6ut4gLrW1SG97W9Z+WpLA6Sx5C2RrXx+yO7K783cZmx4jEoywurSKIAhYLBbWI+sYTUb+2bV/xktrL20TcZr0JtJSmlSmtJklxUARW25sbDA4OKhOS+wXWoLV2dm5o6OixWIhZoqxlFlCNIiYLWZcFhfnGs7R7erOe+zl5WU8Hg+NjY1cvHix4qOwOyGRSHD37l1SqVTeoCqTyZTXF0MhWMvLyzntHYU8lLr6oDWD6uvre2PC6QhAlmX+z//5P/zar/0av/RLv8RTTz11ZMW1RwnHZKFEKJYsBAIBhoeHkWV5RwFjOUYyC61WVBmraKlqYWR9hPbqdkx6E6IkshZdo8fds2cvXFvK7+jooKenJ+cBnG9nrYgCN/wbTC9Ok4wnqXPWHciKGUDMiNxYvsGUfyr7WsgYdUbONZzjVN0pgsEgw8PDGAyGncf3dLrtUxklhJgR0Qm6nJaB0WiktbGV1ngrddY6DBiYnZ0lEAiQ0Wewy3Zu3bjFqrRKRB+hv6Efu92O0WgkKkYx683YjJUROW5sbDA8PIzD4Sjb6ObWChZkdUOza7P834n/SygawpQyEZEjrJpWmVuc47G+x+hp7FFJuZbQ7ORseVSwurrKyMgIDQ0NBRMarS/G1vaOVj+jVB+0BGK/3gypVIqhoSFisdiRq9Ck02l+7/d+j6997Ws89dRTfOADHzgyJOao45gs7AMHaUMongKLi4t7OjDq9fqSp1nuRRa06uFTdaeIp+MsRhaR5KyHQnt1OxcaL+z6AQsEAoyMjKDT6QqO6VVEgRvpDZYTywTqA5CBoBDEKlnzWjErosC9PuzzoXnGN8dpsbdgMWRL1MFkkNdWXyO8HCbqi6r+DoctDvMn/ExuTrIYXkSn09Ht7KbP3aeWzOtt9bTZ27i7dJfoWhSb2UZ9dz2NxkautV2j3lRP3WIdP575Ma/NvIZBNJDWpwnrw/TX9ROPxpGtpR3p3Q2ZTIaJiQmWlpY4ceIEra2th/owNhgMJI1JrC4rp7tPq9WHSCTCuG+cV0ZeYd4zT1VVFVarlUAgoI7tHlXHSO1UxuDg4IHNtfK1d8LhcI4+RHHl1BKIQsSlm5ubDA0N4XQ6uXTp0pFqO6ysrPDBD36QlZUV/vEf/5Fz585V+pTeVDgmCyXCXmQhn4Bxr9KXwWAgHo+X/DwLyXMQBAGH2cHDHQ+zFlsjLsaxGq3U2+p3bEGk02l1odhp8U1lUixHlgklQ5j0JhqrGnFZstWF5cgy1xevIyPjNrsRJZHl2DIWl4WHBh8CmW1WzIqf+24pkgvhBcx6s0oUAHQpHSNjIxhrjLzr8rsOVIbMSBlWoiusRFaQkWmwNdDiaNmzVRNKhnh54WV8MR9ui5uMlOHV5VfZjG9yte0qRr0RWZKpjlQj+ASqa6px1jhxmp0M1A7QXp3tVV/su0h9Qz3jm+N4fB6m1qcQRIGF9QWeWXqGDlsH55rOUeOuOfCucTcEg0GGhoYwGo0VnfNPZBJqhUZbfUhaknQ7u7mn7h41f8JqtRIOh7l+/fo2U62j4HoYDoe5e/cuBoOhbFMZWk1DR0dWzJxMJtX2zsLCwjZxqRLXrVwjrS7pxIkTBYmXDwuyLPPiiy/ywQ9+kIcffpi///u/f1PbOlcKlf80vEWwG1nYScC4F0qtWVCOmS/PYad0SL2gp9nevOdxfT4fo6Oj6vx0voUimoryytIrzIfmERCQZAmn2cl9LffRXt3OlH8KURLV6QsrViwGCwvhBdZiazTbm7dZMWtHNpeWlkgmk6rgTfmSZRmBN7QJi4uLbGxsUFNTw+kzpw9EFCRZ4vbqbUY2RuD1YtOIPMKJ2hPc13zfroRhLjiHL+aj29mtXm+HycFcaI6eaA/VcrW6+L7/0fcjG2V1dNKoz92xtVe34zA58EV9uDvctNhb0Ak6AvEAa6E1MlUZIpGIOtaaL2lz39dAkpiZmcHr9R6JCQKn2YkkS2SkjEoaJFkilUlhxcrt27eRZZkrV65gt9u37ay3XiOtcPKw3pfW4bCzs5Oenp5DrXqZzWYaGxtVnYlyjRQCMT8/r14ju91OKBQik8kUXEk8LGQyGf70T/+UL33pS/zRH/0RH/vYx47kaOmbAcdkYR8oNExqLwHjXii3ZqEUeQ6pVIqxsTHW19fp7+/ftew86Z9kLjhHh7NDXUSXI8vcWrlFnbUOf8KP3ZirFzDpTUiSREyMbTtevnE7ZaJAG+KzySbT6WkS9gThQBiz2UxHXwcJEtTaDqZDWI2u4tnwUGeto8qYJR2JdILxzXGa7c10One2XvXFfdgMuaVdk95ERsowNDGEKWCip6eHzs7Ogh5wvpiPRCaRQz5cVhdhMYxklzjXli27KqJARViqiAK1FZpCrYaj0ShDQ0NIkqTmeVQarY5WWhwteINeaqw1CAhsxDcwJAwsjS7R19lHX19fzijd1p219hppW2Daa1SuMKhUKqXau+/X4bDU0F4jBYlEgoWFBWZnZ9WNza1bt3KMtUo92loMNjY2eOKJJ/B4PPzwhz/k0qVLFTmPtwqOyUKJsLUKoAgYJUni3nvv3dcHvpyVhd2qCYVAMVcaHx/H7XbvmRKYltLMhmZxWVw5u+0GWwPzoXnWomuIaZGpwBQtjhZcFhcOkwMxI2YnAAyF7Xy3Ct5EUWTZt4z/jp+RxREMggFdQodP9HGh+QLGpJGMJes7IcsyETGCgECVsTB1uC/mIy2nVaIAYNabiYkxbq3cospYRa21Nu+xbAYbKSlXkxKNRpmcmqTKVcUvXPqForISRElEQNj2WkadkXj6jXaWxWKhqalJ7X0rQUdKe2dychJg1/aO1mSnvb09Z/GtNCwGC5dbLzNuGWc+NI+YFjH5TdRINTxw8YGCYsS3XiMljTQYDLK5ucnMzEyOpbdyrQ7qSKjt+RczZnrYkCSJhYUF5ubm1AyKrdUH7WirlkAcRoXmxo0bvO997+Ps2bPcvHmzMtHxbzEck4USwWAwkEgkihIwFnLMUlcWFPOoTCaz72pCPB5ndHSUcDhc8EicUsXY+lo6QUdaTnNr9RbzkXlmgjPMheaotdbS5cyWs1sdrTTY9qdSDwaDeCe9XKi9wCMXHsEv+kkmktjSNkxJE3fv3kUURWSrjE/wEdfHqbJV0eZq41TdKWqsBZC819sPkVSE57zP8b/G/xfL0WX12z2uHj5y8SO89/R7VX0GZFsHU4EpNuObuMwuFpcW8Sx4aG9q5+ce+DnsluJClZxmJzpBRyqTwqTPLlqSnK3KNFbt/DfKF3S0tb2jjaGuqqpiZWWFRCLBxYsXS+YwWko4TA7ubb6XZl0zIyMj1NfUc+rUqX0vvnnTSDVhUIovhmLHrA2DKuTzpUwPzc3N0d/ff6R6/luhjG+KosgDDzygElqtIymwbbRVqdAUk0haLCRJ4umnn+bzn/88n/3sZ/n0pz99ZEjsmx2CvFXWf4w9kclktu34vV6v2jO32+2cOnXqwLO7fr+f27dv8/a3v/1Ax1EgyzJDQ0Nsbm5SX1+Py+XC7XYXvBtSdpOTk5M0NjZy4sSJoh6+N5dvMuQbosvZpYZSrcfWWY4sY9AZ6HJ2sRHfYC40x0pkBYPOwKPdj3K17WrRtsWiKDI2NobP59u1PSLLMmvBNZ4de5blwDIm0UQ8HiepT9LqbuXR3kdpqWvBarXm/f3lyDI/9P6Q2eAs/+mV/0Qik9j2M4pewma08a13f4vHuh9TX9uz4eGn8z/F4/WgE3Sc6TnD1e6rtDpai3q/kK3eXF+8ztTmFHaTHb1OTzAZpLGqkWvt13CY9t8iUB76i4uLbG5uAuSdTDkqD2btVMZBklqLgdaOWalCKJkpWmHgVuFkPB7n7t27ZDIZzp49e2STN+GNUK36+noGBgaKXuS1oWvKNRJFkerq6pxrtB8NTSgU4mMf+xjXr1/n29/+No888siRJVxvRhyThX1gK1mIxWLcunWLSCTC2bNnS/ZgCofDvPLKK7zzne880HG0uoRUKsXm5qa6a4xGozn++263O2+ZMBKJMDIyQiqV4tSpU/tqqwSTQV5eeJnV6CoWvQVREtUSeZWxSnUaTGVSxFIxFiOL/Fz3z9Fb01vU6yjxzNXV1QwODu754BnxjfBPS/9Etyvb60+n04TCIcbWxugz9uFMO9Xd0NaFUZIlnr71NJ96/lPI7P5R0pGt4vzP9/xPHut+DEmS8Hq9DE8O42py0dXZRUNVQ96QqL2QyqSIpCJIssRadA1vyEtGytDmaKPX3Uu1+WCis1QqxejoKIFAQP37Kw975V5SUhK1u8ZKlNG1EwRnzpyp2FTGVkOkQCCQU6FxOp2kUimmp6e3ZWUcNUiSxOTkJAsLCwwODqptvoNCcS7VkqxIJKISUW31YTcievfuXf71v/7XtLe38+1vf/vA46XH2I5jsrAPSJKEKIo5AkaXy0UqleLBBx8s2evEYjFeeOEFHn/88X2RD+VPq7QctPnuCpSAI+UrFAqpH1S32011dTU+n4/Z2Vk10e4gD7RIKsJ8aJ712Do2o40WRwu3Vm4RT8ept9Xn/Ox0YJpr7dfoc/cVdOxUKqUa7OyYZJkH1xeu4w16t+3m50JzDNYOcqHhQo7bpLIwulwuBKvAzz37cyQyiT3JAmQJg9Vo5db/d4v5iXkkSeLMmTP7VpDLssykfxLPhodIKoJRb6TD0cHp+tNYjdZtseL7gc/nY2RkBJfLxeDgYN5KlDYlUfnaGgTlcrl2rNCUAlrXwK6urgO1AMuFRCJBMBjE7/ezsrKCKIoYDAbcbveegWKVgrbyce7cubK7HabT6Rxb72AwSCaTybH1VlpnsizzV3/1V/z7f//v+cQnPsHv/M7vHImR17cijq/qPrFVwCjLMsPDwyV9DeWm30/0tVbAKMvyjtqErQFHipBL6VV7PB4A1U8+FAodSOFsN9kZrBvM+beN6g1uLt+kxlKjjrqFk2GsBituy979cMXDwuPx4HK5dk+y3OGcttoiy7JMOpPGZrTljaBWFsanbz9dMFEAkMhqCP74//4xH7vvYweOE54NzvLK0itYDVkPjGQ6ycj6CEkpyYNtByOu6XSa8fFxVldX9yRf+VIStUFQCwsLjIyMbOtX580D2QcSiQTDw8PE4/GKhhXtBYvFQiqVYnJyUm1Xagn77OzstrK8y+UqiwNmIVhbW2N4eJimpiZOnDhxKCTGYDDk1Yco99L09DT/5t/8G+LxOE1NTUxOTvIHf/AHfPSjHz0mCmXEcWVhH1hfX+f69ev09vaqu5dgMMirr77KO97xjpK9TiaT4Qc/+AFvf/vbC35YKORAIQr5qgl7IZ1OMzk5yeLiIt3d3dTU1BAKhfD7/QQCAURRzHmQHbTcHElFeHnhZZYiS1gNVkRJBOBs/VnONZzb9dyTySQejwe/38/AwACNjY1F71w345v8ePbHJDNJtbqxGl2lyljFO7resWMJX5Zlzv3lOWYCMwWTBUBN8hx+YvhAu2xJlnje+zwb8Q1a7C3qvyfSCdbj6zzW/di2ak2h8Pv9DA8PY7FYOH36dEnMgLT9au2OUZu06XQ6i54o0Nognzx58sguGNrKx05+FNpAMWVxVBJbtwony1k1kSSJ8fFxlpeXOXXq1IFzPUqNmzdv8pnPfIZwOExtbS2vvfYayWSS+++/n7/5m785cuf7VsDR/FQdcdTU1HDt2rWcXuhBUid3glINKHQi4qDjkJAlQqOjo1gsFi5fvqyWHF0ulxo/HY/HVeIwPj5OLBbLMflRdA+Fwm6y82Dbg1lhY3QFi95CW3UbrY6dPRtkWVZT9Wpqarh69eq+x9ZqrDVcar3EnbU7rEazYU31tnrONpzdtde/Ed9gOjBd9OvJyMyGZvFFfTTY959FIGZEIqnINm8KiyGrB0mkt4st94IkSUxNTTE3N1fyAKB8FRplokB7LykRy8rXTjbD6XQaj8fD+vr6kVzQtFAiuqPR6K6Vj3yBYtrRVp/Px8TEBMA24WSp9CGxWIw7d+4gCAKXLl2qmOYjH2RZ5u/+7u/4+Mc/zgc/+EG+/OUvYzJlvVjGxsa4fv26GuF9jNLimCzsA8oHWguDwZBjblSq1ykk+KlU5krj4+N7Tg9oH2atrdkev2INq5RRh4eHMZvNKnFQxu12O6cqUxWDdYPbWhT5kEgkGB0dJRQKcerUqZKE/yjjmYFkAMhGce9l1xwVowd6zR/8vx/QX9+fszBqCU8ynUSSJSyG/HPpRr0Ru8nORnwjh9Qk0gmMOmPB3hQKwuEwQ0ND6iJRblW+kgdSVVWl3ktKxLK2Daa1GVZaF8q5Wq3WI53rAFkCPjw8jNvt3ldM806jrcp18ng825IkdyNZu2FlZYXR0VFVcHmUNB/JZJLf/u3f5jvf+Q7PPPMM73nPe9T3p9PpGBwcZHBw7+fHMfaHY7JQIiilz3Q6fWBjlq3H3StzQiEJsD9zJWWH7nK59jRXyoet1rDandDq6ipjY2PqA18hD3v1qlOZFPF0HIveok4HyLLM0tIS4+Pj1NfXc/Xq1ZKq7Y16Y1Fle60R037wtitvQ5fU4ff7mZqaIhKJYLPZsDgsrLNOgAAGk4EGWwMna0/SUJVLinSCjn53P6vRVXwxH06zk2Q6iS/mo7eml1prYUY02vJ4JayFtcgXsawdtVN6+gBut/tI+xFIkqR6rpRyfFPrXKroQxTdgzZJcmuWg9Pp3FFzoA2rOorpm16vl/e9732k02lu3LhBf39/pU/pZw7HZGEfyPeBVxbpUpOFnVwcFZKg/Hc/1QTtDn2//f582LoTUpzdlNaF1+slk8ls0z0YDAYyUobxzXEmNieIp+NYDVb63H102DoYHxsnEolw5swZdTEpF/wJP2vRNTJyBqfZSWNV47ZKQ621lh5Xz740C13OLuw2OzanLcdtcn1znecnn2difQKjaMSgN+AxeRitHuWx/sfobMi1fu50dpLKpBjbHGMttoZJb+JU3SnONJwpaBIiFosxPDxMKpU6cnHCkBtlHovF1JHIlpYWEokEU1NT28yQCqlklRvRaJS7d+8CcOnSpbJPEGwVKmvdFBXLaq2bojYTJBqNcufOHfR6fdnCqvYLWZb5/ve/zxNPPMF73vMennrqqSN1fj9LOBY47hOpVGpbTPXzzz9f8iCV69ev093dnTM3rGgTdhqH3AtKSM3ExASNjY309/eXlOAU8vqxWAy/38/qxiqeVQ/z4XmsVismi4mYPkZ7bTsum4tIKsLc6hyOsIPL3ZeLNoLaD6b909xavUU4GUYQBHQ6Hb2uXu5rvg+jzphzrf/zq/+ZT//w00WRBYD3n30/b+t4Gzajjf6afvpr+tEJOhbDizzvfZ4WewtGnZFoNEokEmHMN0YTTfRYeqiursbtdud4GSg+C0a9sSDzJVmWWVxcZHx8/MjP+CsVpbGxMVpbW+nr68s5V1EUcwSBwWBQJRnanfVhvD/FBt3j8dDa2npkSvlb3RQDgQDhcFh1iXW73fT29pZsOqUUEEWRL37xi/zFX/wFf/7nf8773ve+I1tF+lnAcWWhhCiHyFFbWSh0HHI3RKNRRkZGSCQSnD9/viKe6Uqv2mgxMpWZQkSko6mDQDjA9YXr2CQb0rrEmnkt259NRXC0OOju7y47UQinwry2+hoAPe4eAOJinJcXXmZic4Iaaw0NtgZ63D3U2+p57+n38oUXv0BcjCMhFfQaJp2Jfnc/4VSYUDLEenwdWZbpcffg2fAwtTlFMp2k1lpLbVVtVvnu0OEwObjcdHmbIFArLrW6rHlttbVIJpOMjIwQDof3vAfCqTDLkWVDQ9lRAAAgAElEQVSiqSgOs4MWews24+EJ3rRmUOfOncsrXjMajdtaF9pd9fz8vLqr1k4UlFrnIIoio6Oj+P3+Hc+1UtBGdTc3N5PJZBgZGcHn89HU1IQoity6dQtJkg48nVIKrKys8IEPfID19XVefvllzp49e+jncIxcHJOFEqIcZEE5pqJLUKoJxRIFxS1wZmaGtrY2Ll68WPGd5FJ4iZngDO3V7Rj1RpxWJ8viMslMEoveQjqQxmKxUGOsYWZ+hueiz9FZ31lWe2Ff1EcwFaTb2a3+23JkmdngLIFEgPua72Nsc4yl8BJX26/SYGvgqQef4td+/GsICLtWGJTv//O+f44v7mMjvgECWPQWXjO8xlJkidsrt1mLrZGW08yF5uhydtHn7iOZSdJibsFqs5LQJah11tJzogedpMubjrjVbVK5V1ZXVxkdHaW2tnbPoKLV6CqvLL7CZmITvaAnI2dosDVwufVyYZkZB8TGxgbDw8NUV1dz5cqVghctbUJiZ2dnzq5amdPfOo6oJG3ud+caCAS4e/cuVVVVXL58uWK+CIVAcbg0Go1cvXpVJU1a/5BgMLhtOkWp0pSzxSPLMi+88AIf+MAHePTRR/mHf/iHI5FkeoxjsrBvCIKwrQ1RrsqCKIrqRMR+qgnBYJCRkRGAI9WX3ohvoBf0GPXZBcuoN6KTdSytLIEJHjn1CA6Hg0AiQEOmgfvq7iMZSbK5ucn09LTqorhTMuJ+ICHlJDdGxSjzoXkcJgdOi5Maaw011hpmQ7MMLQ/hDrlpjjXz3x77b/z6j39djdLWkgYlG8Kit/DOrnfSUd1BQ1UDOkGHmBFZiixxa+UWnc5OBuoGyMgZwqkwNoON2eAsOkGH2WDGZXHxwtwLLEeWSUtpHCYHA7UDnGw4qYpLtaZa6+vrTE1NIcsy1dXViKJILBZjYGBAnT7YCRkpw521O4RSITXyWpIlZoOzDPuGudZ+rWwLRiaTUX0+Tpw4sWvseSHYuquGbBVAEU6ura0xMTFRUI7DVsiyjNfrZXp6mt7eXjo7O49sqVzbeurs7NzmcJnPWEs7naIIoRUyphVOlsLbIpPJ8JWvfIWvfOUrfPnLX+ajH/3okWmJHOOYLJQUpSQLSqvBYrEwPT2Nz+dTJwncbndB5XjlobuwsEB3dzddXV1H6sNn0pvURVWWZQLrAWKrMdL6NK0drdiqbISSITYTm5xrOEdLfQu8rmtUdkGKaPL/Z++8w6Mq87f/mUnvhZBKKiQkpIB0SdC4iCzq2vd1FZWyYlkBFRBXBcGO4iprZV0RLKsiq6Koi4oaSKhS0zukkZ6ZZFJmJjNz3j/yO2fPpEB6hnU+15XrknEmeXIyc57v8y33LZp4yVPNfTHJEvFy9MLR1hGNToObgxut7a20GdoQBEFyvhQEAaFF4GDeQa4Zd400lXFl9JV8nPUxb59420x/IdwznKWTlhI1Koqd2TuxVdpKzYd2NnbYKm2p0FQQ7R0tBQAFDQWodWqqW6rxdfFlesB0KpoqONd8jgDXAOyUdqh1ao5VHcPOxg5nO2e0Bm2HkqPnaDP1u4qKCgoKClAqldjZ2ZGTk0N5eblZoNX5JKzSqqhtrcXP+b9Nr0qFktHOo6luqaa5vXlAxlQ9IY5EKpXKIW0MtLOz69KE253Tpvz9JDYEimi1WjIzMyUxoMHsVRpsDAYDOTk5NDQ09Kn82N10ikajkQKIiooK6Tp1bpzsS9BUV1fH0qVLKSgo4JdffmH69On9+j2tDB3WBsd+InpDyDl16hTu7u5EREQM6Ht3HoeU68nLzZ/kwUPn+mt9fT05OTk4ODgQExNjkU521S3VpJxNQTAINFb9n/67nxtl2jJ8XXxxtHXE0daRMI8wEnwTJNvlnhCV78QvcRRRrvdwIW8CQRDIqM3gdM1pFCho0bdwovoEYz3HMtFvIraCLaWlpVSoKggPCefWybd2mZIQBIEGbUOHYJK9K3qDnlM1p8hvyGd/yX4AwjzCCPYIRmfQUdlcCQJMCZxCqEco0HGyb9Q1crbxLJeHXI6fi99/Gx9t/hsoFjYUotKq8HX17ehjUSgJcQthauBUHJQO0gldbnssVwhUqVQ0Nzd3mSZoU7Tx49kf8XX2NbvuLe0tNOubmRcxb8DmVJ2vWWlpKYWFhSM+vikiL12IDYGifoiNjQ01NTWS+6KlqkZChxtjeno6Tk5OxMXFDXqJpLvGSbnxmoeHx3kbJ48cOcLChQuZNGkS27dv75dJnZWhxxos9BODwdBFLCkzMxN7e3uioqL69T17K66k1+ulwEGlUqHRaHB0dMTLyws3NzdUKhX19fVERUVZ9By60Wjkl4xfSCtIw9nLGR8fH9wc3Ij1iWWM+5iOk7KdU79PsGKXvHidmpqapJuYGDzI6/kiJsFEhaaC8qZyWtpbKGksAcDT5ElFeQX2LvbYedkxM3gmsaNju//dTEbONp4lpz6HoxVHsVXaEukVSV59HqWaUjQ6Df6u/vg6+yIgEO4RTk1rDd5O3ng5euHh4CFtzHPC56DRaUgrTyPMI0z6GYIgcKD8ALWttVwz9hrsbe3RGXRUaCoIcw7DvtYeW1tbYmNjz3tCF69TSU0JFQ0VtGpacbd354zpDCZ7E2NHj5Xq1KWaUsa4jiE5NHnQ3leir0NraytxcXGSwqOlYTAYUKlUFBcXo9FopCmkoVJSHCji1FN+fj7h4eGEh4cPy73gfLLeHh4e1NfXM2bMGIKCgnjrrbd46qmnWL9+PatXrx7xANFS6dy0fKEm5qHAcsPhi5CBlCE6j0OerzfB3t6+iwiSaNZTUFCAIAjY2dnR0NCAIAg9boojiUajISsrC2eTM0suX0K7XYfQjrhZAgM+uXbukpffxOT1/M59DzY2NgS7BxPsHgxAZWMlu37dxXHVcfz9/XH3difcI5xI756FYTJqMkivTadJ10SjrhFXO1eKG4vxdfHFhIkqRRXOds5SBgVFh4V3QUMBSoWSUc6jGOc1jin+U/Bx8sFoMmKjsEFr0ErKjOKkQphHGPa2Had/ext72pva2Ze/j1sm3kJkRCRVLVXkVOZgo7DBz8UPf1d/Mw0GpY2SMkMZRRSh9dAiuAs000y4KZy8mjwOZB9AYVJg52hHgGcA/u4d3fOD0SVfU1NDdnY2Pj4+JCQkWMxG2x1arZbCwkJsbGyYNWsWTk5OZqWLqqoq2trazKZT+pOSHwza29vJzs6msbGRyZMnD2sA1pOst5h5+Nvf/saePXvw8fGhubmZ+++/n9///vddesCsdGA0GqVm9MzMTEJDQ0ek6dOaWegnRqOxS2BQWFhIa2srCQkJvf4+8kxCf8chtVotubm5qNVqxo8fj6+vr7QpihkI8QQknqg9PDxGJIo3mUwUFxdTUlIy4ulmUTZXvEZqtRq9Xm82OmYwGCgoKMDJzYlRIaPApsPLYrTz6B5Fj1RaFXvP7MXJ1okmfRPZtdn4u/pT1VxFoGsgvq6+5NXloVAouDLsSs40nsFoMuLn6odKq6KupY66tjouC76M2SGzO/xBTEYOVhykoL4Ag8lAfVs9FZoK6lrr+P3Y3xPhFYFWq+XMmTO0tbfhGeDJtTHXSgJXSoUSAQEbhQ2xPrEk+CVI6y9WFZNWnsYop1G42bthNBmpaqnCxd6FKf5TqG+tp05Th1KnxNngjKHFIJXC+ms/bTAYyMvLo6amhpiYGDMdEUtDrksi2rT39J4VS4by0oU8JT9UUzxyGhsbSU9Px9XVldjY2BEZfTwfp0+fZsmSJfj6+jJ16lTS09M5fPgwCoWC3bt3c/nll4/0Ei0GeQbhscce47PPPuP+++9n9erVw74Wa2ZhEBEFTnpD55JDf8Yh5c1rovyxeGMQI/vw8HAEQZDmzlUqFaWlpRgMBkncR66gOJSIUxkKhcIiGsLksrmiSZZWq0WlUtHQ0EBmZiZGoxEHBwdcHV1xbnfG0+XCJ0WNTkOroRU/Fz8MJgMKhQK9UY+rvStqnZrxo8Yzxn0McaPj8Hf1J7c+l2D3YGyUNvg6++Lr7Ettay2adg0CAgoU2ChtmOI3hbLGMo6eO4pCocDT0ROdQUdufS5Ci0BTbRM+Pj64e7jj7eSNWqumoKGAQNdASTK7Wd9Mdn1H8OLv2rFBn208i72NvVTusVHaEOAawNnGs7Qb20nwS4BOHk1yW+XO9tMX2hQbGxvJyMjA0dGxX/Liw4n8hD5p0qQL1tMdHR1xdHTsMp3S2NhoNsUjL1sM1LVVRN73YYmTGYIg8P7777NmzRpWrlzJk08+Kd1zjEYjmZmZhIWFjewiLQyFQoFOp+PGG28kPz+frVu3SgZjw12KsAYLg0hvyxCD4Q4pF1eKj48/rwCMQqHA3d0dd3d3aVMUFRTlRjRubm5mTZODdSIxGo0UFxdTWlpqkVMZIuKIXXNzM/X19ZKqndjAVVZWZqZjYOdqh5OrE76evjjbyxxIlbYoUWIwGfBw8MDfxZ8KTQVGkxFHO0fKNeV4OHgQ7hmORq9BUAjYKM01L2yVthhMBkyCScoA6Ew6bJW2XB56OU52TjjZOFFcX8x3Wd9Rp6zjipgrEOw7mhxjfGIo05Rhp7STAgXoyIrUtNZQ31YvBQtthjbslOablVKhRIECg9D9+7mzvLBY4mlQNVBdV21W4hEzWm5ubpSXl3PmzBmL3Mw6IwaMbm5uzJw5s1+fBxsbG7y9vc2mU0QtA3npQp6l8fDw6LMJlF6vJysri+bm5vO6Wo4ULS0tPPzww/zwww98/vnnXHXVVWa/n42NDRMnThzBFVouqamp1NfXc/DgQXx9fdFqtZhMJsrKyggNDR22dViDhX7S3Qe5N6ZPA3WHNJlMlJSUUFxcTFBQEJdcckmfMwJytz9xnlo8UavVaklvX7yByScJ+oparSYrKwtbW9thcTIcCO3t7eTn51NTU0NUVBSBgYFSoCXfFKvqqzhacpTC8kIaWxpxVDoSMzqGiWMmMsprFF4uXox2Hs255nMEuQYxftR47JR2HRkE52CivKOI9I7E28kbG6UNLrYuNOoa8XDo0L8QBAG1Vk3MqBizSYsmXRNagxZ/V/+OiYuGBhpLG0kYlQCu4OzijI+TD2O9xhLoFkiZpqxXv3egayCna07j4+QjvR9b21uxs7HD3b532R+FUkEDDRRRRItrC56jPAlyDMLF4CK9B3Q6HUqlktGjR+Po6IhOp7PIrIK8VBYZGUlwcPCgBTXdaRnodDqpdCHP0nR22uwpwFapVGRkZODu7t4vV8uhJjc3lzvvvBMvLy+OHz9OcHDwSC/JYpH3J4g0Nzfz66+/0tbWxo4dOzh69Ch79uyhvLycDRs2sGzZsmH5m1t7FvqJyWSS3O9E6urqyMnJYfbs2V2e3zmb0Fc/B+gYgcrOzsZkMjFhwoQhPT3I08zixIU4Nubo5oiruyu+nr5dTsQico2HsWPHEhISYpHZBBFRLdDV1ZUJEyb0uIkJgsDhisPk1ecx2nk0DjYO1DbVUqWuIsIuAk+DJ+3t7QhOAqWmUrQ22g5BIHsnwtzDSPBLwMXefDIhoyaDU9WnsFHa4GDjgEavwdvRm8TgRDPnyApNBT+d+YkA5wAqyitoamoiLCwMvZ0eF3sX5obPNQsuzqjPsK90H0GuQWZlCLVOze9CfydlFlRaFWllaTS0NeDh4EG7qZ3W9lZiRsUwNXBqrwypsmuzOV51HAcbB5zsnNDoNShRMjNoJvat9uTl5eHr64u3t7fZiN1gqigOBm1tbWRkZGAwGIiPjx+RRjIxSyPvfRCnCTqXLkRBqMEOagYDQRDYuXMnK1asYOnSpWzcuHHYA5n9+/ezadMmjh8/TmVlJV9++SU33HBDj89PSUnhiiuu6PJ4ZWXlkPfViAdIo9HIsWPHCAgIwMfHB0EQuOWWW9i3bx8BAQHceOONTJ06leLiYp555hlKS0uH3FgPrJmFQaW7zII8myDWmPr6gTYajRQVFVFWVkZYWFgX5bWhoHOa2WAwUFlXybGyYxSWFtLc2oy7vTvxfvGMDxhvVqNuaGggOzsbe3t7Zs6cOeSOewPBYDCQn59PVVVVr9QCVVoVpU2l+Ln6SRbVQd5B2DnYdcjnhs9Cr+0ItHzqfThbdxZNgwZPd088FB402TZh42VjFozEjo7F3cGds+qztBpaifCMIMwzTJoKEfFx8sHeYM/+U/sJ9QolLi4OvaCnoaWB2NGxXfQexriNIco7isKGwg7FUVmDo9zu2svRi6TgJIpURVQ2V+Js58xEv4mEe4T3KlBo0beQ15CHm72bJAPt4eBBmbqMH47/wDibccTHxUs3NFFFUW5l3llFsfN0ynBQVVVFTk4Ofn5+jB8/fsTk0HuaJhADh8LCQlpaWqTMZGho6Ih4vJwPrVbLX//6V3bu3Mn27du58cYbRySQaWlpYeLEiSxZsoSbbrqp16/Ly8sz66kaDstupVLJ4cOHWbJkCba2trS3txMaGsquXbv47rvv+Pnnn5k2bRpKpRJXV1eOHDnC119/jV6vH/K1gTVY6De9KUMMRjZBvvGOaBpfCYXaQtT2aqKjorFV2FLRUEGRrgibShuUxUoEQcDW1ha9Xi857lmyWE1DQwNZWVk4OTlx6aWX9qrMojPqaDO0EeAaYPa4i50LLYYW9Ea9VOIJCgriEi5Bp9NJN/qSkhIyMzMlXQxxUwxxD5EEmbrDYDBQlF+EXa0dkcGRCE4CZc1l2NnYMWHUBMZ5jevyGjsbO6YHTmeM2xhqW2tRKpTdjk5CR8AwNWAqJsFc7ro3aPQamvXNjHEb89/HNBoqz1Qi2AtMnD2RUa5dN7PurMzlo4iiAZR8OsXT03PQu/uNRiO5ubnU1NQwYcIEqTnRUpCXDYOCgmhoaCA9PR0XFxfc3d1RqVSUlJRgY2PTpXQxEgHPmTNnuOuuuxAEgV9//ZVx47q+N4eL+fPnM3/+/D6/ztfXd0gzt8XFxUREREjZBIDDhw9zww03sHTpUh5++GEaGhqIiorinnvuYdu2bcyZMwf4r8jWkiVLmDp16rC9Xy33Tn4RIk5DiFmEgYxDivXz6upqxo0bN+IpxuqWaso15QS7B0uKflH+UZQ0luDq7cpYh7FkZWWhVCrx9vampqaGioqKLhMXllBPNRqNFBQUcO7cuT5fWydbJ5xtnSV1RpHm9o5/y5sJRRwcHLroYojqiaLevnijF6+VvEatVqvJzMzEwcGBqy+7GoWdgpqWGtpN7bjZu+Hj7NNjBsBWaUuIRwghHiG9+v16k0nojJ2NXYeddnsLLfoWzlScQdOoIdAvkEDfQFwce5dZUiqVXRpxxeZSlUpFUVGRmSqn+NXXZkA5Go2G9PR0KQvWn76c4UIQBKmXonMWzGQySePSjY2NlJaWmgVaYhAxlAZXgiDw7bffcu+993LrrbeyefNmi+xJ6Q2TJk1Cp9MRFxfHhg0bSExMHLTv/dVXX3HjjTeSlZVFTEyMFDD8+uuvXHXVVTzzzDPo9XqWLl1KSEgId955pxT07du3jx07dvD5559zyy238Oabbw7aui6ENVjoJ93dnMQ/qE6nw8bGpl/jkNDhDJibm4ubm1uvT7xDTWt7K4IgdJFcdlQ6cjLvJC20mEkKC4JAW1ub1DSZl5cnCdaIKdahvnl1h0qlIisrCwcHB2bOnImzc9/slj0cPAjzCCO7LhuDySBpKWgNWib7T+5SCuiO7k7UGo1GulZnz56VatSCINDU1ER4eDgRERHSe6m3m/9w4O3ojZeTFz8U/EBtXS02ChvcvNzI0+Yxzm6cJCLVV3oygJL7N+Tm5mJjY2MWPJyvGVBEEATKysooKCggLCzM7NpaIp19KDr3UiiVSun3B6TPn3itxKblzrLeg+Ug2d7ezoYNG9i6dStvvfUWCxYssOjr2RMBAQFs2bKFqVOnotPpePfdd0lOTubIkSNMnjx5UH7GjBkzmDt3Ln/60584efKk9F4tLCzE2dmZnJwcrr76aiIjI0lLS2PMmDGUlpbi6elJREQEUVFRfPTRR8ydO3dQ1tNbrA2OA0Cn00n/LQgCBoOB/fv3o1AozDbE3jZt6XQ6cnNzUalUREVFERAQYDEfuLKmMn4p+YVgt2CpqbGxsZGj+UcJ8wjj9sTbLxjU6HQ6M5nq/ng39Bd5w+W4ceMICQnp98/RGXRk12VzVn0WnVGHi72LNOHQn5N5ZwRBoLa2ltzcXKk7Wm6SNVKBVk8IgsCXx7/k35n/xtPdE08vT+yUdtja2BLnE8fV467uNuMyGMhP1J2bAb28vLrVMZCPGVqyvLRIXV0dmZmZ+Pj4DMiHor293axpsrGx0cxBsr89IufOnWPhwoWoVCp27txJbGz3EugjjUKhuGCDY3dcfvnlhISE8OGHHw54DWIWITc3l2uu6TChE7/vK6+8wgcffEB+fj4rV65k/fr12NnZYTQa2bBhA25ubqxZs8asdDGcWDMLA0ChUHQpOSQlJUmnxJqaGvLz86WTj9yPQP7Hlosr+fj4mIkrWQq+zr74u/hTpinDx8GHqooqyurL8PfzZ97Eeb3Kfjg4OODv7y91FctPieLImKhh0NdA63yIo3t2dnaD0nDpYOvAJf6XMH7U+I5gwc7lgiZXvUUQBEpKSigqKjJTuJSbGhUXF5uZP4nXaiDp+P6i0+k4nXGa/PJ85sfPx83VjXZTO462jrjYulDeXE59Wz2BboFD8vO7O1HLmwHz8/NpbW2VJJhtbW2pqKjA09PTIscM5ZhMJqmxOTo6WhLj6S92dnb4+PhImiydHSTLy8vR6/VmTpseHh7nnQxKSUlh8eLFXHXVVezZs2dEpkeGmunTp5OWljbg7yPf5E+fPs3ChQvZsGEDV111FXfeeSfz589n69atJCcn85e//EV6b37yySfs3LmTtWvXAozYVJk1szAAdDodBoPhvA2M8hSzeKoWxWq8vLxwcnKirKyMtrY2YmJihmUEpr+otCp+yf2F00WnsXe0JzosmkmBk4jwHJwUrqh2J16nxsbGDqVC2YbYmxSziHizLS0tJSIigtDQUIse32xra5NSzXFxcedtsJKfEkWTLLGLfrhkhWtra8nKysLdy51iu2Lsbe3xdPzvmk2CiZLGEq4Mv5Igt6AhW8eFEDNaJSUlNDU1AUhjwPJrZSlZPOgoO6Snp2M0GomPjx+WxmZ5j4jcuVU+3trU1MT48eNRKBS89NJLvPrqq7z88svcc889Fv3Zgv5nFubOnYubmxtffPFFn17XXQagvLycuXPn4ufnx9ixY9m9ezdNTU0cOHCAKVOmsHXrVl555RWph0alUvH111/z1ltvsWjRoj79/MHGmlnoJ4cOHeL5559n1qxZJCUlMXHixG7Tg2Kaz8PDg7CwMMmPoKGhgXPnztHc3AwgfRDFRreRGtvqCb1eT1l+GR4NHvy/yf8Pn9E+eDp6Dmp6ubPaXU+1fPHGJaaZu7tWTU1NZGZmolQqLV4MShAEzp07R15eHgEBAUyePPmCf//uTolNTU2SVHVxcTGCIHRJMQ/GdIrRaCQvL4/q6mqio6MJCAjAUGEguz4bdwd3qRRT31aPu4N7lxHQ4cZoNFJSUoLJZJJ6gMRAS24oNhTXqj+IQZivr++wjnB21yPSebz1j3/8IxqNBn9/f1QqFS+++CILFiyw2EChubmZwsJC6d9nzpzh1KlTeHt7ExISwmOPPUZFRQUffPABAJs3byY8PJzY2Fi0Wi3vvvsuP//8Mz/88EOffu53333HP//5Tz777DOz7NWbb76Jj48P33zzDa6urmRkZLB69WpuueUW8vLy+POf/0xkZCS7d++moaEBd3d3Tp061W8n48HEmlnoJ6WlpXz00Ufs37+fQ4cOATBz5kySkpJITExk8uTJPZYSRMdFo9FITEwM9vb20glRpVJJZkZi38NI2t4KgiA1XHp6ehITEzNitXJRKlfe9yA3fvLy8sLd3Z2ysjJKSkosWlpaRKfTkZOTQ2NjI7GxseeV7e4LYlAqPyV21/fQ13JXU1MTGRkZ2NvbExcXJ5WfVFoVh8oPUdNSg6OdI3qjHgelA1MCp3Q71jlciE2QgYGBREZGdrvxXuhaiV9D/b43mUwUFBRQUVFBTEyMtGFbEqmpqaxevRo3NzcCAwP59ddfKS8vZ+LEiezevZugoJHLIHVHTyJLCxcuZPv27SxatIizZ8+SkpICwEsvvcQ777xDRUUFzs7OJCQk8OSTT3b7Pc7HiRMnOHHiBHfffbf0mNFoJDk5mcjISN577z2g472Xnp7O/Pnzufzyy/nkk0/6/8sOMdZgYRAwGAycPHmSffv2kZqaSlpaGlqtlunTp5OYmEhSUhLTpk3DYDBIYzgJCQmEh4d3uXnJzYzEL7lvQ39v8v1B3nAZHR2Nn5+fRaVq5ddKrVZTX1+PVquVJIXFWWlLHd8S7Zm9vb2Jjo4e8r+pvDtepVLR0tLS6wZTQRAktcCIiAjCwsK6PE+j11DWWEZ9Wz3Ods4EuQVJKpHDjcFgIDc3l7q6OmJjY/tc3hOvlVgWk/eIDPYkgfjz0tPTEQSB+Ph4ixMyM5lMvP766zz77LM8/fTTPPzww1IQXl5ezoEDB7j55pstWldlJKipqaG4uJiZM2cCsHr1an799Vf+85//SJNYJpOJRYsW8dFHH7Fp0yZWrVo1kkvuEWuwMAQYjUaysrJISUkhNTVVMgIRyxGPPPIIN910U69vNvJZc/Em7+LiYhY8DOaGKAiCNP8/XBvZQDCZTJw9e5YzZ84wZswYPDw8pJu8RqOxiEZAOe3t7eTl5VFbWyul8UdqHfLgoampCTs7uy59D+LYnl6vJy4uDg8PjxFZb28RXS2dnJyIi4sblIxAT5MEnUc2+1MyqK6uJjs7m4CAgB6zHyOJWq3mvvvu4+TJk3zyySckJSWN9JIuGlasWMFbb71FXl4eYwn/6RoAACAASURBVMeOZfv27WzZsoXbbruNBx980Ox5R44cobGxkRMnTvR5pHs4sAYLQ0xjYyNr1qzho48+4pprrsHW1pYDBw5w7tw5Jk2aJGUeZs2ahYeHR682MdG3QQwexA1RDB68vLwuaKPcE1qtlpycHJqamoiJiRkWmdOB0NzcTGZmJiaTibi4uC621waDwWxDbGxslKyUxWs1nH4Eomqki4vLeT0oRgLRk0DeYCpO+bi6ujJu3Di8vLwsbjMT6U32Y7AQ+2nkpYv29vYufQ/nC7KNRqMkNW6JypEAp06d4o477iAyMpIPP/zQ4u8HI0l3JlAtLS0kJyfj7u7O999/D8Bf/vIXTp06xY033sgdd9xBRkYG69at4/XXX2fWrFkjsfReYQ0WhpgnnniCo0eP8s477xAeHg503NTOnDnDvn372L9/P2lpaRQXFxMXFycFD4mJifj4+PTqZtfdCdHe3t4seLjQaVpsssvPz2f06NGMHz/e4sfKRPfNkJAQxo4d26veBHFDFK+VWq2WJi7kfQ+D3ecg6jxUVFSYiVdZKu3t7eTk5FBfX4+vry9GoxGVSjUs8sv9QafTkZmZSVtbG/Hx8cOe/egsgqRWq82cW8UvsczT0tJCRkYGCoWChIQEixBek2Mymdi2bRuPPfYYjzzyCGvXrh32ILGvJlDQ0aOwcuVKsrKyCA4OZu3atUM+RSD6/yiVSlpaWjh79iyOjo6MHTsWgKysLGbOnMl9993Hpk2bKC8v57333mPTpk34+/tTVlbGk08+yeOPPz6k6xwo1mBhiNHr9djZ2V1wo66oqJB6Hvbv309ubi7R0dHMmjWLxMREZs+e3WuRJqPR2OU0LTen6XyabmtrIycnh+bmZosf34SOaD0rK4v29nZiY2MHpOEu+hHImyaNRqN0QhQbTAdSixUnM2xsbIiLi7O4enRnVCoVmZmZuLi4EBsbK6XxL7QhyktiwxkIidMDAxUtGmzkzq1qtVoq8zg6OqLRaPDz8yMmJsZi1ivS3NzMgw8+yM8//8y//vUv5syZMyKB7X/+8x9ppPCmm266YLBw5swZ4uLiuO+++7j77rv56aefeOihh/j222+ZN2/ekK/3xx9/ZMmSJXh5eZGXl8cDDzzAggULmDJlCu+//z6LFy/mk08+4dZbbwXg7NmzVFVV4eHhQUxMzJCvb6BYgwULRBAEampqSE1NZd++faSlpZGenk5YWJhUspg9ezahoaG9+hCbTCazmXz5aVqhUFBfX4+/vz9RUVEWnU0QBIHS0lIKCwsZM2YM48aNG/TTjijqIw8e+jtFIO+luBgmM+S6FL21PJaXxETb6aEQ1uoOucfHYIgWDTV6vZ7MzExUKhWurq60trZiMpmkksVgBKYDJTs7m7vuuotRo0bx6aefWsx0Q280Eh599FG+/fZbMjMzpcf+9Kc/oVar2bNnz5CuLyUlhVtvvZWVK1dy3XXXkZKSwieffIKzszPbt2/H39+fv/zlL3z55Zfs3bvXYlUuz4c1WLgIEAQBtVptFjycOHGCgIAAEhMTpa/IyMhebUYmk4na2loKCgrQ6XTSjVy8YYmpeEuqTbe2tpKVlYVOpyM2NnZYJXrlExfyBtPOUwRyxOyHwWDotpfC0hDT4mI3fn91Kc4nrCWv5Q80aGpubiYjIwOlUkl8fLxFNoTJaW5uJj09HTs7O+Lj43F0dJRGgeXZB3HySX69hqOvRRAEduzYwUMPPcS9997L888/b1EHh94EC5dddhmTJ09m8+bN0mPbtm3joYceorGxcUjX9+KLL7Jr1y5pjB7gyy+/5O9//zvTpk1j06ZNGAwGJk2ahIODAwcPHrQYufbeYln5LyvdInpNXHfddVx33XXSXPjBgwclF7LVq1fj6ekpiUQlJSURExPT7WhmeXk5hYWFZt3X4py5SqWirKwMg8HQRethJE48ouFPYWEhgYGBvRIsGmwcHR0JCAiQphbkp+nS0lLJmEq8TjqdjpKSkiHLfgwmYgksPz9fWu9ANvKehLXEzbC0tFR6b8k3xN5uTPL1BgcH97pXZaSQC26FhIRI8t3Q8bl2dXXF1dWVMWM67L21Wq0UbJ09exaNRmOmoDgUmRqtVsuaNWv44osv+PDDD7nuuussup+mJ6qqqro0ifr5+dHU1ERbW9ug9IV0bmI0Go1Sr4KTkxOtra1S4HrjjTeyd+9eqQHb1taWb7/9lvLy8osuUABrsHBRolAocHNzY968ecybN0+qJR85coR9+/bx7bffsm7dOhwdHZk1a5ZUtgB4+OGHeeCBB7jyyiulGzqAm5sbbm5uBAcHd0nFZ2dno9PpzMSPhsNuuq2tjaysLNra2pg0aZLZekcSe3t7fH19pc5wUeWutraWwsJCDAYDtra2aLVaysvLpR4RS9vUREMljUbDxIkTJRfMwUSuYBoaGtrFu0HuRtq576EzYtOlSqUasvUOJnKth96u19HREUdHxy525qKCYkFBAQqFYsDmTyJFRUUsXLgQGxsbjh07RkRERL++z28BeaBw+vRpxowZg6urKw4ODgQGBnLy5ElycnKYPHmyFGwlJCTwySefoFar8fb2JjQ0lNDQ0JH8NfqNNVj4H0ChUODs7MwVV1whKY3pdDqOHTvGvn37SElJ4amnnsJoNDJ16lSKi4vJy8tjypQp3dbeFQoFLi4uuLi4SCceud203JxH3jQ5WF3x8tOjv78/kyZNsrgmMDm2tra0t7dTWVnJ6NGjiYyMlK6XXHq588TFSGYc6urqyMrKwsvLi0svvXTYUs7y95ZYD9fpdFLwID9Ny/Ue2tvbyczMxNXVlUsvvdQiJjDOh0ajIT09HQcHBy699NJ+nyS7szOXq02WlZX1a0JFEAR2797N/fffz2233carr756UZ525fj7+1NdXW32WHV1Ne7u7gPOKgiCIH1eb7jhBg4fPoyPjw/Tpk1j27Zt3HfffWzfvp1ly5bx/vvvS/LMOTk5zJ0716Ll5nuL5d6BrQwIBwcHEhMT8fT0ZNeuXYSGhrJ69WqamprYv38/b775JlqtlmnTpklli2nTpvXYyS5qxotNZHK7adEFUV7HF7Ue+opWqyUrK4uWlpaL4vQonnYbGhrMZuVFoyL4r5yweL3EG3zniYvh2LA7NwVagg26g4MDfn5+XU7TKpWKqqoqcnNzJa0HLy8vWltbsbW1tbhMDfy3zJefn09YWBgREYNjsiaiVCpxd3fH3d2dkJAQM/MnlUpFUVGRmfW7+CUfndbr9Tz55JNmAkEj/R4YDC699FK+++47s8d+/PFHLr300gF/b4VCQXNzM7t27UKr1fL111+zd+9e3n33XRYvXsy2bdvYvXs3U6ZM4bbbbiMoKAgnJye+/fZbPv/8c4sPbnuDtcHxf5xXXnmF6upqNmzYYBZdiyqTotZDamoqKpWKqVOnSloPogFTX4WixDExuXKi6LDZ0/eS6zz4+vpa/GQGdJzOs7OzcXNzY8KECb0+mYllI3nTpLyxTTxRD/ZJT6PRkJGRga2tLXFxcRbfFKjVasnIyECn0xEeHm6mJzLY462DgbxMEh8fP2JlM/l1Ej+L+/bt4+jRo0ycOJEDBw6g1Wr5/PPPLXpkT24Cdckll/DKK69wxRVX9GgCJY5OPvDAAyxZsoSff/6ZFStWDMro5JEjR7j++uuZPn06Dz30EL/73e9ob29n586d3HnnnfzjH//g7rvvprCwkD179nDs2DEcHBxYt26dlJ292LEGC1aAjvRmfn6+pPWQmpoqqUyKPQ+XXnqpNG55IUTlRHlXvHykzsvLS5K7lqtGTpgwweJ1HkTlvcrKSsaPH09gYOCAT2Zya2DRi0Du2zAQVU5BECgpKaGoqIiwsDDCw8Mt8lQuR5RA9vX1JTo62qxk03mKQKVSodVqhzzYOh+ixLSzszNxcXEWdZI0mUwcP36cbdu2cejQIUpKSlAoFJJ3zXXXXSd5F1gSfTWBEl/z8MMPk52dzZgxY1i3bl2/RJkEQTD7rB07dozHHnuMQ4cOUVhYiL9/h+eJRqPh+eef5+WXXyY9Pd2ig6+BYg0WrHSLXGVSNMcqKiqSVCbF7ENvVSY7j9Sp1WpsbGxwcnKiubkZb29vYmNjLeom2x1qtZqsrCzs7e2JjY0dstO5eDqUZ2pEVU5xQ+yNt4jo66DVaomLixuQgNVwILe/jomJkW7KF6K7YEuUQO8uFT9YiNM6BQUFQy4x3V8MBgMbN27ktdde49VXX+XPf/4z+fn5HDhwgLS0NC655BJWrFgx0su0CEwmkxRIyxsaTSYTe/fuZcGCBfzxj3/krbfekl5TUVHBfffdR2pqKmq1ekTWPRxYgwUrvUJsOty/f79UtsjJyWH8+PFmwUNvT9ltbW1kZmai0Whwdnamra0N6Kr1YCknYJPJRHFxMSUlJYwdO7bXgliDRU/Blrxp0s3Nzex6VVVVkZOTg6+vL+PHjx/xNP2FkJdJ4uPjB9SUJho/yYMtW1tbszp+5+vVn58hTpPEx8dbZCBWU1PDkiVLKCsrY8eOHUyePHmkl2SxyAOFHTt28NVXX+Ho6MjcuXO5+eabsbOzY8uWLaxZs4Z33nmH2267TcpAHDlyhGeeeYZt27b1+gB1sWENFqz0i/OpTMqDh+5OWmJvgtzRUhAENBpNF9ll+WY4kBGxgSCaVQmCQFxcHG5ubsO+hs6I+gXy6yWqAbq7u9PU1CSVdSzRoEhO56bAoSiTGI1Gs+ulVqsRBMFsBNHT07PX7y+1Wk1GRgaurq4WmRETBIGDBw+yaNEiZs6cydatWy0ymLFEVq5cybvvvsvtt99OZWUlP/zwA/fffz+PPPIIHh4ePProo3z66accPnxY8n/oXLb4X8QaLFgZFOQqk2LmQVSZFIWixo8fz8aNGwkICODpp58+b4pZrEuLzpqiiZG8qc3T03NIT8tyeem+mFWNBOL1OnfuHOXl5ZhMJgBJWKuv4kfDhV6vJzs7m6amJuLi4oatKVCcUJGXLvR6/QVlveX9H+PGjSMkJMTiNgmTycRrr73Gc889x3PPPceKFSss9n070sizCQAZGRncfPPNvPPOOyQnJwMdKpCbN2/m9ttv55FHHqGwsJCHHnqI3NxciouLR2jlw481WLAyJIg340OHDpGSksKuXbvIz88nMjKS6OhokpKSmD17drcqkz19P3GCQDwddm5q8/LyGrTNUBSEulhq/fIyybhx4wgODpbGW8XrJdfGGE4p4Z5oaGggMzMTDw8PJkyYMOKBjGiSJV6vlpYWnJ2dpevl4uJCYWHhiDlb9gaVSsW9995Leno6n3766YhaHr/55pts2rSJqqoqJk6cyOuvv8706dO7fe727dtZvHix2WMODg5otdrhWKqkvPjNN99w3333kZKSwtixY6VA8MEHH2Tv3r0cOHAAT09P/vOf//Dqq6+yfft2ixg/Hg6swYKVIUWlUrF8+XK+++47/va3vxEWFiY1TR45cgQHBwdJZTIpKYmJEyf2OlsgejbIb+7yzdDLy6vPHfGCIFBZWUleXh5+fn5ERUVZfK2/tbWVzMxMjEbjecskoviR3PRJ3gR4ofHWwUIMbETDKku169br9VLfQ11dHS0tLSiVSkaNGoW3t7fU92Apaz9+/Dh33nknMTExfPjhh/j4+IzYWnbs2MFdd93Fli1bmDFjBps3b2bnzp3k5eVJyqdytm/fzoMPPkheXp70mEKhGJYS2osvvkhlZSWbN28mLS2N5ORkjh8/zsSJEyWZ6Lq6OgICAvj+++/53e9+J6m0/pawBgtWhpTq6mpWrVrFSy+91MUVUFSZFJsmDx06hCAIzJgxg6SkJBITE3tUmewOvV5vFjyIzZOdN8PzvT4nJwe1Wn1RjHDKfQeCgoL67EPRuQmwsbEROzs7s+s12D4E8sBmIIZVw4U4FXTmzBnGjRuHm5ubmYYB0MUka7j7akwmE++++y5PPPEEjz32GI899tiI+5HMmDGDadOm8cYbb0hrDA4OZvny5fz1r3/t8vzt27fz0EMPjcg0wWuvvcZLL71ETk4Obm5uXHvttVRUVHDy5EnpOYcPH2bhwoXs3r1bUmf8rWENFqxYDAaDgZMnT0rBQ1pamqQymZiYyOzZs8+rMtmZ7sYPRcMncTMUx+lqamrIycnB09OTmJgYi2tY64w8sImNjR2UU6TRaKSpqcmsCVDuGDnQCZXKykpyc3PNDMwsGZ1OJ42dJiQkdMnYiE258r4HUXp5uPpENBoNy5cvZ//+/Xz88cdcccUVI57p0Ov1ODs78+9//9vMJXLhwoWo1Wq++uqrLq/Zvn07d999N0FBQZhMJiZPnszzzz8/qFbOnfsTRFJSUnj00UfZuHEjV1xxBQcPHmTBggWMHz+e5cuXSwJQKpWKb775Zlgdby0Ja7BgxWIxGo1kZ2eTkpIiCUU1NDQwdepUSSiqLyqTchlhlUoljdMplUr0ej0RERGEhoZafDNYfX29Wa1/qAKbzo6R4oRKX5UTDQYDeXl51NbWMmHChG7T0JaGeI29vb2JiYnpVcpZ7KuRB6itra0XtDPvL9nZ2dxxxx34+fnxySefdMncjRTnzp0jKCiIgwcPmkktr1mzhn379nHkyJEurzl06BAFBQUkJCTQ2NjIyy+/zP79+8nKyhp0BcSUlBTJYRU6DhUTJkxgwYIFbNiwAYPBQHZ2NnfffTe1tbUolUrCw8P55ptvRrTHZ6SxBgtWLhpMJhMFBQWSRHVaWhrl5eVMmjRJGtWcNWtWr1UmxQ3BxsYGBwcHNBqNZAfek3bBSGI0GiksLKSiooKoqCiCgoKG9RTZnXKiTqfDzc3N7CQtD16amprIyMjAwcGBuLg4i7/ZyvspBkOds7MMukajkXxD+ms5LQgCH3/8MStXruSBBx7g2Weftaj6eX+Chc60t7cTExPDbbfdxjPPPDNoaxPHIN3c3Hj33Xel9+Tf/vY33nvvPVJTU6WJHI1GQ3NzM5WVlVZ9CqzBQr947rnn+Pbbbzl16hT29va9qrMtWrSI999/3+yxefPmsWfPnqFa5v88giBw9uxZs+ChqKiI2NhYqechMTGR0aNHm92M9Xo9Z8+epaysjMjISIKDg1EoFGbaBeLNXXSLFDdDDw+PEQkeNBoNmZmZKJVK4uLicHFxGfY1dEd3EwTiSdpgMFBTU8PYsWMtUtmwM6IXRXt7OwkJCUPST2E0Gs16HtRqNUqlstelnra2NlavXs1XX33F+++/z7XXXmtx17U/ZYju+OMf/4itrS2ffPJJv9YhV2CUc/z4cd544w2+//57lixZwsMPP0x+fj4rVqzgjTfeYMaMGZhMJhQKhcVd25HEGiz0g/Xr1+Pp6Ul5eTlbt27tdbBQXV3Ntm3bpMfE+rmVweF8KpPitIWrqyuPPvooK1asYMGCBefddOVukeKXmIaXn6SHsvYu13oIDQ0lIiLCYjId3aHX66mtraW4uBidTocgCGZ20/I+EUuitraWrKwsRo8e3cWLYijpqdQjWk4rlUo8PDzw8fGhsLCQO++8EwcHB3bs2EF4ePiwrLE/zJgxg+nTp/P6668DHb9nSEgIy5Yt67bBsTNGo5HY2FiuvvpqXnnllT7/fHmgsGvXLoxGI87OzsyfP196zssvv8zu3btRq9W88cYb3HTTTaxfv55ly5b9JkSW+oo1WBgAfengXbRoEWq1ml27dg3DyqxAx0ZbW1vL/v37SUlJ4YsvvqC6uprJkycTHR0tNU32tk9BEARaW1vNgge9Xj9kDW2iXXdraytxcXEXRWBZV1dHVlYWXl5exMTEoFAoukxciLLL4jUbyfFDk8lEYWEh5eXlxMTEEBAQMCLrEBHfY2Lw8NFHH/HGG28QEhJCQ0MDM2fO5O233yYiImJE13khduzYwcKFC/nHP/7B9OnT2bx5M5999hm5ubn4+flx1113ERQUxAsvvADA008/zcyZMxk3bhxqtZpNmzaxa9cujh8/zoQJE3r9c+VNjIIgcMMNN3DixAn8/PzIycnhwQcfZNWqVYwaNQroCBKXLFlCS0sLKSkpTJ48mdTU1EHrK/lfwnIKXb8BUlJS8PX1xcvLi9/97nc8++yz0pvWyuCjUCjw9fVl0qRJvPrqq7i7u/Phhx/S2trKvn372L59O8uXL8ff399MojoyMrLb4EGhUODi4oKLiwtjxoxBEAQzrYe8vDzJaloUiepOBbA3VFdXk5OTg4+PDwkJCSMuWHQhxH6SiooKoqOjzYRqRo0aJb3PTSaTNHFRV1dHUVFRl1KPu7v7sJzs29rayMjIwGg0MmPGDIso7cjfY0FBQTz11FNotVoOHjxIdHQ01dXVREZGEhoayp///GeeeOKJkV5yt9x6663U1tby5JNPUlVVxaRJk9izZ4+km1BaWmr2GVOpVCxdupSqqiq8vLyYMmUKBw8e7FWgcO7cOd566y3WrFmDu7u79P3uuusuWltbOXHiBKNHj+bVV1/lr3/9K0FBQSxevBhnZ2dGjx7N119/zaeffoq9vT0PPvigNVDoAWtmYQD0JbPw6aef4uzsTHh4OEVFRTz++OO4urpy6NAhix8hu9hJTU1l586dbNy40cwlUq4yKQpFHT16FA8PD6lskZSUxIQJE3r9NxLdD8UAQqzhy9Pw52vyEycHampq+uS6OJK0tLSQkZEBQHx8fJ823c6lHrVajcFg6JKtGewGvpqaGrKysvD39ycqKsoiP4OlpaUsXLiQtrY2du7cyfjx44GOptHDhw8DcNVVV43kEi2CN998k7///e8sWLCA9evXA5CXl8dHH33E3XffTWhoKC+//DLPP/880dHRpKen8+9//5u5c+ea/d1/i0JLfcEaLPwff/3rX3nxxRfP+5ycnByio6Olfw9ESKS4uJixY8eyd+9e5syZ0+fXWxl8xEzBkSNH2L9/v9S5bW9vz6xZs6TMQ19O+vJueJVKZaaaKB+lE9P1GRkZODo6XhSTA6LaZW5uLkFBQT1mZPr6PcU0vBg8yLM1YsDV33FRk8lEfn4+lZWVFhuMCYLADz/8wN13383111/P66+/bhFZD0uhcz+BTqfjySefZP/+/SxbtowFCxZgNBrJysoiISGBdevWsWPHDjZt2sT1119PQkICo0eP5uWXX+aSSy4Zwd/k4sIaLPwftbW11NfXn/c5ERERZjepgaqOjR49mmeffZZ77723X6+3MvTIVSZTU1M5ePAgJpOJmTNnSsHD5MmTey0rLVdNFLUe7O3tsbOzo6WlhZCQEMaNG2fRTYzQ8Xvk5OSgUqkGTRSqJ+TZGrVaTXNzszRx0RtlTpHW1lbS09MBSEhIMMsyWQoGg4HnnntOOi0vWbLE2mgnQ96TsGXLFs6dO8fTTz9NUVERTzzxBHV1dTz//POSB4Vareaaa65h8eLF3H333TQ1NTF//nwOHTrE7bffztatW/ssCf9bxRosDICBBAvl5eWEhISwa9currvuuiFYnZWhwGAwcOrUKalskZaWRmtrKzNmzJBKF9OmTeu1x0JzczPp6eno9XqcnJxobm7GxsZGyjwMheTyQBHtmV1cXIiNjR32m21Pypzy4MHFxcXsmlVVVZGTk0NgYOCgZECGgurqahYvXsy5c+fYuXMnEydOHLG19MUECmDnzp2sW7eOs2fPEhkZyYsvvsjVV189qGuSTzgsXryY999/n88++4xbbrkFgJ9++omNGzfi4+PDm2++ibe3NwcPHmTOnDn85z//ITk5mYKCAt58801uvfVWgoKCCAkJGdQ1/i9jDRb6QWlpKQ0NDXz99dds2rSJ1NRUAMaNGyfNZkdHR/PCCy9w44030tzczFNPPcXNN9+Mv78/RUVFrFmzBo1GIwnW9IX+6DwIgsD69ev55z//iVqtJjExkbfffpvIyMi+XwArEiaTiaysLEnrQVSZnDJlipR5mDlzZpcN32QyUVlZSX5+vpn8sbwBUNwMRcllMXgYKaEouU/C2LFjCQ0NtYggpjvtAhsbG0kXo7GxkYaGBuLi4ixSPVIQBNLS0li0aBGzZ8/mn//854g6WvbVBOrgwYNcdtllvPDCC1x77bV8/PHHvPjii5w4cYK4uLhBXVtFRQVz5szB0dGRf//735IKo8iWLVv44IMPuOyyy9i4cSMASUlJFBcXk5yczPfff88tt9zCP/7xj0Fd128Ba7DQD7oTWAL45ZdfJA90hULBtm3bWLRoEW1tbdxwww2cPHkStVpNYGAgV111Fc8880y/XNX6o/Pw4osv8sILL/D+++8THh7OunXryMjIIDs72+Jr4xcTF1KZTExMJDo6mpUrV5KQkMCDDz54XsMq+Ry+GDwYjUaz4GE4pge0Wi2ZmZnodDri4+OlrnNLRAy4ampqKC8vx2g0SsJHcnEtS2hqNBqNbN68mY0bN/LCCy+wbNmyEc969NUE6tZbb6WlpYVvvvlGemzmzJlMmjSJLVu2DNq6SktLmT9/vtQELOf7779n3rx5GAwG1q1bxy+//MKSJUu45557aG1t5fHHH6exsZHZs2ezZMmSQVvTbwlrsHAR09syiCAIBAYGsmrVKlavXg1AY2Mjfn5+bN++nT/96U/DsdzfJHKVydTUVL7//ntqa2uJiIggKSmJ5ORkZs2aha+vb69O6eL0gLxpsr29XRKK6q1fQ1+oqakhOzub0aNHM378+IuiY/zcuXPk5uYSHBxMREREl6bJodTH6C0NDQ3cc889ZGdn8+mnnzJz5sxh/fnd0R/1xZCQEFauXMlDDz0kPbZ+/Xp27drF6dOnB21tVVVVPPvss6SmprJ582auuOIKioqKuOmmmwgMDOSzzz7Dzc2NsrIyHn/8cc6dO8e6detITk7GaDQCWESAeLFi+Z96KwPmzJkzVFVVceWVV0qPeXh4MGPGDA4dOmQNFoYQhUJBeHg4gYGBZGdntNA6bAAAIABJREFUo1ar2bBhAyEhIaSmpvLCCy+QnZ1NVFSUlHmYPXt2j54ECoUCNzc33NzcCA4ONhOKUqvVZGdnm/k1iJthfzZCo9FIfn4+VVVVknaCpWM0GsnNzaW2tpaEhASp8bLzNZPLVOfn59Pa2oqrq6vZNRvKXoxjx45x5513EhcXx/Hjxy1Gb6Wurg6j0dgl4+nn50dubm63r6mqqur2+VVVVYO6Nn9/f+655x5qa2vZsGED+fn5rF27luuvv57Nmzfj6uqKIAgEBwdz3333sXbtWp599lkmTZqEp6fnoK7lt4g1WPgNIH5oh+MDbaV7ysrKOHz4MMeOHZPGbxcsWCCpTKamprJv3z7eeOMNli5dSmhoqGSMdT6Vyc5CUcCgbITNzc1kZGRgY2PDjBkzLHJyoDNis6idnR0zZ87ssbymUChwdnbG2dlZcmrU6XTSNTtz5sx5R1wHgslk4p133mHdunWsXbuWNWvWWE+7fSAhIYGFCxfy3HPPcf/99/Pee++xaNEixAS5+PdJTEzkrrvuwtvb2xooDBLWYMFC6I/Og5WLh3HjxrF///4uj4sqkzfffDM333wzgiDQ2NhIamoq+/fvN1OZFKctEhMTiYqK6rG27eTkhJOTk5QJkG+ExcXFNDc34+zsbDZxIW6sgiBQXl5OQUEBISEhFu9FAf/1BMnPz+/3mh0cHPDz85MCanHiQq1WU15eTnZ2Nvb29mZ9D32dUmlqamLZsmUcOHCAb7/9lssvv9wiGkTl+Pj4YGNjQ3V1tdnj1dXVPWpS+Pv79+n5/UXUV/j9739PWVkZarWa2tpaoONzJP5/cbxy8eLFg/rzf+tYgwULYdWqVSxatOi8z+mvHrz4oa2urjZLJVdXVzNp0qR+fU8rQ4M4+fCHP/yBP/zhD11UJnfu3MkjjzzSJ5XJ7jZCsWxRWlpKVlYWDg4OeHh40NLSgl6vZ+LEiRaTGj8fBoOBnJwcGhoaBnXNdnZ2jB49Wmo+NRqNNDY2olarqampoaCgwGxKRZSp7ilIyczM5I477iAoKIiTJ09apBgUgL29PVOmTOGnn36SehZMJhM//fQTy5Yt6/Y1l156KT/99JNZz8KPP/5oZk/dF3oycRIDAqVSyS233EJpaSlbt26VDKfE11l6cHuxYm1wvIjpa4Pj6tWrWbVqFdBxyvH19bU2OF5kdFaZ3L9/P4cPHx6QyqTBYKCsrIwzZ86gUCgwGo3Y2dmZZR466xZYAk1NTaSnp+Pk5ERcXNyw6j30NKUiNpqqVCqioqJwc3Pjww8/ZPXq1axYsYKnn37a4htE+2oCdfDgQS6//HI2btzINddcw6effsrzzz/f59FJQRCkYKBzwCAXYxLJzs7m+eefp7CwkE8//ZSwsLBB+f2tdI81WLgI6avOA3SMTm7cuNFsdDI9Pb1fo5MNDQ0sX76c3bt3o1Qqufnmm/n73/8u/ezuSE5OZt++fWaP3XvvvYM6WvVbRafTcfz4cSl4EFUmZ8yYIZUtpkyZ0u1majKZKC4upqSkhMjISIKDgzGZTGZOkXLdArnWw0gFD2KpJD8/n/DwcMLDw0c8kBEEgZaWFil4WL58OSdOnCA4OJiqqioeeeQRHnzwwYsiWwPwxhtvSKJMkyZN4rXXXmPGjBlAx2c5LCyM7du3S8/fuXMna9eulUSZXnrppT6JMsmDg0OHDvHZZ5/h4OBAXFwcd9xxB9B9wLB3715WrlzJtGnT2Lp16wB/ayvnwxosXIT0VecB/ivK9M4776BWq0lKSuKtt94iKiqqzz9//vz5VFZW8o9//IP29nYWL17MtGnT+Pjjj3t8TXJyMlFRUTz99NPSY87OzhY9r3+xIqpMisGDqDI5ffp0KfMwbdo0ysrKWLduHX/5y1+YMmUKbm5u3X4/uVCUGDzInSJFrYfhSP+2t7eTnZ1NY2Mj8fHxFmvbnZ+fz9KlS1EoFIwdO5ZTp06Rl5dHbGwsL7/8MvPmzRvpJVoEclVGgE2bNrF+/XoWLlxIXV0dBQUFJCQk8MEHH5i9Th5c/PjjjyQmJl4UTbgXM9ZgwUqfyMnJYcKECfz6669MnToVgD179nD11VdTXl4udZd3Jjk5mUmTJrF58+bhXK4VOjb77OxsUlJSSE1NJTU1lZqaGuzt7Zk6dSrLli3j8ssv73XDniAIZil4lUolCUWJAcRQiB41NjaSnp6Oi4sLcXFx/TaTGkoEQeDLL7/kgQceYNGiRWzatElaZ01NDWlpaUycOJGxY8eO8EpHllWrVrFmzRr8/Pwkt8eCggLuuOMOHn/8ca6//npUKhVJSUm0tbVx5MiRLuJlPfU2WBkarMGClT7x3nvvsWrVKlQqlfSYwWDA0dGRnTt3SmWPziQnJ5OVlYUgCPj7+/OHP/yBdevWWU8Dw0xLSwsrVqzg888/57bbbqO5uZnU1FRJZVJsmpw1axZeXl69Dh5aWlqkzINKpTITPRIbAPtbqxcEgdLSUgoLCy1KZrozOp2OJ554go8//ph//vOf3HLLLRa5zpEmLy+PP/zhD4wZM4aff/5ZevyLL75g5cqVnD17lrS0NG677TamTJnC22+/TUBAgJSFsAYJI4Nld9pYsTiqqqq66MPb2tri7e19Xs2G22+/ndDQUAIDA0lPT+fRRx8lLy+PL774YqiXbEXG008/TWFhIRkZGQQHBwP/VZkUyxZr166lqKiI2NhYSSgqMTGxR5VJhUKBq6srrq6uZqJHYvCQm5trZjMtBg+9yQzo9XqysrJobm5mypQpFjszX1JSwsKFC9Hr9Rw9erRf5b3fChEREbz22mssXbqUVatW8be//Q34r1Dc448/zuuvv87q1atZu3YtNjY2nDp1ipSUFB566CFroDBCWIMFK0DvdR76yz333CP9d3x8PAEBAcyZM4eioqLffEp2OFm/fj0ODg5mJQJRZTI8PJyFCxciCALnzp2TgoeNGzdKKpPycc2goKAegwdR9CgoKAjo8JYQSxaFhYW0tLTg6upq1vfQuQFTrVaTnp6Ou7s7M2fOHHY55t4gCAJ79uzhnnvu4aabbuK1117rlV32cGFpzcjt7e3Y2dlx2WWXsW7dOlatWsWVV17J/Pnz8fHxITU1lT179rBt2zbJTVIQBHbv3k1paSm1tbXn9VKxMnRYyxBWAKitraW+vv68z4mIiOCjjz7qVxmiM+JmsWfPHmuzl4UjCAJ1dXVS8JCamsrp06cJDQ2Vsg5JSUmEhYX1uslRr9ebOWtqNBqcnZ2lvoeWlhbKysqkCQ1LPE22t7fz7LPPsmXLFl5//XUWLlxoceu0xGbkrKwsnnjiCby8vHj//fcJCAjg4MGDhIaG8uqrr/LEE0+wceNG5syZg5OTE5s2bWLXrl188MEHzJ07d1DWYKXvWIMFK31CbHA8duwYU6ZMAeCHH37g97///XkbHDtz4MABkpKSOH36NAkJCUO5ZCuDTGeVybS0NI4fP46fn5+Z1sP5VCY7Iyom1tfXU1lZicFgwN7enlGjRknZB2dnZ4vZjKuqqli0aBE1NTXs3LmT+Pj4kV5SFyyxGfnkyZMkJyezcOFCbrrpJtLS0vjggw/w9vbm8OHDACxfvpxDhw5J629vb+fLL78kPDx80NdjpfdYg4WLEFG8RKFQjMjNc/78+VRXV7NlyxbptDJ16lTptCJ6zn/wwQdMnz6doqIiPv74Y66++mpGjRpFeno6Dz/8MGPGjOmS7uyJN998U5r7njhxIq+//jrTp0/v8fk7d+5k3bp10tz3iy++2Ke5byu9R2xwPHToECkpKaSlpXH06FHc3d3NgofY2NjzTkg0NDSQkZGBl5cXkZGRZgZZjY2N2NraSv0OXl5efZZbHgwEQSA1NZVFixaRnJzMO++8Y7Hjv5bYjPz222/z3nvvcfDgQams9NVXX7F8+XKuvfZa3nrrLQRBoLKykrNnz6JQKPqtBGllcLH2LFyEdA4Shrs7+F//+hfLli1jzpw5Uh30tddek/5/e3s7eXl5tLa2Ah0Ssnv37mXz5s20tLQQHBzMzTffzNq1a3v183bs2MHKlSvZsmULM2bMYPPmzcybN4+8vLwuzZbQoSh322238cILL3Dttdfy8ccfc8MNN/RZUc5K7xAbHOfO/f/tnXlcTfkbxz+3urciZSlK2rQvqluK7KQphJGlYawz1oiRYTIZMhgz1hn7msoyxtgpFCHSIorGcm0p0iKFNl3d+/z+6He/051CllSc9+t1X17ne77nnOfc3HOf+3yf5/O4wc3NTU5lUrYGHRgYCD6fL9ffws7ODnw+H2VlZQgKCoKJiQnMzMxYLoSqqioTMZJIJEzrITc3F3fu3JGTW5YJRdWk1oNEIsHy5cuxdOlS/Pbbb/Dx8anT0sJ1MRlZ1jitrKyMOQuurq4YPHgwVq5cCTc3NwwYMAA6OjrVjlJyfBy4yEI9QOYMPHr0COfOnUNUVBQaN26MXr16oUuXLnX6gfUhaNeuHZycnLBmzRoA5boBenp68PX1hb+/f6X53t7eKCoqwtGjR9lY+/btYW9vzylG1hJisRiJiYmVVCbt7e3x+PFjFBQU4NixY9VOdpXJLVfMe5AJRVXUevhQn40nT55g3LhxEIlE+Ouvv14b1appqpuMvH//foSEhEAkEsnta968OebPn49JkyZV63pRUVFwdXVlpavvw969e7Fo0SL4+/tjyJAh7EfOpk2bMHHiRADAnTt33rkPDkfNwUUW6gE8Hg8REREYPXo0pFIp+vTpg+vXr+PgwYPQ1NTEwoUL0b1799o2s0YQi8W4dOkSZs+ezcYUFBTQs2dPxMbGVnlMbGws/Pz85Mbc3d1x8ODBGrWV49XIeld06NAB/v7+KCsrw4YNGzB79mxoa2szeWpnZ2fWltvJyemVbaEVFBSgoaEBDQ0NGBoasoZbMufhwYMHKCsrg4aGhlyzp3cRikpISMDIkSNhb2+PS5cuoWnTph/iLXlnqtt0TltbGzk5OXLjZWVlyMvLe6tGVjKZ5w/hLPTr1w8bN27Erl27oK2tja5duwIo7/Ph5+cHCwsLzlGoo3DOQj3g9u3b+Oqrr2BjY4OwsDAoKSlBVVUVz58/R1BQEKZPn46YmBg0bNgQQHkkQiqVfhId2HJzcyGRSFjHRBktWrTAzZs3qzwmKyuryvmvC71yfFw2b94Mf39/rFmzhjnBFVUmg4ODkZubC0dHR7Zs0b59+1f2pODxeGjUqBEaNWoEfX19EBHLecjPz8ejR4/khKJkEYjXlWNKpVKsX78egYGBmDt3LmbOnFknPk8Vu2G+DhcXFzx9+hSXLl1iychRUVHMMasuycnJACDXsfa/yJ43//3bVFwilUgkEAgEWLlyJSZOnAhfX18IhUIIBAIcOHAA27dvR69evaptF8fHhXMW6gGbN2+GQCDA0qVL5fT71dXVMWnSJFhYWDBHASh/cH5oqV0Ojg+Jm5sbEhISYGVlBaA8UmBjYwMbGxtMmTIFUqkUd+7cQXR0NM6ePYvp06fjwYMHsLOzYwmTr1OZ5PF4aNiwIRo2bIhWrVqxPAqZ8yASieSEomTOg0zr4dmzZ/Dx8UFCQgLCw8PZL+D6hKWlJTw8PDBu3DiWjDxlyhR89dVXLB+gusnIXbp0eWXVUsX+DpcuXcKDBw/QunVrGBsbo2HDhmy/oqIipFIpbGxssHnzZpw6dQrHjh0DEeHo0aNo3779R3tvON4ezlmo4xQXF+PkyZPo0aMHe7BW9NaVlZXh4eEBoDxkf+HCBYSGhqJZs2YYOHBglR9AWfe2qrq4yagrkqqamppQVFREdna23Hh2dvYrQ6na2tpvNZ/j42NiYvLa/QoKCjAzM4OZmRnGjh0LIkJaWhrOnj2Lc+fOyalMVkyafJ3KpKqqKlRVVdkX5YsXL5g89b179xAUFISYmBjY2Njg6tWr0NfXx+XLlytFqeoTHyMZWeYozJw5E0FBQWjWrBlKS0thaGiIyMhIOaVO2fPG0tISlpaWmDBhQp0U2+KoAuKo05SUlFCDBg3o119/pbKystfO9fPzI21tbRo4cCD179+fWrVqRUFBQWz/ixcv3ngOqVT6Qez+kDg7O9OUKVPYtkQiIV1dXVq8eHGV84cMGUKenp5yYy4uLjRhwoQatZPj4yGVSikjI4N27dpFEydOJGtra+LxeGRubk5jxoyhrVu3kkgkosLCQioqKqrW6+7du+Tr60tt2rQhHR0dUlBQIGNjYxozZgwdPHiwtm+5TlBaWkp79+6tNL5hwwZq1aoVxcXF0cOHD+nkyZNkampKvXv3rgUrOWoCzlmo4+Tk5FCjRo0oICDgtfPOnDlDDRo0oD///JPEYjEREQUEBJCxsTGJRCIiIgoPD6d27drR5s2b6dChQ3TgwAEqLi4movKHABHR+fPnqWfPnhQZGVmDd/V27N69m5SVlSk4OJiuX79O48ePp8aNG1NWVhYREY0YMYL8/f3Z/JiYGFJSUqJly5bRjRs3aN68ecTn8yklJeW97FizZg0ZGBiQsrIyOTs7U3x8/Cvnbtu2jQDIvZSVld/r+hyvRiqVUk5ODu3bt4+mTp1KDg4OpKCgQIaGhjR8+HBav349paSkUEFBQZWOQk5ODg0fPpw0NTUpPDycpFIpPXv2jI4dO0azZ8+mpUuX1vYt1gl27NhBPB6Pjh07xsYkEgmNGDGCRowYITc3KSmJVFVVae3atURUN3+IcFQfzlmo45SWltKXX35Jbdu2feUcsVhMc+fOJSsrK7nx58+fE5/PpwsXLhARUVBQELVo0YJcXFxo4sSJZGBgQEKhkDkTT548oV9++YVcXFzo+vXrNXdT78Dq1atJX1+fBAIBOTs7U1xcHNvXtWtXGjVqlNz8PXv2kJmZGQkEArK2tqawsLD3uv7u3btJIBBQUFAQXbt2jcaNG0eNGzem7OzsKudv27aN1NXVKTMzk71kzg1HzSOVSik/P5+OHDlC33//PbVv3574fD7p6urS4MGD6Y8//qDExEQqKCigy5cvk7W1Nbm4uFBaWlptm17n+eabb0hPT4/u3r3LxoYPH049e/Zk27II5rRp06hHjx7sRwlH/YVzFuoBR48eJU1NTZoxYwY9e/aMjRcWFhIRUX5+Pg0bNowGDBhAROXLDUREt2/fpkaNGtG5c+eorKyMZsyYQerq6hQbG0tERLm5uWRoaEiLFi0iIqLff/+dGjRoQAKBgDw9PWnTpk1UVFRUpU1vWs741HB2dqbJkyezbYlEQi1btnzlUsi2bdtIQ0PjY5nH8QakUikVFBRQREQEBQQEUJcuXUhFRYU0NDRIIBDQd999x6JrHJWRSqXsM19QUEAODg7Ut29fys/PJyKilStXkpOTEx04cEDuuPHjx5O7u/tHt5fjw1P7dUAcb6RPnz5YvXo1jh07BqFQiHHjxmHp0qXo1KkTDh8+jMaNG+Px48es/luW4HXixAloa2ujRYsWyMvLw61bt9C7d2+W9KiiosL6MwDA5MmT0aZNG3h6ekJfXx9Lly7F/fv3mR0JCQl4+PAhAFSqtqD/l2u+CqrH2l8yrYeePXuysTdpPQBAYWEhDAwMoKenh/79++PatWsfw1yOKqioMrlw4UKcOXMGeXl5CAoKwsyZM7FixYpqtcz+WCxatAgdOnRgzbWqAxFh7ty50NHRgaqqKnr27Inbt29/EHtkFVbx8fFYtGgRbG1tcfToUSaU1r9/f2hpaWHLli2Ij48HUN4sLi0tDVZWVpBKpfX6GcABcM5CPeGrr75CXFwclixZAlVVVYhEIsybNw+urq4AgI4dO+LMmTNITk6GQCBASkoK1q1bh65du8LU1BT37t1DRkYGunTpws75+PFj5ObmsodRXFwcxGIxPD09sXbtWty6dQtWVlZ4+PAh+vXrhylTpsDKygpmZmbYsmWLnH3/1XSQSCTMeSgrKwOPx8OSJUsQExNT02/VB+d1Wg+v0m4wNzdHUFAQDh06hB07dkAqlaJDhw7M2eKoXWTVEV5eXli4cGGdqPypiFgsxuDBg6utsggAS5YswapVq7BhwwbEx8ejYcOGcHd3x4sXL976+o8ePao09tdff6Fr167g8XiwtLRE3759ERgYiH379sHIyAh+fn7g8Xjo0qUL3N3dYWdnh5ycHPz0009QUFCoc+8xx1tSu4ENjg9FcXEx9e/fn3R1dalPnz5kbm5OLi4ulJ6eTkREwcHBZG5uTleuXGHHnDt3jszMzCgkJISIykOJLi4udPr0aTbnxo0bNGrUKPL29qbs7GwqKSmhZcuWkaOjIyUmJhJReRLm7Nmz6erVq5Sbm/tKG8ePH08bN24kiURSA+9AzZGRkUEAWO6HjJkzZ5Kzs3O1ziEWi8nY2JjmzJlTEyZyfKJUdzlLKpWStra2XCLm06dPSVlZmf7888+3uqa/vz916dKl0hLkN998QyNHjmTbRUVF9O2335KWlhbdvHmTiMqXKEJDQ2nFihW0atWqt7ouR92Giyx8IqiqqmLfvn0IDg6GUCiEn58fTp48CT09Pbx8+RLJyclQUVGRa6WbmpqKoqIiFm24cuUKmjdvLifpeubMGZw8eRJEhPv370MsFmPGjBnQ09NjXSaTkpKwYcMGBAQEwMfHB2pqahg/fjwyMjLkbNy4cSPGjx8vF4GgCqFJsViMgwcPorS0tEbeo3flXbQe/gufz4dQKMSdO3dqwkSOz5zU1FRkZWXJLZVpaGigXbt2r10qq4rZs2dj165daNCgAYsOEhHi4uKgqakJoFyrRVVVFYsXL0bTpk3h5+eHvLw8qKmpYcSIEZg+fTp8fX0/3A1y1Dqcs/AJoaioiJ49e2LBggUYP348aykrFouhoaEBOzs7FgosKSlBSkoKtLS0YGhoCLFYjIyMDBgZGUFXV5d9iZ8/fx66urooKiqCt7c3dHV10bZtWxw6dIid68qVKygrK0OLFi0wZ84cHDlyBNHR0cyZAIDjx49j7dq1ePnypZzNFUOTCQkJ8PLyksuTqAsIBAI4Ojri1KlTbEwqleLUqVPVbp8rkUiQkpLyWslcDo53RbYc9r4y51KpFOrq6tDV1cWOHTuwfv16FBUVgcfjoXfv3jh16hRycnKYw9+sWTPY2Njg2LFjCAgI4PISPmE4Z+EzoGHDhggMDERISAgbKyoqwv3792FkZASgvKueiooKnj59ytYXxWIxlJWV0aJFCxw9ehS3b99GUlISpkyZgkmTJrFfMYmJiWjfvj1WrlyJNm3aoHv37mjVqhVSUlLw/PlzAMDy5cuxfft2FBUVMRuuXr2KCxcuQCKRAABiYmJgYWEBAwODj/XWVBs/Pz9s3rwZISEhuHHjBiZNmoSioiKMGTMGADBy5Ei5Zlc///wzIiIicO/ePVy+fBnDhw9HWloaxo4d+152REdHo2/fvmjZsiV4PF61mmOdOXMGDg4OUFZWhomJCYKDg9/LBo53w9/fn/VPeNXrVf1OPhYVo35JSUnw9fVlCYs9evSAuro6FixYAODfPKWWLVvCz88PysrKXF7CJwwn9/yZoqmpiT179rAvcx0dHfTp0wdz5syBUCiEv78/vL29YW9vj8DAQNy/fx+GhoYwMTGBiYkJ63qXn5+PtLQ0uLm5QU1NjZ1fQ0MDSkpKUFIq/y927do1TJ06lfWwmDlzJsLDw/Ho0SPw+Xzs3r0bZ86cQdu2baGiolLJXlk2dW31vPD29sbjx48xd+5cZGVlwd7eHsePH2e/5NLT0+UetPn5+Rg3bhyysrLQpEkTODo64sKFC0yy+10pKiqCnZ0dvvnmG3h5eb1xfmpqKvr06YOJEydi586dOHXqFMaOHQsdHR24u7u/ly0cb0d1u0W+C7LlsOzsbLnoVXZ2Nuzt7V97bEXZd6og8758+XJcvXoVU6dOxeHDh+Hh4YHr169j48aN8PLywpdffon4+HiEhYUhJiYGurq672Q7Rz2hFvMlOOogt27dorlz59L+/fuJiCg7O5sGDRpE/fr1oxMnTlB6ejrt37+fLl26REREUVFRJBQKWZIkEdH9+/epa9euTFUxKyuLeDweU4XcsWMHKSkp0caNG+nJkycUGRlJ7u7uxOPxKDQ0lJ1HKpXSrVu3mJ4EhzwAKtW1/5dZs2aRtbW13Ji3tzdX+15PeNsEx2XLlrGxZ8+evTHBsaKq4uHDh+mHH36g7du3U0ZGBhGVJzFqamqSt7c3FRcXU1FREUVERJBQKCQnJycSCoV1TsCNo2bgnAWON3LlyhUaMWIEaWlpkb6+PnXo0IGioqKIiOiXX36hbt26yUkfHzlyhJydnWnbtm1EVF6J0bRpU3r48CFlZ2fTgAEDaPDgwWx+aWkpDR06lFRUVOjatWtEVC4sNXbsWLKxsSEVFRWysbF5J33+wsJCunXrFhF9enKz1XEWOnfuTNOmTZMbCwoKInV19Zo0jeM9SUtLo6SkJJo/fz6pqalRUlISJSUlUUFBAZtjbm7OnHoiol9//ZUaN25Mhw4doqtXr1L//v3JyMiISkpKqrxGRWG1BQsWkIqKCvXu3ZsEAgF9++23dPnyZSIiio6OJh6PR7/99hs7V3FxMT19+rQmbp2jjsLlLHC8EVtbW4SGhiInJwcXL17EunXr0KlTJwDAxYsXoaSkJJdncPXqVaipqbGQe1hYGOzs7KCjo4PU1FTk5OSge/fuAP7tcW9kZISWLVvCzMwM+fn5mDVrFvbs2YP58+fj5s2b8PDwQGBgIDIzM6tlsyyL+59//oGtrS3++usv8Hi8zy4BKysrq8qkt+fPn6OkpKSWrOJ4E3PnzoVQKMS8efNQWFgIoVAIoVCIxMRENkckEuHZs2dse9asWfD19cX48ePh5OSEwsJCHD9+vMplPaA8Ifr58+fYs2cPUlNTcfbsWYSFhWHXrl24ceMGNmzYgMePH6Nz585YtGgRFiyrbQu6AAASW0lEQVRYgGPHjkEikUBVVRUaGho1/j5w1B04Z4HjrWjevDns7OxYW9mQkBCsWrVK7gvp/Pnz4PF4MDU1BQDEx8ejW7duUFBQgKKiItLS0mBrawvgXyXIxMREODo6QklJCefPn8eFCxewbNkyeHl5wcDAAN988w1KS0uxc+fO19r3+PFjZGVlsTXYR48eQVVVlZWHcglYHPWB4OBgUHnkV+7VrVs3NoeI5HIgeDwefv75Z2RlZeHFixc4efIkzMzMXnkNqVSKyZMnY+rUqbhz5w7atm0LABg4cCAGDhyI5ORkbNy4EUB5OaWVlRXWr1+PsrKyGrlnjroN5yxwvBeNGjWCpaWl3Nj8+fMxbdo0NGnSBHl5eXjw4AHTd7C3t0deXh5SUlLY/Li4OMTGxjI1ykuXLqFZs2ZMlhooV0RUV1dnZWCyCoqKhIWFYciQITA2Nkbr1q2xZcsW3Lx5E02aNIGOjk6lqIJEIqnyPJ8S2traVepDqKurQ1VVtZas4qgN/vt/XUFBATNnzoSJiQmysrLkNECmTZvGyoVlVVTx8fE4fvw4lJWVP6rdHHUDzlng+OA4OTmhb9++kEqlaNy4MaKjo9G5c2cA5b9+5syZg2XLlmHNmjXYuXMnvv76ayaHDJTrQjx//hzW1tbsnMXFxbh//z7s7OwA/BuRkC03hIeHY/bs2dDQ0EBiYiJ+++03nDhxAjt37pRzOmTnkp3jbasr6pvGvYuLi5w+BABERkZWWx+Co/5D/+/boqioiKKiIoSFheHixYvIz8+Hra0tvv/+ewgEAgQFBbFlDUVFRVbquWvXLmRmZspVTXB8htRWsgTH58uTJ0/op59+IhsbG/L19aWhQ4eShoYGPXnyhIiI9u/fTwKBQK6l84EDB4jH47EsbRmypMUBAwaQl5eXnNz02LFjicfj0Z49e9jY7t27aejQoaSjo0NdunShvXv3klgsrsnb/aAUFBSwZDcAtGLFCkpKSmKtlf39/WnEiBFs/r1796hBgwY0c+ZMunHjBq1du5YUFRXp+PHjtXULHLVEZGQk6evrk52dHZmbm5OlpSVLKA4MDKS2bdvS2rVr5Y6Jjo5mczg+bzhngaPWSU1Npb1797LttLQ06tmzJw0bNowSExNpxYoVZGRkRMOHDyciqtRboqCggKytrWnFihVy+/744w9SVlZmX6QrV64kR0dHWrx4MUVFRdHcuXNJKBTSmTNniOjN1RIHDhygYcOGVfnw/FjtjU+fPk0AKr1GjRpFRESjRo2irl27VjrG3t6eBAIBtW7dmlWpvA9nz54lT09P0tHRqVZVxqvszszMfG9bON5MQkIC6enp0W+//UZSqZSkUikpKirSl19+SaWlpVRWVkZDhw4lNzc3OnLkSG2by1EH4ZwFjjrJ+fPnydXVldTV1cnBwYF+/fVXysnJIaLKzsKVK1dIKBRSUFAQGysqKqI5c+aQvr4+29bT06MJEyZQXl4emzdp0iT6+uuvqbi4uEo7ZOVlYWFh9O233xKPx2O17BVLz2bNmkWdO3emly9ffoC7r/uEh4dTQEAA7d+//62cBZFIRJmZmexV35qKvY6FCxeSi4sLqaqqVksbgajcufuvA1UTGhibN2+mAQMGEBFRbm4ueXh4kImJCZ07d47NuXXrFjk4OFD//v3ZZ42DQwan4MhRJ+nYsSNOnjwJoLzCQUtLi+3777pp69atIRAIkJyczMYyMjJw/PhxluF9+vRpPHz4EKdPn4a+vj6aNm3K8iiioqJemewny2mYN28eRo8ejYEDBwIAWwOWERsbC1NTU6ZY+anTq1cv9OrV662Pa968OWuJ/qkhayvt4uKCrVu3Vvs4Dw8PbNu2jW2/TwJheHg4VFVV0b17d8TGxoLP56Nt27bIyMgAj8dDUlISPD094ezsjAsXLkBLSwsikQgNGzaEqakpFixYgObNm8t93jg4AC7BkaMe8KYHl5qaGnr37o2zZ89i3759iImJgZ+fHy5duoS+ffsCKNeDEAqFOHHiBO7du4cVK1agSZMmuHz5MnMaqqqMEIvF2LhxI3JycjBu3Dh4eXkhKipKbk5hYSGSk5PxxRdfVDr+c6i4eBvs7e2ho6MDNzc3xMTE1LY5H5T58+dj+vTpcp1dq4OysjK0tbXZq0mTJu90/dTUVMyaNQvbt2/HrFmz0LFjR6bLYGVlhRs3bqBdu3aYOnUq9u/fzz5X27Ztw++//w4A6N27N3OwOTgq8nn8DOL45PHx8UFWVhZ8fHxgbW3NRKJk+godOnTA1q1bce/ePfTo0YPVkgPy1REyZJnfx44dw969e/HDDz9AIBBAQUEBN27cgIKCApuTkpKCkpISODo6VrKrtnpZ1DV0dHSwYcMGtG3bFqWlpdiyZQu6deuG+Ph4ODg41LZ5tcqZM2fQvHlzNGnSBD169MDChQvRrFmztz6PkZERZs+eDR8fH0gkEhw+fBienp4AyqtiDA0NoampCU9PTyZQtmnTJvz999+YN2/eh74tjk8Mzlng+CTQ1NTEunXrsG7dOhQUFODJkydo1qwZa8zTsWNHtGnTBlu3boWOjg5MTU2Rl5eH4uJiGBoayp2LiKCgoIAnT55gyZIlaNWqFXx8fAAA+vr6sLS0xL1799i5o6KimAIlADx9+hTnzp3D9u3boaioiL59+6JPnz5VKt6VlZWBx+NVciouXboEBweHT0ZEytzcHObm5my7Q4cOuHv3LlauXInt27fXomW1i4eHB7y8vGBkZIS7d+/ixx9/RK9evRAbG1stR1PmsL58+RJ8Ph+pqanQ09MDn89HXl4em9eqVStMnjwZy5cvh6urK5ycnFBWVoYLFy5g69atGDRoUE3eJsenQG0nTXBwfCxEIhG5ubmRiooKWVhY0ODBg1mzq6rw9fUlU1NT4vP51LRpU3J3d6eJEyeShYUFxcTEsHndu3dn5Yp5eXk0YsQI0tDQoAkTJtDkyZPJ0tKSfH195TT6K2r8/5ebN28Sj8eT67dRl0E1Ehyr4vvvv6f27dvXgEUfjh9++KHKKo6Krxs3bsgdU93mT1Vx9+5dAkAnT55849yKybRFRUVERCQWi0ksFpO3tze5urpWKpFNTU2lP/74g+bMmUMBAQGVSpE5OF4FF1ng+GwwMzNDREQEnj17hvPnzyM7OxtOTk4A5FvzAkBMTAxCQ0OxadMmdOrUCQkJCTh9+jQSExMhEonQqFEjAOVLGElJSRgxYgQAYP369Th//jz+/vtvuLm5ASjX8E9PTwefz0dJSQlCQkKwa9cuiEQiuLi44Mcff4SzszO79sWLF9GiRQuYmppCKpWyZMpPJcogIzk5Wa6dcl2kJttKv+pcmpqauHPnDlM0fRWyZNqpU6fi1q1baNeuHfr27Yu2bdsiICAAPj4+CAkJgYGBASwsLACULwdNnTr1g9nL8RlR294KB0ddIzk5mWxsbMjV1bXSvvT0dOrYsSNt3bqViIguXrxICgoKJBKJiIjI09OTxowZw3QXZNoNsn/9/PyoZcuWFBAQQBERETRo0CByd3enBw8esGsMGzaMevfuXaP3+L68rTjUypUr6eDBg3T79m1KSUmhadOmkYKCQrV+Qdc33iey8ODBA+LxeHTo0KE3zn3x4gX179+fnJ2daeLEiSQUCqldu3bsb7B7925ycnIiHx8fSk1NZQJon1K5KsfHg4sscHD8Bzs7O4SEhLDogUQiYevHzZo1g5qaGv755x8A5fkKBgYGMDY2RmZmJkpKSqClpQWBQMDWk2X/FhQUYM2aNVi7di3Gjh0LALC2toaRkRHi4uIwaNAgSCQSXL58Ga6urpg/fz6io6Ph6emJsWPHMnsqIpFIQEQs8kD/j5Dk5+dDIpFAU1OzRt6jxMRE1jkUAPz8/AAAo0aNQnBwMDIzM5Gens72i8VizJgxAxkZGWjQoAFsbW1x8uRJuXPUd9LT05GXl4f09HRIJBJWymtiYgI1NTUAgIWFBRYvXowBAwagsLAQ8+fPx8CBA6GtrY27d+9i1qxZMDExgbu7+2uvdfr0aYSFhUFPTw+hoaFQV1dHdHQ05s2bh2+//RaRkZHw9vZGWloa9u7di44dO6Jhw4bYv38/J9nM8W7UtrfCwVFfkEUHevToQYMHDyYiovbt29OQIUOIqFwsqnfv3jR69GgiokoCTQcOHCANDY1K68Q9e/akqVOnEhHR/fv3ic/nk7GxMW3evJkWL15MrVq1otWrV79RYZLoX6GoefPmkbm5OSfV+xGpSmAJAJ0+fZrNAcAUNIuLi+mLL74gLS0t4vP5ZGBgQOPGjZOTOa+KgoIC8vX1JQ0NDfLw8GDjEomE9uzZQ+bm5jR9+nQ2LhKJKDw8/IPeK8fnBxdZ4OCoJrKcgVOnTuHx48coKyuDoaEhPDw8AJSLRXXq1AmbNm3CqVOn4OrqisLCQgDlWhAJCQkwNTWFuro6O6dIJIKqqiqLXJw/fx4CgQDbt29nzZ6ePXuGxYsXY8qUKQCAkpISbNiwAX/99RdevHgBLy8vTJw4Ec2bN2fnTUlJgYODwzuV4HG8G8HBwQgODn7tHKrQhExVVRUnTpx47XypVAoejyeXr6KmpoYxY8YgMzMTZ8+eZaJlCgoK8PDwQHp6OlavXg07OzuMGjUKZmZmr21VzcFRHbh4FAfHO6ClpQUlJSX8+eefGDVqFBufMWMGXF1dMWjQIHTq1AlTpkzB5cuXAQC6urooKipCWloam5+cnIxHjx6xRMuIiAg4OTmxbQDQ09ODQCAAAOTm5uKnn37CDz/8gKFDh2LMmDEIDw/HL7/8AuBfXYerV6/C2tqacxbqMRKJBAoKCuDxeLhw4QL27t2LiIgIAIBQKMSkSZNgbGwMX19fdkyjRo2YiuSOHTvw8uXL2jKf41OjtkMbHByfIiKRiFatWkU//fQTW3Z49OgRWVtbU0BAAGVnZ9PZs2epZcuWNHr0aNZQydjYmObPn09E//bAGDBgAEt4DA4OJltbW9q+fTu71qZNm0hHR4cSExOJqLxXhq6uLv39998f7X45ag5fX19q3LgxWVlZUZMmTcjV1ZXu3r1LRERbtmwha2trWrBggdwxsv0cHB8Kzlng4PiI7N27l0xMTEhFRYWsrKyof//+rLHVo0ePSEVFRW6Nm4hIW1ubFi9eTEREI0eOpCFDhrCMdyKiO3fukLW1Na1bt46IyisPbG1tmfPAUbepKhdFlnuybt06MjAwoKtXr1JWVhaJRCIyMDAgLy8vysrKomfPntGcOXPI2tparnMrB8eHhluG4OD4iAwcOBC3b9/GvXv3EBoaij179rBeAFFRUSgtLYWlpSWb/+DBA+Tm5qJTp04AgMzMTGhqajK1SKC80iAtLY3V0kdHR8PMzAy6urof8c443gWJRMLyEc6ePYvIyEjk5eWx5aSUlBQ4OjqiTZs2aNasGczMzLBv3z5ERkZi//79UFdXh7e3N4yMjBAUFASxWFybt8PxCcMlOHJw1AI6OjqVBIlsbW2xbNkyucZZYWFh4PP5MDY2BgDY2NggLi5OrrtlbGwspFIp64Nx/fp1DB06lMtXqOPQ/0teS0tLMWzYMGRlZQEABg8ejO+++w4AkJ2djRcvXgAoz0d5+fIlHB0dMWbMGGzevBmTJk2CjY0NfvnlF1hYWIDP59fa/XB82nCRBQ6OOkKbNm3g5+cnVwffqFEjjB49mrV17tixIx48eICDBw/i5cuXCA0NxapVq+Dl5QVFRUX8888/KCws5L446gE8Hg/Xr1+HhYUFXrx4gZCQEBw+fJg5CgAwbNgwJCQk4MiRI3JVEQ0aNECTJk1YJKFNmzbc35ujRuEiCxwcdZivv/4aX3/9Ndvu27cvrly5guHDh0NdXR2NGzdG165dMXv2bADlMtWampowMjKqLZM5qolUKsXSpUvRsWNHbNq0CQ0aNGD76P/iWk5OTujXrx+mT58OU1NTGBoaQiqVIj4+HlZWVqxKhoOjpuERVSj85eDgqBeUlZUhNjYWCgoKcHFxYdGIXr164eXLlwgJCeFyFuo4aWlpcHBwwMqVKzFy5MhXzktKSkJgYCAiIyNha2uLx48fo2nTpjh16pScZgcHR03CRRY4OOohSkpK6Ny5c6XxgQMHQlFRUS7vgaNuUlBQgKdPn8La2hrAv+2mZci2hUIhDh06hNDQUBQXF0NRURHjxo2rLbM5PlM4Z4GD4xNC1nOCo+5TUFAAPp+PuLg42NnZySWtAuWKoNHR0YiIiMDChQtfG33g4Khp/gf+mQACYNWNEgAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f69fd83d590>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x7f69fd9b3c90>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### 1. tu código aquí para substraer el promedio global a todos los datos ###\n",
    "# obtenemos las características globales promedio\n",
    "x_prom = \n",
    "\n",
    "# extraemos las caracteristicas globales promedio de nuestros datos\n",
    "x_entren = \n",
    "\n",
    "### 2. tu código aquí para encontrar las características promedio para cada tipo de vino ###\n",
    "prom_1 = \n",
    "prom_2 = \n",
    "prom_3 = \n",
    "\n",
    "# el siguiente código va a graficar los datos y las características promedio\n",
    "scatter3D(x_entren[1:39,1],x_entren[1:39,2],x_entren[1:39,3], alpha = 0.25, color=\"b\")\n",
    "scatter3D(prom_1[1,1],prom_1[1,2],prom_1[1,3], s = 100, color=\"b\")\n",
    "scatter3D(x_entren[40:78,1],x_entren[40:78,2],x_entren[40:78,3], alpha = 0.25, color=\"r\")\n",
    "scatter3D(prom_2[1,1],prom_2[1,2],prom_2[1,3], s = 100, color=\"r\")\n",
    "scatter3D(x_entren[79:end,1],x_entren[79:end,2],x_entren[79:end,3], alpha = 0.25, color=\"g\")\n",
    "scatter3D(prom_3[1,1],prom_3[1,2],prom_3[1,3], s = 100,color=\"g\")\n",
    "xlabel(\"Contenido de Alcohol\")\n",
    "ylabel(\"Contenido de Flavonoides\")\n",
    "zlabel(\"Densidad Optica Relativa\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación acomodaremos las características promedio para cada clase de vino en una matriz con dimensiones [3x3], donde las ileras corresponderán a los distintos tipos de vino, y las columnas a las características promedio para cada clase de vino. Esto nos permitirá hacer una multiplicación de matrices para encontrar el producto interno de nuestras características promedio con todos los datos que tenemos para entrenar el algoritmo.\n",
    "\n",
    "A continuación, acomoda las características promedio en una matriz llamada `W`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       "  0.628462    1.03718     0.646068\n",
       " -0.705385    0.0433333   0.147607\n",
       "  0.0769231  -1.08051    -0.793675"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Tu código aquí para acomodar los vectores promedio en una matriz llamada W ###\n",
    "W = "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora lleva a cabo la operación $v = W~x_{entren}$, donde $W \\in \\mathbf{R^{3x3}}$, $x_{entren} \\in \\mathbf{R^{3x117}}$, y $v \\in \\mathbf{R^{3x117}}$.\n",
    "\n",
    "Lo que queremos es encontrar la matriz `v`, cuyas columnas contendrán los valores que resultan al calcular el producto interno entre cada uno de los vectores promedio en `W` y las ileras de la matriz `x_entren`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×117 Array{Float64,2}:\n",
       "  2.48257    1.1112     2.08986   …  -1.65155    -1.90213   -0.151432\n",
       " -0.327114   0.292399  -0.439774      0.0310276  -0.255145  -0.980127\n",
       " -2.15545   -1.4036    -1.65009       1.62053     2.15727    1.13156 "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Tu código aquí para calcular la matriz v ###\n",
    "v = "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora que tenemos la matriz v, debemos encontrar en que índice de cada columna se encuentra el valor más alto. Ese valor indica que características promedio de un tipo de vino generaron el producto interno más alto con cada una de las ileras en `x_entren`.\n",
    "\n",
    "El siguiente bloque identifica el índice de v con el valor más alto en cada columna."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# encontrando los máximos valores de cada columna y sus indices\n",
    "v_max = findmax(v,1)\n",
    "\n",
    "# encontrando solo los índices\n",
    "v_max_ind = v_max[2] - range(0,117)'*3;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una vez que sabemos que índices contienen el valor más grande para cada columna de `v`, comparamos estos valores con las clases verdaderas que tenemos en el vector `y_entren`. La fracción de índices en `v_max_ind` que resultan idénticos a los valores en `y_entren` nos dirá la presicón de nuestro algoritmo con los datos de entrenamiento.\n",
    "\n",
    "El siguiente bloque muestra esta operación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La precisión del algoritmo con los datos de entrenamiento fue: 0.8632478632478633 %"
     ]
    }
   ],
   "source": [
    "print(\"La precisión del algoritmo con los datos de entrenamiento fue: \", sum(v_max_ind .== y_entren')/length(y_entren))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lo único que nos falta es evaluar nuestro algoritmo con los datos que guardamos para hacer la prueba final. En este punto ya tenemos la matriz `W` y no la debemos cambiar. Lo único que debemos hacer es evaluar la clasificación con los datos en las variables `x_prueba` y `y_prueba`. \n",
    "\n",
    "En el bloque siguiente, tabaja en equipo para evaluar la presición del algoritmo con los datos que guardamos para hacer esta prueba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Escribe tu código aquí para llevar a cabo la evaluación del algoritmo con los datos prueba ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Preguntas para reflexionar en grupo:\n",
    "\n",
    "1. ¿en qué consistió el entrenamiento que hicimos en este algoritmo? \n",
    "2. ¿Para qué sirvieron los datos en las matrices `x_entren` y `x_prueba`?\n",
    "3. ¿Crees que la forma en que generamos la matriz `W` es la mejor para otros tipos de datos?\n",
    "4. ¿Con qué tipos de datos crees que las características promedio de distintas clases no nos ayude en mucho?\n",
    "5. ¿De qué otras formas crees que podríamos generar la matriz `W` para obtener incluso mejores resultados?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 2: Construyendo Redes Neuronales Artificiales Desde Cero #\n",
    "\n",
    "<img align=\"left\" src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Colored_neural_network.svg/300px-Colored_neural_network.svg.png\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En un espacio \"multidimensional\" (como los espacios 2D y 3D que estudiamos previamente), podemos encontrar relaciones entre distintos puntos de datos en base a que tan cerca o lejos se encuentren unos de otros.\n",
    "\n",
    "Previamente, usamos el [producto interno](https://es.wikipedia.org/wiki/Producto_escalar) para describir la distancia entre puntos distintos. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La siguiente imagen ayudará a generar intuición sobre el producto interno:\n",
    "\n",
    "<img src=\"https://www.mathsisfun.com/algebra/images/dot-product-ex1.gif\"/>\n",
    "\n",
    "Vemos los vectores $$a = [-6, 8]$$ y $$b = [5, 12]$$ en el espacio $\\mathbf{R^{1x2}}$.\n",
    "\n",
    "El producto interno entre estos dos vectores sería: $$a ~ b^T = (-6)(5) + (8)(12) = 66$$\n",
    "\n",
    "Entonces, podemos considerar el valor $66$ como un indicador de la similitud entre los dos vectores."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora recuerda la base de datos de vinos que estudiamos previamente:\n",
    "<img src=\"fake_data.png\" style=\"width: 360px\"/>\n",
    "Te puedes imaginar que para cada uno de los tres colores diferentes de datos, existe un vector que maximiza el producto interno entre dicho vector y la mayoría (o todos) los datos del mismo color.\n",
    "\n",
    "Este vector puede ser considerado el \"promedio\" o \"modelo\" de todos los datos que comparten un mismo color."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pensemos un poco más sobre los datos que acabamos de discutir.\n",
    "\n",
    "Existen tres colores distintos, y cada punto de datos es tridimensional.\n",
    "\n",
    "Esto indica que, usando datos de entrenamiento, podríamos identificar tres vectores \"promedio\" o \"modelo\" $\\mathbf{R^{3x1}}$, uno para cada color.\n",
    "\n",
    "Tras identificarlos, podríamos usarlos para identificar la identidad de datos nuevos no identificadoes en el mismo espacio tridimensional. Todo esto usando el valor de un producto interno."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entonces, el algoritmo para identificar un punto de datos nuevo sería:\n",
    "\n",
    "1. Asumimos que tenemos los vectores \"modelo\" $r$, $a$, y $v$ $\\in \\mathbf{R^{3x1}}$, uno por cada color de datos. Tenemos también un punto de datos $u$ no identificado ($u \\in \\mathbf{R^{1x3}}$). \n",
    "\n",
    "2. Para hacer todo en una sola operación, concatena los vectores $r$, $a$, y $v$ uno junto a otro para generar la matriz $W \\in \\mathbf{R^{3x3}}$.\n",
    "\n",
    "3. Encuentra el producto interno entre $u ~W$ para obtener el vector $y \\in \\mathbf{R^{1x3}}$, el cual contiene el valor de similitud entre el vector $u$ y cada uno de los vectores \"modelo\" de los distintos colores.\n",
    "\n",
    "4. Identifica cual fue el color que recibió el valor más alto en $y$, y ¡vualá!, hemos identificado el vector $u$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el mundo real, los datos pueden ser tan multidimensionales y complejos que encontrar estos vectores \"modelo\" es extremadamente difícil.\n",
    "\n",
    "De hecho, con datos multidimensionales, encontrar estos vectores \"modelo\" se hace más y más complicado si tenemos pocos puntos de datos. ¿Puedes pensar por qué?\n",
    "\n",
    "Aquí es donde las redes neuronales artificiales llegan a salvarnos. En pocas palabras, las redes neuronales artificiales encuentran estos vectores \"modelo\" usando los datos con identidades conocidas que les proporcionamos. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para poder pensar más objetivamente, piensa en la matriz $W \\in \\mathbf{R^{3x3}}$ como los parámetros de la función $$y ~= ~u ~W$$\n",
    "\n",
    "Donde $u \\in \\mathbf{R^{1x3}}$ es un punto de datos desconocido y el vector $y \\in \\mathbf{R^{1x3}}$ contiene el valor de similitud entre en vector $u$ y cada uno de los colores de datos.\n",
    "\n",
    "Ahora imagina que $u$ no es un punto de datos desconocido y en lugar su identidad es conocida. Entonces, usemos el punto de datos $x \\in \\mathbf{R^{1x3}}$, con el cual podemos pensar en la función $\\hat{y} ~= ~x ~W$ como un objetivo. ¿Cual sería dicho objetivo?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos decir que el objetivo es hacer que el valor del color verdadero para $x$ sea tan alto como sea posible.\n",
    "\n",
    "$J = \\text{Maximiza} \\{\\hat{y}_{correcto}\\}$\n",
    "\n",
    "Donde $\\hat{y}_{correcto} \\in \\hat{y}$\n",
    "\n",
    "Afortunadamento, esta es una función matemática y, asumiento que es diferenciable, podemos calcular la derivada del objetivo respecto a los parámetros $W$ para \"ascender\" a un valor más alto para el color correcto."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entonces, queremos:\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W}$\n",
    "\n",
    "Usamos la regla de la cadena para expandir esta expresión a:\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W} ~= \\big(~\\frac{\\partial \\hat{y}}{\\partial W}\\big)^T ~\\frac{\\partial J}{\\partial \\hat{y}} $\n",
    "\n",
    "Como el objetivo solo depende de $\\hat{y}_{correcto}$ (osea, solo nos importa el valor que contiene $\\hat{y}_{correcto}$), la derivada de $\\frac{\\partial J}{\\partial \\hat{y}} = $ ?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La derivada de $\\frac{\\partial J}{\\partial \\hat{y}} = e_{correcto}$\n",
    "\n",
    "donde $e_{correcto}$ es un vector \"one-hot\" $\\mathbf{R^{1x3}}$. \"One-hot\" significa que todos los valores en este vector son cero, excepto en el índice que contiene el valor de la clase correcta en $\\hat{y}$, donde tiene un valor de uno.\n",
    "\n",
    "Así, la derivada completa es:\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W} ~= ~\\big(\\frac{\\partial \\hat{y}}{\\partial W}\\big)^T ~e_{correcto} ~= ~\\big(\\frac{\\partial xW}{\\partial W}\\big)^T ~e_{correcto}  ~= ~x^T~e_{correcto}$\n",
    "\n",
    "Entonces, si queremos actualizar los parametros $W$ para dar un paso en la dirección que maximiza el valor de la función objetivo $J$, tendríamos que actualizar $W$ con la expresión:\n",
    "\n",
    "$W := ~W + ~\\alpha~x^T~e_{correcto}$\n",
    "\n",
    "Donde $:=$ indica que se actualizará el valor de la variable a la izquierda, y $\\alpha$ es un parametro libre que se  afina para determinar que tanto queremos que $\\frac{\\partial J}{\\partial W}$ afecte los parametros $W$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Cual es tu intuición sobre lo que está pasando aquí? ¿Podrías explicárselo a alguien?\n",
    "\n",
    "Discute en equipo y prepárate para compartir tus observaciones con la clase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora comprobemos que todas las expresiones que acabamos de estudiar nos pueden ayudar a maximizar el valor correcto de un punto de datos.\n",
    "\n",
    "Para hacer esto, usaremos una versión pequeña de la base de datos [MNIST](http://yann.lecun.com/exdb/mnist/). Estos datos son los números del 0 al 9 (o dígitos) escritos a mano en papel, y digitizados como pixeles en blanco y negro con definición de 28x28. \n",
    "\n",
    "Por cada número, tenemos 100 ejemplos de escritura a mano. El siguiente bloque carga los datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using MAT\n",
    "\n",
    "# obtenemos los datos que necesitamos\n",
    "mnist = matread(\"mnist.mat\")\n",
    "caracteristicas = mnist[\"cars\"]\n",
    "clase_de_digito = mnist[\"desc\"];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La matriz `caracteristicas` tiene tamaño 1000x784. Cada ilera es un dígito, y las columnas son sus pixeles correspondintes. Las primeras 100 ileras corresponden al dígito 0, las siguientes 100 ileras corresponden al dígito 1, las siguientes 100 ileras corresponden al dígito 2, y así sucesivamente hasta el dígito 9.\n",
    "\n",
    "Por cada punto de datos, los pixeles que generan una imagen 28x28 han sido aplanados en un vector de tamaño 1x784.\n",
    "\n",
    "El vector `clase_de_digito` tiene tamaño 1000x1 y contiene la clase de dígito que le corresponde a cada ilera de la matriz caracteristicas.\n",
    "\n",
    "El siguiente bloque visualiza algunos de los datos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f148a668350>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.image.AxesImage object at 0x7f148588e190>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dimensionalidad = 784\n",
    "pixeles_por_lado = Int(sqrt(784))\n",
    "\n",
    "# escogemos aleatoriamente un número entre 1 y 100\n",
    "aleat_i = rand(1:100,1)\n",
    "\n",
    "# inicializamos una matriz para visualizar un ejemplo de cada dígito\n",
    "mat_p_vis = zeros(pixeles_por_lado*2,pixeles_por_lado*5)\n",
    "\n",
    "# iteramos sobre los digitos (del 0 al 9) para llenar la matriz de visualización\n",
    "for i=0:9\n",
    "\n",
    "    este_digito = reshape(caracteristicas[100*i + aleat_i,:],pixeles_por_lado,pixeles_por_lado)\n",
    " \n",
    " # muy feo pero sirve para llenar la matriz que visualiza los dígitos (¡puntos extra a quien lo pueda hacer más elegantemente!)\n",
    "    mat_p_vis[floor(Int,i/5)*pixeles_por_lado+1:floor(Int,i/5)*pixeles_por_lado+pixeles_por_lado,mod(i,5)*pixeles_por_lado+1:mod(i,5)*pixeles_por_lado+pixeles_por_lado] = este_digito\n",
    "end\n",
    "\n",
    "using PyPlot\n",
    "imshow(mat_p_vis,cmap=\"Greys\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Preguntas para discusión: ¿por qué nos referimos a los pixeles como \"características\"? ¿Cómo son los pixeles similares o diferentes a las características que usamos previamente para describir flores y vinos?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora que hemos entendido los datos MNIST, trabaja en equipo para separar aleatoriamente los datos en dos grupos: de entrenamiento y de prueba. Genera las variables `x_entren`, `y_entren`, `x_prueba` e `y_prueba`.\n",
    "\n",
    "También recuerda que debes substraerle a tus datos las características de promedio globales antes de empezar a desarrollar tu algoritmo.\n",
    "\n",
    "(Tip: puedes reusar mucho código que escribimos previamente)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Separa los datos que servirán para entrenar y para probar tus algoritmos ###\n",
    "\n",
    "### Substrae las características globales ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora, genera la matriz `W` que entrenaremos. Genérala usando numeros aleatorios pequeños con un promedio de cero. ¿Cuales deben ser sus dimensiones?\n",
    "\n",
    "Itera sobre cada uno de los puntos de datos que reservaste para entrenar el algoritmo y calcula la derivada del objetivo $J$ respecto a los parametros $W$. Actualiza los parametros $W$ usando la regla $W := ~W + ~\\alpha~x^T~e_{correcto}$ con cada uno de los puntos de datos. Guarda el valor de $J$ para cada uno de los datos.\n",
    "\n",
    "Cuando termines de iterar sobre todos los puntos de datos, grafica el objetivo $J$ de cada uno de los puntos de datos.\n",
    "\n",
    "Lo que queremos ver es que la mariz `W` puede ser cambiada para maximizar objetivo con los datos que estámos entrenando.\n",
    "\n",
    "Reto: si terminas antes que todos los demás, ¿puedes implementar esto sin usar un ciclo `for`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f147fc74d90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f147fbbe490>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### tu código aquí ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Qué notaste?\n",
    "\n",
    "¿Cuales son las limitantes de este método para entrenar el algoritmo?\n",
    "\n",
    "Discute en grupo y prepárate para compartir con todas las personas en la clase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una gran limitación del método discutido hasta ahora es como está definido el objetivo.\n",
    "\n",
    "Si lo piensas bien, el valor podría seguir creciendo por siempre. Entonces, el proceso de \"apredizaje\" de los parametros $W$ podría continuar por siempre.\n",
    "\n",
    "Debe haber una mejor alternativa.\n",
    "\n",
    "¿Cómo podríamos modificar el objetivo $J = \\text{Maximiza} \\{\\hat{y}_{correcto} ~= ~x ~W\\}$ para asegurarnos que hay un límite de apredizaje?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Muy facilmente podemos hacer que el objetivo sea:\n",
    "\n",
    "$J = \\text{Maximiza} \\bigg\\{\\hat{y}_{correcto}\\bigg\\}$\n",
    "\n",
    "donde\n",
    "\n",
    "$\\hat{y} = \\frac{~x ~W}{\\sum_{i}~x ~W}$\n",
    "\n",
    "¿por qué?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora usamos la regla de la cadena para diferenciar la expresión respecto a los parametros $W$.\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W} ~= ~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial \\hat{y}}{\\partial W}$\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W} ~= ~\\big(\\frac{\\partial ~x ~W}{\\partial W}\\big)^T~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial ~\\hat{y}}{\\partial ~x ~W}$\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W} ~= ~\\big(\\frac{\\partial ~x ~W}{\\partial W}\\big)^T~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial ~\\frac{~x ~W}{\\sum_{i}~x ~W}}{\\partial ~x ~W} $\n",
    "\n",
    "De aquí ya sabemos que $\\frac{\\partial J}{\\partial \\hat{y}} = e_{correcto}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para encontrar $\\frac{\\partial ~\\frac{~x ~W}{\\sum_{i}~x ~W}}{\\partial ~x ~W}$, definamos $v = ~x ~W$, donde $v$ es \"valores\". Entonces tendremos que encontrar el jacobiano:\n",
    "\n",
    "$$ \\frac{\\partial ~\\hat{y}}{\\partial ~x ~W} = ~\\frac{\\partial ~\\frac{v}{\\sum_{i}~v}}{\\partial ~v} = ~\\frac{\\partial ~\\frac{~x ~W}{\\sum_{i}~x ~W}}{\\partial ~x ~W} = ~\\begin{bmatrix} \\frac{\\partial \\hat{y}_1}{\\partial v_1} & \\frac{\\partial \\hat{y}_1}{\\partial v_2} & \\dots & \\frac{\\partial \\hat{y}_1}{\\partial v_n} \\\\ \\frac{\\partial \\hat{y}_2}{\\partial v_1} & \\frac{\\partial \\hat{y}_2}{\\partial v_2}& \\dots & \\vdots \\\\ \n",
    "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
    "\\frac{\\partial \\hat{y}_n}{\\partial v_1} & \\frac{\\partial \\hat{y}_n}{\\partial v_2} & \\dots & \\frac{\\partial \\hat{y}_n}{\\partial v_n} \\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pero en este momento podemos ver que el jacobiano $\\frac{\\partial ~\\hat{y}}{\\partial ~x ~W}$ será multiplicado por el vector \"one-hot\" $e_{correcto}$ con un producto interno. Esto hará que todos los valores del jacobiano se conviertan en cero, a excepción de: \n",
    "\n",
    "$$e_{correcto} \\frac{\\partial ~\\hat{y}}{\\partial ~x ~W} = ~\\begin{bmatrix} \\frac{\\partial \\hat{y}_{correcto}}{\\partial v_1} & \\frac{\\partial \\hat{y}_{correcto}}{\\partial v_2} & \\dots & \\frac{\\partial \\hat{y}_{correcto}}{\\partial v_n} \\end{bmatrix}$$\n",
    "\n",
    "Tambien se nos hace notar que:\n",
    "\n",
    "$$~i = j \\rightarrow ~\\frac{\\partial \\hat{y}_i}{\\partial v_j} = \\frac{\\sum_{i\\neq j} v}{(\\sum v)^2}$$\n",
    "\n",
    "$$~i \\neq j \\rightarrow ~\\frac{\\partial \\hat{y}_i}{\\partial v_j} = -~\\frac{v_i}{(\\sum v)^2} = -~\\frac{\\hat{y}_i}{\\sum v}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entonces, en resumen, recordemos que:\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W} ~= ~\\big(\\frac{\\partial ~x ~W}{\\partial W}\\big)^T~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial ~\\frac{~x ~W}{\\sum_{i}~x ~W}}{\\partial ~x ~W} $\n",
    "\n",
    "Pero sabiendo que $~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial ~\\frac{~x ~W}{\\sum_{i}~x ~W}}{\\partial ~x ~W} = ~\\frac{\\partial J}{\\partial v}$ podemos escribir todo como:\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W} ~= ~\\big(\\frac{\\partial ~x ~W}{\\partial W}\\big)^T ~\\frac{\\partial J}{\\partial v} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sabiendo todo esto, modifica tu programa anterior para que esta vez el objetivo sea: $$J = \\text{Maximiza} \\bigg\\{\\hat{y}_{correcto}\\bigg\\}$$\n",
    "\n",
    "Y la actualización de los parametros $W$ se mueva de acuerdo a:\n",
    "\n",
    "$W := ~W + ~\\alpha~\\frac{\\partial J}{\\partial W}$\n",
    "\n",
    "Nota que en esta ocasión `W` debe ser inicializado para que contenga exclusivamente numeros positivos. ¿Por qué?\n",
    "\n",
    "Experimenta también cambiado el parametro $\\alpha$. \n",
    "\n",
    "(Tip: es posible que tengas que mostrarle los datos a tu algoritmo más de una vez para que el \"apredizaje\" pueda suceder.)\n",
    "\n",
    "¿Puedes anticipar problemas?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fcd05488bd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7fcd053c5c50>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### tu código aquí ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si haces que Julia imprima los parametros `W` y la direfenciación `dJ_dW` en cada iteración, ¿Qué observas? ¿Puede haber algo que imposibilite el proceso de aprendizaje?\n",
    "\n",
    "¿qué hace esto último que hemos intentado un mejor o peor método para aprender los parametros $W$?\n",
    "\n",
    "Discute en grupo y prepara observaciones para compartir con el resto de la clase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El objectivo que describimos previamente dará resultados sin sentido cuando $W := ~W + ~\\alpha~\\frac{\\partial J}{\\partial W}$ introduzca valores negativos a la matriz de parametros $W$. \n",
    "\n",
    "Afortunadamente, existe un mejor objetivo que podemos escoger. De hecho, nadie usa los objetivos que hemos descrito hasta ahora (solo fueron pensados como ejemplos para ganar intuición matemática desde cero).\n",
    "\n",
    "El objectivo que es preferido para entrenar redes neuronales artificales se llama $softmax()$.\n",
    "\n",
    "$Softmax()$ es similar al objetivo $J = \\text{Maximiza} \\bigg\\{\\hat{y}_{correcto}\\bigg\\}$, pero está blindada contra números negativos.\n",
    "\n",
    "Antes de entrar a $softmax()$, hagamos un sumario de los elementos de una red neuronal artificial que hemos estudiado hasta ahora."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una red neuronal artifical simple puede ser descrita con la expresión:\n",
    "\n",
    "$$J = Objetivo \\big\\{\\hat{y} = ~f(x~W)\\big\\}$$\n",
    "\n",
    "* Donde $x$ contiene un punto de dato\n",
    "* $W$ contiene los parametros que se van a \"aprender\"\n",
    "* $f()$ es la función que determina el límite de valores obtenidos del producto interno entre $x~W$\n",
    "* y el $Objetivo \\{\\}$ determina lo que queremos maximizar (o incluso reducir)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De estos cuatro elementos, son dos los que podemos modificar para mejorar significativamente como aprende una red neuronal artificial.\n",
    "\n",
    "El primero es la función $f()$:\n",
    "$$softmax(\\theta) = \\frac{e^\\theta}{\\sum e^\\theta}$$\n",
    "Donde, $\\theta \\in \\mathbf{R^{1xC}}$ es el vector de \"valores\" para cada categoria de objetos.\n",
    "\n",
    "Si lo piensas bien, elevando $e$ al poder del vectore de \"valores\" nos aseguramos que $\\hat{y}$ nunca tendrá números negativos.\n",
    "\n",
    "Cuando los \"valores\" contienen valores negativos, elevando e al poder de cualquier número real siempre nos dará un número positivo.\n",
    "\n",
    "Incluso $e^{-\\infty} = 0$ es un número positivo (si consideras $0$ como un número positivo), pero en la práctica nunca te encontrarás con esta situación.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$softmax(\\theta) = \\frac{e^\\theta}{\\sum e^\\theta}$$\n",
    "\n",
    "Otra cosa importante de $softmax$ es que, al dividir $\\frac{e^\\theta}{\\sum e^\\theta}$ el vector $\\hat{y}$ solo tendrá números entre $0$ y $1$, y los valores en el vector siempre sumarán a $1$, siempre. \n",
    "\n",
    "Finalmente, la función $e^{\\theta}$ es una función no-lineal y, como verás, las no-linearidades son cruciales para ayudar a las redes neuronales a aprender."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto concluye una de las cosas que vamos a modificar. De ahora en adelante $\\hat{y} = f(x~W) =  softmax(x~W) = \\frac{e^{x~W}}{\\sum e^{x~W}}$\n",
    "\n",
    "La otra cosa es la función Objetivo. Hasta ahora, podemos decir que la función objetivo ha sido definida como:\n",
    "\n",
    "$$Objetivo\\{\\hat{y}\\} = maximiza\\{\\hat{y}_{correcto}\\}$$\n",
    "\n",
    "Pero existe una mejor función objetivo, y de hecho es como \"el alma gemela de\" $softmax()$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El objetivo que vamos a usar se llama [entropía cruzada](https://en.wikipedia.org/wiki/Cross_entropy), y es definida como:\n",
    "\n",
    "$$J = minimiza\\{-log(\\hat{y}_{correcto})\\}$$\n",
    "\n",
    "Intuitivemente, esta función busca maximizar el valor de $\\hat{y}_{correcto}$, porque si $\\hat{y}_{correcto}$ se acerca a su máximo posible de $1$ (en práctica es imposible alcanzar este valor), el valor de $J$ sería $$J = -\\log(\\hat{y}_{correcto}) = -\\log(1) = 0$$\n",
    "\n",
    "Contrariamente, cuando $\\hat{y}_{correcto}$ contiene el número menor posible de $0$, el resultado es: $$J = -\\log(\\hat{y}_{correcto}) = -\\log(0) = \\infty$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entonces $\\frac{\\partial J }{\\partial W}$ ahora será:\n",
    "\n",
    "$\\frac{\\partial J }{\\partial W} = ~\\big(\\frac{\\partial ~x ~W}{\\partial W}\\big)^T~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial \\hat{y}}{\\partial ~x ~W}$\n",
    "\n",
    "Donde: \n",
    "$$~\\frac{\\partial J}{\\partial \\hat{y}}~\\frac{\\partial \\hat{y}}{\\partial ~x ~W} = \\hat{y} - e_{correcto}$$\n",
    "\n",
    "Si quieres entender esta última expresión, intenta hacer la prueba tu mismo, o visita este [sitio web (en inglés)](http://peterroelants.github.io/posts/neural_network_implementation_intermezzo02/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modifica tu programa anterior para que esta vez la función objetivo sea:\n",
    "\n",
    "$$J = minimiza\\{-log(\\hat{y}_{correcto})\\}$$\n",
    "\n",
    "Y la actualización en la dirección que minimiza el valor del objetivo sea:\n",
    "\n",
    "$W := ~W - ~\\alpha~\\frac{\\partial J}{\\partial W}$\n",
    "\n",
    "¿Por qué usamos un signo negativo esta vez?\n",
    "\n",
    "[Descenso por Gradiente](https://turing.iimas.unam.mx/~ivanvladimir/post/gradient_descent)\n",
    "\n",
    "Experimenta una vez más cambiando el parametro $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DoD2Wz8cZKQCA8EeIBNGZvpx498GmoDzP+/89qEvm/1tvVu4PyuMBAGALIRKGfvK3DWr0tmnO0krbowAA0COESBC5j7WqhvNAAADoNEIkyO56sSLgtvtYq9ZW1aut3Rdwpcxz7+4+5d8/1NSif5TuVcPRlt4bEgCAEBFne4BIs73GE3D71r+UaccBj+799uiA7f97+NRHTu78+0Zt/OSw/r29Tv+YObHX5gQAIBRwRKSX7TjweZi8+UFNp9Zv/OSwJOk/Ow/22kwAAIQKQqQPxQTrU8z4NDQAQIQgRIKMT/cAAKDzCBEAAGANIdJHgva2DAAAEYQQ6UMxnNwBAEAAQiQMkTMAgEhBiASZOdMXzgAAAD9CBAAAWEOI9CHDxb0AAAQgRMIQV+AAACIFIRJkHPMAAKDzoipEtu53W31+Lt8FACBQVIXI2qp6a88dExPDWyoAAJwkqkKkLxgjNXnbbI8BAEBYIER6wWWPrO7Vx+ctHgBApCBEekFLu8/2CAAAhAVCpJe8t+tgwFs0HMMAAKCjONsDRKrpfy3XpPNSbI8BAEBI44hILyrbfSjgNkdFAAAIRIiEIS4DBgBECkIEAABYQ4j0EY5iAADQESECAACsIUTCEAdXAACRghABAADWECJ9hHNEAADoiBABAADWECIAAMAaQiQMxfA+DwAgQhAifSSGa10AAOiAEOlDHMkAACAQIQIAAKwhRAAAgDVxtgfoS6H81ogxRjsONHZqbej+KwAA6BqOiPSRMzXQii21+s5T/+mbYQAACBGESIj4n4pq2yMAANDnCBEAAGBNVIXI+/89aPX5g3ZuByeJAAAiRFSFyM66I9ae+0ztEMon0gIA0FuiKkRsM7YHAAAgxBAiAADAmi6HyLvvvqsbb7xRI0aMUExMjN54442A+40xeuihhzR8+HAlJiYqKytLO3fuDNrAPRHK736E8GgAAPSaLodIU1OTLrnkEhUVFZ3y/scee0xPPfWUnn32WZWXl+uss85Sdna2mpubezxsWAtiBREtAIBI0eVPVp0yZYqmTJlyyvuMMXriiSf0wAMP6KabbpIk/f3vf5fL5dIbb7yhW2+9tcPf8Xq98nq9/tsej6erI4UNAgIAgEBBPUdkz549qq2tVVZWln9bUlKSJk6cqNLS0lP+nYKCAiUlJfl/0tLSgjlSgJgQTYGy3Z+p+KN622MAANDnghoitbW1kiSXyxWw3eVy+e87WX5+vtxut/+nujr6PmH01r+U2R4BAAArrH/pncPhkMPhsD1Gn2hp9wXlcfjMEQBApAjqEZHU1FRJUl1dXcD2uro6/3022fz9vbm6Qd624IQIAACRIqghMmrUKKWmpqq4uNi/zePxqLy8XJmZmcF8qqji8xn9/B8bVbBih+1RAAAIqi6/NXPkyBHt2rXLf3vPnj2qrKxUSkqK0tPTNXfuXP3+97/XBRdcoFGjRunBBx/UiBEjdPPNNwd18Giyad9hrdr2+VGm/O9caHkaAACCp8shsnHjRn3zm9/0387Ly5MkzZgxQ4sXL9a9996rpqYm3XnnnWpoaNA111yjlStXKiEhIXhTd1O4nlkRrHNLAAAINV0Okeuuu07GfPm3psTExOiRRx7RI4880qPB8OU4VxUAECmi6rtmwvVqk1D9/BMAAHoqqkIEAACEFkIEAABYE1UhEqbvzHSY+zSn6AAAEFaiKkQihftYq+0RAAAICkIkDITpgRwAAM4oqkIkXN+aAQAgUkVViISrcL3sGACAMyFEAACANVEVInwwGAAAoSWqQiRc8c4MACBSESJhrpUvxAMAhDFCJAyc7oDIpfP/LfdRPlcEABCeCJEw19TSrpXbDtgeAwCAbiFEAACANVEVIuF60ueJc7e0dTwnhKuBAADhKqpCJBL8atlm2yMAABA0URMih5pa9MlnR22P0S2L3//E/+flm2s6LuCACAAgTEVNiDQcbbE9QredMj4AAIgAURMikYwDIgCAcEWIhLB1Ow/aHgEAgF5FiISwH71Q3ql1fDsvACBcESIAAMAaQiQCcDwEABCuCJEI896ug7rx6XXaut9texQAAM6IEIkAJ54iMv2v5dqy362fLFpvbyAAADqJEIlQh/lGXgBAGCBEIsCpLpoxxvT9IAAAdBEhEgF+8/pW2yMAANAthEgEONrS3mGbjwMiAIAwQIhEMPcxzhMBAIQ2QiSCbavhEl4AQGgjRCIZb88AAEIcIRLB6BAAQKgjRCLY8s01tkcAAOC0CJEQN3Pxhm7/3aUbqoM4CQAAwUeIhLjij+ptjwAAQK8hRAAAgDWECAAAsIYQAQAA1hAiAADAGkIEAABYQ4hEEPdRvlsGABBeCJEIseOAR5c88m/bYwAA0CWESIRYUr7P9ggAAHQZIQIAAKwhRCKE4SvuAABhiBABAADWRE2INLf6bI/Qq14s+/JzRI5423S4qaUPpwEAoHOiJkSOeNtsj2DNmIdX6bLfrVZVbaPtUQAACBA1IQIp+4l3bY8AAEAAQiTKtLVH9ltUAIDwQohEOGMCr6Zp83F1DQAgdBAiEe7k7vAZQgQAEDoIkQh3cnhwQAQAEEoIkQh3coi0UyIAgBBCiES4k9+JOfmcEQAAbCJEItzBI96A2z4jvbfroKb/tUx7DzZZmgoAgM9FTYh429ptj2DFzUXvBdz2GaPpfy3Xe7s+0+yXP7A0FQAAn4uaENn0SYPtEaw4eCTwo919J5wjUtNwrK/HAQAgQK+FSFFRkc4991wlJCRo4sSJWr9+fW89VafExlh9+pBx4rmqrXy4GQDAsl4JkVdeeUV5eXl6+OGHtWnTJl1yySXKzs5WfX19bzxdp8QQIpKkVzdW+//c5jN8GR4AwKoY0wuXUUycOFFXXHGF/vznP0uSfD6f0tLSNHv2bN1///0Ba71er7ze/zuh0uPxKC0tTW63W06nM2gz/XnNTv3x3x8H7fEi0cRRKbpwuDMio6360FGlpQzocBVRX4rE1xVAeBo60KHcb54f1Mf0eDxKSkrq8u/vuKBOIamlpUUVFRXKz8/3b4uNjVVWVpZKS0s7rC8oKND8+fODPUYHE85N6fXnCHflew6pfM8h22MAAHrZeV85K+gh0l1BD5GDBw+qvb1dLpcrYLvL5dJHH33UYX1+fr7y8vL8t48fEQm2SecNCfpjRoqcy0dq4yeH9MlnR/WL674akf/PvaXNp49qGzVuZJLtUQDAusED4m2P4Bf0EOkqh8Mhh8PRJ8+1t3BqnzwPAADonKCfrDp06FD169dPdXV1Advr6uqUmpoa7KcDAABhLOghEh8fr/Hjx6u4uNi/zefzqbi4WJmZmcF+OgAAEMZ65a2ZvLw8zZgxQxMmTNCVV16pJ554Qk1NTbrjjjt64+kAAECY6pUQueWWW/Tpp5/qoYceUm1trS699FKtXLmywwmsAAAguvXK54j0RHevQwYAAPZ09/d31HzXDAAACD2ECAAAsIYQAQAA1hAiAADAGkIEAABYQ4gAAABrCBEAAGANIQIAAKyx/u27Jzv++Woej8fyJAAAoLOO/97u6uekhlyINDY2SpLS0tIsTwIAALqqsbFRSUlJnV4fch/x7vP5VFNTo0GDBikmJiaoj+3xeJSWlqbq6mo+Pj4EsD9CC/sj9LBPQgv74/SMMWpsbNSIESMUG9v5Mz9C7ohIbGysRo4c2avP4XQ6+Q9RCGF/hBb2R+hhn4QW9seX68qRkOM4WRUAAFhDiAAAAGv6/fa3v/2t7SH6Ur9+/XTdddcpLi7k3pWKSuyP0ML+CD3sk9DC/gi+kDtZFQAARA/emgEAANYQIgAAwBpCBAAAWEOIAAAAawgRAABgTdSESFFRkc4991wlJCRo4sSJWr9+ve2Rwk5BQYGuuOIKDRo0SMOGDdPNN9+sqqqqgDXNzc3Kzc3VkCFDNHDgQOXk5Kiuri5gzb59+zR16lQNGDBAw4YN0z333KO2traANWvXrtXll18uh8Oh888/X4sXL+4wD/s0UGFhoWJiYjR37lz/NvZH39u/f79+9KMfaciQIUpMTNTYsWO1ceNG//3GGD300EMaPny4EhMTlZWVpZ07dwY8xqFDhzR9+nQ5nU4lJydr5syZOnLkSMCaDz/8UF//+teVkJCgtLQ0PfbYYx1mWbZsmTIyMpSQkKCxY8dqxYoVvfOPDlHt7e168MEHNWrUKCUmJuqrX/2qfve73wV8KRv7IwSYKLB06VITHx9v/va3v5lt27aZn/3sZyY5OdnU1dXZHi2sZGdnm0WLFpmtW7eayspK853vfMekp6ebI0eO+NfcddddJi0tzRQXF5uNGzeaSZMmmauuusp/f1tbmxkzZozJysoyH3zwgVmxYoUZOnSoyc/P96/ZvXu3GTBggMnLyzPbt283Tz/9tOnXr59ZuXKlfw37NND69evNueeea8aNG2fmzJnj387+6FuHDh0y55xzjvnJT35iysvLze7du82qVavMrl27/GsKCwtNUlKSeeONN8zmzZvN9773PTNq1Chz7Ngx/5pvf/vb5pJLLjFlZWXmP//5jzn//PPNbbfd5r/f7XYbl8tlpk+fbrZu3Wpefvllk5iYaJ577jn/mvfee8/069fPPPbYY2b79u3mgQceMP379zdbtmzpmxcjBCxYsMAMGTLEvPXWW2bPnj1m2bJlZuDAgebJJ5/0r2F/2BcVIXLllVea3Nxc/+329nYzYsQIU1BQYHGq8FdfX28kmZKSEmOMMQ0NDaZ///5m2bJl/jU7duwwkkxpaakxxpgVK1aY2NhYU1tb61+zcOFC43Q6jdfrNcYYc++995qLL7444LluueUWk52d7b/NPv0/jY2N5oILLjCrV6823/jGN/whwv7oe/fdd5+55pprvvR+n89nUlNTzR/+8Af/toaGBuNwOMzLL79sjDFm+/btRpLZsGGDf83bb79tYmJizP79+40xxjzzzDNm8ODB/n10/LlHjx7tv/3DH/7QTJ06NeD5J06caH7+85/37B8ZRqZOnWp++tOfBmybNm2amT59ujGG/REqIv6tmZaWFlVUVCgrK8u/LTY2VllZWSotLbU4Wfhzu92SpJSUFElSRUWFWltbA17rjIwMpaen+1/r0tJSjR07Vi6Xy78mOztbHo9H27Zt86858TGOrzn+GOzTQLm5uZo6dWqH14z90ff++c9/asKECfrBD36gYcOG6bLLLtPzzz/vv3/Pnj2qra0NeK2SkpI0ceLEgH2SnJysCRMm+NdkZWUpNjZW5eXl/jXXXnut4uPj/Wuys7NVVVWlw4cP+9ecbr9Fg6uuukrFxcX6+OOPJUmbN2/WunXrNGXKFEnsj1AR8Z9Re/DgQbW3twf8D60kuVwuffTRR5amCn8+n09z587V1VdfrTFjxkiSamtrFR8fr+Tk5IC1LpdLtbW1/jWn2hfH7zvdGo/Ho2PHjunw4cPs0y8sXbpUmzZt0oYNGzrcx/7oe7t379bChQuVl5enX//619qwYYN++ctfKj4+XjNmzPC/pqd6rU58vYcNGxZwf1xcnFJSUgLWjBo1qsNjHL9v8ODBX7rfjj9GNLj//vvl8XiUkZGhfv36qb29XQsWLND06dMlif0RIiI+RNA7cnNztXXrVq1bt872KFGrurpac+bM0erVq5WQkGB7HOjzQJ8wYYIeffRRSdJll12mrVu36tlnn9WMGTMsTxd9Xn31Vb300ktasmSJLr74YlVWVmru3LkaMWIE+yOERPxbM0OHDlW/fv06XClQV1en1NRUS1OFt1mzZumtt97SO++8o5EjR/q3p6amqqWlRQ0NDQHrT3ytU1NTT7kvjt93ujVOp1OJiYns0y9UVFSovr5el19+ueLi4hQXF6eSkhI99dRTiouLk8vlYn/0seHDh+uiiy4K2HbhhRdq3759kv7vNT3da5Wamqr6+vqA+9va2nTo0KGg7Ldo2if33HOP7r//ft16660aO3asbr/9ds2bN08FBQWS2B+hIuJDJD4+XuPHj1dxcbF/m8/nU3FxsTIzMy1OFn4YEI3PAAADNUlEQVSMMZo1a5Zef/11rVmzpsOhyPHjx6t///4Br3VVVZX27dvnf60zMzO1ZcuWgP9ir169Wk6n0/8/4JmZmQGPcXzN8cdgn37u+uuv15YtW1RZWen/mTBhgqZPn+7/M/ujb1199dUdLmn/+OOPdc4550iSRo0apdTU1IDXyuPxqLy8PGCfNDQ0qKKiwr9mzZo18vl8mjhxon/Nu+++q9bWVv+a1atXa/To0Ro8eLB/zen2WzQ4evSoYmMDf83169dPPp9PEvsjZNg+W7YvLF261DgcDrN48WKzfft2c+edd5rk5OSAKwVwZnfffbdJSkoya9euNQcOHPD/HD161L/mrrvuMunp6WbNmjVm48aNJjMz02RmZvrvP3656A033GAqKyvNypUrzVe+8pVTXi56zz33mB07dpiioqJTXi7KPu3oxKtmjGF/9LX169ebuLg4s2DBArNz507z0ksvmQEDBpgXX3zRv6awsNAkJyebN99803z44YfmpptuOuXlopdddpkpLy8369atMxdccEHA5aINDQ3G5XKZ22+/3WzdutUsXbrUDBgwoMPlonFxceaPf/yj2bFjh3n44Yej7nLRGTNmmLPPPtt/+e5rr71mhg4dau69917/GvaHfVERIsYY8/TTT5v09HQTHx9vrrzySlNWVmZ7pLAj6ZQ/ixYt8q85duyY+cUvfmEGDx5sBgwYYL7//e+bAwcOBDzO3r17zZQpU0xiYqIZOnSo+dWvfmVaW1sD1rzzzjvm0ksvNfHx8ea8884LeI7j2KcdnRwi7I++t3z5cjNmzBjjcDhMRkaG+ctf/hJwv8/nMw8++KBxuVzG4XCY66+/3lRVVQWs+eyzz8xtt91mBg4caJxOp7njjjtMY2NjwJrNmzeba665xjgcDnP22WebwsLCDrO8+uqr5mtf+5qJj483F198sfnXv/4V/H9wCPN4PGbOnDkmPT3dJCQkmPPOO8/85je/CbjMlv1hX4wxJ3zEHAAAQB+K+HNEAABA6CJEAACANYQIAACwhhABAADWECIAAMAaQgQAAFhDiAAAAGsIEQAAYA0hAgAArCFEAACANYQIAACw5v8D8AsQSKQoYYkAAAAASUVORK5CYII=",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fcd050109d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7fcd04fa8a10>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### tu código aquí ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Qué notaste?\n",
    "\n",
    "¿Qué hace que este sea un mejor método para hacer que una red neuronal artifical aprenda?\n",
    "\n",
    "Discute en grupo y prepara observaciones para discutir con toda la clase.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previamente construimos un clasificador $softmax$ con el objetivo:\n",
    "$$J = minimiza\\{-log(\\hat{y}_{correcto})\\}$$\n",
    "\n",
    "Donde: $$\\hat{y}_{correcto} \\in \\hat{y}$$ $$\\hat{y} = softmax(x~W)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El algoritmo de $softmax$ requiere los siguientes pasos para calcular el objetivo:\n",
    "\n",
    "1. Multiplica tu punto de datos $x$ por la matriz $W$ para obtener los valores (llámalos $v$) para cada clase.\n",
    "2. Calcula $softmax(v)$ para obtener $\\hat{y}$ (las \"probabilidades\" de cada clase).\n",
    "3. Calcula el objetivo de la entropía cruzada (también conocido como \"la pérdida de entropía cruzada\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para actualizar los parámetros $W$, los pasos son:\n",
    "\n",
    "1. Calcula la derivada de la función objetivo respecto a los parametros $W$\n",
    "2. Actualiza los parametros usando la derivada que calculaste.\n",
    "\n",
    "$Softmax$ puede ser convertido en una red neuronal artifical de verdad al agregarle una \"capa oculta\" entre los datos $x$ y el paso donde se calculan los valores. Todos los demás pasos se mantienen iguales."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los pasos para calcular el objetivo entonces son:\n",
    "\n",
    "1. Multiplica tu punto de datos $x$ por la matriz $W^{(h)} \\in \\mathbf{R^{DxH}}$ (donde $(h)$ identifica la matriz, y $\\mathbf{H}$ es el número de columnas) para obtener es estado oculto $h \\in \\mathbf{R^{1xH}}$.\n",
    "1. multiplica el estado oculto $h$ por la matriz de salida $W^{(o)} \\in \\mathbf{R^{HxC}}$ (donde $(o)$ identifica la matriz) para obtener los valores $v$ de cada clase.\n",
    "2. Calcula $softmax(v)$ para obtener $\\hat{y}$ (las \"probabilidades\" de cada clase).\n",
    "3. Calcula el objetivo de entropía cruzada (también conocido como \"pérdida de entropía cruzada\")\n",
    "\n",
    "El objetivo sigue siendo el mismo, pero $\\hat{y}$ ahora es:\n",
    "$\\hat{y} = softmax(x~W^{(h)}~W^{(o)})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para actualizar los parámetros, los pasos son:\n",
    "\n",
    "1. Calcula la derivada del objetivo respecto a los parámetros $W^{(h)}$ y $W^{(o)}$.\n",
    "2. Actualiza los parámetros usando las derivadas que calculaste."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como puedes ver, ahora tendremos que calcular dos derivadas:\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W^{(h)}}$\n",
    "\n",
    "$\\frac{\\partial J}{\\partial W^{(o)}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estas derivadas serían similares a las que calculaste anteriormente (observa que los valores $v$ ahora son $v=~x ~W^{(h)} ~W^{(o)}$):\n",
    "\n",
    "$\\frac{\\partial J }{\\partial W^{(h)}} = ~\\big(\\frac{\\partial ~x ~W^{(h)} ~W^{(o)}}{\\partial W^{(h)}}\\big)^T~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial \\hat{y}}{\\partial ~x ~W^{(h)} ~W^{(o)}} = ~\\big(\\frac{\\partial ~x ~W^{(h)} ~W^{(o)}}{\\partial W^{(h)}}\\big)^T~\\frac{\\partial J}{\\partial v} = \\big(x^T~\\frac{\\partial J}{\\partial v}\\big) ~\\big(W^{(o)}\\big)^T$\n",
    "\n",
    "$\\frac{\\partial J }{\\partial W^{(o)}} = ~\\big(\\frac{\\partial ~x ~W^{(h)} ~W^{(o)}}{\\partial W^{(o)}}\\big)^T~\\frac{\\partial J}{\\partial \\hat{y}} ~\\frac{\\partial \\hat{y}}{\\partial ~x ~W^{(h)} ~W^{(o)}} = ~\\big(\\frac{\\partial ~x ~W^{(h)} ~W^{(o)}}{\\partial W^{(o)}}\\big)^T ~\\frac{\\partial J}{\\partial v} = \\bigg(~\\big(W^{(h)}\\big)^T~x^T\\bigg)~\\frac{\\partial J}{\\partial v}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modifica tu programa anterior par que esta vez entrenemos una red neuronal artifical con una capa oculta. Primero tendrás que cargar los datos MNIST y separarlos en datos que servirán para entrenar y para probar la red neuronal. No te olvides de prepararlos removiendo las características promedio.\n",
    "\n",
    "Experimenta cambiando todos los parámetros que tienes disponibles. ¿Cuáles son estos ahora que tenemos una red neuronal completa?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "### tu código aquí ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Qué notaste? ¿Qué efecto hubo al cambiar los parametros que puedes afinar?\n",
    "\n",
    "¿Es esta la mejor manera posible de entrenar una red neuronal artifical?\n",
    "\n",
    "Discute en grupo y prepárate para compartir tus observaciones con el resto de la clase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El siguiente paso para hacer esta red neuronal aún más potente es agregar una función no-lineal $f()$ justo antes de alcanzar la capa oculta. Esta es una práctica muy común. El modelo entonces calcularía:\n",
    "\n",
    "$$\\hat{y} = softmax( ~f(x~W^{(h)})~W^{(o)})$$\n",
    "\n",
    "Hay una variedad de distintas no-linearides que se pueden usar. De hecho, hay gente que dedican sus maestrías y doctorados a investigar las mejores no-linearidades que se pueden usar en una red neuronal artificial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No-linearidades comunes son:\n",
    "\n",
    "* $\\sigma(\\theta)$ (la [función sigmoide](https://en.wikipedia.org/wiki/Sigmoid_function))\n",
    "* $\\tanh(\\theta)$ (la [tangente hyperbólica](http://reference.wolfram.com/language/ref/Tanh.html.en))\n",
    "* $\\text{ReLU}(\\theta) = f(\\theta)=\\max(0,\\theta)$ (el rectificador lineal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para los propósitos de este curso, nos enfocaremos en las primeras dos, pero ten la libertad de experimentar con cualquier no-linearidad que quieras.\n",
    "\n",
    "Como podrás esperar, es crucial conocer la derivada de la no-linearidad que escojas para poder usarla en una red neuronal artificial:\n",
    "\n",
    "Afortunadamente, las derivadas de $\\sigma(\\theta)$ y $\\tanh(\\theta)$ respecto a $\\theta$ con muy simples:\n",
    "\n",
    "$$\\frac{\\partial \\sigma(\\theta)}{\\partial \\theta} = \\sigma(\\theta)(1-\\sigma(\\theta)) $$\n",
    "\n",
    "$$\\frac{\\partial \\tanh(\\theta)}{\\partial \\theta} = 1-\\tanh^2(\\theta)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para nuestro estudio, enfoquémonos en la sigmoide $\\sigma(\\theta)$ para obtener la siguiente expresión:\n",
    "\n",
    "$$\\hat{y} = softmax( ~\\sigma(x~W^{(h)})~W^{(o)})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modifica tu programa anterior para que esta vez tengas una red neuronal artificial con una capa oculata y la no-linearidad sigmoide.\n",
    "\n",
    "Julia no tiene una función sigmoide, por lo que vas a tener que escribir la tuya.\n",
    "\n",
    "Experimenta cambiando los parámetros afinables. Tabien intenta cambiando como inicializas los parámetros $W^{(h)}$ y $W^{(o)}$. ¿Podría afectar eso en algo?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "### tu código aquí ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y así, hemos concluido la construcción de una Red Neuronal Artifical desde cero.\n",
    "\n",
    "Experimenta con otras no-linearidades y agrega más capas ocultas (incluso mezclando distintas no-linearidades entre ellas). No te olvides de afinar los parámetros.\n",
    "\n",
    "¡Felicidades!\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 3: Optimizando una Red Neuronal Artificial con los datos MNIST #"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En esta sección estudiaremos como se optimiza una red neuronal usando la técnica de validación cruzada y como se regularizan las neuronas. \n",
    "\n",
    "Para esto usaremos una versión un poco más grande de los datos MNIST. Ahora tenemos 1000 puntos de datos por cada dígito. El siguiente bloque carga todos los datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using MAT\n",
    "\n",
    "# obtenemos los datos que necesitamos\n",
    "mnist = matread(\"mnist_mas.mat\")\n",
    "caracteristicas = mnist[\"cars\"]\n",
    "clase_de_digito = mnist[\"desc\"];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como ya lo sabemos, el primer paso es separar los datos en un grupo de entrenamiento y otro de prueba. En esta ocasión usaremos solo 5% de los datos como prueba. El siguiente bloque lleva a cabo esta operación y también substrae las características globales promedio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using StatsBase\n",
    "\n",
    "# aleatorizamos los indices de las ileras que corresponden a cada dígito\n",
    "dig_0_aleat = sample(1:1000, 1000, replace = false)\n",
    "dig_1_aleat = sample(1001:2000, 1000, replace = false)\n",
    "dig_2_aleat = sample(2001:3000, 1000, replace = false)\n",
    "dig_3_aleat = sample(3001:4000, 1000, replace = false)\n",
    "dig_4_aleat = sample(4001:5000, 1000, replace = false)\n",
    "dig_5_aleat = sample(5001:6000, 1000, replace = false)\n",
    "dig_6_aleat = sample(6001:7000, 1000, replace = false)\n",
    "dig_7_aleat = sample(7001:8000, 1000, replace = false)\n",
    "dig_8_aleat = sample(8001:9000, 1000, replace = false)\n",
    "dig_9_aleat = sample(9001:10000, 1000, replace = false)\n",
    "\n",
    "# separamos los datos que nos servirán para entrenar\n",
    "x_entren = [\n",
    "    caracteristicas[dig_0_aleat[1:950],:];\n",
    "    caracteristicas[dig_1_aleat[1:950],:];\n",
    "    caracteristicas[dig_2_aleat[1:950],:];\n",
    "    caracteristicas[dig_3_aleat[1:950],:];\n",
    "    caracteristicas[dig_4_aleat[1:950],:];\n",
    "    caracteristicas[dig_5_aleat[1:950],:];\n",
    "    caracteristicas[dig_6_aleat[1:950],:];\n",
    "    caracteristicas[dig_7_aleat[1:950],:];\n",
    "    caracteristicas[dig_8_aleat[1:950],:];\n",
    "    caracteristicas[dig_9_aleat[1:950],:];\n",
    "]\n",
    "y_entren = [\n",
    "    clase_de_digito[dig_0_aleat[1:950],:];\n",
    "    clase_de_digito[dig_1_aleat[1:950],:];\n",
    "    clase_de_digito[dig_2_aleat[1:950],:];\n",
    "    clase_de_digito[dig_3_aleat[1:950],:];\n",
    "    clase_de_digito[dig_4_aleat[1:950],:];\n",
    "    clase_de_digito[dig_5_aleat[1:950],:];\n",
    "    clase_de_digito[dig_6_aleat[1:950],:];\n",
    "    clase_de_digito[dig_7_aleat[1:950],:];\n",
    "    clase_de_digito[dig_8_aleat[1:950],:];\n",
    "    clase_de_digito[dig_9_aleat[1:950],:];\n",
    "]\n",
    "\n",
    "\n",
    "# separamos los datos que nos servirán para probar\n",
    "x_prueba = [\n",
    "    caracteristicas[dig_0_aleat[951:end],:];\n",
    "    caracteristicas[dig_1_aleat[951:end],:];\n",
    "    caracteristicas[dig_2_aleat[951:end],:];\n",
    "    caracteristicas[dig_3_aleat[951:end],:];\n",
    "    caracteristicas[dig_4_aleat[951:end],:];\n",
    "    caracteristicas[dig_5_aleat[951:end],:];\n",
    "    caracteristicas[dig_6_aleat[951:end],:];\n",
    "    caracteristicas[dig_7_aleat[951:end],:];\n",
    "    caracteristicas[dig_8_aleat[951:end],:];\n",
    "    caracteristicas[dig_9_aleat[951:end],:];\n",
    "]\n",
    "y_prueba = [\n",
    "    clase_de_digito[dig_0_aleat[951:end],:];\n",
    "    clase_de_digito[dig_1_aleat[951:end],:];\n",
    "    clase_de_digito[dig_2_aleat[951:end],:];\n",
    "    clase_de_digito[dig_3_aleat[951:end],:];\n",
    "    clase_de_digito[dig_4_aleat[951:end],:];\n",
    "    clase_de_digito[dig_5_aleat[951:end],:];\n",
    "    clase_de_digito[dig_6_aleat[951:end],:];\n",
    "    clase_de_digito[dig_7_aleat[951:end],:];\n",
    "    clase_de_digito[dig_8_aleat[951:end],:];\n",
    "    clase_de_digito[dig_9_aleat[951:end],:];\n",
    "]\n",
    "\n",
    "# removemos las caracteristicas globales promedio de x_entren y x_prueba\n",
    "x_prom = mean(x_entren,1)\n",
    "\n",
    "x_entren = x_entren - x_prom.*ones(size(x_entren))\n",
    "x_prueba = x_prueba - x_prom.*ones(size(x_prueba));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora recordemos cuales son los parámetros que podemos afinar al entrenar una red neuronal artificial:\n",
    "1. Taza de aprendizaje\n",
    "2. Número de capas ocultas\n",
    "3. Dimensionalidad de la(s) capa(s) oculta(s)\n",
    "4. No-linearidad aplicada en la(s) capa(s) oculta(s)\n",
    "5. La regularización aplicada a los parámetros $W$ y la fuerza ($\\lambda$) con que queremos regularizar dichos parámetros (explicado más abajo).\n",
    "6. Número de épocas (las veces que le mostramos todos los datos a la red neuronal artificial)\n",
    "\n",
    "Como podremos imaginarnos, estos parámetros pueden afectar como la red neuronal aprende los datos. Por eso es importante explorar distintas posibilidades para encontrar el mejor desempeño de la red neuronal.\n",
    "\n",
    "La validación cruzada nos permite explorar el desempeño de la red neuronal al variar estos parámetros.\n",
    "\n",
    "El truco de la validación cruzada consiste en separar nuestros datos de entrenamiento en dos grupos:\n",
    "1. uno para entrenar y \n",
    "2. uno para validar el entrenamiento\n",
    "\n",
    "Normalmente, podemos reservar aleatoriamente 10% del total original de los datos como validación. \n",
    "\n",
    "Entonces, usaremos los datos de entrenamiento para aprender los parámetros W, y usaremos los datos de validación para juzgar como se desempeña nuestro algoritmo tras haber sido entrenado. Si vemos que el desempeño con los datos de validación no es óptimo, podemos cambiar uno o más de los parámetros para así volver a entrenar y ver si el cambio de parámetros mejora el desempeño con los datos de validación. \n",
    "\n",
    "Los datos de validación, entonces, son similares en espítiru a los datos prueba. La diferencia es que los datos de validación son usados para afinar los parámetros de nuestro algoritmo, mientras que los de prueba son usados cuando creemos que nuestro algoritmo está completamente listo.\n",
    "\n",
    "En el siguiente bloque, separa los datos de entrenamiento en cuatro variables: `x_ent`, `y_ent`, `x_val`, y `y_val`, los cuales tendran nuestos datos de entrenamiento y nuestros datos de validación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# tu código aquí #\n",
    "x_ent = \n",
    "y_ent = \n",
    "x_val =\n",
    "y_val ="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora si estamos listos para entrenar nuestra red neuronal artificial y afinar todos sus parámetros. Para demostrar como funciona la validación cruzada, entrenaremos una red neuronal de una capa oculta con no-linearidad $tanh()$ para clasificar los datos MNIST.\n",
    "\n",
    "Recuerda que ahora tenemos 850 puntos de datos para entrenar el algoritmo. Con este número de datos no es ideal hacer el Descenso de Gradiente con cada punto de dato que tenemos. Tampoco es ideal esperar a hacer Descenso de Gradiente tras haber calculado la derivada $\\frac{\\partial{J}}{\\partial{W}}$ con todos los datos.\n",
    "\n",
    "Usualmente, se usa un \"mini-montón\" de datos (~10% del total de datos de entrenamiento disponibles) para calcular $\\frac{\\partial{J}}{\\partial{W}}$ y llevar a cabo el Descenso de Gradiente. \n",
    "\n",
    "Además, se aplica una regularización a los valores de las matrices $W$, lo cual convierte nuestra función objetivo en:\n",
    "$$J = minimiza\\{-log(\\hat{y}_{correcto}) + \\lambda(\\frac{1}{2}\\sum (W^{(h)})^2 + \\frac{1}{2}\\sum (W^{(o)})^2 )\\}$$\n",
    "Aquí, $\\lambda$ determina cuanto influyen los parámetros $W$ al objetivo. Esta regularización se hace para asegurarnos que los parámetros $W$ no se conviertan en valores muy grandes.\n",
    "\n",
    "El siguiente bloque muestra como se entrena una red neuronal de una capa oculta a clasificar los datos MNIST usando validación cruzada y Descenso por Gradiente con \"mini-montones\" de datos. Adicionalmente, se agregan sesgos a cada matriz W, haciendo la expresión del objetivo tener la forma:\n",
    "$$J = minimiza\\{-log(\\hat{y}_{correcto}) + \\lambda(\\frac{1}{2}\\sum (W^{(h)})^2 + \\frac{1}{2}\\sum (W^{(o)})^2 )\\}$$\n",
    "Donde\n",
    "$$\\hat{y} = softmax( ~\\tanh(x~W^{(h)} + b^{(h)})~W^{(o)} + b^{(o)})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------------------------\n",
      "Época: 1\n",
      "Precisión con los datos de entrenamiento:0.4073684210526316\n",
      "\n",
      "Precisión con los datos de validación:0.424\n",
      "------------------------------------------------------------------------------\n",
      "Época: 2\n",
      "Precisión con los datos de entrenamiento:0.6514736842105263\n",
      "\n",
      "Precisión con los datos de validación:0.644\n",
      "------------------------------------------------------------------------------\n",
      "Época: 3\n",
      "Precisión con los datos de entrenamiento:0.6121052631578947\n",
      "\n",
      "Precisión con los datos de validación:0.628\n",
      "------------------------------------------------------------------------------\n",
      "Época: 4\n",
      "Precisión con los datos de entrenamiento:0.5610526315789474\n",
      "\n",
      "Precisión con los datos de validación:0.572\n",
      "------------------------------------------------------------------------------\n",
      "Época: 5\n",
      "Precisión con los datos de entrenamiento:0.5153684210526316\n",
      "\n",
      "Precisión con los datos de validación:0.516\n",
      "------------------------------------------------------------------------------\n",
      "Época: 6\n",
      "Precisión con los datos de entrenamiento:0.5011578947368421\n",
      "\n",
      "Precisión con los datos de validación:0.506\n",
      "------------------------------------------------------------------------------\n",
      "Época: 7\n",
      "Precisión con los datos de entrenamiento:0.5322105263157895\n",
      "\n",
      "Precisión con los datos de validación:0.528\n",
      "------------------------------------------------------------------------------\n",
      "Época: 8\n",
      "Precisión con los datos de entrenamiento:0.5762105263157895\n",
      "\n",
      "Precisión con los datos de validación:0.57\n",
      "------------------------------------------------------------------------------\n",
      "Época: 9\n",
      "Precisión con los datos de entrenamiento:0.621578947368421\n",
      "\n",
      "Precisión con los datos de validación:0.63\n",
      "------------------------------------------------------------------------------\n",
      "Época: 10\n",
      "Precisión con los datos de entrenamiento:0.6694736842105263\n",
      "\n",
      "Precisión con los datos de validación:0.68\n",
      "------------------------------------------------------------------------------\n",
      "Época: 11\n",
      "Precisión con los datos de entrenamiento:0.7111578947368421\n",
      "\n",
      "Precisión con los datos de validación:0.712\n",
      "------------------------------------------------------------------------------\n",
      "Época: 12\n",
      "Precisión con los datos de entrenamiento:0.7476842105263158\n",
      "\n",
      "Precisión con los datos de validación:0.754\n",
      "------------------------------------------------------------------------------\n",
      "Época: 13\n",
      "Precisión con los datos de entrenamiento:0.781578947368421\n",
      "\n",
      "Precisión con los datos de validación:0.788\n",
      "------------------------------------------------------------------------------\n",
      "Época: 14\n",
      "Precisión con los datos de entrenamiento:0.8041052631578948\n",
      "\n",
      "Precisión con los datos de validación:0.814\n",
      "------------------------------------------------------------------------------\n",
      "Época: 15\n",
      "Precisión con los datos de entrenamiento:0.8175789473684211\n",
      "\n",
      "Precisión con los datos de validación:0.83\n",
      "------------------------------------------------------------------------------\n",
      "Época: 16\n",
      "Precisión con los datos de entrenamiento:0.8296842105263158\n",
      "\n",
      "Precisión con los datos de validación:0.838\n",
      "------------------------------------------------------------------------------\n",
      "Época: 17\n",
      "Precisión con los datos de entrenamiento:0.8398947368421052\n",
      "\n",
      "Precisión con los datos de validación:0.838\n",
      "------------------------------------------------------------------------------\n",
      "Época: 18\n",
      "Precisión con los datos de entrenamiento:0.8489473684210527\n",
      "\n",
      "Precisión con los datos de validación:0.846\n",
      "------------------------------------------------------------------------------\n",
      "Época: 19\n",
      "Precisión con los datos de entrenamiento:0.8554736842105263\n",
      "\n",
      "Precisión con los datos de validación:0.854\n",
      "------------------------------------------------------------------------------\n",
      "Época: 20\n",
      "Precisión con los datos de entrenamiento:0.8597894736842105\n",
      "\n",
      "Precisión con los datos de validación:0.866\n",
      "------------------------------------------------------------------------------\n",
      "Época: 21\n",
      "Precisión con los datos de entrenamiento:0.8645263157894737\n",
      "\n",
      "Precisión con los datos de validación:0.864\n",
      "------------------------------------------------------------------------------\n",
      "Época: 22\n",
      "Precisión con los datos de entrenamiento:0.8672631578947368\n",
      "\n",
      "Precisión con los datos de validación:0.872\n",
      "------------------------------------------------------------------------------\n",
      "Época: 23\n",
      "Precisión con los datos de entrenamiento:0.8714736842105263\n",
      "\n",
      "Precisión con los datos de validación:0.872\n",
      "------------------------------------------------------------------------------\n",
      "Época: 24\n",
      "Precisión con los datos de entrenamiento:0.874421052631579\n",
      "\n",
      "Precisión con los datos de validación:0.876\n",
      "------------------------------------------------------------------------------\n",
      "Época: 25\n",
      "Precisión con los datos de entrenamiento:0.8762105263157894\n",
      "\n",
      "Precisión con los datos de validación:0.88\n",
      "------------------------------------------------------------------------------\n",
      "Época: 26\n",
      "Precisión con los datos de entrenamiento:0.8791578947368421\n",
      "\n",
      "Precisión con los datos de validación:0.884\n",
      "------------------------------------------------------------------------------\n",
      "Época: 27\n",
      "Precisión con los datos de entrenamiento:0.8817894736842106\n",
      "\n",
      "Precisión con los datos de validación:0.886\n",
      "------------------------------------------------------------------------------\n",
      "Época: 28\n",
      "Precisión con los datos de entrenamiento:0.8834736842105263\n",
      "\n",
      "Precisión con los datos de validación:0.888\n",
      "------------------------------------------------------------------------------\n",
      "Época: 29\n",
      "Precisión con los datos de entrenamiento:0.885578947368421\n",
      "\n",
      "Precisión con los datos de validación:0.89\n",
      "------------------------------------------------------------------------------"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f28c40bd710>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Época: 30\n",
      "Precisión con los datos de entrenamiento:0.8867368421052632\n",
      "\n",
      "Precisión con los datos de validación:0.89\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x7f289a3a97d0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# definimos parámetros generales\n",
    "C = 10\n",
    "D = 784\n",
    "N = size(x_ent)[1] # número de puntos de datos disponibles para entrenar\n",
    "\n",
    "# definimos los parámetros que podemos afinar (excepto el número de capas ocultas)\n",
    "H = 256\n",
    "M = 10 # número de mini-montones\n",
    "NM = N/M # número de datos por mini-monton\n",
    "alpha = 0.1 # taza de aprendizaje\n",
    "lambda = 0.0001 # fuerza de regularización\n",
    "epocas = 30\n",
    "\n",
    "# inicializamos las neuronas y sus sesgos\n",
    "Wh = (rand(D,H) - 0.5)*0.01\n",
    "bh = (rand(1,H) - 0.5)*0.01\n",
    "Wo = (rand(H,C) - 0.5)*0.01\n",
    "bo = (rand(1,C) - 0.5)*0.01\n",
    "\n",
    "# inicializamos el arreglo para visualizar la pérdida\n",
    "Js = zeros(epocas*M)\n",
    "\n",
    "# ciclo para mostrar los datos más de una epoca\n",
    "for ep = 1:epocas\n",
    "\n",
    "    # generando indices aleatorios (es importante aleatorizar los datos en cada epoca)\n",
    "    x_ind_aleat = sample(1:N, N, replace = false)\n",
    "\n",
    "    # ciclo para iterar sobre los mini-montones de datos\n",
    "    for mm = 0:M-1\n",
    "       \n",
    "        # accediendo los datos del mini-montón de datos actual\n",
    "        mini_x = x_ent[x_ind_aleat[floor(Int,(mm*NM)+1:(mm*NM)+NM)],:]\n",
    "        mini_y = y_ent[x_ind_aleat[floor(Int,(mm*NM)+1:(mm*NM)+NM)],:]\n",
    "\n",
    "        # forward pass\n",
    "        h = tanh(mini_x*Wh + bh.*ones(size(tanh(mini_x*Wh))))\n",
    "        v = h*Wo + bo.*ones(size(h*Wo))\n",
    "        y_hat = exp(v)./sum(exp(v),2)\n",
    "\n",
    "        # calculando la pérdida        \n",
    "        J = 0\n",
    "        for n = 1:NM\n",
    "            J = J + -log(y_hat[floor(Int,n),floor(Int,mini_y[floor(Int,n),:])+1])\n",
    "        end        \n",
    "        Js[((ep-1)*M) + mm+1,:] = J/NM + lambda*(0.5*sum(Wh.^2) + 0.5*sum(Wo.^2))\n",
    "        \n",
    "        # generando e_correcto\n",
    "        e_correcto = zeros(size(y_hat))\n",
    "        for n = 1:NM\n",
    "            e_correcto[floor(Int,n),floor(Int,mini_y[floor(Int,n),:])+1] = 1\n",
    "        end\n",
    "        \n",
    "        # backward pass\n",
    "        dJ_dv = (y_hat .- e_correcto)./NM\n",
    "        dJ_dWo = h'*dJ_dv + lambda*Wo\n",
    "        dJ_dbo = sum(dJ_dv,1)\n",
    "        \n",
    "        dJ_dh = (ones(size(h)) .- tanh(h).^2).*(dJ_dv*Wo')\n",
    "        dJ_dWh = mini_x'*dJ_dh + lambda*Wh\n",
    "        dJ_dbh = sum((dJ_dh),1)\n",
    "        \n",
    "        # actualizando los parámetros\n",
    "        Wo = Wo - alpha*dJ_dWo\n",
    "        bo = bo - alpha*dJ_dbo\n",
    "        Wh = Wh - alpha*dJ_dWh\n",
    "        bh = bh - alpha*dJ_dbh      \n",
    "        \n",
    "    end \n",
    "\n",
    "    # midiendo la precisión con los datos de entrenamiento\n",
    "    h = tanh(x_ent*Wh + bh.*ones(size(tanh(x_ent*Wh))))\n",
    "    v = h*Wo + bo.*ones(size(h*Wo))\n",
    "    y_hat = exp(v)./sum(exp(v),2)\n",
    "    y_max = findmax(y_hat',1)\n",
    "    y_max_ind = y_max[2] - range(0,N)'*C    \n",
    "    print(\"------------------------------------------------------------------------------\")\n",
    "    print(\"\\nÉpoca: \", ep)\n",
    "    print(\"\\nPrecisión con los datos de entrenamiento:\",sum(y_max_ind .== (y_ent .+ ones(size(y_ent)))')/N, \"\\n\")\n",
    "\n",
    "    # midiendo la precisión con los datos de validación\n",
    "    h = tanh(x_val*Wh + bh.*ones(size(tanh(x_val*Wh))))\n",
    "    v = h*Wo + bo.*ones(size(h*Wo))\n",
    "    y_hat = exp(v)./sum(exp(v),2)\n",
    "    y_max = findmax(y_hat',1)\n",
    "    y_max_ind = y_max[2] - range(0,length(y_val))'*C    \n",
    "    print(\"Precisión con los datos de validación:\",sum(y_max_ind .== (y_val .+ ones(size(y_val)))')/length(y_val), \"\\n\")\n",
    "\n",
    "    \n",
    "end\n",
    "\n",
    "using PyPlot\n",
    "plot(linspace(0,epocas,length(Js)),Js)\n",
    "xlabel(\"Época\")\n",
    "ylabel(\"Pérdida\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuando estés satisfecho con los resultados de tu red neuronal, obtén su precisión con los datos prueba."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "# escribe tu código aquí para obtener el desempeño de tu red neuronal con los datos prueba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¡Felicidades! Has entrenado una red neuronal artificial completamente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inténtalo también con los datos [CIFAR-10](https://www.cs.toronto.edu/~kriz/cifar.html). El siguiente bloque carga una versión pequeña de la base de datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6465ae1910>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.image.AxesImage object at 0x7f6465a29410>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using MAT\n",
    "\n",
    "# obtenemos los datos que necesitamos\n",
    "mnist = matread(\"cifar_10.mat\")\n",
    "caracteristicas = mnist[\"imag\"]\n",
    "clase_de_digito = floor(Int,mnist[\"desc\"])\n",
    "\n",
    "# visualización de un ejemplo al azar\n",
    "ind_aleat = sample(1:size(caracteristicas)[1],1)\n",
    "using PyPlot\n",
    "imshow(reshape(caracteristicas[ind_aleat,:],32,32,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 4: Redes Neuronales Artificiales con Tensorflow #\n",
    "\n",
    "Los cuadernos que explican como implementar redes neuronales artificiales con Tensorflow están aquí:\n",
    "\n",
    "1. [Redes Neuronales Artificiales con Tensorflow (Parte 1)](https://github.com/iranroman/algoritmica_ejercicios/blob/master/Tensorflow_pt1.ipynb)\n",
    "2. [Redes Neuronales Artificiales con Tensorflow (Parte 2)](https://github.com/iranroman/algoritmica_ejercicios/blob/master/Tensorflow_pt2.ipynb)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.2",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}