1.7. Бинарная классификация.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Сравнение метрик качества бинарной классификации\n",
    "## Programming Assignment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом задании мы разберемся, в чем состоит разница между разными метриками качества. Мы остановимся на задаче бинарной классификации (с откликами 0 и 1), но рассмотрим ее как задачу предсказания вероятности того, что объект принадлежит классу 1. Таким образом, мы будем работать с вещественной, а не бинарной целевой переменной."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Задание оформлено в стиле демонстрации с элементами Programming Assignment. Вам нужно запустить уже написанный код и рассмотреть предложенные графики, а также реализовать несколько своих функций. Для проверки запишите в отдельные файлы результаты работы этих функций на указанных наборах входных данных, это можно сделать с помощью предложенных в заданиях функций write_answer_N, N - номер задачи. Загрузите эти файлы в систему."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для построения графиков нужно импортировать соответствующие модули. \n",
    "Библиотека seaborn позволяет сделать графики красивее. Если вы не хотите ее использовать, закомментируйте третью строку.\n",
    "Более того, для выполнения Programming Assignment модули matplotlib и seaborn не нужны (вы можете не запускать ячейки с построением графиков и смотреть на уже построенные картинки)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Что предсказывают алгоритмы"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для вычисления метрик качества в обучении с учителем нужно знать только два вектора: вектор правильных ответов и вектор предсказанных величин; будем обозначать их actual и predicted. Вектор actual известен из обучающей выборки, вектор predicted возвращается алгоритмом предсказания. Сегодня мы не будем использовать какие-то алгоритмы классификации, а просто рассмотрим разные векторы предсказаний.\n",
    "\n",
    "В нашей формулировке actual состоит из нулей и единиц, а predicted - из величин из интервала [0, 1] (вероятности класса 1). Такие векторы удобно показывать на scatter plot.\n",
    "\n",
    "Чтобы сделать финальное предсказание (уже бинарное), нужно установить порог T: все объекты, имеющие предсказание выше порога, относят к классу 1, остальные - к классу 0. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# рисует один scatter plot\n",
    "def scatter(actual, predicted, T):\n",
    "    plt.scatter(actual, predicted)\n",
    "    plt.xlabel(\"Labels\")\n",
    "    plt.ylabel(\"Predicted probabilities\")\n",
    "    plt.plot([-0.2, 1.2], [T, T])\n",
    "    plt.axis([-0.1, 1.1, -0.1, 1.1])\n",
    "    \n",
    "# рисует несколько scatter plot в таблице, имеющей размеры shape\n",
    "def many_scatters(actuals, predicteds, Ts, titles, shape):\n",
    "    plt.figure(figsize=(shape[1]*5, shape[0]*5))\n",
    "    i = 1\n",
    "    for actual, predicted, T, title in zip(actuals, predicteds, Ts, titles):\n",
    "        ax = plt.subplot(shape[0], shape[1], i)\n",
    "        ax.set_title(title)\n",
    "        i += 1\n",
    "        scatter(actual, predicted, T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Идеальная ситуация: существует порог T, верно разделяющий вероятности, соответствующие двум классам. Пример такой ситуации:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "actual_0 = np.array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  \n",
    "          1.,  1.,  1., 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])\n",
    "predicted_0 = np.array([ 0.19015288,  0.23872404,  0.42707312,  0.15308362,  0.2951875 ,\n",
    "            0.23475641,  0.17882447,  0.36320878,  0.33505476,  0.202608  ,\n",
    "            0.82044786,  0.69750253,  0.60272784,  0.9032949 ,  0.86949819,\n",
    "            0.97368264,  0.97289232,  0.75356512,  0.65189193,  0.95237033,\n",
    "            0.91529693,  0.8458463 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUkAAAFECAYAAACqFMx2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7825f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "scatter(actual_0, predicted_0, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Интервалы вероятностей для двух классов прекрасно разделяются порогом T = 0.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чаще всего интервалы накладываются - тогда нужно аккуратно подбирать порог. \n",
    "\n",
    "Самый неправильный алгоритм делает все наоборот: поднимает вероятности класса 0 выше вероятностей класса 1. Если так произошло, стоит посмотреть, не перепутались ли метки 0 и 1 при создании целевого вектора из сырых данных.\n",
    "\n",
    "Примеры:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "actual_1 = np.array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
    "                    0.,  0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
    "                    1.,  1.,  1.,  1.])\n",
    "predicted_1 = np.array([ 0.41310733,  0.43739138,  0.22346525,  0.46746017,  0.58251177,\n",
    "            0.38989541,  0.43634826,  0.32329726,  0.01114812,  0.41623557,\n",
    "            0.54875741,  0.48526472,  0.21747683,  0.05069586,  0.16438548,\n",
    "            0.68721238,  0.72062154,  0.90268312,  0.46486043,  0.99656541,\n",
    "            0.59919345,  0.53818659,  0.8037637 ,  0.272277  ,  0.87428626,\n",
    "            0.79721372,  0.62506539,  0.63010277,  0.35276217,  0.56775664])\n",
    "actual_2 = np.array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.,\n",
    "            0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])\n",
    "predicted_2 = np.array([ 0.07058193,  0.57877375,  0.42453249,  0.56562439,  0.13372737,\n",
    "            0.18696826,  0.09037209,  0.12609756,  0.14047683,  0.06210359,\n",
    "            0.36812596,  0.22277266,  0.79974381,  0.94843878,  0.4742684 ,\n",
    "            0.80825366,  0.83569563,  0.45621915,  0.79364286,  0.82181152,\n",
    "            0.44531285,  0.65245348,  0.69884206,  0.69455127])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3cAAAFRCAYAAADXWVQUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa70aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "many_scatters([actual_0, actual_1, actual_2], [predicted_0, predicted_1, predicted_2], \n",
    "              [0.5, 0.5, 0.5], [\"Perfect\", \"Typical\", \"Awful algorithm\"], (1, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Алгоритм может быть осторожным и стремиться сильно не отклонять вероятности от 0.5, а может рисковать - делать предсказания близакими к нулю или единице.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# рискующий идеальный алгоитм\n",
    "actual_0r = np.array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  1.,\n",
    "            1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])\n",
    "predicted_0r = np.array([ 0.23563765,  0.16685597,  0.13718058,  0.35905335,  0.18498365,\n",
    "            0.20730027,  0.14833803,  0.18841647,  0.01205882,  0.0101424 ,\n",
    "            0.10170538,  0.94552901,  0.72007506,  0.75186747,  0.85893269,\n",
    "            0.90517219,  0.97667347,  0.86346504,  0.72267683,  0.9130444 ,\n",
    "            0.8319242 ,  0.9578879 ,  0.89448939,  0.76379055])\n",
    "# рискующий хороший алгоритм\n",
    "actual_1r = np.array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,\n",
    "            1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])\n",
    "predicted_1r = np.array([ 0.13832748,  0.0814398 ,  0.16136633,  0.11766141,  0.31784942,\n",
    "            0.14886991,  0.22664977,  0.07735617,  0.07071879,  0.92146468,\n",
    "            0.87579938,  0.97561838,  0.75638872,  0.89900957,  0.93760969,\n",
    "            0.92708013,  0.82003675,  0.85833438,  0.67371118,  0.82115125,\n",
    "            0.87560984,  0.77832734,  0.7593189,  0.81615662,  0.11906964,\n",
    "            0.18857729])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAJoCAYAAADBOF29AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npJrZgEmSJNXs/wPry0rNihC4zAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x90f2be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "many_scatters([actual_0, actual_1, actual_0r, actual_1r], \n",
    "              [predicted_0, predicted_1, predicted_0r, predicted_1r], \n",
    "              [0.5, 0.5, 0.5, 0.5],\n",
    "              [\"Perfect careful\", \"Typical careful\", \"Perfect risky\", \"Typical risky\"], \n",
    "              (2, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Также интервалы могут смещаться. Если алгоритм боится ошибок false positive, то он будет чаще делать предсказания, близкие к нулю. \n",
    "Аналогично, чтобы избежать ошибок false negative, логично чаще предсказывать большие вероятности. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "actual_10 = np.array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
    "                0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
    "                1.,  1.,  1.])\n",
    "predicted_10 = np.array([ 0.29340574, 0.47340035,  0.1580356 ,  0.29996772,  0.24115457,  0.16177793,\n",
    "                         0.35552878,  0.18867804,  0.38141962,  0.20367392,  0.26418924, 0.16289102, \n",
    "                         0.27774892,  0.32013135,  0.13453541, 0.39478755,  0.96625033,  0.47683139,  \n",
    "                         0.51221325,  0.48938235, 0.57092593,  0.21856972,  0.62773859,  0.90454639,  0.19406537,\n",
    "                         0.32063043,  0.4545493 ,  0.57574841,  0.55847795 ])\n",
    "actual_11 = np.array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
    "                0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])\n",
    "predicted_11 = np.array([ 0.35929566, 0.61562123,  0.71974688,  0.24893298,  0.19056711,  0.89308488,\n",
    "            0.71155538,  0.00903258,  0.51950535,  0.72153302,  0.45936068,  0.20197229,  0.67092724,\n",
    "                         0.81111343,  0.65359427,  0.70044585,  0.61983513,  0.84716577,  0.8512387 ,  \n",
    "                         0.86023125,  0.7659328 ,  0.70362246,  0.70127618,  0.8578749 ,  0.83641841,  \n",
    "                         0.62959491,  0.90445368])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3cAAAFRCAYAAADXWVQUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X2YXXV97/33JBFKJJABRyV6OwaVb62ntYqgoYiS2tve\nFYoRqwcrWtT4VGmpnjaHnlutPa3Y8ZRi24MPgVpMW9S7xxjRgtU2VqVRqRYfWvxGwUbb+BCYPNnI\nQ2DuP/YessmVzOyZrLXXb695v66La2bttWft74S9P7O+a/3Wb41MTU0hSZIkSRpui5ouQJIkSZJ0\n5GzuJEmSJKkFbO4kSZIkqQVs7iRJkiSpBWzuJEmSJKkFbO4kSZIkqQWWNF2A2iUi3gGc1V38CeA2\n4E5gCliVmXfNYVvnAj+bmZfMo45x4GuZuWyuPytpuEXEEuDbwM2Z+QtHsJ23AN/IzL846PETgR2Z\n2fcB0oj4FPAoYFf3oRFgKjOfHBF/DjwL+AGdrDwK+CawNjNvn2/9ksoypNn0VODJmfmjnp/ZCzwh\nM789399B9bG5U6Uy89env4+I24AXZeY/z3Nb1wHXHUE53sRRWpjWAF8GTo2IyMycz0Yy882HWTXC\n3PNlCnhDZm48zLrLM/Py6Qci4n8B7wR+aY6vI6lcw5hN48A7gFce9LgKZXOnOo10/yMiXgT8amb+\nTHf5UcAW4NHAPuAK4GxgKfA/MnNjRLwUeH5mnhsRDwPeBfw4cC/w7sz8k4h4GvAHdI50nwR8IjPX\nDvB3lFSe1wLXAt8ALgFeExF/CXwpM/8QICJeDTwjMy+IiFcCFwP7ge8Dr8vMb0bEe4GvZublEfE8\n4PeA/wT+afqFutn0PuDE7kN/k5lvOkxdI3P4Hf6OTrZJao9hzKZ3AC+JiOdl5of6eL4a5jV3GpT/\nDzg5In68u/xy4L2ZeQ+wGLg9M58CvBD4s+7QAjhwdOidQGbm44EzgLURcTKd0HtjZq4CngCcFxFP\nGsyvJKk0EfETdIYRfYDOjs2FETEKrAde2vPUXwHeExFnA/+Nzs7Uk+jseG06aJsPBa4G1mTmacC2\nntVrgVu7+XUW8NiIONxw8LdHxJci4p+7X3/+ML/DMcBLgM1z+NUlFWyIs2lHt773RMQj5vO7a7Bs\n7jQQ3SbuKjpN2SI64fXunqf8afd5XwW+woHr9qb9LPCe7nP2ZOZPZeZt3e2MRsSlwJXAMcCx9f0m\nkgr3auBjmbk7M/8J+DfgVZn5KeDoiHhyRDweeEhmbgZ+HvhAZk4CZOY1wIrudbvTzgS+0jOEqje7\nbgDOj4iPAa8C/ntm7j1Mbb+ZmU/OzCd1v97Qs+710ztXwOeB24FL5//PIKkww5pNZOYngT8H/iIi\nPGtXOIdlapDeA3wB+DSd4QTf6Vl3b8/3iw9ahs6QhPvHeEfESjo7P58E/plOiH2QzlExg0dagCJi\nKZ0zXj/qXvM7AiwDfjUi3k7nCPdLgbu638OhD3IuAh7Uszx10PPuz6fM/KduHj0LWA3cFBHnZebn\n5lj+A665k9QeQ55N0y6lcznNb+M1d0XzzJ0GptvMbQH+iM4wy14vAYiIJwMB/MNB6z8BXNR9zvF0\nrkd5HPBkYF1mfhh4JPBYOs0h2ORJC82L6cwUd1JmnpyZK4HH0NmJegFwDfCLwPOB93Z/5uPACyPi\nIQARcRGdYeLf7NnuZ4CfiIif7C7/yvSKiLgMeFNmfqQ7s++/AKfU9QtKGkpDn03dEVgvojNU9Jj5\nbkf1s7lTnQ51ZOe9dN53f3PQ4z8TEV+kM3TzBZm5+6D1F9MJsC/TCbPfz8wvAZcB/xwRXwDWAZ+l\n0+Ad7vUltdergT/sfaCbJX8MXJKZ3we+BHw5M7/XXf9JOgec/j4ivgpcCDyn++NT3efcTmen5q8i\n4p/ozB437QrgpyPiKxFxE53bv1x7iNpmyiOzSmq3VmRTZm6l09zZPxRsZGrKvykajO61dn8KfCsz\n397z+H3AiZm5s7HiJEmSpCFn562BiIhj6Vwj92i6k6f0mMIhlJIkSdIR8cydJEmSJLWAZ+4kSZIk\nqQVs7iRJkiSpBYbqPnc7duytfAzp6OhSdu7cV/VmK2WN1bDGalRd49jYslZcb1l1Pi3E90IdrLEa\nC7XGNuST+07lssZqLMQaZ8qmBX/mbsmSxbM/qWHWWA1rrMYw1NgGw/DvbI3VsMZqDEONbTEM/9bW\nWA1rrMYga1zwzZ0kSZIktYHNnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDNnSRJkiS1gM2dJEmSJLWA\nzZ0kSZIktYDNnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDNnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDN\nnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDNnSRJkiS1QO3NXUQ8NSI2H+LxcyPiCxFxY0S8ou46JOlg\n5pOkEplNkuar1uYuIn4TWA8cfdDjS4DLgWcBzwReGRFjddYiSb3MJ0klMpskHYm6z9x9E1hziMcf\nD3wjM/dk5j3AZ4Gzaq5FknqZT5JKZDZJmrdam7vM3AjsP8Sq44DdPct7gePrrEXSkZmc3MXatRs5\n/fTrWLv2Q+zcuavpko6I+SSpRGaTpCOxpKHX3UMnpKYtA2bdUxwdXcqSJYsrL2ZsbFnl26yaNVbD\nGufvda/7KJs2XQiMAFMcffT7+cAHLmi6rDoUk0+lvhd6WWM1rLEaw1DjESgmm2A4/q2tsRrWWI1B\n1Tio5m7koOVbgMdGxHJgH51hBW+fbSM7d+6rvLCxsWXs2LG38u1WyRqrYY1HZuvWYzjwUR5h69Zj\nKqm1gEAuMp9Kfi9Ms8ZqWGM16qix4XwqMptg4b4fqmaN1ViINc6UTYNq7qYAIuIC4MGZeVVEvB74\nWzrhdVVmfndAtUiah/Hx3dx88xTTZ+7Gx/c0XVJVzCdJJTKbJM1Z7c1dZm4Dzuh+f23P4x8DPlb3\n60uqxsTEamAD27ePsmLFTiYmzm66pCNmPkkqkdkkab6auuZO0pAZHV3O+vVrhmL4gyRJ0kJU+03M\nJUmSJEn188ydJEkaWpOTu1i3bnN3yPgkExOrGR1d3nRZktQImztJkjS01q3b/IDbtMAG1q8/1D3A\nJan9HJYpSZKG1rZtx9F7m5bOsiQtTDZ3kiRpaI2P76Z71wBadpsWSZozh2VKkqSh1cbbtEjSfNnc\nSZKkoeVtWiTpAIdlSpIkSVIL2NxJkiRJUgvY3EmSJElSC9jcSZIkSVIL2NxJkiRJUgvY3EmSJElS\nC9jcSZIkSVIL2NxJkiRJUgt4E3NJkjS0Jid3sW7dZrZvH2XFikkmJlYzOrq86bIkqZF8srmT1Bd3\noCSVaN26zWzadCEwAkwBG1i/fk3DVUlSM/lkcyepL+5ASSrRtm3H0cklgJHusiQ1r4l88po7SX1x\nB0pSicbHd9M54AQwxfj4nibLabXJyV2sXbuR00+/jrVrP8TOnbuaLkkqWhP55Jk7SX0ZH9/NzTdP\nMX3mzh0oSSWYmFgNbOgOGd/JxMTZTZfUWo7gkOamiXyyuZPUF3egJJVodHQ569evYWxsGTt27G26\nnFZzBIc0N03kk82dpL64AyVJC5sjOKTy2dxJ6ouzZUrSwuYIDql8NneS+uK1FpK0sDmCQyqfs2VK\n6ovXWkiSJJXN5k5SX5xuXJIkqWwOy5TUF6+1kCRJ6t+tt27j/PM/wq5dj2T58u+wceN5rFw5Xutr\n2txJ6ovXWkiSJPXv/PM/wvbtlwIj7Ns3xZo1l3HzzRfX+poOy5QkSZKkiu3cuYLe+Qo6y/WyuZMk\nSZKkit133zfona/gvvu+WftrOixTkiRJkir2oAcdz113/QGwAtjOgx5U/0zjnrmTJEmSpIotWnQn\n8ChgFPi/usv18sydJEmSJFVs6VLYs+cCOtfdTbF06e/V/pqeuZMkSZKkio2N/QS9E6qMjT2+9te0\nuZMkSZKkip188n/SO6HKySfvq/01HZYpSZIkSRWbmFgNbGD79lFWrNjJxMTZtb+mzZ0kSZIkVWx0\ndDnr169hbGwZO3bsHchr1trcRcQIcCXwROBO4BWZeVvP+l8GXg/sB96bme+qsx5JArNJUplKz6bJ\nyV2sW7e5exZikomJ1YyOLh9kCZJmUfc1d88Fjs7MM4BLgcsPWv92YDVwJvCGiDi+5nokCcwmSWUq\nOpvWrdvMpk0XctNN57Jp00v4rd/aPMiXl9SHupu7M4EbADLz88BTDlr/ZTo3fjimuzyFpCJNTu5i\n7dqNnH76daxd+yF27tzVdElHwmySVKKis2nbtuPonfmvsyypJHU3d8cBu3uW90dE72v+C/BF4KvA\nRzNzT831SJqn3/iNj7Fp0xJuugk2bVrCJZd8tOmSjoTZJKlERWfT+Phuemf+Gx83GqXS1N3c7QGW\n9b5eZt4HEBE/CTwHGAceDTwsIs6vuR5J87Rly17gAuBc4EVs2fLDhis6ImaTpBIVnU0TE6s577wN\nnHbadZx33oaBzPwnaW7qni3zRuAc4K8j4ml0jjRN2w3sA+7KzKmI+AGdoQaHNTq6lCVLFlde5NjY\nstmf1DBrrIY1zt/IyBi9w3FGRsaKrbUPlWYT1JNPw/Dva43VsMZqDEONsyg6m8bGlvHhD7+kkm0N\nwjC8H6yxGtZ4QN3N3Ubg5yLixu7yRRFxAfDgzLwqIt4DfDYi7gJuBf58po3t3Fn9jf8GOTXpfFlj\nNazxyDztafdw/fVTdBq8KZ72tP2V1NpQIFeaTVB9PpX8XphmjdWwxmrUUWMD+VR8NsHCfT9UzRqr\nsRBrnCmbam3uMnMKeM1BD2/tWf9u4N111iCpGldc8fMcdVTvjTif3XRJ82Y2SSqR2STpSHkTc0l9\naeJGnJIkSepf3ROqSJIkSZIGwDN3kiRJklSxycldrFu3uXtJyyQTE6sZHV1e62va3EmSJElSxdat\n28ymTRcyPRkdbGD9+jW1vqbDMiVJkiSpYtu2HUfvbaQ6y/WyuZMkSZKkio2P76Zzxg5givHxPbW/\npsMyJUmSJKliExOrgd7bSJ1d+2va3EmSJElSxZq4jZTDMiVJkiSpBWzuJEmSJKkFbO4kSZIkqQVs\n7iRJkiSpBWzuJEmSJKkFZp0tMyKOAn48M78SES8CngRcnpnfrb06ScWYnNzFunWbu9P5TjIxsZrR\n0eWN1mQ+SSpRW7Pp1lu3cf75H2HXrkeyfPl32LjxPFauHG+6LEk9+rkVwl8AX4+IY4C3AO8DrgH+\n7zoLk1SWdes2s2nThcAInRtybmD9+jUNV2U+SSpSK7Pp/PM/wvbtlwIj7Ns3xZo1l3HzzRc3XZak\nHv0My1yZmW8Czgeuysz/CYzWW5ak0mzbdhydxg5gpLvcOPNJUolamU07d55E79+BzrKkkvTT3C2J\niIcAzwU+FhEPB5bWW5ak0oyP76Zzxg5givHxPU2WM818klSiVmbT1NSt9P4dmJq6rclyJB1CP8My\n3w58HvhIZn4tIrYCb6y3LEmlmZhYDWzoXnO3k4mJs5suCcwnSWVqZTatXPk4brnl/cCxwA9ZufKx\nTZckFa2J+Qpmbe4y86+Av4qI6eEEP5GZ+2utSlJxRkeXs379GsbGlrFjx96mywHMJ0llams2nXIK\n3HLLf2X62utTTtnQdElS0V772g/z939/YndpCT/84UauvfaiWl+zn9kynwh8AFgaEauAf4iIF2Tm\nl2qtTJJmYT5JKlFbs6nQERxSsT7zmT3A65g+IPLpT7+19tfs55q7PwHWAHdk5n8ArwHeVWtVktQf\n80lSiVqZTdMjOL7whXNZv35N47fDkUp3770PoXcSos5yvfpp7pZm5i3TC5n5CeDo+kqSVKLJyV2s\nXbuR00+/jrVrP8TOnbuaLgnMJ0llMpsk8dCHfo/eSYge+tAf1P6a/UyoMtkdXjAFEBG/DEzWWpWk\n4hR6nzvzSVKJzCZJbNp0PmvWXMauXY9k+fJ/Z+PG+veb+mnuXkPnxptPiIhdwDeAF9dalaTiFHqf\nO/NJUonMJkmsXDnOzTdfPNDJ6PqZLfNW4MyIeDCwODOLuLmVpMEaH9/NzTdPMX3mroT73JlPkkpk\nNklqymGbu4h4T2a+MiI2c2CwKBEBQGaurr88SaUoaZY080lSidqeTU3cs0vS3Mx05u7d3a+/M4A6\nJBWusPvcmU+SStTqbCr02mtJPQ7b3GXmF7vfPj8zL+5dFxHXAP9QZ2GSdDjmk6QStT2bCr32WlKP\nmYZlXgWcDDwlIp5w0M94Dl5SY8wnSSVqezaVeO21pAeaaVjm7wGPBt4BvKXn8f3ALYf6AUkaEPNJ\nUolanU0lXXstDYMmrlOdqbm7MzM/FRHnHmLdsXi/FknNMZ8klajV2VTYtddS8Zq4TnWm5u4q4BwO\nPT58is6wA0lqgvkkqURmk6T7NXGd6kwTqpzT/bqy9iokaQ7MJ0klMpsk9WriOtWZJlT5s5l+MDNf\nVn05kjQ780lSicwmSb2auE51pmGZQz1dr6RqFXbzWvNJUonMJkn3m5p6wNJAXnOm5u7jmfm9iHjU\nQCqRVLRLLvk4N9zwcqaHFtx999Vcc80LmyrHfJIEFHfgyWySdL+SJ1SZHiw6zYuCpQXmc59bRO9F\nwVu2LGqyHPNJEtDMztMMzCZJ97v11qX07jvddtvS2l/TCVUk9el2DuyrTAF3NFaJ+SRpWhOz0R1O\n27OpsLOkUvEmJ5Pefac77tgKPLvW15zpzB0AEXE88CbgmcA9wCeAyzJzX62VSSrKqlXHcv311wLL\ngL2sWnVs0yWZT5IamY1uNm3NpsLOkkrFO+GER7N9+/vp3Obyh5xwwnjtrzlrcwdcDdwK/AqdT/PL\ngPcAL57tByNiBLgSeCJwJ/CKzLytZ/1pwB92F78HvDgz755D/ZIG5IorzuWoozazfTusWLGfiYlz\nmi4J5plPZpPUHk3MRteHVmZTSWdJpWHwmMfs52tfewnTB0Qe85gNtb9mP83dYzPz+T3Ll0TEV/rc\n/nOBozPzjIh4KnB597Fp7wHOz8zbIuJlwDjwjT63LWmARkeXs379GsbGlrFjx96my5k233wym6SW\nMJsGl00lniWVStbEwad+ZkTIiFg1vRART6T/IDkTuAEgMz8PPKVnO6fQuWjn9RHxKeCEzHTnSSrU\n5OQu1q7dyOmnX8fatR9i585dTZcE888ns0lSnVqZTRMTqznvvA2cdtp1nHfehlLOkkrFmj749IUv\nnMv69WsGco3qTDcx/xadAdXHAM+PiK8D9wKPp//m7jhgd8/y/ohYlJn3AQ8BVgGvBW4DPhoR/5SZ\nn5rzbyGpdiVda1FBPplNkirX9mwq9CyppB4zDct8ZgXb30Nn9oVp0wEFnaNP38zMrQARcQOdI1Sf\nOtzGRkeXsmTJ4grKeqCxsWWzP6lh1lgNa5y/7dtH6b3WYvv20SZrfeYR/nyl2QT15FOp74Ve1lgN\na6xGATU+8wh/fiiyCYr4t56VNVbDGqsxqBpnuhXCNoCIOBr4BTrTvIwAi4GVdGaBms2NdO738tcR\n8TTgqz3rbgOOjYiTuxcLP53O/WEOa+fO6ieZGoajT9ZYDWs8MitWTNI7ne+KFTsrqXU+YVdBPlWa\nTVB9PpX8XphmjdWwxmrUUeNc82khZBMs3PdD1ayxGguxxpmyqZ8JVT4ELAUeC3wGOAvY0udrbwR+\nLiJu7C5fFBEXAA/OzKsi4uXAtREB8I+ZeX2f2z1i3qtFmptCZ6Sbbz4Vm02SWsFsktSIfpq7AB4H\nvAP4M+C/AX/dz8Yzcwp4zUEPb+1Z/yngqf1sq2olXT8kDYNCr7WYVz6VnE2SWsFsktSIfmbL/H43\nbL4O/FRmbgeOrres+nmvFqkVWplPkvpX6Ey+ZpOkRvRz5u5fIuJPgHcCfxkRK4AH1VtW/bxXi9QK\nrcwnSf275JKPc8MNL2f67/ndd1/NNde8sOmyzCZJjeinuXsNcEZm/mtEvAl4FvCiesuqX6HXD0nF\nKvQ61Vbmk6T+fe5zi+gdibNlSz+DkmpnNklqxKzNXWbeGxG7I+Ji4B7gyszM+kurV6HXD0nFKvE6\n1bbmk6S5uJ3emXw7dwxoltkkqSmzHt6KiF+jcxHwo4FTgOsi4qU11yWpMCVep2o+STr11MXA24D3\nAW/j1FObP3NnNklqSj/DMtcCp2bmXoCI+J/Ap4Fr6ixMUlkKvU7VfJIWuKOOOh44cM3dUUdd3XBF\ngNkkqSH9NHf/SWdIQe/ynfWUMziFXj8kFavQ61RbmU+S+vfd7z6E3lEFneXGmU2SGnHY5q57ATB0\nBq/fGBHvB/YDzwe+MYDaalXi9UNSyUq6TrXt+SSpfyWNKjCbJDVtpjN304fBvtD9urT79W/rK2dw\nSrx+SCpZYWe7W51PkvpX2KgCs0lSow7b3GXmW6a/j4gx4Knd52/JzO8PoLZalXSkTxoGJZ3tbns+\nSepfSaMKzCZJTetntsxnAzcDFwEvBb4SEefUXVjdJiZWc955GzjttOs477wNTR/pk4pX4tnutuaT\npOFmNklqSj8Tqvw+cGZmfgsgIk4GPgR8tM7C6lbSkT5pGBR6truV+SRp6JlNkhrRT3P3oOlwAsjM\n2yKi+ZvISBqowq5rmWY+SSqR2SSpEf00d9+OiEuA6RvHvALYVl9JkkpU6Nlu80lSiVqZTYVNrCXp\nEPpp7l4O/AnwP+iMx/p74JV1FiVJfTKfpAWu0IajldlU0sRakg6tn+bu1zLzhbVXIklzZz5JC1yh\nDUcrs6nEibUkPVA/47/PjYiR2Z8mSQNnPkkLXKENRyuzaXx8N50GGgqaWEtSj37O3N0BfD0ivgT8\naPrBzHxZbVVJUn/MJ2mBK3Qm31ZmU6ETa0nq0U9zd03tVfTpN6/8x8q3uXjxCPfeOzX7ExtkjdWw\nxmpUXeOfv/nZR/Ljrc2nhfheqIM1VqPkGo974kM551Ef5t57F7F48X0cNzpW2efxCPKptdm0/EkP\n48SnjHDvvQ/jrdf+a6XbrlLJ79lp1liNhVjjTNk067DMzLwG+DJwInA88PnuY5LUKPNJ0qJFizjx\nxKWcdNIxnHjiUhYtav6OA2aTpKaMTE3N3EVGxBuAVwObgMXAOcBbM/O99Zf3QDt27K28LS9sWvdD\nssZqWGM1qq5xbGzZvK9LaXM+LcT3Qh2ssRol11jnbJnzzac2ZxOU/X6YZo3VsMZqDHLfqZ9hma8C\nTs3MPQAR8bvAjcDAA6pKhU6dLGluWplPkvpX6GyZZpOkRvTT3E0C9/Qs/xAouz3uQ6F/DCTNTSvz\nSVL/Cp0t02yS1Ih+mrtbgS0RcS2wH1gD7ImINwFk5u/WWF9tCv1jIGluWpdPjiqQ5ubhD99B5yBt\n52DtSSfd3nBFQAuzSdJw6Ke529r978e6y5/ofh3q+7cUOnWypLlpXT45qkCam5GR/cC1wDI6J8fu\nmfkHBqN12SRpOMza3GXmWwZRyKBdeump3HTTZeza9UiWL/93fvu3f7HpkqSilXhGqY355KgCaW6+\n+92TgOf2LH+4uWK62phNkoZDP2fuWumyy77E9u2XAiPs2zfFW9+6gfXrx5suSyqWZ5QGw1EF0tz4\nmZGkAxZsc+fRcWlu/MwMxsTEamBD9wzpTiYmzm66JKlofmYGp8QRHJIeaME2dx7pk+bGz8xgjI4u\nZ/36NUNx3x6pBA+8XW/lt3RTD0dwSOU7bHMXEffxwJS8B7gPOBrYk5mjNddWK4/0SXNT0mem7fkk\nqX8lNRxtzyZHcEjlO2xzl5mLACLinXRuvPmXmTkVEecDPz+g+mrj0XFpbkr6zLQ9nyT1r6SGo+3Z\n5AgOqXz9DMt8ama+ZnohM/9PRLyxxpokqV/mk7TAFdpwtDKbShrBIenQ+mnu/jMiLgI+CCwCLgTu\nqLWqAbj11m2cf/5HurdC+A4bN57HypXOlikNmVbmk6T+FdpwtDKbShrBIenQ+mnuXgz8KfDHdMaN\nf5JOSA2188//yANuhbBmzWXcfPPFTZclaW5amU+S+ldow2E2SWpEPzcx3wacGxEnZObkAGoaiJ07\nH0nvGP3OsqRh0tZ8kjTczCZJTZm1uYuInwbeDyyNiKcBnwZekJlfqru4Oo2Ofocf/ejAGP3R0X9v\nuiRJc9TWfJI03MwmSU1Z1Mdz/hhYA9yRmduB1wDvqrWqAdi48TxWrLiMpUvfx4oVl7Fx4y82XZKk\nuWtlPkkaemaTpEb009wtzcxbphcy8xN07tcy1I4//nhOO+2RPOEJo5x22iNYvvz4pkuSNHetzCdJ\nQ89sktSIfiZUmYyIJ9K9KWdE/DLQ1/jxiBgBrgSeCNwJvCIzbzvE895N5+jWb/db+JG65JKPc8MN\nL2d6WObdd1/NNde8cFAvL6ka88qnkrNJUiuYTZIa0c+Zu9cA/xt4QkTsAi4BXtXn9p8LHJ2ZZwCX\nApcf/ISIeBXwX/rcXmU+97lF9E6osmVLP/8Ukgoz33wqNpsktYLZJKkR/XQ0P5aZZwInAI/KzNO6\n3/fjTOAGgMz8PPCU3pURsQo4DXh33xVX5na6B9S6X4f+9jPSQjTffCo4myS1gNkkqRGHHZYZET8D\nLAauiojp8YtExBI6FwWf0sf2jwN29yzvj4hFmXlfRDwceDOdo1QDHw+5atWxXH/9tcAyYC+rVh07\n6BIkzVMF+VRsNkkaXmaTpKbNdM3dzwHPAE4Cfrfn8f30f8RoD53uadqizLyv+/0vAScCf9N9jWMi\n4uuZ+b4+t31ErrjiXI46ajPbt8OKFfuZmDhnEC8rqRpHmk/FZpOkuZmc3MW6dZvZvn2UFSsmmZhY\nzejo8qbKMZskNWpkampqxidExIXAtZm5PyIeBByVmf/Zz8Yj4nnAOZn5su59Xt6Ymc85xPNeCsRs\nFwbv33/v1JIli/t56VndcccuXvva6/nWt45l5cq9vPOdv8AJJzT2x0BayEZmf8qhzTefqs4mqDaf\nJPXvhS+8lg9+8L8yPUHaC17wfj7wgQuq2vy88slsklSzw2ZTP7Nl3gX8M/CTwKOAT0XE6zJzUx8/\nuxH4uYj7IMpHAAAUnElEQVS4sbt8UURcADw4M6/q4+cfYOfOfXP9kcNau/YjbNp0ITDCTTdNcddd\nG1i/fk1l26/S2NgyduzY23QZM7LGaizEGsfGls3+pMObbz5Vmk1QbT7Bwnwv1MEaq1FyjVu3HkPv\nBGlbtx5TWa1HkE+tzSYo+/0wzRqrYY3VGOS+Uz/N3f8LPAsgM2+NiFOBvwVmbe4yc4rOjFG9th7i\nedf0UUeltm07jt4/Bp1lSUNmXvlUcjYVNsRMKt74+G5uvnmK6TN34+N7mi4JWphNkoZDP83dUZn5\n/emFzPxB9z4sQ63QPwaS5qZ1+bRu3eb7RxV0ZvItd1SBVIKJidXAhu4BkZ1MTJzddEnQwmySNBz6\nae4+GxHXAn/ZXX4BsKW+kgaj0D8GkuamdfnkqAJpbkZHl7N+/ZrShma1LpskDYd+mrtfBS6mc/PN\ne4BPA1fWWdQgFPrHQNLctC6fHFUgtULrsknScJjpPncPz8zvAQ8DPtj9b9rDgW/XXJskHVKb88lR\nBdLwanM2SRoOM525uwo4B/gHOhd+jBz09eTaq5OkQ2ttPjmqQBpqrc0mcMInaRgctrnLzHO6X1cO\nrhxJml2b88mdJ2l4tTmbwAmfpGEw07DMP5vpBzPzZdWXI6lUJTUdbc4nd56k4dXmbAInfJKGwUzD\nMv+h+/UcYBnwF8B+4IXA7prrklSYwpqO1uaTO0/SUGttNoETPknDYKZhmdcARMRrgVWZeV93+YPA\n5wZTnqRSlNR0tDmf3HmShlebswmc8EkaBv3cCuF44ATg9u7yw4Bja6tIUpEKbTpal0/uPEmt0Lps\nAid8koZBP83d7wNfiYgbgcXAU+ncu0XSAlJo09G6fHLnSWqF1mWTpOEwa3OXmRsi4pPAGXQutHl1\nZv6g9sokFaXEpsN8klQis0lSUxbN9oSIOAq4CDgP+Dvg1d3Hhtrk5C7Wrt3I6adfx9q1H2Lnzl1N\nlyRpjtqaT5KGm9kkqSn9DMv838AO4MnAPcBjgauBC2usq3aFzfwnaX5al08l3XJCGgaFfmZal02S\nhkM/zd2pmfnkiPh/MnNfRLwU+GrdhdWtpJn/JM1b6/LJA0/S3BT6mWldNkkaDrMOywSmukMJprrL\nD+n5fmiNj+/mwK9RzMx/kuamdfnkgSdpbgr9zLQumyQNh37O3F0BfBJ4eERcAawB3lJrVQNQ6Mx/\nkuamdflU6C0npGIV+plpXTZJGg79NHfXA18EzqYzne+5mfmVWqsagBJn/pM0Z63LJw88SXNT6Gem\nddkkaTj009x9JjMfD/xr3cVI0hy1Lp+mHjBwy1Fc0mwKPVjbumySNBz6ae6+HBEXAl8AfjT9YGZ+\nu7aqJKk/rcunSy75ODfc8HKmh5jdfffVXHPNC5suS9LctC6bJA2Hfpq7p3b/6zUFnFx9OZI0J63L\np899bhG9k0Ns2dLPvFeSCtO6bJI0HGZt7jJz5SAKkaS5amc+3U5nH3B6Wvc7mi1H0py1M5skDYPD\nNncRsQL4U+BxwGeBSzNz16AKk6TDaXM+rVp1LNdffy2wDNjLqlXHNl2SpD61OZskDYeZxvu8F/g6\n8JvAjwF/NJCKJGl2rc2nN7/5LFas+DeWLt3JihXf4nd+5+lNlySpf63NJknDYaZhmY/IzGcDRMTf\nATcPpiRJJZqc3MW6dZu7041PMjGxmtHR5U2V09p8uuyyL7F9+6XACPv2TfHWt25g/frxpsuS1J/W\nZpOk4TBTc3f39DeZeU9E3D3DcyW13Lp1m9m06UIOXAu2gfXr1zRVTmvzadu24+idUKWzLGlItDab\nJA2HuUzD5g2XpAWs8KajNfn08Ifv4MCvM8VJJ93eZDmSjkxrsknScJjpzN0TIuK2nuVHdJdHgKnM\ndDpfaQEZH9/NzTcfmMVxfHxPk+W0Np9GRvYDByZUgXuaLUjSXLQ2myQNh5mau1MGVoWk4k1MrAY2\ndK+528nExNlNltPafPrud08Cntuz/OHmipE0V63NJknD4bDNXWZuG2Qhkso2Orqc9evXMDa2jB07\n9jZaS5vzqbAzpJLmoM3ZJGk4zHoTc0nS4BR2hlSS7lfYrMmSDsHmTpIKMvWA6Reci0FSOQqbNVnS\nIdjcSVJB3HmSVKrCZ02WxNxuhSBJqpk7T5JKNT6+m95btXhNsFQez9xJUkGcUEVSqbwmWCqfzZ0k\nFcSdJ0mlKmnWZEmHtmCbO2d8klQid54kSdJ8Ldjm7jd+42Ncf/30tSxLuPvuj3LNNS9utCZJkjQ3\nHqyVpAMWbHO3Zcte4FVMX9eyZcv/argiSZI0V84wK0kH1NrcRcQIcCXwROBO4BWZeVvP+guAXwfu\nAb6ama+ts54HOpHeGek6y5IWgrKzSdJctGmGWbNJ0pGq+1YIzwWOzswzgEuBy6dXRMSPAb8LPCMz\nnw4sj4hzaq7nfqtW3UvvdL6rVt03qJeW1Lxis2lychdr127k9NOvY+3aD7Fz565BvbQ0lFo2PX+x\n2SRpONQ9LPNM4AaAzPx8RDylZ91dwBmZeVdPLXfWXM/9rrji5znqqN4Z6Z49qJeW1Lxis8khZtLc\ntGyG2WKzCby+URoGdTd3xwG7e5b3R8SizLwvM6eAHQARcTHw4Mz8ZM313M8Z6aQFrdhsatMQM2kQ\npqYesNRUGVUpNpvAg0/SMKi7udsDLOtZXpSZ949/7I4tnwAeBzxvto2Nji5lyZLFlRc5NrZs9ic1\nzBqrYY3VGIYaZ1FpNkF1+XTKKfsecBPzU075UdH/3iXXNs0aq1Fqja973Ucf0HAcffT7+cAHLmi6\nrPkqNpsAtm1bRu/Bp29/e1mx7wso9z3byxqrYY0H1N3c3QicA/x1RDwN+OpB698D/Cgzn9vPxnbu\n3FdxeQzFmTtrrIY1VqPqGhsK5EqzCarLp9e//qf47GcvY9euR7J8+b/zhjf8YrHviYX4fq2DNR6Z\nrVuPobfh2Lr1mMpqbSCfis0mgB/84F/pXBbYaaS///1b2LHjWZVtv0olv2enWWM1FmKNM2VT3c3d\nRuDnIuLG7vJF3ZmeHgx8EbgI+ExEbKZzfv8dmbmp5pokqdhsuuyyL7F9+6XACPv2TfHWt25g/frx\nQby0NJTGx3c/4Gz3kE+oUmw2AZxwwqPZvv39wLHADznhBLNJKk2tzV13fPhrDnp466BeX5IOpeRs\n8po7aW7aNKFKydkE8JjH7OdrX3sJ0430Yx6zoclyJB2CzZUkFaRlZyGk2jlB2uC0qZGW2srmTpIK\n4s6TpFLZSEvlW7DNnfdqkVQid54kSdJ8Ldjmznu1SCrRrbdu4/zzP9KdLfM7bNx4HitXOmmBJEma\n3YJt7py0QFKJ1qz5MN/73v9gerbM8877fb7ylV9vuixJkjQEFjVdQFPGx3fTOWMHTlogqRQ/+MEK\neg88dZYlSZJmt2DP3DlpgaQSLV78Le6778BsmYsX/1vDFUmSpGGxYJs7Jy2QVKKzzjqev/u7twGP\nAP6Ds846vumSJEnSkFiwzZ0klejKK1/Ib/3W9Ey+OKpAkiT1zeZOkgriqAJpbry1kSQdYHMnSZKG\nlrc2kqQDFuxsmZIkafh5ayNJOsDmTpIkDS1vbSRJBzgsU5IkDS1vbSRJB9jcSZKkoeUkRJJ0gMMy\nJUmSJKkFbO4kSZIkqQVs7iRJkiSpBWzuJEmSJKkFbO4kSZIkqQVs7iRJkiSpBWzuJEmSJKkFbO4k\nSZIkqQVs7iRJkiSpBWzuJEmSJKkFbO4kSZIkqQVs7iRJkiSpBWzuJEmSJKkFbO4kSZIkqQWWNF1A\nUyYnd7Fu3Wa2bx9lxYpJJiZWMzq6vOmyJEmSJGleFmxzt27dZjZtuhAYAaaADaxfv6bhqiRJkiRp\nfhbssMxt246j09gBjHSXJUmSJGk4Ldjmbnx8N50zdgBTjI/vabIcSZIkSToiC3ZY5sTEamBD95q7\nnUxMnN10SZIkSZI0bwu2uRsdXc769WsYG1vGjh17my5HkiRJko7Igh2WKUmSJEltYnMnSZIkSS1g\ncydJkiRJLVDrNXcRMQJcCTwRuBN4RWbe1rP+XOCNwD3AezPzqjrr6eVNzKWFq+RskrRwlZ5N7jtJ\n5at7QpXnAkdn5hkR8VTg8u5jRMSS7vKpwI+AGyNiU2buqLkmwJuYSwtcsdkkaUErOpvcd5LKV/ew\nzDOBGwAy8/PAU3rWPR74Rmbuycx7gM8CZ9Vcz/28ibm0oBWbTZIWtKKzyX0nqXx1N3fHAbt7lvdH\nxKLDrNsLHF9zPffzJubSglZsNkla0IrOJvedpPLVPSxzD7CsZ3lRZt7Xs673kM8yYFfN9dzPm5hL\nC1qx2SRpQSs6m9x3kspXd3N3I3AO8NcR8TTgqz3rbgEeGxHLgX10hha8faaNjY4uZcmSxZUUNja2\njA9/+CWVbGsQxsaWzf6khlljNaxxICrNJqg2n6YNw7+zNVbDGqsxDDXOouhsct+petZYDWs8YGRq\namr2Z81Tz6xPP9V96CI6FwI/ODOviojnAG+mM4D76sx810zb27Fjb+XFjo0tY8eOvVVvtlLWWA1r\nrEbVNY6NLRuZ/VnVqjqboPp8WojvhTpYYzUWao2DzqdhyCZYuO+HqlljNRZijTNlU61n7jJzCnjN\nQQ9v7Vn/MeBjddYgSQczmySVyGySdKS8ibkkSZIktYDNnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDN\nnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDNnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDNnSRJkiS1gM2d\nJEmSJLWAzZ0kSZIktYDNnSRJkiS1gM2dJEmSJLWAzZ0kSZIktYDNnSRJkiS1gM2dJEmSJLWAzZ0k\nSZIktYDNnSRJkiS1wMjU1FTTNUiSJEmSjpBn7iRJkiSpBWzuJEmSJKkFbO4kSZIkqQVs7iRJkiSp\nBWzuJEmSJKkFbO4kSZIkqQWWNF3AIETECHAl8ETgTuAVmXlbz/pzgTcC9wDvzcyrCqzxAuDXuzV+\nNTNfW1qNPc97N3BHZv72gEvs59/xNOAPu4vfA16cmXcXVuMvA68H9tN5P75rkPX1ioinAm/LzLMP\nerzxz0xbmE+DqbHneebTkdVYRD6ZTfUzmwZTY8/zzKYjq7GIbOrW0mg+LZQzd88Fjs7MM4BLgcun\nV0TEku7ys4BnAq+MiLHCavwx4HeBZ2Tm04HlEXFOSTVOi4hXAf9l0IX1mK3G9wC/kplnATcA4wOu\nD2av8e3AauBM4A0RcfyA6wMgIn4TWA8cfdDjpXxm2sJ8qrnGaeZTX4rPJ7NpYMymmmucZjb1pfhs\ngjLyaaE0d2fSeTOSmZ8HntKz7vHANzJzT2beA3wWOGvwJc5Y413AGZl5V3d5CZ2jFoM2U41ExCrg\nNODdgy/tfoetMSJOAe4AXh8RnwJOyMxvlFRj15eBUeCY7vLU4Ep7gG8Caw7xeCmfmbYwn6phPtVc\nY1cJ+WQ2DYbZVA2zqeYau0rIJiggnxZKc3ccsLtneX9ELDrMur1AE93+YWvMzKnM3AEQERcDD87M\nT5ZUY0Q8HHgz8DpgpIHaps30//ohwCrgj+kcOXlWRDxzsOUBM9cI8C/AF4GvAh/NzD2DLG5aZm6k\nM7zhYKV8ZtrCfKq5RvNpTorPJ7NpYMymmms0m+ak+GyCMvJpoTR3e4BlPcuLMvO+nnXH9axbBuwa\nVGE9ZqqRiBiJiLcDPws8b9DFdc1U4y8BJwJ/A/x34EUR8ZIB1wcz13gH8M3M3JqZ++kcATr4yM8g\nHLbGiPhJ4Dl0hjw8GnhYRJw/8ApnVspnpi3Mp2qYT9UY5nwq5fPSFmZTNcymagxzNsEAPzMLpbm7\nEfgFgIh4Gp2uftotwGMjYnlEHEXnFOmWwZc4Y43QGe98dGY+t2eIwaAdtsbM/JPMPC0zVwNvA/4q\nM99XUo3AbcCxEXFyd/npdI70DNpMNe4G9gF3ZeYU8AM6wwyadPDRxFI+M21hPlXDfKrGMOWT2VQv\ns6kaZlM1himboMF8GpmaampI6uD0zLDzU92HLgJOpXOK/qqIeA6d0+IjwNVNzLAzU410TjPfBHym\nu24KeEdmbiqlxt4ZfyLipUA0POPT4f5fPxP4g+66f8zM3yiwxlcBL6NzvcCtwNru0bKBi4hx4NrM\nPKM761gxn5m2MJ/qr9F8qrTGIvLJbKqf2VR/jWZTpTUWkU3dWhvNpwXR3EmSJElS2y2UYZmSJEmS\n1Go2d5IkSZLUAjZ3kiRJktQCNneSJEmS1AI2d5IkSZLUAjZ3kiRJktQCNneqTUQ8IyI29/nc8Yj4\n1hy3vzkizppfdZIWKrNJUqnMJx0pmzvVbS43UvSmi5IGxWySVCrzSfO2pOkCtLBExGLgncATgIcB\nCTyvu/qYiPgAEMA3gZdn5u6IeArwR8AxwO3AqzJzW882HwH8JbAUuA/4tcz8woB+JUktYDZJKpX5\npLnwzJ0G7Qzgrsz8GeBxdELlF7rrHgpckZk/DdwKvCkiHgRcBVyQmU8BLu8u93o5cF1mng78FnBm\n/b+GpJYxmySVynxS3zxzp4HKzM9ExB0R8Vrgx4HHAsd2V389M7d0v/8L4M+BU4DHAB+JiJHuumN5\noE8CH4qIJwMfA/60xl9BUguZTZJKZT5pLjxzp4GKiHPpDAP4IfBnwGeA6eC5t+epI8A9dN6jt2bm\nkzPzScCTgaf3bjMz/xF4PHAD8ALgo3X+DpLax2ySVCrzSXNhc6e6jRy0/CzgA5n5PuAHwFnA4u66\nx0fEE7vfvwz4BJ1x5SdExPRwgVcAf9W7wYj4A+AlmbkBuBh4UuW/haS2MZsklcp80ryNTE05yY7q\nERHPoHPa/0d0gmoK+Dyd8eH7gbuA/wBuAa4Gru9+/zjgK8ArM3NfRDwV+GPgaGAPnTD6t4j4e+B3\n6IwxvxZY1t3u2zLz/wzo15Q0ZMwmSaUyn3SkbO4kSZIkqQUclilJkiRJLWBzJ0mSJEktYHMnSZIk\nSS1gcydJkiRJLWBzJ0mSJEktYHMnSZIkSS1gcydJkiRJLWBzJ0mSJEkt8P8DTncvGqFmwl4AAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa831470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "many_scatters([actual_1, actual_10, actual_11], [predicted_1, predicted_10, predicted_11], \n",
    "              [0.5, 0.5, 0.5], [\"Typical\", \"Avoids FP\", \"Avoids FN\"], (1, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы описали разные характеры векторов вероятностей. Далее мы будем смотреть, как метрики оценивают разные векторы предсказаний, поэтому обязательно выполните ячейки, создающие векторы для визуализации."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Метрики, оценивающие бинарные векторы предсказаний"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Есть две типичные ситуации, когда специалисты по машинному обучению начинают изучать характеристики метрик качества: \n",
    "1. при участии в соревновании или решении прикладной задачи, когда вектор предсказаний оценивается по конкретной метрике, и нужно построить алгоритм, максимизирующий эту метрику.\n",
    "1. на этапе формализации задачи машинного обучения, когда есть требования прикладной области, и нужно предложить математическую метрику, которая будет соответствовать этим требованиям.\n",
    "\n",
    "Далее мы вкратце рассмотрим каждую метрику с этих двух позиций."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Precision и recall; accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для начала разберемся с метриками, оценивающие качество уже после бинаризации по порогу T, то есть сравнивающие два бинарных вектора: actual и predicted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Две популярные метрики - precision и recall. Первая показывает, как часто алгоритм предсказывает класс 1 и оказывается правым, а вторая - как много объектов класса 1 алгоритм нашел. \n",
    "\n",
    "Также рассмотрим самую простую и известную метрику - accuracy; она показывает долю правильных ответов.\n",
    "\n",
    "Выясним преимущества и недостатки этих метрик, попробовав их на разных векторах вероятностей."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_score, recall_score, accuracy_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Алгоритмы, разные по качеству:\n",
      "Perfect: precision = 1.0 recall = 1.0 ; accuracy = 1.0\n",
      "Typical: precision = 0.857142857143 recall = 0.8 ; accuracy = 0.833333333333\n",
      "Awful: precision = 0.181818181818 recall = 0.166666666667 ; accuracy = 0.208333333333\n",
      "\n",
      "Осторожный и рискующий алгоритмы:\n",
      "Typical careful: precision = 0.857142857143 recall = 0.8 ; accuracy = 0.833333333333\n",
      "Typical risky: precision = 0.8 recall = 0.857142857143 ; accuracy = 0.807692307692\n",
      "\n",
      "Разные склонности алгоритмов к ошибкам FP и FN:\n",
      "Avoids FP: precision = 1.0 recall = 0.466666666667 ; accuracy = 0.724137931034\n",
      "Avoids FN: precision = 0.619047619048 recall = 1.0 ; accuracy = 0.703703703704\n"
     ]
    }
   ],
   "source": [
    "T = 0.5\n",
    "print \"Алгоритмы, разные по качеству:\"\n",
    "for actual, predicted, descr in zip([actual_0, actual_1, actual_2], \n",
    "                                    [predicted_0 > T, predicted_1 > T, predicted_2 > T],\n",
    "                                    [\"Perfect:\", \"Typical:\", \"Awful:\"]):\n",
    "    print descr, \"precision =\", precision_score(actual, predicted), \"recall =\", \\\n",
    "        recall_score(actual, predicted), \";\",\\\n",
    "        \"accuracy =\", accuracy_score(actual, predicted)\n",
    "print\n",
    "print \"Осторожный и рискующий алгоритмы:\"\n",
    "for actual, predicted, descr in zip([actual_1, actual_1r], \n",
    "                                    [predicted_1 > T, predicted_1r > T],\n",
    "                                    [\"Typical careful:\", \"Typical risky:\"]):\n",
    "    print descr, \"precision =\", precision_score(actual, predicted), \"recall =\", \\\n",
    "        recall_score(actual, predicted), \";\",\\\n",
    "        \"accuracy =\", accuracy_score(actual, predicted)\n",
    "print\n",
    "print \"Разные склонности алгоритмов к ошибкам FP и FN:\"\n",
    "for actual, predicted, descr in zip([actual_10, actual_11], \n",
    "                                    [predicted_10 > T, predicted_11 > T], \n",
    "                                    [\"Avoids FP:\", \"Avoids FN:\"]):\n",
    "    print descr, \"precision =\", precision_score(actual, predicted), \"recall =\", \\\n",
    "        recall_score(actual, predicted), \";\",\\\n",
    "        \"accuracy =\", accuracy_score(actual, predicted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Все три метрики легко различают простые случаи хороших и плохих алгоритмов. Обратим внимание, что метрики имеют область значений  [0, 1], и потому их легко интерпретировать.\n",
    "\n",
    "Метрикам не важны величины вероятностей, им важно только то, сколько объектов неправильно зашли за установленную границу (в данном случае T = 0.5).\n",
    "\n",
    "Метрика accuracy дает одинаковый вес ошибкам false positive и false negative, зато пара метрик precision и recall однозначно идентифицирует это различие. Собственно, их для того и используют, чтобы контролировать ошибки FP и FN.\n",
    "\n",
    "Мы измерили три метрики, фиксировав порог T = 0.5, потому что для почти всех картинок он кажется оптимальным. Давайте посмотрим на последней (самой интересной для этих метрик) группе векторов, как меняются precision и recall при увеличении порога."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_recall_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3IAAAFRCAYAAAAxcJ9QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4XNW18OHfFM2o9271dixbttw7BptqMDWUUBMIhJDG\nzU1yCffLTbncQBLSE5JAQoDQIXSDqW7YxrjJsi3bR5Zt9S5ZfSRN+/4YSXbc1EZzZkbrfR4eLGnm\nnDUqa846e++1dU6nEyGEEEIIIYQQvkOvdQBCCCGEEEIIIUZHCjkhhBBCCCGE8DFSyAkhhBBCCCGE\nj5FCTgghhBBCCCF8jBRyQgghhBBCCOFjpJATQgghhBBCCB9j1DoA4X0URfk9sHzgw2nAUaAXcAKL\nVVXtG8WxrgQuVFX1P8YQRzqwX1XVsNE+VwjhuxRFMQKVwB5VVS8fx3F+ChxWVfW5Uz4fAzSpqjri\nm5mKomwA0oC2gU/pAKeqqnMURXkauAhoxJUnTUAZcI+qqs1jjV8I4X18ND8tBOaoqmo56TmdwHRV\nVSvH+hqE9qSQE6dRVfX+wX8rinIUuEVV1aIxHusd4J1xhCMbHQox+VwLFANzFUVRVFVVx3IQVVV/\nfJYv6Rh9bnEC31VV9Y2zfO03qqr+ZvATiqL8CvgLcMMozyOE8G6+mJ/Sgd8DXz3l88LHSSEnhqMb\n+A9FUW4BvqGq6tKBj9OAz4AMoAf4HbACCAb+n6qqbyiK8iXgelVVr1QUJQH4KzAVsAOPq6r6R0VR\nFgG/wHUXOwn4SFXVezz4GoUQ3uXrwIvAYeA/gPsURXke2K2q6q8BFEX5GnC+qqo3K4ryVeBbgA1o\nAL6pqmqZoihPAftUVf2NoijXAf8HdAM7B080kJf+CcQMfOo9VVV/dJa4dKN4DZ/gymtCCP/ii/np\n98AdiqJcp6rq6yN4vPARskZOjMarQJaiKFMHPv4K8JSqqlbAADSrqjoPuAn4x8D0ADhx1+cvgKqq\naj6wBLhHUZQsXAnuf1RVXQxMB65WFGW2Z16SEMKbKIoyDdc0oJdxXcDcrihKFPA34EsnPfTLwBOK\noqwAvofromk2rgust045ZjzwJHCtqqrzgYqTvnwPcGQgdy0HchRFOdt07kcVRdmtKErRwP8vO8tr\nCALuANaP4qULIbycD+enpoH4nlAUZcpYXrvwTlLIiREbKNj+jqsA0+NKVI+f9JA/DTxuH7CXE+vs\nBl0IPDHwmA5VVWeqqnp04DhRiqI8CPwZCAJCJ+6VCCG82NeAd1VVbVdVdSdQDtyrquoGwKwoyhxF\nUfKBWFVV1wOXAS+rqtoKoKrqM0DywBrbQcuAvSdNgTo5b70PfEFRlHeBe4EfqKraeZbYvq+q6hxV\nVWcP/P/9k772n4MXUcDnQDPw4Ni/DUIIL+Sr+QlVVT8GngaeUxRFRuP8hEytFKP1BLAd2IRrSkDV\nSV+zn/Rvwykfg2tawdCcbEVRMnFd7HwMFOFKWK/gutslSUaISUZRlGBcI1mWgfW5OiAM+IaiKI/i\numv9JaBv4N9w5huSeiDgpI+dpzxuKDepqrpzIBddBKwEdiiKcrWqqttGGf6/rZETQvgXH89Pgx7E\ntSTmv5E1cn5BRuTEqAwUbp8Bv8U1VfJkdwAoijIHUICNp3z9I+DOgcdE4FpDkgvMAR5QVfVNIAXI\nwVUIghR0Qkwmt+Hq1pakqmqWqqqZQDaui6UbgWeAq4DrgacGnvMBcJOiKLEAiqLciWuad9lJx/0U\nmKYoyoyBj788+AVFUR4BfqSq6tsD3XVLgLyJeoFCCJ/l8/lpYGbVLbimewaN9TjCe0ghJ4Zzpjs2\nT+H63XnvlM8vVRRlF67plzeqqtp+yte/hStZFeNKXD9TVXU38AhQpCjKduABYDOuYu5s5xdC+Kev\nAb8++RMDeeQPwH+oqtoA7AaKVVWtH/j6x7huLK1TFGUfcDtwxcDTnQOPacZ18fKCoig7cXVwG/Q7\nYJaiKHsVRdmBa7uVF88Q27lykeQpIfyfX+QnVVVLcRVyUgP4AZ3TKe8/YuQG1sb9CTimquqjJ33e\nAcSoqnpcs+CEEEIIIYSYJEZUjSuKslBRlNO6bymKcqWiKNsVRdmiKMrd7g9PeBNFUUJxrWnLYKCx\nyUmcyDRIoQHJT0IIbyS5SQgx0YYdkVMU5fu4hoK7VFVdctLnjcBBYC5gAbYAV6iq2jRx4QohxAmS\nn4QQ3khykxDCE0YyIleGaxf7U+UDhwfayFtxrWs6td28EEJMJMlPQghvJLlJCDHhhi3kVFV9A1fb\n+FOFAyc3s+gEItwUlxBCDEvykxDCG0luEkJ4wnj2kevAlZAGhQFtwz3J6XQ6dTr3LqWq72rigQ8e\nxua085MV3yE3JtOtxxejY7XZufG/3yU0yER+ZrTW4YgJFh0eyNeum+lt6yMnJD/96fOn2VT+OQ9d\n+D2U2OzxRymGpVa08r0/fMqUuBDSEsOHf4KYNMwmA7evyic+Kni4h3pTfvLYtdPPNv6B4vqDPLb6\n/4gLiRldlEL4uR88tpmSoy28+ehVGPSapYhxn3g0hdypJzsI5CiKEgn04Joa8Ohpzzr1IDodTU1n\n25R+bAwEcuf0W/hL8VP8fNOf+a953yI6MOq0x8XFhbn93CM1mc5dXt+Bze5k8cwkblie5bHznmwy\nfb+95dwa80h+KoiYziY+52P1M6Kd8eOJ16M/K0//XrjzfI1NXQDMzYvjmvNOzyfyfZzk57LZhz1W\nXFyYe841NppdO+VH5FNcf5D16nZWpC4b1XPPxZveZ7wpFvCueCSWMxuMpaOrj0CTgdaWLk1jGa/R\n7CHhBFAU5WZFUe5WVdUG/CfwIa7Fun9XVbVu3BGN0fSYqVyfexWd/V38de/T9Np6tQpl0iuvc/2x\n5qZEahyJmEQ8kp+mRuUSEhDM7sZi7A77eA8nRsBqdwAQYJQtj4RP0uzaaWbsdHTo2NO0byIOL4RP\ns/TZCDKPZ2KidxjRK1BVtQJYMvDvF0/6/LvAuxMT2uidn7KEhp5GNtV8xlMlL3LvzC+h18mbv6eV\n13cAkJMqhZyYeJ7MTwa9gdlxM9hc+zmH244yNTrXnYcXZ9BvdRVyJqNB40iEGB2tr50izGFkRaRz\npK2cjv5Owk2ajkwK4VUsfTYiQ81ahzFuflXl6HQ6rs+9ivzoPPa3HOSNMq+pMSeV8rpOAox60hLk\nTUP4n3kJswDY1bBH40gmB6vNNfIpI3JCjN6suAKcONnXdEDrUITwGk6nE0ufnUCz798g9Lt3RoPe\nwF3TbyUxOJ51VZ+yuWab1iFNKlabnZrmbtLiQzEY/O7XSwiyIzOJMIVT1LQfm+NMTemEO1ltMrVS\niLEqjCsAYE/Tfo0jEcJ79FsdOJxOv5ha6ZfvjMEBQdxXeCchAcG8XPomh1oPax3SpFHV2I3d4SRD\nussJP6XX6ZmbUIjFZuFga6nW4fi9finkhBizmKBoUkOTUY+X0WO1aB2OEF7B0u+6CRsshZz3ig2K\n4aszvoQeHX/f/xwN3Y1ahzQpDK6Py0iSaZXCf81NKARgp0yvnHCDI3KyRk6IsSmMm4HdaWd/y0Gt\nQxHCK1j6XIVcoEkKOa+WE5nJLVOvx2Kz8Je9T9HZp12L0clisGNlRqIUcsJ/pYelEhsYzd7mA/Tb\n+7UOx68NrZEL8Ou3KyEmzKx41/TKYpleKQQAPX0yIuczFibN5bL0lTRZWvj1lidkTcsEK6/vwBSg\nJykmROtQJq0f/vC/zvq15557mkOHZNH7eOl0OuYmzKLf3s++ZrnLPZGGplbKmlufJ7lJG4nB8SQE\nx1HSosqNJyGA3j7XDcKgk5qd+Gp+mhTvjFdkXcLsuBkcaDrMi+rrOJ1OrUPyS31WO7XNPaQlhKHX\nj3uzejFG//d/vzzr12677ctMnTrNg9H4r6HulY3FGkfi34amVsqInM+T3KQNnU5HYVwBVodV1vUK\nwUlTK08akfPV/OT7Y4ojoNfpuWPaTXTs7WBb3U4Sg+O5OP0CrcPyO1WNXTicTp+eVvnKujJ2HBrf\nekqDQYfdfuJmwfyp8dy4Muecz1m7dg2bNm2gp6eHjo42vvzlu3nyycdJTU0jIMDE97//II888hCd\nna41iPff/z2ysrJZs+ZN3nzzdRwOB8uWLeeBB77L1VdfyltvfcDrr7/K+++/i8GgZ+rU6dx//3d5\n+OGfctFFlzJnzjweeeSn1NbW4HA4uemmW1m58iK+9a17yc3N4+jRI/T09PDQQz8nISFxXN8Pf5Uc\nmkhSSAIlLYew2CwEGYO0DskvWWVEbog78tOphstP7spNd9311aHc9Pzzz/Ovf70uucmDZsUV8GHF\nevY07R/qZCmEuwyXm069LhqJibp2ioubxab171Hx6Zv8vdhM1cUX/lt+8rVrp0lRyAGYDCb+67z7\neOCDR3jryFrigmOZJcnMrcrrXH8omdKxckz6+nr5/e//zPHjrdxzz5dwOBzceedXycnJ5S9/+SPz\n5i3gmmu+QHV1FQ8//FN+9rNHee65f/Lssy8TEBDA448/Rk9PD+AaDV27dg3f/e4PmDo1nzfffA27\n3T50rrfeep3IyGj+538eoqenh6985Tbmzp0HwLRpBXz729/liSf+zMcff8Ctt35Ji2+HT5iXMIt3\njn5AcVMJi5LmaR2OX+ofWiMnzU604o7cZLFYGMxNb775Jv/5nw9IbvKgtLAUosyR7Gs+iM1hw6if\nNJd/ws+NNj89/vhf2PDha6Qt/Rbfun42O9a/8m/5ydeunSbVX3JUUARfm3knv9n9Z54peZHoufeR\nFpaidVh+o7ze1egk3YdH5G5cmTPsHaDhxMWF0dTUOernzZo1B4CoqGjCwsKoqKggNTUNgKNHy9i9\neyfr1n2E0+mks7OD2toasrOzCQgIAODee79BcHDw0PEefPBHvPTSc9TV1VJQMPPfphRXVBxj/vyF\nAAQHB5ORkUlNTTUAeXkKAPHxCRw/3jqG78DkMSe+kHeOfsDOhj1SyE2QE10rZUTOHflpLNyRm072\n8MMP8+c/Py65yYN0Oh2z4gpYX72Zw8ePkh+Tp3VIwo8Ml5vGel00EqPNT1VVVcTEp6LTGwkyGU7L\nT7527TTp3hlTw5L58rSbsTps/LX4adr62rUOyW+U13diNhlIjA4e/sHiNKrqaprR2tpCd3c3UVFR\n6PWuP9H09ExuuukW/vCHv/K///tzLrnkcqZMSaGiogKbzTXX+4c/fICGhgbAlXTeeedNvv/9/+aP\nf3wcVT1EScm+oXNlZGSxZ08RAD093Rw9eoTk5MGbGrK+caTig2NJD0tFPV5GZ790xZ0IsiG49tyR\nm5qbmxjMTa+88orkJg2c2Bx83zCPFMJ3jDY/paam0txYg9NhJyjQeFp+8rVrp0n5zlgYN51rci6n\nvb+Dv+59mj7p4jRuvf026lq6SZdGJ2PW0tLC/fd/nQce+A7f+96D6PUnppLdccedfPLJR3zrW/fy\nve99m6ysbCIjI7n11jv4xjfu4b777mLq1HwSEhIYTCbZ2dl8/etf4f777yMmJoZp005MJb7qqmvp\n6Gjn61+/m29/+z7uuuurREZGotPJz2605iYU4nA6KGqUi6OJ0C8jcppzR26KjY1jMDfl5eVJbtJA\ndmQGoQEhFDeX4HA6tA5HCLcYbX6Kjo6mYNFqqrb+hYf+59un5Sdfu3bSadDB0TlRw6vDOXlo1+l0\n8sKhf7G1bgez4gr4SsFt6HUTd6EwkcPK3nDu0qo2fv78bi6Zn8oXL8z12HnPxtfOvXbtGiorK04b\n4vfEud0hLi7MX66yRp2f2vra+eGWh8mOzOA7c+4b8fM8+bPy9O+FO8/38+d3U1rVxpMPrDjjm6V8\nHyf2XO7KTSM510Txk/zklmunFw79iy212/nOnPvIicwc0zG0fH89lTfFAt4Vz2SIZSz5KS4ujJ88\nsZVdahO/+9YywkNMbo9rFLGMOzdNqjVyJ9PpdNykXEuTpYU9Tft55sBLJIWcu8NMbGAU8xJneyhC\n3zK4Pi4jyXfXxwkxFpHmCLIjMyhrO8YrpW8Sbjp3s58wUwhLkhZ4KDrfZ7XZCTDqZURGCDcojJvB\nltrtFDftH3MhJ4SvG9x+IMgPNgT3/VcwDka9kXtm3MGvdv6JnQ17RvQcs9HMjFjv3EtCS+X1ro6V\nGdKxckxWrVqtdQhiHBYmzqWs7Rgbq7eO6PFJIYnEx0vX3JGw2hwyrVJDkpv8ixKVTaAhkD1N+7ku\nZ7XcIBE+baz5ydJnx2jQ+8Xa60ldyAGEBATzwPxvc6yjcnCd4xn12Hp4+sBLvFr6FkpUDiaDdkOx\n3qi8rpMgs4H4KNlLS0w+i5LmER8ch9VuPefjDh4v5ZPKTTR0u3cvMH/Wb3Ng9IM3WyG8gVFvpCB2\nKjsb9lDVVSOdu8WkZOmzEWT2jy1tJn0hBxBoDCQ/evhWvFWdtXxUuYG15Z9wdfYqD0TmGyx9Nhpa\ne1DSItHL3T0xCel1+hFNUzLqDXxSuYkmS4sHovIPMiInhHvNipvBzoY97GncL4WcmJRchZx/lEDy\n7jgKqzIvIjowio8rN1LX3aB1OF6jsqETJ5CRJNMqhTiXuOBYAJoszRpH4jtchZx/3DkVwhtMi1EI\nMgaxrupTqjtrtQ5HCI+z9EshNymZDSZuzLsah9PBy+obaNDxU3OHq9v41UtFbCquHdrf6VjdQKMT\nH94IXAhPCDeFEaAP8MsRuZ2HGvnZP3fy2Bv7+Mc7JazbXc3eIy3UtXRjtdnHfNx+m12mVgrhRmaD\niTvyb8TqsPK3ff+kx9qjdUhCeIzN7qDf6iDI5B83CP2jHPWgGbHTmBk7nb3NJWyv383CpLlah+RR\n739eyYHy4xwoP84bnx7lknmpHK52baouhZx3uOGGq3jhhdd49NGHueiiS1mwYJHWIYkBep2euKAY\nmnqa/e5G0PqiGo7Uupoe7VKbTvt6ZKiJ2Mgg4iICiY0IIjYykLiB/0eHBZ5x/0mn04nVKlMr/cVg\nbnrwwQdZtmyl5CYNzYybzmXpK3m/Yh1PH3iJr8388oRuwSSEt+jpPXPHSl+9dpJCbgxuyLuKQ62l\nvF62hoLYfEICgrUOySOsNjsHyo8TFxnIXCWeDUU1vLrhCADBZiNxkdLoxDvIOkVvFhcUQ213PR19\nnfjLz8rpdFLV2EVsRCD/7/a52HR6Dpe30NTeS3ObhaY2C83tvRyt6aBs4MbPyQx6HdHhZuIjg1g0\nPZFF0xMw6PXYHU6c4BedxQT4y++7v7gi6xIqOqspaTnE2mMfc0XWJVqHJMSE6+l1NSULPm1qpW/m\nJynkxiA6MIrLMy/mzSPv8daRtdwy9Qtah+QRamUbfVY7s3OTuXFFDqsXp7O+qIZ1u2uYmR3jF22M\nXy9bQ1HjvnEdw6DXYXecGG2ZHT+D63LO3SJ37do1vPvu2zidTq677kZeffVFDAYDM2fO4t57v0Fb\nWxs/+9mP6epyTWP94Q//F5PJxK9+9QhWq5WWlmbuuec+rr1WWoV7u9jgGADqu5qIJl7jaNyjrauf\nLosVJTWSiFAzcXFhxIQEnPY4u8NBa0efq7hr76W53UJzWy9NA/8vKT9OSflx3tlSzhWL05mV61pT\nKGvkXNyRn041XH5yV25atux8t8Ytxk+v03Pn9Fv4xY7f8175x6SFp8j2SmJMhstNp14XjcREXTv1\nY6Rmx1N8fNDIplctPp+fpJAbo5Wp5/F5/S621H7O4qR5ZEakax3ShCsuc63rKcxxXVwFBwZwxeIM\nrlicoWFU/iMsLJz//u8fc999X+HJJ5/FbDbz0EM/YseOz9m6dTPLlp3P1Vdfx/79+zhwYD/R0THc\nfPPtzJo1h/379/KPfzwhhZwPiA9y/f3UdzYRHeofhVxVo+tNMjU+9JyPM+j1xEUGERcZRP4Zvt7S\n3st7n1fwaXEtT609RMSnrm1eZEROW+7ITb58oeTPQgKCuWfGHfx612M8c+Al/mvet4kfaMokhC8Y\nbX7CHE5U1vnccOVK8qK7fD4/SSE3Rga9gS8q1/Hb3X/hRfV1Hpj3bQx6/71r7HQ6KT7STJDZQG5K\nhNbhTJjrclYPewdoOHFxYTQ1dY76eWlp6VRXV9LWdpzvf/9+nE4nFouF2toaqqoqWL36agAKCmZQ\nUDCDY8eO8swzT7JmzVsA2Gy2ccUtPCNusJDramLauesen1HZ0AVAasL4XlBMRCC3X6KwenEGa7dV\nsLHY1VEv0E8WpY+XO/LTWEhu8m+pYVP4onIdzx58hb/t+yffm/dNzLJXrhiF4XLTWK+LRmK0+Wnz\nrhLaK7bx0euHOBAb4vP5SQq5cciJzGRR0jy21e1kY/UWVqYt1zqkCVPb3E1zey/zp8ZjNMjd8Ymg\n1+tJSppCQkIiv/3tYxgMBtauXUNurkJlZQUHD+4nOzuH4uIitm7dTHV1JVdddR0LFy7mvffeYe3a\nNQNH8q8mGv4mbmBqZV2X/2wKXtU4UMgNMyI3UlFhZm65OI/LF6fz+YEGZmbHuOW4YmwkN/m/RUnz\nqOioYlPNZ7xw6F98edrNfrFcQvi/0eanA6VHCE+Zy013XEVP7W6fz09SyI3TtdlXsK/pAGuOfcjs\n+JlEBUZqHdKEKD4yOK1SLqgmUmRkJDfddAvf/OY92O0OkpKSWbnyYm6//U4eeeSnfPDBWvR6PT/4\nwf9QUrKPP/3ptzz77FPExcXT0THYRELefL1ZpDkCo95IQ+fpnR19VWVjF8FmIzHhgW49bmSomUsX\npLn1mGJsJDf5vy/kXklVZy07G/aQEZ7GitRlWockxIiMJj/pP9rCyy8+zVN/2E5W+hSfz086DVpg\nOydqeHU4EzW0u7V2O88f+hez42Zw94zbPXrukXDHuR95bhdlNe387lvLCAse2ZQLX3/Ncu5Rndc3\nM+DpPJKfHtr2Kzqsnfxy2U88ctd7In8v+vrtfP03G8lLjeSBW+dM+PlO5a/n8vT5/PVcA+fzh/zk\nkdzU1tfOz3f8nm5rD/fPvpecyMzTHqPle9ypvCkW8K54JJYz27C3jn++d5Dv3FjIjCxtByfckZtk\njpwbLEqaR1ZEOkVN+yhpOaR1OG7XZbFSVtNO9pSIERdxQoiziwuOocdqodvm+xvxVjd14WT86+OE\nENqLNEfwlem3AfD3/c/S1nf6diFC+LJui2v7gSCTf0xKlELODfQ6PV9UrkOv0/OK+ib9dqvWIbnV\nvqMtOJ1QKOtUhHCLwYYnTT0tGkcyfpVuXh8nhNBWblQW1+ZcQWd/F0/ufw6bw7ebQQhxshMbgvtH\nEy0p5NxkSmgSK1KX0dzbygcV67QOx62Ky5qBE9sOCCHGZ6iQszRrHMn4DTY6SYsP0zgSIYS7rEhZ\nxryEWRxtr+C1w2uGf4IQPuJEIScjcuIUl2dcTJQ5ko8qNlDf7R8d6Wx2B/uPthITHsiU2BCtwxHC\nLwx2rmzq8YNCrqETg15HsuQHIfyGTqfjlqnXkxySyKaarXxet0vrkIRwi+7egamVUsiJUwUazVyf\ndxV2p52X1TfQoJGM25VVt9PTZ6MwJ0ZaEQvhJidG5Hx7aqXD4aS6qZukmGDZtFsIP2M2mLhnxh0E\nGQN5UX2Nqs4arUMSYtx6eq3oALOf7E/qH+WoFymMnU5BTD77Ww7yw60Po9e5Lm4Meh12h3sKO71O\nz3U5qymMm+6W451L8RGZVimEu0WZIzDoDRQ17ePI1vKhz+dFZXN7/o3aBTZKjW0W+qx2UmVapRB+\nKT44li9N+yJ/3fs0f9v3LA/M/zZxyN+78F09vTYCzUb0fjI4IbdQ3Uyn03Fj3jWkhCYPFXHuZHfY\naba0UNJy0O3HPpPishZMAXqmpvnn/nhCaMGgN3Bh5lLCTScuiLqt3Wyr20mzD43SuXsjcCGE95kR\nO41VGRfR0tvK0yUv4nA4tA5JiDHr6bX6TaMTkBG5CRETFMWDC/7j3z7nrj00jve28cOtD9Nn7x/3\nsU5ldzjo6LYSFWYGoKG1h/rWHmbnxhJg9J9feiG8wd3zbubq9NVDH2+t3cHzh15ld+NeLklfoWFk\nI1fZ4MppabL1gBB+7fLMi6jsrKak5RCvlrzLysQLtA5JaMzhdNLe1T90zegrunttRIb6z1ZaMiLn\nY0wG1y+fu7c46Om18Yvni/jeY1vYVFwLQPER18iATKsUYuIVxk1Hr9NT1LhX61BGTEbkhJgc9Do9\nX572RWIDo3ntwHvsbSrROiShsWc/UPnuY1t497Nyn+kJ4XQ6sfRa/abRCUgh53NOFHLuG5Hr6bXy\n65f3UFbTjk6n4+m1h/hwe+XQtgNa73wvxGQQEhCMEpVDZWeNz0yvrGrsIirMTFiw/9zdFEKcWXBA\nMPfMuAOTIYBnDrxMY0+T1iEJjRypaWfjHtdN/9c2HuW5D0ux+8CU2z6rHYcTgqWQE1ox6gzodXq3\nTa3sslh59MU9HKvrYGlBIj+5az6RoSZeWlfGoYrjpCeG+dywuRC+ak78TACKGvdpHMnwOnv6Od7Z\nJ6NxQkwiKWHJfHXerfTae/nbvmfptfVpHZLwMIfDyXMflgLwtaunkxIXyvqiGh57fT99/XaNozs3\nS58rvkA/6VgJUsj5HJ1Oh0lvot8x/kKuo6efR18soqKhk+WFSdx5RT4pcaH84La5xEYE4gQKs2U0\nTghPmTkwvXK3D0yvPFrbAci0SiEmm+UZCzk/ZSm13fW8USabhU82m4prqWjoZPH0RBbkJ/DgbXOY\nnhHFnrJmfvnibjq63d/DwV0sfa7NwGVETmjKbAgY94hce7eriKtq7GLF7CnccdnUoVas8ZFBPHjb\nXFYvyWDl3BR3hCyEGIHQgJCB6ZXVNFtatQ7nnAbX0s7OjdM4EiGEp30hZzWJIQlsqd1OTVed1uEI\nD+myWHlt4xECTQZuWJENuDbWvv+GQpYWJHKsrpOfPbuT+tYejSM9s8FCTtbICU2ZDKZxrZFr6+rj\nly/spqapm4vmpnDbJXmn7acRFWbmuuVZhMvaFyE8anb8DACvbnrS3G5hT1kzmUlhZCWHax2OEMLD\nDHoDX8iXB8zFAAAgAElEQVRZjRMnrx1+x2eaXYjxeX3jEbp7bVyzLJPI0BPLbowGPXddkc9VSzNo\nauvl4Wd3UVbdrmGkZzZYyAVKISe0NJ5CrrWjl188v5u6lh4uXZDKzRflovOTTRGF8AeFsQUD3Su9\nd53chqJanE5YOUdG7IWYrKbFKEyLUVCPl7Gv+YDW4YgJVl7fwcY9tSTHhpxxtpZOp+Oa87L48qqp\n9PTaePSlIvYeadYg0rOzDKzhk6mVQlNmg4k+e/+o74C1tPfyixd203DcwhWL07lxRY4UcUJ4mVBT\nCHmR2VR0VtHihdMrrTY7m4prCQ0KYEF+vNbhCCE09IWc1eh1et4oexebw6Z1OGKCOJyuBidO4NaL\n8zAazl4+LC9M5v4bZuJ0wouflHkuyBE4MbVSmp0IDZn0Jpw4R5U0m9ss/OKF3TS19XLV0gyuW54l\nRZwQXmqoe2WT943KbT/YSJfFynmFSQQY/efNUAgxeokhCZw3ZRGNlmY2VW/VOhwxQbbsq+NobQcL\n8uPJT48a9vEzsmKYmR1DQ2sPdS3dHohwZHp6Bwo5k4zICQ2ZB/aS6xth58q65m5+/sJumtt7ufa8\nTK45T4o4IbxZYVyB13avXLe7Gp0OVsyaonUoQggvcHnmxQQZg3iv/BO6+r3nol24R3evlX9tOII5\nwMCNK3JG/LzZubEAFB32numV0uxEeIXRbApe39rDDx7bTGtHH9dfkM2VSzMnOjwhxDgNTa/sqKLF\nclzrcIYcre3gWF0nhdmxxEYGaR2OEMILhAaEcHnGhVhsFt499pHW4Qg3e/PTY3T2WLlyaQbR4YEj\nft7M7Bh0OtjjTYVcvxRywguMtJCrbe7mF8/vprWjly+uzOHyRemeCE8I4QZD3SubvGdUbt3uagAu\nlG1JhBAnWZ6yhPigWDbXbqOuu0HrcISbVDZ0sm53NQnRwVw8L3VUzw0LNpGbEsmRmnaOd/ZOUISj\n449r5IYtSRVF0QF/BgqBXuBuVVWPnvT1W4H/BGzAU6qq/nWCYhUDhqZWnqOQq27q4tEXi+jssXLv\ntTNYqMheT8K/+HtuKowr4OXSNylq3MdFaedrHQ4dPf1sP9hIQnQw+RnDr5EQYrLy99x0Jka9kWtz\nruDxfc/wetkavlH4Fa1DEuPkdDp5/qNSnE649aJcAoyjH/uZlRNLaVUbOw40MDsregKiHB1Ln6tr\n5WQbkbsGMKuqugR4EPjNKV9/FFgJLAO+qyhKhHtDFKcabkSusqGTX77gKuLuuFRh9bIsT4YnhKf4\ndW4KM4WSG5lFeUclrb3aT6/8tLgWm93ByjlTTtt3Ugjxb/w6N53NjNhpKFE5HGhRKWlRtQ5HjNO2\nkgYOV7czJy+OgqyYMR1jdp5rndzn++vdGdqYTdY1csuA9wFUVf0cmHfK14uBKGBwwYTsCjnBzPqz\nj8iV13fw6ItFdFus3LlqKhfMloYEwm/5fW6aPdi9UuM95RwOJxuKajAHGFhakKRpLEL4AL/PTWei\n0+n4Qu6V6NDx+uF3sDvsWockxsjSZ+OV9WUEGPV8ceXIG5ycKiEqmOTYEPaUNtLXr/3vg6XPhsmo\nP+f2Cb5mJCVpOHDy9uw2RVH0qqo6Bj4uAXYBXcDrqqp2uDlGcYrBEbljHZUYdCfm+da1dvPahqP0\nm+2sOi+N2JQuDraUUmsPor3NMqJjR5jDSQ5NnJC4hXAzv89Ns+IKeFl9gx31u0kOGfvf5ZlyQHev\nlThzPOmxw0+7Li5rpqWjjwtmTyE40H/uZAoxQfw+N53NlNAkliTPZ0vtdjbXfs75KUu0DkmMwdtb\njtHe3c8152WOu7HV7NxY3v2sggPlrczO03aZj6XPRnBQgKYxuNtI3pE7gLCTPh5KRoqizACuANKB\nbuB5RVG+oKrqa26PVAwJCQgG4P3yT07/YjaYgPXtO1lfPPpj69Dx0JIHiQqMHF+QQkw8v89NYaZQ\n8qKyUY+X8afiv7v9+I7eIPK6r+bCOWkUZMWcdcrkYJOTlXNkhF+IEfD73HQuq7MuZVdDMe8e+5D5\nCbMIHrhmEb6hprmbj3dWExcZyKqFaeM+3qyBQm53aZP2hVy/nbDgyVfIbQFWA/9SFGURcPIcn3ag\nB+hTVdWpKEojrukC5xQXFzbcQyaMP5z7wqhF6Mx2LLYTXYCq6jvZsLuaqRlRzJ82tjv3pS3H2F27\njzZdC3lxo+tOdDb+8P2Wc3stt+cm8Oz3byTn+sbi29lWXYTD6Rj2saPx0o516AO7OFC3l32vtpEQ\nHczlSzK4aEE64SGmocdVNXRSUn6cguwYZk8b+bRKb/s++uK5PH0+fz2XBnw+Nw3nXLHEEcZ101fx\nwt432dDwKV+afb1msWjBm+IZbSxOp5Pf/WsvdoeTr11XSHLS+G/qx8SEEht5gD1HWoiMChlT0xR3\n6e2zER8d7FU/o/EaSSH3BnCxoihbBj6+U1GUm4EQVVX/rijKE8BmRVH6gCPA08MdsKmpc6zxjktc\nXJjfnHte1L9Puf/dhmJsdWZuXLWAlLjQMZ07ShfD7tp9HKo9RqY5e9wx+tP3W849/Hk14PbcBJ7L\nTyP9WRkIYmns+KYnnelcLx3pgfz1ROdWkZc0lx0HWnhqzQGee/8QC/LjWTknhcykcF77pBSA82Yk\njfh748nfQ389l6fP56/nGjyfh/l0bhrOSH5+C6Lm80HgJt4/vIF50XOID56YkRgt32/PxJviGUss\n2w82sLesmZnZMWTGh7jttSydmcxbm46waWcFM7Nj3XLM0bLZHfTbHIQEGr3qZzRewxZyqqo6gftO\n+XTpSV9/HHh83JGIMWvt6GXf0RayksNJiQ8d/glnMbg2rrbbO7oLCXEukpvGx2k1E9yZTVdEKVkz\n2vniyqVs3lvH+t01bNlXz5Z99WQmhVPX0k1kqInZudq8+QrhayQ3QYAhgGtyLufJ/c/xRtl73Dvz\nS1qHJIbR22/j5XVlGA06br4o163HXjbLVcjtONioWSE32LEyONC/plb6T9uWSWzz3jqcTlhemDyu\n40SZIwk0BFLbJYWcEP7O4XQS0jkVs8HEBxXrCAhwcumCNB6+dxHfubGQwuwYyus66O23c8GsKX7V\n5UsIMfFmx80gOyKTvc0lqK1lWocjhrFmawXHO/u4bGE6CVHuXdeopEURE25m9+FmrDb3LhMYqROF\nnH817JJ3Zh/ncDj5dG8tZpOBBfnx4zqWTqcjOTSBRkszVofNTREKIbyR0wlGp5kVqefR2d/Fxuqt\nAOh1OmZkxXD/DYX8/GuLufPyqaxaNP4F70KIyUWn03H9wHYEr5W94/Z1vr7M4XDidHrPrhP1rT18\nsL2SmHAzVyxOd/vxdTodc5V4LH02Sspb3X78kRjcDDxERuSENzlQ3kpLRx8L8xMINI3/LkNySCIO\np4P67kY3RCeE8FYOhxO9TseFqcsJMgbxUeUGek9qoAQQFxnEeTOTCTAaznIUIYQ4u7TwFBYkzqGm\nq47PandoHY7mnE4n63dX883fbeI//riZx97Yx0c7q6hs6MShUWHndDp54aNS7A4nN63MxRwwMfl+\n/sBgw85D2lxf+uvUSv8aX5yENhbXAuOfVjkoOdTVla6uu57UMPccUwjhfZxO113S4IAgLkxdzppj\nH7C+agurMi/UOjQhhB+5Kvsyihr38s7RD5iTUEiQMVDrkDTR1tXHP947yP6jrQSbjRgNenapTexS\nmwAINhvJS40c+i89MRSDfuLHW4oON7P/WCvTM6KYq0zc9gBZSeHEhJspOtyE1ebwePdKf51a6V+v\nZpJp7+5nz+FmUuJCyUxyT1eu5JAEAFknJ4Sfczid6Ae2jVuRupT11Z/ySdVGzk9ZLPs+CSHcJtIc\nwSXpK1hz7EP+UPQ4EeYItx07ONDMiqTzvf7G885DjTzz/iG6e20UZEZz5+X5RIaaaG7vRa1so7TK\n9d+esmb2lDUDYDYZyJkSgTJQ2GUmhbu9+Om32nnx48MY9DpuuTgP3Vn2EnUHnU7HvKnxfLC9ipJj\nrczycAOtHhmRE97A6XRSXObqULl1fx12h5PlhUlu++MbHJGr6a5zy/GEEN5ncG3GYN4INAZycdoF\nvHnkPT6p+pQrsy7VMjwhhJ+5MG052xt2U9lZA501bj12iC7Uawu5nl4bz39Uymcl9ZiMem67JI8V\ns6cM5d64yCDiIoNYNtN17dXa0UtpdRullW2oVW2UHGul5JhrTVmAUU92cjh5qZEoqZFkTYkY9zTI\n97ZV0NLRy6qFaSTFhIzvxY7A/KkJfLC9ih2HGj1eyPX2D6yRC/Kv0se/Xs0ksKGohmc/LOWC2VM4\nWHEco0HP4oKxbQB+JiEBwUSYwmVETgg/NrgWQ68/cQPo/JQlfFK1ifVVn7IiZRmhpol/UxdCTA4m\ng4n/Wfg9+ux9bjtmfXcjv9r1GDYvbc52qOI4T757gJaOPjKTwrh79bRhi6Xo8EAWTUtk0TTXdV1H\nd//QaJ1a1YZa2cahyjYADHodmUkDhV1aJDlTIggyj/yyvrHNwnvbKokMNbF6ScaYX+doZCaFERMe\nyJ6yJqw2u0fXXw+NyJllRE5opKa5m5fWuVr4biupp7ffzqLpCW7vwJMcmsjB1lJ6rBaCA4Lcemwh\nhPYcA83jTh7INxlMXJq+kn8dfpuPKzdyTc7l2gQnhPBLep2eIKP7rilCBqaAe1shZ7XZeX3TUT7c\nXoVOp+OqpRmsXpIxpi1cwkNMzJsaz7yprkYh3b1WDle1DxR2xzla20FZTTvvbatAp4P0hLChwm5x\niPmcx37p48PY7A5uXJkzqgJwPHQ6HfOnxvP+9kr2H2tldu7Erck71dAaORmRE1qw2hw88XYJVpuD\nYLNx6M7C+W5qcnKy5BBXIVfbXU9OZKbbjy+E0Nbg1Er9KVOylyUv5OPKjWyo3sKK1POIMLtn7a0Q\nQribUe+6hLU67BpHcsKx2nZ+8c+d1DR1kxAVxN1XTiM72X1rAkMCA5iVGzs0LdHSZ+NIbfvQOrtj\ndR2U13fy4Y4q/vjaPlLiQlBSo8hLc62ziwgxAVA8sBZPSY1kYX6C2+Ibifn5rkJux6FGjxZyvQPX\nzf62/YAUcj7itY1HqGrsYnlhMnodbNhTS0JUEHmpkW4/V3Koa0i/tksKOSH80ZmmVgIEGAK4LGMl\nL6lv8FHFeq7Pu0qL8IQQYliDhZzNqf2InMPh5P3tlbz56VFsdicrZk/hxhU5mE0TO3UwyGykIDOG\ngswYwNW85GhtB6VVbRyt7+RQeSvVTd18srsagMToYPJSIzlY0Ypep+PWSya2wcmZZCSGERsRyJ7D\nzR6dXtlzUtdKR7/2vzPuIoWcD9h/rIUPd1SREB3MzRfmsv1QAxv21LJ8VvKE/AEOFXLdsk5OCH/U\n3tUPcMapPouT5vNRxQY+rd3GhWnLiQp0/80iIYQYL6NuoJDTeGplU5uFv685wOHqdqLCzHzpsqnM\nzI7RJBZTgIGp6VFMTY8iLi6Muvp2yus6UauOo1a1UVbdzqaBbasumpdCSlyox2N0bQ4exwfbqyir\nbic/I9oj5x3cEDw4MIAuKeSEp3T29PPkmoMY9DruvWoaZpOBxdMTCTIZmZ03MR1/EoMT0KGThidC\n+KlPdrnuzp5pzyCj3siqjIt47tCrvF+xjpuV6zwdnhBCDGtoRE6jQs7pdLJ5Xx0vfHyYvn47c5U4\nvnPLXPot/ZrEcyZGg56clAhyUiK4YjHYHQ4qG7qob+lh3lTPTWs8VXyUa31je4/nvleWfhs6HQSa\nDHR57KwTz7O78YlRcTqdPPXeIdq7+7lueRYZieGA6w9z3tT4Cdso0mQIID44ltru+qG1NEII/9DT\na+XTvXVEhZmZP7CA/lQLEucQHxTLZ7U7aLa0ejhCIYQYnlHvmpKnRSHX0dPPn17fx1PvHUKvg7tX\n5/P1awqICD13gxGtGfR6MpPCWVyQ6NGOkacKGdiUu9viuZ+dpc9GkMno8amkE00KOS+2cU8te8qa\nmZoWyaUL0zx67qSQRCw2C2197R49rxBiYm3cU0uf1c5F81LO2kXNoDdweebF2J121pZ/7OEIhRBi\neHqdHoNOj83DzU72lDXzo79/TtFhV7OQn961gCUF7tvPdzIICXI1HOm2WD12TkufzWPdOT3J/16R\nn6ht7ualTw4TEmjk7tXTTusuN9GSQxPZ07SPZw68NNTid1BIQDDX516FyWDyaExCiPGx2R18vKsa\ns8kwbMfbuQmFvF+xju31u7HYehlJBooJjGa1bCYuhPAQoyHAY81OevttvPRJGZuKazEadNy4IodL\nFqR6/PrMH4QOdI7s6vVkIWcnJjzQY+fzFCnkvNDgVgP9Ngd3r55GtAa/eEpUDu+Xf8LhtqNn+Xou\ncxMKPRyVEGI8dhxq5HhnHxfNSyF4mBbMep2ea7JX8fjeZyhu2j/ic7T2HueBhK+NN1QhhBhWgN7o\nkamVZdXt/H3NARrbLKTEhfLVK6eREu/5RiH+IiTIs1MrHU4nvX02gszaTSedKFLIeaE3Nh2lsrGL\n82YmDW0C6Wk5kZk8et5PT7vTVdVZw5/2/J2ytqNSyAnhQ5xOJx9sr0Sng4vnpY7oOTNip/Gr5f87\nojveDqeDJ/c/R1HTPp7d8zqXp8jInBBiYk10IWezO3h7yzHe/awCnLBqURrXLMsiwCgrk8ZjcC+3\nbg+NyPX123GCTK0UE+9gxXHe315JQlQQN1+Uq2ksgUYz8O8Ld/MiszHpA846UieE8E6HKtuobOhi\nnhJHXGTQiJ93pjxwNvfO+BK/3vVn3i39hCBnCCtSl40xWiGEGJ7RYMRmm5g1crXN3fztnQNUNHQS\nGxHI3aunTcjevZNRoMmAQa/z2Bo5y+Aecn5YyMktBS+zdV8dAF9eNZVAk/f9whn0BrIiMqjrbqCr\nv1vrcIQQI/Th9koALl0wcY2TggOC+XrhV4gMDOe1w+9Q1Lhvws4lhBATMSLncDr5aGcVP316BxUN\nnSybkcRP71ogRZwb6XQ6QgKNdPV6ZmrlYCEXKIWcmGh9NgcAiTEhGkdydjmRmQCUtR/TOBIhxEhU\nNXRSfKSFnCkRZE+JmNBzxQRF8YPzvkGAIYBnDrzI0fbyCT2fEGLyCtAb3drspLWjl9+8vIcXPz6M\nOcDAN66dwV1X5PvllDythQQFeHBEzjVq649r5KSQ8zK2gUIu4Cxtwb1BTmQWAGUyvVIIn/DWpiMA\nXDJ/ZGvjxisrOo27C27H7nTw171P09DT5JHzCiEmF6PBfSNy2w7U86Mnt3Og/Dgzs2N46CsLmKto\nt2m2vwsJCqC714rDA/sVW/plaqXwEOvAXG9vXkibEZ6KUW+k7LgUckJ4u46eftbvrCIuMpA5eZ67\nKJkeo3Czch3d1h7+vOdJOvu7PHZuIcTk4Jpaacc5jmKgu9fKX9/azxNvH8DucHLHZQr3Xz/T6zf3\n9nWhgQE4ndDbN/HTKwenVvrjyKr3VguTlNXuSkZGg/fuSxJgCCAjPJXqrjosNovW4QghzuHT4lr6\nbQ4unpeKXu/ZvLIkeQGrMi6kubeVvxQ/RZ+936PnF0L4twCDESdOHE7HmJ5fcqyVHz25ne0HG8lO\nDucnd83ngllTZHNvDwgJdBVVnlgn1zNYyHlh74nxkkLOy1htDowGvdcnkZzILJw4OdJWrnUoQohz\nOFrbAcD8/ARNzn9F5iUsTJxLRWcVT5U8j90xMR3mhBCTj1HvamNvHeX0SrvDwQsflfLrl/fQ0d3P\ntcuz+MFtc0iICp6IMMUZhAQNbEHggXVyvUNr5KSQExPManN49bTKQblD6+Sk4YkQ3qy2pYewYBPh\nwefeAHyi6HQ6bpn6BaZG5bKv+SCvHn57XNOghBBiUIDedWE+2oYnRaXNfLyrmqSYYP7fHXO5ckkG\nBr33X3v5k6FCzgN7yQ2NyEmzEzHRbHbfKOQyI9LR6/Syn5wQXsxqc9B4vIe0xDBNR/mNeiN3z7id\nKaFJfFrzGR9VbtAsFiGE/zAaBgq5UY7ItXT0AnD9+dlkJIa7PS4xvNCBqZXdFlkjNx7eXzFMMlab\nw6s7Vg4yG0ykh6VQ2VlNr61P63CEEGfQ0NqD0wkp8aFah0KQMZCvF95FpDmCt46sZUd9kdYhCSF8\nnGlgauVoC7nBUaDBUSHheYPf+y6PTK2UQk54iNXuwOgDI3LgWifncDo41lGhdShCiDOobekGIC0h\nTONIXCLNEXy98C4CDYE8e/AVSo8f0TokIYQPCzYFAdBjHV3jtcFRoMGGG8LzQgK1mFrpfz9v36gY\nJgmrzUFfv50AL+5YebKhjcFlnZwQXqm22VXIpXpJIQcwJTSJr864A4An9j1DbVe9xhEJ4Z8ef7uE\nX76wm8bjPVqHMmHCza7ZBl3W7lE9T0bktBc61OzEc1MrA02yRk5MoHc/K6fPamdqepTWoYxIdmQG\nOnQclv3khPBKg4VcWqL3FHIASnQOt+XfgMXWy5+L/0FbX7vWIQnhdyJCTByqbOPHT+1g8946v2wy\nFGYaYyE3MJ1PRuS0M/i998SInKXfjilAj9EHli6Nlv+9Ih9V3djFu59VEBVm5trzsrQOZ0SCjEGk\nhCVT0VGJ1T7xf4hCiNGpbekhyGwgOjxQ61BOsyBxDldmXcbxvjb+UvwUvbZerUMSwq988cJc7rly\nGnod/OO9g/z1rRKPXDR7Upg5BIBu6+hGHbt6bZgC9AQY/W+Exld4co2cpc/ml9MqQQo5r+BwOHlq\n7UHsDid3XKr41C9bTmQmNqed8o5KrUMRQpzEZnfQ0NpDckyI1+5LeWn6CpYmL6S6q5a/739O9pgT\nws0WT0/kJ3cuIGdKBDsONfLjf2xHrTyudVhuEzYwtbJ7DCNyoTKtUlOBJgMGvc4zI3J9Nr/cDByk\nkPMKH+2s4lhdJ4umJ1CYE6t1OKMyuJ/cwdbDdFm7/+0/uSgTQjuNxy3YHU6SYkO0DuWsdDodN+Vd\nQ0HMVA62lvKi+rpfTv8SQktxkUE8cOtsrlmWSVtnP798oYjXNh7BZndoHdq4hZlc+a1rlCNy3b22\noWYbQhs6nY6QQKOH1sjZfWqQZDT881X5kMbjPbyx6SihQQHcfGGu1uGMWvZAw5MPKtbxQcW6f/ta\nRmQK3539TfQ6uV8ghKdVNHQCkBzjvYUcgEFv4M7pt/L7or/yWd0OciOzWJg0V+uwhPArBr2eq5Zl\nMi0zmifeLuHdzyrYvLeOOXlxzFXiUNIifWpD7O5eK+9sKWdTyVF0BaMbkbM7HFj6bLI+zguEBAXQ\n1tWPze6YsPVrVpsDm91BsB9uBg5SyGnK6XTy9NpD9Nsc3Hl5PmHBJq1DGrXQgBCuyb78tKmV9T1N\nlLdVc6BFpSA2X6PohJi8Nu2pBWBGVrTGkQwv0Gjmzum38tNtv6SoaZ8UckJMkJwpEfz0rgW8vuko\nnx9oYH1RDeuLaggNCmBWbizzlDjy06MJ8NJtkGx2B+t31/D2lmN099pAZyCI0Y3IdfcObD0gUys1\nNz0jmo93VbN1fz3LC5Mn5BxDHStlRE6426d76zhU2casnFgW5MdrHc6YXZx+wWmfq+qs4ec7fs+G\n6i1SyAnhYRX1nahVbUzPiGJKnPabgY9EfHAs8UGxlB4vw+awYdTL25MQEyHIbOTWi/P44oU5lFa2\nsbO0id2lTWzeW8fmvXUEmQ0U5sQyNy+egqxozAHaj2Q4nU6KDjfz6voyGo5bCDIbuHpZJm9tPobe\nETCqEbkTHSulkNPaqkXpbNhTw5qt5SwpSJyQUTmLH+8hB1LIaeZ4Zx8vrztMkNnAbZfkeW0zgrFK\nDZvC1NhsDjaX0tDdSEKI7xaqQviaj3dWAXDx/DSNIxmd/Jg8NlZv5Vh7BblR2VqHI4RfM+j15GdE\nk58Rza0X53Gkpp1dahO71Ea2lTSwraQBU4CemVkxzFXimZkdo8nFcHl9By9/UoZa1YZep2PlnClc\ntSyTsKAA3ttWgc5hGlXXyhMjcnIJrLWoMDPLC5NZt7uGz0rqOW+m+0flLP2un3ewFHLCXZxOJ899\nqGLps3PHZYpXtgZ3h1V5KzjUfISNNVu5Me8arcMRYlJo7+rj84MNJEYHU+AD0ypPlh/tKuQOtJZK\nISeEB+l1OnJTIslNieSmlTmU13cOFXU71SZ2qk0YDXoKMqO5YF4q2YmhEz6i1drRy2sbj/JZST0A\ns3JiuWFFNkknrfuNCDVjsQbQZe3C6XSO6Kb44IhcqIzIeYXLF6WzqbiWd7dWsKQg0e1rNS29/rsZ\nOEghp4mm9l6KDjeTmxIxYXOCvcH8KbOINEewrW4nV2ZdRpDRPwtWIbzJ+qIabHYnF89LQe9jI/25\nkdkYdAYOtpZydfYqrcMRYlLS6XRkJoWTmRTOF87Poqapm51qI7tKm9hT1syesmYMeh1T06O4YFYy\ns/Pi3JprevttvLetkg+3V9Jvc5AWH8pNK3PIzzj9xlRkmJnO/gD0QTb67P0EGs3DHn+w3b2skfMO\n0eGBnFeYzPrdNXy2v4FlM5PcevyePlcHdRmRE27T3GYBID89yucutEbDqDdw3pTFvHP0fbbV7WRF\n6jKtQxLCr1ltdjYU1RBsNrKkwL1vhp4QaDSTHZFBadsROvu7CDP5xvo+IfyVTqcjJT6UlPhQrjkv\ni/rWHg5Vt7NpdzUlx1opOdZKWnwoVy/LZFZu7LiWiTgcTjbvq+P1TUfp6O4nItTErcuzWFqQhF5/\n5uNGhpqp6AtAj2tT8BEVcgPt7qVrpfe4YlE6m/bUsmZrOYsLEtw6KtfbL2vkhJsd7+wD8NsplSdb\nmryAteUfs7F6C+enLJGtCISYQJ8faKSjx8qqhWmYfXQaSX5MHqVtRzjYWsqCxDlahyOEOElidDAz\nlAQumJlEXUs372wp5/MDDfzx9X2kJ4Rx9bJMCnNiRl3Q7T/Wwivryqhu6sYUoOfqZZlctmD4PBYd\nHgH1i74AACAASURBVAh1rpG1bms3MUFRw55rcERONgT3HoOjchuKathW0sDSGe67Ednj581O5Kpa\nA60dvYBrkae/CzOFMi9+Fk2WFg62lmodjhB+y+l08tHOqoFmAClahzNm+dEKgOQLIbxcUkwIX71q\nOv9790IW5MdT2dDJH17by0PP7GTvkWacTuewx6hp6uK3rxTzm5eLqWnqZtmMJB756mKuXpY5optR\nWVMicFpdWzd1jbBz5YkROSnkvMkVi9Ix6HWs2VqO3eG+zeqla6Vwu6ERuUlQyAGcn7qEbfU72VC1\nhekxU7UORwi/pFa2UdXYxfyp8cRE+O5o/5TQRMJMoRxsLcXhdMgovhBebkpsCF+7uoArl3Tx1pZy\ndh5q5Hev7iUrOZyrl2VSkBl92ghdR3c/b24+xsY9NTidrqUmN63MIS0hbFTnVtKicH46OCI3ss6V\nR+va0elc6+uE94iJCGTZzCQ27qll+4FGFhckuuW4vQNr5KSQE27TOlDIRYX57sXWaKSFpZAVkcGB\nVpWGniYSguO0DkkIv/PR4JYD81I1jmR89Do9+dF5bK/fTU1XPalh/tsQSgh/MiUulK9fU0BVYxdv\nbz7GrtImfvtKMdlTXAXd9IxorDYHH+2s4t3PKujtt5MUE8wNK3IozB79dEyAjORwDE5XQTaSEbmq\nxi6O1XVSmB0jUyu90BWL09m8t463t5azcFrCWddGjsaJqZW+udxgOFLIaaC1o5dAk4HgSbTQ9oKU\npRxtL2dj9VZuzLta63CE8CvN7Rb2lDWTnhhG9pRwrcMZt2nRCtvrd3OwVZVCTggfkxofyjeum0Fl\nQydvbT5G0eFmfvOyq6Br6+yjpaOP0KAAbr04m/NnJY9rE2ijQU9CWCTNQHtv17CP/7S4FsCvO4b7\nstiIIJbOSGJTcS2fH2xg8fTxj8r5+9RKmbOigeOdfZNifdzJZsUVEGmO4PO6nVhsvVqHI4Rf2VBU\ni9MJF85JGVfXOG8xNToXHToOtsg6OSF8VVpCGN/6wkx+/OX5zMqJ5UhNB+3d/axamMbP713MhXNT\nxlXEDZ0n1rUtQX1H2zkfZ7XZ+ayknvAQEzOyY8Z9XjExVi92rZV7Z0s5Dsfw6yyHY/HzrpVSyHlY\nZ08/3b22SdGx8mQGvYHzpiyi197H53W7tA5HCL9htdnZVFxLaFAAC/LjtQ7HLcJMoaSGJXOkvZxe\nW5/W4QghxiE9MYxvXz+TR+5dxC/vW8INK3LcOiMpOyEWgOaujnM+bndpM929NpbOSHRLASkmRmxk\nEEsKEqlv7WH7oYZxH8/SZ0Ov02Ey+ufP3D9flZfqt9p57PV9ACipkRpH43lLkxdi1BvZWL0Fh9N9\nHYmEmMy2H2yky2LlvMIkTAH+swYgP1rB7rRzuO2I1qEIIdwgISqYyFD3z0aamuy6gTXc1MpNg9Mq\nZ8q0Sm93xZIMt43KWfrsBJkNfjFb5UyGvSWiKIoO+DNQCPQCd6uqevSkr88Hfj3wYT1wm6qq/RMQ\nq0+z2x3/v737Do+rvNP//z4zoz7qvdiSZcnHRe7dYGNaSAgttAQIoYcSIH032Wy+u5v9bXZTlmyA\nkBAIJBAgEAi9mmKKKe7dPpZsSbZsy1ZvVtf8/hjJCGNbsjUzZ2Z0v64rV5BmNM89xzMf6TPPOc/D\n/S9sYUdVE3PMdM5dkG93pICLj3QzO2M6n1SvYVt9KVNSTbsjSQhTbfJ6e20VhgGnz8i1O4pPTUqZ\nwOuVb7OtfgdT0ybbHUdk2FSbAisz2Y3RE00b9VTsb6Yg+/PXCR9sbGdbZQMTxiSRmRJrQ0o5ERlJ\nMSwsyeKDjftZtf0g8ydnnvRjtXf2hO1plTC8GbmLgCjLshYBPwbuOuL2PwLXWpa1BHgNCLsOpbun\nj8eX7eDfH1rJW2uqDu8SP1wej4f7ntnIutJaJuUnc9P5U3yyEk8oWpp3CgDLqz6wOYmEgVFfm3bt\na+5fgS2NtKQYu+P4VGFiPtHOKF0nJ6Fo1NemQDIMg+Kk8RgRXfzp7ZVHncH5YON+AJZM991G0+Jf\n5y0qwGEYvPhhBX3D2JPwWNTIwal4Cw2WZX0CzBm4wTTNCUAd8D3TNJcDKZZllfohp23qmzv4n8fW\n8uaaKnYfbOWxZTv4/u9W8Le3SqlpbB/WYzz7/i7e+KSS/Mx4br94KhFhep7ucIxN6N+KoM7i4KEa\nu+NIaBvVtQm8s3EAZ84O3Q3Aj8XpcDIhuYiD7bXUttfbHUfkRIz62hRo88ZMAaC6azdv9dfFAb19\nfazYtJ+YKBezzfC4jng08M7KZbKvto3V2w+e1GP09Xno6Ood9Y1cAtA06Ose0zQHfi4NWAjcDZwF\nnGWa5lKfJhyG9s4elq/fS0V184i69iNtrajn3x9eRfn+ZhZOyeSXtyzkosXjiHQ5eWPVHn50/0fc\n88xGtlc24DnGuG+u3sNLH1aSnRrHdy6fHtYvpuFamrcIgHerPrQ5iYS4oK9N/tR8qIuV2w6QlRLL\npIJku+P4xaSUCQD8cdNfaOxsGuLeIkFjVNcmO5jJ4wGITGrgH+/tor7509WxN++qp6GlkwWTM4kK\no+uIR4PDs3IrTm5WrqPLuxl4bBj/7T2cZ9YMxA/62mFZ1sBKFXVAmWVZOwBM03wN7ydPy4/3gOnp\n8ce7+YS9v34vj7xmAZCSEMXsiZnMnZzFjAnpn2uchjO2x+PhmXfKePSVrTgcBrdcPI1zFxVgGAaT\nijP4xnklfLBhLy+8v4t1pbWsK62lIDuBCxYXctqsvMMLDry3roon3iolOT6Kn928kKzUOJ8+7xPh\n62M+knHPSl3E38teYFP9Vm5L/3pAxw6U0Tp2gPm8NkFgj9/JjuXxeHjgL6vo6fVw4WnjycwYeu+4\nQL8ufDHe4tjZPLnjWfa27ufdA+9z4+wr/DbWcIXicRztY9kg5GvTUIItSzrxZLnTqTMaae7q5pn3\ny/mXa+cB8MlLWwG4YGlRQHIH27EJFieTJT09nqWz83h79R5K97dw6vQTuxb8YMMhAJISoj8zfjAd\nl5EaTiO3AjgPeNo0zQXApkG37QLcpmkW9l/Iuxh4cKgHrKlpOZmsxzQhJ55vfaWE9aW1bNxVx7KV\nu1m2cjcup8HEsclML0pj2vhUJhdnDDn2oY4eHnplG2t31JAcH8VtF5UwPjeR2trProZUMjaJKVfO\nZOfeZpat3sMaq4a7n1rPQy9uYenMHHLS4vjTS9uIjnTy7UunkZUa5/PnPVzp6fG2jH28cVMik9nb\nuo+DB5v9spKQXc95tI5tU1H0eW0C39enYxnJv9UrH1fy0ab9mGOSmF2UOuTjBPp14avxDCL55zl3\n8ovVd1N6sOKojxnI5xaqx3E0jzUwXoCFdG0aip2/4440OMv4hEKqWz8hf1wfH23azxsf7qIwO4FV\nWw8wNtNNYpTT77mD9djYbSRZzp6Vyztr9vDXV7dRnB2P4wT+Ztx70Pu3u4Hn8PjBdlxGajiN3LPA\n2aZpruj/+jrTNK8A4izLetA0zRuAJ0zTBPjQsqxXR5zqBDkMg9lmBrPNDPr6PJTvb2bDzjo2ltWy\nubyezeX1PLYMxmTGU1LgbezG5ybgdHz2zNKqmlZ+949NHGhoZ+LYJG65sISEuMhjjmsYBkV5iRTl\nJVLf3MHba/fy7vq9vPRhJQAup4M7L5nG2Mzw6fx9xR0ZR4+nl47eTmJco2tPPfGZoK9NJ+LPr26n\nvqWDG788+bh1Z0t5Pc+8u5Pk+Chuvagk7PdDGpuQR05cFntb99Pn6cNhhPfzlbAQVrUpVJjJRazY\n9wmTp/ZRVWnw2LIdnFKSTW+fhyXTteVAqMpMiWXB5Cw+2lLNWquGOROHf53jwGbgo/rUSsuyPMCt\nR3x7x6DblwPzfRvr5DkcBuNzExmfm8jFSwqpb+5g4846NpTVsq2ygT0HWnj1k93ERbsoKUxl+vhU\nSgpT2Vxex59f3U5Xdx9fmj+Wi08r/FyjdzwpCdFcunQ8559SwEdbqlm17SBnzx2DOTY8r10ZqfgI\nNwCtXW1q5OSkhFptOp6NO+sO73H0X4+u5ruXzyDrKEtk1za284fnN+N0GNz2leN/0BROct057Gur\npqa9jszYdLvjiBxXONWmUDKh/zq56s49fGnBmbz0YQUvflhBhMvBghEsXy/2O/+UAj7eWs0LKyqY\nZaYPe1auvdPbyEVHhu+1keHbovZLSYhm6cxcls7MJT4xhg/W7PE2djtr+WTrAT7ZegDDAI/H+w99\n20UlJ9TtHykqwsnSGbksDbM9nXzNHem9XrClu5V0Um1OIxIY2ysbeG3lbq7/8iQG2pGe3j6efLsU\nw4DF03J4b8M+fv7oGu68ZBpFeYmHf7aru5d7n91EW0cP13zRZHxO4tEHCUN58dmsOgB7W/erkROR\no4qPdJPrzmZnUznXL8xh5bYDHGxoZ46ZTmx0hN3xZASyUmKZPzmTj7ccYN2OWmabw/s9cKgz/Gfk\nRtU5KtGRLqYXpXH1OSa/unUR/3H9PC5eUkhhTgITxybx02vmjKiJk+FzR3gbudau1iHuKRI+3lm3\nl40763jpw4rD33t3/T721x3itOk5XPuliVz7pYkc6ujhV39bxxrLu0WHx+Phkdctdh9oZcn0HE4b\nZR8U5bm9p0XtbdlncxIRCWZmchHdfT3sPVTF9edOIjs1lnPmjbU7lvjA+YsKMAx4YUX5sFew7Oj0\nrloZzivGh+8zG4JhGIzJcDMmw815iwrsjjPqxEf2n1rZ3WZzEpHAKdvrXZF8+bq9XPnFybR1dPPc\n+7uIiXJy0eJCAJZMzyHJHcXvn9vMfc9u4mtnFeMwDD7cXM247ASuOnuCnU/BFrlu7ya+Va1q5ETk\n2CYkj+ftPe9jNezk/MIi/uumBXZHEh/JTo1j/qRMPt56gPWltcyaMPSs3OFTK8O4kRtVM3ISPAZm\n5Fo0IyejRH1zBw0tncRGuejp9fDkmxYvfFBBW0cP5y0q+Mz1btPGp/Kjq2aREBfJE2+W8viyHcTH\nRvCtr5QQ4Rp9ZTs+0k1iZDxVrfvtjiIiQawoqRCH4cCqL7M7ivjBeYsKMPDOyh1r/+bBdGqliJ9o\nRk5Gm4HZuC8tGEtWSizLVu7m7bVVpCdFc9bsMZ+7f35WPD+5ejbZqbE4HAa3XlhCSsLoXRgo151D\nY2cTbd2H7I4iIkEqxhVNfnwelS176OjpGPoHJKTkpMUxd1IGuw+0sr6sdsj7j4ZTK9XIiS3c/atW\ntnSpkZPRoazK28hNGJPERYvH0dfnobfPw+WnFx9zli0tKYZ/v24uv7hlIRPzR/cKuHnx/dfJ6fRK\nETkOM7mIPk8fZY3ldkcRPzj/lHEYwPMfDD0rNzAjFxMVvqtWqpETW8T3r1rZ2q1TK2V0KNvbhNNh\nUJAVz5yJGcyamMEcM51ZE9KO+3MRLueonokbcPg6OS14IiLHMSG5CACrQadXhqPcQbNyG8rqjnvf\n9sONnGbkRHwq0hlJpDNSq1bKqPDm6j1UVrcwLjuBCJcTh2HwHzct5LavTMUY5n44o13e4QVPdJ2c\niBxbYWI+LodLjVwYO7//Wrnnh7hWrqN/Q/CYSDVyIj4XHxFHi66RkzDW29fHX9+wePzNUuLjIkfl\nipO+kh6TRoTDxV41ciJyHBHOCAoTC9jbul8LqoWp3HQ3sydmUFndwsadx56VO9TZQ1SkE4cjfD8w\nVSMntnFHuGntah3WykMioaa9s4e7n97E22v3kpcex0+/MYf8rHi7Y4Usp8NJTlw21W0H6OnrsTuO\niAQxs//0ytLGXTYnEX+5oH/rsOOtYNne2UNMZPheHwdq5MRG8ZFx9Hh66ejttDuKiE/VNXXw339d\nw6ZddUwtTOXHX59NaqKucxupXHc2PZ5eDhyqsTuKiAQxM3k8AFZ9qc1JxF/yMtzMNtMp39/Cpl1H\nn5Vr7+wN6+vjQI2c2Ghg5cpWrVwpYaR8fzP/+chqqmraOGNWLndeOjXsf5EESm68FjwRkaGNjc8j\n2hnFjoaddkcRP7rglHEAPP9Bxedm5TweD+2dPWG9hxxAeD87CWru/pUrW7pbSSfV5jQiI7fGOsgD\nL26lu7ePK84q5uw5n98fTk5enntgCwJdJycix+Z0OClKKmRz3TZWVq8l2hkVkHETu2Joamof8n6G\nYTA+cRyxETEBSBW+xmS4mT0hnTU7athcXs/Uwk//luzu6aO3z0O0GjkR/zi8KbguRpYw0Nndyx9f\n3IrDMLjjkmnMKDr+tgJy4nLdWYAaOREZ2sSUYjbXbeMvW/9md5SjSoiM58qJlzA1bbLdUULa+acU\nsGZHDS98UE7JuJTDK0G3d4X/ZuCgRk5s5I7wzsgdbK+1OYnIyLW1d9Pd08fCKZlq4vwkxhVDanQK\nVa378Hg82rpBRI7plJx5uBxOunq7Azam2x1Fa+vQ1/03dTXz7p4V/GHjn1mQNYdLJ5xPjEuzcydj\nbGY8M4vTWFday5aKekrGeWflBvaQiw3jzcBBjZzYaHziOCIdEby463Xy3DlMTCm2O5LISRv4pRHu\np3HYbXxSASur17K7pYr8BJ26KiJHF+mMZHHuwoCOmZ4eT01Ny7DuuyBrDo9s/RsfV69me0MpX594\nGZNStUXNybjglHGsK63l+Q/KmVLgnZU7/Ds5jPeQAy12IjZKj03lm9OuAY+H+zf9hV1NlXZHEjlp\nh0/jCPNfGnablTENgDUHN9icRETk5OW4s/jhnDs4d9zZNHe1cO+GB3li+zN09HTYHS3k5Gd5Z+V2\n7m1ma0UDMHhGLrx/J6uRE1tNSpnA9SVX0dPXw30bHmKPVqOTENXR/0sjJsxP47DbxJQJRDujWXtg\no/agFJGQ5nQ4+fK4s/nhnNvJicvig32f8POVv9Fqmyfh8AqW/fvKtR/+naxGTsSvpqeXcPWky+no\n6eDe9Q9woO2g3ZFEjupA/SEqqpuPetvAjFy4n8ZhtwiHi+npU2jobKSieY/dcURERmxsfB7/NPdO\nvpB/OvUdjfx23f08teN5unq77I4WMvKz4plRlEZZVRPbKhs4dPhyh/D+cFWNnASFeVmz+Kp5Ea3d\nbdy9/gHq2hvsjiTyOY8t28HP/ryap5fvpLev7zO31fYvOZ0YF2lHtFFlZsZUANbq9EoRCRMRDhcX\njv8S35/9LTJj03m3agU/X/kbdjVV2B0tZFxwagEAz39QTnun98NVnVopEiCLcxdy0fhzaexs4u71\nf6Sp8+gzHyJ2uXTpeDKSYnjl40p++fg66ps/vZahstp7gXt+Vrxd8UaNiSkTiHFFs+7gJvo8fUP/\ngIhIiBiXOJYfzf0OZ45ZQm17PXet+T3/KHuJ7gCuvhmqCrISmDY+ldKqJtaX1gA6tVIkoM7OX8oX\n88+gtr2Oe9c/SGt3m92RRA4bmxnP/7t2LnMmZlBa1cS/P7yKjTvrAKiobiEu2kVaYrTNKcNfhMPF\ntDTv6ZVldRV2xxER8alIZwQXF5/Hd2bdQmpMCm/tfo//WfVbKnU6+ZAuPNV7rdz23Y2AGjmRgDuv\n8BxOyzuFfW3V3Lf+Idq1gpMEkdhoF7deOIWrvzCBjq4e/u/vG3h82Q4ONrQzNjNee5sFyMDqlR/u\nWWNzEhER/yhKGse/zPsup+UtovrQQX695ne8uPM1evp67I4WtMZle2flBqiREwkwwzC4tPh8FmTN\nobJlD3/Y+LAu+JWgYhgGp8/K4ydXzyEjOYY311QBUKDTKgNmYkoxMa4YPt6zVqdXikjYinJGcvmE\ni7hzxjdJikrktcq3+eXqe7TK93EMrGAJauREbOEwHFw58RJmpk+lrLGcBzY/qk+gJOjkZ8Xzb9fO\nZd6kDABKClOH+AnxFVf/6pX17Y2UN+22O46IiF+ZKUX8y7zvckrOfPa27ueXq+/mlfJl9Pb12h0t\n6BTmJDB7QjrxsRHERauRE7GF0+Hk2ilXMDnFZGudxZ+3PKGCJUEnJsrFzRdM4XffXcKk/GS744wq\nszKmA1q9UkRGhxhXNFdOvIRvTb+BhMh4Xi5fxq/X3Mu+1mq7owWdmy+cwv/cvBCXM7xbnfB+dhLy\nXA4XN029mqKkcayr2cTj1jM6jUqCjmEYYX/6RjCamFxEXGQs6w5uVF0QkVFjcqrJT+Z9j/lZs9nd\nspdfrPotb1S+ozo4iMvpGBW/l9XISdCLdEZyy7TrGBufx8f7V/NM6Yt4PB67Y4mIzZwOJ/NzZ9DU\n1cKupkq744iIBExsRAzfmPxVbp56DTERMTy/81XuWnMfB9oO2h1NAkiNnISEGFc035pxA9lxmSyv\nWsHL5W/YHUlEgsDCsbMBnV4pIqPTtPQp/Ov87zM7Yzrlzbv571X/x9t73tfs3CihRk5Chjsijjtm\n3ERaTCqvVrzFssrldkcSEZtNyTCJi4jV5uAiMmq5I+K4vuQqbij5OlHOKJ4pfZH/eOc31Byqszua\n+JkaOQkpiVEJ3DnjJpKiEnlu5yu8v/djuyOJiI1cDicz0kto7mphZ2O53XFERGwzK2Ma/zr/+0xP\nL2FbTRk/X/Ub3qv6UB9yhTE1chJyUmNSuGPGTbgj4njSepaV1WvtjiQiNvp09cqNNicREbFXfKSb\nm0qu5s4F1+EynDy54znuXf8g9R0NdkcTP1AjJyEpKy6D22fcRLQrike3PcWGmi12RxIRmxQnFeKO\niNPplSIieFdSPjV/Hj+Z/z1KUidiNZTxX5/cxYf7VmqxuDCjRk5C1pj4HG6bfgMuh4uHtzxOQ0ej\n3ZFExAbO/tMrW7pbWVW9zu44IiJBISkqkVumXcfXJ14GGDy2/Wl+v/FhGjub7I4mPhL+GyxIWCtM\nzOey4gt5bPvfeWnXG1w9+XK7I4mIDc7OX8rKA+v4e+kLmClFJEUl2h1JRMR2hmGwMGcuZkoRj217\nmi112/nZx7/ySY2Mj3Rz89RriY2I8UFSORmakZOQtyB7NjlxWXxSvYaqln12xxERG6TFpHJx0Zdp\n72nnsW1P6/QhEZFBUqKTuX3GjXzNvBh3hJtDPe0j+l9zVwtljeWs0dYvttKMnIQ8h+Hg4qLzuHfD\ngzxb9jK3z7jR7kgiYoNTcxawoWYLW+stPty3klNy59sdSUQkaBiGweLcBSzOXTDix2roaOSnH/43\nqw+s88njycnRjJyEhUmpE5iUMoHtDaVsrd9hdxwRsYFhGFw18VJiXNE8U/Yite31dkcSEQlLydFJ\nFCWNo6yxXCti2kiNnISNrxR9GQOD58pepq9PK9eJjEbJ0UlcVnwhnb1d/HXbU1rFUkTET+ZkzgBg\nzQGdXmkXNXISNnLd2czPns2+tmqWV3xkdxwRscm8rFlMT5tCaeMulletsDuOiEhYmpkxDafhZNUB\nrRZsFzVyElbOLzyHCEcET256kc7eLrvjiIgNDMPgiomX4I6I44Wdr1LddtDuSCIiYScuIpbJqSZ7\nW/ezr7Xa7jijkho5CStJUYmcOXYJDR1NvLX7XbvjiIhN4iPdXGFeTHdfD49se5Levl67I4mIhJ25\nh0+vXG9zktFJjZyEnbPHnkZiVDzLdr9LU2eL3XFExCYzMqYyN3Mmlc17WKYPdkREfG5q2mQinZGs\nOrBe277YQI2chJ1oVzSXlZxHV28XL5e/YXccEbHR5RMuJDEygVfKl2mfSRERH4t0RjI9rYS6jnoq\nmnfbHWfUUSMnYenMwlPIjM3gw30r2d92wO44ImKT2IhYrpp0Kb2eXh7Z9iQ9fT12RxIRCStzs7yn\nV2rRk8BTIydhyelw8pWic/Hg4bmyl+2OIyI2mpI6kVNy5rG3dT+vlL9pdxwRkbAyMbkYd0Qcaw5s\n0PXIAaZGTsJWSeokipMK2Vy3Hau+zO44ImKji4vOIzU6mTcq36G8Saf/iIj4itPhZFbGdFq727Aa\n9PdWIKmRk7BlGAYXF50HwLNlL2ljYJFRLNoVzdWTLseDh0e2/Y0ubU8iIuIzA6dXrtbqlQHlGuoO\npmkawH3AdKADuNGyrF1Hud/9QJ1lWf/i85QiJ2lsQh5zM2ey6sA6Vh9Yz7ysWXZHEh9RbZITVZw8\nntPHnMo7ez7ghV2vcWnxBXZHkjCk2iSj0biEfFKjk1lfs4mv9V5MpDPC7kijwnBm5C4CoizLWgT8\nGLjryDuYpnkzUOLjbCI+cX7hF3E5XLyw8zW6ervtjiO+o9okJ+yCwi+RGZvOO3s+YEfDTrvjSHhS\nbZJRxzAMZmfOoLO3i8112+yOM2oMp5E7FXgNwLKsT4A5g280TXMhMBe43+fpRHwgNSaZ0/NOpaGz\nkeVVH9gdR3xHtUlOWKQzgqsnfRUDg79ue4qOng67I0n4UW2SUWlu5kwAVldr9cpAGU4jlwA0Dfq6\nxzRNB4BpmlnAvwG3A4bv44n4xhfyTycuIpbXK96htr3O7jjiG6pNclLGJY7lC/mnU9fRwLM7X7E7\njoQf1SYZlXLcWeS6s9lSt51D3YfsjjMqDHmNHNAMxA/62mFZ1sCqEZcBqcArQDYQY5rmdsuyHjne\nA6anxx/vZr/S2KNj3M+PHc8V0y7kwTVP8Ks19/LthdczPWtygMYOLDvHDjCf1yYI7PEL17ECPd7J\njHVNyldYV7uBVdVruf2Uq3EYw1v7S8cx9MayQcjXpqEoy7EFUx47spxWOJ/HNz5HWXspZ+acamuW\nYwmmLCM1nEZuBXAe8LRpmguATQM3WJZ1D3APgGma1wDmcIpRTU3LyaUdofT0eI09CsY91tgzE2dy\n5cQunrKe4+fv3st5hedwTv7pGIZvPxQNtucdqHFt4PPaBIGrT4H8twr06yJUnlu+O59VbWvZtruC\njNh0v451MkLlOAbzWAPjBVhI16ah2Pk77kjBlAWCK49dWSbGTQKe452yj5mWMN3WLEcTbFlGajgf\nQT4LdJqmuQL4X+C7pmleYZrmjSMeXSTATsmZz3dn30piVAIv7nqNBzY/SruukQlVqk0yInnx0P1t\nkwAAIABJREFU2QBUte63OYmEGdUmGbVSY5IZn1hAaeMuGjubhv4BGZEhZ+Qsy/IAtx7x7R1Hud9f\nfBVKxJ8KEsbyo7nf5qHNj7GhZjPVbQf45tRvkBWXaXc0OQGqTTJSuW5vI7e3dT+zMqbZnEbChWqT\njHZzMmeys6mCNQc2cObYJXbHCWvaEFxGpfhIN7fPuJEzxy7hwKEafrn6HtYf3DT0D4pI2Mhz5wCw\nt3WfzUlERMLHrIxpGBhsqt1qd5Swp0ZORi2nw8nFRedx/ZQr8Xg8PLD5UZ7f+Sp9nr6hf1hEQl58\npJuEyHiqWnRqpYiIr7gj40iKSqRGq4T7nRo5GfVmZ87gh3PuID0mlTcq3+F36/9Ea1eb3bFEJABy\n3dk0dDZqqWwRER9Ki0mhqbOZ7t5uu6OENTVyInj3PvmnOXdSkjqJ7Q2l/GL13exuqbI7loj42eDr\n5ERExDfSYlLx4KG+o8HuKGFNjZxIv9iIGG6edg1fHnc2DR2N3LXmPj7ev9ruWCLiR582ctU2JxER\nCR9pMSkAOr3Sz9TIiQziMBycO+5sbpl2LS5HBI9ue4onrWfp6euxO5qI+IEWPBER8b20aG8jV9tR\nb3OS8KZGTuQoStIm8U9z7iAnLov39n7E/629X/uhiIShzNh0XIZTe8mJiPhQWmwqAHXtauT8SY2c\nyDFkxKbxgzm3MydzBuXNlfxi1d2UNZbbHUtEfMjpcJIdl8n+tmp6+3rtjiMiEhbSor2NXK0aOb9S\nIydyHFHOSK6dfAWXFJ9Pa3cbv113P8v3rMDj8dgdTUR8JNedQ3dfDzXttXZHEREJC3ERsUQ7o6jV\nNXJ+pUZOZAiGYXDGmMXcOeMm4lyx/L30eR7Z9iRdvV12RxMRH8iN9y54otMrRUR8wzAMUmNSqO2o\n14fffqRGTmSYipPH889z76QgYSwrq9fy6zW/0ydNImEgN05bEIiI+FpaTCpdvV00d7bYHSVsqZET\nOQHJ0Ul8Z9YtnJozn72t+/nFqrvZUmfZHUtERuDTGTmtXCki4isDK1ceaNVp6/6iRk7kBEU4XFwx\n8RKumngZXX3d/H7DQ7xW8TZ9nj67o4nISXBHxJEUlcjeFs3IiYj4ysBecmrk/EeNnMhJWpQzl+/N\nupWkqERe3PUaD256lPaeDrtjichJyHVn09TVTGtXm91RRETCQlqMd+XKA21q5PxFjZzICOQnjOGf\n597JhOQiNtRu4eEtj9sdSUROQq7be3rlvjbNyomI+MLAjNxBzcj5jRo5kRGKj3Rz+/QbSI9Jpbyp\n0u44InISUqKTAHRRvoiIj6REJ2NgaEbOj9TIifiA0+EkLSaVQz3tdPZoWwKRUBPrigWgteeQzUlE\nRMKDy+EiKSpRM3J+pEZOxEeSohIBqG9vtDmJiJyouAhvI3eoW42ciIivpMWkUN/eSHdvt91RwpIa\nOREfSYpKAKDuUIPNSUTkRH3ayLXbnEREJHykxaTiwUNdh/428gc1ciI+ohk5kdA1cGplm06tFBHx\nmYEFT2rb62xOEp7UyIn4yEAjpxk5kdATFxED6NRKERFfGtiCoLaj3uYk4UmNnIiPJPeveqcZOZHQ\nE+WMwmE4aNOplSIiPqMZOf9SIyfiI4kD18ipkRMJOYZhEOeKpa1HG4KLiPhKZmwGBgZVLfvsjhKW\n1MiJ+EicK5YIh4t6nVopEpJiI2K12ImIiA/FuKLJS8iisqWK3r5eu+OEHTVyIj5iGAZJUYmakRMJ\nUXERsbR1H6LP02d3FBGRsFGcOo6u3i72tx2wO0rYUSMn4kNJUYk0d7TQ09djdxQROUFxETF48NDZ\n22l3FBGRsFGUOg6A8ubdNicJP2rkRHwoKSoRDx6aOlvsjiIiJ+jwFgQ6vVJExGcm9DdyFWrkfE6N\nnIgPDWxB0NjZZHMSETlRn24Kri0IRER8JS8hmyhnJBVNauR8TY2ciA8lRQ80crpOTiTUaFNwERHf\nczgc5CeMpfrQQS0o5WNq5ER8KPnwjFyzzUlE5EQNbArephk5ERGfKkgYA0Blyx6bk4QXNXIiPqRT\nK0VCl06tFBHxj3EJYwF0eqWPqZET8aGBRq5BjZxIyImN0GInIiL+UJDobeS0cqVvqZET8aH4SDdO\nw0Fjh66REwk1cf3XyB3SNXIiIj6VEBlPanQyFc278Xg8dscJG2rkRHzIYTjIic+kvHk3yyqXq1iJ\nhJCk6EQMDDbWbNEF+SIiPlaQMJa27kPUtNfZHSVsqJET8bE7FlxPUlQiz+18hce3P0NvX6/dkURk\nGBIi4/lC/unUdtTz121P6YMYEREfGpeYD2g/OV9SIyfiYwXJefxwzu2Mcefw4f6V3LfhIdp79Om+\nSCj48rizmZA0ng21W3hrz3t2xxERCRsDK1eqkfMdNXIifpAUlch3Zt3K1LRJbG8o5ddr7qOuvd7u\nWCIyBKfDybVTriQhMp7nd75KWWO53ZFERMJCXnwuLsNJuVau9Bk1ciJ+Eu2K4ptTr+H0MadS3XaA\nX62+V8VLJAQkRsVz/ZSrAHho82O0dLXanEhEJPRFOFzkxedS1bqPrt5uu+OEBTVyIn7kMBxcWnwB\nl0+4iNbuNn677g+sO7jJ7lgiMoTi5EIuKPwiTV3NPLzlcfo8fXZHEhEJeQUJY+jz9FHVutfuKGFB\njZxIAJyWt4hbpl2Lw3Dw4OZHtaKlSAg4c+wSpqZNxmoo45XyZXbHEREJeQMbg+sMJd9QIycSICVp\nk/jerNu0oqVIiHAYDr4x6XJSo5N5teIt1u/fYnckEZGQVtC/cqU2BvcNNXIiAZQXn6MVLUVCSGxE\nLDeWXI3LcHLPxw9T39FgdyQRkZCVGp1MfISbCs3I+YQaOZEA04qWIqFlbEIel064kJauNv60+TF6\n+nrsjiQiEpIMw6AgcQwNnY00djbZHSfkqZETsYFWtBQJLafmzGdx/jwqmnfzbNnLdscREQlZY+Pz\nANjbWm1zktCnRk7EJlrRUiR0GIbBTXOuJCsuk+VVK1h7cKPdkUREQlJiZAIAbd1tNicJfWrkRGym\nFS1FQkO0K4qbSr5OpDOSv257igNtB+2OJCIScuIi4wBoVSM3YmrkRIKAVrQUCQ1ZcZlcNfFSOnu7\neHDzX+nq7bI7kohISHFHeBu5ti41ciOlRk4kSGhFS5HQMCdzBktyF7GvrZq/Wc9qBl1E5AS4I2IB\nzcj5gmuoO5imaQD3AdOBDuBGy7J2Dbr9CuDbQDewybKs2/yUVSTsDaxo+eetj7Opdhu/XnMft027\njtSYFLujBR3VJrHTxcXnUdm8h0+q1zA+qYBTcubbHUmChGqTyPHFRQycWnnI5iShbzgzchcBUZZl\nLQJ+DNw1cINpmtHAz4DTLMtaDCSZpnmeX5KKjBKHV7TM04qWQ1BtEttEOFzcUHIVsa4YntrxPHta\n9tkdSYKHapPIccS6YgAtduILw2nkTgVeA7As6xNgzqDbOoFFlmV19n/twvvpk4iMgMNwcOkErWg5\nBNUmsVVqTArXTP4aPX09PLj5UQ5161RoAVSbRI7L6XAS64qhTTNyIzacRi4BGLxjX49pmg4Ay7I8\nlmXVAJimeQcQZ1nWm76PKTI6Hbmi5arqdXZHCiaqTWK7krRJnJN/BrXtdfzv2vt4fuerbKmzaO/R\n3+ajmGqTyBDcEXG6Rs4HhrxGDmgG4gd97bAsq2/gi/5zwX8JFAMXD2fQ9PT4oe/kJxp7dIwbTmOf\nnj6PcVnZ/Otbv+Llitf5wpRTcDmcARk7yPm8NkFgj1+4jhXo8ewe69rUi2n1NPPRnrW8UfkOb1S+\ng2EYFCaNZVJGMZPTi5mUXkRcZKxPxvOXcB3LBiFfm4aiLMcWTHmCOUtibDx19fWkpbkxDMPWLKFs\nOI3cCuA84GnTNBcAR57f9Ueg3bKsi4Y7aE1Ny/AT+lB6erzGHgXjhuPYcSSxMHsu71Z9yGub32d+\n9uyAjT0cNhVFn9cmCFx9CuS/VaBfF+H63I431pVFl3NxwQXsbKqkrHEXpQ27KG/cw86GSl6y3sTA\nINedTXFSIUXJhRQljsPdv5fSyYzna+E61sB4ARbStWkodv5+PVIwZYHgyhPsWaKIptfTx57qGmL6\nr5mzK4tdfFGbhtPIPQucbZrmiv6vr+tfcSkOWANcB7xvmuY7gAf4rWVZz484mYh8xpljTuP9vR+z\nbPdy5mbNxGGM+t1DVJskqES7opmSajIl1QSgs7eL8oHGrnEXFc17qGrdxztVHwCQE5dFUdI4ipIK\nKU4uJCEyfD4lHuVUm0SGcHgvue5DAW3kws2QjZxlWR7g1iO+veNEHkNERi41Jpk5mTNYWb2WLXXb\nmZo22e5ItlJtkmAX5YxkYkoxE1OKAeju7aaieTeljbsobSynvKmSfW3VvLf3IwAyY9O9TV1/Y5eO\nGrtQpNokMrSBU81bu9tIi0m1OU3oUjERCSFnj13Kyuq1vF7xDiWpkwJ+XrmInLwIZwTFyeMpTh4P\nQE9fD7tbqiht8M7Y7WqqYMW+T1ix7xMAMt3pFMYXUJQ0juKkQu0nKSJhw+3q30uuSwuejIQaOZEQ\nkuPOYmraJDbVbqOssZzi5EK7I4nISXI5XBQmFlCYWMA5nEFvXy97WvdS2rCLssZd7Gyu4KPWVXy0\nfxUAyVFJFCd7Z+yKkgpJj0nVhzkiEpIGZuS0BcHIqJETCTFfyD+DTbXbeGP3O2rkRMKI0+GkIGEs\nBQljOTt/KampcayrsChrLKesYRdljeWsrF7Lyuq1ACRGJlCcXNh/OuY4MmMz1NiJSEj49Bo5zciN\nhBo5kRBTmJhPUdI4ttZZVLXsIy8+x+5IIuIHDoeDsfF5jI3P44wxi+nz9LG/7QCljbso6z8dc/WB\n9aw+sB6A+Ai3d/GU/lm77LhMLYokIkEprr+Ra9WM3IiokRMJQV/IP52yxnKW7V7OdVOutDuOiASA\nw3CQ684m153N0rxT8Hg8HDh0kNLG8sNbHqyr2cS6Gu9q93ERsRQlftrY5bqz1diJSFBwH27kNCM3\nEmrkRELQ5BSTXHc2aw5s4Lxx55AeqxWfREYbwzDIisskKy6TxbkL8Hg81LTXHd7uoLRhFxtqt7Ch\ndgsAMa5oxicWHN7uYIw7F6fDafOzEJHRKC5i4Bo5NXIjoUZOJAQZhsEX8k/n4S2P8+aed7nCvNju\nSCJiM8MwyIhNIyM2jUU58wCoa6/3norZWE5p4y42121nc912wLs9QmFiAcVJhcw1SkjoS8Hl0J8F\nIuJ/sa4YDAzNyI2QKrZIiJqZPpUXo1P4eP9qzi04m8Qo7TklIp+VGpNCakwKC7LnANDQ0Xi4qStr\n3MW2+h1sq9/BC7teI8IRcfga3OKkQgoSxhLhjLD5GYhIOHI6nMS6YrRq5QipkRMJUU6Hk7PyT+Nv\n1rMsr/qAC8d/ye5IIhLkkqOTmJs1k7lZMwFo6myhrHEXVZ172Lx/B1ZDGVZDGeDdHqEgYczh7Q4K\nE/OJdEbaGV9EwkhcZCwNHY00dDSSHJ1kd5yQpEZOJIQtyJrDy+XLeK/qI76QvxTQrJyIDF9iVDyz\nM6fzxfRTqalpobWrjbKm8sOrYu5srKCssRx4C6fhJD8hr3+7A29jF+2KtvspiEiImp81mxd3vc5d\na3/PHTNuJCM23e5IIUeNnEgIi3BGcMaYxTy/81Xer/qYq7IvsDuSiIQwd2QcM9JLmJFeAsCh7kPs\nbKro3/KgnIrmPexqquSNyndwGA7GuHMpSvaeijk+cRyxETE2PwMRCRXn5J8B4G3m1vyeb824kTHa\nUumEqJETCXGLcxfwesU7vF31PpfN/KLdcUQkjMRGxDI1bTJT0yYD0NHTwc6mysPbHVS27KGyZQ9v\n7X4PA4M8d/bh7Q7GJ407vMS4iMiRDMPgiwVnEuuK4akdz/PbdX/glmnXUZQ0zu5oIUONnEiIi3HF\nsCRvIW9UvsPyio+ZmTjT7kgiEqaiXdFMSTWZkmoC0NnbRXlT5eHtDiqbd7OndR/v7PkAgJy4rMPb\nHRQljSMhUqd/i8hnLclbRKwrhr9se5J71z/IjSVfpyRtkt2xQoIaOZEwsDTvVN7e8z4vbH+DaXOn\naW8oEQmIKGckE1OKmZhSDEB3bzcVzbu9jV1jOeVNlexrq+a9vR8CkBmbwdRskzHRY5ieNkWrYooI\nAHOyZhLtiubBzY9y/6a/cM2krzInSx9MD0WNnEgYSIyKZ2H2XN7f+xH3rH+AKydeoouGRSTgIpwR\nFCePpzh5PAA9fT1UNlcd3u5gZ1MFb+58H4DipEK+Nf0GNXMiAkBJ2iRun3ETv9/wMH/e+jcO9XSw\nJG+h3bGCmho5kTBxQeE5tHOI1Xs38POVv+HccWdz5pglmp0TEdu4HC7GJxUwPqkAOIPevl5aXY08\nsf4FNtVu4y9b/8b1JVfhMBx2RxWRIFCUNI7vzLqZ363/E0/ueJZDPYc4J/8MDMOwO1pQUuUUCROx\nEbH88JSbuaHk60Q7o3l+56v8avU97G6psjuaiAjg3f+yKLWAG6Z8naKkcayr2cTfdzyPx+OxO5qI\nBIkx8bl8b/atpEQn8+Ku1/lH2UuqEcegRk4kjBiGwayMafx0wQ9YkD2HPa37+NXqe3mu7BW6ervt\njiciAnhPwbx56rXkurN5b+9HvFrxpt2RRCSIZMSm871Zt5IVm8Hbe97nr9v/Tm9fr92xgo4aOZEw\nFBcRy9WTLueOGTeRHJXEst3L+fnKu9jRsNPuaCIiAMRGxPCt6TeQGp3My+XLeH/vx3ZHEpEgkhyd\nxHdn3crY+Dw+3r+aP215jG59KP0ZauREwtjElGJ+Mv97nDFmMbXt9fx23f08vv1pDnW32x1NRITE\nqARun3Ej7og4nrSeZf3BTXZHEpEg4o6M49szv8mE5CI21Gzmvo0P09HTYXesoKFGTiTMRTkjuaT4\nfH4453Zy3dms2LeS/++TX7O+ZrPd0UREyIhN57bp1xPpjODhrU9QqjMHRGSQaFc0t027julpU9jR\nUMbd6x6gtbvN7lhBQY2cyCiRnzCGf55zJ+cXnkNb9yEe2PQID2x6lKbOFrujicgol58whpumfgOP\nx8MfNv6FqpZ9dkcSkSAS4YzghpKvsyBrDpUte/jN2j/Q2NlkdyzbqZETGUWcDidfLDiTH8/7LuMT\nC1hfs4n//OTXfLhvlVaEEhFbTUqZwDcmf5WO3g5+t+FP1LbX2x1JRIKI0+HkqkmXcsaYxVS3HeB/\n19zHwUM1dseylRo5kVEoKy6D78y6ha9OuIg+Ty+Pbf87d69/gJpDdXZHE5FRbE7mDC4tvoDmrhbu\nXf8ALV2tdkcSkSDiMBxcXHQe5xeeQ31HA3et/f2onsFXIycySjkMB0vyFvHT+T+gJHUiOxrK+K+V\nd/Hm7ne1xK+I2Ob0MafyhfzTqWmv474ND2lhAxH5DMMw+GLBmXx1wkW0drXxf+v+wM7GCrtj2UKN\nnMgolxydxC3TruO6KVcS5Yzk2bKX+fWa343qT7hExF4XFH6Rhdlz2d1SxQObHqWnr8fuSCISZJbk\nLeLayV+js7eLe9Y/wJa67XZHCjg1ciKCYRjMyZzBTxf8gHlZs9jdUsUvVt/NCztf054tIhJwhmFw\nhXkxU9Mmsb2hlEe2Pkmfp8/uWCISZOZkzeTmqdcAHv6w8c+sPrDe7kgBpUZORA5zR8RxzeSvcdv0\nG0iKSuT1yrf5+arfUNZYbnc0ERllnA4n10+5isLEAtYc3MAzpS9qUSYR+ZyStEncPuMmIh2R/HnL\nE7y/9yO7IwWMGjkR+ZwpqSY/mfc9Ts87lZpDdfxm7e95wvoH7bpWRUQCKNIZya3TriU7LpPlVStY\nVrnc7kgiEoSKksbxnVk3446I42/Ws7xW8fao+ODHZXcAEQlO0a4oLp1wAbMzp/PY9qf5YO/HbK7d\nxtfMrzA1bbLd8URklIiNiOX2GTfy69W/4/ldr+KOdLMoZ67dsUQkyIyJz+W7s2/lnnUP8OKu19jX\nup+U6OTP3CdmXyTth7oAyHFnMS9rlh1RfUaNnIgc17jEfH4099u8XvkOr1e8zR82/pnZGdO5bMKF\nxEe67Y4nIqNAUlQit8+4kbvW3sfj25/GHRHLtPQpdscSkSCTGZvO92ffxr3rH2TNwQ3Hva87Io65\nmTMxDCNA6XxPjZyIDMnlcPHlcWczM30qj29/mjUHN7C9vpSLi89jftZsu+OJyCiQFZfBrdOu5+51\n9/PQlse4Y8Y3GZ9UYHcsEQkyydFJ/Gjut9nbtp8jz65MTo6loeEQACnRySHdxIGukRORE5DjzuJ7\ns2/jsuIL6fb08Oi2p/j9xoftjiUio8S4xLHcOPUb9Hr6+P3Gh6ltr7c7kogEoQhnBAUJYxmX+Nn/\nFaeOO/zfiVHxdsccMTVyInJCHIaDpWNO4V/nfZ/JqSa7mirsjiQio8iUVJOrJ11Ob18PNYdq7Y4j\nImIbnVopIiclNSaZb02/QXs7iUjAzcuaxeyM6TgdTrujiIjYRjNyIjIiDkNlREQCT02ciIx2+gtM\nREREREQkxKiRExERERERCTFq5EREREREREKMGjkREREREZEQo0ZOREREREQkxKiRExERERERCTFq\n5EREREREREKMGjkREREREZEQo0ZOREREREQkxKiRExERERERCTFq5EREREREREKMGjkREREREZEQ\n4xrqDqZpGsB9wHSgA7jRsqxdg24/H/gp0A08bFnWg37KKiJymGqTiAQj1SYRCZThzMhdBERZlrUI\n+DFw18ANpmm6+r8+C1gKfNM0zXQ/5BQROZJqk4gEI9UmEQmI4TRypwKvAViW9QkwZ9Btk4BSy7Ka\nLcvqBj4Alvg8pYjI56k2iUgwUm0SkYAYTiOXADQN+rrHNE3HMW5rARJ9lE1E5HhUm0QkGKk2iUhA\nDHmNHNAMxA/62mFZVt+g2xIG3RYPNA7xeEZ6evwQd/EfjT06xtXYo4KvaxMEuD6F61iBHi9cxwr0\neOE6lg1CvjYNRVmOLZjyKMvRBVOWkRrOjNwK4FwA0zQXAJsG3bYNKDJNM8k0zUi8pwd85POUIiKf\np9okIsFItUlEAsLweDzHvcOg1Zem9X/rOmA2EGdZ1oOmaX4Z+DfAAP5kWdYf/JhXRARQbRKR4KTa\nJCKBMmQjJyIiIiIiIsFFG4KLiIiIiIiEGDVyIiIiIiIiIUaNnIiIiIiISIgZzvYDJ2XQxb7TgQ7g\nRsuydg26/Qrg20A3sMmyrNsCNO4lwD8DfcDjlmXd7YtxhzP2oPvdD9RZlvUvgRrbNM3vADcCB/u/\ndbNlWaUBGnsu8L/9X1YDX7csq8uf45qmmQn8DfDgvaB8BvDPlmX9caTjDjV2/+1XAd8DeoCHfXkx\n+zDGvhr4Ad4lrf9iWdZDvhp70Bjzgf+xLOv0I75/PvBTvO/rhy3LetDXY4/UcN6npmnGAm8A11uW\ntcNfY/m6Dgay/gWy3gW6vgWypgWyjgW6btlRq0KxNp3M6w3v8xjy/ReILJZldZmmuYZP98crtyzr\nBn9mOdZ7A3jgePkDmcWyrD8G+rj03/659/Fw63UgsvR/3+fHZZh5PldzbDw2R61/J3ps/DkjdxEQ\nZVnWIuDHwF0DN5imGQ38DDjNsqzFQJJpmucFYFwH8HPgDGARcJtpmik+Gve4Yw/KcDNQ4sMxhzv2\nbOBqy7LO6P+fT5q4YY79R+Bay7KWAK8B+f4e17KsA5ZlnW5Z1hn9t63BW+B9Zajn/Cu8r7NTge+b\npunLDV+P9xpPxfveWgIsBa4yTXOsD8fGNM0f4j2WUUd839Wf5az+sb9pmma6L8f2keP+25mmORt4\nFyj051h+qoOBrH+BrHeBrm+BrGmBrGOBrlsBrVUhXJtO5vU25PsvUFlM04wCGPT+88kf5cfLcpz3\nRsCPy7Gy2HFc+h3tfWzX6+VzWfx4XI6b5zg1J+DH5lhZTubY+LOROxXvmxzLsj4B5gy6rRNYZFlW\nZ//XLrzdql/Htbwbck6yLKsVSMP7/Ec8MzScsQFM01wIzAXu9+GYwxob7x86PzZN833TNH8UqLFN\n05wA1AHfM01zOZDiwyZyqOc84B7gFsuyfLlE61BjbwCSgZj+rwM1diGw3rKspv7nuwpY4MOxAcqA\nrxzl+5OAUsuymi3L6gY+wFukgs1Q/3aReAvwdj+P5Y86GMj6F8h6F+j6FsiaFsg6Fui6FehaFaq1\n6WReb8N93QQiy3QgzjTN103TfLN/VtSvWY4w+L0R8ONynCx2HZejvY/tOi5Hy+Kv4zJUnqPVnIXD\neA6ByrKAkzg2/mzkEvh0ahCgp/8TYSzL8liWVQNgmuYdePdWedPf4/aP3Wea5leA9cByoM1H4x53\nbNM0s/DuG3M73ql3Xzvu8waeAG4BTgdONU3z3ACNnYb3jXI33k9DzzJNc2kAxgUOn06z2bKsMh+N\nOdyxt+D9VG4T8JJlWc0BGrsUmGKaZnr/6YFnAnE+HBvLsp7Fe5rEULlaAF/ORPrKUDXiI8uy9uKb\n92mg62Ag618g612g61sga1og61ig61ZAa1UI16YTfb2dPsTPBDLLUuAQ8CvLss4BbgUeC0AW4Kjv\nDTuOy7Gy2HVcjvY+tuu4HC2Lv47LUHmOVnNih/EcApUlDu/v5BM6Nv5s5JqB+MFj9X8iDHjPHTVN\n81d4w18cqHHBW+wty8rBe/rFNwI09mVAKvAK8CPgStM0AzU2wG8ty6q3LKsHeBmYGaCx64Ayy7J2\n9I/9Gr77tGPIf2u81xL45Lq44Y5tmuZU4Mt4T38pADJN77VJfh/bsqxGvOejPwM8hreA1vpw7KFy\nJQz6Oh7vud/BZjivm4CM5Yc6GMj6F8h6F+j6FsiaFsg6Fui6FSy1Kthr08m83pqO8zOBzmLh/Tek\nf4auDsj2c5YBR743/FXfTybLDgJ8XI7xPr4UG14vx6kp/joux81znJoT8GNznCylnOAv+gRxAAAF\nWUlEQVSx8WcjtwI4F8A0zQV4u/HB/oj33NGLBp1a5NdxTdOMN01zuWmakf3fasN70b/fx7Ys6x7L\nsuZa3nOo/wfvQgOPBGJs0zQTgM2macaa3osvz8D7ovH72MAuwG2a5sD1RovxfkLj73EHzLEs6yMf\njTfcsZvwfuLU2T9lfhDvqQV+H9s0TScwy/Jev/BVYGL//f3hyJmWbUCRaZpJ/e+xJYA/jv1IDed1\nE6ixfF0HA1n/AlnvAl3fAlnTAlnHAl237KpVoVabTvT1thn4EO8fyb6uYyfz2r+B/gVQTNPMwfvH\n634/Zxlw5HvDX/X9ZLJcT+CPy9Hex0n9PxPo18uxaoq/jstx8xyn5nx4nOcQ6CwnfGwMj8eXl+58\nyvx0tZZp/d+6Du91DHF4f8muAt7vv82D9xPV5/05rmVZD5qmeSPe1c26gI3AHZaPrp0aauxB97sG\nMC3/rFp5rOd9Fd7V8TqAtyzL+o8Ajr0U+EX/bR9alvXdAI2bBrxhWdYsX4x3gmPfjPcN2QnsBG7q\n/wQzEGP/P7zXeLUD/2tZ1j98Me4RGfKBJyzLWmR6V14cGPvLeE+pM4A/WT5crdNXTuB9+jbeax18\nsWplQOpgIOtfIOtdoOtbIGtaIOtYoOuWHbUqFGvTybzejvYzI6lVI8wSATyMd+alD++KjR8HIMvn\n3hs2HpejZbHruHzufQz0HvkzATouR8ti4IfjMsw8n6s5Nr5mjpblhF8zfmvkRERERERExD+0IbiI\niIiIiEiIUSMnIiIiIiISYtTIiYiIiIiIhBg1ciIiIiIiIiFGjZyIiIiIiEiIUSMnIiIiIiISYtTI\nCaZpJpim+axpmvmmaZb74fHfMU1zyQnc/9/699c48vvXmKb5sG/TiUiwUm0SkWCl+iTBQI2cAKQA\n0/v/O9g3Fgz2fCLiO6pNIhKsVJ/Edi67A0hQ+C2QA9wFxJqm+QRQAtQDF1mW1WCaZg2wGsgE5gI/\nAC7H+2HA65Zl/cg0zXjgif77APyHZVkv9f/3TaZp3gUkAd+2LOtl0zQzgD8BY4Fu4CeWZb0+OJhp\nmlcDPwGagN1Ai1+OgIgEI9UmEQlWqk9iO83ICcCdwD7gu0A68GvLsqYCB4Gv9d8nFfi5ZVmzgLOA\n2cAcYBaQZ5rmVcBXgHLLsuYCVwOLB43RYFnWHODbwMDU/z3AW5ZlTQcuAx4yTTN94AdM08wGfgGc\nCiwE4n39xEUkqKk2iUiwUn0S26mRk8EMYK9lWWv6v94CpA26fWX//58FzAPWAGvxFqbJwArgItM0\nn8VbQP5z0M8+d5THPAPvp0pYllUOfAzMH/Qzi4AVlmXVWpbVB/x1pE9QREKSapOIBCvVJ7GNGjkZ\nzAP0HPG1MfCFZVmd/f/pBP7PsqxZlmXNxFtA/suyrJ3ARLxFYzGwatBjDTzu4Mc88vXn4LOn+3r6\nxzryMURkdFFtEpFgpfoktlEjJ+B9k7vwFgljiPsCvA1cbZpmnGmaLuB54FLTNL8F/MyyrGeAbwHp\npmkmHOdx3gJuBDBNsxDvp0gfDbr9A2C+aZrZpmk6gK+e4PMSkdCm2iQiwUr1SWynRk4ADuC9GPZh\noO8Y9zm84lH/RbjPAJ8AG4G1lmU9AjwCmKZpbgSWA/9mWVYzx14t6dvAGf33/wdwg2VZBwaNcxDv\nOehv4T11oOlkn6CIhCTVJhEJVqpPYjvD49GKpCIiIiIiIqFEM3IiIiIiIiIhRo2ciIiIiIhIiFEj\nJyIiIiIiEmLUyImIiIiIiIQYNXIiIiIiIiIhRo2ciIiIiIhIiFEjJyIiIiIiEmLUyImIiIiIiISY\n/x8Y+NuV/kBU4gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb744da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "precs = []\n",
    "recs = []\n",
    "threshs = []\n",
    "labels = [\"Typical\", \"Avoids FP\", \"Avoids FN\"]\n",
    "for actual, predicted in zip([actual_1, actual_10, actual_11], \n",
    "                                    [predicted_1, predicted_10, predicted_11]):\n",
    "    prec, rec, thresh = precision_recall_curve(actual, predicted)\n",
    "    precs.append(prec)\n",
    "    recs.append(rec)\n",
    "    threshs.append(thresh)\n",
    "plt.figure(figsize=(15, 5))\n",
    "for i in range(3):\n",
    "    ax = plt.subplot(1, 3, i+1)\n",
    "    plt.plot(threshs[i], precs[i][:-1], label=\"precision\")\n",
    "    plt.plot(threshs[i], recs[i][:-1], label=\"recall\")\n",
    "    plt.xlabel(\"threshold\")\n",
    "    ax.set_title(labels[i])\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "При увеличении порога мы делаем меньше ошибок FP и больше ошибок FN, поэтому одна из кривых растет, а вторая  - падает. По такому графику можно подобрать оптимальное значение порога, при котором precision и recall будут приемлемы. Если такого порога не нашлось, нужно обучать другой алгоритм. \n",
    "\n",
    "Оговоримся, что приемлемые значения precision и recall определяются предметной областью. Например, в задаче определения, болен ли пациент определенной болезнью (0 - здоров, 1 - болен), ошибок false negative стараются избегать, требуя recall около 0.9. Можно сказать человеку, что он болен, и при дальнейшей диагностике выявить ошибку; гораздо хуже пропустить наличие болезни."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__<font color=\"green\" size=5>Programming assignment: problem 1. </font>__ Фиксируем порог T = 0.65; по графикам можно примерно узнать, чему равны метрики на трех выбранных парах векторов (actual, predicted). Вычислите точные precision и recall для этих трех пар векторов.\n",
    "\n",
    "6 полученных чисел запишите в текстовый файл в таком порядке:\n",
    "\n",
    "precision_1 recall_1 precision_10 recall_10 precision_11 recall_11\n",
    "\n",
    "Цифры XXX после пробела соответствуют таким же цифрам в названиях переменных actual_XXX и predicted_XXX.\n",
    "\n",
    "Передайте ответ в функцию write_answer_1. Полученный файл загрузите в форму."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "############### Programming assignment: problem 1 ###############\n",
    "T = 0.65\n",
    "precision_1 = precision_score(actual_1, predicted_1 > T)\n",
    "recall_1 = recall_score(actual_1, predicted_1 > T)\n",
    "\n",
    "precision_10 = precision_score(actual_10, predicted_10 > T)\n",
    "recall_10 = recall_score(actual_10, predicted_10 > T)    \n",
    "\n",
    "precision_11 = precision_score(actual_11, predicted_11 > T)\n",
    "recall_11 = recall_score(actual_11, predicted_11 > T)\n",
    "\n",
    "write_answer_1(precision_1, recall_1, precision_10, recall_10, precision_11, recall_11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def write_answer_1(precision_1, recall_1, precision_10, recall_10, precision_11, recall_11):\n",
    "    answers = [precision_1, recall_1, precision_10, recall_10, precision_11, recall_11]\n",
    "    with open(\"pa_metrics_problem1.txt\", \"w\") as fout:\n",
    "        fout.write(\" \".join([str(num) for num in answers]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### F1-score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Очевидный недостаток пары метрик precision-recall - в том, что их две: непонятно, как ранжировать алгоритмы. Чтобы этого избежать, используют F1-метрику, которая равна среднему гармоническому precision и recall. \n",
    "F1-метрика будет равна 1, если и только если precision = 1 и recall = 1 (идеальный алгоритм). \n",
    "\n",
    "(: Обмануть F1 сложно: если одна из величин маленькая, а другая близка к 1 (по графикам видно, что такое соотношение иногда легко получить), F1 будет далека от 1. F1-метрику сложно оптимизировать, потому что для этого нужно добиваться высокой полноты и точности одновременно.\n",
    "\n",
    "Например, посчитаем F1 для того же набора векторов, для которого мы строили графики (мы помним, что там одна из кривых быстро выходит в единицу)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import f1_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Разные склонности алгоритмов к ошибкам FP и FN:\n",
      "Typical: f1 = 0.827586206897\n",
      "Avoids FP: f1 = 0.636363636364\n",
      "Avoids FN: f1 = 0.764705882353\n"
     ]
    }
   ],
   "source": [
    "T = 0.5\n",
    "print \"Разные склонности алгоритмов к ошибкам FP и FN:\"\n",
    "for actual, predicted, descr in zip([actual_1, actual_10, actual_11], \n",
    "                                    [predicted_1 > T, predicted_10 > T, predicted_11 > T], \n",
    "                                    [\"Typical:\", \"Avoids FP:\", \"Avoids FN:\"]):\n",
    "    print descr, \"f1 =\", f1_score(actual, predicted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "F1-метрика в двух последних случаях, когда одна из парных метрик равна 1, значительно меньше, чем в первом, сбалансированном случае."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__<font color=\"green\" size=5>Programming assignment: problem 2. </font>__ На precision и recall влияют и характер вектора вероятностей, и установленный порог. \n",
    "Для тех же пар (actual, predicted), что и в предыдущей задаче, найдите оптимальные пороги, максимизирующие F1_score. Будем рассматривать только пороги вида T = 0.1 * k, k - целое; соответственно, нужно найти три значения k. Если f1 максимизируется при нескольких значениях k, укажите наименьшее из них.\n",
    "\n",
    "Запишите найденные числа k в следующем порядке:\n",
    "\n",
    "k_1, k_10, k_11\n",
    "\n",
    "Цифры XXX после пробела соответствуют таким же цифрам в названиях переменных actual_XXX и predicted_XXX.\n",
    "\n",
    "Передайте ответ в функцию write_answer_2. Загрузите файл в форму.\n",
    "\n",
    "Если вы запишите список из трех найденных k в том же порядке в переменную ks, то с помощью кода ниже можно визуализировать найденные пороги:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "############### Programming assignment: problem 2 ###############\n",
    "dict_1 = {}\n",
    "for k in range(10):\n",
    "    dict_1[k] = f1_score(actual_1, predicted_1 > 0.1*k)\n",
    "    \n",
    "dict_10 = {}\n",
    "for k in range(10):\n",
    "    dict_10[k] = f1_score(actual_10, predicted_10 > 0.1*k)\n",
    "    \n",
    "dict_11 = {}\n",
    "for k in range(10):\n",
    "    dict_11[k] = f1_score(actual_11, predicted_11 > 0.1*k)\n",
    "k_1 = sorted(dict_1, key = dict_1.get, reverse=True)\n",
    "k_10 = sorted(dict_10, key = dict_10.get, reverse=True)\n",
    "k_11 = sorted(dict_11, key = dict_11.get, reverse=True)\n",
    "write_answer_2(k_1[0], k_10[0], k_11[0])\n",
    "ks = [k_1[0], k_10[0], k_11[0]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3cAAAFRCAYAAADXWVQUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8ec3be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "many_scatters([actual_1, actual_10, actual_11], [predicted_1, predicted_10, predicted_11], \n",
    "              np.array(ks)*0.1, [\"Typical\", \"Avoids FP\", \"Avoids FN\"], (1, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def write_answer_2(k_1, k_10, k_11):\n",
    "    answers = [k_1, k_10, k_11]\n",
    "    with open(\"pa_metrics_problem2.txt\", \"w\") as fout:\n",
    "        fout.write(\" \".join([str(num) for num in answers]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Метрики, оценивающие векторы вероятностей класса 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Рассмотренные метрики удобно интерпретировать, но при их использовании мы не учитываем большую часть информации, полученной от алгоритма. В некоторых задачах вероятности нужны в чистом виде, например, если мы предсказываем, выиграет ли команда в футбольном матче, и величина вероятности влияет на размер ставки за эту команду. Даже если в конце концов мы все равно бинаризуем предсказание, хочется следить за характером вектора вероятности. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Log_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Log_loss вычисляет правдоподобие меток в actual с вероятностями из predicted, взятое с противоположным знаком:\n",
    "\n",
    "$log\\_loss(actual, predicted) = - \\frac 1 n \\sum_{i=1}^n (actual_i \\cdot \\log (predicted_i) + (1-actual_i) \\cdot \\log (1-predicted_i))$, $n$ - длина векторов.\n",
    "\n",
    "Соответственно, эту метрику нужно минимизировать. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вычислим ее на наших векторах:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import log_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Алгоритмы, разные по качеству:\n",
      "Perfect: 0.249212637592\n",
      "Typical: 0.464506822256\n",
      "Awful: 1.52702488092\n",
      "\n",
      "Осторожный и рискующий алгоритмы:\n",
      "Ideal careful 0.249212637592\n",
      "Ideal risky 0.170619479147\n",
      "Typical careful: 0.464506822256\n",
      "Typical risky: 0.613874592234\n",
      "\n",
      "Разные склонности алгоритмов к ошибкам FP и FN:\n",
      "Avoids FP: 0.584933970989\n",
      "Avoids FN: 0.588679128881\n"
     ]
    }
   ],
   "source": [
    "print \"Алгоритмы, разные по качеству:\"\n",
    "for actual, predicted, descr in zip([actual_0, actual_1, actual_2], \n",
    "                                    [predicted_0, predicted_1, predicted_2],\n",
    "                                    [\"Perfect:\", \"Typical:\", \"Awful:\"]):\n",
    "    print descr, log_loss(actual, predicted)\n",
    "print\n",
    "print \"Осторожный и рискующий алгоритмы:\"\n",
    "for actual, predicted, descr in zip([actual_0, actual_0r, actual_1, actual_1r], \n",
    "                                    [predicted_0, predicted_0r, predicted_1, predicted_1r],\n",
    "                                    [\"Ideal careful\", \"Ideal risky\", \"Typical careful:\", \"Typical risky:\"]):\n",
    "    print descr, log_loss(actual, predicted)\n",
    "print\n",
    "print \"Разные склонности алгоритмов к ошибкам FP и FN:\"\n",
    "for actual, predicted, descr in zip([actual_10, actual_11], \n",
    "                                    [predicted_10, predicted_11], \n",
    "                                    [\"Avoids FP:\", \"Avoids FN:\"]):\n",
    "    print descr, log_loss(actual, predicted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как и предыдущие метрики, log_loss хорошо различает идеальный, типичный и плохой случаи. Но обратите внимание, что интерпретировать величину достаточно сложно: метрика не достигает нуля никогда и не имеет верхней границы. Поэтому даже для идеального алгоритма, если смотреть только на одно значение log_loss, невозможно понять, что он идеальный.\n",
    "\n",
    "Но зато эта метрика различает осторожный и рискующий алгоритмы. Как мы видели выше, в случаях Typical careful и Typical risky количество ошибок при бинаризации по T = 0.5 примерно одинаковое, в случаях Ideal ошибок вообще нет. Однако за неудачно угаданные классы в Typical рискующему алгоритму приходится платить большим увеличением log_loss, чем осторожному алгоритму. С другой стороны, за удачно угаданные классы рискованный идеальный алгоритм получает меньший log_loss, чем осторожный идеальный алгоритм.\n",
    "\n",
    "Таким образом, log_loss чувствителен и к вероятностям, близким к 0 и 1, и к вероятностям, близким к 0.5. \n",
    "\n",
    "Ошибки FP и FN обычный Log_loss различать не умеет."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Однако нетрудно сделать обобщение log_loss на случай, когда нужно больше штрафовать FP или FN: для этого достаточно добавить выпуклую (то есть неотрицательную и суммирующуюся к единице) комбинацию из двух коэффициентов к слагаемым правдоподобия. Например, давайте штрафовать false positive:\n",
    "\n",
    "$weighted\\_log\\_loss(actual, predicted) = -\\frac 1 n \\sum_{i=1}^n (0.3\\, \\cdot actual_i \\cdot \\log (predicted_i) + 0.7\\,\\cdot (1-actual_i)\\cdot \\log (1-predicted_i))$\n",
    "\n",
    "Если алгоритм неверно предсказывает большую вероятность первому классу, то есть объект на самом деле принадлежит классу 0, то первое слагаемое в скобках равно нулю, а второе учитывается с большим весом.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__<font color=\"green\" size=5>Programming assignment: problem 3. </font>__ Напишите функцию, которая берет на вход векторы actual и predicted и возвращает модифицированный Log-Loss, вычисленный по формуле выше. Вычислите ее значение (обозначим его wll) на тех же векторах, на которых мы вычисляли обычный log_loss, и запишите в файл в следующем порядке:\n",
    "\n",
    "wll_0 wll_1 wll_2 wll_0r wll_1r wll_10 wll_11\n",
    "\n",
    "Цифры XXX после пробела соответствуют таким же цифрам в названиях переменных actual_XXX и predicted_XXX.\n",
    "\n",
    "Передайте ответ в функцию write_answer3. Загрузите файл в форму."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "############### Programming assignment: problem 3 ###############\n",
    "def weighted_log_loss(actual, predicted):\n",
    "    n = len(actual)\n",
    "    return -1.0/n*np.sum(0.3*actual*np.log(predicted) + 0.7*(1-actual)*np.log(1-predicted))\n",
    "\n",
    "wll = []\n",
    "wllr = []\n",
    "wll_1 = []\n",
    "for actual, predicted in zip([actual_0, actual_1, actual_2], \n",
    "                                    [predicted_0, predicted_1, predicted_2]):\n",
    "    wll.append(weighted_log_loss(actual, predicted))\n",
    "\n",
    "for actual, predicted in zip([actual_0r, actual_1r], \n",
    "                                    [predicted_0r, predicted_1r]):\n",
    "    wllr.append(weighted_log_loss(actual, predicted))\n",
    "\n",
    "for actual, predicted in zip([actual_10, actual_11], \n",
    "                                    [predicted_10, predicted_11]):\n",
    "    wll_1.append(weighted_log_loss(actual, predicted))\n",
    "    \n",
    "write_answer_3(wll[0], wll[1], wll[2], wllr[0], wllr[1], wll_1[0], wll_1[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def write_answer_3(wll_0, wll_1, wll_2, wll_0r, wll_1r, wll_10, wll_11):\n",
    "    answers = [wll_0, wll_1, wll_2, wll_0r, wll_1r, wll_10, wll_11]\n",
    "    with open(\"pa_metrics_problem3.txt\", \"w\") as fout:\n",
    "        fout.write(\" \".join([str(num) for num in answers]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обратите внимание на разницу weighted_log_loss между случаями Avoids FP и Avoids FN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ROC и AUC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "При построении ROC-кривой (receiver operating characteristic) происходит варьирование порога бинаризации вектора вероятностей, и  вычисляются величины, зависящие от числа ошибок FP и FN. Эти величины задаются так, чтобы в случае, когда существует порог для идеального разделения классов, ROC-кривая проходила через определенную точку - верхний левый угол квадрата [0, 1] x [0, 1]. Кроме того, она всегда проходит через левый нижний и правый верхний углы. Получается наглядная визуализация качества алгоритма. С целью охарактеризовать эту визуализацию численно, ввели понятие AUC - площадь под ROC-кривой.\n",
    "\n",
    "Есть несложный и эффективный алгоритм, который за один проход по выборке вычисляет ROC-кривую и AUC, но мы не будем вдаваться в детали."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим ROC-кривые для наших задач:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve, roc_auc_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perfect:1.000000 Typical:0.884444 Awful:0.041667 Ideal careful:1.000000 Ideal Risky:1.000000 Typical careful:0.884444 Typical risky:0.738095 Typical:0.884444 Avoids FP:0.819048 Avoids FN:0.780220 \n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3cAAAFECAYAAACEQsc8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n2FusOXPWX8oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8ee5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 5))\n",
    "plt.subplot(1, 3, 1)\n",
    "aucs = \"\"\n",
    "for actual, predicted, descr in zip([actual_0, actual_1, actual_2], \n",
    "                                    [predicted_0, predicted_1, predicted_2],\n",
    "                                    [\"Perfect\", \"Typical\", \"Awful\"]):\n",
    "    fpr, tpr, thr = roc_curve(actual, predicted)\n",
    "    plt.plot(fpr, tpr, label=descr)\n",
    "    aucs += descr + \":%3f\"%roc_auc_score(actual, predicted) + \" \"\n",
    "plt.xlabel(\"false positive rate\")\n",
    "plt.ylabel(\"true positive rate\")\n",
    "plt.legend(loc=4)\n",
    "plt.axis([-0.1, 1.1, -0.1, 1.1])\n",
    "plt.subplot(1, 3, 2)\n",
    "for actual, predicted, descr in zip([actual_0, actual_0r, actual_1, actual_1r], \n",
    "                                    [predicted_0, predicted_0r, predicted_1, predicted_1r],\n",
    "                                    [\"Ideal careful\", \"Ideal Risky\", \"Typical careful\", \"Typical risky\"]):\n",
    "    fpr, tpr, thr = roc_curve(actual, predicted)\n",
    "    aucs += descr + \":%3f\"%roc_auc_score(actual, predicted) + \" \"\n",
    "    plt.plot(fpr, tpr, label=descr)\n",
    "plt.xlabel(\"false positive rate\")\n",
    "plt.ylabel(\"true positive rate\")\n",
    "plt.legend(loc=4)\n",
    "plt.axis([-0.1, 1.1, -0.1, 1.1])\n",
    "plt.subplot(1, 3, 3)\n",
    "for actual, predicted, descr in zip([actual_1, actual_10, actual_11], \n",
    "                                    [predicted_1, predicted_10, predicted_11], \n",
    "                                    [\"Typical\", \"Avoids FP\", \"Avoids FN\"]):\n",
    "    fpr, tpr, thr = roc_curve(actual, predicted)\n",
    "    aucs += descr + \":%3f\"%roc_auc_score(actual, predicted) + \" \"\n",
    "    plt.plot(fpr, tpr, label=descr)\n",
    "plt.xlabel(\"false positive rate\")\n",
    "plt.ylabel(\"true positive rate\")\n",
    "plt.legend(loc=4)\n",
    "plt.axis([-0.1, 1.1, -0.1, 1.1])\n",
    "print aucs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чем больше объектов в выборке, тем более гладкой выглядит кривая (хотя на самом деле она все равно ступенчатая).\n",
    "\n",
    "Как и ожидалось, кривые всех идеальных алгоритмов проходят через левый верхний угол. На первом графике также показана типичная ROC-кривая (обычно на практике они не доходят до \"идеального\" угла). \n",
    "\n",
    "AUC рискующего алгоритма значительном меньше, чем у осторожного, хотя осторожный и рискущий идеальные алгоритмы не различаются по ROC или AUC. Поэтому стремиться увеличить зазор между интервалами вероятностей классов смысла не имеет.\n",
    "\n",
    "Наблюдается перекос кривой в случае, когда алгоритму свойственны ошибки FP или FN. Однако по величине AUC это отследить невозможно (кривые могут быть симметричны относительно диагонали (0, 1)-(1, 0)). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "После того, как кривая построена, удобно выбирать порог бинаризации, в котором будет достигнут компромисс между FP или FN. Порог соответствует точке на кривой. Если мы хотим избежать ошибок FP, нужно выбирать точку на левой стороне квадрата (как можно выше), если FN - точку на верхней стороне квадрата (как можно левее). Все промежуточные точки будут соответствовать разным пропорциям FP и FN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__<font color=\"green\" size=5>Programming assignment: problem 4. </font>__ На каждой кривой найдите точку, которая ближе всего к левому верхнему углу (ближе в смысле обычного евклидова расстояния), этой точке соответствует некоторый порог бинаризации. Запишите в выходной файл пороги в следующем порядке:\n",
    "\n",
    "T_0 T_1 T_2 T_0r T_1r T_10 T_11\n",
    "\n",
    "Цифры XXX после пробела соответствуют таким же цифрам в названиях переменных actual_XXX и predicted_XXX.\n",
    "\n",
    "Если порогов, минимизирующих расстояние, несколько, выберите __наибольший__.\n",
    "\n",
    "Передайте ответ в функцию write_answer_4. Загрузите файл в форму.\n",
    "\n",
    "Пояснение: функция roc_curve возвращает три значения: FPR (массив абсции точек ROC-кривой), TPR (массив ординат точек ROC-кривой) и thresholds (массив порогов, соответствующих точкам).\n",
    "\n",
    "Рекомендуем отрисовывать найденную точку на графике с помощью функции plt.scatter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "############### Programming assignment: problem 4 ###############\n",
    "best = (0, 1)\n",
    "dists_1 = []\n",
    "dists_10 = []\n",
    "dists_11 = []\n",
    "for actual, predicted, descr in zip([actual_0, actual_1, actual_2], \n",
    "                                    [predicted_0, predicted_1, predicted_2],\n",
    "                                    [\"Perfect\", \"Typical\", \"Awful\"]):\n",
    "    fpr, tpr, thr = roc_curve(actual, predicted)\n",
    "    points = zip(fpr, tpr)\n",
    "    dists = sorted([(np.linalg.norm(np.array(x)-np.array(best)), t) for (x, t) in zip(points, thr)])\n",
    "    if descr == \"Awful\":\n",
    "        dists_1.append(dists[1])\n",
    "    else:\n",
    "        dists_1.append(dists[0])\n",
    "    \n",
    "for actual, predicted, descr in zip([actual_0r, actual_1r], \n",
    "                                    [predicted_0r, predicted_1r],\n",
    "                                    [\"Ideal Risky\", \"Typical risky\"]):\n",
    "    fpr, tpr, thr = roc_curve(actual, predicted)\n",
    "    points = zip(fpr, tpr)\n",
    "    dists = sorted([(np.linalg.norm(np.array(x)-np.array(best)), t) for (x, t) in zip(points, thr)])\n",
    "    dists_10.append(dists[0])\n",
    "    \n",
    "for actual, predicted, descr in zip([actual_10, actual_11], \n",
    "                                    [predicted_10, predicted_11], \n",
    "                                    [\"Avoids FP\", \"Avoids FN\"]):\n",
    "    fpr, tpr, thr = roc_curve(actual, predicted)\n",
    "    points = zip(fpr, tpr)\n",
    "    dists = sorted([(np.linalg.norm(np.array(x)-np.array(best)), t) for (x, t) in zip(points, thr)])\n",
    "    dists_11.append(dists[0])\n",
    "    \n",
    "write_answer_4(dists_1[0][1], dists_1[1][1], dists_1[2][1], dists_10[0][1], dists_10[1][1], dists_11[0][1], dists_11[1][1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def write_answer_4(T_0, T_1, T_2, T_0r, T_1r, T_10, T_11):\n",
    "    answers = [T_0, T_1, T_2, T_0r, T_1r, T_10, T_11]\n",
    "    with open(\"pa_metrics_problem4.txt\", \"w\") as fout:\n",
    "        fout.write(\" \".join([str(num) for num in answers]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Наподобие roc_curve, строят также precision-recall curve и ищут площадь под ней."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Заключение\n",
    "\n",
    "Мы рассмотрели несколько метрик бинарной классификации. Некоторые из них, например, log_loss, обобщаются на многоклассовый случай. Если метрику сложно обобщить в виде формулы, задачу многоклассовой классификации рассматривают как совокупность задач бинарной классификации и затем особыми способами усредняют метрику (например, micro и macro averaging).\n",
    "\n",
    "На практике всегда полезно визуализировать векторы, которые выдает ваш алгоритм, чтобы понимать, какие он делает ошибки при разных порогах и как метрика реагирует на выдаваемые векторы предсказаний."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}