jupyter_russian/tutorials/Gini_coefficient.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Автор: Петухов Дмитрий*<br />\n",
    "*Дата: 04.03.2018*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>Коэффициент Джини. Из экономики в машинное обучение."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Интересный факт: в 1912 году итальянский статистик и демограф Коррадо Джини написал знаменитый труд «Вариативность и изменчивость признака», и в этом же году \"Титаник\" затонул в водах Атлантики. Казалось бы, что общего между этими двумя событиями? Всё просто, их последствия нашли широкое применение в области машинного обучения. И если датасет \"Титаник\" в представлении не нуждается, то об одной замечательной статистике, впервые опубликованной в труде итальянского учёного, мы поговорим поподробней.\n",
    "\n",
    "Коэффициент Джини (Gini coefficient) - метрика качества, которая часто используется при оценке предсказательных моделей в задачах бинарной классификации в условиях сильной несбалансированности классов целевой переменной. Именно она широко применяется в задачах банковского кредитования, страхования и целевом маркетинге. Для полного понимания этой метрики нам для начала необходимо окунуться в экономику и разобраться, для чего она используется там."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center>Экономика"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Коэффициент Джини - это статистический показатель степени расслоения общества относительно какого-либо экономического признака (годовой доход, имущество, недвижимость), используемый в странах с развитой рыночной экономикой. В основном в качестве рассчитываемого показателя берется уровень годового дохода. Коэффициент показывает отклонение фактического распределения доходов в обществе от абсолютно равного их распределения между населением и позволяет очень точно оценить неравномерность распределения доходов в обществе. Стоит заметить, что немного ранее появления на свет коэффициента Джини, в 1905 году, американский экономист Макс Лоренц в своей работе \"Методы измерения концентрации богатства\" предложил способ измерения концентрации благосостояния общества, получивший позже название \"Кривая Лоренца\". Далее мы покажем, что Коэффициент Джини является абсолютно точной алгебраической интерпретацией Кривой Лоренца, а она в свою очередь является его графическим отображением.  \n",
    "\n",
    "<center>\n",
    "<img src=\"../../img/gini_curve.png\" style=\"width: 600px\">\n",
    "\n",
    "Кривая Лоренца - это графическое представление доли совокупного дохода, приходящейся на каждую группу населения. Диагонали на графике соответствует \"линия абсолютного равенства\" - у всего населения доходы одинаковые.\n",
    "\n",
    "Коэффициент Джини изменяется от 0 до 1. Чем больше его значение отклоняется от нуля и приближается к единице, тем в большей степени доходы сконцентрированы в руках отдельных групп населения и тем выше уровень общественного неравенства в государстве, и наоборот. Иногда используется процентное представление этого коэффициента, называемое индексом Джини (значение варьируется от 0% до 100%). \n",
    "\n",
    "В экономике существует <a href=\"https://en.wikipedia.org/wiki/Gini_coefficient#Calculation\">несколько способов</a> рассчитать этот коэффициент, мы остановимся на формуле Брауна (предварительно необходимо создать вариационный ряд - отранжировать население по доходам):\n",
    "\n",
    "$$\\large \n",
    "G = 1 - \\sum_{k=1}^n(X_k - X_{k-1})(Y_k + Y_{k-1})$$\n",
    "\n",
    "где $n$ - число жителей, $X_k$ - кумулятивная доля населения, $Y_k$ - кумулятивная доля дохода для $X_k$\n",
    "\n",
    "Давайте разберем вышеописанное на игрушечном примере, чтобы интуитивно понять смысл этой статистики.\n",
    "\n",
    "Предположим, есть три деревни, в каждой из которых проживает 10 жителей. В каждой деревне суммарный годовой доход населения 100 рублей. В первой деревне все жители зарабатывают одинаково - 10 рублей в год, во второй деревне распределение дохода иное: 3 человека зарабатывают по 5 рублей, 4 человека - по 10 рублей и 3 человека по 15 рублей. И в третьей деревне 7 человек получают 1 рубль в год, 1 человек - 10 рублей, 1 человек - 33 рубля и один человек - 50 рублей. Для каждой деревни рассчитаем коэффициент Джини и построим кривую Лоренца.\n",
    "\n",
    "Представим исходные данные по деревням в виде таблицы и сразу рассчитаем $X_k$ и $Y_k$ для наглядности:"
   ]
  },
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Person</th>\n",
       "      <th>Cum_population</th>\n",
       "      <th>Income_Village_1</th>\n",
       "      <th>Cum_Income_Village_1</th>\n",
       "      <th>Income_Village_2</th>\n",
       "      <th>Cum_Income_Village_2</th>\n",
       "      <th>Income_Village_3</th>\n",
       "      <th>Cum_Income_Village_3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Person_1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>10</td>\n",
       "      <td>0.1</td>\n",
       "      <td>5</td>\n",
       "      <td>0.05</td>\n",
       "      <td>1</td>\n",
       "      <td>0.01</td>\n",
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       "    <tr>\n",
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       "      <td>Person_2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>10</td>\n",
       "      <td>0.2</td>\n",
       "      <td>5</td>\n",
       "      <td>0.10</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Person_3</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10</td>\n",
       "      <td>0.3</td>\n",
       "      <td>5</td>\n",
       "      <td>0.15</td>\n",
       "      <td>1</td>\n",
       "      <td>0.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Person_4</td>\n",
       "      <td>0.4</td>\n",
       "      <td>10</td>\n",
       "      <td>0.4</td>\n",
       "      <td>10</td>\n",
       "      <td>0.25</td>\n",
       "      <td>1</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Person_5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>10</td>\n",
       "      <td>0.5</td>\n",
       "      <td>10</td>\n",
       "      <td>0.35</td>\n",
       "      <td>1</td>\n",
       "      <td>0.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Person_6</td>\n",
       "      <td>0.6</td>\n",
       "      <td>10</td>\n",
       "      <td>0.6</td>\n",
       "      <td>10</td>\n",
       "      <td>0.45</td>\n",
       "      <td>1</td>\n",
       "      <td>0.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Person_7</td>\n",
       "      <td>0.7</td>\n",
       "      <td>10</td>\n",
       "      <td>0.7</td>\n",
       "      <td>10</td>\n",
       "      <td>0.55</td>\n",
       "      <td>1</td>\n",
       "      <td>0.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Person_8</td>\n",
       "      <td>0.8</td>\n",
       "      <td>10</td>\n",
       "      <td>0.8</td>\n",
       "      <td>15</td>\n",
       "      <td>0.70</td>\n",
       "      <td>10</td>\n",
       "      <td>0.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Person_9</td>\n",
       "      <td>0.9</td>\n",
       "      <td>10</td>\n",
       "      <td>0.9</td>\n",
       "      <td>15</td>\n",
       "      <td>0.85</td>\n",
       "      <td>33</td>\n",
       "      <td>0.50</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>15</td>\n",
       "      <td>1.00</td>\n",
       "      <td>50</td>\n",
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      "text/plain": [
       "      Person  Cum_population  Income_Village_1  Cum_Income_Village_1  \\\n",
       "0   Person_1             0.1                10                   0.1   \n",
       "1   Person_2             0.2                10                   0.2   \n",
       "2   Person_3             0.3                10                   0.3   \n",
       "3   Person_4             0.4                10                   0.4   \n",
       "4   Person_5             0.5                10                   0.5   \n",
       "5   Person_6             0.6                10                   0.6   \n",
       "6   Person_7             0.7                10                   0.7   \n",
       "7   Person_8             0.8                10                   0.8   \n",
       "8   Person_9             0.9                10                   0.9   \n",
       "9  Person_10             1.0                10                   1.0   \n",
       "\n",
       "   Income_Village_2  Cum_Income_Village_2  Income_Village_3  \\\n",
       "0                 5                  0.05                 1   \n",
       "1                 5                  0.10                 1   \n",
       "2                 5                  0.15                 1   \n",
       "3                10                  0.25                 1   \n",
       "4                10                  0.35                 1   \n",
       "5                10                  0.45                 1   \n",
       "6                10                  0.55                 1   \n",
       "7                15                  0.70                10   \n",
       "8                15                  0.85                33   \n",
       "9                15                  1.00                50   \n",
       "\n",
       "   Cum_Income_Village_3  \n",
       "0                  0.01  \n",
       "1                  0.02  \n",
       "2                  0.03  \n",
       "3                  0.04  \n",
       "4                  0.05  \n",
       "5                  0.06  \n",
       "6                  0.07  \n",
       "7                  0.17  \n",
       "8                  0.50  \n",
       "9                  1.00  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "village = pd.DataFrame({'Person':['Person_{}'.format(i) for i in range(1,11)], \n",
    "                        'Income_Village_1':[10]*10, \n",
    "                        'Income_Village_2':[5,5,5,10,10,10,10,15,15,15],\n",
    "                        'Income_Village_3':[1,1,1,1,1,1,1,10,33,50]})\n",
    "village['Cum_population'] =  np.cumsum(np.ones(10)/10)\n",
    "village['Cum_Income_Village_1'] =  np.cumsum(village['Income_Village_1']/100)\n",
    "village['Cum_Income_Village_2'] =  np.cumsum(village['Income_Village_2']/100)\n",
    "village['Cum_Income_Village_3'] =  np.cumsum(village['Income_Village_3']/100)\n",
    "village = village.iloc[:, [3,4,0,5,1,6,2,7]]\n",
    "village"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ThzVr1hAeHk6lSpWYO3du4Xvt2rW7bFX98uXLr1rRv3XrVgYMGMC5c+dYtWoV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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2692ed13550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (8,8))\n",
    "Gini=[]\n",
    "\n",
    "for i in range(1,4):\n",
    "    X_k = village['Cum_population'].values\n",
    "    X_k_1 = village['Cum_population'].shift().fillna(0).values\n",
    "    Y_k = village['Cum_Income_Village_{}'.format(i)].values\n",
    "    Y_k_1 = village['Cum_Income_Village_{}'.format(i)].shift().fillna(0).values\n",
    "    Gini.append(1 - np.sum((X_k - X_k_1) * (Y_k + Y_k_1)))\n",
    "    plt.plot(np.insert(X_k,0,0), np.insert(village['Cum_Income_Village_{}'.format(i)].values,0,0),\n",
    "             label='Деревня {} (Gini = {:0.2f})'.format(i, Gini[i-1]))\n",
    "        \n",
    "plt.title('Коэффициент Джини')\n",
    "plt.xlabel('Кумулятивная доля населения')\n",
    "plt.ylabel('Кумулятивная доля дохода')\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видно, что кривая Лоренца для коэффициента Джини в первой деревне полностью совпадает с диагональю (\"линия абсолютного равенства\"), и чем больше расслоение среди населения относительно годового дохода, тем больше площадь фигуры, образуемой кривой Лоренца и диагональю. Покажем на примере третьей деревни, что отношение площади этой фигуры к площади треугольника, образуемого линией абсолютного равенства, в точности равна значению коэффициента Джини:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DkcAL1tr1xph7gW+ste8DNwDPGmOux9OVP91aq5srRUSCzO7duxkwYAA///wz\n9ZvnkZuVSXRMrNOxgtL+3O3kujJoWK0hjRMaO5oloMvaWmuXAktLHLvL5/ufgHMCmUFERE7Nzp07\nSUpKYsuWLTRs1Z45Dy2mWs3aTscKWsWL4DjcVQ9au15ERI5j27ZtJCUl8euvv9KkTWdmP/Q8VRNq\nOR0rqBUvguNwVz2oyIuIyDGkpKTQp08fdu7cSbP2XZm94HniqyWUfWEltyNIJt2BiryIiBxDYmIi\njVt3JCohkcvuf5a4qtWcjhT03NbFrqyfABV5EREJUm635fPNaYy98Y+4XAXExld1OlJI2Jv9C/nu\nHJrXaE5iVedv+dYudCIiUmzt2rVMmDCRJWt+ZcOew0TFxKjAn4CdWd5b5xzclMaXWvIiIgLAN998\nw6BBg0hLS+NQXD0GT77K6Ughp3gRHAe3l/WllryIiPC///2PAQMGkJaWRpezBjDgwllORwpJxYvg\nqCUvIiLB4Msvv2To0KFkZmbS7bzBTL7tj0RGRTsdK+QUuvPZlbUBgF4NezmcxkMteRGRSuzzzz9n\n8ODBZGZm0qP/CCbf/qgK/En6LXszLltAuzrtqBFXw+k4gFryIiKV2jPPPkd2djanJ5/PhLkPEBEZ\n6XSkkLUjiBbBKaIiLyJSSeUWuBhx1XwK6rThrBGTiIhQ5+6pCJad53zp/6iISCWzbNkyDh7K4L3v\ndrEvy805oy5WgS8HwbLznC/9XxURqUTefvttkpOT6ZM8jJT9h52OEzbyXTn8lr2ZCBNB9wbdnY5T\nTEVeRKSSeO2115g4cSKFhYXUb9VRE+zK0e7sn3HjonNiZ6rGBM/iQRqTFxGpBBYvXszMmTOx1jJo\n8pUMnnI1xhinY4WNYNqUxpda8iIiYe6ZZ55hxowZWGsZOv06hky9RgW+nKUE4Xg8qCUvIhLWPvro\nI2bPng3AyMtupv/4SxxOFJ6Kb58LkpXuiqjIi4iEsd5n96Fnn8E069ybPudPdTpOWMotzCQ151ei\nI6I5rd5pTsc5goq8iEgYys/PJ7MAlvywl4vveFzd8wGUkrUei6Vbg27ERsU6HecIGpMXEQkj1lrm\nz59P/wEDeX3FJjJyC1XgA2xHkO0850steRGRMGGt5Y477mDBggWYiAi6rPmaDr3PczpW2EsJsp3n\nfKnIi4iEAWstN954I48++igREZFcfOsjKvAVJFhvnwMVeRGRkOd2u7n22mt58skniYyKZsrtf6Lr\nuclOx6oUsgrSOJiXQnxUPJ0SOzkd5ygq8iIiIcztdjNnzhyeeeYZoqKjmXbnn+l8Zn+nY1UaRevV\n92jYg6iI4CupwZdIRET85napGsQrAAAgAElEQVS72bV3P9Exscy45yl10VewnVnBuQhOERV5EZEQ\ntvtQPslX3Ef7wVNo0ib4uovD3c4g3EPel26hExEJMQUFBdx7772s27aXJd/vwm2iVOAdUtRdH4yT\n7kBFXkQkpOTl5TF+/HjuvvtuLpo8mUK3dTpSpXU4fx+H8veSEJtA2zptnY5TKnXXi4iEiNzcXC64\n4AKWLl1KfLUEBk663OlIlVrRrXO9GvYiwgRnm1lFXkQkBGRnZzNmzBj+7//+j6oJNbl84WIat+7o\ndKxKbWeQ7jznS0VeRCTIZWZmMnLkSJYtW0a1mnWYs3AxDVu2czpWpbcziBfBKaIiLyIS5B5//HGW\nLVtGQu1E5jz8EvWbtXY6UqVnrf29JR+Ey9kWUZEXEQlygy+azb9X/8x5Y6aQ2LiF03EESMvbRVZh\nGnXi69C8RnOn4xyTiryISBA6ePAg0dHRbDpYyBdbDjL2yjudjiQ+fFvxwbzLX3BOBxQRqcRSU1Pp\n378/fQYM5v/Wbnc6jpRiR5AvglNERV5EJIj89ttv9OvXjx9++IHde34jLzvT6UhSipSs4F4Ep4i6\n60VEgsSuXbtISkpi06ZNNGjeljkPL6Z6rbpOx5IS3NYd9CvdFVFLXkQkCOzYsYO+ffuyadMmGrXq\nwBWLXlaBD1L7c7eR68qkUfVGNKreyOk4x6WWvIiIw/bs2UOfPn3Yvn07Tdp2ZvaCF6iaUNPpWHIM\nobAIThEVeRERhyUmJtKqcw+oUotZDzxLfLUEpyPJcewIgUVwiqjIi4g4yO22fLZxP8OufoDC/Dxi\n46s6HUnKkBJCLXmNyYuIOGDdunWMGXM+/1y9hfW7DxMZGaUCHwJctpCUrJ8A6NWol8NpyqaWvIhI\nBfvuu+9ITk7mwIEDZMQlMuKSG52OJH7am/0LBe5cWtZsSd0qwT8xUi15EZEKtHr1apKSkjhw4AAd\nz+jL4ClXOx1JTkDRpjTBvF69LxV5EZEKsnLlSgYOHEh6ejpdzhrAjLueJDom1ulYcgKK749vGPyT\n7kBFXkSkQixfvpxBgwZx+PBhuvUZwrQ7HycqJsbpWHKCQq0lrzF5EZEK8PIrr5KZmUnP/iOYdPNC\nIiP16zfUFLrz2Z29EYOhZ8OeTsfxi/6ViYgEWF6hi4GX3s7hqk35w5BxRERGOh1JTsKe7I24bAEd\n6nYgITY01jJQd72ISIAsW7aMvfsP8t63u9hzOJ+zhk9QgQ9hobQIThEVeRGRAHjvvfcYNGgQ5yUl\ns31futNxpByE0nK2RVTkRUTK2VtvvcX48eMpKCigcfvumkEfJnaqJS8iUrm9+uqrTJo0CZfLxcBJ\nlzPyspsxxjgdS05RviuH37K3EGki6d6gu9Nx/KYiLyJSTl588UWmTp2K2+1m8NSrGTr9OhX4MLEr\n6ycsbrrU60KV6CpOx/GbZteLiJSDZcuWMXPmTACGzZjLwEmzHU4k5al4EZwQ6qoHFXkRkXLRtfeZ\nnDX4fBKbt6ffuBlOx5FyVjSzPpQm3YEfRd4YcybwZ6AjEANEAlnW2tC4SVBEJIDy8vLIcRn+8d1u\nxs1doO75MBWKk+7AvzH5J4FJwGYgHrgUT9EXEanUHnjgAc4+9zxe/u8GMnILVeDDVE5hBqm524iJ\njOG0+qc5HeeE+DXxzlq7BYi01rqstS8C/QMbS0QkeFlrufvuu5k3bx7frfmGH1avdDqSBFBKlmc8\nvlv9bsREhtZ+A/6MyWcbY2KA740xDwN7gKqBjSUiEpystdx2220sXLgQExHBRTctpPNZSU7HkgAK\nxUVwivjTkp/iPe8qIAtoClwQyFAiIsHIWsvcuXNZuHAhEZFRTLn9UXoNGOV0LAmwUB2PBz9a8tba\n7d5vc4H5AMaYnsaYPsBP1tr9AcwnIhIU3G43V199NX/5y1+IjIpm2rzH6HL2QKdjSQUobsmHyPay\nvvyZXf9EKYcn4Cn4uwAVeRGpFA4cyiAqOobpdz9JpzP6Oh1HKkBmwUEO5u2iSnQVOtTt4HScE+bP\nmPxo4K4Sx0ZZa/8SgDwiIkFpV3ouZ0+7nSbnXkDj1h2djiMVpKgV37NhT6IiQm9pGX8SH7DWvuR7\nwBhzXYDyiIgEjcLCQu677z4umDaL5duycRGhAl/J7AzRRXCK+DPxrq0x5lNjzFvGmEeNMUmAbgYV\nkbBWUFDAxIkTuffee5lw4UQKXNbpSOKAUJ50B/615PvhWeWuGtASuBE4zRjTFNhvrc0JXDwRkYqX\nl5fHhRdeyPvvv0981eoMmnq105HEIaF8+xz4N7t+TYlDz3vvl58P/BVYHYhgIiJOyMnJ4YILLuCj\njz6iSvUazF7wAk3bdXE6ljggPW8vhwtSqRFbg9a1Wzsd56T4NYvAGFMfKPozZpW19ubARRIRcUZ2\ndjajR4/m008/pWqNWlz+0GIatw69GdVSPlKyfu+qjzChuTN7mamNMRcCq4DxwIXA18aYcYEOJiJS\n0f72t7/x6aefUr1WXa5c9IoKfCW3I8TH48G/lvwdwOnW2n0AxphE4FPgnUAGExGpaEkXTKffV+s4\nc+h46jVt5XQccVioj8eDf0U+oqjAex3Az41tRESCXVpaGtZadmRF8PnGVEbNusXpSBIErLXFRT7c\nW/L/NsZ8DLzhfTwB+ChwkUREKsaBAwdITk4mt9DN5PnPEV8twelIEiQO5qWQXZhOYpVEmtVo5nSc\nk+bP7PqbjDFjgXPx3B//jLX2vYAnExEJoH379jFw4EB+/PFH6jZqTl5Otoq8FCteBKfx6RgTukvD\n+LN2fSdr7T+Af/gc62etXRbIYCIigbJnzx4GDBjAhg0bqNe0FXMeXkyNOvWdjiVBpLirvmHodtWD\nf2PrbxljbjYe8caYPwMLAh1MRCQQUlJS6Nu3Lxs2bKBB87Zc+cgrKvBylB0+LflQ5k+R/wPQDPgK\nz8I3u4FzAhlKRCQQ9u/fT9++fdm8eTONWnXgikUvU71WXadjSZBxWzcpWeuB0J50B/5NvCsAcoB4\nIA741VrrDmgqEZEAqFWrFh16nkVBVBVmPfg8VRNqOh1JglBqzq/kubJoktCEBtUaOB3nlPhT5FcD\nS/CseFcH+JsxZpy1VgviiEjIsNby+cb9JF06j3Nzs4mrUs3pSBKkQn1TGl/+dNdfYq29y1pbYK39\nzVo7Gk/RL5MxZogxZqMxZosx5tZjnHOhMeYnY8x6Y8zrJxJeRKQsGzZsYNiw4by78md+3HWIiIgI\nFXg5rp1Zob8IThF/bqH7xhjTDTjPe2i5tfaVsq4zxkQCTwHJQAqw2hjzvrX2J59z2gK3AedYa9OM\nMfVO5kOIiJTmxx9/ZMCAAaSmppIZW4fzr5jndCQJAeGwCE4Rf9auvxZ4Dajn/XrNGOPPvotnAFus\ntVuttfnAm8DoEudcBjxlrU0DKLGynojISfvuu+/o378/qamptO91LsNn3uB0JAkBLlvIrixPWzQc\nirw/Y/KXAH+w1mYBGGMWAiuBP5dxXWNgp8/jFDwz9X21877mCjx71t9jrf23H5lERI5p9erVDBo0\niPT0dDr9oR/T7nyC6JhYp2NJCPgtewsF7jxa12pN7fjaTsc5Zf4UeQO4fB67vMf8ua4kW8r7twX6\nAU2AL4wxXay16Ue8kDGzgFkAzZqF7vKCIhJ4X331FUOHDuXw4cOcdk4yU25/lKjoGKdjSYgIp0l3\n4F+RfxHP9rJFS9mOAV7w47oUoKnP4yZ47rEvec7/rLUFwK/GmI14iv5q35Ostc8AzwD07t275B8K\nIiLF3n77HQ4fPkz3vkO5+JZFREZFOx1JQkjxcrZhMOkO/Jt496gx5r94FsAxwAxr7Xd+vPZqoK0x\npiWwC5gIXFTinH8Ck4DFxpi6eLrvt55AfhGRYvmFbs6cdC0TIurSO3kMkZH+tGNEfhdOk+7Av5Y8\n1to1wJqix97u8wbAO76z5UtcU2iMuQr4GM94+wvW2vXGmHuBb6y173ufG2SM+QnPMMBN1toDp/SJ\nRKTSWbZsGW07dGTFznx2H8rjD0O0jIecuAJ3HnuyN2Ew9GzY0+k45cKfDWp+KHkIaIVncZyU411r\nrV0KLC1x7C6f7y0w1/slInLCPvjgA8aNG0fDFm24fNGrxMZXdTqShKjdWRtx2QI61u1I9djqTscp\nF/605COBYT6PDfDhsVrwIiIV5d1332XixIkUFhbSrFMvYuKqOB1JQlhKmGxK48ufIp9nrd3ue8AY\nkxegPCIifnnjjTeYMmUKLpeL/uMvYcSlN4X0vt/ivB1hsr2sL3+KfDtjTAaQjWcC3b+AhICmEhE5\njpdffpkZM2bgdrtJvmgOQ6ZdqwIvp6x4OdswasmXueKdtbaatbY60AgYj2dHuubGmKnGmOaBDigi\n4mvlypVMnz4dt9vNkKnXMHT6dSrwcsryXNnszd5CVEQU3ep3czpOufH7/hJrrQv4BVhgjFkHhP5S\nQCIScjp170Xf0ZOoWqchAybMcjqOhIldWT9hcdOlXlfio+OdjlNuTuomUmvtB+UdRETkeHJzc8lz\nR/LOt7sYOecutd6lXBXdHx8ui+AU8WerWRERRz388MP0Pv0MXvzsBw7nFKjAS7nbEWbL2RZRkReR\noHbfffdxyy238NP6dXz/9Qqn40iYSgnTlrw/i+GUuiOMtXZH+ccREfGw1nLXXXdx//33Y4xh4g0L\n6NZniNOxJAzlFB4mNXcbsZGxdKnXxek45cqfMfmfgS38vtLdVjy7yXUNYC4RqcSstdxyyy0sWrSI\niIhIJt28kF5JI52OJWFqZ+Z6ALo36E50ZHhtaORPkd9ore0BYIz53lrbPcCZRKQSs9Zy/fXX8/jj\njxMRGcWU2/6oFrwEVLhtL+vLnzH5eGNMjDGmJtDMGLPYGBMX6GAiUnkdzs4jMiqa6Xc+rgIvAReu\nM+vBv5b8a8BO7/e3A/uA/+DZelZEpFztSs+h58S51Ok1lEatOjgdRyqBnWG4Zn0Rf/aTv88Y85j3\n+wwAY8zaQAcTkcrD5XIxf/58xk6+hC9T8ilwWRV4qRAZ+QdIy99N1eiqtK/T3uk45a7M7npjTE+g\nLdDWGNPT+7hGwJOJSKVQUFDA5MmTue+++xg7diz5hW6nI0klUrRefa9GvYiMiHQ4Tfnzp7v+v8Bq\nPLPri1ggKSCJRKTSyM/PZ9KkSfzjH/8gtkpVRlx6oxa6kQpVPOkujHae8+VPkd9irVVBF5FylZeX\nx/jx4/nggw+Ir1qdWQteoHkH3ZkrFat40l0YjseDf0U+0RhzHZAL7Aa+ttbuDWwsEQlnOTk5nH/+\n+Xz88cdUqV6Tyx96gSZtOzsdSyoZa21Y3z4H/t1C9yyeHedaAxOAVcaY6YEMJSLh7ZVXXuHjjz+m\nWs3aXLHoJRV4ccSh/L1kFOynZlxNWtdq7XScgPBndv1838fGmLrAF8DiAGUSkTB31rALGXTxWrr3\nG06D5m2cjiOVlO+mNOE6F8TvrWaNMdUBa63dD3QMXCQRCUeHDh0iNzeXvQWx/GfDPoZMu9bpSFLJ\nheumNL78uYXuNGPMd8A64CdjzBpjjPrWRMRvaWlpJCcnc06ffixZ+bPTcUSA31vylbrIA38D5lpr\nm1trmwE34BmnFxEp0/79+0lKSmL16tWkHc4kPy/H6Uginkl33nvkw3XSHfjXXV/VWvt50QNr7TJj\nTNUAZhKRMLFv3z4GDBjAunXrSGzcgjkPv0TNxAZOxxLhQN5OcgoPUb9qfZokNHE6TsD4U+S3GmPu\nBF7xPp4M/Bq4SCISDvbs2cOAAQPYsGED9Zq24oqHXyKhTj2nY4kAR+48F66T7sC/7vqZQCLwD+A9\noC4wI5ChRCS0paen07dvXzZs2ECDFu248pFXVOAlqITzznO+/LmFLg24xveYMaaBMaYZkGqt1QCb\niBwhISGBbmcnke2OYvZDL1CtRm2nI4kcYUeYL4JTpMwib4yZW8rh64E3gFeBH8o7lIiELmst/920\nn7Muup5eY2cTG68pPBJc3NbFrsz1QPgXeX+6628Cqpf4irTW3mytVYEXEQA2btxIcnIyb3+xnu93\npmOMUYGXoLQv51fy3Nk0TWhK/Wr1nY4TUP5MvNtTyqp3YwKUR0RC0E8//URSUhJ79+4lM+Z+Lrzu\nXqcjiRxTuG9K48ufIt/cGPMccBBIAT7Es9WsiAg//PADAwcOJDU1lbY9zmL07FudjiRyXDsrwSI4\nRfwp8rOASKAa0BJ4F+gUyFAiEhq+/fZbkpOTOXjwIB16n8f0u58kJjbO6Vgix1XUkg/38Xjwb3b9\nu76PjTH3Aa8aYz4D7rXWLgtQNhEJYqtWrWLw4MGkp6fT+awkpt3xOFExMU7HEjkul7uA3dkbAOjV\nsJfDaQLP7w1qilhr84ELA5BFRELI+x/8i/T0dLqeO5jJtz1CVLQKvAS/PdmbKXDn0aZ2G2rF13I6\nTsCdcJEXESlwuek++jIuyq9Oj/7DiYzUrxIJDUXr1VeG8XhQkReRE7Bs2TJatm7Lqr1uUtJy6D1w\ntNORRE7IzkqyCE4Rf+6TFxFh6dKlDBkyhLP79GPTjt+cjiNyUirLcrZF/Fnx7rPSjltrk8o/jogE\noyVLljB+/HgKCgpo0eV04qpWdzqSyAkrcOexJ3sTESaCHg17OB2nQvjTXd8IuBgweHaimxzQRCIS\nVN5++20uuugiCgsLOe/8qYy5/Paw3rVLwte2jG9x20JOq3ca1WKqOR2nQvhT5HOttWsAjDE1gZrW\n2v8ENpaIBIPXX3+dKVOm4Ha76X/hpYy45EYVeAlZ6w56SteIdiMcTlJx/CnyacaYJ/CsWb8auNIY\nc27JpW5FJLx8++23TJ48GWstyRdfwZCp16jAS8iy1rLugKfIj25feSaM+lPkx+LprncBr1hrM40x\nNwU2log4rU3HLgyZdBk2Ko5Bk690Oo7IKdmVtYG0/N00rNawUqxZX8Tf/eSfLHFsUcASiYijcnJy\nyCeKd9fsYuC0uWq9S1go6qof1X4UEaby3FhW5ic1xiQaYxYZY5YaYz4r+qqIcCJSsf70pz/RtVs3\nnv33Gg7lFKjAS9hYd/BTAMZ0qFybqPrz58xrwM94NqeZD2zDMzYvImFk4cKFzJ07ly2bN/P9qhVO\nxxEpNwdyd7I7+2eqx1Snf4v+TsepUP4U+TrW2ueBAmvtf621M4EzA5xLRCrQfffdx6233ooxhguv\nv59eSSOdjiRSbtYf9HQ+D207lNioWIfTVCx/Jt4VeP+7xxgzHNgNNAlcJBGpKNZa7rzzTh544AFM\nRASTblxA74GVqztTwt+PRV317Svfv21/ivz9xpgawA3An4EE4PqAphKRgLPWcsstt7Bo0SIiIiK5\n+NZH6NFvmNOxRMpVVkEavx5eQ3RENMPaVr5/3/7Mrv+X99tDQOUazBAJc3luQ2RUNFNuf5Su5w5y\nOo5Iufsp7b+4cTGgRRI14mo4HafC+bN2/YuALXncOzYvIiFqz6Fc2g67lBva96FBi7ZOxxEJiMo6\nq76IP931RS35h4GbA5hFRALM5XJx1113MeaiGazaBwUuqwIvYSvflcvG9C8Bz/3xlVGZs+utte9a\na98FDhd9730sIiGksLCQadOm8eCDDzJ2zGhy8wudjiQSUJsPfUW+O4fejXrTJKFyzhf3pyVf5Kgu\nexEJDQUFBUyePJm33nqL2PiqjL78diIiKs+qX1I5VeZZ9UX8GZP/EU+Bb2OM+QHPlrPWWts10OFE\n5NTl5+czceJE3nvvPeKqVOOyB56lZeeeTscSCSi3dfHTwc8BGN2h8mxIU5I/LfnKsyefSJjJzc1l\n3LhxfPjhh8RXS2D2gudp1l5/n0v425bxHZmFB2ldqzWdEzs7Hccx/ozJbwfSvf9tCJwG7Ap0MBE5\nde+88w4ffvghVRNqMufhl1TgpdIo2pBmTIcxlXoPBn+6618H+hlj/gW0AbKBycDEAGcTkVPUo/9I\nhs24nk5n9qdRy/ZOxxGpENba4vH4yrR3fGn86a7vDbQCdgL1rbVuY8y6wMYSkZOVkZHBoUOHSDfV\n+XTDXgZOutzpSCIVam/OFg7k7qBulbqc3fRsp+M4yp/ptZnW2lxgp7XW7T2WH8BMInKS0tPTGTRo\nEGef24e3l/+A1T0xUgkVddWPbDeSyIhIh9M4y5+WfDdjzGGgive/BogLbCwROVEHDx5k0KBBrFmz\nhlr1GuEq0N/iUjn9WMlXufPlz9r1lfvPIJEQkJqaSnJyMmvXrqVOw6bMefglatdv7HQskQqXnreX\nnZk/UiW6Csmtkp2O4zh/Jt6VekOttfbb8o8jIidq7969DBgwgPXr15PYpAVzFr5EzcQGTscSccT6\nNE9X/aDWg4iPjnc4jfP86a7/BtiM57a5ovsQLJAUqFAi4p/MzEz69evHzz//TP1mrZmzcDEJdeo5\nHUvEMcW3zlXiVe58+VPkk4G7gDXAAmvtwcBGEhF/Va1alTMHDOdQnpvLH1pM9Vp1nI4k4picwgy2\nHPqaCBPBiHZaxw38G5P/D/AfY8xY4EPv/fJ/stZmBzydiByTtZb/bkrltFGX0X7QZGLjqzgdScRR\nP6cvx2UL6Nu8L3Wq6A9e8OMWOmPMXGPMXKAF8B4wAdga4Fwicgxbtmyhb9++vPn5t3y3Ix1jjAq8\nCPDjAc2qL8mf7vrqJR5rm1kRh/z8888MGDCA3bt3k/XgvVx8yyKnI4kEhUJ3PhvS/wtolTtf/hT5\nNdbafwU8iYgc17p16xg4cCB79+6lddczGHfNPU5HEgkaWw59TZ4ri671u9KyVkun4wQNf1a8uzfg\nKUTkuNauXUv//v3Zu3cv7XqczWX3P0NsfFWnY4kEjXXaO75U/rTkqxhjevD77XOA7pMXqShr1qwh\nOTmZtLQ0Opzehxl3P0l0TKzTsUSChtu6WZf2GVC5944vjT9FvjHwR44s8rpPXqSC/Oc/n5GWlkbn\ns5KYdsfjRMXEOB1JJKjszFzH4fx9NE1oSo8GPZyOE1T8KfJbrLUq6CIOKHC5aZs8iSmHojntnIFE\nRavAi5S0zmet+sq8d3xp/CnyaQFPISJHWL58OQ0aNeHHQzHsOJhNj37DnI4kErSKVrnTrPqjlTnx\nTq14kYr1ySefMHjwYM7r24+ftqY4HUckqO3L+ZW9OVuoGVeTPs37OB0n6PizQU3JhW8MYK21rQIT\nSaTyWrp0KWPHjiUvL49u3c6kSkJNpyOJBLWiVvyIdiOIjox2OE3w8ae7PhPoj6e4fwb0o8RMexE5\ndf/85z+58MILKSgo4JyRF3H+lXcSEeHPXa4ildd6ddUfl1+/Qay1B4CDeGbaj/I+FpFy8vbbbzN+\n/HgKCgroO3Y6Y6+6SwVepAwZ+fvZlvEdsZGxDG492Ok4Qcmv2fXGmPeBKsA/gJ7GmL7W2hmBjSZS\nOWzYsIGJEyfidrtJmjCL4TPnaoawiB/Wp32OxTKg1QCqx5ZcgV3AvyI/ARgMuIBPrLUuY8x4f17c\nGDMEeByIBJ6z1j50jPPGAW8Dp1trv/EruUiYaNqqLaNnXktWbj6Dp1ytAi/iJ+0dXzZ/tpotAP5V\n4tjbZV1njIkEnsKzH30KsNoY87619qcS51UHrgG+PoHcIiEvKysLd2QM765J4bwLL3c6jkhIyXNl\nsSl9BQbDyPYjnY4TtPzZajbDGHPY5yvDGHPYj9c+A89COluttfnAm0BpMyPuAx4Gck8ouUgIe/LJ\nJ+nUuQt//dfXpGUXOB1HJORsTF9Boc3nzCZn0qBaA6fjBC1/ZvZssdYm+HxVt9Ym+HFdY2Cnz+MU\n77Fi3jXxm2qXO6lMHn30Ua6++mp2bN/Gd19/6XQckZDku8qdHJs/RT7OGNPNGNPBGFPjBF67tIFF\nW/ykMRHAn4AbynwhY2YZY74xxnyTmpp6AhFEgsuCBQu44QbPP/nx197LGYPGOpxIJPS43AWsT1sG\nqMiXxZ8i/xvwZ+AV4CdjzI/GmN5+XJcCNPV53ATY7fO4OtAFWGaM2QacCbxf2mtba5+x1va21vZO\nTEz0461Fgou1lvnz53P77bdjjGHiDQ9y1vAJTscSCUlbM9aQU3iIDnU70K5OO6fjBDV/Jt71931s\njDkXeBooq9CvBtoaY1oCu4CJwEU+r3sIqOvzusuAGzW7XsLRvHnzePDBBzEREUy68SF6D9TCHSIn\nS3vH+8+fiXeRvo+ttV8CZU4FttYWAlcBHwMbgLesteuNMfcaY0adZF6RkGSi44iIjGLKbX9UgRc5\nBdZa1h307B2vrvqy+bsYzjvAi0W3v/nb2rbWLgWWljh21zHO7efPa4qEmt8O5dKo3yRuatqb+s1a\nOx1HJKTtzv6ZtLxdNKzWkNMbn+50nKDnz5h8V2AT8Jwx5n/eSXD+zK4XqbTcbje33347/1u7gXe/\nTSGvwK0CL1IOfjzg6aof1X4UEUZLP5fFn61mM6y1z1przwZuBu4G9hhjXjLGtAl4QpEQ43K5mDlz\nJgsWLGDMqBHk5OU7HUkkbKxP04Y0J8KfrWYjgeHADKAF8EfgNeA8PF3xmtoo4lVYWMi0adN4/fXX\niYmLZ+yVdxEZ6c+omIiU5WBuCruyNlAtphpJLZOcjhMS/Pntsxn4HFhkrf3K5/g7xpg+gYklEnoK\nCgq46KKLeOedd4iNr8pl9z9Dq9P8udtURPxRtFb9sLbDiI2KdThNaPCnyHe11maW9oS19ppyziMS\nkvLy8pgwYQJLliwhrko1Zj34HC069XA6lkhYWae940+YP0X+idJ2xbLWziz/OCKh6cMPP2TJkiXE\nV0tg9oLnada+q9ORRMJKVkEaWw9/Q1REFMPaDnM6Tsjwp8gPBrYDrwJ7AxtHJDR1OnsgY+bcTqvT\nTqdJm05OxxEJOz+l/Rc3Lga0SKZmXE2n44QMf4p8U2AIMAXPvvAvWms/CmgqkRCQlZXFvn37yI6t\nzf/9tJc+509zOpJI2FYdfeAAACAASURBVFJX/cnx5xY6t3dRm/uAbDyr2IlUaocPH2bIkCGcdc55\nvPmfb7C27GtE5OTku3LZmP4F4Lk/Xvznzy10s4AxwBbgcWvtdwFPJRLE0tPTGTJkCF9//TU16zbA\n5XI5HUkkrG0+tJJ8dw69GvaiaY2mZV8gxfzprn8aT4FvCvQrmoRnrdXMIql0Dh48yKBBg1izZg21\n6zdmzsMvUaehfumIBJL2jj95/hT5lgFPIRICUlNTSU5OZu3atdRp1IwrHn6JWvUaOR1LJKy5rYv1\n2pDmpPlT5K8GXijanEakMsrNzSUpKYl169ZRr0lLLn/4JWrWre90LJGwtz3jezILD9KqVis6J3Z2\nOk7I8afI/ww8a4yJAl4E3vDuBS9SacTGxtJvxHj2Z+Rx+cIXSaid6HQkkUrhR5+940tbs0WOz5/Z\n9c9Za88BpuJZu/4HY8zrxpj+gQ4n4jRrLdZavtyyn1ZJE7nuyXdU4EUqiGfveM+tc+qqPzl+7dPn\n3aSmg/drP/D/7d13fFRV/v/x1ye9EkoCQXpXBBSpohTpSHUVUVdR6a76W8Wy67oqFmzsruvaQGyI\nX8Vd174WBEQR6UpJKAIB6SQkIb3OnN8fM4lDSMgEZnJnJp+nDx7e3Llz5z13IJ+55557zhZgtogs\n8WI2pSy1b98++vfvz7vfrGfj/kwAwsIjLE6lVN1xvGAvJwp/JT4qnn4t+lkdxy9VW+RF5B84muyv\nBJ40xvQwxjxjjBkL6ODcKiDt3r2bAQMGsHr1auY98YjVcZSqk8p61Y/tOJbgoGCL0/gnd67JJwF/\nNcbkV/JYbw/nUcpyO3bsYMiQIRw9epQ2XXowafaTVkdSqk7SpvpzV+WZvIiMBjDGvOFa4EUkVkRe\ncD6mHfBUQElKSmLQoEEcPXqU9hf1YcbchUREx1gdS6k652TRcQ7kbiUyJJKhbYdaHcdvnam5/nkR\nmeq6QkRuALYCqV5NpZQFNm/ezKBBg0hNTaXjJZcx7fEFhEdGWx1LqTopOdNxFj+i/QiiQqMsTuO/\nztRc3x/4n4g0A5YALwPFwFBjzN7aCKdUbVq9+kfS09Pp3GcQNz/0L0LDwq2OpFSdpRPSeEaVRd4Y\nc1REBgIfAn8BbjHGaG96FZBKbXaaXzaeWx42dO4zkJDQMKsjKVVnFZTmsCdrHUESxJiOY6yO49fO\n2PHOGJMjIqOAN4AbRORjY0xh7URTyvt++OEHGjSK55fCGPafyKfb5cOsjqRUnbfz5PfYTAkDWw0k\nPire6jh+rcoiLyI5QNkEmgJEAxkiYgOMMaZeLeRTymtWrFjB2LFjiYipx53P/5u4RjpMrVK+QJvq\nPedMzfWxtRlEqdr09ddfM2HCBAoLC7nw8pHE1tezBaV8Qam9mO2ZKwEYf74W+XPl1oh3SgWSzz//\nnHHjxlFYWEjfKycxafZcgoJ1oA2lfMGerHUU2fLo1qQbbRu0tTqO33NnMBylAsZHH33EpEmTKCkp\n4fLxN3LVH/6qk14o5UO0qd6ztMirOiMlJYVrr72W0tJSBl59K+Nm/EkLvFI+xG7sJGXqKHeepEVe\n1RlNmrXk2tsf4Nix44yeMlsLvFI+5lBuEtnFqbSo14LuiTo1iidokVcBLycnBwmL5L+bDtFz9I1W\nx1FKVcG1qV6/hHuGdrxTAe2VV16hY8dOvPDhd2TkFVsdRyl1Btucs85pU73n6Jm8CljPP/88d911\nFwA/rV1NvzHXWZzIGsWFBfz07eck/biMI3t3kpudSZAEEV2/ITH1G9K0dQfade1Nu269aJjY3Oq4\n5+xk2jFWfbKY7Wu/JTP1KEHBwTRKbE6Xy4bSf/xNRMXGndP+Zw/vVOPn/PXt5acdW7vdTurBFA7s\n2sqBnVs5+Ms2juzbha2kBIA/zHub9hf1Oaes/iStYD/HC/ZQP6I+A1oNsDpOwNAirwLSvHnzuP/+\n+wG46vaH6myB/3XHFhY/eTcZxw+f9ljx8cNkHj/MwV3bWP/1hwA88/lWvx6zf8eG73nnqXsoyM0+\nZf3hvTs4vHcHa7/4N1PmvEyLjl1qLVNEdCyxDRNOW79p2Se897c/11oOX1fWVD+6w2hCg0MtThM4\ntMirgDN37lz++te/AjDxj49x6ehJFieyRtrh/Sx4YAqF+bkAdO4ziIv6jyShRRtCw8LJzz7JkX27\n2LtlPbt+Wk1JkX+PWH0kZSeLHv8jxYX5hIVHcsWkaXTsfik2m43kH5ez6uPFZJ04zmsPz2L2S/89\n6xEO71vwWbXbbF+/kv+9/ncALh54ZaVfnEz5gKIQHBJKYusO2G2lHN33y1nl8ndJ2lTvFVrkVUCZ\nM2cOjz76KCLCpNlz6T3iaqsjWeaLN58rL/DX3v0EfUdNPG2bDt0vZeDvbqEwL5f1Sz8kKMh/u+l8\n/MqTFBfmExQUzPS5C2nXrVf5Y+279aZZ+868++z95GSk8eVb/+S6e546q9dp2qZjtdt88eY/ypd7\nDau8aDVp2Z4Jtz1Iy/O70azdBYSGhfPV2y/UySKfU5zO/pyfCQsOY0S7EVbHCSj++y9aqUpExNYn\nKCiYG+5/tk4XeLvNxvZ1KwFo0bFLpQXeVUR0DAOumkxwiH82kx78JYk9W9YB0Gv4VacU+DI9h46n\nw8V9Adj4zSfkZKZ7JUvuyQx2bFgFQEKz1rS58JJKt2t1fjcGXDWZ1hdc7NeXSDwhOXMFBsPQtkOJ\nDdcR1T1Ji7wKGMezC4nrMZY/vf4lPYaMszqOpXKzMsqb3xs1bWlxGu/btvqb8uU+I6+pcruyL352\nu43ktSu8kmXTik+x20oB6FnFWbw6VbLzevyETnq8PE2LvPJrdrudBx98kO/X/8x/fzpEYYmNhGat\nrI5luZDQsPLl4wf3WpikdqQkbQIgLDySFp26Vrld+4t/662+z/kcT9u47BMARISeQ3Vo1uoU2fLY\ndXI1gjC201ir4wQcLfLKb9ntdmbOnMmTTz7J7yaMIy/fvzuOeVJUbBwNmzQD4GjKLpa9Nx+73W5x\nKu85fmAPAPHNWhEcXHVXo7hGTYiIigHgmPM5nnRk3y4O79kOQPuL+tCg8Xkef41As+vkakpNMX2b\n9yUxJtHqOAFHO94pv2Sz2Zg6dSqLFi0iNCyca+589JSzVwX9r5rMJ/Mdncu+ePM51vzvfS68dDCt\nO3enRceuxJ/X0mOjiq1f+iFL/vbAOe+nsvvJq1NaXExeViYA9ROqLxJxCYkU/rqHk2nHzirjmWz8\n5uPy5Z7DrvL4/gORTkjjXVrkld8pLS1l8uTJvPfee4RFRDL1sfnlHarUbwZcdTPHD6Sw9ov3AchM\nPcIPn7zDD5+8A0B0XAPadu1F94Gj6Hr58DOeAfuywoLc8uWwiKhqtw93blNckOfRHHabjZ9WOG6v\nC4+Motvlwz26/0BkM6UkZ34L6K1z3uKf/6pVnVVSUsINN9zABx98QHhkNNPnvkrbLj2tjuWTRIRr\n73qM7gNH8d2Hi9i16QdspSXlj+dlZbLth6Vs+2EpjVu05cYH/k7z9p3P6rW69htKiwXnPsBMXHzN\n710vKSoqXw4Jrf7ugLIWH9fnecKuTT+QnZEGQLf+IwmPrP4LR12Xkr2RgtIszo8/n07xNR9JUFVP\ni7zyK8uXL+eDDz4gMjqW6U++RusLLrY6ks/r0P1SOnS/lKKCPPZv38yBXVs5tDuZlG0byMs+CUDq\nwRReuvdG/vjP90ls3aHGrxEZU4/ImHqeju6W0PDfbj8rLSk5w5Zl2xSf9jxP2ODSVF/VvfHqVNpU\n731a5JVfadv9Mq696zGatb+wVocmDQThkdF06nEZnXpcBoDNVkrymhV8/PJcTp44RlF+Hh+/8iSz\nnnnT4qQ1ExEZU75cXJhf7fZFzm3CIqM9lqEgL4ekNY6C1bBJM9p16+2xfQcqY0x5kdemeu/RIq98\nXn5+PocPH8YW24Svko7R98q6OUytpwUHh9Dt8uHEN2vFc3dcja2khN1b1pKXfZLoevVrtK+C3GyP\ndGRr3KJNjQfkCQkLIzquAXlZmW5lyHJu404nPXdtXvkFpcWO5v+ewyboNKluOJK/i8yiwyTGJNK7\nmX4p8hYt8sqn5ebmMnbsWLYmJTPjmUU0btHO6kgB57w2nWjV6SJSkjZi7HbSjx6ocZHf9uMyy3rX\ng2OI2JRtGzhx+FdsttIqOxFmpR8vH+o3sWX7c8rqauMyl171Q/Ws1B1lY9WP6ziOING7ub1Fj6zy\nWdnZ2YwcOZKVK1diMwLo2ZG31GvUuHxZ/PAXbtsuPQAoLirg4K5tVW63Z8v68uU2zuecqxNHDrAv\n+afyfcafF/gjDHqCTkhTO/RMXvmkzMxMRo4cyfr166mf0JTbnl2kI9l5iTGGQ7uTAUeP/AZNaj6A\nS+/hv6P38N95Oprbul42jGXvzQdg3Vcf0Lpz90q3W//1fwEICgrmwr6DPfLaG775qHy5l94b75aM\nwsMczttBTFgMg9t45nNQlfO/r+wq4KWnpzNkyBDWr19Pw8Tm3PH3d7TA11BRQR7P3XkNSWuWY7fZ\nzrjtV2//ixNHfgWgTZeexMQ1rI2IHtWiYxfaX+QYsnbD0o9I2bbxtG02Lf+U3T+vAaDnsPHENmh0\n2jYZxw4xe3gnZg/vxEv33lTt6xpj2OQcxjY0PIKLB4w6l7dRZyRlOjrcjWo/ivCQuj05j7fpmbzy\nKcXFxQwZMoQtW7aQ0Kw1s555iwaNm1odyy8d3LWNNx75A/UaJtCl3xBaXdCdRonNCY+Koaggl6Mp\nu9i4/FN+3bEZcNw/Pn7mnyxOffYm3PYX/nXX9RQX5vPqX6YxeNJ0OnS/FLvNRtKa5az66G0AYhvE\nM+qWuzzymnu3bSDj+GHAMVZARHRMNc841fqlH57y85G9O8qXd25cVb5vcOS+oNeAc0jrO5LStam+\ntmiRVz4lNDSUEdfcxLHMXGY98yZxjWo+OIqCoOAQYhsmkJORRnZGGj9+voQfP19S5fb14xO5/r6n\nadGx6sldfN15bc/n5oee552n7qEgN5uv3v4XX739r1O2iYtvwpQ5L3vs79XGc2yqP1NnxRXvLzzl\n53bdegdEkc8rOUlK9kZCgkK4ssOVVscJeFrklU8wxgDw4950EvuMZXb34XV+ju1zERoWzpz3VvHr\njs3s/nkNv+7cQurBfWRnpFFaXERoRAT1GiTQtE0nOvcdxMUDRhEWEWl17HN2Qa8B3LfgM1Z9/Dbb\n160kM/UoQUFBNExsTtfLhtF/wk1ExcZ55LWKCwvYsuprwPHlocMl/Tyy30C3I3MldmwMbj2U+hE1\nu4tD1ZyU/XL1Fz179jQbN55+vU35r19//ZVJkyZx20PzyAjTM3elAtmbO+9kW8ZSXhz1Irf3vt3q\nOH5BRDYZY85q/G7teKcslZKSwoABA1i3bh3PPv6w1XGUUl5UbCtk18kfABjXaZzFaeoGLfLKMr/8\n8gsDBgzgwIEDtLrgYn7/579ZHUkp5UW7s9ZQbM+nR9MetIhrYXWcOkGLvLLE9u3bGThwIIcPH6ZN\nlx7MfOp1IqNjrY6llPIiHau+9mmRV7Vu69atDBo0iGPHjtH+oj7MmPsaEVE1u/VIKeVf7MZGcuYK\nQGedq01a5FWt++mnn0lLS6NTj8uZ9vgCnXdbqTrg15zN5Jak07ZBW7o01hkka4veQqdqVanNTsPu\nw5j2+AI6dL9Ub5NTqo5wnTteZ+mrPVrkVa1Ys2YNYeERHApqTEpaHp37DLI6klKqlhhj2KYT0lhC\nm+uV133//fcMGzaMwUOGsnHbLqvjKKVq2fGCvZwo/JX4qHj6tdBBg2qTFnnlVcuXL2fkyJHk5eXR\nsWd/4hISrY6klKplZU31YzqOISRIG5BrkxZ55TVff/01Y8aMoaCggN4jrua6e54iOFj/gStV15TP\nHd9Jm+prmxZ55RWfffYZ48aNo7CwkH5jruPau58gKDjY6lhKqVqWVXycA7lbiQyJZFi7YVbHqXP0\ntEp53KFDh5g4cSLFxcX0n3ATE257UHvTKlVHJWc47o0f3m44UaF6u2xt0yKvPK5h40RunP0YKXt+\nYcy0+7TAK1WHaa96a2mRVx6TlZVFSEQ0H/50iAuvmMCFV1idSCllpcLSXPZkrSNIghjTcYzVceok\nvSavPOL111+nXfv2PPf+N5zILbY6jlLKB+w4+T02U8LlLS8nPire6jh1khZ5dc5efvllpk2bRvqJ\nE2xau9rqOEopH6G96q2nRV6dk3/+85/cfvvtAIyf+QADrppscSKllC8otRezI/M7AMafrxPSWEWL\nvDprzz77LHfffTcAV9/xMAOvvsXaQEopn7E3ez2Ftly6Nu5K2wZtrY5TZ2mRV2dl7ty5/OlPf0JE\nuPbuJ7hs3O+tjqSU8iHb0rVXvS/Q3vXqrMTFNyEoOIRJdz9Br+FXWR1HKeVD7Mauc8f7CC3yqsZS\ncwoJOf8KHnjjKxo1bWF1HKWUjzmUm0RW8XGa12vOJU0vsTpOnaZFXrnFGMNDDz3EoBFj2G1LoLDE\npgVeKVWppEzHhDQTOk3QwbAsptfkVbXsdju33347c+fO5ZqrJpCdm2d1JKWUD0tKdxR57VVvPT2T\nV2dks9mYOXMmr7/+OiGhYVx79+OEhUdYHUsp5aPSCn7lWMFu4sLjGNhqoNVx6jwt8qpKpaWlTJky\nhcWLFxMaHsHUR1+h4yX9rI6llPJhyc6540d3HE1ocKjFaZRXm+tFZKSI7BKRPSLy50oeny0i20Vk\nq4gsF5FW3syj3FdSUsJNN93E4sWLCYuIYvrchVrglVLV2qaj3PkUrxV5EQkGXgJGAZ2B60Wkc4XN\nfgZ6GmO6AR8Az3orj6qZH3/8kffff5/wqGhmPvUa7bv1tjqSUsrH5RSnsz/nJ8KCwxjZfqTVcRTe\nba7vDewxxqQAiMgSYDywvWwDY8y3LtuvBW70Yh5VA80uuITf3/8MjZq1odX53ayOo5TyA9szv8Vg\nGNJmCLHhsVbHUXi3yDcDDrr8fAjoc4btpwJfejGPqkZBQQEpKSmExrfky23HuGSI9oxVSrkvSeeO\n9znevCZf2c2RptINRW4EegLzqnh8hohsFJGNaWlpHoyoyuTl5TFmzBj6XXYZr360HLup9KNSSqlK\nFdny+SXrRwRhXKdxVsdRTt4s8ocA19FSmgNHKm4kIkOBB4FxxpiiynZkjHnVGNPTGNMzISHBK2Hr\nspycHEaNGsWKFSswQaEEh4RZHUkp5Wd2nVxNib2IPs37kBiTaHUc5eTNIr8B6CAibUQkDLgO+NR1\nAxHpDizAUeBTvZhFVSErK4sRI0awatUq6jVqzO1/W0xiq/ZWx1JK+RmdO943ea3IG2NKgTuAr4Ed\nwL+NMcki8piIlLXlzANigP+IyGYR+bSK3SkvyMjIYOjQoaxZs4YGjc/jjr//H41b6JSQSqmasZlS\ntmeuBHSUO1/j1cFwjDFfAF9UWPewy/JQb76+qprNZmPEiBFs3LiRhonN+cO8t2nYpJnVsZRSfmhf\n9ibyS0/SqVEnzo8/3+o4yoWOeFdHBQcHM/aGaRw4ls6sZ96ifoJeQ1NKnZ1t2qveZ2mRr2OMs9f8\n2pQMYrtcwb3zLyMkTDvaKaXOjjGmfChbnTve9+gsdHXIoUOH6NOnD298vIK1KekAWuCVUufkSP4u\nMooO0yS6CX2an2koFGUFLfJ1xP79+xkwYAAbNmzgmccfsjqOUipAlPWqH99pPEGiJcXX6CdSB+zd\nu5eBAweyb98+WnTqys1/fd7qSEqpAJGUoXPH+zIt8gFu165dDBw4kAMHDtC6c3dmPf0mUbFxVsdS\nSgWAjMLDHM7bTkxYDIPbDLY6jqqEdrwLYNu3b2fw4MEcP36ctl17Me3x+URExVgdSykVIJIzVwAw\nsv1IIkIiLE6jKqNFPoAlJ28nLS2NDhf3ZcqjrxAeGWV1JKVUgMgrOcmPx5YAOsqdL9MiH6BsdkNk\np35Mn/sabbr0ICxcv2UrpTwjtySDBduncLxgD+0atNMJaXyYFvkAs27dOkptdtKjW7E3NZdOPS6z\nOpJSKoDkFJ/gleRbOFawm46NOrJ88nKdO96Hace7APLDDz8wbNgwho8YyZpNW62Oo5QKMFnFx3kp\n+SaOFeymc0JnVt68kub1mlsdS52BFvkAsXLlSkaOHElOTg6devan0XktrY6klAogmUVHeSnpJlIL\nUujauCvf3vwtTWObWh1LVUOb6wPAsmXLGDduHAUFBfQcOoHr7nmSoOBgq2MppQJERuEhXk6+mYyi\nQ3RP7M43N31Do6hGVsdSbtAzeT/3xRdfMGbMGAoKCugzaiLX3fuUFnillMekFfzKi0k3klF0iN7N\nerN88nIt8H5Ez+T9WGpqKhMnTqSoqIh+Y67nd3c8TFCQfm9TSnlGakEKryTfTFZxKv1a9OPL339J\nvfB6VsdSNaBF3o/F1m/ErQ88TdLmnxk340+IiNWRlFIB4lj+bl5JvoWckhMMbDWQz2/4nJgwHUzL\n32iR90OZmZmER8fy358O067PCNr1GWF1JKVUADmct5P5ybeQV5rJ0LZD+eS6T4gK1cG0/JG27fqZ\nRYsW0bZtW55Z/DkncoqsjqOUCjAHc5N4JXkyeaWZjGo/is+u/0wLvB/TIu9HFi5cyK233srJkyf5\nae2PVsdRSgWY/TmbmZ98C/mlWYzrNI6PJn2kY9L7OS3yfuKll15ixowZGGMYM+1eBl87zepISqkA\nkpK9kQXbp1Bgy+HqC67mPxP/Q3hIuNWx1DnSIu8HnnvuOe644w4Axs96gMHXTrc4kVIqkOzJWser\n26dTZMvj+i7Xs+SaJYQFh1kdS3mAFnkfN2/ePGbPng3A1Xc8zMDf3WJtIKVUQNl1cjULd8yg2J7P\n5Isms/iqxYQEaZ/sQKGfpI9LOK8FwSGhXH3nI/QdNdHqOEqpALI98zve2nkHpaaYad2nsWDsAoJE\nz/0CiRZ5H5aWU0RR81488ObXNGzSzOo4SqkAsi19GW//chc2U8Ifev6BF658QQt8ANIi72OMMTzy\nyCP06X8FB8NaUlBs0wKvlPKozSe+5J3d92I3pdzd927+PvzvOphWgNKvbT7EGMPdd9/N448/zqRr\nribzZJbVkZRSAWZT2mcs/mU2dlPKny/7sxb4AKdn8j7Cbrdz++23M3/+fEJCQ7nunieJiNIhJJVS\nnrM+9UPe3/MXDIaHBzzMnEFztMAHOC3yPsBmszFjxgzeeOMNQsPCueWRF7mg1wCrYymlAsiaY+/z\nn5SHAXjiiid4cMCDFidStUGLvMVKS0u59dZbeeeddwgNj2DqY/Pp2P1Sq2MppQLIqqPv8NG+xwGY\nN2we9/a71+JEqrZokbfYpk2bWLJkCWERUUx/4lXadetldSSlVABZeeRNPt3/NADPj3ye/9fn/1mc\nSNUmLfIWi297ITf95TliGsTT5sJLrI6jlAogyw4t4IsD/wBg/uj5zOw50+JEqrZpkbdAYWEhO3fu\nJOa8dvxv6zG6Xj7c6khKqQBijGHpoZf4+uALCMJr415jSvcpVsdSFtBb6GpZQUEB48eP57LL+/Pi\nki+xG2N1JKVUADHG8MWB5/j6oGNwm7evelsLfB2mRb4W5eXlMXr0aJYuXUpQaBihEZFWR1JKBRBj\nDJ/9+izLDy8gWIJ593fvcmO3G62OpSykzfW1JCcnh9GjR7Nq1SpiGyZw2zNvkdiqvdWxlFIBwhjD\nR/vm8sOxxYQGhfL+Ne9z1QVXWR1LWUyLfC04efIko0aNYu3atcTFN+G2ZxfRuHkbq2MppQKE3dj5\nIGUOa4+/T1hwGP+99r+M6TjG6ljKB2iR9zK73c7o0aNZu3YtDZo04w/PLqJR0xZWx1JKBQi7sfH+\nnr+yIe1DIkIi+HjSx4xoP8LqWMpHaJH3sqCgICZMnsmeA0eZ8dTrOtmMUspjbKaU93b/iZ9OfE5U\naBSfXf8Zg9sMtjqW8iFa5L3EGIOIsC4lnZC2fbnv1c8IDgm1OpZSKkDY7CW8s/tetqR/RUxYDF/c\n8AX9W/W3OpbyMdq73guOHDlCr169eHnJZ/y4Nx1AC7xSymNK7cUs+uUutqR/Rb3weiy9cakWeFUp\nLfIedvDgQQYOHMimTZv429xHMXofvFLKg0rsRby58w6SMpZRP6I+yycv59IWOt+Fqpw213vQ/v37\nGTx4MPv27aN5+wuZMuclncZRKeUxxbYC3th5O79kraZRZCOWTV7GxYkXWx1L+TAt8h6yZ88eBg8e\nzMGDB2l5/kXMfPI1ImPqWR1LKRUgimx5vLZjFnuz19M4ujHLJy+nS+MuVsdSPk6LvAfs3LmTIUOG\ncOTIEdpceAnTn1hIRHSM1bGUUgGisDSXhTtmsC9nE01jmrLi5hWcH3++1bGUH9Ai7wF796aQmppG\nu4t6M+2x+YRHRlsdSSkVIApKs1mwfRoHcrfQvF5zVkxeQYdGHayOpfyEFvlzZLMbpGV3Zjz9Bi07\ndiVMx6NXSnlIXslJFmyfwqG8ZFrFteLbm7+lTQMdLVO5T4v8Wdq4cSNZ2TkUxHdi9/Fc2nfrbXUk\npVQAyS3JYH7yrRzJ30m7Bu1YcfMKWsa1tDqW8jN6C91ZWLt2LUOGDGHMmDF8t2aj1XGUUgEmuziN\nl5MmcyR/J50adeK7W77TAq/Oihb5Glq1ahXDhg0jOzubjj3607hFW6sjKaUCyMmi47ycfBPHCnbT\nOaEzK29ZSbN6Ohy2OjvaXF8D3377LWPGjCE/P5/uV4zhhvufIThYD6FSyjMyi47wcvLNpBceoFuT\nbiy7aRkJ0QlWx1J+TCuUm5YuXcr48eMpLCyk59AJXHfPkwQFB1sdSynlZ4wxFNpyyS5OJbskjezi\nNHKK08guSWPLia/ILD7CJU0vYemNS2kU1cjquMrPaZF3Q2ZmJhMnTqSwsJA+oyYy8Y+PERSkVzqU\nUr+xGzt5JZnOZ2EyrgAAEdNJREFUwp1aXrizi9PIcf4/27muxF5Y5X76NOvDVzd+Rf2I+rWYXgUq\nLfJuiIypx/SHn2P96u8YP/MBLfBK1SE2ewnZJSecxTrVWaxPkF2SRk5xannhzilJx25K3dpndGg0\nTWOb0jSmKYkxiTSNaUrT2Ka0imvF+PPHExUa5eV3peoKLfJnkJ6eTlRsfT78+RDNul3OVd0utzqS\nUspDimz55JSccDSbu551ly871ueVZrq9zwYRDcqLd/n/XZed/48Nj/XiO1PqN1rkq/Duu+8ya9Ys\n7nx6IfEdulsdRynlBmMMBbZsl6bx1AqFO638WniRLc+tfQZJEI2jG5+xcCfGJJIYk0hESISX36FS\nNaNFvhJvvfUWU6ZMwRjDzxvWMkyLvFKWshsbuSUZLmfcZde8T7hc83YU9FJT7NY+w4LDTivciTGJ\np511N45uTHCQdrJV/kmLfAWvvvoqM2fOBGDULXcx7IbbLE6kVOAqtRc7m8xPPfM+tbNaKrklGdix\nubXPmLCYapvLm8Y2pUFEA50KWgU8LfIuXnzxRe68804Axk6/nysmTrU4kVL+qciWR3bxiVPOsLMr\n9DDPKU4lr/Sk2/tsFNmo2uvdiTGJxITpDJBKldEi7/T8889z1113ATDhtgcZcNVkixMp5VuMMeSX\nZp1yhn164XasL7Lnu7XPYAmmSUyTapvNE2MSCQsO8/I7VCrwaJF3Oq9VW0LDwhk/6y/0G3Od1XGU\nqjWO693pzkJ94rR7vF0LuLvXu8ODw93qZR4fFa/Xu5XyIi3yQHpuEZkNO/PAW99QP76J1XGU8ohS\ne3GFW8NOP/POLk4jtyQdg92tfdYLr+fW9e648Di93q2UD6izRd4Yw5w5c+jWsy8n6nUkv9imBV75\nBceQqKd3TvutmDsGasmvwfXuhKiESs+8Kzab6yAtSvmXOlnkjTHce++9/OMf/yAiOoYHFy0nup4O\nIamsY4whrzTTpXCfKC/cFZvOi9283h0SFFI+mprrqGoV/98kugmhwaFefodKKSvUuSJvt9v54x//\nyIsvvkhwSCjX3fO0FnjlNTZT+tv17tPu8U5zOSM/gc2UuLXPyJBIt653N4pqRJDoEMxK1WV1qsjb\n7XZmzZrFwoULCQkN5eaHXuDCvldYHUv5oRJ7URXDoaaeUtDzSjIwGLf2WT+ifrW3hzWNaUq98Hp6\nvVsp5ZY6U+RtNhtTp05l0aJFhIaFM2XOy3TqqWPRq9+caQrQijOJFdiy3dqnIDSJbnLqte1KzroT\nYxKJDI308jtUStU1dabIJyUlsWTJEsIiIpn66Ct06H6p1ZFULSmbArS8SJ/STH7qmfeZpgB1FRoU\nWm3hbhrrGBI1JKjO/DNTSvmYOvPbp16z9tz6yIuEhEfRtmtPq+MoD7DZS8gpSa9iUJazmwI0KjTK\nrVvEGkY21OvdSimfF9BFvqioiK1bt9Kw9QX8b+tROvYcYHUk5YZiW8EpU32eemvYb7OK5ZVmun29\n250pQBNjEokNi9Xr3UqpgBGwRb6wsJCrr76a5StWMPWxBbS/uK/Vkeq0silAXQv1aT3OncW80Jbr\n1j7LrndXd9atU4AqpeqqgCzy+fn5TJgwgW+++YboevWJjI2zOlLAclzvzqj0zPuUKUBLTlBqL3Jr\nn2HBYaff111JAU+ITtDr3UopdQYB9xsyNzeXsWPHsnLlSmLqN+K2Z96iaZuOVsfyO25NAVqSRm5x\n+jlNAVrZ/N0NIxtqk7lSSnlAQBX57OxsrrzySlavXk29hgnc9uwimrRsZ3Usn1Jkyz/1DNsDU4A2\njGzoVmc1nQJUKaVqV8AUeWMMEyZMYPXq1dSPT+S2eYtIaNba6li1whtTgAZJkFvXu5tENyE8JNzL\n71AppdTZCJgiLyJcfevtJO/ez/S5C2nUtIXVkc6ZYwrQjDMOh+qJKUArG9c8ISpBpwBVSik/5/dF\n3m63ExQUxIb9GRQnduW+hZ8THOzbb8udKUBzih33d9dkClB3OqvVj6iv17uVUqqO8O1qWI1jx44x\nevRoJv+/B7Cf1w3A0gJfZMs77bawisOh1nQK0Pio+GoLd2JMItFh0V58Z0oppfyR3xb5w4cPM3jw\nYH755RfSnnyUP/7rPwQFeX4EMsf17pMVOqid2xSgwRJc5ZCoruubxDQhLDjM4+9JKaVU3eDVIi8i\nI4HngWDgNWPM0xUeDwfeBnoA6cAkY8z+6vZ74MABBg8ezN69e2nathPTn1hY4wJf/RSgJ8qXazoF\naHmzeRWd1eKj4nVIVKWUUl7ntSIvIsHAS8Aw4BCwQUQ+NcZsd9lsKpBpjGkvItcBzwCTzrTfoqIi\nBg4cyP79+2ne/kJmPv060fUalD9e6RSgpw3OkkZuSbrbQ6LGhce5NX+3TgGqlFLKl4gx7hW6Gu9Y\n5FJgjjFmhPPnBwCMMU+5bPO1c5s1IhICHAMSzBlChUaHmtK2pdRvdx5dhg0mn6yzngI0ITrhtLm6\nKyveOgWoUkopq4jIJmPMWc2s5s3m+mbAQZefDwF9qtrGGFMqIllAI+BEVTstjSuFa+AkR/jhxDun\nPR4SFOJWL/PG0Y0JDQ491/eolFJK+SxvFvnK2q0rnqG7sw0iMgOY4fyxiDkkVfWipZRyyPmfOmvx\nnOGLlvIYPc7ep8fY+/QYe1+ns32iN4v8IcB1RJrmwJEqtjnkbK6PAzIq7sgY8yrwKoCIbDzbZgvl\nHj3GtUOPs/fpMfY+PcbeJyIbz/a53uzivQHoICJtRCQMuA74tMI2nwI3O5evAVac6Xq8Ukoppdzn\ntTN55zX2O4CvcdxC94YxJllEHgM2GmM+BV4HFovIHhxn8Nd5K49SSilV13j1PnljzBfAFxXWPeyy\nXAhMrOFuX/VANHVmeoxrhx5n79Nj7H16jL3vrI+x126hU0oppZS1dNg1pZRSKkD5bJEXkZEisktE\n9ojInyt5PFxE3nc+vk5EWtd+Sv/mxjGeLSLbRWSriCwXkVZW5PRn1R1jl+2uEREjItpL+Sy4c5xF\n5Frn3+dkEXm3tjP6Ozd+X7QUkW9F5Gfn74wrrcjpz0TkDRFJFZFKbxMXh385P4OtInJJtTs1xvjc\nHxwd9fYCbYEwYAvQucI2fwDmO5evA963Orc//XHzGF8BRDmXb9Nj7Plj7NwuFvgeWAv0tDq3v/1x\n8+9yB+BnoIHz58ZW5/anP24e41eB25zLnYH9Vuf2tz/AAOASIKmKx68EvsQxxkxfYF11+/TVM/ne\nwB5jTIoxphhYAoyvsM14YJFz+QNgiOjA8TVR7TE2xnxrjCmbWm8tjrEOlPvc+XsM8DjwLFBYm+EC\niDvHeTrwkjEmE8AYk1rLGf2dO8fYAPWcy3GcPi6KqoYx5nsqGSvGxXjgbeOwFqgvIk3PtE9fLfKV\nDYnbrKptjDGlQNmQuMo97hxjV1NxfINU7qv2GItId6CFMebz2gwWYNz5u9wR6Cgiq0VkrXOGTOU+\nd47xHOBGETmE466qO2snWp1S09/bPjufvMeGxFVVcvv4iciNQE9goFcTBZ4zHmMRCQKeA26prUAB\nyp2/yyE4muwH4WiRWiUiXYwxJ72cLVC4c4yvB94yxvzdOUHZYucxtns/Xp1R47rnq2fyNRkSlzMN\niauq5M4xRkSGAg8C44wxRbWULVBUd4xjgS7AShHZj+Ma26fa+a7G3P198YkxpsQYsw/YhaPoK/e4\nc4ynAv8GMMasASJwjGuvPMet39uufLXI65C43lftMXY2JS/AUeD1GmbNnfEYG2OyjDHxxpjWxpjW\nOPo9jDPGnPU41XWUO78vPsbRkRQRicfRfJ9Sqyn9mzvH+AAwBEBELsBR5NNqNWXg+xSY7Oxl3xfI\nMsYcPdMTfLK53uiQuF7n5jGeB8QA/3H2aTxgjBlnWWg/4+YxVufIzeP8NTBcRLYDNuA+Y0y6dan9\ni5vH+B5goYjcjaMJ+RY98aoZEXkPxyWleGffhkeAUABjzHwcfR2uBPYA+cCt1e5TPwOllFIqMPlq\nc71SSimlzpEWeaWUUipAaZFXSimlApQWeaWUUipAaZFXSimlApQWeVVniEiuy3JTEdkrImOtzKSU\nUt6kRV7VOSISi+N+02eMMZ9ZnUcppbxFi7yqU0QkFPgQ+NQY86pz3VQRec5lm+ki8g8Rae2c432W\nc32wiBwWkbdEJFZE9jn3h4jUE5H9Lj+vdM69vbmsBUFEwkTkIxFJEpFtzqFscc7BvVlEcl2eM05E\n5ojIvc5thrjONy8iNud2e0TkPecIWK1d56EWxxz1bzmXx4rIOudc38tEpIlzfUNn1q3O115ZxXG7\nRkQynK95zCVXQxH52Pn8tSLSzeU5c5zHq+y9lWV/yOV9FohI60pez7XVpWdZLhHpLSI/Ot/HjyLS\nyeWz+ZvzuG4VkTud63uIyHcisklEvhaXGbuq+IyCRWSeiGxw7memc/0gEfnc5bn3isgcl/2Uvbcn\nKmSfLyI7nK9hq+zYKuVNWuRVXfMGjol23nNZtwQYV1agcYwi9aZzeQ8wwbk8kt9mPswBVgKjnY9d\nB/zXGFPi/DkYuN4Yc7HL64wAQo0xXXAOserc1xXO7TYCvzfGXFzJaHiPOLOUKXA+p6tzX/Wred8/\nAH2NMd2d7/d+5/rf45i7uptzuSrBwMfO15zvsv5R4Gfn8/8CvF3hOX93eW+ISD0cs5Nd7Fy/t5rc\nFe0EBjjfx8PAk871M4A2QHdnlv9zfp4vANcYY3rg+OznVshX8TOaimOo0F5AL2C6iLRxJ5iINMY5\nrKvz565AP+BC52sU1PC9KnXOfHJYW6W8JBpoiGPWt5dw/kI2xuSJyApgjIjswFGItznPMIuAPSJy\nIXAT8A6OGfkAXsNRLD/G8cVgustrRXL6/PA2IEpEgmsSWkSuxjF2eA/X/YvIZhwTVHxsjMkUkTig\nnXM9OCZt+s653Bx433kmGwbsc8kU60aMGCqfAOpy4GoAY8wKEWkkInHGmCwcx6CycbXF+diZil6k\ny/tw3U8csEhEOuAYOrXsi9lQYL5z2mmMMRki0gXHBEDfiGNY5uAKeSr7jIYD3UTkGpfX6wAUA/1d\nMiUACys89yEcXzrKvkDacBzrsEpeR6laoWfyqi4pAq41xrwLlIiI65nraziKv+tZfJk3cRTzEOBY\n2UpjzGqgtYgMBIKNMUkuzzmP0wvcUhyToqQB37qZOdj52k9VWF92Jp+Io7D3c67f62wJuBi4z2X7\nF4AXjTFdgZk4Jg8BWAw0FJFjwP+dIUcbHDNgVXSmqS/Po8IMWcaYbBxn4HtFZAvQrorXK3B5H66f\n0+PAt87WkLEu70OofDrq5LL9GGO6GmOGuzxe2WckwJ0uz2ljjFnqfGyVS6bnKjyvNdDFtY+HMWY7\njlnZUp1fDiKreK9KeY0WeVWXlBpj8pzLdwBznWe/GGPW4ZjC8QZObcrHGLMJaMzpxR8czdPvuT4m\nIpcDmcaYzAr7KcVx9nofLs311bgR+J8x5kRlDzr3mU/1U3rGAYedyze7rM8FSoHJVNFcL45Zx8YC\n/6vk4e/Lnicig4ATxphsccz01h9YV8lzUoHPjTEXUfPmetf3cYvL+qXALHFMO42INMQxnWyCOOY2\nR0RCnS0yVX5GOCZguU1+61vRUUSi3cj1iPNPRVnA89pcr6yiRV7VScaYPTgK85Muq/8NrK7kFz/G\nmFHGmMqK3P8BDXB+MRCRXsC/gCkVNxSRa4F6xpjXaxC1CaefNYKzOVtEkoE84Ktq9jMHx2yCqwDX\nLwz3AVtdzlYr8w5wofP5m4FZwN0icp5zvz1FZCvwNL99gfgBmFNxGkwRaQ/c69zH2XgWeEpEVuNo\n5SjzGo6pTrc6WwhuMMYU45iG+hnnus1AvzN9Rs79bAd+EkcnxgW4d1nzkDHme9cVztaV4TiOkVKW\n0FnolHJy9p5+zhizvAbPuQYYb4y5yXvJrCUiK40xgyqs+xuO5v/9loRSSrlFO96pOk9E6gPrgS01\nLPAvAKNwzO8cyB6rZN07OPoWKKV8mJ7JK6WUUgFKr8krpZRSAUqLvFJKKRWgtMgrpZRSAUqLvFJK\nKRWgtMgrpZRSAUqLvFJKKRWg/j+JokbLseOw+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2692d3b5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "curve_area = np.trapz(np.insert(village['Cum_Income_Village_3'].values,0,0), np.insert(village['Cum_population'].values,0,0))\n",
    "S = (0.5 - curve_area) / 0.5\n",
    "\n",
    "plt.figure(figsize = (8,8))\n",
    "plt.plot([0,1],[0,1],linestyle = '--',lw = 2,color = 'black')\n",
    "plt.plot(np.insert(village['Cum_population'].values,0,0), np.insert(village['Cum_Income_Village_3'].values,0,0),\n",
    "             label='Деревня {} (Gini = {:0.2f})'.format(i, Gini[i-1]),lw = 2,color = 'green')\n",
    "\n",
    "plt.fill_between(np.insert(X_k,0,0), np.insert(X_k,0,0), y2=np.insert(village['Cum_Income_Village_3'].values,0,0), alpha=0.5)\n",
    "plt.text(0.45,0.27,'S = {:0.2f}'.format(S),fontsize = 28)\n",
    "plt.title('Коэффициент Джини')\n",
    "plt.xlabel('Кумулятивная доля населения')\n",
    "plt.ylabel('Кумулятивная доля дохода')\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы показали, что наряду с алгебраическими методами, одним из способов вычисления коэффициента Джини является геометрический - вычисление доли площади между кривой Лоренца и линией абсолютного равенства доходов от общей площади под прямой абсолютного равенства доходов.\n",
    "\n",
    "Ещё один немаловажный момент. Давайте мысленно закрепим концы кривой в точках $(0,0)$ и $(1,1)$ и начнем изменять её форму. Вполне очевидно, что площадь фигуры не изменится, но тем самым мы переводим членов общества из \"среднего класса\" в бедные или богатые при этом не меняя соотношения доходов между классами. Возьмем для примера десять человек со следующим доходом:\n",
    "\n",
    "$[1, 1, 1, 1, 1, 1, 1, 1, 20, 72]$\n",
    "\n",
    "Теперь к человеку с доходом \"20\" применим метод Шарикова \"Отобрать и поделить!\", перераспределив его доход пропорционально между остальными членами общества. В этом случае коэффициент Джини не изменится и останется равным 0,772 , мы просто притянули \"закрепленную\" кривую Лоренца к оси абсцисс и изменили её форму:\n",
    "\n",
    "$[1+11.1/20, 1+11.1/20, 1+11.1/20, 1+11.1/20, 1+11.1/20, 1+11.1/20, 1+11.1/20, 1+11.1/20, 1+11.1/20, 72+8.9/20]$\n",
    "\n",
    "Давайте остановимся на ещё одном важном моменте: рассчитывая коэффициент Джини, мы никак не классифицируем людей на бедных и богатых, он никак не зависит от того, кого мы сочтем нищим или олигархом. Но предположим, что перед нами встала такая задача, для этого в зависимости от того, что мы хотим получить, какие у нас цели, нам необходимо будет задать порог дохода четко разделяющий людей на бедных и богатых. Если вы увидели в этом аналогию с Threshold из задач бинарной классификации, то нам пора переходить к машинному обучению."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center>Машинное обучение\n",
    "### 1. Общее понимание"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сразу стоит заметить, что, придя в машинное обучение, коэффициент Джини сильно изменился: он рассчитывается по-другому и имеет другой смысл. Численно коэффициент равен площади фигуры, образованной линией абсолютного равенства и кривой Лоренца. Остались и общие черты с родственником из экономики, например, нам всё также необходимо построить кривую Лоренца и посчитать площади фигур. И что самое главное - не изменился алгоритм построения кривой. Кривая Лоренца тоже претерпела изменения, она получила название Lift Curve и является зеркальным отображением кривой Лоренца относительно линии абсолютного равенства (за счет того, что ранжирование вероятностей происходит не по возрастанию, а по убыванию). Разберем всё это на очередном игрушечном примере. Для минимизации ошибки при расчете площадей фигур будем использовать функции scipy <b>interp1d</b> (интерполяция одномерной функции) и <b>quad</b> (вычисление определенного интеграла).\n",
    "\n",
    "Предположим, мы решаем задачу бинарной классификации для 15 объектов и у нас следующее распределение классов:\n",
    "\n",
    "<center>\n",
    "$[1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]$\n",
    "\n",
    "Наш обученный алгоритм предсказывает следующие вероятности отношения к классу \"1\" на этих объектах:\n",
    "\n",
    "<center>\n",
    "<img src=\"../../img/data.png\">\n",
    "\n",
    "Рассчитаем коэффициент Джини для двух моделей: наш обученный алгоритм и идеальная модель, точно предсказывающая классы с вероятностью 100%. Идея следующая: вместо ранжирования населения по уровню дохода, мы ранжируем объекты по предсказанным моделью вероятностям по убыванию и подставляем в формулу кумулятивную долю истинных значений целевой переменной, соответствующих предсказанным вероятностям. Иными словами, сортируем таблицу по строке \"Predict\" и считаем кумулятивную долю истинных классов вместо кумулятивной доли доходов.\n",
    "\n",
    "<center>\n",
    "<img src=\"../../img/data_sorted_cum.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kEfFauXsfdezoaAy/kJS0hj592pKSkkylSlW4++7b1RyJFJFj6ceYt3UeoOl1Imezc8dO\nenTowYH9ByhVphRP9nuSIOPMyQSdwhARr/Tjj/D111CiBLRr53Qa3/bTT1vo2bMVKSnJtG17D507\n36rruUSK0OxNs0nPSqdRTCMuLavhcJHT7du7j+4dunNg/wEa3dSIfr37ERwU7FgelUgR8UqTJ7u/\ntmzpng4mBbN79y66dWvB0aOHadasNbNmTSY01LmiIxKIclev61hPw+Eipzty+Ajd23fn152/csXV\nV7BowSIii0c6mkkNkoh4nezsPxskLc5QcAcP7ueee25n377fadDgJubPn0OxYmFOxxIJKD8e/pGv\nf/uaEqElaFdPw+EieaUkp9CrSy9+3PojterWIiEhgbKlyzodSw2SiHifFSvgt9+gShW46San0/iu\nAQN6snPnz8TFXc3ixQsoWbK405FEAs7kJPfZnpY1W1IyXMPhInm99OxLrFu7jpjYGBITE6lcsbLT\nkQA1SCLihXIXZ2jfHkK0lEyBDR78Lxo1upXExESio7Wct0hRc2W7/phe16W+hsNFTvf0i09zw003\nkJCQwKXVvOf6PH30EBGvcuIEzJ3rvt21q7NZfJG1FmMMWVkQG1ufFSuWExHhdCqRwLRi5wp2n9hN\nlZJVuClWw+Ei8GedcmW7KFWhFMuXL6d4qHfNcNAIkoh4lTlzIC0NGjaE2rWdTuNbXC4Xjz7anYkT\nx5GWBlWrouZIxEG5o0ft67YnJEjnpEWstQweNJg3h7xJSkYKMVExXtccgRokEfEyk9yfJ7T30QWy\n1jJoUD8++2wWw4c/R1jYAYoVczqVSOA6kXGCuZvdw+Fd62s4XATg7eFvMyF+AuPeHUfynmSiwqOc\njnRGapBExGvs2AGrVkGxYu7rjyR/rLUMHTqQGTMmEB4ewccfL6RGjQpOxxIJaHM2zyEtK42GlRtS\nu5yGw0XGjx3P2yPeJigoiPETx3P91dc7Hems1CCJiNfIu/dRaa0pkG+jR48gPn4UISEhTJkyl1at\nbnY6kkjAm7h+IqC9j0QAZk+bzeDnBgPwzph36NW9l8OJzk0Nkoh4hezsP6fXderkbBZfMmnSOEaM\neAFjDOPGTaFr1zudjiQS8LYf2c5/fv0PxUKK0b6ehsMlsCUsTOCZAc8A8PqI13m83+MOJzo/NUgi\n4hVWrYKdO6FSJWjWzOk0viElJZl33x0CwMiR4+jbt5vDiUQE/rr3UekIDYdL4MrKymLkkJG4XC6e\nfPZJXhr4EsYYp2Odl5ZUERGvkDt6pL2P8i8yMopJk75k/fovePrpfk7HEREg22YzeYO7QeoUp+Fw\nCWwhISF8OOdDFs1ZxOsvve4TzRGoQRIRL5CSAh9/7L7dRXspntfhwwcpVy6a1FS48sratGxZGx+p\nOSJ+b9WuVew8tpNKkZVoVr2Z03FEHHH40GHKlitL2qk0qsZUZcjLQwgyvjNxzXeSiojf+uQTSE2F\na6+FuDin03i3DRvW0qRJLUaPfofixaFiRdQciXiR3MUZOtTroL2PJCDt+mUXLW5swasvvkpIUAiV\noyr7VHMEapBExAtMnOj+qr2Pzu3nn7fSs2crkpNP8MMP33DJJZYgvYuLeI2UzBTmbJ4DQOf6nR1O\nI1L09u3dR7f23di/bz8b128kOiKa4KBgp2NdMJVWEXHUrl2wYgWEh2vvo3PZvXsX3bq14MiRQzRr\n1prZs6cQHKyhIxFvMnfzXFJPpXJtpWuJK6/hcAksRw4foUeHHvy681euuPoKFi1YRIliJZyOVSBq\nkETEUbl7H91+O5Qr52wWb3Xw4H7uued29u7dzXXXNWH+/DkUKxbmdCwROc2kJPdqMx3rajhcAktK\ncgq9uvRi25Zt1KxTk4SEBMqWLut0rAJTgyQijrH2z9XrOms2yhkdP36MHj3uYOfOn4mLu5olSxZS\nsmRxp2OJyGl2HtvJip0rCA8O195HElDS09N5oMcDrFu7jpiqMSQmJlK5YmWnY10UNUgi4pjVq2H7\ndvdCA82bO53GOx06dIAjRw5RvXptEhISiI7Wnioi3mhK0hQAbr/0dsoV13C4BI4Tx0+wf99+ylco\nT0JiAjWr13Q60kXT8ioi4pjcxRnatYPQUEejeK1q1eowbdpXxMQYYmMrOh1HRM7AWsvEpImAFmeQ\nwFMuuhyT508mNC2Uy+MudzpOodAIkog44uRJmD3bfbtrV2ezeBuXy8XKlYm4XJCWBo0bV6du3WpO\nxxKRs/jq16/YcXQHFUtUpHl1DYeL/7PWsixxGa5sF6mZqVxe/XIaXN3A6ViFRg2SiDji008hORmu\nugrq13c6jfew1vLcc/3p2bMVo0e/RUwMFCvmdCoROZfcxRna1W1HaLCGw8X/vTPiHXp17cXLg16m\nUlQlosKjnI5UqNQgiYgjchdn6NhRG53mstbyxhuDmD59POHhETRr1pDISKdTici5nDx1ktmb3MPh\nXetrOFz83/ix43lr+FsEBQVxa9NbKRVRyulIhU4NkogUud9+gy++gLAwbQ6b1+jRIxg37h+EhIQw\nefJcWre+xelIInIen275lOTMZK6qeBX1ozUcLv5t9rTZDH5uMABvj36b3t17O5zIM9QgiUiRmzrV\nvcT3bbdB+fJOp/EOkyaNY8SIFzDGMG7cFO6++06nI4lIPuQuztAxriNGw+HixxIWJvDMgGcAeG34\nazzR/wmHE3mOGiQRKVLW/rl6nUaP3BYs+JgXX3wMgJEjx9G3bzeHE4lIfvx2/DeW7VhGWHCYNocV\nv/bN6m94pM8juFwunnz2SV4e9LJfnxDQMt8iUqS+/RZ+/BGio6FFC6fTeIfLLruaSpWqcv/9j/D0\n0/2cjiMi+TRlwxQslttq3Eb5EhoOF/91aa1LqVG7Bo2bNGbUiFF+3RyBGiQRKWK5o0dt27qvQRKo\nWLE2y5YlUbduaS1YIeIjrLV/rF7XsZ5Gj8S/RZaJ5JMln1Cnch2Cg4KdjuNxmmInIkUmLQ1mznTf\n7tLF2SxO++GH//Hhh++RmgrFi0OdOmqORHzJN7u/4cfDPxJdPJoWNTUcLv5n1y+7eOfNdziZeZLQ\n4FDqxtQlJDgwxlYC47cUEa/w2Wdw/DhcdhlceaXTaZzz889b6dHjDo4cOUS5cpfQr19XgnS6SsSn\nTFw/EYC2ddoSFqzhcPEv+/ftp3v77uzauYvwYuG8+vyrATFylEslWUSKTO70uk6dAnfvo927d9Gt\nWwuOHDlE06at6NOnvZojER+TdiqNWZtmAdDlsgAfDhe/c/TIUXp06MGunbu44uoreOrRpwgJCqwx\nFZVlESkSe/bA0qUQGupukALRoUMH6NatBXv37ua665rw2WdzKVZMZ55FfM38bfM5nnGcyytczpUV\nAng4XPxOakoq93W5j62bt1KzTk0SEhIoV6ac07GKnBokESkSU6dCdjY0awYVKjidpugdP36MHj3u\n4JdffiIu7mqWLFlIyZLFnY4lIgWQd3EGf1/NSwJHeno6D/R4gHVr1hFTNYbExEQqV6zsdCxHqEES\nEY+zFia5P0/QubOzWZwyaFA/Nm1aT/XqtUlISCA6urTTkUSkAPYk72Hp9qWEBoXSqV6ADoeLXxrx\n2gi+WvkV5aPLk5CYQM3qNZ2O5Bg1SCLicWvWwObNULZs4O59NGjQm9xww60kJHxObGxFp+OISAFN\n3TCVbJtNs+rNqBAZgMPh4rce+/tjNG7amIVLFnJ53OVOx3FUYF1xJSKOyB09atsWIiKczVKUrLUY\nY3C5oHz56qxYsZxixZxOJSIFZa39Y/W6znEBOhwufsVa6/6KJTwqnMTERKLCoxxO5TyNIImIR2Vk\nwPTp7tuBtPeRtZZBg/rz7rvDSE21xMSg5kjEx32/53u2HNpC2WJlaXFpgA6Hi1/555v/5MVnXuR4\n2nEqRVVSc5RDI0gi4lELF8LRoxAXB9dc43SaojNs2HNMm/YB4eER9OjRjcjIS52OJCIXadJ693B4\n2zptiQgNoOFw8UsTxk1g1LBRBAUF0aNnDy5repnTkbyGRpBExKNy9z7q0CFw9j4aPXoEY8eOJCQk\nhMmT53LVVWqORHxdRlYGMzbOAKBLXAANh4tf+nj6x7wy6BUA3h79Ni2btnQ4kXdRgyQiHrN/PyxZ\nAiEhgbP30eTJ8Qwf/jzGGMaNm8Ldd9/pdCQRKQQLflzA0fSjxJWP45pKATQcLn4ncVEiTz/2NACv\nDnuVJ/o/4XAi76MGSaSARo6EFSv++tiKFe7HvfnYRXn8adPA5YKmTeGXX2Ds2MI5vreaN28GL7zw\nKAAjR46jb99uDicSkYs1cvVIVvyy4o/FGTrGdeTr375m7Pd+/oYmfumrL7+if+/+uFwunnz2SV55\n7hXt5XUGugZJpIAaNoS774Y33oBKlWDDBndjMHAgLFhwccc+dco9JW3gQLjyysI9dlEev3TOVj+X\nXQb9+0N8/MUf21tlZmbyj3+8grWWF18cztNP93M6kogUgoaVG9Ll4y4cSztGSFAIsSVj6b+oP/Ft\n/PgNTfyStZZRb4wiMzOTPg/3YdSIUWqOzsLkLu/nKxo0aGDXrFnjdAwRAN5/3/3BX84uIsK9etv7\n70OTJk6n8azt23ezfPnHvPLKU35/vZUxZq21toHTObyR6pT/eWThI8Svjad66eqcyDhBfJt4msT6\n+Rua+KW9B/Yye9Js3hj8BiHB/j1OcjF1yr//ZkQ8bMOGP29XqwaXFvK1+Dt2wK5dnjl2UR6/f3//\nbY4OHz5IuXLRpKbCpZdWoUkT/2+ORAKJtZavfvsKgJ3HdvLkDU+qORKfcvjQYcqWK0t6Vjrly5Vn\n2KvDCA4KdjqWV1ODJFJA6ekwebL7drdusHQpPPJI4TUCq1e7G4snn3T/nMI8thPHv/FG/2uSfv55\nKx073kz37v0ZOPB1KlUyBOnKThG/sm7fOjYe2IjB8FjDx5i8YTI3Vr1RTZL4hP379tOxZUduuOkG\n3njnDWJKx6g5ygeVcpECGj4cUlLcoy+jRrmvr+nf390YXKzc5iI+Hp59tnCP7Q/H9wa///4r3bu3\n5MiRQ2zcuIYKFbLUHIn4oaGrhgJwW43beP7m54lvE0//Rf1Z/asfvaGJXzp65Cg9OvRg185dbP5h\nM+VCyxESpLGR/FA5Fymg2bPdX++9172/T5Mm7kYgKenij52U5D5W7ohLYR7bH47vtEOHDtCtWwv2\n7PmN665rwmefzSUiItTpWCJSyDJdmST+nAjAgOsHANAktgnxbeJJ2u8nb2jil1JTUrmvy31s3byV\nmnVqkpiYSJlSZZyO5TO0SINIAezbB1WquBujb75xr2IngeH48WN07XormzatJy7uar78cgXR0aWd\njlXktEjD2alO+Y9Pt3xKp9mdqFO2Dst6LSNIw8TiAzIyMujVtRdfrfyKmKoxrFy1klrVazkdq8hd\nTJ3S/+kiBZC7v0+zZmqOAkla2kn69GnLpk3rqV69NgkJCQHZHIkEiklJkwDoUK+DmiPxCVlZWTz2\nwGN8tfIrykeXJyExISCbo4ul/9tFLpC1MHGi+3anTo5GkSJ29OgRDhzYxyWXVCEx8QtiYys6HUlE\nPORg6kEW/bSIYBNMl/pdnI4jki+pKan8vvt3SpYqycIlC7k87nKnI/kkXaklcoHWrYONG6FMGWjZ\n0uk0UpQqVqzClCn/oWTJE9SpE+t0HBHxoOk/TCcrO4um1ZoSUzLG6Tgi+RJVKooJcyaQcSiDG667\nwek4PksjSCIXKHf0qG1b9wao4t+stSxfvgSXy5KaCldffQlXXlnH6Vgi4mETkyYC0Dmus7NBRPJh\nxecrcLlcJGckU7tybZpcr2XoL4ZHGyRjTCtjzDZjzM/GmOfO8P1YY8wKY8w6Y8wGY8ydnswjcrEy\nM2H6dPftzqqZAWH48Oe57747eeONl6lcGSIjnU4kIp6WtC+J9fvWUyq8FK1rtXY6jsg5fRj/Ifd2\nvpfH+z1OxRIVKRVRyulIPs9jDZIxJhgYA7QG6gPdjTH1T3vaS8Bsa+01QDdgrKfyiBSGRYvg8GGo\nWxeuvdbpNOJpY8a8yZgxbxISEsKttzamZEmnE4lIUchdnKFN7TYUDyvucBqRs5szYw4vD3wZgFub\n3UrZ4mUdTuQfPDmCdD3ws7V2h7U2E5gJtD/tORbI/chRCtjjwTwiFy13el2HDmhTUD83Zcr7DBv2\nHMYYxo6dzD33tHE6kogUgVMC7VPMAAAgAElEQVSuU0zdMBXQ9DrxbomLEvn7o38HYPAbg3mi/xMO\nJ/IfnvyIFwP8luf+7pzH8noVuNcYsxtYDDx+pgMZYx42xqwxxqw5ePCgJ7KKnNeBA7B4MQQHa3qd\nv5s/fybPP/8IAG++OZaHHurucCLxdqpT/iPh5wQOnjxIzTI1uT7meqfjiJzR6lWreaTPI7hcLv72\nzN8Y/PxgjDFOx/IbnmyQzvSvdPqutN2BidbaKsCdwBRjzP/LZK39wFrbwFrbIDo62gNRRc5v+nTI\nyoKbb4YYLWjkt778cilPPHEf1lpeeGEYzzzT3+lI4gNUp/xH7uIM2vtIvNUP63/g/m73k5GRQe+H\nevPWm2+pOSpknlzmezdQNc/9Kvz/KXQPAq0ArLX/NcZEAOWBAx7MJVIgk9xT0jV65Odq165PtWq1\nadnyLoYMeQ7VHJHAcfjkYRZsW0CQCdLeR+K1qlarSt36dalWvRrjx40nOCjY6Uh+x5MN0vdAbWNM\nDeB33Isw9DjtOb8CtwETjTFxQASguQnidZKSYP16KF0aWrVyOo14UqlSVViw4Bvq1IkiKEjdkUgg\nmbFxBqeyT3Fz7M3EltJeZ+KdwiPDmfrJVGqUr0FIsLY09QSPjR1ba7OAAUAisAX3anWbjDGvG2Pa\n5TztaeAhY0wSMAPoY609fRqeiONyR4/uvBOKa0Ejv/Pzz9t4773hnDxpCQ+HOnVKEhys5kgk0OSu\nXtexXkeHk4j81f59+3nz9TdJzUjFGEPtSrWJCI9wOpbf8mjbaa1djHvxhbyPvZLn9mZAO1mJVzt1\nCqa6FzSia1dns0jh+/33X+nevQV79vxGZGQZnnuuP8GarSAScDYd2MSaPWuICovirjp3OR1H5A9H\njxylR4cebN28lazsLP458p+EBGnkyJN09aHIeSQkwMGDUKsWNGjgdBopTIcOHaBbN3dzdN11TRgw\n4D41RyIBKnf0qHWt1pQIK+FwGhG31JRU7utyH1s3b+XS2pfy4sAXCQ0OdTqW31ODJHIeuXsfdeyo\nvY/8yYkTx+nZsxU7dvxIXNxVLFmykFKl9KFIJBBlZWcxZcMUAC3OIF4jIyODB3s+yLo164ipGkPi\n0kQqV6zsdKyAoI97Iudw+DAsWOBujLqoZvqNtLST9O59Fxs3rqN69dokJCQSHV3a6Vgi4pCl25ey\nL2Uf1UtVp3GVxk7HESErK4sBDw7gPyv+Q/no8ixJWEKt6rWcjhUw1CCJnMOMGe5rkG66CapUcTqN\nFJbXXnua7777iksuqUJCwufExlZ0OpKIOCjv4gza+0i8wZh3xrD4s8WULFWSBYsXcEX9K5yOFFD0\nLiByDnmn14n/+NvfBtO48W0sXvw5detWczqOiDjoaNpR5m2dh8HQub42uhPv0OfhPjRt0ZS58+bS\nqEEjp+MEHC2BIXIWGzfC2rUQFQVt2jidRi5W7g4C1hpKlLiEpUu/IDLS4VAi4rhZm2aR6crkxio3\nUqNMDafjSID7Y7ebcJj/2XxKRZRyNlCA0giSyFnk7n3Upg2U0LX7Pm/48OcZMmQgycmWypVRcyQi\nAExcPxGATnGdnA0iAe/D+A954uEnOJJ6hIqRFdUcOUgjSCJnkJX1595HnTXjwueNGfMmY8a8SUhI\nCD169CQu7mqnI4mIF9h6aCvf/v4tkaGR2vtIHDVnxhxeHvgyAPd0v4cr2uuaIydpBEnkDJYuhX37\noEYNaKSpvz5t6tQPGDbsOYwxjB07mVtuUXMkIm6T1runCrSq1Yqo8CiH00igWrp4KX9/9O8ADH5j\nMF3baVd6p11Qg2SMCTPG6B1E/F7u9DrtfeTb5s+fxXPP9QfgzTfH8tBD3R1OJL5MNdC/uLJdf+x9\n1DlOUwXEGatXraZ/7/64XC7+9szfGPz8YIwxTscKeOf96GeMecoYs8YY0wv4EfjJGPOs56OJOOPo\nUZg3D4zR9Dpftnz5Ep544l6stbzwwjCeeaa/05HEB6kG+q9lvyzj9+TfqVqyKk1imzgdRwLQ+rXr\nub/b/WRkZNC7b2/eevMtNUdeIj/XID0GdAOWA9WBdGAN8A/PxRJxzsyZkJkJN94I1as7nUYKIjs7\nm3/842WysrLo3/8Zhgx5DtUcKSDVQD+VuzhDh3odCA4KdjaMBKR3//EuqSmpdOjagfHx4/XfoRfJ\nT4N0wlq7xhiz3Vp7BMAYk+7hXCKOyZ1ep9Ej3xUUFMQHHyQwb954hg4dRFCQuiMpMNVAP3Q8/Tif\nbv0UgK71db2HOGNU/Cg+GvcRwwYPIyRY66Z5k/z8a1xqjPkMqJHz1QDaKED80tat8O237iWgtfeR\n7zl8+CBly5YnPd1wySXlGTr0OYJ1Qk4ujmqgH5q9aTbpWelcH3M9NcvWdDqOBJAjh49QqnQpTtlT\nlIgswcihIwkJUnPkbfLzL9I+5+tbeR4b5YEsIo7LHT1q3dq9Qaz4jt9//5UOHW6iefN2vPbav6hS\nJUjNkRQG1UA/NCnJ/WbfqZ72PpKic/TIUe6+626qXVqNt95/i9oVaqs58lLn/Vex1n5pjKkINMx5\n6Dtr7QHPxhIpei4XTJ7svt2li7NZ5MIcOnSAbt1asGfPb2zevI7o6AyCg4s5HUv8gGqg//np8E+s\n/m01xUOL065uO6fjSIBITUmlV9debNm0hYzMDMoElyE0ONTpWHIW+VnF7m7gO6ArcDfwrTFGHx/F\n7yxbBnv2QLVq7gUaxDecOHGcnj1bsWPHj8TFXcWSJYuIilJzJIVDNdD/TE5ynwlrWbMlpSJKOZxG\nAkFGRgZ9e/blf9//j8pVKpO4NJFKFSo5HUvOIT/jei8CDXPPmBljooEvgDmeDCZS1CZOdH/t0EF7\nH/mKtLST9O59Fxs3rqNatVokJCRSoUJpp2OJf1EN9CPZNpvJG9wNUpc49bnieVlZWQx4cACrVqyi\nXHQ5EhITqFW9ltOx5Dzy8zEw6LTpBIfz+ToRn3H8OHzqXtBI0+t8RGZmJg8/3IXvvvuKihVjSEz8\ngtjYik7HEv+jGuhHVu5cya/HfyUmKoabq93sdBzxc9nZ2Qx8YiCLP1tMVMkoFi5eyBX1r3A6luRD\nfkaQEowxicCMnPv3AEs8F0mk6M2eDenp0KgRXHqp02kkP1JSTrB37++UKVOexYs/p27dak5HEv+k\nGuhHcvc+al+3vS6OF4/LSM/g112/ElEsgrnz5tKoQSOnI0k+5WeRhmeNMZ2Am3Avb/qBtfZTjycT\nKUK50+s6dnQ0hlyA0qXL89FHK4HdXHttnNNxxE+pBvqP5Ixk5m6ZC2jvIykaEcUiGDN1DEd3HaX5\nzc2djiMX4LwNkjGmBrDYWvtJzv1ixpjq1tqdng4nUhR++gm+/hpKlIB2WtDI6y1fvoSmTVuRmmqI\niytDyZJlnI4kfkw10H/M2TyHk6dO0qByA+qUr+N0HPFjXy77ksY3NybdplMtuhrXxF7jdCS5QPmZ\nR/0xkJ3nvivnMRG/kLv3UcuWULKks1nk3MaOHcl9993Js88+SsWK+veSIqEa6CcmJk0EoEPdDs4G\nEb82d+ZcenTswQM9H6BseFnKFivrdCQpgPw0SCHW2szcOzm3wzwXSaToZGdr7yNfMXXqB7zxxiCM\nMTRvfjNlNHAkRUM10A/sOLqDVbtWERESQYd6apDEM5YuXspTjzwFwM0330x0ZLTDiaSg8tMgHTTG\n/DHxyBjTHjjkuUgiRWfFCvjtN6hSBW66yek0cjbz58/iuef6AzBixBgefriHw4kkgKgG+oE/9j66\ntCVliunsihS+1atW0793f1wuF0888wSvvvAqxhinY0kB5WcJl/7ANGPM6Jz7u4FenoskUnRyp9e1\nbw8hWtDIKy1fvoQnnrgXay3PP/8Gzz77iNORJLCoBvq4bJv9R4PUKa6Tw2nEH61fu577u91PRkYG\nvfv25u0331Zz5OPys4rddqCRMSYSMNbaZM/HEvG8EydgTs5Wj121oJFXWrv2Gx56qDNZWVn07/8M\nQ4c+j2qOFCXVQN/3n13/4Zdjv1ApshLNqjdzOo74me0/befezveSmpJKh64dGB8/nuCgYKdjyUU6\n7xQ7Y8wwY0xpa22KtTbZGFPGGDO0KMKJeNKcOZCWBg0bQu3aTqeRM6lRoxa1atWne/e+jB49kqAg\ndUdStFQDfV/u4gzt6rYjNDjU2TDidypVrsRlV11G8zuaM2PKDEKCNR3FH+TnGqTW1tpjuXestUeB\nOz0XSaRo5E6v095H3isiojyzZ69k4sR4goPVHIkjVAN9WEpmCh9vci86qL2PxBOCwoP4YPoHzJs7\nj4jwCKfjSCHJT4MUbIwJz71jjCkGhJ/j+SJeb8cOWLUKihVzX38k3uP3339j1KjBpKZmExICdepE\nEham6QriGNVAH/bJlk9IPZXK1ZdcTb3y9ZyOI37i2NFjDBs8jBOpJ7DWUiu6FlElopyOJYUoP+OA\nU4FlxpiPAAs8AEzyaCoRD8td2rtlSyhd2tks8qdDhw7QvXsLtm/fRlBQOCNGvECweiNxlmqgD5uU\n5P6n6lSvky6al0JxMvUkvbr2Yu13azl67Cgf/fsjTd30Q/lZpGGkMeYH4DbAAEOstYkeTybiIdnZ\nf06v66QFjbzGiRPH6dmzFdu3b6NevSt59tlHtLKgOE410HftOraL5b8sJyw4jPb1NFVALl5GRgYP\n9niQtd+tpXKVyrz68quEBWtbNH+Ur48f1tolwBIPZxEpEv/5D+zcCZUqQbNmTqcRgLS0NPr0acvG\njeuoVq0WiYlLqVhRe5WId1AN9E1TNkwB4PZLb6d88fIOpxFfl5WVxYC+A1i1YhXlosuRkJhA7Rpa\n4clf5WcVu0bGmO+NMSnGmExjjMsYc6Iowol4wsSJ7q8dOmjvI29w6tQp+vXryrff/oeKFWNITPyC\n2NiKTscSAVQDfZW19o/pdV3iujicRnydtZZBfxvE4vmLiSoZxcLFC7mi/hVOxxIPys8iDaOB7sBP\nQDGgL/CeJ0OJeEpKCnzsXtCIzp2dzSJub7/9GsuWLaJ06XIsXvw5detWczqSSF6qgT7o69++5ucj\nP1OxREWa12judBzxcZMnTGbmlJlEFItg7ry5NGrQyOlI4mH5aZCw1v4MBFtrXdbaj4BbPRtLxDM+\n+QRSU+HaayEuzuk0AvDQQ09z882tmD8/gWuv1T+KeB/VQN8zcf1EQHsfSeHo2qMrLe9qydSZU2lx\nawun40gRyM8Eo5PGmDBgvTFmJLAXKOHZWCKekTu9TnsfOc9ai7WGkJAyLFy4hJIlnU4kckaqgT7m\n5KmTzNo0C4Au9TW9TgrOWgtAVnAWM2bPoGyxsg4nkqKSnxGk+4BgYACQClQFNDlJfM6uXbBiBYSH\na+8jp40b9w+eeeYhjh93UbEiao7Em6kG+ph5W+eRnJnMlRWu5LLoy5yOIz7qk1mf8GCPBzl47CDl\ni5VXcxRg8rPM966cm2nAa56NI+I5uXsf3X47lCvnbJZANm3avxk6dCDGGHr0uI/LLmvqdCSRs1IN\n9D250+s6xHXQ3kdSIEuXLOXJ/k/icrnosKwD/fr0czqSFLHzNkjGmGTcm+P98RBgrbU65ys+w9o/\n9z7S4gzO+eyz2Qwa5C40w4ePpm1bNUfi3VQDfcvuE7v5YscXhAWF0ameNrqTC/f1f76mf6/+uFwu\nHn/6cfr16adGOwDl5xqkn62113g8iYgHrV4N27dDxYrQXAsaOWLFigSeeOJerLU899xQBg581OlI\nIvmhGuhDpiRNwWK5tcatRJeIdjqO+Jik/yXR554+ZGRk0OvBXrwz8h01RwEqPw1ShDHmKiAD2Gut\nPe7hTCKFLnf0qF07CNWCRkXuu+++om/fTjl7Hj3NG2+8gGqO+AjVQB+Rd++jTnEaPZIL8+PWH+nZ\nqSepKam079KeCe9PIDgo2OlY4pD8LNKwD/eeD1OAzcaYH4wxDTwbS+TijRzpXpTh5EmY5V7QiNq1\nYexYZ3MFGmstb7/9GunpadxzzwOMGfMPgoLUHYnPUA30ciNXj2TFLyv49vdv2XZ4G+WLlycqLIqx\n3+vNXvJv3LvjOHrkKM1bNmfm1JmEBGsn+UCWn0Ua/rLfgzHmJiAeUIEQr9awIdx9Nzz8MCQnQ82a\nMGIExMc7nSywGGN49925TJv2L4YNe57gYDVH4jtUA71fw8oNuXvO3TSu0hiABpUaMGDJAOLb6M1e\n8u/VUa9SObYyr7/4OhHhEU7HEYeZ3DXeL+hFxlxvrf3OA3nOq0GDBnbNmjVO/GjxQStWwB13wKlT\nULy4ex+kJk2cThUYjhw5ROnSZcnICCI4GKpWhWDNVvAbxpi11tqAbBLOVwNVp4pe4s+JtJ7WGoul\nZHhJxrcdT5NYvdnLuZ04foLwiHAIhmybTWypWG0s7Ecupk6dd4qdMab3affjgLcK8sNEilqtWu7m\nCODee9UcFZXDhw/SocNNDBjQi6ysU1SpouZIfJNqoG84ln4Mm7PY4P1X36/mSM7rZOpJ7u18L73v\n6c2J5BNULVVVzZH8IT/XIHUyxgwyxoQaY14DpgGDPJxLpFC8lrNrSc2aMGeOezU78awTJ47Ts2cr\ntm/fxrZtP1CmTCohmsotvks10Ae8/d+3Abip6k1M2TCF1b/qzV7OLiMjg749+7L2u7Vs/3E7JbJL\nEBYc5nQs8SL5aZA6ArWA33Lu32Ct/dpzkUQKx/Ll7il1AIMGua896t9fTZInpaWlcf/97fjhh/9R\nrVotEhISqVChtNOxRC6GaqCX+3jTx3y35zuCTTD/av0v4tvE039RfzVJckYul4vHH3qcL5d/Sbno\ncixJWEKt6rWcjiVeJj8N0tW4L0j9HqgPXGGMudajqUQKwSefgMsF0dHQooV7el18PCQlOZ3MP7mX\n8O7KN9+somLFGBITP6datUucjiVysVQDvdzE9RMBaF6jORUjK9IktgnxbeJJ2q83e/kray2D/jaI\nRfMWEVUyigWLFnDlZVc6HUu8UH4mvryFexdxA0Tmua/tNsWrZWW5v7ZtC2E5I+dNmug6JE9wuVw8\n+WRvli1bROnS5Vi8+HPq1q3udCyRwqAa6MWstew8vhOAjvU6/vF4k9gmug5J/sJay5CXhjBj8gwi\nikUwd95cGjds7HQs8VIXvMy3iC9IT4eZM923u3RxNksgSEs7ye7duyhRIor58xO49to4pyOJFArV\nQO+2du9aNh/cTNliZbmj5h1OxxEv5nK5+GX7L4SGhjJ15lRa3NrC6UjixXTptPil+fPh+HG4/HK4\nUqPnHle8eBTvv7+U5OSt3HLLdU7HEZEAkTu9rm2dtkSEau8aObvg4GBGjR/Fnm17uKOZmmk5t/xc\ngyTicyZNcn/t2BGM9iX1mJUrE8nKcpGSAjVqlKBpUzVHIlI0MrIymLFxBgCd4zo7nEa81VdffkVa\nWhrJGclUKllJzZHkixok8Tt79kBiIoSGQqdOTqfxX9Onj6dnz1b069eD6GhLmTJOJxKRQLLwx4Uc\nSTtCvXL1uLaS1s2Q/+/zJZ/To0MPunfsTongEpQrXs7pSOIj8rNR7BBjTEie+yWNMR95NpZIwU2d\nCtnZ0KwZVKjgdBr/tGDBxwwc+DAATZveQrlyGqYT/6Qa6L0mJbmnCnSM64jRVAE5zX+/+i/9e/fH\n5XLRqHEjqpSpov9OJN/yM4IUAnxrjLnSGNMS91Knaz0bS6RgrP1zel1nzbjwiBUrEnj88Z7u5VIH\nDWHQoMecjiTiSaqBXmh/yn4W/7SYkKAQOsVpqoD8VdL/kuhzTx/S09O574H7eGfkO2qO5ILkZxW7\n540xy4BvgaPALdbanz2eTKQA1qyBzZuhbFn33kdSuL7/fjV9+3bK2fPo7wwb9qKu8RK/phronab9\nMA2XdXFrtVupHFXZ6TjiRX7a9hM9O/UkJTmFdp3bMeH9CQQHBTsdS3xMfqbY3QK8C7wOrARGG2P0\nbiReKXf0qF07iNCCRoVq69aN9OrVhvT0NO655wHGjBlFUJC6I/FvqoHex1r7x+p1WpxB8trz+x66\nte/G0SNHubXFrcyaNovQkFCnY4kPys8y36OArtbazQDGmE7AcqCeJ4OJXKiMDJg+3X1b0+sKX0xM\nLPXqXU25cuWZPPkDgoPVHElAUA30Muv3reeHAz9QOqK09j6SvyhXvhzXNryWgwcOMu+TeUSE60yp\nFEx+GqTG1lpX7h1r7SfGmC89mEmkQBYuhKNHIS4OrrnG6TT+JySkJJMmLaFq1SDCwjRdQQKGaqCX\nyV2coU3tNhQPK+5wGvEqwfDOv98hOiyakpElnU4jPiw/DdKLZ7mw7fVCziJyUSZOdH/V3keF5/Dh\ng3zwwTsMGPAaoaGh1KpVjBBtLy2BRTXQi2S6Mpn2wzQAutbv6nAa8QYnU0/y9oi3GfDsAEIjQqle\ntjphwWFOxxIfl5+POql5bltAHz3F6+zfD0uWQEiI9j4qLMnJJ7j33tZs2LCWkyczGDfuLTVHEohU\nA73Ikp+WcOjkIWqXrc11lbQxdaDLyMigb8++fLn8S3bu3Mkncz5RcySFIj+r2L0FYIypDbwKhALD\nPBtL5MJMmwYuF9x2G1Sq5HQa35eWlkafPm3ZsGEtsbE1eeWVZwlTzZEApBroXSYmTQSgQ70OBAVp\nr/tA5nK5ePyhx/ly+ZeULV+WEW+MICJE1xxJ4biQd5exuC9MnQ6875k4IhfO2j+n12n06OK5l/Du\nyjffrKJChcosXfoF1apd4nQsEaepBjrsYOpBFv64kCATRJf6XZyOIw6y1jLob4NYNG8RkVGRLFi0\ngCsvu9LpWOJHLqRBKmetnWCtnQdkeiqQyIVavx5++AHKlIE7tKDRRcnOzuapp/qwbNkiSpcux+LF\nn1O3bnWnY4l4A9VAh83YOIOs7Cxujr2ZKiWrOB1HHGKtZejLQ5kxeQYRxSKYO28uN15/o9OxxM+c\nd4pdzpKmAKWNMR1xN1VlPZpK5ALkjh61aQPFijkaxef9+9//5NNPp1O8eCTz5i3huuvqOx1JxFGq\ngd4jd++jjvU6OhtEHLXg0wXE/yuekJAQpsyYQsvmLZ2OJH4oP5dct835+iXQLuf2d56JI3JhMjP/\n3Puoi2ZcXLSePfuxevUqnnrqSZo2beh0HBFvoBroBTbs38C6fesoGV6SO2vf6XQccVCru1rR/u72\ntL2rLV3aq/CLZ+RnkYb7C3pwY0wr3DuQBwPjrbUjzvCcu3Ff+GqBJGttj4L+PAk8ixfDoUNQpw5c\npwWNCsxa9+Jc2dkl+PjjeZQp43QiEe9wMTVQCs+k9e69j+6sdSclwko4nEacYK3FGEN6djrjPxxP\n+RLlnY4kfiw/U+w+wt28/IW19oHzvC4YGAO0AHYD3xtjPsvdjTznObWB54Em1tqjxpgKF5hfAtwk\nd82kQwfQgkYFM336eL78cilvvDGFKlXC1RyJ5FHQGiiF55Tr1B97H2lxhsD0+ZLPmRA/gXcmvEOV\n6CqUK17O6Uji5/IzxW5hzteRwMALOPb1wM/W2h0AxpiZQHtgc57nPASMsdYeBbDWHriA40uAO3gQ\nFi6E4GBNryuoBQs+ZuDAh7HW0rlzd668UnP7RU5T0BoohSRxeyL7U/dTo3QNboi5wek4UsT++9V/\n6d+7P+np6SR+ksjzf3+es2zeLFJo8jPFbi6AMeal3Nv5FAP8luf+buD0d7Y6OcdejXsa3qvW2oTT\nD2SMeRh4GCA2NvYCIog/mzEDsrKgaVOIiXE6je9ZuTKRxx/vibWWgQNfp3dvNUcip8tvDVSd8pxJ\nSe6pAp3qddLeRwFmw7oN9LmnD+np6dz3wH0MemqQmiMpEhfyTvP/phicx5n+Cz79GCFAbaAZ0B0Y\nb4wp/f9eZO0H1toG1toG0dHRFxhD/FXu6nWdOzsawyd9//3X9O3biVOnTvHQQ08xfPhLqOaInNM5\na6DqlGccSTvCZ9s+c+99dJmmCgSSn3/8mZ6depKSnEK7zu2Y8P4EgoOCnY4lASI/1yD9gLsw1DLG\nbMDd+Fhr7fl25NoNVM1zvwqw5wzP+cZaewr4xRizDXfD9H0+80uA2rAB1q2DUqWgdWun0/iWTZuS\n6NXrTtLSTnL33fczbtxbBAWpOxI5k4uogVIIZm6cSaYrkyZVmxBbSiNzgWL3r7vp1r4bRw4f4dYW\ntzJr2ixCQ0KdjiUBJD/XIN1VwGN/D9Q2xtQAfge6AaevUDcP98jRRGNMedxT7nYU8OdJAMldnKFN\nGyhe3Nksvmb06OGcOHGcVq06MXnyBwQHqzkSOYeC1kApBLl7H3WO01SBQPLh+x+y9/e9NGzckHmf\nzCMiPMLpSBJg8tMgXejUOveLrM0yxgwAEnFfX/ShtXaTMeZ1YI219rOc77U0xmwGXMCz1trDBfl5\nEjhOnYKpU923Nb3uwg0b9hE1a9ZnyJBBhIfn5y1AJKAVqAbKxdt8cDPf7/meyLBI7qqjPjWQPPPK\nM5SIKsHzTz9PyciSTseRAJSfT0eLcr5eCmwnZ3oBcN7pBdbaxcDi0x57Jc9tC/w9549IviQmwoED\nULMmXH+902l8w7FjRylRIhKXK5RixYoxcuQrhKg3EsmPAtdAuTi5ex+1rtVaex8FgJOpJwEIiQjB\nGsvw14cTFhzmcCoJVPlZxe4KAGPMOmvtNZ6PJHJuuYszaO+j/ElOPkH37i2Ijq7MP/85izp1iqk5\nEskn1UBnZGVnMWXDFAC6xGlxBn+XmZnJQ/c+xInkE8RPi+eK6leoORJHXcjHJE0zEMcdPgwLFrgb\nI+19dH5paWn06dOWDRvWEht7jJIlTxAWVszpWCK+SDWwCH2x4wv2puylWqlq3Fj1RqfjiAe5XC4e\nf+hxVi5bSdnyZYnIjCAiRNccibPys4pdp5ybpfPcxlr7icdSiZzFzJmQmQk33QTaauTcTp06Rb9+\nXfnmm1VUqFCZxMTPid5xBBYAACAASURBVI2t6HQsEZ+iGuiM3MUZOtTroL2P/Ji1lkF/G8TCTxcS\nGRXJgkULuKL+FU7HEsnXCFLbnK9f5rltARUHKXK5q9d16nTu5wW67OxsnnqqD8uWLaJUqbIsWrSU\nevVqOB1LxBepBhaxY+nHmLd1HgZDl/qaKuCvrLUMfXkoMybPIDwinDmfzuHG6zVaKN4hP9cg3V8U\nQUTOZ9Mm+P57iIqCu7Sg0VlZa3nxxQF8+ul0ihePZP78BBo0uMzpWCI+STWw6M3aOIsMVwaNqzTm\n0jKXOh1HPOS9t94j/l/xhISEMGXGFO647Q6nI4n8IT9T7P51psettU8UfhyRs8sdPWrdGkpoQaOz\nyszMZOfO7YSFhTNr1mc0bdrQ6UgiPks1sOhNSnK/2Xes19HhJOIp1lp+2vYTxhjiP4yna4euTkcS\n+Yv8bhR7AhgHpHs2jsiZZWX9ufeRFmc4t7CwcN577zP27VtHy5aNnI4j4utUA4vQtkPb+O/u/1Ii\ntARt67Y9/wvEJxljGPLuEO5/8H7uaqEpIeJ98nPlYx3g30BfIBSYYq2d5NFUIqf5/HPYuxeqV4fG\njZ1O451Wrfqc9PQMkpOhSpVwNUcihUM1sAhNTpoMwB0176BkuDYI9Tfffv0tySeSSc5IplyJcrS5\nvY3TkUTO6LwNkrU2y1o7BrgFiAa+NsboHL4UqdzpdR3/j707j4uqbP84/rlZBFlERUHEfdfSLDUr\nLbfclc1MwXIpLXtK05afPZqpZZtlZk8upRnuua8p7lqae4r7gru4K6IICjL3748JQkUZlOEwM9f7\n9eLFMHPmzBfKueY+5z7XHSprH2Vm0aJZREQ0p3PnIHx8blO4sNGJhLAPUgNzT6oplUm7zAMkac5g\nfzau30hESATtWrfDKdkJP08/lFJGxxIiU5Zcg7Sbf9d/UIAPMANwtmIuIdLFxcH8+aAUtGtndJq8\nZ82aKHr16oTWmnr16lOsmKwCK0ROkRqYe1YfW83pa6cpUaAE9UrVMzqOyEHRf0fTtUNXbt68yZNP\nPUm5YuVkcCTyNEuvQRLCMDNnwq1b8NxzUFY6Vd9h69YNdO8eRkpKCj169OXLLz9Gao4QOUpqYC5J\na84QUjkEFyc50GMvDh88TKewTiRcT6BtWFsm/DwBZyc5viDyNkvegQZord+wehIh7iMy0vw9VBoa\n3WHv3mg6d27NzZtJvPxyN8aMGY6Tk4yOhMhhUgNzwbVb15i737y0VPtq0tHMXpw+eZqOwR2JuxJH\nwxcbMmPqDFxdXI2OJUSWLLmao7bVUwhxHwcPwqZN4OUlax9ldPLkMSIimnHtWjwtWoQxadLPODvL\n4EgIK5AamAtm7Z1F0u0k6hSvQwXfCkbHETngyuUrdAjqwLkz56jzbB0WzFtAfvf8RscSwiKWnEEq\nkdk6ELIGhMgNac0ZmjeHAtLQKJ2fXwA1atQlOfkms2dPw81NpqMIYSVSA3NBZHQkIGsf2ROfgj7U\nrVcXDy8PlixeQgEvKeLCdljyqSoJ2G7tIELcLTUVJpkbGsnaR/dwZ/ToOfj7J+Pp6WZ0GCHsmdRA\nK4u5EsP6k+vJ75Kf4CrBRscROSSVVD797lMKOxemSKEiRscRIlssGSBdkTUfhBFWr4bYWChZEupJ\nQyOuX7/GyJFD6d17CC4u+Slb1pV8+WQutxBWJjXQytLWPmpWvhkF3QsanEY8iuTkZIZ9Noy3+r6F\nm6cbpQqWwt3F3ehYQmSbJQMkKQzCEGnNGUJCwNnBG94kJSXRtWtbNm36g/PnLzJt2q/ky2d0KiEc\ngtRAKzJpU/oAqV1VWcfBlqWmptKrRy8Wz1tM9M5oVq5YKYMjYbMsadJwQinlk/aDUqqgUirEipmE\nID4e5s0z327v4A2NUlJSePPN9mza9Ad+fsX5/PNPcJNZdULkFqmBVrTu+DpOxJ+guHdxGpRpYHQc\n8ZC01vR7tx+L5y3Gy9uLYV8PI7+rNGQQtsuSAdIgrXV82g9a66vAIOtFEgJmzYKkJHj6aShf3ug0\nxjGZTPTt25VVq37Hx6cwv/++nCpVZDEoIXKR1EArSmvOEFw5WNY+slFaa4YOHMr0SdNxc3dj9rzZ\n1Ksr8+KFbbNkgJTZNvIuJqwqrXtdWJixOYyktebjj3sxb940PDy8WLAgitq1HzM6lhCORmqglSQk\nJzBn3xwAXqomnXhs1Y/f/cjYH8bi4uLC5OmTad6kudGRhHhklgyQtimlvlNKlVdKlVNKjUA6+ggr\niomB9evBwwOCgoxOY5xZsyYxceJo8uVzY8aMhTRoUMfoSEI4IqmBVjJ732xupNzgqYCnqFKkitFx\nxEP4Y80ffDXkK5RSjPllDO1DHHxOvLAblhwF6wUMBGYAClgOvG3NUMKxpbX2btYMfHwevK09Cw4O\nZ+XKZYSHd6BNm0ZGxxHCUUkNtJKJ0eapAmFVHHiqgI2r36A+r3R/hZrVa9K9c3ej4wiRY7IcIGmt\nbwAf5UIWITCZ/p1e185BGxpprQHFrVv5mDhxGr6+RicSwnFJDbSOY3HHWHt8LW7ObrL2kQ3SWqOU\n4kbKDb4d8S1+nn5GRxIiR2U5xU4ptTCzr9wIJxzP2rVw8iQEBsILLxidJvctXjybV19txYULN/D1\nhcKFjU4khGOTGmgdk3dNBqBpuaYUzi9vdLZk4/qNhLUI49SZUxRwK4Cfpx9KKaNjCZGjLJliVwjw\nBr4Azls3jnB0aWePgoPBxcEug167dhnvvBNBSkoKa9f+Rp8+ryM1RwjDSQ3MYVrr9Ol17ao56FQB\nG7Vrxy66duhKwvUEZk6cyTeffyODI2GXLJli97xSqjXQH1gDDNNaX7N6MuFwrl+H2bPNtx1t7aOt\nW/+ie/cwUlJS6N69D++++5oMjoTIA6QG5rz1J9dzNO4o/p7+NCoj11faiphDMXQK60TC9QTahrXl\nq0+/wklZ0utLCNtj0f/ZWuvftdb1gL3ACqXUB9aNJRzRnDmQmAi1a0OlSkanyT1790bTuXMrkpIS\nad++K2PGDMfJSUZHQuQVUgNzVuTOSMC89pGrs6uxYYRFTp88Tcfgjly5fIWGLzZkxtQZuLrIfzth\nv7I8g6SUug7otB8xD6pqA99aMZdwQJGR5u8hDrRG/dGjh4mIaMa1a/E0bx7K5MnjcHGRI3JC5BVS\nA3PWjeQbzNo3C4D2jznYVAEbdfHCRToEdeBs7Flq1a3FgnkLyO+e3+hYQliVJVPsvHMjiHBsx47B\nunXg7u5YA6Rx40Zw6dIF6tVrwuzZ03Bzc7ALr4TI46QG5qx5B+ZxPfk6T/g/QdUiVY2OIywwfdJ0\njh89TtXqVVn6+1IKeBUwOpIQViefxkSekLb2UdOmUKiQsVlyU//+I/H1Lc7AgX3w8nI3Oo4QQlhV\n2vS60CqhcnG/jXizz5topXm7x9sU9S1qdBwhcoXM5REPNGwYrFlz531r1pjvz6l9Z1z7qFo1GD36\n0fedl12/fo2kpCSSk8HZ2ZWvvvqYQoW8jI4lhBBWMWzDMNYcW8PJ+JOsPraafM75CPQOZPRWO3+z\nt2HJycnEX43ntuk2KakpDPl4CKUCSxkdS4hcI2eQxAPVqQMvvwxvvAE+PnDkCEydCp06Pfog6cgR\n+PRTaNXKPMWuUCEYNw7Gjs2Z7HlRUlIS3boFYTLBmDELqVatAPnyGZ1KCCGsp07xOrw8+2WCKgWh\n0dT0r0m/Vf0Y29qO3+xtWGpqKr169CLmYAzjZo6jVqVauLvIDAfhWCxp0pDpIQOt9cmcjyPymkaN\n4IMP4KO71pH/+eece41Z5ut1SUoyT7WrVy/n9p2XpKSk0LPny2zcuI6iRQPw8LiCm5vM5RYiL5Ma\n+OgalW3EjHYzaDalGQD7Lu1jQtAE6pWy0zd7G6a15qM+H7F43mK8vL1QCYr8rtKQQTgeS84gHQBi\nMHfvKQccxdzRp4YVc4k8ZPv2f2/XrAm1auX8/nfuhK5d7XdwZDKZ6Nu3KytXLsbHpzBLlqygcuUy\nRscSQmRNamAOcHd1J1WnAtCtZjcZHOVBWms+/+Rzpk2chpu7GzPnzqReXfnvJByTJQOkg1rrJwGU\nUju11jWtnEnkIXFxMG+e+XbXrrBwIfTvn3MDmQ0bzPvv08d89qhxY/sbJGmt+fjjXsybNw0PDy/m\nzVtK7dqPGR1LCGEZqYE54Ms/vwSgZrGaTN09ledLPS+DpDzmx+9+ZMzIMbi4uDBp+iRavtjS6EhC\nGMaSJg35lVL5lFIFgVJKqUillExGdRBDhsDt2/DYY/D55+brg3r2NA9sHtWGDeZ9jR0LH36Ys/vO\nS4YNG8jEiaPJl8+N335bQKNGTxsdSQhhOamBjyjqcBS/H/4dgC+bfMnY1mPp+XtPNpy0szd7GzZx\n/ES+GvIVSinG/DKGl0NeNjqSEIayZIA0FTgFHAT6AwuBVdYMJfKOuXPN37t1M3+vV888kImOfvR9\nR0eb95V2xign951XpKamcvToIZydnZkwYQZt2zY2OpIQInukBj6iSbsmodE87vc41f2qU69UPca2\nHkv0eTt6s7dxRw4fAWDY98Po3rm7wWmEMJ7SWme9kVLeAFrr6//8XF5rfcTK2TJVu3ZtvW3bNiNe\n2uHs329uu+3lBdu2gbcsl5htWsPVq6mcOLGJVq1kOomwH0qp7Vrr2kbnyA3ZrYFSp+7UYkoLlh1Z\nxicvfMKbtd80Oo7IxLWb1zj490GCmgXJ+lTCbjxKnbKki91TGW4/zGsIG5W2NlGLFjI4yq6//lpL\nzZp1SE31xM/PmWrVZHAkhC2SGvhoYq/FsuLoClydXAmtEmp0HJHB31v/pnTZ0rgXcMfH3UcGR0Jk\nYEmThnXAVswdfNJoQOYK2bHUVJg82Xz7pZeMzWJr1q1bTpcubXjssdrMm7eKIkXyIzVHCJslNfAR\nTNk1BZM28WLZF/Hz8jM6jvjH7p27iQiNoKh/UeYvm0/5MuVlcCREBpYMkGK01lIIHMzKlXDmDJQq\nZX9d5axp69a/eP31UFJSUqhduy6lSrnL4EgI2yY18CFprYmMjgSgXdV2xoYR6WIOxRARGsH1a9dp\n0KQBVUpWwUlZckm6EI7DkgFSUaVUH+AmcAbYrLU+b91Ywmhp0+tCQsBJ3jctsm/fLrp0aU1SUiLt\n23dlzJjhODnJ6EgIGyc18CFtPbOVA5cO4JvflxfLvWh0HAGcPnmajsEduXL5Cg2aNGDmtJm4urga\nHUuIPMeSj77jgMJAeaADsEUp1dWaoYSx4uP/XfuofXtjs9iKY8diiIhoRnz8VZo3D2Xy5HG4uMjI\nUgg7IDXwIUXujASgbaW2uLtKZ3SjXbxwkY7BHTkbe5ZadWuxcP5C8rvnNzqWEHlSlmeQtNZDMv6s\nlCoC/AlEWimTMNjMmXDzJtStC+XKGZ0m77t48Tzh4U25ePE89eo1Yfbsabi5WXJyVgiR10kNfDg3\nb9/ktz2/AfBSNbmQ1Wg3Em7QKawTx44co2r1qiz9fSkFvAoYHUuIPMviT3H/tDnVWutLQFXrRRJG\ni4w0fw8LMzSGzShYsDC1atXH19efRYvm4+UlR0qFsDdSA7Nn0cFFxN2Mo1qRatQsVtPoOA7Pw9OD\n+g3qcyPhBlFLoyjqW9ToSELkaVnOAVJKVVdK7QD2APuUUtuVUo9ZP5owwuHD8Ndf4OEBbdsancY2\naO3K119PZOXKFRQq5GV0HCFEDpIa+HAmRpsvZA2pGiLd0fKAVJ1Kn4F92LRlE6UCSxkdR4g8z5KL\nJH4C3tNal9ZalwLexzwnW9ihtOYMzZuDj4+xWfKypKQkPvvsQ65cuUZKCpQu7YSvrywWJYQdkhqY\nTWevnyUqJgoXJxfCqshUBKOkpqby5ZAvOXPmDEkpSZQuWBp/X3+jYwlhEyyZYueptV6T9oPWeq1S\nytOKmYRBTCaYNMl8u510ZL2vlJQU3nqrAytWLOLgwYMsWbIQNzejUwkhrERqYDZN3T2VVJ3Ki2Ve\nJMA7wOg4DklrzX/7/pepkVNZvWI1GzdtJL+rNGQQwlKWDJCOKqUGAv8sG8orwDHrRRJGWbMGTp2C\nEiXg+eeNTpM3mUwm3nvvNVasWISPTyG+/voL3OWSIyHsmdTAbNBap0+vC60aanAax/XFoC+YGjkV\nN3c3vh3+LQXyS0MGIbLDkil2rwFFgbnAPKAI0M2aoYQx0pozBAWBizRhu4fWmoEDezN37hQ8PDyZ\nO3cpdeo8bnQsIYR1SQ3Mhr/P/s2eC3so5F6I5uWbGx3HIf343Y+M/n40Li4uTJw2kZYvtjQ6khA2\nx5I233FA74z3KaWKKaVKARe11knWCidyz7VrMGeO+basfZS5b775hMjIUbi65mP69AU0blzX6EhC\nCCuTGpg9aWeP2lRqI1O6DDDpl0l8OfhLlFKMHj+aDqEdjI4khE3KcoCklHovk7v7AtOBKcCunA4l\nct/s2ZCUBHXqQKVKRqfJe5YvX8TIkUNxdnZmwoQZBAU1MTqSECIXSA20XHJqMtN2TwNk7SMjRP8d\nTf/3+gPw9Yiv6dGlh8GJhLBdlkyk+hAYe9d9zlrr/7NCHmGQtO51ISHG5sirGjduRfv2PWjYsD6v\nvCJ/JCEciNRAC/1+6HcuJ12mkm8lnir2lNFxHE6NJ2vw1ntvUdCrIB/0/sDoOELYNEsGSGczWUlc\nPiHakaNH4Y8/IH9+GSDdTWuNUoqkJGdGjfqZIkWMTiSEyGVSAy0UGR0JQGiVUJycLLnEWeSEtDqV\nmJLIx4M+pphXMVl7SohHZMk7WGml1Hil1DClVG+lVHlAWzuYyD1prb2bNoWCBY3NkpesW7ec9u0b\nERsbR8GCUKQISM0RwuFIDbTAhRsXWHJ4Cc7KmXZVZZ2I3LJ7527aNmlLzLEYPFw98Pfyl8GREDnA\nkgHSG8By4ADmTj5zAGndZSdMpn+n18naR//atm0jr78eysaN61iwYDx+fjI4EsJBSQ20wLTd07ht\nus3zpZ8nsECg0XEcQsyhGCJCI9ixbQcTx0wkwDsAJyVn7oTICZZ0sZuT8Wel1GfAFKXUauBTrfVa\nK2UTueCPP+D4cQgIgIYNjU6TN+zbt4vOnVuRlJRI+/ZdGTz4fRkcCeGgpAZaJnJnJADtqsiRttwQ\neyqW8JBwrly+QsMXG/LjiB9lcCREDsr2ajda62TgZStkEQZIO3sUHCxrHwEcOxZDREQz4uOv0rx5\nKJMnj8PFRYqOEMJMauC9dp7bSfT5aHzcfGhRoYXRcezepYuX6BjckTOnz1D7mdosmLeA/O7SUl2I\nnCSf/BxYQgLMmmW+/ZJ0ZOXs2Vg6dnyRixfPU69eE2bPnoabm4wahRDiQSbuNB9pa12pNR75PAxO\nY9/ir8YTERrB0ZijVK1elSWLl1DAq4DRsYSwOzJAcmBz58KNG/Dkk1ClitFpjDd58lhOnz5BzZp1\nWbRoPl5e7kZHEkKIPC0lNYWpu6cC8FJVOdJmbQvnLmTvrr2UKVeGqKVRFPUtanQkIeySHB53YJGR\n5u9hYdKAAKB37yG4unrx/vs9KFTIy+g4QgiR5y2NWcrFxItUKFyBOsXrGB3H7oV3DSchKYFXX36V\nUoGljI4jhN3KcoD0z4Wo99BaN875OCK3nDgBa9aAm5v5+iNHdfPmTVJSknF3L8Dt204MHdoPNzej\nUwkh8gqpgQ82Mdo8vS60sqx9ZC2pqanEX43Hp5APSSlJ9H+/P/ld5ZojIazJkjNIxYFOgAImA69Y\nNZHIFWlrH734Ivj6GpvFKCkpKfTs+TJnz8YyblwUNWsWlcGREOJuUgPv43LiZRYdXISTcuKlx2R6\nnTVorflv3/+yft16xs8czzPVn5HBkRC5wJIB0k2t9XYApVRBoKDWepV1Ywlr0lrWPjKZTLz33mus\nWLEIH5/CuLpexN1d5nILIe4hNfA+pu+ZToophRdKvUCJAiWMjmOXvhj0BVMjp+Lm7kZqfCpebjL9\nW4jcYMkAKU4p9QPgDWwF3lZK1ddaD7FuNGEtGzbAkSPg7w+NHXCSiNaagQN7M3fuFDw8PJk3bym1\nalUzOpYQIm+SGngfaWsfhVYNNTaInfrxux8Z/f1oXFxcmDhtIs2bNDc6khAOw5IJw2HAIWALEKG1\nDgMSrZpKWFVac4agIHB1NTSKIb755hMiI0fh6pqP6dMX0KjR00ZHEkLkXVIDM7Hnwh62n92Odz5v\nWldsbXQcuzPpl0l8OfhLlFKMHj+aDqEdjI4khEPJ8gyS1joO+PGu+76xWiJhVYmJMHOm+bYjrn30\n00/fMXLkUJydnZkwYQZBQU2MjiSEyMOkBmYube2jVhVb4ZnP0+A09mX+rPn0f68/AF+P+JoeXXoY\nnEgIx2NJF7uiwP8BjwHpC8NIBx/bNG8eXL8ONWrAY48ZnSZ3aa2JiTkAwMiRE3jllRCDEwkh8jqp\ngfe6bbrN5F2TAXipmgMeabOyY0eOobWm/6D+fND7A6PjCOGQLJliNxU4AJQFhgDHMc/DzpJSqoVS\n6qBSKkYp9dEDtntJKaWVUrUt2a94eGnNGUJDHW/tI6UUAwf+xMKFf/Kf/3Q2Oo4QwjY8dA20V8uP\nLOf8jfOULViWZwKfMTqO3enRtwfzoubx2SefoRytUAuRR1gyQPLVWv8CpGit12mtXwOyfEdUSjkD\no4CWQDUgXCl1z5XwSilvoDewOVvJRbadOgUrV0K+fObFYR3F1q1/ERd3hYQEKFhQ0aZNfYcbHAoh\nHtpD1UB7lt6coYqsfZRT9u7eS+zpWG4k38AjnwdBzYLkbyuEgSz515fyz/ezSqnWSqknAUv6eT4N\nxGitj2qtk4HfgMyWJP0MGAbctCSweHhTpphbfDduDEWKGJ0md2zfvomIiGaEhTUkJSUOf3/HO3Mm\nhHgkD1sD7VJcUhwLDi5AoWhX1UHXichhMYdjCA8OJ6RZCJfOXiLAKwAnJYMjIYxkyb/AoUopH+B9\n4ANgPNDXgucFAqcy/Hz6n/vS/VNoSmqtFz9oR0qpN5RS25RS2y5evGjBS4u7af1v9zpHOXu0f/9u\nXn21JYmJN3jiiVpUruwjgyMhRHZZVAMdpU79tuc3klOTebbks5QpVMboODYv9lQs4cHhXL50mYqV\nK1KzQk2cnZyNjiWEw7Oki13a4CUeaJSNfWf2UVSnP6iUEzAC6GpBhp+BnwFq166ts9hcZGLzZjh0\nCIoWhaZNjU5jfceOxRAR0Yz4+Ks0bx7K5MnjcHGRI3JCiOyxtAY6Sp2aGG2+kLVdFTl79KguXbxE\nx+COnDl9hlp1a7Fw/kLyu+c3OpYQAsu62P1KhoFNmn/mYT/IaaBkhp9LAGcy/OwNPA6s/ecixGLA\nQqVUkNZ6W1a5RPaknT1q29Z8DZI9O3s2lvDwply4cI7nnmvC7NnTcHOzZE1kIYS40yPUQLuz/+J+\nNsduxsvVi9aVZO2jR3Et/hoRoREcjTlK1cersvT3pRTwKmB0LCHEPyz51Jh29GwY5lanltoKVFRK\nlQVigY5ARNqDWut4IP1KGKXUWuADGRzlvKQk+O038217X/vo2rV4IiKacerUcZ544mkWLZqHl5d7\n1k8UQojMPWwNtDtpZ49aVmyJt5u3wWlsV3JyMl1e7sLeXXspU64MUVFRFPUtanQsIUQGlkyxmwOg\nlPo47bYltNa3lVLvAMsAZ2CC1nqvUupTYJvWeuHDhhbZs3AhxMeb1z2qUcPoNNbl5eXNM880RmtF\nVNRSCheWIi6EeHgPWwPtTaop9d+1j6ra+ZE2K8uXLx+NmjXi5ImTRC2PolRgKaMjCSHukp15R9me\nU621XgIsueu+T+6zbcPs7l9YJm16nSOsfZSa6kT//j9QuPB1ihaV6QpCiBxjt9cVWWLl0ZWcuX6G\n0j6lea7kc0bHsWmpplS6vdONd995l4AiAUbHEUJkIsur1pVSu5VSu4AqSqldGX4WNuDMGVi+HFxd\n7bd7XUpKCp9/3o/z5y9y6xaUKqVkcCSEyBFSA83SpteFVAmR9Xkegtaa4V8M5/ix49xIvkGgd6AM\njoTIwyw5g9TG6imE1UyZAiYTNGkC/v5Gp8l5JpOJ9957jblzp7Bp0wb++ONP8ue389NkQojc5PA1\nMP5mPPMOzANket3D+nLwl4waMYrZv83m711/4+XmZXQkIcQDZHkYSGt9Arj6z/cAoDrmpgsij9Ma\nJpoP+tnl2SOtNZ988i5z507Bw8OTb74ZjqenDI6EEDlHaiDM3DuTm7dv8kzgM5QrXM7oODZn1IhR\njBoxChcXF4YNH4avt6/RkYQQWbCkzfc0oKFSajFQAUgEXsHclU7kYdu2wb59ULgwNGtmdJqcN3z4\nYH799UdcXfMxffoCGjeua3QkIYSdkRoIkdGRAIRWCTU2iA2a8usUvhj0BUopRo8fTYewDkZHEkJY\nwJIpdrWBcsApwF9rbVJK7bFuLJET0s4etW0L7nbW6XrcuO8ZMeJTnJ2dmTBhBkFBTYyOJISwTw5d\nAw9fPsxfp/7C09WToCpBRsexKQvmLOCjPh8B8PWIr+nRpYfBiYQQlrLkSssErfVN4JTW2vTPfclW\nzCRywK1bMG2a+ba9rX20Zct6Bg/uC8D33//CK6+EGJxICGHHHLoGpjVnaF6+OQXcpPmNpY4dOUbv\nHr3RWtN/UH8+6P2B0ZGEENlgyRmkJ5RS1wCPf74rwM7OR9ifRYsgLg6qVIEnnzQ6Tc6qU6cer7/+\nIWXLBvL2212MjiOEsG8OWwNN2sSk6EkAtKvWzuA0tqVs+bJ8OOhDrl66ymeffIay9zU2hLAzliwU\n65wbQUTOSpteZ09rH2mtUUpx44Zi6NBh+Pvbz+8mhMibHLkGrjm2hlPXTlGiQAnql6pvdBybkF6n\nkm/wn97/obh3cZyUtEUXwtZYsg7SU5l95UY48XDOn4elS8HFxX66123fvong4HocPXoWT09kcCSE\nyBWOXAPTmjME+KgOdAAAIABJREFUVw7GxSk768o7ppjDMbRp1IZ9+/eRzzkfAV4BMjgSwkZZ8o63\nDTiMua1p2kdSDTS2VijxaKZOhdRUaNwYihc3Os2j279/N6++2pL4+KtMn/4D//vflzI4EkLkFoes\ngdduXWPOvjkAtK/W3uA0eV/sqVjCg8M5c/oMo4aPYvb02Tg7OezJRyFsniWHNpoC54DtQDutdSOt\ntV0XBlumNURGmm+3s4Mp48eOxRAR0Yz4+Ks0axbCd999hiziLoTIRQ5ZA2fvm03S7STqFK9DRd+K\nRsfJ0y5dvETH4I6cOX2GWnVrETk+UgZHQtg4SxaKXaW1bgBsBH5XSg1QSnlYP5p4GDt3wu7dUKgQ\nNG9udJpHc/ZsLOHhTblw4RzPPtuYOXOm4+Ym0zyEELnHUWtgWvc6Wfvowa7FX6NTWCeOxhyl6uNV\nWfL7Eny8fYyOJYR4RJYsFPtehh/nYV4grxdQzFqhxMNLO3vUujXkz29olEdy5cplIiKacerUcZ54\n4mkWL56Pl5dDNI4SQuQhjlgDj8Yd5Y8Tf5DfJT/BVYKNjpNnJSUm0eXlLuyJ3kPpsqWJiorCz9fP\n6FhCiBxgyeF477t+nmONIOLRJSfbz9pHs2dP4tChfVSs+BhLly6hcOG7/zcUQohc4XA1MK21d7Py\nzSjoXtDgNHnXiqgVbNm4Bf8Af5atWEapwFJGRxJC5BBLBkjbtdaLrZ5EPLIlS+DSJahUCWrVMjrN\no+natQ/JydCjRwcCAnyNjiOEcFwOVQNN2pQ+va5dVTu4kNWKWoe0ZuiIobRs3JLK5SsbHUcIkYMs\nudz9U6unEDkibXpdcDA22cggJSWFuLgr3L4NycmKgQP7UrasHbThE0LYMoeqgX+c+IPjV49T3Ls4\nDco0MDpOnqO15tLFS5i0iRvJN3j3rXd5qoZDdH0XwqFY8jHaQyn1pCOuAZEThg2DNWvuvG/NGvP9\nObn/ixfh99/B2RnKlIHRo3Nm/7nFZDLx/vuvExJSjyNHTlGihG1fQyWEsBsOUQOHbRjGmmNr0s8e\nBVcOZvPpzYzeamPFxMq+GvIVzeo3Y8euHRT3Lo6Xm5fRkYQQVmDJFLtAYDj/rv8ADrAGRE6pUwde\nfhlmzoTnnoPVq6FzZ5g0CRITH33/1aub9//SS3D7NtSoAQMHwtixj77v3KK1ZtCgPsyZMxkPD0/g\nLB4eJY2OJYQQ4CA1sE7xOrSf1Z4byTcAKF+4PD1/78nY1jZUTKxs9Pej+fG7H3FxcSHxQiIF3AsY\nHUkIYSVKa/3gDZTaobV+MpfyZKl27dp627ZtRsfIljVrICgIEhKs/1qenvDrr1CvnvVfK6d8++0g\nRoz4FFfXfMyevYSgoCZGRxJCZEEptV1rXdvoHNb2MDXQFusUwH9X/pevNnxFMa9iJKcmM7b1WOqV\nsqFiYkVTfp1Cv3f7oZRi7ISxvNH1DaMjCSGy8Ch1ypIzSHEPs2Pxr4YNIV8+820np39v56SUFEhN\nha5dbWtwNG7c94wY8SlOTk788stvMjgSQuQ1DlMDN8duBuBcwjn61O0jg6N/LJizgI/6fATAV999\nJYMjIRxAlgMkR1gx3NpGjYIrV8DDA9zdzdPfcnIQs2ED9Oz579S9Bg1sY5A0Y8avDB7cF4CRIyfw\n6quyIKEQIm9xlBp44uoJ1hw3XzD7Zq03mbRrEs+VfM7hB0mrl6+md4/eaK357yf/5cN3PzQ6khAi\nF2TZpEEpdfSur2NKqaO5Ec4erFkDH/7zfhoebh4c9expHtTkhLTB0dix5tfJ6f1b09GjhwAYOvR7\n3n67i8FphBDiXo5SAwevHQzAM4HP8EmDTxjbeiw9f+/JhpM2UEys6MSxE9y+fZuevXsydNBQlFJZ\nP0kIYfMsmWKXADTCfIHqaqAhd16sKh7gr7/MneXA3EihRg3zICY6OmfO8kRH33lGql69nN2/NfXq\n9SUvvtiaoKD6SM0RQuRRdl8DtdYsPLQQgDdqm6eP1StVj7GtxxJ9PtqhzyJ16NaBqtWrEtw0GCdb\nXD9DCPFQLBkgobW+rJRywtzNJ0hrHWnVVHakfHm4cQMef9zccQ7MA5ecGrz85z/33peT+89pu3Zt\nx9+/OJ6eAXh6IoMjIUSeZ+81cMOpDVxJuoK/pz+Ny/w7o7BeqXoOOTg6cvgIAMXLFCefSz6Cmwbj\n7ORscCohRG6y5HBIjFJqIbAcmAs8pZT61bqx7Efa4q1hYTj8QGD//t2EhzclJOR5rl07S0CA/E2E\nEHme3dfAyJ2RAARVDsLV2dXYMAaLPR1Lx+COhLYI5fjh4wR6B8rgSAgHZMkZpA5AcyAVWK61TlVK\ntbduLPsQGwsrVpi71oU6eP+B48ePEBHRjKtX46hT5wWqVy+KzFYQQtgAu66BiSmJzNw7E4D21ezm\n13ooly5eIjw4nDOnz/DU009Ru1ptGRwJ4aAs6WKXAiy+675ZVktkR6ZMAZPJ3Obbz8/oNMY5d+4M\n4eFNuXDhHM8+25i5c3/Dzc2i2Z1CCGEoe6+B8/bP43rydZ7wf4JqRasZHccw1+Kv0SmsE0cOH6HK\nY1VY8vsSfLx9jI4lhDBIlp9SlVLXMa8ann4XoLXWsoT0A2gNEyeab7drZ2wWI125cpnw8KacPHmM\nJ554msWL5+Pl5W50LCGEsIi918CJ0eZCFVo11GE7tCUlJtG1Q1f2RO+hdNnSLFu2DP8i/kbHEkIY\nyJLD+DHZXUVcwNatsH8/+PpC06ZGpzHGzZs36dy5FYcO7aNixcdYunQJhQt7Gx1LCCGyw25r4Kn4\nU6w8upJ8zvkIreyY88BNJhNvdH6DzX9txj/An2UrllEqsJTRsYQQBrPkKhB3pdQTSqkqSik532yh\ntLNHbduCm5uxWYzi5ubG88+3oESJsixbtpyAAF+jIwkhRHbZbQ2csmsKGk2Tsk0o4lnE6DiGcHJy\nokmLJvgW9WVJ1BIql69sdCQhRB5gyQDpHPA/YDKwTym1WylV27qxbNutWzB9uvn2Sy8Zm8VIqamK\nt98ewtatOyhbtrjRcYQQ4mHYZQ3UWhMZHQlAWNUwY8MYyKRNhL0SRvSeaJ6q8ZTRcYQQeUSWAySt\ndSOt9Qta6zpa60DgLWCs9aPZrkWLIC4OqlWDmjWNTpO7TCYTw4YN5NSpUyQmQokSUKyYXR10FUI4\nEHutgZtjN3Po8iGKehTlxXIvGh0n143+fjT79+0nITmB4t7FCfQLNDqSECIPyXKApJS6o8el1no9\n0NNqiexA2tpHISGOtc6P1prBg/sycuRQOnVqQbFiqXh4GJ1KCCEenr3WwIxrH+VzzmdsmFw2ZuQY\nPv/kczq27Yin9qSAu1302xBC5CBLF4r9RimV3v9Ta73Nipls2rlzEBUFLi7mxWEdyXffDeGXX37A\n1TUfw4ePpGBBWT9CCGHz7K4GJqUk8due3wB4qZpjzQOfGjmVoQOHopRi6NdDKVm0pNGRhBB5kCUD\npBrAIWC8UmqTUuoNpZQcbrmPqVMhNdW89lFAgNFpcs/48SP57rshODk5MX78dIKDHW/KhhDCLtld\nDVx4cCHxt+J53O9xqvtVNzpOrlk4dyH93u0HwJfDv+TNbm8anEgIkVdZcg3Sda31OK31c8D/AYOA\ns0qpiUqpClZPaEO0/nd6XagDdUydMSOSQYP6APD997/QubODnToTQtgte6yBac0ZQqs4ztpHa1as\noXeP3mit+eiTj/i/Pv9ndCQhRB5m0TVISqkgpdQ8YCQwHCgHLAKWWDmfTdmxA/bsgUKFoHlzo9Pk\njgMH9vDBB68D8NlnI3jnna7GBhJCiBxkbzXwzPUzLD+yHFcnV8KqOMbBrAvnL9Dj1R6kpKTwZq83\n+XzQ5w4zMBRCPBxLFoo9DKwBvtFa/5Xh/tlKqResE8s2pZ09atMG8uc3NEquqVLlcfr2/QKT6QYD\nBvRxqKYUQgiHYFc1cMquKZi0iSZlm+Dn5Wd0nFzh5+/HoK8HsefvPYz6fhROTpZcXSCEcGSWDJBq\naK0TMntAa907h/PYrORkmDbNfNsR1j7SWqOU4sYN6Nu3H8WLO1bHPiGEw7CbGqi1ZmK0eRXzdlXb\nGZzG+tLqVGJKIh1f6UiJ/5TA2UmaBwkhsmbJYZQflFIT7v6yejIb8/vvcPkyVKoET9n5WnP79++m\nTZu6HDx4DHd3czMKGRwJIeyU3dTAbWe2se/iPnzz+9K0XFOj41hV7OlY2jRqw/a/t+OiXChRQAZH\nQgjLWXIGqTlwApgCnLduHNs10XxQjtBQsOez9ydOHCUiohkXLpxj3LgvmTz5Z7v+fYUQDs9uamDa\n2aO2ldri7upucBrruXzpMuHB4Rw5fIThQ4ezctlKGRwJIbLFkgFSSaAF8CrgDPyqtV5q1VQ25uJF\n8xkkZ2doZ8ezFs6dO0PHji9y4cI5nn22ET///APOUnOEEPbNLmrgrdu3mLbbPA/cntc+uhZ/jU5h\nnThy+AhVHqvCjOkzcHGy5KOOEEL8y5I23yat9RLgMyAReMfqqWzMtGlw+zY8/zwEBhqdxjquXLlM\nREQzTp48Ro0adVi8eAFeXvZ7BFIIIcB+auDiQ4uJuxlH1SJVqVmsptFxrCIpKYluHbuxe+duSpct\nTVRUFP5F/I2OJYSwQVkeVlFKvQGEADHASK31DqunsjFp3evs9exRQsJ1OnduxcGDe6lQoRpRUUsp\nXNjb6FhCCGF19lID09c+qmqfax+lpKTwZuc32bRhE/4B/ixbvozSJUobHUsIYaMsOe88FnNhKAk0\nTHtj1VrXsGIumxEdDTt3go8PtGhhdBrrWLp0Hjt2bCEwsAzLli0nIMDX6EhCCJFbbL4Gnk84z9LD\nS3FxcrHbtY82rt/I6uWrKVi4IEuillC5QmWjIwkhbJglA6SyVk9hw9KaM7RuDR4exmaxltDQzly9\nmshLLzWlXDk7nUMohBCZs/kaOHX3VFJ1Kk3KNCHAO8DoOFZRv2F9vv3pW2o/Vpunath5K1khhNVZ\nMkDqBUzQWu+zdhhbk5ICU6aYb9vb2kcmk4m4uMsULFiUxET48MOedjsAFEKIB7DpGqi1JnJnJIBd\nnj26dPEShYsUJiE5ge6vdqeAewGjIwkh7IAlDZoPAOOUUpuVUj2VUj7WDmUroqLMHewqVIA6dYxO\nk3O01gwe3JeWLWuzd+9hAgPt9+yYEEJkwaZr4M5zO9l9YTeF3AvRvEJzo+PkqDEjx9CgdgM2btqI\nv6e/DI6EEDnGki5247XW9YDOQBlgl1JqmlKqkbXD5XVpzRlCQuxr7aPvvhvCL7/8wIUL50hOPom3\n9GMQQjgoW6+BaWeP2lRqQ37X/MaGyUFTI6cydOBQ4q/GE3cmjkL5CxkdSQhhRyz6WK+Ucgaq/PN1\nCYgG3lNK/WbFbHna5cuwaJF5YGRP0+vGjx/Jd98NwcnJifHjpxMU1MToSEIIYShbrYHJqclM22Ne\n+6hdVftps7pw7kL6vdsPgC++/YI3ur5hcCIhhL3JcoCklPoO8xSDVsAXWutaWuuvtdZtgSetHTCv\nmj7dfA1SvXpQsqTRaXLGjBmRDBrUB4ARI8bTubP9zVdPk5iYyPjx42nTpg0lS5Ykf/78eHp6UqZM\nGZ5++mlee+01Jk6cyPHjx42OmiNOnz5Nv379qFatGl5eXhQsWJAnn3ySTz/9lLi4uBx5jVOnTjFn\nzhw++ugjGjduTIECBVBKoZRi8ODB2drXyZMn6d+/P08//TSFChXC1dWVQoUKUadOHf773/9y8uRJ\ni/azZcsWunfvTtWqVfH29iZfvnz4+/vTuHFjRo4cSUJCQpb7SE1NZfr06bRt25aAgADc3Nzw8/Pj\nhRde4McffyQ5OTlbv5uwLbZcA5ccXsKlxEtU8q1ErYBaRsfJEWtWrKF3j95orek3sB/9+vYzOpLV\nSJ3K2ToVGxvLhAkTeOutt3jmmWcoU6YMXl5euLu7U7x4cVq0aMHYsWNJTEy0eJ8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fPmEhdX8JKjiIgERpYnizHrvePAb29Q8NbfysjI4P7e97NyxUoqVanE/PnzOa9GgZuoVkQkVwEr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\nRETE5/8B12PDlJfYofsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2692fdc0b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import interp1d\n",
    "from scipy.integrate import quad\n",
    "\n",
    "actual = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
    "predict = [0.9, 0.3, 0.8, 0.75, 0.65, 0.6, 0.78, 0.7, 0.05, 0.4, 0.4, 0.05, 0.5, 0.1, 0.1]\n",
    "\n",
    "data = zip(actual, predict)\n",
    "sorted_data = sorted(data, key=lambda d: d[1], reverse=True)\n",
    "sorted_actual = [d[0] for d in sorted_data]\n",
    "\n",
    "cumulative_actual = np.cumsum(sorted_actual) / sum(actual)\n",
    "cumulative_index = np.arange(1, len(cumulative_actual)+1) / len(predict)\n",
    "cumulative_actual_perfect = np.cumsum(sorted(actual, reverse=True)) / sum(actual)\n",
    "\n",
    "x_values = [0] + list(cumulative_index)\n",
    "y_values = [0] + list(cumulative_actual)\n",
    "y_values_perfect = [0] + list(cumulative_actual_perfect)\n",
    "\n",
    "f1, f2 = interp1d(x_values, y_values), interp1d(x_values, y_values_perfect)\n",
    "S_pred = quad(f1, 0, 1, points=x_values)[0] - 0.5\n",
    "S_actual = quad(f2, 0, 1, points=x_values)[0] - 0.5\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1,ncols=2, sharey=True, figsize=(14, 7))\n",
    "ax[0].plot(x_values, y_values, lw = 2, color = 'blue', marker='x')\n",
    "ax[0].fill_between(x_values, x_values, y_values, color = 'blue', alpha=0.1)\n",
    "ax[0].text(0.4,0.2,'S = {:0.4f}'.format(S_pred),fontsize = 28)\n",
    "ax[1].plot(x_values, y_values_perfect, lw = 2, color = 'green', marker='x')\n",
    "ax[1].fill_between(x_values, x_values, y_values_perfect, color = 'green', alpha=0.1)\n",
    "ax[1].text(0.4,0.2,'S = {:0.4f}'.format(S_actual),fontsize = 28)\n",
    "\n",
    "for i in range(2):\n",
    "    ax[i].plot([0,1],[0,1],linestyle = '--',lw = 2,color = 'black')\n",
    "    ax[i].set(title='Коэффициент Джини', xlabel='Кумулятивная доля объектов', \n",
    "              ylabel='Кумулятивная доля истинных классов', xlim=(0, 1), ylim=(0, 1))\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Коэффициент Джини для обученной модели равен 0.1889. Мало это или много? Насколько точен алгоритм? Без знания точного значения коэффициента для идеального алгоритма мы не можем сказать о нашей модели ничего. Поэтому метрикой качества в машинном обучении является <b>нормализованный коэффициент Джини</b>, который равен отношению коэффициента обученной модели к коэффициенту идеальной модели. Далее под термином \"Коэффициент Джини\" будем иметь ввиду именно это.    \n",
    "\n",
    "$$\\large \n",
    "Gini_{normalized} = \\frac{Gini_{model}}{Gini_{perfect}}  (1)$$\n",
    "\n",
    "Глядя на эти два графика мы можем сделать следующие выводы:\n",
    "- Предсказание идеального алгоритма является максимальным коэффициентом Джини для текущего набора данных и зависит только от истинного распределения классов в задаче. \n",
    "- Площадь фигуры для идеального алгоритма равна:\n",
    "$$ S = \\frac{Число\\enspace объектов\\enspace класса\\enspace 0\\enspace в \\enspaceвыборке}{2}$$\n",
    "- Предсказания обученных моделей не могут быть больше значения коэффициента идеального алгоритма.   \n",
    "- При равномерном распределении классов целевой переменной коэффициент Джини идеального алгоритма всегда будет равен 0.25\n",
    "- Для идеального алгоритма форма фигуры, образуемой Lift Curve и и линией абсолютного равенства, всегда будет треугольником\n",
    "- Коэффициент Джини случайного алгоритма равен 0, а Lift Curve совпадает с линией абсолютного равенства\n",
    "- Коэффициент Джини обученного алгоритма будет всегда меньше коэффициента идеального алгоритма\n",
    "- Значения нормализованного коэффициента Джини для обученного алгоритма находятся в интервале [0, 1]. \n",
    "- Нормализованный коэффициент Джини является метрикой качества, которую необходимо максимизировать.\n",
    "\n",
    "### 2. Алгебраическое представление. Доказательство линейной связи с AUC ROC.\n",
    "Мы подошли к самому, пожалуй, интересному моменту - алгебраическому представлению коэффициента Джини. Как рассчитать эту метрику? Она не равна своему родственнику из экономики. Известно, что коэффициент можно вычислить по следующей формуле: \n",
    "\n",
    "$$\\large \n",
    "Gini_{normalized} = 2 * AUCROC - 1 \\hspace{35pt} (2)$$\n",
    "\n",
    "Я честно пытался найти вывод этой формулы в интернете, но не нашел ничего. Даже в зарубежных книгах и научных статьях. Зато на некоторых сомнительных сайтах любителей статистики встречалась фраза: *\"Это настолько очевидно, что даже нечего обсуждать. Достаточно сравнить графики Lift Curve и ROC Curve, чтобы  сразу всё стало понятно\"*. Чуть позже, когда сам вывел формулу связи этих двух метрик, понял что эта фраза - отличный индикатор. Если вы её слышите или читаете, то очевидно только то, что автор фразы не имеет никакого понимания коэффициента Джини. Давайте взглянем на графики Lift Curve и ROC Curve для нашего примера:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RZuJE5+fFF0OVkht3oEScfXYHunS5grPPPpthw/p7HY6JEL/t+Y0vNn9BQkwC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o58gVGjXmLbtmVkZcUkRBFJUr8M/2x15OGfK75dwQ2/voFli5eR90oe9arXU+NPpAJTA1BEJIoC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2692fcc36d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, roc_auc_score\n",
    "\n",
    "aucroc = roc_auc_score(actual, predict)\n",
    "gini = 2*roc_auc_score(actual, predict)-1\n",
    "fpr, tpr, t = roc_curve(actual, predict)\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1,ncols=3, sharey=True, figsize=(15, 5))\n",
    "fig.suptitle('Gini = 2 * AUCROC - 1 = {:0.2f}\\n\\n'.format(gini),fontsize = 18, fontweight='bold')\n",
    "ax[0].plot([0]+fpr.tolist(), [0]+tpr.tolist(), lw = 2, color = 'red')\n",
    "ax[0].fill_between([0]+fpr.tolist(), [0]+tpr.tolist(), color = 'red', alpha=0.1)\n",
    "ax[0].text(0.4,0.2,'S = {:0.2f}'.format(aucroc),fontsize = 28)\n",
    "ax[1].plot(x_values, y_values, lw = 2, color = 'blue')\n",
    "ax[1].fill_between(x_values, x_values, y_values, color = 'blue', alpha=0.1)\n",
    "ax[1].text(0.4,0.2,'S = {:0.2f}'.format(S_pred),fontsize = 28)\n",
    "ax[2].plot(x_values, y_values_perfect, lw = 2, color = 'green')\n",
    "ax[2].fill_between(x_values, x_values, y_values_perfect, color = 'green', alpha=0.1)\n",
    "ax[2].text(0.4,0.2,'S = {:0.2f}'.format(S_actual),fontsize = 28)\n",
    "\n",
    "ax[0].set(title='ROC-AUC', xlabel='False Positive Rate', \n",
    "              ylabel='True Positive Rate', xlim=(0, 1), ylim=(0, 1))\n",
    "for i in range(1,3):\n",
    "    ax[i].plot([0,1],[0,1],linestyle = '--',lw = 2,color = 'black')\n",
    "    ax[i].set(title='Коэффициент Джини', xlabel='Кумулятивная доля объектов', \n",
    "              ylabel='Кумулятивная доля истинных классов', xlim=(0, 1), ylim=(0, 1))\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Прекрасно видно, что из графического представления метрик связь уловить невозможно, поэтому докажем равенство алгебраически. У меня получилось сделать это двумя способами - параметрически (интегралами) и непараметрически (через статистику Вилкоксона-Манна-Уитни). Второй способ значительно проще и без многоэтажных дробей с двойными интегралами, поэтому детально остановимся именно на нем. Для дальнейшего рассмотрения доказательств определимся с терминологией: кумулятивная доля истинных классов - это не что иное, как True Positive Rate. Кумулятивная доля объектов - это в свою очередь количество объектов в отранжированном ряду (при масштабировании на интервал (0, 1) - соответственно доля объектов).\n",
    "\n",
    "Для понимания доказательства необходимо базовое понимание метрики ROC-AUC - что это вообще такое, как строится график и в каких осях. Рекомендую статью из блога Александра Дьяконова <a href=\"https://alexanderdyakonov.wordpress.com/2017/07/28/auc-roc-%D0%BF%D0%BB%D0%BE%D1%89%D0%B0%D0%B4%D1%8C-%D0%BF%D0%BE%D0%B4-%D0%BA%D1%80%D0%B8%D0%B2%D0%BE%D0%B9-%D0%BE%D1%88%D0%B8%D0%B1%D0%BE%D0%BA/\">\"AUC ROC (площадь под кривой ошибок)\"</a>\n",
    "\n",
    "Введём следующие обозначения:\n",
    "\n",
    "- $n$ - Количество объектов в выборке\n",
    "- $n_0$ - Количество объектов класса \"0\"\n",
    "- $n_1$ - Количество объектов класса \"1\"\n",
    "- $TP$ - True Positive (верный ответ модели на истинном классе \"1\" при заданном пороге)\n",
    "- $FP$ - False Positive (неверный ответ модели на истинном классе \"0\" при заданном пороге)\n",
    "- $TPR$ - True Positive Rate (отношение $TP$ к $n_1$) \n",
    "- $FPR$ - False Positive Rate (отношение $FP$ к $n_0$)\n",
    "- $i,j$ - текущий индекс элемента.\n",
    "\n",
    "#### Параметрический метод\n",
    "\n",
    "Параметрическое уравнение для ROC curve можно записать в следующем виде:\n",
    "\n",
    "$$AUC = \\int_{0}^{1} TPR \\enspace dFPR = \\int_{0}^{1} \\frac{TP}{n_1} \\enspace d\\frac{FP}{n_0} = \\frac{1}{n_1*n_0}\\int_{0}^{1}TP  \\enspace dFP \\hspace{35pt} (3)$$     \n",
    "\n",
    "При построении графика Lift Curve по оси $X$ мы откладывали долю объектов (их количество) предварительно отсортированных по убыванию. Таким образом, параметрическое уравнение для Коэффициента Джини будет выглядеть следующим образом:\n",
    "\n",
    "$$AUC = \\int_{0}^{1} TPR \\enspace d\\frac{TP + FP}{P+N} - 0.5 \\hspace{35pt} (4)$$ \n",
    "\n",
    "Подставив выражение (4) в выражение (1) для обеих моделей и преобразовав его, мы увидим, что в одну из частей можно будет подставить выражение (3), что в итоге даст нам красивую формулу нормализованного Джини (2) \n",
    "\n",
    "#### Непараметрический метод\n",
    "\n",
    "При доказательстве я опирался на элементарные постулаты Теории Вероятностей. Известно, что численно значение AUC ROC равно статистике Вилкоксона-Манна-Уитни:\n",
    "\n",
    "$$\\large\n",
    "AUCROC = \\frac{\\sum_{i=1}^{n_1} \\sum_{i=1}^{n_0} S(x_i, x_j)}{n_1*n_0} \\hspace{35pt} (5)$$\n",
    "\n",
    "$$S(x_i, x_j) = \\begin{cases}\n",
    "  1, \\enspace x_i > x_j\\\\    \n",
    "  \\frac{1}{2}, \\enspace x_i = x_j \\\\  \n",
    "  0,\\enspace x_i < x_j \n",
    "\\end{cases}$$\n",
    "\n",
    "где $x_i$ - ответ алгоритма на i-ом объекте из распределения \"1\", $x_о$ - ответ алгоритма на j-ом объекте из распределения \"0\"\n",
    "\n",
    "Доказательство этой формулы можно, например, найти <a href=\"https://stats.stackexchange.com/questions/272314/how-does-auc-of-roc-equal-concordance-probability\">здесь</a>\n",
    "\n",
    "Интерпретируется это очень интуитивно понятно: если случайным образом извлечь пару объектов, где первый объект будет из распределения \"1\", а второй из распределения \"0\", то вероятность того, что первый объект будет иметь предсказанное значение больше или равно, чем предсказанное значение второго объекта, равно значению AUC ROC. Комбинаторно несложно подсчитать, что количество пар таких объектов будет: $n_1*n_0$. \n",
    "\n",
    "Пусть модель прогнозирует $k$ возможных значений из множества $ S =\\{s_1, \\dots, s_k\\}$, где   $s_1< \\enspace...\\enspace < s_k$ и $S$ - какое-то вероятностное распределение, элементы которого принимают значения на интервале $[0,1]$.\n",
    "Пусть $S_{n_1}$ множество значений, которые принимают объекты $n_1$ и $S_{n_1} \\subseteq S$. Пусть $S_{n_0}$ множество значений, которые принимают объекты $n_0$ и $S_{n_0} \\subseteq S$. Очевидно, что множества $S_{n_1}$ и $S_{n_0}$ могут пересекаться.\n",
    "\n",
    "Обозначим $p_{n_{0}}^{i}$ как вероятность того, что объект $n_0$ примет значение $s_i$, и $p_{n_{1}}^{i}$ как вероятность того, что объект $n_1$ примет значение $s_i$. Тогда $\\sum_{i=1}^{k}p_{n_{0}}^{i}=1$ и $\\sum_{i=1}^{k}p_{n_{1}}^{i}=1$\n",
    "\n",
    "Имея априорную вероятность $\\pi$ для каждого объекта выборки, можем записать формулу, определяющую вероятность того, что объект примет значение $s_i$: $$p_{n}^{i} = \\pi p_{n_{0}}^{i} + (1-\\pi)p_{n_{1}}^{i}$$ \n",
    "Зададим три функции распределения:\n",
    "- для объектов класса \"1\"\n",
    "- для объектов класса \"0\"\n",
    "- для всех объектов выборки\n",
    "$$CDF_{n_{1}}^{i} = \\sum_{j=1}^{i} p_{n_{1}}^{i} \\hspace{10pt}i =1, \\dots, k$$\n",
    "$$CDF_{n_{0}}^{i} = \\sum_{j=1}^{i} p_{n_{0}}^{i} \\hspace{10pt}i =1, \\dots, k$$\n",
    "$$CDF_{n}^{i} = \\sum_{j=1}^{i} p_{n}^{i} \\hspace{10pt}i =1, \\dots, k$$\n",
    "\n",
    "Пример того, как могут выглядеть функции распределения для двух классов в задаче кредитного скоринга:\n",
    "\n",
    "<center>\n",
    "<img src=\"../../img/KS.png\">\n",
    "\n",
    "На рисунке также показана статистика Колмогорова-Смирнова, которая также применяется для оценки моделей. \n",
    "\n",
    "Запишем формулу Вилкоксона в вероятностном виде и преобразуем её:\n",
    "\n",
    "$$AUCROC = P(S_{n_1}>S_{n_1}) + \\frac{1}{2}P (S_{n_1}=S_{n_1})= \\\\\n",
    "\\sum_{i=1}^{k} P(S_{n_1} \\geq s_{i-1}) P(S_{n_0} = s_{i}) + \\frac{1}{2}\\sum_{i=1}^{k} P(S_{n_1} = s_{i}) P(S_{n_0} = s_{i}) = \\\\\n",
    "\\sum_{i=1}^{k} \\big((P(S_{n_1} \\geq s_{i-1}) + \\frac{1}{2}P(S_{n_1} = s_{i})\\big) P(S_{n_0} = s_{i}) = \\\\\n",
    "\\sum_{i=1}^{k} \\frac{1}{2} \\big((P(S_{n_1} \\geq s_{i}) + (P(S_{n_1} \\geq s_{i-1})\\big) P(S_{n_0} = s_{i}) = \\\\\n",
    "\\sum_{i=1}^{k} \\frac{1}{2} (CDF_{n_{1}}^{i} + CDF_{n_{1}}^{i-1})(CDF_{n_{0}}^{i} - CDF_{n_{0}}^{i-1}) \\hspace{35pt} (6)$$\n",
    "\n",
    "Аналогичную формулу можем выписать для площади под Lift Curve (помним, что она состоит из суммы двух площадей, одна из которых всегда равна 0.5):\n",
    "\n",
    "$$AUC Lift = Gini_{model} + 0.5 = \\sum_{i=1}^{k} \\frac{1}{2} (CDF_{n_{1}}^{i} + CDF_{n_{1}}^{i-1})(CDF_{n}^{i} - CDF_{n}^{i-1}) \\hspace{35pt} (7)$$\n",
    "\n",
    "И теперь преобразуем её:\n",
    "\n",
    "$$AUC Lift = Gini + 0.5 = \\sum_{i=1}^{k} \\frac{1}{2} (CDF_{n_{1}}^{i} + CDF_{n_{1}}^{i-1})(CDF_{n}^{i} - CDF_{n}^{i-1}) = \\\\\n",
    "\\sum_{i=1}^{k} \\frac{1}{2} (CDF_{n_{1}}^{i} + CDF_{n_{1}}^{i-1}) \\big(\\pi(CDF_{n_{1}}^{i} - CDF_{n_{1}}^{i-1}) + (1-\\pi)(CDF_{n_{0}}^{i} - CDF_{n_{0}}^{i-1})\\big) = \\\\\n",
    "(1-\\pi)\\sum_{i=1}^{k} \\frac{1}{2}(CDF_{n_{1}}^{i} + CDF_{n_{1}}^{i-1})(CDF_{n_{0}}^{i} - CDF_{n_{0}}^{i-1}) + \n",
    "\\pi\\sum_{i=1}^{k} \\frac{1}{2}(CDF_{n_{1}}^{i} + CDF_{n_{1}}^{i-1})(CDF_{n_{1}}^{i} - CDF_{n_{1}}^{i-1}) = \\\\\n",
    "(1-\\pi) AUCROC + \\frac{1}{2} \\pi \\sum_{i=1}^{k} \\big( (CDF_{n_{1}}^{i})_{}^{2} - (CDF_{n_{0}}^{i-1})_{}^{2} \\big) = \\\\\n",
    "(1-\\pi) AUCROC + \\frac{1}{2} \\pi \\hspace{35pt} (8)$$\n",
    "\n",
    "Для идеальной модели формула запишется просто:\n",
    "\n",
    "$$Gini_{perfect}= \\frac{1}{2}(1-\\pi)\\hspace{35pt} (9)$$ \n",
    "\n",
    "Следовательно из (8) и (9), получим:\n",
    "\n",
    "$$\\large \n",
    "Gini_{normalized} = \\frac{Gini_{model}}{Gini_{perfect}} = \\frac{(1-\\pi) AUCROC + \\frac{1}{2}}{\\frac{1}{2}(1-\\pi)} = 2AUCROC - 1$$\n",
    "\n",
    "Как говорили в школе, что и требовалось доказать."
   ]
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    "### 3. Практическое применение.\n",
    "\n",
    "Как упоминалось в начале статьи, коэффициент Джини применяется для оценки моделей во многих сферах, в том числе в задачах банковского кредитования, страхования и целевом маркетинге. И этому есть вполне разумное объяснение. Эта статья не ставит перед собой целью подробно остановиться на практическом применении статистики в той или иной области. На эту тему написаны многие книги, мы лишь кратко пробежимся по этой теме.\n",
    "\n",
    "#### Кредитный скоринг\n",
    "\n",
    "По всему миру банки ежедневно получают тысячи заявок на выдачу кредита. Разумеется, необходимо как-то оценивать риски того, что клиент может просто-напросто не вернуть кредит, поэтому разрабатываются предиктивные модели, оценивающие по признаковому пространству вероятность того, что клиент не выплатит кредит, и эти модели в первую очередь надо как-то оценивать и, если модель удачная, то выбирать оптимальный порог (threshold) вероятности. Выбор оптимального порога определяется политикой банка. Задача анализа при подборе порога - минимизировать риск упущенной выгоды, связанной с отказом в выдаче кредита. Но чтобы выбирать порог, надо иметь качественную модель. Основные метрики качества в банковской сфере:\n",
    "- Коэффициент Джини\n",
    "- Статистика Колмогорова-Смирнова (вычисляется как максимальная разница между кумулятивными функциями распределения «плохих» и «хороших» заемщиков. Выше в статье приводился рисунок с распределениями и этой статистикой)\n",
    "- Коэффициент дивергенции (представляет собой оценку разницы математических ожиданий распределений скоринговых баллов для «плохих» и «хороших» заемщиков, нормализованную дисперсиями этих распределений. Чем больше значение коэффициента дивергенции, тем лучше качество модели.) \n",
    "\n",
    "Не знаю как обстоят дела в России, хоть и живу здесь, но в Европе наиболее широко применяется коэффициент Джини, в Северной Америке - статистика Колмогорова-Смирнова.\n",
    "\n",
    "#### Страхование\n",
    "В этой области всё аналогично банковской сфере, с той лишь разницей, что нам необходимо разделить клиентов на тех, кто подаст страховое требование и на тех, кто этого не сделает. Рассмотрим практический пример из этой области, в котором будет хорошо видна одна особенность Lift Curve - при сильно несбалансированных классах в целевой переменной кривая почти идеально совпадает с ROC-кривой.\n",
    "\n",
    "Несколько месяцев назад на Kaggle проходило соревнование \"Porto Seguro’s Safe Driver Prediction\", в котором задачей было как раз прогнозирование \"Insurance Claim\" - подача страхового требования. И в котором я по собственной глупости упустил серебро, выбрав не тот сабмит. \n",
    "\n",
    "<center>\n",
    "<img src=\"../../img/porto.png\">\n",
    "\n",
    "Это было очень странное и в то же время невероятно познавательное соревнование. И с рекордным количеством участников - 5169. Победитель соревнования <a href=\"https://www.kaggle.com/c/porto-seguro-safe-driver-prediction/discussion/44629\">Michael Jahrer</a> написал код только на C++/CUDA, и это вызывает восхищение и уважение. \n",
    "\n",
    "Porto Seguro - бразильская компания, специализирующаяся в области автострахования.\n",
    "Датасет состоял из 595207 строк в трейне, 892816 строк в тесте и 53 анонимизированных признаков. Соотношение классов в таргете - 3% и 97%. Напишем простенький бейзлайн, благо это делается в пару строк, и построим графики. Обратите внимание, кривые почти идеально совпадают, разница в площадях под Lift Curve и ROC Curve - 0.005. "
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ECmf79u1cfenV/LnmT04/+3TGvDSGpMTIpwpUOSEipdOiRb5aIm9iomNHX0+s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\ntcvXJsH08ThI+u2L7ElOjl8W9OKLc8e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VQkKaExkZQfv2Xfnkk3HIzDVhEpvm4sSZE9I5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\niIiIp/4fX24jekuy7IMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2692ef3d9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "import xgboost as xgb\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.integrate import quad\n",
    "\n",
    "df = pd.read_csv('train.csv', index_col='id')\n",
    "unwanted = df.columns[df.columns.str.startswith('ps_calc_')]\n",
    "df.drop(unwanted,inplace=True,axis=1)\n",
    "df.fillna(-999, inplace=True)\n",
    "\n",
    "train, test = train_test_split(df, stratify=df.target, test_size=0.25, random_state=1)\n",
    "estimator = xgb.XGBClassifier(seed=1, n_jobs=-1)\n",
    "estimator.fit(train.drop('target', axis=1), train.target)\n",
    "pred = estimator.predict_proba(test.drop('target', axis=1))[:, 1]\n",
    "test['predict'] = pred\n",
    "\n",
    "actual = test.target.values\n",
    "predict = test.predict.values\n",
    "\n",
    "data = zip(actual, predict)\n",
    "sorted_data = sorted(data, key=lambda d: d[1], reverse=True)\n",
    "sorted_actual = [d[0] for d in sorted_data]\n",
    "\n",
    "cumulative_actual = np.cumsum(sorted_actual) / sum(actual)\n",
    "cumulative_index = np.arange(1, len(cumulative_actual)+1) / len(predict)\n",
    "cumulative_actual_perfect = np.cumsum(sorted(actual, reverse=True)) / sum(actual)\n",
    "\n",
    "aucroc = roc_auc_score(actual, predict)\n",
    "gini = 2*roc_auc_score(actual, predict)-1\n",
    "fpr, tpr, t = roc_curve(actual, predict)\n",
    "x_values = [0] + list(cumulative_index)\n",
    "y_values = [0] + list(cumulative_actual)\n",
    "y_values_perfect = [0] + list(cumulative_actual_perfect)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1,ncols=3, sharey=True, figsize=(18, 6))\n",
    "fig.suptitle('Gini = {:0.3f}\\n\\n'.format(gini),fontsize = 26, fontweight='bold')\n",
    "\n",
    "ax[0].plot([0]+fpr.tolist(), [0]+tpr.tolist(), lw=2, color = 'red')\n",
    "ax[0].plot([0]+fpr.tolist(), [0]+tpr.tolist(), lw = 2, color = 'red')\n",
    "ax[0].fill_between([0]+fpr.tolist(), [0]+tpr.tolist(), color = 'red', alpha=0.1)\n",
    "ax[0].text(0.4,0.2,'S = {:0.3f}'.format(aucroc),fontsize = 28)\n",
    "ax[1].plot(x_values, y_values, lw = 2, color = 'blue')\n",
    "ax[1].fill_between(x_values, x_values, y_values, color = 'blue', alpha=0.1)\n",
    "ax[1].text(0.4,0.2,'S = {:0.3f}'.format(S_pred),fontsize = 28)\n",
    "ax[2].plot(x_values, y_values_perfect, lw = 2, color = 'green')\n",
    "ax[2].fill_between(x_values, x_values, y_values_perfect, color = 'green', alpha=0.1)\n",
    "ax[2].text(0.4,0.2,'S = {:0.3f}'.format(S_actual),fontsize = 28)\n",
    "\n",
    "ax[0].set(title='ROC-AUC XGBoost Baseline', xlabel='False Positive Rate', \n",
    "              ylabel='True Positive Rate', xlim=(0, 1), ylim=(0, 1))\n",
    "ax[1].set(title='Gini XGBoost Baseline')\n",
    "ax[2].set(title='Gini Perfect')\n",
    "for i in range(1,3):\n",
    "    ax[i].plot([0,1],[0,1],linestyle = '--',lw = 2,color = 'black')\n",
    "    ax[i].set(xlabel='Share of clients', ylabel='True Positive Rate', xlim=(0, 1), ylim=(0, 1))\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Коэффициент Джини победившей модели - 0.29698\n",
    "Для меня до сих пор загадка, чего хотели добиться организаторы, занонимизировав признаки и сделав невероятную предобработку данных. Это одна из причин, почему все модели, в том числе и победившие, по сути получились мусорные. Наверное, просто пиар, раньше никто в мире не знал про Porto Seguro кроме бразильцев, теперь знают многие.\n",
    "\n",
    "#### Целевой маркетинг\n",
    "\n",
    "В этой области можно лучше всего понять истинный смысл коэффициента Джини и Lift Curve. Почти во всех книгах и статьях почему-то приводятся примеры с почтовыми маркетинговыми кампаниями, что на мой взгляд является анахронизмом. Создадим искусственную бизнес-задачу из сферы <a href=\"https://ru.wikipedia.org/wiki/Free-to-play\">free2play игр</a>. У нас есть база данных пользователей когда-то игравших в нашу игру и по каким-то причинам отвалившихся. Мы хотим их вернуть в наш игровой проект, для каждого пользователя у нас есть некое признаковое пространство (время в проекте, сколько он потратил, до какого уровня дошел и т.д.) на основе которого мы строим модель. Оцениваем модель коэффициентом Джини и строим Lift Curve:\n",
    "\n",
    "<center>\n",
    "<img src=\"../../img/CAP_per.png\">\n",
    "\n",
    "Предположим, что в рамках маркетинговой кампании мы тем или иным способом устанавливаем контакт с пользователем (email, соцсети), цена контакта с одним пользователем - 2 рубля. Мы знаем, что <a href=\"https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D0%B6%D0%B8%D0%B7%D0%BD%D0%B5%D0%BD%D0%BD%D0%B0%D1%8F_%D1%86%D0%B5%D0%BD%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D0%BA%D0%BB%D0%B8%D0%B5%D0%BD%D1%82%D0%B0\">Lifetime Value</a> составляет 5 рублей. Необходимо оптимизировать эффективность маркетинговой кампании. Предположим, что всего в выборке 100 пользователей, из которых 30 вернется. Таким образом, если мы установим контакт со 100% пользователей, то потратим на маркетинговую кампанию 200 рублей и получим доход 150 рублей. Это провал кампании. Рассмотрим график Lift Curve. Видно, что при контакте с 50% пользователей, мы контактируем с 90% пользователей, которые вернутся. затраты на кампанию - 100 рублей, доход 135. Мы в плюсе. Таким образом, Lift Curve позволяет нам наилучшим образом оптимизировать нашу маркетинговую компанию. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Сортировка пузырьком.\n",
    "\n",
    "Коэффициент Джини имеет довольно забавную, но весьма полезную интерпретацию, с помощью которой мы его также можем легко подсчитать. Оказывается, численно он равен: \n",
    "\n",
    "$$Gini_{normalized} = \\frac{Swaps_{random} - Swaps_{sorted}}{Swaps_{random}}$$\n",
    "\n",
    "где, $Swaps_{sorted}$ число перестановок, которые необходимо сделать в отранжированном списке для того, чтобы получить истинный список целевой переменной, $Swaps_{random}$ - число перестановок для предсказаний случайного алгоритма. Напишем элементарную сортировку пузырьком и покажем это:\n",
    "\n",
    "$$[1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]$$\n",
    "$$[1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Число перестановок:  10\n"
     ]
    }
   ],
   "source": [
    "actual = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
    "predict = [0.9, 0.3, 0.8, 0.75, 0.65, 0.6, 0.78, 0.7, 0.05, 0.4, 0.4, 0.05, 0.5, 0.1, 0.1]\n",
    "\n",
    "data = zip(actual, predict)\n",
    "sorted_data = sorted(data, key=lambda d: d[1], reverse=False)\n",
    "sorted_actual = [d[0] for d in sorted_data]\n",
    "swaps=0\n",
    "n = len(sorted_actual)\n",
    "array = sorted_actual\n",
    "\n",
    "for i in range(1,n):\n",
    "    flag = 0\n",
    "    for j in range(n-i):\n",
    "        if array[j]>array[j+1]: \n",
    "            array[j], array[j+1] = array[j+1], array[j]\n",
    "            flag = 1\n",
    "            swaps+=1\n",
    "    if flag == 0: break\n",
    "        \n",
    "print(\"Число перестановок: \", swaps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Комбинаторно несложно подсчитать число перестановок для случайного алгоритма:\n",
    "\n",
    "$$Swaps_{random} = \\frac{6*9}{2} = 27$$\n",
    "\n",
    "Таким образом:\n",
    "\n",
    "$$Gini_{normalized} = \\frac{27 - 10}{27} = 0.63$$\n",
    "\n",
    "Видим, что мы получили значение коэффициента, как и в рассматриваемом выше игрушечном примере."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Литература:\n",
    "1. <a href=\"https://books.google.ru/books?id=tTs2DgAAQBAJ&printsec=frontcover&dq=jiri+credit+risk&hl=ru&sa=X&ved=0ahUKEwjG38i599LZAhUJWSwKHXQxCwMQ6AEIJzAA#v=onepage&q=jiri%20credit%20risk&f=false\">Jiri Witzany \"Credit Risk Managment\"</a>\n",
    "2. <a href=\"https://link.springer.com/content/pdf/10.1023%2FA%3A1010920819831.pdf\">A Simple Generalisation of the Area Under the ROCCurve</a>\n",
    "3. <a href=\"https://www.kaggle.com/c/porto-seguro-safe-driver-prediction\">Porto Seguro’s Safe Driver Prediction</a>\n",
    "4. <a href=\"http://pubs.rsna.org/doi/pdf/10.1148/radiology.143.1.7063747\">The Meaning and Use of the Area under a Receiver Operating Characteristic(ROC)Curve</a>\n",
    "5. <a href=\"https://www.business-school.ed.ac.uk/crc/wp-content/uploads/sites/55/2017/03/Paper-65-Paper.pdf\">Measuring the Quality of Credit Scoring Models</a>\n",
    "6. <a href=\"https://www.youtube.com/watch?v=reiZ61V2OlI\">Assessing your model using the cap curve</a>"
   ]
  }
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