{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><img src=\"img/logo_hse_black.jpg\"></center>\n",
    "\n",
    "<h1><center>Методы машинного обучения</center></h1>\n",
    "<h2><center>Семинар: линейные модели</center></h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.style.use('ggplot')\n",
    "plt.rcParams['figure.figsize'] = (12,8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Линейная регрессия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Пример: Стоимость автомобиля"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Загрузите тренировочные данные и тестовые данные - уже знакомые нам данные по автомобилям."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train = pd.read_csv('./data/accord_sedan_training.csv')\n",
    "df_test = pd.read_csv('./data/accord_sedan_testing.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>mileage</th>\n",
       "      <th>year</th>\n",
       "      <th>trim</th>\n",
       "      <th>engine</th>\n",
       "      <th>transmission</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14995</td>\n",
       "      <td>67697</td>\n",
       "      <td>2006</td>\n",
       "      <td>ex</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Manual</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11988</td>\n",
       "      <td>73738</td>\n",
       "      <td>2006</td>\n",
       "      <td>ex</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Manual</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11999</td>\n",
       "      <td>80313</td>\n",
       "      <td>2006</td>\n",
       "      <td>lx</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Automatic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12995</td>\n",
       "      <td>86096</td>\n",
       "      <td>2006</td>\n",
       "      <td>lx</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Automatic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11333</td>\n",
       "      <td>79607</td>\n",
       "      <td>2006</td>\n",
       "      <td>lx</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Automatic</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   price  mileage  year trim engine transmission\n",
       "0  14995    67697  2006   ex  4 Cyl       Manual\n",
       "1  11988    73738  2006   ex  4 Cyl       Manual\n",
       "2  11999    80313  2006   lx  4 Cyl    Automatic\n",
       "3  12995    86096  2006   lx  4 Cyl    Automatic\n",
       "4  11333    79607  2006   lx  4 Cyl    Automatic"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11d4ae128>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_train.plot(x='mileage', y='price', kind='scatter', s=120)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Кажется, что между стоимостью и пробегом зависимость линейная - давайте ее найдем!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = df_train.mileage.values.reshape(-1, 1)\n",
    "y_train = df_train.price.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обучим модель"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Модель:\n",
      "price = 16762.02 + (-0.05)*mileage\n"
     ]
    }
   ],
   "source": [
    "print('Модель:\\nprice = %.2f + (%.2f)*mileage' % (model.intercept_, model.coef_[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нарисуйте предсказание модели (прямую) вместе с данными на плоскости. Здесь можно либо явно взять уравнение прямой и посчитать значения в каждой точке, либо через predict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a2047a208>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_train.plot(x='mileage', y='price', kind='scatter', s=120)\n",
    "y_hat = model.predict(X_train)\n",
    "\n",
    "plt.plot(X_train, y_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Меры качества"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "**1. (R)MSE ((Root) Mean Squared Error)**\n",
    "\n",
    "$$ L(\\hat{y}, y) = \\frac{1}{N}\\sum\\limits_n^N (y_n - \\hat{y}_n)^2$$\n",
    "\n",
    "**2. MAE (Mean Absolute Error)**\n",
    "\n",
    "$$ L(\\hat{y}, y) = \\frac{1}{N}\\sum\\limits_n^N |y_n - \\hat{y}_n|$$\n",
    "\n",
    "* Чем плохи такие метрики?\n",
    "* Отличия - http://yahwes.github.io/2016/03/22/mae-rmse/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**3. RSE (Relative Squared Error)**\n",
    "\n",
    "$$ L(\\hat{y}, y) = \\sqrt\\frac{\\sum\\limits_n^N (y_n - \\hat{y}_n)^2}{\\sum\\limits_n^N (y_n - \\bar{y})^2}$$\n",
    "\n",
    "**4. RAE (Relative Absolute Error)**\n",
    "\n",
    "$$ L(\\hat{y}, y) = \\frac{\\sum\\limits_n^N |y_n - \\hat{y}_n|}{\\sum\\limits_n^N |y_n - \\bar{y}|}$$\n",
    "\n",
    "**5. MAPE (Mean Absolute Persentage Error)**\n",
    "\n",
    "$$ L(\\hat{y}, y) = \\frac{100}{N} \\sum\\limits_n^N\\left|\\frac{ y_n - \\hat{y}_n}{y_n}\\right|$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**6. RMSLE (Root Mean Squared Logarithmic Error)**\n",
    "\n",
    "$$ L(\\hat{y}, y) = \\sqrt{\\frac{1}{N}\\sum\\limits_n^N(\\log(y_n + 1) - \\log(\\hat{y}_n + 1))^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 10)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = 100\n",
    "y_hat = np.linspace(0, 300, 151)\n",
    "# log error\n",
    "error1 = np.sqrt((np.log(y+1) - np.log(y_hat + 1))**2)\n",
    "\n",
    "# squared error\n",
    "error2 = (y - y_hat)**2 /1000.\n",
    "\n",
    "plt.plot(y_hat, error1, label='RMSLE')\n",
    "plt.plot(y_hat, error2, label='MSE')\n",
    "plt.xlabel('$\\hat{y}$')\n",
    "plt.ylabel('Error')\n",
    "plt.title('true value y = %.1f' % y)\n",
    "plt.legend()\n",
    "plt.ylim(0, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_absolute_error\n",
    "from sklearn.metrics import median_absolute_error\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat = model.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя абсолютная ошибка 1182.21\n",
      "Средняя квадратичная ошибка 2412292.55\n"
     ]
    }
   ],
   "source": [
    "print('Средняя абсолютная ошибка %.2f' % mean_absolute_error(y_train, y_hat))\n",
    "print('Средняя квадратичная ошибка %.2f' % mean_squared_error(y_train, y_hat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Можно рассмотреть более сложную меру: коэффициент детерминации $R^2$:\n",
    "\n",
    "* $TSS = \\sum_i (y^{(i)}-\\bar{y})^2$ - общая сумма квадратов (total sum of squares)\n",
    "* $RSS = \\sum_i (\\hat{y}^{(i)}-y^{(i)})^2$ - сумма квадратов остатков (residual sum of squares)\n",
    "* $ESS = \\sum_i (\\hat{y}^{(i)}-\\bar{y})^2$ - объясненная сумма квадратов (explained sum of squares)\n",
    "\n",
    "Для простоты будем считать, что\n",
    "$$TSS = ESS + RSS$$\n",
    "\n",
    "Тогда Коэффициент детерминации $R^2=1-\\frac{RSS}{TSS}$\n",
    "\n",
    "Рассчитайте его для нашей модели\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.43096955626446276"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_train, y_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Оценка значимости коэффициентов с помощью бутстрепа"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Интро в бутстреп\n",
    "\n",
    "Иногда для анализа данных полезно знать не только среднее значение какого-нибудь признака, но и его [доверительный интервал](http://www.machinelearning.ru/wiki/index.php?title=%D0%94%D0%BE%D0%B2%D0%B5%D1%80%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D0%B8%D0%BD%D1%82%D0%B5%D1%80%D0%B2%D0%B0%D0%BB). \n",
    "\n",
    "Из курса статистики известно, что если выборка $x$ подчиняются нормальному закону распределения и нам известно стандартное отклонение $\\sigma$ на *генеральной совокупности*, то доверительный интервал c доверительной вероятностью $(1-\\alpha)$ для среднего можно вычислить по следующей формуле:\n",
    "\n",
    "$$\\left( \\bar{x} - z_{1 - \\alpha/2}\\frac{\\sigma}{\\sqrt{n}}, \\bar{x} + z_{1 - \\alpha/2}\\frac{\\sigma}{\\sqrt{n}} \\right),$$\n",
    "\n",
    "где $\\bar{x}$ - выборочное среднее , $n$ - это размер выборки, а $z_{\\gamma}$ - это квантиль нормального распределения уровня $\\gamma$.\n",
    "\n",
    "Выберем какой-то признак и посчитаем доверительный интервал"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df_train.price.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2.,  8.,  4., 29., 19., 32., 54., 20., 64., 39., 52., 45.,  6.,\n",
       "        19.,  2., 11.,  7.,  1.,  1.,  2.]),\n",
       " array([ 6900.  ,  7504.75,  8109.5 ,  8714.25,  9319.  ,  9923.75,\n",
       "        10528.5 , 11133.25, 11738.  , 12342.75, 12947.5 , 13552.25,\n",
       "        14157.  , 14761.75, 15366.5 , 15971.25, 16576.  , 17180.75,\n",
       "        17785.5 , 18390.25, 18995.  ]),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsMAAAHVCAYAAAAU6/ZZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAHeVJREFUeJzt3W9sXfVh//GPY6elIcTYuSHIMAYhoIksNF0TkdJBKPU2ad1Y1AdMa4OgqEwllIpkrcj6IFQrEd7a1BFrMhitaEUfVH1APMY2VllpjDqEZJKGhbCl0LKKDZq/JolJwMQ+vwf8sErj1CaxfQ3f1+tR7vG9Pt97v/fc+87JyTkNVVVVAQCAAk2r9wAAAKBexDAAAMUSwwAAFEsMAwBQLDEMAECxxDAAAMUSwwAAFEsMAwBQLDEMAECxxDAAAMVqmuwVvvTSS5O9yve8Wq2W/fv313sY/H/mY+oxJ1OPOZlazMfUY05OT1tb25jva88wAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUKymeg8A4J0YvOW6d/yYPeOw3sYHHhmH3wLAVGPPMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxWoay51effXV3HfffXnxxRfT0NCQW2+9NW1tbens7My+ffsyZ86crFq1KjNnzpzo8QIAwLgZUww/+OCDWbRoUf7qr/4qx48fz+uvv57Nmzdn4cKFWb58ebq6utLV1ZUVK1ZM9HgBAGDcjHqYxNGjR/Nf//Vfufbaa5MkTU1NOfPMM9Pb25tly5YlSZYtW5be3t6JHSkAAIyzUfcM7927N7NmzcqmTZvyi1/8IvPmzctNN92UQ4cOpaWlJUnS0tKSw4cPT/hgAQBgPI0aw4ODg3nhhRdy880355JLLsmDDz6Yrq6uMa+gu7s73d3dSZKOjo7UarVTHy0jampq8rpOIeZjYu2p03rN6fiynUwt5mPqMSeTZ9QYnj17dmbPnp1LLrkkSbJ06dJ0dXWlubk5fX19aWlpSV9fX2bNmjXi49vb29Pe3j58e//+/eM0dN5Sq9W8rlOI+XhvMqfjy3YytZiPqcecnJ62trYx33fUY4bPPvvszJ49Oy+99FKSZOfOnTn//POzePHi9PT0JEl6enqyZMmSUxwuAADUx5jOJnHzzTfn3nvvzfHjx3POOedk5cqVqaoqnZ2d2bJlS2q1WlavXj3RYwUAgHE1phi+8MIL09HRccLytWvXjvuAAABgsrgCHQAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxWqq9wCAUzd4y3V1WW/jA4/UZb0AMN7sGQYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBAChWU70HAMBvNnjLdXVZb+MDj9RlvQCTyZ5hAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKNaYr0N12220544wzMm3atDQ2NqajoyP9/f3p7OzMvn37MmfOnKxatSozZ86c6PECAMC4GfPlmO+6667MmjVr+HZXV1cWLlyY5cuXp6urK11dXVmxYsWEDBIAACbCKR8m0dvbm2XLliVJli1blt7e3nEbFAAATIYx7xlet25dkuQP/uAP0t7enkOHDqWlpSVJ0tLSksOHD4/4uO7u7nR3dydJOjo6UqvVTnfM/Jqmpiav6xQymfOxZ1LWcqJ6vt8858kzkc/Z59bUYj6mHnMyecYUw1/96lfT2tqaQ4cO5e67705bW9uYV9De3p729vbh2/v373/no+Q3qtVqXtcppIT5eK8/v5F4zuOrhO3k3cR8TD3m5PS8k1Yd02ESra2tSZLm5uYsWbIkzz//fJqbm9PX15ck6evre9vxxAAA8G4wagy/9tprOXbs2PCf//M//zMXXHBBFi9enJ6eniRJT09PlixZMrEjBQCAcTbqYRKHDh3K17/+9STJ4OBgfv/3fz+LFi3KxRdfnM7OzmzZsiW1Wi2rV6+e8MECAMB4GjWG586dm6997WsnLD/rrLOydu3aCRkUAABMBlegAwCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIrVVO8BADA1Dd5y3YT97j2/4WeNDzwyYesF+HX2DAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABSraax3HBoaypo1a9La2po1a9Zk79692bBhQ/r7+3PRRRfl9ttvT1PTmH8dAADU3Zj3DP/rv/5rzjvvvOHb3/ve9/KJT3wi9957b84888xs2bJlQgYIAAATZUwxfODAgWzfvj0f//jHkyRVVWXXrl1ZunRpkuSaa65Jb2/vxI0SAAAmwJiOa/jOd76TFStW5NixY0mSI0eOZMaMGWlsbEyStLa25uDBgyM+tru7O93d3UmSjo6O1Gq18Rg3v6KpqcnrOoVM5nzsmZS1nKie7zfP+b3P59nk8z0y9ZiTyTNqDG/bti3Nzc2ZN29edu3a9Y5X0N7envb29uHb+/fvf8e/g9+sVqt5XaeQEubjvf78RlLic64Xr/XkK+Fz693GnJyetra2Md931BjevXt3nnrqqfzkJz/JwMBAjh07lu985zs5evRoBgcH09jYmIMHD6a1tfW0Bg0AAJNt1Bj+1Kc+lU996lNJkl27duWf//mf84UvfCHf+MY38uSTT+ajH/1otm7dmsWLF0/4YAEAYDyd8nmGP/3pT+fRRx/N7bffnv7+/lx77bXjOS4AAJhw7+jEwAsWLMiCBQuSJHPnzs0999wzIYMCAIDJ4CoZAGMweMt19R4CABPA5ZgBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBAChWU70HAO92g7dc97bbe+o0DgDgnbNnGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFijXnRjYGAgd911V44fP57BwcEsXbo0119/ffbu3ZsNGzakv78/F110UW6//fY0NbmGBwAA7x6j1uv06dNz11135Ywzzsjx48ezdu3aLFq0KI8++mg+8YlP5KMf/Wj+8R//MVu2bMkf/uEfTsaYAQBgXIx6mERDQ0POOOOMJMng4GAGBwfT0NCQXbt2ZenSpUmSa665Jr29vRM7UgAAGGdjOq5haGgod955Z375y1/mj/7ojzJ37tzMmDEjjY2NSZLW1tYcPHhwQgcKAADjbUwxPG3atHzta1/Lq6++mq9//ev5v//7vzGvoLu7O93d3UmSjo6O1Gq1UxspJ9XU1OR1raM99R5AHdTz/Vbi610an2eTz/fI1GNOJs87+h9vZ555Zi677LI899xzOXr0aAYHB9PY2JiDBw+mtbV1xMe0t7envb19+Pb+/ftPb8ScoFareV2ZVN5vTCTvr8nne2TqMSenp62tbcz3HfWY4cOHD+fVV19N8uaZJXbu3JnzzjsvCxYsyJNPPpkk2bp1axYvXnyKwwUAgPoYdc9wX19fNm7cmKGhoVRVlY985CP58Ic/nPPPPz8bNmzI97///Vx00UW59tprJ2O8AAAwbkaN4d/+7d/O3/3d352wfO7cubnnnnsmZFAAADAZXIEOAIBiuWQc427wluvqst7GBx6py3oBgHcve4YBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhiGACAYolhAACKJYYBACiWGAYAoFhNo91h//792bhxY1555ZU0NDSkvb09f/zHf5z+/v50dnZm3759mTNnTlatWpWZM2dOxpgBAGBcjBrDjY2NueGGGzJv3rwcO3Ysa9asyeWXX56tW7dm4cKFWb58ebq6utLV1ZUVK1ZMxpgBAGBcjHqYREtLS+bNm5ck+cAHPpDzzjsvBw8eTG9vb5YtW5YkWbZsWXp7eyd2pAAAMM5G3TP8q/bu3ZsXXngh8+fPz6FDh9LS0pLkzWA+fPjwiI/p7u5Od3d3kqSjoyO1Wu00h8yva2pqmlKv6546rbder0G9nm89Dd5yXb2HwHvYVPo8K8VU+x7BnEymMcfwa6+9lvXr1+emm27KjBkzxryC9vb2tLe3D9/ev3//Oxsho6rVal7XeG/Be4VtefL5Hpl6zMnpaWtrG/N9x3Q2iePHj2f9+vW56qqrcsUVVyRJmpub09fXlyTp6+vLrFmzTmGoAABQP6PGcFVVue+++3LeeeflT/7kT4aXL168OD09PUmSnp6eLFmyZOJGCQAAE2DUwyR2796dxx9/PBdccEG+9KUvJUn+4i/+IsuXL09nZ2e2bNmSWq2W1atXT/hgAQBgPI0aw7/zO7+TH/zgByP+bO3ateM+IAAAmCyuQAcAQLHe0anVYCpzui/gdNXrc6TxgUfqsl7AnmEAAAomhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWGIYAIBiiWEAAIolhgEAKJYYBgCgWE31HgAAUD+Dt1yXPXVYb+MDj9RhrXAie4YBACiWGAYAoFijHiaxadOmbN++Pc3NzVm/fn2SpL+/P52dndm3b1/mzJmTVatWZebMmRM+WAAAGE+j7hm+5ppr8uUvf/lty7q6urJw4cLce++9WbhwYbq6uiZsgAAAMFFGjeHLLrvshL2+vb29WbZsWZJk2bJl6e3tnZjRAQDABDqls0kcOnQoLS0tSZKWlpYcPnz4pPft7u5Od3d3kqSjoyO1Wu1UVslv0NTUNKVe13r8r2TgvaOen2f1+vzynPl1U+27/b1swk+t1t7envb29uHb+/fvn+hVFqdWq3ldgfeMEj/PPGd+ne/209PW1jbm+57S2SSam5vT19eXJOnr68usWbNO5dcAAEBdnVIML168OD09PUmSnp6eLFmyZFwHBQAAk2HUwyQ2bNiQZ599NkeOHMnnPve5XH/99Vm+fHk6OzuzZcuW1Gq1rF69ejLGCgAA42rUGL7jjjtGXL527dpxHwwAAEwmV6ADAKBYYhgAgGKJYQAAiiWGAQAolhgGAKBYYhgAgGKJYQAAijXqeYY5PYO3XDfh69gzwrLGBx6Z8PUCALzb2TMMAECxxDAAAMUSwwAAFEsMAwBQLDEMAECxxDAAAMVyajUAYNJNxqlHT8bpR/lV9gwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsZ5MAYEqp51kGgPLYMwwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFAsMQwAQLHEMAAAxRLDAAAUSwwDAFCspnoPgIkxeMt19R4CAMCUZ88wAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAscQwAADFEsMAABRLDAMAUCwxDABAsZrqPYDJMHjLdfUeAgCclO8pJlq93mONDzxSl/W+E/YMAwBQLDEMAECxxDAAAMUSwwAAFEsMAwBQrCLOJgEA8JZ3w9k79tR7AAWxZxgAgGKJYQAAiiWGAQAo1mkdM7xjx448+OCDGRoaysc//vEsX758vMYFAAAT7pT3DA8NDeXb3/52vvzlL6ezszP/8R//kf/93/8dz7EBAMCEOuUYfv7553Puuedm7ty5aWpqypVXXpne3t7xHBsAAEyoUz5M4uDBg5k9e/bw7dmzZ+e555474X7d3d3p7u5OknR0dKStre1UV3nq/uWpyV8nAABT3invGa6q6oRlDQ0NJyxrb29PR0dHOjo6TnVVjGLNmjX1HgK/wnxMPeZk6jEnU4v5mHrMyeQ55RiePXt2Dhw4MHz7wIEDaWlpGZdBAQDAZDjlGL744ovz8ssvZ+/evTl+/HieeOKJLF68eDzHBgAAE6rxK1/5yldO5YHTpk3Lueeem7//+7/PY489lquuuipLly4d5+ExVvPmzav3EPgV5mPqMSdTjzmZWszH1GNOJkdDNdLBvwAAUABXoAMAoFhiGACAYp3W5ZiZOI8++mi2bNmShoaG/NZv/VZWrlyZV155JRs2bEh/f38uuuii3H777Wlqasobb7yRb37zm/n5z3+es846K3fccUfOOeecJMnmzZuzZcuWTJs2LZ/5zGeyaNGiOj+zd49NmzZl+/btaW5uzvr165Mk/f396ezszL59+zJnzpysWrUqM2fOTFVVefDBB/OTn/wk73//+7Ny5crhY722bt2ahx9+OEnyyU9+Mtdcc02S5Oc//3k2btyYgYGBfOhDH8pnPvOZEU9PyJtGmo+HHnoo27ZtS1NTU+bOnZuVK1fmzDPPTHLy9/7JLiO/d+/eEbcvTm6kOXnLI488ku9973v51re+lVmzZtlGJsnJ5uTf/u3f8thjj6WxsTG/93u/lxUrViSxnUy0kebjf/7nf/LAAw9kYGAgjY2N+exnP5v58+fbRuqpYso5cOBAtXLlyur111+vqqqq1q9fX/3oRz+q1q9fX/34xz+uqqqq7r///urf//3fq6qqqscee6y6//77q6qqqh//+MfVN77xjaqqqurFF1+svvjFL1YDAwPVnj17qs9//vPV4OBgHZ7Ru9OuXbuqn/3sZ9Xq1auHlz300EPV5s2bq6qqqs2bN1cPPfRQVVVVtW3btmrdunXV0NBQtXv37uqv//qvq6qqqiNHjlS33XZbdeTIkbf9uaqqas2aNdXu3buroaGhat26ddX27dsn+Rm+u4w0Hzt27KiOHz9eVdWbc/PWfJzsvT84OFh9/vOfr375y19Wb7zxRvXFL36xevHFF6uqqk66fXFyI81JVVXVvn37qrvvvru69dZbq0OHDlVVZRuZLCPNyc6dO6u/+Zu/qQYGBqqqqqpXXnmlqirbyWQYaT6++tWvDr+Xt23bVt11113Df7aN1IfDJKaooaGhDAwMZHBwMAMDAzn77LOza9eu4TN2XHPNNcOXv37qqaeG/5a4dOnSPPPMM6mqKr29vbnyyiszffr0nHPOOTn33HPz/PPP1+spvetcdtllmTlz5tuW9fb2ZtmyZUmSZcuWvW0Orr766jQ0NOTSSy/Nq6++mr6+vuzYsSOXX355Zs6cmZkzZ+byyy/Pjh070tfXl2PHjuXSSy9NQ0NDrr76apczH8VI8/HBD34wjY2NSZJLL700Bw8eTJKTvvdPdhn5qqpOun1xciPNSZJ897vfzac//em37aGyjUyOkebkhz/8Yf7sz/4s06dPT5I0NzcnsZ1MhpHmo6GhIceOHUuSHD16dPgaDbaR+vFvG1NQa2tr/vRP/zS33npr3ve+9+WDH/xg5s2blxkzZgx/8be2tg5/8f/qpbEbGxszY8aMHDlyJAcPHswll1zytt/71mM4NYcOHRr+4Gppacnhw4eTvDkHtVpt+H6zZ8/OwYMHT7hs+VtzMNLlzM3N6dmyZUuuvPLKJPmN7/2RLiN/5MiRk25fvDNPPfVUWltbc+GFF75tuW2kfl5++eX893//d77//e9n+vTpueGGGzJ//nzbSZ3ceOONWbduXR566KEMDQ3l7rvvTmIbqSd7hqeg/v7+9Pb2ZuPGjbn//vvz2muvZceOHSe9f3WSS2OPtJyJcbI5GIm5GX8PP/xwGhsbc9VVVyUZeT5OttzxdePn9ddfz8MPP5w///M/P+FntpH6GRoaSn9/f9atW5cbbrghnZ2dqarKdlInP/zhD3PjjTfmH/7hH3LjjTfmvvvuS2IbqScxPAXt3Lkz55xzTmbNmpWmpqZcccUV2b17d44ePZrBwcEkb/4NsrW1NcnbL409ODiYo0ePZubMmSdcMvtXH8OpaW5uTl9fX5Kkr68vs2bNSvLmHOzfv3/4fm9dnry1tfWEOWhpaRnxcubm5tRs3bo127Ztyxe+8IXhL46TvfdPdhn5s84666TbF2O3Z8+e7N27N1/60pdy22235cCBA7nzzjvzyiuv2EbqqLW1NVdccUUaGhoyf/78TJs2LUeOHLGd1ElPT0+uuOKKJMlHPvKR4cMXbSP1I4anoFqtlueeey6vv/56qqrKzp07c/7552fBggV58sknk7wZAG9d/vrDH/5wtm7dmiR58skns2DBgjQ0NGTx4sV54okn8sYbb2Tv3r15+eWXM3/+/Ho9rfeExYsXp6enJ8mbH2hLliwZXv7444+nqqr89Kc/zYwZM9LS0pJFixbl6aefTn9/f/r7+/P0009n0aJFaWlpyQc+8IH89Kc/TVVVefzxx13O/BTs2LEj//RP/5Q777wz73//+4eXn+y9f7LLyDc0NJx0+2LsLrjggnzrW9/Kxo0bs3HjxsyePTt/+7d/m7PPPts2UkdLlizJM888kyR56aWXcvz48Zx11lm2kzppbW3Ns88+myR55plncu655ybxPVJPrkA3Rf3gBz/IE088kcbGxlx44YX53Oc+l4MHD55wSpvp06dnYGAg3/zmN/PCCy9k5syZueOOOzJ37twkb/7z8Y9+9KNMmzYtN910Uz70oQ/V+Zm9e2zYsCHPPvtsjhw5kubm5lx//fVZsmRJOjs7s3///tRqtaxevXr41Grf/va38/TTT+d973tfVq5cmYsvvjjJm8eybt68Ocmbp8T52Mc+liT52c9+lk2bNmVgYCCLFi3KzTff7J8if4OR5mPz5s05fvz48H9QueSSS/KXf/mXSU7+3t++fXu++93vZmhoKB/72MfyyU9+MsmbezVH2r44uZHm5Nprrx3++W233ZZ77rln+NRqtpGJN9KcXH311dm0aVN+8YtfpKmpKTfccEN+93d/N4ntZKKNNB9tbW3Dp62bPn16PvvZz2bevHm2kToSwwAAFMthEgAAFEsMAwBQLDEMAECxxDAAAMUSwwAAFEsMAwBQLDEMAECx/h/ngxPSNiYYUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% доверительный интервал: (11886.620, 12281.864)\n",
      "Среднее 12084.242\n"
     ]
    }
   ],
   "source": [
    "# Посчитаем 95% доверительный интервал (alpha = 0.05)\n",
    "# Тогда просто согласно формуле\n",
    "\n",
    "sigma = x.std() # Вообще говоря, это неправда, но будем считать, что это знание свыше\n",
    "n = x.shape[0]\n",
    "z = 1.96 # 0.975 квантиль\n",
    "xm = x.mean()\n",
    "\n",
    "lb, rb = xm - z*sigma/np.sqrt(n), xm + z*sigma/np.sqrt(n)\n",
    "\n",
    "print('95%% доверительный интервал: (%.3f, %.3f)' % (lb, rb))\n",
    "print('Среднее %.3f' % xm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(417,)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Есть другой, более универсальный способ для расчета доверительных интервалов любых статистик - метод [bootstap](https://en.wikipedia.org/wiki/Bootstrapping_(statistics)), идея которого заключается в многократной генерации выборок на базе имеющейся выборки.\n",
    "\n",
    "Для того, чтобы найти доверительный интервал методом bootstrap проделайте следующие шаги:\n",
    "1. Создайте случайную матрицу размера $417 \\times 1000$. $417$ - есть измерения по $417$ объектам, а $1000$ - это количество bootstrap-выборок, которое мы отсэмплируем. Значения в этой матрице должны быть целочисленными от 0 до 416 (включительно). Полученная матрица - матрица со случайными индексами элементов массива, для которого мы считаем доверительный интервал\n",
    "2. Выполните сэмплирование - должна получится новая матрица размера $417 \\times 1000$, но заполненная значениями из массива.\n",
    "3. Посчитайте среднее по каждому столбцу - получится массив выборочных средних.\n",
    "4. По массиву из пункта выше посчитайте 2.5% и 97.5% персентили - это и будут границы доверительного интервала."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "rnd_idx = np.random.randint(0, 416, size=(417, 1000))\n",
    "bootstap_sample = x[rnd_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "bootstrap_means = bootstap_sample.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11872.18782974, 12281.29070743])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(bootstrap_means, [2.5, 97.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12075.540944844122"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bootstrap_means.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Зачем это нам? Для моделей мы можем точно также делать оценки каких-то их параметров.\n",
    "\n",
    "В частности, для линейной регрессии мы можем методом бутстрепа генерировать выборки для обучения, строить модели и запоминать полученные коэффициенты. \n",
    "\n",
    "Затем точно так же можно смотреть на доверительный интервал для коэффициентов\n",
    "\n",
    "Используйте бутстреп для данного датасета"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "betas_mileage = np.empty((1000,))\n",
    "betas_intercept = np.empty((1000,))\n",
    "\n",
    "for i in range(1000):\n",
    "    rnd_idx = np.random.randint(0, X_train.shape[0]-1, size=(X_train.shape[0],))\n",
    "\n",
    "    y_bootstap = y_train[rnd_idx]\n",
    "    X_bootstap = X_train[rnd_idx, :]\n",
    "\n",
    "    model.fit(X_bootstap, y_bootstap)\n",
    "\n",
    "    betas_mileage[i] = model.coef_[0]\n",
    "    betas_intercept[i] = model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.05771692, -0.04583858])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(betas_mileage, [2.5, 97.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16163.66493411, 17322.26897075])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(betas_intercept, [2.5, 97.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/andrey.shestakov/anaconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a21da8550>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nmO3nvV547PPsVFdXT/yguAmHUhcuXIiqqqq0bVu3bsW1114Lh0NqO9fW1gIA2tvbcckll8DhcGDOnDloamrCu+++i3fffRdNTU1obGyE3W7HJZdcgvb2dmitsW/fPlx00UUAgDVr1qC9vT3rxqvGZhhXXgf1P/8e6ubvAMsulo+BYzHgzT3Qj/1v6B9+F+ZTj0J/VKR8bFMD/qHk8unB0lw+vRjynR87XfNvxzsvq845834cBe+7ic6n3FYnna73JCWV+zUu9/YTFVtOOdZHjhzBW2+9hcceewwOhwM33ngj5s+fj76+PpxzTvKj4vr6evT19QEAGhoahrc3NDTgnXfewcDAADweD2w226jHZ7Jt2zZs27YNAHDnnXeirq4u+cOGi4HWi6HDIYT3tCPU/ntE3nwDCPiB9t9Dt/8ehrcRzhWXwrny07DNbsrl1Eex2W3p7chGLAzDUwlVWQVlK+s09yk57uuBqqpJqwuubZXQvh54vd5xn2u32yd8zFT2X8rGOy8AlpxzpmPAboNR4L7L6hqubZOvMpDLPZnNvU7Wmkqfl/vrTjHbz3u98Njn1sspqjNNE4ODg7j99ttx8OBB/NM//RP+9V//dcyR2Ezbc1lkZd26dVi3bt3w/30+X+YHzl8EzF8ENdAPdO2E7twOHPkYZk83As/8CoFnfgWcdhbU0lXABa1Tyseuq6sbux3jkiAILhfgroJyzrzJjmadd3R+bCgI1HnR09Mz7nO93okfM5X9l7LxzguAJeec6Ri2aARmgftuul3DXM4nm3udrDWVPi/3e7aY7ee9Xnjs8+w0N2efBpXTrLr6+nqsWrUKSinMnz8fhmFgYGAADQ0N6O3tHX5cX18f6uvrR23v7e1FXV0dqqur4ff7EYvF0h5vFVVdC3XJ5TBu/Vuo//E94NNXAjXx0eWP34N++ueSKvLoA9D7O6GjEcuOnbVgEPD1QPd0Qw8NzqiSfaptPRCNyou21vI9GpXtZbD/YhnvvKw658z7iRS876bbNZxu50Ojlfs1Lvf2ExVbToH1ihUrsHfvXgDA4cOHEY1GUV1djeXLl+PVV19FJBLBsWPHcOTIEcyfPx9nn302jhw5gmPHjiEajeLVV1/F8uXLoZTCokWL8PrrrwMAXnzxRSxfvty6s0uRlo9903eAZRfF87GjwJud0D9/oLj52NEoMNAPHO+G7vdBh0OFPX4R5Ds/ttzyb7M13nlZdc6Z9lP1p/+z4H033a7hdDsfGq3cr3G5t5+o2JSeIIK85557sH//fgwMDKC2thY33HADVq9ejfvvvx8ffvgh7HY7brzxRlxwwQUAgM2bN+OFF16AYRi46aabsGzZMgDArl278JOf/ASmaWLt2rVYv17e/XZ3d48qt5eYFDmRT3ZlP9ExEx0OySTHzu3AwTfl3XlC/WyoJSuBpaug6mePuY/cU0GyYLcDnkrA5WHJvhH48VXhsc+Lg/1eeOzz4mC/Fx77PDuTSQWZMLAuZVMNrFPpgX7gjXYJso8eSv/h6WdBLcmcj53XwDpBKcDlloVnHBX5PVaZ4ItB4bHPi4P9Xnjs8+Jgvxce+zw7kwmsZ25JihFUdS3wqXVQn1oHffQT6D3bgT07JD3jo/egP3oP+O0voRdcIJMeFyyCsmc3sj5lWkt1k4CfC88QERERlSgG1hmoplOgmtZDX/FF4P23ZRR7f6csPvFmJ/SbnYC7ErqlFZFL10HP8uZU5SQnkQgQOQEM9kO73FJRJMvUGSIiIiLKHwbW41CGAZx9PtTZ50N/IQTs75SR7INvyYqKO17GyR0vA/WzgSzysS1lasDvB/x+aEeFrJDFUWwiIiKiomFgnSVV4ZTAeekq6JMnkvWxjx4C+o5Dv/Ab4IXfQJ9+drw+9oVQ7tzrY09KJCxfg/3QLg/gruQoNhEREVGBMbDOgaqZNZyPXe0/if6XnwPeaI/nYx+E/ugg8Jv/hD63RYLscxZB2QvQ1Ynl0/1DMortiediFypNhTIyuzpkOeCebsDbCNW2nqWr4tg3REQ0ndg2bdq0qdiNyNXAkcPFbgIq5zQhdOqZwMWXQc2bLxt9PUA0Ahw/CnTtBNpfhj7RK4FuzazCBLpmTAr7B4YA0wRsNijDlv/jFojH44Hf7y92MyZkdnVAP/qAfKLg9gD+QWBPO9DYDNWY/SzjUmB1n0+nvsmncrnXpxP2eXGw3wuPfZ6d6urqrB9b3iPWNbOAYEAmFRaZMgxg/vlQ88+HDgWlPnYiH9sv+dh6x8tAwxxgySpg6UqoxBLU+WSawNAgMDQIXREfxXZyFLtQ9JbNUo88sTyw0wUgKNtn+Mgs+4aIiKabsg6slacS8FTKMuDBYOkE2U5Xej52oj529ydA7zHo558Gnn8aet7Z8frYBcrHDofly+iHdnsAt6dwJQNnqp5uoHLEO90Kp2yf6dg3REQ0zZR1YJ2gDJuMxJZikF0zC7j0CqhLr4A+ckhGsRP52B8ehP6wCPnYaaPYTsDj4Sh2vngbgX5fclQWkPvS21i8NpUK9g0REU0z0yKwTjU6yA5IoF0KQfbcU6Hmngp95XXAe28l62NHwsD+3dD7d0u7W5bLSPapZ+Q/2A2H5Gt4FLuyMBMtZwjVtl7yiBGU0dhwCIhGodrWF7tpRce+ISKi6WZaR1ASZFcBniroWAwIBeIj2eEit8sA5i+Emr8wmY/duR14L56Pvf0l6O0vFTYfm6PYeWG0tMLcsJGVLzJg3xAR0XSjtNa62I3I1eHDuVUFsTLIrqurg8/nm9I+htt18gTwxg7ozh2Sj51q3nxJFVl0IZTbY8nxJmQYUq2hBHOxvV4venp6it2MGYV9Xhzs98JjnxcH+73w2OfZaW7OvlLVtB6xHouylehIds0s4NIroS69MkM+9rvQH74L/OYX0OcuhlqyMv/52CMrirhZF5uIiIhoLDMysE6VFmSnTnyMhIEiDuaPm4+9bxf0vl3xfOwVMpJ9yrz8BryJiiID/dAuN1d3JCIiIhphxgfWqTJWFwnFJz4WKcjOnI/9OvDe2/F87Beht78o+dhLVwFLVkHVNeSvQaaZvrqj2yOj2IaRv2MSERERlQEG1mNID7JNCbBDASBUxCB7VH3sHdC7twPHDkt97N89DfzuaehC5WNHwvI12A/tdAOeSihHRf6OR0RERFTCGFhnQaVM4tOmCYSD8RJ+weK1KZ6PjU9dARw9JKkib7QDgydH52Mn6mPb8rSkuamBgB8I+KHtdsnFdrun1RLqRERERBNhYD1JyjAAlwdweaC1hlFVCQRDMpptFn4kWykFzD0Nau5p8XzstyXIfnNkPnaV1MfOdz52NCqTLQdPQjtdUlEkdQEQIiIiommKgfUUKKVguD1QtXXQepbkYofiC9KYZuHbY7MB5yyEOieej72/UyqLvPc24B9M5mN7G4ElK/Obj611fHGeALTNFh/xr8zfqDkRERFRkTGwtohSSpZmdrqAGkCH4kF2KAjEYoVvj9MFLLsIatlF0P0+4I12Gck+dhjo6U7mY59xjpTuy2c+diwGDA4AgwPDo9hwuli2j4iIiKYVBtZ5opxOwOkEAOhwSALsYKA4QXZtHfDpK4FLM+Rjf/AO9AfvFC4fOxSvtGIY8SXUS2/xGSIiIqJcMLAuAFXhBCqcQHUtdCQ8nCJR6CB7dD72Wyn52JH0fOzFy6GW5DEfe+TiM55KLqFOREREZY2BdYEpRwXgqIgH2REJsEMBmfRXyHbYbDIyfc4iycfet1vysd8/IPnYr78I/fqLko+9dBWwZCXUrDzlYycWnzH6OYpNREREZYuBdREphwNwOIDqGgmyEznZkUhh2+F0ARdeDHXhxdD9fcCedgmyjx2RfOxtTwHbnpJ87ER9bJfb+oakjWI7AY+Ho9jTiNnVAb1lM9DTDXgbodrWw2hpLXaziLLGe5iIJqK0LuK63VN0+PDhYjcBXq8XPT09lu5TRyPxnOyglMzLgnlgH/DKVsDXA9R5gUuvhLFgUe5t0Bo4ckhWeezaKfnYCXYHcF48H3v+wqzzsXNqo2HE62J7oOzJ94GT6ffJ/jHkH8/MJurzsfrN7OqA3vwT4PBHcu/U1AF2OxCNQm3YOOm+tfr6jLe/XI5ldfvy8RqTiVXtng6/P5n63OzqgH70Abl3K5xSBSrHe7gcFeK6FupepyT2eXaam5uzfqxt06ZNm/LXlPwaGBgodhPg8Xjg9/st3acybFAVTihPpQSVNhsAPWZOtnlgH/DrxyQId7plsZa3u6AbGqEa5uTWBqWgqmuhzlkEXHwZ1GlnSgk933EgGpHR7DfagfaXoftPAJVVQHXtmKPLObdRa3mOf0hG8pWCsjuy7vfhP4aRsFQj8Q8Ce9qBxmaoxtG/KJN9/EwyXp+P1W86MAT89nGg93jywQE/4HJLgHLoAxiXXJ51G6y+PuPtTx87Mulj5eP+ycdrzEhWtXu6/P5k6nPzp/fFX79cgFJy/2pz0vdwOSrUdS3EvU7p2OfZqa6uzvqxRh7bQRZQNhtUZRVU/WxgThNQMyv5wp7wylYJviucsr3CKf9/Zat1bVhwAYwb/jvUX/0D1HV/DJx1rhxraBB4/QXoH90J/S/fh37pWegTfaN3YkUbQ0HgRB/08aMwT/ZDZzH5U2/ZLH8AE33mdAF2u2y34PEkxuo3PPekfDdjcr0NQ35+8oTcAz3dlhwn1+sz3v5yOVa53j9Wtbtczz8rPd1yz6bK4R4uR9P6uhJZjDnWZUQZNqme4alMX1rd1yMj26kcFbLd6ja43KPzsTu3A8ePAMePQm97Etj2JPSZC6SqyKJl8hwr2xiLwRzoB3y+5OqOY+V893QDlSPeaY73x3Cyj5/GRn70G/yjm4B552T8GY58DIyc3FrhlHkDFU2SAhKLJgPraEQ+Svc2Tq4d/T45Tmp8M5XrM9H1nuy9UK73j1XtLtfzz4a3Ue6/1JVks7yHy950vq5EFmNgXaZSl1bHnGbgRJ8Eqjq+4mMkLHnM+WxDbT2wuk1qZB/5OFkfe2gAeP8A9PsHgF8/Bn3eYvljFA6l/1Gyoo3xutjaZpO+GJGLPek/hjP5j2eKtHzSymqg34fBB++G+eU/BYBRP0PALyPSNXXJnYRDkvYTDgG1s4C+48kVSW02yU9tWz+5dpzsl3QkpeRNZuI4uV6fia73ZO+Fcr1/rGp3uZ5/FlTberkXEUzPsZ7gHp4WpvF1JbIaU0GmAfXZL0nAEosCNpkUBtMEPt1WmOMrBdV8OozP/xHUX/4A6sZvAi3LZZQyGgH2dgDdhyWw6uuJL/0eX5Hy0iutaUQsJgF9Tze0r1dKCEL+GCIaleNpLd/H+WM42ceXG7OrA7G7bkPsu7cgdtdtMLs6Mj4u80e/jrFTJCqrZYLriH7DFdfKd8Mmb6KUIWkhs5uymvQ16lh19fKD/j5Lrs941zuXe6Fc7x+r2l2u558No6UVasNGoLZOXmtq62bMxMXpfF2JrMbJi1NUCon/qrEZaGwGDn0gowoNs6HW/zGM5Z8CKioAQ0ngWYACMMowoBrmQC26ELhoDZR3jrwIJwKhaEQmIkYjUke7pTWn0n1utxvBYDDzD2NRqQ8e8EPNmQvdPA/45ENpQ70X6robx/xjmN6XEz++nExmApJ+6ufymJRcfsNRAe3rkes34mdwumRy6eymtH6zffrKZH8ODcqCQxu+AduX/3tWk55GtcNRIW/Ygn5JK5ni9RnveudyL+Tj/inEa4xV7Z4uvz9j9blqbIZxyeUw1l0D45LLy2pC5lQU6rqWwt/TmYZ9np3JTF5kub0pKqdSNToUAkJ+yctOfCRfqGOPzMdOUApI1MdeuCzrILuurg4+ny+7gysF870DwO+3yKh5mZYAm6rYXbeN/jg3FARq62D7i9snfKwtGkGsqkb+k+V+Ctnm6aqcXmOmC/Z5cbDfC499np3JlNtjKsgMopxOqJo6qDlzgXqv5KhmWYN6yseurYda3Qb1re9BfeO7wMVrJX1Aa8nHfuKn0P/w1zD/89+hD+zNquJHtsy39wJP/B+ZKOl0Ab5e6J/9aMw0iGlrElUNMn/0G8k5RSJX/AiaiIjKCVNBpqhcP0ZRNjuU0wVVWSXBlRHPfc1lAw3lAAAgAElEQVTzBxhKKaiaWaPrY/cl6mMfjtfH/j30SZ8E31U1o+pjj5sKMoJ+8meS/pAIKhPn+tFBqFWfyXqBm3KnO7dL+kfq5M5wCKj3jqrDm+mj35obb0VkwQUZf4ZlFwHbX4J+6udynOpZlnxMPl1SC6aiXF9jyhn7vDjY74XHPs/OZFJBWBWEoCqcEnRW10JHwpKfHAyMuSCNZce12YAFF0AtuAA6GAD275ag7P0DMjnotRegX3sBmD0XWLoKWLJCKpFM1lil/nqPAb3HoR0O+bnLLdVWpqnJVjUwWlqBlADW5fViMP6RYerPMlUQ0Y8+ANOiiV0j20FERFSqGFhTGuWokKBzOMgOykSxfAfZLjdw4SVQF14iC8zs2QG9Zztw/Chw/Aj0c/8l9bHj+djmJWuz33mdFxjoT0+DSC31F4kAkRPAYD+0yw24K6UfphmjpRXmho2WL0ucVrkDiH8PyvYSD4inw/LbRERUOhhY05iSQXYNdCQio9ihgOS85vO4s+qBz3xWamQf/khGsbvapapEvD6279e/AM5bLJMezz5//HSOS6+U5dTDITmfSDhzqT9TA34/4PfHR7GlTvh0GsXOy+hvmS4eke+RdiIimnkYWFNWlMMBOBzJIDsUkIlkkUj+jqmUlGc7ZR70Z78EvLtfguy39khw3LUTumsnUFUD3bJcguy5p43KxzYWLIJ59Vdk+XRfj4xUX3oljAWLxj54JAJE+oGBk/FRbI+kzJSYkhhxLdPFI8p5pJ2IiEoTA2uatOEgu6oGOhqRADsYyG+QbbMB57ZAndsCHQzA8/5bGHr1BeCDd2Rhkteeh37t+THzsY0Fi4DxAumxaC2rCgb80Ha75GK73bK8fJGVyohr2a5IV6Yj7UREVLoYWNOUKLtDFuyorIZOlEULBmREOV/HdLnhuuQyBM5fBu3rTeZj93Sn52OfuQBqySpg0TKo1NHUXEWjkqs9eBLa6ZJcbGfxRrFLZcQ1X7nbeVemI+1ERFS6GFiTZZTdDtirgMoqqUMdilcXCecxyK5rANZ8TnKyP/lQAuw3dkpZuffehn7vbeDXP4c+f6mkipx13tTL62k9XDlF22ySi+2uLHzZvhIacU3kbidSU/TP/g2xEg+wy3aknYiIShYDa8oLZbMBnirAUwVtxuLVReIj2Xmola2UAk49A+rUM6A/e/2IfOwI8EY79Bvtkr6yeIUE2U2njsrHnrRYDBgcAAYH4qPYHsDpmvp+s1FiI66lkpqSrbIdaU9REjn2REQ0jIE15Z0ybLLKo6dSguxQKD6SHcpPkJ2ajx3wA/t2Qe/ZkczHfvV30K/+DpjTHM/HXglVM2vqBw4F5ctmg3Z5ZMKjPX+/YqU24loqqSmTUc41ssvtjQwR0UzAwJoKShmJ1AkPtGnGg9GABNv5CLLdHmD5pVDLLx2dj33sMPTWJ4Dn/kvysZeuAhZakI8di8kCN0MD0BVOwOMBnG7LR7FLbsS1hFJTZoJyfCNDRDTdMbCmolGGkR5kh4OSMhIOSk1pq483Mh+7czvQNSIf++nHUvKxz5163nQ4JF9GP7S70vJR7JIacS2x1JRpj29kiIhKDgNrKgnKMACXLMiitU6mVYQClgfZafnYn7seeGefBNlvvyE54G/sgH5jh7X52KY5YhS7snC52AVSaqkp0x7fyBARlRwG1lRylFKAyw243NB6lgQLoYCMZpumtcey2WQFx/MWJ/OxO7cDH76bv3zsxCi2zQZdrIoieVByqSnTHN/IEBGVHqV1HhJbC+Tw4cPFbgK8Xi96enqK3YwZQ4ckyK7zuOHLY79rX4/kY3duB3qPJX+glKSILFkFLFxqTX1spQCnE3BXFbUu9kR4rxfHeP3OqiD5wXu9ONjvhcc+z05zc3PWj+WINZUV5XQCTifsXi9gIrkgTSxm7XHqvMCazwOf+Rxw6AOZ8Ni1E/APAQffgj74FvB0vD72snh9bMPI7WBax8sRBktudUcqbSWVY09ERAysqXypCqd8BF5dCx0JDy/aYmWQrZQCTjsT6rQzpT72O/ukdN/IfOzqWsnHXrIKau6puR8wdXVHl1smO1aU7ig2ERERJTGwpmlBOSoAR0U8yI5IgB0KSKBq1THsduD8JVDnLxmdjz3QD/xhG/QftkE3ngK1dCWweAr52FoDAT8Q8MsotqcScHlyHxUnIiKivGNgTdOOcjgAhwOoroGOJoLsoKzAaNUx0upjj8jH7v4EessTwNb/gj7rPKkqcv6S3POxo1HgZD8wcDK+umNlSediExERzVQMrGlaU3YHUOWQ0nnRSDIn28oge9x87DehD74JOCqgFybqY+eYj631cLqLtsUX2nHld3VHIiIiyh7/ItOMoewOwO4AKquho9F4CT/rguwx87Hfiudj79kh/0/kYy9dBdWUYz52LAYMDgCD8brYbo/UxWaqCBERUdEwsKYZSdntgL06f0F2Wj72ELB3l4xkf3gwQz72KmDxitzzsRN1sZWSCY8utzVlAImIiGhSGFjTjJf3INtdCaz4NNSKT0P3HU/mY/cdj+djbwa2PgF99nnJ+ti5VAJJnfBos8UX2fFIzjkRERHl3YSB9f33349du3ahtrYWd999d9rPnnrqKTzyyCP48Y9/jJqaGmit8dBDD2H37t1wOp249dZbcdZZZwEAXnzxRWzevBkAsH79eqxZswYA8N577+G+++5DOBzGsmXLcPPNN0+rZZ5LkdWLSuSyv2IvbDHW8ZXdDvPNA/Kz40eBei9w6ZUwzj5v8sc4sA94ZSvg6wHq4vtZsAhYexV08zzgd0/JZMdoRFaUfPdN6HffBJ52Sn3spatkMZpc0jtiMWBoEBgahHZUwHz/APDCb+R48fMFMKlrEOx4DbFfPjz8eJzbArzdlfH5Vl1fK/YTe/ox4Lkn5Q2T0w2cdhbw8XvJ/19xLWxf+MrEx3e5ZTGfkyfkTZfNDtTOkm0Bf9btG9WexSuAE715+13I1IdA/Np/8hEQi8pk37mn5eX30OzqgN78E+DoJ7KhsRnqSzdJGzJsL/cFbor92kZExWXbtGnTpvEeUFlZibVr16K9vR1tbW3D23t6evDb3/4WsVgM69atg9PpxO7du9HZ2Yk77rgDZ555Jv7jP/4Dl19+OQYHB3HvvffiBz/4AS6//HLce++9WL16NSoqKvDDH/4Qt9xyC772ta/h2WefRXV1NebOnZtV4wcGBqZ08lbweDzw+/3FbkbWzK4OWQY5Epa8XP8gsKdd/qg1Zr+y0FT2Z0UbptLv4x1fHzuS8rNKCZje6oI+4xypT601YE5cJ9s8sA/49WOyH6db9vN2F3RDI3TvceA3v5B9VdVILW7DAOaeJnnT0QjQ/QmwZzvQ8QfowZNAVQ1UVc3kzvPAPugnfwb9218CO38vEzcrq2RS5c5XgN2vS0CfxTUwuzoQ+T//Kitfuj2A7zjQ1SFtra4dpw9zv8esuE9iTz8G/PoXgBmVQDgcAnq7pd12h3w/sA8agHHuBWMfX2ug56hUZwmH5B4Ih2TZ+8GTgKcKCIcnbN+o9kTCwKH35f6YVZ/xHC2/19vj194/BAwNSGAdCUtf7Nud82vBmMd/+F75dAaQNyGD/UDndmD3a8CJvvTt+3YDzadbdvxc5drnVr++zjTZ9LvZ1QHzp/dBP/Vz+eSvehb7dgrKLYYplurq6qwfO+FQ2MKFC1FVVTVq+09+8hN89atfTRtd3rlzJ1avXg2lFBYsWIChoSH4fD50dnZi8eLFqKqqQlVVFRYvXozOzk74fD4EAgEsWLAASimsXr0a7e3tWTeeJk9v2QzY7YDTFV9K2wXY7bK9QPuzug1Wtnmsn2Hbk1CV1VANs4HZTRJMVlSMfZBXtgI2mwTNSsl3m022v7JVSuj1nwC6D0uwZtgAmw3qr++EumYDcPrZsp+BfuCV56Dv+3uY990uedkD/ROe43BgP9Avf+RNU4KogF/a4R8Cgv5k+ya4BtIvjmS/+P2Aguwvyz5M3bfZ1YHYXbch9t1bELvrNphdHZO6Tll77klpp80u+9A6+TOl4tvjjxvv+AP9gDIAaPmy2eW7acr2k/3ZtW+s9mToRytk7MOAX0bLE8e02eUc/H7Lfw/1ls3x4xhy3xmG/DsUiN9Do7cX6nUgH4r92jbdDb9x6fcBldVAvw/60Qcyvn4QFUtOOdY7d+5EfX09zjjjjLTtfX198Hq9w/9vaGhAX18f+vr60NDQMLy9vr4+4/bE48eybds2bNu2DQBw5513ph2rWOx2e0m0I1vHfT1QVTVpb4i0rRLa15PTeeSyPyvaMJV+H+/4ACbVNh2LQgcD0AG/jObG9fX7oDxV6ftx2aD7fdDhUEpQYwDalJGt4ybqm08Fmk8FrrwGsZ5uhNpfQWjH72EePwocPQT97CFgy2bYz1sM58pPo2Lx8owTFftffx6mowLK6ULM1yvBiwYwOABbZTViZgxQCjZoAPF2eCoRO3oIxj9vQuzYEdjmzIXni1+Fq/Vi6bPqGtgh5xONReXNQCwKe7zcX7Z9GOx4DYO/eFAC9do6GfH9xYOoqqmBq/XirK5Ttte+OxSUc8+UXpbYZtiAUHDUPlOPL+drAFGdfG4iKDaM4X6YqH2j2pOI87U5qh8T+7D6Xo/Grz1gxgNaNXwONk/urwVjHd80Y+nnnNqPieMn/m2aUEc/yXgPFlKufZ7a39o/CNPXJ6vC9h5D1YfvFPw8ys1E/d73/NMwnU4ol1s2OBzQwQCM559G/dq2MZ9HYyu3GKYcTDqwDoVC2Lx5M/7u7/5u1M906mhQ3Fj50kqpjI8fz7p167Bu3brh//f09Ezq+fng9XpLoh3ZMuu88m4/NRgLBYG63M4jl/1Z0Yap9Pt4xweQY9ts0HZnss50bZ2MLKdOQgyHJJA8/LEE04ZNtivIyGckAp/Pl7LLCuCiy6BXrYU69L587NnVAQSGEHlzDyJv7pH9J+pjn5nMxzaPH5VUlkQAbMYAQwHRCGKJIFEBscTKlBFIgOsfROR4N+DywOw5hv4f/SNObtgIXeeFGjyJmD0+EdJmB6JhwF6BaGIfWfZh7JcPy+ik3SG54PHv/b98GIPzzsnqOmV97Z0uIBzMHFgnXn/MGOB0jdpn2vFtdunL4YBYJ4Nr0wRsdumHido3sj0KElwrY1Q/JvZh+b1u2OS4yojfH8bwOcT8Qzm/Fox5fF+f7D8xV8A0432H0duhof2DiPQcG3UPFjJPOdc+H+5vMxZPf1FyrkoV5TzKzUT9HjtySEaqU1fUtdkRO3KorP4Ol5Jyi2GKpbk5+3SjSc+K6u7uxrFjx/CXf/mX+OY3v4ne3l789V//NU6cOIGGhoa0C9Tb24u6ujrU19ejt7d3eHtfXx/q6urQ0NCQtr23txf19fWTbRJNgmpbLy9KoaAEBaEgEI0OT2gqxP6sboOVbZ5K25TNBlVZJekin78BMHUyPzcckiDy0ivlo2JAfp76fYyFXpRSUKedBeML/w3qr+6E+m8bgYVLkznDnduhH74X+u7bYG55Arr7EwlwI2HZQVWNtCEWHzkMhyTvu8Il/060zz8kucI2uwQ5Fc7hj7FV23qYQwPypuDj9+MTLrXkkU62D3u6099wAPL/nu6sr1PWFq+Q806UJEyltQSWGsAV147u99TjV9fKmyGJSOV5iI/0ahOoqc2ufVdcK8eLRZPBOZCxH62QsQ/dHrn+iWPGonIOHo/lv4eqbX38OKZcB9OUfzvdcryR201TAqcyTaUY7m9fX8qnERqorS+r8yhZ3sbRv8fhkGwnKhETTl4EgKGhIfzhD39AW1sbamtrcc011+Cqq67CVVddhRdeeAF33nknamtroZTC7373O1x66aV45513sG/fPlx99dWor6/HI488gs985jMIh8N45JFHcOONN6K2thYvvfQSTj/9dNTX1+NnP/sZVq9ezcmLeaQam4HGZuDQB0B/H1DvhbruxpxHUXLZnxVtmEq/j3d8q/rHaDoFaDoFOPyRVJGoawCuvA7GOQuhD+yVYCYWiwe7dplUOLsJatn4HxUrw4Ca3QTVshxY+RmougbJle73SdD00UFgx8vJShUKUs0CkGM6XVLppG09cP5SmSQ50C9/+BMBpEJyJFYZ0g+LV0Dt2SEBtdYSoDsq4hPuhibVh7pzu6S+pL6RCIeAei+MSy7P6jplw+zqAF7eIv+JRgHEA9nmefL/xMTSz30pY1WQtOP7B4FZDUDNrPh+DHmut1H6LBLOqn3GuRdIvPXhweTxWz8FOJ1jnqPl9/r1N0Etuwg4eggIBOTNgcsNNJ06pdeCMY/ffLpM0PTHX6+bToG68ZtQF14yajtMLfdU6icMNhvQ3wdj3TWWtWsiufb5cH+3vywb7A65bzyVRTmPcjNhv1fPksmg2kwOEkSjUNfdyAmMOSq3GKZYJjN5UekJ8jHuuece7N+/HwMDA6itrcUNN9yAyy67bPjn3/zmN/GDH/xguNzev//7v2PPnj2oqKjArbfeirPPlklYzz//PJ544gkAUm5v7dq1AICDBw/i/vvvRzgcxtKlS/Enf/InWZfbO3z4cNYnmi/8GKU4yrXfdTQCc/d24JcPSV6zo0ICrFgMuPorUo4vl/32HZeR6z07khUYEuwOCezXXQtj4dIx92H+xz9JkD0yfaW6FgBgBPwwE5MdAQnEa+tg+4vbJ9XW4QlIdrscK/HH0eKPyWN33ZY5lSSHNhdTud7ruSiVazbVPi+V8yg32fQ7yxlaaya9vkzFZFJBJgysSxkD65mr3Pvd7OqAfvZXUiu7rgH41BU5B9WptNbAx+9Dd74O7O2QUeuECiewaJksQnPmglH1sYcriSRGo1MCfjz9KIyqWpmIplQyP9w/CNudP550OwvxxzH23VskrSD1jbrWwNBATm0ulnK/1yejUG+6JjLVPi+V8yg3M+leLxXs8+xMJrDmyotERWC0tAIpf2B1Ig82GEjmRudAKQWcfhbU6WdBf/6PpEZz53bgQJf8cd/9OvTu14GaWdCLV0ItXQnVeIq0acEimFd/JeOiNmadVxacsduTebnhMDCrHjoShnKMU3owi/PPC2/j6FFD5mOWNKOlFeaGjWU/IjldzoOIJo8j1lPEd3vFMZ37XcdiEmCHAhK8WrFP/xCwtwN6z3bgo/fSf9h0quTctiyHiqd9jGQe2Ac88VMg5AdipqSxVLiA9V+XkXaHQyapuTy5rRSZB9Nl1LBQ9zo/Yk+azq8vpYz9Xnjs8+xwxJqojCmbTSYzVlZZFmQrTyWwcjXUytXQfcdlFDuRj330EPQzjwPP/gp6/vmSKnL+UqiRC+AkSsNpHa94kJJiEYkAkX5g4CS0yw14Kic9im01jhpmL+1NSOrCG2X2JoSIqNgYWBOVsFFBdigABIPJMn657LN+NtRlV0OvvQr4+D0JshP52O/sh35nP1DhhF60TOpjn7EAeGUrDHclzNQR7XBI0kZSc8O1lv0E/NAlMIpdkJSTaSBtxUAg/j0o21taOZpNRJQlBtZEZULZbFJn2lMFbcaAUEhGsxO1qCe7P6WA08+GOv3slHzs14EDe0fkY9fJUtOzGtJ34KiQXOwxmPs6k/naDXOAtvWwLbto0u2kAujplpHqVPHa4hzNJiLKHgNrojKkDJuMBrs90KYpq/kFAxJs5xJk2x2yguPCpdD+QcnH7twBfPwecFJWg9Tdn8RzqSuTqzrWZV4KN63CiLtSJhH+/H8j5h+CsWxVSeViE8ad6DnRaDYRESXxLxtRmVOGAeXyQM1qAObMBWbVyYIfRnb14Eftz1MFtfIzMP7sL6H+r/8FrL1KVm8EJJf65AlZWOZEH3DKGdCZcr9f2SpBdaLudYVT/v/SM8DJfuD4Ueh+H/TIVdSoKMZd5TLLlTKJiIgj1mQxs6sD+lcPA93xii1Np0Ct/3pRPzKeSfmhSinAJXnNOhEghYKSm23mMJLdMGc4H9u1+1UEtj0NDJ6U4CsaAV7ZCt3+MvTCZVBLVwJnxOtj+3pkpDpVaupIai623R4fBXfLSDwV3HgTPWMsW0hElDUG1mQZs6sD+qF/liWKlSHB05GPoR++F+ZN3y5KMDuT80MlyHYDLje0njWlIFspBc/lVyN04aegoxHg7b0y6fGdvbLP3a9B734NqK2DXrxS+joUTB/pjIQzp45Eo7Li4+BJaKcTcFdCpQZxUzST3lhNxVgTPVXbevkdQjC9bGHb+sI3Mo7XlIhKFVNByDJ6y2YJ2pQBGIZ89K8MGZXcsrl4bUrkhyol3+32orWnWJRSUC43VG0dMHuurPbo9uSULqLsDqhFy2B89RtQf3Un1NVfAU47U37Y7wN+vwX45EMZne73SeAcDskqjpdeOfaOtZaKJ75e6ONHoQdOysI5UzD8xqrfl/7GqqtjSvudSYyWVqgNG4HaOmBoAKitK2otcF5TIiplHLEm6/R0S/CUOinNMCSwKlY+5jjVDmYqlXiD4XQlR7KDgWR+7SToQx8C+3bJiPOpZwB1s4FD7wG+XrkXhgbky10JtH4K6sxzsttxynN1hTNets8tbZ9M+zjxLieZRoRtf3F7sZsFgNeUiEobA2uyjrdRAizTlNFhQP5tsxcvH5P5oeNKSxeZZHWRUZU/ggHg0PvAVV+BcrmS9bGDASAwlMzHXnSh1MeeNz+7yiDhkHwNnJDFZ9yTWHyGb6wmreTTp3hNiaiEMRWELKPa1gNON6BNCahjMfm321O0fMxxqx1QmrTqIrOb5KP/RApNJmNV/vjDc1Dz5sO49qtQf/UPUF/+U+C8xfLpRSgI7HoV+j/+Cfr/+x7M5/4L+tiR7BpoasDvB3qPQ/cegx4alHre4/E2SlCeim+sxlXy6VO8pkRUwhhYk2WMllaom78DNJ0a36CAuadBFWni4nCbSig/tFwow4Bye6DqkkG2crnTg2xfj1T6SDVi0RjlcEBdcCGMr/65BNlXf1lSRgCgvw94eQv0v3wf5o/uhH7teejBk9k1MBKRT0eOd0Of6IUOBTOfB99YTV6Jl9fjNSWiUsZUELJUKS4hXYptKifKMAC3B7YGLxDTyZzsOq8Et9lU/gCgKquAVWugVq2B7umWVJE9O4ATvcAnH0J/8iHw7K+g5y+UVJHzFk+c8pGY8BgMQttsUmrQ7ZYFbzB+GTkaQ4mnT/GaElEpY2BNRFkJdrwG85cPDwczuKAV+MPvZPTYbpegeqLKH3HK2wi17hroy64GPjoIvWdHMh/7wF7oA3tlcuVk8rHTJjxWSN6308U3VpNUiuX1RuI1JaJSpbTOYf3jEnH48OFiNwFerxc9PT0TP5AsxX4vLLOrA8YvHkRMGWnBFi65DHi7Czh+FKifDaxug3HWuTktq64jEeDtLug924EDeyVPP6G2HliyEmrpKqjZTdnv1EhMzvRAjUxvGHF+pToCWox7vZT7oxD4+lIc7PfCY59np7m5OevHMrCeIt6UxcF+L6zYXbfBNngSsXiKBQBJCamtG1WGLVldJCjfc1jxUQ8NAl07Jcg+9EH6D0+ZB7VkJbB4BdTI6hDjsdulbJ/bk7bCY1oVjNQR2hLJxee9Xnjs8+Jgvxce+zw7kwmsmQpCRBPr6ZYJoLGUKhxjTGhThjHGsurB9FHocajKKuCiNVAXrZHFYvbsyJyPfc4iqCWrgPNaJs7HjkaBgZPA4EDaCo+si0xERFZhYE1EE/M2AoMngdQR6ywmtKUvq66BcFhW5wwF04P08fYxuyk9H7tzuyxKEwxI6sjbXZKPfcGFEmRPlI89csLjsSNAVU36Y0qoCgYREZUPBtZENCHVth74xYMSDOc4oU1WfHTKFwAdCUtwHAxkFWQrwwDOOAfqjHOgr/oy8PYbEmS/s08C9Y5XoTteBWbVQy/OMh87FgNm1Ut1E6dbam0rVVJVMIiIqHwwsCaiCRktraiqqUF/SlWQqU5oU44KqXtdXTv5INvhAC5ohbqgFXpoAOjqSOZjn+gDXn4W+uVnoU+ZJ1VFWpaPnY996ZWygmQoIO2JRCRlZd21OZ8bERHNTAysiSgrrtaLMTjvnLzsOy3IDofiy6pnly6iKqtH5GMn6mP3JfOxn3k8JR97sQTmccaCRTCv/oqsJOnrkTrcl14Jo+kU6L7jUrbP5ZYRdyIionEwsCaikqIqnMOLzuhwKDnxMRqd+Lmzm6DWXQt92RcmyMdulZHs08+GMgwYCxYBCxaN3mE4LF8D/dCJiiKpeeZEREQpGFhT0Y1XM3em19MtF5muE4Bxr924zznyMRAIAGYUUAbQdApw7ddgnHO+TDyMhMduy4F96aPPq9YAb3YCfT1ANBLPx/4DdMcfJB97yUqoJaug93bIgjfhIFDhAj51OYy1V8V3agJDg8DQ4PDiM+Y7+4GtT0hbIxHAZgdOOT3jPTp8rp98BMSigMMB1MySiZQD/RM+HwBiTz8GPPekpKw43cDiFVIlJbFgz7ktUlP8o4PyRkJryRevnw311T+XFQvz+LuW9ny3Jz5JNDDpfZldHdCbfwIc/UQ2NDZDfemmCZ8/fPwxrkfaz4OB5D1k2ICmUyY8Rrb9w9csopmNdayniDUgp2a8GsIAxvzZnLVt7PcCG+tez3gNhwYlqPNUZqwNPeo5AydkGW2tAShAp5TlU0omFVbWQN30bRgtrdBmLJmTHU4G2eaBfZIvbbNJasnQgJTYq6oBqqolqA74pV29x0afpFISaGkT0ADWfj4ZXKeec+I4ZkwCY6Wk3dW1gN2RVgN7+FyjEXksdLK2t4Kcs2GM+Xyv14vuh/4V+PUvkv2SeNl2uYE5zcDJE/LlqJDAeyR3JXDFtcCrz0/6dy2boDDtesaiQN/x+HnZ5E2JzQZ87nrYvvCViffz8L3A0EnpDxW/FzzVUDd/Z8w3ATi3Rc4tFpF+SHRuvD9xyWXJn5/wpd9fQPL+itMyaMYAACAASURBVB9j5L2eba3zUq+JXur497Tw2OfZmUwd6wnWCCbKr7QawkrJd7sdesvmcX9GuTO7OhD7X99G7M+/JF+bvgWzqyPn/WW8TqGABLBjXLu05wT9EnCapgRjI4OeRBAZ8A8/Xxk2KE8VVP1sYHYTUF0jo8CvbJUgrsIpxw0EJHgNBuT/LjdQWQXUzIL69v8DrP6srOqYeqxYNH5MDbyyLfNJJ47j98uIemLBGf/QqHt0+FwDfmmDzS77hk7W9bbZ4+31Z77Hn3syHuzr9FUtgwHpv4BfzjNTUA3IY557Mm+/a2nPP9kvG01T+tJmkzcgz/xywvtMb9kcPxdDnmcY8u9QYLgtw8Frvw+orJbvzzwuQXPieozoz+Fz9/vjfZ9KSVtTjjHu+Y3TP3zNIiIG1lRcPd3D+bTDEjWEx/sZ5WR4RPDIx8kA7egh6If+OWPQY3Z1IHbXbYh99xb0fe9/ZA6MMl2nWEyCqlSp1y71Of0nIFHheA2PB2mZFqSx2aAqq6Ea5kiQ5XTHR5AhzzFs6W1xVAC+HqjZTTCuuBbq//5/4ztKaUMigA0HYf7XI9AfvCMrSib4emQ/sagsm4542kU0IgHh8aOj+ycaSR4jNUBOfE88P9M9nhowj5xE2X9CnpeymuQoWss+8vW7lvr8aCT5hiGRjmKzAzFz3ADT7OoADr4FRELSr4mJq0rJv+NtyRi8xmLA0FC8H4zk8xL9mTj3aCT9jQmQvPVSjjHu+Y3XP3zNIprxmGNNxeVtjAdDruS21BrC4/2MJi1tRDARgJhIjtaN9bF2ZTVMXy/0ow/AHPmxdqZraLONHhhMvXapz4lGJoyrobW0Y6JrP7spuV+tJQ0gGgZsKRMOI2HJvY5ThgHtdEtAZ7PJ8xKj50BKPnaD5GMvXSXPH+iXgNGMSXCttfw/vtS7Pn5UVqBsmCPpCXaHBIxKpQfYqf+2OzLf4043EBjKfM7RSPI8x6KU7CMcys/vWur1tDuAUDR5XED60+4YM8AcvtdU/J5MfHKQ2IfNlmxLT7eMVKdyOCSvevjNjpHen4lztzvkeqUG14l/ph5jvPMbr3+yfVwWmKtNVJ44Yk1FpdrWS7WHUDA+qhYcXnhkvJ9Rjnq6k4FHwogRwYSRI4PK5c74sXbG6+R0ywS2Ma5d2nNs9qwqfsDtmfDap+0XACorAcRzvZUh+dixmNSuTvWpyyXAMk15XCJn+pxFQPPp8pgTvcBLz0D/8yYJqocGZbEbbco+tZZUk8T+YzHJ8V61BgiFAJcrOfKO+P4T1yGRfuL2ZL7HrxijpnZiNNjtkfY73Zkf5/LIPiz4XUv9FCN2120wuzrSn19Tm3xwIscaWq6Fyz3quUDKvVZXnz7ybsakf53uZFu8jRKspnJXAjYD8Hji1yO9P4fP3ePB6Hdx8Rz31GOM7OYs+8eq16xM6S760QemlLJFRIVh27Rp06ZiNyJXAwMDxW4CPB4P/H5/sZtRtlRjM9DYLAt79PcB9V6o626E0dI67s/Y77nRndvjkwTN9JFSmw04ZR6MSy5PPvapn0tgEn+cYRgwlQL6+2Csu2b4cRmv0/U3y8huhms36jlBvwQghjF6lDuhoRHqj7854YjdqLbMnisT10IBGTX2zgGu+SqMRcukD+IpC+rMBXLoTz6Skd8KF/CZNhhf/BrUik8DF7RKYHyiT9rqj6cdhEMSCBrxvO45c4F110r5vkQ/9h4H3j+Q7He7QwL92U3JpdSVIcece2paPwHyGhM87SzoY0eATz6EdJJKpry43UDTqXKesSjgH0wf7W2YA3XTd2D79JXj/q7pwBCwvxPwHZfgcM3n5DkphgO+SFjuDf8gsKcdqmU5VMty2ffQIOCpSqav2OwycTQakzc2ZiztuWhsBra/KNscFUBFRfJxgHw6YLcDrzwH/Zv/lGsWDMj9YrPFg2wFXHZ1sv75iP4cPvejh+TxiU8lEm9M5p4KteEbw/0+8vVlvNeice+/MR43EfOn90kfJ9Jd7Ha5dw59kPY7Ot3wdb3w2OfZqa4eY4GxDFgVZIo4o7Y42O+5ybbqAgDE7rot7WNtu92O6NAgUFsH21/cbmm7Ypu+JXnJsVgyVSIWk4BidlNOZduyoaORZDAWiUz8eNMEPnw3WR87MTIOyGh1an1spUZXKYnER8yv/gqMRUtlJNnthhonPzr1Xs9XekC21SxG3hMAhlNfRt4Toyp3DA1IwJ7huQAy79dulxxy/4AEy4lJpU6XBNx5ui+K/foS++4tMlI9Mu9/aAC2O39ctHblW7H7fSZin2dnMlVBmGNNNM2MF3wZLa0wb/q21Anu/kQGP5tOzVjDV7Wtl2ALQaDCCR0M5C0VR33pprFL9sVi6R+HW1i6TNkdQJUDqKpJBtnx88z4eMMAzlwgI9xXfxl4cw/0nh3Au/vleTtfgd75ClDXAL1klWxPVCkBkuf2ylZZkCbSDwyehHa6AHcllNOZ8bgJRktrWh68VdLSfoD49+CovPuM+c1jTM4b2dbhYDHDc9VX/zztXksE9rDZZOQ7bU6ACUSiQFUNbJv+ZeonX4oszNUmosJiYE00jYyccJgpGM02ODNaWmFu2DgcpBtzT4V52RfyMoFq5LHgbZRzSB3hHCvYs0hakB1JjGSPE2Q7KoDFK6AWr4AePAl07ZSR7MMfAb5e4MXfygMdFZL64fZIyki8KkmC+fbelAVtZgPrroFx4cVQ9gK+PGcbME8l4BvnuZmuv2pbD/2zf5M3VqlzAgxDrsk0rrQx8k3t8CcInF9CVPIYWBNNI1mPPGYpNQivn+JHhhOlMUxmhDPflMMhlSaqE0G2XwLtRAm4kY+vqgEuvgzq4sugjx2RAPuNHRJIRsJAf1j+7XJLYN0wG8CIBW3clbJQzuMPwQwGYFxwIeDxoCDZelkGzMMBX9AnVUoi8fKCK1dPeIiJgsVMb/hi3sZkjfPUCiO2LCrElLGx3miwKghR6ePkxSli4n9xsN8zGznhEIAEPiMmHOZiKn0+1qQ3NDbLhK8MdOd2eVzqyG04BNR7CzqBS9lsUE4XVGUV4HBKUQkzOuZES1VZDXX2ecBFayWIPvR+sq5zNCrn4B+CPtEL7NkuP0tMUrPFJ6l1fwK1eIUs3/5GO0I/+Rfopx+TtJPqWWP2Wc6qZ8n10GZyQmA0CnXdjWnHSk5y3C2TEe0OoKpKJn2Ocy0Tz530xL7qWUBXh5RCBJIVRjxVUNffZH0/xJXC64tqbIZxyeUw1l0D45LL83aupaQU+n2mYZ9nZzKTFzliTTSdlGhuZi4j6aX4cbhyOgGnE1rPkjSRYEBK6WUYVVaGAbW6DWbTqcDLzwLHj0gwHvTLuex8RR6YGK32VEqgmpIqYh7YB/9v/zO5EErvcehH/g2xDRthW7LCsvOa1Ajp211AQ+OoiYbZfCoy2Rxxo6UV5s3fgf7Vw0D3YakX3ngq1Pqvc/SWiEoSA2uiaaQUg1EAWeXwZkoVURZ/HG5VVQ2llFT0cHmgzZiMLAf9UiZuBGPBIpmoGJfMx34dOPyxpJcMnpQvR4X0S8McefArW2UUOzFqX1Eh1/Q3v4A+/SwZ/Xe6pD1TPNesg94jH8v5xqLyRqB2lvRFnlJ0xmoXF1AholLEVJAp4scoxcF+z8yqOrqZTKXPJ0rrGK8+su26r/3/7L15eBz1lff7/VX1rqXVWixZtjEGbCcYYRsbDAYSwMaGBAKYIWFIeF+Ylxnm5r1Jntw3kzCXWXjvPCTkDpmQ3JDJDMyEDDOBDOCwTQjgsG+2EZYQNmCz402L1ZJ6X6p+949T1XtLvXdLOp/n0SO7VV11fqd+XX3q1Pd3TkUeh5ciRykEIRQIqw3C2UQBpqpSDebUFuip29vsEEuWQZx+LmSzG/jkvWSnR10j+3yTkEc+JYlFUwsSupNQiHTY46OQ7+2DVK0QriZ6v6JCqGpVx6oP9QOvPktSGLPrpNkRsmthzSQ61RqfCV9f6gP7vfawzwuDpSAMM4+pVkm2cpgpk17pRZe5qMUxhMUCWFqAppaCKosoZ5wLva0dePFJquMthFHuLwa8PUh2hwJGZ0ELZbUFKFPsmwQevx86jKx4wA9ptQFOJ+TvH6rKWOWT2ynQT11QqOuAfwri2v+z5P2WZEeVzyXDMEwpcGDNMEzVmVHDW0R95JIp4hilygzyvW+6IDtLKhKNAu8MUpb/vX2UyQ76U94hqLNhZk1sgDK4sSgwcpjGquvJUnWV8OfYMNDaRpKVqQm6AbBYAau9thKd1HMZDCRtGRuGPtSf9d65JhuZa+Nh6ke4/1VoD9zDc6mCsBSkTPgxSn1gv9eecn0+XZWDYiqA6EP90O+9E/LR++h9BVbJKPQYpcoMpnsfxoYhf3M35I5HIffvhfR0QrR35l70qKoQ3YsgVp8BnH4ubFJCGz6cXurPXDipqEAoAHH25vSxvvMmBZyKkpSkRCNAe1dZco2ED50uasduBtldPSXvt6yKMdEIMD6a9KOiAgf2pr23lP038vWl2jKYetLIfp+L6EP9iP3bzyAjkTk3lypNMVIQZeZNGIZhqovYuo0yuZEwBUmRcM5Fl4mgYtKb3gBnqL9ix0iTGZjVOCwWen0a8r5v+6/SbfZNAr+9F/LoIWrLnVkeMdXm5la0XPOnUP76DmDR0mSTGYACqykvMDUB/de/gNy7h7pHAsA5WygQj0aohJ5ZiWTjJshggBZcFok+1E9tyUcO0wLGgD+vD4uhFH8nzuXkeNJ3AoCnPeu9OfevxSDvuh3aTTdAu/3mguZPo1Dq/GSYTGguWXkuVRgOrBmGqTtK3zqIa24E3B4K3tweiByty8sJKgo9BsaGky3ITQqRUeR73/ChpM2hIHVlHB+FvOt2yP1vQbg9QFcPZX9ttvz7v+BSWhzp6QDauwxdsRFUvj0Ief8/Q/6/N0F/9NcQDgfwxa8ALW5aXNjiBi65GsoJK0k2MToMOTEOGQnP2IBGH+qH9r+/CfmzvwNGjlCmWgIYHwFUNbcPi6FIfydkENEw3VxoGunP27tIi5753sz9hwzpSCRc9M1ZQ1Dq/GSYTMaG08tmAjyXKgBrrBmGaQgKWnRZpha7oGOUWgs83/ukYWMwQLIFIahySCSc3m7eRbWsZTyelHrEYknbV6yCfsnVyfbnvccBG86HiEchB3cC771NgfvuFyF3v0iB5uozIC77KoRZvs9EStp/OAQoCqTDCThd1KY9hbQnBMKQlQT8tG9VBZpby9djFuHvhD0WC9DWYXTDjFPJP2dT7vdm7n9ygn5bbcmbs9m08LFBa9Uzs5DObloQbbEmX+O5VDacsWYYZvbQ2U0X/lQq/EVQqGSk0Pehu5dsnJqgQE5R6O9WW85su7BYqHtjxwKgcwGUFjcFsaDgWvmTb0P5X7fS71VrIFafAeW/fQPiL34AcdGVQM9i2tH4KPDsf0He8bfQ//nvIXe9ABkMZBuu6xT0HxuFHBuGDPgouEfKEwJdIxsUhcYwNVGxzFYx/s56YuFupz94x/O+N2v/sSgAQU8ITGZRlq7U+ckwmdBcivFcqjC8eLFMeLFFfWC/156G8HmBrbfLodRa4PneJ05eQzYHfMmgGpIkHXbntO3mhaKiydOOkFAomFSMGtm5Fj3aHRDHnQBxxueAVWsBmwOYOEZfllNeYP9bwKvPQB7+lKQTnk4IJSO3ouuJluuIRiCf/C3pukNBOq6pZ9Y0wOGsSHv5YvwtH70vXZNutQGqlTTkipLzvVn7l9QSHS2tyR1nLGJtiLmeh2rWqq83jez3uYjo7kXziSsRef/dOTeXKk0xixeFnElg18AcPny43iags7MTY2Nj9TZj3sF+rz2N4vNKlBqrdbkyfagf8q7bKci12pLShUgYcHugfufWvO/N5fdE+b5wML1aSAZS14EP36UqGvsG0rP9ziagbx3E6g3AkmW5uzf+649psaWUFKRDJLPurXk06lVEu/3mbBlEAT5MJU1OklpTPWUsjTLX5xvs99rDPi+M3t7CEzecsS4TvsOuD+z32tMoPp+ubF8h1KNcmejuBRYvIx10UzNlqgvMtufyu1BVCLsdwtyXouTMZAshINq7KGt+1vkQCxZS23XvGI3/0MfAG68Ag7toUZ/bQx0kDWRTK/DuEO3fZqf3aiRvEV+5ofaZrQo8sSgk49soc32+wX6vPezzwuCMdQ3hu736wH6vPXPF55XIepZKKZnyYvwuo5HkosQ8LdUBQPomgTd3Uyb76MH0Px53IsSaDcApp0E4m6Dv35tcMOnpBM7ZQk1trFaqUuJ0QpglAGtALZ42zJW5Pttgv9ce9nlhFJOx5qogDMPML2rR5TEP1W43L2x2wGaHbHFTNtfs9qhnZLJb3MDZmyHO3gx59BBVFRncRbKPT96H/OR94L/+E3LlKSQV+W/foHbtqcRiQGwS8E9B2u0UZNsdOSUllaTaPmQYhikHDqwZhplfzINyZcIsI2d3QMo2Cq5DIaP8X0aQ3bMIomcb5IWXZ+ux9w1A7hsAnE2Qfesok704Q48tJRAO0880pfsYhmHmAxxYMwwzrxBbt5HGGuH0xWtztMSUEIKyyQ4XdVwMG0F2LJq+naIAJ34W4sTPQl5qBNWDO4H33yH99a4XIHe9AHQsAFafQTWy27vSD2aW7gsGIFWVNOwOJ0RqnVyGYZg5DAfWDMPMK5S+ddCvubGmVUEaBaGoVGrO1Uy1qsNBKqWXUVlE2OzAmg0QazZk67GPjUA+8zjwzOOQGXrsNDQN8PsAvw/SagOcTgqya6jHZhiGqTUcWDMMM+9gnS41okFzK9DcChmLUoCdY9Fjlh574DXgzd059Nh9FGQvX5VDjx2lH5+hx3Y2QWS2UmbqQq1LTzLMXIcDa4ZhmHmOsNoAq40WPUbClMmO5NFjX3Ql5JYrgA8MPfbbph57D+S+PdSW/ZSZ9dhSVanJjMMFYWWpSD1Iq+nd1AJMeiF//U/Qa1yfnGHmEjMG1j//+c/xxhtvwO1240c/+hEA4N5770V/fz8sFgu6u7vx9a9/HU1N9Bjwt7/9LZ555hkoioLrr78ea9asAQAMDAzgl7/8JXRdx6ZNm3D55ZcDAEZGRnDHHXfA7/dj2bJl+MY3vgFLZraDYZiaUckMVqX2Veh+ZlP2TR/qh3zoHmDYKBvaswg4bSPQ/3LyNXc7Rpuboft9FIQKQZnlKjTGyfwbLrwcyvLPQv/lT4HBnckg22IFliyjsnt/dB2V+EvVYwdT9NgWK6TFAnT2AOd/kcr0mWgaEPBD37MTePlpwHsMcBlyknCIbFjZR3W0CziflWwcNOodg+7pLPj4tZqfae9PnQ9Ol3HTEsq533zHTWsRDxi/w/R6jT43qbaNL1wM7YTPJH0+w5yvxed9Nl1TmMZgxjrW+/btg8PhwJ133pkIrAcHB3HKKadAVVX8+7//OwDga1/7Gg4ePIif/OQn+P73vw+v14u/+7u/w09+8hMAwLe+9S381V/9FTo6OvCXf/mX+Na3voXFixfjH/7hH7BhwwacffbZ+Od//mccf/zx2LJlS0HGcx3r+Uu9/D7XL7LTdaVbcP7WonxeSIe7Su6n2OMVcy4rfd71oX7IX/4ECPoAYbQ513X6LUAtx3Utuxa1UIDOBfT3In2ZOGYkREGtqgJ2J8T13wKAnL5Dexewfyh7ZxYLNWu55Oq0YFlOTUD+4THgzV30/sz3nPhZ4Ngo1cQGgBZ3slGPplHDFoDqZcfjJDdxt9GxTJs2XpAV7OazP9U/M53D1PmjupqgjY8BUxMzHh8r+4BXnsn2XYHbFXoO0+Z3PA54R+kPTa1AYMrwW1fy7+bxD30CRIIk+0kZh7jmRsj/+EfKVGc+VQj4oN52d/qxM3wHoDI3MinnTfinICfGyeeqNTnG9q6sOV/UdaFEOyt1DWtkOIYpjGLqWCszbXDyySejubk57bXVq1dDVWkByooVKzA+ThfD3bt3Y+PGjbBarViwYAF6enrw3nvv4b333kNPTw+6u7thsViwceNG7N69G1JK7N27F2eeeSYA4LzzzsPu3bsLNp5hakniIjvpTX9sOtRfb9MqRloGyyzZZrHQ63nQh/qh3X4ztJtugHb7zQl/lLKvcmwq5njFnMtqnHf55HYKcIVCXQ1VFYA0fkCv5cp5SB2YGC/Jl/KheyiQ13WjU6MOBH2QD92T13c5g2qAAjctTo1jUo9x9BDw4X5Q63MlPWCLx41A8ygF0bpObdKDfkDTaaGjUOhnapIqkUACgUDSpngMeOKBrHMhH7pn2nNfyDlM9YEws6QCQDA47fHxxAP0euqxtRjwxIMZ2z1Ir5f4eUg7R77JpK8y/515/FiEfO2bJIlP6nE7u9Pb3ANZpSdz+u6u2yHvvBU4sA/wTwHDh0v6TMgnt5PvvMeAQx9DThyjOR4Mpo9rajLLX4V83sv97FbqGsbML8rWXDzzzDPYuHEjAGB8fBzLly9P/K29vT0RdHd0dCRe7+jowIEDB+Dz+eByuRJBeur2udixYwd27NgBALjtttvQ2dlZrvllY7FYGsKO+UY9/D7+zGPQ7XYIh5NesFohwyEozzyG9vO31tSWajHqHYNobk3TxUq1CdI7ltPn4f5X4f/NXSQPcHvoS/Y3d6G5tRW+afZVzLmbzqbU/RS6HVDcuazGeR/1jkHXNUBRk8GnGUhLSa/lfJgogHgMFoulaF8OjxyhIEVNqcqhARg5AiUWzek7LXs3ScJhCN8k2nt6ICMUnE2+9gx0qw26lIBFJXt1ncajaRQ00d7Tx+ubpAy9auR6dOPIigpocaiSbga0UADQdViajGSPcS60kSNQlyzLe+4LOYep80cI0I2DcXxTnhgPB7OOHx89AoSDsHQkSw/Gg0FA17K3CwZhSSlRWMw5TLUvrsXp5gigwFQxNOqGrebxFQC6WbtcCMB7DJYWd+K4LX/2Hfjv+lHyxiASBqSO5quug8OwKdN3ejQCPRSg49nsdH79UxCtbbAU+ZkYPnoQCPjJNlUFosZTjliEfG+O0RhXqr8K+byX+9kt5poyW+EYpvKUFVhv374dqqri3HPPBQDkU5Xker2U7lybN2/G5s2bE/9vhMcX/BilPtTD79qRg5T1SH3ErVqgHTk4Z+aA7unM3e7b04l4PJ41Tu2BeyhYs1gpcDJ+Tz5wDz3Oz7OvoiQlBe6n0O2A4s5lNc677umkzLOZPQaSwXTeoBqgjLZAPB4v2JeJR+GpdavNjHU8Rtv4poBolG6OTCLh6QcRj0F2LIAXKqRqA8JB6KPDJOtQVAqOFWNcqZIWRaUAO3WM8SiAlPGrxleTFgNUKzTT99EoYLEgHonQGBLbSmjBQN5zn/McRiPQ3h3C8A2XU4bWaiN9uN1BgbRqIbssNvJ34vjW5P8BkixEo+mvxaIUTKe+ZrEC0QjiBz8mv1usgMsFLOgtaB6lzW/VQoE/QJ8/07+qhY4ZiwKKAn30aPoNTCyK+NQkBbGeTviXLof+lT/Nkkr4ly6H37Apy3feY+mGGfNVBnyIFfuZiEZpLiiW5FikTuPRjSc4qpo8BynntJDPe7mf3WKuKbMVjmEKo6JSkHw899xz6O/vxze/+c1EkNzR0YFjx5IfuvHxcbS3t2e9fuzYMXg8HrS0tCAYDEIzaqia2zNMQ1LAY9PZjti6jb6EImH6Io6Ep2+eMjZMWatUjPbgRe+rTJuKOl4x57IK511s3QbYnckgQtNAugMj4ZBLW22iWgr2ZdqjcLMTYjxGfjKCalhtgMNBeuJJb5rvsKIv/85VJXF8YbFANLcC3b1ku9sNQFJwJCVlolUjWy4EPV63WNKlIpCGPzRAakbwL6n+tZTkc7PpjK4Z44jRgr0FvdOf+8xzGAoA46PkV1Oq4Zui7GkkTMkgp4vuY1yu5D5VFWjKqNfd1ESvpx5bVYDMut6qhcYXp6AX8SgwOUHa6wJIm98tbuPmRM/+t3l8GDcpmc15JsfTfKP0rYP6nVuh3nY31O/cmq0dzvSdOW9Sz50Q1OK+2M+EWQ3GnO+p0yGRrdaS2fQUuwv6vJf52a3UNYyZX5QUWA8MDOCRRx7B9773PdjtyS/V9evX45VXXkEsFsPIyAiOHDmCk046CSeeeCKOHDmCkZERxONxvPLKK1i/fj2EEFi1ahVee+01ABSsr1+/vjIjY5gKMx8uskrfOohrbqTMZcAHuD3TL9SZ5our6H2VaVMxxyvmXFbjvCt962jRYM9i4wUBLDoO+NIfA73H0Wuq8ShcNQJQxciiupoK9mWaRrStg7LFQLrUoq0DaPXQgrFIOM136l/cmju4ttqAi6/KOr7Yus14cmGjBWdCoWO1dwGfu4g6QEojG6kbgZ/DSYvu7I4UeUOcNOiKoH9PeWnx3ee2kg9MeUMkTNnZTZeS71paSY6U4Z+sc+g1JIfu9qR21tVEPnB7IP1TdJNwyVcoaDd8gov/iDLUaUG0lV5PmXe4+CoKaFO3i0WBpmbyja7T79Y20p0XOmfM+S11mjsLl1BwunAJ/V/qyeObi2GVlBsaIyNczOcwy3eqmtQ+mwGxTothi/5MLFxCPlAtySZFpp3mTYHFAoT8Wee0kM97uZ/dSl3DmPnFjFVB7rjjDuzbtw8+nw9utxtf/vKX8dvf/hbxeDyxqHH58uX4sz/7MwAkD3n22WehKAquu+46rF27FgDwxhtv4Fe/+hV0Xcf555+PbdtoYg8PD2eV27MWWNOUq4LMX7gqSO3J5fPZvGq+nlVBirHR8sxjiB05WNJxtZtuSK/6EAxQkBoJUzDZ6kmWuMtRDSLVjnJ8JU45DYiEoL+xE/iv3wDHRig72dENbLkiUVlEalp6fexU+YqrGehbT0H62wO08NHTSWX/Usv4KQpl4B0u6iCZy65JL91QNKUszE8Z/3TXl1JL6+HIp3TMGSpwVArtf38TGD5CQa/FcdxpgQAAIABJREFUSjcNigq4PVC/c2tR+8oq8+eboqx4IEAZbFUBLr4K6qVXF7/f1OvHoY8ACDrHBczLom2fZ9fsQuAYpjCKkYLMGFg3MhxYz1/Y77Unn8/5i6u6FDPXs4I5/1TyUbpJJEyBpduT/XoJQVexTNdKPW27SDhZH/uDd9M12Z3dEKs3AGvOgGjryLuPhHTE4UrrBqndfnNu7awx/mpcX2Y6ZqWp5k1vtWrdi3AQ0mrP1vrXYF7OV/i7tDA4sK4hPCnrA/u99rDP60Ohfs8ZSAUDFJA2NWfXWC6jpnKlkJEw6Z1zdHlM227SC7y5mzLZIxnX/eOXQ6w+AzhlXbL6Qy6sNtJrO5yQewemDTrzPp0pt7lLjZ/uzLab3uaPD2DyF39f93k5n+DremFwYF1DeFLWB/Z77WGf14dC/Z43I2q2q84Irhop6JK6ZrQ6D1KliHzbSQkcPUgB9pu7KSNvYrEAn1lNrdRPOhkitaxgKkIAVhv0D94Fnv0vkqVkjD/T5xVtdtQgPm9EOjs7MfLsk+yjGsLX9cLgwLqG8KSsD+z32sM+rw8FB9aZemqgqhreUigksJTmwsVQMLt7Y+p2aXrsPVSVwqSJ9Nhi9QZg0dL85V2FoEDZ4aTGMMbiyUyf11rGMV/ha0ztYZ8XRjGBddkNYhiGYZgGoLM7O/hroHKQaVnf1C54mZUcLBbA0gI0tUDGYiQVCYeyShAKVQWWnwyx/GTIyB8D+/ZQkP3hfiqb99pzkK89R+PPp8c2K0VEwoAQkHYHabIzGRsmm1MxykoyhcHZema+wIE1wzDMHEBs3UaBK8LpcoUGKQeZVvoPMH6H6fU8AZawWgFrG6RZnzkUzNm4RtgdwNqzINaelaLHfg0YOQKMDUP+4VHgD49CHr+cpCKrTsvWY0tJAXw4hLgqIENhWvRotTb8TUujU+hNFcPMBTiwZhiGmQMofeugX3Nj42YFy8j6CrPetcNJEpBwEPrALuD5JwDvWFrZPeH2AOduAc65EDhykKqKmHrsjw5AfnQAeOw+SDOw7loInLs1vWSfplHWO+CHtFqBz18MPPSrpM0NdtPS6JRyU8UwsxUOrBmGYeYISt+6xg1UKpT1FaoK/YP9wOO/MTohtlBd5cfvh37J1YkAWQgB9C6B6F0CueUK4IN3SCqydw+1Aw/4aYfB94Ajn0LfdCnEmedn67FjMShLlkH/wlXAy09TS++uHoiLrmycm5ZGh6U0zDyCA2uGYRim6lRSqpKVAVUtJON4+WkgNfNsHltVgeWrIJavgj75I6oEEo2kd3D83QOQu14E1pwB7XMXAiL961FZsSp93zY7ZDAAOBwQSp4KJAzBUhpmHsGBNcMwTIk00oKs6WxpBDsrKlXJzICaUpFJL9C5AAiFqHRfrgY0k+NAi5veo8WBYJBaZsfjwNhRyB2PYmLHo1QfO58eG0gG5j4BabNTjWy7E/KtN6YdYyOci1rT6Pp/hqkkXG6vTLhUTX1gv9ce9nk6tWr4UYjf02zR4sCEF9BiwMIlwLqzG6IZTCUptPydjESASNCoKkJfdfq//hjwTZIvUt9rdwDHL89RH9sKfObUmetjA9AP7AMev5/eY3dQS/YUX9ejSUyjUMgNBV9jag/7vDC43B7DMEyVaaQFWQlbdI0W80EAigqMHgWeeABoaqXaznW2s1IUmgEVdjtgt0O2tFHwHA7SwsbH7qf3WG0U/Oo6sOlLUFasgtxyBZqHP4XvpT8A7wxSfey3+iHf6geamiH7Tqcgu/e4bD32i08CimLc4Gj0W+oJXzfSnKk1Da3/Z5gKwoE1wzCMQVGP6RtpQZZpy/BhUFCtkHZY0+h3KAC4PfW3s0IUKytJrSqinL0JurMJePphYHw0raIIQHps26q1UHqPhwyHgH0DVFkkUR/7WcjXngU6e4A1ZwCrN0C0tdOBvGOAs8k4qqQsuaICw4chpyboRqe5Nd24WX4uGIZJhwNrhmEYlFBrt5EWZJm2xGNUKQOggNpipd+pXQnraGcl9cWlZkCFokJdfzaw/mzIeIxqY4dDOfXYwuEETjsL4rSzICfHgcHdVFlk9EhCj40dj0IuW0FdHt0eCr5TZSaxKODpAILGzY1vioJ8YdwA8SI+hplTKPU2gGEYphFIe0wvBP22WOj1HIit22jBWyScrCxRgQVZ+lA/tNtvhnbTDdBuvxnh/ldnfE/CFkWlAFHXyabWNqCpiYLtCttZLIkbl0lv+o3LUH9N7UhFWKwQLW6Irh4Kfs2AN9e27naIz22F+MZfQ/wffwmcdUHyicWH+yEfvhc4+BGNzz9F5yAaofNxzhba7pwtpIEPB+kmKOAHolFg06W1GTDDMFVHveWWW26ptxGl4vP56m0CXC4XgsFgvc2Yd7Dfa89c97l89D5qZ50aWKkqMDkOZfOXsrYX3b1Ad68RTI0D7Z0QV1xb1iK0RPAZi5ItQT/i/a9A71pIx8tDwpZP3wd8E1R+rq2DbhQggAu+SMFehewsBf3eO2lc5o1LNAJMeYFdL0C+8ybQ0jbtGIs+3lA/9HvvhHz0Psoyz7B/YbFQhtrVhKbWVoSCgdxZbCEoGF++CjjrAogly+iGZXyUgmZdo5uXgI/8f/ZmiNWn0/s6FkB2dAPDh2gBpdsDbP4SlONPosy5rgFCQKjz82HyXL/GNCLs88JoaWmZeSMDrgpSJryitj6w32vPXPd5oZUmam2DGo9Ba24t2IZGLeem3XQDZXiFIFnE+Cj9W9eBBQsrWh2j3Oob5lyX8Xiyy+MLv8/q8pgK6bH3UBD/4f70HXb1QKw5E1h9OoS7feYBqCrNAYcTIlVWUidqNafm+jWmESnG5416bakFXBWEYZiKkHohHV+4GPoFl87ZC2lD1NrNtSDS7ihqcVvDVl9I1aRPTSSfDFhtFa+OUanqG8Jigf7hAeC//hNQFTo3YyPAff8E3e6gGwKzlbrDCZy2EeK0jZAT48DgLlr0OHoUGD0K+fTDwI5HII9fTkH2qrUQqTdxqWga3XwEA5B1DrKLXnvAzEl4HhQOa6wZhslJpiZW9x6ruya2mih96yCuudFYgOYD3J7a1xfu7KaAPpVIeE4sbkvTpMdjJJ+ABNxttEElq2OMDacvICxj/4kg3eEiPXTAR5KNaJTkHI/fD33/3rT3iLZ2iM9fBPGNv4H485uAs86ncodSkh77t/8G+cPvQv/Pf4Hc/xZkrkY2JmaQPT4GOXoUcmoCMnOOVJFi1x4wcxOeB4XDGWuGYXKSmfUTDiegaXO65m69s705s+ZSnxMd6rJK5AkF8LQny9NVsjpGJSu2pD5FmJqgSh6KQgGvq4m6PL70VO5W6kIAi5ZCLFoKufVK4L19JBV5502q1DL0OuTQ60BzK2TfeqqPvXBJdn1sk8xMtlFCUFhtxY+rlPGbcInA+QfPg4LhwJphmNzwhbTm5KrP3HzVdfAvXV5v0yqCeeOSeBqiqJTFrbDspqKyntQgPR6joFrXqZShUGiR6aSXnnSEApTJzmWTqgIr+yBW9pEee+8bFGR/dIAWlr76DOSrz5C8ZPUGYPUZEKm1xzPRNKoqEvBXN8hupLKSTP3geVAwXBWkTHhFbX1gv1cfObATCPqNyhKAoijQwyGgvRPKxk11tm7uIrp7oWzcBGXzl6Bs3ITWk1bOublejYoqldx/2vWlpQ0Y3A1IHYiGqfKHAJXns9oouGjvgvL5iyCcTcmSfVrckLvksM9iheg9DuK0s6hOdlMzMDVJn7eAH/jgHQq0PzpA+2jvgrBMkweTkiquhIL0o8UrV10kdfyqmrxJueLailZxAfi6Xg8K9nkN50EjwlVBagivYq4P7Pfqk1lZQdXi0CKR2uuO5zk812tPps8Ti3gPfQJEgtQ9saVt2moj0qwZHgrS7xmQUgKHP6Eb2qHdFGCbWK3AZ1ZDrD0TOOEzlP0uBHPho91J7d1LhKuCzF24KkhhFFMVhAPrMuELQX1gv9eG1AupdeFixOdwVZBGhed67ZnO56UEF1LTqClMKEgLOGdAalqKHnsw/T3NrcCpp1Onx4WL8+uxM1EUwOEA7K6yguxqwnO99rDPC4MD6xrCk7I+sN9rz3zzeaNkZ+ab3xuBavpcRiMUZIdDgD7z12+WHjuVBQspwJ5Jj51JgwbZPNdrD/u8MDiwriE8KetDqX5vlGBpNlL0I8PtvwKOHqIXunshrrxuWl9X+twUs7+0R/2akR2Mx2jxZqvxyD/gp9JwoWDa/tKO43SR3jUcqtj8av74ACYfuCfvOEoa59hwUgscChpdHgNU9QIAehZBbPvvJdmuPXY/8PQjQCQE2J3AhZdBvfTq/HZU6XOYOMaRT0mKEYvSYskC5mK1rutZ/td18r+nI2fTmUyk91iyPnbqImIhgO5FNGdjUaC9K7E/ff9eqlqSr7lNEUH2TOet3PNajN+z5tmppwMTxyoyp+b69wQ/iSyeYgJrXrxYJrzYoj6U4vdc7aIxuJu+aOfB4otyKdTn+lA/5D0/pc56AH3p+yeBvXuA3uNy+rrS56aY/SW2HR+hGsXxmFFnWaf3W20ULE95gWCQghZjfzIUAH73IG0HCYweoQoPzmZ6rcz5pQ/1I/ZvP4OMRHKOo6RxxqI0nrGjZKtqpQAiFEg2bfFPAvsG8p6vfGiP3Q88/htAj1Nb9XgM2L8XEoCy8pSiz02pJI7hn6RFgYm62aBzPM1cBADl7UGE7v4Haof+8g7I534H+fvtBbVGn9GmxFw5SrY0tdDN3DtDkF09EO1defchnC6I45cDGz4PseIU0l6Pj9E+/VN0cxSJ0Lnc/xZkJAy8+KTRSt5JQfy7Q5Ad3RAdC2inUlLpv3CQ3q9pAATk24NpLeHlsdHkXC9zLuaj0GtM1jyLRYGDH9L42trLmlNz/Xsic3wiGIA+sHPOjK9aFLN4kRvEMPMGLnBfG+ST2+kLTii0eEpR6N+RUF5fV/rcFLM/+eR2QItRUAEkg0uzgcnUhNEpUKHGICn7w9OPJI8zNUnbCIUah1RgftE4rHnHUfQ4zW19Gbaa6MaKf6EAoWDxtj/9CFXMUC1kj2qh/z/9SG47qvQ5TBwjGAQgQUaAzukMc1Ef6of/rh9RaTFFoYz30YP0PrPbXAlNktLGnTlXHE7AZgNee5ay1+bThDwIISAWHw/li1+B+O5tVAEl0RDHWDTpnwKe+53xWTT2ZbPT+X3pqdw71nUgGIC+83nIe++koN3ZRL544kH6nFRgLpZN5jwzb5rMsZZx7Ln+PZE5PuFwzqnxNQJcx5qZP3Bd5towNkwZuNTyYEJQJiyfryt9borZ39gwEAjkLo2maQBiyf9brOn7i4QAWw/9Px6joEVK+ne5YzBtc3sMO3KMo9hxmtua9ZiFSNoKJH2gKLRgrljbIyEKdlJRVHo9lx0z2Vwq5jHMTLUQFF+b/84zF/Whfsi7bocWDQMWm3EjZeSffJNAzyKU3Ho90/+qSj6Oh6ksoMUC+H3U5tzugNQ1khSFgpRRzoNQVcpMdyyg8YWCRj1toztjOEg/FisFyU4nyUKm46WnyD6rlXygGLb6/UBripY79bwd+gSIUZUUWKwkoXK6qnN9zZxn5ryVem7bimGuf0/M9fE1ABxYM/MHLnBfGzq7KSOn6xSgAfTFp6r5fV3pc1PM/jq7Ae+x9MxXKhYLva7Fk+23zf3ZncZvBwUTpj7bDMDLnV+d3ZR5TA3oU/dZ7DjNbU1bzQwuZDLoBIzMtaV42+1OqvWcGvToGr2ey46ZbC4V8xgWIzA0T6t5jnPMxcQj8kiY/q7FKQC2WMhH5d4sZfo/FiE/A8aNTAzQNehD/VD61kEoKuBqBlzNkLEYBcvhUPI9qXg6KfC32al1elMzBdhTEwAk3UjEY4Bvgn4cLsg9rwInr6VAPhPvWLIjJkD7sBjSnphxU6YIaobT2U0Z/EjQ+MwbvhsfBVrclE2vNJnzzDyvIuUhfKlzqkbfE6XouCui/ebvwarDUhBm3iC2bqNsSiRMF+FIuKLd3hhCbN1mLOLT6Qtd1+nfdmdeX1f63BSzP7F1G6CmXArN4FoIAAKw2oGuHqCpNdkp0NgfLrwseZxWN41T6hRQVGB+0ThiecdR9DjNbVsybDUxW3VLnfSXxdp+4WUUxJpBuxan/194WW47qvQ5TBzD5QJpBlLOaZ65mHhEbnYuNDP6mkZ2lnmzlDbuVncyQDZv3ISg1uY5HskLqxWitY3mYVt7elAEAOdsITujkWQnSwD4/EVUb9vdTkG6eeMUDkJu/zfIH34P+gO/hDywj0r8mXg6DS14Cg4XfU7MJjnBAI3lcxdBPvEglQE0A1zFuFkL+Kpzfc2cZ+a4zMXDZcypWszPxE3cpJeyxwVIjEp5Ty4yxyfDIf4erDC8eLFMePFifSjF79Xu9jbXKdTnorsX6D2OFhMFjc9ozyKIa/48r68rfW6K2Z/o7oXUJfDBuxTsCCOgsliBS74C9Zt/A+W8LxhjSt+feu6W5HECfgpImlspGK7A/BLdvWg+cSUi77+bcxzFjjOxbdAPtHVQUK3rtCDTYqWATBFAz2KIPy6+EZCy8hQKYT9+P7lg7uIr06qC1OJzmDjG0YPJIFMa2dQ8c1E+eh8FZqpK2V4pKSbXdZoP7nbaR4nd5tLGHfAnM64S5HtPhxEwjUPZ/KXc+xCCujY6XZRRVkn3LzydkB3dwPAhyly724HNl0FZfzZkZzctqo1FgJ7FwJqz6DjeUZqnw4eAwV3A6y9B+iaB5haqMPLuUNJnsSj54MzzKKBOPcYJKyF3PEKBu9VGWWxNo0WxTifUa/9nwT4q9BqTc56tOxuw28ueU7WYn/q9dxp2Gzpui4V8ffCjvF1tS3lPLjLHZ+nqgfzSNfw9OAPcebGGcLm9+sB+rz1z3eeNWmJrrvu9UdBuvznxiFyJhKF7j1EgY7FQpniGEorFzp/U4yWIhAG3B+p3bi3K9mJrYwOADAWpPvbgrhz1sXuBxcdTQO6bzF2mLwX9X3+clKIAFPjFooC7Hep3f1DwOObLXNduuoFublIXqErK8Ku33V2x9xTCfPF5uRRTbo811gzDMAAFQQ0QSDP1QWzdRo/aEYZwGfriPO3KM0k8prdY0h/TT/Pe1OPBZk+2Ry9FvmCzAzY7ZLM7ZcFjNGu7nDWt/8f/ZdTH3knlBI+NACOH6UcI4ISV1IRm6Yn5DThnC/D4/TQGq41+axpw5vmQo0dJRuJwQJgym/lOKTpn1kbPGlgKUiYsBakP7Pfawz6vD+z32pD6iFxMeSHbOgqWAJTymL4akgMhBITVRjcGZsk+Q4es799LwW+OmtbK4qWg+tjnQSxfRfZ7jfrY3jHg7UHg1WchR47STYCnI62VuuhYkFuKsmKVUSc7alQrMRc4CghVzbJ/3sz1ljaqjS2N8pbmTdV0EqNS3lMA88bnZcJSkBrCj1HqA/u99rDP6wP7vfZk+nwmmUfWY/pQAJjwAvEosHxVdTtLziA9kcYCPP2Ov6WMpy2lu2I0ArS4ofzJt7PfF48DB/aSVOSdN5MVbwBaR7D6DIjVGyAWLi5tAKpKwb/Dmchkz6e5XreqIBnMJ5+XA0tBGIZhGKYCFCTzSH1MHwpQqTkpSRZRgCykKjYZCCEogJ0YpwWGUhoVYQz78tS0FhYL8NnVEJ9dTR1G33qDWql//D6VgHx5B3Wl7F4EsWYDcOrpkEcPTd8+PRVNo0WcAT+kqlIJQHdrRfwzGyhFesZytdkBB9YMwzBMQ9IIC0rTOtUBxu/0JjFpeukJr1GyUVAzlRzb18KmLNI0ukbZyHCQAuAZEM4m4PRzIU4/F9I7BgzsoiD72AgwfIiO+9RvqcqJw0nBvm8SePx+6JdcnT+4NtE0IOCDNnIU0udLZrJT67czzCyBA2uGYZgq0AhB4WxGe+x+o422Rh0ANa3imd+CKKBTndK3Dvo1N9L5HjlMmeBWD2AugqxWZ8lpbMok52JJXQKXXE3dPYOBnAses/bj6QTO/wJw3sXAwY8owH7zdcrUx2OAPwYEjODYagN+/xD0jCw2gPyZ7Xgc8PsAvw/SaqUbAbsTwspBNjM74AYxDMMwFaZSzRzmK/pQP/DEA9Q1UVUpuPZNAvFYzgYqVaWzO1kL2yRHNQalbx2VyVu+ioJFV9O029fCpkz7xDU3UhAd8AFuD8Q1N0I9dT2E0wXR0UVt0V0uqmU+A0IIiCXLoFxyNcR3b6Nujw6jw6bZWn1qgkr2HT1Itbp9k8D2fwO2/4r+7WxKZrb3780+SCxGQfaxEcjRo5C+SSotyDANDGesGYZhKkxJj+qZBPLJ7YCmkw8BWhSo65QVrWTmtwCKLYtXyTJ6lbLJZCaNrrBaAatnxrJ9We+zWCAX9FKQ3NZhVAAJJIN/syKI2WJeUSjAB5L2v/QUsOGc/AdJ1WQrCuBwAHYXhN2e/z0MUwc4sGYYhqk0JTyqL4dGkZ1UzI6x4fQgDKDgOhIBlABV4ajRONNkHgWMq9jt85HLlwCSr5ntuwO+ivtCKApl3F1NkLEoBckzNZ8xa1kD9F6rlex0uCg41+IkFQHoJunYCGWsTclIyiLKnPW2U3Xaug4Eg0AwyEH2LKFRrlG1gMvtlQmXqqkP7Pfawz4vnEp21ZvJ72kVIlKzlzXWIlfSDu32m0mr7JsEICi4jkUpkPR0UE3fKo6z3nNdH+qHvOenlOXV4rQo0GqhNuFNzXn9W83gReq6kcUOkEQjl92ZAXEwQPZbbXT+ggEg6E9/kxCJ2tjt//ffY3z3KxSgq2ryfZoGFLIIUlGSCx9tHGQXQi3meqNco8qhmHJ7rLFmGIapMGLrNlqEFQlTMBgJV1wOYJImOxGCflssNdciV9IOsXUbBZEtbkBRyZcA0NRKiwLrOM5aILf/CghMUVk8s9lMMACE/Hn9W21dv1AUCFcTRMcCoKMrpxZbWbEKyp98G8r/upVqY2+5goLiWJSCZFcT4Goh283A1/x8HD0E71//T+DR/6Dx2uzJoFtVKWCfCd3w0/gYabKnJliT3QA0yjWqVnBgzTAMU2HyLRSrSnZmbDi96QdQVdlJLexI+G9BL9DSCiw/mYLsjq6K7L/hOXoIiUw9kPwdj6dvlzL+WgYvwmqDaPUAnT1Aq5tkHzlQVqyiqiMtbsp0t7iBK/878OUbgEVLgdY2WjDZtZDGMOmlG4OJcWDkCNXL1rRp623nRdOyg+wIB9l1oVGuUTWCNdYMwzBVoGbNHNLqExtUugpFHezI9F9OeU09xlkrxMyVOdLGXyVd/3TyEtJiNwOu5rxabGXFKiCXhCPjNTk+Csf+IYSefJi02PEYVRWZmqDAuq0dMhopTeJhBtnBQIom2wnY7Gmt2Zkq0SjXqBrBGWuGYZhZTC1lJ/W0o1HGWRO6e0kOoRsdEnWdstaKkn/8JZTgm4li5CXpWew2wGYr6liivQuui68Erv4zymw7nIAwQpRYFBg9CvnD70F/6B7I998mzXdJgzIWPnqPAaNHICfGIcPB0vfHzMi8+uwCUG+55ZZb6m1Eqfh8vnqbAJfLhWAwWG8z5h3s99rDPq8PM/lddPdSIHbwI2ByHGjvhLji2povCqq2HbUcZ93nekc3sHcPVUXRddIYO5uBrVeQPCLX+FvagMHdFJCranKB2BXXku9KQL/3TgpqTXmJqfc++BGUjZtyvkcIQUG2WfFDKDSOAuokOJ1ORJpaIbsWkvRD1wB3O0mA/D7KYh89BAzsBN54BdI/BbS0QjSX2ApdggK+cJgy2nGjtKCizptMdi3meqNco8qhpaVl5o0MWArCMAwzy6mZ7KQKdhRTyaJRxlltlL510K//Vu5ye+8O5X9PBcr8pVGmvERYrECLFWhphYyESSoSicwYZOeSj8hgANj7BuTAa8AnH5BE5KWnIV96GrJnMcSaDcCpp0O0uIsaYvIAkgLscBgQAtJupxsDm4MkL0xZzJfPLsDl9sqm3mWZ5ivs99rDPq8Pc9nvjVqGqxF9Xg9fVbJspInUtZTmM+ll+zweD7xe78z7GB8FBnZCDu4CxkeTfxACOPGzFGR/dnVlSu6ZC0EdTsDumHOZ7Eac641IMeX2OGPNMAzD1AXuUFk49fBVNbpICkVNWfAYA8JGV8YiNM6ivQu44BLg/C8Cn35IWey3+mk/7+2DfG8fYLNDrloLsXoDsGxF6VlnKelGIBwCFAFpm7tBNlMZOLBmGIZh6kONO1TOaurgq6rIS1KgFupuyOZWIBKCSM2MF/J+IYDjToA47gTIL1wF7N8LObAT2D9ENwF7XoPc8xrQ2gZ56hkQa86A6F5UusF6RpBtdxpyEa4uwiThwJphGIapD/OsDFdZ1MlXtdDGCiEAhwtqZycQ1yjzXGwW22IFTl4DcfIayKAfeKsfcmAX8Kmpx34K8qWnSI+99kygb33pemyAgmzTTjPItjs4k81wYM0wDMPUh2pIDeYq88VXtOAxmcVGMJhdRnCmfbiagTM+D3HG5yGPjZAWe2AnVRo5ehDyiQeBJ7dDmnrsz6yGKLI8YBqZQTbLReY1HFgzDMMwdaHaUoO5xHzzlZnFhsMFGY9T0BoOUrOXYvbTsQDigksgz/8i8MkHkIM7gaHXSc5xYC/kgb2A3QF58loKso9fXl4VkEy5iM1BDWm4usi8gQNrhmEYpm5UQ2pQTAm/2cR8KlmWirBYqLV9kWX70vYhBLD0RIilJ5Ie+923KMje/xZVOtnzKuSeVwG3x9Bjb4BYsLA8w1ODbCEgbXajwoiDFnEycxIOrBmGKZq5Grgws5+0snSp3QLrXMKPqQzC0DFLXQNCIQqy4/Hi9mGxAqvWQqxaS3rsoX4Ksj/9kHTsLz4J+eKTkL1LqKrIqaeX3oTGxOw4GAkDU4C02Qy5iBNC5SB7LjFjYP3zn/8cb7zxBtxuN370ox8BAPx+P3784x9jdHQUXV2q9HGIAAAgAElEQVRd+Pa3v43m5mZIKfHLX/4Se/bsgd1ux9e//nWccMIJAIDnnnsO27dvBwBs27YN5513HgDggw8+wJ133oloNIq1a9fi+uuvZ00SwzQwHLgwjQyX8JsfCEUFmpqBpmbIaISkIpEQZYmL2Y+rGdjweYgNhh57YCcwuJNanh/+FPLwp+l67M+uhrCWocc2iUbpB5OQVltSk23hfOdsZ8YzeN555+Giiy7CnXfemXjt4YcfRl9fHy6//HI8/PDDePjhh/G1r30Ne/bswdGjR/HTn/4UBw4cwN13343vf//78Pv9ePDBB3HbbbcBAG666SasX78ezc3NuOuuu3DjjTdi+fLl+MEPfoCBgQGsXbu2eiNmGKYsOHCpD9M9JWjkJwg1ty1fWbpDn1DDk8xOhkXYVq2xFLPfxLaHPgG0OGC1AguXlDSeWpJrjEC6veGrrgOWLp/xfZljEjY71a3W3SnNZ6JF2yg6FkBsuhTygkuAT96nIPut/mw9tlkfu1w9tkksCsSi0PtfAV5+moL6rh6Ii66syfnL5+NqzPdGvlZVCvWWW265ZboNurq6EIvF8PLLL2Pr1q0AgH/5l3/BddddB6fTie7ubvz617/GxRdfjMceewzr16/H0qVL0dHRgUcffRRnnnkmhoaGoCgKzjrrLNhsNhw8eBCapqGlpQU7duzAV7/6VQghIITA4OAg1q0rzMk+n69sB5SLy+VCMBistxnzDvZ77TF9Lh+9D3C6qCOZiaoCk+NQNn+pfgbOUVwuF/w7X6SnBLEo+T7oBwZ3A929kCNH8v5NdBfeLawaJJ5u1NA2ObCTjpOa+ZuaAEJ+QFGTdux6ERjcBehalm1Ny07Kur5UayzF7DexrW8SCPgosI5FgXgMeOPVvONpyHmQw//x/legdy1M2Jv2PimB4UPAa89CvvEK0LEga1xCCAirDcLVBNidgAD5qMj+0kIIiLZ2iM+cCpx1AcTCxVQG0DtG3SKPHAQGXiNdtt8HtLghMm/mivXR/r3A4/fTWO0OOr8DuyDbOiC6F1ZNk628PYjwL3+aNf9kKAD87sGKzvd6XA8qRUtL4ee3pFutyclJeDweANSCdGpqCgAwPj6Ozs7OxHYdHR0YHx/H+Pg4Ojo6Eq+3t7fnfN3cnmGYBqazO7v8FdcerippTwnMFssWC+ST26f9W72ph21i6zbS3EbCSV1rwAc0t6bbETEymwXaVq2xFLPfxLahIG2rWgChUEm6IsdTS3KOMae91jR7E+/TjKBW12m8w3QzqQ/15z2msFohWtuAroWA2wOUWE5PWK0Qq06D8tU/h/jubRCXXA0sWUZ/NPXY/9//A/0ffwD56jOQ/qmSjoOXnqIEhc1O/rDZAVUBnn4YGBshmUrABxmPzbyvIgg+/B855x+efqTi872Rr1WVpKJiHpljhW4+vbQQIuf207Fjxw7s2LEDAHDbbbelBfH1wmKxNIQd8w32e+0xfR6+6jr47/oRZcnsDiOA0dF81XVw8DmpOBaLBYp3DKK5Ne16KtUmSO8YAOT9Wy0/I+H+VxF8+D+gjRyBumAhXJd/Fb5p7K6abedvRbi1Nc2W2NQEBXG+KQiLFaKtHbquAZL8m2lbruvLaJXGMuodgxQKMHwYMh6DsFghHQ7g2AjkzTcmfOlYd1bCBm1sGFAUCk4UhbKykHnHU+9rZS7fxXP4HxYVSoq95vv0w59CKgqNVUpA16Ha7VCeeQzt528t2A4Zi0EG/dCDgaKazyTweIBFS4CLLoc2fBiR3S8hsvtF6MdGgcOfQB7+BPj9Q1AWL4OMhqFHIrB0LoBj85dgX7Vm2l2PT3ohXM3p88uhQk56E4lMAIAWg1AA4WyCcDipe2UZjI0cgZpjXmsjR6C6mio636v1GWo0Sgqs3W43vF462V6vF62ttFq2o6MDY2Njie2OHTsGj8eD9vZ27Nu3L/H6+Pg4Tj75ZHR0dODYsWNp27e3t+c97ubNm7F58+bE/1OPVS86Ozsbwo75Bvu99iR8vnQ59K/8aZZOzr90Ofx8TipOZ2cndE9ndte9SBjwGF9Gef5WzmekaN2vuaDV4YI+NoLJX/w9YLcDwUDFbZuRpcuBb90CASA+1A+8+30KpBQVMh6DHDlCEgQA8YMfA+42wNmUsC0ej2fZN905KMvPVhtw9CBlYoWAjEWoXrNqgZ7iy6lrboQ0bVAtFEwrCo1LtQBSByQQT62QUQtfF4Du6QRGDlNmPR4DLEYwqKhp9qrxGPQUexM+j0XTgmqoFmiqBdqRgyWNTVrshhY7YCwgLAGbEzj7QsiNmyEy9NjaJ+/TNkIgHvTDf+/P4b/8WigrT8lvk9sD6ZukTLVJNAK4Kc7Ki9WarC5SwsJHZcFCxMZGsue13QGtwp/dan2GakFvb+FSlZKkIOvXr8fzzz8PAHj++edx+umnJ15/4YUXIKXE/v374XK54PF4sGbNGgwODsLv98Pv92NwcBBr1qyBx+OB0+nE/v37IaXECy+8gPXr15diEsMwNUTpWwf1O7dCve1uqN+5dc4tPmk0csobjK570/2tVBKB8qQ3vfJLnkfv+R7xQoiK21Ys8sntJAMRwqh7LBNBNRQViEeBYyPAlHda26rhZ9qxSP+3mUk1M9Ipj8sTNjhdZIMWp4Da5SJNsdNVV1/nZWUfMDlBvlYU+h3XAKslw95Ymr2J8apqMqiGpBuhMuRnQggIpwuivQvoXEDVRUpchCiEgFh6EpTLvgrx3R8CCxYmg2NzXP4p4L5/gv70w3RTl4tztpDkJWrU545G6P/nbJnegFgM8E0BY8MpcpHCyw+6Lv9qznmNCy+r+Hyv2meowZhx8eIdd9yB3/zmNzh27Bh27NgBl8uFTZs24ZFHHsFDDz0En8+H66+/HjabDT09Pdi/fz/uueceDAwM4MYbb0R7eztsNhucTid+9rOf4Q9/+AOuvPJKrFy5EgCwbNky/OIXv8Djjz+Ok046CV/4whcKLrfHixfnL+z32sM+rw8ulwuhljaguxc4+BEwOQ60d0JccS2UvnW06CfP30pFv/fO5CIqIShIljpw8CMoGzdlbZ93QWswAPHVP6+obcUiH70PaHYDVhtlJ2OGRlVRgY4F9H+jm5+47ptQ+tblnOvV8DMAyN8/BLiaDTviVC5OVWnBXWsbbWQsDla/+udkw9GDVMNZUShb2bMY4o+up3JwdfR1PuRj91GmWtfJ1xYbNXxpbaMfw97Wa7+O2IpkVjfh84/fA3wTgGIBPB2UoY/HIa64tuxFb0JRqTa2q5kCfdPGUvalqpAvPQW0euiG1GLsT9fo8/Px+8Cu5yHfHSJ/eDqoogmoIons6KYFmr5JwN0ObL4MyopVhRug6xSQB80GOvSUZrrKJa0nrUSwpS1r3qjnbqn4fK/WZ6gWFLN4Uchihc4NxOHDh+ttAksS6gT7vfawz+tDPfyu3XQDBQapgbKUQMAH9ba7s7e//ebcj3jdHqjfubUGFucny7aDHyUX/vUsotcyxlZLn2fZd/QQZXQttqR9DeLLUil0Pk3n91qWaZPxGGnyQ8Gitdj6v/6YAuNUSUcoYDwtEcBEUv4KRQFOOpluiD5zamXqY+fCaqO26jnkInxdL4xipCBciZxhGIZJp7M7O1Ce5tG72LqNpCMIU0ARjTTMI94s2xQV0OPJbDBQsao2pQR/Wfa5XMBkNCn3aCBflkyR8ykXtWznLixWoMUN2dxK1UuCRWixz9lCZfOiEQpoY1EAArj0jyFO+izVxx7clayPvf8tyP1vGfWxT6Mge+lJlamPbWLUyYZvCjKhyXbQOJmKM6MUpJFhKcj8hf1ee9jn9aEufm9po/qyUicZghnc5Xn03siPeLNsa2snuYXdkXdspfi81Bq9WfZ1LQQ2XkBBV4P5smQKnE+Ndo0RQlAVGWcTBaNCGLr2/A/6p5N0UH3sjmR97J7FJAnxjtHvI58Ce14D9rwGGfADrW0QTc2VHVSaXCQMp82GYCRStTrZcwWWgtQQfoxSH9jvtYd9Xh/q5fe50iEtbRxmcDThzepamDq2UnyekHTomrFQL0bZ8e6FUP/2p5Ue1qyjkPk0G64x0lx0FwrS70rsM+ADhvohB3fSDVYqi5ZCrD4D6FsP0dxakeOlYlZ3o4o+TsDh5Ex2DlgKwjAMw5RFLR+9V4u0MoBCoUV/ANDelVwAV6kbBrO2tHcMgKDMrKYBhz+BPtQ/K29KKslcmE+A0ZvDCEBlPE6lEUPBkhc8AqCujWeeB3HmeZCjRynAHtwFTIwDhz6GPPQx8PuHIE86GWLNmcBn+iqvx47HAb8P8PsgzSDbXn6d7PkIB9YMwzDMnCStDKD3EAXXADA1aSwMDNM2lQj4OruBD/YDEMnSbUIAqrVyx2AaCmGxUCnH5lbISJgWKUYi00pFZtxnVw/E5ssgL7iU9NhmfexIOF2PfcppFGQfd2Jl9dhAdpBtNzLZHGQXBAfWDMMwzNxkbJiqUQCGNMOoDW22hbbZaZsKILZug/zZ35H8Q8rkT6unYsdgGhdhd1DAq2mUxQ4GystiKwpw/HKI45dDfvHLwDtDlMk+sJeC7P5XIPtfAdraIVefAbF6A0RXT+UGZBKPA3EfEPBBqirgcAEOR/UqmMwBOLBmGIZh5iap1Sgs1uTCM1NDWqFqIABJHbSFS4DRo0atZitVHlFVwO2ZeQfMnECoKt3MNbVARiJGFjtcXhbbagP61kH0rTP02K9TJvvQxyQXef73kM//HnLRUspi962v/KJHgOZ1IDXINjPZHGSnwoE1wzAMMydJK2XX4ga8o/SHVndVur6JK69LarobrOwgU3uE3Q7Y7ZC6Rg19QgHKAJezz6YW4MzzIc48n/TYA4YeezJFj/3EA5DLV1HpvpWnVkfCoWlAwA8E/BxkZ8CBNcMwDDNnyKw+gY0XAO8O0f97FpMUZGqCOh2q1CpcByqyuFDpWwf9mhurXk1lrlRsKYRaj7UaxxOKSm3Tm5ohoxFa7BgOlZXFBgw99oWXQW66FPj4PZKKvPUG3TS+O0QdHh3OZH3sCumx9f17gZeeooW6nk7gnC3UITI1yLY7El0lK8FsmvNcbq9MZkN5oLkI+732sM/rA/u9cNKqgKRmjK+5MfElXMg2jezzQuyfrWT6vdZjreXxKpnFTttvLJqux07tHNnWAaw+A2LNBghDApUot1cg+v691ABHVZMNcDQNuOTq7PbrqkoyLIezrCC7EeZ8MeX2KryUlGEYhmHqQ1oVECEMbTVlpYvZppGZ7fYXQ63HWsvjCUWFaGqmALe9k5oKpbZ8L3W/VhtE3zooX/s6xF/8AOILVwGLltIfJ44Bzz8B+ZNboP/TDyFfew66f6q4A7z0FAXMNjvZa7PT/196KntbTaNFnONjJFuZmqCMfZHMtjnPUhCGYRhmbpBaBcQks/JHIds0MrPd/mKo9Vjr5FthswM2O2SLO1kXOxYrf7/NrdTh8awLsvXYBz+CPPgRvE88CCw36mOv7JtZj+0dA5xN6a9ZbUb99mkwg+xggOQidgfVybYXkMmeZXOeA2uGYRhmbpBaBcQks/JHIds0MrPd/mKo9Vjr7FuhKICrGXA1k6QjFCAttl6+YjdLjz2wE9ibQ499yjrq9JhPj+3ppFbtqdKOWJReL5TUIFtRks1o8gXZs2zOsxSEYRiGmROIrdtIr2qWN8tR+aOQbRqZ2W5/MdR6rI3kW2G1QbR6gM4eKttYoWobQlEglq2AcsW1EN/7IZqv/yaw4hSq8R4OAa+/BPkv/wD547+BvuNRyMys8DlbKDCOGo1wohH6/zlbSjNI1ynI9o5BjhyBnPJCRsJIXf7XSOelENRbbrnllnobUSo+n6/eJsDlciEYDNbbjHkH+732sM/rA/u9cER3L9DdCxz8iB53t3dCXHFt2gKnQrZpZJ8XYv906EP90O+9E/LR+yhr2dJG+2wAMv1e7liLpdbHK8gmISjIdjVRB0RFJOuxl7tvVUXzCSsQWdEHnH4uhNtDQa5vkoLsj98Ddj4HeWAvHdPTCWXhYsiObmD4EG3nbgc2X5a9cLEUpCQJTDgEhPyJRZ2idwnQvaiu56WlpWXmjQy4KkiZNPLq8bkM+732sM/rA/u99sxVnzdCdYXpmKt+rzRSSiASAoJBOodlkKsqiBw5QlVFBneRBMNEUYAVp0Cs3lCYHrtSKAKwOQCHocuuwCLPYimmKghrrBmGYRhmHpBWXQEwfofp9QYIrJnCEEIYrcVd1EI9FKAFj2W0UE/b/4KFEBdeDrnpS9l67HfehHznzaQe26yPXc1gV5eUxQ6HADEBaTeCbJujInW5Kw0H1gzDMAwzH5hl1RWYmRGqCjS3As2tkJEwSTki4crsW1GAZSsglq2A/OJXgHcGIQd3Ae/tS+qxX38J8HRArt5A9bE7FlTk2HmRqUG2gLTbafFjAwXZHFgzDMMwzHxgllVXmInZ1I2vFgi7A7A7KIsdDFDpvkplsW024NTTIU49HdI/BQy9Tpnsw58A3mPAc7+DfO53kIuPpyx233oIV3NFjp0XKYFwmH6EgLTZk10f6xhkc2DNMAzDMPMAsXUbaawRTtdYN2h1helI04s3tQCTXshf/xP0BtGL1xOhqkBLK2RzS8W02Gn7T62PnanHNupj44kHIZefArHmDNJjW6qsxzarhUQyg2w7tZSvIRxYMwzDMBWHs4mNh9K3Dvo1N86J88J68ZlJ02LH46TDDgXS25yXe4xUPfZHByjI3rvH0GMPQr4zWFs9NpA7yDZ02bUIsjmwZhiGYSoKZxMbF6Vv3awOPBM3bAf2AhYb0OZJdgJkvXhehMVS3Sy2ogAnrIQ4YSXkF6+moHpgJ/D+2/XTYwPpQbZPQFptlMmuYpDNgTXDMAxTUTibyFSDtBs2qw2Ix4DxUaAdFFzPYr14rUjPYsegOB3A5GRls9iZeuw3d1OQfeTTdD32kmVUuq9vXfX12ECyoU00AkwB0maj2uB2B914VAgOrBmGYZjKwtUnmCqQdsPW6qGgWkpgwgso6qzVi9cLYbFCcXuAaJyyysEAtSev5DGaW4GNmyA2boIcPmzosXcDU17g0w8hP/0QeOIBQ4+9AVh5SvX12CbRKP34JiGt1uTCxzKPz4E1w8wxWNtaGuy3ClJg9YlG8XmmHeGrrgOWLq+ZjY3ih4Yn9YbNZcg/prwUDLo9Cb8V4s9CfV7KuSn2PdU6/9Pt1/zbqHcMuqcz8TcZi1HXw3CI6kdXAH3/XuClpwDvGODpBC79YwibFXJgF9XHjkaSemynK6nHXnJC7ZrBxGL045uiINtuNKMpoQkOtzQvk0ZufTuXYb/nJvGoNBYFnC4g6KfsQHdv2W2L57LPq+m3cpmVfm9pI/9JHVDVZPWJK65N+DPL595R4JUdkDseh3yrv2attnOd+3j/K9C7FlLFgxLnRaGtw2eae43cgrzSzDTX5cBO8o/52N5qo5/e46B+59aEv2Y6Z4Vuo//jD4BnHgMmJ2i7aHTG81/staQS155cc2S6uZv6N6WpheQaxt+UhYsh7E6S1qgqSUTKkIno+/cCj99PdtidtIBy/1vASaugnHMhVRdZsJD+7h2j4PbwJ8AbrwCDuyBDAbppMnX0tUDX6VyHAnSDoelo7ews+O0cWJfJrPzSmwOw33Oj33uncQFzAELQF5DUgYMfQdm4qax9z2WfV9Nv5TIb/S66e4HuXuDgR8DkONDeCXHFtWlZuDSfh4O0nZQAJCCUmt3Y5Dr3CgD90w9o4VUJ86KYYGm6uYeWtoa94asGM871Qm7YCvgs593mnTchX38Z8qFfAa8+C/imqI03JM1RhxNQLdOe/2KvJeVee/LOtQN7aYNc8yplXquqCl1R6G/vDkG+/hIF6IO7gPYFUI5fTjIuANDiM9qTiXzkP+hYNjvZoRp2DB+CWHsWhKpC9CwirfX6cyBa24CAD/BPURD+0QHgtWfpZlsogKcTwmor2o6S0XUgFkXrwkUFv4WlIAwzl2Bta2mw3yrOjNUnUn0+OUFfYOYKfu8xeiRci8WOuc693ZE89yXMi6IWb04z93gRaDoFlQss5LOca5t4HBg5DCzopYYjukbNVRSVzoGu0zzt7p3+/Bd7LSnz2pNvjuDoIaD3uPz7zTymljL+XJV8bHbIllYgFKLgvdDGM96xZNUWE6uNXs9AtLiBjZsgO3uAR/6dAvJIhM7F6FHIx+4DfvcA5ApDj71iVe302EXAgTXDzCXmWGe1msF+qz2pPo9GKItlosUB3yQFO7W0wyQSTp77UuZFMcHSdHOvwP3MJ432jDdshXyWc20z5QVUQ1urxSmzqmnJeakoVIVkpvNf7LWk3GtPvjli7ifffjOPOeEFLNZpb+KEogJNzUBTM2QkQlKJSNh40pQHTyd9lk2bAAqYPdNIK156irZvbk1W8vBP0W8tDrw9APn2QP302DPQGI3VGYapCGLrNgpGzItdJMwr5QuA/VZ70nyeisWafPxewqPnsuxInPsYxNZtpc+Lzu7sGsF5gqVpj1HAfhJSgElveqZxqL9Ul8xqCjln+c452jy0gcVKGWrVQn/X9WT2eobzX+ycKfvak2+OdPfm3W/qMaX5Ny1GlVZSmSZzLux2iLZ2oKsbaGklaU4uztlCvotGkkGyptHr+fCOUVYbIPmI3QG0dwGtbRB/dD2w/GR6PRQEdr8IedftkHf8LeQzj0OOjxbmtyrCGusymY36x7kA+z03hWhbS2Uu+7yafiuXuer3NJ8fG6EXVTW5YAoScDihbL2idnYY57712q8jtuKU0udFAVrg6Y6fOEaFNMWzhUrM9ULOWa5t4HDSHy0W8nUoAEAmb/R0DVi4GOLL/2Pa81/snCn72pNvjnzlBoi+9Tn3m3pMMeWFbOtInz8m0QjQ3jntPBJCgbDZIZqaAaudfJYiExEdCyA7uoHhQ5S5drcDmy+DsmJV3n3Kd96koFlNsSUWBdraoVz8R0k9dosb8OfQY7//NtlQQT12MRprIeV0OfzG5vDhw/U2AZ2dnRgby9YKMdWF/V572Of1YT74Xbv9ZtJ3BoOUObRYAZcLWNAL9Tu31tyeSvi8UvKMmfaj3XQDZapTH4NLCQR8UG+7u6wxVJJC/FHPuZ7WfMZmB3wTFLDZXcCi4xpaXlPOXDN9njV+M0AvoVuq1DXSYocCJcm5EpVEVJUy17EoBcqXXJ0zIJfDh6h035u7gKmJ5B9UC9XFXr0BWHFKWU1gFp12esHbcmBdJvPhS68RYb/XHvZ5fZgPfq/kl3olmE0+126/ObdG3O2py01JLgo9v/X2+3zSqpuk+rwa45fRCGWTw6HptdgZZNW+PmfLtFluAJC6Dny4H3LgNWDfQLpExtlEHR5XbwCWLCtaj82BdQ2p94VgvsJ+rz3s8/owX/zeSEHNbPJ5o92U5KLQ4H82+X2uUCufS12nkoWhINWqrvbxohHg7UGq6/3+2+lBfXsXxOozgDUbINq7CtpfMYE1VwVhGIZh6s6M1R6YnBRUgq7ecDnLeY/4/9u7t9iornuP4789M74wvo7HsWkgiHCTWkIwtVNcqiTQ0CI1RYp4aFXSB+hDCSZBbg5VXEXqyUNR0p5jYjUYgZQoiUjywIOdllQtEjIOilxOjak5hjQOF7clJwRjj3F8AY89s87DjqcYbMqM99wy38+Lw8oe7zV///f4P9tr/svlkrz5kjf/i90dR+xC26HdHW87X3aOtPIbslZ+Q2ZoUPrfdrvI/uwTKXBV5tgfpGN/kFmw2O4q8sDXHduEhsIaAIA0lvJvSmhniZtYWVlSVrFMQZG9ROT6iL3TYbzOV1AkfWu9rG+tl/ns/2RO/490+i/2hyn/eUHmnxekPxyScWg9NoU1AACIG2vDJnu5im5MXa5CO8uMZlmWvVvkHK/MxLi9TOT66Ky2UP+355w7T9bcTTLfeULq6bbvYk+ux/6wU+bDTsmb96/+2POjX49NYQ0AAOImLZarIKksT5ZUUCSTX2ivv78+enuPeyfP53JJi78qa/FXZTZOrsc+IV34SBodkf5yXOYvxyV/mbRytcQaawAAkCpSfrkKUoJlWXZP8dw5MqGQvUzk+ujdb6EeyznvtB67v1em5bD0H/9519+PwhoAAAApxXK77W3N8wtlxm7Yd5LjeBdbusN67ChQWAMAACBlWTm5Uk6uzMTEF32x43sXW7plPXYUKKwBALOSSj2oAdydcFeHAi2HFbr8SUpft9O9vlgPfN2+ez06MnUjmDiwXK6ojo/uaAAAbhLZoGRwwO5VPDgg884Bhbs6kj01ADOYvG7DA/0pfd3O9PpizpySlTtHVkmp3bYxr0CKsgCOl9SYBQAgLZkjTfaufzm5kmXZXz0eexxASpq8bq3cOSl93d7N64vl8cgqKJTumSsV+6Ts7CTOmKUgAIDZYFc9IP2ky3UbxTztjiJeKXeyL/YXm8/EsS/2dCisAQCxY1c9IGXc9ecdJq/brKx/jaXidRvj64vdFztLJr8gIX2xb8ZSEABAzKwNm6SJCfuXljH2V3bVAxIums87TF635sb1lL5uZ/v6YlmWvRbb57eXihQUSm53XOdMYQ0AiJlrRaWszdukIp80MiQV+WRt3paS3QWAL7NoPu8wed26fP6Uvm6dfH2x3G5ZeQWy7pkr+fxSbu6/f1AMWAoCAJgVdtUDUkCU66ZdKypVsm6D+vr6EjC52MXj9SXSFzsOuztyxxoAACDdlZbf3tM5FddNpxDL7ZaVX2jfxS4umbqWO0YU1gAAAGmOzzvMTmQt9iz7YlNYAwAApDk+7+CM2fbFZo01AADAlwCfd3DOzX2xo8EdawAAAMABFNYAAACAAyisAQAAAAdQWAMAAAAOmNWHF9977z21tLTIsizdd999qqmp0bVr19TQ0KDh4WHdf//9euaZZ+TxeDQ+Pq69eyWd9bsAAA+2SURBVPfq4sWLKigoUG1trcrKyiRJzc3Namlpkcvl0tatW1VRUeHIkwMAIF2EuzrsXfL6rkil5bI2bKKjQ4ZLdE5Ec747HZvJuRzzHetAIKA//vGPeumll1RfX69wOKy2tja99dZbevzxx/Xb3/5WeXl5amlpkSS1tLQoLy9Pr7zyih5//HG9/fbbkqRPPvlEbW1t2rNnj55//nm99tprCofDzjw7AADSQLirQ+adA9LggN1Dd3BA5p0DCnd1JHtqSJJE50Q057vTsZmey7NaChIOhxUMBhUKhRQMBlVcXKyzZ8+qurpakrR27Vq1t7dLkk6ePKm1a9dKkqqrq3XmzBkZY9Te3q41a9YoKytLZWVlmjt3rs6fPz+7ZwUAQBoxR5okj8fe+c2y7K8ejz2OjJTonIjmfHc6NtNzOealICUlJdq4caO2b9+u7OxsrVy5UosWLZLX65Xb7Y4cEwgEJNl3uP1+vyTJ7XbL6/VqaGhIgUBAS5cunfJ9Jx9zq6NHj+ro0aOSpJdeekmlpaWxTt8xHo8nJeaRaYh74hHz5CDuiZeMmF8d6LO3VrasyJhx58kM9GXMz//LkOs3Ov6s0XffVqj3stxlX5H3iSeVW/nNmL5XInLi5phHc747HSspo3M55sJ6eHhY7e3tamxslNfr1Z49e9TZ2Tnj8caY28Ysy5p2fCbr16/X+vXrI//u6+uLbtJxUFpamhLzyDTEPfGIeXIQ98RLRszDvlL7T+c5uf8aHLsh+TLn55/uuR5ZAuHxSLlehft6Nbj/v/R5jLsfJiInbo55NOe707GSvnS5fO+99971sTEvBenq6lJZWZkKCwvl8Xi0evVqdXd3a3R0VKFQSJJ9l7qkpESS5Pf71d/fL0kKhUIaHR1Vfn7+lPFbHwMAQCawNmySJibsAsQY++vEhD2OtOD0EohE50Q057vTsZmeyzEX1qWlpTp37pzGxsZkjFFXV5fmz5+v5cuX68SJE5Kk1tZWVVVVSZIqKyvV2toqSTpx4oSWL18uy7JUVVWltrY2jY+Pq7e3V5cvX9aSJUtm/8wAAEgTrhWVsjZvk4p80siQVOSTFeOdTiRJ3xUpO2fqWHaOPR6DROdENOe707GZnsuWiWYtxi0OHTqktrY2ud1uLVy4UE899ZQCgcBt7faysrIUDAa1d+9e9fT0KD8/X7W1tSovL5ckNTU16dixY3K5XNqyZYtWrVp1V+f/9NNPY526Y9L9T1fpirgnHjFPDuKeeMQ8OdI97qH/fn76JRBFPrl37U7exO4g3WOeKNEsBZlVYZ1sFNaZi7gnHjFPDuKeeMQ8OdI97lPWWGfnSMExewlECt+tTfeYJ0pC1lgDAADAlulLIGCb1c6LAAAgfaTKjnjTzUPrNiR8Hk5zraiUKKQzGnesAQDIAKmyI95M87jR8eeEzgOIBwprAAAyQKrsiDfTPEbffTuh8wDigcIaAIBM4HA7OKfnEeq9nNh5AHFAYQ0AQCYoLbc7VdwsOGaPp8A83GVfSew8gDigsAYAIAOkyo54M83D+8STCZ0HEA90BQEAIAO4VlQqvHlbXLqCRNNtZKZ55FZ+U8P0VEaao7AGACBDxKMd3JSNUW7uNnKHHs60pcOXFUtBAABAzFKl2wiQCiisAQBA7FKl2wiQAiisAQBA7FKl2wiQAiisAQBAzFKl2wiQCiisAQBAzFwrKmVt3iYV+aSRIanIJ+sOH1wEvszoCgIAAGaFLh+AjTvWAAAAgAMorAEAAAAHUFgDAAAADqCwBgAAABxAYQ0AAAA4gMIaAAAAcACFNQAAAOAACmsAAADAARTWAAAAgAMorAEAAAAHUFgDAAAADqCwBgAAABzgSfYEAAAAIIW7OmSONEl9V6TSclkbNsm1ojLZ00IUuGMNAACQZOGuDpl3DkiDA1JegTQ4IPPOAYW7OpI9NUSBwhoAACDJzJEmyeORcnIly7K/ejz2ONIGhTUAAECy9V2RsnOmjmXn2ONIGxTWAAAAyVZaLgXHpo4Fx+xxpA0KawAAgCSzNmySJiaksRuSMfbXiQl7HGmDwhoAACDJXCsqZW3eJhX5pJEhqcgna/M2uoKkGdrtAQAApADXikqJQjqtcccaAAAAcACFNQAAAOAACmsAAADAARTWAAAAgAMorAEAAAAHUFgDAAAADqCwBgAAABxAYQ0AAAA4gMIaAAAAcACFNQAAAOAACmsAAADAARTWAAAAgAMorAEAAAAHUFgDAAAADqCwBgAAABxgGWNMsicBAAAApDvuWM9SXV1dsqeQkYh74hHz5CDuiUfMk4O4Jx4xdx6FNQAAAOAACmsAAADAAe4XXnjhhWRPIt0tWrQo2VPISMQ98Yh5chD3xCPmyUHcE4+YO4sPLwIAAAAOYCkIAAAA4AAKawAAAMABnmRPIBX09fWpsbFR165dk2VZWr9+vb73ve9peHhYL7/8sq5evap77rlHP/vZz5Sfny9jjF5//XX99a9/VU5OjmpqaiJrlFpbW9XU1CRJ2rRpk9auXStJunjxohobGxUMBrVq1Spt3bpVlmUl6ymnlHA4rLq6OpWUlKiurk69vb1qaGjQ8PCw7r//fj3zzDPyeDwaHx/X3r17dfHiRRUUFKi2tlZlZWWSpObmZrW0tMjlcmnr1q2qqKiQJHV2dur1119XOBzWY489pieeeCKZTzUljIyMaP/+/bp06ZIsy9L27dt17733kutx9t5776mlpUWWZem+++5TTU2Nrl27Rq47bN++fTp16pSKiopUX18vSQl5LZ/pHJlgupgfPHhQHR0d8ng8Ki8vV01NjfLy8iRFn8Ox/E7IBNPFfdLvf/97vfXWW3r11VdVWFhIrieSgQkEAubChQvGGGNGR0fNzp07zaVLl8zBgwdNc3OzMcaY5uZmc/DgQWOMMR0dHWb37t0mHA6b7u5u84tf/MIYY8zQ0JDZsWOHGRoamvLfxhhTV1dnuru7TTgcNrt37zanTp1KwjNNTYcPHzYNDQ3mxRdfNMYYU19fbz744ANjjDEHDhwwR44cMcYY86c//ckcOHDAGGPMBx98YPbs2WOMMebSpUtm165dJhgMmitXrpinn37ahEIhEwqFzNNPP20+++wzMz4+bnbt2mUuXbqUhGeYWl555RVz9OhRY4wx4+PjZnh4mFyPs/7+flNTU2PGxsaMMXaOHzt2jFyPg7Nnz5oLFy6YZ599NjKWiPye6RyZYLqYd3Z2momJCWOMHZvJeMSSw9FeJ5liurgbY8zVq1fNr371K7N9+3YzODhojCHXE4mlIJJ8Pl/knducOXM0b948BQIBtbe369FHH5UkPfroo2pvb5cknTx5Uo888ogsy9KyZcs0MjKigYEBdXZ26sEHH1R+fr7y8/P14IMPqrOzUwMDA7p+/bqWLVsmy7L0yCOPRL5Xpuvv79epU6f02GOPSZKMMTp79qyqq6slSWvXrp0S98l30tXV1Tpz5oyMMWpvb9eaNWuUlZWlsrIyzZ07V+fPn9f58+c1d+5clZeXy+PxaM2aNRkf99HRUf3tb3/Tt7/9bUmSx+NRXl4euZ4A4XBYwWBQoVBIwWBQxcXF5HocfO1rX7vt7lki8numc2SC6WK+cuVKud1uSdKyZcsUCAQkKeocjuV3QqaYLu6S9Oabb+rJJ5+c8pdCcj1xWApyi97eXvX09GjJkiUaHByUz+eTZBffn3/+uSQpEAiotLQ08hi/369AIKBAICC/3x8ZLykpmXZ88nhIb7zxhn784x/r+vXrkqShoSF5vd7IC/JkDCVNiaPb7ZbX69XQ0JACgYCWLl0a+Z43P+bWuJ87dy4hzytV9fb2qrCwUPv27dM//vEPLVq0SFu2bCHX46ykpEQbN27U9u3blZ2drZUrV2rRokXkeoIkIr9nOgeklpYWrVmzRpKizuFYficUFhYm5HmlopMnT6qkpEQLFy6cMk6uJw53rG9y48YN1dfXa8uWLfJ6vTMeN9074pnWkFqWlVHvoKPR0dGhoqKiu+6hOVPcZ4pvND+nTBEKhdTT06Pvfve7+s1vfqOcnBy9++67Mx5PrjtjeHhY7e3tamxs1IEDB3Tjxg11dnbOeDy5nhjkd/w1NTXJ7Xbr4YcfljR9zGca/3c5TN5PNTY2pqamJv3whz+87f+R64lDYf2FiYkJ1dfX6+GHH9bq1aslSUVFRRoYGJAkDQwMRN4F+/1+9fX1RR7b398vn8+nkpIS9ff3R8YDgYB8Pp/8fv+U8f7+fpWUlCTiaaW07u5unTx5Ujt27FBDQ4POnDmjN954Q6OjowqFQpLsGE7G6uY4hkIhjY6OKj8//7b4Tj5murhPvsvOVH6/X36/P3LHqLq6Wj09PeR6nHV1damsrEyFhYXyeDxavXq1uru7yfUESUR+z3SOTNba2qqOjg7t3LkzUsRFm8MFBQVRXyeZ6sqVK+rt7dXPf/5z7dixQ/39/Xruued07do1cj2BKKxlv5Pbv3+/5s2bp+9///uR8aqqKr3//vuSpPfff18PPfRQZPz48eMyxujjjz+W1+uVz+dTRUWFTp8+reHhYQ0PD+v06dOqqKiQz+fTnDlz9PHHH8sYo+PHj6uqqiopzzWVbN68Wfv371djY6Nqa2v1wAMPaOfOnVq+fLlOnDghyX5hnoxVZWWlWltbJUknTpzQ8uXLZVmWqqqq1NbWpvHxcfX29ury5ctasmSJFi9erMuXL6u3t1cTExNqa2vL+LgXFxfL7/fr008/lWQXfPPnzyfX46y0tFTnzp3T2NiYjDGRuJPriZGI/J7pHJmqs7NTv/vd7/Tcc88pJycnMh5tDluWFfV1kqkWLFigV199VY2NjWpsbJTf79evf/1rFRcXk+sJxM6Lkj766CP98pe/1IIFCyIX5Y9+9CMtXbpUL7/8svr6+lRaWqpnn3020qLptdde0+nTp5Wdna2amhotXrxYkr2WrLm5WZLdtmbdunWSpAsXLmjfvn0KBoOqqKjQT37yk4x+AbjV2bNndfjwYdXV1enKlSu3tVbKyspSMBjU3r171dPTo/z8fNXW1qq8vFyS/efGY8eOyeVyacuWLVq1apUk6dSpU3rzzTcVDoe1bt06bdq0KZlPMyX8/e9/1/79+zUxMaGysjLV1NTIGEOux9mhQ4fU1tYmt9uthQsX6qmnnlIgECDXHdbQ0KAPP/xQQ0NDKioq0g9+8AM99NBDcc/voaGhac+RCaaLeXNzsyYmJiIxWLp0qX76059Kij6HY/mdkAmmi/vkB9MlaceOHXrxxRcj7fbI9cSgsAYAAAAcwFIQAAAAwAEU1gAAAIADKKwBAAAAB1BYAwAAAA6gsAYAAAAcQGENAAAAOIDCGgAAAHDA/wNo3SdWBv6FFQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Но есть различные статистические оценки для доверительных интервалов. Их можно либо считать [самому](https://math.stackexchange.com/questions/871601/confidence-interval-for-regression-coefficient-beta), либо использовать пакеты, в которых все расчитывается автоматом"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train2 = np.c_[X_train, np.ones_like(X_train)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "ols = sm.OLS(y_train, exog=X_train2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = ols.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>OLS</td>         <td>Adj. R-squared:</td>      <td>0.430</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>         <td>y</td>               <td>AIC:</td>          <td>7315.6635</td>\n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2018-11-21 20:28</td>        <td>BIC:</td>          <td>7323.7297</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>417</td>         <td>Log-Likelihood:</td>     <td>-3655.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>1</td>           <td>F-statistic:</td>        <td>314.3</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>415</td>       <td>Prob (F-statistic):</td>  <td>9.22e-53</td> \n",
       "</tr>\n",
       "<tr>\n",
       "      <td>R-squared:</td>            <td>0.431</td>            <td>Scale:</td>        <td>2.4239e+06</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>Coef.</th>   <th>Std.Err.</th>     <th>t</th>     <th>P>|t|</th>   <th>[0.025</th>     <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>      <td>-0.0521</td>   <td>0.0029</td>  <td>-17.7288</td> <td>0.0000</td>   <td>-0.0579</td>    <td>-0.0464</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>16762.0249</td> <td>274.6464</td>  <td>61.0313</td> <td>0.0000</td> <td>16222.1534</td> <td>17301.8965</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td>Omnibus:</td>    <td>32.530</td>  <td>Durbin-Watson:</td>    <td>1.688</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Prob(Omnibus):</td>  <td>0.000</td> <td>Jarque-Bera (JB):</td> <td>58.603</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Skew:</td>      <td>0.487</td>     <td>Prob(JB):</td>      <td>0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Kurtosis:</td>    <td>4.557</td>  <td>Condition No.:</td>   <td>336445</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                  Results: Ordinary least squares\n",
       "===================================================================\n",
       "Model:              OLS              Adj. R-squared:     0.430     \n",
       "Dependent Variable: y                AIC:                7315.6635 \n",
       "Date:               2018-11-21 20:28 BIC:                7323.7297 \n",
       "No. Observations:   417              Log-Likelihood:     -3655.8   \n",
       "Df Model:           1                F-statistic:        314.3     \n",
       "Df Residuals:       415              Prob (F-statistic): 9.22e-53  \n",
       "R-squared:          0.431            Scale:              2.4239e+06\n",
       "-------------------------------------------------------------------\n",
       "            Coef.    Std.Err.    t     P>|t|    [0.025     0.975]  \n",
       "-------------------------------------------------------------------\n",
       "x1           -0.0521   0.0029 -17.7288 0.0000    -0.0579    -0.0464\n",
       "const     16762.0249 274.6464  61.0313 0.0000 16222.1534 17301.8965\n",
       "-------------------------------------------------------------------\n",
       "Omnibus:              32.530        Durbin-Watson:           1.688 \n",
       "Prob(Omnibus):        0.000         Jarque-Bera (JB):        58.603\n",
       "Skew:                 0.487         Prob(JB):                0.000 \n",
       "Kurtosis:             4.557         Condition No.:           336445\n",
       "===================================================================\n",
       "* The condition number is large (3e+05). This might indicate\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.summary2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Эффект регуляризации\n",
    "\n",
    "Теперь, давайте попробуем добавить столбец с \"километрами\" в наш датафрейм (линейная зависимость) и \n",
    "\n",
    "1. Посмотрим что будет с коэффициентами\n",
    "2. Добавим регуляризации"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge, Lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train2 = np.c_[X_train, X_train*0.62]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=1000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False)"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# model = LinearRegression()\n",
    "model = Lasso(alpha=1.0)\n",
    "model.fit(X_train2, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.05213421, -0.        ])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16762.02477739712"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Преобразование переменных"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Давайте попробуем  добавить остальные переменные"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>mileage</th>\n",
       "      <th>year</th>\n",
       "      <th>trim</th>\n",
       "      <th>engine</th>\n",
       "      <th>transmission</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14995</td>\n",
       "      <td>67697</td>\n",
       "      <td>2006</td>\n",
       "      <td>ex</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Manual</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11988</td>\n",
       "      <td>73738</td>\n",
       "      <td>2006</td>\n",
       "      <td>ex</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Manual</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11999</td>\n",
       "      <td>80313</td>\n",
       "      <td>2006</td>\n",
       "      <td>lx</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Automatic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12995</td>\n",
       "      <td>86096</td>\n",
       "      <td>2006</td>\n",
       "      <td>lx</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Automatic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11333</td>\n",
       "      <td>79607</td>\n",
       "      <td>2006</td>\n",
       "      <td>lx</td>\n",
       "      <td>4 Cyl</td>\n",
       "      <td>Automatic</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   price  mileage  year trim engine transmission\n",
       "0  14995    67697  2006   ex  4 Cyl       Manual\n",
       "1  11988    73738  2006   ex  4 Cyl       Manual\n",
       "2  11999    80313  2006   lx  4 Cyl    Automatic\n",
       "3  12995    86096  2006   lx  4 Cyl    Automatic\n",
       "4  11333    79607  2006   lx  4 Cyl    Automatic"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ex     288\n",
       "lx     120\n",
       "exl      9\n",
       "Name: trim, dtype: int64"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.trim.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "def data_preproc(df_input):\n",
    "    df_output = df_input.copy()\n",
    "    \n",
    "    df_output.loc[:, 'transmission'] = df_output.transmission.replace({'Automatic': 0,\n",
    "                                                                       'Manual': 1})\n",
    "    df_output.loc[:, 'engine'] = df_output.engine.str[0].astype(int)\n",
    "    df_output.loc[:, 'trim'] = df_output.trim.replace({'ex': 0,\n",
    "                                                       'lx': 1,\n",
    "                                                       'exl': 2})\n",
    "    df_output = df_output.drop(['year'], axis=1)\n",
    "    \n",
    "    \n",
    "    return df_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train_preproc = df_train.pipe(data_preproc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = df_train_preproc.iloc[:, 1:].values\n",
    "y_train = df_train_preproc.iloc[:, 0].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 67697,      0,      4,      1],\n",
       "       [ 73738,      0,      4,      1],\n",
       "       [ 80313,      1,      4,      0],\n",
       "       [ 86096,      1,      4,      0],\n",
       "       [ 79607,      1,      4,      0],\n",
       "       [ 96966,      1,      4,      0],\n",
       "       [126150,      1,      4,      0],\n",
       "       [119255,      1,      4,      0],\n",
       "       [ 73513,      2,      4,      0],\n",
       "       [ 50649,      0,      4,      0]])"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Pipeline([\n",
    "    ('ohe', OneHotEncoder(n_values='auto', categorical_features=[1], handle_unknown='ignore')),\n",
    "    ('linreg', LinearRegression(fit_intercept=False))\n",
    "])\n",
    "\n",
    "# Избегаем мультиколлинеарности сами!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/andrey.shestakov/anaconda3/lib/python3.7/site-packages/sklearn/preprocessing/_encoders.py:341: DeprecationWarning: Passing 'n_values' is deprecated in version 0.20 and will be removed in 0.22. n_values='auto' can be replaced with categories='auto'.\n",
      "  warnings.warn(msg, DeprecationWarning)\n",
      "/Users/andrey.shestakov/anaconda3/lib/python3.7/site-packages/sklearn/preprocessing/_encoders.py:385: DeprecationWarning: The 'categorical_features' keyword is deprecated in version 0.20 and will be removed in 0.22. You can use the ColumnTransformer instead.\n",
      "  \"use the ColumnTransformer instead.\", DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('ohe', OneHotEncoder(categorical_features=[1], categories=None,\n",
       "       dtype=<class 'numpy.float64'>, handle_unknown='ignore',\n",
       "       n_values='auto', sparse=True)), ('linreg', LinearRegression(copy_X=True, fit_intercept=False, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [],
   "source": [
    "ohe = model.named_steps['ohe']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0., 1., 2.])]"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ohe.categories_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.55046625e+04,  1.44122069e+04,  1.59703332e+04, -5.22010985e-02,\n",
       "        3.37203254e+02, -8.41350658e+02])"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.named_steps['linreg'].coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.named_steps['linreg'].intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "А теперь для статс моделс"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [],
   "source": [
    "def data_preproc(df_input):\n",
    "    df_output = df_input.copy()\n",
    "    \n",
    "    df_output.loc[:, 'transmission'] = df_output.transmission.replace({'Automatic': 0,\n",
    "                                                                       'Manual': 1})\n",
    "    df_output.loc[:, 'engine'] = df_output.engine.str[0].astype(int)\n",
    "#     df_output.loc[:, 'trim'] = df_output.trim.replace({'ex': 0,\n",
    "#                                                        'lx': 1,\n",
    "#                                                        'exl': 2})\n",
    "    df_output = pd.get_dummies(df_output, columns=['trim'], drop_first=True)\n",
    "    df_output = df_output.drop(['year'], axis=1)\n",
    "    df_output.loc[:, 'dummy'] = 1.0\n",
    "    \n",
    "    \n",
    "    return df_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train_preproc_stats_models = df_train.pipe(data_preproc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>mileage</th>\n",
       "      <th>engine</th>\n",
       "      <th>transmission</th>\n",
       "      <th>trim_exl</th>\n",
       "      <th>trim_lx</th>\n",
       "      <th>dummy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14995</td>\n",
       "      <td>67697</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11988</td>\n",
       "      <td>73738</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11999</td>\n",
       "      <td>80313</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12995</td>\n",
       "      <td>86096</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11333</td>\n",
       "      <td>79607</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   price  mileage  engine  transmission  trim_exl  trim_lx  dummy\n",
       "0  14995    67697       4             1         0        0    1.0\n",
       "1  11988    73738       4             1         0        0    1.0\n",
       "2  11999    80313       4             0         0        1    1.0\n",
       "3  12995    86096       4             0         0        1    1.0\n",
       "4  11333    79607       4             0         0        1    1.0"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train_preproc_stats_models.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train = df_train_preproc_stats_models.iloc[:, 0].values\n",
    "X_train = df_train_preproc_stats_models.iloc[:, 1:].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "ols = sm.OLS(y_train, X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = ols.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.556</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.550</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   102.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 21 Nov 2018</td> <th>  Prob (F-statistic):</th> <td>3.77e-70</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:06:05</td>     <th>  Log-Likelihood:    </th> <td> -3604.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   417</td>      <th>  AIC:               </th> <td>   7221.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   411</td>      <th>  BIC:               </th> <td>   7245.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     5</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>   -0.0522</td> <td>    0.003</td> <td>  -19.962</td> <td> 0.000</td> <td>   -0.057</td> <td>   -0.047</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>  337.2025</td> <td>   73.074</td> <td>    4.615</td> <td> 0.000</td> <td>  193.557</td> <td>  480.848</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td> -841.3507</td> <td>  246.604</td> <td>   -3.412</td> <td> 0.001</td> <td>-1326.113</td> <td> -356.588</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>  465.6708</td> <td>  476.592</td> <td>    0.977</td> <td> 0.329</td> <td> -471.191</td> <td> 1402.533</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>-1092.4555</td> <td>  159.656</td> <td>   -6.843</td> <td> 0.000</td> <td>-1406.300</td> <td> -778.611</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>  1.55e+04</td> <td>  450.080</td> <td>   34.449</td> <td> 0.000</td> <td> 1.46e+04</td> <td> 1.64e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>40.761</td> <th>  Durbin-Watson:     </th> <td>   1.922</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  72.412</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.601</td> <th>  Prob(JB):          </th> <td>1.89e-16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.650</td> <th>  Cond. No.          </th> <td>6.84e+05</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 6.84e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.556\n",
       "Model:                            OLS   Adj. R-squared:                  0.550\n",
       "Method:                 Least Squares   F-statistic:                     102.8\n",
       "Date:                Wed, 21 Nov 2018   Prob (F-statistic):           3.77e-70\n",
       "Time:                        21:06:05   Log-Likelihood:                -3604.3\n",
       "No. Observations:                 417   AIC:                             7221.\n",
       "Df Residuals:                     411   BIC:                             7245.\n",
       "Df Model:                           5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1            -0.0522      0.003    -19.962      0.000      -0.057      -0.047\n",
       "x2           337.2025     73.074      4.615      0.000     193.557     480.848\n",
       "x3          -841.3507    246.604     -3.412      0.001   -1326.113    -356.588\n",
       "x4           465.6708    476.592      0.977      0.329    -471.191    1402.533\n",
       "x5         -1092.4555    159.656     -6.843      0.000   -1406.300    -778.611\n",
       "const        1.55e+04    450.080     34.449      0.000    1.46e+04    1.64e+04\n",
       "==============================================================================\n",
       "Omnibus:                       40.761   Durbin-Watson:                   1.922\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               72.412\n",
       "Skew:                           0.601   Prob(JB):                     1.89e-16\n",
       "Kurtosis:                       4.650   Cond. No.                     6.84e+05\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 6.84e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Логистическая регрессия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Игрушечный пример"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сгенерируем выборку и опробуем логистическую регрессию"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "X = np.r_[np.random.randn(20, 2) + [2, 2],\n",
    "          np.random.randn(20, 2) + [-2, -2]]\n",
    "y = [-1] * 20 + [1] * 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 7))\n",
    "ax.scatter(X[:, 0],\n",
    "           X[:, 1],\n",
    "           c=y,\n",
    "           cmap=plt.cm.Paired)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обучим логистическую регрессию на этих данных и нарисуем разделяющую гиперплоскость"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LogisticRegression(C=1.0, \n",
    "                           fit_intercept=True, \n",
    "                           penalty='l2')\n",
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print('w_0 = %f' % model.intercept_)\n",
    "print('w_1, w_2 = ', model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Нарисуем эту гиперплоскость\n",
    "w_0 = model.intercept_[0]\n",
    "w_1 = model.coef_[0][0]\n",
    "w_2 = model.coef_[0][1]\n",
    "\n",
    "x_1 = np.linspace(-4, 4, 10)\n",
    "x_2 = - (w_0 + w_1*x_1)/w_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 7))\n",
    "ax.scatter(X[:, 0],\n",
    "           X[:, 1],\n",
    "           c=y,\n",
    "           cmap=plt.cm.Paired)\n",
    "plt.plot(x_1, x_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Пример с текстами"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Возьмем текстовые данные [отсюда](https://archive.ics.uci.edu/ml/machine-learning-databases/00331/). Архив содержит 3 файла с положительными и отрицательными отзывами с ресурсов\n",
    "* imdb.com\n",
    "* amazon.com\n",
    "* yelp.com\n",
    "\n",
    "Формат файла следующий:\n",
    "<отзыв>\\t<метка>\\n\n",
    "\n",
    "\n",
    "### Задача\n",
    "1. Загрузите тексты и метки классов в разные переменные\n",
    "2. Выберите меру качества классификации\n",
    "3. Обучите логистическую (без подбора гиперпараметров). Тексты представляются в виде мешка слов\n",
    "4. Выведите наиболее значимые слова из текста\n",
    "5. С помощью кросс-валидации найдите хорошие значения гиперпараметров для `CountVectorizer` и `LogisticRegression`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('data/sentiment/imdb_labelled.txt', sep='\\t', header=None, names=['text', 'label'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.model_selection import StratifiedKFold\n",
    "from sklearn.model_selection import RandomizedSearchCV GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Pipeline([\n",
    "    ('vect', CountVectorizer(min_df=4, max_df=0.95, stop_words='english', ngram_range=(1,1))),\n",
    "    ('clf', LogisticRegression())\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your Code Here"
   ]
  }
 ],
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