{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "tags": []
   },
   "source": [
    "# Las pruebas de Box-Pierce y Ljung-Box.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Cargar paquetes necesarios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn')\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "from scipy.stats.distributions import chi2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## EJEMPLO 1: Crecimiento del IMAE de Costa Rica, serie tendencia-ciclo\n",
    "\n",
    "¿Es es crecimiento mensual del IMAE tendencia-ciclo un proceso ruido blanco?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "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>fecha</th>\n",
       "      <th>Original</th>\n",
       "      <th>Tendencia_ciclo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01</th>\n",
       "      <td>1991-01-31</td>\n",
       "      <td>3.543337</td>\n",
       "      <td>3.436627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02</th>\n",
       "      <td>1991-02-28</td>\n",
       "      <td>3.444160</td>\n",
       "      <td>3.438203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03</th>\n",
       "      <td>1991-03-31</td>\n",
       "      <td>3.389929</td>\n",
       "      <td>3.439999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04</th>\n",
       "      <td>1991-04-30</td>\n",
       "      <td>3.391805</td>\n",
       "      <td>3.444238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05</th>\n",
       "      <td>1991-05-31</td>\n",
       "      <td>3.406380</td>\n",
       "      <td>3.448570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-04</th>\n",
       "      <td>2021-04-30</td>\n",
       "      <td>4.628316</td>\n",
       "      <td>4.657012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-05</th>\n",
       "      <td>2021-05-31</td>\n",
       "      <td>4.657245</td>\n",
       "      <td>4.667075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-06</th>\n",
       "      <td>2021-06-30</td>\n",
       "      <td>4.660920</td>\n",
       "      <td>4.676299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-07</th>\n",
       "      <td>2021-07-31</td>\n",
       "      <td>4.682706</td>\n",
       "      <td>4.685173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-08</th>\n",
       "      <td>2021-08-31</td>\n",
       "      <td>4.659956</td>\n",
       "      <td>4.691523</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>368 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              fecha  Original  Tendencia_ciclo\n",
       "1991-01  1991-01-31  3.543337         3.436627\n",
       "1991-02  1991-02-28  3.444160         3.438203\n",
       "1991-03  1991-03-31  3.389929         3.439999\n",
       "1991-04  1991-04-30  3.391805         3.444238\n",
       "1991-05  1991-05-31  3.406380         3.448570\n",
       "...             ...       ...              ...\n",
       "2021-04  2021-04-30  4.628316         4.657012\n",
       "2021-05  2021-05-31  4.657245         4.667075\n",
       "2021-06  2021-06-30  4.660920         4.676299\n",
       "2021-07  2021-07-31  4.682706         4.685173\n",
       "2021-08  2021-08-31  4.659956         4.691523\n",
       "\n",
       "[368 rows x 3 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_imae = pd.read_csv(\"https://github.com/randall-romero/econometria/raw/master/data/log_imae.csv\")\n",
    "log_imae.index = pd.period_range(start='1991-01', freq='M', periods=log_imae.shape[0])\n",
    "log_imae"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "growth = log_imae['Tendencia_ciclo'].diff().dropna()\n",
    "T = growth.size  # número de datos\n",
    "M = 7   # máximo número de rezagos\n",
    "rezagos = np.arange(1, M+1)\n",
    "alpha = 0.05  # significancia de los test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos las autocovarianzas, a partir de un rezago"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "rho = sm.tsa.acf(growth, fft=True, nlags=M)[1:] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos el estadístico de Box-Pierce, para todos los rezagos desde el 1 hasta el 7\n",
    "\n",
    "\\begin{equation*}\n",
    "Q^{*} = T\\sum_{j=1}^{m}\\hat{\\rho}_j^2 \\; \\overset{\\text{asy}}{\\sim} \\; \\chi^2_{m-k}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "Qstar = T * (rho ** 2).cumsum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos el estadístico de Ljung-Box\n",
    "\n",
    "\\begin{equation*}\n",
    "Q = T(T+2)\\sum_{j=1}^{m}\\frac{\\hat{\\rho}_j^2}{T-j} \\; \\overset{\\text{asy}}{\\sim} \\; \\chi^2_{m-k}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "Q = T * (T+2) * ((rho ** 2)/(T-rezagos)).cumsum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos los valores críticos, tomando en cuenta que $k=0$ porque los datos que estamos usando no son residuos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "vcrits = np.array([chi2(k).ppf(1-alpha) for k in rezagos])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Con carácter informativo nada más, calculamos la autocorrelación parcial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "rhop = sm.tsa.pacf(growth, nlags=M, method='ols')[1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Juntamos todos los resultados en una tabla de resumen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "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>AC</th>\n",
       "      <th>PAC</th>\n",
       "      <th>Box-Pierce</th>\n",
       "      <th>Ljung-Box</th>\n",
       "      <th>$\\chi^2(m-k)$</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rezagos</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.246</td>\n",
       "      <td>0.246</td>\n",
       "      <td>22.150</td>\n",
       "      <td>22.331</td>\n",
       "      <td>3.841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.178</td>\n",
       "      <td>0.126</td>\n",
       "      <td>33.829</td>\n",
       "      <td>34.139</td>\n",
       "      <td>5.991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.117</td>\n",
       "      <td>0.052</td>\n",
       "      <td>38.845</td>\n",
       "      <td>39.223</td>\n",
       "      <td>7.815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.075</td>\n",
       "      <td>0.020</td>\n",
       "      <td>40.893</td>\n",
       "      <td>41.306</td>\n",
       "      <td>9.488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.035</td>\n",
       "      <td>-0.006</td>\n",
       "      <td>41.350</td>\n",
       "      <td>41.771</td>\n",
       "      <td>11.070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.021</td>\n",
       "      <td>-0.002</td>\n",
       "      <td>41.510</td>\n",
       "      <td>41.935</td>\n",
       "      <td>12.592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.029</td>\n",
       "      <td>0.019</td>\n",
       "      <td>41.822</td>\n",
       "      <td>42.255</td>\n",
       "      <td>14.067</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            AC    PAC  Box-Pierce  Ljung-Box  $\\chi^2(m-k)$\n",
       "Rezagos                                                    \n",
       "1        0.246  0.246      22.150     22.331          3.841\n",
       "2        0.178  0.126      33.829     34.139          5.991\n",
       "3        0.117  0.052      38.845     39.223          7.815\n",
       "4        0.075  0.020      40.893     41.306          9.488\n",
       "5        0.035 -0.006      41.350     41.771         11.070\n",
       "6        0.021 -0.002      41.510     41.935         12.592\n",
       "7        0.029  0.019      41.822     42.255         14.067"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resumen = pd.DataFrame({'AC':rho, 'PAC': rhop, 'Box-Pierce':Qstar, 'Ljung-Box':Q, f'$\\chi^2(m-k)$': vcrits}, index=rezagos)\n",
    "resumen.index.name = 'Rezagos'\n",
    "\n",
    "resumen.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Graficamos los datos y el autocorrelograma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7wujSsi6v/KErjer6sfdoCovWHSxzu26ZtJNTzVxMy6ZD82A8rt6GLtDoxdQhEZhzrfxj+T4+355AXn4BOw4lA9C3YwMAOresi00pDt0whpCUYkKBPTG1bx6ETSl2/15yV3pJdlztdrcpxcpNx52ufyTx2o9fdU/wyrMU8P2eM/z021n2H08pdnLyW/wl9h+/TETTAAZENgagUV0/9DotZy6WfUKSkpHD6x//ypZ951i56Thb9p+7aftxs2XnWnn1wz389cM9t8UchwKbDVNOPnvjL3EiKZPkVDNLvj2Ch15L9NDWaDTw2U/HbuuTmNtJvrWAfcdS2HEoWS73rIALadnsO5ZCswZGJg5sSfvmQdzTM5RGdf3YcegCR89m0L55EI3r+gHQrIE/sx7pSd+ODbicWfpkaXCDB4aUJPZ4Yfd2ZKu6Du/379yIlIwcfvj1LN/sTOTQyTRS0nMw+nrQsUUwAJ3Dg/li+0kOnkilV7sG9s8mpRTOHG8SYgBgYGRjfvztLF9sP0m3iBDqGLzKrFOmKY8DJy7TJMSAv58Hh0+nczwpg1ZNAkr9TPyZDAB0Wg0HT6YycVDLCsWhKr7ZdZoNuxLtr4P9vfhrdHcCjV6kZuby6Y/H8NBrefjeNmg1GgD0Oi1163iXeVBZ8gv49+eHSM/K4+4eTdkZd4EVG4/Rq119fLyq93Cz2RRaraZK21i7LYFLV3tuFqzYz7wnejk9FlzBnJtPVnY+DYJ8b3pZUBirL385xfd7ErEWXEvIGkABD9zTmju7NOb3U2nEHEvh3GUzTUIMpGbm4uGhxc9bz1e/nOK3I5eIjAhhZJ9mTv/eSik0mqr9fcTNk56Vx6J1Bzl9dTgs0OjFU6M70LJJnRquWe23My4ZBdzds6n9GNdqNdwX1YJ/f3GINqEBTBvW1uEzGo2Gwd2aFBvivZFbtrT3n7iMRgMdw4OLLRs3IJxFz0XRq119Ei9kkZ1nZXjvZuh1hbvatJ6BIH8vDp1MdZi0VtSd3aRe4ZlPHYMXo/s1x5xr5aXFO3n1//awYmPprefffr9IgU3Rp0MDRvVtDsA3OxNLXd9mUxw9k07dOt50aB7E+cvmMi9Hq6zkVDPf7U50aCVmZVvYGJNEHT9P/jimA3dGNib1Sh4LV8VyIimTf609iCknn4kDW1L/hqQRXMcbU04+eZaCEsvbFJPEmUsm+nduyOTBrRjUtTHWAsXvp69N6tu6/xz/+z6eDbtOsy32HDl55R+CKK8jp9N49t2f2RpbeivfWWvxQlo2W/efo3FdPyYNaklefgHf7TnjtOwLadnEHr9caoyciU9M49UP9/Dqh3tIOF+1YZMr2RY270viSGI6Npvj/ppz8+0x+OS7eL7ZeRqjrycdWwQzqm8zIlvVpWWTOjwxqj0DOjcCoHubegDsjb/E4dNp/OX9nTz37i889o+tfLMzkYvpOXy/5wxLvosvNb4FNhv/+z6eF/69o0bmR1jyC27qHBKllH371gIbG/eerZWTTYv+PubcfC5l5DgcH6eSrzBr6W+cvpBFr/b1Gd47jAxTHvOX72PzvqQSt3f0TDoLVuwn1UlLsaqysi2lXgFUW8Qev4xep6VLS8eGZbfWIfzzj314aUokgcbiJ//NGvgT4eSkyC1a2kopsrLzsRbYSMnIISEpk5ZN6uDv61ni+l4eOh4d2Y577gglwOCFv9+19TQaDZ3D67Jl/zlOJGXSOrRwTDwpxYxGA42C/ezrDuneFIBfj1zk3GUzP+09S/c2ISW2nmOPpQDQoUUQTUIMtG4awKGTqWzce5a7ujelwGZDg8be8jt7yYQ510pkRAj1A304kJDKqeQrBPl7uyRmSSkmfjmYzJb95+yXaE24M5x7e4Xx429nybMUMDaqBd3b1KNb6xA89Vp+/O0scz6NAQp7GgZ1bVxsu8H+hQfa5Su59q6dIjal2BZ7Hg+9lokDC3sNOoYH8/WO0xxMSKVb63rsPXKR//1w1OFzX/1yikdGtKN9syCgcNb+d3sS8fX2YFivUJo18K/Qvl/JtvDf9b9jzrWydksCPdrUw8/b49pys4V31hwgOTWb0PoGIluFMKRHE3Rax3PYg1eHLO7u0ZTeHRrw096zbNl/zn5cleRSejZzlsVgysnH10vP85M6E96o5C/h5cwcMk0W6gf5YvAprF9qZi6vL/mVnDwrSsFH3xzhjYd74OlR8tOI0rPySDiXidHXw34sF0m6ZOJfaw+SevVkMLS+gQGdG5GWlcehhFTOXDLRMNiXVk3q8MuhZMIaGHl5chd8r4vVjTqFB+Oh17L794vsjLtw9fsUTHaelQZBvozt34L3vjjE3vhL7GoZTJ8ODR0+n5dfwAdfHbZPJP3X2gO89lCPUuPpKtYCG4dOprLvaAp7jlwEoG/HhjwwtHWFWvtKKX6Lv8T6naeJaBrAH4ZEOHz+eFIGy344RtqVXIb3CWP/8cucSMrE00PLX//QjdD6pT9ysbrYbIoffjvDNzsT8dRrycrOx6YUBh8PHh/ZDj8fD/6xYj8WSwETB7Zk6NXWYofmQbz/ZRzLfzpOl5Z1HX6rlFKs3nKCU8lZLP0+nucndi4xrkopMkwWvDx0+HpXPP0cO5vBonUHyc6zckfb+kwb3tbeIIPC737SJRNhDYwO3/nqdDkjh6QUMx1bBOPtWXwfnf3GPzuhc5nL3SJpL/k2nl+ujk1rNYWJb2z/FmV+RqvRlPoF6dwymC37z3HgRCqtQwNRSnEuxUS9QF+HH0etVsPQnqEM7RnKsbMZzPtsHxt2JfLchACH7dmU4sDxFOoYPO2J7IF7WvOP5ftZvrFwTDftSh5NQvx4YVIXfLz09vHstqGB+BsKTypOX8iiW+t6Ze7XxbRsTpzLpE+HBqX+2Bw4cZl/fxGHtcCG0deD8QPC+XZPIl/8fIrWoYH2VvaALoWtJ41Gw6RBha3q7bHnGdytCX06lrz94KsHXGpm8aQdn5jOpYwc+nZoYP/hL5rYd+hkKtm5+byzch96nYY/jumIVgsnzl3h+z2J/L9VB+jdoT4ZJovDpXYJ5zJ567E7Sjz4S/Pjr2fJNFsIa2Ak8UIW3+5KZMLVk4h8q41/rT3A6QtZhAR4c+JcJseTMtFq4O6eoQ7bKapH++ZB6HVaRvRuxv9+OMq3uxOZeldEsXIzTHm8s6awl6Jn23r8Fn+Jf605SKNgX6w2hb+vJ/UCffDz8cCck8+mmCQKbAofLx1/HteJpvWM/N83v5Oda+Whe9twLqXwRPG7PWcY3a+5Q1kFNhtrtyawcW/hNgAmD27F3T0KTzQPnLjMf74+TJ6lgKE9m5JpsrD794ss+/EYUDgk07JxHU5fuEJyajaeei2Pj2xXZsIG8PHS0zk8mL1HC09S77kj1H6CVuTR4W15Y8lvfPJdPBqNhnbNgtBpNcSdTOWHX8+SeDGLds0Cadm4Dl/vOM2GnYncf3fxeLpKnqWARZ8ftF8NUi/QB5ut8ASzbVggPdvWJ9dipcCm8PXSl3jcZ5jyOJKYzsGEVPb8Xpj0z6WYaVrPwJ1dCk9u07PyeHtVLPn5NvR6LWu2JAAQ0TSAY2czWPxFHG89fkexk8OKOp6UwYfrf6duHW8CjV60aFSHgV0b24exnPluTyLrtp3Ez1uPXqehWUMj9QJ82Hs0hYWrD6AB0MCTYzrQo82136PWoYGMHRDOJ9/FszX2HGP7h19Xp0xOJWehAeJOpfHrkUvc0a4+UPj7+OvvF/nxt7NcTM8hJ8+Kp4eWP4/rRLurJ+rlkZqZy8JVsRTYFA2CfNn9+0WaN/K3N65+2nuWdVsTsFht6LQanhnXiU4l9Ma6wqX0bNZsSSDHYuXFSV0cjhn7lU03DN+Wl7NhpVqftFMzc9kRl0yQvxeh9YycPJ/JhIEti7UqKqJtWCA+Xjp+PnieYb3DyLfaMOdaaVPGNiOaBtCqSR0OXm0RNwnxY8/vl/D38yDA4EWGKY/e7a8luobBfky/vysrNx3n99Np+HjpSTh/hUXrDvLi5C7EX52B2yYsEE+Pwi/x6eTCLuzzl814eegIruN4RmazKd5dd5Dk1GzSs/IY0adZsXqev2zmvc8PodNqeHxUO7pF1MNDr6WOwZP/fHWYeZ/FYC1QjI1q4XCCotFoGBjZmIGRxVvX1yuqU2oJXfnbYs8DMKDLtW1otRo6tghi1+GL/Hf972SaLNwX1dx+QHcKr0vHFkG89/kh+1hOeCN/pg6JYN+xFDbsSuTLn08xeXCrMutVRCnF3qOX8PLQ8dLkLrz6f3vYGnuOEVfHWHcdvsCp5MIuv8dGtCPTbOHVD/fw9Y7T9OnY0N7izbfaOHomncZ1/exnxv06NWTDrkS27j/PkO5NCQnwsZdrysln/vL9XEzL5t5eoUy4syWtQ8+x7IejHD+XiVajsSfXIoFGL7q2CmFr7DnmL9+Pp16LxWqjV4cGRHVqSK6lgF/jL/Ld7kR8vPS0DQukab3CORefbz/JD7+epW4db/p3bsSmfUms3HQco48HAQbPwmNAp+GPYzrYu7Tv7tmUC2nZ+Hl70LJxHXy89Jhz8zl+NpMAoycNgx1Pwkrz4L1t6BoRQnaelahOjYotrxfoyzPjOvH/Vsfy4frfiy3v3b4BD93bBo0GfjmUzM+HzjM6qrk99lWVnpVHfGI63l46vD10rNmawOkLWXQKD2ZYrzBaNqlDSkYOM//vV5b9cJTdhy9yMCEVm1LUD/JlRO8wendoYE+CR8+k8+8v4uwTscIb+TNuQDj//uIQy386RsMgX1qHBrJ2awKWfBsP3NOatmGBHDyRSssmdWjWwMj/fjjKttjzxB6/XOzE3FpgI/5MOjqNhuaN/Nm6/zwFNhv39gorlohTM3N57/NDmLLz7XNLdh2+yO+n03hiVHty8wvYHJNE2pU8WjcP4o7WIQ4t0Zw8K9/vOYOft563Hu/l0Fs56FwmX/58EmuBYnC3Jg4Ju8gd7eqzZssJtsWeZ2Sf5njoC7dddJXIIyPasuTbeL7ecYoebeqRlpXLxxuOEH8mA51WQ4NgX+r61+Hw6TT+tfYgf4su3vtw/rKZd9ceJDKiLhPubGnvnfxm12ksVhsP3duGLq3q8soHu/j6l1P0bt+ArGwLqzefwM9bz4AujdkUk8Sqzcdp3zyw3CdJl9KzuZieQ8MgX+pe991WSnH6QhZpV/Jo3zyQTJOFN5fuJfvqsF6BTaHXFdYx32pj49VLjG/sGneVWp+0N+9LQikY3a95iT8QleGh1zGyT3NWbznBFz+fpMPVs73GIWX/aI2JasGCFfv55Lt4TDn59gvli8Ym2jd3TPoNgnx5bkJnbEqBgn9/cYj9xy/z/Z4zHD2bQf0gX/tn6wX6cPpCFhfTsnljyW9otfDg0Db07nBtstye3y+SnJoNwBfbT9KxRbB9tjsUHlyFN5hRPDm6vcOPQ4829UhKMbMpJolAo97eyq6o61va17titrDvWAqN6/oR3tixO/uu7k359cglDiak4ufjwV1Xz4yLtGoSwIKn+pB6JRdvT709Jo3r+vHbkUv8+NtZIpoG0KVlXacTy86lmLmUnkP3q13igyIb88XPp9hxKJlB3Zrww69n0Gk1jB8QjkajIcDgxai+zVi5+QTf7b7WIj+elIHFaqN982stAb1Oy8i+zfjku3j+9uEeRvQOY0TfZmg1Gpb/dIyLadkM7dmU8QMKWyADIxvTtVVdfL098NBruWK2cDkzl+y8fPLzbbQODcTXW0+XiLp8uyuRtKw8+nRowB+GtSMzIxsfLz3jB4Tz0YYjrNx0HI0GhvUKI6y+ke92n6FeoA+vPdgdX28PukaE8NayGD7+9ghKgVYLz47vTNuwa8dkswb+xYYa/Lw9Ktwi8PP2oFf7BmWu0zYskL9Fdyfm2CWSL2eTZy2gZaM69GxX32Fy3d3dm7Jy8wl+/O2MQ8utMjLNFtZuOcHOwxe4cTi9b8cGPHhPG3sCqx/oy5S7WrFq03FiT1ymUV0/gv29+f10Gh9tOMJPe88S1akRuRYrX/58Cii86VLDYD+6XU2ET43pwP9bfYB/rT1IeCN/Dp9OJ6y+kf6dGqHVahjS49p+3tW9Kdtiz7MpJsnhe1lgs/HuuoPEnSzs1dFpr53cXUjN5uHhbe2JWynF0h/iycrO5/4hEfRuX59Ms4VPfzzG/uOXmf2/GC5lZGPJLxwO++VQMtua1OG58Z3tXdE/7T2LOdfKff1bFBtebNm4Di9Njiwzxl4eOvp1asgPv54l9sTlwsR8JZfY45cJrW+gd/sGxJ/J4JeDyfzfN79zIOEyOXkFdGlZl6l3tbInw/3HUlj0+SE+3nCEVx/sbv+75Ftt/Pfrw1y6OqH4cmYuT45uz6X0HH45mEyDIF/6dmyATqu1/4Z/9fMpLmZkU2BTRA9tQ7fWIeTlF7D9wHl2xV2kX6eGJe6LtcDGsTPpZJtyOZWcxf9+iMdaoNAA3drUo0ebeqRn5bF1/zkupBX+7nrotXjqtfaEDYWNKa62f37ae5ZL6Tnc1a1JiWPWrlCppG2z2XjjjTc4evQonp6ezJ49m7CwMPvyzZs38+9//xu9Xs+4ceOYOHGi08+U5rs9ZzD4eHBH2/qVqWqp7urehO0HzrN13zn7bPRO4WX/eLUNC6RTeDAHE1LRajQM6d6UI4lpJKdmM6h7U3q0KbmOWo0GNPDwsLac+HA367adtG+vSLMGRn49csnere2h0fJ/3/xO3QBvfLz0bNl3jh1xyei0GsZENWfdtpMcPZvhkLR/T0wn7lQa7ZoF0jUixKEOGk3hkMLIPs1QSpU6RupMUUv7xklzO+KSKbAp+ndpVKx7sXlDf8b2b8GarQmM7h9eYvePp4euWEvP00PHU2M6MOfTGN77/BB6nYY2YYHcF9WC5g39OZiQym9HLuLtpefuHoUt371HLwHQ7er+D4hszPqdiWzYnUhyajbJqdn07dDAYVxpYNfGfLvnDFtjzzG8dzN8vfVsvdpr0PmGs+WoTg2x2RTrd57my19OcSr5Cm3CAgu76hr6M/7OcIf9v36mub+fp8P8iiLtmwXZx/OL9rtInw4NqGPwJD0rjw07E9mwKxEN4Omh5en7Otq7sxvV9eOpMe15b90hGof4Mbpfc4fjqyaENTA6HJ8lierciB9+O8u3u87QuWXdUsf/y3L2kokDJy7z3Z5EcvIKaBLiR9+ODbEpxRWzhZaN65Q47DQwsjF9OxReYtMw2BeNRkNqZi7rtiWw5/eLfPZT4VCCn7eeP97XsVg82zUL4tER7fjsp2McPp1O84ZGHh/ZvsQTy8Z1/WjXLJDfT6dzMOEyncLrYrMpln5/lLiTabQJDSCsgZHf4i/RoqE/qVfy2BF3gTZhgeRaCtgWew6tVsOZiybaNQtkUNfGaDQafL09eG5CZ977/BCHTqYSaPRiwp1htGsWyLd7zrLj4Hk++e4IT43pQML5K6zfcRp/Xw8Gd21S4TgX6duxMGnvPJRMjzb1+PlgMjalGBhZWKfhvcPYFXeB3b9fxNtTx8PD2tCvY0OH70VkRAj9OjXkl4PJvLUshoGRjWkTGsD6nac5c8lE7/b1SbuSR8zRFBatO8SF1MKkPLZ/C3vL+a7uTdgae45NVyfGtQ0LpGtE4fd1VN9m7IxL5usdp+jVvr5DbwMUTmZ7Z80BTiVfmwjp7anjnjuacighlb3xl9gbX/hbotNq6Nm2HvUCfYg9nsq5yybu6RnK+VQzBxNS7SeI1gIb31/NV2OiHIezXKlSSXvjxo1YLBZWrVpFbGws8+bN4/333wcgPz+fuXPnsnbtWnx8fJgyZQoDBw5k//79pX6mLF0jQhjSvUmlk0xp9DotT4xqz5xPY0jPyqNfp4a0aOR8wtP9QyLw9T7JnV0aE9E0gAKbDUu+jdAmgaSklD0T1uDjwbRhbVm3LQFfLz13XtfabdGoDr8euURSiokOzYMY2bcZ8z7dx9urYu1nzsH+XowbEE6TegbWbTvJ+cuO10v/8GvhzOYbE8f1irqzKivQ6IVWo+Hy1aR9KSOHTFMe3+0+g4deS58OJbfA7rkjlNahgXTv0JC0NHOJ65QkrIGRZ8Z1ZMu+c6Rk5BB3Mo2jZzJo1sDocEOaX49c5A93t2bj3iS8PHX2sSx/X8/CE4YtJ9iy/xzB/t6MumF82EOvY0j3JqzbdpLv9iTSr2NDYuIvEVbfSJvQAId1NRoNd0Y2pnubevznqzgOJKRyICEVg48Hj45oW+XxyhsVTgAq3JfIViEsWLGfs5dMPHRvG5pc7Sov0qF5MO+/OMCtLqPy8dLz2Ih2LFixn8VfxPHKH7pSt46P8w9etfv3C/z368IueF8vPX+4O4I7uzQu96V+nh46Gl03NyO4jjePj2rP+DvDOXwqDatN0Tk8uNTJQ3e0q0+31iFcTMumYbBfmeVOHNiS2f+L4cP1vzMmqgX7jqVwJDGd0PoGnhnXCR8vPZMGFQ4DXc7M4W8f7uHjDUdQgF6nwVqg0Gk1TLnLcfKbh17L02M72i8xLfqOv/yHbqS8a2bv0RReWryTTJMFheKJUe0rNQmsSJMQA2H1jRw6mcaR02ls3peEt6fOPoZdP9CXmQ92x5xrpUmIH8ZSJgxPGdwKS34Bvx65xCffxdvfb97QyAND22BTiv+3+oB9QuiIPmH2oR4o/A2fNKgli9YdokUjf/54Xwd7XIL8vbkzsjEb9yax/cB5Bl13kpKTZ2XBiliSUkx0b1sfg5cOb089fTo2oEmIgfuimpNw/grxiekEGr1o3zzIPlFybP9w+6Wk/1pzACgcsweIO5mGKSefId2bOp0bUhWV+svFxMQQFRUFQJcuXYiLi7MvS0hIIDQ0lDp1Cs+Yu3Xrxt69e4mNjS31M2V5emzHylSxXMIaGHliVHt2xV1gwp3l65oLCfDh8ZHt7a91Wi0+XuX/oe7csm6x1htA/84N8dBr0Ws19GhbD29PPcN6h7FhVyIdmgcxMLIxnVoGo9NqsRYUTrQ4d/la8jt/2UzcyTQimtSp8GzritBptQQaPUnNzCXuZCoLVx+wL3vgntalztjUaDS0aOSPTlfxpNahebA9cRVNsDqRlElEkzpMGNiS0xeyWLHxOO9/WXhM/eHuCIfW/D13hBLWwEh8YjpDe5b8hRoY2Zif9iaxYVdi4ZAMMKx3WKkJ0ODjwfMTO/PVL6c4djaTh4e1oX7gzb2m2uDjwV+ju5GSkWO/n8CN3ClhF2kTFsiEgS1ZveUE/1wZyyv3dy3XtfDpWXl8+sMxvDx0TB3SishWIS4bFw/y9yaqc/mGkPQ6LY1L+XtcL7S+kfuHtGLp90ftrfgOLYJ4anSHYr1Pdev4cO8doXy94zTtmwfx2Ih2mHLyybfaik0AhcLEfeOkLt3VLvzlG48TfyadsAZG7rkjlLYVmPxVmqjODfn0x2MsWBkLFDZmrp8sWp5Z8j5eep4c3YExUdnEnUzl6JkM8vILeHRkO7w8Cxtp0++P5PSFLK6YLCUO40S2CuHNR++gXoBPsQbJ8N7N+PlAMmu2JNAgyJd2zYLIt9p4/8s4klJMDOjSiBf/0J3LNzR+NJrCSZotG5fc61N0Ylb0/0WXzu06XDgnp1d71/YK36hSSdtkMmEwXDtIdTodVqsVvV6PyWTCaLz2B/Pz88NkMpX5mbIEBvqi17u2lX29oSFGhvYteyZ6eYWEVO1yjqaNHbvfnhjXmQdGtC8xyTQK8SM5NZu6dQ1oNBq+vPpo0rGDI6pcD2ca1DXw+6lU1lzt5u/XuRH9ujSmbznnHFSlfneFGOnXrSkFBQq/qz/QvYAubeuzeO0BQgJ8mTCkTbEWT0iIkf7dQ0vY4jULnxvAwuUxXEzLZkS/Fgzt2wKdkxbbE+O6VHpfylJWjJo0CrgpZdak6BHtQadl9cZjvLP2IHP/1K/UFlqRn+MukJ1n5Y/jOnFvn5vXHelK44e0oU+XJhxKuEyzhv5EhAaWeqL1yJhODOgeSnjjOpU62QVo2bwurz3m+glRE4a0wdfXiy0xZ7mzWxNGRVV+PkJIiJGOrUtPdA3qlz1kUtp3JSQEXry/G/9YtpeFqw8wsFsTLqRmc/hUGt3a1OP5qd3QaDSV/j3yvvq7HBhkIDUzhwMnLtM4xECPjsWHCF2pUknbYDBgNl9r5dlsNnvyvXGZ2WzGaDSW+ZmypKdnV6aK1S4kxOi0e7yyzFnFZ2rXC/Dh7EUTx05eJtDoxc+x5/D10tOint9Nq0eR/p0acvhkKmcvZhHZqi7T7m0DUK5yXRmnbNO1uAT7ejDzge4ApKZW7ilkWuClSV3sr9MquZ2qupnHUm02tFtjUtOz2RSTxN8W7+ClyV1KvfwlJMTInrhkPD20dG4e5Fbx8gC6Xh2+ubGVd6NAH32FhpOud7OPo15tQujVpnDuSG2Nf8sGBl6c1JlPvj/Kpqsz3Lu0rMvjI9qSlmauUozyLYWT0U6eSWPB8n1YrDZG9glz+jctj7JOJCp1+ta1a1e2b98OQGxsLBER166xDA8PJzExkYyMDCwWC3v37iUyMrLMz4iKK+oiO59q5vSFLNKz8ujcsm6xCRc3Q4829RjTr/ASnRuvHxaisjQaDVPuakXfDg04lVx4eWS+teS7yl1KK5xU2DY0sMrzNMStrXVoIG8+0pO//qEbrz/Ug6fHdbQ/s6IqilrTCecyuZKdz909mtLTxROmS1KplvaQIUPYsWMHkydPRinFnDlzWL9+PdnZ2UyaNIkZM2bwyCOPoJRi3Lhx1K9fv8TPiMormjxzLsVsv370xhnjN9Oofs0Z0adZle/tLcT1tBoNDw1rQ66lgJhjKbyz5iBPjelQbKw65upVAh1a3JybZ4hbi16ndfk904t++wqu3rL2Zl3idaNKJW2tVsusWbMc3gsPvzamMWjQIAYNGuT0M6LymjcsnGwWdyqNS+nZeHpo6dCi6hNMKkIStrgZdFotj49qz3++imP/8cu88sEuerVvwKRBLe09STFXb0XasZqPeSGKFA1bW69eV1/eO9JVlfQruamQAB+aN/Tn8Kk0UjJy6dG6Hl4uvixOiJriodfyp7EdGTegBR56LZtikvhie+HExzxLAfuPXqJhsC/1bvKMfSFKU5SkC64+Fa+6LtyQpO3GerW7Nn5S3stThHAXWo2G4b2bMefxXtQP9OG7PWc4eiadQydTsVhtTu/TL8TNVJSki54WWV09j5K03VjPtvUK7+cbVPikJiFuRd6eeh4d2Q4N8NlPx/j1atd4t2qcwyHEjewt7WruHq/19x4Xpatj8OKlyV3w9/N0y5tqCFFe4Y3q0PfqbS+TUsw0CPYltL7zG5oIcbNoaqh7XJK2m6vK086EcCfjBoRz/rKZIKMXD47sICeqokYVdYdbi7rHpaUthBDX1PHz5NWrN9C5XW9AI2oP+5j21Za2jGkLIYQQtdSNY9oye1wIIYSopa7NHpfrtIUQQoha7dp12nLJlxBCCFGrFe8el6QthBBC1Eqaq9nTWtTSljFtIYQQonaqqZurSNIWQgghKqj4zVUkaQshhBC1ktb+lK+iiWjVVG71FCOEEELcOm58yletviNabm4uL7/8Mqmpqfj5+TF//nyCghyfa7t69WpWrlyJXq/nqaeeYuDAgWRlZfHyyy9jMpnIz89nxowZREZGumRHhBBCiOqi0brR7PEVK1YQERHB8uXLGTNmDIsXL3ZYnpKSwrJly1i5ciUfffQRCxcuxGKxsGTJEnr16sWnn37K3LlzmTVrlkt2QgghhKhOWvvNVap39nilWtoxMTE8+uijAPTv379Y0j548CCRkZF4enri6elJaGgo8fHxPPTQQ3h6egJQUFCAl5dXFasvhBBCVL+i7nBrNd973GnSXrNmDUuXLnV4Lzg4GKPRCICfnx9ZWY437jeZTPblReuYTCb8/f2Bwpb4yy+/zF//+lenFQwM9EWv1znfk1ogJMTofCUhcSoHiZFzEiPnJEbOVTZGBoM3cK1bPDDQr1ri7TRpT5gwgQkTJji89/TTT2M2mwEwm832ZFzEYDDYlxetU5TEjx49ygsvvMBf/vIXevbs6bSC6enZzveiFpCnDpWPxMk5iZFzEiPnJEbOVSVGOdl5AORZrABcycxxWbzLSv6VGtPu2rUr27ZtA2D79u1069bNYXmnTp2IiYkhLy+PrKwsEhISiIiI4MSJEzz77LO8/fbbDBgwoDJFCyGEEDVOc+NtTKvpWqxKjWlPmTKF6dOnM2XKFDw8PHj77bcBWLJkCaGhoQwePJjo6GimTp2KUornn38eLy8v3n77bSwWC2+99RZQ2CJ///33Xbc3QgghRDUoGsN2i0u+fHx8ePfdd4u9//DDD9v/PXHiRCZOnOiwXBK0EEKIW4Gm2OzxWnzJlxBCCHE7u3H2eDXlbEnaQgghREVda2nLA0OEEEKIWu3aU74Ku8c11XSdtiRtIYQQooJufMqXPE9bCCGEqKWKnuol3eNCCCFELXfjA0Kke1wIIYSopW5sWUv3uBBCCFFL3dgbLt3jQgghRC11Y5Ku1c/TFkIIIW5nNybp6no0pyRtIYQQooK0N2RPuSOaEEIIUUsVa2lL97gQQghROxWfPS5JWwghhKiVpHtcCCGEcBMyEU0IIYRwE27VPZ6bm8szzzzD1KlTeeyxx0hLSyu2zurVqxk7diwTJ05ky5YtDssSEhLo1q0beXl5lau1EEIIUYNubFjX6u7xFStWEBERwfLlyxkzZgyLFy92WJ6SksKyZctYuXIlH330EQsXLsRisQBgMpmYP38+np6eVa+9EEIIUQPcqns8JiaGqKgoAPr378+uXbsclh88eJDIyEg8PT0xGo2EhoYSHx+PUoqZM2fywgsv4OPjU/XaCyGEEDWgprrH9c5WWLNmDUuXLnV4Lzg4GKPRCICfnx9ZWVkOy00mk3150Tomk4n33nuPAQMG0KZNm3JXMDDQF71eV+71a1JIiNH5SkLiVA4SI+ckRs5JjJyrbIzSsvPt/9Zqqi/WTpP2hAkTmDBhgsN7Tz/9NGazGQCz2Yy/v7/DcoPBYF9etI7RaOTrr7+mQYMGrFu3jpSUFKZNm8Znn31WZvnp6dnl3pmaFBJiJCUly/mKtzmJk3MSI+ckRs5JjJyrSowyM3Ps/9ZoNC6NdVknAE6Tdkm6du3Ktm3b6NSpE9u3b6dbt24Oyzt16sQ777xDXl4eFouFhIQEIiIi+Omnn+zrDBo0iI8//rgyxQshhBA16vru8Ooaz4ZKJu0pU6Ywffp0pkyZgoeHB2+//TYAS5YsITQ0lMGDBxMdHc3UqVNRSvH888/j5eXl0ooLIYQQNeX6IezqmjkOlUzaPj4+vPvuu8Xef/jhh+3/njhxIhMnTix1G5s3b65M0UIIIUSNc2hpV2PWlpurCCGEEBV0fZ6WpC2EEELUYtePY1dn97gkbSGEEKKCNDU0EU2SthBCCFFBWukeF0IIIdzD9S1t6R4XQggharGauk5bkrYQQghRQTJ7XAghhHATMntcCCGEcBMaubmKEEII4R4cZo/LmLYQQghReznOHpekLYQQQtRajvcer8Zyq68oIYQQ4tYgs8eFEEIIN+E4e1ySthBCCFFrOd5cpfrKrdTztHNzc3n55ZdJTU3Fz8+P+fPnExQU5LDO6tWrWblyJXq9nqeeeoqBAwdSUFDA3LlziYuLw2Kx8MwzzzBw4ECX7IgQQghRXdyqe3zFihVERESwfPlyxowZw+LFix2Wp6SksGzZMlauXMlHH33EwoULsVgsfPXVV1itVlauXMn7779PYmKiS3ZCCCGEqE5u1T0eExNDVFQUAP3792fXrl0Oyw8ePEhkZCSenp4YjUZCQ0OJj4/nl19+oUGDBjz++OO8+uqrDBo0qOp7IIQQQlSz69N0dc4ed9o9vmbNGpYuXerwXnBwMEajEQA/Pz+ysrIclptMJvvyonVMJhPp6ekkJibywQcf8Ntvv/HKK6/w2WeflVl+YKAver2u3DtUk0JCjM5XEhKncpAYOScxck5i5FxVYqTVgE2Bp5e+2mLtNGlPmDCBCRMmOLz39NNPYzabATCbzfj7+zssNxgM9uVF6xiNRgICArjzzjvRaDT07NmT06dPO61genp2efajxoWEGElJyXK+4m1O4uScxMg5iZFzEiPnqhojjUYDSlFgtbk01mWdAFSqe7xr165s27YNgO3bt9OtWzeH5Z06dSImJoa8vDyysrJISEggIiKCbt262T8XHx9Pw4YNK1O8EEIIUeOKxrJrVfd4SaZMmcL06dOZMmUKHh4evP322wAsWbKE0NBQBg8eTHR0NFOnTkUpxfPPP4+XlxcTJ07k9ddfZ+LEiSil+Pvf/+7SnRFCCCGqS1Gyrs6JaBqllKq20irBXbp3pCuqfCROzkmMnJMYOScxcq6qMXpq4TbyLAV0Cg/muQmdXVqv0sjNVYQQQohKKGpp1/rrtIUQQojbXVGyrsacLUlbCCGEqIxrE9GkpS2EEELUavaJaNU4fVySthBCCFEJNXHJlyRtIYQQohKK7j8u3eNCCCFELaepgeu0JWkLIYQQlaCV7nEhhBDCPWhkIpoQQgjhHrRyyZcQQgjhHmT2uBBCCOEmimaPS/e4EEIIUctp5N7jQgghhHuQe48LIYQQbkJa2kIIIYSbsM8er8YxbX1lPpSbm8vLL79Mamoqfn5+zJ8/n6CgIId1Vq9ezcqVK9Hr9Tz11FMMHDiQrKwsnn/+eXJycvDw8GDBggWEhIS4ZEeEEEKI6mSfiFbbu8dXrFhBREQEy5cvZ8yYMSxevNhheUpKCsuWLWPlypV89NFHLFy4EIvFwueff05ERASfffYZw4YN46OPPnLJTgghhBDVzW26x2NiYoiKigKgf//+7Nq1y2H5wYMHiYyMxNPTE6PRSGhoKPHx8URERGA2mwEwmUzo9ZVq6AshhBA1riZuruI0a65Zs4alS5c6vBccHIzRaATAz8+PrKwsh+Umk8m+vGgdk8lEUFAQO3bsYNiwYWRmZvLZZ585rWBgoC96va5cO1PTQkKMzlcSEqdykBg5JzFyTmLkXFVi5OlZmEINBq9qi7XTpD1hwgQmTJjg8N7TTz9tbzGbzWb8/f0dlhsMBvvyonWMRiPvvfcejz76KJMnTyY+Pp5nnnmG9evXl1l+enp2uXemJoWEGElJyXK+4m1O4uScxMg5iZFzEiPnqhqjAmsBADk5FpfGuqwTgEp1j3ft2pVt27YBsH37drp16+awvFOnTsTExJCXl0dWVhYJCQlERETg7+9vb4EHBwc7JHYhhBDCnWhqY/d4SaZMmcL06dOZMmUKHh4evP322wAsWbKE0NBQBg8eTHR0NFOnTkUpxfPPP4+XlxfPPvssr776KsuXL8dqtfLmm2+6dGeEEEKI6lITs8c1SilVfcVVnLt070hXVPlInJyTGDknMXJOYuRcVWO0cHUscSfTmDAwnHvvCHNpvUojN1cRQgghKkEezSmEEEK4iWv3HpekLYQQQtRq126uUn1lStIWQgghKqEm7j0uSVsIIYSoBI1WuseFEEIIt6CV7nEhhBDCPcjscSGEEMJNFOVq6R4XQggharlrE9GqsczqK0oIIYS4ddTEvcclaQshhBCVUNTClu5xIYQQopbTyHXaQgghhHu4Nnu8GsusvqKEEEKIW4fMHhdCCCHchNtcp52bm8szzzzD1KlTeeyxx0hLSytxvbS0NO6++27y8vIq9DkhhBCittO4yyVfK1asICIiguXLlzNmzBgWL15cbJ2ff/6ZadOmcfny5Qp9TgghhHAHbjN7PCYmhqioKAD69+/Prl27im9Yq2XJkiUEBARU6HNCCCGEO6iJ7nG9sxXWrFnD0qVLHd4LDg7GaDQC4OfnR1ZWVrHP9e3bt9h7JpPJ6eduFBjoi16vc7pebRASYqzpKrgFiZNzEiPnJEbOSYycq0qM/Py8gMI8VV2xdpq0J0yYwIQJExzee/rppzGbzQCYzWb8/f3LVZjBYKjw59LTs8u17ZoWEmIkJcX5ScjtTuLknMTIOYmRcxIj56oao9xcCwBXMnNcGuuyTgAq1T3etWtXtm3bBsD27dvp1q3bTf2cEEIIUds0rWfE4ONBvUCfaivTaUu7JFOmTGH69OlMmTIFDw8P3n77bQCWLFlCaGgogwcPrtDnhBBCCHfTo009urcOqdaJaBqllKq20irBXbp3pCuqfCROzkmMnJMYOScxcq62xsjl3eNCCCGEqH6StIUQQgg3IUlbCCGEcBOStIUQQgg3UesnogkhhBCikLS0hRBCCDchSVsIIYRwE5K0hRBCCDchSVsIIYRwE5K0hRBCCDchSVsIIYRwE5K0y+HAgQNER0cDcPjwYcaPH8/UqVN58803sdlsAPz3v/9l9OjR3H///WzZssXh8wkJCXTr1o28vLxqr3t1qWyMMjIyeOyxx5gyZQpPPfUUqampNbYPN1N+fj4vv/wyU6dOZfz48WzatInExESmTJnC1KlTef311+1xWr16NWPHjmXixIm31bFU1RjdDsdSRWIEkJaWxt13313seJHjqPQY1frjSIky/fe//1UjRoxQEyZMUEopdd9996mYmBillFILFy5UX375pYqPj1cjR45Uubm5Kjc3V40ZM0ZlZ2crpZTKyspSjz32mOrVq5fKzc2tsf24maoSo3nz5qn3339fKaXUjh071F//+tca24+bae3atWr27NlKKaXS0tLUgAED1BNPPKF2796tlFJq5syZ6scff1SXLl1SI0aMUHl5eerKlSv2fyt16x9LVY3R7XAslTdGSim1fft2NXr0aBUZGelwvMhxVHaMavtxJC1tJ0JDQ1m0aJH99cWLF+natStQ+HzwmJgYEhIS6NmzJ15eXnh5eREWFsbRo0dRSjFz5kxeeOEFfHyq73mr1a0qMTpx4gT9+/d3WPdWdM899/Dss8/aX+t0Og4fPkzPnj0B6N+/Pzt37uTgwYNERkbi6emJ0WgkNDSU+Pj42+JYqmqMbodjqbwxAtBqtSxZsoSAgAD7+nIcOY9RbT+OJGk7MXToUPT6a48db9q0Kb/++isAW7ZsIScnh9atW7N3715MJhPp6ens37+fnJwc3nvvPQYMGECbNm1qqvrVoioxatu2LZs3bwZg8+bN5Obm1sg+3Gx+fn4YDAZMJhN//vOfee6551BK2Z/D6+fnR1ZWFiaTCaPR6PA5k8l0WxxLVY3R7XAslTdGAH379iUwMNDh83IcOY9RbT+OJGlX0Jw5c/jggw94/PHHCQ4OJjAwkPDwcO6//34ee+wx5s+fT+fOnQkMDOTrr79m3bp1REdHk5KSwrRp02q6+tWiIjF6/PHHOXfuHA899BDJyck0aNCgpqt/0yQnJ/PAAw8wevRoRo4ciVZ77etnNpvx9/fHYDBgNpsd3jcajbfNsVSVGN0ux1J5YlQaOY6cx6jWH0c12DXvNs6ePWsfr/3444/VhQsXlFJKzZo1S23dulWlpqaqDz74QCml1JUrV9T48eOV1Wp12MbAgQNvyfGjIpWN0ZYtW9SuXbuUUkp9//33av78+TWzAzdZSkqKuueee9TOnTvt7904zrZhwwb7eG1ubq66cuWKGjp0aLHj5lY9lqoao9vhWCpvjK5X2vFyux9H17s+FrX9ONI7T+viemFhYTz++OP4+Phwxx13MGDAAJRSJCUlMW7cODw8PPjLX/6CTqer6arWmIrEqHnz5kyfPh2AevXqMWfOnBqu/c3xn//8hytXrrB48WIWL14MwN/+9jdmz57NwoULadGiBUOHDkWn0xEdHc3UqVNRSvH888/j5eVVw7WvHlWN0e1wLJU3Rrezqsaoth9H8pQvIYQQwk3ImLYQQgjhJiRpC1EN8vPz6devH48++mi51j979izPPPPMTa5VxSQlJREZGVnT1RDitiZJW4hq8NNPP9GmTRvi4uJISEhwuv758+c5depUNdRMCOFOZExbiGoQHR3NsGHDOH78OFarlVmzZrFnzx7efPNNvvnmGwD766+++op77rmHixcv0qNHDz766CM2btzIe++9h81mw8/Pj1deeYVOnTphtVpZsGABW7duRafTERkZyeuvv45Go2HevHns2rULnU5Hp06deOWVVzAYDAwaNIhOnTpx9OhRXnjhBebOnevwulOnTsyaNYvk5GTy8/MZPnw4Tz75JElJSYwcOZL9+/eTn59f6vYPHjzIG2+8QX5+PqGhoZw/f54ZM2YA8NZbb+Hr64vZbGbdunX84x//4MCBA5jNZpRSzJ49m27dujFjxgy8vb05duwYqampDBo0iICAALZs2UJKSgqzZ8+md+/enDp1ilmzZmE2m0lJSaFNmza88847t83kPXEbqrF560LcJo4fP67at2+v0tLS1IEDB1SnTp1UWlqa2r17txo+fLh9vetfX//vEydOqD59+qgzZ84opZTauXOn6tu3r8rKylJLly5V999/v8rJyVEFBQXq2WefVV988YX617/+pZ5++mllsVhUQUGBmjFjhpo5c6ZSqvDylvfee89e7o2vo6Oj1aZNm5RSSuXm5qro6Gi1YcMGdfbsWdWlSxellCp1+/n5+ap///5q69atSimldu3apVq3bq12796tdu/erdq0aaOSkpKUUkrt27dPPfPMM6qgoEAppdQHH3ygnnjiCaWUUtOnT1cTJkxQFotFXbp0SUVERKj//e9/SimlPvnkE/Xwww8rpQpvOfnll18qpZSyWCxqxIgR6vvvv3fNH06IWkgu+RLiJluxYgUDBw4kMDCQwMBAmjRpwurVq+nSpUu5Pr9792569epF06ZNAejduzdBQUHExcWxc+dORo8ejbe3NwDvvPMOAOPHj+f555/Hw8MDKGzp/+lPf7Jvs3v37g5lFL3Ozs7mt99+IzMzk3/961/29+Lj4+nUqZN9/e3bt5e4/WPHjgEwYMAAAHr16kWrVq3sn2vYsCGNGzcGIDIykjp16rBy5UrOnj3Lnj178PPzs687cOBAPDw8CAkJwdfXl6ioKKDwtrkZGRkAvPzyy+zYsYMPP/yQ06dPc+nSJbKzs8sVVyHckSRtIW6i7OxsvvrqKzw9PRk0aBAAJpOJTz/9lMjISNR1o1P5+fklbsNms9lvwVhEKYXVanW4fSzA5cuXsdlsxT5js9kctu/r6+vwuaLXNpsNpRQrV66035s6LS0NLy8v0tPTS61T0fZ1Op3DPgEO9yy4vtytW7fy1ltv8fDDDzN48GBatGjB119/bV/u6enpsJ0b9xXghRdeoKCggHvvvZc777yT5OTkYuULcSuRiWhC3ETr168nICCAn3/+mc2bN7N582Y2btxIdnY2+/bt4/z586SmpqKUYsOGDfbP6XQ6e5Lt3bs3v/zyC2fPngVg165dJCcn07lzZ3r37s0333yDxWLBZrPxxhtvsGHDBqKiolixYgX5+fnYbDY+++wz+vbt67S+BoOBLl26sGTJEgCuXLnClClT2LRpk8N6pW0/PDwcT09Ptm/fDsDBgwc5duxYsZMOgB07djBw4ECmTp1Khw4d2LhxIwUFBRWK7y+//MKf/vQnhg0bBhQ+Irai2xDCnUhLW4ibaMWKFTz88MMOrU1/f3+io6P56aefmDx5MuPGjSMkJIQ777yTQ4cOAdCyZUu8vLwYP348a9as4fXXX+fpp5+moKAAb29v/vOf/2A0Gpk8eTLnzp1j7NixKKXo2bMn0dHRWK1W5s+fz5gxY7BarXTq1ImZM2eWq87//Oc/efPNNxk5ciQWi4URI0YwatQokpKS7Os89dRTJW5fr9ezaNEiXn/9dRYuXEizZs2oW7cu3t7e5OTkOJQzefJkXnzxRUaOHInVaqVv3778+OOPDs86dub555/nT3/6E76+vhgMBnr06MGZM2fK/Xkh3I3MHhdCuNT8+fN55JFHqFu3LsnJyYwePZqNGzeW+ZAGIUT5SEtbCOFSjRs35qGHHkKv19sv45KELYRrSEtbCCGEcBMyEU0IIYRwE5K0hRBCCDchSVsIIYRwE7V+IlpKSpZLtxcY6Et6utwxyVUknq4jsXQtiadrSTxdx1ksQ0KMpS677Vraer3O+Uqi3CSeriOxdC2Jp2tJPF2nKrG87ZK2EEII4a5uStI+cOAA0dHRxd7fvHkz48aNY9KkSaxevfpmFC2EEELcslw+pv3hhx/y9ddf2x82UCQ/P5+5c+eydu1afHx8mDJlCgMHDiQkJMTVVSjRpYwcPt5whIRzmYQ3rsO04W2pF+Dj/INCCCFELeHylnZoaCiLFi0q9n5CQgKhoaHUqVMHT09PunXrxt69e11dfKk+3nCEY2czKLApjp3N4OMNR6qtbCGEEMIVXN7SHjp0qMODBYqYTCaMxmsz4vz8/DCZTE63Fxjo65IJEAnnMou9LmuGnig/iaPrSCxdS+LpWhJP16lsLKvtki+DwYDZbLa/NpvNDkm8NK66xCC8cR2Onc1weO3qy8luRyEhRomji0gsXUvi6VoST9dxFstacclXeHg4iYmJZGRkYLFY2Lt3L5GRkdVVPNOGt0WvK3ymb0TTAKYNb1ttZQshhBCucNNb2uvXryc7O5tJkyYxY8YMHnnkEZRSjBs3jvr169/s4u3qBfhQx88LnU7DjPu7Vlu5QgghhKvclKTdpEkT+yVdI0eOtL8/aNAgBg0adDOKFEIIIW55cnMVIYQQwk1I0hZCCCHchCRtIYQQwk1I0hZCCCHchCRtIYQQwk1I0hZCCCHchCRtIYQQwk1I0hZCCCHchCRtIYQQwk1I0hZCCCHchCRtIYQQwk1I0hZCCCHchCRtIYQQwk1I0hZCCCHchCRtIYQQwk1I0hZCCCHchCRtIYQQwk24NGnbbDZee+01Jk2aRHR0NImJiQ7Lv/76a+677z7GjRvH8uXLXVm0EEIIccvTu3JjGzduxGKxsGrVKmJjY5k3bx7vv/++ffk//vEPvvnmG3x9fRk+fDjDhw+nTp06rqyCEEIIcctyadKOiYkhKioKgC5duhAXF+ewvHXr1mRlZaHX61FKodFonG4zMNAXvV7nkvrpdIXlhYQYXbI9UUji6ToSS9eSeLqWxNN1KhtLlyZtk8mEwWCwv9bpdFitVvT6wmJatWrFuHHj8PHxYciQIfj7+zvdZnp6tsvqV1Cg0Ok0pKRkuWybt7uQEKPE00Uklq4l8XQtiafrOItlWQndpWPaBoMBs9lsf22z2ewJOz4+nq1bt7Jp0yY2b95MWloa3333nSuLF0IIIW5pLk3aXbt2Zfv27QDExsYSERFhX2Y0GvH29sbLywudTkdQUBBXrlxxZfFCCCHELc2l3eNDhgxhx44dTJ48GaUUc+bMYf369WRnZzNp0iQmTZrE1KlT8fDwIDQ0lPvuu8+VxQshhBC3NJcmba1Wy6xZsxzeCw8Pt/97ypQpTJkyxZVFCiGEELcNubmKEEII4SYkaQshhBBuQpK2EEII4SYkaQshhBBuQpK2EEII4SYkaQshhBBuQpK2EEII4SYkaQshhBBuQpK2EEII4SYkaQshhBBuQpK2EEII4SYkaQshhBBuQpK2EEII4SYkaQshhBBuQpK2EEII4SYkaQshhBBuQu/KjdlsNt544w2OHj2Kp6cns2fPJiwszL784MGDzJs3D6UUISEhLFiwAC8vL1dWQQghhLhlubSlvXHjRiwWC6tWreLFF19k3rx59mVKKWbOnMncuXNZsWIFUVFRnDt3zpXFCyGEELc0l7a0Y2JiiIqKAqBLly7ExcXZl506dYqAgACWLl3KsWPHGDBgAC1atHBl8UIIIcQtzaVJ22QyYTAY7K91Oh1WqxW9Xk96ejr79+9n5syZhIWF8eSTT9KhQwd69+5d5jYDA33R63UuqZ9OpwEgJMToku2JQhJP15FYupbE07Uknq5T2Vi6NGkbDAbMZrP9tc1mQ68vLCIgIICwsDBatmwJQFRUFHFxcU6Tdnp6tsvqV1Cg0Ok0pKRkuWybt7uQEKPE00Uklq4l8XQtiafrOItlWQndpWPaXbt2Zfv27QDExsYSERFhX9a0aVPMZjOJiYkA7N27l1atWrmyeCGEEOKW5tKW9pAhQ9ixYweTJ09GKcWcOXNYv3492dnZTJo0ibfeeosXX3wRpRSRkZHceeedrixeCCGEuKW5NGlrtVpmzZrl8F54eLj9371792bt2rWuLFIIIYS4bcjNVYQQQgg3IUlbCCGEcBOStIUQQgg3IUlbCCGEcBOStIUQQgg3IUlbCCGEcBOStIUQQgg3IUlbCCGEcBOStIUQQgg3IUlbCCGEcBOStIUQQgg3IUlbCCGEcBOStIUQQgg3IUlbCCGEcBOStIUQQgg3IUlbCCGEcBMuTdo2m43XXnuNSZMmER0dTWJiYonrzZw5k3/+85+uLFoIIYS45bk0aW/cuBGLxcKqVat48cUXmTdvXrF1Vq5cybFjx1xZrBBCCHFbcGnSjomJISoqCoAuXboQFxfnsHz//v0cOHCASZMmubJYIYQQ4ragd+XGTCYTBoPB/lqn02G1WtHr9Vy6dIn33nuP9957j++++67c2wwM9EWv17mkfjqdBoCQEKNLticKSTxdR2LpWhJP15J4uk5lY+nSpG0wGDCbzfbXNpsNvb6wiO+//5709HQef/xxUlJSyM3NpUWLFowdO7bMbaanZ7usfgUFCp1OQ0pKlsu2ebsLCTFKPF1EYulaEk/Xkni6jrNYlpXQXZq0u3btypYtWxg2bBixsbFERETYlz3wwAM88MADAHz++eecPHnSacIWQgghxDUuTdpDhgxhx44dTJ48GaUUc+bMYf369WRnZ8s4thBCCFFFLk3aWq2WWbNmObwXHh5ebD1pYQshhBAVJzdXEUIIIdyEJG0hhBDCTUjSFkIIIdyEJG0hhBDCTUjSFkIIIdyEJG0hhBDCTUjSFkIIIdyEJG0hhBDCTUjSFkIIIdyEJG0hhBDCTUjSFkIIIdyES+897s4uZeTw8YYjJJzLJLxxHaYNb0u9AJ+arpYQQghhJy3tqz7ecIRjZzMosCmOnc3g4w1HarpKQgghhANJ2lclnMss87UQQghR0yRpXxXeuE6Zr4UQQoiaJkn7qmnD26LXaQCIaBrAtOFta7hGQgghhCOXTkSz2Wy88cYbHD16FE9PT2bPnk1YWJh9+TfffMPSpUvR6XRERETwxhtvoNXWjvOGegE+1PHzAmDG/V1ruDZCCCFEcS7NmBs3bsRisbBq1SpefPFF5s2bZ1+Wm5vLO++8w//+9z9WrlyJyWRiy5YtrixeCCGEuKW5NGnHxMQQFRUFQJcuXYiLi7Mv8/T0ZOXKlfj4FF5GZbVa8fLycmXxQgghxC3Npd3jJpMJg8Fgf63T6bBarej1erRaLXXr1gVg2bJlZGdn07dvX6fbDAz0Ra/XuaR+uqtj1iEhxkotFyWTeLmOxNK1JJ6uJfF0ncrG0qVJ22AwYDab7a9tNht6vd7h9YIFCzh16hSLFi1Co9E43WZ6erbL6ldQoNDpNKSkZJW6HCh1udyApbiQEGOp8RIVI7F0LYmna0k8XcdZLMtK6C7tHu/atSvbt28HIDY2loiICIflr732Gnl5eSxevNjeTe5O5AYsQgghapJLW9pDhgxhx44dTJ48GaUUc+bMYf369WRnZ9OhQwfWrl1L9+7defDBBwF44IEHGDJkiCurcFPJDViEEELUJJcmba1Wy6xZsxzeCw8Pt/87Pj7elcVVu/DGdTh2NsPhtRBCCFFdasdF0m5CbsAihBCiJslTvipAbsAihBCiJklLWwghhHAT0tJ2IbkkTAghxM0kLW0XkkvChBBC3EzS0nahilwSppRCARoNoK6+d/UfSt2kCt6EbVvyC7AW2CpdRmm31ynvJlQpa97MGN4s2bn55FoKqrnUygWqOsJbkb+hKmFlL1Meptx8Jx+sYKVuklpSjTJ5ZOWSleMknq7ghl9eHy89el31tIElaZdAKUWBTaEU2K7+22ZT2FThfwCpmTnYwP6+UtCknoHEC9fuctM4xI9T56/YP1P0/0oBqvSEU3q9XLJ7LnXZlE9GhuvuWnc7S8+2SixdKCvPJvF0IbNF4lmapvUNkrSrS67FSkpGLgU2m73FeOxsRqkJssB29VanGbnFlg3t0ZSPNhyhwKZoEmLgnp6h5OVXd8tJCCHEreq2T9pWm8J8tcunKE9XtkUbYPDCz8cDgKl3tSq2PMOUx7e7z3D+solGdQ0M6xVKgEGedCaEEKJ8ZCJaNfp29xmSUkzYFCSlmPh295marpIQQgg3Ikm7Gp2/bCrztRBCCFEWSdrVqFFdQ5mvhRBCiLJI0q5Gw3qFotMWXuTUJKRwTFsIIYQor9t+Ilp1cjZRDapnspqzMmTCXMVIvIQQ1UVa2rWMKyarZZjyWL7xOP9cuZ/lG4+TYcqrUBnlqUNRGa9+sLPEMm4nMsFQCFFdpKVdyzibrFaeVl1REoFrSeT6lr2zMsozYc5ZGbeK8sTbFX8zIYQoD5e2tG02G6+99hqTJk0iOjqaxMREh+WbN29m3LhxTJo0idWrV7uy6FuGs8lq5WnVOUsizsooz4S522UmfHniXdW/mfRaiNpMjs/axaVJe+PGjVgsFlatWsWLL77IvHnz7Mvy8/OZO3cuH3/8McuWLWPVqlWkpKS4svhbgrPJauVJls6SiLMyyjNh7naZCV+eeFf1b2ZP6jYl3euiWjkbSgPnx2d5tiFcR6NKutN+Jc2dO5dOnToxfPhwAKKiovj5558BiI+PZ8GCBXz00UcAzJkzh8jISO69994yt/nQ339wVfVIz8oFjYbA67omlVJYr96aNCvbAoDR17PUbThbp6rLna1jzsm330oVQKfV2Ce3FbHZFKard3nTaTX4eOnRah0fzVHVejorw2ZT5ORZKbCpUutQGzirZ3niDVX7m10xW4p9xt/PcTvuEs/aRKvVYLPVwhv2VyNXHN/Ojs/yfkduNmf7WtXlZa2j12rQaMr/fdTpNBQUlH5sfvL60FKXuXRM22QyYTBca3HpdDqsVit6vR6TyYTRaLQv8/Pzw2Ry3qWq1WlKfRJURdUt4dnWNnWtu6FOOcYZna1T1eXO1vH18SA7N5+CAoVOp8HX26PYgaXVaggw3tx6OivDnHvti1xgU+RYrMUSWubVM/KyynK2TlW34aye5Ym3s/KdbePGL7BOpylWhiviWdVYFdgUWVd/wIv2Q3dDPcuzzs2upyuWO9uPqi6vrno6O24KbjipKbCpYsees+PT2TZccdyUZxvO9rWqy8taR6vToK1A0i7aj8pwadI2GAyYzWb7a5vNhl6vL3GZ2Wx2SOKlmf9Eb1dWkZAQIykp157EZcrNJ+nirTkeWx0CAnxLfPLPP1fud3itbIrHR7RzeO8/Xx8GKPZ+RdZxtjzDlGd/iIvB26PYJLDy1PNms09USzXTKNivxIlqzurpbD+h6vFevvG4/YezoEBRx9ez2OTD8qxT1b9pebeh1WpKXF6eWDnbj6ouL089XFFPZ8fN8o3H7RNKoXB4p6R6lnV8OtuGK46b8mzD2b5WdXlZ6zStb8DPu/y9CzfmoYpw6Zh2165d2b59OwCxsbFERETYl4WHh5OYmEhGRgYWi4W9e/cSGRnpyuJFLVJbxry/3X3GfmZc0nhcbahngMGLqXe1YvYTfZh6V6sSZ5aXZ7JbWfuZYcrDnJPPFbOl1HFHZ+uUZ3y/PDPpndXjZnMWK6j6FRblvQKjrHq4op7lmd/SJMSAVlP6/BVnx6ezbbjiuHHFXB5XTMCtDb8XLk3aQ4YMwdPTk8mTJzN37lxeeeUV1q9fz6pVq/Dw8GDGjBk88sgjTJ48mXHjxlG/fn1XFi9qEWdfZFf8eJdnG86+7OX50aoNqvrDWJ4E4IoTnKqeXLhC0XGRkZVX6ZOP6kgA1ZGonB03RQn5pcmRpZ4wOuNsG644bsqzDWf7WtXl5V3nZnNp97hWq2XWrFkO74WHh9v/PWjQIAYNGuTKIkUtVfRFLk1JP94ldcsVTXJZvvF4sW658myjUV2DQ9fdjV92Z/WsLZzV09l+uqK1M6xXaLHrzW/kbJ3ytsRL+5uXZx1nx4WzWJVnP6q6vDz1cEU9a8Px7YrjpjzbcLavVV1e3nVuNrm5iqgRle0+rMhNYqB8X/ZbgbP9LE8CcMUJTlVPLspzIlbV46K2JIDqSFS1gSuOG3fYz+oiSVvUiPIkkfKM1znbxu3yZXe2n65o7bhCVVvi5VnHXXpXJFGJypCkLWqEK7oPb5dWtCvUlq6/qrbEy7OO/bi4brazELcKl95c5Wao7LT40sglX65V2iVfrnC73bP7ZsbSXZTnb17e40Li6VoSz9K5+pKvkJDSL4eWlraotaR78PZTW3oEhKit5NGcQgghhJuQpC2EEEK4ids+aWsovI92BW8bK4QQQlS7235M28/bg4imAdiUDZsNlCq8EbxNKWw2Vfhvm0IVvVbXlilVuH7R66L1r5/bV7un+QkhhHAnt33SLqLVaNHqCv9d1YfKKaVQKHvCLkru9uXXLbv2mWtLr/1vaduvYgUrqaQLDYIC/TB6ld1hU6XqlvDhYm+VEpCaCFNV/jZBQb746Guuy6e2XUhSenXKc1BAQJAvnpqy96nW7HEti31JAgJ98MB208up/ZEozkOnq7ayJGnfBBqNBg0aXPZM0VrM3+BFXk7x5+2Kigvy96Egz1rT1bhlhAT6orEW1HQ1bhkhwX7obDc/aYuy3fZj2kIIIYS7kKQthBBCuAlJ2kIIIYSbkKQthBBCuAlJ2kIIIYSbqPUPDBFCCCFEIWlpCyGEEG5CkrYQQgjhJiRpCyGEEG5CkrYQQgjhJiRpCyGEEG5CkrYQQgjhJm6bB4bYbDbeeOMNjh49iqenJ7NnzyYsLKymq+V2Dhw4wD//+U+WLVtGYmIiM2bMQKPR0KpVK15//XW0WjkPLI/8/Hz++te/cu7cOSwWC0899RQtW7aUeFZSQUEBr776KqdOnUKn0zF37lyUUhLPKkhNTWXs2LF8/PHH6PV6iWUVjBkzBqPRCECTJk148sknKx3P2ybqGzduxGKxsGrVKl588UXmzZtX01VyOx9++CGvvvoqeXl5AMydO5fnnnuO5cuXo5Ri06ZNNVxD9/H1118TEBDA8uXL+fDDD3nzzTclnlWwZcsWAFauXMmf//xn5s6dK/Gsgvz8fF577TW8vb0B+a5XRdHv5bJly1i2bFmVj83bJmnHxMQQFRUFQJcuXYiLi6vhGrmf0NBQFi1aZH99+PBhevbsCUD//v3ZuXNnTVXN7dxzzz08++yz9tc6nU7iWQV33XUXb775JgDnz5+nbt26Es8qmD9/PpMnT6ZevXqAfNerIj4+npycHKZNm8YDDzxAbGxsleJ52yRtk8mEwWCwv9bpdFit8uziihg6dCh6/bURFaUUGk3hQ8P9/PzIysqqqaq5HT8/PwwGAyaTiT//+c8899xzEs8q0uv1TJ8+nTfffJOhQ4dKPCvp888/JygoyN7IAfmuV4W3tzePPPIIH330EX//+9956aWXqhTP2yZpGwwGzGaz/bXNZnNIQKLirh+DMZvN+Pv712Bt3E9ycjIPPPAAo0ePZuTIkRJPF5g/fz4//PADM2fOtHdLgsSzItatW8fOnTuJjo7myJEjTJ8+nbS0NPtyiWXFNG/enFGjRqHRaGjevDkBAQGkpqbal1c0nrdN0u7atSvbt28HIDY2loiIiBqukftr164de/bsAWD79u107969hmvkPi5fvsy0adN4+eWXGT9+PCDxrIovv/ySDz74AAAfHx80Gg0dOnSQeFbCZ599xqeffsqyZcto27Yt8+fPp3///hLLSlq7dq19DtXFixcxmUz07du30vG8bR4YUjR7/NixYyilmDNnDuHh4TVdLbeTlJTECy+8wOrVqzl16hQzZ84kPz+fFi1aMHv2bHQ6XU1X0S3Mnj2b7777jhYtWtjf+9vf/sbs2bMlnpWQnZ3NK6+8wuXLl7FarTz22GOEh4fL8VlF0dHRvPHGG2i1WollJVksFl555RXOnz+PRqPhpZdeIjAwsNLxvG2SthBCCOHubpvucSGEEMLdSdIWQggh3IQkbSGEEMJNSNIWQggh3IQkbSGEEMJNSNIWQggh3IQkbSGEEMJNSNIWQggh3MT/BwLgFWqVh9I6AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2,1, figsize=[8,6])\n",
    "growth.plot(ax=axs[0], title='Evolución del crecimiento del IMAE')\n",
    "sm.graphics.tsa.plot_acf(growth, ax=axs[1], lags=48, alpha=0.05, title='Autocorrelograma');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## EJEMPLO 2: Crecimiento del tipo de cambio Euro/USD\n",
    "\n",
    "¿Es es crecimiento diario del tipo de cambio euro-dólar un proceso ruido blanco?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "euro = pd.read_csv(\"https://github.com/randall-romero/econometria/raw/master/data/euro.csv\")\n",
    "#euro.index = pd.to_datetime(euro['fecha'])\n",
    "euro.drop('fecha',inplace=True,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "depreciacion = euro.diff().dropna()\n",
    "T = depreciacion.shape[0]  # número de datos\n",
    "M = 7   # máximo número de rezagos\n",
    "rezagos = np.arange(1, M+1)\n",
    "alpha = 0.05  # significancia de los test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos las autocovarianzas, a partir de un rezago"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "rho = sm.tsa.acf(depreciacion, fft=True, nlags=M)[1:] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos el estadístico de Box-Pierce, para todos los rezagos desde el 1 hasta el 7\n",
    "\n",
    "\\begin{equation*}\n",
    "Q^{*} = T\\sum_{j=1}^{m}\\hat{\\rho}_j^2 \\; \\overset{\\text{asy}}{\\sim} \\; \\chi^2_{m-k}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "Qstar = T * (rho ** 2).cumsum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos el estadístico de Ljung-Box\n",
    "\n",
    "\\begin{equation*}\n",
    "Q = T(T+2)\\sum_{j=1}^{m}\\frac{\\hat{\\rho}_j^2}{T-j} \\; \\overset{\\text{asy}}{\\sim} \\; \\chi^2_{m-k}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "Q = T * (T+2) * ((rho ** 2)/(T-rezagos)).cumsum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Calculamos los valores críticos, tomando en cuenta que $k=0$ porque los datos que estamos usando no son residuos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "vcrits = np.array([chi2(k).ppf(1-alpha) for k in rezagos])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Con carácter informativo nada más, calculamos la autocorrelación parcial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "rhop = sm.tsa.pacf(depreciacion, nlags=M, method='ols')[1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Juntamos todos los resultados en una tabla de resumen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AC</th>\n",
       "      <th>PAC</th>\n",
       "      <th>Box-Pierce</th>\n",
       "      <th>Ljung-Box</th>\n",
       "      <th>$\\chi^2(m-k)$</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rezagos</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0042</td>\n",
       "      <td>0.0042</td>\n",
       "      <td>0.0948</td>\n",
       "      <td>0.0949</td>\n",
       "      <td>3.8415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.0063</td>\n",
       "      <td>-0.0064</td>\n",
       "      <td>0.3144</td>\n",
       "      <td>0.3146</td>\n",
       "      <td>5.9915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.0002</td>\n",
       "      <td>0.3145</td>\n",
       "      <td>0.3147</td>\n",
       "      <td>7.8147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0082</td>\n",
       "      <td>0.0082</td>\n",
       "      <td>0.6825</td>\n",
       "      <td>0.6831</td>\n",
       "      <td>9.4877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.0022</td>\n",
       "      <td>0.0021</td>\n",
       "      <td>0.7082</td>\n",
       "      <td>0.7088</td>\n",
       "      <td>11.0705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.0076</td>\n",
       "      <td>-0.0076</td>\n",
       "      <td>1.0282</td>\n",
       "      <td>1.0293</td>\n",
       "      <td>12.5916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0106</td>\n",
       "      <td>0.0108</td>\n",
       "      <td>1.6485</td>\n",
       "      <td>1.6507</td>\n",
       "      <td>14.0671</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             AC     PAC  Box-Pierce  Ljung-Box  $\\chi^2(m-k)$\n",
       "Rezagos                                                      \n",
       "1        0.0042  0.0042      0.0948     0.0949         3.8415\n",
       "2       -0.0063 -0.0064      0.3144     0.3146         5.9915\n",
       "3        0.0001  0.0002      0.3145     0.3147         7.8147\n",
       "4        0.0082  0.0082      0.6825     0.6831         9.4877\n",
       "5        0.0022  0.0021      0.7082     0.7088        11.0705\n",
       "6       -0.0076 -0.0076      1.0282     1.0293        12.5916\n",
       "7        0.0106  0.0108      1.6485     1.6507        14.0671"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resumen = pd.DataFrame({'AC':rho, 'PAC': rhop, 'Box-Pierce':Qstar, 'Ljung-Box':Q, f'$\\chi^2(m-k)$': vcrits}, index=rezagos)\n",
    "resumen.index.name = 'Rezagos'\n",
    "\n",
    "resumen.round(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Graficamos los datos y el autocorrelograma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qiQI5IWboZab0EZ1naapf70kIMQ0UyAkxQ5UDM1d9+SghxNRQICfEDFW+YEHJa8QJISaGAjkh5kjJu5Ik5eXIzC2ug8QQQqrDJIdoJYRUz6sS+asi+ZYDN/Dvg3R89m43eLrZ103CCDEREokE69Z9hhcvnkMsFmPq1Pfwww/b8eGHC9C8eUv8+msUsrOz0bnz69i372cUFhZi5swP8Px5MqKi9oDH46FNm7aYM2detdOidyBftWoVEhMTweFwsHjxYnTo0IGdd+HCBXz55Zfg8Xjo06cPIiIicOPGDcyYMQNNmzYFALRu3Roff/wxUlJSsGDBAkgkEggEAnz++eewsrKq9oERQjSTrVn/90E6ACApLZ8COTEp/zvzAP/cSQOPx4FEYpg3c3f18cCo/i1Vzj958hjc3NyxaNEnyM7OxuzZ74HPd1S67MOHD7B37wGIxWIsXboIP/zwC+zs7LBgwQdISLiMLl38qpVWvQL5pUuX8PTpU0RFReHBgwdYtGgRoqOj2fkrV67Ejh07IBQKER4ejpCQEBQWFiIkJAQfffSR3LY2btyI8PBwDBw4EOvWrcP+/fsRHh5erYMihBBCatKNG9eQmHgV1679CwAoKSmBra1Y6bItW7aClZUVHj9+BC+vJrCzswMAdOjQEffu3ambQB4XF4egoKCKBLZEbm4u8vPz4eDggKSkJDg5OcHT0xMAEBAQgLi4OHh5eSndVnx8PJYvXw4ACAwMxI8//kiBnJCaZphCCyFGYVT/lhjVvyUEAn6NvB1TGQsLS0yYMBnBwaHsZ7NmTWf/FotfBXVLS0sA0s6ljEz/FIZhwOVWv6uaXoE8PT0dvr6+7LSbmxtEIhEcHBwgEong6urKznN3d0dSUhJcXV1x5coVTJ06FUVFRZg1axa6d++OoqIitipdIBBAJBJp3L+Li12NvOVG1SviiDzKJ+0Ycz5ZWUt/+hYW3CrpdHS0rdW0G3M+GRPKJ+3UVj517+6H06dPIzx8JDIyMrBr1y64uDhBLC6EQMDHvXu30KpVKzg728Ha2hICAR/29r5ISUmGrS0HDg4OuHkzEe+//36106xXIGcUerwyDMN2mlGcB0g71Pj4+CAiIgKBgYF4/PgxJk2ahBMnTsh1tlG2rjI18b7Z2ryTM2WUT9ox9nwqrhiaVSIpr5LO3NyiWku7seeTsaB80k5t5pOfXy/Exv6F4cNHQiKRYPLkaWjRoi0++WQZGjdujEaNvFBQUILs7EKUlJSx6XrvvVmYOHESOBwuOnTohKZN22idZlUBX69ALhQKkZ6ezk6npaXB3d1d6bzU1FQIBAK0aNECLVq0AAB4e3vD3d0dqampsLW1RXFxMWxsbJCamgoPDw99kkQI0UvVB8k59HA5IRpZWFggMvLjKp/37NmrymeybeABAf0RENDfoGnRq3Le398fx48fBwDcunULHh4ecHBwAAB4eXkhPz8fycnJEIvFiImJgb+/P/bv34+ffvoJACASiZCRkQGhUIiePXuy2zpx4gR69+5tiOMihKjBjuxGMZsQk6dXibxLly7w9fXFmDFjwOFwsHTpUhw4cAB8Ph/BwcFYtmwZ5s6dCwAICwuDt7c3XF1dMW/ePBw/fhylpaVYtmwZrKysMGvWLCxcuBBRUVFo2LAhhgwZYsjjI4SoQXGcENOn93Pk8+bJP8Tu4+PD/t21a1dERUXJzXdycsL27durbMfDwwM//PCDvskghFQHRXJCTB4N0UoIkUOxnRDTQoGcEDOk7RMihBDjR4GcEDPEjrVO5W9CTB4FckLMGcVxQkweBXJCzBD7+FndJoMQYgAUyAkxQ0xF5To9R06I6aNATohZo0hOiKmjQE6IOVLTaZ1K6YSYFgrkRqCkTIKEeyKIJeV1nRRiJthe6xS0CTF5FMiNwN5T97H5wHUcv/SsrpNCzAzFcUJMHwVyI3AvKRsA8Cw1v24TQsyH2gFhKLwTYkookBsBquYktY0N43TOEWLyKJATYoZePUdOkdxcHfr7MbYcuF7XySAGoPfbzwgh9QDFcbN16O/HdZ0EYiBUIifEjD16nosPN/+NZ6l57GfUxEOIaaFAbgzoTVSklr3IKAAAlDMMsvNLceDcozpOESFEXxTIjcCrzm5UFCI14+aTTDxPL2Cnc/JL5ebX1b1kWlYhvjl4A+k5RXWTAELqAb3byFetWoXExERwOBwsXrwYHTp0YOdduHABX375JXg8Hvr06YOIiAgAwLp163DlyhWIxWJMnz4dAwYMwIoVK3D16lXY29sDAKZMmYK+fftW76hMFIVxUlPW7/sXALAzsr/GZWvzPPz212u4fCcNJaUSfDCqYy3umWijTCyBpQWvrpNBNNArkF+6dAlPnz5FVFQUHjx4gEWLFiE6Opqdv3LlSuzYsQNCoRDh4eEICQlBeno67t+/j6ioKGRlZWHo0KEYMGAACgsL8dlnn6Ft27YGOyiTQzXrpAaVlknYvzNzi2FtVfXCzNTRSVhUIgYgn0YAKCmVIP52Kt5o6wEbK90uU8WlYqzZk4Cw7k3xRluh3mmTlJeDy+GYbU1Zek4RFnwbh8AuXnh7QOu6Tg5RQ69AHhcXh6CgIABAy5YtkZubi/z8fDg4OCApKQlOTk7w9PQEAAQEBCAuLg7h4eFsqd3JyQlFRUWQSCQoKChQuR+zY57XC1LD7jzLYv+e980FcDUFJj3PQ4apfKOa7huoXCWvsBQ3n2Ti0YtcnLqcjCcpuZgQ6qPTtq49zMCz1HxsPXRTp0D+8HkOhK52cLC1hFhSjmmfx6JzK3fMGt5B88r10IPnOQCA0wnJ8PMRwNbaAk2E/DpOFVFGr0Cenp4OX19fdtrNzQ0ikQgODg4QiURwdXVl57m7uyMpKQk8Hg92dnYAgOjoaPTp0wc8Hg8FBQXYvHkzcnNzIRQKsWTJEjg7O6vdv4uLHSxqoLpHIKj+SXog5gHsbCwQ2qOZ1utwedKrmI21JQQCPiSScjAALHjG2YXBEPlkDowln5zSC+Wmy5U0iFvJlHqdHG3ZtDMMo3Vgnvn5GYgl5dgaGaRzGi0tLSAQ8LHm67O49yyb/Tw1u1jnfHRMzmX/1nbdlxkF+Gz3FQhcbLFzyQBk5RUDAK7eTzea77Gm0qFqu06OOezfa3+5CgD4ff1/aiQNhmQs31dt0iuQMwoXAtkfu+I8QP4O/dSpU9i/fz927twJABgzZgxatmwJb29vfPvtt9i0aRM+/vhjtfvPyipUO18fAgEfIlGe5gU1+OHITQDA6y3dtF5HUvGylJKSMohEeZi14RxKxeX4bl7faqfH0AyVT/WdMeVTdrbm30tpRRU3ABw+9xA//3kbT15K069NuzoAPK1YXp/jLisTY9XOeLkgLv1covX2UrMKsffUfbRp7Mx+pu26DypqLURZRRCJ8pBb8KozoDF8jzV5Pqnabm5usdbLGgtj+t3VBFU3KXoV+YRCIdLT09nptLQ0uLu7K52XmpoKgUAAAPjrr7+wdetWbN++HXy+NEHBwcHw9vZm/757964+SapzadlF+OXkPYNsq6BYjDKx6b0JLSOnGCWlEs0L6qmkTEJviNOgTCyBKLt6PcCvPcxgg7ghFJWI2fcJKKq88RdlFyPu5kuN2yosFquc98PRO7j2MAPRsQ/1SieRfh8pGQVKC2TEeOkVyP39/XH8+HEAwK1bt+Dh4QEHBwcAgJeXF/Lz85GcnAyxWIyYmBj4+/sjLy8P69atw3fffSdXdf7ee+/hxYsXAID4+Hi0atWqmoeku5irz/HV3oRqbWPT/ms4dSVZr3Xrw2+mpEyC+d9eQOS2OJXLxP77HNcepqucr8n7689i/rcX9F5fF5UXtNtPMlUuU84wyMipWmqpS2v2JGDh1jhkypSmtDm9bjxWfZyAND8ycop1vsBfvPkSczb9jTV7Etg2V/ntVqZR+XZlP3/4IgczN5zDr2eVB2pjvvnNzi+p1rlfW84kPMdH2+NxjN7EaFL0CuRdunSBr68vxowZgxUrVmDp0qU4cOAATp48CQBYtmwZ5s6di7fffhthYWHw9vbG0aNHkZWVhTlz5mD8+PEYP348Xrx4gXHjxmHWrFkYP348zp49i5kzZxr0ALWx+/hdnLmcpLG09+hFLm48zlA6LyuvRG46r7AUB/96hILiMh1SYrq93YorSuKKzyfL+unYXWyIvqZy/vnrKSrzt5K67euqTCzBob8fKw3Gm369jo+2x+Pzff+yPasl5eVy7cvRMQ8w/9sLuPZQfZpr0+MUaUk6XfaYDHCjeOpKMuZ/ewFnE19ovU5hcRm2/X6LDbCpmYWQlJcjv0iX38Qr1yvy+Y+4p1qv8yw1D+UMg+fpBVi87SIep+RqXgkwyE9Rtnr+kx2XsCH6Gp6LjPsNh/8+kN5sXLkrohH+TIjez5HPmzdPbtrH51XP0q5duyIqKkpu/ujRozF69Ogq22nYsCF69eqlbzJq1cqfLgMANs7uDQdbS7XL/nziHv65k4bs/BJMHKjdo3WKP5z07CK4O9uCYRi8zCyE0MUOXK7yXxfDMCgqkcDOpm6GzzfEb37HH7cBaN8mW11nEp7j0N+PceVuGj6d0k1uXuUFDZA+GmVrbYGZX/0FF741Vk3rjpJSCc4kPAcA3HqSiQ4tqvaJSM0qREpGITq1dK/ZA1HC0FWjl26lAgCu3ElD306NtFqnTCKfBrGkHGv2JODh81xsntNH7lxVef5oeRjlDKM08Cz74R+M6d8St59m4WVmIX46dhdLJ3XVbqPVcPlOGr45eAMj+7XAwG5N2ZuX7IJSNBLU+O7l6HJtqMzD+lBLaE6Ms1u0kYtJ0FyFnlFRtZmZW6JhSdU/mgVb45BfVIbrjzLx0fZ4/HxCdf+B6JiHmLnhHJ68rFriyMgpxrpfEpCUpro0wDAMDv39WOn6WjHBu/fcQmmJ6WWm+jblyq+npEyCl5nSjmPvf3mWLWmq+v4WfXcRG/df07sEqgt1gdsgz4jr8/0qpGnXsbt4+Fx6fuUUlFQsojltmbnFmLPxL1y9L181XblucakYU9fG4NEL5efu9UevakyepuapbK83pMt30wAA5/7VvgZDV49TctnaInV2H7+LmRvOISVD86O+lW/DozZy00KBXB861Dnp8nNQttW8wlL2whP77wv8+yBdaRNAZZvWsfhnkJTLz//13EPceZaNrYduqNz3oxe5OPT3Y3z642UdUmyaDv/9GAn3ROx0eTmDpy/zlD6WBWgundxNyqrStCKruFTzxVYfKRkFePoyD/lFZZiyNgaHz796m5Uhr8Oy5xsD4OjFp1i7J6FaF/tth2+huFQs8/tQ/Zs6l/gCuYVlcjeihcXSY9584Drmf6Nbv4k1e6rXH0Yb7FM8ijMM9L0ki/KxYtdlrNt7VeOysRU3E/eTq/ZRUETV6aaJAnkNMeTvQfbHtXH/NRyX6YiiGHwu3U7Db+fkX09YXs5ULKt6HyVl1ettrsvxPhflY+raGLlgqqiguAx7Tt5T25ns9tMsXLqdqsOepUHp4N+PsfnAdbb0Uc4wWP7jPzh79blO26r0LDUf87acV72AAYPq5TtpuFnRAe+j7fFY/uM/eFBxgT7416vvXSxzM3f9kfqObJpM+zyWLUkDwP7Yh7iblI2iEv3PmaepeVj50xW986ay9J1wT4QCNT3ZAQAcjs67SctSXUsjlpTL3dzkFJTij7gncr8h9vdQQwXb1IpapKc6PF0g+xtVVzsH1M5gkwzDqLx5Vufoxac4Fk+d8WRRIJehyzmldeDTaqOVj+AUITrmQZXVFe+Sn1R0aPru8E1MXRtTpYSu8jEeLQ/wNz3ehKVp0JArFVWNAHA64TnKGQa7jt1Rm4bTFR2sVPl871VsPXRT6TxV349sFigm+dYT6bPEv5ySf4xQseR59GLVzlbqcra6F8WYq88xd8t5FJWI8c3BG+y46ZVOX0mqss7mA9fZv2P1vEFRpjKPZOl7E/givRqjOupy56hHsNj+u/LzCpDe2Cz5Pl5u2V/PPsKfsudFZVuzwrdvuKFwdd/Ok5d5KCoRo5xhsHTnJaXLyN6AKPtN51R04Lv5OBM3NTzpoMlnu6/gg01/67ze/tiH+J/CddLcUSBXIz2niC3tyIq9+hzvrz8r18O6yjmvR5H8XnIO/lS402TUbCy+ogOSYolEXTWvNn6/8KRa609ecwZn/5UPHof+frXNyqNRd33VtV35WPwz9rGk2H+l38+1hxm4dDsVV2VK/pqqg+8lZePUZfV9IPbr+Jxyddsbdx+/i6y8EpVtuzeVBNfSsnLcfZalttbDEE78k4T315/FnadV06DdLax0qQwlg48YyosM3QeQUve8OiBfYk+p2H6mzO9O5TmuJlNOXk7CvtP3dUmmTmKuPseCby8g/qbqWix1A3sBwE8VN9/ro/7F+qh/q5WeRy9ykVeof/+RJd/Hs9dAYyOWlGvVJ8FQKJDLkT95F3wbh1U/X6nS5lwZKC+q+UFUyi8S470vYnHyn1elJkl5OS7cSGGDlboL3pqfr+CIQmC9q29nnVpsANt1TM3APhXJyC+SVp8DwD930uQWkb2OKNY43H2WVeW1l/+LecA+lnT8kjSvL9xIwdZDN7FJpnSqLq+LyyQ10n5qqDKYbAlJmyaFtb9clSuZGx7Dnpv/3E2rOleLA7+v4Vx++CJX6XY4Otwp63pjuyE6UXN1vTKMdPAb6fVCefq+/F8iW6Nz7WEGpqw9g6cv88AwDPaeuo8T/1StXVFO8/Fn55dUuSEuKBbLPZEBSH+H95Oztdprdn71CgmG9CK9AN8dVl1zUpemfR6Lj7bH46GSsRNqQt08q2SkVF14GEZFdaqaC1Vl29XTVOn/e0/fx97T98HhAMP6NMevZx+htZcTIse9rjZNyi4o+UVleJaqx8hbahJcnTbynPwStc+HA/L3ELLtc6evJONlZmGVarocmWdwy8sZQGZo/cpxn5VhGEbtccqWNBTva8rUVMdr0ztY9U71X3WbzIVKtipaVZNCbSqTMCprTh69yGWfClBH38qKv65Vrzf4H3FPMEjF+xCqMy5AxFfn4OFii5aNnAAoP779sQ8R1r0p9py8C4YBTvzzDD3beeq9T1lFJWLceJyJLq3d8eFm5f02FG+al/9wCRm5JVg1rTv7maqvRfF4bj/JRNtmrsoXriCWlGP+txeQk1+KMYGtEOTnBbEBB+/R5X0Ata22bnwokGshI7dYaXWqWFKO2KvP8Xqbqg+GiiXKfwoMAxyoaIO+l5yDklKJXhcz2U5gmu76tDnJT2pZEpBIpIOiyL5Ba+nOS8hVU0VWzjBywVuxuUIxiB/++7FcNfLLzEJI1PTUk+0wM2VtDPu3suOWrVw5ckH+5kzlxQsMIr46p3L/mugTq6JjH+DGo0y5fDO2dkHZ9k3ZqvXo2Af482LNdka6dLtqDYAufj37CD18G8DV0Uan9VJl3vNw4UYK9py8z97kVTYTpGUVoVVFINf229f9EUXl2608T8cGaT9CZkbFI7JZeSXszW12foncW/NU7fXzff9qHPchNauIHchp3+n7iLv5UqdOepqcupyM4K6NAUivT//eT0fbZi6wtqz796hrfNOggZh9IJctoan6yRWr6J37z500/HMnTa4jl3b7fPV35fO01aGu+vTWk0y1pfeTl5Nga2WBOwovqwCk7YSf/vgPBvdshl4dPFFezmDIgt8BADOGtIOfjwcAqA3igLSntS4O/i3f637ZD/+oXf6HioFktKGus5HKdtFq1o3nFZbCxooHZwdrrdep6UBoaCky7dCGTnt1+2wAykvGZVqO2//zibsI694ULnxrLPruIvv590cUzjvZfXCqfqROYXVqfJTQdwS5ypvfvMIyxCQo7yRZru7xFyUyFJrBVAVxsaQc8bdS0bmVO+xs1A+4JeufO2lsIP/970fYcfgmenfwxKQw7Qbiqkm1VVNg9m3kci+HYKR3pc8VetMu/1F9IHmk7bCPKtTEi0byi8rw9GUevtj3r9xFVtHeU/ex82jVQHjychJmbjiHtOwi7Dx6GyWlEvaxJwD45qD0mfTbSjo5ybr9NEvjMtV1/obyXvrKOsKoq/1Q/N4rabpRqbTn5D38WzFoSbHMhXn1zwn4cPN59qaRYRj1A7jQYBwGJzsoTKVfzz5i81pxsBlZZxKeY8cft7FXQ0c02fh2/rr0nJRIGI21XZdup2H3cd1eFpUtM1SxKLsIk9ecYfubAPo1WWjTfPT0ZR6mrouR+2zn0dts2/7FWy+rDIP7zW+qx6+QdfpKMnb8cRs7/riN648y5PrBXL0nwu/nHyu9iXj04tXAOA8ravvuPMvC4b8f46+KIYXTs4two+IcuPEoAz8duwOGYVBaJtH6xuS3c4+qPFWkUS3V+Jt9iVw2iIrLyzG34nngheGdtd5GUYkE9noOjXrinyS97sbzNFTFfbIjXu7Hrqu9p+QvWu9/ebbKMqevJMtdPBT9cvKe3i+SMbQysQRiCYPZG//Sed11v2jXAe70lWScvpKMTyb64dM1Z6rMf2/9WXz7YQA+3hEPB1tLLJLpHyEpL8eVuyL4NHHBfhUvBSGGdflOGhal5mH8gDYaO5mlZBRovCEtE1e9Ic8pKFV6A1BQXAZRtrR5TF2zkSqyv7sN0YkApOdfJX1uBb89eEPpUMOa/H0tBQDQq30DbDt8CwDQ1ccDLnxrjAlshVIN7eHJaflwdbRB1BlpkLx6P529sdoZ2R9iSTnbYdXR3qrK+uUMg6/+l4jF41+XG2K2smavfQs3LNgqfZnTskld8eX/pPn1uo8H1u/7Fw3d7bFyarcq2wWk4+Wv/vkKRvVvydYMjezXUqt8AQAVI2obnNkHctmxy2dteHWRP1pLVZtnVFRfafLjn6qfwQagNIinZknv3GeP6IAmQn6Vnt+6UhfEARhNEAeko1sVFYv1KqlouhApUjU6Xpm4HCVlEraGZMtv1zHtTV9YWnBx4Nwjk6tOrw/Ssoq0eoxKm9Pm8l3tH/X7Wk3nUF07bymrcdOnVkdSzmg1+psqM2Wun5Ud6kb2a6FxvU92XoK3p/L3bN94nIEvoxLZ6WSR8lqzyjfrvXp87tU82U5/lUEcADsew4v0gopaMlR5l8Xf11OQmlWETb/q+/QHtZHXClWdEZRVxalTUma8r1BU9PV+9T3M66O9p+4j9I0mdZ0M/H09hf37yl0R/m2bDt9mLhTEjZwh37oHQOkrXSsdu/QM9jaWaN3YGQ1c7fTafrmelyNDvxfg3XWxWi1X+dY+RYqjVCZrGJGukqpxCWTfSCerspNsZce9u8+y4GBnpTYMf7HvKlwcrDFl8GvsZ4o3YVQiryUcA/US0PQKVFL3nqUZrqesvhSbLL49eAPtm+tenUnqr+iYV00rWz7og4s3X+LNvtr3QgfUjO5oYhTb29WNoXHx5ks81zLQq1IZiNU94vr0ZR4autuxoxxWBvKvoxOR+DAD2+b3fbUwBfLaUVuPB5C6p2x4UWOga+0PMR+rf76CZFEBsovE6NDMBc/TC+DfvkFdJ8sobfv9VrW3ISln8PH3F9Uus/zHf9Cl9atHjvOLyrD5wHX2kdkCmVqN2uq1ToGcAjkhxEhVtgnHXE7C739Jx5+obt8WolrM1edIVfPCnEqyQx//92v5DrSy7fi1FV3M/vEziuOEEGMn23atOJARMRzFpi99yHaerK3woneJfNWqVUhMTASHw8HixYvRoUMHdt6FCxfw5ZdfgsfjoU+fPoiIiFC5TkpKChYsWACJRAKBQIDPP/8cVlZVHzGoKYq9FAkhhBBDMOoBYS5duoSnT58iKioKK1euxIoVK+Tmr1y5Eps2bcLevXvx119/4cGDByrX2bhxI8LDw/HLL7+gUaNG2L9/f/WPSgdUtU4IIaQm1FZ40SuQx8XFISgoCADQsmVL5ObmIj9f2lswKSkJTk5O8PT0BJfLRUBAAOLi4lSuEx8fj8DAQABAYGAg4uLiDHFcWqMSOSGEkJpg1J3d0tPT4evry067ublBJBLBwcEBIpEIrq6v3obj7u6OpKQkZGVlKV2nqKiIrUoXCAQQiTQPquDiYgcLC8MMiC821PNnhBBCiAzvxi4QCBxqfD96BXLFUYNkH4JXNqIQh8NRuY7sHYu2oxFlZakeO1xX2dnUA5QQQojhWYKBSGS48SsEAuUj4OkVyIVCIdLTX71kIC0tDe7u7krnpaamQiAQwMLCQuk6tra2KC4uho2NDVJTU+Hh4aFPkvRGVeuEEEIMzdFO+ze4VZde9cr+/v44fvw4AODWrVvw8PCAg4O0+sDLywv5+flITk6GWCxGTEwM/P39Va7Ts2dP9vMTJ06gd+/ehjgurRnrC+kJIYSYLr6SF7zUFL1K5F26dIGvry/GjBkDDoeDpUuX4sCBA+Dz+QgODsayZcswd+5cAEBYWBi8vb3h7e1dZR0AmDVrFhYuXIioqCg0bNgQQ4YMMdjBaYNK5IQQQgxtWO/mtbYvDmOCLz82ZJtDbkEp5mz622DbMwWTBvrghz/voF1zV9x4lKl5BVIrevgKEXez6jvUCSHGZ/X07lj0nXQ4108m+lV56+GnU96Al4E7uqlqI6cu22ZYIO/dsSG2fNAHH47qVNdJqdd4Gmp7FN9hT808RNGs4e3ZN3LVVy5867pOArw9HfH5+z3ZaTtrCwwPaI7v5gWoXEfoYgcXvjU6t3JHswaO6NxK2k9swdjOeHfwawYP4uqY/Vjr5nrptLWWfvXuTjZIzylGD18henVoiM/3qn7rD9FNv86NVL6TfWTfFmjl5YxVP19hP9MU+In5qTwnrCy4aNXYGTcf168atG3z+4JhGEz/4iwAwNnBCtkqXhk7sFsT9OnUkC0FG9KicV1gwXtVrt38QR/2752R/ZGTX4IPZN5r7tPEGQDwxYye7A34rOEddH6XvKFQidzMyZ5zbZu61F1C6iEba9X3yUJXO7T0cpL7jArk9c9Xs3qxf7/RVvsncgK7eAEAmjVwBABErx6MD0d1NGziakjzho5KPw/r3rTKZ9Lg+erE92ujOo9G9msJoYsd5o7upFU6KvMQAEb1awlAvif5xIE+CulQzcnBGkF+XvAS2AMA++phxaBdV7VqZh/I7Wzqd6XE6zKv21Omkbu0+sfdyVblMtvm90Wnlu4GTZehNGugvM2ouoJe96oSaAFgbKB274Xu0d4TA7s1qfK5rTUP/To3QseWyt5BLn8R6N3BU6t9EePk364BnGR6LlspDGIVHvTqXArr3hT9ujRip98e0Brb5veFY8X6XK50zI2+nRrWcKqV2zhbu6eJPN3ssGSCX5XP2zZ1wYi+LbBqWndEDG0nN0829nXV4mbH19tVq+YGd2cb9u9+XRqhT8eGmDe2M0LeaIwxga3Q7TUhOrV0x8Lwzuxykwb6YN6YTkq3Fx7UGssmvYGlE7si5I2qv+26ZPaBnMflYsfCfirn+7d79e7f7Qv6oolH7bV76MLSgovlk9/A7BGvXl7TztsVkwe1lVuugaud3PTkQW0xNrAVBvWoerdcyYLHhZuTjcr5+tL2zlqdheFdqp8QJcKDW8PRTv7xkXbergju2pi9u1elgasdFk98A7bWFvBr8+pG6p3QNtg8pw/Gh7QBj1v1p1d5l19pTGArjA1sRe+frgOebnZV+jCo07dzo6ofKhTOeincmFXeHI/s2wIj+rZAB4XvX1kpsbyOuiZb8DiwtZbeiCyb1BXD+rzqkT24ZzP2b1XvruhZcR1t4GpX5RokS6gwz9NN9bLdXxOqTXN/mRK5tSUPEwf6wEvggNH9W2FA18awtuThvyM6oE2TVzWRvTs2xGvNXJVtDoD0hqppA77RPe1k9oEckFaHRK8eVOXzZZO6Ysrg17B5Th98MaMneFwuOLXwBYa80Vir5QZ2f3VX+O3cADT2cEBHmZLz620EbFs4IK3a+3TKG3LbcLC1RHDXxrCyVD/k7bA+zTE8oDneGfSa2uV0GQTB11v1D0Zb1lY8eLiork1QpVd7zaVdxW/a0kL6c1G8IFdydbTGiqnd8Nm73djPZgxtz/7t28y1StXb5jmvSjqWFly5mg9bawsEd22McQPaaEwrMSwLHhcf6NAZdEBX1b/ZaW++hqDXvdC6sTO8PV/VILk72+L7hf0wsKLKWZta2broRzE8oDlsrCywYko3zBjSDk2EfLngHeznhS4VNX9aHYPCDYrsOo52Vtg851X79Gfvdle5HdlCirVV1etX5e/VHJjPkWpgY1X17ruJUPqjs7OxgKujtEQqeycKAEsndoWtNQ/+7Rsg8u1XpcPqlNyVldaUEbrYYXDPZpg9ooPSO2HFBwunv+WrsS1IloOtJYQVQdLW2gKDejRTWt1c6b8jOqhtI5oU9qpNSuCsXQnf080OYwNbYUxgKzRv6AgLHoe9aFQHl8vBrOHt0dWnalWeqtqJzq1U73fpxK74YoY/Grnbq8wDxQsYANjZWGLq4LZoInRAm4oONID8+WOt4SarNrSW+d7rIj2ybc2GNLin6pqo5g0dsTOyv1a9qtXlSXffBggPbg2gaolVdlqb9tW3/JuhQwtlzTKG09DdHjOHvboBHdSjGQDA1dEGfkp+L7JDcFceg42SwFpJ6GKL0G5NMLeiCpujcMtsZ2OBfp0bsW3YC8Z2lru2VpK9lm2RCf5cDgdDenurO8R6p343EFfDqmnK7wTbN3fDjoX9MGVtDACgaQM+Ns/pw57AlhZclInL0bdzI/x0/K7G/dha89DQ3R4Pn+eiXXNXDO/TApfuqH6W2K+NAJfvSl8s01TIR5+OVdvMpr35GqJjH+L1NvKBR9eOGBtn964y/n3HVgLMHNYemw9cl/s8rHtTdGrpjvONnHDlnjR9jdztkZ1fgoJiMQCgd4eGeKOtEC8zCiFwlt4g9O/SCGcSnqtMw7wxndkL6YCujdleoV9HJ8LeVv8hEDkcaWDu3EqA3o8z4OZog4+2xwMAhge0qFhI+l9Dd3vMGdlBaT+C5g0d8ehFrtrqwsi3u+Dh8xyVAaFnO0/0bKe+hmDiQB/8+OcdLY6shsicO+8PaYfSMgm+OXjDIJv+cHRHfBmVqHYZJ3srNBXy8TRV/zEk/Ns1wPkbL+U+a+KhvI+F7Gk/eVBbbP/9FhaGd8ahvx/j0u20KstzOICXwAHJonyZjVTdrrqqcW1+nk4O1pgzsiMmrzkDQFqrZeie7CunSmuUNs7urXUNQGV+VS7dp2NDnPgnSemyHA5Hrnmq8rhlS9XjQ17VQvmo6YS7cmo32NtaylV1v9WrGd7yp0Bu9mYMaaf2wqyup+Ln7/dERm4xRFq+jMXO2gIfjZfvHHLptvJAvnp6d6SkF74K5Co6enX3bYDuvoZpV1V2rF1aC/DxO35IFuXDxsoC23+/hT4dpYFoyuC2KNhfhqF9mqOVlzOKSsSI+Oocu761JU8u3W8Ht8ab/t74QMtBeSrTM3uk4XrwtvPWXMKRDeKypY0JIW3g5eGg9r32rRs7o3VjZ63SYsGTbkex9P56G0GVQP7u4New/cgtpdtp0dARD1/karVPbcgenZ2NhUFLhZry38lAQ11aWfHAgXx8Vfa1tWjkiPEyzRm+zVyxoaJGQNXwWU72Voh8uzOSRQXY/vtNZOSWKF2uXE0k16fH85yRHfDweS7W7EnQab3/juiAjfuvqV3GQYcb5dGBLZFXWIp3Qn00L6yAw+Hgixk95ZoBtdXQ3Z79u/trQly8laqy13x9RlXrSnjKnByqLJvUVa4ttJKjvRW8PTWfSOo6MHWpKEl3VLhY2lpboG0zFzTxcMC7g9W3VetLsQ1dFW9PR/Tu0BBdfTywbX5feLhIb3xsrCywILwLWnk5AwAkGnrncDgclRdq/3YN4Oxg2PGKK9vwtblkCiuOqaFChxvZKj0ej6s2iOtqdP9W6NDCDVMHy3dStLepelHt0U71OaSuCURbQpm+B7KHWPlnxND2mDFEvgeyj0zzgCpfzfSv8pmqDqcBnaQ9jQHgnYHV6yvQ3tsNQxSaxpT5aLwf26ymqPJslq1KH9SjKTgcDuxsLOVv2JScFpLycpX7bVwxgEhPNd+rIg44Wt8kyjLkUygcjvS38tEEP3ipaFLU9BNxdbTRK5DLmjyoLTbO7avVjXl9Q4FcT02EfHi6aQ74qvTtJO3lylbjymjR0Alb5wZggpK7W2tLHpZNfkPtRbw6DD0aUWXpVZubG1kdWrhhyuDXdC6laFp8VH9plV5vJU0SH41/HREyndPe9G+GsUGt8M7Aqt/Dh6M6IrCLV5UgX11uTjaYM7Jjtc4toGq7ozZeayZfhSn7pILc+Vax6dfbCKq0mb4/pB3aNXfFmP6qe/Y7OVhjvsIjPqq+53dCfdCo4sa68plqfXVq5Y43ezbD1rmqR+vS5K2ezeBob4U5I189HaLLOerTRHU1saO9FbbODcAUhSdN1FKxa1163FeXsiQoNiPVxkDgFjwuvBtW/wbWFFHVujIGOOtUPZddOYKQt6cjvl/YT2VpzsqSBytLHta+1wO7j9/FjceZsKvmHWtdsOBxseWDPrXSQar7a0I0FjogOuYhOJyqX2M7b1f0bOeJ7r4NlOZ7i0byFwFrSx6C/ZT3Rm7X3A3tmhvfnb+VBRelYtWlPnXe7NkMt55ksdOVOdTQ3R7dX2uAH47eqfhcdeDi21nhw1GdIJaUY9+ZByqXc3RQ3YFs+eQ3sHTnJd0SrwP5JzR0u+Hx8nBgq9n12cKo/i1x51kWBnZT3slO09MjilTte9G413Hwr0e4fFeERgJ7PBcVVFmmsYcDktLy5T7T7zn1qqno38UL5QyD6JiHemyP6Mr0IkMNcnKwQk5+Kfh21a/Obd7QEXPHdML6ff/KfV5Z5QyofuZSlsDZFh+M6ghJOaNTj3NjUt0qM1307dQI95NyMKhHU3y2Wzr8qaujNZZNeoO9ETJkVXhtatqAj6cvDffCII0q8snWiif3KI822VfZ+aiyM2CVTStZZ/Oc3rCy5NXKeV45NLGNdfVvMHU5nSx4XHw6pWqTnK4WhndGalYRWxvAt7NEXmEZO7+huz1mDG2PlIwCuPJt8P6XZ6ts45OJfnguKsD232/hebo00Kt7hloVZcdvacHFwG5N6zyQfzWrFyQS/W5sTQkFchmfTe2GjNwSdjSl6vLV40ehDIfDYTtB6WPJBD9k5RUbJC21pbGej+/ZWlvgvxWD4kQMbY89J+/ig1GddOq4Y6wWjO2MtKwiLP/xnxrf15r3euDniqcuFOun1D1aVInL4eC7eX1hweOwT3jIcqjoqyBbBWynpB+AoShW5X/2bjcUlkjgYGuBTi3d4d/eE3w7SxSViHXetsrBQWqwOrlNExe5gUw+f78nCkvE+FBmPHAAaptoeFwumgj5WDG1G649zMDpK8kqRhw0XYbqKGnsKJDLsLOxNPjFZGhvb/z212ODblNX0l6c2rcvTnvrNbg5Gn4kN229++ZrciOiacK3s0RaVlGVkv/rbQRVHsEzZbbWFmjagI/3h7RDQVGZ+oU50o5nd55l67UvD+dXTUOVTRSfTnkD95NztG6/Vzcgh6OdFT5+xw9tmrujtEj5SzKUpsvFFmlZVZ8IWT2tOxZtU/0yDcXftaUFD04VQ6b+V2Y0RH0YQw2PLjUZyjq6dWjhpveTCNocvhFkUb1GgbyGvenvjbAeTXEvKcdkRhrq/lrtDwm6MLwz1v4iffNaDx0fnZv+pi+OXnyKoVr0SK4PlA1io0xjD77egRyATP23NJJ7CRyq3RlSdhhab09HODlYQ6RDIK+sSlZs91Uc2rPSrGHt8c+dNDQW1tzQyiqDVG0HLzX7s7bkQVJejo2zexu8v4q6PhOebnZIySis04KBOaBAXgt4XC69WUyD6rSLujvbKu3hb05aNHREp1bu+P38E/YzRk3drrLXRSp2DtS157ti9bWi9RH+cLSvXo1X5QBFXgIHNpBXDmCiTOfWAnQ2wEiApkDdt7VpTm9wONqPGmmoHUsHQ8qVawYghqfXt1pWVoa5c+di7NixGDduHJKSqo7gc/jwYQwfPhwjR47E/v37AQBisRgLFy5EeHg4Ro0ahcuXLwMA3nvvPYwdOxbjx4/H+PHjceOGYUaMIsRcjO7fih1KU5Gyzob9lL3kQwVtH+JQNUBRJRe+dbUDyauhQF991lBh3IcPR9fO6z4rX0vaXOHRyqYVj8mpG1SqJqh7DM6Cx62ZIA71NxB8Oyt0amWcb06sT/QqkR85cgSOjo5Yv349zp49i/Xr12PDhg3s/MLCQmzZsgX79++HpaUlhgwZgqCgIJw+fRq2trb45ZdfcP/+fSxatAj79+9HQUEBvvvuOzg6mt+IPETKS+AAHpeDUCWv/iSaVZa+GfkPddyGvEE9muL6o4wq7xfQdv1K40PaIDWzULfEqNoHOxSo6vDRwKV2AujUwa9hcM9mVZobJof5oGMLN4ONrmjsqP277ul1ixYXF4fg4GAAQK9evXDlyhW5+YmJiWjfvj34fD5sbGzg5+eHhIQEvPXWW1i0aBEAwNXVFdnZ2QCAgoKqzzgS82JtxcO2+X2VDpBDtFc5ylcDVzs2sHIgbSvWSKHo3bqxM3Ys7Fft5+X7dW6EMVq+x12TyuDYvrmaJ0JqKbBY8LhK+wzY2Viid8eGJtMnpvooktc1vUrk6enpcHWV/pB4PB64XC5KS0thZWVVZT4AuLu7QyQSwdLyVfvYrl27MHjwYADSEvzy5cuRkpKC1q1bY9GiRbC2Vj1ghIuLHSwsDD/AiECgvmqQSFE+aac28mnioNdw8OxDdPH1hI2VBZZM7oYrd9LQq1MjfH9I+mIbLpeDAf7NEZuYgusP0wEA9vbyv6+lU7vLBR590u7u5gAHPcZgULavRe90RU5+SZV57w7tgDcDWsDTzR7f/3Eb5eUMu0yrxs64n5QN78avrj316VzV5Vhq87gFAr5R3bTUp+9cWxoDeXR0NKKjo+U+S0yUf1NR5RupZKfVzd+zZw9u3ryJrVu3AgCmT58Of39/CAQCfPLJJ9izZw8mT56sMk1ZWYapppMlEPAhEtXiYBsmivJJO7WVT33aN0Cf9g2Ql1OEyr291tgJmRn5KKoYIIRhGIhEeSgre/WMdEGB/Es9HCy5SJX5XemT9vSMfBQV6NaZTVU+tfLkA1A+zxJAeno+vvmgD8orjg0AFozthOJSCfJyXz2eVl/OVV3Pp9o87vT0PKMZrKq+X59U3aRoDOQjR47EyJEj5T6LjIyESCSCj48PysrKwDCMXGlbKBQiNjaWnU5LS0OnTp0ASG8Mzpw5g2+++YZdZ+jQoeyyQUFBOHr0qNYHRgjRjtzNtsI8F761XCDXxZBe3kh8mF6rI/gBVYcz5XG5sLcxjoBiTqiNvO7pddb7+/vj2LFjAICYmBh06yb/+EfHjh1x/fp15ObmoqCgAAkJCfDz80NSUhL27duHzZs3s1XnEokE77zzDvLzpWP+xsfHo1Urw7SnEWLO1D1+pkjl6GRaeKuXNz5+p6tRDIxCap8+L+ghhqXXLXRYWBguXLiAsWPHwsrKCmvWrAEAbNu2DV27dkXnzp0xd+5cTJkyBRwOBxEREeDz+di+fTuys7Mxbdo0dls7duzAsGHDMGHCBNja2kIoFGLWrFmGOTpCzBjb2a0iwDZ0s8ftp1mqVyAm7/P3e8JaiyF0DYrieJ3TK5DzeDysXr26yueyATo0NBShoaFy8z/88EN8+OGHVdb7z3/+g//85z/6JIUQoqXhfZvD090OPXwb4OTlqmM/1MKbJkkNk331bG2hOF73aGQ3QuorhchsY2WB/l28tF6eEG3o8j52UjOoZwgh9dSrqnX1y62Z3h0A4O4sLc1Vdzx1QkjtohI5IfVU5atbXfnqq1s9KkZCE7rYYfnkNyBwphdcEGJKKJATUk8N7NYEZWIJAl9XU52uQN/3wBsba0telTHYiWGNDWyFp6n195ltU0KBnJB6ytbaAqP7q3iUs563h2/5oA8931zDgrs2ruskkAoUyAkh9U51nosnxNRQZzdCCCHEhFEgJ8QcUYGVkHqDAjkh5qiet5ETYk4okBNCCCEmjAI5IYQQYsIokBNCCCEmjAI5IWaImsgJqT8okBNCCCEmjAI5IWaInj4jpP6gQE4IIYSYML2GaC0rK0NkZCRevHgBHo+H1atXo3Fj+XF3Dx8+jF27doHL5WL06NEYMWIEjh8/ji+++AINGjQAAPTs2RPvv/8+7ty5g2XLlgEA2rRpg+XLl1fvqAghhBAzoVcgP3LkCBwdHbF+/XqcPXsW69evx4YNG9j5hYWF2LJlC/bv3w9LS0sMGTIEQUFBKCwsxNtvv42JEyfKbe+zzz7D4sWL0aFDB8yePRtnz55FQEBAdY6LEKIGdXYjpP7Qq2o9Li4OwcHBAIBevXrhypUrcvMTExPRvn178Pl82NjYwM/PDwkJCSgoKKiyrdLSUjx//hwdOnQAAAQGBiIuLk6fZBFCCCFmR68SeXp6OlxdXQEAPB4PXC4XpaWlsLKyqjIfANzd3SESiVBYWIizZ8/i3LlzYBgGCxcuhIuLCxwdHdllBQIBRCJRdY6JEEIIMRsaA3l0dDSio6PlPktMTJSbZhgGHJmX/zIMo3R+9+7d0aFDB3Tv3h2XL1/G/Pnz8f3331dZVhMXFztYWPA0LqcrgYBv8G3WR5RP2jHmfLK3s2L/rut01vX+TQXlk3bMMZ80BvKRI0di5MiRcp9FRkZCJBLBx8cHZWVlYBgGlpaW7HyhUIjY2Fh2Oi0tDZ06dWKrzwHAz88PmZmZcHFxQXZ2Nvt5amoqPDw81KYpK6tQU7J1JhDwIRLlGXy79Q3lk3aMPZ8KCkvZv+syncaeT8aC8kk79T2fVN2k6NVG7u/vj2PHjgEAYmJi0K1bN7n5HTt2xPXr15Gbm4uCggIkJCTAz88PW7ZswfHjxwEA9+7dg6urK6ysrNC8eXNcvnwZAHDixAn07t1bn2QRQgghZkevNvKwsDBcuHABY8eOhZWVFdasWQMA2LZtG7p27YrOnTtj7ty5mDJlCjgcDiIiIsDn8/Gf//wHixYtwu7duyEWi/HZZ58BABYvXoxPPvkE5eXl6NixI3r27Gm4IySEEELqMQ6jTaO0kamJqpP6XiVjKJRP2jH2fDr092Mc+vsxAGBnZP86S4ex55OxoHzSTn3PJ4NWrRNCTJsJ3r8TQlSgQE4IIYSYMArkhBBCiAmjQE6IGZId94EQYtookBNihqiNnJD6gwI5IYQQYsIokBNCCCEmjAI5IYQQYsIokBNCCCEmjAI5IYQQYsIokBNCCCEmjAI5IYQQYsIokBNCCCEmjAI5IYQQYsIokBNCCCEmjAI5IYQQYsIokBNCCCEmzEKflcrKyhAZGYkXL16Ax+Nh9erVaNy4sdwyhw8fxq5du8DlcjF69GiMGDEC3377LS5cuAAAKC8vR3p6Oo4fP4733nsPOTk5sLCQJmfhwoVo165dNQ+NEKJKt9eEOHz+CSaEtqnrpBBCqkmvQH7kyBE4Ojpi/fr1OHv2LNavX48NGzaw8wsLC7Flyxbs378flpaWGDJkCIKCgvD+++/j/fffBwD89ttvyMjIAAAUFBTgu+++g6OjY/WPiBCikaebPXYs7EevMyWkHtCraj0uLg7BwcEAgF69euHKlSty8xMTE9G+fXvw+XzY2NjAz88PCQkJ7HyxWIy9e/di3LhxAKSBnBBSuyiIE1I/6FUiT09Ph6urKwCAx+OBy+WitLQUVlZWVeYDgLu7O0QiETt94sQJ9OrVCzY2NgCkJfjly5cjJSUFrVu3xqJFi2Btba33QRFCCCHmQmMgj46ORnR0tNxniYmJctMMw8jd3TMMo3b+r7/+iuXLl7PT06dPh7+/PwQCAT755BPs2bMHkydPVpkmFxc7WFjwNCVdZwIB3+DbrI8on7RD+aQdyiftUD5pxxzzSWMgHzlyJEaOHCn3WWRkJEQiEXx8fFBWVgaGYWBpacnOFwqFiI2NZafT0tLQqVMnANLSd2pqKry8vNj5Q4cOZf8OCgrC0aNH1aYpK6tQU7J1JhDwIRLlGXy79Q3lk3Yon7RD+aQdyift1Pd8UnWTolcbub+/P44dOwYAiImJQbdu3eTmd+zYEdevX0dubi4KCgqQkJAAPz8/AMCdO3fg7e3NLiuRSPDOO+8gPz8fABAfH49WrVrpkyxCCCHE7OjVRh4WFoYLFy5g7NixsLKywpo1awAA27ZtQ9euXdG5c2fMnTsXU6ZMAYfDQUREBPh86Z2ESCSSaz/n8XgYNmwYJkyYAFtbWwiFQsyaNUvt/muq6sQcq2T0QfmkHcon7VA+aYfySTvmmE8cRrFBmxBCCCEmg0Z2I4QQQkwYBXJCCCHEhFEgJ4QQQkwYBXJCCCHEhFEgJ4QQQkyYXo+f1SerVq1CYmIiOBwOFi9ejA4dOtR1kurEvXv3MGPGDEycOBHjxo1DSkoKFixYAIlEAoFAgM8//xxWVlZK32qnzdvw6ot169bhypUrEIvFmD59Otq3b0/5pKCoqAiRkZHIyMhASUkJZsyYAR8fH8onFYqLizFo0CBERESgR48elE8Kbty4gRkzZqBp06YAgNatW2Pq1KmUT7IYMxYfH89MmzaNYRiGuX//PjNixIg6TlHdKCgoYMaNG8csWbKE2b17N8MwDBMZGckcPXqUYRiGWbt2LbNnzx6moKCAGTBgAJObm8sUFRUxISEhTFZWFnPgwAFm2bJlDMMwTGxsLDN79uy6OpQaFRcXx0ydOpVhGIbJzMxkAgICKJ+U+OOPP5ht27YxDMMwycnJzIABAyif1Pjyyy+ZYcOGMb/++ivlkxLx8fHMypUr5T6jfJJn1lXrcXFxCAoKAgC0bNkSubm57Ahz5sTKygrbt2+Hh4cH+1l8fDwCAwMBAIGBgYiLi1P5VjtNb8OrL7p27Yqvv/4aAODk5ISioiLKJyXCwsLw7rvvAgBSUlIgFAopn1R4+PAhHjx4gL59+wKg350yyt6OSfkkz6wDeXp6OlxcXNhpNzc3ube0mQsLCwv2TXSVioqK2LfZCQQCiEQilW+1U/U2vPqGx+PBzs4OgPRlQn369KF8UmPMmDGYN28eFi9eTPmkwtq1axEZGclOUz5VVVhYiCtXrmDq1Kl4++23cfHiRconBWbdRs5oeEubOVP2NjtV+WVu+Xjq1Cns378fO3fuREhICPs55ZO8ffv24fbt25g/fz6dT0ocPHgQnTp1kmuvpXyqysfHBxEREQgMDMTjx48xadIkiMVidj7lk5mXyIVCIdLT09nptLQ0uLu712GKjIetrS2Ki4sBAKmpqfDw8FCaXwKBAEKhkK3JUPY2vPrkr7/+wtatW7F9+3bw+XzKJyVu3LiBlJQUAEDbtm0hkUgon5SIjY3F6dOnMWrUKERHR+Obb76hfFKiRYsWbDW6t7c33N3dkZubS/kkw6wDub+/P44fPw4AuHXrFjw8PODg4FDHqTIOPXv2ZPPmxIkT6N27t8q32ml6G159kZeXh3Xr1uG7776Ds7MzAMonZS5fvoydO3cCkDZfFRYWUj4psWHDBvz666/43//+h5EjR2LGjBmUT0rs378fP/30EwDpS7cyMjIwbNgwyicZZv/SlC+++AKXL18Gh8PB0qVL4ePjU9dJqnU3btzA2rVr8fz5c1hYWEAoFOKLL75AZGQkSkpK0LBhQ6xevRqWlpY4duwYduzYAQ6Hg3HjxuGtt96CRCLBkiVL8OTJE/ZteJ6ennV9WAYXFRWFTZs2yb2Gd82aNViyZAnlk4zi4mJ89NFHSElJQXFxMWbOnIl27dph4cKFlE8qbNq0CY0aNUKvXr0onxTk5ORg3rx5KCwsRGlpKWbOnIm2bdtSPskw+0BOSF0aM2YMCgsLcfjwYY3LpqenIzExka1mNAbJyckYMGAAbt26VddJIcRsmXXVOiF16f79++Dz+WjYsCGuXr2qcfn4+HicOXOmFlJGCDElFMgJqSMHDhxAaGgoBg8ejIMHDwKQBuvKZ15lp2/evIlPP/0Ux48fxwcffAAA+PPPPzF48GCEhoZiwoQJePbsGQBp1faCBQvQv39/DBw4EIcOHQIAlJSU4JNPPkFISAgGDhyINWvWQCKRAAD69++PzZs3IyQkBC9evMD48ePx1VdfYeDAgUhISEBeXh7mz5+PkJAQBAYG4tdff61yPOXl5fjqq68QGhqK0NBQREZGorCwEABw8+ZNvPnmmwgJCcHmzZvx5ptvIj4+HsnJyejVqxdWrVqFcePGAQBOnz7NLjts2DDcvn2bzYvRo0dj1apVCAwMxLBhw5CYmIjx48fD398fGzduZNOyZcsWhISEICgoCNOnT0dubq4hvzpCjEvNjjdDCFFGLBYzgYGBTF5eHlNYWMj07duXKSkpYS5evMgEBQWxy8lOb9y4kVm8eDHDMAzz/Plz5vXXX2eePHnCMAzD7Nixg3nnnXcYhmGYLVu2MHPmzGEYhmFSUlIYPz8/5uXLl8x3333HvPvuu0xZWRlTVFTEDB8+nDl48CDDMAzTr18/ZsmSJex+x40bx0yePJmRSCQMwzDM8uXLmQULFjASiYTJyMhgAgICmLt37zJJSUlM27ZtGYZhmCNHjjBDhgxhCgoKGIlEwrz//vvMli1bGIZhmKFDhzJ79uxhGIZhfvjhB6Zdu3bMxYsXmaSkJMbX15c5cOAAwzAMU1ZWxvj5+TFXr15lGIZhNm3axB7XxYsXGV9fX+bixYtMeXk5M3z4cGbYsGFMYWEhc/fuXea1115jiouLmevXrzM9evRg8vLyGIlEwkycOJFNByH1EZXICakDf//9N9q3bw8HBwfY2trijTfeQExMjNbrnz9/Ht26dWPHnx45ciTi4+NRVlaGc+fOYdCgQQCABg0aIDY2FkKhELGxsRg1ahQ7ANCbb76J8+fPs9usHF2sUkBAALhc6SXizz//xJgxY8DlcuHq6org4GCcOHFCbvnY2FgMGTIEdnZ24HK5GDZsGM6fP4/i4mLcvHkTgwcPBgC8/fbbcs/2lpWVsbUQFhYWuHDhAjp16gQA8PPzQ1JSEruso6MjunXrBg6Hg1atWuGNN96Ara0tWrVqBYlEgszMTLRr1w6xsbFwcHAAl8tF586d5bZBSH1j1gPCEFJXDhw4gHPnzsHPzw8AIJFIkJOTg0mTJmm1flZWFhwdHdlpPp8PhmGQnZ2NrKws8Pl8dp69vT0AIDMzE05OTuznTk5OyMjIkJuWJTudl5eHBQsWgMfjAZBW04eGhsotr2r7OTk5AMCm19LSEm5ubuxyPB5P7rHP3bt347fffkNpaSlKS0vlBu+oPBYA4HK57Eh7HA4HXC4XEokERUVFWL16NeLj4wFIez0r3qQQUp9QICekluXm5uLSpUuIj49nh5kUi8UICAgAj8dj260BsEFQkZubm1wHuZycHHC5XLi4uMDFxQVZWVnsvJcvX8LJyQnu7u7Izs5mP8/OztZ6ACQPDw9s2bIFrVu3lvs8OTmZ/VvV9iuDdH5+PhwcHCAWi5GZmal0PwkJCdi+fTuio6Ph5eWF8+fP4+OPP9YqjZV27dqFJ0+e4MCBA7C3t8dXX32F1NRUnbZBiCmhqnVCatmRI0fQvXt3NogD0irlXr164datW+ygFxKJBEeOHJFbJi8vD4B0MKPLly+zVcb79u2Dv78/LCws0L9/fxw8eBAMw0AkEmHIkCHIzMxEQEAA9u/fD4lEgsLCQhw6dAgBAQFapbl///7Yt28fAOlNx6pVq3Dz5k25ZQICAnD48GEUFRVBLBYjOjoaAQEBsLe3R4sWLdiq+KioKJVDZGZmZsLNzQ2enp4oKirCgQMHUFhYiPLyci1zF8jIyIC3tzfs7e3x/PlzxMbGKn3xBiH1BQVyQmrZwYMH2bfuyQoODsbBgwcxfPhwDBkyBOHh4ejevTs739/fHxcvXsTw4cPRoEEDrFixAjNmzMDAgQPxzz//4NNPPwUATJw4EW5ubujXrx/Gjx+PhQsXolGjRpgwYQIaNGiAQYMGYfjw4ejbty8GDhyoVZrnzJmDvLw8hISEYNCgQSgvL68yeNLAgQPRp08fDBs2DIMHD4anpycmTJgAAFi6dCm2bt2KQYMGoaCgAEKhUGkw7927Nzw8PBAQEIDJkydj4sSJ4PP5iIiI0Dp/x4wZg3/++Qf9+/fH2rVrsWjRIly4cAE//PCD1tsgxJTQgDCEkFrByLysonv37vjxxx/NciRFQgyNSuSEkBr33//+F9u3bwcAxMXFgWEYNGvWrG4TRUg9QSVyQkiNe/jwIRYtWoScnBxYWlpi/vz5WrfPE0LUo0BOCCGEmDCqWieEEEJMGAVyQgghxISZ5IAwIlFetdZ3cbFDVlahgVJDAMpTQ6P8NDzKU8OjPDUsTfkpEPCVfm6WJXILC15dJ6HeoTw1LMpPw6M8NTzKU8PSNz/NMpATQggh9QUFckIIIcSEUSAnhBBCTBgFckIIIcSEmWSvdUMrE5ejpEyieUEzIDs+kNxIQYzSP4GK5S2sLZGTX6J+2zqlQ4eFdaRuDCR998vodHRabI/HQ0ZOkUG3qXxHaie1PyotzhsNu65xpeAgM9NwPaxNdSwtQya7uBzIzNT8Zjm1u1SSIJXLGzDtNf3tOTtYgW9npXlBA6BADqCguAwvM+gRiuookgDZ2ZSHhiIGF9nZxXWdjPqFx0N2nvqbTaIbrqUFcgtK6zoZRsnepvbCK1WtE0IIISaMSuTELGTnl+DoxWd4kZ6Phu4OCOveBM4O1nWdLEIIqTYK5GbMnILb0YvPkCzKBwAki/Jx9OIzhAe1quNUEUJI9VHVuhmrDG7lzKvgVl+9SM9XO00IIaaKArkZM6fg1tDdQe00IYSYKgrkZsycgltY9ybgcTkAAC+BtBmBEELqA2ojN2Nh3Ztgxx+3ISln6n1wc3awhr2tJQBQ2zjMq38EIfUdlcjNWGVwc7S3QnhQK7qQmxFz6h9BSH1HgZwQM2RO/SMIqe8okBNihsypfwQh9R0FckLMEHX+I6T+oM5upM5Rx6vaR53/CKk/DF4iX7VqFUaPHo0xY8bg2rVrcvMuXLiAESNGYPTo0diyZQv7+bp16zB69GgMHz4cJ06cMHSSiJGjjleEEKI/g5bIL126hKdPnyIqKgoPHjzAokWLEB0dzc5fuXIlduzYAaFQiPDwcISEhCA9PR33799HVFQUsrKyMHToUAwYMMCQySJGjjpeEUKI/gwayOPi4hAUFAQAaNmyJXJzc5Gfnw8HBwckJSXByckJnp6eAICAgADExcUhPDwcHTp0AAA4OTmhqKgIEokEPB7PkEkjRqyhuwM7DnrlNCGk/qLmNMMyaCBPT0+Hr68vO+3m5gaRSAQHBweIRCK4urqy89zd3ZGUlAQejwc7OzsAQHR0NPr06aMxiLu42MHConqBXiDgs3/zrC1RLKnW5kwWt6LDk7OzXbW3pe82xgxog6/2JUAiYdDM0xEj+reCs6NNtdOjyJDHWhtqOp2mlh+GYE7HWlv0ydP/xT6Ue4nRicvJmDakvaGTVqfc3Ozh7myr83qysUlbBg3kDMNUmeZwOErnAWDnAcCpU6ewf/9+7Ny5U+N+srIKq5VOgYAPkSiPnc7OL0F2dvW2aarKy6XfS3WP39nZTu9tcAHY20g7Xo3q2wIoL6+R78NQx1obqpOf2jKl/DCE2shTc6Nvnj57mVtlur59N1YcBkyZWKd1FGOTsvnKGLSzm1AoRHp6OjudlpYGd3d3pfNSU1MhEAgAAH/99Re2bt2K7du3g8/X/W6EEEKI6aBxDAzLoIHc398fx48fBwDcunULHh4ecHCQfkFeXl7Iz89HcnIyxGIxYmJi4O/vj7y8PKxbtw7fffcdnJ2dDZkcQgghRojGMTAsg1atd+nSBb6+vhgzZgw4HA6WLl2KAwcOgM/nIzg4GMuWLcPcuXMBAGFhYfD29mZ7q8+ZM4fdztq1a9GwYUNDJo0QQoiRoHEMDMvgA8LMmzdPbtrHx4f9u2vXroiKipKbP3r0aIwePdrQySCEEELMAg3RSgghhJgwCuSEEEKICaNATgghhJgwCuSEEEKICaNATgghhJgweo0pIYQQo0PjsWuPSuSEEEKMDr3eWHsUyAkhhBgder2x9iiQE0IIMTo0Hrv2KJATQogG2fkl+OXUfXyx7yp+OXUf2fkldZ2keo/GY9ceBXJCCNGA2mtrX+V47I72VggPakUd3dSgQE4IIRpQey0xZvT4GSFaosdhzFdDdwcki/LlpgkxFlQiJ0RLVL1qvqi9lhgzKpEToiWqXjVf9P5sYsyoRE6IluhxGEKIMTJ4IF+1ahVGjx6NMWPG4Nq1a3LzLly4gBEjRmD06NHYsmUL+/m9e/cQFBSEn3/+2dDJMWv0yIxhUfUqIcQYGTSQX7p0CU+fPkVUVBRWrlyJFStWyM1fuXIlNm3ahL179+Kvv/7CgwcPUFhYiBUrVqBHjx6GTAoBtekaGj0OQwgxRgYN5HFxcQgKCgIAtGzZErm5ucjPl7YjJiUlwcnJCZ6enuByuQgICEBcXBysrKywfft2eHh4GDIpBNSmSwgh5sCgnd3S09Ph6+vLTru5uUEkEsHBwQEikQiurq7sPHd3dyQlJcHCwgIWFrolw8XFDhYWvGqlVSDgs3/zrC1RLKnW5oxSkwaOeJKSKzft7Gwntwy3oqpY8XN9VGcbhkxHTe6jutvIzC3G/jP38Sw1D02EfIzo3wqujjZKl63JvABqJ8+NjbGfo6ZI3/zQJj9NOc/d3Ozh7myr83qysUlbBg3kDMNUmeZwOErnAWDn6Sorq1Cv9SoJBHyIRHnsdHZ+CbKzq7dNYzTAzws7/rgNSTkDL4EDBvh5VTnO8nLp91Ld43d2tqvWNgyVjpreR3W3se/UffZ55Ccpudh34q7SXtDVzU9t1EaeGxNTOEdNTXXyVJv8NOU8t+IwYMrEOq2jGJuUzVfGoIFcKBQiPT2dnU5LS4O7u7vSeampqRAIBIbcPVFAj8wYH2ruIIQYmkHbyP39/XH8+HEAwK1bt+Dh4QEHB+kjOl5eXsjPz0dycjLEYjFiYmLg7+9vyN2bDOpNbr7oETZCiKEZtETepUsX+Pr6YsyYMeBwOFi6dCkOHDgAPp+P4OBgLFu2DHPnzgUAhIWFwdvbGzdu3MDatWvx/PlzWFhY4Pjx49i0aROcnZ0NmTSjUtmbHHjVm5xKzOYhrHsTueYOeoSN6IKGCSbKGHxkt3nz5slN+/j4sH937doVUVFRcvPbtWuH3bt3GzoZRo2qV80XNXeQ6qBCAFGGhmitA/QCBkKkqISpGyoEEGVoiNY6QCOEESJFgxbphvpYEGWoRF4HqHpVN1Rqq7+ohKkb6mNBlKFAToyeKbUL0k2HboyhmcmUvjMqBBBlqGqdGD1TKrVRVbFujKGZib4zYuqoRE6MnjGU2rRlSjcdxsAYSpj0nRFTRyVyYvSModSmLeqMZHroOyOmjgK5Ahp1zfiY0utDTemmg0jRd0ZMHQVyBdReRqrDlG46iBR9Z8TUURu5AmovI8R4mFKPckLqCpXIFVB7GSHGg2rICNGMArkCai8jxHhoU0NG/VqIuaOqdQXG8DgMQFWKhADaPXpoSgMGEVITqERupKhKkRDtasioXwsxd1QiN1J0cSJEuxoyUxowiJCaQCVyI0Wd7gjRDvVrIebO4IF81apVGD16NMaMGYNr167Jzbtw4QJGjBiB0aNHY8uWLVqtY67o4kSIdug5cGLuDFq1funSJTx9+hRRUVF48OABFi1ahOjoaHb+ypUrsWPHDgiFQoSHhyMkJASZmZlq1zFFhuioZiyd7gghhBg3gwbyuLg4BAUFAQBatmyJ3Nxc5Ofnw8HBAUlJSXBycoKnpycAICAgAHFxccjMzFS5jqmiXrSEEF3RkypEXxyGYRhDbezjjz9GQEAAG5jDw8Px2WefwdvbGwkJCdixYwdbpR4dHY2kpCRkZWWpXEeVicuPVyudPB4HEsmrwy5nGEjKX03nFZYCAPh2VnptP7egtMpnjvby29JmH9VNhzbbMMQ+AIDL5aC8XP9TqTbSWVvbMMSxVDc/tWGo776m02Go34q6PK2t36M6BUVlctchHpfD1srVZjp0UZ3z1BjyvCbxuBxwORzd1lGITYp+XBqi9HODlsgV7wkYhgGn4kCU3S9wOBy166jC5XGgW/ZUxeO92gKnHJBNhZOGu+CcigEnVC2n+GXweBxwufIp1rQPQ6RDm20YYh+alqmNdGqzn9raRn3Jc2NJR238Vmrr96huGYlCQJSUM1WuG7WRjtrahjHkeU1ug8vlsP2cdCEbm7Rl0EAuFAqRnp7OTqelpcHd3V3pvNTUVAgEAlhYWKhcR5W103tUK50CAR8iUR47nZ1fgpcZhVqvv/XwTQDAtMGvKZ1fW1VkmtJRW/vYevgmuFyOymVqI52G2k9tpVVTGtTlZ3Z+CXb8cRuScgYONpZKz6/aygtNyxhDflamQ12eGmofgP759cup+3KP0XkJHPRqkqut780Yfve1eay6bsPDxRaujjYqt6mMYmzSlkF7rfv7++P4cWm1961bt+Dh4cG2dXt5eSE/Px/JyckQi8WIiYmBv7+/2nVMlbODNcKDWmHemM7Ui5YY3NGLz9jSGw0WVH+EdW8CL4EDuBx6UoXoxqAl8i5dusDX1xdjxowBh8PB0qVLceDAAfD5fAQHB2PZsmWYO3cuACAsLAze3t7w9vausg4hRDUaLEg32fklbPvzL6fuG20nssoCACG6MvjIbvPmzZOb9vHxYf/u2rUroqKiNK5DCFGNRjLTjbIaDAqYqpnKjQ95hUZ2I8TEUBWsbqgGQzfUdGN6aKx1QkwMVcHqhmowdGNONz6GqH0whhoMKpETYkQqLwrZeSV6v1u7chu5BaX0fm7I1GBwOVSDoQVTec+DIc5zQ9Q+GEMNBgVyQoxIfbmwGJPKGoyV03vSUyRaMJWmG0Oc54aofTCGGgyqWifEiNSXC4u5MYbqVUMxlaYbQ5znhmh2MYamGyqRE2JEDFGtaSpVo/UJ1YLUPkOc54aofTCGGgwqkRNiRMK6N5GOCphRgIZu9npfWBRHFiQ1i2pBap8hznND1D4YQw0GBXJSL9SXqs3Ki4Kzsx2ys7UfNljZNkjtMYbqVXND5/krVLVO6gWq2iR1yRiqV4n5ohK5jupLya++oapNUpeodEjqEpXIdUQlP+NEHbwIIeaKArmOqORnnKhq07BoUBnDM5Y8NZZ0EMOhQK4jYyn5GcuP0RAjkRkCvTrWsKjmyfCMJU+NJR2mwliutepQINeRsZT8jOXHaCzpIIZFNU+GZyx5aizpMBWmcI2jzm46MpZOLcbyYzSWdBDDosepDM9Y8tRY0mEqTOEaRyVyE2UsVfzGkg5iWMZS81SfGEueGks6TIUpXOOoRG6ijGX0LkOMREaMj7HUPNUnxpKnxpIOU2Es11p1DBbIy8rKEBkZiRcvXoDH42H16tVo3Lix3DKHDx/Grl27wOVyMXr0aIwYMQIAcOnSJcyePRurVq1Cv379DJWkes1YfoyGGImMEGJazGk8DWO51qpjsKr1I0eOwNHREXv37sW7776L9evXy80vLCzEli1b8OOPP2L37t34/vvvkZ2djWfPnuGHH37A66+/bqikECNiCj0+K5lSWgmpS6bQAcycGCyQx8XFITg4GADQq1cvXLlyRW5+YmIi2rdvDz6fDxsbG/j5+SEhIQECgQCbN2+Gg4PxtTuQ6jOlH7wppZWQumQKHcDMicGq1tPT0+Hq6goA4PF44HK5KC0thZWVVZX5AODu7g6RSARbW1ud9+XiYgcLC1610isQ8Nm/edaWKJZUa3P1FpfLAQA4O9tpXFbZMi8yCqpMa7OtumBsaTXWfJKl6fzQ5fypDcaSjppUG3nepIEjnqTkyk0r7s9Yvvu6Soebmz3cnXWPb7KxSVt6BfLo6GhER0fLfZaYmCg3zTAMOByO3LS6+brIyqpeW6xAwIdIlMdOZ+eXUPuuCuUVJVRN+aOqjbyhm738oy5u9kab18aUVlPpc6Dp/ND2/KkNppKn1VUbeT7Az0uuk+sAP68q+zOW776u0mHFYcCUiXVaRzE2KZuvjF6BfOTIkRg5cqTcZ5GRkRCJRPDx8UFZWRkYhoGlpSU7XygUIjY2lp1OS0tDp06d9Nk9MSGm0OOzkimllZC6ZCqdXM2lU57Bqtb9/f1x7Ngx9O7dGzExMejWrZvc/I4dO2LJkiXIzc0Fj8dDQkICFi9ebKjdEyNlCj0+K5lSWgkhminr91Iff+MGC+RhYWG4cOECxo4dCysrK6xZswYAsG3bNnTt2hWdO3fG3LlzMWXKFHA4HERERIDP5yM2NhY7duzAo0ePcPPmTezevRs7d+40VLIIIYSYKXPplGewQF757LiiadOmsX+HhoYiNDRUbn7fvn3Rt29fQyWDEEIIAWA+w9HSEK2EEELqJXMZjpaGaCWEEFIvmUu/FyqRE0JqBI2UR0jtoEBOCKkRNFIeIbWDAjkhpEaYS49hQuoaBXJCSI0whfc4E1IfUCAnhNQIc+kxTEhdo17rhJAaYS49ho2JuQxJSuRRiZwQQuoJ6mBoniiQE0JIPWEsHQzp0cPaRYGcEELqCWPpYEg1A7WLAjkhhNQTxtLB0FhqBswFdXYjhJB6wlg6GJrLy0qMBZXICSGEGJSx1AyYCyqRE0IIMShjqRkwF1QiJ4QQQkyYwUrkZWVliIyMxIsXL8Dj8bB69Wo0btxYbpnDhw9j165d4HK5GD16NEaMGAGxWIyPPvoISUlJEIvFWLBgAfz8/AyVLEIIIaReM1iJ/MiRI3B0dMTevXvx7rvvYv369XLzCwsLsWXLFvz444/YvXs3vv/+e2RnZ+PQoUOwtbXFL7/8gs8++wxr1qwxVJIIIYSQes9ggTwuLg7BwcEAgF69euHKlSty8xMTE9G+fXvw+XzY2NjAz88PCQkJeOutt7Bo0SIAgKurK7Kzsw2VJEIIIaTeM1jVenp6OlxdXQEAPB4PXC4XpaWlsLKyqjIfANzd3SESiWBpacl+tmvXLgwePFjjvlxc7GBhwatWegUCPvs3z9oSxZJqba7e4nI5AABnZzuNy2qzDNGeKeSnLueHMTCVdJoSylPl3Nzs4e5sq/N6srFJW3oF8ujoaERHR8t9lpiYKDfNMAw4HI7ctLr5e/bswc2bN7F161aN+8/KKtQn2SyBgA+RKI+dzs4vQXZ29bZZX5VXjM6kKX+cne0oDw3IVPJT2/PDGJhKnpoSylPVrDgMmDKxTusoxiZl85XRK5CPHDkSI0eOlPssMjISIpEIPj4+KCsrA8MwcqVtoVCI2NhYdjotLQ2dOnUCIL0xOHPmDL755hu5dQghhBCinsHayP39/XHs2DEAQExMDLp16yY3v2PHjrh+/Tpyc3NRUFCAhIQE+Pn5ISkpCfv27cPmzZthbU2v2yOEEEJ0YbA28rCwMFy4cAFjx46FlZUV2/t827Zt6Nq1Kzp37oy5c+diypQp4HA4iIiIAJ/Px/bt25GdnY1p06ax29qxYwfbtk4IIYQQ1TiMYuO1CVDXhqANZW3kLzOonUeZrYdvAgDee8tX7XLUVmZYppKf2p4fxsBU8tSUUJ6q5uFiC1dHG53W0beNnEZ2I4QQQkwYBXJCCCHEhFEgJ4QQQkwYBXJCCCHEhFEgJ4QQQkwYBXJCCCHEhFEgJ4QQQkwYBXKiUnZ+CQqKypBbUIpfTt1Hdn5JXSeJEEKIAgrkRKWjF59BUvFSjGRRPo5efFbHKSKEEKKIAjlR6UV6vtppYt6oxoYQ42CwsdZNmZUFD04O5jO2u7pBeWVnNRHy8eTlq+ECGwv5cLCzlFuo8k8HO0uUlah/c111RwOuqcGEGZkDMpYBi62teLC24tXKvhSPmUGVD5Q6Fi9fY/Nn/DOMD2lTZZ0q21Oz75rE5XLY96ebg1oZfZsDcLTIUmP5XdVXFMgB2NlYwM6GskLRe0PaYecft/HweQ5aNHLC5EFt4eFsq3RZgYAPB0uq4DEUgYAPka1xn5PP0wvkpl+kF6BlI6c6So1m0nGszeeGvTZoGhtcG6puONTG/hq4MVB3w6kPjjZ3OAZi3FcKUqc8nG0R+XaXuk4GMVItGjnhXlK23DQhulIV8NSGwRqJkaZbW0NFKEKIXiYPaovWjZ3B43LQurEzJg9qW9dJIsQsUYmcEKIXqrEhxDhQiZwQQggxYRTICSGEEBNGgZwQQggxYRymVh42JIQQQkhNoBI5IYQQYsIokBNCCCEmjAI5IYQQYsIokBNCCCEmjAI5IYQQYsIokBNCCCEmzOyGaF21ahUSExPB4XCwePFidOjQoa6TZJLu3buHGTNmYOLEiRg3bhxSUlKwYMECSCQSCAQCfP7557CyojdNaWvdunW4cuUKxGIxpk+fjvbt21N+VkNRUREiIyORkZGBkpISzJgxAz4+PpSn1VRcXIxBgwYhIiICPXr0oPyshhs3bmDGjBlo2rQpAKB169aYOnWqXnlqViXyS5cu4enTp4iKisLKlSuxYsWKuk6SSSosLMSKFSvQo0cP9rONGzciPDwcv/zyCxo1aoT9+/fXYQpNy8WLF3H//n1ERUXh+++/x6pVqyg/qykmJgbt2rXDzz//jA0bNmDNmjWUpwbw7bffwtnZGQD95qursLAQISEh2L17N3bv3o2PP/5Y7zw1q0AeFxeHoKAgAEDLli2Rm5uL/Pz8Ok6V6bGyssL27dvh4eHBfhYfH4/AwEAAQGBgIOLi4uoqeSana9eu+PrrrwEATk5OKCoqovysprCwMLz77rsAgJSUFAiFQsrTanr48CEePHiAvn37AqDffHUVFBRU+UzfPDWrQJ6eng4XFxd22s3NDSKRqA5TZJosLCxgY2Mj91lRURFbBSQQCChfdcDj8WBnZwcAiI6ORp8+fSg/DWTMmDGYN28eFi9eTHlaTWvXrkVkZCQ7TflZPYWFhbhy5QqmTp2Kt99+GxcvXtQ7T82qjVxxNFqGYVS+1J7oRjYfadRf/Zw6dQr79+/Hzp07ERISwn5O+am/ffv24fbt25g/fz6do9Vw8OBBdOrUCY0bN2Y/o/ysHh8fH0RERCAwMBCPHz/GpEmTIBaL2fm65KlZBXKhUIj09HR2Oi0tDe7u7nWYovrD1tYWxcXFsLGxQWpqqly1O9Hsr7/+wtatW/H999+Dz+dTflbTjRs34ObmBk9PT7Rt2xYSiYTytBpiY2ORlJSE2NhYvHz5ElZWVpSf1dSiRQu0aNECAODt7Q13d3ekpKToladmVbXu7++P48ePAwBu3boFDw8PODg41HGq6oeePXuyeXvixAn07t27jlNkOvLy8rBu3Tp89913bEciys/quXz5Mnbu3AlA2qRWWFhIeVoNGzZswK+//or//e9/GDlyJGbMmEH5WU379+/HTz/9BAAQiUTIyMjAsGHD9MpTs3v72RdffIHLly+Dw+Fg6dKl8PHxqeskmZwbN25g7dq1eP78OSwsLCAUCvHFF18gMjISJSUlaNiwIVavXg1LS8u6TqpJiIqKwqZNm+Dt7c1+tmbNGixZsoTyU0/FxcX46KOP2BLOzJkz0a5dOyxcuJDytJo2bdqERo0aoVevXpSf1ZCTk4N58+ahsLAQpaWlmDlzJtq2batXnppdICeEEELqE7OqWieEEELqGwrkhBBCiAmjQE4IIYSYMArkhBBCiAmjQE4IIYSYMArkhBBCiAmjQE4IIYSYMArkhBBCiAn7Pzp9TVheB/KdAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2,1, figsize=[8,6])\n",
    "depreciacion.plot(ax=axs[0], title='Evolución del cambio porcentual en EUR/USD')\n",
    "sm.graphics.tsa.plot_acf(depreciacion, zero=False, ax=axs[1], lags=48, alpha=0.05, title='Autocorrelograma');"
   ]
  }
 ],
 "metadata": {
  "kernel_info": {
   "name": "python3"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "nteract": {
   "version": "0.22.0"
  },
  "vscode": {
   "interpreter": {
    "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}