{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import sqrt\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io as sio\n",
    "import os\n",
    "import random\n",
    "import time\n",
    "import sys\n",
    "from matplotlib import rcParams\n",
    "from scipy.linalg import eigh\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from scipy import stats\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "mpl.rcParams['figure.dpi'] = 400 \n",
    "plt.rc('text',usetex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Duncan Prestige data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Carregando a base de dados\n",
    "duncan_prestige = sm.datasets.get_rdataset(\"Duncan\", \"carData\")\n",
    "Y = duncan_prestige.data['income']\n",
    "X = duncan_prestige.data['education']\n",
    "X = sm.add_constant(X) # adicionando uma constante para que ajuste o modelo beta0 + beta1 * X. \n",
    "\n",
    "# inicializando as classes do statsmodel e ajustando o modelo. \n",
    "model = sm.OLS(Y,X)\n",
    "results = model.fit()\n",
    "model_prediction = results.predict(X[['const','education']])\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "\n",
    "plt.plot(X['education'],Y,'o',color='C0',alpha=0.2,label=r'Dados')\n",
    "plt.plot(X['education'],model_prediction,'r-')\n",
    "plt.xlabel(r'$X$ (education)',fontsize=16)\n",
    "plt.ylabel(r'$Y$ (income)',fontsize=16)\n",
    "\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Resumo da regressão"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>income</td>      <th>  R-squared:         </th> <td>   0.525</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.514</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   47.51</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 22 Sep 2023</td> <th>  Prob (F-statistic):</th> <td>1.84e-08</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:27:52</td>     <th>  Log-Likelihood:    </th> <td> -190.42</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    45</td>      <th>  AIC:               </th> <td>   384.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    43</td>      <th>  BIC:               </th> <td>   388.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</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>const</th>     <td>   10.6035</td> <td>    5.198</td> <td>    2.040</td> <td> 0.048</td> <td>    0.120</td> <td>   21.087</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>education</th> <td>    0.5949</td> <td>    0.086</td> <td>    6.893</td> <td> 0.000</td> <td>    0.421</td> <td>    0.769</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.841</td> <th>  Durbin-Watson:     </th> <td>   1.736</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.007</td> <th>  Jarque-Bera (JB):  </th> <td>  10.609</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.776</td> <th>  Prob(JB):          </th> <td> 0.00497</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.802</td> <th>  Cond. No.          </th> <td>    123.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                 income   R-squared:                       0.525\n",
       "Model:                            OLS   Adj. R-squared:                  0.514\n",
       "Method:                 Least Squares   F-statistic:                     47.51\n",
       "Date:                Fri, 22 Sep 2023   Prob (F-statistic):           1.84e-08\n",
       "Time:                        13:27:52   Log-Likelihood:                -190.42\n",
       "No. Observations:                  45   AIC:                             384.8\n",
       "Df Residuals:                      43   BIC:                             388.5\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         10.6035      5.198      2.040      0.048       0.120      21.087\n",
       "education      0.5949      0.086      6.893      0.000       0.421       0.769\n",
       "==============================================================================\n",
       "Omnibus:                        9.841   Durbin-Watson:                   1.736\n",
       "Prob(Omnibus):                  0.007   Jarque-Bera (JB):               10.609\n",
       "Skew:                           0.776   Prob(JB):                      0.00497\n",
       "Kurtosis:                       4.802   Cond. No.                         123.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tabela ANOVA"
   ]
  },
  {
   "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>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>education</th>\n",
       "      <td>1.0</td>\n",
       "      <td>13790.229826</td>\n",
       "      <td>13790.229826</td>\n",
       "      <td>47.51072</td>\n",
       "      <td>1.839946e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>43.0</td>\n",
       "      <td>12480.970174</td>\n",
       "      <td>290.255120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             df        sum_sq       mean_sq         F        PR(>F)\n",
       "education   1.0  13790.229826  13790.229826  47.51072  1.839946e-08\n",
       "Residual   43.0  12480.970174    290.255120       NaN           NaN"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "X['income'] = Y\n",
    "lm=ols('income ~ education', data=X).fit()\n",
    "table=sm.stats.anova_lm(lm,typ=1)\n",
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculando $R^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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yeqdQqgduEjFbO4Z6mx5XnXQd7RjqVSIW/mrsB9I7hZKMwjN3lwtllTy/qTUAQJK2LF2MkKR0j1vPS+QXvZa9z5Q8vz7Ry7LCddfqB13kd34n/D8zii2gZmbCK2K9vc3XAgAAmxbHuQDA9lKRKRQKOn36tPL5vGZnZ3XmzBnl83ml02nt2rVLw8PDymQyeuihhzrdKgAAAACsexfzxfpda7nFispemLhxHUv3pXsiG1Pt2GG9C7lFeb5R2QuUW6xouDchY8I+Mtv6I1kLwOaVdB31JRwtlH3FHUdDfa5m58MLBZcKJe0Y6o10/L4fGF0qlOofD/W5ijthULEv4TQdWkSb/c3fSB/8YDS1nn1WOnw4mloAAGDT4zgXAAjdNOWtt97SV77yFU1NTWlmZua2v298fFz79u3TE088oVQq1cIOAQAAAKD7lDxfC+XwjriK7yu34NU/d08qGfm+8I5t6Z5UUhdyRUlSbsFTfyKmuBOeOCx5PifuADTtvnSP3r48L2Okod64Fsq+yl4gzze6mC9GFij0A7O0XV6YXEy4toZ6wzt+LSvsA12iXJaSyWhqPfig9O1vR1MLAACgAce5ADY7tpe6C1/96lf14IMPas+ePTp27Jimp6dljLntPy+++KImJiY0NDSkp556SufOnev0SwIAAACAdePqwvLe7/miV594k+51WxZ+SbqO0r3hSGpjwnXX6gcA7lbSdbQ9lZAkWbJ0byopZ+nMXLka6EJusekR/CXP14XcosrVcDqYY0v3ppKyFF7k2J5KECLsFpYVXeDGGAI3AACgZTjOBbDZEbq5A88//7wefPBB7d+/X2fOnKmHaCTJsqzb/tMYwJmcnNSuXbv01FNPqVAodPgVAgAAAEBnBYFRbink4hujuVJVUnjtsXYHW6sM9cbr+8/PlaoKln7fyy1UFASmpWsD2By29SfUEw8vBriOvXTXb/g5zze6kCvq3fmy/Dt8z/EDo3fny7qQW77z17HDu33dpQV64o629SeiezFojQ9/WPV/jJpVKKieXAUAAGghjnMBbGaEbm5DoVDQRz7yEU1MTNTDNjcL0tzqz1rfNzk5qUwmo7/4i7/o9MsFAAAAgI5ZqFTr1wfny1WZ8CY2DSRjkW8rtZpjWxpIhLswm0CaK4eBH2PCvgCgWZZl6YEtvYrHwlNyiZijHUO9SrjLp+jyi57OXV3Q5UJJJc+v3/C1mjFGJc/X5UJJ564uKL+4PKEr4dph3Vh44SMes/XAll5ZUYU5EL3f//0wbPONbzRf6/XXw3+8BgaarwUAAHAbOM4FsJnFOt3AevfWW29p7969yufz9cBMzeopN7er8R+R2vcZYzQ7O6vR0VEdO3ZMn/70pyN6BQAAAADQPYoNI6dLleXHqaTblvVTPa4KS9N1ShVfg0vrFj1fA23qAcDG5jq2Rrb26ey7C6pUA7mOrR1DPcotVpRbCLfUM0YqlKr196NEzJYbs2VJMpK8alAfrd/IsqShPjec3LU0aj8eC9er3QmMdeY735He//5oav3qr0q//uvR1AIAALhDHOcC2KwI3dzEq6++qn/6T//pinCNpBXTamof367V37dW7UOHDunq1av6rd/6rcheCwAAAAB0g2JD0KZUXX6ciLXnJFrjOo3rN/YFAM2Kx2xltvXp/NVFFSu+LFka7k2oPxFTvuhprrQ86UuSyje4+FBj2eFEsHSPq7jj1J/viTt6YEsvFyLWI8+T4hFtm/ie90gXL0ZTCwAAoAkc5wLYjAjd3MCbb76pffv2SVo7bNMYtBkbG9O+ffuUyWSUTqc1PDysdDqtfD6v2dlZ5fN5ZbNZvfHGG5qamlI+n7+u7uraR48e1a5du/SJT3yivS8cAAAAADqo5IUn2wJj5FXD37sSrt22UdGWZSkRs1WuBvKqRoExsi2r3hcARMV1bO3a1qcr82VdLpRljBR3HG3vd7S1z2iuXFWp4qtU9evvhyu+P2YpGXOUjDsaSMRkN7xPWpa0PZXQtv4Eo/bXoyj/PwmCaOsBAAA0ieNcAJsNoZs1nD17Vnv37pV0feCm9nh0dFRHjx6tf92d1n/22Wd14sSJ69aofWyM0cGDB5XJZPSjP/qjTb8mAAAAAOgGfhD+XlQNlkMu7b5zzV0K3dT6iDtOvS8AiJJlWdo+kFQq6epivqiFcjhVy7YsDSbd+hZ3gTGqBoGMCS80xGx7xcWHRn0JR/ele5R0nTU/jw76iZ+Qvva1aGrNzkpDQ9HUAgAAiBjHuQA2E2ZurWH//v3K5/MrJtrUHo+MjGh6elqnT5++q8CNJI2MjGhyclJBEOjZZ5+9boupxvX279/f/AsCAAAAgC5hFP5+1LiLb7vvXWtcr9ZHrS8AaIWk6yizrV8P3tOv4f74dYNLbMtS3HGUiDmKO851FyIsSxruj+vBe/qV2dbPhYj15stfDv9PiiJw841vhP84EbgBAABdgONcAJsBoZtVTpw4oZmZmXropfZfY4wmJib09ttva/fu3ZGtd+jQIZ0+fVo7d+6UpOu2rsrlcjpy5Ehk6wEAAADAemYtRV4az7O1O+7SuF6tD6vt0R8Am1HSdXR/ukff+56Udm7t1T2DCaV6YorHbDm2JduWHNtSPGYr1RPTPYMJ7dzaq+99T0r3c9fv+nP+fPgPyc/+bPO1Pv3pMGzzoQ81XwsAAKDNOM4FsJFZpjHhscldu3ZNIyMjunbtWv25WvDm0KFDeuaZZ1q2dj6f1549e3Tu3LkV69b+e+bMmXowB1jt9ddf12OPPbbiuddee02PPvpohzoCAAAA7s633plTpRooMEbZKwuSpIRr671DvW3r4buzi/XtpTLb+sI772K2/r17B9rWAwCgi/m+FItFU6unR1pcjKYWAAAAACByTLpp8Mwzzyifz9c/rgVexsfHWxq4kaR0Oq3p6WmNjIxIWrnVlCQdO3aspesDAAAAwHqQdMNfU23LkhsLfy8qe4Hadb+IMaYeuHFjVn20da0vAABuyrKiC9wEAYEbAAAAAFjnOGvY4MUXX7wu7JJOp3XixIm2rJ9Op/WFL3xhxcnk2rSbr3zlK23pAQAAAAA6qSe+PDI6GVt+XAvCtFrjOo3rN/YFAMB1fvZnV+6N2IzLl8OtpKKqBwAAAABoGUI3S958801ls9n6x7UpN08//bRSqVTb+hgbG9Pjjz9+3V2c+Xxeb731Vtv6AAAAAIBO6GnYpz3ZEHQplLy2rF8oLq/TuH4P+8cDANby8sthOObLX26+1h/9URi22bat+VoAAAAAgLYgdLPkRpNkfvmXf7nNnUhHjhxZ83mm3QAAAADY6PrisfqN/f2JmKyl31rnSlX5QWu3mPIDo7lyVZJk2dJAItwexLLCvgAAqPv7vw//gfjYx5qv9clPhmGbj3yk+VoAAAAAgLbirOGStabcjI2NdaSX3bt3K51O69q1ayuen5mZ6Ug/AAAAANAutm1pqC+u2fmKHMvSQDKmwmJVxki5xYq29idatnZusaLa0NGBZEz2UvpnqC8u22aLDwCApCCQnAinn5nWBkoBAAAAAK3FpJsljaGbmtHR0Q50EhobG1uxxZQxRrOzsx3rBwAAAADaZUtfvP443ePWJ9/kFz2VPL8la5Y8X/nFcGspywrXXasfAMAmZlnRBW58n8ANAAAAAGwAhG6WZLNZWdbKOxd37drVoW6k4eHh+uNaX2sFgwAAAABgo0m6jvoS4UXNuONoqG85AHOpUIp8myk/MLpUKNU/HupzFV+6qNqXcJR0I5xoAADoPgcPSlZEE88uXgzDNjanZQEAAABgI+C3uyX5fP665xqDL+2WTqeve26tHgEAAABgI7ov3VO/vjnUG1fCDX999Xyji/liZMEbPwjreX5YL+HaGuoNJ9tYVtgHAGCT+tf/OvzH4MSJ5mv9H/9HGLZ5z3uarwUAAAAAWDcI3SzJZDLXPdfJ7ZzWCtisFcQBAAAAgI0o6TrankpIkixZujeVlLP0G2y5GuhCbrHpraZKnq8LuUWVq4EkybGle1NJWQrTPttTCabcAMBmdPlyGLb5sR9rvtbP/VwYtvmP/+PmawEAAAAA1p1YpxtYL9LptIwxK7aYOnPmTMf6adxKyizt77xWMAgAAAAANqpt/QkVilUVK75cx9Z96Z6lKTfhxJsLuaLSva6GeuNy7Nvf9sMPjHKLFeUXvfpzjh1OtXGXkj09cUfb+hORvyYAwDoW9bZPJtrtEAEAAAAA6w+TbpasDrQYYzQ1NdWhbqSpqakVASDLsgjdAAAAANhULMvSA1t6FY+Fv7omYo52DPXWt5qSpPyip3NXF3S5UFLJ8+s3LaxmjFHJ83W5UNK5qwsrAjcJ1w7rxsKpNvGYrQe29K74nQwAsMHF49EFbqpVAjcAAAAAsEkQulnyyCOP1B/XTqzOzMyoUCi0vZeXXnppzecbewQAAACAzcB1bI1s7asHb1zH1o6hHg33u6plYoyRCqWqLuSKOnNlQd+dXdQ7hZIuFUp6p1DSd2cXdebKgi7kiiqUqvXroJYlDfe72jG0POEmHgvXq30MANjgfumXwn8QPO/WX3sr58+H/yg5bE0IAAAAAJsFZxGXHDx4cM3nP/vZz7a5E+nw4cNr3lE5Pj7e9l4AAAAAoNPiMVuZbX3qiYcXMS1ZGu5N6L3DPUr1xmSt+s22XA00X6pqrlTVfKmqcjVY8XnLllK9Mb13uEfDvQlZCn//6ok7ymxbDvgAADawb3wjDNt8/vPN1/rDPwzDNv/oHzVfCwAAAADQVTiTuGRwcFBjY2P1UeSWZckYo8nJSZ0/f75tfZw4cULZbPa65zOZjHbu3Nm2PgAAAABgPXEdW7u29emewUR9wk3ccbS9P6mRLX3alkpoIBmTG1t7Syg3ZmkgGdO2VEIjW/q0vT+p+NIkAsuS7hlMaNc2JtwAwIY3Oxu+8X/4w83X+smfDMM2H/9487UAAAAAAF0p1ukG1pPx8XFNTU3VP64Fb/bt26dvf/vbLV//zTff1MTERH3dxv9OTEy0fH0AAAAAWM8sy9L2gaRSSVcX80UtlH1Jkm1ZGky6Gky6kqTAGFWDQMaE11Vjti17jWmiktSXcHRfukdJl61AAGBDM0ayIwxW1vYqBAAAAABsatzC1+DgwYMaGRm57vkzZ87oox/9aEvXfvPNN/Xwww/Xt5Vq3F4qnU7rl3/5l1u6PgAAAAB0i6TrKLOtXw/e06/h/rhW52lsy1LccZSIOYo7znWBG8uShvvjevCefmW29RO4AYCNbtu26AI3lQqBGwAAAABAHaGbVSYnJ+tbTDVOmzl16pTe//73t2Srqeeee04PP/zwinUb1z9x4kTkawIAAABAt0u6ju5P9+h735PSzq29umcwoVRPTPGYLce2ZNuSY1uKx2ylemK6ZzChnVt79b3vSel+ptsAwMb3K78SJi3ffbf5Wt/5Thi2cd3mawEAAAAANgy2l1plbGxMjz/+uF566aXrtnl6++23lclkdOzYMR04cECpVKqptb7+9a/r8OHDmpmZuW47qdp/R0dH9bGPfSyiVwcAAAAAG49tWxpIuhpIciEUACDptdekH/7haGr9/u9Lv/AL0dQCAAAAAGw4TLpZw8mTJ7V7925JWhGAqT0+dOiQhoaGdOTIEb311lt3VPvcuXN6/vnn9eCDD2rfvn1rBm5q0um0Xn311ShfGgAAAAAAALAxFQrhZJsoAjdjY+FkGwI3AAAAAICbsIxhE+K15PN57dmzR+fOnZOkFYGY2v9kjQGZsbExZTIZpdNpbdmyRel0Wvl8XlevXlU+n1c2m9Xp06eVz+dX1KjVaaxZW2t6eloPPfRQ618sut7rr7+uxx57bMVzr732mh599NEOdQQAAAAAANBGDefpmsbpUgAAAADAbWJ7qRtIp9Oanp7WyMiICoXCdcEYaWVwZmpq6pY1VwdtVj/fuMYrr7xC4AYAAAAAAAC4mV27pGw2mlqlkpRIRFMLAAAAALApsL3UTaTTaZ09e1Yf/vCHr9tiqvHjxudu9qfx6yVd97wxRplMRtPT09q7d2+HXz0AAAAAAACwTj3zTDjdJorAzd/8TTjdhsANAAAAAOAOEbq5hXQ6rVOnTunZZ59dMySzVqDmRn8krfk9tefHxsY0PT2t3bt3d/IlAwAAAAAAAOvT9HQYtjlypPlav/u7Ydjme76n+VoAAAAAgE2J0M1tOnTokN5++209/vjjt5xcc6fTbkZGRnTy5Em98sorGhwc7OTLBAAAAAAAANafhYUwbPPww83X+sEfDMM2n/pU87UAAAAAAJsaoZs7kMlkdPLkSZ05c0YHDhxYEaaRdFvTbhq/pxa2qYV5AAAAAAAAAKxiWVJ/fzS1jJH+7M+iqQUAAAAA2PQI3dyFkZERTU5OKggCnTp1SocOHdLIyMhtTboZGxvT5OSkzpw5Q9gGAAAAAAAAuJGHHgoDN1FYXAwDNwAAAAAARMgyht82o3Tt2jVls1nNzs4qn88rnU4rk8loeHiYraPQMq+//roee+yxFc+99tprevTRRzvUEQAAAAAAwF36l/9S+q//62hqvfWW9P3fH00tAAAAAABWiXW6gY1mcHBQu3fv7nQbAAAAAAAAQHf5q7+S/sk/iabW5z4nffrT0dQCAAAAAOAGCN0AAAAAAAAA6JxSSerpiabW936v9Nd/HU0tAAAAAABugdANAAAAAAAAgM6wrOhqGRNdLQAAAAAAboPd6QYAAAAAAAAAbDL//r8fXeBmbo7ADQAAAACgIwjdAAAAAAAAAGiPEyfCsM2f/mnztf78z8OwTX9/87UAAAAAALgLbC+1hnPnzmlmZkajo6PauXNny9c7e/asjh8/rnw+r2w2q2w2q9nZWT3yyCP6oz/6o5avDwAAAAAAALTUt74lfeAD0dT6F/9C+m/+m2hqAQAAAADQBEI3axgfH9ebb75Z/3h0dFQPP/ywJiYm9NBDD0W+3sjIiE6dOlVf0yyNwz116pRefvll/eRP/mTkawIAAKw3QWC0UKmq6PkqVnyVvEB+YGRkZMmSY1tKurZ64o56XEd98ZhsO6ItCQAAANAalYqUSERT673vlf7u76KpBQAAAABABCxj2PC40UsvvaT9+/df9/zQ0JDOnj2rVCrVknWz2aze9773yWrYy9oYo+HhYb377rstWRMbx+uvv67HHntsxXOvvfaaHn300Q51BADA7St5vq4uVJRbqOhOjkwtSxrqi2tLX1xJ12ldgwAAALg7VoQBaU5hAgAAAADWIbvTDaw3hw8flmVZ9T+SZFmWjh8/3rLAjSRlMhk9++yzWp2ByuVyOnLkSMvWBQAA6JSS5yt7ZV7fuTSv2fnrAzeBMar4vspVXxXfV7DqC4yRZucr+s6leWWvzKvk+W3sHgAAADf0Yz8WXeAmlyNwAwAAAABYt5h00+DVV1/Vvn376mEbY4wsy9LY2Jj++I//uC09DA8P69q1a/WPjTEaGhrS1atX27I+uhOTbgAA3cQYoyvzZV0ulFdcP/GN0Xy5qlLFV6nqy6tef5jqxiwlY46ScUf9iZichos5hxB1KwABAABJREFUliVtTyW0rT+xYnogAAAA2uR//V+l//Q/jabWn/yJ9B/8B9HUAgAAAACgRZh002BycnLN548ePdq2Hj772c9eN+0mn8/r5ZdfblsPAAAAreL5gc5cWdCla8uBm4rv6/J8SeeuLuhKoay5UnXNwI0keVWjuVJVVwplnbu6oMvzJVX8cMKNMdKla2WdubIgzw/a9ZIAAABw9myYgI4icHP4cHhgR+AGAAAAANAFmHSz5Nq1axoaGurolJuaxmk3newD3YNJNwCAblCpBjr77oIq1TAQY2SUW6wot+CtuWNAwrXlOrYsSUZhYKfsXR+msSxpqM/VUG9clsJjuXjM1sjWPsVjZMwBAABaplqVXDeaWqmU1DD9GQAAAACAbhDrdAPrxdTU1JrP79+/v82dSE888YSOHz8uy7JkWZaMMZqamlKhUFAqlWp7PwAAAM3y/JWBG88P9E6htCJEY1nSQDKmVNJVImavuUWUMUblaqBCydNcqSpjwhuhZ+c9LZR93ZtKynXsesAns61PrkPwBgAAIHJRbucZBNHWAwAAAACgTbgCseSNN95Y8/mxsbE2dyLt27dvzedPnz7d5k4AAACaZ4zR+auL9cBNuerrQm5xReAm3etq55Y+bR9IKuk6awZuJMmyLCVdR9sHktq5pU/p3uU7q8teENathttNVaqBzl9dvG7rTgAAADTh4x+PLiDz7rthgprADQAAAACgSxG6WTIzM3Pdc+l0Wjt37mx7LzcK+pw6darNnQAAADTvynxZxUoYhPH8QBfzRflLeRvXsbRjqEdb+xNy7Du72OLYlrb2J7RjqEeuE36vH0gX80V5SwsUK76uzJejezEAAACb1cmTYTjmhRear3XqVBi22bKl+VoAAAAAAHQQoZsl2Wy2fke1MUaWZenhhx/uSC+Dg4MaHR297q7stYJBAAAA61nJ83W5EIZejIzeKZTqgZtEzNaOoV4lXaepNZKuox1DvUrEwkNbP5DeKZRkFB5LXS6UVfL8ptYAAADYtC5cCMM2TzzRfK3/4r8IwzYdmCwNAAAAAEArxDrdwHoxOzt73XOZTKYDnYSGh4frjy3LkjFG2Wy2Y/0AAADcjYv5omo54txipb6llOtYui/dc8fTbW7EscN6F3KL8nyjshcot1jRcG9CxoR9ZLb1R7IWAADApuD7UizCU4ds+QkAAAAA2ICYdLMkn89f91w6nW57HzVrBX7WCgYBAACsVyXP10I5nDBT8X3lFrz65+5JJSML3NQ4tqV7Usn6x7kFTxU/XH+h7DPtBgAA4HZZVnSBmyAgcAMAAAAA2LAI3axTawV+1goGAQAArFdXFyr1x/miV7/Wku51m95S6kaSrqN0ryspvLaTLy4HfRr7AQAAwBr+s/8sDNxE4R/+ITwgi6oeAAAAAADrEKGbJYRcAAAAohMERrmlkItvjOZKVUnhNZeh3nhL1x7qjdev7cyVqgqW0j65hYqCgLusAQAArvN//V/hgdq/+lfN1/o//88wbHPvvc3XAgAAAABgnSN0sySTycisGnWbzWY71M3aa6+15RQAAMB6tFCp1ifbzJerMkH4eCAZi3xbqdUc29JAItwOwQTSXDkM/BgT9gUAAIAl77wThm1+/Mebr/XP/ll4wPUf/UfN1wIAAAAAoEtEtDlz9xseHq4/tixLxph1E7oxxsiyLEI3AACgaxQ9v/64VFl+nEq6bVk/1eOqsDRdp1TxNbi0btHzNdCmHgAAANYtYyQ7wnvxDNMEAQAAAACbE5NulqwVaMlmszp37lzbe7l27ZpmZmZkrdrzeq0tsAAAANajYkPQplRdfpyItefws3GdxvUb+wIAANiULCu6wE21SuAGAAAAALCpEbpZsm/fvjWfP378eJs7ufGaN+oRAABgvSl54X5SgTHyquGFmIRrXxcqbhXLsurBG69qFCxdDKr1BQAAsOk8/HAYuInC3/1dGLZxnGjqAQAAAADQpQjdLHn88cdXfFzbYmpycrKtfVy7dk3PPPPMmheknnjiibb2AgAAcLf8IAy5VIPlkIvrtPfQ022YdlPro9YXAADApvGlL4Vhm+np5mudPBmGbd773uZrAQAAAACwARC6afD444/LrBqJm8/n9VM/9VNt6+Hw4cPK5/P1j40xsixLY2NjSqVSbesDAACgGUbhMVXjoVV7ZtysvV6tj1pfAAAAG97f/30Ytvn5n2++1v794QHV+HjztQAAAAAA2EAI3TT45Cc/WX9cC7sYY3Ty5En99m//dsvXf+6553T8+PH6uo0mJiZavj4AAEBUrKXIS+PwvnbHXRrXq/VhtT36AwAA0GbGhAc/O3ZEV++FF6KpBQAAAADABkPopsHevXu1e/duScvbS9X+e+jQIR05cqRlaz/99NP67Gc/W99WqnH90dFRfexjH2vZ2gAAAFFz7PCYJmYvH256fnCjL28Jr7q8Xq2PWl8AAAAbkmVJdkSn+zxv5dhCAAAAAABwHUI3q5w8eXLFlJnG4M3Ro0f10Y9+VOfPn49svXPnzukjH/mIjh07Vl939ZSbEydORLYeAABAOyTd8DDTtiy5sTDoUvaC645zWsUYo/JS6MaNWbKXgs21vgAAADaUsbGVIwabkc2GYZtYLJp6AAAAAABsYFx1WCWTyejZZ5+th22klcGbV155RZlMRk899ZTeeuutu17n3Llz+tSnPqVdu3ZpampqxRqN/z148KAeeuihaF4cAABAm/TEnfrjZGz5cbnanmk3jes0rt/YFwAAQNd78cUwbPPqq83X+tKXwrDNyEjztQAAAAAA2CQs067bjbvMvn379Oqrr9YDMJKueyyFIZ3x8XE98sgjGh0d1c6dO9esVygUdPr0aZ06dUpTU1OamZmRpOtqWw13JY2NjemP//iPW/USsYG8/vrreuyxx1Y899prr+nRRx/tUEcAgM1uruTp3LuLkqRrJU9XCmVJUqonpu0DyZavf7lQUqFUlSRtSyU0mHQlSTu39mpg6TEAAEDXunJF2r49mlqOI1Wr0dQCAAAAAGCTYU7sDZw6deq64M3q6TeSdObMGR07dmzF96bTaQ0PD0uSZmdnlc/nV3y+Mee0eppO7fGePXsI3AAAgK7VF4/JssKbpfsTMb1rl2UCaa5U1ZY+I8eOaPuDNfiB0Vw5vHBk2dJAIjzktaywLwAAgK4W1TZSUniwBgAAAAAA7hrbS93EqVOn9Pjjj9cDMavDN6ufq/3J5XI6c+aMzpw5o1wud93nJa1ZTwoDN6Ojo5qamurkSwcAAGiKbVsa6otLkhzL0kAyDLsYI+UWKy1dO7dYqV8/GkjGZC8dZw31xWW3MOwDAADQUpYVXeCmWCRwAwAAAABABAjd3MLJkyf17LPP3jAs0/jcnfxZHd6RwsDN4cOHdfr0aQ0ODnbsNQMAAERhy1LoRpLSPW79GlF+0VPJ81uyZsnzlV/0JIXXpNI9y1tJNfYDAADQNQ4dii5s82d/FoZtkq3f7hMAAAAAgM2A0M1tOHTokN5++2099NBD1wVtJK05yabR6s+vFbYZHBzUqVOn9Mwzz7TvhQEAALRQ0nXUl3AkSXHH0VDfcgDmUqEkP4j27mo/MLpUKNU/HupzFXfC9fsSjpKuE+l6AAAALfXGG2HY5rnnmq/1i78Yhm1+8AebrwUAAAAAAOoI3dymTCaj6elpvfDCC9q9e/dNJ92sdrNJNyMjI5qcnNTs7Kz27t3b7pcFAADQUvele+o3Zg/1xpVww8NPzze6mC9GFrzxg7Ce54f1Eq6tod5wso1lhX0AAAB0hfn58ADmB34gmnrGSJ//fDS1AAAAAADACoRu7tD4+LhOnz6t6elpHThwQIODg2tOsqlZ63PGGI2Pj+vkyZN6++23deDAgQ6+IgAAgNZJuo62pxKSJEuW7k0l5SwdgZargS7kFpveaqrk+bqQW1S5GkiSHFu6N5WUpTDtsz2VYMoNAADoDpYlDQxEU8uY8A8AAAAAAGgZy6y1HxLuyNmzZzU1NaXp6Wlls1nNzs4qn89LktLptIaHh5XJZLRr1y6NjY1p9+7dnW0YG87rr7+uxx57bMVzr732mh599NEOdQQAwDJjjM5cWVCxEoZrylV/acrN8teke10N9cbl2NdPDbwRPzDKLVaUX/Tqzzl2ONUmEQtDNj1xR7u29a05jRAAAGDd+L7vk775zWhqzc1J/f3R1AIAAAAAADdF6AbYAAjdAADWO88PlL2yoMrSNBrPD/ROoaSyt5y8sSxpIBFTqsdVImavGZQxxqhcDVQoeporV1fcvJ1wbd2bSspdGqUTj9nKbOurfwwAALDu/Hf/nfTpT0dT69/8G+lHfiSaWgAAAAAA4LbEOt0AAAAANj7XsTWytU9n3w2DN65ja8dQj3KLFeUWvPruB4VSVYVSVZKUiNlyY7YsSUaSVw3qW0g1sixpqC+clFPbUioeC9cjcAMAANalv/xL6fu/P5pan/iE9Pzz0dQCAAAAAAB3hNANAAAA2qI2eeb81UUVK74sWRruTag/EVO+6GmuVJVpyNSUbxCyqbFsaSAZU7rHVdxx6s/3xB09sKWXwA0AAFh/ikWptze6egywBgAAAACgowjdAAAAoG1cx9aubX26Ml/W5UJZxkhxx9H2fkdb+4zmylWVKr5KVV9e9fqLSG7MUjLmKBl3NJCIyW7YgsqypO2phLb1J9bcmgoAAKCjojw+IWwDAAAAAMC6QOgGAAAAbWVZlrYPJJVKurqYL2qh7EuSbMvSYNLVYNKVJAXGqBoEMia8RhWz7RUhm0Z9CUf3pXuUdJcn3gSB0UKlqqLnq1jxVfIC+YGRkZElS45tKena6ok76nEd9cVjsm3COgBwN3jPBW7iscek11+Pptb8vNTXF00tAEBLcFwEAACwuRC6AQAAQEckXUeZbf0qeb6uLlSUW6isuGnbtqwV20atZlnSUF9cW/riK8I2N6q3kpEfGFWqgQrF6k3rAQBujPdc4Ca+8AXpU5+Kptbp09KePdHUAgC0BMdFAAAAmxOhGwAAAHRU0nV0f7pH70klm7obsOT5KybnrHaryTnGSLPzFc3OV9acnAMAWMZ7LnATf/u30vd+bzS1fvM3pSNHoqkFAGgJjosAAAA2N0I3AAAAWBds29JA0tXA0vZSt8sYoyvzZV0ulFfcTegbo/lyVaWKr1LVl1e9/lZDN2YpGXOUjDvqT8TkLJ34XCj7evvyvLanEtrWn5B1g22tAGCz4T0XuIlKRUokoqk1MiJls9HUAgC0BMdFAAAAkAjdAAAAoIt5fqDzVxdVrCzfUVjxfeWLnuZKVZngFt9fNfKqVc2VqnrXLmsgGVO6x1XccWSMdOlaWYViVQ9s6ZXr2C1+NQCwvvGeC9xElBdFb7wnCQBgneC4CAAAADWEbu7QW2+9pdnZWeXzec3OzurMmTNtW/uZZ55p21oAAADrXaUa6Oy7C6pUw7OZRka5xYpyC96a16oSri3XsWVJMgpPkpa95TOhJpAKi1XNFasa6nM11BuXJUvFiq/slQWNbO1TPMbJTgCbE++5wA185CPSK69EU+vaNSmViqYWAKBlOC4CAABAI0I3t+H555/XyZMnNTU11dE+CN0AAACEPH/lSU7PD/ROobTixKVlSQPJmFJJV4mYveZYbmOMytVAhdLS3YgmvLl8dt7TQtnXvamkXMeun1TNbOvjLkMAmw7vucAa/pf/Rfpn/yyaWn/6p9Jjj0VTCwDQUhwXAQAAYDVCNzfx/PPP6/Dhw8rn85LCA+FOYe9WAACAkDFG568u1k9ylqu+LuaL8hvGd6d7w7sDHfvmx1CWZSnpOkq6jrb0hXcn5he9sK4X6EJuUfele5SIOapUw/Hhu7b1cWwGYNPgPRdY5cwZ6X3vi6bWkSPSb/5mNLUAAC3HcREAAADWQujmBj71qU/p+PHjK4I2nTqg7WTYBwAAYL25Ml9WseJLCu8qbDzJ6TqW7kkllXSdO67r2Ja29ifUn4jpUqEkzzfyA+livqgdQ71yHVvFiq8r82VtH0hG+ZIAYN3iPRdYUq1KrhtNreFh6erVaGoBANqG4yIAAACshXmEa/jUpz6lyclJGWNkWVb9jzGm7X8AAACwrOT5ulwoS5KMjN4plOonORMxWzuGeu/qJGejpOtox1CvErHwUNkPpHcKJRmFx2aXC2WVPL+pNQCgG/CeCyyxrOgCN0FA4AYAuhDHRQAAALgRQjervPrqq5qcnKwHbSStCMA0hnDa8QcAAADLLuaLquWSc4sVlb3wLKfrWLov3XPLEd63y7HDeq4T1it7gXKLFUmSMWEfALDR8Z6LTe/xx8PATRSuXg1/oDnXAwBdieMiAAAA3Aihm1UmJibqj1dPm1kdwmHaDQAAQPuUPF8L5fCuvorvK7fg1T93TyoZ2UnOGscOx4PX5BY8Vfxw/YWyzx2GADY03nOxqX3lK2E45qtfbb7Wq6+GV0mHh5uvBQDoCI6LAAAAcDOxTjewnpw9e1bZbLa+lVRNY9gmnU7riSee0J49ezQ8PKx0Oq1hTpwAAAC03NWFSv1xvujV7zJM97pNj/G+kaTrKN3rKr8Yrpcvetre79T7uT/d05J1AaDTeM/FpvR3fyc98EA0tX7xF6XPfz6aWgCAjuK4CAAAADdD6KbB5OTkdc81BnCOHj2qz3zmM+1uCwAAYNMLAqPc0olO3xjNlaqSwpvQh3rjLV17qDeua0snVudKVW3tM7ItS7mFit6TSsqO+K5GAOg03nOx6fi+FIvoFJnrSpXKrb8OANAVOC4CAADArbC9VIOZmZkVH9cCN5Zl6dSpUwRuAAAAOmShUq3fTThfrsoE4eOBZCzyUd6rObalgUR4Ic4E0lw5PMlqTNgXAGw0vOdiU7Gs6AI3QUDgBgA2GI6LAAAAcCuEbhrMzs7WHzcGbg4dOqS9e/d2sDMAAIDNrdiwZ32psvw4lXTbsn6qZ3mdxvUb+wKAjYL3XGwKP//zYeAmCpcuhVdAo6oHAFg3OC4CAADArRC6aZDNZmWtcYLk6aef7kA3AAAAqCk2nFwsVZcfJ2LtOZxtXKdx/ca+AGCj4D0XG9rXvhaGY770peZr/T//Txi22b69+VoAgHWJ4yIAAADcCqGbBvl8vv64NuVmbGxMqVSqc00BAABAJS+c4R0YI68azvZOuPaagelWsCyrfrLTqxoFS/PFa30BwEbCey42pH/4hzBs8xM/0XytJ58Mwzb/4X/YfC0AwLrGcREAAABuJaJNqzeGTCajs2fPrnhudHS0Q90AAACgxg/CE4vVYPnEouu0Nz/uxmyVq0G9j7jj1PsCgI2E91xsKEEgOU509Qw/hwCwmXBcBNydIDBaqFRV9HwVK75KXiA/MDIysmTJsS0lXVs9cUc9rqO+eEy2zVadAIDuROimQSaTuW6LqV27dnWwIwAAAEiSUXhCsfE6V7tPxTSuV+uj1hcAbCS852LDiHIKge9LNgOjAWCz4bgIuDMlz9fVhYpyC5WbZJWN/MCoUg1UKFYlhYdtQ31xbemLK+lGGJgGAKANOFvQIJ1OX/fc8PBw+xsBAADACtbSacbGa2ftPsXYuF6tD6vtp1sBoPV4z0XXe+qp6AI3Fy6EVzgJ3ADApsRxEXB7Sp6v7JV5fefSvGbnrw/cBMao4vsqV31VfL++VVqNMdLsfEXfuTSv7JV5lTy/jd0DANAcJt00eOKJJ/Tiiy+ueG52drZD3QAAAKDGsS35gVGs4YKX57d3D3uvurxerQ+H0ccANiDec9G1XnlF+shHoqn10kvSxz4WTS0AQNfiuAi4OWOMrsyXdblQXhG08Y3RfLmqUsVXqerLq14fV3NjlpIxR8m4o/5ETM5Sqmyh7Ovty/PankpoW39ixe4UAACsR9ym02B8fPy656anpzvQCQAAABol3fCw1bYsubHwZEvZC2RuPKs4UsYYlZdOdLoxS/bSCZ9aXwCwkfCei65z5Up4638UgZuf/unwVmsCNwAAcVwE3IznBzpzZUGXri0Hbiq+r8vzJZ27uqArhbLmStU1AzeS5FWN5kpVXSmUde7qgi7Pl1Txwwk3xkiXrpV15spC24NuAADcKY7MVnn88cdljJFlWTLGaGpqqtMtAQAAbHo98eX9vJOx5cflantOvDSu07h+Y18AsFHwnouuYUwYttm+Pbp6X/5yNLUAABsCx0XA2irVQNkrCypWlkIyMppdLOu7s0UVFqsyq/6KJFxb/cmYBpIx9SdjSqwKjplAKixW9d3ZomYXyzJLG6sVK76yVxZUadPfOQAA7gahm1WOHj264uNsNquXX365Q90AAABAknrchhOdDScXCyWvLesXisvrNK7f2BcAbBS856Ir9PdLdkSntTxPatPEAgBAd+G4CLie5wc6++5yEMbzA13IFTU779UPqSxLSvXEtGOoR7u29em9Q726N5XUPamk7k0l9d6hXu3a1qcdQz1K9cRU20HKGGl23tOFXLE+4aZSDddj4g0AYL0idLNKJpPRs88+u2LazZNPPqnz5893ujUAAIBNqy++fAKmPxGTtXQUO1eqyg9ae5HMD4zmylVJkmVLA4lY+NgK+wKAjYb3XKxrhw6FPxALC83XOns2vLIT42cLALA2jouAlYwxOn91sR64KVd9XcgtquwtB2LSva52bunT9oGkkq4jq/aXaBXLspR0HW0fSGrnlj6le93658peENathpN0KtVA568utm1rNwAA7gShmzUcOnRIu3fvlhT+o5/L5bRv3z6CNwAAAB1i25aG+uKSJMeyNJAMTzAaI+UWKy1dO7dYqd+pNZCMyV46WTTUF5dtr33iCAC6Ge+5WJf+5E/Cq4zPPdd8rT/4g/AHeufO5msBADY0jouAla7Ml+tbSnl+oIv5omoDaFzH0o6hHm3tT8i5w59Rx7a0tT+hHUM9cp3we/1AuphfnnhTrPi6Ml+O7sUAABARQjc3cPLkSaVSKUlh8Obtt99WJpPRkSNHVCgUOtwdAADA5rNl6USnJKV73PrdhvlFTyXPb8maJc9XfjEc521Z4bpr9QMAGw3vuVg3crnwB+JHfqT5Wj/+4+FV0p/5meZrAQA2DY6LgFDJ83W5EIZejIzeKZTqgZtEzNaOoV4lm9z6LOk62jHUq0QsvHzpB9I7hZKMwgTa5UK5ZX/vAAC4W4RubiCTyWh6enpF8MYYo6NHj2poaEhPPfWUvv71r3e4SwAAgM0j6TrqS4Qnb+KOo6G+5ZOOlwqlyEd7+4HRpUKp/vFQn6u4E67fl3CaPpEEAOsZ77noOGPCq4zDw9HV+9rXoqkFANhUOC4CQhfzxfr0pdxipb6llOtYui/dc8fTbW7EscN6tYk3ZS+oT5YyJuwDAID1xDJsgLjC6ik2Z86c0d69e3Xt2jVJqu8X2bgHZTqdViaTUSaT0fDwsNLpdEt6e+aZZ1pSF93v9ddf12OPPbbiuddee02PPvpohzoCAKA1Sp6vty/Py5jwrqoLuWL9JE8iZkd2kscPjC7miyov7VGecG3tGOqRJUuWJb1vez8nOgFseLznomPuv1+6eDGaWpWK5Lq3/joAAG6C4yJsdiXP13cuzUuSKr6v784uB3B2DPW05Oey5Pm6kAsDNpYlvXe4px5Ae/Ae/i4AANYPQjcNPvvZz+q5G+wNvjpss9b/bI1BnFbwfUbmYW2EbgAAm8nluZIuXQvHGXt+oAu5xRX7h9+TSjZ14qXk+bpUKMnzw+M9x5Z2DPXKdcIhkfcMJrR9INnciwCALsF7Ltrq135N+vVfj6bWt78tPfhgNLUAABDHRdjc/j5f1Ox8OG3m8nxJhcWqJCnd62prf6Jl6747X65vtZbqjWl7f/h3YLg/rvvTPS1bFwCAO8H2UqsYY9b8s/rzlmWt+HOz743iDwAAAELb+hPqiYcnMl2ndkdh+DnPD+84fHe+fMcjvv3A6N35si7kiitOcoYjjcMFeuKOtrXwZBIArDe856It/vzPw9uXowjcnDgR7jtA4AYAEDGOi7BZBYFRbiEM3PjGaK4UBm4sSxrqjbd07aHeuGr3u8+VqgqWrpflFioKIt7aDQCAuxXrdAPr0VoTa1YHXxo/bgzetAKhGwAAgGWWZemBLb3KXllQpRooEXO0Y6hX7xRK9fHe+UVP14qeBhIxpXpcJWL2DY/xytVAhaKnuXJVjYddCdfWvalk/SRnPGbrgS29LZ9uCADrCe+5aKm5OSmViqbWhz4kfeMb0dQCAGANHBdhs1qoLP+MzperMksTngaSsUi2VbsZx7Y0kIipUArXnStXNZh0ZUzY10CSbUQBAJ1H6OYG7iTo0spQDAfSAAAA13MdWyNb+3T23fBkp+uE+9znFivKLXgyJrzJvVCqqrB0B1YiZsuN2bIkGUleNVC5GlxX27KkoT43vJtK4bFYPBauVzvpCQCbCe+5aIkoz3dwsxIAoE04LsJmVPT8+uNSZflxqk2Bl1SPW//7VKr4Glxat+j5hG4AAOsCoZsbIOwCAACwvsVjtjLb+nT+6qKKFV+WLA33JtSfiClf9DRXWr77SpLKNzixWWPZ4V1a6R5XccepP98Td/TAll5OcgLY1HjPRWQ+8AHpW9+KplaxKCWT0dQCAOA2cVyEzabYELQpVZcfJ2Lt+dlsXKdx/ca+AADoJEI3a2A7JwAAgO7gOrZ2bevTlfmyLhfKMkaKO4629zva2mc0V66qVPFVqvryqtcf47kxS8mYo2Tc0UAiJrsheG1Z0vZUQtv6EwSyAUC856JJx45Jhw9HU+ub35Q++MFoagEAcBc4LsJmUlraPi0wpv7znHDX3jqtFSzLUiJmq1wN5FWNAmNkW1a9LwAAOo3QTYOnn35aExMTnW4DAAAAd8CyLG0fSCqVdHUxX9RCObzTybYsDSbd+tjhwBhVg0DGhCcxY7a94sRmo76Eo/vSPUq6zpqfB4DNivdc3LE335RGR6Op9T/8D9I//+fR1AIAoEkcF2Gz8IMwaFMNlkMu7Z7A5C6Fbmp9xB2n3hcAAJ1G6KbB4OCgBgcHO90GGrz44ovav3+/JicndfDgwU63AwAA1rGk6yizrV8lz9fVhYpyCxU1DjC0LWvFqO7VLEsa6otrS1+cE5wAcAu85+KWFhelvr5oau3ZI50+HU0tAAAixnERNjqj8Ae68ee63TOYGter9VHrCwCATiN0g3Urn8/rwIED9cdROH78uE6ePKlsNqtsNqt0Oq3h4WGNjY1pYmJCo1HdfQcAADom6Tq6P92j96SSWqhUVfR8FSu+Sl4gPzAyMrJkybEtJV1bPXFHPa6jvnhMts3obgC4E7znYk1RbjXAFuAAgC7BcRE2KkuWJLPiEK/dR2iN69X6sNoe/QEAYG2EbrBuHThwILKwzeHDh3Xs2DFJ0tjYmA4fPqxMJqN8Pq833nhDx44d0/Hjx5XJZHTy5EnCNwAAbAC2bWkg6WpgaaQ3AKB1eM+FJOmRR6KbSLOwIPX2RlMLAIA24rgIG41jW/IDo5i9vKWU5wc3+Y7oedXl9Wp9OITVAADrRHs3XQRu09TUlF588cWm6+Tzee3Zs0fHjh1TOp3W9PS0Tp06pYMHD2psbEzj4+M6evSojDE6ePCgstms9uzZo+PHj0fwKgAAAAAA2AR+53fCW46jCNzMzITTbQjcAAAArAtJN7yUaFuW3FgYdCl7gUybJhIaY1ReCt24MUv20qibWl8AAHQak26wLu3fvz+SOnv27FE2m5UkTU9PK5PJ3PBrJycnJYVbUE1MTEiSDh48GEkfAAAAAABsOH/zN9IHPxhNrWeflQ4fjqYWAAAAItMTd1QoViVJyZgjrxo+LlcDJV2n5euXG6bcJGPL6/XEW782AAC3gxgo1p2JiYlItpXav39/PXBz9OjRmwZuaiYnJ+tfNzExoZmZmab7AAAAAABgQymXw8k2UQRuHnwwnGxD4AYAAGBd6mkI1iQbgi6FkteW9QvF5XUa1+9pQ+AHAIDbQegG68rMzIyOHz+usbGxpuvUtqdKp9M6dOjQbX/v4YYTfQcOHGiqDwAAAAAANhTLkpLJaGoZI33729HUAgAAQEv0xWNa2tFJ/YmYrKUri3OlqvygtVtM+YHRXDmcrGPZ0kAi3MDDssK+AABYDwjdYF3Zv3+/xsfHm95eqjEs88QTT9zR9zZuKdUY3gEAAAAAYNP60R9V/WpLswqFMHADAACAdc+2LQ31xSVJjmVpIBmGXYyRcouVlq6dW6zUDxsHkjHZS8ejQ31x2XZEx6YAADSJ0A3WjcOHD2t2dlYnTpxoqk42m12xLdSePXvuuMbo6Gj98eTkZFP9AAAAAADQtX7/98Owzb/5N83Xev318OrMwEDztQAAANA2W5ZCN5KU7nHrWez8oqeS57dkzZLnK78Ybi1lWeG6a/UDAECnEbrBujAzM6Njx47pxIkTSqfTTdVaHZK5m62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\n",
      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.rsquared\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "\n",
    "plt.plot(X['education'],Y,'o',color='C0',alpha=0.2,label=r'Dados')\n",
    "plt.plot(X['education'],model_prediction,'r-')\n",
    "plt.xlabel(r'$X$ (education)',fontsize=16)\n",
    "plt.ylabel(r'$Y$ (income)',fontsize=16)\n",
    "plt.title(r'$R^2 ='+str(np.round(results.rsquared,4))+'$')\n",
    "\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cuidados com a interpretação de $R^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemplo com \n",
    "$$ y = - x^2 + 10 + \\varepsilon $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x = np.linspace(-5,1.5)\n",
    "e = np.random.normal(loc=0,scale=1.0,size=len(x))\n",
    "y = -x**2 + 10 + e\n",
    "\n",
    "df = pd.DataFrame(x, columns=['x'])\n",
    "df['cte'] = 1\n",
    "df['y'] = y\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "\n",
    "model = sm.OLS(df.y,df[['cte','x']]).fit()\n",
    "model_prediction = model.predict(df[['cte','x']])\n",
    "plt.plot(df['x'],model_prediction,'r-')\n",
    "\n",
    "plt.title(r'$R^2 ='+str(np.round(model.rsquared,4))+'$')\n",
    "#model = sm.OLS(y,x)\n",
    "#results = model.fit()\n",
    "#model_prediction = results.predict(df)\n",
    "\n",
    "\n",
    "plt.plot(x,y,'o')\n",
    "plt.xlabel(r'$X$',fontsize=16)\n",
    "plt.ylabel(r'$Y$',fontsize=16)\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.savefig('underfit_example.png',dpi=300)    \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemplo com \n",
    "\n",
    "$$ Y = - \\sin(X) + \\varepsilon .$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lIQCApSmJeYRz5yL+5V+uXCy68LGxscJ8EJhMAwCK0n/c8070Z4aTjhFd6db40Y67IqI4MwEAQC4sfUy4gqRSqRgYGIjHHnssDhw4EDt27IiPP/44/vqv/zrn1xodHY2IiJGRkZy/NwAAUH5638wkUhiKiHj3s9HofTNz5XmEqqqIpqa5Wzqd3ZufOTNXHrpUqeji+8PDEbOzK/+gKtFvfxvx6adzt2xkO5k2/5jJNABgiT78fKwoyjkREf2Z4fj5ibE4dy6KLtPNbc1JRwEAoEwoDV3GJ598Er29vXHkyJGIiDh37lzs3r07ent7o7u7O775zW9Gd3d3NDf7CzoAAFA4gyfG4/t9v0g0w3N9H0X3xmtzP49QXx+xbt3cLRszMxEjl5lKW+yxqancZq4UMzMRJ0/O3bKVSl2+WHTxY42NeYsPABS/fe8MJR1hgX39Q1FsUw37+ofirx65LekYAACUCaWhRbzwwgvR29sbhw8fXvB4VVVVnDt3LkZGRuLAgQNx4MCBiIhIp9PR3d0dDzzwwIpLRKlUaiXRAQCACrDrtaNxdibZb19MzczGrteOJj+PcOHpNxs3Xvn5F06mXekUo/lfj4/n/+MoV6Ojc7ePPsru+fOTaVc6xWj+16nU3IlWAEDJO31mOl49cjzpGAv874ePFd3fNV45cjz+4k82xqp6394BAGDl/K3yX/3TP/1T9Pb2ni8CnTv31S/Anzt3Lqr+9ROEC3//448/jkwmE3v27ImI5ZWIvvzyy1x8GAAAQJkrxsmGkppHWM5k2uTk4pNpl7o/PDxXTmLpljqZVlsb0dp65VOM5u9fffXcawCAonNoaCQmpmaSjrHAb88W3wzuxNRMHBoaiXtvuibpKAAAlIGS+ErZ2NhYRETOZ8Dm58f27NkTo6OjEbGwDFR1wU8QzD8+XxyquuinC1ZaIpo/1WjNmjW5+eAAAICyVIyTDWU/j9DQELF+/dwtGzMzEV9+mX3JyGTa8k1PL30yraXl0qWixR4zmQYABfHB8VNJRygZHxw/pTQEAEBOlERp6Pd///djbGwsfvzjH8d/+A//YcXvd/H82JWKQhda7KSh5ZaIOjs7Y8uWLZHJZCKTyXzlPQAAAC5UjJMN5hEWUVPzu+JJtpNp4+NLKxmZTFu+kZG5W7aTaY2Nlz+96OL7JtMAYFneOzaadISS8f4xBSsAAHKjJL6qOzo6GlVVVfGzn/1s2aWhy82PZVsUuvA5lysJZVsiuthi1wYAAJhXjJMN5hFyoKoqorl57mYyrfhMTEQMDc3dslFbO1cgyrZkZDINACIiYvCEUnS2Bk/6ZwUAQG6U1Fel5ifEsrWc+bELLfb76XQ6UqnU+VOKFnvuYte53O/PP0dpCAAAuJxinWwwj5AAk2nFa3o64sSJuVu2splMu/C+yTQAytD45HTSEUrG+OTZpCMAAFAmSqI0lEql4tSpU4uezrOYXMyPXfj76XQ6enp6YseOHbF69erzv/+Tn/wk3njjjejr61txiQgAAOBKinWywTxCCTCZVtyWM5l2canIZBoAJW5qZjbpCCXjzLR/VgAA5EZJlIbWrFkTo6OjcejQoUs+J1fzYxf+/o4dO6Knpyc2bdq06DXvv//+uP/++8/fX0mJCAAA4EqKdbLBPEIZWu5k2vDw5UtGJtNyY2Ii4tNP527ZMJkGQAmoq6lOOkLJqK/1zwoAgNwoqa8AjY6OxiuvvBKPPPJIRORnfqy7uzt6enriG9/4xpLzraREBAAAcCXFOtlgHoGImJtMW7du7pYNk2mFYzINgBLQ1FAbw6f9WZ+Npoarko4AAECZKInSUCqVioi5Ys8TTzwR/+N//I84fPhw9PX1nX98Xi7nx1Yq2xKRAhEAAJCNYp1sMI/AsuRrMu3Cx0ymLZ/JNAAKrKOtKT4Znkg6RknouLYp6QgAAJSJkigNzauqqoqRkZF45plnIuJ3pZ98zY/l2sUlogMHDsSePXuir69PcQgAALiiYp1sMI9AQZhMK24m0wBYodvXp+L1oyeTjlESblufux9+BgCgspXcV1uqqqpWVBZayfxYrj366KPx6KOPRk9PT+zduzfpOAAAQJEr1skG8wgULZNpxctkGgAXuXWdIky2/LMCACBXSq40FPG7MlDS82O50tvbG3v37nXaEAAAcFnFOtlgHoGyYTKtuOViMu1y902mASRqS3tLNNbVxMTUTNJRzvvaVdURVVXx2yLK1FhXE1vaW5KOAQBAmSi50lAxz4+txObNm+Pw4cNJxwAAAIpYsU42mEegYuVrMu3C+ybTlm85k2mtrQtLRSbTAApmVX1tPLxpXbx0MMv/3y6A/7B5fZyLKKpMj2xaF6vq/fkDAEBulPTfLIt9fmwp0um00hAAAHBZxTpDUKy5oCgtZzJtZOTSJxeZTMud6emIkyfnbtkymQaQU9vuai+qgs62rvY4d664SkPbutqTjgAAQBkpydLQxfNkxT4/lo01a9ZERMSXX36ZcBIAAKBYFeNkg3kEWOj0mek4NDQSHxw/Fe8dG43BE+MxPjkdUzOzUVdTHU0NtdHR1hS3r0/FretWx5b2lsufFlBTM1c6ufpqk2nFyGQaQE5tvK45utKt0Z8ZTjpKdKVb4+a25vO/LrZMAACQCyVXGqqqqjpfFiql+TEAAICVKsbJBvMIMOfDz8di3ztD8eqR45ct9g2fnopPhifOTw021tXEw5vWxba72mPjdTn4JmCuJtMuVzQymbZ8uZhMu7hkZDINKDO7HrolHnz+rZiamU0sQ11Ndfzln95S1JkAACAXSuqrCPNlod27d8d3v/vdhNPkViqVioiI0dHRRHMAAADFrRgnG6CSDZ4Yj12vHV326QMTUzPx0sFP46WDn0ZXujV2PXRLdLQ15TjlFSxnMu3LL698gtGFt7Nn8/sxlKvlTqZd6QSjCx8zmQYUmY62pniq+8Z49vXBxDI81X1j3HTt7/48LsZMAACQCyVRGpov0lRVVcUPf/jD2L59e7KBAAAAElKskw1QaaZnZqP3zUw81/dRzk4d6M8Mx4PPvxVPdd8YPfeko7amOifvm3M1Nb8rnWRjfjLtcsWii+//y7/k92MoZ/OTab/4RXbPb2zM7hSj+dvq1SbTgLzruScd//jPJ+Pdz0YLfu07rk9Fzz1fPa2vGDMBAMBKVZ07V/znSd9www2RyWSiqqoqZmYufcR3KfvVr34VPT09kU6n44c//GHScaDg+vv74+67717w2Ntvvx1dXV0JJQIAKF6DJ8aLYh7h//V//SM/7UxF+mJsMrbvG8jrNw3vuD4Ve7d1xtrmhrxdo6hNTl65WHTh/S+/NJlWKLW1Vz7F6ML7ra0m04Bl+WJsMrb29sfQ8ETBrtne2hj7n+yKtU2L//lbjJkAAGAlSqI0tGbNmjh16lR0d3fH66+/nnQcIA+UhgAAluYHP/1lovMI3/16R3znvhsSuz4k5djIRDz+wsGCfLOwvbUxXnzizljfYj7qii6cTMv2NCOTaYWzZs3SikZf+1rSiYEiUYx/7hZjJgAAWK6S+jGfVCqVdAQAAICiYB4BCu+LscmCfZMwImJoeO6bkvt7uir3xKFsmUwrbl9+OXfLdjJt1aqllYxMpkHZWt/SGPt7ugpzwt+3OrM6zacYMwEAwHKVRGlodHQ0qqqqYs2aNUlHAQAAKAq1NdWxd1tnIvMIe7/VGbU11QW7JhSD6ZnZ2L5voKD/vUXMFYe27xuIl5/s8t9dLlVVRTQ3z902bMjuNSbTCuf06bnb0FB2zzeZBmVtbXNDvPxkV/S+mYnn+j7K6URvXU11PNV9Y/Tck17Sn7PFmAkAAJajpD47dtIQAADA76xtbogXn7iz4PMIftqZStT7ZiaRk70iIt79bDR638yYBExaQ0PE+vVzt2yYTCuc6emIEyfmbtkymQYlpbamOr5z3w3RvfHa2PXa0ejPDK/4PbvSrbHroVuio62pbDIBAMBSlURp6Bvf+Ea8/PLLsSHbn/wCAACoEOYRIP8GT4zH9/uynFXKk+f6Porujdf6JmIpycdk2sWPmUxbPpNpUJI62priRzvuig8/H4u/fWcoXjlyPCamZrJ+fWNdTTyyaV1s62qPm9uayzYTAABkq+rcOeckA8nr7++Pu+++e8Fjb7/9dnR1dSWUCACgtEzPzJpHgDz5j3veycnpASvVlW6NH+24K+kYFBOTacXLZBoUxOkz03FoaCQ+OH4q3j92KgZPjsf45Nk4Mz0b9bXV0dRwVXRc2xS3rV8dt65bHVvaW2JVfX7/WyvGTAAAcClKQ0BRUBoCAMiNwRPj5hEghz78fCz+/XP/PekY5/3D//bvnELA8plMK24tLQtLRSbTAAAAyDP1dQAAgDJiHgFya987Q0lHWGBf/1D81SO3JR2DUmUyrbiNjMzdTKYBAABQIE4aAoqCk4YAAPLDPAIs3+kz0/GHf9W3pOJdvjXW1cTP/m/d/juleF08mXalk4xMphWOyTQAAAAu4rM+AACAMraqvjbuvemauPemLE+VAM47NDRSVIWhiIiJqZk4NDTiv2mKV0NDxPr1c7dsmEwrnOnpiBMn5m7Zungy7UqlI5NpAAAAJUVpCAAAAGARHxw/lXSERX1w/JTSEOXDZFpxW+pkWmPj5UtFJtMAAACKitIQAAAAwCLeOzaadIRFvX+sOMtMUBBVVRHNzXO3DRuye43JtMKZmIgYGpq7ZcNkGgAAQKJ8hgUAAACwiMET40lHWNTgyeLMBUXLZFrxMpkGAACQKKUhAAAAgEWMT04nHWFR45PKCZBXJtOKW64n0y6+bzINAACoIEpDAAAAAIuYmplNOsKizkwXZy6oWLmYTLtS0chk2vKtdDLt4lKRyTQAAKCM+GwGAAAAYBF1NdVJR1hUfW1x5gKWYKmTadPTv5tMy7ZsZDJteZYzmbZmzZVPMLrwMZNpAABAkVAaAgAAAFhEU0NtDJ+eSjrGVzQ1XJV0BKDQamsj1q6du2X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NAQAAAAAAAABAyQgNAQAAAAAAAABAyfx/egM+OuuiMekAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x = np.linspace(0,3.0*np.pi)\n",
    "e = np.random.normal(loc=0,scale=0.3,size=len(x))\n",
    "y = -np.sin(x) + e\n",
    "\n",
    "df = pd.DataFrame(x, columns=['x'])\n",
    "df['cte'] = 1\n",
    "df['y'] = y\n",
    "\n",
    "model = sm.OLS(df.y,df[['cte','x']]).fit()\n",
    "model_prediction = model.predict(df[['cte','x']])\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "plt.plot(df['x'],model_prediction,'r-')\n",
    "plt.title(r'$R^2 ='+str(np.round(model.rsquared,4))+'$')\n",
    "#model = sm.OLS(y,x)\n",
    "#results = model.fit()\n",
    "#model_prediction = results.predict(df)\n",
    "\n",
    "\n",
    "plt.plot(x,y,'o')\n",
    "plt.xlabel(r'$X$',fontsize=16)\n",
    "plt.ylabel(r'$Y$',fontsize=16)\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Efeito do intervalo de $x$ em $R^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimento\n",
    "\n",
    "Gerando dados com: \n",
    "$$ Y = 10 + \\beta_1 X + \\varepsilon. $$\n",
    "\n",
    "Vamos aumentar $S_{XX}$. A cada iteração $i$: \n",
    "\n",
    "$$x \\in [-5-i,1.5+i].$$\n",
    "\n",
    "\n",
    "Valor esperado de $R^2$: \n",
    "\n",
    "$$ \\mathbb{E}(R^2) \\approx \\frac{\\beta_1^2 S_{XX}/n-1}{ \\frac{{\\beta}_1^2 S_{XX}}{n-1} + \\sigma^2} \\textrm{ (Veja Seção 2.6, Montgomery  5 ed.)}$$\n",
    "\n",
    "A equação acima na 4 ed. do mesmo livro está errada: deve ser $\\beta_1$ em vez de $\\hat{\\beta}_1$. O livro cita o resultado deste artigo: \n",
    "\n",
    "http://www2.hawaii.edu/~cbaajwe/Ph.D.Seminar/Hahn1973.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sxiWXwHPPwS23wDHHhBqvJ0ydWBh1hE6mlsRWHkmSwmbxR5IkSZIkSZIkSQpTYyOUlcHw4bBkSbAZI0fCihXw859DUVGo8XrSiOOzKSnKizoGACVFeQzPz446hiRJPcrijyRJkiRJkiRJkhSG9nb42c86Cj833wxNTd2fkZsLd98Nzz4LH/hA6BF7Q9nkkaSlRPtjyLSUZG6+aGSkGSRJ6g0WfyRJkiRJkiRJkqSj9eyzHVd6ffzj8PLL3X8+ORk+9znYvh2+8AVITQ07Ya8pzs9i9qShkWaYPWkowwZlRZpBkqTeYPFHkiRJkiRJkiRJCurvf4eZM2H8eFi5MtiMf/s3WL8e/vu/4Z3vDDVeVErPLmLskJxIzh47JIfSs/vO9WiSJB0Niz+SJEmSJEmSJElSdx06BAsWwNChUF4ObW3dn1FYCEuWwO9+B2PGhJ8xQqkpySyaOp7CvMxePbcwL5NFV4wnNeKrxiRJ6i19d0egJEmSJElSDzhwsIU11bVs3rWfjTvrqNzTQENTC82tbaSlJJOVkUpxfhZjBucwqmAAEwpz6Z/uSyySJEkJZfly+OIX4bnngj3/jnfAV74C117b8ec4NTA7gwemncHl966muqaxx88rzMvkgWlnMDAro8fPkiQpVviqlCRJkiRJErB1dz2LV1Xz6PpdNDa3Hvbjag4082JNI09s2QtAZloKF48rYOrEQkYcn91bcSVJkhSFF16Aq6+GX/wi+IxPfALmz4chQ8LLFcMG52aypLSE6YvXsuHluh47Z+yQHBZdMd7SjyQp4Vj8kSRJkiRJCa1yTwNly7ZQUVUT6PnG5lYeXP0SD65+iZKiPMomj6Q4PyvklJIkSYrUq6/CrbfCHXdAc3OwGaecAnfdBe97X6jR+oKB2Rk8PLOE8pVVLFixg+bWANeiHUZaSjKzJw2l9Owir/eSJCUkP/tJkiRJkqSE1NLaxj1PPs+Fdz8VuPTzRhVVNVx491Pc8+TztIT4wwxJkiRFpK0NFi+GYcPgttuClX7e+U4oL4c1axKy9POa1JRkrjz3JB676ixKivJCmVlSlMdjV53FleeeZOlHkpSw3PgjSZIkSZISzr76ph67aqC5tY3bn6jkN8/tZdHU8QzM9qoBSZKkPumZZ2DWLFi1KtjzqanwhS/ATTdBbm642fqw4vwsHpoxka2767l/VTWPvM1Vu2+UmZbCJeMKmFpSyPB8r9qVJCmpvb29PeoQkvq+iooKzjzzzE7ve/rppykpKYkokSRJkiR1bWdtI5ffu5rqmsYeP6swL5MHpp3B4NzMHj9LkiRJIdmzB667Dn70o+AzPvhBuPNOGDEirFRx68DBFtZU17J513427dxP5d4GGpoOcbCljfTUZLIy+lE8KIvRgwcwqmAAEwpz6Z/ubgNJkl7jZ0VJkiRJkpQw9tU39VrpB6C6pqNktKS0xM0/kiRJsa65GRYsgG98Axoags048US44w648EJISgo3X5zqn57KOcOO45xhx0UdRZKkPsnLLiVJkiRJUkJoaW1j+uK1vVb6eU11TSPTF6+lpbWtV8+VJEnSEWpvh1/+EkaNgjlzgpV+jjkGbrsNtmyByZMt/UiSpF5j8UeSJEmSJCWE8pVVbHi5LpKzN7xcR/nKqkjOliRJ0lvYtg0uuKBjQ8+OHcFmXHEFVFbC3LmQnh5uPkmSpLdh8UeSJEmSJMW9yj0N3Llie6QZFqzYQeWegFdGSJIkKVz798PVV8Po0fDrXwebcfrpsGoV/PjH8K53hZtPkiTpCFn8kSRJkiRJca9s2RYOtbZHmqG5tY2yZVsizSBJkpTwWlvh3nth6FC44w5oaen+jPx8+NGPoKICzjgj9IiSJEndYfFHkiRJkiTFta2766moqok6BgAVVTVs21MfdQxJkqTE9Kc/dWzpmT4d/va37j/frx/MmdNxrdd//ick+2M2SZIUPb8ikSRJkiRJcW3xquqoI3SyuCK28kiSJMW9nTvhU5+Cs86CdeuCzfjoR2HLFpg3D7Kzw80nSZJ0FCz+SJIkSZKkuHXgYAuPrt8VdYxOHlm/iwMHA1wpIUmSpO75xz/glluguBgeeijYjOHD4fHH4bHHOq4HkyRJijEWfyRJkiRJUtxaU11LY3Nr1DE6aWxuZU11bdQxJEmS4ld7O/z853DyyXDjjdDY2P0Z2dlwxx2wcSN86EPhZ5QkSQqJxR9JkiRJkhS3Nu/aH3WELsVqLkmSpD5v0yaYNAkuvRRefLH7zyclwfTpsGMHfOlL0K9f6BElSZLClBp1AEmSJEmSpJ6ycWdd1BG6tGmnxR9JkqRQvfIK3HQTfP/70NYWbMZ73wt33QWnnhpuNkmSpB5k8UeSJEmSJMWtyj0NUUfoUuXe2MwlSZLgwMEW1lTXsnnXfjburKNyTwMNTS00t7aRlpJMVkYqxflZjBmcw6iCAUwozKV/uj9uiUxLCyxc2HGl1yuvBJsxeDDMnw+f+ETHxh9JkqQ+xK9EJUmSJElS3Gpoaok6Qpcamg5FHUGSJL3B1t31LF5VzaPrd9HY3HrYj6s50MyLNY08sWUvAJlpKVw8roCpEwsZcXx2b8UVwJNPwuzZHdd7BZGeDnPmwNy50L9/uNkkSZJ6icUfSZIkSZIUt5pbA17z0MMOtsRmLkmSElHlngbKlm2hoqom0PONza08uPolHlz9EiVFeZRNHklxflbIKdXJiy/CNdfAww8Hn3HppfDtb8N73hNWKkmSpEgkRx1AkiRJkiSpp6SlxOZLH+mpsZlLkqRE0tLaxj1PPs+Fdz8VuPTzRhVVNVx491Pc8+TztMRoAblPO3Cg40qv4cODl35GjYLf/haWLrX0I0mS4oIbfyRJkiRJUtzKykil5kBz1DHeJCujX9QRJElKaPvqm5i+eC0bXq4LfXZzaxu3P1HJb57by6Kp4xmYnRH6GQmnvR1+8pOOa7l27gw249hj4RvfgBkzINUfj0mSpPjhr5dJkiRJkqS4FavXbBQPis1ckiQlgp21jUwpr+iR0s+/2vByHVPKK9hZ29ij58S9devgfe+DT30qWOknORmuvBK2b4fPf97SjyRJijsWfyRJkiRJUtwaMzgn6ghdGj14QNQRJElKSPvqm7j83tVU1/ROGae6ppHL713NvvqmXjkvruzbB9Onw4QJ8Kc/BZtx7rnw7LPwve9BXl6o8SRJkmKFxR9JkiRJkhS3RhXEZsEmVnNJkhTPWlrbmL54ba+Vfl5TXdPI9MVraWlt69Vz+6xDh+C734Vhw+Deezuu+equ97wHHn4YfvtbGD069IiSJEmxxOKPJEmSJEmKWxMKc8lMS4k6RieZaSlMKMyNOoYkSQmnfGVVj1/vdTgbXq6jfGVVJGf3KU88AWPGwJe/DPv3d//5zEz4xjfguefg3/8dkpLCzyhJkhRjLP5IkiRJkqS41T89lYvHFUQdo5NLxhXQPz016hiSJCWUyj0N3Llie6QZFqzYQeWehkgzxKwdO2DyZPjQh2DbtmAzPvUpqKyEr34V3vGOcPNJkiTFMIs/kiRJkiQprk2dWBh1hE6mlsRWHkmSEkHZsi0cag1wZVSImlvbKFu2JdIMMaehAebOhZEj4bHHgs049VR46il44AEYPDjcfJIkSX2AxR9JkiRJkhTXRhyfTUlRXtQxACgpymN4fnbUMSRJSihbd9dTUVUTdQwAKqpq2LanPuoY0Wtrgx//GIYNg/nz4dCh7s847jhYtAj+/Gd473vDzyhJktRHWPyRJEmSJElxr2zySNJSon0ZJC0lmZsvGhlpBkmSEtHiVdVRR+hkcUVs5el1q1dDSQl8+tOwZ0/3n09NhS9/ueN6sGnTICUl9IiSJEl9icUfSZIkSZIU94rzs5g9aWikGWZPGsqwQVmRZpAkKdEcONjCo+t3RR2jk0fW7+LAwZaoY/S+3bvhP/8TJk7s2NITxIc+BJs2wXe+AwMGhJtPkiSpj7L4I0mSJEmSEkLp2UWMHZITydljh+RQenZRJGdLkpTI1lTX0tjcGnWMThqbW1lTXRt1jN5z8CDcdlvHtV7/+7/BZpx0Ejz2GPzf/8Hw4eHmkyRJ6uMs/kiSJEmSpISQmpLMoqnjKczL7NVzC/MyWXTFeFIjvmpMkqREtHnX/qgjdClWc4WqvR2WLYORI+G66+DVV7s/IysL5s+HzZvhox+FpKTwc0qSJPVxvuIkSZIkSZISxsDsDB6YdkavlX8K8zJ5YNoZDMzK6JXzJElSZxt31kUdoUubdsZ58Wfr1o5ruS66CF54IdiMz3wGtm+Ha6+F9PRw80mSJMURiz+SJEmSJCmhDM7NZElpSY9f+zV2SA5LZpYwOLd3NwxJkqT/r3JPQ9QRulS5NzZzHbW6OvjiF2H0aPjNb4LNmDgR/vxn+J//gfz8MNNJkiTFJYs/kiRJkiQp4QzMzuDhmSVce34xaSFfwZWWksy15xfz8MwSN/1IkhSxhqaWqCN0qaHpUNQRwtXaCgsXwtChsGBBx9vddfzx8L//C3/6E5x2WvgZJUmS4lRq1AEkSZIkSZKikJqSzJXnnsSkEYMoW7aFiqqao55ZUpRH2eSRFOdnhZBQkiQdrebWtqgjdOlgS2zmCuSPf4TZs2H9+mDPp6XB1VfD9dfDMceEm02SJCkBWPyRJEmSJEkJrTg/i4dmTGTr7nruX1XNI+t30dh85L+lnpmWwiXjCphaUsjw/OweTCpJkror7M1+YUlPjc1c3fLyyzBnDvzkJ8FnXHQRfOc7cOKJ4eWSJElKMBZ/JEmSJEmSgBHHZ3PrJaO5/oIRrKmuZfOu/WzauZ/KvQ00NB3iYEsb6anJZGX0o3hQFqMHD2BUwQAmFObSP92XWCRJikVZGanUHGiOOsabZGX0izpCcP/4B9x+O9x2W8efgxgxouNKsPPOCzebJElSAvJVKUmSJEmSpH/RPz2Vc4YdxznDjos6iiRJOkrF+Vm8WNMYdYw3KR7UB68FbW+Hhx+Ga66B6upgM3Jy4Oab4XOfg359uPwkSZIUQ+Jgl6QkSZIkSZIkSdKbjRmcE3WELo0ePCDqCN2zcSO8//0wZUqw0k9SEpSWwvbtMGuWpR9JkqQQufFHkiRJkiRJkiTFpVEFsVmwidVcb1JTAzfeCOXl0NYWbMbZZ3dc63XKKaFGkyRJUgc3/kiSJEmSJEmSpLg0oTCXzLSUqGN0kpmWwoTC3KhjvLWWFvje92DoUPj+94OVfoYMgZ/+FH7/e0s/kiRJPcjijyRJkiRJkiRJikv901O5eFxB1DE6uWRcAf3TY/hCht/+tqOoc9VVUFvb/eczMuBrX4Nt2+BjH+u45kuSJEk9xuKPJEmSJEmSJEmKW1MnFkYdoZOpJbGV53V/+Qv8+7/DpEmwZUuwGR/7GFRWQlkZZGaGGk+SJElds/gjSZIkSZIkSZLi1ojjsykpyos6BgAlRXkMz8+OOkZnr74KX/0qjBgBjzwSbMbYsR1Xev30p/Dud4caT5IkSW/N4o8kSZIkSZIkSYprZZNHkpYS7Y9E0lKSufmikZFm6KS9HR54AIYPh1tvhYMHuz8jLw++/31YuxbOOSf8jJIkSXpbMXyJrCRJkiRJkiRJ0tErzs9i9qSh3P5EZWQZZk8ayrBBWZGd38natTBrFjz9dLDnU1Lgyis7rvTKzQ01mnrWgYMtrKmuZfOu/WzcWUflngYamlpobm0jLSWZrIxUivOzGDM4h1EFA5hQmEv/dH+cKElSLPMztSRJkiRJkiRJinulZxfxm+f2suHlul4/e+yQHErPLur1c99k3z64/nr4n//p2PgTxKRJcOedMDKGthfpbW3dXc/iVdU8un4Xjc2th/24mgPNvFjTyBNb9gKQmZbCxeMKmDqxkBHHx9g1dZIkCbD4I0mSJEmSJEmSEkBqSjKLpo5nSnkF1TWNvXZuYV4mi64YT2qUV401N8Pdd8PXvw719cFmnHAC3HEHXHQRJCWFm089pnJPA2XLtlBRVRPo+cbmVh5c/RIPrn6JkqI8yiaPpDg/RjZXSZIkAKK90FaSJEmSJEmSJKmXDMzO4IFpZ1CYl9kr5xXmZfLAtDMYmJXRK+d16fHHYcwYuOaaYKWf/v3hm9+E556Diy+29NNHtLS2cc+Tz3Ph3U8FLv28UUVVDRfe/RT3PPk8La1tocyUJElHz+KPJEmSJEmSJElKGINzM1lSWsLYITk9es7YITksmVnC4NzeKRm9yfbt8NGPwgUXQGVlsBn/8R8dz153HWREWF5St+yrb+LSH1Rw+xOVNIdc0GlubeP2Jyq59AcV7KtvCnW2JEkKxuKPJEmSJEmSJElKKAOzM3h4ZgnXnl9MWshXcKWlJHPt+cU8PLMkmk0/9fVw7bUwahT86lfBZkyYAE8/DYsXQ0FBuPnUo3bWNjKlvIINL9f16DkbXq5jSnkFO2t779o8SZLUNYs/kiRJkiRJkiQp4aSmJHPluSfx2FVnUVKUF8rMkqI8HrvqLK489yRSQy4Uva22NvjhD2HYMPj2t+HQoe7PGDQI/ud/YPVqKCkJP6N61L76Ji6/dzXVNb1TxqmuaeTye1e7+UeSpIilRh1AkiRJkiRJkiQpKsX5WTw0YyJbd9dz/6pqHlm/i8bm1iN+PjMthUvGFTC1pJDh+dk9mPQtVFTArFmwZk2w5/v1g9mz4cYbITuifwcdlZbWNqYvXttrpZ/XVNc0Mn3xWh6eWdL7ZTdJkgRY/JEkSZIkSZIkSWLE8dnceslorr9gBGuqa9m8az+bdu6ncm8DDU2HONjSRnpqMlkZ/SgelMXowQMYVTCACYW59E+P6Mctf/0rzJ0L998ffMZHPgJ33NGxKUh9VvnKqh6/3utwNrxcR/nKKq4896RIzpckKdFZ/JEkSZIkSZIkSfqn/umpnDPsOM4ZdlzUUQ6vqQm++1249VY4cCDYjGHD4M474cMfDjWael/lngbuXLE90gwLVuxg0ohBFOdnRZpDkqRE5M49SZIkSZIkSZKkvqC9HX7xCxg5Eq6/PljpJzsbvv1t2LTJ0k+cKFu2hUOt7ZFmaG5to2zZlkgzSJKUqCz+SJIkSZIkSZIkxbrnnoPzz4eLL4aqqu4/n5QE//VfsH07XH01pKWFHlG9b+vueiqqaqKOAUBFVQ3b9tRHHUOSpIRj8UeSJEmSJEmSJClW1dbC7NkwZgwsXx5sxplnwp//DPfeC4MGhZtPkVq8qjrqCJ0sroitPJIkJQKLP5IkSZIkSZIkSbGmtRV+8AMYOhTuuqvj7e5617vg/vvhqadgwoTwMypSBw628Oj6XVHH6OSR9bs4cLAl6hiSJCWU1KgDSJIkSZIkSZIUbw4cbGFNdS2bd+1n4846Kvc00NDUQnNrG2kpyWRlpFKcn8WYwTmMKhjAhMJc+qf7kr3+aeVKmDULNmwI9nx6OlxzDXzlK3DMMeFmU8xYU11LY3OAQlgPamxuZU11LecMOy7qKJIkJQy/i5AkSZIkSZIkKSRbd9ezeFU1j67f9ZY/kK850MyLNY08sWUvAJlpKVw8roCpEwsZcXx2b8VVrKmuhjlz4Gc/Cz7jkkvg29+GoqLwcikmbd61P+oIXdq8a7/FH0mSepHFH0mSJEmSJEmSjlLlngbKlm2hoqom0PONza08uPolHlz9EiVFeZRNHklxflbIKRWzGhth/nyYNw+amoLNGDkSFiyAD3wg3GyKWRt31kUdoUubdsZmIUmSpHiVHHUASZIkSZIkSZL6qpbWNu558nkuvPupwKWfN6qoquHCu5/iniefp6W1LZSZilHt7R3bfYYPh5tvDlb6ycmBu+6CZ5+19JNgKvc0RB2hS5V7YzOXJEnxyo0/kiRJkiRJkiQFsK++iemL17Lh5brQZze3tnH7E5X85rm9LJo6noHZGaGfoYg9+yzMng0rVwZ7PjkZSkvh61+Hd74z1GjqGxqaWqKO0KWGpkNRR5AkKaG48UeSJEmSJEmSpG7aWdvIlPKKHin9/KsNL9cxpbyCnbWNPXqOetHf/w4zZ8L48cFLP+ecA+vWwX//t6WfBNYcoxvBDrbEZi5JkuKVxR9JkiRJkiRJkrphX30Tl9+7muqa3injVNc0cvm9q9lXH+AaKMWOQ4dgwQIYOhTKy6EtQDni3e+GJUvgySdh7NjwM6pPSUuJzR/zpafGZi5JkuKVn3klSZIkSZIkSTpCLa1tTF+8ttdKP6+prmlk+uK1tMTohg+9jeXL4ZRT4ItfhLq67j//jnfAzTfDtm1w2WWQlBRyQPVFWRmpUUfoUlZGv6gjSJKUUCz+SJIkSZIkSZJ0hMpXVvX49V6Hs+HlOspXVkVytgJ64QW4+GL44AfhueeCzfj4xzsKPzfd1FEAkv6pOD8r6ghdKh4Um7kkSYpXFn+UsJYuXcqUKVM48cQTyc3NJSkpidzcXMaPH8/cuXNZsWJF6GcuXLiQ8847jxNPPPH180488URKS0tZt25d6OdJkiRJkiRJCk/lngbuXLE90gwLVuygck9DpBl0BF59Fa67Dk4+GX7xi2AzTjkFVq6En/yk44ov6Q3GDM6JOkKXRg8eEHUESZISisUfJZyFCxeSm5vLlClTWLp0KQBFRUUUFRVRV1fHunXrmD9//usFnYULFx71mXPnziUpKYnS0tLX316+fDmLFi3isssuY+HChYwfP54TTzzRApAkSZIkSZIUo8qWbeFQa3ukGZpb2yhbtiXSDHoLbW2weDEMGwa33QbNzd2f8c53Qnk5rFkD73tf+BkVN0YVxGbBJlZzSZIUryz+KKFMmTKF0tJSjj32WJYsWUJ7ezsvvPACa9eu5YUXXqC2tpZ58+a9/vFVVVWUlpZy3nnnURfg3uW6ujrGjx/P/PnzycnJYe3atSxfvpwZM2YwadIkLrvsMubNm0d7ezszZsygqqqK8ePHh1I2kiRJkiRJkhSerbvrqaiqiToGABVVNWzbUx91DL3RM8/Ae98LV1wBu3d3//mUFJg9G7ZvhxkzOt6W3sKEwlwy02LrvyeZaSlMKMyNOoYkSQnF4o8SxnnnncfSpUuZMWMGL7zwApdddtmbPiYnJ4c5c+ZQW1tLUVHR6+9fsWIF48eP73b5Z/z48a9v8Fm7di2nnnrqYT+2vLycGTNmAFBaWmr5R5IkSZIkSYohi1dVRx2hk8UVsZUnoe3ZA5/5DJx+OqxaFWzGBz8IGzfCnXdCrqUJHZn+6alcPK4g6hidXDKugP7pqVHHkCQpoVj8UUKYO3cuK1asYMaMGZSXl7/tx+fk5LB8+fJO76uqquIDH/jAEZ85ZcoUqqqqAJg3b16nItHhlJeXv/5xpaWlXvslSZIkSZIkxYADB1t4dP2uqGN08sj6XRw42BJ1jMTW3Ay3395xrdePfhRsxoknwi9+Ab/+NZx8cqjxlBimTiyMOkInU0tiK48kSYnA4o/iXl1dHfPnz6eoqOiISj+vKSoqYs6cOZ3et27dOubPn/+2z65bt46lS5cC/3+L0JGaO3fu63+ePn36ET8nSZIkSZIkqWesqa6lsbk16hidNDa3sqa6NuoYiam9HX75Sxg1CubMgYaG7s845hi47TbYsgUmT4akpPBzKiGMOD6bkqK8qGMAUFKUx/D87KhjSJKUcCz+KO69VqTpTunnNdddd91h572Vfy3sfOxjH+vWma9d9wWdC0SSJEmSJEmSorF51/6oI3QpVnPFtW3b4IIL4MILYceOYDOuuAIqK2HuXEhPDzefElLZ5JGkpUT7I7+0lGRuvmhkpBkkSUpUFn8U9372s58BHYWd0tLS16/fOhI5OTlcdtllb3r/W5VxqqqqOl3RNX78+G6k7XDqqae+/ucghSVJkiRJkiRJ4dm4sy7qCF3atNPiT6/Zvx+uvhpGj+64liuI00+Higr48Y/hXe8KN58SWnF+FrMnDY00w+xJQxk2KCvSDJIkJSqLP4prdXV11NXVAR3bcxYuXMiJJ574+vuORFFR0Zvet3z58sN+/BuLOpMmTTris14zYcKE1/+8YsWKbuWVJEmSJEmSFK7KPQGucuoFlXtjM1dcaW2Fe++FoUPhjjugpaX7M/Lz4Uc/6ij9TJwYekQJoPTsIsYOyYnk7LFDcig9+80/S5EkSb3D4o/i2uG2+yxcuPCIZ5x44olHPBfevA3o2GOPPeKzDnfma1uLJEmSJEmSJPW+hqYAZY9e0NB0KOoI8e1Pf+rY0jN9Ovztb91/vl8/mDOn41qv//xPSPZHMuo5qSnJLJo6nsK8zF49tzAvk0VXjCc14qvGJElKZH4WVlzLyck56hldbfx55ZVXuvzYurq6N5WCgmR44zNr167t9gxJkiRJkiRJ4WhubYs6QpcOtsRmrj5v50741KfgrLNg3bpgMz76UdiyBebNg+zscPNJhzEwO4MHpp3Ra+WfwrxMHph2BgOzMnrlPEmS1DWLP4prRUVFXRZ3LrvssiOe0Z1rttasWdPp7aDFozduCVqxYkWgOZIkSZIkSZKOXlqMbrJIT43NXH3WP/4Bt9wCxcXw0EPBZhQXw+OPw2OPdVwPJvWywbmZLCkt6fFrv8YOyWHJzBIG5/buhiFJkvRmfleguLd27VomTZoEdBSBli9f3mUZ6HC6utbrcM+ve8NvfwS55gveXBh6q6vFJEmSJEmSJPWsrIzUqCN0KSujX9QR4kN7O/z853DyyXDjjdDY2P0Z2dlwxx2waRN86EPhZ5S6YWB2Bg/PLOHa84tDLy6mpSRz7fnFPDyzxE0/kiTFiNj8bkUKUU5ODsuXLw/8/DPPPPOm95133nldfuwLL7zwprOD6KowVFVV1a3CkiRJkiRJkqRwFOdn8WJNgDJIDyselBV1hL5v0yb44hfhd78L9nxSEvzXf8Gtt8LAgaFGk45GakoyV557EpNGDKJs2RYqqmqOemZJUR5lk0dSnO/fPZIkxRKLP9Lb6Oqardc2CL3RK6+80mM5unPlmCRJkiRJkqTwjBmcwxNb9kYd401GDx4QdYS+65VX4Kab4Pvfh7a2YDPe+1646y449dRws0khKs7P4qEZE9m6u577V1XzyPpdNDa3HvHzmWkpXDKugKklhQzPz+7BpJIkKSiLP9JbWLp06ZsKN5dddtlhN+/0ZDmnqqqKU3vwG8iKioqjen7Tpk0hJZEkSZIkSZJiy6iC2CzYxGqumNbSAgsXdlzpFfQXOQsK4Pbb4ROf6Nj4I/UBI47P5tZLRnP9BSNYU13L5l372bRzP5V7G2hoOsTBljbSU5PJyuhH8aAsRg8ewKiCAUwozKV/uj9OlCQplvmZWnoL5eXlb3rfvHnzDvvxYW38CXpF2NE488wze/1MSZIkSZIkqS+YUJhLZlpKt7Zk9LTMtBQmFOZGHaNvefJJmD2743qvINLTYc4cmDsX+vcPN5vUS/qnp3LOsOM4Z9hxUUeRJEkhSY46gBSr1q1b96ZrvsrLyw+77QfevPHn2GOPDS1PT14jJkmSJEmSJOnw+qencvG4gqhjdHLJuAK3cBypF1+Eyy6D978/eOnn0kth2zb4+tct/UiSJCmmWPyRDmP69Omd3r7sssuYMWNGRGkkSZIkSZIkRWnqxMKoI3QytSS28sSkAwfgpptgxAh4+OFgM0aNgt/+FpYuhfe8J9R4kiRJUhgs/khdWLhwIevWrXv97UmTJrFkyZIIE0mSJEmSJEmK0ojjsykpyos6BgAlRXkMz8+OOkbsam+Hhx6C4cPhG9+Apqbuz8jNhe99D9av79gUJEmSJMUo94BKb1BVVcXcuXNff/vUU09l+fLlESbqHU8//fRRPb9p0yZKS0tDSiNJkiRJkiTFnrLJI7nw7qdobm2LLENaSjI3XzQysvNj3rp1MHs2PPVUsOeTk+Fzn4Obb4a82Ch6SZIkSW/F4o/0BlOmTKGurg7oKP2sXbv2iJ/NyckJJcNr5/+rY489NpTZh1NSUtKj8yVJkiRJkqS+rjg/i9mThnL7E5WRZZg9aSjDBmVFdn7M2rcPbrgB7ruvY+NPEOeeCwsWwOjR4WaTJEmSepBXfUn/YsqUKa9f8TVp0qRulX668sorr4QRS5IkSZIkSVKMKD27iLFDciI5e+yQHErPLork7Jh16BB897swbBjce2+w0k9hISxdCr/9raUfSZIk9TkWf6R/mj9/PkuXLgXgsssuC3S9V1FRz33T3ZOzJUmSJEmSJB2Z1JRkFk0dT2FeZq+eW5iXyaIrxpOa4sv6r3viCRgzBr78Zdi/v/vPZ2bCN74BW7fCpZdCUlL4GSVJkqQe5ncIErB06VLmzp0LwIwZM1iyZEmgOW+8jqurK7uORFebgsK6RkySJEmSJEnS0RmYncED087otfJPYV4mD0w7g4FZGb1yXsx7/nmYPBk+9CHYti3YjE9+Eior4atfhXe8I9x8kiRJUi+y+KOEt2LFCqZMmQLAnDlzKC8vDzzrxBNP7PR20Ku+uioMvbFUJEmSJEmSJCk6g3MzWVJa0uPXfo0dksOSmSUMzu3dDUMxqaEB5s6Fk0+Gxx4LNuPUU+GPf4QHH4TBg8PNJ0mSJEXA4o8SWlVVFeeddx4A5eXlzJs376jmnXrqqWHEoqqqqtPbOTk5bvyRJEmSJEmSYszA7AwenlnCtecXkxbyFVxpKclce34xD88scdNPWxv8+McwbBjMnw+HDnV/xnHHwaJF8Oc/w1lnhZ9RkiRJiojFHyWsuro6xo8fD8CSJUuYMWPGET23cOHC168Fe6MJEya86YwgampqOr09adKkQHMkSZIkSZIk9azUlGSuPPckHrvqLEqK8kKZWVKUx2NXncWV555EasiFoj5n9WooKYFPfxr27On+86mp8KUvwfbtMG0apKSEHlGSJEmKUmrUAaQovFb6qaurY8mSJVx22WVH/Gx5eTlFRUVd/rOcnByKioo6beypqqo67Mcfzhs3/px22mndel6SJEmSJElS7yrOz+KhGRPZurue+1dV88j6XTQ2tx7x85lpKVwyroCpJYUMz8/uwaR9xO7d8JWvwP/+b/AZ558P3/0ujBgRXi5JkiQpxlj8UUL6wAc+QFVVVbdLPwDr1q3j4x//+GH/+aRJk1i4cOHrbwcp/rxxU1B3M0qSJEmSJEmKxojjs7n1ktFcf8EI1lTXsnnXfjbt3E/l3gYamg5xsKWN9NRksjL6UTwoi9GDBzCqYAATCnPpn+5L9hw8CHfeCbfcAq++GmzGSSd1FH4+8hFISgo1niRJkhRr/C5CCWfKlCmsW7cuUOnntU08p5566mE/Zu7cuZ2KP+vWrev2VV1r1qx5/c+nnnpqt4tDkiRJkiRJkqLVPz2Vc4YdxznDjos6St/Q3g6//GXHtVwvvBBsxjHHwI03wuzZkJ4ebj5JkiQpRiX45cBKNKWlpSxdupTly5cH2qKzdOlSgLcs4hQVFXUq+ixfvrxbZ1RVVXXa+FNaWtq9kJIkSZIkSZLUl2zdCh/6EEyeHLz08+lPw44dMGeOpR9JkiQlFDf+KGHMnz+fhQsXMmfOHI499ljWrVv3ts+88sorQMfVW1VVVXzrW98C3rr4Ax1bf1asWAHAihUrqKurIycn54hylpeXv/7noqIiZsyYcUTPSZIkSZIkSVKfUlcHN98M3/setLQEm3HGGXDXXXD66aFGkyRJkvqKpPb29vaoQ0g9benSpUyZMiWUWUVFRbxwBL91MmXKlNc3BM2ZM4d58+a97TN1dXWccMIJr2/8Wb58ebevCYtKRUUFZ555Zqf3Pf3005SUlESUSJIkSZIkSVJMam2F++6DG26Av/892Iz8fJg3D/7jPyDZyw0kSZKUuPxqWHFvxYoVoZV+AE499dQj+rhFixa9vhlo/vz5R7RhaPr06a+XfubMmdNnSj+SJEmSJEmSdET++Ec47TQoLQ1W+klLg698BbZvhyuusPQjSZKkhOdXxIprdXV1oZZ+4O2v+XpNTk4Oa9eufb0oNH78+Nc3AL3Razm7uyFIkiRJkiRJkvqEl1+GT34Szj4b1q8PNmPyZNiyBb71LcjKCjefJEmS1EelRh1A6klVVVWvb9AJy2mnnXbEH/ta+Wf+/PnMnTuXKVOmcOqpp1JaWkpRURF1dXU888wzLFy4kLq6OoqKiigvL3fTjyRJkiRJkqT48I9/wO23w223dfw5iBEj4M474YMfDDWaJEmSFA+S2tvb26MOISWCuro6fvazn7FkyRKqqqqoqqoiJyeHY489lkmTJlFaWnrE14jFooqKCs4888xO73v66acpKSmJKJEkSZIkSZKkyLS3w8MPwzXXQHV1sBkDBkBZGVx5JfTrF2o8SZIkKV648UfqJTk5OcyYMYMZM2ZEHUWSJEmSJEmSes7GjTB7Nvz+98GeT0qC6dPhllvguONCjSZJkiTFG4s/kiRJkiRJkiTp6NXUwE03wQ9+AG1twWa8732wYAGMGxduNkmSJClOWfyRJEmSJEmSJEnBtbR0lH1uuglqa4PNGDIEbr8dPvaxjo0/kiRJko6IxR9JkiRJkiRJkhTM737Xca3X5s3Bns/IgDlzYO5cyMwMN5skSZKUACz+SJIkSZIkSZKk7vnLX+Dqq+GRR4LPmDKlY8tPYWF4uSRJkqQEY/FHkiRJkiRJkiQdmQMH4Fvfgm9/Gw4eDDZjzBhYsAD+7d9CjSZJkiQlIos/kiRJkiRJkiTprbW3w4MPdlzJtWtXsBnHHgu33ALTp0OqP56QJEmSwuBX1pIkSZIkSZIk6fDWroVZs+Dpp4M9n5ICn/88lJV1lH8kSZIkhcbijyRJkiRJkiRJerN9++D66+F//qdj408QH/gA3HknjBoVajRJkiRJHSz+SJIkSZIkSZKk/6+5Gb73Pbj5ZqivDzbjhBPgjjvgoosgKSncfJIkSZJeZ/FHkiRJkiRJkiR1+PWv4YtfhMrKYM9nZsINN8CXvwwZGaFGkyRJkvRmFn8kSZIkSZIkSUp0O3bAl74Ev/pV8BmXXw7z5kFBQXi5JEmSJL0liz+SJEmSJEmSJCWq+nq45Ra48044dCjYjPHj4a674MwzQ40mSZIk6e1Z/JEkSZIkSZIkKdG0tcGPfwzXXQd79wabMXAgfOtb8OlPQ3JyqPEkSZIkHRmLP5IkSZIkSZIkJZJVq2DWLHjmmWDPp6bC7Nlw440wYEC42SRJkiR1i8UfSZIkSZIkSZISwV//Cl/5CixeHHzGhz8M3/0uFBeHl0uSJElSYBZ/JEmSJEmSJEmKZ01NHWWdW2+FAweCzRg2rGPGBReEm02SJEnSUbH4I0mSJEmSJEkx7MDBFtZU17J513427qyjck8DDU0tNLe2kZaSTFZGKsX5WYwZnMOoggFMKMylf7ov/Qpob4dly+DLX4aqqmAzsrLgpps6rgZLSws3nyRJkqSj5nd/kiRJkiRJkhSDtu6uZ/Gqah5dv4vG5tbDflzNgWZerGnkiS17AchMS+HicQVMnVjIiOOzeySbZaQ+4Lnn4ItfhOXLgz2flASf+UzHlqD8/FCjSZIkSQqP32lJkiRJkiRJUgyp3NNA2bItVFTVBHq+sbmVB1e/xIOrX6KkKI+yySMpzs8KJVssl5H0T7W1UFYG99wDrYf/z+gtlZTAXXfBhAmhRpMkSZIUvqT29vb2qENI6vsqKio488wzO73v6aefpqSkJKJEkiRJkiRJfUtLaxvlK6tYsGIHza1toc1NS0lm9qShlJ5dRGpKcqAZR1tG+ldhl5H0T62tcO+9cMMNUBPwP6d3vQvmzYPLL+/Y+NML3B4lSZIkHR2LP5JCYfFHkiRJkiQpuH31TUxfvJYNL9f12Bljh+SwaOp4BmZnHPEzsVxG0r9YuRJmzYING4I9n5YG11wD110HxxwTbrbDONLtUW/k9ihJkiSpM4s/kkJh8UeSJEmSJCmYnbWNXH7vaqprGnv8rMK8TB6YdgaDczPf9mNjtYykf/HSS3DttfCznwWfcfHF8J3vQFFRaLHeitujJEmSpHD5qxSSJEmSJEmSFJF99U29VvoBqK7pKBntq296y4/bWdvIlPKKHi39AGx4uY4p5RXsrO2df/+40dgIN98Mw4cHL/2MHAnLl8Mjj/RK6aeltY17nnyeC+9+KpTSD0BFVQ0X3v0U9zz5PC0hbqSSJEmS+hKLP5IkSZIkSZIUgZbWNqYvXttrpZ/XVNc0Mn3x2sMWJWK1jCSgvb2j6DNiBJSVwT/+0f0ZOTlw113w7LMwaVLIAbu2r76JS39Qwe1PVIZ6ZRxAc2sbtz9RyaU/qPC/Q5IkSUpIFn8kSZIkSZIkKQLlK6t6fKPO4Wx4uY7ylVVven+slpEEbNgA554LH/94xxVf3ZWcDDNnwo4dcNVVkJoafsYuuD1KkiRJ6lkWfyRJkiRJkiSpl1XuaeDOFdsjzbBgxQ4q9zR0el8slpES3t//3lHYOfVU+MMfgs045xxYtw6+/3145zvDzfcW3B4lSZIk9TyLP5IkSZIkSZLUy8qWbeFQa3ukGZpb2yhbtuX1t2O1jJSwDh3quJJr6FAoL4e2ANuQ3v3ujqvBnnwSxo4NP+NbcHuUJEmS1Dss/kiSJEmSJElSL9q6u56KqpqoYwBQUVXDtj31QGyWkRLWihVwyikwezbU1XX/+Xe8A26+GbZuhSlTICkp7IRvy+1RkiRJUu+w+CNJkiRJkiRJvWjxquqoI3SyuKI6ZstICeeFF+Dii+G88+C554LN+PjHYds2uOkmyMwMNd6RcnuUJEmS1Hss/kiSJEmSJElSLzlwsIVH1++KOkYnj6zfxQ//9JeoY3SyuCK2ylE97tVX4frr4eST4Re/CDbjlFPgD3+An/yk44qvCLk9SpIkSeo9qVEHkCRJkiRJkqREsaa6lsbm1qhjdNLY3Movnv1r1DE6eWT9Lq6/YAT90+P8Jey2NnjgAZg7F3bvDjbjne+EW2+F//ovSEkJN18Asbg9anh+dtRRjtqBgy2sqa5l8679bNxZR+WeBhqaWmhubSMtJZmsjFSK87MYMziHUQUDmFCYG///+5EkSRJg8UeSJEmSJEmSes3mXfujjtClgy1tUUfopLG5lTXVtZwz7Lioo/ScZ56BWbNg1apgz6ekwBe+AF/7GuTmhpvtKMTiVXa3XjI66hiBbd1dz+JV1Ty6ftdblgZrDjTzYk0jT2zZC0BmWgoXjytg6sRCRhzf94tPkiRJOjyv+pIkSZIkSZKkXrJxZ13UEfqMWC1JHbU9e+Czn4XTTw9e+jnvPNi4Ee68M6ZKP7F6ld2Bgy1Rx+i2yj0NfHLhKj684I88uPqlbm8Ka2xu5cHVL/HhBX/kkwtXUbmnoYeSSpIkKWoWfyRJkiRJkiSpl/jD9yO3aWecFX+am+H222HYMPjhD4PNOPFE+MUv4Ikn4OSTw80Xgli9ym5NdW3UMY5YS2sb9zz5PBfe/VRoV6ZVVNVw4d1Pcc+Tz9PSGlvbvSRJknT0LP5IkiRJkiRJUi9paOp7m0eiUrk3jkpSv/oVjBoFc+ZAQ4B/r/794Vvfgi1bYPJkSEoKP2MIYnVLU6zmeqN99U1c+oMKbn+ikuaQCzrNrW3c/kQll/6ggn31TaHOliRJUrQs/kiSJEmSJElSLwn7h/nxrKHpUNQRjl5lJVxwAXz0o7BjR7AZV1wB27fDV74C6enh5gtZrF5l1xe2R+2sbWRKeQUbXq7r0XM2vFzHlPIKdtY29ug5kiRJ6j0WfyRJkiRJkiSpl6Sl+JLskTrY0odLUvv3w9VXd2z5efzxYDNOOw0qKuDHP4Z3vSvcfD0kVq+yi/XtUfvqm7j83tVU1/ROGae6ppHL713t5h9JkqQ44XeZkiRJkiRJktRLsjJSo47QZ6Sn9sGXr9va4L77YNgwuOMOaAlwtdugQfDDH8KqVTBxYvgZe1CsXmUXy9ujWlrbmL54ba+Vfl5TXdPI9MVraXELmSRJUp/XB79zkiRJkiRJkqS+qTg/K+oIfUZWRr+oI3TP00/D6afDtGmwb1/3n+/XD+bM6bjW69OfhuS+9/J9rF5lF8vbo8pXVvX49V6Hs+HlOspXVkVytiRJksLT975zkCRJkiRJkqQ+aszgnKgj9BnFg/pISWrnTrj8cnjve2Ht2mAzPvpR2LIF5s2D7Oxw8/WiWL3KLla3R1XuaeDOFdsjzbBgxY6YvaJNkiRJRyY2v9qVJEmSJEmSpDg0qmBA1BH6jNGDY/z/V01NcOutUFwMDz4YbEZxMTz+ODz2GAwdGm6+CMTqVXaxuj2qbNkWDrW2R5qhubWNsmVbIs0gSZKko2PxR5IkSZIkSZJ6yYTCXDLTUqKO0UmsbkOJ2ZJUezs88gicfDJ89avQ2Nj9GdnZ8J3vwMaN8KEPhZ8xIrF6lV0sbo/aurueiqqaqGMAUFFVw7Y99VHHkCRJUkCx+R2dJEmSJEmSJMWh/umpXDyuIOoYnVx0yrtiroyUmZbChMLcqGO82ebNMGkS/Pu/w1/+0v3nk5Jg2jTYsQO+/GVISws/Y4Ri9Sq7WNwetXhVddQROllcEVt5JEmSdOQs/kiSJEmSJElSL5o6sTDqCJ189qwTYq6MdMm4Avqnx9C1Ua+8AlddBaecAr/7XbAZ730vPPMMLFoEAweGGi9WxOqWpljLdeBgC4+u3xV1jE4eWb+LAwdboo4hSZKkACz+SJIkSZIkSVIvGnF8NiVFeVHHAKCkKI/h+dkxV0aaWhIjeVpa4L//G4YOhe99D1pbuz+joAAefBD++EcYPz78jDEkFq+yi8XtUWuqa2lsDvDfpR7U2NzKmuraqGNIkiQpAIs/kiRJkiRJktTLyiaPJC0l2pdn01KSufmikUBslpEi9/vfdxR1rryyY+NPd6Wnw1e/CpWV8MlPdlzzFedi8Sq7mNseBWzetT/qCF2K1VySJEl6axZ/JEmSJEmSJKmXFednMXvS0EgzzJ40lGGDsl5/O9bKSJGproYpU+Dcc2HjxmAzLr0Utm6Fb3wD+vcPN1+Mc3vU29u4sy7qCF3atNPijyRJUl9k8UeSJEmSJEmSIlB6dhFjh+REcvbYITmUnl3U6X2xWEbqVQcOwE03wfDhsHRpsBmjRsFvf9vx/AknhJuvj3B71Nur3NMQdYQuVe6NzVySJEl6axZ/JEmSJEmSJCkCqSnJLJo6nsK8zF49tzAvk0VXjCe1i+0+sVZG6hXt7fCTn3QUfr7xDWhq6v6M3Fz43vdg/Xp4//vDz9jHuD3qrTU0tUQdoUsNTYeijiBJkqQAYutiW0mSJEmS1GMOHGxhTXUtm3ftZ+POOir3NNDQ1EJzaxtpKclkZaRSnJ/FmME5jCoYwITCXPqn+9KBJPWkgdkZPDDtDC6/dzXVNY09fl5hXiYPTDuDgVkZXf7z18pIU8oreiXPv+Y6XBmpR61fD7NmwVNPBXs+ORk+9zm4+WbIi40tN7Hgte1Rtz9RGVmGSLdHvY3m1raoI3TpYEts5pIkSdJb89U7SZIkSZLi3Nbd9SxeVc2j63fR2Nx62I+rOdDMizWNPLFlLwCZaSlcPK6AqRMLGXF87F2TIUnxYnBuJktKS5i+eC0bXq7rsXPGDslh0RXjD1v6eU2slZF6xN/+BjfcAPfe27HxJ4hzz4UFC2D06HCzxYnSs4v4zXN7e/S/04cT2faoIxT1NqTDSU+NzVySJEl6a34VJ0mSJElSnKrc08AnF67iwwv+yIOrX3rL0k9XGptbeXD1S3x4wR/55MJVVO5p6KGkkqSB2Rk8PLOEa88vDr0UkJaSzLXnF/PwzJIjLte8Vkbq6Wu/xg7JYcnMEgbn9tJ1Z4cOwZ13wtChsGhRsNJPYSEsXQq//a2ln7cQi1fZxYqsjNj8neysjH5RR5AkSVIAsfuVryRJkiRJCqSltY17nnyeC+9+ioqqmlBmVlTVcOHdT3HPk8/TEqPXU0hSX5eaksyV557EY1edRUlRONdGlRTl8dhVZ3HluSd1uwgRa2Wko/bEEzBmDHzpS7B/f/efz8yEb3wDtm6FSy+FpKTwM8aZ17ZH9Vb5J5LtUQEU58fmFWTFMXo1miRJkt5abNbKJUmSJElSIPvqm3rsqpjm1jZuf6KS3zy3l0VTxzMwO7Z/qCZJfVVxfhYPzZjI1t313L+qmkfe5qrGN8pMS+GScQVMLSlkeP7RXdX4Whlp0ohBlC3bEkqhtKQoj7LJI3uv/PD88/DlL8NjjwWf8clPwrx5MGRIeLkSRKxdZRcLxgzOef1q1VgyevCAqCNIkiQpgKT29qAXGEvS/1dRUcGZZ57Z6X1PP/00JSUlESWSJEmSEs/O2kYuv3c11TWNPX7Wa79R32tXs0hSAjtwsIU11bVs3rWfTTv3U7m3gYamQxxsaSM9NZmsjH4UD8pi9OABjCoYwITCXPqn98zvfMZCGemINTTALbfAd7/bccVXEOPGwV13wVlnhZstAbW0tlG+sooFK3bQHOL2wLSUZGZPGkrp2UUxfb3Xv/rD9r/xn//z56hjvMmPP3s65ww7LuoYkiRJ6iaLP5JCYfFHkiRJita++iamlFf0SunnNYV5Hb/B7+YfSUo8sVRGepO2Nli8GL7yFdizJ9iM446Db34TPvMZSEkJN1+Cq9zT0He3R4XkwMEWTrt1RbfKcz0tMy2FZ26Y1Hv/O5UkSVJo/ApOkiRJkqQ+rqW1jemL1/Zq6QeguqaR6YvX8vDMkj7zG/aSpHD0T0/lnGHHxd52kNWrYdYs+HPAbSqpqXDVVXDTTZCTE2o0dYilq+yi0j89lYvHFfDg6peijvK6S8YVWPqRJEnqo/wqTpIkSZKkPq58ZRUbXq6L5OwNL9dRvrKKK889KZLzJUkCYPduuO46+PGPg884//yOa8FGjAgvlw5rxPHZ3HrJaK6/YETsbo/qQVMnFsZU8WdqSWHUESRJkhRQ3//qWJIkSZKkBFa5p4E7V2yPNMOCFTuYNGJQn7tmQ5IUBw4ehDvvhFtugVdfDTbjpJM6Cj8f+QgkJYUaT28vZrdH9bARx2dTUpQXypVnR6ukKK/Pbk+SJEkSuIdbkiRJkqQ+rGzZFg61tkeaobm1jbJlWyLNIElKMO3t8NhjMGoUfOUrwUo/xxwD8+bB5s3w0Y9a+lGvK5s8krSIr0tNS0nm5otGRppBkiRJR8fijyRJkiRJfdTW3fUx8VviABVVNWzbUx91DElSIti6FT70IZg8GZ5/PtiMT38atm+HOXMgPT3UeNKRKs7PYvakoZFmmD1pKMMGubVRkiSpL7P4I0mSJElSH7V4VXXUETpZXBFbeSRJcaauDr70JRgzBn7zm2AzzjgDVq+GH/4Qjj8+1HhSEKVnFzF2SE4kZ48dkkPp2UWRnC1JkqTwWPyRJEmSJKkPOnCwhUfX74o6RiePrN/FgYMtUceQJMWb1lZYuBCGDoU774SWAJ9r8vPhxz+Gp5+G008PPaIUVGpKMoumjqcwL7NXzy3My2TRFeNJjfiqMUmSJB09v6KTJEmSJKkPWlNdS2Nza9QxOmlsbmVNdW3UMSRJ8eSPf4TTToPSUvj737v/fFoazJ3bca3XFVdAsi+JK/YMzM7ggWln9Fr5pzAvkwemncHArIxeOU+SJEk9y+9yJEmSJEnqgzbv2h91hC7Fai5JUh/z8svwyU/C2WfD+vXBZkyeDFu2wG23QVZWuPmkkA3OzWRJaUmPX/s1dkgOS2aWMDi3dzcMSZIkqedY/JEkSZIkqQ/auLMu6ghd2rTT4o8k6Sj84x/w9a9DcTH85CfBZowYAU88Ab/4BZx0Urj5pB40MDuDh2eWcO35xaSFfAVXWkoy155fzMMzS9z0I0mSFGdSow4gSZIkSZK6r3JPQ9QRulS5NzZzSZJiXHs7PPwwXHMNVFcHmzFgANx8M3z+89CvX7j5pF6SmpLMleeexKQRgyhbtoWKqpqjnllSlEfZ5JEU57v5SpIkKR5Z/JEkSZIkqQ9qaGqJOkKXGpoORR1BktTXbNwIs2fD738f7PmkJJg+HW65BY47LtRoUlSK87N4aMZEtu6u5/5V1TyyfheNza1H/HxmWgqXjCtgakkhw/OzezCpJEmSombxR5IkSZKkPqi5tS3qCF062BKbuSRJMaimBm68EcrLoS3g54/3vQ8WLIBx48LNJsWIEcdnc+slo7n+ghGsqa5l8679bNq5n8q9DTQ0HeJgSxvpqclkZfSjeFAWowcPYFTBACYU5tI/3R8BSZIkJQK/6pMkSZIkqQ9KS0mOOkKX0lNjM5ckKYa0tMAPfgA33QS1tcFmDBkCt98OH/tYx8YfKc71T0/lnGHHcc4wt1pJkiSpM4s/kiRJkiT1QVkZqdQcaI46xptkZfSLOoIkKZb99rcd13pt2RLs+YwMmDMH5s6FzMxws0mSJElSH+Sv4UmSJEmS1AcV52dFHaFLxYNiM5ckKWJ/+Qv8+7/DpEnBSz9TpsC2bXDzzZZ+JEmSJOmfLP5IkiRJktQHjRmcE3WELo0ePCDqCJKkWPLqq/DVr8KIEfDII8FmjBkDTz4JP/sZFBaGm0+SJEmS+jiv+pIkSZIkqQ8aVRCbBZtYzSVJ6mXt7fDggx1Xcu3aFWzGscfCLbfA9OmQ6kvZkiRJktQVv1uSJEmSJKkPmlCYS2ZaCo3NrVFHeV1mWgoTCnOjjiFJitratTBrFjz9dLDnU1Lg85+HsrKO8o8kSZIk6bC86kuSJEmSpD6of3oqF48riDpGJ5eMK6B/ur9jJEkJa+9emDYNTjsteOnnAx+AZ5+Fu+6y9CNJkiRJR8DijyRJkiRJfdTUiYVRR+hkakls5ZEk9ZLmZvjOd2DYMLjvvo5rvrrrhBPgkUdg+XIYNSr8jJIkSZIUpyz+SJIkSZLUR404PpuSoryoYwBQUpTH8PzsqGNIknrb44/DmDFwzTVQX9/95zMz4dZb4bnn4OKLISkp9IiSJEmSFM8s/kiSJEmS1IeVTR5JWkq0396npSRz80UjI80gSepl27fDRz4CF1wAlZXBZlx+ecec66+HjIxw80mSJElSgrD4I0mSJElSH1acn8XsSUMjzTB70lCGDcqKNIMkqZfU18O113Zcx/V//xdsxvjx8Kc/wf33Q0FBuPkkSZIkKcFY/JEkSZIkqY8rPbuIsUNyIjl77JAcSs8uiuRsSVIvamuDH/4Qhg2Db38bDh3q/oyBA+G+++DPf4Yzzww/oyRJkiQlIIs/kiRJkiT1cakpySyaOp7CvMxePbcwL5NFV4wnNeKrxiRJPayiAs44Az77Wdi7t/vPp6bC1Vd3XOv12c9Csp83JEmSJCksfoclSZIkSVIcGJidwQPTzui18k9hXiYPTDuDgVkZvXKeJCkCf/0rTJ3asZ1nzZpgMz78Ydi8uWNL0IAB4eaTJEmSJFn8kSRJkiQpXgzOzWRJaUmPX/s1dkgOS2aWMDi3dzcMSZJ6SVMTfOtbHdd63X9/sBnDhsGvfgX/939QXBxuPkmSJEnS6yz+SJIkSZIURwZmZ/DwzBKuPb+YtJCv4EpLSeba84t5eGaJm34kKR61t8Ojj8LIkXD99XDgQPdnZGXB7bfDpk1wwQWhR5QkSZIkdZYadQBJkiRJkhSu1JRkrjz3JCaNGETZsi1UVNUc9cySojzKJo+kOD8rhISSpJjz3HMwezasWBHs+aQk+Mxn4NZbIT8/3GySJEmSpMOy+CNJkiRJUpwqzs/ioRkT2bq7nvtXVfPI+l00Nrce8fOZaSlcMq6AqSWFDM/P7sGkkqTI1NZCWRnccw+0HvnniE5KSuCuu2DChFCjSZIkSZLensUfSZIkSZLi3Ijjs7n1ktFcf8EI1lTXsnnXfjbt3E/l3gYamg5xsKWN9NRksjL6UTwoi9GDBzCqYAATCnPpn+5LB5IUl1pbYdEi+OpXoSbgZrh3vQvmzYPLL+/Y+CNJkiRJ6nW+eidJkiRJUoLon57KOcOO45xhx0UdRZIUpZUrYdYs2LAh2PPp6XD11XDddXDMMeFmkyRJkiR1i8UfSZIkSZIkSUoE1dUwZw787GfBZ1x8MXznO1BUFFosSZIkSVJwFn8kSZIkSZIkKZ41NsL8+R3XcjU1BZsxciTceSdMmhRqNEmSJEnS0bH4I0mSJEmSJEnxqL0dliyBa6+Fl14KNiMnB77+dfjc5yDVl5MlSZIkKdb4nZokSZIkSZIk/dOBgy2sqa5l8679bNxZR+WeBhqaWmhubSMtJZmsjFSK87MYMziHUQUDmFCYS//0GHyZ9dlnYfZsWLky2PPJyVBa2lH6eec7Q40mSZIkSQpPDH5HKkmSJEmSJEm9a+vuehavqubR9btobG497MfVHGjmxZpGntiyF4DMtBQuHlfA1ImFjDg+u7fiHt7f/w5f/SosWgRtbcFmnHMOLFgAY8eGm02SJEmSFDqLP5IkSZIkSZISVuWeBsqWbaGiqibQ843NrTy4+iUeXP0SJUV5lE0eSXF+Vsgpj8ChQ/D978PXvgZ1dcFmvPvd8O1vw2WXQVJSqPEkSZIkST0jOeoAkiRJkiRJktTbWlrbuOfJ57nw7qcCl37eqKKqhgvvfop7nnyeltaA23aCWLECTjml42qvIKWfd7wDbr4Ztm2DKVMs/UiSJElSH+LGH0mSJEmSJEkJZV99E9MXr2XDy3Whz25ubeP2Jyr5zXN7WTR1PAOzM0I/43UvvABXXw2/+EXwGR//OMyf37HtR5IkSZLU57jxR5IkSZIkSVLC2FnbyJTyih4p/fyrDS/XMaW8gp21jeEPf/VVuP56OPnk4KWfU06BlSvhJz+x9CNJkiRJfZjFH0mSJEmSJEkJYV99E5ffu5rqmh4o43ShuqaRy+9dzb76pnAGtrXB/fdDcTF861vQ3Nz9Ge98J5SXw5o18L73hZNLkiRJkhQZiz+SJEmSJEmS4l5LaxvTF6/ttdLPa6prGpm+eC0trW1HN+iZZ+C974WpU+Gvf+3+8ykpMHs2bN8OM2Z0vC1JkiRJ6vMs/kiSJEmSJEmKe+Urq3r8eq/D2fByHeUrq4I9vGcPfPazcPrpsGpVsBkf/CBs3Ah33gm5ucFmSJIkSZJiUmrUASRJkiRJkiSpJ1XuaeDOFdsjzbBgxQ4mjRhEcX7WkT3Q3AwLFsA3vgENDcEOPfFEuOMOuPBCSEoKNkOSDuPAwRbWVNeyedd+Nu6so3JPAw1NLTS3tpGWkkxWRirF+VmMGZzDqIIBTCjMpX+6P5aSJEkKm19hSZIkSZIkSYprZcu2cKi1PdIMza1tlC3bwkMzJr79B//qV/ClL8GOHcEOO+YY+OpX4YtfhPT0YDMk6TC27q5n8apqHl2/i8bm1sN+XM2BZl6saeSJLXsByExL4eJxBUydWMiI47N7K64kSVLcs/gjSZIkSZIkKW5t3V1PRVVN1DEAqKiqYdueeobnH+YH3pWVHYWfxx8PfsgVV8C3vgXvelfwGZLUhco9DZQt2xL479TG5lYeXP0SD65+iZKiPMomjzzyLWiSJEk6rOSoA0iSJEmSJElST1m8qjrqCJ0srugiz/79cPXVMGpU8NLP6adDRQX8+MeWfiSFqqW1jXuefJ4L734qtCJlRVUNF979FPc8+TwtrW2hzJQkSUpUFn8kSZIkSZIkxaUDB1t4dP2uqGN08sj6XRw42NLxRmsr3HcfDBsGd9wBLS3dHzhoEPzwhx2ln4lHcI2YJHXDvvomLv1BBbc/UUlzyAWd5tY2bn+ikkt/UMG++qZQZ0uSJCUSiz+SJEmSJEmS4tKa6loam1ujjtFJY3Mra6pr4U9/6tjSM20a7NvX/UH9+sGcObB9O3z605DsS72SwrWztpEp5RVseLmuR8/Z8HIdU8or2Fnb2KPnSJIkxSu/G5QkSZIkSZIUlzbv2h91hC5tvmMhnHUWrFsXbMBHPwpbtsC8eZCdHW44SaJj08/l966muqZ3yjjVNY1cfu9qN/9IkiQFYPFHkiRJkiRJUlzauLMu6ghd2rT3QLAHhw+Hxx+Hxx6DoUPDDSVJ/9TS2sb0xWt7rfTzmuqaRqYvXktLyFeKSZIkxTuLP5IkSZIkSZLiUuWehqgjdKnyuPd074HsbLjjDti4ET70oR7JJEmvKV9Z1ePXex3OhpfrKF9ZFcnZkiRJfZXFH0mSJEmSJElxqaGpJeoIXWpIzzyyD0xKgmnTYMcO+NKXoF+/ng0mKeFV7mngzhXbI82wYMWOmC1uSpIkxSKLP5IkSZIkSZLiUnOMXhdzMOUICjzvfS+sWQOLFsHAgT0fSpKAsmVbONTaHmmG5tY2ypZtiTSDJElSX2LxR5IkSZIkSVJcSkuJzZc/01sPHf4fFhTAgw/CH/8Ip57ae6EkJbytu+upqKqJOgYAFVU1bNtTH3UMSZKkPiE2v/OVJEmSJEmSpKOUlZEadYQuZR1sfPM709PhxhuhshI++cmOa74kqRctXlUddYROFlfEVh5JkqRYZfFHkiRJkiRJUlwqzs+KOkKXiv/2Yud3XHopbNsGX/869O8fSSZJie3AwRYeXb8r6hidPLJ+FwcOtkQdQ5IkKeZZ/JEkSZIkSZIUl8YMzok6QpdG73m+4w+jRsFvfwtLl8J73hNpJkmJbU11LY3NrVHH6KSxuZU11bVRx5AkSYp5Fn8kSZIkSZIkxaVRBQOijtClUQf2wve+B+vXw/vfH3UcSWLzrv1RR+hSrOaSJEmKJbF5ybUkSZIkSZIkHaUJhblkpqXE1BaLzPYWJjyxBI4fGHUUSXrdxp11UUfo0qadFn8kSZLejht/JEmSJEmSJMWl/umpXDyuIOoYnVwysYj+ln4kxZjKPQ1RR+hS5d7YzCVJkhRLLP5IkiRJkiRJiltTJxZGHaGTqSWxlUeSABqaWqKO0KWGpkNRR5AkSYp5Fn8kSZIkSZIkxa0Rx2dTUpQXdQwASoryGJ6fHXUMSXqT5ta2qCN06WBLbOaSJEmKJRZ/JEmSJEmSJMW1sskjSUuJ9qXQtJRkbr5oZKQZJOlwov478nDSU2MzlyRJUizxKyZJkiRJkiRJca04P4vZk4ZGmmH2pKEMG5QVaQZJOpysjNSoI3QpK6Nf1BEkSZJinsUfSZIkSZIkSXGv9Owixg7JieTssUNyKD27KJKzJelIFOfHZjGx2MKkJEnS27L4I0mSJEmSJCnupaYks2jqeArzMnv13MK8TBZdMZ7UGL1GR5IAxgzOiTpCl0YPHhB1BEmSpJjnd5uSJEmSJEmSEsLA7AwemHYGhQPSe+W8wrxMHph2BgOzMnrlPEkKalRBbBZsYjWXJElSLLH4I0mSJEmSJCkxHDzI4EXfY8mdn2HsXyt79KixQ3JYMrOEwbm9u2FIkoKYUJhLZlpK1DE6yUxLYUJhbtQxJEmSYp7FH0mSJEmSJEnxrb0dHnsMRo2CuXMZuG8nD99/Ldf+4cektRwK9ai0lGSuPb+Yh2eWuOlHUp/RPz2Vi8cVRB2jk0vGFdA/PTXqGJIkSTHP4o8kSZIkSZKk+LVtG3z4wzB5Mjz//OvvTm1v48pVS3jsx1+kpHpDKEeVFOXx2FVnceW5J5Ga4kuvkvqWqRMLo47QydSS2MojSZIUq6xKS5IkSZIkSYo/dXXw9a/D3XdDS8thP6z479U89JMb2Hrce7h/3AU8MvJcGtPeccTHZKalcMm4AqaWFDI8PzuE4JIUjRHHZ1NSlEdFVU3UUSgpyvPvVEmSpCOU1N7e3h51CEl9X0VFBWeeeWan9z399NOUlJRElEiSJEmSJCWk1lb4n/+BG26Av/2t248f6JfBmtHvZfOnStk08AQq975KQ9MhDra0kZ6aTFZGP4oHZTF68ABGFQxgQmGuV9FIihuVexq48O6naG5tiyxDWkoyv5x1FsMGZUWWQZIkqS/xO1JJkiRJkiRJ8eGpp2DWLFi/PtjzaWn0/9JszrnhBs7J8gfOkhJPcX4WsycN5fYnKiPLMHvSUEs/kiRJ3WDxR5IkSZLUbQcOtrCmupbNu/azcWcdlXsaaGhqobm1jbSUZLIyUinOz2LM4By3IUiSet7LL8PcufDQQ8FnTJ4M3/kOnHRSeLkkqQ8qPbuI3zy3lw0v1/X62WOH5FB6dlGvnytJktSX+aqrJEmSJOmIbd1dz+JV1Ty6fheNza2H/biaA828WNPIE1v2ApCZlsLF4wqYOrGQEcdn91ZcSVK8+8c/4Nvfhttug8bGYDNGjIDvfhfOPz/cbJLUR6WmJLNo6nimlFdQXRPw79YACvMyWXTFeFJTknvtTEmSpHhg8UeSJEmS9LYq9zRQtmwLFVU1gZ5vbG7lwdUv8eDqlygpyqNs8kiK813fL0kKqL0dfv5zuOYaePHFYDMGDICyMrjySujXL8x0Usxya6OO1MDsDB6YdgaX37u6V8o/hXmZPDDtDAZmZfT4WZIkSfEmqb29vT3qEJL6voqKCs4888xO73v66acpKSmJKJEkSZLC0NLaRvnKKhas2EFza1toc9NSkpk9aSilZxf5G72SpO7ZtAlmz4Ynnwz2fFISTJsGt94Kxx0XbjYpRh3p1sY3cmuj9tU3MX3x2h699mvskBwWXTHe0o8kSVJAFn8khcLijyRJUvzptRf5p45nYLYv8kuS3kZNDdx0E/zgB9AWsIx61llw110wbly42aQYdbRbG/+VWxsTl78MIEmSFNv8SkqSJEmS9CY7axuZUl7Ro6UfgA0v1zGlvIKdtT1/fYAkqY9qaYF77oGhQ+G//ztY6WfIEPjJT2DlSks/SggtrW3c8+TzXHj3U6GUfgAqqmq48O6nuOfJ52kJsfyh2JeaksyV557EY1edRUlRXigzS4ryeOyqs7jy3JMs/UiSJB0lN/5ICoUbfyRJkuLHvvomppRXUF3Te2WcwrxMlpSWuPlHktTZ737Xca3X5s3Bns/IgDlzYO5cyMwMN5sUo9zaqJ62dXc996+q5pEAV8ddMq6AqSWFDM/36jhJkqSwWPyRFAqLP5IkSfGhpbWNS3/Q85t+ujJ2SA4PzyzxN34lSfCXv8A118DPfx58xpQpMH8+vOc9ocWSYt3O2kYuv3d1rxS4C/MyeWDaGQzOtVSXqA4cbGFNdS2bd+1n0879VO5toKHpEAdb2khPTSYrox/Fg7IYPXgAowoGMKEwl/7pqVHHliRJijt+hSVJkiRJel35yqpISj/Qce1X+coqrjz3pEjOlyTFgAMH4Lbb4Pbb4eDBYDPGjIEFC+Df/i3UaFKs21ff1GulH4Dqmo6SkVsbE1f/9FTOGXYc5ww7LuookiRJCc1fo5QkSZIkAVC5p4E7V2yPNMOCFTuo3NMQaQZJUgTa2+HBB6G4GG65JVjp59hj4b//G9autfSjhNPS2sb0xWt79apW6Cj/TF+8lpbWtl49V5IkSdL/Z/FHkiRJkgRA2bItHGqN9jbo5tY2ypZtiTSDJKmXrV0L73sfXH457NrV/edTUuALX4AdO+Bzn4NUl5wr8cTC1kZJkiRJ0bD4I0mSJEli6+56Kqpqoo4BQEVVDdv21EcdQ5LU0/btg2nT4LTT4E9/CjbjAx+AZ5+Fu+/u2PgjJSC3NkqSJEmJzeKPJEmSJInFq6qjjtDJ4orYyiNJClFzM9xxBwwdCvfd13HNV3edcAL8/OewfDmMGhV+RqkPcWujJEmSlNgs/kiSJElSgjtwsIVH1we4WqUHPbJ+FwcOtkQdQ5IUtscfhzFj4OqroT7AdrfMTLj1VnjuObjkEkhKCj+j1Ie4tVGSJEmSxR9JkiRJSnBrqmtpbG6NOkYnjc2trKmujTqGJCksO3bARz8KF1wAlZXBZlx+OWzfDtdfDxkZ4eaT+ii3NkqSJEmy+CNJkiRJCW7zrv1RR+hSrOaSJHVDfT3MmQMjR8KvfhVsxvjx8Kc/wf33Q0FBuPmkPsytjZIkSZLA4o8kSZIkJbyNO+uijtClTTst/khSn9XWBj/8IQwbBrffDocOdX/GwIFw333w5z/DmWeGn1Hq49zaKEmSJAks/kiSJElSwqvc0xB1hC5V7o3NXJKkt7FqFUycCJ/9LOzd2/3nU1Ph6qs7rvX67Gch2Zcwpa7E6nbEWM0lSZI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      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "\n",
    "bounds = np.linspace(1,30)\n",
    "rsquared_list = []\n",
    "Sxx_list = []\n",
    "for bound in bounds: \n",
    "\n",
    "    x = np.linspace(-5-bound,1.5+bound)\n",
    "    Sxx_list.append( np.sum((x - x.mean())**2) )\n",
    "    e = np.random.normal(loc=0,scale=10.0,size=len(x))\n",
    "    y = x + 10 + e\n",
    "\n",
    "    df = pd.DataFrame(x, columns=['x'])\n",
    "    df['cte'] = 1\n",
    "    df['y'] = y\n",
    "\n",
    "    model = sm.OLS(df.y,df[['cte','x']]).fit()\n",
    "    model_prediction = model.predict(df[['cte','x']])\n",
    "\n",
    "    rsquared_list.append(model.rsquared)\n",
    "\n",
    "model = sm.OLS(df.y,df[['cte','x']]).fit()\n",
    "model_prediction = model.predict(df[['cte','x']])\n",
    "plt.plot(df['x'],model_prediction,'r-')\n",
    "plt.title(r'$R^2 ='+str(np.round(model.rsquared,4))+'$')\n",
    "\n",
    "\n",
    "plt.plot(x,y,'o')\n",
    "plt.xlabel(r'$X$',fontsize=16)\n",
    "plt.ylabel(r'$Y$',fontsize=16)\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#mpl.rc('text.latex', preamble=r'\\usepackage{amsmath},\\usepackage{amssymb},\\usepackage{amsfonts}') \n",
    "#params= {'text.latex.preamble' : [r'\\usepackage{amssymb},\\usepackage{amsfonts}']}\n",
    "#plt.rcParams.update(params)\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "\n",
    "plt.plot(Sxx_list,rsquared_list,'.',label=r'Dados')\n",
    "n = len(y)\n",
    "Sxtheo= np.linspace(np.min(Sxx_list),np.max(Sxx_list),100)\n",
    "s2 = np.sum(((y - model_prediction)**2)/(len(y)-2))\n",
    "\n",
    "Fr = ((Sxtheo/(n-1))/((Sxtheo/(n-1)) + s2))\n",
    "\n",
    "plt.plot(Sxtheo,Fr,'r-',label=r'$E(R^2)$')\n",
    "\n",
    "\n",
    "plt.xlabel(r'$S_{XX}$',fontsize=16)\n",
    "plt.ylabel(r'$R^2$',fontsize=16)\n",
    "plt.legend(loc='upper left',fontsize=13)\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Equivalência teste $\\mathcal{F}$ e teste $t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pVIpisbhmbTqdjrGxsRgZGdmBSi8bGxuLiYmJiIjIZrMxPDwc6XQ6SqVSPP3006tfS6fTMT09HZlMZsdqBQAAoLsJAQAAAAAtNTw8HDMzM5FOp2N8fDyGhobWfL1UKq2GBK6UzWZjeno6UqlUy2otlUpx9OjRKBQKkUql4uTJk5ue4M/lcjE1NRUREZOTkzsaWgAAAKB7CQEAAAAALTM4OBj5fD5GRkZicnKy6tpSqRQDAwNrOgOk0+mYm5trWRCgv79/9fXn5+cjnU5XXS8IAAAAwE7r3ekCAAAAgO4wNjZWcwAgIiKVSsXs7Oya+4rFYhw9enS7SlxjeHh4NQAwPj6eGACIuHzif2VdLpeLQqGwrTUCAADAejoBAAAAANuuVCrFwYMHI51Ox/z8fF2PHRsbi4mJiTX3jY+Px+joaDNLXKNQKMTAwEBEXA4jnDt3rubHTk1NRS6Xi4iITCYTc3Nz21IjAAAAVCIEAAAAAGy7lTb5s7Ozkc1m63rsSoBgve08pDEwMLB6FX+tnQuu1NPTs/r36enpGBoaamp9AAAAsBnjAAAAAIBtd+LEiYi4fFV/LpdbbbNfi1QqVfEk+szMTNPqu1KxWFzTxn+lI0A9MpnM6t/rDRAAAADAVggBAAAAANuqVCpFqVSKiMtt9qempqK/v3/1vlqk0+kN983OzjapwrXWn7Svt3NBRMSRI0dW/57P5+v6XgEAAGArhAAAAACAbbXZVf9TU1M1P0d/f3/Nz7tV6zsM9PX11f0c6+td6YQAAAAA200IAAAAANhWqVRqy89RqRPAwsLClp93vVKptCFc0Ej96x8zNze3haoAAACgdnt3ugA6x/nz5+MHP/jBmvvuvvvuuP7663eoIgAAANpBOp2OdDq94eT60NBQzc/Rqnb6p06dWnO70QDD+u4B+Xy+0ZJaxr4eAACgMwgB0DQ/+MEP4r777ltz35NPPhn33nvvDlUEAABAu5ibm4vh4eHI5/ORTqdjcnKy4tX9m6nU+r+ex9eqUCisud3IKICIjeGB7Rpd0Ez29QAAAJ1BCAAAAADYdqlUKmZnZxt+/NNPP73hvsHBwa2UVNH8/Pya283qBBBxOQiwHcEFAAAAuFLvThfAL83MzERPT09MTU3tdCkAAADQViq1089ms01/nYWFhaY/54pWjTQAAACgu+36TgBTU1MxPT0dxWIxisVipFKp6Ovri2w2G7lcLjKZzE6XWJNSqRTHjh1b/TsAAABw2czMzIa98tDQ0LZcVb+de/JisbitxymeeuqpLT3+mWeeaVIlAAAA7KRdGwIYGxuLiYmJiLic/B8bG4t0Oh2lUimefvrpmJiYiKmpqUin0zE9Pd32YYBjx445+Q8AAAAVTE5ObrhvfHx8W16rWZ0AGh0jsBX33Xdfy18TAACA9rPrQgClUimOHj0ahUIhUqlUnDx5csMJ/qGhoRgfH49cLhdTU1MxMDAQk5OTMTIyskNVV5fP52NmZmanywAAAIC2UygUNowCmJyc3JYuABEbOwH09fU17bm3c9QAAAAArNh1IYCBgYEoFosRETE3N1d1079ypcDU1FTkcrmIiLYMAgwPD+90CQAAANCWVkbnrRgaGmrLvT0AAAC0i96dLqAew8PDqwGA8fHxmlL/V14dkMvlolAobGuN9crlcsYAAAAAQAVTU1Nr9vHZbDamp6d3sCIAAABof7umE0ChUFhtmZ9KpWJ0dLTmx46Nja12Ajh27FjMzc1tS431KhQKMTU1FdlsdkNrQwAAAOhmxWIxxsbGVm9nMpmYnZ3dwYra35NPPrmlxz/zzDOrx08AAADYvXZNCODK9n8PPfRQXY8dGRlZ3cSuhAmGhoaaWl8jhoeHY2hoKAYHB4UAAAAA4ArDw8OrnfMymUzLAv2pVKopz1Op619fX19Tnnsz995777Y+PwAAALvDrhgHUCwW17T/GxgYqPs5MpnM6t8nJyebUtdWjI2NxcLCQhw/fnynSwEAAIC2Mjw8vHocIJvN7mhHv4WFhR17bQAAAGjErggBrD9pn81m636OI0eOrP49n89XTOS3SqFQiImJiTh+/HjTrjAAAACATjAxMbE6DnBoaKjlIwDS6fSufG4AAABYsStCACub/xWNtM/r7+9fc/vEiRNbqmkrjh07Ftlsti1GEgAAAEC7mJmZibGxsYi4PNpvenq65TWsP+bQ6EUElToIuBAAAACAVti70wUkKZVKUSwW19zXyKZ5/WN2qpXgxMREFAqFOHfu3I68PgAAALSjfD4fw8PDERExOjoa4+PjO1LH+osIGh0HUCk80MhFDQAAAFCvtg8BnDp1as3tRlPz6zfa+Xy+0ZIaViwWY2xsLCYnJ6X/AQAA4I8Vi8UYHByMiMsjAUdGRnaslkwm05TnqXRBg2MBAAAAtELbjwMoFAprbjeaml+/0V6/GW+FXC4XmUxmRw9mAAAAQDsplUoxMDAQERHT09M175mnpqZWRwc005EjRzbU14izZ8+uuZ3NZhstCQAAAOrS9iGA+fn5Nbeb1QkgorVBgKmpqcjn8zsyzxAAAADa0UoAoFQqxfT0dAwNDdX82MnJyW3Z16dSqUin02vua+R11j/mnnvu2VJdAAAAUKu2DwE0OnuvFo2m+Rt5nVwuF+Pj4xsOJAAAAEC3Onr0aBSLxboDABGXOwdu14n19VftNxICWH/Mod7vDwAAABq1d6cLSLKdJ+qLxWLTZv1Vc+zYsUin0zE6Orrtr7UVTz311JYe/8wzzzSpEgAAADrd8PBwFAqFhgIAKyflt2tPPzY2FlNTU6u3C4VC3e38T506tfr3TCbjogAAAABapu1DAM3qBNDoGIGtmpmZiZmZmZibm9uR16/Hfffdt9MlAAAA0AVyuVzMzMzE7Oxs3SfXIy7vtSOi5hPrY2Njkc/nI51O19SlL51ORzabjXw+HxERs7OzdQX7i8XimosacrlczY8FAACArWr7EMD6TgB9fX1Ne+7tHDUQcbn2Y8eOxcjISEs6DgAAAEC7m5iYiKmpqRgdHY2+vr4oFAqJj1nZv5dKpSgWi/Hoo49GRG0hgMHBwdWT+YVCIWZmZmJ+fj7xsSvBgYiIfD4fpVKp5gsMJicnV/+eTqdjZGSkpscBAABAM7R9CGA3Gxsbi4i1m38AAADoVjMzM6t75YmJiZiYmGj4uWoJABSLxdUT+evrSLqyP5vNxtDQ0GrXgUcffTTGx8cTX7NUKq0ZJeCYAAAAAK3Wu9MFdKp8Ph9TU1MxPT2906UAAADAjsvn8zE8PNy059tKx72zZ8/WtO748eOrYYOJiYmauhYcO3Zstavh6OhoQ+MOAAAAYCt0AtgmuVwuhoaGdtVm/8knn9zS45955hlzDgEAANigVCo1NQAQUVsngHQ6HZlMZsPJ+4cffrim10ilUjE3NxdHjx6NQqEQAwMDMT09HUNDQxvWrowEXOkcMDo6WlPnAAAAAGi2tg8B1DpvL8lKCv9KfX19TXnu9cbGxmJhYSGOHz++Lc+/Xe69996dLgEAAIAOVCwWK+7Lt+Kee+6pad3JkydjeHg48vl8pNPpmJycrKuLwEoQYGJiIsbGxmJ4eDgymUzkcrlIp9NRKpXi6aefjqmpqSiVSquvsZsuCgAAAKCztH0IYL2FhYWdLqGqQqEQExMTMT093bQAAwBQu7cvLMZzr74VF5eWN11z49X74q5bbog9vT0trAwAulcmk4lyubwjr51KpWJ2dnbLzzM6OhojIyNx4sSJmJ6ejvHx8SgWi5FKpaKvry8eeuihyOVyWxpTAAAke/vCYrz+1vuxr7c3PnLTNTtdDgC0pbYPAaTT6Zpm7jX63M02PDwc2Wy2YmtAAGB7lMvl+MMX34i//dhLcerHC7FcwzmG6/bvjX/tV26Jf/vB2+OjN127/UUCALteKpWKkZGRGBkZ2elSAKDrLC+X4786+WL8/W+9HOffX4yIiCMfPRj/9z/1qfjsbamdLQ4A2kzbhwDWt+xvtH1gpQ4Czb5Sf2JiIorFYszNzTX1eQGAysrlcjz2/On4r06+FN//Wamux759YTFOnPp5/OPCK/FnPndr/J+/fHt8/GZhAAAAAGhHfyv/Qvw3X39pzX2nfnIu/vI/eDr+6b/9hbitT1cAAFjR9iGA/v7+NbcbHQdQKTywPmCwFcViMcbGxmJyctIYAADYZuVyOfLPno7/+uSL8cwrb27puZaWy/GPCz+Pf/Ldn8ef/tyt8W8/eHvcfvi6JlUKAAAAbNXZty9sCACsWHjnYvydx1+KR//sZ1pcFQC0r96dLiBJs2bpFYvFNbdTqVRTT9bPzMxEREQul4uenp66/uRyuTXPNTY2VnEdAHS75eVyfO0Hr8W//l9/M479D6e2HABY89zliH/y3Vdi8G89Ef/u//LdePH18017bgAAAKBxp35yrurXv11s7OJBAOhUbd8J4MiRI2tuNzoO4OzZs2tuZ7PZRkuqKJ1ON/ycp06dWvN9pdPpSKfTTaoMADrD6bfej3/vf/1ePFU8m7x4C8rliN/7/i/if/9Xv4i//sDt8e8P3hF7eoXxAAAAYKecPn+h+tffer9FlQDA7tD2IYBUKhXpdHrNlfzFYrHuk+TrOwHcc889TalvxdDQUAwNDTX02MHBwcjn86u3c7lcjI6ONqs0ANj1Xim9F79z/Nvxk7Pvtuw1l8sR/+1jL8Urpffibw59JvbuafsGSgAAANCRlpaWq379wmL1rwNAt9kVR7PXX2G//oR+LdZ3EGj0hD0A0Fo/W3g3Hp58qqUBgCv9k+++En/jq9+LSwkHHAAAAIDtsVSu/vXF5XIs2rcDwKpdEQIYGxtbc7tQKNT9HKdOnVr9eyaT0W4fAHaBH7/xTjw8+VT8/Nx7O1rH//6vXo1/53/+blx0ZQEAAAC03NJy8n78ohAAAKxq+3EAERHpdDqy2exqy/zZ2dm62uUXi8U1nQByuVzNjx0bG4t8Ph/pdDrGx8eFBwCgRV46/Xb8zvFvJ879W++aq/bEX7z3o/EXfvWjce3+jb/q/PjsO/F3Hnsp8s+erut5v/bD1+Kv/6O5+Nt/PhP79+6p67EAAABA42o5v3/h0nJcc9X21wIAu8GuCAFE/PJkfEREPp+PUqkUqVSqpsdOTk6u/j2dTsfIyEhNjxscHFx9zUKhEDMzMzE/P9/0IMDCwsKa22fPnm3q8wPAbvPC6+fjd45/J954u/YAwLVX7Ym/dN/H4t/6Yjr6rt1819937VXx9/7SPfGDV96M//rki/Evf/R6za+Rf/Z0jPwPczH5FwfiwD5BAAAAAGiFWjoBXNC9DwBW7YpxABER2Ww2hoaGVm8/+uijNT2uVCrF1NTU6u0rAwHVFIvF1QDAlWZmZmp6PADQmB/94q34P0x9u+YAwPX798a/8+Xb41v/8Zdj9DfuqhoAuNLdt94YU//Gkfjn/+4X4zfvvqXm+p544Uz81X/4dLx3canmxwAAAACNq6kTwKJ9OgCs2DUhgIiI48ePr16FPzExEYVCIfExx44dWx0FMDo6Gtlsdks1NPsq/UKhsOH7mJqaWjO+AAC6xQ9eeTN+5+99OxbeuVjT+ns+djC+MfZg/Ae/fmekGuz596kP3RB/9y8MxD/+a/fFDQdqa5L0rZfOxr/53/9RvHNhsaHXBAAAAGqnEwAA1GdXhQBSqVTMzc1FJpOJiIiBgYFNr8wvlUoxPDy8+vXR0dEYHx+v+bXS6fTq61zp4YcfbqDyX9Y0ODi4+qe/vz8GBgYqrjt48GD09/evrs3lcg2/LgDsBs+/dj5+5/i3o/TupZrW35u+Kf7BX/6TDZ/8X2/gowfjfz72+Th4zb6a1n/n5YX4y//gaVcaAAAAwDZbKpcT11y4JAQAACtqu9ytjawEASYmJmJsbCyGh4cjk8lELpeLdDodpVIpnn766dWr6dPpdExOTjbUAeDkyZMxPDwc+Xx+9XkqBQPqsTJiIJVKRV9f32png0oWFhZiYWFh9fsAgE713sWl+Gv/aC7eer+2K+u/+ImbY+ovHomrr9rT1DruvvXG+F9GPh9//vh34mwN3Qj+6OWF+Jtfez7+kz/1qabWAQAAAPzS4nINIQAhfQBYtetCACtGR0djZGQkTpw4EdPT0zE+Ph7FYnH15PpDDz0UuVxuSyftU6lUzM7ONq3mVCoV5RoSiwDQbf6zf/FsFM+8U9PaB+88FH/3LwzEgX3NDQCsuOuWG+J/Hfl8/M7f+06cOX8hcf3f++bL8eW7Dsd9t9+8LfUAAABAt1taqiUEoBMAAKzYtSGAiMsn1UdGRmJkZGSnSwEAGvTEC2fiHz71k5rWZj/5gfjbf/5PxP692xMAWPGJD1wfXx35fPzO8e/Ea2+9n7j+P5j+fnztb3wpbry6tlECAAAAQO1qGgegEwAArOrd6QIAgO517p2L8R9Nf7+mtb959y3xd/58ZtsDACvSh66Lr+Y+H7emrk5c++qb78d/+k9/0IKqAAAAoPss1TIO4JJOAACwQggAANgR5XI5/pPf/UGcrqHl/m999kPx3/wf/0Rctbe1v7p89KZr438d+Xx8+GByEOB3v/eL+P3v/6IFVQEAAEB3qSkEYBwAAKwSAgAAdsTvfu+V+GfPvJq47rO3peJvPfTZ2LtnZ35tua3vmvgHf/me2F9DAOE/+d0fxGtvJo8PAAAAAGpXWwjAOAAAWCEEAAC03Cul9+L/8bs/TFx39b49OxoAWHH74evjkd+8K3Hdm+9div9o5vuxXMPBCQAAAKA2tYQALuoEAACrhAAAgJZaXi7Hf3Die3H+wmLi2v/bv/7JSB+6rgVVJfs37v1YfPETNyeu+8aLb8T/+O2ftKAiAAAA6A7GAQBAfYQAAICW+vvfejm+XVxIXPfAnYfiz//qR1pQUW16e3vibw59Nm68el/i2v/vP382Xjr9dguqAgAAgM63VBYCAIB6CAEAAC3z/GvnY+JrzyeuO3jNvpj4c5+Jnp6eFlRVu1tuPBD/7z9zd+K6C4vL8e9/9XtaEQIAAEATLNbSCeDSUgsqAYDdQQgAAGiJC4tL8Te++r24uJR8YvzRP/srcfiGAy2oqn6/9dkPxZ/+3IcS1z3zypvx33z9xRZUBAAAAJ1t2TgAAKiLEAAA0BKTTxTj2VffSlz35zIfjt+4+4MtqKhx/6/fvjs+eGNySOFvP/ZSTd8zAAAAsLmaOgEIAQDAKiEAAGDbnTl/ISafmE9cd2vq6vhPf/tTLahoa268Zl/858OfTVy3XI6Y+NpzLagIAAAAOtdSTSEA4wAAYIUQAACw7f7br78Y71ysvhnv6Yn4Lx76bNxwYF+LqtqaL9x+c/yVL3w8cd1jz5+JbxfPtqAiAAAA6Ew1hQAu6QQAACuEAACAbfXTs+/G//xHP01cN/LFdHw+fVMLKmqe0d+4Mz5x+LrEdf/Zv3guyuXkAxYAAADARrV1AhACAIAVQgAAwLb6L2afj0tL1Tfrd3zguvi//PodLaqoeQ7s2xN/6+HPxZ7enqrrvvezUvzBD19vUVUAAADQWYwDAID6CAEAANvmh794M/7p936RuO7/+q99Mvbv3dOCiprv7ltvjOGBDyeu+5t/8FwsLrkqAQAAAOqlEwAA1EcIAADYNhNfez5xzefTfXH/HYdaUM32+RvZO2L/3uq/Vs2feSf+ceHnLaoIAAAAOsdSDSP2LlwSAgCAFUIAAMC2eGr+bDzxwpnEdf/xb34yenqqt9Nvd7fceCD+zS98LHHd35p9Md6/pD0hAAAA1GPROAAAqIsQAADQdOVyOf6zrz2XuO43774lPndbavsLaoG/fv/tccOBvVXXvPbW+/EPn/xxawoCAACADrFsHAAA1EUIAABouj/44Wvx/Z+Vqq7Z09sT/+FX7mxNQS1w4zX74q8/eHviur/z+Hy8+e6lFlQEAAAAnaG2TgBCAACwQggAAGiqxaXlmPiD5xPXPXTkw9F/6LoWVNQ6/+Z9H4tbbjhQdc2b712Kv/vEfIsqAgAAgN2vpk4Axu8BwCohAACgqabnfh7FM+9UXbN/b2/8e0fvaFFFrXNg3574G9lPJK7777/1crz25vstqAgAAAB2v8Xl5Kv8dQIAgF8SAgAAmua9i0vxX+ZfSFz3V37t43HLjdWvmN+thgY+HP2Hrq265sLicvxXJ5PfJwAAACBiyTgAAKiLEAAA0DT/4Mkfx+tvXai65sar98X/6f7+FlXUenv39MZ/9JU7E9edOPXzmD/zdgsqAgAAgN1tqVxLCMA4AABYIQQAADTFm+9eir/7+EuJ6/76A/1x49X7WlDRzvnKp2+Jz92Wqrpmabkc//kfPN+aggAAAGAXW1pKDgFcWirHcg0dAwCgGwgBAABN8fe/9XK89f5i1TUfvPFA/KX7PtaagnZQT09PjP3GXYnr/sUPXotnX32rBRUBAADA7lVLJ4CIiItLRgIAQIQQAADQBO9fWor/6ds/SVz3N7KfiAP79rSgop13b/9N8cCdhxLX/f1vvtyCagAAAGD3WqrxCv8Ll4QAACBCCAAAaIJ/+r1X4uw7F6uuuf3wdfHnMh9uUUXtYfQrd0VPT/U1//R7v4jT599vTUEAAACwC9UcAlhc2uZKAGB3EAIAALakXC7Hf1fD1ez/4a/fGXv3dNevHp/60A3xpz/7oaprLi4tx//07Z+2qCIAAADYfRZrDgHoBAAAEUIAAMAWfePFN+KF19+uuub2w9fFr3/qAy2qqL38tQduT1zzj779k3j/kqsVAAAAoJJlnQAAoC5CAADAlvy9GroA/JUvfDx6exP64neoO2+5Pr74iZurrjn7zsX43e++0qKKAAAAYHeptRPA+5d0AgCACCEAAGALXnz9fPzhC2eqrjl4zb74s5lbW1RRe/qrv/bxxDX/3TdfjnK5toMaAAAA0E2WjAMAgLoIAQAADfv730ruAvAXPv/ROLBvTwuqaV/333Eobj98XdU1L55+O/7wxTdaVBEAAADsHks1huaNAwCAy4QAAICGnH37QvzjQvUW9vv29MRf/PxHW1RR++rp6Ym/8oXaugEAAAAAv7S8XI5aG+fpBAAAlwkBAAAN+Uff+WlcTNhc//Znb43DNxxoUUXt7c9mbo2D1+yruuYPXzgTL7x+vkUVAQAAQPurtQtARMSFS0IAABAhBAAANODC4lL8D0/9JHHdX/215Kvfu8WBfXviL9TQFeHv6wYAAAAAq5aW6wgBGAcAABEhBAAANOD3vveLeOPtC1XX3Ju+KT71oRtaVNHu8Bfv/Whctaf6r1//23dfSXxvAQAAoFvUFwLQCQAAIoQAAIA6lcvlmmbX/1tf1AVgvcPXH4jf+uyHqq65uLgc/+jbP21RRQAAANDeFoUAAKBuQgAAQF2enD8bz71WfW59+uZr48E7D7eoot2llhEJ/+O3fxzvX9LCEAAAAJbrCQHYSwNARAgBAAB1qqULwF/+tY9Hb29PC6rZfT71oRvivv6bqq554+2L8Xvf/0WLKgIAAID2pRMAANRPCAAAqNlLp9+Orz93uuqaG6/eF38uc2uLKtqdahmV8Pe/+XKUy7Uf6AAAAIBOtFzH3lgIAAAuEwIAAGr2338ruQvA7/zqR+Kaq/a2oJrd64E7Dkf60LVV1zz32vn41ktnW1QRAAAAtKf6OgEYBwAAEUIAAECNzr1zMf5x4edV1+zt7Ym/dO/HWlPQLtbb2xN/5QvJ3QD+3jeLLagGAAAA2tfSUh0hgEs6AQBAhBAAAFCjf1z4ebyfsJn+U5/5YNxy44EWVbS7/bnMhyN1zb6qax5//kz8bOHdFlUEAAAA7WfJOAAAqJsQAACQqFwux4lTP0tc91d/Ld2CajrD1Vftid/5kx9JXDczV737AgAAAHSypeXaT+wbBwAAlwkBAACJvv/zN+OF19+uuuZPfrwvfuXDN7aoos7wl+77WOzb01N1zczcz2OpjvmHAAAA0EmW6ri4/6JOAAAQEUIAAEANaukC8G/c+9EWVNJZPnDDgfj1T99Sdc0rpffiyfk3WlQRAAAAtJfFujoBCAEAQIQQAACQ4L2LS/H73/tF1TWpa/bF4Kc+0KKKOsvDR25LXPPVp5NDGAAAANCJ6sgACAEAwB8TAgAAqvoXP3g1zl9YrLrmz3zu1ti/d0+LKuosX7j95vjQjQeqrvmXP3w9Su9ebFFFAAAA0D7q6gRwaWkbKwGA3UMIAACoqpar0B+q4Wp2KtvT2xNDCe/fxaXl+N3vvtKiigAAAKB9LJfLNa/VCQAALhMCAAA29eM33onvvLxQdc2v3HpjfOpDN7Soos40PPDhxDUnTv28BZUAAABAe1lcEgIAgHoJAQAAm5qeq6ELwD26AGzVbX3XxBduv6nqmh+9+lb84JU3W1QRAAAAtIel5XpCAMYBAECEEAAAsIml5XLMzFW/+nz/3t747c9+qEUVdbZaRiqcOJUcygAAAIBOslTPOIBLOgEAQIQQAACwiT984Uy8/taFqmt+8+5b4sar97Woos72lU/fEtcf2Ft1ze9+95V4/5KrGgAAAOgei3V1AhACAIAIIQAAYBO1XHVey9Xr1ObAvj3xZz53a9U1b72/GH/ww9daVBEAAADsvGXjAACgbkIAAMAGZ9++EPlnX6+65ra+q+Pz6epz7KlPLaGK6VPVRzQAAABAJ9EJAADqJwQAAGzwT777Slxaqr7JHh64LXp7e1pUUXe4+9Yb4pMfvKHqmm++9Eb8bOHdFlUEAAAAO6ueTgAXF5ejXK59PQB0KiEAAGCNcrmcOAqgpydiaODDLaqoe/T09MRDR5Lf15k53QAAAADoDvV0AojQDQAAIoQAAIB1vv/zN+OF19+uuuaLnzgUH0pd3aKKusuf+dytcdWe6r+izcz9PJbqPAgCAAAAu9FynVf2CwEAgBAAALDOV5+u3gUgIuLhGmbX05iD114Vg5/+QNU1r5Teiyfn32hRRQAAALBzFhPGFa53YXFpmyoBgN1DCAAAWPXexaX4/e//ouqag9fsi+ynDreoou5US8iilrAGAAAA7HZL9XYCuKQTAAAIAQAAq/75M6/G2xcWq675M3/i1ti/d0+LKupOX7j95vjQjQeqrvmXP3w9Su9ebFFFAAAAsDPqHYdnHAAACAEAAFc4cSr56vKHjALYdnt6e2Io4X2+uLQcv/vdV1pUEQAAAOyMxbpDAMYBAIAQAAAQERE/W3g3vvPyQtU1n/nwjfHJD97Qooq62/DAhxPXzBR+3oJKAAAAYOcs6wQAAHUTAgAAIiLi977/i8Q1w7oAtMxtfdfEff03VV3zg1feiuKZt1tUEQAAALRe3Z0ALgkBAIAQAAAQERG/nxAC2L+3N377sx9qUTVERDx8T3Lo4ve//2oLKgEAAICdUW8ngItLQgAAIAQAAMQLr5+P5147X3XN4Kc+EDdeva9FFRER8ZVP3xLXXrWn6prf+/4rUS7Xd0AEAAAAdov6OwEsbVMlALB7CAEAAIldACJCF4AdcGDfnvj1T99Sdc38mXfi2VerBzgAAABgt1quM/h+YVEnAAAQAgCALlculxNDANcf2Bv333moRRVxpVrCF79XQ4gDAAAAdqPFJSEAAKiXEAAAdLlnXnkzfnz23aprfuPTt8T+vdXb0rM9vnD7zZG6pvoYht///i+MBAAAAKAjLdXdCcA4AAAQAgCALlfTKIDPGQWwU67a2xu/efcHq655pfReFH5aak1BAAAA0EJLy/Vd2X/hkk4AACAEAABdbHm5HP/7v3q16pqbr7sq7k3f1KKKqOS3Pls9BBBRW5gDAAAAdpvFZeMAAKBeQgAA0MVO/eRcvPrm+1XX/Gu/8sHYu8evDDvpVz9+Uxy+fn/VNf/smVdjqc4DIwAAANDulusOARgHAACO6ANAF/u977+SuOa3PmsUwE7b09sTf+oz1T+HM+cvxHeKZ1tUEQAAALSGTgAAUD8hAADoUpeWluOfP/Na1TUfuvFADHzkYIsqoppaRgL8npEAAAAAdJi6OwFcEgIAACEAAOhST86fjYV3LlZd86c++6Ho7e1pUUVU87nbUnFb39VV1/yLH7wWF13xAAAAQAepvxOAcQAAIAQAAF3q976XfNX4bxsF0DZ6enritxJGArz53qX4xotnWlQRAAAAbL/lsnEAAFAvIQAA6ELvX1qKf/nD6qMAPn7ztfHpD93QooqoxW9/LjmUYSQAAAAAnWRxSQgAAOolBAAAXejx58/E+QuLVdf81mc/FD09RgG0k7tuuSHu+MB1VdfM/uj1eO+i1ocAAAB0hqV6OwFcsicGACEAAOhCv/+vahkF8MEWVEK9kkYCvHtxKU4+93qLqgEAAIDttbSsEwAA1EsIAAC6zDsXFuPks9VPEn/ygzfE7Yevb1FF1OO3PlvDSIDvGQkAAABAZ6g/BKATAAAIAQBAl8k/+3q8f6l6Kv63azjRzM742M3Xxmc+fGPVNY8/fybeev9SiyoCAACA7aMTAADUTwgAALpMLVeJ/6nPGAXQzpJCGheXluMPfvBai6oBAACA7bNYbwgg4cIHAOgGQgAA0EVK716MP3zxTNU1mY+k4ra+a1pUEY341z/zwejpqb7m9//Vq60pBgAAALbRsnEAAFA3IQAA6CJf+8FrcWmp+ua5lpnz7KwP3nh13POxvqprvvXSG3H27QstqggAAAC2R92dAIwDAAAhAADoJr//r6qPAujtuXyVOe0vaSTA0nI5/vkzugEAAACwuy2XhQAAoF5CAADQJRbeuRhPzZ+tuubz6Zvi8PUHWlQRW/Gbd98Se3qrzwT4Fz94rUXVAAAAwPZYTOhouN5FIQAAEAIAgG6R/9HrkdRBL+nqctrHTdftj1+7/eaqa77z8kIsvHOxRRUBAABA8y3V3QlgaZsqAYDdQwgAALrE135Y/arwvb098Rt339KiamiGP5UwumFpuRz5Z19vUTUAAADQfEtJVzSsc2FxOcp1BgcAoNMIAQBAFzj//qX45otvVF1zb/9NkbrmqhZVRDMMfuoDiSMB/sBIAAAAAHaxekMA5XLEpTpHCABApxECAIAu8NjzZ+LiUvWZeF/5tC4Au03qmqvi3vRNVdd848U34u0Liy2qCAAAAJqr3hBAhJEAACAEAABdIOlq8J6eiF//1AdaVA3N9JWEEQ4Xl5bjsedOt6gaAAAAaK7GQgDVL4QAgE4nBAAAHe79S0vx2PPVTwIPfORgHL7hQIsqopm+8qkPRE/1iQDxtR8aCQAAAMDuJAQAAPUTAgCADvfNF9+Idy9Wb4P3GwlXk9O+Dt9wIDIfOVh1zePPnY73L2mFCAAAwO6zuFz/Cf0L9sAAdDkhAADocLVcBf6VTwsB7Ga/kfD5vXNxKb710hstqgYAGpfL5aKnpyeKxeKO1lEsFiOXy0U+n2/osWNjYzE1NbUNlQFA92mgEYBOAAB0vb07XQAAsH0uLS1H/tnXq6751AdviNv6rmlRRWyHr3z6lvj//PNnq6752g9ei6Of/ECLKgKA+uTz+cjlcqsn/0ul0o7XMzU1FVNTU5FKpeKhhx6KwcHBSKfTkUqlIp1Or9a5sLAQhUIhnn766cjn81EoFCIiYnp6eie/BQDoGA11AhACAKDLCQEAQAf7o5cXovTupaprjALY/T5y0zXxyQ/eEM+++tama2affT0Wl5Zj7x6NoABoD8ViMSYnJ2NmZmbHr/yvplQqrQYCajU6OhpDQ0PbWBUAdI8GMgDGAQDQ9YQAAKCDfe0HyaMAhAA6w298+paqIYDSu5fij15eiPtuv7mFVQHAZaVSKYaHhyPi8sn/K0/6r1xdv9NX/zfL+Ph4jI6O7nQZANAxdAIAgPq5FAwAOtTycjn+4IfVQwDpm6+NTxy+rkUVsZ1qCXN8LeHnAQC2Uz6fj3w+HxER2Ww2xsfHY25uLubn56Ovr2+Hq9u6dDodc3NzAgAA0GRLjXQCEAIAoMvpBAAAHeq7PyvF6fMXqq75yt23RE9PT4sqYjvd8YHr4uM3Xxsvv/HOpmv+4Ievxf/ztz4dvb0+cwBaK5VKRblc3ukytkUmk4lHHnlE+38A2CZLDXUCMA4AgO4mBAAAHSqpC0DE5RbydIaenp74yqdvif/fE/Obrnn9rQvxvZ+XIvORgy2sDAB2r9nZ2Uin01EoFKJYLMbZs2cjIuKmm26KdDod2Ww2UqnUzhYJAB1uabn+IOGFSzoBANDdhAAAoAOVy+X42g+qhwA+eOOB+MyHb2xRRbTCb9xdPQQQEfEHP3hNCAAA6pBOpyOdTu90GQDQtRoKARgHAECX693pAgCA5nv21fPx04V3q675yqeNAug0n7n1xvjgjQeqrvnaD1/r2HbMAAAAdJ7FhkIAxgEA0N2EAACgA9U0CuBuowA6TW/v5ZEA1fzk7Lvx/OvnW1QRAAAAbM1yA0F2nQAA6HZCAADQgZJCAH3XXhX3fKyvRdXQSr/+6Q8krkkaFQEAAADtoqFOAJeEAADobrs+BDA1NRWDg4PR398fPT09cfDgwejv749cLheFQmGny1uVz+cjl8vFwMBAHDx4cE2tw8PDMTMzs9MlAtAhXn7jnXjutepXeg9+8gOxp9cogE70Jz/WFwev2Vd1jRAAAAAAu8HycjkamWhnHAAA3W7XhgDGxsaip6cncrnc6u3Z2dk4fvx4DA0NxdTUVAwMDER/f/+OhgEKhUIMDAzE4OBg5PP5OHLkSDzyyCMxOTkZDz30UEREzMzMxPDwcPT398fU1NSO1QpAZzAKoLvt3dMbg5+q3g3gudfOx4/feKdFFQEAAEBjlhpJAETEReMAAOhye3e6gHqVSqU4evRoFAqFSKVScfLkychkMmvWDA0Nxfj4eORyudUwwOTkZIyMjLS01pXXz2azMTc3t6HOFRMTEzE2NhbFYjFyuVyMj4/H7OxspNPpltYLQGdIusr7uv17477bb2pRNeyE37j7ljhx6udV1/zBD1+L3P39LaoIADpLsViMiIi+vr5IpVI7WwwAdLClBkYBRERcEAIAoMvtuk4AAwMDq1f2VzuxHhFrTvyvnJBvlZXXm5ycjNnZ2ap1jo6Oxvj4+OrtYrEYAwMDqwcVAKBWr775XnzvZ6Wqa7581+HYv3dPawpiR9zXf3Nct7961vNrNXSMAAB+aWJiIgYGBqKnpyf6+/ujv78/Dh48GAcPHmy7kYQA0CkaDwEYBwBAd9tVnQCGh4dXT4yPj4/XdKX85ORk5PP51avsjxw5UvWEfDPk8/mYmpqK8fHxmrsPjI6OxqOPPhqlUikiLnc8GB4ejrm5uW2sFIBO8y9/+HriGqMAOt+BfXviwbsOx+9//xebrvnuT0vx2pvvxy03HmhhZQCw+0xNTcXY2Fj09fWtdu87cuRIREScOnUqxsfHY2pqKqampmJkZCTGx8d3rDvAU089taXHP/PMM02qBACao9FxADoBANDtdk0IoFAoxMzMTEREpFKpGB0drfmxY2NjkcvlIiLi2LFj235ifeWq/rGxsfjqV78a4+Pjkc1mEx/30EMPrelWUCgUIp/P1/RYAIiI+Jc/qn519/69vXH/HYdaVA076Tc+fUvVEEBExOyPXou/eO/HWlMQAOxCY2NjUSgUNh0xmM1mI5vNro75m5qainw+H3NzczsSBLjvvvta/poAsJ2WlhoMAVwSAgCgu+2acQDHjh1b/ftDDz1U12Ov3KhfGSbYLvl8fs3rDQ4Orl7hX83AwMCG+6anp5tZGgAd7K33L8V3igtV13zpjkNxbUKbeDrDA3ceiqv2Vv9VL//s6RZVAwC7U6FQiLm5ucQuf6OjozE0NBQRvxzxBwBsXeOdAIwDAKC77YoQQLFYXDNbr5HN9JUjACYnJ5tSVyUr4wrWuzIYsJm+vr6anw8A1nvi+TOxmDAr7yufNgqgW1y7f2986RM3V13z1PzZeOfCYosqAoDdY2V/Pj09XfNIwZWugBGX9/LDw8PbUhsAdJOlhOMcmzEOAIButytCAOtP2jfSHn9lXl/E5RPytVyZ34h0Or0tzwsASfLPvl716709EV++63CLqqEdZD/5gapfv7i0HN948UyLqgGA3WNoaCjm5+dXr+6vRTqdXnNMYGZmpqYLAgCAzSVd7LAZIQAAut2u6Ae8vn1/pSvmk/T396+5feLEicR2fo0aGRmJqamp1dvpdLqmAweVrvoXKgCgFpeWluOx56q3dh/46MHou/aqFlVEO/jyJ5NDH/lnT8dv3P3BFlQDALtLI/vxbDa75njA+Ph4QxcyNOrJJ5/c0uOfeeaZyOVyTaoGALZuueEQgHEAAHS3tg8BlEqlDSfHU6lU3c+z/jFzc3NbqKq6ycnJGBwcjKeffjr6+/trDhvMz89vuG9wcLDZ5QHQgU79+Fy89X71tu5HE64Kp/Mcvv5AfPa2VHz/Z6VN13z9udOxtFyOPb09rSsMADrU4ODgmhDASifCRo5jNOLee+9tyesAQKs03Angkk4AAHS3th8HcOrUqTW3G904r+8esN0t+YaGhmJ8fLyubgPra6q1gwAAnEwYBRCR3BqezjSY0A1g4Z2L8b2fnWtRNQDQ2Sp1Dzhx4sQOVAIAnWHJOAAAaEjbhwAKhcKa242MAojYGB6o1Hp/JxWLxQ01TU5O7lA1AOwm5XI58gkhgI/ddE30H7q2RRXRTmrpADH7o+qjJACA2lS6cGE7OxECQKdrPARgHAAA3a3tQwDrW+Q3qxNARHsFAcbGxtbczmazLZ0bCMDuNX/mnfjx2Xerrsl+8gPR06Pdeze665br49bU1VXX1NJJAgBoTDsdewCA3UYnAABoTNuHABYWFrbtuUul0rY9dz3y+XzMzMys3s5mszE7O7uDFQGwmyR1AYio7WpwOlNPT09kE0YCvHj67fjJ2XdaVBEAtK9CoRADAwPR09MTAwMDdZ/Ar3QBwnYe1wCATtdwCOCSEAAA3W3vTheQZDtP1BeLxchkMtv2/LUoFAoxODi4entkZGTHxgA89dRTW3r8M88806RKAKhH0lXcN169L4587GCLqqEdZT/1gfiHT/2k6pr8s6fjr/7ax1tUEQC0p6NHj64eh1gJBJw7d25Lz9noWEMAIGKp3Pg4gHK5rCsiAF2r7UMAzUrMNzpGoNlKpVIsLCxEsViM6enpmJqaiojLV/+PjY3t6AiA++67b8deG4DGLLxzMeZ+Uv3A9AN3Hop9e9q++Q/b6Fc/flNct39vvH1hcdM1J599XQgAgK5WLBY3XIhQKpWiWCxGOp2u6TkqHcNol+MRALAbLS03dkX/cjlicbkc+/YIAQDQndo+BLB+A97MBH0rW/LlcrnVE/7rDQ0Nxfj4eM0HFQBgxWPPnY6kznhZowC63lV7e+P+Ow7FP3vm1U3X/NHLC/Hme5fixqv3tbAyAGgfm3UirOc4RKXnuOeeexqsCABYXGqsE0BExIXFZRdFANC1/B+wRcbHx2N2dnb1z/T0dIyPj0cmk4mZmZno7++PgYGBmJmZ2elSAdhF8gmjAPb29sT9dx5qUTW0s6OfPFz164vL5XjihTMtqgYA2k+lYP7o6GhdV/IXi8UN9w0NDW2lLADoao2OA4iIuHBpqYmVAMDu0vadADpFKpWq2Op/dHQ0ZmZmYnh4OAqFQgwPD0cmk4np6WmdAQCo6sLiUvxhwknbX033xQ0HXNlNxIN3Ho7enqjaOSL/o9fjtz/7odYVBQBtJJVKre7Dx8bG4siRI5HJZOp6jqeffnrN7XQ6bW8PAFuwlNT+sIoLi42NEgCATiAE0AaGhoZidnY2BgcHIyKiUCjEwMBAnDx5su4DDlvx5JNPbunxzzzzTORyuSZVA0CSbxcX4p2L1VPtR+8yCoDLDl57VRz5aF/80Y83H4f0+POn49KSdokAdI6xsbHI5/ORTqdrGsM3NDQUExMT8dBDD9XVAWDF+u5+4+PjdT8HAPBLQgAA0Ji2DwE0sumupNJcvnrm+m23bDYb2Ww28vl8RFyud2BgIObn51t21cC9997bktcBoDlOJowCiIjIflIIgF86+snDVUMAb72/GE//eCHu67+5hVUBwEYLC5v//6pWg4ODq3vsQqEQMzMziXvsRx55JCYmJmJsbCwmJyfrer18Pr9mHEAmkzEKAAC2aCshgItCAAB0sV13mVczDgS0q7GxsQ33rXQHAIArlcvlyP+oegjgjg9cFx+56ZoWVcRukP1Ucijk5LOnW1AJAKy1fq9fKchfj2KxuBoAuNL6K/XXS6VSMT4+HlNTUzE1NVXXa17ZGS+VSsXJkyfrejwAsNHWOgFU754IAJ2s7UMA23kVfLvN5ctmsxs6HxSLxboPPADQ+Z599Xz84s33q67RBYD1+g9dFx+/+dqqa/LPvh7lcuMHWQCgXhMTExtO+j/66KNbDgJUcvbs2cQ1o6Ojkc1mI5fL1bwfHxwcXO0CsBIAaFZnQwDoZsYBAEBj2j4EsL5lf6MHASp1EGjHDfmRI0c23FdvC0IAOl++hlEAR4UAqCD7ycNVv/6Ts+/G/Jm3W1QNAN1kbGwsBgcHV/8MDAxET09Pxa54hUIhDh48GP39/TEwMLDmcbUcF0in05HJZDbc//DDD9dU6+zs7GoQYGBgIAqFQsV1+Xw++vv7V7sOpNPpmJubq/jaAED9lrYQUr9wSQgAgO61d6cLSNLf37/mdqPjACodJFgfMGgHlboTFAqFKJVKbRlaAGBnnEwIAdx83VXxudtSrSmGXeXoJz8Qx7/xctU1sz86Hbcfvr5FFQHQLQqFQuTz+dW9bV9fX00d+orF4upV9qVSKRYWFmraH588eTKGh4cjn89HOp2OycnJuk7Oz87OxsTERIyNjcXAwMBqsKCvry8WFhaiUCisufr/kUceidHR0ZqfHwBIZhwAADSm7UMAzUrPr2zMV6RSqW05qT4zMxNjY2NRLBYjk8nE8ePH6/oeNqtp5fkA4PW33o/v//zNqmsevPNw7OntaVFF7CZHPnowbrx6X7z53qVN15x89vX4aw/0b/p1AGjE7OxsS18vlUpt+TVHR0djZGQkTpw4EdPT06sn/lOpVPT19cXQ0FA8/PDDMTQ01KSqAYArGQcAAI1p+xDA+vb4jY4DWD/3L5vNNlrSpgqFQgwPD6+5ffTo0Xj55ZdrDhzcdNNNTa8LgM7y9edOJ67JfsooACrbu6c3HrzzUPzu936x6Zq5n56Ls29fiJuu29/CygCgPaVSqRgZGYmRkZGdLgUAus6iTgAA0JDenS4gSSqV2tAecP1V/bVY/5h77rlnS3VV8tWvfnXDfaVSKU6cOFHzc6wPK6yopUUiAN0h/6PqowCu2tsbX/zEzS2qht0oKSRSLkc89vyZFlUDAAAAlW2pE8AlnQAA6F5tHwKI2HjVfiMhgPUdBLajVV8jda23WaeD7RhdAMDu897FpfjmS29UXfOF/pvimqvavtkPO+hLdxyKvQnjIk4+Wz1sAgAAANvNOAAAaMyuCAGMjY2tuV0oFOp+jlOnTq3+PZPJbMuV9Zs9Zz2jB66sc4XZggCs+OZLbyRuYo9+0igAqrvhwL741XRf1TVPvHBG60QAAAB21NZCAPa0AHSvXRECSKfTa06kz87O1vX4YrG45gr7XC5X82PHxsZiYGAghoeHE6/0HxwcXHM7lUrF9PR0XYGDSgGHRx55pObHA9DZvv5c8tXZRz95uAWVsNtlE8Ii715ciu8UF1pUDQAAAGxkHAAANGZXhAAi1nYDyOfzm7bNr2RycnL17+l0OkZGRmp63ODgYExMTEShUIiZmZno7++vGgTIZrOrJ/ynp6fj3LlzdV3FPzMzs+G+oaGhyGQyNT8HAJ2rXC7HY89Vn9N+9603xAdvvLpFFbGbJYUAIiIee/50CyoBAACAyowDAIDG7JoQQDabXXNC/dFHH63pcaVSKaamplZvXxkIqKZYLEY+n99wf6UT9Vdaef5jx47VFVSI2Pg9pVKpOH78eF3PAUDnevbV8/HaW+9XXXP0LqMAqM1tfdfEHR+4ruqax54TAgAAAGDnLJWNAwCARuyaEEBExPHjx1evtF+5Qj/JlSfjR0dH14wVaMTZs2erfj2bzcb4+HiUSqUYGBioGCSoZGxsbM33k0qlYm5uLlKp1FbKBaCD1HJV9pfvMgqA2j2Y8PPy47PvRvHM2y2qBgAAANbSCQAAGrOrQgArJ8ZX2uMPDAxsemV+qVSK4eHh1a+Pjo7G+Ph4za+VTqcrtuF/+OGHEx87Ojoa09PTUSwWY3BwMAYHBzcNA5RKpcjlcjExMbF6XyaTiZdffnk18AAAERFfT7gq++brropfufXGFlVDJ3jwzuTQSNLPHQAAAGyXLYUALgkBANC99u50AfVaCQJMTEzE2NhYDA8PRyaTiVwuF+l0OkqlUjz99NMxNTUVpVIp0ul0TE5ONtQB4OTJkzE8PBz5fH71eSoFAyoZGhqKc+fOxbFjx2JmZmY1BJDNZldP7p86dWrD1f/j4+MxMjJSd60AdLZz71yM7/70XNU1999xOHp7e1pUEZ1g4KMH4/oDe+P8+4ubrnn8+TPxb31RMBEAAIDWW9xSJwDjAADoXrsuBLBidHQ0RkZG4sSJEzE9PR3j4+NRLBYjlUpFX19fPPTQQ5HL5Wo+aV9JKpWK2dnZLT1+eno6SqVSnDhxImZnZ6NQKMSpU6eiVCpFKpWKTCYTR44cieHh4S2PKgCgc/3hi2ciad9rFAD12renN750x6H4Z//q1U3XfOfls/H2hcW4bv+u/bURAACAXWppufGr+Y0DAKCb7eqjualUKkZGRtr+yvndUicA7SupJfue3p744h03t6gaOsmX7zxcNQRwaakc33zxjfiNu29pYVUAAAAQsbSF8/hCAAB0s96dLgAAqG5puRxPvHCm6pojHz0YNxzY16KK6CT333koehKmSDyWEEIBAACA7bC1TgDGAQDQvYQAAKDNfe9n56L07qWqa4wCoFE3X7c/PvPhVNU1jz1/OsrlxucwAgAAQCO21Angkk4AAHQvIQAAaHNJowAihADYmi/fWf3n5/T5C/HDX7zVomoAAADgsq10Ari4lQQBAOxyQgAA0OYee676KIBbU1fH7Yeva1E1dKJaQiRGAgAAANBqS1voSqcTAADdTAgAANrYa2++Hz96tfoV2F++63D0JA11hyo+/aEb4tD1+6uu+frzQgAAAAC01tLyFkIAi0tNrAQAdhchAABoY4/VcOLVKAC2qre3Jx6441DVNd/7WSkW3rnYoooAAABgqyEAnQAA6F5CAADQxr6e0IJ9/97euLf/phZVQydLCpOUyxFPvKAbAAAAAK2zKAQAAA0RAgCANnVhcSm+9dIbVdfc139THNi3p0UV0cl+7RM3x7491cdKfP25My2qBgAAACKWtxICuGQcAADdSwgAANrUH728EO9erL5hNQqAZrn+wL6452N9Vdc88fzpWFxyJQUAAACtoRMAADRGCAAA2lTSKICIiAfuFAKgeR5M+Hl66/3F+O7PSq0pBgAAgK63tIUQwOJyWZAdgK4lBAAAberx56u3Xv/E4evitr5rWlQN3eDBGjpL1BJOAQAAgGbYSgggIuKiEAAAXUoIAADa0MtvvBMvv/FO1TVGAdBs/YeujY8kBEseEwIAAACgRbYaArhwSQgAgO4kBAAAbaiWq61ruWob6tHT05MYLnnutfPxSum9FlUEAABAN1sqbzEEsCgEAEB3EgIAgDb0+PPVQwDXH9gbAx892KJq6CYP3HkocU3SzycAAAA0w5Y7ASwuNakSANhdhAAAoM28c2ExvlNcqLrmS584FPv2+N84zff59E1x9b49VdcYCQAAAEArbD0EoBMAAN3J2QMAaDPffOmNuLhUfZNqFADb5cC+PfGF22+quuZbL52N9y+5mgIAAIDttbjVEMAlIQAAupMQAAC0maSrrHt6amvZDo1KCpm8d2kpvl0826JqAAAA6FbLxgEAQEOEAACgjZTL5XgsYd76Zz6cipuv29+iiuhGD9yZ3Gni8efPtKASAAAAutmWOwEYBwBAlxICAIA28qNX34rX37pQdc2DugCwzW5NXR133XJ91TVff+50lMtbOxgDAAAA1Sxvcd+pEwAA3UoIAADaSC1XV385oVU7NEPSSICfLrwbL7/xTouqAQAAoBstLm0xBHBJJwAAupMQAAC0kccTRgHcfN3+uPtDN7aoGrpZLWGTx4wEAAAAYBstGQcAAA0RAgCANvHme5ei8NNS1TX333Eoent7WlMQXe1P3JaKGw7srbomKbQCAAAAW7FkHAAANEQIAADaxDdffCMx4f7gXYdaVA3dbu+e3vjiHdV/3r7z8kK8d9EBFQAAALbHVjsBXNQJAIAuJQQAAG3isYSrqnt7Ir54uxAArfNAQgjg4uJyPFV8o0XVAAAA0G2MAwCAxggBAEAbWF4uxxMvVJ+vnvnIwbjxmn0tqggi7r8zOXTy2HPVf24BAACgUUIAANAYIQAAaAM/evWtOHP+QtU1D951uEXVwGWHrz8Qn/7QDVXXPP7C6ShvcUYjAAAAVLLlEMAlI+wA6E5CAADQBh5PGAUQEXF/Qmt22A4P3lk9fPKzhfei+MY7LaoGAACAbrKoEwAANEQIAADawOPPV2+pfuj6/YlXZMN2eKCmkQDJIRYAAACo1/IWO88JAQDQrYQAAGCHvfnupSj89FzVNQ/ccSh6enpaVBH80uduS8UNB/ZWXfPEC9VDLAAAANCIxaWtncS/sGgcAADdSQgAAHbYN146E0nd7R5IaMkO22Xvnt74UsIoiu8UF+Ldi4stqggAAIBusbTVcQCXdAIAoDsJAQDADnvsuepXUe/p7Ylf+8TNLaoGNkoKoVxcWo6n5s+2qBoAAAC6xZJxAADQECEAANhBy8vlxFbqAx85GDdeva9FFcFG9yd0AoiIeOz50y2oBAAAgG6y5U4AxgEA0KWEAABgB/3o1bfijbcvVF1z/53JJ2BhOx26fn/cfesNVdc8/vyZKG/xCg0AAAC4UlII4Op9e6p+XScAALqVEAAA7KDHnku+evoBIQDawIMJIwF+fu69mD/zTouqAQAAoNOVy+VIagRwzVUJIYBLQgAAdCchAADYQY8njAI4fP3++NQHq1+BDa1QSxjlcSMBAAAAaJJaRgFcsz+pE4BxAAB0JyEAANghpXcvxnd/eq7qmgfuPBQ9PT0tqgg297nbDsaNV++ruubx56uHWgAAAKBWi7WEAPbtrfp14wAA6FZCAACwQ/7wxTcS29o9kNCCHVplT29PfOmO6t0A/ujlhXjnwmKLKgIAAKCTLZeb0QlACACA7iQEAAA7JKl1+p7envjC7Te3qBpI9kBCCODi0nI8NX+2RdUAAADQyWrpBHDtVQmdAC4ZBwBAdxICAIAdsLxcjj98oXrr9IGPJrdfh1ZK6gQQEfFYQrgFAAAAarFcQwjg6qt0AgCASoQAAGAH/OAXb8Ybb1+suuaBO5NPuEIrHbp+f/zKrTdWXfP482eiXEPLRgAAAKimtk4AQgAAUIkQAADsgMefr94FICLigTsOt6ASqM+DCeGUV0rvxfyZt1tUDQAAAJ1qqaZOAAnjABaNAwCgOwkBAMAOeDyhZfoHbtgfn/zg9S2qBmp3/53J4ZRaQi4AAABQTS0hgKROAJeWyjU9DwB0GiEAAGixc+9cjO/+rFR1zQN3HI6enp7WFAR1+NxtqUhds6/qmscSQi4AAACQpJaT99ckhAAiIi4aCQBAFxICAIAW+8MXz0TSyPQHElquw07Z09sTX/pE9Z/Pp18+F+9cWGxRRQAAAHSimkIA+6uPA4gQAgCgOwkBAECLPZHQKn1vb0984RM3t6gaqF9SSOXi0nI8OX+2RdUAAADQiRab1AngwuJSM8oBgF1FCAAAWmh5uRxPvFA9BDDw0YNxw4Hq7dZhJ33pjuROFUYCAAAAsBXLSW0UI+Kaq5I7AVzQCQCALiQEAAAt9Mwrb8bZdy5WXfPAnYdbVA005ubr9sdnPnxj1TVPPH8myjUcsAEAAIBKFpd0AgCARgkBAEALPZ4wCiAiudU6tIOksMorpffipdNvt6gaAAAAOk1tnQCSQwDvX9IJAIDuIwQAAC30+AvVW6TfcsOBuOuW61tUDTSulrBKLaEXAAAAqGRxOTkEcO1+4wAAoBIhAABokXPvXIzv/axUdc0Ddx6Knp6e1hQEW/DZD6fi4DX7qq5JCr0AAADAZpaWk0/eX73POAAAqEQIAABa5A9fPBNJneyMAmC32NPbE1/8RPWf16dfPhfvXFhsUUUAAAB0kqUaLuDXCQAAKhMCAIAWeSKhNfre3p74wu03t6ga2Lqk0MrFpeV4cv5si6oBAACgkyzW0Angmqtq6ARwSQgAgO4jBAAALbC8XI4nXqgeAhj46MG4/kD19urQTr50R3LnisefNxIAAACA+tWQAYj9e3sjaaqicQAAdCMhAABogR/84s04+87FqmvuNwqAXebm6/bHZz58Y9U1jz9/JspJczAAAABgnVo6Aezp7Yn9e6uf5jAOAIBuJAQAAC3weMIogIiIB+443IJKoLkeSOgG8ErpvZg/83aLqgEAAKBTLNcQKN/b2xv791YfCSAEAEA3EgIAgBZIaon+gRv2xyc/eH2LqoHmuf/O5PBKLSEYAAAAuNLiUnIIoLc3kjsBXDIOAIDuIwQAANus9O7F+N7PSlXX3H/HoehJGmIHbehzt6Uidc2+qmuEAAAAAKhXzZ0A9hkHAADrCQEAwDb7xotvxHLCvvWBGq6mhna0p7cnvviJ6iMB/ujlhXjnwmKLKgIAAKATLCYdTImI3p4wDgAAKhACAIBtlnQV9J7envjC7Te3qBpovgfuqB4CuLi0HE/Nn21RNQAAAHSCpYQQwJ7enujp6UkeB7BoHAAA3UcIAAC20fJyOZ54oXoIYOAjB+PGq6u3U4d29qWEEEBExOMvnG5BJQAAAHSKWkIAEZEcArikEwAA3UcIAAC20Y9efSveePtC1TX335l8AhXa2aHr98ev3Hpj1TWPP38myjXMcwQAAICI5HEAe3pWQgDGAQDAekIAALCNHn8++ernB4QA6ABJP8c/P/dezJ95p0XVAAAAsNstJ4QA9q50AthnHAAArCcEAADb6PHnq48COHz9/vjUB29oUTWwfWoJs9QSigEAAICI5E4AvbWOA9AJAIAuJAQAANvkzXcvReGn56quuf+OQ9Hzx+3rYDf73G0H48ar91Vd88QL1UMxAAAAsGI5YaTcaieAhHEAF4UAAOhCQgAAsE2+8dKZSAitxwN3Hm5NMbDN9vT2xBc/cXPVNd8pLsS7FxdbVBEAAAC72eKSTgAA0CghAADYJkmjAPb09sSvJZw0hd0kKdRycWk5npo/26JqAAAA2M1q7gSwLyEEcGmpaTUBwG4hBAAA22B5uZzY+jzzkVRi+3TYTe6/41DimqRwDAAAAERELCa0V+ztqW0cgE4AAHQjIQAA2AY/evWtOHP+QtU1RgHQaQ5dvz/uvvWGqmsef+F0lBOu5gAAAIClhBDA3j3GAQDAZoQAAGAbJHUBiKjtqmnYbR64o3q45WcL70XxjXdaVA0AAAC7VVIIYE9vrZ0AjAMAoPsIAQDANnj8+dNVv37o+v3x6Q9Vv2IadqMH7jQSAAAAgK1LDAGsjAPYl9AJ4JJOAAB0HyEAAGiyN9+7FIWflqquuf+OQ9Hzx5tV6CSfuy0VNxzYW3VNUkgGAAAAau8EYBwAAKwnBAAATfbNF99I3KjWcrU07EZ79/TGFxNGXXzn5YV476J2jAAAAGxu0TgAAGiYEAAANFnSVc69PRFfvF0IgM71QEII4OLicjxVfKNF1QAAALAbLZerhwD26gQAAJsSAgCAJiqXy/H4C9XnnWc+cjBuvGZfiyqC1ru/hk4Xjz9f/d8JAAAA3W1xqXoIoHclBLCv+mmOi4vLUU4IFABApxECAIAm+uEv3ooz5y9UXWMUAJ3u8PUH4tMfuqHqmq8/d9pBGAAAADZVayeAq/Ykn+bQDQCAbiMEAABNlDQKICLigTsPt6AS2FlJYZefn3sv5s+806JqAAAA2G0Wl6ufuO/tWekEsCfxuYQAAOg2QgAA0ERJLc4PXb8/PvXB6ldIQyd4sIawSy2hGQAAALrTUsJ5+717/jgEsLeWTgBLzSgJAHYNIQAAaJLSuxej8NNzVdc8cMeh1Zl10Mk+d1sqbrx6X9U1SaEZAAAAutdSrZ0AagkBXNIJAIDuIgQAAE3yhy++EcsJI86NAqBb7N3TG1/8xM1V1/zRywvxzoXFFlUEAADAbpLYCaB3JQRgHAAArCcEAABNktTafE9vT/xawklR6CRJIwEuLi3Hk/NnW1QNAAAAu0lSJ4A9vZdPb+zfZxwAAKwnBAAATbC8XI4nElqbD3z0YGJ7dOgk9995KHHNYwnhGQAAALrTYkK7xT1/fHajpnEAOgEA0GWEAACgCZ555c04+87FqmseqOGEKHSSm6/bH5/58I1V1zz+3OkolxPmaAAAANB1lhP2intXOgHUMg7gkhAAAN1FCAAAmuDxhC4AEcmt0aETPZDwc/+LN9+PF0+/3aJqAAAA2C0Wl6qHAHp7eyLCOAAAqEQIAACaIKml+S03HIi7brm+RdVA+6ilA8ZjzxkJAAAAwFrJnQD+OARQwziAi8YBANBlhAAAYIvOvn0hvv/zUtU1D9x5KHp6elpTELSRz344FQev2Vd1TVKIBgAAgO6zuJzQCeCPj7NctaeWTgBCAAB0FyEAANiib7z4RiSNNE9qiQ6dak9vT9x/R/VuAKd+fC7Ov3+pRRUBAACwGywlhABWOgH09PQkdgMQAgCg2wgBAMAWJV3FvG9PT3zh9ptaVA20n6QQzOJyOb710hstqgYAAIDdICkE0Nv7y46LySGApabUBAC7hRAAAGzB0nI5nnjhTNU193ysL64/UL0dOnSyL91xKJKmYTz2XPV/RwAAAHSXWjsBRETs37en6toLl3QCAKC7CAEAwBZ8/+elKL1bvY35A3dWb4UOna7v2qvic7elqq55/IXTUU6aqwEAAEDXSAoB7KmrE4AQAADdRQgAALbg8eeqjwKIiHgwoRU6dIMH7qj+7+D1ty7Es6+eb1E1AAAAtLulhKB4fSEA4wAA6C5CAACwBY89X72F+a2pq+P2w9e1qBpoXw/eldwR47Hnk0M1AAAAdIe6xgHsTRgHoBMAAF1GCAAAGnTm/IV45pU3q6554M5D0ZM0DB26wN0fujFuvu6qqmueSAjVAAAA0D0Wl6qHAHqvDAHsS+gEcEkIAIDuIgQAAA164oXkE5ZGAcBlvb098aU7qncDmPvpuXjz3UstqggAAIB2tpwwDmCvcQAAsCkhAABoUFLr8qv29MZ9t9/Uomqg/SWFYpaWy/GNl3QDAAAAIGIxYRxAb49xAACwGSEAAGjA4tJyfCOhE8Cvpvvimqv2tqgiaH9f+sSh6E2YjvG4kQAAAABExHJCCKC+TgBCAAB0FyEAAGjAd39WirfeX6y65gGjAGCNG6/ZF5mPHKy65vHnzyQe6AEAAKDzJXYCuDIEsK96J4D3LxkHAEB3EQIAgAY89lz1UQAREQ/eWX3+OXSjB++qHo554+0L8cNfvNWiagBoN7lcLnp6eqJYLO50KRtMTU3F4OBg9Pf3R09PTxw8eDD6+/sjl8tFoVDY6fIAoOMs1dEJ4NqrqocAFt652JSaAGC3EAIAgAYktSz/SN818fGbr21RNbB73H9Hcjjm8eeTQzYAdJZ8Ph/9/f0xNTUVERGlUmlnC7rC2NhY9PT0RC6XW709Ozsbx48fj6GhoZiamoqBgYHo7+8XBgCAJkoKAey5IgRw6Pr9VdeePv9+U2oCgN3CoGIAqNNrb74fP3q1+pXKD955KHp6EoafQxf69IduiMPX74/T5y9suuax50/Hv3P0Ey2sCoCdUCwWY3JyMmZmZtryyv9SqRRHjx6NQqEQqVQqTp48GZlMZs2aoaGhGB8fj1wutxoGmJycjJGRkR2qGgA6x1K59hDA4aQQwFsXolwuO1YDQNcQAgCAOj3xQvJVyg8ktDyHbtXT0xMP3HkoTpz6+aZrvvuzUpx752IcvPaqFlYGwHYqlUoxPDwcEZdP/l950j+dTkcqlWqrq/8jIgYGBlbrnJubi3Q6venaycnJiLg8MmClY4AgAABsTT3jAA5df6Dq2guLy3H+wmLccGBfU2oDgHZnHAAA1Omx56qPAti/tzfuTd/Uompg93ngzuohmXI54g9frP7vDIDdJ5/PRz6fj4iIbDYb4+PjMTc3F/Pz89HX17fD1a01PDy8GgAYHx+vGgBYMTk5uboul8sZDQAAW7S4tFz1671XdgK4oXongIjL3QAAoFvoBAAAdbiwuBTfSDg5eW//TXFg354WVQS7z6994ubY09tT9aqOk8+ejj/9uVtbWBUA2ymVSkU5oaVvuygUCjEzMxMRl+seHR2t+bFjY2OrnQCOHTsWc3Nz21IjAHSDhEYAazoBJI0DiIg4ff79uP3wdVstCwB2BZ0AAKAOT798Lt65uFR1zYMJVzlDt7vhwL448tGDVdc88cKZxKs+AGA7HDt2bPXvDz30UF2PvXIEwJVhAgCgfovLCZ0Aeq4cB5AcAjhzXicAALqHEAAA1OHrz51OXPPlu4QAIEnSv5M337sU3/1ZqTXFAMAfKxaLa9r4DwwM1P0cmUxm9e+Tk5NNqQsAulFCBiD27vllCGD/3j2RumZf1fXGAQDQTXZ9CGBqaioGBwejv78/enp64uDBg9Hf39928/dmZmZieHg4+vv74+DBg6u1DgwMxNjY2OpcRADa29efe73q1z9x+Lq4re+aFlUDu9fRTyaHZWoJ3QBAM60/aZ/NZut+jiNHjqz+PZ/PR6lU2mpZANCV6ukEEJE8EuD0+fe3XBMA7Ba7NgQwNjYWPT09q7P2xsbGYnZ2No4fPx5DQ0MxNTUVAwMD0d/fv6NhgKmpqTh48GAMDw+vtgFMp9ORTqejVCpFoVCIiYmJ1SDD1NTUjtUKQHXFM2/Hj8++W3WNLgBQm/5D18VtfVdXXfP1Z4UAAGit9e37+/r66n6O/v7+NbdPnDixpZoAoBuVy+VYLldfs7d37emNw9cfqLr+tHEAAHSRXRcCKJVKMTAwEBMTE5FKpWJubi5mZ2djZGQkstlsDA0Nxfj4eJTL5RgZGYlisRgDAwM7cnJ9eHg4crlc9PX1xfT0dJTL5Zifn4+5ubmYn5+Pc+fOxfj4+Or6YrEYuVwuBgcHXSkA0IZquSr5QSEAqElPT098+c7q/16ef/18vFJ6r0UVAdDtSqVSFIvFNfelUqm6n2f9Y+bm5rZQFQB0p6WkBEBE7Fl3diOxE4BxAAB0kV0XAhgYGFi9sn9ubm7NrL31JicnY2RkJCIicrlcS4MAg4ODMTMzEyMjIzE/Px9DQ0Mb1qRSqRgdHY1z585FOp1evT+fz8fAwIAgAECbSQoBXH9gbwx89GCLqoHdr5bQjJEAALTKqVOn1txuJAAQsbF7gPF/AFC/pXItIYC1pzcO3WAcAACs2FUhgOHh4dVU/vj4+JoT55uZnJxcXZfL5VoyGmBsbCzy+XyMjIxsmCdYSSqVitnZ2TX3FYvFOHr06HaVCECdzr9/Kf7o5YWqa+6/41DsWx9DBzb1+fRNcfW+PVXXPCYEAECLrD9e0MgogIiN4YH13QUAgGSNdQIwDgAAVuyaMxWFQmF1Nt/KFfS1GhsbW/37sWPHml7blUqlUkxMTEQ6na4pALAinU5v+J4KhUJMTEw0u0QAGvDNF9+IxYQN6JeNAoC6HNi3J75w+81V13zrpTfivYtLLaoIgG42Pz+/5nazOgFECAIAQL1qCwGsPb2RNA7g/PuL8f4l+0sAusOuCQFcefL+oYcequuxKyMBItaGCbbDSuCgngDAikceeWTT5wNgZyW1JO/pudwJAKhPUnjmwuJyPFV8o0XVANDNFhaqd33aCuP+AKA+tYQA9vb2rLl9KCEEEBFx+i3dAADoDnt3uoBaFIvFNW35BgYG6n6OTCaz+hyTk5MxNDTUtPqudOLEiYi4fPL+yJEjMTY2VtPYgojLVxkMDQ1tCCnMzMxsW70AJFteLsdjz1cPAfyJ21Jx03XJm01grVo6aHz9udPx5bs+0IJqAOhm23mivlgsRiaT2bbnX/HUU09t6fHPPPNMkyoBgK1J6sYYEdHbszYEkNQJICLi9Pn34yM3XdNwXQCwW+yKEMD6q+qz2Wzdz3HkyJHVEEA+n49SqdRwa7/NlEql1YMGhUIhCoVCTE1Nxblz52p+rUqBgdnZWSEAgB30zCtvxhtvX6y6xigAaMwtNx6IT33whvjRq29tuuax585EuVyOnnUHeACgmZrVCaDZxxrqcd999+3YawNAMy3X0glgz7oQwA0HEh9z5rxOAAB0h10xDmD9lfGV5usl6e/vX3N75Yr9Ztpsxt/U1FTNz7G+zmrPC0BrJI0CiIh4UAgAGpYUonml9F48//r5FlUDQLda3wmgkWMPm9nOUQMA0Ika6QRw3f69cc1Ve6o+5rQQAABdou1DAKVSacNJ8EZS9esfMzc3t4WqanuNRlTqBOBgAcDOSgoB3HLD5SuZgcbUEqKpJYwDAABAZ1iqpRNA78ZucUkjAU6ff7/hmgBgN2n7EMCpU6fW3G70RPv6BH8+n2+0pE2l0+mKJ/HraeW/nTMIAajf6bfej2deebPqmgfvOqxNOWzB525LRd+1V1Vd85gQAAAAQNeoJQSwp2IIoPpIgNNv6QQAQHfYu9MFJCkUCmtuN9qOb314YLta7M/NzcXw8HDk8/lIp9MxOTlZMRiwmUp11fN4AJrr8efPJK5JamUOVLentyceuONQ/G/ffWXTNXM/OReldy9G6prqYQEA6GZPPvnklh7/zDPPRC6Xa1I1ANC4pXJjIYBDNyR1AhACAKA7tH0IYH5+fs3tZnUCiLh8wr3ZJ9hTqVTMzs42/Pinn356w32Dg4NbKQmALUhqQX7V3t74wu03taga6FwP3nW4aghguRzxxAtn4k9/7tYWVgVAN2nGiL+Iyh3+Gr2goV733ntvS14HALZb450AhAAAIGIXjANYWFjYtudux9b7lcYUZLPZHagEgAuLS/GNF6t3Avh8+qa45qq2z9RB2/vSHYcqHsC5UlIoBwCaaTuPRwAA1W3XOIAz599vuCYA2E3a/qzFdp6oLxaLkclktu356zUzM7Ph+x0aGmrZOICnnnpqS49/5plnmlQJQHt4+uVz8c7FpaprjhoFAE1x49X74shHD8Z3Xt78hMsTL5yJpeVyYlgAABqRTqc3jCRs5nMDALWrJQSwt4FOAGffuRiLS8uxd0/bXx8JAFvS9iGAZiXvm9XWbztNTk5uuG98fLxlr3/fffe17LUAdoNarjr+shAANM2X7zpcNQRQevdSfPen5+LIx1rTUhmA7rK+ZX+jFyVUOo6xG45JAEA7WawhBNDbUyEEcEP1EEC5HPHG2xfjlhurdwwAgN2u7eNu6zfdzZyj106t/QqFwoZRAJOTk64WANhBX3/u9apfv/3wdXFb3zUtqgY6Xy2hmpNGAgCwTfr7+9fcbvSYQaXwQDOPZQBAN6ipE8Ce+scBREScNhIAgC7Q9iGAbnHs2LE1t4eGhmJkZGSHqgGgeObt+PHZd6uuMQoAmutysObqqmseEwIAYJs0a1xgsVhcczuVSukEAAB1qiUEsKdCJ4BDCeMAIiJOv3WhoZoAYDcRAmgDU1NTa+YOZrPZmJ6e3sGKAKhlFMCDQgDQVD09PfHlO6v/u3rutfPxSum9FlUEQDc5cuTImtuNjgM4e/bsmtvZbLbRkgCga9UUAujdGAI4eM2+2FehQ8CVTp8XAgCg8+3d6QK6XbFYjLGxsdXbmUwmZmdnd6SWJ598ckuPf+aZZyKXyzWpGoCd9djz1UMA1x/YGwMfPdiiaqB7PHjX4fiHT/2k6prHnjsdf+HzH21RRQB0i1QqFel0es2V/MVise4xfes7Adxzzz1NqQ8AukmjIYCenp44dN3++MWbm7f8PyMEAEAXaPsQQLNa5rXrTL7h4eHV2jKZTMzNze1YLffee++OvTZAOzn//qX4TrH6DNgv3XEo9u3RUAea7fPpm+LqfXvivUtLm675uhAAANskm83G1NTU6u1GQgDrjz8MDQ01ozQA6CpL5cZCABERh244UDUEcPr85l8DgE6x685eLCxUPymzmwwPD6+OAchmszsaAADgl77x4huxmJA4P2oUAGyLA/v2xBduv7nqmm+99Ea8d3HzkAAANOrKTn0RsWZ0X61OnTq1+vdMJlN3iAAAiFhaXk5cs1kI4PD1+6s+zjgAALpB24cAtnOzvJMb8YmJiZiZmYmIy1cF7NQIAAA2yj/7etWv9/RE3H/HoRZVA93nywkhmwuLy/Gtl95oUTUA7GZjY2MxMDAQw8PDG9r0V5JOpyObza7ernevXiwW13QCMDIPABqzlJwBEAIAgCraPgSwvmV/pbb+tajUQaBZowbqNTMzs3p1wcjISExPT+9IHQBstLi0HI89d7rqms/dloqbrqu+oQQalxQCiEgO6wCwuzWjC+Dg4GBMTExEoVCImZmZ6O/vrykIcGU3gHw+X9dxiMnJydW/p9PpGBkZqatmAOCymjoB9GwWAjhQ9XFn3jIOAIDO1/YhgP7+/jW3Gz0QUGnTvj5g0Ar5fD6Gh4cjImJ0dHTNAQIAdl7hp6U49+6lqmuyn/xAi6qB7nTLjQfi7ltvqLom/+zpWE4Y2wHA7rF+r9/oBQArisVi5PP5DfevdOSrJpvNxtDQ0OrtRx99tKbXLJVKMTU1tXrbfh8AGrelTgA3VL9w48zbF6Jctp8EoLO1fQggk8k05XnWp/1TqVTLOwEUi8UYHByMiMsHA8bHx1v6+gAkq+Xq4sFPCQHAdksK27zx9oX4/s9LrSkGgG01MTGx4aT/o48+uuUgQCVnz56tad3x48dXRwiudBNIcuzYsdWaR0dH14wVAADqs5jQCWBPb0/0bNoJoHoI4NJSOfECEADY7fbudAFJjhw5suZ2owcB1m/0W70ZL5VKMTAwEBER09PTa64qqGZqairm5+cFBgBaJCkEcFvf1fGJw9e1qBroXtlPfiD+y/yLVdecfPZ0/ImPHGxRRQBs1djY2JqT6QsLC5ueXC8UCnHw4MFIp9ORSqXWdPKbnp5ODPWn0+nIZDIbnv/hhx+uqdZUKhVzc3Nx9OjRKBQKMTAwsOlevlQqxbFjx1a7DIyOjtrDA8AWLSV0fttsFEBE8jiAiIjT59+PvmuvqrsuANgt2j4EkEqlIp1Or7mSv1gsribya7W+E8A999zTlPpqsRIAKJVKdQUAIi53DKj3ewWgMfNn3o7imXeqrsl+8gObJs2B5vn0h26ID954IF59c/NZjflnX4//8Ct3trAqALaiUChEPp9fPYHf19dX0363WCyu7ulLpVIsLCzU1Nnv5MmTMTw8HPl8PtLpdExOTtbVbXAlCDAxMRFjY2MxPDwcmUwmcrlcpNPpKJVK8fTTT8fU1FSUSqXV19ABAAC2LjEEsMkogIjkcQAREaffuhB33VJ3WQCwa7R9CCDi8lX7V87VayQEsL6DQD0n4rfq6NGjUSwW6w4ARFw+SFLrlQoAbM3JWkYBJLQoB5qjp6cnjn7ycPxP3/7ppmuee+18/Gzh3bit75oWVgZAo2ZnZ1v6eqlUqimvOTo6GiMjI3HixImYnp6O8fHxKBaLqx0KHnroocjlck0bZwgAbC0EcNO1V0VPT0S5ylOcPn+h0dIAYFfo3ekCajE2Nrbmdi2z+NY7derU6t8zmUzLrq4fHh6OQqHQUABg5UoHBxIAWiP/o9NVv379gb1xz8f7qq4BmidbQ+gmaYQHADRDKpWKkZGRmJ2djfn5+SiXy3Hu3LmYn5+vu8MAAJBsqdoZ/KgeAti7pzduSmj1f/r85l3nAKAT7IoQQDqdXtNOr94kf7FYXNMJIJfL1fzYsbGxGBgYiOHh4Q0jBZLkcrmYmZmJ2dnZhjoPrMwTNA4AYPude+dinPrJQtU1D9x5OPbt2RX/64SOcG//TXHtVXuqrjn5bPXwDgAAALvPVjoBREQcuv5A1a+ffksnAAA6264YBxBx+WR8Pp+PiIh8Ph+lUqmmGYAREZOTk6t/T6fTMfL/Z+++w+O6y7z/f6aot1Gx5F5GjnviRHKKnZ7ISagJIIUWygKWWNiFLTzWj+dZ2AJLkGFZOiuFXhaIBSSQBBIrjSR2iC05sRN3jXu3pVGvM/P7Q7GwHWvOkTRzZs7M+3VdvqSRvjNzO5GPTvmc+66uNvW81atXj75nS0uLGhsb1draauqi/Lp169TQ0KC1a9eqoKDAVPeCtraRi09+v18+n0/333//aM0AgOh6evcpGRxfqmJxsTXFAJAkpbldumnBFP3x1RNjrnnRd1ad/UPKTU+xsDIAAAAAQDRNNgRQnJOmncfH/v5pxgEAABKcbUIAFRUVqqysHL07/v7771ddXZ3h8/x+vxoaGkYfnx8ICMfn840GAM7X2NiotWvXhn1uY2Pj6AiDdevWad26dabe81IIAACANYxairudDt2ygBAAYLXbF5eEDQEMB0N6dvdpvW35dAurAgAAAABEk2EIwGEcAgiHEAAAINHZqqfxAw88MHpRfN26daburl+zZs3oKIC1a9deMFZgIs6ePRv2+01NTaqqqprUe5yPuYIAEH0DwwE9u/t02DXXzCtQXiZ3GgNWu3XhFBnc4GEY4gEAAAAA2MukOwHkhg8BnOrqH3dNAADYia1CAB6PR83NzaMXxsvLy0c7A1zM7/erqqpq9Ptr16411TngHK/Xe8kL8O9+97vHfM6594wkOgEAQPS96GtTz2Ag7JqKxSUWVQPgfIXZaSqfkx92zdO7TmkoELSoIgAAAABAtA0bhADcLqNOAOlhv3+KTgAAgARnqxCA9NcgwLkL+lVVVSovL1dDQ4OamppGW/HPmzdPjY2N8nq92rBhw7gCAOc8+eSTo50Dzr1OuDvzfT7faNeBSLn66qsj+noAgDd60sRdxIQAgNgx+vfX2T+sLQfaLaoGAAAAABBtwSiPA+gdDKh7YHjcdQEAYBfuWBcwUWvXrlV1dbUefPBBrV+/XnV1dfL5fPJ4PCooKNC9996rmpqaSbXT93g82rBhg+n1ZWVlCoXC75wAAOJLKBRS047wIYAFJdmaXZhpUUUALlaxpET3/3FX2DVNO09qZWmhRRUBAAAAAKLJqBPAZMcBSNKpzn5lT8keV10AANiFbUMA0shF+urqalVXV8e6FACATe043qljHeHnwNEFAIit0inZmleUpf1nesZc07TzpP7lLYvlMLgbBAAAAAAQ/wKTDQEYjAOQRkYCeAkBAAASlO3GAQAAEElNO04ZrqlYQggAiLWKxcVhv3/wbK/2neq2qBoAAAAAQDQFDDruGoUAphiMA5BGQgAAACQqQgAAgKT25K7wowCKslN15UyPNcUAGJOZjhxNO41DPQAAAACA+DfZTgDpKS7lpodvhHyqM3xnSAAA7IwQAAAgaZ3o6Ne2Ix1h19y2qFhOgwNLANFXPidfnsyUsGuadoYP9QAAAAAA7GGyIQBJKs4NPxLgNJ0AAAAJjBAAACBpGXUBkMzdfQwg+twup25dGH4kQMuhdp3p5iQOAAAAANidYQjAYSIEYDASgHEAAIBERggAAJC0mnaEDwGkuZ264bIii6oBYMQolBMKSU/tYiQAAAAAANhdJDoBTDEMATAOAACQuAgBAACSUu/gsF5oPRt2zfXzi5SZGn5+HADr3LSgSCmu8Cd6nmQkAAAAAADY3nAkxgEYhQA66QQAAEhchAAAAEnpub1nNDgcDLuGUQBAfMlJT9F13sKwa/6854z6hwIWVQQAAAAAiIZgREIA6WG/zzgAAEAiIwQAAEhKRqMAJOn2xeHnjwOw3uol4cM5fUMBbTLo8gEAAAAAiG9GnQDcZkIAueE7AXT0DWlgmBA5ACAxEQIAACSdQDBkODd8+cw8leSGT4wDsN5ti4zDOU+YCPkAAAAAAOJXIBi+e6OZTgBTDMYBSNJpugEAABIUIQAAQNJpPtiusz2DYdfczigAIC7NzM/U4mm5Ydc07Txp2DoSAAAAABC/AgaHdJEYByAxEgAAkLgIAQAAks7jr50wXFNBCACIW6sNRnWc7hrQ1sPtFlUDAAAAAIi0SHQCMBoHIEmnOgkBAAASEyEAAEBSCYVChiGAGZ4MLZ6WY1FFAMZr9ZKphmsef42RAAAAAABgVwGD7m4up/GljZw0t9JTwq873dU/rroAALALQgAAgKSy43injrT3hV1z59KpcjiME+UAYmPZjFzN8GSEXfP4aycUCjESAAAAAADsyDAEYOK0jcPhMBwJwDgAAECiIgQAAEgqZu4OvnMpowCAeOZwOLR6Sfh/pwfP9mr3yS6LKgIAAAAARFIkOgFIUnFO+JEAjAMAACQqQgAAgKTy+KvhRwEUZqVqxdwCi6oBMFF3LjUeCfAng3/vAAAAAID4NGwYAjD3OsW5BiEAxgEAABIUIQAAQNI4cKbH8M7g1UtK5HIyCgCId1fPzVdBVmrYNWY6fwAAAAAA4k/QYLyb+U4AjAMAACQnQgAAgKTx+GvGdwWbubsYQOy5XU5VLC4Ou2bn8U4dbuu1qCIAAAAAQKQMB8KHANwmb+CYYjQOgBAAACBBEQIAACQNoxBAdppbq+YXWlQNgMkyE9oxE/4BAAAAAMQX404AkQkBnO0eUMBg9AAAAHZECAAAkBROdvar5ZA/7JpbFk5RmttlTUEAJu36+UXKSg3/b/ZPrxICAAAAAAC7GTa4MG82BFBsEAIIhkaCAAAAJBpCAACApPDEDuPZ4IwCAOwlPcWlWxaGHwnQfKhdp2nvCAAAAAC2YnR3vvkQQLrhGkYCAAASESEAAEBSeMKgJXiqy6lbF4W/mAgg/ty5LHx4JxSSNpgIAQEAAAAA4kfEQgC54TsBSCI4DgBISIQAAAAJr6N3SJtaz4Zdc8NlRcpOc1tUEYBIuXXhFKW6wu/SPm4QAgIAAAAAxBfDEIDDXAigIDNVboPAwKmuftN1AQBgF4QAAAAJ76ndJw1nyd25tMSiagBEUk56ilbNLwy7ZmPrGXX2D1lUEQAAAABgsiLVCcDpdKgoO3w3gFOddAIAACQeQgAAgIT3p1fD3wXsdEgViwkBAHZ159LwIwGGAiE9veuURdUAAAAAACYrUiEAyXgkwCnGAQAAEhAhAABAQusbDOjZPafDrrl6boEKDVLhAOLX6iUlMuoEyUgAAAAAALCPQCiCIYAcoxAA4wAAAImHEAAAIKH9ee9p9Q8Fw64xuosYQHwryk7T1XMKwq55Zvdp9Q8FLKoIAAAAADAZw4HIhQCm5KSH/T6dAAAAiYgQAAAgoZm5+/eOpYwCAOzO6N9x72BAz+89Y1E1AAAAAIDJCBp0AnBHshNAJyEAAEDiIQQAAEhYQ4GgmnacDLtm2YxczczPtKgiANFipqPHnxgJAAAAAAC2MByM4DiA3PAhgNNdAwoZhA4AALAbQgAAgIT1F1+bOvuHw665cwmjAIBEMKsgU0um5YZd8+TOkxoOhB8PAgAAAACIvUAkQwAG4wAGA0F19A2Zfj0AAOyAEAAAIGGZGQVw1zJCAECiMPr33N47pJcOtFlUDQAAAABgoiIZAphiMA5Akk51MRIAAJBYCAEAABJSMBjSEzvChwC8RVmaX5xtUUUAos3MSIAnXgs/IgQAAAAAEHuGIQDHeDoBmAgBdBICAAAkFkIAAICE9MoRv04aHMDdsXSqHOM4aAQQ3xaUZGtuYWbYNY+/doJZjwAAAAAQ5yLZCaAo20wngH7TrwcAgB0QAgAAJKQ/mRgFcOfSEgsqAWAVh8Nh2A3geEe/th3psKgiAAAAAMBERDIEkOp2qiArNeyaI+19pl8PAAA7IAQAAEg4oVBIj78aPgRQkpum5TM91hQEwDJ3mBgJ8EeD7QMAAAAAILYCBh3cxhMCkKQZnoyw3999omtcrwcAQLwjBAAASDivHevUgbO9YdfcuXSqnOM8YAQQ/66a5TGc9/jY9uOMBAAAAACAOBUKhSLaCUCSFpTkhP3+rhOd43o9AADiHSEAAEDCeXT7ccM1Ri3DAdiT0+nQHQajPg619erVo5zgAQAAAIB4ZHD9X5LkHmcIYPG08CGA/Wd61D8UGNdrAgAQzwgBAAASSigU0mMGIYCCrFRdO6/AoooAWO3Nl08zXGMmLAQAAAAAsN5wMGi4xukYXwhg4dTwIYBgSNp3qntcrwkAQDwjBAAASCivHevUQYNRAHctmyq3i1+BQKK6dl6hirJTw655dPsxRgIAAAAAQBwykQGQ2zW+EMCiqbmGa3Yep2McACBxcAUEAJBQHtlmfHfvW0zcJQzAvlxOh+5aFn7kx+G2Pm0/2mFRRQAAAAAAs8x0AnA5x3dpY0pOmgqzwofFd53oGtdrAgAQzwgBAAAShplRAIWMAgCSwlsun264hpEAAAAAABB/AkHjrm2ucY4DkKRF08KPBNhNCAAAkEAIAQAAEsarRzt1qI1RAACka+YVqCg7LeyaR7cdZyQAAAAAAMQZUyEA5/hDAAtLwo8E2HWCcQAAgMTBVRAAQMIwc1cvowCA5OByOvQmg5EAR9r7tO0IIwEAAAAAIJ5EKwRg1AngTPegTncNjPt1AQCIR4QAAAAJIRQK6dHtx8KuKcpO1TWMAgCSxluuMA79GI0QAQAAAABYK2CiY9tEQgCLp4bvBCAxEgAAkDgIAQAAEsL2ox063NYXdg2jAIDkcvVc45EAjzASAAAAAADiynAgOiGAy0qyZfQ0RgIAABIFV0IAAAnBzCiANzMKAEgqLqdDb748/EiAo/4+vcJIAAAAAACIG0ETQW33BEIA6SkuzS3KCrtmF50AAAAJghAAAMD2QqGQHt0WPgRQlJ2qa+cVWlQRgHjxFhPhH0YCAAAAAED8GA4ahwCcjvGHACRp0dScsN9nHAAAIFEQAgAA2N62Ix060h5+FMCblk2bUKs4APa2Ym6BpuSEHwnwKCMBAAAAACBuBE2EANyuiYYAcsN+f8/JLg0HghN6bQAA4gkhAACA7Zm5i5dRAEBycjkdevMy45EALx/2W1MQAAAAACAsM50AJnqjx0KDTgADw0EdONs7odcGACCeEAIAANhaKBTSI4ajANJ0zbwCiyoCEG/ecsV0wzWMBAAAAACA+BAwEwKY4DiAxQadACRGAgAAEgMhAACArW070qGj/vCjAN58+VRGAQBJbMWcfBUzEgAAAAAAbMFUCGCC53lm5mcoM9UVds2uE50Tem0AAOIJIQAAgK09yigAAAacTofhduBYR7+2MhIAAAAAAGIumuMAnE6H4UiAXXQCAAAkAEIAAADbCoVCetRgFMCUnDRdPZdRAECyMxMGesxgewIAAAAAiL6giS5t7kl0fFxkMBKATgAAgERACAAAYFuvmBkFsIxRAADMjQR4bPtxBU3ccQIAAAAAiJ7hgPFxmXNSIYDwnQAOt/Wpe2B4wq8PAEA8IAQAALCtR7cdM1zDKAAAEiMBAAAAAMAuot8JIHwIQJJ2MxIAAGBzhAAAALYUCoX02PYTYdcU56RpBaMAALzuLVeYGAmwnZEAAAAAABBLwyY6tE2uE0D4cQASIQAAgP0RAgAA2NLLh/3GowAun8YoAACjymfnqySXkQAAAAAAEM/MHJNNphNAXmaKpuWlh12z60TnhF8fAIB4QAgAAGBLf3jF+G5dRgEAOJ+ZkQDHO/rVfKjdoooAAAAAABcz1QnAMbmbPhYajATYdZxOAAAAeyMEAACwnUAwpD9sOxZ2TXFOmlbMybeoIgB28RYT4aCHth61oBIAAAAAwKUEotwJQDIeCbDrRKdCIbrEAQDsixAAAMB2Nrae0emugbBr3nz5tEnNhwOQmMpm52tqbvi2j49uP67B4aBFFQEAAAAAzmcmBDDZ8Y+LDDoBdPYP63hH/6TeAwCAWCIEAACwnYe2hu8CIElvWz7dgkoA2I3T6dBbrwjfDcDfO6Q/7zltUUUAAAAAgPMNB8OHsp0OyTHJcQCLpoUPAUjS7hOMBAAA2BchAACArfQPBfT4ayfCrpldkKmy2R5rCgJgO/dcNcNwzUMvMxIAAAAAAGIhaNCG3+2c/GUNb1G2UlzhgwQ7T3RO+n0AAIgVQgAAAFtp2nlS3QPDYdfcc+X0SSfCASSupdNzNb84O+waM9saAAAAAEDkDQfChwAikAFQqtup0inhjwvpBAAAsDNCAAAAWzEzCuBuE3f5AkheDodD91wZfmRI/1BQj78avusIAAAAACDyrOgEIEmLpoYfCbDrOCEAAIB9EQIAANhGe8+gntl9Kuyay2fkGSa5AeDuKxkJAAAAAADxaDho0AkgQs0fF07NDfv91tPdGhwORubNAACwGCEAAIBtPLr9uOGB4N0Gd/cCgCTNKshU+Zz8sGte2HdGp7r6LaoIAAAAACBJQYNzP25XhDoBTAvfCWA4GFLr6e6IvBcAAFYjBAAAsI2HDe7KdTqkty8nBADAHKORAMGQ9IdXjltUDQAAAABAMtMJIDKtAIzGAUjS7hOMBAAA2BMhAACALRxp79XmA+1h16wqLVJxbrpFFQGwu7dcMV1ugz6SRuEjAAAAAEBkBYw6AURoHsDU3HTlZaSEXbPzRGdE3gsAAKsRAgAA2MLDLx8zXMMoAADjUZCVqpsWTAm7ZtuRDvlo/wgAAAAAljEKAbgiFAJwOBxaaNANYNdxOgEAAOyJEAAAIO6FQiE9tDX83bhpbqfuWjbVoooAJIp7rpphuOYhEyEkAAAAAEBkBELWhAAkabFBCIBxAAAAuyIEAACIezuOd2rvqfB34lYsKVFOevgWbgBwsdWLS5SV6gq75qGtRxUyOAkFAAAAAIiMQMCacQCStGhabtjvn+jsl793MGLvBwCAVQgBAADinplRAPdcaXw3LwBcLCPVpTuXhu8icqitV1sP+60pCAAAAACS3LDBOABnBEMARuMAJGkX3QAAADZECAAAENcCwZB+bxAC8GSm6GaDud4AMJa7TYwEeNhgJAkAAAAAIDKCBp3YItkJYGGJiRDA8c6IvR8AAFYhBAAAiGt/2X9WJzr7w6558+XTlOrmVxqAibm+tFBF2alh1zyy7biGAkGLKgIAAACA5GXYCcARuRBAVppbswsyw67ZfZJOAAAA++GKCQAgrj28lVEAAKLL7XLqrVdMD7vmbM+gnt93xqKKAAAAACB5BQ1CAG5X5EIAkrTIYCTAzuOEAAAA9kMIAAAQt/qHAnrs1eNh18zwZGjFnHyLKgKQqO5hJAAAAAAAxAUrOwFIxiGAPSe7DIMJAADEG0IAAIC49fSuU+rqHw675u4rp8sZwVlwAJLT8pl5mleUFXbN46+dVM9A+G0SAAAAAGByAkadACJ8HmjRtNyw3+8dDGj/2Z6IvicAANFGCAAAELceetn4rlszd+8CgBGHw6G7rww/EqBvKKANO05aVBEAAAAAJCejEECkbwZZaNAJQJI2Mh4OAGAzhAAAAHGpo29IT+86HXbN4mm5WlBifKAGAGbcc6VxqMhMOAkAAAAAMHGBkLWdAOYWZikn3R12zXN7CQEAAOyFEAAAIC49su2YBgPBsGvuMbhrFwDGY25RlpbP8oRd89zeMzrV2W9NQQAAAACQhAKB8CEAV4RDAC6nQyu9hWHXbGo9q2GD81QAAMQTQgAAgLj04JYjYb/vcEhvJwQAIMKMwkWBYEi/3Uo3AAAAAACIlmGDcQCRDgFI0o2XFYX9ftfAsF450hHx9wUAIFoIAQAA4s7uE1165bA/7Jpr5xVoWl6GNQUBSBpvvWK64QmlB7ccVsigPSUAAAAAYGKCFo8DkKQbL5tiuOZ5RgIAAGyEEAAAIO6s33LYcE1l+SwLKgGQbKbkpOmWBeFP/vhO96jlULtFFQEAAABAcjHqBOB0RD4EMKcwUzPzw99s8vy+0xF/XwAAooUQAAAgrgwFgvqdQavtrFSX3nz5VIsqApBsqlYYh4we3Bx+ZAkAAAAAYGKCBiEAtyvyIQCHw2E4EmDrIb+6B4Yj/t4AAEQDIQAAQFx5atcpne0ZDLvmbcunKzPVbVFFAJLNbYuKVZiVGnbNI9uOqXeQkz8AAAAAEGnDwWDY70ejE4Ak3TA/fFe44WBIL7aejcp7AwAQaYQAAABxxcwoADN36QLARKW6nXrHVTPCrukZDOix7ScsqggAAAAAkkcgfAZAbmd0QgCrSgtllC94ft+ZqLw3AACRRggAABA3TnX26+nd4eerlU7JUtlsjzUFAUhapkYCmAgtAQAAAADGJ2DUCSBKIYD8rFRdPiMv7Jrn9oY/bwUAQLwgBAAAiBu/3XpUAYO5b1UrZskRpbZvAHDOwqk5Wj4z/Mmfl/a3af+ZHosqAgAAAIDkEAh/aihqnQAk6Yb5RWG/33q6R8f8fVF7fwAAIoUQAAAgLoRCIcO7al1Oh95p0KIbACLFTDeAxma6AQAAAABAJBl1AnBFMwRwWfgQgCQ9v5eRAACA+EcIAAAQF1oOtct3OvwdtbcunKLi3HSLKgKQ7N62fLrS3OF3l3/TbNzBBAAAAABgntExVjRDAOVz8pWR4gq75rl9hAAAAPGPEAAAIC6s33LEcI2Zu3IBIFLyMlL0pmVTw6450dnPTEgAAAAAiCCjEIDbGb3LGmlul66ZVxB2zQv7zihIGBwAEOcIAQAAYq53cFh/eOVY2DVF2am6bVGxRRUBwIh7TYSPzISYAAAAAADmDBtcYHc6otcJQJJuNBgJ0NYzqB3HO6NaAwAAk0UIAAAQc49tP6GewUDYNfdcOUMpLn5tAbDWdd5CzczPCLvmiR0n1NYzaFFFAAAAAJDYjO6yd7uiGwK4wSAEIEnPMxIAABDnuJoCAIi5B7ccNlzDKAAAseB0OlRZPjPsmqFASA+/fNSiigAAAAAgscW6E8DCkhxNyUkLu+b5vYQAAADxjRAAACCm9p/p0Uv728KuWT7Lo4VTcyyqCAAuVFk+U0bnmH69+bBCIWZCAgAAAMBkBYw6ATijGwJwOBy6cX74bgAvHWhT/1D4rpYAAMQSIQAAQEw1Nht3Abh3Rfi7cAEgmmbmZ+r60vAngHad6NJrx5gJCQAAAACTZRQCcEY5BCAZjwQYHA5q84HwN7UAABBLhAAAADETCIb0m+bwLbTT3E69bfl0iyoCgEurMhFGWm9itAkAAAAAILyAQZe1aHcCkKQbDDoBSIwEAADEN0IAAICYeW7vaZ3o7A+75s2XT1NueopFFQHApd25dKpy091h1zz08jHaQQIAAADAJBl1AnBZEAIozk3XwpLwoyn/TAgAABDHCAEAAGJm/ZYjhmuqyhkFACD20lNcevuV4buSdPQNacOOkxZVBAAAAACJKR5CAJLxSICdxzt1umvAkloAABgvQgAAgJg40z2gJ3acCLtmZn6GrvMWWlQRAIR374pZhmt+tfmQBZUAAAAAQOIyCgFYMQ5AMg4BSNLGVroBAADiEyEAAEBMPLjlsIYC4Q/qqspnyWnRgR0AGLl8Rp4WTQ3fDvKFfWfVerrboooAIHE0NDRo9erVKi0tlcPhUH5+vkpLS1VTU6OWlpaY1eXz+VRTU6OmpqYJPbe2tlYNDQ1RqAwAgMQ1bBACcDqsOVd07bwCpbrCX0J5jpEAAIA4RQgAAGC5QDCkX7wY/m5Zh0N6V/kMiyoCAGMOh0NVJroBGG3fAAB/VVtbK4fDoZqamtHHGzZs0AMPPKDKyko1NDSovLxcpaWlMQkDNDU1jQYU8vPzVVNTo8bGRrW0tMjn842u8/v98vl8amxsVG1t7WjN69atU0FBgeV1AwBgZ0GjTgAua0IAmalulc3xhF3z/N4zCoXC1wsAQCy4Y10AACD5PLP7lI76+8KuuWF+kWbmZ1pUEQCY846rZqjuT7s0OBwcc8365sP6zJ0LlJnKrjYAjMXv9+v2229XS0uLPB6PnnzySZWVlV2wprKyUnV1daqpqRkNA9TX16u6ujpmNTc0NIzrzv61a9eqsrIyilUBAJB44qUTgCTdeNkUvehrG/P7Jzr71Xq6W/OLw3eNAwDAanQCAABY7mcvHjRc88GVc6NfCACMU0FWqt56+bSwa7r6h/WHV45ZVBEA2FN5efnonf3Nzc1vCACc7/wL/+cCAXZQV1enurq6WJcBAIDtGHYCsHB05A3ziwzXMBIAABCPbB8CiNe5gWbU1NTI4XBc0EIQABLdwbM9enbP6bBrpuel67ZFxRZVBADjc9/KOYZrfrrpIC0hAWAMVVVVo8fBdXV18nq9hs+pr68fXRfvx/ter1fNzc1au3ZtrEsBAMCWDDsBWBgCWDYjT57MlLBrCAEAAOKRbUMA8T43MJympiaVlpaO3r3g9/tjWxAAWOh//3JIRtfF3nftbLksPKADgPG4apZHS6blhl3z2rFOvXzYb01BAGAjLS0tamxslCR5PJ5xXSivra0d/XzNmjURr22yysrKtH79erW2tobtbAAAAMILGJw4srITgMvp0PWl4bsBPL/3jDp6hyyqCAAAc2w3qNSOcwMlyefzqb6+Xo2Njdz5DyBp9Q8F9Osth8OuSXE5dO/VsyyqCADGz+Fw6AMr5+izv90edt3PXzykq2bnW1QVANjD+Rfv77333nE9t7q6evRGgHNhgsrKyojWN5YNGzbI6/WqpaVFPp9PZ8+elSQVFhbK6/WqoqJCHo/HkloAAEh0AYNOAFbfOHLDZUV6dPvxMb8/GAjq99uO6QPXGXeNAwDAKrYLAZSXl49eRG9ubg7bNrC+vl7SyMiAcycKrAgC+P1+VVVVSRq5+H/+RX+v1yuPx8Pd/wCS0qPbjstvkIy+a9k0FeekW1QRAEzM3VdO15ce3amugeEx1/xh2zH9y1sWKz8r1cLKACB++Xy+Czr1lZeXj/s1ysrKRl+jvr7eshCANHI8b2Z0AQAAmLhQKBR3IYBbFk4xXPOb5iOEAAAAccVW4wDsNDewqalJTU1NkqSKigrV1dWpublZra2tKigosKQGAIg3P3vxoOEaDpgA2EFmqlvvKp8Zds3gcFDrm8N3PwGAZHIuqH9ORUXFuF9jxYoVo583NTURsAcAIMEYXP+XJLkc1oYApuVlaKW3MOyalw/71Xq626KKAAAwZpsQgJ3mBno8HoVCIYVCIbW2tmrDhg1au3YtMwEBJLVXj3YYzsdeWJKjq+fSOhuAPdxnIrT08xcPKWjmLBYAJIFzx/TnTCQgX1paesHjBx98cFI1AQCA+GLUBUCyvhOAJMMQuDTSDQAAgHhhmxDAZOcGnnN+mAAAYJ2fm+gCcN/KOXJYnOYGgImaX5ytVaXh7wY51NarP+89bVFFABC//H7/BaPypJEA/Xhd/Jzm5uZJVAUAAOKNmRCA22X9uaM3LZuqzFRX2DW/23rUVP0AAFjBFiGASM0NPOfiFoQAgOjq6BvSQy8fDbsmK9Wld1w1w6KKACAyzIwwMROCAoBEt2XLlgseTyQAIL2xe8C5MXwAACAxDAeDhmucMbiBJCvNrTctmxZ2zfGOfm1sPWNRRQAAhGeLEABzAwHA3n7TfET9Q+EP4t5RNkPZaW6LKgKAyKhYUqKS3LSwa57adUpH2nstqggA4tP5wX5pYqMApDeGBy7uLgAAAOzNRAZAbmdsLmu8q9z45hVGAgAA4oUtQgDMDQQA+wqFQuZGAZi4mxYA4k2Ky6n3XjM77JpgSPrlS4csqggA4lNra+sFjyPVCUCKbRDA5/PJ5/NxowEAABFiqhNAjK5qXDevUDM8GWHX/Om1E+rqH7KoIgAAxhb3IQDmBgKAvW1sPSvfmZ6wa66ZW6BFU3MtqggAIuu918yWyxm+HeWvNx/WwHDAoooAIP60tbVF7bWtvgC/bt06lZeXy+FwqLS0VKWlpcrPz1d+fr5qamre0PUAAACYFwiFDNfEqhOA0+nQO8vCdwPoHwrqj9tPWFQRAABji/u+y8wNBAB7+9kmE10AVtIFAIB9leSm686lJXoszImeM92D+tOrJ3T3lcbtIwEgEUXzQr3P51NZWVnUXv+choYG1dbWqqCgQDU1NaqrqxsdPbhlyxbV1dWpoaFBDQ0Nqq6uVl1d3YTPYUzUpk2bJvX87du3R6gSAAAmJhA0DgG4Ynhr47vKZupbT+0Lu6ax+YjuvXqWRRUBAHBpcR8CYG4gANjX8Y4+bdh5MuyaouxU3bV0qkUVAUB03HfdnLAhAEn6+YsHCQEASFqR6gRg9UX1c2pra9XS0qL6+npVV1e/4fsVFRWqqKjQunXrVFtbq4aGBjU1Nam5udnSmletWmXZewEAEA3mQgCxSwHMLcrSijn52nKwfcw1Lx1o06GzvZpdmGlhZQAAXCjuxwEk6txAAEgGv3zpsOHB23uunq1Ud9z/OgKAsFZ6C1U6JSvsms0H2rXzeKdFFQFAfLm4E8BEA/6XEs1RA+e0tLSoubn5kgGA861du1aVlZWSRs45lJeXR702AAASiakQgCP8OLZoe1f5TMM1v2k5YkElAACMLe6vuiTS3EAASCb9QwH971/CjwJwOqT3XjvboooAIHocDofuu854tMmPXthvQTUAgEg5F1ZYv3696ZEDdXV1o5/7fD5VVVVFpTYAABKRuU4AsQ0BvOWKaUozuKHlt1uPKGji7wIAQLTEfQgg2nMDAQDR8dDWozrTPRh2zW2LSjTDk2FRRQAQXe8sm6mMFFfYNQ9tPaZTXf0WVQQAmKzKykq1traO3t1vhtfrldfrHX3c2NiopqamaJQHAEDCMRMCcLtiGwLITU/RHQajLQ+39Wnzgeh3KwIAYCzuWBdgxO5zA+1k06ZNk3r+9u3bI1QJALsLBkN64DnjoNUHVhrfNQsAdpGXkaJ7rpquX750eMw1g4GgfrrxoD5z50ILKwMATMb5F/TNqqioUENDw+jjuro6VVRURLKsS9q4ceOknr99+3bV1NREqBoAAMZv2EQIwBnjcQCSVFk+U3945VjYNY3NR3Stt9CiigAAuFDchwDsPjfQTlatWhXrEgAkiGf2nFLr6Z6wa7xFWbpxfpFFFQGANT60am7YEIAk/fwvB/WJW0uVmRr3u+IAEDGRCuZfqltgJM8TRMrq1asvCAE0NTXJ7/dH/QaFlStXRvX1AQCINlOdAGI8DkCSbphfpJLcNJ3sHBhzzWPbj+vf717KsR8AICbifhwAAMB+Gv5s3AXgYzd65YyDgzYAiKRFU3N142XhA07+3iE1Nh+xqCIAiE+JHsq/VPeABx98MAaVAABgL2ZCAK44OJ/kcjp0z1Uzwq7pGQzo8ddOWFQRAAAXIgQAAIioV4926EVf+JO6hVmpemdZ+AMlALCrNTcat43+wfP7TZ3cAoBEMZGW+vHw2hN1qTv+m5ubrS8EAACbCYTsEQKQpMqymYZrftN81IJKAAB4I0IAAICIeuA54y4AH1g5R+kpLguqAQDr3XhZkRZNzQm75uDZXm3YwR0hAJLHxS37L9XW34xLdRCIdov9SPH5jPeTAQBIdnbpBCBJl5Xk6IqZeWHXvNB6Rsf8fRZVBADAX8X9MJpkmxsYSxs3bpzU87dv366ampoIVQPAjo76+/TItuNh16S5nfrAdXMsqggArOdwOPSxG736zPpXwq574Ln9umvZNIuqAoDYKi0tveDxRMcBWHVs39LSojVr1qilpUVlZWVav379uDoOXKqmRB+BAABAJNgpBCBJleUzte1Ix5jfD4WkX28+rH9cvcDCqgAAsEEI4GIcNEfPypUrY10CAJv78QvG7a3fVT5ThdlpFlUEALHx9uXTte5Pu3Sqa2DMNc0H29V8sF3lc/ItrAwAYqOsrCwir3Px3fQejycqnQBuv/320cBBS0uLysvL1d7ePqnX5EYEAACMmQoBOOInBPC2K6brC4/s0FBg7Lp/sumA1tzkVXaa7S7HAABsLO7HASTb3EAAsKvO/iH98qXDhus+esM8C6oBgNhKdTv14evnGq77vokRKgCQCFasWHHB44mOAzh79uwFjysqKiZa0ph8Pt8b6vP7/eNq52/nsQUAAMSSqRCAK35CAPlZqbp9UUnYNf7eIf3ixYMWVQQAwIi4DwEwNxAA7OHXLx1W98Bw2DUVi0tUOiXboooAILbef80cZaa6wq55/LUTOni2x6KKACB2PB7PG4L447moPtZzrr766knVdSljnXcYz538l3qNaNQKAECisVsnAEm69+qZhmseeG6/+ocCFlQDAMCIuA8B2G1uIAAko6FAUD96Yb/hujU30gUAQPLIy0zRvStmhV0TDEk/fN54+wkAieDiu/YnEgK4+Ni+srJyMiVd0qW6Bq5du3ZcNxJc6u8WjVoBAEg0pkIAzvgKAdyyoFgLSsLf9HKme0C/3mzcQRMAgEiJ+xCA3eYGAkAyemz7cR3r6A+75oqZebpmHuErAMnlI9fPk9H5qQe3HJG/d9CaggAghmpray943NLSMu7X2LJly+jnZWVlURnzd65rgdfrVX19vZqbm1VXVzeu19i8efMFj8+9HgAACG/YRAjAHWchAKfToU/eOt9wXf2zrRocDlpQEQAANggB2GluIAAko1AopAdMzLRec6NXjjhr1wYA0Ta7MFN3LZsadk3fUEC/+MshiyoCgNjxer0XHItv2LBhXM/3+XwXnBOoqakx/dza2lqVl5erqqrKVAeCyspK+Xw+3XvvvRO6OaGxsfGCx+MNEQAAkKzs2AlAkt5y+TTNKcwMu+ZYR79+t/WIRRUBAJJd3IcA7DQ3EACS0Yu+Nr16tDPsmhmeDL3J4CIYACSqNTca3/n5440HNDDMfEgAie/8bgBNTU3jCvrX19ePfu71elVdXW3qeatXr9a6devU0tKixsZGlZaWGp5X+OxnP/uGes1qamq64PXLysoYBQAAgEmBUPgQgNOhuLzJxO1y6hO3lBqu+94zrRoO0A0AABB9cR8CkOwzNxAAkpGZLgAfuWGe3C5b/MoBgIi7ana+VszJD7vmdNeAHn75mEUVAUDsVFRUXHA8fv/995t6nt/vV0NDw+jj8wMB4fh8PjU1Nb3h6xffqX8xj8ejuro6NTQ0XPC+ZpzfocDj8ejJJ58c1/MBAEhmgWD4C+Tx2AXgnHdcNVPT89LDrjlwtlePbj9uUUUAgGRmiysydpkbCADJZt+pLj2161TYNTnpbr376lkWVQQA8eljJroBfP85n0IGd70AQCJ44IEHRo/Jz92hb2TNmjWj4f61a9dOesTfxSMDL+Xc+9TU1JgOAqxevXr0xoVzAQCPxzOZUgEASCpGN8nHcwgg1e1Uzc3G3QC+/dQ+BU2MPQAAYDJsEQKw09xAAEgm332m1XDN+66drew0twXVAED8Wr2kRHMN5kPuOdmtpp3hg1UAkAg8Ho+am5tVVlYmSSovLx/zzny/36+qqqrR769du1Z1dXWm38vr9Y6+z/ne/e53m3r+hg0bRoMA5eXlYwYWmpqaVFpaOtp1wOv1XvB3BAAA5hh2AojDUQDne/fVs1SUnRZ2zd5T3Xpix0mLKgIAJCtbhAAk+8wNnIi2traIvyYARNuBMz2GravdToc+vGquNQUBQBxzOR366A3zDNd948k9dAMAkBTOBQHOXdCvqqpSeXm5Ghoa1NTUpMbGRtXW1mrevHlqbGyU1+vVhg0bxhUAOOfJJ58cvbHg3OuM5+L8ufdtaWlReXm5SktLVVVVpZqaGlVVVam0tHS0A8C5MQKtra10IAQAYALs3AlAktJTXFpzo/Gx37ef3suxHwAgqmwTArDL3EAzLr7oP55AAwDEi28/vU8Bg9Zlb18+XdPyMiyqCADiW2X5LOVnpoRd8+rRTsMxKwCQSNauXav29nbV19eroKBAdXV1Wr16tdasWaPGxkbde++9am5uVmtr64RHAHg8Hm3YsEGhUGjCr3N+nV6vVy0tLaOBBUmqrKzU+vXr1d7errVr106oTgAAYKITQJyHACTp/dfNkcfEsd+ze05bVBEAIBnZJgQg2WduYDjr1q17w0X/+++/nyAAAFs5eLZHv9t61HCdmRnYAJAsMlJd+sDKuYbrvvEkd4QASC4ej0fV1dXasGGDWltbFQqF1N7ertbWVtXX18dNS/1wda5fv/6CGxcAAMDEGN1w4nLG/yWN7DS3/maViW4AT+3j2A8AEDXx/xvzPHaaG1hbW6vVq1eP/ikvL5fD4bhgrME5LS0tys/PV2lpqcrLyy94HuEAAPHoOya6AKxeUqIl03MtqggA7OEj189Vdpo77JptRzr0DHeEAAAAAEhCwwbnm9w26AQgSR9eZXzst+Vgu/6yn1HBAIDoCP9bKA6dCwKsW7dOtbW1qqqqUllZmWpqauT1euX3+7V582Y1NDTI7/fL6/Wqvr5+Qh0AnnzySVVVVampqWn0dczegdDS0qKmpiZ5PB5JUkFBgal5gD6fTz6fT9JIkKGtrW30NQAgHhxu69VvW4y7AHz69sssqAYA7MWTmaoPrZqj7zzdGnbdN5r26pYFU+Rw2OMEFwAAAABEQtDgzng7jAOQpLzMFH1g5Rx975nwx37ffmqfrvMWWlQVACCZ2C4EcM7atWtVXV2tBx98UOvXr1ddXZ18Pp88Ho8KCgp07733qqamZlJtA8/NDZyIiT4PAOLdd5/ZZ5jKvn1RsZbNyLOoIgCwl4/e4NWPXjig3sHAmGtePuzXn/ee0c0LplhYGQAAAADEltE5J7uEACTpozfM049e2K/+oeCYa57fd0bP7z2jGy4rsrAyAEAysNU4gIvZZW4gACSKI+29Wr/liOG6T1fQBQAAxlKQlaoPrpxruO4bTXuYDwkAAAAgqQQCiRMCKMpO03uvmW247vO/f1WDw2MHBQAAmAhbhwAAANb67jOthonsWxdO0RUzPdYUBAA2tebGecpIcYVd03LIrxf2nbWoIgAAAACIvUCCjAM4p/omr1Jd4S/D+E736AfP77eoIgBAsiAEAAAw5ai/T+u3HDZc96nb6QIAAEYKs9P0wZVzDNd940m6AQAAAABIHgGjcQAOe4UApuVlqHLFTMN133xyr476+yyoCACQLAgBAABM+d4z+zRk0JLtpgVTdNXsfIsqAgB7W3OTV+kp4XfHNx9o16ZWugEAAAAASA6GIQCbdQKQpE/ddpkyU8N3gusbCuiLj+ywqCIAQDIgBAAAMHS8o08Pbj5iuO7TdAEAANOKstN037XG3QC+/uReC6oBAAAAgNhLxBDA1Lx0U+fM/vjqCT2757QFFQEAkgEhAACAof95plWDgWDYNTdeVqTyOXQBAIDxqL7ZqzR3+F3yl/a30Q0AAAAAQFJIxBCAJH3khnm6rDjbcN2//f41DQwHLKgIAJDoCAEAAMI62dmvX24+bLjuU3QBAIBxK85J1/tNdAP4Jt0AAAAAACSB4QQNAaS4nPr3u5cartt/pkfff26/BRUBABIdIQAAQFjfe6ZVg8PhuwCsKi3U1XMLLKoIABLLx010A9jkO6uX9rdZVBEAAAAAxEYwlJghAElaVVqkty+fbrjuW0/t1eG2XgsqAgAkMkIAAIAxnejo1y9fOmS4zsxcMwDApRXnpuu918w2XPffG/YoZHBCDAAAAADszKgTgNvGIQBJ+n9vWaysVFfYNf1DQX3hkR0WVQQASFSEAAAAY/rvDXs0YNAF4Dpvga71FlpUEQAkpo/fXKpUl3E3gGf3nLaoIgAAAACwXiCQuJ0AJKkkN13/uHqB4bondpzU07tOWVARACBREQIAAFzS7hNdWt982HDdp+gCAACTNjUvXe+5Zpbhui//cZcCBnfGAAAAAIBdBRJ4HMA5H1o1VwtLcgzX/dsfXlP/UMCCigAAiYgQAADgkr78x50yus50zdwCraQLAABExN/eYtwNYNeJLv2m5YhFFQEAAACAtYxCzy6H/UMAKS6n/uPupYbrDp7t1feeabWgIgBAIiIEAAB4g437zujp3cYtp/9x9QI5EuDgCwDiwbS8DL3XRDeArz2xR32D3A0CAAAAIPEYhgASoBOAJF3rLdQ7rpphuO7bT+9T88F2CyoCACQaQgAAgAsEgyHd/8ddhutuW1SslaV0AQCASPr72y9Tdpo77JoTnf364Qv7LaoIAAAAAKyTLCEASfrsmxcpx+D4LxAM6VO/3KqOviGLqgIAJApCAACAC/xh2zFtP9oRdo3TIdXetciiigAgeRRlp+njN3sN133vmVad7R6woCIAAAAAsE4yhQCKc9L1T3csMFx31N+n//u77QqFDOZ2AgBwHkIAAIBRA8MBfeXx3YbrqspnaeHUHAsqAoDk89EbvCrJTQu7pntgWN96ap9FFQEAAACANYaTKAQgSR+4bo4WmTjH9ui24/r15sMWVAQASBSEAAAAo3626aCOtPeFXZOe4tQ/rjZOKQMAJiYj1aV/MrGd/fmLB3XgTI8FFQEAAACANYIGd7snWgjA7XLqy++6wtTf69/+8Jr2nuyyoCoAQCIgBAAAkCR19A6Zuqt0zY1eTc1Lt6AiAEheleWztKAkO+ya4WDIVPcWAAAAALALw04AjsQKAUjSlbM8+mcTYwH6h4L6+19uVf9QwIKqAAB2RwgAACBJ+u4z+9TRNxR2TWFWqqpvMp5VDQCYHJfToc++abHhuke3H9fWQ+0WVAQAAAAA0Rc0CAG4XYkXApCkj99UqhvmFxmu23WiS//56E4LKgIA2B0hAACAjrT36kcbDxiu+3TFZcpJT4l+QQAA3bJwilZ6Cw3X3f/YLoUMWmYCAAAAgB0MB4Nhv59o4wDOcTod+tq9y1WYlWq49mcvHtSfXj1hQVUAADsjBAAA0Nee2KPB4fAHWfOKsvTea2ZbVBEAwOFw6LNvXmS47qUDbWraecqCigAAAAAgugJJOA7gnOLcdH313uWm1tb+ZpuO+vuiXBEAwM4IAQBAknv1aId+9/JRw3Vr71yoFBe/NgDASlfM9Ojty6cbrvvyH3dqOBA+zAUAAAAA8c4wBOBM7HNTty4s1sdumGe4rqNvSP/wq60cBwIAxpTYvzEBAGGFQiF96bGdMuoiXTbbo7uWTbWmKADABf7PnQuVahDCaj3do19uPmxRRQAAAAAQHcYhAIsKiaG1dy3S5TPyDNdtPtCuLz6604KKAAB2lAS/MgEAY3lk23FtbD1ruO7/vnmxHAncbg0A4tmsgkx9cOUcw3VffXy3znQPWFARAAAAAERHwOBOlUTvBCBJqW6nvvXeq5SV6jJc++ONB/TD5/dbUBUAwG4S/zcmAOCSuvqH9IVHdhiuu3NpiVbMLbCgIgDAWP7utvnKTXeHXdPRN6Qv/3GXRRUBAAAAQOQNB+gEIElzi7L0xXcsM7X2C4/u0OOvnYhyRQAAu0mSX5kAgIt9vWmvTnWFv2PU5XRo7V2LLKoIADAWT2aqPnnrfMN1jc1H9NL+NgsqAgAAAIDIC9IJYNQ7rpqpd5bNMFwXCkmf/tVWvXzYH/2iAAC2kTy/MQEAo3Yc69SPNx4wXPfea2apdEp29AsCABj60Kq5muHJMFz3uYde1VAgaEFFAAAAABBZw0GDEECSjav8wt3LNK8oy3Bd/1BQH/vJZh1u67WgKgCAHRACAIAkEwyG9LmHX1XA4KCqICtVn7ljoUVVAQCMpKe49K9vW2K4bvfJLv34hQPRLwgAAAAAIixocL7K7UquEEBWmlvfu69M2Wnhx8NJ0pnuQX34Ry+po3fIgsoAAPGOEAAAJJnG5iNqPthuuO6zb1okT2aqBRUBAMxavaREty8qNlz33017dLyjz4KKAAAAACByDDsBOJMrBCBJi6bm6jvvLzP1d2893aOan2/RwHDAgsoAAPGMEAAAJJH2nkHd/8edhuuunpuvd5XNtKAiAMB4OBwO/dvblyrNHX43vncwoC88ssOiqgAAAAAgMow6VybbOIBzbl4wRV+8Z5mptS/62vTZ32xXKBT+vyUAILERAgCAJLLu8V1qN2gJ5nI69IV7lsmZhMlqALCDWQWZ+rtb5xuue2z7CT2z+5QFFQEAAABAZBiGAJL4fNV7r5mtT9xSamrtb7ce1dc27IlyRQCAeEYIAACSRMuhdv3ypcOG6z5y/VwtmpprQUUAgImqvtmreUVZhuv+9fevqX+INpAAAAAA7IEQQHifuWOh3rZ8uqm133pqn7755N4oVwQAiFeEAAAgCQwHgvqX371quG5qbro+XbHAgooAAJOR5nbpP+5earju4Nle/c+zrRZUBAAAAACTFzBoYZ/sIQCn06GvVF6hq+fmm1r/tQ179N8b9jAaAACSECEAAEgCP3vxoHYc7zRc9/m3LVF2mtuCigAAk3XjZVP01iumGa777jOtOnCmx4KKAAAAAGByAgFCAEbSU1xq+MAKU93hJOkbT+7V1wgCAEDSIQQAAAnuVGe//usJ4xlgNy2Yojctm2pBRQCASPncW43DW4PDQX3+969xwgcAAABA3KMTgDn5Wan60YevVn5miqn133pqn77y+G6OCwEgiRACAIAEFgqF9LmHX1X3wHDYdalup/7j7UvlcHAgBQB2UpKbrn9cbTzG5c97Tuuhl49aUBEAAAAATNxw0CAEwLmrUXOLsvT9D61QqtvcZZ7vPtOqL/9pF0EAAEgShAAAIIH9butRPf7aScN1f3tzqeaabCEGAIgvH1o5R4um5hiu+9eHX9OJjn4LKgIAAACAiQkahADcLkIA5yufU6Bvvucq0x0S6p/16T8f3UkQAACSACEAAEhQx/x9+tffv2a4bk5hpv72llILKgIARIPb5dR/vmOZ4brO/mGt/c02TvYAAAAAiFtGnQCcdAJ4g7uWTdV33neV3CaDAN9/fr/+45EdHBsCQIIjBAAACSgUCqn2N9vU1R9+DIAk/dvblyo9xWVBVQCAaCmfU6B3r5hluO7Pe07rf186ZEFFAAAAADA+Rl0AJJm+0J1s7lo2Td95f5lSTHZK+NELB1T7m20aCgSjXBkAIFYIAQBAAvr5Xw7pub1nDNe9+fKpunVhsQUVAQCirfZNi1SQlWq47j8f3amDZ3ssqAgAAAAAzDPqAiDJdNv7ZHTn0qn63vvLTQcBHtxyRB/+0Uvq6BuKcmUAgFggBAAACebg2R596dGdhusKs1L1H3cbt48GANhDQVaqvniP8Xa9dzCg/7N+mwImTrABAAAAgFXMHKMQAgivYkmJ6j9QrlSXuUs/L+w7q3d9b6MOt/VGuTIAgNUIAQBAAgkEQ/rnB19R31DAcO1/vuNyFWWnWVAVAMAqb758mu6+crrhupcOtOmHz++3oCIAAAAAMCdgYkY9IQBjty0qUf0Hy5XqNnf5Z9+pbr3juy9o66H2KFcGALASIQAASCDff86nLQeNd9jfedUM3bVsqgUVAQCs9h9vX6aSXOOQ11ee2K09J7ssqAgAAAAAjAUChAAi5daFxfr+B1cozWQQ4Ez3oN7T8KIe2348ypUBAKxCCAAAEsSek136ryf2GK6bmpuuf337UgsqAgDEQl5mir78risM1w0OB/XPD76ioUDQgqoAAAAAIDw6AUTWTQum6AcfulrpKeYuAw0MB/WJX7Toe8+0KmTi/wUAIL4RAgCABDAUCOqfHnxZgyYu5KyrvEJ5GSkWVAUAiJVbFxbrvdfMNly3/WiHvvP0PgsqAgAAAIDwhoPG57VcDkIA43HDZUX68d9co9x0t+nn1P1pl/6/32zXwLDxuFEAQPwiBAAACeBbT+3Tq0c7Ddfdd91s3bRgigUVAQBi7f+9ZbFmFWQYrvv2U/u0/UiHBRUBAAAAwNhMZADkdhECGK/rvIX67Seu1+yCTNPP+fWWw3rX9zbq4NmeKFYGAIgmQgAAYHPNB9tM3cU5uyBTn33TYgsqAgDEg+w0t75auVxGN8oMB0P6h19vVc/AsDWFAQAAAMAlmOkE4KQTwITML87W7z6xSuVz8k0/59WjnXrrN5/XH7cfj2JlAIBoIQQAADZ2pntAn/zFVgWC4ed0ORzSf927XFlp5lt/AQDs71pvoT56/TzDda2ne/T//XY7cx8BAAAAxIypTgBOLmlMVGF2mn7xsWv1tuXTTT+na2BYf/uLFv3b719jPAAA2Ay/MQHApgLBkD79q6060dlvuLb6Rq+unltgQVUAgHjzmTsXan5xtuG6P7xyTD978aAFFQEAAADAG5npBOBy0glgMtJTXPrGu6/U3982f1zP+/HGA6r6n0063NYbpcoAAJFGCAAAbOrrTXv0wr6zhusWlGTrH1cvsKAiAEA8Sk9x6Wv3Ljd1suwLj+zQy4f90S8KAAAAAC5i1OlSIgQQCU6nQ/98x0J9tWq5Ulzm/3tuO9KhN3/zOf3p1RNRrA4AECmEAADAhp7edUrfemqf4Tq306Gv3Xul0lNcFlQFAIhXV8z06JO3Gt/pMRQI6ZO/aFF7z6AFVQEAAADAXwVMjCcjBBA5leUz9dOPXKvcdPPjQ7v6h/Xxnzfrcw+9qp6B4ShWBwCYLEIAAGAzR9p79Q+/ftnU2n++Y6GWzciLbkEAAFv4+9vmq3xOvuG6o/4+/cOvX1bQxF04AAAAABApwwFCAFZbWVqoh//uBi2Zljuu5/3sxYO66xt/1qZW4y6lAIDYIAQAADYyMBzQJ37Roo6+IcO1FYtL9PGbvRZUBQCwgxSXU99+31UqyEo1XPvsntP69tPGHWcAAAAAIFKCJjoBuAkBRNy8oiz99hOr9L5rZ4/reYfb+vTeB17U5x+mKwAAxCNCAABgI194ZIe2HekwXDerIEP/de9yORwcGAEA/mpaXoa++Z6rZObXw3837dFze09HvygAAAAAkDRsohuZkxBAVKSnuPSld1yub7znSmWljm+s6E83jXQF2Nh6JkrVAQAmghAAANjEQ1uP6ucvHjJcl+p26nvvL1deRooFVQEA7OaGy4r0TxULDNeFQtKnf/Wyjnf0WVAVAAAAgGRnZiQZnQCi6+4rZ+j3f3+DFk3NGdfzDrf16X0P/EWfe4iuAAAQLwgBAIAN7DnZpc/+druptf/x9qVaNiMvyhUBAOzsk7fO1y0Lpxiua+sZ1Cd/0aLB4aAFVQEAAABIZqY6AdD1MupKp2TroU9er/deM2vcz/3Ziwd159f/rKd2nYxCZQCA8SAEAABxrr1nUDU/a1bfUMBwbWX5TL376vHvoAMAkovT6dB/33ulZngyDNe2HPLrX3//qkIm5nMCAAAAwETRCSB+pKe4dP87r9DX332lMsc5HuBIe58+8uMt+uiPN+vg2Z4oVQgAMEIIAADiWP9QQGt+ukX7zxjvMC+amqMv3L1MDhLRAAAT8rNS9d33lynFZfx745cvHdb/POuzoCoAAAAAycpUJwBCAJa656oZevRTN2rFnPxxP/fJXae0+mt/1lcf363eQUYEAIDVCAEAQJwKBkP65/WvaMvBdsO12Wlufe++cmWMM5kLAEhuy2d59Pm3LjG1tu5Pu/T7V45FuSIAAAAAySpgovsYnQCsN68oS7+uWal/ectipbnHd0lpMBDUt5/ep4r/elaPbT9OhzkAsBAhAACIU+se361Htx03tfarVVdoXlFWlCsCACSi+66bo7uvnG5q7WcefEUv7W+LckUAAAAAklEgYHyB2EUIICZcToc+dqNXf/qHmybUFeBYR78+8YsW3feDv2jvya4oVAgAuBghAACIQ7/4y0H9z7OtptZ+7IZ5umvZtChXBABIVA6HQ196x+W6rDjbcO1gIKjqn21R6+luCyoDAAAAkEzMjAMgBBBb57oCfP6tS5SeMv7LSy/sO6s7v/5n1TZu0zF/XxQqBACcQwgAAOLM07tO6XMPvWpq7bXzClT7pkVRrggAkOiyXh8rk5PuNlzr7x3S3/xos850D1hQGQAAAIBkETTRKt7lIAQQay6nQx+5YZ7++OmbdPXc8XcFCIakX285rFu++oz+89Edau8ZjEKVAABCAAAQR1492qFP/m+LTASfVTolSw0fWKEUF5tyAMDkzS/OVv195UpxGZ9UO9TWq4/9ZIv6BgMWVAYAAAAgGRh1AnA4JCedAOLGvKIs/bp6pf797UuVk2YcKL/Y4HBQDzy3Xzete1rffmqvegeHo1AlACQvrhwBQJw45u/TR368Wb0mLqgUZafqx39zjfIyUyyoDACQLFbNL9KX33mFqbUvH/brH369VQEzyTUAAAAAMBA0OLZwEwCIO06nQx9aNVdPfeYWVZXPnNBrdA0M66tP7NFN657RTzcd0OBwMMJVAkByIgQAAHGgs3+ktfKpLuPWyukpTv3gQ1drVkGmBZUBAJLNu8pn6h8rFpha+/hrJ/Wlx3ZGuSIAAAAAycCoE4CTUQBxa0pOmr5StVy//cQqXT4jb0KvcaZ7QJ9/+DXd8pWn9eMX9qt/iM5zADAZhAAAIMa6B4b14R++pN0nuwzXOhzSN99zlZbP8kS/MABA0vrU7fNVafIujh88v19fb9oT5YoAAAAAJDo6Adhf2ex8PfTJ6/Wld1yu/Al2MD3W0a9/+8MO3VD3lL73TKu6+ociXCUAJAdCAAAQQ+cCAC2H/KbWf/6tS3TH0qnRLQoAkPQcDoe+9I7Ldf38QlPrv960V998cm+UqwIAAACQyAw7ARACsAWX06H3XTtbT3/mFn3gujma6P+2M92DqvvTLl3/5af0tSd2q71nMLKFAkCCIwQAADHSMzCsj/xos7YcbDe1/iPXz9PfXD8vylUBADAi1e3U9+4r14KSbFPrv7Zhj77z9L4oVwUAAAAgUQVCdAJIJJ7MVH3hnmV69FM36rZFxRN+nc7+YX3zqX26vu4pffGRHTrq74tglQCQuAgBAEAM9A4O6yM/3qyXDrSZWn/n0hL9v7csjnJVAABcKDc9RT/6m2tUnJNmav1XHt+t7z3TGuWqAAAAACSiQCAY9vsuJ5cz7GjxtFz98MNX68GalSqfkz/h1+kdDOj7z+/XTeue1id+0awtB9oUMgiOAEAy47cmAFisbzCgj/54i/6y31wA4MpZHn393VfJRdoZABADMzwZ+uGHr1ZmqsvU+ro/7VLDnwkCAAAAABifgMH1XBdXM2ztmnkFavz4Sn3/gyu0sCRnwq8TCIb02PYTqvyfTXr7t1/Qb1uOaHA4fIAEAJIRvzYBwEJ9gwF99Cebtcl31tT6uYWZ+v6HVijD5IUXAACiYdmMPH3nfWWm229+6bFd+v5zvihXBQAAACCRBILhL+S66QRgew6HQxVLSvTYp2/U1+5drhmejEm93vajHfqnB1/R9XVP6RtNe3W6ayBClQKA/fFbEwAs0j8U0JqfbtHGVnMBgDmFmfpl9XUqyjbXghkAgGi6dVGxvj2OIMAXH92pHzy/P8pVAQAAAEgUw8HwrQDIACQOl9Ohd5bN1FOfuVn/cfdSTc9Ln9Trne4a0H837dGqLz+pT/yiWc/tPa2gwc8TACQ6fm0CgAV6B4e15qdb9Py+M6bWzy7I1C/XXKdpeZNLwwIAEEl3LZuqb73X/IiaLzyyg44AAAAAAEwxumhLJ4DEk+Z26YMr5+qZ/3Or1lVeoXlFWZN6vaHAyKiAD/zgJd381af17af26mRnf4SqBQB74bcmAETZme4BvafhRT2311wAYGZ+hn5ZfZ2mT7IdFgAA0fCmy6fpm+8xHwT44qM79aXHdnIXBgAAAICwDDsBmDsEgQ2lup26d8UsNf3TzfrWe6/Soqk5k37Nw219+uoTe7Tqy09pzU+36KldJzUcCD9yAgASiTvWBQBAItt/pkcf+uFLOtTWa2r9DE+GfrnmuknPwwIAIJrecsU0BUMhffpXW2Xm2n7Dn3063tGvr1ZdoTS3K/oFAgAAALAdOgHA5XTobcun661XTNOTO0/p20/v08uH/ZN6zUAwpA07TmrDjpOakpOmu5dP1z1XzdDS6blyOEiWAEhchAAAIEpaDrXroz/erPbeIVPrp+el61fV12lWQWaUKwMAYPLetny6gqGQ/vHXL5sKAvzhlWM61dmvhg+uUF5GSvQLBAAAAGArhp0AaAWQNBwOhyqWlOj2xcV60demH72wXxt2nlRokg3mTncN6PvP79f3n9+vBSXZuueqGbrnyhl0ZAWQkIjOAUAUPPHaCb3vgRdNBwCm5aXrV9UrCQAAAGzl7itn6Gv3Xmm6Ledf9rep6n826qi/L7qFAQAAALCdgMEVXjchgKTjcDi0srRQDR9coWc/c6s+esM85aRF5t7WPSe7te5Pu3V93VN6T8Mm/XrzIfl7ByPy2gAQDwgBAECE/WzTAX38583qHzI3Y2pqbrp+ueY6zS4kAAAAsJ97rpqhr1Ytl9kuintOduud331BO451RrcwAAAAALYSCNAJAGObXZipz711iTb939v1b29borkROpcaCkkv+tpU+5vtWvHFJn3why/p15sPqb2HQAAAeyMEAAAREgyG9OU/7tLnHn7NVFtkaaQDwC+rr9PcoqzoFgcAQBS9s2ymvlK5XC6TJ+VOdg7o3vpNemHfmShXBgAAAMAu6AQAM7LT3Prw9fP01D/foh9+eIVuXjDFdCjdyHAwpD/vOT0SCPjPJn3gB3/RL186pDYCAQBsKDJ9UwAgyXUPDKu2cZse3X7c9HMWTc3Rj//mGk3NS49iZQAAWKOyfKYKslL0yV9sVd9QwHB998CwPvTDl/Svb1ui+66bI0ekztoAAAAAsKWAwV01ZkPHSA5Op0O3LSrRbYtKdKS9Vw9uOaIHNx/Wic7+iLx+IBjSc3vP6Lm9Z/QvD72qa+YWaPWSEq1eUsJIVwC2QAgAACZpz8kuffznzfKd7jH9nOvnF+p795UrNz0lipUBAGCt2xaV6FfV1+kjP96ssybulBgOhvS5h19T88F2femdlyszlcMTAAAAIFkNG4UACA5jDDPzM/VPqxfoU7fN17N7TuuXLx3W07tPGQZLzAoEQ9rkO6tNvrP6j0d2aGFJjiqWFKticYmWz/QwqgJAXOIsGwBMwkNbj+qzv91u6o7Hc+65crrWVS5XqpuJLACAxLN8lke//cQqffhHm7X/jLmA3EMvH9Nrxzr1vfvKNb84O8oVAgAAAIhHQYMLtm4XF1oRntvl1O2LS3T74hKd6OjX+i2Htb75iA619Ub0fXaf7NLuk136ztOtKspOU8XiYt2ysFjXzy9UDjd9AYgThAAAYAIGhgP64iM79bMXD47reX97S6nW3rmQlscAgIQ2pzBLjR9fqY/9dIu2HvKbes7eU926+9vPq67yCr31iunRLRAAAABA3DHqBODkfBrGYWpeuv7+9sv0d7fNV8uhdv1u61E9su24/L1DEX2fM90D+tXmw/rV5sNyOx0qm5OvmxdM0c0LpmjJtFy6BACIGUIAADBOR9p79clftOiVIx2mn+N0SP/+9qX6wMq50SsMAIA4Upidpv/92HX61K+2asOOk6ae0zMY0N/971Y1H2zXZ9+0mK45AAAAQBIx7ATAxVRMgMPhUPmcApXPKdDn37pUz+w+pd9tPaond57SYCAY0fcaDob00v42vbS/TV95fLeKslN102VTdNOCKVo1v1DFOekRfT8ACIcQAACMwzO7T+kffv3yuBKj6SlOffM9V+mOpVOjWBkAAPEnI9Wl/7mvXP/6+1f18xcPmX7ej144oFcO+/Wd95dpWl5GFCsEAAAAEC8MOwEQAsAkpbqdumPpVN2xdKo6eof02KvH9YdXjulF31kZ/PhNyJnuQf1261H9dutRSdJlxdlaVVqolaVFWuktVF4mowMARA8hAAAwoXdwWOv+tFs/2XRAoXHsEBZlp6rhgytUNjs/esUBABDHXE6HvnD3Ms3wZGrd47tM/x5tOeTXm77xnP797Uv19uXTGaUDAAAAJLiAwcECnQAQSXmZKXrvNbP13mtm60z3gB5/7YT+uP2ENvnOKhCNRIBGxuDtPdWtn2w6KIdDWjY9T6tKC3VdaaHK5+QrN51QAIDIIQQAAAZe2t+m/9P4ig6e7R3X866em69vv69MJbm0eQIAJDeHw6G/vaVUS6fn6tO/2qp2kx11/L1D+vSvXtaj247ri+9YRutEAAAAIIEFAnQCQGwUZafp/dfO0fuvnaOz3QN6YsdJPbb9uDa2Ri8QEApJ2492aPvRDtX/2SenQ1o8LVdXzy3QtfMKdPW8AhVlp0XlvQEkB0IAADCGid79L0lrbpyntXctUoqLWcYAAJxz04IpevRTN+qT/9uirYf8pp/3xI6TeulAG10BAAAAgARGJwDEg8LstNEOAe09g3pq1yk17TypZ/ecVu9gIGrvGwxJrx3r1GvHOvXjjQckSd6iLF0zr0Dlc/JVNidf3qIsjocBmEYIAAAuYaJ3/2enufXVqit017JpUaoMAAB7m+7J0K+rV+pLj+0cPbFhBl0BAAAAgMRmdMe1i4ufsFh+VqreVT5T7yqfqf6hgF70nVXTzpNq2nFKJzr7o/7+vjM98p3p0a82H5YkeTJTdNUsj8pm5+uq2flaPitPOYwQADAGQgAAcJ7J3P2/aGqOvndfueYVZUWnOAAAEkSq26l/e/tSlc/JV+1vto3rbgq6AgAAAACJyTAEQCcAxFB6iku3LCzWLQuL9YW7Q3rtWKeadp7UM7tP65Uj/nGfS54If++Qnt59Wk/vPi1JcjikhSU5Wj7Toytm5Wn5TI8WlOQo1U13WgCEAABAkhQKhfTY9hP60mM7ddTfN+7nv7Nshv7znsuVkeqKQnUAACSmty2frsXTcvTxn7do36lu08871xXgNy1H9fm3Ltb84pwoVgkAAADACkYhALeLEADig8Ph0LIZeVo2I0//ULFA7T2Den7fGT2757Se3XNap7sGLKkjFJJ2nejSrhNd+vWWkW4BqW6nFk/L1fKZebpipkdXzMyTtyhLbsbWAkmHEACApPfasQ79+x926KX9beN+bqrbqX9721K995pZ3IkIAMAEzC/O0cOfvF7/73fb9dDLx8b13D/vOa07v35GH7hujv6xYoHyMmmDCAAAANjVcDAY9vtOzr0hTuVnpepty6frbcunKxQKaefxLv1572k9u/u0mg+1a3A4/M92JA0OB/XKYb9eOeyXdFCSlJ7i1KKpuVo6PVdLp+dp6fRcLZyao/QUbmgDEhkhAABJ60z3gP7rid361ebDE2rXVDbbo69ULVfplOzIFwcAQBLJSnPr6++5SquXTNXnHn5VbT2Dpp8bCIb0440H9PDLR/VPqxfovdfM5g4HAAAAwIYMMgByMw4ANuBwOLRkeq6WTM/Vx28uVf9QQC0H2/VC6xltbD2rbUc6DLteRFr/UFAvH/br5cP+0a+5nA5dVpytJdNytWhajhZOzdXiqTmakpPGzW5AgiAEACDpDA4H9ZONB/TNJ/eqa2B43M9Pczv1mTsW6iM3zGMWGQAAEfSWK6bpWm+BPv/wq3ps+4lxPbe9d0ife/g1/fzFQ/r825bo+vlFUaoSAAAAQDQYdgLgPBxsKD3FpVXzi7Tq9WPUrv4hbT7Qpo37zmpj61ntPNE5oRvUJisQDI2OEtDWv369ICtVi6bmaOHUHC2emqsFU3M0vzhb2WlcTgTshn+1AJJGIBjSo9uP67837NH+Mz0Teo2rZnv0Ve7+BwAgaoqy0/Td95frkW3H9PmHXxtXVwBJ2n2yS+///l9UsbhE/7R6gZZMz41SpQAAAAAiKWBwIZROAEgEOekpum1RiW5bVCJJ6ugbUsvBdr10oE0v7W/TtiN+DRn9Y4iitp5BbWwdCSicb4YnQ5eVZGtByUgoYEFJji4rzlYW4QAgbvGvE0DCCwRDemTbMX3rqX3ad6p7Qq+R6nbqM3cs0Edv8HL3PwAAFnjrFdN1nbdQn3voVf3x1fF1BZCkpp0n1bTzpO5YUqJP3X6Zls3Ii0KVAAAAACIlQCcAJKG8jBTduqhYty4qliT1DwX08mG/Xtrfps0H2vTyYb+6+sffzTbSjvr7dNTfp2d2n77g69Py0lU6JVulU7JUWpz9+ufZKsllrAAQa4QAACSs4UBQf3j94r/v9MTu/JdG7v7/SuVyzS/m7n8AAKw00hWgTI9sO67PP/yq2nuHxv0aT+w4qSd2nFTF4mJ9+vYFunwmYQAAAAAgHgXCZwDoBICkkJ7i0nXeQl3nLZQkBYMhtZ7uVsuhdrUc9KvlULv2TvBGt2g43tGv4x39en7fmQu+npXqkndKtuYWZWleUZbmFWVqXlG25hVmKS8zJUbVAsmFEACAhDMcCOrhl4/p20/vm3Dbf0nKz0zRP92xUO+7ZjZ3/wMAECMOh0NvWz5dq0oL9dUn9uhXmw9NaF5i085Tatp5SrctKtanbr9MV87yRLxWAAAAABNn1AnAxV3FSEJOp0OXleTospIcvfvq2ZJGRgi8fNivVw77te2IX68c6dDproEYV3qhnsGAth/t0PajHW/4Xn5miuYVZWluYZZmF2ZqTmGmZhdkaU5hpgqzUukgAEQIIQAACaOjd0gPbjmsn754QIfb+ib8Om6nQx9YOUf/cPsCUokAAMSJwuw03f/Oy3XfdbP1H3/Yob/sb5vQ6zy165Se2nVKq0oL9aFVc1WxuISwHwAAABAHAsHwaV+X02lRJUB8y8tI0c0LpujmBVMkSaFQSCc6+7XtSIe2HfG//rFDHX3j76ZnhfbeIbUf8qvlkP8N38tKdWlWwblgQKZmFWRqVn6mZuZnaGZ+pjJSXdYXDNgUIQAAtrfrRKd+svGAfrf1qPqHDPqGGbh5wRR97q2LNb84J0LVAQCASFo6PU+/qr5Of3z1hL702E4daZ9Y8G9j61ltbD2rGZ4MfWDlHL17xSzlZ6VGuFoAAAAAZhmFANwuwrvApTgcDk3Ly9C0vAzduXSqpJFgwJH2Pr12rEOvHevUq0dHPp6Ks44BF+sZDGjXiS7tOtF1ye8XZadpVkGGZuVnakZ+hqZ7MjTTk6EZ+Rma4clQVhqXPYFz+NcAwJaGA0E9seOkfrLxwITvBDyftyhLn3vrEt26qDgC1QEAgGhyOBx68+XTdNuiYn3/OZ+++0yregcDE3qto/4+ffmPu/TfG/bo7iun60Or5mrp9LwIVwwAAADAyLBBCMBJi3DANIfDMXIXfUGm7lo2bfTrp7sGRoMBu050adfxTvnO9BiGcOLFme4Bneke0NZLdBGQRrokzPCMhAOme9I1Le+vH6flpWtqXrpSXHQVQXIgBADAVvaf6dHvth7V+i2Hdbyjf9Kvl5eRor+/bb4+uHKuUt388gcAwE7SU1z6u9suU9WKWar70y49tPWoJnreYmA4qAe3HNGDW45oxZx8Va2YqTddPk256YwGAgAAAKwQNOoEwBgvYNKm5KTploXFumXhX2+G6x8KqPV0t3Yd79KuEyPhgJ3Hu3SmO767BlxKR9+QOvqGtON45yW/73BIU7LTNC0vXSW5I6GAqXnpmpo78qfk9c/pKIBEwE8xgLjX1jOoR7Yd029bjurlw/6IvGZ+Zoo+dqNXH1w5Rzmc3AcAwNZKctP1tXuv1Cdvna9vP7VPD7888TCAJG052K4tB9v1uYdf0+rFJXrHVTN088Ip3C0AAAAARJFhJwBCAEBUpKe4tHR63hu64rX3DGrvqW7tOdmlvSe7tOdkt/ae6rZlOOCcUEg61TXw+liEjjHXZae5VZybpuKcNJXkjgQGinPSVPz6xyk5I9/LTnPLQZcSxClCAADiUv9QQE/uPKXfbT2iZ3afNjwIMKsgK1VrbvTqAyvnKJs0HwAACaV0Srb++91X6u9vm6/vPN2qh14+OqmWhoPDQT26/bge3X5cBVmpetsV0/SOsplaPjOPg3wAAAAgwoIhOgEA8SQ/K1XXzCvQNfMKLvj6uXBA6+lu+U53q/V0j1pPd+twW++kAvnxpHtgWN2nh+U73RN2XXqKU1Ny0jQleyQYMPJ5uopyUlWYlaYpOakqyk5TUXaaMlNdnEuApbgCBiBudPYP6Zndp7Vhx0k9s+uUugaGI/bahVmpqr7Jq/uum0MrHwAAEpx3Srb+697lr4cB9um3WycXBpBGOhP9ZNNB/WTTQc0uyNTqJSW6Y0mJyufky02HAGDSGhoatH79evl8Pvl8Pnk8HhUUFKiiokI1NTUqKyuLdYmj7FQrAAB2QicAwB7GCgf0DwV08GzvaDhg/5leHTjbo/1netTWMxijaqOrfyiow219OtzWZ7g2PcWpouw0FWanqTArVYVZqSrITlVRVpoKslJVmD0SHCjITlVBZqoyUl0W/A2QyGx/JcxOB992qhWwyjF/n5p2ntSGHSf1ou+shgKRjQpOzU3XR2+Yp/dfN1uZqbbf5AEAgHGYW5Slr1Qt19/fdpm+9+w+/ablqAaHg5N+3UNtvfrB8/v1g+f3Kz8zRbctKtHqJSW6aUER+xvAONXW1mrdunWSpIqKCtXW1srr9crv92vz5s1at26dGhoa5PV6tX79+pgeN9upVgAA7MgouEsnACC+pae4tHBqjhZOzXnD9zp6h7T/bI8OnOmR70yPDp7t0cGzvTrU1puwAYGL9Q8FdaS9T0fajQMD0khooCBzJCiQn5mqgqyRj/mZqcrPSpEncyQs4MlMUX5WqvIzU5SRQrcB/JUjFDLosROnLj74rqqqesPBt6S4OPi2U62TsWnTJq1ateqCr23cuFErV66MUUWIR4PDQW091K4XWs/q6V2ntP3o2HN3JuOaeQX60Mq5umNpCfN7AQCApJG7+X+1+ZB+vumgjnX0R/z109xO3TC/SDctmKLr5xeqdEo2B9/AGPx+v26//Xa1tLTI4/HoySefHPNYuKamRg0NDZKk+vp6VVdXW1mqrWqdLI7rAQCxtOTzf1LvYGDM76971xW69+pZFlYEwApd/UOjgYCRjz0jd9e39+qYvy/iNw4mslS3U56MFHkyU+TJSFVeZspfH2emKjdj5HHeRX9yM1LkImiVcGwXArDTwbedao0EThbgUoLBkHYc79QL+87ohdaz2ry/TX1DY+/MT0Z6ilP3XDlDH1w5V0um50blPQAAgP0NB4Jq2nlSP954QC/62qL2PiW5abq+tEir5hfp+vmFmpaXEbX3AuymtLRUPp9PktTa2iqv1xt2fSyPme1U62RxXA8AiKWF//JHDYTp3PVfVcv1rvKZFlYEINYCwZBOdvbrcFuvDrf3vf5xJBxw1N+n4/5+w1EiMCcnza3c1wMBuekjn+dlpCg3PUW5GW7lpqcoJ92tnEs8zkl3czNmHLJdr8ry8vLRg+/m5uawB9/19fWSRtrw19TUSJKlB992qhWIlMHhoF471qGWQ35tOdCmTb6z8vcORfU9Z+Zn6APXzdG7r54lT2ZqVN8LAADYn9vl1F3LpumuZdO060SnfrrpoH7XcjTiQcWTnQP67daj+u3Wo5Ikb1GWVpYWqnxOvspm52tOYSadApCUqqqqRo+V6+rqDC+qSyPHzE1NTfL5fKqpqdGKFSss6aJnp1oBALA7o3EA3KUKJB+X06HpngxN92To2kt8PxAM6VRXv475R9rsH/X36djr4YBjHf063tEX9esTiaJrYFhdA8M66jc3ruBiGSkuZae7R4IBaSPhgOw092hQIDvdrew0l7LTLvo8za3sNLey0lzKSnMrze3kXEmE2KoTQFVVlRobGyWNHHyvXbvW1PPOT+03NzdbdqLALrVGCncMJKcTHf1qOdSuloPt2nrYr+1HOyIya9dIRopLdy2bqndcNUPXzy/iIAAAAExKR9+Q/rj9uH679ahe2h+97gDnK8hK1VWzPCqbk6+rZnu0fKZHWWm2y2kD49LS0qLy8nJJksfjUXt7u+nnnh+aLysrU3Nzc1RqPMdOtUYKx/UAgFia99lHFe5qxbfee5Xetny6dQUBSAi9g8M63tGv4/6RUMDxjn6d6OzXyXMfO/t1pnsw1mXidSkuh7LS3MpKvTAcMPL5yMebF0zRrYuKY11q3LNNCMBOB992qjWSOFmQ2ILBkI6092nH8Q7tONapHcc79dqxTh2PwjzdsTgd0vXzi/TOshm6Y8lUTpIDAICoONzWq4dfHrmD33e6x7L3dTqky4pztGR6rpZMyx39mJ9FpyMkjvLycrW0tEga6X53riueWeffEbJ+/XpVVlZGtL7z2anWSOG4HgAQK8FgSN7/+1jYNd97f5nedPk0iyoCkEwGhgM61Tmgk539Ovn6x1NdAzrV2a+TXf2j3+vsH451qZD0qdsv0z+tXhDrMuKeba6grVmzZvTze++9d1zPra6uHr2w3tLSosbGxqgefNupVuBSznYPqPV0j/ad6taek13acaxTO493qmsgNr/gFk/L1TuvmqG3XzldJbnpMakBAAAkj1kFmfq72y7TJ2+dr+1HO/TblqP6wyvHdLYnuncGBEPS7pNd2n2yS797fYSAJE3LSx8NBcwvztb84mx5i7KVkeqKaj1ApPl8vtGL6pJGw/PjUVZWNvoa9fX1UTtetlOtAAAkAjMzvZ10AgUQJWlul2YVZGpWQWbYdX2DAZ3pHtCprgGd7hrQ6e7XP573+EzXgM50D2jAgo7JySo7jfMhZtgiBGCng2871YrkNjAc0JH2Ph0826PWUz1qPd2tfae61Xq6W+0xnpHjcEgr5uRr9ZISrV4yVfOKsmJaDwAASE4Oh0NXzPToipke/ctbFmvLwXZt2HFSG3ac1KG2XsvqON7Rr+Md/Xpy16nzapNmeDJUOmUkFFA6JVveKVmaU5ipkpx0TpAiLl18J31FRcW4X2PFihWjx8tNTU3y+/3yeDyRKO8CdqoVAIBEEDTRsNjNPi6AGMtINRcWCIVC6hkMjAYCRv4M6kz3gNp6BnW2Z1Bnz33ePaj23kGZyELhdXSJNscW/5XsdPBtp1qR2IYDQZ3qGtDxjj4dbuvTobbe0T+H23p1orM/7Iwtq6WnOHXD/Cm6Y0mJbltcrKLstFiXBAAAMMrtcuo6b6Gu8xbqX96yWHtOdmvDjhPasOOkXjnSYXk9oZB0pL1PR9r79Oye0xd8L9Xt1Mz8DM0uyBz9M6sgUzM8GZruyVB+ZsoFbcoBqzQ2Nl7wuKCgYNyvUVpaesHjBx98UNXV1ZOq61LsVCsAAImATgAAEonD4VD26/Pr55q4yTEQDMnfOxIGOBcKaOsZUlvPgNp6hka+3jM4uqa9Z0jdMercHA+yCQGYYov/SnY6+LZTrbCnUCikroHhC1rMnOzsf/0Osb6Rj/5+nerqj/vk2LyiLK0qLdTNC6boxsum0NIWAADYgsPh0MKpOVo4NUd/d9tlOtHRr6adJ/X83jPa5Durjr7YdlUaHA7Kd7pHvtM9l/x+mtupaXnpmpaXoWme9NHPi3PSNOX1P0XZaUpPYd8MkeP3++Xz+S742kTC7hc/p7m5eRJVXZqdagUAIFEETJzIpBMAgETlcjpUmJ2mwuw0zS8295zB4aD8fYPy9w6pvWdQ7b1D6nj9sb9vSP7zH/cOqaNv5E8ihAeyUm1xeTvm4v6/kp0Ovu1UK+JHMBhS9+Cw/D1DausdVHvPoNp6ziW9/pr8On+2jF1nyRTnpOn6+UVaVVqo6+cXabonI9YlAQAATNrUvHTdd90c3XfdHAWCIe041qkXWs/ohX1ntPlAm/qH4mvfbWA4qANne3XgbPiRBrnp7gtCAQVZqcrPTB35mJWqgsxU5WeljH49ze2kwwDGtGXLlgseT7Tb3cVB+6ampomWNCY71QoAQKIwEwJwsa8JAKNS3U4V56SrOCd9XM8bDgTV2T8sf+/gaDCgo29InX1D6uwffv3jkDr7hl//OPL9rv6Rx0OB2N99yjgAc+L+v5KdDr7tVCsiYygQVO9AQL1Dw+oZGFZX/7B6BgLqHhjZIHYPDKv79Y/nNpoXbFRf34DG+x37EzU9L11XzcnX1XPydf38Is0vzubEMAAASGgup0OXz8zT5TPz9PGbSzUwHNDWQ35tbD2rloPtevmw3zap+87+YXX2D6t1jI4CF0t1OZWbkaK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      "text/plain": [
       "<Figure size 2400x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as st\n",
    "\n",
    "alpha = 0.05\n",
    "\n",
    "deg_of_freedom = 20\n",
    "\n",
    "x = np.linspace(-4,4,100)\n",
    "\n",
    "fig = plt.figure(figsize=(6,2))\n",
    "plt.subplot(121)\n",
    "plt.title(r'$t$ Distribution')\n",
    "plt.plot(x,st.t.pdf(x,deg_of_freedom),'-')\n",
    "plt.subplot(122)\n",
    "plt.title(r'$\\mathcal{F}$ Distribution')\n",
    "plt.plot(x,st.f.pdf(x,1,deg_of_freedom),'-')\n",
    "\n",
    "\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Realizando os testes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.351243503329171\n",
      "4.351243503329288\n"
     ]
    }
   ],
   "source": [
    "#st.t.ppf?\n",
    "\n",
    "alpha = 0.05\n",
    "\n",
    "print(st.t.ppf(1 - alpha/2,deg_of_freedom)**2) # funcao quantil\n",
    "\n",
    "print(st.f.ppf(1 - alpha,1,deg_of_freedom))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "st.t.ppf?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}