1_Ridge_Regression_Solutions.ipynb

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   "source": [
    "# Introduction to regression\n",
    "\n",
    "Linear regression is one of the typical ways to compute the relationship between independent variables $X$ and a dependent variable $Y$. Linear regression relates $X$ and $Y$ with a series of weights, which we will denote with $\\beta$ here.\n",
    "$$\n",
    "Y = \\beta X\n",
    "$$\n",
    "We usually know the values of $X$ and $Y$ so we must use these to then solve for $\\beta$. The typical way for solving a linear system of equations like this is to use ordinary least squares (OLS). OLS is the best unbiased estimator for a system of equations, but there are other types of regression that can achieve lower mean-squared errors, especially on unseen or held out data. OLS performs poorly in the following scenarios:\n",
    "- The number of predictors is high compared to the number of observations! OLS also has no unique solution when there are more predictors than samples (this is referred to as an underdetermined system), therefore it will cross-validate quite poorly in this regime. \n",
    "- *Multicollinearity*. Multicollinearity occurs when independent variables in a regression model are correlated . Correlated independent variables will lead to very poor cross-validation, and in some cases OLS will not even work!\n",
    "\n",
    "**Both of these scenarios are quite common in neural encoding models!** So we need a solution: **regularization**.\n",
    "\n",
    "Regularized regression (which includes ridge regression and lasso regression) works by punishing solutions with large $\\beta$ values, where OLS implies no restrictions on the $\\beta$ values that are found. This penalization reduces model variance, which translates to improve model predictions on held out data (ie. cross-validation).\n",
    "\n",
    "**In this notebook, we will implement OLS and ridge regression to see how their performance compares in different situations**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/cheninstitutecaltech/Caltech_DATASAI_Neuroscience_23/blob/main/07_10_23_day1_ethics_regression/code/diy_notebooks/dimensionality_reduction.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "# install dependencies\n",
    "!pip install gdown scikit-learn tqdm pandas matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import a dataset that describes the average miles per gallon (MPG) for many different cars. The displacement (the total cylinder volume of an engine), horsepower, cylinder number, and other information about the cars is also included. We will try to see how well we can predict fuel efficiency from these variables.\n",
    "\n",
    "Visualize the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model_year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165.0</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration  \\\n",
       "0  18.0          8         307.0       130.0    3504          12.0   \n",
       "1  15.0          8         350.0       165.0    3693          11.5   \n",
       "2  18.0          8         318.0       150.0    3436          11.0   \n",
       "3  16.0          8         304.0       150.0    3433          12.0   \n",
       "4  17.0          8         302.0       140.0    3449          10.5   \n",
       "\n",
       "   model_year origin                       name  \n",
       "0          70    usa  chevrolet chevelle malibu  \n",
       "1          70    usa          buick skylark 320  \n",
       "2          70    usa         plymouth satellite  \n",
       "3          70    usa              amc rebel sst  \n",
       "4          70    usa                ford torino  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PREDICTOR_LABELS = ['cylinders','displacement','horsepower','weight','acceleration','model_year','american','japanese']\n",
    "dataset = pd.read_csv('https://raw.githubusercontent.com/mwaskom/seaborn-data/master/mpg.csv')\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The shape of x is (392, 8)\n",
      "The shape of y is (392,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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HHxg5ciR69+6N119/HRcuXHDE/IgbbMk/b3FMEG0Rb9cjaWhs36kK6G/E3sxVpNaFB+KNSQOQ1C0Mb0waAACYnp6Db4+WI33vadnzlFXVWTwueZAJogmrjSatVosJEyZgy5YtKC0txaxZs/DZZ59Bp9PhL3/5C7Zs2QKjUXn9EEIZ7X01FscE0Rbxdj2ShsYmJHYRjWNCAvjSAlwYb8vhc3hmQx5yTlfimQ15+CCrmM9Zqm804vXvTyC7uEJUkoBCcAShjFYlgkdERODWW29FUVERioqKcPToUUybNg2hoaFIT0/HyJEj7TRN4qSkmKV0TBBtHW/UI7nFFdw4JiQAMzJyUac3wE+rhgpNRpFGJT7GwZIrovG3R8v58gLC1XC0iIMgWsam4pYXL17E8uXLcdNNN2HkyJGoqanBtm3bcPr0aZw7dw73338/pk2bZu+5tmmuNTRaHBNEW8Xb9UgaGuPG+WVVfOiuodHIe5MMksZYPTu3N3tsYSiuNSE4zstFRTEJb8dqT9Pdd9+NH374AT179sSsWbMwdepUhIU1u3LbtWuHBQsW4M0337TrRNs6IYE+qK1uEI0Joq3TVvWopKIWKzKL+LGvRgW1SoX6RiOf0M3RJTQQWrUKjUbTNqP2CMVRHSeiLWG10dS5c2dkZWUhJSXF7D6dOnXC6dPyCYeEbXQI8AUERlOHAF8XzoYg3IO2pkdcZe6Kaw2i2ksLxvRCZJA/PsspQWQHf2w90rxQJCTQB2/dNxDzN+bDYGTw0aiw/N6B0BsZbzB9ebDM5rAc1XEi2hJWG03r1q1rcR+VSoXY2FibJkTIowsNQOGFq6IxYRvUEsJ7aEt6JPTo+GvV8NOq0dBoRICPBpFB/nhmQx6/r69GxbdRGRgTghkZubzB9MmjQ5GcEG5yTFu9REo7AdB9R3gDVhtNTz/9NLp3746nn35atP3dd9/FyZMnsWrVKnvNjRBwuLTK4phQBoUSvIu2pEdCj059oxFL0nojvL0fkuLCsHrXSdG+w7t3ROcgf0xI7IKyqjr+fXoDw9Ltx7EkrQ+SE8Lt4iVSkkRO9x3hLVidCP7VV19h+PDhJtuHDRuGL7/80i6TIkzpFdHB4phQhtwfCcJz8XY9EiZYC8sC+GvVuFJ7HRXXmkL2w+LDRe/be7ICG3JLMT09BzEhAfAXVATPL6vGA2uzkV1cobjUgFyit3BbS0nkdN8R3oLVnqaKigoEBwebbA8KCsIff/xhl0kRphySLBuWjgllUFNh78Kb9UjOO/PD3BHYXlCOt3YU4v2sUwCA5T+cgErVXGdAo1LhuqG5LlN+WRXm3dkTS7efEB1/c945vD5pAH9Ma+YBwCrPEd13hLdgtaepe/fu+P777022b9++HfHx8TLvIOxBnd5ocUwog1pCeBferEfmQmfh7f1wXbA6Tm+EaGxgpqvk0vpFwVdSwGlCYhf+/yszi7B0+wmMWZllUjZAbh7Weo7oviO8Bas9TfPnz8ecOXNw+fJl3HHHHQCAnTt34q233vKq/AF3IyRAi6q6RtGYsA1deCCJtpfgzXqUFBcGf60a9Y1G+GvViAkJwLLtx1F44So0KtN6TBzS8gIDY0KgCw/Ej/NH4vOcsyitrMOYvhEoq6pDSUUtPs85K6oYvr2gHI+lJojmIeclstZzRPcd4Q1Y/Zf30UcfRUNDA1577TW8+uqrAIC4uDisWbMGU6dOtfsEiSYMkhor0jGhHFrF4z14ux5xd7mRMUz96IDIo6RRq/gVccK6TEaJp4kzjnLOVOKhpKZVhFxozU+rblFLzCV6p08fgs155zAhsQvdR0SbwSZ3xRNPPIEnnngCly9fRkBAANq3N19xlrAPtdcNFseEMmgVj/fhrXqUc6aSr8V0XcatdNdNkbi9d2fEhATgkY8O8IaTkYH3RPlqVIgJCRB95+eO7iGqJC5Eq1YhrV+UybmkXqKSilq+hcvWvPN0HxFtBpvaqHB06tTJawTK3Ynv1M7imFAGreLxXrxNj4Qr2/y0apOcpEeSY3Hv4BgkJ4Tjk0eHwufG635aNR+6u25gyCq6LPrOAxAdl1tZ56NR4dOZQxUZP3QfEW0Vqz1NFy9exMKFC7Fz505cunQJTOIKNhjIA+IIekYE4fdLf4rGhPXQKh7vwpv1SBoWA4APsopRcL4ajw7vJipQmV9WhZm3dkNooC+OlFXzDXkBoKSyVvSdHxgTgrmjewAA71VqqcYSt7ourV8UdOGBovvI54Y3iyDaAlYbTdOnT0dJSQleeOEFREVFiZa6Eo7j94s1FseEMqibu3fh7XokDIuVVNRi0+FzqNMbsHjTUQzShQIA7lyZxYfZ/LVq3HdLjOgY3To2f+djQgL4sFqAj4Y3gszdByUVtaLjr8wswo55qdCFByJ9+hA+LDgjI5dCdESbwGqjac+ePdi9ezcSExMdMB3CHEUCL5PcmFAOreLxHtqSHpkLiQnzkuobjfjx+CXR+348fgkLx/aGLjwQXx4ss6oCuDCvijs+956yqjo+j4p6zhFtBatzmrp27WriAiccT3igj8UxQbRFvFmPpFW4pdW7Y0ICUHGtQZTr5KtRI6KDn+g4IQHNWqG0Arhwfz9BNXFfjYp/j7XHIghvwGpP06pVq7B48WJ88MEHiIuLc8CUCDniOrZDRUmVaEzYBpUc8B68VY/MrfKUC7MJjabrBiPiOrZDXlk1v+2WuFD+/9aGp3Xhgfh4RhIfhlMLwp+tCXXTPUh4KlYbTZMnT0ZtbS0SEhIQGBgIHx+xx6OyklZROIL8siqLY0IZVHLAu/BWPTJXDZz7EYbZpOUI9pz8Q3Isccsla8PTwjCcMDwnPBbnFVNiBNE9SHgyNnmaCOcztFs49hZXiMaE9dijqzvhPnirHrW0ylP4uq9GJTKcHhjSFe/+XMyPpyTpAIi9OwB4j1VZVR3/r5zRI52Lj1qFRV8dwYTELkhOCBcli/tp1ci8kShuDroHCU/GaqNp2rRpjpgH0QJnKq5ZHBPKoJID3oW36lFLoS9pqI6rFu6rUSE00NfkeELvjp9WDRXAt04RIuf5EZ7LR63CMxvyAAAbckuxflYy8suq+GTxhkYjPs85i+6dO5j1OtE9SHgyNlUELy4uRnp6OoqLi/H222+jc+fO2L59O3Q6HW666SZ7z5EAcK6qweKYUAaVHPA+vFWPWgqjCUN1nKfpuoHh0wMlov0+yymB3sjMVgEXUqc3mPSeE3qoVu86Kdp/c945xEvyK9ftOQ29gZkNvdE9SHgyVq+ey8rKQv/+/XHgwAFs2rQJ1641eTzy8/Px0ksv2X2CRBPh7Xwsjgnl6MIDce/gGBJrL4D0yHQV28NDdaLXpyTpTKqL+2vNS/+KzCJ+xR7noVq4MR+jVuxCz87iiusTErsgrV9Uc1VxtcqkDIEcdA8SnorVRtPixYvxz3/+E5mZmfD1bXYD33HHHcjOzrbr5IhmuoYGWhwTypEu5SY8F9KjZs/N8vsG4oe5IzDztnjckxgNP60Kd/bpDP2NhrzcPpnzUpExIwmTh3TFC+P68O1XOBpuJHsD4vwjvYFh2fcnoL2xu48aiA4JgC48EK9PGoCkbmFYnNZbURkCugcJT8Xq8NzRo0fx+eefm2zv3Lkz/vjjD5l3EPagUFIBXDomlEErd+yHOywbJz1qQhjKW7f7FL7OOw8AyDx+CZnHL/Hf9XsHx4ia7fpomj1DHEJjJykuTLSPcF+9EdheUI6BMSF8nlPO6Uq8PTkReiOz2JaF7kHX4A73rKdjtacpJCQE5eXlJtsPHz6MLl262GVShCl1emZxTCiDGo3aB2HYZuyqX1zmMSA9MkWa0wSIv+tS75Gw0e+StN4iI0YXHihqBqxVi71SVbV6fJJ9VrRtx7GLFkNvdA+6Bne5Zz0dq42mBx54AIsWLcKFCxegUqlgNBqxd+9eLFy4EFOnTnXEHAlQTpO9oCrG9sFd/vC1NT2yFNbiXru1u2k5Eu67XlJRi4prDXwOkr9WjZm3dsOStN54Y9IAnPrjT5yvqhO9NzkhHDvnj8Ty+wbifklfOwaGrmHiZr3BAVqLoTe6B12Du9yzno7V4bl//etfmD17Nrp27QqDwYC+ffvCYDDgoYcewvPPP++IORIA6vUGi2NCGbRyxz64y7LxtqRHlsJawtekDIsPw7JJAwFAVHbgidQEfLT3NN7POgU/rZpfVceVEkhOaDa+uPBfxTXxqt3QQF+k9YvCR3tO47qBwUcNfHXoHD7PKYW/Vs039xVC96BrcJd71tOx2mjy9fXF2rVr8cILL6CgoADXrl3DoEGD0KNHD0fMj7jBn9eNFsfuAsXM2wbu8oevLemRpaKQwtekHDlXbVJFvKHRiMra66L6SkI2550TGU0caf2isCKziC9kmdYvCrrwQPw4fyRyzlSi+NI1rMlqKqxZ32gUlS+QaoP0O0Pa4Vjc5Z71dGyq0wQAOp0OOp2u5R0Ju9DeV41rAkOpva/VkVWH4wkJntZWLybMY207DkfSFvTIkqcgJiRANqkbACYM6iIKy9U3GuGjUUGjAl9N3EfdlNjNMSzefMcBo9Eo+hdo/i58kFUs+56WtCG7uILvb+eu2uENuNM966koMprmz5+PV199Fe3atcP8+fMt7rtixQq7TIwQo9WoARglY/fCE9ojbC8oFz1dSwv5Ee5PW9Ujc54CbjUcl9S9+K7eePXb4wCaklbH9Y/mDRbfG8aS3sDweU4pf2wGFYBmg+tCTb3sHD7IKuaNK72xafzaxP7863KeKMCyNpRU1PIGk9zrBOFOKDKaDh8+DL1ez//fHCqVyuxrROuoqmu0OHYHKGZOOIO2rEdyngLpariiS80tloxoCrWZa+7L0WhUthq34Hy17FgYWsucl2pi2FnShpwzlSIPmY9GRdpBuC2KjKaff/5Z9v+E8+jZuR2KLv0pGrsbnhAzN/ckTHgOpEdipAbJsPhwbMht9iINiw/H1rzzqNMb4K9Vw8iYifEk3G7pvnh0eDe+JhMA/GVgND7IKsZbOwr592bOS8W9g8Wr7Cxpg3D+PhoVPnl0qFtqB0EANuQ0VVdXw2AwICxM/CRQWVkJrVaLoKAgu02OaKZHRJDIaOoR4Z6fsyfEzBljon8J23CHxF3So6Z7Ln36EGzOO4cJiV1QJikZoDcy/DB3BLYXNNWzGhgTgq355/Db+Rrc1qMjfjtfg/rrBnTq4AcDAx5JjhX9PoW/5/GDuuCPaw349EAJxvWPxPIdRaIEdEshb3PaYM3Dlqu/c64+P+F6rDaaHnjgAdx999148sknRdu/+OILbN26Fd99953dJudM3P1m2HfyssUxoYztBeWi5qaU02Qb7pL07616xKFEl4QVvrfmnUf69CGyobBVP/7O5zVx90B+WbXJ8X48fpFfICH9PadPH8IbSh/8cko28byqVm/1dSl52HL1d87V5yfcA6uziQ8cOIDbb7/dZPvIkSNx4MABu0zK2XhCpdQrkhwm6ZhQxpXa6xbHhDLcpVCeN+oRh1Jdkv4uyqrqRL3odOGBon3M5TVxmOs9V6c3iPKjhNXEhTAwi8UtbdVbV3/nXH1+wj2w2mhqaGhAY6PpH2y9Xo+6ujqZd7g/nnAzxIUHWBwTyggN9LU4JpSRFBcmqirtqsRdb9QjDqW6pKTCtnAfXxlDR4ivIBFbeuwJiV3gd+P37qdV45NHh2JJWm/+mL4aFdL3nrFoENmqt1xZBUvX6Ui8oZI5NUpuPVaH55KSkvD//t//wzvvvCPa/v7772Pw4MF2m5gz8YRVX2Ht/HCmok40JqxnYEyIxTGhHCb51xV4ox5xKNUlaU4QANkwknCfwyVXMH9jPgxGBnExE3Gun/R956vqTApiPpaagLR+Ucg5U4mKaw1Yuv0EAPOlA2zRW2lZhfTpQ5weGvOEhS6WoPCifbDaaPrnP/+J0aNHIz8/H6NGjQIA7Ny5E7m5udixY4fdJ+gMPOFmKDhXZXFMKEOaJCsdE8rIOVMp+uPpqro63qhHHNbokjAnSFj5W2i4CPfJOVMJw40yA9LeAnojRL9P4ftW7zop2perHM7tU1JRy+dOmTOIbNFbaVmF1ty32cUVfNK8XNVzS3jCQhdzeEIdPU/AaqNp+PDh2L9/P95880188cUXCAgIwIABA7Bu3TqPbl3g7jdDas/OyDx+STQmrMdH0qVdOiaU4S7eWW/VIw5bdMnS74ZLwI4JCeD3ESaGA4DmxjHkkJYz6Nm5Pb48WCZK6FZiEFl7XVw4uL7RaHU4WJh0fr6qDg+szQYg32PP3Pvc+W+DUtzlnvV0bGqjkpiYiM8++8zecyEsYJQsj5eOCWW8L2nz8H5WMcYP6uKi2Xgu7uSdJT0SY6lyuHQlXFlVHZLiwvDFryV49+eme8MA4HDJFdnfqbRS+LLtJ6A3ilufOOoB1JZwsPSak+PFhsIn2WdljSZvDGW50z3rySgymmpqavh6JzU1NRb39dS6KO7+VHGopMrimFDGeYlbXzomlOMq72xb0CNLKNGqliqHc6vsuCKUOWeuiPb9LKdE0cOE3uic1ie2hoOl1yxFFyZ/DG8NZbl7RMUTUGQ0hYaGory8HJ07d0ZISIhsewLGGFQqFQwG+U7b7ownPFWk9uyEr/POi8aE9fwlMRqfZJeIxoRn4e16ZInWaJWl8ExSXChyTleKxsJzckaasKK+r0YFtUqF+kajw8M9toaWpO+7J7ELfi5srnFnTkcplEWYQ5HR9NNPP/EVd+3ZtmDp0qXYtGkTTpw4gYCAAAwbNgyvv/46evXqxe9TX1+PBQsWYP369WhoaMDYsWPx3nvvISIiwm7z8ISnCmkRObmickTLDOwaKjKaBnYNtbA34Y54ux5ZojVaZSk8c/oP8RL0y9ea6pfJGWkfz0jiE6mjQwJEx3OUx56b+/tZJ/Hb+Rqz4cOWrlla3sBcQjmFsghzKDKa3n77bQwaNAhBQUE4e/YsJk+eDD+/1i95z8rKwuzZszFkyBA0Njbi73//O8aMGYNjx46hXbum3mrz5s3Dt99+i40bNyI4OBhz5szBxIkTsXfv3lafn8MTnirq9Y0Wx4Qy8kuvmIylfbII98bb9cgSrdUqufBMSUUtdvxWLto2LL4pz0dqpG0vKOdXx23NO48f5o7g7x9He+wPl1zB5zlNSehc/zslIcTzVXXIvZH8HhMirm8nHQuhUBYhhyKjadu2bfjzzz8RFBSEGTNm4K677kLnzq1fvfX999+LxhkZGejcuTMOHjyIESNGoLq6GuvWrcPnn3+OO+64AwCQnp6OPn36IDs7G8nJya2eA+AZTxXck5+5sbvg7rlhGw+WmYxfvae/i2bj2bjqd+3temQJR2hVzplK6CV1B7hcJa6gpN7A+MKO5jxdjvbYf7T3tMm4JaMpu7hCtFruLwPEjYh3FV2yuuyAI3B33SSaUWQ09e7dG0uWLMHtt98Oxhi++OILswmWU6dOtXky1dVNfZA41/vBgweh1+sxevRo0Vx0Oh32799vV5Fy96eKmZLu4jOHd3PdZMzgCblhBoPR4phQRklFLe5cmYWGRiPf2d5Zv+u2oEeWUNqnTUnPOq78ALecH2iq9J0UF4bs4go88tEBUUHJ6JAArMwskl36L/SC+WhUFr04ttDOR/znqqOCAr+b886JxrlnxZ7mwgtXrZpDSUUt3/g4rV+UXb7znqCbRDOKjKY1a9ZgwYIF+Pbbb6FSqfD888/LJl+qVCqbRcpoNGLu3LkYPnw4+vXrBwC4cOECfH19ERISIto3IiICFy5ckD1OQ0MDGhoa+HFLq2s8hT+uNVgcuwOekBsW4KuBvt4gGhPW89+cEtFqpv/mlGBRWm+nnJv0yDJK/ghL98mYkYT8sioATcYAAN5gApoLSkaHBJhd+q8LD0T69CH8+2Zk5NrNACipqEX2mQrRNn8F9660rlS38ECUVzeXTYgOVm7YlVTUYszKLN64XJFZZJeHBU/QTaIZRUbT8OHDkZ3d5OJUq9UoKiqyiztcyOzZs1FQUIA9e/a06jhLly7FK6+8YqdZuQ+fHigxGc+8Ld5Fs5HHE3LDNGo1mirRCMeEtZRU1locOxLSI8so+SMsV37gsdQE/vUvD5aJFpv43OhH19LS/7KqOv599jQAcs5Uwiix0sb0bTn5Xi95U6jEO2XN3HLOVPIGE2C/SvhKdZNCeO6Bor8YEydO5J+Q0tPT0aFDB7tOYs6cOdi2bRt+/vlnxMQ0J+VGRkbi+vXrqKqqEu1/8eJFREZGyh5ryZIlqK6u5n9KS0tl95Pi7o0MHx6qszh2B7h8C2F3dXfjZl2IxTGhDOkfLCV/wOxFW9AjDlt0ydoGvgE+GsSEBOD17Scw+7NDyC6uEL3uo1Hhk0eHQhce2OKxk+LCRA197fXglBQXxjfr5ZAaRGbfd+OvnI/a9HtqqfdkdnEFFn11BNnFFfyxuCbVQNP1xYQEtPrvhlA306cPQc6ZSpPjcZ5BS42QCedgdSL4o48+irS0NAQEtD5ezRjDU089hc2bN2PXrl3o1k2cpzN48GD4+Phg586dmDRpEgCgsLAQJSUlSElJkT2mn5+f1StpPCGm3LG9n8Wxu+DuuWEnymssjgllHL9QYzIeD+dUVvd2PeKwVZeUJIsL94kJCcC09Bzeg/Tt0XKsn5Usewwlx1ZJ/rUHuvBAfPLoUD70p9STfbjkCp/krjcCH+8XJ5N/niNfEVyaQM61W9kxL5XPaRoYE4IZGbl2+bvBvc/c75tCeO6DSxPBZ8+ejc8//xxbtmxBhw4d+LyA4OBgBAQEIDg4GDNnzsT8+fMRFhaGoKAgPPXUU0hJSbFr0qUnfCE/yykxGVP7D+s5V91gcUwoo7SyzuLYkXi7HnG0tiZTS/ty+3x5sIw3mDg2553D65MGmDW4zB1bGMKqt3Mj5+SEcOycP9KqEJVUNwvOiY19c50VpAnkwsbEXBjTXGNkW7H0+3Zk6gOF/axDkdH0/vvvY/78+XZPvFyzZg0AYOTIkaLt6enpmD59OgBg5cqVUKvVmDRpkqiYnD3xhFycKUk6UcXeKUnuF57zBOLCA3Cmok40JqxnTN8IfHu0XDR2Ft6uRxzO0iUupCY0nCYk2vZA5ug5W+vJHts3QqSbqT07iRqfzxgWJ/u+np3bm4ylxoU9r7WkohYV1xr434P0eFySPVdU1F7GjSdEWdwNRUbTsGHDHJJ4yRQ0nfX398fq1auxevXqVp/PHI76QtqT8YO64I9rDfj0QAkeHqojL5ONBAX4AqiTjAlrOSFZqn3iwlWMd9K5vV2POJylS7rwQGTOS8UHWcU4er4aM4d3s7l2kZLwXWs8G9a+NzhQfH+P7ReFdn5abC8oR1q/KLOLaYouXROND5VU4c0fCvlSCzturJqzR80soeHir1Xj8dR4hErmXVJRi+npOahvNGLL4XP8+VuLJ0RZ3A1FRpOQ06dPo1Mn7+p7VlJRy8emuSq37vbFKamoxfIdRajTG7B8RxHu7BvpdnP0BIolYigdE8o4XHLF4thZeKMecThblzYdPoc6vQGLNx3FIF1oq/JzLNWGstWzYct7q2vFRYD3/H6Z7+H5dd553N6rs+wDqK8k6by8uk4UdtxeUI7HUhPsksMpNFzqG434IOsUGIBVP/7OX+P2gnLZ87cWT4iyuBuK11u/8cYbqKurQ2xsLFQqFfbu3SuqP3L16lU8+eSTDpmko5Gztt0NT5ijJ/DndYPFMaGMy1cbLI4djTfrEYcz73lnnas157HlvVvyz4vG30vaxayTVBnnEDb1BYAiiWf1isQYaw3SIqCcv1N4jdLz2ev8nrDi2d1QbDQtWbIEV682f3HS0tJw7lxzslxtbS0++OAD+87OSShZoutqPGGOnoBWZXlMKKNWb7A4djTerEcczrznHXkuYdmE1pzHlvf2jw4WjWNCAi2+ziEtReJIY8Jc02CNCvw1SsN10rFS5EpY6MIDce/gGDKYFKI4PCeN9yuJ/3sKntB7zhPm6An878Bo3j3PjQnrie/YTlRZOb5jO6ee35v1iMOZ97yjziUXUrP1PLbM8bHUBGw8WIbrBiN8NWo8dUcPUTuqu83c/w8lxWJrfrNX6rERCXj2y3xcv1G4M2PvGTyUFGuXz8lcu5m//08f/vhp/aJE7Wu4qu3WQEnf9sHqnCZvxd3rCwGeMUd357zgD73cmFBG4cWrFseEfXDmPe+Ic0lDaqt3ncTskd1x7+CYFt4pj7Vz1IUH4sf5qbyhJQ3pmfPySLfrjQwLxvTC0u0nANi3nIK5OQiT2HXhgdgxL7VVRi0lfdsH6iFBtCnGSpbGS8eEMm7t3tHimCAAcYVwoKlQpCsrWisN8UkriSfFhWFgTAhfldyeIcykuDCTxHNpM2QAOF9Vh9wzlThvxshqCR+1yuLYnmw5fA73f7AfWw6fa3lnD8MqT9OHH36I9u2b6lc0NjYiIyMDHTs2iaUwv4Ag3JWdxy+ajN2th58nkCt5YpeOnQHpkWcg/dPsTC+HreFBaSXxzGMXsHxHEfQGBh+NCunTh9h1/k11xppCfxoVkDEjSXR8cxXKrWHHsYsmY0eUrtly+BwfAuVqZHlTiRzFRpNOp8PatWv5cWRkJD755BOTfQjCnckrq7Y4JpRRXlVvcexoSI88A2mTW8C5C1nkQlJKkp6llcQ/PVDCH0dvYGZDarbOUVhY1MBMQ3bmKpRbQ9ewAItje+Ht3SsUG01nzpxx4DQIwjlMurkLPskuEY0J69FJKqvrnFxZnfTIMxDWAfLXqjHvzp5I6xfltFwaW+sQSTswPDxUx9fJs7fRx4XnuCRzwDQ5fFh8ODbklorG1tInMsji2F5Iq7B7WwoEJYITbYpX7+mPY+drcKikCjfrQvDqPf1dPSWP5FqDweKYIADXr/q19fzjB3XBr2crsfnwOUwY1AUzb4vHTdHBDqnOrgsPxKO3dsP7Waf4bXKJ6JbGSth3qsJkbIsHSFqVXTqWVmGXjq09vrtBRhPRpli3+xQO3mjSebCkCut2n6KcJhtoNBgtjgmCw9Wrfm05/5bD53iP9CfZJYgLb8d7muxdnb2kohbpe8+Itkk9TdLK5tKxEjq197U4VoI0Ryx9+hC+aj2XMyadu7mSCkqO745lEWj1HNGm+PSAaa4CYT1VdY0WxwThyVjKabJ3xXRpThNg6mn6QZLELR0r4Zff/7A4VoI0R2xz3jmTz0U6d2vyvzyh8wUZTUSb4uGhOotjQhkRHXwtjgnCk5mSZKoTjqqY3pTT1PynmCtxYGk+0rEUucrf0urn5qqhtzRX4ecwIbGLyeciLKHgq1HZreq73DUJX1u2/Thmf3YI2cUVJq/bEwrPEW0KLhT36YESPDxUR6E5G6mp11scE4Qnw+X6fJZTgilJOowf1AV39o10SK7N+ao6XBeEt/XGpm3Cc/xxTdzbUToWYi7EFdrOR7SfdKwEuRwx6Ti7uIJPar9uYCbXYu3xLV0T99roFbv4c357tNymkgxKUWQ01dTUKD5gUJBjMvIJwl7MvC2ejKVWUqdnFseOhPSIcAbjB3URJUo7KjdLWk6A2yb8oy+XVmBOw8xV/v726AXRft8evYCFY3tbPV/p5yAdt7Y8gtznbKmaec6ZStHKQ1vOaQ2KwnMhISEIDQ21+MPtQxCE99POV21x7EhIjwhvYkKi6Qq20EAfURjKmrQCcyEuc8fILq7Aoq+O2C2sJb0eueuzFmFleT9JtXS5iur2OKc5FHmafv75Z4dNgCAIz8MoaZArHTsS0iPCm7hYIy4MqwHwftYpfLzvLB+GukmSfyQdCzEX4jp6TlzI9+i5artUGpfy2/lqk7E9vD4qyb8cTf0FR+LznLMorazDI8mxDvMyAQqNptTUVIdNgCAIz8OV4TnSI8KbkK7U4yqeCcNQ1oa85EJc2wvKTcZ+NzxSSo+rBGtCiUoRVpaXa5asCw/E4rQ+rTqHUmzyqe/evRsPP/wwhg0bhnPnmn6Zn3zyCfbs2WPXyREE4Z4E+Kgsjp0J6RHhyUhXwnGNgoWhNXuEvNL6RZmMHRFKc8QKZaWNlp2B1UbTV199hbFjxyIgIACHDh1CQ0NTFn91dTX+9a9/2X2CBEG4H8df/R9ePNQ3xq6A9IjwdMYP6oK3JyciqVsY3p6ciJ0Lbsfy+waKVoglJ4Rj/axkTB7S1eYQ2qoHBmF4QjjUKmB4QjhWPTDIpuNaWvoPNC20mXN7Ajq298Wc2xOs9jLJHZ8LOUo/F2vmZS9UjFmXjDBo0CDMmzcPU6dORYcOHZCfn4/4+HgcPnwYaWlpuHDhQssHcSI1NTUIDg5GdXU1raQhCDvxwtdHRT38HknWmW1J48h7kPSIIJQhzF8CYJPxpaRid2uqetv6Xmve19p70GpPU2FhIUaMGGGyPTg4GFVVVVZPgCAIz2Pz4XMWx86C9IgglCGXF2UtSip2t6aqt63vdWYlcauNpsjISJw8edJk+549exAfT7VvCKItMEHS6FM6dhakR0RbobXhJ3vkLynJLUqKC4P/jfIA/pLyAEqOb8t7nZnzZHVF8FmzZuGZZ57BRx99BJVKhfPnz2P//v1YuHAhXnjhBUfMkSAINyMuvJ3FsbMgPSLaAvZoZBsdEgA/rRoNjUb4adWItqKRLoe5cgZSmORfa7DlvUrnZQ+sNpoWL14Mo9GIUaNGoba2FiNGjICfnx8WLlyIp556yhFzJAjCzXDEsmJbID0i2gKWKmJbcwyuMXCDzLJ9pbRUGb0152nNex1VsV2K1eE5lUqF5557DpWVlSgoKEB2djYuX76MV1991RHzIwjCDXGXxsekR4S3IReGs0f4ydwx7L3qrDVzdafSAuawevWcp0GrVQjC/lizEofuwWbosyAs0VJj2taGn6THsEfYT8l5nPVeJbT2HrQ6PHf77bdDpTJfyO6nn36yehIEQXgWrW3KaS9IjwhvwlIYzh7hJ+kx7BH2U3IeZ73XGVhtNCUmJorGer0eeXl5KCgowLRp0+w1L4Ig3JgJiV2wIbdUNHYFpEeEN8GFpzjPj6PDU84+nzdgtdG0cuVK2e0vv/wyrl271uoJEQTh/iQnhOPtyYn4LKcEU5J0LvEyAaRHhPfAhaXSpw9BWVWdw1eBAc5ddeYt2C2n6eTJk0hKSkJlpeOKStkC5RAQhP1xZgVeWyA9IjwJR+UWEaY4vSK4Ofbv3w9/f397HY4gCDfGmRV4bYH0iPAk3P1+IpqxOjw3ceJE0ZgxhvLycvz6669UTI4g2gjukgtBekR4A+5yPxEtY7XRFBwcLBqr1Wr06tUL//jHPzBmzBi7TYwgCPfFXXIhSI8Ib8Bd7ieiZRTnNJ06dQrdunWzuLzXHaEcAoJwLY64B0mPCIKwBaflNPXo0QOXL1/mx5MnT8bFixetPiFBEERrIT0iCMIVKA7PSR1S3333HZYuXWr3Cdkbbt41NTUunglBtE24e8+ezQdIjwiCsIXW6pHVOU2extWrVwEAXbt2dfFMCKJtc/XqVZMcpLYG6RFBuAe26pFio0mlUpnkD3hCPkF0dDRKS0vRoUMHj5ivJWpqatC1a1eUlpZSPkQroM/RPij9HBljuHr1KqKjo+12btKjlvHG7zldk2fgztfUWj2yKjw3ffp0+Pn5AQDq6+vx+OOPo127dqL9Nm3aZNNEHIVarUZMTIyrp2FXgoKC3O6L6InQ52gflHyO9vYwkR4pxxu/53RNnoG7XlNr9Eix0STt4/Twww/bfFKCIIjWQHpEEIQrUGw0paenO3IeBEEQiiE9IgjCFditjQrhePz8/PDSSy/xIQnCNuhztA/0Obo33vj7oWvyDLzxmjjs1rCXIAiCIAjCmyFPE0EQBEEQhALIaCIIgiAIglAAGU0EQRAEQRAKIKOJIAiCIAhCAWQ0eRjLli2DSqXC3LlzXT0Vj+PcuXN4+OGHER4ejoCAAPTv3x+//vqrq6flURgMBrzwwgvo1q0bAgICkJCQgFdffdWufeUIy/zyyy+4++67ER0dDZVKha+//lr0OmMML774IqKiohAQEIDRo0fj999/F+1TWVmJKVOmICgoCCEhIZg5cyauXbvmxKtoZunSpRgyZAg6dOiAzp0745577kFhYaFon/r6esyePRvh4eFo3749Jk2aZNKguaSkBOPGjUNgYCA6d+6MZ599Fo2Njc68FJ41a9ZgwIABfHHHlJQUbN++nX/d065HDrm/Rd5wXS1BRpMHkZubiw8++AADBgxw9VQ8jitXrmD48OHw8fHB9u3bcezYMbz11lsIDQ119dQ8itdffx1r1qzBu+++i+PHj+P111/HG2+8gXfeecfVU2sz/Pnnnxg4cCBWr14t+/obb7yBf//733j//fdx4MABtGvXDmPHjkV9fT2/z5QpU/Dbb78hMzMT27Ztwy+//IL/+7//c9YliMjKysLs2bORnZ2NzMxM6PV6jBkzBn/++Se/z7x58/DNN99g48aNyMrKwvnz5zFx4kT+dYPBgHHjxuH69evYt28fPv74Y2RkZODFF190xSUhJiYGy5Ytw8GDB/Hrr7/ijjvuwPjx4/Hbb7955PVIMfe3yNOvSxGM8AiuXr3KevTowTIzM1lqaip75plnXD0lj2LRokXs1ltvdfU0PJ5x48axRx99VLRt4sSJbMqUKS6aUdsGANu8eTM/NhqNLDIykr355pv8tqqqKubn58f++9//MsYYO3bsGAPAcnNz+X22b9/OVCoVO3funNPmbo5Lly4xACwrK4sx1jR/Hx8ftnHjRn6f48ePMwBs//79jDHGvvvuO6ZWq9mFCxf4fdasWcOCgoJYQ0ODcy/ADKGhoezDDz/0+Osx97fI069LKeRp8hBmz56NcePGYfTo0a6eikeydetW3HLLLbjvvvvQuXNnDBo0CGvXrnX1tDyOYcOGYefOnSgqKgIA5OfnY8+ePUhLS3PxzAgAOH36NC5cuCDSieDgYAwdOhT79+8HAOzfvx8hISG45ZZb+H1Gjx4NtVqNAwcOOH3OUqqrqwEAYWFhAICDBw9Cr9eLrql3797Q6XSia+rfvz8iIiL4fcaOHYuamhreu+MqDAYD1q9fjz///BMpKSkefz3m/hZ5+nUpRXEbFcJ1rF+/HocOHUJubq6rp+KxnDp1CmvWrMH8+fPx97//Hbm5uXj66afh6+tr0seMMM/ixYtRU1OD3r17Q6PRwGAw4LXXXsOUKVNcPTUCwIULFwBA9EeJG3OvXbhwAZ07dxa9rtVqERYWxu/jKoxGI+bOnYvhw4ejX79+AJrm6+vri5CQENG+0muSu2buNVdw9OhRpKSkoL6+Hu3bt8fmzZvRt29f5OXleeT1AJb/Fnnq78layGhyc0pLS/HMM88gMzMT/v7+rp6Ox2I0GnHLLbfgX//6FwBg0KBBKCgowPvvv09GkxV88cUX+Oyzz/D555/jpptuQl5eHubOnYvo6Gj6HIlWM3v2bBQUFGDPnj2unkqr6dWrF/Ly8lBdXY0vv/wS06ZNQ1ZWlqunZTP0t6gJCs+5OQcPHsSlS5dw8803Q6vVQqvVIisrC//+97+h1WphMBhcPUWPICoqCn379hVt69OnD0pKSlw0I8/k2WefxeLFi/HAAw+gf//+eOSRRzBv3jwsXbrU1VMjAERGRgKAyYqlixcv8q9FRkbi0qVLotcbGxtRWVnJ7+MK5syZg23btuHnn39GTEwMvz0yMhLXr19HVVWVaH/pNcldM/eaK/D19UX37t0xePBgLF26FAMHDsTbb7/tsdfT0t+iiIgIj7wuayGjyc0ZNWoUjh49iry8PP7nlltuwZQpU5CXlweNRuPqKXoEw4cPN1nGXFRUhNjYWBfNyDOpra2FWi2WDY1GA6PR6KIZEUK6deuGyMhI7Ny5k99WU1ODAwcOICUlBQCQkpKCqqoqHDx4kN/np59+gtFoxNChQ50+Z8YY5syZg82bN+Onn35Ct27dRK8PHjwYPj4+omsqLCxESUmJ6JqOHj0qMgYzMzMRFBRk8rDkKoxGIxoaGjz2elr6W3TLLbd45HVZjasz0QnrodVz1pOTk8O0Wi177bXX2O+//84+++wzFhgYyD799FNXT82jmDZtGuvSpQvbtm0bO336NNu0aRPr2LEj+9vf/ubqqbUZrl69yg4fPswOHz7MALAVK1aww4cPs7NnzzLGGFu2bBkLCQlhW7ZsYUeOHGHjx49n3bp1Y3V1dfwx7rrrLjZo0CB24MABtmfPHtajRw/24IMPuuR6nnjiCRYcHMx27drFysvL+Z/a2lp+n8cff5zpdDr2008/sV9//ZWlpKSwlJQU/vXGxkbWr18/NmbMGJaXl8e+//571qlTJ7ZkyRJXXBJbvHgxy8rKYqdPn2ZHjhxhixcvZiqViu3YscMjr8cc0r9F3nJdliCjyQMho8k2vvnmG9avXz/m5+fHevfuzf7f//t/rp6Sx1FTU8OeeeYZptPpmL+/P4uPj2fPPfecxywX9gZ+/vlnBsDkZ9q0aYyxprIDL7zwAouIiGB+fn5s1KhRrLCwUHSMiooK9uCDD7L27duzoKAgNmPGDHb16lUXXA2TvRYALD09nd+nrq6OPfnkkyw0NJQFBgayCRMmsPLyctFxzpw5w9LS0lhAQADr2LEjW7BgAdPr9U6+miYeffRRFhsby3x9fVmnTp3YqFGjeIOJMc+7HnNI/xZ5y3VZQsUYlfIlCIIgCIJoCcppIgiCIAiCUAAZTQRBEARBEAogo4kgCIIgCEIBZDQRBEEQBEEogIwmgiAIgiAIBZDRRBAEQRAEoQAymgiCIAiCIBRARhPhNOLi4rBq1Sp+rFKp8PXXX7fqmBkZGSZdtQmC8GxGjhyJuXPnAjDVjdZiD90h2i5aV0+AaLuUl5cjNDTU1dMgCMKNyc3NRbt27Vw9DY9k+vTpqKqqIiPRjpDRRLgMd+lqrdfr4ePj4+ppEAQhQ6dOnVw9BYLgofAcYRVGoxFvvPEGunfvDj8/P+h0Orz22mu44447MGfOHNG+ly9fhq+vr6jrtRChm/zMmTNQqVTYtGkTbr/9dgQGBmLgwIHYv3+/6D0ZGRnQ6XQIDAzEhAkTUFFRYXLcLVu24Oabb4a/vz/i4+PxyiuvoLGxUXTeNWvW4C9/+QvatWuH1157DVeuXMGUKVPQqVMnBAQEoEePHkhPT2/lp0UQREv8+eefmDp1Ktq3b4+oqCi89dZboteF4TnGGF5++WXodDr4+fkhOjoaTz/9tGjfV199FQ8++CDatWuHLl26YPXq1RbPv2jRIvTs2ROBgYGIj4/HCy+8AL1eL9rnm2++wZAhQ+Dv74+OHTtiwoQJ/GsNDQ1YuHAhunTpgnbt2mHo0KHYtWsX/zqXQrBt2zb06tULgYGBuPfee1FbW4uPP/4YcXFxCA0NxdNPPw2DwWD1cX/44Qf06dMH7du3x1133YXy8nIAwMsvv4yPP/4YW7ZsgUqlgkqlEr2fsBEX974jPIy//e1vLDQ0lGVkZLCTJ0+y3bt3s7Vr17LPPvuMhYaGsvr6en7fFStWsLi4OGY0GhljjMXGxrKVK1fyrwNgmzdvZowxdvr0aQaA9e7dm23bto0VFhaye++9l8XGxvLNHLOzs5larWavv/46KywsZG+//TYLCQlhwcHB/DF/+eUXFhQUxDIyMlhxcTHbsWMHi4uLYy+//LLovJ07d2YfffQRKy4uZmfPnmWzZ89miYmJLDc3l50+fZplZmayrVu3Ou6DJAiCMcbYE088wXQ6Hfvxxx/ZkSNH2P/+7/+yDh068I1ghbqxceNGFhQUxL777jt29uxZduDAAVHj7djYWNahQwe2dOlSVlhYyP79738zjUYjapYr1B3GGHv11VfZ3r172enTp9nWrVtZREQEe/311/nXt23bxjQaDXvxxRfZsWPHWF5eHvvXv/7Fv/7Xv/6VDRs2jP3yyy/s5MmT7M0332R+fn6sqKiIMcZYeno68/HxYXfeeSc7dOgQy8rKYuHh4WzMmDHs/vvvZ7/99hv75ptvmK+vL1u/fr3Vxx09ejTLzc1lBw8eZH369GEPPfQQY4yxq1evsvvvv5/dddddrLy8nJWXl1NjbTtARhOhmJqaGubn58fWrl1r8lpdXR0LDQ1lGzZs4LcNGDBAZKwoMZo+/PBD/vXffvuNAWDHjx9njDH24IMPsv/5n/8RnXfy5Mkio2nUqFEiQWOMsU8++YRFRUWJzjt37lzRPnfffTebMWNGC58AQRD25OrVq8zX15d98cUX/LaKigoWEBAgazS99dZbrGfPnuz69euyx4uNjWV33XWXaNvkyZNZWloaP5YaTVLefPNNNnjwYH6ckpLCpkyZIrvv2bNnmUajYefOnRNtHzVqFFuyZAljrMm4AcBOnjzJv/7YY4+xwMBAdvXqVX7b2LFj2WOPPdaq465evZpFRETw42nTprHx48ebvVbCeig8Ryjm+PHjaGhowKhRo0xe8/f3xyOPPIKPPvoIAHDo0CEUFBRg+vTpVp1jwIAB/P+joqIAAJcuXeLPP3ToUNH+KSkponF+fj7+8Y9/oH379vzPrFmzUF5ejtraWn6/W265RfS+J554AuvXr0diYiL+9re/Yd++fVbNmyAI6ykuLsb169dF93VYWBh69eolu/99992Huro6xMfHY9asWdi8ebMo9A6YakJKSgqOHz9udg4bNmzA8OHDERkZifbt2+P5559HSUkJ/3peXp6s5gHA0aNHYTAY0LNnT5HmZGVlobi4mN8vMDAQCQkJ/DgiIgJxcXFo3769aBundbYeNyoqij8G4RgoEZxQTEBAgMXX//rXvyIxMRFlZWVIT0/HHXfcgdjYWKvOIUzIVqlUAJryqJRy7do1vPLKK5g4caLJa/7+/vz/patx0tLScPbsWXz33XfIzMzEqFGjMHv2bCxfvtyq+RME4Ti6du2KwsJC/Pjjj8jMzMSTTz6JN998E1lZWTYt5ti/fz+mTJmCV155BWPHjkVwcDDWr18vyquypHvXrl2DRqPBwYMHodFoRK8JDSLp3FQqlew2Tutac1zGmKVLJloJGU2EYnr06IGAgADs3LkTf/3rX01e79+/P2655RasXbsWn3/+Od599127nr9Pnz44cOCAaFt2drZofPPNN6OwsBDdu3e3+vidOnXCtGnTMG3aNNx222149tlnyWgiCAeSkJAAHx8fHDhwADqdDgBw5coVFBUVITU1VfY9AQEBuPvuu3H33Xdj9uzZ6N27N44ePYqbb74ZgKkmZGdno0+fPrLH2rdvH2JjY/Hcc8/x286ePSvaZ8CAAdi5cydmzJhh8v5BgwbBYDDg0qVLuO2225RfeAvY67i+vr6i5HKi9ZDRRCjG398fixYtwt/+9jf4+vpi+PDhuHz5Mn777TfMnDkTQJO3ac6cOWjXrp1ohYk9ePrppzF8+HAsX74c48ePxw8//IDvv/9etM+LL76I//3f/4VOp8O9994LtVqN/Px8FBQU4J///KfZY7/44osYPHgwbrrpJjQ0NGDbtm1mhZYgCPvQvn17zJw5E88++yzCw8PRuXNnPPfcc1Cr5TNHMjIyYDAYMHToUAQGBuLTTz9FQECAyKO9d+9evPHGG7jnnnuQmZmJjRs34ttvv5U9Xo8ePVBSUoL169djyJAh+Pbbb7F582bRPi+99BJGjRqFhIQEPPDAA2hsbMR3333Hr7qbMmUKpk6dirfeeguDBg3C5cuXsXPnTgwYMADjxo2z6XOx13Hj4uLwww8/oLCwEOHh4QgODqbyKq2EcpoIq3jhhRewYMECvPjii+jTpw8mT54siqE/+OCD0Gq1ePDBB0XhMHuQnJyMtWvX4u2338bAgQOxY8cOPP/886J9xo4di23btmHHjh0YMmQIkpOTsXLlyhbDhL6+vliyZAkGDBiAESNGQKPRYP369XadP0EQprz55pu47bbbcPfdd2P06NG49dZbMXjwYNl9Q0JCsHbtWgwfPhwDBgzAjz/+iG+++Qbh4eH8PgsWLMCvv/6KQYMG4Z///CdWrFiBsWPHyh7vL3/5C+bNm4c5c+YgMTER+/btwwsvvCDaZ+TIkdi4cSO2bt2KxMRE3HHHHcjJyeFfT09Px9SpU7FgwQL06tUL99xzD3Jzc3nPma3Y47izZs1Cr169cMstt6BTp07Yu3dvq+ZEACpGAVDCjpw5cwYJCQnIzc3l3eUEQRDOIC4uDnPnzuVbsBCEvaHwHGEX9Ho9Kioq8PzzzyM5OZkMJoIgCMLroPAcYRf27t2LqKgo5Obm4v3333f1dAiCIAjC7lB4jiAIgiAIQgHkaSIIgiAIglAAGU0EQRAEQRAKIKOJIAiCIAhCAWQ0EQRBEARBKICMJoIgCIIgCAWQ0UQQBEEQBKEAMpoIgiAIgiAUQEYTQRAEQRCEAshoIgiCIAiCUAAZTQRBEARBEAogo4kgCIIgCEIBWlvepNfrceHCBdTW1qJTp04ICwuz97wIgiAUQXpEEISzUOxpunr1KtasWYPU1FQEBQUhLi4Offr0QadOnRAbG4tZs2YhNzfXkXMlCIIAQHpEEIRrUDHGWEs7rVixAq+99hoSEhJw9913IykpCdHR0QgICEBlZSUKCgqwe/dufP311xg6dCjeeecd9OjRwxnzbxGj0Yjz58+jQ4cOUKlUrp4OQbQ5GGO4evUqoqOjoVa3PiOA9IggCFtptR4xBTzwwAOsoKCgxf3q6+vZmjVr2Lp165Qc1imUlpYyAPRDP/Tj4p/S0lK73NOkR/RDP/TT2h9b9UiRp8mTqa6uRkhICEpLSxEUFOTq6RBEm6OmpgZdu3ZFVVUVgoODXT0dl0J6RBCupbV6ZFMiuCfBucCDgoJIpAjChVA4ivSIINwFW/VIsdFUXl6Od999F6+99hoA4NZbb0VtbS3/ukajwddff40uXbrYNBGCIAilkB4RBOEKFGdBvffee7hy5Qo/zs/Px2233Ybx48dj/Pjx0Gg0WLlypUMmSRAEIYT0iCAIV6DY07Rt2zb8+9//Fm175plnEB8fDwBITk7G/PnzsXz5cvvO0IMpqahFzplKJMWFQRce6OrpEITXQHpkf0ivCKJlFBtNZ86cQbdu3fjxnXfeiXbt2vHjXr164fTp0/adnQdTUlGLsat+QZ3egAAfDX6YO4KEiCDsBOmRfSG9IghlKA7P6fV6XL58mR9v2rQJERER/PjKlSt2qcHiLeScqUSd3gAAqNMbkHOm0sUzIgjvgfTIvpBeEYQyFKtKr169sG/fPrOv7969Gz179rTLpLyBpLgwBPhoAAABPhokxVFrB4KwF6RH9oX0iiCUoTg898ADD+DFF1/EbbfdhgEDBohey8/Pxz/+8Q8sWrTI7hP0VHThgfhh7gjKESAIB0B6ZF9IrwhCGYqLW+r1eowePRr79u3DnXfeiV69egEACgsLkZmZiZSUFOzcuRM+Pj4OnbC11NTUIDg4GNXV1VQXhSBcgCPuQdIjgiBsobX3oFUVwa9fv44VK1Zg/fr1KCoqAgD06NEDDz74IObNmwc/Pz+rJ+Bo3EGkaFUK0ZZx1D1IemQKaQ1BWMapRpMnYu0HZG/RoVUpRFvHHR5c3AVHfhat0Roytoi2QmvvQavaqGzYsAFbt27F9evXMWrUKDz++ONWn9CdMSc6rREUuVUpJEoE0Xq8XY+sxVatEeqen1aN+Xf2RFq/KNIpgpBBsdG0Zs0azJ49Gz169EBAQAC++uorFBcX480333Tk/JyKuWW3rfEUcatSuPfTqhSCaD1tQY+sxVatEepeQ6MRS7efwKoffyevOEHIoLjkwLvvvouXXnoJhYWFyMvLw3/+8x+89957jpyb00mKC4Oftukj8dOqkRQX1ur6JdyqlOX3DSQRIgg70Rb0yFps1RphuQEOpVpXUlGLLw+WoaSitsV9CcIbUGw0nTp1CtOmTePHDz30EBobG1FeXu6QibkL9qhfogsPxL2DY8hgIgg70Vb1qCVa0ho5I4cztpak9Yb/jYdGJVrHhfUWbszH2FW/kOFEtAkUh+caGhpEbQrUajV8fX1RV1fnkIm5gu0F5WhoNAJoclNvLyjHY6kJVL+EINyMtqBH9sZSorguPBCPpSYgrV+UYq2jfE2iLWJVIvgLL7yAwMDmm+L69et47bXXEBwczG9bsWKF/WbnJujCA0kMCMLNaKt6ZCtKjBxrtI7yNYm2iGKjacSIESgsLBRtGzZsGE6dOsWPVSqV/WbmAtL6RWFFZhEaGo3w06qR1i/K1VMiCEKGtqBH9sbeRg5VESfaIlSnSQLVKyEI+0J1mppx9WdB+ka0dZxap6ktQKE4giC8FdI3gmgdio2mf/zjH4r2e/HFF22eTFuHngIJQhmkR46DdIggzKM4PKdWqxEdHY3OnTvD3FtUKhUOHTpk1wm2Fle7w5VC7VYIb8UR9yDpkWMgHSK8ndbeg4rrNKWlpaGiogI6nQ6vvPIKDh48iMOHD4t+WiNQy5Ytg0qlwty5c/lt9fX1mD17NsLDw9G+fXtMmjQJFy9etPkczsaawm+tLaJJEG0JR+sR4J2aZImSilqs3nWSdIggLKDYaPr2229RXFyMoUOH4tlnn0WXLl2waNEikxUstpCbm4sPPvgAAwYMEG2fN28evvnmG2zcuBFZWVk4f/48Jk6c2OrzOQNrC7/Zo4gmQbQVHKlHgHdqkiU4vdqQW8pvIx0iCFMUG00AEB0djSVLlqCwsBAbNmzApUuXMGTIEAwfPtzmonLXrl3DlClTsHbtWoSGhvLbq6ursW7dOqxYsQJ33HEHBg8ejPT0dOzbtw/Z2dk2ncuZWOs5onYrBGEdjtAjwHs1yRJCvQKAyUO6kg4RhAxWGU1ChgwZgttvvx19+vTB4cOHodfrbTrO7NmzMW7cOIwePVq0/eDBg9Dr9aLtvXv3hk6nw/79+22dttOwxXNE7VYIwjbspUeA92qSJaR6NXtkd9IhgpDB6pID+/fvx0cffYQvvvgCPXv2xIwZM/DQQw/ZlFC1fv16HDp0CLm5uSavXbhwAb6+vggJCRFtj4iIwIULF8wes6GhAQ0NDfy4pqbG6nnZAyr8RhCOx556BNhfk9xFj1qC9IoglKHYaHrjjTeQkZGBP/74A1OmTMHu3btN4v3WUFpaimeeeQaZmZnw9/e3+ThSli5dildeecVux2sN5mqi0JJegmgd9tYjwDGa5E56ZA6hHt07OMbV0yEIt8aqkgM6nQ7/+7//C19fX7P7Ke319PXXX2PChAnQaDT8NoPBAJVKBbVajR9++AGjR4/GlStXRE92sbGxmDt3LubNmyd7XLknu65duzpkia8l48fca7Skl2hrOKrkgD31CHCMJjlSj2zRH7ljkB4RbQmnVQQfMWIEVCoVfvvtN7P7WNPradSoUTh69Kho24wZM9C7d28sWrQIXbt2hY+PD3bu3IlJkyYBAAoLC1FSUoKUlBSzx/Xz84Ofn5/iediKJbGx9Bp1BieI1mNvPQIco0mO0iNb9UcK6RFBWIdio2nXrl12PXGHDh3Qr18/0bZ27dohPDyc3z5z5kzMnz8fYWFhCAoKwlNPPYWUlBQkJyfbdS62YElsLL1GncEJovXYW48Az9IkW/VHCukRQViHW/eeW7lyJdRqNSZNmoSGhgaMHTsW7733nqunBcBUbGJCAvDlwTIkxYUhJiQAPhoV9AaGAB8NfNQqLPrqCCYkdkFyQnirEy4pJ4ogXIO7aJIlY8fca9nFFdicdw7D4sOhNzJeP4R6BIDXMW/QFtJKwt4oymlatmwZnn76aQQGtvylO3DgAP744w+MGzfOLhNsLY5sW8DdkDEhAZiRkYs6vQG+GhUYAL2BwUejwuK7euPVb4/z71k/KxnJCeGtOiflIBCehL3vQdKjJqzJacoursADa8W1pAJ8NEifPgRlVXW8weRN2kJaScjhlJymY8eOITY2Fvfddx/uvvtu3HLLLejUqRMAoLGxEceOHcOePXvw6aef4vz58/jPf/5j9UQ8EW513JcHy3h3+HVDsw2qNzD8cEzcYmFz3rlWGU2Ug0C0dUiPmjC3Olfutc1550z2qdMb8MhHB3iP+NzRPbxKW0grCUegqLjlf/7zH/z444/Q6/V46KGHEBkZCV9fX3To0AF+fn4YNGgQPvroI0ydOhUnTpzAiBEjHD1vt0JYGE6Ij0aF7p3aibYNiw9X3I+upXNRDgLRFiE9sp4JiV1MtmnUTSkEAHjjwl+r5v/1dG0hrSQcgeKSAxxGoxFHjhzB2bNnUVdXh44dOyIxMREdO3Z01BxbhbO6ipdU1GJ7QTlWZhahvtEIH7UKAIPeCPiogVt7dEJUsD++OnQODY3GVrmLW4rTUxyfcCcceQ+SHilny+Fz+CynBElxoXg/6xQajc3Sz4XqpqXnoKHRCD+tGpnzUm3WD3fRIHeZB+E+OK3kAIdarUZiYiISExOtPpk3owsPxGOpCUjrF4WcM5U4eekq3s86BQDQG4E9J//gn+qA1rmLLbnlKY5PtCVIj5RRUlGLxZuOok5vwKGzlWg0Nr82rn8UFt3VGzlnKtFw44WGRqPN+uROGmRJKwnCFmzuPUfIw/WPCw0UF9wTGkyA49zF1jYKJgjC+xHqgtBgAoABMcHQhQfaLZzlSg0qqahtVfoDQbSEW5cccHeErl8AIjdwWr8oPlQnxE+rxozhcSKjigvtAUBav6gWK/hK3c3CbVR3hSDaFuZKCQgR6oJWDahValw3GOGvVSOtXxSApge+9OlD+GMJjZ2WQlzuoEHu5OEivBerc5o8DUflEAhvUD+tGioA9ZJcpeziCkz5MBtCJ9PjqfH4eN9Z/sYW5hEATQmYOwS5BFLDTCoK5rZRHJ9wF1yZx+Nu2PuzMFdKgNMgoX6cr6rjV8v5adWYf2dP0UOaUNM4zGmbEDljBXC+Bn15sAwLN+bz4+X3DaReeoQJTs9pIpoQuqAbBN4kYa5SWVWdyGDy0agQGugrcl1vzjsnen+9IJdAKkZyS4K5/wu33Ts4howlgmgDmCslwGmDVD+4NIGGRiPC2/uJdEKoaRzmtE2IXDjOFRpEXnbCGVid05Seno7aWooXC+P/flo1fDUq/v/czSrcx0ejwiePDsXAmBD43Ng3wEeDCYld4Kdt/jUIl/pKxYh7D/cv5wr3pmXCBGEN3qxHLeXnlFTUIizQtFkxpw1K9EOIXOkUP62a1xdzhoiSXChn5Bpx1c2X3zeQQnOEw7A6PBcREYG6ujrcd999mDlzJoYNG+aoudkFZ1UEn56eg/rGphyBjBlJoiq7cuE1zohKTgg3m9OkxO1dUlGLO1dm2WWZMEE4Akfeg96qRy3l50jTA0b3icCYvhGinCZbwmZCTeM07HxVHTbnnePbQJmbr6Xq5JRrRLgLTg/PnTt3Dt988w0yMjIwcuRIxMfHY8aMGZg2bRoiIyOtnoAnI6wIziV81zcazeYNCCuH6w0M+WVVSE4I58sVyB1frk+d1KVuj2XCBOGJeKsetVTNWpoecHvvzhg/SFzAUol+SI0d7qekohZlVXU4X1XHt4jamnferMFjaWk/VeYmvAmrw3NarRYTJkzAli1bUFpailmzZuGzzz6DTqfDX/7yF2zZsgVGo7HlA3kR0jCcMG9g6fYTGLMyC9nFFai41sCH8QBgRWaRRdf7lwfLAMBifgBVvSXaMt6qRy3d10rve64ECmcIfZBVjA+yilFSUct7gBZuzMfYVb/wWiTc/vC6A60uH0AaRXgTrUoEj4iIwK233oqioiIUFRXh6NGjmDZtGkJDQ5Geno6RI0faaZrujfCJTti8l6O+0civotOqm42mhkYjtheUm3iZrHFnC5cJT0jsQk9wRJvFm/TInJdI6etShGF8AFiZWYR5d/aU9QBtLygX1HQSZ28UX7qGkopaRaUHhJ4ta+ZKEO6MTcUtL168iOXLl+Omm27CyJEjUVNTg23btuH06dM4d+4c7r//fkybNs3ec3VruCe65IRw/DB3BMb1jxK9zq2ik4rQldrrAMSJkuaKw8klU5ZU1GJGRi425JZienoO/xRJEG0Fb9UjoZfIlteFbC8oN1mlC0DkIY8JCUBJRS1WZhaZPc6arGKRV0qIOc+VdK5UgJLwZKz2NN1999344Ycf0LNnT8yaNQtTp05FWFizu7Vdu3ZYsGAB3nzzTbtO1JPQhQdi0V298ePxiyKhAgC1ChDaTSqoTDxL6dOHmCydNed9EhpY9TfCgat+/J2SLYk2AelRy5RU1GKFxBDiiloOjAnhczBnZORi7ugeooK8GhUgaWZgVekBSgonvA2rjabOnTsjKysLKSkpZvfp1KkTTp8+3aqJuRtc1V1LK0iE6MIDkTkvVdzEV6PCfYNj8HlOKb9fSKCPyB1epzegrKrOxJ0tTCIXCpKwNgmHkmRLamRJeANtVY+EtKRNwsUiQHOvOe6hi8vBFJYl4IyaiYO64LOcEtHxWio9YKlOkjkvOmkR4SlYbTStW7euxX1UKhViY2NtmpA7suXwOTyzIQ8AsCG3FOtnJSs2nIRNfDkR+erQOb5EwMCYEExLz+Hfw9Vakq5GMSdIXL7A9oJyrMgsQsONyr2Wki3d8WmPjDjCFtqiHgkRVgQ3p01C7fDTqjEgJlj2tQAfDdL6RfF6FRMSINImX40KC8b0MtvqSUnukvR8MSEBdtEi0g/CWVhtND399NPo3r07nn76adH2d999FydPnsSqVavsNTe3oKSiFvMFpfmBpiq8SowmOTgPFCdK0org04fHWS1IcsaZJeFwtyXA7mjEEZ5BW9MjKdKK4HLaJHywWplZZBLCl1tIwnm3hdq0YEwvftGKpb6blu5dqY7ZQ4tIPwhnYrXR9NVXX2Hr1q0m24cNG4Zly5Z5nUjlnKmEQZK8PSGxi+y+0qcdrmjlWzsKcf1G3abMeak4X1WHn09cks15St97Bg8lxZo1nLg5CcfC1925oaY53M2IIzyHtqZHUiYkdsGG3OZwf2igj+zqNm7M5SvV6Q3YXlCOtH5RojpM6dOH8EUt5bxQUk3z1aigVqks9qaTItUpqefpy4NlVnmMSD8IZ2K10VRRUYHg4GCT7UFBQfjjjz/sMil3QigcGrUKK+4bKOtlkkvmFjbiBZpKDHyQVWySIyDEXBkCuXMofaKSe587LQF2NyOO8Bzamh5JSU4Ix/pZyfgk+ywyj13A+1mn8PG+syJtaDZ0xMngb3x/AlW1epHBwSWFy+kEAJOGvtcNDEBzTpS1Bou5ci3W6BvpB+FMrDaaunfvju+//x5z5swRbd++fTvi4+PtNjF3QWmNEenTzifZZ028SABwsOSKyTa5FSpKzqFUoNyloaY5qI4LYSttTY/kSE4IR1lVHb492tSKSagNwgcmKQYGrN1dzBfkFRbmldMJ4WIUIT5qFfRGZrPBwh1/9a6TNukb6QfhTKw2mubPn485c+bg8uXLuOOOOwAAO3fuxFtvveW1rvCW4vSA6dOOLkx+/+JLV003qlTAjRaAPuqm/nNKzqFUoDzhSUzJZ0wQUtqiHslh7h4XPjDJ0fRc12QwLb93IBZvOmpWJ+RW6kp7bSopsik1buQMO2t1ivSDcBZWG02PPvooGhoa8Nprr+HVV18FAMTFxWHNmjWYOnWq3SfoDihZmSF92gGAj/aeRkOjEWoAnM9JbwSSu4Uh+3RzOwJhzpTRjMeJm0P69CHIL6uyav70JEZ4K21Bj1pqhsu9JnePCw0dFbhAmil6A4PeyMzqhFB/yqrqRA19leqJtMkw15dTathNHtIVs0d2BwCr85sIwtGoGGMKAkPyXL58GQEBAWjfvr0952RXWtvR2JY8ImmypJS3Jyfib18dQUOjEb4aFYxMXCn88dR4PJQUK5tL4K9VgwF8aQFaKUK4O629B5XijXpkSX+UalN2cQUeXpcNabaARtVUbFdvBL9IRc4oE9aaa43mfHmwDAslK5G5/E9pLhMAp6yIo1IFbY/W6lGres916tSpNW/3CKzNI7KUQ8ChNzK+7EBSXBg+zzmL97NO8a9/uPs00vee4Q2juaN7iKp+c9BKEYJoxhv1yJL+KNWmsqo6E4MJaMppUqub/E8q05dltaw1mmOuEK81xXztCZUqIGzB6t5zFy9exCOPPILo6GhotVpoNBrRj7dhbYfulnIIfDVqxIQEiATioaRYUSPfRiPjk8jr9AYcKauGv7bpV+WnVePGf902P4kgnIW365El/VGqTUlxYfDTmkq9MPG7vtGI/wpW9WYXV2Dhl/kmWmbpPNnFFVj01RFkF1fIvs6lCSxJ683rGXc8aR89a3XXFqzp8UkQHFaH59LS0lBSUoI5c+YgKioKKpX4GWX8+PF2nWBrsUdowBoXbnZxBb9sVw4fNaBWq03Ca8Kq40BT9V1haM9Pq8ajw7vxeVI+GhU+eXSoqPwBuZoJd8SR4bm2oEdKc5q41XLmcpI+zzmLdbtPQ29sTvzm0gQ41s9KBgC+yjiHMAfJXAhQ+J6Wuia0pFVcWBCA2XO2FjlPE+CcsCDhOpwentuzZw92796NxMREq0/mqShdmVFSUYsZGbnQG5jZMgJ6IwCjuMDcY6kJ0EsywBeM6YVTf/zJF65raDSisvY6L3B6A0NZVZ3o3HSzE22NtqBHlvRH+JrwgU2qAbrwQHTv3IHXGS7xe3SfCL5UAdBUUfxafaPoHEndwrD83oEW9URJZXKl1yTVMnOriVuL3AIZZ4QFCc/G6vBc165d0YrccY9A6p5V6q4VunsNrMn9LYcwaLAyswglFbWICQng9w/w0WBgTAjiO7bj3eoBPhoMiw/nQ3N+N3rUyZ1b6GomCG+mLeiREkoqakUebu6BDGjqnXn/B/tRXXtdFPKKCQkwKY0yLD4cPx6/KNo2JUkHABY1UNolQa5rgi066mgtc0VYkPBsrPY0rVq1CosXL8YHH3yAuLg4B0zJtchV9lZapVZaK4VbnnvobCU+z2ludSDMEqi/UQF81Y+/8wXmlk3sz5/TX6vGkrTefGNfuYROuXM742ancCDharxdj5SSc6bSJCVgRWYRtGoVXv32eNM+pyvxwrg+CA70FVXf9tOqMbpPBB5JjkVZVZ1JUd5FXx1pccUuV5mc62En9TKZC4XJ6Ycr68pReRaiJaw2miZPnoza2lokJCQgMDAQPj4+otcrKz3bwyF9ytmcd06xu9bcDZcUF4bNh8/zrViEdZk0NxLAuXPoDQz7TlWIVsuFt/czEbOGRqNoLuYabzoKCgcS7oC365FS5FamNTQa8ekBccumH45dxBePpYjCUA2NRtzeuzOSE8JRUlFrchylK3aTE8LNhuSkuso9KEr1Q1oPyhWGCxXKJCxhk6fJm5E+5UxI7IKteecVP/XI3XBCY8pHrRIlfK+4byAG6UJFAiI8p59WjYprDRgYEwI/rZo3nPwl4Tkun4prvOloI4aaZBLugLfrkVI4jdleUI4VmUW8V+jhoTre0wQ0h9rMeXPkjiOtDWeL50d6PgAm+gG4PgmbvOdES7SquKUnYI/VKva+kbKLK0zc2FsOn8NnOSWYkqTD+EFd+NUuH+4+jUYj49sVcNXAB8aE8E9iQFPfJmG3c66qrrXzVXqt5GkilOKs4paegDM+C+k9LNUWc/sBzdrUs3N7HCqpQtewADyUFAsAfFNdayqCC8/BHUNasFerBmbdloCQQB8s3X6Cf+/y+wbi3sExFudrT0jT2gatvQdtMpqKi4uRnp6O4uJivP322+jcuTO2b98OnU6Hm266yepJOBJPEGy55brRIQEYtWKXKE9hSVpvPJaaYNKOQAWxC51DmFeltC+UNaJBT2WEEhx9D5Ie2QepDnFw5QPM9YgzpxPm9ITTDR+1Cgs25vF5mr4aNa4bxOUPuIdKZxg00orlUqON8A5aew9avXouKysL/fv3x4EDB7Bp0yZcu3YNAJCfn4+XXnrJ6gm0VYQrSeSW68oldnLvE3YDb2g0yhpMQJPb+5GPDmDhxnyMXfULsosrLK5esXbVinTlCUE4G9Ij+yHVIel2ucK9lnRCLo+JM34WbszHwi/zRQtbhAYTAFFJFUevqCupqEXFtQaTopsEIcXqnKbFixfjn//8J+bPn48OHTrw2++44w68++67dp2cJ2GN10X61LRsYn9RaG1CYhdEhwSIcpgAQKtWmXifmnrXMdlVdcKKv5wBJVfDhcOVq1YIwhZIj5ppred3WHy4SIeE2788WIaYkACTJHEAiAkJkD0eV4mc07CVmUUAxItetGrw2iVdJBMTEsBfU4xAD6XlVoTY8hlIPfdL0no7rKAm4flYbTQdPXoUn3/+ucn2zp07448//rDLpDwNa13H0qcmvZHJLtedf2dPUYz/X98dNymY2dTs1/Qcj6fGY2TPznxyuNSAkkvctnYFHoXnCFdDetREa8NXJRW1+NtXR0Tbbu/VCfckdsHiTUdFZVQ2550TGVdCj5AQXXigSMM4j7i0LMuuokt87qaQT7LPYufxi6i/YShxyFe/s/0zEOpxw43Vys7UM9JRz8JqoykkJATl5eXo1q2baPvhw4fRpYtpQbO2gLUryYQeHR+NCjEhAbLLddP6RfGr6oRGjxCp0HBcqdUjOSGcX7UnrMtizotkzQo8Spok3AHSoyZau5o150ylSX2mzkH+0BuZ6LhlVXWYPbK74hXFQg3jqnun9YviC29GhwQgNNBXVseElcqFc6u/UW6FmzdnbNj6GbjSw0466nlYbTQ98MADWLRoETZu3AiVSgWj0Yi9e/di4cKFmDp1qiPm6BTkVrQppaWbTrqCZHtBOSYMisbGX8ugNzDMyMjFson9se9UBX9+rvfSxEFdUFWnx5i+EVj4Zb6J4aRVq2QFR6tS4YOsYqT1i+KTGVsq2qZEdLhrqbjWQCUHCJfjrXpkLUlxYfDXqlF/o0SAVIOyiyvwSfZZ6MIC8WCSTjY0L00H4Kp6cw9sflo1Pt1/Bh/uPoWZt8bh8rXrJh5pudVy0sUoJRW1vCG1fEch7pMkWw+ICcaRsmrRNuGCF66audTYsNX4cWVBSyrd4nlYvXru+vXrmD17NjIyMmAwGKDVamEwGPDQQw8hIyPD7TqLK8mUt7bZpByWGmVyN7e/Vg0jY6JGvHK8PTnRpJGmn1aNNyYN4A0nroEmAFEIT4qfVo3MeamKe+dZeuoxt2qPnpAISzhyxZg36pEtlFTU4s6VWXzOj/Cel+qbOU0oqajFf3NKUFJZi0eSYxEtMEzM9dKUrooTap25KuLSVWpatQqMMRhY09w+npEkqlbONQoGmj1LOWcqZVe6eVqoizxNzsfpDXt9fX2xdu1avPDCCygoKMC1a9cwaNAg9OjRw+qTuwvWNpuUw1wVWeGThLlVblJBWrXzdxNXeUOjEXojw875I01qSHFPbXI0mHFlm7sGS09c0tj/krTesschCGfhjXpkC8LwmrRbgFTfpK9z6MIDsUhwTwurhpt7zhN6R8xpndSDkhQXJko34DzlPhoVPp6RJEorkNZ3EpYA4LxKXAHgkopat6nmrdR4o7YtnofVRhOHTqeDTqez51xcxoTELiar1+yF0GUs9TT5alRYMKYXIoP8RVXCT//xp8lxuBUjUlHQhQdi2cT+mP9FnqywadWQdWUr6Zpu6Vq4psLcE+GqH3+npyTCZXiTHtmCpdCUVN8srT4zd0xfjcqsh5xbPSfVOnNVxHXhgfjk0aGiBsNA02o6Lqmc0xFphXNOY4SVy1dmFmHp9hNuo0HWeo/cxdAjlKHIaJo/fz5effVVtGvXDvPnz7e474oVK+wyMWfSUrPJ1iB9kgCahOBK7XWEBvqKlrau2vm7yGAa1z8KIQE+OF9dh96R5kOL8zfmiwwmznOlVQNL0vpgxY9FrYqbC5+ahNeyvaCc4vGE0/F2PbIFSx4LTt8s5TRxSD0k3DGra69j48Ey6BuNqNUbUF5dz79HuHpu7ugmD580nMadT1hCYOGYXqiq1eOjvad5o8hHrcKir45gWHw4v2qPQ6oxuvBAhLf3471aXC2o8PZ+LvXaUJ6Sd6PIaDp8+DD0ej3/f3OoVOYWg7o/lppNKsGSO1b6JJHWL4p/Eln14+9Inz7ERCACfDR4JDkW09Jz0NBoxM+Fl5G+9zR2CHIRSipq8chHB0S1TXzUKqhUgMHAoFapRH2nuONaszpE7qmJyx1YcaPuCmDaC48gHEVb0CNbsOSxUKJv0pxFLpfIRy3WkRfG9cHyHUUir5ZUJ7iHQXM5kRwBPhp8PCMJZVV1or6ccvWi5LRL6N3y06qxMrPI5XmWVO/Ou1FkNP3888+y/yeaaG2dps1550RCwvWNky4DrpfkIshVDR8cG4rs0005TFJ3elK3MCy/d6DVS5Hlnpqkc5t3Z0+H9OkjCCmkR45BmrPIhbx6RLQX7ffDsYsmXi1h/pM574q5iuJlVXW4d3AMFknqRGlUKhhurFPSqoH06UMsNkMvvnQNa7KK+eO6yutEeUrejdVtVKqrq1FZaVrCvrKyEjU1NXaZlKdhbYl/7kkEaHp6mpDYBb6apqdiX42Kb7TLLQPm8NWoRE8tXEKlEM5g4vYX0sFXi6f+ewhbDsu3SzA3V661gNCbJL2GtH5RohYJY1f9YrZdC0HYC9Ij+xETEmCiJ3V6A/pHB4u2je0bYWIQCHXCR62Cj1rFt2ziWkZxFcWFCD0xw+LFnrAhcaH8/xuNpkU0ueNy5/9o72n+NT+tGisyi7BwYz5GrdiF7OIKqz+PlhC2wpJCLaa8F5vqNN1999148sknRdu/+OILbN26Fd99953dJucpWOuOlT6JnK+q471C1w0M56vqeNf2xzOS+IRJ9Y1wg9CbI5dQ2YwKQPP2nYWXAADPbMjDH9caEBzoq+hJiEn+lbsGpU+bBGFPSI/sA1fYVtraBADuHhiNpG5h+CynBGP7RohCc0KvuvGGV0hvZHyYTVqaZNnE/nzZFB+NivcelVTUYvGmowAAtaqpDIHwAVCqqyUVtRizMouvSzXvzp4iz/foPhF8cUy9geGRjw5g5/yRdtMjKhXQdrHa03TgwAHcfvvtJttHjhyJAwcO2GVSngZnQCy/b6Dim0f4JCJX8oCjrKqON4jqG43YXlAu8uZEhwRg5/yRGBAjfhoETBtgCnntu+OKPEJyS5nlrgEw9T5RLJ9wNKRH9kHoLZdWRimrqsP4QV3wxWMpCA70lfWq55yplF1dJ2woXqc3YN+pCl7PhKvlhOc3MnFqwbj+USa6ur2gnD9ufaMRVbV6kfY8khwr8prpDcyuTX4d3UCYcF+sNpoaGhrQ2Nhosl2v16OuTr4HkbfgKHestMTBhMQusi5tf60aR8qqTTqHA8AwmSRPYWhPCpc7Lr3hpdcobcZprjknYNl4tPTZEYSttGU9sifCBx5/rZrXDmGi95cHy5pCbzeMEeGDkTSVgEOrVjWH7TQqDIsPF52Hq68kDA36alTQCqKEO45dwHkz/e04SiprkT59CJak9cbc0T0QHRKATx4dKjtXe+CKB0TSUPfA6orgt99+O/r164d33nlHtH327Nk4cuQIdu/ebdcJthZ7VeB1tDtW2MYlWlJXKX36EOSXVfH1SoT4alRQq1SobzTCV6PCnX0jMaZvBPRGJlqNIkSrArQatckqE7lrNFd51xrIld22cWRF8LaqR45ArgUK93/pqjcfjQqfPDpUtCKvpKIWn+ecxbo9p/nw2yePDgUAPoVATs+ENZ20akCjVpvonI9GJQqvCSugc8h1KRBeh701x5mLXkhD7YfTK4L/85//xOjRo5Gfn49Ro0YBAHbu3Inc3Fzs2LHD6gl4Co6uvSFcEizNDSqrqkN4ez8TIQE4N3ZzPlR7fy0G6UKbqvtKVqNwNDLg2Tt7mqwskbtGYU8qpUXxpFDdEsJRtFU9cgRyhXMBsR5xCENrwv0Xp/XBQ0mxJrmOXEhOTs+E1cMbjUCj0VTnuPCasEZT5rxUrN51ki9PINRHTmek3n9PXd1LGuo+WG00DR8+HPv378ebb76JL774AgEBARgwYADWrVvn1a0LnFl7w9y55Krt+mnVYIIq4xtyS7E17zx+mDvCpBIwV9VXWEdFyXk5T7mtVW+obgnhKNqqHjkT4f3LYek+lhpf1uoZ5y3y1ajAWFNiudz5dOGBmD2yO74+fA4NN/bnvO7mGqfby1vjbM8Paaj7YHV4ztOwpzvc3k8p0uOZc49Lq+lyK+42553DsPhwLPrqiElfu+X3DURSXBg+yCpGwflqPDq8GyKC/PFJ9ll0DQvAyJ6dRZ3HOYRhwuSEcJPmmlwNKWuv31Of8IjW484hKWfjqZ+FsJK3nG5w+5jrdsC9BoDfbikcaE4HuRBgaWUd31RYuIru9UkDsO9UhWxnB6mWyaUaWNIp4Wv2SFuwFtJQ+9Dae1CR0VRTU8MfvKXaJ+4mBO4qUtInlfTpQ/g+bi09uQjfK2x8ycEdb3p6Dm9M+WpUUKlUJiG+lnKaAJjkDnCvcYabvVvPEN6Fve9B0iP3Q1gCgMNPq0bmjQ4G5jwzSo0UXXggsosr8PCH2WgUyN3jqfF4P+sUP+b0UE5DW/IOSXVVmLPVGr0m3Aun5DSFhoaivLwcnTt3RkhIiGx7AsYYVCoVDAaDzBEIKZaqgrcUsxa+l0u41BsYX68krV8Ucs5UigRMmPskxFyXcm57TEiAiaFVpzfgvzklfPXdDbmlWD8rmQwnwimQHrkfUr0BmkuUmNMWAGaNGDkj5ZGPDogMJgAorazjw1bCB0g5DW2pUrdUV4W1naTzL6uqo6rfbRRFRtNPP/2EsLAmVym1LbAP0gTrCYldsDXvvKKYNbc8V29g8NOqMWN4HEIDfTEwJoRPzuQq9HJC5qMG1DKrUqTLhoV5BhXXGvDziUsm5w/w0aCkUrzsdXPeOTKaCKdAeuR8WgoNSfUGaPI0xYQE8KVTpAtKpA2/hW1P5B4q5Qr4PpIci0V39eYf8Djvj7CcASAO8ZkzcLgOC8I6UpzhJZdTZOlYhPeiyGh6++23MWjQIAQFBeHs2bOYPHky/Pz8Wn3ypUuXYtOmTThx4gQCAgIwbNgwvP766+jVqxe/T319PRYsWID169ejoaEBY8eOxXvvvYeIiIhWn9/VCBOso0MCFD25lFTUYqqgAnhDoxHvZ50SJVNyT20ZgmriGrUaGTOSkF9WBQC8gSU8ly48EOnTh+CT7LPIPHYBS7efgI+k9MqUJB0eS03A+ao6vuIuYFpriiAcBemRc1GS9KwLD2zSm3UHmsqdaFR4Y9IA3ogR1nBSAThfVSdq+M21PeH0K336EJGRInyo1KqB23p0wmMjEvgHNW4+P8wdge0F5ViRWYSl209gRWYRn1gubEIsp6+68EBRhwXhAyXnpdpeUI6qWj22F5SbPQ7h3Sgqbrlt2zb8+eefAIAZM2agurraLifPysrC7NmzkZ2djczMTOj1eowZM4Y/FwDMmzcP33zzDTZu3IisrCycP38eEydOtMv5XYnQnS1sxNtSgcztBeWylXfrG428F4lzTUuriZdV1eGx1AQ8lpqAaEGRSq5oWnZxBaan5+Dbo83n0EtW/3JPV8kJ4Vg/KxmTh3Sl0BzhVEiPnIvS6tdlVXXQG5u9NPtOVYgaAAtLDGzOO2fS9kSoX1z4iyuUm5wQzo8/nZmMcQOiRRrGoQsPFJUzEFYk55oQC7sgSAtGJieEY+f8kWa7O6zMLMKarGIs3X4Cd67MwpbD57DoqyMO6W1HuCeKPE29e/fGkiVLcPvtt4Mxhi+++MJsAtXUqVMVn/z7778XjTMyMtC5c2ccPHgQI0aMQHV1NdatW4fPP/8cd9xxBwAgPT0dffr0QXZ2NpKTkxWfy92w9xJSzY02c4Yb/5er3M1tExaG81GrAJU4N0qIVq1Co1F+rYCwtpQUe670oFUjhBDSI+ci1Sou5Ca9H4X7cdW/Oe+QtPDkhMQufKkAP60ajyTH4qcTlyyGv3ThgThfVSfyBMkllEvTF7jzctTpDVi96yQmJHbhF8v4a9XYMS8VAPhQH2ccCuvYCY/T0Gjkiweby+uU0y7SM89GkdG0Zs0aLFiwAN9++y1UKhWef/552eRLlUpllUhJ4Z4YuXyFgwcPQq/XY/To0fw+vXv3hk6nw/79+2VFqqGhAQ0NDfzYXTudt5SUaI6BMSGi8SPJOnySXQKhrWNgwNSPDmDmrfGiffPLqpCcEI7/5pTwT2J6gUEkNZjG9Y/CmL4Roqri0vPL4cn1UAj3h/TIuQi1Spg3JL0fufA+Z9Qs3nQU6dOH8GkAgLiUgLXpCSUVtaLm5HIJ5ZyRpDcwaFTAG5MGICLI36Sp+YbcUnx1sIx/IKxvNOK/OSXI2HfGpB4Vd43CPFSgqbGw8HlSmtdpbjUy6Zlnoyg8N3z4cGRnZ+Py5ctgjKGoqAhXrlwx+amstL1podFoxNy5czF8+HD069cPAHDhwgX4+voiJCREtG9ERAQuXLgge5ylS5ciODiY/+natavNc3I0tvSr43KSOI6UyYcmrhuYSbI2h7ntPhoVfG/0avLTqrHort64UFNv8fxy2LOZpfRYXK0Xou1CeuR8OK0qq6qzeG8LUwK4MBuncUK9syU9IedMpcjw8dGoTJLGheE4AwMWfpmP/LIq2SRyqQf9xIUak8rn5vRLqwae+58+om3SvE45HTSnjdRXznNQZDRNnDiRf0JKT09Hhw4d7D6R2bNno6CgAOvXr2/VcZYsWYLq6mr+p7S0tOU3eTD9ooNlt/uom1aWcAmYflo10vpFAWjabrL/jbok/3l0KCYP6YqPZyTZ/AQk18zSVlHgVuVwrMgsEh2DxKbtQXrkOlpqVKu0ka0tDW+F7+H0SriyDWjSOR91s9eRM5bkmhH7adX8Q6KvRoV9MnlJwrnlnKnkvUxN7V4Y3p6ciKRuYXh7cqKJl6niWoPoXBXXGkQN2IXaOHbVL1i4MV+Ub0W4J4rCc1ziZVBQEB599FGkpaUhIMB8t3trmTNnDrZt24ZffvkFMTHNVVUjIyNx/fp1VFVViZ7uLl68iMjISNlj+fn52WUljbuS1i+KX2Xip1XjsdQExHdqh3d/PokrtXp+v5m3xSM5IRwfz0jiC1AC4HMRHknWYfPhcxjdJwK39uhk0phza955pE8fAgCipcJAkyBYMqikoUfhca11SevCAzHvzp5Yuv0EAHHtFwrdtU1Ij1yHNFQnrfKtNO1ATiPk8qSUvCcmJABzR/fgK5FHBvlj4Zf5fN5TWr8ovnaduYrjFdcaeI0BmlYJn6+uQ911Az7POYuHkmJNwnPc6r+GRiOOllXzPT+FuuSvVePx1Hhk7D3TtBpZo8LyewdCb2Si3nzUV85zcGkiOGMMTz31FDZv3oxdu3ahW7duotcHDx4MHx8f7Ny5E5MmTQIAFBYWoqSkBCkpKYrP480cLrmCV789brJdBRVKKmr5/IMth8/xJQk0KvA5UF/nnUf/LsGyNy+XB+CjBnpHdkDxpatYuv0EVv34e4sGijCJs7WikNYvCqt+/N0kad5SE0tKtvReSI9cC3c/CSuAr8gs4qt/K61fxO1nzcOP3HukBPho8MmjQ2VLqkivgfu/dPXbhtwSvpBm9ulKfLTnNH6cPxLzJQ9wHEL9Edafqm804kqtnv+c9AaGeV/k4fO/JvNzsHZREGmba1FkNL3//vuYP3++3RMvZ8+ejc8//xxbtmxBhw4d+LyA4OBgBAQEIDg4GDNnzsT8+fMRFhaGoKAgPPXUU0hJSfHalSotIXQRNzQa8VlOiex+IYE+IqNCuOpDGt7/9EAJZt4Wb7L6RS8oO3DiwlV+f2sNn9aKgrmnV3PHJQ+Ud0N65HrkVpLZ6iGx9PCj5D1ShLlUSuGKAnNIK49fv1HoUvgAJ62Nx4XahPWn/G8ULt50qIzXUyMDHl6XjZ8W3G5R38ytvCNtcy2KjKZhw4YhOzsbQFNV6aKiInTu3LnVJ1+zZg0AYOTIkaLt6enpmD59OgBg5cqVUKvVmDRpkqiYnLdj7mlCaihMSdIh57Q4UdFXo+Lzlzh3sq9GBYORmRhMAPDwUB2ApieuhWN64tMDJRjXPxLr9pyRFSb/GxV9lc67taIAmDYvtnRcW0SY8BxIjxyHUi+GtAK4nwVNaAklD1XShr/C90jRqlU4dLYp5CZXxNfc8YRayRgT1ajzUYM/hjA8uavoEkor6zCmbwRyzlSi+NI1kQdq+vA4lFXVIe2mKGw9cp7f3miESJeEHjQu5Ci3SpG0zfUoMpqEnD59Gp06dbLLyRX0Coa/vz9Wr16N1atX2+WcnoClpwluWa8wT0mK8Klb+PwtZzABQMf2TTkXWw6f40N97/5cjBfG9cGpy3+aeLPM/dZamrfw5s4urpCttyK3Wk4YmpM+WcmFAqQ1quRqVrUEucA9A9Ij+2FtmGzHvFSTnCZbaCkPSlhXDmgqMLljXqrIeMkvq8LyH05AfyNB+/McccK9tKaTNLT48YwkXivVKhUyHh2Kb/LP4785JTAC0KibF6PIhSeF3RE4/LRqpO89Y9K6intN6BmXlnMw10fP3vX9COtRtHoOAN544w3U1dUhNjYWKpUKe/fuFdUfuXr1Kp588kmHTLKtYWnJPpentCG3FDMycvFJ9lmT93OucqELXa6KOAdnFEmNox+OXcSg2FCzx7dm3kIs1VuRrqrhXuf+/TznrMmxpKvnpK526bglaDWL+0N6ZH+sLRWiCw/kOwy09sHCUrkBYUoCYFqiIDkhHOHt/Uy6FwgRXo9caPGT7LOiEghlVXUYFBsKbq96iebJNSiWMiwhXNZgGtc/is//EmrNIx8dMGnEDkBUUBSAqFK6uc/d0qpiWnHcOhQbTUuWLMHVq815LWlpaTh37hw/rq2txQcffGDf2bVRLC3HlQqbLsz0puHeo9TDMiVJJ/pXuF3uGOaecCzNW3ijSuutaNUqkx5PnCik9YvilwUDwPtZp/ikTXPGDedqB2wLG9izzhThGEiP7I8tZQCcgfB+BuTTA6T7SJE2JheWMfFRA5nHmutscccXfh7SBsDSY8ixr7jCZE4BPhosuqs3gKYFMsKkcamh9MmjQ7EkrTemDYvFtPQcLNyYjzErs7C9oNxiAdAPsooxZmWW7EMfPRC2HsXhOanrWokrm7ANS+5qqXv2wSQdUnt2wua8cxgWHy5ayir9Y/9EagIqa69jWHw4Fm7Mg97YJBiDdE3epPGDmsJ9n+WUYEqSDuMHdcHrgmW4AHB7r0545S/9ZG9YS7lLQrd/+vQhonwItcr0OMLjD+/eET8XXubHn2SfRXJCuMX4vrDaMIc1+RrkAndvSI/sj61dChyNLjwQmS2EAoX7VNXqwcAQGuhrtjG5sJk5VCqRJ37enT35faUNgIUrh3fMS8UHWcUiD71GpYKBNTdTX5LWG+Ht/RATEiCqjC6sYM5pIaeNwv24cB1H/Y3+eXIrmOVWFEp1UWlOFKUnmMfqnCbCOZhbtisnbLrwQNkecHIGFldagHNl6yUJieMHdeGNJ8C0enigr9bqm0h6o5ZV1YlqL3ErU8zdvFK6hgXIXp+wFIG02jCgvFaUvf54kPAQnobScgHOhgsFtnYfDmHlcmHfTa6uk/CYwgbAQkNDFx6IQbGhIqNp1ohu+HjfWV5n5Aw8YQkWoWElfdBcveukxRWCq3edxOyR3WUNIg7pQ5/SpHtOK7kiotSQvRkymjwQa+qgWLNUX45HkmNFSY5y1cQ5zCWSmjuftPaS1MiQe3Ly1ajwUFKs1ddn7aqT1v7xoKXBBOG+SDVC6OGR3qeWSptwVb+5sgMPJcXioaRYiw9L0uNJDSs53fPXqjF9eJwosXxDbim25p2X1Vk/rRrz7+xpcmwlD4RCrdQbGB756AB2zh9J+nUDq4ymDz/8EO3btwcANDY2IiMjAx07dgQAUX4B4T7I/fHXhQdi2cT+fBhOuqqNW5mXnBCO5IRwvD05kd/X0hOHOcPE3I3aUtVw6ZNTUrcwzB/d00QEpIKTc6YSM2+Nw7dHL+Dhoc3XZ4+Qm1LvUVtYGuxqTxrpEWErSowH4fdbuq/QsNGoVHgoqSseT232+lhK0M45U2nWSJPzME0e0hWzR3YHAIQG+uJIWTX/IKtEZ4XXAYBfqSdNbOder7jWIK7TJxMJUHrvu1ojHIFio0mn02Ht2rX8ODIyEp988onJPoT7k11cgWc25AEAck5XIiLIH8kJ4cgursADa5vq32zILcX6WcmIDgnA4k1HUac3iFoFyCGs3SJN1jRnvHHb5KqGS2ux5JyuxIyMXIud06VPaK9+exwd2/th/KAurQ65CZc++2nV/AoYOawte+Bp4uJqTxrpEdFaLHmT5b7fwmKZwociA2sqcfCXgV1aNCAs3TNyHqYAHw1vMMnlQfloVBa1RahZGhWgUYvzt4QFOrmkda5WlVatQqORyS7qUXLvu1ojHIVio+nMmTMOnAbhTDbnnTMZJyeEy24fEhdmlceESf5VipwLnHtyWr3rJDbklvJz4BI4pRV5547uIZsD8FlOCcYP6tLqkNv2gnJRNfbtBeVmcyisKXvgieLiak8a6RHhSFr6fifFhUGjbioYzMHpqK3HlHrWOQ8Tl4cqzIN6PDUe6/acht7AMCMjly8CLNURoWYZGGCQlJ6Rll7guG5geCI1AQmd25s8yCm9912tEY5CcckBwv5kF1dg0VdHTPoeORppUUxuLLfdmuX70hYvLS3VF5YhkJYaELq5Z4/sLupuzrmN6xuNogRNoLm2kxBpKQUltLaWiTXLt62pb+Uu9VXcdXk6QViDuXtK+v3m6iQJ93vglq6i98gVGxYe39wxs4sr8OXBMvioVXzJAX+tmvcwcRXCuRIH/lo1QgN9TercSXVk9a6TqBI0cZfDX6vm9V1qDDAwvnaWpeswd+97q0ZQIriLkAuFOWuFQnRIAHw1TW5aX40K0Tfcu8kJ4Vg/K1mU01RSUSu7fF8OaxLMzXlXWloxKKya66tR47qh+ekoMsgfP8wdgVe+KcDOE80lCn6/ZF1+i7m5DYwJEe0nHZubc0shNyWhPHfzRrnr8nSCUEpLHQzkNIdLGpeWAvDTqnkdtXR8uWPKYWQM56vq+H38tGq+rAZDk/bIaa0wnWFDbqmoxh0A+GrUWDCmp6gUw/mqOlGxYY70vWf4RTfmrsPSve+tGkFGk4swFyJzBjlnKvm4tnS5P5f8LdxXunzfHjdJa1azcef4+cQl0cq+facqMH5QF+SXVYvem7HvDO6/Raf4pjU3N2srjSsNByo5rju6ut11eTpBKKGle4r7fkvzLTfnnTMxduQaFssdn/PcCI8px3UDE52nQRJGK6uqM7u4RpjOIO0EsWBM04o64fukxYal18TNX+46WsIbNYLCcy7CXIjMGVjjNrXWxaoLN98OwdrjCl3C0lDevYNjTMofDIsPx5cHy5DWL1K0/VqDAbe/tQtbDosNVbnzcHOTC0mam3Nrw6xKPgt7u7rlwhLmQhWuCiMThL2xR5hpQmIXkzQAufcL3+cnqSgeExLAh+Lk8NeqRefhkr+F55JqLbeYZFh8OH9sX40aXFFyH40KkUH+fLXwO1dmYdn24zh56Sp/bB+NCj439vfVqFBxrUEUGtSqVTh56WqLKQJcZfIPsordIp3AnqiYl5fSrampQXBwMKqrqxEUFOTq6YiQLu93Jtas1nLUyi5LxxW6tv20aqgAvmqu0I3OfYbD4sP5VX7SBE0h0jConAsdaG7G6a9VY4dglZx0zsIwq9zx7fFZWLOP0nPJXbNcqMIe1+fO96Czoc/CdZj73tuydF7YZNdcfSfufdsLyrEys0hU9VvYmHf5vQOhNzK+8TDQXPVcrlxAS3ppCR+1CnoZbfTVqGBkTc2Opfhr1TAYjaLefpZWD0sbLEs11NW09h5UFJ6rqalRfEASAuVIQ2HOxBq3qaNcrJaOK3RtC13TUjc69xkK3d3mDCbANAxqLgnbXEhSOmd7hVmVfMb2+j2Yu2a5UIUrw8jmID0ibMFSuKwlpPee0ntRF95UUbxesGBFGHbTGxj0RsaXM5DeW3LnbenaLCFnMAGWG7rLNSaWC0cK52KuwbI3oMhoCgkJgUplOQ2YMQaVSgWDoeVfHEG0hLS6rdDTZCl81ZKnSRoGNZe8rjShfUJiFz5/QO747og11+yO10d6RNiCq3pKSs87IbELtuadt+s8pDXtzOGvVcPImImRJKzRpOQ9llZSc+kNQk+Tt6ycAxSG57KyshQfMDU1tVUTsjfkDndPSipq8XnOWZRW1uGR5FhZ74XQNX2+qk42lCkMcUbfqHKbFBeGeRsO41BJFW7WheDZsb1NGhoDsOj2Nhc6ldu+/IcTWJ9bigeGdMXCsb1t/jycucpE7jrMzaG1YWR734OkR4StyH3HnXHvmQvvWZqHuRCguZAdAFHD4po6Pcqr69ErsgNG9uxsUhCYCwdy+6ugQkigDwbGhPDbheMrtddxta4RVXV6jOkbIWoOL3e9nL4L9zWn4474jM3R2nuQcpoIp1NSUYvRK3aJnlws5cqYWxpsLt9m3e5TePXb4/z2F8b1wZ19IxXlSFl7vos19Xx1dQB4e3KiqOGx0s/DmeUEnH0+ugeboc/CvXCXUh7SeciVNZBulxb3Fb4m9PQA5vVVLv8oY0aS7DmEuimck9xnJpdjpXROtmDN77G196BNq+d2796Nhx9+GMOGDcO5c005D5988gn27Nljy+GINoaw5AGHNHdGur9cDo5cvg0AfHqgRLT90wMlJjlSwhwDaTFJa84n7HAOwGSsBKXFLe2Fs8/naEiPCFtxl3tBOg+5sgbS7dLivuZKFADm9VUu/8jcOYS6KZyT3Gcml2OldE624Mzfo9VG01dffYWxY8ciICAAhw4dQkNDAwCguroa//rXv+w+QcL7SIoLMym6ZilXxtzSYHNlGx4eKq4A/vBQncnyX+HyXWm1X3NLheXOJ602LhwrXaqvdOmzvSqCW1u+wJ0qkUshPSJag7tUrVZa1kC4XVjNW/oat53DnL4Ky6twxzR3Dl+NyqRMgrncJuH1CPdVMieh3mw5fA73f7DfbLkYufM5+vdodXhu0KBBmDdvHqZOnYoOHTogPz8f8fHxOHz4MNLS0nDhwgVHzdUmyB3unijJaZLub02+zbrdp/DpgRI8PFSHmbfFmxwDaI7rC6v9cm5duaXCP8wdIRuT33K4yeM0JUnHh+asXarfUjze3mEEa7qUt/a8jrwHSY+I1uIuzbJbm9MkfU1p/hCndYD5UgfbC8qxIrMIDY1GaNWAWtXUjcFSOQG5+bc0J6HeSDs+tJT64KycJqsrghcWFmLEiBEm24ODg1FVVWX1BIi2iS48EIvT+li1v9yNYK5sw8zb4nljydwx5Kr9cktj5ZYKc0uUpecbP6iLyc1s7VL9lpYw27siuNIl0+5YiVwI6RHRWtylarXSsgaWyhAIX9OFByrKGdKFB5o0HpeeI7y9Hx9ea/qn5S4RcvNvaU5CvREaTEBz43VL1+GM36PV4bnIyEicPHnSZPuePXsQHx8v8w6CcD5KQ0qW3Lqtcfnau+K7rSE1rhmoMxoPuwLSI8LTcOdwtxBz1dPlqpNbeq81CM/jqxGbJ2P7RrjF52a1p2nWrFl45pln8NFHH0GlUuH8+fPYv38/Fi5ciBdeeMERcyQIq7AmpKQLN98vz9JrLREdEsCvFpFr5mkt1sxFbuWKraG11nwGzoD0iPAk3GW1XktYajZsTXVya69RqjeHS67gs5wSjO0bgeU7itzic7PaaFq8eDGMRiNGjRqF2tpajBgxAn5+fli4cCGeeuopR8yRIKyiNc2ArXmtpTkIV53YI6xlS0iNozWhNXcJX8hBekR4Eu4e7uZQUj1dSXVyW65RGmIcP6iL2TQKV2C10aRSqfDcc8/h2WefxcmTJ3Ht2jX07dsX7du3d8T8CMJqXFX5113mIFcd2B1Da/aA9IjwJNxBm5TQmnk64hrd6XOj4paEV+IOK2Jc0ehYuo+5hqLO/HzoHmyGPgvCHbRJCbZ2ApBbjWcP7PW5OX313O23326x79NPP/1k9SQIwt64Q0jJEXNQmi9g6dyeklehBNIjwtNwB21qiZKKWr4Uy9a884o1Qqotaf2i7DYnd/ncrDaaEhMTRWO9Xo+8vDwUFBRg2rRp9poXQRAy2CMnwlPyKpRAekQQ9sdWjfAmbTGH1UbTypUrZbe//PLLuHbtWqsnRBBtHUtuaHvE9t0pP6C1kB4RhP2xVSMsvc9TwpItYbecppMnTyIpKQmVle7Vx4pyCAhPQknozB7i4+05TaRHBNE6bNUIufe5U0qA03OazLF//374+/vb63AE0SZR4t62R2zfXfIDHAXpEUG0Dls1Qu593hS2s9pomjhxomjMGEN5eTl+/fVXKiZHEK3Em0JnzoD0iCDcH2/SNauNpuDgYNFYrVajV69e+Mc//oExY8bYbWIE0RZx9wrc7gbpEUG4P96ka4pzmk6dOoVu3bpZXN7rjlAOAUG4Fkfcg6RHBEHYQmvvQcUNe3v06IHLly/z48mTJ+PixYtWn5AgCKK1kB4RBOEKFIfnpA6p7777DkuXLrX7hOwNN++amhoXz4Qg2ibcvWfP5gOkRwRB2EJr9chuq+fclatXrwIAunbt6uKZEETb5urVqyY5SG0N0iOCcA9s1SPFRpNKpTLJH/CEfILo6GiUlpaiQ4cOVs23pqYGXbt2RWlpqVfmHtD1eS6edm2MMVy9ehXR0dF2O2Zb0yN74mnfH1uh6/Qu7HWdrdUjq8Jz06dPh5+fHwCgvr4ejz/+ONq1ayfab9OmTTZNxFGo1WrExMTY/P6goCCv/iLS9XkunnRt9vYwtVU9siee9P1pDXSd3oU9rrM1eqTYaJL2cXr44YdtPilBEERrID0iCMIVKDaa0tPTHTkPgiAIxZAeEQThChSXHGhr+Pn54aWXXuLd/94GXZ/n4s3XRjietvL9oev0LtzlOu3WsJcgCIIgCMKbIU8TQRAEQRCEAshoIgiCIAiCUAAZTQRBEARBEAogo4kgCIIgCEIBbd5oevnll/nqwtxP7969+dfr6+sxe/ZshIeHo3379pg0aZLbNgb95ZdfcPfddyM6OhoqlQpff/216HXGGF588UVERUUhICAAo0ePxu+//y7ap7KyElOmTEFQUBBCQkIwc+ZMXLt2zYlXYZ6Wrm/69Okmv8u77rpLtI+7Xt/SpUsxZMgQdOjQAZ07d8Y999yDwsJC0T5KvoslJSUYN24cAgMD0blzZzz77LNobGx05qUQDsaZ35Vdu3bh5ptvhp+fH7p3746MjAxHXx7PmjVrMGDAAL6YYUpKCrZv386/7g3XKMeyZcugUqkwd+5cfps3XKs9/ta6xTWyNs5LL73EbrrpJlZeXs7/XL58mX/98ccfZ127dmU7d+5kv/76K0tOTmbDhg1z4YzN891337HnnnuObdq0iQFgmzdvFr2+bNkyFhwczL7++muWn5/P/vKXv7Bu3bqxuro6fp+77rqLDRw4kGVnZ7Pdu3ez7t27swcffNDJVyJPS9c3bdo0dtddd4l+l5WVlaJ93PX6xo4dy9LT01lBQQHLy8tj//M//8N0Oh27du0av09L38XGxkbWr18/Nnr0aHb48GH23XffsY4dO7IlS5a44pIIB+Gs78qpU6dYYGAgmz9/Pjt27Bh75513mEajYd9//71TrnPr1q3s22+/ZUVFRaywsJD9/e9/Zz4+PqygoMBrrlFKTk4Oi4uLYwMGDGDPPPMMv90brrW1f2vd5RrJaHrpJTZw4EDZ16qqqpiPjw/buHEjv+348eMMANu/f7+TZmgbUqPCaDSyyMhI9uabb/LbqqqqmJ+fH/vvf//LGGPs2LFjDADLzc3l99m+fTtTqVTs3LlzTpu7EswZTePHjzf7Hk+6vkuXLjEALCsrizGm7Lv43XffMbVazS5cuMDvs2bNGhYUFMQaGhqcewGE03DUd+Vvf/sbu+mmm0Tnmjx5Mhs7dqyjL8ksoaGh7MMPP/TKa7x69Srr0aMHy8zMZKmpqbzR5C3X2tq/te5yjW0+PAcAv//+O6KjoxEfH48pU6agpKQEAHDw4EHo9XqMHj2a37d3797Q6XTYv3+/q6ZrE6dPn8aFCxdE1xIcHIyhQ4fy17J//36EhITglltu4fcZPXo01Go1Dhw44PQ528KuXbvQuXNn9OrVC0888QQqKir41zzp+qqrqwEAYWFhAJR9F/fv34/+/fsjIiKC32fs2LGoqanBb7/95sTZE87EUd+V/fv3i47B7eMK7TMYDFi/fj3+/PNPpKSkeOU1zp49G+PGjTOZjzdda2v+1rrLNSpuo+KtDB06FBkZGejVqxfKy8vxyiuv4LbbbkNBQQEuXLgAX19fhISEiN4TERGBCxcuuGbCNsLNV/iF48bcaxcuXEDnzp1Fr2u1WoSFhXnE9d51112YOHEiunXrhuLiYvz9739HWloa9u/fD41G4zHXZzQaMXfuXAwfPhz9+vUDAEXfxQsXLsj+frnXCO/Dkd8Vc/vU1NSgrq4OAQEBjrgkEUePHkVKSgrq6+vRvn17bN68GX379kVeXp7XXCMArF+/HocOHUJubq7Ja97y+2zt31p3ucY2bzSlpaXx/x8wYACGDh2K2NhYfPHFF067YQj78MADD/D/79+/PwYMGICEhATs2rULo0aNcuHMrGP27NkoKCjAnj17XD0Vws3x9u9Kr169kJeXh+rqanz55ZeYNm0asrKyXD0tu1JaWopnnnkGmZmZ8Pf3d/V0HIa3/K2l8JyEkJAQ9OzZEydPnkRkZCSuX7+Oqqoq0T4XL15EZGSkayZoI9x8pasRhNcSGRmJS5cuiV5vbGxEZWWlx10vAMTHx6Njx444efIkAM+4vjlz5mDbtm34+eefERMTw29X8l2MjIyU/f1yrxHehaO/K+b2CQoKctofOV9fX3Tv3h2DBw/G0qVLMXDgQLz99ttedY0HDx7EpUuXcPPNN0Or1UKr1SIrKwv//ve/odVqERER4TXXKsTav7Xuco1kNEm4du0aiouLERUVhcGDB8PHxwc7d+7kXy8sLERJSQlSUlJcOEvr6datGyIjI0XXUlNTgwMHDvDXkpKSgqqqKhw8eJDf56effoLRaMTQoUOdPufWUlZWhoqKCkRFRQFw7+tjjGHOnDnYvHkzfvrpJ3Tr1k30upLvYkpKCo4ePSoyDDMzMxEUFIS+ffs650IIh+Os70pKSoroGNw+rtQ+o9GIhoYGr7rGUaNG4ejRo8jLy+N/brnlFkyZMoX/v7dcqxBr/9a6zTXaLaXcQ1mwYAHbtWsXO336NNu7dy8bPXo069ixI7t06RJjrGkZpE6nYz/99BP79ddfWUpKCktJSXHxrOW5evUqO3z4MDt8+DADwFasWMEOHz7Mzp49yxhrKjkQEhLCtmzZwo4cOcLGjx8vW3Jg0KBB7MCBA2zPnj2sR48ebrEknzHL13f16lW2cOFCtn//fnb69Gn2448/sptvvpn16NGD1dfX88dw1+t74oknWHBwMNu1a5doSW5tbS2/T0vfRW5J7pgxY1heXh77/vvvWadOnajkgJfhrO8Kt3z72WefZcePH2erV6926hL1xYsXs6ysLHb69Gl25MgRtnjxYqZSqdiOHTu85hrNIVw9x5h3XGtr/9a6yzW2eaNp8uTJLCoqivn6+rIuXbqwyZMns5MnT/Kv19XVsSeffJKFhoaywMBANmHCBFZeXu7CGZvn559/ZgBMfqZNm8YYayo78MILL7CIiAjm5+fHRo0axQoLC0XHqKioYA8++CBr3749CwoKYjNmzGBXr151wdWYYun6amtr2ZgxY1inTp2Yj48Pi42NZbNmzRItT2XMfa9P7roAsPT0dH4fJd/FM2fOsLS0NBYQEMA6duzIFixYwPR6vZOvhnAkzvyu/PzzzywxMZH5+vqy+Ph40TkczaOPPspiY2OZr68v69SpExs1ahRvMDHmHddoDqnR5A3Xao+/te5wjSrGGLOf34ogCIIgCMI7oZwmgiAIgiAIBZDRRBAEQRAEoQAymgiCIAiCIBRARhNBEARBEIQCyGgiCIIgCIJQABlNBEEQBEEQCiCjiSAIgiAIQgFkNBEAgJEjR2Lu3LmungZBEIRbEhcXh1WrVine/8yZM1CpVMjLy3PYnAjnQ0YTQRAEQbRAbm4u/u///s+ux8zIyEBISIhdj0k4FjKaCIdw/fp1V0/BabSlayWItkqnTp0QGBjo6mkQLoaMJoLHaDTib3/7G8LCwhAZGYmXX36Zf62kpATjx49H+/btERQUhPvvvx8XL17kX3/55ZeRmJiIDz/8EN26dYO/vz8A4Msvv0T//v0REBCA8PBwjB49Gn/++Sf/vg8//BB9+vSBv78/evfujffee49/jXNvr1+/HsOGDYO/vz/69euHrKws0byzsrKQlJQEPz8/REVFYfHixWhsbAQAbNu2DSEhITAYDACAvLw8qFQqLF68mH//X//6Vzz88MP8eM+ePbjtttsQEBCArl274umnnxbNOS4uDq+++iqmTp2KoKAguz99EgTReqy995Xc98Lw3IkTJ3DrrbfC398fffv2xY8//giVSoWvv/5aNI9Tp07h9ttvR2BgIAYOHIj9+/cDAHbt2oUZM2aguroaKpUKKpVKpLmEm2LXTnaEx5KamsqCgoLYyy+/zIqKitjHH3/MdxQ3GAwsMTGR3XrrrezXX39l2dnZbPDgwSw1NZV//0svvcTatWvH7rrrLnbo0CGWn5/Pzp8/z7RaLVuxYgXfqXz16tV8g9xPP/2URUVFsa+++oqdOnWKffXVVywsLIxlZGQwxhg7ffo0A8BiYmLYl19+yY4dO8b++te/sg4dOrA//viDMcZYWVkZCwwMZE8++SQ7fvw427x5M+vYsSN76aWXGGOMVVVVMbVazXJzcxljjK1atYp17NiRDR06lJ979+7d2dq1axljjJ08eZK1a9eOrVy5khUVFbG9e/eyQYMGsenTp/P7x8bGsqCgILZ8+XJ28uRJUdNJgiDcA2vufaX3/cqVKxljjDU2NrJevXqxO++8k+Xl5bHdu3ezpKQkBoBt3ryZMdasX71792bbtm1jhYWF7N5772WxsbFMr9ezhoYGtmrVKhYUFMTKy8tZeXm5WzQPJyxDRhPBGGsymm699VbRtiFDhrBFixaxHTt2MI1Gw0pKSvjXfvvtNwaA5eTkMMaajCYfHx926dIlfp+DBw8yAOzMmTOy50xISGCff/65aNurr77KUlJSGGPNorNs2TL+db1ez2JiYtjrr7/OGGPs73//O+vVqxczGo38PqtXr2bt27dnBoOBMcbYzTffzN58803GGGP33HMPe+2115ivry+7evUqKysrYwBYUVERY4yxmTNnsv/7v/8TzWn37t1MrVazuro6xliTeN5zzz0WP0+CIFyP0ntf6X3PGU3bt29nWq2WlZeX8/tnZmbKGk0ffvghvw+nm8ePH2eMMZaens6Cg4MddPWEI6DwHMEzYMAA0TgqKgqXLl3C8ePH0bVrV3Tt2pV/rW/fvggJCcHx48f5bbGxsejUqRM/HjhwIEaNGoX+/fvjvvvuw9q1a3HlyhUAwJ9//oni4mLMnDkT7du353/++c9/ori4WDSPlJQU/v9arRa33HILf97jx48jJSUFKpWK32f48OG4du0aysrKAACpqanYtWsXGGPYvXs3Jk6ciD59+mDPnj3IyspCdHQ0evToAQDIz89HRkaGaE5jx46F0WjE6dOn+XPccssttn3IBEE4DaX3vtL7nqOwsBBdu3ZFZGQkvy0pKUl2DkJdjYqKAgBcunTJzldKOAutqydAuA8+Pj6isUqlgtFoVPz+du3aicYajQaZmZnYt28fduzYgXfeeQfPPfccDhw4wCdUrl27FkOHDjV5nz0ZOXIkPvroI+Tn58PHxwe9e/fGyJEjsWvXLly5cgWpqan8vteuXcNjjz2Gp59+2uQ4Op2O/7/0WgmCcD+U3vtK73tbEOoq93Bnja4S7gV5mogW6dOnD0pLS1FaWspvO3bsGKqqqtC3b1+L71WpVBg+fDheeeUVHD58GL6+vti8eTMiIiIQHR2NU6dOoXv37qKfbt26iY6RnZ3N/7+xsREHDx5Enz59+Lnt378fjDF+n71796JDhw6IiYkBANx22224evUqVq5cyYskJ5y7du3CyJEj+ffefPPNOHbsmMmcunfvDl9fX9s+QIIgXILSe9/a+75Xr14oLS0VLYbJzc21en6+vr58ojrhGZDRRLTI6NGj0b9/f0yZMgWHDh1CTk4Opk6ditTUVIthqgMHDuBf//oXfv31V5SUlGDTpk24fPkyb/C88sorWLp0Kf7973+jqKgIR48eRXp6OlasWCE6zurVq7F582acOHECs2fPxpUrV/Doo48CAJ588kmUlpbiqaeewokTJ7Blyxa89NJLmD9/PtTqpq93aGgoBgwYgM8++4wXyREjRuDQoUMoKioSeZoWLVqEffv2Yc6cOcjLy8Pvv/+OLVu2YM6cOfb8SAmCcAJK731r7/s777wTCQkJmDZtGo4cOYK9e/fi+eefBwBRqkBLxMXF4dq1a9i5cyf++OMP1NbWtu6CCYdDRhPRIiqVClu2bEFoaChGjBiB0aNHIz4+Hhs2bLD4vqCgIPzyyy/4n//5H/Ts2RPPP/883nrrLaSlpQFoWu774YcfIj09Hf3790dqaioyMjJMPE3Lli3DsmXLMHDgQOzZswdbt25Fx44dAQBdunTBd999h5ycHAwcOBCPP/44Zs6cyQsYR2pqKgwGAy+cYWFh6Nu3LyIjI9GrVy9+vwEDBiArKwtFRUW47bbbMGjQILz44ouIjo5u7cdIEIQLUHLvW3vfazQafP3117h27RqGDBmCv/71r3juuecAgC+3ooRhw4bh8ccfx+TJk9GpUye88cYbrbtYwuGomDCuQRBuxJkzZ9CtWzccPnwYiYmJrp4OQRCEWfbu3Ytbb70VJ0+eREJCgqunQzgISgQnCIIgCCvZvHkz2rdvjx49euDkyZN45plnMHz4cDKYvBwymgiCIAjCSq5evYpFixahpKQEHTt2xOjRo/HWW2+5elqEg6HwHEEQBEEQhAIoEZwgCIIgCEIBZDQRBEEQBEEogIwmgiAIgiAIBZDRRBAEQRAEoQAymgiCIAiCIBRARhNBEARBEIQC/n97dx4f07n/Afwz2RdZJMhCRkhttZQiJEq0trq9rtLbomppXb8utEj14t6irba0VXRBe5Xooo2qqraqaIqiIqGxpIiKJUFiSWQh+8zz+yPmZM5k5uScmWfWfN+vV148MydnnpnM+c4zz/J9qNFECCGEECIDNZoIIYQQQmSgRhMhhBBCiAzUaCKEEEIIkYEaTYQQQgghMlCjiRBCCCFEBg9zfqm6uhr5+fkoKytD8+bNERISwrtehBAiC8UjQoityO5pKi0txerVq5GQkIDAwEBER0ejU6dOaN68OVq3bo2pU6ciPT3dmnUlhBAAFI8IIfahYoyxhg5atmwZ3njjDcTExGDEiBGIjY1FZGQkfH19UVhYiMzMTOzbtw/fffcd+vTpgw8++ADt2rWzRf0bpNVqceXKFQQEBEClUtm7OoQ0OowxlJaWIjIyEm5uls8IoHhECDGXxfGIyTB27FiWmZnZ4HEVFRVs9erVbO3atXJOaxO5ubkMAP3QD/3Y+Sc3N5fLNU3xiH7oh34s/TE3HsnqaXJmxcXFCA4ORm5uLgIDA+1dHUIanZKSEkRFRaGoqAhBQUH2ro5dUTwixL4sjUdmTQR3Jrou8MDAQApShNgRDUdRPCLEUZgbj2Q3mvLy8vDhhx/ijTfeAADcd999KCsrE+53d3fHd999h5YtW5pVEUIIkYviESHEHmTPglq1ahVu3rwplI8dO4b+/ftj5MiRGDlyJNzd3bF8+XKrVJIQHnIKyvDNkUvIKShr+GDi0CgeEeIYGltcld3T9OOPP+L9998X3TZjxgy0bdsWANC3b18kJiZi6dKlfGtICAc5BWUYtuI3lFdr4Ovpjh0zB0Ad6mfvahEzUTwixP4aY1yV3dN04cIFtGnTRigPGTIE/v7+QrlDhw44f/4839oRwknahUKUV2sAAOXVGqRdKLRzjYglKB4RYn+NMa7KbjRVV1fj+vXrQvnbb79FWFiYUL558yaXHCyEWENsdAh8Pd0BAL6e7oiNpqzRzoziESH21xjjquzhuQ4dOuD3339Hjx49jN6/b98+tG/fnlvFCOFJHeqHHTMHIO1CIWKjQ1y+C9nVUTwixP4aY1yV/VVs7NixWLBgAY4fP17vvmPHjuG1117DuHHjuFaOEJ7UoX74Z89WjeLCdnUUjwhxDI0trspOblldXY3Bgwfj999/x5AhQ9ChQwcAQFZWFnbt2oW4uDikpKTA09PTqhVWqqSkBEFBQSguLqa8KITYgTWuQYpHhBBzWHoNKsoIXlVVhWXLliE5ORlnzpwBALRr1w7jxo3DrFmz4O3trbgC1kZBynI5BWWNqvuV8GWta5DiESH252yfDzZtNDkjClKWaYxLSh2NswUlQ3QN1qHXgriSnIIyDF2+FxU1Wvh4uGHnrASHj1GWXoOKtlHZuHEjvv/+e1RVVWHQoEF45plnFD8gcS7GlpQ6+kXhShyt0epIDTiKR4TY1/bMPFTUaAEAFTVabM/Mw9MJMXapi61ik+xG0+rVqzFt2jS0a9cOvr6+2Lx5M7Kzs/HOO+9YrXLE/nRLSnUf2o1hSakjcaRGqyM14CgeEUJ0bBmbZK+e+/DDD7Fw4UJkZWXh6NGj+Oyzz7Bq1SqrVIo4Dt2S0qWP3mP3Xo7GyBZ5UORug+BIiewoHhFif8O7RMDLvXbjWy93FYZ3ibBLPWwZm2Q3ms6dO4dJkyYJ5ccffxw1NTXIy8uzSsWI42hsS0odga4hA8CqjVbdN7TZm45h2IrfJBtOjpTIjuIRaewcZc83N5VK9K892DI2yR6eq6ysFG1T4ObmBi8vL5SXl1ulYoQ0Vsa6mv/Zs5VVHkvJ8J8jJbKjeEQaM0cZKk+7UCia02Sv6QO2jE2KJoLPnz8ffn51lamqqsIbb7yBoKAg4bZly5bxqx0hjZAt5zEpnbOmDvVzmB5HikeksXKUuY6ONOfVVrFJdqNpwIAByMrKEt0WHx+Pc+fOCWWVHbvnCHEVtgxEjtR7pATFI9KYOUpjxVnjhyUoTxMhDsiRlvZbiq7BOvRaEF5cKUbYkk3zNBHSELqQ+XCkYTBCiONxlBjR2GK+7EbTa6+9Juu4BQsWmF0Z4twcZXIicX0Ujwixv8YY82U3ml555RVERkaiRYsWMDWip1KpzA5SS5Yswbx58zBjxgysWLECAFBRUYEXX3wRycnJqKysxLBhw7Bq1SqEhYWZ9RjEuhxlcqI1NLZvU47O2vEIoJhESENcOeabIrvRNHz4cPz666/o1asXnnrqKfz973+Hm5vsNE+S0tPT8fHHH6Nbt26i22fNmoVt27Zh06ZNCAoKwvTp0zF69GgcOHCAy+MSvhxlciJvjfHblKOzZjwCKCYRIkerYF/JsiuSHWW2bduG7Oxs9OnTBy+99BJatmyJOXPm1FvBotStW7cwfvx4rFmzBk2bNhVuLy4uxtq1a7Fs2TI88MAD6NmzJ5KSkvD7778jNTXVosck1uGq2cMdKRM2qWWteARQTCJErktF5ZJlV6Toq1lkZCTmzZuHrKwsbNy4EdeuXUPv3r3Rr18/s5PKTZs2DQ899BAGDx4suv3IkSOorq4W3d6xY0eo1WocPHjQrMci1ueK2cMdKRM2qWONeARQTCJErsYYG81ePde7d29cuHABJ0+eREZGBqqrq+Hrq6xrLjk5GX/88QfS09Pr3Zefnw8vLy8EBweLbg8LC0N+fr7Jc1ZWVqKyslIol5SUKKoTIYYaYy4SZ8MjHgH8YxLFI+LKGmNsVDwJ4ODBg5g6dSrCw8PxwQcfYNKkSbhy5YrifAe5ubmYMWMGNmzYAB8fH6XVMGnx4sUICgoSfqKioridm7g2qb2cXLEHzRXwikeAdWISxSNiLY6y91xji42yG01vv/027r77bowcORJNmjTBvn37kJ6ejueee67eNy85jhw5gmvXruHee++Fh4cHPDw8sHfvXrz//vvw8PBAWFgYqqqqUFRUJPq9q1evIjw83OR5582bh+LiYuEnNzdXcd2I4zAVGHgHDCUb1xL74x2PAOvEJIpHxBpcLV6lZhdgzubjSM0usHdVGiR7eG7u3LlQq9V47LHHoFKpsH79eqPHyd3radCgQThx4oTotieffBIdO3bEnDlzEBUVBU9PT6SkpOCRRx4BAGRlZSEnJwdxcXEmz+vt7Q1vb295T4o4NFOr1qyxmq0xLp11ZrzjEWCdmETxiFiDK8Wr1OwCjF1Tu5BiY3oukqf2Rd+YUDvXyjRFe8+pVCr8+eefJo9RstdTQEAAunTpIrrN398foaGhwu1TpkxBYmIiQkJCEBgYiOeffx5xcXHo27ev7MchzstUYLBGwHDVdAmuinc8AigmEefhSvFqy9HL9cou0Wjas2ePFath3PLly+Hm5oZHHnlElEiONA6mAoM1Aob+hMZWwb5CWgFn/fbm6uwRjwCKScQxONIEbEsT/47q3hIb03NFZUdGG/YSrvQvIABmX0y687QK9sWlovJ652jofkvqT4ks+aJrsA69FsSV8IqXqdkF2HL0MkZ1b2l2L9PafefwxaEcPNFHjSn925o8ziYb9i5ZsgQvvPAC/PwafjEOHTqEGzdu4KGHHlJcGeLc9C8gbw83qABU1GgVX0xyLkRdWf+4pMm9LW5AudJcAVdF8YgQx8ArXkYG+6J3dAgizcwovnbfOSzadgoAhH+lGk6WkLV67uTJk2jdujWee+45bN++HdevXxfuq6mpwfHjx7Fq1SrEx8djzJgxCAgIsEpliWPTv4Aqa7SoqNECUJ5F2/BCXLnnrNHVIYbHTVh3yOLVJI0xWZuzoXhECB+WrkKOjQ6Bt0dtM8Lbw82seMljJeAXh3IkyzzJajR99tln+OWXX1BdXY3HH38c4eHh8PLyQkBAALy9vdGjRw+sW7cOEydOxOnTpzFgwACrVZg4LsN9h7zca99ePgovJv2GC1C7osLYxaR/nKe7CtWa2pFmOY00U8FCzlYwjpIfpbGieESI5XilLdDN8DF3pg+Pbaqe6KOWLPMkeyL4PffcgzVr1uDjjz/G8ePHcfHiRZSXl6NZs2bo3r07mjVrZrVKEudguO+QltX2NCm9lHQNl5V7zgoTBI11/RpO3n5yfbqsyeENDf+pQ/1MdjHTnCfHQPGIEMvwGFrbnpmHqjtfVqs0DNsz8/B0Qoyic/DY9HfI3eFY/NMp1DDAQ1VbthbF26i4ubmhe/fu6N69uxWqQ5yZ/qo2/Z6fyhqt4gtSHeqHaQPvwvdHr0g2hPQbOHJXk1gSLKR+19JVJEQ5ikeEmMdR0hbw2PQ37UIhau58O69hsOpcVLP3niPOj8eHfE5BGb5Mu4jcwnJM6NtasudH6eOpQ/2QNLm3sKqC10VgKljIqZ/U71IPFCFEDh6x19IVZzzSFtzTKliyLAePxltsdAjcAWgAuN8pWws1mhopHh/yOQVlGPTublTXjsJh24k8JE/ti3/2bAVA3PMDQPHj5RSUCQ2v749ekfwdJc/HWLCQ+/umAg2tuiOEyMEj9jpKFm0evUQ8Gm9fH86B5s7/NXfKs4d1VHweORRv2EtcA4/Jd9sz84QGk45+dlf9jRzNeTwlv6P0/IabTCr5fWMbVNKqO0KIHDxir7Es2krxmAjOK+5ZuulvcnquZJkn6mlqpKw1nm0qm6uSx9NPXCn3dyx9Ppb+viNl6CWEOC4esZdHFm0eveO84p6lw5Vje0fhw93ZorK1KM4InpSUhDFjxshKLOcIKAOvaZa+UXMKyjB0+V5U1GjhrgKWPdYdI3u0rHeMkgzhhl3XShJWynk+UsfQRG7rsOY1SPFIGr2nHZMjzGniNQ+Tx+cIj3os3XEayem5GNs7SnJoztJrUHGjKSwsDOXl5Xj00UcxZcoUxMfHK35QW6JGk3WZumBSswvweepF7DqZjyoNk30xfHPkEmZvOiaUlz56jzBHikddabK27VnzGqR4ZBq930lDHKHhZc2Yb4yl16DiOU2XL1/Gp59+ihs3bmDgwIHo2LEj3nrrLeTn5yt+cOIYLEnWaGwsWjdJcduJuhweUmP3+o9vmLDSnJwdpvCYS0AcC8Uj0+j9TqTkFJRhclIaNqbnYnJSmlnxn8d7jEeeJltS3Gjy8PDAqFGjsHXrVuTm5mLq1KnYsGED1Go1/vGPf2Dr1q3QarUNn4g4BF5ZYfUZm5To4+GGgluV9c6v//hDlu/F9sw8LBndVcjz9OT6dKN1MqehxyPlP3EsFI9Mo8UJRMr2zDxhq6uKGi22Z+YpPgePBs+xS0WSZblSswswZ/NxpGYXmPX7clm0ei4sLAz33Xcf4uLi4ObmhhMnTmDSpEmIiYnBnj17OFWRWJOl3xSMNV4MJyWOj1WDAVi8/XS9hpnhfnWLt5/G7G+OSW6JYo2GHnF+FI/E5GwJRBqvm2VVkmU5eKQcKCqrlizLoRvd2Jiei7FrUq3acDKr0XT16lUsXboUnTt3xsCBA1FSUoIff/wR58+fx+XLl/HYY49h0qRJvOtKrMCS3hdTjZe+MaFIntoXY3pHIXlqX/Ro3RSVJjbvNdxnDgCqNQye7ioAxr8hb8/MM6uhtz0zT6hHpZnfrIjjoXhkmqVLuYl12KpXREpTPy/Jshw8epqYwUZbhmU5eKRgkEtxyoERI0Zgx44daN++PaZOnYqJEyciJKTuQ83f3x8vvvgi3nnnHa4VJdajMvi3IbrJ3wW3Kk0uWe0bEypMLMwpKDO5xFaX9fuJtam4056Bj4cb1j8Za3TVXE5BGZbtOiOUDTcD1k9XIHfVHXFeFI+IErx2QbDkHI6SmJJHNm8ePU08Gm88UjDIpbjR1KJFC+zduxdxcXEmj2nevDnOnz9vUcVIfdZYPpx2oVA0rt1Qrg791RLeHm7w8XBDRY1WcjuShnJ5XCoqFxpMADBrSHuTQSTtQqHQW6Q7Vn/vN13ddPRXdAzvEoFlu86gskYLbw83DO8SoezF0nsNaBm3Y6B4ROTitQuCpecw1iti7so1S+IQjwaPbqRCF1PNmTfHo/GmG92wZCWgXIobTWvXrm3wGJVKhdatW5tVIWKctZYPK020ZjgHad7wjght4t3gdiT6G+s2VAepxozhRXpPq2B8c+QSYqNDRHXT0e8BU4f6YdesBIfIKUL4oHhE5OKRzJHHOXj0ivCIQ7wSHOuyFinMXiQwNhHcnEaP/uiGNSluNL3wwgu466678MILL4hu//DDD3H27FmsWLGCV92IHmvtbaY0o6uxBo7+75iqp1SSS6V10B9GnJSUhso7PV1Jk3sLddPx9XRHq2BfoWEl1XiTg/aYcywUj4hcvDaGtfQcPHpFHCWb9/bMurQyVRqG7Zl5eDohRtE5eEwEtyXFjabNmzfj+++/r3d7fHw8lixZQkHKSgwvVsOGgCXkNCRyCsqEidNSWbqNBRX9b0U+Hm5ggKihozuXnIRm+sOJ+sN05dUaXCoqF4KAbk5Tq2BfYdNfc76RGc6RUrK1i5Lz01CfeSgeNR6WJmLk0UjQzcHU1cPca9bSXhFevURXisqRfie+mdvzLlWWg8dEcADYmnEZG9JyMD5WXW9nCp4UN5oKCgoQFBRU7/bAwEDcuHGDS6VIffoXvKUNAaX0t0sBalfZ7ZqVYPQxdfXUX5mm/62owqChM2HdIVQryBiuHyx0w3Q6ugtf/xzfHLlk8htZQ1u8mJojpWRrFyk01Gc5ikeNA6/J05b2NOcUlAmx9/ujV+y29QiPxhuP17SovFqyLAePieBbMy5jxsajAIC087Wrqa3VcFKccuCuu+7Czz//XO/27du3o23btlwqRYzTLR++VFRu00y/+r07QG0PT0OPueKXv4S8TLreGaB2tZsuxYEugSUg/3no555JHNJedJ/+REZd/ij9xzacrK5LlzB0+V4MWb63XuoEU3OkLhWVc1nGTRmbLUfxqHGw5ZJyKTyuWR555nSNt43puSYTADeEx2s6oW9rybIcPCaCb0jLkSzzpLinKTExEdOnT8f169fxwAMPAABSUlLw7rvvUle4jfDqmlXyeLpVckD9fE6G35oMA4v+sJl+r45hj5n+kKPuGFNzoHTzpFb88le910G/B8fTXYWl/7wH1Vom+lYn1ful643Sn3Suw3No1NZ/R1dE8Uiaqwz/2nJJuRQe16wrTUiPDPaFl7sKVRoGL3cVIs3I08RjFd/4WLXQw6QrW4viRtNTTz2FyspKvPHGG1i0aBEAIDo6GqtXr8bEiRO5V5DUx2NsXunj7ZyVIAy56U/+NjbEZCywGHaL6/5vbMjR28MNKtQ2ZgznQOl3h5t6HfQDSrWGYfY3x5CSOFD0+Pp1NHwMXSC8UlQuajA9mxCDhPbNhXr6eLhh1pD29SbDK3ldbfl3dEUUj0xzpeHfqyUVkmVb4XHN8mh48UgqyWtCuv5EcHMabzzSFtiS4kYTADz77LN49tlncf36dfj6+qJJkya860UaYOnYvDmP93RCjPDNVXebsW88/+zZSnZg0T0P/blH+g0VU71AUmKjQ0RDf9VGLmbD4AfUn9Nk2F1dWFYlGhqtuLPty4pf/jL7A8nWf0dXRPHIOFda6Wls+MWak32lWHrNqkP9sGR0V2HSsr1yLAGOMyFdaYJlQ7Z8f5jVaNJp3rw5r3oQGzOn295Ur5Ju6E6XnduccxtO8Nb1NHl7uKFGo4WGGR8WNJUT6vOn+ogmmRu7mE31fukY676O1Fs9p2OLDyRXGWaxJopHYs72DV6KLYdfrC01u0A0aTks0Edxw8VY3LUHHhPSlSZYNsahh+euXr2K2bNnIyUlBdeuXauX0Eqj0Zj4TeIozO22N/bNNTY6RFggylA7pGVqZZ/UFifGen62Z+bh3Z1Z0JhYgSr1TbpvTChSEgda1NAw1X1du+3LIdRoayumNGgpbQC50jALbxSPTNMfXq6s0eJKUbnTvm90vQa2WFJubR//ll2vbE5vDzP41x5yCsowcd0hVGkYtvxxCb8YTIOQg8dQoy3fH4obTZMnT0ZOTg7mz5+PiIgIqFTmdqgRa2noQ9ncbntjXbH625pU1mix5ehlk8ktpbY4Aer3/IQ28RbGy3XnX7nnLKYNvEuYqC3VNcxj6MtY93Xtti919dLfyqUh5jSAXGmYhTeKR6bx2q7DUYzs0dIhGkuO0OtrGHftFRO+TLsomtP0ZdpFzB3eSdE5eGUEt9X7Q3Gjaf/+/di3bx+6d+9uheoQS8n5UDZ3HNrUJEj9c43q3hLfH71S79wNbXFijLHVaxvTc0X5UewxkVrJti+GzGkA0So70ygemeYoK85cCY9e36cHxGB31nVRWSkevTM85BaWS5ZdkeJGU1RUlNl7zBDzyf12I+dD2dzGhv7wmv5kcP0x7b4xoUbPrf/Br2PYADDM+KsOrd0r7su0iziYXYBjl4rrPS97TKS2ZBzfnAaQqb+XI3zjtTeKR6bZchPThvB4r/I4h6VZxXn0+vaNCcV7Y7oLQ0nm1IPXRHBLX9MJfVtj24k8UVmp4V0isHzXGWF+lqNvpK640bRixQrMnTsXH3/8MaKjo61QJWJIybcbuR/KShsbUtmxjWXIlWqoGZvTJJWd9tPfL0o2tmzNkqzA5jZYDV9TmudUi+KRNFttYiqFx3uVxzl4ZMD2dFNJluXIKSjD3G9PoLxagxOXitFD3dSsZfqW9j7zeE15NMx1KW2cZSN1xY2mMWPGoKysDDExMfDz84Onp6fo/sJCymrMm5JvN9YasjI1vGZqDpOpupm6z9T8C8PHHdM7SpjTZC+Wftvk0TtG85xqUTxyfI6SzJHHHK/fzxXUKyudR+Mom+3yiiE8GuaWxkRbxkOzepqIbSn9VmGNISvDrOBAbY9PfNtQfHvkEqq1rN4qMlPdpca6yOPbhormX8S3rb29VbAvPNyAGm1tygHDBhPPLlm559L/e3i6qxqcT2CNbmOa51SL4pE0S4ejeJyDx3uVR/oEHnO8eJyD17VraZznNS+Kx3vM0hgZGx0iykxuzXiouNE0adIka9SDSLDXhGdDupkjXu4qvDi0A+5pFYzJSWmovrOSTKs3t8RUd6mpLvJqrXheSrWWIaegDJOS0qDXThPh2SWr5Fy6OU26PFBPrk83eby1uo0d5T1hbxSPTOMxHMXjHLzeq5YmQHSUOV6Ocu3ymBfF4/3BI0ZeKSoXreKzZnoNxRv2AkB2djZefvlljBs3DteuXQNQu0Hmn3/+ybVypI461I/LJrHm0l/iWqVhOHfjNo5dKhL1POnS6OuON7axpalNInXfvoC6OUv6jwnU3yiY54a3Ss91qahc1mbD1tyU197vCUdB8cg4Hhuy8too19L3qrEEiOboGxOKtx7pZnaDyVFeD6BuU3JzNusF6kYPAOW55nR4vB48YqQtN3RW3Gjau3cvunbtikOHDuHbb7/FrVu3AADHjh3DwoULuVeQOAb9Rg1Q+61i2a4z8Paoewt53Rmq+ubIpXoTJFsF+yKnoAwhfl6i2z1UKny8tzbZ246ZA7D00XuEbxq6Lnkdw255w4aW7rGlgoipQGMqgEgdb9jIM0bucc7I0qDNgyvHI0tfX8OhI3OHoyw9Bw+Och05yuuRU1CGIcv3YvamYxiyfK/Z7xHd6IDWzBWoPF4PHo03W/5dFA/PzZ07F6+//joSExMREBAg3P7AAw/gww8/5Fo5Yj1Kx5B1Xcor95wVxvQra7QYH6sW9v2p0jBMSkpDZY0Wnu7iRtOxS0WiDXnjY0Jx4GyB8LvLdp3BrlkJ+GfPVqLH/PTJWDyxNtXoEJ3hijxTmcj1n7NUN7Bhhl2p4+V2sTtKVzxvjrJ6z1XjkaO8vpHBvqK5RObsYs+Do1xHkcG+orkz9no9tmfmiZJbbs/Mw9MJyvI9bc/MEw1pmXMOXkOelmY3//NKcb2ytYZfFfc0nThxAqNGjap3e4sWLXDjxg0ulSLWpQvIszcdw7AVvxn9lmLsW6461A/TBt4l+sZXVF4t+j3dhVytYULDSXe8/oa8LQJ9UKUxPfSmc+xSkdBgMnaMrptbfyNdU128ht3A2zPzRPcZZthtqNtYbhe7Kw6jWXPYUQlXjUeOMmRh7LqwF0e4jtIuFIoaGvZ8PSx1s6xKsixXZLAvekeHmN2A5PEe++JQjmSZJ8WNpuDgYOTl5dW7PSMjAy1bUsZZZ9BQQJZqVOm+8emG0QyTmemG03w93fH5U32E44Z3iRA1tkZ1byl0yep+z7BbNqegDMt3nZE8RkdO971+NzBQ27ule27Gft9Rsu46IkcZLnHVeMTj9eU1dOIIf2dH4SgxYXiXCNGQljkJIZsaTJUwLMsh5wt4Q3jkvnqij1qyzJPi4bmxY8dizpw52LRpE1QqFbRaLQ4cOIDZs2dj4sSJ1qgjsZDhUFxDS15N5bzQP4/+MNo/ukXij9ybeDI+GkPuDjfZha7rXi8uq8KyX87gpWEdhD3chneJqHe8/uRPAHiqXxvFw2CGz31yv2h8tPccAHG3trHfN2xMmpt1FzC9LNdZs3o7ynCJq8YjdagflozuKmSNNjd/jqWZpy3Jfq+Px7L0pTtOIzk9F2N7R2H2sI5mncNSjpKJm0dCSB6ZuHnkR+KR+2pK/7a4WVYlvD+m9G+r6PeVUNxoevPNNzFt2jRERUVBo9Hg7rvvhkajweOPP46XX37ZGnUkFjA1N0LqA89Yo8rYeQBg8LI9Qnf1om2n0DkySNSg0qcO9UNGzk0s2nYKAJB2vhDvjemOHuqmom1Z9Ouhnxtq3YHzGCfxAdJQ1uykyb2RdOCC6HeW7TojNNgMf59XPhVTy3IdZd6KuayRD0wpV41HqdkFmLHxKIDa6yQs0MespdyWZp62JPu9Do9l6Ut3nMaHu2sXjOj+tUfDiUdPU05BmRA3vdxV+CVxoNkNJ0uuPx4NLx4x0lSOPiVyCsqwdv8FlFdrsHb/BTzWy7wvGnIobjR5eXlhzZo1mD9/PjIzM3Hr1i306NED7dq1s0b9iIWMzePR9awo6bX55sglo0N6ugaTTkNZdtceOC8qr9qbjZyCMpOTrWcNaY/F208DUL6bt+Fz33L0siiFQUPnNLc3xfBbpJxs5405q7clXDUe8che7UqZuJP1PlR1ZXs0mnj0NH2ZdlE0L+rLtIuYO7wTl/rZGo8eZ2M5+pRy6IzgOmq1Gmq19cYNCR/6mXQBYLlez4opxrqO9Xt99JeF6laS6OjmTZjqfo4O8cfxS3UrHUJ8PZEl8Wa/p1UwPNxUqNEy0Zwm3fk93VT4/VxBvW7/1OwC7D59TXjuunlU3x+9omgfO6Xf5oz1HpnKIkxZvflxtXjEK/O0sWvW1ufg8VzG9o4Seph0ZXPwyG5uaWby3MJyybJclg7x8erpdoTM5Dzep3LJajQlJiZi0aJF8Pf3R2JiouSxy5Yt41Ixwoc61A+Jer01FQ301khdSIbLQtWhfvglcSC+TLuI3MJyTOjbWnLYKaegDDtP5guP5emmwozB7XFUL1WA4TYsk5PShHlPut3sjW0erN/trz8cAADPJsQIw3pSmwbzYOwbzz97tjK6LNdR5gU5G4pH8lm6lJvHOXgsS3+slxqrd2dDA8D9TlkpHsOEV4rKRSu9zMk8PaFva2w7kScqK8WjweMoPd285onxeK/LIavRlJGRgerqauH/pqhU5ia4J9Y0vEsEVvzyl6weDVMXkrFlobpvGIZdy1Ln0J/YPXtYB/SNCRU1ZPTnNhker7/E13DzYKCu299wOKCwrEo05GfNwGDqm6ipTS3NrY+zTiDnoTHEI17Dc8auWVufA7B8U9e0C4XQXfGaO2V7DBPyOAePCfo8Gjy8erp57BtnaT14vU/lkNVo2r17t9H/E+egpEfDWDdnTkEZCm5VCkNxht3SUqvz3N1UwhJS/dvdVIDHndt19TH85mQ4tKj/uLrz6NN1+xsOB5gzsdASlu6R1RBnn0BuqcYQjxxlY1hewx48hsUs3ZCVx2vKa9KypRP0efxtefR084hFPFZo2nJ4TnGepuLiYhQW1k8+VVhYiJKSEi6VInwp/Sag3815pagcw1b8hsXbTwtzl/QbA8bydKhD/TB7aHsAgEbLMGPjUaRmF4hu17La1XZbM2q/uTWUO8rDDfj0yVihZ2bHzAGYN7wjvO4k0NTPVqz7JqdL9/HvzcdtttUHrz2yGnoMU0k6GxuKR6YZ5lQzt2Ft6bCHblhsY3ouxq5JRWp2QcO/ZMDYhqz2kF9SIVmWg0fiUl1Kitg2IVgyuqvdvjTxeC66FZob03Px5Pp0s2O1rYbnFDeaxo4di+Tk5Hq3f/311xg7diyXShF+9Bs1g5btaTBgGXZzbjl6uV6Pjn5jwNhFk1NQhjfvzKHS0XVr7zh5VXS7bhuVhjbsrdGKx7rVoX4IbeItBFLDTLL5JRXQLcLQ5WOyBVskAzTck2+5XpLOxsZV45GjbAzLI1uzo2wcbMtNXaXwiBG6lBRp5wuFL6VK8UhMyWMSN4+Gly0z1ytuNB06dAj3339/vdsHDhyIQ4cOcakU4Uf/DVmtYZiw7pDkxWF4QY/q3lK0Ua/udt2FbqqxozFYNqrrCh8fK57AqSsb+1Zs7Nz627s4YrZiXt/uG3qMxCHthbK1erScgavGI0fZGNZRMpM7yjmGd4kQvrB4m5kQkkeM4LVFjqWNFR6TuHmtnrPVZ4HilAOVlZWoqampd3t1dTXKy+3TZUpMi40Ogae7CtV3emSq70ymVpKjSVfWX96vP7Ha2Hi0/tyl//6tkzCPQZfpVTcJUirzq2FdgPrzngyzJuuGIu9pFSwa424ouPGcWG2LpI9KJveb4gqTyV01HvHaCJVH5mlHyEzO4/XoGxOKCX3V2JJxGaN6mHcOdagfdlmYEFJ3HkuuOR5zq3ilpLB0bhWPhpctVyIrbjTFxsbif//7Hz744APR7R999BF69uzJrWKED3WoHz5/qg8mrDuEag2T9cY2vKANJ2rrZwY2lTE4aXJv4TGX7jyDIXeHC+cZ2aNlvcaSqQmF+nUxTLD5VVoOVu+tzd2Sdr72W5JugqWvpzveeqRbvUaeMc44sdrSIOGMz9kYV45Hlq444/E3dpTM5IDlr8fafefweWrtdIDPU3MQHepv1e02rIlHQkjA8nlAPBorvFbx2eLLKmBGo+n111/H4MGDcezYMQwaNAgAkJKSgvT0dOzcuZN7BYnl+saEIiVxoEVvbKk0AsZuv1RULvRuNbQkNqegDCv3nG1wCa3hxZVTKB5mXHfgvOgcs785hmoNa3D7B0fJV6KUJUHCWZ+zIYpHpjlKNm9Hea8Z7nz/xaEcxY0mR/my4UjL9C1trPBYPWdLiuc09evXDwcPHkRUVBS+/vpr/PDDD7jrrrtw/Phx9O/f3xp1JBxYOiHU1JhxbHQIPO+8izzdasejvzlyCa2CfY0en1NQho/3ZuPjO9un6IKQflezYVexbh4TANFcAMOkcKfy6lZL6Q9J6o/X68+Jaui5mTreFTjifDBzuHI8svS9pxt+AepfU3LxmAekv3DB3CzaPBjufG9YloPHPCDA8r8tj3lRPOYS8cBr9ZytYrVZ26h0794dGzZs4F0X4sBMdcNm5NxE9Z38k9VaYOK6NFRptMIGufpZt3MKyjB0+V5hSf6yXWfwVL829Vbn6XcVG/tmp9sQWB3qJ8xzCPHzEobqAGDKfW3w6e8XG9x0WD+FgeFzc5RvldbgStnIXTEe8Xrv2WoZdkOsnbtMjiF3h2PJz6dRrWHwdFdhyN3his+hyzlnqiyHo8QVXpm4LcWjJ9KWr6msRlNJSQkCAwOF/0vRHUcck5yJoaaOMdYNq0sZoFOlqW0QlVdrcKmoXGjgAOIcRkBtl/CafdkwpN9V3NAFpZvnkFNQhvW/XxAumsdjW+Px2NYNbjoslSncUYYVrMVWcwB4awzxiNdmu5YOv/AanjPMXWaP913ahULZC2JM+f1cQb2y1GIWU/VwhEaCLRNCNlQPHkONDrVhb9OmTZGXl4cWLVogODjY6PYEjDGoVCpoNPW3tyCOQc6FJnWMscbU+Fi1MAkbALzc3VCl0cLTXYXisirM2XxcWO1i2P3rrqrNv6TjoQJqmHgoQe6FbarnRP/5Kb04pY63NMMxMV9jiEc8MmDz+DDilZnc0ufCg6NsPsyjt4pXI8EReiIdaTK5HLIaTb/++itCQmorwXPbgsWLF+Pbb7/F6dOn4evri/j4eLz11lvo0KGDcExFRQVefPFFJCcno7KyEsOGDcOqVasQFhbGrR6NhZwLzdQxphpThikEwgJ9hFVzi7adAlC3OaZh9+//DYgReod8PNygZQzQsHoXsGGGclMXV0M9J0ovTlPH89j4k5ivMcQjYxmwlX6YOMoQLI/nwosjbD7Mo7eKV1JJW+3X1hAek8kdKuXAe++9hx49eiAwMBAXL17EmDFj4O3tbfGD7927F9OmTUPv3r1RU1OD//znPxg6dChOnjwJf39/AMCsWbOwbds2bNq0CUFBQZg+fTpGjx6NAwcOWPz4jY2c1ripY6QaXPopBL45cknoAte35ehlTBt4l+jc42LVGBerxvbMPBy/VCzs/G04PKd/YY//JBWaO71Rs4a0x/AuEaL8TA1dMLqLUzdpUO7xhs/FsEyNJttpDPGI13vM0g8jR9nklgdH2XyYR2/VsUtF9cpK62Rqc3Fn5VApB3788Ufcvn0bgYGBePLJJ/Hggw+iRYsWFj/4zz//LCqvX78eLVq0wJEjRzBgwAAUFxdj7dq1+PLLL/HAAw8AAJKSktCpUyekpqaib9++FtehMZGztNNUi11u96f+cfp0j2d47pyCMizfdUY018lYxnHd+XTtsYoaLRZvP40Vv/yFJaO7CukF5Izv5xSUYcjyvUKw2DUrQdHFxiPoEfM1hnjkKO8xHvVwlOdiyyEcKZHBvqLhykgzeon+vFwiWXY2zpRoV1ajqWPHjpg3bx7uv/9+MMbw9ddfm5xgOXHiRLMrU1xcDABC1/uRI0dQXV2NwYMHi+qiVqtx8OBBajQpZCoRpaErReVIv1CIVsG+orlBcnJp6DeM9DOI674F6X5Pt1T3q7QcUYNJpYJoA0rd4y775Yxo7pROebUGiZuOCdu2GPaCGbsYt2fmib5xbs/Mw9MJMSZfM8Pf55HhmJivMcQjXhnBedSDRzbv6ffHIDk9F2N7Rzl1dnPA8vmMaRcKRcOV5vR4ZeTelCzLoSQOWpOjrCaUS1ajafXq1XjxxRexbds2qFQqvPzyy0YnX6pUKrODlFarxcyZM9GvXz906dIFAJCfnw8vLy8EBweLjg0LC0N+fr7R81RWVqKyslIoN/adzvXJmdNkar6O3AYXIO4mlcr87ePhhmqNVnQ/Y8Dsb44JWYP1H1fH010FFWoDjn4+Jt19+jmhjF2MRWXVosc0LBurq/7v88pwTMzTWOKRpcNAPPB4r2/NuIwPd9eukv1wdzbatQhQPIfHUbKb85jPyKPHy/Ddbk4qh5tlVZJlW3G2Vcqyklv269cPqampuH79OhhjOHPmDG7evFnvp7DQ/E1Dp02bhszMTKM7liuxePFiBAUFCT9RUVEWnc+VmEpomJpdgDmbjwvfoPTpyuYkdTOWbEz/PBU1WhiZ/iQsBzY8HgDG9I5CSuJA/JI4EEsfvQefP9VHeE7ubios/ec9ot4sY3UO9vMUPZ5h2Vhdy6s1WLnnrPBtl0eCO2Ieike2w+O9bpiWxLBsq3rw2OSWxzl4JKa8r10zybIcTf28JMu24myJdmU1mkaPHi18Q0pKSkJAQADXSkyfPh0//vgjdu/ejVat6vL6hIeHo6qqCkVFRaLjr169ivBw44nJ5s2bh+LiYuEnNzfX6HGNkeHFCgBLtp/C2DWp2Jiei7FrUtG+RRPR7+jmHyh9Y+sSWc7edAxDl+8VGk61y49r33ae7iohU7CHqjYFASDOGmz4uNMG3iX0ZP2zZytEBvtiUnxreLqpoNEyzP32hOixjGUiNrZTua6Bl5pdIDT09B8bqP1mOWzFbyaznVubq2YnV4rikXxbMy7jsY8PYmuG8g93gE827/GxasmyrerBI7s5j3PwEOLvJVmW455WwZJluRwhu7ktKZ4I/tRTT2H48OHw9bU85TpjDM8//zy2bNmCPXv2oE2bNqL7e/bsCU9PT6SkpOCRRx4BAGRlZSEnJwdxcXFGz+nt7c1lJY2r0l89puvu1vdHTpHRSYpKl3Ruz8wTJbTTjZdn5NwUEmBWaxjmP9QRQX5e8HRTCV3nlTVaYVmy1OMaew6G3bvGMhGrQ8U7lQOodx4fDzfsnJWAHTMHYOWes8JEVl3STlsv5Xa2cX9rongkz9aMy6LhKKD+cLkclmbzDgv0kSzbqh6Ogse1vO1Efr3y7GEdFZ2DR0ZwXnHJmRLt2nUi+LRp0/Dll19i69atCAgIEOYFBAUFwdfXF0FBQZgyZQoSExMREhKCwMBAPP/884iLi6NJ4BYyHPbSiQrxNTlJkccb27BrfsfJq/j66TjM2XxcdPvnqRdFW7AYe1xjz8EwTYKpTMT659TPFK6ja+gN7xKBts38haR4uvPb+iJ3tnF/a6J4JI+xYTFzsldbms3bUbKKO0r6BB7X8kNdw4V5YrqyUjxSDjTGuCSr0fTRRx8hMTGR+8TL1atXAwAGDhwouj0pKQmTJ08GACxfvhxubm545JFHRMnkGgPd/JlWwb6iBkRDx8vp/TBMhnZ/h+Z4ekAMIoN9sW7/eUXZe7dmXBZWpOiC8vAuEXh3ZxaqNAzuKiA80AffHLmEYXeHiVbB6brqDZcl/3LqKradyIOvpztmD22PHSevis4PiCdUenu4IVEvb5Ph/eakSbhZViXsleflrsK84R1F5+dB7t/MUZZLO4LGEo+MXVdKGGbrt2RYzJIPVl5ZxR2hHvFtQ0XniG+rfKI+j8SU0c2aSJZtpTHGJVmNpvj4eKSm1q4YcHNzw5kzZ7jkRWGs4bysPj4+WLlyJVauXGnx4zkTY0NPUt2fSrtJDbtiH+oWib4xodiacVlR9l45QwAaBuEY3bwEHVNd9bqlsOXVGiGzuOH5GxoylDukqDtue2ae0NDT1VP37Vb3mvBuMMn9mzlKdmdH0BjiEa+hNR4sHRbbf/Z6vbI5qwItrcfVkgrJshz5Br9jWJaDx7AYj61YeKQcaIxxSdZEcH3nz59H8+bNrVEXosfY0JPUqhGp1SXGJurp9mEC6vZ6yykow6yvj4rOu+yXM5IT/EytjNHPRaKvUi8nE1DX3W3Y7e1+JwgYhoIVKX+J6qObEC7V2IiNDkHahULJ56EO9cPTCTHCqrxdsxKsvppE6Yqghp5rY+Sq8YjHijNeq9YMh8WUSk7PlSzbqh48Xg8eeExq33nyqmTZlnjEJWda5CK70fT222+jvLwcrVu3hkqlwoEDB0T5R0pLS/Hcc89ZpZKNkeHKLUB6pZap1W263ozZm45h2IrfRG9Kw32YtmfmQWvQzkk7X1jv9/SZWhmjHxj0Gd6m6yI37Cpf9ug9mDe8Izzcxc2m8zduS9bHkNTzN0Y/ABhbZceTsy21dSSuHo94rDjjtWrN0vfo2N5RkmVb1YPH6xFu0DNuWJbjSlG5qIfnihk9TUG+HpJlOXitnrOU0hhtb7Jf6Xnz5mHy5MnCKpXhw4fj6NGjaNu2LQCgrKwMH3/8caOZb8SLqTkt+t2ehnOajP2OqW5SUxP1jO3DZIrUBD/DDXv1hxASh7THzbIqNPXzwj2tgnGpqBytgn3xw7ErOHGlGFP6tRG66Y1lQDa1j52SCYeWTFRUh/rh0ydjG8yCbi65WdZJfa4ej0b2aIkbtyrxxaEcPNHHvDlNPM7B4z2qW9WlywiudJWXrh6WDgPxeD14bLbLYzJ561B/ybIcPIYJeXC2yeSyG02G4/1yxv+JtIbmtBhboSX1O4ZblOiGpoxN1DOcRF1wqxL3tAoWVonpa6gLWX/DXqk66nI36c7/783HRRmGDTMgG9ZRhdqueU93lezJk5ZMVFSSBd0c1j6/K3P1eJRTUIalO8+gvFqDpTvPYMjd4YrfG7zOweM9OntYR7MaS/osXbHK4/VwlMnkPHqJeMyL4sHZJpMr79Mj3JjTwpb6HVONFWPf0PQnPy/fdQaLt5+Gr6c71t/pWdG/qBOHtFcUXKR6t/QbZPo9XA31tsVGh+BKUTkmrDuEag3Dk+vTZQVwS76hWvsbkLN9wyK2w+O94SjncBSO8lyqDeZAGJbl4NFLZGxelD0WGzjbZHLFE8GJNCUT2uSM0xueT2oS4fbMPKMTi6Um6p27cVtoyOgSN04beJeoXrq5PKaem/42LFLPS3/yOQB43ekxkhrP1q/7paJyYbhO9/zkvN765zCsq6nXWep58EJzmogpxhZq2OscPN6jpq47JXhkN/e6M0dSbjoVQzy2UeFRDx5pC6JCfCXLtuRMi1wU9TR98sknaNKkNh9ETU0N1q9fj2bNave8KS0t5V87J6N02X9DLWxj5wOML73NKSjDsl1nhHJDQdJUSgNdPQzrZeq5mdrA0lTv1vonY/HE2kOo0TKoVCocu1Qk+9ufYTeursEl9/WW2ozY2Hms/Q3I2b5hORpXj0eGCzXscQ4e71Eem9zySMFQuxtBXTqVjJybip8Pj6G1K0XlitK6GMOjp+nx2NainHyPx7ZWfI7GSHajSa1WY82aNUI5PDwcn3/+eb1jGjNzun+lxukNz7c9M0/UM6SfGVd/YjcADOoUJruuQO1GuLp93XT10h0HmO7FWvbLGf3TCpMaTT2vS0XlqLnTHa2rr9zxbMMArvT1NjUBU+o8ls6jaIi1z++qXD0eGVuoYc7QmqXnACx/j/KY+MwjuzmPc/AYWuPxevCYB6QO9cNnT/WhhSgKyW40XbhwwYrVcFxKsmzrusMrarT1enpSswtEK8PkaBXsC093FarvJFtcvuuMaE6Q/mMYZrXediIPv56+hh0zB+BKUXm9xzasq36DKaegTJjrpLtfqzfRVn9YzTCXlG5ipKnXzfBiH94lAsO7RMh+jQ0DuKnX2xhTkzilApCp56HkfSGF13kaG1ePR7HRIXAHoAHgfqdszjl4TLA1J3bp4zF5mkd2cx7n4DEs1ryJl2RZDh49gLQQxTw0EVyCOZsRGusON6d7WveGrtYweLqr8FS/Nli9N1t0jP5j6C4iw81lv0rLEX7P8LGN1dXYsJ3hajrGIBpWA4DYNiFIHNxecrhLv57Ghu7MoWT4wVhaA6k6Sa0C5LFJJW3CS0z5+nAOdFeX5k5Z6eozRxla45GJu4e6KTzdgGot4OlWW1bqxq1KybIcPIbF9v11o1559jDFp7G4B9BRJsY7G5oILkFpxmZTuY/MmTyo/9jVGoZgP896yS4N8yupQ/3qTeLOKRRPkP489SK+OXKpXgp9/VVshr1HPh5u0M9JqeuS1n+cpf+8RwimDb1uvCb9Kck1pdM3JhRvPdKtXuA3VidTz0Pp+0Kq/jzOQ1wPjyzagOXXGo+Jz7wyk1ff+e5WrYVZ18oXh3Iky3LwyObdOTJQsmwrtBDFPNTTJEFp97ap483pnjY1jLU9Mw/Ldp1BZY3WaJ2MLdPfdiJPuF+3Ea6Ph5uwAaZU/ibdJrj6y/0bGlazVd4Naz+OnBxXljyus+UnIbYztneUaBd7c7Jo8+AoQ2s8rpUn+qiFfSx1ZXNYugfeMwl3YdPhXKHX7JmEu8w8k2VoIYp5VMzVssIZKCkpQVBQEIqLixEYaLpFb2puianxfKVzXdbuOydkop3Sv62sups6l6ndz03VVXd7iJ+XaIhvfKwaf12/Ve88pura0Pn1b5eaq8NznpC15wTRnCbLyb0GGwMlr8Ujqw7gj5wi3KsOxubn+pn1eObEHUNLd5y2KJs3AMz/7gS2ZFzGqB4tsejhrmadwxGeyzdHLmH2pmN153v0HvyzZyvF52kM172jsjQeUaMJyueuKJ2Loj8vAIBZ8wIaOpecx9Cvt66XyfB4/aW9APDemO4Y2aOlrJQDcp6btecJEcdDjaY6cl+LpTtOi3qapt8fo/hDfu2+c6KelfkPdVLc2DAVD5zxHDxiDMUp52dpPJI1p6mkpET2jzNSOndF6VwUHvMCGjqXnMfQdccuffQeDDZISaA73tT8A1PPWelzs/Y8IeL6XD0eAXzmNPGYw8NjPpKjnINHjNGPodRgapxkNZqCg4PRtGlTyR/dMc5IKoO1kttNMZwHIHdegLEsuqbOJfUY+tmudRNDJ/QVJzIL8fNCTkGZyZ3ATWWxlfu4OnKyhZubvZg0Dq4ej4D6c5jMmdNkOGfHnDk8puKBM56DxyRuANh1Mh8rd5/FrpP5Zv0+cW6yJoLv3r3b2vWwK6ll8EpuN8XUUncpppb6mjrXthNXRL+/7cQVyeX/f14pFh2/em821v9+AUmTextd2msqi21ksK8w1Oft4YbIO3lLzMmyzSMDMnF9rh6PAAhDcZbMv+kcGSRZluOva6WSZTl2Z12rV1Y6tMYj5QBg+SRu/SFP3b/mzq8izklWoykhIcHa9bA7UzkvlN5uiq7BI5dU1lhj59pisB/TlozLWPRwV5O5OIx11ZdXa7Dl6OV6S3vVoX6S2bSNZR1WmmWbV/Zi4voaQzwCahtO5k68BvhknjY2TKi0Ttsz8+qVV6CHonMYSzlgToZ0Y7spKGFsyJMaTY2LWXma9u3bhyeeeALx8fG4fLn2wvz888+xf/9+rpVrzKSGvYwO2xl8c9OVTQ2rGeuq9/V0x6juLY12YZuqD68hTMoZQsxF8cg4c6cF6OMxTKjb8NtUWQ4e8YHHOXgMeRLnpjhP0+bNmzFhwgSMHz8ef/zxByora7OqFhcX480338RPP/3EvZKNUWSwL7zcVcJmirphL1PDdrplvIbLek0Nq+m+HX1xKAcPdQ1HdLMmQhAx1oWtNJu20iFMyhlCzEHxyDRTMUSJx3qp8dGebNQwwENVW1aqa8sgfHf0iqisFI/4wOMc+nHTktQHxHkpbjS9/vrr+OijjzBx4kQkJycLt/fr1w+vv/4618o1ZmkXCkWNnYaGyQBg0cNd6+VAkTp+Sv+29S76b45cMtmFbWqIkdcQJm1eS5SieGSaqRii9Bw1dyYZ1jDzhsV4DWnxiA88zmEsbpLGQ/HwXFZWFgYMGFDv9qCgIBQVFfGoE4HprmSlXe5Kj6dhMuJMKB6ZRkNahPCnuKcpPDwcZ8+eRXR0tOj2/fv3o21ban3zog71w5LRXYXM3/q9PUpW4ik9Xh3qh6TJvYXjrZEFmxBeXDkeWXq98RrSMhUP5JrSvy0uFNwWpg5QLw1xZoobTVOnTsWMGTOwbt06qFQqXLlyBQcPHsTs2bMxf/58a9SxUUrNLhAy4KadL0RYoI/k6jkpSo7PKSjDk+vTUV6twfdHr1DGbuLQXDUe8breLB2OMhUPlEjNLsDnqbVDdJ+n5uChrpFm74hAiL0pbjTNnTsXWq0WgwYNQllZGQYMGABvb2/Mnj0bzz//vDXq2CjxWC5sDlOpAqRSCBBiL64ajxzleuNRD3vFMkKsQfGcJpVKhf/+978oLCxEZmYmUlNTcf36dSxatMga9Wu0eCwXNgfPjN3GMoITwpOrxiNe2at51MPSOU32imWEWIPiniYdLy8v3H333TzrQvSYk0WcB14Zu2k4j9iSq8WjK0XlomSvulQhtsZjXpS9Yhkh1qC40XT//fdDpTKdhP7XX3+1qEKkjtK5S7zwyNjtKMMLxLW5ajxypCEtHsv07RXLCOFNcaOpe/fuonJ1dTWOHj2KzMxMTJo0iVe9iIPRddPreo7kZviWe7y90cpA5+Sq8WhU95bYqLeFCQ1pEeIYFDeali9fbvT2V155Bbdu3bK4QsQxuXKGbxpKdF6uGo9MbYRNCLEvs/aeM+aJJ57AunXreJ2OOCB1qB/+2bOV7AaF0uPtxdhQInFuzh6PjA2HE0Lsj1uj6eDBg/Dx8eF1OkJshrKgux5nj0f0niTEMSkenhs9erSozBhDXl4eDh8+7NTJ5Ejj5UxDiUTMVeMRvScJcUyKG01BQeIdqt3c3NChQwe89tprGDp0KLeKEWJLtFmwc3LleETvSUIcj+xG07lz59CmTRskJSVZsz6EENIgikeEEHuQ3Whq164d8vLy0KJFCwDAmDFj8P777yMsLMxqleOBsdpUjCUlJXauCSGNk+7a012LPFA8IoSYw9J4pGIyf9PNzQ35+flCkAoICMCxY8ccfifxS5cuISoqyt7VIKTRy83NRatWrbici+IRIcQS5sYjs7dRcRaRkZHIzc1FQECAZOZgayspKUFUVBRyc3MRGBhot3rYEj1nes5A7Te60tJSREZG2qF2jkVJPGqM7yVro9eUP2d7TS2NR7IbTSqVqt5Fbs9GiFxubm7cvt3yEBgY6BRvLJ7oOTcOUs/ZcMK2pRpTPGqM7yVro9eUP2d6TS2JR7IbTYwxTJ48Gd7e3gCAiooKPPPMM/D39xcd9+2335pdGUIIkYPiESHEHmQ3mgz3cXriiSe4V4YQQuSgeEQIsQfZjSZa2msZb29vLFy4UPhm3BjQc24c7PGcG0M8aozvJWuj15S/xvaayl49RwghhBDSmHHbe44QQgghxJVRo4kQQgghRAZqNBFCCCGEyECNJkIIIYQQGajRxNlvv/2GESNGIDIyEiqVCt99953ofsYYFixYgIiICPj6+mLw4MH466+/7FNZThp6zpMnTxaSEep+HnzwQftUloPFixejd+/eCAgIQIsWLfDwww8jKytLdExFRQWmTZuG0NBQNGnSBI888giuXr1qpxpbTs5zHjhwYL2/8zPPPGOnGjuH6Ojoeq+ZSqXCtGnTALje+8gWGnpN6X2qnEajwfz589GmTRv4+voiJiYGixYtEu3f5oqfbcZQo4mz27dv45577sHKlSuN3v/222/j/fffx0cffYRDhw7B398fw4YNQ0VFhY1ryk9DzxkAHnzwQeTl5Qk/X331lQ1ryNfevXsxbdo0pKamYteuXaiursbQoUNx+/Zt4ZhZs2bhhx9+wKZNm7B3715cuXIFo0ePtmOtLSPnOQPA1KlTRX/nt99+2041dg7p6emi12vXrl0AgEcffRSA672PbKGh1xSg96lSb731FlavXo0PP/wQp06dwltvvYW3334bH3zwgXCMK362GcWI1QBgW7ZsEcparZaFh4ezd955R7itqKiIeXt7s6+++soONeTP8DkzxtikSZPYyJEj7VIfW7h27RoDwPbu3csYq/2benp6sk2bNgnHnDp1igFgBw8etFc1uTJ8zowxlpCQwGbMmGG/SrmAGTNmsJiYGKbVahvF+8gW9F9Txuh9ao6HHnqIPfXUU6LbRo8ezcaPH88YaxyfbTrU02RD58+fR35+PgYPHizcFhQUhD59+uDgwYN2rJn17dmzBy1atECHDh3w7LPPoqCgwN5V4qa4uBgAEBISAgA4cuQIqqurRX/njh07Qq1Wu8zf2fA562zYsAHNmjVDly5dMG/ePJSVldmjek6pqqoKX3zxBZ566imoVKpG8T6yNsPXVIfep8rEx8cjJSUFZ86cAQAcO3YM+/fvx/DhwwE0rs822RnBieXy8/MBAGFhYaLbw8LChPtc0YMPPojRo0ejTZs2yM7Oxn/+8x8MHz4cBw8ehLu7u72rZxGtVouZM2eiX79+6NKlC4Dav7OXlxeCg4NFx7rK39nYcwaAxx9/HK1bt0ZkZCSOHz+OOXPmICsri/Z/k+m7775DUVERJk+eDMD130e2YPiaAvQ+NcfcuXNRUlKCjh07wt3dHRqNBm+88QbGjx8PoHF9tlGjiVjd2LFjhf937doV3bp1Q0xMDPbs2YNBgwbZsWaWmzZtGjIzM7F//357V8VmTD3n//u//xP+37VrV0RERGDQoEHIzs5GTEyMravpdNauXYvhw4cjMjLS3lVxGcZeU3qfKvf1119jw4YN+PLLL9G5c2ccPXoUM2fORGRkZL19IF0dDc/ZUHh4OADUW/1y9epV4b7GoG3btmjWrBnOnj1r76pYZPr06fjxxx+xe/dutGrVSrg9PDwcVVVVKCoqEh3vCn9nU8/ZmD59+gCA0/+dbeHixYv45Zdf8K9//Uu4zZXfR7Zg7DU1ht6nDXvppZcwd+5cjB07Fl27dsWECRMwa9YsLF68GEDj+myjRpMNtWnTBuHh4UhJSRFuKykpwaFDhxAXF2fHmtnWpUuXUFBQgIiICHtXxSyMMUyfPh1btmzBr7/+ijZt2oju79mzJzw9PUV/56ysLOTk5Djt37mh52zM0aNHAcBp/862lJSUhBYtWuChhx4SbnPF95EtGXtNjaH3acPKysrg5iZuLri7u0Or1QJoZJ9t9p6J7mpKS0tZRkYGy8jIYADYsmXLWEZGBrt48SJjjLElS5aw4OBgtnXrVnb8+HE2cuRI1qZNG1ZeXm7nmptP6jmXlpay2bNns4MHD7Lz58+zX375hd17772sXbt2rKKiwt5VN8uzzz7LgoKC2J49e1heXp7wU1ZWJhzzzDPPMLVazX799Vd2+PBhFhcXx+Li4uxYa8s09JzPnj3LXnvtNXb48GF2/vx5tnXrVta2bVs2YMAAO9fc8Wk0GqZWq9mcOXPq3edq7yNbMfWa0vvUPJMmTWItW7ZkP/74Izt//jz79ttvWbNmzdi///1v4RhX/GwzhhpNnO3evZsBqPczadIkxljt0sz58+ezsLAw5u3tzQYNGsSysrLsW2kLST3nsrIyNnToUNa8eXPm6enJWrduzaZOncry8/PtXW2zGXuuAFhSUpJwTHl5OXvuuedY06ZNmZ+fHxs1ahTLy8uzX6Ut1NBzzsnJYQMGDGAhISHM29ub3XXXXeyll15ixcXF9q24E9ixYwcDYDQOuNr7yFZMvab0PjVPSUkJmzFjBlOr1czHx4e1bduW/fe//2WVlZXCMa742WaMijG9lJ6EEEIIIcQomtNECCGEECIDNZoIIYQQQmSgRhMhhBBCiAzUaCKEEEIIkYEaTYQQQgghMlCjiRBCCCFEBmo0EUIIIYTIQI0mQgghhBAZqNFE7Gb9+vUIDg622+NfuHABKpVK2HuKENK4DBw4EDNnzpR9vL1jFrE/D3tXgBBbmDx5MoqKivDdd98Jt0VFRSEvLw/NmjWzX8UIIYQ4DeppIk6turra7N91d3dHeHg4PDzouwMhxDVYEhNJw6jR1Mj9/PPPuO+++xAcHIzQ0FD8/e9/R3Z2tnD/pUuXMG7cOISEhMDf3x+9evXCoUOHhPt/+OEH9O7dGz4+PmjWrBlGjRol3FdZWYnZs2ejZcuW8Pf3R58+fbBnzx7J+mzduhX33nsvfHx80LZtW7z66quoqakR7lepVFi9ejX+8Y9/wN/fH2+88QY0Gg2mTJmCNm3awNfXFx06dMB7770n/M4rr7yCTz/9FFu3boVKpYJKpcKePXuMDs/t3bsXsbGx8Pb2RkREBObOnSt6/IEDB+KFF17Av//9b4SEhCA8PByvvPKKGa88IcSUgQMH4vnnn8fMmTPRtGlThIWFYc2aNbh9+zaefPJJBAQE4K677sL27duF32no2r19+zYmTpyIJk2aICIiAu+++269xzUnZhlz4cIFuLm54fDhw6LbV6xYgdatW0Or1QIAMjMzMXz4cDRp0gRhYWGYMGECbty4IRzfUHzWxbCNGzciISEBPj4+2LBhg+L6EgXsvWMwsa9vvvmGbd68mf31118sIyODjRgxgnXt2pVpNBpWWlrK2rZty/r378/27dvH/vrrL7Zx40b2+++/M8YY+/HHH5m7uztbsGABO3nyJDt69Ch78803hXP/61//YvHx8ey3335jZ8+eZe+88w7z9vZmZ86cYYwxlpSUxIKCgoTjf/vtNxYYGMjWr1/PsrOz2c6dO1l0dDR75ZVXhGMAsBYtWrB169ax7OxsdvHiRVZVVcUWLFjA0tPT2blz59gXX3zB/Pz82MaNGxljjJWWlrLHHnuMPfjggywvL4/l5eWxyspKdv78eQaAZWRkMMYYu3TpEvPz82PPPfccO3XqFNuyZQtr1qwZW7hwofD4CQkJLDAwkL3yyivszJkz7NNPP2UqlYrt3LnTSn8hQhqfhIQEFhAQwBYtWsTOnDnDFi1axNzd3dnw4cPZ//73P3bmzBn27LPPstDQUHb79m1Z1+6zzz7L1Go1++WXX9jx48fZ3//+dxYQEMBmzJghHKM0ZkkZMmQIe+6550S3devWjS1YsIAxxtjNmzdZ8+bN2bx589ipU6fYH3/8wYYMGcLuv/9+4Xip+MwYE2JYdHQ027x5Mzt37hy7cuWKGa84kYsaTUTk+vXrDAA7ceIE+/jjj1lAQAArKCgwemxcXBwbP3680fsuXrzI3N3d2eXLl0W3Dxo0iM2bN48xVj8ADRo0SNToYoyxzz//nEVERAhlAGzmzJkNPo9p06axRx55RChPmjSJjRw5UnSMYaPpP//5D+vQoQPTarXCMStXrmRNmjQRglRCQgK77777ROfp3bs3mzNnToN1IoTIY3id1dTUMH9/fzZhwgThtry8PAaAHTx4sMFrt7S0lHl5ebGvv/5auL+goID5+voKjSZzYpaUjRs3sqZNm7KKigrGGGNHjhxhKpWKnT9/njHG2KJFi9jQoUNFv5Obm8sAsKysLKPn1I/PjNXFsBUrVsiqE7EcTeZo5P766y8sWLAAhw4dwo0bN4Ru45ycHBw9ehQ9evRASEiI0d89evQopk6davS+EydOQKPRoH379qLbKysrERoaavR3jh07hgMHDuCNN94QbtNoNKioqEBZWRn8/PwAAL169ar3uytXrsS6deuQk5OD8vJyVFVVoXv37g0+f32nTp1CXFwcVCqVcFu/fv1w69YtXLp0CWq1GgDQrVs30e9FRETg2rVrih6LECJN/zpzd3dHaGgounbtKtwWFhYGALh27VqD1+7NmzdRVVWFPn36CPeHhISgQ4cOQtmcmCXl4YcfxrRp07BlyxaMHTsW69evx/3334/o6GgAtfFu9+7daNKkSb3fzc7ORvv27SXjc5cuXYTjjcVEYh3UaGrkRowYgdatW2PNmjWIjIyEVqtFly5dUFVVBV9fX8nflbr/1q1bcHd3x5EjR+Du7i66z1iQ0P3Oq6++itGjR9e7z8fHR/i/v7+/6L7k5GTMnj0b7777LuLi4hAQEIB33nlHNPeKJ09PT1FZpVIJwYwQwoex60z/Nl0Dide1Z07MkuLl5YWJEyciKSkJo0ePxpdffimaa3nr1i2MGDECb731Vr3fjYiIACAdn/UZxkRiPdRoasQKCgqQlZWFNWvWoH///gCA/fv3C/d369YNn3zyCQoLC432NnXr1g0pKSl48skn693Xo0cPaDQaXLt2TTh3Q+69915kZWXhrrvuUvQ8Dhw4gPj4eDz33HPCbfqTJYHaAKbRaCTP06lTJ2zevBmMMSEgHzhwAAEBAWjVqpWiOhFCbKehazckJASenp44dOiQ0GN88+ZNnDlzBgkJCQDMi1kN+de//oUuXbpg1apVqKmpEX0hvPfee7F582ZER0cbXcHbUHwm9kGr5xqxpk2bIjQ0FP/73/9w9uxZ/Prrr0hMTBTuHzduHMLDw/Hwww/jwIEDOHfuHDZv3oyDBw8CABYuXIivvvoKCxcuxKlTp3DixAnhW1P79u0xfvx4TJw4Ed9++y3Onz+PtLQ0LF68GNu2bTNanwULFuCzzz7Dq6++ij///BOnTp1CcnIyXn75Zcnn0a5dOxw+fBg7duzAmTNnMH/+fKSnp4uOiY6OxvHjx5GVlYUbN24YXZb73HPPITc3F88//zxOnz6NrVu3YuHChUhMTISbG10qhDiqhq7dJk2aYMqUKXjppZfw66+/IjMzE5MnTxZd1+bErIZ06tQJffv2xZw5czBu3DhR7/y0adNQWFiIcePGIT09HdnZ2dixYweefPJJaDSaBuMzsQ/6JGjE3NzckJycjCNHjqBLly6YNWsW3nnnHeF+Ly8v7Ny5Ey1atMDf/vY3dO3aFUuWLBG6rgcOHIhNmzbh+++/R/fu3fHAAw8gLS1N+P2kpCRMnDgRL774Ijp06ICHH34Y6enpwjc9Q8OGDcOPP/6InTt3onfv3ujbty+WL1+O1q1bSz6Pp59+GqNHj8aYMWPQp08fFBQUiHqdAGDq1Kno0KEDevXqhebNm+PAgQP1ztOyZUv89NNPSEtLwz333INnnnkGU6ZMabDRRgixLznX7jvvvIP+/ftjxIgRGDx4MO677z707NlTdB6lMUuOKVOmoKqqCk899ZTo9sjISBw4cAAajQZDhw5F165dMXPmTAQHB8PNza3B+EzsQ8UYY/auBCGEEOKKFi1ahE2bNuH48eP2rgrhgHqaCCGEEM5u3bqFzMxMfPjhh3j++eftXR3CCfU0EUIIIQp17twZFy9eNHrfxx9/jF27duGrr77Cww8/jC+//LLeijzinKjRRAghhCh08eJFk/u8hYWFISAgwMY1IrZAjSZCCCGEEBloThMhhBBCiAzUaCKEEEIIkYEaTYQQQgghMlCjiRBCCCFEBmo0EUIIIYTIQI0mQgghhBAZqNFECCGEECIDNZoIIYQQQmSgRhMhhBBCiAzUaCKEEEIIkcHDnF+qrq5Gfn4+ysrK0Lx5c4SEhPCuFyGEyELxiBBiK7J7mkpLS7F69WokJCQgMDAQ0dHR6NSpE5o3b47WrVtj6tSpSE9Pt2ZdCSEEAMUjQoh9yNqwd9myZXjjjTcQExODESNGIDY2FpGRkfD19UVhYSEyMzOxb98+fPfdd+jTpw8++OADtGvXzhb1b5BWq8WVK1cQEBAAlUpl7+oQ0ugwxlBaWorIyEi4uVk+I4DiESHEXBbHIybD2LFjWWZmZoPHVVRUsNWrV7O1a9fKOa1N5ObmMgD0Qz/0Y+ef3NxcLtc0xSP6oR/6sfTH3Hgkq6fJmRUXFyM4OBi5ubkIDAy0d3UIaXRKSkoQFRWFoqIiBAUF2bs6dkXxiBD7sjQemTUR3JnousADAwMpSBFiRzQcRfGIEEdhbjyS3WjKy8vDhx9+iDfeeAMAcN9996GsrEy4393dHd999x1atmxpVkUIIUQuikeEEHuQPQtq1apVuHnzplA+duwY+vfvj5EjR2LkyJFwd3fH8uXLrVJJW8gpKMM3Ry4hp6Cs4YMJIXbl6vGIEKKMrT7DZfc0/fjjj3j//fdFt82YMQNt27YFAPTt2xeJiYlYunQp3xraQE5BGYat+A3l1Rr4erpjx8wBUIf62btahBATXDkeEUKUseVnuOyepgsXLqBNmzZCeciQIfD39xfKHTp0wPnz5/nWzkbSLhSivFoDACiv1iDtQqGda0QIkeLK8YgQoowtP8NlN5qqq6tx/fp1ofztt98iLCxMKN+8eZNLDhZ7iI0Oga+nOwDA19MdsdGUUZgQR+bK8YgQoowtP8NlD8916NABv//+O3r06GH0/n379qF9+/bcKmZL6lA/7Jg5AGkXChEbHUJDc4Q4OFeOR4QQZWz5GS77q9jYsWOxYMECHD9+vN59x44dw2uvvYZx48ZxrZwtqUP98M+erajBRIgTcPV4RAhRxlaf4bKTW1ZXV2Pw4MH4/fffMWTIEHTo0AEAkJWVhV27diEuLg4pKSnw9PS0aoWVKikpQVBQEIqLiykvCiF2YI1rkOIRIcQcll6DijKCV1VVYdmyZUhOTsaZM2cAAO3atcO4ceMwa9YseHt7K66Atcl9gXIKymh4jhArsFZDwZXjESFEGbmf4TZtNDkjOS9QTkEZhi7fi4oaLXw83LBzVgI1nAjhhBoKdZS8FvRFjhB5lKQcsDQeKdpGZePGjfj+++9RVVWFQYMG4ZlnnlH8gI5oe2YeKmq0AICKGi22Z+bh6YQYO9eKECLFVeMRUPshMGT5XlTWaOHt4YZd9EWOEJOMpRywe56m1atXY9y4cTh8+DD++usvPPfcc3jppZesUilbu1lWJVkmhDgWV45HQO0Xuco7X+Qq73yRI4QYZ8uUA7IbTR9++CEWLlyIrKwsHD16FJ999hlWrVpltYrZUlM/L8kyIcSxuHI8IoQoo0s5sPTRe6y+o4fsRtO5c+cwadIkofz444+jpqYGeXnO/w3onlbBkmVCiGNx5XgEUEwiRClbpRyQ3WiqrKwUbVPg5uYGLy8vlJeXW6VitnTsUpFkmRDiWFw5HgEUkwhxVIomgs+fPx9+fnWtuKqqKrzxxhsICgoSblu2bBm/2hFCiAkUjwghtia70TRgwABkZWWJbouPj8e5c+eEskql4lczGxreJQLLdp0RVqoM7xJh7yoRQiS4cjwCKCYR4qgoT9MdlBOFEOugPE11KE8TIfZlaTyibcAJIYQQQmSQPTz32muvyTpuwYIFZlfGXpRkEyWE2J8rxyOAYhIhjkp2o+mVV15BZGQkWrRoAVMjeiqVyimDlC2ziRJCLOfK8QigmESIUrYazpY9PDd8+HAUFBRArVbj1VdfxZEjR5CRkSH6+eOPP8yuyJIlS6BSqTBz5kzhtoqKCkybNg2hoaFo0qQJHnnkEVy9etXsxzClVbCvZJkQ4lisHY8A+8YkW2Y4JsTZ6XpmZ286hmErfkNOQZnVHkt2o2nbtm3Izs5Gnz598NJLL6Fly5aYM2dOvRUs5khPT8fHH3+Mbt26iW6fNWsWfvjhB2zatAl79+7FlStXMHr0aIsfz9ClonLJMiHEsVgzHgH2j0m2zHBMiLMz1jNrLYomgkdGRmLevHnIysrCxo0bce3aNfTu3Rv9+vUzO6ncrVu3MH78eKxZswZNmzYVbi8uLsbatWuxbNkyPPDAA+jZsyeSkpLw+++/IzU11azHMoW+1RHifKwRjwDHiEmA7TIcE+LsHHLvOUO9e/fG/fffj06dOiEjIwPV1dVmnWfatGl46KGHMHjwYNHtR44cQXV1tej2jh07Qq1W4+DBgybPV1lZiZKSEtFPQ+hbHSHOjVc8AvjGJHPiESFEGYfce07n4MGDmDp1KsLDw/HBBx9g0qRJuHLliln5DpKTk/HHH39g8eLF9e7Lz8+Hl5cXgoODRbeHhYUhPz/f5DkXL16MoKAg4ScqKkpxvQghzoFnPAL4xySKR4S4Ftmr595++22sX78eN27cwPjx47Fv37564/1K5ObmYsaMGdi1axd8fHzMPo+hefPmITExUSiXlJQ0GKhyCsowZPleIfvurlkJ1NtESAPsmXyRdzwCrBOTzIlHOpTckhB5bPkZLrvRNHfuXKjVajz22GNQqVRYv3690ePk7vV05MgRXLt2Dffee69wm0ajwW+//YYP3GBSXwAALC9JREFUP/wQO3bsQFVVFYqKikTf7K5evYrw8HCT5/X29oa3t7esOuhsz8xDZY0WAFBZo8X2zDw8nRCj6ByENCb2ziPEOx4B1olJ5sQjwP6vLyHOxJaf4Yr2nlOpVPjzzz9NHqNkr6dBgwbhxIkTotuefPJJdOzYEXPmzEFUVBQ8PT2RkpKCRx55BACQlZWFnJwcxMXFyX4cQgh/9s4jxDseAY4Vk+z9+hJCjJPdaNqzZw/XBw4ICECXLl1Et/n7+yM0NFS4fcqUKUhMTERISAgCAwPx/PPPIy4uDn379uVaF9ockxBldKtVdD0htl5xyjseAY4Vk+z9+hLiTGz5GS670WQPy5cvh5ubGx555BFUVlZi2LBhWLVqlVUeS6vViv4lhJimDvXDktFdsSEtB+Nj1Y2mF8RWMamxvr6EmMtWn+EqZmoPAj1LlizBCy+8AD+/hi/cQ4cO4caNG3jooYe4VNBScnY0XrL9FD7ae04oP5PQFnOHd7JVFQlxOqnZBRi7pi43UfLUvugbE2r0WEt3FTfk6vEIUPb6EtLYKfkMtzQeyUo5cPLkSbRu3RrPPfcctm/fjuvXrwv31dTU4Pjx41i1ahXi4+MxZswYBAQEKK6IPWXll0qWCSFiW45elixbk6vHI8C+ry8hzsaWn+GyGk2fffYZfvnlF1RXV+Pxxx9HeHg4vLy8EBAQAG9vb/To0QPr1q3DxIkTcfr0aQwYMMBqFbaGAG9PyTIhRGxU95aSZWty9XgEAPFtQyXLhJA6EUE+kmWeZM9puueee7BmzRp8/PHHOH78OC5evIjy8nI0a9YM3bt3R7NmzaxWSWvLKbwtWSaEiPWNCUXy1L7YcvQyRnVvafOhI1eORwBQrWWSZUJInVsVNZJlnhRPBHdzc0P37t3RvXt3K1THPipqtJJlQkh9fWNC7T7PxhXjEVC7es7bw01YDUSr5wgx7WJhmWSZJ7P3nnMlj/ZsJVkmhNS3NeMyHvv4ILZm0Hwba6i58+Wthr7EESLpqX5tJMs8UaMJwO9nCyTLhBCxrRmXMWPjUaSdL8SMjUep4cTZq9//Cc2d/2vulAkh9keNJgAZuTcly4QQsXUHzkuWiWUO59yULBNC6mxIy5Es80SNJgCP91FLlgkhYp0jAyXLxDK91E0ly4SQOuNj1ZJlnhQ3mpKSklBWZr1JVvbwWC+18EK43SkTQkx7JuEueN65aDzdasv24IrxCAAW/qMz3O/83/1OmRBiXA91U1E86mHFLxmKG01z585FeHg4pkyZgt9//90adbK5r9JyoJtqqb1TJoSYpg71w9JHuyO2TQiWPtrdbtt8uGI80nF3V4n+JYQYtz0zD9V3PsSrtbVla1HcaLp8+TI+/fRT3LhxAwMHDkTHjh3x1ltvIT8/3xr1s4kcg+WJhmVCiFhqdoFoInhqtn0WT7hiPAKAL9MuokpTm5upSsPwZdpFO9eIEAKY0Wjy8PDAqFGjsHXrVuTm5mLq1KnYsGED1Go1/vGPf2Dr1q1Ot+nt0LvDJMuEELGPf8uWLNuKK8YjAPUaofZqlBLiDIZ3iYDHnQ5ZD1Vt2VosmggeFhaG++67D3FxcXBzc8OJEycwadIkxMTEYM+ePZyqaH2HzhdIlgkhYuVVGsmyPbhKPAKAEoOMxoZlQkidjJybqLmTNL+G1ZatxaxG09WrV7F06VJ07twZAwcORElJCX788UecP38ely9fxmOPPYZJkybxrqvVHDpXKFkmhIgZTrS05sTLhrhaPAKAOIO95gzLhJA6q/dmS5Z5UtxoGjFiBKKiorB+/XpMnToVly9fxldffYXBgwcDAPz9/fHiiy8iNzeXe2WtJdDHQ7JMCBHrGB4gWbYVV4xHABDbJkSyTAip4+vhJlnmSXHroEWLFti7dy/i4uJMHtO8eXOcP+88ye5C/L0ly4QQsd/PFdQrj+zR0ub1cMV4BAA7T16tV7bH60uIM4gK8UfGpWJR2VoUN5rWrl3b4DEqlQqtW7c2q0L28Ne1UskyIURsVPeW2JieKyrbgyvGIwBQh/hJlgkhdXIKb0uWeVLch/XCCy/g/fffr3f7hx9+iJkzZ/Kok81Va5lkmRAi1jcmFO+Nqc3T9N6Y7ugbY585N64YjwBgXKwaXu614dnL3Q3jrJjhmBBnV3i7SrLMk+JG0+bNm9GvX796t8fHx+Obb77hUilbC/b1lCwTQsRyCsrw783HkXa+EP/efBw5BfbJbeaK8UiHMa3oX0KIcf7eHpJlnhQ3mgoKChAUFFTv9sDAQNy4cYNLpWyt4HalZJkQIrY9Mw+VNbUf5pU1Wqtm4JXiivEIqE1uqZ/hmJJbEmJacXmVZJknxY2mu+66Cz///HO927dv3462bdtyqZStFdyqkiwTQhyTK8YjAMjKL5UsE0Lq3DD4zDYs86S4DysxMRHTp0/H9evX8cADDwAAUlJS8O6772LFihW862cTAd4eKNJLHhdgxa49QlzB8C4RWLojC9VaBk83lVUz8EpxxXgEAB3CA7A767qoTAgxLiLQBxdvlovK1qK4dfDUU0+hsrISb7zxBhYtWgQAiI6OxurVqzFx4kTuFbSFliG+KLpSKioTQkzLyLkpLJio1jJk5Ny0y6a9rhiPAMDDTSVZJoTUadnUV9RoatnUep/hZmWAevbZZ3Hp0iVcvXoVJSUlOHfunFMHqEuF5ZJlQojYhrQcybItuVo8AoCtR69IlgkhdXJulkuWebIobWbz5s3RpEkTXnWxm86RgZJlQojYMINNrQ3L9uAq8QgAogy+KRuWCSF1noyPlizzpLjRdPXqVUyYMAGRkZHw8PCAu7u76McZ+Xp6SJYJIWLZ129Jlm3FFeMRAFw2+KZsWCaE1Blydzg87oxge6hqy9aiuHUwefJk5OTkYP78+YiIiIBK5fxj7ceuFEmWCSFif+QUSZZtxRXjEQDklVRIlgkhdbZn5qHmTk7qGlZbfjohxiqPpbjRtH//fuzbtw/du3e3QnXsI9jHEzdKq0RlQohpPdVNcVpvGXxPdVO71MMV4xEARAT54KLe3MqIIOutBiLE2RWVVUuWeVI8PBcVFQXGXGubkSiDfZ0My4QQsacTYuB+p1PHXQWrfatriCvGIwAY3jVCskwIqRPs5ylZ5klxo2nFihWYO3cuLly4YIXq2Act7yVEmYycm9DcaatoWG3ZHlwxHgHACb0d242VCSF17mkVLFnmSfHw3JgxY1BWVoaYmBj4+fnB01PcoissLORWOVs5eK5AskwIETOWcmBkj5Y2r4crxiMAOHS+QLJMCKlzqahcssyT4kaTM2fZNWVUj5b4PDVHVCaEmDbs7jCknS8Ule3BFeMRAPRpE4oD2QWiMiHEuNjoEHi5q1ClYfByVyE2OsRqj6W40TRp0iRr1MOugnw9JcuEELFtx/Lqlaf0t/1eb64YjwDg8s0yyTIhpM6VonJU3ZkvUKVhuFJUbrUdCsxKbpmdnY2XX34Z48aNw7Vr1wDUbpD5559/cq2crSSn50qWCSFimXnFkmVbcrV4BAAXDHYlMCwTQupsOXpZssyT4kbT3r170bVrVxw6dAjffvstbt2qTWp37NgxLFy4kHsFbWF4l3DJMiFELKF9c8myrbhiPAKALpEBkmVCSJ34tqGSZZ4UN5rmzp2L119/Hbt27YKXl5dw+wMPPIDU1FSulbOVPy8XS5YJIWJaLZMs24orxiMAYFrpMiGkTsqpa5JlnhQ3mk6cOIFRo0bVu71Fixa4ceMGl0rZWuaVEskyIUTssEEGcMOyrbhiPAKA01dLJcuEkDp/5N6ULPOkuNEUHByMvLy8erdnZGSgZUvnXHX2N4PEcYZlQohYC38vybKtuGI8AoBmTbwky4SQOg69Ye/YsWMxZ84c5OfnQ6VSQavV4sCBA5g9ezYmTpxojTpa3YqxPRDsW7uQMNjXAyvG9rBzjQhxbBUarWTZVlwxHgGAl4e7ZJkQUmdK/7aY0FeNJt7umNBXbdWVvIobTW+++SY6duyIqKgo3Lp1C3fffTcGDBiA+Ph4vPzyy9aoo9U9suoAisprAABF5TV4ZNUBO9eIEMemNthqyLBsK64YjwCgtKJaskwIqZOaXYDPU3Nwq1KDz1NzkJptvWSwivM0eXl5Yc2aNZg/fz4yMzNx69Yt9OjRA+3atbNG/WzCUXZsJ8RZOMo8QFeMRwCEL3GmyoSQOsZSDvSNsc4KOsWNJh21Wg21Ws2zLnbTroU/zly7LSoTQkxrGeSD4vJqUdmeXCkeAYCvpxvKq7WiMiHEuPi2odiol1/RmikHZDWaEhMTsWjRIvj7+yMxMVHy2GXLlnGpmC0Zrpa20+ppQpxG+/AAnMwvFZVtxdXjEQAE+nigvLpKVCaEGJdfUiFZ5knWlZiRkYHq6mrh/6aoVCo+tbKxS0VlkmVCiNj+szcky9bk6vEIAK6WVkmWCSH2IavRtHv3bqP/dxWP9owSbdj7aM8oO9aGEMfXIyoYu/QSyPWICrbZY7t6PAKA6FBfXCgoF5UJIcYN7xKBJdtPgwFQ3Slbi+KB8uLiYhQWFta7vbCwECUlzpkU8qTBJFbDMiFELPdmuWTZVlwxHgFAWZVGskwIqbNmXzZ0s2rYnbK1mJWnKTk5ud7tX3/9NcaOHculUrZ2xGC1nGGZECJmGDjsNU3ZFeMRANy8XSVZJoTU2XTkkmSZJ8Wx7tChQ7j//vvr3T5w4EAcOnSIS6VsLdTfU7JMCBEL9PWULNuKK8YjAIgM9pUsE0LqtDK4PgzLPCluNFVWVqKmpn7OkOrqapSX26eL3lIrH+8pWSaEiMU0byJZthVXjEcAcN9dzSXLhJA6rz/cVbLMk+JGU2xsLP73v//Vu/2jjz5Cz57O2dj480qxZJkQInb+xi3Jsq24YjwCgLQLBZJlQkidyGBfeLnXrpb1cldZtWdWcfKP119/HYMHD8axY8cwaNAgAEBKSgrS09Oxc+dO7hW0hS8O5dQrW3PvGkKc3Z8GiyUMy7biivEIAM5dvy1ZJoTUSbtQiCpN7VTwKg1D2oVCqEOts7WT4p6mfv364eDBg4iKisLXX3+NH374AXfddReOHz+O/v37W6OOVvdEH7VkmRAiFtPcX7JsK64YjwAgKsRXskwIqRMbHSLqaYqNDrHaY5mVZrZ79+7YsGED77oQQpxEgcFqLsOyLbliPCo3SDFgWCaE1LlSVC7qabpSVG61niZZjaaSkhIEBgYK/5eiO86ZJP1+oV6ZhucIMe1qaaVk2ZpcPR4BwHWDDOCGZUJIHYfbsLdp06bIy8tDixYtEBwcbHR7AsYYVCoVNBrn+0akDvHFJb3kfGrqCidE0oOdw/Hd0Suisq24ejwCamPQhUKKSYTI4XAb9v76668ICakdI+S5bcHixYvx7bff4vTp0/D19UV8fDzeeustdOjQQTimoqICL774IpKTk1FZWYlhw4Zh1apVCAsL41YPrVa6TAgRu1ZaIVm2JlePRwBQbbBruGGZEFLH4Tbsfe+999CjRw8EBgbi4sWLGDNmDLy9vS1+8L1792LatGno3bs3ampq8J///AdDhw7FyZMn4e9fO7F01qxZ2LZtGzZt2oSgoCBMnz4do0ePxoEDByx+fB1fL3fJMiFE7I+cm5Jla3L1eAQAV4srJMuEEPtQMcYa/Arj5eWFixcvIiIiAu7u7kLXOG/Xr19HixYtsHfvXgwYMADFxcVo3rw5vvzyS/zzn/8EAJw+fRqdOnXCwYMH0bdv3wbPWVJSgqCgIBQXF5uc35CaXYCxa1KFcvLUvlYbDyXEFfRbnILLeh/kLYN8cGDeIKPHyrkGlXD1eAQAfd7Yhat685jCArxw6L9DLH9ShLignIIyDF2+FxU1Wvh4uGHnrASTE8EtjUeyepo6duyIefPm4f777wdjDF9//bXJB5s4caLiSugUF9cmldR1vR85cgTV1dUYPHiwqC5qtVp2kJIjMtgX7m4qaLQM7m7WTYxFiCsoLKuSLFuTq8cjACgqr5YsE0LqqEP98NYj3bAhLQfjY9VWWzkHyGw0rV69Gi+++CK2bdsGlUqFl19+2ejkS5VKZXaQ0mq1mDlzJvr164cuXboAAPLz8+Hl5YXg4GDRsWFhYcjPzzd6nsrKSlRW1q3kkbPT+dKdp6G5M2dAo2VYuvM03h93r1nPg5DGoEajlSxbk6vHIwCoqmGSZUJIndTsAszYeBQAkHa+EGGBPvZdPdevXz+kptYOX7m5ueHMmTPcu8OnTZuGzMxM7N+/36LzLF68GK+++qqi3/kjp0iyTAgRM5yXbMt5yq4ejwDA8OWkJhMhptky5YCsjOCjR48WviElJSUhICCAayWmT5+OH3/8Ebt370arVq2E28PDw1FVVYWioiLR8VevXkV4uPElzvPmzUNxcbHwk5uba/Q4fU/GR0uWCSFi9swI7urxCABaBntLlgkhdUZ1bylZ5klWo+nHH3/E7du1ex899dRTKC0t5fLgjDFMnz4dW7Zswa+//oo2bdqI7u/Zsyc8PT2RkpIi3JaVlYWcnBzExcUZPae3tzcCAwNFP4QQvs7fuC1ZtqbGEI/yiyoly4QQ+7DrRPBp06bhyy+/xNatWxEQECDMCwgKCoKvry+CgoIwZcoUJCYmIiQkBIGBgXj++ecRFxfHddIlbdhLiDLVWumyNbl6PAIAw5SczpmikxDbsOXwnKyUA7///jsSExORnZ2NwsJCBAQEmJx4WVhYKP/BjZwDqO1ynzx5MoC6ZHJfffWVKJmcqe5wQ3KWF67ddw6Ltp0SyvMf6kSNJkIkKFkSzzvlgKvHIwDo/uoOFJXXCOVgXw8cXThM9nMhpDFRkjbIJikH4uPjrTLxUkZ7DT4+Pli5ciVWrlxp8eOZ0jkySLJMCBG7ZrAXmmHZmlw9HgFAsV6DyViZEFInMtgXXu4qVGkYvNytmzZI1pwmfefPn0fz5s2tURe7Mda1RwgxzVFWd7liPAIc5/UlxBmkXShElab2KqnSMKRdkN/DrJTsRtPbb7+N8vJytG7dGiqVCgcOHBDlHyktLcVzzz1nlUpamy1n3hNCLOfK8YgQokxsdAh8PWu3P/P1dEdsdIjVHkt2o2nevHmiVSrDhw/H5ct1PTJlZWX4+OOP+dbORvrGhOK9Md0R2yYE743pTluoENIAL3eVZNnaXDkeAfZ/fQlxJupQP+yYOQBLH70HO2YOsH9GcKD+eL+c8X9nkVNQhjmbj6OiRovjuUXooW5q1RedEGfXPMALl/WWwTcP8LLp47tyPAKApn6eoon2Tf087VgbQhyfOtTPJp/biuc0uaLtmXmoqKldM11Ro8X2zDw714gQx2bPieCNwfVbVZJlQoh9UKMJwE2DzUYNy4QQscggH8kysYy/l7tkmRBiH7KH5wDgk08+QZMmTQAANTU1WL9+PZo1awYA3LLy2kNTPy/JMiFErKJaI1m2BVeNR4DrDz8S4qxkN5rUajXWrFkjlMPDw/H555/XO8YZDe8SgeW7zqCiRgsfDzcM7xJh7yoR4tCuGgzHGZatzZXjEQDcqtJKlgkh9iG70XThwgUrVsO+1KF+2DkrAWkXChEbHUKTwAlpQIC3O0orNaKyLblyPALs//oSQoxTNDznymw1854QV6D/gW6sTCxDry8hjokmghNCCCGEyECNJkKIYsG+HpJlYhl6fQlxTNRoIoQo9vLfO0uWiWXo9SXEMVGjiRCi2PzvjkuWiWXo9SXEMcnq8y0pKZF9wsDAQLMrQwhxDuXVTLJsTY0hHtnz9SWEmCar0RQcHAyVSnrDSMYYVCoVNBpa5UGIq/P3csNtvdxB/l6267RuDPHInq8vIcQ0WY2m3bt3W7sehBAnojXIUG1YtqbGEI/s+foSQkyT1WhKSEiwdj0IIU7EnsNHjSEe0fAcIY7JrD7fffv24YknnkB8fDwuX74MAPj888+xf/9+rpUjhDgmX0+VZNmWXDEeOdLrSwipo7jRtHnzZgwbNgy+vr74448/UFlZCQAoLi7Gm2++yb2ChBDH88+eUZJlW3HVeOQory8hRExxo+n111/HRx99hDVr1sDT01O4vV+/fvjjjz+4Vo4Q4pi2ZFyWLNuKq8YjR3l9CSFiihtNWVlZGDBgQL3bg4KCUFRUxKNOhBAHN6pHS8myrbhqPHKU15cQIqa40RQeHo6zZ8/Wu33//v1o27Ytl0oRQhzbooe7oqc6GCoAPdXBWPRwV7vUw1XjkaO8voQQMcWNpqlTp2LGjBk4dOgQVCoVrly5gg0bNmD27Nl49tlnrVFHQoiDWbvvHI7kFIEBOJJThLX7ztmlHq4ajxzl9SWEiCneBXLu3LnQarUYNGgQysrKMGDAAHh7e2P27Nl4/vnnrVFHQoiD+eJQTr3ylP6279lx1XjkKK8vIURMcU+TSqXCf//7XxQWFiIzMxOpqam4fv06Fi1aZI36EUIc0BN91JJlW3HVeOQory8hRExxT5OOl5cX7r77bp51IYQ4ic6RQZJlW3O1eORory8hpJbiRtP9998vue/Tr7/+alGFCCGOb8vRy/XKfWNCbV4PV41HjvL6EkLEFDeaunfvLipXV1fj6NGjyMzMxKRJk3jVixDiwEZ1b4mN6bmisj24ajxylNeXECKmuNG0fPlyo7e/8soruHXrlsUVIoQ4vshgX3h7uKGyRgtvDzdEBvvapR6uGo8c5fUlhIiZtfecMU888QTWrVvH63SEEAeWdqEQlTVaAEBljRZpFwrtXCMxZ49Hjv76EtJYcWs0HTx4ED4+PrxORwhxYLHRIfD1dAcA+Hq6IzY6xM41EnP2eOTory8hjZXi4bnRo0eLyowx5OXl4fDhw5g/fz63ihFCHJc61A87Zg5A2oVCxEaHQB3qZ5d6uGo8cpTXlxAiprjRFBQkXvrq5uaGDh064LXXXsPQoUO5VYwQ4tjUoX52/zB35XjkCK8vIURMdqPp3LlzaNOmDZKSkqxZH0IIaRDFI0KIPcie09SuXTtcv35dKI8ZMwZXr161SqUIIUQKxSNCiD3I7mlijInKP/30ExYvXsy9Qrzp6l1SUmLnmhDSOOmuPcMYYgmKR4QQc1gaj8zeRsVZlJaWAgCioqLsXBNCGrfS0tJ6c5AaG4pHhDgGc+OR7EaTSqWqt12B1PYFjiIyMhK5ubkICAiQrG9JSQmioqKQm5uLwMBAG9aQP3oujsmVngsg//kwxlBaWorIyEhuj+3q8QhwrfcLPRfH1Bifi6XxSNHw3OTJk+Ht7Q0AqKiowDPPPAN/f3/Rcd9++61ZFbEWNzc3tGrVSvbxgYGBTv/m0aHn4phc6bkA8p4P7x6mxhKPANd6v9BzcUyN7blYEo9kN5oM93F64oknzH5QQgixBMUjQog9yG400dJeQoijoHhECLEHbtuoODtvb28sXLhQ6O53ZvRcHJMrPRfA9Z6Po3Gl15eei2Oi56KcivFcB0wIIYQQ4qKop4kQQgghRAZqNBFCCCGEyECNJkIIIYQQGVy60bRy5UpER0fDx8cHffr0QVpamuTxmzZtQseOHeHj44OuXbvip59+Et3PGMOCBQsQEREBX19fDB48GH/99Zc1n4JAyXNZs2YN+vfvj6ZNm6Jp06YYPHhwveMnT54sJAjU/Tz44IPWfhoAlD2X9evX16unj4+P6Bhn+bsMHDiw3nNRqVR46KGHhGPs9Xf57bffMGLECERGRkKlUuG7775r8Hf27NmDe++9F97e3rjrrruwfv36escovQZdGcUjikfWRvHIBvGIuajk5GTm5eXF1q1bx/788082depUFhwczK5evWr0+AMHDjB3d3f29ttvs5MnT7KXX36ZeXp6shMnTgjHLFmyhAUFBbHvvvuOHTt2jP3jH/9gbdq0YeXl5Q71XB5//HG2cuVKlpGRwU6dOsUmT57MgoKC2KVLl4RjJk2axB588EGWl5cn/BQWFlr1eZjzXJKSklhgYKConvn5+aJjnOXvUlBQIHoemZmZzN3dnSUlJQnH2Ovv8tNPP7H//ve/7Ntvv2UA2JYtWySPP3fuHPPz82OJiYns5MmT7IMPPmDu7u7s559/Fo5R+vq4MopHFI8c7e9C8ci8eOSyjabY2Fg2bdo0oazRaFhkZCRbvHix0eMfe+wx9tBDD4lu69OnD3v66acZY4xptVoWHh7O3nnnHeH+oqIi5u3tzb766isrPIM6Sp+LoZqaGhYQEMA+/fRT4bZJkyaxkSNH8q5qg5Q+l6SkJBYUFGTyfM78d1m+fDkLCAhgt27dEm6z199Fn5wg9e9//5t17txZdNuYMWPYsGHDhLKlr48roXhUh+KRdVA8sk08csnhuaqqKhw5cgSDBw8WbnNzc8PgwYNx8OBBo79z8OBB0fEAMGzYMOH48+fPIz8/X3RMUFAQ+vTpY/KcPJjzXAyVlZWhuroaISEhotv37NmDFi1aoEOHDnj22WdRUFDAte6GzH0ut27dQuvWrREVFYWRI0fizz//FO5z5r/L2rVrMXbs2Hpbf9j672KOhq4XHq+Pq6B4JEbxiD+KR7aLRy7ZaLpx4wY0Gg3CwsJEt4eFhSE/P9/o7+Tn50ser/tXyTl5MOe5GJozZw4iIyNFb5gHH3wQn332GVJSUvDWW29h7969GD58ODQaDdf66zPnuXTo0AHr1q3D1q1b8cUXX0Cr1SI+Ph6XLl0C4Lx/l7S0NGRmZuJf//qX6HZ7/F3MYep6KSkpQXl5OZf3raugeCRG8Yg/ike2i0eyt1EhzmnJkiVITk7Gnj17RBMWx44dK/y/a9eu6NatG2JiYrBnzx4MGjTIHlU1Ki4uDnFxcUI5Pj4enTp1wscff4xFixbZsWaWWbt2Lbp27YrY2FjR7c7ydyHEHBSPHBPFI/lcsqepWbNmcHd3x9WrV0W3X716FeHh4UZ/Jzw8XPJ43b9KzsmDOc9FZ+nSpViyZAl27tyJbt26SR7btm1bNGvWDGfPnrW4zqZY8lx0PD090aNHD6Gezvh3uX37NpKTkzFlypQGH8cWfxdzmLpeAgMD4evry+Vv7SooHtWieOSYfxeKR8r+Li7ZaPLy8kLPnj2RkpIi3KbVapGSkiL6lqAvLi5OdDwA7Nq1Szi+TZs2CA8PFx1TUlKCQ4cOmTwnD+Y8FwB4++23sWjRIvz888/o1atXg49z6dIlFBQUICIigku9jTH3uejTaDQ4ceKEUE9n+7sAtUvJKysr8cQTTzT4OLb4u5ijoeuFx9/aVVA8onjkqH8XgOKR4r+LomnjTiQ5OZl5e3uz9evXs5MnT7L/+7//Y8HBwcLy0AkTJrC5c+cKxx84cIB5eHiwpUuXslOnTrGFCxcaXeIbHBzMtm7dyo4fP85Gjhxps6WkSp7LkiVLmJeXF/vmm29ES0VLS0sZY4yVlpay2bNns4MHD7Lz58+zX375hd17772sXbt2rKKiwqGey6uvvsp27NjBsrOz2ZEjR9jYsWOZj48P+/PPP0XP1xn+Ljr33XcfGzNmTL3b7fl3KS0tZRkZGSwjI4MBYMuWLWMZGRns4sWLjDHG5s6dyyZMmCAcr1vi+9JLL7FTp06xlStXGl3iK/X6NCYUjygeOdrfRYfikbJ45LKNJsYY++CDD5harWZeXl4sNjaWpaamCvclJCSwSZMmiY7/+uuvWfv27ZmXlxfr3Lkz27Ztm+h+rVbL5s+fz8LCwpi3tzcbNGgQy8rKssVTUfRcWrduzQDU+1m4cCFjjLGysjI2dOhQ1rx5c+bp6clat27Npk6darMPMyXPZebMmcKxYWFh7G9/+xv7448/ROdzlr8LY4ydPn2aAWA7d+6sdy57/l12795t9D2jq/+kSZNYQkJCvd/p3r078/LyYm3bthXld9GRen0aG4pHFI8c6bkwRvHInHikYowxZX1ThBBCCCGNj0vOaSKEEEII4Y0aTYQQQgghMlCjiRBCCCFEBmo0EUIIIYTIQI0mQgghhBAZqNFECCGEECIDNZoIIYQQQmSgRhMhhBBCiAzUaCJOaf369QgODrZ3NQghdjR58mQ8/PDD9q4GaUQoIzhxSuXl5SgtLUWLFi3sXRVCiJ0UFxeDMUZfoIjNUKOJOJ3q6mp4enrauxqEEEIaGRqeI7L9/PPPuO+++xAcHIzQ0FD8/e9/R3Z2NgDgwoULUKlU+Prrr9G/f3/4+vqid+/eOHPmDNLT09GrVy80adIEw4cPx/Xr10Xn/eSTT9CpUyf4+PigY8eOWLVqlXCf7rwbN25EQkICfHx8sGHDBqPDcz/88AN69+4NHx8fNGvWDKNGjRLu+/zzz9GrVy8EBAQgPDwcjz/+OK5duybcv2fPHqhUKqSkpKBXr17w8/NDfHw8srKyrPBKEkJ40B+ek4pPQF0sSU5ORnx8PHx8fNClSxfs3btXOEaj0WDKlClo06YNfH190aFDB7z33ntGH3Pp0qWIiIhAaGgopk2bhurqauGYyspKzJ49Gy1btoS/vz/69OmDPXv2CPdfvHgRI0aMQNOmTeHv74/OnTvjp59+Eu7PzMzE8OHD0aRJE4SFhWHChAm4ceMG51ePmIMaTUS227dvIzExEYcPH0ZKSgrc3NwwatQoaLVa4ZiFCxfi5Zdfxh9//AEPDw88/vjj+Pe//4333nsP+/btw9mzZ7FgwQLh+A0bNmDBggV44403cOrUKbz55puYP38+Pv30U9Fjz507FzNmzMCpU6cwbNiwenXbtm0bRo0ahb/97W/IyMhASkoKYmNjhfurq6uxaNEiHDt2DN999x0uXLiAyZMn1zvPf//7X7z77rs4fPgwPDw88NRTT3F45Qgh1iYnPgHASy+9hBdffBEZGRmIi4vDiBEjUFBQAADQarVo1aoVNm3ahJMnT2LBggX4z3/+g6+//lp0jt27dyM7Oxu7d+/Gp59+ivXr12P9+vXC/dOnT8fBgweRnJyM48eP49FHH8WDDz6Iv/76CwAwbdo0VFZW4rfffsOJEyfw1ltvoUmTJgCAoqIiPPDAA+jRowcOHz6Mn3/+GVevXsVjjz1mxVePyMYIMdP169cZAHbixAl2/vx5BoB98sknwv1fffUVA8BSUlKE2xYvXsw6dOgglGNiYtiXX34pOu+iRYtYXFwcY4wJ512xYoXomKSkJBYUFCSU4+Li2Pjx42XXPT09nQFgpaWljDHGdu/ezQCwX375RThm27ZtDAArLy+XfV5CiO1MmjSJjRw50uh9+vGJsbpYsmTJEuGY6upq1qpVK/bWW2+ZfIxp06axRx55RPSYrVu3ZjU1NcJtjz76KBszZgxjjLGLFy8yd3d3dvnyZdF5Bg0axObNm8cYY6xr167slVdeMfp4ixYtYkOHDhXdlpubywCwrKwsk/UktkE9TUS2v/76C+PGjUPbtm0RGBiI6OhoAEBOTo5wTLdu3YT/h4WFAQC6du0quk03LHb79m1kZ2djypQpaNKkifDz+uuvi7rVAaBXr16SdTt69CgGDRpk8v4jR45gxIgRUKvVCAgIQEJCQr26G9Y/IiICAETDeIQQxyQnPgFAXFyc8H8PDw/06tULp06dEm5buXIlevbsiebNm6NJkyb43//+V+8cnTt3hru7u1COiIgQ4sSJEyeg0WjQvn17UVzbu3evENdeeOEFvP766+jXrx8WLlyI48ePC+c6duwYdu/eLfrdjh07AkC9uEhsz8PeFSDOY8SIEWjdujXWrFmDyMhIaLVadOnSBVVVVcIx+hO0VSqV0dt03eW3bt0CAKxZswZ9+vQRPZZ+QAIAf39/ybr5+vqavO/27dsYNmwYhg0bhg0bNqB58+bIycnBsGHDRHU3VX/D7n1CiOORE58akpycjNmzZ+Pdd99FXFwcAgIC8M477+DQoUOi4wwXohjGNXd3dxw5cqReHNMNwf3rX//CsGHDsG3bNuzcuROLFy/Gu+++i+effx63bt3CiBEj8NZbb9Wrn+6LHLEfajQRWQoKCpCVlYU1a9agf//+AID9+/dbdM6wsDBERkbi3LlzGD9+vEXn6tatG1JSUvDkk0/Wu+/06dMoKCjAkiVLEBUVBQA4fPiwRY9HCHEcSuJTamoqBgwYAACoqanBkSNHMH36dADAgQMHEB8fj+eee044XmnvTo8ePaDRaHDt2jWhLsZERUXhmWeewTPPPIN58+ZhzZo1eP7553Hvvfdi8+bNiI6OhocHfUQ7GvqLEFmaNm2K0NBQ/O9//0NERARycnIwd+5ci8/76quv4oUXXkBQUBAefPBBVFZW4vDhw7h58yYSExNln2fhwoUYNGgQYmJiMHbsWNTU1OCnn37CnDlzoFar4eXlhQ8++ADPPPMMMjMzsWjRIovrTghxDEri08qVK9GuXTt06tQJy5cvx82bN4UFH+3atcNnn32GHTt2oE2bNvj888+Rnp6ONm3ayK5L+/btMX78eEycOBHvvvsuevTogevXryMlJQXdunXDQw89hJkzZ2L48OFo3749bt68id27d6NTp04AaieJr1mzBuPGjcO///1vhISE4OzZs0hOTsYnn3xSr/eK2BbNaSKyuLm5ITk5GUeOHEGXLl0wa9YsvPPOOxaf91//+hc++eQTJCUloWvXrkhISMD69esVBSkAGDhwIDZt2oTvv/8e3bt3xwMPPIC0tDQAQPPmzbF+/Xps2rQJd999N5YsWYKlS5daXHdCiGNQEp+WLFmCJUuW4J577sH+/fvx/fffo1mzZgCAp59+GqNHj8aYMWPQp08fFBQUiHqd5EpKSsLEiRPx4osvokOHDnj44YeRnp4OtVoNoDa1wbRp09CpUyc8+OCDaN++vZBqJTIyEgcOHIBGo8HQoUPRtWtXzJw5E8HBwXBzo49se6PkloQQQpzSuHHj4O7uji+++KLBYy9cuIA2bdogIyMD3bt3t37liEuiZishhBCnUlNTg5MnT+LgwYPo3LmzvatDGhFqNBFCCHEqmZmZ6NWrFzp37oxnnnnG3tUhjQgNzxFCCCGEyEA9TYQQQgghMlCjiRBCCCFEBmo0EUIIIYTIQI0mQgghhBAZqNFECCGEECIDNZoIIYQQQmSgRhMhhBBCiAzUaCKEEEIIkYEaTYQQQgghMvw/VswAsMjdmBMAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Preprocess the data\n",
    "dataset = dataset.dropna()\n",
    "y = dataset.mpg.values\n",
    "x = dataset[PREDICTOR_LABELS[:-2]].to_numpy()\n",
    "\n",
    "is_american = (dataset.origin == 'usa').values #dummy variable\n",
    "is_japanese = (dataset.origin == 'japan').values #dummy variable\n",
    "\n",
    "x = np.vstack((x.T, is_american, is_japanese)).T\n",
    "print(f'The shape of x is {x.shape}')\n",
    "print(f'The shape of y is {y.shape}')\n",
    "\n",
    "# Plot each of the regressors vs MPG\n",
    "fig,axs = plt.subplots(4,2,figsize=(6,8),dpi=100)\n",
    "for i,ax in enumerate(np.ravel(axs)):\n",
    "    ax.scatter(x[:,i],y, s=3)\n",
    "    ax.set_xlabel(PREDICTOR_LABELS[i])\n",
    "    ax.set_ylabel('Fuel Efficiency (MPG)')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ordinary least squares (OLS), ridge, and lasso regression\n",
    "We will use linear regression to model the relationship between each of these variables and gas mileage. \n",
    "\n",
    "**EXERCISE QUESTION**: Given the plots above, what do you expect the $\\beta$ weights for each of these predictors will be?\n",
    "\n",
    "**We will discuss 3 ways of modeling the relationship between the availible car info and gas mileage** \n",
    "1. OLS - used to solve a linear system of equations\n",
    "2. Ridge - adds a squared penalty term to keep $\\beta$'s small\n",
    "3. Lasso - adds a non-squared penalty term to keep $\\beta$'s small. This leads to *sparse* solutions when compared to OLS and ridge (this means that uninformative $\\beta$ values get set to 0).\n",
    "\n",
    "The goal of regression is to minimize the sum of squared errors (SSE) between the real data $y$ and the model predictions $\\hat{y}$. **The major difference between these regression types how SSE is computed.**\n",
    "\n",
    "Below are shown the different SSE formulations for OLS, ridge, and lasso regression.  \n",
    "$$\n",
    "SSE_{OLS} = \\sum_{i=1}^{n}{(y_i - \\hat{y}_i)^2}\n",
    "$$\n",
    "$$\n",
    "SSE_{Ridge} = \\sum_{i=1}^{n}{(y_i - \\hat{y}_i)^2} + \\alpha\\sum_{j=1}^{P}{\\beta_j^2}\n",
    "$$\n",
    "$$\n",
    "SSE_{Lasso} = \\sum_{i=1}^{n}{(y_i - \\hat{y}_i)^2} + \\lambda\\sum_{j=1}^{P}{|\\beta_j|}\n",
    "$$\n",
    "You can see that the ridge and lasso equations include an additional term that penalizes large $\\beta$ values. The only difference between ridge and lasso is that ridge is squared and lasso takes the absolute value of the weights instead. In practice, this means that lasso will have sparse solutions (less informative predictors will have $\\beta$ weights set to 0) while ridge regression will spread out variance across predictors, even if they are correlated. \n",
    "\n",
    "By minimizing the above functions, we can compute the OLS and Ridge estimators! Lasso is not included below because there is no closed-form solution.\n",
    "We will not go over the complete derivation of the closed form solutions, but just know that they come from *minimizing* the above equations (ie. picking the values of $\\beta$ that make the SSE as small as possible).\n",
    "\n",
    "$$\n",
    "\\hat{\\beta}_{OLS} = (X^TX)^{-1}X^Ty\n",
    "$$\n",
    "$$\n",
    "\\hat{\\beta}_{Ridge} = (X^TX + \\alpha I)^{-1}X^Ty\n",
    "$$\n",
    "\n",
    "Where $X$ is our matrix of predictors, $Y$ is our dependent variable (gas mileage), and $\\alpha$ is the *ridge parameter* that determines how strong the $\\beta$ weight penalty should be. $I$ is the identity matrix.\n",
    "\n",
    "Lasso regression must be solved with other techniques such as gradient descent, so we will omit it for now. \n",
    "\n",
    "In this notebok we are going to implement a lot of things \"by hand\" to get an intuition of how the regression is done under the hood. In the next notebook we will make use of Python libraries (mostly sklearn) to do a lot of the heavy lifting for us."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data preprocessing normalization\n",
    "It is important to properly condition $X$ and $Y$ before performing the regression. Both $X$ and $Y$ should be normalized so that the ridge penalty applies equally to all predictors. This also makes the $\\beta$ weights more interpretable. Here, we will use *min-max normalization*:\n",
    "\n",
    "$$\n",
    "x_{scaled} = \\frac{x - x_{min}}{x_{max} - x_{min}}\n",
    "$$\n",
    "\n",
    "**$Y$ must also be mean-centered**. This is really important because ridge regression does not have an intercept term (it would not make sense to include an intercept term because it would be penalized by the ridge parameter).\n",
    "\n",
    "**In the following cell, apply min-max normalization and mean center the data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# More data preprocessing\n",
    "x = (x - np.min(x, axis=0)) / (np.max(x, axis=0) - np.min(x, axis=0)) # normalize columns of x.\n",
    "y = (y - np.min(y, axis=0)) / (np.max(y, axis=0) - np.min(y, axis=0)) # normalize columns of y.\n",
    "y = y  - np.mean(y, axis=0) # mean center columns of y."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1: Implement OLS and Ridge regression\n",
    "Use the equations above to compute $\\hat{\\beta}_{OLS}$ and $\\hat{\\beta}_{Ridge}$ (beta estimates for OLS and ridge regression)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS beta weight for cylinders: -0.03407722627535886\n",
      "OLS beta weight for displacement: 0.2015401862946056\n",
      "OLS beta weight for horsepower: 0.09676076839456776\n",
      "OLS beta weight for weight: -0.6981579520912886\n",
      "OLS beta weight for acceleration: 0.1865453152329084\n",
      "OLS beta weight for model_year: 0.27111501476079825\n",
      "OLS beta weight for american: -0.055987983673881705\n",
      "OLS beta weight for japanese: 0.019426596599336557\n",
      "\n",
      "How do the beta weights match up with what you expected from the plots above?\n"
     ]
    }
   ],
   "source": [
    "def ols_solver(x,y):\n",
    "    betas = np.linalg.inv(x.T @ x) @ x.T @ y # the @ symbol is equivalent to np.matmul()\n",
    "    return betas\n",
    "\n",
    "def ridge_solver(x,y,alpha):\n",
    "    betas = np.linalg.inv(x.T @ x + alpha*np.identity(x.shape[1])) @ x.T @ y\n",
    "    return betas\n",
    "\n",
    "RIDGE_ALPHA = 00 #TODO: What alpha value will make ridge regression equal to ordinary least squares?\n",
    "\n",
    "ols_betas = ols_solver(x,y)\n",
    "ridge_betas = ridge_solver(x,y,RIDGE_ALPHA)\n",
    "\n",
    "for label, ols_beta, ridge_beta in zip(PREDICTOR_LABELS, ols_betas, ridge_betas):\n",
    "    print(f'OLS beta weight for {label}: {ols_beta}')\n",
    "    #print(f'ridge beta weight for {label}: {ridge_beta}')\n",
    "\n",
    "assert np.array_equiv(ols_betas,ridge_betas), \"Betas not equal, change RIDGE_ALPHA so that they will become equal\"\n",
    "print('\\nHow do the beta weights match up with what you expected from the plots above?')\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2: Assessing model performance\n",
    "Here, we will generate model predictions and implement a scoring function. A scoring function quantifies the similarity between the model predictions $\\hat{y}$ and the real data $y$.\n",
    "\n",
    "There are many ways to assess a models performance (many of them are also built into scikit-learn, which we will use later). But for now, lets practice building our own custom scoring function to evaluate the models performance. We will use the *coefficient of determination* ($R^2$), which is a useful scoring metric to evaluate many different models.\n",
    "\n",
    "$$\n",
    "R^2 = 1 - \\frac{\\sum_i(y_i - \\hat{y}_i)^2}{\\sum_i(y_i - \\bar{y})^2}\n",
    "$$\n",
    "\n",
    "This the amount of fluctuation (variance) in y that the model can account for. Usually, its value ranges from 0 to 1, though values can go negative when scoring on held out (cross-validated) data.\n",
    "\n",
    "**EXERCISE QUESTION:** What might a negative $R^2$ mean?\n",
    "<font color='red'>Our model is badly overfitting. Our performance is worse than just guessing the mean of y</font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS R-squared: 0.8164738741138317\n",
      "Ridge R-squared: 0.8164738741138317\n"
     ]
    }
   ],
   "source": [
    "def r_squared_score(y_true, y_pred):\n",
    "    numerator = ((y_true - y_pred) ** 2).sum(axis=0)\n",
    "    denominator = ((y_true - np.average(y_true, axis=0)) ** 2).sum(axis=0)\n",
    "    r_squared = 1 - numerator / denominator\n",
    "    return r_squared\n",
    "\n",
    "y_pred_ols = x @ ols_betas\n",
    "y_pred_ridge = x @ ridge_betas\n",
    "\n",
    "r2_ols = r_squared_score(y,y_pred_ols)\n",
    "r2_ridge = r_squared_score(y,y_pred_ridge) # if the ridge parameter (alpha) was set to zero, these scores should be equivalent\n",
    "\n",
    "print(f'OLS R-squared: {r2_ols}')\n",
    "print(f'Ridge R-squared: {r2_ridge}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try many different $\\alpha$ values and see how ridge regression performs over these values. Larger values mean a larger penalty is applied to the beta weights. \n",
    "\n",
    "**Do you think ridge or OLS will perform better? Where will they be equivalent? Remember, we are not doing cross-validation yet.**\n",
    "\n",
    "<font color='red'>Ridge will not do any better than OLS. We have an overdetermined system, the regressors are not collinear, and we are not yet using held out data.</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ALPHAS = 10**np.linspace(-15,7, 100)\n",
    "\n",
    "scores = np.empty_like(ALPHAS)\n",
    "for i,alpha in enumerate(ALPHAS):\n",
    "    betas = ridge_solver(x,y,alpha)\n",
    "    scores[i] = r_squared_score(y, x @ betas)\n",
    "\n",
    "plt.scatter(ALPHAS,scores, s=10, color='black', label='ridge')\n",
    "plt.scatter(ALPHAS[0], r_squared_score(y, x @ ols_solver(x,y)), s=5, color='red',label='ordinary least squares') # plot OLS score\n",
    "plt.hlines(0,ALPHAS[0],ALPHAS[-1],linestyle='--',linewidth=.5, color='black')\n",
    "plt.legend()\n",
    "plt.xlabel('Alpha')\n",
    "plt.xscale('log')\n",
    "plt.ylabel('$R^2$ (training set)')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Excercise 3: Implement cross-validation\n",
    "\n",
    "As you saw in the previous exercise, ridge regression will actually never perform better than ordinary least squares when assessing performance on training data. The power of regularization comes when generating predictions on held out data (cross-validation). When assessing model performance, it is best practice to do this on cross validated data. This ensures our model is not over-fitting and that it will be able to make reliable predictions on new data. In this toy example about fuel efficiency, we want a model that will give us a good prediction for a *new* car where the fuel efficiency is not availible. \n",
    "\n",
    "Here, we are going to implement k-fold cross validation. K-fold cross validation splits our data sets into k chunks. We will leave one chunk of the data out for testing (with our function `r_squared_score()`). We will train our model on the remaining data, and then go back and make predictions on the held out data.\n",
    "\n",
    "Here's a nice visualization of 5-fold crossvalidation\n",
    "\n",
    "![k-fold crossval figure](https://miro.medium.com/v2/resize:fit:720/1*AAwIlHM8TpAVe4l2FihNUQ.png)\n",
    "\n",
    "https://towardsdatascience.com/cross-validation-k-fold-vs-monte-carlo-e54df2fc179b\n",
    "\n",
    "SKLearn has several useful functions for cross-validation. We will make use of one of them here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "N_FOLDS = 5\n",
    "ALPHAS = 10**np.linspace(-15,7, 100) #try some different alpha values\n",
    "\n",
    "def cross_val_score(x, y, n_folds, scoring_function, fitting_function, **fitting_func_kwargs):\n",
    "    kf = KFold(n_splits=n_folds, shuffle=True)\n",
    "    train_scores = np.empty((n_folds))\n",
    "    test_scores = np.empty((n_folds))\n",
    "    for j, (train_index, test_index) in enumerate(kf.split(x)):\n",
    "\n",
    "        x_train, x_test = x[train_index,:], x[test_index,:]\n",
    "        y_train, y_test = y[train_index], y[test_index]\n",
    "\n",
    "        betas = fitting_function(x=x_train,y=y_train,**fitting_func_kwargs)\n",
    "        y_train_predictions = x_train @ betas\n",
    "        y_test_predictions = x_test @ betas\n",
    "        train_scores[j] = scoring_function(y_train, y_train_predictions)\n",
    "        test_scores[j] = scoring_function(y_test, y_test_predictions)\n",
    "    return np.mean(train_scores), np.mean(test_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS test performance: 0.8028269173448503\n",
      "Best ridge test performance: 0.8082682058284686\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_scores, test_scores = [],[]\n",
    "for alpha in ALPHAS:\n",
    "    train_r2, test_r2 = cross_val_score(x, y, N_FOLDS, r_squared_score, ridge_solver, alpha=alpha)\n",
    "    test_scores.append(test_r2)\n",
    "    train_scores.append(train_r2)\n",
    "\n",
    "ols_train_r2, ols_test_r2 = cross_val_score(x, y, N_FOLDS, r_squared_score, ols_solver)\n",
    "\n",
    "plt.scatter(ALPHAS, train_scores, s=10, color='black',label='ridge train')\n",
    "plt.scatter(ALPHAS, test_scores, s=10, color='red',label='ridge test')\n",
    "plt.scatter(ALPHAS[0], ols_train_r2, s=10, color='blue',label='ols train')\n",
    "plt.scatter(ALPHAS[0], ols_test_r2, s=10, color='orange',label='ols test')\n",
    "plt.hlines(0,ALPHAS[0],ALPHAS[-1],linestyle='--',linewidth=.5, color='black')\n",
    "plt.legend()\n",
    "plt.xlabel('alpha')\n",
    "plt.xscale('log')\n",
    "plt.ylabel('$R^2$')\n",
    "\n",
    "print(f'OLS test performance: {ols_test_r2}')\n",
    "print(f'Best ridge test performance: {np.max(test_scores)}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the above plot and consider the following:\n",
    "- Are the OLS or ridge models overfitting? <font color='red'>Nope. The testing scores are fairly close to the training scores for both regression models, so overfitting is not too bad here</font>\n",
    "- is ridge regression needed in this case? <font color='red'>Nope.</font>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4: Regression with collinear regressors and underdetermined systems\n",
    "\n",
    "In the plot above, you may have noticed that ridge regression test performance is only *slightly* better than ordinary least squares. As we introduced at the beginning of the notebook, where regularization becomes most helpful is when you have few observations relative to the number of regressors or when regressors are collinear. Neither is the case in our dataset currently, so let's manipulate our regressor matrix $X$ and compare OLS and ridge again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of x is originally (392, 8)\n",
      "Shape of x with data augmentation is (392, 32)\n",
      "Shape of x after subsampling is (50, 32)\n"
     ]
    }
   ],
   "source": [
    "# augment the matrix x with noisy versions of itself\n",
    "random_offset = x + np.random.normal(scale=1e-5, size=x.shape) # same as x but with small random differences\n",
    "random_offset_2 = x + np.random.normal(scale=1e-3, size=x.shape)\n",
    "random_offset_3 = x + np.random.normal(scale=1e-7, size=x.shape)\n",
    "x_augmented = np.hstack((x, random_offset, random_offset_2, random_offset_3)) # add columns to x that are nearly identical. This is an \"ill-conditioned\" matrix but still full rank. \n",
    "\n",
    "#x_augmented = np.hstack((x, x)) # This matrix exhibits multicollinearity (it is not full rank). Uncomment and see how OLS vs ridge handle this.\n",
    "x_augmented = x_augmented / np.max(x_augmented, axis=0)\n",
    "\n",
    "print(f'Shape of x is originally {x.shape}')\n",
    "print(f'Shape of x with data augmentation is {x_augmented.shape}')\n",
    "\n",
    "# now let's subsample x and y so that the number of observations is closer to the number of regressors\n",
    "N_SUBSAMPLE = 50 #The number of observations to randomly grab \n",
    "\n",
    "subsample_indices = np.random.choice(x_augmented.shape[0], N_SUBSAMPLE, replace=False)\n",
    "x_subsample = x_augmented[subsample_indices,:]\n",
    "y_subsample = y[subsample_indices]\n",
    "print(f'Shape of x after subsampling is {x_subsample.shape}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS test R^2: -0.8137268011765396\n",
      "Best ridge test R^2: 0.7969822997243099\n",
      "Best ridge parameter (alpha): 0.1\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ALPHAS = 10**np.linspace(-15,7, 100)\n",
    "train_scores, test_scores = [],[]\n",
    "for alpha in ALPHAS:\n",
    "    train_r2, test_r2 = cross_val_score(x_subsample, y_subsample, N_FOLDS, r_squared_score, ridge_solver, alpha=alpha)\n",
    "    test_scores.append(test_r2)\n",
    "    train_scores.append(train_r2)\n",
    "\n",
    "ols_train_r2, ols_test_r2 = cross_val_score(x_subsample, y_subsample, N_FOLDS, r_squared_score, ols_solver)\n",
    "\n",
    "plt.scatter(ALPHAS, train_scores, s=10, color='black',label='ridge train')\n",
    "plt.scatter(ALPHAS, test_scores, s=10, color='red',label='ridge test')\n",
    "plt.scatter(ALPHAS[0], ols_train_r2, s=10, color='blue',label='ols train')\n",
    "plt.scatter(ALPHAS[0], ols_test_r2, s=10, color='orange',label='ols test')\n",
    "plt.hlines(0,ALPHAS[0],ALPHAS[-1],linestyle='--',linewidth=.5, color='black')\n",
    "plt.legend()\n",
    "plt.xlabel('alpha')\n",
    "plt.xscale('log')\n",
    "plt.ylim(-2,1.2)\n",
    "plt.ylabel('$R^2$')\n",
    "\n",
    "print(f'OLS test R^2: {ols_test_r2}')\n",
    "print(f'Best ridge test R^2: {np.max(test_scores)}')\n",
    "\n",
    "best_ridge_alpha_value = ALPHAS[np.argmax(test_scores)]\n",
    "\n",
    "print(f'Best ridge parameter (alpha): {best_ridge_alpha_value}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at this plot after adding in more predictor variables and reducing the number of observations and consider the following:\n",
    "- How are the two models performing? Are they overfitting?\n",
    "- Previously, the OLS and ridge fits had similar $R^2$ values, now they look wildly different for the test data. Why do you think this is?\n",
    "- See what happens when you modify `N_SUBSAMPLE`. How does this affect the results?\n",
    "- Will these methods work on a collinear matrix? Try it and see what happens\n",
    "- What will the $\\beta$ weights look like for OLS and ridge? Will there be a unique solution for OLS and ridge?\n",
    "- In your own data, how might you check to see if regressors are correlated before doing the regression?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Up next: Selecting the proper value of alpha and fitting to neural data!\n",
    "Since $\\alpha$ is a model hyperparameter, it is important that the proper value is selected to get the best model performance. Cross-validating with many different alphas (what we did above) is one way to do that, but there are other ways it can be done. See Karabastos 2017, *Communications in Statistics* for another method of $\\alpha$ selection. The Karabastos method is the one used in the Musall 2019 paper we discussed.\n",
    "\n",
    "In the next notebook, we will fit an encoding model to neural data and solve it with ridge regression!"
   ]
  }
 ],
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