{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinary Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "np.random.seed(9876789)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS estimation\n",
    "\n",
    "Artificial data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "nsample = 100\n",
    "x = np.linspace(0, 10, 100)\n",
    "X = np.column_stack((x, x ** 2))\n",
    "beta = np.array([1, 0.1, 10])\n",
    "e = np.random.normal(size=nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model needs an intercept so we add a column of 1s:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "X = sm.add_constant(X)\n",
    "y = np.dot(X, beta) + e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       1.000\n",
      "Model:                            OLS   Adj. R-squared:                  1.000\n",
      "Method:                 Least Squares   F-statistic:                 4.020e+06\n",
      "Date:                Fri, 20 Mar 2026   Prob (F-statistic):          2.83e-239\n",
      "Time:                        11:18:46   Log-Likelihood:                -146.51\n",
      "No. Observations:                 100   AIC:                             299.0\n",
      "Df Residuals:                      97   BIC:                             306.8\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.3423      0.313      4.292      0.000       0.722       1.963\n",
      "x1            -0.0402      0.145     -0.278      0.781      -0.327       0.247\n",
      "x2            10.0103      0.014    715.745      0.000       9.982      10.038\n",
      "==============================================================================\n",
      "Omnibus:                        2.042   Durbin-Watson:                   2.274\n",
      "Prob(Omnibus):                  0.360   Jarque-Bera (JB):                1.875\n",
      "Skew:                           0.234   Prob(JB):                        0.392\n",
      "Kurtosis:                       2.519   Cond. No.                         144.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quantities of interest can be extracted directly from the fitted model. Type ``dir(results)`` for a full list. Here are some examples:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters:  [ 1.34233516 -0.04024948 10.01025357]\n",
      "R2:  0.9999879365025871\n"
     ]
    }
   ],
   "source": [
    "print(\"Parameters: \", results.params)\n",
    "print(\"R2: \", results.rsquared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS non-linear curve but linear in parameters\n",
    "\n",
    "We simulate artificial data with a non-linear relationship between x and y:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "sig = 0.5\n",
    "x = np.linspace(0, 20, nsample)\n",
    "X = np.column_stack((x, np.sin(x), (x - 5) ** 2, np.ones(nsample)))\n",
    "beta = [0.5, 0.5, -0.02, 5.0]\n",
    "\n",
    "y_true = np.dot(X, beta)\n",
    "y = y_true + sig * np.random.normal(size=nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.933\n",
      "Model:                            OLS   Adj. R-squared:                  0.928\n",
      "Method:                 Least Squares   F-statistic:                     211.8\n",
      "Date:                Fri, 20 Mar 2026   Prob (F-statistic):           6.30e-27\n",
      "Time:                        11:18:46   Log-Likelihood:                -34.438\n",
      "No. Observations:                  50   AIC:                             76.88\n",
      "Df Residuals:                      46   BIC:                             84.52\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "x1             0.4687      0.026     17.751      0.000       0.416       0.522\n",
      "x2             0.4836      0.104      4.659      0.000       0.275       0.693\n",
      "x3            -0.0174      0.002     -7.507      0.000      -0.022      -0.013\n",
      "const          5.2058      0.171     30.405      0.000       4.861       5.550\n",
      "==============================================================================\n",
      "Omnibus:                        0.655   Durbin-Watson:                   2.896\n",
      "Prob(Omnibus):                  0.721   Jarque-Bera (JB):                0.360\n",
      "Skew:                           0.207   Prob(JB):                        0.835\n",
      "Kurtosis:                       3.026   Cond. No.                         221.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res = sm.OLS(y, X).fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract other quantities of interest:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters:  [ 0.46872448  0.48360119 -0.01740479  5.20584496]\n",
      "Standard errors:  [0.02640602 0.10380518 0.00231847 0.17121765]\n",
      "Predicted values:  [ 4.77072516  5.22213464  5.63620761  5.98658823  6.25643234  6.44117491\n",
      "  6.54928009  6.60085051  6.62432454  6.6518039   6.71377946  6.83412169\n",
      "  7.02615877  7.29048685  7.61487206  7.97626054  8.34456611  8.68761335\n",
      "  8.97642389  9.18997755  9.31866582  9.36587056  9.34740836  9.28893189\n",
      "  9.22171529  9.17751587  9.1833565   9.25708583  9.40444579  9.61812821\n",
      "  9.87897556 10.15912843 10.42660281 10.65054491 10.8063004  10.87946503\n",
      " 10.86825119 10.78378163 10.64826203 10.49133265 10.34519853 10.23933827\n",
      " 10.19566084 10.22490593 10.32487947 10.48081414 10.66779556 10.85485568\n",
      " 11.01006072 11.10575781]\n"
     ]
    }
   ],
   "source": [
    "print(\"Parameters: \", res.params)\n",
    "print(\"Standard errors: \", res.bse)\n",
    "print(\"Predicted values: \", res.predict())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare the true relationship to OLS predictions. Confidence intervals around the predictions are built using the ``wls_prediction_std`` command."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xadde5de1e8ed>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fVbduXSZOnMinn35Kw4YNWb9+PS+++GKaxzzxxBNMnz6dmTNn0qBBA1q3bs3MmTOpnrqWm1JKKWxWCy1rlKFL/Qq0rFFG6mpWqyY1Lteuhddf991AM7UyZWDqVEkk+uADaNjQdV90DgvUq7z78Uepoer01lsaaGbCYni7VtFVxMXFERISQmxsbIY2lwkJCezfv5/q1asTFJS9LEOVkb6OSqkCafNmePhh6ebTvr3Zo3GviAjJeO7TR3ptlypl9ojyN7sdhg6FsWOhXTv45Rf/eLPiRleK19LTmU2llFL535o10Lo17Nwps5i+Nc+Sdz//LAXnJ02C2rWlRWZ++xp9xdmz0LmzBJogpY18IZnMh2mwqZRSKn9bswY6dID4eGjbVjoB5bfg4JVXpGxTvXpw4oRkRd9zj7TPVO6zcyfceKP8DBUpAl9/De+8I1UDVJY02FRKKZV//fWXBJrnzsly508/QenSZo/KM9q0ka0Cb78tdTgXLJAuRN99Z/bI8oeffpJAc/duqFxZKgR07272qPyCBptKKaXyp9WrXYHmbbfBokXuLZDsiwICZC/hxo3QuDGcPi0F61XeXLoEzz8vtVhvuUVe3yZNzB6V3yhYu1mVUkoVHJ99JoW2//c/meXL74FmatdfD3//LbU5H3/cdfz06fw7s+tJAQEwbx5Mny57NQMCPH5Ku8PIWK7L6p/bPzTYVEoplT9NmQK1asGzzxasQNOpcGHphOR08aKU5WnQQDoQlStn3tj8wYEDMoN5331y+7rrpLuUFyyNiM7QiCAsJIhhnevRsX6YV8bgTrqMrpRSKv/YuVP6U4MEW6++WjADzcz8+Sfs3Qs//CCB0w8/mD0i3/XHH5Jl3r27bMfwoqUR0QyYvSlNoAkQE5vAgNmbWBrhf/VUNdhUSimVP/zxh9Sa7N/fFXAql9tvl6X1Bg0kY/3+++Ghh+DkSbNH5jvsdnj/fdl6cfKkbEeoWtV7p3cYjFi0ncyKVjmPjVi0HbvDv8paabCplFLK/61cCXfcARcuwOHDkJRk9oh8U5MmsjT8+utSrmfOHJnl/OILrcu5c6ck/7z4IiQnSwOAP/+UzHMvWb//dIYZzdQMIDo2gfX7T3ttTO6gwaZSSin/tnIl3HmnBJodO8L8+RAYaPaofFdAAIwcKS0vr7sOjh+H77/Pf7VHc2L8eGjUSFqXlighLUFnz/b6Fozj8VkHmrl5nK/QYNPLDh8+TJ8+fahYsSIBAQFUrVqVZ599llOpequ2adOGwYMHZ/kcK1asoG3btpQuXZqiRYtSq1YtHnvsMZKTk73wFSillA9ZscI1o9mpk2QMaxve7GnaFDZtkqLkH33kOn7qlGStFyRWKyQmypuVbdskscqE4Lt8iez97Gb3cb5Cg00v2rdvH02bNmX37t188803REZGMnnyZH7//XdatmzJ6Wz8cm/bto1OnTrRrFkzVq1axX///ccnn3xC4cKFcegeJaVUQbJ2rcxoXrwoAeePP2qgmVMBAdJ9qEYN17GXXoJrr5XZPbvdvLF5UlIS7Nvnuj1woJTHWrzYq8vm6TWvXpqwkCCyCnMtSFZ68+r+Vb6qYAebUVHyrjgqyiune+qppwgICGDZsmW0bt2aKlWq0KlTJ3777TeOHDnC0KFDr/ocv/76K2FhYYwbN4769etTo0YNOnbsyPTp0wnwQt0vpZTyGQcPyt66jh1h7lwNNN3h4kXZ03nqlCRatWghSUX5yZYt0Lw5tG8vdVhBZjbvvtv0rQQ2q4VhnesBZAg4nbeHda7nd/U280+wef581peEhIyPnThRMszatZOPEyfK8YsXs/e8OXT69Gl++eUXBg4cSJEiRdLcFxoayiOPPMKcOXMwrrJBOzQ0lOjoaFatWpXjMSilVL7y0EOSgf799xpoukuRIvDPP7KsHhwsgWeLFtCnj+zt9GeXLsGbb0pJoy1b4OxZWTL3MR3rhzGpRxNCQ9L+TIeGBDGpRxO/rLOZf4q6Fy+e9X133AE//+y6XbZs2gDU4YCnnpJL69ay2dypWrXMy0LkMGtvz549GIZB3bp1M72/bt26nDlzhhMnTlzxee6//35++eUXWrduTWhoKC1atOC2226jZ8+eBAcH52hMSinldy5dgthYV0Hyli3NHU9+VLiwFMJ/6CEYMkS6EH32mcweL1gg/yf9zcaN0Ls3RETI7W7d4NNPITTU3HFloWP9MNrXC803HYTyz8xmTvhgeQfnjKblKlP4NpuNzz//nKioKMaNG0fFihUZNWoU1113HdHR/lfoVSmlss0wYMAAWQLdvt3s0eR/FSrA55/DmjVSMikgABo2dN3vD+WlHA7o0kVmMyMiZLJpzhwpaO+jgaaTzWqhZY0ydGlUiZY1yvhtoAn5Kdg8dy7ry9y5aR+7davsz0jNZoNdu2DJkrTHDxzI/DlzqGbNmlgsFrZn8Qdy586dlCpVirJly2br+SpVqsSjjz7Kp59+yvbt20lISGDy5Mk5HpdSSvmNsWNlhu3QIfnbrLyjZUtYvx5WrYKSJeWYYUgB/QcflNwHX5rESb3VzWp1bbHo3l3epDzwgOl7Mwua/BNsFiuW9SX9Xh5nlp3NJrdtNumhe+21sl8lO8+bQ2XKlKF9+/ZMnDiRi+n2hcbExPDVV1/x4IMPXnVmMzOlSpUiLCyM87nYS6qUUn7h+++l9STAxx/L9ijlPTYb1Knjur1xI/z3H3z3neQ+1K0r+zzNLJn033/w5JMyI7trl+v4yJGwZw98/bX2gzdJ/gk2c6pPH3lnvGKFfOzTx+OnnDBhAomJiXTo0IFVq1Zx+PBhli5dSvv27alUqRKjRo1KeeyJEyfYsmVLmktMTAxTpkxhwIABLFu2jL1797Jt2zZeeeUVtm3bRufOnT3+NSillNetWwc9e8r1QYPg6afNHY9yJdk8+aTkTOzaBc89B5UqQa9esGOHd8aRlCRL4m3aSGvJKVNkZjN13/drr4WaNb0zHpU5w8fExsYagBEbG5vhvosXLxrbt283Ll68aMLI3OPAgQNGr169jNDQUKNw4cJG5cqVjWeeecY4efJkymNat25tIF2p0lyGDRtmbNq0yejRo4dRvXp1IzAw0ChTpoxx6623GgsXLsz2GPLD66iUKiD27TOM8uUNAwyjc2fDSE42e0Qqvbg4w5g0yTCuv16+T2AYv/3muv/gQcOIiTEMh8O95x092jAqVXKd02YzjPvuM4w//nD/uVQGV4rX0rMYhi9ttIC4uDhCQkKIjY3NkF2dkJDA/v37qV69OkFa5iLX9HVUSvmNbt2kK1DjxrJn8EqVR5S5DENmoefOhXffde2LfOghScoJCZFZxtq15aPzeoMGrm1tzuc5dQoiI+Wyd698LFFCyhQ6Va0q+3fLl4d+/aQuaHi4d79mH2F3GF7PXL9SvJZe/il9pJRSKv+ZMUP20o8bp4Gmr7NYJJkofTmqc+fkvthY2LBBLk6FC0urUae77oLVq+Wx6VWsmDbYfOghCVTvvx8CA937tfiRpRHRjFi0nehYV0nHsJAghnWu5zM1OTXYVEop5btKlYKvvjJ7FCovfvpJaltHRsLu3XLZtUs+WixQKFUocv68K9AMD5e9lqkvhuGaMR071vtfi49ZGhHNgNmbSL9EHRObwIDZm3ymCLwGm0oppXzLe+/JbOZTT5k9EuUuQUFQv75cruSjj2S2s3r1jNVhVBp2h8GIRdszBJogiR4WYMSi7bSvF2p6jU4NNpVSSvmOuXPhpZfkeoMGcOut5o5HeVfqovHqitbvP51m6Tw9A4iOTWD9/tO0rFHGewPLhF8Gmz6W0+R39PVTSvmkjRvh0Ufl+jPP+E2gaUZyhlLH47MONHPzOE/yq2CzcOHCAFy4cIEiOr2eaxcub8Z2vp5KKWW6I0ekreDFi9CpE3z4odkjyhZ/SM5Q+VP5EtmrJpPdx3mSXwWbNpuNkiVLcvz4cQCKFi2aq447BZVhGFy4cIHjx49TsmRJbKlLTSillFkuXJBA8+hRqFcPvv02bSkcH+UvyRkqf2pevTRhIUHExCZgAKFxJ6l+5ij7S1UkJrgsFiA0RGbazeZXwSZAaGgoQErAqXKuZMmSKa+jUkqZyuGAxx6Df/6BsmVh0SK4Ss0+X+BPyRkqf7JZLQzrXI8Bszfx4L/LGP3LJ9gMA7vFwmsdnuG7hrczrHM9n/j587tg02KxEBYWRvny5UlKSjJ7OH6ncOHCOqOplPIdFgs0by7lcX78Ea65xuwRZYs/JWeo/KvjtWX4qdBW6i0djzOktBkGo3+ZQMcXetLWR2bW/S7YdLLZbBo0KaWUv7NYJPv8kUekaLef8KfkDJUPHTgAU6fCjBlcl8lKr81w0LZQvPfHlQW/DTaVUkr5sYgIqFLFtWTuR4Em+FdyhvJjUVGwZw/UquVqxZmQICWi4uLkdvnycOKEFLx3stmkCL6PsJo9AKWUUgXMoUPwv//BzTfLP1M/5EzOyGo3nAXJSveF5Azlp2bMkP7v7drJG7Pp0+V4UBB07w633QY//CC/Q9OmuZLqbDaYMsWn+sRbDB8rupiTxu5KKaX8zLlz0KoV/PsvXH89/PWX3/Y8d2ajA2kShZwBqGajq1yLipJA0+FwHbNa4eBBCSLt9owVG6KipCVozZpeCTRzEq/pzKZSSinvcDigRw8JNMuXl8xzPw00ATrWD2NSjyaEhqRdKg8NCdJAU+WeYcD48WkDTZDbkZFyPbOclfBwaNPGp2Y0nXTPplJKKe947TVYsAACA2H+fFka9HMd64fRvl6odhBS7nH4MPTrB0uXZrzvKvswDQP++0+6vPpaCXINNpVSSnnerFkwdqxcnzEDWrY0dzxuZLNatLyRyjuHAzp0gB075A3ZXXfJmzLnknkW+zD37IFvvpHLzp2wZo3v/XppsKmUUsqzEhNhxAi5/vrrUuZIKZWW1SpvyEaNgs8/h7p1s9yHefgwzJkjAeamTa6nCAyEbdt8L9jUBCGllFKed+QITJ4sQac1f6QLGAbs2gVLlsD6H6VETWx5KVFToQKZXsqXhzJlwBadSUkbVbAYhmSYlygBDz3kOu5wZPo7cuIEfP+9dHP980/XcZsN2reXBPUuXSAkxAtjJ2fxmgabSimlPCOzjFk/d/48rFghAebixVJb+3FmMJV+2HBgx8qbjGAmvTlHcc5TDHu6RcQnLDOYbMjjDasVpkzF8kQfc74g5V3OuplFisAbb8Bvv0HJkrJ0nkkb6dhYmDdPAszffpNfKadbb5UA8957oVw5730JThpsKqWUMteZMzLd8tJL8OCDZo8m1wwDdu+W4HLJEvjjD9kV4FS9cBR7kqpiw5HlcyRag3i46hr+iGtM0KkoDlEFa6piSXZsfD36AF2fDqdECU9+NcpUM2ZI8k/qLPOgIFk2f/bZNG/MkpLgww/hrbfkDY5T06YyCfrgg+ZPiGuwqZRSyjwXLsDtt0sNzYoVJVorVszsUeXIyZPw6atR7P55D39E1+II4YBBEzbxWMh87rXNZ8+Ib7jxmhMUubNdxiewWtMGFTt2QJ062H9bga19xsd/zCA+KvY6d/Uux4ABUK+e5742ZYLM6maCvHu59dY0h/78EwYMkL2XAHXqwMMPS5BZq5aXxpsNOYnXNEFIKaWU+yQlwQMPSKAZEiLTgX4UaBqG7Itb02cG759zLY3/W6oNNY09BJ89DLHy2EqxC+D6xzIGljYb7N8vGzTj46WQfaVKAKwimNYWC9Z08zzPMp6B5yeydEJHWkz4iqZtgxk4UPbgFT6W/f2ddoehZZjywGOv37//Zgw0Ic2xEyfg5Zdh5ky5XbYsvPsuPPaY75UyyikNNpVSSrmHwwF9+sDPP8vy4E8/SZcgPxEdDU89BevnRXHw8h5MABsOmpxZLg8qWhQ6dYKuXeHOO6FUKZg6Ffr3T1uipnJleXxgoEQNXO449FsM93d4htG/TKCQ4cBusfJz7Zupdiaa649F0rh4JOfPl2DFCtkb+k6JUbx07k2sxuWkkalT5TXOxNKIaEYs2k50bELKsbCQIIZ1ruf1AvP+GPR69PVr2FAixkz6lzscssL+yiuy+wSgb18YM0aSyfIDXUZXSimVd4YBL7wgG81sNinefuedZo8qWwwDvvgCBg+Gs2fhNusKfnNksjQ+ahQ895wkd6R3lVaBdodBq7HLUwKZ0LiTVDt7lAMlKxITXBYLcGPiMb7qXJ0jNdsyZQr8NmkP685cm6b/umGzYTlwIMM5nK0z0/9DN6N1pi8FvdnlkdfPbpdZbWd6+NSpMHBgmjclW27ow4ABsG6dPKRhQyna0KJFXr4a79B2lUoppbzrp58k0ASpEegngeahQ3DHHdCrFxQ9e4TPKrzK+J+uyVh6xmaDnj0zDzThqq0C1+8/nSb4igkuy7oq1xMTLLOeBrAusALrq15PlSoS164e8Rvp5wItdjs75u9Kc8zuMBixaHuGQMn5vAAjFm3H7sjb3JLdYbB27ykWbDnC2r2nMn0+Z9CW+msFiIlNYMDsTSyNiM7TGDzBI6/f2bPQubNcLl2SY/36SfmCFSs4F3GA5yL6cMMNEmgWLy6/Phs3+kegmVO6jK6UUirv7rxTZjYrVYJHH83VU3hz6dXhkImml16Cc+cMnig0i08KDSboWCzsqpD50nge0n+Pxydc/UHpHlf4ns4w+OmMe/2eeZqJf0zksZltKVYsYyCbngFExyawfv/pXHc6ys5s5dWCNgsStLWvF+pTS+puf/22bZNtFpGRsp1k82a48UZ5rkrh/LA2nMGPwNGj8vD775dA8/K23nxJg02llFJ5Z7XCe+/l+tO9ufQaGQlPPCGJwBU5wi8l+3HT2cWQDDRrBrffjr1OXbbUbs7FnTspUqcOjW6qT14qhpYvEZTzx4WHpwl6DYuVRGsQde07qf3DbbRdF8kbn1/D+bI5D2RzIqslZudspXOJ2RtBryfk5o1AlubOlYye8+ehShUpktmkCSD7MR9/XDpQAtSoAZ9+Kh0q8ztdRldKKZU7y5dLTZaE3AUxTt5aerXbZQbp+uvhjz8M+gXMZF+R6yTQDAiAd96BNWtY6ihFq7HLufenQ/SILMq9Px2i1djleRpH8+qlCQsJyrAs7mRBguvm1UunvaNPn5SlV8uhgwQdO8SBzk/zVbH+rIq6hvbtYerbZTDOX/3feXYD3tRyssTs1qDNi3L1RiC1qCipuP7MM3DffRJotm0ra+KXA03n1fnz5Udt2DCIiCgYgSZosKmUUio3Nm6UujzffJOnGU1v7Tc8fx56toti4fMrKH0xijmVX2LKpd4EXoyV2czNm+GVV1i684RHAl+b1cKwzlI8M8M+zMsfh3Wul/nycur9oGXKUG3hJ3Q9OpFnnpEE5z1zD7Hi04F0+nUzhsMgNO4kLQ9uJTTuZMrzZxrIZkNOZivzHLSZJNdvBEDSyKtWlQYGEybIseeeg2XLoFw5DEMO33yzvGe45hpYuxaGD5cV9oJCg02llFI5s2uXlP85dw7atYMXX8z1U+UkmMmtuDj4pNEMvlhVlRW045ClKvf3Li5ZGZdnM6lXz+OBb8f6YUzq0YTQkLRRRmhIUI6znUsEWxg/HlavhlEl3+Ua4wCTNr3B8g+fYc2k3nzz7Wv8Nbk3D/67DLhCIHsVOZmtzFPQZqJcvxGIisrYEchqheefh0KFiI2VTj/PPCM5QvfcA//8kzLZWaDonk2llFLZt2mTJAOdPAk33CDrgnmYovH00uvp0zKjuSDSVTfTajhg1NuwZQvUr5/yWG/sOexYP4z29ULdlgh1002QeOATfut2DS2Xj6RG8oGU+2yGwehfJtDxhZ60zeW+15zMVjqDtgGzN2GBNEH7VWdvTeZ8I5B+33DolfYN//FHxuQthwMiI9lyMpz775f9wYUKyeT/oEH+X5w9tzTYVEoplT1Llkjq7PnzsvFxyRLy2szbk0uvx49L18wK/27L2LvcbpeAOfXjvbTn0Ga1uDVBJjAkiP/9/iqH3q9BsRfT9qG3GQ7aForP9XM7ZytjYhMynfG1IAGZc7YyV0Gbj8j2GwG7XTZdvvNOhu5Rhs3G13/XpM8wSEyUHKHvvktJRi+wNNhUSil1defOubJs//c/ybp1Q+ONnAYz2XX0KNx2GxzaeZ7JhUdCUroHXO7ekpq/7jl0qvLgTRgvW7GkCn4cWNiRWJPrcvmcuZmtdPfsrTdd9Y3A2bPwyCOweLHcvvtu6Zhlt2PYbExvOoV+Q6RE1l13waxZUNq3dg2YQvdsKqWUurrixSXAfOIJ+efqpg5veUqcycLBg3DrrXB0ZywrAjrQIukvaRvpLNSeRd1Mf91zmCI8HMvUqfL1IYHmk0zmhi7hTJoExsXczcjmZq+pM2jr0qgSLWuU8YtA86q2bZNkssWLZevIl19Kp6wDB9j/2QraVjtAv7/7YLPB2LFylwaaQttVKqWUylxSkiQDpdrX6CnuqrO5Z4/MaJ4/fIqVAR1ocOkfKFkSli6VqtlXaCnpHMeA2ZuAzGfxvNn2Mdcut848U6Ymjw0NZ9EiKMwldoc0J+yBWwj88B0oVizHT+uP/c7d5scfZWb/3DnJPv/xR2jSBLvDYPj75xn3ZlEuJVipWNFgzhwLrVqZPWDPy0m8psGmUkqpjOLjZX/m2rWS8tyggcdPmddgZvt2CTQTYs7wd8CtXHspAsqWhV9/hUaNsv08/tjbOyuGAR9/DH++uIC59q4AJFS6hqBvZsItt5g6Nr+xdq1kYoFUX5gzB8qWZf6GaPoNMDjxT0UAgqqd4LqHd/B291p+93OSGxpsKqVUFgr07Ex2RUdLxvnmzVC0qCyfd+xo9qiuaPNmSQY6eRIa1reztvZjFFmzXIpt16uX4+fLbz8nGzbAJ52XMepYHyoThWGxwKBnsTw1UGZCa9XKUzvOfCUqSqbIna+JYcisZtmyMG4cFCrE9EXHGdgniKQTwWAxCLl5NyE3ReL8EfGLGfA80mBTKaUykZ9mrDxmxw6poXnwIJQrJ/szmzUze1RX9PffEgufPQtNm8qKeZmQZIiJ0QAqldhYGPRYLLcueJ4+fAa4epZjtUprzD59zByi+WbMcNXOTP2aOG8D33xj0KOXHcelQliLJVC28xaKVD2V8hTOpLbVr7Tz6zcoV5OTeE0ThJRSBYK3WiL6tT//lFYnBw/KrM7atT4faP7xhyTHlz+7izlhg/ntFztlyiDFDTXQTCMkBGbOC+HSxBn0tn3hCjRBgqn+/WVWr6BKX6Q99WtitZKYCE8/DQ8/bMFxqRCBlU8R1mt1mkAT3NOIIL/R0kdKqXzvap1hLEhnmPb1QvP1TMQVrV0rUdulS9CiBSxaJMuGPmzNGniiYxQPJCzl/UJDKBl9CsaXlF6AKlMWCwwYAO0LhWPpl+5Oux127pREqoJYfXz9+oxF2u12iIxkf1I4DzwgXVoBgltGUrLVbizWrBeH09djzW9bM3JCg02lVL7njc4wfu+GGyRhpEQJ+Oor2avpwyIjYc7tM9iZcLkzUDJSQfupp8weml+o2akWhjVtTU47NuI/nU3J8eOloXeVKiaO0Mu++w6efDLjcZuNZftq8uA9sk2jdGl4bVwcn+zZddWnTF2PtaBv4dFldKWUf0tKkvp3q1bB3r3StiMdb3WG8SsOh9QJjIuT2wEB0nryhx98PtA8eRJ6t4/ig/P90nYGOnIk0++/ykS6mpzJ2HiRcQTOnwOLFmHUqwcffADJySYP1MNOn5aqCw8+CGfOyNaLy3szDZuN7/83hQ59wjl7Vib8N2+Gwb1L5Kgeq27h0WBTKeUvDEMCS6cVK6RlYrFiUgeydWupnxgUBBUqwGefpTy04qV47tqxiiZROwiLO4HNYc/0FL7aGcbtIiLk9erZU9ruORUvnhJ8+KqEBOjaFSod+DPzFpSRkaaMyy/16QMHDsCKFZxYf4D/bnueJmxiFbdgOX8eXnhB9uxu2GD2SD0nIAD++Uf2+L75prxhPXiQE9+toFvjAzzwiyRMDR4s+4OrVMlZI4KrbeEB2cJjd/hUrrbb6TK6Usr3GIbsIdy4UQKj//6T2cv33pMN/ABFishxkKXf8uVlZishQZpiFy6c8nRNju+l2cJxKbeTLVa2VajB6mqNWF2tMZsq1aV0mRK+2xnGXc6fhxEj4MMPZcaqaFGoXNnsUWWbwwG9esHav+xss7xFhv/gmbSgVFcRHg7h4YQBy5bBJ5/UpcPLK+l+aSbvW16k1JYt0tj76afh7bdlJjx1WSB/dOoUlColM5jFi8u2kaAgaNwYgJ//DafXwHBOnpRGWZ9/Dt26pX2K7PaA1y08QoNNpZRv+ftveOklyYxOLyLCdf366yWJpUEDmW6wWCRIPXUKDh9OE0TZigRxuklzLkQeoMK5UxR22GkYs4eGMXt4at33vNbhaW597zXZrH/pkgSq+S1BYsECGDQIDh2S2127SrVvP9qX9/rrUk+7UCEbiW+9Dx8/LmvqdnuWLShV9lmt8Oyz8L//WenR43Fqb7mL93iRnsaXGF/OxlK9Orz4YsayQP7AWTtz1y544w1JInPu723ZEoCjR2UG8/vv5XDjxnK9Ro3MnzI7PeB1C4/QOptKKd9x6BBUry7/zIKCpEp3gwauS61aaWYsc2ppRDRvLYiAI1G0OPQfrQ5sofXBLUR8v4TWHW+UB02YAKNGSWZ2+/ZyCfPzDfwffgjPPy/Xq1aFTz6Bzp3NHVMOTZvmmtSeOVNqbJN8uZbmVVpQqpy7dEnisXfegXbGbzQrvY/RZwekSSjCZpNleF9/3VPXznS66SZ5Q2u1YrfD5Mnw2msycWuzSdD59tvyZygv1u49Rfdp6676uG/6tvC7mU0t6q6U8h8XL8qSuNMTT8g/hbfe8sg/sQzlR6qVwmZLtX39vvukY05q9etL1fCOHeHWW/MU8JoiJkaC9SeekOnBXPTFNtMvv0hDo4H28dR45k6eHZ/FVJNyu9Wr4dFHodqBFaygXcYHvPyy/K4GBnp/cNmxYYNsA0gd6lgs8gblmmvYskVKaa5fL3c1by4T5DnobnpFdodBq7HLiYlNyHTfpj8XgNdgUynl+y5ckGXc996Tgom1a8vxVJ06TJGYCH/9Jf20f/0VNm1y/aMqVEiW6Z1/m+LiXNd9waVL8PvvEizv3StJVE7nzsn+ND+zdSu0agUPxk9jGv0wypXDsmMHUrldeUNcHIzoG8W476pmTMoCCA2VLRr9+0ttIF+R2YzmZRcXr+DN5W348EPZhREcDKNHS/Ujd+fIObPRIe02Y2do6a+tLTXYVEr5LrsdvvhC9k0dOSLHXnhBgk5fdOqU9NdeulRmYb/91nVf8+ZSOsU569mmjfcDuosXZepv7lzZwxob67pv505XEH8Fvlps+sgRKTdTP2oJP9EZG3bJGB4xwuyh5Qs5/b7/M3AGDSf1pxB2krHxe0g3bi28liInL3cdKlpU9nC++67MdKbvMe5pFy/Kz39oqNzesQPq1cvwMIfVRsvQA6w/KmO6/3746COoWNFzQ8uPdTY12FRK+R7DkIDt5ZddiT5Vq8r+yO7dzZ3NzI34eOkdnrquY0CATMPdeKOUFurQwbNjmDhRXs/z513HQkMldfbee2XJv9CV80B99Z9gfLwMny2bWW25hWLGeSnVNHNm/kveMkFuv+/ndkYx791IRn9Xk53nwilEEq/V/I4XeY8SkVvkDdi6dVJ6LLMe4+6SOpA1DJg0Sc7Rvj18843rcfv2yQx///5gt2O32OhnTOEz+lC1Knz6qWzR8AZffVOXWxpsKqV8i90uAaUzzbNkSdk7+NRTed+Bb6b4ePlHtnSpXPbvd93Xq5fUTAFZ3r7nHqhTB+rWldmWunWl/Ep6DocsecfHyyUuzvXxxAmZPb32WnnswoXQpYtk3t97r1xatsz2OqBzeS/9PwGzl/eSk+XL+m/xIdZbWxDqiIbbboPFiyWgV3niju/76dMygfnxxzKhCAYvNl5O736FqXfXNfJGMvXytdUqvyNt2mS95zm7M6Hpl8edlShAUse3b0/zc3LuHMx5P4q5YyPZerEmMbZwnn9eSsz62fZln6LBplLK94wcKZdBgyTt05f2drmDYUjSwa+/Sv3P1q3hoYfkvm3bJMkovdBQ6UM9YIBr1ueff6Bp06zPM3SopMmC1BTdulUKb+dwts+ZuJBVDUCzEhcMAwYOhG8mn+UvSyuuMy6/dqtXQ0iI18aRX7n7+x4dLXsdp0xx9VwYetMK3l6TSTIRSBB43XWSgfPkkzITCmkDSKtVnvDuuyXb/cABuOsuWaaPipJyXelDl5YtpWRa585QqBCGIT8yn38unSidk/833ihP3bDhVb80dRU5ide0zqZSyjtef11mN/Nr0W2LRWZkatXKeF/58vIfbvt22Ue2fbv804yJkUvqGVHnH22bTa4HB0vReuf11BvLgoJc/6xzyFeLTU99M4qdk/dQldKE1SwG5yvKjGYBDTTdvfTq7u97WJhU0nrhBUlKnzULZq6pxQisGZOJihWTqG/zZrk4K6VHRWH06+cqq+RwYPTti6VvX9fnbt0qFRX27MkYaIJEvG3aEBUlW8I//zxtM6lataT6V9++Pt8kK1/SYFMp5RkxMTIL9/HHkjRjseTfQPNqypVzFYl0iouTBJ7jx9Mm8dSoIZn6QUEe3Zvoi8Wmtz47gyfG96M/DhwWK9bnJsjyuR91OXInT+yn9dT3vVo12ab58sswbFg4/b6byhQkmciOjW/aTCGgf2/aXXOAskf+hS1bZEYeWL9sHc3TZYxbkMDXEh4uT+6cNq1VS2Y+Uz3esNlYtL0mE9+RhQXnXcWLwwMPQO/ecPPNutXXTBpsKqXc7+BBKYoeGSkJNLNnmz0i3xMcnPmspNWatu6oh2S3D7y3+sXvXh7FdeP7pcyGWQ0HPPOMLKEWQFntq4yJTWDA7E253k/r6e97nTrS5WnzkD70ebEDh5ZHsoeaHFkZDisBrqFu3Wto0+Ye2vwB9vLHGL/xPKstFmypZiztFitt+k1h6NN3pv06w8Nh6lSM/v2xXE74eS5wCp885drj2bq1BJj33uuX1b7yJd2zqZRyr507JSM0Kkq6Af36a9b93pRpfKnY9KlT8Oz1K5h9NJN9fitWSFJJAeLJ/bTe/r6fPg2rVsHKlXLZujXjKnih0ufoV2wiH0e9SiHDQbLFyvN1hvFF6Yco4ihCu+rhnDlj4fRpOHNGnrPo6SiqOyKJpCZHCKdyZekq1auX/rnxFk0QUkqZY/NmKfdz4oRkW//6qyTAKJ/kC8Wmk5KkRGnR5YtYyN2kCW/8pR2im3m6xaGZ3/fUwefiZcns2WFLOXMloqiJK4C8msBAKfLw+OPQrl3WezHzW8khX6EJQkop71u9WgrWxcXBDTdImZOyZc0elbqCjvXDmNSjSYZ9gaFerLP53HOwe/lhNlr6YjFwlbGx2SSpqoAFmuD5/bRmft9Ll4auXeXSdssxnv58G4lRpUk4VJoTUaU5QSOsQUkUDTqKtUgS1qAkurUox60NQihdWj6/VCn5WLbs1Sth+Wod2YJGg02lVN4lJUnB7bg4qcS9aJFvtXFUWepYP4z29UJNmfmZMgU+//Q8q7mbCsYxyTb+7jtJLqtZs0AGmuCd/bRmft+dypcIwlYkiaK1jlG01rEsH9evbyla5mJp3FP7XlXO5bhlx6pVq+jcuTMVK1bEYrEwf/78NPcbhsHw4cOpWLEiRYoUoU2bNmzbts1d41VK+aLChWHePClttGSJBpp+xma10LJGGbo0qkTLGmW8EnCsXAnPPOXgSx6lMVukPNSiRZJh0qZNgQ00AZpXL01YSBBZfRcsyOxc8+p5q1Vrxvc9NU9+nXaHwYhF2zPdl+o8NmLRduwOn9pJmG/lONg8f/48DRs2ZMKECZneP27cOD744AMmTJjAhg0bCA0NpX379sTHx+d5sEopHxMd7bresCF8/bUUXlbqCvbtg/vug9b23+nGPIyAAHmzUrWq2UPzCTarhWGdpad3+kDMeXtY53p+v+/Qk19nTuqJKs/LcbDZqVMn3n77bbo5i7GmYhgGH330EUOHDqVbt27Ur1+fWbNmceHCBb7++mu3DFgp5SPmzJGlztWrzR6J8iPx8dKK8tQpONu0PZdmfIll+nS46Sazh+ZTnPsqQ0PSLpWHhgTlq+VfT32dvlhHtiBz657N/fv3ExMTw+23355yLDAwkNatW7NmzRr69++f4XMSExNJTExMuR0XF+fOISmlPGHbNkkBvXBBlj5btTJ7RMoPOBzQowdEREinzvnzIaBSD7OH5bN8YV+lN3ji6/S1OrIetWsXfP+9XBYu9MkVArcGmzExMQBUqFAhzfEKFSpw8ODBTD9nzJgxjBgxwp3DUEp5Umys1Bu5cEG6u4waZfaIlJ94/XXYvPAQC63PUGnGFCpVCs3T8xWEkjbOfZX5nbu/Tud+0KvVE83rvlfTpA4wt251Hf/hB+kd6mM8ko1uSdcTyjCMDMecXn31VZ5//vmU23FxcVQuoK3JlPJ5DodUTt6zR1oIfvMNFNKiFurqvv4axo85x190pqFjK0xywB2Lcv18WtJGXYlzP+iA2ZtSWl86+fW+V8OQLSfrUtVhLVRIOrbdf7/UlPJBOd6zeSWhofIu1TnD6XT8+PEMs51OgYGBBAcHp7kopXzU2LGwYIEUt5s7V3p+K3UVGzbAE487mE0PGrJVMs8//TTXz+csaZM+AcRZ0mZpRHQWn6kKknyx7zUyEiZNct22WKRSQ6FC0g1hxgw4dkyqgDz+uBQg9UFunZKoXr06oaGh/PrrrzRu3BiAS5cu8ccffzB27Fh3nkop5W2rV8s6KMCECdCsmbnjUX7hyBEY0DmKaYkv05UFGAEBWObPhypVcvV8VytpY0FK2rSvF+p/s1bK7fx23+vp0zB0qBSjNQxpkVS7ttw3bpwc99HAMjM5DjbPnTtHZGRkyu39+/ezZcsWSpcuTZUqVRg8eDCjR4+mVq1a1KpVi9GjR1O0aFEefvhhtw5cKeVlzZpB376QnCwflbqK2FiY1mIG64/1xXo5PLQ8+ii0bJnr58xJSZuCsNdRXZ1f7Xu122W28rXXpGQDQPv2skfeqXp1c8aWBzkONjdu3Ejbtm1Tbjv3Wz722GPMnDmTl19+mYsXLzJw4EDOnDnDjTfeyLJlyyhRooT7Rq2U8r7AQJg8Wf4YKp/mC4kzly5B/zuj+CqqX0qgCcDMmTB8eK6LtmtJG5VvrV8PTz0FGzfK7fr1ZRWpdWtzx+UGOQ4227Rpg2FkXXHfYrEwfPhwhg8fnpdxKaV8xbx5cPfd0qsaXB+VT/KFxBnDkO1jx/7agw1H2jvtdtmHlstgs0CVtFEFR0KC/J09dkw6sL31FgwcKN3Z8gFNI1VKZW36dFky79gRfv4ZrG7NKVRu5iu9oIcOha++girWWhiGFYuRKuC02aQZQC75ZEkbux3++ksKiBYqJAl0hQvLxwYNpAUnwPnzUqamcGFZKahZE4oU8d44lW+x2+VvqsUCQUHwzjuwYoUkYobmrSyYr9H/HEqpzG3YIEs6ALfcooGmj/OVXtCTJsGkMWe4nV8YPj0cy7SpaWfFp0zJU99zn2vl+McfEhi0bi2/L/37Q+/eUr3+gQdkZcBp1y4pW9OsGVx/vVRzeOAB+PZbaa2kCo6//oKmTeG771zHevWCWbPyXaAJOrOplMrMiRNw772y8a5LFxgyxKun94U9h/7GFxJnFiyAF55KYCldaGX5C6vtc+jdBzp0kKXzmjXzFGg6OUvapN8uEOrp7QInT8oMf7lycMcdcqx2bUnkKFVKOmlZrZCUJL87SUlpu7nYbHDNNXI8Ph7OnnUV5g4MlHJQffp4ZuzKNxw7Bi+/DF98IbffflvecGRRizy/0GBTKZVWcjJ07w6HD8O118o7bS/OavrCnkNvcHdAbXbizLp18MhDdr40HuFW/sQIDoHLJfAID3dLkJma10ra7NsnUfSCBfDnn9LYoF07V7AZGgp//w2NGl19f13DhrB3r1w3DEkE+fFHqVm7Zw/Uq+d67IYNcv899+TLma4CacUK+dt67Jjc7tMHxozJ94EmaLCplErvjTfg99+haFH5RxgS4rVT+8qeQ0/zREBtZuLMnj3Q+S6DsQmDuJcfXbU0GzRw+7lS82hJmxUr4MUXYdOmtMcbNZJgM7Xc1Jy1WOTzmjWD0aNh+3aoW9d1//TpMHWqLM3fdJPMfj3xhPxeFnB+t/LhcEhQ+eabcr1+fSlv1Ly52SPzGotxpdRyE8TFxRESEkJsbKx2E1LK244ehVq1pKbbt9/Cgw967dR2h0GrscuzXAp2Jn6sfqWdb/9juYqsAmrnV5TbgNr5+l0tccbdr9/x45djob2jGc1QDIsFy5w50jrPXzkcsp9u82ZZ+r71VmkDePfdUK2ad8YwdSp89pnMmjpVqgQjR0LPngW2KoRfrnz88Qe0aSPXe/eWckb54E1DTuI13fGvlHKpWBHWrJFsSC8GmpCzPYf+ypNJPGYkzpw/D3fdBa32zmQ0Q+VcH3/sn4GmYbhqyFqtMG0aPPkkxMTA8uUwaJD3Ak2Afv1kb8Lhw/Dxx3LuI0ekplT79jLeAsZv25S2bg2vvCJvHj77LF8EmjmlwaZSKq2GDWUDu5eZvefQGzwdUHuzF3RyMjz0kGwtbBH0rxwcMgSeecZt5/Caw4clEW7kSNexG26Q1PqyZc0bF8he10GDYOdOeO89KFlSxloA9vml5ivVFrLFMGD8eFkpcnrnHZnVLKB0z6ZSChYtkiQEE/udF4Ri3d4IqL2ROGMYspXwp5+kPGDD3z+A07fBnXe67RxeYbdLQPnqq3DunGsG0xd7TgcGwgsvSHmc1B35FiyA+fMlUHZzEpYv8YVqC9ly5ox8jxYuhB9+kJ+pQhpq6cymUgVddLTsAWvZUpIiTOIs1p1VSGRB9mZ5tVi3m3kroHYmznRpVImWNcq4PdD88IUozkz9jurs45tvoOVNFllP96fZtm3bpFTRM89IoHnTTbI/0hcDzdTKlJFi8SB7S195RVqAXnutVNOPizN1eJ7iFysfGzZAkyYSaAYEwCOPFNi9telpsKlUQWYYUoT67FnJsr3lFtOG4nPFuj3A3wNqhwO+6zCDZz+sync8yF5q0PXIp2YPK2cSEiQruHFj2RNZooTUt/zzT7juOrNHlzNWq5Qma9UKLl6UrPaaNeXrSUoye3Ru5dMrH4YhST833wwHDkgt1bVr5W+rP70B8yANNpUqyGbPliX0gACZHTF5ucebew7N4M8BdXIyvPhQFPf92i+l37kF4NlnISrK1LHlSHS07H1MSpK9j9u3Sw9qf+2QdeONsGqVdCq69lppyPD007LndMsWs0fnNj77Ri0+XjYvP/OM/Ex16yblspo08e44fJxuJFCqoDp6VPanAQwbJrXffIDXinWbxLTuN3mQkCD/T4MX/J4SaKaw26U7kL/sF6xeXbK7S5eWwCA/zDxZLFKa6c47JYv+zTfhv/9g/35ZscgHnG/UBszehAXSJAqZ/kYtIkLeqL/3nvxNzQ8/U26mdTaVKogMQ2oG/vST1BNcu9b0Wc2Cxl8KU8fFSRwTt2Ijv3A7ZTiT9gE2mywd+nKwOXu2vJnKJ4HXVR0/DnPmpK0McOFCvii545N1NnfvlpalLVuac36T5CRe02BTqYJoyRJptxcQIEs+/rZXTXnFiRPQqRME/7OcBXShBOek13dUlMxo2mwwZYpv9/P+4APJ4q5QQX7WK1Y0e0TeFxMjy7pPPy1lzfz8jaWpb9Tsdpk5LlVKOkwVYDmJ1/z7J04plTsdOsDEiZCYqIGmytThw1I7fNcuaF2yDEWTrNDiNtkbGBsrS+c1a/rujKZhSHb2mDFy++GHC26P8S++kL2qQ4fK92/WrLR92P2MR9uUXsmpU/JztGyZvNHq2lV+B9RV6cymUipX/GUZWOXczp1w++0ScFauDL/+CrUTt0Lt2lLv0dfZ7TBggOxfBMnSHjKk4O6lMwz46itZVj97VlY0Ro6UGV8tzZM9mzbBvffKlpGiRaV3fffuZo/KVLqMrpTK3Nq1snctdVHoXPDJfVPKLTZuhE4dDfqdGs2BKq15Z3UrKlc2e1Q5kJgo9Q3nzpUM80mTpPWjkqTAvn1h8WK53aKFVKGoXdvUYfm8WbOkdWlCAtSoAT/+CNdfb/aoTKe90ZVSGR09Kvs0r78e9u3L9dP4bX9idVUrVsBtbewMP/U0o3idL2M7UznwuNnDypm33pJAMyAAvvtOA83UKlaUpMDPPoPgYKkzOmGC2aPybc89Jx2BEhLk7+eGDRpo5oIGm0oVBIYh/3TPnpVez1Wq5Opp/Ko/scqRpdOjeO/2X/jyfFeeYiKGxYJ11NtQvrzZQ8uZIUOgXTuZvbv3XrNH43ssFunRHREhH517WkH+Tqi0atSQj8OHS03iUqVMHY6/0mV0pQqCWbPk3Xkes8/X7j1F92nrrvq4b/q2MLc/scq2Cxfg524z6PaLq1i7YbNh+eorePBBk0eXTadPSxDg3JNpGAV3f2ZuORxSp/PWW+Gll/w+Yz1Pzp+HYsXkumHA5s1apD0Tmo2ulHI5ckS6vIC8O89D9rkv9Sc+c0b2F65fD5Erowg4tIdzobWwVA6nXDmZwC1XLu2lbFmJSTzVLMbfkqaWLYPhT0Tx5+F+aYq1WwxDWu/5gx07JJvpyScl2xo00MyNn3+GpUvl8sMPstTesKHZo/KuixddGfv//itbDSwWDTTdQINNpfIzZ+/z2Fho1kxmLPLArP7EiYnyt3/9evj7b/m4e7fc9zgzmI4ES/bdVvoxlY/Iuu6jzQYNSkXRvtoeqt9eixvvDadRo7wHoP6UNHXiBDz/vNQ6b8OejF2BHA7/6AoUEQFt2khJmq++kv11+aBwuSnuuktKJD37rKx+NG0Kr70mwVdAgNmj87x16+Cxx1x/WObPh549TR1SfqLL6ErlZ199BT16yD+LzZvzXFvP7jBoNXY5MbEJme7btCBtF1e/0i5PM3rJyZLjsXq1BJdbtkjb4dSCieWxCr/w8bGHsKQajWGxMObJQ+xNDOfECagW+RtRccHsjS3LvnPleIA5TKW/BKdIcDq/dB/atIHbbpPLtdfmbHLMmTSV/jVxPoWv9HU3DPjySwk0405dItkSwBu9oxg+syoWR6qA0x+6Ah0+LB1bjhyRN1KLF8vUtcqbmBjpFT9vntyuXx8+/1yCz/woIUHa9b73nrzJqlhRyhp16mT2yHyelj5SSgln//MmTWSWwg2cgRVk3p84r4HVsmUyQRW7PYpa7GEPtYgmjNJlbTRvDjc3vsCzMxtR7MierJ9kxQqZ8TIMCbSTk1PuMlKNFSAZG9U4wBFcgVWlSq7As127K8dczgA8fXa+k7sC8Lzat09Wmtf9GscohtK66AYSfvuL5i1tMGOGzIB7oCuQR7YWnDkDt9wC27ZB3bryrqR0abeMVyG/N99/Lx2HTpyQ5fRNmzy3/8QsGzfKbOb27XL70Ufh4481CSibNNhUSqXlcLj1H4Unlox375Ya0z/9BE8ykU95GisGBnCp1nUE7IpwzTZWqwYHD0oUGBWV9omsVtd9Fy5IUHLihFwSMg8It01YwfwzrQn+4hO+2d+S9cmNsV/eZVSJKG6rvIdad9Ti1ofDuemmtLkTvp40lZwsHRuHD4fbL87nU56mEkfkzqVLpZsUyOvo5q5AHtlakJAgY161Smah1q7NdXUFdRUnT8LgwfKGtXlzs0fjfg89JD3ky5eHqVOhSxezR+RXNNhUqqA7c8bj787dNWMVGyvNTMaPB0dSMi9aPmCM8QoZnunQIVKqi//7rwREZcrkbFZuzx6oU0eCbyfnkvHFi7J+DiQXLUFk2C0cOV2UNmd+zLDkfscdcPfdEvOs2HeEZ7/dctWv8+OHGtGlUaWcvjx5snGj1PA+sSWKT3iGe5gvd9SoIa/Tbbd57Nwe21rw449S0ig4GP78U2seets778DevfD661C1qtmjybnUlQpOnJCvY9Qo3YKRCxpsKlWQXbgg/4CbNZOCzWV8swSR3S5x4uuvy9/8//Er04sPpuq57Zl/gnNpPDM5mZXLKjiNiJDB/PGH1CPNRPol98KFoVHzS0QW2UPRmscoFHIxy9N6a2YzLk4mLFfOjmL3op20YC2v8C4liMcoVAjLyy/L11mkSK6ePztvMjy+teDzz2V2u23bnH+uyr3oaKheXTL2ChWSOp2vvSbfC1+XlCSB8u7dsnFZ5ZkGm0oVZK++Kn9UK1WSvUg++Hu0cqWszv37r9yuUwfmtvuUehOfhpIlZboz9Z8mdyesXCk4tdth61bpqz1pUoZP3frxCpZvDCbo57nMPt2JdbRIWXIvXC6OGpX/pW7wVg5fE8KJcqW8smczJgYWLpQE2t9/hx6XZjD1coZ+yh7VFi1kqbBBg1yfJ7vL4h7ZWpCcXLBrP/qKv/6SPRm//Sa3CxWSGr6vvSaBqK9JToYFC2T2cvNmObZqlWyvUXmiwaZSBdXWrZIMZLdL5OFje5D275fqS3PnQhUOcm3xaDqPasGAAVCYJMkIffJJWSr1UMJKtkVFyTJhZkvuEyemdF5JKFKSFUHt+fbMHZTmDO/xYsqy+4Ain/BV1a50v7M4Pe4KpkkT98X+u3bJt3jBAqnaEmhcpD2/8gizuZ+5WFOXM7Ja5cXPw97GnCyLL9ji5q0FX34Jn3wiG3r9raNRfvXXXzBiBPz6q9wuVEiaRzz8sLnjcjp9WrLKP/1UtuCAbC2aMAG6d9darG6gwaZSBZHdDjfdJEUou3WTiM5HGAZMeSOKeeP2cDipPL2ZxWDbeKyVw7Ht2p55HT8PJKzkWFZL7osXS5HKpUtlf2wWZNl9P0eQvaYWC9SuLVVknJfateX1SU52Xez2tLdTLgei2LFwD1+tr8Ufe8MJ4Sx38RP3MI87rEsp4riQ9ddypW0IV5HTZXG3zmwuWyadbZKTJcAfMiQXX4HymDVrJOhcuVL2cjp/V92clJgjW7bI38KLl7e1lC0rb2KffhoqVDBnTPmQBptKFUSffCJZo8HB0lWlYkWzRwRIIPVDJ1c7xDSlh9q2lVqgYebXoMzS1Zbc16+X4HPOHElASmd/jXYYp86wIakxq883YguN+JeGxBNMJVzlnVKXXsrM47iWxu1Y2Ukdalt2U8hwlXWiShVJ+pk1K/MZ2VwG7TkNHt1Wj3XTJmjdGs6dk9mo2bPzX/md/OLgwbQJQ926QUiILK/XquXZczscUturZk25bbfL9ZAQKVLfvTsEubfRhNJ2lUoVPIcPu+pojh3rM4GmwwFv9I7irVR9t1NCi5kzpUOHry9nhYdnHaTZbFJYvGVLmQHNZNm9elIknD3ENWwmdafxswHlCLl0Agtgx8qTlqnUtuwm1HKMQMuly5dEArlEceK44dLfKcXrbTiox3YsBtJ+9J575NK4sbyeN9+ccUY2D7PDOW1TarNaGNa5HgNmb8JC5vVYh3Wud+VAc98+uOMOCTTbtZOkIA00fVfqQHP3bldR+Jkz4ZprXL8nLVtKAqM79t/GxcnPxSefSD/zgwdllcRmkxnX0FDf//tSQGiwqVR+cPiwvIu//nro18/s0QCy6vnEExD7xfqM7RBB/jnlp38E4eGSgJM+yGvXThITtmyRy+bNEBVFyUsnUj7VhoNp1v7yz/HIkWydzgKyl7FHj4x39ukjdZnctA0hN21KO9YPY1KPJhkSikKzU2fz5Eno2BGOHZOC4vPmQWBgrsevvOzaa2Uj8YgRstVk3z65fPWV3P/00xIggmSJx8ZmXnrIMOTifJOxcaNkwkVFyWXdOoiPl/tKlpQi/40by21fXi0pgHQZXan8Ii5OSvb4QIHrS5ckBvr+e6hmOcg+o1raupn+0A4xt7Kz13T+fJmJTG/QIJmVDgiQ4Mr5MT4ennnGrUvjOZGXZfFc1WPt2lUyn6pWlRkqH5mpV7kQGys9Z9eulcu6dRJoPvqo3L9mjczE16olFROsVnnz7Awof/rJVeJq+nQpHJta3brye/Poo1CsmHe/tgJOl9GVKoiCg32izNHFi3D//fDzzxIrffBtVSzHJ8NTT7ltWdenXWnZ3alpU/mnmj54fOmlrD83MNCtS+M5kZdlcZvVkvP6oh98ILOan3+ugaa/CwmB22+XC8jPvN3uut/ZKnLPnkz3PKfpENa4MQwY4Podcwao+WmFJJ/SmU2l/NmQIbJk1bu3T/zBPXdOqi0VW76Qe2wLqbhoKh06XV4C84Xscl+Sm37kJr+GHmk/mZXUnV5U/nb6tMx+btgg71CdwWR4uHQN0y0UPkmz0ZUqCFavdhUm3rgRbrjB1OGcPSv5HLXXfs40+lIIuxRGf+IJU8fl0/wwAHdXm9IMvvlGZsHuuCPvz6WU8jhdRlcqv0tMdCUCPfGE6YHmyZOySva/zeMYxytysFcvuaisZWfJ3cfkaln8ataskZ+V5GRpF9qqlXufXyllKq0joZQ/GjtWamlWqADjxpk6lKNHoc2tDrpvfskVaL70Enz2mbYXVFd36JAkS126JHswbrrJ7BEppdxM/xMo5W927JA+vwAffywt2EwStS6Kod12MCx6CvdzuWPRuHESbCp1NefOwd13w/HjUuLoiy+0lqZS+ZAGm0r5E4dDls8vXZK9bQ88YNpQTo2bQdgr/Zh1uSuQYbFg+ewzXTpX2eNwSLmaf/+VGfqFC6F4cbNHpZTyAA02lfIna9bAX39JPbmJE03L1k3cG0XJV9J1BbJY4H//M2U8yg+98YbUGw0IkKLtPlAfVinlGbpeoZQ/adVKgs3p09O2h/OySYN3ZewK5HBIZrVSV2MYcOqUXJ8xQ1oYKqXyLZ3ZVMrfOPsLm+SLL4CfFmJAxq5ANWuaMyjlXywWmDQJevbUhCClCgCd2VTKHyxaBLt2mT0K/v0Xljwxl8GMl0DTmcyR37sCKfc4cULKG4EEnBpoKlUgaLCplK87fBgeeQQaNYJ//jFtGGfPwqt3/ce0pMcAMAY/BwcPwooV0qP7at1vVMF2/rwUY73zTvlhUkoVGLqMrpQvMwzJPo+Pl6XzRo1MGYbDAU93P8WEqC4U5zyXWv+PgHfHSR1Nnc1UV+NwyJL5li1QvjzExkLJkmaPSinlJTqzqZQv++ILWLpUegN/9pksV5vg3THJ9F76ANewn8SK1QmY+60WbFfZN2wY/PijK/PcxOQ2pZT3abCplK86ehQGD5brI0ZAnTqmDOP33yH+jbHcxnKSAosRuHQBlHFzu0KVf335Jbz9tlyfOlX3aSpVAOnUhFK+yDBgwADZ29a0KbzwginDiIqC7t0hyRjIA5VW0+CjJ6BBA1PGovzQ8uWuvbwvvwyPPWbueJRSptBgUylf9NNP0lGlcGHTeoxfugT33y8JxI0alaLWX4uxFDWniLxZ7A6D9ftPczw+gfIlgmhevTQ2a8F6DXItMVG6SSUlwYMPwpgxZo9IKWUSDTaV8kUdO8LIkRJkmjSTOPzJGOquW8zOkN7MnWuhSAELNJdGRDNi0XaiYxNSjoWFBDGscz061g8zcWR+IjBQSnaNGQMzZ2rPc6UKMIthGIbZg0gtLi6OkJAQYmNjCQ4ONns4ShVI385KpHKvdtzMGnb2GEmdL183e0hetTQimgGzN5H+j6Mz3J7Uo4kGnEqpAi0n8Zq+1VTKl0REyPq1mUP4z+Bin6e5mTVcDCpJnTcfNHU83mZ3GIxYtD1DoAmkHBuxaDt2h0+9T/cNSUlSE/avv8weiVLKh2iwqZSvOHUK/vc/uOEGKZZugvgdUfxz63P0tk/HjpWAH76BWrVMGYtZ1u8/nWbpPD0DiI5NYP3+094blD8wDBg4EL7+Gu6+W2rDKqUUGmwq5TsGD4Zjx6QAdmio988/YwbF6lXlsbMfA5B01z3Y7uzo/XGY7Hh81oFmbh5XYIweDdOny97MmTOhRAmzR6SU8hEabCrlC376CWbPln/Un30myRXeFBWF0bcfVhwph4KWzJfaRwVM+RJBbn1cgTB7Nrx+eV/vJ59A587mjkcp5VM02FTKbGfPQv/+cv355+HGG70+hLh/9mAxHGkP2u0QGen1sZitefXShIUEkVXuvQXJSm9evbQ3h4XdYbB27ykWbDnC2r2nfGfP6PLl8Pjjcv3ll2UpXSmlUtHSR0qZyTCgb1/pFlSrFrz1linDePPLWryPFVuqmU1sNqhZ05TxmMlmtTCscz0GzN6EBdIkCjkD0GGd63m13qbPlmHatQu6ddNamkqpK9KZTaXMNG0a/PCDFG+fPRuKFPH6EBYvho/nhtOfqRjWy73XbTaYMgXCw70+Hl/QsX4Yk3o0ITQk7VJ5aEiQ18seOcswpU9aiolNYMDsTSyNiPbaWDKoUgXat4dWrbSWplIqSzqzqZSZ7rhD/lF36wbNm3v99HGxBpEPvUFNHqPE4D5YXuggS+c1axbYQNOpY/0w2tcLNbWD0NXKMFmQMkzt64Wa09moSBGYMwfOn4cg3cOqlMqcBptKmSk8HFaskJlEE8zrOotB8aN4zPophV4+CGHhBT7ITM1mtdCyRhnTzp+TMkxeG+e5czLr/dxzMpNptWrmuVLqinTNQylvMwz45x/X7UKFwOL9Wam1cw7RdeWzAJzsM4RiYdqxy9f4XBmms2fh9tvhxRclGUgppbJBg02lvG3mTGjaFF56ybQhXDjnwOjdmxDi2FuhJTUmvWjaWFTWfKoM0/Hj0LYtrF0LpUrB/fd7/pxKqXxBl9GV8qbt2+Gpp+R6GfOWZ3/pMpF7Li7noqUI5RfP8vgyvt1hmLr30V85yzDFxCZkum/TgiQtebwMU1SUJALt3AkVKsCyZXD99Z49p1Iq39BgUylvuXABHngALl6UpUiTliH//WEPHZbLuff2G0f9Jp5tR+mzZXv8gE+UYdq7V9qoHjgAlSvDb7/Btdd67nxKqXxHl9GV8pZBg2DbNmlF+cUXXikTk74Q+IWLBrv7vUtRLrKtQjvqT/RsAW6fLtvjJ0wtw5SY6Ao0a9aE1as10FRK5ZjObCrlDV99BTNmSCLQV1/JUqSHZTajmLyhLsfOfEpk0Sr0X9rTowGvz5ft8SOmlWEKDIQPPoCRI6Uga2ioZ8+nlMqXNNhUytOOH4cnn5Trb7wB7dp5/JTOGcXUgd6l4yWIXlkNsBI/4ilKNyrl0TH4ZNkeP+bVMkzJyVIlAeCee+Duu00rz6WU8n+6jK6Up5UvL7Oad98Nb77p8dNlNqNYKCmZB39YR2FHMkVrxbD80iaP99b2ubI9KnuWLYP69eHgQdcxDTSVUnmgwaZS3vDAA7BggVf+aWc2o9jvh1/4MP4VFlvuoFT7/4iJkxlFT/Kpsj0qe+bNg86dpef5O++YPRqlVD6hwaZSnrJyJcTEeP206WcKb9m8lRcOTQHg60YdKFTiUqaPczdn2Z6sdhVakKx0j5ftUdkze7bUzrx0Ce67Dz7+2OwRKaXyCQ02lfKE/fuha1do2FBqE3pR6pnChzf9zBfLXsOGAwMoWyEq08d5grNsD5Ah4PRa2R51dXFxUvv10UfBbodeveCbbyAgwOyRKaXyCQ02lXK3+Hi4916IjYUaNeTiRc4ZxbC4k7z96+SUwM4CjP5lAmFxJzOdUUxfJskdezq9UrbHMCSgX7ky7fFTp+R7kJyc93PkV5GRcN11MHGi3H7+edlfXEhzR5VS7qN/UZRyp8REyd7dvBnKlpUZosKFvToE54zi74N+xpqu8FAhw0HVs0fpNfD2NDOKniy87vayPQkJsHEj/PWXXNaskcAyPBwOH3Y97s474e+/5XpgIBQrBsWLy8cSJWD5crlekFWrJmW4AgJg2jSvVEpQShU8Gmwq5S52O/TsCb//LkHNkiVQtaopQ+lYP4wqm//KcNxusdL/8dtpmyqAzKxMErgKr7tjBtJtZXsefhh++AGSktIeDwqCxo3THktItSc1MVEupy8nRdWsmTbQfPBBOHcObr5ZLs2aQdGieR+vrzEMSQK64w55zQoVgrlzoVy5/Pn1KqV8ggabSrmDYcCzz8J338lM5rx50LSpacNZvRp6n53NdzxAQ+tWrA4HhtWGZfJk2v7vhpTH+Wzh9T174N13Yf16mcV0LusGBUmgWaGCKzC8+WYJNNPvMdy8WQLM8+clkDx/3nW9eHHX4+x2eWMQHy+Fy0HO16SJPPdtt8ksqb87fBgGDICff4ahQ+Htt+W4SW+IlFIFhwabSrnD+fOwbp10CPryS2nxZ5LkZBg4ECKpxcQnNjNtWBRERmKpWRNLeHiax/pc4fWTJ+Gtt2DSJNdey61bJfADeO01CZSuuUZeayRgznSJ3mKR4DQoCMpcYewWi8xGO5fl//oLoqMl0F2/HiIi0gab27ZB3bpeaTfqFg4HTJkCr7wiAXVAQNpgWymlPEyDTaXcoXhxWLFCgpauXc0bh2Hw9dDt/PffdZQuDWPGAGXDZT9jJnym8PrFizB+PIweLdnRIEu9Tz0FtWu7HlezZppPc8teU6tVls2bNYPBg2WW+uBBV+CZenn++HFo0EAK9XfqBHfdBe3bQ3BwLr9wD9u1C/r2hT//lNs33QTTp0uwrJRSXqLBplJ5cegQVKki10uUMDfQBE5P/o4e47pzksGUeOcDypa98uN9ovD60aPQsqW8lgCNGsF778ny9RV4bK+pxSKJM9WqwSOPpL1v2zZ5Y3HsGMycKZfCheGWWyTwvPde18+D2Vavlhn2xETZn/rOOzLl7S8zskqpfEP/6iiVWytXwrXXyj9xw7OtH7PlzBmszw3CikFwpWD69Ln6p/hE4fWwMAnQwsPhiy/gn3+uGmheba8pyF5Tt7fkbNtWlvp/+w2eew5q1ZI9pMuXS9mgFStcjz16VIJTh8O9Y8jM2bPw7bfwyy+uYzVqSKDZsaOM4+mnNdBUSplC//IolRtbtkCXLvLPfP16nwg2jzzyMiUTj7ODOjSd+2q24gpTCq/v2CEzhmfPXj6RBb76CnbvlsLi2Rh4Tvaaul1AgATDH3wgY969Gz78UI516uR63KxZ0mO8ZEmZYRw6FBYulFlRdzhwAD75RJ67XDno3l1mhJ3CwmR2c/FiTQJSSplKl9GVyqm9e2W2KC4OWreGr782fcbo0q9/UGnJdAB+uXcag28MzPbnOguvp9/7GOqmOpspjh+HYcOknqPdDpUqwbhxcl8Ol559Zq8pyOzm4MFySe38eSknFB8ve3l//911X7VqMhtavbrc/u8/qRV6OekJiyXt9Ztucv2MjRolVQ+2bk17vrp1oUWLtMduvtkNX6BSSuWNBptK5cSxY9Chg3xs2BAWLJBs5zzIMps6uxISiH+4H2WAWUX603tGqxyPwe2F19P77z+Z9TtyRG536UK21vmz4BN7Ta/m7bdh+HBZwl63TgrM//23zOzGxKRN2ho6FBYtyvq5kpJcweaff0qgabVCq1byWnbuLEGvUkr5IA02lcquuDgJmPbulRmpJUsgJCRPT+mObOqzL4+mzMndHCWMIh+9k+shua3wenorVkjiVFwc1KkjZXhuvTVPT+ncaxoTm5Dpvk0LMjPr0b2m2VGokLwpadgQ+veXY7GxkiWeurNU5coyM+ncjmEYrkt6zz0n2xDuuOPKJZ2UUspHWAzDBzabpRIXF0dISAixsbEE+2o5EVUwffmldAgqX15K4qQrw5NTWWVTO+cSs5tN/VGTL+i5eTAfXzeN4f/dm7L66hMWL5ZAMylJMrYXLIBSpdzy1M7XD0jzGub09VNKKZVzOYnXNEFIqex69FGZlVuyJM+BpruyqRctguc296S2bS8PzunmW4EmwA03yHLxfffBsmVuCzTBtdc0NCTtUnloSJAGmkop5UPcvoyenJzM8OHD+eqrr4iJiSEsLIxevXrx+uuvY9WyG8rfrF0rySuVKsntfv3c8rTu6Nxz4ZyDQYPkd+rxF0pR7zq3DC3vDMOV3FKhgswCV6jgkSQqj+81VUoplWduDzbHjh3L5MmTmTVrFtdddx0bN26kd+/ehISE8Oyzz7r7dEp5zmefSS/phg3hjz+gSBG3PXWes6mPHCG+0e1cf3I09spdeOMNtw0tbxIS4LHHpL1jz55yLMyzM4we22uqlFLKLdwebK5du5YuXbpw5+VewtWqVeObb75h48aNmT4+MTGRxMTElNtxzlZ1SpklORleeEHaJ4IsA9vtbj1FnrKpo6K40LU7FU5u51XGcPSDzhQv7gOrBmfOyP7MVavg558lmapcObNHpZRSymRu/w/VqlUrfv/9d3bv3g3Av//+y+rVq7njjjsyffyYMWMICQlJuVSuXNndQ1Iq+06dkhqazkBz+HD44QdpUehGue7cM2MGRpUqFP1nNQYQWbMT99zrA4HmoUNShmfVKukTvmiRBppKKaUAD2SjG4bBa6+9xtixY7HZbNjtdkaNGsWrr76a6eMzm9msXLmyZqMr79u2De6+G/btk17SX3wB3bp57HQ5zqaOipJOMKnaHxpWG5aDB9LWbPS2rVtlFvPoUdnbumQJNGhg3niUUkp5nKnZ6HPmzGH27Nl8/fXXbNq0iVmzZvHee+8xa9asTB8fGBhIcHBwmotSXmcYUgdx3z7p7rJmjUcDTchFNvWePRn6bFscdoiM9Og4r2j5cilpdPQoXHedJFRpoKmUUioVt+/ZfOmllxgyZAgPPfQQAA0aNODgwYOMGTOGxx57zN2nU8o9LBapo/nSSzB5MpQt65XT5iib+vjxDIcMmw1LHssw5cmff0qx9ltvhfnz3VraSCmlVP7g9mDzwoULGUoc2Ww2HOlmZJQy3fnz8Ntv0u4PpCvQDz94fRjZzabe+M0amgIOLFgxSLZYGddlME3O2uho1ir6m29KtnnPnnlu26mUUip/cnuw2blzZ0aNGkWVKlW47rrr2Lx5Mx988AGPP/64u0+lVO44HPDdd/D667JsvnAh3HWX2aO6op//jabb3yNoSyeOVQ+idou1HChZkWPBZWH2Ju8WMY+Lg6JFpRWjxeK22qNKKaXyJ7cnCMXHx/PGG28wb948jh8/TsWKFenevTtvvvkmAQEBV/18bVepPMYw4NdfYcgQ2LxZjoWFSeDZqpW5Y7sCu8OgZtfdHFhUG0tgEpWe+ANbcVdSnbMP+OpX2nm+mPmlS9Chg8xifvttnnvDK6WU8k85idfcPrNZokQJPvroIz766CN3P7VSubdhgwSZy5fL7RIl4OWXYfBgt5c1cqtLlzjQczCXlr4CQKlbd6UJNCF73YbcwjDg6adh5Up5zaKiNNhUSil1VW4PNpXyOcnJcP/9cPAgBATAwIEwdKjXkoDyZNw4asyZxEp+5frQdRRvdDDLh2a3K1GuffwxTJsmS+fffivZ50oppdRVaLCp8qeYGAkmCxWSy1tvwe+/w4gRUtrIH+zYgeOtkViBYQynZIftWK5QrCy7XYlyZfFi6aoE8N570o5SKaWUygYfaD2ilBvFxsqsZY0aUpTdqWdPmDXLfwJNux177z5Yky7xE3eyomUrgkIzb+WaZbchd9m2DR56SBKrnngCnnvOM+dRSimVL2mwqfxfbKwk+fTsKcHk6NFw4YJ0svFXEydi+3stcZRgRIVJTPggECBDe0vn7WGd63kmOcjhgO7dIT4eWreGTz+VZXSllFIqm3QZXfm3rl3h559lX6ZT3boScDrrZ/qbgwdxDHkVK/AKYxnyaWXubQHFijdhxKLtRMe69maGhgQxrHM9z5U9slplhvj55+H772XPq1JKKZUDGmwq/5CUBKtXw19/SX1MJ5tNAs06daRW5p13SvtEm828seaRMeItrBfOs4pbONypf0rXzBx1G3KnRo1cWfxKKaVUDrm9zmZeaZ1NRUIC7N8Pe/dK3++1a2HpUikmDrBrF1x7rVzfvl1m28xs2ehm30w/z5G+w/gioC8LdtamenUTBjF5MjRsCC1bmnBypZRSvs7UOptKZUt8vASTzoCyRw+oVEnu+/BDeO21jJ9TrlzGLOh69Tw/Vi86cwaefa0YJ3iP0cMxJ9BctEjKQxUuDFu3Qu3aJgxCKaVUfqHBpnIfw5DZx+hoKT1Uv76rluUvv8AHH8jx6Gg4cSLt59ar5wo2a9aUouE1a0pW+XXXQadO0Ly57CHMj6Ki4KuvGLe1OydOVKFuXVelIa/auhUefli+l48/7ppBVkoppXJJg02Ve5s3wzffwJYtsGePBJIJqQqLz5/vStI5cwaWLUv7+WXLSjBZs2baAuvdusF99xWcrOcZM6BvXzAMRjOEk0zl0cl9vZ+Lc+6cvPbnzkG7djB+fMH5HiillPIYDTbVlV24AP/9JwHl5s0y29W8udy3cye8+27GzwkJgdDQtMduuglmzpTjoaFSoiirVod+nNyTY1FR0K+fzCQipYwmWwZgu6YTEO7dsTz3nGxrqFxZMs8LF/bu+ZVSSuVLGmyqtAwDVqyQwHDjRknGcThc99es6Qo2W7SQvX2NGskyeMWKUKECFC2a8XmrVIHHHvPGV+Bfdu9O+/oCNsMu+1jDvRhsLlwI06fLTOYXX0BpDxWIV0opVeBosKnS+vVX6NAh7bHy5aFxY7ncfLPrePXqUuRb5d6//2Y8ZrN5P7t+7lz5+Pzz0KaNd8+tlFIqX9Ngs6Dbvl3KDDmzvG+7DRo0gFatoHNnmbUM81DB8IIuMhLjjTewAA4sWDEwbDYsU6Z4d1YTZCa7fXvZK6uUUkq5kQabBVFysiybfvqpFOuuUAEOHZJ6lTab7M/Mr1nfvsIwoHdvLOfPs4I2PBk0k9+n7Se8TU3vB5ogy+c9enj/vEoppfI9jSgKkuPHYdQoWf6+914JNK1WKdx9+rTrcRpoep7FwoEXJ/CXpRWP8iWD3qtKeI823g009+6FAQNcxfKVUkopD9CZzYJi3Dh44w24dEluly0r5XaefFKSd5RXJSfDg6Mbst74k/btJebz+gAefVS6M507B19+6eUBKKWUKih0CquguP12WSpt3lyyjQ8fhtGjNdD0tpMnYcMG3nkH1q+X6k+ffWbCZPK4cRJoBgfD2297+eRKKaUKEp3ZzM/273f1O2zUSJZNnV16lPdd7spjLFnCAcdUoDcTJpiwRXPTJhg2TK5PmABVq3p5AEoppQoSndnMjxIT4ZlnoE4d2LDBdVwDTXNNmgSLFpFkt7LB0YR774VHHvHyGC5elESg5GTJPNekIKWUUh6mM5v5zf798MADUpAdYNUqaNbM3DEpiIhIaXb+kjGOmPIN+W2SCd0ghwyBHTuknNXkydqOUimllMdpsJmfLFgAvXrB2bPSAeaLL1z1M5V5Ll6E7t0hIYHFdGI8g1gwDcqV8/I4zpyBOXPk+uefQ5kyXh6AUkqpgkiDzfwgKUlmrD74QG63aCFBhSb/+IaXX4aICE7YKtDLPpPevS3cfbcJ4yhVCrZuhUWLMnaJUkoppTzEYhiGYfYgUouLiyMkJITY2FiCg4PNHo5/mDVLZjRB2g2OGSMF2pX51qxJafHZgaXsqtqBrVslCVwppZTyVzmJ13RmMz949FH47Tcp1N61q9mjKfDsDoMtayJI2LGDoDq1Cez7IYumHWMZHVj+uQmB5g8/gN0ODz7o5RMrpZRSGmz6r9WrZbm8UCEp0qhFuX3C0ohoNg17n1fmfYDNMLBbrAwI+JRpjGHwYGjb1ssDioqCJ56A2Fj5Wbn3Xi8PQCmlVEGnpY/80S+/QJs2cPfdknyifMLSiGhGTFyWEmgC2AwHExOfplrJXbR5JNq7AzIMGDhQAs3mzaFLF++eXymllEKDTf+zebPUR7TbJZs4KMjsESlk6XzEou1UO3M0JdB0KoSdJs2X8c6v27E7vLhF+ocfJBmocGHJPi+kCxlKKaW8T4NNf3LwINxxh/Syvu02mDFD6yR6id1hsHbvKRZsOcLavacyBI3r958mOjaB4onnSB9OJmPlSI1gomMTWL//tHcGfOaMFPYHePVVqFfPO+dVSiml0tGpDn9x+jR06gQxMdCgAcydqxnnXrI0IpoRi7YTHZuQciwsJIhhnevRsX4YAMfjE7jmVBTjlnyCBXAg7+SSsfFah6eICS6b8jivePllOHZMuki99pp3zqmUUkplQoNNf5CQIFnmO3ZIy8nFiyEkxOxRFQhLI6IZMHtThtnKmNgEBszexKQeTehYP4xKCbHM+n4YpRLi2Vi0Id0vfEe49TBxD5zmVNWiKZ9XvoQXtj3s3AnTp8v1adMgMNDz51RKKaWyoMGmP9i2TfZqBgfDkiUQHm72iAoE5z7MzHZZGoAFGLFoO+2rFOeGpx7FEnuMfUWr0OnCr5ykHLF3x1O0qsxkWoDQkCCaVy/t+YHXqQPLlsHatdCqlefPp5RSSl2BBpv+4IYbpMd5bKwsoSuvcO7DzIoBRMcmsHXDThqfPMmF4mW4/ZwEmiVv3UnR2jGABJoAwzrXw2b10h7b9u3lopRSSplMg01fFh8PJUrI9caNzR1LAZTd/ZWHylQkePZa+twZw16upWyjaIq22Jtyf2i6/Z0es2ePVCeoXNmz51FKKaVyQINNX/XDD/DUU7BggRRvV153tf2VlWKPcySkPEGOItzxRGl2x1ekRQv47fdQtka34Hh8AuVLyNK5x2c07Xbo2RMiImDOHKlaoJRSSvkALX3ki1avhh494PhxCRyUKZpXL01YSBCZhYkP/LuM5dP60WPfWsa9XIrdu2VCcf58KFbUQssaZejSqBIta5TxztL5pEmwbp2UwmrY0PPnU0oppbJJg01fs3OndHpJTJSP771n9ogKLJvVwrDOUp8ydbjYZu9GRv8ygUB7MtdHJLL8dwvFikn99AoVTBjo4cNSSxPgnXekYoFSSinlIzTY9CUxMVJL8/RpuPFG+PprsNnMHlWB1rF+GJN6NCE0JIjQuJM8vHkxE+ePoZDhYF39h3hwxzgsFvlWmTKhaBiy3eLcObjpJnjySRMGoZRSSmVN92z6iuRkqaV54ADUrCnTZEWLXu2zlBd0rB/G7Wt/xvJ6fywOBwDxVerRZtsswMI770ibelPMnetqSTl1Klj1/aNSSinfosGmr5gwAf7+G0qWlFqa5cqZPSLlFBWF9cn+cDnQBChyaBdlOU77XuG89JJJ40rdknLIELjuOpMGopRSSmVNg01f8fjjUrz91ltlZlP5jj170gSaAIWwc0/9SN6bHG5ee/rAQMlAX7xYW1IqpZTyWRbDMDJrkGKauLg4QkJCiI2NJTg42OzhKAVRUVC1apqAMxkbsVsOUKahD3RzunQJAgLMHoVSSqkCJCfxmm7wMts//0iSh/ItDgd88gmcPw/h4RhTpmK3SLJWMjaOjZhiXqB56ZLU1XTSQFMppZQP02DTTJs2SdZ5x45w8aLZo1FOcXGSrDVoEPTujT3Z4NmtfahqHKCdZQWrZh2g0pt9zBvfyJFw883w33/mjUEppZTKJt2zaZbERNlvZ7dDSAgUKWL2iBTAvn2SWr5tGwQGktjhbro/YGHePIBwXpsQTrueJo4vIkJqaSYnw+7d0KCBiYNRSimlrk6DTbOMGCEBTfnyMHGi2aNRACtWwH33SZ3TsDDOfD6fO4Y3Z906ycX58ku4/34Tx+dwQN++Emh26QLdupk4GKWUUip7dBndDH//DWPHyvXJk6FsWXPHU9AZhgT87dtLoNmsGfu/30jzpyXQLFUKfvvN5EATXC0pS5SQUlmmpcErpZRS2aczm9528SI89pjMUj3yCNxzj9kjKriioqSsUdmyMHy4bGl45BH+fmIad3UtwsmTUK2alD2tU8cHxupsSTlmDIT7QBa8UkoplQ0abHrbG2/Arl0QFgbjx5s9Gp9mdxis33+a4/EJlC8RRPPqpbFZ3TSbN2MG9OsnQb/VCi+/DKVKMb/WS3TvZCEhAW64AX76CUJD3XPKXHO2pIyPh5YtYcAAkweklFJKZZ8Gm952330Swbz/PpQubfZofNbSiGhGLNpOdGxCyrGwkCCGda5Hx/pheXvy3btl76Oz5JTDAe++y2dvHuCJey0YBtx5J3z7LRQvnrdTuUVcHBw9Ki0pp03TlpRKKaX8ihZ1N0NSkgQOKlNLI6IZMHsT6X8wnXOak3o0yV3AmZAge2RHjICzZzPc3YYV/EEb+veXLZGFfOmtmN0ue31vusnskSillFJa1N0nnTjhuq6BZpbsDoMRi7ZnCDSBlGMjFm3H7sjBe6RLlyS5pmZNeO65TAPNZGxEUpPRo+WhPhVoAthsGmgqpZTySxpsesOKFdLu8L33suwWZHcYrN17igVbjrB276mcBVP5yPr9p9MsnadnANGxCazffzrDfZm+hn/8AbVrw8CBcOQIVK4sS9FTpmDYXB2BBtqmMHZ2OK++6kNJ3n/+CUOHyoysUkop5ad8bf4m/4mPh8cflyz0PXsyjWQ8uj/RzxyPz15glf5xztfQOBxF9TNH2V+qIpbK4Yy9PohbDx+WLJ+hQ6FvXxyFA/nyS/ik7B0UPxbJ8RI1+XRBOG3beuIryqWEBNlXumuX3B41ytzxKKWUUrmkwaanvfgiHDggNXTeey/D3VntT4yJTWDA7E2535+Yikezut2sfImgHD/O+Ro+vOlnRv46GSsGdouF1zo8w2Oxt/P9hC9o2rMrFC3KH3/A889Lp1AIp0aNcObPh/r1PfHV5MHo0RJohobCSy+ZPRqllFIq1zTY9KTly2HqVLn+2WdSjDuVq+1PtCD7E9vXC811cOhvs6bNq5cmLCSImNiETF8XCxAaIgEzdjv2DRs5MGwq30es4YajO1OSiGyGwahfJrCqehOeORPOzKgivDqEy20nITgYXn8dnnkGgrIX33rPtm3SkhLgk0+gZElTh6OUUkrlhe7Z9JTkZBg0SK4PHEhma7R52Z+YHc4Zv/TncM6aLo2IztXzepLNamFY53rA5cAy7iQtD24lNO5kSiA5rHM9bBM/hbJlsbVswZPLPqNpqkDTqZDhIPz4MbbNq079+hJoWq1SpjIyUiYMfS7QdDik/mdSEnTuDPfea/aIlFJKqTzRmU1PmTpVZqhKl4aRIzN9SG73J2ZHXmZNPb7s7uzcU6tWpp1wOtYPY1KPJvw3dAzPL5qAzTAwgOm39aTyR+/IjOy/peDsWZKKB/N7xevYWqEmL6yejS1VAlYyVv7++T7iE66R5+0oOxmuu859X4rbTZ4Ma9ZIgc9PP/WhbCWllFIqdzTY9JTz5yEwEN56K8vi7bnZn5hdOZk1bVmjTMrxXC27XyV4TCN9554PP3TNAG/dCm++CQcP0vHAATqmKlFkAZ5Y/iWWkpcTZe68E9avZ2NIVZ78bAMAJ4uVYvQvEyhkOEjGRn+mcDjhGgqXiWfsOIPnHnfVAfPJfayJifD223J9zBjJnFdKKaX8nAabnvLSS/DAA1CpUpYPydH+xBzKzaxprpKV0gePU6ZAr16uQpVRUTB7NkRHy9r14sWuz3U4YPBg6NZNgtSkJFiwIMuxWgxDniM8XPYxNmtGc4dBWEgQR2LsfGbrzY8V+xB+5DSR1CS6aDlKt/qPWrecYFAv1zYGn93HGhgIa9fKjKa2pFRKKZVPaLDpSVWrXvFu5/7EAbM3YYE0QV6a/Ym5mHHL6axpjpfdHQ5YuTJj28e+fWH/flepnuPH4dVXsx5A6gCyVi2pqF6lCgQEQIcO8pxONpsUZr9s/35YsMDChXmtOLyxMBhWTgF7bXaCmx4gvOVKrIHJDO/aJOU19Eb2f55UrQrjxpl3fqWUUsrNNNh0t5dfhnvugZYts/Vw5/7E9DNtoXmcacvprGn6ZffQuJMp9SpjgsuC4XAtu5+LgtatITY285Pv3u26XqUK9OwJFStCkSIwfHjawvapA8jgYHjySdd9U6dC//7SqtFmw5g8hU3HwlkwVSZAt251PjAQgCIVzlH4mmiKX3+YwiUvXp6tvD7lNfRG9n+uxMbC5s3Qpo33zqmUUkp5iQab7rR4Mbz7Lnz8MRw6BBUqZOvTOtYPo329ULfuIczprGnq5fQH/l3GmF8+SUnMOV6sFAvrtWZUuyfkcTVrSLH6oKCM3W1sNtlv6FS2LMya5bpdqVKaAJIpU7Le59mnDxdv7UDE/EjmR9TkixHhREW57rZa4ZZboEsXuVStVoz1+0tzPL5opq9hbvexetwzz8CXX0ogPmyY986rlFJKeYEGm+6SlCTVwkESXrIZaDrZrBa3Bzg5mTUtXyIIDINuEcsZu3R8SkBqASqcP0OLQ1tdjyteHP77D669VgLJ9MFjqqXuDPr0keXxyEh53OVA8+RJ2LkTduxwXXbuhIMHwzEMVzBarJh8epcukiNUJs1LduXX0JPZ/7n2/fcSaFqt0L69986rlFJKeYkGm+7y6afS8aVcOakW7iOyO2vavGpJFn3zMg0O78j0ecbf1J2w1MlK9aQWZlbBY2aSk+HgQdizJ5wdO8LZ+Y0rsDx5MuuvISwM7rpLAszbbst9bUxPZv/nypEjEqgDvPYa3HSTd86rlFJKeZEGm+5w8iSMGCHXR42CkBBzx5NOlrOmFy5A0aLymEI2SrS+mXNz9lM0KSFNtf9ki5WI0FpZJyuFh6cEmXa77CDYs0cukZGu6/v2ScCZlSpVoG5dudSp47perlwevvhUPJn9n2MOh2TtnzkDTZtKySellFIqH9Jg0x3efBPOnoWGDeHxx80eTeZS18IsXBjGj4eJE+Gnn+DmmwGo9tE7/DbgBda/P52X530o9SotVsbd8xzDBt6eIVkpORk2boRly+SjM6C8dCnrYQQGygRo7dquYLJuXVmRL17cky+AZ7P/c+yTT+C33yRpavZs+Z4opZRS+ZDFMIzMJnlMExcXR0hICLGxsQQHB1/9E8y2YwfUr+8qBdS6tdkjyih1LUyLRfZWOqcYn3xSyg2lYncYbFkTwcWdOylSpw6NbqqfEoDt2yfB5a+/wu+/Z56QHhAANWpIXFurlgSXzuvh4bI90Uym19k8ckReoMRE2X4xcKDnz6mUUkq5UU7iNQ0288rhkCSZjRslcPA1UVFSuzF1vUqARo1kRrZLlytGf2fPwvLlElwuWybBZmolS8L//icxdu3aElBWrizxbGZ8pXOP6eP4/nup3/Tll9qSUimllN/RYFO5LF8uWTWZHW/bNuNx4MQJmexcuhT+/jttnFqokOSxtG8Pt98ON9yQdWCZnukzikoppZRyi5zEa7pnM7cSE2Upulgxs0dyZddeKzNn6Qup16qV4aGxsfD++9Ku/Nw51/HatSWwbN9e6o6XKJHzYfh85x5v2LxZitvnsCyWUkop5c9M3j3nxz7+WKKw+fPNHklGhiEp4SCbJKdNc00/ZlJI/cIF6ZBYvTqMHCmB5g03wPTpUqpo507JJ+rcOXeB5tU694B07rE7fGqS3b1iY6FrV2jQAP75x+zRKKWUUl6jM5u5cewYvP22dNE5e9bs0aQVHy8ldf76S4KaSpWyrIV56ZIElCNHQkyMfHrduvKl3XOP+7YS+mznHm965hl5A3DNNTLbrJRSShUQGmzmxtChEtQ1bSp9v33Fzp0SJe7cKaV0NmyQYBMy1ML8+mvpjLh/v9xdrZqUCn3kkezvwcwun+zc403ffefqEjR7du6mh5VSSik/pcFmTm3eDJ99Jtc//tj8Oj5O8+dL4BsfL/sC586FFi3SPMQw5GGvvw7bt8uxChXgjTegb18pWeQJPte5x5uOHJHyUiBdglq2NHc8SimllJdpsJkThgHPPScfu3c3v71gVJTMYi5YABMmyLFbb5WZtHRJKH/9JUPfsEFulyoFr7wCTz/t+Rwnn+rc403aJUgppZTSYDNHFi+GP/6Q5txjx5o7ltSF2p0GD5ZMn3TdaD7/XB7qTJ5/7jl44QWpkekNPtW5x5tmzNAuQUoppQo8DTZzYuVK+ThokFQuN0tUVMZA02qVCDJVQGMYMpn29tty+4EHJKvcjMo7HeuHMalHkwx1NkPzc53Nhx6Cdesktb92bbNHo5RSSplCi7rn1Jo1krJdqpR5Y/j1Vyl8md6KFVIIEykD2qcPfPWV3DV0KLz1lvlbTE3v3GMGw9AuQUoppfIVLeruSWbv00xIkAyfzAq116wJwOnTkpS+apWrrGafPiaNNx2b1ZJ/yxsBJCXBzJnygjsjew00lVJKFWA+kkrt4377TZauzeZwwOOPw/r1EBiYaaH2ffskHl61CoKDYckS3wk08z3DgIEDZYtDr15mj0YppZTyCTqzeTWxsbL37vx5ieCaNTNvLG++Cd98Iw3Kf/pJ9gGmKtS+bh3cfbf0Nq9cGX7+WRrWKC95912pkm+xwH33mT0apZRSyidosHk1770Hp05BnTrQuLF545gxA0aNkuvTpsFtt8n1y4Xa586FHj1klb1JE1i0SMptelqB3IOZmR9+kFpSAB99JFG/UkoppTTYvKKYGPjgA7k+apTMKJrh11+hf3+5/sYbaZZoDQM+/BBefFGu33knfPstFC/u+WEtjYjOkF0elp+zy7Oybh08+qhcf+YZqVaglFJKKUD3bF7ZyJFw4QLceKNk3Jjh+HFZkrXbZepyxIiUu5KTJbZ54QXXdsH5870XaA6YvSlDz/OY2AQGzN7E0ohozw/CF+zbJ7OYCQlw110S+SullFIqhQabWYmMhKlT5fo775iXUVy+vAQw//ufaz8gEgPfcw98+qkcev99aSLkjclXu8NgxKLtmXYDch4bsWg7dodPVdXyjB07IC5Otlh88437G8srpZRSfk6Dzay88YZMHXbsmFK70jSPPw7LlkkGOjKL+fjjkiMUFCTbBZ9/3nvx8Pr9pzPMaKZmANGxCazff9o7AzLTnXdKsf9Fi7wzpayUUkr5GY8Em0eOHKFHjx6UKVOGokWL0qhRI/755x9PnMozDAOqVoWiRWHMGO+fPzkZXn1V0sqdUkWS774Lc+bILOaSJdCtm3eHdzw+60AzN4/zO4YhSWNOLVpApUrmjUcppZTyYW4PNs+cOcPNN99M4cKFWbJkCdu3b+f999+npLcacbuDxSJL50eOQKNG3j23YUiCyTvvQLt2slczlV9+kTgU4OOPzZl0LV8iyK2P8zujR8P118OWLWaPRCmllPJ5bt/hN3bsWCpXrsznn3+ecqxatWruPo13eDtAjoqSrPfJkyXgHTEizR7AvXul5KfUdjdodPtpFmzxfsmh5tVLExYSRExsQqb7Ni1Iz/Pm1Ut7ZTxe9c030sEJ4O+/vf9mRCmllPIzbp/ZXLhwIU2bNuX++++nfPnyNG7cmGnTpmX5+MTEROLi4tJcTONM6V671vvnnjEDqlSRQBPg/vvTrI+fOwddu8LZs1D7+ktEVFvBw9PX8ey3W+g+bR2txi73Wga4zWphWOd6gASWqTlvD+tcL//V21y92lV26oUXXOWolFJKKZUltweb+/btY9KkSdSqVYtffvmFJ598kkGDBvHFF19k+vgxY8YQEhKScqlcubK7h5R9P/wAkybB7bdL5yBviYqSFoepe53PnZvSItMwoHdviIiAUmXtnG+1imPnL6Z5Cm+XHOpYP4xJPZoQGpJ2qTw0JIhJPZrkvzqbW7ZItH/pkpQBGDfO7BEppZRSfsFiGIZb69MEBATQtGlT1qxZk3Js0KBBbNiwgbWZzBgmJiaSmJiYcjsuLo7KlSsTGxtLcHCwO4d2ZUlJUK+elDwaPhyGDfPeuZcvd3UESm3FCmjThjFj4LXXoHBhg2sf/4dzJY9l+jTO5evVr7Tz2qxigeggNHcu9Owp9aaaNZPs86JFzR6VUkopZZq4uDhCQkKyFa+5fc9mWFgY9erVS3Osbt26zJ07N9PHBwYGEni5pI+pZsyQQLNcOakj5E2ZfZNsNqhZk8WLYehQOfTcsPPMic880IS0JYda1ijjmbGmH6bV4rVzmcIw5GfjwgWZ8Z4zRwNNpZRSKgfcvox+8803s2vXrjTHdu/eTdWqVd19Kvc5f97VmeeNN6BECe+ev2lTqc5uvfztsNlgyhT2XAzn4Ycl3unfH266M3tL+/m25JAZLBb4+mtJ3Pr5Z+8njSmllFJ+zu3B5nPPPce6desYPXo0kZGRfP3110ydOpWnnnrK3adyn48+kj7o1au7NenD7jBYu/cUC7YcYe3eU1fuqDNwIBw8KEvnBw4Q/0AfunaVraM33QTjx2vJIa+JioKxY117aEuWlH0M3mjPpJRSSuUzbv/v2axZM+bNm8err77KW2+9RfXq1fnoo4945JFH3H0q9zh1ypXs8fbbEBDglqddGhHNiEXb03TaCQsJYljneq7kmZkzIT4ennpKZjXDwyE8HIcDet4L27dDxYqStxQQUMBLDnnL339LIlBMDISEwJNPmj0ipZRSyq+5PUEor3Ky4dQtkpPhiy9g3jxYsMC1lJ0HSyOiGTB7U4aA0Jk2M6lHEzqWuAT160tNo6+/hu7dUx43ciS8+aYEmKtWwY03ZnxuIM3zp3nu/JYJ7i2zZ8MTT0BiIjRoAAsXgr/WiFVKKaU8KCfxmvZGL1RIGo0vWuSWQNPuMBixaHumM4/OYyMWbsPo84QEmjffDA88kPKYRYtcifCTJqUNNKEAlhzyBocDhgyBRx+VQLNLF/jrLw00lVJKKTfQTWhutn7/6TRL5+kZQNtV87H8/hsUKQKff57SJWjXLujRQ7YKPvWUxMCZ6Vg/jPb1QvN/ySFviI+HRx6RKB9kb+bIkW5546GUUkopDTbd7mqZ4OGxx3htxWdyY/RoqFULkFrh990HcXFwyy3w4YdXPk++LznkLRs3SpZ5YCB89hk8/LDZI1JKKaXyFQ023eyKmeCGwTtLxlP80kXimrYgeNCglLvee086BJUrB99/D4ULe2GwBdWJE/JCA7RtKy1CGzaE5s3NHZdSSimVD+laoZs5M8YzW9BuEBNJi0P/kVA4kGJffZGyVLt3r6zcAnzwAVSo4L3xFij79kHfvlCpEmza5Dret68GmkoppZSHaLDpZjarhWGdpYNS+oAzIqwWXXt+wK63P8B2rSyfG4aU2ExIkI6Vvlohyq9FRsoG2GuvhenTpTXpwoVmj0oppZQqEDTY9IArZYw//eIDNHx5YMqxOXNg2TLZMjhpkjSsUW6ye7f0NK9dWxKx7Hbo0EEyzYcPN3t0SimlVIGgezY9JHXGuG3+jwTWqU39TrekyRg/exYGD5brQ4em5Aopd7Db4X//g8OH5fadd0or0vS1pJRSSinlURpsepDNaqHl8d3w+iApHv/XX2n2Br76Khw7JhNvL79s4kD9nWHAnj2wejXccQeEhko5qZdegt9+kyCzaVOzR6mUUkoVSLqM7knTp0tj84QECTb//TflrrVrJQkaYMoUWUZX2XTpEqxbB++/D/fcIxlVtWtDnz7w+++uxz39tHSF0kBTKaWUMo3ObHpKVBT065f22IAB0KkTSRXC6d9fDvXuDa1be394fsUwXJtZV6yQ2cuEdPVMAwOhWTMoVsx1TDfAKqWUUqbTYNNTtm6VICk1ux0iI/nw63D++w/KlIFx48wZnk+5cAF+/RWio9NeYmLk48CB0tkHoE4dCTTLlJFWn61ayccbbtDpYaWUUsoHabDpKcuWZTxms3E4sGZKIvT770PZsl4dlfckJUmV+iNHXJeoKNf1bt3grbfksXFx0LVr1s/155+u62FhkmVes6bOXCqllFJ+QINNTzh8GKZOletWKzgcYLNhTJ7Ck2+Hc/EitGkjVXn82qVL0u5xxQqZyb3lFtknCXDqFDRpkvXn1q/vul6unGSJV6ggwWRYmCT5OK9XrZr2czVtXymllPIbGmx6QoUK0vd85Ur45BNpEVSzJnPXhbN4MQQE+GlNTbsdNmyQ4HLlSsn+vnDBdb9huILN8uWhYkV5LcLDpWtP6kvNmq7Ps9kk4UcppZRS+Y7FMNJvLDRXXFwcISEhxMbGEhwcbPZw3CY2FurWlS2Ib74JI0aYPaJsSE6WAVeuLLcTE6FkybTJOWXKyDRtixYyk9munRkjVUoppZQX5SRe05lNdzIMCdAKF85w1+uvS9xWq5bU1/RpK1dKk/aVK6FKFdl7CZKA07mzfI1t20qQed11KT3elVJKKaXS02DTnX74QaLKDz+U8jyXrV8Pn34q1ydPhqCgLD7fbKtWwbBhEmQ6HT0K8fFQooTc/u47U4amlFJKKf+kU1LukpAAr7wimdIbNqQcTk6G/v1l0vPRR310lfmff+C226Tg58qVsql04EA5fuKEK9BUSimllMohndl0l/HjYf9+SYp58cU0h7dsgVKl4L33zBveFR09CsuXy/J/nz5S09K5T1MppZRSKg802MwBu8Ng/f7THI9PoHyJIJpXL43NaoHjx2HUKHnQmDEpXWwOH5ZkIIB335UEbZ/w999w6BDcf7/cvusuGDlSpl7TlxlSSimllMoDDTazaWlENCMWbSc61pWJHRYSxLDO9ej46VtSmPyGG6BHj5T733gDzp+XJje9e5sx6nQ2bJA9mUuWyFRrhw4QHCw1mF5/3ezRKaWUUiof0mAzG5ZGRDNg9ibS14iKiU3ggw/n0WHmVCwgGdyXM7O3bYMvv5THpTpsjvPnZePoV1/JbZtNOvYkJEiwqZRSSinlIRpsXoXdYTBi0fYMgSaAAdy9YxUWhwPjnm5Ybr015b7XX5fGQd26QbNmXhtuRocPQ5cusHmzRLyPPiqDS11UXSmllFLKQzTYvIr1+0+nWTpP771berCpYm2eHtgZZ3PGv/+G+fMltnv7ba8MM3NnzkDz5hATIy0h586VlpJKKaWUUl6ipY+u4nh81oEmABYLy2s253DpMEBKHA0ZInc99ph0DTJNqVLwxBNw/fWyX1MDTaWUUkp5mQabV1G+ROYV2JtGbaPkxbgMj/v1V1epyuHDvTDA9Ox2OH3adXvECFizRrPMlVJKKWUKDTavonn10oSFBEkC0GXBCeeY8uMo/pjSl3rH9xEWImWQHA4pUQlSE71KFS8PNi4O7r4bOnaEixflmNWaUopJKaWUUsrbNNi8CpvVwrDO9QCwAKFxJ3n7l08pczGOE8VKsadMFYZ1rofNamHuXGm6U7y4K+j0mshIaNECFi+G//6DTZu8PACllFJKqYw02MyGjvXDmNSjCX33rOCvyb25e+efAPxTpxmfPNacjvXDSE52lap84QXJx/Ga5cvhxhthxw6oVAlWr4abb/biAJRSSimlMmcxDCOzqj6miYuLIyQkhNjYWIJ9qQZkVBRG1apYHI6UQ4bNhuXAAQgPZ/p06NsXypaFvXu9WL5y4kQYNEj2ajZvLmnwYWFeOrlSSimlCqKcxGs6s5lde/akCTQBLHY7REZy8aLk4QAMHerFQPOdd+CppyTQ7NED/vhDA02llFJK+RQNNrOrVq2Mx2w2qFmTiRMhKgoqV4Ynn/TimB58UBqujx0LX3wBQZlnziullFJKmUWLumdXhQpSp/JP2a+JzQZTphBbIpzRo+XQiBFejveqV4fduyEkxIsnVUoppZTKPg02s6twYVi1SjK9T52Sdo/h4bz/ppS1rFNHOkF63E8/QdGi0K6d3NZAUymllFI+TIPNnGrQIOXqsWPwwQdyfdQoKOTpV3PTJlk6v3QJVqyAVq08fEKllFJKqbzRPZtXYxjwyisyo5nO6NFw/jw0awb33OPhcRw5Ap07w4ULMqt5440ePqFSSimlVN5psHk1ixbBuHFw000QH59y+MABmDRJro8ZAxZL5p/uFufOSaB59CjUqwfffSfL+koppZRSPk6DzStxOOCNN+T6009DiRIpdw0fDklJcNttcvEYux0eeQQ2b5ZK8T/9pPs0lVJKKeU3NNi8ku+/h61bpXDmSy+lHI6IkEpDILOaHvXyy7BwIQQGwoIFkoGulFJKKeUnNNjMSnIyvPmmXH/hBShdOuWu11+XrZzdusl+TY9xOODECbk+axa0bOnBkymllFJKuZ+2q8zKzJnQuzeUKQP79qW0BVq3TmI+q1VmOOvW9fA4DEN6nd9yi4dPpJRSSimVPdquMq8uXXL1n3zllTT9J197TT4+9pgHA82jR2WvJkjmkQaaSimllPJTGmxmxjAkIahBA+k9ftnq1VLesnBhGDbMQ+c+fhxuvhnuu0/qKimllFJK+TENNjMTGCj7NP/9V7r1XPb22/KxVy+oWtUD5714Ebp0kbpK//0nt5VSSiml/JgGm1eSqnjm+vXwyy/SEn3IEA+dr39/2RRasiT8/DOULeuhEymllFJKeYcGm6nFx0PbtvDjj7KUnsqoUfLxkUfgmms8cO4ff4Qvv5Ro9scfoXZtD5xEKaWUUsq7tDd6auPHw8qV0hry7rtTmp3/+6+UurRYXAlCbnXqFAwYINdfeUUCXqWUUkqpfEBnNp3OnIF335XrI0akBJrgmtV84AEPTTgOHiyJQfXquWp7KqWUUkrlAxpsOr3/PsTGQv368OCDKYd37IAffpDrQ4d66NxPPil1lD7/XJKTlFJKKaXyCV1GB9iyRYJNgJEjpWL7ZaNHy/bNrl2lEpJH3HyzZJ/bbB46gVJKKaWUOXRmc8YMaNIEEhLk9smTKXft3Qtffy3XX3/dA+c+ftx1XQNNpZRSSuVDBTvYjIqCfv3SZp4/+aQcB8aMkfbknTrBDTe4+dxLlkC1avDhh25+YqWUUkop31Gwg809eySaTM1uh8hIDh2CWbPkkNtnNWNjJci9eBEOHXLzkyullFJK+Y6CHWzWqpVmfyYgy9k1azJ2LCQnQ7t2cNNNbj7vSy/J7GmNGq5Ud6WUUkqpfKhgB5vh4TB1qmu/pM0GU6Zw1BrOjBlyyO2zmr/9BtOmyfUZM9K0w1RKKaWUym80G71PH+jQASIjoWZNCA/n/RcgMVGSxNu0ceO54uPhiSfk+lNPQevWbnxypZRSSinfo8EmyAxneDgAJ07A5Mly+PXX07RHz7shQ+DgQUkMeucdNz6xUkoppZRvKtjL6Jn48EO4cAGaNpUJT7cxDKhYEQICYPp0KF7cjU+ulFJKKeWbLIaRuu6P+eLi4ggJCSE2Npbg4GCvnvv0aZl0jI+H+fOhSxcPnOToUQk6lVJKKaX8VE7iNZ3ZTOWTTyTQbNAAOnd24xOnLq+kgaZSSimlChANNi+Li4OPPpLrr7+esSJSrv31l1SE/+cfNz2hUkoppZT/KPDBpt1hsHbvKZ5+PZazZ6F2bYN773XTk1+8CI8/Lr3XJ05005MqpZRSSvmPAp2NvjQimhGLtnPkRBJHprcFIPn67fy6ozQd64fl/QTvvQe7d8vS+fvv5/35lFJKKaX8TIGd2VwaEc2A2ZuIjk3g3L9VcFwMpFDIBZKrHWTA7E0sjYjO2wliYmDsWLn+wQdQsmSex6yUUkop5W8KZLBpdxiMWLQdAzCSrcStvwaA4BaRYJXk/BGLtmN35CFR/8034fx5uPFGeOABN4xaKaWUUsr/FMhgc/3+00THJgBwbmtl7OeCsJW4SPEGUQAYQHRsAuv3n87dCSIiSOl3+f77bq4Mr5RSSinlPwrkns3j8Qkp1wuXOUdAxTMUq3cEi83I8nE5Mn26lDvq1k16XiqllFJKFVAFMtgsXyIo5XpQ1VOE9lgj05lXeFyOfPCBtCC68cZcjlAppZRSKn8okMFm8+qlCQsJIiY2AYPLq9ypVrotQGhIEM2rl87dCaxW6NHDDSNVSimllPJvBXLPps1qYVjnekCaGDPN7WGd62Gz5nCv5ZYtkhSklFJKKaWAAhpsAnSsH8akHk0IDUm7VB4aEsSkHk1yXmfzwgW4806oVQv++8+NI1VKKaWU8l8FchndqWP9MNrXC2X9/tMcj0+gfAlZOs/xjCbIPs2jR6FaNQk4lVJKKaVUwQ42QZbUW9Yok7cniYmBd96R62PGQFAuE4uUUkoppfKZ/7d390FR1Xscxz+L8qBcIDMVSEFyCsY0R1EDH5sslDQtm9RyCO1hqtGSdCappgv3znilJ7tTZqaDD92abAp0nLGb4ghooUaJRWroDVJmlBydBNQREX73Dy7cFncXUQ7L7r5fMzuznv39fnzPl6/nfD3unvXZ/0bvUJmZTe/VHD1amj3b3dEAAAB0GTSbN+rwYWnt2qbnb7/NDdwBAAD+hGbzRr38ctMN3B9+WBo/3t3RAAAAdCk0mzeirk76y18kf///v2cTAAAALXz+A0I3JDBQ2rRJOnFCiopydzQAAABdDlc2OwKNJgAAgEM0m9fj4kXphRek48fdHQkAAECXRrN5Pf75T2nlSmny5KYPBwEAAMAhms32+v33phu3S9Jf/yr5kUIAAABn6JTa629/k86fl0aOlObMcXc0AAAAXRrNZntUVNjfwJ2rmgAAAC7RLbXHP/4hXbki3X+/NHGiu6MBAADo8mg2r1VFhbRhQ9PzjAy3hgIAAOApuKn7terVS3rllabvQh871t3RAAAAeATLr2wuX75cNptNaWlpVv8oa910k/T3v0tffunuSAAAADyGpc1mcXGx1qxZo7vuusvKHwMAAIAuyrJm8/z585o7d67Wrl2rXr16OR1XV1enmpoau0eXUlEh3XOPtHOnuyMBAADwOJY1mwsWLNDUqVN13333uRy3fPlyhYWFtTwGDBhgVUjXZ9kyqbBQeustd0cCAADgcSxpNjdt2qQDBw5oefM37bjwyiuvqLq6uuVRWVlpRUjXp7xc2rix6XlmpltDAQAA8EQd/mn0yspKLVq0SDt27FBQUFCb4wMDAxUYGNjRYXSMZcua7qs5ebKUmOjuaAAAADyOzRhjOnLBLVu26OGHH1a3bt1atjU0NMhms8nPz091dXV2r7VWU1OjsLAwVVdXKzQ0tCNDa5/ycumOO6SGBqmoiGYTAADgf9rTr3X4lc1JkyaptLTUbtv8+fMVFxenpUuXumw0u5Rly5oaTa5qAgAAXLcObzZDQkI0ZMgQu23BwcHq3bv3Vdu7rIoK3qsJAADQAfgGIUeiopqazaIiKSHB3dEAAAB4rA5/z+aN6jLv2QQAAIBD7enXLP+6So/T0ODuCAAAALwGzeaf/fqrNGiQ9MEHUte64AsAAOCRaDb/bNky6fhxads2yWZzdzQAAAAej2az2X/+I338cdPzjAz3xgIAAOAlaDabNd9XMzlZuvtud0cDAADgFWg2paarmv/6V9NzrmoCAAB0GJpNiauaAAAAFqHZPHXq/1c1+bYgAACADsU3CEVESHv3Sv/+tzR6tLujAQAA8Co0m5I0alTTAwAAAB2K/0YHAACAZWg2AQAAYBmaTQAAAFiGZhMAAACWodkEAACAZWg2AQAAYBmaTQAAAFiGZhMAAACWodkEAACAZWg2AQAAYBmaTQAAAFiGZhMAAACWodkEAACAZWg2AQAAYBmaTQAAAFiGZhMAAACWodkEAACAZWg2AQAAYJnu7g6gNWOMJKmmpsbNkQAAAMCR5j6tuW9zpcs1m7W1tZKkAQMGuDkSAAAAuFJbW6uwsDCXY2zmWlrSTtTY2KiTJ08qJCRENputU35mTU2NBgwYoMrKSoWGhnbKz/QE5MU5cuMYeXGMvDhHbhwjL86RG8c6Oy/GGNXW1ioyMlJ+fq7fldnlrmz6+fmpf//+bvnZoaGhFK4D5MU5cuMYeXGMvDhHbhwjL86RG8c6My9tXdFsxgeEAAAAYBmaTQAAAFiGZlNSYGCgMjIyFBgY6O5QuhTy4hy5cYy8OEZenCM3jpEX58iNY105L13uA0IAAADwHlzZBAAAgGVoNgEAAGAZmk0AAABYhmYTAAAAlqHZBAAAgGV8otlctWqVYmJiFBQUpPj4eO3Zs8fl+MLCQsXHxysoKEi33XabVq9e3UmRdp7ly5dr1KhRCgkJUd++ffXQQw+prKzM5ZyCggLZbLarHr/88ksnRd05MjMzr9rH8PBwl3N8oWYGDhzo8Pe/YMECh+O9uV52796tBx98UJGRkbLZbNqyZYvd68YYZWZmKjIyUj169NA999yjQ4cOtbluTk6OBg8erMDAQA0ePFibN2+2aA+s4Sov9fX1Wrp0qYYOHarg4GBFRkbqiSee0MmTJ12uuWHDBod1dOnSJYv3puO0VS/z5s27av8SEhLaXNfT60VqOzeOfvc2m01vvfWW0zW9oWau5RztSccZr282P//8c6Wlpem1115TSUmJxo8fr+TkZJ04ccLh+IqKCj3wwAMaP368SkpK9Oqrr+rFF19UTk5OJ0durcLCQi1YsED79u1TXl6erly5oqSkJF24cKHNuWVlZTp16lTL4/bbb++EiDvXnXfeabePpaWlTsf6Ss0UFxfb5SQvL0+S9Oijj7qc5431cuHCBQ0bNkwrV650+Pqbb76pFStWaOXKlSouLlZ4eLjuv/9+1dbWOl1z7969mj17tlJSUvTjjz8qJSVFs2bN0v79+63ajQ7nKi8XL17UgQMH9Prrr+vAgQPKzc3V0aNHNX369DbXDQ0NtauhU6dOKSgoyIpdsERb9SJJU6ZMsdu/r776yuWa3lAvUtu5af17X7dunWw2mx555BGX63p6zVzLOdqjjjPGy40ePdo899xzdtvi4uJMenq6w/Evv/yyiYuLs9v27LPPmoSEBMti7ApOnz5tJJnCwkKnY/Lz840k88cff3ReYG6QkZFhhg0bds3jfbVmFi1aZAYNGmQaGxsdvu4r9SLJbN68ueXPjY2NJjw83GRlZbVsu3TpkgkLCzOrV692us6sWbPMlClT7LZNnjzZzJkzp8Nj7gyt8+LId999ZySZ48ePOx2zfv16ExYW1rHBuZGjvKSmppoZM2a0ax1vqxdjrq1mZsyYYe69916XY7ytZoy5+hztaccZr76yefnyZf3www9KSkqy256UlKSioiKHc/bu3XvV+MmTJ+v7779XfX29ZbG6W3V1tSTp5ptvbnPs8OHDFRERoUmTJik/P9/q0Nzi2LFjioyMVExMjObMmaPy8nKnY32xZi5fvqxPPvlETz75pGw2m8uxvlAvf1ZRUaGqqiq7mggMDNTEiROdHnck53Xkao6nq66uls1m00033eRy3Pnz5xUdHa3+/ftr2rRpKikp6ZwAO1FBQYH69u2rO+64Q88884xOnz7tcrwv1svvv/+ubdu26amnnmpzrLfVTOtztKcdZ7y62Txz5owaGhrUr18/u+39+vVTVVWVwzlVVVUOx1+5ckVnzpyxLFZ3MsZo8eLFGjdunIYMGeJ0XEREhNasWaOcnBzl5uYqNjZWkyZN0u7duzsxWuvdfffd+vjjj7V9+3atXbtWVVVVGjNmjM6ePetwvC/WzJYtW3Tu3DnNmzfP6RhfqZfWmo8t7TnuNM9r7xxPdunSJaWnp+vxxx9XaGio03FxcXHasGGDtm7dqs8++0xBQUEaO3asjh071onRWis5OVmffvqpdu3apXfeeUfFxcW69957VVdX53SOr9WLJG3cuFEhISGaOXOmy3HeVjOOztGedpzpbunqXUTrKy/GGJdXYxyNd7TdWyxcuFA//fSTvvnmG5fjYmNjFRsb2/LnxMREVVZW6u2339aECROsDrPTJCcntzwfOnSoEhMTNWjQIG3cuFGLFy92OMfXaiY7O1vJycmKjIx0OsZX6sWZ9h53rneOJ6qvr9ecOXPU2NioVatWuRybkJBg92GZsWPHasSIEXr//ff13nvvWR1qp5g9e3bL8yFDhmjkyJGKjo7Wtm3bXDZWvlIvzdatW6e5c+e2+d5Lb6sZV+doTznOePWVzVtuuUXdunW7qmM/ffr0VZ19s/DwcIfju3fvrt69e1sWq7u88MIL2rp1q/Lz89W/f/92z09ISPDYfy1eq+DgYA0dOtTpfvpazRw/flw7d+7U008/3e65vlAvzXcuaM9xp3lee+d4ovr6es2aNUsVFRXKy8tzeVXTET8/P40aNcqr6ygiIkLR0dEu99FX6qXZnj17VFZWdl3HHU+uGWfnaE87znh1sxkQEKD4+PiWT802y8vL05gxYxzOSUxMvGr8jh07NHLkSPn7+1sWa2czxmjhwoXKzc3Vrl27FBMTc13rlJSUKCIiooOj61rq6up05MgRp/vpKzXTbP369erbt6+mTp3a7rm+UC8xMTEKDw+3q4nLly+rsLDQ6XFHcl5HruZ4muZG89ixY9q5c+d1/WPMGKODBw96dR2dPXtWlZWVLvfRF+rlz7KzsxUfH69hw4a1e64n1kxb52iPO85Y+vGjLmDTpk3G39/fZGdnm8OHD5u0tDQTHBxsfvvtN2OMMenp6SYlJaVlfHl5uenZs6d56aWXzOHDh012drbx9/c3X375pbt2wRLPP/+8CQsLMwUFBebUqVMtj4sXL7aMaZ2bd99912zevNkcPXrU/PzzzyY9Pd1IMjk5Oe7YBcssWbLEFBQUmPLycrNv3z4zbdo0ExIS4vM1Y4wxDQ0NJioqyixduvSq13ypXmpra01JSYkpKSkxksyKFStMSUlJy6eqs7KyTFhYmMnNzTWlpaXmscceMxEREaampqZljZSUFLu7Ynz77bemW7duJisryxw5csRkZWWZ7t27m3379nX6/l0vV3mpr68306dPN/379zcHDx60O+7U1dW1rNE6L5mZmebrr782v/76qykpKTHz58833bt3N/v373fHLl4XV3mpra01S5YsMUVFRaaiosLk5+ebxMREc+utt3p9vRjT9t8lY4yprq42PXv2NB9++KHDNbyxZq7lHO1JxxmvbzaNMeaDDz4w0dHRJiAgwIwYMcLu9j6pqalm4sSJduMLCgrM8OHDTUBAgBk4cKDTAvdkkhw+1q9f3zKmdW7eeOMNM2jQIBMUFGR69eplxo0bZ7Zt29b5wVts9uzZJiIiwvj7+5vIyEgzc+ZMc+jQoZbXfbVmjDFm+/btRpIpKyu76jVfqpfm2zq1fqSmphpjmm5LkpGRYcLDw01gYKCZMGGCKS0ttVtj4sSJLeObffHFFyY2Ntb4+/ubuLg4j2vMXeWloqLC6XEnPz+/ZY3WeUlLSzNRUVEmICDA9OnTxyQlJZmioqLO37kb4CovFy9eNElJSaZPnz7G39/fREVFmdTUVHPixAm7NbyxXoxp+++SMcZ89NFHpkePHubcuXMO1/DGmrmWc7QnHWds/9spAAAAoMN59Xs2AQAA4F40mwAAALAMzSYAAAAsQ7MJAAAAy9BsAgAAwDI0mwAAALAMzSYAAAAsQ7MJAAAAy9BsAgAAwDI0mwAAALAMzSYAAAAs81/TWzQOOnohDQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_ols = res.get_prediction()\n",
    "iv_l = pred_ols.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_ols.summary_frame()[\"obs_ci_upper\"]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x, y, \"o\", label=\"data\")\n",
    "ax.plot(x, y_true, \"b-\", label=\"True\")\n",
    "ax.plot(x, res.fittedvalues, \"r--.\", label=\"OLS\")\n",
    "ax.plot(x, iv_u, \"r--\")\n",
    "ax.plot(x, iv_l, \"r--\")\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS with dummy variables\n",
    "\n",
    "We generate some artificial data. There are 3 groups which will be modelled using dummy variables. Group 0 is the omitted/benchmark category."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "groups = np.zeros(nsample, int)\n",
    "groups[20:40] = 1\n",
    "groups[40:] = 2\n",
    "# dummy = (groups[:,None] == np.unique(groups)).astype(float)\n",
    "\n",
    "dummy = pd.get_dummies(groups).values\n",
    "x = np.linspace(0, 20, nsample)\n",
    "# drop reference category\n",
    "X = np.column_stack((x, dummy[:, 1:]))\n",
    "X = sm.add_constant(X, prepend=False)\n",
    "\n",
    "beta = [1.0, 3, -3, 10]\n",
    "y_true = np.dot(X, beta)\n",
    "e = np.random.normal(size=nsample)\n",
    "y = y_true + e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         0.         0.         1.        ]\n",
      " [0.40816327 0.         0.         1.        ]\n",
      " [0.81632653 0.         0.         1.        ]\n",
      " [1.2244898  0.         0.         1.        ]\n",
      " [1.63265306 0.         0.         1.        ]]\n",
      "[ 9.28223335 10.50481865 11.84389206 10.38508408 12.37941998]\n",
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 1 1 2 2 2 2 2 2 2 2 2 2]\n",
      "[[ True False False]\n",
      " [ True False False]\n",
      " [ True False False]\n",
      " [ True False False]\n",
      " [ True False False]]\n"
     ]
    }
   ],
   "source": [
    "print(X[:5, :])\n",
    "print(y[:5])\n",
    "print(groups)\n",
    "print(dummy[:5, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.978\n",
      "Model:                            OLS   Adj. R-squared:                  0.976\n",
      "Method:                 Least Squares   F-statistic:                     671.7\n",
      "Date:                Fri, 20 Mar 2026   Prob (F-statistic):           5.69e-38\n",
      "Time:                        11:18:46   Log-Likelihood:                -64.643\n",
      "No. Observations:                  50   AIC:                             137.3\n",
      "Df Residuals:                      46   BIC:                             144.9\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "x1             0.9999      0.060     16.689      0.000       0.879       1.121\n",
      "x2             2.8909      0.569      5.081      0.000       1.746       4.036\n",
      "x3            -3.2232      0.927     -3.477      0.001      -5.089      -1.357\n",
      "const         10.1031      0.310     32.573      0.000       9.479      10.727\n",
      "==============================================================================\n",
      "Omnibus:                        2.831   Durbin-Watson:                   1.998\n",
      "Prob(Omnibus):                  0.243   Jarque-Bera (JB):                1.927\n",
      "Skew:                          -0.279   Prob(JB):                        0.382\n",
      "Kurtosis:                       2.217   Cond. No.                         96.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res2 = sm.OLS(y, X).fit()\n",
    "print(res2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare the true relationship to OLS predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_ols2 = res2.get_prediction()\n",
    "iv_l = pred_ols2.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_ols2.summary_frame()[\"obs_ci_upper\"]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x, y, \"o\", label=\"Data\")\n",
    "ax.plot(x, y_true, \"b-\", label=\"True\")\n",
    "ax.plot(x, res2.fittedvalues, \"r--.\", label=\"Predicted\")\n",
    "ax.plot(x, iv_u, \"r--\")\n",
    "ax.plot(x, iv_l, \"r--\")\n",
    "legend = ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Joint hypothesis test\n",
    "\n",
    "### F test\n",
    "\n",
    "We want to test the hypothesis that both coefficients on the dummy variables are equal to zero, that is, $R \\times \\beta = 0$. An F test leads us to strongly reject the null hypothesis of identical constant in the 3 groups:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 0]\n",
      " [0 0 1 0]]\n",
      "<F test: F=145.49268198028008, p=1.2834419617282137e-20, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "R = [[0, 1, 0, 0], [0, 0, 1, 0]]\n",
    "print(np.array(R))\n",
    "print(res2.f_test(R))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use formula-like syntax to test hypotheses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=145.49268198027983, p=1.2834419617282617e-20, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res2.f_test(\"x2 = x3 = 0\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Small group effects\n",
    "\n",
    "If we generate artificial data with smaller group effects, the T test can no longer reject the Null hypothesis: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "beta = [1.0, 0.3, -0.0, 10]\n",
    "y_true = np.dot(X, beta)\n",
    "y = y_true + np.random.normal(size=nsample)\n",
    "\n",
    "res3 = sm.OLS(y, X).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.224911192540889, p=0.3031864410631281, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res3.f_test(R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.2249111925408895, p=0.3031864410631281, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res3.f_test(\"x2 = x3 = 0\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multicollinearity\n",
    "\n",
    "The Longley dataset is well known to have high multicollinearity. That is, the exogenous predictors are highly correlated. This is problematic because it can affect the stability of our coefficient estimates as we make minor changes to model specification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.datasets.longley import load_pandas\n",
    "\n",
    "y = load_pandas().endog\n",
    "X = load_pandas().exog\n",
    "X = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 TOTEMP   R-squared:                       0.995\n",
      "Model:                            OLS   Adj. R-squared:                  0.992\n",
      "Method:                 Least Squares   F-statistic:                     330.3\n",
      "Date:                Fri, 20 Mar 2026   Prob (F-statistic):           4.98e-10\n",
      "Time:                        11:18:46   Log-Likelihood:                -109.62\n",
      "No. Observations:                  16   AIC:                             233.2\n",
      "Df Residuals:                       9   BIC:                             238.6\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const      -3.482e+06    8.9e+05     -3.911      0.004    -5.5e+06   -1.47e+06\n",
      "GNPDEFL       15.0619     84.915      0.177      0.863    -177.029     207.153\n",
      "GNP           -0.0358      0.033     -1.070      0.313      -0.112       0.040\n",
      "UNEMP         -2.0202      0.488     -4.136      0.003      -3.125      -0.915\n",
      "ARMED         -1.0332      0.214     -4.822      0.001      -1.518      -0.549\n",
      "POP           -0.0511      0.226     -0.226      0.826      -0.563       0.460\n",
      "YEAR        1829.1515    455.478      4.016      0.003     798.788    2859.515\n",
      "==============================================================================\n",
      "Omnibus:                        0.749   Durbin-Watson:                   2.559\n",
      "Prob(Omnibus):                  0.688   Jarque-Bera (JB):                0.684\n",
      "Skew:                           0.420   Prob(JB):                        0.710\n",
      "Kurtosis:                       2.434   Cond. No.                     4.86e+09\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 4.86e+09. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "ols_model = sm.OLS(y, X)\n",
    "ols_results = ols_model.fit()\n",
    "print(ols_results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Condition number\n",
    "\n",
    "One way to assess multicollinearity is to compute the condition number. Values over 20 are worrisome (see Greene 4.9). The first step is to normalize the independent variables to have unit length: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "norm_x = X.values\n",
    "for i, name in enumerate(X):\n",
    "    if name == \"const\":\n",
    "        continue\n",
    "    norm_x[:, i] = X[name] / np.linalg.norm(X[name])\n",
    "norm_xtx = np.dot(norm_x.T, norm_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we take the square root of the ratio of the biggest to the smallest eigen values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56240.86943113035\n"
     ]
    }
   ],
   "source": [
    "eigs = np.linalg.eigvals(norm_xtx)\n",
    "condition_number = np.sqrt(eigs.max() / eigs.min())\n",
    "print(condition_number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dropping an observation\n",
    "\n",
    "Greene also points out that dropping a single observation can have a dramatic effect on the coefficient estimates: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percentage change 4.55%\n",
      "Percentage change -105.20%\n",
      "Percentage change -3.43%\n",
      "Percentage change 2.92%\n",
      "Percentage change 3.32%\n",
      "Percentage change 97.06%\n",
      "Percentage change 4.64%\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ols_results2 = sm.OLS(y.iloc[:14], X.iloc[:14]).fit()\n",
    "print(\n",
    "    \"Percentage change %4.2f%%\\n\"\n",
    "    * 7\n",
    "    % tuple(\n",
    "        [\n",
    "            i\n",
    "            for i in (ols_results2.params - ols_results.params)\n",
    "            / ols_results.params\n",
    "            * 100\n",
    "        ]\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also look at formal statistics for this such as the DFBETAS -- a standardized measure of how much each coefficient changes when that observation is left out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "infl = ols_results.get_influence()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general we may consider DBETAS in absolute value greater than $2/\\sqrt{N}$ to be influential observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.0 / len(X) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    dfb_const  dfb_GNPDEFL   dfb_GNP  dfb_UNEMP  dfb_ARMED   dfb_POP  dfb_YEAR\n",
      "0   -0.016406    -0.234566 -0.045095  -0.121513  -0.149026  0.211057  0.013388\n",
      "1   -0.020608    -0.289091  0.124453   0.156964   0.287700 -0.161890  0.025958\n",
      "2   -0.008382     0.007161 -0.016799   0.009575   0.002227  0.014871  0.008103\n",
      "3    0.018093     0.907968 -0.500022  -0.495996   0.089996  0.711142 -0.040056\n",
      "4    1.871260    -0.219351  1.611418   1.561520   1.169337 -1.081513 -1.864186\n",
      "5   -0.321373    -0.077045 -0.198129  -0.192961  -0.430626  0.079916  0.323275\n",
      "6    0.315945    -0.241983  0.438146   0.471797  -0.019546 -0.448515 -0.307517\n",
      "7    0.015816    -0.002742  0.018591   0.005064  -0.031320 -0.015823 -0.015583\n",
      "8   -0.004019    -0.045687  0.023708   0.018125   0.013683 -0.034770  0.005116\n",
      "9   -1.018242    -0.282131 -0.412621  -0.663904  -0.715020 -0.229501  1.035723\n",
      "10   0.030947    -0.024781  0.029480   0.035361   0.034508 -0.014194 -0.030805\n",
      "11   0.005987    -0.079727  0.030276  -0.008883  -0.006854 -0.010693 -0.005323\n",
      "12  -0.135883     0.092325 -0.253027  -0.211465   0.094720  0.331351  0.129120\n",
      "13   0.032736    -0.024249  0.017510   0.033242   0.090655  0.007634 -0.033114\n",
      "14   0.305868     0.148070  0.001428   0.169314   0.253431  0.342982 -0.318031\n",
      "15  -0.538323     0.432004 -0.261262  -0.143444  -0.360890 -0.467296  0.552421\n"
     ]
    }
   ],
   "source": [
    "print(infl.summary_frame().filter(regex=\"dfb\"))"
   ]
  }
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