Lecture 04_Regression Recap and Asset Pricing Models.ipynb

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    "## <center><font color=navy>Algorithmic Trading in Python</font></center>\n",
    "### <center>Regression Recap and Asset Pricing Models</center>\n",
    "#### <center>Ali Habibnia</center>"
   ]
  },
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   "source": [
    "For individuals who lack prior exposure to regression analysis:[A Refresher on Regression Analysis by Ali Habibnia](https://github.com/AliHabibnia/ECON_5314G_Big_Data_Economics/blob/main/Lecture%2001_Regression%20Recap%20with%20Examples.ipynb)\n",
    "\n",
    "[What the Great Fama-Shiller Debate Has Taught Us](https://hbr.org/2013/10/what-the-great-fama-shiller-debate-has-taught-us)\n",
    "\n",
    "[Empirical Asset Pricing: Eugene Fama, Lars Peter Hansen, and Robert Shiller](https://dash.harvard.edu/bitstream/handle/1/25142544/99130770.pdf)\n",
    "\n",
    "[Fama-French Data Library](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html)"
   ]
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    "### Regression Models in Python:\n",
    "\n",
    "Here's a list of popular Python libraries that can be used to estimate a linear regression model along with the specific function or class typically used to perform the regression:\n",
    "\n",
    "1. Statsmodels\n",
    "    - Library: statsmodels\n",
    "    - Function/Class: statsmodels.api.OLS()\n",
    "      \n",
    "        \n",
    "2. Scikit-learn\n",
    "    - Library: sklearn\n",
    "    - Function/Class: sklearn.linear_model.LinearRegression()\n",
    "    \n",
    "\n",
    "3. NumPy\n",
    "\n",
    "    - Library: numpy\n",
    "    - Function: numpy.polyfit() (with degree=1 for linear regression)\n",
    "    \n",
    "\n",
    "These are just a few libraries and there are others (i.e. TensorFlow (Using Keras API), PyTorch, ...) available. The choice of which to use often depends on the requirements of the specific task, familiarity with the library, and personal preference."
   ]
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    "### Linear Regression Indicator and Regression Channels in Technical Analysis and Trading \n",
    "\n",
    "Befor we explore the mathematical and explanatory description of asset pricing models, let us first quickly review how traders use Linear Regression Indicator (LRI) and the Regression Channels in technical analysis. \n",
    "\n",
    "In the vast realm of technical analysis, the Linear Regression Indicator and Regression Channels stand out as powerful tools that offer traders both a perspective on trend direction and the potential volatility around that trend. At their core, these tools are rooted in statistical analysis, providing a quantifiable approach to market dynamics.\n"
   ]
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   "source": [
    "#### Regression channel\n",
    "\n",
    "Channels are an important component of technical analysis. There are quite a few types of channel trading techniques that can be applied. Some of these include Fibonacci channel, Andrews pitchfork, and the Keltner channel. The linear regression channel is a three-line technical indicator, which outlines the high, the low, and the middle of a trend or price move being analyzed.\n",
    "\n",
    "Upper Channel Line (UCL) and Lower Channel Line (LCL):\n",
    "\n",
    "These are drawn a specified number (usually two) of standard deviations above and below the LRL, respectively. The space between the UCL and LCL represents the expected range of movement for the given asset based on its past volatility and trend. When prices move outside this channel, it might indicate overextension and a potential reversion to the mean."
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "! pip install yfinance mplfinance pandas-ta> NUL"
   ]
  },
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   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
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1ahQeHpdm0j/77LP2Rt7Z/fzzz4WqAMpP1tgC+Ne//sUVV1yBm5sbu3btYuvWrZd1fHB8T4ryfoiIiIgUh3oSiYhUAM2bNyc6OpqFCxcWantfX1/uvfde3nzzTcDxj8uWLVvSvn37Qh1nzpw5WK1WTp06xcqVK9m0aZPD46+++qp9xbXU1FQWL15sf6xmzZp069YtxzFPnz7NL7/8AkBSUhIff/yxw4pNeZk3bx5//vkne/fuBeB///sfDRo04LbbbiMiIoLExES2bt3KTz/9RK1atezJq6ioKHbs2AHA22+/jcViISgoiM8++4yYmJhCvQ6F5eHhwQMPPMArr7wCmJUm11xzDTfffDP79+/n448/LvIx3dzcGDduHBMmTADgl19+oUWLFvTr149q1apx7tw5tm3bxurVq0lKSiI6OhqAtWvXctddd3HNNdfQvHlzQkND8fT0ZM2aNQ6JuawVQNmn9Q0YMICOHTvi7u7OLbfcQuPGjfMd59NPP80TTzwBmA2eW7ZsyT333ENERAT//PMP33//PY8//rhDYjGrFi1asGzZMm644QYSExM5ePAg3bt3Z/Xq1YWafhYVFcXs2bPtY0hMTKRXr150796dTp064evry9GjR1mxYgUxMTEsXLiQzp07F3jcvDRq1Mje9wng8ccfZ/PmzcTHx7No0aJ8pzAWVtb3ZOPGjYwaNYrw8HAAHn300WJXBIqIiIjkyhARkXLhwIEDBmC/TJkyxeHxo0ePGr6+vg7b5Pcxvn79+hzbAsaCBQvy3KdLly657pP9UrVqVeOTTz5x2Pezzz5z2Ob555/P9TkSEhKMoKAg+3bt27cv9Gt07Ngxo3v37gWOLyIiwr7Pp59+mus2gYGBxh133JHna5n1tejSpYvDY7/++qvDfr/++qv9sYsXLxrNmzfP9Tmzjz3re5zfMW02mzF06NBCvTd5vR+5XSIjI43Y2Fj7PidPnjQCAgJy3fazzz4r1DhHjRqV73POnz/fvn10dHSu79n3339veHl52R9r2rSpcerUqYIDJMM777xj+Pv7F3j+CxcuvOz3+5FHHsn12C1btjTatWuX5zHz+7ee1bfffpvn+E+fPl3o10RERESkMDTdTESkgqhTp06eFRi5ad++PS1btnS4z8vLi/vuu6/Qx7BYLHh6ehISEkLTpk3p378/b775JocPH+auu+5y2DbrVLPMiprc+Pn5OUwd27BhA9u2bSvUeMLCwlixYgUrVqzgwQcfpGnTpgQFBeHu7k7VqlW55ppreO655/jhhx/s+/zrX//iyy+/pF27dnh5eVG1alVuueUW/vzzT5o3b17o16KwgoKCWLNmDY8//jhhYWF4eXnRqFEjpk2bxvLly4t1TIvFwttvv83PP//MPffcQ7169fD29sbT05PQ0FC6d+/O1KlTHV7Ha6+9lhdffJFbb72Vxo0bU6VKFdzd3QkODqZdu3Y8++yzrFu3zmF6XM2aNfnuu+/o1q2bw/1FGefLL7/M6tWrue+++2jQoAE+Pj74+PgQERHBXXfdxXXXXVfgcXr16sXixYvtUyx37dpFz549C92IesiQIRw6dIiXXnqJnj17Urt2bby8vPD29qZ+/frcc889fP7559x9991FPsfsXnnlFZ5//nnq16+Pp6cnYWFhjBgxglWrVhEQEHDZx+/bty/vvPMOrVq1ytFAW0RERKSkWQwjS/dRERERERERERGplFRJJCIiIiIiIiIiShKJiIiIiIiIiIiSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQiIiIiIiIiIoKSRCIiIiIiIiIigpJEIiIiIiIiIiKCkkQ5bNy40dlDECk1im9xVYptcWWKb3FVim1xZYpvqaiUJMrG3d3d2UMQKTWKb3FVim1xZYpvcVWKbXFlim+pqCyGYRjOHkR5Eh8fT0BAgLOHIVIqFN/iqhTb4soU3+KqFNviyhTfUlGpkiibXbt2OXsIIqVG8S2uSrEtrkzxLa5KsS2uTPEtFZWSRNn4+Pg4ewgipUbxLa5KsS2uTPEtrkqxLa5M8S0VVYlNNzMMg/T0dKxWa0kczmni4uIIDAx09jBESoy7uzseHh5YLBYuXrxIcHCws4ckUuIU2+LKFN/iqhTb4soU31JReZTEQVJTUzl+/DiJiYklcTinSklJwdvb29nDEClRfn5+hIaGsmfPHjp06ODs4YiUOMW2uDLFt7gqxba4MsW3VFSXnSSy2WwcOHAAd3d3wsLC8PLywmKxlMTYnCI5OVmlgeIyDMMgNTWV06dPc+DAAfz8/Jw9JJFS4e/v7+whiJQaxbe4KsW2uDLFt1RUl50kSk1NxWazUbduXZf4A9TDwwMPjxIpsBIpF3x9ffH09OTQoUNUr17d2cMRKRW1a9d29hBESo3iW1yVYltcmeJbKqoSa1zt5uYaPbBTUlKcPQSREpf57/Pw4cNOHolI6di3b5+zhyBSahTf4qoU2+LKFN9SUblGZqcEubu7O3sIIqUmICDA2UMQKRVBQUHOHoJIqVF8i6tSbIsrU3xLRaUkUTZKEokr0woL4qpCQkKcPQSRUqP4Flel2BZXpviWikpJomxSU1OdPYQyMXjwYPr372+/3bVrV0aPHm2/Xa9ePRYsWFDm46oosr9eFcWxY8ecPQSRUnHw4EFnD0Gk1Ci+xVUptsWVKb6loqq0SaLsSZJM5b2SaPDgwVgsFvulWrVq9O7dm23btpXo86xfv55hw4aV6DFLUlm9Dq5GZa/iqqpWrersIYiUGsW3uCrFtrgyxbdUVJU2SZSX8pIkyq+iqXfv3hw/fpzjx4+zYsUKPDw86NevX4k+f40aNcrFanXOfh1cTXl4T0VKg/ptiStTfIurUmyLK1N8S0VVKkmiFGC3Ey4lsS5ZZlJi1apVXHXVVXh7exMaGspTTz1Feno6AMuWLaNKlSpYrVYAtmzZgsVi4amnnrIfZ+jQodx3333227/99hudO3fG19eXunXrMmrUKBISEuyP16tXj+nTpzNo0CCCgoLyreLx9vamdu3a1K5dm9atW/PUU09x5MgRTp8+bd9m+/btdO/eHV9fX6pVq8awYcOIj48v9OuQfbqZxWLhnXfe4bbbbsPPz4/IyEiWLl3qsM/SpUuJjIzEx8eHbt268f7772OxWLhw4YLTXocJEybQuHFj/Pz8aNCgAc8++yxpaWn2x6dOnUrr1q1ZvHgx9erVIzg4mHvuuYe4uDj7NgkJCQwaNIiAgABCQ0OZO3duoV/H8ubEiRPOHoJIqThy5IizhyBSahTf4qoU2+LKFN9SUZVKkugA0NQJlwMlMHYPDw+OHTtG37596dChA1u3buWNN97g3XffZcaMGQB07tyZuLg4Nm/eDJgJperVq7Ny5Ur7cVatWkXXrl0Bc/nD3r17c8cdd7Bt2zY++eQTfvvtN0aOHOnw3HPmzKFVq1Zs3ryZZ599tlDjjY+P58MPP6RRo0ZUq1YNMJMavXr1omrVqqxfv57PPvuMn3/+OcfzFdW0adO466672LZtG3379mXgwIGcO3cOgAMHDnDnnXfSv39/tm7dyvDhw5k0aZLD/mX9OgAEBgayaNEidu7cycsvv8zbb7/N/Pnzc4zr66+/ZtmyZSxbtoxVq1bx4osv2h8fN24cq1at4n//+x8//vgjK1euZNOmTUV67coLlb2Kq6pevbqzhyBSahTf4qoU2+LKFN9SYRmXKSkpydi5c6eRlJRkv2+XYRg44bKrCOOOjo42br311hz3p6SkGBMnTjSioqIMm81mv//f//63ERAQYFitVsMwDKNt27bG7NmzDcMwjP79+xszZ840vLy8jLi4OOPo0aMGYOzZs8cwDMMYMmSIMWzYMIfnWbNmjeHm5mZ/3SIiIoz+/fsXatzu7u6Gv7+/4e/vbwBGaGiosXHjRvs2//nPf4yqVasa8fHx9vu+/fZbw83NzThx4kSu59+lSxfj8ccft9+OiIgw5s+fb78NGM8884z9dnx8vAEY3333nWEYhjFhwgSjefPmDmOdNGmSARjnz593yuuQm9mzZxvt2rWz354yZYrh5+dnxMbG2u8bN26ccfXVVxuGYRhxcXGGl5eX8emnn9ofP3v2rOHr6+vwepV3mf9ODx486OyhiJSKo0ePOnsIIqVG8S2uSrEtrkzx7TpWrVpl9OvXzwgNDTUA46uvvnJ4PDo62gAcLr169XLY5uzZs8aAAQOMwMBAIzg42HjwwQeNuLi4MjyLwiuVSqL6wC4nXOqXwNjT0tLYtWsXHTt2xGKx2O/v1KkT8fHxHD16FIAuXbqwcuVKDMNgzZo13H777TRt2pTffvuNVatWERYWRmRkJABbt25l0aJFBAQE2C+9evXCZrNx4MCl+qf27dsXaozdunVjy5YtbNmyhb/++otevXrRp08fDh06BMCuXbto1aoV/v7+DuO32WzExMQU+7Vp2bKl/bq/vz9BQUGcOnUKgJiYGDp06OCw/VVXXeVwu6xfB4BPPvmETp06Ubt2bQICAnjmmWc4fPiww3Hq1atHYGCg/XZoaKj9vPbt20dqaipXX321/fGQkBCioqIKNcbyJvO8RFzNP//84+whiJQaxbe4KsW2uDLFt+tISEigVatW/Pvf/85zm6z9co8fP85///tfh8cHDhzI//3f//HTTz+xbNkyVq9eXW4XivIojYN6A01K48BlwMOjcC9J165dee+999i6dSuenp40adKErl27snLlSs6fP0+XLl3s28bHxzN8+HBGjRqV4zjh4eH261mTOvnx9/enUaNG9tvvvPMOwcHBvP322/YpcaXB09PT4bbFYsFmsxV6/7J+Hf744w8GDhzItGnT6NWrF8HBwSxZsiRHT6HLPa+KJOtUPBFXUqtWLWcPQaTUKL7FVSm2xZUpvl1Hnz596NOnT77bZPbLzc2uXbv4/vvvWb9+vb0g4tVXX6Vv377MmTOHsLCwEh/z5SiVJFFF17RpU7744gsMw7BXE61du5bAwECuuOIK4FJfovnz59sTQl27duXFF1/k/PnzjBkzxn68tm3bsnPnToeERkmyWCy4ubmRlJRkH/+iRYtISEiwJ1zWrl2Lm5tbqVXAREVFsXz5cof71q9f73C7rF+H33//nYiICIfeSFmrjAqjYcOGeHp6sm7dOnsi6/z58+zZs8chESgiIiIiIlJh2KyQcBBiYyB2N8Rl/LSlw41rnT26MhEbG+tw29vbG29v72Ida+XKldSsWZOqVavSvXt3ZsyYYf+C/o8//qBKlSoOM2Z69uyJm5sb69at47bbbiv+SZSCIiWJNm7cSI0aNQA4efIkYWFhJCUlkZKSYl8xymq14uXlhdVqxWq14u3tTVpaGjabDW9vb1JTUzEMAx8fH1JSUjAMA19fX/sf9kW5brFY8Pb2Jjk5GYvFgpeXFykpKbi5ueHp6UlKSgru7u64u7uTmprqcN1qtXLhwgX++OMP+7L3VquV4OBghgwZwoIFC3j00UcZPnw4u3fvZsqUKYwaNYqkpCS8vb3x8fGhefPmfPTRR8ybN4+EhAQ6derEpk2bSEtLo3PnzvZVu8aNG8e1117L8OHDGT58OO7u7uzevZvVq1cza9Ys++ubmppKYmJivueUnp5OUlISR44cIS0tjdjYWN566y3i4+Pp1asXqamp9O/fnylTpnD//ffz1FNPceHCBUaOHMm9995LSEgIycnJpKenY7PZSE5Oxmq1YhgG6enpJCQk4O3tjWEY9tcpJcVcN85ms9nPydfXF4CUlBRsNhv3338/8+bNY/z48QwYMIBt27axaNEiAJKSkggMDGTUqFF069aNRx55hPvvv5+AgAD+/vtvfvjhB15++WXc3d0xDIO0tDTS0tJITU3Fw8MDi8VCWlqavcorc+xJSUns378fT09Pzp49y+uvv25/HRISEmjQoAGHDx9m0aJFdOzYkW+++YavvvoKgMTERHs7q8zzyoyrzBXuEhISsFgsPPjgg4wdOxY/Pz/q1q3LxIkTcXNzwzAM+zZFib28zsnT09P+PmT9N1QS/54yH4uJieHs2bO0atWKrVu34ubmRrNmzdixYweenp40atSIXbt24ePjQ3h4OHv27MHf35/atWuzb98+goKCCAkJ4eDBg1StWpWAgACOHDlC9erV8fLy4p9//rF/a5L5GZGamsqZM2eoW7cu8fHxnD9/nnr16nHu3DliY2Np2LAhJ06cICEhgcaNG3P48GGSk5Np2rQpe/fuJS0tjebNm7Nz505sNpt97ECu13VOlfOcMo/vSufkiu+Tzql452S1Wjl58qRLnZMrvk86p6Kf09GjRzl58qRLnZMrvk86p+Kd05EjR6hRo4bTz8mSHkvcsQ3U9r+IW9webBd3E2gcwyNxPxbj0qrPmQzc2fjX70RGXemS79ORI0do3rw5YLYZSUxMtJ/7lClTmDp1ao7XpCC9e/fm9ttvp379+uzbt4+JEyfSp08fe67hxIkT1KxZ02EfDw8PQkJCyufq05fb1Ci3xtUVQW7NpQDjgQceMAzDMFauXGl06NDB8PLyMmrXrm1MmDDBSEtLczjG448/bgDGrl2XWma3atXKqF27do7n++uvv4wbbrjBCAgIMPz9/Y2WLVsaM2fOtD+evVF0YccdGBhodOjQwfj8888dttu2bZvRrVs3w8fHxwgJCTEeeughh8ZYxWlcnb1BV3BwsLFw4UL77f/9739Go0aNDG9vb6Nr167GG2+8YQAOsVHWr8O4ceOMatWqGQEBAcbdd99tzJ8/3wgODrY/PmXKFKNVq1YO+8yfP9+IiIiw346LizPuu+8+w8/Pz6hVq5Yxa9asHK9XeafG1eLq1BxSXJniW1yVYltcWZnGtzXdMOL2Gcax5Yaxa55hrBtuGD91NYwvahvGRxR8+TLMMH7uZhh/jTCMXQsMIy2h7MbuRBcvXnS4JCcnF7hPbn8XZ7dv3z4DMH7++WfDMAxj5syZRuPGjXNsV6NGDeP1118v1thLk8UwDONykkzJyckcOHCA+vXr4+PjczmHKhdSUlKKXWImjmbOnMmbb77JkSNHnD2USi/z32lmBl/E1WT+PyTiihTf4qoU2+LKSiW+0+IuTQ+L3Z1lqtjfYEvJf183bwhqDEFNIDDK/BkUZd7nGVSy43RhFouFr776iv79++e7XY0aNZgxYwbDhw/nvffeY8yYMZw/f97+eHp6Oj4+Pnz22WcVe7pZZZCenq4kUTG9/vrrdOjQgWrVqrF27Vpmz57NyJEjnT0sySLrB5OIKzlz5oz+0BCXpfgWV6XYFldW7Pg2bJBwOGevoNgYSCrEimk+tTMSQJlJoIyffuHg5l708UiRHT16lLNnzxIaGgpAx44duXDhAhs3bqRdu3YA/PLLL9hsNodVtMsLJYmy8fLycvYQKqy///6bGTNmcO7cOcLDwxkzZgxPP/20s4clWeTVcV+koqtbt66zhyBSahTf4qoU2+LKCozvtHgzAXQxWyIobg9Yk/Pf180LAiMvJYCyVgZ5BZfcSQhgrtK9d+9e++0DBw6wZcsWQkJCCAkJYdq0adxxxx323krjx4+nUaNG9OrVCzAXlurduzcPPfQQb775JmlpaYwcOZJ77rmn3K1sBkoS5WC1WnMsiS6FM3/+fObPn+/sYUg+sjZmE3El8fHxzh6CSKlRfIurUmyLK4uPjzerghKPOk4Ns1cFHSv4ID41sySAslQG+ddTVVAZ2rBhA926dbPffvLJJwGIjo7mjTfeYNu2bbz//vtcuHCBsLAwbrzxRqZPn+4wQ+mjjz5i5MiR9OjRAzc3N+644w5eeeWVMj+XwlCSKBur1ersIYiUmuzLPIq4Ck2lFFem+BZXpdgWl5GeALF7HJJBoSc3w8YjYE3Kf183T7MqyKFPUMbFq2rZjF/y1bVrV/Jr5fzDDz8UeIyQkBA+/vjjkhxWqVGSKBtNNxNXVqdOHWcPQaRU1KtXz9lDECk1im9xVYptqVAMw6z+cagKyviZmHOhHv/sd3jXyNknKDAKAuqDm/4sl/JD0ZiNppuJK7t48WK5nPcqcrnOnTtHjRo1nD0MkVKh+BZXpdiWcik90ewL5JAIijH7BqUn5L+vxQMCG0FQFGfTalCt3rWXEkLeIWUzfpHLpCRRNppuJq5Mc//FVWkqpbgyxbe4KsW2OI1hmCuF5VoVdLjg/b2rX6oIyjpNLKC+OX0M2L9+PdUadijlExEpeUoSZZO1uZSIq9EqIuKqGjZs6OwhiJQaxbe4KsW2lLr0JIj7O/dVxNIL+PLU4m5WBTn0CsqsCqpW4FMrvqWiUpIom7S0NDw89LKIazpz5gy1a9d29jBEStyJEycICVEZt7gmxbe4KsW2lAjDgKTjjgmgzJ8Jh4C8Gw4DZnPo7KuHBUZBQANwL36/WsW3VFTKhmRjs9mcPYQycfDgQerXr8/mzZtp3bo1K1eupFu3bpw/f54qVaqwaNEiRo8ezYULF5w91HIp++tVUSQlFbC6gkgFlZBQQI8AkQpM8S2uSrEtRWJNhri9jsvI26uC4vLf1+IG/g2yVQRlVgVVB4ulxIer+JaKqtImibp27Urr1q1ZsGCBw/1LlixhzJgx5TY5kpncyeTp6Ul4eDiDBw9m0qRJWEroA+7uu++mb9++JXKs0lBWr4Or0Soi4qoaN27s7CGIlBrFt7gqxbbkYBiQfDJnn6C4GIg/QIFVQZ5Vck4NC4qCgIbgXrZtRRTfUlFV2iRRXtLT0509BMBsoG2xWHBzc8v18Z9//pkrr7ySlJQUfvvtN4YOHUpoaChDhgwpkef39fXF19e3RI51OZz9Oria48ePaxURcUmHDx+mRYsWzh6GSKlQfIurUmxXYtYUiN+Xe+PotIv572txA//6uSSDmpjLzJeTL4sV31JR5f6X92VKAXY74ZJSCucyePBg+vfvz7Rp06hRowZBQUE8/PDDpKam2rfp2rUrI0eOZOTIkQQHB1O9enWeffZZDONSpjslJYWxY8dSp04d/P39ufrqq1m5cqX98UWLFlGlShWWLl1Ks2bN8Pb25vDhvDvrV6tWjdq1axMREcHAgQPp1KkTmzZtsj9us9l47rnnuOKKK/D29qZ169Z8//33hT7vzPFkmjp1Kq1bt2bx4sXUq1eP4OBg7rnnHuLiLpV2xsXFMXDgQPz9/QkNDWX+/Pl07dqV0aNHO+11WL9+PTfccAPVq1cnODiYLl26ODwOYLFYeOedd7jtttvw8/MjMjKSpUuXOmyzfPlyGjdujK+vL926dePgwYOFfi3Lk5SU0vhXIuJ8ycnJzh6CSKlRfIurUmy7OMOA5FNwajXsfRs2jYGV/WBpJHzqB99eCWvugK0T4cAHcHadY4LIMwiqXQX17odWM6HzF9B3B9yVCLfsha7LoO1caPQQ1LwefGqWmwQRKL6l4iqVSqIDQNPSOHABdgFNLvMYnp6eOe5bsWIFPj4+rFy5koMHD/LAAw9QrVo1Zs6cad/m/fffZ8iQIfz1119s2LCBYcOGER4ezkMPPQTAyJEj2blzJ0uWLCEsLIyvvvqK3r17s337diIjIwFITEzkpZde4p133qFatWrUrFmzUGPesGEDGzduZNCgQfb7Xn75ZebOnctbb71FmzZteO+997jlllv4v//7P/vzFdW+ffv4+uuvWbZsGefPn+euu+7ixRdftL8OTz75JGvXrmXp0qXUqlWLyZMns2nTJlq3bm0/Rlm/DnFxcURHR/Pqq69iGAZz586lb9++/P333wQGBtq3mzZtGrNmzWL27Nm8+uqrDBw4kEOHDhESEsKRI0e4/fbbefTRRxk2bBgbNmxgzJgxxXoNna1BgwbOHoJIqWja1Bn/64iUDcW3uCrFtouwpuZTFXShgJ0t5rLxua0g5lOrXCV9ikrxLRWWcZmSkpKMnTt3GklJSfb7dhmGgRMuu4ow7i5duhiPP/54jvvffPNNIzg42H47OjraCAkJMRISEuz3vfHGG0ZAQIBhtVrtx2ratKlhs9ns20yYMMFo2rSpYRiGcejQIcPd3d04duyYw3P16NHDePrppw3DMIyFCxcagLFly5Z8x33gwAEDMHx9fQ1/f3/D09PTAIxhw4Y5bBcWFmbMnDnT4b4OHToYjzzyiMNxNm/ebBiGYfz6668GYJw/f94+nqyvw5QpUww/Pz8jNjbWft+4ceOMq6++2jAMw4iNjTU8PT2Nzz77zP74hQsXDD8/P/vr7IzXITur1WoEBgYa33zzjf0+wHjmmWfst+Pj4w3A+O677wzDMIynn37aaNasmcNxJkyY4PB6lXeZ/043bdrk7KGIlIrMzzIRV6T4Flel2K5gkk4bxsk1hrH3HcPYNNYwVt5sGEsjDeNjd8P4iPwvnwQaxncdDGPtfYaxfYZhHPrMMM5vN4z0pIKft4JSfEtFVSqVRPUxq3rKWv2CNymWVq1a4efnZ7/dsWNH4uPjOXLkCBEREQBcc801Ds2SO3bsyNy5c7FarWzfvh2r1ZqjeVlKSgrVqlWz3/by8qJly5aFGtMnn3xC06ZNSUtLY8eOHTz22GNUrVqVF198kdjYWP755x86derksE+nTp3YunVrkc8/U7169Ryqb0JDQzl16hQA+/fvJy0tjauuusr+eHBwMFFRUfbbZf06AJw8eZJnnnmGlStXcurUKaxWK4mJiTmmsGV9Pn9/f4KCguzntmvXLq6++mqH7Tt27Fio8ZU35aXnlkhJS0tLc/YQREqN4ltclWK7HLKlQdy+3JeTTz1XwM4W8I8wq4ACoyC4yaVVxHxqV+iqoOJQfEtFVSpJIm8uf9pXaQsKCuLixZxN0RITEwkODi7R54qPj8fd3Z2NGzfi7u7u8FhAQID9uq+vb6FX5apbty6NGjUCzFLGffv28eyzzzJ16tQSG3d22afiWSwWbDZbofcv69fBx8eH6Ohozp49y8svv0xERATe3t507NjRoadUSZxbRVHcqYYi5V3z5s2dPQSRUqP4Flel2HailLO5Tw+L3w9GAV8qevhnmR6WZYpYYCR4OH/hm/JC8S0VVaVd3SwqKooff/wxx/3r16/PUemydetWkpKS7Kt9/fnnnwQEBFC3bl37NuvWrXPY588//yQyMhJ3d3fatGmD1Wrl1KlTdO7cuRTOBtzd3UlPTyc1NZWgoCDCwsJYu3YtXbp0sW+zdu1ah0qfktSgQQM8PT1Zv3494eHhAFy8eJE9e/Zw/fXXA5T56+Dj48PatWt5/fXX6du3LwBHjhzhzJkzRTpm06ZNczSy/vPPP0tszGVp3759tGvXztnDEClxO3fuVGyLy1J8i6tSbJcyW7qZ9Mm6jHxmQiilEL8P+4Xnvpy8b51KVxVUHIpvqagqbZJoxIgRvPbaa4waNYqhQ4fi7e3Nt99+y2effcY333zjsG1qaipDhgzhmWee4eDBg0yZMoWRI0c6LMt++PBhnnzySYYPH86mTZt49dVXmTt3LgCNGzdm4MCBDBo0iLlz59KmTRtOnz7NihUraNmyJTfddFORx3/27FlOnDhBeno627dv5+WXX6Zbt24EBQUBMG7cOKZMmULDhg1p3bo1CxcuZMuWLXz00UeX8arlLTAwkOjoaMaNG0dISAg1a9ZkypQpuLm52auCnPE6REZGsnjxYtq3b09sbCzjxo2zJ/sK6+GHH2bu3LmMGzeOoUOHsnHjRhYtWlTksZYHrlgdJQKKbXFtim9xVYrtEpJ6PmdFUOxus5m0rYApT+5+jkmgzGligY3Bwy//fSVfim+pqCptkqhBgwasXr2aSZMm0bNnT1JTU2nSpAmffPIJvXv3dti2R48eREZGcv3115OSksK9996bY1rXoEGDSEpK4qqrrsLd3Z3HH3+cYcOG2R9fuHAhM2bMYMyYMRw7dozq1atzzTXX0K9fv2KNv2fPnoBZORMaGkrfvn0dVlsbNWoUFy9eZMyYMZw6dYpmzZqxdOnSUp1uNG/ePB5++GH69etHUFAQ48eP58iRI/j4+Ni3KevX4d1332XYsGG0bduWunXr8vzzzzN27NgiPUd4eDhffPEFTzzxBK+++ipXXXUVzz//PA8++GCxxuxMWXtEibiSVq1aOXsIIqVG8S2uSrFdBLZ0SDiYc4pYXIy5zHxB/K7ISAA1zZIIigK/OmBxK3h/KTLFt1RUFsMwjMs5QHJyMgcOHKB+/foOyYCKKiEhAX9/f/vtwYMHc+HCBb7++us89+natSutW7dmwYIFpT/ACiQhIYE6deowd+5chgwZ4uzhVGqZ/07j4+Pp0KGDs4cjUuLWr1+v2BaXpfgWV6XYzkXqhZxVQXExEPd3IaqCfC9VAzlME2ts9hGSMqX4loqq0lYSScnbvHkzu3fv5qqrruLixYs899xzANx6661OHpmIiIiISDlhs2ZUBcVk6ROUkRRKPlnw/r51cu8V5FdXVUEictmUJMqmqP1qxNGcOXOIiYnBy8uLdu3asWbNGqpXr+7sYUkGTTcTV6WSbnFlim9xVS4f26kXsyWCMiuD9oItJf993X3MvkBB2VYRC2wMnoFlM365LC4f3+KyNN0sm+zTzURcgaabiatTSbe4MsW3uCqXiG2bFRIP576cfPKJgvf3Dc1YPj7bFDH/cFUFVXAuEd9SKamSSESKbPvr/6HFI8MK3lBERETEFaTFZSR/si8nv6fgqiA3bwiMdJwaFpSxgphXcNmMX0SkkFRJlI3NZnNY2l7EFWT+O61Tpw5BQUGXfbyPW7ZnwLYNJTAykZKRmpqKl5eXs4chUioU3+Kqyl1sGzZIOJxLIigGkv4peH+f2tn6BGX89IsAN/fSH7+UK+UuvkUKSZVE2SQlJWm6mbismJgYlb2KS9q6datiW1yW4ltcldNiOy0+IwGUvVfQHrAm57+vmxcENrrUJyjrNDFVBUkW+uyWikpJIpFK5HKr5D7p0InU2DgMq5XFUS3xCgrk7vVrS2h0IsWnCtCK5yDwA1ANqAfUB0IAi/OGVG4pvvP3EvA9MBO41sljkaIp1dg2bJB4NPfl5BOPFry/T808egVFgJv+hJKC6bNbKip9wmWj1c3ElTVs2PCy9k+NjcOWlgaAYbORGhtXEsMSuWzNmjVz9hCkkNKB+cAUICnbYwFcShjVy3K9DRBB5U0gKb7zthR4KuN6V+Bl4GFyjxX10yt/SiS20xPNCqCLu3P2CrIm5r+vmycENMplOfkm4FXl8scmlZo+u6WiUpIoG003E1f2999/q+xVXNKOHTsU2xXARuAhYHPGbW8gDbBl3I4HdmRcsqsFXJPl0h4zqVQZKL5zdxoznjKlAY8A64HXgeydMre/qSRReVPo2DYMSDqW+wpiiUcK3t+7erZEUEaFUEB9VQVJqdFnt1RU+lTMxmKprN9TOtfBgwepX78+mzdvpnXr1s4eDvXq1WP06NGMHj3a2UMp0NSpU/n666/ZsmVLgdt6eOifvLgmT09PZw9B8pGAWTk0n0sJoXuABZhTzI4CBzCnoGVeMm8fAwzgJPC/jAuAG9CCS0mjJsAVQG1c75cbxXdOBjACOIWZbPwBeA74BVgIbAe+AMKdNUAplByxnZ4IcX/nTAbFxUB6Qv4Hs3hAYMNcpohFgXe10jsJkTzos1sqKlf7ParQBg8ezIULF/j6668d7vf29nbOgApp8ODBvP/++4D5B/8VV1zBv/71L5577rkKvbpc3bp1OX78ONWrVy/154qNjeWll17iiy++4ODBg1SpUoXmzZvzyCOPcNttt7l0ojA8XL8ui2tq1KiRs4cgefgRGI6Z8AHzj/Y3gL5ZtqmfcclNAmYF0p8Zlz+AE5jJpq0Zl7eybO+GmSiqk3G5IsvPHkDoZZ6PMyi+c/oYMwkEZi+iLpiJoqeBOcAGoB3wKdDNGQOUvBmGuVJYbAxN3LfBhoWXpoklHCp4f6+QS9VAmUmgwCgzQeSmP8ql/NBnt1RUlTZJlJfk5ORyMd0svyUTe/fuzcKFC0lLS2Pjxo1ER0djsVh46aWXSm08VqsVi8VSag3Y3N3dqV27dqkcO6sLFy5w3XXXcfHiRWbMmEGHDh3w8PBg1apVjB8/nu7du1OlSpVSH4ez7N+/n2rV9G2auJ5du3appLucOQ08CXyYcdsNGAVMp2jTxPyB6zMuYFaQHOFS0uhPYBOQkvG4Dfgn47I+27ECgXVA0yI8f3mg+HZ0FHg043pnYHTGdQ9gNuZUxAeBM8ANwCzgibIdogCkJ5lVQXExZr+grMvJp8cDOacE2lncIaDhpSRQ1iliPqX/haJISdBnt1RUpfMXvzXF/M+grC/WlILHVoDMKpJVq1Zx1VVX4e3tTWhoKE899RTp6ekALFu2jCpVqmC1WgHYsmULFouFp556yn6coUOHct9999lv//bbb3Tu3BlfX1/q1q3LqFGjSEi4VDZbr149pk+fzqBBgwgKCmLYsLznzHt7e1O7dm3q1q1L//796dmzJz/99JP9cZvNxgsvvED9+vXx9fWlVatWfP755w7HWLp0KZGRkfj4+NCtWzfef/99LBYLFy5cAGDRokVUqVKFpUuX0qxZM7y9vTl8+DApKSmMHTuWOnXq4O/vz9VXX83KlSvtxz106BA333wzVatWxd/fnyuvvJLly5cDcP78eQYOHEiNGjXw9fUlMjKShQsXAuZ0M4vF4jBlKr/3AKBr166MGjWK8ePHExISQu3atZk6dWqerxvAxIkTOXjwIOvWrSM6OppmzZrRuHFjHnroIbZs2UJAwKU/XRITE3nwwQcJDAwkPDyc//znPw7HmjBhAo0bN8bPz48GDRrw7LPPkpbR1BnMaWCtW7dm8eLF1KtXj+DgYO655x7i4i41ey7MOVy4cIGhQ4dSo0YNgoKC6N69O1u3bs33PPNS3ivlRIqrIldSuqIvMBMxmQmilpjJnPlcfh8hC2Y10l3APOB3zF5GRzCrjD7HbF48DhiAWWHSEDOBEJdx3+X/tlC2FN+XGMAQ4CJmLC0C3LNtczdmvDUErMAYzPc92VevY4kzDEg6Did/hb/fhI2j4dc+8L/68Kk/fNcKfrsLtk+Ggx/BuY32BBGA1S0QqneEBoOh9YvQ+Su4aRfclQg3x0CXpdBmNjQcAjU6KUEkFYo+u6WiKp1KovgD8K0Tvqe7aRcEN7msQ3h5eXHs2DH69u3L4MGD+eCDD9i9ezcPPfQQPj4+TJ06lc6dOxMXF8fmzZtp3749q1atonr16g7JklWrVjFhwgQA9u3bR+/evZkxYwbvvfcep0+fZuTIkYwcOdKeJAGYM2cOkydPZsqUKYUe744dO/j999+JiIiw3/fCCy/w4Ycf8uabbxIZGcnq1au57777qFGjBl26dOHAgQPceeedPP744wwdOpTNmzczduzYHMdOTEzkpZde4p133qFatWrUrFmTkSNHsnPnTpYsWUJYWBhfffUVvXv3Zvv27URGRvLoo4+SmprK6tWr8ff3Z+fOnfbEy7PPPsvOnTv57rvvqF69Onv37iUpKfvaNqaC3oNM77//Pk8++STr1q3jjz/+YPDgwXTq1IkbbrghxzFtNhtLlixh4MCBhIWF5Xg8a4IIYO7cuUyfPp2JEyfy+eefM2LECLp06UJUVBQAgYGBLFq0iLCwMLZv385DDz1EYGAg48ePtx9j3759fP311yxbtozz589z11138eKLLzJz5sxCn8O//vUvfH19+e677wgODuatt96iR48e7Nmzh5CQkFxfv7yEhlbEiRYiBdNUyvLjK8wEjg2zSmAqZkVRaU4C8cCcTnZFPtssA24GtmBOSZpXiuMpaYrvS97EnMII5nvYII/tWmBWkt0HLAeWAGsXL6QbeU9tlHxYkyFub+7LyafF5r+vxQ38G+SyglgU8cleBLtwBbdUbvrslgrLuExJSUnGzp07jaSkpEt3XthlGB9R9pcLuwo97ujoaOPWW2/NcX98fLwxceJEIyoqyrDZbPb7//3vfxsBAQGG1Wo1DMMw2rZta8yePdswDMPo37+/MXPmTMPLy8uIi4szjh49agDGnj17DMMwjCFDhhjDhg1zeJ41a9YYbm5u9tctIiLC6N+/f6HG7e7ubvj7+xve3t4GYLi5uRmff/65YRiGkZycbPj5+Rm///67w35Dhgwx7r33XsMwDGPChAlG8+bNHR6fNGmSARjnz583DMMwFi5caADGli1b7NscOnTIcHd3N44dO+awb48ePYynn37aMAzDaNGihTF16tRcx37zzTcbDzzwQK6PHThwwACMzZs3G4ZhFOo96NKli3Hdddc5HKdDhw7GhAkTcn2OkydPGoAxb968XB/PKiIiwrjvvvvst202m1GzZk3jjTfeyHOf2bNnG+3atbPfnjJliuHn52fExsba7xs3bpxx9dVX228XdA5r1qwxgoKCjOTkZIdtGjZsaLz11lv252nVqlW+55P57/Svv/7Kd7uCfNC4hbGofhP75YPGLS7reCIl5XJjW0rGL4ZheBmGgWEYUYZh/O3c4eQw0jDHhmEY3zl5LEWh+Db9bRiGn2G+f30Mw7Dlv7lhGIZhNQzjWePS+17bMIytpTXAis5mM4zEE4ZxcpVh/P2WYWx4wjB+7WsY/2tgGB+7Ffx7+KdVDOP7qw3j92jD2PGCYRz+0jAu/J9hpCfn+ZSKbXFlim+pqEqnkiigvlnVU9YCLv+7ITc3N3bt2kXHjh0dGhh36tSJ+Ph4jh49Snh4OF26dGHlypWMGTOGNWvW8MILL/Dpp5/y22+/ce7cOcLCwoiMjARg69atbNu2jY8++sh+PMMwsNlsHDhwgKZNzaqr9u3bF2qM3bp144033iAhIYH58+fj4eHBHXfcAcDevXtJTEzMUUmTmppKmzZtAIiJickxP/aqq67K8TxeXl60bNnSfnv79u1YrVYaN27ssF1KSoq9z82oUaMYMWIEP/74Iz179uSOO+6wH2PEiBHccccdbNq0iRtvvJH+/ftz7bXX5nqOhXkPAIfxgVkpc+rUqVyPaRhGrvfnJeuxLRYLtWvXdjj2J598wiuvvMK+ffuIj48nPT2doKAgh2PUq1ePwMDAfMeX3zls3bqV+Pj4HH2EkpKS2LdvX5HOB8DX17fI+4hUBOWhl1xltwm4FUjFrOj5kfK3stQsYCWwA4gGtgG1nDmgQlJ8m9PGooFEzBXx3sWcelgQN8xVz9oCdyUnc8LHh+uBbzD7GVVK1hSI35f7cvJpF/Pf1+IG/vXM3kDBTS9VBgVGgU9NKOLiH4ptcWWKb6moSidJ5O592dO+nKWwSxV27dqV9957j61bt+Lp6UmTJk3o2rUrK1eu5Pz583Tp0sW+bXx8PMOHD2fUqFE5jpO1DLGwHyT+/v72bvnvvfcerVq14t1332XIkCHEx5vzvL/99lvq1KnjsF9R+9H4+vo6JGni4+Nxd3dn48aNuLs7dgDInKo1dOhQevXqxbfffsuPP/7ICy+8wNy5c3nsscfo06cPhw4dYvny5fz000/06NGDRx99lDlz5hRpXFllf78sFgs2my3XbWvUqEGVKlXYvXv3ZR/7jz/+YODAgUybNo1evXoRHBzMkiVLmDt3bpHHl9828fHxhIaGOkxlzFScBttlsXqciDOUReN7ydseoDdmz59qlM8EEYAv8F+gA+bS6Q9gTkMrnQaNJUfxba5Y9nvG9dcp+ip1/YGnhz/KK++/ywXgRuAT4JaSGmB5YxiQcjpnEig2BhL2g5H770p2nkHZlpHP+BnYCNxLrs+KYltcmeJbKiqtbpZNSkoKTZs25YsvvsAwDHuSZO3atQQGBnLFFWbHg8y+RPPnz7cnhLp27cqLL77I+fPnGTNmjP2Ybdu2ZefOnaWyDKKbmxsTJ07kySefZMCAAQ5NprMmqrKKioqyN5POtH599jVgcmrTpg1Wq5VTp07RuXPe37/VrVuXhx9+mIcffpinn36at99+m8ceewwwEzXR0dFER0fTuXNnxo0bl2uSqDDvQVG5ublxzz33sHjxYqZMmZKjL1F8fDw+Pj54eBT8zyKzD9SkSZPs9x06VIhlW4uobdu2nDhxAg8PD+rVq3fZxzty5Ij+wxKXtG/fviL36JKScQzzD+7TmCuRLad8rx7WHJiLuTrWd8CrwONOHVHBKnt8bwcmZ1y/B7MxdXYvLP+Ip/sOzPc4UZu3shroBRwHbgfexkwWVljW1IyqoCw9gjJXEks9X8DOFrMqKCiXZJBP7SJXBRVHZY9tcW2Kb6moKnWS6OLFiw6raYFZpfPII4+wYMECHnvsMUaOHElMTAxTpkzhySeftC8BX7VqVVq2bMlHH33Ea6+9BsD111/PXXfdRVpamkOCZsKECVxzzTWMHDmSoUOH2hs6//TTT/Z9L8e//vUvxo0bx7///W/Gjh3L2LFjeeKJJ7DZbPbl3teuXUtQUBDR0dEMHz6cefPmMWHCBIYMGcKWLVtYtGgRgEPlUHaNGzdm4MCBDBo0iLlz59KmTRtOnz7NihUraNmyJTfddBOjR4+mT58+NG7cmPPnz/Prr7/ap9NNnjyZdu3aceWVV5KSksKyZcvsj2VXmPegOGbOnMnKlSu5+uqrmTlzJu3bt8fT09M+ZXD9+vWFqtCJjIzk8OHDLFmyhA4dOvDtt9/y1VdfFXtceenZsycdO3akf//+zJo1i8aNG/PPP//w7bffcttttxV6imKm7M25RVxF9qmeUjbOYf7BfQizMfVXQM7Jy+XPCOAHYCkwHugKtHLmgApQmeM7Fbg/42co8O88tnth+ccFJonAbGj9O2Zi82/gQcwE5/j8dioPks9cSgJlrQyK3w+GNf99PQKzLSWf8TOgEXg4dxp6ZY5tcX2Kb6moKnWSaOXKlfY+PZkeeOAB3nvvPZYvX864ceNo1aoVISEhDBkyhGeeecZh2y5durBlyxa6du0KQEhICM2aNePkyZP2FbDA7DmzatUqJk2aROfOnTEMg4YNG3L33bl9F1Z0Hh4ejBw5klmzZjFixAimT59OjRo1eOGFF9i/fz9VqlShbdu2TJw4EYD69evz+eefM2bMGF5++WU6duzIpEmTGDFiRIFT0hYuXMiMGTMYM2YMx44do3r16lxzzTX069cPAKvVyqOPPsrRo0cJCgqid+/ezJ8/HzB7HD399NMcPHgQX19fOnfuzJIlS3J9njp16hTqPSiqkJAQ/vzzT1588UVmzJjBoUOHqFq1Ki1atGD27NkEBwcX6ji33HILTzzxBCNHjiQlJYWbbrqJZ599Nsfy9ZfLYrGwfPlyJk2axAMPPMDp06epXbs2119/PbVqFb2TRmHPT6Si0Td1ZS8B6Af8H2ZvmMVAznUlyycLZk+blpgVJfcCGwA/Zw4qH5U1vg1gErA14/Y7mP2ILlc94DegD2YvrQmYiaKXcPLUQ1uamfTJrVdQ6rkCdraAf/il/kDBTS5NF/MNLZOqoOKorLEtlYPiWyoqi1HUbr7ZJCcnc+DAAerXr4+PT8nNUXaWhISEStlkbObMmbz55pscOXLE2UORUpD57zQ+Pj5H0/KiWBzVEltamv22m6cn98dsK4khilyW9evXX1ZsS9GkYTap/i7j9r+BR5w3nGJbgZnYMoDhmMurl0flKb7/Ar7GrOppg5loK+nvyg3ge+AZzCQOwDDgrVy2rfXEbVxISsBqs+Lu5k4VX39Ozs+9svfjlu0ZsG2D/XYscBvwS8btQZiJqMJ1p7wMKWdzX0o+bh8Y6fnv6+GfR6+gSPAor2nOvJWn2BYpaYpvqagqdSVRbrI3ZHZVr7/+Oh06dKBatWqsXbuW2bNnM3LkSGcPS0qZyl7FVVWtWtXZQ6g0bMBgLiWIplIxE0QAPYBxmKuevYU5de42p44od+UhvtcA04GfcnmsEdA649Im42cohVt9LLtVmMmh37Lc1x2zcXVuLiQlkJpufnlhtdm4kJSQY5tPOnQiNTYOw2plcZS5oqhXUCB3r1/LcuA+4HPgA+As8CklUFVmS4f4A7lPEUs5U/D+fuFZEkFZkkG+dcptVVBxlIfYFiktim+pqJQkyqayJIn+/vtvZsyYwblz5wgPD2fMmDE8/fTTzh6WlDI/v4r3LaNIYajfVtkZA3yccX0klxoKV1TTMStJNgBDMVc+K97yCKXHWfFtYFZbTQdWZ7k/DEgCMtsi7824fJ5lmxrA1cB1GZf2QH4T2tdjTi3LmoRqC8zAXDnvctIiqbFx9ipYI2P10NTYOMgY0xLMWH4T+BboxqVqqYIPfj73FcTi95rTx/Lj7gdBjTMSQFmniUWaFUOVgD67xZUpvqWiUpIom9TU1BxLkrui+fPn23sFSeVx4sQJ6tat6+xhiJQ4rdxXNn4CFmRcvwd4mcv747088MJMerXBbMR9P/AzUJ6+Mirr+DYwV6mbAfyZ5f4mmImcezBfnyPAFmBzlp+Z63yeBpZlXMBMxnQAOmEmja7F7C+0HXgW+F+W52mKmZi6nbKJL3fgdaAm8BzmlLqrMBubtwGzKijhYJYkUNaqoNMFP4HfFZeSQFmnifnVAYtTuyA5nT67xZUpvqWiUpIom8Isfy5SUansVVxV9erVnT0El5cKjMq43hJ4Hyc3+S1BkcBrmEuhrwTmUr5Wuyqr+LZhVtDMwEz4ZGqJOQXsdhyTZ+EZl1uy3Hces9H0RsxVxH4DTgEpGdd/w2wQDeY0tX2YSSmABpjTFwdQ9kk6CzAt9QJXx8bweWwMjWJ3cyguhoaxuwmK2wu21PwP4O4LgVmqguzTxKIqTVVQceizW1yZ4lsqKmVEsslvCXiRiq4yVMlJ5eTl5eXsIbi8V4HdGddfw6zAcSXRmH2WPsVMiPQCWjl1RJeURXyfwFzlbWWW+9pjvhY3U/iEYFWga8ZlDGYCaC+XEkS/AXsytt2b8bMOZjXRg5R+02iLxSCgahrBtZJg93zHqqDkk/QF+uZ3AN86OZeSD4oCv7qVviqoOPTZLa5M8S0VlZJE2aSlpekftLisU6dOERER4exhiJS4f/75hzp16jh7GC7rOGaFB5hVHp2dN5RSYwHewExi/AMMxOxTVB7WbS3t+F4D3I35PoM5FexZzETZ5X51ZsGs1IrErNQCs7JoLea0rnDMRui+l/k8OaTF2pM/rbudIDAkmeDqqQRVS8XdM6N2adOTue/r5k1qUGN+DWrCX4FR7A5qQqPgJkwMbIy3Z2BJj7RS02e3uDLFt1RUShJlo+lm4sqqVavm7CGIlIpatWo5ewgubQIQD/hjrgTmqkKARcCNwP9h9t+Z68wBZSit+DaAeZjvrxWzb9BrwBBKtxdQTcxV5C57JTnDRj2fJOp7XaSJXyJRfkk0DUiCr8Ig6bh9sxbX57G/b2juy8n7hePl5k5HzAq6bzM2XwF8mTF+KRn67BZXpviWikoZEREREcnTWmBxxvXJmFODXNkNmL2XXsFMoNyEuQS7q7mIOb3ry4zb9TFXJ2vrtBHlIy3eXEb+Yrbl5OP2EHNVcs7tk7Jcd/Pm/HG4eNqL2DNeXDztxcUzXsRf8Oee7f+X79MGYTbUnoCZLFyL2dD6G6BFCZ2aiIhIeaMkUTbp6el4e+e3SKtIxXX27FkaNGjg7GGIlLiTJ08SHh7u7GG4HCvm0uAAjYHRzhtKmXoR+BGzB1M05gpcVZw4npKO7+3AHcDfGbf7AR9g9hNyGsMGiUdyX04+6ViBu59I8WR3oh97kwMYetOYS8vJ+0WwrGkbbGmOy9G7eRauNbY7MAdzxbWHMVdvuxbz9brsSijRZ7e4NMW3VFRKEmWTV2Pfrl270rp1axYsWJDnvvXq1WP06NGMHj26dAZXjlksFr766iv69+/v7KEU6r0qLxYtWsTo0aO5cOFCmTxfzZoqkhfXFBYW5uwhuKS3MZc2B7OyprJ07PMFPgKuBo4Cj2bcdpaSjO/FwHDMYhs3zKXmn6IMV6pLi4e4PTkTQXF7wJqU/75uXhAYaU4Jy5gmdt0b/2ZHnCcX083f37w8PBna5IkSH/YQzNXYbgfOZfy8C3gZ0ALXxafPbnFlim+pqCrtMgyDBw/GYrHw8MMPO9xvGAaPPvooFouFwYMH2+//8ssvmT59+mU959SpU7FYLFgsFtzd3albty7Dhg3j3Llzl3Xc8uD48eP06dOn1J8nNTWVWbNm0apVK/z8/KhevTqdOnVi4cKFpGX7llBy0mskrio1tYDlqaXIzmL25AG4FbOJcWXSFpiWcf1jYIkTx1IS8Z2MWQkzCDNBVAOzWmoipfDLoGFAwhE4/hPEvAbrR8IvN8DXdeGzQPi+Hfw+EHY8B4c/hQtbHRNEPjWh5vXQ8CFoMxe6LIOb98JdCXDTDuj8BbR+HhoMYn1csD1BVNq6YDbbzpyS9ylmhdHbgK1MRuB69NktrkzxLRVVpa4kqlu3LkuWLGH+/Pn4+prrasTHx/Pxxx/nKA0MCQkpkee88sor+fnnn7FarezatYsHH3yQixcv8sknn5TI8XNjGAZWq7VUm3LXrl3636OlpqbSq1cvtm7dyvTp0+nUqRNBQUH8+eefzJkzhzZt2tC6detSH0dFdv78eWcPQaRUnDlzhvr16zt7GC7lGcyKCW9gvpPH4izjMZsW/w6MAK4DrnDCOIoS3wbmKmX/l3HZkeV6XMY212ImOC67v1R6AsTuyagEyjpNLAasifnv6+YJAY1yX07ey6kT3/LVEFiHWVn3LHABGIZZofUWZtJICk+f3eLKFN9SUZVOJVFKCuzeXfaXlJQiDbNt27bUrVuXL7/80n7ft99+S3h4OG3atHHYtmvXrg7TyE6dOsXNN9+Mr68v9evX56OPCleI7uHhQe3atalTpw49e/bkX//6Fz/99JPDNu+88w5NmzbFx8eHJk2a8Prrrzs8/vvvv9O6dWt8fHxo3749X3/9NRaLhS1btgCwcuVKLBYL3333He3atcPb25vffvsNm83GCy+8QP369fH19aVVq1Z8/vnn9uOeP3+egQMHUqNGDXx9fYmMjGThwoWAmaAZOXIkoaGh+Pj4EBERwQsvvGDf12Kx8PXXX9tvb9++ne7du+Pr60u1atUYNmwY8fHx9scHDx5M//79mTNnDqGhoVSrVo1HH30030qXBQsWsHr1alasWMGjjz5K69atadCgAQMGDGDdunVERkbat7XZbIwfP56QkBBq167N1KlTHY41b948WrRogb+/P3Xr1uWRRx5xGN+iRYuoUqUKP/zwA02bNiUgIIDevXtz/Pil1VIKcw4pKSmMHTuWOnXq4O/vz9VXX83KlSvzPMfSVhbJPBFnqFu3rrOH4FI2Yf7BC2bT3sr6K64H5h//AZjJgME4p2KkoPhejlkldB3mCm11MFdoewJ4F/iTSwmi0cBKipAgMgxIPAonVsCef8OGx+CXG+HrcPg0AL5vC7/fC9unwqElcH6zY4LIuzrU6AQNh0DrWXD9Uui3B+5KhH474fqvoPUL0GAwVL+mXCeIMnkAT2Im3jJrqNcArTGrz4r222jlps9ucWWKb6moSqe05MABaOqE71J27YImTYq0y4MPPsjChQsZOHAgYCYHHnjggQL/kB88eDD//PMPv/76K56enowaNYpTp04V6bkPHjzIDz/8gJfXpS4PH330EZMnT+a1116jTZs2bN68mYceegh/f3+io6OJjY3l5ptvpm/fvnz88cccOnQozx5ITz31FHPmzKFBgwZUrVqVF154gQ8//JA333yTyMhIVq9ezX333UeNGjXo0qULzz77LDt37uS7776jevXq7N27l6Qks/z7lVdeYenSpXz66aeEh4dz5MgRjhw5kuvzJiQk0KtXLzp27Mj69es5deoUQ4cOZeTIkSxatMi+3a+//kpoaCi//vore/fu5e6776Z169Y89NBDuR73o48+omfPnjkSeGD2ksraT+r999/nySefZN26dfzxxx8MHjyYTp06ccMNNwDg5ubGK6+8Qv369dm/fz+PPPII48ePd0jIJSYmMmfOHBYvXoybmxv33XcfY8eOdUgIFnQOI0eOZOfOnSxZsoSwsDC++uorevfuzfbt2x2SWmUlMbGAb3ZFKqisSV65PDbMZtUGEIGZJKrMGgALgKGYS6C/CjxexmPIL77fxRxbbmoBV2a5XAO0yutA6UkZvYKyNY6O2wPpBfz7snhAYMNsy8lnXPeulv++FVg9zEqzTzFXxDsFTMWcmvgfoLOzBlaB6LNbXJniWyqqSj3dDOC+++7j6aef5tChQwD88ccffPrpp/kmifbs2cN3333HX3/9RYcOHQB49913aVqIxNj27dsJCAjAarWSnGwu2zpv3jz741OmTGHu3LncfvvtANSvX5+dO3fy1ltvER0dzccff4zFYuHtt9/Gx8eHZs2acezYsVwTK88995w9KZKSksLzzz/Pzz//TMeOHQFo0KABv/32G2+99RZdunTh8OHDtGnThvbt2wNmI+5Mhw8fJjIykuuuuw6LxUJERESe5/jxxx+TnJzMBx98gL+/PwCvvfYaN998My+99BK1atUCoGrVqrz22mu4u7vTpEkTbrrpJlasWJFnkujvv/+ma9euBb7GAC1btmTKlCkAREZG8tprr7FixQr765E1sVavXj1mzJjBww8/7JAkSktL480336Rhw4aAmfB57rnnHJ4nv3M4fPgwCxcu5PDhw/bGdWPHjuX7779n4cKFPP/884U6l5IUGxtb5s8pUhY0lbLkfAj8kXF9HuDnxLGUFw9iLnueuRz6DUCzMnz+vOL7B8wm1GA2Vb4Rx6RQ9ew7GAYkHc82NSzjZ8IhzNRgPrxCsk0Ny7ge0MCcPlYJWYC7MWNiAvAO5qp41wMPAJMxk0mSO312iytTfEtFVTpJovr1zaqeslaMOZ81atTgpptuYtGiRRiGQZ8+fahePcevVQ527dqFh4cH7dq1s9/XpEkTqlSpUuDzRUVFsXTpUpKTk/nwww/ZsmULjz32GGBW4Ozbt48hQ4Y4JErS09MJDg4GICYmhpYtW+Lj42N//Kqrrsr1uTKTPQB79+4lMTHRniTJlJqaaq/MGTFiBHfccQebNm3ixhtvpH///lx77bWAWTl1ww03EBUVRe/evenXrx833nhjnq9Pq1at7AkigE6dOmGz2YiJibEnia688krc3S8tQRsaGsr27dvzfO0Mo4BfXrNo2bKlw+3Q0FCHSq+ff/6ZF154gd27dxMbG0t6ejrJyckkJibi52f+SeTn52dPEOV2jILOYfv27VitVho3buywT0pKCtWqOeeb1Tp1LrsDhUi5lDWpLcUXi9mHB8w/erXEt8mCWRnyB2a1yEDMPkW+ZfT8ucX3VuBOwIrZJ+d3zGbUAFiTIe7v3KuC0gr4ssDibiZ9siaDMiuEfPL//agyC8FsYH0/Zo+iGGAh5nTFaMwG4Q2cNrryS5/d4soU31JRlU6SyNu7yNO+nOnBBx9k5MiRAMyfX7rtOb28vGjUqBEAL774IjfddBPTpk1j+vTp9pLEt99+m6uvvtphv6yJiMLKmqTJPPa3336bI1Hg7e0NQJ8+fTh06BDLly/np59+okePHjz66KPMmTOHtm3bcuDAAb777jt+/vln7rrrLnr27OnQ06iosk4PA7Ovkc2Wd7eHxo0bs3v37ss+9sGDB+nXrx8jRoxg5syZhISE8NtvvzFkyBBSU1PtSaLcjpE9UZXf88THx+Pu7s7GjRtzvH8BAQGFOo+SdvHiRS3HKS7p3Llz1KhRo+ANJV/TgJOYvxy8gpkcEVNNzKldNwNbgCaYy8cPBIr+P3TRZI/vo8BNhkFA8gm6xcbwduxuajhUBR2k4KqgqpcSQVmniQU0BHev/PeVPF2PmcCbA8wFzmPGzSLMBNJEoOwnm5df+uwWV6b4loqq0k83A+jduzepqalYLBa6d+9e4PZNmjQhPT2djRs32qebxcTEcOHChSI/9zPPPEP37t0ZMWIEYWFhhIWFsX//fnuPpOyioqL48MMPSUlJsSd31q9fX+DzNGvWDG9vbw4fPkyXLl3y3K5GjRpER0cTHR1N586dGTduHHPmzAEgKCiIu+++m7vvvps777yT3r17c+7cuRwrvzVt2pRFixaRkJBgT1StXbsWNzc3oqKiCvW65GbAgAFMnDiRzZs35+hLlJaWRmpqqkNiLC8bN27EZrMxd+5c3NzM3u2ffvppsceVlzZt2mC1Wjl16hSdO5ePzgSaGy2uSlMpL18MZmIIzObGFeernrLTD5gEzAQOY1aIzAZeBPpSSkk1awqppzeD7w6IiyH14m7Ox8Xwf7G7CS6wKsgN/Bvk7BMU1MRsKG1RGrA0eGPGyWPAa5jJonOYiaIPgAGYqwcW/zci16HPbnFlim+pqJQkwqzS2ZUxPS6ziiQ/mVOuhg8fzhtvvIGHhwejR4/G17fohecdO3akZcuWPP/887z22mtMmzaNUaNGERwcTO/evUlJSWHDhg2cP3+eJ598kgEDBjBp0iSGDRvGU089xeHDh+1JHEs+v+wFBgYyduxYnnjiCWw2G9dddx0XL15k7dq1BAUFER0dzeTJk2nXrh1XXnklKSkpLFu2zN5nad68eYSGhtKmTRvc3Nz47LPPqF27dq5T7AYOHMiUKVOIjo5m6tSpnD59mscee4z777/fPtWsOEaPHs23335Ljx49mD59Otdddx2BgYFs2LCBl156iXfffZfWrVsXeJxGjRqRlpbGq6++ys0338zatWt58803iz2uvDRu3JiBAwcyaNAg5s6dS5s2bTh9+jQrVqygZcuW3HTTTSX+nAXRKgviqrJODZXieQZIx2x2/KyTx1KezQDuAJ4CfsRcYr4fZgXJS5jNoYvMMCD5VMaUsJhsvYIO0MKwmVkpwAtokX1/z+BsfYKyVgV5F+s85fIFYVYOPQa8jllddAaz79dHwD2YU9O8Mf/tZb9YM356Am2AurhedZ8+u8WVKb6lolKSKENQUBAASUlJeHgU/LIsXLiQoUOH0qVLF2rVqsWMGTN49tni/Vr9xBNPMHjwYCZMmMDQoUPx8/Nj9uzZjBs3Dn9/f1q0aGFvtBwUFMQ333zDiBEjaN26NS1atGDy5MkMGDDAoU9RbqZPn06NGjV44YUX2L9/P1WqVKFt27ZMnDgRMKfCPf300xw8eBBfX186d+7MkiVLADPJNGvWLP7++2/c3d3p0KEDy5cvt1fiZOXn58cPP/zA448/TocOHfDz8+OOO+5waNBdHN7e3vz000/Mnz+ft956i7Fjx+Ln50fTpk0ZNWoUzZs3L9RxWrVqxbx583jppZd4+umnuf7663nhhRcYNGjQZY0vNwsXLmTGjBmMGTOGY8eOUb16da655hr69etX4s9VGGfOnKF27dpOeW6R0nTixIkcVY1SeBuBzMnDz2L+cSt5a4PZNHoFZrPijcBqoCNmH6fnyaMSy5oK8XtzNo2O3Q1pF/N9TgMLpwPqsyEwit1BTbgyuAm97L2CaqoqqBwLxIyTkcCbwCzM3lb/zbgUVm3gKuDqjEsHKv6/VX12iytTfEtFZTGK0g04F8nJyRw4cID69esXmKSoCLJOkaooPvroIx544AEuXrxYrGomcX2Z/07j4+PtUySL45MOnUiNjcOwWrG4u+MVFMjd69eW4EhFimf9+vWXFduVXS/Mqpj6wAPf/Zdn+9yb7/bbX/8PLR4ZVhZDK/dsmAm2icA+AMOgZsoZnozdzQ2xMYTH7qZqbAzusbsh4QAY1vwP6BmU0SPoUp+gHYfT+KbjbUx0N3/PGgH8G9erKikO74dvJDU9zX7by8OTlDd/dNhmcVRLbGlpDve5eXpyf8y2MhljdomYjdBfAk4UsK0HZjVRbixAU8zEUQfMSqMamKva1cBMIBU2RmxAPBCXsX9Z1Z/ps1tcmeJbKipVEmWT2eenPPvggw9o0KABderUYevWrUyYMIG77rpLCSIp0OWuspCZEPq4ZXsGbNtQAiMSKRnZVxGUwvsVM0EEZuPqR7/9sOAk0ZsFJ4lcPpFkS4O4fbjFxXBX7G7ujI3hVOxuvGN3UzU1/2WPDSwk+deDoCh8gprgliUhhE/tHFVBv1dPtCeIbqLyNRV3tVjyw+z7NZJLjeJzu7hhvs9xmNVq67Jc/sFsTb4z47Iol+fx4lLCKDN5lIq5imFsxnGzXs86vh5An4xLvcs+47zps1tcmeJbKiolibJJTU0t1HQzZzpx4gSTJ0/mxIkThIaG8q9//YuZM2c6e1hSARw/flyrLIhLOnz4MC1a5OjUIgUwgKczrl+J2VD30RI6dmESSRVC8pmcfYJid0P8fjAu1Xi4YU4HyirOI4CYIHN62O6gJvbrewMakexhfrHjDlyB+Yd4RC4/9wGPZlRqtwWWUPl+eXOZWMrGA6hT4FbmdLWuGZdMx3BMGm0FLmTbLxUzmfRPEceVCHyTcQGzWqlvxuU6zORTSdFnt7gyxbdUVJXt94wCXebsuzIxfvx4xo8f7+xhSAWUkpLi7CGIlIrk5GRnD6FCWor5ByaYK3aV9lLu5ZYtzUz6ZE8ExcVAytmC9/ePcFxGPuOnp28YvhYLfkAA5h/7wRk/MyPWChzKuOTJzY1wYFnGcUTqALdnXDKlYDbGPp3tknnfWcxpZEH5XHwxq5a+A37BjNNdGZe5mPHXE7MvV86ulI68MafARQDhmEnU7J8x+uwWV6b4lopKSaJsXKGvkkheGjRo4OwhiJSKzJUYpfCsmMt0g7ki1y1OHEuZSTmXJRGUuZLYbojb51AVlCsP/1wTQQRGgkfuK6P6YFZoXZnLY+eAvzGTQwdz+ZmQZdtgw2C5xUJoUc5VKh1vzORRYaqT8tMRcypcErAKWJ5x2YfZt+jrjEtReWBWzYVzKXFUq0UL0jFX7FMCVFyNfjeRikpJomxSUlLw88v9lz2Riu7w4cNUq1bN2cMQKXF79+6ldevWzh5GhfIx8H8Z15+ncD1usjavXxzVsnw2r7elQ/yB3JeTTzld8P5+dbMlgjKu+9Yp0RXEQri0SlV2BmYS6RBwBPDctYsrmzUrsecWKQxfoHfG5RXMpOZy4HvMuCxIPOa0uMz0azpmAvRg1o2yfDnbEGgFtMzysx4FVyyJlFf63UQqKiWJsqkI081Eiis9vYBvykUqqLRsKxdJ/lKBKRnXbwC6FXa/2Dj7KlGGzUZqbFyObcoskZR6Puf0sNgYc4l5WwHx4O57KQnkUB3U2KwYcjILUC3j0hZYn5CQ/w4iZSASeDzjUlhWzBXcDudx+dtqJcHdnIS2L+PyZZb9A4FmmH+wpORzScNMLN0N3IVZpSTibPrdRCoqJYmy0Qph4soiIyOdPQSRUtG8eXNnD6FCeRs4kHH9+RI+dmESSYVms0LCwZx9gmJ3Q/Kpgvf3uyLHcvIENTHvt1Sc+gTFt1RU7lyaAtcxl8cTU1M56evLVmAb2H/uzXg8jkt90wqyIeMyDrgWM2H0L9A0TXEafXZLRaUkUTZJSUn4+zv/W0SR0rBv3z7atWvn7GGIlLidO3cqtgspAZiecf0OoL0Tx2KXetFMAsVl6RcUGwNxf4MtNf993X0gsLHj1LCgJuZ9nq7R5UTxLa5qV0Zs1wf6Z7k/HtiOmTDajVld553l4pPtthVzGtxSzNXZfs+4jAa6YCaM7gC0vquUJX12S0WlJJFIJWKz2Zw9BJFSodguvFeAk5h9PqYXsG2Jslkh8VBGRVC2aWLJJwre3zcsWxIoCoKbmD2EKlBVUHEovsVV5RXbAZiVR7lVH+UlGjMJ/i3wScbPFGBlxmUkZn+l0UAPCteHTeRy6LNbKiolibLRdDPnGTx4MBcuXODrr7929lBYtGgRo0eP5sKFC84eSqFYLBa++uor+vfvn+92UVFRZTMgkTLWqlUrZw+hQjgPzMq4Hg0Udd0Vr6BAe78hi7s7XkGBObbx9LISUDOJ4OqpBNdIJbhGGnzbIqMqKCX/J3DzNvsCOfQJyrh4BhVxtK5D8S2uqqRj2x+zJ9FdQCxmZdEnwA+YfYu+zbi0wEwWDcCsShIpDfrsloqq0iaJunbtSuvWrVmwYIHD/W+//TYTJkwot8mBgwcPUr9+ffvtqlWr0qJFC2bMmEHnzp2dOLLL9/LLL5dZ4/Bff/2V2bNns27dOpKSkqhXrx59+vThySefpE6dy108tvyKiYmhQ4cOzh6GSInbunWrYrsQZgEXAC9gajH2z2xA/XHLdgz4/QuzEmj3yw69gu55+njOHS/ucLztG5qtV1BGQsgvHNzcizEy16b4FldVmrEdBNyXcTkPfI5ZSbkDcyrbEOBp4BFgBFCzVEYhlZk+u6WiqrRJovLOarVisVhwc8u9hP7nn3/myiuv5MyZM8ycOZN+/fqxZ88eatWqVWpjSk1NxcvLq9SOHxwcXGrHzuqtt97ikUceITo6mi+++IJ69epx+PBhPvjgA+bOncu8efPKZBwiImXpOPByxvURFHL1n7Q4iNsDFx2Xk79rzHZYWj/fXa3pFmLPehJ71oeIfz3m2CvIq2w+70VEAKoCDwFDgRXAfGA5cAozYf4CMBB4AsjaajgFM8F0IeNn5nVPzKlrOWspRUQqvtKZxG9NMX+hLOuLtYAy9kLw9PR0uD148GD69+/PtGnTqFGjBkFBQTz88MOkpl5qpNm1a1dGjhzJyJEjCQ4Opnr16jz77LMOVTEpKSmMHTuWOnXq4O/vz9VXX83KlSvtjy9atIgqVaqwdOlSmjVrhre3N4cPH85znNWqVaN27do0b96ciRMnEhsby7p1l9Z/2LFjB3369CEgIIBatWpx//33c+bMGfvjcXFxDBw4EH9/f0JDQ5k/fz5du3Zl9OjR9m3q1avH9OnTGTRoEEFBQQwbNgyA3377jc6dO+Pr60vdunUZNWoUCVmW53399deJjIzEx8eHWrVqceedd9of+/zzz2nRogW+vr5Uq1aNnj172vfNfK2zvmajRo2iZs2a+Pj4cN1117F+/Xr74ytXrsRisbBixQrat2+Pn58f1157LTExMXm+bkePHmXUqFGMGjWK9957j65du1KvXj2uv/563nnnHSZPnuyw/Q8//EDTpk0JCAigd+/eHD9+6Rvy9evXc8MNN1C9enWCg4Pp0qULmzZtctjfYrHwzjvvcNttt+Hn50dkZCRLly4t8jn873//o23btvj4+NCgQQOmTZtWrOXsNd1MXJVKugs2HUjC7PUxMesDhg0SDnHXlE48+VwTXozYyq//rsY/i3zhsyD4vj38cR/smA6HP4UL2/DwzFL16VMLal4PjYZBm7ms+CiCL+c14KNpjVn6agNWfxYBrWZA/fuhWgcliIpB8S2uqqxj2wL0xJxytgsYDvhiJoPew5yGFgmEAX6YU9FCMafmXgvchJlMuitjm+GA429+Ipfos1sqqtKpJIo/AN8WtdNBCbhpl9nE8jKkZSzbm9WKFSvw8fFh5cqVHDx4kAceeIBq1aoxc+ZM+zbvv/8+Q4YM4a+//mLDhg0MGzaM8PBwHnroIQBGjhzJzp07WbJkCWFhYXz11Vf07t2b7du325clT0xM5KWXXuKdd96hWrVq1KxZcOFrUlISH3zwAYC9yufChQt0796doUOHMn/+fJKSkpgwYQJ33XUXv/zyCwBPPvkka9euZenSpdSqVYvJkyezadMmWrdu7XD8OXPmMHnyZKZMmQKYq2P17t2bGTNm8N5773H69Gl7gmzhwoVs2LCBUaNGsXjxYq699lrOnTvHmjVrADh+/Dj33nsvs2bN4rbbbiMuLo41a9bkOcVs/PjxfPHFF7z//vtEREQwa9YsevXqxd69ewkJCbFvN2nSJObOnUuNGjV4+OGHefDBB1m7dm2ux/zss89ITU1l/PjxuT5epUoV+/XExETmzJnD4sWLcXNz47777mPs2LF89NFHgJloi46O5tVXX8UwDObOnUvfvn35+++/CQy89N3StGnTmDVrFrNnz+bVV19l4MCBHDp0qNDnsGbNGgYNGsQrr7xC586d2bdvnz1hl/m+FFZZTTc7g7kiSR0gAs33l9Knku78bQM+Sk+gdeweJsbupqa9cfRus1LImsSn+eWQ3TwhoJF9Wtgfs/9Lx5eXmNVBXlUdNv1n7yJsufxfKsWn+BZX5czYbgK8CcwE3gJew6y43FvAfj6YSaV44D8Zl/aYCaN7MBPxIqDPbqm4NN2sELy8vHjvvffw8/Pjyiuv5LnnnmPcuHFMnz7dPh2sbt26zJ8/H4vFQlRUFNu3b2f+/Pk89NBDHD58mIULF3L48GHCwsIAGDt2LN9//z0LFy7k+eefB8wE1euvv16orPO1116Lm5sbiYmJGIZBu3bt6NGjBwCvvfYabdq0sR8X4L333qNu3brs2bOH0NBQ3n//fT7++GP7PgsXLrSPLavu3bszZswY++2hQ4cycOBAe8VRZGQkr7zyCl26dOGNN97g8OHD+Pv7069fPwIDA4mIiKBNmzaAmSRKT0/n9ttvJyIiAoAWLVrken4JCQm88cYbLFq0iD59+gBmv6iffvqJd999l3Hjxtm3nTlzJl26dAHgqaee4qabbiI5ORkfn5ypib///pugoCBCQ0MLfI3T0tJ48803adiwIWAm+p577jmH1yar//znP1SpUoVVq1bRr18/+/2DBw/m3nvvBeD555/nlVde4a+//qJ3796FOodp06bx1FNPER0dDUCDBg2YPn0648ePL3KSqLQlA/OA5zFXGMlUB6gPNMjyswHmt3WlN0FSpBIybJB4zGHlsH/iYqgaG8PFxCMF7n4q1ZOYRD92J/qxNymAlx6cZyaG/OuB26VfGQ5s/4mO1a8pxRMRESkb1TCrK8cCXwF/A1Uwp6hVzXI986cPcAR4F3gHOAZsyLg8iVlpNBxoXVYnICJSwkonSRRQ36zqKWsB+fdHKIzs083ALBX08/Oz3+7YsSPx8fEcOXLEnuy45pprsFgsDtvMnTsXq9XK9u3bsVqtNG7c2OG4KSkpVKtWzX7by8uLli1bFmqcn3zyCU2aNGHHjh2MHz+eRYsW2ce+detWfv31VwICcn6XsW/fPpKSkkhLS+Oqq66y3x8cHJzrVKT27ds73N66dSvbtm2zV9MAGIaBzWbjwIED3HDDDURERNCgQQN69+5N79697VOtWrVqRY8ePWjRogW9evXixhtv5M4776Rq1arZn5Z9+/aRlpZGp06d7Pd5enpy1VVXsWuXY2xlfc0ykz+nTp0iPDxnxw3DMBzep/z4+fnZE0SZxz516pT99smTJ3nmmWdYuXIlp06dwmq1kpiYmGOaYNbx+fv7ExQU5HCcgs5h69atrF271qFyzWq1kpycTGJiokNsFqS0ppsZmA0hxwGHcnn8WMblt1weuwmYBrQrlZFJZVHpSrrTE7P1Ctp9aWl5a6LDpjnS/xYPCGyUYzn52tMmcjL50mZeHp68VKdf9r3FCSpdfEulUZ5i2wu4u5Db1sXsZfQM8B1mNdFyIA6zOulN4GrMCqXyc4ZS1spTfIsURekkidy9L3vaV2kLCgri4sWLOe4/c+ZMiTdQjo+Px93dnY0bN+Lu7rhqS9ZEjq+vb6ETGHXr1iUyMpLIyEjS09O57bbb2LFjB97e3sTHx3PzzTfz0ksv5dgvNDSUvXsLKqS9xN/fP8e5DB8+nFGjRuXYNjw8HC8vLzZt2sTKlSv58ccfmTx5MlOnTmX9+vVUqVKFn376id9//50ff/yRV199lUmTJrFu3TqHFduKKmtiL/P1s9lsuW7buHFjLl68yPHjxwusJsqeMLRYLA5T46Kjozl79iwvv/wyEREReHt707FjR4d+VXkdJ/v48juH+Ph4pk2bxu23355jjLlVS+WnNKabbcRcRjZrAmgwMAlIBPYDB3L5mfm3aOZytP0xf+HSf6dSHC5Z0m0YkPSPQ1WQ/Wdi3j3rMp3zrs7OoChiAqNICWrCXUFRVA9qYn6h4pbzC5Hz6Z6Yi0RLeeOS8S1CxY9tD+DmjMthzOqidzG/GFsH9Mr4GeGsAYpTVfT4lsqr0k43i4qK4scff8xx/5YtW3JU/GzdupWkpCR8fX0B+PPPPwkICKBu3br2bbI2jc7cJjIyEnd3d9q0aYPVauXUqVOlskz9nXfeyeTJk3n99dd54oknaNu2rX3VLg+PnG9xgwYN8PT0ZP369fZqm4sXL7Jnzx6uv/76fJ+rbdu27Ny5k0aNGuW5jYeHBz179qRnz55MmTKFKlWq8Msvv3D77bdjsVjo1KkTnTp1YvLkyURERPDVV1/x5JNPOhyjYcOGeHl5sXbtWnu1VlpaGuvXr3dorl1Ud955J0899RSzZs1i/vz5OR6/cOGCQ1+i/Kxdu5bXX3+dvn37AnDkyBGH5uAlpW3btsTExOT7mhdWXqvlFcc/mImg9zEriQCuAxbgWBWUW22cAZzA/NZtBnAQ+DrjcidmsujKEhupVAYlGdtlLj0J4v42K4Iu7s6ynHwMpMfnv6/FAwIbZiwn3wQjKIpvgpowIiiKf7yrYcGcRjGVSvwfvguo0PEtkg9Xiu1wzMroZzF/nxkEnAT6Amsxp6tJ5eJK8S2VS6X9nXHEiBG89tprjBo1iqFDh+Lt7c23337LZ599xjfffOOwbWpqKkOGDOGZZ57h4MGDTJkyhZEjRzr8wz98+DBPPvkkw4cPZ9OmTbz66qvMnTsXMKtXBg4cyKBBg5g7dy5t2rTh9OnTrFixgpYtW3LTTTdd1rlYLBZGjRrF1KlTGT58OI8++ihvv/029957L+PHjyckJIS9e/eyZMkS3nnnHQIDA4mOjmbcuHGEhIRQs2ZNpkyZgpubW4GVTBMmTOCaa65h5MiRDB06FH9/f3bu3MlPP/3Ea6+9xrJly9i/fz/XX389VatWZfny5dhsNqKioli3bh0rVqzgxhtvpGbNmqxbt47Tp0/TtGnOJuf+/v6MGDHCPsbw8HBmzZpFYmIiQ4YMKfZrldk7auTIkcTGxjJo0CDq1avH0aNH+eCDDwgICLC/bwWJjIxk8eLFtG/fntjYWMaNG2dPJJakyZMn069fP8LDw7nzzjtxc3Nj69at7NixgxkzZhTpWFmnzxVXEvC/oQ8wjEt9h+oBs4E7MFcOKYgFc7WQIcD9wCLMZNERzGlrX2A2f5wCaD02KYxmzZo5ewj5MwxIPpF7VVDCIS6lWvPgVRWCml6aHpb5M6CBvSooDrMPxn8zdqkJfAjcUGonJWWl3Md3Kdn++n/Y/uZ/SE9K4uOW7Wnx8DBaPDLM2cOSEuSKse2B+YWXB3A7sDPj9nLMKW1SebhifEvlUGmTRA0aNGD16tVMmjSJnj17kpqaSpMmTVi8eLFDQ2GAHj16EBkZyfXXX09KSgr33nsvU6dOddhm0KBBJCUlcdVVV+Hu7s7jjz9uX4EKzMbQM2bMYMyYMRw7dozq1atzzTXXODQ4vhzR0dFMmjSJ1157jfHjx7N27VomTJjAjTfeSEpKChEREfTu3due2Jo3bx4PP/ww/fr1IygoiPHjx3PkyJECpy+1bNmSVatWMWnSJDp37oxhGDRs2JC77zZncVepUoUvv/ySqVOnkpycTGRkJP/973+58sor2bVrF6tXr2bBggXExsYSERHB3Llz7Y2ps3vxxRex2Wzcf//9xMXF0b59e3744YdcexgVxSOPPELjxo2ZM2cOt912G0lJSdSrV49+/frlqGjKz7vvvsuwYcNo27YtdevW5fnnn2fs2LGXNbbc9OrVi2XLlvHcc8/x0ksv4enpSZMmTRg6dGiRj/X3339fVtlrOtAd+HPUo8ClpbSfoPgrmHkBw4BozAaQMzFXF/kv8AlwX8Z9VxR71FIZ7Nixo3yUdFuTzaqg7Img2BhIj8t/X4u7mfQJjDKnbAdmSQh5V4d8kvibMZdkzpxM3B0zQVRwi36pCMpNfJexFo+YSaGPW7ZnwLYNzh6OlAJXju3+wFzMZtYrgIcxp6IVrrGEuAJXjm9xbRYjr/XHCyk5OZkDBw5Qv379IvdHKY+yNwIePHgwFy5c4Ouvv85zn65du9K6dWsWLFhQ+gMsJQkJCdSpU4e5c+deVqWOlE+Z/06Tk5Ptq80Vxzogcz2jaOAFSv6P0CTMRo8vAJntva8AfgUuf8KduKotW7bQunXrsnkyw4Dkk1kSQFmrgg5SYFWQZxV78ufEzovUvnFQRlVQQ3Av+vfMXwADgFTADbMCbxLgnt9OufB++EZS0y/1JPLy8CTlzZzTsoF8/2hfHNUSW9ql47h5enJ/zLYijkayKtP4Lofyi7fCxG32mATFZXnh6rFtAI8B/864PQPz81kqB1ePb3FdlbaSKC/e3t7OHkKZ2Lx5M7t37+aqq67i4sWL9qXdb731ViePTEpTbiu+FcWvGT8Dz53nvZCqlMZMa1/MRtgPAa9jzu0/CnQFVqJEkeSuJHp25WBNgbi9jj2CMhNCaTkXPnBgcQP/+o5TwzJ/etewVwX9Mrw9A4bcVuwhbsWcspmKmbD9GPPfiriWUolvkXLA1WPbgtmr8SDmIh3PAPUxE/vi+lw9vsV1KUmUTXJyco4VvVzVnDlziImJwcvLi3bt2rFmzRqqV6/u7GFJKdq/fz/VqlUr9v4rM3423bARtxt7lsiY8uIPjMNsfH0r5kohXTETVZGl+sxSEe3atat4Jd2GAcmnsi0jn/Ez4QAYua+UaOcZnDMJFBhlLjHvXjJfOmx//T+59mE5B9yGWX1XA7PSr26OrVxDXq9BZVHs+BYp5ypDbHsAS4DrMacGP4D5WV3yS9lIeVMZ4ltck5JE2WRv3Lxo0aIC91m5cmXpDKYUtWnTho0bNzp7GFLGLqdSLo1Ly9w3W78BSjlJlKkXsBS4hUuJopUoUSSOCpzubE2F+H3ZEkGZVUEXCji6xVw2PjAqZ2WQT618ewWVhO1v5kyQWIGBwAHMaWWf4boJIsj9NahMXGE6f2mp4uvPhaQErDYr7m7uVPGtHF/0uYrKEtsBwDLgaszq6P7AH0DjfPaRiq+yxLe4HiWJsvHy0roD4rpCQ4vfQWg9l1Yza/ZX2TYQvREzUXQr8A+XKor0y5Vksk+lTD5zKQGUuaR8XAzE7wfDmv9BPAKzJICyVgY1Avfy9YveVOD7jOtzgC7OG4qUgcudKuzKTs7/CoCgkTcR+9q3Th6NFFVliu0wzCln12FWgvbFTBTVcOagpFRVpvgW11JiSSKbrYCS/AoiJSUFDw/lzsS1ZP77PHjwIDVqFO/Xkcx+RLWAsAMHS2RcRZGZKLqFS4milShRVCnZ0iBun0OfILd/NoLtKKSeK2BnC/hH5N4ryKd2qVcFlYSvMZufgtnX4nHnDSVXXkGBpMbGYVitWNzd8QoKdPaQKrw9e/ZoyoK4pMoW2y2BzzETRPswK4pWUPwVYqV8q2zxLa7jsrMhXl5euLm58c8//1CjRg28vLxyTNmqSNLS0khOTnb2MERKhGEYpKamcvr0adzc3BxW7iuqzCRRV5y3fOsNwDfAzcBxLlUURTlpPFLKUs7m7BMUuzujKijdYdMcaQgP/0v9geyJoCgIbAwevmV2CiUtBhiUcb0l8DaX/j2Wl749d69fC+S/IpUUTWXplSiVT2WM7RuBN4BhwO/AGC6tfiaupTLGt7iGy04Subm5Ub9+fY4fP84///xTEmNyKpvNhptbaazZJOI8fn5+hIeHEx8fX6z9UzB/kQHoVmKjKp6eOCaKuqFEUYVmSzeTPlmTQJlNpFPOFry/XzgERZHsFYFPzTaXqoJ8wypEVVBRxGE2qo4DqgBfAd906ERqbBwAhtXKlpdfwyso0J6oEddQu3ZtZw9BpFRU1th+CNgBvAIsBuYBlWN95cqlssa3VHwlMq/Ky8uL8PBw0tPTsVoL6PlQzm3fvp0WLVo4exgiJcbd3R0PDw8sFgv79u0jJCSkyMf4C3MFJTCTMs6uDcieKOqKmShq4sQxSQFSzmVLAmVWBe0zp4/lx90v59SwoCgIjDQrhoDt69fTobHrlnQbwGBgF2bl0H+BBsDa2DhsaZdeP8NmsyeNxHUU97NbpLyrzLE9EjNJFIc5fb6XU0cjpaEyx7dUbCXWfMdiseDp6Ymnp2dJHdIpgoKC1IleXFZQUFCx9sucahaGuaqYs5NEYCaKlmEmik4AbYDHgAlANSeOq1KzpUP8gdyXk085XfD+fnUdl5EPzvjpVwcs+Vd4Fje2K4pZwJcZ16cDvZ04Fil7rh7fUnlV5tiOBJpiJv+/RkkiV1SZ41sqNnVozkbZXnFlxY3vzCRRN5zXjyg3PTATRbcBscBs4C1gLDCaXPrUSMlIvZBzGfnY3RC/txBVQb4ZVUBRl/oEBTWFoMb2qqDicOXP7u3XXM2sjOu3Ak87czDiFK4c31K5VfbY7o+ZJFqK2ZdIDS9cS2WPb6m49FmUzcGDB509BJFSU5z4TsZcohXMaV3lTXfMFULGYM7njwUmY07FmY85fikGm9VcQezYctg1D/4aDj93gS9rw+dV4cdr4M/BsPNFOPoVxO5yTBD5XQG1ekDkI9DuFej2A9x6CO6Khz6b4bol0HIa1BsAIW0uK0EErvvZfRB4bdZMbJgr+X1A5fmP+5MOnVgc1ZLFUS1JT0xicVRLPunQydnDcgpXjW+Ryh7bt2b8/IfyUaUtJauyx7crWb16NTfffDNhYWFYLBa+/vrrPLd9+OGHsVgsLFiwwOH+c+fOMXDgQIKCgqhSpQpDhgwpdr/Y0qZKomyqVq3q7CGIlJrixPefmI2rwflNq/NSHZiDWT00A3gHOAM8idkMcjJmP5eKPRm2lKReNCuBsvYJio2BuL/BlpL/vu4+5mphOXoFNQbPsq3jcsXPbgO4H4ivUoUAzOkI5aVwvcXDpb+KWqr6Ldm5YnyLgGK7AxCK2V/xf8BVzh2OlLDKHt+uJCEhgVatWvHggw9y++2357ndV199xZ9//klYWFiOxwYOHMjx48f56aefSEtL44EHHmDYsGF8/PHHpTn0YlGSKJuAgABnD0Gk1BQnvjOnmtXFrM4pz64A3sScbjYFs7nvUcxlZmdjJpD+RfmaMlcmbFZIPJz7cvLJJwre3zfMsVdQZjLIP7zAXkFlxRU/u5cDv2Vcfwuzd0V50eKR0k8SySWuGN8ioNh2A27B/Iz/Gpjp1NFISavs8V0RxMbGOtz29vbG2zvnWoN9+vShT58++R7r2LFjPPbYY/zwww/cdNNNDo/t2rWL77//nvXr19O+fXsAXn31Vfr27cucOXNyTSo5U5GSRBs3bqRGjRoAnDx5krCwMFJTUzlz5gx169YlPj6e8+fPU69ePc6dO0dsbCwNGzbkxIkTJCQk0LhxYw4fPkxycjJNmzZl7969pKWl0bx5c3bu3InNZqNVq1Zs3boVINfrbm5uNGvWjB07duDp6UmjRo3YtWsXPj4+hIeHs2fPHvz9/alduzb79u0jKCiIkJAQDh48SNWqVQkICODIkSNUr14dLy8v/vnnH2rVqmU/p/j4eJKSklzqnFzxfdI5Fe+c1q9fT+3atYt0Tt82awb+/rQ4c4Y9Z88SEhKC1Wpl79695eKc8nqfRu/Ywa2BgbzfqBHLPTz4G7gbmHfxIlNPneKqatXK7ftU7Nir7s/xmJWEuJ8iyHKClNNb8LcewyvlIJYCqoJsFi+SPcNxC25Comc4F6y1qBrRkTOpIVxIsF06p7gEGoc25vCBwyQnbyw3/542bdpEq1atKsb7lOWcDJvB+vXrc5yTh5cXj8QnQFRj6m/bQdqd9/KBxYKHvx+Rb71qPyfDMHK8l4ZhHrOo55TjODYbGzduLPb7ZLPZOHHiRL7/nr7cu4Fh1/TO9X3K7dzAXIW0sn2WW61Wjhw54lLnVJT3yWq1ER8fn+852Ww2Tp8+nes55RZJBnDgwIFy/xlRkd6n4pzT0aNHXe6civo+XWWz8VZYGDuBH/bvJ+Ts2Qp/Tq74PhXnnI4cOULPnj1d6pxc4X06cuQIzZs3ByA0NJTExET7/w1Tpkxh6tSpufyvkT+bzcb999/PuHHjuPLKK3M8/scff1ClShV7ggigZ8+euLm5sW7dOm677bYiP2dpshh5/RZWSR04cID69es7exgipaIw8f3C8o94uu9AABKBKkAasBBzyhbAxy3bM2BbxZk9/ycwHliTcdsHs9JoDBVwCpphg4TDuS8nn/RPwfv71M45PSyoCfiFg5t76Y+/lFTUz+68/i19AtyTcX3soCE0/+13ANw8Pbk/Zpt9u8VRLR2mZOW2TWHVeuI2LiQlYLVZcXdzp4qvPyfnf1Xk42QqzOdE0MibiH3t21wfK8lzq+gqanyXlO2v/6fA6jXFUsVU2WMbzCn9NYA4zKrnsc4djpQgxXf5V9hKoqwsFgtfffUV/fv3t9/3wgsv8Ouvv/LDDz9gsVioV68eo0ePZvTo0QA8//zzvP/++8TExDgcq2bNmkybNo0RI0aUyPmUFE03y8bLy8vZQxApNYWJ7xeWf2xPEv2OmSCC8tm0urCuAVYBizB/+TqHuULUR8B/gI5OG1k+0uJz9gmK3W32CrIm5b+vmxcERuY+RcwruGzGX8Zc6bM7HbOPFkDUn39xZUaCqLRlJoTy+2O7PCtMIqGicqX4Lg5XfV9FsQ3moht9gE8x+xIpSeQ6FN/l3/+zd+dxbtTlA8c/Sfa+uz225/ba7m6BtmgpCIhyC63IUUAsP0QRsEBRwRMUARGKgtxCRVEQW0QQ5EZAQMQDSjlLu7vd7Unv7XbvI7vJ/P74TnaTSTbJ7k4ymcnzfr3yyiSbSb7pPp2dPHm+z7eoaOTdHtesWcOdd97Ju+++i8vljKYWkiQy2LFjB5MmTbJ6GEIkxFDj+3X9epp+sTMX8HXgi6gKooeBtcCRwDeB5aiqqaTS/ND5SeReQV3bY++fMy4oCRRIBFVD/jRbVwUNh5OO3X8E6vTtM391hyN7aAVXLWUvPRFgxJVLH61wbpLISfEtRDCJbeVUVJLo38AeYJy1wxEmkfhOD//617/Ys2cP5eXl/ff5fD6++93vcscdd7B582bGjx/Pnj17Qvbr6+ujqamJ8ePHJ3vIMUmSyCAwx1EIJxpqfAeaVqfqqmbDMRb1Ifx8YClQj2p2/TfgThLU2LqvA1rrDBVBteo+X2f0fd2ZUFARYYpYFWTJqhkBTjl29wDX69uf+te/qfpwLZrbjcujkn5ZRcldNW4koq2A1tzVgbdP1Sn6/P7++0RkTolvIYwktpWFqA9lfcCzwAXWDkeYROI7PZx33nkcf/zxIfd94Qtf4LzzzuPrX/86AIcffjjNzc2sWbOG+fPnA/Dqq6/i9/s57LDDkj7mWCRJJISIqB14W992UpIo4DjgQ9RKIr8EdqEaW/8BuBr4LENMFmmaqgpqq4WWQBJITwp1bou9f/bY8D5B/VVBcqhOF/cDW/Xt3x91JAfXfmi7HmABTq3qEUIIs5WgpvW/gvrSSpJEQqSW9vZ26uvr+29v2rSJ999/n9LSUsrLyxk9enTI4zMzMxk/fjxVVVUAzJ49m5NOOomLLrqIFStW0Nvby7JlyzjnnHNSbmUzkCRRmN27d4eUignhJEOJ73+jvtECZyaJAHKBnwNfQU05+zfwon45GPiW/rOc4J36OlVfoJApYjXQVqcqhqJxZUDhzIEEUHCvoOxS099fOnHCsbsDFY8AZ6NiUAhwRnwLEYnE9oDTUEmil1F/D/ItHY0wg8S3c7zzzjscc8zAJ6Irr7wSgPPPP58HH3wwrudYuXIly5Yt47jjjsPtdrN48WLuuuuuRAx3xCRJZJCKmTwhzDKU+A5MNasAJidkNKnjQOAN4CHgF0CtprGnawcPt9ayvrWG01pr+XRrDTlttdCxJebzNWeV8nFRNXVFVWwsqmZbUTW7iqrYXzCDXHcmhdB/mQzMCLqMIwHT3dKAE47dd6F6UbiBn1k8FpFanBDfQkQisT3gS8AyoBt4CUitBbHFcEh8O8fRRx/NUBaF37x5c9h9paWlrFq1ysRRJY4kiQy8Xq/VQxAiYYYS36/r10cnYiCpoq9LVQW11eJuqeHrbbV8rbUWX2sNGX3tUXfVXB7aCmayqaiad4qq+E9RFTVF1dQWVrEvZ8ywh5RHaNJoBjAGVfWUo18HX3KCrrNJ7EG9C9iPWqa3SB9XZpz7akAjqgdUg369ETXeGcDMoEspQ0+U2f3Y3Yya9gjwNaDKspGIVGT3+BZiMBLbA6YA84E1qFXOJElkfxLfwq4kSWTQ2NjI9OnTrR6GEAkRb3y3AYEOKLafaqZp0L1rYFpYa9Cy8h1bUOmLAS5CD4wdWaNYW1TNx0XV1OqJoMbCKlYXzKDXE7q0qRs1ReirwBH67Tb90h5huwXVf2YTEDiN6ESturZ2mG/XDWShEkaBi/F2tPvd+rj2Gy7NqKbKRiWoZuDj9OvAZTSwl4GEUAPQGud7KCY0cTQb1SNqBoMnj+x+7L4V9W+cCfzU2qFw1cIlFo9AGNk9voUYjMR2qFNRSaJnUFP+5YOavUl8C7uSY4/BlClTrB6CEAkTb3z/C/Dp25GSRNFWLbKMrxva6iMvJ9/XFn1flxvyZ0RYQaya/OwxzHa5eAt4ApXwCHCjvvX7vH75LCppMlR+YAeqsib4skm/3k/kBM1gz9WtX5KhWb9sGMI+2QwkgXpR73Gzvg0qSfWefgk2EfgccJR+fQDqdwD2PnbvAe7Qt5cCU60bCgBXLTzX4hEMzaMLjsTb2obm8/Fw1Vyyigr58up/Wz0sU9k5voWIRmI71GmoLwqaUH0SP2/paMRISXwLu5IkkUF7e/QpJkLYWbzxHehHVAVMiPBzy1Yt0jTo3jOwhHzwKmIdm0HzR98/syR0CfnAdsFM8GQPulsRqon1MlRT6w9QFUNH6j8bKTeqN9FkVPIjkuDkT5fhEri/B1WR1BNjO9rFh6rkGRXhUqJfF6ISOXsHuewB9qGmjVWgkkHB15MYSO4E+IBtqIqjjfp14PKxPv4dwJ/1C/rzH6VfZnm9fGmQf7tUtxzVpDQPtbKeGBpvaxv+XpVi1Px+vK0xksI2JOcmsUkFnD1JbIc6CJiO+pLob0iSyO4kvoVdSZLIYP/+/VYPQYiEiTe+A0mikUw1++je+4efTPL1QHtD5Kqg3pbo+7rckD89YlUQ2WPBNfy20G5goX5JNjcqiZBnwWsngweYpl+OM/ysG3gb1Vz8DeA/qKRKE6pvw1MA5eV8FdX8uTgZAzZJ4/gy7tW3vw2Mt3IwImXJuUlsdquAE4rEdigXasrZHai/bbchi1nYmcS3sCtJEhlMmzbN6iEIkTDxxLeWm98/zWdESaIVMZJEmgY9e8OTQK210LExjqqgoqBl5KuClpWviFoVJOwnB1VhFaiy6gXeZyBp9CYqYfRH4J/Aw6jqIjt48psX4kUltr5v9WBEypJzE+FUEtvhTkMliTYBHwFzrRyMGBGJb2FXkiQyaGpqYuzYsVYPQ4iEiCe+fTMPJJCeMaXM2efVq4Jqw6eJeWN9w+KC/GmRq4JyykZUFSTsKxNYoF++i2rueUVjI/eNGcMWVNz+ELge1Zw7VW0A3jj1FEAliEYN8riU7AEmkkrOTYRTSWyHOxI1nTpQLStJIvuS+BZ2JUkig9bWeNffEcJ+4onvvkp1OnIAUDaUJ+9uHOgP1FrL5xbXwzOV0L4RNF/0fTMKw5NARVVQOAs8OUMZhUhDGcBXN23i/8aM4f9QzcVvBv4O/AkVy6noGsCfkcFY1FSzwVjWA0ykDDk3EU4lsR0uAzgFeAjVl+gaS0cjRkLiW9iVJIkMZs6cafUQhEiYeOLbN0sliSJONfP3qqSPcYpYWy307At56ORZQFtw/yAX5E81JIH07dwJUhUkRmTmzJmUolZE+y5wv749H/glqul4KkXYvcCj+vbVQMEwnyerqLC/UbPm8+HyeMgqKjRhhCKVyLmJcCqJ7chORSWJ3kUt6iBrZNmTxLewK0kSGezatYvS0lKrhyFEQsSK7ybAP2k6pT37WNxaG5oEaq2BtgbQ+qK+Rq/XTWtjNi17M2ltyqGzs4Qj7nlMVQVl5Jr8joRQArFdAPwG+CLwDdRqa98CngN+D0y0boj9ngeW+Xzg8VD19mqKL/gmj+bmDmvZ9uB9Vs09hCUfvmPiSEWqkHMT4VQS25GdiOrH142acrbM2uGIYZL4FnYlSSKDjo4Oq4cgRMKExLe/D9o39SeBVr50D1NHaezJ72RsT2PsJ8srj9gr6M+fOgl/70AiyZ2ZyRGjZEa9SCzjsfsUVMPPC4FnUVPP5qASNIcle3BBPgC+DGgeD+M3buLyb16Ou7MLb2/05KtZRrTqoLCMk89Nlj+/UlYmS2NOju2RyAdOAJ5BkkR2JvEt7EqSRAaVlZVWD0EIc3n391cEzfF/CG/cpG6316vpY7pzA331eoL29eTpyZ+qgZXEiqv1qqD8QV4wlSb1iHQR6dhdBjwN/Ba4AlUp9z3gX0kd2YDtwCKgHSjYv58rvrGUgpaWGHuZK+aqg0lSkptPc1cHPr8Pj9vTf18wmUo3wMnnJsufXyVJojTm5NgeqdNQSaLXgWagxLqhiGGS+BZ2JUkig61btzJnzhyrhyHE0Pj7oGNzUJ+goGli3Xv6HzZoC+i8yfxjeyfrD1xI7YRDqWnYy8a/v07DHa+Dy52ENyDEyAx27HYBF6NOrr8MvAmsBQ5K5uBQiaFTUImiLODbl32Hsi1bkzyK1LH79icBKFq2iNZ7nov4mERMpbNr1Yqcmwinktge3BdRf8P6UFWwS6wdjhgGiW9hV5IkMuju7rZ6CEIMztscngRqrYG2evB7o+/ryaUjYwr5ZZ8Kmh5WBYWVkFnAyd87i97LHlaPffknZPXkSIJI2EasY/fpwHhgF6pn0d1JGFOAD3Vy/55++0Ggb817+JM4Brubs9Sc6qd4qlZScUqeE89Nyq44vb+aLHvpiZTk5vcnD0X6cGJsm2UccCTqy40/oSqL8qwckBgyiW9hV5IkMpg9e7bVQxDpzu+Dzi3QUhOypDytNdC9O/b+uZOC+gQF9QzKm4zW0QkFkddR8h+4YOD1N3xo4hsSIvFiHbszUY2sbwT+CCxn+CuKDdV3UVMGAG4AvgI8nKTXdopkJm1SZUpeMCeemzR3deDtU1OefX4/zV3SuyMdOTG2zXQqKkn0AuqLji8D56OSRzK5P/VJfAu7kiSRQX19PQcffLDVwxDpwNuikj8hiaBaaNsA/p7o+3pyVF+gQCKov1dQJWQO3rMjWnz7539ObdR+AB1tkJE5zDcmRPLFc+y+CLgJaAX+jGpqnWh3A3fq2+cDP07CawrnkXMT4VQS29FdALwMvAS0Ab/TLxXAV/XLVMtGJ2KR+BZ2JUkig97e3tgPEiJefh90bh2oBAqpCtoVe//cCSoBZFxFLK8c9GavQzFYfLcA2uxPqxvvvD7k5xXCavEcu6cCC4HngBUMniQya7rRc8B39O2jgfux7pvfj+69n49W3E9fVxer5h7CnKUXp0S1zFULpctGPOTcxJ5ScepiqpHYjq4UtTrnZlQF6oPARqAe+Kl+OQb4GrAYtSqaSB0S38KuJElkcNBByW5nKhyht22QXkEbwBdjPrI7W68KMiSDCishq9jUYQ4W308DZGappNa7Vq39JMTwxXvsvgSVvFkDvAMcot//6IIjQ1bSev/Oe8gqKgxpnjwU76OmBfiBKuAJVMPqRIrWt2fOpSopZFYDaLPYsYm0FeTcxJ5ScepiqpHYjs804BrgJ6jpZw8Bf0FVF72mXy5B9S06FzgBNc1aWEviW9iVJIkM1q1bx/z5860ehkhFmh86twVVBQVdd22PvX/O+PBEUFEV5E0dVlXQcAwW348FNmo/gLbmpIxFCDPFe+w+CSgHtqKqiX6n3+9tbcMf9I2f5vf3J42Gah9qVZoOYAwqKTVqWM80NPJh1Lnk3EQ4lcT20LiAo/TLXcCTqITRK0AnsEq/jAbORiWMDgdkGRJr2Cq+29qgtlZdWlvhkkusHpGwkCSJDPx+WW8m7fW2Q1tdhOXk68DXFX1fdxYUVgz0CQpeRSyrJCnDjyZSfLegSpkBWPNGMocjhGniPXZ7gItR38Y+AtwKlJg8lisZWOr+KWBmhMdkFRXibW1D8/lweTxkFQ3eS0wIOTcRTiWxHZ/lz68Mq7zMQyWBzgU+QfXaW4mqZN0H3KdfpqIWTDgXOAjoRa30uQPYGeG6GShGTXUbpV9KDdclqISVP+iiGW6D+vs3zqR/AztKufj2+2HbNpUIqqkJvd4e9IV3YSEsXQouaY+eriRJZDBv3jyrhyCSQfND53ZDRZA+Tazzk9j754yLnAjKnwbu1P1vFSm+nwG8oP5wvCtJImFPQzl2XwBch/rW9U/AMhPH8XfU6mkA1wJHDPK4wDS2VJv+JVKTnJsIp5LYjs/y51dFnZ47GfieflnHQEXRJmALcLN+KUElgZJpCmpqd+AyH1XplA4si+/2dqirC08G1dVBV4wvvLOyYMoUaGmBkpKkDFekntT9NGuRDz74gAULFlg9DGGWvk5VARS2nHwt+Dqj7+vOhIKK8OlhRVWQlYzJI+aLFN+BqWau+o/QWvcnf1BCmGAox+4JqL4Nj6OmnF1m0hjaUVVKAPOA75v0vELIuYlwKolt8x0A/By4AXgLVV30KLCXyAmicai/ixP1Swmqynw/0GS4Hs4k7G365cmg+6YzkDSaA8xC9V1y2gfThMa3psEnn0SuCtq2Lfb+Y8dCdbW6VFUNXE+bBhlO+02IoZIIEPanaaonkLFPUGutWlksluwxAwmg/sqgaiiYntJVQWZoZWCqmXvNG/isHIwQSbQUlST6GBhea+pwP0b1OnKjeh1J01AhhBBWcQGf0S+3A6+iKovGM5AUKmNof6t6UYmmFv22W7+4grYDt32ov7HvBF0CqYtN+qW/JybqQ+l0VMKoQr8OXMpJ3w+tWmcnvXV1ZBkTQbW10BnjC+/MTJg5cyABFJwMKi1NzhsQtpSu/98GJWWvKayvU60WZlxOvq0W+jqi7+vKgIIZAwmg4Mqg7HQpeg2P72eAHvQ/7u+9KUkiYVtDPXYfgzrx3ICqJvrCCF//v8Dd+vZ3GVg1TYhY4lkmXc5NhFNJbCdHBnCiCc+TCYzVL/GYZHjd3QysLhq47NR/1of6m7whwvO49deciEpwBS7Bt6fo16nURSfu+NY02L6d/bW17Kmpobu2lsyaGkpraxm/dWvM1VE7x4yhvaoKV3U1xdXVZAWSQdOnS1WQGBaJGgMpe7WYpkHXjoHkT/A0sY6tqLZ4UWSVGhJBejKoYIaaPpbmjPEd+AbnKOB/MtVM2NhQj91u4Juo/g2PAUeMKiF/z95hvXYP8A3U0Wkmqt+REPGKZ5l0OTcRTiWxnV7KgIX6JaCVgeTQBqA+aLtRf4wflWDaDbwX5flLgANRDboPCtqON6kVzI9KXA12ydNfL9qHaWN8e7u62LthA201NfTV1uKpqSG/poYxdXXktbf3NwqPpDcjg4aZM6mprqa2qqr/uraqiqbRA194u1CVWHP1yxz9ejqyyp2InySJhDX6ulRVkDER1FoLfe3R93V5oGBmaDVQYJpYzpjkjN8B2oAX9e2zgP9ZOBYhrHA+aopYD/Cv00/lpN/8bljPcxOwXt/+LerEUQghhHNFWm1MDE8Rqpl1pIXi96OSRltRFUfBq7AFLsFf7zSjppAbp5GPRSWLKlCLtXTol/YI252oaXUxvpbuV4BKFgVWfRulaUzbuZNZtbVkrF7N9pUrGVNby5SaGqZs2cIkLfoz7ystpb66mn1VVfRUV5NTVUVOVRU7Z86kMTOTJtTqdT1AISr5U4xasa5LH3cgyfbXoOfNRyWMzkJ9SZYf5/sT6UmSRAZS9moiTYPuXYY+Qfo0sY4txK4KGqUnf6pCq4MKZoInVuGliCQ4vp9lYKrZYtQUGSHsajjH7jGok6U/Aa99+UxOvP8B3DFO3ow+Apbr2xehprENxZyl0StIzJbs1xPmkHMT54pnuqGT2TW2Y602BvK7NcMoYIF+GYwXVWG0CdUDaW3Q9T79MXuB1/SLWbK7u5m1YQNVtbVU19SEXBe1RW/x3efxsHHGDLZUV7O3qoq+6mpyq6oYX11N5ZgxHMrQp835gY2o85IPgy4NqE9cHagvhP+HOm+5ErVwR9EQX0ekB0kSGUjZ6zD4egy9gmoHlpPvbY2+r8sN+TMiryCWPRZcqTSz2P6C4zsw1eyzqDncQtjZcI/dS1FJot3TprLuyMM56M3/xL2vD7gQ9Y3jBOCXQ351kv4BQj6w2JOcmzhXPNMNnVy14uTYjud3K0YuC9WPaArwuaD7NVTyKDhxtAXIQVXR5KOqgPINt/P058wAMjSNvN27KaqpobC2lvyaGvJqa8mtqSFr82ZcMb5Yai0uZs/s2bRUV+OtqsJdXU1+VRWjZ85kZlYWleb9M+BGVUpVAKcH3d+hv/cPgX8Af0FN47sadd7ybf1iz3WbRaJIksjA7ZbZmhFpGnTvMSwjr193bALNH33/zOLITaMLZoInOznvQfTHdzvwgn7fWZaNRgjzDPfYfQSqBH0t8NqSLw8pSXQX8La+fS+qzByg7IrTae4aaKZfkpvP7tufRFgn8Dvx+X1kLz3Rdr8TOTdJb/FUrdiVxLZIFBdqJbfxwHGxHtzTA/X1kZeTb2mJvq/brRpEB68gNns2VFWxYetW5h9i7VIW+cCh+uVC4GfAzcAfUdPzrgduA5YBVzC8/k3CeSRJZHDAAQdYPQRr+XqgvSHCcvI10BvjIOlyQ/40lQAqrILi6qBeQeOkKigFBOL7WaCbgalmQtjdcI/dLlQ10TLgveOPZf+4sYyKo4H1RuAn+vZZwGlBP2vu6sDb1xtyW1gr+Hfi8/tt9ztJ+3OTEcoqKsTb2obm8+HyePrvE9aT2BZJo2mwZ0/kRNCmTeCP8YV3cXHoEvKB64oKyI78hfcBhal3nJkFPABcA/wC+D2qT+ly4E7gElQLCpllkN4kSWSwdu1ax5a99tM06GkMXUa+vypoY+yqoIxCQ0VQoHl0BXhykvMexLAE4jsw1exI1PKhQthdPMfuwaZsnAd8t6OTnvw83jj7TE69576oz6Ohmj52osqz7x7uoEVKeXTBkf2JhIer5pJVVMiXVxvbn1ojLc5NEijwe1w19xCWfPiOxaNRUjnekkliW5jO6x28Kqi5Ofq+bjdMmxaeCKqqgrKyIX/hncrxPQ24D7WAxy3A/ajzml8B9wBrUKvDifQkSSKDzEwHLZPu80L7xoH+QMEJIW+s5c5delVQVfhy8jnjpSrIpjIzM2kHntdvy1Qz4RTxHLsHm7JRBBz50su8evqp/PMrZ3PKb35HBoNXGjwIvKJv34Za0lfYn7e1DX+vqjbS/H68rYM3Hk12Q1pHnZtYKJUatw8l3pxMYlsMi6ZBY2N4EqimRlUF+XzR9y8sVAmgSFVBOeZ94W2H+J6MqiC6GpUguhdVbSQ1fulNkkQGFRUVVg9h6LobI/cKam8ALcZBMqMgQtPoaiiogIzc5IxfJE1FRQXPoaaagUw1E84x0mP3L08/lUOApgnj+fslF3Hqdy5nH3AjagneZv16P7Ba3+cE4PwRvaqwq2Q3pLXluUkKivY7C1T2BHNidU+qrbglsR3d8udXsvz5VXR6uylatoirFi5xbH+qiHp7oaEhPBFUUwP7Y3zh7XLB1KnhiaDqahifnC+87RTfZahG1j8AdjL01dWEs0iSyGD9+vWpWRbo7x2oCgpOBLXVQs++GDu7IL88cq+g3AlSFZRG1q9fz2N6fB8JTLJ2OEKYZqTH7vmoJXZXA49+53IejfH4POA3yEmUCGdsXA4jb16esucmDhJc2RN8n13Em/xJtRW3JLaju2rhuVy18FyKli2i9Z7noj421RKAQ7JvX+SqoI0boa8v+r4FBZF7Bc2aBbnWfuFtx/geo19EepMkkUGOiSWGw9KzL/JS8m0NoMU4SGbkDyR/giuDCmdBRl5yxi9Smj83V6aaCUcy49h9DWrZWB9q+dtR+qUkaDtw+SIwfcSvKJKlJDe/f3Uzj9tDSW5+wl7L2Lg8cN9IWH5uIlJeqiV/4uXE2Db2m4LEVqUFv977d96TuhVwvb1qKlikZNC+WF94A+XlkaeITZyYsl94OzG+RXqQJJFBeXl54l/E3wftmwYaRwdPFetpjL1/3pSgBFAVFM9W27mTUvYgKVLDLR176NK3ZaqZcBIzjt2nAK3Ao4ceydfe/rdUCTlIoIonnm/jU1FSzk2EsIATY9vYbypwX7Jez/IKuKYmlfwxJoLq62NXBeXlRa4KqqxUP7MZJ8a3SA+SJDKoq6szryzQuz+8Kqi1Ftrr1fSxaDy5A9VAIdVBlapiSIhh+FuGaqB3BKpRnRBOYdaxOw/I7u6RBJFIKaaemwiRQiS2B195M6X19amqoEgriO3dG3v/KVMiJ4MmTVIrjDmExLewK0kSGeTnDzEB4/dBx+bw5eTbaqF7T+z98yZHniKWNxlczjlICut1AL456g+VTDUTTjPkY7cQNiLxLQaT7KlNZkvX2A7uXebz+7ju6YdG3LssIZqbI08Pq69X08eiyctTFUCRqoLS5PeervEt7E+SRAbjx4+P/ANvS2gCqL9x9Abwe6M/qSfHkAgKVAhVQmaB+W9CiAieB8hSc6NlqplwmkGP3UI4gMS3GEyypzaZzW6xHUju+Pw+speeOOzEjrF3mc/vH3HvsmHz+WDz5shVQbt3x95/8uTIVUGTJzuqKmg47BbfQgRIkiiY38e2mjconZYdPkWse1fs/XMnhvYKKqpWK4nlTZGqIGG5x/TrzwBTrByIEAnQ0NBAaWlpxJ8ZT+ph5KtNCZFM0eJbCDuzW2wHJ3csTewMR0tL5ETQhg3gjfGFd05OaFVQIBlUWQmFhckZvw3ZLb6FCJAkUYB3PzwxgXn+Htgc5XHubLVaWFF10EXvFZRZlKzRCjEknUCgVatMNRNOVFQ0+PHXeFIfuE+IYFlFhf3TdlweD1lF4R98jFN7kjWtJ1p8C2FnqRjbdl5K3qVpFPR64YUXwpNBu+L4wnvCBJUAmj07tCqovDztq4KGIxXjW4h4SJIoILNELRPv7VG3cycM0iuoHNweS4cqxFA9g0oUAZxp5UCESJBkf1Nn5w8RIrJAsmfV3ENY8uE7ER9j1SpC8k10ejJralMqS8XY/miFDY7vra39K4jNa9xFUXc3Rb1eivu8eDQNFi4cfN/sbFUBZJwiVlkJktQwVSrGtxDxkCRRgMsFR6xkXcMeDjjsNMgqtnpEQphCA27Vt90bPqJ81hwrhyNEQmzevJmxY8cm7fVs8SFChLlq4RKrhzAsyY5vkRpsPbUpThLbUfj9sHUr1NTw195SuOSSgcqgnTv7HzZ3sP3Hjw/vE1RVBVOngke+8E4GiW9hV5IkCjbxZLI66yVBJBzlH0DgO/HMlx8HSRIJBxo1apTVQxAWiWeaWIDtlpnWSXyLVGNWNWUqxbZV00nze/uoaunioLYe+OlPB6aH1dVBdzcAJwy2c1YWzbhoycikJTOblsws2nLzWPjRGiiWzzNWS6X4FmIoJElkUFAgq40JZ1muX88BNn682sqhCJEwcuxOX/FME7M7iW+RTMufXxkzoWpWNWUqxXZCp5NqWn9VELW13Pmv9VQ0t1Pd3MnkzqCm0a+ujbx/WVnkFcSmTeOZAz7VP24Ad2amJIhSRCrFtxBDIUkig23btslyhcIx3gJe1bd/BFysN+2NpCQ3v7/3gcftoSQ3PxlDFMIUcuwWZpmzNPWmEUp824tVFSlmWf78qqRV3Tkutjs6GNXdRWFXJ8W9PRT3elWvoF6vmualWxphV6/bRVb17MjJoJKSpL0FYR7HxbdIG5IkMhgzZozVQxDCNIEqohnA2cA3Xa5BHxtohlm0bBGt9zw36OOESEVmHrtTMUkgkicVe03JuYm9WNXgPJpUTVzZMrY1jckdPVS1dKopYpdfPjBFbNs2vhhr/7FjedPTy/qiXGpLcqkpzqOmJI8dJYV03v9KMt5BSnHyQhC2jG8hkCRRmKysLKuHIIQpPgae0rd/gP6fffAckRC2Zuax26knq8K+5NzEXobSJytZzEpcmZ1sSuXY9vj98P77IcvI/+/l/zGruYOCvqDK7H/Xhu3rB9oys2jRL205uRzx5GOqKqi0lOOWntjflDwgK02XmHfyQhCpHN9CRCNJIoMdO3YwadIkq4chxIj9Qr8eD5yvb2t+zaLRCJFYNz33J3598Q+tHoYQYVN3A/eNhMS3vTi5T5bZVVKWn3drGuzYAbW1VDbvo7C7i+JeL8XeHgp8ffCpT4U8/FOG3RtzMhkz/9CQqWF/+/b3acWFFlS97c7M5IjDD++/HThOADLN38Esj28hhkmSRAZlZWVWD0GIEdsMrNK3rwRy9G1XlOlmAXZdIlqktz++/zq/Rj5EC+slYuquxHfqiae5s92UXXF6f4Ize+mJlOTm98dzwl4zWefdXV2wYUNIVVD/dXs7AIcNtq/HAxUVUFXFr7Z8wMdFOdQW51FbnEtbQT49K14KeXjb93+C1ts7yJMpwf+u6TrNfyhVaXadkiafK4VdSZJICAe6FfABJURujhiN0056hRAi1QQ+HAEp1yNGxCeZzZ2jMU5tC9wX63GRHtPc1dE/Bcrn9/dXutiGpsGuXeFJoJoa2LJF/TyKHrenf3pYYCn5Y179O8yYAZmZAFxtmCYmk4mGL56qtOBE0vt33iPHSSGSRJJEBrt376a8vNzqYQgxbLuBB/Tty4Hg00AtxgmSEHYlsS3sJPjDEcSetiPxnTqsqLaJJt6pbak6BW5Y593d3VBfHzkZ1BZ9+pvf7cY9c+bA9LDA6mFVVfzls8eFLyVfVTWct5Wy7FaRk4pN4IdCPlcKu5IkkcHEiROtHoIQI3In0A3kAd8y/Mzlls7VwpkktoWTV6WT+E4dtq+2STGDnndrGuzerZI/gQRQIBm0aVPMqiBKSkISQF/7z994L89DXUE2/sxMSnIz2H3LLaa/n1Tn5CbR8Uh2kkw+Vwq7kiSRgdfrtXoIQgxbC/BrffsiIGzhTfkyWjiVxHbac+IHn0DVSp8vNapWhDCbt60NPv44cq+glpboO7vdMH16fyLorb/8lcNWPaySQ2PHQlAfxkeWvjYwTayvN6HJvXinAIrkS3aSTD5XCruSJJFBY2Mj06dPt3oYQgzLvUArkAl8N8LPZcqCcCqJbeFEwVUr3j5nVa0YV4GTlZ2cp79qQ9Ng796I08OmbdoEfn/0JyoqGqgKCr6uqIDs7P6HNbzyBod97nPDHm88fZviMdSpfU5eMMSJDd6HQj5XCruSJJHBlClTrB6CEMPSBdyhb/8fEBzJ/T0U5Nto4VAut9vqIQghhiARq8AJi3m90NDQnwTK++Wt8PAf1O3m5oi79Nf6uFwwbVrkZFBZWUhVkNFQVsmKxqq+TU5OoiSzwXu0qWTGGAGS0gRbPlcKu5IkkUG7vgymEHbze2AP6oTLuFBySA8Fh30bLQRIJZFIDrMqDYSwLU0j29dHca9XXXx9cMopqjJo40bw+fofOhPgf/tC9y8sDEkC7SwuZsLRR8OsWZCTM6wh2b25sRiZeFZAM8ZI4L7BmFUBJZ8rhV1Jkshg//79Vg9BiCHrBQLtFxcDzlqLQ4g4SJJIJEGqrhAlhNky/H6q9nfAU0+FTA87u2E92X5f6IOffTb0tssFU6eyo7GJid/4emhl0IQJIVVBn6xezYQ5c5LwjkSqMSvpnogkoVkVUPK5UtiVJIkMpk2bZvUQhBiyPwNb9O2rrByIEBaR6WZCCDEM+/b1J4Bu/N8GZu1vo6qlk5mt3WRqGvzltJCHZwdt97pctGblMHrx6aHTw2bNgtxcXp97CEvuuCPqy9vtvDsVe2nZtcLRrKR7Kr9/u8W3EAGSJDJoampi7NixVg9DiLj5geX69onApy0cixBWkelmQtiTk5v2poy+PjUVrLaW6r274MILB6qDGhv7H/a9wfYvL+9PAr316F9pdntozcyi05OBOyuL81auHPbQ7HbenYq9tNK9wtGs9x/o3wng88fu4RmtB1KA3eJbiABJEhm0trZaPQQhhuRpYL2+LVVEIm1JkkgIW3Jy096ka2pSiR/jcvINDaBPx/k0wAMPhO+bl8d7eR7WF+VSW5xHTUkeG0uLWP3QK5A/UC1T9/fX+6f2mMHJ591zliZvqXUxcsH9OwF8/ug9PD9aETtJ5OT4Fs4mSSKDmTNnWj0EIYbkF/r1Z4DPWzmQNBLPt0ciuWS6mRAi1SQkSdDXB5s3hy0nf8a6D2D06Ji7d2Rmkv/5z4evIjZpEp+59KSQD8lZGZkhCaJEcPJ5t5wnONNQVtNzcnwLZ5MkkcGuXbsoLS21ehhCxO13qETR2QQtJSsSKp5vj0RyyXQz4USB/id9Ph8ZntTofyLiN6K/E83NLNjdwsymVqpaOqlu7qS6tQt+n9dfFRQsZF2w3FyV+DEuJV9ZyVOHf54lL788/HGZTM67nSkwdSueaVt2M5RG2RLfwq4kSWTQ0SFLgwt7ORD4o9WDEBFJxVESSZJIpBgzeu0EPlQVXHIS7fe9OOLnE6kjq6iQ3pZW8nq6Ke7rpbS3G775zYEKod27eTPWk0yaNJAECiSCqqth8mSwSXWlnHcnx1CqX8wQPHUr1rQtJ5P4FnYlSSKDyspKq4cghHAIqThKHrdNPhCJ9GFmrx2Jb5traQnrFfTlrhbYsgG83oHH3X9/2K5dHjcbinKpKcljw6gCfnzlDf1VQRSmzipOwyXn3eaJNr0xEcvEi9gkvoVdSZLIYOvWrcyZM8fqYQghbCrwbR2QtG/sBPg1v9VDECJhJL5twOeDrVvDm0bX1MCuXbH3nzAhrE9Q5cM3Up/jQXOpyeRZGZn8+FxnNfqW827zyJdSg8sqKuyvpHJ5PP33mfFc0Z7n7dvu5ITrfzqs1xHCSpIkMuju7rZ6CEIIGwv+tg7kG7ukkdlmwskkvlNGgbeP6ftaqWrporqlk9mt3TB3LmzYALHOIbOzYdaskGTQi9fdyEnvvgVFRWEP3/K329D6zFtJLBXFe969/PmVg1bnxfOhPdDfy+f34XFLf690E/iibtXcQ1jy4TtJe65djz8JkiQSNiRJIoPZs2dbPQQhhBBDJNNxhJPFE9/SA81EmkZ+Xx8l3m64666QyqB9O3ZE2GF36M3x48P7BFVVwdSpoFcxBDT98o6ICaJ0Ee959/LnVw2aJIrnQ3ugv1fRskW03vPcMEYqRPyS3QNKCLNJksigvr6egw8+2OphCCGEGAK/X6bjCOeKJ76lB9owtLf39wqa27ibop4uinu9FPV6yQg0w//2tyPu2uN2saEolw2jCjj9KxeGriRWXJzEN2Fvct4tohnK1K5UIj2ghN1JksigN8KyokIIIUS8ZFqD80VrECtSjN8Pn3wS2icocL19e//D5g22f1lZSALo1FceZm1BNpsLcvC7XWRlZNJz441JeStOFO28O7CMOpByS6mbsXqhiM3MaWJCOElXVxcvvvgi69evp6Ojg5/97Gds1/+mTZkyBZfey264JElkcNBBB1k9BCGEEHEKfIjw+ZLzASKeEvLA60froSHsLdkVO26PTKeMqaMD6urCk0G1tdDVFX3fzEyaXW5aMzJpzsymNTOLlsws2vLyOaf+45CHvlj3Yv/S3mLkop13By+jDslbSj2eJLAc24UQVnn22We54IIL2LdvX/99P/vZz/jMZz7D7t27efrpp1m0aNGIXkOSRAbr1q1j/vz5Vg9DCCFEHII/RPj6Ev8BYigl5PIhQpjF75PplABomqr+iVQVtG1b7P3HjAntERS4nj6dZw78dMiiAwBuQ/8gp7OiCjIVz7tl2mbqkepN88gXWPb21ltvsXjxYvr6+tD0adEulwuPx8Ppp5/Offfdx+OPPy5JIrNJXwshhBBCCAt1dqrVwoKXkQ9UBXXESARnZEBFRWjj6MD26NHJGb9NWdHcWc67RTwkcWeeaE3gReq74YYb6O3tpaCggBNOOIEnnxyonv/0pz8NwNtvvz3i15EkkcG8eYPOShdCCCGESLpoFS1DWUUnpb5B1jTYuTNyVdDWrern0YweHV4RVF0N06dDZmZy3oMYMTnvFkKI+P3nP//B5XJx6623cuCBB4YkiaZOnQrQ35toJCRJZPDBBx+wYMECq4chhKkCJeR9vj4yPBnSSFcIIWzkvLmfG/RnQ5kCack3yN3dqiooUq+gthgr/ng8MHNmeCKoqkpNHRNDlmrTduS8W6RaTAqRyjo7OwGYPn162M/a9L+pZizEJUkiIdJAoIS84JKTaL/vRYtHM+Cje2XJZiGEiOVrnzrW6iFEp2mwa1f49LCaGtiyJXZV0KhRkauCZsyArKzkvIcUlIgeQfI3V6Qas2JSkk0iHZSXl9PQ0MAjjzzChRde2H+/pmk88MADAEybNm3EryNJIgMpexVOlmpNOD9aIUkiIYSIJWXOTbq7ob4+fHpYbS20tkbf1+1WSZ9IjaPHjIERLtfrRFb0CDLDUKZAZvzvHTCpkkiSBOlNzidFOvjiF7/IHXfcwUMPPcTf//73/vurqqqor6/H5XJxyimnjPh1JElkIGWvwsn8Pp/VQxAi6YzfxgfuE8Iuknpuommwe/fAlLDgZNDmzRCr0XBxcWgSKLA9cyZkZyflLTjNVQuXWD2EIRnKFMi1K+7nU5dfYsrrSpJACOF0V199NY899hjbt29n165duPQvWBoaGgCYPHkyP/jBD0b8OpIkEsLGyq44PWzJ75Lc/P5vH4UQA9/Gp1TTXiGs1tMDDQ2hSaDAdktL9H3dbpg2LXIyaNw4qQoymROPW4FqI79ebQRErTgSQgxf8OcFn99H9tITo35ekHYQqWvMmDH85z//4ZJLLuGFF15A06dzu1wuFi5cyH333UdpaemIX0eSRAYpU9ItRByauzrw9vWG3TeYVJtuJkQyOfGDlrCnrKLC/uoKzefD5fGQVVQ46OOHfW6iadDY2J/8+fm/18MXv6gSQRs3xq4KKiqK3DS6ogJycoY3JuF4gfiOFtvB1UZ+PQ6jVRwJ4VTJSMgYPy/4/P6InxeCp4q+f+c9krhNUVOmTOHZZ59l//791NfXA1BRUcGoUaNMew1JEhnIdDPhZDLdTAghrBd80r1q7iEs+fCdqI+PdW7i0jQKe70U93op8fvg618fqA7av7//cd8CeH+TYWdXaFVQcGVQWZlUBYkhC8R3PLEtRLpLpf6cQ5kqKqw3atSohOUtJElk4Ha7rR6CEEIIIUS//nOTxsawPkFf2lRLYa+XkLOXBx8Mf5KCAt7NdfPpE08JrQyqqIDc3CS8CyGEEEKMxLXXXsvDDz9MdXU1zz//fMjPFi1axPr16zn//PO59tprR/Q6kiQyOOCAA6weghAJ4/ZIElQIIVJab6+aChaUCDp4/Xqoq4OmprCHFwdta0BHRiYFxx0bXhk0YQJHX/5FWu/5U9LeivQBE0IIIczz17/+lS1btvC9730v7GennHIKL7zwAo899pgkicy2du1amW4mHMvvi9F/QiSdNAcUIk01NUFNDTOaGuGHPxyoEGpogL6+kIeGdZPLz+9PAr3/91dodmfQmplFa2YWWnY25734YtLeRjTLn18lSSIbsttqakIIkS42b94MwKxZs8J+NnPmTAC2bNky4teRJJFBZmam1UMQQqSRVJqLLoQwWV8fbNoUvnpYTY2aOgZ8BuCXv4y8f3k5VFWxt7SUsUcdNVAdNGlSf6+gj6rm9veQAJB6UTFS0RJ78TSlFqIkN5/mrg58fh8et4eS3HyrhySEIwSWvK+pqeGEE04I+VlNTQ1A/4pnIyFJIoOKigqrhyBEwkjPrZEJXvXh4aq5suqDEELZvz+sVxC1tVBfr6aPRdHncpNx8LzwVcRmzYL8fFqBjPZ2KChIznsRIgppSi3iEVha3U5TTgOJLcCWyS07/VuL4ausrOS9997jZz/7GQcccADHHXccAP/4xz+44YYbcLlcVFZWjvh1JElksH79epluJhzLH2u5Y4cb6dQuWfVByLfoaayvDzZvjpwM2rMn9v6TJ0dcQewvC09jybtr+h+mAeuAp4C/AauBg4D3iTDtTAiLzFkqFbBOZWayIdWSFtHiNpDYAihatojWe55LxpCiCnw5GRDty0mZ3pseFi9ezHvvvUdTUxMnnngi2dnZuFwuuru70TQNl8vFmWeeOeLXkSSRQU5OjtVDECJx0nwlY5naJUZKvkVPAy0t4YmgmhpVFeT1Rt83JwcqK2H27NDKoMrKwSuBXC58wH9RSaGngHrDQ9YWFPAEcNYI35oYObOn0dg12SJ/S53LyckGM+M2Gf93g7+cDNxOJPkiLPVdeeWVPPbYY3zwwQcAdHd3h/x87ty5XHnllSN+HUkSGZSXl1s9BCESxu2S6WbCflKxubddP9gJnc8HW7ZErgratSv2/hMnhk4NC1xPmQJxTuttA14D7r/uGr4D7DX8vAT4IrAWVUV0M3AmaZ/rt1yg2sCsSoNUO7YJIeLjxP+78kVY6svJyeGNN97g6quv5pFHHqFJX/V01KhRLFmyhBtvvNGUohdJEhnU1dXJdDPhWOfN+7zVQxAibh/dez8frbifvq4uVQW29OKUOSlLlXGIGFpbIyeCNmyAnp7o+waqgoKnhwWqgoqKhjyUXuAt4BX98hbQB3DGqf2PKQdOA04FjgIygReAhcC7+n6hbSqFcC6794gRIhrpc2kvb7zxBrfccgtr1qxh586dPPnkk5x22mn9P7/uuuv485//zLZt28jKymL+/PnceOONHHbYYf2PaWpq4vLLL+eZZ57B7XazePFi7rzzTgqG2HOwsLCQu+++m7vuuotGfRGMMWPG9De1NoMkiQzy8+WPj3Cuyz57itVDECJucy5VSSH5RktE5ffD1q3hiaCaGti5M/b+EyZErgoqL4+7KigSDfiYgaTQP4H2CI87mIHE0DzCK4VOAiq7u6nLyeFmhpckKrvi9P4pUtlLT6QkNz+k/4YQqSgVe8QIYRbpc2kvHR0dzJs3jwsuuIAzzjgj7OeVlZXcc889zJgxg66uLm6//XZOPPFE6uvrGTt2LADnnnsuO3fu5OWXX6a3t5evf/3rXHzxxaxatWpYY3K5XP3PbTZJEhmMHz/e6iEIkTDJiG+ZzyyESIi2NpX8CU4E1dZCXR0Y5uSHycoaqAoyJoSGURUUy1PAJUCkFNVEVKLneOBY/XY0LuB7fX1cDLyKamQ91Hrn5q4OvH3qw4jP7++vzkgUSUoJMHda7lULl5j2XGL4Av+3g8n/b5EOTj75ZE4++eRBf75kSegx6rbbbuOBBx7gww8/5LjjjmP9+vW8+OKLrF69mkMOOQSAu+++m4ULF3LrrbcycWLks4Fjjz0Wl8vFXXfdxYEHHsixxx4bc6wul4t//OMfQ3h34SRJZNDQ0EBpaanVwxAiIZIR3zKfWQgxbH4/bNsWuSpox47Y+5eVhawc1r89dSp4krM22FrgK0CXfrsIOAaVFDoeqGLofYUOWr+e6QsWsAn4BfC4SWNNlGQnpURqMnNarlMbKdtN8P/t4PtEqP4vTPXVpuQL09TV2toacjs7O5vs7OwRPafX6+X++++nuLiYefPmAfDf//6XkpKS/gQRwPHHH4/b7eatt97i9NNPj/hcr7/+Oi6Xi5aWlpDbgwnE3EgNKUm0Zs2a/pKm3bt3M3HiRLxeL42NjUyZMoX29nb279/PtGnTaGpqorW1lZkzZ7Jr1y46OjqorKxk69atdHd3M3v2bOrr6+nt7eWggw5i3bp1+P1+5s2b19+tO9K22+3mgAMOYO3atWRmZlJRUcH69evJycmhvLycuro68vPzGT9+PA0NDRQVFVFaWsrmzZsZNWoUBQUFbNu2jTFjxpCVlcWOHTsoKyvrf09+v59NmzY56j058fck70m9Jy3Skvaaxpo1ayK+p6amJlavXp2U9+Tz+di+fXvU9+Tz+Whqakra70nTNFavXj3s96RpWug/NVBfXx/ynoyPCey3evXqiO/J5/Ph9XptF3vJ/P/k8/mora2N+J7C/r31f+tUf09O/D0N5T25OjpofecdJrS24qqtxV9TQ9GOHXgaGnDHqAryZ2bSM3kymQcdxL6xY+mYPJmJxx5LjabRm58f+T3t25eU39OmvXu5cO5cujIzGdXbyx9aW6nav5+2oN/TO8P4PRXl5XHW5s38cto0ntA0Hl+7lqnd3cybNy/8uKRptLe3h7wn498KTdPYu3dvwmIP45j8flavXp0SsTfYe9IIP3YDrFu3LuLvye/zpfx7SuVjRMS/lcDq1asT+57S9G9upH/v1atXR3xP/qH8zdX/f8c630ul2Ivn9+SP4xw22nta9Nrfqa+vZ/fu3Xzuc59j3bp1IeffAJmFhXhbW9H8ftweD67cXNasWRPynsL+rTWNdevWRXxPfr+fXbt2RX5PEX5vaFrYOWzgPfl86pid6r+n4f5/2rZtGwcddBAAEyZMoLOzs/+f5dprr+W6664L//eKw7PPPss555xDZ2cnEyZM4OWXX2bMmDEA7Nq1i3HjxoU8PiMjg9LSUnbFs2BGyK8u8t8rM7m0ZLyKjezduzdhc/uEMFv20hPDvtHJysikZ8VLER+fzPiOp5IoWdVGwc0BA1PghtMc8OGquSFLkbozMzmv9sOIrwXE9XpScRVbtH8j4/+BaPEvkszvh08+idw4+pNPYu8/blxo0+hAZdC0aZCReoXQGnAesBJVKfQSqnLIDHv37qVg7FimolZB+wbwO/1n8RyXkv3/xI7/L43/jhD53zJAeuSMzFD/vc2Srr+33807lH+cfQb7x4/npN/9gdFN+4cV20M977Qrs+IknvPuaOc48RzfA6KNOXiaYHAT+MGmCabTuelwKolcLldY42pQfYt27txJY2Mjv/3tb3n11Vd56623GDduHDfddBMPPfQQtbW1IfuMGzeO66+/nksuuSTia23ZsgVQyaysrKz+27FMnTo1rscNJvXOsiy2efNmSRIJx0rX+E5mc8DgZFA6/ZEVaayjQ/UFMiaD6uog6Nu5iDIyoKIifHpYVRWMGpWc8Zvkd6gEEcBPMS9BBOrYvWDsWL4D/Bj4I3A9MMnE1xBCOI8XdWy6+uXnaBmnzv9eP+csvnTfbzkbGNmkGhFLqpx3SxP4wRWZ2JcwPz+fiooKKioq+MxnPsOsWbN44IEHuOqqqxg/fjx79uwJeXxfXx9NTU1Re8YGJ3u6urr45z//CcCBBx7I/PnzTRu7kSSJDEbZ7KRUiKGQ+BZCDIumwfbtkauCtm6Nvf+YMeFJoKoqmD4dIpTU2837wOX69nHANSY/f+DYfSlwM9AG3AHcYvLrCOF06dIA2w88gkpYbwQYNxaXz0dmTw89+fk89r3v8B7qOLJI3yeehvMlufkRK1Kcxqw4kfPu9Ob3++np6QHg8MMPp7m5mTVr1vQnd1599VX8fj+HHXZYXM+Xm5vLhRdeiM/n4y9/+YskiZKpoKDA6iEIkTAS36kjeArcw1Vzhz0FTghTdXXBhg3hiaDaWmiPtIB7kIwMmDkzNAkU2B49Ojnjt0ArcBbQA4xHVROZ3SI7cOwuAb4J3AqsAK42+XWESJZAY1+/z4dbbyqfjOa+Tm+ArQHPoSoOgyclzX/pFc649Q7yW1p57AdX8u/Fp1EPfBGVJLqd+BrOp0tFillxIufdztHe3k59fX3/7U2bNvH+++9TWlrK6NGjufHGG/nSl77EhAkTaGxs5Ne//jXbt2/nrLPOAmD27NmcdNJJXHTRRaxYsYLe3l6WLVvGOeecM+jKZpFMnz6d+vp6srKyTH+PwSRJZLBt27akLBMuhBUkvlNHMqfACRFC02DnztAEUGB7y5bIDS6DlZaG9gkKJIJmzHBEVdBQaMCFQD3gBv4MlCXgdYKP3VcAdwHtwL1AeQJeT8SWLhUpiRL4UuThAz/FeR+/Z/FonOFfwFVA8NdNxwE3AbWXX9l/znHR96/i2Mf+ynN/fph3UUmllwDfaRfAMw9BT/TFA0T8knHebawAA6L2GxLD884773DMMcf0377yyisBOP/881mxYgU1NTU89NBDNDY2Mnr0aBYsWMC//vUvDjzwwP59Vq5cybJlyzjuuONwu90sXryYu+66a0jjuPLKK7nkkktYsWIFixYtwu12m/MGDSRJZBDoQC6EE0l8C6cJlL4Hlvx0Ytn7sHV3D14V1BYjKenxqKSPcYpYdbWaOiYA+DXwmL59A/D5BL1O8LF7IvBVVJ+RO4GbcnLINDQAHomP7r3f1KXLncrpFSnJYsZSzU63BWgA9gPN+nXwpRnYhZr2GnAIsJyB3mihrXJh1nsf8Dbwe1RFYiPASefAYcfB4/fD268m4J04lwbsQf2uApdtQPbMmYwDorUQnrN0ZMdbYwVY4D5hrqOPPjrqqmJPPPFEzOcoLS1l1apVIxrHrl27mDFjBi+++CIVFRWcdNJJatVYw7H0pz/96YheR5JEBoku3RLCShLfwmkC35Rt376dSZPSsI2vpsHu3eGJoJoa2Lw5dlVQSUnkXkEVFSDHi6hWA1fq2ycBP0rgaxmP3d8HHkCtdPavM07l2If+ZNprfbRCkkQimSRJFM2/gKNRPYbiUQ3cCJxO6L9sYHpf8KqrHuAi4EzgWuBunw9GjYWLfgynfR3fG8+xD3DuZOH4acA+VLJuo369GZUM2qpfItZflZZyC+p3eD6wGDBOqhzp8TbwZVmgR1TgPuFM119/fX9CaMuWLfzmN7+J+DhJEplsx44d6flBQ6QFiW/hVI6P7e5uqK8PrwiqqQHD8q1h3G5VFWSsCKqqgrFjQb7JH7L9wNlAL2qFsYdR080SxRjflagPG48Dz3/ja3z+T4/g8fkSOAIhEkPT4k1/pKcbGEgQuVB9yUqAUfolePtTqP5okT7cBab3RVp1dRRqCut9N15C31lLYfanYexEfIsvYhJwDnAZsMDE95WqWoA1qCnEDYQmhWL8pe3nQf1dmAx84PPR4fHwOvA66t/xDFQ16LGY078u8GWZmT2iRlrdJBIrWkUTmFOhKUkig7KyRHQTEE5j13J8iW/hVI6IbU2DPXsGkj/GqiB/jA9TxcWRp4fNnAnZstCxWTTg66hvkT3Ao0CiJ+BFiu8fopJEjZMn8faikzj8aWc2kBXO5nIlMr1qb+8BL+vbv0dVoiTyX8u9YzP86rswYzYcfRosOJqezCweAh5CJYkuA74M5CRwHMniB+qA/wD/1S/rUMf4aDKBacB01DSycv06cJnEwAfs2h07WDNlCg8BrwCdwJ/0yyTg/1B/T6rMelMmseNnnHTxhz/8ISmvI0kiIYZByvGFEMPm9YZXBQWum5uj7+t2w7RpkVcQKyuTqqAkuBN4St9eDhxp0TgOQTWl/Qfw3NKL+MzTz8nEHSEc5Fb9egoqmZC0dNrG9bBxPZlP/Jaf3foY96GmU60GvgZ8F5Ww8h5zGrehki1+VHIl+NqPWvWxCzUVa7DrTNQUrCL9Umi4LgKy9ecNXIhwG9QHW88g1xlAG/AWKiH0P1RVaCTFwEz9MiNoeyaqQijeCqBcTWMJsATYjlr98iFUMmo78Avgl6hE0c+BCYb9I00THClpum9v559/flJeR5JEBrt376a8XNYKEZHZfdlyiW+RapY/v9KUBrApF9uaBnv3hq8eVlMDmzZBrKlBRUWRp4dVVECOE77DtadO4Dp9+xTUh6VkGCy+f4RKEn1SXcWHR3+Oea+/kaQRCWGO0V9aZPUQUtJmVJUiqN5nVqwb6Wpv4UeoHmjPoRr1v4TqzXMbwOKLknYMTKRsYD5wBHA48BlUssaMpHvwsXsS8APUv+e7wB+BVaim4b9H/b5/hPp95+n7R5smOFzSdN++nnjiCf71r3/h9XqZM2cO5513Hvn5iek/JUkig4kTJ1o9BJHC7L5seTLjW+Yzi2iCl2y97umHRrxcq2XHbq8XNm4MTQIFtvcP9h2lzuVSVUGRkkHjx0tVUAr6K6pnBcAdJO+b/cHi+zhg2tqP2XzQgTx3yUXMlSSRsJm5l33T6iGkpNsBH6rn0IXWDgUP8CX9UgesAJ4BGvbtZtroMlyoY2HgOng7G8hFTU/LNWzn6Jc+VL+fVlSlT6Rrrz4WV9DFeFtD/ZvF6nI1BZUMClw+BSRqmYZIx24XKik1H7gZ9bteDrQD1wC/0e//CkmsHhMpra+vj0WLFvHKK6+E3P/LX/6S119/PSFfkkqSyMDr9cZ+kBAmSXZvo2TGtxOn4yWi7DddGZdsHelyrQmP7cbGyNPDGhpiVwUVFAwkgIKTQRUVkJub2HELU/1Wvz4eNQUhWQaLbxfwxd/+nnvu/BV1Cw7hN3fcwjeu+VkSRybEyMh5d7h9wO/07UuBAhOfO9oXeMZVsiKtkFWJqiK6DSi69gI2mtQo2Ux+VLLIh0pABa77UB98k7laW6z4zgWuBi5AJYgeAD5BTS+8C/XvbNWUZpE67rzzTl5++WVcLldI0+otW7bwrW99i7/97W+mv6YkiQwaGxuZPn261cMQaSLZvY0kvkcmEWW/whymxHZvr5oKFqkqaN++2PtPnRq5KmjiRKkKcoBa1HLUoJaNTqZo8X3IS/9g/t9fZs0XTuB/X/oiu2bM4Auob8uFSHVyXhLuPtTU1mzgcpOfO9o5ZyJWybJCoJrJiil6RvHG93jUlxDLUNPNXgXeBj6LWknz8Eky0yWdrVq1ClCrmh199NEUFxfz4osv0tPTw3PPPUdHR4fp084kSWQwZYqcVonUYma1kcS3cKohxXZTU3hFUE2Nqgrq64u+b34+VFaGVwXNmgV5edH3FbYW+GZ/DHBqkl87Wny7/X4uu+w7PHHlt3j20m+y+aADWICaGjeUb6CNPfcA2/XdE/Yj5yWhulAVJKCaQ4+3YAzS2Ng8Q43veahV0J4Fvoea3vcX4ImnHuc94FuoaWoivdTV1eFyubj66qu54YYbAPj73//OySefjN/vp76+nnnz5pn6mpIkMmhvb7d6CEKEMLPaSOJbOFVYbPf1hVcFBa4bG2M/4ZQpkZeTnzRJqoLSkBe1Ig3AV1Hf8CdTrGO32+/nzFvvYMr6Wh745Y3szs3lGOBeVD+TeKaRGHvuBe4bTLKnSwtnkvOSUA8Be1FTSa1qCi2Njc0znPh2oRZGOAlVVXYdsD8riz+iml0fgaowW0xotZQk95yro6MDl8vF8ccf339f8HZnZ6fprylJIoP9sRqNCmFjEt/JJc27k2D/fqitxf3CC6qJdCARVF+vpo9Fk5c3UBUUWE4+cEnQahHCnp5GfXADa5rIxnvsPuy5F5jwyXZ+++SjbENNi/sA+OT2J8nE3GkkyZ4uLZxJzksG+IBf6dunofr/CHsbSXxnoiqHzgMuvf0u/nPFt9gK/Ee/TAQuAS4GxiHJvXSQmTmQFvR4PP3bwX2KzCJJIoNp06ZZPQQhEkbiO7nkA5Q5XJqmpoJFqgrasweI0UR48uSB5E/wNLHJk8Eta4eI2AINq48EZlvw+kM5dk9bt57VwJnAm8A9wMfAYwkZmRAjI+clA/4G1OvbP7BwHPGSypXYzIjvUcApf/gjD1/xLZ4G7gZeB3agml3fAJwDXIaarpbsSleRPJdffjnFxcUx73e5XPzjH/8Y0WtJksigqamJsWPHWj0MYaHlz690bDbeyfHt5N9b2mhpibiC2Nnr1qmVwKLwZ2fjjjQ9rLJSrS4mxDBtBl7Wt5PdsDpgqMfuMuAfqCkJ9wOvAQsA38SpCRmfEMPl5POSodCAX+jbnwU+Y+FY4iXnXLGZGd8ZwBn65UNUsuhPQDf0T0UDKEb9DRinX5cZbhejVswrNFxLUiD1vf/++yG3XXr7g+D7NU3rv38kJB4MWltbrR6CsNjy51cl/A+fsUFospqDOjm+k/F7Eybw+WDLFr6wtZGZTa1UtXRS3dxJVWsX/KYk4i6e4BsTJ4b3CqqqYs3u3Sw47LBkvAORZn6P+gBXBJxl0RiGc+zOAlagvln+NrAJ4Lu/Yg3S+FSkDieflwzFG8BqfdsOVUQiPomK77moCtebgQeAXwNb9Z+16Je6IT5nDipZFEgcvY9aJU6khkRMKYtGkkQGM2fOtHoIIg0YG4RGaw5qplSJb1lFJw20tYVXBdXUwIYN0NPD09H2zc4O6RX0nwf/xBFPPqYSQoWFEXeZWVSUkLch0lsfKkkEcC5g1fp1wz12u4BLgQNQ08/2ZefyZeBdVNJLCKulynmJ1W7Rr2cDi6wciDBVouN7NCqpeCWq/9xOYA+wO+gSfHsf6kuPSLr1SyMqYSQJotTxhz/8IemvKUkig127dlFaWmr1MIRISCIlVeJ7qKvoiBTl98PWrZF7Be3cGXP3nblZ1Bbnsr4kn4ZRBdz60ztVIqi8HIIa8m1+6gWOOOSQqM+VKrEtnOVFYLu+bdVUMxh5fB8NPAl8zu+jwe3hm8AqVBJJCCvJsRvWAoF28t9HPpw7SbLiO4P4KkR9QAfQBrRHue5LzDDFMJ1//vlJf01JEhl0dHRYPQSRBrKKCvsTQC6Ph6yi8OqIRCRSJL7FsLS1QV1deDKorg66u6Pvm5UFs2aFTREbe98PaQyaR5aVkcmtJ5007CFKbItE+J1+PR/4lIXjMCO+jwKynluJ95Sv8mfgOKxZqS1VBf4uA1H/NgtzybEbbtWvJwDSCtpZUi2+PagqUqkkFbFIksigslIWnBTmiNZIOVANtGruISz58J2kjUniWwzK74dPPgmfHlZbC9u3x96/rCysTxDV1TBtWkhVUEDr7zOhL8YS9UMgsS3MthN4Vt+2OpliVnxnvfQYR53y1f6m1p8BDjLlme0vuEo32X+b01m6H7s/QVX1AXwHWZnKacyK7zlLZbVckVySJDLYunUrc+bMsXoYwsbKrjid5q4OfH4f1z39ECW5+ey+/UmrhwVIfAugoyNyVVBtLXR1Rd83M1NVBRlXEKuqgpKShA05npMjiW1htgdRpfl5WP/tvlnxffXJ5/B1VDPrPcDZqGa5+SN+ZiGGJ92P3XcCvahGwd+0eCzCfGbF95xLJUkkkkuSRAbdsaZOCBFDc1cHXr1Cwuf309yVOqWmEt9pQtNUVVCE5eTZti32/mPHhieBAlVBGcn/sxHPyZHEtjCTn4GpZmdjfWm+WfEdqG79E/AFYD3wLdTqOEJYIZ2P3c3Ab/Ttb6KWJhfOks7xLexNkkQGs2fPtnoIQiSMxLfDdHaqqiBjMqiuTlUMRZORARUVEZeTJ44mix/de39KfbMlsS3M9BqwUd+2smF1gNnxfQLwI2A5avW2Y0x9diHil47Hbj+qkfz1qEbBmcC3LR2RSJR0jG/hDJIkMqivr+fggw+2ehgiRcXTcDqVOTG+g6f3ZS89MaWm95lC02DHjsgriG3dGnv/MWMiTw+bPl1NHxumj1akVpLIibEtrBOoIjoAONzKgegSEd8/A94A/g0sBX46bSplG+pNfQ0hYkmnY7cfeAKVHFobdP+VwGRLRiQSLZ3iWyRHW1sbhYXRP3++/PLLnHDCCSN6HUkSGfT2mtdIVTiPVQ2nzeLE+E7l6X1D4fH74cMPI/cKam+PsbMHZs5UCSBjMmj06OS8AYs5MbaFNRpRH+RANaxOhWXiExHfGcAjwMFAE/Dr23/JT844hyyvd8TPXZKb35+897g9lORK1yMRWTocu/3AX1GJ2eDk0GeB64BjLRiTSI50iG+RXMcddxwvv/wyxcWRJ6j+8Y9/5OKLLx7xVEdJEhkcdJCs8yGcS+LbYpoGO3dCbS2Vzfso7O6iuNdLUa+Xgr5emDcv+v6jRoUngqqrYcaMEVUFOYHEtjDLw4AXyALOs3gsAYmK7ynAH4BTga0HzObRq3/Aedf9fMTPG6jmLFq2iNZ7nhvx8wnncvKx2w88jkoOfRx0/1Go5NAxpEYSWiSOk+NbWOOdd97hmGOO4aWXXmLMmDEhP1u+fDk//vGPcblGfmSRJJHBunXrmD9/vtXDECIhJL6TpLsbNmyI3Di6rQ2Awwbb1+NRSZ9Iy8mPGQMmHPidSGJbmEFjYKrZGcCYKI9NpkTG95dQS2/fAfzjq+dS/b+3WPDiywl5LSGM7HbsfhOV4PkXKpGcC+To18bLRqAmaN/P6fsejSSH0oXd4lvYwwcffMDRRx/NK6+8wvjx49E0jcsuu4zf/Ea1ws8wYZEZSRIZ+P1+q4cgLGJFb5t4lvaOJlDSD8RV1i/xbSJNg927IyeCNm1SP4+ix+2mJTOL1sxsWjKzaMvJ5eh/vKimjWVlJelNOIfEtjDDf4F1+vaFVg7EINHxfTPwt7Ufs/mgA/n9zT9n2kcfM3b7joS+phBgn2P3W8BPgZeC7vMCMSaDA/B5BpJDIr3YJb6FfVx//fVce+21rF+/nqOPPpqnn36aH/7whzz99NNomkZxcTGPPfbYiF9HkkQG82JN9xCOZUVvm5E2/g1OYsVT1i/xPQw9PVBfH5IEOrF+vZr61dISfV+3WzWIjrCc/F8+exz+vr6Bh2ZmgqyCMWwS28IMv9WvZ5BaK34lOr6zgcu+832uefIvdBUV8ccbruXKC76Z0NcUAlL/2L0GuBYIPruqQlXf5QFdQLd+bby4gSVIciidpXp8C/u55pprKCsr49JLL2XDhg0ceOCB+P1+NE1j+vTpPPvss6asqidJIoMPPviABQsWWD0MIRJC4nsQmgZ790ZeQWzTJjB8EzQG1BlgQHHxwLSw4F5BFRWQnR35NWXamKkktsVItQN/0be/gfqAlyqSEd9l2z7hKzfezB9u/jkfHf051nzhBA599fWQxzy64Ei8rWrKrObz8XDVXLKKCvsXdRBiqFL12P0hKjn0t6D7Zur3fQX5ACXik6rxLezt4osvZuzYsSxZsoSenh4AjjjiCJ566ilGm7RgjRzjhBBpw61pFPZ6KenuhJtvDk0GNTdH39nlgmnToLqamrfXUH3jzwYqg8rKHJP0Wf78Sq5aeK7VwxAi6Z4BOlG9Qr5q8VisctRjT/CvsxZTP/9TrLrmR8z771shP/e2tuEPWq1H8/v7k0ZCOEEd8BMgeLLGVNRUs/OA9F4iQgiRbBdccMGgP5s1axZr164lIyOD8vJyvv/97wPgcrl44IEHRvS6kiQykLJAYVdXLVwS8zFpEd+BqqCgiqBjtm+msKebwr7egeqAq66KuHuv203m/Plh08OoqICcHADenXsI1d901lSM4J5c1z39EEBS+nKZJS1iWyTUn/Xro4DJVg4kgmTFt1vTOO+nP+O6px+naeJE/nbpxSnVm0k4Tyodu2uBBUAg7TkZlTD6OqpJtRBDlUrxLezpwQcfjLpamcvlwufz8eijj4bcL0kik0lZoBipQDPpeBpJR5NVVIi3tQ3N58Pl8fTfN5h4qj8cFd+9vdDQwCmb9zBzXxtVLZ1Ut3RS1dIF948LeajxA58GuKZNC50apm8/duIXWfL221FfeqQNxxPho3vvH1GPK2NPrsB9duGo2BZJ1wy8qG9/2cJxDCZafBv/VkT7OxGPqetrOP6PK3n561/lxa9/lXXAASN6RvtJxWO8U6XKsbsLOAuVICoGbgAuQq1cJsRwpUp8C3vTYiyGYxQtqRQvSRIJYbJA5UU8jaSjCfR4WDX3EJZ8+I4pY0sVQ0qA7dsXuVfQxo3Q18fj0V4oPx+qq9lUV0+zJ1OtJpaVRXtuPks2rI28TxwH1pE2HE+Ej1aMLEkkRDr7G2qlIjdwprVDGbJE/K04/Y67eXvRybSMG8tlwKuk15LdcixNP98CPtK3/wR80cKxCCFEwGuvvWbJ60qSyEDKAoWTpUp8h32o6etTSZ9nnglNBNXUqCRRDFvys6kpyaOmOI+G0kLuuu4eVR00cSK4XLxZNTekj4bbnUotaYUZUiW2hT0FppodC4yL9kCLxBPfZla/5LW1c85Nv+A3d9zK68AjqFWahDBbKhy7/wT8Tt/+PpIgEuZJhfgW9vb5z3/ekteVJJGBlAUKJ7M8vpuaVAJITwIdtaVBLfve0KCmj0WTlxfeJ6i6mpK7rqTFNbD6WFZGJncdd1yC34hINZbHtrCtRuAVffscKwcSRTzxbXb1y2eefo43zjmb9Z85lO8Ci4bxHPH0yhPpzepj93og0GHwCOBGy0YinMjq+BbOs23bNjZt2oTb7eazn/1syM/efPNN/H4/06dPZ8qUKSN6HUkSGUiFgXCypMR3X59aNt44Pay2VjWUDjIFoLU5dP8pU0KTQYHtSZMgwvi7Mj3Q5w+730mirTgWWJI63ZejlmO3GK6/Aj7UCdHpFo9lMFbEtwv46s9u4prn/8Yu1OpOhwzxOWSlRBGLlcfuDlQfok5gNKqiUFYvE2aScxNhtiuvvJInnniCs846KyxJtGLFCh555BEWL17MX/7ylxG9jiSJDA44IN3aM4p0Ymp8NzeHJ4JqaqC+Pr6qoMpKtmzawtTvfGsgEVRZqfoIiRDLn1816Iet4CWpR7IctbHheuC+YIGEFJBySSk5dovhCqwH8gWg1MqBRGFVfE9q2MiVwC+Be4CbDvk0E995F8C0RtkivVl57L4c+Fjffhj9iyshTCTnJsJs//3vfwE444wzwn526qmnsmrVqv7HjIQkiQzWrl0rZYHCFGaV2ZvZZ2LI8e3zwebNkauCdu+Ovf+kSaHTwwLXkyeD282/5x7C1OuuG+7bESaKp+F6cEIKYielolVAmU2O3WI4dgKv69upOtUMrI3va1A9ibYBT618kDdRDb6duKiCSD6rYvsh4A/69o+Ak5M+ApEO5NxEmG2vPiujoKAg7Gf5+hftew0zN4ZDkkQGmZlSaCrMYdaHYzP7TAwa3y0tIb2C+q83bACvN/qT5uSoCiDj9LDKSiiUb5jTWbQKKLPJsVsMx+OABmQDX7J4LNFYGd8FwB3AYuC/wIPABZaNRjiNFbH9MXCJvn0Uarl7IRJBzk2E2YqLi9m3bx9PPfUUCxcuDPnZU089BUBRUdGIX0eSRAYVFRVWD0GIxPD5mJWRAS+8EJ4M2rUr9v4TJ4ZXBFVVQXl5xF5BZkpmRYqwJzl2i+EIrGq2CBj5KVXiWB3fpwMnAS8CPwBOtXQ0wkmSHdvtqD5EXcAYVJWcfBgSiWL1sVs4z4IFC3jhhRf43e9+R2dnJ4sWqWUlnnvuOVauXInL5TKlek2Oiwbr16+XskBhb21tkaeH1dWR39MTfd/sbJg1q3/lsJCqIBOy0sOVzIoUYU9y7BZDtRX4j779ZSsHEger49sF3A0cBOwDrgasWZRXOE0yY1sDLkWtaOYC/gRMSsori3Rl9bFbOM/ll1/OCy+8AMCqVatYtWpVxMeMlCSJDHJycqweghCx+f2wdWtow+jAdLEdO2LvP358yDLy/dvl5eDxJH78QphMjt1iqALrfuQzvOXdkykZ8Z1VVNi/UqJL/zsQ3JS6AtW75Xrgt0DZpw9O+JiE8yXz2P0HVINqUInOLyTtlUW6knMTYbaTTjqJ6667jusG6en605/+lJNOOmnEryNJIoPy8nKrhyDEgPb2yL2C6uqguzv6vllZqiooaGpY++TJFMyfD8XFyRm/SAllV5xOc1dH/+2S3Pz+RtVOIcduMVSBqWanoBJFqSwZ8R1YpTBaQ+ofoj5kbwRu+u0KuoCfAtJ9TgxXso7dHwKX6dufB65LyquKdCfnJiIRfvrTn7Jo0SL+9Kc/UVdXB0BlZSXnnnsuhxxyiCmvIUkig7q6OikLFDGZueIYfj988kl4VVBNDWzfHnv/srLIvYKmTQurClq/ejULJEGUEgLf2gffTpTmrg68fb0ht51Gjt1iKOqBNfp2Kq9qFpAq8Z2LmqJzBrArM4NbgZXArcBXUFN4hBiKZMR2Mypmu4FxSB8ikTypcuwWzjN//nzmz5+fsOeXY6RBYOk4kTo+uvd+U1f4MsOwxtPRoSqAIvUL6uqKvm9mJlRUhCaCAtslJXEPQeI7dQS+tRfmkNgWQ/Gofl2Masic6lIpvg8HaoFz/riSl756LjuBc4HfAPcAc6wcnLCdRMe2BnwNaADcqArCCQl9RSEGpNKxWzjL6tWreeSRR0Iqib7yla+YlpSUJJHB+PHjrR6CMPhoReoliQalaar6x5gEqqmBbdti7z92bOSqoOnTIWPk/10lvgf36IIj+/txPFw1l6yiQknk2IjEthiKwFSz04BsC8cRr1SL7yLg/269nV9+9VyWAf8E3gA+BSxD9S2SmlURj0TH9i3AU/r2TcAxCX01IUKl2rFbOMPVV1/NL37xi5D7XnjhBe68805+9KMfceONN474NSRJZNDQ0EBpaanVwxCprrMTNmwITwbV1qqKoWgyMmDmzPCm0VVVkODYk/genLe1DX+vmpKl+f0hU8FE6pPYFvH6GFirb9thqhmkbnwfBLyGqsz6LrADuBM1neeXqCqtdqBtkOt2YBRwoH4ZndzhixSQyNh+HbhK3z4N+EFCXkWIwaXqsTsqTQNvE2TLETkVPf7449x88824XC40TQv7+c0338ynP/1pFi9ePKLXkSSRQZGFy3yLFBOoCoo0PWzLltj7jx4dngSqrlZVQZmZiR9/BBLfwqkktkW8AlPNRgPHWTmQIUjl+Hahkm2LgJ8DtwF7UFN8hqqMgYRR8GWUGQMVKSlRsb0d+DLgR63M9yDSM0skXyofu+nrhLYN0FoLrTUD1211kDUKTttq9QhFBL/+9a8ByM7O5rLLLuPQQw/F5XLx1ltvce+999LV1cU999wjSSKz2S7bK0auqws2bGBxwy5mNrVR3dJJVUsnVS1dcP/k6Pt6PKoqKDgRFNgeMyY54x8CiW97CaxK5vP7yF56oiNXJTOLxLaIh8ZAkmgxYE26fujsEN+FwC+ArwOXA68M8jiP/tgC1Kpyu4AW/We79curhn0OBG5GJaLkg76zJCK2e4GzUcnKXOCvyPRHYQ3Lj92aBl07IiSCaqEjyhfefe3Q1wEZ0lMp1bz//vu4XC6WL1/Ot7/97f77zzzzTCZPnswVV1zB+++/P+LXkSSRwebNmxk7dqzVwxCY3CNG02DXrsi9grZsAU1jVbT9R42KXBU0Y4Zaat4mJL7tJXhVMp/f76hVyUpy8/sTYB63h5LckZ2ISGyLeLwP1OnbX7ZwHENlp/iuBl4CPgA6GUgIFejb2YQmejTUNLWPI1wCk34/Bk4BTgZuB6oS/SZE0iQitn8A/Eff/g0w19RnFyJ+STt2+7r1qqCa8IRQX3v0fV0eKJgJRdVQVDVw7bbP55t00qUvdlRRURH2s8B9XbEWRIqDJIkMRo2SouZUMaweMd3dUF8feTn5tuj797lcbCrMoaY4j5qSPBpGFbDi578ZqApy2f/7S4lvkSoCFVFFyxbRes9zI34+iW0Rj0AVURnweSsHMkR2i28XcPAQHjtJv5wYdL8GbAPeQ01jewd4AXgZ+A5wDaqBtrA3s2P7L8Ad+vZS4DxTn12IoTE1vjUNuncbEkH6dsdm1FEziqxRUFgFxdUqEVSoJ4QKZoBHEkJ2MXnyZDZt2sTtt9/OEUcc0R9j+/fv5/bbb+9/zEhJksigoKDA6iGIWDQN9uyJXBW0eTP4/dH3LymJWBVUctvldGi+/odlZWSy4qijEvpWkk3iWziVxLaIRWNgVbOzUdOe7CId49sFlOuXU4CHgB+hphDdCjyMmt52Hmppc2FPZsb2euACfXsBA8kiIawyrPj29UBb/cC0sBb9urUGeluj7+tyQ/6MoIqgoOqgbGd84Z3uFi5cyD333MNrr73GpEmTmDlzJqCapPf09OByuVi0aNGIX0eSRAbbtm2T5QpThNvvp8jbQ1Gvl+LeHop9fXDYYSoh1NISY2e3ahAdqVfQuHERD5K9Hjf0+SI8mXNIfAunktgWsbwFBDow2GmqGUh8u1G9js4Afgbchepd9DXgXuBu4NCgx7cC9UGXDfp1F3CZvp98VEoNZsV2Gyo+OlBN6R9HTW0UwkqDxremQfeeyImgjs2gxfjCO7M4fHpYYRUUVoBHIt/JfvzjH/PYY4+xe/duuru7WbduHUD/SmcTJkzg6quvHvHrSJLIYEwKNht2suXP/YmrFpwYXhFUU8NXGhrCvx18++3Q20VFoQmgwKWiArLlIGkk8S2cSmJbxBKYajYFONzKgQyDxLdSDPwKuAg15ezvwNvAYcBJqOTQBmBvlOe4AHgWuB+VTBDWMiO2O4ELgRpU8m8lqgJNCKuNKS2ClnXhfYJaa6A3xhfeLjfkTx9IAAVPE8uJ/IW3cL6ysjL+85//cOmll/LSSy/1J4dcLhdf+MIX+PWvf01ZWdmIX0eSRAZZNmpCbCteLzQ0hCWDlr63Bnp6I+4SSBBpQHtGJq1Z2Uy6+MLQyqDx4+UgOQROjG+zGyALe3JibAvz+FG9SkBNNbPb9CSJ71DVqP5Ez6KSRRuBFyM8zgNMQy2BXgGsBf4JPAH8FzWF7YSEj1ZEM5zY3g38G3hTv34X6NN/dh3wBZPGJkRcNA169uoJoNBk0LT2TUCMWQqZRQP9gYqDegVJVZAYxPTp03nhhRfYv38/GzZsAFTTajNX05MkkcGOHTuYNGmS1cOwJ02DxsbwqqDaWti4EXzhB8mQdm6FhSHTw/55729pdrtpzcjC73bjzszkPL0hlxgeJ8a32Q2QhT05MbaFeX6JWkEL7DfVDFIzvucsvdjS13ehehWdANyDSvpMYSAhVAFMBTKD9vGjVke7GtiJapT9HWA5kJOkcYtQ8cR2HfAGA0mh+kEetwT4iamjEyKIzwvtDaHLyAemiXn3R9zFFbyVPy10eljgOke+8Bbxu+AC1Xntxz/+MTNnzuTQQwcmWzc2NvL8888D8NWvfnVEryNJIgMzyrMcr7dXJX0M08OorYWmpuj7ulxQXt6fCLry/X9w27V3qdsTJoQcJLc+/Jf+1c2EOSS+hVNJbIvBPI1KCgB8CTjEwrEMVyrG95xLrU0SBeQA34vzsW7gu8DxwLnAx6jmxq+gpijJUunJFy22vcAy4LcRfuYCDgI+CxypX6YivaaECbobB/oDBVcGtTeAFqMqKKNgIAFUWEWjdzRjZh4FBRWQkZuc8QtHe/DBB3G5XFx44YX9TasDamtr+drXvobb7ZYkkUigffsiVwU1NEBfX/R98/MjriDGrFmQO3CQ/N2yRdx27LEJfiPK8udXctXCc5PyWkIIIaz3ESoZoAEHolbEkg+RYh6wGrgKuBM1DW0BqqLoO0SejqgB+4Fd+mUf0BTj4kZVTJcOchkFFOjPbbwQtO1CNWHOCbpkR9jOQk2xG2qM+4BuVGPvbmAs1jd93g8sBl7Tb+egek8FkkKHAyWWjEw4gr8X2jeFLiMfqA7q2RdjZxfklw/0BwqeIpYb+oV359atUCIdskRytLW1AQNNrEdCkkQGu3fvprw8jf4z9/XBpk2Rl5NvbIy9f1BVUMj1xIkpVzq5/PlVaZ8kSrv4FmlDYlsY7UVVDrWjGhQ/DRRZOqLhk/g2Xy6qiuhk1Gpnu1BVRs8BRzGQDNoZtO0dxut8MvKhDokLlSwa7OJFJYKCk0LGr/1yUcmY4/TLp1DJp0SIFNv1wCLUNDOAS4HbsD5xJWyopyk0ARRICLXVgxbjC++M/IHkT8gqYrMgIy+ul5djtzDDU089xVNPPRVy30033cS4ceP6b/v9ft58800ACgsLR/yakiQymDhxotVDSIz9+yMnghoa1PSxaPLyQlcQC64KypcmwXbi2PgWKaXsitP7m4lnLz2Rktz8/t5RiSKxLYJ5gTOBzagTnceBGVYOaIQkvhPnC6iKs4uBJ4FX9UssHkIrgiJVCUF4ddF+w+0YC10PmQb06Jfh6gJe1i+g3ssxqITR8cAszKvIM8b2G8DpDFRi3QFcbtJrCYfy9w1UBbUZmkf3RFvrUJdXrieBDAmh3Ekj/sJbjt3CDO+//37/NDNQlUIvvPBCxMe6XC7mzZs34teUJJGB1zuc74lSRF8fbN4c3ieopgb2xnGQnDw5PBFUXQ2TJoHb3LVgrPgQKWwe38I2mrs68Pap5LPP76e5qyPhrymxLQI01IfKN/Tb9wBHWzYac0h8J9YY4K/A71EVKy5gAjBevxi3y1CJk5EmSvyohKZrkAv6dSDx0x103R3htjfKpVe/zkRN3cplYLpa8HYm8AGqT9OrDCS2ntAvAJNR/YCCzwxdEbZLUVPGTkJVMUUSHNsPARfpYy0AHgUWDrKfSEPe/RGWkq+F9no1fSwaT15oIqh/mtgsVTGUqCHLsVuYSNO0kERRJOPHj+e2224b8WtJksigsbGR6dOnWz2M6JqbVfLHWBVUX6+Wmo8mNxcqK8OniFVWQkFBUoYP1nyIFDaJbyGGQWJbBPwauF/fXgZ808KxmEXiO/FcwDf0S7K4iW9VNRcqkZOstrefQf2/8TOQMPoH8C+gEzWFLt5pdH9ETfc8BzgPOJTQhFJjYyNTp0/nJ6ieUADlwLPAnJG9DWFH/j7o2ByeDGqrhe49sffPmzyQBAquCsqbBC5zv/COhxy7hRm+9rWvcfTRR6NpGsceeywul4u77rqLOXMGjpJut5tRo0Yxe/ZsPJ6RTxCWJJHBlClTrB6C4vPBli2Rp4jt3h17/0mTwquCqqpgyhTTq4KEfaRMfAthMoltAerD7Hf07eNQy507gcS3sIIb1Y/oU8D3UVVLb6EqjLYbHmv8TltDJZjWoJp8/1q/VAL/p1+mA6OnTOFsVCUXqCTSU6iqLeFg3mY9AWToF9RWD/4YX3h7cqGwMkKvoErITN4X3vGQY7cww9SpU5k6dSoAn/vc53C5XBxzzDEceOCBCXtNSRIZtLe3J/cFW1sjryC2YQP0xJhRnpOj+gIZE0FVVWBCwyo7+eje+1NmOd5UlvT4ThFZRYV4W9vQfD5cHg9ZRen1/yMdpGtsiwEbgLNQKzVVAH/BOSc5Et8iFWQDn9Mv8VqPWlVwJbAV1Yz6p/rls0BTSQnr9MeeDTxI8iqmRIL5fdC5JagqKKgyqDuOL7xzJ4YmggJTxPKmWFIVNBxy7BZme/3115PyOk45fzLN/v37zX9Svx+2bo1cFbRzZ+z9J0yIXBVUXg4mlJPZ2aMLjuz/8P/+nfeQVVTIl1f/2+phpayExLcNBGJi1dxDWPLhOxaPRiRCusa2UJqBU/TrIuAZVD8Up0hmfM9ZKl+4CPPMBm4Cfo7qE/YwqpF8K/AmqC88gZ8A1xPa50jYRG+rYXpYoCpoA/hjfOHtyVF9gcKmiFVCpl3Xoxwg5yYikVpaWrjlllt499138fl8HHrooVx++eUhq54NlySJDKZNmzb8ndvaoK4uPBlUVwfd3dH3zcpSfYGMyaDKSiguHv6YHM7b2oZfX51N8/vxtrZZPKLUNqL4FiKFSWynLx/wFaAW9QHzz0C1pSMyXzLjW6pyRSK4UQ3kj0Y1k38alTD60OfjRo+H86wbmoiH3wedWyP3CuqK4wvv3AmRl5PPKwe3c7/wlnMTYYYbbriBG264gdLSUjZv3kxOTg6dnZ0sWLCAhoaG/se98sor/OEPf2D16tVMmDBhRK8pSSKDpqYmxo4dO/gD/H7Yti1yVdCOHbFfoKwsdOWwwPbUqWlfFSQSL2Z8C2FTEtvp6yfAi/r2LcDJFo4lUSS+hZPkAl/WL7X19VRVVVk8ItGvtw3a6qAlqE9QoCrIF+MLb3eW3itIX0UsOCmUlZ5feMuxW5hh9erV9PX1ceqpp5KjV1+uWLGC+vp6XC5XyEpnO3fu5KabbuLuu+8e0WtKksigtbVVbbS3D14V1NUV/UmysqCiIjwRVFkJJSUJfw9CDKY/voVwGInt9PQUcLO+/VXgCgvHkkgS38KpJLYtoPmhc1vk5eS7jC3JI8gpC6oGCu4VNNXRVUHDIfEtzLB+/XpcLheHHnpo/31PPvlk//YZZ5zB+eefz09+8hM++ugj/v73v4/4NSVJFNDWBlddxcFr10JDA3wSx+Ke48aF9wmqroZp06QqyATSbNh8M2fOtHoIQiSExHb6qQfO17fnAfcRurS2k0h8C6eS2E6g3nZVFRS2ilgt+GJ84e3OHKRXUBVklSRl+E4g8S3MsHfvXmBg+mJvby+rV68GwO12c9999zF27Fg6Ozv5yle+wrZt20b8mpIkCsjNhfvvJ1Pvb9MvM1NVBRlXD6uuhlGjrBlrmpBmw+bbtWsXpaVOaucqhCKxnV46gcVAC1CMaoSbZ+mIEkviWziVxPYIaX7o3B7eJ6i1Bjrj+MI7e2yEpeSroGA6uOVj4khJfAszdOmzmAKr5b399tt4vV5cLhfz5s3rn9JYVlYGQGZm5ohfU/73B2RkwJe/zN7WVsYeddRAImj6dPUzIRygo6PD6iEIEeKqhUtMeR6J7fShAZcCH+q3H0Itee9kEt/CqSS249TXGaFXUKAqqDP6vq4MKKwYSAAVz9arg6ogWxIYiSTxLcwwceJEtm7dyr333ktFRQW33HJL/8+OPfbY/u0den/k8ePHj/g1JfsR7OGHyWppkdXEhGNVVlZaPYSEMSvZIJLrqoXnmvI8To5tEep3qMQQwI+AUy0cS7JIfAunktgOommqJ1Ck5eQ7t8beP3t0aJ+gQGVQwXQ1fUwkncS3MMPxxx/PAw88wCuvvMLcuXNDfnbWWWf1b//zn/8EzJnmKEkig61btzJnzhyrhyFEQjg5vs1KNgh7cnJsiwHvAMv07WOAGywcSzJJfAunSsvY7usK6hUUPE2sDvrao+/r8qiqoEjLyWePTs74RdzSMr6F6a677jqee+45du3aFXL/ueeey4IFCwBVtfbYY4/hcrk4/vjjR/yakiQy6O6OsbyjEDYm8S2cSmLb+ZqAMwEvMBF4hPQ5iZH4Fk7l2NjWNOjaOTA1LHiaWMdW1MTZKLJKQ5tFByqECmZIVZCNODa+RVJNmjSJ9957j7vvvpt3332XwsJCjj/+eL7xjW/0P+bdd99l0aJFAJx22mkjfs10Ob+K2+zZs60egrBISW4+zV0d+Pw+PG4PJbn5Vg/JdBLfwqkktp3ND/wfsAV14vIXoMzSESWXxLdwKtvHtq8b2jZEXk6+ry36vi6PSvoEVwQFKoRyxiRn/CKhbB/fImWUlZXx85//fNCfH3XUURx11FGmvZ4kiQzq6+s5+OCDrR6GsMDu258EYPnzKx07dUni23myigrxtrah+Xy4PB6yigqtHpIlJLad7UbgBX37VuBIC8diBYlv4VS2iG1Ng+7dEaaH1UL7JmJWBWWWqMRPsbFX0EzwZCXjHQiL2CK+hYhAkkQGvb29Vg9BWMypCSKQ+HaiL6/+NwCr5h7Ckg/fsXg01pHYdq6XgGv17bOBb1k4FqtIfAunSqnY9vVAW/1AAih4ilhva/R9XW7Inx7eJ6ioWi0z73Il5z2IlJJS8S3EEEiSyOCggw6yeghCJEy6x/ecpRdbPQSRIOke2061FViC+p6+GrWyWTp+1JL4Fk6V9NjWNOjeM5AICq4O6tgEmj/6/pnFQUvJB60kVlgBnuzkvAdhG3LsFnYlSSKDdevWMX/+fKuHIURCpHt8z7l08CSRTNuyt3SPbae6AtgH5AN/BdL1f6XEt3CqhMW2rwfaG8L7BLXWQm9z9H1dbsifFtQjKKgyKKdMqoJE3OTYLexKkkQGfn+MbxCEsDGJ78HJtC3lqoVLrB7CsEhsO89q4Al9+2bgAAvHYjWJb+FUI4ptTYOexgiJoBro2BhHVVBR5KXkCyvAkzP8cQmhk2O3sCtJEhnMmzfP6iGIIYin+qPsitP7Vy3LXnoioFYyCzSqTicS3yIWu/bkkth2nh/r19OBdJ8oKvEtnCqu2Pb3QltD0BSxoGSQd3+MnV2QPzV0GfnAds54qQoSCSXHbmFXkiQy+OCDD1iwYIHVwxBxiqf6o7mrA2+fahzn0zP6zV0dyRlgipH4tpeS3Pz+BKfH7aEkN9/qIaUsiW1neQ14Wd++Hkj39X8kvoVThcR2z77IVUHtG0Hri/5EGQWhy8gHVhIrnAUZuYl/I0JEIMduYVeSJBJCiBQVqHYrWraI1nues3g0A5V7gPRuEgmjAVfr2weiGlcLIRzC36uWjdeTQNN2vwkv68mhnn2x98+fGnmKWO5EqQoSQgiTSJLIQMoChZNJfIuRCFTuQer1bpLYdo5ngP/p2z8HPBaOJVVIfAvb6WkaqAQKniLWVh9SFTQ20r4Z+eENo4uq9aqgvKS9BSFGSo7dwq4kSWQgZYH2JEubx0fiWziVxLYz+BnoRXQocKqFY0klEt8iJfn7VFWQsU9Qay307I29f94UWrQJFE85NDQZlDtJqoKEI8ixW9iVJImEI0Rb2lwIIYQ9PAKs1bdvAuRjohApwLt/YPn44Oqgtg1q+lg0njwoqgxaTj6QDKqEjHzqVq9mwSHyIVoIIVKJJIkMpCww9UiVkHkkvoVZUu3/pcS2/fUCP9W3j9MvQpH4Fgnn90HH5tCKoECFUPee2PvnTjL0CdK38yaDyz3obhLbwskkvoVdSZLIQMoCU49UCZlH4luYJdr/SytWZZPYtr8HgI369k1WDiQFSXwL03hbBukVtAH83uj7enKgsFIlfwqroHi2vl0JmcNbxEBiWziZxLewK0kSGbjdg3/bIYTdSXyLZLBiVTaJbXvrBH6mb5+G6kckBkh8iyHx+6Bza+Tl5Lt3xd4/d2LocvKBqqD88qhVQcMhsS2cTOJb2JUkiQwOOOAAq4cgRMJIfAunkti2t18DO1E9iH5u8VhSkcS3iKi3LTwJ1FYLrXXg74m+rztb9QUqNEwPK6qEzKLkjB+JbeFsEt/CriRJZLB27VopCxSOJfEtnEpi275agJv17f8DDrRwLKlK4juNaX7o2Bp5iljXjtj754wPSgAFJYTyysHtSfz4Y5DYFk4m8S3sSpJEBpmZmVYPQYiEkfi2p6sWLrF6CClPYtu+fgU0AZnA9RaPJVVJfKeB3nY9AWSsDKoDX3f0fd1ZUDgrtCKoUE8KZRUnZ/zDJLEtnEzi2zneeOMNbrnlFtasWcPOnTt58sknOe200wDo7e3lJz/5Cc8//zwbN26kuLiY448/nptvvpmJEyf2P0dTUxOXX345zzzzDG63m8WLF3PnnXdSUFBg0bsanCSJDCoqKqweghAJI/FtT1ctPNfqIaQ8iW172gPcpm9fBEy3cCypTOLbITQ/dH4SuVdQ1/bY++eUhVYDFVZBcTXkTU2JqqDhkNgWTibx7RwdHR3MmzePCy64kUt9nwAAmjlJREFUgDPOOCPkZ52dnbz77rtcc801zJs3j/379/Ptb3+bL33pS7zzzjv9jzv33HPZuXMnL7/8Mr29vXz961/n4osvZtWqVcl+OzFJkshg/fr1UhYoHEviWyRTMiugJLbtaTnQAeQCP7F4LKlM4ttm+jpUX6CwXkG14OuKvq87EwoqDH2C9MRQVklShp9MEtvCySS+U19ra2vI7ezsbLKzs8Med/LJJ3PyySdHfI7i4mJefvnlkPvuueceDj30ULZu3Up5eTnr16/nxRdfZPXq1RxyyCEA3H333SxcuJBbb701pOIoFQwpSbRmzRrGjh0LwO7du5k4cSJer5fGxkamTJlCe3s7+/fvZ9q0aTQ1NdHa2srMmTPZtWsXHR0dVFZWsnXrVrq7u5k9ezb19fX09vZy0EEHsW7dOvx+P/PmzeODDz4AiLjtdrs54IADWLt2LZmZmVRUVLB+/XpycnIoLy+nrq6O/Px8xo8fT0NDA0VFRZSWlrJ582ZGjRpFQUEB27ZtY8yYMWRlZbFjxw7Kysr635PX62XTpk2Oek+p+HvS/P6Q2NI0jb179ybkPRlfC0Dz+1m9enXa/Z4aGxtZvXp1yrwnn89HU1NTzPcEGmvWrEnK78nv11i9erWt/j/V1dXh8/lpamqK+J7QtLD437p1a8Lf0/FjK0PiLZH/nxobG5Pynpx+jEjme/pg/37unTsXXC7O3rkTl8tFvc3fU6J+TxkZGaxevdpR78n2v6cNG3B1bad6kovdG/5Jds9mxmbvo7fpY7L7doeddxj1ekbhLq6mqW8sfXkVFE0+lIa9GWSUzGL8hMnqPeUWUVpYyuZNmxk1qpGCgm7H/Z56e3tt+TdX/j/Je4rnPTU2NtLV1eWo9+SE39O2bds46KCDAJgwYQKdnZ39x+Zrr72W6667LuYxPJaWlhZcLhclJSUA/Pe//6WkpKQ/QQRw/PHH43a7eeuttzj99NNH/Jpmcmma4dNDmmtpaaG4OLXnbztB9tIT8fb19t/OysikZ8VLSXmtRL9eKku1+F419xCWfPhOzMclcyn1eMeUaj66937mXHpxxJ8l8/+bVVIttkV0fcBi4GmgGNgEjLJ0RKlN4ttCfZ2qL1CkXkF9HdH3dWVAYUXk5eSzS5Mz/hQnsS2cTOI79cVbSRTM5XKF9CQy6u7u5sgjj6S6upqVK1cCcNNNN/HQQw9RW1sb8thx48Zx/fXXc8kllwz/TSSATDczqKurk7JA4VgS3841WIIoXUhs20cfcB4qQQRwNZIgikXiO8E0Ta0U1p8ECpoi1rEl9v7Zow1JID0RVDBdTR8Tg5LYFk4m8Z36ioqKTH2+3t5ezj77bDRN47777jP1uZNJkkQG+fn5Vg9BmKwkN5/mrg58fh8evbFjSW56/p4lvoVTSWzbgw/4GvBn/fbFwPcsG419SHybpK8L2jZE7hXU1x59X5cHCmYG9QkKWkUsZ0xyxu9AEtvCySS+00sgQbRlyxZeffXVkATU+PHj2bNnT8jj+/r6aGpqYvz48ckeakySJDJIxV+SGJndtz8JJHfKUqqS+BZOJbGd+nzABcBK/fY3gPsAt2Ujsg+J7yHQNOjeZVhBTN/u2ALE6LKQNcrQNFqvECqYAZ6spLyFdCKxLZxM4jt9BBJEGzZs4LXXXmP06NEhPz/88MNpbm5mzZo1zJ8/H4BXX30Vv9/PYYcdZsWQo5IkkUFDQwOlpTJPXDiTxLdwKont1OYHLgT+qN/+GnA/kiCKl8R3BL5uaKuPvJx8X1v0fV0elfQJLCFfGLSCWPYYcLmS8x6ExLZwNIlv52hvb6e+vr7/9qZNm3j//fcpLS1lwoQJnHnmmbz77rs8++yz+Hw+du3aBUBpaSlZWVnMnj2bk046iYsuuogVK1bQ29vLsmXLOOecc1JuZTOQJFEYs+clCpFKJL6FU0lspy4/8E3gQf32ecDvkATRUKRtfGsadO+O3CuofRMxq4IyS0KXkA9cCmZKVVCKSNvYFmlB4ts53nnnHY455pj+21deeSUA559/Ptdddx1PP606LR588MEh+7322mscffTRAKxcuZJly5Zx3HHH4Xa7Wbx4MXfddVdSxj9UkiQykGyvcDKJb+FUEtupyQ9cikoKASwB/gB4LBuRPTk+vn09qiqorTZ8mlhva/R9XW7Inx7aJygwRSxnnFQFpTjHx7ZIaxLfznH00UcTbVH4eBaMLy0tZdWqVWYOK2EkSWSwefNmxo4da/UwhEgIie/0ZGze7sTG7RLbqUcDLgd+o98+B3gISRANhyPiW9OgZ294n6DWGujYBJo/+v6ZxeENo4uq1RLznujLFYvU5YjYFmIQEt/CriRJZDBqlCzEK5zLTvFddsXpNHd1AODz+8heeiIlufn9jchF/NKhebudYtsKzcDdQAVwBpDoj9Qa8G3gXv32WcDDyEnHcNkqvn1eaG8InRrWol9798fY2QX508IbRxdVQU6ZVAU5kK1iW4ghkvgWdiXnawYFBQVWD0GIhLFTfDd3deDt6+2/7fP7+5NGYniuWrjE6iEkjJ1iO9mageOBNfrtsagm0t8Epibg9dqBK4Hf6rfPQK1oJiccw5dy8a1p0NMYvox8aw20bwTNF33/jMLw6WFFVVA4Czw5yXkPIiWkXGwLYSKJb2FXcs5msG3bNlmuUDiWxHdsc5ZebPUQEuaqhedaPYSEkdiOrBk4kYEEEcBeYDnwC2ARqmfQiZjTSPrvqOTTFv32qcAjQKYJz53OLItvf69K+kRaTt7bFGNnF+RPDUoEBfUKyp0gVUECkGO3cDaJb2FXkiQyGDNmjNVDEAni5CqKeEl8xzbnUucmiZxMYjtcC/AFYLV++x7gWGAFaqWxVuAZ/TIDWAp8HRjOv+Q+4ArUlDJQCafvoJJRsobUyCU8vnv2hS8j31YLbQ2g9UXfNyN/IPlTVD2wpHzhLMjITey4he3JsVs4mcS3sCtJEhlkZcnprFM5uYoiXhLfwqkktkMFEkRv67fvAi7Tt+8EbkJV+NwLvAdsBH4AXAOcBpwOnAzEWrxXA/6M6j+0V79vLvAAcMjI34bQmRLf/l61bHzIFDE9KdTTGHv/vPLwqqCiasidKFVBYtjk2C2cTOJb2JUkiQx27NjBpEmTrB6GEAkh8S2cSmJ7QCtwEvCWfvsO1CpjwfJRfYm+gUok3Qs8CvTo14+ipogdh0oYfQkwFsxvBS4BntdvZwPXAt9DppeZbUjx7d0/0Cg6pDKoPnZVkCcPiioHEkCFVXpl0CxVMSSEyeTYLZxM4lvYlSSJDMrKyqweQlpIhyW5U5HEt3AqiW2lDZUg+p9++zZUlc9gXMBh+uVXqOlifwX+A/QCL+qXpcBnUFVGpwIvA1ehmlQDfA7VqLrStHcigoXFt78POjYbegXp1z17Iz5HiLwpocvIByqD8iaBy4zuVELER47dwskkvoVdSZJIWCIdluQWQohkakNNEfuvfvtXqD5B8RqjP/4KYBeqV9HfgFcAr/68/wV+GLRPEXALqipJUgsJ4N0PrbXk7/4PNO1ViaC2WmjboKaPRePJjZAI0i9SFSSEEEKIQUiSyGD37t2Ul5dbPQwhEkLiWziVHWP7L8DHqClbI137pB1YCPxbv30Lahn64RoPXKRfWlHVRH8DntNvg6oo+jUghfQj5PfpVUFBq4cFpop17wFgdLT9cyeF9wkqqoa8yVIVJFKeHY/dQsRL4lvYlSSJDCZOnGj1EIRIGIlv4VR2iu0+VLXOPfrtXwHfB74LFAzj+fajEjZv6rd/geoLZJYi4Gz94gX+BRQCC1DT1UScvC0DlUAhvYI2gN8bdVfNnY2rKKgiqL9XUCVkFibpDQhhPjsdu4UYKolvYVeSJDLweqOfqAlzybL0ySXxLZzKLrG9H5VseSXovg7gOuA+4HpUM+l4/jiv0fd5BOjU77sZtUpZomShmlmLQfh90Lk1KAkUtJJY187Y++dOCG0arSeFNu/xMX3GzMSPX4gks8uxW4jhkPgWdiVJIoPGxkamT59u9TDShixLn1wS38KpzIrtblS1TEbQxawJO3XAKfo1qD4+1wDLUU2fd6MaRN+OSvacSnilTidqyfn7gHeC7s9ALWv/fZPGKmLobQtvGN1WC6114O+Jvq87S60WFjw1LDBdLLMo4i6N61dLkkg4kpyXCCeT+BZ2JUkigylTplg9BCESRuJbOJUZsf0kqson0iLhgYSRB7W8+yHAMuCL+n2xvAKcBTSjkk63Ad9CJYHuQ61AdhWq708tatn5I1G9hQ4H1gG/AR4CWoKetxy4GLgAmBDf2xTx0vzQuU0tJx/cJ6i1Frp2xN4/Z3xQn6Cg67yp4I4nagbIsVs4lcS2cDKJb2FXkiQyaG9vj/0gIWxK4ls41UhjuwXVQDpSggj9/uCfvaJfpqOSRRcAJYPs+2tUEsiH6u/zKGqZ+mDVqCTVm6hqoP+hmlAfAcwG1gc91oVaxewS/Xpo6QYRprcd2urCl5NvqwNfV/R9+6uCqoKmiOnbWcWmDVGO3cKpJLaFk0l8C7uSJJHB/v37rR6CEAkj8S2caqSxfS1qulcGqsdPEQOJIV/Qdh9qda+HgbeATaiG09cA5wOXo5I6AL2o5NB9+u2ZqGXlAz+P5LPAf4AngB8B9QwkiMahpqhdBEwb/ltNT5ofOj+JPEWs85PY++eMC+sTRFE15E8bclXQcMixWziVxLZwMolvYVeSJDKYNm2a1UMQImEkvoVTjSS2PwDu1revBM6MY5/LUEmiu1FL2XeikkH3ASegegvdC/xDf/zRwOPEWMpc5wIWA18Cfge8CxyPmoKWFcf+aa2vQ/UFCukTVKPu83VG39edCQUVkaeIZY1KzvgHIcdu4VQS28LJJL6FXUmSyKCpqYmxY8daPQwhEkLiWzjVcGPbj0r4+IHJqIqgeB2mX24BVuiXPcDL+iXgm6hkUuYQx5aJmlImDDQNuraHTw9rrVE9hGLJHjvQKDq4OqhgOrhT87RIjt3CqSS2hZNJfAu7Ss2zIQu1trZaPQQhEkbiWzjVcGP7YVTvH1CrihUM4zkmoJauvxpVVXQnanl6N3AHqmeRcZUyEYe+TmjbEHmKWF9H9H1dGVA40zBFTK8Kyi5NzvhNJMdu4VQS28LJJL6FXUmSyGDmTFliVjiXneK7JDef5i71QdDn9+FxeyjJzbd4VCJVDSe29zOwZPwJqCleI5ENnAf8H/AekAMcMMLndDxNUyuFRUoEdWwFtOj7Z5UalpHXrwtmqOljDmGnY7cQQyGxLZxM4lvYlSSJDHbt2kVpqf2+ZUy2j+69nzmXXmz1MMQQ2Sm+d9/+ZP920bJFtN7znIWjEaluOLF9DbAXNa3rHsyr9nEBnzbpuRyjr0tVBbXVqiXlg5eT74ux+ovLo5I+wYmgQHVQzpjkjN9idjp2CzEUEtvCySS+hV1JksigoyNGCbsA4KMVkiSyI4lve/IB+1D9bvagVuEybmcCVail1Kv1bfMW4E59Q43tdxlYdez7QKXZA0pHmgbdu8KrglproWMzsauCRkVIBFVBwUzwpHfLbjl2C6eS2BZOJvEt7EqSRAaVlfJRwSzLn1/JVQvPtXoYIkiqxfecpfElGq9auCTBI0k9PcCDqJ42dajGykM1noGkUTUwAygFSoBR+nUuzuiXM5TY9gOX6tflqF5CYgh83dBWH54IaquF3hj9F1xuyA+uCgrqF5Q9BlxOiEbzpdqxWwizSGwLJ5P4Fnbl0jQtxld76eWjjz5izpw5Vg8j5a2aewhLPnwn6mNkilDqkfhOfV2oZc9/CXwyyGMygXFAmX49Tt+vVr/0DOH1MlHJohJU4mgScBWwYMgjt9ZQYvsB4EJ9+0ngtASNydY0Dbr36AkgQ6+g9k3ErArKLA5NAPX3CpoJnuykvAUnkWO3cCqJbeFkEt/CrqSSyKC7u9vqIQiRMBLfqasDtYT6rcCuoPtPA76CWkErkBgqZvDqHx+wFajRL7VB27sjPL4X1Zdnb9B9z6KWdf9WlNdJNfHGdhPwQ337ZODURA3ILnw90N4QeTn53pbo+7rckD89tGF0f6+gcVIVZCI5dgunktgWTibxLexKkkQGs2fPtnoIQiSMxHfqaQV+DdwGNOr3uYCzgB8Dc4f4fB5gun452fCzHqA56LLfsL0feARVwfQd4J/A71FVRqku3ti+GtXfKRu4C/skwUZE06CnMXIiqGMjaDEmM2YWDfQIKg7qFVQ4S6qCkkSO3cKpJLaFk0l8C7uSJJFBfX09Bx98sNXDECIhJL5Txybgj8CdqOQMgBtVNfRjIBGnFdmoSqSyKI/5AXA+8DxqKtb7wKOk/vSzeGJ7NXC/vv1DoCLBY0o6n1evCgqaGhZYScy7P8bOLsifFt4nqKgacsqkKshicuwWTiWxLZxM4lvYlSSJDHp7e60eghAJI/FtrXrgcf2yJuj+DOA8VC+gWRaMK9gY4BnUtLerUcmsI4FfActI3cqbWLHtQzWr1lBVVj9KwpgSprtxIAkUXBXUvhE0X/R9MwpDp4f19wqqgIzc5IxfDJkcu4VTSWwLJ5P4FnYlSSKDgw46yOohCJEwEt/JV8NAYugDw88KgHNRCYtpyR1WVG5URdGRwJeB7aj+RP9ENX0utm5og4oW2x8CtwOBVvt3oVZ1S2n+XpX0MU4Pa6uFnn0xdnZB/tTwZFBhFeROkKogG5Jjt3AqiW3hZBLfwq4kSWSwbt065s+fb/UwhEgIie/k2Irq5fM48LHhZ0XAl4AzgRNJ7WTFkajpZucBLwJ/Bd4D/gKkWhQZYzvQX+n3hFZtnQJ8MblDi66nKTwJ1FoDbQ2g9UXfNyN/oFF08BSxwllSFeQwcuwWTiWxLZxM4lvYlSSJDPz+GA08hbAxie/EWodaun4lEPzxfhRqlbIzgeNQvYHsYgzwHOp9/QTYCByBmrr1DSBVviPz+/34gVdRiaEnUI26A8ajei392IKx4e9Ty8ZHmiLW0xh7/7wpocvIB65zJ0lVUJqQY7dwKolt4WQS38KuXJqmaVYPIpV4vV6ysrKsHkbKWzX3EJZ8+E7UxxQtW0TrPc8laUQiHhLfifE/4GbgqaD7ioGzUYmhY4BMC8Zltn+hGmtvD7pvAXABcA7JWwVNAzpRq8EFLm/6fPzR42Fr0OMyUJVDFwAnkYRvRbz7w6eHtdZCe72aPhaNJy+0aXT/SmKzVMWQSGty7BZOJbEtnEziW9iVVBIZfPDBByxYkOrr+AgxPBLf5tFQU7B+gerVEzAeuBL4JmpqmZMchZp+9kvgIWAPasWw1cAVwGJUQuZoVF8jIw1oQjXDDlxaUE2lo106UMvWByeFuo1P7vH0bx6oj+P/gHHDfreD8PugY7MhEaRXCHXvib1/3uSBJFBwZVDeJHBF+lcTQo7dwrkktoWTSXwLu5IkkRBCDEEf8BgqORTciLoC1ez5PCDHgnElyxhUkuhG4HnU1K7nUEmblfplGvA1YDQqEbSRgaRQa4LGVdTXx1cyMrgAVd004klY3mY9CWTsFVQPfm/0fT05ehKoKnSaWGElZBaMdGRCCCGEEEIkjEw3M5CywPjIdDN7kvgeua8Afw66/SnU0vVnAJ6IezjfLuBhVMKoJs59PMAUoBT1bYUnyiUXlZwaq19HumQMJ7b9PujcAi0RegV17469f+6k0B5BgSlieVOkKkiYSo7dwqkktoWTSXwLu5JKIgMpCxROJvE9Mv9kIEH0OVQT5BMwoWrF5sYD3we+h+rP9HvUSmgZwAxgun6ZEXQ9GXP7NK2OFtu9raFVQYFkUNsG8PdE3ifAk6MqgIJ7BQV6B2UWmvgOhBicHLuFU0lsCyeT+BZ2JUkiYbqyK06nuasDn99H9tITKcnNZ/ftT1o9LCFGRAN+qG8fAPwDOYAauYDD9ctvk/3imk9fQaw2fEn5rp2x98+dEJQAmj2QFMovl6ogIYQQQgiRNuQzjsG8efOsHoLtNXd14O1TK/n4/H6auzosHpEIkPgevieBt/Ttm5CDp2V62yL2CjqkdQPUh7WzDuXOUquFGZeTL6yErOLkjF+IYZBjt3AqiW3hZBLfwq7kc46BlAUO7tEFR+JtbQNA8/l4uGouWUWFfHn1vy0emYiXxPfw9AFX69tHAF+ycCxpQfND57YIy8nXQNeOiLuETPnLKTMkgfQKofxp4E7XzlHCzuTYLZxKYls4mcS3sCtJEhm43TKtYDDe1jb8vb39tzW/vz9pFKwkN79/upnH7aEkNz+ZwxRRSHwPzx+AWn37F0gPItP0dUBrXWifoNYaaKsDX1f0fd1ZUFjRnwTa1JTN9LknqWRQVklShi9EssixWziVxLZwMolvYVeyuplBV1cXubm5Vg8jJT1cNTckSQTgzszkvNoPIz5eVjdLPRLfQ9cJzAJ2AKcAT1s7HPvR/NC5PbxPUGsNdH4Se//sseF9gvqrgga+55DYFk4m8S2cSmJbOJnEt7ArqSQyWLt2rZQFCseS+B66u1AJIheqF5EYRF+nqgAKW06+Fnyd0fd1Z0JBRWgSKHCdNSqul5fYFk4m8S2cSmJbOJnEt7ArSRIZZGaauSizOT66937mXHqx1cMQDpCK8Z3KmoCb9e3zgYMsHEtK0DTVE8jYJ6i1Fjq3xt4/e0zkXkEFM0KqgoZDYls4mcS3cCqJbeFkEt/CriRJZFBRUWH1EMJ8tEKSRMIcqRjfqexmoAXIBq63eCxJ1dcFbRsiTBGrhb726Pu6MqBwpp4ACl5FrAqyRydsyBLbwskkvoVTSWwLJ5P4FnYlSSKD9evXS1mgcCyJ7/htQ001A1gGlFs4loTQNOjaaZgapl93bAFitKvLKg2fGlZUrVcFJf+bM4lt4WQS38KpJLaFk0l8C7uSJJFBTk6O1UMQImEkvuN3HdADFAFXWTuUkfF161VBhulhrbXQF746YQiXRyV9Ik0RyxmbnPHHSWJbOJnEt3AqiW3hZBLfwq4kSWRQXu64eoEhWf78Sq5aeK7VwxAJku7xHa91wIP69o+AxE2SMommQffu8Iqg1hro2EzMqqDMEpUAKq4OmiZWBQUzwZOVhDcwchLbwskkvoVTSWwLJ5P4FnYlSSKDurq6tC4LXP78KkkSOVi6x3e8rgb8wATg2xaPJYSvB9rqB3oEtQT1Cuptib6vyw350w19gvTr7LHgciXnPSSIxLZwMolv4VQS28LJJL6FXUmSyCA/P9/qIaSsrKJCvK1qeorm8+HyeMgqKhz08VctXJKsoYk4SXzH9m/gKX37OiAv2QPQNOjeM0ivoE2g+aPvn1kc2iw6MEWssAI82cl5DxaQ2BZOJvEtnEpiWziZxLewK5emaTHmIaSXpqYmSktLrR5GiFVzD2HJh+8k9DXKrjid5q4OfH4fHrcHgJLcfHbf/qRlYxLmS8X4TiUa8DngTaAS+JgEZtJ9XmivD58e1loLvc3R93W5IX/aQAIoeJpYzjjbVwUNh8S2cDKJb+FUEtvCySS+hV1JJZFBQ0NDWv5nbu7qwNvXC4DP7++/TzhLusZ3vJ5DJYgAbsKEA6SmQU/jIL2CNoHmi75/RqFhapi+XVgBHmmGGExiWziZxLdwKolt4WQS38KuJElkUFRUZPUQhEgYie/B9QA/1LcPBc4Yys7+XmhrGOgVFJwM8u6PsbML8qdGXk4+Z3xaVgUNh8S2cDKJb+FUEtvCySS+hV1JksjArtnej+69nzmXXmz1MESKs2t8J8NPUKuaAfwCiJia6dlnqArSt9sb4qgKKgjtERSYIlY4CzJyTX0v6UhiWziZxLdwKolt4WQS38KuJElksHnzZsaOHWv1MIbsoxWSJBKx2TW+E+1V4Ff69mX+Xo5u3xSaDApUB/Xsi/1k+VP1/kCGKWK5E6UqKIEktoWTSXwLp5LYFk4m8S3sSpJEBqNGjbJ6CEIkjMR3kJ4maK2lo7WG9W21PNFaw5zWWma0N6jpY9F48iJPDyucBRlJXw9NILEtnE3iWziVxLZwMolvYVeSJDIoKCgw7bmWP7+Sqxaea9rzCTFSZsa3Lfj7oH1TUJ+gQHVQLfTsBSAfuGyw/fOmRE4G5U6SqqAUk3axLdKKxLdwKolt4WQS38KuJElksG3bNsaPH2/Kcy1/fpUkiURKMTO+U4q3ObxPUGuNWmI+RlVQhyePuqJKsouqOSCkX9AsyMhPzvjFiDk2toVA4ls4l8S2cDKJb2FXkiQyGDNmTFJfz64Np+cstd+YRfLj21R+H3RsjtwrqHtP7P3zJuu9glRF0M6iao4rqqImbzJHudy8mvA3IBLJ1rEtRAwS38KpJLaFk0l8C7uSJJFBVlZWUl7n0QVH4m1tQ/P5eP/Oe8gqKuTLq/+dlNc2gx0TWyJ58T0i3pbQqqBAIqitHvze6Pt6cqCw0jBFrFrdlzlQ8tsHnAWsB4qBPwKexL0jkQS2iG0hhkniWziVxLZwMolvYVeSJDLYsWMHkyZNsnoYcQtONj1cNdd2ySaRXCkT334fdG4JSgYFXXfvir1/7sTQ5eQD2/nl4HLH3P0XQOB/yb3A1JG8F5ESUia2hUgAiW/hVBLbwskkvoVdSZLIoKysLCmvE0jkrJp7CEs+fGfYz+NtbcPfq3quaH4/3tY2U8YnnClZ8d2vt3WgUXTINLEN4O+Jvq87G4oqQ6aIqetKyCwa9pBWA9fp218Blgz7mUQqSXpsC5FEEt/CqSS2hZNJfAu7kiRRCpMqIWELmh86tkbuFdS1M/b+OeMjryCWVw5ucyeBtQPnoqablaOqiIQQQgghhBBCKJIkMti9ezfl5eVWDwOQKiFhvhHFd2+7nvwxrCLWVge+7uj7urPUamHBSaDANLGs4uGNZxi+C2wAXKg+RCVJe2WRaKl07BbCbBLfwqkktoWTSXwLu5IkkcHEiROtHoIQCRMzvjU/dH4S3ieotQa6tsd+gZyygURQYJpYcTXkTTW9KmiongLu17d/AHzewrEI88mxWziZxLdwKolt4WQS38KuJElk4PXGWD0phrIrTqe5qwMAn99H9tITKcnNZ/ftT5oxPCFGpD+++zqgtS7CFLE68HVGfxJ3JhRUDKwcFjxNLKsk4e9hOHYDF+rbnwZ+ZuFYRGKM9NgtRCqT+BZOJbEtnEziW9iVJIkMGhsbmT59+rD3b+7qwNvX23/b5/f3J42ESCpNC6sKKv1kNXywQ90fS/bY0GXk+1cQmwZu+xw6NOCbQCOQA6wEZEFS5xnpsVuIVCbxLZxKYls4mcS3sCv7fNJLkilTplg9BCGGpq9T9QUKW0GsTlUMBQnr/uPKgMKKyMvJZ5cm7S0k0p9QU80AbgaqLRyLSBw5dgsnk/gWTiWxLZxM4lvYlSSJDNrb260eghDhNE31BIq0nHzn1tj7Z4+BoipamEjxpAUDlUEF09X0MYfaDlyub38+aFs4jxy7hZNJfAunktgWTibxLexKkkQG+/fvH9H+Jbn5IT2JPG4P/9/enYc3VebvH38npRsthZatFKkgTNllE5BBERQXEEcRV9xABBeYn4oL7iAoos4oLox+XdFRwGXQcVxwwYVhEQtakEWgDNhCKVBaKN1Lk98fpZGG0qRt0pM8vV/XxWVITnI+h9yeJp8+53maRUb5ojRpCI4UwuFtlVcPc40K8vCDxhYC0R3d5gk6eju8OQBbk5Pp361/PRyI9ZyUz0N0CIgC3gDsllYk/lTXc7dIIFO+xVTKtphM+ZZgpSaRm/bt29fp+cdOUB0z5UJyX/ysjhWJcZxOKNxzdKJot1XE8n+nvL1RjbC4ypNFV1wmFn0KhFQ/205d8x1MXgeWHL39N+AUC2sR/2tI2ZaGR/kWUynbYjLlW4KVmkRusrOzadmyZZWPHbtyWQWtXCYnVFYEh1PdGkFHbx85XP1zbSHlTR/3RlBMF4hoUeuSqsu3SX4Hph69fS7lE1eL2RpKtqVhUr7FVMq2mEz5lmClJpGb3NzcEz7mvnJZxX3SgDmdULS3ikmjt0DeDjyOCgptdvwy8jFdyi8b8zAqqDaqy7cpHMCNwGEghvIRRTZLK5L60BCyLQ2X8i2mUrbFZMq3BCs1idx07NjR6hIkEJUV/zEq6PAWOPTbH5eLlXr4AWCzQ1SHqptB4S3BVn8tjIaQ738A3x69/RygdSUahoaQbWm4lG8xlbItJlO+JVipSeQmMzOTuLjAWPo7LKYJJbmHcZaVYQsJISymidUlmc3phOL9x88TlPsb5O8Ap6P654c2rWZUUHj9HIMHgZRvf0gFph29PQq4wcJapH6Znm1p2JRvMZWyLSZTviVYqUnkJj8/cC4fuzJ5BQALTj2NsevXWFyNQcpKIC+16uXkSw96eLKtfNn4Jp2PbwhFtK7XUUG1EUj59rUyYBxQAMQCr6DLzBoSk7MtonyLqZRtMZnyLcFKTSI3SUlJ9bq/nrdMqtf9NRhOJxRnVTMqqKz65zdqcvwy8jFdoEknCImon2Pwg/rOd32aC6w4ense0Ma6UsQCJmdbRPkWUynbYjLlW4KVmkRu0tLS6Nmzp09e6/6RYz1u0/O2ujWJGvwlaY5SOLy96uXkS7I9PNkGUSdXHg1UMUIosk3AjwqqDV/mO5BsBh48evsy4CoLaxFrmJptEVC+xVzKtphM+ZZgpSaRm6KiIp+91v0jr/HZa51Ig7kkrfjA8SOCcn+DvP+B80j1z20UXbkB1PTocvJN/gSNIuun/gDhy3wHiiOUzz1UDLSkfOJq89p74omJ2RapoHyLqZRtMZnyLcFKTSI3Xbt2tbqEhstRWr5s/LHLyFc0hYqzPD+/ceLxl4fFdIbIBCNHBdWGifl+H0g+evv/KG8UScNjYrZFKijfYiplW0ymfEuwUpPITWpqKr1797a6DL/49R+v1PnyNp8ozq66EXQ41YtRQVFHRwR1drtM7E/lj0m1TMz3e0f/OwQYbWUhYikTsy1SQfkWUynbYjLlW4KVmkRuSktLrS7Bb359uR6bRI4jkL/zj8vCjr1UrHi/5+c3bld5nqCmR0cIRbbVqKA6MC3fucCXR29faWUhYjnTsi1yLOVbTKVsi8mUbwlWahK56dGjh9UlBJeSnOOXkj+8BQ5vK798rDohkdAk6ZhLxCouE0vSqCA/MS3fn1E+F5ENjSJq6EzLtsixlG8xlbItJlO+JVipSeRm06ZN9OvXz+oyAouj7JhRQW6XiRXt8/z8yLZVLyff+CSw2f1evvzBtHx/ePS/Z6Al7xs607ItcizlW0ylbIvJlG8JVmoSuXlj7TcN9n/mmJAjdG5cQOeoAro0LqBrVBF81uPoqKCS6p8cEnF0VNDRBtCx8waFNqmfAxCPHA6H1SX4TB7w+dHbl1tZiAQEk7It4k75FlMp22Iy5VuClZpEbv65fhnzmGZ1Gf7jKIOCtMrLyOduYefAlbQJr6IRdMhtpFBkglsj6OjIoKhEjQoKAr169bK6BJ/5HKhYWPRSKwuRgGBStkXcKd9iKmVbTKZ8S7BSk8iNo6zM6hJ8o/Swa66gjc/eR1STw4wYV8SRf4bSKNR53OZtwv+4XVRmY1thY7YWRjFm6KRjLhVLgtCYejwI8bV169bRv39/q8vwiYpLzf4MtLWyEAkIJmVbxJ3yLaZStsVkyrcEKzWJgpnTAfnlo4I6n7YXkm/7Y96gwgzXZt1PP8HzI+JdI4Hu+fI7NhwOZ0tBY34visCBjbBGoRTfPqt+jkWkBgoon7Qa4DIrCxERERERETGImkRu7CEhVpdwnEahZZD98/HLyR/eBmWFAPQbDmx76fgn28M4mGnj4L4wcrPCOJQVxuGcxoz8ci2ENXVt9vwb51FyRMs0ms6UYa9fUN4oAhhjZSESMEzJtkhVlG8xlbItJlO+JVipSeSmusvNmkVGcbAwnzJHGSH2ENd9PuF0QMGuY5pAf6widsVdu2BJ9ZNpF+Y3IrLDn4+ZJ6hirqD2/KdrHxylfzSA7KGhlRpE0nCYMuy14lKzgUCilYVIwDAl2yJVUb7FVMq2mEz5lmClJlEN7H32IwBiplxI7oufedj6BI7kQ+7WKpaT3+IaFXRC9lCI7lR5GfmjK4h9dNq5jF3/Q+1qEgkihcCnR2/rUjMREREREfGnZcuW8fTTT7N27Vr27NnDRx99xCWXXOJ6fPHixbz88susXbuW7OxsfvnlF3r37l3pNYqKirjrrrtYtGgRxcXFnH/++fzjH/+gdevW9XswXlCTyI1PLjdzOqFwd+VGUMXtgnTPzw9v+cfy8ceuIhbdAex6y6T2TBj2+hWQd/S2LjWTCiZkW+RElG8xlbItJlO+zZGfn0+vXr248cYbufTS49dVzs/P54wzzuCKK65g4sSJVb7GnXfeyWeffcYHH3xA06ZNmTJlCpdeeikrVqzwd/k1po6DmxqtbnakoHxeoErNoC3lI4OO5Ff/XFsjaNLxj0vDjl1OPjyubgchcgImDHv94Oh/+wEdrCxEAooJ2RY5EeVbTKVsi8mUb3OMGDGCESNGnPDx6667DoCdO3dW+fihQ4d4/fXXWbBgAWeffTYAb775Jl27duXHH3/k9NNPtNKUNdQkOqr1naM5WJjPkbIjhN9yHs0io8ovL3M6y1cKq2j+HPqNxV1/gn+3L19ZjOOXk68kLO6YOYKOuUwsukP55WMi9chut1tdQp0UA58cvX25lYVIwAn2bItUR/kWUynbYjLlO/Dl5uZW+nt4eDjh4eE+38/atWspLS1l+PDhrvu6dOlCYmIiq1atCu4m0dq1a2nZsiUAe/fuJSEhgZKSErKysmjXrh15eXnk5OTQvn17srOzyc3NpWPHjmRmZpKfn09SUhJpaWkUFRXRtWtXUlNTKS0tpUePHmzatAmHw0GvXr1Yt24dQJW37XY73bp1Y8OGDYSGhtKpUyc2b95MREQEiYmJbN26laioKOLj49m+fTsxMTHExcWxc+dOYmNjiY6OJj09nRYtWhAWFkZGRgatW7fmcEEunSNy6dy4gC5RBXSNKqL0P70Iyd+O3VF5VNDwWCA/y/V3JyEUhbYlNK47B460oiDkJBI6D2NzBpTaY/44jnzo1animFJ8ekxlZWXs2LGj0jFVvE/ubSwnTpKTkyu9TziPb3Y5HQ7y8vIC6n0yMXv1eUwlJSUkJycH7TH90KQJh5OSAPjT+vWUdOli5PukY6r5MZWUlJCWlmbUMZn4PumYandMSUlJJCcnG3VMJr5POqaaH1OLFi1ITk426phMfJ90TLU7ppKSEgoLC406JhPep/T0dHr06AFAmzZtKCioWDMZpk+fzowZM/C1zMxMwsLCaNasWaX7W7duTWZmps/3V1c2p7OK7kAD1GLy2WQN/q76jcJiIaYL72xK49rz/vrHZWLRp0BIWP0UegILTj2NsevXVPnYPzufetzqZtdtWV9pm4qRVO4rt1VM1i1mSE5ODuphr+OAt4DewC+WViKBJtizLVId5VtMpWyLyZTvwFebkUQ2m+24iasr7Ny5kw4dOhw3cfWCBQsYP348xcXFlbYfMGAAw4YN48knn6z1MfiDLjc76nBZIzKKw2gVWsL/iiLZVhjFhWeMc5srqAXYbNz2yYVce8c0q0v2KZ+s3CYBLzQ0eC9xLAH+ffS2VjUTd8GcbRFPlG8xlbItJlO+A19MTEy97Cc+Pp6SkhIOHjxYaTTR3r17iY+Pr5caakJNomOcvqYvmSVhlDrthDUKpfivT1tdkohPderUyeoSam0pcPDobTWJxF0wZ1vEE+VbTKVsi8mUb6nQr18/QkNDWbp0KWPGlK/PvGXLFtLS0hg0aJDF1R1Ps2kdI704glJnw/4nuX/kWKtLED/avHmz1SXU2odH/9sT6GxlIRKQgjnbIp4o32IqZVtMpnybIy8vj5SUFFJSUgDYsWMHKSkprvkws7OzSUlJYdOmTUB5AyglJcU131DTpk2ZMGECU6dO5bvvvmPt2rWMHz+eQYMGBdyk1aAmkbi5f+Q1VpcgfhQREWF1CbVSCnx89LZGEUlVgjXbIt5QvsVUyraYTPk2x5o1a+jTpw99+vQBYOrUqfTp04dHHnkEgE8++YQ+ffpw4YUXAnDVVVfRp08fXn75ZddrPPvss4waNYoxY8YwZMgQ4uPjWbx4cf0fjBd0uZlIA5KYmGh1CbXyPZB99LaaRFKVYM22iDeUbzGVsi0mU77NMXToUKpb72vcuHGMGzeu2teIiIhg3rx5zJs3z8fV+Z5GEok0IFu3brW6hFr54Oh/uwLdrCxEAlawZlvEG8q3mErZFpMp3xKs1CQSaUCioqKsLqHGjgAfHb2tUURyIsGYbRFvKd9iKmVbTKZ8S7BSk6gWNLmzBKtAXGLRk2VA1tHbl1tZiAS0YMy2iLeUbzGVsi0mU74lWKlJVAua3FmC1fbt260uocYqVjVLAnpYWYgEtGDMtoi3lG8xlbItJlO+JVipSSTSgMTExFhdQo2UARVz/l8G2CysRQJbsGVbpCaUbzGVsi0mU74lWKlJJNKAxMXFWV1CjSwH9h69rfmIpDrBlm2RmlC+xVTKtphM+ZZgpSaRSAOyc+dOq0vw2hHg4aO3OwK9rStFgkAwZVukppRvMZWyLSZTviVYqUlkiJ63TLK6BAkCsbGxVpfgtYeB/x69PR1daibVC6Zsi9SU8i2mUrbFZMq3BCs1iQzR87YTN4nCYppgDw3FZrdjDw0lLKZJPVYmgSQ6OtrqErzyOTDn6O3xwHUW1iLBIViyLVIbyreYStkWkynfEqzUJGoArkxewXVb1tOocSTXbVnPlckrrC5JLJKenm51CR6lA9cfvd0DeNHCWiR4BEO2RWpL+RZTKdtiMuVbgpWaRCINSIsWLawuoVqlwFXAASAK+ABobGlFEiwCPdsidaF8i6mUbTGZ8i3BSk0ikQYkLCzM6hKq9SCw8ujt/wO6WFiLBJdAz7ZIXSjfYiplW0ymfEuwUpNIpAHJyMiwuoQT+hR4+ujticA1FtYiwSeQsy1SV8q3mErZFpMp3xKs1CRqQLQCmrRu3drqEqqUBtxw9PapwHMW1iLBKVCzLeILyreYStkWkynfEqzUJGpAqlsBTcQqJcCVQDYQTfk8RJGWViQiIiIiItIwqUkk0oDs3bvX6hKOcz/w49HbrwJJFtYiwSsQsy3iK8q3mErZFpMp3xKs1CQSaUASEhKsLqGSfwPPHL19C+Urm4nURqBlW8SXlG8xlbItJlO+JVipSSTSgJSUlFhdgstOYNzR272BZ60qRIwQSNkW8TXlW0ylbIvJlG8JVmoSiTQgWVlZVpcAgBMYDxwEmlA+D1GElQVJ0AuUbIv4g/ItplK2xWTKtwQrNYlEGpB27dpZXQIA7wPfH709D+hkXSliiEDJtog/KN9iKmVbTKZ8S7BSk+ioZpFRhDUKxW6zE9YolGaRUVaXJOJzeXl5VpdAHnDX0dtDgGstrEXMEQjZFvEX5VtMpWyLyZRvCVaNrC4gUOx99iMAJr/yJPMmTbO4GhH/yMnJsboEZgO7Ke9QvwDYrC1HDBEI2RbxF+VbTKVsi8mUbwlWNqfT6bS6iECyf/9+WrZsaXUZIn5hdb63Ad2BUuCvwPOWVSKmsTrbIv6kfIuplG0xmfItwUqXm7nJzs62ugQRv7Ey307gdsobRC2ARy2rREykc7eYTPkWUynbYjLlW4KVmkRucnNzrS5BxG+szPenwBdHb88BYi2rREykc7eYTPkWUynbYjLlW4KVLjdzk52dTVxcnNVliPiFVfkuovwys/8B/YEfUYdafEvnbjGZ8i2mUrbFZMq3BCt9T3OTmZlpdQkifmNVvv9GeYMI4EV04hHf07lbTKZ8i6mUbTGZ8i3BSt/V3OTn51tdgojfWJHvNMpXNAO4ERhQ7xVIQ6Bzt5hM+RZTKdtiMuVbgpUuN3Nz6NAhmjZtanUZIn5hRb4vBz4EmgJbgVb1undpKHTuFpMp32IqZVtMpnxLsNJIIjdpaWlWlyDiN/Wd76WUN4gAZqIGkfiPzt1iMuVbTKVsi8mUbwlWahK5KSoqsroEEb+pz3yXAn89ersHcFu97VkaIp27xWTKt5hK2RaTKd8SrHS5mZu8vDyio6OtLkPEL+oz388Adx29/T1wVr3sVRoqnbvFZMq3mErZFpMp3xKsNJLITWpqqtUliPhNfeU7E5hx9PZVqEEk/qdzt5hM+RZTKdtiMuVbgpWaRG5KS0utLkHEb+or33cDh4HGwNP1skdp6HTuFpMp32IqZVtMpnxLsNLlZm4KCwuJjIy0ugwRv6iPfL8KTDp6ezZwv1/3JlJO524xmfItplK2xWTKtwQrjSRys2nTJqtLEPEbf+f7J2DK0dtnAff4dW8if9C5W0ymfIuplG0xmfItwUpNIjcOh8PqEkT8xp/53geMAUqAtsB7QCO/7U2kMp27xWTKt5hK2RaTKd8SrHS5mZuSkhLCwsKsLkPEp8qAlUBIaSm9QkOJ8vHrHwHOpXwVszBgGTDQx/sQqY7O3WIy5VtMpWyLyZRvCVYaSeRm3bp1Vpcg4jMlwOtAF2AIMDg0lCZAJ+AS4GHKR/xsAuoytd79lDeIAF5ADSKpfzp3i8mUbzGVsi0mU74lWOlqEBED5QOvAX8Ddrk95gS2H/3z72PuD6W8mTSC8qZPMy/39f7R/QDcCEysVcUiIiIiIiJiNV1u5kbDAiWYHQTmAXOBrGPuvwi4D2hWUsLWsDB+BTYAvwJbKb8c7VitgKeA66h+uOFGykcN5QOnAf8FIup6ECK1oHO3mEz5FlMp22Iy5VuClS43c6NhgRKM9lI++icReIjyBpEduBpYB3wC/BnIX7fuuMvM8oEU4B3gVspHFO0DxgFnHn2sKoeA0Uef3wL4F2oQiXV07haTKd9iKmVbTKZ8S7BSk0gkyN0DtAfmAIcpb/JMBLYAC4BTPTw/HOgFXAP8A1hP+STUUD7ZdT/Kl7XPOeY5DuB6YBvlJ5FFlDeoREREREREJHjpcjM3GhYoweZW4GWgMXAzMBU46QTbeptvJ7AYuBNIP3pfS8obUeOA2ZSPRgJ4Eri3dqWL+IzO3WIy5VtMpWyLyZRvCVYaSeRGwwIl2NxL+SVmvwPPcOIGEXifbxswBtgMPED5svb7gQlAX+CRo9uNoXwkk4jVdO4WkynfYiplW0ymfEuwUpPIjd2ufxIJLh2AWZTPC+RJTfMdBTxO+QTX5x+9bx3lI426Am9S3lASsZrO3WIy5VtMpWyLyZRvCVa63MxNYWEhkZGRVpch4hd1ybcT+DdwN1AMfAN09l1pInWic7eYTPkWUynbYjLlW4KV2ptuNmzYYHUJIn5Tl3zbgEuAVGAnahBJYNG5W0ymfIuplG0xmfItwUpNIjehoaFWlyDiN77Kd4hPXkXEd3TuFpMp32IqZVtMpnxLsNLlZm7y8vKIjo62ugwRv1C+xVTKtphM+RZTKdtiMuVbgpVGErnZvHmz1SWI+I3yLaZStsVkyreYStkWkynfEqzUJHITERFhdQkifqN8i6mUbTGZ8i2mUrbFZMq3BCs1idwkJiZaXYKI3yjfYiplW0ymfIuplG0xmfItwUpNIjdbt261ugQRv1G+xVTKtphM+RZTKdtiMuVbgpWaRG6ioqKsLkHEb5RvMZWyLSZTvsVUyraYTPmWYKUmkZv4+HirSxDxG+VbTKVsi8mUbzGVsi0mU74lWKlJ5Gb79u1WlyDiN8q3mErZFpMp32IqZVtMpnxLsFKTyE1MTIzVJYj4jfItplK2xWTKt5hK2RaTKd8SrNQkchMXF2d1CSJ+o3yLqZRtMZnyLaZStsVkyrcEKzWJ3OzcudPqEkT8RvkWUynbYjLlW0ylbIvJlG8JVmoSuYmNjbW6BBG/Ub7FVMq2mEz5FlMp22Iy5VuClZpEbqKjo60uQcRvlG8xlbItJlO+xVTKtphM+ZZgpSaRm/T0dKtLEPEb5VtMpWyLyZRvMZWyLSZTviVYqUnkpkWLFlaXIOI3yreYStkWkynfYiplW0ymfEuwUpPITVhYmNUliPiN8i2mUrbFZMq3mErZFpMp3xKs1CRyk5GRYXUJIn6jfIuplG0xmfItplK2xWTKtwQrNYnctG7d2uoSRPxG+RZTKdtiMuVbTKVsi8mUbwlWahK5sdv1TyLmUr7FVMq2mEz5FlMp22Iy5VuClc3pdDqtLkJERERERERERKyl9qaIiIiIiIiIiKhJ5G7Dhg1WlyDiN8q3mErZFpMp32IqZVtMpnxLsFKTyE1hYaHVJYj4jfItplK2xWTKt5hK2RaTKd8SrDQnkZu8vDyio6OtLkPEL5RvMZWyLSZTvsVUyraYTPmWYKWRRG5SU1OtLkHEb5RvMZWyLSZTvsVUyraYTPmWYKUmkZvS0lKrSxDxG+VbTKVsi8mUbzGVsi0mU74lWOlyMzeFhYVERkZaXYaIXyjfYiplW0ymfIuplG0xmfItwUojidxs2rTJ6hJE/Eb5FlMp22Iy5VtMpWyLyZRvCVZqErlxOBxWlyDiN8q3mErZFpMp32IqZVtMpnxLsNLlZm5KSkoICwuzugwRv1C+xVTKtphM+RZTKdtiMuVbgpVGErlZt26d1SWI+I3yLaZStsVkyreYStkWkynf5li2bBkXXXQRCQkJ2Gw2Pv7440qPjxs3DpvNVunPBRdcUGmb7OxsrrnmGmJiYmjWrBkTJkwgLy+vHo/Ce2oSiYiIiIiIiIhUIT8/n169ejFv3rwTbnPBBRewZ88e15+FCxdWevyaa65h48aNfP3113z66acsW7aMSZMm+bv0WtHlZm40LFBMpnyLqZRtMZnyLaZStsVkyreZbDYbH330EZdcconrvnHjxnHw4MHjRhhV2Lx5M926dSM5OZnTTjsNgCVLljBy5Eh27dpFQkJCPVTuPY0kcqNhgWIy5VtMpWyLyZRvMZWyLSZTvgNfbm5upT/FxcW1fq3vv/+eVq1a0blzZ2699VYOHDjgemzVqlU0a9bM1SACGD58OHa7ndWrV9fpGPyhUU02Xrt2LS1btgRg7969JCQkUFJSQlZWFu3atSMvL4+cnBzat29PdnY2ubm5dOzYkczMTPLz80lKSiItLY2ioiK6du1KamoqpaWl9OjRg02bNuFwOOjVq5frf6iqbtvtdrp168aGDRsIDQ2lU6dObN68mYiICBITE9m6dStRUVHEx8ezfft2YmJiiIuLY+fOncTGxhIdHU16ejotWrQgLCyMjIwMWrdu7TqmvLw8duzYYdQxmfg+6Zhqd0yZmZkkJycbdUwmvk86ppofU2ZmJmlpaUYdk4nvk46pdsdUVlZGcnKyUcdk4vukY6r5MeXn55OcnGzUMZn4PumYandMmZmZFBYWGnVMJrxP6enp9OjRA4A2bdpQUFBAhenTpzNjxgxq6oILLuDSSy+lQ4cObN++nQceeIARI0awatUqQkJCyMzMpFWrVpWe06hRI+Li4sjMzKzx/vxNl5u50bBAMZnyLaZStsVkyreYStkWkynfgS83N7fS38PDwwkPD6/2OVVdbubuf//7Hx07duSbb77hnHPOYfbs2bz11lts2bKl0natWrXi0Ucf5dZbb631MfiDLjdzo2GBYjLlW0ylbIvJlG8xlbItJlO+A19MTEylP54aRN465ZRTaNGiBampqQDEx8ezb9++StscOXKE7Oxs4uPjfbJPX1KTyI3drn8SMZfyLaZStsVkyreYStkWkynfDdeuXbs4cOAAbdq0AWDQoEEcPHiQtWvXurb59ttvcTgcDBw40KoyT0iXm7kpLCwkMjLS6jJE/MLqfCf3HkSxh+tuw+Pj6Z+yqp4qElNYnW0Rf1K+xVTKtphM+TZHXl6ea1RQnz59eOaZZxg2bBhxcXHExcXx6KOPMmbMGNfcSvfeey+HDx/m119/dY1OGjFiBHv37uXll1+mtLSU8ePHc9ppp7FgwQIrD61Kam+62bBhg9UliPiN1fkuzswkrqCo2j+emkgiVbE62yL+pHyLqZRtMZnybY41a9bQp08f+vTpA8DUqVPp06cPjzzyCCEhIaxfv56//OUvJCUlMWHCBPr168d///vfSpevvfvuu3Tp0oVzzjmHkSNHcsYZZ/DKK69YdUjVqtHqZg1BaGio1SWI+I3yLaZStsVkyreYStkWkynf5hg6dCjVXYD15ZdfenyNuLi4gBw1VBWNJHLTqVMnq0sQ8RvlW0ylbIvJlG8xlbItJlO+JVipSeRm8+bNVpcg4jfKt5hK2RaTKd9iKmVbTKZ8S7BSk8hNRESE1SWI+I3yLaZStsVkyreYStkWkynfEqzUJHKTmJhodQkifqN8i6mUbTGZ8i2mUrbFZMq3BCs1idxs3brV6hJE/Eb5FlMp22Iy5VtMpWyLyZRvCVZqErmJioqyugQRv1G+xVTKtphM+RZTKdtiMuVbgpWaRG7i4+OtLkHEb5RvMZWyLSZTvsVUyraYTPmWYKUmkZvt27dbXYKI3yjfYiplW0ymfIuplG0xmfItwUpNIjcxMTFWlyDiN8q3mErZFpMp32IqZVtMpnxLsFKTyE1cXJzVJYj4jfItplK2xWTKt5hK2RaTKd8SrNQkcrNz506rSxDxG+VbTKVsi8mUbzGVsi0mU74lWKlJ5CY2NtbqEkT8RvkWUynbYjLlW0ylbIvJlG8JVmoSuYmOjra6BBG/Ub7FVMq2mEz5FlMp22Iy5VuClZpEbtLT060uQcRvlG8xlbItJlO+xVTKtphM+ZZgpSaRmxYtWlhdgojfKN9iKmVbTKZ8i6mUbTGZ8i3BSk0iN2FhYVaXIOI3yreYStkWkynfYiplW0ymfEuwUpPITUZGhtUliPiN8i2mUrbFZMq3mErZFpMp3xKs1CRy07p1a6tLEPEb5VtMpWyLyZRvMZWyLSZTviVYqUkkIiIiIiIiIiJqErnbu3ev1SWI+I3yLaZStsVkyreYStkWkynfEqzUJHKTkJBgdQkifqN8i6mUbTGZ8i2mUrbFZMq3BCs1idyUlJRYXYKI3yjfYiplW0ymfIuplG0xmfJtjmXLlnHRRReRkJCAzWbj448/dj1WWlrKtGnT6NmzJ1FRUSQkJHD99dcfN3F5+/btsdlslf7MmTOnno/EO2oSucnKyrK6BBG/Ub7FVMq2mEz5FlMp22Iy5dsc+fn59OrVi3nz5h33WEFBAT///DMPP/wwP//8M4sXL2bLli385S9/OW7bmTNnsmfPHtefv/71r/VRfo01srqAQNOuXTurSxDxG+VbTKVsi8mUbzGVsi0mU74DX25ubqW/h4eHEx4eftx2I0aMYMSIEVW+RtOmTfn6668r3ffiiy8yYMAA0tLSSExMdN3fpEkT4uPjfVC5f9WoSbR27VpatmwJlE/ElZCQQElJCVlZWbRr1468vDxycnJo37492dnZ5Obm0rFjRzIzM8nPzycpKYm0tDSKioro2rUrqamplJaW0qNHDzZt2oTD4aBXr16sW7cOoMrbdrudbt26sWHDBkJDQ+nUqRObN28mIiKCxMREtm7dSlRUFPHx8Wzfvp2YmBji4uLYuXMnsbGxREdHk56eTosWLQgLCyMjI8O1PGHF5GKFhYVGHZOJ75OOqXbH9Ouvv5Kenm7ZMTkdTo/nGYfDQXJycoN+n3RMNT+mTZs2uYZ1m3JMJr5POqbaHVOTJk1IT0836phMfJ90TDU/pkOHDhl3TCa+Tzqm2h3T/v37adq0qVHHZML7lJ6eTo8ePQBo06YNBQUFVJg+fTozZsygrg4dOoTNZqNZs2aV7p8zZw6zZs0iMTGRsWPHcuedd9KoUeCN27E5nU7P39oakOTkZPr37291GSJ+YXW+l8d3IK6gqNptshtHcEbmjnqqSExhdbZF/En5FlMp22Iy5TvweTuS6Fg2m42PPvqISy65pMrHi4qKGDx4MF26dOHdd9913f/MM8/Qt29f4uLiWLlyJffffz/jx4/nmWeeqfJ18vPzCQsLIzQ0FIAVK1bw+eefAzBy5EgGDx7s7WHWmOYkctO+fXurSxDxG+VbTKVsi8mUbzGVsi0mU74DX0xMTKU/nhpEnpSWlnLFFVfgdDp56aWXKj02depUhg4dyqmnnsott9zC3//+d1544QWKi4urfK0hQ4awZcsWAF577TVGjx7N4cOHycvL47LLLuP111+vU63VUZPITXZ2ttUliPiN8i2mUrbFZMq3mErZFpMp3w1LRYPo999/5+uvvyYmJqba7QcOHMiRI0fYuXNnlY9v27bNdVnc3//+d5YuXcrzzz/Pc889x7fffsvs2bN9fQguahK5cR9yJmIS5VtMpWyLyZRvMZWyLSZTvhuOigbRtm3b+Oabb2jevLnH56SkpGC322nVqlWVjzdr1ozdu3cDkJOTQ+fOnV2PdezYkf379/um+CoE3ixJFuvYsaPVJYj4jfItplK2xWTKt5hK2RaTKd/myMvLIzU11fX3HTt2kJKSQlxcHG3atOGyyy7j559/5tNPP6WsrIzMzEwA4uLiCAsLY9WqVaxevZphw4bRpEkTVq1axZ133sm1115LbGxslfucMmUKN9xwA6+++ipTp05l8uTJTJ8+HYDHH3+c8847z2/HqyaRm8zMTOLi4qwuQ8QvlO/aSXosiYzcjGq3SYhJYOtDW+upInGnbIvJlG8xlbItJlO+zbFmzRqGDRvm+vvUqVMBuOGGG5gxYwaffPIJAL179670vO+++46hQ4cSHh7OokWLmDFjBsXFxXTo0IE777zT9TpVuffee4mKiuKMM86goKCAQ4cO8cYbbxAWFub3OYnUJHKTn59vdQkifqN8105Gbgb5odX/23lqIol/KdtiMuVbTKVsi8mUb3MMHTqU6haF97RgfN++ffnxxx9rvN/Jkydz6623smvXLnbv3k1kZCRJSUk0bty4xq9VE2oSuUlKSrK6BBG/Ub7FVMq2mEz5FlMp22Iy5Vt8wW63k5iYSGJiYr3tU00iN2lpafTs2dPqMkT8QvkWUynbYjLlW0ylbIvJlG/xh927d5OSkkJGRgaFhYVERkaSkJBA7969adu2rU/2oSaRm6KiIqtLEPEb5VtMpWyLyZRvMZWyLSZTvsWXVq5cyb333suqVauA4y9xs9lsnH766Tz11FMMHjy4TvtSk8hN165drS5BxG+UbzGVsi0mU77FVMq2mEz5Fl/55ptvGDlyJCeffDKPP/44AwYMoE2bNkRERFBUVMSePXv48ccfmT9/PmeffTafffYZw4cPr/X+bE5Psyw1MCkpKcfNSi5iCqvzvTy+A3EF1f9WJbtxBGdk7qinirwTfW+0x4mro0qjyHsqr54qEndWZ1vEn5RvMZWyLSZTvsVXTj/9dBo1asTSpUsJDw8/4XYlJSUMGzaMsrKyWk2UXcFe62caqrS01OoSRPxG+RZTKdtiMuVbTKVsi8mUb/GV9evXM27cuGobRABhYWGMGzeO9evX12l/ahK56dGjh9UliPiN8i2mUrbFZMq3mErZFpMp3+IrsbGxpKamerVtamoqsbGxddqfmkRuNm3aZHUJIn6jfIuplG0xmfItplK2xWTKt/jKtddey7PPPsuzzz5LXl7V01vk5eXxzDPPMHfuXK699to67U8TV7txOBxWlyDiN8q3mErZFpMp32IqZVtMpnyLr8yaNYu0tDTuuusupk2bRlJSEm3atCE8PJzi4mL27NnD1q1bOXLkCJdffjmzZs2q0/40cbWbkpISwsLCrC5DxC+szrcmrhZ/sTrbIv6kfIuplG0xmfItvvbTTz/x4YcfkpKSwp49eygsLCQyMpI2bdrQu3dvLrvsMgYMGFDn/WgkkZt169bRv39/q8sQ8QvlW0ylbIvJlG8xlbItJlO+xdcGDBjgkyaQJ5qTSERERERERERE1CRy16tXL6tLEPEb5VtMpWyLyZRvMZWyLSZTvsUKhw8fJi0trU6voSaRm3Xr1lldgojfKN9iKmVbTKZ8i6mUbTGZ8i1WeP755+nQoUOdXkNNIhERERERERER0cTV7jQsUEymfIuplG0xmfItplK2xWTKt/jK22+/7fW2v/zyS533pyaRG81CLyZTvsVUyraYTPkWUynbYjLlW3xl3Lhx2Gw2nE6nV9vbbLY67U9NIjd2u67AE3Mp32IqZVtMpnyLqZRtMZnyLb4SGxtL7969eeqppzxu+/rrr/N///d/ddqfmkRuunXrZnUJIn6jfIuplG0xmfItplK2xWTKt/jKgAED+O233+jXr5/HbZcsWVLn/am96WbDhg1WlyDiN8q3mErZFpMp32IqZVtMpnyLrwwYMIDff/+dffv2edy2WbNmJCYm1ml/ahK5CQ0NtboEEb9RvsVUyraYTPkWUynbYjLl2xzLli3joosuIiEhAZvNxscff1zpcafTySOPPEKbNm2IjIxk+PDhbNu2rdI22dnZXHPNNcTExNCsWTMmTJhAXl6eV/u/99572bFjB7GxsR63nTx5Mjt27PD62KqiJpGbTp06WV2CiN8o32IqZVtMpnyLqZRtMZnybY78/Hx69erFvHnzqnz8qaee4vnnn+fll19m9erVREVFcf7551NUVOTa5pprrmHjxo18/fXXfPrppyxbtoxJkyZ5tf+oqChOPvnkems8qknkZvPmzVaXIOI3yreYStkWkynfYiplW0ymfJtjxIgRPPbYY4wePfq4x5xOJ3PnzuWhhx7i4osv5tRTT+Xtt98mIyPDNeJo8+bNLFmyhNdee42BAwdyxhln8MILL7Bo0SIyMjLq+Wg8U5PITUREhNUliPiN8i2mUrbFZMq3mErZFpMp34EvNze30p/i4uIav8aOHTvIzMxk+PDhrvuaNm3KwIEDWbVqFQCrVq2iWbNmnHbaaa5thg8fjt1uZ/Xq1XU/EB+r0epma9eupWXLlgDs3buXhIQESkpKyMrKol27duTl5ZGTk0P79u3Jzs4mNzeXjh07kpmZSX5+PklJSaSlpVFUVETXrl1JTU2ltLSUHj16sGnTJhwOB7169WLdunUAVd622+1069aNDRs2EBoaSqdOndi8eTMREREkJiaydetWoqKiiI+PZ/v27cTExBAXF8fOnTuJjY0lOjqa9PR0WrRoQVhYGBkZGbRu3dp1TE2bNmXHjh1GHZOJ75OvjunqJVeTcbC8e2sPseMocxx3u22ztiy4YEHQHFN179OhQ4dITk627H1yOpwezzMOh4Pk5OSAyp43dTudTrZs2dKg/3+y8pgOHTpEWlqaUcdk4vukY6rdMbVv357k5GSjjsnE90nHVPNjioyMJDk52ahjMvF90jHV7pjy8vIoLCw06phMeJ/S09Pp0aMHAG3atKGgoIAK06dPZ8aMGdREZmYmgKuuCq1bt3Y9lpmZSatWrSo93qhRI+Li4lzbBBKb0+n0/O2nAUlOTqZ///5WlyH1JPreaPJD86vdJqo0irynvJtULNBZne/l8R2IKyiqdpvsxhGckVm3ydZ8raHlJBhZnW0Rf1K+xVTKtphM+Q58ubm5lf4eHh5OeHh4tc+x2Wx89NFHXHLJJQCsXLmSwYMHk5GRQZs2bVzbXXHFFdhsNt577z1mz57NW2+9xZYtWyq9VqtWrXj00Ue59dZbfXNAPqLLzdxERUVZXYKI3yjfYiplW0ymfIuplG0xmfId+GJiYir98dQgqkp8fDxQPrLpWHv37nU9Fh8ff9zy9UeOHCE7O9u1TSBRk8hNIL5JIr6ifIuplG0xmfItplK2xWTKd8PQoUMH4uPjWbp0qeu+3NxcVq9ezaBBgwAYNGgQBw8eZO3ata5tvv32WxwOBwMHDqz3mj1Rk8jN9u3brS5BxG+UbzGVsi0mU77FVMq2mEz5NkdeXh4pKSmkpKQA5ZNVp6SkkJaWhs1m44477uCxxx7jk08+4ddff+X6668nISHBdUla165dueCCC5g4cSI//fQTK1asYMqUKVx11VUkJCRYd2AnUKOJqxuCmJgYq0sQ8RvlW0ylbIvJlG8xlbItJlO+zbFmzRqGDRvm+vvUqVMBuOGGG5g/fz733nsv+fn5TJo0iYMHD3LGGWewZMmSSivcvfvuu0yZMoVzzjkHu93OmDFjeP755+v9WLyhJpGbuLg4q0sQ8RvlW0ylbIvJlG8xlbItJlO+zTF06FCqW+/LZrMxc+ZMZs6cecJt4uLiWLBggT/K8zk1idzs3LmTli1bWl2GiF/4M9/JvQdR7GEJR0dBIWDzy/6lYdO5W0ymfIuplG0xmfItwUpNIjexsbFWlyDiN/7Md3Fmpsfl7bOcTrCpSSS+p3O3mEz5FlMp22Iy5VuClZpEbqKjo60uQcRvlG8xlbItJlO+xVTKtphM+RZ/KiwsZMmSJWzevJn8/HxmzpzJ7t27AWjXrh22OvxiXk0iN+np6Vqu0BBJjyWRkZtR7TYFJQUQWk8FBQDlW0ylbIvJlG8xlbItJlO+xV8+/fRTbrzxRg4cOOC6b+bMmZx++uns3buXTz75hAsvvLDWr2/3RZEmadGihdUliI9k5GaQH5pf7Z/qJiAzkfItplK2xWTKt5hK2RaTKd/iD6tXr2bMmDEcOHAAp9Pp+j4bEhLC6NGjcTqdfPjhh3Xah5pEbsLCwqwuQcRvlG8xlbItJlO+xVTKtphM+RZ/mDVrFqWlpURFRTF69OhKj/Xt2xeAn376qU77UJPITUZG9ZcniQQz5VtMpWyLyZRvMZWyLSZTvsUfVq5cic1m429/+xtTp06t9NjJJ58M4JqbqLbUJHLTunVrq0sQ8RvlW0ylbIvJlG8xlbItJlO+xR8KCgoA6NChw3GPHT58GIDS0tI67UNNIhERERERERGRAJeYmAjAwoULK61g5nQ6ef311wFo3759nfah1c3c7N271/UPL2Ka2ubb00pxCTEJvFGXwkTqSOduMZnyLaZStsVkyrf4w6hRo5g7dy5vvfUWX375pev+zp07k5qais1m46KLLqrTPjSSyE1CQoLVJYj4TW3z7WmluOoaSCL1QeduMZnyLaZStsVkyrf4wwMPPEDbtm1xOp1kZma6RhNt374dgJNOOol77723TvtQk8hNSUmJ1SWI+I3yLaZStsVkyreYStkWkynf4g8tWrRg5cqVjBw5Eii/zMzpdAIwcuRIli9fTlxcXJ32oSaRm6ysLKtLEPEb5VtMpWyLyZRvMZWyLSZTvsVf2rVrx6effkpWVharV69m9erVZGVl8emnn9KuXbs6v77mJHLji39UkUClfIuplG0xmfItplK2xWTKt/hbbGws/fv39/nraiSRm7y8PKtLEPEb5VtMpWyLyZRvMZWyLSZTviVYqUnkJicnx+oSRPxG+RZTKdtiMuVbTKVsi8mUb/GXN954g4EDB9K8eXNCQkKO+9OoUd0uGNPlZm7at29vdQkifqN8i6mUbTGZ8i2mUrbFZMq3+MPDDz/M7NmzAVwTVvuamkRusrOzadmypdVliPiF8i2mUrbFZMq3mErZFpMp3+IPr732mqs51KRJkzqvZFYVNYnc5ObmWl2CiN8o32IqZVtMpnyLqZRtMZnyLf6Ql5eHzWZjxowZPPzww37Zh5pEbjp27Gh1CSJ+Ewz5dhQUsjy+Q7XbhMfH0z9lVT1VVP+Sew+iODPzhI+bfvy1EQzZFqkt5VtMpWyLyZRv8Ydhw4bx2Wef0aVLF7/tQ00iN5mZmX4ZsiUSCIIi304ncQVF1W6SXU0DxQTFmZnV/huYfvy1ERTZBpIeSyIjN+OEjyfEJLD1oa31WJEEg2DJt0hNKdtiMuVb/GHevHls3LiRO+64g4KCAvr160dMTMxx2yUmJtZ6H1rdzE1+fr7VJYj4jfItpgqWbGfkZpAfmn/CP9U1kKThCpZ8i9SUsi0mU77N0b59e2w223F/Jk+eDMDQoUOPe+yWW27xSy2tW7fmjDPOYM+ePdx444306tWLDh06VPpzyimn1GkfGknkJikpyeoSRPxG+RZTKdtiMuVbTKVsi8mUb3MkJydTVlbm+vuGDRs499xzufzyy133TZw4kZkzZ7r+3rhxY7/Uctddd/HOO+9gs9m0ull9SUtLo2fPnlaXIeIXyreYStkWkynfYiplW0ymfAc+98nFw8PDCQ8PP24791Xq5syZQ8eOHTnrrLNc9zVu3Jj4+Hj/FHqMBQsW4HQ6sdvtdOvWjbi4OOx2314gVqMm0dq1a13/QHv37iUhIYGSkhKysrJo164deXl55OTk0L59e7Kzs8nNzaVjx45kZmaSn59PUlISaWlpFBUV0bVrV1JTUyktLaVHjx5s2rQJh8NBr169WLduHUCVtyv+MTZs2EBoaCidOnVi8+bNREREkJiYyNatW4mKiiI+Pp7t27cTExNDXFwcO3fuJDY2lujoaNLT02nRogVhYWFkZGTQunVr1zHl5eWxY8cOo47JxPfJm2PCh43V5OTkgDimur5PO3fupKioqMbvk6d/S6fD6bdOdlUcZQ6Sk5PrLXtOh+djczqdbNmyxSfvk6PM4WFn5ZkMpuz5+33auXMnTZs2Dfhjcjiqf28dZQ527Nhh7PukY6rdMZWVlZGcnGzUMZn4PumYan5MBw4cIDk52ahjMvF90jHV7pjS09Pp1KmTUcdkwvuUnp5Ojx49AGjTpg0FBQWuz2HTp09nxowZx30+O1ZJSQnvvPMOU6dOxWazue5/9913eeedd4iPj+eiiy7i4Ycf9stooorL2V599VXGjx/v89cHsDnr85tdEMjLyyM6OtrqMsQHou+NJj/Uw7XAeYCHtzuqNIq8p/J8VpeVaptvT/+WUaVRLHm7pccJp7OcDlrYqu90e7NNduMIzsjcUe02vuRNlnyZk+XxHaqfuLqejz8YBMu525v/l0w534jvBEu+RWpK2RaTKd+Bz9uRRMd6//33GTt2LGlpaSQkJADwyiuvcPLJJ5OQkMD69euZNm0aAwYMYPHixT6v+f/9v//HvHnzePXVV7nxxht9/vqgy82Ok5qaSu/eva0uQ8QvTMn31SN3kXNv9T90tUpUw2JKtkWqonyLqZRtMZnyHfiqWhXMk9dff50RI0a4GkQAkyZNct3u2bMnbdq04ZxzzmH79u107NjRJ7VWGDlyJF988QV33HEHO3bsYMCAAa7R9McaMmRIrfehJpGb0tJSq0sQ8RtT8n0gsoxCDyN76nuVqIKSAqIbcOPK09Lu4N/jNyXbIlVRvsVUyraYTPk2z++//84333zjcYTQwIEDgfJGoT+aRBWTVs+ePbvKbWw2G0eOHKn1PtQkclNxfaKIiZRv/3E6nR4vSavvxlV9Nm4qlnb3tI2/KNtiMuVbTKVsi8mUb/O8+eabtGrVigsvvLDa7VJSUoDyOY/8oWLGIK1uVk82bdpEv379rC5DxC+U74bF6sZNfVK2xWTKt5hK2RaTKd9mcTgcvPnmm9xwww00avRHG2X79u0sWLCAkSNH0rx5c9avX8+dd97JkCFDOPXUU31exw033ODz13SnJpEbTyvPiAQz5VtMpWyLyZRvMZWyLSZTvs3yzTffkJaWdtxk0WFhYXzzzTfMnTuX/Px82rVrx5gxY3jooYf8Usebb77pl9c9lppEbnr16mV1CSJ+09Dyndx7EMWZmSd8PDw+nv4pq+qxIt/x5tg4rx4LslhDy7Y0LMq3mErZFpMp32Y577zzqry8q127dvzwww8WVOQ/ahK5WbduHf3797e6DBG/aGj5Ls7MrH4p+WqaLIHO5GOrjaqybfVk2iK+0tDO3dJwKNtiMuVb/OHtt9/2arvrr7++1vtQk0hERIzUkOZkEhERERHzjRs3DpvNVu02NptNTSJf0rBAMZnyLaZStsVkyreYStkWkynf4i/+WtWsgppEbjQsUEymfIuplG0xmfItplK2xWTKt/jD9OnTj7svKyuLr7/+mq1bt9K1a1euvPLKOu1DTSIRERERERERkQBXVZMIykcXXXjhhXz55Zd07969TvtQk8iNhgWKyZRvqQ1PK6kBOC4rhKb1VFAVlG0xmfItplK2xWTKt9Qnm83GRRddxJIlS5g1axZjxoyp9WupSeRGwwLFZMq3uCsoKSD63uhqt1mcFsVJR+zVv5Cfr432RNkWkynf/uNNEzw8Pp7+KavqqaKGRdkWkynf4g9paWnH3VdWVkZmZiavvfYaAFu2bKnTPtQkcmO3e/giJBLElO/jefqCEB4fD+fVY0H1zOl0elwBzOlsXE/V1J6yLSZTvv2nODOTuIKiarfJ9tBEktpTtsVkyrf4Q/v27atd3cxms5GYmFinfahJ5KZbt25WlyDiN8r38Tx9QdCXg+CgbIvJlG8xlbItJlO+xV+qW93Mbrcza9asOr2+mkRuNmzYoGGBfpT0WBIZuRknfDwhJoGtD231+DrBMEdKIFK+xRTu5xJHmQN7SOXf2BWUFEBofVcm4ns6d4uplG0xmfIt/jBkyJDjRhLZbDaaNm1Kp06dmDBhAl26dKnTPtQkchMaqm8U/pSRm1HtpS3VNZCO5c3wcKvnSAlEyreY4rhzSVXRLq63ckT8SuduMZWyLSZTvsUfvv/+e7/vQ00iN506dbK6BBG/Ub5FRIKPzt1iKmVbTKZ8iy8sW7asVs8bMmRIrfepJpGbzZs3a1igGEv5FhEJPjp3i6mUbTGZ8i2+MHTo0Gonqq6KzWbjyJEjtd6nmkRuIiIirC5BxG+Ub7Gar+YlE2lIdO4WUynbYjLlW3yluomq/UFNIjd1XS5OJJAp32I1X81LJtKQ6NxdO14tclFQCNTsN7TiO8q2mEz5Fl+44YYb6n2fahK52bp1q4YFirGUbwkG3ow2EmlIdO6uHW8WuchyOqGGw/jFd5RtMZnyLb7w5ptv1vs+1SRyExUVZXUJIn6jfEsw0Ggjkcp07hZ/svIyYGVbTKZ8S7BSk8hNfHy81SWI+I3yba1XF0Sy/O0O1W4TrvcoIHm6bCU8Pp7+KavqsSJpSHTuFn+ysjGvbIvJlG/xp+TkZBYuXMjWreVN/KSkJK6++mqfjF5Tk8jN9u3biYuLs7oMEb9Qvq0Vl28jrqz6Sx+yPcyfIdbwdNmK3jfxJ527xVTKtphM+RZ/eeCBB3jyyScr3ffFF1/w3HPPcd999/H444/X6fXVJHITExNjdQkiHnkaGg5VDw9XvkVEgo/O3WIqZVtMpnyLP3z44YfMmTMHm81W5apnc+bMoW/fvowZM6bW+7DXpUATqdsrwaBiaHh1f6pqIinfIiLBR+duMZWyLSZTvs0xY8YMbDZbpT9dunRxPV5UVMTkyZNp3rw50dHRjBkzhr179/qllnnz5gEQHh7OXXfdxXvvvcf777/PXXfdRWRkJE6nkxdffLFO+9BIIjc7d+6kZcuWVpch4hfKt0hlBSUFRN8bXe02CTEJvFFP9YhUReduMZWyLSZTvs3SvXt3vvnmG9ffGzX6o5Vy55138tlnn/HBBx/QtGlTpkyZwqWXXsqKFSt8XkdKSgo2m40nnniC22+/3XX/ZZddxkknncSdd95JSkpKnfahJpGb2NhYq0sQ8RvlW6Qyp9NZ7YStUDFpqz7kiXV07hZTKdtiMuXbLI0aNapyMvJDhw7x+uuvs2DBAs4++2ygfNn6rl278uOPP3L66af7tI7CwkIAOnXqdNxjFfdVbFNbahK5iY6u/jfKIsGsqnx7s/StiIhYR59NpDa8nb/QSsq2mEz5Dny5ubmV/h4eHk54eHiV227bto2EhAQiIiIYNGgQTzzxBImJiaxdu5bS0lKGDx/u2rZLly4kJiayatUqnzeJTjrpJHbs2MGzzz7Ln//8Z1czMicnh2effda1TV3UqEm0du1a15C5vXv3kpCQQElJCVlZWbRr1468vDxycnJo37492dnZ5Obm0rFjRzIzM8nPzycpKYm0tDSKioro2rUrqamplJaW0qNHDzZt2oTD4aBXr16sW7cOoMrbdrudbt26sWHDBkJDQ+nUqRObN28mIiKCxMREtm7dSlRUFPHx8Wzfvp2YmBji4uLYuXMnsbGxREdHk56eTosWLQgLCyMjI4PWrVu7jikvL4/CwkKjjimQ3ieHw1FtxhxlDlZ074cj6wBOhxObzQY2/rgNEBcLVUzS5c7zFt5LTk4OqPfJUeaA0OprrriMxlFW/m9uD7FTdqQMm82GPcSOo8xBi8YtyC7KJj/sxCMpdh3chd1W/fRlToezyonT/MWbPTnKHF7lzZWrarZxOurv2Cr2WS0nHo/N6XR6lRNf8fY9sYdUnyWHw+FV3qj+bfMpR5nD43viKHOwdu1aj+cIbzK5Y8eOgD+Xm/jzKZCPqaysjPT0dKOOqT7eJ4/nUi85yhwcOnQoII6pJu/T7oO7KQgvqPbYdh3cVX4Cr+ZnhaPMQXJysl+OadeuXUZmT8ekY0pNTSU9PZ3hw4cbdUwmvE/p6en06NEDgDZt2lBQ8Md5cvr06cyYMeO48+DAgQOZP38+nTt3Zs+ePTz66KOceeaZbNiwgczMTMLCwmjWrFml57Ru3ZpMP6x+O3LkSF588UW+++472rZtS8eOHYHy1fSKi4ux2WxceOGFddqHzVmf3+yCwI4dO+jQoYPVZRgr+t7oai/tiCqNYsnbLatfarpxBEC12wCcdt1eCpt5iHce4KHJH1UaRUJMgsfRNu4rifmTp39HwOtjAzy+J95s4+l9A8hyOmjhoQHgzTbevLe+ylJ24wguuH6/T/69l/yjJe3KQqrdxtuavNmmPuv29j0B3+TN0zaAV8fm7f8n3mTpjMwdHnbm3Tkw76k8j68jDYs+m9TO8vgOPvm55O3/34HGm88K3p5z/XVeUrbFZMp34KvJSKJjHTx4kJNPPplnnnmGyMhIxo8fT3FxcaVtBgwYwLBhw45bqr6u9u7dS+/evV0TY1f8wruirdOmTRt+/vlnVzOtNrS6mZuwsDCrS5AA5Gk1MU/DuUVERGpLn03EVMq2mEz5DnwxMTGV/njTIAJo1qwZSUlJpKamEh8fT0lJCQcPHqy0zd69e6ucw6iuWrduzapVqzj//POx2Ww4neVXdNhsNi644AKWL19epwYRaE6i42RkZNC2bVuryxARkSCj+b3EX/TZREylbIvJlG9z5eXlsX37dq677jr69etHaGgoS5cuZcyYMQBs2bKFtLQ0Bg0a5JP93XzzzVx99dWcddZZ2Gw22rdvzxdffEFOTg7btm0DyietjouL88n+1CRyU9eum4iINEwVIw6re1ykNvTZREylbIvJlG9z3H333Vx00UWcfPLJZGRkMH36dEJCQrj66qtp2rQpEyZMYOrUqcTFxRETE8Nf//pXBg0a5LNJq1999VVee+01WrduzRVXXMFVV13F6aefTmxsLAMGDPDJPo6lJlED5+3KF/U5346IiIiIiIhIINi1axdXX301Bw4coGXLlpxxxhn8+OOPrkW9nn32Wex2O2PGjKG4uJjzzz+ff/zjHz6vY+/evbzwwgu88MILnHzyyVx55ZVcddVV9OrVy6f70ZxEbiomgGooPM21o/l2RERErNXQPptIw6Fsi8mUb3MsWrSIjIwMiouL2bVrF4sWLXKtKgYQERHBvHnzyM7OJj8/n8WLF/t0PqJp06ZxyimnuOYfcjqd/P777zz11FP07duXbt26MWvWLLZu9c3ADjWJ3CQkaM4IERERCRz6bCKmUrbFZMq3+MoTTzzBtm3bWLt2Lffddx8dO3as1DDasmULM2bMoGvXrvTt25enn366TvvT5WZuSkpKrC5BRESk3ngz4bYuObaWPpuIqZRtMZnyLb7Wp08f+vTpw+zZs/nll1947733+PDDD/nf//7n2iYlJYV169Zxzz331Ho/ahK5ycrKokOHDlaX4VFy70EUZ2ae8PHw+Hj6p6yqx4pERCQYacLtwBcsn01EakrZFpMp3+JPFQ2jOXPm8OWXXzJp0iR27dqF0+ms82urSeSmXbt2VpfgleLMTOIKik74eHY1DSQREQlcWlBA3AXLZxORmlK2xWTKt/hTdnY2ixcv5v333+f777+nrKzMZ6/d4JtE7h/GnQ4nNrvN9Xd9EBcRkfrkaWRPxTbScOTl5fnttT2NTAbfjk7W5Y2eNaRGsT+zLWI15Vt87eDBg67G0HfffceRI0cAKo0eat68OZdddlmd9tPgm0QaZi8iIiKBLCcnx2+v7WlkMvh2dHIwfu66euQucu6NrnYbXzZtGlKj2J/ZFrGa8i2+Mn/+fN5//32WLl1aZWOoSZMmXHLJJVx11VWce+65NGpUtzZPg28SiYiIiASy9u3bW11Cg3YgsozCBtK0qW/Ktn9pDlNrKd/iKzfeeCM2m61SYygiIoILL7yQq666igsvvJCIiAif7U9NIhEREZEAlp2dTcuWLa0uQ8TnlG3/0hym1lK+xZecTieNGjXi3HPP5eqrr+aSSy4hOrr6Ua61pSaRiIhIkHl1QSTL365+xRT9htgcubm5VpcQcLyZt2dxSRRx2OupIqkNZVtMpnyLr5x11llcffXVXHbZZcTFxfl9f2oSiUcFJQVE1+O1+CIiUr24fBtxZfU3j4xYq2PHjsfd19AvI/Fm3h6ns3E9VSO1VVW2RUyhfIuvfPfdd/W6PzWJxCOn0+nxg1hqVqpXjSQRERGpmczMzON+c6jLSAKPVm6ruaqyLWIK5VuClZpE4hPeNJI0qaOIiEjN5edX//NVAkMwrtzmS95cAujeKFO2xWTKtwQrNYkM5mkoOoDjskJoWk8FiYhIvXEUFLI83vO8RZxXTwVJrSUlJVldgohH3lwC6N5EUrbFZMq3BCs1iQKQN/MMeMPTUHQAjllGT0REDOJ0evwZ4O0lSbqMxlppaWn07NnT6jLEB7z6jBeAjVtf1e0+6b7D4cBurzy5uOnzaUn98eYX5v7Mm87dEqzUJApAmmdAREQCSUO/jMZXavuFpajIwy98JGgE62c8X9WtSfelPnnzC3N/5k3nbglWahKJiIiI1IPafmHp2rWrv0oSERE/0blbgpWaRCL1yJtLNt79sLnmkhIREZfU1FR69+5d4+d58zPnjTrU5S/e1C0iEuhqe+4WsZqaRF6ozWoNIlXx5pKN4sxSzSUlIiIupaWltXqed5cJtqxlVf6jyxs9c5/bpyr6hZKItWp77haxmppEXqjNag0iIiIivtCjRw9L93/1yF3k3Btd7Tb6ZVn98mZuH/1CScQzf57frD53i9SWmkQiIiISVKxesaa+bdq0iX79+lm2/wORZRTql2ViKG9WbjPlXCLH8+f5zepzt0htqUkk4iOaQ0FEpH7U94o1VjelHA6HX15XxHRezcvl4TJ/rbYmtaVztwQrNYlEfERzKIhIQ2Z1I8WfrF5GuVevXn57bRGT+WpeLs1PKrWhc7c5nnjiCRYvXsxvv/1GZGQkf/7zn3nyySfp3Lmza5uhQ4fyww8/VHrezTffzMsvv1zf5daZmkQiIiJSZ1Y3Uky2bt06+vfvb3UZ1SooKSDai3k9RIJRIM5P6s1lcvVJjbTjBcO5W7zzww8/MHnyZPr378+RI0d44IEHOO+889i0aRNRUVGu7SZOnMjMmTNdf2/cuLEV5daZmkQiIiJSLxwFhSyPr35FpmAdbdTQOZ3OgPsSLcFJE6V7x1Njvr6b8oHYSBPxlSVLllT6+/z582nVqhVr165lyJAhrvsbN25MfD03aP1BTSIRERGpH06nRhvVgi5ZkIZEE6WLKXTuDny5ubmV/h4eHk54eLjH5x06dAiAuLi4Sve/++67vPPOO8THx3PRRRfx8MMPB+Vooho1idauXUvLluXX7e7du5eEhARKSkrIysqiXbt25OXlkZOTQ/v27cnOziY3N5eOHTuSmZlJfn4+SUlJpKWlUVRURNeuXUlNTaW0tJQePXqwadMmHA4HvXr1Yt26dQBV3rbb7XTr1o0NGzYQGhpKp06d2Lx5MxERESQmJrJ161aioqKIj49n+/btxMTEEBcXx86dO4mNjSU6Opr09HRatGhBWFgYjjIHhJ74mJ0OJ06ns9pt4Ogw63uicTgd4AS73e6arMweYsdR5qDUUUp4aHj5Po+5H/7YvmXjlrzrtFe7L6fDCbbq63E6vFv2tD4XR3WUOTzW7ShzeKzdUebAZvfwQvj22DzlBOfRyemqy5LTWX5sHvJWkYnq+OrYHGUO7Pbq8+ZwOLDbPGfSWY9L7XqzJ0eZw+OEgY4yBzZb9VnyJpO+5jEDTs+TITqdTs+59SFv3xN7iG/y5ulc4kuOMofH98S1TTX/3t6eAz1l0td8cX7D6UVua1DP/v37q/0c4c2+HGUOSkpKfPI5wpvzm9PhJDk5udrPRt6cSxwOB4kPJZJdnF3l/+f2EDtxYXG8U+b53OXNOdCbmnx2BvQmS/gokz7ks/NbmcPjizkcnrfxlld1V+zPw7nLq3Ogjybp9aZup9PJli1bPH7X8KYmr37mevHz1FHmIDU19bjvGhkZGbRu3Rrw7fcnj1ny8mfuoUOHavz9qapj8vb8lpycXG/fCb15/73NW2pqao3fp/T0dIYPH27Z91x/Zc/K7+6+OKb09HR69OgBQJs2bSgoKHC919OnT2fGjBkec3zHHXcwePBg1+sAjB07lpNPPpmEhATWr1/PtGnT2LJlC4sXL/YiZYGlRk2iY5fwS0xMdN3u0OH4oeMVzSSo3GHr2bOn63bv3r2rfO1jr92sy+1j93tsPccOAfN08rTZbdi8+DbidDrJD6vmtx6hQB4cCT1S+YeM2w+cA8UHwFb9BHreNEi82Qbq9XuWx3/rim081e7N64Bvj83jPm1eZMlmwxZSfVU2u82r4/PVsXn1nnhoIsHR/0/q8YutN3uyh9g91u6rTPqar/Lm7f8rvuDte+JxGy/zVp/sIXaPtXu7jTf7qm++yJtX23iruJgtPQe4/rrpmId+PWYbT6mzh9gJCwvzyeeI/V6c32x2W6XnVvXZaIsX2bXb7WSX7K/+M0UJ2EOq/6zg7TnQq88UHrfwkpc5qde8ecFn57cQu8cXs9s9b+Mtr+r24pzr9TnQi9fyhjd122y2ShPGnui7hrfH56kgb9/fTp06AZW/a7Rt29Z125ffn5Z7ypKXP3ObNm1a4+9PVR2TN+cSu93u2ld9fCdc7s1nCo9blOet4r0F79+n0tJSIiMjLfue66/sgXXf3X1xTE2bNnXd3rNnT6XneDOKaPLkyWzYsIHly5dXun/SpEmu2z179qRNmzacc845bN++nY4dO3p83UCiy81EREQkcHhxSVqW0wleNG68Wf7aV/OaeDOPyuKSKOKo/0agiIhpvJko2+pzri43C3wxMTE12n7KlCl8+umnLFu2jJNOOqnabQcOHAhAamqqmkQiIiIigcC75a99w5t5VJzO4JuXQETqnzcN7jfqsZ765s3KbRnneZ4o2+pzrtWrm2nFOd9xOp389a9/5aOPPuL777+vcuSSu5SUFKD8krZgoyaRiIiINFiBtoy0iIh3De7qLzkNZoG2cltt1fYSTE8/l8C7lUC14pzvTJ48mQULFvDvf/+bJk2akHn0/WnatCmRkZFs376dBQsWMHLkSJo3b8769eu58847GTJkCKeeeqrF1decmkQiIiLSYJnyZUREpDa8GW1ScqSEsEZh1W5TUFJQb5PJB4tu3brV6nmefi6BfjbVt5deegmAoUOHVrr/zTffZNy4cYSFhfHNN98wd+5c8vPzadeuHWPGjOGhhx6yoNq6U5NIRERERESkDl5dEMnyt6u/BGXsX/aQ3az6r18JMQm+LMsjb0abUAylkaUet5HKNmzYYOnlZuI7nlY5bdeuHT/88EM9VeN/ahKJiIiIiIjUQVy+jbgyD5Puh5ZQGFp9N8X0y38a0nxLoaHBMbTKm8uuPV3aJmZRk0hERERERET8LhjnW/JmlFhVjZROnTr5syyf0WXX4k5NIhEREREREZEqeDNKLDsz87gROY4yB/aQPyav1ogcCRZqEomIiIiISNAoKCkg+t7oarep77l9ROpzRM7VI3eR4+H/AU0mLrWlJpGIiIiIiAQNp9Oppb2lQTsQWUahFxOOi9SG3fMmIiIiIiIiIiJiOjWJRERERERERERETSIREREREREREVGTSEREREREREREUJNIRERERERERERQk0hERERERERERFCTSEREREREREREgEZWFyAiIiIiIiJiuuTegyjOzDzh4+Hx8fVYjUjV1CQSERERERER8bPizEziCopO+Hh2NQ0kkfqiy81ERERERERERERNIhERERERERERUZNIRERERERERERQk0hERERERERERFCTSERERERERERE0OpmNA5tjDPUeeLHaQxQ7TYAhAGhHnbmxTaNaYy9cSQ2bCfcxt44AqDO2wA0DmuMrR6PDar/t/TV8YPvjs3bun21jafjh8A8Nm/qtjud2Gx138ab4/fl/0uezhOAV//eIY0bYyurvjfvq/+/67tub98TqJ//l4B6Py/74ueJt8fmVZa8+f/Nh3XX5znAl8dWnz9zvD0H+KpuX7wOBObPHE/bgO/+P/Hl+c0X7xvU/3k50Oqu78+dwfqeQP19VjD5Panvz2+etgHf/n/ibZak4bA5nU4P6RIREREREREREdPpcjMREREREREREVGT6Fi5ublERUWRm5trdSkiPqd8i6mUbTGZ8i2mUrbFZMq3BDM1idwUFBRYXYKI3yjfYiplW0ymfIuplG0xmfItwUpNIhERERERERERUZNIRERERERERETUJKokPDyc6dOnEx4ebnUpIj6nfIuplG0xmfItplK2xWTKtwQzm9PpdFpdhIiIiIiIiIiIWEsjiURERERERERERE0iERERERERERFRk0hERERERERERFCTSEREREREREREUJNIREREJOjt2rWL33//3eoyREREJMipSSQiVdLCh9IQOBwOq0sQqbNNmzYxePBgnn/+eUDnbzFTRa7LysosrkTEt3JyctiyZQvbt2+ntLTU6nJE1CSqrVWrVvHaa68xf/58UlJSrC5HxGf2798PgM1m0xcNMconn3zCtGnTuOGGG3jxxRc5cOAAdrtdjSIJaikpKZx22mnk5+ezZMkSnE6nzt9inI0bNzJhwgQOHDhASEiIGkVijA0bNjB8+HAuv/xyevTowdNPP618i+XUJKqFN954gzFjxjB//nxmzpzJo48+Snp6utVlidTZe++9x9ixY/nqq68ANYrEHG+++SZjx47Fbrdz8OBBFi5cyMCBA9myZQt2u105l6CUkpLC4MGDue+++0hNTeXgwYM89dRTQPn5W8QEDoeDiRMnMn/+fMaNG6dGkRhj48aNDB06lLPPPpuFCxcyY8YMHn74Yfbs2WN1adLA2Zz6ZFwjCxcu5NZbb+WVV15hzJgxfPHFF0yYMIEVK1bQqVMnq8sTqbXPP/+cq6++mujoaP785z9z8803M3z4cADXb6ZFglFqaiqXXHIJDz30EFdddRUAH3/8MZdeeimJiYn8+9//plevXjgcDux2/e5EgsOGDRvo378/d955J7NnzyYvL49rr72WI0eO8J///EfnbDHKxRdfTGRkJIcOHQJg/vz5tG7dWp9PJGhlZWVx6aWX0rdvX+bOnQuUX0o5atQopk+fTuPGjYmLi+Okk06ytlBpkPRpuAbS0tJ45ZVXmDlzJldccQUhISGMGjWK7t27s2jRIubOncvnn39udZkiNXbo0CEWLlzI+PHjefnll8nMzOTFF1/km2++ATSiSIJbTk4Ohw8fpm/fvq77hg4dypAhQ2jdujUXXXSR69IzkWCxePFiHnroIWbPno3T6SQ6Opo777yTJUuW8PHHH1tdnohPDR48mJ49ezJp0iSys7O56aabAHj//ffJyMiwuDqRmsvKymLEiBFMmTLFdd/jjz/OV199xS233MKoUaOYOHEiK1eutLBKaaj0ibgGoqOjueuuu7j44otd940ePZr169eTnJzM119/zdixY1m4cKGFVYrUXNOmTZkwYQKjRo3ioosu4oknniArK+u4RpFIMKlobIaEhBAVFcW6detc9y1ZsoT09HRmzZpF06ZNef31160sVaTGHnnkER588EHX3x0OB/379+fiiy/mvffeIz8/X819CXoVGbbb7WzcuJHRo0dz9913k5eXR3x8PJMmTSImJkZzy0nQ6dKlC9dff73rSpSKy80WLFjA0qVLeeutt8jKyuLbb7+1uFJpiNQkqoG4uDjOOussTj75ZABeeukl1q1bx3//+1/+/e9/884773DeeeexePFiiouL9eFMgsrgwYNdl5edccYZlRpFS5cuBSA7O1s/rCRoVDQ2u3TpQseOHXn++ee5/vrrue+++xg7diwzZ87kvPPOIykpiZ9//tniakU8q5iD5djPFxWX29jtdho3bsywYcP47LPP2Ldvn0aBStCraP6cd955ZGdnA3D55Zdz5MgRDh8+TI8ePVyXCqtRJIGurKys0uplbdu2dd0+/fTTWbNmDVdeeSXNmzdn2LBhtGzZkuTkZCtKlQZOTSIPtm7dysaNG1m/fj0ATZo0cT126623smbNGrp27QpAbGwskZGRNGrUiPDwcI28kIC2ceNGfvzxR77++msAQkNDcTgcri8UZ555JrNnzyYrK4t58+bx4YcfMnr0aO677z596ZCA9ssvv/DBBx+wePFiNm/eTOPGjXn77bcZOHAg2dnZpKSk8Pnnn3PNNdcA0KJFCxo3bmxx1SLV27JlC1OnTuWcc87hoYceYvny5cAfzdCK8/KUKVPo3Lkz06dPp6ysTJ9FJKgUFBRw6NAhcnJygPKRoFA+mr9icvabbrqJ7du389BDDxEWFsaIESPIzs7WJcMS0H777TcmT57M8OHDufPOO/n+++8rPd6hQwfXZfEOh4OioiJiYmIYNGiQBdVKQ9fI6gIC2WuvvcacOXM4fPgwkZGR9O7dm3/84x8kJCS4tomNjXXdzs3NZe/evZx55plWlCvitfnz5zNnzhzKysooLCzk4osvZt68eZU+YDmdToYMGcKTTz7JPffcw5VXXknPnj1JTk7Wlw4JWG+88QaPPvoozZo1Izc3l7Zt2/Lss8/Sv39/nnzySUJCQsjPzycqKgoo/0Ly66+/csEFF1hcuciJbdiwgaFDhzJq1Cjatm3L8uXL2bx5Mx07dqRNmzbAH80ih8PBX/7yF/75z3+yZ88eTXoqQWPjxo3cf//9bNu2jdatWzNixAimTZsGlI+46NixI+effz579uzh66+/pnv37rRp08Z1eWVcXJzFRyBStY0bNzJs2DAuuOAC+vTpw7fffsuOHTvo2bMnzZs3P257u93O7Nmz+fHHH5k1a5YFFUuD55QqLV261NmkSRPne++951y5cqXzP//5j7NLly7Obt26OVetWuV0OByubY8cOeLcs2ePc9SoUc7TTjvNWVpaamHlItX75z//6WzcuLFz0aJFznXr1jmff/5556mnnuo8dOiQaxuHw+HKeElJibNHjx7OgQMHurKtjEsgWrx4sbNZs2bOhQsXOnNzc53fffed87zzznP+7W9/czqd5efqCsXFxc4ffvjBef755zt79uypTEvAysjIcPbt29d57733uu77+uuvnS1btnSuWLGiyuds27bN2aFDB2d6enp9lSlSJxs3bnTGxcU5b7/9ducrr7zivOOOO5ynnXaa8+uvv3Ztc8sttzgTEhKcP//8s+u+srKySp9fRALNnj17nP369XPeddddrvs2bdrkbNy4sfM///nPcdu///77zsmTJzubN29eKesi9UnjMk9g27Zt9O7dm0suuYRBgwYxatQo1q5dS3R0NDfccANbtmwBoLCwkHfffZebbrqJffv2sXLlSho1auSaN0AkkPz888/MmDGDl19+mSuvvJJTTz2VP//5z8THx7NixQo++OADHA4HNpsNm81GaWkpo0aNYt++ffz3v/+lUaNGHDlyhEaNNAhRAsu+fft46623uP3227nqqqto0qQJQ4cO5ZRTTnGt9FRx2QLAwYMH+e9//0tZWRlr167VeVsC1i+//EJiYiLXX3+965Ky4cOH07lzZ1JTU4HKcxSVlZXRqVMnfv31V40ikqCQnZ3NX//6V66//nrmzp3LxIkTuf/++ykuLubHH390bffSSy+xZs0a+vTpA5Tn3m63ExMTY1XpIh5VnMPHjx8PQGlpKV27duXPf/4zWVlZx21fWlrKvn37WLZsmSvrIvVNTaIT2Lt3LxkZGYSFhQFQUlJC48aNWb58OZGRkdxyyy0AREZG0qFDB0aNGsXKlSsJDQ3lyJEjlb6MiASKk046idtuu40hQ4a47nv44YdZt24d9913H1OnTmXgwIHk5+cD5fMUPf/88+zatcuVbTWIJBDZ7Xa6d+/uuty3YgLTQYMGuW4f+0W6ZcuWTJ48ma+++krnbQlorVu35sILL6R79+6uiaidTidFRUXs27cPqLz6ZEWOKy6pFAl0e/fupUWLFlx44YVA+fm7VatWnHfeeezatQvANdlvmzZtXOdyXfouwaBjx46cffbZdO/eHSj/bA3ln0l279593PZjx47lzTffpFu3bvVap8ix1CQ6gbFjx5KTk8Njjz0GQFhYGCUlJYSGhvL222+zZcsW3n//faB8gt9bbrmFkJAQysrK9CVaAlarVq247bbbXCv0Pfjgg+zevZtvv/2Wb7/9luTkZHbv3s3s2bOB8t9Id+7cWQ0iCXgtWrRg0qRJnHPOOcAfXx5atGgBwJEjR1z3bdiwAZvNRrNmzVxfupVtCVT9+vXjpptuAv5Yyawiv8c2NufNm8eSJUusKlOk1lq1asX111/vWmG14lxdVlbmmsD62HO0mkMSTJKSkpgyZQpQ+ZdVFaPzK/zf//0fCxcuBNTkF+upSXQCCQkJTJ48mY8++ohXXnkFwDWqKD4+nsjISHJzc497nn4TLYEuIiLCdfuiiy7iq6++olu3bjRv3pyYmBg6dOjgyvGxedaXaAl0Fc3Pii/SADk5ORw6dMiV3/PPP5/JkydXep6+cEiwODarTZo0ITw8HIAHHniAe+65h8TERKtKE6m15s2bu0YRHXv+rvgFFZRnf/r06Tz00EOW1SlSVxW/mILy3Ddr1gwoP4fffvvturxMAoa+9Z1A48aNue6660hPT+fVV18lLy+PqVOnAuUrmsXGxqohJEHv9NNPr/T3oqIiQkND6dixo0UVidSde9On4ov0hRdeyO+//86vv/5qRVkiNXbsF2Z3OTk5lJWVMWfOHJ599lmWL1+uyxMk6B2b99jYWNcvaB944AFXzkWCWUXG8/PzcTqdPPbYY8ydO5fly5fTpUsXi6sTKWdzHjvuTY6zZcsWXn75Zd577z169epFz549Wb16NQcOHCAlJUWjK8QITqeTw4cPM3bsWA4cOMDy5cvVBBUjfPPNNzz88MOEhYWxe/duNm/erMsnJWCVlZUREhJCVlaW61LJE/nLX/7CihUrKC4u5vvvv+e0006rpypFfKe6RugjjzxCWloaSUlJzJw5k5UrV9K3b996rlDEP8aMGcMXX3wBwLJly3QOl4DSoC8386Y/1rlzZx566CH++c9/YrPZSEtLo0uXLvzyyy9aDUcCVk16v8XFxfz73//m4osvZs+ePSxbtsw1v5ZIoKnI9rEZr5iYuirZ2dmsXr2avLw8NYgkYG3dupWPPvqIkJAQPvjgA66//nrXpNQnEhcXR2hoKKtWrdKXCwkaFefuqiZdd3fkyBHefvtt5syZw4oVK9QgkoBWke01a9aQkpLicdtmzZrRpEkTfvrpJ53DJeA02CbRsb+5eO211/jyyy9PuG3z5s0555xz+Pzzz1m0aBH/93//p9VwJGDVJNsAhYWFlJaWMnjwYFavXq1sS8ByOByubO/fv5+8vDzXEsgnkpSUxJ133lkp22oQSSBxOBwsWLCAMWPGcPfdd3PllVdy1VVX0apVq2qfd/3117Nq1Sp69uxZT5WK1J3NZiM5OZkJEyaQnZ1d7bZdunQhKSmJlStX0q9fv3qqUKTmKj57L168mIsvvpgXXniB/fv3n3B7m83GlClTWLlyJT169KjHSkW80yAvN3M4HK4vFT///DN33303u3fvZv78+QwaNKjK51Q3HFYkUNQm21C+tGzFkpwVlzuIBKrp06fzr3/9C7vdTsuWLXnuuedcy4NXRw0iCWQjR47kyy+/5NZbb+XFF1+sdD4XMckvv/xCv379ePfdd7n66qtPuN3u3bsJCQkhPj6+HqsTqZ3vvvuOUaNGMW/ePC666CKaN29udUkitdYgP31UfOiaPn06M2fOpKioiLS0NCZOnMh3331X5XPUIJJgUJtsA64GEWiFPgk8x15ONn/+fJ5//nluv/12br75Zux2O2eddRaff/45UPkyNPffgahBJIGmIqOlpaU0b96cIUOG8NJLL7Fo0SLsdjtOp/O4HDfA3+2JASpyW1ZWRp8+fXjggQd45ZVX2L179wmf07ZtWzWIJGh89dVXXHnllYwbN861apmmbpBg1SCbRAAvv/wyf//735k6dSr//ve/WbBgAR06dOD222/nhx9+sLo8kVpTtsU0Fc3PTz/9lP/973/MnTuXiRMnMnnyZL7++mtGjRrFDTfcwJ49eyo19NXcl0BWMUJ5zZo1LF26lJdeeonvvvuOe+65h2uuuYaFCxdWyvDvv/8OKNcSnAoKCoA/zueDBg1i9+7d/O9//wOqn1tOJBikpKSQlZUFlP/C1el0un7xmpGRYWVpIjXWYJtEycnJXHLJJQwZMoSWLVsyevRo7r77bmJiYrjttttYuXKl1SWK1IqyLSZas2YNd911F3/7299cXzJKSkoAeOutt2jXrh1PP/20lSWKeK2iQfSvf/2LESNGsHr1anbt2gXAgw8+yD333MN1113nahTNnj2bKVOmkJ+fb3HlIjW3Zs0azj77bBYuXEhOTg4AF154IT179uSOO+7gyJEjurRSgprD4aB///4cOnSIbdu2AeUNfYfDQUZGBnfddRe//vqrxVWKeK9BnJGr+u1E8+bN2bFjB7m5ua77zjrrLEaPHs3mzZuZPHkyy5Ytq88yRWpM2RZTuV9S06lTJ2677TaaN2/OP//5TwDCwsI4cuQIZWVlnHTSSRQVFVlRqkiN2Ww2VqxYwYQJE3j88ceZNm0aXbp0AaBJkyY8+OCD3H///VxzzTUMHjyYxx57jEcffZSoqCiLKxfxXsV5/MCBA/Tv35+bb76ZcePGMXPmTADuvfdeYmNjWbx4caXtRQJZRU737NnD77//zr59+7Db7Vx66aX8/PPPPPvss2zevBkov9zs1VdfZc2aNTRt2tTKskVqpEE0iSp+O7FkyRLXfT169GDPnj385z//qfSbuY4dOzJ69Gh69OjBiy++yMGDB+u7XBGvKdtiomNXMQPIz8+nWbNm3HzzzTz44IP873//49prrwXK5xkKCQlh7969hIeHW1WyiNcqvmB8+eWXDB06lEmTJhEREQH8MX9FkyZNmDVrFp999hlXXnklv/76q5b/lqBx7PxDAOeffz4vvvgiX375JaeeeiqvvfYagwYN4vPPP2fPnj2uORN1KaUEuopRoB9//DHDhw/nwgsvpE+fPtx333106NCBjz/+mI8//phJkyZxxhlnMGbMGObOncv7779PYmKi1eWLeK3BrG62ceNGevbsyYQJE3j11VeB8uVjly5dysMPP8xZZ51Fy5YtufHGG+nfvz9t27bljjvuYM2aNSQlJVlcvciJKdtikmNXdPr73//O2rVr+fnnn7npppsYOXIknTt35uWXX+aJJ54gLi6OLl26EBISwpo1a9i8ebMmp5aA5b5K6k033cTevXv5z3/+c9xKZj///DPdunUjIiJCq6tKUKnI69KlS/noo4/Iycmhe/fu3HTTTbRq1YqSkhIKCwt54IEHyMrK4oMPPiAkJIT9+/fTtGlTZV0C3tKlS7nkkkt4/PHHmTRpEn/729945JFHWLhwIVdeeSVr167lp59+YtWqVXTp0oUxY8bQuXNnq8sWqZEG0yQqLCzkww8/ZPLkyVx11VW88sorAEyaNInVq1ezc+dO4uPjsdls/Pbbb2zZsoWLLrqITz75xDUEXCQQKdtiovvvv58333yTadOmERUVxbRp0zj77LN56623AHj77bd57rnnCA0NZe7cuQwfPhzQMvcSeAoLC7Hb7ezdu5fWrVu7RrzNmDGD559/nq1bt9KiRQvXl+vDhw/z2GOPcd5553HOOedYXL1IzX388cdcffXVXHvttfz+++/k5OSwf/9+li9fzkknneTabs+ePXzxxRcMGDCAHj16WFixiGcV5+jJkyfjcDh46aWX2LVrF8OGDeOcc87h5ZdftrpEEZ9pMJ+kIyMjufzyy7Hb7UycOBGn08mrr77KK6+8wpo1a8jIyMBmszFy5EgA5s2bR+PGjWnVqpXFlYtUT9kW06xZs4bFixfz8ccfc/rpp7NmzRoOHz7MxRdfTHR0NADjx4+nrKyMd955h0WLFrmaRPottASSzZs389BDD7F161Z+++03evTowbnnnstTTz3FPffcwyeffMKwYcP45ptvaNWqFUeOHOGJJ55g4cKFTJkyxeryRWosKyuLRx99lJkzZ3LPPfcAsGHDBu666y7OOusskpOTiYuLA6BNmzbceOONVpYrckIVTSH3kZ779+/n4osvprCwkIEDBzJq1CheeuklAN5//31atmzJsGHDrCpbxCeMbhL9/e9/58CBA8yePRuAiIgIxowZg9Pp5MYbb6Rx48Y899xznHbaaa7nLF++nDfeeINPPvmEpUuXun6QiQQSZVtMUlxcXGk+IafTSdOmTTn99NN5//33mTBhAi+88ALXX389eXl5rFq1inPPPZdx48YB5aubXXnllbz33nuu5WZFrPbrr79y5plncu211zJy5Eji4uJ46623eO6559i8eTMffPABb7zxBjfffDNdunShe/fuhIaGsmHDBr766ivatWtn9SGIeJSfn09UVJTri3ReXh579uyhd+/erm26du3KU089xY033siiRYu47bbbdBmlBI3Dhw9XuhQyPj6exx57jPvvv58xY8bw97//HZvNRmlpKR999BFJSUmceeaZGtUsQc3YiasLCwvJz8/nueeec32Rhj++TI8dO5YXXniB8ePHV3peo0aNyMrK4vvvv6dXr171XbaIR8q2mOSrr77i+eef56effnLdV1JSQkZGBq+99hqTJk3iySef5NZbbwVg9erVvPTSS/z22280adKE8ePHc8UVV7Bnzx727Nlj1WGIVLJ//35uuOEGbr31Vl588UUmTJjA6NGjefXVV3nmmWdYunQpEydOpHfv3vz444/MmjWLs88+m5EjR/Ljjz/Sp08fqw9BxKN9+/bRvn173n//fddIi/j4eNq1a8cPP/zg2i4kJIRTTz2VRo0auVZ9UoNIAtnOnTt5/PHHOfPMM+nVqxfXXHMN7777LgB33XUXsbGxOJ1O5syZQ2hoKGVlZcyYMYMVK1Zw7bXXqkEkQc+YBFf8BqPiv5GRkdx2221ERUUxa9YsHA4HDz30EFB+ec6f/vQnRowYwZ49eyoNI6z4zXXFSiMiVlO2xVRvvvkmDz/8MH/5y18YOnSo6/7BgwczZMgQJk2axIwZM7jtttuA8hFHc+fOJTw83DXpenR0NLfddhsTJ04kNjbWisMQOc6uXbsoLS3lmmuuoaysjJCQEBwOBy1btuTaa6/l4MGDPP7441x66aWMHj1al5ZJULLb7fzlL3/huuuuIzw8nIsvvhi73c7AgQP59ttvWbx4MZdeeilQ3hRq27YtzZo1c61+pkaRBKJff/2VMWPGcNppp9GtWzcuuOACXn/9db7//nu2bNnCzJkzueuuu5gxYwbdu3enf//+FBQU8NNPP/Hll1/ypz/9yepDEKkzI5pEixYt4quvvuK+++6jbdu2REVFAdCiRQuuv/56HA4Hs2fPxmaz8eCDD5KXl8evv/7KZZdd5hptceyXaX2JlkChbIupFi1axJQpU3jzzTe54IILiImJqfT4X//6VzIzM5k/fz7t27cnJyeHzz//nN27d/PLL7+4Gqc2m801T5FIoFi3bh2pqamuyXidTqfrPNy0aVPGjh3L008/zfbt2ys9T5fgSDBp0aIFTzzxBNHR0YwePZp//etfjB49mkcffZRrrrmGp59+mmXLljF48GCWLVvG0qVLXZ9ZRALRunXrOOOMM7jtttu4//77adasGQCXX345jz32GC+//DLNmzfn9ttvp2fPnrzxxhscOHCA3r17M3fuXDp16mTtAYj4SNCvbpabm0vfvn3Jzc0lPj6eAQMGcOaZZ3LDDTe4ttm7dy+LFi3innvuoUOHDthsNsLCwvj5559p1KiRPpRJQFK2xVT79+/niiuu4LLLLmPy5Mmu+/Py8ti4cSONGjWiX79+bN26lTlz5vDNN9/QqVMnTjnlFF5++WUaNWqkVcwkoC1fvpxzzz2Xd955hzFjxlS5Td++fTnrrLN49tln67k6kdrLz8+nrKysUmN/z549zJ49m3nz5vHBBx8wZswYDhw4wJw5c1ixYgVZWVnEx8fz/PPPV5qrSCSQpKam0rNnT+6++25mzZrlGgVa8Xlj+/btTJkyhfT0dD766CONGBKjBf0n7KioKK644gpOPvlk+vfvz7fffssdd9zBV199Rffu3bnnnnto3bo1t99+O0OGDOHjjz8mNjaWKVOm0KhRI9cJQCTQKNtisn379tG2bVvX31966SW+/fZb/vWvf9G6dWu6devG0qVLeeONN8jKyqJFixaubdUgkkDXvn17YmJiePvttznttNM4+eSTgT9Gdubk5BAZGUm/fv0srlTEe9u2beOKK64gOjqaiRMnEh8fz3nnnUebNm3429/+htPp5PLLL+e9997j8ssv54knnsBms5GdnU3jxo1do6FFAo3D4eCNN96gSZMmtGzZEiifS6usrMz1S9eOHTvywAMPMHToUDZs2FCpSaRfyoppgv5TdkhICGeeeSZXXnkly5cv5+6772bKlCnMnj2bhx56iA8++ICrr76ac889lz59+lSaDFJfNCSQKdtistzcXD777DNiYmL4xz/+wdatWznjjDP48ssvOXToEPfeey+zZs3i4Ycfdg33hvIPYsq2BLqTTjqJl156iauvvpqHH36YadOm0b17d9clZ8888wwZGRmceeaZFlcq4h2Hw8H8+fNZt24dERERHDx4kIKCAuLi4hgwYAA33ngj48ePp3nz5lx55ZXExMRw/vnnA7i+dIsEKrvdzpQpUygoKGDBggUUFBRw3333ueaTq2gA9evXj+bNmx+3UIYaRGKaoL/crELFJQvz5s0DoHv37iQlJdGpUyfWr1/P119/zWuvvcaNN95oZZkiNaZsi4mWLl3KmDFjaN68OU2aNOGZZ56hV69eNG/enJycHM4++2wuvvhiZsyYYXWpIrVSVlbGa6+9xpQpU+jYsSODBw+mTZs27Nixgy+++IKlS5dqFTMJKpmZmTz55JNs376dTp06MXnyZN59913++9//sn79euLi4jjllFNYu3Yt+/bt4/vvv2fIkCFWly3itczMTB5//HGSk5MZPXo006ZNA3CNzl+xYgWTJ0/mjTfeoG/fvhZXK+I/xvw6tm/fvrz55pvk5ORwzjnnEBsby1tvvUVMTAy7d+9m+fLlJ5wXQCSQKdtionPOOYdt27aRl5dHhw4djnu8SZMmJCQkWFCZiG+EhIRw880307t3b5566ilWr15Ns2bN6NWrFytXrqRLly5WlyhSI/Hx8dxzzz3Mnj2b5cuX86c//YlHHnkEgNWrV5ORkcErr7xCq1at2LdvX6XLhEWCQXx8PA8++CCPP/44H330EQDTpk1zTd9QcUl8+/btLaxSxP+MGUkEMGDAANasWcOQIUNYvHgxcXFxx22jy3AkGCnb0lDs37+f8ePHk5WVxYoVKzSvlhihrKwMu92OzWartOKkSDCqmKh69erVXHLJJTzwwAOux0pLS3E4HBw6dIhWrVpZWKVI7VU1ouixxx7jmWeeYdmyZa6VK0VMZUSTqGKysHfeeYcnn3yS+fPn069fP00iJkFP2ZaGIisri9dee43ly5ezb98+VqxYQWhoqCZgFyMce87W+VtMcOyX6EsuuYT77rsP0C+sxBwVGV+3bh3FxcWsX7+eFStW6DIzaRCM+FVWxYetYcOGceDAAb7++utK94sEK2VbGopdu3axYsUKOnXqxMqVKwkNDeXIkSNqEIkRjj1n6/wtJqi4LKd///58+umnTJ8+HUANIjFGRcY7depEdnY2q1atUoNIGgwjRhId64UXXuDRRx9l2bJldOvWzepyRHxG2RbTHTx4kKZNm2Kz2TSCSEQkCGRmZnL//feza9cuFi1aRPPmza0uScSn9u/fj8PhoHXr1laXIlJvjGv3jxw5kjVr1mhCSDGOsi2mq1jq3ul0qkEkIhIE4uPjmTNnDoAaRGKkli1bWl2CSL0zbiQR/HG9v34TLaZRtkVERERERMRfjGwSiYiIiIiIiIhIzRgxcbWIiIiIiIiIiNSNmkQiIiIiIiIiIqImkYiIiIiIiIiIqEkkIiIiIiIiIiKoSSQiIiIiIiIiIqhJJCIiIiIiIiIiqEkkIiIiIiIiIiKoSSQiIiIiIiIiIqhJJCIiIiIiIiIiwP8HKhN0TUU2qAIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1500x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Bollinger band and a regression channel together are used to develop trading strategies. \n",
    "\n",
    "\n",
    "import pandas as pd\n",
    "import yfinance as yf\n",
    "import mplfinance as mpf\n",
    "import pandas_ta as ta\n",
    "import numpy as np\n",
    "\n",
    "# 1. Fetch NVIDIA stock data:\n",
    "start_date = \"2020-08-01\"\n",
    "end_date = \"2021-01-01\"\n",
    "stock_symbol = \"NVDA\"\n",
    "\n",
    "data = yf.download(stock_symbol, start=start_date, end=end_date)\n",
    "\n",
    "# 2. Calculate Bollinger Bands using pandas-ta:\n",
    "data.ta.bbands(close='Close', length=20, append=True)\n",
    "\n",
    "# 3. Calculate Regression Channels:\n",
    "x = np.array(range(len(data)))\n",
    "y = data['Close'].values\n",
    "slope, intercept = np.polyfit(x, y, 1)\n",
    "data['Regression'] = slope*x + intercept\n",
    "\n",
    "residuals = y - data['Regression']\n",
    "std_error = np.std(residuals)\n",
    "\n",
    "data['Upper Regression'] = data['Regression'] + (2 * std_error)\n",
    "data['Lower Regression'] = data['Regression'] - (2 * std_error)\n",
    "\n",
    "# 4. Plot candlestick chart with Bollinger Bands and Regression Channels:\n",
    "ap = [\n",
    "    mpf.make_addplot(data['BBL_20_2.0'].values, color='cyan', label='Lower Bollinger Band'),\n",
    "    mpf.make_addplot(data['BBU_20_2.0'].values, color='cyan', label='Upper Bollinger Band'),\n",
    "    mpf.make_addplot(data['Lower Regression'].values, color='orange', label='Lower Regression Channel'),\n",
    "    mpf.make_addplot(data['Regression'].values, color='red', label='Mid Regression Channel'),\n",
    "    mpf.make_addplot(data['Upper Regression'].values, color='orange', label='Upper Regression Channel')\n",
    "]\n",
    "\n",
    "mpf.plot(data, type='candle', style='charles', title=f\"{stock_symbol} Candlestick Chart\",\n",
    "         ylabel='Stock Price', addplot=ap, volume=True, figsize=(15,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear Regression Indicator in Technical Analysis:\n",
    "\n",
    "The Linear Regression Indicator plots the ending value of a Linear Regression Line for a specified number of bars; showing, statistically, where the price is expected to be. For example, a 20 period Linear Regression Indicator will equal the ending value of a Linear Regression line that covers 50 bars. The Linear Regression Indicator (LRI) can be calculated using the following formula:\n",
    "\n",
    "LRI = (Ending Value of Linear Regression Line) / (Number of Bars)\n",
    "\n",
    "The interpretation of the Linear Regression Indicator is similar to that of a moving average although it does have an advantage when compared to a moving average. Instead of plotting an average of past price action, it is plotting where a Linear Regression Line would expect the price to be, making the Linear Regression Indicator more responsive than a moving average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1500x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import yfinance as yf\n",
    "import pandas as pd\n",
    "import mplfinance as mpf\n",
    "import pandas_ta as ta\n",
    "\n",
    "# 1. Fetch stock data:\n",
    "start_date = \"2020-01-01\"\n",
    "end_date = \"2021-01-01\"\n",
    "stock_symbol = \"NVDA\"\n",
    "\n",
    "data = yf.download(stock_symbol, start=start_date, end=end_date)\n",
    "\n",
    "# 2. Apply linear regression trend using pandas-ta:\n",
    "linreg = ta.linreg(data[\"Close\"],length=50)\n",
    "data[\"LINREG\"] = linreg\n",
    "\n",
    "# Convert the index and LINREG column to numpy arrays\n",
    "x_dates = data.index.to_numpy()\n",
    "y_linreg = data[\"LINREG\"].to_numpy()\n",
    "\n",
    "# 3. Plot the candlestick chart with the regression trend:\n",
    "ap = [\n",
    "    mpf.make_addplot(y_linreg, color='red', width=1.5)\n",
    "]\n",
    "\n",
    "mpf.plot(data, type='candle', style='yahoo', addplot=ap, title=f\"{stock_symbol} with Linear Regression Trend\", volume=True, figsize=(15,10))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's briefly explore the mathematical and explanatory description of key asset pricing models (i.e., CAPM, Fama-French 3 Factor, Fama-French 5 factor), and how to run these models in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Capital Asset Pricing Model (CAPM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All finance students should have some knowledge of one of the most important topics in finance, that is the Capital Asset Pricing Model (CAPM). The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and cost of capital.\n",
    "\n",
    "The formula for calculating the expected return of an asset given its risk is as follows:\n",
    "\n",
    "### $ r_i = r_f + \\beta_i (r_m − r_f)$\n",
    "\n",
    "where:\n",
    "\n",
    "\n",
    "$r_i$ : The expected return of the investment in asset i. This can be the return of the any stock (i.e., Apple, Google, Tesla) or investment portfolio (i.e., any mutual/hedge fund portfolio).\n",
    "\n",
    "$r_f$: The return of the risk-free asset. The risk-free asset is usually given by the US 3-month Treasury bill. It is assumed that the US government will not default on a short-term government security, thus the US 3-month Treasury bill is widely assumed in finance to be risk-free. \n",
    "\n",
    "$r_m$ : The return of the market. This is usually given by the S&P500 return as it is the largest market index in the world.\n",
    "\n",
    "$(r_m − r_f)$ : Market risk premium\n",
    "\n",
    "\n",
    "Investors expect to be compensated for risk and the time value of money. The risk-free rate in the CAPM formula accounts for the time value of money. The other components of the CAPM formula account for the investor taking on additional risk.\n",
    "\n",
    "The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.\n",
    "\n",
    "A beta coefficient can measure the volatility of an individual stock compared to the systematic risk of the entire market. In statistical terms, beta represents the slope of the line through a regression of data points. In finance, each of these data points represents an individual stock's returns against those of the market as a whole.\n",
    "\n",
    "A stock’s beta is then multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required return or discount rate they can use to find the value of an asset.\n",
    "\n",
    "The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared to its expected return.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Factor Investing and Fama-French model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### FF3 Factor Asset Pricing Model\n",
    "\n",
    "The Fama and French Three-Factor Model (or the Fama French Model for short) is an asset pricing model developed in 1992 that expands on the capital asset pricing model (CAPM) by adding size risk and value risk factors to the market risk factor in CAPM. This model considers the fact that value and small-cap stocks outperform markets on a regular basis. By including these two additional factors, the model adjusts for this outperforming tendency, which is thought to make it a better tool for evaluating manager performance. The model is essentially the result of an econometric regression of historical stock prices.\n",
    "\n",
    "The Formula for the Fama French Model Is:\n",
    "\n",
    "### $ r_{it} - r_{ft} = \\alpha_{it} + \\beta_1 (r_{mt} − r_{ft}) + \\beta_2 SMB_t + \\beta_3 HML_t + \\epsilon_{it}$\n",
    "\n",
    "$SMB$ : Size premium (small minus big)\n",
    "\n",
    "$HML$ : Value premium (High minus low)\n",
    "\n",
    "\n",
    "SMB accounts for traded companies with small market caps that generate higher returns, while HML accounts for value stocks with high book-to-market ratios that generate higher returns in comparison to the market.\n",
    "\n",
    "\n",
    "#### FF5 Factor Asset Pricing Model\n",
    "\n",
    "The theoretical starting point for the five-factor model is the dividend discount model as the model states that the value of a stock today is dependent upon future dividends. Fama and French use the dividend discount model to get two new factors from it, investment and profitability (Fama and French, 2014).\n",
    "\n",
    "### $ r_{it} - r_{ft} = \\alpha_{it} + \\beta_1 (r_{mt} − r_{ft}) + \\beta_2 SMB_t + \\beta_3 HML_t + \\beta_4 RMW_t + \\beta_5 CMA_t + \\epsilon_{it}$\n",
    "\n",
    "$RMW$ : Return spread of the most profitable firms minus the least profitables\n",
    "\n",
    "$CMA$ : Return spread of firms that invest conservatively minus aggressively\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistical Analysis with statsmodels\n",
    "\n",
    "https://www.statsmodels.org"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "statsmodels provides a large range of cross-sectional models as well as some time-series models. Basic linear regression is provided by OLS. Estimating a model requires specifying the model and then calling a method to estimate the parameters (named fit in most models). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "! pip install yfinance > NUL\n",
    "! pip install pandas-datareader --upgrade > NUL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import yfinance as yf\n",
    "import bs4 as bs\n",
    "import numpy as np\n",
    "import os\n",
    "import requests\n",
    "import pandas as pd\n",
    "import datetime\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.dates import DateFormatter\n",
    "import statsmodels.formula.api as sm # module for stats models\n",
    "from statsmodels.iolib.summary2 import summary_col # module for presenting stats models outputs nicely\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "\n",
    "warnings.simplefilter(action='ignore', category=FutureWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  504 of 504 completed\n",
      "\n",
      "5 Failed downloads:\n",
      "- BF.B: No data found for this date range, symbol may be delisted\n",
      "- OGN: Data doesn't exist for startDate = 1136091600, endDate = 1593489600\n",
      "- CEG: Data doesn't exist for startDate = 1136091600, endDate = 1593489600\n",
      "- BRK.B: No data found, symbol may be delisted\n",
      "- GEHC: Data doesn't exist for startDate = 1136091600, endDate = 1593489600\n",
      "                    A        AAL         AAP       AAPL       ABBV        ABC  \\\n",
      "Date                                                                            \n",
      "2006-01-03  20.400560  35.305664   38.423595   2.265983        NaN  16.258938   \n",
      "2006-01-04  20.455357  36.955463   38.697315   2.272653        NaN  16.151209   \n",
      "2006-01-05  20.991257  37.436260   38.882702   2.254768        NaN  15.951151   \n",
      "2006-01-06  21.100876  36.766918   38.838551   2.312970        NaN  15.774172   \n",
      "2006-01-09  21.039982  36.399254   39.341808   2.305391        NaN  15.774172   \n",
      "...               ...        ...         ...        ...        ...        ...   \n",
      "2020-06-24  84.758995  13.040000  133.327560  88.257690  82.679939  94.541733   \n",
      "2020-06-25  85.444443  13.170000  133.243652  89.429359  84.287651  96.292152   \n",
      "2020-06-26  84.112755  12.380000  130.521164  86.681580  83.540291  94.866966   \n",
      "2020-06-29  85.653297  13.320000  133.094452  88.679321  83.809700  94.685226   \n",
      "2020-06-30        NaN        NaN         NaN        NaN        NaN        NaN   \n",
      "\n",
      "                  ABT       ACGL         ACN        ADBE  ...       WYNN  \\\n",
      "Date                                                      ...              \n",
      "2006-01-03  12.530259   6.120000   21.450239   38.520000  ...  29.625664   \n",
      "2006-01-04  12.549263   6.151111   21.567379   38.419998  ...  29.570749   \n",
      "2006-01-05  12.710846   6.061111   21.728443   38.070000  ...  29.395031   \n",
      "2006-01-06  12.954793   6.173333   22.804605   39.000000  ...  29.675089   \n",
      "2006-01-09  13.436364   6.116667   22.738722   38.380001  ...  31.075380   \n",
      "...               ...        ...         ...         ...  ...        ...   \n",
      "2020-06-24  82.754738  28.450001  192.953873  431.679993  ...  74.841599   \n",
      "2020-06-25  84.953941  28.879999  207.752365  436.950012  ...  73.199677   \n",
      "2020-06-26  84.091316  27.700001  203.115906  426.920013  ...  68.711769   \n",
      "2020-06-29  84.375710  28.370001  203.354889  424.200012  ...  73.856445   \n",
      "2020-06-30        NaN        NaN         NaN         NaN  ...        NaN   \n",
      "\n",
      "                  XEL        XOM       XRAY        XYL        YUM         ZBH  \\\n",
      "Date                                                                            \n",
      "2006-01-03   9.751626  32.048004  23.966692        NaN  12.062395   60.362865   \n",
      "2006-01-04   9.798885  32.102802  24.188478        NaN  12.165599   60.935837   \n",
      "2006-01-05   9.793634  31.943861  23.913458        NaN  12.684220   60.292362   \n",
      "2006-01-06   9.830395  32.574192  24.286070        NaN  12.648103   59.983845   \n",
      "2006-01-09   9.804136  32.557747  24.525604        NaN  12.746144   62.108185   \n",
      "...               ...        ...        ...        ...        ...         ...   \n",
      "2020-06-24  58.529015  37.677601  41.371834  60.307781  81.987091  112.077583   \n",
      "2020-06-25  57.812103  38.244884  41.429882  60.027725  81.456696  109.309280   \n",
      "2020-06-26  57.269821  36.932518  41.720146  60.993427  80.310593  109.660789   \n",
      "2020-06-29  57.407696  37.525200  42.484497  62.055691  82.384903  111.057327   \n",
      "2020-06-30        NaN        NaN        NaN        NaN        NaN         NaN   \n",
      "\n",
      "                  ZBRA       ZION         ZTS  \n",
      "Date                                           \n",
      "2006-01-03   42.830002  56.404537         NaN  \n",
      "2006-01-04   42.410000  56.802811         NaN  \n",
      "2006-01-05   42.529999  57.319096         NaN  \n",
      "2006-01-06   44.119999  57.916447         NaN  \n",
      "2006-01-09   44.790001  57.437077         NaN  \n",
      "...                ...        ...         ...  \n",
      "2020-06-24  250.500000  29.837135  131.358551  \n",
      "2020-06-25  253.639999  30.762249  132.346436  \n",
      "2020-06-26  246.419998  29.001839  129.754471  \n",
      "2020-06-29  252.050003  29.684444  129.089325  \n",
      "2020-06-30         NaN        NaN         NaN  \n",
      "\n",
      "[3648 rows x 504 columns]\n"
     ]
    }
   ],
   "source": [
    "### Historical Stock Price Data\n",
    "\n",
    "resp = requests.get('http://en.wikipedia.org/wiki/List_of_S%26P_500_companies')\n",
    "soup = bs.BeautifulSoup(resp.text, 'lxml')\n",
    "table = soup.find('table', {'class': 'wikitable sortable'})\n",
    "tickers = []\n",
    "for row in table.findAll('tr')[1:]:\n",
    "    ticker = row.findAll('td')[0].text\n",
    "    tickers.append(ticker)\n",
    "\n",
    "tickers = [s.replace('\\n', '') for s in tickers]\n",
    "start = datetime.datetime(2006,1,1)\n",
    "end = datetime.datetime(2020,6,30)\n",
    "tickers=tickers+[\"SPY\"];\n",
    "\n",
    "data = yf.download(tickers, start=start, end=end)['Adj Close']\n",
    "\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "if not os.path.exists('Stock_Data'):\n",
    "    os.makedirs('Stock_Data')\n",
    "data.to_csv('Stock_Data/SP500Prices.csv')\n",
    "\n",
    "#data.to_hdf('Stock_Data/SP500Prices.h5', 'fixed', mode='w', complib='blosc', complevel=9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABC</th>\n",
       "      <th>ABT</th>\n",
       "      <th>ACGL</th>\n",
       "      <th>ACN</th>\n",
       "      <th>ADBE</th>\n",
       "      <th>ADI</th>\n",
       "      <th>...</th>\n",
       "      <th>WTW</th>\n",
       "      <th>WY</th>\n",
       "      <th>WYNN</th>\n",
       "      <th>XEL</th>\n",
       "      <th>XOM</th>\n",
       "      <th>XRAY</th>\n",
       "      <th>YUM</th>\n",
       "      <th>ZBH</th>\n",
       "      <th>ZBRA</th>\n",
       "      <th>ZION</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2006-01-03</th>\n",
       "      <td>20.400560</td>\n",
       "      <td>35.305664</td>\n",
       "      <td>38.423595</td>\n",
       "      <td>2.265983</td>\n",
       "      <td>16.258938</td>\n",
       "      <td>12.530259</td>\n",
       "      <td>6.120000</td>\n",
       "      <td>21.450239</td>\n",
       "      <td>38.520000</td>\n",
       "      <td>23.851408</td>\n",
       "      <td>...</td>\n",
       "      <td>64.403900</td>\n",
       "      <td>13.357165</td>\n",
       "      <td>29.625664</td>\n",
       "      <td>9.751626</td>\n",
       "      <td>32.048004</td>\n",
       "      <td>23.966692</td>\n",
       "      <td>12.062395</td>\n",
       "      <td>60.362865</td>\n",
       "      <td>42.830002</td>\n",
       "      <td>56.404537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-04</th>\n",
       "      <td>20.455357</td>\n",
       "      <td>36.955463</td>\n",
       "      <td>38.697315</td>\n",
       "      <td>2.272653</td>\n",
       "      <td>16.151209</td>\n",
       "      <td>12.549263</td>\n",
       "      <td>6.151111</td>\n",
       "      <td>21.567379</td>\n",
       "      <td>38.419998</td>\n",
       "      <td>24.072374</td>\n",
       "      <td>...</td>\n",
       "      <td>65.072762</td>\n",
       "      <td>13.679873</td>\n",
       "      <td>29.570749</td>\n",
       "      <td>9.798885</td>\n",
       "      <td>32.102802</td>\n",
       "      <td>24.188478</td>\n",
       "      <td>12.165599</td>\n",
       "      <td>60.935837</td>\n",
       "      <td>42.410000</td>\n",
       "      <td>56.802811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-05</th>\n",
       "      <td>20.991257</td>\n",
       "      <td>37.436260</td>\n",
       "      <td>38.882702</td>\n",
       "      <td>2.254768</td>\n",
       "      <td>15.951151</td>\n",
       "      <td>12.710846</td>\n",
       "      <td>6.061111</td>\n",
       "      <td>21.728443</td>\n",
       "      <td>38.070000</td>\n",
       "      <td>24.839266</td>\n",
       "      <td>...</td>\n",
       "      <td>64.087074</td>\n",
       "      <td>13.559610</td>\n",
       "      <td>29.395031</td>\n",
       "      <td>9.793634</td>\n",
       "      <td>31.943861</td>\n",
       "      <td>23.913458</td>\n",
       "      <td>12.684220</td>\n",
       "      <td>60.292362</td>\n",
       "      <td>42.529999</td>\n",
       "      <td>57.319096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-06</th>\n",
       "      <td>21.100876</td>\n",
       "      <td>36.766918</td>\n",
       "      <td>38.838551</td>\n",
       "      <td>2.312970</td>\n",
       "      <td>15.774172</td>\n",
       "      <td>12.954793</td>\n",
       "      <td>6.173333</td>\n",
       "      <td>22.804605</td>\n",
       "      <td>39.000000</td>\n",
       "      <td>24.936747</td>\n",
       "      <td>...</td>\n",
       "      <td>63.312599</td>\n",
       "      <td>13.579657</td>\n",
       "      <td>29.675089</td>\n",
       "      <td>9.830395</td>\n",
       "      <td>32.574192</td>\n",
       "      <td>24.286070</td>\n",
       "      <td>12.648103</td>\n",
       "      <td>59.983845</td>\n",
       "      <td>44.119999</td>\n",
       "      <td>57.916447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-09</th>\n",
       "      <td>21.039982</td>\n",
       "      <td>36.399254</td>\n",
       "      <td>39.341808</td>\n",
       "      <td>2.305391</td>\n",
       "      <td>15.774172</td>\n",
       "      <td>13.436364</td>\n",
       "      <td>6.116667</td>\n",
       "      <td>22.738722</td>\n",
       "      <td>38.380001</td>\n",
       "      <td>25.287697</td>\n",
       "      <td>...</td>\n",
       "      <td>65.882416</td>\n",
       "      <td>13.547583</td>\n",
       "      <td>31.075380</td>\n",
       "      <td>9.804136</td>\n",
       "      <td>32.557747</td>\n",
       "      <td>24.525604</td>\n",
       "      <td>12.746144</td>\n",
       "      <td>62.108185</td>\n",
       "      <td>44.790001</td>\n",
       "      <td>57.437077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-23</th>\n",
       "      <td>87.422417</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>139.826126</td>\n",
       "      <td>89.843628</td>\n",
       "      <td>97.086075</td>\n",
       "      <td>86.546471</td>\n",
       "      <td>29.559999</td>\n",
       "      <td>198.269089</td>\n",
       "      <td>440.549988</td>\n",
       "      <td>116.737549</td>\n",
       "      <td>...</td>\n",
       "      <td>185.444489</td>\n",
       "      <td>19.926138</td>\n",
       "      <td>84.096046</td>\n",
       "      <td>58.997757</td>\n",
       "      <td>39.540314</td>\n",
       "      <td>43.215523</td>\n",
       "      <td>83.275253</td>\n",
       "      <td>119.415413</td>\n",
       "      <td>260.769989</td>\n",
       "      <td>31.866991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-24</th>\n",
       "      <td>84.758995</td>\n",
       "      <td>13.040000</td>\n",
       "      <td>133.327560</td>\n",
       "      <td>88.257690</td>\n",
       "      <td>94.541733</td>\n",
       "      <td>82.754738</td>\n",
       "      <td>28.450001</td>\n",
       "      <td>192.953873</td>\n",
       "      <td>431.679993</td>\n",
       "      <td>113.157280</td>\n",
       "      <td>...</td>\n",
       "      <td>182.452225</td>\n",
       "      <td>19.033527</td>\n",
       "      <td>74.841599</td>\n",
       "      <td>58.529015</td>\n",
       "      <td>37.677601</td>\n",
       "      <td>41.371834</td>\n",
       "      <td>81.987091</td>\n",
       "      <td>112.077583</td>\n",
       "      <td>250.500000</td>\n",
       "      <td>29.837135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-25</th>\n",
       "      <td>85.444443</td>\n",
       "      <td>13.170000</td>\n",
       "      <td>133.243652</td>\n",
       "      <td>89.429359</td>\n",
       "      <td>96.292152</td>\n",
       "      <td>84.953941</td>\n",
       "      <td>28.879999</td>\n",
       "      <td>207.752365</td>\n",
       "      <td>436.950012</td>\n",
       "      <td>113.753990</td>\n",
       "      <td>...</td>\n",
       "      <td>190.539932</td>\n",
       "      <td>19.243555</td>\n",
       "      <td>73.199677</td>\n",
       "      <td>57.812103</td>\n",
       "      <td>38.244884</td>\n",
       "      <td>41.429882</td>\n",
       "      <td>81.456696</td>\n",
       "      <td>109.309280</td>\n",
       "      <td>253.639999</td>\n",
       "      <td>30.762249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-26</th>\n",
       "      <td>84.112755</td>\n",
       "      <td>12.380000</td>\n",
       "      <td>130.521164</td>\n",
       "      <td>86.681580</td>\n",
       "      <td>94.866966</td>\n",
       "      <td>84.091316</td>\n",
       "      <td>27.700001</td>\n",
       "      <td>203.115906</td>\n",
       "      <td>426.920013</td>\n",
       "      <td>111.641830</td>\n",
       "      <td>...</td>\n",
       "      <td>185.989410</td>\n",
       "      <td>18.806004</td>\n",
       "      <td>68.711769</td>\n",
       "      <td>57.269821</td>\n",
       "      <td>36.932518</td>\n",
       "      <td>41.720146</td>\n",
       "      <td>80.310593</td>\n",
       "      <td>109.660789</td>\n",
       "      <td>246.419998</td>\n",
       "      <td>29.001839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-29</th>\n",
       "      <td>85.653297</td>\n",
       "      <td>13.320000</td>\n",
       "      <td>133.094452</td>\n",
       "      <td>88.679321</td>\n",
       "      <td>94.685226</td>\n",
       "      <td>84.375710</td>\n",
       "      <td>28.370001</td>\n",
       "      <td>203.354889</td>\n",
       "      <td>424.200012</td>\n",
       "      <td>112.712105</td>\n",
       "      <td>...</td>\n",
       "      <td>185.087570</td>\n",
       "      <td>19.409822</td>\n",
       "      <td>73.856445</td>\n",
       "      <td>57.407696</td>\n",
       "      <td>37.525200</td>\n",
       "      <td>42.484497</td>\n",
       "      <td>82.384903</td>\n",
       "      <td>111.057327</td>\n",
       "      <td>252.050003</td>\n",
       "      <td>29.684444</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3647 rows × 417 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                    A        AAL         AAP       AAPL        ABC        ABT  \\\n",
       "Date                                                                            \n",
       "2006-01-03  20.400560  35.305664   38.423595   2.265983  16.258938  12.530259   \n",
       "2006-01-04  20.455357  36.955463   38.697315   2.272653  16.151209  12.549263   \n",
       "2006-01-05  20.991257  37.436260   38.882702   2.254768  15.951151  12.710846   \n",
       "2006-01-06  21.100876  36.766918   38.838551   2.312970  15.774172  12.954793   \n",
       "2006-01-09  21.039982  36.399254   39.341808   2.305391  15.774172  13.436364   \n",
       "...               ...        ...         ...        ...        ...        ...   \n",
       "2020-06-23  87.422417  14.000000  139.826126  89.843628  97.086075  86.546471   \n",
       "2020-06-24  84.758995  13.040000  133.327560  88.257690  94.541733  82.754738   \n",
       "2020-06-25  85.444443  13.170000  133.243652  89.429359  96.292152  84.953941   \n",
       "2020-06-26  84.112755  12.380000  130.521164  86.681580  94.866966  84.091316   \n",
       "2020-06-29  85.653297  13.320000  133.094452  88.679321  94.685226  84.375710   \n",
       "\n",
       "                 ACGL         ACN        ADBE         ADI  ...         WTW  \\\n",
       "Date                                                       ...               \n",
       "2006-01-03   6.120000   21.450239   38.520000   23.851408  ...   64.403900   \n",
       "2006-01-04   6.151111   21.567379   38.419998   24.072374  ...   65.072762   \n",
       "2006-01-05   6.061111   21.728443   38.070000   24.839266  ...   64.087074   \n",
       "2006-01-06   6.173333   22.804605   39.000000   24.936747  ...   63.312599   \n",
       "2006-01-09   6.116667   22.738722   38.380001   25.287697  ...   65.882416   \n",
       "...               ...         ...         ...         ...  ...         ...   \n",
       "2020-06-23  29.559999  198.269089  440.549988  116.737549  ...  185.444489   \n",
       "2020-06-24  28.450001  192.953873  431.679993  113.157280  ...  182.452225   \n",
       "2020-06-25  28.879999  207.752365  436.950012  113.753990  ...  190.539932   \n",
       "2020-06-26  27.700001  203.115906  426.920013  111.641830  ...  185.989410   \n",
       "2020-06-29  28.370001  203.354889  424.200012  112.712105  ...  185.087570   \n",
       "\n",
       "                   WY       WYNN        XEL        XOM       XRAY        YUM  \\\n",
       "Date                                                                           \n",
       "2006-01-03  13.357165  29.625664   9.751626  32.048004  23.966692  12.062395   \n",
       "2006-01-04  13.679873  29.570749   9.798885  32.102802  24.188478  12.165599   \n",
       "2006-01-05  13.559610  29.395031   9.793634  31.943861  23.913458  12.684220   \n",
       "2006-01-06  13.579657  29.675089   9.830395  32.574192  24.286070  12.648103   \n",
       "2006-01-09  13.547583  31.075380   9.804136  32.557747  24.525604  12.746144   \n",
       "...               ...        ...        ...        ...        ...        ...   \n",
       "2020-06-23  19.926138  84.096046  58.997757  39.540314  43.215523  83.275253   \n",
       "2020-06-24  19.033527  74.841599  58.529015  37.677601  41.371834  81.987091   \n",
       "2020-06-25  19.243555  73.199677  57.812103  38.244884  41.429882  81.456696   \n",
       "2020-06-26  18.806004  68.711769  57.269821  36.932518  41.720146  80.310593   \n",
       "2020-06-29  19.409822  73.856445  57.407696  37.525200  42.484497  82.384903   \n",
       "\n",
       "                   ZBH        ZBRA       ZION  \n",
       "Date                                           \n",
       "2006-01-03   60.362865   42.830002  56.404537  \n",
       "2006-01-04   60.935837   42.410000  56.802811  \n",
       "2006-01-05   60.292362   42.529999  57.319096  \n",
       "2006-01-06   59.983845   44.119999  57.916447  \n",
       "2006-01-09   62.108185   44.790001  57.437077  \n",
       "...                ...         ...        ...  \n",
       "2020-06-23  119.415413  260.769989  31.866991  \n",
       "2020-06-24  112.077583  250.500000  29.837135  \n",
       "2020-06-25  109.309280  253.639999  30.762249  \n",
       "2020-06-26  109.660789  246.419998  29.001839  \n",
       "2020-06-29  111.057327  252.050003  29.684444  \n",
       "\n",
       "[3647 rows x 417 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleaned_data = data.copy()\n",
    "\n",
    "# Remove companies (columns) with all missing values for whole time range\n",
    "cleaned_data.dropna(axis='columns', how='all', inplace=True)\n",
    "\n",
    "# Remove days (rows) with missing values for all of companies\n",
    "cleaned_data.dropna(axis='index', how='all', inplace=True)\n",
    "\n",
    "# Finally, remove the columns with at least one Nan (missing value)\n",
    "cleaned_data.dropna(axis='columns', how='any', inplace=True)\n",
    "\n",
    "cleaned_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3646, 417)\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABC</th>\n",
       "      <th>ABT</th>\n",
       "      <th>ACGL</th>\n",
       "      <th>ACN</th>\n",
       "      <th>ADBE</th>\n",
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       "      <th>WTW</th>\n",
       "      <th>WY</th>\n",
       "      <th>WYNN</th>\n",
       "      <th>XEL</th>\n",
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       "      <th>ZBH</th>\n",
       "      <th>ZBRA</th>\n",
       "      <th>ZION</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2006-01-04 00:00:00</th>\n",
       "      <td>0.002682</td>\n",
       "      <td>0.045670</td>\n",
       "      <td>0.007098</td>\n",
       "      <td>0.002939</td>\n",
       "      <td>-0.006648</td>\n",
       "      <td>0.001515</td>\n",
       "      <td>0.005071</td>\n",
       "      <td>0.005446</td>\n",
       "      <td>-0.002599</td>\n",
       "      <td>0.009222</td>\n",
       "      <td>...</td>\n",
       "      <td>0.010332</td>\n",
       "      <td>0.023873</td>\n",
       "      <td>-0.001855</td>\n",
       "      <td>0.004835</td>\n",
       "      <td>0.001708</td>\n",
       "      <td>0.009211</td>\n",
       "      <td>0.008519</td>\n",
       "      <td>0.009447</td>\n",
       "      <td>-0.009855</td>\n",
       "      <td>0.007036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-05 00:00:00</th>\n",
       "      <td>0.025861</td>\n",
       "      <td>0.012926</td>\n",
       "      <td>0.004779</td>\n",
       "      <td>-0.007900</td>\n",
       "      <td>-0.012464</td>\n",
       "      <td>0.012794</td>\n",
       "      <td>-0.014740</td>\n",
       "      <td>0.007440</td>\n",
       "      <td>-0.009152</td>\n",
       "      <td>0.031361</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.015263</td>\n",
       "      <td>-0.008830</td>\n",
       "      <td>-0.005960</td>\n",
       "      <td>-0.000536</td>\n",
       "      <td>-0.004963</td>\n",
       "      <td>-0.011435</td>\n",
       "      <td>0.041747</td>\n",
       "      <td>-0.010616</td>\n",
       "      <td>0.002826</td>\n",
       "      <td>0.009048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-06 00:00:00</th>\n",
       "      <td>0.005209</td>\n",
       "      <td>-0.018041</td>\n",
       "      <td>-0.001136</td>\n",
       "      <td>0.025485</td>\n",
       "      <td>-0.011157</td>\n",
       "      <td>0.019010</td>\n",
       "      <td>0.018346</td>\n",
       "      <td>0.048340</td>\n",
       "      <td>0.024135</td>\n",
       "      <td>0.003917</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.012158</td>\n",
       "      <td>0.001477</td>\n",
       "      <td>0.009482</td>\n",
       "      <td>0.003746</td>\n",
       "      <td>0.019540</td>\n",
       "      <td>0.015462</td>\n",
       "      <td>-0.002852</td>\n",
       "      <td>-0.005130</td>\n",
       "      <td>0.036703</td>\n",
       "      <td>0.010368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-09 00:00:00</th>\n",
       "      <td>-0.002890</td>\n",
       "      <td>-0.010050</td>\n",
       "      <td>0.012874</td>\n",
       "      <td>-0.003282</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.036499</td>\n",
       "      <td>-0.009222</td>\n",
       "      <td>-0.002893</td>\n",
       "      <td>-0.016025</td>\n",
       "      <td>0.013976</td>\n",
       "      <td>...</td>\n",
       "      <td>0.039787</td>\n",
       "      <td>-0.002365</td>\n",
       "      <td>0.046108</td>\n",
       "      <td>-0.002675</td>\n",
       "      <td>-0.000505</td>\n",
       "      <td>0.009815</td>\n",
       "      <td>0.007722</td>\n",
       "      <td>0.034803</td>\n",
       "      <td>0.015072</td>\n",
       "      <td>-0.008311</td>\n",
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       "    <tr>\n",
       "      <th>2006-01-10 00:00:00</th>\n",
       "      <td>0.012940</td>\n",
       "      <td>-0.021202</td>\n",
       "      <td>0.001122</td>\n",
       "      <td>0.061329</td>\n",
       "      <td>0.000243</td>\n",
       "      <td>-0.009715</td>\n",
       "      <td>0.006338</td>\n",
       "      <td>-0.021807</td>\n",
       "      <td>0.005975</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.010204</td>\n",
       "      <td>0.013228</td>\n",
       "      <td>0.001236</td>\n",
       "      <td>0.004809</td>\n",
       "      <td>0.007714</td>\n",
       "      <td>-0.008537</td>\n",
       "      <td>-0.000810</td>\n",
       "      <td>-0.004267</td>\n",
       "      <td>0.036607</td>\n",
       "      <td>-0.011753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-11 00:00:00</th>\n",
       "      <td>-0.000286</td>\n",
       "      <td>-0.082691</td>\n",
       "      <td>-0.008555</td>\n",
       "      <td>0.036906</td>\n",
       "      <td>-0.000243</td>\n",
       "      <td>-0.007095</td>\n",
       "      <td>0.003424</td>\n",
       "      <td>0.008193</td>\n",
       "      <td>0.018476</td>\n",
       "      <td>0.004871</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.004599</td>\n",
       "      <td>-0.000585</td>\n",
       "      <td>0.029562</td>\n",
       "      <td>-0.007491</td>\n",
       "      <td>0.006826</td>\n",
       "      <td>0.022724</td>\n",
       "      <td>-0.008053</td>\n",
       "      <td>0.025749</td>\n",
       "      <td>-0.009516</td>\n",
       "      <td>0.005829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-12 00:00:00</th>\n",
       "      <td>-0.022252</td>\n",
       "      <td>0.005445</td>\n",
       "      <td>0.002935</td>\n",
       "      <td>0.004638</td>\n",
       "      <td>0.007774</td>\n",
       "      <td>-0.002175</td>\n",
       "      <td>-0.008128</td>\n",
       "      <td>-0.001634</td>\n",
       "      <td>0.003807</td>\n",
       "      <td>-0.008476</td>\n",
       "      <td>...</td>\n",
       "      <td>0.017471</td>\n",
       "      <td>-0.017686</td>\n",
       "      <td>-0.009469</td>\n",
       "      <td>0.010152</td>\n",
       "      <td>-0.010508</td>\n",
       "      <td>-0.001606</td>\n",
       "      <td>-0.016304</td>\n",
       "      <td>0.005955</td>\n",
       "      <td>0.010591</td>\n",
       "      <td>-0.015228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-13 00:00:00</th>\n",
       "      <td>-0.007627</td>\n",
       "      <td>-0.027232</td>\n",
       "      <td>0.000225</td>\n",
       "      <td>0.015306</td>\n",
       "      <td>0.002418</td>\n",
       "      <td>-0.003635</td>\n",
       "      <td>-0.005820</td>\n",
       "      <td>-0.012500</td>\n",
       "      <td>-0.016344</td>\n",
       "      <td>0.006428</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.004807</td>\n",
       "      <td>-0.011516</td>\n",
       "      <td>0.009297</td>\n",
       "      <td>0.000532</td>\n",
       "      <td>0.022056</td>\n",
       "      <td>0.004988</td>\n",
       "      <td>-0.000208</td>\n",
       "      <td>-0.025453</td>\n",
       "      <td>-0.007554</td>\n",
       "      <td>0.010307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-17 00:00:00</th>\n",
       "      <td>-0.005907</td>\n",
       "      <td>-0.126633</td>\n",
       "      <td>-0.019573</td>\n",
       "      <td>-0.010335</td>\n",
       "      <td>-0.012389</td>\n",
       "      <td>-0.002917</td>\n",
       "      <td>-0.016183</td>\n",
       "      <td>0.020640</td>\n",
       "      <td>0.015330</td>\n",
       "      <td>-0.031236</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.014564</td>\n",
       "      <td>0.001052</td>\n",
       "      <td>-0.025164</td>\n",
       "      <td>0.011096</td>\n",
       "      <td>0.009306</td>\n",
       "      <td>-0.004096</td>\n",
       "      <td>-0.012355</td>\n",
       "      <td>0.001416</td>\n",
       "      <td>-0.020132</td>\n",
       "      <td>-0.004814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-18 00:00:00</th>\n",
       "      <td>0.020522</td>\n",
       "      <td>0.032790</td>\n",
       "      <td>-0.008308</td>\n",
       "      <td>-0.026557</td>\n",
       "      <td>0.003904</td>\n",
       "      <td>0.003646</td>\n",
       "      <td>-0.015695</td>\n",
       "      <td>0.004852</td>\n",
       "      <td>0.007326</td>\n",
       "      <td>-0.004505</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.012025</td>\n",
       "      <td>-0.003462</td>\n",
       "      <td>-0.022932</td>\n",
       "      <td>0.002624</td>\n",
       "      <td>-0.014073</td>\n",
       "      <td>0.002139</td>\n",
       "      <td>0.005673</td>\n",
       "      <td>0.009992</td>\n",
       "      <td>-0.006876</td>\n",
       "      <td>0.002345</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 417 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                            A       AAL       AAP      AAPL       ABC  \\\n",
       "Date                                                                    \n",
       "2006-01-04 00:00:00  0.002682  0.045670  0.007098  0.002939 -0.006648   \n",
       "2006-01-05 00:00:00  0.025861  0.012926  0.004779 -0.007900 -0.012464   \n",
       "2006-01-06 00:00:00  0.005209 -0.018041 -0.001136  0.025485 -0.011157   \n",
       "2006-01-09 00:00:00 -0.002890 -0.010050  0.012874 -0.003282  0.000000   \n",
       "2006-01-10 00:00:00  0.012940 -0.021202  0.001122  0.061329  0.000243   \n",
       "2006-01-11 00:00:00 -0.000286 -0.082691 -0.008555  0.036906 -0.000243   \n",
       "2006-01-12 00:00:00 -0.022252  0.005445  0.002935  0.004638  0.007774   \n",
       "2006-01-13 00:00:00 -0.007627 -0.027232  0.000225  0.015306  0.002418   \n",
       "2006-01-17 00:00:00 -0.005907 -0.126633 -0.019573 -0.010335 -0.012389   \n",
       "2006-01-18 00:00:00  0.020522  0.032790 -0.008308 -0.026557  0.003904   \n",
       "\n",
       "                          ABT      ACGL       ACN      ADBE       ADI  ...  \\\n",
       "Date                                                                   ...   \n",
       "2006-01-04 00:00:00  0.001515  0.005071  0.005446 -0.002599  0.009222  ...   \n",
       "2006-01-05 00:00:00  0.012794 -0.014740  0.007440 -0.009152  0.031361  ...   \n",
       "2006-01-06 00:00:00  0.019010  0.018346  0.048340  0.024135  0.003917  ...   \n",
       "2006-01-09 00:00:00  0.036499 -0.009222 -0.002893 -0.016025  0.013976  ...   \n",
       "2006-01-10 00:00:00 -0.009715  0.006338 -0.021807  0.005975  0.000000  ...   \n",
       "2006-01-11 00:00:00 -0.007095  0.003424  0.008193  0.018476  0.004871  ...   \n",
       "2006-01-12 00:00:00 -0.002175 -0.008128 -0.001634  0.003807 -0.008476  ...   \n",
       "2006-01-13 00:00:00 -0.003635 -0.005820 -0.012500 -0.016344  0.006428  ...   \n",
       "2006-01-17 00:00:00 -0.002917 -0.016183  0.020640  0.015330 -0.031236  ...   \n",
       "2006-01-18 00:00:00  0.003646 -0.015695  0.004852  0.007326 -0.004505  ...   \n",
       "\n",
       "                          WTW        WY      WYNN       XEL       XOM  \\\n",
       "Date                                                                    \n",
       "2006-01-04 00:00:00  0.010332  0.023873 -0.001855  0.004835  0.001708   \n",
       "2006-01-05 00:00:00 -0.015263 -0.008830 -0.005960 -0.000536 -0.004963   \n",
       "2006-01-06 00:00:00 -0.012158  0.001477  0.009482  0.003746  0.019540   \n",
       "2006-01-09 00:00:00  0.039787 -0.002365  0.046108 -0.002675 -0.000505   \n",
       "2006-01-10 00:00:00 -0.010204  0.013228  0.001236  0.004809  0.007714   \n",
       "2006-01-11 00:00:00 -0.004599 -0.000585  0.029562 -0.007491  0.006826   \n",
       "2006-01-12 00:00:00  0.017471 -0.017686 -0.009469  0.010152 -0.010508   \n",
       "2006-01-13 00:00:00 -0.004807 -0.011516  0.009297  0.000532  0.022056   \n",
       "2006-01-17 00:00:00 -0.014564  0.001052 -0.025164  0.011096  0.009306   \n",
       "2006-01-18 00:00:00 -0.012025 -0.003462 -0.022932  0.002624 -0.014073   \n",
       "\n",
       "                         XRAY       YUM       ZBH      ZBRA      ZION  \n",
       "Date                                                                   \n",
       "2006-01-04 00:00:00  0.009211  0.008519  0.009447 -0.009855  0.007036  \n",
       "2006-01-05 00:00:00 -0.011435  0.041747 -0.010616  0.002826  0.009048  \n",
       "2006-01-06 00:00:00  0.015462 -0.002852 -0.005130  0.036703  0.010368  \n",
       "2006-01-09 00:00:00  0.009815  0.007722  0.034803  0.015072 -0.008311  \n",
       "2006-01-10 00:00:00 -0.008537 -0.000810 -0.004267  0.036607 -0.011753  \n",
       "2006-01-11 00:00:00  0.022724 -0.008053  0.025749 -0.009516  0.005829  \n",
       "2006-01-12 00:00:00 -0.001606 -0.016304  0.005955  0.010591 -0.015228  \n",
       "2006-01-13 00:00:00  0.004988 -0.000208 -0.025453 -0.007554  0.010307  \n",
       "2006-01-17 00:00:00 -0.004096 -0.012355  0.001416 -0.020132 -0.004814  \n",
       "2006-01-18 00:00:00  0.002139  0.005673  0.009992 -0.006876  0.002345  \n",
       "\n",
       "[10 rows x 417 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This converts prices to arithmetic or log returns.\n",
    "\n",
    "prices = cleaned_data.copy()\n",
    "return_values = np.log(prices).diff().dropna()\n",
    "print(return_values.shape)\n",
    "return_values.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def assetPriceReg(df_stk):\n",
    "    import pandas_datareader.data as web  # module for reading datasets directly from the web\n",
    "    \n",
    "    # Reading in factor data\n",
    "    df_factors = web.DataReader('F-F_Research_Data_5_Factors_2x3_daily', 'famafrench')[0]\n",
    "    df_factors.rename(columns={'Mkt-RF': 'MKT'}, inplace=True)\n",
    "    df_factors['MKT'] = df_factors['MKT']/100\n",
    "    df_factors['SMB'] = df_factors['SMB']/100\n",
    "    df_factors['HML'] = df_factors['HML']/100\n",
    "    df_factors['RMW'] = df_factors['RMW']/100\n",
    "    df_factors['CMA'] = df_factors['CMA']/100\n",
    "    \n",
    "    df_stock_factor = pd.merge(df_stk,df_factors,left_index=True,right_index=True) # Merging the stock and factor returns dataframes together\n",
    "    df_stock_factor['XsRet'] = df_stock_factor['Returns'] - df_stock_factor['RF'] # Calculating excess returns\n",
    "\n",
    "    # Running CAPM, FF3, and FF5 models.\n",
    "    CAPM = sm.ols(formula = 'XsRet ~ MKT', data=df_stock_factor).fit(cov_type='HAC',cov_kwds={'maxlags':1})\n",
    "    FF3 = sm.ols( formula = 'XsRet ~ MKT + SMB + HML', data=df_stock_factor).fit(cov_type='HAC',cov_kwds={'maxlags':1})\n",
    "    FF5 = sm.ols( formula = 'XsRet ~ MKT + SMB + HML + RMW + CMA', data=df_stock_factor).fit(cov_type='HAC',cov_kwds={'maxlags':1})\n",
    "\n",
    "    CAPMtstat = CAPM.tvalues\n",
    "    FF3tstat = FF3.tvalues\n",
    "    FF5tstat = FF5.tvalues\n",
    "\n",
    "    CAPMcoeff = CAPM.params\n",
    "    FF3coeff = FF3.params\n",
    "    FF5coeff = FF5.params\n",
    "\n",
    "    # DataFrame with coefficients and t-stats\n",
    "    results_df = pd.DataFrame({'CAPMcoeff':CAPMcoeff,'CAPMtstat':CAPMtstat,\n",
    "                               'FF3coeff':FF3coeff, 'FF3tstat':FF3tstat,\n",
    "                               'FF5coeff':FF5coeff, 'FF5tstat':FF5tstat},\n",
    "    index = ['Intercept', 'MKT', 'SMB', 'HML', 'RMW', 'CMA'])\n",
    "\n",
    "\n",
    "    dfoutput = summary_col([CAPM,FF3, FF5],stars=True,float_format='%0.4f',\n",
    "                  model_names=['CAPM','FF3','FF5'],\n",
    "                  info_dict={'N':lambda x: \"{0:d}\".format(int(x.nobs)),\n",
    "                             'Adjusted R2':lambda x: \"{:.4f}\".format(x.rsquared_adj)}, \n",
    "                             regressor_order = ['Intercept', 'MKT', 'SMB', 'HML', 'RMW', 'CMA'])\n",
    "\n",
    "    print(dfoutput)\n",
    "    \n",
    "    return results_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    },
    {
     "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>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2006-01-03</th>\n",
       "      <td>3.064167</td>\n",
       "      <td>3.208333</td>\n",
       "      <td>3.054167</td>\n",
       "      <td>3.185000</td>\n",
       "      <td>2.922242</td>\n",
       "      <td>47281200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-04</th>\n",
       "      <td>3.209167</td>\n",
       "      <td>3.279167</td>\n",
       "      <td>3.175833</td>\n",
       "      <td>3.274167</td>\n",
       "      <td>3.004054</td>\n",
       "      <td>51007200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-05</th>\n",
       "      <td>3.275000</td>\n",
       "      <td>3.354167</td>\n",
       "      <td>3.269167</td>\n",
       "      <td>3.348333</td>\n",
       "      <td>3.072100</td>\n",
       "      <td>64609200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-06</th>\n",
       "      <td>3.386667</td>\n",
       "      <td>3.415833</td>\n",
       "      <td>3.254167</td>\n",
       "      <td>3.403333</td>\n",
       "      <td>3.122564</td>\n",
       "      <td>62338800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-09</th>\n",
       "      <td>3.401667</td>\n",
       "      <td>3.516667</td>\n",
       "      <td>3.394167</td>\n",
       "      <td>3.498333</td>\n",
       "      <td>3.209726</td>\n",
       "      <td>56048400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Open      High       Low     Close  Adj Close    Volume\n",
       "Date                                                                   \n",
       "2006-01-03  3.064167  3.208333  3.054167  3.185000   2.922242  47281200\n",
       "2006-01-04  3.209167  3.279167  3.175833  3.274167   3.004054  51007200\n",
       "2006-01-05  3.275000  3.354167  3.269167  3.348333   3.072100  64609200\n",
       "2006-01-06  3.386667  3.415833  3.254167  3.403333   3.122564  62338800\n",
       "2006-01-09  3.401667  3.516667  3.394167  3.498333   3.209726  56048400"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_stk = yf.download('NVDA', start=start, end=end)\n",
    "df_stk.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Date'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_stk.drop(['Volume'],axis=1,inplace=True)\n",
    "df_stk['Adj Close'].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Returns</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2006-01-03</th>\n",
       "      <td>3.064167</td>\n",
       "      <td>3.208333</td>\n",
       "      <td>3.054167</td>\n",
       "      <td>3.185000</td>\n",
       "      <td>2.922242</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-04</th>\n",
       "      <td>3.209167</td>\n",
       "      <td>3.279167</td>\n",
       "      <td>3.175833</td>\n",
       "      <td>3.274167</td>\n",
       "      <td>3.004054</td>\n",
       "      <td>0.027611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-05</th>\n",
       "      <td>3.275000</td>\n",
       "      <td>3.354167</td>\n",
       "      <td>3.269167</td>\n",
       "      <td>3.348333</td>\n",
       "      <td>3.072100</td>\n",
       "      <td>0.022399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-06</th>\n",
       "      <td>3.386667</td>\n",
       "      <td>3.415833</td>\n",
       "      <td>3.254167</td>\n",
       "      <td>3.403333</td>\n",
       "      <td>3.122564</td>\n",
       "      <td>0.016293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-09</th>\n",
       "      <td>3.401667</td>\n",
       "      <td>3.516667</td>\n",
       "      <td>3.394167</td>\n",
       "      <td>3.498333</td>\n",
       "      <td>3.209726</td>\n",
       "      <td>0.027531</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Open      High       Low     Close  Adj Close   Returns\n",
       "Date                                                                   \n",
       "2006-01-03  3.064167  3.208333  3.054167  3.185000   2.922242       NaN\n",
       "2006-01-04  3.209167  3.279167  3.175833  3.274167   3.004054  0.027611\n",
       "2006-01-05  3.275000  3.354167  3.269167  3.348333   3.072100  0.022399\n",
       "2006-01-06  3.386667  3.415833  3.254167  3.403333   3.122564  0.016293\n",
       "2006-01-09  3.401667  3.516667  3.394167  3.498333   3.209726  0.027531"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_stk['Returns'] = np.log(df_stk[['Adj Close']]).diff().dropna()\n",
    "df_stk.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Date'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_stk['Returns'].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_stk['Returns'].hist(bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    3646.000000\n",
       "mean        0.000945\n",
       "std         0.030545\n",
       "min        -0.367108\n",
       "25%        -0.013310\n",
       "50%         0.001139\n",
       "75%         0.015712\n",
       "max         0.260876\n",
       "Name: Returns, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_stk['Returns'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "===============================================\n",
      "                  CAPM       FF3        FF5    \n",
      "-----------------------------------------------\n",
      "Intercept      -0.0067*** -0.0075*** -0.0075***\n",
      "               (0.0012)   (0.0011)   (0.0011)  \n",
      "MKT            1.5120***  1.6305***  1.4925*** \n",
      "               (0.0707)   (0.0637)   (0.0684)  \n",
      "SMB                       0.5429***  0.3230*** \n",
      "                          (0.1235)   (0.1222)  \n",
      "HML                       -1.0400*** -0.7702***\n",
      "                          (0.1092)   (0.1168)  \n",
      "RMW                                  0.6162*   \n",
      "                                     (0.3413)  \n",
      "CMA                                  -1.5601***\n",
      "                                     (0.3989)  \n",
      "R-squared      0.5343     0.6073     0.6250    \n",
      "R-squared Adj. 0.5333     0.6047     0.6209    \n",
      "N              464        464        464       \n",
      "Adjusted R2    0.5333     0.6047     0.6209    \n",
      "===============================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "df_regOutput = assetPriceReg(df_stk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "    import pandas_datareader.data as web  # module for reading datasets directly from the web\n",
    "    \n",
    "    # Reading in factor data\n",
    "    df_factors = web.DataReader('F-F_Research_Data_5_Factors_2x3_daily', 'famafrench')[0]\n",
    "    df_factors.rename(columns={'Mkt-RF': 'MKT'}, inplace=True)\n",
    "    df_factors['MKT'] = df_factors['MKT']/100\n",
    "    df_factors['SMB'] = df_factors['SMB']/100\n",
    "    df_factors['HML'] = df_factors['HML']/100\n",
    "    df_factors['RMW'] = df_factors['RMW']/100\n",
    "    df_factors['CMA'] = df_factors['CMA']/100\n",
    "    \n",
    "    df_stock_factor = pd.merge(df_stk,df_factors,left_index=True,right_index=True) # Merging the stock and factor returns dataframes together\n",
    "    df_stock_factor['XsRet'] = df_stock_factor['Returns'] - df_stock_factor['RF'] # Calculating excess returns\n",
    "\n",
    "    # Running CAPM, FF3, and FF5 models.\n",
    "    FF5 = sm.ols( formula = 'XsRet ~ MKT + SMB + HML + RMW + CMA', data=df_stock_factor).fit(cov_type='HAC',cov_kwds={'maxlags':1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>XsRet</td>      <th>  R-squared:         </th> <td>   0.625</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.621</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   152.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 23 Aug 2023</td> <th>  Prob (F-statistic):</th> <td>3.36e-95</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>00:56:33</td>     <th>  Log-Likelihood:    </th> <td>  1117.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   464</td>      <th>  AIC:               </th> <td>  -2223.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   458</td>      <th>  BIC:               </th> <td>  -2198.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     5</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>         <td>HAC</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -0.0075</td> <td>    0.001</td> <td>   -7.034</td> <td> 0.000</td> <td>   -0.010</td> <td>   -0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MKT</th>       <td>    1.4925</td> <td>    0.068</td> <td>   21.812</td> <td> 0.000</td> <td>    1.358</td> <td>    1.627</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SMB</th>       <td>    0.3230</td> <td>    0.122</td> <td>    2.644</td> <td> 0.008</td> <td>    0.084</td> <td>    0.562</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HML</th>       <td>   -0.7702</td> <td>    0.117</td> <td>   -6.592</td> <td> 0.000</td> <td>   -0.999</td> <td>   -0.541</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RMW</th>       <td>    0.6162</td> <td>    0.341</td> <td>    1.805</td> <td> 0.071</td> <td>   -0.053</td> <td>    1.285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CMA</th>       <td>   -1.5601</td> <td>    0.399</td> <td>   -3.911</td> <td> 0.000</td> <td>   -2.342</td> <td>   -0.778</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>275.665</td> <th>  Durbin-Watson:     </th> <td>   1.878</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>7075.563</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-2.057</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>21.683</td>  <th>  Cond. No.          </th> <td>    376.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction"
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &      XsRet       & \\textbf{  R-squared:         } &     0.625   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared:    } &     0.621   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       } &     152.8   \\\\\n",
       "\\textbf{Date:}             & Wed, 23 Aug 2023 & \\textbf{  Prob (F-statistic):} &  3.36e-95   \\\\\n",
       "\\textbf{Time:}             &     00:56:33     & \\textbf{  Log-Likelihood:    } &    1117.6   \\\\\n",
       "\\textbf{No. Observations:} &         464      & \\textbf{  AIC:               } &    -2223.   \\\\\n",
       "\\textbf{Df Residuals:}     &         458      & \\textbf{  BIC:               } &    -2198.   \\\\\n",
       "\\textbf{Df Model:}         &           5      & \\textbf{                     } &             \\\\\n",
       "\\textbf{Covariance Type:}  &       HAC        & \\textbf{                     } &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                   & \\textbf{coef} & \\textbf{std err} & \\textbf{z} & \\textbf{P$> |$z$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept} &      -0.0075  &        0.001     &    -7.034  &         0.000        &       -0.010    &       -0.005     \\\\\n",
       "\\textbf{MKT}       &       1.4925  &        0.068     &    21.812  &         0.000        &        1.358    &        1.627     \\\\\n",
       "\\textbf{SMB}       &       0.3230  &        0.122     &     2.644  &         0.008        &        0.084    &        0.562     \\\\\n",
       "\\textbf{HML}       &      -0.7702  &        0.117     &    -6.592  &         0.000        &       -0.999    &       -0.541     \\\\\n",
       "\\textbf{RMW}       &       0.6162  &        0.341     &     1.805  &         0.071        &       -0.053    &        1.285     \\\\\n",
       "\\textbf{CMA}       &      -1.5601  &        0.399     &    -3.911  &         0.000        &       -2.342    &       -0.778     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 275.665 & \\textbf{  Durbin-Watson:     } &    1.878  \\\\\n",
       "\\textbf{Prob(Omnibus):} &   0.000 & \\textbf{  Jarque-Bera (JB):  } & 7075.563  \\\\\n",
       "\\textbf{Skew:}          &  -2.057 & \\textbf{  Prob(JB):          } &     0.00  \\\\\n",
       "\\textbf{Kurtosis:}      &  21.683 & \\textbf{  Cond. No.          } &     376.  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  XsRet   R-squared:                       0.625\n",
       "Model:                            OLS   Adj. R-squared:                  0.621\n",
       "Method:                 Least Squares   F-statistic:                     152.8\n",
       "Date:                Wed, 23 Aug 2023   Prob (F-statistic):           3.36e-95\n",
       "Time:                        00:56:33   Log-Likelihood:                 1117.6\n",
       "No. Observations:                 464   AIC:                            -2223.\n",
       "Df Residuals:                     458   BIC:                            -2198.\n",
       "Df Model:                           5                                         \n",
       "Covariance Type:                  HAC                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -0.0075      0.001     -7.034      0.000      -0.010      -0.005\n",
       "MKT            1.4925      0.068     21.812      0.000       1.358       1.627\n",
       "SMB            0.3230      0.122      2.644      0.008       0.084       0.562\n",
       "HML           -0.7702      0.117     -6.592      0.000      -0.999      -0.541\n",
       "RMW            0.6162      0.341      1.805      0.071      -0.053       1.285\n",
       "CMA           -1.5601      0.399     -3.911      0.000      -2.342      -0.778\n",
       "==============================================================================\n",
       "Omnibus:                      275.665   Durbin-Watson:                   1.878\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             7075.563\n",
       "Skew:                          -2.057   Prob(JB):                         0.00\n",
       "Kurtosis:                      21.683   Cond. No.                         376.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF5.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter Terminology\n",
    "\n",
    "In general, we do not know the underlying true values of the coefficients β. We will denote $\\widehat{\\beta}$ the estimation of the unknown parameter β.\n",
    "\n",
    "We note that we can talk about $\\widehat{\\beta}$ in two ways:\n",
    "\n",
    "- $\\widehat{\\beta}$ as a concrete estimated value, or more generally, as a result. Then we say that $\\widehat{\\beta}$ is an estimate of β based on an observed data sample;\n",
    "\n",
    "- $\\widehat{\\beta}$ as a random variable, or more generally, as a rule for calculating an estimate based on observed data. Then we say that $\\widehat{\\beta}$ is an estimator of β.\n",
    "\n",
    "When we are talking about $\\widehat{\\beta}$ as an estimator, we can also talk about its mean, $\\mathbb{E}(\\widehat{\\beta}_1)$ , variance $\\mathbb{V}{\\rm ar}(\\widehat{\\beta}_1)$ and distribution, which are very important when determining if a particular estimation method is better than an alternative one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Key assumptions in Regression Analysis\n",
    "\n",
    "<p>Let our <em>(random) samples</em> of <span class=\"math inline\">\\(\\epsilon\\)</span>, <span class=\"math inline\">\\(X\\)</span> and <span class=\"math inline\">\\(Y\\)</span> be: <span class=\"math inline\">\\(\\boldsymbol{\\varepsilon} = (\\epsilon_1, ..., \\epsilon_N)^\\top\\)</span>, <span class=\"math inline\">\\(\\mathbf{X} = (X_1,....,X_N)^\\top\\)</span>, and <span class=\"math inline\">\\(\\mathbf{Y} = (Y_1, ..., Y_N)^\\top\\)</span>.</p>\n",
    "<p>The required conditions are:</p>\n",
    "\n",
    "\n",
    "<p>\n",
    "<strong>(UR.1)</strong> The Data Generating Process (<strong>DGP</strong>), or in other words, the population, is described by a linear (<em>in terms of the coefficients</em>) model: <span class=\"math display\"><span class=\"math display\">\\[Y = \\beta_0 + \\beta_1 X + \\epsilon\\]</span></span>\n",
    "</p>\n",
    "</div>\n",
    "\n",
    "<p>Another example of a linear model is: <span class=\"math display\">\\[\\log (Y) = \\beta_0 + \\beta_1 \\dfrac{1}{X} + \\epsilon \\iff U = \\beta_0 + \\beta_1 V + \\epsilon,\\ \\text{where}\\ U = \\log(Y),\\ V = \\dfrac{1}{X}\\]</span> In a linear model <span class=\"math inline\">\\(\\epsilon\\)</span> and <span class=\"math inline\">\\(Y\\)</span> are <strong>always dependent</strong>, thus <span class=\"math inline\">\\(\\mathbb{C}{\\rm ov} (Y, \\epsilon) \\neq 0\\)</span>. However, <span class=\"math inline\">\\(\\epsilon\\)</span> may (or may not) depend on <span class=\"math inline\">\\(X\\)</span>. This leads us to further requirements for <span class=\"math inline\">\\(\\epsilon\\)</span>.</p>\n",
    "\n",
    "\n",
    "<p>\n",
    "<strong>(UR.2)</strong> The error term <span class=\"math inline\"><span class=\"math inline\">\\(\\epsilon\\)</span></span> has an expected value of zero, given any value of the explanatory variable: <span class=\"math display\"><span class=\"math display\">\\[\\mathbb{E}(\\epsilon_i| X_j) = 0,\\ \\forall i,j = 1,...,N\\]</span></span>\n",
    "</p>\n",
    "</div>\n",
    "\n",
    "\n",
    "<p>This means that whatever are the observations, <span class=\"math inline\">\\(X_j\\)</span>, the errors, <span class=\"math inline\">\\(\\epsilon_j\\)</span>, are on average 0. This also implies that <span class=\"math inline\">\\(\\mathbb{E}(\\epsilon_i X_i) = 0\\)</span> and <span class=\"math inline\">\\(\\mathbb{E}(\\epsilon_i) = \\mathbb{E}\\left( \\mathbb{E}\\left( \\epsilon_i | X_i\\right) \\right)=0\\)</span>. An example would be the case, where <span class=\"math inline\">\\(X_j\\)</span> and <span class=\"math inline\">\\(\\epsilon_i\\)</span> are independent r.v.’s and <span class=\"math inline\">\\(\\mathbb{E}(\\epsilon_i) = 0\\)</span> <span class=\"math inline\">\\(\\forall i,j = 1,...,N\\)</span>. Furthermore, This property implies that:\n",
    "<span class=\"math display\">\\[\\mathbb{E}(Y_i|X_i) = \\beta_0 + \\beta_1 X_i\\]</span>\n",
    "On the other hand, if <span class=\"math inline\">\\(\\mathbb{C}{\\rm ov}(X_i, \\epsilon_i) \\neq 0\\)</span>, then expressing the covariance as <span class=\"math inline\">\\(\\mathbb{C}{\\rm ov}(X_i, \\epsilon_i) = \\mathbb{E}\\left[ (X_i - \\mathbb{E}(X_i))(\\epsilon_i - \\mathbb{E}(\\epsilon_i))\\right] = \\mathbb{E}\\left[ (X_i - \\mathbb{E}(X_i))\\epsilon_i\\right] = \\mathbb{E} \\left[ (X_i - \\mathbb{E}(X_i))\\mathbb{E}(\\epsilon_i | X_i) \\right] \\neq 0\\)</span>, which implies that <span class=\"math inline\">\\(\\mathbb{E}(\\epsilon_i| X_j) \\neq 0\\)</span>, i.e. assumption <strong>(UR.2)</strong> does not hold.</p>\n",
    "\n",
    "\n",
    "<p>\n",
    "<strong>(UR.3)</strong> The error term <span class=\"math inline\"><span class=\"math inline\">\\(\\epsilon\\)</span></span> has the same variance given any value of the explanatory variable (i.e. homoskedasticity): <span class=\"math display\"><span class=\"math display\">\\[\\mathbb{V}{\\rm ar} (\\epsilon_i | \\mathbf{X} ) = \\sigma^2_\\epsilon,\\ \\forall i = 1,..,N\\]</span></span> and the error terms are not correlated across observations (i.e. no autocorrelation): <span class=\"math display\"><span class=\"math display\">\\[\\mathbb{C}{\\rm ov} (\\epsilon_i, \\epsilon_j) = 0,\\ i \\neq j\\]</span></span>\n",
    "</p>\n",
    "</div>\n",
    "<p>This implies that the conditional variance-covariance matrix of a <em>vector</em> of disturbances <span class=\"math inline\">\\(\\boldsymbol{\\varepsilon}\\)</span> is a unit (or identity) matrix, times a constant, <span class=\"math inline\">\\(\\sigma^2_\\epsilon\\)</span>:\n",
    "\n",
    "    \n",
    "$\\mathbb{V}{\\rm ar}\\left( \\boldsymbol{\\varepsilon} | \\mathbf{X} \\right) =\n",
    "\\begin{bmatrix}\n",
    "\\mathbb{V}{\\rm ar} (\\epsilon_1) & \\mathbb{C}{\\rm ov} (\\epsilon_1, \\epsilon_2) & ... & \\mathbb{C}{\\rm ov} (\\epsilon_1, \\epsilon_N) \\\\\n",
    "\\mathbb{C}{\\rm ov} (\\epsilon_2, \\epsilon_1) & \\mathbb{V}{\\rm ar} (\\epsilon_2) & ... & \\mathbb{C}{\\rm ov} (\\epsilon_2, \\epsilon_N) \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "\\mathbb{C}{\\rm ov} (\\epsilon_N, \\epsilon_1) & \\mathbb{C}{\\rm ov} (\\epsilon_N, \\epsilon_2) & ... & \\mathbb{V}{\\rm ar} (\\epsilon_N)\n",
    "\\end{bmatrix} =\n",
    "\\sigma^2_\\epsilon  \\mathbf{I}$\n",
    "    \n",
    "    \n",
    "This means that the disturbances $\\epsilon_i$ and $\\epsilon_j$ are independent $\\forall i \\neq j$ and independent of $\\mathbf{X}$, thus:\n",
    "\n",
    "$\\mathbb{C}{\\rm ov} (\\epsilon_i, \\epsilon_j | \\mathbf{X} ) = \\mathbb{E} (\\epsilon_i \\epsilon_j | \\mathbf{X} ) = 0,\\ \\forall i \\neq j.$\n",
    "</p>\n",
    "\n",
    "\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "<strong>(UR.4) (optional)</strong> The residuals are normal: <span class=\"math display\"><span class=\"math display\">\\[\\boldsymbol{\\varepsilon} | \\mathbf{X} \\sim \\mathcal{N} \\left( \\mathbf{0}, \\sigma^2_\\epsilon \\mathbf{I} \\right)\\]</span></span>\n",
    "</p>\n",
    "</div>\n",
    "<p>This <strong>optional condition</strong> simplifies some statistical properties of the parameter estimators.</p>\n",
    "<p>We can combine the requirements and restate them as the following:</p>\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "The Data Generating Process <span class=\"math inline\"><span class=\"math inline\">\\(Y = \\beta_0 + \\beta_1 X + \\epsilon\\)</span></span> satisfies <strong>(UR.2)</strong> and <strong>(UR.3)</strong>, if: (conditionally on all <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbf{X}\\)</span></span>’s) <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbb{E} (\\epsilon_i) = 0\\)</span></span>, <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbb{V}{\\rm ar}(\\epsilon_i) = \\sigma^2_\\epsilon\\)</span></span> and <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbb{C}{\\rm ov} (\\epsilon_i, \\epsilon_j) = 0\\)</span></span>, <span class=\"math inline\"><span class=\"math inline\">\\(\\forall i \\neq j\\)</span></span> and <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbb{C}{\\rm ov} (\\epsilon_i, X_j) = \\mathbb{E} (\\epsilon_i X_j) = 0\\)</span></span>, <span class=\"math inline\"><span class=\"math inline\">\\(\\forall i,j\\)</span></span>.\n",
    "</p>\n",
    "</div>\n",
    "<p>The linear relationship <span class=\"math inline\">\\(Y = \\beta_0 + \\beta_1 X + \\epsilon\\)</span> is also referred as the <em>regression line</em> with an <em>intercept</em> <span class=\"math inline\">\\(\\beta_0\\)</span> and a <em>slope</em> <span class=\"math inline\">\\(\\beta_1\\)</span>. From <strong>(UR.2)</strong> we have that the regression line coincides with the expected value of <span class=\"math inline\">\\(Y_i\\)</span>, given <span class=\"math inline\">\\(X_i\\)</span>.</p>\n",
    "<p>In general, we do not know the true coefficient <span class=\"math inline\">\\(\\beta_0\\)</span> and <span class=\"math inline\">\\(\\beta_1\\)</span> values but we would like to estimate them from our sample data, which consists of points <span class=\"math inline\">\\((X_i, Y_i)\\)</span>, <span class=\"math inline\">\\(i = 1,...,N\\)</span>. We would also like to use the data in the <em>best</em> way possible to obtain an <em>estimate of the regression</em>: <span class=\"math display\">\\[\\widehat{Y} = \\widehat{\\beta}_0 + \\widehat{\\beta}_1 X\\]</span></p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Properties of the OLS estimator\n",
    "\n",
    "From the construction of the OLS estimators the following properties apply to the sample:\n",
    "\n",
    "1. The sum (and by extension, the sample average) of the OLS residuals is zero:\n",
    "\n",
    "$\\begin{equation}\n",
    "\\sum_{i = 1}^N \\widehat{\\epsilon}_i = 0\n",
    "\\end{equation}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Date'>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "FF5.resid.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.6215588839535955e-16"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF5.resid.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. The sample covariance between the regressors and the OLS residuals is zero:\n",
    "\n",
    "$\\begin{equation}\n",
    "\\sum_{i = 1}^N X_i \\widehat{\\epsilon}_i = 0\n",
    "\\end{equation}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.6104877808019733e-16"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(FF5.resid.values * df_stock_factor['MKT'].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.73913033e-04, -4.87890978e-19],\n",
       "       [-4.87890978e-19,  2.95093793e-04]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(FF5.resid.values, df_stock_factor['MKT'].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that both the sum and the sample covariance are very close to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ol start=\"3\" style=\"list-style-type: decimal\">\n",
    "<li>The point <span class=\"math inline\">\\((\\overline{X}, \\overline{Y})\\)</span> is <strong>always on the OLS regression line</strong> - if we calculate <span class=\"math inline\">\\(\\widehat{\\beta}_0 + \\widehat{\\beta}_1 \\overline{X}\\)</span>, the resulting value would be equal to <span class=\"math inline\">\\(\\overline{Y}\\)</span>.</li>\n",
    "</ol>\n",
    "\n",
    "However, these properties are not the only ones, which justify the use of the OLS method, instead of some other competing estimator. The main advantage of the OLS estimators can be summarized by the following Gauss-Markov theorem:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gauss-Markov theorem\n",
    "\n",
    "<p>\n",
    "Under the assumption that the conditions <strong>(UR.1) - (UR.3)</strong> hold true, the OLS estimators <span class=\"math inline\"></span> and <span class=\"math inline\"><span class=\"math inline\">\\(\\widehat{\\beta}\\)</span></span> are <strong>BLUE</strong> (<strong>B</strong>est <strong>L</strong>inear <strong>U</strong>nbiased <strong>E</strong>stimator) and <strong>Consistent</strong>.\n",
    "</p>\n",
    "\n",
    "## What is an Estimator?\n",
    "\n",
    "\n",
    "<p> An <strong>estimator</strong> is a rule that can be applied to any sample of data to produce an <strong>estimate</strong>. In other words the <strong>estimator</strong> is the rule and the <strong>estimate</strong> is the result.</p>\n",
    "\n",
    "<p>The remaining components of the acronym <strong>BLUE</strong> are provided below.</p>\n",
    "\n",
    "### OLS estimators are Linear\n",
    "\n",
    "\n",
    "<p>From the specification of the relationship between <span class=\"math inline\">\\(\\mathbf{Y}\\)</span> and <span class=\"math inline\">\\(\\mathbf{X}\\)</span> (using the matrix notation for generality):\n",
    "<span class=\"math display\">\\[\n",
    "\\mathbf{Y} = \\mathbf{X} \\boldsymbol{\\beta} + \\boldsymbol{\\varepsilon}\n",
    "\\]</span>\n",
    "We see that the relationship is <strong>linear</strong> with respect to <span class=\"math inline\">\\(\\mathbf{Y}\\)</span>.</p>\n",
    "\n",
    "\n",
    "### OLS estimators are Unbiased\n",
    "\n",
    "<p>Using the matrix notation for the sample linear equations (<span class=\"math inline\">\\(\\mathbf{Y} = \\mathbf{X} \\boldsymbol{\\beta} + \\boldsymbol{\\varepsilon}\\)</span>) gives us the following:</p>\n",
    "\n",
    "$\\begin{aligned}\n",
    "\\widehat{\\boldsymbol{\\beta}} &= \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\mathbf{Y} \\\\\n",
    "&= \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\left( \\mathbf{X} \\boldsymbol{\\beta} + \\boldsymbol{\\varepsilon} \\right) \\\\\n",
    "&= \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\mathbf{X} \\boldsymbol{\\beta} + \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \\\\\n",
    "&= \\boldsymbol{\\beta} + \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \n",
    "\\end{aligned}$\n",
    "\n",
    "\n",
    "<p>If we take the expectation of both sides and use the law of total expectation:</p>\n",
    "<p>\n",
    "    $\\begin{aligned}\n",
    "\\mathbb{E} \\left[ \\widehat{\\boldsymbol{\\beta}} \\right] &= \\boldsymbol{\\beta} + \\mathbb{E} \\left[ \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \\right] \\\\\n",
    "&= \\boldsymbol{\\beta} + \\mathbb{E} \\left[ \\mathbb{E} \\left( \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \\biggr\\rvert \\mathbf{X}\\right)\\right] \\\\\n",
    "&= \\boldsymbol{\\beta} + \\mathbb{E} \\left[ \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\mathbb{E} \\left(  \\boldsymbol{\\varepsilon} | \\mathbf{X}\\right)\\right] \\\\\n",
    "&= \\boldsymbol{\\beta}\n",
    "\\end{aligned}$\n",
    "    \n",
    "    \n",
    "since $\\mathbb{E} \\left( \\boldsymbol{\\varepsilon} | \\mathbf{X}\\right) = \\mathbf{0}$ from <strong>(UR.2)</strong>.</p>\n",
    "<p>We have shown that <span class=\"math inline\">\\(\\mathbb{E} \\left[ \\widehat{\\boldsymbol{\\beta}} \\right] = \\boldsymbol{\\beta}\\)</span> - i.e., the OLS estimator <span class=\"math inline\">\\(\\widehat{\\boldsymbol{\\beta}}\\)</span> is an <strong>unbiased</strong> estimator of <span class=\"math inline\">\\(\\boldsymbol{\\beta}\\)</span>.</p>\n",
    "<p>Unbiasedness does not guarantee that the estimate we get with any particular sample is equal (or even very close) to <span class=\"math inline\">\\(\\boldsymbol{\\beta}\\)</span>. It means that if we could <em>repeatedly</em> draw random samples from the population and compute the estimate each time, then the average of these estimates would be (very close to) <span class=\"math inline\">\\(\\boldsymbol{\\beta}\\)</span>.</p>\n",
    "</div>\n",
    "\n",
    "\n",
    "\n",
    "### OLS estimators are Best (Efficient)\n",
    "\n",
    "<p>When there is more than one unbiased method of estimation to choose from, that estimator which has the lowest variance is the <strong>best</strong>. In other words, we want to show that OLS estimators are <em>best</em> in the sense that <span class=\"math inline\">\\(\\widehat{\\boldsymbol{\\beta}}\\)</span> are <strong>efficient</strong> estimators of <span class=\"math inline\">\\(\\boldsymbol{\\beta}\\)</span> (i.e. they have the <strong>smallest variance</strong>).</p>\n",
    "<p>To do so we will calculate the variance - the average distance of an element from the average - as follows (remember that for OLS estimators, condition <strong>(UR.3)</strong> holds true):</p>\n",
    "<p>From the proof of <strong>unbiasedness</strong> of the OLS we have that:\n",
    "<span class=\"math display\">\\[\n",
    "\\begin{aligned}\n",
    "\\widehat{\\boldsymbol{\\beta}} =  \\boldsymbol{\\beta} + \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \\Longrightarrow \\widehat{\\boldsymbol{\\beta}} - \\boldsymbol{\\beta} = \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \n",
    "\\end{aligned}\n",
    "\\]</span>\n",
    "Which we can then use this expression for calculating the <strong>variance-covariance matrix</strong> of the OLS estimator:\n",
    "    \n",
    "$\\begin{aligned}\n",
    "\\mathbb{V}{\\rm ar} (\\widehat{\\boldsymbol{\\beta}}) &= \\mathbb{E} \\left[(\\widehat{\\boldsymbol{\\beta}} - \\mathbb{E}(\\widehat{\\boldsymbol{\\beta}}))(\\widehat{\\boldsymbol{\\beta}} - \\mathbb{E}(\\widehat{\\boldsymbol{\\beta}}))^\\top \\right] \\\\\n",
    "&= \\mathbb{E} \\left[(\\widehat{\\boldsymbol{\\beta}} - \\boldsymbol{\\beta})(\\widehat{\\boldsymbol{\\beta}} - \\boldsymbol{\\beta})^\\top \\right] \\\\\n",
    "&= \\mathbb{E} \\left[  \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon}  \\left( \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \\right)^\\top \\right] \\\\\n",
    "&= \\mathbb{E} \\left[  \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\boldsymbol{\\varepsilon} \\boldsymbol{\\varepsilon}^\\top \\mathbf{X} \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\right] \\\\\n",
    "&= \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top  \\mathbb{E} \\left[  \\boldsymbol{\\varepsilon} \\boldsymbol{\\varepsilon}^\\top\\right]  \\mathbf{X} \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\\\\n",
    "&= \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top  \\left(\\sigma^2 \\mathbf{I} \\right)  \\mathbf{X} \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\\\\n",
    "&= \\sigma^2 \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\mathbf{X} \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1} \\\\\n",
    "&= \\sigma^2 \\left( \\mathbf{X}^\\top  \\mathbf{X}\\right)^{-1}\n",
    "\\end{aligned}$\n",
    "\n",
    "\n",
    "### Estimating the variance parameter of the error term\n",
    "\n",
    "\n",
    "<p>We see an immediate problem from the OLS estimator variance formulas - we do not know the true error variance <span class=\"math inline\">\\(\\sigma^2\\)</span>. However, we can estimate it by calculating the <strong>sample</strong> residual variance:\n",
    "<span class=\"math display\">\\[\n",
    "\\widehat{\\sigma}^2 = s^2 = \\dfrac{\\widehat{\\boldsymbol{\\varepsilon}}^\\top \\widehat{\\boldsymbol{\\varepsilon}}}{N - k} = \\dfrac{1}{N-k} \\sum_{i = 1}^N \\widehat{\\epsilon}_i^2\n",
    "\\]</span></p>\n",
    "\n",
    "<p>Note that this is an <strong>estimated variance</strong>. Nevertheless, it is a key component in assessing the accuracy of the parameter estimates (when calculating test statistics and confidence intervals).</p>\n",
    "<p>Since we estimate <span class=\"math inline\">\\(\\widehat{\\boldsymbol{\\beta}}\\)</span> from the a random sample, the estimator <span class=\"math inline\">\\(\\widehat{\\boldsymbol{\\beta}}\\)</span> is a random variable as well. We can measure the uncertainty of <span class=\"math inline\">\\(\\widehat{\\boldsymbol{\\beta}}\\)</span> via its standard deviation. This is the <em>standard error</em> of our estimate of <span class=\"math inline\">\\(\\boldsymbol{\\beta}\\)</span>:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>\n",
    "The square roots of the diagonal elements of the variance-covariance matrix <span class=\"math inline\"><span class=\"math inline\">\\(\\widehat{\\mathbb{V}{\\rm ar}} (\\widehat{\\boldsymbol{\\beta}})\\)</span></span> are called <strong>the standard errors (se)</strong> of the corresponding OLS estimators <span class=\"math inline\"><span class=\"math inline\">\\(\\widehat{\\boldsymbol{\\beta}}\\)</span></span>, which we use to <strong>estimate</strong> the standard <strong>deviation</strong> of <span class=\"math inline\"><span class=\"math inline\">\\(\\widehat{\\beta}_i\\)</span></span> from <span class=\"math inline\"><span class=\"math inline\">\\(\\beta_i\\)</span></span> <span class=\"math display\"><span class=\"math display\">\\[\n",
    "\\text{se}(\\widehat{\\beta}_i) = \\sqrt{\\widehat{\\mathbb{V}{\\rm ar}} (\\mathbf{\\widehat{\\beta}_i})}\n",
    "\\]</span></span>\n",
    "</p>\n",
    "<p>\n",
    "The standard errors describe the accuracy of an estimator (the smaller the better). The standard errors are measures of the <strong>sampling variability</strong> of the least squares estimates <span class=\"math inline\"><span class=\"math inline\">\\(\\widehat{\\beta}_1\\)</span></span> and <span class=\"math inline\"><span class=\"math inline\">\\(\\widehat{\\beta}_2\\)</span></span> in <strong>repeated samples</strong> - if we collect a number of different data samples, the OLS estimates will be different for each sample. As such, the OLS estimators are <strong>random variables</strong> and have their own distribution.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    0.001069\n",
       "MKT          0.068412\n",
       "SMB          0.122155\n",
       "HML          0.116806\n",
       "RMW          0.341355\n",
       "CMA          0.398788\n",
       "dtype: float64"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF5.bse\n",
    "\n",
    "# Note: the b in bse stands for the parameter vector β, and se - standard errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence Intervals\n",
    "\n",
    "In this section we will introduce the notion of interval estimation - a procedure for creating ranges of values, called confidence intervals, in which the unknown parameters are likely to be located. Confidence interval creation procedures rely heavily on (UR.4) assumption."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>-0.009595</td>\n",
       "      <td>-0.005404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MKT</th>\n",
       "      <td>1.357822</td>\n",
       "      <td>1.625993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>0.082963</td>\n",
       "      <td>0.561804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>-0.998712</td>\n",
       "      <td>-0.540839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RMW</th>\n",
       "      <td>-0.051692</td>\n",
       "      <td>1.286393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CMA</th>\n",
       "      <td>-2.346915</td>\n",
       "      <td>-0.783695</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "                  0         1\n",
       "Intercept -0.009595 -0.005404\n",
       "MKT        1.357822  1.625993\n",
       "SMB        0.082963  0.561804\n",
       "HML       -0.998712 -0.540839\n",
       "RMW       -0.051692  1.286393\n",
       "CMA       -2.346915 -0.783695"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF5.conf_int()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis Testing\n",
    "\n",
    "in practice, we usually want to answer very specific questions about the effects of specific variables:\n",
    "\n",
    "Does income affect expenditure?\n",
    "Do more years in education lead to an increase in wage?\n",
    "Hypothesis tests use the information about a parameter from the sample data to answer such yes/no questions (though not necessarily in such strong certainty)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Null Hypothesis\n",
    "\n",
    "<p>The <strong>null hypothesis</strong> is denoted by <span class=\"math inline\">\\(H_0\\)</span>, and for the univariate regression can be stated as:\n",
    "<span class=\"math display\">\\[\n",
    "H_0: \\beta_i = c\n",
    "\\]</span>\n",
    "where <span class=\"math inline\">\\(c\\)</span> is a constant value, which we are interested in. When testing the null hypothesis, we may either <strong>reject</strong> or <strong>fail to reject</strong> the null hypothesis.</p>\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "<strong>The null hypothesis, is presumed to be true, until the data provides sufficient evidence that it is not.</strong>\n",
    "</p>\n",
    "</div>\n",
    "<p>If we fail to reject the null hypothesis, it does not mean the null hypothesis is true. A hypothesis test does not determine which hypothesis is <strong>true</strong>, or which is most likely: it only assesses whether available evidence exists to <strong>reject</strong> the null hypothesis.</p>\n",
    "</div>\n",
    "\n",
    "\n",
    "###  The Alternative Hypothesis\n",
    "\n",
    "<p>Once, we state our null hypothesis, we must test it <em>against</em> and <strong>alternative hypothesis</strong>, denoted <span class=\"math inline\">\\(H_1\\)</span>.</p>\n",
    "<p>For the null hypothesis <span class=\"math inline\">\\(H_0: \\beta_i = c\\)</span> we may specify the alternative hypothesis in thee possible ways:</p>\n",
    "<ul>\n",
    "<li><span class=\"math inline\">\\(H_1: \\beta_i &gt; c\\)</span> - rejecting <span class=\"math inline\">\\(H_0\\)</span>, leads us to “accept” the conclusion that <span class=\"math inline\">\\(\\beta_i &gt; c\\)</span>. Economic theory frequently provides information about the <strong>signs</strong> of the variable parameters. For example: economic theory strongly suggests that food expenditure will rise if income increases, so we would test <span class=\"math inline\">\\(H_0: \\beta_{INCOME} = 0\\)</span> against <span class=\"math inline\">\\(H_1: \\beta_{INCOME} &gt; 0\\)</span>.</li>\n",
    "<li><span class=\"math inline\">\\(H_1: \\beta_i &lt; c\\)</span> - rejecting <span class=\"math inline\">\\(H_0\\)</span>, leads us to “accept” the conclusion that <span class=\"math inline\">\\(\\beta_i &lt; c\\)</span>.</li>\n",
    "<li><span class=\"math inline\">\\(H_1: \\beta_i \\neq c\\)</span> - rejecting <span class=\"math inline\">\\(H_0\\)</span>, leads us to “accept” the conclusion that <span class=\"math inline\">\\(\\beta_i\\)</span> is either greater <em>or</em> smaller than <span class=\"math inline\">\\(c\\)</span>.</li>\n",
    "</ul>\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "<strong>We usually talk about hypothesis testing in terms of the null</strong>, i.e. we either <strong>reject</strong> or <strong>fail to reject</strong> the null - we <strong>never</strong> <em>accept</em> the null. As such, if we reject the null, then we “accept” (i.e. we are left with) the alternative.\n",
    "</p>\n",
    "</div>\n",
    "</div>\n",
    "\n",
    "\n",
    "\n",
    "### The Test Statistic\n",
    "\n",
    "\n",
    "<p>The <strong>test statistic</strong> is calculated under the null hypothesis (i.e. assuming the null hypothesis is <em>true</em>). Under the null hypothesis the distribution of the statistic is <em>known</em>. Based on the value of the test statistic, we decide whether to reject, or fail to reject the null.</p>\n",
    "<p>Under the null hypothesis <span class=\"math inline\">\\(H_0: \\beta_i = c\\)</span> of our univariate regression model, we can calculate the following <strong><span class=\"math inline\">\\(t\\)</span>-statistic</strong>:\n",
    "<span class=\"math display\">\\[\n",
    "t_i = \\dfrac{\\widehat{\\beta}_i - c}{\\text{se}(\\widehat{\\beta}_i)} \\sim t_{(N-2)}\n",
    "\\]</span>\n",
    "If the null hypothesis is <em>not true</em>, then the <span class=\"math inline\">\\(t\\)</span>-statistic does not have a <span class=\"math inline\">\\(t\\)</span>-distribution with <span class=\"math inline\">\\(N-2\\)</span> degrees of freedom, but some other distribution.</p>\n",
    "</div>\n",
    "\n",
    "\n",
    "### The Rejection Regions\n",
    "<p>The <strong>rejection region</strong> consists of values that have low probability of occurring when the null hypothesis is true. The rejection region depends on the specification of the alternative hypothesis. If the calculated <em>test statistic</em> value falls in the rejection region (i.e. an unlikely event to occur under the null), then it is unlikely that the null hypothesis is holds.</p>\n",
    "<p>The size of the rejection regions are determined by choosing a <strong>level of significance <span class=\"math inline\">\\(\\alpha\\)</span></strong> - a probability of the unlikely event, usually <span class=\"math inline\">\\(0.01\\)</span>, <span class=\"math inline\">\\(0.05\\)</span>, <span class=\"math inline\">\\(0.1\\)</span>.</p>\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "To determine, whether to reject the null hypothesis or not, we will compare the calculated <span class=\"math inline\"><span class=\"math inline\">\\(t\\)</span></span>-statistic <span class=\"math inline\"><span class=\"math inline\">\\(t_i\\)</span></span> to the critical value <span class=\"math inline\"><span class=\"math inline\">\\(t_c\\)</span></span>.\n",
    "</p>\n",
    "</div>\n",
    "\n",
    "\n",
    "### Type I and Type II Errors\n",
    "<p>When deciding whether to reject the null hypothesis or not, we may commit one of two types of errors:</p>\n",
    "<ul>\n",
    "<li><strong>Type I error</strong> - <strong>to reject the null hypothesis when it is true</strong>. The probability of committing Type I error is <span class=\"math inline\">\\(\\mathbb{P}(H_0 \\text{ rejected} | H_0 \\text{ is true}) = \\alpha\\)</span>. Any time we reject the null hypothesis, it is possible that we have made such an error. We can specify the amount of Type I error, that we can tolerate, by setting the level of significance <span class=\"math inline\">\\(\\alpha\\)</span>. If we want to avoid making a <strong>Type I</strong> error, then we set <span class=\"math inline\">\\(\\alpha\\)</span> to a very small value.</li>\n",
    "<li><strong>Type II error</strong> - <strong>to not reject the null hypothesis when it is false</strong>. We cannot directly calculate the probability of this type of error, since it depends on the unknown parameter <span class=\"math inline\">\\(\\beta_i\\)</span>. However, we do know that by making <span class=\"math inline\">\\(\\alpha\\)</span> smaller we increase the probability of <strong>Type II</strong> error.</li>\n",
    "</ul>\n",
    "<p>It is believed that a <strong>Type I</strong> error is more severe, hence, it is recommended to make the probability <span class=\"math inline\">\\(\\alpha\\)</span> small.</p>\n",
    "</div>\n",
    "</div>\n",
    "\n",
    "\n",
    "### The <span class=\"math inline\">\\(p\\)</span>-value\n",
    "\n",
    "<p>When reporting the outcome of statistical hypothesis tests, we usually report the <span class=\"math inline\">\\(p\\)</span>-value of the test. The <span class=\"math inline\">\\(p\\)</span>-value is defined as the probability, under the null hypothesis, of obtaining a result, which is equal to, or more extreme, than what was actually observed.</p>\n",
    "<p>Having the <span class=\"math inline\">\\(p\\)</span>-value allows us to easier determine the outcome of the test, as we do not need to directly compare the critical values.</p>\n",
    "<div class=\"THEOREM\">\n",
    "<ul>\n",
    "<li>\n",
    "If <span class=\"math inline\"><span class=\"math inline\">\\(p \\leq \\alpha\\)</span></span>, we <strong>reject</strong> <span class=\"math inline\"><span class=\"math inline\">\\(H_0\\)</span></span>.\n",
    "</li>\n",
    "<li>\n",
    "If <span class=\"math inline\"><span class=\"math inline\">\\(p \\geq \\alpha\\)</span></span>, we <strong>do not reject</strong> <span class=\"math inline\"><span class=\"math inline\">\\(H_0\\)</span></span>.\n",
    "</li>\n",
    "</ul>\n",
    "</div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept     2.305164e-12\n",
       "MKT          1.962882e-105\n",
       "SMB           8.312035e-03\n",
       "HML           4.392977e-11\n",
       "RMW           7.052368e-02\n",
       "CMA           8.667348e-05\n",
       "dtype: float64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF5.pvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Goodness-Of-Fit\n",
    "\n",
    "<p>In order to have an accurate prediction of <span class=\"math inline\">\\(Y\\)</span>, we hope that the independent variable <span class=\"math inline\">\\(X\\)</span> helps us <em>explain</em> as much variation in <span class=\"math inline\">\\(Y\\)</span> as possible (hence why <span class=\"math inline\">\\(X\\)</span> is usually referred to as an <em>explanatory</em> variable). Ideally, the variance of <span class=\"math inline\">\\(X\\)</span> will help <em>explain</em> the variance in <span class=\"math inline\">\\(Y\\)</span>. Having said that, we would like to have a way to <strong>measure</strong> just how <em>good</em> our model is - how much of the variation in <span class=\"math inline\">\\(Y\\)</span> can be explained by the variation in <span class=\"math inline\">\\(X\\)</span> using our model - we need a <strong>goodness-of-fit</strong> measure.</p>\n",
    "<p>Another way to look at it is - a <strong>goodness-of-fit</strong> measure aims to quantify how well the estimated model <em>fits</em> the data. Fortunately, there are many ways to measure the goodness-of-fit of the estimated model.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R-squared, <span class=\"math inline\">\\(R^2\\)</span>\n",
    "\n",
    "\n",
    "<p>It is often useful to compute a number that summarizes how well the OLS regression fits the data. This measure is called the <strong>coefficient of determination</strong>, <span class=\"math inline\">\\(R^2\\)</span>, which is the ratio of explained variation, compared to the total variation, i.e. the proportion of variation in <span class=\"math inline\">\\(Y\\)</span> that is explained by <span class=\"math inline\">\\(X\\)</span> in our regression model:\n",
    "<span class=\"math display\">\\[\n",
    "R^2 = \\dfrac{\\text{ESS}}{\\text{TSS}} = 1 - \\dfrac{\\text{RSS}}{\\text{TSS}}\n",
    "\\]</span></p>\n",
    "<ul>\n",
    "<li>The closer <span class=\"math inline\">\\(R^2\\)</span> is to <span class=\"math inline\">\\(1\\)</span>, the closer the sample values of <span class=\"math inline\">\\(Y_i\\)</span> are to the fitted values <span class=\"math inline\">\\(\\widehat{Y}\\)</span> of our regression. Ir <span class=\"math inline\">\\(R^2 = 1\\)</span>, then all the sample data fall exactly on the fitted regression. In such a case our model would be a <em>perfect fit</em> for our data.</li>\n",
    "<li>If the sample data of <span class=\"math inline\">\\(Y\\)</span> and <span class=\"math inline\">\\(X\\)</span> do not have a linear relationship, then <span class=\"math inline\">\\(R^2 = 0\\)</span> of a univariate regression.</li>\n",
    "<li>Values <span class=\"math inline\">\\(0 &lt; R^2 &lt; 1\\)</span>, the interpretation of <span class=\"math inline\">\\(R^2\\)</span> is as <em>the proportion of the variation in <span class=\"math inline\">\\(Y\\)</span> around its mean, that is explained by the regression model</em>. For example <span class=\"math inline\">\\(R^2 = 0.17\\)</span> means that <span class=\"math inline\">\\(17\\%\\)</span> of the variation in <span class=\"math inline\">\\(Y\\)</span> is explained by <span class=\"math inline\">\\(X\\)</span>.</li>\n",
    "</ul>\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "When comparing <span class=\"math inline\"><span class=\"math inline\">\\(\\text{RSS}\\)</span></span> of different models, we want to choose the model, which better fits our data. If we want to choose a model based on its <span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> value we should note a couple of things:\n",
    "</p>\n",
    "<ul>\n",
    "<li>\n",
    "<p>\n",
    "<span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> comparison <strong>is not valid</strong> for comparing models, that <strong>do not have have the same transformation of the dependent variable</strong>, for example two models - one with <span class=\"math inline\"><span class=\"math inline\">\\(Y\\)</span></span> and the other with <span class=\"math inline\"><span class=\"math inline\">\\(\\log(Y)\\)</span></span> dependent variables cannot be compared via <span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span>.\n",
    "</p>\n",
    "</li>\n",
    "<li>\n",
    "<p>\n",
    "<span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> does not measure the predictability power of the model. For example, a linear model may be a good fit for the data, but its forecasts may not make economic sense (e.g. forecasting negative wage for low values of years in education via a simple linear model).\n",
    "</p>\n",
    "</li>\n",
    "<li>\n",
    "<p>\n",
    "<span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> is based on the sample data, so it says nothing whether our model is close to the true population DGP.\n",
    "</p>\n",
    "</li>\n",
    "<li>\n",
    "<p>\n",
    "<span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> may be low if: the error variance, <span class=\"math inline\"><span class=\"math inline\">\\(\\sigma^2\\)</span></span>, is large; or if the variance of <span class=\"math inline\"><span class=\"math inline\">\\(X\\)</span></span> is small.\n",
    "</p>\n",
    "</li>\n",
    "<li>\n",
    "<p>\n",
    "<span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> may be large even if the model is wrong. For example, even if the true relationship is non-linear, a linear model may have a larger <span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span>, compared to the quadratic, or even the log-linear model.\n",
    "</p>\n",
    "</li>\n",
    "<li>\n",
    "<p>\n",
    "On the other hand, <strong>the goodness-of-fit</strong> of the model does not depend on the unit of measurement of our variables (e.g. dollars vs thousands of dollars). Furthermore, comparisons of <span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> are valid, if we compare a simple linear model to a linear-log model, as they both have the same dependent variable, <span class=\"math inline\"><span class=\"math inline\">\\(Y\\)</span></span>.\n",
    "</p>\n",
    "</li>\n",
    "</ul>\n",
    "<p>\n",
    "In any case, a model should not be chosen <strong>only</strong> on the basis of model fit with <span class=\"math inline\"><span class=\"math inline\">\\(R^2\\)</span></span> as the criterion.\n",
    "</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6247845025614316"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF5.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6206971877745191"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF5.rsquared_adj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression Diagnostics and Graphics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In many cases while carrying out statistical/econometric analysis, we are not sure, whether we have correctly specified our model. As we have seen, the <span class=\"math inline\">\\(R^2\\)</span> can be artificially small (or large), regardless of the specified model. As such, there are a number of regression diagnostics and specification tests.</p>\n",
    "<p>For the univariate regression, the most crucial assumptions come from <strong>(UR.3)</strong> and <strong>(UR.4)</strong>, namely:</p>\n",
    "<ul>\n",
    "<li><span class=\"math inline\">\\(\\mathbb{V}{\\rm ar} (\\epsilon_i | \\mathbf{X} ) = \\sigma^2_\\epsilon,\\ \\forall i = 1,..,N\\)</span></li>\n",
    "<li><span class=\"math inline\">\\(\\mathbb{C}{\\rm ov} (\\epsilon_i, \\epsilon_j) = 0,\\ i \\neq j\\)</span></li>\n",
    "<li><span class=\"math inline\">\\(\\boldsymbol{\\varepsilon} | \\mathbf{X} \\sim \\mathcal{N} \\left( \\mathbf{0}, \\sigma^2_\\epsilon \\mathbf{I} \\right)\\)</span></li>\n",
    "</ul>\n",
    "<p>We note that the residuals are defined as:\n",
    "    \n",
    "    \n",
    "$\\begin{aligned}\n",
    "\\widehat{\\boldsymbol{\\varepsilon}} &= \\mathbf{Y} - \\widehat{\\mathbf{Y} } \\\\\n",
    "&= \\mathbf{Y} - \\mathbf{X} \\widehat{\\boldsymbol{\\beta}} \\\\\n",
    "&= \\mathbf{Y} - \\mathbf{X} \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\mathbf{Y} \\\\\n",
    "&= \\left[ \\mathbf{I} - \\mathbf{X} \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\right]\\mathbf{Y}\n",
    "\\end{aligned}$\n",
    "    \n",
    "   \n",
    "Hence, for the OLS <strong>residuals</strong> (i.e. not the true unobserved errors) the expected value of the residuals is still zero:\n",
    "\n",
    "\n",
    "$\\begin{aligned}\n",
    "\\mathbb{E} \\left( \\widehat{\\boldsymbol{\\varepsilon}}| \\mathbf{X} \\right) &=  \\mathbb{E} \\left( \\left[ \\mathbf{I} - \\mathbf{X} \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\right]\\mathbf{Y} | \\mathbf{X} \\right)\\\\\n",
    "&= \\mathbb{E} \\left( \\left[ \\mathbf{I} - \\mathbf{X} \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\right] \\left( \\mathbf{X} \\boldsymbol{\\beta} + \\boldsymbol{\\varepsilon} \\right) | \\mathbf{X} \\right) \\\\\n",
    "&= \\mathbf{X} \\boldsymbol{\\beta} + \\mathbb{E} (\\boldsymbol{\\varepsilon}) - \\mathbf{X} \\boldsymbol{\\beta} - \\mathbf{X} \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top \\mathbb{E} (\\boldsymbol{\\varepsilon}) \\\\\n",
    "&= 0\n",
    "\\end{aligned}$\n",
    "\n",
    "\n",
    "For simplicity, let $\\widehat{\\boldsymbol{\\varepsilon}} = \\left[ \\mathbf{I} - \\mathbf{H}\\right]\\mathbf{Y}$, where $\\mathbf{H}\\ = \\mathbf{X} \\left( \\mathbf{X}^\\top \\mathbf{X}\\right)^{-1} \\mathbf{X}^\\top$.</p>\n",
    "\n",
    "\n",
    "<p>Consequently, the variance-covariance matrix of the residuals is:</p>\n",
    "\n",
    "$\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\mathbb{V}{\\rm ar} \\left( \\widehat{\\boldsymbol{\\varepsilon}}| \\mathbf{X}\\right) &= \\mathbb{V}{\\rm ar} \\left( \\left[ \\mathbf{I} - \\mathbf{H}\\right]\\mathbf{Y}|\\mathbf{X}\\right) \\\\\n",
    "&= \\left[ \\mathbf{I} - \\mathbf{H}\\right]\\mathbb{V}{\\rm ar} \\left( \\mathbf{Y} | \\mathbf{X}\\right) \\left[ \\mathbf{I} - \\mathbf{H}\\right]^\\top \\\\\n",
    "&= \\left[ \\mathbf{I} - \\mathbf{H}\\right] \\sigma^2 \\left[ \\mathbf{I} - \\mathbf{H}\\right]^\\top \\\\\n",
    "&= \\sigma^2 \\left[ \\mathbf{I} - \\mathbf{H}^\\top - \\mathbf{H} + \\mathbf{H} \\mathbf{H}^\\top\\right] \\\\\n",
    "&= \\sigma^2 \\left[ \\mathbf{I} - \\mathbf{H}^\\top - \\mathbf{H} + \\mathbf{H}^\\top\\right] \\\\\n",
    "&= \\sigma^2 \\left[ \\mathbf{I} - \\mathbf{H}\\right]\n",
    "\\end{aligned}\n",
    "\\end{equation}$\n",
    "\n",
    "\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "This result shows an important distinction of the residuals from the errors - the residuals may have different variances (which are the diagonal elements of <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbb{V}{\\rm ar} \\left( \\widehat{\\boldsymbol{\\varepsilon}}| \\mathbf{X}\\right)\\)</span></span>), even if the true errors (which affect the process <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbf{Y}\\)</span></span>) all have the same variance <span class=\"math inline\"><span class=\"math inline\">\\(\\sigma^2\\)</span></span>.\n",
    "</p>\n",
    "</div>\n",
    "<p>The variance for the fitted values is smallest for observations near the mean and the largest for values, which deviate the most from the process mean.</p>\n",
    "\n",
    "\n",
    "### Residual Diagnostic Plots\n",
    "\n",
    "<p>One way to examine the adequacy of the model is to visualize the residuals. There are a number of ways to do this:</p>\n",
    "<ul>\n",
    "<li>Plotting the residuals <span class=\"math inline\">\\(\\widehat{\\epsilon}_i\\)</span> against the fitted values <span class=\"math inline\">\\(\\widehat{Y}_i\\)</span>;</li>\n",
    "<li>Plotting the residuals <span class=\"math inline\">\\(\\widehat{\\epsilon}_i\\)</span> against <span class=\"math inline\">\\(X_i\\)</span></li>\n",
    "<li>Plotting the residual Q-Q plot, histogram or boxplot.</li>\n",
    "</ul>\n",
    "<p>In all cases, if there are no violations of our <strong>(UR.2)</strong> or <strong>(UR.3)</strong> assumptions - the plots should reveal <strong>no patterns</strong>. The residual histogram, Q-Q plot should be approximately normal so that our assumption <strong>(UR.4)</strong> holds.</p>\n",
    "<p>As we are not guaranteed to specify a correct functional form, residual plots offer a great insight on what possible functional form we may have missed.</p>\n",
    "<p>We should note that when having multiple models, it is only meaningful to compare the residuals of models with the same dependent variable. For example, comparing the residuals of a linear-linear model (with <span class=\"math inline\">\\(Y\\)</span>) and of a log-linear model (with <span class=\"math inline\">\\(\\log(Y)\\)</span>) is <strong>not</strong> meaningful as they have different value scales.</p>\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "Transforming the dependent or the independent variables may help to alleviate some of the problems of the residuals:\n",
    "</p>\n",
    "<ul>\n",
    "<li>\n",
    "If nonlinearities are present in the residual plots - we must firstly account for them, and only after can we check, whether the errors have a constant variance.\n",
    "</li>\n",
    "<li>\n",
    "Transforming <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbf{Y}\\)</span></span> primarily aims to help with problems with the error terms (and may help with non-linearity);\n",
    "</li>\n",
    "<li>\n",
    "Transforming <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbf{X}\\)</span></span> primarily aims to help with correcting for non-linearity;\n",
    "</li>\n",
    "<li>\n",
    "Sometimes transforming <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbf{X}\\)</span></span> is enough to account for non-linearity and have normally distributed errors, while transforming <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbf{Y}\\)</span></span> may account for non-linearity but might make the errors non-normally distributed.\n",
    "</li>\n",
    "<li>\n",
    "Other times, transforming <span class=\"math inline\"><span class=\"math inline\">\\(\\mathbf{X}\\)</span></span> does not help account for the nonlinear relationship at all;\n",
    "</li>\n",
    "</ul>\n",
    "</div>\n",
    "<p>Remember that the Q-Q plot plots quantiles of the data versus quantiles of a distribution. If the observations come from a normal distribution we would expect the observed order statistics plotted against the expected (theoretical) order statistics to form an approximately straight line.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip uninstall statsmodels\n",
    "!pip install statsmodels\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "from matplotlib import pyplot as plt\n",
    "import scipy.stats as stats\n",
    "\n",
    "fig = sm.qqplot(FF5.resid.values, stats.t, distargs=(6,), fit=True, line=\"45\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residual Heteroskedasticity\n",
    "\n",
    "\n",
    "<p>If <span class=\"math inline\">\\(\\mathbb{V}{\\rm ar} (\\epsilon_i | \\mathbf{X} ) = \\sigma^2_\\epsilon,\\ \\forall i = 1,..,N\\)</span>, we say that the residuals are <strong>homoskedastic</strong>. If this assumption is violated, we say that the residuals are <strong>heteroskedastic</strong> - that is, their variance is not constant throughout observations.</p>\n",
    "<div class=\"THEOREM\">\n",
    "<p>\n",
    "The consequences of heteroskedasticity are as follows:\n",
    "</p>\n",
    "<ul>\n",
    "<li>\n",
    "OLS parameters remain <strong>unbiased</strong>;\n",
    "</li>\n",
    "<li>\n",
    "OLS estimates are no longer efficient (i.e. they no longer have the smallest variance). The reason for this is that OLS gives equal weight to all observations in the data, when in fact, observation with larger error variance contain less information, compared to observations with smaller error variance;\n",
    "</li>\n",
    "<li>\n",
    "The variance estimate of the residuals <strong>is biased</strong>, and hence the standard errors are <strong>biased</strong>. This in turn leads to a bias in test statistics and confidence intervals.\n",
    "</li>\n",
    "<li>\n",
    "Because of standard error bias, we may fail to reject the null hypothesis whether <span class=\"math inline\"><span class=\"math inline\">\\(\\beta_i = 0\\)</span></span> in our estimated model, when the null hypothesis is actually false (i.e. making a Type II error).\n",
    "</li>\n",
    "</ul>\n",
    "<p>\n",
    "There are a few possible corrections to account for heteroskedasticity:\n",
    "</p>\n",
    "<ul>\n",
    "<li>\n",
    "Take logarithms of the data, this may be able to help <strong>linearize</strong> the data and in turn, the residuals;\n",
    "</li>\n",
    "<li>\n",
    "Apply a different estimation method. We will examine this later on, but one possibility is to use a <strong>Weighted Least Squares</strong> estimation method, which gives different observations different weights and allows to account for a non-constant variance;\n",
    "</li>\n",
    "<li>\n",
    "It is possible to correct the the biased standard errors for heteroskedasticity. This would leave the OLS estimates unchanged. <a href=\"https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors\">White’s heteroskedasticity-consistent standard errors</a> (or, robust standard errors) give a consistent variance estimator.\n",
    "</li>\n",
    "</ul>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>There are a number of methods to test for the presence of heteroskedasticity. Some of the tests are:</p>\n",
    "<ul>\n",
    "<li><strong>Goldfeld–Quandt Test</strong>. It divides the dataset into two subsets. The subsets are specified so that the observations for which the explanatory variable takes the lowest values are in one subset, and the highest values - in the other subset. The subsets are not necessarily of equal size, nor do they contain all the observations between them. The test statistic used is the ratio of the mean square residual errors for the regressions on the two subsets. This test statistic corresponds to an F-test of equality of variances. The Goldfeld–Quandt test requires that data be <strong>ordered</strong> along a known explanatory variable, from lowest to highest.</li>\n",
    "</ul>\n",
    "<p>If the error structure depends on an unknown variable or an unobserved variable the Goldfeld–Quandt test provides little guidance. Also, error variance must be a monotonic function of the specified explanatory variable. For example, when faced with a quadratic function mapping the explanatory variable to error variance the Goldfeld–Quandt test may improperly accept the null hypothesis of homoskedastic errors.</p>\n",
    "<p>Unfortunately the Goldfeld–Quandt test is not very robust to specification errors. The Goldfeld–Quandt test detects non-homoskedastic errors but cannot distinguish between heteroskedastic error structure and an underlying specification problem such as an incorrect functional form or an omitted variable.</p>\n",
    "<ul>\n",
    "<li><p><strong>Breusch–Pagan Test</strong>. After estimating the linear regression <span class=\"math inline\">\\(Y = \\beta_0 + \\beta_1 X + \\epsilon\\)</span>, calculate the model residuals <span class=\"math inline\">\\(\\widehat{\\epsilon}_i\\)</span>. The OLS assumptions state that the residual variance does not depend on the independent variables <span class=\"math inline\">\\(\\mathbb{V}{\\rm ar} (\\epsilon_i | \\mathbf{X} ) = \\sigma^2_\\epsilon\\)</span>. If this assumptions is not true, then there may be a linear relationship between <span class=\"math inline\">\\(\\widehat{\\epsilon}_i^2\\)</span> and <span class=\"math inline\">\\(X_i\\)</span>. So, the Breush-Pagan test is the based on the following regression:\n",
    "<span class=\"math display\">\\[\n",
    "\\widehat{\\epsilon}_i^2 = \\gamma_0 + \\gamma_1 X_i + v_i\n",
    "\\]</span>\n",
    "The hypothesis tests is:\n",
    "\n",
    "$\\begin{aligned}\n",
    "H_0&: \\gamma_1 = 0 \\text{ (residuals are homoskedastic)}\\\\\n",
    "H_1&: \\gamma_1 \\neq 0 \\text{ (residuals are heteroskedastic)}\n",
    "\\end{aligned}$\n",
    "\n",
    "It is a chi-squared test, where the test statistic:\n",
    "$\n",
    "LM = N \\cdot R^2_{\\widehat{\\epsilon}}\n",
    "$\n",
    "is distributed as $\\chi^2_1$ under the null. Here $R^2_{\\widehat{\\epsilon}}$is the R-square of the squared residual regression. One weakness of the BP test is that it assumes that the heteroskedasticity is a <strong>linear</strong> relationship of the independent variables. If we fail to reject the null hypothesis, we still do not rule out the possibility of a non-linear relationship between the independent variables and the error variance.</p></li>\n",
    "<li><p><strong>White Test</strong> is more generic than the BP test as it allows the independent variables to have a nonlinear effect on the error variance. For example, a combination of linear, quadratic and cross-products of the independent variables. It is a more commonly used test for homoskedasticity. The test statistic is calculated the same way as in <strong>BP</strong> test:\n",
    "<span class=\"math display\">\\[\n",
    "LM = N \\cdot R^2_{\\widehat{\\epsilon}}\n",
    "\\]</span>\n",
    "the difference from <strong>BP</strong> is that the squared residual model, from which we calculate <span class=\"math inline\">\\(R^2_{\\widehat{\\epsilon}}\\)</span>, may be nonlinear. A shortcoming of the White test is that it can lose its power if the model has many exogenous variables.</p></li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(94.90890408824038,\n",
       " 1.9935113331602095e-22,\n",
       " 118.79970601959461,\n",
       " 8.966508040873986e-25)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.stats.diagnostic as sm_diagnostic\n",
    "\n",
    "# Breusch–Pagan Test\n",
    "sm_diagnostic.het_breuschpagan(resid = FF5.resid.values, exog_het = sm.add_constant(FF5.resid.values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(464.0, 1.7525894717410334e-101, 1.0104392007997422e+29, 0.0)\n"
     ]
    }
   ],
   "source": [
    "# White Test\n",
    "print(sm_diagnostic.het_white(resid = FF5.resid.values, exog = sm.add_constant(FF5.resid.values)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residual Autocorrelation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>If <span class=\"math inline\">\\(\\mathbb{C}{\\rm ov} (\\epsilon_i, \\epsilon_j) \\neq 0\\)</span> for some <span class=\"math inline\">\\(i \\neq j\\)</span>, then the errors are correlated. Autocorrelation is frequently encountered in time-series models.</p>\n",
    "\n",
    "<br>\n",
    "Assume that our model is defined as follows:\n",
    "</div>\n",
    "\n",
    "<p><span class=\"math display\">\\[\n",
    "\\begin{aligned}\n",
    "Y_t = \\beta_0 + \\beta_1 X_t + \\epsilon_t \\\\\n",
    "\\epsilon_t = \\rho \\epsilon_{t-1} + u_t,\\ |\\rho| &< 1,\\ u_t \\sim \\mathcal{N}(0, \\sigma^2)\n",
    "\\end{aligned}\n",
    "\\]</span>\n",
    "Then we say that the model has <strong>autocorrelated</strong>, or <strong>serially correlated</strong> errors.</p>\n",
    "<p>In this case, we have that:\n",
    "<span class=\"math display\">\\[\n",
    "\\mathbb{C}{\\rm ov}(\\epsilon_t, \\epsilon_{t-1}) = \\mathbb{C}{\\rm ov}(\\rho \\epsilon_{t-1} + u_t, \\epsilon_{t-1}) = \\rho \\mathbb{C}{\\rm ov}(\\epsilon_{t-1},\\epsilon_{t-1}) = \\rho \\sigma^2 \\neq 0\n",
    "\\]</span>\n",
    "Estimating the coefficients via OLS and ignoring the violation will still result in unbiased and consistent OLS estimators. However, the estimators are inefficient and the variance of the regression coefficients will be <strong>biased</strong>.</p>\n",
    "<p>On the other hand, autocorrelation in errors may be a result of a misspecified model.</p>\n",
    "\n",
    "\n",
    "<p>There are a number of tests for the presence of autocorrelation:</p>\n",
    "<ul>\n",
    "<li><p><strong>Durbin–Watson Test</strong> for the hypothesis:\n",
    "<span class=\"math display\">\\[\n",
    "\\begin{aligned}\n",
    "H_0&:\\text{the errors are serially uncorrelated}\\\\\n",
    "H_1&:\\text{the errors follow a first order autoregressive process (i.e. autocorrelation at lag 1)}\n",
    "\\end{aligned}\n",
    "\\]</span>\n",
    "The test statistic:\n",
    "<span class=\"math display\">\\[\n",
    "d = \\dfrac{\\sum_{i = 2}^N (\\widehat{\\epsilon}_i - \\widehat{\\epsilon}_{i-1})^2}{\\sum_{i = 1}^N \\widehat{\\epsilon}_i^2}\n",
    "\\]</span>\n",
    "The value of <span class=\"math inline\">\\(d\\)</span> always lies between 0 and 4. <span class=\"math inline\">\\(d = 2\\)</span> indicates no autocorrelation. If the Durbin–Watson statistic is not close to 2, there is evidence of a serial correlation.</p></li>\n",
    "<li><p><strong>Breusch-Godfrey Test</strong> is a more flexible test, covering autocorrelation of higher orders and applicable whether or not the regressors include lags of the dependent variable. Consider the following linear regression:\n",
    "<span class=\"math display\">\\[\n",
    "Y_i = \\beta_0 + \\beta_1 X_i + \\epsilon_i\n",
    "\\]</span>\n",
    "We then estimate the model via OLS and fit the following model on the residuals <span class=\"math inline\">\\(\\widehat{\\epsilon}_i\\)</span>:\n",
    "<span class=\"math display\">\\[\n",
    "\\widehat{\\epsilon}_i = \\alpha_0 + \\alpha_1 X_i + \\rho_1 \\widehat{\\epsilon}_{i - 1} + \\rho_2 \\widehat{\\epsilon}_{i - 2} + ... + \\rho_p \\widehat{\\epsilon}_{i - p} + u_t\n",
    "\\]</span>\n",
    "and calculate its <span class=\"math inline\">\\(R^2\\)</span> (R-squared), then testing the hypothesis:\n",
    "<span class=\"math display\">\\[\n",
    "\\begin{aligned}\n",
    "H_0&:\\rho_1 = \\rho_2 = ... = \\rho_p = 0\\\\\n",
    "H_1&:\\rho_j \\neq 0 \\text{ for some } j\n",
    "\\end{aligned}\n",
    "\\]</span>\n",
    "Under the null hypothesis the test statistic:\n",
    "<span class=\"math display\">\\[\n",
    "LM = (N-p)R^2 \\sim \\chi^2_p\n",
    "\\]</span></p></li>\n",
    "</ul>\n",
    "\n",
    "Note There is also the Ljung-Box Test for testing the null hypothesis of no autocorrelation of residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8783699845436945\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.stattools import durbin_watson\n",
    "# Durbin–Watson Test\n",
    "print(durbin_watson(FF5.resid.values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2.889760555209726, 0.2357743023303879, 1.454856925216001, 0.23451519609285382)\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.diagnostic import acorr_breusch_godfrey\n",
    "# Breusch-Godfrey Test\n",
    "print(acorr_breusch_godfrey(FF5, nlags = 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residual Normality Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The normality requirement is necessary if we want to obtain the correct <span class=\"math inline\">\\(p\\)</span>-values and critical <span class=\"math inline\">\\(t\\)</span>-values when testing the hypothesis that <span class=\"math inline\">\\(H_0: \\beta_j = c\\)</span>, especially for significance testing, with <span class=\"math inline\">\\(c = 0\\)</span>. Assume that we want to test whether our residuals <span class=\"math inline\">\\(z_1,...,z_N\\)</span> come from a normal distribution. The hypothesis can be stated as:\n",
    "<span class=\"math display\">\\[\n",
    "\\begin{aligned}\n",
    "H_0:\\text{residuals follow a normal distribution}\\\\\n",
    "H_1:\\text{residuals do not follow a normal distribution}\n",
    "\\end{aligned}\n",
    "\\]</span></p>\n",
    "<p>There are a number of normality tests, like:</p>\n",
    "<ul>\n",
    "<li><p><strong>Anderson-Darling Test</strong>. The test statistic is calculated as:\n",
    "<span class=\"math display\">\\[\n",
    "A^2 = -N - \\sum_{i 1}^N \\dfrac{2i-1}{N}\\left[ \\log(F(z_{(i)}) + \\log\\left(1 - F(z_{(N+1-i)}) \\right)\\right]\n",
    "\\]</span>\n",
    "where <span class=\"math inline\">\\(z_{(i)}\\)</span> are the <strong>ordered data</strong> and <span class=\"math inline\">\\(F(\\cdot)\\)</span> is the cumulative distribution function (cdf) of the distribution being tested (for the univariate regression residuals - we are usually interested in testing for the normal distribution). The test statistic is compared against the critical values from the normal distribution. <a href=\"https://web.archive.org/web/20150630110326/http://instatmy.org.my/downloads/e-jurnal%202/3.pdf\">Empirical testing indicates</a> that the Anderson–Darling test is not quite as good as Shapiro-Wilk, but is better than other tests.</p></li>\n",
    "\n",
    "<br>\n",
    "<li><p><strong>Shapiro-Wilk Test</strong>. The test statistic is:\n",
    "<span class=\"math display\">\\[\n",
    "W = \\dfrac{\\left(\\sum_{i = 1}^N a_i z_{(i)} \\right)^2}{\\sum_{i = 1}^N (z_i - \\overline{z})^2}\n",
    "\\]</span>\n",
    "where <span class=\"math inline\">\\(z_{(i)}\\)</span> is the <span class=\"math inline\">\\(i\\)</span>-th <strong>smallest value in the sample</strong> (i.e. the data are ordered). <span class=\"math inline\">\\(a_i\\)</span> values are calculated using means, variances and covariances of <span class=\"math inline\">\\(z_{(i)}\\)</span>. <span class=\"math inline\">\\(W\\)</span> is compared against tabulated values of this statistic’s distribution. Small values of <span class=\"math inline\">\\(W\\)</span> will lead to the rejection of the null hypothesis. Monte Carlo simulation has found that Shapiro–Wilk has the best power for a given significance, followed closely by Anderson–Darling when comparing the Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests.</p></li>\n",
    "\n",
    "<br>\n",
    "<li><p><strong>Kolmogorov-Smirnov Test</strong>. The test statistic is given by:\n",
    "<span class=\"math display\">\\[\n",
    "D = \\max\\{ D^+; D^-\\}\n",
    "\\]</span>\n",
    "where:\n",
    "<span class=\"math display\">\\[\n",
    "\\begin{aligned}\n",
    "D^+ = \\max_i \\left( \\dfrac{i}{N} - F(z_{(i)})\\right)\\\\\n",
    "D^- = \\max_i \\left( F(z_{(i)}) - \\dfrac{i - 1}{N} \\right)\n",
    "\\end{aligned}\n",
    "\\]</span>\n",
    "where <span class=\"math inline\">\\(F(\\cdot)\\)</span> is the theoretical cdf of the distribution being tested (for the univariate regression residuals - we are usually interested in testing for the normal distribution). The <strong>Lilliefors Test</strong> is based on the Komogorov-Smirnov Test as a special case of this for the normal distribution.. For the normal distribution case, the test statistic is compared against the critical values from a normal distribution in order to determine the <span class=\"math inline\">\\(p\\)</span>-value.</p></li>\n",
    "\n",
    "<br>\n",
    "<li><p><strong>Cramer–von Mises Test</strong> is an alternative to the Kolmogorov–Smirnov test. The test statistic:\n",
    "<span class=\"math display\">\\[\n",
    "W = N\\omega^2 = \\dfrac{1}{12N} + \\sum_{i = 1}^N \\left[ \\dfrac{2i-1}{2N} - F(z_{(i)}) \\right]^2\n",
    "\\]</span>\n",
    "If this value is larger than the tabulated value, then the hypothesis that the data came from the distribution <span class=\"math inline\">\\(F\\)</span> can be rejected.</p></li>\n",
    "\n",
    "<br>\n",
    "<li><p><strong>Jarque–Bera Test</strong> (valid for large samples). The statistic is calculated as:\n",
    "<span class=\"math display\">\\[\n",
    "JB = \\dfrac{N-k+1}{6} \\left(S^2 + \\dfrac{(C - 3)^2}{4}\\right)\n",
    "\\]</span>\n",
    "where\n",
    "<span class=\"math display\">\\[\n",
    "\\begin{aligned}\n",
    "S = \\dfrac{\\dfrac{1}{N}\\sum_{i = 1}^N (z_i - \\overline{z})^3}{\\left( \\dfrac{1}{N}\\sum_{i = 1}^N (z_i - \\overline{z})^2 \\right)^{3/2}}= \\dfrac{\\widehat{\\mu}_3}{\\widehat{\\sigma}^3}\\\\\n",
    "C = \\dfrac{\\dfrac{1}{N}\\sum_{i = 1}^N (z_i - \\overline{z})^4}{\\left( \\dfrac{1}{N}\\sum_{i = 1}^N (z_i - \\overline{z})^2 \\right)^{2}} = \\dfrac{\\widehat{\\mu}_4}{\\widehat{\\sigma}^4}\\\\\n",
    "\\end{aligned}\n",
    "\\]</span>\n",
    "<span class=\"math inline\">\\(N\\)</span> is the sample size, <span class=\"math inline\">\\(S\\)</span> is the skewness and <span class=\"math inline\">\\(C\\)</span> is kurtosis and <span class=\"math inline\">\\(k\\)</span> is the number of regressors (i.e. the number of different independent variables <span class=\"math inline\">\\(X\\)</span>, with <span class=\"math inline\">\\(k = 1\\)</span> outside a regression context). <br> If the data comes from a normal distribution, then the <span class=\"math inline\">\\(JB\\)</span> statistic has a chi-squared distribution with <strong>two degrees of freedom</strong>, <span class=\"math inline\">\\(\\chi^2_2\\)</span>.</p></li>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7075.5627332582235, 0.0, -2.0568441457575295, 21.68301237474802)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.stattools import jarque_bera\n",
    "jarque_bera(FF5.resid.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standardized Residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When we compare residuals for different observations, we want to take into account that their variances may be different. One way to account for this is to divide the residuals by an estimate the <strong>residuals standard deviation</strong>. This results in calculating the <strong>standardized</strong> residuals:\n",
    "<span class=\"math display\">\\[\n",
    "s_i = \\dfrac{\\widehat{\\epsilon_i}}{\\widehat{\\sigma}\\sqrt{1 - h_{ii}}}\n",
    "\\]</span>\n",
    "where <span class=\"math inline\">\\(h_{ii}\\)</span> is the <span class=\"math inline\">\\(i\\)</span>-th diagonal element of <span class=\"math inline\">\\(\\mathbf{H}\\)</span>. Standardized residuals are useful in detecting outliers. Generally, any observation with a standardized residual greater than 2 in absolute value should be examined more closely.</p>"
   ]
  }
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