5. Analyzing returns using the AR Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the relevant packages\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.graphics.tsaplots as sgt\n",
    "from statsmodels.tsa.arima_model import ARMA\n",
    "from scipy.stats.distributions import chi2\n",
    "import statsmodels.tsa.stattools as sts \n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the Data and Pre-processing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_csv_data = pd.read_csv(\"Index2018.csv\") \n",
    "df_comp=raw_csv_data.copy()\n",
    "df_comp.date = pd.to_datetime(df_comp.date, dayfirst = True)\n",
    "df_comp.set_index(\"date\", inplace=True)\n",
    "df_comp=df_comp.asfreq('b')\n",
    "df_comp=df_comp.fillna(method='ffill')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_comp['market_value']=df_comp.ftse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "del df_comp['spx']\n",
    "del df_comp['dax']\n",
    "del df_comp['ftse']\n",
    "del df_comp['nikkei']\n",
    "size = int(len(df_comp)*0.8)\n",
    "df, df_test = df_comp.iloc[:size], df_comp.iloc[size:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LLR Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LLR_test(mod_1, mod_2, DF=1):\n",
    "    L1 = mod_1.fit().llf\n",
    "    L2 = mod_2.fit().llf\n",
    "    LR = (2*(L2-L1))\n",
    "    p = chi2.sf(LR, DF).round(3)\n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The DF-Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.9041551418836873,\n",
       " 0.330108932770283,\n",
       " 6,\n",
       " 5014,\n",
       " {'1%': -3.4316548765428174,\n",
       "  '5%': -2.8621166146845334,\n",
       "  '10%': -2.5670769326348926},\n",
       " 54854.15304507557)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sts.adfuller(df.market_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['returns'] = df.market_value.pct_change(1).mul(100)\n",
    "df = df.iloc[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-12.7702657194972,\n",
       " 7.79805833603984e-24,\n",
       " 32,\n",
       " 4987,\n",
       " {'1%': -3.431661944885779,\n",
       "  '5%': -2.8621197374408225,\n",
       "  '10%': -2.5670785949998973},\n",
       " 15696.7672456975)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sts.adfuller(df.returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ACF and PACF for Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "sgt.plot_acf(df.returns, lags=40, zero = False)\n",
    "plt.title(\"ACF FTSE Returns\", size=24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "sgt.plot_pacf(df.returns, lags = 40, zero = False, method = ('ols'))\n",
    "plt.title(\"PACF FTSE Returns\", size=24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## AR(1) for Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_ret_ar_1 = ARMA(df.returns, order = (1,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "results_ret_ar_1 = model_ret_ar_1.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(1, 0)</td>    <th>  Log Likelihood     </th> <td>-7929.749</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.174</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 05 Sep 2019</td> <th>  AIC                </th> <td>15865.497</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:14:38</td>     <th>  BIC                </th> <td>15885.061</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15872.353</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0188</td> <td>    0.016</td> <td>    1.159</td> <td> 0.247</td> <td>   -0.013</td> <td>    0.051</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.0230</td> <td>    0.014</td> <td>   -1.631</td> <td> 0.103</td> <td>   -0.051</td> <td>    0.005</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>         -43.4386</td> <td>          +0.0000j</td> <td>          43.4386</td> <td>           0.5000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(1, 0)   Log Likelihood               -7929.749\n",
       "Method:                       css-mle   S.D. of innovations              1.174\n",
       "Date:                Thu, 05 Sep 2019   AIC                          15865.497\n",
       "Time:                        10:14:38   BIC                          15885.061\n",
       "Sample:                    01-10-1994   HQIC                         15872.353\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0188      0.016      1.159      0.247      -0.013       0.051\n",
       "ar.L1.returns    -0.0230      0.014     -1.631      0.103      -0.051       0.005\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1          -43.4386           +0.0000j           43.4386            0.5000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_ret_ar_1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Higher-Lag AR Models for Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(2, 0)</td>    <th>  Log Likelihood     </th> <td>-7923.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.173</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 05 Sep 2019</td> <th>  AIC                </th> <td>15854.911</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:14:39</td>     <th>  BIC                </th> <td>15880.996</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15864.052</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0188</td> <td>    0.015</td> <td>    1.220</td> <td> 0.222</td> <td>   -0.011</td> <td>    0.049</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.0242</td> <td>    0.014</td> <td>   -1.716</td> <td> 0.086</td> <td>   -0.052</td> <td>    0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.0500</td> <td>    0.014</td> <td>   -3.550</td> <td> 0.000</td> <td>   -0.078</td> <td>   -0.022</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -0.2417</td> <td>          -4.4635j</td> <td>           4.4701</td> <td>          -0.2586</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -0.2417</td> <td>          +4.4635j</td> <td>           4.4701</td> <td>           0.2586</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(2, 0)   Log Likelihood               -7923.456\n",
       "Method:                       css-mle   S.D. of innovations              1.173\n",
       "Date:                Thu, 05 Sep 2019   AIC                          15854.911\n",
       "Time:                        10:14:39   BIC                          15880.996\n",
       "Sample:                    01-10-1994   HQIC                         15864.052\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0188      0.015      1.220      0.222      -0.011       0.049\n",
       "ar.L1.returns    -0.0242      0.014     -1.716      0.086      -0.052       0.003\n",
       "ar.L2.returns    -0.0500      0.014     -3.550      0.000      -0.078      -0.022\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -0.2417           -4.4635j            4.4701           -0.2586\n",
       "AR.2           -0.2417           +4.4635j            4.4701            0.2586\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_2 = ARMA(df.returns, order = (2,0))\n",
    "results_ret_ar_2 = model_ret_ar_2.fit()\n",
    "results_ret_ar_2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LLR_test(model_ret_ar_1, model_ret_ar_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(3, 0)</td>    <th>  Log Likelihood     </th> <td>-7906.738</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.169</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 05 Sep 2019</td> <th>  AIC                </th> <td>15823.477</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:14:39</td>     <th>  BIC                </th> <td>15856.083</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15834.902</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.330</td> <td> 0.184</td> <td>   -0.009</td> <td>    0.047</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.0283</td> <td>    0.014</td> <td>   -2.011</td> <td> 0.044</td> <td>   -0.056</td> <td>   -0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.0521</td> <td>    0.014</td> <td>   -3.705</td> <td> 0.000</td> <td>   -0.080</td> <td>   -0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.returns</th> <td>   -0.0815</td> <td>    0.014</td> <td>   -5.792</td> <td> 0.000</td> <td>   -0.109</td> <td>   -0.054</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           0.9233</td> <td>          -2.0210j</td> <td>           2.2219</td> <td>          -0.1818</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>           0.9233</td> <td>          +2.0210j</td> <td>           2.2219</td> <td>           0.1818</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>          -2.4855</td> <td>          -0.0000j</td> <td>           2.4855</td> <td>          -0.5000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(3, 0)   Log Likelihood               -7906.738\n",
       "Method:                       css-mle   S.D. of innovations              1.169\n",
       "Date:                Thu, 05 Sep 2019   AIC                          15823.477\n",
       "Time:                        10:14:39   BIC                          15856.083\n",
       "Sample:                    01-10-1994   HQIC                         15834.902\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.014      1.330      0.184      -0.009       0.047\n",
       "ar.L1.returns    -0.0283      0.014     -2.011      0.044      -0.056      -0.001\n",
       "ar.L2.returns    -0.0521      0.014     -3.705      0.000      -0.080      -0.025\n",
       "ar.L3.returns    -0.0815      0.014     -5.792      0.000      -0.109      -0.054\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            0.9233           -2.0210j            2.2219           -0.1818\n",
       "AR.2            0.9233           +2.0210j            2.2219            0.1818\n",
       "AR.3           -2.4855           -0.0000j            2.4855           -0.5000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_3 = ARMA(df.returns, order = (3,0))\n",
    "results_ret_ar_3 = model_ret_ar_3.fit()\n",
    "results_ret_ar_3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LLR_test(model_ret_ar_2, model_ret_ar_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                              ARMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                returns   No. Observations:                 5020\n",
      "Model:                     ARMA(4, 0)   Log Likelihood               -7901.330\n",
      "Method:                       css-mle   S.D. of innovations              1.168\n",
      "Date:                Thu, 05 Sep 2019   AIC                          15814.661\n",
      "Time:                        10:14:40   BIC                          15853.788\n",
      "Sample:                    01-10-1994   HQIC                         15828.371\n",
      "                         - 04-05-2013                                         \n",
      "=================================================================================\n",
      "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "const             0.0188      0.015      1.267      0.205      -0.010       0.048\n",
      "ar.L1.returns    -0.0245      0.014     -1.739      0.082      -0.052       0.003\n",
      "ar.L2.returns    -0.0496      0.014     -3.531      0.000      -0.077      -0.022\n",
      "ar.L3.returns    -0.0802      0.014     -5.701      0.000      -0.108      -0.053\n",
      "ar.L4.returns     0.0464      0.014      3.291      0.001       0.019       0.074\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1           -1.8888           -0.0000j            1.8888           -0.5000\n",
      "AR.2            0.3231           -1.9331j            1.9599           -0.2236\n",
      "AR.3            0.3231           +1.9331j            1.9599            0.2236\n",
      "AR.4            2.9701           -0.0000j            2.9701           -0.0000\n",
      "-----------------------------------------------------------------------------\n",
      "LLR test: 0.001\n"
     ]
    }
   ],
   "source": [
    "model_ret_ar_4 = ARMA(df.returns, order = (4,0))\n",
    "results_ret_ar_4 = model_ret_ar_4.fit()\n",
    "print(results_ret_ar_4.summary())\n",
    "print (\"LLR test: \" + str(LLR_test(model_ret_ar_3, model_ret_ar_4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                              ARMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                returns   No. Observations:                 5020\n",
      "Model:                     ARMA(5, 0)   Log Likelihood               -7892.390\n",
      "Method:                       css-mle   S.D. of innovations              1.166\n",
      "Date:                Thu, 05 Sep 2019   AIC                          15798.779\n",
      "Time:                        10:14:42   BIC                          15844.428\n",
      "Sample:                    01-10-1994   HQIC                         15814.775\n",
      "                         - 04-05-2013                                         \n",
      "=================================================================================\n",
      "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "const             0.0189      0.014      1.348      0.178      -0.009       0.046\n",
      "ar.L1.returns    -0.0217      0.014     -1.544      0.123      -0.049       0.006\n",
      "ar.L2.returns    -0.0544      0.014     -3.865      0.000      -0.082      -0.027\n",
      "ar.L3.returns    -0.0831      0.014     -5.914      0.000      -0.111      -0.056\n",
      "ar.L4.returns     0.0449      0.014      3.190      0.001       0.017       0.073\n",
      "ar.L5.returns    -0.0596      0.014     -4.232      0.000      -0.087      -0.032\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1           -1.5481           -0.0000j            1.5481           -0.5000\n",
      "AR.2           -0.2860           -1.7252j            1.7487           -0.2761\n",
      "AR.3           -0.2860           +1.7252j            1.7487            0.2761\n",
      "AR.4            1.4366           -1.2157j            1.8819           -0.1118\n",
      "AR.5            1.4366           +1.2157j            1.8819            0.1118\n",
      "-----------------------------------------------------------------------------\n",
      "LLR test: 0.0\n"
     ]
    }
   ],
   "source": [
    "model_ret_ar_5 = ARMA(df.returns, order = (5,0))\n",
    "results_ret_ar_5 = model_ret_ar_5.fit()\n",
    "print(results_ret_ar_5.summary())\n",
    "print (\"LLR test: \" + str(LLR_test(model_ret_ar_4, model_ret_ar_5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                              ARMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                returns   No. Observations:                 5020\n",
      "Model:                     ARMA(6, 0)   Log Likelihood               -7886.945\n",
      "Method:                       css-mle   S.D. of innovations              1.164\n",
      "Date:                Thu, 05 Sep 2019   AIC                          15789.890\n",
      "Time:                        10:14:44   BIC                          15842.059\n",
      "Sample:                    01-10-1994   HQIC                         15808.170\n",
      "                         - 04-05-2013                                         \n",
      "=================================================================================\n",
      "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "const             0.0189      0.013      1.414      0.157      -0.007       0.045\n",
      "ar.L1.returns    -0.0245      0.014     -1.740      0.082      -0.052       0.003\n",
      "ar.L2.returns    -0.0523      0.014     -3.716      0.000      -0.080      -0.025\n",
      "ar.L3.returns    -0.0870      0.014     -6.174      0.000      -0.115      -0.059\n",
      "ar.L4.returns     0.0424      0.014      3.009      0.003       0.015       0.070\n",
      "ar.L5.returns    -0.0607      0.014     -4.309      0.000      -0.088      -0.033\n",
      "ar.L6.returns    -0.0466      0.014     -3.302      0.001      -0.074      -0.019\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1            1.2869           -0.9022j            1.5716           -0.0973\n",
      "AR.2            1.2869           +0.9022j            1.5716            0.0973\n",
      "AR.3           -0.0727           -1.5282j            1.5299           -0.2576\n",
      "AR.4           -0.0727           +1.5282j            1.5299            0.2576\n",
      "AR.5           -1.8659           -0.4836j            1.9275           -0.4596\n",
      "AR.6           -1.8659           +0.4836j            1.9275            0.4596\n",
      "-----------------------------------------------------------------------------\n",
      "LLR test: 0.001\n"
     ]
    }
   ],
   "source": [
    "model_ret_ar_6 = ARMA(df.returns, order = (6,0))\n",
    "results_ret_ar_6 = model_ret_ar_6.fit()\n",
    "print(results_ret_ar_6.summary())\n",
    "print (\"LLR test: \" + str(LLR_test(model_ret_ar_5, model_ret_ar_6)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(7, 0)</td>    <th>  Log Likelihood     </th> <td>-7886.647</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.164</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 05 Sep 2019</td> <th>  AIC                </th> <td>15791.294</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:14:47</td>     <th>  BIC                </th> <td>15849.985</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15811.860</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.399</td> <td> 0.162</td> <td>   -0.008</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.0240</td> <td>    0.014</td> <td>   -1.702</td> <td> 0.089</td> <td>   -0.052</td> <td>    0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.0517</td> <td>    0.014</td> <td>   -3.663</td> <td> 0.000</td> <td>   -0.079</td> <td>   -0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.returns</th> <td>   -0.0874</td> <td>    0.014</td> <td>   -6.202</td> <td> 0.000</td> <td>   -0.115</td> <td>   -0.060</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.returns</th> <td>    0.0433</td> <td>    0.014</td> <td>    3.064</td> <td> 0.002</td> <td>    0.016</td> <td>    0.071</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.returns</th> <td>   -0.0601</td> <td>    0.014</td> <td>   -4.263</td> <td> 0.000</td> <td>   -0.088</td> <td>   -0.032</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L6.returns</th> <td>   -0.0463</td> <td>    0.014</td> <td>   -3.282</td> <td> 0.001</td> <td>   -0.074</td> <td>   -0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L7.returns</th> <td>    0.0109</td> <td>    0.014</td> <td>    0.772</td> <td> 0.440</td> <td>   -0.017</td> <td>    0.039</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -1.6490</td> <td>          -0.5384j</td> <td>           1.7347</td> <td>          -0.4498</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -1.6490</td> <td>          +0.5384j</td> <td>           1.7347</td> <td>           0.4498</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>          -0.1189</td> <td>          -1.4954j</td> <td>           1.5001</td> <td>          -0.2626</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th> <td>          -0.1189</td> <td>          +1.4954j</td> <td>           1.5001</td> <td>           0.2626</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th> <td>           1.2790</td> <td>          -0.9786j</td> <td>           1.6105</td> <td>          -0.1039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.6</th> <td>           1.2790</td> <td>          +0.9786j</td> <td>           1.6105</td> <td>           0.1039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.7</th> <td>           5.2269</td> <td>          -0.0000j</td> <td>           5.2269</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(7, 0)   Log Likelihood               -7886.647\n",
       "Method:                       css-mle   S.D. of innovations              1.164\n",
       "Date:                Thu, 05 Sep 2019   AIC                          15791.294\n",
       "Time:                        10:14:47   BIC                          15849.985\n",
       "Sample:                    01-10-1994   HQIC                         15811.860\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.014      1.399      0.162      -0.008       0.045\n",
       "ar.L1.returns    -0.0240      0.014     -1.702      0.089      -0.052       0.004\n",
       "ar.L2.returns    -0.0517      0.014     -3.663      0.000      -0.079      -0.024\n",
       "ar.L3.returns    -0.0874      0.014     -6.202      0.000      -0.115      -0.060\n",
       "ar.L4.returns     0.0433      0.014      3.064      0.002       0.016       0.071\n",
       "ar.L5.returns    -0.0601      0.014     -4.263      0.000      -0.088      -0.032\n",
       "ar.L6.returns    -0.0463      0.014     -3.282      0.001      -0.074      -0.019\n",
       "ar.L7.returns     0.0109      0.014      0.772      0.440      -0.017       0.039\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -1.6490           -0.5384j            1.7347           -0.4498\n",
       "AR.2           -1.6490           +0.5384j            1.7347            0.4498\n",
       "AR.3           -0.1189           -1.4954j            1.5001           -0.2626\n",
       "AR.4           -0.1189           +1.4954j            1.5001            0.2626\n",
       "AR.5            1.2790           -0.9786j            1.6105           -0.1039\n",
       "AR.6            1.2790           +0.9786j            1.6105            0.1039\n",
       "AR.7            5.2269           -0.0000j            5.2269           -0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_7 = ARMA(df.returns, order = (7,0))\n",
    "results_ret_ar_7 = model_ret_ar_7.fit()\n",
    "results_ret_ar_7.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.44\n"
     ]
    }
   ],
   "source": [
    "print (LLR_test(model_ret_ar_6, model_ret_ar_7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalizing Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "benchmark = df.market_value.iloc[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['norm'] = df.market_value.div(benchmark).mul(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.8928710132672344,\n",
       " 0.33542220743300755,\n",
       " 6,\n",
       " 5013,\n",
       " {'1%': -3.431655136974821,\n",
       "  '5%': -2.8621167297421373,\n",
       "  '10%': -2.567076993884522},\n",
       " 19553.90073102193)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sts.adfuller(df.norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-12.77026571949722,\n",
       " 7.798058336038942e-24,\n",
       " 32,\n",
       " 4987,\n",
       " {'1%': -3.431661944885779,\n",
       "  '5%': -2.8621197374408225,\n",
       "  '10%': -2.5670785949998973},\n",
       " 80114.49116124898)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bench_ret = df.returns.iloc[0]\n",
    "df['norm_ret'] = df.returns.div(bench_ret).mul(100)\n",
    "sts.adfuller(df.norm_ret)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalized Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>     <td>norm_ret</td>     <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(1, 0)</td>    <th>  Log Likelihood     </th> <td>-40351.743</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>749.388</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 05 Sep 2019</td> <th>  AIC                </th>  <td>80709.487</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:14:52</td>     <th>  BIC                </th>  <td>80729.050</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th>  <td>80716.342</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>          <td>  -11.9731</td> <td>   10.339</td> <td>   -1.158</td> <td> 0.247</td> <td>  -32.237</td> <td>    8.291</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.norm_ret</th> <td>   -0.0230</td> <td>    0.014</td> <td>   -1.631</td> <td> 0.103</td> <td>   -0.051</td> <td>    0.005</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>         -43.4387</td> <td>          +0.0000j</td> <td>          43.4387</td> <td>           0.5000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:               norm_ret   No. Observations:                 5020\n",
       "Model:                     ARMA(1, 0)   Log Likelihood              -40351.743\n",
       "Method:                       css-mle   S.D. of innovations            749.388\n",
       "Date:                Thu, 05 Sep 2019   AIC                          80709.487\n",
       "Time:                        10:14:52   BIC                          80729.050\n",
       "Sample:                    01-10-1994   HQIC                         80716.342\n",
       "                         - 04-05-2013                                         \n",
       "==================================================================================\n",
       "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------\n",
       "const            -11.9731     10.339     -1.158      0.247     -32.237       8.291\n",
       "ar.L1.norm_ret    -0.0230      0.014     -1.631      0.103      -0.051       0.005\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1          -43.4387           +0.0000j           43.4387            0.5000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_norm_ret_ar_1 = ARMA (df.norm_ret, order=(1,0))\n",
    "results_norm_ret_ar_1 = model_norm_ret_ar_1.fit()\n",
    "results_norm_ret_ar_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>     <td>norm_ret</td>     <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(2, 0)</td>    <th>  Log Likelihood     </th> <td>-40345.450</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>748.449</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 05 Sep 2019</td> <th>  AIC                </th>  <td>80698.901</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:14:52</td>     <th>  BIC                </th>  <td>80724.985</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th>  <td>80708.041</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>          <td>  -11.9731</td> <td>    9.834</td> <td>   -1.218</td> <td> 0.223</td> <td>  -31.247</td> <td>    7.301</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.norm_ret</th> <td>   -0.0242</td> <td>    0.014</td> <td>   -1.716</td> <td> 0.086</td> <td>   -0.052</td> <td>    0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.norm_ret</th> <td>   -0.0500</td> <td>    0.014</td> <td>   -3.550</td> <td> 0.000</td> <td>   -0.078</td> <td>   -0.022</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -0.2417</td> <td>          -4.4635j</td> <td>           4.4701</td> <td>          -0.2586</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -0.2417</td> <td>          +4.4635j</td> <td>           4.4701</td> <td>           0.2586</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:               norm_ret   No. Observations:                 5020\n",
       "Model:                     ARMA(2, 0)   Log Likelihood              -40345.450\n",
       "Method:                       css-mle   S.D. of innovations            748.449\n",
       "Date:                Thu, 05 Sep 2019   AIC                          80698.901\n",
       "Time:                        10:14:52   BIC                          80724.985\n",
       "Sample:                    01-10-1994   HQIC                         80708.041\n",
       "                         - 04-05-2013                                         \n",
       "==================================================================================\n",
       "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------\n",
       "const            -11.9731      9.834     -1.218      0.223     -31.247       7.301\n",
       "ar.L1.norm_ret    -0.0242      0.014     -1.716      0.086      -0.052       0.003\n",
       "ar.L2.norm_ret    -0.0500      0.014     -3.550      0.000      -0.078      -0.022\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -0.2417           -4.4635j            4.4701           -0.2586\n",
       "AR.2           -0.2417           +4.4635j            4.4701            0.2586\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_norm_ret_ar_2 = ARMA(df.norm_ret, order=(2,0))\n",
    "results_norm_ret_ar_2 = model_norm_ret_ar_2.fit()\n",
    "results_norm_ret_ar_2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>     <td>norm_ret</td>     <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(7, 0)</td>    <th>  Log Likelihood     </th> <td>-40308.642</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>742.977</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 05 Sep 2019</td> <th>  AIC                </th>  <td>80635.283</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:14:53</td>     <th>  BIC                </th>  <td>80693.974</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th>  <td>80655.849</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>          <td>  -11.9731</td> <td>    8.630</td> <td>   -1.387</td> <td> 0.165</td> <td>  -28.887</td> <td>    4.941</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.norm_ret</th> <td>   -0.0240</td> <td>    0.014</td> <td>   -1.702</td> <td> 0.089</td> <td>   -0.052</td> <td>    0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.norm_ret</th> <td>   -0.0517</td> <td>    0.014</td> <td>   -3.663</td> <td> 0.000</td> <td>   -0.079</td> <td>   -0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.norm_ret</th> <td>   -0.0874</td> <td>    0.014</td> <td>   -6.202</td> <td> 0.000</td> <td>   -0.115</td> <td>   -0.060</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.norm_ret</th> <td>    0.0433</td> <td>    0.014</td> <td>    3.064</td> <td> 0.002</td> <td>    0.016</td> <td>    0.071</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.norm_ret</th> <td>   -0.0601</td> <td>    0.014</td> <td>   -4.263</td> <td> 0.000</td> <td>   -0.088</td> <td>   -0.032</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L6.norm_ret</th> <td>   -0.0463</td> <td>    0.014</td> <td>   -3.282</td> <td> 0.001</td> <td>   -0.074</td> <td>   -0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L7.norm_ret</th> <td>    0.0109</td> <td>    0.014</td> <td>    0.772</td> <td> 0.440</td> <td>   -0.017</td> <td>    0.039</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -1.6490</td> <td>          -0.5384j</td> <td>           1.7347</td> <td>          -0.4498</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -1.6490</td> <td>          +0.5384j</td> <td>           1.7347</td> <td>           0.4498</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>          -0.1189</td> <td>          -1.4954j</td> <td>           1.5001</td> <td>          -0.2626</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th> <td>          -0.1189</td> <td>          +1.4954j</td> <td>           1.5001</td> <td>           0.2626</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th> <td>           1.2790</td> <td>          -0.9786j</td> <td>           1.6105</td> <td>          -0.1039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.6</th> <td>           1.2790</td> <td>          +0.9786j</td> <td>           1.6105</td> <td>           0.1039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.7</th> <td>           5.2270</td> <td>          -0.0000j</td> <td>           5.2270</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:               norm_ret   No. Observations:                 5020\n",
       "Model:                     ARMA(7, 0)   Log Likelihood              -40308.642\n",
       "Method:                       css-mle   S.D. of innovations            742.977\n",
       "Date:                Thu, 05 Sep 2019   AIC                          80635.283\n",
       "Time:                        10:14:53   BIC                          80693.974\n",
       "Sample:                    01-10-1994   HQIC                         80655.849\n",
       "                         - 04-05-2013                                         \n",
       "==================================================================================\n",
       "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------\n",
       "const            -11.9731      8.630     -1.387      0.165     -28.887       4.941\n",
       "ar.L1.norm_ret    -0.0240      0.014     -1.702      0.089      -0.052       0.004\n",
       "ar.L2.norm_ret    -0.0517      0.014     -3.663      0.000      -0.079      -0.024\n",
       "ar.L3.norm_ret    -0.0874      0.014     -6.202      0.000      -0.115      -0.060\n",
       "ar.L4.norm_ret     0.0433      0.014      3.064      0.002       0.016       0.071\n",
       "ar.L5.norm_ret    -0.0601      0.014     -4.263      0.000      -0.088      -0.032\n",
       "ar.L6.norm_ret    -0.0463      0.014     -3.282      0.001      -0.074      -0.019\n",
       "ar.L7.norm_ret     0.0109      0.014      0.772      0.440      -0.017       0.039\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -1.6490           -0.5384j            1.7347           -0.4498\n",
       "AR.2           -1.6490           +0.5384j            1.7347            0.4498\n",
       "AR.3           -0.1189           -1.4954j            1.5001           -0.2626\n",
       "AR.4           -0.1189           +1.4954j            1.5001            0.2626\n",
       "AR.5            1.2790           -0.9786j            1.6105           -0.1039\n",
       "AR.6            1.2790           +0.9786j            1.6105            0.1039\n",
       "AR.7            5.2270           -0.0000j            5.2270           -0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_norm_ret_ar_7 = ARMA(df.norm_ret, order=(7,0))\n",
    "results_norm_ret_ar_7 = model_norm_ret_ar_7.fit()\n",
    "results_norm_ret_ar_7.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysing the Residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['res_ret'] = results_ret_ar_6.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5.3754069915803e-05"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.res_ret.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.355980211076917"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.res_ret.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-70.78380337886345,\n",
       " 0.0,\n",
       " 0,\n",
       " 5019,\n",
       " {'1%': -3.4316535759402753,\n",
       "  '5%': -2.8621160400844468,\n",
       "  '10%': -2.567076626752987},\n",
       " 15692.570834180244)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sts.adfuller(df.res_ret)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": [
    "sgt.plot_acf(df.res_ret, zero = False, lags = 40)\n",
    "plt.title(\"ACF Of Residuals for Returns\",size=24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NLwrgHu2zf4CamLoMaiu5Ow2fzYRvA+iHerw3CSGqhRCVUI/Ff4Ya5Jrp/UBERJSXGDwiIiLKb7cACENtXfOU/qbW8uKPoHZvK4fazetjADoAPAPgeillpXFGWjLoL0FtHTMKNXDwX6B26boDwJ9IKd1GEdPncxhqXp8XoLZQ+SSAJqg37CscvnMcaneuzVCTOH8M6s399wH8PRKtjIx+AODfoAZlFgL4lLYt1kFNJq4HBr6k53ZyKfMTUAMku6Dm7bkewNVQu6z9B4C/kVJGnOdgmtdhqOv8GNQA2Cegjlh2AMBiAF+RUgY26pzHMk1BHT0OUBOaLzF8Vg11fX8DteXQRwD8AdTWXQ8D+EMpZYtlfnsA/AxqYOn3APyh3k1R25bfgLrtLtDmVwE1OOWWbD1QUspGADcAWAmgGeqIch+B2jLuEQAfl1KenanyEBER5bMiRVFyXQYiIiIiIiIiIpql2PKIiIiIiIiIiIgcMXhERERERERERESOGDwiIiIiIiIiIiJHDB4REREREREREZGjBbkugINFAD4HdSjVaI7LQkRERERERERUCOYDeC+AEwCmvH5ptgaPPgd1eFciIiIiIiIiIgrWFwEc8jrxbA0edQLA4OAYYjEl12WhDF111aXo7w/luhgUEO7PwsL9WVi4PwsL92dh4f4sLNyfhYX7s7Bwf7qbN68IV155CaDFXbyarcGjKADEYgqDRwWC+7GwcH8WFu7PwsL9WVi4PwsL92dh4f4sLNyfhYX70xNfKYKYMJuIiIiIiIiIiBwxeERERERERERERI4YPCIiIiIiIiIiIkcMHhERERERERERkSMGj4iIiIiIiIiIyBGDR0RERERERERE5IjBIyIiIiIiIiIicsTgEREREREREREROWLwiIiIiIiIaI7atL8ez247m+tiENEsx+ARERERERHRHPXm0WYcre7OdTGIaJZj8IiIiIiIiIiIiBwxeERERERERERERI4YPCIiIiIiIiIiIkcMHhERERERERWYxs4RDIWmcl0MIioQDB4REREREREVmPteLMPPnzua62IQUYFg8IiIiIiIiKgATUxFc10EIioQDB4REREREREREZEjBo+IiIiIiIiIiMgRg0dEREREREREROSIwSMiIiIiIiIiInLE4BERERERERERETli8IiIiIiIiIiIiBwxeERERERERERERI4YPCIiIiIiIiIiIkcMHhERERERERERkSMGj4iIiIiIiIiIyBGDR0RERERERERE5GhBul8UQtwI4FbDWx8E8LKU8lbDNL8CsBjAoPbWc1LKp9JdJhERERERERERzay0g0dSyucBPA8AQoiPA9gK4B7LZDcA+KaUsjTd5RARERERERERUe6kHTyyeBrAz6SUfZb3bwDwMyHE7wE4AOAOKeVkQMskIiIiIiIiIqIsyzh4JIT4CoCLpJQbLe9fCqACwI8B1AFYA+CXAH7udd5XXXVppsWjWeKaay7LdREoQNyfhYX7s7BwfxYW7s/Cwv1ZWPJlf3otZ76sT7bM9fUvNNyfwQui5dFNAJZb35RShgB8VX8thFgGYDV8BI/6+0OIxZQAiki5dM01l6G3dzTXxaCAcH8WFu7PwsL9WVi4PwsL92dhyaf96bWc+bI+2ZBP+5NS4/50N29eUVoNdTIabU0IcQGALwHYZvPZB4QQiw1vFQEIZ7I8IiIiIiIiIiKaWZm2PPoUgBop5ZjNZxMAHhJC7APQBOAWAFsyXB4RERERERGl6bnt1egbnsBd//LZXBeFiPJIRi2PAHwIQJvxDSHEm0KIG6SUvVC7tG0HIKG2PFqW4fKIiIiIiIjIh/HJCPaWt0FRFJSe7UJt23Cui0REeSajlkdSyg0ANlje+6rh/5sBbM5kGURERERERJS+l3dLHKvuxvuuuSTXRSGiPJVpyyMiIiIiIiKaxUITaurZ6UgsxyUhonzF4BEREREREVEBK9L+KhzImojSxOARERERERFRIdOjR2D0iIjSw+ARERERERFRAStKRI+IiNLC4BEREREREdEcwG5rRJQuBo+IiIiIiIgKWJHW8IixIyJKF4NHRERERERERETkiMEjIiIiIiKiuYBNj4goTQweERERERERFTA9XbbC6BERpYnBIyIiIiIiogJWxKRHRJQhBo+IiIiIiIiIiMgRg0dEREREREREROSIwSMiIiIiIqI5gL3WiChdDB4REREREREVsHjKI0aPiChNDB4REREREREREZEjBo+IiIiIiIjmBOemRxNTEdR3DM9gWYgonzB4RERERAUppiho6hrJdTGIiHKuSOu35tZtbcWWM7j/pXJMTkdmqFRElE8YPCIiIqKCtOtoM+5dU4a6Nj5JJ6K5rcjDNI2dowCASJSJkYgoGYNHREREVJBae0IAgP6RyRyXhIgoxzxEj4q8RJiIaM5i8IiIiIgKmsLhhYiIALhlPCIicsfgERERERWkeI6PHJeDiCjX9EZFDKYTUboYPCIiIqKCFO+CwXslIprrfPRJY4CJiOwweEREREQFKRE74o0QEc1tXkJHRUx6REQuGDwiIiKiApV6aGoiornEy/mQp0wissPgERERERUk/SE6g0dENNfFz4cMDRFRmhZk8mUhxD4AvwMgrL11k5TymOHzrwBYDuAiAK9JKX+RyfKIiIiocIxNhvG9Rw/iB39/PT71B1cFPn92WyMiSgNPmURkI+3gkRCiCMBHAPyelDJi8/lFAFYD+BKAVgA7hRB/KaXcle4yiYiIqHC09YQAAG8ebc5K8AhMmE1E5BlTHhGRm0y6rQnt724hxCkhxK2Wz/8IQK2UslELLq0F8PcZLI+IiIjIMz35K2NHREQa5jwiojRlEjy6EsBeAF8H8GcAbhZC/E/D59cC6DS87gTwvgyWR0RERLNUTFHwk6eP4Gh1V66LEseH6EREKi/BdJ4zgzMUmsp1EYgCl3a3NSllKYBS/bUQYhWArwJ4R3trHsznpyIAMT/LuOqqS9MtHs0y11xzWa6LQAHi/iws3J+FJVf7c3Iqgr7hSazZJfHXX/qwp+90DauV64UL52el3BdddAEA4NJLF+XtcZ6v5SZ73J+FJV/25zXXXIYLFy0EAFx22YWm943mzVPbFVz17ktw5eUXYq4Jan/K5gHc8eRh/OCbn8Gffe4DgcyT/MuX32c+ySTn0RcALJJS7tXeKkIicTYAtAF4r+H1ewB0+FlGf38IsRgbTua7a665DL29o7kuBgWE+7OwcH8Wllzuz6lwVP2Ponguw9DQOAAgHI5mpdyTk2q1ZGR0Mi+Pc/4+Cwv3Z2HJp/3Z2zuKqWn1fDg6Mml63yimDU3Z3x9CZCqMuSTI/VlV2wsAKKvuwqd+/8pA5kn+5NPvMxfmzStKq6FOJqOtXQHgXiHEHwNYCODfANxs+PwYACGEuA5AI4BvQU2gTURERAVqNj3yKWLCbCIiEy+jT/KUSUR20s55JKXcAWAngAoA5QBWSylLhRCVQohrpZSTAP4fgM0AqgGcB7Ap8yITERHRbJNJroxs5dmI5/hQeCtERHOL9bwXj6W7nA6Z8yhgvPRQgcmk5RGklL8E8EvLe582/H8vgOszWQYRERHlj3TiNNmqX7PhERGRzntoiPF2IrKTyWhrRERERLOXdq/EGyEimmuspz29G++qneecv8SmR0TkgsEjIiIiCpD3SE1Lt5rMMmvd1rI0XyKiQsauvpnhtYcKFYNHRERElLF0bjVeLa4LvBxGRWDOIyIiwD6gMTg6NePlIKL8xeARERERBWZWxWn0bmu5LQUR0cxL6reWPMmPnjqclUU3do5g1Y5qxGbVBYGIMsXgEREREWVOu0eIxmbPzUL8Xmn2FImIClBlbR96BsdzXYyMeRmRzYvHNp7C4aouVDcNZFymfKbw4kMFhsEjIiIiytisrCSz5RERzYDHN5/GXc8czXUxTKzn5CI/o61leNbUHyIsf+1URvMhotmFwSMiIiLKqaIsZRedV8ScR0Q0MwrhLFNUxIg7ETlj8IiIiIgylkl8JtuxHcaOiGjO8xGk5ykzQxxujQoUg0dEVLDW7pb4z+UluS4GEeVItlo0ERHNdhkF9NP4zj0vHMcjG9hNjaiQMXhERAWr+GQ7JqejuS4GEaVQVATEFAWLlxTj9QP1Ac6X3daIiACfjWHSOGe2dIdwpqHf9/eIKH8weEREBW9zSXA3o0SUrPRsF2555EBG84hpCVZ3HW0JokgADCMHBTZHIqL85KclJs+ZAeGGpALD4BERFbydpc25LgJRQTtW3R3YvAJtJKTnfmXLIyKa81JHj4pSRNzLZQ/2nWxLOR/rKTemKJicjqT8HpFubDKMcCSW62KQBYNHREREVJD8DE1NRFRIspHz6KktVXh5d43v+W3eX4//XH5g7gWQeAlK2/cePYiHX63IdTHIgsEjIpoTth5sQIytD2gWq2kdwuqd5/Kylcw8m/4QG/fVYcXWqhyUJiE+6nT+bVIiokB56bYWb3iU4UnT+u0jVV0AgImpOZaHkteejNS2Dee6CGTB4BERzQnbDjehtnUo18UgcvTgKydx6ExnwQQ5dx1rQdn5Hs/TZ3O1C2OLElE+i8UUdPSNzciy+oYmMGFp5ZPTRjBsgUNpGhydynURyIDBIyIqCIqi4GzTgOvTshjvIGkW07tY5WPsyE8iVn1UtbeP2yfGVgIM9STyd+ThRiWigvL6gQb84vlj6B4Yz/qyfrKyFPetKTO/6elEHdR1iOdcCsaPnjqMnsHs/2bIGwaPiKgglJzqwLJXK3E0wMS9RDPJTwAmn0Wj6k3Fpv3WURCzcbNRlLU5ExH5Udumtn4eHpuekeX1j0ym/d1Mz5nW4NMcubzFMd9esGbqN0OpMXhERAWhd2gCADCQQWWJKFempqOIak3j8rGRTJEl8jUVds5r4RQky8Z6z2POIyIiAN4COEG11nT6dj7m9KPcWzCfIYvZgnuCiMhGNBYrmNwzNPvd++KJ+P/zsXJtvSn57rISx2mdVi+TtX7pbYnFS4pdlpl/25SIKFA+GsMEfca0PmAg8mPhAueQxa/XnMAtjzjXOShYDB4RUWEIuKbzHw/tx1Ovnwl2pkQOOvsT/fnzMczh575AD+QkxXMyWPH9Fe227/OGhYhmWn37cNKQ9M1do/k1cpTP83FFTW92ypHn8vF6PhvNn+d8LW/uGp17o/jlEINHRHNM9+B4UqWG7FXU9uW6CDQH5WUrGR9BGn3tHNczwNW/6IL5ABKjtVTW9mHNrvPBLYCIyGBsMoz7Xy7HyjfOmt7/zUtlDt+Ynfyehp+wPmzLw8sYEaXG4BHRHHPXM0ex7NXKXBcjeGxgQAUiL2NHfiZ2jBkFv+IXLloAAOgbVnOhPb75NA6c6gh8OUREABCOxACorSGc5OoBgZ+cR5mUMRyJIRKN2X6Wj9c3mjk9QxPx35ARj5vZg8EjojmovmMk10UIRGVtHxYvKUZoIhy/IW3vHWOuIspr+XT4KoqC7Uea1N+gR/rvM6nXWhbXu6lrBOOTbHFJROl561gL6ju8dztzO51NTuemi006I4BFYzG8U9bqGAyyc9PD++MDQMSXPcce8M219U1XaCKMmHasTE1HcefKUqx+81zSdHnZIrtAMXhERHnrreMtAIC2nlD8vaPV3dhxpClHJSIKgoJINIZozHtlPVdkyxC2HGjAuebBXBfF1cRUFI9sKMAWl0Q0Izbsq8P9L5WnnO72Jw+nnOaxTachW3JwzvQQ0NADTPq9+v6KDqzfU4t3TrQGUoRstDCl/DQ1HcVtjx3Eq8W1AIDpiBpUPds4kDQtj5rZg8EjIspbTvWgpk7n5uJ+PfByOdp6Q6knJApITAG+s3Q/7l51PNdFScnP02id3QPE8y1DWW9xVSgtLonIu3Akhr3lbfHWDbNFXXt+JM8en4qY/qZrLjfEiURjOHq2i61nLEbHpwF4TLauqK3g/nN5CQ6f6cxyycgNg0dElPcUZO+pRF37MDbsq8vS3ImcGUdgm63S+d2levLM6jURBeWhV05i3Ts1OFLVFX8vpijYWdqEiQwDIn5YuzHlIo7gKYCj5zzK1pl4jp3gFQXYfrgJz26vxkmOSGcyGVZbGi26QM0R7oiuAAAgAElEQVRN6HZoKFBbEE9OR7F+T232C0eOMgoeCSF+JYQ4q/17yOHzZiFEpfbvlkyWR0RkNFN9ytPJE0CJnFSd/WO5LopvI2PTeGLzafQOTcz4svMpZ1c6RXX+TvDrbXzSy18x0dxS3TQQb3E4YRhltqKmF5tLGrAxhw+GcnKW93ESDP4ypC589nfGDt7AqDpgA/PumU1pub8WLZyfclrTtZwX85xKO3gkhPgKgD8H8BkAnwbwWSHE1y2T3QDgm1LKT2v/nkq/qERktHhJMda9U5PrYmD5hkosWZs6D0DWZbEmxgtVeo6f6wYANLmMOjNb7SxtRkVtHypr+2w/P3CqA4uXFMebXQfJKbdE8ck23PjgvlkTXBoZn8ajG08FNj+3tRodn8aGfXV5kQeKaCZNTEVwyyMHbPOEzHXDY4bzs+EEM6W1eNBbPriJxmJYsu6k6zTeusQF1/RI0VpOjU16H6igtm0IZxpSHyPW6k7Q1Z/TdfbX1EKmX7bmzUvemi3dowhH3I/DzSX1qGkdykbRckr/HS5aOA8DI5N4wCWn2Cyp9hAya3nUCeBHUsppKWUYwDkAH7BMcwOAnwkhTgshnhRCXJjB8ojIYm95m6/p/fa3Ljvfk3IUpaqGAdS05bjvfsBXFet2sqs89QyOz5qb+KDtO9mGgwEMZx7RKtTzbSpMs52ey2f+fPuyl1S2AwB6hyYzXpa14riztNl2uvV7ahFTlFmTu2N/Rbuv6X+7thy3PFLi+Ltx+zm9sqcWbx1rQWVtv69lmuTfYUiUUnvfGCamIthysCHXRZnVjKcX/Vwzz8OToeHQdMob9zcONWZUHr+qmwexuaQBL78tPX/nt2tPonvAe1do6/nY+tpvvjt9U7/io8vR5HQEfTlo/Rs0vU5pPd6GQ1O454UTePGtxH68e9UxvPjWedN0O0ubUwYw85E+It/8+fOwv7IDPWns65nsekqqBel+UUp5Vv+/EOLDAP4BwJ8Y3rsUQAWAHwOoA7AGwC8B/NzrMq666tJ0i0ezzDXXXJbrIhQsP9vWeNPp9L01O87isx/7XVx79SVYsbUKn7ruatz/3T8xTWP33Vzs4wu0ftLvuuJiXHRxyPS+XXmuuOKi+Pv9wxP4f/fuxn03fR6f/sjvmKazDjF74YULTfNr6RrBnc8cxb/85Ufxj18RgaxLW88oLr9kES6/5AJf32toH8YH3nMZFsxP/1mAdVu9vFtt0fYNH+s2MjaNCxbMw4WLEpcVvdXOu6+8OO/OARdo63H5ZRfaln2h1sz6XYZjKl2vvuN8A+D0W3Pb3zO1rS+9ZJGn6fTy1GpB5qvebX9tbzXkeLKuwzxtfS+73H5/6K6++lIUGSrol16aeGZVVFQUr8Tn0/GYT2Wl1ILen/1j6gOehQvm81ixuPzyxIOtSy5ZhGuuuQyDI5OQ2rnooosWptxmRQvNt0rW6a+55jLU2STjHxmbRtHCBbj6iovU+VjiVBdfdEHa++vSPvVcGVGCOZ6M81iwQD3X6vWlS7Tz/MUXm8tbeq4X3/gf13me/zzDNctrmX/4yH7UtQ1j+7KveZo+CEH9hi6/XB1N78ILFyAaVa8773qXub4wrT3RaOwajb/f1juGtt4x3PF/P5e1ss0WV/SrwaKFC+fjoosWxt+fN68oaV2vuOJiXPXui5M+P3m+Jz7NbLk3KXRpB490QoiPA9gJ4MdSyng4WUoZAvBVw3TLAKyGj+BRf39o1jxhLRR9wxO45MKFuGhRxrves2uuuQy9vfnXbSVf+Nm2xt+T0/c276vD5n11ePDmzwMAOnpDpmmd9mcu9vG0lsNgaGgc4+NTpvftyjM0NBF//wePHwQA/OaF43j69i8BAE7V9aGufRhf+8IHk5ZjnF9No9r64ZTsxZ9ef20g6/LdB4tx+SUX4NHvfcH288bOEYxPRvDxD747/l5n/xh+/twx/Pnn3o9v/tmH01qu2+9Tf384NIV3XeoeKFi8pBi/e+VF+O1Nn4+/pz+ZDI1OxefV3DWKwdAUPn3d1WmVNx2RaAyPbDiFv/3iB/Hh913h6TvjWne0sbEp1DX14+JF87FwQaJffiSirtvg4Dh6L15oOw+vBoacnwav2nIaf2M5Hnt7Rx2DRzNxvlUUBeeaBxEam0o9MZLPDX399qMXLjV0f7V+Z1p7ujgyPOG6fmt3VuMv/luiEfRoKNEyzHjvli/XJF4/C0s29uegdv6IRKI8VixGRxItGUKhSfT2juLOlaXxFg5TU/Z1BaOBEXPrUrv6UNih+9sTr1Xg1m980vaz0NhU2vtrZMR7+b1oak10Z4togQ792jamnefHx6dNy+odCHledm/vKGKGlkpev1enBflm6rgO8vc5oh03k5MRhPW6kHYM6ga1lmDRSCxpubOlnp1NwyPq+oenI5iYSHQxjcWUpHUdGBzDvFg06fPh4UT9yfidyekIajtH8YkPXGF6oEQJ8+YVpdVQJ9OE2X8CYC+AO6WUL1o++4AQYrHhrSIA3jvnUlb85OlS/HY25KehnPDTzUo/1c6WoUWbu0YxYskvk84FYfGSYrz41nmMjGunI8PqPbbpNHaWNqdc51i8CbLvxbsaGXPOn3Pfi2VY9lql7fSNndkZgnxiKgLZMogfPnkYJwxPd5x0D9o3OTZ2/fr1mhN4fNPpwMroRf/wJM41D2LVjnOevxMzNDP/4ROHcNPDJfjl88fin8cPvQB+Hm5dJ7badIfI9U+y9GwXHn61EodOpzlcbhor4PUb5dJynM6O0xcR5Zh+2jF2jfHSbS2zZWbnBJS4/iiYDkex5UADwpEojp7twuIlxRgc9RbY163ZlegmNa7lUdJLzvvuTClQYvbd1vSKds/QBBpsWq/NFdZfSWgijI4+80AripL4DRvr/k6/sHXv1OCR9RWoa89xWo0ClEnC7PcD2ArgW1LKV20mmQDwkBDig0KIIgC3ANiS7vIoOG29+TfyEWXXXc+UYtWOatN7+sl5ttx7/XrNCfz6hRO2n1nL6FRh0y83JZWJfD52w9Fac/Jag1RuyQ9zIVuluOWRA6huUpte12dwAZ7pnEetPSFzItE0hh6O58QwlL3dUJnRR+ALYjhjv5XzXAd0+4bVJ6r9w+nle/LSoHh8MozFS4pxut6cXNVuWxm3h/6/qoZ+LF5SjP6RzHNSEeWD+jl88+koxbnVyzU8qFYL1rkoivqQIp3cifr1J6YAu0+0YvuRJuwpa8OhM2pA33rjnYpxFLBRy4O10rPd2ktrOf1tFz+bsbSqC2UeHljlC30fW48l4+vfvFQ2o2WaFbRDSt085m3zC8PDOgCQrYO+6j5DWgBVH9EtV6KxGM41D+a0DEHLpOXRHQAuBLBcCFGp/btZCPGmEOIGKWUvgJsAbAcgoR4VyzIvMhGle/Po9LXuwQkcruoyvadf03LdysHI69O0uvZh7DvpMZm4zfpZK3PJlT6Hp0g5ks1dNKw1Wde7STV2juDJ18+k7FJsPEZnOnj0q9XH8eC6ivhrw0NazxKVPffpgvh9FHmshMd/k9rrNbvO57SCnc3jrrVH7drmlDzcqRwNHSPo7B/DAa1VlPFp7iz5uRIFynhYD4X8tTiZSzbsq0t6L9vnBLfrgwLgxgf34d419g/F3BjLHda6UE9HEk+9/D7UsKtTKlDQ2DniOxBlZ/mGSl+DSzy3oxortlaltaxwJBZImYOk15fmWe66vRx+mTwsGhmfxrPbz2JyenYmlfazZhv31Xt68JQki7/x0EQ45X3JG4casXR9RUaj5U2Ho2jqmj0PB9IOHkkpvy+lvExK+WnDv5VSyq9KKcu0aTZLKT8hpfyIlHKxlDL4MY2J5qAMBnj1PGW85dFsih45sRRxbDIST/ps9ND6iqT37NbOusrWCmY8sJDjlkcz0Y9br5Au0LqePb21Cidreh1bdJSd70Fj54hpG8631pgCcK55EAe0EeE6+8fwk6ePmLr9tfUa8uqksZ30yp5TYCfITe97Xtq2PXCqI+0Kdib8FtdaufJzTrHrPhuOxEyjBlnnV1LZEe9Sag5yeiv5stcqcfPD+z2Xkea2xs4R7w8rsiwfLtdW311egp2lTYHOMxqLYf2eWjy7rdp1unlZHoLRdG4qsv+spTuESDSGtbul5+Cf8byYeNCnpL02dseNoiQCU5mqahgwvX7rWAsWLynGU6+fSWt+L78tsXhJse1nL711Hr94/hhGx51vOdt6Q/H6Q7YYr+v6Zcj6wNFb8Cj9Mmw90ICjZ7vjrceClG7LYzte6wSz7X7k+48dxI+eOuw6Tac2EMiwS1qKVFa/eQ73rilLSt0BqK0M71513NzaPsuCr9EXiJbu0ZRDlBPlTJrnz1RRe9unT7PrXG1ivA6nW067dU5qRp7UbS07OY/sTE5HsGpnogI8MDKJLu3G2a7sPYPjgZ67jmqVjpHxMMYnwym384qtVbjvxTLzk88sbKel6yvieRrePt6CvuFJnKzttZ02ncXr6xmx9mG0zDOIykyqFmzl0rxeQXSVm0nFJ9tMFSc/myx50iKs2XUedz17NJGbw+Xnatw/XoN0ZxsHTE/xyZuKmt45WW+678Uy24cVueDWDatc9mLxkuL49WO2mJqOYnNJQ6DzLJe9eKesNeV0RQHdBTmdk72e6qoaBlB8sh0vv+088qYuYkg8HVT9zOk65tZqOJPLut4KrLzG/pqdyr6KdsfPzreoLTzW76lNSnYOAMfPdePuVcdNeZ6yLd5a3bo9PWxEP90aj57twuEziVyEk1oi90ULg73dP3G+Bz9++giqtMFj0uUSW3Wd3su1fCZqSV6WYVdXVBQFL7113nNrpPp2tdWRXRe8bYcb0dYbwpmGzPaFHwweObjnhRNMLE2zVto3j6mCR8b/aye6fLhNzeRm2v6Jm323tZiiYNvhxniybWtFoLK2zzXpdTr2nWzH4TOJLoV3rDiCnz171LZ8AHDnM0dx22MH0dId7Kgc+yva8bPnDAmjU0zfZ3wqlfWDyNKfy0E63daiThHXeMs8b/Nbv6cWP3n6iNusHD21xfx0NucBXZ9NpYqKikzdCDINflU3q0+xp8L2AZ6Kmr54QC7Xm2quGBmbxhOvn8GTabYkoGAYf5kxRcGre2vRN6wmiD5xXn0Q0JSlARZmE2OAxU0uu54bz+Px+paHE9Z3lu7HU1vUFqcT0xFsO9yU/F2fJz6nrWUc7MIqqE3X2DmCqhQ3vv4e0qjTHq3uxh0rjiAciWEqHMWPnjqM6qYBrHzjbAalTY/XbvB2/Kz6s9ursWpnYmAQPdiwaOF8p6+kpaFDzYGpdy9Pn78D9XyL/9xBxtbj4YiaXH7aYXTEbLDrIaAA2F/ZgSXrTnqch4eJZrCyw+CRC72pGdFsk3YrmxRnF+MFWr/5t7tohybCuPOZUnPXoBzIpO7yyQ9dBQC2Q8Zb4wX6iVu2DGHrwUa8urcWgLniORWO4vHNp7HcMiJaJpq6Rjyt5OhEGBv31ZkCRvcYkot39I2h9GyX3Vd9UQNj3g6+u55JBLjSCRa8dawFlbV9qSdEci4go7NNA/jpylI4T2FPP+yjUfvvzPMWr4p7p6zVHFAz8lAzaPfwW5ucjuCZLacxNYMVIy+S1s7H4WD97nQ4iuGQOUBrPUf1DE3EE1Qan9oWuXxHNz6DTb8LiX6z3jtkP+IiZZGxpZ3h7eauUew+0Ypntqk3y7NtEIzZwEvwKJPWpZ39Y/GuX9Yu0JkE0cen1Bw2Ld2J60JG+9XhIZpbl3PjsjNx34tlWL7hlOs0MUXBztImDHvo1mddlaHQFDr7xzA4OoWN++qTpq9q6MfPnj0aWBc9u/LEHEZbsx5ax6qTu5dlcvxNh7MTPNJ5zdeYiqJ4C5AYA2MTUxEMjEz6uh/aU96G7Uea8PaJ1K0Sg6Kvl6kFWYDP/3NxXmfwiCgPpd9Fy/vnekTc7jun6/vQMziBN4+mTmY7E9JJRPf+37kUAPDeqy9J+szuYr14STFWvmHOL2OsCOhBhp6Abp7KZQ/uXVOG0qrUQZ/O/nHsOtZiChgZ/eL5Y3huu3vuh3SUne9B1KFbl1E6x+uGfXV4fPNpT9PG94KiJO271/YmkqQqUANpXiqJemUvmuIJdjDd1lJP8/qBBuhr6rTMt461YMehRuzx0F0jE36ri9uPNJlee6miH7WpRANAq00QzW5z6CMGGT8zJ5S1Z5dUNxOxmIKzjQOpJ8xzegU2nZGjKDjmrhHq30T+Nv2DmS3TbBZUtzUnvUOTeG6Hw7U38P2QSQts+++63dBX1vWhvmNmhkFv7BjF5pKGpDqOoigYGZs2nXfcTkHNlhbZiqJg7e4adA2MY2A0eyNz6g8krUWzvtYDvaZpMjhO9GvewgWJA31iKoIHXi733X01HIli5RtVAec60v76/F4R1NHp7lhh35rbOG+jsNZaOVuBQleG8qR9nbT5Xi7aTjJ4RJSX0jvxpA4eOU8QiymoqO2FoiiJYcxtahY1rUMzN+KLtvwdR5pRJv2NOpVY1+R1tm4GfT3jQ9jq75vOoO7NkodCU74CS92D6rSZtIA809CP8x6GCG3sHPGUH8KoTPZixdYqvHWsJd3iBSZx4+r+yxgZC+MXzx/zlFdCPz7suq0tXlIcz6sQRP3fS+JztTjuXUn1sqY1IslM8lBxKqnUkplato3dOcet66njohSge2Aci5cUo9HQjWfaoSucrq0nhIkp7yPX7DrWjGWvVeJ0/czlI6C5yynxMQBD797ZfoLInNd7My8tj5weypgX6PxRfETMpITZqWfrRybzC00mn9MUBZZcBsnf07sj2+UWCtL+SjXHkTXpcP/IJH7wxCHc+OA+xwTagPO2URQkfhfZ/FnEr0eK5e3UC7UGGurbhz23Lo7Xcg2zONPQj7r2Ye2BlHen6vpx/FwP1mst772KxmJ4dW+tbcLoTDa557qxzU/c7VevKAr2lLX6SkBdWdfnmIDdrmWQcX9sO9SYcv5uretzgcEjG5k8ST5a3TXrkhFScF4rrsXRALr/ZCr9QzTxRbvEpnY3nfrv4e0TLXhi8xkcOd3p2n97ybqTuGf18fh3/dxoJcqh4M2jzRjXKjReovSDI/4CVnYX1fjyk/qt2c+jtm04HjxJfMV+4tufPIw7V5aiIkWCSH2EkHkBPMl/ZMMp2xHmrO57sQzr9/irEAyPqds71TClQDCtc1w5JEjW3on/T+9a46Wlmr4/IymzzHspoDsvzbUr6/oQiSYCIq7bNKDtPRyawvFzwY/S4qt0lnWxSwhsdzOc+H3bL+3Gh/bFW0SZWvel2Bd3rz6O5Ru8d03t0YLAg1l8qj0bxI/h2VK7naMURUH3wDh+u7YcU9rw3JbYERl4Ofd6SQKfzmGfThAvZZAmzURE3Tb3LQpS1z96h9Ty/NyQDzEbjji0wM60FUzMMEJd0PUUU5cup7t/D4s0FmsoNIX7Xy7HakP3rXAkdSDJPHBEeiMppztAzfnmIew+0YoX3RKU+932aR7nvcOpH+DWd4zglT21WLPrPOrahj2lT3h802nHBOx2LT6N236rl+CRl7yeM3jtnXPBo9aeEN5x6Ouo78xMbtae3VaNX2T5JEq58/bxVjybhe4/fnk5QnuHJpKfchj+H38aZvzc5tjX39Iv0sY+xsZEzkZ6Qum3jrXglkcO2LZEau4axdaDyU8+psNRnJS92LS/Huv31jiWCzBXhufP93c6c2uZ4JQw26qzfzzezSWpawDUwIo1cecTKRLK6rGKHObxdNWvBenio17MgluSeYbuXF5O36kq7eveqYmPXJGy21qKeY1Phk3BSLvKfzrb0G49gz5mlr1WiZVvnE0rAOwmkzq6XRe/dONoetBoT3lbIiDusmx9Gn3kEy/00YpSxSAHR6d8P70/fKbTU8vCmZCtGzDyJ6Yo2HygAbVtwzijD4+u7RJ9uO65vouKTP+fueuXdUl+98NUOOq7m04mrL/lXTatjHdoAfig8uzFYoqnYIguYpOT0Gv9TV/eTFa2/MSOItEYWntCpjqGngC7uUvtfldZ24ebHi4xtZ61Y6zFJM7V3sqsTpuoW/k9x+td5myDsNqsatuH44nfg7b7eGu8Hu50z2Kk54kamwjjgbXlSekTFEXB4iXF+OGThzwtPxE3TGw33z9Vt9hRDqrgcy549KvVxx2b3H37wX1Y9lql7xPwcGgq3kICyE6f/w3FdQEMiTjHawx55Fh1N+rbnfuSW4d8tKpvH8ZPV5ai5FQHSqu6DEO7J6axu17aHSLjUxGs2XUu3kdYgWJ7jIcmwlj95jnTe3pltXtgPClh86/XnMC2w01J87r10YNYsVXNLTQ5HcWKrVUorUrd+mHhAn9n0ERf6+R1SV4/93mHJsJJrbEi0Rh+9NRh0xMi57KYHklo85mZdqpjGQ6t7WnI1GyfegzNzj0Fj1JMs7e8Lf5/x9HW4jOzf7u9bwztfWO49dGD2Lg/kUfn1eLknDpech6ZFqnY/wbtHD7Tico6b4nHrfpH7JPmZ1rX9nMtqmkbNlU6bVseuQaPnD80zitVi0DApkWiB0V68CjFd3/01GHXG0M7q3ae89SycCawdpG4oculmGLfTWqu1f+CWt3ZtN1SjRCV0c2p3fw8Xk+D9PTWKtz0cInn6a0P5841DWAo5H3E22gs0fIoGlWw9q1zmJxOfljS3DWK7yzdn3ZKBqfgutvxtXR9BX61+rhr6yr9IVdDR4oHGqa6f3LLo3Ak5hq0e624Ll4v90tP1j1hs131Y9Z3wyMf055p6MeesjbTe251mHhLTYeJGrRAnXXgDmfJI/P6bvXla+rsm3PBo1TONg74riD+8MnDuPXRA4E/nTV663gLlr/mPhpBKnZrddtjB7G5JHn0AUpPaCIcSN/vZ7adxf0vl5veW7e7But26y1xEu9bz0HhSCweLKptHcZzO6pxzwuJbmQ62+EjHQ79A6c6Ud2kPsXcXFxre6xvO9SIQ6c7Te/pF/aXd9fgue3VtsN6Wk+i1spA2fmepKCUHbdRQezoix0dSw6eWLdDqpvl2x47GD9vjE1GUFrVFQ86HK3uTnmhMH6qn378juaVjpiiYMlLiXwO9714Ag+94m3o0N16C04vwaN0CueDsceMl4uynwu302hr8Xk5vP/L54/hl8+rrVD1ICpgv7m85DwyLVNxCkYk961ftfMcHt9kfnI2ODoVf4LpLrhRPOxaOnqlP90GzDlK4q0HXUrodjk3bvfpFAk09aGedUfPdnkaDny+tgz9/FmoEsH4/LH9cCN+/tzR1BN69Os1HnLjZNmRM4lrcOK8aP6FzKJ4SNaCM64tQt1uHBVzy5edpcEMClLTOoRJyznX76qnnFwJ9ibTz0OKoJR7COIbWVseLX3V32i3iqLE63dHqrrw2js12HKgMWm6d8rU1itvHWvBK+/UYP2eWu/bxqW+7jaL2jb1AbKXbpMpi2BYULxuaVj2j5467Bi0G58MJ+p78HfcDo5O4ZjW9d1bnSMd9gUyrrNdQDBd0y7rYZeIu8hme6f7s3I7X85kLrs5Gzyy/ujtRqgAgOPnuj3fTHUPuuc6iikKdh1tzijIpCgKNpfUo7N/zPd3x20S4oUmwp4vjlPT0ZlLhJynbn/ykO+nx17tPdmGvSfbkt4vPtmGu55RhyLv6BvDTQ/vj7c00I/z6XAMK7ZW4aktiScHdverEZeRsy6/5AIAwMDIFDbZDHdqPW0tWXcyPpzsiJYoz+7JmdtgXSkrQoYJFsz3eQOulfjQmU70WH671ptCL32ejTfzz+2oNp1TUiXKNk677LVK3P7kId8BBS+sLdZufHAfKg2VtcbO0XgiaK88NfvPcgW0yHB1Tl6UXY4c76zHQlOX+Qmfp4SXhmOjqEjNURCLJfKB+d3VapAs8XpwdAr3v1QW/525icbUFnFPv5H6KWI6zdud7Ktoj//f7/yMATzfLY9c9rYx3pwYjdB+Z3T2j5kS5j+7vTrejWNqOuoYSNLLW+HhHJLPUiYon4W2HGzMaECCoNS1D+Pmh/djZNx7iwknphtNQ1TddO7P8k1G39AEymXiutLWE7Ktf+bC8XPdtsfo4OgUWrpHUXKqAzc9XBJ/CGj3u52ajmLT/npfIzbpo9caGe9DPOVK9dEINojfYcxjN/Bc8jLaqxvjw4Wwdg6ftmmBo/+Udp9oxZ7yNrxT1mqbJyqVxzadNnUx8/awy+bNImDtbmm6rroxPUSJV5cSb7oFqO7Wcpim48F1J+N5Qe3Woy/dnFW+W2v7OFZS7BK3udz08H48utHc0EPP12VqGejxh3W+eVANZrtUEjnamo2YomDjvjr02tx8HanqxOIlxa7BmLHJMNa9U5N0krc+tTU+ETCe0Fe+cdbzzVSqm6hTtX3YuL8er9l0W/BqKDSNnaXNWP6av+g6AMdkXl49tL4Ctz95OPWENiLRWNZHY5gN7PpfZ8LpBGN8+5U9tfGRufSWPXrFzRisKTvfY0oUbDfKyM4jzoFEU9TcdgLzy5rWIceb2dq2RDnSffJYdr4HXYaK/wKfOY+M5dWTPuqso1CMewj4Ri3rcfeqxAXX6bg43zyI0ETYtG07+sYwFJq2vUm28rvpVr95Lj6CRFCVwtDENA6f6XSdJtuDouqHsjramnXFklfUad037qtLGrFlT7k5YHvvmjJP8zKydn276eES3PjQPtzyyAEcPN3hO1AYi5mfCBefbEN9xwgOOoz2YaRX1s55yJWTrVQQfn/zYUNgxlimWDxg4dLyyKXpkZeRltwMaw9Tvru8JN5SdOn6CtP12bgMfWQiq1KHZLBBC02Efbes7h4Yx0+ePpLywVG6+TCyId/qGruONmM6EkNta+bDnheftL+ZNO2WLO+ie144gae2JHL73b36OG599AD229zoZlKUw2c6ceczpfbHnMOMV75x1nayH684gnteOCIO0UYAACAASURBVIHTdWo3ILccMjuPNuHNo83xEcCA9K6nxnO4PhKVe8uCFBTYZ+dNk/31dHZJ1TI4lVhMSboOBH0KO9PQb7pumR6kePi+cR/c9ezR+Bedfuu287DpdeC27NP1fbjr2aPYX9GOAZfBaPT1qmrst32A0m84F9sdS34HakmXAuDxTe75RhPTquU07rOJqQjqtJZgqXaa48iqqe6hLLoGxvHQ+gq8/HZNIA/yRsenkx5+pmvWB4/aekLYdawFTxv6WjZ0jKBc9uDt42ozOn00EzubSxqwt7wtKd+KtQJlrJzaJw1Ofi8ciZpuxlPVQ/VRe8Z9DP9nXbbb8NGp9GdYodIvptZtNzUdTdl8c82u87hjxZHAkuq5iURjOe8isOzVikDyHziNMOF06rEGSd22d8mpDvzkaXMrKbsgrfsSjZ+7VHosx4cxqOR66Lj8qFZsrTI9tfAbPLL2PzYew+m0ErD+LoxlU2x+r5FoDA+tr8AjG07Znl+8DCfv1+EzXdiuJSVM5xxip/RsN1alyOu050Rr0rGWrtBE2BSYs8rk4mqXEDQVL4szPvGylu9UXb/vnEe/Wn3cdLz6SY+lH6d+Wuol5zzKLOjidxdFo7H4dttoaPWYaVcpP8GjVMeVfr4/1zyIqsbE9ccYBP7F8/aDaTy3I7hBGBRFQX3HMGTLYDy4BagP0m577CCWvVbpqxvE7rJW9A1PmlqSOC13Nqis7cMdK47gVJp5vnIp3Z+V04NLRTvttPSETA9aMhGJxlLm3nF62PKS3TUtg8Nmza7z6BmcwMRUcnn8zlY/n15x2SIAcM2bo9ezMg1cGIOFbj+faCyG2x47iGMpRvo11sGcBgby4/FNp2d9yyMvXYcB5+0bjSlJTTdsz2U+B2owGrO0ujPOytM80tgH0VjM1LDCpuGR67If3Xga3QPjtr9Z6/apbRvC8tdOJT10Tf5eqlJnzq17mp4fKiWtnMb99PTWKjywthzjkxFf17pthpHU/LYM1Pdfa2/IUx3Pek9jbWn1wMvlpoefY5PhtOvlszp4FJoIxzdek+FG/DcvleGpLVW4QMvg7tZ0VB8px7qz9RsnRVFw/Fw3agyti2yHK7eZ98tv19g2RVXLFMU7J1pNN5R6HdLvTZseJDNKp/LuNmpQZ/8Yvr2k2FPT2ZAh+BWOxPDd5SV4ba97ayq9H/OWFCeXIGw92IiHX600tW6ZaWebBvHS28ktvYpPtuGsj8BWg83Tr8HRKftjVFHiwaKLFqkJ6qbDzvu8rm04qcmo62GV4rB1+9haXuNNW1B96j01+zYwVrRiCnDsbGZDkrs90bdbR336tt5QypGYnGRyD59pc28/TtX3+2qe7HZMnK7vQ1tvIndWXduwaTQLL02xg7zRVUchUbCztMkx+Go8NuyW7fd8bm2ttsOlxaAuHIlpFR+9HKmX4+UJZTr8bv6Iww/ES1cpt9+W3U2un27lRSjCM9vOuk7jlIotEo3h6NmutI/Filr7YE7xyXbc/1I5HnylAr95KZE3T7+BOdc8iNseO5h4gp2CXm+YnyLYqK9FcC0aw566YVrpD7maZkHy6lQi0RhO1fXFt1nQDf2M59F7XkjkY3ohRSv0SDSGJzafRkt38ja8d00Zbl7mLaGxfm500tE3Zmq945felX7QECStaxvOKLeKPjqiWz09EbTO7GA3XseM14669mFTPXF8MoLQRNh2sAW7cgFqHTQIsyUobGQ8ZpyuDUbuN9xK0u/Obnq7AK0+Xd/wBBYvKUZ9h7eWg+Yh7zMrv5PVO8/jlkcO2CbqtkuYnYkRLW+oXTc+u5bCQXAKwL19vBXT4SiWrq+w3D95X7Y+pfHQ0q8nkVjMc319cHQKW43BI0NBrdsiNBHGg+tOYnA0cS7T75OMD59jMcUmYJp8bO4obcZ/PLTf1F2429LQpm8o/QYlszp4dO+aE3jwFeeRRPTh/6z9U4tPtsWbgEqHLmf6Tiw+2Y6Vb5w1ZZG3O8DVJ5/m963Jf41dU7Yfacb6vbWmliP6E0i/v59N+xNPWtMZ7UXndjE8Vt0NBWoSUCf6ScBYudaDFUeq3LutRLQA3+4AnoYAwKm6PscuAHo+qBGbRMhBGR6bTkoObdXYOYrFS4qxz5CnaO3uGizTEvoNjEw6N2/UzLdpkuA0NHPXwDjWvaMm1NZPOqmeEALmE5rbk/iU07kempaWC4b1cruAZbMvr3mxdidkf9x+mnbnFPNTiPR+1+l8Ld7FK6CWR9lgLNsDL5djg6HSfOEFC0zTPrC2PFGxU8z74bbHDqKtN/k8oU8SicZw75oTOJdhS8X+kUlsLmnAE5YhXXXGJ9TWfdbWG0prNDTX/Wfz0dL1Fbj10QNpVUSDvn/we+w5/Tbjc3Hr6uGj8Ot21/jbF0XqtVNnF6x0OqduO9yIZ7dX41RdeqOoOn2v3XBdNLY2tlb2vObr0Os1C1IMSJBIXp4QU5S0u5Dd9thB/OAJb0MhGyXSn83M+e2+F70nyZ6cjmDXkcZ42X79wgk8tum0qQV7kGIuNytuuvrHUVHbh+dtWsQZAx6pnKrrdx0p6lerj2OtNggI4D+pvv4AWW9tMByawgNry/HoxlO+8hEZu2R6OX4S3WWN72Z2vBnPOw+8XB6vJyYvZ2bNwtgRXnor0RrGS71NAdDaYx9M7uwfT9QR4g9WPK60Nt1ZraXpq3trTTf/zvwPkJFyjkUwjcht7W2jKOq9W9n5HtNgLL98/pjvVmpuxWnrCWHxkmLb60u2jiXjbEfHp7HyjbM41zzo+vDcKhKNJdVLnLr2e8pzqSimATas5bTO4siZTsjWIew61owfrziCu1cdM6RjUOIBv3vXnMB3lu43fddaxXh046l4Q42QS0+nTIJ5szp4lMoF2vB/xlFSugbGsXZ3DX74xCFsP9KUlKhW38iPbTqNSDRme0Kx62Jy08MleFE7YYUjMdsTlvFJvj46jDGwpVci/bY8Mu7gFpvRqkzTxhQsXV9hezPk1sTW+rSlpVsNfLQZlqffoBl/YPGnkin6XXg5SGOKgi0HGuKBPzePbTrt2AXAzthkONBk309vOYPVb55D37B7ImRAHWnMzn0vliUlVrv/5TJTsNCuK9bCBfNsT16mEYm0/aEH99z2jl33FzvGJfoc2CxxQ6/N33i4bD3YGM/DY3XCpjJ5ur4/kBsDY1fVmAJcdvEFGc3PteWR5XShKIq5//MMVtCK0jwPBa1cmvdt79BEvNWAsWx17cN463iiO9miC+YnzctPty0gsb0HRqfQ1DWa8km8+8wSN9j6tShpQAbD/62f9QxOpAwi2/FyTn11byKfQF27+lTU7iY/laBvxP1WWiIR+5x5+mxc42g+lmU3IIFuxZbU+RJOnEtuvWhXtq6B8XhrMbvhi/2685nSRCsdp/VNMxKv13WM3RyPVnclVawVm/9tP9yEO1Ycce0OHbTEU3X36U7XJ27WM6lEN3ba35TKlkEs31Bpui68VlyHFZtPx1uV6IG+eAs4h30Umghj8ZLilF0HrdJdrYUeWvV78fjm06YWT1bWa5DfocD1b+vd8/T6jmwdij9I88LcQ0DdCW45j/TpZypAaa0nOslGcY7ZnNNmE09dBxUlfv9mtcyQny7eksy+6ZHz7LW/9e0j5oCBw3eKitTWSuWyN9B9Zjd0vD5im6IoePGt81ixtSr+4F1RFLT3jWH9Xv95h+zKXVHbhwfWqq1dE6PmJTbCyNg0GjpG8MMnDmHpeueGIV4YA0PGe/bik+1pPYz7ztL9uPGhfZiYiqTcJ1722cN26+cWPTJUYvtHJtHWO2ZqcKJvRS8tIo31Sf171vp2pvI6eKRvIP0Ct/rNc/Gs7oB9Fyn9wlDbNow3DjXaHgRO++aAloz0pof3474Xy5I+t0uKa+yO0Kw1AdYrKrc9dhCPbEhcFFp7Qnh046n4BXBqOpr0I3jydecKbDgSxehEGOeaB7H01Urc8kgJ1uw6j8VLihGz6f9oNF8LUugHZplWSbFrGm/cPvo6p0ru6+XHVtMyhO1HmrDGMiz7sepuLF5SjD6PFdB4E3BDkX705GHc/uRh7ClrxeIlxZ5a5LgZ0Ubd8RPZNpoKR+NBMmMgsr59BG8eTXRBsQvmLFgwz/baZjyp6KMC6TezbvvHeFi4jTxj7k9r87njNxOVrAOVHRgcnTI9jd9T3mZqWZLK3vI2fPvBfZ6nd2JsOZaqeb0Xbjcg1hZ9ipKYPhyJpRwm3O/y3LT2hGyfssw048h/APDTlaW478Uy7DjS5Fi2kfFp+4uW4Wmxp+2iTTPP/DItMSURRNeDvevfca6MBVVZ9DIfu5ae+o28scJ1rLobbT0h1LQOoXdoAoqiYHR8Ot6SJqmek36xAaTX8sjuwcnrJfUpn/Rmsr3VG3a10tVvkzQ0aTsYzmt6awjruiqKYmppkurBi7PEfHsGJ1IOce1pVEQb+s2Z8UHGs9uqsXR9hem8Zredd5Y2AchuAuuW7tFEIlOYA8lbDjSg2CEg+OjGRCvBbJwLn91ejaqGAdPxqf+e7HL06KIxdThwY+BGb0391nH77qlOD33czoVuXQL1+sJ0JIaYomQ0QrCXwSbcTE5H8IPHD+J0fR9e2VODtbsNQYB48Fj9j7E+7YexfqT///i5HkSiMdsgkn68TE5H8fwbVepoSFnktQvmUGjKtaVXOvb7SMqcqXS6qZZ4GCTCaxBUT0Dt9XTgNBDK5pJ6LFlbbvsZoHZn+tVqNam8t66PydNYv6co7tc6RUm0RNV/k9UBdG20nnr0waecrja/eakMw2PTngbscGM8r3jZX9Z9VXKqA/Udw4jFFNMgKWoMwXmGRfAWNLYbaMv8EDF5vtZp9PhBe9+Ya/7aVFf2g6c7TPVt/Xw5Z1se6fSb70OnO+MBHifGYM5waNr+JtjDBm3tCSU1UbdrjWRtYQEkLjyhiTDONPTj19qTmUc2VOJ0fT++u6wE4UgU311egsc32XeDsGrpHsVND5eY1n9iKhp/HY0qrn2DF2gF1dfB7mDUN92k4UcbcWh51Ng5kvLksLmk3tQsXR8mPj5cZjiKcCQazynR5tBNzYmxRPrN+c5StfKl53+IKeqJ4+3jLRgZm8a6d2o8NYPVK9KlZ7s893M2Mj6JnQpHHSuvdofiBQvm2Z7b7J7AeFkX47LbXbZxyouca9cR9e/B0514fNNpU7c1Yxm8nMw8J73zQVEyb4lT4pK7wTpiV0xR8MtViZZz63b7T46d7g3P2cYBvHGoMSctj7ycW18/0GBbtu6Bcfzg8UN4ckvy02n9xvjt463YfqgpdTn078Vz+mSyLZR4xUQ/D7oNnxtUv3+3/T8xHXF8cv7EZvUBxLShBe0z287i7tXHsWTdSfx0ZSneONRo6k4yMBrsDYnfY89p+jLZi+d3VLseV5kGhfUE87YsF0rjTfztTx5GVUN/UmJyRTFPN9+mGedv15Zjwz7v+U0AoDnFKCrpbId3ylrjQan584uwp6zV1Ari2e2Jbk3W/FOhiXD8d9HYOYqj1cld4mMxBZtL6jHqMkT9Ay+XY0+Zc7eKe144EX/aDRiTwSrYfqQJa3fXoGdowpRDxtq62c/x2Ds0gXaXrlv67/tCrYWksWWZfn7YuK/OcUCNA6c6sWFfHXYZHyIZDjRFq7Ns2l+PvqEJ18Cc2y7/wROHsMFhJGN9HQZHp7D9cBNueeSA5yTrmQ6KYk26W1LZgZHxMJ7bXo09ZW0oPtkef0ign7f1c6E1p4cXZxr6TS3sjd193iy1D9bph8vO0ma8caAe+ytSBzC8OpVGK1TdifM9rg8A0zGTtYR0uql66X77S5cBNuwl1vr4uW6Une+xvSf69ZoT6OgbM3WjA9TjoqbNfF9gDCacru+PB2R9POvyUGqX6yAS15pwivuCVAHImtYhU2Lq8ankc0OijuU6q0B4ubbttdTBh0PTuP+l8qTAogKgoy/5mIo/SEMGvwlDOZPKbBM9Mt4mWZOu23npbZnUi6NrYBwvvGluWT+kP9DI4MddEMEjPxvAdM9aZP9jc6rcf/q6q02vraOX2d2o2yVCtV6Em7tHoSiKaXSHbW4VVouVb1TFmwY73Vj/+OkjGJswH3zGg1dveTQ1HcXiJcXYrnWBstsS+pDEQCKi3z8yZXrCdt+LZVi6vgIjY9M45pAPaWdpc/xJw1Q4Gl+YvsVuXlaC7z12MD6915Fx9JNyNKZg9c5ztsPC68eB3kJn2+EmbNpfj73lbdhZ2ozjNk113zZ0nVm4oCi+Dve/5PyEwUk4Eov3139m21nc+NA+U7cznd0N4ryiItuTpV0FWA8oud2wer2ZNU7m9wbYOPnw2FTSvlyodUF1qqxlWxDBowOn3HNgGe0pazMNf1rmszsCoB4b6ZZ4Z2lzyuSb2WA9bJxuCu2S++sJfu2eguvHY2gi7Nr1SDc6Hsa6d2oM+S1SfsWRsRWZngdvwQLnc1Wmw8Pr3H6Dbx9vtW0da+V0Q1hS2WGqVOnnuN6hCdcAs1d+Axluv03jSGx2Mo2RtvSEHFuqWlvzGF9NTkexfMMpXPWuC03ThKMx0/fsElHXtg2bWlF7oZ9/nFbX6XhZ+UaV40Mq4zDK4UgMr+ypdexiqc9e/2vcZhv21eHZbeb8Oc1do1i7W2JnabNrF6O69mG84mc4Z5vf150rS7Hs1cp4wMY6kqXbYCJWP11Z6nozOqb9pvTcbJPTUYQmwth2qDH+2+8bnsRvXkr+ffYNTcaTPW891IgfPH4QQ6EplOqBN8O55s2jzfjJyv/P3nkH1lFd+f87r+qpd1m9WXqSZcuSJVkuchPuNmBjjMEY00wxvQTsUNIIIetAYAmkkMTJ7qbtj/2l7GaT7CbZkJ4FfgECSfzo1YALuFdJ7/fHezNvyp2ZO/NmXpHO5x/L782budPuPffcc77nj/jIF/+g+36YvWc/+983pX7i5KlRyYaV2x2iDpFe2v9dX/tffFvmaP7GT4wrb5rx4z+8jp/+6Q188Ycv4I33DkuRQFNbyqRtvvXzF7HlH36FvXHB17Fo1NDBaMQb7x3G52URS/LUnwM6kTBqu2wsGs1IbaBUkaxeZKYhv5VqTVw18kwBW8ey6Tw6pnImvPjWAcN9HTxyUhrvjVL9nnjmHdxmUoHrxKlR/FYWua92TgBKrV634ZmP6EafqYaLv7y8z3jhJmp/QUrebej5juTi/7+SRf3xBCiPjI5JQSoirGjMj3wxdn+T6bKyynn08jsHFeKUdpA7c44eP80cdL+jk3Lg8xlfLtYLyZoovLXniGZVWC1uZqbPI+724NFTePLvslxGnafh0NFTmg5e/vCKq6PH1VUqorFOSU9QTe7BvvXR32uO8eDjz+HT31AaWk/+/X2FgfHBoRPY+sCvpZBRQRAkw1meFsajs/PS2wcQiacEvPjWAfzu+XcVoo/q0EXRA5sf8klGyo9+9xq+/CNlBZ1oNIp/lU22vSotomg0imctlHc/PTIm6Qq88GpsRZRV5vLk6VFNWsb933tWOkc5rDzfRFVB/bbwO4/kXnPG9wa/lT8XUWg7wudf2Y8X3zqAP5ukXrjFP//XLsVKr9uYRRXwMBaNIvKm/dBfq+KkTqB+1r7zi5c0unSA9dVrPpFKJfKVqGSiU6LQ9v0sceHK4lDs35KQ7WMpjuvAbEVtgIrkBLxMp8a2L/8Rd1vQmtPDatScYR+l40x3Er0Jgnp4Z1bNUzXte798Cbv3JxxwRw0iOl586wBuevAJnB4Z0zzjPGcsCLHx9o9/fU/Xifbk3/dwaUSox0SR0bGxePW/qOpz7QGPHD+Nnz/1FqLRKD75zafwxLOxiI1kqmOp8Rg4hD/5zdgim9pZ9HA8Gu/Q0USq5rETIzg9Mob3PzwmE0g2v+piZJ8YeXTi1Ai+84sX8cPfvYa/yaKfWO/Ad3/5kkLn79Cx09jxnWekScQruw/h6V3aMVLP9uB5z8Tz3fr5X+PT//Q0Xnr7gOJ3H8SfO70Ij937juKXf35bSv14431jXc6R0THTNK/Hn3gFT+/agx/89lXmffyVKpVqLBq15mDkZERnwql+tt0Krth/8ATu/CpfVcR0wnIeZDXRmE0hf051izYkOfbw/J4VFKCORHlq1x7DfX3nFy9JWkdGkUf//F/Wo+CNMHo3nBq3k4rmVv3UbHEs6pCjeJfKdhdtB/kcSJ6xYFiRV/YVr231waETSV1/n/kmmcNn/oUd4cGz/i5eePn1f0ZnwNUzpMwu9AhDU0jvfqtDhb/2Y+VqjZmWzoHDp/CXV/ZrhPTe3c+/KqwUShaFubTn+Nlv/xkAW5tB7c0dHY3CJ9OzZYVmq41QsYS3eN1HRseYk2u9l+f4yRF86ptPYcvqKYrjibm38qprYp6s+H6Jk1Sf1yMZeyzUxsJ7qtDgP7zwHr7+n/wrbqdGRhHwe01DEX/97G78+tndePD6IemzsWhU15BXYzVtLRm4Q2uj2nu5/9AJfPbbf0ZDZb4jbbHK4WOnpSi0bCEatRahmAkwn5FoVBECDShFLHmwu6igjpawt4+oxhjz+TyAyp8VyokNt05VnHTitX3p7QPIz/VrPs8J+OBniPVLJDlb+tz3rN1fo5VSj+B+agXve8YU9Vb9/2+vfyBFTAAwHDf++b8i2L3vKJ5/dT8e+f7zOGd+C1bPacIzL+1lVvv86n/8FX/8a+JdECBIY8X01jLN9nK+/5tXsXSgHnk5PmNDVcUfXngP3/jJLszumgQgYY+xxp6d//l3PPvyPrTWFik+jyKWel9XmW8YmSdfdDFDz14bHRvTaACKGlQ3feF3EATg69uGcd1Dv0FRXgAHj57CWXObsGZeiyQ+a8TL7xzEbV/8g+QkfuHVD/Cn+D2Rt0jvmVUvLKqdNmIavxy9Mfy3JhVhpd/Hr9Wbe47gvm/9GRcsbpO+EyM9H/3BC9i5fVj6/Olde9DVXKrYD89kRKwUJN+XHq/uPoRwfTEArc2lPK7prmzBsuljx1OHDQiu9EFPPPuO42lobsCK1M9mxEpZU1sSz7eeLmWyzx5PxLtRGrydtiSr+SrHKIL9v5580/D89thIM2URTSLwTR31ajb0jUXtO6vk/YaV+SLAn/7H27J7/+X/4aqzuiy1QU5WOY/0sHIfk0kZeOO9w4bVLqysfueHtAa7HDOBt7FolFmBgScvUtz/Vfc/If1fvCpqI0QetsvqBDTOo7ExfHDI2iRcXVGMJTQGJMLk9nyoHExffucg3v/wOH7w21cxs7NK+lwSHmd0lOJnCa0daIzS0bExKUdYPXlRp3uYdQRHT5xWTMY+/6/WhB0P2xASBPgGJt5JqJER4/UI3KH/0WhUV8A73RXAsolUVXpxEmYapkfAj36nDLWVT65dbY8DwoFf/tFfce3aqYrP1Do3AJhVPJPBCQPwn34Wwf/9tTbicc+B445UAXMKo35BMIk8SuV7wlNy3UpzxKdIHG/+9Lf3sXpOkxTdokbuOAKUzzVLS0Wu1/fjP7yO3z63GwePnsJD1w+hMI+v+qQY9SJGT4sLX6wFsENxbaP/fkqZkvfq7kNS6v3Xti3Cfz+pdbD+9H/fwOO/egXbL5yB9rhDQc3Tu/YgErcf9C7zFTueMDwfZYp1rL1P7dqDvQeOK65vNBrVdbLtP3QCxfmx6yd3FpsVFmG2h2ub5J5xddTtdzmieL74wxc0DsmPff1JHDHQr7LKkeOn8e/xdH6x4AyLlzmcenbQE0RW64emQteFSD1iVgAAlBbkMLcxsh14Hgsnxyfeqq1ORnoa8a8m0ghOnXky84bfPa90sOu98yLJRB79+rnd+ONf30NdhXaR3KwP4e1ieJ8nO9H6crIqbU0PnoFOJJlOft/BE3jUoFzv47/S5niOjkXx3gfHFOHKgLkBmazooBlvqgbi9+IOGXW7njDxeJ9QdULPvLRPyqfkxSxFT0QQBIyNRbH9K8owXnFlLBT0KRxARvf6jsf+hJHRMeyIl1OMRqMa58hruw9LL1iyTo3rH/qtFDJvB6dEdpn7dmBSOzYWxdt7+aLe1IKxcoxE3Qkl2XipfvBbdgVMrnK7LmBFtNIIdT+pdogDzt+vL1ksa60HS/fo+MkRw1VBu5W77GLURwkmkUduPllPqETyWQsfr+5WRpKY9eUK4y9+mcXzd/qqq/X6RGeJWs/RCFbq4wuv7WeOd+K1UKTaQ/kM/tsTrzAjj0X7SoyEVvPsS/vwxR++gBdei9laVsc1ecUdVrEPtWPOLPWYdZ9ZpbQzAT3xbjXqCE91isc7+45yL2Dy2n08E92nXErB1lsQU6d8u9Ubumn32YG1KAJkXjuThdV1/FxHU0s9B7KKkwumvCXqk22zU1jRmjPcj0ElcaeJRu0769/ZexSvvXuYGRFq1ocYRgPLmmPFGTlh0tb0sFIK1Eo4thOcHhnDHY9pc5bNHvZTLpf+/IyqjORP/xRbCeQdBF5/7xBOnBzFydPKa88T1q3mke/rO+TkRKE1VsbGopKR6PUICPj0U8/UyDVP9nx4XDNZEq/Rxy8ZQGlhkHu/eiQTfuxmRM5zr/BrNekRhfHKIPMHDJwuMzueycbII72UraBByqibiEUKjhw/jesf+o3t/ajfT5bz6G2DCk12sFNZKLnjpS99wsipHIs8Mvixi6+JWXo5oE0ll6dRs5Ab9qfj+z8cd64cPn6aO4UhVbDsrx8w9Pt44REKf+bFvWitK0JhbiI66nVVtblk0kM/F19UEmGN3U88uxsbhts0n4ukMoo22aHAbLVdRJ0yp5fKw8Mtj/ze9m/VhILujB+810Uw82CPE6pKc5mfu22KbF4e1lQ0c5PTFhbvjaJ9eOZT6XC8nXA5OIEXp/rI1Pa1Lonj2/BNvL33CF7bfUghm2ClcE8y5zEunEdW4M2Xdwo9kcGHHmdXNxFxeyVe76HhfQk/9U12JZ/fPOdcgdyeaQAAIABJREFUyVI1f33tA02O/ZYdv8Lkuph+wumRMfzqmYRDSL26qcYspFLknX1H8KpO2etU4eYAk8pBGYhN1B/RieAbb1U73CQLfUdMolF2BTUglt7LWyLaDvKKILwr5izkEScjo2OSMOV44qNfSZ9w65jBYouAzHakqlPlzfq4ax9MODFFMXnRGXPo6ClNpTA32L3vKLcG3LET2u14J912+cL3n0drbSHu2NQnffbjP6S2UqeZBMKbJsLRmYTdyZeT2inJEPS75TxKsz2Sud1aSnGqQikvrBRfO/D0g8+8mPzirVVOnMyM99Yx51EKI9ejcMfe+P6vjavTHVRJlzy1a48Ufd7bVs76iSnJnMWEcR59/9evYHBKFQpC/qRz/azwno7zyAynRIyz5bg8/ORPbzDD6cV891MjY/jb6/arT+kxMhpNicFuxL8xUiKzmUwN388mMnnCbIXf/mW3VGlRTUGuu84jp6OBABjq4hH2ME5bM448UhtdqSYb9VCsiHnuP6S1p1KhqbF73zHFeJ/qFXwb8kUZi10nSaakK+npZCYLr3PMLcHozLi6CTLkdmcNr7xjnomRjkhSN+weO/BEmfKQysij4ydHcMSF4jpWFy/lsgUFjKInPCRTvX7cOI/MjJVDx07j0R88jwJOEUin0FtRN2M0Tb10JjuPAK1WkxwroaZW+OtrH5hv5DIRDiFWYmKR7kmxUxhVsspGY9VqFQ3CHOO0tcybZMlJdap8JnCUEY3kBm5rQxqRSfc12X7SrDy1Hjxpm9kMb2rwS28fRGNVgfMNyLCOTRCMbXC3SHsEmE14qx1OVJzSKkvl8yEWdsgk7FaK/s1zu6WqoFZJynkUDoc3ArgLgB/AQ5FI5FHV9z0AvgagEMBvAFwdiURcKeHyzZ/tMt3mhVc/wKwpVabbOYlaLJOXdDlxMt1JYaQb9KJLFTfcEmMkiGT4xk/M+7xsJxujq7LV0LVCqufNRmHpHkHIaC8jS3x5vGNFh9Iux0+O4N9//5r5hi5hp3KaWyTbTx4aJwsRTsMSg08lP3vSmcgMp/B6hLRMnpNJKSfGP3aDNMYLz7yU+tRH2wJA4XC4FsC9AIYA9AC4MhwOT1Ft9i0A10UikXbEpAmusHs8M3jDr1LdCdkd0u16EgmCmBhkUil1t0hlODLBD69enFOYVlujxySjSNX9SKeu0KGjpxRFN9IJPf7uYKWqkt0KTNlCWWEwbYvaGeSnnZCwCoBkEj91KP2N4CeZJ2IxgP+JRCIfRCKRowD+DcC54pfhcLgRQCgSiYgqm98EsD6J4znC8686I4TmNm7qfBAEkf14J4BFRc4jAjBO4xYEYVxO28b/2539fPvnL6a7CYSLWHKCjsdOSIaT/Sz1bdnFRIimJqyRjPOoBoA8ofNdAHUWvicY9LRVpLsJ45Ycl8qB+7w0FBIJNi3vSMlxjFI4eQkFM1v2LlMEWYn0YrTi/ZdX9mPv4fGXdnPX5YO4+/LBdDeDSCN1lflc24Vy7AmmOsnnbpiX7iaklQ/HeREQn88Dj8eZCBSrac/5+TmOHDeTmFxfbG37eFXpbGUCrHWmjLKiHLRZfH6cJpmewAOlr10AMGbhe4LBqIGH98Il7Slsyfijx2Y5QzPKikKOT8I3LW3HIzfNd3SfbjF32qR0NyGjOHqMz4i0K1TnJHOmZva9o6p8BGCseTQyOoZHHn82ha2xx0BHpaXtjx05ifrS9PcRqaCiWH9y+OB1c1PYEi2FNivZqDlrbpPl33Q1lXBt9+M0aj+JnDiauirGmchhznE/W3lv/zG85ZhYtjVPwpEj2irL2U53c6ml7aNZHoXtlOORAC44ow0NBgsLrbWFrrchmbv5NoBq2f8nAdht4XuCgVEqSiYJNPIws7MS918zx/bvb1jX7WBrgNldk7B8ZoOj+xQxuzMBv7VXrbulDKGgO5FSTmM0sZsI5OXYcxw2uFGdxSJ+X+YN6FVxp1qvS85eIvvI9Ai0es4IEUsIyWtNrJjlzni3bkGLo/u746J+5uf9HZUoyg9izVCzpf0F/c6NnU71kdlmv4nkh/icZ06eXzJ2YzZz3qLJ6W5CSsigQoVpw2sxY8EpmYKgSxkYZlg9X8v79wgoK1QuQmwYZr9PJQVBx48/hdPR7wTRKPDau/rFuIrznT8/NcmMir8AcEY4HK4Ih8O5ANYB+Jn4ZSQSeQPAiXA4LC4bXQTgp0kcb9xwtoEhZPSCOdF3XLNmqvR3KjqRwryA7d/yGi28VJfloqXGvke2uZo92V82UG86GFYW860gywcIVing+dOrNZ+lC7F5p0YmdkCh5hnnnOj6MyDdMf0t0LJpaRhfvX0hasrz0t0UguCCZ+JsdcJ01AHdQ49Ls7Q8h8fmXJ3IXbGKmN/i4ktxfqxPrinPw8M3JpdO5fM5YydluP9TF95KRl4HRXVLCzM/TclJB6VIbQWNeSwyOejGbhfrtfhDJ5yzd1/cjweucTaSk9dpUpDkmNFostjq8QgaB5veFXNaL/Ti5WEs7Kl1dJ9GRKNRFOnMrTcMT8YlK9yXzrDd20cikXcA3AngVwCeBfCdSCTyZDgc/kk4HBaXkS4E8GA4HN4FIB/Aw8k22IyyQvc9bslSazApcjLyiJUWIx+c8lURE3UVzq+e+rwezO+191I56ale0l+P8qIQ+sIVuO38HoRt5ItWleYyP+dJ2+IV/hVXOfUEYnOD6dc2EBGNp9MT3HmkdvLx2jlOGtsslg7UG36/uK/Ode/R9NYyy7/xeQV4KcQ5JfS1k8aeE7ghXt9UnXzoOWsBwgmsTnzM0HvdxWHQb7GvrK3IR16OD/On11hahJpcq9UV8Tl0b6M2vEcCBLQmseDlBPO6+RasnLpO2UJVkmnnrAme1ec8W7HaffC8O/dcPtNma9KDej6njppRk2xffvfF/WiuLkSuzUh5Pc6Z38q1ndcjoMtiqp4cn8/4/D0eAYLaeaRzzcRrr9aR6miwpyMkCEJKI0ujAC5d2YnLVnYqPl87vwVLB+qRlwINvKR6qkgk8p1IJDI1Eom0RyKRHfHPVkYikafjfz8XiURmRiKRjkgksjESibieFL1l9RTH9uWGwHJ/R6VhKLqeEfrAtXMVq4g3nzdd+vv+a+bgxnO78dmrZyt+w+qM5A94rcpZVFPOdo7YRezvRefC6jmNln7vhkEuCAI6m0oVE/xVsxPtuu+qWbq/7Zlcjs9t1YZTezyCopNiRXSZDQwi5y6MdcTFeWwnqJlDbcWgO2kKLAJxR9fpkVF023ASTHTSbSgu7K2F4LL3aPpk66ln/vhKf6at1N9wrrNptGboRToaUWdx5bozhaHW4xmnSxn3tVdwR6saY/4S2QnhVxvKAYPUrpmd5lpPeka+mLptNXXM7/Pg4RvnmTrQ5dx9cT/uuKgPX9+2SKFheOLUqGZb3vFczlg0im0bexFusPbOrZxlzW5yknu2DGLTsjDXtvJn4p4t41/oPdnJ4vzpNZp3z5eBaeRuYNURomcLyB3D6vlMqrCbIqRePGx22UncnORiROOkAmb0D+88zW1zzisI2uwc2f/LixJ9tjiXzg36FKnddiMeBdiPQLPjZ4hGo8gP+THUXY1Hb05o4545p8n03frMlco5rt0IynHXU1kdmNXIdTbKi5wXqxQARA1eI70Vd49H6dmUr3qUFAQxfXK5xtgUvfVn9CWK3HkEQXqJ2lReV3lwzNQkPMTS8eP/noiHPVt9MeWdq9oxZhX1+yRfyZCnEZoNBGVFObjyTKWDUp0a0Kl6BvNDflx5VhdXO+dOq8bO7cO6KYVmk5T1KcyZF+9PNMpeRZsoqLtq+ftmhBvOUTkVxSFDp17M6elqE2wZ2GL1QqN+Mh2UOpAn3ziJ3yFkJxL0jov6LBmzvBGRhDFOp6DyvpdGQtMAMMYRFGqnGxLf6/KiHFy2shMFBqLSK2c1oj9sHOGmHkNry/Nw/vBkbFwcKxISsJg6Fo1GFUb02vktpv2y+H4LgqBYgd5/6IRGf1GvbxpiROmIotfRaMw+7TG5FmrUq+mpJMfvZaY+spxy8vFML6WCh42L23S/u+9K/cW9ZDByfurhRFSf+tame0EpVVi9cnqRR+rIi1SyoKcGAGyn16vtP7PXnLcb6LdYmIGX0dExZoSopdcgiRVBs4VO9Rw59psEH7tkQLEtEHPoy/drt3K2IAi2U8TtaPtOkmXBWF24mqTKoLHb7gnRU21Z3YlLV/JNbt2qyCUiCMbvj15kiUdQdjbyG242iMnT1zyCIEUD+FUGmbyDntriXCSJuHKnp2ugR1Cmc1Bs0Ri5/YJew+9HZCLP8pePx4iY1aVMUxME5SR8RGWxf+bKWcgP+aXwb6OUObPOy27npmZ4RvL5uWJbxqJR1x0hqeSBay3mhKtOPS/Hj3aOsqosx0qfxYmFEYtm1OK6c6bpHz8Ft8zOwCQObm5GRV3F6cyV44Qock0Zv6FpZ0wXBAEHjvAH+GZ7BZdMQT2WsrAy/vFOTK84swvzp9fofs+T7mFnEiwWCeiZXI6h7mpDDaTCvACuWavfD7G4Z8sgls5skCKAjCKPdm4fxt0XKwW31ad95pwmXLikHZ+4dEA3DUwe9ZETUN4r9fHHGO+Nz+vBOfNjQuLyVPZLV3aivChHuk+WtU4Ym/PqVa6Z18wtmn7xcm2EkZ7z//wztA4e+TUzslPkK+Us2g3sI7eEYO30gk6Mn+p3jyKP2OgNU+kUob94eQcuXdlhy5YAWM4j43NRXzN5xkSTfFEqCQfN7K4q3fS/0bEoCnK18zDuexlNMvpIgGnhBHXfKm+bR/F3ok3yn9itCCcIfNeB1W9bfYYfvG6uotiO2Nfa1TC26wOfED2V1+MxrQhVkOvHqtmNmN2l1a/ZvDzsaMqCofNI50HyeARFeJnZA3f5qoRHXvHSeAQcPBorKVqYpzT45AYRyzjSY/WcJvYX8RM9eTrmPLJazj4vx4/OxhIU5gUs6x+pc1nVjI6yl2QFQcDXty2ydCw18mtXVhiUQmvF+z7boDy62QDiVHqEURt4ETtaK84jloGaafBUxtt+4Qzpb9aZb9/UZ7qPonztQGwnHUIPjyDA5/Wgs5Edjal2erqB1f1/+dYFCMT7uaBFkVwrWI1qaq4ucGSl2dourB/P6DVUR6nccG63rrYaEUMdKVacH2CWjueZ9J2zoFUT7asH6zlh9f0+r4CLl8cE5lmY3d6i/AC2yopo8DKtpQyXrOjAuniatdw5pB7DnBDtNrN31OkUeqfdUFWAOzdrK7sNTatWOPfOmtuE/nAFBLCdGXrmUXF+EDu3D2Pu1EQEUmlhDnZsnYOKeGS4/FwCPo8idalUrdmpMyn52MXs6nRqzpzThFCAz+5iPV/qy75uQQvTcQQoHWx6dsrGxW2mdqCRLeF2xSYrOBN5lNhHfsiP4ARxHlkd2vSc4KletPy4LHoFAOZ1W9NUk6MRdzZ5ntQObL2o8uRGdEE3/W90NIotq6do+nPe1yDZiqmnR8ZQZ7CAd+T4ac04IY+IFYRElVDxHNTPld3HySMIiqgsvT7unsu0jjl1m81StItUDnRBEHDzedPxD1fpZ+eoJRAK5ZHCFHmkTzQaxanT2rx1OaGgD+sWtDIHvZbqwqTF8UQEQTBcDdQzkjyCgGmyzsLMmJo7LWG8eBQRS0BnPCRbnQMbjSZCMfXaWJQfwEc3JSbOoaBXWm3TtDl+XDEUN+Dz4As3zcO0eFTTGTOMw8hzAl7cdkEvHrp+CF6PRxGxs2hGLXZsVb4sAQ7jRWTEwDkmCILlUrHyuyF3VHbLNF/EztPImDYbQJxaafElIUi8KZ6iJjZlbMy4XWLE1aIZtehsspcOObmuSN9JaQH1qvP167Qr4jwRL/J3x+7kaEk/I/TfBeNYr3keQXBd88gq8udfvfrvKGnymaivtjqEWLGtzcgjPdR9Yijg5V4k4NGtGY/ctVnpBI5GY8bbot5aRaouT7pJTsCrcNSohYhvv6BXmojI76PoUJjRro2Kzs3xQxD0BeZFJ6le1NM1a6ba0sIQBAHzp9dIC1rylHm1Y1bvkbQc4cngKx9ZCEA7/phFXKl1Hi5b1am45lWlubhm7TR89fZF2LaxV7N/K4trauT78nqV9mBJQZBL34nXDrCyQMCaiKuPs2p2E5eOlN6kfjFjzBM5a24TzpnfIqUBsZx2Rs6C9Yv4hHt50DjxGCTjOxK16eT7ePjGea4X0chW9F5n9fN5HodswyKOqHtW2mUw4NVNO7/vyllcx5ajbruZSV5WmIPLV3XioRuGcP81c9BWl3g/5JfHio9G22b9H4+OjSE/5MfWNcpIKyv2bzL+o7GxqKm1qr6meuLgbfXFaK4uwPpFk3Wjk6ygjjy67YIe5nblxSFNISv1MT9x6QAGp1RZOv60ljJN1We5xlNJgXLh8H7Z2EuRRwaMRaOYM824YgQr4sgN1PdJre6u9/B64jmVYlSElYdcUf7dI2Bhby0euWkeqkpyccemPqkDaakplIxMXS9xFGirK8ZHzu/B8Ixa3H5BzJHU2ViCjYvb8IlLBzAUv9biy1QcX1mLRmPRRGJ7OhqLDdN71BOhctnK+UVLwxpNqk9bEGkc0Yk8ErEsnCZrq56OiGikG00YzXBqpSUnaF8MvjAeuiq2JRZ5pN+ViMZwTVme7Zz+4ryArpPSCnLx0cV9dZIjUw7PqyUPy9eLOjDLhWev9LrvzBFXY2IDnuuHAxCbFMkHMz3k7ZnaonU02qmSyCIaBc4f5jf2xO7wgWvnWhLhNcPofbZzawQB2KqTQ8969+R9lbwt6lSXCkfEm7OHM/rqcMt50zX9mjjRv2hZWJEupp7wX3VWl8YxrTYwl85UXuOOxhJcEI/qkN/7f/r4cuzcPqxYEW6vL8btF/QaimqvntOElbMaUV6Ug1vPZxuzdqInzIoyqE0H0aA/a26T4nMrQt16rdR1tJhMUnZsnY1PMlaB1YjFMML1xYqxg+Wckl9Ko8PPkkUlFYQCmm3li2ABnwcjjGqmViqcmo0p5y2ajKL8ANPmsbpY9YWb5uELN81TPFdfuGke12+LC4JYLRN8ZT3fRs+rUbqbGeqIX55xWBAEXH22vZQl0TmhPp9Ujcdpx6ITQf6+yXVp7djDRg6Mj18ygJ13LcWZqr7KjKrSXN0Ibz20ETwm5yLEggIKcxPv6p2b+2I6YLJzslLVcbmFAjui1EdfWLmQlKpnlkefUaM/21giFV0AEhGjOQEv7r54AA1VBYqxxfbivKB0pjRNMliQUZ2G1yMoCgwU5wdtp0LKWSlLa1Sfls/rQVt8Qd5uBOWEcB5Fo+ZGutqw0Wxj4wIzRSSFxLPTH67A7RtnKL7W97Arv/d4BFx3zjScqYrGGJxSpSmHqMjpFGLGUG68lN/kuiIsH2zAPZfPxMrZjaiOa3JUFIfQY1ApaUpTKTYtDUue+Nsu6MXi/no0VBVIg7h4ya9b34PVcxqlz8XOzevx4Mb107U7R0zHQM2p0yYOH47JqYhZGiNgbWVU/nTIHVPyzmx4Ri3uvWLQNKXO8DhJ9tRi6koypRzFNkihn2P6aWs7tw9L241Fo1yRNWoPOgBDXQ8eCnP92Ll9GL2y0uSttUW2Bz75fdBziPEM4oWqPsIN55H6vRGPkAq9APF0gn4vlqicLvKcfRF5m6oZ+kBWBOGNomWiiGom70aId7KkIGi7IgcAzSzY8B5YfBauO2cavB4PVs5plj6TR8yyVrXlERRTZFGBcxi6bhOJpQP1TN0/PftV3f+11hZqFgkEKKvB1JTlaox3cdGGdblXDDZgVnxFMifgRYfJZOWc+S0oyA1gx9Y5unpddu4qq3+WI0+Zjx0jdhRecfZPsZw6soY+dP2Q6T7MUiQKcgOWNMw8HkGqhBrbv3Yb+SGNFknqqwqkijcdjcWKyYT6PRucUoXTjIUuK+O32bs7OKUKD143xIxO4x2PxGuTl+PXtC0vx48dW2drIsXVqKO5PB4BH7sklp63YrABd+ikgoupoMlEU5/RV4c5slR+s0wFIGbfsqpP8SDeE/XldaqfDfq9tqp1uond9C5A+W4pIvc0qV8Wd6aicVIBKmxmmdRV5im0zsxQ32uzogIsWmuKUFWaq3AUJFMEw+iXevu1Fnlkv22jY1HTAUv+bNx7xWB88Sc+T4mCee+Vmkc2HSmCwC0BIEbmikcShFiBCBGr8i48sPqVj27qwznzWyjyyIho1PgB9/s9rhjHW1ZP0XwmIOFUYa2a5etULRHbJzmPBGBGewXWqqIxrjqrC7duUK4yKoXC2OdZW5EPjyBg7rRJ+OimGRjoqMR1jJQentdDcnTF/19cEMQ581ulF3MgPqmrrciz9OBOYZSVvml9YpXdyh2c1RUzwmd36YcHlhQELVcRq6/MV/xmzbzERE4QBOaE2ArycxSdWzyDsjjI3nJeD3ZuH9YN5zRDrpsiSJFHyg5Y7RQQRaA7Gkq4Io8uWtqu+P/O7cNJC7gPdGjv88zOSkecNf4ktHkeumGeYtXBjTm6utS0vK+z0+/NsaCXJU4cBUHZ98zumsSMZjFrjVORd5ZtGPkEL4njqtMEjYwVq8eZ0a41PuVpImoR21iaciKEX55uVFuRL03cAHBFjU0EdI1fQZkCMMayOQTl/RYEQRNNKe6e9V76vB6pko7Vfktve/VxHrttofT317YtYk6OjY7cOKkAc6dV4zZZpBPvnP6Gc7tx31WzmLoWclvJzHnlNkV5AY1zqrYiD3dclFgIbK01TgWcVJqL2y/oxaalYemtqy3Pw6YlibHvgWvnorosT3L+z506CWvnt2DD8GSUFASxeo7W+c7C7FERI8BY4xjvc2YWRVZeFFJEiqu1YwD25DQ3x4+v3b4I5y5slRbdLloWxs3nJRYdrzyzC6tmN6K+yn5BA4+g1JDhGR4EQbA9GKgX4EScGt9i/UxmOfzl52ZVc1C+6CgvOmFUXSsY8OJ6RsEQHt+KPCVMwuR3Xo8Hl6/Szvn0UN/q7tZyfG3bIlyrU1zASGJgoKNSmvdZiUq0wqhO6U7eoShZecXR0THzimuqQAkAuOOSAUxtLkVO0CvdQj271+77JwgCjhw/bbJN7F/pOsT/79oirmJRQn8zu0cf986jmvI8dLeWGT/gOg+16Lm3OtEW0y3YD4WAnrZyrJjVgAsWt2u+ba8rws7twxjqrlZ0IolBRlyZNL/l8iglaT8md1wQBLTVFeuXHuToAaQyiDq99Jyp1fjq7QtRURyS0gLMjC0gFn1y7xWDioig7tZEdJQgCKiryGNq46hPZe38Fnzxlvm44kzj8MD502skZ0iTgTaEuP8b1nUrlPCTifBhHyjxp9cr4Ku3L1RoUAHsSmqiN1vsHD2CYEsjQL76J+5LXRZ53QLlfsMNJdi5fRj1lfmaCextjKp4bnSmLGNFiEfhqQkFfTj/jDZNBR89ki2vK58YuaFffPL0iPID2SBm50qbVbxgodbe8Hj0Uj+MW2TXuSY+q+IkRy8yQc8RG3XOe6SAR9+EB70oUXkKDMswkk/61JdEHnrNKkGebkTxy1Ri9H7K0xZy/F5tVAEYzkPVRtKqpM4zJr4zVvtIvf2pP5en0sZEQBk/1NnZjq2zsW1jrD+XR0WJ7/SKwQbMn16DqpIQiuPFAu7ZMihFpPRMLkdVCTule0pTKdYvasUjnClQbunAf+nWBdixdbam79owPFnxvvDYZx2NJfB5PVL0+McuiadRqKJSxMgjvy+27bJ4xGR+iM+JZpQ+XVuR+I41jon24sM3zsPDNxpce4vXu3FSgcbhpGcviqmDIot6axXp5mVFOVi3oDWphSD1kXn25LHvO5ImuernJD/kd6T8vJvFJnhgaQMZ9Vlm4+Dq2U3S32cNJf7WjGmq69nTVo5bzlNmN/BEv9RX5nPNSZKBdc4eQcCkUnbkk1nUvri/pJxHBpdGL1uDfwEyamFbxvE5Io8U+4//2dNeiVs29MAjCInFGdlvrFQu1z0ugP6wsS6kOrJTtAXcEn3n7ZLtnrOLiqTpY9vGXhTmBRRRHkYvlN5F3rQ0jIW9tSgvCmHPh8cMj3nVWV34yr//FQBwczwVK/LmAc12ghDzUK9fqE2/2H7hDCm1SxxAblrfjV8/u1vjtbRiPPJEHvHC80CKDiEjUUlxG7/Pg09vGUQo6MOtj/7ecL88kTufupxP98gjCNyCvOsWtGocIqy2xf7l2qWGRb21zPD0K86cgvKiHNz3rT9rvvN5YkKp6s5n6cwG/M+f31F8lhPw4sjx04rQyhWDjfjdX97Fu/v1n+2b1k/HQ48/J/0/N8cnPQNyzSNe1KkzIYb2klMV5eRYnUssHag31cUS0TN8eC+L3GhPZs4j6Px+87IO/NsTr+CN9w9L28XaZ897ZKeNgqB0zJweGbO5H3svWMDvwfGTo4oSrSx0B3J3fEeGjkcrp6qXoid/N9XXTvzmjk19eOP9w3j2pb26+/cIAibXFeHltw/yN8plmqoL4fUISYXp68ESTAUMVsxlHwd8HhTmBTSpL4IgaBZv1Pc44Iv1h7lBthNTPFWrr4Hee8ObdnPlmVPw2H/8zXAbeWQJS4Q0N8evieStNdGFk+9jxSBfpA2QXHqEEaLQtpOr+2f01eGMPm3xkES0eexc7BYQmNZShk9dNhMf2/kkAOCSFR345k93AVAWbQj49ctIs5zqC3tq8MSzu2NtZLwXFy8PG2pyqd9bN95jXmw9LjqLT3w/1f/dUHc1vvvLF3H8pHnqnB5RpE6LhsWmpe0oK8zBLY8kbHrF3MPC9W6tLUQw4MWM9gr8+cW98Ho88AiCeZXfaOw6q6PWee+1TqCNY+TopCfppS2ZORlEPdxTI/afGzW9beV45qV9ABKaR2p455RRxORh/v7Gh7baolchW9mWxN+sd0yck8q/kqcv25Y8ErTzloaaRwxoAAAgAElEQVTKfLy55wiAmFanOPZF5WN4NDWSAEbHsDvbyvjIo6rSXO4Iic9tjVXICjeUaJwMRhE3eoaG3+eRRI7NBEOb41WcyotypIgGlqfY6DFhle7ubi3H9eu6NTffihNIHSqfDDwdr9g2XmOgpjwPOQH7As5OkO5Q+MX9dcwVp9ldk9ghtEg44DTPAuMmidFTBarVSkNhN2iNe9akQOyQV85qZEYSydGIBDLeCFc88TaMQ93VetX/9USceQ+pjDyyb0DLtXjkbe9qLsXHL02kCSzqjUWm5eb43A9sF1dYIaC/o1KKkDHTL9Pdnc0GJ5w08QlZ/H9XrJ6iiBjRc8rL70oyfaj6p0YrrkYh2v9wtVI/RK9Kj7wL1nutJtcV4Yy+Ogx0Glf48KW4LDJgsiLtouHFmkgDxikPonB+i1jRkdE0M5HUgY5KnLdoMs7RiaoSUwec6CMrinN0n/eyeLUpsXnyvsWqaH06JrFuV61yK7JJjnjZhqZVY0l/vWURXznyVEC5fqC84p/YRyoiRA1u3ublHYZp/wt6jKurinZDiVRQJX3OIzWHjhmnoACx62T30e6MSzCcOBWLCmbp/1lFLUzu1GtXX5mPB6+zVhnR5/GgWFVS3KjPMrr1N8UX469ZMxVfvnVBbP/xuZWmYpnCP8XeKe9zpl4UtZpqZ0ZIZ85TWpiDW86brokmNpvz+X0Jx/a1a6cabquHeIaio0M+/uotEsubZZbeHm6wJiouh2c+ecmKxByKdbU+OHwCQKKIEwD0tlcgL55dpBbO54XlXP/EZTMlcfcz+upQJWkgxs6DFQWVDuzKbmS88+i+K2dhYY95aUUgFr6qh5GRqX4nrjxzihR+Lf99g0FOtdgRdJhMRIzawWMIix0wj0Emnpa8GVZLgYulza2IuYlttLKSJL9W9101i/t3vJiVPvzsVbOMw7I5EZ+lm8+bjk9dbl7NxSryia5XZwBVP8+NkwqwoKeWqXV08fKw4fGYz4sqdUIcVM5d2Gq54gTzmG6krdkwTNXvo+jEVldXm9aqo8dkcEy50a5O5bNLV3Pi2otGFovVc5rwtdsXxVayHZrZCQJw4RJtGq4YqltfmQePIEgr7CdPjyo8MusXtXJVX1Lfk0tXdOA6hq6BmoQRJA7csX9nT52kuBe6gUcGj49RYQE16updAZtpa2qnit47o4j+NHEyq0vHqynITb2D/WOXDLALT8RxqqvgXTww6kdqynKxcXEbrjo7ZrizIm/NxniPR8DywQZNKfnE8ePbOfDeyqOft23sxeb4WHD3xf24O65JwzqeXrlqPVJRQVLOspn1uGiZ8biWLBq9IQfnlVKUefz/Ab8XFyxu00QkBBxITVIUfoj3KdEo+3sj7Ph9xPdDnLil03ckCMrj81RfFovPmMHS6hQjvkQ9Qrk2XbxFpvuVE/B5lBIJUcu70GX7hTNQlM9fGZEHK7daXETxeATJqS9Geaht33nTaxLOe52D8E5LjDInnMBIGHlqS5kmKt/MLhYd/ksH6tHZqO+0NUIc38Txh+edlL8D8qIC2n3H/l0201612pGxqOkjLfcBsF7NBdNr4fN60Kuy2arji+RVpbm476pZlscPM6cYK+jOLEU9VdjV4c1o55EYjSJ/aVgdMQ9qA0ZezUv9gszqmsR8GMQS9CwKcgO494pBbJY9dKyXnRVhIzaNxxC+c3M/1gw1W0rtUWgeWXxS79zcj0dvni9NDHkm4eI55lnQipK3S0/3wC47tw+bRtjkBHxJVYNIGHyx6zOtpQx1FfrOxqnN9jp3+bVJOBLZ6Sgid17ErlIC6K+wi2hXdhL/FydcrPdiYU+NQkBWD9bjKF81/tIt+k4QK9gxA9TviljNRd1mjyAoxIXNuPrsLlwqizIzuwd6yHOo79zch/nTY072UNArrUKpaakpjKfPxJ8dW0dmw4oSqSwJ4fYLerF5eWwlSzRKTp4eVURzLhto4KpuqHCEewTMm17DFIpWI/aXoj2o9zzorzzJ07+U39xwbjd4UY8JRpE1Rk4T9TvP4zwy6/rNJkKbl4cVaS6pIDfoQ5dO9EI0SQ0FOdx7MehIBEHA4v56KeWNFeavFwHNOy6zwu552X7hDEkPcFFvrSS+DcSMX3GRrrm6EIUqR6Gd421c3AavR3DNOBYnS2o2DLfpph06xTnzW7FylnG0SF97BarLnLVl5MzrrjacrFnF4xEwraWMKTKsj/2bKy46iX2zE5FHdq7H8IxaDE2rltoxr7sakzjumwC+9yJkkG4oylRoK91ZvBbqdQEYR65a2rWN3bB+c+zkiPZDm/sSF9zUj0zQ78UlcVuDdQVry/O4I4j0nEeXr+rUVJS0g3kaqsr2Npkg5gR82Ll9GAt6ak3v2TVrphpGu6kd2EZYXcARn8v1C1ul4AQeRkfHLD2LrDF1cl0RHrttocYZKi0tRqOoKsmVovOtEvB5FBVuWaifWdfS1uSSBQab6UXAmZHRzqMb1sWMcnn0A8+E1Cq8nQkrL11OdVmewqmjXmUG2HmuteUxJwNP+fj6ynycxSlYuyxeGttKSVoWoaDPUhh4uKEYFy5px4VL+L23Xq+AssKgI51yOpCeUM4xX52HbacDEX8jThxFA0RthCUjQK1JVRESpxgKePHYbQuZAuWbl3doylDrcf6w8p2WT4SDDqUzOrGqKd4iVsUslnNS75CsFNSuuFPcin7UjniaLhAr2ZoQMGdv/8Vb5mP7hUpxdcfGrSjb+PcIAjoaSySnkbgyNK2lDF0yB6peO4xW1x+9eT5389TRYno351qOiROrqWfNbcLifuPxAdBG8hk5j9oN0oPUixB6EaUKzSNVy62+Enk5fqyYxfdOO4lROx0T1+fcjd77yfqUVWiDZdBuXh7mjlIVo/OMFib0aK8vtuFUsR9bv7i/Hl+9fZErxvGXbl2Az1xpXPrdbcyKj1x7zjTce4X1KOqELWH8hno9HlMHllVuPm86ejmc8SLt9bEKaHZWr8XJuY8R8WSXlbMaTaOp1WxaGkbA70VvWznWzmvG+We0IarjOPiELP2b97k2imq84swpuPeKwaQLJzDb4lTXmIRtKkfukLNyr1mHXxKf27CidwQDO2jrmqmaCpd66GVOzJ1WjbkGgQS85DD0Po2wEpFvdsv6OyoNdVyntZShpaYQa2XVovWPJTD/1v+B7E8L5zQyGtWNyE0WdTVzu3zxlgW490rOPl+ufWTApqXaiH7LGBwjaFNLL6OdR+XxlWkn1NAN4XxgrB5bXvFAfPHzGQblzedNx+o5jag08Vhapbe9Aju3D2tWEd1GiKenWKlS5xEEfO6auY50yukh3vm4tPdPXT5TKsW5bWMvlg4kIgAKcv0Y6q7GBYvbmL9NJm2AVQpVWv32CPB5PZbfC3mlFEEQ0KeqUuBO9YHk74zeeeqef/yQ6mofzK05Bq9tG3ulSo5nDzVrI6A8xs9gTsCXtBi51yMYpgcDwCyZDoa6jSUFQTx0w5BGv0PvGt69WT+iy0rElqjn0RYv9yyvMiS/XnqpWYprymjrmnktaK/TW0VO4PV4sEOmV+T3Gp+DXhpo0O/FF26aJ4Xo+3RmsvLV0wuXJPqH5uoCtNYUGR6bRapTkGLpJDpPdNS5tDXe3eg1pYsREV2cH1Tca4D9nC/sqTWsiCVnSlMptl84A8s4HfNqrKwoZzJBv1cz4d62sRc3reePAgRiBUnUDnVe5O+Co9dTcNeW4OGuzf1c1QznT6/B57bOSaQKWUB0xPqlqFBnztjuHMHjEXDm3GaEgj7dtqi1T82OtXP7sKGDO+j3Mh1vVi+FeAQpMjRqnuJjdd/J/qbEZuob6xqvmt2EnduHmZkcRmOC3+dBeVGIa0KueQY47wlP+j1gPpbq2Xc82H0HxFMOBX24a3M/l1NYbJeZ3a4ex6Owbk+0y4SnzbByDaRxMck+yOPRqVIuQ30MswhB+easStq6v4v/u9AkiioYGKeaR0DiIQgFfYoLn0yakZxkhyyW1geQiDISECt1unSgHosYN7+kIIhz5re6Fr7mxOqs2DSnSks7ydVnd2GWiaaRW4iCkcN9sfvK+0xavSN1FflSpEa4oQTnn5GYCAqCgMtWdkqON6fS/jyCoBkQBEGQqpDpTVjNuPm86ZKjVIA2PccN55Gj6evqQV3XdxQ7qPYaMnYpiPvSP/dwQ4lkaNdX5uuLRVpa1eO/1h0NxXj4xnnMNsoPKf+Wtf/C3AC30cA7qTZDXN2e2VmFz183V1eEHtC5B3IdEJ3ficamUWq11yOgvDiEW8/vwczOSlMNOiNjJi/HL62OaiKrVG1aMasBlbJ+4e6LB2xF9bnlO9KbqBodLgrnFpPsartcdVYXbj2/R+MAFykvDulWwrNLe32xbSceb1SL9nepdRraIdxQgu5Wfv0xIFaQxCjCzwiF88jB8UW0IVJRhUePlppCrJKVR9dDEMwXE/QQ+y6rOpxmOOHg1rufWsF7830dO2Euvp0s4rMiX1R0zHnklPdIgfoC679ARuYg6zvRLgomqQlmV/PogWvnMovfWEV9atYqbCd9eG7E58Pn9UhtntFegXtU0bTi1ZTM1GjUesqbIGD+9BquZ9LKcytFHllrji02Lm5HfsiP/Fyxn2dvt2ZeM2Z1VUk24Bkz6rBpqXUtP/nuWfqceTn2gkvsxSulgSvOnILWmkJJYA4Abt3Qg8ZJBbjss/+TsnbcsmE6Pv+vzyk+0/MGSmlEiDm+5BP+VOKEDZKX48c581vQZ0E4O1XM7KzCTJNKQW5xWTzNbsVgo6VSwuIbPaWpBNWleY5GnckHmcm11qMLgFg1p2DAy0y9FMsUJ2P0SYaxEIsg2bl9WHqPXamU48CoIE7ExbPOCXhx4tSowsiXh6hLYrOaEVJ73USjdHJtEVbNbsT+Qyfwp7++b9ge9W4TkUf8J8tzB29Y1439h06Ypu1KxoHseiRryCczgZLbftLq9lhUUwVGTX6uH4eOnlJ8pow8Yv9OdEid0VeHpyPKsvfBgBcnT41K70xXUym6mkrxvV++ZH4iBpyMj4d64puiASzeh772ChxUnZsRn79uLkZkZckdSxNToTbUP7ppBn72v28ainRHo0BdRR52vXnAlTaxj6lsp1khBgC48kylxtm6BS2Y2qwjsu82Fo3kDCqAlXE47fQQuXn9dDz78j7XdZvSjfhs+VV6dMnCo1dkhjiGrpnXjB/+9jXpc7k5JAh84+fRE/a0fqxwZlw6QBFZ6KJjXRzPdH/D+Ex+e62lremfB+s7uX2WDFYK/lilNK7XVl2Wi3f3H+P6jRUNWbuuwyUDWk3DgN+jqY7bNKkAr793GEDiXsoLvwgA8vXGblnTnFwobq5WFnKwF3nkWHPUR5D+6u+oRH9HJX7wm1fxH394XTdD56y5zQCAnz/1lnoXXLDOpb9DO3+3O6fPvDASHWZ3TUJlSa4qvzLxvd2qNVZhGX16D6mYIlKqI+yYKpxKNVg9p8m2Mvt4heVc4UG8I9Wlebhwabtr6SB3GIhlG1FRHEJhboBpf0grhkl0/ILqXyA2EQTcmaA6UWY16Peir70CN6oEksXm3rNlULPaAmifEdbpVcbD4fNCPqxb0IorVk8xbY9GO8kjtxw54bjUPW3lpo4jZbvYf7O44dxuRZqbU/i8HoyOJgweMWKSJzWCleYrdxronVJJQRA7tw8rii2IJXPFZ5snCk2O2btw8nTceaRjKIv2r3jca8+ZZqlPKM4PSunjgHsRKGpDva2uGNev64bHIxgadDyV9vSQC53zdjl2ehGPR1BoNaya3WS5YplTJFZ9Lf4u8wOPUs7iPvlEy7lZR1lRjqX+NttxUjAbiC3ATNergMqJVEZbE2lk/H8W3TbaIr8SX7t9keG2X9u2SNKXlGu3uPnKbjRbCLfYYRjdeqNdsezmk3FHh5EgNc+jduKU0uln5ek0sje3bezF3RfHtLOMRKvVN3AWRwVA6ac2bv5jty1kLjb/4w3aKtQf3ZSwIUTborct4YRgnr0knyebw6sG3mRkFdTRv1YuQeK9Sd1qyZp5zfjKRxZKz+l5iybjlg3TNdupI7YsIyQKwbAyY+z6TrIm8oiFeMM/e/VsS4rhazhEwHi4/5o5OHzMOCR128ZeRbpAOkhn+DNhjBNODaeRixSznh0xbS0p55Gg/gP4yAW9eHvPEXg5ntf6yny8tecI/wEdusxsQeVYe2t1Uqw0DgDG6a1fNBmdjSVS9IogCAgFfTiuU6EkGmXkxNsRtow3prWmEK/sPmT598pGxfdpQaOuZ3K5pVL3vGN7KOhVRLMYOo9UHxXm+YG92s1ErPSnfeFKPHTDEJ57eR9eeeeQJee7IEBZfpmBGImrl4I2qoo8ShabvnJTjJx6+gZdFLk5fpw5pwn/8YfXLR3voqXtmN5ahrLCIPYfOgkj0yzg8+DUyJju91mFdJp8L9LcadV4/b3DkvFpZyI8XgkGvJjWUobnX92f7qZw0V5XhI64htplKzvxhxfeTXOLYvhsRnBt29irG90Qs7nt3xexP9KL7gX4x4FFvbXwez34xk932WqL2WHkX8vb65TZzxo7zBY1NNfNVAdG/zujBQvWbitLQigrzNHVAJUzr7saS/rr8bGdT2q+O3EyNrb2hyvwdGSvY9fTrKy7HlbGcDtt1ds/S6RaLl8SCvrwua1zUJQfwHMv75M+FzNvzh5qxo9+95o04iwZqMdr7x7C/Ok1eOntg4r9djQW44VXP7DeeAbW0tZi/7oYbMY4pgC/L9FIvQJDxfmxPq7cYnrw7K5J+Msr+7F6dhMKcv1orCpQ6M0mS5Y7j2L/VhZbS/mZ0ZZc6tW1a6firT1HUFqYg1Ld0s4x7HYUxPgmlTm2VrnIJK9WrAqYTHqZZHjJrIbC3ACmNJXig0MnABgPllYHRycGBY3QnUkbEmlrys9ZxpDf57FU5QZIXJ+huNaVVG3Nwj7Ec3AyfFjPmHUC3nOrr8xXRLOIqRFRhg9A7cBlRx5xN1FDYW4AQ9OqUVeRj+ZqpbDs0LRq/NeTbxn+Vs5dm/txeiSRLnD23CZ8739e1pSDXthbi4NHTmJmRyV+/IfX0dfhrO6O08TExt+w9Vs7DvhFM2KRHZ++YhZGR6N4/8Nj+On/vomnd+3RbNsXrsQf//qerbZlGlYjj4Zn1GLRjFp4BAGP3DTfsPohkdlsl0ULDHVXY6g7M4qT+GwKZhvZ1smKb0tjtzq6V74wAr7xSBAEDHVXY3JdEe786v9yNkD5e7P9825rC8YurS5GfOGmefjGT/4u/X/z8jC+8RM+Z5rRocTzlUcvB/1efO6aOXo/UeDzeVCnU41avAVnz2vB05G9trMM7JJMlK+9Cnm2DyfpnomLWPkhH/w+D3ZuH8bBo6fwo9+9Jr1URXkB3HZBLwBnC3Bo7XMLzjax4FEG5mkPdFQi4POie7I1x09ujg83y4r19DtsA2a1JWBbUT7J4/aFK7FmHl+5R4IwJPP6Ko3h9cC1cxX/TwhmJ5+2xuqrxVUto7Ha+qCT/IVWt3XZQGylQG9ClRDM1niPHEEQBDx683yp+kQy5Uad1JlSpK2lUrlRxjVrpiqcR+K14ZlUlDDSjPUEwXkRBEHjOAKA2op8yZBicfa8Zsk5CMSEbOWTpqUzG5gVfTYvC+P6dd2oq8zHzu3DulFxVnEjbe3hG+dhqsGKmNkdO3JcG5332av4yuUG/V7k5vjQXF2Ia9ZMZW5jpWpopmPVZhKERPWY3JzkqzWON+ZMjaWS1JazJ6CEOaLYv5PzNrk+TCFDO8qssIk4iZS/L5rJlwDuRguCYEvy4XqrabmKyCNn+mrWXkyjoVQbhII+qR/fumYq5nXX8B/f5GCP3DQfl69KXqBazYbhycgP+SU719ICG+ezbPj4yA5n9fys3Hkx8tvoOhflBdDbZh4h3tVUik1L2xX6vnk5PpQUBHEhY1HaLQ1FwJoz7KJl7ZjdNQlTmkpda49dBEFAT1t5yivdmpHVloDdSymGyX5WVUaXGF80VqVHV4IHhbBhpqFqlLr06JgDmkcwOH9xEDPqLK0OOk5cZ/U+zhpqxs7tw7oTKtEwCPg9uGXDdFvljM0IBX3cpVJZOKFfpSWxr3QNeLmySmSblrZLjkge59HcqYwVefnvHD4lo2ufH/JLovyZQDDgdaSSjBxTYVOdWybeklJV/zTUXY3Kklxcu3YaVs+xUMRAh3MXtOL8M9rQ1VSCa9fa11jKJDJy3MlCBqdUYef2YdsVxwhZVKiD3iN5pTjWEPTwjVodFzljY9rfqncT8HnZ9gtXC/lotVnwxElYTgUz+8voW/G7RbIS4h2N9ioeAjGnNm9UECuqGACWzazHltWdqs8a8PCN81yJzrbCJSs6pErKvFhxHG5dMxX3m0RqPXj9EK5f1224jXjc4Rl1Cr0pn9eDB66diwFG5EuaLqmG8qIQrjhzimk18Z3bhzXVoac2Z57DKRVk9ZKaXoUZM8QVALXRSYwvtl3Yi6OMVelMoCMePcDqUNONmQm3YUkY+z88hgU97CqDPCQij7RHE8c9IwPFjcCj5uoCDHToizfbNW4FxIT2f/H025Z/p2ZybRGeeWkfM/85cb3428nSr1q3oAX/99evWmmq4qhWBLOtH4T/3EQnZ31lvqYyiBwxIkh0DNQwonSUkUfOnpSbq29W+cSlA5rKKmqGuquxU5aC4Db6ikcxVsxqwPd/k3heRWOuL1zhSEWsYMCLpQP1ijLYWQ95j4gMwe9C5JF8EijvAYIBr/T/z1w5CwcOn2T+Pj8Um1sYac5tXNJm2lfaRYxatjp+GtlVTmLqnOBo90XLwigpCOL7v3kVTZMKceuGHtzy6O9x8Ah/NVCr6GkDbhjW10eSFjMtjNNOXH1nnZD6C5d+n8dUfsUt7No+AgRNurr4yItaoW5ZVepX65YNPbrbDk6pwjMv7UN95fgrNJXVziN1RIRVMsloTwXWSj1mPzkBn2HFhXRSU56HnduH090MJmbRGYV5AVzOUQ3MGAPHUPxfo6iVnsnleOUdY4Hnhqp8vPl+TFSbJ+JErIChh117TFOhhft32s+WDTagp62cGQIvXi8r7RxR6VfVV+Yn/c4Iir+d7WOrddKv7r64H8+/ul9RVlkSi/YkUm/UJeGB2GLC17ct4l6t49lsaFo1jp/ic1yna0WTRUMaojXNtcP0Qo9i/xitOlsRYx8vXLikHW117IiFhHuZvEdEZiAK67rl75D36w9cM0ca3yaV5mJSKbuYzYpZjSjMC2DOtEm6jvKYY0lbMMfJ07CTZpr428GGqI+T5PfSdlIEejTW9gzslsTxJ9XjdEIWNLmLcv81c0wLb9jhzov6cDrJQhKOah45tictl67okIJVVs5qxP/51ctcv5vZWYWZnc5XE84Esi5tTXzUaiuS9+RlWg6hm9x5UR/u2TKY7mYQWUAqNOMYetma47Ocu+IKyspZ5ukoXQ7nL1sV4UzoJoj/T74NHgPtBDt6jqPx+HzxUgtCLL/dFgZRZE6h12c3VxfirLnNis/Ec/N6BCllsEpnsmBqpFu8d5et6uROcdI7J6qSGeP8M9owua5ofEX+uMgZfXX6TkDrwYlEhnPjuYl0kjNm1EmTXLtVzFKN14W0NT0EQeBaNPZ5PVjQU2s6R8jL8eP+G+Y571iQKpfG/r3joj48cO1c3cgZFm7efauaRwCyts+RUvtTrvdmX8NSTmlhjqXnhpfW2kT1RrsYvYtGwSGiLX79umlY3FeXVBvMWNBTg3nTayTNs+WDDRm78J9Kss55RNijtbYIxfmUpucUH900Q1dgNVtpqIqJfuqtWjuJkfEhlcllDCzbNs7AozfP55pYy1NWnLBLre5D3FxtgLrlE7DjDI9KRmrstwIE9IUrcNN68/x2rjalMapmdVz3oqokF/O6q3HvFYPotGnsyCM1HHeIMa7R4v46TM4AvYtUYBadVlEcwh2b+jQOY4qeUdLRYK4bIlWVcbsxRMqQ6+JMaSqRBKLvuzI7ND2dXFwx2r/6b6cIN5YiwChn7gRicyfXFsUm0xaEmN0sVuH3eXD2UDO2bexlOilZRzZsupTz7kDjHMYdXUhzJsLakZHN+vFLjDMBAKC9vjjhGJM6EGc7kouXdzi6v/FC1jmP8uNiVU5HFRCEFdrqih0vfZhuuppLsXP7MOoq3K8cI05iWNE8+SE/8kN+bFyszUP3eT3cWmc+WSiOI8OJTe+R6JgR9YXccqiI+7XSTM1qrxBrb3erM+k+bpzqPVsG8ZHz9fPMRfo7KrFz+zBCQZ/tajciSr1s9zWPNi5uV3x+yYoOLmMq1Vx1VlfyO+G8nIV5AezcPmyaijZRI7ZuPHe6aREQtyfqROqRP+5RZM+ks7k6Fh0npVu75NJ0M406gVsvlLX2ig6OSWW5CLrk0AJifezZQ80IN5TgxvXTGRsY/Va5n7TCcdvERfcFPfwV4pxkPHfV2kLE8ofD/PdBv1fT3y3ui0UoJ+vQLWVU3SUS2Ba3CIfDcwE8CCAAYD+AyyKRyBuqbRoBvADglfhH70cikWV2jwnEXuQdV89mllM247KVnRqh2d62cszumpRMkwhiXJDSNE6DQ/m8HtNqKDwoI4+SH4KT3cPhYzF9hIKQzbQwE0Rnw0Anv1OT4TuyxK3n9+CB7z2r2olcdyH5Z+rTWwbxrf+O4NyFkwEAteV5jpWet4XDr0nApMIHAMyfnh7D1YyudFYa0a3CNp7NbX2CAS8qAyHOrSfmNRqPyCdc2fTsf3RTH0bHovj98+8CcNOh6b5d43TbWcUnYp8bHygU9OGm9dPRXF2A7/ziJWcbJUPQ+TvxmfZTo2fT7ae2ojgH3S32FsTyQ37s3D6c8ncrS3zASZHsnENe6Vi8O2vnt2Dt/Jak9gvEIjetSlVMJJJRRv02gLMikchfwuHwZQAeBlG3jK0AACAASURBVHC2apt+AN+JRCJXJXEcDeXFvAaSkqFubblDnvKDBDERSKXzSAyqcLNzlg8sTlgndtPWxMsqavCoS33qYdXx4hEEPHT9EHItCOOL5yT+Rl5p7Lbze1BsUpRA7oxnli124JGqKc/D7RtnJL+jJJjRXiH9bbfKpx5urhC7Dc/9PWd+i6IammYfDraHMGYi6TxOFBSRR7JOONPTOn1eD3zexDjn1uRcMPN0OIC85U2TCqTqnsmieV05LlF3axkAYCRJMWMj7CwKiVFRClFv9X5lf5+3aDLqq5yJgv+Hq5Wl6O10g2mLkrL5XszrrkZvW4X5hmnEKLWS/2q7c1/8HIt6ExlbVnA4HA4CuCsSifwl/tFfAFzP2HQAwNRwOPwsgA8A3BiJRJ631VKCIFwltfo0UpkN15DnqMsPc/fF/Th5atTy/iwbt6Jgdvy/150zDU/v2pN0lUgjCi2KXYsTjOqyPNy6oQeTZXpXnRypwSyDSv5JOiarPNovVvjHG4YU1Uqmt5Zh8/Iw/vlnEUf2n9XOI5Pv1ww1Y+XsRkPnkeVjmnQdaU+FyGD6OyoReetDnDO/Nd1NIVwi255+8XVlFMJ0dP9uIrcNyopyknYeqbUI7XB61Fnn0WeunIU7HvtT7D+mgtnazy5cGkZRflBybplRWhjMWnkSJxyhg1Oq8MSzuxFusKfTeOnKzqTb4DZG9qH82f/UZTMR8CecObee34NXd6uqLWe2r3zcYct5FIlETgL4FgCEw2EPgE8A+CFj0xPx7b4CYDmAH4bD4c5IJHKK5zhlZe5rrxCpoaIi9SWgCWvXPT8/aLq9+H2y97O7rQKvvXsIDXXFqCh35z0vLkpEKAYCXtO2m51TKDdg6bzFVZWy8nyUFOSgoqIA3R38KbJqZ54b71BO3ClSkB/EwpnmFezUlJUmIpXy82JOsZxQwtFSWVmYZAut8Y27l6IgL+CoQ6alUWvsrl9SKDmPkr0vY4xZU7L7TFV/W15ufJzL15pH9rKeEaP2B+ORX4WFOcztWhpKuPsxu9+nGifbc9vmmY7ti7CHk/fzxMkR6e+CwhwsGWzC934eQWNdCXJdKNHtNIUFsejVYNDnynsnr5JVUVFge2xQt0/Z1sRYHQj4dLaB6efS3oTEdmbt1dvXljXT8Mjjz+LFNw8Y/t4Mud1UX1WAt94/jJLiXOnz4gMnNL8pLc1HRUlIsY+KCuCmJuVYmhe3GUKhmG3V11mFXz71FgCgsDDkWj+cnx975nJCfuYxkj1uaQm7qqt63wUFH+oes6KiAEN9DUm1I9PJUy12BmRV4cpl84LeLmXW0MKKAixU7SM3T3/+4uZ4nmm2QqowdR6Fw+H1iGkbydkViUQWh8PhAIB/iu/nM+rfRiKRT8j++5NwOHwfgE4Az/E0bv/+I0zDmsguKioKsHevM2G8BB87ts7GkeOnLV3348dOmW6/d+9hR+7nqsF69E0ugz8ade3ZOH4s4aM+cWKE69yMOHLkpKW2jo7G+q4P9h/FyInT3L8TEfu+7tYyy/eSl+NxHaajR62d260bevDcy/vw4YdHpc8OHzkJADhxPHGu6XjvDx0YMd/IAsk+N24c04hU9rf79h0x/J6nHaxtjH53Mj5ZPnjwuGa7j18ygLJcf1L3rL2+OKPGKxo/xxdO38+TpxNRtAcPHseSGTVYNL0aRw+fwNHD2ol9plEYdwbXluW68pzL5xD79x2G32fPebSsv07RPvHviooCRaTJKZkzT+98zM5T3J+6vazZkN6+8v0ebN84A5d99n8Mj2WGfP8jI7FnTd73HjxwTPObDz44AoyYX4dpTSUoL8rBYEcF9u49jA0LW/HSmx/izfeP4PDhE671e0eOxN6LEwy7yon3c0p9EQY6KvHUrj2Kz++/Zo5i34fj7+ecqZMmZB9/UmUXn5JlBOzfn7AtjK7NsaMxO1/PhnVr/BQwPu6bxyPYCtQxdR5FIpHHATyu/jwcDucD+HfExLLPjkQimtlROBy+HjHNo/3xjwQA1mdRBEFYorwohPIia9pgqUxb83k9qKt0N7JQoXnkALbd2DYvq7j6eNnKTsvpaLyMxc/Kanh8V3MpuppLsf9gYnIittHNtDwiMxCQvspORs9q4yT9VcBr1kzFF3/4guG+H7ttIekCEVmF/GltrSmCIAjw+7LnGZ5cV4QdV89GmaqYjVM4dSVqDarQyrOUvIzS9fZR7uuOTX345DefcnD/9pCbiixnHK89UVIQxI6tCT0in9eDiuIQ3nzfeFEiWdzWQfZ6PDh7qFnjPCotdOcZz1YM09Y495Efj3S3ovXpBF/fPpzS42UayVztbwF4GcDVkUhEL7l2AYAQgB3hcHgBAC+AXUkckyAIl8i2SZM4gdVDbsTxilQbkU2VbLiRtBXs/Vz+u/5wBa5ZMxW97eWOatwQmYcgCGl/H6wevr+jEnds6sPBo/pZ8047nAnCbeQTdbccMG5jtwiOdawPdLlBH46dNItmTXRGG5e048m/7zHY1j5GznGnCQV9OG563kBrrTup6SmxRl08SHWZfuqayHg0Ka1gvGDNd3OG+2rh83kwf7q2IBbhHnYFs3sRq6z2NwB/DofDALA7EomsDIfDVwOoiUQiHwNwI4BvhsPhzQCOA7jAwNFEEEQaSaletgOEG4qxyyCfX+4Mu2Bxm61jXLt2KiJvHsAv/t/bqLcYKRVVCWZbJT/kx+Fjp101cKSKcDZ/r6icIgjo76gEECs/f8rFai9EehHintt0+JtFo9xONJ5cEJ4gxgNZtuaTcpRjlPXf33fVLBw7YexEkTsBCnOTjxLeevZU/ORPb8DHiGKqKgkhFPQ5VtFNj09vGcQHqrRHlpC3IAgoygsYOuWtUBnXSnJiwS+dCIKAyuIQ9hw4br5tCtqTiRgLZvPtw+vxYFFvrUMtInixK5j9DHSe90gk8mXZ3+8AWGKvaQRBpBKjspmZyPXrurHv4Al8fOeTAICq0ly8/0Ei/16MPKouy0VOwF6QZV+4En3hSizur0OlgQiiEXYrptxyXg+ee2WfI8aoLtHkQo9CQbZ+xKcun4k3XA49J9KHxyNg1GE9wsduW4grP/eE6XZnDzWjo7EE7fXOVtUjCGL8kaxzrSA3gAKTMVgdQbLj6tkYSaJ/7G2vQG87u8z6fVfNxsnTo9j6wK+lxRo3KCkI6qagu+mwXDuvBeH6EttVxjKJbLOpU01qKzwTTpLaJEGCIDIWo1WAHVtnx6JgMohQ0KeIBrrn8pmKyadYpcSJ0GA7jqNkB8ayohwMz6hLah9miPat3ZbmBHzoC1egu0VZRaWyJNe2s43IfATpX+eMP96UMZ/Xk7UlnAnCabIt3TzbuWtzv2KRCgCiqgR6t9Pwgn4vHrphCHkp1nmRIpVdfOZ8Xg+6W7UVTrMRMxNQ/dxMNNTXR/5YUbeW2VCCP0EQAIBpBgN2eVEIzdWpLbtuFfnk80u3LEBAch6lZ4C+/YJerJrdmHIDzxqiYLb9PVy7dhrmTa9xqD1ENiBOHsYmumgDQaQbmmQZ4rSjo6WmELOnTlJ+mIZusDA3AK8nxVM4nVR89enTxD/GpqXhdDcho9m9X1upT8TJhSnCech5RBAEAKAyZaKVznLX5n5s29ir+CwY8MIfdyala4JbW5GPdQtaXV2lS5YxhoYBQZghzlnId0QQ6YV6bmPk18etYe684cnu7DjD0I08Ug0Emf5MTiqNRUVb1bG0SmdjiaGQ80R3kMir9YoIibBmIoMh5xFBEFlNS02hlB9/98X9uHxVJwBIYpM0wTUgybS18co1a6amuwkZzfx4pJnfZ92E6G0rd7o5BDFhEQQBc6dNwm0X9JpvPAFRpMK4NNItm9ngyn4zlWxfa+pqLsUnL5uJBSmImBbtz7PmNmm/m+BpaywmukMtW8jkfAqCIFLAwzfOS3vZbadori6U0ut8vvRGHmUD0n2n8VqBm0Kk44H1iyZj7bwWW84jgiCc5fJVU9LdhIzj3isGkRPw4cH/81y6mzJ+0KmvobGwssC75HbUkZrSwhzNZ2K0f31VQUrbkslIlVzT3RDCEHIeEcQEJz+U3SVR9fDFc2vId6SPeGlIdJWwgkcQJE2xT28ZxI7vPoNDDpVqJgiCSJbqsjzthzTMOQJvdMj918zBydOjLrcmszEyP8MNJfj4JQNoqEqtIytTMDI7ySTNbGjZkCCIcYlY7WzM4ZLi44nxEnGWDiqKtSuJTrDj6tmu7Nctasrz0Bdml5UmCIJIJ1QN3DmiOgU21GaE+HVpYQ7biUdINE4qmLCak6yznqCXIuugyCOCIMYlkvPIxEGyYrABBydo1ARFHtnnE5fOxCkXVlXdLvPsBh4LS/rkryQIImUIzD8JB+lsLMFTu/ZI/ydzgrBPLG+N7ITMhiKPCIIYl+TlxHzja+a1GG63ftFkbFk9MTUjpAGajD3LhII+FOUH092MzMDB52daS5lzOyMIYkJTX5FICZqoER5OIdoL6sWmLas7sXl5oix9QW4glc0ishXG+zgQ15v0UMhgRkPOI4IgxiU+rwc7tw9jUW9tupuSsYhpa2RTE8nA+/w8dMOQ4fdfvX0hblzf7UCLCIIggIuWhc03ItBSU8i/saq/9/u8qImnp1WX5TrYquynoiiW3l6YRw41NVObSzWfXbqyAw9ePwSfl9wTmQylrREEQUxQEsXWyHtE2If3+Sk0WZH2eshgJAjCOURhf8IYHm1IyV6g1SZuVs5uRH1VAaa3UkStmpWzG/H937yq+Mzn9aCIHG0ZD1lqBEEQE5RVsxtRURJCF2MFiCB4sTKXcEOkvaacRFkJgiDsYqVbZnX3YiobOZaUeD0e9Ewup+vCgLQ2sxeKPCIIgpigNFQVYOddS7F37+F0N4XIYqzYgMsHG/DcK/sdPf4nLxsggU2CIJh0t5bhLw73OeMNs8IiMQzS3MkPQBATBoo8IgiCIAjCNlbSHsMNJdi5fdjR43s9HtJIIAiCybVrp+L+a+akuxlp4cIl7bjyTPOCIHzOoxisKBpB9S9BEOMXijwiCIIgCBWfuHQAuUEaIrmgGQNBEBmK3+dFaeHE1D46o68OAPDYf/zNcDsuzaP4v4aRRzQWEBa494pBvPbuIXztx39Pd1MIC5BlTBAEQRAqGqoK0t2ErIHmCwRBEMbM667GkeOn090MJjzOIxG270jQ/Y4g9Kguy8P7Hx5PdzMIi5DziCAIgiAI25AYKEEQhDGXruxMdxN04claM6q2lviIxgKCGO+Q84ggCIIgCNuwfEdeT+LDS1d24MDhkylsEUEQBMGLJc0j1meC8l+C4IaKXWQd5DwiCIIgCMIx7ryoDyUFQen/87pr0tgagiAIwogoh/NI3IYtmE1eIyI56AnKHsh5RBAEQRCEbdRzidbaovQ0hCAIgrCMBckjw+gicgAQxPiHatsSBEEQRAZwy4bp6W6CLWjVmSAIInuxVm1N299HxW9pKCCIcQ85jwiCIAgiA5icpRE7pHNBEASRvVjRPGIhiWmT94ggxj2UtkYQBEEQGUC2Gt52qq3dfXE/Xn/vsAutIQiCIKzAE3nEJWycnUMYkUYqS0IAgCnNpWluCcELOY8IgiAIgrCNnflCc3UhmqsLHW8LQRAEYQ0rviPWWkGUstYIm9SU5+HB6+aiMC+Q7qYQnJDziCAIgiAygSy1vIe6q/HD372W7mYQBEEQNhDT1pb016O8KIe9kVhtzWA/lMJM2KEoP6j57N4rBrH3wPE0tIYww7bzKBwOXwzgswDej3/0n5FI5E7VNsUAvg2gBcBeAOdFIpH37B6TIAiCIIjMorRQZ7JBEARBZDzRuGOora4I/R2VxhsbCWYThENUl+Whuiwv3c0gGCQTedQP4JZIJPJdg20+DeC3kUhkVTgcvgjAPwLYkMQxCYIgCGJcQou2BEEQRKoZG4v9a6RfZ+gekr6kUYwgxjvJVFsbAHBxOBx+PhwOfyscDpcwtlmFWOQRAHwXwIpwOOxP4pgEQRAEQRAEQRCEA4iRRx6OWSHLPWSkh0QQxPgiGefRuwDuAdAN4C0AjzC2qYlvh0gkMgLgEICKJI5JEARBEOOS8WB4nz3UnO4mEARBEDLuu2qW4fditTWPUeSRUegRCWYTxITBNG0tHA6vB/Cg6uNdkUhksWybHQBeYfxc3Y8IAMZ4G1dWls+7KZHhVFQUpLsJhIPQ/Rxf0P3MDMrLCxDwe5PeTzrv55a13Wk7thHZ/Ixnc9sJLXQ/xxfy+5mp97aiogB+nwenR5RTsPaGYrz45gFcsWYaHvvh8xiYVsMULwYAjyc2pSsvz9dss/fIKQCA3+/N2GvAS7a3n1BC99N5TJ1HkUjkcQCPyz8Lh8NF4XD45kgkIjqVBAAjjJ+/A2ASgLfD4bAPQAGA/byN27//iOQNJ7KXiooC7N17ON3NIByC7uf4gu5n5rBv3xH4fckEBKf/fmbqs5Sp7TIj3feTcBa6n+ML9f3M5HvLihxaPtCAzUvDqCnPw6ztwzh1/BT2Hj/F/L04H9u//whOqbb58MNjAICRkbGMvgZm0Ps5vqD7aYzHI9gK1LFrpR4BcHs4HB6M//86AD9gbPcTAJvjf29ATDz7tM1jEgRBEARBcJMTSD6SiyAIItsJMBYmPB6gppyvopWoi2Qkqk15awQx/rFVbS0SiYyGw+HzAHwpHA6HALyIuJMoHA5/CsDuSCTyZQB3A/hmOBz+K4ADAC50ptkEQRAEMb4YD5pHmcY9lw/i3Q+OprsZBEEQaUVMO7PLBYvb8C///SI55AligmPLeQQAkUjktwBmMD7/mOzvDwCcZfcYBEEQBEEQdikrykFZUU66m0EQBJHVzJlajTlTq5nfSVFJqWwQQRBpITlxBYIgCIIgCIIgCCLLcMbdU1IQE9DubCxxZH8EQWQutiOPCIIgCIIgCIIgiOyjINfvyH4qS3LxD1fPpihPgpgAkPOIIAiCIAiCIAjCBpuXhbHrzQ/T3QxDoqpya7ed34Pm6kLH9l9RHHJsXwRBZC7kPCIIgiCIDIAEswmCILKPhb21WNhbm+5mWKKzqTTdTSAIIgshzSOCIAiCSCPkMyIIgiAIgiAyHYo8IgiCIIgMQMhiN9LlqzqRGySTgiAIgiAIYrxClh5BEARBEEkxdxq7hDNBEARBEAQxPqC0NYIgCIIgCIIgCIIgCEIXch4RBEEQRBo5Z0ELABLMJgiCIAiCIDIXSlsjCIIgiDSyanYTVs1uSnczCIIgCIIgCEIXijwiCIIgCIIgCIIgCIIgdCHnEUEQBEEQBEEQBEEQBKELOY8IgiAIgiAIgiAIgiAIXch5RBAEQRAEQRAEQRAEQehCziOCIAiCIAiCIAiCIAhCF3IeEQRBEARBEARBEARB/P/27jXKzqo84Ph/ZnLhkhDWgrAAKbaa8kgrGIrRoiJdLXgrGpdAKSJqCyi1XJa3lEWppdoWXd7aUlyiLpPYNIJIQVFSL9BWXEpbq4G26iNF0SJQMLYSr1wyfth7zDCdl2TmvHnfmcP/9yXn7Pdynp0n55ydZ/beo0YWjyRJkiRJktTI4pEkSZIkSZIaWTySJEmSpCE1Pt53BJKGgcUjSZIkSZIkNbJ4JEmSJEmSpEYWjyRJkiRJktTI4pEkSZIkSZIaWTySJEmSJElSI4tHkiRJkiRJamTxSJIkSZIkSY0WzOaiiNgP+OSkpmXA8sxcMuW8xwL/AdxWm/4nM589m9eUJEmSJM3MeN8BSBoKsyoeZeY9wEqAiBgFrgf+cJpTnwxszMxXzjpCSZIkSZIk9WZWxaMpfgf4YWZunObYKuCJEbEZ+C5wXmb+ewuvKUmSJEmSpA4MVDyKiDHKjKPVDaf8GNgAXAY8B7gmIg7NzPt35v777LNkxydpXli+fGnfIahF5nO4mM/hYj6Hi/kcLuZzuMyXfI6OPPz5fIm7a/69DBfz2b4dFo8i4iTgnVOav5qZx1IKQrc2zSbKzIsmPb0uIi4GDgVu3pngtmz5Ptu2uUp3vlu+fCn33ru17zDUEvM5XMzncDGfw8V8DhfzOVzmUz6n/ndqvsTdpfmUT+2Y+Xxko6Mjs5qos8PiUWZeCVzZcPiFwOVN10bEOZQ9j7bUphHggZkGKUmSJEmSpH6MDnj9UcCNj3D8GOB0gIg4BhgDvjrga0qSJEmSZujM43+p7xAkzVODbpj9OOCOyQ0RcRZwYGa+ATgPWBcRLwV+BJySmdsGfE1JkiRJ0gwd9cT9+w5B0jw1UPEoM/eYpu3dkx5/GzhukNeQJEmSJM2We8hKGtygy9YkSZIkSZI0xCweSZIkSZIkqZHFI0mSJEmSJDWyeCRJkiRJkqRGFo8kSZIkSZLUyOKRJEmSJA2pg/db2ncIkoaAxSNJkiRJGlLnnHBY3yFIGgIWjyRJkiRpSO2x28K+Q5A0BCweSZIkSZIkqZHFI0mSJEmSJDWyeCRJkiRJkqRGFo8kSZIkSZLUaEHfAUiSJEmSdp0LXnIkt999X99hSJrHLB5JkiRJ0hBbcdAyVhy0rO8wJM1jLluTJEmSJElSI4tHkiRJkiRJamTxSJIkSZIkSY0sHkmSJEmSJKmRxSNJkiRJkiQ1sngkSZIkSZKkRhaPJEmSJEmS1MjikSRJkiRJkhpZPJIkSZIkSVKjBX0H0GAMYHR0pO841BJzOVzM53Axn8PFfA4X8zlczOdwMZ/DxXwOF/PZbNLfzdhMrhsZHx9vP5rBPQO4se8gJEmSJEmShtDRwGd39uS5WjxaDKwC7gIe6jkWSZIkSZKkYTAGHAD8K/CTnb1orhaPJEmSJEmSNAe4YbYkSZIkSZIaWTySJEmSJElSI4tHkiRJkiRJamTxSJIkSZIkSY0sHkmSJEmSJKmRxSNJkiRJkiQ1sngkSZIkSZKkRgv6DkDzV0TsBXwOOD4zb4+IlwNrgIeAG4DXZuaDEfEU4FJgMfAt4IzMvDsiFgFvA44GFgGvzsxP9tAV0Vo+1wKH12tel5mf7qErj3oR8cfAb9WnH8/MNRFxLPAOYHfgisy8sJ67EngfsBfwGeCsmueDgQ3AfkACp2bm9zvuimgtn08H3kn5rN0C/G5mfrPjroh28jnpXkcAN2Xm4i77oO1aen8eUNsPBH5I+by9vdueCFrL588DH6jt/we8zM/bfswkn5Ou+QBwQ2auq88dD80RLeXT8dAAnHmkWYmIpwKfBQ6pzwP4U+A3MvMwYCFwbkSMAB8G1mTm4ZQv0/fU26wB9gV+hfJBsLaer461lM/TgLF6/mnAuk47IQDql+izgCOAlcCREXEK8H5gNXAosCoinlsv2QCcnZmHACPAmbX9XcC7MvMJwBeAP+quF5rQYj7/llLoXVkf/1V3vdCEFvNJROwBXEIZAKsHLebzb4BrM/OI+vgt3fVCE1rM55uAD9bP26uAP+uuF5ow03xGxIERcS1w4pRbOR6aA1rMp+OhAVg80mydCfw+cGd9fjjw+cy8qz7/GPBCSnFo98z8h0ntz4mIxcDJwJszczwz/xM4jvLlq+61kc8xYM+IGAP2BH7UVfB6mLsos8Tuz8wHgK9QioK3ZuY36qyFDcBJEfFYSj5vqteuq+0LgWdSCoU/a++wD9qujXwuBi7MzFtq+y3AwZ32QhMGzueke70d+IvuQtc02nh/7gs8Cbistq8FHvaTc3WmrffnGGXWETge6tNO57OefyrwEeBDEzdwPDSntJFPx0MDctmaZiUzzwAoE1QAuBl4R0T8HKUAcSKwP/Ad4AcR8ay6JO23KbNY9gFWAMdExKWUf4sXZOaXO+2IgNbyuQ54eT1/b+CU7nqgCbUQC0BE/CJlVt8llC/dCXcBB1GWSEzXvi9w36TlMRPt6lgb+czMn1AGVETEKHARcM0uDVzTaun9SUS8ANgjMz886XNbHWspn4+nLAF/e0QcDdwNnL1rI9d02np/UmamfC4izqXMDDxqF4atBjPMJ5n51nruMyYddzw0R7SRT8dDg3PmkVqRmV8Dzgc+CtxIqeTen5njwAnABRHxJUpRYQtwP6VgdBClov9KYGNELOshfE0xy3xeBHyeUmQ6DPjL+pM59SAifhn4FPB64OvA+KTDI8A2ynfAzrRT29WTAfM5cY9FlCnaC4A/38Uh6xEMks+I2J8yM+WcbqLVjgz4/lxAWYZxQ2auovykfH0HYatBC5+364FXZOZjgLOAq92WoT87mc8mjofmmAHzOXEPx0OzZPFIrYiI3YB/ycwjMvNpwLeB2+rhBzLz1+pa/g2U6bzfpfx07fK6bO0W4L8Bf4Q6B8wyn6uBtTWfXwNuAp7SQ/iPenUzwOuB8zNzPXAHcMCkU/anzBBrar8HWFaXIFLPuRP1ooV8EhFLgL+nDJRW1ynf6kEL+TyeMtvzMxGxud5zc0Qs7SB8TdFCPu8Gtmbmx2r7Rvzu7M2g+YyI5cATMvMjAJl5VT22bwfha4oZ5LOJ46E5pIV8Oh4akMUjtWVP4PqIWFqruecAV9RjayNiVX38GuDKzNwGXEvZ94iIeBxlzWl2G7YazCafN1P2RaIOnp4MbO42bNWlhtcAL87My2vzP5dDsaIOgF4MbKq/XeLH9csYykbnm+oX6Y3U9yfwUmBTZ53Qz7SRz/p4A/BfwMl12rZ60NL7832Z+fjMXFk3/KQ+3tpxdx71WsrnbcAdkzZhfj7wb931QhNa+rz9Tm0/ut7z6ZTi4L1d9kUzy2fTPRwPzR1t5LNyPDQA9zxSKzJzS0T8CWW2yUJgY2ZurId/D7gsym+GuQU4vbafD/x1REysYT0jM7/XZdya3izz+WrgPTWfD1H2sLq149AFrwN2o+xZNdH2bsp+VFfVY9exffPHU4H3RsRewBfZ/lsnXgWsj4gLKftxuIdVPwbOZ5Rf574a+DLwxXqfOzPzeR31Qdu19f7U3NBWPl9E+V59K3Af8LIu/t1ZWwAAAjxJREFUgtf/M3A+M3M8Il4EXBIRuwNbKcv91b2Z5rOJ46G5YeB8Oh4a3Mj4+NRlnJIkSZIkSVLhsjVJkiRJkiQ1sngkSZIkSZKkRhaPJEmSJEmS1MjikSRJkiRJkhpZPJIkSZIkSVIji0eSJEk7ISJOjIh/3ME5b4iI1R2FJEmS1AmLR5IkSe35dWBh30FIkiS1aWR8fLzvGCRJkuakiHgjcCqwBbgVeAzwCuBSYClwALAZOBk4HXgLcC/wGuDj9fkxwBjwJeDczLyv215IkiQNxplHkiRJ06jLz04AVgJPA5bVQ2cC6zPzV4EVwC8Av5mZlwJfAF6fmVcD5wMPAkdm5pOAO4E3d9sLSZKkwS3oOwBJkqQ56ljg7zJzK0BEvB84F/gD4LiIWAMcAhwILJnm+uOBveu5AIuAezqIW5IkqVUWjyRJkpqNTHr8YP3zg5Qx1IcoS9MOnnLehDHgvMzcBBARS4Dddl2okiRJu4bL1iRJkqa3CTgpIvaOiFHgtNr+bOCNmXlFff5USqEISoFpYsPsTwBnR8Siev17gYu7CV2SJKk9zjySJEmaRmZeFxGHUfYx+l/gZmA5cAFwdUT8APge8E+UvY8APgpcHBGLgDcBb6NslD1G2Vj7tZ12QpIkqQX+tjVJkiRJkiQ1ctmaJEmSJEmSGlk8kiRJkiRJUiOLR5IkSZIkSWpk8UiSJEmSJEmNLB5JkiRJkiSpkcUjSZIkSZIkNbJ4JEmSJEmSpEYWjyRJkiRJktTop+v13oB18fJ4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.res_ret.plot(figsize=(20,5))\n",
    "plt.title(\"Residuals of Returns\", size=24)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}