smason/muscle ups.ipynb

## muscle ups.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "eec36f4e",
   "metadata": {},
   "source": [
    "# Data reanalysis\n",
    "\n",
    "Data pulled from [How Much Weighted Pull-up Is Required to Achieve the Muscle-up?](https://www.youtube.com/watch?v=c90yZnUXdQM) by [Geek Climber](https://geekclimber.com/).\n",
    "\n",
    "---\n",
    "\n",
    "Start by pulling in various libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1252c6fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from io import StringIO\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import PercentFormatter\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set(style='ticks')\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "199973d6",
   "metadata": {},
   "source": [
    "The data presented at [13:55](https://www.youtube.com/watch?v=c90yZnUXdQM&t=835s) is transcribed below.\n",
    "\n",
    "The ratio is recalculated to check for transcription errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "961ce8b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>bodyweight</th>\n",
       "      <th>success</th>\n",
       "      <th>extraweight</th>\n",
       "      <th>pct</th>\n",
       "      <th>ratio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ben</td>\n",
       "      <td>163</td>\n",
       "      <td>1</td>\n",
       "      <td>110</td>\n",
       "      <td>67</td>\n",
       "      <td>0.674847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>henry</td>\n",
       "      <td>150</td>\n",
       "      <td>1</td>\n",
       "      <td>95</td>\n",
       "      <td>63</td>\n",
       "      <td>0.633333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>derek</td>\n",
       "      <td>155</td>\n",
       "      <td>1</td>\n",
       "      <td>110</td>\n",
       "      <td>70</td>\n",
       "      <td>0.709677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>andrey</td>\n",
       "      <td>198</td>\n",
       "      <td>0</td>\n",
       "      <td>95</td>\n",
       "      <td>47</td>\n",
       "      <td>0.479798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>hieu</td>\n",
       "      <td>144</td>\n",
       "      <td>1</td>\n",
       "      <td>80</td>\n",
       "      <td>55</td>\n",
       "      <td>0.555556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>kaleb</td>\n",
       "      <td>202</td>\n",
       "      <td>0</td>\n",
       "      <td>45</td>\n",
       "      <td>22</td>\n",
       "      <td>0.222772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>bryan</td>\n",
       "      <td>155</td>\n",
       "      <td>1</td>\n",
       "      <td>110</td>\n",
       "      <td>70</td>\n",
       "      <td>0.709677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>kuvam</td>\n",
       "      <td>125</td>\n",
       "      <td>0</td>\n",
       "      <td>35</td>\n",
       "      <td>28</td>\n",
       "      <td>0.280000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>satvik</td>\n",
       "      <td>137</td>\n",
       "      <td>0</td>\n",
       "      <td>55</td>\n",
       "      <td>40</td>\n",
       "      <td>0.401460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>harrison</td>\n",
       "      <td>152</td>\n",
       "      <td>0</td>\n",
       "      <td>45</td>\n",
       "      <td>29</td>\n",
       "      <td>0.296053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>sanjay</td>\n",
       "      <td>132</td>\n",
       "      <td>0</td>\n",
       "      <td>45</td>\n",
       "      <td>34</td>\n",
       "      <td>0.340909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>garrett</td>\n",
       "      <td>160</td>\n",
       "      <td>1</td>\n",
       "      <td>105</td>\n",
       "      <td>65</td>\n",
       "      <td>0.656250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>ajani</td>\n",
       "      <td>153</td>\n",
       "      <td>1</td>\n",
       "      <td>160</td>\n",
       "      <td>104</td>\n",
       "      <td>1.045752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>jess</td>\n",
       "      <td>139</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>sean</td>\n",
       "      <td>140</td>\n",
       "      <td>0</td>\n",
       "      <td>60</td>\n",
       "      <td>42</td>\n",
       "      <td>0.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>nick</td>\n",
       "      <td>139</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>71</td>\n",
       "      <td>0.719424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>ibrahim</td>\n",
       "      <td>140</td>\n",
       "      <td>1</td>\n",
       "      <td>115</td>\n",
       "      <td>82</td>\n",
       "      <td>0.821429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>spandan</td>\n",
       "      <td>126</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>35</td>\n",
       "      <td>0.357143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>wilson</td>\n",
       "      <td>180</td>\n",
       "      <td>1</td>\n",
       "      <td>95</td>\n",
       "      <td>52</td>\n",
       "      <td>0.527778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>kevin</td>\n",
       "      <td>143</td>\n",
       "      <td>0</td>\n",
       "      <td>105</td>\n",
       "      <td>73</td>\n",
       "      <td>0.734266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>geek climber</td>\n",
       "      <td>135</td>\n",
       "      <td>1</td>\n",
       "      <td>95</td>\n",
       "      <td>70</td>\n",
       "      <td>0.703704</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            name  bodyweight  success  extraweight  pct     ratio\n",
       "0            ben         163        1          110   67  0.674847\n",
       "1          henry         150        1           95   63  0.633333\n",
       "2          derek         155        1          110   70  0.709677\n",
       "3         andrey         198        0           95   47  0.479798\n",
       "4           hieu         144        1           80   55  0.555556\n",
       "5          kaleb         202        0           45   22  0.222772\n",
       "6          bryan         155        1          110   70  0.709677\n",
       "7          kuvam         125        0           35   28  0.280000\n",
       "8         satvik         137        0           55   40  0.401460\n",
       "9       harrison         152        0           45   29  0.296053\n",
       "10        sanjay         132        0           45   34  0.340909\n",
       "11       garrett         160        1          105   65  0.656250\n",
       "12         ajani         153        1          160  104  1.045752\n",
       "13          jess         139        0            0    0  0.000000\n",
       "14          sean         140        0           60   42  0.428571\n",
       "15          nick         139        1          100   71  0.719424\n",
       "16       ibrahim         140        1          115   82  0.821429\n",
       "17       spandan         126        1           45   35  0.357143\n",
       "18        wilson         180        1           95   52  0.527778\n",
       "19         kevin         143        0          105   73  0.734266\n",
       "20  geek climber         135        1           95   70  0.703704"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csvdata = \"\"\"name,bodyweight,success,extraweight,pct\n",
    "ben,163,1,110,67\n",
    "henry,150,1,95,63\n",
    "derek,155,1,110,70\n",
    "andrey,198,0,95,47\n",
    "hieu,144,1,80,55\n",
    "kaleb,202,0,45,22\n",
    "bryan,155,1,110,70\n",
    "kuvam,125,0,35,28\n",
    "satvik,137,0,55,40\n",
    "harrison,152,0,45,29\n",
    "sanjay,132,0,45,34\n",
    "garrett,160,1,105,65\n",
    "ajani,153,1,160,104\n",
    "jess,139,0,0,0\n",
    "sean,140,0,60,42\n",
    "nick,139,1,100,71\n",
    "ibrahim,140,1,115,82\n",
    "spandan,126,1,45,35\n",
    "wilson,180,1,95,52\n",
    "kevin,143,0,105,73\n",
    "geek climber,135,1,95,70\n",
    "\"\"\"\n",
    "df = pd.read_csv(StringIO(csvdata))\n",
    "\n",
    "df['ratio'] = df['extraweight'] / df['bodyweight']\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f6542e8",
   "metadata": {},
   "source": [
    "# Binomial regression\n",
    "\n",
    "Regress probability of success against the extra-/body-weight ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3ada5978",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                success   No. Observations:                   21\n",
      "Model:                            GLM   Df Residuals:                       19\n",
      "Model Family:                Binomial   Df Model:                            1\n",
      "Link Function:                  Logit   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:                -7.9569\n",
      "Date:                Tue, 29 Nov 2022   Deviance:                       15.914\n",
      "Time:                        14:48:15   Pearson chi2:                     21.7\n",
      "No. Iterations:                     6   Pseudo R-squ. (CS):             0.4556\n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -5.2637      2.293     -2.296      0.022      -9.757      -0.770\n",
      "ratio         10.6585      4.283      2.488      0.013       2.264      19.053\n",
      "============================================================================== \n",
      "\n",
      "even chance when able to do pullup with 49% of added weight\n"
     ]
    }
   ],
   "source": [
    "res = smf.glm('success ~ ratio', data=df, family=sm.families.Binomial()).fit()\n",
    "print(res.summary(), '\\n')\n",
    "\n",
    "midpoint = res.params[0] / res.params[1]\n",
    "print(f\"even chance when able to do pullup with {-midpoint:.0%} of added weight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5c37b14",
   "metadata": {},
   "source": [
    "Lets use this to draw a similar plot to the one that appears in the video.  Note that filled areas are 70% and 95% CIs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a9f37221",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "sns.scatterplot(df, x='ratio', y='success', hue='bodyweight', ax=ax)\n",
    "ax.margins(0.1)\n",
    "xlim = ax.get_xlim()\n",
    "ax.set_xlim(xlim)\n",
    "ax.xaxis.set_major_formatter(PercentFormatter(1))\n",
    "\n",
    "x = np.linspace(*xlim, 201)\n",
    "r = res.get_prediction(dict(ratio=x))\n",
    "\n",
    "[mu] = ax.plot(x, r.predicted_mean)\n",
    "\n",
    "for alpha in [0.3, 0.05]:\n",
    "    ci = r.conf_int(alpha=alpha)\n",
    "    ax.fill_between(x, ci[:,0], ci[:,1], edgecolor='none', facecolor=mu.get_color(), alpha=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "948b4a68",
   "metadata": {},
   "source": [
    "We see two obvious outliers:\n",
    "1. Spandan was successful while doing chinup with only 36% extra weight\n",
    "2. Kevin was unsuccessful while lifting 73% extra weight\n",
    "\n",
    "---\n",
    "\n",
    "Lets see if a multivariate regression does any better!  This time, rather than putting the ratio in, I'm putting the weights directly into the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8406a2d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>success</td>     <th>  No. Observations:  </th>  <td>    21</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>    18</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>        <td>Binomial</td>     <th>  Df Model:          </th>  <td>     2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>         <td>Logit</td>      <th>  Scale:             </th> <td>  1.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -7.6221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 29 Nov 2022</td> <th>  Deviance:          </th> <td>  15.244</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>14:48:15</td>     <th>  Pearson chi2:      </th>  <td>  22.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>          <td>6</td>        <th>  Pseudo R-squ. (CS):</th>  <td>0.4727</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>   <td>    1.5568</td> <td>    4.716</td> <td>    0.330</td> <td> 0.741</td> <td>   -7.687</td> <td>   10.800</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bodyweight</th>  <td>   -0.0494</td> <td>    0.038</td> <td>   -1.295</td> <td> 0.195</td> <td>   -0.124</td> <td>    0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>extraweight</th> <td>    0.0783</td> <td>    0.032</td> <td>    2.423</td> <td> 0.015</td> <td>    0.015</td> <td>    0.142</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                 Generalized Linear Model Regression Results                  \n",
       "==============================================================================\n",
       "Dep. Variable:                success   No. Observations:                   21\n",
       "Model:                            GLM   Df Residuals:                       18\n",
       "Model Family:                Binomial   Df Model:                            2\n",
       "Link Function:                  Logit   Scale:                          1.0000\n",
       "Method:                          IRLS   Log-Likelihood:                -7.6221\n",
       "Date:                Tue, 29 Nov 2022   Deviance:                       15.244\n",
       "Time:                        14:48:15   Pearson chi2:                     22.4\n",
       "No. Iterations:                     6   Pseudo R-squ. (CS):             0.4727\n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "Intercept       1.5568      4.716      0.330      0.741      -7.687      10.800\n",
       "bodyweight     -0.0494      0.038     -1.295      0.195      -0.124       0.025\n",
       "extraweight     0.0783      0.032      2.423      0.015       0.015       0.142\n",
       "===============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res2 = smf.glm('success ~ bodyweight + extraweight', data=df, family=sm.families.Binomial()).fit()\n",
    "res2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c66d756",
   "metadata": {},
   "source": [
    "The intercept and bodyweight are considered non-significant, but it makes physical sense to include them.\n",
    "\n",
    "Looking at the coefficients we can see that `extraweight` is almost twice as important as `bodyweight` (i.e. `0.08 / 0.05`).\n",
    "\n",
    "Visualising this is kind of awkward, here's my best attempt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "997b1dac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eemuJpM211/ZHREQE3lqwRHADdYZhcPGSd0dpYWERKisrOf1t2qTB6XSioirXS5eE18dr1641AKC8wvd+6BKNNRWqKBEEYQk1WQyxsZsYYiMlAYqKijFw4Ehcd/3VaNu2NWJja2PLlm3444+/8dQ/JgAARo4civ+s+S8eyHoCN1w/CMePn8R3/16D5ilNOb6GD78e3373H7zyynz88cdf6N79CpQUl2LLr9tw25ibkJFxFXr37oZhw67HsuUrcOToCVzVrzc8jAfbt+9G715dcccdI9C8eVM8+sh9eH3OIpw8dQYZg65CXFwsTpw8hR9//AW3jroR9957G3799XfMfPENXH/9ALRsmQJ3pRvf/fs/iHA6ce11VwMA3np7KbZt24Wrr05HkyaNcOH8RXzy6Tdo1Kg+une7XOKoyBxHnzkDGDArpiKeBUFqMCSUCIIwDRJHXuwtjpQrWbVq1cKY227C5k2/Ye3aDWA8DJo3b4oZMx7DbWNuAgD069cLT/1jApZ+8DleenkeLr+8LRa+/Qpemb2A4ysiIgLvLJyNhe98iJUrf8TaNeuRmORC925XoE2bNL/drBenom2bVKz4aiVe/dfbSEiIQ8eObdGl6+V+m/Hjx6JFyxR8+MEXeOutpQCARo3ro2/fnhg4qB8AoF27NPTt2xP//Xkzcs7molatWmjXLg3vvPMqunT2XlJm0MC+OHXyDL76ahUuXsxDnTqJ6NmzMyZOuNe/4Fv2GDIscRQEaMOsuTgYfs2SkMR3C5Mfv7sr2KkQhG0hceTF7uKITWl5bRw/0wUtWzZFrVpREqPCEf2fEQOgtLQCR46cQpOGvyMmukRgM3T4x3A4E2VvjRUIGRkZcHvy8PHX6q9nJcXtN3+MCBNzDWWookQQRECQMPISSsKoZhOYOLIjjBXzezUYEkoEQWiGxJEXOwsQO+dmLdYKo2AcdxJK5kJCiSAIRUgYebGr+LBrXsHB+oqRdxF8MK+jZIwfQhwSSgRBCCBh5MXOAsTOuVlLYMeBjiKhBAklgiAAkDjyYWcBYufcrEffsbDiCFr7KTkMujwATd9JQUKJIGowJI682FmA2Dk3a7H3Iuxgfkq0RslcSCgRRA2ChJEXO4sPK3NjeP+1H/YWR8GIRVgPCSWCCGNIGHkhYeSLZXdCQxjJwV5YbdGFuQ25KS4hDQklgggjSBh5IWHEjmdnQl8YAcbtPNMfn4SSmZBQIogQh8SRFxJH7Hh2JjzEEVFzcAY7AYIgtONhGP+jJsOw/mc3rM7N3ve115cdA+PfV3b2Udx332Po3v16XHXVzfjXv95GeXmFQd6t/xz4xyiQByEOVZQIIkSo6aLIhx1FEUBVIy72rBrl5RXgnnumoEWLZnjzzReQk5OL2bPfQmlpGaZPn6zbb7CFBq1RMhcSSgRhU0gYeSFh5Itnhk+j9r3ZUxjx+eyzb1FYWIy5c2ciKckFAHC73XjhhTfwwANj0aBBPUUfjMRzKRsi9KGpN4KwCezptJoskhje/+yC1XmZMS1i3HvQn12lh8HuQ/lYv+Mcdh/Kh9tj3Wf8yy9bkZ7e3S+SAOCGGwbC4/Fg06bfRMeoeafBnsJiGEfAD0IaqigRRJCoyWKIjZ3EEJ/wqhoF7inQkVv+uIB3vzuK83nl/r66idG4f1gLpHdKDjA/ZQ4fPoZbbhnMaXO5ElC/fl0cPnxMkG8gWKj/aNebyVBFiSAshCpGXuxYMfIRDouwjXsP+rPjj9zyxwW8suwARyQBwPm8cryy7AC2/HEhwFyVyc8vQEJCvKDd5UrApbz8gD8HD1P9sBIPHAE/CGlIKBGEyZA48kLiyBfLzuJIf3ZyI90eBu9+d1R2/HvfHbV0Gg4w4DOoGhwMcURYBwklgjAYWmvkxa5rjQBrc7NCGOl9Dx4w/of2+Orf197DBYJKEp9zeeXYe7hAcx5acLkSUFBQJMg5P78AiYkuqWHVKLzp4KxVcoAx4EE3xZWG1igRRIDUZDHExm5iiE043CbEiPegRxBVx9fPxXx5kaTVTi38nFu1ao7Dh7mVrYKCQuTmnkerVs2VHUjEEBNGVn3jGMCQxdj2/esNPlRRIggdUMXIC1WMfPHsWTECjKsaBUIdV7ShdlIoVXSuuqo3tmzZjvz86srVf/7zXzidTvTt21PoxMDYROhCQokgVELiKHSm06yJZ9d1RvYQR2w6tEpA3UR5EVQvMRodWiVo9q0l31tHD0dcXCwemTQdmzb9hq+/WoXX/vU2br11GBrUr6dLHEnhgcOyvxBazG0uJJQIQgJaa+TFrsIIIHHEJiBxxJhbCYlwOnD/sBayNvcNa4EIp7oTtt7PITExAe+9/zoiIiLwyKT/w5w5izBixFD84x8TVPuQix0s4cGvZul5ENLQGiWCqKImiyE2dhREPsLhukZev0FebxSEjzi9UzKeuvMywXWU6iVG4z6F6ygZkm6Vk7TUlnjvvde1DpPFA+5tROz7F0TogYQSUWMhYeSFhBE7nhk+jfEaasJIjPROyejVsQ72Hi7Axfxy1HF5p9v4lSQjhZEVw4JdlaELTpqLrabejh49ihkzZmD48OHo0KEDhg4dKmv/448/om3btqJ2BQUFmDZtGnr16oWuXbvikUcewdmzZ81KnQgRaCrNC02n+WLZdzqNPZWmVSQxDPdhJyKcDnRKc6F/13rolObyi6SAPwedH6aR3wHhlntr8DCOgB+ENLaqKB04cADr169H586d4fF4wMj8hZeWlmLWrFmoV0/8JoaTJ0/GwYMH8eyzzyImJgZvvPEGxo8fjxUrViAy0lZvmzCZmi6KfNhRFAFUNWJjddXIl3cwvhmhVjWS98cVRvSTE17YSjEMGjQI11xzDQBg6tSp+PPPPyVt33nnHTRp0gTNmjUT2O3YsQMbN27Ee++9h379+gEAWrVqhcGDB2PNmjUYPHiwmEsijCBx5IXEkS+eGT5DWxwFg/AQRw7R58H6yfFWwug6SmZiq6k3p1NdOseOHcOSJUswffp00f4NGzbA5XKhb9++/rbU1FS0b98eGzZsMCRXwl7QDjUvtH3fF8u+U2qA/h1qeqfUgvmdCNaUmiGx/ThYD65/gPtZBGPnmzFX5iaksFVFSS0vvvgihg8fjnbt2on2Z2dno1WrVnA4uB9+amoqsrOzZX1nZGRI9p0+fRqNG8VpT5gwnJoshtjYTQyxoathe7F7xchIMRnMipFh8QFI3c5DzL+vohO8XW9GiTISS1KEnFD66aefsGPHDqxevVrSJj8/HwkJwguXJSYmyk7nEfaFhJEXEka+WGb5Df/pNOPX5wTPQTCEkZQd35YqNeFDSAmlsrIyzJo1C5MmTUJysvQ1NwJh3bp1kn0ZGRkAk29KXEIIiSMvJI58sczyWzOqRkYSLHFk7PsQihgjdr1ZjlE7G+37MxN0QkooffDBB3A6nRgyZAjy872CpaKiAh6PB/n5+ahVqxaio6Phcrlw5swZwfi8vDwkJiZanTahARJHXuwqjsJhEbbXL4kjHx6VtiSOpGFXj4JxOxCqXJlLSAml7OxsHD16FOnp6YK+nj174tlnn8Vtt92G1NRUbNmyBQzDcNYpHT58GG3atLEyZUIBEkZe7CqMgPAQRzSlxsVjsD+jndhlSk0t/MXbJFzCi5ASSuPHj8fNN9/MaVu0aBEOHz6Ml156CS1btgQA9O/fH2+99Ra2bNmCK6+8EoBXJO3duxf333+/1WkTLEgYeSFhxI5nhk8SRmzUCCOfz4COnM2F0bGjJ7B06afYvWsvDh48jFatmuPrbz/QFEE8V/51lKy+1xsJMzOxlVAqKSnB+vXrAQAnT55EYWGhf9F2r169kJaWhrS0NM6Yr7/+Gjk5Oejdu7e/rWvXrujXrx+mTZuGp556CjExMZgzZw7atm2L6667zro3RAAgceTDruKIhFE1NUkYMRLPNWFzYcTn4KHD2LBhC67o1AEexgPGoy4TJSvv5Rqqc1ErTI2AgTHTffb8dbIHthJK58+fx6OPPspp873+8MMPOWJIiTfeeAMvvfQSZsyYgcrKSvTr1w/Tp0+nq3JbAAkjL3YVRgAtwmajVxzp/ZqbIY60VIwCIsR3qA0Y0BeDBl0FAPi/abOwd88+3b7411bifwbedUtEOGAr1dCsWTPs2yf+xZXi5ZdfFm1PSEjArFmzMGvWLCNSIxQgceSFxJEvlll+g7sIG7BP5cgocaQ43WawOGI8HpSdOAh3YT4i4l2IadYaDsWLDRuz1kjuosbqxRF3jLeiA0QgeFNgVk/11TRsJZSI0ILEkRcSR75YZvmlHWo+jBRHgRnoG1a8bycurfsC7oJL/raIhCQkZYxCbNsuPGtzdqjx/Sn7FL8aN7eteo1SMMSSfX+BwgNb3cKEsDd0mxAvoXKbELNzY3gP4/wG/h7Ytwix4jYhWnNWe+w8vIdef0r9/qU6Gj9MLd+B4n07cf6bxRyRBADugks4/81iFO/bCf50ltHfMXW+HJyHmhzYtwIJxi1MCHMhoURIQsLICwkjXywSRv4xYSCM2A+16P0OMB4PLq37Qtbm0rov4fF4TBNG0v60CyNhHK8wcjNOMIzD/7DqtiB2uNfboUOHcM8996BLly7o27cvZs+ejfLycsVxFy9exIwZMzBgwAB06dIFQ4cOxSeffBJwPkZCU2+En5oshtjYTQyxoR1q1dh5Ok2Le6OuaaRkIyeI5KslgVN24qCgksTHXXARZScOolZz/de607vOKFD84ihIVSRPkNco5eXlYdy4cWjZsiXmzZuHnJwcvPzyyygtLcWMGTNkxz766KPIzs7GY489hsaNG2PDhg149tlnERERgVtvvdWidyAPCaUaDokjLySOfLHM8htccWSnHWqAMeIoEGGkNN6474H3BO4uVHfrJ09hnuYIVosjRuS51JW5rfrLDfZ1lD799FMUFRVh/vz5SEpKAgC43W4899xzyMrKQsOGDUXH5ebmYuvWrXjppZdwyy23AADS09Pxxx9/YOXKlbYRSjT1VgOh6TQvdp1OA6zNzYzpNK9fY96DEVNqmsbpnFKTQ8+Ump5+pek0tf4Dg7vOCAAi4hNVjXSqtNO+1iiw77lwrPDSAL51SWb9PdmZDRs2ID093S+SACAzMxMejwebNm2SHFdZWQkAgpvYx8fHg7HR+YkqSjWAmi6IfNhREPmgKbVqaEpNm43SlFogsdWhvHU/ullrRCQkyU6/RSTUQUyz1pL9yvkq75IrKSnFxg1bAACnTuWgqLAIa//zMwCge88uSE6uIzFWumLDsP7LveikteuTjPCjl+zsbIwYMYLT5nK5UL9+fWRnZ0uOa9y4Mfr164eFCxeiVatWaNSoETZs2IBNmzbhX//6l+58jIaEUhhCwsgLCSNfLLP8kjDyYeQFH+VszJhO81ZCtKD9mkYOpxNJGaNw/pvFkjZJGSM511PSKozUHNsLFy7iice4a2Z8rxcvmYuevXxCSZ1oYHz/x3gXcle3W3wLE4P+yE+fPo2MjAzJ/nXr1om25+fnw+VyCdoTExORlyc/nTpv3jxMmTIFQ4YMAQBERERg+vTpuP766zVkbi4klMIAEkZeSBix45nhM/yFkddeHaFcMdJe7Qj8mka123ZF3ZvGi1xHqQ6SMkaiVtuupogjNk2bNsauPb+IjNUgjETw8KYag71mKFRgGAZPP/00jhw5gtdeew3169fH5s2bMWvWLCQmJvrFU7AhoRSikDjyQuKIHc8Mn+EvjmrKdJqYOGJ4/+Vi/AUfa7ftilqXdUbZiYPwFObBGZ+IaNkrcxu7Q81IccT244ETDt96JcZ6wWTUNF/jxo0lq0ZyuFwuFBQUCNrz8vKQmCi97uy///0vVq9eje+++w5t27YFAPTu3Rvnz5/Hyy+/TEKJ0A6JIy8kjtjxzPBJ4ohNqO5Qkzt5SvsTXvvHyO8YAwBOJ2JkLwFgzg41Md/qx4nBXiju8K9PCs6VuYNbwUpNTRWsRSooKEBubi5SU1Mlxx08eBARERFo04b7fWjfvj2++OILlJSUoHbt2qbkrAXa9WZzaIeaF7vuULP6YpQM72GMT2PeQyhd9FEONTvU1HwOSv1yO9SU/Ev1SV0VWsqf2AUHjf6OqfNl3Q41o/Jkf1e5F2/0+nDXoOm3/v37Y/PmzcjPr74MxOrVq+F0OtG3b1/JcU2bNoXb7Rbc43XPnj2oW7euLUQSQBUl21HTBZEPuwkiH1QxqoYqRtpsrFxrJC3eRKbTOCf8wFFfjdE6Rk08IytGXH9S31mfMOJcP8k3/WbRz0WwK0pjxozBsmXLMGHCBGRlZSEnJwezZ8/GmDFjONdQGjduHE6dOoW1a9cC8AqsJk2a4JFHHsGECRPQoEEDbNy4EV9//TUmTZoUrLcjgIRSkCFh5IWEkS+eWX4D92xnYeS1V4fdhZFcv1HCSE9OUgRXGAl9qx8nhrIwYvvzmbgZB8CberNSvAT7NJKYmIgPPvgAL7zwAiZMmIC4uDiMHDkSU6ZM4dh5PB643W7/6/j4eCxduhRz5szBv/71LxQUFKBZs2aYOnUqxo4da/XbkISEUhAgcWRfYQSEhziqCVUjr7067C6OrKgayfn1j1E97amG8KkaSfqsGsD47xPHvo6SZQUlW5CWloalS5fK2ixbtkzQ1qJFC7zxxhvmJGUQJJQsgISRFxJH7Hhm+CRxxIbEkTq/DABHZDnAuFFSUo5ataM0xa7G2F1y5okjnoDTKo5YPkpLK+CBB0yEG2Bdj4qx+N5rwZ56C3dIKJkEiSMvJI7Y8czwGdwpNUC7OAqmMFLjLxBhpDTezCk1QJs4YuN0uhEVdxq5uV6RVLt2tEptEn5Taqp8MkBpaTnO5Z5Dea0L8Dg9Qdv1xsAYYWbfX+rgQ0LJIEgYeSFhxI5nhs/QqxqZJYyA0K0aBVsYifmslXQSJXAg52wlHA5rrmukFkbyBRtlsRBovgznuQdltS6iIuEiUHVVbv+Ncf3CxarrKBFmQkJJJySMvJAwYsczwyctwmYTbtc0CqYw4o9zOIDadU6iVuJpeCqj4dsCzx0j71PuNb/qwV/PI5k/4/Bbiq6rUv28GrEpMm7uDo4d29Zrx4CJqKzSRw7eRSar/dn315HQAgklHdR0kWRXcUTCqJpwEUehWjECzN2hpkYcifkTXl9JJEcHA2dUGWtMNREiY7iCh+ePJSAckBYx7FEMSxgJfYo/lxI8vmMiunWfZSsl2vjTaRw7xgEw/CqTQxDDCmiNkrmQUCJUQeLIF88MnySO2JA4UudXTdVIbKx4TH61Sd6vnDiSrtLwK0LSOaipHHlE1gRxq0baxZGinT+mSG6MrwrFtTEfh0HCjMSWFCSUCFHsKowAEkds7CyOasJaIyA0xZHYiVVOHClN2+kRR0JxJiZ8eDY6xJGk0JLJXbjWSJs4quGTDmEHCSXCD4kjXyyz/NJ6Ix8kjPT7tVvVSM7WqKoRu92OVSP258n2GZTF7oThkFCqoZAoYsczw2f4V4y89uogYaTObzhNp0lVjNg+pCpGXBsJHwZUjNgxjRBG3Lysg9YomQsJpRoEiSNfLLP8UsXIh92vaWTnRdhiPsXHyVd5tO5Qk6rO8G3Nrhix/Rq1CJv9XG46jS+MODaMeGy+MPJw2knAhAMklMIcu4qjcKgaef2SOPJB4ki9b5pOE7MR8WGwOJLboSa2CFufOLK2msSOS5gDCaUwhMSRL54ZPsN/So0WYUv50i+OwmlKjT9O7w41tl8r1hpx7AyYUpMSR9X21ggmBsbEsedZwx6QUAoD7CqMAGtzs3PVCAgPcWT3qpFcXyhc9FHMJhhTat4+8RyMqBqx/UhfA8knZoR5BFo1YtuprRr5xnPz5eXC8I6/RT9/tEbJXEgohSAkjHyxzPIbXGFE02naxpMwqjnCSG/FiG0X6HQau2IkN57ES/hgK6F09OhRvPfee9i1axcOHDiA1NRUfP/99/7+wsJCLFmyBOvXr8eRI0cQHR2NK664AlOmTEHbtm05vgoKCvDSSy/hxx9/REVFBa666ipMnz4dDRo0sPptBQwJI18ss/xSxciHUcJIyaamCCOxsSSMuM+DtQjbN06pYsSNIz1eSkCZDqPv90PMDyGOrYTSgQMHsH79enTu3BkejwcM79M/deoUPvvsM4wYMQKTJ09GWVkZ3n//fYwePRorVqxAWlqa33by5Mk4ePAgnn32WcTExOCNN97A+PHjsWLFCkRG2upti0LiyBfLLL+Bew5EGAHaf9xqatXI7HVGQM2oGhm1zkhoI8wrVKbTjKoaKdmZDVWvzMVWimHQoEG45pprAABTp07Fn3/+yelv1qwZ1q5di9q1a/vb+vTpg0GDBuHjjz/GM888AwDYsWMHNm7ciPfeew/9+vUDALRq1QqDBw/GmjVrMHjwYIvekTZIHPlimeU3uOKIptTUjzdbHJm9fd/oRdj8GHYRR+G0Q81IcVT9vkjAhAO2EkpOp1O2PzY2VtAWFxeH5s2b4+zZs/62DRs2wOVyoW/fvv621NRUtG/fHhs2bLCVULKrOKIdatXYWRxpcV9TdqiF45Qa35/aHWpSwojvQ3x6S75qJJWT1h1qaqbU2HGlqkZi44wQR1KLteV3u1krkOjyAOZiK6Gkh/z8fBw4cABXXnmlvy07OxutWrWCw8H98qSmpiI7O1vWX0ZGhmTf6dOn0bhRXED5kjDyxTPDJwkjNqEqjKREkdQYEkbiY+wgjPSuNWLHDSlhZPX6JH8uhJmEvFB69dVX4XA4cNttt/nb8vPzkZCQILBNTEwUTOeZDQkjXzwzfJIwYhOqwggIj4qRd4yMvQ2EESB+TSMzK0bcmDwbGwgjvl0gwojhjbPnrz+hlZAWSitWrMDnn3+Ol19+GY0aNTLE57p16yT7MjIyACZfdrxdhRFgbW52XmcEkDjS0m/lDjWpMTV5Eba3TzyHUF6EzYnr98mzlRAtvrFG71ATE0cCwaYgjvixrIAWc5tLyAql9evXY8aMGXj44Ydx8803c/pcLhfOnDkjGJOXl4fExETDcyFx5Itlll8SRz5o+z6JI7uLI3YcqUXYHJsAxZHUVJnPh9HiiC2GuO9DRBxZ8PPrFWrG+CHECUmhtHPnTjz66KO46aab8Oijjwr6U1NTsWXLFjAMw1mndPjwYbRp08aQHEgc+WKZ5Tdwz3YWRl57ddAONfW+Q1kc8XO3ww41vVNq7LF226EmJbTExBHDy50jvMSqZhZfFoCwBvltZjbk4MGDyMrKQp8+ffDcc8+J2vTv3x95eXnYsmWLv+3w4cPYu3cv+vfvH3AOdhNJDO9/5sbiPozzG/h78IDhPDTFZ7gPVWM05qz22Hl4D73+lPo9DPehdrycXw8cnIeyLwfnAUh/FmK+xfzyfYqP49owDPfB/wwE9jIx3IyT649l54az2q6qOuF/sMa4GbadkxWn+rmbccLDOOCpsmfnwgBwV8Xg5+SpsvXA6ffntfO+VzfPjh2XG9Mbx+OzqYrhZpz+/H3v0VP1WfrG+mJ7GN+jymfVGL+PqnZfHP94/4M73v85yNn5jwnXhvP5M1J+HJycfJ+boI9xwOOxbjpM6fup5kFIY6uKUklJCdavXw8AOHnyJAoLC7F69WoAQK9evcAwDO677z7ExMRg3LhxnIXZ8fHxaN26NQCga9eu6NevH6ZNm4annnoKMTExmDNnDtq2bYvrrrvO+jdmMFQx8kIVI239VDFix6SKkZQd+3koVoz4dmZWjDjHj+2fH8tkDLkyNyGJrYTS+fPnBVNpvtcffvghAPjXHt19990cu169emHZsmX+12+88QZeeuklzJgxA5WVlejXrx+mT58eElfl5lMjdqg5G8FR0QyAE4g8DYY5LmpmZ3GkxX2o7lCz4yJssbFmCiO+P1kRJTHGzK37kkJLhZ3RW/fFFlsbsXVfzy42vnhhxMaJrDPixOeLYgn/1v5iG1URoqqSFLZSDc2aNcO+fftkbZT6fSQkJGDWrFmYNWuWEalZTo0QRwCAGDgq+6P4wD4U7FwBeDyI79gLcZffACbqF4ApInGkoZ92qLHjWVM1EthK5CBVNWK/tusibE5cv0+erWhe4jmbJY6M2qGmRRzxq1LsNiI8sJVQqunUxCk1R2U/nF2xBOU5R/xtFzd8jYKdG9Fo7KNwR/6gPQebiCO7T6nJ9dEONXlxFC471Dh582KE6w41qQXXYtNuYjkIxJFov7XQzJu5kFAKIjWnaiSOw5mMshOnOSLJR2V+Lgr/2I7Y7s3BeI7J52CyMPLaqyNUp9QA89YbmTml5o2pXxwZPaXGtpMSRgBbqMgLI7Z/tVNq7H4xQcYXI+yxUlUjn73YGCOqRn7/GqbU/K9Fqka+sWJCSSz/gKpGbGHEjmPhzzs/f8JYSChZSE0XRmw8YOD0NEbh7i2SNkV7fkXcFbeBieAKpXCrGKmxsWqtUTArRmJjlSpG3jEy9gpVKSlhFKyKEdu/2ooRu1/LdJqWipFvnFyVS40w4lewzLymEfs1P75hFSP2e2JY/2G4uRKhDQklk6mJ02liSK4zkrsRsjPCG50qRqrHUsVIQfDoqBjxx+kVR6FQMeL814IdalZVjNiv5fwLRQ+7HwA/DsNt5/ZZV+UhPWYuJJQMhqpG1SgtwmYcx5DQ7SqUZO8U7U/o0h+eyOOqSzd2XoStxobEkS+efmEk6t/A6TS2DylhxLWR8GGAOJKrGrHHBvseakbtUPONNWo6zZ9f9UEQ6QfEptNUiSOaegsbSCgZAImjarTsUGOYfEQ3TECtlpej9Aj3ZsVR9Zujdpt2cHv+I++DxBHXn4QwkhpjxZSa1Yuw+f70iCOrt+9bvUPN99ysHWo+u0DFkaU71HhTan47jeJIUG0iQh4SSjoIB2Hk9Ru450C37lc6N6Hu4GGoODsQBds3gPG4EX9FOmJSmsAd8V/hGI3x1FrbQRgpjdcqjgKtGkn5FpyoVFSNxOzMmlJTtJUYZ6cdanJTahw7iaqRt49na+GUms9OyUZMvCjtUNN70Ueu6GH3Q1oYsfr4thC1BcDybQUMjAlHok4aEkqaMf/rFC4VI0EOokMr4Y5Yj4gmLtRp0hsOxgmP8xTcnr3eMWEsjJTGhrIwCue1Rmy/eq6GzbYlYRS4MDJ0Oo3Vx7cV+vA18oRREBSHVGWYMAYSSjbAzhUjQL840rIIm2HywWCPN2e128kQWsJIaby8MIoBUKbK3ujpNGlhFAHvkWVE7eiaRsI8SBgFLoz8/pUqRv74vsF8AVXdzmqWFkb+JwrCKEjrlAjzIKEUJOwsjux8JWyvvTrsII70CCPAe3KLdDZBXEVvMCXlcJcWIjKhLtzRRShwrANQyfOlrmpkxCLsOEc7xFakwF2QD2dUNJhYJ/Ii96DCcz5sqkZiwojtW9KXTO5y4ogRiVFTd6iJrTMS888VL/x+QM06I9E2rVUjGwgjutebuZBQshAzvsvBrhoBJI60jFUSRz6iIlIQW9QdOV++ispLOf722HZ9kJwxBhcdK0SPodk71JLQBxXb/sCZrYsBxnu0I+ISUe+WibjkOohynLXNBR/5PkJZHInFNnOHWvVra8QR+7XPv9KUmjA+VIkjsUqS4eLIcuEi/NsljIOEksmQOGKN0RBPi/tQFUdya41iy3vhzKfPw114idNX/PeviIhPRuyV6SjybPbaGyiO5BZhR0c0AHPoHPJ/XcXpdxfl4ewnr6LB/TNwxrlOVhiJxTByh5oRU2ps/1qn1Dh2Bu1QExvDSObLj1P9mj9eT3VJTLz4/ancoSYmjMT8CwSsoN/XrnJKjdfGtQXAe2/C5zLiSMrOCgHD6Ps9FvNDiENCyWBIGLHGkDDi+pP50WSPcToTUZl7TiCSfBTu/BGu7hkoZP31WrF1P64iDXkb3xXPv7IcZdn7EN22Pkrd52VjhJow8toq25Ewsk4Y+e3sJoykfBEhDQmlACFhxBpDwojrT6Uwqm7z2kc4k1F54bT02MpyMJWV8ETyKzfSPuVyUrsIOwK1UJmXK5lXZe4pONu1gAcXJP2FgjCiilF1JwkjDXZVzx385xYgNm1OGAcJJY0wsK84srMw8tqrww7CSGm8VnEkZS/2A1dRcQ616veUjO2MiYUjKlLUr5p1RuILv8XFEXtMJYoRVbcpKs6fFM0rumlLFHnybbNDzait++zntENN/DMTE0eGL8Jm9fFtwbf1D3DwEgYXxiHezm+TEUcOiXYrocXc5kJCKYiQOKrGDuJIjzACjL+uEYNCRCQmIbJOI1RePCOwdfUcgpLoE2Dc0v7MuODjpYhDqHP1LTj/1TyBb2eteEQ2a4Uy93rBuGDvUOPaCsWR1kXYHDub7lDz2cnaiFSN+P6DfsFHq3eoGSGOqsZRjSd8IKFkITVhSs1rrw4SR9J+L0X+gkajpyL332+j7OQ+AIAjIgoJ3a9HbOc+yHV/C/5PsdkXfSzzXEJ5oxTUue5OXPrvl2DKSwAAUfWaIXn4A8iJ2A3GwxUOXh9y8c0RR2rXGnF9SosjRiSGkjgSG2OkOArWDjWlKbXq9w9Bm1ZxJFZJEoojkapQoOJIxJdDRQxZGyJkIaFkMlQ1qkbtdSSV/IWjMOJT4TmPC1HrkHzTODjLouApL4WzdhzKonOR6/lWcmygVSPZahDjwHn8ibg2zVAv9WmgtAKOiEiUR5fipHMXKjyFAKTvxSXwZ+OqkR5hxPmvBVUjtb7ACI9joFv3/f71CiN/Xr7nPHFk96pR1ViBMJKLayK0RslcSCgZDAmjaqhipM6v+O+sAxWePJzDau9FuWOqxnoAiJzoq2PqF0Zqd6cVuk8i33EKqM3K3yMVP3wrRpz/2kUYGVAxYr+W829dxQgwVRixK0YCe+44NcLIQVWksIOEUoAEWxgB2sWR3StGamx84ijC2QCVlW3gYSJQK/oYPJ4jsu9PqscIYQQELo6UxxlZMXIiztkKMe5EeByVKHAeQ7k7X9Q2FG8TwrFTsUNNbLpQ6yJsXx/3XKtzmowXR65i5PcrOBbiOfHbDFlnBMDW1zQS8SUQPmIVI4UYDsnxsAQG2s8BUn4IcUgo6SDY4ijUqkZq/GmvGkWionIwtu6rxKrNZ1Be4Ubfzqm4pldP1I7+DzxMnqLvYN9cVsynVTeXreWoj3qVnVC0ZR2KjuxBRO14JPe6DkyTdjjDbAPA0A61IFSNfHZKNl5hIV4FYkRiicYP5nQa21aqaiR4AyLiSc5O0K5hOk0sjkpxJDneRGjqzVxIKFlITRJHRlaNxCivvA5zPjmFvYcv+du+WFeEtf87g1cm3IDo6C9EMw22OBLzZ5U48uFEbdQr7YCzHz4PpqIUAFB5ESj75iBiO16Jev374ix2i1YgxHwGWxzJTalx7EgcmbtDjdXHtwXfVkocqa0aqbUNpjiiEk3YQELJZOwsjrS4N0IcBSKM2OOdjgQcOxPNEUk+LhWUYeWmsxiZ0Rpuz37dF30UtIsYG3kPNWOn1KRFCAC4HK2R99MXfpHEpnjPZjTodS1QKwIMUx21pkyp+cbxc+ZfzJEbR3q8FgElN6XmeyklfKTEkaQwqjKQFEb+ft9gseoShMKI18b1AdhlSk3URuS1gxFpVxVD3J9pkCgzFRJKBqNXGOmdYzZDGNlhd5rceKezGX787bxEL7Bh51kM6dcSkVEHFH2Fx1ojeWHEry7V9tTBucO7RTL3UnrwD0R3ro/iyrOC8XYRRmoqRmw7tRUj33i+MOIKIXnBIxpPozBSWzHy2ShWjKoG6hVGqipGAlvACmFkRcUIUCeMRMWXBZBOMhcSSgFCFSNtNkbsUGPAIMIpbRvhdEDqSNm1YuQdI+1XcS2ThBCRXGfkcAKMxKceEekXB4K4oiJGPC9ZwaOQu5aKETuu3ooRN19+HGFcvlCjipHPwOYVI16bqDhix5CKoySMLFUuDqFg1euHEIWEkg7CQRwFY4ea1rFSfRWe47iuTwds3CV+P7RrejVCdMxBuH1b1sOwasT3p0ocVY0pdJ5H7cu6oWT/NkHOABCT1gnFlf8DA4dt76Fm5A418TjS4kpN1UhunZHvtZQYoh1q4r50iyOrqkZBrioR5kFCyWRCbRG2Gn+BCCOl8VJ9nJM/U4zG9fKQfnkDbPnzLMeuSb04ZPSsg0rPUfD/hWT2DjUxGyun1Lh94jl44MB55jBaDRiBshP74SnO54yL7zMEedEX4PYwAK+iJCc02PmoXYTNfq5FHHHfm3hsu23fl1uELZYTv8024sjfqVIcKVVbAhRHolUf3muzxZFs5ckiSJeZCwklE7BL1QgIrSk1gU+pShAAR8R/ce+wQbi2dyes3HQGZRUeDOhWD1dcFoOIqFX+fKzeoWbVlBrfVk4Y8WO7mUocj9yFZnc9jfJ9O1F28A84YuMR1yMDhS43znj+AngndrtdDVvsGJq5Q03rmiQpcSQllPhtAlHMcH37YnFFD78ffiHC8NtZfXxboQ9fo4OXMPu5TNWI3Saypon9XFa0VI1XqugAAe5Qk7JhvVbyYfVFJ+mmuOZCQskASBipH6tXGIlZI3IdWjSLx4TRqWCYCDid21DhzvVPucn5VlMxEh8XesJI7HmxuxD7sQlxHRoitt31cDs8OO05ALenTBjLZGGkZa2R2LhgCSOz1hrJ+a9RwijQtUbsGLJxDBZGJFrCDpklsfK0b98e//73vyX7V61ahfbt22vyefToUcyYMQPDhw9Hhw4dMHToUFG7L774Atdffz06deqEYcOG4eeffxbYFBQUYNq0aejVqxe6du2KRx55BGfPnhXxph2G4T5UjeH9T96W+5DDw3vo9adk42G4D7Vj5fo8iIIHDv9DaYxvcTF7kbHbU4hKz264mR2ocOeyfDs4DzGfYv6E44Q2DOPwP7xjuA+2vQdO3muef5YvDyNt62a9Bw9rjJtxSubLju1mnPBU2btZcQoqzyLHcxBn3YdRwZR7YzFOQU4eOP3+3HDAA8DNOOCWs/PH9D7YOXqqYvjyd/v8+r9j3vVR7PfhYZxVD2+fb4zvPfna/ceD4T+449l2nPEqfHE+N44fsbgOzufmYRxwe5w8X9Xv2eNhfye48RnGAcZTPcb33ONv9x4/729T1XeUly/DOACPVwR5fVTbe9urHh7WHwyn3SH2xyRuy2n3CgoHAziqnnNiMAAYBxz+R5WNSAwHz5dsDH4cKRu2f96D70MuPvjtluAw4EFIobuixCgoBLfbDYdD28E/cOAA1q9fj86dO8Pj8YjGWLlyJZ555hk8+OCD6NOnD1atWoWJEyfio48+QpcuXfx2kydPxsGDB/Hss88iJiYGb7zxBsaPH48VK1YgMjKAQpqGL34oV43MWmfkdMSjtrsrHKUx8JQWISLOhcroXBQ7dgFw8/xIVJhEAoTqNY0CrRpJVYzsek0jTly/T54t73jJ5SyMIx6XUWnjaw/6DjVem/e5r12iaiRy/EN6ETavTfGaRlJxpPLQkKdsxYgJ/jolmnozl4Cm3qSEUGFhITZu3Ig6depo8jdo0CBcc801AICpU6fizz//FNjMnTsXQ4YMweTJkwEAffr0wf79+7FgwQIsXrwYALBjxw5s3LgR7733Hvr16wcAaNWqFQYPHow1a9Zg8ODBmvLSAu1Q4/ljnfScjgTElfXDuS/fQsWFU/722m26I+naYch3/Ch5/EJZHPH9caet+H7Exxgtjtj+1Yojdr8WcWTEBR+5+fLjyI8XEz5GXNdI7DU/Pm3flx4rKlx4rzVd8JH92gBxJBm/6rUacUR1mvBAk1CaP38+FixYAMArkp588kk8+eSTorYMw+DOO+/UlIzTKT8TePz4cRw5ckQQc/DgwZg9ezbKy8sRHR2NDRs2wOVyoW/fvn6b1NRUtG/fHhs2bDBUKNXUHWpyw6TWGsVWdkfuZ3NRmcedAi3Zvx0RsQmIuaotSpm/vf4lAoTbDjXB76/B4ijY91Bj29nhNiE+OykbteJI7HNTFEeC98+NxxFAgEAciQkhQRtHRPk6ZcSRnDASjJEWR4qigQmNHWqa48uNJ8IGTUKpU6dOuP3228EwDD7++GP07dsXLVu25Ng4HA7Url0bHTt2xHXXXWdkrsjOzgbgrQ6xSUtLQ0VFBY4fP460tDRkZ2ejVatWgopXamqq34cUGRkZkn2nT59Go4axmsSR1cJIjY2ZVSNp+0gwhW6BSPJRuHsjGvUegJLIvxV921EY8f3ZoWpk5ZSakdc1kqoGVb8mYRQKVaOQE0YidoGOtwqpZQqEMWgSSldffTWuvvpqAEBJSQnGjBmDzp07m5KYGHl5eQAAl8vFafe99vXn5+cjISFBMD4xMVF0Os9IrBZGgYgiufFyw7TtTvP+ETsdtVGZf0HGaSVQWQlPZGgIo5pQMWLHCYYwooqRSBvbh79TpTCSEBMCOwlfYSeMpHyrHa81vzDn0KFDmDlzJnbs2IG4uDgMHz4ckydPRnR0tOLYnJwcvP7661i/fj2Ki4vRtGlTPPTQQxg2bJgFmSuje43SSy+9ZGQetmHdunWSfRkZGWA8eZw2LX8PNWfrvojIYEoQmVRf0r8jMhqIipT0aed1Rnxbzm+nhDDi+xAXKfIVI6mcxMRRoOuM2HGlhJHYOL44ssPWfd9YKaHEbzN9676KihF/nO6t+1J2gr4Q27ovU8kJSJzJjZfLz2qhFGRhlpeXh3HjxqFly5aYN28ecnJy8PLLL6O0tBQzZsyQHXv27FmMHj0arVq1wgsvvID4+HgcOHAA5eXlFmWvTECLud1uNzZu3Ijjx48jLy9PsEvN4XBgwoQJASXIJjExEYB363/9+tUn3fz8fE6/y+XCmTNnBOPz8vL8NoFQE8SRlDCSGiNV+q3+SrjBxLkRVb85KnKPCewSel6H4qijnNuPhZs4koodjNuEsOMGIo74i6jZtkbsUPPZBSqOjL6uEV948cURX/DoEUcMx0Bl1Yjfzm8zaxE2r033Imh2HhLjlfK0YjpNzodk7mHMp59+iqKiIsyfPx9JSUkAvPrgueeeQ1ZWFho2bCg59tVXX0WjRo3w7rvvIiIiAgCQnp6uOYfMzEwMHz4cN954I5o2barrfUihWyj98ccfeOSRR3DmzBmBQPJhtFBKTU0F4F2r5Hvuex0VFYWUlBS/3ZYtW8AwDGed0uHDh9GmTRvD8hHDqrVGpt8mRIW9sjji+i5wbke9kQ/i4qqPUHp0j7fDGYmEboNQq1sXXPKsD7o4Ujul5u0Tz6GmrDXyjePnzMjGkR6vpbpEO9SEYzmosQtUHElVXtTEYL+Ws1GZZ6BVH2PFEetDt0IsMeK/uXr86GXDhg1IT0/3iyTAK1z++c9/YtOmTbjllltExxUWFuKHH37ArFmz/CJJL40bN8a8efMwd+5cdO3aFTfddBNuuOEG0WU4WtEtlJ577jmUlpZiwYIF6NGjh2DdkBmkpKSgZcuWWL16tf8yAoD34pbp6en+udD+/fvjrbfewpYtW3DllVcC8IqkvXv34v777zc8r1CtGgHGiCO1W/fdTCkuRPyE+KHXIKn8VjAVFXDERKMk6jguMr8A/hO/vLDxxtQvjoyoGvHH6RVHYsKI7VvSl0zuaqpG7LFSVSMxn2ZMqelarC0Qb9XvSUkY+drEqkZi/oWih90P2GJKTcpW4wnf1lNqGuIbNl5VHyPTF1qcPn1adkOT1NKU7OxsjBgxgtPmcrlQv3592Q1Ue/bsQUVFBSIjIzF27Fjs2LEDSUlJuOmmmzB58mRERUWpzv3999/HuXPn8P333+Pf//43nnnmGbzwwgsYMGAAhg0bhquvvlqTPza6hdK+ffswZcoUDBo0SK8LASUlJVi/fj0A4OTJkygsLMTq1asBAL169UJycjImTZqEJ554As2bN0fv3r2xatUq7N69G8uXL/f76dq1K/r164dp06bhqaeeQkxMDObMmYO2bdsashOvpggjrRUjNT49TDnysQOIhvcBtoAQnui98cSqTNK56p1OM7JiBLBFinzFiO0/mMLIrOk07nlG52JtEWEUzAs+CsUTVAkj7jiDKkZsWzWCQSSGbmGkRnxVPddcMVITX248z5elwshykST+W20V+fn5osWSxMRE/yYrMc6dOwcAmD59Om699VZMnDgRu3fvxty5c+F0OvH4449ryqNevXq4++67cffddyM7OxvfffcdVq5cibVr18LlciEzMxPDhg1Dt27dNPnVLZQaNWokOeWml/Pnz+PRRx/ltPlef/jhh+jduzeGDh2KkpISLF68GIsWLUKrVq0wf/58dO3alTPujTfewEsvvYQZM2agsrIS/fr1w/Tp0wO7Kjf0CxQ1/cEWRt52seoN4EAkYhytEelOhMdZimJHNjxMoSq/SsJFzCaUdqi5Ipog3l0XHnhwKSIHxZXnhSddmZxEBY9auxCoGPHtrKoYsV/L+ReKHnY/AH4cnmjiDFdRMaodEYXL4xPhinDgfKUHfxVcQpnbLS+MBG9UwpZRI1oCv7Gs953IxVCorKjIU218p8OBFvXrIDEuFm63G8fOXUReUam+6TjJPkamTzwvSzEoXuPGjWU3NBmNx+P9pbvyyisxdepUAN6LSBcVFeH999/HhAkTUKtWLV2+U1NTMXnyZNxxxx148cUXsXr1anz66af47LPPkJKSgnHjxuG2225TvH4jEIBQGj9+PN577z2MHj0a8fHxet1waNasGfbt26doN2rUKIwaNUrWJiEhAbNmzcKsWbMMyU0MNd/NUBZHPqIdzRFb2g75W1aj4OQhRCbURcKVN8BTz4NCbBf5vRCrAMkLGzOrRnx7NYuwhXbC59HOeDT3dEXpzi0o/WslHJFRaNh1ABypvZHt+R0eVFq6Q4091i471Hyvrdqhxn4t558revj9gOR0Gr+P9Vrow9dYLbx6JNVFO3cZyjd/jsqLZ1C3fgtc3mcYtpe58Vc+71/egj8sEXEkd3I2WByprhrJxDGk6sNqrxsfiytaNsParcew+8BxxMdG4fr05mjXNAa/7TvKrX4rvAdRcSTZp+CzhuFyuVBQUCBoV9pA5atC9enTh9Oenp6OhQsX4ujRo2jbtq3mfIqLi7F27Vp899132Lp1KwBgwIABuOmmmxAVFYXPP/8cM2fOxL59+/D8888r+lMtlJYsWSJoi4uLw7XXXoshQ4agUaNGgsVYDocDd999t9oQIYPS34PV4sj4HWrVOJ3JqHWhOU5/8hzg8d6LrfJSDko/24vEfjejdue2KMY+Q8SRnXao8X0IhYoDzT1dcWH5K3AXXvTblf/nA0Q3uQwth43FQWa76eLIDtv3uUJNnYCSE0dG71Dz+dctjgSim9fGgOPbi4OXMNA6PhFtzmYjf+37/ubKSzkoPfAbut80BRdj43GmuJD1xmUqTEqiw25rjdj9UrE1xo+OjEDH5k3xzMJfUVJW6W08Dxw4fglXdmqMgb2aYtfBk0ERR1ZeoZuRTkOzH72IXcy5oKAAubm5nI1XfFq3bi3rt6ysTHUOvl343333HX766SeUlJSgY8eOeOqppzBkyBAkJyf7bTMyMvD666/jo48+MlYovfLKK5J97PVBbMJVKPEJRBgpjdcqjqTs9a43ine3x4UfPvCLJDZ5m75Fo47Poyhyv2ROdphS8/aJ56B3EXZSZFOUbPuFI5J8lJ86gLjcC4iq70JZ1fSkX/SI5CEnyLi/7VwBwhdG3j6erYVVI58dP2c164HEhI+UMGK/FstB4F+03zdY5UUf+RVPgTgSCiOuvQPd4+NR9JXYbyWDorXvofeo6fi2sEjchyrREuIXfdQ4vnWjevh87YFqkcRi8x+nccOVLRDldKLS7ZHxzXD+I/q+lIQTxASfiCo0EwuFmRj9+/fHwoULOWuVVq9eDafTybmVGJ+mTZuiTZs22Lx5M8aOHetv37x5M2rVqqUopNj07dsXeXl5aNiwIcaOHYubbroJaWlpkvZt27ZFUVGRZD8b1ULJynlLuxPOwojv11keg4oLpyWCeFBx9iQcTePhZopE45q1O03RVmKcUVv3EyrroWTvF5CibPcmuK67Cmc81X+IfGEkt9aIYxciwkjKxlRhJHj/4Laxz4MqptP4thC1BdQII3af0+FAZFEemErxi+i5i/IQX1nGPuCWCCM1FSPAJGEkJ0BUjE9OiMfv+/4QScrLjn25qJ8UjzPn87kfHts3P65SXmI5AYIfVsnrSIUpY8aMwbJlyzBhwgRkZWUhJycHs2fPxpgxYzjXUBo3bhxOnTqFtWvX+tumTJmChx9+GC+++CIGDBiAP/74A++//z7uu+8+xMbGqs5hwIABGD58OPr06SO4fZkYQ4YMwZAhQ1T5Vi2UjL6AUzgRTsJI4FPhC+dwRnhPdiJTQd5Y8nnatWLE9ym4ppGTgUNuEaDTCTfjExKBVYzYdnqFka9PzzQZPw4/Z63XNBITRnzftqwY8ZPmiRbRdvZrpUWjDof3BGuiMAJCp2IkNd6fH7wC1C2xqSjC6QDDeHxf9OpxYSmMlIWBmSQmJuKDDz7ACy+8gAkTJiAuLg4jR47ElClTOHYejwduN3d2YtCgQXj99dfx1ltv4ZNPPkGDBg0wadIkPPDAA5pyGDFiBNLS0iRF0oULF3Do0CH07NlT25tDgFfmrsmEwiJsOb+SwohHZVQRohu0QPnZo8IBzghE1m+ESs8esP9QjRJHatcZ8ceZdU0jtu055wU0uOIqFPzyFcSo1aU/jrhPw4Pqk2NN3KHme21Z1QgQF0cq1hnxfRt5TSMPA5TVSoAjuhaY8lKBeYSrHvIQVXWwuDGCKo7kREQg8dWOr3otFj/3Yj76dGqETbvEK97d2tbHtj8PCcWnUl5iOQHqxVEwxFLQBFo1aWlpWLp0qazNsmXLRNsHDx6MwYMHBxT/rrvuwuzZs3HjjTeK9v/66694/PHH8ddff2n2rVsoDRo0SLa85XA4EBMTg0aNGqF3794YPXq0IbcPsQNiIikUxJGYX6VF2AXOv1FnyN04u/wVMBXcH/jk6+5EgfNQ1Rh5v0ZMqYmdZMXtzBFHbF8XK8+g6eW9EbV3KyrOn+TkUqt1N5TUiUOZu6xGiiMxocR/z1rEEVv0CPsB4S40rmji9lknjvjt/7uUj6syH0TBt29yjZ2RiM98CD9cLKgSSjbdoaYhPmCOOGL7PnLqPG6+ujX2ZF/ApQLuot/BV7ZAXkER3G5GdKzZ4sjBjkVYgtLlisrLy3Vf/Vu3UOrVqxf27NmDAwcOoE2bNmjRogUA4OjRo9i/fz/atGmDli1b4tixY3j99dexfPlyfPTRR/7bjIQDesSRmTvUAqkcSe34qmQKkRe3Fw3vnYHiP35F+fEDiEisi/geg1Acm4tC/C3qU64a5M1fe+VIzQ41vVNqbP+SQotn95d7N9qOehjM8cMo+2MLHJFRqNVtIErrJmJf5V8sAcQVKey4fHHEj82fOuOMDWCHmp6b0IqJIzHhIzzXCO2r+8T9c0UPvx9Qs0NNShzxhZducaTGjnXCPJ5fhN+TktH9rlmo2LUWzIXTcDZohchOA/HLhSJcKCqEgz8FyPYhG195672sOJISEVLCRiq+Qg4BX/SR9eFVVrqx4+8j+L+7e2DXwXPYse8cEmpH4ZpeKWA8Ffhz/0lpn1I5AQGLI+4X0hosDGUrTp06hZMnq/+hmp2djd9++01gl5+fj08//RRNmjTRFUe3ULrmmmvw888/Y/ny5ejRowen73//+x8mTZqExx57DAMGDMDWrVuRlZWF119/HXPmzNEb0jYo/WOSTagJo+p41a/LmHM4HfEjandvhuiug+B2lOOMZysYVAA8MSDp3yRhxH5utjDi25Uz5dhVuRNxKUmokzIYjAPIdp9Fqftk1TjWtFuQhZHPjoQRYJUwEmv/+2IeDlyKQFraILjaOnCx3IMjR8/Cwy0jen1oFSZhLozExhUWlmHj9v1okByPwX0aw+324GD2CZSWV0pu0TdNGPmeBkO11FCl9NVXX2H+/PlwOBxwOBxYuHAhFi5cKLBjGAYRERF47rnndMXRLZTefPNNjB07ViCSAG+16Y477sDrr7+OAQMG+KfevvnmG73hbEc4CyOvvTBOsfsEiqteeMfLCJkwFEbCmF4KKvNQgDxW/o6gCyO7VowEU55hLozYY302Hnhw4MIloQ8SRorCSGpc7vlC5J4T3ilAkBNgnDASGadUvTIP6fNOOJOZmYnLLrsMDMNg8uTJuPPOOwWaxOFwoHbt2mjfvj3q1aunK45uoXT06FHZG+EmJibi6NGj/tdpaWkoKSnRG85W8P8Ggr1DTY0wErML16374ju+RESPSB5y4oj7G82NQVv3xd+zwL9ov2+wSdc0EryBwMWRomgwYIeacowqH2IxVPowe4ea3DEQ9omIIznBJ9bPzwlQL4xE2vSJI0ZgQ5hDWlqa/1pJL730Enr06GHK8h7dQiklJQXffPMNRo8eLbgXS0lJCb766is0a9bM33b27FnOlTFDnZoojvgxwk0cicUMV3Hke224OBK8f248wTlEjzgS+AAE2/elBA+/T842COIICOL2fTkRYhdxJPEDa+QONSVxxPk2yYgj8V98wixuvvlm03zrFkoTJ07EY489hszMTNx0001o3rw5AG+l6dtvv0VOTg5ee+01AN5Li3/33Xea79hrRxjIiwBuu4hw0SmMpPwpTal5Y+oXR0ZMqfHHmbVDTe2UGtentDhiRGLQDjXu++b7F543eOIogCk1/jgzd6ipEg28KTW5GJbcJsRIcaZnvKo+zh+MvvcllhOgWxxx/SiIIxlbUQEldXIwGqvi2Iinn34aDocDL7zwAiIiIvD0008rjnE4HLru/6pbKGVmZqJ27dp47bXX8Pbbb3P6LrvsMsyYMQMDBw4EADAMgyVLloTN5QECFUaAfnFk16qRGcKI7deom8uyn2sRRhw7gfCwThjx7YysGvlstAgjvw8pYQQg4KoRWxjxk+aJFtE3JRgjYatKtIRR1UhP/ip8CHNjZPpEfIr183MCrBFGnPH8L7bU51ADVUsQ2Lp1KxwOBzweDyIiIvw3v5VDzRW7xQjogpMDBgzAgAEDcPbsWZw6dQoA0KRJEzRo0IAbJDIyLK/sHUjFyDte2WdNEkZsn0YJI6oYcd8f9/dcaF/dJ+5feM7gCSN+nECFkYxgEW3XYqtFGCnECFQYyQkEOwgjufgBCyMJXWG3ipGondgPPukkS/jpp59kXxuJIVfmbtCggUAchTNCoSK0CZWKEd+fHdYZsf1rXWfEsROZzpFaZ8SxEQgP7hifrXi+/DjVr43c3i8mXtTuUFMURlVOBAKW4ff72lVWjHhtXFtAtmIkMpb7xlTYqRItDnEb3uuAhFHVayUBJufDsh1qqgQOI+yT8ynmVywnQFwcKQljjh9xYSSeiwphJJKTWHxvDhYqJhJnpqJaKPm29g8fPhwOh0P1Vv+bbrpJR1r2J5TFUbgtwubYWbQI29fHj8OvQBk9nSZWNeK/FvvMdIkj0X7f4NARR6qrRgoxbDudpme8lvzUiiO5cWL9ojmJCCOp8XYWRyRcwgrVQmnq1KlwOBwYPHgwoqOjMXXqVMUxDocjLIUS+2/GrjvUwn37vtyUGsfOQHEUdtv3Be8f3Db+b36ga438Txy8hMElRMSRcowqH2IxVPoI6R1qYv38nABpcaQgjLi+xMUR55dNiziSqgaROLIN7dq107zmyOFwYO/evZpjqRZK69atAwBER0dzXtdE1Ox6UyOOlISRd4y0XztMqQFsoSIvjNj+1Qojdr+a9UZi+fN/+8T88SsxesQRX6ipEVByi7B9L6WEj5Q4MmtKzf8fK6tG7DazptR4baInajXCRIUwUsxTKn7Va0VxhsDEFbdPRBhp8SmVE6BbHMneJkQyF0aFjTAn0XzAm1IT/ZwtVkwMuH8bgfgJISZMmKB7cbZWVAsl/mLscFycrRY1woim08TFDvu5GdNpbDu1FSPfeP4aJMn1QeAKIy2VJa270/ixROObNJ1WPcZCYaTGTo1gUFkxAlQIIzXCQ6cwsmw6Ta5PQnzorRgJ8grWdJpSvmYLoxATHqHGpEmTLIsV8GLu8vJy7NmzB+fPn0e3bt3C6qKScuipGAGBiSOjbxPCtpONa1DFyGsrnbuaihF7rNIONbExPhMjptN0TbkJxFt1flJCid8mEMVsEccXRrw2vjDy22kURtxxBlWM2LaaRYuOihG7XYWo8D1XEmByAkMyvtHjVfWJCCMtPlnYtmLE7rZQGFm6kJswnYCE0ocffoj58+ejoKAAAPD+++8jPT0dFy5cQGZmJp588kmMHDnSkETtAv8EHPg91NRXjfj+7FA1Yvs3omrEjmNE1YhtG8h0mp71SKFQNRITQlLiiHteMr9q5I+iRxxJCQt2n5oYVa8DqRoJclAjvDSMF43P7/O/tlgcKQljmCCOuD9+ivG9OYS4OKqBuszKDWa6hdKKFSswa9YsDBkyBH379sW0adP8fcnJyejTpw9WrVoVdkIJsFYc1YQpNXacQNYaKW3f5/7+mr9Dze9XcCzEc+K30fZ98bFKFR3AwB1qEnGUxE2g2/dN36Em51PMr1he4b5DLRBx5PddAxWMRVi5wUy3UFqyZAkyMjLw2muv4eLFi4L+jh07YtmyZXrd2xorp9TkbKWEkdBOnzjSc9FHtq2aKTWOncSUmrdPPLaZO9S0rkkSEy+B7lCTE158YeT/j9SUGquPbyv04Wt06BNGam3FRIPgJGvNDjVZkaBV3GgUNrLjVcQXFRVaBJ9YPz8nQFocKQijaltGaCObp4TI44xXJ4y8OegQR1qEkUJ8wjis3GCmWygdPXoUd955p2R/UlISLl26pNe97dEijLRMp/Ht7S6MtK414tgpCCOx90HCiISRP9NQE0a8OOEsjAQVI/bTcBNGdhBFdsjBYqzcYKZbKLlcLtFKko+DBw+ifv36et3bGoZxWF4x4o+jilHgwohvR8KInzwJI83CSM94FfH1CiPZfn5OgG5hVG1bA4SRVv+EpbjdbuzZswcnTpwAADRr1gwdO3ZERESEbp+6hVL//v3x+eef4/bbbxf0HThwAF988QVGjBihOzE746+m6Kwaya5JkhgjJYz4r8PlmkZsW6t2qAnu6ybIUVr4SIkjO+xQYzgGDp4x/7lKcWTWImxemyHXNBKLI5WnVHyROIriTGG8ZH6ifRKCQq1PqZwA3eIo7Heoqa0akTiyDV999RVef/11nD9/HkzV5+JwOJCcnIwpU6boXjOtWyhNnjwZt956K4YOHYqBAwf6V52vWLECa9asQf369fHwww/rdW9bGIif3IHQ36HmtZXOXcsibC071Lh5cXM2+4KPPl9ilR3fS7XiiN8vlqdAHIn2+wbb7LpGbFsjxZEacaFS2PgFjIwAk81TKr7R41X11QBxxP0jgoBQFEfBEE6k1fDpp5/i2WefRfv27TFx4kS0bNkSAHD48GF89tlneOaZZ1BRUYHbbrtNs2/dQqlhw4Z+9fbDDz+AYRh8++23iIuLw5AhQ/DEE0+E7TWVJKfKbDKlxvZj5Q61QC76qHaHmp4pNZ+d3JSaP47gWIjnxG+TFEciwgui/b7BAe5Q83caJI4CrBwpVXQAA3eoSYgjpcqPoVNqWvIT7av+QohWWpTyYqFqh5qSMIaMOGIfA8F4oZAyRBxJCYJgiqOgL+R2gPdtCcBP6LJ48WL06NEDS5YsQVRUlL+9T58+GDlyJMaNG4d3333XWqEEAHXr1sWLL76IF198ERcuXIDH40FycjKcTmcgbm2P0toevo23j/U8iFUju27dF49T/Zo/Xosw8tlZIoyqnGiZUgtIGPkN7CGMRG14rwOt2EiKH5U+At26L/BhkDDy98n5FPMrlhMgLo4kxKS4HxsII4l+W1WNBGaWKyUCwLlz53DvvfdyRJKPqKgoDBkyBK+++qou37qFUnZ2NlJTU/2vrawerVu3DgsXLsTBgwcRFxeH7t2744knnkBKSgrH7osvvsC7776LU6dOoVWrVpgyZQoGDhwYcHwxgVETrmkUyAUfrb6mkdPhBMMw3vFmCiPB++fGE5w/wkwYhVzFSMQuWBUjf5+cTzG/YnmJnNRFhZGoKBHPLSjCSEpj2LpipNRvPoLvaA2kffv2OHz4sGT/4cOH0a5dO12+dQulwYMHo27duujevTu6d++OHj16oEOHDqbfpG7r1q2YOHEibrrpJkyZMgWXLl3Cm2++iXvvvRf//ve/UatWLQDAypUr8cwzz+DBBx/0X/xy4sSJ+Oijj9ClS5cAMqi+Mne4bd0XWzOkVDHi+DZxh5pam7YxDZEa4YKj4BIcUTEorhWD38tzcLGiSFT4iH1uUuJIriIF0X5AchE2q49vK/Tha3TwEmY/lxFGam0ZBdFSNVZOtPgzlRE+ihUbKRsNPkJ6674aYQQITuC0dV9inFbxpehD3j/dviQ4PPPMM8jKykJKSgpGjx7t1wKlpaX49NNPsXr1aixatEiXb91C6fXXX8f27duxbds2/Pjjj2AYBrGxsejatSt69OiBHj164IorrvBfDMooVq5ciSZNmmDWrFl+UZacnIxx48bhzz//RI8ePQAAc+fOxZAhQzB58mQA3nnK/fv3Y8GCBVi8eHFAOYhvb5erLsmLIy3TaWx7I8WRluk0sXHBEkf+1wyQHtsS8bs3I/+3HwDGe0Qi4hLR7+bJ2BwZgbPlhRw/fN9W7lATbWO4vr0YII4UqktKVaOqLIInjuRO3kbFVxivFF+zOFISTmI5ARaLI6FtIOJIcTpNhS9LF2GTOLI1N954o6DN6XTi5ZdfxquvvooGDRoAAM6ePQu324369etj6tSp+O677zTHCqiiNHjwYABAQUEBtm/f7hdOb731FioqKhAdHY1du3bpDSFKZWUl4uLiOJWrhIQEAIBvO+Dx48dx5MgRPPnkk4KcZ8+ejfLyct0CjgH790FcHEkJI8D67ftGrzXyjRPL2ewdanKLsOtGu5B44jAK/rcSbNxFecj77GX0uvsF/NsnlCTEUVjtUDNrrRGvTfcNZqXy0JKnVPyq59aKI0amT4VPqZwA48SRWoGnJt9wXGsk8BOgOCLxZCpJSUmibS1atOC0GXEhyoAWc/tISEhA69atcenSJVy8eBFnz57FyZMnTVnUfcstt+Dbb7/FRx99hGHDhuHSpUt4/fXX0aFDB3Tr1g2Ad/0UALRq1YozNi0tDRUVFTh+/DjS0tJE/WdkZEjGPn36NOo2jJdYsyNfNWK3Kwkjrq1xVSP2WClhJObTios+qq0acfOrfk/tI5NRvHkpxGAqyoBjfyOpQV1cKC9Utd5IeI5h9wPg5esXPCqqRtXtvkYDqkZStqpEi82qRjICwLTbhOgSONUfpq73JZYTYIAw4uYmyEMwXkLkccYbJIxU+JIVIHr9S/UJTKX9q6oaBUsc1UBNZuUt0nQLpf3792Pbtm3+KlJOTg5cLhe6deuG2267DT179kTHjh2NzBUA0KNHD8yfPx+PP/44nn/+eQDeRVzvvvuu/8qbeXl5ALxXD2fje+3r14sH1euUgMCFkaQvnh3Xp7HCSGyMkcJI12JtGWHEfg4AtRyRKM0/Byk8uSdQu3ETeDxF1e9VQhjpnU7j20JgCwRUMZKyVXNSFxlHwogqRhwbdrfdKkZS/uViKPqQ929rYURYim6hNGzYMERERGDAgAF44IEH0KNHD7Rp08b0xdy///47/vGPf+DWW2/FgAEDcOnSJbz11lt44IEH8PHHH/sXcOlF7sZ6GRkZKPcUwIPqSpndF2Fz7ATCw/qKkc9OypeYeFG6TQgAFLorUDu5MSounIYYzsZpyC8vqxJZYqKHVzECoHqHmpqKET9p/5sLsGJU9VxZtITgDjUjhZEKHwFXjMT6+TkBBggjbm6ieXDGC4WU+OegTpgEfYeaURUjkZeGTKepnRIkTKGiogLZ2dkoKCjwL8dh07NnT80+dQulyy67DAcPHsQvv/yCvLw8nD17Frm5uejSpQvi4+P1ulVk5syZ6NOnD6ZOnepv69KlCwYMGIBvv/0Wo0ePRmJiIgDv2in2/eby8/MBwN+vF7uLI7HfPttOp1UZqKkacd8Xt21X+SUMuGoUKr6dCz7O2vFwN07FhUtHwZ7mUj2dxurj27IHCMSRjGgRbddiyyiLhrDdoaZ2vIr4esWRuCCRyAmwRhzJ2YrZ0Q4146pGGo6lKZAgg8fjwWuvvYaPP/4YpaWlknZ//fWXZt+6hdK///1v5OXl4ffff8e2bduwdetWvPfee2AYBm3btvVfNuCGG27QG0KUQ4cOCdYRNWrUCHXq1MGxY8cAwH99J/61nrKzsxEVFSW43pIWBNNUVf+lHWoafAnEW/XxUCuO+DvULpQV4URyYzTNuAtFv3wOptz7hxJVLwWxNz6MNYVnq8dIiSP+uSAY4oj3vhTFkUiMoIojuZN3IOJITkAYIY5kRYeMT6mcAAPEESO00SCORMWc3cSR3AmexBGhgYULF+K9997D6NGj0b17d/zjH//AE088AZfLhY8//hgOh0OwwUstAS3mTkxMxMCBA/0XcSwrK8PKlSuxePFiLF++HMuXLzdcKDVp0gR79+7ltJ08eRIXL170r25PSUlBy5YtsXr1alxzzTV+u1WrViE9PT3gSxZICQ1vn/C51os+cn/buTECmVLzjZeaBvP50iR6JOyMmlLTcjXsXwty0KJJc3S+63lElZXAERGFXAfwU/F5FFaUcQQQ/1zEF0ICYVTVyB3HfW/C5zLiSI2dKtES4lNqesbL5SfXJ/qhy1es5MSRamEk419oyxMn7GMgGCsUHOLHQN0JPaR2qAnMAhRHhgojUkvB4Ouvv0ZmZiaee+45XLx4EQDQsWNHpKen46abbsKYMWPw66+/4sorr9TsO+Bdb9nZ2di2bZv/cfr0aTAMg3r16vmvaWQkY8aMwaxZszBz5kwMGjQIly5dwttvv426desiMzPTbzdp0iQ88cQTaN68OXr37o1Vq1Zh9+7dWL58ecA5uJnqNUpWCSOx371gTKf57Pg5q51O873Wc8FHWf9V/YeL83C4OI8nahy8cdXt1e+B+1poC8hWjPjjSRiJ+zZzvGSfxcJI4piJ+xIXRqLVIL6tVL4kjIIvjBi5L4OxOCDy3dTpJ5Q5c+YM7r//fgDwF0PKy8v9r4cNG4YlS5bgscce0+xbt1B65JFHsH37dly4cAEMw6BFixbo06eP/2KTzZs31+talrvuugvR0dH45JNPsGLFCsTFxaFLly544403UKdOHb/d0KFDUVJSgsWLF2PRokVo1aoV5s+fj65duwaWAOcEHdoVI58PPQJKrmLkjysifITnGp33TxPt9w2mihH/eaDCSMlHOFaMBHlRxYiEkVQj7X4LOklJSSguLgYAxMXFIT4+HsePH+fY+NYpa0W3UDpx4gQGDx7sF0Z169bV60oTDocDt912m6o7AI8aNQqjRo0yPAcGDt3rjDh2EuIo2Nc08tkp2bDFCl/siAklsGwUxZGI8IJov2+wSTvUpASP6BuTsA1RcaS76qNC2MiOV8pPNDdGpk+FT7GcAGlxpFoYcXMT5CEYz/9iGySOpM7jCuLINtc0EnlpW3FEmikodOjQAX/88Yf/de/evfHBBx+gffv2YBgGH374Idq2bavLt26h9NVXX+kdGtIwANxhvEPNZ2fmDjVTL/jI6uPbcv2xBzu4CXOSlaka8duMEEcKMQIVR7IVFKPEkR5xpyJ+wOJIrJ+fE2CNOJKzFbMzexE2P35N2b4vmYdEo4bPgbFKMTHSOWj2E8Lceuut+Prrr/133pgyZQruuOMOjB07FgzDIDExkbNbXguGXJm7piGYeuOfmNk2NtihpmexthFTanx7sRykxJGwH1xxJNLOzsm0HWpSduw+VaLFIW4jYqtph5pa8aE2T4X4ho1X3ccoix8lQcjPCTBAHIkICA3iSLS6ZNSUmgpfNKUm02FHcUQIyMjI4OyIb926NX788Uds3boVERER6Nq1q+htT9QQkFD6+++/sXz5cuzduxcFBQXweDycfofDgR9//DGQELaEu5jb91/7CCO+XaDCyDeW/Zzdx2+rccKo6nlQhJFaG9broAkjufxIGJEwkstLTVw5G6uFEeklW5CQkMDZ+a4X3UJp69atuP/++5GYmIjLL78ce/fuRZ8+fVBWVoadO3eidevWuPzyywNO0G74TvB2EkZWVIzYrwXxbSCMhOcvEkZBF0ZywoGEEQkjubzUxJWzqWnCiP9bVYP5+eefsX79epw8eRKA96a4V199tf8yRnrQLZTmzp2LlJQUfP755ygvL8eVV16JrKwspKenY9euXRg/fjyeeOIJ3YnZGU9VRcmMdUa+MYEswubbad2hZtbWfTU71MSEEF8sCW0BwSJswXMd4kizaAnxRdh6xmvJT7RPRFDIjRPrF81JQhjJ+BfacnPjHAPBWKFYED+OBokj2qEm0iZqqN6/UeKIdsAFhfz8fEyYMAHbtm1DRESE/64cW7ZswWeffYYePXpgwYIFgnvAqkG3UNq7dy8mTZqE+Ph4/01mfVNvnTt3xujRo/Hmm2/i6quv1hvCtihVjtSKI1+fnoqQXBwlccQXO1LiyGejKI5EhJfh4oh3zhIVR4LkSRxpiq9nvFJ+orkZI46EeUmIIwVhxPUjLo5EK0KCL2WIiyMtAiaMxZHsOiObiiMjrqMU6rz44ovYvn07nnjiCdx2222IjY0FABQXF+Pjjz/G66+/jhdffBGvvPKKZt+6hVJERATi4uIAAC6XC5GRkTh//ry/PyUlBYcOHdLr3tZ4OL8X+ipHRuxQk/UlJl4gLny4v+kqK0ciwgui/QD4cfSII/8AnVNqam2VRIdBU2qiPtTkoTZPPfHVjlcRX04caZ4qZBES2/fNnlJj50jb96UbzZ5Sk82flIvV/Pjjj7j99ttx3333cdpjY2Nx//334/Tp0/jmm290+dYtlJo3b44jR44A8C7aTk1NxY8//ohhw4YBAP773/+iXr16et3bGq84sE4Y8e30XtfI91p4rgnidY3YbVLCiPOa/WaE03GSr2WEkT+KjACrcVUjLfmJ5qZRGIn1i+UVKlUjyfci9Mcdp3zCpq37Eo1BnVIjYRRsIiMj0apVK8n+1NRUREbqkzy6hdLVV1+NFStW4PHHH0dkZCTuuecePP3007juuusAAMeOHdN1qXC7w8C7RslMYRToNY3848ycTuOIGoMrRvykxYSRhJiofm7AdJpCjJAQRnqEnQofZgmjkKgYieRFwkhjbDmbQISRUaJIyr+agcHQTKTTcP3112P16tUYM2YMIiIiOH2VlZX44YcfdN97VrdQevjhh3HXXXf5E7r55pvhdDqxZs0aRERE4MEHH8Qtt9yi172tcZtQDTL7mkZiwkjOP1f0sIWZr11HxUhgC1ixCNsfRSGGJmEh4k82BttGJo6Sj4B2yCmMF40v2ccI++R8ivkVywkwQByJiBPJXIRiQ5UwEssHNlhnJBdD0YfNhZGm8UaLI6X3Lt9NGM+ePXs4r4cNG4bnn38eY8aMwa233ooWLVoAAI4ePYrPPvsMFRUVuPHGG3XF0iWUKioqcOjQISQlJcHhqD5BDR8+HMOHD9eVSOjg4AoP1sLp6tfqKkK2vIcary2cxZHsCdznQ6uw0CIUVIgbVeIsgPGS+ZkojmiHmkiOJI7EG+08nab01hlG2YbQzYgRIzj6AwCYqs/zjz/+8PcxrM/4zjvvxF9//aU5li6h5HQ6MWLECDz11FO466679LgIaTws4aNnrRH3PGDxDrWqgUHfvi9IPnBxpHpKTSGGbafUzBwv2ScijiSOnSlTaiJtAa01UsqXxFFIiSPjd6gZII6CQQ0UZC+99JJlsXQJpYiICDRp0gTl5eVG52N7GLDu5aaiIqR3h5rRF33UUjXy27HPQ1ZWjaRsNYsWmSk1XpuouJA9oXKfa55SUxPf6PGq+kSEkRafLGw7pcbuDkdhJPAToDBSiq0qB9lGDcJKRhzVJGFE4Oabb7Yslu41SmPHjsVHH32EkSNH6r5/SkjCsG96q04Y6Z1OY7/mt5lVMaoeE5rTaaI2IraiJ2k1wkhOuKjM07ILPqrqqwHCiPtHBAEkjNTHVZ2DTGOoT6cF0m8SDmWTGkVRURHOnDkDAGjUqJH/UkZ60S2UPB4PoqOjce211+L6669H06ZNUatWLY6Nw+HA3XffHVCCdoQrlPRVjLw2gd0/Tcy/8BzD7gcCqRjxx4HlW5i8gRUjdl+gwkgkDlWMxMdJ5iWWE2CAMKrqDFQYsbvtJoyk/MvFUOVDOv+wrxhJ+VczMFBhpNaGsITdu3fj1Vdfxe+//+6/ALbT6UT37t3x5JNPolOnTrr86hZK7Ktbfvnll6I24SuUvLcwERNHclUjr42yOOL3+3yz/UmJI6OrRtW2gO2rRnInYDHhI5ujDnGkIb4p4/l9/tfqxRFVjRT88GxDdp2RUmyp/pAQR0rvS77brlUjQp5du3bhzjvvRFRUFEaOHIm0tDQAwKFDh7By5UqMHTsWy5YtwxVXXKHZt26htG7dOr1DQxrG/1Anjozevq93rZGYEJISR9zzkj3EkewJ3OdDRnSIiiMpG4k+pTzDcYeaeF4GiyP2MRCMJXEk2aBVHNloEba3mcSRYdg8PSuYM2cOGjZsiI8//th/nzcfkyZNwm233YY5c+ZgyZIlmn3rFkpNmzbVOzTEccDDVF+ZW0y8GHaDWdZz4TlG5ZQaq49vC76tf4DMlBp7vIxo4cfVKhqM2KGmZkoNkJ+60yRuNAob2fFy8SX7GGXxo0IcGSWMuL7ExZF4HhIijzNe7QmdJSAkz7HKvmxx0UetwkgptpyNCeKIptQIM9m1axcmTJggEEkAUK9ePdx666146623dPl26k2qffv2+Pe//y3Zv2rVKrRv316ve1vjYZxgGK9g8lQJJ9/D7XF6/8v4BJV3TRPDcO38bR5Wm8dn5+T4ZhivmGI81X6Ez733oPPbMg6g6r/sBzxeEcQwAOOptve2Vz08qFJ5voevvXo854Tne3B8sOw83hOmgwEcVc997eyxDqbq4XFU2/AeDp4vbTGENg7ee1HyIRefM57ROJ5Rji/sq/7QHQwjjCvml98PsT6G8+DEFclZ6IvxP/x+PLzjz8mj6gk/HtjHgPMFF373fJ8hWPE93ge/n//++L4cHobzHqqFFm8c27eSf6k+znvgvSFev2hOfORiq3z/HOHNb5TyL2bK+5+crbr8ZQbK+QzkuASClUJL6m9SyyPEcTqdcLvdkv0ejwdOpz7Jo7uixCh8Cdxut+BiUOFC9WJuGFYx8tuL9gO6K0ZVjZzfPqoYqfZh14qRP7bEsbNdxYgznlG20VCpoIqRDhvRYWJ26j+HGl8xogpUUOnatSs++ugjDB06VDDjderUKXz88cfo1q2bLt+6hRIASSFUWFiIjRs3ok6dOoG4tyUMuELJ3x6kaxqJtokJI0HC7Ocy64ykbNWc2EXGyYkWH7RDDdwPUK0oE8tLLCdAtzgSCCP2U7n3AAkbznh1J/SQWmck8CMvnKwVRyqOgZJpTRZHJIxsxWOPPYY77rgDmZmZuPbaa9GyZUsAwOHDh7Fu3TpERETg8ccf1+Vbk1CaP38+FixYAMArkp588kk8+eSTorYMw+DOO+/UlZTdqf5dVy+OvP8JwR1qbFs1ooHEUYDiiJHpU+GTBe1QA+8zUikMpM5/oSaORIfYTRwpvK9AxVFNqBoxIn/rOv2EMh06dMAXX3yBOXPm4KeffkJJSQkAoHbt2rjqqqswefJktG7dWpdvTUKpU6dOuP3228EwDD7++GP07dvXr9p8OBwO1K5dGx07dsR1112nKylbwwivzO197uvWOKUGCMSRmBCSEkfc85JB4siC7ftm3yZEyYdlO9RUCTeLxZGCaOX64X1Z2cdAMFYopEJCHOk6wSv5CFAc2WhKzdusURzprRopdYfClJodxVSYU15ejl9++QVNmzbFggUL4PF4cOHCBQBAcnKy7rVJPjQJpauvvhpXX301AKCkpARjxoxB586dA0ogFPFXkphqMcQWQlzRw+8H+FNq+oURILveyK7CSMSfbAy2jUwcM4WRwEcoCSOZvIR+dAgjpXxJGAVfGGkar0MYSflXHKTcbfuqEQmjoBMVFYVHH30U//d//4d27drB6XSiXr16hvnXLbNmzZqlKJIKCwv1urctDODfoSa1+823Q82/Y421s837vGrDjIe3Ow1eEeZrg8e34w1VO9TYO8p8z6uSYiC964z/kNmdBoa1w6nquVgM9u400V1WcrvDPKwYHpEYDCsPli/Rfok8HbwdVtz3L+HbIxFf7D2IxZfMzfcheh9yO+PkdqcBYv0SvhV2qFX7EN+d5reBdCzJfD08O4jkgOrYvh1q/H41O6z4O9SqbdjvScS3mJ1g6krOB+8NCY6vwg41ubhyNiLHUbRR8FnJjQc071CT8i87SF234rFRc+y0oNWf0fGNgH9M9TwC5NChQ7jnnnvQpUsX9O3bF7Nnz9Z8P9ilS5eibdu2yMrK0jTO4XCgZcuWuHjxoqZxatEtlG6//XYcO3ZMsn/9+vUYMmSIXvc2ploYVf+tVG/X9wkjhiWYuH9X1SKFAQTCCD67qq37XGEE9cII4P0hsGwFP+oyoqJqrH/rPtsG0n60x5ARRlDnQ04YQcq3VI5ywk0khpyAUTUO5gqjal++E7fPB2SEEXxfQr+t34adr0ph5M1BRhgBQj8ivhSFESPhW8xOro/jg5eETE6qtu5LofT+5RpVHLvq5gC37gsTlxik4JPvN5BjpxYrhJHf1oB8Q4C8vDyMGzcOFRUVmDdvHqZMmYLPP/8cL7/8smofubm5WLBgAerWrasrh6ysLHz00UfIzs7WNV4O3bvejh8/juHDh+Pxxx/H2LFj/e2FhYV46aWXsGLFCt33VbE7/rVJrHNCIDvU+OOgdzpNrW3VyY7TLjJOaaoLqDpZqo2h1ob1WtNaIZHnutdKyeUnmRsjn7dSXmI5AYIfZ93Taeynsnky4jac8RInRB6K02kqfNEONZlG1WMB2qFmor3eMWHCp59+iqKiIsyfPx9JSUkAvJcIeu6555CVlYWGDRsq+nj11VcxaNAgnDp1SlcOu3btQlJSEm688Ub06tVL9P6zADB9+nTNvnULpZUrV+K5557DzJkzsXbtWsyaNQtHjx7F9OnTkZubi8mTJ+OBBx7Q697W+P8eVIij6nOVSTvUpGzViAYpcaQQQ1RcqBQ2qsWRTnFm2HhVfRKCQq1PFqavNZLNRSg4TBVHksJHwofU2HASR2qFkZR/o8SRXmGkopvEkYkEOY0NGzYgPT3dL5IAIDMzE//85z+xadMm3HLLLbLjt23bhh9//BGrV6/WvYV/+fLl/udbtmwRtXE4HNYKpcTERLz++uu47rrr8Pzzz2PIkCEoKytD+/bt8fbbb6Nt27Z6XdsedkVJTAjxxZJk1Yj9OlBhJGhXI1ocAW/dB5QEmISNhjyDUjWS7GNk+lTkJZYTYIAw4uYmyEMwXiikVC3E1iOMxPzw7GUFSCD+xfoEpgGKo2BUjaRM9VR5wqVqpNVfKAsjkzh9+jQyMjIk+6Xu8ZqdnY0RI0Zw2lwuF+rXr684FeZ2u/HCCy/gwQcfRIMGDbQnXcXff/+te6wSAV1wEgDq16+P2NhY/1a89u3bIyUlJeDElPj666/xwQcf4NChQ4iNjUWnTp0wf/58f6ntp59+whtvvIHDhw+jSZMmeOCBBwQfpF4Yj9aKEWDqdBr/hCgWJwSuaeSsuoAp45E4MQYqjFQcJ80VI6W8xHICjBNGat+f1Hth29mtYiTlXy6GKh/S+Yd9xUjKv5qBJIy0DdU9UjsOZRNTyc/Ph8vlErQnJiYiLy9PduzHH3+MkpIS3H333Ybksn//fqxfvx4nT54EADRr1gz9+/dHmzZtdPvULZTKy8sxZ84cfPjhh2jdujW+/PJL/PLLL3jrrbfwv//9D7NmzULPnj11JybH22+/jcWLF+PBBx9Ely5dcPHiRWzZssV/n5dt27Zh4sSJGDlyJKZNm4Zff/0V//d//4e4uDjccMMNgQVnn5tE1yr5OmWm00RuMSL5OsCt+4GuM1KOIWHD6lcSV40TE3BZgwYoLXPD7QESYiNx+Nx5HMu9WO1bZrxQhKjMTzQ3RqZPxKdYv1heOoUR1w9X7JhSMZLMQeiPO8YgcWS2MBJ5SRUj7V3KfjXYaIGEkanBGzduLFk1MoPz589j7ty5eOWVVxAdHR2Qr/LycsyYMQPffvstGIbxXzvJ4/Hgtddew4033oiZM2fqiqNbKA0fPhzHjh3D/fffj4kTJyIqKgqXX345Bg4ciKeffhrjxo3D2LFjMW3aNL0hRMnOzsb8+fPx1ltv+a/pBADXX3+9//nbb7+NK664As8//zwAoE+fPjh+/Djmzp0buFAC4N85BhFxJHXis3o6TSyOSnEUUNVIpQ9f/Bb16qAWYvH84t9QUlYJAIiOdOKOzHZo36Qh/j6Zoy1/FfHNEkdGVY24vhTEEWesCnGkoVphmjgK16qRaB4SjVQ1Ug+JI9vjcrlQUFAgaM/Ly0NiYqLkuDfffBNt27ZFjx49kJ+fDwCorKxEZWUl8vPzERsbi8hIdTLl1VdfxTfffIPbb78dY8eORfPmzeFwOHD06FEsW7YMn3zyCRITE/F///d/mt9fQJer/OSTTzBlyhRERUX529q1a4cvvvgCDz74ID7++ONA3Ivy1VdfoVmzZhyRxKa8vBxbt24VCKLBgwfj0KFDOHHiRMA5cHaKymy752zfZ7f7HbEf6rbve/0Kx7K373PiyPlR2Sdrw3ovqrf/V72OcDjQvE5dvPHJDr9IAoDySg+W/HsvYqNqoXZUlHKOKuILt+BXf4iS70tybPXb5owVfDlY/R5x30Jf6rbvV4/l2ipu34d0fG8OItv32TDyvlRd10gmvuw2bFkfvA+c519x675SbJXvX7ZR9VhAdOu+jL1y/jID5Xwq+tVgoxa2L7XCTGvsAPJVOlw1kdTUVMFapIKCAuTm5iI1NVVy3OHDh/Hbb7+hZ8+e/sfvv/+OjRs3omfPnti8ebPqHL777jsMHz4cM2bMQGpqKiIjIxEREYHU1FT885//xI033ojvvvtO1/vTXVH65ptvEBMTg/LycuzZswfnz59Ht27dkJycjMjISDzyyCO45ppr9LqXZNeuXWjTpg3eeustLFu2DAUFBbj88svx9NNPo3Pnzjh27BgqKioEH05aWhoAb0WqWbNmkv7lFrKdPn0asXXrgF1RAsB7LlM5UmPHBFg1YrVpXqsjZSMXQyZPpapP87p18NNvJyR/q77dcBjXX9kYfx3LUf8eJHNjZPpU+GShakpNxr/Qlpsb5xgKxvJOslL52m29kdxZRW3lSGAmIiJYhNKUmrdZm73uqpGKbsVjE2pVowDGhYQgCnKS/fv3x8KFCzlrlVavXg2n04m+fftKjps2bZq/kuRj1qxZqFWrFh577DFNm8IqKytlL4LdtWtX/Pzzz6r9sdEtlGJiYvDhhx9i/vz5/pLb+++/j/T0dFy4cAGZmZl48skn0aFDB70hRMnNzcWff/6J/fv345///Cdq166NhQsX4t5778WaNWv8C8f4C8t8r5UWlqnCw3oebGGkRpioEDVqhJHu3WkS42tFRuHUuSKRYF5yzhcjJrK6oiSZn2huxggj1dNpMv6FtiSMVPWRMFLnX3aQuu6wE0Z2mE4z+pjZmDFjxmDZsmWYMGECsrKykJOTg9mzZ2PMmDGcayiNGzcOp06dwtq1awF4N3/xcblciI2NRe/evTXl0K9fP2zcuBG33367aP8vv/wiK9rk0C2UVqxYgVmzZmHIkCHo27cvZy1ScnIy+vTpg1WrVmHkyJF6Q4jCMAyKi4vx5ptvol27dgCAzp07Y9CgQVi+fDn69esXkH+5hWwZGRnIKy8FfxF3dXLs54Etwha1EbEVXfcie0JVyENDnoGsEwKAktIytGycgD3Z50USAJo3SkBJWXn1FJJYbv7XxggjwLi1RoZf04iEEQdDhJGYHQmj4AojvfGDXTGqQcKIT2JiIj744AO88MILmDBhAuLi4jBy5EhMmTKFY+fxePybrozm0UcfxeTJkzFx4kTccccdaN68OQDg6NGj+Oijj3Dq1CnMmTMHly5d4oxjX/tJCt1CacmSJcjIyMBrr70men+Vjh07YtmyZXrdS+JyuZCUlOQXSYD3jXbo0AEHDx703zaFv7DMV96TW1imComTtvd56FeNlHwEsvWeP/5Ebh6u7tYa//n1GCrd7DId4HAAw/u3wo79R/3HnHaohYg40nISDoY4sqhqZOkONRXdthZHVDUKCME/7oJAWloali5dKmujRhPo1Q2DBw8G4L08AL/gwVR9TmK3Vfvrr78UfesWSkePHsWdd94p2Z+UlCRQbkbQunVryXvMlZWVoXnz5oiKikJ2djauuuoqf59voZncwjLVhJk40j2lJudbajyrzwMGB07mYNrdPfD2ij+Qe6kEAJAYH437hnVEzoU8VFS4JdcahdwONc54neJIUugJ/XHHBVEcKb6H8BFH3ma1sRT8Kw0MVBiptdECiSMiSEyYMAEOhzlXlNItlFwul+ydeg8ePIj69evrdS/JwIED8dVXX+Gvv/7yz29evHgRe/bswd13343o6Gj07t0b//nPfzBu3Dj/uFWrViEtLU12Ibc6HMriSEpYANXiSEK0+KPIiBNTtu8LTk7SvgHl96l2Wu7MuXyUlVVg0uhOcDqcYBggwgkcOpmD3AtF1QOUxI/Se+bnBOgWR3QPNRn/Un1ix0HipbUXfZToUC2sJISRbDwJ/2oG2k0c2XhKDTBIHJEwCgkmTZpkmm/dQql///74/PPPRRdOHThwAF988YVhV8Jmc80116BTp0545JFHMGXKFMTExGDRokWIjo725/LQQw/hrrvuwrPPPovMzExs3boV33//PebMmWNMEqyTYsgKIw3xAeOEkZiPS/kl2Lb3CLfaQsJIgK6qUU0WRiKxJBtJGKmDhJE9CcGUQwndQmny5Mm49dZbMXToUAwcOBAOhwPffPMNVqxYgTVr1qB+/fp4+OGHjcwVAOB0OrFo0SK89NJLmDFjBioqKtCjRw989NFH/gpWjx49MG/ePLzxxhv48ssv0aRJE8ycOROZmZkBx3cA3mvi+CBhxOlrVCcBDZJccAA4eykfZ84XCOxE1xqRMBJAwkiHDQkjEkYWxg+KX8JydAulhg0b4quvvsLrr7+OH374AQzD4Ntvv0VcXByGDBmCJ554AsnJyUbm6ic5ORmvvvqqrE1GRobsNZECgiMSDLymkVYbVr/RW/dlx4vY1YqORK92LbHzwHks23wQAHBV58a4qnNr/Lb3CMrKK7nCSOl9KQknsbykhJGMf6EtT5ywj4FgrFBwhPQibLkYij4CFEehsM5Ixp4WYZsYgz1MXzTD4gfNLxFUAropbt26dfHiiy/ixRdfxIULF+DxeJCcnOy/x0rYYpNF2Eo+zBZH7Pi92rXEm5/uxsncQr/Jx2sK8N/fT2LymM7YuPOAfN78PrF+sbzUVo1E2gJahK2UL4mjkBJHtEONxJHt/BK2ISChxMas6pHtYOQFhG0rRyoEiux4GR/1EuPw1+GLHJHk49S5Iuw9fBH1E+Nw7lKRLnFk/JQaq1OLOGIfJ7EYFu1QU7wNh0J82qHma7JQHAUqjNTaaIF2qNnHZ4DY4fIA4YxhQqlGYaEwUvKhVPUxsmoklVuDJBe++u9RfvZ+Nu46jVEDW+DcxSKuTzG/knmJiCMFYcT1Iy6MxHPRKYwkc1AQL8GsGtUgYeRt1mZfY4WRFfb84QGNNiYHy3wSIQUJJR0oXg07AGFkSMVI7Xgt+YnmVn0gIiKkr18R4XSA8TDi4kYsL50VI64fcWEUChUjjg+5sXpO7iSMZO1rrDCiipG5PomQhoSSHlgnX6WpLEnxw3qte+u9keNV9TGifTm5eRjUvRn+PnIRYgzq0Qw5uXkKgk2fONJ3mxChvanXNKJ1RiJtooYBjtchjKT8Kw5S7rb1OiO98YMtjmidkRCZf4Bq9kOIQkJJB4KTuOqTM69fQsBYNp0m1ychQMTGXcwrRttWjdG2eR3sO8YVS21SktC8QSy2njpjvjhiHwPBWKFYIHEk/jLo4siuVSMV3SSOeEN1jzQmflD8EmEHCSU98BW8lPhR6pcSNyJCIejiSE7wAdi++zDGZbbBmYulWL/jFBgwGNC1KRrVqYXf/zhSNe0mIYxk/AttDRJHnNgkjkgc6e+2tTiiHWrW+BWNZV0owlxIKOmhSihprhrxXpu2Q02tMPK/FhFGEuOk8qp0e/C/XdlIjKuF67o3BACczb2A40dKOHbmTqnJCCN2t92EkZR/uRiKPgIURkqxVeUg26hBWOkQRlL+1QwMVBiptdECrTeyj0/ZeNaGC3rcGgIJJa0w4F6Zu6oNCEzYKF6NW2G8P76qPvXCSOvutPyCEuQXlAj7SRjJ+1aKIdZHwkjet+Igdd2WCyOaTrOfX8l41oaTwpxbwRI+SCjpQW3lRY2w0SmsJONXvZbb8q6rEiaWEyD4YbL6mka2vbEsf6yeE7yWHWpWCSOlPDSP9TVrFEZS/tUMtJsw0uovFIVRgDlY6lM2nrXhCHtAQkkHcmtr7L5DTZ2okskJMEAcMcJ+2TxVvBe7VY2k/MvFUPQh7z/sq0ZS/hUHKXfbep2R3vjBFkdUNbKOUMgxhCGhpAepqg+vz7IpNaVqi53Eke8p+xiKjpV4L2w7u4kjvdWPUF6ErWl8iFWOSBxZGj8ofkVjWReKCA1IKOnA0B1qWkSMaJ+IoJAQL6bcJkSkzbSrYWvYGRX0iz7KxlCq2Ej3WzulJtFo1x1qgQojtTZaoCk1+/iUjWdtOCK0IKGkB41Vo5oujHRfDdtsYaS2OmOlMNJaMZKLq2RjgjAKqYqRWhstkDCyj0/ZeNaGM51wez82g4SSDuRuYcLp59tUvSZhJJFvuFSMFH3IC6egT6cZIYwk48n4lx2kopuEEXeo7pHG5RAUv6KxrAtFhB8klLTCQCAMABN2qKkY5++X+BGgHWrgfUZ6hY2Mf6k+21aNVIhDBXOqGpE4so1P2XjWhgsWDoj81uv0Q4hDQkkPvhO/HnEk2ichKOwkjlSLPwvFka13qPEarBJHaqtGUv4lD2kNFkc1YRF2gDlY6lM2nrXhiJoBCSWNcNS7lHhQJXBUiCMl4eTLyXBxJF41Es9FKAZCYvu+3hN8KE+paRpvtDhSeu/y3bRDjTdU90hj4gfFr2gs60Jpx9bJERogoaQHBqZWjYIujBTzDMGqEQkjZVMSRubZ6x3jG6p7pDHxg+JXNJZ1obQTxOSsrtzVMEgo6cDBEkpA9XM9FaOY6Ei0beZCQowT+SUe7D+Rh/IKtzAemwCEUVRkBJo3r4vasTEoK6vAiWPnUFJSUW0jGEsVI8kGDcIoPrE2Gqc2QER0FArPF+BUdg48bhFDEkb6+rVCwsh+fkVjWRcKAKJrRaHZ5c0R44pFeUEJjv95DOUl5RLWJE5qCiSU9FB1r7dAbxNyecsktE6sROlvX8B98TQS66Xgsh7Dsfcsg/3H81hj9Akjji0YNG2ajMZN6+G7jYdx+HQ+GiTHYljfVnAXl+DAvtNCR2xxwo+h4YRc07fuX96vLc5XAJ9vPYa8ojJc3qoubrihC7K3Z+PCmbzAxBEtwlYPLcK2j0/ZeNaG89H8ihZIvKwpvt18FMd3nEOz+nEYdkN3FB05gyM7Dgc3OSKokFDSgaByJFdpYb1mj2veMAGpzHHkfb7Ib1Z5KQelB7eh3ZBHkV83EWfOFVbH1CmOfP9JrhOH2CQX/u+dLfBUNZ85X4zdB85hXGY7NEtJxonj54XvhR1Dw0k5UHEULjvULuveCj//fR7rfj/hbztzvhi/7DqFZ+/pieL1e1BaXC6Rh0QjiSP1kDiyj0/ZeNaG41O/eX1UNKiLZ97/zd+Wc6EY2/fl4uGbOqJhqwbIOZwTxAzlMWLXGyGNM9gJhCQM4384GNYCb5GHg/Vg/xh0ah6Pwp8/EHVf+NP7uKJlQvVYD8sneDHAjeFg5QYG3uoXA7RMbYhF3+7xiyQ2H63Zj6bN61e/F3YMD8uf//2L5cBUPzwMN1/eMZPyxfYhdbz974vvn2/Hh98n8MFqkHlvkojEdkY4EFc/kSOSfJRVuLF87X4079BMOg+OYFP3OXibq//HzVFoK+tfzUA5n4p+NdhoQYs/PbEDyFfpcFmRg6U+ZePBoIMROM27p+LdVX+L9i35YR9SuqVZnBFhJ6iipBUR0eNrB9Rf9DGqohDFFWWiITwlBajFlHKFkYQffyfPVlARckbgQn6paLxKtwcX8ssQGRGBykq38IdS4ocs0Is+2qZqJPLSiIXYiXXi8efhC5L9ew5fwF0ZrcWSUzx23Ca54yDVLpe/Dn+q/Gqw0QJVjezjUzaeteG0UO5wooi1VpNNSVklSj0WJ0TYChJKemBXGwAZIcEfx2pwKF3ey8ESFPzgrJhSwkjMVgZnhANgPNUVG342gQiXGiKMhDYMIiKkP2eHgy2sJao1YmFoOs0c20DG+IbqHmlcDpb6lI1nbTj1CBNT/DW2+9UYbXuswwMSSjoQrSix+9jwfpx8Y8ucsXDGxMJTVizwERFfB8We6Cpf4sIIkF9MzrdhKirQqG4szpwXxouJjkBSbBQqK7j/bKqpO9QU48rZsJou5Raia8/LJId3bVMfeWcuqjoWlt1YVkW34rEJpjCywp4/PKDRxuRgmU/ZeNaG04Z8chGVlUiKj8GlQmGVPyE2CtGiW1SJmgKtUdIDRwjw1yExnAd7nZF/rRGAnQfzkXD9Q4CD9xE4I5Bw3UPYeSCvurrDWqPkW0NUvSaq6glr7Y7AxsPg8P7TeOimToiK5MZzOIAHhl+OowfOVL0fkXVG7N8YqXUMLFt1a41EfCvGYBR88Bp4LxXXGuldTyP6XhgwjAcXjuVi5ADh+oaE2CjcNrA1jv91UvJYiK41YiBpb8g6I6XPI5BjpwW964zUxjdonVFA75bWGZmM+uSO/u8AHh7eARFObunI6XTg4eEdceS3A+akSIQEVFHSgRHXNco5V4Q/Yly44vZZKP/jR3gunoSzXgtEdxyE3w8U4cKFfK8v0fEM5z9qdqjl55Ug5/AZvJSVjvU7T+HQqTw0So7FtT1ScO7kORw/dVF654SKaaGAKkdGTampzUltbDkb0WHCxiO7j6J9j1Q8O64H1vx+EnlF5biiVTJ6XlYPf/3yF8pZ6yJoSk2DP5pSM9enbDxrw2lDX3IXzlxE9N/H8NL9vfDzrtM4erYQKfXiMKhrE5zacQjnT0qvNQw6jEG73mz9uQYXEkp60SGOOHZgcOREHo6fzEdK0/5IaOBEfrEbxzeeAeNhxC9eyXqq52rYuTn5OHd2L9Ka1sHlXRuhorQCuzftg9vNW6lY06fUxOxUCiMx/we2ZSM6JgpXtWqAiJg4FJ7Lx/++O1LlQaM4CuaUmlobtVgxRaYzX1sLIzP9isayLpR2jEvuzMHTOJt9Bu0ua4IuafEoKyjBji83wcP/fSRqHCEvlIqKipCZmYmcnBx8+eWX6NSpk7/viy++wLvvvotTp06hVatWmDJlCgYOHBhgxKppqeqX/G4OSvdPc4PB0WMXeWNlhBHbv8pKB0c8eIBTx3j/OqrpwiiAipGaYwcA5aUVOPrXydASRqFWMQpgHAkjdizrQmnH3OQ8HgYn9500NQYReoT8GqW33noLbrdwod3KlSvxzDPPIDMzE4sXL0aXLl0wceJE7Ny5M7CAjPyDfT0jqWsasa+9xFnXhGpbB8/OO57tjxHPBzLXNGJXnhTW2jg8jPiaHvY4qXVMcjHE+jg+eG9IcHwl8lITV8pO4jiKNqo4dlydy/2fkr18/lKD1HVbvtZI69ohPbG1xmAPhfShsiJ+UPxKxoMBB8MMlL7UBADhYdLzICQJaaF06NAhfPzxx5g0aZKgb+7cuRgyZAgmT56MPn364Pnnn0enTp2wYMGCwAPzvlyciz2yxA5HGDEqFmELbKB8wUf4cmCJB6UTsMR7MW0RtpwPRuQNCY6vwYuwxcSR2AFR8i9xLDRf8FE2f4VfMqUfOi3CyGhxZIa93jEw8LxgloAJljCy3UnStokRNZSQFkozZ87EmDFj0KpVK0778ePHceTIEWRmZnLaBw8ejC1btqC8XOomh+pREkfwiR6A9XcvIo4gdmVvjeKIdqiptwl1caR0grO6aqTVnx5hFqCYM+SUS1Ujk7F1ckQNJ2TXKK1evRr79+/HvHnzsGfPHk5fdnY2AAgEVFpaGioqKnD8+HGkpYlfkj4jI0My5unTp5GQUEd4RWrfyR3c15wXfBvOeIkTogim3UNNTBCo9a/Kh7x/O+xQ0/I51Ogdalp96YkdQL6GvFOzhIsVgogTz9pw2rB1ciEF3evNXEJSKJWUlODll1/GlClTEB8fL+jPy8sDALhcLk6777WvXzdVmyBIGJEwImFkUOxgC6MAc7DUp2w8a8Npw9bJEYQkISmU3n77bdStWxcjRoww3Pe6desk+zIyMlBYWCp7SxESRuIvSRiRMAp4jG+o7pHG5WCpT9l41obThq2TIwjVhJxQOnnyJN5//30sWLAABQUFAIDi4mL/f4uKipCYmAgAKCgoQP369f1j8/O9F3H09evHOHFEtwlRwGhhJDlehzhSzN9EcWT0CbkmiKNwmE6ztfawdXLWwUg8tyomYTghJ5ROnDiBiooKPPDAA4K+u+66C507d8Zrr70GwLtWKTU11d+fnZ2NqKgopKSkBJYEY+B1jUgcqbMJCXGk9N7lu0kcsYbpGmVc/KD5FY1lXSjt2Do56wj2YQh2/DAn5IRS+/bt8eGHH3La/vrrL7z00kt47rnn0KlTJ6SkpKBly5ZYvXo1rrnmGr/dqlWrkJ6ejujo6IBy4Ey9aRVHWk/ARokj3VNqIg0hLI4khZFkPBn/soPku5T9arDRghZ/oVg1CjAHS33KxrM2nDZsnZx10GGoMYScUHK5XOjdu7doX8eOHdGxY0cAwKRJk/DEE0+gefPm6N27N1atWoXdu3dj+fLlgSXAQIWwoKqRIoEII03jqWpkqr3eMb6hukcaEz8ofkVjWRdKO7ZOzjpsfBgcyiZEAIScUFLL0KFDUVJSgsWLF2PRokVo1aoV5s+fj65duwbuXGfFyOFwoGmLukhIjoe70o0zx84j/2Kx0IfIWLnYonZy7aEmjOw6nRbqFSMr7PnDAxptTA6W+ZSNZ204bdg6OesImcPAGPT9DZk3bDlhIZR69+6Nffv2CdpHjRqFUaNGmRJTsWIEcL68SclxaNu1FX7cfgI7fzuIuNpRuKF3ClLbRWP3rwfBcO4fp1yxErWT62MkX2gXRkqxVeWg0BGuO9RCTRjpHeMbqnukMfGD4lc0lnWhtGPr5KyDDgMhQVgIJavx3yZEDJEf36ioSFzWpSWmv7sVJWWV/vb5Jy6hT8eGuKFrS/y1LZvlQyZ4uE6nmV01kouhNNBulSMSR/bzKxrLulDasXVy1kGHgVBBSN/CJGiw/7gYhvtg21Q9WqTVx+f/PcQRST5+3ZMDZ2wMoiIjqscI4on4F40Png9eA+9ljbpNiOA9MDID5btkc1cVWwdafemJrTNfhSNpevyg+RWNBQMOhFnYOjnrCMfDwP8j1PMgJKGKkh4UKid84ZHUIBHbv/1b0t32fblo0cCFnJMXpf1LxRaYMpJ91l70UUZAqDWtyVUjrf5CsWoUYA6W+pSNZ2049dg2MWupAYeBFnObCwklvcgIo2obpuo/DJxOBzxucbuICCcYT4WEiJATRvKiydq1RiSMAqImTKcFmIOlPmXjWRtOPbZNzFroMBAGQ1NvOnB4GOlpK5GpsPMnL+LKTo0l/fVoUw/nc/JFxlf7qC6P8mqlvJeaptO02IiWaEUaVUxFVjdx/8fNQSyeUv4ytWSlMrPe4xIIWnzpiR1AvkqHS70jg4+ZWT5l48Ggg2E0tk3MWmr6YeC//0AehCgklAJFTthUcSL7LIZf2RJ1EmIEwzN7N0fx+QK4K90SooT3Tea9ZAsjQ9caSf4BKYgjMTMJccSNLxVPKX+Zv3KlHwA9xyUQtJ7g9cQOIF/Dfi/NEDFWCiPAxicP2yZmLXQYCAuhqTc98AWBgp27wo09m/dj+thu2Jl9Ab8fOIf42lG4tntTRJaW46/fsvkDZV8askNNzE5ymJgIkRAmoqMlO6ShKTVzx/iG6h5pTPyg+BWNZV0o7dg6Oeugw0AECRJKWvFVjeT6RSgqKMX//rMb9Rq6MKxjPXgq3Ti27RDKSip8A3l+uC/Dfvu+XmGk1G21MNLqLxSFUYA5BMWvaCzrQmnH1slZBx0GddBxMhUSSoGiNG3jf+79z7kz+Th3Jh8kjEgYmTrGN1T3SONyCIpf0VjWhdKOrZOzDjoMuqBdb+ZCQkkPcmuB/M8FnbIvSRjp71Y8NiSMLM0hKH5FY1kXSju2Ts466DAQIQAJpUBQXOMjLZysvaaRRKMGcSQpjCTjyfiXHSTfpexXg40WSBzZx6dsPGvDqce2iVkLHQZzsPrvrIZBQkkPdqscSQ5RKY6MqhpJ+VczkMSRtqG6RxqXg6U+ZeNZG049tk3MWugwmA8dY1MhoaQHRvKF/abUNI03WhyF8ZSa3vjBFkc0pWYytk7OOugwEGEECSVdBGFKjapGJIx0OSFhZC62Ts466DAQYQwJJT2wfhSsrRhJdFDFSB0kjOznVzSWdaG0Y+vkrIMOg72wwedx6NAhzJw5Ezt27EBcXByGDx+OyZMnIzo6WnLM2bNnsXTpUmzatAnHjh1DQkICevbsicceewxNmza1MHt5SCjpIOjTaXbdoUbrjLQN1T3SuBws9Skbz9pw2rB1ctZBh8GWOGDM5QEC8ZGXl4dx48ahZcuWmDdvHnJycvDyyy+jtLQUM2bMkBy3Z88erF27FiNGjEDnzp1x8eJFvP322xg1ahS+//57JCcnB5CVcZBQMgobiSPaoUbiyDY+ZeNZG04btk7OOugwECr49NNPUVRUhPnz5yMpKQkA4Ha78dxzzyErKwsNGzYUHde9e3f88MMPiIysliLdunXDgAED8M033+Dee++1In1F6F5vgcAw1Q8tNgzrIWhg1I/lNNfge6hp9acndgD5Kh0uK3Kw1KdsPBh0MIxG7g+lBkGHITThf256HgGwYcMGpKen+0USAGRmZsLj8WDTpk2S41wuF0ckAUCjRo2QnJyMs2fPBpaUgVBFSQ9KAkDQJmqo3i9VjQLzR1Ujc33KxrM2nDZsnZx10GEIA4z5EE+fPo2MjAzJ/nXr1om2Z2dnY8SIEZw2l8uF+vXrIzubfy9TeQ4fPozz588jLS1N0zgzIaEUKCSM9NtogYSRfXzKxrM2nHpsm5j10KEgDCY/Px8ul0vQnpiYiLy8PNV+GIbBzJkz0aBBAwwZMsTIFAOChJJWGAhPPmqFEUTGyplatQhbRTftUOMN1T3SmPhB8Ssay7pQ2rF1ctZBhyH8Megzbty4sWTVyArmzZuHX3/9Fe+++y5iY2ODlgcfEkp6MaFq5G22SBxR1UjbUN0jjcvBUp+y8awNpw1bJ2cddBhqFI4gf94ulwsFBQWC9ry8PCQmJqry8fnnn2PBggV48cUXkZ6ebnSKAUFCSQ+M5IuqJppSUw2JI/v5FY1lXSjt2Do566DDQASJ1NRUwVqkgoIC5ObmIjU1VXH82rVr8eyzz+KRRx7ByJEjzUpTN7TrTRciWwXM3KHG9h3qO9QU34sBsYO9Q03rewy2X8l4MOBgmIHUH0oNgw4DYRP69++PzZs3Iz8/39+2evVqOJ1O9O3bV3bs1q1b8dhjj2HUqFGYMGGC2anqgipKerDrdJqKblprxBqma5Rx8YPmVzSWdaG0Y+vkrIMOAyEGA4P+Eat/6JgxY7Bs2TJMmDABWVlZyMnJwezZszFmzBjONZTGjRuHU6dOYe3atQC8V/OeMGECWrZsieHDh2Pnzp1+2+TkZDRv3lx/UgZCQkkzjOhTroVGYQSEz3SajYURYHNxRGuNqrBtYtZCh4EIERITE/HBBx/ghRdewIQJExAXF4eRI0diypQpHDuPxwO32+1/vWvXLhQUFKCgoAC33XYbx/bmm2/Gyy+/bEn+SpBQ0oOWtUZUNTImfrDFEVWNTMbWyVkHHQYiRElLS8PSpUtlbZYtW8Z5fcstt+CWW24xMStjIKEUALRDzUb2/OEBjTYmB8t8ysazNpw2bJ2cddBhIAKFvkOmQkJJB6KLsCWNw0Qc1YSqUYA5WOpTNp614bRh6+Ssgw4DYSDBvjxAuBNyu95++OEHPPTQQ+jfvz+6dOmC4cOH48svvwTDOxl98cUXuP7669GpUycMGzYMP//8s3FJyO02kd2ZJDNQaQeLmh1PRu+K0rs7TW3sAPJVOlzqHRl8zMzyKRsPBh0MM7B1ctZBh4EgQpaQE0pLly5F7dq1MXXqVLz99tvo378/nnnmGSxYsMBvs3LlSjzzzDPIzMzE4sWL0aVLF0ycOJGzot4wwlUYqVnnRMLIPJ+y8WDQwTADWydnHXQYCEvhf+H0PAgpQm7q7e2330ZycrL/dXp6Oi5duoQlS5bg4YcfhtPpxNy5czFkyBBMnjwZANCnTx/s378fCxYswOLFiwNPgqbTzB3jG6p7pDHxg+JXNJZ1obRj6+Ssgw4DEUzo+2cqIVdRYoskH+3bt0dhYSGKi4tx/PhxHDlyBJmZmRybwYMHY8uWLSgvLzc4IwVVriTY7Tydpsde7xjfUMgfLrPjB8WvZDzY9AeQ/hUKgA4DQdQQQq6iJMb27dvRsGFDxMfHY/v27QCAVq1acWzS0tJQUVGB48ePIy0tTdJXRkaGZN/p06eREJuIkKoa6fFHO9TM8ykbz9pw2rB1ctZBh4EgahwhL5S2bduGVatW4amnngLgvQkf4L1JHxvfa1+/oQQqjkJNGOkd4xuqe6Qx8YPiVzSWdaG0Y+vkrIMOAxEKWP2PuhpGSAulM2fOYMqUKejduzfuuusuQ3yuW7dOsi8jIwOFecUkjLQO1T3SmPiW+pSNZ204bdg6Oeugw0AQBI+QW6PkIz8/H+PHj0dSUhLmzZsHp9P7VhITEwF471zMt2f3G4rWHWpWxAvEXu8Y31DeQzdmrAkK1jojW56AbZ2cddBhIEId/o+ungchSUgKpdLSUmRlZaGgoADvvvsuEhIS/H2pqakAgOzsbM6Y7OxsREVFISUlxZgk1JxwaRG2Rif6xZlqv2Zj6x8fWydnHXQYiDDDYcCDkCbkhFJlZSUmT56M7OxsvPvuu5w7EwNASkoKWrZsidWrV3PaV61ahfT0dERHRweWAAMSR76hMOBcEw471Gx90rV1ctZBh4EIZ/j/yNTzICQJuTVKzz33HH7++WdMnToVhYWFnItIdujQAdHR0Zg0aRKeeOIJNG/eHL1798aqVauwe/duLF++3PiEgrneKBTXGgWYg6U+ZeNZG049tk3MWugwEARhECEnlDZt2gQAePnllwV969atQ7NmzTB06FCUlJRg8eLFWLRoEVq1aoX58+eja9euxiRh9LSQmXFJGBkUz9pw6rFtYtZCh4EgCJMIOaH0008/qbIbNWoURo0aZXI2OiBhZB+fsvGsDacNWydnHXQYCMK4KWX6e5Ik5IRSyFETtu4HmIOlPmXjWRtOPbZNzHroUBAEYTEklMygJoijcLjgI2DzE6+tk7MGOgQEoYBRi7Hpj00KEkpGQVNq9vMrGsu6UNqxdXLWQYeBIAgbQUJJLySM7OdXNJZ1obRj6+Ssgw4DQRA2hoSSHsy6RYnOcSSM2LGsC6UdWydnHXQYCMJY6DpIpkJCySioamSuT9l41obThq2TswY6BARBhDAklAKBxJG5PmXjWRtOPbZNzHroUBCENdDfmqmQUNKDFbvafEN1jzQmflD8isayLpR2bJ2cddBhIAgiDCGhZAYkjAyKZ204bdg6Oeugw0AQQcdBa5RMhYSSEZAwMiCWdaG0Y+vkrIMOA0EQNRASSnoItjAKMIeg+BWNZV0o7dg6Oeugw0AQRA2HhJJmtJ85SByxY1kXSju2Ts466DAQRGhBU2+mQkLJJGwtjmitURW2Tcxa6DAQRGhDf8OmQkLJQGy73oiEEQtbJ2cddBgIgiBUQUJJJ1QxYsezNpw2bJ2cddBhIIgwhv7AzYSEkg4C+krSOiOTsXVy1kGHgSBqDvT3bioklKyAxJHJ2Do566DDQBAEYTgklMyCxJHJ2Do566DDQBA1GwbGnBfot0QSEkpGQuuNTMS2iVkLHQaCIATQD4OZkFDSSzhUjAAb/33ZNjFrocNAEIQS9DthKiSU9GCkmCFhVIVtE7MWOgwEQRC2goRSMCBxVIVtE7MWOgwEQQQCXZnbVEgoWQUtwq7C1slZBx0GgiCIkICEkllQ1YiFrZOzDjoMBEEQIQcJJaMgYcTC1slZBx0GgiBMhzHo/EM/WFKQUNILCSMWtk7OOugwEARBhB0klPRglUiy7YnXtolZCx0GgiCIsIeEkt2w7cnXtolZCx0GgiDsBu16MxUSSsHG1t9vWydnHXQYCIKwMySUTMUZ7ATM5NChQ7jnnnvQpUsX9O3bF7Nnz0Z5eXlwk2J4D1thbXIRkRGmx9CFrT8jgiAIwkrCtqKUl5eHcePGoWXLlpg3bx5ycnLw8ssvo7S0FDNmzLAuEVufaK1PLjahNlr3bQ9nfCyKSiuQGBeN/BO5OPjrfnjcHsvzAWDzz4ggCIIIJmErlD799FMUFRVh/vz5SEpKAgC43W4899xzyMrKQsOGDc0LbusTb/CSi3XVxuWDe2LOV3/iZG6hv71n+wYYfVNvbPv6V3g8NX2hPEEQhEZo6s1UwnbqbcOGDUhPT/eLJADIzMyEx+PBpk2bjA9o66kaeyTXpv/lePWL3RyRBAC//XUWq3flIKVTC/OC03QaQRDhCAMwDBPwg34XpQnbilJ2djZGjBjBaXO5XKhfvz6ys7Mlx2VkZEj2nT59Ggm1XdUNtv1i2S+xyKgIlEdEIudCsWj/f3eexLXjuuPoriPGBbXfYSAIgiBCjLAVSvn5+XC5XIL2xMRE5OXlBebclidgWyblJ7p2NM7ll0r2V7oZVBox7Wbvw0AQBGE89LtnKmErlPSybt06yb6MjAwUXiqyMBspQu+voqy4DGl1akv2x0RFINKh0WnoHQaCIAgToB9DMwnbNUoulwsFBQWC9ry8PCQmJgYho0AJ7QU27koPHMWlaNEoQbT/ht7Ncfbv48qOQvswEARBECFG2Aql1NRUwVqkgoIC5ObmIjU1NUhZaSW8VMG+9X/i0Zs6olNaXX9bZIQDmb2bo08LF47vPSE+MLwOA0EQhLEwTOAPQpKwnXrr378/Fi5cyFmrtHr1ajidTvTt2zfI2ckRvl/YspJybP9qC27q2RpjB6ahvNKDmEgHcvefxM6Vv3GNw/cwEARBGAv9XppK2AqlMWPGYNmyZZgwYQKysrKQk5OD2bNnY8yYMeZeQ0kzNesbXlFWgX0b/xJ21KzDQBAEQYQIYSuUEhMT8cEHH+CFF17AhAkTEBcXh5EjR2LKlClBzowUAQA6DARBEEZBU2emErZCCQDS0tKwdOnSIGdBX2AAdBgIgiBMwagFnPQjLUVYC6XgQV84AHQYCIIgiJCHhJJhkCoAQIeBIAjCauh311RIKOmGvpl+6FAQBEEED1qjZCoklHRRw7+UNfztEwRB2AmGhJKphO0FJwkDYXgPgiAIgmBx6NAh3HPPPejSpQv69u2L2bNno7y8XHEcwzBYtGgRBgwYgCuuuAKjR4/Gzp07zU9YAySUCCEkjAiCIEII/o+2nod+8vLyMG7cOFRUVGDevHmYMmUKPv/8c7z88suKYxcvXoy5c+fi7rvvxjvvvIP69evj3nvvxfHjKm5pZRE09UZ4IUFEEAQRetjg6gCffvopioqKMH/+fCQlJQEA3G43nnvuOWRlZUle5LmsrAzvvPMO7r33Xtx9990AgO7du+OGG27Ae++9h2effVZ/UgZCFaWaDFWNCIIgiADZsGED0tPT/SIJADIzM+HxeLBp0ybJcb///jsKCwuRmZnpb4uOjsa1116LDRs2mJmyJqiipIGzZ8+isqIS8799Ldip6IMEEUEQhGXkF+ehuKLI1Bh5xXlYYMA5Ka84DwWl+cjIyJC0WbdunWh7dnY2RowYwWlzuVyoX7++4Ob0/HEABDeqT0tLwwcffIDS0lLUqlVL7VswDRJKGoiJiYHD4UB8UlywUwlLTp8+DQBo3LhxkDOpWdBxtx465sHB6uNeUlmM6Oho0/wb+T7i68Th7Nmzusaybz7PJjExEXl5ebLjoqOjERMTw2l3uVxgGAZ5eXkklEKNbdu2BTuFsMb3Lxmpf7UQ5kDH3XromAeHcDvuy5cvD3YKNQJao0QQBEEQhG5cLhcKCgoE7Xl5eUhMTJQdV15ejrKyMk57fn4+HA6H7FgrIaFEEARBEIRuUlNTBWuRCgoKkJubK1h/xB8HAIcPH+a0Z2dno0mTJraYdgNIKBEEQRAEEQD9+/fH5s2bkZ+f729bvXo1nE4n+vbtKzmuW7duiI+Pxw8//OBvq6iowJo1a9C/f39Tc9YCrVEiCIIgCEI3Y8aMwbJlyzBhwgRkZWUhJycHs2fPxpgxYzjXUBo3bhxOnTqFtWvXAvBukMrKysK8efOQnJyMNm3a4JNPPsGlS5dw3333BevtCCChRBAEQRCEbhITE/HBBx/ghRdewIQJExAXF4eRI0diypQpHDuPxwO3281pGz9+PBiGwfvvv48LFy6gffv2eO+995CSkmLlW5CFhBJBEARBEAGRlpaGpUuXytosW7ZM0OZwOJCVlYWsrCyTMgscB0O3HSYIgiAIghCFFnMTBEEQBEFIQEKJIAiCIAhCAhJKBEEQBEEQEpBQIgiCIAiCkICEEkEQBEEQhAQklAjTOHr0KGbMmIHhw4ejQ4cOGDp0qKz9jz/+iLZt24raFRQUYNq0aejVqxe6du2KRx55RPedrsMdtcc9Pz8fM2fORL9+/dCpUydcc801eP/99zk25eXleOWVV9C3b1906dIF99xzj+BWBYQXNce9pKQEr732GjIyMtC5c2dcf/31WLhwISorKzl29H1Xxw8//ICHHnoI/fv3R5cuXTB8+HB8+eWX4G/m/uKLL3D99dejU6dOGDZsGH7++WeBLzrmhBR0HSXCNA4cOID169ejc+fO8Hg8gh8vNqWlpZg1axbq1asn2j958mQcPHgQzz77LGJiYvDGG29g/PjxWLFiBSIj6WvMRs1xLy4uxp133omIiAhMmzYNdevWxZEjR1BYWMixmzlzJlatWoWpU6eiYcOGWLhwIe6++26sXLkSCQkJVr2lkEDNcX/++eexZs0aPPbYY0hLS8POnTsxd+5clJSUcC7OR993dSxduhRNmzbF1KlTUadOHWzevBnPPPMMzpw5g4kTJwIAVq5ciWeeeQYPPvgg+vTpg1WrVmHixIn46KOP0KVLF78vOuaEJAxBmITb7fY/f+qpp5ghQ4ZI2r7xxhvMHXfcIWr3+++/M23atGF++eUXf9uhQ4eYtm3bMitXrjQ+8RBHzXGfM2cOk5GRwRQVFUn6OX36NNO+fXvm008/9bddvHiR6dKlC7No0SJjkw4DlI672+1mOnfuzMydO5fT/o9//IPJyMjwv6bvu3rOnz8vaJs+fTrTrVs3/+dx3XXXMY899hjHZvTo0cz999/vf03HnJCDpt4I03A61X29jh07hiVLlmD69Omi/Rs2bIDL5eLcXDE1NRXt27fHhg0bDMk1nFBz3L/88kuMGDECsbGxkjYbN26Ex+PBDTfc4G9LSkpC37596biLoHTcGYZBZWWloBKXkJDAqT7R9109ycnJgrb27dujsLAQxcXFOH78OI4cOYLMzEyOzeDBg7FlyxaUl5cDoGNOyENCiQg6L774IoYPH4527dqJ9mdnZ6NVq1ZwOByc9tTUVFovo4MTJ04gNzcXderUwYMPPojLL78cvXr1wvTp01FUVOS3y87ORt26dZGYmMgZn5aWRsddBxEREbjllluwfPly7N69G0VFRdi8eTO+/fZbjB071m9H3/fA2L59Oxo2bIj4+Hj/8WrVqhXHJi0tDRUVFTh+/DgAOuaEPCSUiKDy008/YceOHXj00UclbfLz80XXwyQmJiIvL8/M9MKSc+fOAQBeeeUVJCYmYvHixZgyZQpWr16NZ555xm8nddxdLhcdd53885//RJ8+fTBq1Ch069YN99xzD2677Tbcc889fhv6vutn27ZtWLVqFe69914A8B8vl8vFsfO99vXTMSfkoBVqRNAoKyvDrFmzMGnSJNESOmEOHo8HgPdf2a+88goAID09HZGRkZg+fTqmTJliqzt3hxP/+te/8N///hczZ85Ey5YtsXPnTixYsAAulwv3339/sNMLac6cOYMpU6agd+/euOuuu4KdDhFGkFAigsYHH3wAp9OJIUOGID8/HwBQUVEBj8eD/Px81KpVC9HR0XC5XDhz5oxgfF5enmBaiFDGd8x69+7Nae/Tpw8A7+6tlJQUuFwuwS44wPuvbzru2tm/fz/ef/99vP322xg0aBAAoGfPnqisrMSbb76JMWPGID4+nr7vOsjPz8f48eORlJSEefPm+deL+Y5XQUEB6tevz7Fn99MxJ+SgqTciaGRnZ+Po0aNIT09Hz5490bNnT3z//fc4dOgQevbsiRUrVgDwrhM4fPiwYLv14cOHkZqaGozUQ5qUlBRER0dL9peVlQHwHvdz584Jph6ys7PpuOvg4MGDALyLjdl06NAB5eXlyMnJAUDfd62UlpYiKysLBQUFePfddzlTaL7jxV9nlJ2djaioKH/llI45IQcJJSJojB8/Hh9++CHn0a9fPzRt2hQffvih/1/d/fv3R15eHrZs2eIfe/jwYezduxf9+/cPVvohS3R0NPr27cs5ngCwefNmAEDHjh0BAP369YPT6cSaNWv8Nnl5edi4cSMddx00bdoUALBnzx5O+59//gmHw4EmTZoAoO+7FiorKzF58mRkZ2fj3XffRcOGDTn9KSkpaNmyJVavXs1pX7VqFdLT0/3/YKBjTshBU2+EaZSUlGD9+vUAgJMnT6KwsND/g9WrVy+kpaUhLS2NM+brr79GTk4OZ1qoa9eu6NevH6ZNm4annnoKMTExmDPn/9u7/5iqq8eP40+vBGiEdRVBBMpZXDMmAZfBmECiM3+RYDkJbS5WQk0XKrFrI7JFtShFMo2rppHEcmtSQlFTa1JpTCCGaMx0k4W0liCioCKD7x99eX+8wbWs/Ho/X1+PjT/e55z3Oed9YOzFeR92C7BYLMycOfP/7oH+S/zZupvNZpYvX05KSgqrV68mOTmZ5uZm1q1bR2JiIkFBQQD4+fnx2GOPkZ+fj8lkwtfXF7vdzh133EFKSspNez5X9WfrHhISQkhICC+99BJtbW0EBQXR0NDAli1bePTRRxkxYgSgn/fr8fLLL/P1119js9m4cOEC9fX1Rt3kyZNxd3dnxYoVZGVlERQURFRUFJ9//jkNDQ2UlJQYbbXmci3D+v+41yjyL2lpaWH69OlD1n3wwQeDzsgA2Gw2GhsbqaiocCg/f/48r7/+Onv37qW3t5epU6eSk5Mz6C9I+evrfujQId566y2OHz/OqFGjSExMZOXKlQ6v5Xp6eigoKODTTz+lq6uL8PBwcnJyBgVc+Wvr/ttvv1FYWMjBgwdpa2vDz8+PefPm8fTTT+Pp6Wm018/7X5OQkMDp06eHrNu/fz8BAQHA7x9hsnXrVlpbW5kwYQKrVq1i2rRpDu215uKMgpKIiIiIEzqjJCIiIuKEgpKIiIiIEwpKIiIiIk4oKImIiIg4oaAkIiIi4oSCkoiIiIgTCkoiIiIiTigoibiIjRs3YrFYaG9vv6HjJCQkYLPZbugYf8fA8/+Te2/02onIrUdBSURuKUVFRezbt+9mT0NE/ksoKImIS3jmmWdoaGi44ePY7XYFJRH5y/ShuCLiEtzc3HBz068kEXEt2lEScTFnz57lueeeIzw8nKioKPLy8rh8+bJR39vby6ZNm5gxYwYhISEkJCSwfv16enp6HPrp7+9n8+bNxMXFERoayhNPPMFPP/3k0Obnn3/GYrHw/vvvD5pHXV0dFouFiooKmpqasFgs7N+/36hvbGzEYrGQnJzscN9TTz3FwoULHcoOHDhAamoqDz74IGFhYSxbtmzQXIY6o3Tp0iXy8vKIiooiLCyMjIwMfv31VywWCxs3bhw05/Pnz2Oz2bBarURERLBmzRouXrxo1FssFrq7uykrK8NisWCxWFzyvJaIuA4FJREXk5mZyeXLl1m9ejVxcXHs3LmTF1980ajPycnh7bffZvLkyaxZs4bIyEjsdjsrV6506KewsJDCwkImTZpEdnY2gYGBpKWl0d3dbbQJDAwkPDycPXv2DJpHeXk5t99+O9OnTyc4OBhvb29qamqM+pqaGkwmE01NTVy4cAGAvr4+fvjhB6xWq9Huk08+IT09nZEjR5KVlcWzzz7LiRMnSE1NpaWl5ZprYbPZ2LlzJ/Hx8WRlZeHp6cmyZcuuuXZdXV2sWrWK2bNns3v3bt555x2jPj8/H3d3d6xWK/n5+eTn57No0aJrzkFEbm3a5xZxMQEBAbz77rsALF68GC8vL0pLS0lLSwOgrKyMhQsXkpeXZ7Qxm81s376d77//nujoaNrb29m2bRsPPfQQRUVFDBs2DICCggKKioocxktKSiI3N5eTJ08yceJEAK5cuUJlZSUzZ85kxIgRAISHhzsEpdraWmbMmMH+/fupq6sjLi7OCE0DQamrq4tXX32VhQsX8sorrxj3JicnM2vWLOx2u0P51Y4ePUplZSVLly7lhRdeMJ51zZo1NDU1DXnP/fffz2uvvWZcd3R08PHHH/P8888DMH/+fNauXUtgYCDz58//0++FiIh2lERczOLFix2ulyxZAkBVVRUHDhwA4Mknn3RoMxCiBuoPHjzIlStXWLJkiRGSAJYuXTpovNmzZ+Ph4UF5eblR9u2333L27FkeeeQRoywiIoJjx44ZO1K1tbXExcUxadIkamtrgd93mYYNG0ZERIQxj87OTubOnUt7e7vxZTKZCA0Npbq62uk6fPPNNwCkpqYOuR5DSUlJcbi2Wq10dHQYO14iItdLO0oiLubuu+92uA4KCsJkMhmvqUwmE0FBQQ5tfHx88Pb25vTp0wC0trYCcM899zi0M5vNjBo1yqHM29ubadOmUVFRQWZmJvD7azdfX1+io6ONdlarld7eXurr6/Hz86OtrQ2r1cqJEyeMnaaamhruvfde7rzzTgBOnToFDB3QALy8vJyuQ2trKyaTiYCAAIfyP67P1fz9/Qc9G8C5c+euOZaIiDMKSiIu7uodoWuV/RNJSUl88cUX1NXVERwczFdffcXjjz+OyfSfTeeQkBA8PDw4fPgw/v7+jB49mgkTJmC1WiktLaWnp8d4HTegv78f+P1skI+Pz6Bxhw8f/q8+x9XzvdrAPERErpeCkoiLaW5uJjAw0OG6r6+PgIAA+vv76evro7m52ThPBHDmzBk6OzsZP3488J+dlVOnTjn01d7ezrlz5waNGRsbi9lspry8nNDQUC5evDjoDI+7uztTpkyhpqYGf39/4xxSREQEPT097NmzhzNnzhAZGWncMzD26NGjiYmJua518Pf3p6+vj5aWFoedsebm5uvqR0Tkn9AZJREX8+GHHzpcl5SUABAXF0d8fDwAxcXFDm127NgBYNTHxMRw2223UVJS4rCb8sf7Bri5uTF37lwqKyvZvXs3wcHBTJo0aVC7iIgIGhoaqK6uNs4hmc1mJk6cyNatWwEc/uMtNjYWLy8v7HY7V65cGdTftT5yZOrUqQCUlpY6lA+sx981cuRIOjs7/1EfInLr0I6SiItpaWkhIyOD2NhY6uvr2bNnD/PmzTOCS3JyMrt27aKzs5PIyEiOHDlCWVkZM2bMMM4Umc1m0tLSsNvtpKenEx8fz7Fjx6iqquKuu+4actykpCR27txJdXU1WVlZQ7axWq0UFRXxyy+/OAQiq9XKrl27GD9+PH5+fka5l5cXa9euJTs7mwULFjBnzhzMZjOtra0cOHCA8PBwcnNzhxwrJCSEhx9+mOLiYjo6OggNDeXw4cPGuae/+/rxgQce4NChQ+zYsYOxY8cSEBBAaGjo3+pLRP7/U1AScTEbNmygsLCQdevW4ebmxpIlS8jOzjbq8/LyCAgIoKysjH379jFmzBjS09NZvny5Qz+ZmZm4u7vz0UcfUV1dzZQpU9i+fTvp6elDjhsSEsJ9993HyZMnHf7b7WphYWEMHz4cT09Phx2ngaB0dXgakJiYyNixY9myZQvvvfcePT09+Pr6YrVaWbBgwTXX4o033mDMmDF89tln7N27l5iYGAoKCpg1axbu7u7XvNcZm81Gbm4uGzZs4NKlSyQnJysoiYhTw/p1ylFE/ldSUhKjRo1y+orOFfz4448kJSXx5ptvOg10IiL/Fp1REhEAjhw5YoQQV3Hp0qVBZcXFxZhMJodD4yIiN4pevYnc4o4fP87Ro0fZvn07Pj4+zJkz52ZPybBt2zYaGxuJjo5m+PDhVFVVUVVVxaJFixg3btzNnp6I3AIUlERucV9++SWbNm1iwoQJrF+/Hg8Pj5s9JUNYWBjfffcdmzdvpru7m3HjxrFixQoyMjJu9tRE5BahM0oiIiIiTuiMkoiIiIgTCkoiIiIiTigoiYiIiDihoCQiIiLihIKSiIiIiBMKSiIiIiJOKCiJiIiIOKGgJCIiIuKEgpKIiIiIE/8DnIHlVTy/ZfIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(df, x='bodyweight', y='extraweight', hue='success')\n",
    "xlim, ylim = plt.xlim(), plt.ylim()\n",
    "\n",
    "bodygrid, extragrid = np.meshgrid(\n",
    "    np.linspace(*xlim, 300),\n",
    "    np.linspace(*ylim, 300),\n",
    ")\n",
    "\n",
    "prob_succ = res2.family.fitted(\n",
    "    bodygrid * res2.params['bodyweight'] +\n",
    "    extragrid * res2.params['extraweight'] +\n",
    "    res2.params['Intercept']\n",
    ")\n",
    "\n",
    "# mean of function\n",
    "# plt.plot(xlim, (np.array(xlim) * -res2.params['bodyweight'] - res2.params['Intercept']) / res2.params['extraweight'])\n",
    "\n",
    "plt.imshow(\n",
    "    prob_succ,\n",
    "    origin='lower', aspect='auto',\n",
    "    extent=[*xlim, *ylim],\n",
    "    cmap='viridis', vmin=0, vmax=1,\n",
    "    alpha=0.5,\n",
    ")\n",
    "\n",
    "plt.colorbar(label='probability');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7524ce0a",
   "metadata": {},
   "source": [
    "This time the only real outlier is Kevin (`bodyweight=143, extraweight=105`), where the model says he was probably strong enough when he could do a chinup with 70lbs (i.e. `(143 * 0.05 - 1.6) / 0.08`) and might just need to work on technique."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}