BXD Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bf84b99a",
   "metadata": {},
   "source": [
    "#  Time Series Analysis of BXD Aging Colony Body Weight\n",
    "\n",
    "The BXD family of mice is a recombinant inbred strain of mice which can be reproduced by crossing a female C57BL/6J (B6 or B) and a male DBA/ 2J (D2 or D).  They are used to map Mendelian and Trait Loci.\n",
    "\n",
    "In this explorative exercise, we apply some time series analysis to investigate body weight across several months of collected data.  We first do some data cleaning, and from the various data points, pick one experiment(represented as one vector) to model and attempt forecasting.\n",
    "\n",
    "The dataset provided in this exercise was provided by [Prof Roy Suheeta](https://www.researchgate.net/profile/Suheeta-Roy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7edfb91e",
   "metadata": {},
   "source": [
    "### Data Cleaning\n",
    "\n",
    "The first part of this exercise is to store the data in a panda's data frame; remove metadata that is useless; and reshape some of the titles to make visualisation easier."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "147c68c3",
   "metadata": {},
   "source": [
    "We first get an overview of what this dataset looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e512de8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Columns:\n",
      "EarTagNumberCurrent EarTagNumberOriginal StrainName Sex Diet CauseOfDeath AgeAtDeath DateOfBirth DateOfDeath DateDietStart Age diet started Weight00Baseline Weight01 Weight02 Weight03 Weight04 Weight05 Weight06 Weight07 Weight08 Weight09 Weight10 Weight11 Weight12 Weight13 Weight14 Weight15 Weight16 Weight17 Weight18\n",
      "\n",
      "Count of individual columns:\n",
      "EarTagNumberCurrent     2506\n",
      "EarTagNumberOriginal    2506\n",
      "StrainName              2506\n",
      "Sex                     2506\n",
      "Diet                    2506\n",
      "CauseOfDeath            2506\n",
      "AgeAtDeath              2505\n",
      "DateOfBirth             2506\n",
      "DateOfDeath             2505\n",
      "DateDietStart           2506\n",
      "Age diet started        2506\n",
      "Weight00Baseline        2506\n",
      "Weight01                2473\n",
      "Weight02                2266\n",
      "Weight03                2160\n",
      "Weight04                1939\n",
      "Weight05                1639\n",
      "Weight06                1423\n",
      "Weight07                1100\n",
      "Weight08                 824\n",
      "Weight09                 629\n",
      "Weight10                 416\n",
      "Weight11                 255\n",
      "Weight12                 153\n",
      "Weight13                  81\n",
      "Weight14                  49\n",
      "Weight15                  16\n",
      "Weight16                   8\n",
      "Weight17                   4\n",
      "Weight18                   1\n",
      "dtype: int64\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>EarTagNumberCurrent</th>\n",
       "      <th>EarTagNumberOriginal</th>\n",
       "      <th>StrainName</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Diet</th>\n",
       "      <th>CauseOfDeath</th>\n",
       "      <th>AgeAtDeath</th>\n",
       "      <th>DateOfBirth</th>\n",
       "      <th>DateOfDeath</th>\n",
       "      <th>DateDietStart</th>\n",
       "      <th>...</th>\n",
       "      <th>Weight09</th>\n",
       "      <th>Weight10</th>\n",
       "      <th>Weight11</th>\n",
       "      <th>Weight12</th>\n",
       "      <th>Weight13</th>\n",
       "      <th>Weight14</th>\n",
       "      <th>Weight15</th>\n",
       "      <th>Weight16</th>\n",
       "      <th>Weight17</th>\n",
       "      <th>Weight18</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1231</td>\n",
       "      <td>1231</td>\n",
       "      <td>B6D2F1</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Other</td>\n",
       "      <td>193.0</td>\n",
       "      <td>2013-02-03</td>\n",
       "      <td>2013-08-15</td>\n",
       "      <td>2013-08-08</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1570</td>\n",
       "      <td>1537</td>\n",
       "      <td>B6D2F1</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Natural</td>\n",
       "      <td>880.0</td>\n",
       "      <td>2013-07-27</td>\n",
       "      <td>2015-12-24</td>\n",
       "      <td>2014-04-11</td>\n",
       "      <td>...</td>\n",
       "      <td>31.3</td>\n",
       "      <td>21.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2281</td>\n",
       "      <td>2281</td>\n",
       "      <td>B6D2F1</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Natural</td>\n",
       "      <td>879.0</td>\n",
       "      <td>2015-04-28</td>\n",
       "      <td>2017-09-23</td>\n",
       "      <td>2015-08-05</td>\n",
       "      <td>...</td>\n",
       "      <td>38.7</td>\n",
       "      <td>39.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2282</td>\n",
       "      <td>2282</td>\n",
       "      <td>B6D2F1</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Natural</td>\n",
       "      <td>992.0</td>\n",
       "      <td>2015-04-28</td>\n",
       "      <td>2018-01-14</td>\n",
       "      <td>2015-08-05</td>\n",
       "      <td>...</td>\n",
       "      <td>41.5</td>\n",
       "      <td>40.6</td>\n",
       "      <td>33.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2283</td>\n",
       "      <td>2283</td>\n",
       "      <td>B6D2F1</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Natural</td>\n",
       "      <td>912.0</td>\n",
       "      <td>2015-04-28</td>\n",
       "      <td>2017-10-26</td>\n",
       "      <td>2015-08-05</td>\n",
       "      <td>...</td>\n",
       "      <td>37.7</td>\n",
       "      <td>39.5</td>\n",
       "      <td>38.0</td>\n",
       "      <td>35.7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   EarTagNumberCurrent  EarTagNumberOriginal StrainName Sex Diet CauseOfDeath  \\\n",
       "0                 1231                  1231     B6D2F1   F   CD        Other   \n",
       "1                 1570                  1537     B6D2F1   F   CD      Natural   \n",
       "2                 2281                  2281     B6D2F1   F   CD      Natural   \n",
       "3                 2282                  2282     B6D2F1   F   CD      Natural   \n",
       "4                 2283                  2283     B6D2F1   F   CD      Natural   \n",
       "\n",
       "   AgeAtDeath DateOfBirth DateOfDeath DateDietStart  ...  Weight09  Weight10  \\\n",
       "0       193.0  2013-02-03  2013-08-15    2013-08-08  ...       NaN       NaN   \n",
       "1       880.0  2013-07-27  2015-12-24    2014-04-11  ...      31.3      21.2   \n",
       "2       879.0  2015-04-28  2017-09-23    2015-08-05  ...      38.7      39.6   \n",
       "3       992.0  2015-04-28  2018-01-14    2015-08-05  ...      41.5      40.6   \n",
       "4       912.0  2015-04-28  2017-10-26    2015-08-05  ...      37.7      39.5   \n",
       "\n",
       "   Weight11  Weight12  Weight13  Weight14  Weight15  Weight16  Weight17  \\\n",
       "0       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "1       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "2       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "3      33.8       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "4      38.0      35.7       NaN       NaN       NaN       NaN       NaN   \n",
       "\n",
       "   Weight18  \n",
       "0       NaN  \n",
       "1       NaN  \n",
       "2       NaN  \n",
       "3       NaN  \n",
       "4       NaN  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_excel(\"BXD_BodyWeights_12Nov2021.xlsx\", header=[3])\n",
    "print(f\"Columns:\\n{' '.join(df.columns)}\")\n",
    "print(f\"\\nCount of individual columns:\\n{df.count()}\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81c1e003",
   "metadata": {},
   "source": [
    "From the above, it's immediately obvious that data collection happened over the span of 18 months, with some experiments-- represented by a single row, running for less than the aforementioned 18 months.  One task, is to determine a minimum threshold for which to conduct our analysis.  With regards to this, for this analysis, experirements that have less than 15 data points are filtered out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d0417aa8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Count of individual columns:\n",
      "EarTagNumberCurrent     16\n",
      "EarTagNumberOriginal    16\n",
      "StrainName              16\n",
      "Sex                     16\n",
      "Diet                    16\n",
      "CauseOfDeath            16\n",
      "AgeAtDeath              16\n",
      "DateOfBirth             16\n",
      "DateOfDeath             16\n",
      "DateDietStart           16\n",
      "Age diet started        16\n",
      "Weight00Baseline        16\n",
      "Weight01                16\n",
      "Weight02                16\n",
      "Weight03                16\n",
      "Weight04                16\n",
      "Weight05                16\n",
      "Weight06                16\n",
      "Weight07                16\n",
      "Weight08                16\n",
      "Weight09                16\n",
      "Weight10                16\n",
      "Weight11                16\n",
      "Weight12                16\n",
      "Weight13                16\n",
      "Weight14                16\n",
      "Weight15                16\n",
      "Weight16                 8\n",
      "Weight17                 4\n",
      "Weight18                 1\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "df = df.dropna(thresh=df.shape[1]-3)\n",
    "print(f\"\\nCount of individual columns:\\n{df.count()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70d23545",
   "metadata": {},
   "source": [
    "Each month's entry is represented under \"Weight**\".  With this in mind, we use these columns to represent a time entry by renaming these columns into an index.  \"Weight00\" becomes \"0\", \"Weight01\" becomes \"1\", and so forth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6e8c912f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Columns:\n",
      "EarTagNumberCurrent EarTagNumberOriginal StrainName Sex Diet CauseOfDeath AgeAtDeath DateOfBirth DateOfDeath DateDietStart Age diet started 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 identifier\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>EarTagNumberCurrent</th>\n",
       "      <th>EarTagNumberOriginal</th>\n",
       "      <th>StrainName</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Diet</th>\n",
       "      <th>CauseOfDeath</th>\n",
       "      <th>AgeAtDeath</th>\n",
       "      <th>DateOfBirth</th>\n",
       "      <th>DateOfDeath</th>\n",
       "      <th>DateDietStart</th>\n",
       "      <th>...</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
       "      <th>identifier</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2817</td>\n",
       "      <td>2817</td>\n",
       "      <td>BXD1</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Euthanized</td>\n",
       "      <td>1007.0</td>\n",
       "      <td>2018-04-24</td>\n",
       "      <td>2021-01-25</td>\n",
       "      <td>2018-07-12</td>\n",
       "      <td>...</td>\n",
       "      <td>29.6</td>\n",
       "      <td>30.4</td>\n",
       "      <td>29.0</td>\n",
       "      <td>28.2</td>\n",
       "      <td>27.7</td>\n",
       "      <td>26.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2817-BXD1-F-CD-Euthanized</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>2228</td>\n",
       "      <td>2228</td>\n",
       "      <td>BXD168</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Natural</td>\n",
       "      <td>1092.0</td>\n",
       "      <td>2015-06-24</td>\n",
       "      <td>2018-06-20</td>\n",
       "      <td>2015-08-05</td>\n",
       "      <td>...</td>\n",
       "      <td>24.8</td>\n",
       "      <td>28.2</td>\n",
       "      <td>24.9</td>\n",
       "      <td>26.3</td>\n",
       "      <td>23.9</td>\n",
       "      <td>20.9</td>\n",
       "      <td>19.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2228-BXD168-F-CD-Natural</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>2667</td>\n",
       "      <td>2667</td>\n",
       "      <td>BXD168</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Euthanized</td>\n",
       "      <td>999.0</td>\n",
       "      <td>2016-12-04</td>\n",
       "      <td>2019-08-30</td>\n",
       "      <td>2017-02-24</td>\n",
       "      <td>...</td>\n",
       "      <td>32.8</td>\n",
       "      <td>33.9</td>\n",
       "      <td>33.8</td>\n",
       "      <td>29.1</td>\n",
       "      <td>27.8</td>\n",
       "      <td>28.1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2667-BXD168-F-CD-Euthanized</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>230</th>\n",
       "      <td>2306</td>\n",
       "      <td>2306</td>\n",
       "      <td>BXD175</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Natural</td>\n",
       "      <td>1091.0</td>\n",
       "      <td>2015-07-10</td>\n",
       "      <td>2018-07-05</td>\n",
       "      <td>2015-09-09</td>\n",
       "      <td>...</td>\n",
       "      <td>21.2</td>\n",
       "      <td>17.2</td>\n",
       "      <td>17.2</td>\n",
       "      <td>16.2</td>\n",
       "      <td>14.3</td>\n",
       "      <td>14.5</td>\n",
       "      <td>13.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2306-BXD175-F-CD-Natural</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>273</th>\n",
       "      <td>2210</td>\n",
       "      <td>2210</td>\n",
       "      <td>BXD19</td>\n",
       "      <td>F</td>\n",
       "      <td>CD</td>\n",
       "      <td>Natural</td>\n",
       "      <td>1068.0</td>\n",
       "      <td>2015-06-09</td>\n",
       "      <td>2018-05-12</td>\n",
       "      <td>2015-08-05</td>\n",
       "      <td>...</td>\n",
       "      <td>28.0</td>\n",
       "      <td>28.4</td>\n",
       "      <td>23.8</td>\n",
       "      <td>23.2</td>\n",
       "      <td>21.3</td>\n",
       "      <td>18.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2210-BXD19-F-CD-Natural</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     EarTagNumberCurrent  EarTagNumberOriginal StrainName Sex Diet  \\\n",
       "19                  2817                  2817       BXD1   F   CD   \n",
       "179                 2228                  2228     BXD168   F   CD   \n",
       "190                 2667                  2667     BXD168   F   CD   \n",
       "230                 2306                  2306     BXD175   F   CD   \n",
       "273                 2210                  2210      BXD19   F   CD   \n",
       "\n",
       "    CauseOfDeath  AgeAtDeath DateOfBirth DateOfDeath DateDietStart  ...    10  \\\n",
       "19    Euthanized      1007.0  2018-04-24  2021-01-25    2018-07-12  ...  29.6   \n",
       "179      Natural      1092.0  2015-06-24  2018-06-20    2015-08-05  ...  24.8   \n",
       "190   Euthanized       999.0  2016-12-04  2019-08-30    2017-02-24  ...  32.8   \n",
       "230      Natural      1091.0  2015-07-10  2018-07-05    2015-09-09  ...  21.2   \n",
       "273      Natural      1068.0  2015-06-09  2018-05-12    2015-08-05  ...  28.0   \n",
       "\n",
       "       11    12    13    14    15    16  17  18                   identifier  \n",
       "19   30.4  29.0  28.2  27.7  26.5   NaN NaN NaN    2817-BXD1-F-CD-Euthanized  \n",
       "179  28.2  24.9  26.3  23.9  20.9  19.9 NaN NaN     2228-BXD168-F-CD-Natural  \n",
       "190  33.9  33.8  29.1  27.8  28.1   NaN NaN NaN  2667-BXD168-F-CD-Euthanized  \n",
       "230  17.2  17.2  16.2  14.3  14.5  13.6 NaN NaN     2306-BXD175-F-CD-Natural  \n",
       "273  28.4  23.8  23.2  21.3  18.9   NaN NaN NaN      2210-BXD19-F-CD-Natural  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def rename_columns(name: str) -> str:\n",
    "    name = name.replace(\"Weight\", \"\").replace(\"Baseline\", \"\")\n",
    "    if name.isdigit():\n",
    "        return str(int(name))\n",
    "    return name\n",
    "\n",
    "df = df.rename(columns=rename_columns)\n",
    "print(f\"Columns:\\n{' '.join(df.columns)}\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d8f7da8",
   "metadata": {},
   "source": [
    "Next, we collapse various columns that contain metadata into one column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "cac51200",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>identifier</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2817-BXD1-F-CD-Euthanized</th>\n",
       "      <td>20.1</td>\n",
       "      <td>27.0</td>\n",
       "      <td>32.6</td>\n",
       "      <td>30.8</td>\n",
       "      <td>30.8</td>\n",
       "      <td>29.2</td>\n",
       "      <td>28.8</td>\n",
       "      <td>27.7</td>\n",
       "      <td>30.2</td>\n",
       "      <td>31.2</td>\n",
       "      <td>29.6</td>\n",
       "      <td>30.4</td>\n",
       "      <td>29.0</td>\n",
       "      <td>28.2</td>\n",
       "      <td>27.7</td>\n",
       "      <td>26.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2228-BXD168-F-CD-Natural</th>\n",
       "      <td>15.4</td>\n",
       "      <td>20.4</td>\n",
       "      <td>23.1</td>\n",
       "      <td>24.7</td>\n",
       "      <td>26.5</td>\n",
       "      <td>27.0</td>\n",
       "      <td>27.1</td>\n",
       "      <td>25.9</td>\n",
       "      <td>25.3</td>\n",
       "      <td>24.9</td>\n",
       "      <td>24.8</td>\n",
       "      <td>28.2</td>\n",
       "      <td>24.9</td>\n",
       "      <td>26.3</td>\n",
       "      <td>23.9</td>\n",
       "      <td>20.9</td>\n",
       "      <td>19.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2667-BXD168-F-CD-Euthanized</th>\n",
       "      <td>20.6</td>\n",
       "      <td>23.7</td>\n",
       "      <td>26.8</td>\n",
       "      <td>30.8</td>\n",
       "      <td>27.7</td>\n",
       "      <td>28.5</td>\n",
       "      <td>29.3</td>\n",
       "      <td>31.2</td>\n",
       "      <td>31.3</td>\n",
       "      <td>32.4</td>\n",
       "      <td>32.8</td>\n",
       "      <td>33.9</td>\n",
       "      <td>33.8</td>\n",
       "      <td>29.1</td>\n",
       "      <td>27.8</td>\n",
       "      <td>28.1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2306-BXD175-F-CD-Natural</th>\n",
       "      <td>16.2</td>\n",
       "      <td>17.2</td>\n",
       "      <td>19.0</td>\n",
       "      <td>19.6</td>\n",
       "      <td>19.6</td>\n",
       "      <td>20.3</td>\n",
       "      <td>22.0</td>\n",
       "      <td>22.6</td>\n",
       "      <td>22.5</td>\n",
       "      <td>21.3</td>\n",
       "      <td>21.2</td>\n",
       "      <td>17.2</td>\n",
       "      <td>17.2</td>\n",
       "      <td>16.2</td>\n",
       "      <td>14.3</td>\n",
       "      <td>14.5</td>\n",
       "      <td>13.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2210-BXD19-F-CD-Natural</th>\n",
       "      <td>19.2</td>\n",
       "      <td>29.1</td>\n",
       "      <td>29.9</td>\n",
       "      <td>32.5</td>\n",
       "      <td>32.4</td>\n",
       "      <td>30.6</td>\n",
       "      <td>32.4</td>\n",
       "      <td>29.5</td>\n",
       "      <td>28.3</td>\n",
       "      <td>29.1</td>\n",
       "      <td>28.0</td>\n",
       "      <td>28.4</td>\n",
       "      <td>23.8</td>\n",
       "      <td>23.2</td>\n",
       "      <td>21.3</td>\n",
       "      <td>18.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                0     1     2     3     4     5     6     7  \\\n",
       "identifier                                                                    \n",
       "2817-BXD1-F-CD-Euthanized    20.1  27.0  32.6  30.8  30.8  29.2  28.8  27.7   \n",
       "2228-BXD168-F-CD-Natural     15.4  20.4  23.1  24.7  26.5  27.0  27.1  25.9   \n",
       "2667-BXD168-F-CD-Euthanized  20.6  23.7  26.8  30.8  27.7  28.5  29.3  31.2   \n",
       "2306-BXD175-F-CD-Natural     16.2  17.2  19.0  19.6  19.6  20.3  22.0  22.6   \n",
       "2210-BXD19-F-CD-Natural      19.2  29.1  29.9  32.5  32.4  30.6  32.4  29.5   \n",
       "\n",
       "                                8     9    10    11    12    13    14    15  \\\n",
       "identifier                                                                    \n",
       "2817-BXD1-F-CD-Euthanized    30.2  31.2  29.6  30.4  29.0  28.2  27.7  26.5   \n",
       "2228-BXD168-F-CD-Natural     25.3  24.9  24.8  28.2  24.9  26.3  23.9  20.9   \n",
       "2667-BXD168-F-CD-Euthanized  31.3  32.4  32.8  33.9  33.8  29.1  27.8  28.1   \n",
       "2306-BXD175-F-CD-Natural     22.5  21.3  21.2  17.2  17.2  16.2  14.3  14.5   \n",
       "2210-BXD19-F-CD-Natural      28.3  29.1  28.0  28.4  23.8  23.2  21.3  18.9   \n",
       "\n",
       "                               16  17  18  \n",
       "identifier                                 \n",
       "2817-BXD1-F-CD-Euthanized     NaN NaN NaN  \n",
       "2228-BXD168-F-CD-Natural     19.9 NaN NaN  \n",
       "2667-BXD168-F-CD-Euthanized   NaN NaN NaN  \n",
       "2306-BXD175-F-CD-Natural     13.6 NaN NaN  \n",
       "2210-BXD19-F-CD-Natural       NaN NaN NaN  "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns = [\"EarTagNumberOriginal\", \"StrainName\", \"Sex\", \"Diet\", \"CauseOfDeath\"]\n",
    "\n",
    "df[\"identifier\"] = df[columns].apply(\n",
    "    lambda row: \"-\".join(row.values.astype(str)), axis=1)\n",
    "\n",
    "weights = df.drop(df.columns[[i for i in range(0, 11)]],\n",
    "                       axis=1).set_index(\"identifier\")\n",
    "\n",
    "weights.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f4424ce",
   "metadata": {},
   "source": [
    "### Visualisation And Analysis\n",
    "\n",
    "We make a time series plot for every row in the same figure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "a05eb49f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f475e261220>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e2611f0>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e2613a0>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e2614c0>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e2615e0>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261700>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e2b5d90>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261820>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261a30>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261b50>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261c70>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261d90>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261eb0>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e261fd0>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e268130>,\n",
       " <matplotlib.lines.Line2D at 0x7f475e268250>]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZsAAAEJCAYAAABCNoqwAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAADcqUlEQVR4nOydd3gc1dm375nZplXvXbKqZclN7r1jG0wzvZfkJQUSILSENAjkS0IogSQECAmE3osNbrgb9yIXyVaX1Xsv23fm+2NtyWNJtmRLlsve16VL2jMzZ86sduc35zlPEZqbmxXcuHHjxo2bQUQc6gG4cePGjZuLH7fYuHHjxo2bQcctNm7cuHHjZtBxi40bN27cuBl03GLjxo0bN24GHbfYuHHjxo2bQcctNm7cuHHjZtBxi40bN27cuBl0Llixyc/PP+/6Oh/H5O7L3Ze7L3df57qvnrhgxcaNGzdu3Fw4uMXGjRs3btwMOm6xcePGjRs3g45bbNy4cePGzaDjFhs3bty4cTPoaIZ6AG7cuDk9Da3VHK07jOTlwM8rEB9jABrJ/fV1c+Hg/rS6cXOesztnPSt2vY+syHyf52oTEPA2+uPnFYifV5Drx1P9t1ajG9qBu3FzAm6xcePmPEVRFNZlfM6WzG+7b0Oh1dRIq6mR0tqe4yM8DT74ewXh6xWIn2cQ/seEyNcrELvTNtjDd+NGhVts3Lg5D3E4HSzb/hYHCredcR8dllY6LK2U1xd12yYKIpNbF3D5xNsQBOFshurGTZ9wOwi4cXOeYbGZeX/9S92ERiNqiQpKwMvD96zPISsyO458R1HVkbPuy42bvuCe2bgZEmRFxmxrR1ZkRMH9zHOcNlMz7657kerGUlW7p8Gb2ck3MnXcbADsDhutpkaa2utpbq+nub3B9bvD9XerqRFFUU57vqzi3SREpA3KtbhxcyJusXFzzskrP8i3u96jqa2ONYf9SYudyMi4yUQFx1/SwlPbXMl7a1+kuaNe1R7gHcJdlz1GY01rZ5tWoyPQJ4xAn7Ae+3LKDlo7mmjuOCZC7fU0dzRQ31JJaW1B5345Zfu5Srn7kn7f3Zwb3GLj5pzRYWllxa4PyDy6s7Ot1dTEjuzv2JH9Hb6eAaQNm8TIYZOICoq/pNYSSmry+GD9y5htHar2yKA47pj/CF4ePiqxOR2SqMHfOxh/72BVu8Np588f/QybwwJAu7mFivqjRAcnnP1FuHFzCtxi42bQURSFg0XbWbX7Q0zW9l73a+loZPvh1Ww/vBo/zyBGxrmEJyJw2EUtPEdK9vLZltdxOO2q9uSoMdw8+wF0Wv2AnUsjaUmKHMXhkj2dbTmlGW6xcTPouMXGzaDS3F7Psu3/o6Ays3/HddSzNWslW7NW4u8VzMhhkxgZN4nwgNiLSnh2Zq9l5a4PUFCvr0xIns2VU+5GEqUBP2dKTLpKbLLLMrhs/I0Dfh43bk7ELTZuBgVZltmVs451GZ9jc1i7bQ8LiGFs5Fz8Ar3JKt5NbvkB7I6eYz+a2uv4PmsF32etIMA7tHPGE+YffcEKj6zIrN33GVuzVnbbNm/sUuaMuWbQri05agwCQqfA1TVX0tBaQ6BP6KCcz40bcIuNm0Ggpqmcr7e9RXl9YbdtGknL3LFLmZ62iKLCoyQNSyJt2ERsdiu55QfIKt5NXvnBbial4zS21bDl0DdsOfQNgT5hjBw2iVFxk/vkeXW+4HA6+GrbfzhUtEPVLgoiV0+7l/FJswb1/Ea9F6G+MVS3lHS25ZTtZ3ra4kE9r5tLG7fYuBkwHE47mw99w/eZ3+KUnd22DwtN4drp9/boQaXT6hkVN5lRcZOx2i3klrmEJ7/8EA65Z+FpaK1m86HlbD60HB9DAMHF4WgkbdePqFW/lrRoJM1Jr3VoJS3SCe3NpnqccvygmLAsNhMfbfxHt/gWnUbPzXMeIDlqzICfsyeiA4arxaY0wy02bgYVt9i4GRBKa/P5ettb1LVUdttm0BpZNPFmxiXN6pOLrV5rYHT8FEbHT8FiM5Nbtt8lPBWZOGVHj8e0WhpprWw86+s4zurM/xETksSwsOEMCx1OZFD8WSe+bDU18e7aF6lpKlO1exp8uHPBI0QGxZ1V//0hOiCZPUe/63xdUptHh6UNT4P3ORuDm0sLt9hcxDS11bF8xzsUVR0hICuE6KAEooLjiQpOINQ/Ckk8+3+/1W5m7b7P2J2zodsiN8CImPFcOeVOfIz+Z9S/QefBmIRpjEmYhsVmIrs0g6zi3RRWZvU4exoobA4LBZWZnY4NWklHdEgisaHJxIWmEBWc0K9El7XNFby79gVaOtSCGOgTyl2XPUaAd8iAjv90eBn8CPWP7hQ+RVHIKz9IeuKMczoON5cObrG5SDlcvIevt72FxW4CoL6livqWKvYXbgVcaycRgbFEBSUQFZxAVFA8fl5B/VqUzi07wPId79Bq6j6j8PLw5crJd5I2bOLAXBBg0BlJT5xBeuIMzNaOE4TnMLIyeMIDYHfaKKo6QlHVETbiimOJCop3zXzCUogOTkSvNfR4bHFNLh+sfxmLzaRqjwpK4I4FD+Np8BnUsfdGSnS6apaVXZrhFhs3g4ZbbC4y7A4bq/Z8yJ7cjafcz+G0U1pboIom9zT4uGY+QQlEBycQGRSHQWfsdmy7uZWVu9XBmScyPmkWiybcgofe8+wu5hR46D0ZlzSTcUkzMVs72Je5k9DwEBxOe88/sqP3bSf9NLbWYbF3nPL8TtlBSW0eJbV5bD70DaIgERE4rNPsFhuajEFnpKQ+m207lndbd0qJTufG2T9Fpxm4GJr+MiJmHJsPLe98XVCZid1hc5cmcDMouMXmIqK2uZJPN79KTVP5GR3fYWklt+wAuWUHOtuCfMNV5rfC2kN8tnc9Zmv3m3GAdwjXTLuX+PDUM72EM8JD70mobwxJkUkD0l9eXh7+IV4U1+S6fqpzaDU1nfIYWXFSXl9IeX0hW7NWIggCIX5R3dZnACYmz2XJlDsHxQGhP0QEDsPH6N95bXaHa/Y2PHrskI7LzcWJW2wuAhRFIaPge1bsfK9bnRJJlEiPmcuo4eMpqyukor6I8roi2szNfer7ZPNbT4iCyLS0xcwde+2QPqkPFIIgEOwXQbBfBBOHz0VRFJra6yiuzqG42iVATe11p+xDUZQehWZ++vXMHn3VeREfJAgCKdHp7M7d0NmWXZrhFhs3g4JbbC5wLDYzy3f8r0eTVoB3CDfNvh9Tk4P48KTOGYeiuApvldUVUV7nehqvbCjuNajyVIQFxLB0+g+JCBx2tpdy3iIIAgHeIQR4hzDuWAxMS0cDR6tzKKnJ5Wh1Lg2t1afsQxQkrpl2L+OSZp6LIfeZlJhxKrHJLTvgzsTtZlBwi80FTEX9UT7Z/CpNbd2fskfHT+WqKXdj0HmQ36Su5CgIAr6egfh6BjLy2AK+U3ZS21xxTHxcIlTXXNmjhxmogzMHwqvtQsPXM5CxCdMZmzAdcJUGONHsVttc0bmvTmPglrk/Iyly1FANt1fiwlLQaw1Y7ccSc1paqKgrIjokcYhH5uZi49K7S1wEHC98tXbfp93cf7UaHVdOvpP0xJn9MtVIokR4QAzhATFMHD4XcM2aKhuOdjO/JUaM4sopd/Sa3v5SxNvo1xmUCtBhaaOkJpeikgJmjl+Ir2fAEI+wZ1yJOUeTVby7sy27LMMtNm4GHLfYXGB0WFr5cut/yCs/2G1bqH80N82+nxC/iAE5l0HnQXx4qsr8lpefx/Dk4QPS/8WMp8Gb1NgJaG2+563QHCclZpxKbHJK97Nw/E1DOCI3FyNusbmAKKrK5vMtr/e4uD8pZT6LJ9wyqG6rgiC4bfkXIcmRoxEFqTNWqa6lkobWavfM1c2A4habCwCn7GTTwWVsPri82xqKQWfk2uk/JC12whCNzs2Fjofek2Fhw1X52rJLM5gx8oohHJWbiw33Y+p5TktHA2+v/gubDi7rJjQxIYk8cPWzbqFxc9akRKerXueU7h+ikbi5WHHPbM5jsksz+Grrf7qVChYQmDn6SuaNXTrkgYFuLg5GxIxj5e4POl+X1uXTYWkdslQ6bi4+3GJzHmJ32NhdtIacqj3dtnl5+HLDzB+TEJE2BCNzc7Hi5xVEmH8M1U2lgMsZJLfsQGdckRs3Z4tbbM4jbHYrB4u2s/3wGupbq7ptT4wYxfUz78PLw3cIRufmYiclJr1TbACyS/e7xcbNgOEWm/OAprY6duWsZ1/+5m6ZgcEVfX7Z+BuYlrbY7Q3mZtAYETOOTQeXdb4urMxyJ+Z0M2C4xWaIUBSFo9XZ7Diyltzy/b2WNfbzCuKm2fcTHZxwjkfo5lIjPCAWX8+Azpo7dqeNwqrD3ZwH3Lg5E9xic445birbmb1WldLkZAQExiZM5/JJtw1qqn43bo5zPDHnrpz1nW05pRlusXEzILjF5hxxOlPZcYx6LyYkzyFYH8fYkW6XZjfnlpSYcWqxKTuALMuIott86+bscIvNINJXUxlAmH8MU1IvY3TcFLQaHfn5+b3u68bNYDEsNAW91gOr3Qy40iOV1xcSEzIwtYLcXLq4xWYQ6KupTBRERsSMZ0rqZcSGJJ8XNU7cXNpoJM2xxJy7OtuySzPcYuPmrHGLzQDSbmlm9Z6P+2wqm5QyD1/PwHM4QjduTs+ImHSV2OSU7mfRhJuHcERuLgbcYjMA2B02Vux6j4z873ut/wLdTWVu3JyPJJ2UmLO+tYq6liqCfcOHeGRuLmTcYnOWyIrMF9//m8Ml3aP94eIxlSmKwoG3M8j5LhvbdRZSbxx5wV6Lm1PjofckLiyFwqrDnW05pRkEj1oyhKNyc6HjFpuzZM2ej3sUmovNVHbo3QNs+cNGANbtqKZ6fxVz/7gAUXJ7KV2MpMSkq8WmbD8z3WLj5ixwi81ZsP3warYfWaNq8/cKZvaYqy8qU5mt3caul7er2rI+PISlycyiV5ag0bs/RhcbKdHjWLHr/c7XZbUFtJtb8fJwJ+Z0c2a4H0vPkKzi3aze87GqzUPrxQ8W/4rxSbMuGqEB2P/fvZgbzd3aC1bls+yeL7G124ZgVC4sLRY2/m4dW3+6iU2/X09jQcOQjeViws8rkPCA2M7XCgq55QeGbkBuLnj6LTYvvvgifn5+PP74451tiqLw5z//mZSUFMLCwliyZAnZ2dkDOtDzieKaXL7Y8m+VM4BOY2B+6i34eQUN4cgGHnOjiYx/7+11e/n2Ur645RNMDb173w0WNZnVfLTkPQ69e4DW/BYOvrOf9+a/zVd3fs7R9YUocu/OGm5OT0rMyTVuMoZoJG4uBvolNnv27OGdd94hLU2d3v6VV17h1Vdf5bnnnmPDhg0EBwezdOlS2traBnSw5wO1zZV8uP4VHLK9s00UJG6d+zMCvC6+Mrp7/7VbNXPRemvxTwhQ7VObWcNnN3xEa3nLORmToihkfnCQz677iNay7ucs3VLM8h98xTtz/8v+t/ZhbbWek3FdbKREj1O9Lqw8jM3hfi/dnBl9FpuWlhbuu+8+/vGPf+Dn59fZrigKr732Gg8//DDXXHMNqampvPbaa7S3t/P5558PxpiHjDZTM++tfbFbMbNrp/+AxMhRQzSqwaOtqo2D76orNibcmsyNn99C6Fi1sDYXNfHZ9R/RkFc/qGOym2x894tVbPj1Wpw25yn3bSluZssfNvLfKa+z8Xfr3Ca2fhIeEKNybrE7bRRWHj7FEW7c9E6fxea4mMyePVvVXlJSQk1NDfPmzets8/DwYNq0aezatevkbi5YrHYz7617ieYO9c10fvp1pCfOGKJRDS67X9mB09p1Q/cK8yL2mjg8Aoxc9+FNxMyMVe3fXt3OZzd8TFVG5aCMp7GggU+u+YCcr4502xaxIIqw9J7jQOwddg69e4D35r/N13d9ztENRW4TWx84npjzRNymNDdnitDc3Hzab90777zDW2+9xdq1a9HpdCxZsoTU1FSef/55du3axaJFi8jMzCQ6OrrzmAceeICqqiq+/PLLHvu8kHJ/ybKTDdmfUNlcpGpPCk1nSsIVF2W8SUd5O1t+sEF1Ux758BhirhzW+dppc3LwLxlUb1GLi2SQGPfUJIInhgzYeCo3lpP50gGcZvVsRjJIjHp0LBFzowBozmmi+OsiqjZVoDh6/2gbIz2JvSaOqIUxaL20AzbOi43K5iLWHf6w87VBa+SGiQ+76yq56UZS0qlTGp3WZzU/P59nnnmGVatWodP17mF18g1XUZRT3oRPN7C+jOts++hLX4qi8NW2/3QTmuSoMdw27+dIonTOx3Qu+lr1929VQuM7zI85P5tHUXGRqq/k/yWz6ffryXz/YGeb0+Jk3+93sfClKxh+dcpZjcthdbD1/23m4Dv7u20LSApkyWtXE5AU2NVXEky8ahIdtR1kfXSQQ+8dxFTX0e1YU0UH2f/KouCdXEZcn8aYu9MJSAzs87j6yoXeV7wcx9a8r7HYXQ4gFrsJg69AbGjXsRf6Nbr7Gvi+euK0jye7d++moaGBqVOnEhgYSGBgINu2beM///kPgYGBBAS4Fotra2tVx9XX1xMcHDw4oz6HbDjwFfsLtqraIgPjuGn2/SqhOV9R7G3orEXI1r6vV9QdriVveY6qbeoj05G03a9XlETm/nEBkx6aqmqX7TKrH/y2R5HoK63lLXx+08c99jH82hHcsvx2ApJ6Dpj1DPFk8kPT+MH2H7HolSVuE9sZIokakqJGq9qy3aY0N2fAaWc2S5YsIT1dbbd94IEHSEhI4JFHHiExMZHQ0FA2btzIuHEu7xWLxcKOHTt45plnBmfU54i9eZtUZXLBFbR5x4JfoNcahmhUfcfZlo/14O8JsjVhrgXRZzhS0FQ0QVMQPGN7nXluf/571eug1GCSr+p9hiIIAlMfmY6Hvwebn97QtUGBTb9fj7nRxOSHp/XL3Fi8sYg1D6/E0mxRtUs6idlPz2PkbaP71J+kk0i5dgQp146g+kAVB/+3n7xvc5Dtcrd9SzYXU7K5GGOkJ+LvBRIXuzMdg6tcdObRnZ2vc8r2s3jiLUM4IjcXIqcVGz8/P5X3GYDRaMTf35/U1FQAfvrTn/Liiy+SlJREYmIiL7zwAp6entxwww2DMuhzQV75Qb7Z8Y6qzaj34q7LHsPLw3eIRtV3ZGsD1oNPo9iautpac5Fbc7EX/Q/BEI4UPAVN0BRE35EIx2ZpFXvKKd54VNXXtMdmIIinv7GPvXccBn8P1j66CtnRdTPf9fIOzA1m5jwz/7T9yE6ZXX/bzu5/7Oy2zSfKhytev5rQUWfmYh42Npywl8OZ8evZpzWxrfjxMpa8fjWJlyef0bkuJpIiRyOJEk7ZtV7W0FpNXXMlwX4RQzwyNxcSA5Jn5KGHHsJsNvP444/T3NzM+PHj+fLLL/H29h6I7s85FfVH+XjTP5GVrhumRtJy+/yHCfI9/2NpFKcF66GnUWy9m84USxWOsq9wlH0FGi+kwIlIQVPY/VKxar/wCZEMmxff53OnXDsCg6+eFT9ZjsPi6Gw/9N4BLM1mFr50BZKuZ/Ojqb6DVT9fQfn20m7b4ubHs/BvV2DwPfsZ5XET24SfTiZ/ZR4H/5dB9f6qbvutfXw1Qakh+MX6nfU5L2QMOg/iwkZQUJnV2ZZdtt8tNm76xRmJzYoVK1SvBUHgySef5MknnxyQQQ0ljW21vLfuJeyOrkBGAYEbZ/3kgiggpSgy1iMvILf1w9vP0Y6zZiPOmo3Mv1egaqo/JRnBlB4MZvovZ/bb227Y3Hiu+/Amlt37JdaWLjNY3je5WFqsLHn9anSeameTij3lrHrgWzpq2lXtgigw7YkZjP/xpD7NrvqDysR20GViy12WjeJ0rdnY2mys/OlybvryNjSGSzv/W0p0ukpsckozmOVOzOmmH7j9F0/AZGnn3bUv0mFpVbVfMfl2UmMnDNGo+of96Ps469QODRZDGh7T3kM3/OdIgRNB7N3VV9IoRI1sZPpdudz64lYC+DO2o+/jbCs4ZVnrkwkfH8ENn92MZ6iXqr10SzFf3f4Z5iZXrjVFUdj3xh6+uPmTbkJjDDZy3Uc3MeGnkwdcaE4mbEw4i/52BTN/O0fVXne4ls3PbBzUc18InJy6pryukHbzuckY4ebiwC02x7A7bHyw4W80tFar2meMvIIpIy4bolH1D0f1RuzFH6raBM9hNAXejWgIRhu5BMOYZzHO+BT9yN+iCVsA2lNn8ZXbC7EffR/Lnp9h3n4Xvk2f4mzN7dN4goYHc9MXt+IX569qr95fxec3fETb0VZW/HgZW/+0uXM2cZzIKVHctuIuoqZEcy4Ze+84wmaqPdeyPjjYYyDppYSvZyARgerEnDllZ+5p6ObSwy02uAqgfbbldUprC1Tto+Imc9n4G4doVP3D2ZKNNecldaPWF8Pop1FED1WzoPFAEzIDfepjGKd/hG70c+RuT6al2njKcyjWOjzbv8ey9yHM+3+NsznrlPsD+ET7cuPntxCcpg7wbCxo5Pv7NlK4pqDbMRMemMx1H9zUbVZ0LhAEgVGPpuM7zE/Vvv7J7wY9Fc/5zsm50nJK3WLjpu9c8mKjKAp7j64lu3Sfqn1YaArXzbjvgoiUli21WDOfgROSgyJoMYz6PaLHqR0aBFEid63A92/G8NmTU/nsyans+TwRWZ8M9G66kpsysGQ8hjnjCZyNB05pYjMGeXL9Jzefdpai99Fz1VtLmf7ETETN0L3vWi8tS/51NZK+y5HBYXaw8v5vsJuGrpzCUJMSc1JizqrD2OzuxJxu+sb5fycdZLYdXkVOlbrSZohfJLfNexCNdP6nMVEc5mOeZ02qdl3KQ0h+aT0fdAIOi/2EwmgCLdWeOH2uxnv63zHO+Ahdyi+QgqaCqO/xeLn5EJYDv8KS8SiOhr29io7eW88171xPwqKenSxCRoVy64o7iZ+fcNoxnwuC00KY84f5qrbG/AY2/GZdv9auLibC/KPx8+wqoeFw2imozBzCEbm5kLikxeZQ0U7W7P1E1eZt9OPOBY/iofccolH1HZfn2V+R29WpdLSxN6MNX9CnPg69e4D26q6FeUkvdWYDEHR+aCMWYRj9FMaZn6If9RRWfWKP/cgtR7Ae/C2WvQ/hqN/V4w1ZY9Bwxb+uIu1mdYbsUXeM4cYvbsU3xq9PYz5XpN0yipTrUlVtOV8e4fDHl+YNVhCEHmrcuE1pbvrGJSs2NU3lfLn1TVWbXmvgzgWP4ufVcwqU8w174f9w1u9QtUnB09DG392n461tVvb8a7eqbfSdY/EO7x4fJUh6NMFTaQh5CEP684j+6d32AZDb8rAeegrLnp/hqN2Koqgj9UWNyPznFnLZi4uJviKWq9++jnn/77LzsrS0IAjM+38LuqXE2fTUeuoO1/Zy1MXNiJNMabnlB1TxaG7c9MYlKzabDy3HKXcFHboKoD1IeEDMEI6q79irvsNe+qmqTfRKQJ/6BEIf15ky3tyLpamr3LPOS8fEByaf9jjJfxQe6X/GMP4llyt1D8jthViz/oh59/04ajajKF3ZmgVBIPWGkYx6ZCxx/QgYHQq0Rh1LXrsajUeXGDqtTlb8dPklWZQtNjQZg67LkcRkbaeutXwIR+TmQuGSFJumtjoOF6vXaa6eejcJEadf4zgfcDZnYcv5u6pN0PmjH/00gtS3CHtTg4n9/1GXe06/bwIeAaf2SDsRyTcVw5hnMUz4O1LQlB73UTqKsR7+M+ZdP8FRvR5FPnXBs/ORgKRA5v95oaqtpaSZdU+svuTWbyRRQ3LUGFVbWWPeEI3GzYXEJSk2O7K/U039fT2CGJc0awhH1HdkcxWWzGdB6ZqVIerQj34a0dD3LNt7Xt2FvaPLe80jwINx/3dmgauSTzKG0U9jmPgqUnDPheQUUxnWI89j3nUf9srvUE6YVV4IpCxNZeTt6ptswap8Drx96WVAPrmgWllj7iUnum76zyUnNmZrB/vyNqva0iKnXBAF0BRHB5ZDT4FdHbmtH/Eoks/wPvfTWtFK5nsHVG0THpiMzqv3ekV9QfJOwDDqt3hMeh0pdA49uU4r5kpsOS9h3vlDjO1bUZwXjivx7N/P7RYvtPX/bR60yqTnK8cTcx6nzdJEXcul9R646T+XnNjsyd2IzdFla/fy8CUueOQQjqhvKLIT6+G/oHSok1Rq4+5AEzq7l6N6ZvcrO3DaTij3HOHN6DvGDsQwARC9hmFI+xUek//tylLQwxqSYqnBr+kTTFtvxpL5R5eJzd42YGMYDDQGDVe8djU6ny43cNkhs/KBbzrT71wKuBJzqr303DVu3JyOS0psHE47O7PXqtqmjLgMSTz/PKFOxlb4H5wN6nUmKWQ22mG396ufpsJGjnymjvyf/NC0QUk0KXpGo099DI/J/0ETvgiEHrI9O80467ZiPfI8pq03Y854Anvpl8im8/NJ2S/Wj8ueX6xqa69s47tfrLykiq6NcLtAu+knl5TYHCraSZu5ufO1TqNn4vC5QzegPmKvWOkqBXAConcy+hGP9Nv8t+PFraqbon9CAKk3DK5jhGiMQD/iF3hMeQtN5BIQegmWVWTk5kPYCv6NeecPMO36MbbCt3G2ZHdzoR5KEhcnkf7D8aq24o1H2fva7l6OuPg4ed2mvL6QdRlfuDMKuOmVS0ZsFEVh2+FVqrZxSbMw6s99/q3+4Gw8gC3vVVWboA9CP/opBKnnqP7eqM2sIX+F2nNo6qPTz1lqGNEjFP3wn+Mx9S000UtxiqdOAqp0lGAv+QTLvl9g3nY71uyXXQGjzqG/oU1/chbh49T1XHa8sJXynWVDNKJzi49nAJGBcaq2zYeW88pXv+JQ0Q63w4CbblwyYpNfcYja5orO14IgMC110RCO6PTIpnIsWX+EE2JUEPUuzzN9/wNPTy73HDIydEgqUYqGYPRJP6Ym4lkM419GG3sLgmfsKY9RbE04qlZjPfQUpu9vwnLoDy6vNlvzuRn0SUhaictfvRKDf1eSU0VWWPWzb+mo7V7982JkYsq8bm2tpkY+2/I6/131JyobSoZgVG7OVy4Zsdl2eLXqdVrsJPy9++4qfK4RZJPL88yhrvGiT3sCybvnlDGnonxnGSWbi1VtUx/vW7nnQUMQkXxT0CXcg3HyG3hMeQtd0o8R/Ub36FTQiWzFWb8DW85LmLbeinnfI3i1rjvnwuMd4cOil69QtZnqOlj94LfIzvPH7DdYjE+axXUz7sOg7Z7aqaQ2j9e/eYpl29/qVh/KzaXJJSE2lQ3FFFWp65HMGHn5EI3m9Ciyg4D6/6KYKlTt2vh70QRP739/isL259SzmsjJUcTOHnY2wxxwRGME2uileIz7K8YZn6BPfQIpZCZIpwo0VZBbjuDTsgzTzv/D2Xz4nI0XYNicOCb+TB3QWr6jjF1/297LEf1HURRaK1ppL2/HaT+/gmLTE2dw7bj7mTHyCpU7NLhq3uzN28zLX/yS7YfXqDJ2uLn0OP/dsAaAk2c1w0JTiAyK62XvoUWxt2Mr+Dd6q3ptRRO2AG3sTWfUZ+2umm6xINOe6H+553OJoPVGEzYPTdg8FNmGsykTZ/0OnPU7Uay91JVxtGM58Gv0I3+NJuj0aXcGiimPTKNqXwXlO7rWa3b/YyfhEyIhsn99OSwOGvLrqT9SR312HXXZtdRn13eW194bvJPRd45h5G1j8Aw+P5LF6jR6Fk24mfFJs1m150Pyyg+qtlvsJlbt+ZC9eZu4YtJtJEaO6qUnNxczF73YNLc3kHV0l6rtfJvVKIqC3JqNo2IVjtotIKsXwEXfVHQpD56ROCiyQt5b2aq2uPnxREzo511wCBFEHZrA8WgCx6MkP4DcXoizziU8cnuhemfZijXzDzDiUTRh83vucIARJZHFf7+SD694F1Nd13rNmodXMvXVmdBzVQU6ajuoO1JLfXYtdcfEpamosVvV0hMx1XWw86Xt7P7HTpKvTGHMvemEjQnvdf9zSZBvGHcueIS88oOs3P1ht6q3dS2VvLP2BVKi07l84q0E+IQO0UjdDAUXvdicnJomyDecpKjRQziiLhR7G47q9dgrV6F09LyYKhhCMYz6PYJ4ZtH9uctzaCs6wWYuwNTHZ55RX+cDgiAgeSe61q3i70S21OIo/wZ76WddOyky1iPPo9hb0UYvPSfj8gzx5PJ/LOHL2z7rdC23NJnZ/8c9jPhyBC0lzdQfOT5TqaMuuw5zvemMzyfbZXK+OkLOV0cISw9n7L3jSLw8GUnXQyzTOSY5agzx4Wnsyl7LxoPLsNrVAa85ZfvJr8hkWtoiZo++Cr3Wo5ee3FxMXNRiY7Z2sDd3k6ptRtrlQ1p9U1EU5JbDOCpX4aj9HuRTpGvR+mEY/TSCzu+MzuW0O9n50jZV2/CrRxA84vx1jOgvoiEEXeIPqWsT8Gv6DOiaFdjy30CxtaCNv/ucmAyjpsYw5dHp7Hh+a2db85EmXkv9+1kHfGo9tchOGael+5pN9f4qVu9fgTF403ljYtNIGqaPvJwxCdNYl/E5Gfnfo5zwv3HKDr7PXMGBgm1cNv5GxiRMuyCq4ro5cy5qsdmbtwmbw9L52svgy+j4qUMyFsXe6prFVKxCMZWecl9BH0KLfiJho+88Y6FRZIWNv1lHS0lzZ5uoEZnyaP8dDC4ETF4zCY1IxHrkr6okpfaSj1HsLeiG/wyhpwwGA8zE+ydTuaeCkk1HO9v6KzQ+UT4EpYYQNCKY4BHBBKWG4BvtS/bBbKz7zRx8Zz8txc3djjtuYtvzz10kLRl+XpjYvDx8uXb6D5k4fB4rdr1PWV2BanubuZkvt77J7pwNLJncv2wYbi4sLlqxcTgd7Mj+TtU2ecQCtJqzSzbZHxRFQW7OxF65CmfdVpDtve8siEhBU9BEXIEUkE5FQdFZCc2GX6/l8CfqipJpt4zCL/bM+rwQ0ITOQtB6Ycl8BpxdDxmOylUo9jb0aU+csTmyrwiiwKKXr+DDK96lvfLUud4kvYaglCCVqASlBKP36TlYV+ulJfUHqYy9ZxzFm45y8H8Z3dzZAZw253lnYosMiuO+K37LoaIdrNn3CW2mZtX28vpC3ljxDAkhowmL/CHeRr8hGaebweOiFZvMoztVH2itRsek4d2D0AYDxdaCo3qday3GdOrCUoIhFE3E5WjCLzujQM1u51YUNv5uHVkfHVK1e4Z6MfnhaWfd//mOFDAOQ/pzWA7+Duxda1XOuq1YDra71r80fa/ZcyZ4+Htw5RvXsOzeLzvXZTxDvVyikhpM8LFZi1+cP6LUf9ORIArEzYsnbl48TYWNHHxnP0c+z1KVjDjO+WRiEwSBMQnTSIkZx5bMb9metRrHSQ9ghbWHePnLJ5g+8nKmp12OXtu3+kxuzn8uSrHpMTVN4iyMhsFLTaMoCjpLHpasz3HWbQflVLMYCSloKpqIy5EC0vtcWbMvY9j0u/Vkvq92PdUH6Ln+o5uG3I5/rpB8huMx7gUsB36tcpOWmw5g2f9LDGOePeNZY18JHR3G3Rt/SNa2TFInp/arKF1/8E8IYM4z85n62AyOfJ7VNxPblcMJmBfUq5fcYKPXGrhs3A2MT5rF6j0fdcsYbXNY2Xjga/bkbmR++nWkJ87sFsPj5sLjohSbwsosapq6ZhSCIDAtbfBS0yi2ZiyZzxDUcoRThdwJhnA0kZejDb8MQec/sGNQFDY/vYFDJ9WpMQYbmfDcFPwTAgb0fOc7omcMhvEvuQTnhNml3JaPOeNRDGP+hOgxuK63eh89Pom+gyY0J58r/Qfj+2Zi+/IIfAkN3+xhzi+DkXR6EHUgal1mRlELos71t6RDELWu5KmiDkHSde6LoD0rx4sA7xBum/cQhZWHWbn7A1U6KYB2cwvLtr/NjiPfsXD8TSRHjTmvY8PcnJqLUmy2ZqlnNamxEwjwDull77NDcdqwHPoDcmt2zzsIGqTgaWgjLkf0HzNgsxjVGBSFLc9s5OD/1GnePYKMXP/RzTTQOODnvBAQDSF4jHsRy8HfIbd1BckqpgosGY9iGPNHRK9hQzfAQaA/JrbcNWa8PDeQflXxmZ9Q1BEqGLFpl6KNvemMxCAhIo37r36WvbkbWbvvC6wOtUt4bXMF76//G3FhI1g88RYiAoed+XjdDBkXna9hVUMJhVXqlCXT0wYniFNRZKzZL/YoNIJHBNqEH2Kc/j6Gkb8eUHOZegwK3z+7iQNvqU0RHoEeXP/RTQQknf060IWMoPPFkP4XRH91SnzFWo854zGcLb08JFzgKE4L3t5ZTLlxB7e+sJkpt+biE9I9rmf/sngaSs/CvCzbkJzN2Ivexlmz8Yy7kUSJySMWsHT8/cwadSUaqXsZiqPV2bz2zVN8tuV1mtt7ySLh5rzlopvZnJyaJjY0mejghEE5l73oXZy16hLTos8IdAn3IPqNHvQpv6IobP3TZvb/d5+q3SPAg+s+vInA5KBBPf+FgqAxYhjzB6xHnsdZe0KOOEc7lv2/Qj/qd2gCJwzdAAcIxWnF2bAHR+0WnPW7OjNR6AwwcqGJtAVllGcGsvk/aVjaXV55slNk05tpXPv73Ujas4sFsua9iug3EtFw5lYEncbAZeNvZFLKPNZnfMmBwm2q+ByAQ0U7OFK8lymplzFr1JV46C+NtcgLnYtKbFo6Gsg8KTXNYM1q7JVrsJd8rG7ThOE75lkE7eDXyFEUhW1/2ULGv/eq2g3+Hiz98CaCUi6ewM2BQBB16NN+hU3rg6NiRdcG2Yr10NOQ+hia0DlDNLozR3HacDbuPSYwO1Uu3ycjiBA9poEZ91Wx7m9dJR2ayr05sH4Bk+52uNzzZTuKbHMFHMs2FNl+7O/j7cdeKycl1nR0YD3yIob0P5/1LN7XM5DrZt7H1NSFrNn3CYWVamuFQ7azNWsl+/I3M2f0NUxKmY9GuqhuZxcdF9V/Z8eRtcgn1H4J8glnePTYAT+Ps3E/tty/qxs1vhS33MIIsxZ9L4UoBwpFUdj+/Fb2va4uE23wM3DdBzdeVBkCBhJBkNAl/wxB64u9+MOuDYoD6+HnXOltoq4eugH2EUW24WzMwFGz2TWDcZ4+7Y2gD0ETOhMpZBapc5M5cugTKtd3OU4c+AySbrmzW0G4U45DceIoX44t/43ONrn5II6yr9HGXNe/i+qF8MBY7ln4BPkVmazZ+7HK8QdcWUJW7fmQnTlruWzcjYwcNsntRHCectGIjcVmYm+e2mY8feTiAU+BIXeUdCtopqBl7SujKd2bxTZDDmk3jyL9/8bjG+M3oOcGl9DsfHEbe19Vz+D0vgaWfnAjwWmD4whxsSAIArr4uxC0PtjyXz9hi4It718othZQzl3G6L6iOMzozVlYjyzDUbe9jwIThBQyE03IbESf4aqbcNrPRtGS1UxHjatekiIrfPfoKm5beRdaj749LQmChCbqGtpKN6G35na224reRgoYN6DOF0mRo0gIT+NA4VbW7f+iW1BoU1sdn27+F9sPr2HxxFuIDT33RQHdnJqLRmz25m3Cau8yIXgafBgTP7BBjIqtCcvB34NDXYlx83/SKN3rivp2WBwcfGc/h947QNKSZMb9eCKho8IGbAy7XnZl/D0RvY+epR/cQMhIdxbdvqKNvhZB64s1+wXVg4O9+AN8vUpRlF+dk/Q2x1Hs7ciWGhRLLYql5oS/a5EtNWBvJRA4XUUYQRfoEpjQWYg+Kb2as7TeOhb8dRHL7v6is625qIntz33P7Kf7HvwsCCJNAbcTVvfXrkJ/sh3rkb9imPDygGZsEEWRcUmzGBk3me2H1/B95gpVOipwZSL4z6r/x4iYcQwPmsyQBRO56cZFITYOp4MdRwY3NY3itGA59DSKpUbVvufLZAq2dV+IV2SFvG9yyfsml6hpMUz4yURiZg3r0xS/ra2N6upqV4ZjSUIURTQaDTlvHybrTXVmAJ23jiv/dy3BaSEoiuI2IfQDTdhc0HphzfyjqqyDZ/v3mHfkIXhEIhpCEAwhiB6hCIZjP/qAfgmRoihgb+kmIIqlBtnsauvLTKU3BJ3/sRnMLETf1D6vlwybE8fI20aT9WHXZ+rA2xnEL0wkelpMn88va/zRD/8Z1sN/6WprL8J+9H10CT/o+4X0EZ1Gz5wxVzMheQ4bD37N3tyNqszuANmlGeSU7qewKYOxCdNJiBjpDgwdYi4Ksckq3kWrqanztVYa2NQ0iiJjPfICcmuuqj1nSxQHv4k+7fHl20sp315K0Ihgxv9oIklXDUfS9vzBz8vLY+vWrTidTnJycjrb7d9bsG9W17lBD8INWlZlrIZjns+SJKHRaJAkqfPH6XTS1tbGyJEj0enOXW643jCbzWRmZlJaWorD4SAlJWXIRFITOBEh/c/HZqxdJbiV42LQ00GChKAPQjCEHhOj0BP+DgGdH3JzFs7a7wmuz8RU0dStRtFZo/VDEzLDJTB+aWc8C5v5mzmUfl9Ca1lLZ9vax1dz++q70Xv3nKOtJzShc3DU78RZs6mzzV7yGVLgJCS/kWc0ttPh5eHDVVPuYkrKAr7b9xk5ZWr3fwWFzKO7yDy6Cy8PX8bET2VswnTCAvoupG4GjgtebBRFYVuW2t05PWkmngbvATuHvfBtVyLNEyjPCmTbu8lA101y3fzRtHp7MH1bDqF1LZxMfXYda36xkm3Pf0/6D8cz8pbR6LyOuaDKMjt27ODIkSPdjrNv60FodKC/zRMpUv0vdDqdOJ3d8xjs27ePw4cPM378eFJSUhDFcx9i5XA4yMzM5ODBg9jtriDDrVu3Ul1dzaxZs5CkoXnylHxTj6W3+Q2KreH0ByjOU4vRCQyYr4gg4ZD8MYROPiYwIwfEzKfz0nHZC4v54pZPOqsztJW38v0fN7Hguf5l3dAnP4C5OeuEFEEK1iPP4zHpXwiawXNPDvaL4Pb5D1Fck8uaPR9TXl/UbZ92cwvbDq9m2+HVhPnHMDZxOqPjprgTfp5DLnixKao6QnVTV8p+AYFpqQOXmsZesVJdmAtoLPdk/b9GoTi7btjfXjGBPZNc9uFDo+NILKhk+rYc4kpqu/XZXtnG989uYvcrOxh151iG3zyCHYd2UF1d3W1f+3Yr9o09CM2t3YXmdFgsFrZt20ZWVhaTJk0iNjb2nMwoZFkmPz+fffv20dHR0W17QUEBZrOZBQsWDNnMS/QahmH8i9hy/46zMeP0Bwz4AHQIhmDE46Y6Q8ixv0M6TXcFBUUkJQ38GkTUlGjSfzBeFa91+ONMEhYmEje/7zFqgtYb/YhHsBz4dWebYqnBlv8G+hGPDOiYe2JY6HB+tOT3ZBXvZl3GFzS21fS4X3VTKav3lLJm78ckRoxibMJ0RsSMO6cZ4S9FLnix2Zq1UvV6ROx4Ageo3KyjYR+2vH+q2kzNOtb8LR272fXWyYLA19dM5uDYOACCDCL1Fpn85EjykyOJLG9g+vZsRmSXIyrq4DRrq5W9r+5i7+u7kEZp0U7VIwa6nlZFUcQrx4PqDeoZkqATCPxRKJoYLU6nE4fD0TmbUZS+BeW1tLSwdu1aQkNDmTJlCiEhg+fBVlZWxu7du2lsPHXKnIqKCr755hsWL16Mp+fQBOmJHmEYxv6JgtyDxEV4d81eji3an7hYf0boApG8EzoF5LiYiB6hoPUb0vW2aU/MoHjTUZoKu/5P6375HXesvQcP/75X0pQCxqGJuhZH+dedbY6q71zlM4IHP+u4IAiMiptM2rCJbN+3gXprCVnFu1XOQ8dRFIX8ikPkVxxCr/Vg5LCJjE2YTkxosruQ2yBwQYtNdWMpBZVZqrYZAxTEKbcXY836f3DCwqPDKvLdK2PpaHSlPXdKIp9dP43sVNe6TZqXkw3XRfBuXgd/2d9Gg1WmIiqQT2+aQUBDG1N35JB+4Chax0lmLic4D9hxHrAjJWvwme+Hn9mPo5+qC01pjVqueed6IidF9TxmWe4UnuM/DoeDvXv3UlFRgcOh9mWqqalh2bJlxMfHM3HiRHx8fM72beukoaGBXbt2UVFR0eN2vd61HmC1ds3aGhsbWb58OYsXL8bff2ATlfYHRTQieceDd7zrteJEbj6Mo3YLsqXuzDu2NSAF3YY2cskAjXTg0Bi0LHzpcj697kMUp+uhxVTXwabfr+fyf1zZr750CffibMxQFQm05ryC5DtiwBPQ9oYoiIT6xjIjaQFXTL6DnNL9HCjcRkFlZo8PZVa7mX35W9iXvwU/ryDGJkxnbMI0An0GzpP0UueCFpuTU9PEhCQRHZJ41v3K1gbXgvEJHkKKDBvfGEl98bEbsk7iwxtnUJDUFQT3WIIdvSRw3wgvbkow8kpmG/863I7FCY2B3qy4ciKb5oxi8u5cpu/JRWPuvrbizHPQlFdPE+rcTxoPDVe/fV2vQgOu2ZAoimi16pWCuLg4ZsyYwb59+8jNze32ZSsqKqK4uJjU1FTS09MxGM68hkh7ezt79+4lPz+/x+2SJJGWlsbYsWMpKCggPz+furo61fHffPMNCxcuJCxs6L7oiiIjtxxxRebXfo9iazr9QRovNMHTkYKnIRjCkFsOY839J8IJKzu23H+A4jwvg0fDxoYz8f7JKtf6vOU5JC5OImnJ8D73I0h69GmPY9n7cJdbub0Fa/bL6Ec/fc5ncDqNntHxUxgdP4U2UzOHju5kf8FWaprKety/ub2eTQeXsengMqKDExmbMB2j4k79dLZcsGLTYW3lUJE63mQgUtMoTgvWQ0+jWNVrLbs+SaJkv8vcpDFq+fC2WRREdZmfbk00MtK7S5x8dSK/H+/LD4Z78v/2t/FxgQkFkDwhdVYH3lM8cRy04dhlRWk+tflLY9BwzdvXETXl9J5vvWE0Gpk5cyZpaWns3r2bsjL1F02WZbKyssjLy2Ps2LGkpaWh0fT942Gz2Th48CCZmZk9OigAJCYmMmHCBLy9Xc4bOp2OJUuWsH79etV4rFYrK1euZO7cucTFxZ3B1bpQFMWVUqUz1Yr9hBQsXWlX1O12fJoOYN6W2TdnAY0XmuBpSCGzkPzHIohd75nkFUt1vYmAxv+pUrvY8v7lEpzopWd8bYPFpAenUrS+kPojXQ8AG36zjohJUf2qhyR5J6GNuxN70f8625wNu3BUrkYbOTgppPqCt9GP6WmLmZ62mKrGUg4UbuNQ4Q7aLd0degDK6gooqytAQGBVph9eHj54efjh5eGLl8HH9fv4z7HXBp3RHYLQAxes2ORU7VGlpgn0CSUlOv0UR5weRXFiPfwccpv6qfzI+iiyvnO5S+p9DRx9bCGHnV1fPG+twFPjfWir6J6JNspLw2sz/bk/zYu/bS0irWYXPlhBJ6CdqEczXoc120nTLgHfyvZux0t6DVe/dR1RUwfGXTMgIIDFixdTUVHBrl27aGhQ31BtNhu7d+/myJEjTJw4kYSEhFN+cWRZJjs7m4yMDCyWnvNyhYeHM3nyZIKDu6fR0Wq1LFy4kG3btqlcvZ1OJ+vWrWPq1KmMHNm766xsbcBe8gnBNXsw1cnd83fR/+SSXqc7SjIeE5iZSAHjXPVeTqDZKvNduYXVZRby6ifxQHQgV5leRDhRcPLfQJEd6GJv7Pf4BhNJJ7HwpSv4+Kr3kO2uGZmlycyGJ7/jyjev7ddNVBtzI86G3cgtXR6WtoI3kPzHIBr7nhZnsAgPiCE8IIaF42+isDKLA4XbyC7NwOHsXo5BQaHV1HQsxKLklP1KouaYAB0TI4Ov6nVbm5kEOWFIPEKHkgtSbCw2M3nVao+haamLz/qfZyv4D876Haq2skOB7PjQ5eJsDDaS+s9reTJbfSt6fIw3YUaJ3irOK4qCVJ3PtNrt3TLYNoqevDN6HFWjvYk7WsNlu3KIzK0CXGs0V755LdHTBz4uIDIykqVLl1JQUMDevXtpb1cLXXt7Oxs3biQzM5PJkycTEaG+OSiKQnFxMbt376a1tecFcz8/PyZPnkx0dPQpb1KiKDJjxgw8PT3Zt0+dwXrHjh10dHQwaZI655Ui27CXLXPlOHOa0XLq4qhnjeThWuQOnX1MYNSeS8VtDlaWWlhVamZ7jQ1n579Z4qdHklnm+SCvB/0DLV2DtBf+FxQHumG3DuLA+0/wiGCm/GI62//alSG7aG0h2V8cJvWGvsfMCKKEfsRjmPfc35Ug1GnBeuR5DONeQDhPgiwlUSI5agzJUWOw2EwcLt7DgcJtFNfknv7gHnDKDlo6Gmjp6H1mnFO3kzvm/+KS8oC7IMVmX/5m7M6uhWWj3pv0xBln1ae9fDmOsq9UbQ2lXmx4bRSKLOIV4c3S92/g9lwZBVvnPok+Gn6S2nuWZ4fDwbZt28jLy+u27agUzNuMwSy4PnBH48P4d3wYU5pyWNSShzJjCu8Z/SHjDL2fjtHRrOE6PxsTgtUfbEEQSEpKIi4ujsOHD3PgwAFsNptqn/r6elasWEFMTAyTJk0CXI4Fu3btoqamZ9dSDw8PJkyYQHJycp8fAARBYNy4cXh6evL999+r1pUOHTpER0cHs2fPRhRFnA27XTMDc2V/3ob+IxlcAhMyCylgPILUFeQoKwr76+2sLDWzqtTCkeZTJ5JZ3ZHGHc4H+V/wP/AQu95je9E7LpPasNvPK9PL+B9PpGhtAdX7qzrbNj+9gehpMXhH9N2RRDRGoEv6MbacVzrb5NZs7KWfnnciC2DQGRmfPJvxybNpaqvjQNF2DhXuoL616vQH94OiqiN8tuV1bpnzs0tmhnPBiY1TdrDjyBpV2+QR88/qCUFvPoyt7N+qto4mPWteHovdosE31o/rPryRtTYtO2rUC8V/muSLTur5JtHe3s7atWupr+9uXhs7diy3jkknINvMK5lttNldN9fLPA7wZsy/0ApOHMo3PFzwQ77qmHLG1+ZCx79K6pgVrueJsd7MCFNHhms0GsaMGcPw4cPZv38/R44cQZbV4YqlpaWUlZXh7e3d60xGo9EwevRoRo8e3c1Joa8MHz4co9HIunXrVN5zhYWFmNqbmBWxH6l17yl6OAlBOlbG+Fh54xNLHnf+rVXt09xmI3DYdKTAiQhSl7OE2aGwpcrKqlIzq8ssVJtPF9KpZqsllTtrH+KdkL/jKXY9LNmPvg+yA2383eeN4IgakYUvXc6Hl7+Lw+L6P9jabKx9fA1L37+hX+PUhC/GWb/TlaH6GPaj7yMFTEDyOX9zl/l7BzN3zDXMHXMN2TlHCIsMpt3cQrul1fX7+I+llXZzM+1mV7vN0bdsEdml+1i5+wOWTL7jvPm/DyYXnNhkFe+hpaMrFkAjaZmcMv+M+3O2FeLf8Dac4DFkt0h898oYTE0GApMDWfr+jRBg5Pdfqp0GFkbpWRjds+dWVVUV69at67aOodVqmT17dufC92NjvLk72chzB9rYVpTHP4P+jVZwrUVpBJm/B/4HT8HC++1zzvgaj7OlysqWKitTQ3U8McabORF61YfcYDAwderUTieCo0ePqo5XFKVHoREEgeHDhzN+/HiMRuNZjzM6Oporr7ySNWvWYDabO9urahpZ0+TLnHADRs0J76vGixavRYSNuBJE7TEh0YGgPSNTTWt+PqEhrptgvcXJmjILq0otbKi0YnL0bQ0oxU/DFTEGLC2NfFpjoN7i+nztsKZwe+0veD/kb3idKDglH4PiQJvww0G/8bTZZZrtrtmZeIpz+ccHMP1Xs9j89IbOtrKtJRx67wBj7ur7+qggCOhTHsa06ydgP7YQrzixHvkrHhP/qZoxnq9oJC3+3sH4e5++fIfVbqHD3EJbD8JUVHWExrau+8iunHX4eQUyY+QVgzn884LTis2bb77J22+/3ektlJKSwmOPPcaiRa4ofUVR+Mtf/sI777xDc3Mz48eP54UXXmDEiBEDPlhXappVqrb0xBl4Gs4sPkS21mM99BSi0vWll2XY8PpIGkp8CBkdyrXv3oCHvwd/zGilwtTlkKAVXbOansZ4+PBhdu7c2c3F2MfHh4ULF3aLIQn2kHh+gkSr/Boaq/qpSBQUngt8D0/ByhttA5MZYUeNjaXfNTAhWMsTY3y4LEotOj4+PixYsOC05jKAmJgYJk6cSEBAwICM7TjBwcFcddUSVq/4mtaOrhlOs82P7yrmMjd8K766DjSRl6OLu4vKklpEj/ABOXeJWWBVZhuryizsqrUh90FfRAGmhuq4IsaDy6MNxPu4vlr5+bX8dlYo/8s18ffMNqrNMnusSdxa8ygfhP4NH7FLTO2ln9NisROU9pMBFZwmq8yOGivbqm1sq7ZyqNGOrBiJP1LDfSO8uC3JiK+uZ1POmLvTKVydT/nOLm/BrX/aTOysYfgN63vMjKDzR5/yMNbMP3S2KaYybIVvoU/+6Zlf3HmIXmtArzUQ0ENweUtHI/9a9ntMtq4V3jV7P8HHGMDo+LO1YJzfnFZsIiIi+MMf/kBCQgKyLPPRRx9x++23s2nTJkaOHMkrr7zCq6++yquvvkpSUhJ//etfWbp0KXv27Ol0cR0oWk2NtJmbO1+7UtMsPqO+FKcV68GnTsjj5GLnh8mUHQwmYlIUV7+1FL23nuI2B//IUi///zTVi0RftanI6XSyadMmCgrUwZjguinPnTu3x3QsiuzEkvUnNNbe7cK/D/iUxREyuz1uhH7eiNYWNbO3pfsT/t46Ozeta2BsoJbHxnhzRYxB9aQbGhrKVVdd1aMjQFBQUI+OAwOFs/kwuvzXWBBcymbHNBqsgZ3bTA4jayvns2D2RCITxh9r7Z4WqL/kt9h54Ptmdtd5AKdfJ/PSCMyP0nNFjAeXReoJMPQ8izJqRO5P8+IHwz15L7+Dlw+1k2FK4JaaR/kw5CX8pC6XeWPtMr6rMxGf/jOS/M7sib/O7GR7jY2t1Va2V1s50uTo0buuqM3Jk7tb+H8ZrdyaaOS+EZ4k+6k/04IocNkLi/lg8TvY2l1rTQ6zg+8eXc0Nn96MKPV9vUETPBVn+CIcVV1mcEf5MjRBk5ECxp3RtV5o+HoGMD/1Vr47/B5We9eDxpdb38Tbw5e48IF/SD9fEJqbTxPk0QPDhg3jqaee4p577iElJYX77ruPxx57DHBl9E1KSuLZZ5/l3nvvHfABO5x2DhXtYEPGMiKCY7ht3kNn1I+99EtsBep1mqy10ez8cDgxs4Zx5b+v6SwideeGBr4p6TLbhHiI7L0uFJ8TngZbWlpYuXJlN68ugHHjxjFu3Lhen1atea+r0nsAWPQpGOyFLhfeE9BEX4cu8b5+Pfnm5+fT4BPD8wfbWF/Ruz05zV/D42N8uHqYoZt55Xh+s4KCAkaMGEFcXNxZP33n5+d3y/UlW+qwFb6Fs6arEJ5DlthWM4kKk1rYRFFk7ty5xMfH99hXf/jqqImfb22m/TRmsgijyOUxHlwRY2BGmB59L+t1x+lpXFanwkcFJl461IaPrYiPQ17EX1LnjHu/bTZ7fO7jkbG+pPpre+0LoLLDyfYaK9uqXbOXvJbTVb3pnfmRen40wovLovSqz0DWx5ms/6V6rXTGr2cz/scT+/XeKw4T5t33o1i68gAKukA8Jr+OoPU+6//jiZzPfUledt5d+wJOuctaYtAa+b8rfkOof++B24M9rsHIvXecfq3ZOJ1Ovv76605X1JKSEmpqapg3ryudv4eHB9OmTWPXrl2DIjYaScu4pFl4KWFEx0aeUR+KomArW6FqK9kfxK6PkklYlMTifyxBo3e9NZsrLSqhAXh6vA+izUR+SRVVVa6fntYytFotc+fOJTY2ttu249gr13QTGtE3jUbv/yM+yIol82lVXXlH2ZfgNKMb/rN+Zf2dEqrni4V69tXZ+OvBNtaUdY+JOdzk4J5NjaT4aXh0tDfXxXkgia4bjiiKDB8+HFEUiY+P7/N5+4ritGEv/Rx7ySfd0vFrRCczIzLIMEeTV9H15ZRlmfXr19PR0XHGWQ9sToXf7WnhjezuCUKPMypAy+UxBq6INjAmUHvWIquXBO4Z7sntSUY+KfTmF1m/5EWvvxIodT2o3OG9GanNyYyv72ZJrJHHx3hzPENZSZuDbdVWtte4zGJH23oOoj0VEgpOul/H+gor6yusxHtLKhNb2s0jKVydR/HGrnW8HS9sZdjcOHroplcEjRF96uNYMh7n+DqpYmvAmvtPDCOf7Pd1XKjEh6eydMZ9fL6lq1qsxW7i3bUv8uMlv8PHc2DN0ucDfZrZHD58mIULF2KxWPD09OTNN99k0aJF7Nq1i0WLFpGZmUl0dFd0+wMPPEBVVRVffvllr332ls7kXKCzFhJU+3Lna9kh8NGjM/CflMDox9M7TQMOBW7fb6CoQyAQE/FKI+OkBtLEBlVOr54wGo2MHDnylAvmWmsRQbV/R6DrZuGQ/KkPfRxZ8j62z1EC615DVMyqY03GCTQH3OHytjoDctoF/lumZVND788bMQaZe6PtLA52ohks70xFwWA+iE/zV2icPSfrNHuk0+p3LQ7Jn9LS0m6OCwBRUVGnDUA9mWqLwJO5OrLaur+H6T5OFgQ5mRXgJMzQ/8DQ/uBQYE9NDXMsfydQUj+0fN4+lV80/AAZkXQfJ1VWgWpr//4ZAgqJngrjfJyM85UZ6+NEBr6q1vBFlZYGe+/vmVFSWBLi4KZwB2EmE9/ftxF7W9ds2yfJl2n/mIXYzw+Id/NyvNvWqtqaAu7G7DmhX/1c6GSVbyejZIOqzd8YwqJRd6HTnHnaqKHgdLOiPomNzWajvLyclpYWli9fzjvvvMO3335LW1sbixYtIisri6iorqnf/fffT01NDV988cUpej07zmbKZznyPM7q9Z2vj+4Jobrxdub/eSGCKKAoCs3NzXyaUczBoxXEK4340vfiV8OGDWP27NmnTJcvW+qw7H1QnXNL1GMY/yKSd6Lq+pxtha607cc9eY4hBU1Fn/YkgnRqt+9TvVeHG+28eKiNr46ae42aj/WSeHSMN7ckGCkpKhiwqfbRw5sJs61CbjrQ43bRKx5d0k+Q/Eer2vPy8tiyZUs3B4yIiAhSU1OJiYk5bW2cdeUW7tvSSJNV3YdOhEfibPxyZt+qqp6O/nxO7W2ltGb8EoNT7V7/dcckHqz/P5z07cFCFGBMoJbpoXqmhemYFqrHT68Wg+PjsjkVlpeYeeNIO3vqTh0VOz9Szy3llVT+QV0VN+mu4Vzx7FV9GttxFNmOZe/DyO2FXY0aL6qDnyBhxKR+9dUb56uJ6cS+FEXh213vsTtnvWqf+PBU7lzwKBrp1Man8/Uae6JPZjSdTtdpOklPTycjI4N//etfnes0tbW1KrGpr6/vMTXJ+YBib8dR871q5p+7LZJpfx/F4SOHqa6upqqqCovFggj01cFTEAS8vLwYO3Ysw4cPP+WNSnFasWY+0y25o37EI0je3ROJSt4Jx4p7PalyaHDW78By6CkMo59SxYP0h7QALW/NCeCXY12i83mRuZv3VUm7kwe3NfPXA23cFqbh3kgnoR7iKd1me0JRFBRzFc7mQzibDhBcswW5p/JjWh908XejiVjco6kwOTkZDw8P1q9f31mEDaCyspLKykr0ej0JCQkkJSURHBys+l84ZYW/HGjjhYNt3cQ12kvi3bkBeDWVDEncg9Y7Bv+JL2De/wRYu6LPr/XcjQYnD9T/CEcPX1mNAOOCdEwP0zE9TM+kEJ1qPfFU6CSBG+KN3BBvJKPOxhvZ7Xx51Iy9h3/L+gor6wng3jExDDvYldG54IM8am6sJnR03xOnCqIWferjmPf+vGtd0tGOf+P7KMqEPpe2vtARBIElk+6gtaNJVWm0qOoIX2/7L9fP/NFFE4NzRnE2sixjs9mIjY0lNDSUjRs3Mm6cy5vEYrGwY8cOnnnmmQEd6EDhqNmIoHRFcLfVG6gxhfLt2hWnOKo7oigSEhJCeHg4YWFhhIaGUlxcfNonA0VRsOb8rVv+NW3sLWhCZ/d+Ps9oDONewLL/SRRLl9ea3LQfy4FfYxjz7FlVQxzup+XfswL45RgHL2W28UmBiZPXyss7nPy1UMdfC6vRiRDlKRHtpSHGSyLaSyLGS0P0sb8jjBKS4HJvdTZn4mzORG5SJ7fs9hUSRDSRV6GLuwNBe2pPxuOxOKtXr1bF4oArkeeRI0c4cuQIvr6+JCUlkZiYiEVj5P82N7G5qvssdVG0gddn+uOvF8nvQ4LnU+F0Oqmrq6OqqqqzIF5sbGyfCsOJxkg80p/Hsv9XqmSwV3ruQxJe56d1P0GUNEwIds1YZoTpmBiiwzgAds5xwTreCA7gmQlO/pfXwVs5HdScHLgqCHyycAIPFNTg1eF6HxWnwsdXv49fnD/BI4IJGhFCUGowwSOC8Qr37vVmKXoNQxd/r8pRR2/Nw178EdrYW84qnY0iKyh98Vk/DxBFkRtn/4S3Vz9HeX3XTO9g0XZ8vQK5bNwNQzi6geO0YvP000+zcOFCIiMjaW9v5/PPP2fr1q18+umnCILAT3/6U1588cXOL/QLL7yAp6cnN9xw/r1BiqLgqFSXJcj7PgJh+Omj3RVRIjIslPDwcMLDwwkODu5XVuTj2Es/U9VpB5CCJqONv+u0x4oeYRjGH5vhdHQ9WcotR7Ds/yWGMf8PQdc99qc/JPhqeHWGP4+P8eblQ218UGDq8SnXJrtcZ4tOWJwWkEnRVjDFkMc0Qy5TDHkEiL1ljDvp2vzT0Sf9GNFrWJ/HGhQUxNVXX82GDRtUZQpOpKWlhb1797J3717KpEA6lAj0QhhWwfU/FwX43TgfHhrl1e+Z2nEcDgc1NTWds+La2lpV5uvy8nJEUSQ6Opr4+HhiYmJOKTyiMQLDuL+6BOcEr63Ljfs5OPIt/Mf+Hg/t4OUVCzVK/HKsD78Y5d2jic3kqWf5VZO47eOu3Gko0FzURHNRE/krulIzGfwMBKUEE5QaTNCIYIJTQwhICux0wNFEX4ujfhdy88HOY+xH38NRsRJNxEI04YsQPbrPmGSnTEdNO63lrbSVt9Ja3kJrRSttFa2utspWECBvTjaTfj6FkJEDU1BxsNBp9Nyx4GH+veKPqgqjWw59g68xgEkp805x9IXBae+WNTU1/OhHP6K2thYfHx/S0tL4/PPPmT/fFbX/0EMPYTabefzxxzuDOr/88ssBj7EZCOS2fJWNWJYhb2sE0j3d3wYLEsVCAEVCADbPYD6/LgkP3dklXHDU78Je+LaqTfCMQZ/6RJ/NBqI+0PXke+DX6mtpK8C8/3EMY/+MqA88RQ99Y5i3hpen+/PYGG9eyWrn3bwOrCc5PUk4SdWVMVXvEpZJ+jz8T4gZ6QsNBFMd9kNGJ/d/kRlcAajXXHNNZ9bpwsLCXp03op0N3EwDSzlMlhBGoSGK385LZlZE3ytRgmsN80Rxqaur65be52RkWaakpISSkhIkSVIJT0+pfUSPMAzjnsey/wkUc9dM1rdtF9rGrXCKWfBAcSoTW25KFPvHxJF+sLuzxolYmi2U7yxTBYWKGhH/hACX+IwIJjDxVjzNJRg9mzv3cZgaadn9Ne31a+iwpNBhSaaj0Zu2inZay1tor25Hdpw+XVDh6nwKV+czbF48kx+cSlj6wAT+DgaeBh/uvuxR/r3yWTosXQ9p3+56Fx9P/7POaj/UnFGczfnAmSxmWXNewVHZlYGg9GAg65ZNxHC7JzqdjrCwMOp0QfzlqIFKfJCPCcCnCwJ7TUvT1zHJHaWY9z6sKsiGxguPCX/vMd366a5PsbdjOfR7Vfp2AMEQjiH9z6qnwYFY+KsyOXkjq5mj5ZkkiAWM1eYySZ+Pt9hzWYHeMMs69loT2Gkdzk5LMnusiTiR8NEJLInxYOkwD+ZE6HvNN9cbx6/R6XRSVlZGfn4+paWlpxUBo9FIYmIiSUlJnVkQTn6/rFYr1dXVneJSX1/f5xLcp0OSJGJiYoiPjyc6Orqb8MjWeiz7f4li6qp4KnonYZjw97Oy5Z/pZ6LG1GVia2i1s2DdAZLzK/FvbOdsDXkePja8gsx0NOkxNetBGfi1iphZw5j84FQiJvYvbOJcLsSX1xXy1uq/YHd2mfu1ko4fLP4VUcEJQzaus+WSERvFYca07TZwdtn31/59NJVhMRineHHXXXdhdsKkL2tVaWkWRen55LK+VenrbUyKvQ3z3odRzCeWSBYxjP1jr5HTfbk+xWnBcujpbt5cgj7INcPxjO5zXz33b0Nuze1ac2k50i0G5nS0y3p2W5PYaXGJyyHbMOynmVD76gSujPXgujgPZoXr0Yqnv+mcfI2HGmz8aH01/m3ljJcriKX5tH0EBgaSlJSELMv4+Ph0isvJNX/6gqenJ+Hh4VgsFlpbW3tNXnoiGo1GJTzHzbRyRxnmXfep9jWkP4fkP6ZPY5FlGZPJRHt7O+3t7bS1tVFfX8/EiRPx8/Pr97UBnV5sb2Z3sLvWitbqIKS2hbDqJsJqmgmtbia0phm9/cwDTAeTqKnRTH5oKpFTTl3+4jjn+qaeU7afDze8onqo8TR4c98VvyPwhDQ4F5LYXHCJOM8UR+0WldCYmnWUZgZhmK0lODgYURT524Ge8p/5ndV5XQXZ/nKS0IAu6b6zTtEhSAYMo5/BevhPOOu7qpYq1nrMGY9hGPtnJO++B2AqTgtyS3aXuLTmdMtgcFo0Xkh+aTh9RlGrTaVQjqW+A/QdDuLanWjanZS1O6gyyb26WrfYFD7IN/FBvgl/vcBVsa4Zz8xwPZo+CM+7eR08vrMZq1MCMZYdYizBSjvThEpma6pwWnoO4GxoaDgjYQHw9vbuXM8LCwvD29u1MJ6fn09iYiINDQ0UFRVRVFREW1vP61gOh6NzH41GQ2xsLPHx8URFRSEFTVH9j+2lX3SKjdPppKOjg7a2tk5BOS4qx//uaSZWUVHONddc2y1XX1840cS2LzufWs8otlX7s70mnFUNdpwKCLKCf1M7oTXNKhHyb+k9gLY/GLxseAXb8YnywychAd9hEfhE+eAd6YNPpA97v91L+WclqjIJxynfUUb5jjIiJkYy6cGpxMyMPa+8vlKi07lqyt0s3/G/zrYOSxvvrn2RHy357RnngxxKLh2xqVQn8MzbGoEQoUXwEgkODu41/1mC79m9RbaCt3A2qguCacIuQxN17Vn1exxB0qEf+Vus2S+oHQ/sLVj2P4FhzLP09m9WHB04W7KRmw/hbMp0ecgp/XwS1foi+Y1C8huJ6Dca0WtY5/pT3LGfnrA6Fb7aX8QeeyDLi83UWXo2dzVZFd7NM/FunolAvchVsQaWxhmZHqbrJjwmh8xjO1r4sKD7ulFEkD9/mJtArJdEVVUV+fn5HD16VOU63R98fX1V4uLl1XtNI0EQCAoKIigoiIkTJ1JfX98pKj2lNwKX8BQWFlJYWIhWqyUtJp5UusTG2bCb9d/8j5o2HR0dZ3bzttsdbPxuDdfccONp45JOhY8Gxsd4cHmMa+2rzS6zq8Z2LIWOnoxgb7JTu4K+DWabS4Bqmgk9JkIhtS1oHepFwXZvD8QgLWEhLUQHVuAX1IZXoMX1E2RGq1d/ZkT/sWgjLkcKjkEQdYRMCmXabdMp21bK7r/voGJXebexV+6p4Os7Pyd0TBATfxRPzCQN2FtQbI0otmYUWxOKrQnR87Yzfn/OlInD59Lc0cCWQ990tjW21fD+upe5d/Ev0WnO/2zZJ3JJiI3cXux6Sj+B3C0RSOO0GAwGfH19+d2eFtUCeKiHyGNjzs7JwV61DkeZOrBV9ElBl/LzAX2KEkQN+tTHsUkealF1tGM58CQ6/x8ASSj2NpzNWTibs5CbDyG3FUJPcS6nwCn6oAtKdwmM/ygEY8wZXYteEhjvK3NLkh/PTfZlW7WNr4tNLC+20GDteUwNVpn/5XXwcV4dMboW5gSbGOXdhr/QTHFtLVv3RZFhjkUgHOWEAMgfDPfkT5N8MWhc44yIiCAiIoLp06dTXFxMfn4+FRUVp1yH8ff37xSW8PDwMy6lIAgCwcHBBAcHM2nSJOrq6jqFpzfRsNvtHChUCIn0J8jQ5Zcd5NxJUcf4Ho/pKw2tbezdtIHJ8y87q35OxFsrsiDKwIIo1zqnySGzp9bOtmP52/bWQYlHCCXDQjqPEZ0yAY1teHZYafP2oNXHiOMEjzujYOFqzz3c7rWZaH3Ps0+56QDWpgOg9UUbvgCNLQG5TSEipYlrXvajYreVvf9roGJ/989XzcF6vn2gnsDYVtKvOkpseh0n+uxIhuYBeW/6y4L062npaOBg4fbOtvL6Qj7b/Bq3zn1wSMZ0plwSazbWvNdwlC/rfF1xxJ9Vz4/H8JA3qRNTKTVE8ECW2gHgXzP8uC2pf3Erqqj/lhws+x9XmaEEfRCGCa/0yVvsTOyniqJgK3jTlT/tGFYZdAK0yjqOmkXanf18gpU8ET1CEQwhCIZQmlrtRIRFYdAZMeg8MOg8T/jbiEFr7HPlwZ6u0e50sr6knjVFleyvqkF0NOJNMz40400T3jSjE2y99OjCpuioIpZaMZ6bRo3irjEjThuJ3dHRQWFhIQUFBTQ3N+Pn56eauZxp7rW+/h8VRaG2trZTeEym7rOzaM9yZoZ1FSBzKiLLSi7H4jz92AySiE9LHT6WDjp0HlT5qIOul0yZSMSosae/oB7o72fV6lTYV+fK67atxsbuWluf6wQBpGlLuc17C9d57lSVaOgrNfm+7P8mjvLM3tdi/aPaSL/qKMMm1CKK0BD0E2JGX9vvc/VEf98vh9PBe+tepKhK7Qw0afg8hgdOJTk5eUjG1V8uerFRnDaXY4Cjy1yx4bWRFFdGYrjHi0WLL+fa7QpFpq4b5PggLWuvDO533MXxMcnWBix7fo5iOyHXl6jFMO4FJJ/h/eqrvyiKgv3o+9QVfIjJKRGhV5vFMtsNbGr2okMevDgNVz0PIwadEQ+dEf0xIXL97fpt0Bmpr6vH4KWjub2e5o56mtvraWlvxNHfdaLToJV0RIckEhuaTFxoClHBCaes7DrUi66KolBTU0NhYSFHjx7tDFoVULgqZjVe2i4hympK4VBjGkajES8vL7y8vPD29lb97Vt0GO9Xn0I4FvtjkXS8n34FbYauhykvu4XrrlqCPrr/SVbP9v2yywoH6u2u5KIljVTLHhS0Ok4rQB6ClauMe7jdawsTDIWn3Lcn6op82P9NHKUHes924hveQfpVR/FfNJeYCXf3+xw9cSbvl8Vm4j+r/kRNU5mqfVzsPJbOHbpx9YeL3ozmrNumEhpLm5bijBCkuVr0ej2rWn0oMqnXav46xe+MA/wUp+1YKhp1Ukl9yi/6LDRng91hY0uzkbY2bxb6d/eAGuVlIdloZXuLJ3vbjD1m/j1brHYLVruFVlPPiTXPNXanjaKqIxRVHWEjIIkaooLjGRY6nGFhKcQEJ6HTnj/2b0EQCAsLIywsjKlTp1JTU0NRUZHL7Vo7DS/Wde6bFlTGuCufRavv2eQrHd6L4bU/dAoNgF52MKu1ghX6pM7aSO1aA9s//ZC5t98DYX1PcT8QaEWBiSGuTAhLPKpJSopFVhQqO5wUtDrIb3H9FLQ4yGtxUN7huhazoufTjhl82jGDFG05t3lt4Qav7fj2cbYTHN/KwocO0lDqw4Fvkzi6p7ujREuVJ5v+PRKv1R3cvc7RGYx6rjHojNy14BHeWPGs6nuVUbKB+KJkxsRPHZJx9YeLXmzsJzkG5G8PR3aI6IZrCYuO5b4D6gXa2xKNjA8+fVqRHlEUbLmvILfmqpq1MTegCRvcCGBFUcg8upM1ez9FY6vl3rDeXW31osJc/3bGeJlZ3+RNoUVHv/LEDzFaSYdGH0Cz4s9Riw8Nsh9ONEQKJSRpipEdPS+6H8cpOyipyaOkJo/Nh75BFCQiAocxLGw4cWEp2B3nT14uURQ7zXn5+fkkxl+JadvOzgcowdkBtRsg+prux+YewvDybxFOcoKw/t8v6QgZxvjNa9hHV0BrgU8ow954gfifPoESMjhF8fqKKAhEeWmI8tIw56ShmBwyha1OClrsnSKU3xrHX5uj+VPz9Vxp3MdNXtuI09TQLHtS5/Shzunb9Vv2oQNfRoWFsCA+nIlzAom5R6I+t449/9xF3jc5nOwq6ZsSOGRCcxwfzwDuuuxR/rPy/2Gxu2a3Rp03oX5nVmrlXHNRi41sqkBuPqRqy90SgRghIfqJbLGH0GLr+lR5awWeGn/mLoWebRtwtKizt0qBE9EmDHxdnxOpbChmxa73Ka3NR0ThrrAWtCfcL+2ygF3yxKiob8IBWic3hjTTrImi2DgNi+TX8wlkGaGjDaG9hY76WiS9hNlhxSrbMct2LIodi+LEjBOL0D+Hg54waI34eQXh5xV47HcQfp5dfxv1Xp1OCRaHwsZKC7uLqrk9fSkJPhrqWqooqcnlaHUOxTU5tJmaT3k+WXFSXl9IeX0hW7NWIiCQWD6KqSMuIyFyJOIQJ4VUFIXS2nwKaw8RGhGIIfJK7CUfd263l32FJvJKVS4xsTAbj5d+hWBTB91a7nkEx4xFkJ/PmHt+Stn/3qSWrkDSzaHJRLz4awyP/Rkl+PyMtjdqREYFiIwKUAfAKopCtVkmvyWSvObL+VtuI7uapV7Leq8phBcK7cR41XFzgpFbEvy5/B9XMvmhqex5dRe5y7JRnAqCKJBw28Csi5wtof5R3DbvQd5Z+wKBPqHMTLyOsICYoR5Wn7ioxebkPGg1+b40V3qhnadF0up4rdxL9UD/xBhvQo1ntpbhaNiLT8syVZtgjEKf+st+FTnrD+3mVtZlfE5G/haUY49iM33bCdOp12naA28jcsxtOCpXYCt6V2VWBPBzlDO27Qu0IYvQC5OQausRq0oRq8sQq8oQ6ioRThOJfxwZsEoCZo2IWSNiOfa7+2sBuyTiY3Xib3Hg7xTwiR+D96SF6MZMgz4mYTRoBC6P8SDR6ugs0x3iF0GIXwQTh89FURSa2mo5WpNLcXUOxdW5NHfUn7JPBYX8ikPkVxwi0CeMKSMWMDZhBgZd/9LanC0dllYOFGxjT94mGlpdOdJ2Fq5iQuJUJsk6PEWXo4RiqcZZvw1NyCwAxJJ8PF54HMGidjKw3vYAjrlXd76WtFpm33ALX332OY5j4m2XtKwJHc6Nf3kE25N/QwnqeybnoUYQBMKNEuFGiVnhemZrqvCOjOezIhMfFZg40tSzW39pu5PnD7bx/ME2JgXruCXRyNK/LGbyw9PY++ouZIcTr6jeXdvPNXHhI7hjwS+IDIyjvLRyqIfTZy5asVFkB/YqdXGmnM2u6aaUoqHSEI7T3PXEmuij4cepZ/aBcrblYz38Z4QT594aTwyjnkLQDvyH1Ck72JW9jo0HlnVOpwFi9Dam+KhvMFLITMy6yQiihDbqajQB07Bn/xt7y/eobAWKE3vNShzmFXjtd6AvcCKcgeuICHg4FTycTrolUzsd1d/D9u+R/QJxTF2AY/oi5DNYsD4RQRAI8AklwCeU8Umum3Fzez3FNbkUV+dSXJNDQ2tNr8c3tFazYtf7rMv4nPTEmUwZsYBAn8G7AcuKTHF1DntyN5FduldVNhiO/e/zvidDDGS8VxuTvTvwkBTsJZ8jBc9ErCzB4/nHEEzqBwrrDf+HfdGN3c7n5x/A1Bkz+H7bts62Gu8g9hiDmfKXX2B+8hWUwJBux10ohBklfj7Sm5+P9Caz0c7HBSY+KzJRe3I262PsrrOxu87Gr3Y1szjawC0/m8WCSD0lRf13QBhMEiNGDvUQ+s1FKzbO+p1gb+58bTNJHN0TihAqIgZIfNsRzInJnJ6d6NPvfFwAzubDWA7+Tp3zDAF92q8608UMJPkVmazc/QH1LeqoaIMoc2VgCyf6NQj6IIzCHCLXfYbh2zbEylKE+moERcbuL9A2SYs9TG0iUjwE2qZpMQ+X8N5lR1d37p0VxeYGdKs+QbfqE5wxiTimL8IxdT6K78CUyvXzCmKsVxBjE6YD0Gpqorg6l5KaXIqqs7u9t+ByetiZvZad2WtJihw94Ca2dnMr+wu+Z2/eZlXW396wyzI7Wz3Z3+bBJB8TE+R89Ec34vHKqwht6iJ7tqvuwH7VHb32NXzECErLyigp7cokvjs6jZjMdUT8+WHMv34ZJeDCFZzjjArQMmqSL3+Y4MPGSisfF5hYUWrG0sMzkU2G5SUWlpdYCNSLXB2s5W+D56h1SXDRis3JJrSCneE4bBLaEVocopZ8ocvHPtlTZnEfEm2ejLMxA8uhP3TLF6ZN+AGawIlnNvBeaGitYdWeD8ktO9DDVoWrQ2z4aE58WhPwPuiJx67f0FP4obZJwX+NDWusSNsELbKXWmgdgSJNV+gxFDnx2mdH0Achh8fQbPDCJywCtDoUrU71G4226+8T27Xa7vtqdZTu2UFieS6a7WsRG3q+wUqlBUilBeg+eQ3nqEku4UmfBrqB8x7zMfozOn4Ko+OnALA9YxMV7TkcLt7dbWYBnGBiC2XKiMvO2MQmKzJHq7LZk7eRnNKMHs91HFGQ0GkMWOzqwE+rIvJ9ixd724zMqPoXC1obOdG9xbboRmzX//CU4xAEgVmzZ/PF559jOuZmrQgiq5Onc8f+FXj85ReYf/UySsDgFkQUKorxKciE2JgB/f+ejEYUuCzKwGVRBlpsMsuKzXxcYGJ7Tc/xWw1WmXrbheNAc75yUYqNbK7pliImd4vLpUVK0bKfEJwnPJHeHWXvdxS8o24H1qw/gaL29NHG3IA2ZuBq+VjtZjYf/IbtR9bglLvbnPVaD65PTiLmpHruxiw7Hvtyu+1/IgJgKJHRl1vpGCnRMVLb7RNhiZewJBrRxl6HNuZ6yopKB8wX3xoYhm3KTGzX/QAp9yCabd+h2bMJwdLddVWQZTQHd6I5uBPF6Ilj4lzsMxYiJ41CUexI9joUR8RZFZA7TrB3JNPGzWHxhFvYk7uRPbkbabe0dNuvobVGZWKbnLKAIN/Tm9jaTM3sL9jK3vxNNLX1XIfnOAHeoUxInk164gzKSytplsvZfPCbbuMxyyJr8WT3VD0Lj7Ywuaodec7V2G69H/rw2TYYDMyeM4dVq7q8N9sMnmxMmMjledtdgvPkyyj+fUtK22ccDjR7N6Nd+xVSQRYJgPzdR1h+8jvk4aNPe/jZ4qsTuSvZk7uSPSluc/BpoYmPC0yqOk0AS0LOz4SiFxIXpdg4qr7jxPWI+mJvGkp8EIJFxCCJg3TdEOK9JeYH9W9twVG9EWv286Co7b6tPksIS/jhgKSiURSF/QVbWbvvM9rMzd22CwiMS5rJgtQZCId+pdqmaZDx2t/7l0MODEUOi0YOj0YJi0YOj0EIj8HDQ8ZW9DbO2s0nHWDFfvRdHFVrMHheiaIkntU1Nlllvj5qZkexlti2VmK8JGJ8RxB90ygib3sQz4Pb0Gxbg5S1D0HpblsXTB1oN3+LkLECU7oP5mFOQgUHpmoQdP4IxijEYz+uv6MRDKE9Vn40OWTK2p2UtjuP/XZQUa9lptLBvAgv5qUvZdboqzhcvJud2Wspry/q1kdfTGyyIlNYeZi9eZvIKd2PrPT+mZNEidTYCUxInsOwsJTOfiSxlinDL2Nc4ix25qxja+YKzDb1TKdFp+Gz4YGsTw5j7vRJjFaUPseMRUVFMXLkSLKysjrbckLiGNZUyYiaYjyeOzbD8Tv7eklCaxOajd+g3bAcsVntsCE21uHx54exLb0H+1W399lZ5GwZ5q3hibE+PD7Gmz11Nj4uMPPFURPeWpF037P3srzUuegyCCiKE/P2e1CsXU+MW99JIWdTFJqZeuTZXjwtzcd5zEPslWl+TBMr+/y0bq9chS3n75zsiG+OvpMdVSL+AWdXKdN1DQoZuduob6/ocXtMSCJXTLqDiIBoLPseRW47YQbjUAj8xoamtWt8bcNGoL38BuTwGOSwKNCf2uTjbMrElv8acnv3Gyu46qlowheiCZ2NoO2bq7jNqbC23MJHBSbWlFt6rP4JrtlWmFF0lZjWOYhtLCGuOINh1TnEWuqJsdSjCXNgGiFhi+r7TUhGQ6sURg3hHHWGkW0NY197CPtNITTLvTtxJPtqmBepZ16EgelhOhqbj7Ize22vJrbjHDexae3etCm17MvfTHP7qb3gAn3CmJg8h7GJ03vM6nvyZ97SVMP2Tx9lm0HApvS8dhTsF8H8sdeRGjtB9YDQ2/fH4XCwbNkyGhu7Agd1Dht37F+Jr7UDOTzGNcM5Yf2sP5Hn4tFctGu/RLNrA4Lj9JkiHCljsf7kt2c0oxqIiHiLQ6G43YFUd/qS7+dyXOd7Xz1x0YmNo3431kO/73xtt4p8+PAs7BYNhh95sT80mo+lsQCEG0UO3BBGaVFBn95ke+mXqnrpAIoicMC4mLV5B5B7eAofSLyNfiwafzOj46ciAPZtf8Rm26beZ4cdY57rJuiMHIbt5p+S4+FPUj/zJymKE0flamxF74C9lwBRQYMUNAlN2AKkwIkIYve4h/31dj4qNPFFkZnGXhJs9gVPwcyNXtv5gfd6ErSnX0DvDw1OLwrtYRQ6wii0h1FgD2eXJZlWRb3apRNhaqieeZF6pgZaaa/5vlcTG4BF8aCZQEKoQOzFtU8SNaQNm+iaxYQOP+WMUfWZN3fg8dyjiMU5lFxjYIfsRUa7EUcvBcciAoexIP16EiNHdZY+6O0z39jYyNdff60qbR3RUsuNmesQUXBGDMPy5N9QfPy7j6snTjKV9RfF2xfL//0K59j+RcmfrzfiS6GvnrjozGgnOwYc3R2K3aJBCBARgkUOCV2Bag+keaHvgweaoijYiz/EfvQ9VbtdkVjrnMyh3IyBGXwvaEQt00YuZtaoK9FrDYj5WYgr/kbHyHI4Ic2+vtSJR54T2S8Q29J7ccxcDJIG8vP7fU5BkNBGLkETMgvb0fdxVHzTzWyI4sBZtx1n3XbQeKMJnYMmfAGVQjyfHbXwcYGJvJazs3XHaWq4x3s9N3ttO2VV0FbZA4NgQyf0090aCJTaCZQKmERBZ5tV0bDZnMY3pol8ZxpLu+KBTYbNVVY2V7kcQkI8pjA3fDrjdEew122mptE1E2xXvNnLXA4zARkN/tRylfIuvkLXbCHYN4IJybMZmzADo6Gf7vFWMx4v/QrpqCuTeUiOnXmT25nobWJ7qycH2z2QT8oIUdlQzLvrXiQ2JJkF464Hep8VBgQEMHnyZLZv78o0XOkbwp7oNCaXZSFVFmM45jSAj1+v/ZzKVHYiit6AfcZi7AuWUnUog/gV7yK2dmW3Ftpa8Pjbk9gW34TtxvtA072Mtpvzn4tKbGRrA86Gnaq2nC3HY2u0WAUNece80Pz1AvcMP/1isqIo2Av/g71UXSqg2ann67ZEqlsH1/9+RMw4Fk+8lQDvEISacvSf/hvx4BYartLBCdmVRZOC9z4J29I7sF9+02lNZX1F0HqjT/4p2ojLsRX+F2fDnp53dLThqPgGR8U3NNrDaGqfRnvHFKBn+36Cj8RsXwu+fv6d6yVlHa6iagIyswxH+KH3OuYbM085vgPWYbzVNp9vOibiRCRGU0+CtpoETTXx2moStNUkaqsJlk5fKfNE9IKDhcaDLDQexKJo2GQeyTcdE1lrHkOH4npva80ynxTJfEISkMREr2qc9lYOWuNwnhCV30QIX/AjrhfeZVb8MCYmzyUmJOnM1r1sVgwv/wYpr+t9MRQ4aR+vx1sjsyigjck+JrYr48isLutWNqGkNo//rv4z4X7xeAXcQ3hgbI+nSU1NpaysjLKyrsSPO2JGEdNURXh7A1JFMR7PPYL5Vy91O7avpjI5OAL7ZUuxz1gMnq7cbm0dNszP/gf9v/+E5rDayUe3+lOk3INYfvo7lNBzm7/NzdlzUZnRbMWfYC96u/N1U4UnX/x2CiBg+KEXByOi+FBKB+CXY715Mt2n174AFEXGlvcqjooVqvZimyfLGoMwn5QKRCvpmDB8DuIAZAxoa2lj0qjZxIYmQ1szumXvot2wDMHppGWGFkuC+hxetemw+LEeF28HcnpclL2LKI8iHNXrUEw9rymdyDZLCp+3T2WFaTxarauy4y2JRsYHaSkoUJsvFYcJS+VabGXL0Vh779uuSHxrmsBbrfPJsMVzqrxuetlGjKWBEfZy0oVikjUVxOrqCPJoxdNoRvSWoR/xVWZZywbzKL41TWSdeTQmpe8u8/56ga8WBjE26Mxy7xXkZDNy5TtoDqofqJwJqbTcPBZ7RVdpCcEQTvuIZ9hwYBmHS3p+QBAFiXnpS5k5ckmPZSFMJhNffPEFFkvX59zX3MYdB1aic7pmrM7oBA7f+DPi00b12VTmGDkR+2VLcY6e3G3xv/OzKstoV3yE7sv/dsteoRiMWO95FMfU+ac8z/lqYroU+uqJi2Zmoygyjiq1Cc2VMUBA8BMQwrpMaJ4agR+POPWsRpGdWLNfxFmz4YRzwO4OPzY1GlBQC02QbzjT469hwpiByb6an59PrH8M2m8/QPfthwhml9eROU7sJjRa//ko8x4fkPOeDqcmgELfcXxcezmHm7KYq9nGNcZd+Evd668ATDfkMN2QwwvCB2iCp6MLX4AUMFb1VC+bKrCXL8dRtRacpt4/lFo/pIgraPRfRJzNjx8d8x4ra3dS1tBKQogv0Z4SMV4S0V4aoj1FQs0NaMqrEEvbEEubkUqrEWrKEY498SsCOD0FnL4CDl8Bp4+ALVzE6dPzgruHaGeJZwZLPDMwyzrWm0ex3DSJ9eZRWJRTx4Y0WRWuWFnH5zMNTIswuuKN+upp5XQQ+9WbaHLUJltnbBLmR59Do7Fhr1zeWWlVsVQRYC/hlrk/o7KhhPX7vyCv/KDqWFlxsi7jc/LLD3H9zB/h762OozEajcyaNYvvvvuus63Fw5tNceNZWOCqqyOVFZL8znPonI4+m8qUiJ5nUypEEftVt+NMGYPhtWdVcViCxYTh9WexH9mH9Y6fD9gs3s3gctGIjdx0CMXcFfnttAsUbHe5OEspWmyChhzB9WW6Z7gnAYbev+SKbMN6+C+utYhj2GRY1RxEdrvEyZ5oI2LGcd2MH1FW0r3s7JldjEzAoe0Y//UbxMbarmvyhLYpanu14DkM7eiHBua8p8DkkPkw38R/Mg3kdBwfUxzriOMPjTczzyOTG7y2M9/jUI/rJpJiQ6ndiLV2I+gCydHNYHNDKDPK/ksaB0557lLi2SwsYr9zCs5yLZQDqF1+PTUw3FfD/EgD8T5Sl5h5huIMCsU5dlrXzlYzYvlRxNJCxLJCV9BoWSH6imMBjYDDX8ASJ2EdJuL07k14bFzpuY8rPfdhknWsNY/hm46JbLSMwqL0PHsxOeGKjWYWN+zkx1XrmN+ajYckuAJeNdpuga/H/xbaWvAqylb15Ywchvnx58HTGxHQhM075vbvwl76OVLwdCICY7lzwSOU1OSxLuMLimvUVWtLavN4dflvuXLKXYyJn6Z6EIiNjSU1NZUjR7oKdx0OS2RYUyXJDS4Tm6GhusdrhRNMZTMvB2P/UzfJSSMxPfsfDG89j2bvFtU27ZaVSPlZWO5/Cjkmod99uzm3XDRic3IpgeJ9IVg7XF94aYSWTCEEhyChFV2OAb2hOC1YM5/B2dj1BNnskPiiPpC6k6KIBQTmpV/HrNFXDkzaEllG2rcF3bL3iC1TrwUpArTM1KHoThiDqMWQ9ksE6QxLIvSBeouTN7M7eDO745g3WffrtKFltXkcmcJEjobaudVvH4EtG7uVWug6oIEU2zJSTjER6NlU5jj20xMaVtS2AC3EeEnMj9QzN8LArHA9fvqTxqz3QE5IRU5I7WqTZYT6asTSQpoy9xGME4/6aow7qnA6a7FGyViGScjePZvcjKKNazz3cI3nHjpkPd+Zx7K8YyKbzSOxctKCtiCwOmgsq4PG4uG0cllTJlfVZ7CkYT8h9lO7R3cONzQKyxMvgrdfZ5s2+jqV2MitOcgtR5D80gCIDU3mB4t/RXbpPr78/r9YHV2zUavdwhff/5vcsgNcPfUePPRdM//JkydTWVlJc3NzZ9u64dMJ37sMb1vPtWNcprLrjpnKzvK74emN5Wd/QLNhOfqP/qkqmSBWleLxzE+w3vozHPOu7lMAq5uh4aIQG8XWopqFQJdjgOAjIEZIHBJcs5xbE41EePY8q1EcHVgOPoXc0mVzLjLrWN7gj+UkRyyD1siNs39CctSYs78A2Ylm1ya0y99DqizucZeOdCP2UPUgdAk/RPSKO/vz98DRVgevHm7ng3wTZmfvy3qeGoGrh3lwS4KRmeG6YwGE0cC1yB1lOKrXY6tej2A9daT8ceqcPrzXNpv322dT4+xezKovlLY7eTvXxNu5JiQBJgTrOmNlxgVpkcQebkiiiBISgTMkghrfMHxOsF3LsszX2fX8OdOMZ3spVxn3cJXnXiI1PReH8xStLPXcxVLPXZidOt5sW8CLLdfg6OHrZpb0LA+awPKgCQiKzJTWAq6q38fVDfsYbqrqcTVKDgrD/MuXuq3PiV7DkAInqpw47KWfd4oNuFLTpMZOwNEucaByA/kV6hIcWcW7Ka0t4PqZ9xEf7hJjjUbDvHnz+Prrr5GPrZ9YRYnV6Yu4YdfXnWPst6msPwgCjvnXICeNxPCvPyBWdeVxE+x2DO/+DceRfVh+8Hins4Gb84uLQmwcNRtUaWNaajyoynHdqKQULXZBQ44QgijAQyN7/iAq9lYsB36D3OZyE1YU2NlqZHNL9/1D/Fw1JQJ9Qs9u4E4Hmh3r0X3zPmJ1WY+7KJIG8+Vz6AjaobLeSQET0ER1L5h1tmTU2fh7VjvLS8y91gERgDkRem5JNHJljAFPbc9Prq2aSP7ddh2vlyxghJDDDZ7bWWLch6do7bbviV5ltpNnAmeBU4FdtTZ21dr48/42fHUCcyL0zI80MDdCT7RX718BRVFYU27hjxltZDXacX1d4jlgi+ePzTeSrjvKUq+93OizF2+lZ+HxkGw86LeSO8Ud3F9zH1t0vVdrVQSRHb7J7PBN5tcJt5JkquLKhgyuqs9gWmseGkVGDgp1CU0vmZi1MTeoxMZZvxO5o6xbUlgPnRd3LniE3TnrWb33YxzOru9Pq6mRt9c8x/S0xSwYdwMaSUtgYCATJ05k165dnfuVaz3ZtfBOhpcexjhu6hmbyvqDHJOA6Q9voH//H2i3rFRt0+zdgvFoLpaf/g456cLLinyxc8GLjaIo3UxouVsiXXYnXGKTJQRjFySuG+ZBgm/3SxadLZgzXkDpKAHAKgusbPAh19zd0yht2ESWTv8/9Nr+J+7sxGFHs3UNum8/RKzruR6FgoBj8lysS+/AVPxHMJ+wDqL1RTfikQFJiwOu93BdhZVXMtvYWt1zMkIAH53A0hAbT0yLJrKX2SG40tH863A7b2S302pTAIFtjGCbZQS/bryDy40Z3OS1g1H6Sjo8R1LicwXNumQWCwKLz/AaMktryLR5s73GesrKBi02hWXFFpYVuxw8kn01zD0mPtPDdJ3CuaXKyrP7WthT17PrrkYUGZ8wmhtHTyfUQ0BuycZRuwVn7ffdSoID+Ps08XHwW3zn/Rj37gs+uRBk9/5lB3ZBIsMrjnqtNzsDRpAm15McE0b03i1g9EIxenX+VoyeYPRC9ExB9E5EbjseM6RgL/sKfcqD3c4hCAKTRywgLjyVz7e8TlVjiWr7tsOrKag8zI2zfkKofxSjRo2irKyMysquz+wuC9gW3cG4ceNOc0UDiN4D6w+fwJk6Dv3/XlLV7REbavD404PYrvshDJ9w7sbk5rRc8GIjt2ajdHRNqWWnQP62Y4GbXgJitNTphfbwqO5PXbK5hqDaV1AcLjNPo13iy3o/6u3qt0YQBC4bdyMzRl5x5jd5uw3NllXoVnzYa5ZjRRBxTJlH/phZxEydhTX7byhmtSDpR/wCUX/26fZtToUvjpr5R2YbR5p7D76MNEr8NM2TH/g1Yd65meDydORhyaBXC269xcmrWe28md1Bu6Pn26lGYyAu4TImpi2lsayI5KQkBqIG4ljZQVJSECaHzI4aG+srLGyosJJziusCyDtW1/6N7A50IkwJ1WMy6dnb0vPaiSi4Soc/MdabmBNmRZJfGpJfGkrSj5FbjuCo3YKjZjPYu7ILKNZ6LrP/jlXjfsSV+8dx8lu0tG43D5avJtZST6S1EaknSSrp3nQymkQdrdO7ZpuO8lV4bapF1Pt3ClOgyYroISFHxhHiF8GPlvyeDfu/ZGvWys5CfAA1TWW8/s3TLJxwE5NHLGDOnDl88cUXWK2u2aksy2RnZzN69Gg0mnN7O3FMXYAzPgXDv55BKs7rbBdkGf3nb5IQtxXh4T8OSC43N2fPBS82jgr1rKb0QBDmFtfKs2a4FocgkSMEc1mkntGB6oV02VSOZf+TaI4JTYFZxzf1vlhPyjPloffkptn3n3nBIpsV7aZv0a74qFf3UEUUcUxbSMsVd/CXKm/WHG3h2rWr+Jm0RrWfJuIKNEFTzmwcx2i1ybyT18HrhzuoMPU+DUj11/DgSG+ujzNgXPMpuhf/7Yp5+OZtFFFEjopHThhBZcwoXiaF/1ZoMPUiMr46gZ+kevHTVK/OBfueDU/9xOlAqK/Gs6wAIcAXY0Aw8yMNzI90CWFFh5MNFRY2VlrZWGmhydr7nMImu2Y0vUXXXx/nwZPp3p0VQXtCEEQkv5FIXinoPWbTkvsCGvGE+jiynVENr7Jb9meW8gztYldKnK+CJxFnruW5oo9OETl0egyFNtrH6LvKRogKdtNOvHZ0CW8MwMr3kP2CcI6cgGbURBamLSQpajRffP9vWjoaOvd1yHZW7v6A3PIDXDfjPmbOnMm6des6t5tMJlatWkV0dDQBAQEEBgZiNBoHbOZ9KpTQKMy/exXdZ2+iW/2papvP0Wzkp36M5fHnkaMGZ23TTd+5oMVGcXTgqFW7Qx53DACXF9oRIRiboOEXo9VrL3L7USwHfo1ia0JRYFurJ1tbPDk5QDDMP4bb5j3YLQahT1jNaDcsR7vqY8SWph53USQNjhmLsV15G4WGEO7a2EhWYzthUiu3+/1HtW+BPYwb911FVH4tib4aknw0JPtpSfTRkOCjwaA59Ze7yuTkjSPtvJXbccy81TOzwvU8ONKL+ZF6BFM7hn/+Hk3GVtU+gixTVdPICzp//uNIwiJ1dwkHVyDjA2ne3DfCE1/dWXgltbe6ylRXliJWlyJWlSFWlyHUVCA4HZ2zI0VnQA6LQg6PQQmPJjYshrvDo7lzShROnT8HG+yuWU+llT21tm6zi55YHG3gN+N8utW8B6Ct2VVC+9h4XL9LEWorEZxOPAVoH6/BlKb+qoUOayKj4XEua/89JXSt/b0UcyXtGg/+mfc24mmNbT0jKGA84qB9Utd4TSkSnlkOTvZKF5vrEbeuRrt1NYogkDosmZi0dL4KauJgvdpFurDyMP9c9huumfYD4pKSWVdQT54QRAsGAmtMhNeUEKFk4Y8Zg15PYGBgp/gEBgbi5+eHJA1CBmeNFtut9+MckY7hzT8jtHdlixCb6/H404OYH/kLcmLaKTpxM9hc0GLjqNmkKlzW3qCnIvPYlNkoIMa4TGhTQnRMC+vys3W25mI58BtwtGOVBb5t8CG/h/WZ0fFTuWbaveg0/SzkZO5Au+5rdGs+7VY18TiKVot91hLsS25FCQxlebGZn31XS6tdQUDm5cD/4i91xZLYFIkH6n9ErU1Hbb2djHr1WoIARHtJJPlqSPTRkOSrIclXS5KvhiKTwCtbm/ik0NRrtmVRgGtiPXhwlBfpxyLcxZJ8DP94qtu6Uo3Ghz/FXsubkfOwiT0/5YfYWnikbAU/Mh/E2JiAs2IEzoTUHs1vnTgcCHWVrht2Vemxm7frd2/v48kINktnwbWTkf2DmBYew5TwGH4dFk3z2Bg2SZFsaPNgfaWV4pNqmMwO1/PbcT5MDBAQaisR95V2Exah49RpcAQFvPc60DTItE7TwgkPBJ6BFrYYf8udDQ+xxdk1a/53xHw6RD1vVn2KFBiCMzCEMo8QNjaJVLbZ8XGY8XWY8HN04Osw4+vowM9hcrU5TWgUGY98Jx1jNZ2u8opBwJwoYcztfSYrKArS0Vx8j+ZyD7Av0o/Pk/ywnJBE1Gzt4OON/yBPGM8G6UrsdP9uGBQ74Y42IqpbCa9qJkIpI4w2dIKCv79/pwAd/+3hMTBBmc6xUzE9+1/0b/w/NDkHuq6row2P5x7F8vM/uFyx3QwJF3S6mqjmV05YCIWMr+PIWOYK7pLStYhLvPiDtID3Lgtl4bFKnM6mQ1gOPQVOMw12iS/q/Gh0qDVXFEQWTbiZqamL+mUKKMo8yPDCA+i++xyho63HfRSdHvucq7BfcQuKfxB2WeHpva28erirZvyPvdfw+wC1SeDZpht5vfVMl897x0MSuCPJyAMjvRjmrUFoaUQsLUCz6Vs0+77vjLQ/mTbJwHf+o1geNJ5VgWNp1LpmjuHWJh4r+5b7KjdglLs7G7jMb3HI8anU6DwJkZSuWUqdazZwrlG0OuTQKAoiUvnOfzS5Dj3XitXMqd1/bFxV3VKmnAl2f4HmuVrkk4JEFUXg2cZbeaNdnX7lyhgD/50T0JksNj8/H2NEPG/ndPB2bgcNPWXRVhQ8nVaiRDMvR69gtGZj5yZR8cXbdCWiyYQ5Lwuf0nwEW+/JTQGa9BIfjAii0L/7A0KLEsB33Eg1p3dzFhSFYDoIV1qJUNoIp5UIpRUfrBg9PDrFx+FwMGnSJLTas/BIlJ3o3v8HuvVfq5oVScJ6369Pm+amJ87XtDDna189ccGKTfHhDQTX/LXztSLDJ09Mp73B9ZSkv9VIdmIU+4Kn8P3VwQiCgKNhL9bMZ+iw29nR6sn+NiPOk8xmRr03N895gPjwEX0fjOxEu+IjNN98gGTtOchN0Ruwz1+KffGNnbVAKjuc/GBTIztrXTflEKmZB31WcIf3ZrQn2DvySOMX7Y+T3yLT0Re7Tx8I1cr8MrSZ23SV+FQfj6Yv6NXcdyqcCOz1ScCByIS2IvTKua1qKPv6YzF44dHWiGDqOP0B5wjZN4AO3yAMMfEoQaHIQWE4A7wxt3+Fs+Nwt/2/NM/m0dpbVa7f8yL0vD8/AKNGVN0MLA6FL46aeONIB4cae/aYC5Oa2BH5S1VGB/2o36EJnu7qa1gsUsFhpMzdSFl7kUp6zg4uA5uifVgZ74fz5BglBcqtY1muW4pT6L9AGBUbEUor4bQRobgEKM7gYNLECQwffuqSC6dEUWj770uEf/+NulkQsN3+c+yXXdfnrtrb2sk+mMWEaZMQzjZAlfNXINy50XrB2K4O4izPCuwUGgwC4jANh4QwfjHKyyU0tVtpOfQcu1p17G3zxd5DsamIwGHcOvdB/Lz64b1iasfw+h+7JUc8juLhiX3BUmyLblBFe2+qtPB/m5uot8j4i+3c77OKe7034CGeNBvQeDFm0q/YZAhGURQqTTIFLXbyWxxdP60OytudvVr4/e3tjGkvYXR7KdNsZcyylRPcUNqn4lV9QUJhcmvXDFPx9EbR6hDamgdspqJotcihUZ2VRY9XGpXDosHT2/VFSUxEaG1C6DRzlXaZ4QZodtJ9XK5Z0fE1IrlzfFFg9KKghy+wXpmKvfAd7KXq2et1HptJjijj7pr7qT4W0Lqh0sr13zXw8QL1Z9KgEbg9yZPbEo3sqrXxxpEOlpeYOTH+ttrpz9cdk7nJq+u7UpHzKYG+U1wxVFodR6NH8f/bO+/4qsrzgX/P3St775ABIYO9p4CAiKIi7mpdWLe2tXW01p+jrbXUOorWUVfdAxUUEWVvkB0IkASyyN65e5zz++NCwiU3k6DEnu/ncz733jOevOfknPc5z/s+Y41iIKvCF3CwqJrR1fuZVb+PmfX7iT7hSacAppc2M6jBxn8zw6kynuJoI0C8bg+P2nYSbItnueZ8vjMMQupmRg2roKFACKeAtuJoIS4rIzYd5/zcY8yfPIKoqF7EswkClVPnEZo0AM17L7Za6IIkoX33BYSWJpyX3dhhxgGnw8mBNRtRbfqWkaU/ME3ykPdpCq4Ft5IycbycqaAX9EvLRvLYMa+/GoXUNgTw/b+GULTTG+imHKJGOc/EW8Gz2HR5PI7jK9j8w3/Y1qxv52l2kmGpE5k3/kbUqu6nfhGqytA/9wcU5e39USWDCeesBbhmXe4T0SxKEov2tvDX3S0YBRsLA1fyq8CVHdZq0Wb/AVXk5C7bYnNLFDa7KWhyc6TJRUGTG0/pMe7c+QZT69u/RfeUYm0Y+0xJ1KuMzGzYT6yzsVvHScYAbwesUmNubqbcA8eDoigLjMSsNZBWW8qMwu1oTwQVisHhp5SrTkCMTkSMTfQGMXaStLLrAl4u77xL61xQaevcUFfzLuCd7xFjEr1K5RRFJ4VFdZqOpbN2uavW4zj0LHh8//f1YhC3VN/OdkebU/iwMDV/T2tidGbH55jf5OKVAxY+Pmql2eV9rMMUzcwx7KLGE0SNJ5AaTyDHPWFICGiVAvaO3gUkiSGWEmbWe5XPpKbDaCU3ToXAV6nBbIj3X6E1wOFmUp1IdOgotiRNZoUmhdwGN8daevfSkSg1MCfMyT2T04kP7VlmgJPXXrVlFdrX/tLuxcc1/RIc19/bel9Jokj+7gM0rf6GIYfXE+Yy+xPLoehMAq5dSNDQ4b06p3PVGpGH0fzgqliJM6+tjoatRcv7v56I5PE+9NqrDBwaGMfQiVNJa3iDjQW7sYr+O4RAQyg5cROZPeHyHpnsyoO70P3rsXZzM5IxEOecK3GdfxnofTNL19k93La+gU3lzdwYsIa7Ar8hVOn/hnYrQzFm3oUqYmK329SKy4lm2Xuov3oPwdOzIS27oCbXGM8+U+KJJYl9xkQa1UYMKoFhAW5uyg5lAaVo92xCuXszyjL/5aPbNUuhpCQ4hsLQOAqVMVjdOoRQBaGBGuaMGo5xQDroDV3KcXvc1DSVU1lfQmVDKZX1JdQ0VKLT6VAp1KiU/haVn3Ua1Eo1OruTgMZGTA0NGOrr8dTVEZaWgyIu5YRSiQdd1+3yR1cPsGguwr7/cZ8ksgBuScmf6q/mbfM0TnpIphhE7hkaSrXdQ7VNpNrm+9lXQ6ynMjhYxfQ4HTMjJCY3HkJ/cAeq3B84bK/ig4wwWrT+B0e0bpHx5WYmWTQEDD+P5hFT2RuYQm6jm9x6F7n1Lg40uDt0lT8dJSITgpwsHB7FBYlGNN0oC3HqtVfu24buxcfazVG5xk6j+MKbKf7uO5L3fE+q2X+QtT8Kk0cQfsNtKFMzun3M6e06U85VWf7ol8rGtvM3iE1tWWj3fp3Ejk9PXCQt6H5tYrtByyDNVloc/i0Goy6QqUMuZtTA8yg6Vtyji6xa9YXXFD9tWMYSmwy/X+S3XvqOaicL11YzVVjDvUFfEa3y710laEJRJ19DkTWN9IE9mDc6gSI/F90bf/drbZ1OuSbYq1CMSew9oVyO6GPwnGJB5ISqW5NajovS+C2hLdRUoNy1EXasR1twAKEb5bElCY43h3CsKZyy0CgaRyQye+GlREb6pmGx2JuprPcqlIqGEirrS6ltKscjnl1HArVSw+CkkQxPnUhKTJbfei/doTsPsORqwXHwGb+F6T42T+Dh+us7zCLdHZR42hWVMyocfGoez1p7jt9jInQKzo/XMS9Jx6QYLQFqhddbsL4aRV0ViqIjePJ2UlFxmGqlh9xwPQfD9O2GlxSixIhqC9NKmonWh+EeMw332GmISemIwLFmD7kNLvbXu9hf52RtuR2H2LkiCVZJXJFm4po0A8PD1R2+JJ5+7RUFB9A/+xCCpYUWhZa9piSMooOh5pJeu5kDHM+cSMh1t3Y7ludcVRCysjkN0VyEbfvtPus+fmgCzVUGJEHCNceMZUwlHsG/ktGpNEwaMo9xg2e2ppzp9kV2u9G+9yLq1V+22+QaN4MDU+eTlunryy9JEq8dbGb3wRXcG7SMRFUHWX1VAWiSr0IVdxGCUtfzf7zNiubT11Cv+sKvB1muIZ7dAck+yqVW034oJNLZxPRgN9NGpnJerI4og//iVqIoUl9fT2VlJRUVFVRWVmK329E4HCQVl5FaW8YAdyU6RfcsK48oUGEPoT42kcYxcRwO8VDaUkGLrbH71+AsEWAIZmjKBIalTiQqpGcVIrv7f5QkD65j7+Iq+qDdtlx7Al8cGk9MQxNWpZZGlYFGlYHmE5+NKiNNSj2SBmJ0DV6lcnJRVZKsru6wXPY/Gy/mH03zkFCg8zhJdNSSZG9bEu21DHDUkOasI9zegKKTF4m8UD2fDQyhTu/fUSCjzsb0kibSGh1IkbFexTPmPMTEtFYltTsvn1xlLO8cbGRHN3xVBgapuDrNwJUpeuJPy3N3+rX3uN3kLf8W96qvGN5ciNGPt+SpNKiM7B04mYDpczhWVUvk+mVMqdrjd18RgYZR09FdeTNSVJzffTpq15lwrsryR79TNo78V3CXft76u6ownKVPDcWZ0Yx1ehWeqPZJHgHUgsS4tNFMHnWzT/p06OZFNjeh+9f/ocrb3b5NCxbiuuha8k+rPNnscPPWppVMdX1MmrqDmh9KA+rE+agTLkNQtbWrJ/945d6taN961qf2zUkq1UHcM/BGPg8f7XdSU+1xM7L+KNMaDjBDOE76tVfiiU3C4/H4XYqLi3G73VRWVuJwOJAaJcTjbsRyD+JxD2KlB070awpBJCm4jvSwKgaGVxGk8++p5w+PBMd1OgoiNRQGazkapMPeQcLPH5PYsCSGpU4iZ8A4THr/8xan0tMH2F2zCcfBReDxvVaCXSJ4nQt1lYgnoK3Qm/dTgTtIQNL1btLaVq5Dt0Ek2t6z0tn+8CiVrE0K4ZsEQ3vPtRPENzuYXtLMkForSgnE6ATcY87DPWYah21u0gd656qKmp0s3lbKF2UiNXQ+jCkAk2O0XJ2qZ16yHpO6zXvv2MF8ar77hsEH1xJj7zxvhUtQsjN+BM4Js8maPhmtzhtHlJ+fz4DUNFZ8v52E5W8yseGQ3+M9CiX2SXPgshuQQv0nSz1XFYSsbE5BEp1YN/0CXN6HQpLgiyUDKYx14o7z35EpkRgR6GTqhPsJivaf5qWriywcL0L/z0faBTdKWh322/+IZ8QkHzmSJHGsaAvN+W+RrirxJxIUWtTx81AnXYGgbt9pdesf39zotbS2rvK7+Y3oqfw+9Toa1b7KNbymibTCSlILK0guqkbjOjXJJwhGBYJJQDAKrd8xCggmBYICxAoPnnIPYrkHrN29fSSiTM2tiicmoHtBmicRgXKTmsJgHYXBOmpiogmMHkB0aCLRIQnYmtwkJSXh9rhaF4/oxnXK744Wp82JrdCOPd+Fo9CNrdqG22THE+7AHe7AE+bAE+YEbdtbvUJQkB43hGFpExkUP6xDx5IePcB2K6o9W2DvN5gj9+MJOq2zPpmGu4NO/ExQ1YsEr3ZyShzxGVEZGMmLg0ayy6hBgx3ticX73YYGJ2F2J9NKmxlTYUFz4twcIRGoIqLbCsip1LgVSgrqLRy2KjiuCMKs0OFQqLGftpxch1rDiBgj2bV5ZBzZSmZj13OKBwxx1KlNDFbZMDzwZLsSCaf+H+tsbj5fuoFJG/7LqBb/st1KNZ7zL8F90XVIgb6lMs5VBSErm1MQbRU4cv+C2JJPqV3NusZAypz+JygVSAwx2ZgQCpGjnkIZ2HFq984usnLvVnQvPeGTWRa8NUXs9/8FMSHFR05KuJXyA28Q6vRfOExEhSZuDurkq1FoO3axPnjwIDExMdhsttbFarV6v1utRB3cxcjc9RjE9pZcoS6SOwbdwuoQb1S6yuVm4JFy0gorSC2sJLjJfwnns4WgEAhOD8YdZ6Uy4BjOODOmQAsD6+2kl3pIbXEQquq+1XMST1wynoxhiIOGkq82MWD4qC5dUiVRouFoPZV7KqjcXUHVnkpqD9UgurueZ/IEOvGEO73KJ7xt0YSpyU4dw7DUiSRGpvvMIXT5ADtsqPZsRbV9Dcq9WxFc3qEdUQ3Nk9Q4EvsmvYvCJqFsklA1iyjMEtbBKiS90G6foDVONDUddwkVmmCKdeEUa8Mp0YVTqg1jQc02pjT5f9P/IHI8v0u9jkrt6bWJRDQ40GJHL9mIdFhIsDQT72jk5oq1jO6gE+9LynWhHA5JIbGhmFR7W70lyRSI7bfPIKa0Tfz7+z/uq3Xw1ZLvuWbPB+RY/FfpdWt0iLMX4JxzVatX6rmqIGRlcxoNLTUs3fgyBVWFHe6TZbAxKchCqDEQ3bC/dFlgzO9FliTU33yE5uNX2s2BeAYOwXbPExAY3Lau5SgN+55H7/CvZDySgCN8BmEDf4FCH+13H4vFQkFBAfn5+TQ0+A5YS5KEVCViLGhkqmsfg9XtvWY8CPwz4UIeT74cm1JLUKOF0TvyGbmrEIOt8/HpvsQUE0D0sGiihsUQnBnIYekHfihei1vsOK4nqtpE1n498fXVJBjqCDf0/BVbUmuQgkKRgkK8n4GhONUmGpsU1FSIVBY5KM2z0NAg4PL0XYiZpBbxhHoVjzpWRWL2AFKyMtFHmaisr2LUqFGYTKdkHHfYUe7bhmr7WlR7tnQYxS8BliFKLMO7GSzpkVA1n1QqEsomsfW34rRL7zFC43QN7tDThiZFMB2NQiMNRAqPRgyLosIQwQZ3CF9ZAvi+WmqfV0+S+EXVRp4pfJ9IV/uhuCalnj8NuIKX42YidiP+RiO6+HL/ImY25Ha5b08xK7XsTpmAeuoFZE4YhcLjRvfKn9uVnJa0Ouz3PYUny1umoKOOWJIkvjxqZvvSb7n30Cek2f1nc/foTbjnXo1r5nzyS4+fkwpCVjanYXWY+eenv8Puav92rneHMTnEzIiQEgRtBLrhf0Vh6HpCt91FdjrQvvUs6k3fttvXNXUujhvuB1VbByCai7Ds/A0Kj3+LYa9iPMNG3IwhMKHdNpfLRVFREfn5+Rw/ftxnm2QW8Rx14znqxlXkJmlgHZcH/YBRaq849hgTuS3jNnYFDCC5qIqxu/PJdFehGaBEkaQCSUIyS0gWCckstn5i8a7DIiGaxdb5lu6iNqqJyokmangM0cNiiB4egynKhM1hYdOBFWw5+C1Ot/95tGBDBGMGTyMmNJHo0EScNg8rvllB875GtHubiaurJjGojsSgeiJN/tP/9BanR4nFqcXs1GI5ZTE7tVhcWuxuFQ63GrtbjePEd6kXuZiFAAFVipqsywaQE2cl5OAujAf2oHD6vyanIkbE4B4zDXt2BLa6D1qHjwVNKIIhAYUxHoUhHsFw4lMXieARwWoBSwtVG49QuGQPLfnH0ancaJUu76fKhVIhYpY0RMxrJDS7vfu9GDwX0/A7EQRfy8otSuyscbKq3MGa43Z21rpaR/dCXGaeOvoRCyvW+PXu2mVK5q6BN7MjMLXLc9eKTr7Z+7cOLaaeICKwOzqHlnGzGDxzGkaT8bQdPN7nfd3XPqslpco7TD7mvC47Yqtb5F97Gqn/7msePPY5CQ7/c0NiYAjlY84ndPQkby0i44m6RFp9r8pny8rmLLN275es2r2k9bc630RAYRwBM8K4LPlr9KYwdMOeRqHvXuTxqRdZaKxD9+KfUBb4BkJKggLntXd501ycNlRTvfP/MDa1zyCwyjYUIfl6Ls7yLU0gSRJlJWUc2pVHyaESXI3O05SAhFjrQaoWseo11I0I5NagdYyyHmv3N+yCmieS5/NC9CxyisuZ3VTACH0xkZoajB47Rqcdg8uOSnSjEj0oRQ/ijEsRL70BpUbr49IrSRLOZgeWGgvWWivWE5+WGov3e42Fptpm4rLjiBoWQ/TwaELTwlAo22Q4XQ625K1kY+5y7E7/yjckIIIZw+aj84QxaKDv8KbVauW7776juroasUXEs9eJe7cTndVBYlAdCUH1JAXXEWVq/tGDuNsUkK8i8n6qsXvabw/Q2MmIrGBgWCVaVdeavEGnIjcmmLy4MKpDA1GpNKgUarRKBTqPg+E5c8lIntDh8R6XhyPLDrHzlR3UHerA8/FUBIkRlxxlxCXt762asnjc4fcwYGY2SrX/4bxGh8iaA8cIjIqjySHS7JIwFucx69vFxNW2lyki8GbcdB5MvqrdXOLpaHHyScIxpuvd4HJ6hxhPLILLCW4XLquF2vLjWBsbUIoiSsmDU1RgF5XYFBqOhicz+LL5DMruIhZGktB8+jqar97zXS0IOG64n7yEzG51xKVmN09uqSV6y1c8VLKUSFczkgDuEAFXuAJPgEDAzvYempIggN7oUwhPMpiQ9KcWyTu53dS6b77FQWr2kC7b1R1kZeMHu9PKX/5zD8oqDcZV0ahLjGgu0RM/poEZ6aXeobNO5kNO5+RFVhTno3vuD+28uiSDEfud/4cnZ3S7Y8triwnYezuKUzLj7mhK5cuSmcwJSSHMam/tsJsrmmiqaMJWZ0OydD5HUBkVzK7RA7gwZB+/K/sKjdS+o1oXNJiHk69jQtNxfl38IXFS576iksGEfeHDeEb0IlD0BB3dkC63kx+OrGXdvmVYOvBqCjSEcN7QSxiRPhmlQtWhLLfbzdq1azl2zNtZSZKEeNSNe7cTMd+D5JHQqlwkBNV7LZ/geiKNzaiVfZ+O5segQatkT6SRPZEGSgI0Xc47XTPtHjKTfKtQOs1Ocj/Yx+7/7MRc0bEVGDYonJG3j0aIq8G6YRt5yyzUFgWSMqaSKbccRKXxvYaN5QY2vDuOhGnjyLp6CMFJwe1k+v0/etyoV32J5rP/tJvvBDA7NXxTOoSt5hTsOi12nYbipAjWnucb96PFxgvDarly2NhOg64rKyvZsmULtbXtFaxCoWDs2LFkZWV1GbitXvEx2g9eare+fOolBN50f9dzgpKE5KjhYEkuewt2M8axk1hjvU9isIgP7fipjN4rCq+8i6i5V/SJLFnZ+KF67xHe/cWnKJrVCAigBP2vAxmXdpyc83/r17urM/Lz88loPI7u1afbjZ+L0QnY7v8zUkxiu+MaHSLfrPw784xtmXVriwP44v/GcHpdnK6wGDQUJ0VSlBRJcXIkA/Q1vHL4NTKt7edmmpR6Xok5n3RbORfX70bVjSBKT1o29l89ghQZ26N2nU672AXRze6Cjazd+yVNFv9DB0ZdAFNyLmb0oGk+Xlud3dySJLFjxw727t3ru94sElIejHlrM80lp3q0SWiUbowaByaNo/XTpHURFgnBwRImnROdZEFpaeqzvHC9pdmhI686hryaWErdJhyZzTizmnAlW7zJyDpBo9KycO6jRIckYKkys+etXex7dy/O5o57sPjxCYy8fQxJU5MRBKEtXsp8jOMr3+Xgl3U0lhuYdvsBjCG+cuxmFatfGkJ5XigJExPJvnYIqbPSUWq81s7p/0dJkqjPr6N4XRHV63PJrP+OzHDfIeKTFDeGsuJIDrVW7+T5homD+X7mMJ99dJKF38Ss5/Yp8wk0dlyhVhRFjhw5wg8//IDN1t7hJCkpiSlTpqDTdV7SXbXxW7T/+Vu7oG131ijcY87DM2x8a/VPyW1BbD6Cp/kwYvMhxObDSM7OX/qCv3eiPd43L0b51z9AzPkX9Y0sWdn4ItoqWPvQs+z/om2ITJGmQne1geuuuRxDT5JoAogiLW/+k5j1y9ptcmeNwn7XYz65zQBEt0jhuiLe/89m7rv+A9TaNqtj7atZFGyJ6fLPtph0XuWS7FUwNRGBDLJWMKUpjxkNucyv2eF33Hu3MQmt6CLT1nlaDUmtwZMxFE/2aI4GRJIwYWqfJA9s7aQkkf3HtrF69+fUt/ifFNWpDUzMnsP4zFmtAbT+ZHXGoUOH2LhxI9JpThqxMbEMNg7i0CcHKVxZgHiiUE9gQhDRJ+ePhsUQkRWJSufrDCCJIo0Vx6nNP0Rj8VHsFWXoHNbWIUeD047W40TjdqH1ONG6nWh7mPbHHy0OLXk1MeRVx1LWHIK/FxLR6MKR2Ywjuwl3YseKJ8QSzeCjkylcmo/H6X94TlAIpF04kJG/Gk3UEF+nlHYvDU2HsBx4m2NrywlLMBMS5+ugIXoEtrw/kLzV3nlHfZiezAXZZF0zhFp3LfFhcZRsLKFkfRElG4owV/rOAw0IqWF2ei5hfhw/PJLAYdVI6sdcxuaXf+DbYYNYd5qFY5BauFbzDr8YP5ehKRM6tVCcTifbtm3j0KH28z1Go5Fp06YRE9P5M6rcvRnd4v9r9Q4EfIbDnCkhuCKUiIpm/BUN7Izyw2FYDxpbaxKFSzZ0rs5LPXTEoYV/In7S9F4dezqysjkNx5GX+PCX1TSWt3n3aC7Wk3hBInMvuriHwuxoX3sa9Y617TY5Z12O8+o7QNnWUdXk1XDoswMc+iIPa42FoXOPMXpBm1ecpV7LR7+fiOhp30M0BhlOWC4RFCdHUh9qIttSxuTGQ0xpymNy4yGi/HjynMSs0CIhECB2fFN64gfgyR6NJ2cMnoE5oGkLSOurm+jIkSN4dGa+3/UZ1Y3+3T01Ki3jMmcxKWtOuwDaU+luu44fP87333+P0+nrGBESEsLs2bNRe1Tkbs4lc0wmhnD/f89ut3P8+HHKyso4fvw4FkvPvN0ESSRAqSDSpCfcoCdMpyFYpcSkBKXdChYzgs2CYDUjWM1gsyBYzDjsNsqMoezWR1BWF4zrkAfPITfYu37s9BF64mbEEXt+DI3hlazeuwRViQH9xgi0hzu23lU6FZlXZjNi4SiCEoP97tPRtfc07MVR+Cb2igK0xvYKNm91HJvfH9SahxDAEGfEWm7pss9VKjyMTyhkYlIBKkX7N3sxLIpDObNY+YqLJdlpbJ7om67JJDVyufAqYxJTmDf+lwQY/J/bSTZt2kR+fj4u12mFBgWBESNGMGzYsHZpiCRJ9FbvtVfD0R0o132AqHHhDlHgChN8it/1BEETgkU/kCW1ibxTM5gDLt84nnQjvD5GyzC9o/U+wmpGsJ56T5lbv3u3W8i7dCHJI/umINxPrmyeffZZli1bRkFBARqNhlGjRvHYY4+RmZnZuo8kSTz99NO8/fbbNDY2MnLkSBYtWsTgwT3P7dUVm7eXseOKD9tWKED/6wAmnT/Zp01dYrOg/9tvUB7zdVWWlCocN9yP+zyvaWqptnD4yzzylhyg9mCbL75CKXLV3zdiDGnrALd/ksa+1QPAJNAYbaIoKYqimHCKwiJo0ukZZi5mSqNXsUxqOkyY238SztMR8f+CKwUE4c4ahSd7FJ7s0X5zssGZ30SSJNFgrqG0uoC1u5dR20GyQqVCxZhB05ky5CJM+qAu5fakXQ0NDaxYsQKz2fea6fV6Zs2aRVNTk48sURSpqqpqVS41NTWni+yUoKAgn2qSoaGhGI3GHtdXyc/PJyEhgWXLltHY2AiA5JEQi9yE1oZQv60WRyfDXycxRpmw68x4Okl5pwvRM/TG4Qy9YRj60M4j7rsawnTXbsd1+HlER307g7g8L4RVi3NwWLqfr80UrSdxfBAJozQkJNYTsmYdmqMVfvdtidXw9qrJvDdyEjvGDPTZFijWc7niVSK0Li4afRXZqVM7zFuXn59PVFQUq1evbv3/C4joVTaMKitx4RoyU8NReRoQ7dVI9iokew1IZzjEKipQqmIRokagDMtGEZiBoPXW1PKIEo+uLeLVEk27kuRKAR4cFsBvhgSg6mbg7s/KG23+/PnMnz+fESNGIEkSf/nLX9ixYwfbtm0jJMQbqPXcc8+xaNEiFi9eTHp6Os888wxbt25lx44dBAT0LC14Vzx0/2piPt/V+luRokJ/nYlrr70Wg6H7mXm1b/y9vatjQBC2u5/AmZxJ4cpC8j47QMn6IiSx/SVKn1jO1FvbkoG6XEoeOXIreYY4jgqhWCQ1I1uOMaXpEFMa85jQdIQgT88DF33ap1Qipmfjzh6NJ3s0YlJ6t9wle3oT2RwWymqPUlZTeOLzKFZHx5POCkHBiPTJnDf0EoKMPXfM6C6neqqdilKpJCMjg+zsbMrKyigrK6O8vLzdG21nGI1G4uPjiY+Px2639+zFpRNOnmNLSwtffvllu7mE6VOnoyiF/K8PU7iyAGdLz+OhdDFaxt05icwrslF3kJeso3Z1hiSJOAvfwF3yGaebLc3VelY+P9RnhOFUVFqRmIxm4rKqiM+uIyja6qu0JAl1hYi2zIOkU+AOFLwZEyTQlIsIlRL/XTuBN0bNYvfwFB/ZIWIN8xWvYhAsDDI4uSBKhdEQgqA5uQQjaEOprmkgIkjAY6uipaYAyVGDQWXzceY5YyRvHJO6RkRd6/1UNUoIkvfF1TN4OJ7hE3APn+gtk4H32ptDkli4roGC5vbW45gIDa9ODSE5oOtYsJ+Vsjkds9lMYmIi7733HnPmzEGSJDIyMli4cCEPPPAAADabjfT0dJ588kluuummPmtspdXD89PeJLqysXWd5kI9CXOTuOii7k+SKQ/sRP/Mb33WueMGUDj1PvJWVZG//HAXD73EZU9sIyyh7S377abz+KZo1IlhsUOMb8rH6Ce6v6eIUfG4s0d5h8YyhnUrBf/pdFpTxeOmsqGE4zVHKa0tpKzmKHXNHeRxOw0BgZyUcUwfdhlhgT0vcNWbm/t0T7XeolQqiY2NJT4+nri4OIKDg1utlrP1ANfW1vLVV1/5KEGlUsmFF15IdHQ0boebkg3F5H91mKPfFeA0d654XLFWbBNr8WSZuenCh0iKGtjp/h21qys8zYXY9z7cGufT+vcdCla/nEPp3ggAwhJbiMuuIz6rjqj0RpTq3nfqgktCc0zki89H8FzWJeTm+A47hXsquUz5GjrBhkEhMju0mUGGPnLx6qxdmhAU+hRUTSq0BbVodh1BaeveS40nKR3P8AkURiSTMGkaFpfIozuaeeNw+yFdk0rgb+OCuDbN0Kk13Z+UTY/DqM1mM6IoEhwcDEBxcTFVVVVMn942SaXX65kwYQLbtm3rU2WjrWr2UTQIoBykYsCA7qX2BsBuRfvmotaf9VYju5sHcTB/EM3vfd/5sYLXkkqY3uijaERJYM7m/fy+ekX329EJkkZLzfApGC+/scsMsj2Se2I4rKzGq1TKagupqCvpNLK/IwYnjmDG8Mt7nAX5TFGpVMyYMcOvp1pXhIaGtlov0dHRKJV9kwqmu4SHhzNjxgy+/fbbVocHj8fDypUrmTdvHsHBwaScn0rK+am47W6K1x3jyFeHOfZ9IS5r2/8oemI0BYO2Y09savUx+GDNi9x+0f/1rMpsN1EGpmIY+yr2/U8iNrXFn6m1IrPu20tLjQ6NwY3O1HflwCW1gGOgkgt/vYeUzdX85shN7BnYFgxaq4zmS/fNXKp6HUQHn9cGk2mwMTOkBb3yDC0XlRGFLsobJKuLRKGLorJBIm7QlNbhMADPdLDZrShzf0C1e5M3G4S543lXZXE+yuJ8orLGwKRpGNUKnp0QzKwELXdvbKTW3jaPZXZL3LWxkW9L7Tw3IZhQ3Y97r54NemzZ3HjjjRQWFrJ27VqUSiXbtm1j9uzZ7N+/n4SEtgj5u+66i4qKCpYsWeJXTn6+/3rnneFosHP0y0KKvjuKVCWiSFKiu97E+PHj0Wq13ZIR9+2HRGxfRXFjGBuL0ylu9D/PcSpClAJVjgZVlhohQMF50RuJNbZ5YLlLVcSt7nr+RVRpEER3h+WJPRot5cMmcDAzkzqFi556uXSE022n1lxObUs5Dnfv8qKpFBrCTDGEB8SRHD6YMFPXHndnm/LycvLz89t5qp1ErVYTGhpKSEgIISEh3b5HzjYVFRUcPuw7V6jT6Rg+fLjfNnocHmp2VGGttBI+IpLAlECKag+y/rDvsxVqjOaCnF+iUnYzvU1PkdwENXyC0bK56337GIdFzStlM/mnbh5O2s4v1lXCxeo30AheK9Co8HBBaAvpnVg5HoUJm8dIvUWFxW3A4jJ4P91G7KKJAenZraWoJY+EvdaGPqobIwqiB2NZIUFH9hJ0ZA86P1nYAY5ddhuNWb4xe3VOeCpfy8aG9kolQiPyWLqTsSHndhxZV1ZRjyybRx55hK1bt7JixYp2b4Wnm3qSJHVq/vXWXPNoRaqSaxDrPeCA6OhosrOzuz4QEA7vo+Lb/XxTNIGy5o799QEwCaiy1ahyNCii2s41UN3so2gAIvb792wSg0IRUwd7c2Ed2Y/C5X9YxKlRsyc9kW+jlNRLR6H47Cch7AxBEIgMjichIoX48FTiIlKIDIpDoVCcU2Z7eno6aWlprF69GrvdjkKhIDo6mri4OBISEggNDe3xhH5ftKsrWenp6ZhMJnbu3Nm6zm63k5+fz0UXXYRa3V5ZZGRn+MhKT09H0LpZt29p6z71lkr2Va7lyql3dHnevT1HSXoUd9lSnPmv4HVd6SWCCpcyjEa7geoWNS2uAJqdAURpqhkSmIeg832B0Bpd3DtoOVfaN/N3y6V8Yp6AByXl6kSWO37JRdo3UQluLKKSz2qDyQkPZXyIgajoVARdFIIuCsUJS0VQ6ggEpMpK9qxZ087pJC8vD1uNDeMxPXmfHEBj1DD2pYkMHNiNYcpBGTBjLm7AUl6MavdmVLs2oSg8gCBJSEoVzalZ7e8JYFmmxJuHrfxhexM2T9v51zgV3H1Axx2ZRh4bGYTuFI+4c+l57IpuK5uHH36YJUuWsGzZMpKTk1vXn3wDqK6uJj6+bUiltraWiIiIvmvpCU6O1StCvQqgO0NokiRxbMVhfnjkCyrqx3S8owqUA9WohqpRDFAhnOIR4kGgQAhjYojvXIG6WvTJkluZMozgqecjxiSi2rEO9bqvEDrIg2VRKVgfH8D6+EDsajdIfTcM0RMCDSHER6QSH55CfEQqsWHJfuNizkXi4uK4+uqryc3NJTs7229HfS4yfPhwzGazj4VTW1vL999/z+zZs7tVGXT68MuoaijjUGmbw0xu0TaiQxOYOqSHYQDdRBAE1AmXoDAmYM/9C3ThUSloQlpzt6GPo8Gqo7DCwZFjDbg97S3SWkcYhU3JzHOtQp1mR9L4Ks1oXSP/0L3FXYHfsKjxEpZaR1OqHcA3thu4UP82yhNF4vbX1lPQ7GJB0kgGxg3127bo6Gguu+wyNmzYQFGR1xFILHTj3uXkYMFen4GFhgP10P0pMQCk2CRcsUm45l6D0NyAcs9WFHWViB2UGBcEgZszjEyO0bBwXQN76nyHt18+aGFtuYPXpoaSHdo/7vNT6ZayefDBB1myZAlfffVVO+2elJREVFQUa9asYcSIEYD3LW3Lli088cQTfdrYlpaWdi6snSkbSZQoWJHPjhe3UnOwGjoowKRIUKIaokE5WI1wSgEqCcgXwtgrxJIrRGFQ2vhjwBs+xxoOtimIlVEjSbvmOqSVHxP5zg6UHv/Bdma1grUJgWyMC8Ch+nELgmlUWuLCBxAfnkp8RArx4SmdRmX3B9RqNSaTqd8oGvB2LJMmTcJqtVJaWtq6vqysjI0bNzJ58uQurROFoGDBlNt49esnqW5si9BfteszokLiyUgYftbarwwdgX7UczjynsPdXIDSEI3C4JsYVGGIR1CbqKurIz8/n4IfCrDZui6/aVfo+Uw9h7mr1xEZW4N1sBLUvtciRV3FSxGvcrdzOc80XsZ3DGWl5RfMNv4XheC1uGzOFv77/bOMTJ/CBaOvRafRt/tbOp2OsYPHYF9j4diyo0jN/q210q+LGHuZ/3pY3UEKDME9ZY73RxdTCOlBalbOjeCZPS08u7+FU51h8xrdTF9WzZ9GBnJnln9PwHOVLpXNAw88wEcffcS7775LcHAwVVXeISSj0YjJZEIQBO644w7+8Y9/tA5rLFq0CKPRyIIFC/q0sYIgkJOTw7FjxzCbzURFRWE0tg/iEz0i+V8fYceLW6g7UtehPEWaCvUkLcr4tssgCAIxMTHskKJ5rToEi9A2hv5M3ErUtL1tKFpEtCXem/Ob0KHsCzAw/S+/QdXBVEuzRsGahCA2x5lwKv0rGbVKQ3RIAlohgPCwvrEMm5uaSU/OJD4itXU4TOanR6FQMGPGDL766iufnF6HDx/GZDK1vrx1hlat57rp9/Hvrx/H5vAO50pIfLr+39w2909EBvedg0m79hvi0Y9c5Hf4xWq1UpDnLZdRX995dUyAyMhI0tPTOX78OCUlJXiAr1LP44Ijm0nLK8aao8I6SOkNRjmFTE0Zb0W+yC7HAJ5pnM+G+l8y2fCWj3vzzvz1FJTnctnEW0mN9ZZtF90ix1YfJff9vRSv8x/e0IoKmizNOByOH23eT6MU+OPIQKbHafnVhgZKzW0vrk4R/rijmZVlDn4fL3D2Br76li6Vzeuvvw7AJZdc4rP+wQcf5OGHHwbgvvvuw2az8bvf/a41qHPJkiV9HmNjMpkYN24cY8eOZdeuXcTG+ub5Et0ih5fmseNf22go7PgGVw5UoZqkRRnbdvoxMTGkpKSQnJzM4iNuntvd4pNNZFSoxKWaVXDKSJcxz4MgwZrgTB4dsIDtO//kN/iyUaNkdVIgW2NMuE5RMkHG0BOVJr0p9mNCEwgJiEQhnFtzIzJnD7VazezZs/nyyy995g527tyJ0Whk0KCOi/6dJDQwiqum3sU73y1CPJEnz+Gy896q57n9osc6zeLQl7jdbp9yGR05bpzEZDK1vqCe9G5Vq9WMGjWK9evXU11dzTeDJnB+gYrsHYUYDrixDFVhS1O2q1Y6QnuMD6P+weagQXxTcxFG6WtOnVNqstTz1spnGB4ylYjDKRz+9BCWqi6GACMVCCO1mLMDMRpc2O32H93JZEK0lo2XRPLg1kY+LPSN0Vpf4WB3tY41CS7Sgs59q75LZXMy6rkzBEHg4YcfblU+ZxtBEAgMDGzNb+RxeTi05CA7Fm+jqbixg6MkVBkqVJP1vhP+gYEMGjSIYcOGAfBevoU/7/YNYEwwKfkoaxtCSZtbo+CU0OV72ByYzqXZv+W1w6+1y2VWr1WyKimIXbHBhIbHk3NCqUSHJBAVmoBB27/MYJmzg8FgYM6cOSxduhSHo21+b8OGDRgMBh8vz45Ijc3igtHXsHx7W4r8+pYqPlq3mOvP/y1KxdlxnZUkicbGRtatW8exY8e6DKRVq9UMGDCAgQMHEh0d7XeoMCQkhHnz5nHw4EF27NjBd2ljcSpVjCg/TOAWN4ZcD5ZhKuwDFO3y/U3QHWZCwmH2WzM4ZHdQYTWjFCX0xUYMeYFYK49xXFVIUJhIaLQIWnAGqXAGqnAGqPAEqlDFGPAYwCE5QbAQKjQxLsCNSVELdJ0Zo68J0ij495RQZidYuX9zI02nFK/LChBJCey7QoBnk/7Ryg5wO9wc/CSXH17eTkuZf/92AYnIZAtNs6NRRPg+cHFxccyYMYOSkhIAVh+3c9+mRp99gjUCn04LwLj9TTynzJnrj3jYpRvARUN+T4KjjstrtrVuazIZKBgzBseEGYwIH8CsoJiz9rDL/DwIDg5m1qxZLF++HM+JuT5Jkli1ahUXXXQR4eFdu+iPGzyTyoZSduW3VZ0sLD/Ayh8+Ys6Ya7vdFkmScDqd7cuRn/b95CJ24Mp/EkEQiIuLIz09neTkZFSqrrsdQRDIysoiKSmJjRs3sg5wKtWMK81F1SIRtMGFYb+AebgaZ2L78YQcwyFyDMDJ6cjEWpjc7UvgF/uOraiTFqAe8AsERfdT9fQVlw0wMCZSyx0bGlhf4SBEK/CndCeKH7uwUy/pl8rGbXdR9PlR1n+2ql122ZMISoHMlGY8IyRK0hPaDW9lZWUxbty41vmLfXVOblhd75OvSKuED6YHk7H8D5jjT0mAKUoUF0dy4dAHaVYZWHzkTZQnrBrnnKtQXrGQQcp+eWllfkKio6OZNm0a33/fFlzscrlYsWJFu2FsfwiCwMXjbqC2qZyS6oLW9ZsPfkt0aCLDUidis9kwm81UV1d3qFBsNlurwjsTQkNDW4fJepJK6lRMJhOzZ8+msLCQLVv0uJQqJhftAUDdKBGyxokjXMHxiXEYg3uW/67niLiKP8Zduw3t4AdQBv74Q9NxRiVfzA7jpQNmkgJURDh7Xj79p6Lf9YgNR+v59MqPsNb4v8gKlYLBC7IYOriGzQ0uqk+LqD7pBZSR0Va5r8IucNt3dZhP0TQC8OqkYMYs+SvO4FygzTJxlGqZNfCP1KsDGGgt58rqLQDU5YxHe9XtfZLKX+Z/kwEDBjB+/Hi2bNnSus5ms7FixQqysrI6PVYURew2B9Mzr2ZZ/Xu4HC5Ukg4lWras3cWudYe7tELOFL1eT1paGunp6YSF9U02A0EQSEtLIz4+ni1b4lm1Qc2Mwh2t27W1IilflrIpewyNgy2MMhR2Iu3MkSzF2HfehzrpatTJ1yAoftz5EoUgcHe2dz68F7HxPxn9TtkEJQWjDdS2UzZKjZLMK7MZdccYHOZSVq46jPU0RaPVapk5c6ZPLYtGh8h9B7RU2nwfwkeHqhj5ya8xVORTP893UvBW7qBa4x27faT4S5RIuLNGUnrRDaTJikbmDMnOzsZsNrN///7WdY2NjeTm5hIbG4vFYsFsNmM2m2lpaWn9tFgsrZPyRtp7oYndKLLXG1QqFYmJiQwcOJC4uLPn7ajT6Zg2bRqlaWms/egNpuxf6zNPOjF3O8srx3Hz0Lu4Nfx7sjQluCUlTkmNXVLjkFQ4JHXr4jzxW5QUIAkIkoBCAqUooZYk1JKIWhJRIZIddhStcMooiiTiKnofT+1WNIMfQBmQ0r7BMj70O2WjUCoYffdYVv76GwCUWhU51w5h5O2jMUUHkH/kCBvWb8Jzmk99SGAgs+bMITCwrQ6I3S1x7ao6jtl8H465YceZ8sVfyChupGmS71vLLusAVuOt+Z1mreTq6s14ElKx3/MEUlnnBc1kZLrL2LFjsVgsHD3alk2iqamJTz755Ef5+0qlEoPBgF6vR6/X+3w//XdRUdGP6u2YkJBA9H2PsO+jGHK+/xDlKUr0wtqtKHc7uDb5LpoCjShFkXDJRYTOhcndQoC7hVBshGAjRLIRhL11CNwfgiAQERHBQeUMRkfm4q78zme7aD6K/Yd7UCdfizrpKgRFv+tSfzT65ZUZNG8wW/61ifQZAxmxcDTGSCOiKLJ9+3ZvckbBV3kkmXScd9llaDRtk3pVVg+/2dLI5irfFDKDFHnc8cOLnFfchMeA1+PlFF4wt2WXfqT4CxQh4dh+8zTofxz3Upn/DQRBYOrUqVitVioru5eFuzuIuFFrlASZwoiMjOxQgajV6l6l+vmxUKvVpP3iNqoSk4h88xlUYtsc0+z63azULmK5ehwGtcc7X9vN6h4SIg6hBZVeYvywaWQNHIparSY/Px9t+myUkZNwHnrOt/Sz5MF17L94areiHfxbFKbkvjzVnw39UtkoVAomvXweAwd5sxk4nU7WrFnT6lV2KiPtdQy/5fcIJ0z7couH5/e38PYRC/bT5kBjKOIvRS9xQbG3tr01Q+Xjz1/oiuJ7m9eqSbFVcU3LHux/eAEptO/T8sjIqFQqZs2axdKlS7sVggDeoeKAgABMJlPrsvPoGkrqD+HGjiR4QIKRYTOYPPkM3bPOAQKnzMYeHonu2YdQudrcxkdWHEErevg+bQyS0PGwnlKpRKH1UGMvxiE04xRakAQRXPD5Dwepc17M1CHzWvdXhY9FOfZVHEdewlO1xkeW2JKPbcc9qFOuR51wOUI/8kA9W0Osp9IvlQ3QmresubmZlStX0tDgmwZDKXqYWbSLxN8+gaRQUGJ289w+M+/mW3D6ua4hVLOo7HkuOeoNBhVVYBvoe7O81jwL6YRf20NlX+G+9wnE+B6UN5CR6SFarZY5c+awevVqqqur0ev1rUrkVKVy8ru/lD3pg1J55esnqG1qm+fcWbQK/Q9aNH2QA6+xvgltkEB8RAqKTjr2s0bmcJyPPI/w9wdQWtvmVbKrCgmym9makE1ZUBQIAiqViqioKGJiYoiJiSEiIgKlUkl+2T6+2PwGDmtb5yBKImv3fsmh0t2MSpwNJ2L1BXUAuqwHcUdOwnHoBXA1tbVFcuEqfANPzWavlWPsOkbqx8TqMFPbVEltU4V3aa6gtqmSZms9V4z+zVn92/1W2YA3xfz333/vEwgHYHDamHdwHSHzrydfE86zGxv4oMDargzrSYKp5ZmKf3BVQVtKcHuaEknbZtXUe0x8YhkPwABbNVdcPBHP4LOXe0pG5iQmk4l58+Zx5MiR7mUePg2dxsAvZtzPv796HLuzrcTExtzlfdbGXcWrMOoCyUgYxqCE4aTGZqFR/XjR9mJKBo5HXkD3zG9RNLe9eCY0VZHQVEVLVALWmZejP28uCn8KOX4Id1/yZ77Z8T67Czb6bKusL2F5w38oqPuhNWFtXHgKuoiJKIOycBxZjKd6g297mg9h23EnmpQbUSVciiD8eFaOR3RT31JDbVMFdc1exVLT5FUqnVXcNdsbz2q7+q2y6aiWSWRLHfPy1lGaNo7fqafwyZIq/CSXBcBEIyNYzw1Va7jhcJuikQSwZPpemndazsMueR+eByIbEcbP6NsTkpHpgjOZQwkLjOaqqXfyzvf/6DKNTG+x2JvZmb+enfnrUSs1pMZmkZE4gkHxQzHpz37kvZiQgu0PL6D/229RnFZLJqCqlIB3n0P89mNcF1yBa/Ic0PpadXqtkfmTFpKZNIovN7+J2dZmsYiSyKHS3Rwq3Q14q9SGB8eQEJ5KXPh4BiRlYDj+EbhPCS4XXTgLXsNds8lr5Rj6thCi2dZEdXMpzUfKqW0+aa1UUt9SjSj1PE6q2dZxHsm+oN8pG1EU2bJlC0eOHGm3bWBNEXFlJdwweCFfh4xBLPQ/KxhAA6NYx2B2Mqy2hesP1fgEfdqT1YgBbQ+2Q1LxVou3EmkCFq64dGqfnpOMzI9BWlwOc0Zf65PS5mzh8jhbO2cBgfiIVDISR5CRMJyIoJiz5nwgRSdg++OL6F79C8pD7Su5KmrK0f73eTSfv4nr/Mtwnn8ZBAT77JORMJzES9P5etu77Du6pZ0M8CY7rWksp6axnF0FXqsmSG3iokg1CUrfTltsOoht+51oUm9GFd+90g+iKNJia6DBXEujuZZGcx1NltoTv+tostTh9vS8wm5nmB1NXe90BvQ7ZbN7924OHjzYbn1QQxl/Dh7H9pg7Ozw2iDpGsYZB7EEpiAxvFrjuYB2nVpGVlEos05LAU9a67nPLWGpE75vZb8bFoPmRywLIyPQV4zNnERkcx668LYSEhPSJzKLjBVQ2H8XhsvvdLiFRWlNAaU0B3+38mLDAKDIShpORMJyEyPQ+T+UkhUVhe/h5yld/Q8r+jah2bWq3j2BuRvPF26iXf4hr8hxcF1yJFNmW2NegNXHFlNvJTBrF8m3v0WztOnN1k8vDe8eVZBoC25enFh0481/GWb0BpeFy3J4BNFvqaLTU0Wj2KpEmcx2NJxRKs6WhV9ZJV6gUakIDowgPiiY8KIbwwLbPspKzG7rR75TNyRIDJx0CJElkpTKK7yMu7PCYEKoZxVoGso/okBgyEi5kqDqSAS/82adEsyQosNx6Ex77uz7Hv9o8C4B4g4JrB8rJM2X6N6mxWYgWTd9lFQ/IZ0DKAIoq81qtmSZLx51zXXMVmw6sYNOBFRi0JgbGDyUjcQRpsd2ruNtdLAlp2KfPQSgvRrPiY1SbViK4fa0BwelAs+oL1KuX4h49FdeFVyEOaMsukpU0ioyE4fywdzMKg5uymkJKawupbaxA8hufI3DQqqfEoeGC0GbS9KdV523KJaThAC/sDKPBffbmcQL0wV4lEhRNeGBMq3IJNob/ZCVG+p2yUalVNOuP4WoIwIaW/6jGUS4E+t03jErGCGuZEeUiM3EYGQnXEhoYBZKE/i/3IZxWptlx6+9x2pb6lBZYa8visMtbgfT+IQFoledu7IGMzE+FSqkiLS6HtLgc5o69nor6Eg6V7uJw6W7K64o7PM7qMLOncBN7CjehVKiIDkpC0l/CwHj/1TV7gxSbhOPm3+GcfzPqlZ+hXvMlgtU3A4kgiai3r0G9fQ3uwcNxXXg1npwxIAgoFUpCTdGkp6czetA0AOxOG+V1xyitKaSs5ihltYU+czxmj5JPa4LJMdqZEdKCTtGmmIrsGhrcZ97h69QG9JoAYiMSiQiKbbVSwgKj/RaK+6npd8rmuEXk303TsSl1NKDHLLT3eImggvkRJVyVEUVG/K8w6HytEdX2NSiP7PNZZ7/hfjxaFy57oU9us1dOWDWxBgXXD5QDN2VkukIQBGLDkogNS2L6sMtostRxqHQPh0p2c6zyIB7R//CQR3RzvKGQ/37/LOlxQ5gz5loigmL87tsbpOAwnFfehvPiX6Be9xXqbz9BUd8+eacqbzeqvN144lNwXXg17rHT2+2j0+hJickkJSbTK1uSaLLUU1bbpnzKa4vYbxEosmuYE9pMit6J1SOwoj4AnzfaDjBoAwgxhRNkCiPYFO79bvR+DzaGodca+1Wtqn6nbMJ0Cqo8YTQJ7d0XU3RN3D1YwfXZQ1CrRvkX4LCh+fDfPqua0nJQJ6XjWfkbyGi7CfKccay3e5Mf3p8jWzUyMr0hyBjG2IwZjM2Ygd1po6B8P3kluzhSttfHFftU8o/vo/CLA4zLnMm0oZeg0/Qua7Rf9AZcF1yJ6/z5qLatRr38Q5RlR9vtpiw7ivLVvyB++hqRI86D1BToYH5JEASCTWEEm8LITh4DgEf0UN1QRlntUQqqCyhv3kGNuRmr6JURoA/2Kg5TGMHG8LbvpgiCjWFo1D9uobazTb9TNgaVgnvc+3iKka3rRprzeWR8LNNHDu7Sy0Xz9Qc+bpGSUkXN6OkMePEhzKdN+3jnagSi9QpukK0aGZkzRqfRk508huzkMXhENyVV+eSV7uJQyW4azL5Whih52HxgBXsLNzNzxAKGp0/u26BRlQr3xFm4J8xEuX876m8+QnVwV7vdFPU1BB/8odNMBP5QKpTEhCURE5Z0YvhtIQ6XjYOHcsnJHIZKee5X1+xL+p2yUebt5rcbXmLxuOcZYi7hD8WfM3H8UFyjzuvyWKGmAvXyD33Wuc6bS8I372OPsyKdEuxV7QnkC8tYAO7LCUCnkq0aGZm+RKlQMSBmMANiBjNn9LUcrzvGF+vfpKrZN+2Uxd7MF5vfYPvh1cwd+wsSI/t42EgQ8AwZi2fIWBTHDqFe/hGqHesQTknhUjV+NpF94K6tVesx6YL/5xQN9Ddl43ahfePv6D129u54kFhnI2JUPNb5N3brcO2HL/s4BYiBISgLDqJoqqF5hq/J+lbLdJyoidIruHGQbNXIyJxNBEEgPjyFWdnX41A38O0PH7bzaCuvK+K15U8xJGU8s0deSaAxtANpvUcckIHjrsdwVpejXvEx6g3fIIWE0zRoOJF9/tf+t+hfykalxnHd3WjfepbYhlokQcB+6+9BowW3G2xmBKsZwWpBsJrBakaweb8rigtQ/bDeV57oQVmcj22AAtHU9tZiEzW80+L1Ork3JwC9bNXIyPwoCIJAzoCxDEoYxsb9y9mQ+3W74MV9R7eQV7KTKTkXMzHrAtSqvi/RLEXG4rzhfpyX3YiithL6wHvsf53+pWwAz7AJOGeXolz2LkpAt/gJr4Jx+g8o6wyFuRkJsJ6WmuZjywQaRBMROgU3DerDiUkZGZluoVFpmT78MkakT2bFDx9yoGiHz3aX28mq3Z+xK389F4y+msGJI89OVoKAYMSA4P5VEvMcpd8pGwCFpQW15WRCuY4Ty3UHV5SAO7ztrUWUBF5vngnAvdkmDHK2ABmZn4xgUzhXn3c3xyoPsXzbe1Q2+M7nNJhr+GDNi6TEZHLhmOuICon/iVoq0xX9sieVDH0XxX+6VfOdbShH3dGEaRXcnCHP1cjInAsMiM7gjosf5+Jxv8Sgbf/8H604yEtLH+Xrbe9ic1j8SJD5qemXlo0/ZSMJCjAYkfRGJIPJu4/BiFBegrKytG0/tQb79fdBRAwelRVH2Z/hlLQTJ1PT3JNtwqjul7pYRuZniUKhYEzGdLIHjGHNni/YfmiVT9EvURLZmvcd+45uYcbw+QQp/Fs5bo8Lu9OG3WnF7rRgd538fvrStt5mt3G0KYe02GwSI9PPyjzRz51+qWw8Q8dx5IbfEz8wo02x6PQ+kf8AiuJ89I/d5rPOOf9mPFPnAuA4/C9OVTR7HUlsdQwkVKvg1sGyVSMjcy5i0JqYO/YXjBp4Hsu3v8fRCt/EvFaHmWVb3yFIH87Wopg25eHyfvY2W3J1bikbc5ejVmpIjs4gLTabtLics5rF+udEv1Q2Ukg4lsR0xISUTnaS0L77IsIptTvEqHhcsy5HcltwV67BXfGdzyEngzjvzjZhkq0aGZlzmqiQeG6c9XvySnaxYscH7YJCm2y1NNlq+/zvujxO8o/vI//4PtgBQcbQVsWTEpPpd5hPpp8qm+5wev4zCbBceQnO/BdxV60D0be6Z7k7hK+sowjRCiyUrRoZmX6BIAhkJo0kPS6HzQe/Zd2+pbjczq4P7EOaLPWtReMEQSAuLIW0uGzSYrOJj0jt8xIK/ZWfp7Jx2NB8+DIAohrsqUqsQwLwNP8Hmv0f8nrzTNyouDPTRIBs1cjI9CvUKg1Th1zM8NSJfLvz4w6LngEoBCU6jQGdRn/i85RF7WedxkD+0UNYpDoKju+n2drQoWxJkrzJOGsLWbv3S7Rqb8LOtNhs0uNyCAmIOBun3y/4WSob9dfv41bWYpuoxp6sAJUA+I/D8UgCn1vG8UbLDII0ArdlyiawjEx/JdAYyhVTbmfGsMvYdWAbiQlJpykTA2qVpsdzLO4WJenp6UiSRE1TOQXH91NQnktR5WFcno4tKYfLRl7JTvJKdgIQFhjFgLAh/SZTc1/ys1I2kqsFd8ES7HyM58LOM6ZKmnBeqpvIW02TKPd4017cmWUiSCNbNTIy/Z3QwCiSwgeTHt+3nbogCEQGxxEZHMeErAtwuZ2UVOeTf0L5VDWUdnp8XXMV8UGOTvf5udLvlY0kSYhNB3AdX46nZgOILgju4K1FUKAMG0NV0Cwu35FMQUub80CgRuBXg2WrRkZGpvuoVRpSY7NIjfWWImmxNlJQnktBeS6F5blY7O2DzmODO3Fs+hnTb5WNwmPGVfIZrvIVSNbO3yYEbSSq2AtQxc5iVY2JW9bW0+zyLel6e6aJYK1s1cjIyPSeAEMww9MmMTxtEqIkUllfQsHxXArK91NSnY9apSUsIPanbuZPQr9TNpLbguPwi0RVbcSJu+MdRQlNvRFh2kMow0cCChYfMPOnH+oQTysdPjzQw69zAs5qu2VkZP63UAgKYsOSiQ1LZsqQi3C47NQ2VWBt6KTf+hnT75QNSj1i82GEDhSNskVEf8SDrtCD43f/RIzIxOGR+PXmRt4vaF8V8Lp0A3dG1MqZnWVkZM4qWrWOuPAB5Df8byb17HfjRoKgQBU757SVSrSlAsErnYQtcWLM9SCOnI2YmkmNzcO8FbXtFI1CgD+PCeJfE4ORfQJkZGRkzi79sptVx8xEQoGgj0GdejPBpRMJXm1DWyEiAJJOj/OK29hf72Lashq2Vfu6JgaqBT4+P4y7skxymgkZGRmZH4H+N4wGCJoQaqIeJDlzMsqSQjSrX/bZ7rzklyxtMvCr9TVY3b4TNCkBSj48P4yBwf97ZVllZGRkfir6pbIBcGtiERD85j97OmomT66ub3fM1Bgtb00LJUT2OpORkZH5UenXva5q22qf/GcAf8u5gSf3tc8WsHCwkU9nhcmKRkZGRuYnoN9aNgqnA81H//ZZtzF6OI+6s3zWqQT4+7hgbpILocnIyMj8ZPRbZRO5eQWK+raU4k5BycLE63z2CdUqeHtaKJNjOk9dIyMjIyNzdumXykaoqSBqywqfdS/GX0C+Iab19+BgFR+cH0ZyQL88RRkZGZmfFf2yJ9Z++DIKT1tQZ6U6iKeSLm39PTtBx2tTQgiUA2hkZGRkzgn6nbJRHtiJ6of1PuseSbmKFpUBgPtzTDw6IhClQo6fkZGRkTlX6F/KxuNG+O+LPqu2B6Ty3+jJaBTwwsQQrk4z/ESNk5GRkZHpiP41zuTxsCt5LHahLSDz/vQbiDCo+HpOhKxoZGRkZM5R+pdlo9GS86vbeSh+KlPXvEGzUo9jwGBWTw8l3tS/TkVGRkbmf4luWTabNm3i6quvZvDgwQQHB/Pee+/5bJckib/+9a9kZGQQHR3N3LlzycvLOysNFgSBP14wmCfG38s3s+/hmwvDZUUjIyMjc47TLWVjsVjIzMzk6aefRq/Xt9v+/PPPs3jxYv72t7+xevVqIiIiuOyyy2hpaV+lri/QqQReyHLw2vQIDKr+NRIoIyMj879It3rqWbNm8ac//YlLLrkEhcL3EEmSePnll7n//vu55JJLyMzM5OWXX8ZsNvPpp5+elUYDmFTIGZtlZGRk+glnbBYUFxdTVVXF9OnTW9fp9XomTJjAtm3bzlS8jIyMjMzPAKGxsVHqerc24uLieOaZZ7juOm9qmG3btjF79mz2799PQkJC63533XUXFRUVLFmyxK+c/Pz/zWp1MjIyMj9H0tPTO93eZzPrpw9pSZLU6TBXVw3rivz8/DOW0deyzsU2ybJkWbIsWdaPLcsfZzyMFhUVBUB1dbXP+traWiIiIs5UvIyMjIzMz4AzVjZJSUlERUWxZs2a1nV2u50tW7YwduzYMxUvIyMjI/MzoFvDaGazmaNHjwIgiiJlZWXs27ePkJAQEhISuOOOO/jHP/5Beno6aWlpLFq0CKPRyIIFC85q42VkZGRk+gfdchDYsGEDF198cbv111xzDS+//DKSJPH000/z1ltv0djYyMiRI1m0aBGZmZlnpdEyMjIyMv2LHnujycjIyMjI9BQ5/F5GRkZG5qwjKxsZGRkZmbOOrGxkZGRkZM46srKRkZGRkTnr9Dtl8/rrrzNkyBCioqKYOnUqmzdv7pWcrsomdJdnn32WadOmkZCQQGpqKldddRUHDx7slazXXnuNCRMmkJCQQEJCAjNnzuTbb7/tlazT+cc//kFwcDC/+93venzsX//6V4KDg32WgQMH9rotlZWV3H777aSmphIVFcXYsWPZuHFjj+Xk5OS0a1dwcDBXXnllj2V5PB6eeuqp1ntryJAhPPXUU7jd7h7LAmhpaeGhhx4iOzub6OhoZs2axa5du7o8ri/LeXQla+nSpcyfP5/U1FSCg4PZsGFDr9rlcrl47LHHmDBhArGxsQwaNIhbb72V0tLSXrXrqaeeYvTo0cTGxpKUlMS8efM6zLPYk+f4vvvuIzg4mBdffNHv9q5k3XHHHe3utfPPP7/X7SooKOAXv/gFiYmJxMTEMGXKFA4fPtxjWf6egeDgYB544IEeyzKbzfzud78jMzOT6OhoRo0axeLFi/2eY0/pV8pmyZIlPPTQQ/z2t79l/fr1jBkzhiuuuKLDm7ozuiqb0F02btzILbfcwrfffsvSpUtRqVRceumlNDQ09FhWbGwsjz/+OOvWrWPNmjVMmTKF6667jtzc3F63D2DHjh28/fbbZGVl9VpGeno6hw8fbl16q+QbGxuZPXs2kiTx8ccfs23bNp555pleZZtYs2aNT5vWrVuHIAhceumlPZb13HPP8frrr/O3v/2N7du38/TTT/Paa6/x7LPP9lgWwL333svq1at5+eWX2bx5M9OmTePSSy+lvLy80+P6spxHV7KsVitjxozhz3/+c5fn05ksq9XK3r17eeCBB1i3bh3vv/8+x48fZ8GCBX6VdVftSk9PZ9GiRWzevJkVK1aQlJTEggUL2mUp6Y6sk3z55Zfs2rWLmJiYXp3jSc477zyfe+6TTz7playioiJmz55NUlISS5cuZcuWLfzxj3/EaDT2WNap7Tl8+DAffvghgN/noCtZf/jDH1i5ciX//ve/2bZtG7/97W95/PHHW2WeCf3K9XnGjBlkZWXxwgsvtK4bMWIEl1xyCY899liv5Z6eXPRMMJvNJCYm8t577zFnzpwzlpecnMxjjz3GTTfd1Kvjm5qamDp1Ks8//zzPPPMMmZmZ/P3vf++RjL/+9a+tD8SZ8sQTT7Bp06Y+s9hOZdGiRbzwwgscOnQIg6FnJcKvuuoqQkJC+Pe//9267vbbb6ehoYGPPvqoR7JsNhvx8fG88847zJ07t3X91KlTmTlzJn/84x+7Jef0+1KSJDIyMli4cGHrW6vNZiM9PZ0nn3yy03uks3u8rq6O1NRUli1bxuTJk3vcLn8cOnSIcePGsWnTpk5fcrojq7m5mcTERD777DNmzJjRY1klJSXMnj2bL774ggULFnDbbbdxzz33dHKG/mXdcccd1NfX9/h+8Cfr1ltvRRAEXnvttTOWdTr33nsvmzdv5ocffuixrPHjx3PxxRfzyCOPtK678MILycrK6nG/cTr9xrJxOp3s2bPHp5QBwPTp08+pUgZmsxlRFAkODj4jOR6Ph88++wyLxcKYMWN6LedknaGpU6eeUXuKiooYPHgwQ4YM4eabb6aoqKhXcr7++mtGjhzJTTfdRFpaGpMmTeLVV19Fks7snUeSJP773/9y1VVX9VjRAIwbN46NGzdy5MgRwNtZbtiwgZkzZ/ZYltvtxuPxoNPpfNbr9fozUtj9qZzHSUvrTJ8Dp9PJ22+/TWBgIDk5OT0+3u12c+utt/LAAw8waNCgM2oLwJYtW0hLS2PkyJHce++91NTU9FiGKIqsWLGCQYMGcfnll5Oamsq0adM6zJDfE8xmM0uWLOGXv/xlr44fN24cK1asoKysDPBm9c/Nze1UyXeXflNPua6uDo/H0264JSIiwq95/VPx0EMPkZOT02sFceDAAWbNmoXdbsdoNPLuu+/2evjr7bff5ujRo7zyyiu9Ov4ko0aN4qWXXiI9PZ3a2lr+/ve/M2vWLLZu3UpoaGiPZBUVFfGf//yHO++8k/vvv5/9+/fz4IMPAnDbbbf1uo1r1qyhuLiY66+/vlfH33///ZjNZsaOHYtSqcTtdvPAAw9w66239lhWQEAAY8aMYdGiRQwePJioqCg+/fRTtm/fTkpKSq/aB1BVVQXg9xmoqKjotdy+xul08sc//pELLriAuLi4XslYsWIFt9xyC1arlejoaD7//HMiIyN7LOevf/0rISEh3HLLLb1qx6mcf/75XHzxxSQlJVFSUsJTTz3FvHnzWLt2LVqttttyampqMJvNPPvsszzyyCM89thjrF+/noULF2IwGLjgggt63cZPP/0Uh8PBNddc06vj//a3v/HrX/+a7OxsVCqvenjmmWfOqE0n6TfK5iQ9LWXwY/LII4+wdetWVqxYgVKp7JWM9PR0NmzYQFNTE0uXLuWOO+7gq6++6nHqn/z8fJ544gm++eYbNBpNr9pyktPf7keNGsWwYcN4//33ufvuu3skSxRFhg8f3jrsOXToUI4ePcrrr79+Rsrm7bffZsSIEQwZMqRXxy9ZsoQPP/yQ119/nYyMDPbv389DDz1EYmIiN9xwQ4/lvfLKK9x1111kZmaiVCoZOnQoCxYsYO/evb1q36mcy8+A2+3mtttuo6mpiQ8++KDXciZPnsyGDRuoq6vj7bff5sYbb+S7774jOjq62zI2btzI+++/36njQ0+4/PLLW79nZWUxbNgwcnJy+Pbbb5k3b1635YiiCHiHp04+P0OGDGHPnj28/vrrZ9Sxv/3228ydO5fw8PBeHf/KK6+wbds2PvjgAxISEti8eTOPPvooiYmJHTpDdJd+M4wWFhaGUqk8Z0sZPPzww3z22WcsXbqU5OTkXsvRaDSkpKS0dsg5OTm89NJLPZazfft26urqGD9+PGFhYYSFhbFp0yZef/11wsLCcDgcvW6jyWQiIyOjNTlrT4iKimo3nDFw4MBWs7031NTUsHz58l4PHQD86U9/4u677+byyy8nKyuLq6++mrvuuot//vOfvZI3YMAAli9fzvHjxzlw4ACrV6/G5XKRlJTU6zae6+U83G43t9xyCwcOHODLL7/ssdV7KkajkZSUFEaPHs2//vUv1Go177zzTo9kbNiwgcrKSgYNGtT6DJSWlvLYY4/1Sd7GmJgYYmNje/wchIWFoVKp+vw52LdvH7t37+71c2Cz2XjiiSd4/PHHmTNnDtnZ2dx2223Mnz+/Qw++ntBvlI1Go2HYsGE+pQzAO3zyU5cyePDBB/n0009ZunTpGbkE+0MURZxOZ4+Pmzt3Lps3b2bDhg2ty/Dhw7n88svZsGHDGVk7drud/Pz81s6vJ4wbN46CggKfdQUFBT5VXnvK+++/j1arZf78+b2WYbVa21mjSqWy9S20txiNRqKjo2lsbGTVqlVceOGFvZZ1LpfzcLlc3HTTTRw4cIBly5b16t7ojN48B7feeiubNm3yeQZiYmK48847+fLLL8+4TXV1dVRUVPT4XDUaDSNGjGhXrfhMn4O3336bxMREzjvvvF4d73K5cLlcZ+U5gH42jHbXXXfxq1/9ipEjRzJ27FjeeOMNKisre+Wp1VXZhO7ywAMP8NFHH/Huu+8SHBzcOq5uNBoxmUw9atP//d//MWvWLOLi4jCbzXz66ads3LiRjz/+uEdyoM33/lQMBgMhISE9fqs7Of4eHx/fOmdjtVp7NS585513MmvWLBYtWsT8+fPZt28fr776Ko8++miPZYF3COmdd95h/vz5BAQE9EoGwAUXXMBzzz1HUlISGRkZ7Nu3j8WLF3P11Vf3St6qVasQRZH09HSOHTvGo48+Snp6epcej31ZzqMrWQ0NDZSWltLU1ATAsWPHCAoKIioqql0H2pmsmJgYfvnLX7J7924++OADBEFofQ4CAwPbudh2JisoKIgXXniBCy64gKioKOrq6njttdcoLy/368rb1TmebvGpVCqioqL8VqTsTFZISAhPP/008+bNIyoqipKSEp544gkiIiK46KKLetyue++9l5tuuokJEyYwZcoUNmzYwJIlS/zG43Snr7JarXzyySfce++9nQ6pdiVr4sSJPP744xiNRhISEti0aRMffvghjz/+eIcyu01jY6PUn5ZFixZJCQkJkkajkYYOHSp9/fXXvZKzbNkyCWi3XHPNNT2S408GID344IM9btM111wjxcfHSxqNRgoPD5emTp0qffbZZ3127SZOnCgtXLiwx8fNnz9fio6OltRqtRQTEyNdfPHF0tatW3vdjo8++kjKysqStFqtlJqaKj399NNSQ0NDr2QtXbpUAqRVq1ad0bUpLS2Vbr/9dik+Pl7S6XRSUlKS9Jvf/EaqrKzslbw333xTSk5OljQajRQVFSUtXLhQKi4uPuP7sqGhQXrwwQelqKgoSavVShMmTJA2b97cK1mLFy/u9r3bmay9e/d2+BwsXry4R7LKy8uluXPnStHR0ZJGo5Gio6OlOXPmSN9//32vzvH0JSEhQXryySd7LKuiokKaPn26FB4eLqnVaik+Pl665pprpNzc3F63a/HixVJqaqqk0+mkzMxM6fXXX++1rH/961+SUqmU8vLyzuj+Onz4sHTttddKMTExkk6nk9LT06Unn3yy18/nqUu/irORkZGRkemf9Js5GxkZGRmZ/ousbGRkZGRkzjqyspGRkZGROevIykZGRkZG5qwjKxsZGRkZmbOOrGxkZGRkZM46srKRkZGRkTnryMpGRkZGRuasIysbGRkZGZmzzv8DIas+RWQvHL0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "plt.plot(weights.transpose())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45c7133c",
   "metadata": {},
   "source": [
    "From the above, we can see that all the BXD colonies seem similar in shape.  To make our analysis easier, we choose one experiment, and in this case, we opt for one which has no missing entry(that is, one that ran for a period of 18 months):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "33573529",
   "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>identifier</th>\n",
       "      <th>2534-BXD29-F-CD-Natural</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>21.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>23.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>25.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>25.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>27.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "identifier  2534-BXD29-F-CD-Natural\n",
       "0                              21.5\n",
       "1                              23.2\n",
       "2                              25.8\n",
       "3                              25.8\n",
       "4                              27.7"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "single_bxd = weights.dropna(thresh=weights.shape[1]-0).transpose()\n",
    "plt.plot(single_bxd)\n",
    "single_bxd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "6856a3cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     21.5\n",
       "1     23.2\n",
       "2     25.8\n",
       "3     25.8\n",
       "4     27.7\n",
       "5     27.7\n",
       "6     27.5\n",
       "7     27.9\n",
       "8     27.1\n",
       "9     25.7\n",
       "10    27.0\n",
       "11    25.3\n",
       "12    23.0\n",
       "13    21.5\n",
       "14    19.3\n",
       "15    17.1\n",
       "16    16.4\n",
       "17    16.8\n",
       "18    17.3\n",
       "Name: 2534-BXD29-F-CD-Natural, dtype: float64"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "single_bxd[\"2534-BXD29-F-CD-Natural\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8726973a",
   "metadata": {},
   "source": [
    "Here, we try to model the time series as an additive time series[1]:\n",
    "\n",
    "```\n",
    "Value = Base Level + Trend + Seasonality + Error  \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "7f797de9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Additive Decompose')"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.tsa.seasonal import seasonal_decompose\n",
    "\n",
    "bxd_additive = seasonal_decompose(single_bxd.iloc[:,0],\n",
    "                                  period=1,\n",
    "                                  model='additive')\n",
    "bxd_additive.plot().suptitle(\"Additive Decompose\", fontsize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52265ce3",
   "metadata": {},
   "source": [
    "Here, we try to model the time series as a multiplicative time series:\n",
    "\n",
    "```\n",
    "Value = Base Level * Trend * Seasonality * Error    \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc3c3a88",
   "metadata": {},
   "source": [
    "We perform an Augmented Dickey Fuller (ADF)[2] Test to check whether the series is stationary or not:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "939c2ec0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -0.0544396646351928\n",
      "p-value: 0.9537916493653631\n",
      "Critial Values:\n",
      "   1%, -3.859073285322359\n",
      "Critial Values:\n",
      "   5%, -3.0420456927297668\n",
      "Critial Values:\n",
      "   10%, -2.6609064197530863\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.stattools import adfuller\n",
    "\n",
    "def print_test_statistics(values):\n",
    "    result = adfuller(values)\n",
    "    print(f'ADF Statistic: {result[0]}')\n",
    "    print(f'p-value: {result[1]}')\n",
    "    for key, value in result[4].items():\n",
    "        print('Critial Values:')\n",
    "        print(f'   {key}, {value}')\n",
    "    \n",
    "print_test_statistics(values=single_bxd.iloc[:,0].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a4d483c",
   "metadata": {},
   "source": [
    "From the above, the obtained p-value is greater than significance level of 0.05 and the ADF statistic is greater than any of the critical values.  We therefore do not reject the null hypothesis, and we can conclude that this series is non-stationary.\n",
    "\n",
    "The next step in our analysis is to try to make this series stationary, and we first try to do this by differencing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "f1b05b15",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -963.6122928751103\n",
      "p-value: 0.0\n",
      "Critial Values:\n",
      "   1%, -4.331573\n",
      "Critial Values:\n",
      "   5%, -3.23295\n",
      "Critial Values:\n",
      "   10%, -2.7487\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffed_single_bxd = single_bxd.diff().dropna()\n",
    "plt.plot(diffed_single_bxd)\n",
    "\n",
    "print_test_statistics(diffed_single_bxd.iloc[:,0].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5513fa5d",
   "metadata": {},
   "source": [
    "From the above, we see that differencing once made the time series stationary because the p-value is less than 0.05 and the ADF statistic is less than all the critical values.  Next, we plot the PACF and ACF to help us determine which model(AR[I]MA(p,q), AR(p), MA(q)) model to fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "b888df02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "\n",
    "plot_acf(diffed_single_bxd)\n",
    "plot_pacf(diffed_single_bxd, lags=8, method=\"yw\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd8c4136",
   "metadata": {},
   "source": [
    "From the above, we see a tail-off at the ACF plot, and a cut-off at lag 1 in the PACF.  This indicates an AR(1) process of the form:\n",
    "\n",
    "x<sub>t</sub> = ϕ<sub>0</sub>x<sub>0</sub> + ϕ<sub>1</sub>x<sub>t-1</sub> + ω<sub>t-1</sub> + μ\n",
    "\n",
    "We can now use Yule Walker equations to get the value of ϕ.  For this, we split the data into a training and test set, so that we can perform how our model performs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "3daef587",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [-0.183827   0.3372827]\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.ar_model import AutoReg\n",
    "X = diffed_single_bxd.iloc[:,0].values\n",
    "train, test = X[0:len(X)-5], X[len(X)-5:]\n",
    "model_fit = AutoReg(train, lags=1).fit()\n",
    "print(f'Coefficients: {model_fit.params}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80aa9a03",
   "metadata": {},
   "source": [
    "We thereafter inspect the errors from our model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "e1159394",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error: 1.5102489398206589\n",
      "Error: 1.7835318929135164\n",
      "Error: 0.3757055062078283\n",
      "Error: 0.6932059282904643\n",
      "Error: 0.7827202928638868\n"
     ]
    }
   ],
   "source": [
    "predictions = model_fit.predict(start=len(train),\n",
    "                                end=len(train)+len(test)-1,\n",
    "                                dynamic=False)\n",
    "for i in range(len(predictions)):\n",
    "    print(f\"Error: {abs(predictions[i] - test[i])}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c4bc380",
   "metadata": {},
   "source": [
    "We use the root mean square error to see how our model performs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "96ca623c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test RMSE: 1.157\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "rmse = sqrt(mean_squared_error(test, predictions))\n",
    "print('Test RMSE: %.3f' % rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7065e45",
   "metadata": {},
   "source": [
    "And finally we plot how predicted values against the actual values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "bbb64bb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot results\n",
    "plt.plot(test)\n",
    "plt.plot(predictions, color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e653ca10",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "In this data-exploration exercise, we obtained real world data on BXD Mouse colonies which were represented in excel format as vectors.  We extracted the longest running experiment and did some time series analysis on it.  For this chosen experiment, the data was non-stationary, and we had to difference it once to make it stationary.  The PACF and ACF plots of the differenced data allowed us to infer that this data could be modelled using an AR(1) process.  As an exercise in forecasting, the experiment was split into a test and train data set, and used in forecasting.  The results were satisfactory, albeit 18 data points being too little to make a definite conclusion.  In conclusion, this exercise shows that an AR(1) process can be used to model the aging process of a mouse colony."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae80663c",
   "metadata": {},
   "source": [
    "## Future Work\n",
    "\n",
    "There were 2506 experiments in this data set and only one was chosen.  Coming up with a generalized model that performs well, if feasible, for all this experiments should be explored.  This would prove useful to researchers as an extra quality control check after completing an experiment, before uploading their data, for example, to a website like www.genenetwork.org."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bad909d9",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[0] Ashbrook, D. G., Arends, D., Prins, P., Mulligan, M. K., Roy, S., Williams, E. G., ... & Williams, R. W. (2021). A platform for experimental precision medicine: the extended BXD mouse family. Cell Syst 12 (3): 235-247. e9.\n",
    "\n",
    "[1] Time Series Analysis in Python – A Comprehensive Guide with Examples. Dec. 27, 2021. url: https://www.machinelearningplus.com/time-series/time-series-analysis-python/\n",
    "\n",
    "[2] Augmented Dickey Fuller Test (ADF Test) – Must Read Guide. Dec 28, 2021. url:https://www.machinelearningplus.com/time-series/augmented-dickey-fuller-test/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e07bd95",
   "metadata": {},
   "source": [
    "# Appendix\n",
    "### Using GNU/ GUIX To Manage Dependencies\n",
    "\n",
    "In this exercise, [GNU Guix](https://guix.gnu.org/) was used to handle dependencies.  The following manifest file was used:\n",
    "\n",
    "```\n",
    "(specifications->manifest\n",
    " '(\"python-matplotlib\"\n",
    "   \"python-notebook\"\n",
    "   \"python-numpy\"\n",
    "   \"python-pandas\"\n",
    "   \"python-scikit-learn\"\n",
    "   \"python-scipy\"\n",
    "   \"python-seaborn\"\n",
    "   \"python-statsmodels\"\n",
    "   \"python-wrapper\"))\n",
    "```\n",
    "\n",
    "This file was saved in a `manifest.scm` file and loaded with `guix shell -m manifest.scm`.  The command used to start the notebook file was: `jupyter notebook --ip=0.0.0.0 --port=8080`"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "/gnu/store/3282r97il61j9jkv2aaifa3nwdylzfsv-python-wrapper-3.9.6/bin/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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}