{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Covid-19 Timeseries Forecasting\n",
    "\n",
    "The aim of this notebook is to identify the optimal model from a given simple\n",
    "parametric family that best characterizes the growth curve of COVID-19 cases without \n",
    "overfitting the data.  \n",
    "The first part of the dataset (up to 20 March) will be used for training, along [Bayesian Information Criterion](https://en.wikipedia.org/wiki/Bayesian_information_criterion) for selecting the degree of our polynomial.  \n",
    "The chosen model will be tested on the rest of the dataset.  \n",
    "  \n",
    "Intuitively, is a timeseries forecasting model able to accurately predict the future number of cases?  \n",
    "I believe that it is not for most countries. There are many factors that a time series model will not be able to forecast. A country may decide to take some measures like lockdowns, increase the number of tests, promote self isolation, etc.\n",
    "  \n",
    "  \n",
    ">This is most obvious with weather forecasting where we have excellent models based on the physics of the atmosphere. No time series model will perform as well as a good atmospheric model for forecasting short-term weather. That is why meteorologists do not use time series models [(ref)](https://robjhyndman.com/hyndsight/forecasting-covid19/).  \n",
    "  \n",
    "However, it is an interesting exercise on the field of forecasting in a domain that is highly interpretable (at least at the depths I am reaching).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:00:57.737730Z",
     "start_time": "2020-04-01T16:00:57.163348Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "import datetime\n",
    "import logging\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.preprocessing import normalize\n",
    "\n",
    "from statsmodels.tsa.seasonal import seasonal_decompose\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from statsmodels.tsa.stattools import acf,pacf\n",
    "from statsmodels.tsa.arima_model import ARIMA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data gathering\n",
    "\n",
    "As in the [previous notebook](https://github.com/MikeXydas/Weekend-EDAs/blob/master/Covid19_Testing_Importance.ipynb) the number of confirmed cases will be taken from the [John Hopkins](https://github.com/CSSEGISandData/COVID-19/blob/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv) dataset which is daily updated.  \n",
    "We will group by country name and sum over provinces/states so as to have the cases per country."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:01:04.573835Z",
     "start_time": "2020-04-01T16:00:59.063815Z"
    }
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>1/22/20</th>\n",
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       "      <td>197</td>\n",
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       "      <td>243</td>\n",
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       "      <td>107</td>\n",
       "      <td>107</td>\n",
       "      <td>119</td>\n",
       "      <td>119</td>\n",
       "      <td>135</td>\n",
       "      <td>135</td>\n",
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       "    <tr>\n",
       "      <th>Vietnam</th>\n",
       "      <td>0</td>\n",
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       "      <td>2</td>\n",
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       "      <td>35</td>\n",
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      ],
      "text/plain": [
       "                    1/22/20  1/23/20  1/24/20  1/25/20  1/26/20  1/27/20  \\\n",
       "Country/Region                                                             \n",
       "Afghanistan               0        0        0        0        0        0   \n",
       "Albania                   0        0        0        0        0        0   \n",
       "Algeria                   0        0        0        0        0        0   \n",
       "Andorra                   0        0        0        0        0        0   \n",
       "Angola                    0        0        0        0        0        0   \n",
       "...                     ...      ...      ...      ...      ...      ...   \n",
       "Venezuela                 0        0        0        0        0        0   \n",
       "Vietnam                   0        2        2        2        2        2   \n",
       "West Bank and Gaza        0        0        0        0        0        0   \n",
       "Zambia                    0        0        0        0        0        0   \n",
       "Zimbabwe                  0        0        0        0        0        0   \n",
       "\n",
       "                    1/28/20  1/29/20  1/30/20  1/31/20  ...  3/22/20  3/23/20  \\\n",
       "Country/Region                                          ...                     \n",
       "Afghanistan               0        0        0        0  ...       40       40   \n",
       "Albania                   0        0        0        0  ...       89      104   \n",
       "Algeria                   0        0        0        0  ...      201      230   \n",
       "Andorra                   0        0        0        0  ...      113      133   \n",
       "Angola                    0        0        0        0  ...        2        3   \n",
       "...                     ...      ...      ...      ...  ...      ...      ...   \n",
       "Venezuela                 0        0        0        0  ...       70       77   \n",
       "Vietnam                   2        2        2        2  ...      113      123   \n",
       "West Bank and Gaza        0        0        0        0  ...       52       59   \n",
       "Zambia                    0        0        0        0  ...        3        3   \n",
       "Zimbabwe                  0        0        0        0  ...        3        3   \n",
       "\n",
       "                    3/24/20  3/25/20  3/26/20  3/27/20  3/28/20  3/29/20  \\\n",
       "Country/Region                                                             \n",
       "Afghanistan              74       84       94      110      110      120   \n",
       "Albania                 123      146      174      186      197      212   \n",
       "Algeria                 264      302      367      409      454      511   \n",
       "Andorra                 164      188      224      267      308      334   \n",
       "Angola                    3        3        4        4        5        7   \n",
       "...                     ...      ...      ...      ...      ...      ...   \n",
       "Venezuela                84       91      107      107      119      119   \n",
       "Vietnam                 134      141      153      163      174      188   \n",
       "West Bank and Gaza       59       59       84       91       98      109   \n",
       "Zambia                    3       12       16       22       28       29   \n",
       "Zimbabwe                  3        3        3        5        7        7   \n",
       "\n",
       "                    3/30/20  3/31/20  \n",
       "Country/Region                        \n",
       "Afghanistan             170      174  \n",
       "Albania                 223      243  \n",
       "Algeria                 584      716  \n",
       "Andorra                 370      376  \n",
       "Angola                    7        7  \n",
       "...                     ...      ...  \n",
       "Venezuela               135      135  \n",
       "Vietnam                 203      212  \n",
       "West Bank and Gaza      116      119  \n",
       "Zambia                   35       35  \n",
       "Zimbabwe                  7        8  \n",
       "\n",
       "[161 rows x 70 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# In case the link fails I am including a stored dataset which is not up to date\n",
    "try:\n",
    "    confirmed_cases_df = pd.read_csv('https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv', \n",
    "                                     index_col=['Country/Region'])\n",
    "    \n",
    "    # Drop unused columns Lat, Long\n",
    "    confirmed_cases_df = confirmed_cases_df.drop('Lat', axis=1)\n",
    "    confirmed_cases_df = confirmed_cases_df.drop('Long', axis=1)\n",
    "\n",
    "    # Group by and sum number of cases of each country\n",
    "    confirmed_cases_df = confirmed_cases_df.groupby(['Country/Region']).sum()\n",
    "\n",
    "    # Filter the countries that had no cases up until 20/3/2020 to avoid divisions by zero\n",
    "    confirmed_cases_df = confirmed_cases_df[confirmed_cases_df['3/20/20'] != 0]\n",
    "except:\n",
    "    logging.warning(\"GitHub link not working. Using stored csv file...\")\n",
    "    confirmed_cases_df = pd.read_csv(filepath_or_buffer=\"datasets/covid_19_country_cases.csv\")\n",
    "\n",
    "\n",
    "display(confirmed_cases_df)\n",
    "\n",
    "# Uncomment below if you want the DataFrame created to be saved on disk\n",
    "# confirmed_cases_df.to_csv(path_or_buf=\"datasets/covid_19_country_cases.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly we will sum over all the countries and try to fit a polynomial that forecasts the global number of cases as days pass. I avoid fitting a model to each country from the start since it will be more difficult to debug them.  \n",
    "  \n",
    "Steps:\n",
    "    1. Fit a global polynomial model\n",
    "    2. Examine the results, find and correct any bugs\n",
    "    3. Fit a different model for each country "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:01:06.512881Z",
     "start_time": "2020-04-01T16:01:06.503865Z"
    }
   },
   "outputs": [],
   "source": [
    "test_days = 7    # How many days will be used for testing\n",
    "bic_criterion = 2    # Tolerance of BIC (0 - 2 strict, 2 - 6 intermediate, >6 loose)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:01:09.650331Z",
     "start_time": "2020-04-01T16:01:09.115804Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mikexydas/pythonEnvs/thesisEnv/lib/python3.6/site-packages/pandas/plotting/_matplotlib/converter.py:103: FutureWarning: Using an implicitly registered datetime converter for a matplotlib plotting method. The converter was registered by pandas on import. Future versions of pandas will require you to explicitly register matplotlib converters.\n",
      "\n",
      "To register the converters:\n",
      "\t>>> from pandas.plotting import register_matplotlib_converters\n",
      "\t>>> register_matplotlib_converters()\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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zHuf99V//9T1qT3/60/P0pz99Q9qxEqEUAAAAwDRN+w2AU2JNKQAAAAAGJ5QCAAAAYHBCKQAAAIAN1lqbdhMGtZ7+CqUAAAAANtDpp5+eI0eOzEww1VrLkSNHcvrpp6/pOgudAwAAAGyg888/P4cPH85NN9007aZMxG233XaPAOr000/P+eefv6b7CKUAAAAANtCpp56aCy64YNrNmJj9+/fnG7/xG+/zfUzfAwAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwEw2lqupFVfXRqvpIVf12VZ1eVRdU1Xur6vqqektVndaf+1X9/vX98fll9/nJvv6JqnrSsvoVfe36qnrZsvqKzwAAAABgc5hYKFVV5yX5sSR7WmuPSnJKkmckeXWSn2utPTzJF5I8v7/k+Um+0Nd/rj8vVXVhf90jk1yR5Jeq6pSqOiXJLyZ5cpILk3xff25O8gwAAAAANoFJT9/bmeSMqtqZZC7JjUm+Ncnv9MffmOSp/fen9Pvpjz+xqqqvX9Va++fW2t8muT7JY/rP9a21T7fWbk9yVZKn9Nec6BkAAAAAbAITC6Vaa59N8jNJDqULo76Y5ECSm1trd/SnHU5yXv/9vCSf6a+9oz//nOX14645Uf2ckzwDAAAAgE2gWmuTuXHVA5O8Lcn3Jrk5yf9IN3rpyn5aXarqoUne0Vp7VFV9JMkVrbXD/bFPJfmmJFcmeU9r7Tf7+uuTvKN/zBWttRf09Wcfd/49nrFCGxeSLCTJueeee8lVV1210T/DYG699daceeaZ027G4Ga138ns9l2/Z4t+zxb9nj2z2nf9ni36PVv0e7bMar+TtfX9sssuO9Ba27PSsZ0b2qpjXZ7kb1trNyVJVf1ukscnObuqdvYjmc5P8tn+/M8meWiSw/10vwckObKsftTya1aqHznJM47RWltMspgke/bsaZdeeul96vA07d+/P1u5/es1q/1OZrfv+j1b9Hu26PfsmdW+6/ds0e/Zot+zZVb7nWxc3ye5ptShJI+tqrl+nacnJvlYkj9N8j39Oc9N8vv996v7/fTH/6R1w7iuTvKM/u18FyR5RJL3JXl/kkf0b9o7Ld1i6Ff315zoGQAAAABsApNcU+q96abr/VWSD/fPWkzy0iQvrqrr063/9Pr+ktcnOaevvzjJy/r7fDTJW9MFWn+U5Edaa//Sj4L60STXJLkuyVv7c3OSZwAAAACwCUxy+l5aay9P8vLjyp9O9+a848+9LcnTTnCffUn2rVB/e5K3r1Bf8RkAAAAAbA6TnL4HAAAAACsSSgEAAADbx3iczM8nO3Z02/F42i3iBCY6fQ8AAABgMONxsrCQLC11+wcPdvtJMhpNr12syEgpAAAAYHvYu/fuQOqopaWuzqYjlAIAAAC2h0OH1lZnqoRSAAAAwPawa9fa6kyVUAoAAADYHvbtS+bmjq3NzXV1Nh2hFAAAALA9jEbJ4mKye3dS1W0XFy1yvkl5+x4AAACwfYxGQqgtwkgpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAYHMaj5P5+WTHjm47Hk+7RWygndNuAAAAAMA9jMfJwkKytNTtHzzY7SfJaDS9drFhjJQCAAAANp+9e+8OpI5aWurqbAtCKQAAAGDzOXRobXW2HKEUAAAAsPns2rW2OluOUAoAAADYfPbtS+bmjq3NzXV1tgWhFAAAALD5jEbJ4mKye3dS1W0XFy1yvo14+x4AAACwOY1GQqhtzEgpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAACGMR4n8/PJjh3ddjyedouYop3TbgAAAAAwA8bjZGEhWVrq9g8e7PaTZDSaXruYGiOlAAAAgMnbu/fuQOqopaWuzkwSSgEAAACTd+jQ2upse0IpAAAAYPJ27VpbnW1PKAUAAABM3r59ydzcsbW5ua7OTBJKAQAAAJM3GiWLi8nu3UlVt11ctMj5DPP2PQAAAGAYo5EQirsYKQUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4IRSAAAAAAxOKAUAAADA4CYaSlXV2VX1O1X18aq6rqoeV1UPqqp3VtUn++0D+3Orql5bVddX1Yeq6uJl93luf/4nq+q5y+qXVNWH+2teW1XV11d8BgAAAACbw6RHSr0myR+11r4+yTckuS7Jy5K8q7X2iCTv6veT5MlJHtF/FpL8ctIFTElenuSbkjwmycuXhUy/nOQHl113RV8/0TMAAAAA2AQmFkpV1QOS/O9JXp8krbXbW2s3J3lKkjf2p70xyVP7709J8qbWeU+Ss6vqa5I8Kck7W2ufb619Ick7k1zRH7t/a+09rbWW5E3H3WulZwAAAACwCVSX50zgxlUXJVlM8rF0o6QOJPnxJJ9trZ3dn1NJvtBaO7uq/iDJq1prf94fe1eSlya5NMnprbWf7us/leSfkuzvz7+8r39zkpe21r6rqm5e6RkrtHEh3aisnHvuuZdcddVVE/kthnDrrbfmzDPPnHYzBjer/U5mt+/6PVv0e7bo9+yZ1b7r92zR79mi37NlVvudrK3vl1122YHW2p6Vju3c0Fbd894XJ3lha+29VfWaHDeNrrXWqmoyqdgqntFaW0wXnGXPnj3t0ksvnWRTJmr//v3Zyu1fr1ntdzK7fdfv2aLfs0W/Z8+s9l2/Z4t+z5aZ6/d4nOzdm/0vfGEu/YVfSPbtS0ajabdqMDP3915mo/o+yTWlDic53Fp7b7//O+lCqn/op96l3/5jf/yzSR667Prz+9rJ6uevUM9JngEAAADcV+NxsrCQHDzY7R882O2Px9NtF1vKxEKp1trfJ/lMVX1dX3piuql8Vyc5+ga95yb5/f771Ume07+F77FJvthauzHJNUm+vaoe2C9w/u1JrumPfamqHttP0XvOcfda6RkAAADAfbV3b7K0dGxtaamrwypNcvpekrwwybiqTkvy6STPSxeEvbWqnp/kYJKn9+e+Pcl3JLk+yVJ/blprn6+qVyZ5f3/eK1prn++//3CS30hyRpJ39J8kedUJngEAAADcV4cOra0OK5hoKNVauzbJSotZPXGFc1uSHznBfd6Q5A0r1D+Q5FEr1I+s9AwAAABgA+zadffUvePrsEqTXFMKAAAA2I727Uvm5o6tzc11dVgloRQAAACwNqNRsriY7N7d7e/e3e3P0Nv3uO8mvaYUAAAAsB2NRt1n//7khhum3Rq2ICOlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAACAwQmlAAAAABicUAoAAABIxuNkfj7ZsaPbjsfTbhHb3M5pNwAAAACYsvE4WVhIlpa6/YMHu/0kGY2m1y62NSOlAAAAYNbt3Xt3IHXU0lJXhwkRSgEAAMCsO3RobXXYAEIpAAAAmHW7dq2tDhtAKAUAAACzbt++ZG7u2NrcXFeHCRFKAQAAwKwbjZLFxWT37qSq2y4uWuScifL2PQAAAKALoIRQDMhIKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAAAAGJ5QCAAAAYHBCKQAAANhuxuNkfj7ZsaPbjsfTbhHcw85pNwAAAADYQONxsrCQLC11+wcPdvtJMhpNr11wHCOlAAAAYDvZu/fuQOqopaWuDpuIUAoAAAC2k0OH1laHKRFKAQAAwHaya9fa6jAlQikAAADYTvbtS+bmjq3NzXV12ESEUgAAALCdjEbJ4mKye3dS1W0XFy1yzqbj7XsAAACw3YxGQig2PSOlAAAAABicUAoAAACAwa05lKqqHVV1/0k0BgAAAIDZsKpQqqp+q6ruX1X3S/KRJB+rqp+YbNMAAAAA2K5WO1Lqwtbal5I8Nck7klyQ5NkTaxUAAAAA29pqQ6lTq+rUdKHU1a21ryRpk2sWAAAAANvZakOp/57khiT3S/JnVbU7yZcm1SgAAAAAtredqzmptfbaJK9dVjpYVZdNpkkAAAAAbHerXej83Kp6fVW9o9+/MMlzJ9oyAAAAALat1U7f+40k1yT52n7/b5L8x0k0CAAAAIDtb7Wh1INba29NcmeStNbuSPIvE2sVAAAAANvaakOpL1fVOenfuFdVj03yxYm1CgAAAIBtbVULnSd5cZKrkzysqv4iyVcn+Z6JtQoAAACAbW21b9/7q6r6liRfl6SSfKK19pWJtgwAAACAbWu1b997WpIzWmsfTfLUJG+pqosn2jIAAAAAtq3Vrin1U621W6rqCUmemOT1SX55cs0CAAAAYDtbbSh19E1735nkV1trf5jktMk0CQAAAIDtbrWh1Ger6r8n+d4kb6+qr1rDtQAAAABwjNUGS09Pck2SJ7XWbk7yoCQ/MbFWAQAAAHcZj5P5+WTHjm47Hk+7RXDfrfbte0tJfreq/lVV7erLH59cswAAAICkC6AWFpKlpW7/4MFuP0lGo+m1C+6r1b5977ur6pNJ/jbJu/vtOybZMAAAACDZu/fuQOqopaWuDlvZaqfvvTLJY5P8TWvtgiSXJ3nPxFoFAAAAJEkOHVpbHbaK1YZSX2mtHUmyo6p2tNb+NMmeCbYLAAAASLJr19rqsFWsNpS6uarOTPJnScZV9ZokX55cswAAAIAk2bcvmZs7tjY319VhKztpKFVVD6+qxyd5SpKlJC9K8kdJjiR54eSbBwAAALNtNEoWF5Pdu5Oqbru4aJFztr57Gyn180m+1Fr7cmvtztbaHa21Nyb5vSRXTrx1AAAAQEaj5IYbkjvv7LYCKbaDewulzm2tffj4Yl+bn0iLAAAAANj27i2UOvskx85YzQOq6pSq+uuq+oN+/4Kqem9VXV9Vb6mq0/r6V/X71/fH55fd4yf7+ieq6knL6lf0teur6mXL6is+AwAAAIDN4d5CqQ9U1Q8eX6yqFyQ5sMpn/HiS65btvzrJz7XWHp7kC0me39efn+QLff3n+vNSVRcmeUaSRya5Iskv9UHXKUl+McmTk1yY5Pv6c0/2DAAAAAA2gXsLpf5jkudV1f6q+m/9593pQp4fv7ebV9X5Sb4zya/1+5XkW5P8Tn/KG5M8tf/+lH4//fEn9uc/JclVrbV/bq39bZLrkzym/1zfWvt0a+32JFclecq9PAMAAACATaBaa/d+UtVlSR7V7+J4I1UAACAASURBVH60tfYnq7p51e8k+a9JzkrykiTfn+Q9/QimVNVDk7yjtfaoqvpIkitaa4f7Y59K8k3pFlR/T2vtN/v665O8o3/EFa21F/T1Zx93/j2esUL7FpIsJMm55557yVVXXbWabm1Kt956a84888xpN2Nws9rvZHb7rt+zRb9ni37Pnlntu37PFv2eLfo9W2a138na+n7ZZZcdaK3tWenYztXcoLX2p0n+dPXNS6rqu5L8Y2vtQFVdupZrh9JaW0yymCR79uxpl1566XQbdB/s378/W7n96zWr/U5mt+/6PVv0e7bo9+yZ1b7r92zR79mi37NlVvudbFzfVxVKrdPjk3x3VX1HktOT3D/Ja5KcXVU7W2t3JDk/yWf78z+b5KFJDlfVziQPSHJkWf2o5desVD9ykmcAAAAAsAnc25pS69Za+8nW2vmttfl0C5X/SWttlG7E1ff0pz03ye/336/u99Mf/5PWzS28Oskz+rfzXZDkEUnel+T9SR7Rv2nvtP4ZV/fXnOgZAAAAAGwCEwulTuKlSV5cVdcnOSfJ6/v665Oc09dfnORlSdJa+2iStyb5WJI/SvIjrbV/6UdB/WiSa9K93e+t/bknewYAAAAAm8Akp+/dpbW2P8n+/vun07057/hzbkvytBNcvy/JvhXqb0/y9hXqKz4DAAAAgM1hGiOlAAAAAJhxQikAAAAABieUAgAAgIGNx8n8fLJjR7cdj6fdIhjeIGtKAQAAAJ3xOFlYSJaWuv2DB7v9JBmNptcuGJqRUgAAADCgvXvvDqSOWlrq6jBLhFIAAAAwoEOH1laH7UooBQAAAAPatWttddiuhFIAAAAwoH37krm5Y2tzc10dZolQCgAAAAY0GiWLi8nu3UlVt11ctMg5s8fb9wAAAGBgo5EQCoyUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAgPtgPE7m55MDB7rteDztFsHWsHPaDQAAAICtajxOFhaSpaVu/+DBbj9JRqPptQu2AiOlAAAAYJ327r07kDpqaamrAycnlAIAAIB1OnRobXXgbkIpAAAAWKddu9ZWB+4mlAIAAIB12rcvmZs7tjY319WBkxNKAQAAwDqNRsniYrJ7d7e/e3e3b5FzuHfevgcAAAD3wWjUffbvT264Ydqtga3DSCkAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAAGBwQikAAAAABieUAgAAgGXG42R+Ptmxo9uOx9NuEWxPO6fdAAAAANgsxuNkYSFZWur2Dx7s9pNkNJpeu2A7MlIKAAAAenv33h1IHbW01NWBjSWUAgAAgN6hQ2urA+snlAIAAIDerl1rqwPrJ5QCAACA3r59ydzcsbW5ua4ObCyhFAAAAPRGo2RxMdm9O6nqtouLFjmHSfD2PQAAAFhmNBJCwRCMlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAABgcEIpAAAAAAYnlAIAAGDbGo+T+flkx45uOx5Pu0XAUTun3QAAAACYhPE4WVhIlpa6/YMHu/0kGY2m1y6gY6QUAAAA29LevXcHUkctLXV1YPqEUgAAAGxLhw6trQ4MSygFAADAtrRr19rqwLCEUgAAAGxL+/Ylc3PH1ubmujowfUIpAAAAtqXRKFlcTHbvTqq67eKiRc5hs/D2PQAAALat0UgIBZuVkVIAAAAADE4oBQAAAMDghFIAAAAADE4oBQAAAMDghFIAAAAADE4oBQAAAMDghFIAAAAADE4oBQAAAMDghFIAAABsGeNxMj+f7NjRbcfjabcIWK+d024AAAAArMZ4nCwsJEtL3f7Bg91+koxG02sXsD5GSgEAALAl7N17dyB11NJSVwe2HqEUAAAAW8KhQ2urA5ubUAoAAIAtYdeutdWBzU0oBQAAwJawb18yN3dsbW6uqwNbj1AKAACALWE0ShYXk927k6puu7hokXPYqrx9DwAAgC1jNBJCwXZhpBQAAAAAgxNKAQAAADA4oRQAAAAAgxNKAQAAADA4oRQAAAAAgxNKAQAAADA4oRQAAABTMx4n8/PJjh3ddjyedouAoeycdgMAAACYTeNxsrCQLC11+wcPdvtJMhpNr13AMIyUAgAAYCr27r07kDpqaamrA9ufUAoAAICpOHRobXVgexFKAQAAMBW7dq2tDmwvQikAAACmYt++ZG7u2NrcXFcHtj+hFAAAAFMxGiWLi8nu3UlVt11ctMg5zIqJhVJV9dCq+tOq+lhVfbSqfryvP6iq3llVn+y3D+zrVVWvrarrq+pDVXXxsns9tz//k1X13GX1S6rqw/01r62qOtkzAAAA2FxGo+SGG5I77+y2AimYHZMcKXVHkv+rtXZhkscm+ZGqujDJy5K8q7X2iCTv6veT5MlJHtF/FpL8ctIFTElenuSbkjwmycuXhUy/nOQHl113RV8/0TMAAAAA2AQmFkq11m5srf1V//2WJNclOS/JU5K8sT/tjUme2n9/SpI3tc57kpxdVV+T5ElJ3tla+3xr7QtJ3pnkiv7Y/Vtr72mttSRvOu5eKz0DAACACRmPk/n55MCBbjseT7tFwGa2c4iHVNV8km9M8t4k57bWbuwP/X2Sc/vv5yX5zLLLDve1k9UPr1DPSZ4BAADABIzHycJCsrTU7R882O0npuQBK6tukNEEH1B1ZpJ3J9nXWvvdqrq5tXb2suNfaK09sKr+IMmrWmt/3tffleSlSS5Ncnpr7af7+k8l+ack+/vzL+/r35zkpa217zrRM1Zo20K6qYI599xzL7nqqqsm8AsM49Zbb82ZZ5457WYMblb7ncxu3/V7tuj3bNHv2TOrfdfv2TJL/f7wh5Pbb+++n3/+rTl8uOv3aaclj370FBs2oFn6ey+n37NnLX2/7LLLDrTW9qx0bKIjparq1CRvSzJurf1uX/6Hqvqa1tqN/RS8f+zrn03y0GWXn9/XPpsumFpe39/Xz1/h/JM94xittcUki0myZ8+edumll6502pawf//+bOX2r9es9juZ3b7r92zR79mi37NnVvuu37Nllvr9rd+aHB3z8DM/sz8vecmlSbq36t155/TaNaRZ+nsvp9+zZ6P6Psm371WS1ye5rrX2s8sOXZ3k6Bv0npvk95fVn9O/he+xSb7YT8G7Jsm3V9UD+wXOvz3JNf2xL1XVY/tnPee4e630DAAAACZg16611QEm+fa9xyd5dpJvrapr+893JHlVkm+rqk8mubzfT5K3J/l0kuuT/GqSH06S1trnk7wyyfv7zyv6Wvpzfq2/5lNJ3tHXT/QMAAAAJmDfvmRu7tja3FxXB1jJxKbv9WtD1QkOP3GF81uSHznBvd6Q5A0r1D+Q5FEr1I+s9AwAAAAm4+hi5nv3dtvdu7tAyiLnwIkM8vY9AAAAtr/RqPvs35/ccMO0WwNsdpOcvgcAAMAWNh4n8/PJjh3ddjyedouA7cRIKQAAAO5hPE4WFpKlpW7/4MFuPzElD9gYRkoBAABwD3v33h1IHbW0dPeaUQD3lVAKAACAezh0aG11gLUSSgEAAHAPu3atrQ6wVkIpAAAA7mHfvmRu7tja3FxXB9gIQikAAADuYTRKFheT3buTqm67uGiRc2DjCKUAAABmwHiczM8nO3Z02/H43q8ZjZIbbkjuvLPbCqSAjbRz2g0AAABgssbjZGHh7rfpHTzY7SeCJmB6jJQCAADY5vbuvTuQOmppqasDTItQCgAAYJs7dGhtdYAhCKUAAAC2uV271lYHGIJQCgAAYJvbty+Zmzu2NjfX1QGmRSgFAACwBa3lbXqjUbK4mOzenVR128VFi5wD0+XtewAAAFvMet6mNxoJoYDNxUgpAACALcbb9IDtQCgFAACwxXibHrAdCKUAAAC2GG/TA7YDoRQAAMAW4216wHYglAIAAJiytbxJL/E2PWB78PY9AACAKVrPm/SOHhNCAVuZkVIAAABT5E16wKwSSgEAAEyRN+kBs0ooBQAAMEXepAfMKqEUAADAFHmTHjCrhFIAAABT5E16wKzy9j0AAIAp8yY9YBYZKQUAAADA4IRSAAAAG2w8TubnkwMHuu14PO0WAWw+QikAAIB7cTRk2rHj3kOm8ThZWEgOHuz2Dx7s9gVTAMcSSgEAAJzE8pCptXsPmfbuTZaWjq0tLXV1AO4mlAIAADiJtYZMhw6trQ4wq4RSAAAAJ7HWkGnXrrXVAWaVUAoAAJgpa1kfKll7yLRvXzI3d2xtbq6rA3A3oRQAADAz1ro+VLL2kGk0ShYXk927u/3du7v90Whj+gCwXQilAACALW0tI5/Wswj58pCpanUh02iU3HBDcskl3VYgBXBPO6fdAAAAgPU6OvLpaNB0dORTsnIQtN5FyEcjwRLARjNSCgAA2DTWut7TWkc+WYQcYPMQSgEAAJvCetZ7WuvIJ4uQA2weQikAAGBijo58OnBgMus9rXXk03rWhwJgMoRSAADARCwf+ZTc+8in9az3tJ6RT0cXIb/zTouQA0yTUAoAAFiVzbjek5FPAFuXUAoAALhXm3m9JyOfALYmoRQAAHCvrPcEwEYTSgEAwIxay3Q86z0BsNGEUgAAsE2sJWRa63S8+7reU2LkEwDHEkoBAMAmtNZFxdcaMq11Ot59Xe/pkkuMfALgWEIpAAAYwNGQ6cCBjR/FlKw9ZFrrdDzrPQGw0YRSAACwRvdlFFOy8aOYkrWHTOudjme9JwA2ilAKAADWYDOOYkrWHjKtdzoeAGwUoRQAADNvLSOfNusoprWGTKbjATBtQikAADa19UyVm+QC4Zt1FNN6QibT8QCYJqEUAACDmuSC30NMrdvMo5iETABsJUIpAIBtaq0jhtZzzWZb8HuIqXX3dRRTYhQTACRCKQCAqVjLaKHjr1lNALSeEUObcVTSWgOjIabW3ddRTJdcImQCgEQoBQDMgM02Ymito4WOv2Y1AdB6RgxtxlFJaw2MhphalxjFBAAbQSgFAGw5W33E0BCB0XpGDG3GUUlrDYyGWiAcALjvhFIAwFStdRrbZgyANmNgtJ4RQ5txVNJaAyMLhAPA1iGUAgA21KSnsW3GAGgzBkbrGTE09KikZDILfguYAGBrEEoBABtmiFFMmzEA2oyB0XpGDA09KsmC3wAw24RSAMAJrXWx7yFGMW3GAOi+BEbJZAKjo9esdcSQUUkAwFCEUgDAitazQPgQo5i2y4ih9YwWEgABANuJUAoAWNF6ptYNMYrJiCEAgO1BKAUAM2Qt0/HWM7VuiGlsR68TAAEAbG1CKQCYEWudjreeqXVDTWMDAGDrE0oBwIxY63S89UytS4xiAgBgdYRSADAj1jodbz2jngAAYLV2TrsBAMAwdu3qpuytVD+R0UgIBQDAZBgpBQAzYr3T8QAAYBKEUgAwI0zHAwBgMzF9DwBmiOl4AABsFkZKAcAmMR4n8/PJgQPddjxe/TU7/v/27j1csqq88/j3pZtuaO7IRRRo4gW5CKKNGHVUUFE0GmUEFTqgPmMYcVAkaqIigoNOMsoQ74MiKoqRgfGSoI6XMYB3Ax1R4igEudpRkAByv3W/88daRReHPt2n6pzadWrv7+d5zsOpvXd1rx+reteut9Zae4OZP0eSJEmaDyxKSZI0IoMUjD7/eTjqqDULkV9zTXk80+dkzuw5kiRJ0nxhUUqSpBkYdETSoAWj44+HO+988LY77yzbpzPMcyRJkqT5wqKUJEnrMcyIpEELRtdeO9j2YZ8jSZIkzRcWpSRJnTTIyKdhRiQNWjDaeefBtg/7HEmSJGm+sCglSZp4o55aN8yIpEELRu99LyxZ8uBtS5aU7dMZ5jmSJEnSfGFRSpI00ZqYWjfMiKRBC0bLl8MnPgFLl5bHS5eWx8uXT/939D8nYmbPkSRJkuYLi1KSpHmnN/JpxYr5MbVumBFJwxSMli+Hq6+GZcvKf2dSXOo9Z/XqmT9HkiRJmg8WjrsBkiT164186hWaeiOfYO0Fl2Gn1l1zzdq3r03v7z3++PLn7rxzKUitrwC0fLlFIkmSJGk6jpSSJI3cKBcVb2JqHTgiSZIkSZprFqUkSSM16kXFm5paJ0mSJGluWZSSJA1k0DvdjXrk07AFJkc+SZIkSeNlUUqSNGPD3OmuqZFPFpgkSZKkyWJRSpI6bpTrPcHsRj6BU+skSZKktrIoJUkdNur1nmB2I5+WLXPkkyRJktRWFqUkqUXm23pP4KLikiRJktbOopQktcR8Xe8JXPNJkiRJ0kNZlJKkeaw38mnFivm33pOjniRJkiTNhkUpSWrIoFPr+kc+wfxb78lRT5IkSZJmw6KUJA1pkCLTMFPrXO9JkiRJUptZlJLUSoOOShr0OYMWmYaZWud6T5IkSZLazKKUpNYZZlTSqItMw0ytc70nSZIkSW1mUUrSrA2zVtKwo5hGteD3qItMw0ytc70nSZIkSW3W2qJURBwUEZdFxBUR8bZxt0eaK4MUZ/qPH1XBaNARRrMdxQSjWfB71EWmYQtMvZFP4MgnSZIkSe3SyqJURCwAPgq8ANgDOCwi9hhvq6TZG7Q400TBaNARRk2MYhpmVNKoi0zDTq3rjXxatsyRT5IkSZLapZVFKWA/4IrMvDIz7wXOBl4y5jZJszbqAlATi3E3MYppmFFJTRSZnFonSZIkSWtEZo67DXMuIg4BDsrM19bHRwBPycxjphx3FHAUwPbbb7/s7LPPbrytc+X2229n0003HXczGte13CtWrPl9xx1v5ze/WZN92bJ1Hz/VXBwPcOmlcO+9D92+aBHstdfsj5/6nP7c63rOTTfBypXleYsWwSMfCVtvvfZjZ/OcpnTttd5j7m4xd/d0Nbu5u8Xc3WLubulqbhgs+wEHHLAiM/dd687MbN0PcAjwyb7HRwAfWddzli1blpPs/PPPH3cTxqJruZcuzSwT6zJPOeX8B35funT9x/f/zNXxmZlnnZW5ZMmDj1+ypGyfi+OnPqeXe33PaZuuvdZ7zN0t5u6ermY3d7eYu1vM3S1dzZ05WHbg4pymFtPW6XsrgZ36Hu9Yt0kTbdApZqM+HgafxjbstDcX/JYkSZKkdlk47gaMyEXAYyPijyjFqFcCh4+3SdLs9YowvTWeli4tBaN1FYB6x197bVm0ey6P73/eIAWiQY/vf84FF5T1mCRJkiRJk62VRanMvD8ijgG+CSwAPpWZvxhzs6Q5MWhxpomCkSRJkiRJg2plUQogM78OfH3c7ZAkSZIkSdJDtXVNKUmSJEmSJM1jFqUkSZIkSZLUOItSkiRJkiRJapxFKUmSJEmSJDXOopQkSZIkSZIaZ1FKkiRJkiRJjbMoJUmSJEmSpMZZlJIkSZIkSVLjLEpJkiRJkiSpcRalJEmSJEmS1DiLUpIkSZIkSWqcRSlJkiRJkiQ1zqKUJEmSJEmSGmdRSpIkSZIkSY2zKCVJkiRJkqTGWZSSJEmSJElS4yIzx92GeSEifg9cM+52zMI2wI3jbsQYdDU3dDe7ubvF3N1i7u7panZzd4u5u8Xc3dLV3DBY9qWZue3adliUaomIuDgz9x13O5rW1dzQ3ezm7hZzd4u5u6er2c3dLebuFnN3S1dzw9xld/qeJEmSJEmSGmdRSpIkSZIkSY2zKNUenxh3A8akq7mhu9nN3S3m7hZzd09Xs5u7W8zdLebulq7mhjnK7ppSkiRJkiRJapwjpSRJkiRJktQ4i1KSJEmSJElqnEUpTYyIiHG3Qc2xvyVJk8z3sW7pen93LX/X8k7V9fyaWxalJkhELOr7vTMngoh4b0Tsnh1bAM3+7lZ/d1UUL4+Ih427LRq92t//OSJ2GHdbNHpd7++uvo9FxJ9HxCPG3Y6mdbi/3xoRj+pa/q7l7elqf3dRfQ8/MCI2G/XfZVFqAkTEERHxI+ADEXEcdONEGBGHR8R3gdcDfzbu9jTF/u5WfwNExFERcXJEbDzutjQpIl4EXA4cAHQme/3A9rGIePS429KkiHg+8CvgacCi9RzeGvZ3t/obICKOjIivRcRJEfHH425PUyLilRFxCXAC8Phxt6cp9brt/Ih4f0QcOu72NCUiDouInwBvBp477vY0xf7uXH8fFRHH1t+7NEjgYODXwEHApqP++xaO+i/Q8CJiMfB2yge2twIbAu+OiJ9l5j+OtXEjFBGbA+8HdqHk3x3You6LNhZo6kluMfA2OtTfEbEBsBnwPjrU3/BAny8EXgv8FXA38C3ge+NsV1MiYglwCPDazLxwyr5W9nt9vR8K/CXwW+ApEbEyM+8eb8tGLyIWAi8E3piZ35yyr639vYDyGre/H7yvrf0dwObAR4EdgPcALwCOjIjfZ+avx9m+UanntW2As4HbgTcCbwCitz8zV4+vhaMTEZsAfw3sBZwI7Aa8IiKuzMwVY23cCEXEVsDpwBLgLcCLgTvrvlb2d/33vYSO9XfNvRXwcWATOtLfABGxEaUA93pgSUT8fWZePd5WNSMitgSOAI7MzO838Xc6Umoey8x7gH8BXlpfEN8HfgBsP9aGjVhm3gqcnpnPz8wfAAm8vO5r44XshlncDVwKHNyF/q65V2fmH+hQf0OZmln7/D7gnymFuI8Dr2nzNLbom5JKef/ZEvh5RGxTp/gsg/b2e71wuwR4MvA/gWdS+r71MvN+YFfguojYIiLeXIeEt65AEREbAmTmKuCnwH50oL97ueGB/n4cHehvKAXIek7/A7CCct12PnAm5T38vrE2cERq7tWZeQPwPzLzTzPzu8BlwGvggfNeK2XmHZRz+ktq7n8AbqZ8ydhamXkz8OHMfGFmfg+4gRb3dy28ZO3vn1H+fbe+v/ty3wR8tEP9vQCgfi67ODMfSSnCvmesDRuxXu5qS+COzPx+RDw8IpZHxB+N8u+3KDXPRMQ7IuIpfZu+npk31xPDfcDewG1jat7I9OeuFzkX9+3+InB/ROw9ntaNTkS8HTgjIl4TZb7ul4Au9Hd/7m0y8+K+IbGt7W+AiDgR+LuIeHVEbJ2ZP8nMuygfWncEnlu/eW6VvtyvioitKRdx9wJPpfT5nsCHIuK/1+NbMUR6yrktgCsz8xbgf1NGEjyjfuvcKlPP6RGxBeWD6pOBLwPbAu+gTFMe+VoFTek7t/X+fV9eP8C1vb97uV8VEdvWkd6X0/L+BoiIkyjnrkPqpg8Dd9RrmV9QilKtygwPzZ2ZX4tiAXAxcEP9tr1VIuKYiNirb9PZmXlr7e/fAY+hjhJrk/7cNeuF9fcA/i/l2nXpONs4ChHxDuD9ff++zwK60N+93C8DyMwL6va29/dJlPPay+qmb9f/vpsy2vmAelyrrtP7cv/HumkjYOco08/PpUzXPC0i3lWPn/P8rfofOskiYoeI+CJlmP9ZfbvuglKJjrLezP2Ub2VaYW2567fL/bYCrqJFr9eI2C0ifkj5IH4u8DLgSKA3aqqt/b223K/ojRyqh7Wuv3uirBH2dEoB6jnAiVEXAK7fyHwaOJwylbE1puR+LmXY+x2UKU3HAx/PzDdS/g0sj4hHTPpoimnObZmZ99XRIvdRinHLgCdNee7EXuBOd06vI0huA5YDX8vMt1HWjnsq8KhxtXeurOXcdghwWNTRgS3u76m5DwVeUUd630JL+7unXsjvR/ng8oZ6rtuijh5aFRG7U6a5/GqMzZxzU3IfExHH1SJs1mu4e4An1AJ8K0TE0oi4EHgncGrfrt51+qqIeDgl+8/H0MSRWFvu/uv0+l69IWVdyDb1994R8WPKue0i4ISIeGFm3tN7nbe0v6fmfldE/EndF23tb5j2fL4lPDAq8kOUZVWiTSPEpuQ+NiL+IjN/BdwIfAR4Z2a+BngTcFwdTDDn+Vv3oW+C/QE4NzO3BG6JiL+o2/v7aHNg08z8TUQ8ISIOb7yVc2+tuaOsRwFAZl4FLAX2qfva8Lq9DTgnM/8sM8+jjJB6ambe25evjf29rtwBre3v3rDYJwLvzszvACdTPqy8qXdMZn4BuBV4VkQ8OSKWj6Wxc2ia3PcCxwEnUYqQC+qb/K8pU1YfO6bmzqVpz229gltmfgu4GtgrIv4kIv5L3T7JBbnp3ssATgNWAYsiYklmrqSMphnpkPCGrPec3tL+Xlvup9d9p9Pe/u5NV/wPwJsz8yvAu4BHAK/sO+xRwLX1A+weEfHUMTR1Tq0l94mU3If1jsnM/wNsHxHPHk8rR+Im4POU96fVEfGqur3/GmV74K7MvC0i9oqIFzTdyBGYmvvV8OCpPpl5EeXf9bPrvokttPfZAPhUZi7PzLNZU3Tvvy5tY39PzX0O5UsWqCPC2tjfMzyvfRhYABwcETv3inWTbJr3sZ0i4jDgWMq6ab1r1l8CXwUePoq2tOLDXhtk5p3A1+rD44Dj6+iRVX0n/mXARrWi+SlKpXqirSP3/RGxQV/2c4ED63MmvjpdL85P79v0E2CLiFjcl6+N/b2u3NmW/p76Bl0LLquA6ykLmwNcQfkAt3vUtZSqzwIfq/s2aqC5c2aA3OdQ3gQ3AU4BngK8LiJOBXairKU3MdZ2QTaDc1vv/fcblGlNpzNhdygbJHfdtxL4DPAw4J21v3ejrKs2MabJvc5zeov7e225N61FqOtoQX/DWs9tvSn2v2TNh5YfUkYW7B0Ru9VtuwALI+IEyvpSI7+D0VwaIveu9bjFlNf6Ng02d85M8152G/C5+t/TKCMpNpxynb4HpQh7AmXk80TdVXaGuY/py91/nf6/qHdcnLRC+zRFlX8Fzuo7d18AZH3cy9eq/q6m5r6Qmru+l7Wuv2d6XqtOoUzH/y5l4fuJMUDuMZ7eOgAAD01JREFUH1FmNdxMyXt4RLwwIj5AKdRdPYr2WZQak7WN/qiV9siyyPWFlJN//zDZ3YEnUNZieUZmntlUe+fKgLlX92W/B/jypFbjp8l9R9/DZwPX1SkPPW3t72lz9/X33Uxwf099g+57/Algx4hYVottVwP/xJpRYY+hjCQ6C3hcZp7RWKPnwBC596dcyH2c8uHtLuDAzPz3hpo8J6a7IFvPuW11RGxLudPoecBjMvNvG2v0HBg0d3UO5SLnFsqoqmdl5rUjb+wcWkfudZ3bev39PtrX32vLfWd9PPH9vTZ9X5Z8jbLuxm714v5SSs7eN8kvpowyWAzsn5nffsgfNkFmkPsR9bh7KHcg/MNYGjrH+ka33lU3/T1l1N+76/betcvTKO9rGwHPzMwvNdvSuTWD3P3X6RtTFgGfaL3rzsy8IzPv7HvNvwD4Xc3cOxc+DXgWLejvmeSu+9vQ35vCgxY0n9F5rX6BfALlmnWPzDy36YbP0iC5b6EUHd9DWXrgpZQbdrw4M28fReNiwoqbEy0i/pRyIXpq9N1Cs+9EkFGmdtwfEdtTKpe7UoaH3kS5yLkjMy8fU4ShzCL3tsDCzLy0fiszUXevGTD3B4AfZ+bZEbEvZf2J3YBbW97f/bmfBNyUmVdPYn8DRBnKu5xy0XZWZl5Rty+o3youokzXW5aZr6j7PgT8LDPPiLIA+KIsi2dOjFnk/nlmfrI+nrjbCq8j9wbUJaSmObdtB6zOzF9FmZt/47gyDGOWuTfIzH+pRauJugAZMPfUc9v1mbmyA/3dn3sZcGNmXjOJ/Q0QEQcBR1Mu0r+S9SYsfee2nSijQBdl5tvrvq8Cn83McyLiUOCyzJyoNWdmkfvTmfnF+njjvmLGRFhH7gde633HLqN84bI/pQB3NWXq6vWZ+f+abfnszCL3dsD99d/44nzwF6vz3kxy953bzgX+NjN/GBGPr+9jzwF+28b+nib3HsANmXnjpPV3/QyyLeWLkut716J134zOa3U/WUYBT4RZ5j6zV3hr4nOZI6UaEBELI+KvKAuknRIR+2TfEMis6reoC+u26ynTd26gDH/fKjN/OkkFijnIfSbQq8xPTIFiwNy928huAmwbEZ8G/iuwTWZe3OL+Xlvuk1kzX31i+hsgIjaKiNMoc7G/QJlr/7qot0/NNd8sbQF8DnhYRBwfEY+m3Db9/nrcTZNUkJqD3Pf2/qxJKkjNIPfqGZzTe/8uJqZAMUe5e9+8T0yBYsDc053belMY29rf072X9dbTmqT+jpr9M5TFnc+gfMP8nyLiYbXA1ju33QZ8C9gzIt4YEQ+jvPZvA8jMcyelIDVHuR/4Bn1SClIzzN17rW8ZZQ0WMnMFZaTITZRz2w6Zef6kFCjmKPeZrLlum4gCxaC5WbN0xu2UtXbOAv5bRGyXmd9pa38zTW7WXLtMRH/31Pegu+vP3lHX/6rFlvWd1+6of8Z1k1SQglnnvrXvzxn957LM9KeBH+BgyvDON1G+Rezft4DyQf4rlPnJGwBHUL51eeu4227ukeZ+LHWhRMo6Om8ad9vNPXT2Y4Gd6u+7Af9IuUiF8ub+YcrQ94dT7mryXspts9817rabeyS523puM/e6c7fq3NbV3DXfwcCC+vszgdP69gVl7b9PUdZNejJlKvKlwEnjbru5R5L7o5QizC5123HAdS04t5l73bm3p9ywYDXwU+DYcbfd3EPl3oByXfI3wEuAH/Xt27DF57WJyT32/1lt/QHeWF8AL+91fN++q4DD+x4/ob4Iturbti+w5bhzmLux3McBW487h7mHyn5ofbxxfUNfXB9/G3hS/X2fqdnr9sXjzmHuZnK34Nxm7sFyT+S5rau5p2R/+ZTthwK/B86njHp7GuX22Z+Zkn0BsNG4c5i7sdzPmcTXurkHz02ZpvgOc0/OT1/ul/Vt25Iycnub+t/XAY+mXKe07bw2cbnH/j+vbT+Ui7fjKLc1P4Sylsarge36jjkYWDnN8xeOO4O5G829YNwZzD1n2bftO2anun/ztmQ399C523ZuM7ev89bkXk/27er+/YG9KNMZjgY+CWw/6dnNPXTutp3bzL2O3JP6Y+6H5N6aUoR5Vz3uLZRpeedNeX7bzmsTk3shmlOZmRFxAPDOzDw/Im4HngesoqypQmZ+uc7ZfEtmnhIRB2bmt6Ms9Hv/ONs/LHMPnXvVuv78+aqruWFm2Slv9Jdl5q0R8QjKG/1PJzm7uYfO3dpzG+b2dT7huWGd2ZOy0OsFvWMj4lLKlJc7IiIoNwyayOzmHjp3285t5q6myT0x6132M/eDch9EmVr+A+CZEfF1YGl9fCU8sCB4285rE5Xbhc7nUJS7FkBZL+UZAJn5DeBfKYuHPa7v8KOB90XE71hzC92JPAGY29xdyA0zyr5n3b8tcHdEvAH4JrBjPXYis5vb3OY2Ny3LDevNvntE7DrlKc8D7gTuymIis5vb3OY2d5+2576MsoTIE4HfABdl5p7AK4H9I+KR5h4/i1KzEPWuYrXK2H9hdgWwWUTsVR9fSLn71Gb1+H2A04EvUtZmOLPJds+Wuc1dd7U6NwyVfeP6+KWUOduPAQ7KzPMaa/QcMLe56y5zF+YuJjo3DJV984hYFBFHRMTPgV2At8+Hb5UHYW5z113mLszdrdzfpXw2uQF4XWaeWI+/CXh6Zq5stOGz1NbcFqWGEBFPj4gzgXdGxNaZdTJnvV0q8E+UW7w/LyIWZrld6CMpczoB/h14fWYempn/1nT7h2Vuc9ftrc4Ns8q+X93/OeA5mXnsfDvpr4u5zV23m9vcrckNs8q+LDPvpdxt7OjMPDIzbxhHhmGY29x1u7nN3eXcv6BMW3tiZt4dEQv6Cjq3jyPDMNqe26LUgCLiUZTbJ55P6eiTI+KFAJl5X/3vFZQhdI8G3lafeg9wTd1/XWZe2nDTZ8Xc5u5Cbph19ivr/i9l5vkNN31WzG1uc5ubluWGOXs/uyAzf9Bw02fF3OY2t7kxd3/uq+v+Vb2CzqToQm6LUoPbD/hlZn6GsoL9JcCLI2IHgIh4T0ScAawAPgTsFxErgJsoazBMKnObuwu5YXbZvzWeJs8Jc5vb3OZuW27obnZzm9vc5ja3uScid8zjgtm8EBEvplQkL87MH9dK5eeAwzLz2ojYAzgSuB64CHg95baLV9Tnb0q5jeot40kwHHObmw7khu5mN7e5Mbe5W5Ybupvd3ObG3OY2t7mZzNyOlJpGROwQEecBfwlsBXw6Ip6fmVcCPwIOrYdeBvwC2By4NDMPz8wroq6En5m3T9ILwtzm7kJu6G52c5vb3OamZbmhu9nNbW5zmxtzm3uCc4NFqXXZF/heZj4jM08GPggcVfd9D9grIp6S5U4FK4FnZuYfACJig5wnt1ccgrnN3YXc0N3s5ja3uc3dttzQ3ezmNre5zW1uc09ybotS/SLiyIjYPyIWA9+hDJPr+Xfg8vr7T4CfAqfW4XF7AtdExBJ40K0ZJ4K5zd23u7W5obvZzW3uvt3mNncrckN3s5vb3H27zW1uc5t74nJPtXDcDRi3iAjg4cDfAauBXwN/Dhybmb+NiA2zrGq/A2UYHZn5O+CDEbEU+BRlzueRmXnnODIMw9zmpgO5obvZzW1uzG3uluWG7mY3t7kxt7nNbe4Jzr1OmdnZH2BB/e+uwFm9bcCHgS9NOeY84Ln19+3qfxcCm407h7nNbW6zm9vc5jZ3m3N3Obu5zW1uc5vb3JOce30/nRwpFRELgJOBBRHxdcoiYasAMnNVRBwL/FtEPCszL4yIRcDvgcsj4r3AiyJi/8y8GbhtTDEGZm5z04Hc0N3s5jY35jZ3y3JDd7Ob29yY29zmNvcE556pzq0pFRHPAlZQhsJdQXlx3AccEBH7wQNzMk8C3l2fthHwaso8z80oFcubG234LJnb3HQgN3Q3u7nNjbnN3bLc0N3s5jY35ja3ucHcE5t7IHM99Gq+/wDPAI7oe/wx4GhKp6+o2zagzPM8B9gR2A/4LLDPuNtvbnOb2+zmNre5zd2F3F3Obm5zm9vc5jb3JOce6P/RuBswhhfFEmAxa+ZqLgf+uv5+CfCG+vu+wNnjbq+5zW1us5vb3OY2dxdzdzm7uc1tbnObe/xtNnczP52bvpeZd2bmPZm5qm46kDJfE+A1wO4R8VXgC5Rhdr0V8ieauc1NB3JDd7Ob29yY29wtyw3dzW5uc2Nuc5vb3B3RyYXO4YHFxhLYHviHuvk24B3A44GrMnMlQNbSZRuY29x0IDd0N7u5zY25zU27ckN3s5vb3Jjb3Ji7DbqaeyY6N1Kqz2pgQ+BGYO9anTwBWJ2Z3++9IFrI3ObuQm7obnZzm9vc5m6jrmY3t7nNbe62MXe3cq9XdKwI9yAR8cfAD+vPpzPzjDE3qRHmNveYm9SYrmY3t7nH3KRGmLtbuaG72c1t7jE3qRHmNveYm9SIruZen64XpXYEjgBOzcx7xt2eppjb3F3R1ezmNncXmLtbuaG72c1t7i4wt7m7oKu516fTRSlJkiRJkiSNR5fXlJIkSZIkSdKYWJSSJEmSJElS4yxKSZIkSZIkqXEWpSRJkiRJktQ4i1KSJEnzQESsiohLIuIXEfGziHhzRKzzWi0idomIw5tqoyRJ0lyyKCVJkjQ/3JWZ+2TmnsCBwAuAE9fznF0Ai1KSJGkiRWaOuw2SJEmdFxG3Z+amfY8fBVwEbAMsBT4HbFJ3H5OZP4yIHwO7A1cBZwIfAv4G2B9YDHw0Mz/eWAhJkqQBWJSSJEmaB6YWpeq2W4DHAbcBqzPz7oh4LPCFzNw3IvYH3pKZL6rHHwVsl5nviYjFwA+AQzPzqkbDSJIkzcDCcTdAkiRJ67Uh8JGI2AdYBew6zXHPA/aOiEPq4y2Ax1JGUkmSJM0rFqUkSZLmoTp9bxVwA2VtqeuBJ1DWBL17uqcBb8jMbzbSSEmSpFlwoXNJkqR5JiK2BU4DPpJlrYUtgN9m5mrgCGBBPfQ2YLO+p34TODoiNqx/zq4RsQmSJEnzkCOlJEmS5oeNI+ISylS9+ykLm59a930M+GJEHAl8A7ijbv85sCoifgZ8Bvgg5Y58/xwRAfweeGlTASRJkgbhQueSJEmSJElqnNP3JEmSJEmS1DiLUpIkSZIkSWqcRSlJkiRJkiQ1zqKUJEmSJEmSGmdRSpIkSZIkSY2zKCVJkiRJkqTGWZSSJEmSJElS4yxKSZIkSZIkqXH/HyJPYfAeAHCPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "global_cases_df = confirmed_cases_df.sum()    # Sum over all countries to get global number of cases for each day\n",
    "\n",
    "# Plot the number of cases for each day globally\n",
    "x_values = [datetime.datetime.strptime(d[:-2]+ '20' + d[-2:],\"%m/%d/%Y\").date() for d in global_cases_df.index]\n",
    "y_values = global_cases_df.values\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(20, 10))\n",
    "ax = plt.gca()\n",
    "formatter = mdates.DateFormatter(\"%Y-%m-%d\")\n",
    "ax.xaxis.set_major_formatter(formatter)\n",
    "\n",
    "locator = mdates.DayLocator(interval=5)    # Add an interval on the x-axis so as to not be cluttered\n",
    "ax.xaxis.set_major_locator(locator)\n",
    "\n",
    "# We will use the last 6 days as a test set\n",
    "plt.scatter(x_values[:-test_days], y_values[:-test_days], color=\"blue\", label=\"Train\")\n",
    "plt.scatter(x_values[-test_days:], y_values[-test_days:], color=\"red\", label=\"Test\")\n",
    "\n",
    "ax.set_xlabel(\"Date\")\n",
    "ax.set_ylabel(\"Cases\")\n",
    "plt.title(\"Number of Cases Globally\")\n",
    "plt.legend()\n",
    "\n",
    "plt.grid()\n",
    "plt.gcf().autofmt_xdate()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Global Cases - Polynomial Regression\n",
    "\n",
    "Firstly, we will create a model able to forecast future global number of future cases. This will help us have a greater understanding of a pipeline we could later create to train a model for each country separately.  \n",
    "On the above plot we will use the blue part in order to find the degree of our polynomial and train our linear regression model, and the red part for testing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:10:11.205257Z",
     "start_time": "2020-04-01T16:10:11.155777Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "x_series = np.arange(len(x_values))    # Transform dates to an integer mapping for easier parsing\n",
    "\n",
    "\n",
    "# Split the data in training and testing and\n",
    "# add a new axis so as the PolynomialFeatures input has the expected 2D shape\n",
    "train_X = x_series[:-test_days, np.newaxis]\n",
    "train_Y = y_values[:-test_days, np.newaxis]\n",
    "\n",
    "test_X = x_series[-test_days:, np.newaxis]\n",
    "test_Y = y_values[-test_days:, np.newaxis]\n",
    "\n",
    "# Calculate the models up to 9th degree and cache them in a dictionary\n",
    "models_dict = {}\n",
    "for degree in range(1,10):\n",
    "    # Create the new features\n",
    "    # eg degree=2, [a] => [a^0, a^1, a^2]\n",
    "    polynomial_features = PolynomialFeatures(degree=degree)\n",
    "    x_poly = polynomial_features.fit_transform(train_X)\n",
    "\n",
    "    # Train a linear regression model with our new polynmial feature set\n",
    "    model = LinearRegression()\n",
    "    model.fit(x_poly, train_Y)\n",
    "    \n",
    "    # Cache the model and the new set of features\n",
    "    models_dict[degree] = [model, x_poly]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:10:15.198110Z",
     "start_time": "2020-04-01T16:10:13.834471Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15, 15))\n",
    "plot_index = 1\n",
    "\n",
    "# We will create 9 plots one for each degree\n",
    "for degree, model_features in models_dict.items():\n",
    "    ax = fig.add_subplot(3, 3, plot_index)\n",
    "    \n",
    "    # Plot our true data\n",
    "    plt.scatter(train_X, train_Y)\n",
    "    \n",
    "    # Use our new model to predict on our train set\n",
    "    pred_train_Y = model_features[0].predict(model_features[1])    \n",
    "    \n",
    "    plt.plot(train_X, pred_train_Y, linewidth=3, label=f'Degree: {str(degree)}', color=\"orange\")\n",
    "    plot_index += 1\n",
    "    \n",
    "    plt.title(f\"Degree: {degree}\")\n",
    "    \n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need a robust and unbiased way of deciding how good each degree fits our model. How good each model is depends on its accuracy and its simplicity (lower degree).\n",
    "  \n",
    "### Metrics\n",
    "**BCI**: Bayesian information criterion (BIC) is a criterion for model selection among a finite set of models. It deals with overfitting since it **penalizes models that need many parameters**. So in our case as the degree of the polynomial increases the penalty will increase too.\n",
    "\n",
    "$$BIC = kln(n) -2ln(\\hat{L})$$\n",
    "* $n$ is the number of data points (number of days used for training)\n",
    "* $k$ is the number of free parameters (in our case degree + 1 due to intercept)\n",
    "* $\\hat{L}$ is the maximized value of the likelihood of our model\n",
    "\n",
    "In order to calculate the $\\hat{L}$ we first make some assumptions.  \n",
    "Linear regression is in the form of $Y = Xβ + ε$ where $ε$ is the residue between the prediction and the true data result.  \n",
    "Assuming that our residue $ε$ is **independent Gaussian noise** we can prove that the **maximum likelihood equals the mean squared error metric** [(ref)](https://www.stat.cmu.edu/~cshalizi/mreg/15/lectures/06/lecture-06.pdf).\n",
    "  \n",
    "Under these assumptions we calculate BIC [(ref)](https://en.wikipedia.org/wiki/Bayesian_information_criterion#Gaussian_special_case):\n",
    "$$BIC = nln(mse) + kln(n)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:08:48.513453Z",
     "start_time": "2020-04-01T16:08:48.324378Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate MSE of Linear regression model\n",
    "mse = mean_squared_error(train_Y, pred_train_Y)\n",
    "\n",
    "# Calculate BIC for each model degree\n",
    "bics = []\n",
    "for degree, model_features in models_dict.items():\n",
    "    # Use our new model to predict on our train set\n",
    "    pred_train_Y = model_features[0].predict(model_features[1])\n",
    "\n",
    "    mse = mean_squared_error(train_Y, pred_train_Y)\n",
    "    n = len(train_Y)\n",
    "    k = degree + 1    # We +1 for the intercept\n",
    "    \n",
    "    bics.append(n * np.log(mse) + k * np.log(n))\n",
    "\n",
    "\n",
    "plt.plot(np.arange(1, len(bics) + 1), bics, marker=\".\")\n",
    "\n",
    "plt.xlabel(\"Degree\")\n",
    "plt.ylabel(\"BIC\")\n",
    "plt.title(\"Bayesian Information Criterion vs Degree\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the above plot we can see that the major on BIC happens from the 3rd to the 4th degree. However we need a rule in order to decide from the other models of degree 4 to 9.  \n",
    "A usual criterion is [(ref)](https://en.wikipedia.org/wiki/Bayesian_information_criterion#Gaussian_special_case):  \n",
    "  \n",
    "Let $B^{\\ast}$ be the lowest BIC value and $B$ a different BIC than $B^{\\ast}$\n",
    "* if $B - B^{\\ast} < 2$, the difference is not important\n",
    "* if $2 \\leq B - B^{\\ast} < 6$, the difference is positive\n",
    "* if $6 \\leq B - B^{\\ast} \\leq 10$, the difference is strong\n",
    "* if $B - B^{\\ast} > 10$, the difference is very strong\n",
    "\n",
    "So we will deem as the best model **the one that has smallest degree and its BIC is not bigger than `bic_criterion` from the model with the lowest BIC**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:12:37.357431Z",
     "start_time": "2020-04-01T16:12:37.348028Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best BIC Degree: 9\n"
     ]
    }
   ],
   "source": [
    "def find_simplest_min_bic(bics, criterion=2):\n",
    "    \"\"\"Finds the smallest bic following the above rule\"\"\"\n",
    "    true_min = np.argmin(bics)\n",
    "    for which_bic in range(true_min):\n",
    "        if bics[which_bic] - bics[true_min] < criterion:\n",
    "            return which_bic    # Return the bic index that was the simplest model and B - B* < criterion(2)\n",
    "    return true_min    # No B != B* with B - B* < criterion(2) found, return the index of the smallest bic \n",
    "\n",
    "\n",
    "bic_degree = find_simplest_min_bic(bics, bic_criterion) + 1\n",
    "print(f\"Best BIC Degree: {bic_degree}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the model that covers our criterion is the one of the **7th degree**. Following [Occam's razor](https://en.wikipedia.org/wiki/Occam%27s_razor) we could relax our above criterion to a higher value and pick a more parsimonious model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing\n",
    "\n",
    "Having found the degree of the polynomial that best fits our data without overfitting we must now forecast some dates that were not used in training (the last 7 days in our case) and evaluate our model's performance.  \n",
    "  \n",
    "In the cell below I compute the test set predictions along with the train set making it easier for me to plot them together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:12:39.975306Z",
     "start_time": "2020-04-01T16:12:39.715644Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Transform our train and test data to much the expected input degree of our chosen model\n",
    "polyn_test_features = PolynomialFeatures(degree=bic_degree)\n",
    "x_poly_train_test = polyn_test_features.fit_transform(np.vstack((train_X, test_X)))\n",
    "\n",
    "# Predict on the train set and on the test set\n",
    "chosen_model = models_dict[bic_degree]\n",
    "pred_train_test_Y = chosen_model[0].predict(x_poly_train_test)\n",
    "\n",
    "# Plot the predictions on the train and test set\n",
    "plt.scatter(train_X, train_Y, color=\"blue\", label=\"Train\")\n",
    "plt.scatter(test_X, test_Y, color=\"red\", label=\"Test\")\n",
    "plt.plot(np.vstack((train_X, test_X)), pred_train_test_Y, color=\"orange\", label=\"Prediction\")\n",
    "plt.xlabel(\"Days\")\n",
    "plt.ylabel(\"Cases\")\n",
    "plt.title(\"Final Model Predictions for Global Cases\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the predicted line has a higher rate of increase than the actual rate. This can be expected since a lot of countries have taken measures (lockdowns and curfews) on the previous days and the results are showing up on our test dates. Consequently, our model is making pessimistic predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Country Cases Pipeline\n",
    "\n",
    "On the first part of this notebook we predicted the global number of cases. This way we ended up having a simple problem that we can easily supervise its results and any mistake could be easily debugged. Using the above methods we will continue by creating a separate model for each country in the John Hopkins dataset.  \n",
    "This pipeline will be used to forecast future (yet unknown) number of cases for each country. \n",
    "  \n",
    "Algorithm:  \n",
    "\n",
    "```python\n",
    "for country in countries:\n",
    "    for degree in range(1, 10):  \n",
    "        create_polynomial_features(degree)\n",
    "        train_linear_regression_model()\n",
    "    select_best_bic_model()\n",
    "    save_best_model()\n",
    "        \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:12:47.761263Z",
     "start_time": "2020-04-01T16:12:46.752634Z"
    }
   },
   "outputs": [],
   "source": [
    "country_models = {}    # Dictionary where key:country_name, value:[LinearRegressionModel, degree]\n",
    "\n",
    "x_data = np.arange(len(x_values))\n",
    "\n",
    "# Iterate through the countries\n",
    "for country, row in confirmed_cases_df.iterrows():\n",
    "    train_X = np.array(x_data[:-test_days, np.newaxis])\n",
    "    train_Y = np.array(row[:-test_days, np.newaxis])\n",
    "    \n",
    "    test_X = np.array(x_data[-test_days:, np.newaxis])\n",
    "    test_Y = np.array(row[-test_days:, np.newaxis])\n",
    "    \n",
    "    models_list = []\n",
    "    for degree in range(1, 10):\n",
    "        # Creating polynomial features\n",
    "        polynomial_features = PolynomialFeatures(degree=degree)\n",
    "        x_poly = polynomial_features.fit_transform(train_X)\n",
    "\n",
    "        # Train a linear regression model with our new polynmial feature set\n",
    "        model = LinearRegression()\n",
    "        model.fit(x_poly, train_Y)\n",
    "        \n",
    "\n",
    "        # Predict on the train set\n",
    "        pred_train_Y = model.predict(x_poly)   \n",
    "        \n",
    "        # Calculate BIC value\n",
    "        mse = mean_squared_error(train_Y, pred_train_Y)\n",
    "        n = len(train_Y)\n",
    "        k = degree + 1    # We +1 for the intercept\n",
    "        bic = n * np.log(mse + 1e-2) + k * np.log(n)    # We do mse + 1e-2 to avoid log(0) \n",
    "        \n",
    "        # Save the model and its bic\n",
    "        models_list.append([model, bic])\n",
    "\n",
    "    # Find the best BIC model \n",
    "    best_model = find_simplest_min_bic(np.array(models_list)[:, 1], criterion=bic_criterion)\n",
    "    \n",
    "    # Save the best model as the country modeland its best BIC degree\n",
    "    country_models[country] = [models_list[best_model][0], best_model + 1]    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having created a forecasting model for each country we will then plot some example countries and see how good of a fit are our lines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plots per Country"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:12:51.489733Z",
     "start_time": "2020-04-01T16:12:50.296893Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j+cRxLLvP37gVeMvdewNvhe8hmJ/RO/zJBp6EIAkEbgeOIRiSc3uFRPBJ4JcVrhtUyz1ERKQpiuV+DU2MmV1OsGhOlu9cvW4lsH+Faj3CsurK84E0M2tVqXyXtsLz7cP6IiLSHOR/HAxTjcEsg6gljlXN32DXuRWV51yM98DHBB1eN+BMYKq7r3P39QQLBwwKz7Vz94/DjnU8Vc/fqHgPERFpirRnI7BjhdTfAD9294pjdycCF5pZUrhaam/gE2A60NvMeplZIsECOhPDfvFt4Lzw+qHAKxXaKh+9cx7wnwoJqoiINGXF66FgPnQ6Nia3b+w5jl3cfXX4+lugS/i6vvM3uoevK5fXdI/dNPU5HPn5+fTv35/+/fvTtWtXunfvvuN9cXFxndsZM2YM3377bRQjFRFpgBa4Z6OZPQd8BBxiZivMbBjwGJAKTDWzWWY2CsDd5wAvAHOBN4Br3X17OEfxOmAKMA94IawL8FvgRjNbSDCH8Zmw/BmgY1h+I810VI76RxFpkfKnB8cYzG8EaFV7lehwdzezqH7LWds93H00MBqCfaqiGcue6NixI7NmzQLgjjvuoG3bttx88831bmfMmDEMGDCArl27RjpEEZHIyMraqxPFytz9oiqKn6mirLx+DrDbI1h3nwRMqqJ8McEUj8rlRcD59Qq2CVL/KCIt0tppgEGHo2Jy+8Z+4vhdOMyU8LgmLK/v/I2V7FymvGJ5TfeIvkbch2zcuHEcffTR9O/fn2uuuYaysjJKS0u59NJLOfzwwznssMMYOXIkzz//PLNmzeKCCy6o9zexIiJR0fL2bBT1jyIiDZc/Ddr1gcT2Mbl9Yz9xLJ9bcTe7z7m4zswmECyEs9HdV5vZFOBPFRbEOQO4zd3XmVmBmR0LTAMuAx6t5R7RVb4PWfmS8uX7kEHEv0WfPXs2L7/8Mh9++CGtWrUiOzubCRMmcOCBB7J27Vq+/PJLADZs2EBaWhqPPvoojz32GP37949oHCIi9daIvyuliVD/KCLScO5B4tj9nJiFEM3tOKqav3E3cLqZLQBOC99DMMxmMcGmxk8B1wC4+zrgLoIFAKYDd4ZlhHWeDq9ZxM79rqq7R3Q14j5kb775JtOnTyczM5P+/fvzzjvvsGjRIg466CDmz5/P8OHDmTJlCu3bx+bbCBGRamnPxpZH/aOISMNt+Qa2rQ1WVI2RqD1xrGb+BsCpVdR14Npq2hkDjKmifAZwWBXl+VXdI+oacR8yd+cXv/gFd911127nvvjiCyZPnszjjz/OSy+9xOjRoyN+fxGRPaY9G1se9Y8iIg23dlpwjGHi2NhzHPdejbgP2WmnncYLL7zA2rVrgWB1uWXLlpGXl4e7c/7553PnnXfy6aefApCamsqmTZsiHoeISL1pz8aWR/2jiEjDrf0Y4ltD2uExCyFmq6rudXJydp3DAVHbh+zwww/n9ttv57TTTqOsrIyEhARGjRpFfHw8w4YNw90xM+655x4ArrjiCq688kpat27NJ598QmJiYsRjEhGpk0b8XSlNhPpHEZGGy58GHTIhLnbpm2nf30BmZqbPmDFjl7J58+Zx6KGH1r2R3NxgzsayZcE3qTk5zW6xh3p/ZhGR+orx70ozm+numY12w2ZO/eNO6iNFJCa2F8M/UuGQ4fD9+6J6q5r6SD1xjKQWtg+ZiMge0e/Klkf/m4uI7Lm1H0FZMXQ6PqZhaI6jiIiIiIhIU7V6Mlgr6HpKTMNQ4liLljSUtyV9VhERaZiW1me0tM8rIk3IqknQ+QRIaBfTMJQ41iA5OZn8/PwW0Vm4O/n5+SQnJ8c6FBHZm+TmQkYGxMUFx9zcWEckEdCS+kdQHykiMVS4AjZ8CfudFetINMexJj169GDFihXk5eXFOpRGkZycTI8ePWIdhojsLXJzd11Nc+nS4D1ovlsz19L6R1AfKSIxsuqN4Ljf4NjGgRLHGiUkJNCrV69YhyEi0jyNGLHrFgwQvB8xQoljM6f+UUSkkayeDCk9oH2/WEeioaoiIhIly5bVr1xERER2KiuB1VOh21lgFutolDiKiEiU9OxZv3IRERHZKe8DKN3UJOY3ghJHERGJlpwcSEnZtSwlJSgXERGRmq2aDHEJ0PXUWEcCKHEUEZFoycqC0aMhPT0YYpOeHrzX/EYREZHarZ7cJLbhKKfFcUREJHqyspQoioiI1Ff5Nhz97411JDvoiaOIiIiIiEhTsmpycGwi8xtBiaOIiIiIiEjTsmoypOzfJLbhKKfEUUREREREpKnYXgzfvhk8bWwC23CUU+IoIiIiIiLSVKz9MNiGo1vTGaYKShxFRERERESajlWTmtQ2HOWUOIqISGTk5kJGBsTFBcfc3FhHJCIi0vysKt+GIzXWkexCiaOIiDRcbi5kZ8PSpeAeHLOzlTyKiIjUR8HXsHE27Hd2rCPZjRJHERFpuBEjoLBw17LCwqBcdmNmY8xsjZnNrlDWwcymmtmC8LhPWG5mNtLMFprZF2Y2oMI1Q8P6C8xsaIXyI83sy/CakWbB6grV3UNERJqIxWPA4iGj6e2BrMRRREQabtmy+pXLWGBQpbJbgbfcvTfwVvge4Cygd/iTDTwJQRII3A4cAxwN3F4hEXwS+GWF6wbVcg8REYm1shJYPBa6nwOtu8Y6mt0ocRQRkYbr2bN+5S2cu78LrKtUPAQYF74eB5xboXy8Bz4G0sysG3AmMNXd17n7emAqMCg8187dP3Z3B8ZXaquqe4iISKytfB2KvoMDhsU6kiopcRQRkYbLyYGUlF3LUlKCcqmrLu6+Onz9LdAlfN0dWF6h3oqwrKbyFVWU13SPXZhZtpnNMLMZeXl5e/hxRESkXhY9A627Bfs3NkFKHEVEpOGysmD0aEhPDzYrTk8P3mc1vTkazUH4pNBjdQ93H+3ume6e2blz52iGISIiAIUrYfUk6HU5xLWKdTRVappRiYhI85OVpUSxYb4zs27uvjocbromLF8J7F+hXo+wbCVwcqXy/4blPaqoX9M9REQklr4ZB14GB/4i1pFUS08cRUREmoaJQPnKqEOBVyqUXxaurnossDEcbjoFOMPM9gkXxTkDmBKeKzCzY8PVVC+r1FZV9xARkVjxsmCY6r4nQ+pBsY6mWnriKCIi0sjM7DmCp4WdzGwFweqodwMvmNkwYCnw87D6JGAwsBAoBK4AcPd1ZnYXMD2sd6e7ly+4cw3Byq2tgcnhDzXcQ0REYmXNO7B5MRx+Z6wjqZESRxERiR4vg1VvQOFSyLgEElJjHVGT4O4XVXPq1CrqOnBtNe2MAcZUUT4DOKyK8vyq7iEiIjG08GlIaA/7/zTWkdRIQ1VFRKT+cnMhIwPi4oJjbu6u57etg3kPwKu94Z2zYfo1MPFAmP8obC+ORcQiIiJNT/F6WP5S8OVqq9axjqZGMUkczewGM5tjZrPN7DkzSzazXmY2zcwWmtnzZpYY1k0K3y8Mz2dUaOe2sHy+mZ1ZoXxQWLbQzLS5sYhIJOXmQnY2LF0K7sExOzso37oapv0S/tUDPrsZWneH4yfA6R9A2mEwczi8dgh887fgaaSIiEhL9k0ulG2DA5vm3o0VNXriaGbdgeFAprsfBsQDFwL3AA+5+0HAeqD8X28YsD4sfyish5n1Da/rBwwCnjCzeDOLBx4HzgL6AheFdUVEJBJGjIDCwl3LCgvhztvgP2fAkr8F35yeNQtOfxfSL4DOx8Epb8HJb0DiPvDRpfDWKVC2PTafQUREJNbcYdHTsM8A6PD9WEdTq1gNVW0FtDazVkAKsBo4BXgxPD8OODd8PSR8T3j+1HCVuCHABHff5u7fECwacHT4s9DdF7t7MTAhrCsiIpGwbNnuZfHAecuh4Cs46TU4ZjTsc8SudcxgvzNh0AwY8HCwGMA3YxsjYhERkaZnxb9gw+dw8DWxjqROGj1xdPeVwP3AMoKEcSMwE9jg7qVhtRVA9/B1d2B5eG1pWL9jxfJK11RXLiIikdCz5+5l2QTjP44dA11rWXvF4uCQ4dDpOPj8f6FkUzSiFBERabrKSuHz26BdH+g1tPb6TUAshqruQ/AEsBewH9CGYKhpozOzbDObYWYz8vLyYhGCiEjzk5MDKSk7358PnAD4+dDr0rq1YQYDHoSib2HuPdGIUkREpOla9AwUzIf+d0Nc89joIhZDVU8DvnH3PHcvAf4JHA+khUNXAXoAK8PXK4H9AcLz7YH8iuWVrqmufDfuPtrdM909s3PnzpH4bCIie7+sLBg9GtLTg40dzgX8h3Dx8/Vrp9MxkH4xfPUAbKli+KuIiMjeqHQLfHkHdD4euv841tHUWSwSx2XAsWaWEs5VPBWYC7wNnBfWGQq8Er6eGL4nPP+fcE+ricCF4aqrvYDewCcEGyH3DldpTSRYQGdiI3wuEZGWIysLpo2FYXGw32C46N/BU8T66v/n4Pj57yIanoiISJM1Lxxx0//ePes7YyQWcxynESxy8ynwZRjDaOC3wI1mtpBgDuMz4SXPAB3D8huBW8N25gAvECSdbwDXuvv2cB7kdcAUYB7wQlhXREQiZfs2+ORX0OYAOP75PR9m06Yn9LkJluTC2k8iG6OIiEhTU7QG5t0LPX4SrDjejMRkQK273w7cXql4McGKqJXrFhHMoKmqnRwgp4ryScCkhkcqIiJVmnc/bPo62F4joW3D2ur722A58s9uhNPea1bfvoqIiNTL7Ltg+9adI26akVhtxyEiIs3V5iUwJwf2/1mwvUZDJaTC9/4IeR/A8hdrry8iItIcbVoIC0bBgVdCu0NiHU29KXEUEZH6mXl9sKXGgIci1+YBV0Da94LFAkRERPZGs26DuEQ4vPLAy+ZBiaOIiNTdildh5UQ47HZos3/t9esqLj74BnbjXChYELl2RUREmoKFTwejavrdBq27xTqaPaLEUUREapabCxkZkGzwr5+Ad4c+v478fbqfHRxXvR75tkVERGIlfzrMuBa6ng59b4t1NHtMiaOIiFQvNxeys2HpUvgR0GE73L8Wnnsh8vdqewC07wsrX4182yIiIrFQlAfv/Sx4ynjc34MRNs2UEkcREaneiBFQWAhdgHOA94FZ24LyaOj+I1jzLhRvjE77IiIijaWsFD64KNiC48R/QnKnWEfUIEocRUSkesuWBcefAmXAc5XKI22/c8BL4dt/R6d9ERGRxvL5CPjuLTh6FHQYEOtoGkyJo4iIVK9nT+gGHAdMBTZUKI+GTgMhsUOwCI+IiEhztewlmHcvHHQVHHB5rKOJCCWOIiJSvZwc+Fk8lADla9akpATl0RAXD/sNhtWToGx7dO4hIiISTYvGwIcXQcdj4ciHYx1NxChxFBGR6v0oE44tg2ntYJNBejqMHg1ZWdG7Z/dzYFs+5E+L3j1EREQirWw7fHYLTBsG+/4QfjgZ4pNiHVXEtIp1ACIi0oTN/iO0SoaHF8CofRvnnt3OBGsVrK7a+bjGuaeIiEhDlGyCDy6GVa/BwdfBgIcgbu9KtfTEUUREqlYwH5b+HQ6+FpIbKWkESEyDfU+Ela813j1FRET21OZv4N/HwerJkPk4ZD661yWNoMRRRESqM/uPEJcMh97S+Pfe7xzYOBs2L2n8e4uIiNRFUR58ejO83hcKV8AP34CDr6m6bm4uZGRAXFxwzM2NfFmUmbtH/SbNQWZmps+YMSPWYYiIxFxuLjzz0Hym/rovT71/E6kn3hvVKY1VKlgArx0MRz4Kh1wX0abNbKa7Z0a00b2Y+kcR2Zvk5gZbES9bFiwQXr7WW33KCtau5w8XPcBVJz9MAoXwWQqM3wIp6VVfPHgwjBsX7ItcLiEBzKC4ODJlKSkRWYOgpj5SiWNIHaOISNChZmfDqKGX8tPMf9Lrhm/YUrpv1NfDqdKrh0DbXsE3uBGkxLF+1D+KNF+RSJKaS9ngwTBpUu119jR/a5tSxIkHv8fph03iih88S1qbjXwy7RgGvPI5rZYW1XyxGTRGzpWeDkuWNKgJJY51oI5RRCQY7ZK47Wvm3XcoD0y6id8+dy8Qkb6o/j69Cb5+DH6WDwltI9asEsf6Uf8oEj17mthFO0naszInJamQzu02sE/b9bRJ2EC71gW0Td5MWttNpCZvJrnVZlonbiWxValBkl0AACAASURBVDGtE7eRnLCNeCsmLq4MgPg4BwsWJy3ZnkBxaSKlnkhJaSJbixPZsq0Nm4vaUlTahi3b2rJhc1sKtrZj49b2bCwMfjYVpeIe18D8zdm33RoyOi/hqAOmM+iIN/jhoW/TJrmQouIkXp91Nne+/H+8smwIGSytS4ONwwzKyhrYhBLHWqljFBEJpko8ccVVXH7iWNKvX8qagi5ARPqi+vvuv/DWD+HEf8L+P4lYs009cTSzG4ArAQe+BK4AugETgI7ATOBSdy82syRgPHAkkA9c4O5LwnZuA4YB24Hh7j4lLB8EPALEA0+7+901xaP+USQyKieJDUnsKov8Qy4ntfUmOrVdS6fUtXRulxccU4Njp9S1dGybHxxT8+nYNp992qwnsVVJrS2XlRnbSpPYVpLEttIkiksT2V4Wv/PObpg5reJLSYwvJrFV8JOUsI34uNo7orIyY1NRKhsL2+9IKgu2tmNrcWuKSpJ3HEtKE0hoVRK0Hx+03z5lIxmdlpDeaSkpSVt3tLng24N44/NBTP78LN756iQKt7UBYDtxxNGEcqkoP3Hc+5b7ERGRPfb9Q9cw9MRxjH//sh1JIwR/5DS6zsdDQvtgddUIJo5NmZl1B4YDfd19q5m9AFwIDAYecvcJZjaKICF8Mjyud/eDzOxC4B7gAjPrG17XD9gPeNPMDg5v8zhwOrACmG5mE919biN+TJG9Xm1J4tKlMGrU7oldSRV5V1VltddxEuKLaZO0hbbJm4OnfikbaJ+ykfatN9I+ZSNpKRvo0HZd8NMmOJYng51S11abBBaXJrB2UyfWbupE/uaOzF3Zl/xNHVm3pQPrt+zDhi1pwbEwjY2F7dm8rS2bi3b+lGxPrP0DVclJSti24zO1SdpCavKmXT5T+edq17qA9ikbg2PrjXRsm0/rxK0kJxTtOCbEl1BcmkhxaeKOBHZzUVvmrOzH67POZkleBkvWZjBv5aEsXnNglREto2fdnzhWzuSjMcex/NFzlChxFBGRHZ793RO0tiIenHTjjrJG6IuqFpcA3X8E2wtrr7t3aQW0NrMSIAVYDZwCXByeHwfcQZA4DglfA7wIPGZmFpZPcPdtwDdmthA4Oqy30N0XA5jZhLCuEkeRctuLYOvqnT/b1kLJRigpYP7sjcz+rAAv3UJa6jb69dlGHMWsXL6N7aWlJCU6aWlOv3zn5ewgSSjzOMo8jstvteB1WRzby+Ip8+BY/rr8nGOUlQUbH5g5ZkE7hhMft51W8aW0iiulVXwpCfElJCVsIzmhiKRW23YkRm2StpDQqrTWj7qtJJH8zR1Zt7kD67Z0YPGaA5i26JhdEsO1mzqRV9A5OG7qzKatqYBF7Z+/esa2kmS2lSSzbnPHPW8lgvnbHxJyeMqyaVVcy2PjlBQYOrT28cUNLYvyYgRKHEVEJFC6le8lP86KonMoSuyDWaP1RdUbOD7ogFsId19pZvcDy4CtwL8JhqZucPfyvwJXAN3D192B5eG1pWa2kWA4a3fg4wpNV7xmeaXyYyrHYWbZQDZAz5g8bhaJstKtUDA32K+24GvYFB63fAPF66u8pMzj6FzYngE92lNYnMK2kiSWLkoKh12mUrq9Fe7GsjzDPfiBIPmLszLi4sqCY/gTH7edhPgSkhOKdtapUK/8emdnW6VlrSjdHvwUlSSzZVsbikqSg5/iZLaVJlFUkszmorZs2RbMA9xcFMwL3FCYxpbi9hRsTSNvY3s2FKaxtbg1CQlWr8SpoujOmaxfWWWNkb+dlpMVJFMNSeqqKm9IWRQpcRQRkcA342HbWnqcdjNLYpUoVtaCkkYAM9uH4AlgL2AD8A9gUGPH4e6jgdEQzHFs7PuLRJR7kCDmT4P8T8j/ehrtyj4nIb40PG1sJoOZXx/CvOXHsLmsO117deOfk7qx+Nv9yCvozMat7dlanLIjgYuUPX36VVlNSdKb1SRJRRuDKXFNaWXUaK+qGp38LatJJHWNQYvjhDT5X0RaNC+D1/oEcwrP/GSvTtia8uI4ZnY+MMjdh4XvLwMGAucDXcOnigOBO9z9TDObEr7+yMxaAd8CnYFbAdz9z2E7U9g5pPUOdz8zLL+tYr2qqH+U5qLivMK+vQt44v/eZD8m0bZgMl3brwJga2kq0xYcxYdfH8OnSwbw1ao+LF13EMWlyVHfPaFymw15+tXQJEmkOlocR0REarbyVdi0AI6fsFcnjc3AMuBYM0shGKp6KjADeBs4j2Bl1aHAK2H9ieH7j8Lz/3F3N7OJwN/N7EGCxXF6A58QTEzqbWa9gJUEC+iUz50UabZyc+E3v17Pj4+YwM8veYETDn6fBCtlQ2F7pn51OlO+OJOPFgxk/uo+u6zgWZ2GJo11TRIb+vRrT+qI7CkljiIiAvPuhzbpsP/PYh1Ji+bu08zsReBToBT4jGDI6OvABDP7Y1j2THjJM8Bfw8Vv1hEkgrj7nHBF1rlhO9e6+3YAM7sOmEKwHccYd5/TWJ9PJFLKny6uWlnCJadMYcj3xrH4/okkJRQzZ0Vf7p90M5M/P4uPFgykdHtCxO5bl6Gl9U0SRZoLJY4iIi1Ybi68OOpjXr76fe587SEO3NxKf9zEmLvfDtxeqXgxO1dFrVi3iGAYa1Xt5AC7rYfr7pOASQ2PVKRxVLW1xWsvreUXJzzG1b99ki7t15BX0Ikn37ya8e9fxmdLvk8kVv1syNBS/R6VvZESRxGRFio3F7KzYeyVD7BhS3vue3kYZeEASP3RIyKxUjFR7NABNm3a+UQvrnAx/Qof5P67x5CStJVXPz2Hp97+JZM/P6vOTxaj8dRQvzOlJVDiKCLSQo0YAfu2+YafHvVP7nvtFjYXpe4o1x9BItIYqnqaOG4cFIbb4uXnB8eDu83nDz+7nfOP+Qfby+L56/uXcv/rN/PVqkOrbbuh2zHo96DIrpQ4ioi0UMuWwX0XP4a78djU63YpFxGJtvJRD+VJ4tKlMGrUrk8DO6XmcftP/8BVp46isDiF+167hZFThrN6w367tdexI7RtG9ntGERkJyWOIiItVJ+DNjPspGd48ZPzWLmux45y7fcuIo1hxIidSWO58qQxKaGI4WeOZMSQHNokbWH0f7K54593kFewL1D1/MNHHmkx2+mJxERcrAMQEZHYGHv7eNLabGTklOE7ylJSdn5LLyISSbm5kJEBcXHBcenSquudcfgU5t17KPde9Fvem38ih9/6JdeOfWJH0piSAlddFWxebxYcR49WgigSbXriKCLSEnkZR7d/lPyNmawqHoiZ5vWISPRUNSy18lPD9ikbeCDrJoadPIZ5K/tw2p+m8tac00hICIahrlun31MisaTEUUSkJVo9FQq+ouNxf2XJkoYvWy8iUpPqhqWWJ4+D+7/OX4b9im5pq5my/FaGP3U7CxYnk56uRFGkqYjJUFUzSzOzF83sKzObZ2YDzayDmU01swXhcZ+wrpnZSDNbaGZfmNmACu0MDesvMLOhFcqPNLMvw2tGmpn+KhIRqejrkZDcBXpWuQWgiEiD1HVYapukTfzjxst5/ZZz2FKSxr/tY8787Z+ZvzCZsjJYskRJo0hTEas5jo8Ab7h7H+AIYB5wK/CWu/cG3grfA5wF9A5/soEnAcysA8EGyccQbIp8e3myGdb5ZYXrBjXCZxIRaR4KvoZVk6D31RCfFOtoRGQvUz4sdenS4Gli+bDUyvr1mM2su4/ivMy/Qr8RHDJ8JmdlHdX4AYtInTR64mhm7YEfAM8AuHuxu28AhgDjwmrjgHPD10OA8R74GEgzs27AmcBUd1/n7uuBqcCg8Fw7d//Y3R0YX6EtEZEWq/wJwKP/8xjFpQm89MWvYh2SiOyFahqWWu6SE/7KJ3cezX6dNsApb8ERf9QXWSJNXCyeOPYC8oBnzewzM3vazNoAXdx9dVjnW6BL+Lo7sLzC9SvCsprKV1RRvhszyzazGWY2Iy8vr4EfS0Sk6Sp/ArB+zUYu/8GzTPjoQi7L7kpubqwjE5G9TXV7wbrDwQcW8Zdhv+KvV1/GpsSjaP3Tz6DLyY0an4jsmVgkjq2AAcCT7v59YAs7h6UCED4p9CqujSh3H+3ume6e2blz52jfTkQkZsqfAFxx0rOktt7MyCnDKSwMykVEGqLyfMYOHaqud9Rhq5j/2AlknzIa+v6WLhe9Ba27NWaoItIA9U4czSzOzNo14J4rgBXuPi18/yJBIvldOMyU8LgmPL8S2L/C9T3CsprKe1RRLiLSYi1bBmZlXHf6Y3zw9XHM/CZzR7lERgT6R5Fmp6r5jAUFkJi4a73Mg2bz9q3HQsF8+MG/oP/dEKfF/UWakzoljmb2dzNrFw4pnQ3MNbNb9uSG7v4tsNzMDgmLTgXmAhOB8pVRhwKvhK8nApeFq6seC2wMh7ROAc4ws33CRXHOAKaE5wrM7NhwNdXLKrQlItIi9ewJg/tP4qCuixg5Zfgu5bLnItk/ijRHVc1nLCmB1FRITw/mNV50ylt8cMfxtEkphdPfgx5DYhOsiDRIXZ849nX3AoJFZiYTzFO8tAH3/R8g18y+APoDfwLuBk43swXAaeF7gEnAYmAh8BRwDYC7rwPuAqaHP3eGZYR1ng6vWRTGLCLSYuXkwK/PepSV6/bjn9N/CkBKSlAuDRLp/lGkSavrNhvr1gVbaZQtHM/frxxEYtr+cMbHsE//RoxWRCKprmMEEswsgaBjfMzdS8xsj+cguvssILOKU6dWUdeBa6tpZwwwporyGcBhexqfiMjeJuucr8D+zf1T72J7WYI21Y6ciPaPIk1Z+bDU8ieM5dtseBX/j+/Z02F2Dnzxe+hyCpz4EiSmNW7AIhJRdX3i+BdgCdAGeNfM0oGCaAUlIiIR9vVjEJfIzU9ma1PtyFL/KC1GXbbZAEhJcV7PuTVIGjMuhZMnK2kU2QvUKXF095Hu3t3dB4f7KS4Ffhjl2EREJBKKN8I3YyH9QkjeN9bR7FXUP0pLUtM2G+XzGdPTnRmjb6Sf3Qu9r4aBYyE+seoLRaRZqeviOF3M7Bkzmxy+78vOhWxERKQpWzwWSrfAIcNrrSr1o/5RWpLqFtNKTw/nM24vY8k//odD7WE45HrIfBwsFju/iUg01PW/5rEEq5juF77/Gvh1NAISEZEI8rJgmGqngdDhyFhHszcai/pHaSFycoJFtSrasciWl8H0q2HB43DozTDgod3HsIpIs1bXxLGTu78AlAG4eymwPWpRiYhIg5SvfHj2gDdg80Lez9PTxihR/ygtRlYWjB5dcVhq8D7r4jKY9ktYOBr6/Q7636ukUWQvVNdVVbeYWUfAAcr3U4xaVCIisscqrnw46oKRrFrfjbNv+xlPoAVxokD9o7QoWVmVfo+4w6c3weIxcNj/weF3KGkU2UvV9YnjjcBE4EAz+wAYT7AXo4iINDHlKx8e3G0+g46YwpNvXk3BpgRGjIh1ZHsl9Y/Sss3JgfnhnEYljSJ7tTo9cXT3T83sJOAQwID57l4S1chERGSPlK98eN3pj7GtJJHR/8nepVwiR/2jtGgLnty55caAB5U0iuzl6rqq6vlAa3efQ7DJ8fNmNiCqkYmIyB7p2RNSWxdw+Q/G8sK0n7OmoMuOcoks9Y/SYi15DqZfC91/BMc+o9VTRVqAuv5X/nt332RmJwCnAs8AT0YvLBER2VM5OXDVaWNIbb2ZR964Hqiw8qFEWsT7RzNLM7MXzewrM5tnZgPNrIOZTTWzBeFxn7CumdlIM1toZl9UTFrNbGhYf4GZDa1QfqSZfRleM9JMj4mkauWLbMXFBcfc3PDEqsnw0WWw74lw/PMQlxDDKEWksdQ1cSxfIe5s4Cl3fx3Qbq4iIk1Q1kXb+f0FI5m+5Hg+XZK5c+VDLYwTDdHoHx8B3nD3PsARwDzgVuAtd+8NvBW+BzgL6B3+ZBMmrWbWAbgdOAY4Gri9PNkM6/yywnWDGhiv7IXKF9laujRY/2bp0uD9pNxP4b3zIO1w+MFEaNU61qGKSCOpa+K40sz+AlwATDKzpHpcKyIijWnVa6TaNxx1yfWUlQUbcytpjJqI9o9m1h74AcGTS9y92N03AEOAcWG1cQTDYgnLx3vgYyDNzLoBZwJT3X2du68HpgKDwnPt3P1jd3eCxXzK2xLZoXyRrYrSklYyoOBHkNQJTp4Eie1jE5yIxERdO7efE2xwfGbYgXUAbolaVCIisue+ehhS9oceP4l1JC1BpPvHXkAe8KyZfWZmT5tZG6CLu68O63wLdAlfdweWV7h+RVhWU/mKKsp3YWbZZjbDzGbk5eU14ONIc1V5Ma02SZt59aYfkZK4CU5+DVp3jU1gIhIzdUoc3b3Q3f8JbDSznkAC8FVUIxMRkfpbPwvW/BcO/h+Iq+tWvbKnotA/tgIGAE+6+/eBLewcllp+TyfcNzJa3H20u2e6e2bnzp2jeStpoiouphVn28m9Nosj0j9n+PPPB8NURaTFqeuqqj82swXAN8A74XFyNAMTEZE9MH8kxKfAQVfGOpIWIQr94wpghbtPC9+/SJBIfhcOMyU8rgnPrwT2r3B9j7CspvIeVZSL7CInJ1hUC+Dei3/DkCMncvNzIzl96FmxDUxEYqauQ1XvAo4Fvnb3XsBpwMdRi0pEROqvaA0syYUDhkLiPrXXl0iIaP/o7t8Cy83skLDoVGAuMBEoXxl1KPBK+HoicFm4uuqxwMZwSOsU4Awz2ydcFOcMYEp4rsDMjg1XU72sQlsiO2RlBYtq3Xb+X7hp8IM8++FwMi++VvOlRVqwuo5jKnH3fDOLM7M4d3/bzB6OamQiIlI/C/4CZcVw8PBYR9KSRKN//B8g18wSgcXAFQRf9L5gZsOApQRzKwEmAYOBhUBhWBd3X2dmdwHTw3p3uvu68PU1wFigNcHTUY0gkiplnf4+xF0H3QZzxcgHtSyiSAtX18Rxg5m1Bd4l6MzWEMy7EBGRGMvNhTv+r5h3b3qC+d8NYqX30VOBxhPx/tHdZwGZVZw6tYq6DlxbTTtjgDFVlM8ADmtIjNICFK6E98+Dtr3guL9DXHysIxKRGKsxcTSzgwhWbhsCbAVuALKAdIJvREVEJIbK91r7yfdfoFvat1w+6te8vyg4p+QxetQ/yl5t+7Zgr8bSzXDKW9p2Q0SA2gcdPAwUuPsWdy9z91J3Hwe8DNwR9ehERKRGwV5rzq8HPczclYfy7y/PoLAwKJeoUv8oe6+ZwyH/Yzh2HKT1i3U0ItJE1JY4dnH3LysXhmUZUYlIRETqbNky+EGfd8k8YCaPvHE9YDvKJarUP8reaeFTsHA09L0Vev4s1tGISBNSW+KYVsO51pEMRERE6q9nT7jlnPtYs7Ez49+7bJdyiSr1j7L3WTsNZlwHXc+A7/0x1tGISBNTW+I4w8x+WbnQzK4EZkYnJBERqatHc+Zyzvdf57Gp11FUEuQrKSnBHmwSVeofZe+yLT9YDKd1dzj+OS2GIyK7qW1V1V8DL5tZFjs7wkwgEfhJNAMTEZHa/ejAByhd1JpXv7oGs+BJY06OFsZpBOofZe/hZfDR0GAv2DM+hKQOsY5IRJqgGhNHd/8OOM7MfsjOpbtfd/f/RD0yERGp2dbVsORvtDr4Sj6b2ynW0bQo6h9lrzLvAVj1OmQ+Bh2OjHU0ItJE1WkfR3d/G3g7yrGIiEh9fP0YlJVAnxtiHUmLpf5Rmr28D+Dz26Dn+dD7mlhHIyJNWG1zHEVEpCkq2QwLnoT9fwKpB8U6GhFpjorWwgcXQpsMOPopMIt1RCLShNXpiaOIiDQxi8dA8Xo49JZYRyIizZGXwcfl8xo/gsT2sY5IRJo4JY4iIs1NWSl89RB0Ph46HRvraESkOZr3AKyaBJmPQ4cBsY5GRJoBDVUVEWlGcnPhuiEvwZYlZD94M7m5sY5IRJqd/Onw+e9g//Og99WxjkZEmgk9cRQRaSZycyE723nntvv4enVvnp7yY3LfDc5p+w0RqZOSTfDBxdC6GxwzWvMaRaTOYvbE0czizewzM3stfN/LzKaZ2UIze97MEsPypPD9wvB8RoU2bgvL55vZmRXKB4VlC83s1sb+bCIi0TBiBJxw4L/JPGAm971+C+5xFBYG5SIidTJzOGxZDMflQuI+sY5GRJqRWA5VvR6YV+H9PcBD7n4QsB4YFpYPA9aH5Q+F9TCzvsCFQD9gEPBEmIzGA48DZwF9gYvCuiIizdqyZTDi3ByW5/dg3LtDdykXEanVkgmweCz0+1/Y98RYRyMizUxMEkcz6wGcDTwdvjfgFODFsMo44Nzw9ZDwPeH5U8P6Q4AJ7r7N3b8BFgJHhz8L3X2xuxcDE8K6IiLN2nk/eJcf9HmP+16/hZLtiTvKe/aMYVAi0jxsXgLTfwWdBsJhv491NCLSDMXqiePDwG+AsvB9R2CDu5eG71cA3cPX3YHlAOH5jWH9HeWVrqmufDdmlm1mM8xsRl5eXkM/k4hIVD38yxzWFOzL029fuaMsJQVycmIYlIg0fWWl8GE4Efq4XIjTEhciUn+Nnjia2TnAGnef2dj3rszdR7t7prtndu7cOdbhiIhUL386+9m/WZl6I/t2S8EM0tNh9GgtjCMitZj9R1j7IRw1Ctr2qrJKbi5kZEBcXHDUis0iUlksvnI6HvixmQ0GkoF2wCNAmpm1Cp8q9gBWhvVXAvsDK8ysFdAeyK9QXq7iNdWVi4g0T3NyIHEfvj/kapYoURSRulo7Deb8ETIugYyLgCApHDEimB/dsycMHgzjxkFhYXDJ0qWQnR281hdTIlKu0Z84uvtt7t7D3TMIFrf5j7tnAW8D54XVhgKvhK8nhu8Jz//H3T0svzBcdbUX0Bv4BJgO9A5XaU0M7zGxET6aiEh0bPgSVrwCBw+HhHaxjkZEmouSzfDhJdC6O2Q+BpRv6xMkh+7BcdSonUljOa3YLCKVNaVB7r8FJpjZH4HPgGfC8meAv5rZQmAdQSKIu88xsxeAuUApcK27bwcws+uAKUA8MMbd5zTqJxERiaQ5f4JWbeGQ4bGORESak89ugs2L4NS3IbE9ECSDlZNE96ov14rNIlJRTBNHd/8v8N/w9WKCFVEr1ykCzq/m+hxgt2Uh3H0SMCmCoYqIxEbB17D0eTj0FkjqEOtoRKS5WPEqLBzNXL+FwcectGNY6tKldW9CKzaLSEWx3MdRRERqkJsL//jDn9lanETmpTdqsQoRqZuiNfDJlazzIzj+mrt2GZZqVvUllcu1YrOIVKbEUUSkCcrNhXt//zU/6f9X/vLWr5g5pwvZ2VrpUERq4Q7TroTijVw48m9sKEja7XRVSeJVVwUrNWvFZhGpTlOa4ygiIqERI+DP59zOtpIk/jzxNmDnYhX6Y05EqrXoaVj5Kgx4kDenH1ZlFfcgOSwfvpqTo98rIlI7PXEUEWmC2vsXXHTcBB6Zcj1rCrrsKNdiFS2DmcWb2Wdm9lr4vpeZTTOzhWb2fLhqOOHK4s+H5dPMLKNCG7eF5fPN7MwK5YPCsoVmdmtjfzaJos2L4dMboMspcMj11c5RTE+HJUugrCw4KmkUkbpQ4igi0gTdf+nv2bClPfe9dssu5VqsosW4HphX4f09wEPufhCwHhgWlg8D1oflD4X1MLO+BKuQ9wMGAU+EyWg88DhwFtAXuCisK81d2XbWvDKUgs3xpF/4LBm94hg8OBiGWpHmLorInlLiKCLS1Kydxul9J/LI1JvZULjPjmL9wdcymFkP4Gzg6fC9AacAL4ZVxgHnhq+HhO8Jz58a1h8CTHD3be7+DbCQYOXyo4GF7r7Y3YuBCWFdaeY+fe5B9rX3ue7ZR1m2tidLl8K4cTB0qOYuikhkaI6jiEhT88X/QlIn+gy5nvRPNA+pBXoY+A3w/+zdeXxU1fnH8c+TDQi7iKJACCguuIAQFau/atW6UOu+FoG6NHWrW11Q2mqxsS6tinUrKooaUdyqtajFte4QFDcWRZYAIjsECAJJnt8f9yYMIQlEZnJnku/79ZrXzD13O2cY5uSZs7UOtzsAK9y9LNyeB3QOX3cG5gK4e5mZrQyP7wx8FHPN2HPmVks/sHoGzCwfyAfIUTN38lvxBXuV/4HnPjmZx98bVJVcWgrjxgXdUUVEtpUCRxGRZLLwbfj+ddjv75yxZ2vOUKDYpJjZccAid59kZodFlQ93HwmMBMjLy6tleXhJCuXr4YNBrFjTjgtGPQBsOmWqxkWLSLyoq6qISBIoLITcXOf9+4fx/cqdeeqTC6POkkTjYOB4M5tN0I30cGAE0M7MKn/s7QLMD1/PB7oChPvbAktj06udU1u6pKov/wwrPmPYiw+yZFXHzXarwVhE4kWBo4hIxAoLIT8ferV7hYN3+4Abnv0T5+W30JqNTZC7X+fuXdw9l2BymzfdfSDwFnBqeNgQ4MXw9UvhNuH+N93dw/Qzw1lXuwM9gQnARKBnOEtrVniPlxqgaBJnhYVw8v99SPkXt/B00blk9TheE+GISEIpcBQRidiwYfDD2nL+esZ1fLuwB6PeObdqzUaR0LXAlWY2g2AM48Nh+sNAhzD9SmAogLt/BYwFpgCvAhe7e3k4TvIS4DWCWVvHhsdKCikshCt+t5rbThrE3KVd+c0Dd2oiHBFJOI1xFBGJWHExnHfYKHp3+5zTRoylrDyzKl2aLnd/G3g7fD2TYEbU6sf8AJxWy/kFwGbtTe4+DhgXx6xKAxs2DG484Rp67DCTnxW8xaq1bQBNhCMiiaUWRxGRiPXqWcJfTvsD7047hGcnnFqVrrFJIlKTPdq+xkU/v587X72C/007tCpdPzaJSCKpxVFEJGJP/+lmdrRF/OL2/1A5I6LGJolIjdYt49ELzuWreb0YNnbTLwn92CQiiaQWRxGRKK2exV7pdzLTB7OkIk9jk0RkM8Gsy5CWBi/+6RI6tl5E/iOPsW5D86pj9GOTiCSaWhxFRKL06TVgGfQ46WZmr0BbkgAAIABJREFUK1AUkWoqZ10uLYXT+z/NCb3HMPxfw+n9s37MXxt0T83JCYJG/dgkIomkwFFEpIEVFgaTW+S0eJf//fFZPvM/0zu7c9TZEpEkNGxYEDR2areA+359ER/POIDhz11Hl66aCEdEGpa6qoqINKDK1oPi4gruGHgFc5d24YhLrtKajSJSo2DCG2dU/rm0yFrLkAdGU16RoYlwRKTBKXAUEWlAla0Hgw55nLwekxj61C0sXZGtNRtFpEY5OXDhkfdzbO9XuXrM7UxfsEdVuohIQ1JXVRGRBlRcDO1bLuP2s67mw2/6M+bDs6rSRUSqu7tgOkeuv4pXPzua+8ZfBGgiHBGJhlocRUQaUE4O3HbWNWzXahm/ffifuKdVpYuIwMZZVLMyN9Bt/tlUpLXgT+NGYWaadVlEIqMWRxGRBvRgwf/4uT3Mrf++hi/m7guo9UBENoqdRfXGU/5C7y5F/Or+Z7ls6M4KFkUkUmpxFBFJoNj113bbZR0HkM8q784jRTdozUYR2UzlOOgDd/2IYScU8Oj/hjDmvVM0DlpEIqcWRxGRBIltOQA4q88ttLXpvOmvMu2b7GgzJyJJqbgYWjZbzeMXDmLesi5c9tiIqnQRkSipxVFEJEEqWw4Adt9pGtcffzNPfnAW5w47OtqMiUjSysmBuwZdzi47fMvgBx6jZG3bqnQRkSgpcBQRSZCNLQTOA+deQOn6bK54/E61HIhIldju7Lm5MGzQM5z/s4e5+aXreXfaTwGNgxaR5KDAUUQkQSpbCM49dBSH9XqHq5+8nUUlO6rlQESAjd3Z58wBd6hYXcypOfnMKjmQRzUOWkSSjMY4iogkSEEB3Hz9TO4adDlvTTmMUe+cq5YDEakS2509zcp54qKzSU8rZ/B9TzJjZma0mRMRqUaBo4hIggw8q4yjGIT/kM6v/zmanJw0CgrUciAigdhu69ed8Fd+use7nH3f47z/WY/oMiUiUgt1VRURiZPqY5U+G3MLHe0D2hxxP3MW5zB7toJGEdmostt6/10/5MaTb+SJ9wZS+P7Z6s4uIklJgaOISBxUH6u0Q/oE9qq4kdl+FuSeFXX2RCQJFRRApw4rKbx4IMVLc7j40XvVnV1EklaDB45m1tXM3jKzKWb2lZldFqZvZ2bjzeyb8Ll9mG5mdreZzTCzz82sb8y1hoTHf2NmQ2LS+5nZF+E5d5uZNXQ5RaRpiR2rlN1sDU9cdDbfLd+Z42+6N9qMiUjSGvgr5+MR59G1w1zOvq+Q9ju01UQ4IpK0omhxLAN+7+69gP7AxWbWCxgKvOHuPYE3wm2AY4Ge4SMfuB+CQBO4ATgQOAC4oTLYDI/5Tcx5xzRAuUSkCYsdq/T3gb9n1x1nMOSfo/ny6/a1nyQiTUr17uwTn7yHHHuOzLy/8sHXB6k7u4gktQYPHN19gbt/Er5eBUwFOgMnAKPDw0YDJ4avTwAe88BHQDsz2wk4Ghjv7svcfTkwHjgm3NfG3T9ydwcei7mWiEhCVI5JOr7fi1xwxD/527ireHvKzzRWSUSAmruz9y7/PfP8l7DH76POnojIFkU6xtHMcoH9gI+BHd19Qbjre2DH8HVnYG7MafPCtLrS59WQLiKSMAUFsG/3r3nsgsFMmtWXPz5zk8YqiUiV2O7s7bKXM/bS0/lu+c784i+PgkbUiEgKiGw5DjNrBTwHXO7uJbHDEN3dzcwbIA/5BN1fyVGzgIhsg4Gnr+I4TqSsNItT7nqenTo309IbIlJlY3d255HfnsPO7b/j/4a/yxczt4syWyIiWy2SFkczyyQIGgvd/fkweWHYzZTweVGYPh/oGnN6lzCtrvQuNaRvxt1Hunueu+d17Nhx2wolIk3KpmOVnOKxv6Zt2nQ6/PJpZi/uprFKIrKJyt+nrzj2Tk7Me5FrxtzGhG8PVHd2EUkZUcyqasDDwFR3vyNm10tA5cyoQ4AXY9IHh7Or9gdWhl1aXwOOMrP24aQ4RwGvhftKzKx/eK/BMdcSEdlm1ccqndX7FnLseSZV3AadDo86eyKShAoK4Mje73Lrmdfy/MSTGPHqZerOLiIpJYoWx4OBQcDhZjY5fAwAbgF+bmbfAEeG2wDjgJnADOBB4CIAd18G3ARMDB/DwzTCYx4Kz/kWeKUhCiYiTUPsWKWj932VgtOGMeaDMzll2JXRZkxSnpasajyqz6CazVxeuvpUipf34LwHR9Gtm2npDRFJKRZMPCp5eXleVFQUdTZEJAWkpQUtjT12+JaJN+3P3KVd+cmfP2Dt+pZUVESdO9kSM5vk7nlR56Mm4VCNndz9EzNrDUwimBn818Ayd7/FzIYC7d392vCH198BAwiWpxrh7geGS1YVAXmAh9fp5+7LzWwCcCnBxHTjgLvdvdYfWFU/1l9lr4TKH5iaZ67l/Rv/j326fU3mcROg7R7RZlBEpBZ11ZGRzqoqIpKKcnJghzYLee3ao3E3Tr7reUrXtdRYJdlmWrKqcYjtlQDOyPPz6Zs7iQseL1TQKCIpK7JZVUVEUtWtBavYrXgAO7f/jiNufoOZi3bRWCWJuyiXrNKs49tm4wyqwWQ4gw55gj8+M5xH/vtLHo4uWyIi20QtjiIi9VG+jjM6nUTvnM+4aMyzfPztQXTrhsYqSVxVX7Iqdl/YUpjQcSaadXzbVMbaR+z1Orf/6mqem3AyBS8OU68EEUlpChxFRLaWV8CHQ2DhG6QdNIpH/zuAigq09IbEVbIsWSU/XkEB9O4+nbGXns7U+Xvy638+SosWaeqVICIpTYGjiMjWcIdJl0Px09DnNugxOOocSSOkJatSU/UZVJvzPe/ddAwVZHDCHS/RYcfW6pUgIilPYxxFRLbEHT67Hr7+B+xxJex5VdQ5ksarcsmqL8xscph2PcESVWPN7DxgDnB6uG8cwYyqM4BS4BwIlqwys8olq2DzJaseBVoQLFelJau2QfUZVJd8v5ruc46jebdFtDrlbb7N7xFtBkVE4kSBo4hIXbwCJl0BX98Nu/4W9rsdtOydJIi7vwfU9gE7oobjHbi4lmuNAkbVkF4E7L0N2ZQYsTOopqeVMfbS0+md8ynnP/YSjwzcP9rMiYjEkbqqiojEiO1y1qN7OTOezIev7+bBd68krf/95HZPo7Aw6lyKSLLYOIOqc/+5FzKgzytcOOp+Ro//RZTZEhGJOwWOIiKhyi5nc+ZAetoGbhowmF3tYQpe/CP5D/wNd2POnOAYBY8iAhtnUP3jSTfxm589xE0v/IEH38rXDKoi0ugocBQRCVV2OcvKWMfTvzuDgQc/ydCn/sofxg4ntvdgaWlwrIhIQQFcd+LfGH7qDTz6vyH86dnhWtdVRBoljXEUEQkVF8OObb/nhStO4qCeH3HpYyP4x2uX1nqsiMjAfneCXc3Ln5/Obx56iG7djIICzaAqIo2PAkcRkdCxB37KA786ng6tlnLqiGd4bsKptR6rbmgiwrQR8MmV0PVUjjvzCTbcoj+rRKTxUldVEWnSKifDOb3/Mzzz24NxjIP//H5V0JiZCVlZm56jbmgiTVfld8alR/8DPrmcYj8ZDn4S0jKjzpqISEIpcBSRJquwEH772wp+3e9Gxl56OpNn9+Enf57I3NX7YQbdusEjj8CoUcHryjQt5C3SNFVOoHXcbvdw95BLeWHiiex74RgKxyhoFJHGT30qRKTJKCwMJrUpLg66mrbOmMeLlw7hiL3f5JF3fs0Fox5gfVkzunWDJUs2PVeBoogMG+Zc/4s/MOzEm3lx0vGc8Y+n2VCexbBh+o4QkcZPLY4i0iTELrXhDvvv+AzvXLMvB+76MeeNfIhzR45ifVkzQBPfiEggdl3X3XZZR8EvzmbYiTfz4Fvnc+qIZ9lQHvRj13eGiDQFanEUkSahcqmN1i1K+Mfg3zHkp4/x8YwDOPu+J5ixsOcmx2riGxGp/LGptBTaZS9n5FkncVivd7j+6QL++tJ1xC7Ro+8MEWkK1OIoIo1SbEtBbm7Q0jigz3/47ObenH3IEwx//o8cMvy9zYJGTXwjIrDxx6ac7efw/o0H85PdPuBX9xZyy7+vJzZo1HeGiDQVChxFpNGp3i3VSmfxrytP4D9XH8e6smb89Kb/ccNzwykrz6RDB018IyI1/9j0i/1eZtJf+rFTuwUcdct/GfPBr3DXd4aINE3qqioijU5lS0HzzLVc88vbGPrLWyivSOfaMbdy5yuXV41Lys6GESP0R59IUxfbLRVgwfx1jBh8DZcefTefzu7Dmfc8xdcLdgeCYHH27OjyKiISFbU4ikjKq95SMG9uGUN++ihf3bYXfz7lRl765Hj2uHoat718DTt3yVJLgYhsovLHJoDddprOR3/uz6VH382IVy+j/w0fVQWN6pYqIk2ZWhxFJKXFthSkWTn/1/VJ/nTpcHp2msEns/bjiJtf582vjgDUUiAiNSsuDr4/fnP4g/z9V79n7YYWHPe3f/OfT4+jW7eNS/gUFOjHJhFpuhQ4ikhKGzYMNqxbz8CDx/KHE//CHjtPZ/Kc3px4x794cdLxVE5ioZYCEalUfU3XY/q9z00nXkq/7p/wxpeHM/iBx/hueWf92CQiEkNdVUUkpcR2S91/7+8Z0u/PzBnRjScuGsSG8kxOvvM5+g77hBcnnUC3bqZuqSJNXPWu7BddtHHyrE5tv+OmAYMYd8Uh7Nh2IWfd8yRH/vV1vlveWT82iYhUoxZHEUla1VsFBgyA0aOdPl0+oODC+zjtwGfIytjAuMnHct6Dl/Dq58fgHvweppYCEak+6c2cOfDAA7B960Vce8o9XDngDjLTN/CXfw3jwfeGYlmtMFO3VBGRmihwFJGkVP0PvhYbptJ5SSFfFDxJjx1msbK0DfeNv4h7x1/Mt4t64r7xXLUUiAhsOukNwB47T+XKAXcw6ODHaZ61jucnnsTVT97OzEW7YAYVFdHlVUQk2SlwFJGkUL11cfVqp1v7qfzy8H9zRv+n6dv9U8or0nj9yyP58/M38PzEk1n9Q+uq8zWBhYhUV1wMWRnrOGqf//LbI/7Jcfv9h7XrmzP63SHc+coVTF+wR9WxOTkRZlREJAUocBSRBldzF1QoW7+OI/d+h+P2e5nj9nuZHjvMAmDCt/tz2WN38fRHZ7BwZafNrqduqSICG79bvv9uHQMP/y9PXTaWo/d6ibbZJSxa2ZEbnruR+8ZfxNLVHdVLQUSknhQ4ikhC1RYklpZC88y15GZ/zI6L3ublK96h/64f0SLrB9aub87rXx7Jrf++lv9M/gXzl3Wpup4Z+oNPRDZVUc64MZ/z2dPvcOdJ73D4Xm/SNruEZavb83zRqTz94Wm8+dXhbCjPIjsbLrgAxo1TLwURkfpQ4CgicVNXkGhWQYsN01n9RRE3n1LE/j0m0q/7JJplrqeiwvh0zn7c//qFvPHVEbw15WesXZ+92fWzs2HIEP3BJ9LkrVvKm88WMWl8EXt2/JCf7vEeA1qsZMCZ8O3CHoz9+HSem3AKb3x1BG3bZdKqFZRVBL0T9J0hIvLjKHAUkS2qHhBWtvDVFiR2aLWE3OwvSf/2S/5+5pfs3eVL9s35nDYtVgGw+oeWfDK7L3e/dinvTDuU96YfwsrSdpvdt0MHaNVKQaJIk1axgVfGfMaE/7zP7h0+5KDdJtKtw0wONzj8KJj23e489eHpvDP1UN6ZdugmPRQAli2DJUsiyruISCNiHtvnqwnLy8vzoqKiqLMhklBbGwDGtujFBoSVmmWVs3P7BezUdg6528+mZ6dv2LXTDHru+A277jiDDq2XVR27bHV7vpy3N1/M3YeJM/enaGYeU+fvSYWnb5K3mrqgau1FSQQzm+TueVHnI1XEs37cuu8gZ/7nEzlg55c4Yt/36NttAlnpawEoXtKVCTMPoGjm/kz4dn8+md23xh+dYmkMtIjI1quzjnT3RvkAjgGmAzOAoVs6vl+/fh4PTzzh3q2bu1nw/MQTyZN24YXJkY9kSmtK78mFF7pnZ7sH4VnwyMx0z8rauJ1mZd6xzULv1flLP6zXm37WTwr99wP+5n8beKUXXnyWv/2Hn/rMO3N9/egM90KqHuWPm8+6q5uPv+4Iv++cC/zyY+7wI/f+r+/Ubr5DxSb3hCBPsdvZ2TX/W4gkAlDkSVBPRfmoTx0Zz/qx9u+gCt+/x8d+21lX+ay7urkX4hseS/cJw/P8rkGX+WkHPu2dt5u72XfJlh7Z2fouERGpj7rqyEbZ4mhm6cDXwM+BecBE4Cx3n1LbOfH4RbX6unMAmZlBS8r69dGnVZdMedN7Eo80JytjPa2ar6Z9q9W0ar6aZumradOihDYtSmibXUKbFitpm72S9tnLad9yOdu1Wlb13LH1Yjq0Wkpa2ubfCaXrWrBgxU58t3xn5izpRvHSnKrn2YtzmbW4O+s2NK/xPa2pJVHjFCVKTb3Fsb51ZLxaHHNzYc6cTdPS08oY8n+jGXZiAT12mMX6skzGf/FznplwGi8WncCK0vb1uoe6t4uIbJu66sjGOsbxAGCGu88EMLOngBOAWgPHeKhcaPiY3q+wT9cv6Nh6Mdu3XkLHNsFzmxYlNMtYR1bGepplrKNZ5jrSrALHcA8fGOUV6Wwoy2RD+cbH+rIs1pdl1fi66riyTMoqMigrz6CsIoPyinTKyjOo8DTcjQpPq3pdnZmTZhVVz5WP9LTyGh8Z6WVkpJVVvU5PK691OzYtPa18k+vG3rPqGcfMq/JVXWX+Y8sVW76KijTKK9Krtitfl1ekVz3KyjM2vq7I2DTd0zc5tvqj6poVG69f+W9YmZfKf8vqKstZWcaa3uPK9zYzfQOZGRvISCsLPjOZ66o+N80y1tEia23wyFxb9TojvXyrPqsla1uzfE17lq3ejmWrt2PK/F4sLunI4pKOLCrZgcWrgtffLd+ZBSt2omRtG6ihPJt/jhQkiqSASOrI4uLYLee4/V7mljOHsleXKXw040CGv/CnegWLNX3fjBih7xcRkURprIFjZ2BuzPY84MDqB5lZPpAPkBOHlX8rK8XzD3uIUw54nrXrm7O4pCNLVm3PktXbM29ZF9ZtaBY8yoLnCk/bJJAwc9LTyoOgofKRETxnZawPHunradlsTdW+rIz1VcdWD+gy0spqDAprCmoqA6HYALOmwCk2KI19XT0IW7eh2WZptQVfVUEXRkVFGkBVHmMD3aqAMibwii1X5fuXZhWkpVVsFqhWPSx4f5plrqNl+hrSbfMAt6Zz0tPKSUvbGFRXPlcPBmsKeM2cioq0TX4oqB7QVr5fG8ozKSvP2OSHg8rPzcrStqzb0IwfNjSndH02a9e3qHqsXteKNetasvqHVqz+IXhdsrYNJWvbsLK0bdXr8or6/dev/gdaTS2fChJFUsYW68h414/BdYIWxwN2+Zjbf3U1P93jXaZ/txsn3/kcLxSdRF0/TulHKRGR6DXWwHGruPtIYCQEXXG29XqVleJvHnqQwQ88Rum6bLamlUakoWxNAFhdbX+gweaTXOiPNpHGId71IwTfEff9ZRLv/7E/C1fuwIWj7mP0++dTXpFZ53kKEkVEkkNjDRznA11jtruEaQlVUBCMcVy+ZruqtOjHvdWe32TKm96TxKdtbQBYfVbVuv5A0x9uIikpkjoy+L7oyzXPPcQDr5zOdju05sGHgn0/9jtIREQaUG2z5qTygyAgngl0B7KAz4C96jpHs6o2zbSm9p6ISN0zxjWFR33ryHjVjyIikvzqqiMb5ayqAGY2ALgLSAdGuXtBXcdrHUcRkaahqc+qCvWrI1U/iog0HU1xVlXcfRwwLup8iIiIJBvVkSIiUl9pUWdAREREREREkpsCRxEREREREamTAkcRERERERGpkwJHERERERERqZMCRxEREREREamTAkcRERERERGpkwJHERERERERqZO5e9R5SApmthiYE8dLbg8sieP1otAYygCNoxwqQ3JoDGWAxlGObSlDN3fvGM/MNGYJqB9Bn8FkoTIkj8ZQDpUhOWxrGWqtIxU4JoiZFbl7XtT52BaNoQzQOMqhMiSHxlAGaBzlaAxlaMoaw7+fypAcGkMZoHGUQ2VIDoksg7qqioiIiIiISJ0UOIqIiIiIiEidFDgmzsioMxAHjaEM0DjKoTIkh8ZQBmgc5WgMZWjKGsO/n8qQHBpDGaBxlENlSA4JK4PGOIqIiIiIiEid1OIoIiIiIiIidVLgKCIiIiIiInVS4JgAZnaMmU03sxlmNjTq/GwNMxtlZovM7MuYtO3MbLyZfRM+t48yj1tiZl3N7C0zm2JmX5nZZWF6ypTDzJqb2QQz+ywsw5/D9O5m9nH4mXrazLKizuuWmFm6mX1qZi+H26lYhtlm9oWZTTazojAtZT5PAGbWzsyeNbNpZjbVzA5KpTKY2e7h+1/5KDGzy1OpDLJRKtaPoDoyWaiOTB6NoX4E1ZH1pcAxzswsHbgXOBboBZxlZr2izdVWeRQ4plraUOANd+8JvBFuJ7My4Pfu3gvoD1wcvvepVI51wOHu3hvoAxxjZv2BW4E73X1XYDlwXoR53FqXAVNjtlOxDAA/c/c+MWsipdLnCWAE8Kq77wH0Jvg3SZkyuPv08P3vA/QDSoEXSKEySCCF60dQHZksVEcml1SvH0F1ZL1vqEccH8BBwGsx29cB10Wdr63Mey7wZcz2dGCn8PVOwPSo81jP8rwI/DxVywFkA58ABwJLgIwwfZPPWDI+gC7hF9XhwMuApVoZwnzOBravlpYynyegLTCLcCK0VCxDtXwfBbyfymVoyo9Urh/D/KqOTKKH6sjIy5DS9WOYR9WR9XyoxTH+OgNzY7bnhWmpaEd3XxC+/h7YMcrM1IeZ5QL7AR+TYuUIu69MBhYB44FvgRXuXhYekgqfqbuAa4CKcLsDqVcGAAf+a2aTzCw/TEulz1N3YDHwSNgl6iEza0lqlSHWmcCY8HWqlqEpa0z1I6TwZ1B1ZOQaQx2Z6vUjqI6sNwWOslU8+MkiJdZuMbNWwHPA5e5eErsvFcrh7uUedDnoAhwA7BFxlurFzI4DFrn7pKjzEgeHuHtfgq51F5vZT2N3psDnKQPoC9zv7vsBa6jWXSUFygBAON7neOCZ6vtSpQzSeKXSZ1B1ZLQaUR2Z6vUjqI6sNwWO8Tcf6Bqz3SVMS0ULzWwngPB5UcT52SIzyySoEAvd/fkwOeXKAeDuK4C3CLqstDOzjHBXsn+mDgaON7PZwFMEXXFGkFplAMDd54fPiwjGDBxAan2e5gHz3P3jcPtZgkoylcpQ6VjgE3dfGG6nYhmausZUP0IKfgZVRyaFRlFHNoL6EVRH1psCx/ibCPQMZ8fKImg2finiPP1YLwFDwtdDCMZDJC0zM+BhYKq73xGzK2XKYWYdzaxd+LoFwfiTqQSV46nhYUldBne/zt27uHsuwef/TXcfSAqVAcDMWppZ68rXBGMHviSFPk/u/j0w18x2D5OOAKaQQmWIcRYbu+BAapahqWtM9SOk2GdQdWRyaAx1ZGOoH0F15I9h4aBJiSMzG0DQfz0dGOXuBRFnaYvMbAxwGLA9sBC4AfgXMBbIAeYAp7v7sqjyuCVmdgjwLvAFG8cNXE8whiMlymFm+wKjCT47acBYdx9uZj0IfpncDvgUONvd10WX061jZocBV7n7calWhjC/L4SbGcCT7l5gZh1Ikc8TgJn1AR4CsoCZwDmEny1SpwwtgWKgh7uvDNNS6t9BAqlYP4LqyGShOjI5NJb6EVRH1vteChxFRERERESkLuqqKiIiIiIiInVS4CgiIiIiIiJ1UuAoIiIiIiIidVLgKCIiIiIiInVS4CgiIiIiIiJ1ytjyISKSSsysnGC69UygDHgMuNPdK+o8UUREpBFT/SiybRQ4ijQ+a929D4CZ7QA8CbQhWHdMRESkqVL9KLIN1FVVpBFz90VAPnCJBXLN7F0z+yR8/ATAzB4zsxMrzzOzQjM7wcz2MrMJZjbZzD43s55RlUVERCReVD+K1J+5e9R5EJE4MrPV7t6qWtoKYHdgFVDh7j+EldwYd88zs0OBK9z9RDNrC0wGegJ3Ah+5e6GZZQHp7r62YUskIiKy7VQ/imwbdVUVaVoygXvMrA9QDuwG4O7vmNl9ZtYROAV4zt3LzOxDYJiZdQGed/dvIsu5iIhI4qh+FNkCdVUVaeTMrAdBJbgIuAJYCPQG8oCsmEMfA84GzgFGAbj7k8DxwFpgnJkd3nA5FxERSRzVjyL1oxZHkUYs/IX0AeAed/ewm808d68wsyFAeszhjwITgO/dfUp4fg9gprvfbWY5wL7Amw1aCBERkThT/ShSfwocRRqfFmY2mY3TjT8O3BHuuw94zswGA68CaypPcveFZjYV+FfMtU4HBpnZBuB74OYGyL+IiEgiqH4U2QaaHEdEADCzbIL1rfq6+8qo8yMiIpIMVD+KBDTGUUQwsyOBqcA/VCmKiIgEVD+KbKQWRxEREREREamTWhxFGikze9vMDos6HyIiIoliZjea2Y1R50OkKVDgKLIFZnammX1sZmvMbFH4+iIzs6jz9mOZ2WFmVmFmq8PHPDMba2b7R523H8vMOprZk2a20syWm1lh1HkSEZFNmZmb2a7V0m40syditq83s1kx9dPT23i/NeG1lprZG2Z2xraUISpm9n8x9Xblw83slKjzJk2DAkeROpjZ74ERwO1AJ2BH4ALgYDZd4yn2nPSa0pPQd+7eCmgN9AemAe+a2RHxvpGZNcQMzs8TzGyXA+wA/K0B7ikiInEULoUxCDgyrKPygDe28bK9w2vtTrC0xj1mdsM2XnMzFkjY39bu/q67t6p8AMcBqwlmgRVJOAWOIrUI13QaDlzk7s+6+yoPfOruA919XXjco2Z2v5mNM7M1wM/MrJmZ/c3Mis1soZk9YGYtYq59nJlNNrMVZvaBme0bs6+rmT1vZovDX0fvidl3rplNDVvUXjOzbtujRjA0AAAgAElEQVRazrBM89z9T8BDwK0x99vDzMab2TIzm25mp8fs62Bm/zazEjObaGZ/MbP3Yva7mV1sZt8A32zF9ep8z+piZkcBXYGr3X2lu29w90+39b0REZEGtz/wmrt/C+Du37v7yHhc2N2XuPvjwIXAdWbWAYL63sweNrMFZjY/rM/Sw33pZvZ3M1sStoJeEtZvGeH+t82swMzeB0qBHnVdLzwnXnX5EOBZd1+zxSNF4kCBo0jtDgKaAS9uxbG/AgoIWu/eA24BdgP6ALsCnYE/AZjZfsAo4LdAB+CfwEth4JQOvAzMAXLD854KzzsBuB44GegIvAuM2fZibuJ5oK+ZtTSzlsB44EmCFrwzgfvMrFd47L0E61x1Iqi8htRwvROBA4FeW3G9Wt8zgDDIPqSWfPcHpgOjw2B7opkd+mPeABERidRHwGAzu9rM8hLUi+dFgrXMDwi3HyVY13FXYD/gKOD8cN9vgGMJ6qa+BPVadYOAfIK/AebUdb0t1eVm9rKZDd1SAcI69VRg9NYUWCQeFDiK1G57YIm7l1UmhK2DK8xsrZn9NObYF939fXevANYRVCBXuPsyd19FsDDwmeGx+cA/3f1jdy9399HhOf0JKrGdCVrO1rj7D+5e2Yp3AfBXd58a5ulmoE88Wh1jfAcY0I6gC8xsd3/E3cvCFrzngNPCivwU4AZ3L3X3KdRcef01fA/WbuF6toX3DHdvF/NeVNeFoGJ+iyCQ/Tvwopltv61viIiINBx3fwL4HXA08A6wyMyujfM9NgBLgO3MbEdgAHB5WO8uAu5kY/1zOjAi7JmznOBHzuoedfevwrp5uy1cr8663N2Pc/ea7lHdyWEZ3qn/OyDy4zTEuCORVLUU2N7MMiqDR3f/CYCZzWPTH17mxrzuCGQDk2zj/DkGVP5q2g0YYma/izkniyBgLAfmxAarMboBI8zs7zFpRtAyN6f+xatRZ8CBFeH9DjSzFTH7M4DHCcqYwabljn1dU9qWrlfXe7YlawmC0ofD7afMbBjBWNStaTEWEZGGUQ5kVkvLBDZUbrh7IVBoZpkELXyFZjbZ3V+LRwbC63YElhHUTZnAgpj6J42N9dfO1L+uq+t68arLhwCPudbVkwakwFGkdh8StASeQNAyVpfYL+4lBIHMXu4+v4Zj5wIF7l5QfYeZHQTkxAarNZyXyNlCTwI+cfc1ZjYXeMfdf15DPtMJuuF0Ab4Ok7vWcL3Y96Wu66VR93u2JZ8Dv6zj3iIikhyKCYZiTI1J687GuqRK2DL4TNjiuDcQl8CRoF4vAyYQ/HC7Dti+lh9tFxDUdZW2pq6r63rbXJebWVfgMIIhLyINRl1VRWrh7iuAPxOMwzvVzFqbWZqZ9QFa1nFeBfAgcKeZ7QBgZp3N7OjwkAeBC8zsQAu0NLNfmFlrgkpsAXBLmN7czA4Oz3uAYDD/XuE125rZadtazjAPnS2YYe58grEXEIy13M3MBplZZvjY38z2dPdygvGQN5pZtpntAQzewq3qut6W3rMteQFob2ZDwokMTiWo6N+v15shIiKJ9jTwBzPrEtapRxL88PcsgJn9urJODPcfC+wFfLytNzaz7cxsIMEY/Vvdfam7LwD+C/zdzNqE99wlZpz8WOCysE5qB9TZbXYrrhePunwQ8EHlBEIiDUWBo0gd3P024ErgGmBh+PgnQcXxQR2nXgvMAD4ysxLgdYJpwHH3IoLB9vcAy8Pjfh3uKyeoQHcl+FV2HnBGuO8FghlPnwqv+SXBgP0fa2czW00wlfdEYB/gMHf/b3i/VQTjBs8kGPv4fXj/ZuH5lwBtw/THCQb3r6vtZltxvVrfMwAL1qv6v1quvQw4HrgKWAkMBU5w9yVb/3aIiEgDGE5Qf75HUAfeBgx09y/D/SUEP2AWEwybuA24sI4x7lvjs7C+m0HwA+kV4UzilQYTtDxOCfP0LLBTuO9BgkDwc+BTYBxBa2V5Hfer9XpbqsvN7BUzu36zK25+fU2KIw3O1DVapHEys7eBG9397Qa6361AJ3evaXZVERGRuDOzGwHc/cYGut+xwAPuHs+J6URSglocReRHsWBNxn3Drq4HAOcRdBkVERFpFMyshZkNMLMMM+sM3IDqOmmiNDmOSOP1KDA7gddvTdA9dWeCLrx/RzOYiohIw3o7wdc3gvkOniaYxO0/xKwxLNKUqKuqiIiIiIiI1EldVUVERERERKRO6qoa2n777T03NzfqbIiISIJNmjRpibt3jDofqUL1o4hI01FXHanAMZSbm0tRUVHU2RARkQQzszlR5yGVqH4UEWk66qoj1VVVRERERERE6qTAUUREREREROqkwFFERERERETqpDGOddiwYQPz5s3jhx9+iDorDaJ58+Z06dKFzMzMqLMiIiJJrKnVj6A6UkREgWMd5s2bR+vWrcnNzcXMos5OQrk7S5cuZd68eXTv3j3q7IiISBJrSvUjqI4UEQF1Va3TDz/8QIcOHZpEpWhmdOjQoUn9eiwiEgUz62pmb5nZFDP7yswuC9NvNLP5ZjY5fAyIOec6M5thZtPN7OiY9GPCtBlmNjQmvbuZfRymP21mWWF6s3B7Rrg/98eUoSnVj6A6UkQEFDhuUVOpFKFplVVEJEJlwO/dvRfQH7jYzHqF++509z7hYxxAuO9MYC/gGOA+M0s3s3TgXuBYoBdwVsx1bg2vtSuwHDgvTD8PWB6m3xke96M0tTqjqZVXRKQ6BY4iIiINyN0XuPsn4etVwFSgcx2nnAA85e7r3H0WMAM4IHzMcPeZ7r4eeAo4wYII53Dg2fD80cCJMdcaHb5+FjjCFBGJiMhWUOCYxJYuXUqfPn3o06cPnTp1onPnzlXb69ev36prnHPOOUyfPj3BORURkR8j7Cq6H/BxmHSJmX1uZqPMrH2Y1hmYG3PavDCttvQOwAp3L6uWvsm1wv0rw+Or5yvfzIrMrGjx4sXbVMZEUP0oIk1e6Xz438mw5OMtHxsnChyTWIcOHZg8eTKTJ0/mggsu4IorrqjazsrKAoIB+xUVFbVe45FHHmH33XdvqCyLiMRPYSHk5kJaWvBcWBh1juLKzFoBzwGXu3sJcD+wC9AHWAD8Paq8uftId89z97yOHTtGlY1aqX4UkSZv1dcw7wUoW91gt1TgGEcN9TfOjBkz6NWrFwMHDmSvvfZiwYIF5Ofnk5eXx1577cXw4cOrjj3kkEOYPHkyZWVltGvXjqFDh9K7d28OOuggFi1alJgMiohsq8JCyM+HOXPAPXjOz280waOZZRIEjYXu/jyAuy9093J3rwAeJOiKCjAf6Bpzepcwrbb0pUA7M8uolr7JtcL9bcPjE0r1o4hInK2eGTy36tFgt1TgGCcN/TfOtGnTuOKKK5gyZQqdO3fmlltuoaioiM8++4zx48czZcqUzc5ZuXIlhx56KJ999hkHHXQQo0aNSkzmRES21bBhUFq6aVppaZCe4sIxhQ8DU939jpj0nWIOOwn4Mnz9EnBmOCNqd6AnMAGYCPQMZ1DNIphA5yV3d+At4NTw/CHAizHXGhK+PhV4Mzw+YVQ/iogkwOpZYOmQ3XXLx8aJAsc4aei/cXbZZRfy8vKqtseMGUPfvn3p27cvU6dOrbFibNGiBcceeywA/fr1Y/bs2YnJnIjItiourl96ajkYGAQcXm3pjdvM7Asz+xz4GXAFgLt/BYwFpgCvAheHLZNlwCXAawQT7IwNjwW4FrjSzGYQjGF8OEx/GOgQpl8JVC3hkSiqH0VEEmD1rCBoTMvY8rFx0nB3auQa+m+cli1bVr3+5ptvGDFiBBMmTKBdu3acffbZNa41VTnuAyA9PZ2ysrLNjhERSQo5OUHTVE3pKc7d3wNqmsl0XB3nFAAFNaSPq+k8d5/Jxq6usek/AKfVJ7/bSvWjiEgCrJ7ZoN1UQS2OcVPb3zIN8TdOSUkJrVu3pk2bNixYsIDXXnst8TcVEUmkggLIzt40LTs7SJeUovpRRCQB1syCVt0b9JYKHOMkyr9x+vbtS69evdhjjz0YPHgwBx98cOJvKiKSSAMHwsiR0K0bmAXPI0cG6ZJSVD+KiMRZWSn8sBBaNmzgaAkeE58y8vLyvKioaJO0qVOnsueee271NQoLgzEbxcXBL6kFBan3N059yywikmrMbJK75235SAHVj7FUR4pIUljxFYzbG35SCLm/iuul66ojNcYxjgYOTM2KUEREJJFUP4qIxNGaWcGzxjiKiIiIiIhIjVaHgWMDd1VV4CgiIiIiIpIqVs+E9GxovkOD3laBo4iIiIiISKqonFHValrZKXEUOIqIiIiIiKSK1bMavJsqKHAUERERERFJDe5BV9UGXsMRFDgmtaVLl9KnTx/69OlDp06d6Ny5c9X2+vXrt/o6o0aN4vvvv09gTkVERBqO6kcRabLWLYWy1Q0+oypoOY6k1qFDByZPngzAjTfeSKtWrbjqqqvqfZ1Ro0bRt29fOnXqFO8sioiINDjVjyLSZFUtxaEWx9RWWAi5uZCWFjwXFibsVqNHj+aAAw6gT58+XHTRRVRUVFBWVsagQYPYZ5992Hvvvbn77rt5+umnmTx5MmeccUa9f4kVEWkwDfj9KRFQ/SgiEh8RLcUBanGMn8JCyM+H0tJge86cYBvivurxl19+yQsvvMAHH3xARkYG+fn5PPXUU+yyyy4sWbKEL774AoAVK1bQrl07/vGPf3DPPffQp0+fuOZDRCQuGvD7UyKg+lFEJH5Wzwyem3qLo5mNMrNFZvZlTNrtZjbNzD43sxfMrF3MvuvMbIaZTTezo2PSjwnTZpjZ0AbJ/LBhGyvFSqWlQXqcvf7660ycOJG8vDz69OnDO++8w7fffsuuu+7K9OnTufTSS3nttddo27Zt3O8tIhJ3Dfj9KRFQ/SgiEj9rZkGz7SGzdYPfOtlaHB8F7gEei0kbD1zn7mVmditwHXCtmfUCzgT2AnYGXjez3cJz7gV+DswDJprZS+4+JaE5Ly6uX/o2cHfOPfdcbrrpps32ff7557zyyivce++9PPfcc4wcOTLu9xcRiasG/P6UCKh+FBGJn4iW4oAka3F09/8By6ql/dfdy8LNj4Au4esTgKfcfZ27zwJmAAeEjxnuPtPd1wNPhccmVk5O/dK3wZFHHsnYsWNZsmQJEMwuV1xczOLFi3F3TjvtNIYPH84nn3wCQOvWrVm1alXc8yEiEhcN+P0pEVD9KCISPxEtxQHJ1+K4JecCT4evOxMEkpXmhWkAc6ulH1jTxcwsH8gHyNnWCqygYNMxHADZ2UF6nO2zzz7ccMMNHHnkkVRUVJCZmckDDzxAeno65513Hu6OmXHrrbcCcM4553D++efTokULJkyYQFZWVtzzJCLyozXg96dEQPWjiEh8VJRDaTHknBbJ7c3dI7lxbcwsF3jZ3feulj4MyANOdnc3s3uAj9z9iXD/w8Ar4eHHuPv5Yfog4EB3v6Su++bl5XlRUdEmaVOnTmXPPffc+swXFgZjNoqLg19SCwpSbmKHepdZRCQeGvD708wmuXteQi7eCKl+3Eh1pIhEak0xvNgNDvgn7JqfkFvUVUemRIujmf0aOA44wjdGuvOBrjGHdQnTqCM9sQYOTMmKUEQkcvr+bNz07ysisu0qZ1TVGMeamdkxwDXA8e4eOy3bS8CZZtbMzLoDPYEJwESgp5l1N7Msggl0XmrofIuIiIiIiMRN5RqOEY1xTKrA0czGAB8Cu5vZPDM7j2CW1dbAeDObbGYPALj7V8BYYArwKnCxu5eHE+lcArwGTAXGhsf+KMnWlTeRmlJZRSRCDbgYvCROU6szmlp5RSQJrZkFlgbZ0Uwel1RdVd39rBqSH67j+AJgs9H17j4OGLet+WnevDlLly6lQ4cOmNm2Xi6puTtLly6lefPmUWdFRBqzBlwMXhKnKdWPoDpSRJLE6pnQogukRzORV1IFjsmmS5cuzJs3j8WLF0edlQbRvHlzunTpsuUDRUR+rLoWg1fgmDKaWv0IqiNFJAmsnhVZN1VQ4FinzMxMuneP7h9HRKTRacDF4CVxVD+KiERgzSzY6ZjIbp9UYxxFRKSRa8DF4EVERBqNsrWwdkFkM6qCAkcREWlIBQXB4u+xErQYvIiISKOxZnbwHGFXVQWOIiLScAYOhJEjoVs3MAueR47U+EYREZG6VC3F0SOyLGiMo4iINCwtBi8iIlI/a6JdwxHU4igiIiIiIpLcVs+E9ObQvFNkWVDgKCIiIiIiksxWz4KWucEwj4gocBQREREREUlma2ZFOr4RFDiKiIiIiIgkL/egq2qES3GAAkcREREREZHktX45bCiJdGIcUOAoIiLJzCuCh4iISFO16pvgufWukWZDgaOIiCQndyi6BCbkN6rg0cy6mtlbZjbFzL4ys8vC9O3MbLyZfRM+tw/TzczuNrMZZva5mfWNudaQ8PhvzGxITHo/M/siPOdus2A2hdruISIiSaxkevDcevdIs6HAUUREko87fHoVfHM/ZHUAoptFLgHKgN+7ey+gP3CxmfUChgJvuHtP4I1wG+BYoGf4yAfuhyAIBG4ADgQOAG6ICQTvB34Tc94xYXpt9xARkWRVMg0sA1rvEmk2FDiKiEjiFBZCbi6kpQXPhYVbd97nf4Jpd8Buv4M+t0Q6/Xi8ufsCd/8kfL0KmAp0Bk4ARoeHjQZODF+fADzmgY+Adma2E3A0MN7dl7n7cmA8cEy4r427f+TuDjxW7Vo13UNERJLVqunBjKppmZFmIyPSu4uISONVWAj5+VBaGmzPmRNsAwwcWPt5X90MX/0Fdjkf+t3VqILG6swsF9gP+BjY0d0XhLu+B3YMX3cG5sacNi9Mqyt9Xg3p1HGP6vnKJ2jdJCcnp56lEhGRuCqZDm2i7aYKanEUEZFEGTZsY9BYqbQ0SK/NtDvhs2GQezbs/wBY462mzKwV8BxwubuXxO4LWwo9kfev6x7uPtLd89w9r2PHjonMhoiI1KWiHFbNUOAoIiKNWHFx/dJnPASfXAk5p0H/RyAtPXF5i5iZZRIEjYXu/nyYvDDsZkr4vChMnw90jTm9S5hWV3qXGtLruoeIiCSj0jlQsQ7a7BF1ThQ4iohIgtTWxbGm9CUToOgi2OkYOOgJSGu8IynCGU4fBqa6+x0xu14CKmdGHQK8GJM+OJxdtT+wMuxu+hpwlJm1DyfFOQp4LdxXYmb9w3sNrnatmu4hIiLJaOW04DniGVVBgaOIiCRKQQFkZ2+alp0dpMdatwzePx1a7Aw/KYT0rIbLYzQOBgYBh5vZ5PAxALgF+LmZfQMcGW4DjANmAjOAB4GLANx9GXATMDF8DA/TCI95KDznW+CVML22e4iISDJaFS7FkQRdVRvvT7oiIhKtyglwhg0Luqfm5ARBY+zEOF4BHw6Gtd/Bke9Bs+2iyWsDcvf3qH19kSNqON6Bi2u51ihgVA3pRcDeNaQvrekeIiKSpEqmQ1Z7aLZ91DlR4CgiIgk0cGDdM6hOvR2++w/0+wdsf0DD5UtERCQVlEwPuqkmwQzj6qoqIiLRWPS/YAbVnNNgtxob1ERERJq2kmnQNvqJcSDJAkczG2Vmi8zsy5i07cxsvJl9Ez63D9PNzO42sxlm9rmZ9Y05Z0h4/DdmNqSme4mISITWLoT3zwwWND7woaT4JVVERCSpbCiBH76veWKcwkLIzYW0tOC5sDDh2UmqwBF4FDimWtpQ4A137wm8EW4DHAv0DB/5wP0QBJrADcCBwAHADZXBpoiIJAF3+PhcWL8cDnkGMttEnSMREZHkU1LLxDiFhZCfD3PmBHXqnDnBdoKDx6QKHN39f8CyasknAKPD16OBE2PSH/PAR0C7cE2qo4Hx7r7M3ZcD49k8GBURkajMLoTvxkHvm6F976hzIyIikpxqCxyHDYPS0k3TSkuD9ARKqsCxFjuGa1IBfA/sGL7uDMyNOW5emFZb+mbMLN/MisysaPHixfHNtYiIbO6HRTDpMujQH3a7NOrciIiIJK+S6WDp0GqXTdOLi2s+vrb0OEmFwLFKOCW5x/F6I909z93zOnbsGK/LiohIbYp+B2Wrof/DkJYedW5ERESSV8k0aNkd0pttmp6TU/PxtaXHSSoEjgvDLqiEz4vC9PlA15jjuoRptaWLiEiU5v4LisfC3n+Etr2izo2IiEhyWzV9826qEKyJnJ29aVp2dpCeQKkQOL4EVM6MOgR4MSZ9cDi7an9gZdil9TXgKDNrH06Kc1SYJiIiiVTXDG/rV0DRRdBuX+h1bVQ5FBERSQ1eAau+qTlwHDgQRo6Ebt2CWcm7dQu261o3OQ4yEnr1ejKzMcBhwPZmNo9gdtRbgLFmdh4wBzg9PHwcMACYAZQC5wC4+zIzuwmYGB433N2rT7gjIiLxVDnDW+Vg/coZ3iCoyD69KhjfeOi/IS0zunyKiIikgjXFUP4DtKllDceBAxMeKFaXVIGju59Vy64jajjWgRpXjHb3UcCoOGZNRETqUtcMb0d0gm8fDloat+sXTf5ERERSSW0zqkYoFbqqiohIsqttJrf5c6DoYmi1K+x9Q8PmSUREJFWVTAueWytwFBGRxqS2mdzOaB/8atrvLsho0bB5EhERSVWrpkNmW2i+Q9Q5qaLAUUREtl1NM7x1agHHroWdB0DnX0STLxERkVRUEs6oahZ1TqoocBQRkW1X0wxvf8uD9HLoe1fUuRMREUktJdNrnxgnIgocRUQkPgYOhNmzoaICip4Cexf2uBLa9Iw6ZyIiIqljwypYOz+pJsYBBY4iIhJvXgFFv4MWO8Few6LOjYiISGpZ9XXwnEQT40CSLcchIiKNwMxHYVkRHPQ4ZLaOOjciIiKpJQmX4gC1OIqISDytXwGTh8L2P4Hchl2YWEREpFEomQ6WBq13jTonm1CLo4iIxM9XBbBuCfzs1aSaCU5ERCRllEyHlrmQ3jzqnGxCLY4iIlJ/hYWQmwtpacFzYSGsng3T74YeQ2C7vhFnUEREJEWVTEu68Y2gFkcREamvwkLIz4fS0mB7zpxgm/0gIw32GR5p9kRERFKWVwST4+z4s6hzshm1OIqISP0MG7YxaKzUsRTsfdj9cmjZNZp8iYiIpLo1s6F8LbTdM+qcbEaBo4iI1E9x8eZpvwJWAb2GNnRuREREGo/lnwfP7XpHm48aKHAUEZH6ycnZdHsfYG/g7faQ9f/s3XecVNX5x/HPsxWWKkUUcRcL0dhRVCyJPSoaNdEYFZWoCYkaY0kzEsVGYknsRiWKYlxbLJEYEuMPTYwNRUWxAiK7gEhf2vad5/fHvbM7uyzb2GHmzn7fr9e8ZubcO/eeMzs7zzz33nNOn1TUSEREJDOUfQAY9N2toay5cQVSQImjiIi0z4QJUFAQPDbgdGCpwfG3prJWIiIi0Vf2fjANR06P4Hl8XIGSEnBvGFcgBcmjEkcREWmf0aNh4kQoKoJvAEXAwAth9JhU10xERCTaVn3Q+DLV5sYVKC8PyjczJY4iItJ+o0fD3E/g0iHQb184445U10hERCTaatbBus+h7x4NZc2NK9BSeRIpcRQRkY6ZfSeUL4ThN4NZqmsjIiISbas/BBy2SDjj2HRcgdbKk0iJo4iItF/1avj4Bhg8CgYdkuraiIiIRN+q94P7xDOOieMKxBUUBOWbmRJHERFpv0//CNWrYI/rU10TERGRzFD2AeT2hh5FDWWJ4wqYBfcTJwblm1nOZt+jiIhEW+VS+PQWKDwV+g1PdW1EREQyQ9n7wdnGpt0/Ro9OSaLYlM44iohIy5rOH/X0GKirhD2uTXXNREREMoN7OKLqHq2vmyI64ygiIhsXnz8qPhT4uhKoLYGcQ6D3Tqmtm4iISKZYPx9q1zYeGCfN6IyjiIhsXNP5o74T3t80NyXVyRRmNsnMlprZhwllV5vZIjObGd5GJSz7jZnNNbPPzOzohPJjwrK5ZnZ5Qvl2ZjY9LH/CzPLC8vzw+dxw+dDN02IREWlR2QfBfRqfcYxM4mhml5rZR2b2oZk9ZmbdFBhFRJIscZ6orYBvAv8HzPoyRRXKGA8BxzRTfqu77xXepgKY2S7AacCu4Wv+ZGbZZpYN3A0cC+wCnB6uC3BjuK0dgVXAeWH5ecCqsPzWcD0REUm1VR8ABn12S3VNNioSiaOZbQP8DBjh7rsB2QRBVIFRRCSZEueJOhmoAaaQkvmjMom7vwKsbOPqJwKPu3uVu38BzAX2C29z3X2eu1cDjwMnmpkBhwNPha+fDJyUsK3J4eOngCPC9UVEJJXK3oeeO0Buz1TXZKMikTiGcoDuZpYDFACLUWAUEUmu+PxRhcCBwL+A2tTMH9VF/NTMPggvZd0iLNsGWJCwzsKwbGPl/YEyd69tUt5oW+Hy1eH6IiKSSmUfpHX/RohI4ujui4A/AKUECeNq4B02MTCa2Vgzm2FmM5YtW5bcRoiIRFF8/qizusN64INtUzZ/VBdwD7ADsBdBrPtjqiqi+CgishnVroe1c9O6fyNEJHEMj7qeCGwHDAZ60HzfkHZx94nuPsLdRwwcOHBTNycikpmOHga7VMAB18GnpUoak8Tdl7h7nbvHgD8TXIoKsAjYNmHVIWHZxspXAH3DK3QSyxttK1zeJ1y/aV0UH0VENpeyDwHXGcdOciTwhbsvc/ca4BngIDYxMIqISBvMugry+8NOF6e6JhnNzLZOePodID7i6hTgtHDgt+2AYcBbwNvAsHCguDyCvv9T3N2Bl4FTwtePAZ5L2NaY8PEpwEvh+iIikipl7wf3aX7GMSrzOJYCI82sAKgAjgBm0BAYH6f5wPgGCowiIh237DVY/ALsdRPk9kp1bTKGmT0GHAoMMLOFwHjgUDPbC3BgPvBjAHf/yMyeBD4GaoEL3b0u3M5PgRcIBo2b5O4fhbv4NfC4mV0PvAc8EJY/APzFzOYSDM5zWpKbKiIirVn1AeT0gh5DU12TFllU8mlq5U8AACAASURBVCkzuwb4PkHQfA/4IUFfxseBfmHZme5eZWbdgL8AwwkDo7vPa2n7I0aM8BkzZiSxBSIiETTtcFj9MZwwD3IKUl2bTmFm77j7iFTXIyoUH0VEkuzFbwAOR70KxcXBHMqlpcEI5hMmbNYuIi3FyKicccTdxxMckU00j4Y+IInrVgLf2xz1EhHJWEteDm5735YxSaOIiEhacQ9GVB16ZpA0jh0L5eXBspKS4DmkxfgCUenjKCIim0lxMQwd6rz6pytZvHobHnvnx6mukoiISGZaXwI1a4L+jePGNSSNceXlQXkaiMwZRxERSb74wc5v7PgCB+/0GudP+hMPv9GNGGlxsFNERCSzlH0Q3G+xZ3B5anM2Vr6Z6YyjiIjUCw52OtedciXzlxXxwH/OS6eDnSIiIpll1fuAQZ/dgj6NzdlY+WamxFFEROqVlsLxw59n3x1mcN2zV1JTl1dfLiIiIp2s7APouQPk9gwGwiloMqZAQUFQngaUOIqISL3CQufaU65i7lc78PCrZyeUp7BSIiIimarsA9ginL9x9GiYOBGKisAsuJ84MW36iiS9j6OZZQE93X1NsvclIiKb5uEJzzLcZnL2PZOprcsF0upgZ1pTvBMRkXapWQNr5wQjqsaNHp02iWJTSTnjaGaPmllvM+sBfAh8bGa/TMa+RESkk3iMb/Ydz2rfidcWnZGOBzvTjuKdiIh02Iq3AYcB+6e6Jm2SrEtVdwmPuJ4E/BPYDjgrSfsSEZHOUPoUrP6QPgeN5/N5OcRiMH++ksZWKN6JiEjHrJge3PffYFr6tJSsxDHXzHIJAukUd68BPEn7EhGRDgrmbISc7DrmPHs1Zb4LFJ6a6mpFieKdiIh0zPI3offOkNc31TVpk2QljvcB84EewCtmVgSoz4eISBqJz9lYUgKnjnyCYVt+wk/vu5rix7JTXbUoUbwTEZH2cw/OOPaPxmWqkKTE0d3vcPdt3H2UB0qAw5KxLxER6ZhgzkbIzqpl/Heu4YPS3Xn01ZM1Z2M7KN6JiEiHrC+ByqWR6d8IyRscZ5CZPWBm/wyf7wKMSca+RESkY+JzM44+qJidBs9m/NPX4J6lORvbQfFOREQ6ZPmbwX3/kamtRzsk61LVh4AXgMHh89nAJUnal4iIdEBhIeRk13DVd67l3S+G87cZJ9WXS5s9hOKdiIi014rpkN0d+u6e6pq0WbISxwHu/iQQA3D3WqAuSfsSEZEOmDABfnTEZHYYNI/xT18DmOZsbD/FOxERab8V06HfPpCVk+qatFmyarrezPoTjixnZiOB1Unal4iIdMDo06o4ieuYuWA//jHzeIqKgqRR02+0i+KdiIi0T101rHwXdroo1TVpl2QljpcBU4AdzOw1YCBwSpL2JSIiHfH5A/SwUvY6+8/Efm2prk1UKd6JiEj7lL0PsSr4uBq+MzQYdKCwMO2P3iYlcXT3d83sEGAnwIDPwrmtREQkHdRWwEcTYODBsNVRqa5NZCneiYhIuy2fHtz/eiIsqgwel5QEc2RB2iaPyRpV9XtAd3f/iGBS5CfMbO9k7EtERDpg7n1Q8SXscR2YzjZ2lOKdiIi024o3YXV2Q9IYV15OOs+JlazBca5097VmdjBwBPAAcE+S9iUiIu1Rux4+/j0MOhwGHZrq2kSd4p2IiLTP8ukweyPjqKXxnFjJShzj78RxwJ/d/R9AXpL2JSIibVBcDEOHwuXfvQsql/LCV9elukqZQPFORETarnI5rJsLK/o2vzyN58RKVuK4yMzuA74PTDWz/CTuS0REWlFcHHSdWLl0Db887iamzjyW7449kOLiVNcs8hTvRESk7Va8FdwffSEUFDReluZzYiUruJ1KMCHy0e5eBvQDfpmkfYmISCvGjQu6Tlx89O3077WSq566Nt27UkSF4p2IiLTdiulgWXDq5TBxIhQVBWMNFBUFz9N0YBxI3qiq5cAzZralmcXPt36ajH2JiEjrSkuhb8Eqfj7qj/xtxom888WI+nLpOMU7ERFpl+VvQp/dILdnkCSmcaLYVLJGVT3BzOYAXwD/De//uYnb7GtmT5nZp2b2iZkdYGb9zOxFM5sT3m8RrmtmdoeZzTWzDzTCnYh0dYWF8Ivj/kDfHqu56qlrG5VLxyUj3omISIbyWHCp6oCRqa5JhyTrUtXrgJHAbHffDjgSeHMTt3k78C933xnYE/gEuByY5u7DgGnhc4BjgWHhbSwa4U5Eurg/TljCJcfexqOvn86sBXsAad+VIiqSEe9ERCQTrZ0DNWXQf/9U16RDkpU41rj7CiDLzLLc/WVgREc3ZmZ9gG8SDHOOu1eHfUlOBCaHq00mmEOLsPxhD7wJ9DWzrTu6fxGRqDt5p9/RPa+KiW9cE5WuFFHRqfFOREQy2PLwuGJEE8ek9HEEysysJ/AKUGxmS4H1m7C97YBlwINmtifwDnAxMMjdF4frfAUMCh9vAyxIeP3CsGxxQhlmNpbgjCSFul5LRDLV+lKYey9ZO57Df94ZluraZJrOjnciIpKpVkyHnF7Qe+dU16RDOvWMo5ntaGYHEZzxKwcuBf4FrAAu2oRN5wB7A/e4+3CCoHx54gru7oC3Z6PuPtHdR7j7iIEDB25C9URE0tiHYZ/G3a5KbT0ySBLjnYiIZKrl06H/fpCVneqadEhnX6p6G7DG3de7e8zda919MvAscPUmbHchsNDdp4fPnyJIJJfEL0EN75eGyxcB2ya8fkhYJiLStayZDfMegmHnQ49tW11d2ixZ8U5ERDJRdRmUzYSBB6a6Jh3W2YnjIHef1bQwLBva0Y26+1fAAjPbKSw6AvgYmAKMCcvGAM+Fj6cAZ4ejq44EVidc0ioi0nXMGg/Z3WCX36S6JpkmKfFOREQy1NJXglFVBx2R6pp0WGf3cezbwrLum7jtiwj6j+QB84BzCBLfJ83sPKCEYCJmgKnAKGAuwSVE52zivkVEomfV+1DyOOw6DroPan19aY9kxjsREck0S16C7O6RnYoDOj9xnGFmP3L3PycWmtkPCQa06TB3n0nzI9VtkLaH/R0v3JT9iYhE3vu/hdy+8PVfpLommShp8U5ERDLQV9Ng4MGQnZ/qmnRYZyeOlwDPmtloGgLnCCAP+E4n70tERDZm6avw5fOw5+8gr6WTY9JBinciItI2FUtg9YfwxEI4MgsKC4OJlCM2J1anJo7uvgQ40MwOA3YLi//h7i915n5ERKQF7vD+5dB9a9jp4lTXJiMp3omISJs9cz0Y8FpZMAdESQmMHRssi1Dy2NmD4wDg7i+7+53hTUFURGRzWvR3WPYa7H415BSkujYZraPxzswmmdlSM/swoayfmb1oZnPC+y3CcjOzO8xsrpl9YGZ7J7xmTLj+HDMbk1C+j5nNCl9zh5lZS/sQEZEkevuhYDLB+Qll5eUwblxq6tNBSUkcRUQkRWK18P5vWONfY4dvnUtWFgwdCsXFqa6YNPEQcEyTssuBae4+DJhGw3zFxwLDwttY4B4IkkBgPLA/sB8wPiERvAf4UcLrjmllHyIikixF6+BTINakvLQ0FbXpMCWOIiKZ5IuHYfXH/OTe3zHvixzcG66IUfKYPtz9FWBlk+ITgcnh48nASQnlD3vgTaBvOHfx0cCL7r7S3VcBLwLHhMt6u/ub4WBxDzfZVnP7EBGRZFhfAoOAj5pZVli4uWuzSZQ4iohkitoKmDWemQv247FXv9toUQSviOmKBiXMOfwVwU8NgG2ABQnrLQzLWipf2Ex5S/toxMzGmtkMM5uxbNmyDjZHRET4KuzF8Hm3xuUFBcEAORGixFFEJFPMvgvKF3LJ5JsIeuE3FrErYrq08Eyhp2of7j7R3Ue4+4iBAwcmsxoiIpltyUvQbUu4+s9QVARmwf3EiZEaGAc6fzoOERFJhepV8NHvYPAo5pcf0uwqEbsipitaYmZbu/vi8HLTpWH5ImDbhPWGhGWLgEOblP8nLB/SzPot7UNERDqbOyyZBoMOh4POhNFnprpGm0RnHEVEIq64GO696AZiVas55vLfM2pUcAVMogheEdMVTQHiI6OOAZ5LKD87HF11JLA6vNz0BeBbZrZFOCjOt4AXwmVrzGxkOJrq2U221dw+RESks635DCoWB4ljBtAZRxGRCCsuhmsvL2XmdXdQ/PpoXpi+BwWzYMwYmDo1uDw1ovMMZzQze4zgbOEAM1tIMDrqDcCTZnYeUAKcGq4+FRgFzAXKgXMA3H2lmV0HvB2ud627xwfcuYBg5NbuwD/DGy3sQ0REOtuSsH/jVkekth6dRImjiEiEjRsH13/7iuDxk8EpxfLyIGmcPz+FFZMWufvpG1m0wa+LsC/ihRvZziRgUjPlM4Ddmilf0dw+REQkCZZMgx5F0GO7VNekU+hSVRGRCBuU8xZnHlzMLVMvY8GKhk6MGghHREQkhTwGS14OLlO1DQesiyIljiIiUeXOnef+nCWrt+SGvzeex10D4YiIiKTQqveDgesGZc5FHrpUVUQkqhY+y35DX+WnD9/Huspe9cUaCEdERCTFlkwL7gcdltp6dCKdcRQRiaK6anjvV9BnVw4869yoTw0lIiKSWb56CXp/HQoGp7omnUZnHEVEomjO3bDuczj0n5wxOIczlCiKiIikh9r1sPRl2GFsqmvSqXTGUUQkaqpWwofXwdZHw+BjUl0bERERSfTEOKirhDF3wNChwdxZGUCJo4hI1Hx4LdSshuF/SHVNREREJFFxMbx5F6wFPgVKSmDs2IxIHpU4iohEyepPYPbdsMMPoe8G0/SJiIhIKl15BexeB+8BsbCsvDyYeDnilDiKiESFO7zzM8jpCXtcn+raiIiISFMFpdATmNGkPAMmWFbiKCISFQufha/+D/a4FroNTHVtREREpKlDe0EVMKtJeQZMsKzEUUQkTRUXB33qs7Jgpx0rWPfKZazy3dnh2PPJysqo/vYiIiLR5w4H5MHH2VCdUJ4hEywrcRQRSUPFxUFf+pKSIA6dtudN9LQSvnfjncz7Igf3jOpvLyIiEn2r3gNbAXudRyZOsKzEUUQkDY0bF/SlBygaMJ/Lv30Dj7/xfabNOqTRehnS315ERCT6Fv4NLAtOngDz50MsFtxnQNIIEUsczSzbzN4zs+fD59uZ2XQzm2tmT5hZXlieHz6fGy4fmsp6i4i0V2If+j+O/jmxWBa/fPTmVtcVERGRFFn4Nxj4Deg2INU1SYpIJY7AxcAnCc9vBG519x2BVcB5Yfl5wKqw/NZwPRGRyIj3oT9i1//j5P2e4XdTrmDhym1bXFdERERSZO3nUDYLhpyU6pokTWQSRzMbAhwH3B8+N+Bw4KlwlclA/C91YviccPkR4foiImkpcSCcoUNh1Cjo27uKO8dcxOdLtuePU39Obi7k5TV+XYb0txcREYm2hc8F90NOTG09kigyiSNwG/ArGqbS7A+UuXtt+HwhsE34eBtgAUC4fHW4fiNmNtbMZpjZjGXLliWz7iIiG9V0IJySEpg8GSZffjNf3+ZTLpp8F1sN7saDD8KkSRnZ315ERCTaFj4LffeEntuluiZJk5PqCrSFmR0PLHX3d8zs0M7arrtPBCYCjBgxwjtruyIi7ZE4EE7c4F5zOHrw9VB4KlNnHttomRJFERGRNFK5FJa9BrtdleqaJFUkEkfgIOAEMxsFdAN6A7cDfc0sJzyrOARYFK6/CNgWWGhmOUAfYMXmr7aISOs2HNzGuefc86msySd/n9tSUSURERFpq0V/Bxy2/U6qa5JUkbhU1d1/4+5D3H0ocBrwkruPBl4GTglXGwOEFxczJXxOuPwld9cZRRFJS00Htxl9UDFH7jaNm1+8AbpvnZpKiYiISNsseAZ6DIW+e6S6JkkVicSxBb8GLjOzuQR9GB8Iyx8A+ofllwGXp6h+IiKtmjAhGOQGoF/PFdx65qW8NW9/vn7Cj1NbMREREWlZ8d2wYCo8Ph+22y4YuCBDReVS1Xru/h/gP+HjecB+zaxTCXxvs1ZMRKSD4n0Wx42DK7/1a7bosYq3ek1k9OioH9sTERHJYMXF8NSlQdbxX2BxSTDaHWTkgAT6VSIikgZGj4b5b/2P8w59gJzdLuO40Zl9uYuIiEjkjbsCDqyB2cDisKy8PDgSnIGUOIqIpIPaCnjrR9CjCHYfn+raiIiISGtyS4NJAP/TpHzDUe8yghJHEZEkKi6GoUMhKyu4Ly5uvoxZV8Gaz2C/P0NOj5TWWURERNrguJ5QCUxvUt501LsMEbk+jiIiUVFcHHR1iM/RWFIC55wDZlBd3VB2/w1vcMblf8SGjYWtj0pdhUVERKRtasth31p4Ixsq6xrKCwqCUe8ykM44iogkybhxDUljXE1NQ9II0C23gnvH/IBFZdvC8Js3bwVFRESkYxY8A1YJB1wORUXBUeGiIpg4MSMHxgEljiIiSdOWLg7Xfe9Kdho8m3PufQByeye/UiIiIrLp5k2CntvDGdfB/PkQiwX3GZo0ghJHEZGkaa2LwwHDXueyY2/h3mk/Zs7aIzdPpURERGTTrPsClrwM24f9T7oIJY4iIkkyYULQ1SFRbi7k5QWXqD449hxKVxQy/tmbM7U7hIiISOaZ9xBgsN2YVNdks9LgOCIiSRK/WmXcuOCy1cLChv7yFa+NY6fBsznjgf/jljt7ZfKVLSIiIpnDY0HiuNVR0GPbVNdms1LiKCKSRKNHN9Pd4csXwG6FYRfy6LQjUlIvERERaZ/iYpg66SWKzyvlokk3MnJxRndp3IAuVRUR2Zwql8KbY6DPrhpFVUREJCLiU2ydsOufWbW+L3/+10mMHRvOxdxFKHEUEdlc3OHNc6C6DA56DHK6p7pGIiIi0gbjxsGgHvM4Zb+nuP/lH1JV043y8qC8q1DiKCKyucy+E76cCnv/EfrunuraSJoys/lmNsvMZprZjLCsn5m9aGZzwvstwnIzszvMbK6ZfWBmeydsZ0y4/hwzG5NQvk+4/bnha7vOkIAiIh1UWgo/P+6P1NblcOs/L21U3lUocRQR2RxWvQ/v/RIGHw/DLkh1bST9Hebue7n7iPD55cA0dx8GTAufAxwLDAtvY4F7IEg0gfHA/sB+wPh4shmu86OE1x2T/OaIiETb8K8v5dxDJvGXV89icdng+vLWpt7KJEocRUSSrbYcXjsd8vvDyEldas4n6TQnApPDx5OBkxLKH/bAm0BfM9saOBp40d1Xuvsq4EXgmHBZb3d/090deDhhWyIishGTr7iD/Jwqbv7HL+vLCgroUtNpKXEUEUm2d34Gaz6BAx6GbgNTXRtJfw7828zeMbOxYdkgd18cPv4KGBQ+3gZYkPDahWFZS+ULmylvxMzGmtkMM5uxbNmyTW2PiEi01axlt7y7WWjfoSpvJ8ygqAgmTuxao6pqOg4RkWSaez98/gDsegVsdWSqayPRcLC7LzKzLYEXzezTxIXu7mbmyayAu08EJgKMGDEiqfsSEUl7cydCTRmFR/+a+V0oUWxKZxxFRJJlxdsw40LY6luw+7Wpro1EhLsvCu+XAs8S9FFcEl5mSni/NFx9EZA4A/WQsKyl8iHNlIuISILiYhg6FLrlVfHVf27hKz8MBuyX6mqllBJHEZFkqFwG/zsZum8NBz0KWdmprpFEgJn1MLNe8cfAt4APgSlAfGTUMcBz4eMpwNnh6KojgdXhJa0vAN8ysy3CQXG+BbwQLltjZiPD0VTPTtiWiIjQMGdjSQmccWAxW/X5krG3Xd6l5mxsjhJHEZFOEj86mZNdx6s3nU7d+qXwjWeCQXFE2mYQ8KqZvQ+8BfzD3f8F3AAcZWZzgCPD5wBTgXnAXODPwAUA7r4SuA54O7xdG5YRrnN/+JrPgX9uhnaJiETGuHFQXg5mMX51/E28+8Vw/j7jqC41Z2Nz1MdRRKQTxI9OlpfD777/Ww7ecRo/eXAS32DvLtVxXjaNu88D9mymfAVwRDPlDly4kW1NAiY1Uz4D2G2TKysikqHiczOeuM9z7Dz4M0678zHAutScjc3RGUcRkU4QPzr53X2f5jcn3MC9037Mff93Tpc/OikiIhI1hYWQnVXLdadcydyvduCpt06pL+/KdMZRRKQTlJbCvtu/xV/OP4vXZx/AxQ/fXl8uIiIi0TFhAsx49D522/YjTrrlWepiOV1uzsbmROKMo5lta2Yvm9nHZvaRmV0clvczsxfNbE54v0VYbmZ2h5nNNbMPzGzv1LZARDLdgXt+wd9/8W0Wl23Nibc8R3VtPqCjkyIiIlEz+pQV3HDGlbz2+eFMeffELjlnY3MikTgCtcDP3X0XYCRwoZntAlwOTHP3YcC08DnAscCw8DYWuGfzV1lEuozqMv7xi+PIzanhuJv/wfK1AwF0dFJERCSKZl1NftZqDrroNmIxY/58JY0QkcTR3Re7+7vh47XAJ8A2wInA5HC1ycBJ4eMTgYc98CbQNz7/lYhIZ4iPoJqfW81rN55MT+byTsEzVObtjBk6OikiIhJFZR/BnHtgx59A391TXZu0EonEMZGZDQWGA9OBQeGcVABfEQxjDkFSuSDhZQvDsqbbGmtmM8xsxrJly5JWZxHJLA3zOzn3nvtjDtrhJX7y4P0s5VDmz4dYDB2dFBERiYj4weCsLOeV2y+lKtYLdr8m1dVKO5FKHM2sJ/A0cIm7r0lcFg5J7u3ZnrtPdPcR7j5i4MCBnVhTEclk8RFUrz3lKs455CGufno89087WyOoioiIREzDwWA4fvjf+eawFxn3+DUUPz0g1VVLO5FJHM0slyBpLHb3Z8LiJfFLUMP7pWH5ImDbhJcPCctERDZZaSn86vgbufI713P/y+dxzTPj68tFREQkOuIHg/Nyqrhl9GV8vOjr3P7P83UwuBmRSBzNzIAHgE/c/ZaERVOAMeHjMcBzCeVnh6OrjgRWJ1zSKiKySX576l3cePrlPPr66fz4gfsAAzSCqoiISNTED/r+8vib2XGrz7n0L7dSW5erg8HNiMo8jgcBZwGzzGxmWHYFcAPwpJmdB5QAp4bLpgKjgLlAOXDO5q2uiGSszx/k2hMu4u/vnciYeycT82xAI6iKiIhEUWEhDMqZztXfvZrH3/g+/551dH25NBaJxNHdXyV+SH9DRzSzvgMXJrVSItL1lDwBb/0QtvoW6/Z6gm2GBEckCwuDpFGD4YiIiETLjRPWsO+yM1i0aht+MuleQAeDNyYSiaOISMqVPg2vnwkDDoJvPsvpOfmcrkRRREQk0r6/3U+JMZ/v3fcKayr6UlSkg8EbE4k+jiIiKfX5JHjtVOi/Hxz6POQUpLpGIiIi0gENU2/AxScWw/y/kLXHVTz9ykGaTqsVShxFRFryyS0w/TwYdCQc/m/I7Z3qGomIiEgHJE69MXTAPK474Xxen3MQj36gIVTbQpeqiog0xx1mjYcPr4NtT4YDiyE7P9W1EhERkQ6KT72Rk13Doz89g1gsi9PvKsZ65HCGzjK2SomjiEhTHoN3LoHZd8L258J+90GWvi5FRESiLJhiw7ntrEsYueN0Tr3jCUqXF2ErUl2zaNAvIRGRRDXr4I2zYOHfYOfLYPgfwDY2qLOIiIhERWEhnDX8ei486k/c/Pwv+Ov0U+vLpXVKHEVE4taXwH9PgNUfwt63wk4XK2kUERHJEE9MuI/97Somv3I2v378RkBTb7SHBscREQFY+ir8a98geTxkKux8iZJGERGRCEscQfUnxz3NvlzAIj+O6/59P5BFURFMnKhRVNtKiaOIyOcPwkuHQ15fplRPZ+iBR5OVFQSb4uLGgSdeJiIiIukrcQTVQ77+MrefegZvfb4//+NJ5s7L1dQbHaBLVUWk66pdz9wnfsaONokXZx3JTx55koVLt6C6OlhcUgLnnBOceEwsGzs2eKxgIyIikp7iI6juv+ObPHfZicxdsiOjbnqe3gMKOE3xu0N0xlFEuqaV77Lmib3Z3h9kwt+u4Nib/sm8hQ1JY1xNDRuUlZcHAUlERETSU2kpnLzfU7w87jCWrRnI0Te+wKr1/cKRVaUjlDiKSNfiMfjkFvj3SNavWc8Rv5/Gb/86gbpY+y7AUOARERFJH427lTjjv3cTT138Pd6dvzcjx7/JopVDAI2guil0qaqIZKTi4uCsYGlpECQmTIACFrDF7LEcutO/+PfHJ3L67Q+wcl3/Dm1fgUdERCQ9xPszlpdDTnYN4466gB8ddj9PTv8+Z9/zEFU13QCNoLqpdMZRRDJOYod4d1i4oJaZj9/CUVVfZ9+iVzh/0p84esKzrFrfetKYmwt5eY3LFHhERETSR7w/Y7+eK5j6y1H86LD7uf5v47jw0UfZanA3zNAIqp1AZxxFJOPEAwjAiO3fZuJ5Yxk+dCbPv3ccP33oLkqWDwWCpNIsuI/LzYXevWHlyoYzlfFtJp69VOARERFJD6Wl8N19n+ZP51zAFj1W8YP7HmTyKz/ADJYtS3XtMocSRxHJOKWlMKDXMsZ/9xouOPJPLC7bmpNve4pn3v4u0HhuRvfgKGRrSaESRRERkTRUuZS///pCjtv9Kd75Ym+O+v2LzFqwB6BuJZ1NiaOIREpzfRehoezrO67l92fcwgWH/YGC/HLufvFCxv11Amsreje7vaKiYB4nERERiY7iYufNJ55g/HE/5civr+XKpyZww5RfUluXC6hbSTIocRSRyEjs/A6N51kkVsXPjr6HcSdOYGDv5Tz99imMe+I6Plu8MxBcgpo4HyMoqIiIiESOOy89+gLDvria0adNZ/rc/Th34iTmLN2VPn0bdzXR1UKdS4mjiERGYt/FuILcMn502J/52dF3sG3/hbw460iuePJ3fLF6X3r2DJJF9VUUERGJruBqI2fnPv/md6dfzeGFb1LSu5Cx99/HpP+eWz+lVs+esHx5iiubwZQ4ikjaanpZaklJw7Ltt/yci4+5nXMPmUTPbut56aPDOOe+B5n20ZFA5RTLmAAAIABJREFUkDA2FzyUKIqIiKSvprH/O8evo/yzp3jsnPs4YNiblCwPEsaHXvkBNXWNhz3XHMvJpcRRRNJSc5el5udWcdxezzPmG5M5fvjz1MZyeOz107n1X5fyfslejV6vDvEiIiLprWmSOGoUTJ4MFRUxDv36f/jBNx/i5L2fpseB5cxePGyjCWOcYn9yKXEUkbTUcFmqc9DXXuOsg//CqSOfZIseZXy5amt+N+UK7n7xQlas3zro45hAfRdFRERSp7WB7BKTxPgB4nUrlrPyvWncfsaLHL3HC2zbfyGry3vzyGtnMvl/Y3hjzgE0HRk9kWJ/8ilxFJG0kBhkdtphPbv3e4lfHz6V4/b6B4UDFrC+soBnZnyXv7x6FnPXHsH8kmwKC+HBu4LXq++iiIhI52lL8teWhDBxILv4AHWlpTGm/W0ux+/xHvts9w6H7/ISew99l6wsp2x9H176+HB++ejNPPfOiVTWdG+2fv37B30aFfs3I3fPyBtwDPAZMBe4vLX199lnHxcR90cecS8qcjcL7h95JPllP72gyr+565t+6bF/9Km/OsYrHsx3L8bXPtDDn7nkJD/r4MneI3+tQ7C+yKYAZngaxKlU3toTIzszPrbl++D88zf/d1C6l3X196Srtz8V78n557sXFLgHsx0Ht9xc97y81svMGh736r7a9yic6SeNeMYvG/UHv+sHF/grVx7sa+7v6V6MezFeNTnXX7nyYP/tSdf6/ju+4dlZNY2213SbENTtkUda/86R9mspRlqwPLOYWTYwGzgKWAi8DZzu7h9v7DUjRozwGTNmbPK+O3p0ZnOUjRoFU6emvh7pVKb3pHFZv36wdm3jKSuam8ZiU8q6d6th2FZz2GnQh+yz3TscOOx19t3+bbrlVQEwe/Ew/jHzOP7x3nG8OvsbVNXk17+2oAAmTtQRRdk0ZvaOu49IdT1Spb0xsjPjY2K/ZWj+O6Kpzv4OimJZV39Punr7k/eeOFkWIz8/RnZWjNqaGNlZdeRk15KbXUt2Vi052bXkZVfTLa+SbrkNtx756+nVfS29u6+pv/XvuYItey+tvw3qs4S+PVY3qmfZ+j58tGhX3ps/nHfn781784fz8aJdqK5tiPVmQXoYV1AAY8Zs+HtNvwWSo6UYmamJ4wHA1e5+dPj8NwDu/vuNvaYzAmNrQdEsxlZ9vmKHrUoYOnA+2/QtYWDvZfTuvoYteqymT8FqenVbTX5OFdlZdeE/bR1ZVkddLJuaulxqY7nU1OVSXZtLRXV3yqsKqKwtoLy6gHUVBayr7Mm6qp6UV/diXVUvytb1ZG1lL9ZW9Gp0v66yJ3V0w8zS4guwo2VmMXoVVNIjv5wcK6cgr5yC/HJ6F5TTI7+c3KxyuudVUJBXTs/uFRTkVZCbXdHoy69bbiXd8irJy6mme14VeTnV5GRVh/e15OXUkBP/As2qJctiZGXFyDLHLIYR/A85FtxiwX1dLJu6WA51sWxq67LDv1seNbE8autyqazOo6o2n8qablTXdqOypjvrq7rV/12r6gqoqC5gTXkB5VUFrK/qQVVdDypqCihb1yP4W1f2pDrWg5jnJC0YdUT3vHIK+5dSOKCUogElFA0oYcdBc9ltyId8bevZ5OXUAFBVk8e78/fm9TkH8vrsA3ljzgEsLhvcaFtFRQoU0rmUOLYvRnZW4jh0KKxZvpIffPMhCvLL6Z5bQUF+8L3dPa8i/LFaQ074YzUnuzaoL41/pziGuxHzrPr7WCyLOs8mFssi5lnUxbLr7xMfx2INy+pvsSwcq793D29NHjd6D8M6mXlww5t9nGWxhnucrKyG+yyL1ccTC3/AN1se3idur2l5vCyxTs29d82JtxNott1N3+uN3Td6L8PHTZc39zjxvtFjGr/3G/tbNCfxfUl8nvj3aPQ44X0PfneF91kNZRvcrJmyVm6J22q0v8S/e5P6bPA5asPfur7MvNF7kpWVvN/8dbEsVq7rx5LVg1i6ZkuWrtmSZWsGUrqikC+Wbce8pdvzxdLtKCvfovHfSkli2mkpRmZqH8dtgAUJzxcC+yd7p4lzzOXlVLFn4fuM2H4G+27/NiO2n8HXtppNfm7jX+jrKwtYXdGH1eV9WFPRm9UVfais7hYkG2HSURfLDhPJmuCWU0NedjXd8yro33NFfbLUI389PfLXb7CPjamty2ZdZc/6RLK8OkhOyquCRLS8qoDKmm71t6qafKpq86mpy6WmNkhga+pyqa3LqQ+6MW8IvIlfcPEvvPofBtlBEpabU0N+TpCsxe/jiVxiYhdP/rrnVTR6XJBf0aG/VXVtbtCu6rBttflU1eRTXRskc9W1eZRXFdS3rzaWQ21dw9+jUXvdNgjcWVkNwSEnq7bh7xf/2+Wup2/Byob2JrSze14F2VmxdrWnsjqf9VU9mr2VVxfUJ6MV1d2pqOle/7dMbHPTH1cxz6o/8phtdfV/u/hnrSCvvP6IY/+eKxjQazkDei2nf88V9ClYs8FnrXRFIR8u2I2/v/dtPlq4Kx8u3I1Pv9yZqppuG21XURHMn9/uP6+ItKzVGGlmY4GxAIWdNExhaSkMHVDGLWf+HAi+F+KxpqK6e3hwNPiuranLDb5r4wlNQrIQT7Ka+9GflRWr/0Ef/x5u7sd6YkLQNKFrmoxt7Md2LNZQt+aSzUZJUZPEtD55ba5sI8lsYkLVUpKbWKem711T8bbGH8OGyXB9LE94nG11G5Y1fS/j72/Cek0T5cS/YeL73t4Y2FaxWOPEdYP3PX4QIqGs6UGIttyqavKp8w3Lm24nHmsT99NSwp34twaafR6XmHDXlzVJxIENPncxz9rgt09NXXCyIvE3YXlVAWsqetffKqq7kzhwTdOEMH6gOpGSxOjJ1MSxTTo7MMbnjnngR+dy5sGP1J9VWbp6IG/P25epM0dRsryI+cuGUrK8iNIVhayr7LXJ+20qN7uant3W0bPbOnp1W0uv7muD+/Bx7+5rguX5Dev07LauPiHYoscqtum3KEhCc6rolltJfm5VhxKatojFrD5Zq67Na/TFVFEdJDlrK3uxZPWg+iSoorp7fVIUT3TjyVH9D5Ga7o3K4q+rqO5OzLM7vR2dx+sTtHhylnhgIPHWs9u6+vv448Tblr2Xbphs55WTm1O7ybUsrwr+Busqe7J87QBWrOvP7MVfY/naASxds2X9Z7xkeRFfrhpcPznvxjR31FGjo4mkhrtPBCZCcMaxM7ZZWAglpUX0+WEZ5dUF1NbldsZmJaMlJLMJSW4iM2+UHNW/sklS1dJonNK8jSV/zV25lGhjCSFoILuoy9TEcRGwbcLzIWFZI50dGOMTlL89b1+WrBnEjHkjeHvevixYsS2b8wurpi6PVev7sWp9v07fdpbVkZtT03D2Mzx7mHjpTPySnMSzj/GjZU2PYlXX5lEXy0Zf6ImMmro8Vpfnsbq8b3L2YLFGZ3nzc6saXaITPwJcF8smKyubOs+hojK43La8uoBa7w5ktflS2LpYy+vpqKPIZtWmGNnZJkyAsWOzWVPep75M/dnUx6/lssQza8TzyDSpW2rLmurs7bcn+WuubGPxW3E94jY2ak6UbwQJ8TxgOyAPeB/YtaXXdMaocY880vERqDZHWdNbOtVN70l6lfXvv/lHjBPZXOjio6q2N0ZqVNXUl3X196Srtz9V74l0TS3FyJQHsGTdgFEEo8Z9Doxrbf3OCozp8oWiL169JwoWIs3r6omjtzNGaroqEZGuo6UYmZGjqnZEZ40aJyIi6a2rj6raXoqPIiJdR0sxMmtzV0ZERERERESiRYmjiIiIiIiItEiJo4iIiIiIiLRIiaOIiIiIiIi0SImjiIiIiIiItEiJo4iIiIiIiLRIiaOIiIiIiIi0SImjiIiIiIiItMjcPdV1SAtmtgwo6cRNDgCWd+L2UiET2gCZ0Q61IT1kQhsgM9qxKW0ocveBnVmZTJaE+Aj6DKYLtSF9ZEI71Ib0sKlt2GiMVOKYJGY2w91HpLoemyIT2gCZ0Q61IT1kQhsgM9qRCW3oyjLh76c2pIdMaANkRjvUhvSQzDboUlURERERERFpkRJHERERERERaZESx+SZmOoKdIJMaANkRjvUhvSQCW2AzGhHJrShK8uEv5/akB4yoQ2QGe1QG9JD0tqgPo4iIiIiIiLSIp1xFBERERERkRYpcRQREREREZEWKXFMAjM7xsw+M7O5ZnZ5quvTFmY2ycyWmtmHCWX9zOxFM5sT3m+Ryjq2xsy2NbOXzexjM/vIzC4OyyPTDjPrZmZvmdn7YRuuCcu3M7Pp4WfqCTPLS3VdW2Nm2Wb2npk9Hz6PYhvmm9ksM5tpZjPCssh8ngDMrK+ZPWVmn5rZJ2Z2QJTaYGY7he9//LbGzC6JUhukQRTjIyhGpgvFyPSRCfERFCPbS4ljJzOzbOBu4FhgF+B0M9sltbVqk4eAY5qUXQ5Mc/dhwLTweTqrBX7u7rsAI4ELw/c+Su2oAg539z2BvYBjzGwkcCNwq7vvCKwCzkthHdvqYuCThOdRbAPAYe6+V8KcSFH6PAHcDvzL3XcG9iT4m0SmDe7+Wfj+7wXsA5QDzxKhNkggwvERFCPThWJkeol6fATFyHbvULdOvAEHAC8kPP8N8JtU16uNdR8KfJjw/DNg6/Dx1sBnqa5jO9vzHHBUVNsBFADvAvsDy4GcsLzRZywdb8CQ8IvqcOB5wKLWhrCe84EBTcoi83kC+gBfEA6EFsU2NKn3t4DXotyGrnyLcnwM66sYmUY3xciUtyHS8TGso2JkO28649j5tgEWJDxfGJZF0SB3Xxw+/goYlMrKtIeZDQWGA9OJWDvCy1dmAkuBF4HPgTJ3rw1XicJn6jbgV0AsfN6f6LUBwIF/m9k7ZjY2LIvS52k7YBnwYHhJ1P1m1oNotSHRacBj4eOotqEry6T4CBH+DCpGplwmxMiox0dQjGw3JY7SJh4csojE3C1m1hN4GrjE3dckLotCO9y9zoNLDoYA+wE7p7hK7WJmxwNL3f2dVNelExzs7nsTXFp3oZl9M3FhBD5POcDewD3uPhxYT5PLVSLQBgDC/j4nAH9tuiwqbZDMFaXPoGJkamVQjIx6fATFyHZT4tj5FgHbJjwfEpZF0RIz2xogvF+a4vq0ysxyCQJisbs/ExZHrh0A7l4GvExwyUpfM8sJF6X7Z+og4AQzmw88TnApzu1Eqw0AuPui8H4pQZ+B/YjW52khsNDdp4fPnyIIklFqQ9yxwLvuviR8HsU2dHWZFB8hgp9Bxci0kBExMgPiIyhGtpsSx873NjAsHB0rj+C08ZQU16mjpgBjwsdjCPpDpC0zM+AB4BN3vyVhUWTaYWYDzaxv+Lg7Qf+TTwiC4ynhamndBnf/jbsPcfehBJ//l9x9NBFqA4CZ9TCzXvHHBH0HPiRCnyd3/wpYYGY7hUVHAB8ToTYkOJ2GS3Agmm3o6jIpPkLEPoOKkekhE2JkJsRHUIzsCAs7TUonMrNRBNevZwOT3H1CiqvUKjN7DDgUGAAsAcYDfwOeBAqBEuBUd1+Zqjq2xswOBv4HzKKh38AVBH04ItEOM9sDmEzw2ckCnnT3a81se4Ijk/2A94Az3b0qdTVtGzM7FPiFux8ftTaE9X02fJoDPOruE8ysPxH5PAGY2V7A/UAeMA84h/CzRXTa0AMoBbZ399VhWaT+DhKIYnwExch0oRiZHjIlPoJiZLv3pcRRREREREREWqJLVUVERERERKRFShxFRERERESkRUocRUREREREpEVKHEVERERERKRFShxFRERERESkRTmtryIiUWJmdQTDrecCtcDDwK3uHmvxhSIiIhlM8VFk0yhxFMk8Fe6+F4CZbQk8CvQmmHdMRESkq1J8FNkEulRVJIO5+1JgLPBTCww1s/+Z2bvh7UAAM3vYzE6Kv87Mis3sRDPb1czeMrOZZvaBmQ1LVVtEREQ6i+KjSPuZu6e6DiLSicxsnbv3bFJWBuwErAVi7l4ZBrnH3H2EmR0CXOruJ5lZH2AmMAy4FXjT3YvNLA/IdveKzdsiERGRTaf4KLJpdKmqSNeSC9xlZnsBdcDXANz9v2b2JzMbCJwMPO3utWb2BjDOzIYAz7j7nJTVXEREJHkUH0VaoUtVRTKcmW1PEASXApcCS4A9gRFAXsKqDwNnAucAkwDc/VHgBKACmGpmh2++mouIiCSP4qNI++iMo0gGC4+Q3gvc5e4eXmaz0N1jZjYGyE5Y/SHgLeArd/84fP32wDx3v8PMCoE9gJc2ayNEREQ6meKjSPspcRTJPN3NbCYNw43/BbglXPYn4GkzOxv4F7A+/iJ3X2JmnwB/S9jWqcBZZlYDfAX8bjPUX0REJBkUH0U2gQbHEREAzKyAYH6rvd19darrIyIikg4UH0UC6uMoIpjZkcAnwJ0KiiIiIgHFR5EGOuMoIiIiIiIiLdIZR+lyzOxeM7uyE7c3Pzwi2ZHXfmRmh3ZWXZps281sx2Rsu8l+fmBmDyV7PyIi0jWZ2TfM7LNNeL3Okoh0AiWOEjnNJURmdrWZPdKW17v7T9z9uvB1h5rZwmTUM9z+Q2Z2fcLzXc1ssZn9IqzLru7+n2TtPx2EiXWFma01szIze93MfmJmkf3+MbOLzewLM1tvZp+Y2ddSXScRkVQzs4PD7/jVZrbSzF4zs303dbvu/j9336kz6thU+PuhJoxRa81stpndZWZbJ2N/yWZm/zSzdQm3ajOblep6SWaI7A83kagxs+HAy8D17v6HVNdnM/u2u/cCioAbgF8DDyRjR2aW3fpam7T9HwLnAccBPYHjgeXJ3KeISLozs97A88CdQD9gG+AaoCqV9WqjJ8IY1Q/4DrAV8E4ykkczS+qMBu5+rLv3jN+A14G/JnOf0nUocZSMEz+LaGY/N7Ol4Rm+cxKWP2Rm15tZD+CfwOCEI3ODzSzLzC43s8/NbIWZPWlm/RJef5aZlYTLxrWxTvsBLwJXuPvdCeX1l7mGRz2fNLOHw6OeH5nZiIR19zaz98JlfzWzJ5qczfxl2NYvzezcJvvvE253WVj338bP+IWXmr5mZreGZwTnmdmBYfmC8D0c096/Q3PcfbW7TwG+D4wxs93COuSb2R/MrNTMloSXE3dPqP+vEtr2w8SzzuHf8x4zm2pm64HD2rC9481sZsIZ0D3aUv/wPRsPXOruH3vgc3df2Rnvj4hIhH0NwN0fc/c6d69w93+7+wfQKNbcFZ6R/NTMjoi/2MzOCa/gWBvGoR8nLGt0dVAYO39hZh+E23rCzLptagPcvcbdPyKIUcuAnyfsc6Nxo6X4nPCb5Ndm9hXwYBu2N9jMng5j9hdm9rOOtMfMhgLfAB7uyOtFmlLiKJlqK6APwRHP84C7zWyLxBXcfT1wLPBlwtG5L4GLgJOAQ4DBwCrgbgAz2wW4BzgrXNYfGNJKXfYjmBPqUne/v5V1TwAeB/oCU4C7wv3mAc8STELcD3iM4Kgo4fJjgF8ARwHDgKZ9Lu8M34/tw3adDZyTsHx/4IOwPY+GddgX2BE4E7jLzHq2Uvc2c/e3gIUEAQ2Cs5BfA/YK97kNcFVC2y4L27QjcGgzmzwDmAD0Al5tZXvDgUnAj8P23gdMMbP8cPmfzOxPG6n6kPC2W5hUf2Fm11iEL7sVEekks4E6M5tsZsc2jbmh/YHPgQEEB+GesYYDs0sJruDoTRCfbjWzvVvY36nAMcB2wB7ADzqlFYC71wHPEcaoluJGa/E5tFW4rAgY28r2soC/A+8TxK4jgEvM7OiwLgebWVkbm3I28D93n9/e90CkOfqxI5mqBrg2PHo4FVgHtLV/xE+Ace6+0N2rgKuBUyy4vOQU4Hl3fyVcdiUQa2V7I4HVBGc3W/Oqu08Ng9ZfgD0TtpED3BG26RngrYTXnQo86O4fhgnx1fEFFly6eRrwG3dfGwaQPxIkv3FfuPuD4X6fALYleP+q3P3fQDVBAtaZvgT6mZkBYwkS65XuvpZgIuXTmrTtI3cvT2xbgufc/TV3jxFcFtXS9sYC97n79PCo+OTwNSMB3P0Cd79gI3WOHyT4FrA7cBhwOsHBCRGRLsvd1wAHAw78GVhmZlPMbFDCakuB28I49gTwGcFl/7j7P8IrONzd/wv8m4aDi825w92/DK/4+DvBgcLO9CVBsgctx43W4jMEvxPGhzG1opXt7QsMdPdr3b3a3ecRvJ+nAbj7q+7et41tOJsgoRXpFEm9zlokSeqA3CZluQTJYtwKd69NeF5O0B+tLYqAZ80sMSGsAwYRnGVcEC909/VmtqKV7d1NkHS9aGaHu/uqFtb9qkmdu4UJ62BgkTeeP2dBwuPBwDsJz0sSHg8geH9KmizfJuH5koTHFQDu3rSs0844hrYBVgIDgQKC/iTxZQbE+yoOBmYkvC6x3c2Vtba9IoLLZC9KeE1euJ/WVIT3N7l7GVBmZvcBowgCu4hIl+XunxCe+TOznYFHgNsIDrDBhnGshPC718yOJTgL+TWCExsFQEuDujSNl235Dm+PeIyCluOG03J8Bljm7pUJz1vaXh1BF5rEs4rZwP/aU3kzO5jgTOdT7XmdSEt0xlGiqBQY2qRsOxonRm3V3BDdC4Bj3b1vwq2buy8CFhOcjQPAzAoILjNpSR3BpZSlwAsWDCDQXouBbSwhE0qsR9N68f/s3Xl4VeXV9/HvShiDIINMAknQ4oBaEVLBqVpFRK0PWmejItVGW60t2jo8aV+tNq36aK1T1aio1KM4V2pRxIFaW0GiRUUQQSBhnglgZAhZ7x97Bw4xBCE5Z5/k/D7XlWuffe9pnXiZm7X3fa8N2XGfVxAk1Tk1ti/cjTgahAVV9noQDCtdQZCQHRT3+94znNQPwXeLHw7ci2+K/++4s/PNB4pq/PfNcvdnvkXoMwmevsZfT2XeRURqcPfPCZ52HRzXXLMfywYWhVMFXgTuBLqGT9TGEdz0S7pwuOhpbEvW6uo3dtY/wzf7ibrON59gFFD8trbufsoufo3hwEvuvn4XjxPZISWO0hg9C/zGzHpaUMhmMMEf+N25q7YU6GRme8a1PQQUmVkOgJl1NrNh4bYXgB+GcwxaALfwLf4/cvfNwNkESc04Cwrz7Ir3CRLQq8ysWRjP4XHbnwMuMbO+YTJ7U9y1t4Tbi8ysbfi9riG4E5xUZtbOzH5IMIfyKXf/NBxe+gjBfJYu4X49qudzhLGPMLMDw+9W5zs4v8X5HgGuMLOBFmhjZqeaWdudxR8OlX0WuC78XfYkGHL06i7+KkREmhQzO8CConQ9w/VeBE8aJ8Xt1gW42syam9nZwIEECWILoCVBQZrK8OnjkKR+AYKKp2Z2IME8xW7An8JNdfUbO+ufa1PX+T4A1llQTKe1mWWa2cG2C681saAY3DlomKo0MCWO0hjdQlBe+j2CwjV3APnuPm1XTxTeEX0GmGNBZbO9gXsICtO8YWbrCDq9geH+nwFXEhSQWRxe/1u9B9LdNwE/AjYAf7e4Kp+7cOylwBqCgjWvEpY5d/fXCIYDvQ3MDpfxfg58Bcwh+L09TTAxP1n+Hv4u5wOFBJ1xfHGe6wninmRma4E3Ceekht/tXoJXmcxm2z9C6irxXtf5SoCfEBQeWh3ud0n1gRZUYH2ojnNfRTBndhHBPxiS/bsUEUlF6wj6yskWVLieBEwjrjIpMJmggNsKgoJmZ7n7ynAu+tUENwpXE4zSGZvE2M81s/UE9QjGAiuBAR4UzKuz39hZ/1ybnZxvC0GRoH7AXILf1aMEBe4ws2PCWOtyehjLO9/6NyDyLdj2Q7JFpLEws8nAQ+7+eMRxXAIc5+6XJOl6BxL8Y6RljXmsIiKSosK+4jJ3PzqCa7u7J23Ya6r0zyINTU8cRRoJMzvWzLqFQ2GGE5Qffz3quJLBzM6woEx5B+B24O9KGkVEJBWkc/8s6UVVVUUaj/0JhvG0IRhyepa7L442JACmEgyJSaTLCeZqbAH+CezodRkiIiI1/S7B50/V/lmkQWmoqoiIiIiIiNRJQ1VFRERERESkThqqGtprr708Nzc36jBERCTBPvzwwxXu3jnqOBoL9Y8iIumjrj5SiWMoNzeXkpKSqMMQEZEEM7PSqGNoTNQ/ioikj7r6SA1VFRERERERkTopcRQREREREZE6KXEUERFJMjMbZWbLzGxaXFtHM5tgZrPCZYew3czsXjObbWafmFn/uGOGh/vPCt8fV90+wMw+DY+518ysrmuIiIjsjOY41mHz5s0sWLCADRs2RB1KUrRq1YqePXvSvHnzqEMREWnqngDuB0bHtd0AvOXut5nZDeH69cDJQJ/wZyDwIDDQzDoCNwF5gAMfmtlYd18d7vMTYDIwDhgKvFbHNXZJuvWPoD5SRESJYx0WLFhA27Ztyc3NJbxZ22S5OytXrmTBggX07t076nBERJo0d3/XzHJrNA8Djgs/PwlMJEjqhgGjPXjx8iQza29m3cN9J7j7KgAzmwAMNbOJQDt3nxS2jwZOJ0gcd3SNXZJO/SOojxQRAQ1VrdOGDRvo1KlTWnSKZkanTp3S6u6xiEiK6erui8PPS4Cu4ecewPy4/RaEbXW1L6ilva5rbMfMCsysxMxKli9f/o3t6dQ/gvpIERFQ4rhT6dIpQnp9VxGRVBY+XfSoruHuxe6e5+55nTvX/srLdOsz0u37iojUpMRRREQkNSwNh6ASLpeF7QuBXnH79Qzb6mrvWUt7XdcQEZHGxD34SSIljils5cqV9OvXj379+tGtWzd69OixdX3Tpk3f6hwjRoxg5syZCY5UREQawFigujLqcOCVuPaLw+qqg4DycLjpeGCImXUIq6MOAcaH29aa2aCwmurFNc5V2zUaFfWPIpL2vpoLL+8Ni15L2iWVODagWAxycyEjI1jGYvU7X6dOnZg6dSpTp07liiuuYOTIkVvXW7RoAQQT9quqqnZ4jscff5z48a23AAAgAElEQVT999+/foGIiEShof+ophAzewZ4H9jfzBaY2aXAbcCJZjYLGByuQ1AVdQ4wG3gE+BlAWBTnVmBK+HNLdaGccJ9Hw2O+JCiMQx3XSCj1jyIiDWzFZNiwBFp1S9ollTg2kFgMCgqgtDR4alxaGqwn4t85s2fPpm/fvuTn53PQQQexePFiCgoKyMvL46CDDuKWW27Zuu/RRx/N1KlTqayspH379txwww0ceuihHHHEESxbphFKIpKikvlHNQLufr67d3f35u7e090fc/eV7n6Cu/dx98HVSaAHrnT3fd39EHcviTvPKHf/TvjzeFx7ibsfHB5zVTifkR1dI5HUP4qIJMDKyZDZGtofkrRLKnFsIIWFUFGxfVtFRdCeCJ9//jkjR45k+vTp9OjRg9tuu42SkhI+/vhjJkyYwPTp079xTHl5Occeeywff/wxRxxxBKNGjUpMcCIi9ZXsP6qSMOofRUQS4PN/wJdV0KxF0kblKHFsIGVlu9ZeX/vuuy95eXlb15955hn69+9P//79mTFjRq0dY+vWrTn55JMBGDBgAPPmzUtMcCIi9ZXsP6qSMOofRUQaWOxJqJwNn21M6qicpCeOZtbLzN4xs+lm9pmZ/SJsv9nMFprZ1PDnlLhjbjSz2WY208xOimsfGrbNNrMb4tp7m9nksP1ZM2uR6O+Vnb1r7fXVpk2brZ9nzZrFPffcw9tvv80nn3zC0KFDa33XVPW8D4DMzEwqKysTE5yISH0l+4+qJIz6RxGRBvaXG6A5wSz2akkYlRPFE8dK4Fp37wsMAq40s77htrvdvV/4Mw4g3HYecBAwFPiLmWWaWSbwAHAy0Bc4P+48t4fn+g6wGrg00V+qqAiysrZvy8oK2hNt7dq1tG3blnbt2rF48WLGjx+f+IuKiCRS9R/VIwl+IHl/VKVBqX8UEWlgeywJll/WaE/wqJxmCT17LcIy4YvDz+vMbAbQo45DhgFj3H0jMNfMZgOHh9tmu/scADMbAwwLz3c8cEG4z5PAzcCDDf1d4uXnB8vCwuC/WXZ20ClWtydS//796du3LwcccAA5OTkcddRRib+oiEgiVf/xXPBjKN8EC3OS90dVGpT6RxGRBvbdNrD6K1hZoz3Bo3LMk/ziyO0ubpYLvAscDFwDXAKsBUoInkquNrP7gUnu/lR4zGNsKys+1N0vC9svAgYSJImTwqeNmFkv4DV3P7iW6xcABQDZ2dkDSktLt9s+Y8YMDjzwwIb7wo1AOn5nEUlRXgXPtYXvFMCAuxvstGb2obvn7XxPAcjLy/OSkpLt2tK1r0jX7y0iKSbWHaYuhzu3bGvLyoLi4nrflaurj4ysOI6Z7QG8CPzS3dcSPBHcF+hH8ETyrkTH4O7F7p7n7nmdO3dO9OVERGRXrJ8LWyqg/Tfu+4mIiKSnjavAlkC/MyEnB8yCZQMkjTuT9KGqAGbWnCBpjLn7SwDuvjRu+yPAq+HqQqBX3OE9wzZ20L4SaG9mzdy9ssb+IiLSWJRPC5Z7KnEUEREBYOUHwfKEyyH/2aReOoqqqgY8Bsxw9z/FtXeP2+0MIPwXA2OB88yspZn1BvoAHwBTgD5hBdUWBAV0xoYvOX4HOCs8fjjwSiK/k4iIJMCa6sSxb937iYiIpIuVkwGDTsmfcRHFE8ejgIuAT81satj2vwRVUfsBDswDLgdw98/M7DlgOkFF1ivdfQuAmV0FjAcygVHu/ll4vuuBMWb2e+C/BImqiIg0Jms+hTa9oXnbqCMRERFJDSsmBzdUm7dL+qWjqKr6HmC1bBpXxzFFwDcKd4ev7PjGcWGl1cNrtouISCNSPk3zG0VERKq5w6oPoMewSC4fWXEcERGRHdqyCdbO1PxGERGRauu/hI0rYa+BkVxeiWMKW7lyJf369aNfv35069aNHj16bF3ftGnTtz7PqFGjWLJkSQIjFRFpYOtmgldC+0OijkRSkPpHEUlLKyYHy05KHBu/WAxycyEjI1jGYvU6XadOnZg6dSpTp07liiuuYOTIkVvXW7Ro8a3Po45RRBqd6sI4GqraNKh/FBGpv5WTITML9jwokstH8jqOJikWg4ICqKgI1ktLg3VIyDtVnnzySR544AE2bdrEkUceyf33309VVRUjRoxg6tSpuDsFBQV07dqVqVOncu6559K6dWs++OCDXepURUQiUT4NrBm03T/qSKS+1D+KiDSMlZODaqoZ0aRwShwbSmHhtk6xWkVF0N7AHeO0adN4+eWX+c9//kOzZs0oKChgzJgx7LvvvqxYsYJPP/0UgDVr1tC+fXvuu+8+7r//fvr169egcYiIJMyaT6Hd/pCpf8g3euofRUTqb8tGWD0V9v9FZCEocWwoZWW71l4Pb775JlOmTCEvL3h/y9dff02vXr046aSTmDlzJldffTWnnnoqQ4YMafBri4gkxZpp0EnFsZsE9Y8iIvW3eipUbYpsfiNojmPDyc7etfZ6cHd+/OMfb53PMXPmTH7729/SqVMnPvnkE4455hgeeOABLr/88ga/tohIwm1eD1/N1fzGpkL9o4hI/cRi8POTg88//EW954nvLiWODaWoCLKytm/LygraG9jgwYN57rnnWLFiBRBUlysrK2P58uW4O2effTa33HILH330EQBt27Zl3bp1DR6HiEhClH8WLFVRtWlQ/ygisvuq54l3XA2rgE8XBusRJI8aqtpQqudpFBYGw2+ys4NOMQET/w855BBuuukmBg8eTFVVFc2bN+ehhx4iMzOTSy+9FHfHzLj99tsBGDFiBJdddpkm/4tI41AeVlTVOxybBvWPIiK7r3qe+L7Al2FbguaJ74y5e1IvmKry8vK8pKRku7YZM2Zw4IEHRhRRNNLxO4tIivlwJMwuhnPWgTX8wBgz+9Dd8xr8xE2U+sdt0vV7i0iEMjKgjcPDwDPAq2G7GVRVNfjl6uojNVRVRERSy5pPg3dUJSBpFBERaVSys6FP+Hl2jfYkU68sIiKppXyaCuOIiIhAMLT/4GZQybahqgmaJ74zShx3Ip2G8qbTdxWRFBOLQW4u7GmwYSl8uTHqiGQn0q3PSLfvKyIpIj8fTtoHFrWASoOcHCguTvr8RlDiWKdWrVqxcuXKtOgs3J2VK1fSqlWrqEMRkXRTXTGutBR6hm13vxhZuXHZuXTqH0F9pIhEaMtGyCyFIT8P5jTOmxdJ0giqqlqnnj17smDBApYvXx51KEnRqlUrevbsufMdRUQaUnXFONiWOH65MZKKcfLtpFv/COojRSQiqz6Eqo3Q+aioI1HiWJfmzZvTu3fvqMMQEWnaysq2fe4JrAPWAOVlOzhAoqb+UUQkSZb/O1judWS0caChqiIiErX4ynC9gAW1tIuIiKSj5e9B2z7QumvUkShxFBGRiBUVBRXiIEgc5xNZxTgREZGU4Q4r/pMSw1RBQ1VFRCRq1fMY77geWi+Eio5QfK/mN4qISHpb9wVsXAF7KXEUEREJ5OfDce3hnz+E+1+BLkdHHZGIiEi0quc3psgTRw1VFRGR1FA+LVi2PzjaOERERFLB8n9Dy07Q7oCoIwGUOIqISKpY8ym07gEt2kcdiYiISPSWvxdUUzWLOhJAiaOIiKSK1f+FDodFHYWIiEj0NiwP5jimyDBVUOIoIiKpoPIrWPs5dOwfdSQiIiLRW/GfYJkihXFAiaOIiKSC1Z+AVylxBMxspJl9ZmbTzOwZM2tlZr3NbLKZzTazZ82sRbhvy3B9drg9N+48N4btM83spLj2oWHbbDO7IfnfUEREdigWg9xcuO50qAQmzIo6oq2UOIqISPRWfxQsO6R34mhmPYCrgTx3PxjIBM4DbgfudvfvAKuBS8NDLgVWh+13h/thZn3D4w4ChgJ/MbNMM8sEHgBOBvoC54f7iohI1GIxKCiA0lLYD5gDFFwVtKcAJY4iIhK9VR9By70gq2fUkaSCZkBrM2sGZAGLgeOBF8LtTwKnh5+HheuE208wMwvbx7j7RnefC8wGDg9/Zrv7HHffBIwJ9xURkagVFkJFBTQHegNfEKwXFkYcWECJo4iIRG/1R8HTxhSpHBcVd18I3AmUESSM5cCHwBp3rwx3WwD0CD/3AOaHx1aG+3eKb69xzI7at2NmBWZWYmYly5cvb5gvJyIidSsrC5a9CZLHL2q0R0yJo4iIRGvLRlgzDToOiDqSyJlZB4IngL2BvYE2BENNk8rdi909z93zOnfunOzLi4ikp+zsYLlfuP5FjfaIKXEUEZFolU8Dr1RhnMBgYK67L3f3zcBLwFFA+3DoKkBPYGH4eSHQCyDcviewMr69xjE7ahcRkagVFUFWVpA4LgLWEawXFUUcWECJo4iIRGtVWBhHiSMEQ1QHmVlWOFfxBGA68A5wVrjPcOCV8PPYcJ1w+9vu7mH7eWHV1d5AH+ADYArQJ6zS2oKggM7YJHwvERHZmfx8KH4YDsgInjbm5EBxcdCeAprtfBcREZEEWvURNN8T2vSOOpLIuftkM3sB+IigEPt/gWLgH8AYM/t92PZYeMhjwF/NbDawiiARxN0/M7PnCJLOSuBKd98CYGZXAeMJKraOcvfPkvX9RERkJ049DMZVwfWjoHhE1NFsJ+mJo5n1AkYDXQEHit39HjPrCDwL5ALzgHPcfXV4x/Ue4BSgArjE3T8KzzUc+E146t+7+5Nh+wDgCaA1MA74RXgHVkREUs3qj4KnjWleGKeau98E3FSjeQ5BRdSa+24Azt7BeYqAb4xvcvdxBH2jiIikmmUTg2XXH0QaRm2iGKpaCVzr7n2BQcCV4TukbgDecvc+wFvhOgTvmuoT/hQADwKEieZNwECCzvSmsKgA4T4/iTsu6YUFRETkW6jaDKs/Tvv3N4qIiACwdCK0yYE9cqOO5BuSnji6++LqJ4buvg6YQVAKPP5dVDXfUTXaA5MICgR0B04CJrj7KndfDUwAhobb2rn7pPAp4+i4c4mISNRiMcjNhYwMOCIHqjZqfqOIiIh78MSxy3FRR1KrSIvjmFkucBgwGejq7ovDTUsIhrLCrr+Lqkf4uWZ7bdfXe6pERJIpFoOCAigtDTrIVuGf/X+rsKeIiKS58s9g4wroelzUkdQqssTRzPYAXgR+6e5r47eFTwoTPidR76kSEUmywkKoqNi2ngtsAH5zf0QBiYiIpIilE4OlnjhuY2bNCZLGmLu/FDYvDYeZEi6Xhe27+i6qheHnmu0iIhK1srLt13OBUqB0fi07i4iIpJFlE1N2fiNEkDiGVVIfA2a4+5/iNsW/i6rmO6outsAgoDwc0joeGGJmHcKiOEOA8eG2tWY2KLzWxXHnEhGRKGVnb/tsQA5BHe34dhERkXTjVbDsnyn7tBGieeJ4FHARcLyZTQ1/TgFuA040s1nA4HAdgpLhc4DZwCPAzwDcfRVwK8HLjKcAt4RthPs8Gh7zJfBaMr6YiIjsRFERZGUFn7sBrYBFLYJ2ERGRdBJfLG5Qz5Se3wgRvMfR3d8juM9cmxNq2d+BK3dwrlHAqFraS4CD6xGmiIgkQn5+sCwshB6lwedLbt7WLiIikg6qi8VVz/vfMywW9/4a2Ce6sOoSaVVVERFJQ/n5MG8e3HctZLSE838VdUQiIiLJVbNYXF9gOVD456gi2ikljiIiEo3VH0H770JG86gjERERSa74YnEGHEDwdvuaReRSiBJHERFJPndY9RF0HBB1JCIiIskXXxSuB9COIHFM4WJxShxFRCT5vpoLm8uhY/+oIxEREUm++GJxfcO2ua1SulicEkcREUm+VR8FSyWOIiKSjvLzobgYcnLgQGBVJvzx0ZQuFqfEUUREkm/Vh2DNYE8VwBYRkTSVnw9z58AxnSDvopROGkGJo4iIRGHl5KAwTmbLqCMRERGJTvlnsHEldDku6kh2SomjiIgkV9UWWPkB7HVE1JGIiIhEa+nEYNnl2EjD+DaUOIqISHKVT4PKr5Q4ioiILJsIbXJhj9yIA9k5JY4iIpJcK94Plp2VOIqISBrzKlj2z0bxtBGUOIqISLKteB9adoY2vaOOREREJDqr/xvMb+w2OOpIvhUljiIiklwr3g+GqZpFHYmIiEh0Fk8IlkocRUREati4EtbN0vxGERGRJW8EFcZbd4s6km9FiaOIiCTPiknBUomjiIiks8qvYPl70H1I1JF8a0ocRUQkcWIxyM2FjIxgOfERsEzolBd1ZCIiIslTsz989ndQtRm6NZ7EsVnUAYiISBMVi0FBAVRUBOulpfD5fDigFzRrE21sIiIiyVJbf/jm3TC4OXQ+OtrYdoGeOIqISGIUFm7rJAEMyK2CySsjC0lERCTpavaHAAdWwuxMaNY6mph2gxJHERFJjLKy7dd7Aq2B/66PIhoREZFo1OwPOxD0iVM2RBHNblPiKCIiiZGdvf16n3D51d5JD0VERCQyNfvDQ8Lliu5JD6U+lDiKiEhiFBVBVta29T7AOuDa26OKSEREJPlq9oeHAOXAz++IKqLdosRRREQSIz8fioshJwfM4MBmsMdhkH9h1JGJiIgkT3x/mAF8NwPaHdXo+kMljiIikjj5+TBvHny9HDpXQr+zo45IREQk+ar7w+UfwR5VcOTlUUe0y5Q4iohI4q2YHCz3OiLaOERERKK05I1g2W1wtHHsBiWOIiKSeCveB8uATt+LOhIREZHoLJ4A7Q+B1o2rMA4ocRQRkWRY8T60/y40axN1JCIiItGorIDl/4JuQ6KOZLcocRQRkcSq2gIrJ2uYqoiIpLdl70LVJuiuxFFEROSb1k6HyvVKHL8lM2tvZi+Y2edmNsPMjjCzjmY2wcxmhcsO4b5mZvea2Wwz+8TM+sedZ3i4/ywzGx7XPsDMPg2PudfMLIrvKSKSdpZMgIyW0PmYqCPZLUocRUQksVa8HyyVOH5b9wCvu/sBwKHADOAG4C137wO8Fa4DnEzwhsw+QAHwIICZdQRuAgYChwM3VSeb4T4/iTtuaBK+k4iILB4PXY6BZq2jjmS3KHEUEZHEWvYvaNUF9tg36khSnpntCXwfeAzA3Te5+xpgGPBkuNuTwOnh52HAaA9MAtqbWXfgJGCCu69y99XABGBouK2du09ydwdGx51LREQS5atSKP8Mujfee3VKHEVEJHHcYek70OU40IjIb6M3sBx43Mz+a2aPmlkboKu7Lw73WQJ0DT/3AObHHb8gbKurfUEt7SIikkgL/xEse5wWbRz1oMRRREQSZ/2X8PVC6Hpc1JE0Fs2A/sCD7n4Y8BXbhqUCED4p9EQGYWYFZlZiZiXLly9P5KVERNLDwlehbR9ot1/Ukew2JY4iIpI4S98Jll1+EG0cjccCYIG7Tw7XXyBIJJeGw0wJl8vC7QuBXnHH9wzb6mrvWUv7dty92N3z3D2vc+fO9f5SIiJpJRaD3FzIyAiWscdg6duw9w+jjqxelDiKiEjiLJ0IrbpBu/2jjqRRcPclwHwzq/6FnQBMB8YC1ZVRhwOvhJ/HAheH1VUHAeXhkNbxwBAz6xAWxRkCjA+3rTWzQWE11YvjziUiIvUVi0FBAZSWBtM1SkvhgZ9B1UboocRxl5jZKDNbZmbT4tpuNrOFZjY1/DklbtuNYcnwmWZ2Ulz70LBttpndENfe28wmh+3PmlmL5H07ERHZyh2WvRMMU9X8xl3xcyBmZp8A/YA/ALcBJ5rZLGBwuA4wDpgDzAYeAX4G4O6rgFuBKeHPLWEb4T6Phsd8CbyWhO8kIpIeCguhomL7toM2wQaDzkdHE1MDaRbBNZ8A7ieo5Bbvbne/M77BzPoC5wEHAXsDb5pZ9cDgB4ATCYb1TDGzse4+Hbg9PNcYM3sIuJSwPLmIiCTRulnw9WLoqmGqu8LdpwJ5tWw6oZZ9HbhyB+cZBYyqpb0EOLieYYqISG3KyrZfN4JbgB87ZDbu51lJf+Lo7u8Cq3a6Y2AYMMbdN7r7XIK7o4eHP7PdfY67bwLGAMPCYTfHE8wJge1LlouISCLVnNPx9/ChWJfjIgxKREQkibKzt1/PAToAZZ2iiKZBpdIcx6vM7JNwKGv1S4p3tcx4J2CNu1fWaK+VqsaJiDSQ2uZ0TBkN3iGoIiciIpIOioogK2vben+gCjjr91FF1GBSJXF8ENiX4EHuYuCuZFxUVeNERBpIbXM69tsCH2/U/EYREUkf+flQXAw5OUH/N7AFWB/IvyLqyOotJRJHd1/q7lvcvYpgcv/h4aZdLTO+EmhvZs1qtIuISCLVnNPRHWgPlFTUtreIiEjTlZ8P8+bB+gXQcxP0GxF1RA0iJRLH6ndThc4AqiuujgXOM7OWZtYb6AN8QFAhrk9YQbUFQQGdsWGRgHeAs8Lj40uWi4hIotSc09E3XK7ZO+mhiIiIpIRF44JlI38NR7UoXsfxDPA+sL+ZLTCzS4E7zOzTsPT4D4CRAO7+GfAcwTusXgeuDJ9MVgJXEbynagbwXLgvwPXANWY2m2DO42NJ/HoiIump5pyOvsAqg2tvjywkERGRSC16FbKyYc+mUcg66a/jcPfza2neYXLn7kVAUS3t4wjeX1WzfQ7bhrqKiEgy5OcHy8JCKCuFgzOgzZGQf2G0cYmIiERhywZYPAH2uaTJzPVPiaGqIiLSBFTP6Vj9GexRBYOaxpwOERGRXbZ0ImypaDLDVKEBE0czyzCzdg11PhERaaSWvhMsu/4g2jiSTP2giIhstfBVyMxqUn1hvRJHM3vazNqZWRuCgjbTzezXDROaiIg0SksnBnM62uRGHUnCqR8UEZFvcIeFY6HbYMhsFXU0Daa+Txz7uvta4HTgNaA3cFG9oxIRkcbJq2DZxOAOaxOZ07ET6gdFRGR7K6dAxXzodWbUkTSo+iaOzc2sOUGHOdbdNwNe/7BERKRRKp8OG1dA1+OijiRZ1A+KiMj25r8A1gx6nhZ1JA2qvonjw8A8oA3wrpnlAGvrG5SIiDRSS98Olk1oTsdOqB8UEZFt3GH+i8Ew1RYdoo6mQdUrcXT3e929h7uf4oFSgvcwiohIOlr0GrTdD9rkRB1JUqgfFBGR7ayeCuvnNLlhqlD/4jhdzewxM3stXO8LDG+QyEREpHGprAjmN+59StSRJI36QRER2c78F8EyoefpUUfS4Oo7VPUJYDywd7j+BfDLep5TREQao6UTgxcep1HiiPpBEZH0FotBbi5kZEBuDkx7DLocB632ijqyBlffxHEvd38OqAJw90pgS72jEhGRxmfRuOCdVV2+H3UkyaR+UEQkXcViUFAApaXB3MYtZWBLYEmvqCNLiPomjl+ZWSfCCnJmNggor3dUIiLSuLjD4teg2wmQ2TLqaJJJ/aCISLoqLISKim3rhxPcRvzjm1FFlFDN6nn8NcBYYF8z+zfQGTir3lGJiEjjsu6LoBjAgb+OOpJkUz8oIpKuysq2Xz8cmAlMXxhFNAlXr8TR3T8ys2OB/QEDZobvsBIRkXSyaFyw3PvkaONIMvWDIiJpLDs7GKYK0B3oBYwO25ug+lZVPRto7e6fEbz8+Fkz698gkYmISOOxaBzs2TdtXsNRTf2giEgaKyqCrKzg8/fCtmmtgvYmqL5zHH/r7uvM7GjgBOAx4MH6hyUiIo3G5vWw7N10q6ZaTf2giEi6ys+H4mLIyYGBQGlLuP3RoL0Jqm/iWF057lTgEXf/B9CinucUEZHGZOnbULUpXRNH9YMiIuksPx+mvQ25wOlFTTZphPonjgvN7GHgXGCcmbVsgHOKiEhjsmgcNNsD9joq6kiioH5QRCTdlb0YLHudGW0cCVbfzu0cghcfn+Tua4COQNqV1BMRSVvuQeLY7UTITMsHbeoHRUTSXdnz0HEA7JEbdSQJVa/E0d0r3P0loNzMsoHmwOcNEpmIiKSuWAxycyE7Ayrmw/yOUUcUCfWDIiJpbu1MWDUFci6IOpKEq29V1f8xs1nAXOCf4fK1hghMRERSVCwGBQVBCfJDw7brY0F7mlE/KCKS5uY+BZYBuedHHUnC1Xeo6q3AIOALd+8NDAYm1TsqERFJXYWFUFERfO4HlAILNwTt6Uf9oIhIunKHeU9B18HQunvU0SRcfRPHze6+Esgwswx3fwfIa4C4REQkVZWVBcvWwH7AxzXa04v6QRGRdLX83/DVPOh9YdSRJEWzeh6/xsz2AN4FYma2DPiq/mGJiEjKys4OhqkeTNCLfBzXnn7UD4qIpKt5T0FmFvQ8I+pIkmK3njia2XfM7ChgGFABjAReB1YCP2+48EREJOUUFUFWFhwOrAW+IFgvKoo4sORRPygikua2bISy56DXGdB8j6ijSYrdHar6Z2Ctu3/l7lXuXunuTwIvAzc3WHQiIpJ68vOh+H4YYFAC9MqB4uIm/dLjWqgfFBFJZ4vGwabVkHtR1JEkze4OVe3q7p/WbHT3T80st14RiYhI6ju2I7zrcOt4eHRI1NFEQf2giEg6m/cUtOoK3U6IOpKk2d0nju3r2NZ6N88pIiKNRdkL0KIjdP1B1JFERf2giEi62rQaFr4KOedDRn1LxjQeu5s4lpjZT2o2mtllwIf1C0lERFLalo2wcCz0PB0ymkcdTVTUD4qIpKuy56FqE/ROn2GqsPtDVX8JvGxm+WzrIPOAFkB6lBUSEUlXSybA5rWQfVbUkUQpof2gmWUSzCBd6O4/NLPewBigU3i9i9x9k5m1BEYDAwgK85zr7vPCc9wIXApsAa529/Fh+1DgHiATeNTdb6tvvCIiaWXuX6HdgdDhsKgjSardeuLo7kvd/Ujgd8C88Od37n6Euy9puPBERCTllL0AzdtD1/SZ11FTEvrBXwAz4tZvB+529+8AqwkSQsLl6rD97nA/zKwvcB5wEDAU+IuZZYYJ6QPAyUBf4PxwXxER2YlYDI4+bC4sf487nr+Q2NMWdUhJVa9BueGLjt9poFhERCTVbdkEC16BnsMgs0XU0UQuEf2gmfUETgWKgGvMzIDjgQvCXZ4kqMODaqoAACAASURBVNz6IMHrQG4O218A7g/3HwaMcfeNwFwzm03wAhWA2e4+J7zWmHDf6Q35HUREmppYDAoK4JcnPg3AA+PyWfFCsC1diorv7hxHERFJR0vfgs1rIPvsqCNpyv4MXAdUheudgDXuXhmuLwB6hJ97APMBwu3l4f5b22scs6P27ZhZgZmVmFnJ8uXLG+I7iYg0aoWF8PXXVfz42FFMnH4sZStyqKgI2tOFEkcREfn2yp6H5u2g2+CoI2mSzOyHwDJ3j7TAjrsXu3ueu+d17tw5ylBERFJCWRkc3/dt9u06h+J3CrZrTxeRJI5mNsrMlpnZtLi2jmY2wcxmhcsOYbuZ2b1mNtvMPjGz/nHHDA/3n2Vmw+PaB5jZp+Ex94bDdkREpD6qNsOCv0GP/4HMllFH01QdBfyPmc0jKIZzPEEhm/ZmVj29pCewMPy8EOgFEG7fk6BIztb2GsfsqF1EROqQnQ0FxxezYl0nXpryo+3a00VUTxyfIJisH+8G4C137wO8Fa5DMIG/T/hTQDCnAzPrCNwEDCSYt3FTdbIZ7vOTuONqXktERHbV0neCd1dpmGrCuPuN7t7T3XMJitu87e75BPMoq8vYDgdeCT+PDdcJt7/t7h62n2dmLcOKrH2AD4ApQB8z621mLcJrjE3CVxMRadTuKlrKGXkv8+S/hrNxcysAsrKgqCjiwJIoksTR3d8FVtVoHkYw4Z9weXpc+2gPTCK469odOAmY4O6r3H01MAEYGm5r5+6Tws5zdNy5RERkd5U9D83aQvchUUeSjq4nKJQzm2AO42Nh+2NAp7D9GsKbru7+GfAcQdGb14Er3X1LOA/yKmA8QdXW58J9RUSkDmce9gTNm1UybuZPMIOcHCguTp/COFDPqqoNrKu7Lw4/LwG6hp93dYJ/j/BzzfZvMLMCgqeYZKfTc2YRkV0Ri8Fv/xeuL4Mvs2Dzi+nVU0bE3ScCE8PPc9hWFTV+nw1ArY+A3b2IoDJrzfZxwLgGDFVEpGnzKphdDF2+z1tTDog6msikZHGc8EmhJ+E6mvwvIlKX6vrjbcqgLfBORbAei0UdmYiISHIsfRvWz4HvXB51JJFKpcRxaTjMlHC5LGzf1Qn+C8PPNdtFRGRXFRZCRQV8H/gK+BjSrv64iIikt1kPQ8tO0OtHO9+3CUulxDF+gn/Nif8Xh9VVBwHl4ZDW8cAQM+sQFsUZAowPt601s0FhNdWL484lIiK7oqwMsoDvAf8BNse1i4iINFGxGOTmQrf2S9k872/M2DAcMltFHVakonodxzPA+8D+ZrbAzC4FbgNONLNZwOBwHYJ5GHOA2cAjwM8A3H0VcCtBhbgpwC1hG+E+j4bHfAm8lozvJSLS5GRnwxFAC8LZdnHtIiIiTVD1LI3SUhh+zBM0z6zkgv/3k7SfpWHBdELJy8vzkpKSqMMQEUktsRjMvRiaVcGNYVtWVqMuJWdmH7p7XtRxNBbqH0Uk3eTmBkmjWRWz7urDglU9Oe73/yQnB+bNizq6xKqrj0yloaoiIpJqTu0H+1TBpx1I2/rjIiKSVqpnYxzf92327TqHh9++fLv2dJVKr+MQEZFUM+dxsGbw2EyIqfq0iIg0fdnZwRPHn534F1au68hLU360tT2d6YmjiIjUrmozzPsr9DgNWilpFBGR9FBUBAfnzOb0AX/jobeuYOPmVmRlBe3pTE8cRUSkdotegw3LYJ8RUUciIiKSNPn5kMc9VG5pxgNvXkVOTpA0pvssDSWOIiJSuzmPQ6uusPfJUUciIiKSPJtWs3+zUbDPBSxa1T3qaFKGhqqKiMg3bVgGC1+F3hdBhu4xiohIGpn1MGypgANGRh1JSlHiKCIi24nF4NZLnwKvZPDlI9L+vVUiIpJGtmyCL+6DboOhw6FRR5NSlDiKiMhWwUuPndO/+ziTZg/krSl9KShAyaOIiKSHsufg60VwwDVRR5JylDiKiMhWhYVwcPcPOKTXNB7/Z1AUp6IiaBcREWnS3OHzu2DPvtB9aNTRpBwljiIislVZGfxi6D2UV7Tj6f9csF27iIhIk7ZsIqyeCvuPBLOoo0k5ShxFRGSrww9ewNmHP8+jEy9j/Ya2W9vT/aXHIiKSBmb8CVp2ht4XRh1JSlLiKCIiWz12/QNkZFRx/xtXbW3TS49FRKQpi8XghO99Dote5e5/XElsTKuoQ0pJShxFRCRQWcFBLR9moZ2OZ/XGDHJyoLhYLz0WEZGmKSgKBxcc9n9s2NSSP774UxWF2wG9nEtERAJz/wqbVpN94kjmKVEUEZE0UFgIXdvMYfgxT/LAhCtZvrbL1nbdNN2eEkcREQGvgpl/ho4DoPNRUUcjIiKSFGVl8MhlRVRuacbtf79+u3bZnoaqiogILH4D1n4O+/9SleRERCRtHN3vS4Yf8yQPv305i9fsvbVdReG+SYmjiIjA53dD6+6QfU7UkYiIiCTN49cWsXlLc277+w1b21QUrnZKHEVE0t2az2DJG9DnSshsEXU0IiIiybHuS/bNGE1p88tpuWd3FYXbCSWOIiJpLBaDp2++l683teKwcy5XFTkREWnSYjHIzYWMDHj+5t9TWdWcA350PfPmQVUVzJunpHFHlDiKiKSpWAz+95rlnNFvNH997yKmzthLJchFRKTJqn71Rmkp7NNlNmf0+ysPvXkFsZe6Rx1ao6DEUUQkTRUWwlUn3EGLZpv407hrAKioCNpFRESamsLCoJ8D+M3pv2fzluYU/e069Xvfkl7HISKSpjaWL+HKEx/g6f9cwMzFB2xtVwlyERFpiqr7t327zubCo57i3vFXs2RNd6w82rgaCz1xFBFJU0UX3EaLZpv43Us3bdeuEuQiItIUVfdvRecUsqmyBXe8et127VI3JY4iIumoYiHDj3yI2PvD+XLpd7Y2qwS5iIg0VUVFcPwh/+bcQc9xx6vXsbS8m/q9XaDEUUQkHX32BzIztrDnUb8hJweVIBcRkSYv/4Iqnr1+JEvK9+bOcb9Wv7eLNMdRRCTdfFUGXz4C+17K6Yf35nR1mCIikg7mPc1eNgVOepL1X7eJOppGR08cRUTSRPW7qx75xe/ZuMl4eZbKyImISJqorICPb4SOedD7wqijaZSUOIqIpIHqd1dlVMzhku8/TvFbBVxY0EvvbBQRkfQw406oWAD9/wSmFGh36LcmIpIGqt9d9dszbqWyqhl/GPu/emejiIikh4qFMP126HUWdDkm6mgaLSWOIiJpoKwMDuo5jYuPGc2Db/6UJWu6b20XERFpiqqnaDxxTSEbN1byStntUYfUqClxFBFJA9nZzv3Dr2LNV+0peqUwrj3CoOQbzKyXmb1jZtPN7DMz+0XY3tHMJpjZrHDZIWw3M7vXzGab2Sdm1j/uXMPD/WeZ2fC49gFm9ml4zL1mZsn/piIiiVU9RWOvjBIu+f6T3D1uJBcU7KMpGvWgxFFEJA08VTSG4/r+kxuf/SOr1ncC9M7GFFUJXOvufYFBwJVm1he4AXjL3fsAb4XrACcDfcKfAuBBCBJN4CZgIHA4cFN1shnu85O444Ym4XuJiCRVYSFs2riZRy77CYtWd9cUjQaQcomjmc0L74RONbOSsK3B7rSKiKSD6uE5GRlw0H7r6M+vWOkDeHPupXpnYwpz98Xu/lH4eR0wA+gBDAOeDHd7Ejg9/DwMGO2BSUB7M+sOnARMcPdV7r4amAAMDbe1c/dJ7u7A6LhziYg0GWVlcO0pd3FY7lSufOIB1n3dbmu77J5UfY/jD9x9Rdx69Z3W28zshnD9era/0zqQ4C7qwLg7rXmAAx+a2diw8xQRadKqh+dUVATrw/NuJcsW8a6/xJy5mdEGJ9+ameUChwGTga7uvjjctAToGn7uAcyPO2xB2FZX+4Ja2mteu4DgCSbZGs8sIo3QsYd9wc0/upkXPjiTv5WcsbVdf9J2X8o9cdyBBrnTmuygRUSiUF1BFWD/7p8zcujdPDbxx1xRODDawORbM7M9gBeBX7r72vht4ZNCT+T13b3Y3fPcPa9z586JvJSISMPzKsZc8xO+3tyaq564f2uzpmjUTyomjg68YWYfhnc8oeHutG7HzArMrMTMSpYvX96Q30FEJDLbhuE49w3/Oes37sENY27T8JxGwsyaEySNMXd/KWxeGt4YJVwuC9sXAr3iDu8ZttXV3rOWdhGRRi1+isb/nvsIXe1dPs+6i1btu2mKRgNJxcTxaHfvTzAM9Uoz+378xoa806o7qiLSFFUPwznz8Bc58ZA3+e3zt7JiXWcNz2kEwgqnjwEz3P1PcZvGAtXz9YcDr8S1XxzO+R8ElIc3WscDQ8ysQ1gXYAgwPty21swGhde6OO5cIiKNUvUUjdJS6N5+IdcPuY53pp/AHEYwbx5UVcG8eUoa6yvlEkd3XxgulwEvE1SDa6g7rSIiTV5REXTrVM6f8q9haumhPPTWFRqe03gcBVwEHB8WiZtqZqcAtwEnmtksYHC4DjAOmAPMBh4Bfgbg7quAW4Ep4c8tYRvhPo+Gx3wJvJaMLyYikijbpmg4fxnxM5pnbubS4mIKC/W2oYaUUsVxzKwNkOHu68LPQ4Bb2Han9Ta+eaf1KjMbQ1Acp9zdF5vZeOAPcaXHhwA3JvGriIhEJj8fjuBqevhCzr3vOXr2akZRke60Ngbu/h6wo3/pnFDL/g5cuYNzjQJG1dJeAhxcjzBFRFJK9VSMC49+imEDxnJt7E7mLt8HvaW2YaVU4kgwd/Hl8F3EzYCn3f11M5sCPGdmlwKlwDnh/uOAUwjumlYAIyC402pm1XdaYfs7rSIiTVvZC+xjo+GQ/8f7swZFHY2IiEhCZWdDi41f8OCIn/Lu58dwz+u/2NouDSelEkd3nwMcWkv7ShroTquISJNWsQg+uBw6fg8O/k3U0YiIiCTcH4s20Hf+uWzY3IoLHniaLVXNNEUjAVJujqOIiOya6kpymZlVvHvHCCo3boAjn4KM5lGHJiIiknDn7/9rDs2eynUvPcGi1T1VQTVBUuqJo4iI7JrqSnIVFXDVkAf4/n5vcPVTDzKQ/dRhiohI0zf/Zfjifth/JKPG/1DDDRNITxxFRBqx6kpyB/aYzh3nX8er/z2V+167nMLCqCMTERFJnFgMjupXyurXf8wnCwbwzOe37fwgqRc9cRQRacTKyqB1iwpiP8tn/YY9uOyRRwHbWmFORESkqYnF4Gc/3cxr15xPZsYWzrjrWZasb0EVGp6aSHriKCLSiGVnO6MKfsyh2R9zycNPsLS8W9gecWAiIiIJUljo3H72zzlyv/cpeLSYOcv2paICjbZJMD1xFBFpxF4pKuJQe5brnrmdcVNPBVAlORERadLOPOhurjjhYf449gaenXTe1naNtkksPXEUEWms5r/EofZb5vhFPPfprzFDleRERKRpW/AK/3f+r3jhgzMpfG77u6QabZNYShxFRBqj1VPhPxdBp4Hsc14x8+YZVVUwb56SRhERaVqqXzs1YJ+PqHjzAsq+yuOKJ0fjvi2V0WibxFPiKCLS2GxYBv8cBi06wPdfhsxWUUckIiKSENWvnapct4Cx15zG8rV7cfzNYznn/CxyctBomyTSHEcRkcZk87ogady4HE78F7TuHnVEIiIiCVNYCJm+lr9fexptW6/jqN/9m7lLujFuXDDKRpJHTxxFRBqLyq9Y9typVC6bwo/uipHbfwCxWNRBiYiIJM6qZet4/bqhHNxzGufe9yzT5h8CqBBOFJQ4ioikqOo5HRkZcECfCmYWn0Yn/zf5f4nx8pQzKC0Nhu8oeRQRkaYivu87aL91vHHjyXxvnymcc99zvP7xyVv3UyGc5FPiKCKSgqrndJSWQstmX3PfWcPo024iwx96kucmnbt1P723SkREmor4vi+rxXoeOu8U8nInceFDY/hbyRlb91MhnGgocRQRSUGFhUFS2LL5Bl4a+SNOOOgtRhQ/TuzfF35jXw3XERGRpqC672vTcj3jrjuFI/q8z/n3P8NbX5ypQjgpQMVxRERSUFkZ7NFqHc9ffTZDDx3PpcWPMvpfw2vdV8N1RESkKSgrg3aty3nlmmEctd+/ueCBp3nhg7MxgxUroo5OlDiKiKSgQYeU8dD5P6Rvj+lcWvwoo/55KRDcbXXftp+G64iISFMx6JAyHr7gVA7o/jkX/uWprVMzdIM0NWioqohIqlnxAW9ddzjZe5Vx8h2vbU0as7LgiivQcB0REWkS4gvhnHZUCa+NHEivTvMZesfrjHn/fEA3SFOJnjiKiKSAWCyY2/G9ri/w159dRGWz7vyr9dvMWtcXs+Bua1GRkkQREWkaqgvhVFTAsAF/4+nLLmDZ2q6MLn2LL9er70tFShxFRCIWi8FPr6hk5JAifnfmzfzniyO44KG/UXRXF73cWEREmqSgEI4z8uS7ufOCXzFlzvf4n7vG0rpDV/V9KUpDVUVEIvbgnXMZd81x/O7Mmxn9r4s4/g9vU7q0i16zISIiTUb8sNTcXFi3ciUv/fJH/OnCa3mp5Ef8oOgdlq3tqkrhKUxPHEVEkqx6WGpZmTNy2GjGXfVz3I0LHojxzH8u2LqfOk8REWkK4oelAuRmTeSpX11Il3bLuOapu/jz67/EPXiepUI4qUuJo4hIElV3ni1tFWOuuoJzBj3PP2d8n4sfGk3Zipzt9lXnKSIijdG2G6RBX7Z+fZA0ZmZUctOPfkfhsCJmL/0OR9w8iY/m9t96nArhpDYljiIiSfTb32zhoiMe4fdn/4Y9W5dzw5g/8n+v/honc7v91HmKiEhjVPPpYmlpsDw0ZyoP/fgKBn1nMqMmjuDq0ffy1cY9yMnZlmCqEE5qU+IoItJAat5hrU78qtvOOXYiLxf8gkNzPmHi9GP5xV/v4ZOyQ7cer85TREQau6Dozbb1dq3LueWs/8dVQ+5n1fqOnHffMzw76Twg6PdUCKfxUOIoItIAarvDOmJE8L7FXh1m8+zPb+TsgS8wb3kOZ93zPC9+cCZgW49X5ykiIk3Btvn5Tv5RMe684Fd0abeMh966gt88/3tWf9UR0MiaxkiJo4hIA6h5hxWg795TueG02zh74PNs2NSK3zx/K3f941o2Vrbebj91niIi0lRkZzu920zkljP/H8cc8B4ffPk9fnjnq8xbm0e7vWBNhUbWNFZKHEVEdkPNYanVczjAOeaAf3HDabdxSr/XWPt1W/7v1V/z59d/ydLybluP17BUERFpUtxh6Tt8UHQzXexfLFrdnYJHH+bRiZfRunUGxcXq6xo7JY4iIruotmGpe7VdwQVHxhhx7OP0y/mYZeWdufHZP/Dgmz+lvKL9dsdrWKqIiDQZXgWL34DP/gDL/0WXrL2ZUnEfF959GbPmtNIN0iZEiaOIyC6qHpbaLHMzQw55gxHHPs7/9B9Li2abmfJlHleMepAn3x3OFlpjtv2xGpYqIiKNVfxom/59l/LIjY/zHR6hrc1hwaoePPze/fQ97VLOz2/FTCWKTY4SRxGRODurjHrwfqs5ssdr3HbaWIZ+93XatylnWXln7n/jKh5/dwTrMg7Z4bG66yoiIo1Fzf7wlFPg6ac2MTD3HW6/ahRn5L1MC9vMxBnH8dCbRbxccgabKluS9XeoQn1dU2TuHnUMKSEvL89LSkqiDkNEEmhnSWHHjrBuHWzatO2Ydm0qGLjvZAbt+y+O7/s2R+//Hs0yt7C0vAt//+g0XvlwGOM/OYnNW1poCGojYWYfunte1HE0FuofRdJP/JSMVs2/Zsh33+DM773Iaf3/Toc2a1i1vgNPvHsJxW8X8P/bu/sYOer7juPv7z6d73w2fuTJxsYYAwUFG/OQkAIhJFQQRYCaNgqCxEVVKBaRAmnVQvpH1ahEyh8J0FBaocSAiyFPkISmkJYQGlltypMx4OIYbIODDbaB89Od7bvbnW//mNm92b29vTtu7d2Z+7yk0e789un3nZ2bz/5mZvc2vXvGsMcrD5OrUUbqiKOIJN5oA8LyntIHH6z/7zLKA8U9PSVOO+F1li54meWL1nHx6Ws5d9GLFHKDBIHxyttn861/+xseX3cVL7x5PkGQqfRBp6CKiEgSjJaZCxcGLJj2Kl++5Bk+eeYzfOqsp+me0kdP70x+/uLVPPrc53hqw+X0D04Z8TWG/iWHpImOOEa0R1WktcYy+BvLgBAgn68eEEI4X97cdXX0sfjYLZx63GZOPX4zpx3/OmcveIWPnPQqnYXDAAwU8zy/9XzW/u5i1m66mP95/ePsPTizqs/6ZdRk0hHH8VE+irRevdNGn3iiOZl57Iwezln4Eh+Zv44Ll/yWT5zxG2ZP6wFg887FPLXhch57/o/5r42XUizlx9RfHXFMroYZ6e6pnIArgE3AZuC20e5/7rnnejM89JD7woXuZuHlQw+1T9vKle3Rj3Zq0zJpj2WycqV7V5d7OLQLp3zevVAYvc2sfD3waZ37fNHcLX7+Kc/6lUv/3b908QN+21Xf9O+uuNkfu+Uaf+4b5/k79xzvvoaqade9c/1Xt1/m377uVv/iRQ/62QvWez7bX/U6tdPChePaNEgbAV7wNsipVk7jychm5aN7+26D2r1tsi8T1T88I2un0TMz8GOn7/SLTl/rf3bJKv+HP/26P3bLNf7mXQur8nDLnYv8+1++wa+/aLXPn/X7Ya8zlLkjv25XV1iDJFOjjEzlEUczywKvA5cD24HngWvd/bWRHtOMPaq1P9EP9Y98tKqtVjv1TcvkaLU5g4NOxgIyFtDREZDNBJSKJcyG2jMWkMmEl4W8k80EFIvD2wYHvdLWkQ+wjFOK7pe1EoVCQC5TolQKyGZKZDMlphSK5LIlglKJXLZIPjtIITdILjsYXR+gI9cfXub76cj101k4RFfhIFM7+ujqCC+7p/RyTOc+pnfur0z5XLHu+7qnbwY7euaxY888dvTMY8vuxWzedSpv7FzCll2L2X/omBHWiPrLsqsL/T+qBJvsRxzHm5HNOuK4Zg3c9BclMkEvvYe7CTyr7bKy6kPU7xQKsQyyADOnkHcymTDjDB/xuXI5AzP6+w3HCIIM2VwGMA73h5ftVn/8jJn4cujI99Pd0cvMqXuY1d1TuZwz7X1OmPEuJ854h3mzdnDizHc4adbbTOvsrTy6WMqyZddiXtp2DuveWs66N5ezftsyPuidM9KCp6sLVqwY25FO5WNyTcbvOF4AbHb3rQBm9gPgamDEgWMzlH+i/5GvfIErlz5JX/9Ueg9309c/lb7+qRwa6GSgWKC/2MFAscBAsUCxlCPwDKUgSynIEniGwDNVz2s4Zl71wd7MKx/EMxbUvR6fatvL85XLzPABQ/l1ypfxfpT71YhjuIcbYHerzJevB0Gm0hZ4pnJZdT2I5qP7196v/BxV12suy69Zfp54H2qvD6uhpq1e/eW2+PIxfPjyiw/MomVcfg9ql3ulPRPUf7/GcpuVqu4TtidvR1EQGAcHujjY3xVeRtcPHJ7Gm+8tYv+h6ZXpg97ZvH9gTtW0c9/xHOyfCgwP33JAx+XzMH069PQoFCW1WpaRc7u2sfWuxQAcONTNgcPT2H9oOgcOTaO/2EH/YAcDpUIlI+Pb/PL2urItzQQYXjfzylMuUySXLVauZzOlYfO12VgvD8vb93B5jbwdrcq4miyL51h5KgXZSlv5M0D8snx7yYffLz5f+9xVy2yErKuXeeX6ajMtvgzi2VYvy8qfKUb6TDJa20iZlrGAXLbU5LWyvmJpaBnXvh/FIFe5XgqyFEu5uu3xqer9jq3LMPRZqXbnbTZTIp8bpJAdoJAbmuI7ULOZYMQaBos53tl7Iu/sOZGNO/6AX234dGWH6Rs7l7Dt/YWjnnY6ezZ0d48t+5SJk0NaB47zgLdj89uBj9beycxuBG4EWLBgwYRftPxF4CdfvpKde4+ne0ovUzv6KlNXx0FmdO2lI99fOapSb8NZL5RqB1XuRsmz1cESZCvhUrXR8ur79A92VN2vdoNWO0CbSPDA0ACrHPJVQRQLp3qD1fgyGXZEzAJyuWLVh4fKoC1qG+01awfDVTWMMDCuV39l+dQMVOPvl2N1l3EpyDJQKlQGtqN9kBjptvj7XvvBJP642teI92PYgDz+IafBIL0UZId9QIr3pfx69QJ3sJSvnop5Dg9OqXyILAWjb6ZGGhDWHiWcyJ5ShaKkyKgZ2ex8hPBvbEbXDL720LeZ3rmfaZ0HKmcLTJtyoHKmQfeU3kpO1tsJV297VC/ziqUcA8UChwY7hz7cl3KUfOjDfr2pdhtZ3tZBuK2H+tk32g7EeFZVDU5rBltj2SFYzr/y/ePZV3fHb6xvUL3js+5O0zFkWm3WlN+HwVKe0mB2WAbVZkKjtnjO1WbTWAfHI75HNnREMv5ZobJTvs5O16qdEdGOh6xVz+eyxUpbvZ0R2UyJfHaw6nNe/LNI7bIMPMPB/i72lY6p7EgZKBY4ONBVOSBRnnp6Z7GnbyY9vbPo6ZtFT+8sPuidjdcciBhaDmPLzLvvVvZJtbQOHMfE3e8D7oPwVJyJPt+CBeEvNa5eu4LVa1dMuH8ik0m9IMvmoDTKKTzNOHVGwShSrdn5COWMnMWdT36tGU8nMqnUP111yFhPe9XppjIR9XdFJN8O4KTY/Pyo7Yi6447wDzIun4dCoT3aarVT37RM2qet1tF4za4uuOmm8FfYzMLL+++HVatGb7vvPrj33vDX24IgvLzuunCqbRMRoM0zslY7bR8n03a5ndpqtVPfWpWRK1cqM6UFRvrVnCRPhEdStwKLgALwMnBWo8foV1UnZ5uWSfssE5GjhUn+q6rjzUj9qmrr2yb7Mpns9Ssj5WhqlJGp/FVVADP7DHAXkAVWufsdje6v/1MlIjI5TPZfVYXxZaTyUURk8piMv6qKuz8BPNHqfoiIiLQbZaSIiIxXWr/jKCIiIiIiIk2igaOIiIiIiIg0pIGjiIiIiIiINKSBAZibJAAAB85JREFUo4iIiIiIiDSkgaOIiIiIiIg0pIGjiIiIiIiINKSBo4iIiIiIiDSkgaOIiIiIiIg0ZO7e6j60BTN7D9jWxKecA7zfxOdrhTTUAOmoQzW0hzTUAOmoYyI1LHT3uc3sTJodgXwErYPtQjW0jzTUoRraw0RrGDEjNXA8QszsBXc/r9X9mIg01ADpqEM1tIc01ADpqCMNNUxmaXj/VEN7SEMNkI46VEN7OJI16FRVERERERERaUgDRxEREREREWlIA8cj575Wd6AJ0lADpKMO1dAe0lADpKOONNQwmaXh/VMN7SENNUA66lAN7eGI1aDvOIqIiIiIiEhDOuIoIiIiIiIiDWngKCIiIiIiIg1p4HgEmNkVZrbJzDab2W2t7s9YmNkqM9ttZhtibbPM7CkzeyO6nNnKPo7GzE4ys2fM7DUz+z8z+2rUnpg6zGyKmT1nZi9HNfx91L7IzJ6N1qkfmlmh1X0djZllzewlM/tFNJ/EGt4ys1fNbL2ZvRC1JWZ9AjCzGWb2EzP7nZltNLMLk1SDmZ0eLf/ytN/MbklSDTIkifkIysh2oYxsH2nIR1BGjpcGjk1mZlngn4ArgTOBa83szNb2akweAK6oabsNeNrdlwBPR/PtrAj8pbufCXwMuDla9kmqox+4zN2XAsuAK8zsY8C3gDvd/VRgD/DnLezjWH0V2BibT2INAJ9092Wx/4mUpPUJ4G7gl+5+BrCU8D1JTA3uvila/suAc4GDwE9JUA0SSnA+gjKyXSgj20vS8xGUkeN+QU1NnIALgf+Izd8O3N7qfo2x7ycDG2Lzm4ATousnAJta3cdx1vNz4PKk1gF0AeuAjwLvA7movWoda8cJmB9tqC4DfgFY0mqI+vkWMKemLTHrE3AM8CbRD6ElsYaafv8R8N9JrmEyT0nOx6i/ysg2mpSRLa8h0fkY9VEZOc5JRxybbx7wdmx+e9SWRMe5+7vR9Z3Aca3szHiY2cnAOcCzJKyO6PSV9cBu4ClgC7DX3YvRXZKwTt0F/DUQRPOzSV4NAA78p5m9aGY3Rm1JWp8WAe8B90enRH3PzKaSrBrivgA8El1Pag2TWZryERK8DiojWy4NGZn0fARl5Lhp4Chj4uEui0T87xYz6wYeBW5x9/3x25JQh7uXPDzlYD5wAXBGi7s0Lmb2WWC3u7/Y6r40wUXuvpzw1LqbzeyS+I0JWJ9ywHLgn939HKCPmtNVElADANH3fa4Cflx7W1JqkPRK0jqojGytFGVk0vMRlJHjpoFj8+0ATorNz4/akmiXmZ0AEF3ubnF/RmVmecJAXOPuj0XNiasDwN33As8QnrIyw8xy0U3tvk79IXCVmb0F/IDwVJy7SVYNALj7juhyN+F3Bi4gWevTdmC7uz8bzf+EMCSTVEPZlcA6d98VzSexhskuTfkICVwHlZFtIRUZmYJ8BGXkuGng2HzPA0uiX8cqEB42frzFffqwHgdWRNdXEH4fom2ZmQHfBza6+3diNyWmDjOba2YzouudhN8/2UgYjn8S3a2ta3D32919vrufTLj+/9rdryNBNQCY2VQzm1a+TvjdgQ0kaH1y953A22Z2etT0KeA1ElRDzLUMnYIDyaxhsktTPkLC1kFlZHtIQ0amIR9BGflhWPSlSWkiM/sM4fnrWWCVu9/R4i6NysweAS4F5gC7gL8Dfgb8CFgAbAM+7+49rerjaMzsImAt8CpD3xv4OuF3OBJRh5mdDTxIuO5kgB+5+zfM7BTCPZOzgJeA6929v3U9HRszuxT4K3f/bNJqiPr702g2Bzzs7neY2WwSsj4BmNky4HtAAdgK3EC0bpGcGqYCvwdOcfd9UVui3gcJJTEfQRnZLpSR7SEt+QjKyHG/lgaOIiIiIiIi0ohOVRUREREREZGGNHAUERERERGRhjRwFBERERERkYY0cBQREREREZGGNHAUERERERGRhnKj30VEksTMSoQ/t54HisBq4E53Dxo+UEREJMWUjyITo4GjSPoccvdlAGZ2LPAwMJ3w/46JiIhMVspHkQnQqaoiKebuu4Ebga9Y6GQzW2tm66Lp4wBmttrMrik/zszWmNnVZnaWmT1nZuvN7BUzW9KqWkRERJpF+Sgyfubure6DiDSRmfW6e3dN217gdOAAELj74SjkHnH388zsE8Ct7n6NmR0DrAeWAHcC/+vua8ysAGTd/dDRrUhERGTilI8iE6NTVUUmlzxwj5ktA0rAaQDu/hszu9fM5gKfAx5196KZ/Rb4WzObDzzm7m+0rOciIiJHjvJRZBQ6VVUk5czsFMIQ3A3cCuwClgLnAYXYXVcD1wM3AKsA3P1h4CrgEPCEmV129HouIiJy5CgfRcZHRxxFUizaQ/ovwD3u7tFpNtvdPTCzFUA2dvcHgOeAne7+WvT4U4Ct7v6PZrYAOBv49VEtQkREpMmUjyLjp4GjSPp0mtl6hn5u/F+B70S33Qs8amZfAn4J9JUf5O67zGwj8LPYc30e+KKZDQI7gW8ehf6LiIgcCcpHkQnQj+OICABm1kX4/62Wu/u+VvdHRESkHSgfRUL6jqOIYGafBjYC31UoioiIhJSPIkN0xFFEREREREQa0hFHERERERERaUgDRxEREREREWlIA0cRERERERFpSANHERERERERaUgDRxEREREREWno/wGqsO9ba9chmgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x1080 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Which countries will be plotted\n",
    "example_countries = [\"Italy\", \"China\", \"Greece\", \"US\", \"United Kingdom\", \"Spain\"]\n",
    "\n",
    "cols = 2\n",
    "rows = np.ceil(len(example_countries) / cols)\n",
    "fig = plt.figure(figsize=(15, 15))\n",
    "plot_index = 1\n",
    "\n",
    "for country in example_countries:\n",
    "    # Get the dataset\n",
    "    full_x = np.array(x_data[:, np.newaxis])\n",
    "    full_y = np.array(confirmed_cases_df.loc[country][:, np.newaxis])\n",
    "    \n",
    "    # Create the features and predict using the best model of each country\n",
    "    model, degree = country_models[country]\n",
    "    polynomial_features = PolynomialFeatures(degree=degree)\n",
    "    x_poly = polynomial_features.fit_transform(full_x)\n",
    "    pred_Y = model.predict(x_poly)\n",
    "    \n",
    "    # Plot the true train, test points and the predicted line\n",
    "    ax = fig.add_subplot(rows, cols, plot_index)\n",
    "    plt.plot(full_x, pred_Y, color=\"orange\")\n",
    "    plt.scatter(full_x[:-test_days], full_y[:-test_days], color=\"blue\", label=\"Train\")\n",
    "    plt.scatter(full_x[-test_days:], full_y[-test_days:], color=\"red\", label=\"Test\")\n",
    "    \n",
    "    plt.xlabel(\"Days\")\n",
    "    plt.ylabel(\"Cases\")\n",
    "    plt.title(f\"{country} | Degree: {degree}\")\n",
    "    plt.legend()\n",
    "    plot_index += 1\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see for some countries that are experiencing great increase of cases our model is doing a good job with acceptable forecasts on the test set.  \n",
    "For some others like China our model predicts an increase which is currently not true. Increasing the tolerance of the `bic_criterion` will decrease the degree and create simpler models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of Degrees\n",
    "\n",
    "Following I calculate and visualize the distribution of degrees for all the best models of each country.  \n",
    "Increasing the `bic_criterion` value we will have bigger tolerance of error choosing simpler models and vice versa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:13:59.987898Z",
     "start_time": "2020-04-01T16:13:59.755624Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "models_degrees = np.array(list(country_models.values()))[:, 1]\n",
    "\n",
    "values, counts = np.unique(models_degrees, return_counts=True)\n",
    "plt.vlines(values, 0, counts, color='C0', lw=8)\n",
    "plt.xlabel(\"Degree\")\n",
    "plt.ylabel(\"Number of Models\")\n",
    "plt.title(f\"Distribution of Degrees/Complexity | BIC Tolerance = {bic_criterion}\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ARIMA\n",
    "\n",
    "[Autoregressive integrated moving average (ARIMA)](https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average) models are used for better understanding time series data or for predicting future values.  \n",
    "\n",
    "We will undergo the following stages:\n",
    "1. Stationarize the time series\n",
    "2. Find the best parameters for our model (p,d,q)\n",
    "3. Fit the model\n",
    "4. Perform predictions\n",
    "\n",
    "### Global Forecasting\n",
    "I will perform the above  steps on the global statistics (like I did with polynomial fitting). Again, the model is not perfect. Actually, there is no simple perfect model since a whole field named epidemiology is dedicated on predicting these numbers. However, for educational reasons I found interesting of following the above steps.\n",
    "\n",
    "#### Stationarize the time series\n",
    "\n",
    "In order to decide our parameters p, q, d we must first reach to a stationarized time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:08.138275Z",
     "start_time": "2020-04-01T16:14:07.964422Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First we plot the line of the global cases\n",
    "plt.plot(np.arange(len(global_cases_df)), global_cases_df)\n",
    "plt.xlabel(\"Day\")\n",
    "plt.ylabel(\"Cases\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected our series has no seasonality but is in an upward trend. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:09.678730Z",
     "start_time": "2020-04-01T16:14:09.650947Z"
    }
   },
   "outputs": [],
   "source": [
    "# We will use a part of the data for training\n",
    "testing_arima_days = 10\n",
    "global_cases_df.index = pd.to_datetime(global_cases_df.index)    # Cast our index from type Object to Datetime\n",
    "global_cases_df_train = global_cases_df[:-testing_arima_days]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:11.374561Z",
     "start_time": "2020-04-01T16:14:10.580799Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Seasonal decompose to extract trend, seasonality and residues\n",
    "result = seasonal_decompose(global_cases_df_train, model='multiplicative')\n",
    "result.plot()\n",
    "plt.gcf().autofmt_xdate()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we consider a multiplicative model (since we have an exponential increase as time increases) our model has the form of  \n",
    "$$y(t) = Level * Trend * Seasonality * Noise$$\n",
    "With seasonal and residuals being close to 1, we can see that our time series has **a trend, no seasonality and little to no noise.**  \n",
    "  \n",
    "Most of the forecasting models need our series to be stationarized (almost stationary) since this has the nice property of easily \"predicting the future will be the same as the past\".  \n",
    "  \n",
    "The test we will use for determining if our data is stationarized is the [Augmented Dickey–Fuller test](https://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test).\n",
    "\n",
    "**Null Hypothesis**: The series has a unit root\n",
    "\n",
    "**Alternate Hypothesis**: The series has no unit root.\n",
    "\n",
    "If we **fail to reject the null hypothesis**, we can say that the series **is non-stationary** [(ref)](https://www.kdnuggets.com/2020/01/predict-electricity-consumption-time-series-analysis.html) and we must transform it to stationarize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:13.643816Z",
     "start_time": "2020-04-01T16:14:13.614680Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results of dickey fuller test\n",
      "Test Statistics                 3.031854\n",
      "p-value                         1.000000\n",
      "No. of lags used                1.000000\n",
      "Number of observations used    68.000000\n",
      "critical value (1%)            -3.530399\n",
      "critical value (5%)            -2.905087\n",
      "critical value (10%)           -2.590001\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Perform dickey fuller test  \n",
    "print(\"Results of dickey fuller test\")\n",
    "adft = adfuller(global_cases_df, autolag='BIC')\n",
    "output = pd.Series(adft[0:4],index=['Test Statistics','p-value','No. of lags used','Number of observations used'])\n",
    "for key,values in adft[4].items():\n",
    "    output['critical value (%s)'%key] =  values\n",
    "print(output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected we are not at all able to reject the null hypothesis with a p-value of 0.998.  \n",
    "To get a stationary series we must eliminate the trend.  \n",
    "\n",
    "**Stationarization**:\n",
    "1. Take the log of the cases in order to have a constant standard deviation\n",
    "2. Subtract the moving average of each time step so as to have mean = 0\n",
    "3. Take care of any seasonality (in our case there is none)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:15.876796Z",
     "start_time": "2020-04-01T16:14:15.641744Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rolling_mean_window = 6\n",
    "\n",
    "# Take the log of the values to stabilize their rate of increase\n",
    "global_cases_df_log = np.log(global_cases_df_train)\n",
    "\n",
    "# Calculate the rolling average (the window is define by rolling_mean_window)\n",
    "moving_avg = global_cases_df_log.rolling(rolling_mean_window).mean()\n",
    "\n",
    "# Subtract the rolling average from the log number of cases\n",
    "global_cases_log_moving_avg_diff = global_cases_df_log - moving_avg\n",
    "global_cases_log_moving_avg_diff.dropna(inplace=True)\n",
    "\n",
    "plt.plot(global_cases_df_log, label=\"Log(cases)\")\n",
    "plt.plot(moving_avg, label=f\"Rolling Mean ({rolling_mean_window} days)\")\n",
    "plt.plot(global_cases_log_moving_avg_diff, label=\"Log(cases) - rolling_mean\")\n",
    "\n",
    "plt.gcf().autofmt_xdate()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:17.235222Z",
     "start_time": "2020-04-01T16:14:17.208827Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results of dickey fuller test\n",
      "Test Statistics                -2.753799\n",
      "p-value                         0.065182\n",
      "No. of lags used                0.000000\n",
      "Number of observations used    54.000000\n",
      "critical value (1%)            -3.557709\n",
      "critical value (5%)            -2.916770\n",
      "critical value (10%)           -2.596222\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# We again do the ADF test\n",
    "print(\"Results of dickey fuller test\")\n",
    "adft = adfuller(global_cases_log_moving_avg_diff, autolag='BIC')\n",
    "output = pd.Series(adft[0:4],index=['Test Statistics','p-value','No. of lags used','Number of observations used'])\n",
    "for key,values in adft[4].items():\n",
    "    output['critical value (%s)'%key] =  values\n",
    "print(output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a p-value of 0.06 and due to some anomalies (big jump around 2/15) I will consider this enough and continue with finding the p, q values for the ARIMA model.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define p, d, q\n",
    "\n",
    "ARIMA has 3 values that must be carefully defined:\n",
    "* **p**: Number of autoregressive terms\n",
    "* **d**: Number of nonseasonal differences needed for stationarity\n",
    "* **q**: Number of lagged forecast errors in the prediction equation\n",
    "  \n",
    "**In order to define p, q we will plot the Auto Correlation Function(ACF) and the Partially Auto Correlation Function(PACF).**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:21.433193Z",
     "start_time": "2020-04-01T16:14:21.088644Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mikexydas/pythonEnvs/thesisEnv/lib/python3.6/site-packages/statsmodels/tsa/stattools.py:572: FutureWarning: fft=True will become the default in a future version of statsmodels. To suppress this warning, explicitly set fft=False.\n",
      "  FutureWarning\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf = acf(global_cases_log_moving_avg_diff, nlags=15)\n",
    "pacf= pacf(global_cases_log_moving_avg_diff, nlags=15,method='ols')\n",
    "\n",
    "# ACF\n",
    "plt.subplot(121)\n",
    "plt.plot(acf) \n",
    "plt.axhline(y=0,linestyle='-',color='blue')\n",
    "plt.axhline(y=-1.96/np.sqrt(len(global_cases_log_moving_avg_diff)),linestyle='--',color='black')\n",
    "plt.axhline(y=1.96/np.sqrt(len(global_cases_log_moving_avg_diff)),linestyle='--',color='black')\n",
    "plt.title('Auto correlation function')\n",
    "plt.tight_layout()\n",
    "\n",
    "# PACF\n",
    "plt.subplot(122)\n",
    "plt.plot(pacf) \n",
    "plt.axhline(y=0,linestyle='-',color='blue')\n",
    "plt.axhline(y=-1.96/np.sqrt(len(global_cases_log_moving_avg_diff)),linestyle='--',color='black')\n",
    "plt.axhline(y=1.96/np.sqrt(len(global_cases_log_moving_avg_diff)),linestyle='--',color='black')\n",
    "plt.title('Partially auto correlation function')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe a continuous decrease of the ACF while PACF remains significant until value 3. This means that we have an **AR process** where p = 3, q = 0. q = 0, can also be explained by the fact that we have no residues from previous forecasts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting ARIMA model\n",
    "\n",
    "Having determined the nature of our process (AR(3)) and its values  we will then proceed on fitting on our training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:27.788661Z",
     "start_time": "2020-04-01T16:14:27.467953Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mikexydas/pythonEnvs/thesisEnv/lib/python3.6/site-packages/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency D will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/mikexydas/pythonEnvs/thesisEnv/lib/python3.6/site-packages/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency D will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RSS : 2.488376\n"
     ]
    }
   ],
   "source": [
    "model = ARIMA(global_cases_df_log, order=(3,1,0))\n",
    "fit_result = model.fit(disp = 0)\n",
    "\n",
    "plt.plot(global_cases_log_moving_avg_diff)\n",
    "plt.plot(fit_result.fittedvalues, color='red')\n",
    "plt.title(\"sum of squares of residuals\")\n",
    "\n",
    "plt.gcf().autofmt_xdate()\n",
    "plt.show()\n",
    "print('RSS : %f' %sum((fit_result.fittedvalues-global_cases_log_moving_avg_diff).dropna()**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Forecasting with ARIMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-01T16:14:30.016721Z",
     "start_time": "2020-04-01T16:14:29.570510Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We then forecast our last testing days\n",
    "fc, se, conf = fit_result.forecast(testing_arima_days, alpha=0.05)\n",
    "\n",
    "# Match the index of the correct dates so as to be on the correct day on the below plots\n",
    "fc_series = pd.Series(fc, index=global_cases_df.index[-testing_arima_days:])\n",
    "lower_series = pd.Series(conf[:, 0], index=global_cases_df.index[-testing_arima_days:])\n",
    "upper_series = pd.Series(conf[:, 1], index=global_cases_df.index[-testing_arima_days:])\n",
    "\n",
    "fig = plt.figure(figsize=(10,5), dpi=100)\n",
    "\n",
    "# Log Cases Plot\n",
    "ax = fig.add_subplot(1, 2, 1)\n",
    "plt.plot(global_cases_df_log, label='Training')\n",
    "plt.plot(fc_series, label='Forecast')\n",
    "plt.fill_between(lower_series.index, lower_series, upper_series, \n",
    "                 color='k', alpha=.15)\n",
    "plt.plot(np.log(global_cases_df[-testing_arima_days:]), label='True')\n",
    "\n",
    "plt.title('Forecast vs True (Log Cases)')\n",
    "plt.ylabel(\"Log(Cases)\")\n",
    "plt.legend()\n",
    "\n",
    "plt.grid()\n",
    "plt.gcf().autofmt_xdate()\n",
    "\n",
    "# Actual Scale Cases\n",
    "ax = fig.add_subplot(1, 2, 2)\n",
    "plt.plot(np.exp(global_cases_df_log), label='Training')\n",
    "plt.plot(np.exp(fc_series), label='Forecast')\n",
    "plt.plot(global_cases_df[-testing_arima_days:], label='True')\n",
    "\n",
    "plt.title('Forecast vs True (Actual Cases)')\n",
    "plt.ylabel(\"Log(Cases)\")\n",
    "plt.legend()\n",
    "\n",
    "plt.grid()\n",
    "plt.gcf().autofmt_xdate()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that we are getting close to true results that with great confidence (the grey area is the 95% confidence band). Admittedly, the problem with the global cases is easy for he polynomial and the ARIMA fitting. However, as days pass our forecast seems to predict higher number of cases than true. This is explained since on the testing days we can see the effect of the measures taken. An event that is not possible to be predicted by these models (at least with the data I have given them)."
   ]
  }
 ],
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    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
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    "function",
    "builtin_function_or_method",
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    "_Feature"
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 },
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}