Forecasting-VAR-Granger-Causlity.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forecasting Asset Prices Using VAR and Granger Causality\n",
    "\n",
    "Forecasting Gold and Oil has garnered major attention from academics, investors and Government agencies alike. These two products are known for their substantial influence on the global economy. However, what is the relationship between these two assets? What generally happens to Gold prices when Oil takes a plunge? We can use a statistical technique known as Granger Causality to test the relationships of Gold, Oil, and some other variables. We can also use a VAR model to forecast the future Gold & Oil prices.\n",
    "\n",
    "\n",
    "## Exploratory Analysis\n",
    "\n",
    "Lets begin to load the data and conduct some analysis with some visualizations to understand more of the data. We begin the importing the following packages:\n",
    "\n",
    "* **Pandas**\n",
    "* **Numpy**\n",
    "* **Matplotlib**\n",
    "* **Warnings**\n",
    "* **Quandl**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import quandl\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `pandas`, `numpy`, and `matplotlib` should be familiar with everyone conducting Data Science in Python. However, one particular module that is particularlly new is the module is `quandl`, which allows users to extract financial and economic data. You can acqure all sorts of data from all different types of asset classes and data types from many different regions in the world."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Importing the S&P 500 Close from Google Finance\n",
    "\n",
    "sp500 = pd.read_csv('GSPC.csv', usecols =['Date', 'Adj Close'])\n",
    "sp500['Date'] = pd.to_datetime(sp500['Date'])\n",
    "sp500.set_index('Date', inplace=True)\n",
    "sp500 = sp500.rename(columns = {'Adj Close': 'S&P 500'})\n",
    "\n",
    "# starting the quandl API\n",
    "quandl.ApiConfig.api_key = 'tJKSQn1pHLbyo1mu1wYn'\n",
    "\n",
    "# importing the tickers\n",
    "gold = quandl.get('LBMA/GOLD')\n",
    "silver = quandl.get('LBMA/SILVER')\n",
    "oil = quandl.get('CHRIS/ICE_G6')\n",
    "dollar = quandl.get('CHRIS/ICE_DX1')\n",
    "treasury = quandl.get('FRED/DGS10')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purposes of this tutorial, we will extract six different variables: Gold, Silver, Oil, US Dollar, Interest Rates, and the Stock Market Index. The interest rate of our choice will be based on the 10-Year Treasury, while the stock market index we're using is the S&P 500.\n",
    "\n",
    "The stock market index are the only variables that we were unable to extract directly from the quandl database. Instead, we have decided to download the information from the [Federal Reserve Economic Database](https://fred.stlouisfed.org/) (FRED) directly and import using  `pd.read_csv` argument.\n",
    "\n",
    "We're interested in discovering the degree to which commodities, currencies and interest rates have on U.S. stocks. For this reasons, we have decided to use the following variables.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# conducting an inner merging each dataframe onto one another \n",
    "# based on the index 'date' \n",
    "df = pd.merge(gold['USD (AM)'], silver['USD'], how='inner', on ='Date')\n",
    "df = df.merge(oil['Settle'], on='Date', how='inner')\n",
    "df = df.merge(dollar['Settle'], on = 'Date', how='inner')\n",
    "df = df.merge(sp500, on='Date', how='inner')\n",
    "df = df.merge(treasury, on='Date', how='inner')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From there, we will rename the columns of the dataframe to make it easier to call the information within."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gold</th>\n",
       "      <th>Silver</th>\n",
       "      <th>Oil</th>\n",
       "      <th>Dollar</th>\n",
       "      <th>S&amp;P 500</th>\n",
       "      <th>Value</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1990-08-17</td>\n",
       "      <td>410.50</td>\n",
       "      <td>5.2100</td>\n",
       "      <td>220.5</td>\n",
       "      <td>85.79</td>\n",
       "      <td>327.829987</td>\n",
       "      <td>8.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-20</td>\n",
       "      <td>410.90</td>\n",
       "      <td>5.2010</td>\n",
       "      <td>232.0</td>\n",
       "      <td>86.45</td>\n",
       "      <td>328.510010</td>\n",
       "      <td>8.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-21</td>\n",
       "      <td>407.85</td>\n",
       "      <td>5.1600</td>\n",
       "      <td>244.0</td>\n",
       "      <td>86.44</td>\n",
       "      <td>321.859985</td>\n",
       "      <td>8.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-22</td>\n",
       "      <td>410.00</td>\n",
       "      <td>5.1165</td>\n",
       "      <td>251.0</td>\n",
       "      <td>85.99</td>\n",
       "      <td>316.549988</td>\n",
       "      <td>8.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-23</td>\n",
       "      <td>415.70</td>\n",
       "      <td>5.2160</td>\n",
       "      <td>268.0</td>\n",
       "      <td>85.25</td>\n",
       "      <td>307.059998</td>\n",
       "      <td>9.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Gold  Silver    Oil  Dollar     S&P 500  Value\n",
       "Date                                                        \n",
       "1990-08-17  410.50  5.2100  220.5   85.79  327.829987   8.80\n",
       "1990-08-20  410.90  5.2010  232.0   86.45  328.510010   8.81\n",
       "1990-08-21  407.85  5.1600  244.0   86.44  321.859985   8.84\n",
       "1990-08-22  410.00  5.1165  251.0   85.99  316.549988   8.91\n",
       "1990-08-23  415.70  5.2160  268.0   85.25  307.059998   9.00"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Renaming the columns for the sake of ease\n",
    "df.rename(columns={'USD (AM)':'Gold',\n",
    "                   'USD':'Silver',\n",
    "                   'Settle_x':'Oil',\n",
    "                   'Settle_y':'Dollar',\n",
    "                   'Value_x':'Index',\n",
    "                   'Value_y':'Interest'},\n",
    "         inplace=True)\n",
    "\n",
    "# populating the first 5 values\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following shows the first 5 values of the dataframe that we just created. As usual with data, it would be easier to assess a trend through visualization. We can create a script that allows us to plot all six of our variables into a single graph. We can do this easily with the `plotting` submodule in the `pandas` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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IRgEAykcQjGrYMN6eHHyaNEnq1CnettNOUvfu/kEtmEG1ySbxPgcdFD+ePr1m4wUAACikdAnMf/vN7ygcWLSouGMC8oBgFACgfPz6qy+Tk5evumr8uG1b6Ysv4m0//iiNGuUDWZdf7tuaN4/3eeQRaZ99pGuv9ccEowAAQDl74IGwHsyMeuedeJ9Jk4o3HiBPCEYBAMrHFVf4csiQeHvfvql9W7eWHntM6tkz8/1WWil+vPrq0uDB0nbb+eNDD5UuuST38QIFYGYNzWy0mb2WOO5kZsPNbIKZPWtmjUs9RgBAkfznP2E9mBm1cGG8zxlnFG88QJ4QjAIAlI8XX/TlPfdI990XtjdtGtbXWy+sn3Za5cGk9u3Tt6++eli/9VZp4sTsxwoUzvmSvokc3yzpDudcZ0mzJPFXBwDUR8HMqF694u3pdtkDyhzBKABA+dlxR+nkk6Vtt5Veey1+LnmnvWigqrqSl+899FD290B5WL5cmjOn1KPIGzPrKOlASY8kjk3SnpKeT3TpL+nQ0owOAFBSmYJOBKNQCxGMAgCUnzXX9DvoDR8uHXhg/FzyTjKZglHjx2e+f3SbZMnPjkLttPfefjnmjz+WeiT58m9Jl0gKftDbSvrTObcscTxFUodSDAwAUGKZdtMDaiGCUQCA8tOyZWpbsBwveWe9dH0lacMNM99//vzcxoXy8957vnz33ZIOIx/MrKek6c65kdHmNF1dkYYEACi1s84K647//aPuqKi6CwAARRA8YB1xRPrzwdvAhg3j7clJyiXpr3+t/LO6d5caNOANY10yYUKpR5APO0k62MwOkNRUUmv5mVJtzKwiMTuqo6RfSzhGAEAxLV4c1jMFo046qThjAfKImVEAgNKZP1869VSfH6pB4ldSo0bp+wYPYJY0USQ6U6p7d2nZMulf/6r8cysqfH6FAQNyGjZKYO5c6f77U3cQCkQT3tdSzrnLnHMdnXPrSjpW0jvOuRMkvSvpyES3UyQNKtEQAQDFFv29N2yY9NVXqX2SX9QBtUBOwSgze8zMppvZ2EjbNWb2i5l9kfg6IHLuMjObaGbjzWy/SHuPRNtEM7u0Zt8KAKDWuf12qX9/6Yknwrbk5OKBxond7Js1i7dHg1evvZbdA9lee1W/L0qrdWupd29p003Tvxl+8MHij6l4/ibpQjObKJ9D6tESjwcAUCzRYNTtt0u//Zbah5neqIVyXabXT9I9kpJfKd/hnIu9jjazTeTf7m0qaU1Jb5tZkMjjXkn7yCfj/NzMXnHOfZ3jmAAAtc2kSalt7dun73vRRdLkydJ116Weu+UWqVMnaY01svv8NdeUNtggc94plIfvvgvrkyb5GVK9e/vjjTf25dFHF39cBeSce0/Se4n6D5K2LeV4AAAlkjwj+K23UvsQjEItlFMwyjn3gZmtW83uh0h6xjm3WNKkxFu94IFqYuIBS2b2TKIvwSgAqC/SzXBJ3ukusMoq0sCB6c9dfHHuY2jY0C/tQ/lKDkDee6+0885St27S77/7QCQAAHVRcjDqtttS+xCMQi2U75xRfcxsTGIZ38qJtg6Sfo70CbYkztQOAKgv+vVLbSt2YCHIH4Xy9eST8eOvv5Y231z69FNpxgxptdVKMy4AAAot3bK8ZASjUAvlMxh1v6T1JW0haaqkIGSbaUtitioGAKRasqS4n1dRwcyocrfllunbx4zx5aabFm8sAAAUyx9/SN9/n/7cGWeEL9My7bIHlLG8BaOcc9Occ8udcyskPaxwKd4USWtFugZbEmdqBwDUFxWR1eKXX+5nRR1/fHHH0LCh36kt0y5tKL1MieY//dSX2eYKAwCgNsiUnkDyOTaDHYYrmxlFoAplKm/BKDOLZpw9TFKw094rko41syZm1klSZ0mfSfpcUmcz62RmjeWTnL+Sr/EAAMrcjBnhjKR//1u6/nrphx+kVVct7jgaNvRT4DPt4ofSmzfPl+PHx9sff9yXbGkNAKiLkncQjmrQoOpgVO/evh8zwFGGckpgbmZPS9pd0qpmNkXS1ZJ2N7Mt5JfaTZb0f5LknBtnZs/JJyZfJulc59zyxH36SHpLUkNJjznnxtXouwEA1B6PPRbWzz+/dOP4NTIp97ffmGVTjoJg1CqrpD9/5pnFGwsAAMVSWTAqCEQ1aJA5GHX//b6cN09q0ya/YwNqKNfd9I5L0/xoJf1vkHRDmvbXJb2eyxgAALVcEGBo2bK045g5M6wvXly6cSCzefP87Ke2baV33pFmz5YOO8yfa9u28od1AABqI+d8XqhMqhOMCjTI975lQM3xUwkAKL4RI/yyPEl67bXSjiW6kx7T2MvP/PnSyy9LLVr4B+899pAOPVR6+GGfZ+xX0k0CAOqgpUulRYsyn3/vPV9WJxhl6fYOA0orp5lRAABkZcQIPz18gw38m75ttgnPrbZa6cYl+Ye9wJ9/hvXZs6Vx46Qddyz+mOCNHi1ttZWvz5kTP9erV/HHAwBAsVT1giwajKoqSTlJzFGGmBkFACgc53yS6W22kTp39m/u5s+P99loo9KMLZ1Zs8L6fvtJO+0kfftt6cZT3wWBKAAA6pvoy7LKNuowq3pmFMEolCGCUQCAwhk0SDr99PB4xx2lq6+O9ymnPAb77CN99JGvDx/uS5aBAQCAYosGo3bYIXO/Bg2kH3/0z1hffZW+D8EolKEy+gsAAFDnzJgRPx4+XPr99/D42GOLO57q2Hnn+HHfvqUZBwAAqL+iy/QaN87cr0EDn1bgk0+kc89N36eqF2t//in99FP2YwRqgGAUAKAwnPN5l5K1bu3LddcNtxwuZ5neMqK4SC4PAKhPojv8pgtGrbeeL6MzzEeMSH+vceMyf87UqdLKK0vrrFP1cj8gjwhGAQAKo39/6eKLU9vvuceXX3zhk5rXZv/9r8/V8PXXpR5Jqvnz4w+ytVHPnr68+urK82UAAFDXPPZYWG/UKPX8q6/6MhqMWrgw3CV4wYKwPbpzcLI11wzryZuFAAVEMAoAUBjRh6h0ghlSpTZkiLT33rldGwRLHnkkf+PJl5YtpaZNpQcfLOzn/PKLD3wVIh/F4sX+5+Saa/J/bwAAytkaa4T1dMGoYGaUWbz9jTd8ucceYdtaa1XvM0eP9ve7667qjxPIEcEoAEBhDBtW+fnkh6dS2Xtv6frr423JS8Ieflh6++3M9+jUKf/jypezz/YBo5pMvV+6VBo6NDXgtGCB1LGjD3yddpr04Yf+rWy+DBnCW1oAQP0UnbH0l7+knm/SxJfJG8EEM6I++yxsu+ii6n3mnnv68vzzq9cfqAGCUQCA4vj221KPILNNNw0f6lZbLTWQdtZZfqe9aEAnGpiJBtac88GtUi7dSw4adewoHXVU7ve7/noftEueATZvXljv31/aZRepeXNpwIDs7v/nn9K22/pgViC6ixAAAPXNokVhPd1uesGzxx9/xNvTzTz/9NP8jQvIE4JRAIDi6NIlrHfsWLpxpNOypX/o22svvwNg8GYw2ZIlYf3pp8P6JZeE9dGjpSuv9AGuUknexVCSXnwxPuZsDB/uy/fei7efdVb6/ldckd39n35a+vxzH8wKlOPSRwAAimXUKF++8opUURG2L10an4WcPPP51Veln3/O7TM33jisF2L5PRBBMAoAUHivvBI/PuKI0oyjKulyMkRFE4JH3zIuXBjmyOrePWxPfltZLG++mb79+ONzu99bb6VvHzQoffvPP/sldtWxYoXUu3d4/O67vgwS3QMAUB/dcosvk3f1rajwOSEzue++9M8f48dX/ZnffBPWp0+vuj9QAwSjAACFsfLKYf2gg+LnTjqpuGOprqqCUTfdFNaTd3c744zwLWagbVtp2rT8jC0bp5xSmPsOHFj9vvvuW723qsnLGffc0weoevTwxzfeWP3PBACgrqmoyD7PZtA/+iy20UbZ3ePPP7PrD2SJYBQAIP8WLJBmzZI6d44noP7hB+nRR+Ozh8pJVcGo+fPD+vDhPtgUle77+uij9PcaPDi/yb4lvzwv+ja0W7f4bjqSf0CtyRI4M79EoDoPqQ0aVJ04PV2C8v33D/NOHXts9mMEAKCu6NAh+2uC3fBOPrnyfpW9NPrtt+w/F8gCwSgAQP498IAvJ0yQWrUK2zt1kk4/vTRjqo7kYFTz5vHjVVYJ6wsWSG3aVH3P5DxLkvTkk9J++6Xev6ZWXz0eIPvPf6T//tcveYvm7DrzzPTXjx/vg0OPPy4dcIAPJN19d2q/xo3Dt62XXuofZoOvaFJzqfKlir/8Iu20U2r74MHS77/7evTnBwCA+iLIPXnccf5F0AUXSC+9VL1rH33Ul3feGW9PfpEUTT+QbPfd/efOnl29zwSylFMwysweM7PpZjY20narmX1rZmPM7CUza5NoX9fMFprZF4mvByLXdDezr8xsopndZVYu+3wDAGrkiSd8ucUWpR1HtpJ30XvwwfjxtdeG9TlzfOLzqqQL5kTzP9Q0Qahz0ty56c81aCA1ayade27VY502zU/h32UXHzB84w1p5sz020lHbbJJ/LhFi/hxEFRK5+KLK7+3RDAKAFA/tW4trbGG/10uSbffLh16aM3umfyCKJihvdpqma+pzos3IAe5zozqJ6lHUtsQSV2dc90kfSfpssi5751zWyS+zo603y/pLEmdE1/J9wQA1EbB7Jjnny/tOLJ18MHx486d4zu8BYYOlSZNktq394GlXr1S+9x2W1hPDhZ16xbWZ83KfbyStM02/oH1uutSz0XfeEbf96RLZB7kthozJmyrTgL26M47gfHjfc4oyc/MyiSad2vYML/jX3LwqUmTqscAAEBds3Bh/mdQ9+yZ+hmSdMwx+f0coBpyCkY55z6Q9EdS22Dn3LLE4aeSKt2328zaS2rtnPvEOeckDZBUw1AvAKAkBg2S2rXzuYQkaeJEX66/funGlIt11w3rn3wibbdd6o4148ZJe+/t685JXbtKDz+cGnC68MLw+3/22fi56DT5muZkGDnSl1ddlXpupZXC+ogRYb1du7C+fLmfybb55qnX77BDWB89Ov3np0uIuuGG0lpr+fpFF2Xekeerr3xAzzlp552lww6Lzxp79dX01wEAUNctWlT5rnnV8cQT0jXXhMfR3fKCz5D8LOp0zwFAARUqZ9Tpkt6IHHcys9Fm9r6ZBa+YO0iaEukzJdEGAKhNFi3y08anT/eBh+Qd5WqTTz4J69tv78sjj4z36do1rDduHNajy9PeftuXl17qy9de8zOTxo3zx9G8SjNn1mzMmRx9tNQx8l4omg8rePiUfH6oTAlOo7O2ttjCB42WL5eeeSZsz7T8L9iSWpI+/TT1/Jgx0pdfpj78rrNOmH8q+Q1uHWdmTc3sMzP70szGmdm1ifZOZjbczCaY2bNm1riqewEAarnFi2sejGrfXrr66szng5lRzZpVvtNxTVMKAGnkPRhlZpdLWibpqUTTVElrO+e2lHShpIFm1lpSuvxQ/JQDQG3y0kv+ASYwalT6JWC1RbqHvjPPlL7/Pn3/aCLw6DK4vfby5QYb+HLQIF8Gu9j95z9h35oEo6L3SRbM3gr8/LPUu7evB3mcli/PnMw8KjpDqUEDv3yxKtFk71dcEdZvvtn/swqCUJXllKp/Fkva0zm3uaQtJPUws+0l3SzpDudcZ0mzJJ1RwjECAArFOf8y7PTT8zMzKvgd++uv6c8/+aQvP/3UJyyXfML0ZAsW1GwcQBp5DUaZ2SmSeko6IbH0Ts65xc65mYn6SEnfS9pQfiZUdClfR0kZ/isBAJSlW2+NH6+zjs8XJPkd3Gqb1q1T28yk9dbzSUSTHXRQ/Pjbb6XPPguPg2BUwDl/TbC0TpI+/zysX3FFuB1zdRx9dOZzyQlH27ULd9UJglhBnqh0okv0kmcobbWV9Nhj8SV16QT/LIJ+CxaEs8UC6RK811POC6bNNUp8OUl7SgoSsPUXaQ0AoO6ZOdO/8Bk+3M9anjMn+7yJ77wTP/7iC19Gl+dHPZWYP/Lzz1L37n5G9N//ntpvyZLsxgFUQ96CUWbWQ9LfJB3snFsQaV/NzBom6uvJJyr/wTk3VdJcM9s+sYveyZIG5Ws8AIA8ufLKzFO3o7NfpHhw4txzCzemQoCzwyEAACAASURBVFm2LPO5l1+OHwdBt6guXXxC8UDHpPSJgwf7JXtRN97o7zV9unTDDdL552c35kyiM9YCFRVhfdkyqUPS6viBA8P6BRdUfv/TTosvWUynffuwfvrp6YNfwXJISJLMrKGZfSFpuvzmMN9L+jOSl5O0BgBQF40dGz+eP196993qX7/zzvHfu1I4W71BA7+xSPImIcHufMGGM23axJ8VAtHl/UCe5BSMMrOnJX0iqYuZTTGzMyTdI6mVpCFm9oWZPZDovqukMWb2pfxbvbOdc0Hy83MkPSJpovzDVjTPFACgHFx/fTiNO1mDpF8jwU5sye21RRCMOuCA1HNdusSPN9ww+/snJw4NbLRR/K1lrrkZbr89rEd30kvn449T29q29XmzRoyofJvn6lpzzbD++ON+hhkq5Zxb7pzbQn7G+LaS0mxXSFoDAKhzKnshVh0dOsR3qZXiL42aN/cBrhUrwrZg45nVVw/bos8PwSzrr7+u2diANHLdTe8451x751wj51xH59yjzrkNnHNrOee2SHydnej7gnNuU+fc5s65rZxzr0buM8I519U5t75zrk+wtA8AUEtk2u1sk02KO458CZa9nXpq6rk2baS+fbO/Z/JSxupo0CBMdl4drVv7ANYFF/ilguecIx1xROXX/PJLatsqq/iZSt27+zes55wTT+qerQYNpB9/zHyeHBQZOef+lPSepO0ltTGz4FU1aQ0AoC4KAkNRN9yQ3T3++CN+HM1nuc46PhA1cmQYkAqW30U3ZOnWLax36uTLINE5kEe19NU1AKDoom/SqhLkIKhtevaU5s6Vjjoq/fmg/frrq3/P007LfC45p1TUfffFj++9Vxo9On3faBL0Ll1Sr4265BJfDhgQtp1/vnT44dLWW4dtFRX+PjVdRrf22qltTZv6XFHplhLWY4nUBm0S9WaS9pb0jaR3JQXbOp4i0hoAQN2TLhiVnP+xMmapM6OigtnK224r/eUvvp4uGGUmbbqprwczmg86SJoxo/pjAaqBYBQAILM5c8J6ZfkCeveOBy0226xwYyq0li0zn9txR//PJF1yz0zatk0fyOvaNTUPVVQ0oDRrltSnj08cnm4ScWUPn+k+V5LefDNsu+km6YUXqn+PXO27ry8nTPDfD5K1l/SumY2R9LmkIc651+Rzcl5oZhMltZX0aAnHCAAohHTBqHSbp1TG0m1Yn9C8eVi/915fBsGoRo3ifd98U7rttnjuy+hSPiAPCEYBADIbMSKsT54szZsXHt9xR1i/9974cq7KHoZqu1atsv/+kvvfeKP05ZfxBPCvvy598IG06qphW7CMLZq/4emnw/pWW/kp9NmMJ3lHnZ9+qvnW0VV56y2/+95bb/nAXHJid0iSnHNjnHNbOue6JdIY/CPR/oNzbttESoSjnHNVJAQDANQqixeHScSjsgkANWkSf4ZIFg1GSX65/pIl/oVW8kutjh2lCy/MPYclUA1pUuUDAJAQDXJsuqmfrv399/74wgt9ed55YZ/zzpM2TpdvGf9z4IHSZZf5evShcbfd/IPijBnhP/c+ffwOhdFlgS1ahPW5cyufyZXOPvvEj7N965qLYEaUVLcDlQAA5OLCC+MvmwLZ/I7/5z/ju+kFy/IDrVvHj2+91b8YW7688nvedVd4vHRp6iwqIEfMjAIAZHb//fHjH37wb9GieQNmzQrrd93lk14js7vvDuvRB7po/qQbb/Tl44/72Wk9eoTnZs8O6/PmpW7TXBUzv3Qw3RgAAEDxRWeiR0VfQFUlCEQFZXRHWyl1VvKdd0qTJlV+z+TZVNOnV388QBUIRgEAMkt+CJF8fqjotHGCGdXzxht+hlOwM01g7lzp11/jM4aOOy7zfaLBv7lzsw9GSfGE5wAAoLSizwAPPRTWqxOMGjYsvsQvyD2V/HyWTX7JqOgs7qFDc7sHkAbBKABAZiuvnNr2aFLu5L/+tThjqe169JAuvzy1vWXL+LR6SVpppcz3CZLKz53rZ0blsuzt4Yd9mS4/BQAAKJ3oTOl0LwWT7byzdMQRhRvPjBnSSSf5+imnFO5zUO8QjAIAZBZ9O5fOZZeF2/8if5LzOkQNH+7Lc8/1ZXRXvOrq1csnJS3kwysAAMhe48ZhPZtlelXJNDOqX7+qr50/P3/jABIIRgEAMgt2c8vkyCOLM476prKp9J984mdFPfGEP07O6wUAAGqvmqZCyLQD3pZbxjdECQSznioT3U0ZyBOCUQCA9KqznW/nzoUfR33XoIEPOP30kz/+4w/pvffC8/vvX5JhAQCAPGkQ+bO8prOhMj2/mfl0AWecEbb16hX/7EyOPtqXTZvWbGxAREWpBwAAKFOLFvnypJPCWTiByy+Xdtstt+TZyE63btLZZ8fbDj44rK+1VnHHAwAA8qsi8mf5VltJ111X89lImXJKPvSQ31W3RQvpyiurd6/TT/eBq733rtmYgAiCUQCA9Hr39mXz5tKTT/qp4scc49v69o3vroL8e/556eKLpU8/zdznhBOq90YTAACUr+hyvIYNpSuuyP1ee+whvfCCtN566c83aCDdfHN29zTzwatly3IfF5CEJ1gAQKoffwwTWq5Y4YMewRRtiUBUMRxxhPTDD1KTJmHb22/H+7CTIQAAtV8uuaEy6d9fGjJE2nff/N1T8rO3CEYhj5gZBQBI1adPWJ8+vXTjQNxee4X1Hj18MlIAAFC7VbZxSbZatCjMcjqCUciznGZGmdljZjbdzMZG2lYxsyFmNiFRrpxoNzO7y8wmmtkYM9sqcs0pif4TzOyUmn87AIC8iAY9mjUL65Mn+1lTKJ3PP5c+/lh6441SjwQAAORDpvxO5aSiQlq6tNSjQB2S6zK9fpJ6JLVdKmmoc66zpKGJY0naX1LnxNdZku6XfPBK0tWStpO0raSrgwAWACCDhQula68t/Ba7334b1v/yl7C+zjrS2msX9rNRua23lnbYodSjAAAA+RIEoz77rLTjqEymmVETJ0rDhxd/PKj1cgpGOec+kPRHUvMhkvon6v0lHRppH+C8TyW1MbP2kvaTNMQ594dzbpakIUoNcAEAoi67TLrmGulvfyvcZzz3nPTgg74+dCiBDwAAgEL59lvptdd8Ps5ttin1aDJr1MgHnYLdlgOdO0vbb1+aMaFWy2cC83bOuamSlChXT7R3kPRzpN+URFumdgBAJsESuT+S3wfk0WmnhfV8JtQEAABA3MYb+/L330s7jqpMnuzLDhn+ZF++vGhDQd1QjN300i2AdZW0AwAyWbDAl02b5nb9L79I778fb5s1y++Yl/wZkrTaarl9DgAAAOqeTC9En322uONArZfPYNS0xPI7Jcpg+6UpktaK9Oso6ddK2gEAmQwe7MvWrePtAwdW7yFg/fWl3XcPA05ffSWtsop00UXp+2+0Uc5DBQAAQB3k0swhGTeu+ONArZbPYNQrkoId8U6RNCjSfnJiV73tJc1OLON7S9K+ZrZyInH5vok2AEA60enPK60UP3fCCdKxx0qLF1d+j+D8woW+DGZJ3XFH2Kd5cz/zav78mo0XAAAAdc/06altN95Y/HGgVsspGGVmT0v6RFIXM5tiZmdIuknSPmY2QdI+iWNJel3SD5ImSnpYUm9Jcs79Iek6SZ8nvv6RaAMApDNtWlhPnhkV+PTT6t0rCEJFc0ING+Z3c1mwwCctb948t3ECAAAgOy1blnoE1bd0qS8nTCjtOFCrVeRykXPuuAyn9krT10k6N8N9HpP0WC5jAIB6Z+7csH7xxX72Up8+8anSq6yS+fpovyOOkD74QHr44bBt113D+qhRNR8vAAAAqmfgwFKPoHI9ekhvvunrL7/sn0EnToz3ufRSafPNpeMyhQuAUDESmAMA8uGf/4wfn3eeL7/5JmwL3lSlM2ZM6vHIken7zp6d/fgAAACQm4MOKvUIKvfMM2H9vPOk0aNTX4LefLN0/PHFHRdqLYJRAFAb3HGH1L9/avuRR0rdu4fH77yT+R7JAaaLL87cNzlwBQAAgPyK7mZc7pLzlY4bF9+BOZMlS1JnUAEiGAUAtcOFF6Zvf+EFadGi8DhYXtevnz8X9fjj8eMgiXmyoUOlzTbLaZgAAACopspeIpajffYJ6++/nzkYFW0/4gipc2fpu+8KOzbUOgSjAKDc/fBD9fuOGOHL007zs6ai+vWr+vqrrpL23LP6nwcAAIDcBEGbE08s7Tiqa/PNw/ojj2QORr34Ylh/7TVfTpoU77NihfT66/HdolGvEIwCgHI3eHD1+7ZtK02enN39n3tO+vpraZddpKOOyu5aAAAA5KZXL19+8UVpx1FdV18t7bZbePznn+n7tWqV2tajR3wznUcekQ480L8IRb1EMAoAyt3ixWG9Uyf/yzydTp18306dUs/9/HNYP+aY+LnNNpM23tjvrte1a83HCwAAUEqzZ0tDhpR6FFWbMcOX3bqVdhzV1bKl9N57vtxvv3Cn59694/1mzUp//S+/+HLxYun//s/Xb7yxIENF+SMYBQDlLprc8v3341Ofo1q0kObPT20fMEBae+3wOLobiiStvnrNxwigxsxsLTN718y+MbNxZnZ+on0VMxtiZhMS5cqlHisAlC3npDZtpH33DXNplrvbby/1CLLTpIkPKAXL9M46K37+o4/CekVFWJ83z5dz5sT7p3t+Lab77sv8fI2CIRgFAOXupZfC+lprSc2aSffcE+/TrZsPRqXLL3XKKWG9bVtfXn65LzfcMHVbXgClskzSX51zG0vaXtK5ZraJpEslDXXOdZY0NHEMAEhn2bKw/scfpRtHNmrbi8EmTfzspyuv9MfNm8fPP/KINGyYNHVq/N9HsLlOcv6oaGL0Ylq+XDKTzj3XJ1pHURGMAoByN2xYaltyssd//cu/eYr+wk/n9NN9ed11fobUu+/mZ4wAasw5N9U5NypRnyvpG0kdJB0iqX+iW39Jh5ZmhABQC0ycGNZbtCjdOKprxx19QKQ2adJE+vLL8Lh5c2nMGOlvfwvbdt1VWnPN+HVXXCGNH5+6o/MnnxRurJUZOjR+PHJkacZRTxGMAoBytHSpdO+9fvrzqqv6tujbvWOO8b/gX33VT0ffZx+f96kqQRDLLLwHgLJjZutK2lLScEntnHNTJR+wklTLXqEDQBFNmBDWq3pJV0rBUraPPy7tOHIxZUr8uHlzn4P0ppuqvnajjaQ77vD1vn3D9mnT8je+6kr++dh6a/+MvGRJ8cdSDxGMAoBy9NBDUp8+/o2ec1L79tLKkTQx7dr5JJA9e4Zt0TeBgWi+KYlfrkAtYGYtJb0gqa9zbk5V/QEAETNnhvVyCUb94x8+yPH77+GYgt2SjzyydOPK1dKl8eNmzSrvH50xJUmDBvlyu+3CtjXWqPm4stW4cfr2zz8v7jjqKYJRAFCOoruQzJwpdelS9TXvvZfaNnt2/Hhl8h4D5czMGskHop5yzgXZVKeZWfvE+faSppdqfABQ9qKBEefC+ooVfge4Rx4pzOe+9VZ8VlbU1Vf7crXVpEaNfD14RuvTpzDjKaYmTcL6+eennu/aVXrqqdT2rbf2y/lKJVPi9FtvLe448unjj6WttirNTLMsEYwCgHLUqlX8eIMNcrvPzjvHj1dbLbf7ACg4MzNJj0r6xjkX3VrpFUnBTgSnSBpU7LEBQK3RsGFYj84Qnz3bz0Y688z8f6ZzUo8efmOYL75IzYmUbPx46c47fX2ddfI/nmI69th4zqv11w/rQ4dKe+8tHXSQdPzxqdd27BjOEJNSl/8VWnQWXdSgQdJPPxV3LPly0knS6NFSv36lHkmVCEYBQDlKTriZ64PK11/7snlz/yBw2mk1GxeAQtpJ0kmS9jSzLxJfB0i6SdI+ZjZB0j6JYwBAOtGUBJ99Fs42j86Syrfoc9qWW0p77RUeJ89Sl+LJv4PcoLXR449LTz8dbzv7bL8s8fffpT33lIYMkVZayZ/r3z+cGSZJTZv6WVW77+6P7767KMP+n+BnZciQ1HPrrBMuJ4xavtz3T95MqFwE43rnndKOoxoIRgFAOUp+a5c8UypbXbpIr7witWxZs/sAKBjn3IfOOXPOdXPObZH4et05N9M5t5dzrnOirCV7lQNACSxeHNYvvzxcBlbIndJ+/jl+HOwOt3Ch1KZNav9jjgnrtfHZ7KKLfHnggannGjWSrrxSats29dzJJ/sA0MUXx4MlJ53ky+gsqcDEiYULJAbBqOgyw6g33gjrP/3kZ4BVVEj77iv17p3af9ky6c8/8z/ObPz4oy8HD/bB2CC/V69e0tFHl25caeQ1GGVmXSJv8r4wszlm1tfMrjGzX5Le8gXXXGZmE81svJntl8/xAECdsf32Vffp0SPzuehbKAAAgLoqGoySpLFjpc6dfQAh31askJ5/PvP5H37I/2eWg1tu8TNwck3/cMst0h57hMdBkGSzzeL9nn7a/7u79trcPqcqw4b5snFjH0BMDlhGE7Unr1J46KHU+/3f//n8rOWSr2m77fz35pz06KPSf/7j/3soE3kNRjnnxgdv8iR1l7RA0kuJ03dE3/JJkpltIulYSZtK6iHpPjNrmO7eAFBvRPMb/Otf0uuvx3cbyeS556RTTkl/rthr8AEAAEohXR6g5B2H87XE6vzzpaOOyny+rj5/mUkN8hhKaNnSf33+eTwAFCSbTw5GDR0q/fZbbp/188/SKqv4pXbRQOL22/vE3xUVYVsQHJs0Kf29VqyIz9p67DFf3lRmq+mjAaiXXy7dOJIUcpneXpK+d879WEmfQyQ945xb7JybJGmipG0LOCYAKH+vvhrW//pXaf/9q3ddq1bSAQekP1fZWzsAAIC64sorq+7z8MM1/5xFi6R77sl8fsiQymetS9K779Z8HHXFvHnSt9/6mTyBbt1S+/38s0+K3r17bp/zxBM+j1h0ptyiRWF92bKwHuy2t956qfdp396PYe21/XE0iDZkiE9kH5gzR+rZU/rqq9zGXF2ZZmRFP/fEEws7hiwUMhh1rKRoNrM+ZjbGzB4zs2Bv8Q6SogtspyTaAKD+evLJ3K+dOze1bZ11pB12yP2eAAAAtcFLL1XdR5LOOafmn3XssZWfz7Qs8OSTfTl+fJi4G3GffSaNGRNuxCNJf/wh3X+/9MAD/vjXX3O79+WXp7btskv6vldcEX9JHDV1qg84TZniZ0cNHBieGzfOJ7I3kz7+2Cdw/+9//cwryV9z1ln+uf2OO6Trrsvte0nWq1f69hNO8OVbb0nrrpufz8qDiqq7ZM/MGks6WNJliab7JV0nySXK2ySdLsnSXF7AbQ4AoMz9+ms4iyn6RqW61lorte3HyiaoAgAA1BGHH169fmuuWfPPSrfTWiZLl/qvkSOlnXf2u8ohbt11pcmTff2cc6RRo+Lng4Toue4wXZnoksNhw6TRo6W//MUfH3xwav9DD40vd3vySenUU9Pfe6edwvqyZX6W1AUX+Of9334Lg13VmdFXlddeq/x85841/4w8KtTMqP0ljXLOTZMk59w059xy59wKSQ8rXIo3RVL0L6eOknIMcQJAkTgn3Xabf6OVb9FfRLk8KO27r3/zcued+RsTAABAuYvmgVpjjcr7VrV8LheXXZb5XEWF1KyZD0QhvejuesmBqKjoS9Z8LHv79NP48c47Z545F+y6t+WW8fZgtlt1rLRS+OI5OusqmjM2F9Flgldc4ZczJu92WIhAXg0UKhh1nCJL9MysfeTcYZKCDFqvSDrWzJqYWSdJnSV9VqAxAUB+jBnjt7TdaKP83zua6HLVVXO7xwEHxHfPq+5bQgAAgNrqH/8I6xdfLI0Ykdrn+ON9Gc0RlC/PP+9fWB5xRLz9uefy/1l1UadO2a8K2Hvv1LaJEysP7GyxRfx49dVT+1SkWUA2YID/uXEunlcq2c03+3K33eKzoqp6rr/rrsrPV6Vv37B+3XVSx47Ss8/6GV4bbeSTq+cz6Xwe5H00ZtZc0j6SXow032JmX5nZGEl7SLpAkpxz4yQ9J+lrSW9KOtc5l6etDQCgQJK3DM6nwYN9OXu2X2eeqyVLwnqmHfYAAADqiqFDw3rfvj659MUX++MTTvDLwO66yz9fLVyY3b2XLvV/4C9Y4I/T7cb3xhu+TJ51Vdlue4hr0ya7/tOnS998Ex4/8YRfitawYfr+997rA17RvEnpglGSz+UUddJJYT0IaLVrJ622WrzfJZf4gNV770nbRvZme+ihyr4Tv3TPVZKx6McffUDLTPruu9Tz6XYXbNHCr5b45hvptNMq//wSyHswyjm3wDnX1jk3O9J2knNuM+dcN+fcwc65qZFzNzjn1nfOdXHOvZHv8QBA3mX6BVddc+f6XwzJDzLRX0CtW9fsM4JgVLt26de6AwAA1HaPPur/OP/ll/isj6B+ww3S++/7nD6TJvm8Q82aZR+MWm896aqrpC5d/PG8efHzzknrr+/rhx2W2/eCzMvIbrop8zW9e/uZSs7Fl8tFXx6PGOETl/fp44+7dZM22MDXW7RIf9++fTPPZjr8cGnCBOmnn+KBrbFj4/3+/DOsH3aYH+PChf6l84IF/vzMmWGf4cPTf14QQAv6br55auAqWBVx4YXp71GGymueFgDUBunePFTH3Xf7HUA6d/a/4Coq/C/PpUv9sr/gF1A+3lzsuacvL7205vcCAAAoR+ed58u335a+/NLXozPLGzWSdt01fs1KK0mzZmX3OUEahaAMlvn16CHNmBHvG02V8Mor2X0OUr32WjzlxA03+JxSDz7oj997z/8zT16C9tNPYb1HD+nGG8Pjdu18vqlosCid11/3z+3pclhtsIHUuHF8ZtWmm8b7nH22L6O7PDZt6l86N2vmfxZXWSXc4W+HHXw6kGTJOaoWLYp/vw8+6JfkNWni89rWEgSjACBbL74YPx44sOod6xYv9mu2zzlHmjYtbG/VyucSuO02/wtIktq3T3+PbHTv7t/anX9+ze8FAABQjoLAz6JFfpcyyc9Yqczqq6cGkLIV7KS20Uaps2ei+YZ69qzZ59Rn333nZ/8ceGA46+zww6W//90HZ846q/LroxsNRWcfST6/V9OmPhhUmW228eNIDgZFBWNLl8R8223993DooZV/zoYbhvW7704936FD+ut22cXfPwh6FTKVSAEQjAKAbAVby0p+548TTpD22KPyaw46KH37okXSiSfG2zbZpGbjC7RoUbO8UwAAALkaOdI/h0RzOeVbsFwu+GNcCoMDmXz5pfTDD9l9TnTp3Zw54ecFu6tFNWvmnwuPO47nsFx89JHPodq5c9jWoIEPurzwQvXv8+23vozuMhfYbruajTHqhht8vqd//zv3e5x4otSrl68/8oj/b+fYY/2mRHPn+mWokp/9tP324XUffhifIRUNatUCBKMAIFvTp4f14O3FpEmZt6FdvlwaMiTeFp0qnKyqtycAAADl7pZbfBnsLlYdy5dLp58eJgOvSvKuadk8Q1W249rChfFZJtFlVq+/HtbTzVgx8y8rBw6s/lgQ2nFHaZ99qte3sh3onnxS+uST+HK95s2lyy7L7/LJli2l22+XVl4593s0aBCfEbX11j7w9MYbYR7Z1q2lo4/2yxKnTk17G336ae5jKAGCUQCQjblzpf79w+Ngmrbkl8ZFA1WHHOKnzybPfJL8L8J0S+h22SVzIkUAAIDa4KeffBoCKbvt5CdMkB5/3M8IWbw4/ayWylQ3iCFVvnPZaqv5Z7J0rrsurLdqVf3PQ/717p353Jdf+sBWkKj8hBN8EOfGG+N5vcpF06aV/w0Q/M3RpIm0xhqpwdQFC2oWECsBglEAkI0gOWYm7dr5slcv/9blww+lZ56J97nmGl/++9/heveRI/1D0Qcf5HW4AAAARRckZJZSd55LtsUWYRLo++4L25s29Qmi//gj/XXjxqW2ZQogRQUBq+RdjQNz50rz50uff+6PgyTpga+/DuurrFL156FwGjb0/66GDvUBppNOkr7/Pn3fNdao+W7VhZZpxpOUmhLEzO+e3auXny3VrFlBh1YIFVV3AQD8T6YHlyjn/FbDyWbN8r80ortuPPhguBsIAABAXRANQH30UeZ+8+eHL/pGjkyfvPmCC/yuZwMHhjNHRozwyaWTrbtu1WMLAhLHHZc+B9Gvv4b1DTesPCH6wQdX/XkorObN/S7SS5aEbc8+Kx1zTLxf8MK4nLVqJb31lv8ZPPVUH2j66Sfpv/9N379RI+nhh4s6xHwiGAUAuTjiCOmLL9K/fYm+MYtq06awYwIAACgHc+dWr9/o0WG9T5/0fQYM8OVFF/kdh//yl9RA1L/+5YMR1Vk2FwSgXnxRuvde6dxz4+fffz+sT5gg7befDxCkC3CgPB19tH/5G51NFE38Xc723TesP/JI6cZRBCzTA4BsPPWUL488MtytpWlTPz020LWrL2+80SdOlKSrry7aEAEAAEoqORg1e7YvnZP22ku6/35/fP31YZ+qki8/8IB/nlpvvXh7377SX//q83Fmq08fadmyeFvyUqm33vLlIYfE22fOzP7zUDy77+5/3pYtkyZOrN4SThQVwSgAyEYwFXbTTcOHpkWLpN12ky69NN53++391/LlYZ4oAACAuu6zz+LHjz3my6lT/U5zvXv7BOVBoCedTInPZ80Kz/XrJ91xR83G+uOP8eM770zfr3HjsP7kk+SLqi0aNgxfIKOsEIwCgKosX+53yVu0KGzbbDNpzpx4v+hOepLUtq0vs9lFBgAAoK7p1Mk/R3XoELa98krl11x/vTRlSvodwoKdxE45JfuxJOeJij7fST7YlY5ZWC/H3diAWoa/kACgKiee6JMeBrtUHHRQ/HyQC+r00+PtG29c+LEBAACUu3/+088qjxo50pfbbhtvf/996eSTpUsu8cGrTLvp5erww6WePcPjaOLrqK22Sm0LZsjvtFN+xwTUQwSjAKAyH30kYooWrwAAIABJREFUPfNMvG233Xx5ww2+HD/elzvtJI0a5d/+TZ/OWzMAAADJ7343f3687eabfXn77dK330qdO0tjxki77ir17++XVwU++cTnmnr55bDtnXdyH8+aa4b1xYvD+g8/hPUgWBbVq5fPQxSd4QUgJwSjAKAyO++c2hY8tPz97/6BZPXVw3NbbukfZFZbrTjjAwAAKCdjx4b1777z5YoV0rRp6fvvtJPUpYvvu9lm6ftsv7309tt+y/vodblq3jysR5f6JY9x4kRp772lGTNy/ywAaeU9GGVmk83sKzP7wsxGJNpWMbMhZjYhUa6caDczu8vMJprZGDNLMxcSAErAOf9mLp2zzy7uWAAAAGqLSZN82b59fAZSIEh7kIsgJcKuu8YTimeroiKsBwGzl16SdtzR13v39uX660tDhkirrpr7ZwFIq1Azo/Zwzm3hnNs6cXyppKHOuc6ShiaOJWl/SZ0TX2dJur9A4wGA7MycKQ0bFh6/+qp/O+Ycu6cAAABkEgSJrrnGz0BKDj4tXBjWBw/O7t5Nmvhnsfffr9EQY0sAA4cfHtb3379m9wdQpWIt0ztEUv9Evb+kQyPtA5z3qaQ2Zta+SGMCgMx++SV+3LMn28ICKDgze8zMppvZ2Ehb2hnmAFCWPv7Yl2b+q7KXeDvsUJwxJfvss7C+116p5zfcsHhjAeqpQgSjnKTBZjbSzM5KtLVzzk2VpEQZJFjpIOnnyLVTEm0AUFoffhjWd9mldOMAUN/0k9QjqS3TDHMAKD/vvuvLINCU/ILvpJN8efTRUsuWxRtX1GGHhfWhQ6XLLoufZ1keUHCFCEbt5JzbSn4J3rlmliHpiiTJ0rS5AowJALLTp09Yv/XW0o0DQL3inPtAUvI+5plmmANAeXnyyTDNQbrZRd9/Lw0Y4BOaP/tscccW1aePNGVKOMabbgrPXXihtDITUIFCq6i6S3acc78myulm9pKkbSVNM7P2zrmpiWV40xPdp0haK3J5R0m/CgBKZeJEaerU8Pj446Wt2FsBQEnFZpib2epVXQAARXfqqVL//uFxcoLxG2+U1lvP1y3dnIQiMpM6dAiTl0fddlvxxwPUQ3mdGWVmLcysVVCXtK+ksZJekRTsmXmKpEGJ+iuSTk7sqre9pNnBwxYAFN2ll0qdO4e76G23nfTUU1KjRqUdFwAAQDmbPz8eiOrXL7XPxRcXbTg5e+GFUo8AqDfyPTOqnaSXzEe6KyQNdM69aWafS3rOzM6Q9JOkoxL9X5d0gKSJkhZIOi3P4wFQX02eLLVp47+q6+ab48fbbpvXIQFAjjLNMAeA0nJOeuCB1B3zTjklrI8fLy1eLFXkfVFO/q25ZqlHANQbef0/gnPuB0mbp2mfKSllmwLnnJN0bj7HAAB69VXp4IN9fcWKcCq4c6nTwp2TfvtNeuKJ1PtcSo5gAGUhmGF+k+IzzAGgtJ59VurdO94Wzb8klffOdHvt5ROYB7bfvnRjAeqZQiQwB4DSCgJRUvimbscdpQYNpOeek4YP921mvm3NNaW//c237b+/f3s3fjxvxwAUnZk9LekTSV3MbEpiVvlNkvYxswmS9kkcA0DpffNN/Pj442vHcrzAfvv58oYbpAULSjsWoJ6pBXMlAdRLy5b5YNCNN0q9evkZTE8+KR1yiNS6debrkmc+LV4cbzvmmMo/95lnfMLNcn6LB6DOcs4dl+FUygxzAEixaJH02WfSLrsUJ0n4iy+G9VtvlS66qPCfmU8XXCAdeKC0ySalHglQ7zAzqjreeMPvsIXCWrjQ/xL77bdSjwTl4MorpRkzpDPPlB5+WDrxROnkk6WVVsp8TYcOYb1nz+wewpo1k156qfJAFwAAQDn797+l3XaT7ruv6r7LlklnnJH7s/fUqdLYseFxbQtEST6PFYEooCQIRlXlmWekAw7wO2yttJLfKSKwYoX07rt+xka5u/NO6Z13Sj2Kyl16qXTJJVL79tLy5bXjnysK45574vkGzjpLGjgwPA5+Nvr08QGno47y5a+/hn1eftkHs6LGjZP23jueVDMwbZp06KH5+x4AAKjL7rjDv8RBefnsM1/ec0/VfQ88UHrsMf/snS2zeDoDXtwDyBLBqKpsHsnHPmeOtOqq4fEBB0h77ik99FDxx1VdS5b4XxZ9+/oEfencc4/0r3/5mUmSNGGCf1MSeO01/71H72fm34ZkctNNfieyqVOlefPC65M557/eeEO6666wvaLC5/Jp1Uq6997UoALqnhkzpNmzpfvvl847r/K+K6/sfwbvvdcfP/98eK5DB//z27Ch1Lat//l66ilp1Cj/5mvIEL/d8LJlfglf8DPYqlXBvjUAAOqcCy+UDj+81KNAsiBA2KhR5f0eekgaPDje9uab/vmqefOwrWNH37Z0adh2ww3x60aNktZfP/cxA6iXyBlVlY03jh8vWuT/h9yxozRlim/79tvij6s6vv9e6t+/8j5Nm/o/yKXskw2uuaa09tp+6dTy5T6QcO210mqrxftkcsIJPkhQmXnz/OyXPn388corS02a+ASD660nbbGF/+V3wQVSixbZjR+F9/PPfnbhRRdVvmRu4UJp9dVT25ct88vnog9Akv9ZS+e44+IzqALHH5/a1rCh/wIAALlbtMg/T6L0orOTvvoq/S7Ckg9E/d//hcdHH+3L/ff35cKFqdc1buzLk0+WBgyIn9tyy5qNG0C9ZK6WL4Uys00ljR07dqw23XTTwnzIRhv5nbUqs3Chn81TkYjvTZzod5eoqPAzhNq2jfdfscIvGeratTDJBR94QDrnnNT2Rx6RTjvN7ywW7ChWLo46yu90NmWKD0INHuyTV0+bVr3rv/zSz3ypIMZaNoKf7RdeCN+ezpvnZycdemh4Pt1/A1OnSmus4ev//a/0+efS5ZeHD0OSD0wGwdSFC3kYBlAQ48aNU9euXSWpq3NuXKnHk4uiPC+h/lixInyh88IL0mGHFSdZNjJbssQ/F0UtWBDuKixJn3witWuXfhbTWWdlv9oj2Hm4Zcvsxwugzsn2eYlletUxbpzPZVSZZs38dNguXaSvv/Y5pg4+2C/lW3VVadAg3+/6630AqmFDqVs3H3ypyqhR0qxZ2Y05ORDVvbsve/WSNtssHog6+2xp993D4w02iF/bv780YoSfifT/7N13mBRV1gbw98AAAoKAGBBQUBEFs5gxJ4yYWDGCsssquuqawxo+XdfEGnF1V0VFEeMquCKIiglBUJaMBEFhJEdJEmbO98epu1XdXd3T3dN53t/zzFNVt6qrbhfD9O1T957brJl96Ve1IFHfvuHX/8tfrDfLBx9Y7p7Nm4EJE4B77gE6d7bA00svAW+/Dfz0k53P3YtWrSwAeO21llBRFfj8c9s3eLA/q1q0/fazXECVlcCgQfF7z1BuBAPdw4f764ceaoGpWrXsdyKs8TpokB+IAiynwb332v+xQw6xsh49/N8PVQaiiIiIcmXTJn/9vPPs83nUqPzVpybbssVGG0QHogA/Bcejj1p764gjIgNRRxzhrycKRJ12WmzZ+PE28zADUUSUJvaMSsWwYdZ9dfRoG3508MHArbcmF1BKVkWFfUl3xo/3A0nz5llupf3397+Qh1m8OPKL/LHHWhAnbBayJ56woE90QGD8ePuiH/bhE2bBAqBJE//pSy6fjq1YYU95gnmunC+/tH077shZ0nIt+nfgySfDf9ecU0+1p2s9eth0xImsXx+Zz4CIKIvYM4ooYMQI64V+/PGx+yZPtoeulDtffBH5UBkAeva0/JgTJthD5rCA0Y47Wi/0U0+17zjOSSf5uaR+/tlScohYO7usDHjzTXvQHi8XLRHVWKm2lzieKRVduvi9PQ47zJavv269oGbNig1KTZxof8CbNk3+GrVrW7Dpzjut91DQzjv761dcAbz4og15Cn7AVFREBqKCwcbBg4GuXW39ggts9ox4X+gPPDD5OgOJc0NlW7Nm1vPq+ONtdsOgo4+O3F66NDIJPWXHDTfEll13XeTvcLT3348cgpcIA1FERFQK1q61ZNAHHhjb7itEX3wBnHxy/P377MPZkHMtOpn4K6/YSAzAvlPEM2SILT/6yCYz+uc/rf123nn+Mbvs4q+7NBgXXFD9OhMRgcP0qq92bfuD/+ab9uG7fr31ElK1YXhNmth627Z2fM+eNozMDS3q1w9YssSGqzkTJkQ2SM44I/a6/fvbU4pGjWzZurUtg/mSome7O/10W15yiSWVLrUv9J99VvUxe+5pT/TmzbNkjSIW1Munioriarj9+qsF9Soq4h/z+OP+enCWxHPOsWVweGezZnbOZANRRERE+TZ5srUhvvzS2h///Ke1/xxV6+V73XWJP+MbNbIZiF0Caffa88+33uth+vb1ZzYeODC3E+lE98AJs2WL9ahx9Ytn40brDf3cc+G924OmTrXzTZ6cUnVL3po11q51XnnFEoyHTdwCWF7W88+338uDD/bLr7nG7u3ll3MkARHlDIfpFZKvvortyfPee9abqUMHa2wsWmS5kNq3T3yuww8Hvvkme3UtVKrAgw/arGpt2wJff+0PqWzXLv7rNm/OT+Lzdev8nm3B/4uqwNy59h4KKSHo5s2xQaPp02NnnXQqK63+jRtbgym6PN4sL0REBYTD9JJQCn/PKyosAHTeeUCbNrH7t2yxvDqffWZJu8Psuivw9NP+A0DHfe5Fl4XN6vrKKxakiTZokCWMvvfe8GuffbblBorO/RmPKrB8uU2yk+jfTtXuzbJlQIsWkfs2bQL+8Aerb9iwPff6t96yYV1uQp+NG4Hu3a1XNGA5TW+4wdq7J55oOUdnzrR8oOeeC/z73/75KittOW2aPQweMACYMycyzUWpWr/e7k3XrsCkSZaH0wm2I997z584xlmxIrXRGkREKUq5vaSqRf0DoCMAnTJlitYoixerbtqkumGD6p13ql5zjWrLlqo336y6dm2+a1eYzj7b9UcL/6msjDx+yxbVunVt3+23Z6dO113nX3/OHL/8yiut7IQTsnPdZG3ZolpRYfdm8eLE9y/65957/fNUVvrls2bl7/0QEaVhypQpCkABdNQCaPuk85P19lLfvvY3vn//7Jw/2xYt8j+nOneO3FdZqXrkkal9Bob9jB0bed4+fap/zmR+Ro5U/eWXyGvPnBl5TPT+oO22iz3nrbeqjh4dedxhh1Vdl913V50+PXvvtU4d1csvV737btVu3VSnTIlt3+XKqFGqU6eqXn+96nvvVe9cF1yQ+H0vXx55fGWlauPGtm/UKNUVK6p3fSKiJKTaXsprwygTPzU2GEWpW7FC9aqrrPG0bp1qebnqf/7jf5AfeqjqkCHxP+jPOkt1wABrwDm1atm+O+5Qfe212EBgVQ2gVq388++5p+q4cVYevG5FRWbvQ7IqKuLfi4svji3bfntbbrON6tNPx773DRtUV67Mz3shIqoGBqOScP31kZ8Jmzdn5zqZtm6d6ocfql50UWT9y8v9Y+K1DYLBlyOOiN0/e3bkQ6fgT8+efpDHfX6G/dx0k2rr1pFll19un7GTJqkuWaJ6yy1+4CFTP6tX23t///3YfYceGn4vV63KbB2y8dOhgwWpfv5Zde5c1c8+U+3d24KR6ZgxQ/W+++zhnao9KN64UXX8+Nhrr1kT+/qFCyOP2bDByidOtO2+fS2Imeg9jR+fXt2JiDKMwSiiVA0fnt2Gz4QJqn/5S3iPoLvvjj2+rCx+A6ZrV9u+/vr03us776hOmxZZ9vjj/nXcl4eNG1VPPz38/Xz1lR2zYoVfFuzVRURUYhiMSlKbNv7nwpVXJveas86y42+7zb7I51qiz+8pU6zXeXT5iBH+68vLLSgU9M03qvPmJX+dhQv946ZPVx00yHrURNu4UXXp0vjvZfly/34CqpdeWnUb5emnU2vT7L134vv55puqTzyh+ttvtu0e2sX7mTXLjnXbzzzjr/foofr226pff606ebIFfH7+WfXVV1XfeMOCX4sXqy5YEPm7l+7P735n/24//GDbnTpF/tu88oqVu55zP/6Y/rXat0//tdts469/913ifw8iohzKazAKQGsAIwFMBzAVwHVe+b0AfgEwwfs5LfCa2wHMBjADwClpXJPBKKq+k08O/8A/5hjV9eur38BxP9G9hYKBoHR+TjlFtV8/eyq6bJk9URs3LjzwFWzsvfyy9Xy6//7Yc+65Z/i1br7ZGsJERDUMg1FJWrTIeu24z42OHVUfesgeslxwgR0zbZr1uvn1VwssBD9n9t3XjvnDH1R79bIv2r/8Yp+du+1mx/z976offWSfdZs2WbBgzZr0ehEPGhT7WdexY/zP3OoMdXr77eTbBpnkzj1+vAWJLrhA9dhj7bouiPb661W3N776SvXzz1Ov65Il9iBs82b7/di8WfXaa1W//z6z7zORdeusV/z69Xbd/fbLXLuuqp9585K7v8n8uAd/lZUWiCMiKjD5Dka1AHCgt94IwEwAHbxg1E0hx3cAMBFAPQBtAfwIoHaK12Qwiqpv0SL/SVPHjlZWWRnZuC0vV50/37p1u4ZBmzaR5xk/XvXgg21f796qjRrFNiaCQ/luucXKZs60IYDB47p1i83pkOrPuefa8v33VVu0SO8c+cy3QERUABiMSlG8z5Pzz6/eZ1qyP4sXW0+aVatU3303fMhg2NC7bbe1fddcE7vvk08ye48+/VT1hRcye85M6d3bf9833ZTv2mTPli3WA23TJtUDDkj/923HHf31p59WHTrUhtkFLVtmPb2CgalLL7XeVs78+apjxti+xx+3srfftkAaHwYSURFItb2U1dn0RGQwgH4AjgSwVlX7Ru2/HQBU9UFveziAe1V1dArXKJ3Z9Cj/KiuTm41l4UJgyBCbQaaq4ysqbMa5ffaJf8z69UD9+sDixcD220fOavP99zaLXY8eNrPMJ5/YdNFHHQWMHZvc+6rKwIE2g81XXwE33wzsthswerTN8tOwYWauQURUpDibXoqWL7cZ0SZMSO74TZvss+fJJ7Nbr112sVmJ99kH+O47v3zjRpvx1c30NmmSzeIG2OfiQQfZZ3RNsmwZ0Lx5vmuRf5s324x/N95osxieey4wZgxw6qm2/5dfgB13tHacmx2ZiKiGSrW9lLU5UEWkDYADAHzrFV0jIpNEpL+IuHlFWwKYH3hZuVdGlB/JTgvcogXwxz8md3zt2sDeewN33x2+v2FDv5G7ww6x0ysfdBBw2GE2nbOqTY1cty7w7bf+c7mKCuC++4DTTgNWr7app8PceadNhTxnDjBiBDBxor3+oouA/fcH/vQn4LffgKlTgcaNGYgiIqLUbbst8N//2ufLli32oCfojjuAoUOByZPtmDp1gCeeAH76CTj/fPuC7z7ftmyxhy/9+sX2Sfn1V/v8UwXmzgVeeilxvX7+2QJPwUDUmDH2meoCUQCw774WjKmoADp3rnmBKICBKKdOHaBbN2DePOCKK4AmTYAuXfzfwZ12srYgA1FERCnLSs8oEdkawBcAHlDVf4vIDgCWwbps3Q+ghapeISLPABitqq95r3sRwFBVfTeFa7FnFBWX114Dbr8d+OtfLTB0zTVA69bZudaGDdaI3rzZgmLJBtuIiOh/2DMqQ6ZOtR7Axx+fvWts2WJBpHr1Iss3bbLeK3XrAh99ZA9/OnfOXj2IiIhqmFTbS2WZroCI1AHwLoCBqvpvAFDVxYH9zwP4j7dZDkt67rQCsCDTdSIqKJdcYj+54J7m1qmTm+sRERHF07Gj/WRTWZn9RKtb134A4LzzslsHIiIiqlJGu0mIiAB4EcB0VX0sUN4icNg5AKZ460MAdBeReiLSFkA7ABlKgkNERERERERERIUm0z2jjgRwKYDJIuKyVt4B4EIR2R82TO8nAH8EAFWdKiJvAZgGYAuAq1W1IsN1IiIiIiIiIiKiApHRYJSqfg1AQnYNTfCaBwA8kMl6EBERERERERFRYWI2YyIiIiIiIiIiypmMJzDPg7oAMHv27HzXg4iIiEpQoI1RN5/1qCa2l4iIiChrUm0viapmrzY5ICJnARic73oQERFRyeuqqkPyXYl0sL1EREREOZJUe6kUglHbADgGwHwAm/JcHSIiIio9dQG0BvCFqq7Od2XSwfYSERERZVlK7aWiD0YREREREREREVHxYAJzIiIiIiIiIiLKGQajiIiIiIiIiIgoZxiMIiIiIiIiIiKinGEwioiIiIiIiIiIcobBKCIiIiIiIiIiyhkGo4iIiIiIiIiIKGcYjCIiIiIiIiIiopxhMIqIiIiIiIiIiHKGwSgiIiIiIiIiIsoZBqOyQET6i8gSEZkSKNtPREaLyGQR+UBEGnvldUXkJa98oogc65U3EJEPReQHEZkqIg/l6e2kLRP3IbDvXyIy07sf5+Xh7VSLiLQWkZEiMt3797zOK28mIiNEZJa3bOqVi4g8JSKzRWSSiBwYOFcP7/hZItIjX+8pXZm8F97+xiLyi4j0y8f7SVeGfyce8c4x3TtG8vW+0pHGvdjT+zuyUURuquo8xSJT98Hb10RE3vH+Zk4XkcPz8Z7Slca9uNj7fzFJRL4Rkf0C5+oiIjO8/zu35es9USxhewkA20tBGf5sLNr2Uibvg7e/KNtKANtLQWncC7aXwPaSFHJ7SVX5k+EfAEcDOBDAlEDZOADHeOtXALjfW78awEve+vYAvocFCRsAOM4rrwvgKwCn5vu95fo+eNv/B+Cv3notAM3z/d7SuBctABzorTcCMBNABwCPALjNK78NwMPe+mkAPgIgAA4D8K1X3gzAHG/Z1Ftvmu/3l497ETjfkwBeB9Av3+8tT78TRwAYBaC29zMawLH5fn9ZvhfbAzgYwAMAbqrqPPl+f7m+D96+VwD83luvC6BJvt9flu/FEe5vIYBTA/8/agP4EcCu3n2YWEy/E6X+A7aXMnYfvG22l0qkvZSp+xA4X1G2lTL8O8H2UhXnyff7y/V98PaxvaT5ay+xZ1QWqOqXAFZEFbcH8KW3PgKAe1rVAcCn3uuWAFgFoJOqrlfVkV75JgDjAbTKctUzKhP3wdt3BYAHvX2Vqrosi9XOClVdqKrjvfU1AKYDaAmgK+yPILzl2d56VwAD1IwB0EREWgA4BcAIVV2hqith97BLDt9KtWXwXkBEDgKwA4CPc/gWMiKD90EBbAX74KgHoA6AxTl7IxmQ6r1Q1SWqOg7A5iTPUxQydR/EelAcDeBF77hNqroqJ28iQ9K4F994fxMBYAz8z8tDAMxW1TneZ+kb3jmoALC9ZNhe8rG9ZNhW8rG95GN7ybC95Cv29hKDUbkzBcBZ3no3AK299YkAuopImYi0BXBQYB8A6z4I4Ex4jY8il9J98N47ANwvIuNF5G0R2SG3Vc4sEWkD4AAA3wLYQVUXAvbHBBa5B+yPyPzAy8q9snjlRak690JEagH4O4Cbc1XfbKnOfVDV0QBGAljo/QxX1em5qXnmJXkvUj1P0anmfdgVwFIAL4nIf0XkBRFpmMXqZlUa96IX7Kk4UGJ/M2sItpcM20tsLwFgWymI7SUf20uG7SVfMbaXGIzKnSsAXC0i38O60G3yyvvD/rG/A/AEgG8AbHEvEpEyAIMAPKWqc3Ja4+xI9T6UwSK2o1T1QFiX2r65rnSmiMjWAN4FcL2q/pro0JAyTVBedDJwL/oAGKqq80P2F43q3gcR2R3AXrD/Jy0BHC8iR2e+ptmXwr3IyXnyJQP1L4MN+XlWVQ8AsA7WRbvopHovROQ4WOPqVlcUclhR/s2sQdheMmwvsb3EtlIA20s+tpcM20u+Ym0vlWX7AmRU9QcAJwOAiOwB4HSvfAuAP7vjROQbALMCL/0XgFmq+kTuaps9adyH5QDWA3jP2/U27D9O0RGROrA/EgNV9d9e8WIRaaGqC70uxEu88nJEPvFtBWCBV35sVPnn2ax3NmToXhwO4CgR6QNgawB1RWStqhbNh0iG7sMlAMao6lrvnB/BciR8iSKS4r1I9TxFI0P3oRxAuaq6p5zvoAgbV6neCxHZF8ALsHxBy73ieP9vqECxvWTYXmJ7iW0lH9tLPraXDNtLvmJuL7FnVI6IyPbeshaAvwB4zttu4LoDishJALao6jRv+68AtgFwfV4qnQWp3gdVVQAfwG9QnABgWq7rXV0iIrDxyNNV9bHAriEA3AwvPQAMDpRfJuYwAKu9LpbDAZwsIk3FZkU42SsrGpm6F6p6sarurKptANwEyw9QNB8gGfydmAfgGLEhG3UAHAMbL1400rgXqZ6nKGTqPqjqIgDzRaS9V1R0fzdTvRcisjOAfwO4VFVnBo4fB6CdiLQVkboAunvnoALF9pJhe6lmt5fYVvKxveRje8mwveQr+vaSFkAW+FL7gXUTXwhLklYOezJ1HSy7/UwADwEQ79g2AGbA/hh+AmAXr7wVrGvcdAATvJ/f5/u95fo+ePt2gT21mATLA7Fzvt9bGveis/fvOSnw73kagG299zTLWzbzjhcAz8BmNZgMS9LqznUFgNnez+X5fm/5vBeBc/ZEkc0Qk6n7AJv94p/e/51pAB7L93vLwb3Y0fub8isseW85gMbxzpPv95fr++Dt2x82jGcSgPdRRLNIpXkvXgCwMnDsd4FznQb7zPkRwJ35fm/8ifh3ZnspQ/fB28f2Uom0lzJ5HwLn7Ikiaytl8l6A7SW2l9heAgqsveQ+2IiIiIiIiIiIiLKOw/SIiIiIiIiIiChnGIwiIiIiIiIiIqKcYTCKiIiIiIiIiIhyhsEoIiIiIiIiIiLKGQajiIiIiIiIiIgoZxiMIiIiIiIiIiKinGEwioiIiIiIiIiIcobBKCIiIiIiIiIiyhkGo4iIiIiIiIiIKGcYjCIiIiIiIiIiopxhMIqIiIiIiIiIiHKGwSgiIiIiIiIiIsoZBqOIiIiIiIiIiChnGIwiIiIiIiIGCSKGAAAgAElEQVQiIqKcYTCKiIiIiIiIiIhyhsEoIiIiIiIiIiLKGQajiIiIiIiIiIgoZxiMIiIiIiIiIiKinGEwioiIiIiIiIiIcobBKCKq0USkp4ioiPSMKv9JRH7KT62IiIiI8ktE7vXaSMdGlauIfJ6fWhFRqWAwiohKioh0EpGXRGSOiGwQkV9FZLKIPCoiLfNdPyIiIqJ0eYGg4M9GEVkqIuNF5AUROVVEaue7nkREVSnLdwWIiDJBRATAQwBuAbAFwAgAbwOoC+AIADcB6CMiPVT1ncBL3wMwBsDC3NaYiIiIKG3/5y1rA2gCoCOASwH0AvCdiFysqjPzVTkioqowGEVEpeIuWCDqJwBnqOrU4E4ROQ/AawDeEJGTVHUkAKjqagCrc1xXIiIiorSp6r3RZSKyA4CnAXQD8ImIdFLVJbmuGxFRMjhMj4iKnoi0gQWjNgM4KzoQBQCq+i6AP8OeID4rIrW814bmjCIiIiIqJqq6GEB3AJ8DaA3gjuhjRKSdiAwQkV9EZJOILPC221Xn2iKyk4jcLSKjRGRR4Nyvi8heIce38dpfL4vIHiLypogsEZHK6BxVRFSaGIwiolJwOayn53uqOjnBcS8AWACgPYBjclExIiIiolxR1UoAf/U2L/TSGAAARORgAN8BuATAOAB9YakKLoYN7etUjUsfDeA2AKsAvAvgce/c5wMYJyL7xXndbgC+BdAGwEAA/wLwazXqQURFgsP0iKgUdPaWnyQ6SFW3eLO/XATgSAAjs1wvIiIiolz7GpY/c3tYkGeuF5QaAKAxgEtUdaA7WEQuAPAGgNdEpIMX0ErVZwB2UNU1wUIvCDUKltfz1JDXdQbwoKrG9OIiotLGnlFEVApaeMv5SRzrjtkpS3UhIiIiyhtV3Qhgube5nbc8AsCeAEYHA1He8W/CAljt4T/gS/WaS6IDUV75RFig6jgRqRPy0sXwk7ETUQ3CYBQRlQLXBV0zfCwRERFRMYpu7xzoLT+Lc7wrPyDtC4qcLiIfiMhCEdns5YRSAGcCqAegecjLJnrBMyKqYThMj4hKwULY076dkzi2VeA1RERERCVFRLYC0MzbXOott/GW8do/rrxJmte8FsCTAFYCGAFgHoD1sGDY2QD2gwWkoi1K53pEVPwYjCKiUvA1gOMAnAjg+XgHiUhtAMd6m6OyXy0iIiKinOsM+563WFV/8spWe8sd47ymRdRxSRORMthQu0UADlTVhVH7D0/wcvZUJ6qhOEyPiErBywAqAJwjIh0THHcFLFfUDABf5KBeRERERDkjIrUA3Oltvh7Y9V9veWycl7ry8WlctjmsR9U3IYGoreEPESQi+h8Go4io6KnqHAB/A1AHwBAR6RB9jIicDes+XgGgT5ozxRAREREVJBHZHjYr3rGwYXJ/C+weBXsY11lEzo963fkAjgYwE9bbPFVLYEPyDvKCT+68dWBtr7BcUURUw3GYHhGVinsBNARwA4CJIjIcwFRYgOoIAIcC2ADgQlWNl7yTiIiIqOCJyL3eai1Yr6SOsOF5dQGMBXCxqi5zx6uqikgPWD6nN0VkMIAfYDPonQ1gDYDL0nlYp6qVIvIUgNsATPbOXReWQqEZgJHeOhHR/zAYRUQlwWs83SgibwK4GvaE7wRYT6ifAPwdwBOqWp63ShIRERFlxj3echMskPQzgAEA3gXwcVhQSVW/FZGDAfwFlmfzTADLAAwCcL+qzqhGfe6CJUv/PYA/wnJPjfCu9X/VOC8RlShRZc44IiIiIiIiIiLKDeaMIiIiIiIiIiKinGEwioiIiIiIiIiIcobBKCIiIiIiIiIiyhkGo4iIiIiIiIiIKGcYjCIiIiIiIiIiopxhMIqIiIiIiIiIiHImrWCUiPQXkSUiMiVk300ioiLS3NsWEXlKRGaLyCQROTBwbA8RmeX99Ej/bRARERERERERUTFIt2fUywC6RBeKSGsAJwGYFyg+FUA776c3gGe9Y5sBuAfAoQAOAXCPiDRNsz5ERERERERERFQE0gpGqeqXAFaE7HocwC0ANFDWFcAANWMANBGRFgBOATBCVVeo6koAIxAS4KqKiGwlIh1FZKuU3wgRERFRFUqhrVEK74GIiIgKV6ptjbIMXvgsAL+o6kQRCe5qCWB+YLvcK4tXnqrdAEyZMiVmxCARERFRtU2ZMgV77703AOwNYGqeq5MutpeIiIgoa1JtL2UkGCUiDQDcCeDksN0hZZqgnIiIiIiIiIiISlSmZtPbDUBbABNF5CcArQCMF5EdYT2eWgeObQVgQYJyIiIiIiIiIiIqURkJRqnqZFXdXlXbqGobWKDpQFVdBGAIgMu8WfUOA7BaVRcCGA7gZBFp6iUuP9krIyIiIiIiIiKiEpVWMEpEBgEYDaC9iJSLSK8Ehw8FMAfAbADPA+gDAKq6AsD9AMZ5P/d5ZUREREREREREVKLSyhmlqhdWsb9NYF0BXB3nuP4A+qdTByIiIiIiIiIiKj6ZyhlFRET5tHkzUFGR71oQERGVjrVrAeX8SkRE2cBgFBFRsdu4EahbFzj33HzXhIiSICL9RWSJiEwJlD0qIj+IyCQReU9EmgT23S4is0Vkhoickp9aE9Uw5eVAo0bAtdfmuyZERCWJwSgiomJ3yy22HDIkv/UgomS9DKBLVNkIAHur6r4AZgK4HQBEpAOA7gA6eq/5h4jUzl1ViWqoyZNt2a9f4uM2bQKWLMl+fYiISgyDUURExe6zz/JdAyJKgap+CWBFVNnHqrrF2xwDoJW33hXAG6q6UVXnwiaEOSRnlSWqqX77Lbnjjj4a2GEHYOHC7NaHiKjEMBhFRFTsRPJdAyLKrCsAfOSttwQwP7Cv3CsjomxZty75oe/ffmvLH3/MXn2IiEoQg1FEREREBUJE7gSwBcBAVxRyGDMqE2VTVUPzwhx1FDByZObrQkRUohiMIiIqduwZRVQSRKQHgDMAXKz6vym8ygG0DhzWCsCCXNeNqEb54YfI7crK5F53222ZrwsRUYliMIqIqNitXZvvGhBRNYlIFwC3AjhLVdcHdg0B0F1E6olIWwDtAIzNRx2JaoyXX47cXrMmudeNHQvMnJnx6hARlSIGo4iIitX06dYras6cfNeEiFIgIoMAjAbQXkTKRaQXgH4AGgEYISITROQ5AFDVqQDeAjANwDAAV6tqRZ6qTlQzJZvMHADat89ePYiISkhZvitARERpeuONfNeAiNKgqheGFL+Y4PgHADyQvRoR1RDffAOMGQOsXg3cdBPQqFFyr9u4MbZswQLgjDPCj1+3DmjYMP16EhHVAAxGEREVq/r1810DIiKi4tG5M+DSsf3yC/DCC7HHrFgRWxYWjHr4YeC//w2/zrBhwHnnpV9PIqIagMP0iIiKFYNRREREydPARJTLlsXur6iwn2h9+8aWNWgQ/zoPP5x63YiIahgGo4iIilWihjARERHFVxY1QOTJJ63M5WHcdVd/34ABkceOGQMMHuxvn3lm5P5x4zJXTyKiEsVgFBFRsapbN3J7663zUw8iIqJiU7t25Pb119vy/vtteeaZQKdOth6dwPzww20SEadDh8j9V12VuXoSEZUoBqOIiEpFnTr5rgEREVFhCg7RA4DWrcOP+/BDW06YAPzxj355ohn1ove9+Wbq9SMiqmEYjCIiKhWrV+e7BkRERIUpOhdUvXqJj2/QADjmGH977VpbhuWacj2h9tvPlmFJ0ImIKEJawSgR6S8iS0RkSqDsURH5QUQmich7ItIksO92EZktIjNE5JRAeRevbLaI3Fa9t0JEVMNUVsZuMyBFREQUadYsoHHjyLKwGfKCmjcH2rXzt11y89/9LvbY9u2B9euB8eOrX1ciohoi3Z5RLwPoElU2AsDeqrovgJkAbgcAEekAoDuAjt5r/iEitUWkNoBnAJwKoAOAC71jiYgoGVu2+Ovdutly5cr81IWIiKhQ3XILsGFDZFmiYXcA0Lu3Ldu0seWwYZa4fOTIyOPuuMOW9esDtWoBZ5wRm9ORiIhipBWMUtUvAayIKvtYVd03ozEAWnnrXQG8oaobVXUugNkADvF+ZqvqHFXdBOAN71giIkpGMBjVtq0tq3rSS0REVNP89FNsWVXBqM6dbelmyuvZE+jbN/Y4F7RyGjYENm3i5zERURWylTPqCgAfeestAcwP7Cv3yuKVExFRMoLBqPr1bVlV45qIiKimmTAhtiz4eblqVfzXBo8bNSp2f/TkIS55+fnnJ18/IqIaKOPBKBG5E8AWAANdUchhmqCciIiS8e23/vpWW9mST2KJiIiqFgwyff99/OPat/fXly6N3R9vSN5//pNevYiIaoiMBqNEpAeAMwBcrPq/+VPLAQTnTm0FYEGCciIiSsbAgf666xnlZvshIiKi+N59F5g719ajZ9oLJjvfZZfw13fsaMutt44sP/nkzNSPiKjEZSwYJSJdANwK4CxVXR/YNQRAdxGpJyJtAbQDMBbAOADtRKStiNSFJTkfkqn6EBHVKOXltuSTWCIiovh69PDXh3hfPaKDUe+846/Xqxd+nv/+F/jlF79nsrPtttWvIxFRDZBWMEpEBgEYDaC9iJSLSC8A/QA0AjBCRCaIyHMAoKpTAbwFYBqAYQCuVtUKL9n5NQCGA5gO4C3vWCIiSoZLrgoARx1ly6ZN81MXIiKiYrDDDv6661VcVmbL5s2BOXOAk07yj4kONgHA5MmWK2qnnWL3uXMREVFCaf21VNULQ4pfTHD8AwAeCCkfCmBoOnUgIqrxli2z5b77+g1iTidNREQU3733Ao88Yuvus9NNCPLww/7stE5Yz6i9945//nPPBV59tdrVJCIqddmaTY+IiLJtxQrgyCNtliCXiPWxx/JbJyIiokLmekMBwPLlwMSJwGmn2XZYr6bNm1M7/9lnA506AU2apF9HIqIagP1IiYiKVWWlNZxF/Nl+OJseERFRpCZNgFWrYst79ozcrlMn9piGDVO/3tq1dr3164EGDVJ/PRFRDcCeUURExaqyEqjl/RnfbjvLa3HEEfmtExERUaGJDkT17WvLDh0iy8OCUYcdFrl9zjlVX++HH2x5663J1Y+IqAZiMIqIqFhVVAC1a/vbDRsCGzbkrz5ERESF5sMP/fVff7WlCyideWbksfGSjwc/Wx9+OPlru+sREVEMBqOIiIpVsGcUYE90U81tQUREVEp23hn405/8bddLCQAaNbKlCzpFf2aG9YwCImfUa9Om6jq8/74td9yx6mOJiGooBqOIiIrVpk2Rs+eVlQGjRgHl5fmrExERUb4MGwbMnw/06+eXffRR7HEuGBU96UdlZdXXiBewCnJJ0t2sfUREFIPBKCKiYqRqycqDU067INTxx+enTkRERPl06qmR26rAp5/GHhcvoLTttvHPPW8eMGNGcvUQSe44IqIajMEoIqJi5IYWBHtGObNm5bYuRJQSEekvIktEZEqgrJuITBWRShHpFHX87SIyW0RmiMgpua8xUZF6+21//ayz/PV4uaEOPTT+uVq3BvbYI7nrduzor0+bltxriIhqGAajiIiK0caNtgz2jCKiYvEygC5RZVMAnAvgy2ChiHQA0B1AR+81/xCR2iCixFSBu+/2t10eJyA8GDViROSkINWx007++vnnZ+acREQlhsEoIqJixGAUUdFS1S8BrIgqm66qYWOAugJ4Q1U3qupcALMBHJKDahIVt99+8z8rgcihc8GE5M6JJ2b2+l272rJPn8yel4ioRDAYRURUjDZtsmUwGJVMUlUiKjYtAcwPbJd7ZUSUyLp1wEUXhe/LxeflDTfYUjX71yIiKkIMRhERFaOwnlFh+aOIqNiFZULmt1uiqqxbZ72jAH92u1xyva9cHYiIKAKDUURExWjo0Niyxo1zX4/qqKwEXn8dGDky3zUhKmTlAFoHtlsBWJCnuhAVtuBQvHXrgMces/W5cxO/7vbbM18X97AoOFSQiIj+h8EoIqJidM01thwxwi/bddf81CVdTz8NXHwxcPzxke8jWdOmATNnZr5eRIVlCIDuIlJPRNoCaAdgbJ7rRFSYgrmgPv/cX2/aNPHr/va3zNfF9VbetAkYNQpYtCjz1yAiKmIMRhERFbPg0LxRo/JXj3RMnuyvjxmT2ms3b7aps9u35xAIKjoiMgjAaADtRaRcRHqJyDkiUg7gcAAfishwAFDVqQDeAjANwDAAV6tqRb7qTlSwKiqADRv87auv9tfzMYzd5aUaPRro3Blo0QI46SRgm22sBxdzSRFRDRcyrykRERWN4DTUu+8OzJ5t65s2FX4OqSVL/PV161J77fTp/nr9+mzUU1FR1Qvj7HovzvEPAHggezUiKgHRnyNNmwIrV1b9uhNOyE59tt/elsEHJp984q+vXg00aZKdaxMRFYG0ekaJSH8RWSIiUwJlzURkhIjM8pZNvXIRkadEZLaITBKRAwOv6eEdP0tEelT/7RAR1TCVlf56t27+eqrBnXxYvdpfr2oIRbT99stsXYiIqLitWWPL9u1tWVUgato062H71lvZqY/L4/j11+H7R4/OznWJiIpEusP0XgbQJarsNgCfqmo7AJ962wBwKiy/QTsAvQE8C1jwCsA9AA4FcAiAe1wAi4iIkhQMRt13H3Diiba+fn1+6pOKBg389c2b81cPIiIqfmvX2rJ58+SO32svYMoUoFmz7NUpkfnz83NdIqICkVYwSlW/BLAiqrgrgFe89VcAnB0oH6BmDIAmItICwCkARqjqClVdCWAEYgNcREQULTgkLRiMKisDDj7Y1ouhZ9Q++/jrv/4K3HOPLdNRv37kvSAiopolXjDq3ntzXpWkFPpQeiKiLMtkzqgdVHUhAKjqQhHxBkqjJYBg6L/cK4tXTkREiXz6qb9+112R+1zCVDdcoVD99hswY4a//eijthw7FrjpptRzePz2G7B4sSWIJSKimsd97kUHo7p2zX1dkpHuwxciohKRi9n0JKRME5QTEVEiI0f669GNbJcU/Nxzc1efdNSvDwwZEls+bJgNNRw3Lv5rK7yJxMqinqewZxQRUc3lZtKLHna3ZUvu65KM664Drrkm37UgIsqbTAajFnvD7+At3TRJ5QBaB45rBWBBgnIiIkrkoINs2bt37L6jj7blvHmFm4+iIolZ6Z94Iv6+l16y5ZYtkcMvUsmTNWcO8MgjnIWPiKhUuGCUSxzuRG/n29Sp/vozz+SvHkREeZbJYNQQAG5GvB4ABgfKL/Nm1TsMwGpvON9wACeLSFMvcfnJXhkRESUiXsfSY46J3RecJrpQg1HJDCHcc8/4+/7wB3/94ov9dfdFxNm4ERg+PDzgtNtuwK23Av37V10XIiIqXAsXAqec4gd5Gjb0951yCrDHHvmpFwAcemhs2fbbR267Hs1ERDVMWsEoERkEYDSA9iJSLiK9ADwE4CQRmQXgJG8bAIYCmANgNoDnAfQBAFVdAeB+AOO8n/u8MiIiSuS332y51Vax+4IJUevXz019UhWcOS9eD6ifforcDjbWXe+vjz4Cdt/dejgBkcGoOXPs/nTpAgwcGL8u//1v0tUmIqICtP/+wMcfA3ffbdu77+7ve+21/NTJ+d3vYsu23TZye9my3NSFiKjApJXAXFUvjLMrJuOsqiqAq+Ocpz8APpYmIkpFssEod1yh2bjRX1+6NPyYpUuBN94ALrgAeP99y4H13HNAgwbAl1/aMfvvb0sXdAsO0wvmzOrVywJYO+9s28H7Uq9e9d4LERHlV3TPovXr7WHFV1/FBn5y7eKLgRtvjCyTqLS5ixYBHTrkrk5ERAUik7PpERFRLiQKRi1eHHtcoVkR6AR7xhnAAw/EHvPBB/azcSPQs6eV3X135JeOpk1t2aCBLZcv9/dNnOivb9oE7LKLP1wvOEwwG0+k3XWiv3AQEVH2HX20zazapUu+awI0auSv/+c/wLp1scfcfjvw7be5qxMRUYFgMIqIqJh89x3Qp4+thwWj9tnHXy/UYNT339vyyiuBww5LfOysWf569NNv16vpu+9s2a2bBYKqSkq+cqW/vny5HZ9K4Kiy0o4Pe826dcDWW9s6k6MTEWVXWH7BFi1yX494gsPlTz89/JgTYgaWEBHVCJlMYE5ERNl28MH+elgwyvUSAgo3GFVZacuOHas+tqICaN488TGbNkVux0sGKwLccQfQvr1f9uGHQK1awJAhscevXGlDBZ01a4A2bYDatW3oX5jy8sR1JSKizJkxI3Lb9ZgtFPEedNQKfAVzDzCIiGoYBqOIiIpVnTqxZcWQM8rVe5ddqj72oYfCh9Ldequ//vDDtuza1ZbBBOnRHnwwvPz552PLDjkEuPBC/2n2V18BP/9s6y+9ZEMi99wT+Owz/zULF/rrLuhGRESpWbbMZsL74ovUXjdsWHbqk2nffQc8+qitf/BBfutCRJQnHKZHRFSsaoU8TwgGqAo1GOVyZgR7caWiS5fIoFKzZrZ0M+O5ROYdO/pTfVdlu+1iy2bPtuXQoeFPt3fc0ZbBIRYDBvjrCxYArVold30iIvINGGAz5G3Y4E9aUZVJkyKHqheK8vLYz5ADDrCHRzffDIwZk596ERHlGXtGEREVq7AASTH0jHLBqIYN03t9hw6R792tz5tnvaJcMOrII5M/Z3Ao4PffA8OHp1e3yy7z11u3Dh/+R0REibnPr7lz4x8T3fu0EANRANCyJbDTTrHle+3lr69enbv6EBEVCAajiIiKVbEGo9xQNheMcgnZk5WoR9Vbb9kTZ8CG2YUNvwOATz8Fvv7a3/71V1u+8QbQqVPmZmHq2pWJzImIUjF/vj8jaqKHFhs35qY+2VKrFrD99rZ+0UX5rQsRhXO94x9/PN81KUkMRhERFauwnEvFMEzvscds6WbDe+aZ2CTkibRsGX/fL7/46w0aAL//vc2YF/TII8Dxx1vPqcGDreyf/7QcJRdemHw9kvXpp5k/JxFRqdp5Z3uwAACNGsU/zgWjjjkGmDMn+/XKBjfhxtCh+a0HEYVzeUNvuCG/9ShRDEYRERWj+vXDewgFe0sVYjAqOGwtGDirU8cCQUcd5Zcdf7y/Hgzo9O4de97XXrNlcIZB1yOpWTNgxQpg1Spg4EDgppv8Y045xV8PyxuVrlmz/PWTTgK2bMncuYmIisXnnwPvvZf88dE9ScMm6vjpJ8vZ5x4mdOwItG2bbg3zq379yO01ayzfIBFRDcBgFBFRsQjmx0iUmPvSS21ZiMGo4KxB0V8eBg60RLVnnWXbI0f6+4KBqbDE7W467zVr/LLu3SP3b7ONDYUIBuzq1QN23z32fC4penCmPAC46qrI+/rVV/76/Pn2RUrVznn44f6+SZNir0FEVIoef9xmGu3RAzjuOODcc5N/bfRseGvXxh7Ttq3NZtqzp227XrbFaM89I7c7dbLevxzeTVQYdtjBX1cF+vf3UztQtTEYRURULIKN8kRPgR9+2JaFGIxKlOPDBYkGD/aDOkFDhgD9+oW/1j09/8tf/LKwoFUYN2te0K672vWPO86G/q1ebV+Snn7avvi4+nXuDNx4I1BW5s+u5wQDVQMHJlcXIqJiNmmSDWeZMSNydtFkrVoVuZ3Ml75EQ/kKXf/+kdszZ9rSTcRBRPlTUQFsu62//corQK9e9nCTMoLBKCKiYpHsbDtuqFohBqP23deWb7+d+mvPPBO4+urwfWVlkdtdu6Z+/qAePfz1nXYCGje2IX21a8ce27evzeIXXYfatf2eVS5PFhFRqRk92iaO+PnnxLPfJSN6iFoyScpdT9ZitP/+4eXz5uW2HkQUa999gWnT/O3vv89fXUoUg1FERMVi5UpbhiUuDyrkYJR7yt2hQ9XH3nWXLaNzaoSJ7kXVpk1K1YoR3cspXYce6q+nkqSdiCifFiwATj7Zhh9H+/5768nqhtTdfTcwYQLw3HPA1luHny/ZYWfBnH4AsGgR8M47lvcPCM+/9913yZ270FVU+OvJfEYSUXYFA1FAZO/8sCHElDIGo4iIisXPP9vy7rsTH+fyZxRiMMrNGNS4cdXHuoBSMMdTPIsWRW7ff39K1fqfq66yHB4nnZTe66M1aGAzQwHA2LGZOScVPRHpLyJLRGRKoKyZiIwQkVnesqlXLiLylIjMFpFJInJg/mpONcaNNwIjRgDXXx+77447bHnqqfa55HqAbtgQf7KGzZurvuY774SXd+tmQ2VWrAj/AhgM+hejyy+3ZbK9n4ko+4J5WsM0agQsXZqbupQwBqOIiIqFy220226Jj6tVywI4waeshWDDBr+LczLj7d2T9GSCUW7qXSeVHCKffGLL9u2Bf/wDmD49s/kAXB6rYHJ1quleBtAlquw2AJ+qajsAn3rbAHAqgHbeT28Az+aojlSTuc+PUaNi9wUndmjTxv/Spho/6JTMcLtu3fz1Sy+1hwNBxx0XHniKPq7YbL+9LYO5aYgov9atq/qYUumVmUcZD0aJyJ9FZKqITBGRQSKylYi0FZFvvad9b4pIXe/Yet72bG9/m0zXh4io6H34oSUld8GosNnfopWVJfckOpcmTvTXGzas+nj3BSeZROTbbAMce2xa1cIJJ9gT6QkT0nt9VVxgjAlpyaOqXwJYEVXcFcAr3vorAM4OlA9QMwZAExFpkZuaUo3lZgBdvDh23377hb9mwwbL7RcmXjBK1RKeb7ddZPmAAUCTJrF1cgm+g8Jy+RUT13s2GmfUI/KpAvfdl1repnHj0n8QmMwwPM6qV20ZDUaJSEsA1wLopKp7A6gNoDuAhwE87j3tWwmgl/eSXgBWquruAB73jiMioqAzzgBuuw2YM8fyQbVI4ntoWVn84RL5EkxMm0yAyQXdTjklufNfd13qdXIaN/ZzbWVagwa2ZH4BSmwHVV0IAN7S6y6BlgCCiXvKvTKi7Jkzx19//vnIffGGMUcfFxQvGDV7NvD448CyZbH7EvVQrSp3YjGJF4xasgsnGhsAACAASURBVCS39SAqZOXlwD33AJ06JXf8uHHAIYcArVund71gmy1eu3vWrPTOTf+TjWF6ZQDqi0gZgAYAFgI4HoAbCB79tM89BXwHwAkiyYzHICKqgYYNszxQyQRyROwpdSH54gtb/v3vyR1/3HHAyJE2lW4yCvXjwzWEfvopr9WgohX2i80uE5RdwZ61vXtH7ku2p8HgwcDFF9t6vGBUos8pN2lHmBEjgJ49/TyExSxeT2HmkCLyBR+wHnFE1ccfcogtV68GXn3Vgr7JDBd2XDCqcWNg/Hi/vG1bf/2uu5iCoZoyGoxS1V8A9AUwDxaEWg3gewCrVNX9BgWf6P3vaZ+3fzUADpgmIqqu9estkFMo1q0DnnrK1lOZqe7YY/2eRVUptJ5gzh572DJseAmRb7EbfuctXbeIcgDBR7utACwAUT6sW5dcb4D33wfOOgvYdVfbjvclMNEXuURfHHffHXjpJUuiXuziPWB6//3c1oOokAUn5Rk9OnFe1Ojk45ddZjOD/vWvyV/PBaPuv9/arW5yoGAwCgCOOir5c1KMTA/Tawrr7dQWwE4AGsISb0ZzT/T4tI+IKJFSGdoVzMd0wAHZucY++9jyiiuyc/50NWxoeaM45IISGwKgh7feA8DgQPll3qx6hwFY7YbzEeVcu3bAxx9XfVzXrrZ0X+DiBZZef91fP/hgW956qy1dr6owhdoTNh3xennMnRu5PXiwve/PP896lYgKTvQM0Ynyor75Znj5mDHJX8/lad16a1tOmmR/r/7858jjgvlQC8XSpcALLwB/+hOwsLCbC5kepncigLmqulRVNwP4N4AjYMk2y7xjgk/0/ve0z9u/DWITehIR1Uzr1gFffhlZ5hr4xea44/z1vfbKzjX22MPynDzzTHbOXx3Nm9usfV9/ne+aUAEQkUEARgNoLyLlItILwEMAThKRWQBO8rYBYCiAOQBmA3geQJ88VJlqmng5UsK+2GzYALz9tr8d7P1aVTDqH//w13/91Xo0PPigbe+/vwWk3n3X1ktVnTr2xfqeeyLLn3sucvtsL8tJ8POUqKaI/huSKBjlZqiM9vPPyV1r1Sr/waYbRrvHHsCFFwKHH57cOfLpsMOAP/wB6NcP2GmnfNcmobKqD0nJPACHiUgDABsAnADgOwAjAZwP4A3EPu3rAWuQnQ/gM1VOHUFEBFXrCrx0aWT54MHhxyc6TyE8QXaNhmuvze51ortPFwrXiDrqKM6QRFDVC+PsOiHkWAVwdXZrRBQlOpfTxo1+YCnaVlsB55/vb7v8gID/mlWrqr7mIYdEfl6VlQGvvWbrN9zgl7/6atXnKjZlZQX/pZEor1LpGRWv3TtrlvXsPPnkxNcK/g1r3Dhy37bb2rXr1El8jnyZOjVyAgrAcq+qWp69ApPpnFHfwhKRjwcw2Tv/vwDcCuAGEZkNywn1oveSFwFs65XfAOC2TNaHiKhoDRoUG4hKhZtpKHrcfK5VVgI33+xvP/FE/uqSTwuY4ocorlNOsb9ZDNQWjt9+i5zN7rDDwvPeuVyAAPDWWzaEzOXJA4BFi2x5xhnh1+ne3V//5z/j1yeY5LtUZ7CK/tLboUN+6kFUiKKDUS+/bMtZsyz4tN9+fu7QRPmkkpmhOZhztVGj2P1lZf5Dxr33rvp82bJpE/DDD8Cdd9rf33XrwuvTsydw+eXAL7/kvIpVyfhseqp6j6ruqap7q+qlqrpRVeeo6iGquruqdlPVjd6xv3nbu3v751R1fiKiGqG6jW2XgyLfwajXXwf69rX1nj0Lo5cWERWWjz8G5s0r7GGsqsBHHyV+Gl8qVO2L34kn+mUTJgDt2/vbn31mCYH/9Ce/rFs34JhjIs914IG2jDfBxPr11sOgshKoXz9+nYIPZy6M17GwyO2+uy3PPtuCs9H3ww1VLIZhQkSZFh2MGjjQlm7G5UmTgDfesPVzzqnetZ580l+PDhI7desC++6b2gx9mVJebu/3uuss9cXf/gZccIGVJzJ2bG7ql4KMB6OIiCgD4gVtXnghudfXrm3LRE+HqksVuOYaexoTz9NP++v77pu9uhS6Tp38dZcUk4gi/0YV8lT2b70FnHaafQEp5KBZJrgvV/EeZtx1l+UtatWq6nMdeaQtr7wyfP+qVUCTJlU/qHDTtAOWg68UdeoEjBplX7Lr1o0MfK5da8ODAKBp0/zUjyifooM+48fb343Fi/2yefNsuW5d5LH/+U/ic3/4oZ1rypTYfWE9o5wNG/yeWdn8XLjxRuuNtWmTbbdubT3BovPKnX564vOce2526lcNDEYRERWi5csjt92wh169knu9myo6mz2j1q61ZOEXXBC+/+STI5/CxEuIWxN8842/XuAzmxDlVHDG0CVLgGnT8leXRNyXHMByv40enb+6ZMPpp/u9nNwMd++95/fWCUr05Syay6viZhOtrLTeUI4LRlXl3//21xP1oCp2RxwBNGhg/y/c79zw4XbPP/3UtocOjc3pRVTqontGOcGHtHfeGX7MbrtFbkcHqx54wJbPPmvLunX9fYn+3gRHMRx1VPzj0lVZaYGuxx6zBzcDByZ+aPPjj/76c88BZ54Ze4xIcjOi5giDUUREhcg13J3Jk1NrfLqGe7Zya6jG77rsjBgRuR2cYammqVMHuOMOW4+errsm2bix6m7kVLMEZ2Hr1Qvo2DF/dYln5Uobphbk8pWUgieesABHv3627R5iPPEE8MEHscenEowq8+ZKcp9Jt95q+Z9c7pJJkyIDkvEEvxw2aJD89YvVwoV+0vdgIM4ZOjS39SHKNxeMCvaSrMrYsfb3JTpX0rJl/vq8ef7DhV9/taXrgXT44cB226VX33SVl/u9wG66KXJfo0bJBe9PPBHo3TtyYomgAspjymAUEVEhCs489Oyz1hDfaqvkX+8a98EvepkU/cXMGT/ef7IUraYPLXC923r0yG898qlrV+teXlWXeao5/vCHfNfAt2GDJdEOPoFfuxZo1szvLeTss09u65ZNf/6zv752rf/+998/Mhm5E91zN5FgEOmnn/wcgjNmACtW2HqyvUUPPtiS89aE3IPBz/tCHr5KlCvu79KDDyY+Lvj34eCDLfgd/DsEAPfd568H0yhMnBh53Dff+GkvwgR78mbiM2H9emsjneBNrPv445H7L7oo/HXR7et33rH7cOmlNowxenKQAppVj8EoIqJCtGABsOuu9gESL9dGIu5piOt6nGnxEjYedBDQp0944zk4G1JN5J601WTDh9ty6tT81oMo2rJl1uPmyiuBW27xy11y3GjJPJ0udNOmxQZ2Jk70h9HVr29Dvl98MfKYbt2Sv0ZwiMtLL/nrdetaHpRUjB1rvYRrAje8pqICePPN2P3sGUU1jWt3br11cscHh81FJ/3v399fD06OMHmyzRwK+AGhRPbaCxgyxH9tdblA/6hR4fvDJtB45x2/beW43qsiwPbb23r0A5UCwWAUEVEhWrOmel92fve7zNUFsKDYJ5/4X1KqGjL48cd+rhDApvXeZZfM1qnYnHZavmuQf26oJvOdUKEJTuUdnHjhmmvCj9+8GXj44cQTOBS6sCGRRx1lQ+kAP5B0xRWRx+y8c2rXcUGnYEB+/frSGuqYae4Ld3RuG8clhieqKVzPqK22imxfJsMNF44W1tPo229t2bJlcucO5mUaNiy1ekVzwwRTcd551gPM+e47P29skKvnJZekV7csYTCKiKg61qyxJw8iNrwjUzZsSG1YXrRE3YqTNXu2PX39/HP7cD7pJH9K7eAwQsCepgcT+taqZV/WTjvNhmJ88EHqjYdS07KlDXupycMV3e9lvN4mVPPkuofRiBHADz/ElkcPY6iosGFl8VxxBXDbbfEncChWwfsQbzhcqp9N7nPjoYf8spUr/fVrr03tfDWBC0Z9/31kuRu206xZbutDlG+ujV2nTngPoWjxevA7q1cDgwbF3//zz8nXzalu22bNGn/d5RkFbLKgZLmeUNG23to+1wYMSK9uWcJgFBFRdQS7z6cznC7MihXAokWRM7ClKuypSKratbMZlo47znL9AH535OhhePvvb7MAOb//vS0bNKjZwZdoO+5YM4brffQR8P77seXui26iL/lUs4TNshkdGMqUF16wWT732it236uvRm7/9puf3ygoLF/J/PmZqV8uVVRUfUzwS0337ulfK+xvXvfu/jCasPtc07leY8cfH1nuemtU9UWbqFSsX29D51zS7R12SO510bPvTZwYmbri6KMTvz56IqFkHHhg6q8BbNKIxx+P/BwKftb06VN1j6a//tV6TLZuHf+YWrUKLuceg1FERNURNstNdX31VfXPkYmeUUHBD+UNG4DLL098vOs59c47ma1HsWvQwBpW2fqyXShOOw0455zIMtXI36MxY3JbJypMq1bF9rRJJlCSqhtvjEyWPmdO5Bf66KT669fH9qA64IDI4RBOWOC10EXPLhWtrCwyGOV6JQTzaSUr7J4B/mddTe81GyZsKPMllwD16tk6g1FUUzzxhD90Dki+V2CwlxEA7Lsv0Ly5vz1pUuLXB3v7V2XcOFsGPzOWLrXAz0EHJX7t1KnWZr/hBuAf/4jd797vli1+2TPP2BDyYDvqzjuBr79Ovs4FgsEoIqJ0vP22JRr86CO/LBO9kQA/kHPuuemfI1iXTAc+kknqSOEaNLB/j1L+IhH8fVu8GJgyxdbLyiIbU+l0gafSUF5ujfRHHrG/d9EJaSsrM3/Nxx6L3N5tN+v5CYQP+Vi5MjIBbr9+NmQq7O+fCxAUk7lzE++PvieNG9v/7YcfTv1aZWXANtuk/rqaLJi3zHn1Vf93LV4uKaJSk0xP6rCE/tE9o4DI/E7RnnrKX58yJbW/WS7gtGiRX3bDDbYcPz7xa/feO/H+Y46xpcu9969/WU+pp58GDj00+ToWKAajiIhS1bmzJQg/4IDI8spK4L33Uj/fc8/5SRTHj/enXHV5NtJxyCH+eia/9NetG/m06PbbEx/vEp6Tcd2jS/m+BL8k7bijTXf8ySexAYZS7x1G8bkeMbfeaj1AontyZqNnVJhPP7VlWNLYww8HfvzR1idMAK6+2v//+9prkccuW5a9OmZLor9BM2Zk/nrJzoBFpkuX8HI3lXyfPvZ7WIy/e0SZFpyMwQ1TcxOmBLVoAfTuHX6OYI+rsMkdEhEBttsusjfW7rv76//6V3rtvoYNgXfftfVOnazdFOzhWwIYjCIiSkVFhT/laliekHRmsbvqKkuiuHy5zTrnRAe7UrHddv761KnJvebXXy3vk5tVqmHD2GOic3/ss0/88zVtGjmtNwHz5tmyqiEyxSzsi2ww98GTT9rSJeINU8rBOoodghQ9jCvXvebCnqCvWOHn74jOsRH9JHvhwuzUK5sS/R/bY4/MXy/YKzLouusyf61SEJ1r0Q3/OfFEv+zSS+MPgSQqFcF8pO73Pfg3+M47I/Mkud5Pu+0Wfr7bbgsvP+44Wz7/fHr1XLrUHrR8+aU9lLv3Xn/fH/8Y3qaO549/tGWLFgWX4ynTGIwiIkpFvC8dZ59ty6uuSu18wd4hzZtHnr9Bg9TOFc19mCX7RPqzz6zX0/HHW7CkqmEAPXok7sb83XfJXbcm6dzZlmvX5rce2RSd3B6w3y3HPa0cOzb89Y89Zo22Ro3Cz0XFLziUAQCmT4/crs4Q5TBhwSbAJmkAqp5UoEOHyO1gsB+wIXwixZWY3w23e+wxS+j+1lvZvd7y5eHlwRn2yBf92epmnYx+AFRMv3NE6QgOGXbtBtfWbtbMEncHAzZ//rM9AHvxxfDztWkTXr7TTtYmdxPwpOuYY4A//Sm5Y8OGpG/Z4r/P2bOrV5ciwGAUEVEqwhrUZ53lPwEJy/OQSKI8U2GzTKVi//1tmcwUuIANwXPcB2nv3vHr8cIL8T/UAWDnnZO7bk3Stq0tXV6wUjRnTvx9I0ZUHWhweRHWrrWhUVRaNm+OzaGx7bZAr17+dnRwqrriBULck2qXw6179/Aer2Vlkds77WS9t6KHUp92WvXqmUsu4e5uu9nQr27dsnu9eD2jopPXU7hizEtGlAl33WXLYHvABXGCQ7xdb8JttrHeT40bh59PBBg+PLKsffvq1zPYHn7ppeReE3wA3batPQSuXRt49FErcyMxShiDUUREqXBTywYddFDioEw8ifKipJN7KpoLLlXVC2fDBhsCEAyQuOs3axY/qFRWFj4L0o03Wo+D6C9w5D/dLtVg1IYNifMZtGhhvxe77grst1/V55s4MXN1o8Lw8MN+DgzngQeym/tm6dLw8gkT7O+w6xm1115Aq1b+cI1Edt4ZeP31yLJMB9GyJfg0PlFC32z5+WfgppuAv/8999cuVvGCUdHD+YhKjcvpFwz2n3OOtT/dLJ+ApaT47LPYnqthXNu1eXPrDRU9c2o6grlak+WGBO63n83u50ZEnHCC1Ss4RLFEMRhFRJSK8vLYsk6d7ElMcBrsZMQL1my3nT/srzpc74M770x8XKdO9iXs+utj9zVtar0WgMgnUK+8Ysuw99C3b3YS4JYCF4CM/jIOWOLLAQOKO7F3VT2ZXF6H1q3De6BEByTi9aag4hWWw65uXT9QC1iA/4Yb7Al2WK+mTZtS+92IDv4GZ9b74AO/Z5T7wl/qgfTgA4rg8JaZM8P/X2bS1VdbIO/RR/3Zpqhq8YJRJZ5Phmo4VT/HYDCpf8uW9jlwzjl+WYsWyT1IAGym1CuvtHytmXLqqbFl558fuR1McA4A//d/ttxuuxo7yUPGg1Ei0kRE3hGRH0RkuogcLiLNRGSEiMzylk29Y0VEnhKR2SIySUQOzHR9iIiScu219mUo+oMimhuCdPfdFuz54APglFOszH1pqir/yPz5sT0+grNudO2afL0Tcddws+/E4/aH9R5YvtyG4/XpA7z8sl/uppONfq8uoMUGcjjXgy5seGa3bpaHKywoWCyCXdPXr7cvnCed5Je5bvOtW1uCaPf/raLCZpSMfqKZKEE+FaewQE/dujZ7nbNqlZ/gPqy3Ub16fv61ZLhgk9Onj78+YUJsMKrUDR4cXt6unfUMy6bmzbN7/lISzJkX/MwI9oaKnokyaMGCzPSyTmTuXGsPxOt9SFQdwTZmorQWqSorA559NnJCgOq67LLIpOWA5eIbNswmGwCARx4Jf637HlEDZaNn1JMAhqnqngD2AzAdwG0APlXVdgA+9bYB4FQA7byf3gCezUJ9iIiq9vTT1vBr3Dg28faee/p5LVyy1TPPtNnuzjjDbwy6hIrx8pM4O+/s53NygjPnZSp3xx13VP8czZrZ06ZnnrF8Ko5LQh0cZ79hA4ddVMUFW3bZJXafy2Hw/+zdebxN1fsH8M/DTVIaKDIVIikNNElJqYh80TynOY2a0/Rtnvtq/jaqVEoSiiYa1bdQIhkSoiKRoWQW6/fHs9dvr73PPuM9472f9+t1X3s4e1jnuO7Z+9lrPc+jj+avPdlgTGxvrt69tZLi1VcDo0YBM2fqj7XLLjq1gYaBA4NPKO3wpzfeyF27qTCibp6rVdPhnbaS5+zZ/mvxKnKOG5fa+Vatiu1x5+bHu+02/4bHrndvrIcMSe08Vin05nP/L+bLiSfq9Nhj83/uUrXllvpwIpybzL1eSFQVsUEDzdGX7IFUeTRtqsmW69Qpjd99Ki3hyqvFrEoV4Prrg+tENNBkg/B33hm97xVX5LZtRSyrwSgR2RLAwQD6A4AxZp0x5k8APQB4YzowAIAdf9IDwEtGjQWwtYiUM2MvEVGawk/N3Twgc+fqkLO1a4OJwHfbLfY4dpiJTQwbJeop5YQJfoJGADjwwKRNTonb0yCeRHmrAD9oAOiTJHsj6SaG3HlnbXP16tl9clUR2XwAiW4ggPgXLMVm3Tq9GenbV/PAWHfcEdyuWbNg7z9bKcp+DuFhne7/r9WrE/dYNCZ5b0QqHlE9o9at078dhxwS+1pUXjrr+eeTn2/zzYHTTguuEwn+joV7Rk2apNN69ZIHT2xg3iqFG/K2bXWaz4cHgwZprir2dkzPQw/F5iZzhyutXBl9XeFe10SlF8iFe+7Jz3mo8rC9Ay+5pLDtSJX7oMNle/qG1a8P7Ltv4h6OFVy27xqaAvgDwAsiMlFEnhORzQHUNcYsAABvahOrNADgDk6f560jIsqfbt2CyxMm+PNuwvLPP/fno57Wv/OOTu0wuwsv1C8mNz9HuAvvFltoL6lWrfx1tsJTeblDTuLlIRo0KPExwpX4fv1Vc764w/BmzAC++CKzNlY2Nhi1cmXi7W6+GRgzJvftKa8bb9SA7f33BxOJJkuqa3saxhsetcce/nyNGn7wc+XKYM/DjRs1iLHppskDfFQcoi66E/3NCwd33OTb55yTeWn7E07w521i3PCNhFvpKJ7p07Un1xln6HKyAH8xsH9/GuT5kpvDt7PjyiuDQd2oHIR2KD3gJ4DOBTcYu3Bh7s5DlZPN95dKUvJic+aZ/nzUQ+o1a/QeI6owUiWS7WBUGYA2AJ40xrQGsBL+kLwoUd9KJZy5lYhK0ocfBpfdIIB742u737o9PFxXX+3Pd+0KPPWUBnNq1vTXH3VUcJ9vvtGbaREdvx7v6Ukm3Bv8NWuit7HBkXjC+avq1QN23bV87arMbIJK+zv28cdaSeyrr2K37dAhf+3K1IMP+vM2GAskf8png1F2OJRNmvzii37gNDxcdcQI7YXn5px5911/voJc0IlIHxGZIiJTReRyb11k7s2SFNUzKlFvmXAwatSo4PKiRfH3DQfhW7YEOnXS+agn2JnkjNp6a+0daB9QlEJQ1H6v1apV2HZQZqpWDX6nRwX53LyUbo60bHN7pT7xhAZmN24Ezj/fz7FJlKlly3RaSlUjv/5aH9S5PXf32Uer7bk5+ezw8fr189u+IpPtYNQ8APOMMXYg/xBocGqhHX7nTRc52zdy9m8IoGJcTRJRaVu5UocGucPnxo/Xaffu0fscdpg//9570duEexq5T3t6985u8mp3yJybCNUVvhnp0ydYESTREBlKn71pmDMHGD1af2duuqk0y/e6PVQALUsMJK+oB/g3/aefrnmCnntOl90knuHeMt27xwac3LL09qK1hIlIKwDnAdgPmnezm4g0R/zcm6XHvXG+4ILkvTbCwahwxaJE1UJfeim4/M47fm42N7G+ZZ/CH3NM4jZF+fJLnd52W/Kej4W2dKlOGYwqXW7AP9nQ0D/+yN3w0fA1zYgR2rZnnw0O8yfKhO2dWkrBqH320VQL4SDxFlvod8N332lvRpszM9EDlUogq8EoY8zvAH4VEZvR9jAA0wC8DaCXt64XAFvG420AZ3hV9doC+MsO5yMiyrkZM+IPG2jXTocGhaveAcD//he9j5tHKYqI35Pkl180qWi+bgaGD/dvllzhp/jVqmlvk6ik1JRdUUGbli3z345MxcuN9thjyfedP9+f79jRn3dLGycauvXll7HVmypAMApASwBjjTGrjDH/APgMwNGIn3uz9Lg9KXbdNdhzNIp7sxu+8QWAiRPj7xv+m+fewO+9d+z29vvgrLMStynK99/r9Ikn9Pe4mPOY2SfyyXrGUmlINtwe0HQEM2YE0wak49NPgUMPDT7YWrxYH9o1cvoVXHmlPx/1/5UoHaecotNwXslS9PHHep2y117AcccBd9+t6yv5/5NcZJq9FMBAEZkMYC8AdwO4F8ARIjITwBHeMgC8C+AnALMAPAsgh/1IiYhC3F5PYbaXR5Tw0DUrXtUnwH/ibjVsmJ/Ag63+d+GF0YnRw0/w2RMq94YP12lURavHH9enZLVqxU+EWSxeeUWn4d+ZVPLCxPu/4gaj4vXmA/R3uU6d4Lrzz09+3uI3BcDBIlJbRGoA6ArtQR4v92bpcYcXRZWztkOV27fXqdujI+qmO1H1UtsDyIoaIuiyFd86ddL5qAB+PIceGlyOysfUpQvQr1/qx8wV+xmXQn4ris8+EAh/V0Q9SPrgA+2p1KxZZj0xunfXgNSBB+rxFy/2e3b/6qT/DZ+7EJUbqeI577xCtyD7Pv1Up/ffX9BmFFrWg1HGmEnGmH2MMXsYY3oaY5YZY5YYYw4zxjT3pku9bY0x5mJjzE7GmN2NMd8kOz4RUdaEn0YYk1q3cjc3VFi4hLjNEdU3NKomX4lck/W8CveMKoVKUKUuUcCvZk29wF+6VHtWuMn0i8WQIfr7+/jjupzJ0NJzzoldF+5R9cYb6R3TLQJQoowx0wHcB2A0gPcBfAegYv2ntMGof/4BWrSIfb1PHw0w2YTg7t/peL2N4pX/dnOKAcn/7trerdWqaeArlYqk1r//HVxevBi45hp/uUkT4P33gauuSvywI58qcQWnCmGffTSAHw6EJhr6unAhULdu4iBuFPvgaupULVjSp09q+2Uz9QBVPnXrauXTHXYodEvK75lnotfbStyVFGtwE1HlZcvLA35vp732it3OvXHu1y9xMKF2bc2lM3SoDiOyZcHdSmP5ZBNFxxO+iSuF5Lul7u+/47+2447B5f79c9uWTFxxRXDZHZ46e3Zqxwj3UOnZM3bY4m67pd6mX34B3n479e2LmDGmvzGmjTHmYABLAcxE/NybpWfNGs0ZFi8QIqJBdPv6a6/p9IgjgMsui94n/BDA2nnn4HIug+1RPU/dBP9u1b/ww4lCYU6f0rfFFsGhd99/n9rNrVsIIpmffw7mCFy1Cnj11eA2Ub//gAaEw/kFS8W6dVowgSkLCuOddzR4WoqV9KKEr+8st0d4JcRgFBFVXgMG+PO2QlNUrpDVq7Xa2c8/x96IRxEBjj5aL/bCSRf33z+/F2bJLqJsMMoG2Cr52PW8sAHKKOGebM8+m9u2ZGLevOCyOwS1adPUj/PRR/784YfH9lp58EHtoTJtWvxjHHigDudr1CiYsL+EiUgdb7oDgGMAvIb4uTdLz5o1yYPkgD9MpIzXAAAAIABJREFU0yYh//DDYLD8wgv9+XhPzcO/j4mS4Ma7mU7VJpsAbdoE19m8VOH8ZvEKXJTHihVaEOCbBIMMjAkOXcxXD13KnTVrgnks99gj9X3Xrk1tu969g8vh64S2bWOLBbhKNZ/fVlvpUOKKMQS89HTrptNEeQFLSbxr/2T5Ziu4inHlRkSUiuXL/aCTTTZr2RKsnToB990XfO3kk/ViK5NuwuEeIOPG5fcGIJyrKt7rNokwc4jkXllZ/MTB4d+XYhs2GQ5uvv22JuE85pj0hx7ts48/H5XE+tBD9WYpXm61Dz/U4SIV70LuTRGZBmAEgIuNMcsQP/dm8Zk8WXuqxWN7RiXj/n6Ef+9efRX473+B669PfIyhQ3V6yinAXXfFPoGeOhV4+GFgzBj9fSqvcHJoO8x2ypTg+vbtY/NZldfZZ2set+OPT7xN7drZPS8Vlv0Ot1Ui0/Hii6lt9/77wWX7/8q67LLEBSeKvbpkPHZIsa32mi3JKohSUKL8kaWkcePYdb16Aa1b570pxYTBKCKqPI49Vp9yjR0L3Hpr8LX99vPn3ZxQixf7T2cyseeewWWbZydfbIJEyybPtmyCXtvOYgt+VFT2pjjeTbn7e5LLqlzpDj9wLwqNAf71L+299OabwO67p3cs9+Zl3LjE27qf0003aeDgsMPSO1+JMMa0N8bsaozZ0xjzkbcuMvdmUdpzz/jDEQANMKYSjDroIH/+4IODrx19tE5TOQ4ADBwI3HBD7Ppdd9XcN+3bp9ZbK5kff4xd99lnsblCPv88u0GhGTP8HGtz5wYTSgNaFXb48NSDD1R6jjwydl2ynJHhHk+peuGF4HlPPjlxr8NMK/jl07Jl+nm9/LIuu9+NyQofpOP++7XH1fTp2TtmRZTsQWopihoWfccd+W9HkWEwiogqD/vke/784FCGZ54JDueoUgWYNQsYMaL8Nwx16/rzO+4Ymxcn18IJeI8+Wi+yfv1Vx+KPHq3rbc+UUn2CWWrs5+0GZNyhFu7vycUXa+6EMWOyO8RTRH/XR4+OnwDaNXy4f8ORqBJlqtycQckSRU+YANx2m77/O+6osIGoSiHVYJTriy+Cy7Z6WDjYXowOOQT46Sedf+ed3JwjfJOzww5+r6wVKzQXog3gWVFP6an0uA8uwkUgHnwwugKlK9nf/mQPqGxV1WrV/Id8LVpoWgMrUZ7EYnHNNRqQsoUT3OHhF2Wx2LvNFzd+fPaOWRG5wc10hv8Xu+++0/+z69bp9UyjRoVuUcExGEVElZMdRjJ+fHTJ2J12Kl+PKMstuRxO+JkPxx0Xu+711/Vm5YIL/HXXXadTNw8L5Y4bjBo/Hhg2DGjXLrjN2Wfr9Lnn9HexQwfgP//Jzvmvusqf79RJhw3OnKlBynh5w9yb2Wx3m7cFBOLZbTetVsYcN6UvnWBUvMS1Nj9Ys2bx9w0PLcqHeIlox4/XHIJdu2bnPA8+qHnWgPjDY/fZRx84uENg3aIdUT1pqPS4gZJwgn8R4MQTE+eCTFZVz/1bH/X3131gZ3//GzTQawz7PTNyZOJzFNratbHFQtx8WtnsnWx7YJZqUvdCSLUwSinYYw99wLjJJrye8TAYRUSVz+uv+8PS9t03f+ctROn5Jk1ib5Bsfqy3vBzII0dqIMSY2BLRlBvffafTX3/V38GePWO3ad8+dt0jj6SedDaRfv1i1+28s/aWuPTS2NfCucTuuqv8bQC0h1Xz5pW+mkylkk4wKpz4O8x9qvz778HXZsxIr13ZkCg4tv32sesyTex8zTVaAGDevOihgYD2PAxXmPzrL+1l8N57wKOPZnZuKi4i8XuKNmigU3eY2dVXB5ONJ+sZ5faWvu224GtPPBFcvugi4PLL/QdvNvH0/fcnPkehDRwYu87tEZZKz+FULFniH8vmo6JYrF5YqTAYRUSVzxtv6EVBw4b5Od+//qXTQt1wd+4cXLZD86xs5Eqh9KRyseVWDrPmzwdOOCGzc27YAFx7bXA4YNjGjcDTT8euHzMmuJyt3+Xbb9ebaT4hrBiSBYCMAebM8YOx5eUmtw8H0t1hQvny7rt64z1zpuaecfOB2CHb9vsASJzoHdBAdaIhKt9+GyzG4Q4/79IlOBTWql1be0XZCqpU+qJ6EA4f7veeA/zhYX37atVF+/uY7P+JG4y66abga82bB5c32wx46CH/2A89pNPLL48+tjHADz8UvpfQ2LHB5SlT9LvWmjtXCx1EfSenw+3FxmBUfIsW+fMMTFV4DEYRUeUQfmo+b17+gjDDhmk370KVnk920ZOoCg7lxu236/Trr+NvE9VbCojt7ZCqY44BHnggmBj6wQeju8AfeqhfAWzcOH/IIJD8Bpoqr6gErS6bOynVqp3JquW5w5Ddm9oRI/wb4aiATK7Uq6e9lpo1A047TYdIWTYh7/DhmlMHSH4T/s03GrxzPy+3l0aPHv7fkpdfBvbe2795GzkSOOec2GO6Q/WoYohKVN6jRzDIf/fdGliyw+psUv158xIf+8YbdbrLLrEPDZLlmLRBKZvAfMUKrWw5a5Yuv/OOBpRtnqZCCb+P447T70vrs8+AK64ALrmkfOdxg/XZ6OFcUdmho+kWRaGSxGAUEVUOUd3E8xWMqlq1sE+hO3VK/DoT2ebfTTfpTaVbvj6sfv3Ew34S+fPP2CeK4SBW376a06Np09hhHp9+qkMyfv4ZaNtWnwwDemPMhJsUxU34C0QPsUu3WmeyYJSI5hKzbM+F7t39dc8+m945s8nN12QTilepApx/vs4nCgSceqo/7+b8ibeP2wsmEVvIgyqOVP5NRTQ3oGV7Uy1enHi/YcN0+sMPOnV71iYb1r/11jpdtkzPX7Mm8Nprfo8qW4AgaphcPoUrt8Xr4Vne3pZuIPn661MPylc29gHqyScXth2UFwxGEVHlEPU02Pb8qOjOO0+HWbl5IlzxkgRT7oikFgzdckud7rFHcL0t4x5l8mStRGOfaA8ZosOi7LGsbbf156MuiqtX1/xqLgYuKZ5wJS+bL8aV7s2XG8yJxx22GtXboJBDQOO13/ZOcYNmrrffDha8cINR8Uqeu5Vbw5YsYXGKiixe3rBE7O9gsgTmlg3quoU2kvWy23RTfRBne0a5Bg7MXkGO8kq1IEd5c0fZnqFWvGuyyuyzz7SHJ5B+1VUqSQxGEVHlYEsOV0abbabJsKMSYgP5HcZC6bEX+wccEOxpkihvlM1Jc889Oqzg+OO1tHt4KIIdxgT4T6hdq1cDCxZk1GyqhEaMCC7bYOuaNVpZSwRYvlzXub2ZysvNXxYVjEpUSSzX3J4oRxzhz7sVyKJ89llw2e3lGBWMmj8/GHRzq7iOHKnDuB56SKv5DR+evN1UWsI9r1P5N7a/g+EASTxnnunPz52begBs/frYPJWADmN1ZbNiXbpS/Rvx1VflO0+4Z+jff5fveBXRIYf481OnFqwZlD8MRhFR5eImzrW5NiqLqKf0Rx2V/3ZQ6mwukNWrgz2Z4lm9OpjTya12FO6V4j4Rj+oO/8svmrQV0JvbZJXNqHIL98yxvQ3OPVerRgJ+kCXcSy8RNzBTt672/HO5Veqi8uMV8ibXDRC1bu3PJxtS16VLcNkY/TxFYoddX3aZDul1/fYb0KGDft/Zv/Gbbqo5enr0SO89UPG74Ybgcip5wewQusGDU0sS7Vbk23HH2OTliaSSrDtfBWWi5CtgHQ4a1qmTn/OWqmT5zKhCYDCKiCoXd7jTNtsUrh2FEA5GffedPjWn4vX449rT6d57ddkOm4t3s/HAA6kf+8kn/flXXtHcIIMG+evc5OqzZqUWDKPK6847g8u2l5KbD8Y+AHB/95Jxk9jWqhWb1NYdyhF101vInlEutxJZ9eqaq80NUCWycaMGnVw2d1uvXrHb166tvR3Dw3upYnLziwGpDb1ze0TbgO2SJdozxQaAP/hAp24FyHSlmi/zjz80aN2hgwZd338/83OmK1/fbbZYTO/eOt1ss/yct5Q0aODPP/JI4dpBecNgFBFVfOGnfjZ3xumn578theQO3QBYqaQUbL+95o+pV0+XTzhBL2jj5bhIp0KPO+yiShWt3hev4iOTllMyXboEe+LNmRO7Tdu2Oo1X6j2KW+0zXs6pa6/V6fTpsa8V+obvt9+AL76IfRhQo0b8UvHh9zlqVGzVy2ef1e+2Nm2y11YqTc2b6+/C2LHAkUfG9qxLxgZx33pLA1FnnqkBoSOPLH/b0gkGP/ec5rcE0n8P5ZGv/0N2iK2taFssgfJMGQPstJMmpc+GtWt1yLG1887ZOS4VNQajiKjiszfuZ52l08cf14Salb3EdSET+1LmbK6PcJB11Sot3w1ouexMHH000KpV5m2jyu2ii4ADD9T5qIpU9m9ux46pH9MNotuhRWFDhuj0uONiXzv77NTPlQv16vmfiauszP+MbLUxW3QgnCj5pJOCVcwAoHPn7LeVStv++wPvvRfMVZbIfvvpdNIkndrgqK2eaoXzwaXjqqviv9asmQZZbQ++RYuCr2/cmPl502FzOb3wQnD9woW5OZ/Nczd0aG6On2sLF+rfq4cf1pxjp5ySneO6AfcNG+I/HKMKJSf/yiJSVUQmishIb7mJiIwTkZki8rqIVPPWb+otz/Jeb5yL9hBRJWeTIO6wg06rVAk+bScqJbacdrhCkXshN3Cg9qZw9eyp27zwQvxErGVlwPffBxP+h3P0ECXy9NM6bdgwtgefLROfLIF3mA0oxQug33WXPx8+Z6rDhPLNBgBEgG7ddN4Gk59/Pv5+ffumloOHKJnx43XatatOP/44++eYNi24fO65Oj34YGDmTB2uatc99VRw26pVYwtv5IINRrm57GrVis7pFK83YzpsVdps9Sgqj+uui62am4zN03flldltyzXX6HTXXRmIqkRy9S/dB4DbV/o+AA8ZY5oDWAbgHG/9OQCWGWOaAXjI246IKHOzZ8cO1fjtN53uskv+20OUbTapeTgvyMSJ/vzmmwd7n5xyigYCmjbVIRh2uFQ8t9ziz3M4J6XD3tC9/bbmf4mSbo4W+zvoJit32WEvQOJKk8Xqyy+Dy4mGp9xxB0ueU3a0a6fTVas0h6QNFoeVJ+m9+7t6443AM89ogMktTGArb0bJx8MQO1zOHUq7dGlwm2OP1Wm8IfLJ2J7M7drp0LZi8PXXwP33a8/LYvDuuzp9883CtoPyKuvBKBFpCOAoAM95ywKgIwCvDzUGAOjpzffwluG9fpi3PRFR+v75R7t977prcL3tah2u9lQZ/fCDJhEOd8On0mErk4WfIrvDoqpXDyaoveOO9M/z6aeaQ4QoHTYYNXFisHqp1bBh8HczFZdeqsn5w8NoLDfpbS56d+TLvvvq1AacH3449iGKW9WMqDzc75C99oq/3auvZn6Op5/W4OrAgfo9JBI7jDCc123AAH8+H1Vc7QPLqIrDlv1/uHx5ZuewSeIbN/aH6QHAJ5/kbjhgMnaYJpBaRcVvvtGk9uVJaJ8KPjiuVHLRM+phANcCsAN9awP40xjj9YHEPAD2qqEBgF8BwHv9L297IqL0XXyxP2+HMN13n97IACyjCwAtWgA336ylmak0zZql0/uczsStW/tDfIDYfGh2iGo6OnQAundPfz+q3NwbrSjxkpAnUrUqcPXV8Sugus8x7ZCbUtKkiU5teXvbU+PQQ4MVT885B0RZs/vumpMt0c1/r16p56CKUqeOPig55ZT4w2ybNg0uuz11LrpIp//8oxUl7fDWbPn7b2D4cJ2Pykk3fTowbpz/GYRzt6XKDq0NB946dtQen+E8cbk0b55f9MGaMiX5fvvuq0nty5NDLJFMHlRQyctqMEpEugFYZIyZ4K6O2NSk8BoRUXqeecafr1lTy8L27euvY88oqgjcfDJr1gAvvxy8QP/4Yz8Y1b+/3sSzNwXlS7KbiQUL8tOOUmIrD9pej7bq1lZb6ZCe0aO1h8hzzxWmfVRxHXZYdOVLABg0CHjxxdy3wc0h9957GiCzvbfnz9f2jRwJPPaYPnjJJrenU1Swe5ddtAfRt9/qcqYBYRtsijckcfTozI6biVNO0Z6mru+/T7xPsvxWK1bE/z1K1bx5mT2soJKW7avTAwF0F5GuAKoD2BLaU2prESnzej81BOD1h8Q8AI0AzBORMgBbAVgae1giohR06xZ8ihwuH55u0lyiYtSihT//+uuaA8rl5oMqdCUxIkrdN98Ee49st51ODz+8MO2hiq9OHWDt2ujXEg1byya3J++RR+rU7b192WXBqprZ5B433GvJFS9fXSqmTAEmeP004gXje/RIbahcNvz4Y+y6U09NXBUvWcW8I4/UXmOvv55Z3j43hxhVKlntGWWMud4Y09AY0xjASQA+NsacCuATALbebi8ANgnF294yvNc/NiZf/xOJqMJxA1FRmJKOKoIaNfybhGXLYnN9JLqgJioU2zP1kEPyd047/KZUlWd4FFEqEhUTSDbkNltsjjS3EAEAPPGETkeOBIYOzc253dvORInU27fP/By77+4/NLLv4+abMz9eeeUiR5UdvnjjjZnt/8MPOm3WLDvtoZKRr7qJ1wG4UkRmQXNC9ffW9wdQ21t/JYC+cfYnIkosWRx76tT8tIMoH2yS5tWrgT32KGxbiMLCeVUaNfJzObVpk5tzNmoUXO7YsXxVwIgqg3AvmV9+8efz1TOqWjVNIh7ORdS7d/T2kyZpDxybW6083OrLbi+pcLDoxBN12rlz+c8JAGecEVzORRBm7Njo4X/xcoZu3Bi9ftWq1M+ZaWW+v//Waf/+ibejCidnwShjzKfGmG7e/E/GmP2MMc2MMccbY9Z669d4y82813/KVXuIqALbuDHYxffkk4Ovt2gRW2GPqJTZRKtTpwIvvVTYthCFtWsH3Hmnvzxrlp+PxVbby7YvvwSaN/eXN9kkN+fJlunTtUgAUSGFA0BuUDefg1Xq1YtNIF4lzm3qI49o0CMbVd3iVQoMFwEBtNdxeRNs28IjdgiuZQuTuMqTP2ndOuCAA4BOnYL/jsYAP/8cvc/110evt/myUrFmjZ7bTYg+eXLinFRz5wLXXKPziXrqUYWUr55RRES5c/jhWnUI0KdNDz0UfN0tE0xUEdiL9oEDC9sOonhuvBH46CNg0SLtcWBvtrLRmyFKw4bA11/7y8UejNplF/18iArp9tvjv7bnnvlrRypsgNsmVf/gg/IfM17A59RTY9dVq6ZD3B5+OPNAUadOOo0Kym/YAHzyif4ta9RIC49kWh10/nx/ftkyf37ePH/++uuD+cLuv1+nNWoE01rYXks33KDHatw4tgKiNXs28N//6tDEU0/VwkJ77qk9uOMND3TzUXGYXqXDYBQRlbaJE/XL2zrllNg8G7vtlt82EeVa1FNbIHdDoChvROQKEZkqIlNE5DURqS4iTURknIjMFJHXRSRH2XyzrGPH2B4AY8bk7nzu3/5SqCAZ7mWx3XbAypXArbcGq8MS5Uq9erHrli7VwEF5ewFlgw0wf/dd9BA5W6UuU/EK20QlLF+/XhORX3FFan9fVq6M/ftnh9W7wR6bK2vtWu3ZP3++HzT6KcNBQ25g3v2MVq7Uac2awN13a4DNJlffYQdg8WJ/+3XrtCeV3Wf33fVB2Jw58XtkT5vm54169VXgggv818aODW77zjtAnz7+7+CECblLVE9FqwS+qYmI4pg6Nfbme9tt9Uv222+BSy7R4Xn5SsJJlC/hXh/Vq+vvfJMmhWkPZYWINABwGYBdjTGrRWQwtCBMVwAPGWMGichTAM4B8GQBm5q+7bcHfv8989LoqdhkEx3as3Fj8feMClu4UIcB1agB3HJLoVtDlUWvXsDMmX6vGMAfUlsM9tkn8XDB994Djjkm8+PbXkP33pt823RyJxkTfe0ZNfSwQQOdrlkDrFgRfC1epcNEVqzwc1zZYzz2mPZQskG0f//bf71NG/3b07KlnzQe0KGQw4b5y5tv7s/b3tlVq+rvT9eumoR8xoz47erZE7jwQs1T9tBDWgHbxYdplRKDUURUev7+W2+8o6oyNWyo09atY5PoElVUv/7KXAsVRxmAzURkPYAaABYA6AjAjmUYAOBWlFow6rffNFdJ48a5PU+1anpTVwo9owC9wVu5EqhTp9Atocpok000ELN+vZ/uoJT89Vfm+65Z4+eM2nlnnd5xR/wE32Fffqn58aLY3kSJdOoEjBrl/99fuzZ2v1SDURs2aG+otm2BL74IvjZvHnDZZTpv8+qFCz6sXq3DHtet89e5gSggOISuZUtN8n7SSfoQbPr01CpWP+l9bbHwCnk4TI+ISsvGjTrWPioQ1a2bXz6cqDIptV4gFMkYMx/AgwB+gQah/gIwAcCfxhibPGQegAaFaWE5iOQ+EAX45dlL5f/Ezz9rnhWiQhEB+vXLTkLwfPvjj8z3veQSP/hTv75Ob7oJOP301PYPB31ca9bErnvjjeDye+9pTqhNN42/jxscSuSWWzRh+WuvAZ9/HnztrLP8+ZkzdRo1DBEIpr0Ia9HCn69SRfONucWBnnoqer/27eMf0zr++OTbUIXEYBQRlZbHH49d17Sp9pYKV4UhqgxefTV+DikqKSKyDYAeAJoAqA9gcwBdIjbNY5mrEvPnnzqNurErRrVrx08GTERBv/yi0379dHrddZkfq39/fz6TnpTXXRe/59KkScHl8eOB444LrqtSRYe52QC6m2jcSjUY9e67Ov36a80F5YrKO9Ug9Dwj6gFvWLzqhtZJJwWXa9cGatUC3n8/fkBqr710ymIslRaDUURUWvr0iV3XqRPzQlHldeCBhW4BZc/hAOYYY/4wxqwHMBRAOwBbi4i9W2oI4LdCNbBkDB5c6BYQUbY1aqT5mM48M7vHTSUY1bp17DobSApzg2SrVwP77hv/uDa9xI8/xr4WziEVz8SJ/rms3r3jb7/TTsHlTz8NLoffl5svKp6tttLeXtbixcCSJZoH78MPY7c/4AAtaLF4cen0ZKWsYzAqVVOnAnfdlTiJHlG+LV6sJWZffNEvm10Z3XBDoVtAVDjFUPGIsuUXAG1FpIaICIDDAEwD8AkA+1i9F4C3CtQ+IqLCy3aS9VS+R20aiHDF5qhemAccoNMOHeIHrCwbjLJD6AA/WDR1avJ2ud5805+PVykQSJzfqWZNzcV11lnAo4/qujPOSO387dvrcL6HHw6ur1ZNA16nngpceaWuO+IIPVeidlKFx2BUqlq10nHEybooEuXTdttpidmzztJkghXdc8/ptGNHYMECrQby+eexiRiJKoP+/bVrfbzcD1RyjDHjAAwB8C2A76HXac8AuA7AlSIyC0BtAP3jHoSIqDKwFeOWL89s/+228+dT6Rlle+8cfnhwfffu/vzGjcA11/i5lx54IPlxbXDrP//x173/vk779gUuvzz5MSx3OJwNiFn77BN/P9uL6vzzgcmTNXj0/PPApZfqkMNHHknt/JtvrlX1okYxdOgAvPKKvs///S9Y0Y8qLUZWiCqKf/5Jvk0pe/994LzzdP6HH/QG/LbbgIMOKmy7iArl7LP1gpc9oyoUY8wtxphdjDGtjDGnG2PWGmN+MsbsZ4xpZow53hiTQb3vSsKWaE+lVDsRla6NG3Waac7ELbf051P5Ht1/f50efHBw/ejR/vykScCDDwLTpulyzZrJj2srArqVAd22pRoIAoChQ/35Vq10GJw1dqxW74saDvjII8CMGcDTT8cWmthzz+wPo2vXjtcuBIDBqNTccUdwmUP1qBisX1/oFuTPffcBXZwcvjZxJRERkevaa4GlS8uX2JiIip/bK/jmmzWZ+Jw5qe/v5ldKpWfUtddq4KlPn/jBmSVLgsvNmyc/bufOweUnnwS23Tb5fonsvTew447aU6pnT/2sqlbVoXFRbapWDdh55/KdkygDDEYls3ZtbDfCVJPJEeXSDz/Erisr06pyxWTDBn06c9ttmR+jb9/gsu2aTURE5BLJfj4ZIio+m27qz995pw4pa9oU+O671PZftcqfT3WY3uGH67buA+GjjvLnw6MUUun9s9lmweWtt45NC7NyZfz9o6rl2bQWADBsmKa2ICpCDEYlE5WU7quv8t8OImvSJP1iGTs29rUNG4Jde6PMmKFPjfNh7Vr90p46Fbj11tjXN2wATjtNS95GEYlNslinTtabSUREREQl5IILgsvPPqvTzz/X689EXnsN+PNPf7latfTO7Q6de+cd/1o1G6MWoq7jX3st/vannx67bs89y98OojxgMCqZqD9mnTtnv6QoUapatwaOOUaTDALAb78FS7vHewpjjHbN3WWX/FWuOP74+K/NnauBqoEDdRz+f//rv7ZxY3Slj7PPBr78MuvNJCIiIqIS0qwZMH26zh9zjL9+wgStYDdwYPx9TzkluJzudfFll0WnbclG/lYbjDr2WH+dzZkaJeoBc6JqeURFhMGoZOINyRswoPiGQ1HFtmFDdOWJevU0QWH9+rq8caM+mVm9GvjjD123fr1W1Zg1K3g8QMu23nFH5rnQhgzRL73WrWO7EY8Y4c+7Y/vvvBNo0iS47cUX69Ol6dOjA2rffKPVw2y5WyIiIiKqvJo31wpubkDmxRd1Gs75m0gqw/SSOe64YHLwcKLzRNxiPDYYNWCAX+UOCA4rdC1cmPp5iIoMg1HJuF04w956C2jbluNwKT/KymK/WM86S6dVqgDz5wM9emhQado0oE0bHdL26KNA167AuHGxxxPRRIz//rf2sEpmw4Zgb8G1a/3eT5MmAVts4W/nPpU58UTg99+Bdet0bPvNN0cfv1s3YNddY9d36aLJGImIiIiIAH14uXIl8Omnsa/NmJHftrz5JnD99Tp/3XXAe++lvu+oUf785pv703POCa7/+2+tLn377XoP+sMPwLJl5W87UYFkNRglIo1E5BMRmS4iU0Wkj7e+loiMFpGZ3nRNrWDpAAAgAElEQVQbb72IyKMiMktEJotIm2y2JyvcYFS7dsHXTj9db/Dd4UVE2bJxow7FGzUqthdejRrA0UdrDyPX4sU63WsvP8F5nz7Ahx/621xySfT5bC+qKI88osGlsjLt+rxokZbNrl49dtvp04NPmA46yA9MnX12bM+me+6Jf9558zS49u678bchIiIiIkqVvX498UTg8cczP86YMdHrL7pIr9VT5SYxdxOz77VXcLvtttMHtLfcovegJ5wQeywWcKASku2eUf8AuMoY0xJAWwAXi8iuAPoC+MgY0xzAR94yAHQB0Nz7OR/Ak1luT/m5pTvdLpSudJPeEaVi7lxNxti5M/Drr/76PfYAZs8Ghg71h+ZZ11yT+Jjr1weTLrpsICtqn8svD66rW9d/+gMAnToBLVvqfLhn0+efA4MG6Xx4/P7vv2ulvBtvjD3vV18BDRpEt4mIiIiIqH37+K+tWxe9fueddYjfoEGaJqI853Yr11mNGqV/rHvu0f3q1vXXlZUFc0eFcxl//70/36WLTlu3Tv/cRAWS1WCUMWaBMeZbb/5vANMBNADQA8AAb7MBAHp68z0AvGTUWABbi0i9bLap3Nw/cBs3Rm/z11+JjzF/vkbdjdFeI/GOEzZ9ugbAUhk+VRl98QUwcWKhW5Ebq1YFexDZBOU33KAla938S66OHYPLzZv785dcol9qVapoLrSLLtIhc888o68fcUT0MXv1St7et9+OrTJ53nl+Dim3HYD2qjLG/8J1g2rjxmkVy7Ztk5+XiIiIiCovtydR+Npx2rTofVau9IfDlVeHDrHrMkkg3rcv8MsvwY4QgI5wSIXtiZWN/FdEeZKznFEi0hhAawDjANQ1xiwANGAFwNZmbwDA6fKBed664mQTPIf/k++2W+L9Dj8cuPRSYPfdtddI1aqaxyeR99/Xbf/3P+0dsuOOGsRKNZBV0Q0YoIHCNm20tOtdd2kZ00MPLXTLyu/nn2O/IO1w0WRPb2rWBLp31/nx4zWRos0h5faI2nxz4IknNIm427Mvasx9vHKyW20FLFmilUM23VSXXU895X8xTpgQrARy6aXBbS+8EHj+eR0quN9+wQsLIiIiIqIojz3mzw8ZEnwtXiGqFSuyF4xq1iw7x4mnfXugcePk29mhh+FgFlERy0kwSkS2APAmgMuNMcsTbRqxLsOSXjk0f77ezO+/vy7fcEP8il6LFwP9+mlS59mzNTJuc/dMnepv16dP/Opln3/ud7W0fvlFg1hVq+oxx46N315jNHjxxx9+xbSKZNQo4Mwz/eVnngFuugmYPFmDKSLBz3bIEB1GFv68x4zRzzmqJGq+/PYb8PDDmnxQBLj1Vm2rFR4rHh6WF+Wtt/S97ruvv65lS+0RFWWXXfz5Qw/V3lKW+5kNGADMmaNVO/r21UBUrVrByndPPKHT++8Pnq9mTf13MkZ/wuPoRTQZ+7bbJn9/RERERERA8Dq2Zk3tYW+vn1evjt4nmz2jgOSdDMornC4jrGVLPyfsddflti1EWZT1YJSIbAINRA00xgz1Vi+0w++86SJv/TwA7qDahgCKb0xa/fr6n/z447W8/L//Dcya5UffZ87U6fLlmljuqqv0tWSR8nDvEEC7erqlQMNDn6wDDvDz8AAadNphB72pr1JFk9fVqaO9uGyJUys83jgVGzZoVYh4AbR8WblScyglU6WKfsmMGKH/bqNH62c7apR+RiLAtddqD7TatTW4km/33qu93q64QoM6AHDbbX5Z2EGDdBjirFn6HuJ9oZbX/vtrbiprp510GKAIcOqp/vozztAnM3Xq6Lh2NwhlXXih9si6+urctJWIiIiIyDVnjj6M3XJL7WF/xRW6fs2a2G2NyX4w6tJL4+cWzobLLkv8+ooVOkTRmMQ5tIiKTLar6QmA/gCmG2P6OS+9DcAmnukF4C1n/RleVb22AP6yw/mK1t57+zfh222n03vuAQ47TIeJhe20kwamJk3Sig0LF/pJ7Z54Anj5ZT84IhKsyvDZZ/4flrFjgddfD5YJPflkf7+ysmCSa9dZZwXPUb26BiBSCSz9/bcmzisrA7p2zW+0fflyraYGaO8lEWCLLfzXhw3TINmSJdq7aPz4YGW2Vav8IWuA9jhzA1njxvnz990XLKuaa336BBOAR7EJC3faCRg8OLpyXbacey5w0kn+8sKFOrVD9FLtgiyiPbIyGStPRERERJSuxo2D1/z2mtkNRtl7rtmz9R4om8EowC/G4yYcz5Zk19Xx7gGJily2e0YdCOB0AB1FZJL30xXAvQCOEJGZAI7wlgHgXQA/AZgF4FkAF2W5PbnVrp0///HHWv0M0MTjq1YBixZpr6ljj9VA1aBB2qvk55/9/c44I/a4Tz+tfyTdHlL776/lO488UgNEiQwd6ueXOv/86G3Gj9feQxMmxD/OAQfoE4ahQ/11DzzgB7W+/Tb+vm4PpNq1Nem2NXu2fjauNWv8HkGABvC22koDd/YYrrlzgZ499T3UqqXBnX331R5OrVrFb1eYG5zq3NkfZpZLIvG789auDbzwgg43zHcCwrvvjv+a+ztARERERFSsbDBq8WJNXdKggX/PZYvquA+4s+HII7XHVThvFRHFle1qel8YY8QYs4cxZi/v511jzBJjzGHGmObedKm3vTHGXGyM2ckYs7sx5ptstifnyspiS4becouOXd5sM+05FRXJFvGrjIUNGxY/gGRtsYUGqy6+2E/03LmzRsWNAY4+2g8EPf20Bj4aN9YypmHdusWuW7EieV4qQHuJieh77tdP8ziNHq1/jN0gz9KlOnbbtqlZM62i9vvvuv2JJ+rn1aKFtnfHHXVYWpSbb9bqhTvuGL9d33+vwbbVqzUnk81TtGaN/mzcqMvLl+swPWP0SwrQ8dYi+oX14Yf6nv78M7OhjVHClRF/+kkTi48cqe1YvFjPGVWZI9eaNAku23/D+fM1+T4RERERUbFr2lSnI0YA++wTXZk8XqW98gjnRM0ld1igm++VqISIKXQOoHISkd0ATJkyZQp2S1bVLle23loDJC+8EEysncyGDZp4u2dPPzl6vrzyCnD66altW7cuMGOGJmA/8MDUz7HVVhrQGDw4szYCmvT6jz+0N1jfvrEV27Ip2Wcyb54ftErXjz9qryc3QffKlfn90krFO+9oULN370K3hIioaEydOhWttNdtK2PM1GTbF6OiuF4iIsqHFSs0mXkiN98M3H57ftqTDdtsow/Iu3TRDgmHHAIsWJD7an5EaUj3einP44AqqD//zGy/qlWDOY7y6bTTNEn1EUfE32bRIj8vFqDDEm3wcvRofa179+hxyuPGaQJBQPMOffedVhVs0EB7NbklSm+6Sf+o1qvnr3vttWAOo3w47TT9UrIJ6cMaNvS3e/llHbJ47bUaTBw2LHqfP//UL4+o9cUWiAKAo44qdAuIiIiIiDKXyjV2ixa5b0c2TZ+uI1HuuMMfGcNAFJU4BqMqs8MP1x47l1yiScCPOcZPvvf668FAVJgNYv3yS/LzVKkCtG6tP1ZUj7z16zUPVSETYNu8VYMH6/BBAHjjjeCwwVde0R9r+HBt75IlflU8KyoQ9eCDue3hRURERERUWVVJIRNNvJQgxWr77YH77y90K4iyKtsJzKnUNG8OfPAB8M03wA03+PmVTjgh/20pK9PeVMVQie2EE7RM60svAccdp4GyK69MvE84yfqkSf785Zf781ddlb12EhERERFReqpVK3QLiCo9BqOI4nn0UT+HVFkZ8J//aKDu9df9bUaODO5Tq5YOv/ziC//pxbXXAg89pFUUWXqViIiIiCj/XnxRpx07FrQZRKQ4TI8oXSecoEkD16wBdthBA1T33KM9y5Yt023at/e3v/dene6wQ96bSkRERERU6b3/vhZW6tWr0C0hIg97RhFlok6dYHDJHYbnat++OIYdEhERERFVFt266bR6deCxxzQQRURFhcEoomzYbDNg7Vpg6VLtKfXRR0CfPsCYMYVuGRERlQgRaSEik5yf5SJyuYjUEpHRIjLTm0ZUxyAiov83eDAwcCCwapUWayKiosNgFFG2VKvmV8/r2BF4+OHCtoeIiEqKMWaGMWYvY8xeAPYGsArAMAB9AXxkjGkO4CNvmYiI4tlsM+CUUzhCgaiIMRhFREREVHwOAzDbGPMzgB4ABnjrBwDoWbBWEREREWUBg1FERERExeckAK9583WNMQsAwJvWKViriIiIiLKAwSgiIiKiIiIi1QB0B/BGodtCRERElAsMRhEREREVly4AvjXGLPSWF4pIPQDwposK1jIiIiKiLCgrdAOyoBoAzJo1q9DtICIiogrIucaolqdTngx/iB4AvA2gF4B7velbGRyT10tERESUM+leL4kxJnetyQMR6Y7MLsqIiIiI0tHDGPN2Lk8gIjUA/AqgqTHmL29dbQCDAewA4BcAxxtjlqZ5XF4vERERUT6kdL1UEYJRWwHoAL1wW1fg5hAREVHFUw1AIwCf2QBRqeH1EhEREeVYWtdLJR+MIiIiIiIiIiKi0sEE5kRERERERERElDcMRhERERERERERUd4wGEVERERERERERHnDYBQREREREREREeUNg1FERERERERERJQ3DEYREREREREREVHeMBhFRERERERERER5w2AUERERERERERHlDYNRRERERERERESUNwxG5YCIPC8ii0RkirNuTxH5SkS+F5ERIrKlt76aiLzgrf9ORA7x1tcQkXdE5AcRmSoi9xbo7WQsG5+D89ozIvKj93kcW4C3Uy4i0khEPhGR6d6/Zx9vfS0RGS0iM73pNt56EZFHRWSWiEwWkTbOsXp5288UkV6Fek+ZyuZn4b2+pYjMF5HHC/F+MpXl34n7vWNM97aRQr2vTGTwWezi/R1ZKyJXJztOqcjW5+C9trWIDPH+Zk4XkQMK8Z4ylcFncar3/2KyiHwpIns6xzpSRGZ4/3f6Fuo9USzh9RIAXi+5svzdWLLXS9n8HLzXS/JaCeD1kiuDz4LXS+D1khTz9ZIxhj9Z/gFwMIA2AKY4674G0MGbPxvAHd78xQBe8ObrAJgADRLWAHCot74agM8BdCn0e8v35+At3wbgTm++CoBtC/3eMvgs6gFo483XBPAjgF0B3A+gr7e+L4D7vPmuAN4DIADaAhjnra8F4Cdvuo03v02h318hPgvneI8AeBXA44V+bwX6nWgH4H8Aqno/XwE4pNDvL8efRR0A+wK4C8DVyY5T6PeX78/Be20AgHO9+WoAti70+8vxZ9HO/i0E0MX5/1EVwGwATb3P4btS+p2o6D/g9VLWPgdvmddLFeR6KVufg3O8krxWyvLvBK+Xkhyn0O8v35+D9xqvl0zhrpfYMyoHjDFjACwNrW4BYIw3PxqAfVq1K4CPvP0WAfgTwD7GmFXGmE+89esAfAugYY6bnlXZ+By8184GcI/32kZjzOIcNjsnjDELjDHfevN/A5gOoAGAHtA/gvCmPb35HgBeMmosgK1FpB6AzgBGG2OWGmOWQT/DI/P4Vsoti58FRGRvAHUBjMrjW8iKLH4OBkB16BfHpgA2AbAwb28kC9L9LIwxi4wxXwNYn+JxSkK2PgfRHhQHA+jvbbfOGPNnXt5ElmTwWXzp/U0EgLHwvy/3AzDLGPOT9106yDsGFQFeLyleL/l4vaR4reTj9ZKP10uK10u+Ur9eYjAqf6YA6O7NHw+gkTf/HYAeIlImIk0A7O28BkC7DwL4F7yLjxKX1ufgvXcAuENEvhWRN0Skbn6bnF0i0hhAawDjANQ1xiwA9I8JNHIP6B+RX53d5nnr4q0vSeX5LESkCoD/ALgmX+3NlfJ8DsaYrwB8AmCB9/OBMWZ6flqefSl+Fukep+SU83NoCuAPAC+IyEQReU5ENs9hc3Mqg8/iHOhTcaCC/c2sJHi9pHi9xOslALxWcvF6ycfrJcXrJV8pXi8xGJU/ZwO4WEQmQLvQrfPWPw/9x/4GwMMAvgTwj91JRMoAvAbgUWPMT3ltcW6k+zmUQSO2/zPGtIF2qX0w343OFhHZAsCbAC43xixPtGnEOpNgfcnJwmdxEYB3jTG/RrxeMsr7OYhIMwAtof9PGgDoKCIHZ7+luZfGZ5GX4xRKFtpfBh3y86QxpjWAldAu2iUn3c9CRA6FXlxdZ1dFbFaSfzMrEV4vKV4v8XqJ10oOXi/5eL2keL3kK9XrpbJcn4CUMeYHAJ0AQER2BnCUt/4fAFfY7UTkSwAznV2fATDTGPNw/lqbOxl8DksArAIwzHvpDeh/nJIjIptA/0gMNMYM9VYvFJF6xpgFXhfiRd76eQg+8W0I4Ddv/SGh9Z/mst25kKXP4gAA7UXkIgBbAKgmIiuMMSXzJZKlz+E0AGONMSu8Y74HzZEwBiUkzc8i3eOUjCx9DvMAzDPG2KecQ1CCF1fpfhYisgeA56D5gpZ4q+P9v6EixeslxeslXi/xWsnH6yUfr5cUr5d8pXy9xJ5ReSIidbxpFQA3AXjKW65huwOKyBEA/jHGTPOW7wSwFYDLC9LoHEj3czDGGAAj4F9QHAZgWr7bXV4iItDxyNONMf2cl94GYCu89ALwlrP+DFFtAfzldbH8AEAnEdlGtCpCJ29dycjWZ2GMOdUYs4MxpjGAq6H5AUrmCySLvxO/AOggOmRjEwAdoOPFS0YGn0W6xykJ2focjDG/A/hVRFp4q0ru72a6n4WI7ABgKIDTjTE/Ott/DaC5iDQRkWoATvKOQUWK10uK10uV+3qJ10o+Xi/5eL2keL3kK/nrJVMEWeAr2g+0m/gCaJK0edAnU32g2e1/BHAvAPG2bQxgBvSP4YcAdvTWN4R2jZsOYJL3c26h31u+PwfvtR2hTy0mQ/NA7FDo95bBZ3GQ9+852fn37AqgtveeZnrTWt72AuAJaFWD76FJWu2xzgYwy/s5q9DvrZCfhXPMM1FiFWKy9TlAq1887f3fmQagX6HfWx4+i+29vynLocl75wHYMt5xCv3+8v05eK/tBR3GMxnAcJRQFakMP4vnACxztv3GOVZX6HfObAA3Fvq98Sfw78zrpSx9Dt5rvF6qINdL2fwcnGOeiRK7VsrmZwFeL/F6iddLQJFdL9kvNiIiIiIiIiIiopzjMD0iIiIiIiIiIsobBqOIiIiIiIiIiChvGIwiIiIiIiIiIqK8YTCKiIiIiIiIiIjyhsEoIiIiIiIiIiLKGwajiIiIiIiIiIgobxiMIiIiIiIiIiKivGEwioiIiIiIiIiI8obBKCIiIiIiIiIiyhsGo4iIiIiIiIiIKG8YjCIiIiIiIiIiorxhMIqIiIiIiIiIiPKGwSgiIiIiIiIiIsobBqOIiIiIiIiIiChvGIwiIiIiIiIiIqK8YTCKiIiIiIiIiIjyhsEoIiIiIiIiIiLKGwajiIiIiIiIiIgobxiMIiIiIiIiIiKivGEwioiIiIiIiAAAItJMRIyIPFfothBRxcVgFBFlnYhUFZHzROQzEVkqIutFZJGITBaR50Ske5z96ojIQyIyU0RWi8gCEflQRM5Ncr4XvYsm92eliEwRkXtFZJsU29044jjuz6AE+/YSkfEiskJE/hKRT0WkW5LP6HLvM1ntfU7viki7VNpKRERElYuIvOpdj1yYwrajvW175qNtRETpEmNModtARBWIiFQFMBLAkQD+BPAOgHkAagHYCcABAL41xhwU2m8zAN8BaO5NPwRQE8DeAGobY5okOOeLAHoBeAvAJG/19gD+BaA+gNkA9jPGLE3S9sYA5njnHx6xyRRjzJCI/R4EcJX3PocAqAbgJO89X2qMeTy0vQAYDOA4ADMAjPC2PRFAdQDHGmPeStRWIiIiqlxE5BAAnwCYaIxpk2C7xgB+AvA7gB2MMf+keZ5mAGYC6G+MSfhAkIgoU2WFbgARVTgnQwNR3wHoYIz5y31RRGoA2D9ivyOggagvABxijNng7FM/xXMPN8a86Ox3NYBxAHYFcCmA21I8ziRjzK2pbOj1ZLoKGvDa1xizzFv/AIAJAB4UkZHGmLnObidBA1FfAjjMGLPG2+cp6Pt/VkQ+Nsb8nWJ7iYiIqIIzxnwqIj8CaC0ibYwx38bZ9FwAAuCFdANRRET5wmF6RJRtdpjZi+FAFAAYY1YZYz6J2G+FN53sBqK8fX7LpCHGmBUABniL+2VyjBT09qZ32UCUd+65AJ4AsCmAs0L72O71N9lAlLfP1wBeB7AdNFhFRERE5HrWm54X9aLXQ/1MAAbAc966BiJyi4h8KSK/i8g6EZkvIgNFZJdUTywiX4hIZHBLRM71hgWeFvFaIxH5r4j8JCJrRWSJiLwlInunem4iqngYjCKibFviTXdOc78xAMYDOFVEWmaxPeJN0xmTXF9ELhCRG7zpHgm27ehN34947b3QNhCRTaEBu1UAPk9lHyIiIiLPAADrAJzi9TYP6wqgAYAPjTFzvHWHArgWwFIAbwJ4GHrNdQKA8SLSKleNFZF9oCkUegP4AcCj0PQEhwD4UkQ65ercRFTcOEyPiLJtKIDrAPQWkZoAhgGYYIz5Ocl+WwP4B8BWAD4RkU7GmMnlaYiIbAHNJQXocL1UHeH9uMf6FEAvY8wvzrrNoRd8K4wxCyKOM9ObuoG5ZgCqAvgpTtf5qH2IiIiIYIz5Q0SGQwNJJwB4MbSJzfH0jLNuNIC6Xo/x/yciraHpAe6B5tnMKhHZBJojswaAg40xXziv3QTgawDPi0hTY8y6bJ+fiIobe0YRUVYZYyYCOA3AQm/6JoC5XpfsYSISc7HjPdn7CMAe0OFpywF8JiIHRWz7o4jEDP/z9BSRW72fJ6HJwVtC8zk9Hmcf1yoAd0CTpm/j/XSAJgs9BMBHXgDK2sqbxmuPXb91OfchIiIismygKZBcXETqQXtGLYQWdQEAGGMWhgNR3vqJAD4DcJg3vC/bugNoAuBhNxDlnXsegAehD/UOycG5iajIsWcUEWWdMWawiAyDdgs/CEBrb9oTGjB6CcCZxi/neQM0ENXbGPOmiIwF8CmAUSJygjFmJPD/Q9waQRN/R+nh/QDAagBzAQwEcK+bzylBuxcB+Hdo9RivC/kX0MTr5wJ4JNmxwodOY9tMhhUSERFR5fEx9EHbgSLS0hgz3Vt/FvT+7kVjzHp3BxHpDuACeFWKEXsfWAvAH1lu5wHetImI3Brxegtv2hLAqCyfm4iKHINRRJQT3kXQKO/HJtQ8FsDzAM6ADt8b7m1+KjT/wYvevvO98sWfARgmIucYY16CVumrDu3yHeUst5peFt/LPyLyHDQYdTD8YJTtxbRV5I7RvaCS7bNlxD5EREREAABjjPGuS+6BPiS7SkQEwDlwEpdbInIlgP9Ac0Z9COBn6EM7A+AYALtDC65kW21vemKS7bbIwbmJqMgxGEVEeeFVyBssIrsDuAmaoNsGo+oD+NsYs9bZ3g1IvSgi20EvZn4H8FI+2+6xTwv/f5ieMWaliMwH0EBE6kXkjWruTX901s0CsAFAUxEpi8gbFbUPERERkesFALcDOENErgfQHkBTAB8bY2bZjby8TbcC+A1AG2PMQvcgItI+jXNu1F2kijFmY+i1qPQC9sHaUcaYd9M4DxFVAswZRUT59rc3FWfdXAC1w9VcvHwChwCYA80rsC+APsaY1blvZoy23vSn0PqPvemREft0CW0DL+D2JTSZZ9QFYMw+RERERC4vqPQ2gG2haRDO8156JrRpXQA1AXwREYjaEppKIVXLoPePDSJe2ydi3Vhvmk7Ai4gqCQajiCirRORkETlCRGL+vojI9vAvlsY4L/X3pi+LSOPQbguhXcqt+llqagwR2V9EqkWs7wjgCm/xldDLT3nTG0VkG2efxgAuBrAW+vTS9aQ3vVNEqjv77Avt/fUHNPE7ERERUTzPetOroAGpxdA0CK4FANYA2NctwuJd7zwGLdaSqvHe9Dx3pZdb8/iI7YdBHzheJiKdow4oIu3cayEiqjw4TI+Ism1/AH0A/C4iX0B7NQFaTeUoAJtBK7wMcfbpB+31dByAaSIyEpqYcztoT6H6AAYA6Aygn4gsMsa8moO23wdgNxH5FMA8b90e0CGFAHCzMSaQPN0Y86WI9ANwJYDJIjIEQDVoUKkWgEuNMXND5xkEzdFwHICJIjICmlfhRABVAZxnjFme5fdGREREFcso6HXWft7y48aYde4GxpgNIvI4gKsBfC8ib0PzQ3WE5q/8DFo5OBX9oYGvm0WkNYDpAHaB9g4fBs0N6p57rYgcA+B9AO+LyP8ATILmq9oBeu3XBHq9tyaN901EFQCDUUSUbf8BMBPA4dBATmdo0vEl0Ap5rwJ41amkBy9v0vEicio0+WYn6DC2hdCLpMe9oM9+3jFeFJGlxpj3s9z2lwEcDb046gJgE68Ng702fB61kzHmKhGZDOASAOdDcyp8C+ABWwkwtL0RkZOhw/XOBnAp9CJsDIA7wwEvIiIiojDveqI/gDu9Vc/G2fR6AIug1xwXAPgTwGgAN0KToKd6vt9FpAOA+6FpFA4F8DWAw6CV8Y6N2GeiiOwBfWjXzWvDRmiPrQkAboYO/yOiSkac+0EiIiIiIiIiIqKcYs4oIiIiIiIiIiLKGwajiIiIiIiIiIgobxiMIiIiIiIiIiKivGEwioiIiIiIiIiI8obBKCIiIiIiIiIiyhsGo4iIiIiIiIiIKG8YjCIiIiIiIiIiorxhMIqIiIiIiIiIiPKm5INRIlJdRHYTkeqFbgsRERFVPBXhWqMivAciIiIqXulea5TlukF5sBOAKVOmTCl0O4iIiKgCmjJlClq1agUArQBMLXBzMsXrJSIiIsqZdK+XSr5nFBERERERERERlQ4Go4iIiIiIiIiIKG8YjCIiIiIiIiIiorxhMIqIiIiIiIiIiPKGwSgiIiIiIiIiIsobBqOIiIiodK1fD0ybBqxYUeiW0Nq1gKf4XyQAACAASURBVDGFbgURERGVAAajiIiIqHT9/DOw227A7bcXuiWV27x5QPXqQJUqwAknFLo1REREVOQYjCIiIqLSNX++Ths0KGw7Krvp0/35N94ANmwoXFuIiIio6DEYRURERKXr0Ud1WoWXNAW1+ebB5fHjC9MOIiIiKgm8ciMiIqLSNXSoTrfZprDtqOzWrQsut2tXmHYQERFRSWAwioiIiErT0qX+/P77F64dBKxcWegWEBERUQlhMIqIiIhK0wcf+PPNmxeuHQSMGVPoFhAREVEJKSt0A4iIiIgyMnu2TgcPLmw7COjVC5gzB/j+e+CHH3SdMYBIYdtFRERERYk9o4iIiKg0/fabTg8+uLDtIGDXXTUoeMgh/rqrry5Yc4iIiKi4MRhFREREpWfKFODJJ3V+u+0K2xbytWrlz/frV7h2EBERUVFjMIqIiIhKz6GH+vNVeDlTNHr3LnQLiIiIqATw6o2IiIhKz+LFhW4BRalaFdi4sdCtICIioiLHYBQRERGVlkWLCt0CSsRNWv7PP4VrBxERERUtBqOIiIiotLzzjj8/YkTh2kHx7bKLTv/6q7DtICIioqKUUTBKRKqLyHgR+U5EporIbd76JiIyTkRmisjrIlLNW7+ptzzLe72xc6zrvfUzRKRzNt4UERERVWDTp+t0xgygW7fCtoWiHXusTpP1YluwAJg5E/jxx9y3iYiIiIpGpj2j1gLoaIzZE8BeAI4UkbYA7gPwkDGmOYBlAM7xtj8HwDJjTDMAD3nbQUR2BXASgN0AHAngvyJSNdM3Q0RERBXQ5MnAqlX+8rRpQLVqQNOmhWsTJbZ8uU4POijxdvXrAzvvDLRooRUSiYiIqFLIKBhl1ApvcRPvxwDoCGCIt34AgJ7efA9vGd7rh4mIeOsHGWPWGmPmAJgFYL9M2kREREQV0NNPA3vuCRxwAPDuu8CAATpMr359oKys0K2jeJYs0enSpTo1Jvk+u++eu/YQERFRUck4Z5SIVBWRSQAWARgNYDaAP40xNlPlPAANvPkGAH4FAO/1vwDUdtdH7ENERESV2fr1QO/eOj95MnDUUcCZZ+ry3LmFahWl4pFH/HkRoEoVYO1aoHNnP8H5unWFaRsREREVXMbBKGPMBmPMXgAaQnsztYzazJtKnNfirSciIqLKbuLEQreAMrXttsBhhwXXzZkDjBql8xs2ROeTssP7iIiIqEIrdzU9Y8yfAD4F0BbA1iJi+8w3BPCbNz8PQCMA8F7fCsBSd33EPkRERFQZTZ2qw7yGDYu/TSUMVInIFV7hmCki8pqIVC90mxIaPz64PGeOP19WBjTyLgHvugvYYgudt8P6iIiIqELLtJrediKytTe/GYDDAUwH8AmA47zNegF4y5t/21uG9/rHxhjjrT/Jq7bXBEBzAKErFyIiIip5xgAvvQT88EPi7SZMAFq10p41994bf7u6dbPbviInIg0AXAZgH2NMKwBVoUVgitfddweXu3aN3q5WLeDSS3X+n3+ityll69cXugVERERFJ9PMn/UADPAq31UBMNgYM1JEpgEYJCJ3ApgIoL+3fX8AL4vILGiPqJMAwBgzVUQGA5gG4B8AFxtjNmT+doiIiKjobNwIHH88MHSoLq9cCdSoEb3t4YendsxttslO20pLGYDNRGQ9gBoo9t7km26a2nYLFwKbbabzS5YAzZrlrk35Nn8+0LChzq9Zk/pnQkREVMFlFIwyxkwG0Dpi/U+IqIZnjFkD4Pg4x7oLwF2ZtIOIiIhKwFtv+YEoQAMOUcGoDRvwf+zdebxNVf8H8M+615yZzIqQDIWkNFGmiFKolKT0pKeQhqdUKhoMjdIgSSrpIZGpRyFjlCGRMZnKkHmeue76/fE967f3Pmef8Z7x3s/79bqvvfba++yzDPfefb77u74Lhw6Fds18yT1DLdq01juUUm8B2ArgJIAZWusZCR5WYOdCfL7YsiWwapW0p08HrroqdmOKN/t00okTgY7JncxGREQUL1muGUVEREQ52HffBZ96d/Kkc9/fSnjz5kVlSNmRUqoYgLYAKgMoB+A8pdS9iR1VEEWLBj/n4EEJPi1eLPt9+8Z2TIn04ouJHgEREVHSYDCKiIiIInP6NHDLLUANtwV1PQ4dAjp1cvZt3ep+7siRvn3eK7L9+iuwfXt448wemgHYorXeq7U+C+BbANckeEyB+ft/8c8/wMCBwNGjVsCqVy/ruL9gZSpasMBqb9wIKAV88EHixkNERJQkGIwiIiKiyOzaFfwce22nt96Srb/pW1995dtnClsb9esD5cuHNr7sZSuAhkqpAkopBaApZPGY5FWnDvDLL8Dhw8Dtt0vf+ecDZcsCzz5rraAHALVqWe2uXeM7zlh6/XXfvp49gU2b4j8WIiKiJMJgFBEREUXmnyD1s7V27l9yiWy/+AJYv955bM8e92vkzQss8Sy0O3p0+GPMJrTWiwGMB/AbgFWQe7jhCR1UKBo2BAoXtlaU27vX/TylrPacObEfVzysXu3/2M6d8RsHERFREmIwioiIiCJj/0B98qQz+JSRAQy3xUquuw5IT5f27NkSmNqxwzpeurTV/ve/rXbevECDBnJt7+l+OYzWuq/W+hKtdW2tdWet9elEjylkDRvKNqv/hloDa9b4BjqT0aWX+j/GVfWIiCiHYzCKiIiIItOtm9UuUADo3Nnaz53bGVSaN883gGCWvJ8929n//vtWmx/as4fnn5dpnYGy2+wrKQ4Y4Pz/ZcyZA9SuDfTpE/0xxtL99zuDU0uXJmwoREREyYDBKCIiIorM/v3OfVPzyTvoNH48kJYG/P23+3UmT7baQ4cCuXJZ+3nyZH2clHhKObPf3BQpYgUw+/QBPvnEd1rfqlWyHTgQ2LLFd6XGZPXZZ8Dvv1v73bsnbixERERJgMEoIiIiiq4pU5z7rVvLdssW9/OnT7faBQo4j5mpfZQz1K7t3PeurZQvn9W+6CLf/y/JqE4d2SoFvPmm1Z8qgTQiIqIYYDCKiIiIomflSuC225x9JoDgr4aOKWbeogXQsaO0V60CnngCuOyy2IyTkpN9VT1AprfZZWTEbShZ8uuvVvunn6z2vfda7aNH4zceIiKiJMNgFBEREYXP30p6JgvEzd13+/YdP261J0ywakTVrg288w4zo3Kaxo2d+8uXW+3Tp4EePXxfY681FW+//w5ceSWwbRtw4AAwaZL0d+gg26ZNgUKFrPPTbLfep07Fb5xERERJhsEoIiIiCl/58qGd17u31XYLLJlpWEWKAAULZn1clNqU8u0z0zgbNHB/Taj/F2Ph3/+WYuSDB0tm3+23S1aUqY/28MPO888/32pfeCGQmRm/sRIRESURBqOIiIgoPOfOBT/njjvkvEGDAp9XrZps27TJ+rgoe/rwQ9ma4uXeTpxIXFDH/r2wbJlsV660+vLnd56vlDM7avfu2I2NiIgoiTEYRUREROF56KHg5wwc6PzQHYxZiY9o4kSgc2drf/9+YN++wK95773YjsmfpUtlO3iw1ffgg1bbbTXImTOtdiiBXSIiomyIwSgiIiIKz2efyfb224FKldzPMbWfvM2e7d7/8stZHhZlE7fdBowaBTz6qOwfPgxs2hT4NX37xn5cbsz/f3/fB82b+/bZi7SzbhQREeVQDEYRERFR6OwZKqNHO2vgGB98AFSo4P76G2+UKVX33OPsf+ml6I2RsgczPW/NGmfmUfnygNbAAw9YfUeOJCbL6IorrDF5y5/fvQZWiRJWe9eu2IyLiIgoyTEYRURERKE5ccIZfCpQAMjI8D2ve/fA11EK6No1umOj7O3rr632hg2yveYa5zlHj8ZvPEauXLJduND32MmTgV8DANdfz7pRRESUI0UUjFJKVVRKzVFKrVNKrVFK9fL091NK7VBKrfB83Wx7zXNKqY1KqfVKqZts/S09fRuVUs9m/Y9EREREMVGypG/fCy/I9vvvpX32bGjX8i7sTBSKKlWs/zsPPAD0728d8zcFNFa2bgXGjvV/fN48/8fMVFdApiQSERHlMJFmRmUAeEprXQNAQwDdlVI1PccGa63rer6mAYDnWEcAtQC0BDBUKZWulEoH8CGAVgBqArjbdh0iIiJKFrt2OTM9/vxTtu3aybS7li2BV191Zn0EYg9GDRgQvXFS9uKdcWQKhgNAejrw/PNWkDRQYCgWHn/c/7E77wQaNfJ//MwZq/3MM8D06dEZ07lzwObN0bkWERFRDEUUjNJa79Ra/+ZpHwWwDoDLZPn/1xbAWK31aa31FgAbAVzp+dqotd6stT4DYKznXCIiIkomq1fLNi1Ngk/VqlnH3OriBFO4sNWuWDFrY6Psq0wZ536BAr7nmCBUkyaxH4+d1r59M2dKEGrkyMCvLVTIud+yZdbHs2ULULWqZI+NG5f16xEREcVQlmtGKaUqAagHYLGnq4dSaqVSaqRSqpinrzyAbbaXbff0+esnIiKiZGJWBZs7N7Lgkzf7h/EjR7J+PcqezjvPuZ8nj+856emynTvX2b90qfxfjdX0vd9+8+1r1kym53mP29tddwG33GLtp0WhjOuttwJ//SXtH38EZs0KbZXKefOA3r0lyExERBQnWfrNp5QqCGACgMe11kcAfASgCoC6AHYCeNuc6vJyHaCfiIiIEu3oUaB6deCRR6y+6tWjc+28ea32okXRuSZlP/ZMqA4d3AOhZmro1187s5XMCnxNmzqn90XL1q2RvzYtDZgyBfj7b9lv3z7r4zHZiwDwyScSGOvXD/j118Cvu+EG4I035FwiIqI4iTgYpZTKDQlEfaW1/hYAtNa7tdbntNaZAD6BTMMDJOPJnoNfAcA/AfqJiIgokU6ckKl0f/4JDBsmfa1bA6VKRef69mBUuXLRuSZlP/baYm5T9ADnCo/2oNOYMVb7vfeiO65z53z7akZQ9tRMUXWb8heqtWsDZyt26uT/mD0Q/OqrkY+BiIgoTJGupqcAfApgndb6HVt/WdtptwMwj2imAOiolMqrlKoMoBqAJQCWAqimlKqslMoDKXI+JZIxERERUZT88IP7NCN7hlRW2adbRWPaH2VP9oL49gL6dvb6ZSYLyDsbaPTo6I7r6FHn/uzZwPz54V9HKfleOH068rGMHx/4uFlswE2wrCkiIqIYiTQz6loAnQE0UUqt8HzdDOANpdQqpdRKADcCeAIAtNZrAIwDsBbADwC6ezKoMgD0ADAdUgR9nOdcIiIiSpRWrdz7W7eO3nvYa+Q8+WT0rkvZ18yZ7v1pacAXX0jb1I9yW51uw4bojeXAAav999/AjTcCJUpEdq3cuYGMjMjHUqRI5K/Nl8+5rxRw8GDk14unzZuBFi2AfzipgogoFYW4/rKT1noB3Os9TQvwmv4A+rv0Twv0OiIiIoqxPXuAokUlQ6NbN/dzYlUEGnBOsyLyp2lT/8fMFLmnnpLgjFum0cUXA7t3R2eq6e+/y7ZKFeCCC7J2rfT0rAWj3Iq6h+qhh3z7Vq4EGjeO/Jrx0qSJBAJffx0YMiTRoyEiojBFYekOIiIiSln79wOlS0sNp8GDpfAxANSvD9StC+zaJfVsbrwxseOknMusvDh8uP9zihaV7fHjwN13A3XquJ+3alV0xmTer2fPrF/ryBH/WV/BnDgBPPdc8PN++slqaw08+CAwaZL7ucePRzaWeDPF36NdD4yIiOKCwSgiIqKcbMUKq22fLjdgALB8uQSqiBJp/Xpg3jygeHH/55jgkGEyo158EejVy3mtaDh1SrYFC0bnegDw88/hv+b554HDh639yy5zn6K4b5/VHjoUGDkSuP122feuD7d3b/jjSLQJExI9AiIiChODUURERDmZqbXj7eKL4zsOIn/KlgUaNQp8jncw6q+/ZHvVVcBrr1n93btHZ0wmKyeaU0zbtJHtrl1Su6lSpeCv2b7duf/VV0DJkr7ntWsHnD0r7R49nMeOH5fsLLPC5bJlYQ07Ibz/3K+8ItuTJ4FRoyRjjIiIkhqDUURERDmZW1HnuXND+yCcVSNGyAdHoqzK5VUGtU8f2ebPL9lLU6dG9/1MQMct8BOpgwdl2mxZz+LUJuAViH1K3cKFQO3aVhF3ALjuOqtdv777ioS1a8tUyMWLZf/9963Mr2TlPZVw5UrZdusGdOnivhooERElFQajiIiIcqpjx4BFi4AbbgC2bJEsjw8/jF/x4gcfBDp3js97UfanXNbWMVP72rQBatUCChTI+vtoDZw7J+1oZOCMHSvbK690Lyjuz9mzwJ9/WvsNG8rWXtD86qutdv78wJQpvtcx9arsq/Llzx/6OBIhd27n/n33yXb06PiPhYiIIsJgFBERUU6UmenMwKhUSVbVe/TRhA6LKGJutZLshczXrJHgUVazpEwWTrTcfLNsa9a0spOA4Kv+de0KbN5s7ad5butr1ACaNQPuussZ7L3+eqBjR9/rlCkj23hkQ0bLP//I1gQgR42ypiESEVFKYDCKiIgop+nYUabyHDsm+02bJnY8RNHQvDnw9NPOPrdsqVtvzdr7HDxotYPVsgqFqdX0+efWyoGAbx0sb/YsoI0bncdmzpSMq0svBXbulL5wi3wrJV8tWoT3unjo0EG2AwZYfZddZgXYAQaniIiSHINRREREOc3XXzv3P/ooMeMgirZWrfwfK1w4Ou/RtavVtk+Ji5R9yplZ7a9UKcl6CrV2U7Fi/o+Z6XemqDvgfypulSq+fTNnytTEZGICgmZ6HgD88YfUvzK++iq+YyIiorAwGEVERJSTnTjhW/yZKFXly+f/mHcQNlKVK8vWZOdklVv2VoMGQEaG1G5auDD4NQIV7Har/+Tv/D/+cO8/fTr4GOJFa+DMGWmXKwd8/LG0q1QBDhywzrPXwCIioqTDYBQREVFOMmuW1V61KvkLFROFo359/7WPWrYEqlaV1fWyomJF2b7wQtauE4i9XtTAgcHPDzdD6803pZh7377Ofn+B6U2bwrt+LGzdCtxyC/D227Jfvrxsu3UDKlSQlQL377fOt68qSERESYfBKCIiouzq77+tui+mpkyzZrItVMg5pYUoO8iTB1i7VtpuwYhataRW2owZMtXr3DngvffCy/z54gvZZjWoFUhGhtV2mzoHSFYQIIsOuGVX2ZkAGiCr9tWsCRw6BPTr53tu9eq+fXPmALt3B36PWDh61KptV7s28N13Vl2wG26wztu+XYqa26citm0LDB8e+lRHIiKKKwajiIiIsqPZs50ZItWqyfL2RrjFjCnhlFJFlVLjlVJ/KKXWKaWuTvSYklL+/DKVyx7QMQoUkO1NNwHFi0smUK9egaf3+RPLzJu777baZkqa3blzEnypVg348MPg1zt0yGoPGSJbe60qu19+sdpXXSXbnj2tVffiqXBhqx7W0aPOY99/7/4ae3bXww8DDzwQm7EREVGWMBhFRESUHbVu7dv3v/9Z7ebN4zcWipYhAH7QWl8CoA6AdQkeT+oxwaho8DcdMBrshdiHDZPAk93w4bLdsCG0661aZbWDrdJnL4a+d29o148lt6Ai4KwPZVevnnN/7tyoDoeIiKKDwSgiIqJk0ayZfFgeM0ayHVaujOw6p08DdetK+9NPfY/37x/5GCkhlFKFATQC8CkAaK3PaK0PBX4VhWXfvuDnnDsnwZpoT3F9773Ax019JGPz5vCuf+GFVttfRpSbSy8N732iYd8+mXb4xBNWnwm+2Y0fb7XvvddqlyjhPG/XLiAzM7pjJCKiLGMwioiIKFFy55YPXffdJ9tZs6QI7z33AD16AHXqAOs8yS/nzgGvvAIsXmwta2537pzUhVqxQqYcLVokdWLsy9AbXGUqFV0EYC+Az5RSy5VSI5RSAZZQI1duwVkjlGBUr17y/Xf2bPTGBMg0uA8+kPagQbLV2nlOo0ZW+623wn+P+fOB557zX4PK7pprZDtypLP/1Cn/GUnRYrI2333X6nv4Yec5770HtG9v7b/xhtX+4Qffa27fHr3xERFRVDAYRUREFE+HD0sB3j/+sKaffPml//Nr1pTthx/KylcNG0qtG2/t20v9GPsUlW3bZHvsmLNmTDIt006hygXgcgAfaa3rATgO4NnEDimbqVFDAjXHj/s/x9RnCiVwFa7u3SUA1bu31derl9X+6aesXf/664EBA0I7d+ZM+fnh/bMmf37JPPI3dS4aVqwIfo538Xj71MIXX7SKzBuPPw7s2eMb4CMiooRhMIqIiCheHntM6rW89ZY1jS4U5845P5QCkkllPhDu3AlMnuz/9eedJ9lQZhWq+vXDGzclg+0AtmutF3v2x0OCUxSOm24KfHzzZmDaNGtfawkSTZkCXHCB1b9/f2zG581kSRnegeRY1a0qUACoUEHa8+b5Hjcr3CXKjTc69+0F6OvWlWxTrYHKlaVv4kSgdGkgLQ34+efErAxIREQOEQWjlFIVlVJzPCu5rFFK9fL0F1dKzVRKbfBsi3n6lVLqPaXURqXUSqXU5bZrdfGcv0Ep1SU6fywiIqIkc/o08P77zn1vvXtbK115v9bNnj2y9Tft5rHHnPsDB8q0v8aNg4+XkorWeheAbUqp6p6upgDWJnBIqclMhbO7+27n1NU777Tae/YAQ4cCbdtamYbmNfGQLx9w5Ihz//hxyZAEgNWrYz+GRo2cNacAmU7s7cCB2Ndm2rpV/k0CBeHsWVIjRvgev/ZaZ4F4IiJKiEgzozIAPKW1rgGgIYDuSqmakHTxWVrragBmwUofbwWgmuerG4CPAAleAegL4CoAVwLoawJYRERE2cro0YGP//CDZEHYA0imbou/YNTevZI15fbBEADy5HHup6cDl1wS2ngpGfUE8JVSaiWAugBCnHNF/69iRWs7Zox8X/73vzJ91s2pU+79//1vbMbnplAhZ4HzggUls6dCBcl6jAf7SpwAUK6cZB4tWQKMHSuLLZQoIT9jsjIVLthrK1YEzj8/8Dk33GC1vYuZG8uXhzUsIiKKvlyRvEhrvRPATk/7qFJqHYDyANoCuMFz2hcA5gLo7ekfpbXWABYppYoqpcp6zp2ptT4AAEqpmQBaAhgT4Z+HiIgoeWzZAnTrBjz5JPCvf7mfM24ccPHFUqzcOHVKatIMHChTSjZtcn/twoXOpdcnTgS+/15WmTpwQAJVlG1orVcAuCLR40hpefMGD3jkz2+1r78+tuMJVYECzv0tW6RGXLzUqiUZWfbg16lTwFVXSbtDB6v/xInIg2RHj0Y+xpkz5WelUlZfoUKRX4+IiGIqyzWjlFKVANQDsBhAaU+gygSsSnlOKw/AltuM7Z4+f/1ERESp6cwZqbHy7bfARRcBP/4I3Hyz//PvuMMZiALkA3P58lZmU4MG1rFu3az29u3yekBWoLrtNuDjj60pKEWLZv3PQ5QTbN5stU+elJUpAefUvETKndu3b8OG+I6hQAFnhqc9QDZ+vNX2l6kZirlzZWsPbgGSJRpooQcAaNbMd9W9iy5y1vqyO3MmoiESEVF0ZCkYpZQqCGACgMe11kcCnerSpwP0ExERpaYBA2SaiH3ZceOhh5z7//534GtNnOjc791bgk1mWfcLLrBWybvCljDz0UdA//7OVbmIyL/KlYHp0639JUv8n+v2vR1ryRI46dQpcHAdkKB4pNq2le3FF1t9WksW6L33RnbN3393LuBgTJgQ2fWIiCgqIg5GKaVyQwJRX2mtv/V07/ZMv4Nn66msiu0AKtpeXgHAPwH6iYiIUs/y5cDLL/s/vnu3POG/7Tb5gPXRR4Gv5718fI8esjVTY+z1bPr2tdqFCgHPPy8ZVkQUmhYtgK+/lrZ3ds+uXVb7m2/iNyajadP4v6c/waYuLlwohcazInduqcv16adZuw4gGaL79gFvvOHs//zzrF+biIgiFulqegrApwDWaa3fsR2aAsCsiNcFwGRb/32eVfUaAjjsmcY3HUALpVQxT+HyFp4+IiKi1HP55b59TzxhtYsXlw9q3hlP/njXOynlmf1ugkz2azPwRJR1VavK9p9/gIwMad95J1C6tGRODRvmrEkUL5Ur+y5kYKboxpt95UF/GjYEZs3yDagHYq8XlZ4uKxZ27Rr++Nzk8pTJHTTIytzascP93LNngddekyxXIiKKmUgzo64F0BlAE6XUCs/XzQAGAWiulNoAoLlnHwCmAdgMYCOATwA8CgCewuWvAljq+XrFFDMnIiJKKWfPWu3XX3dvh1vDKV8+576pIeXdT0TRUbiwbEeNAlavlnbBgrJt0cK3JlE85ckj2ZWABEvGjUvMOPwFo265xVrpbudOqeEUbOU7O1OnK5Z69wY++UTaa9a4n5M3L/Dii0CfPrEfDxFRDhZRMEprvUBrrbTWl2mt63q+pmmt92utm2qtq3m2Bzzna611d611Fa31pVrrX23XGqm1rur5+ixafzAiIqK42LQJmDrVqmfyr38BzzxjHbcXHn7kkfCuXbq0e3/Nms79++4L77pE5C49XbYbNwL16kl75MjEjcdbqVJAZqZMw00U72BU7dqyvfNOYNIk3/ODBZmOHJEstBMnrL4uXfyfn1XBMrvsqy1WrQosWhT6tWfPdk7pJCIiv3IlegBEREQp67nnZNqHnZmqd+iQ73SeUKa32JlMKG/mA7Pxr3+Fd10iclesWKJHEFwipgna2acEX3MNMHmyZGzVqiXFwr1Vq+YM8NgtXy4/My+4AGjUyOr3twJeNOTOLQH9tWuDn7tpE3D11f7Hb9ehg1UUPZTziYhyuCytpkdERJTj7NgBfPstsHevbyAKsD5QFSliTfkxH3DNfqgaN5btzTdLMV9/Klb0f4yIQuc2lXbevPiPI5ldfTXQpAkwdqzUwCtZUgJRgASewmGKim/dClSqJG37YgyxYgJRs2ZJRpepD7Z9e+TXtK/Ot3Ej8NdfkV+LiCgHYGYUERFRqDIygAoV/B/fvFkKDXubNAlYtgzInz+89+vb+m3kTQAAIABJREFUV1bRatTINxvi+++BVq2k7V3onIii5+KLEz2C5HLeeRLEcVOggEwjVEp+XubOba3+6aZdOwlqAdbKebGcouetWTPZKiUrKf7nP77npPl5dp+RIasuuv38NUE5ZkhFz+HD8kAn0ZmBRBQ1zIwiIiIK1ccf+z+WP797IAqQYJJ95btQpadLdpTbzXfLltbKXyxoThQ7JUokegSpxfy8MivYLV7s/1z7wg87d8rWFIyPpddec+6bn6Fff+17bmam+zXatpXgiPcqh+Rrwwb5f/Hqq5G9fuVKyVp8883ojouIEorBKCIiolAoBfTo4ewrXBjYtk2CRl9+Gf8x/fqrTDc577z4vzdRdvXuu859+yIEFF3Hj/v2hTudORKlSjn3R40Czp3zf75SzqBURgYwbZq0W7aUrb2WlnHqVNbGmer27JEpnb16yf5LL0V2HVNEvnfvwMFNIkopDEYREREFs2mTe/+RIzJtLyMDaN8+vmMCpC5VjRrxf1+i7OyxxyTw8NprvgFoCs9NNwUOlrsFo9yCOtHmFnjq3dtq33mn7/GjR632wYNWe+5cYMUK9wypnJ7JU7o0MGeOTCs3Dh0K/zr27N+GDbM+LiJKCgxGERERBWOmw3nzfrpORKlPKfnq0wd4//1Ejya1zZ0rASczBc/bmjXO/c6dYz4kAEDr1r59b79ttb/+2rkPOINN3lP36tWT7b33OvsjzQTKDvxlhV1ySfjXOnEia2MhoqTEYBQREVEg9hWRrrlGPoSYuhfhrhxFRJSTmABO9+6+xzIzgREjnH01a8Z+TIAUWvfWrp1sO3WS7ZNPOjO3Tp602kOGuF/Xrb6Y/XU5Sb9+7v27d4d/Le9sqmPHwr8GESUdBqOIiIi8HTkC7NgBDB7sLEo+a5ZkTHTvLtM4Ro9O3BiJiJLdHXfIds8e32MZGVb7hRec58eaW5H0b7+VrT0DqkAB4NprpV2pErBvn7QHDnS/bqFCEmSzZ/K4TUXMCV5/3f+xwYPDu5Z38Onw4fDHQ0RJh8EoIiIiu1OnpBZThQryZNwYPtyqW1GsmEzjqFQpIUMkIkoJr7wi20aNJCNm2DBAa+mzB2lefVXqOFWpEp9x2etSFSvmPDZ+vHPfHrh67rng11VKVlc1vz9y+hSzF1+02tdcI1v779ZQ9O/v3P/xx6yNiYiSAoNRREREgDzxPnsWuPpq9+Ply8d3PEREqS5PHtkOHAjcfTfwyCPA0KHAuHFA8eLOc9Pi/LEkPV22weo6PfOM1T53zpnR5W3oUKttpuddeKGVURVvmZnA448DP/8c3/c1AUdAApJbtki2sVtGmt3y5UD16sD69e7Hzd+vW7F4Iko5DEYRERFt2ACcf758cFqxwv2cK6+M75iIiFKdPcBkViXt0QO46y6r/7HH4jsm4+hRCX48/rizf+FC57595bwlS4AzZ6x974CavVD7Rx9Z7cmTszbWSHz+uQTchgyxphrGy6pVzv1KlYBy5ayp7TVrynT4CROcfzfduwN//un8P2Eyy5o2lUAVADz8sDPgRUQpicEoIiKiOXOc+xUr+p5TuHB8xkJElF3YAzdbt7qf06pVfMbiLX9+oG5dadtrGJmpZMZNN1ntNWskO8q49FLJlDKr8y1ZYh1r08ZqHzkSnTGH44EH4v+exvTpsq1Vy9l//vlAs2bA2rUyHb5DB+C226zjv/wi2xkz5O/55ElrRcuMDGD/fuvcv/+O3fiJKC4YjCIiIpoxw7lvX3r6/fflybiZbkJERKHJnz/4OeefH/txBHPLLf6PFSwIdOtm7dtXx9u7V7KPvvtOMnUaNLCOPfKI1Ta1sxJp7dr4vM/8+dbUxuef9z1eu7Zv37lzwPbtzr7t24GyZYFnn5X9Fi0kO8rYsCE64yWihGEwioiIcra//5apAnYnTgB//SVFU3v0AIoWTcjQiIhSmluWqbeSJWM/jmBM4XR/NQOHDbPapUtb7UD1o+wZX4cORT62aIlF3ahTp6TWop19mqNbRpjbtMzu3YE6dZx9tWs7V81r3tw5LXLkSCkWX66c7xiIKCUwGEVERDmb24p43btL0Vm3p7pERBS6qlUDH0+GzChAAksLFrgfU8q9/3//8389pZxTwP/4I/KxGSdPhl4ryXtq+apVoa3sl5EhGcH21Q79adBApioaWltT7QD3WouVK/s+APr4Y+DAAWffsWPOfTPlr1Qp2Y4dK9udO4HNm4OPlYiSTkTBKKXUSKXUHqXUaltfP6XUDqXUCs/XzbZjzymlNiql1iulbrL1t/T0bVRKPZu1PwoRUYo6eRKYNcvaf+opuYkN5UaQInf8uO8HjBIlZFujRvzHQ0SUHXXsGPh4gQLxGUcw6enhrejXq1fwQJspuA3IioJZ8cEH8nfVu3do53tPkXzvPZnqFsyIEZK9VK5c4PNWrgRWr5aV7z7/XAJRXbsCU6fK8RIlgMsvd39tsWL+r+sdqDLM/5O2bX2P2adOElHKiDQz6nMALV36B2ut63q+pgGAUqomgI4AanleM1Qpla6USgfwIYBWAGoCuNtzLhFRzrBjB9Cli9xgNWsGvPyy3My9844cL1iQyxfHknfW04wZMmVv4UKrqC0REWWN9/QrY//+1FoR7e23nfvp6cFfU7as1c6dO/L3PnIE6NlT2m++Gfz8ffuA3bulbV+50HulQDem1lWwout9+ljtBx4AnnhCglLG+vX+X2uym9w0b+7cP3DAOQ3PXmzeCCXji4iSTkTBKK31fAAHgp4o2gIYq7U+rbXeAmAjgCs9Xxu11pu11mcAjPWcS0TGhg3yZMv7aZpJ0x4xApg7NyFDoyw6dAioUAEYNcrq++ADoHFj53mLFgW+oaPI9OwpT4ntrr0WOO8835WUiIgochdf7NtXtaqz/k8q6NzZuZ8rV3ivz0owasoU5/7vv0vQ6Lvv3M+fOFG2efIA7dtH/r72mk3eli1z7g8Z4tw3mcZuatWSqYDTp1vFzgG5D/IO8hUr5vy7Pu883+vNnOn/vYgoaUW7ZlQPpdRKzzQ+k39ZHsA22znbPX3++onI+P57KQ75/PPWE6rt26WYcr16wEMPATfemNgxUvi0dk9RL1oU+OknZ98NN8jKbkePxmVoOcLKlXLDa2RkyL9JskwVISLKTuwrkfbsKVkuqfiQpWRJZ0ZtKJlRdlmpa+QdCKtbV4qq33KLrER36pTzuFn9r1IloGYWJp6MH+/c37AB2LVL2jt3ur/mqacCF3Y3evSQaYMm4wuQaX7238X+gmEvveTc79cv+PsRUdKJZjDqIwBVANQFsBOAyWV1q/inA/QTkWH/Zf7dd5KaXbEicOaMPBUzzI0BpYaPP3bv37jR/2vsBUIpa15/3bkf7gcKIiIKnT0Y9fTTkuUSTm2mZKGUrLBqhJoZZRbJmDEj6kP6/3Hkzw/8+afvsdq1rcLfbjZuBC66SIqbA75BpHz5rPaZM5LlduWVUmbAn7Jlw/u9WqqUFFtv08aqc6W1fHkXYTeqVQv9+kSUtKL2m0BrvVtrfU5rnQngE8g0PEAynuzrulYA8E+AfqKca9cuqRNkilfPnm0d69TJmcps9+qr8RkfRe7kSeC++6SGg/3ftUkTuTn39tVXzv2//47t+LKjlSulEHmhQtZ01q1bgf/+V9pPPGFNZSAiotjIm9dqV6zo/7xUE2gamp2/B1DR9ttvvn1ffy3bxx5zf83LLwNbtgCXXSaZW96rA9rvPUwm1LZtVl0pwCpY7vaaUOTJI1n/4fw+dgsE2h/SElFKiFowSillq9CH2wGYlfamAOiolMqrlKoMoBqAJQCWAqimlKqslMoDKXLuNSGaKAfRWlKVzQpqZcsGXjLYbuhQSXtPpUKgOcmxY5J2/uWXUsj1m2+kPzNTVtHzztQBgNKl4zvG7GjoUFlK+9gxmc6akQFceKF1/J13gNtuS9z4iIhyAntmVE5kX9Xuscek2Pbvv8s9wLlz0XufggVlm5kp2zp1rKDNu+9a5yklGVGZmVIc3KhSxTew1KePVfS8Sxer35w3bpxkNNkXW/nPf8Ife6FC4dXgat0auOIKYNIkq2/bNv/nA/JQkAEroqQSUTBKKTUGwC8AqiultiulHgTwhlJqlVJqJYAbATwBAFrrNQDGAVgL4AcA3T0ZVBkAegCYDmAdgHGec4myt3XrgBUrnH2ZmZKybp+bH0qNoAEDrHaePKmZ9p6d7dghN32FCll9ZnUbQI7Zt8bHHwNNm/pezwQqjX79gPr1g694k5198IF77ZG///Z9Gm0vHvvjj7EdFxERiexaj+/MmdDOa9DAar//vtRKqltXprLlyhW9B4mLFsm1tm+XfXsWmvd9RrVq8v7Tpjn7P/1UtnfcYfU9/LBs583zfc/rr5dtnjzW1LoLLoj8zxCqQoWApUuBtm2tqXy33CIlDbzrZxlPPy1/725/DiJKCKVTPJNCKVULwOrVq1ejVqA50UTJIDPTmkefmWndHGzcGPr8988/B9askfpRf/1l1SIwUvx7OttYvTpwnadx45w3e19+KdP4AOvf0Pvm0X5syRLgqqukfdFFwKZNWR9zqmnRwlpBp1AhWaEwLU3+joIFZjdskNWciEKwZs0a1K5dGwBqp+qDM94vUcLY732ywz2K+d08bRrQqlV4r3Hz/PPA5Zf7X/XO/jstLc3KfHJTpgxw3XXWw03733egMXg7e9b5AMc8NHUbW6K9844UTTfcVssFpJD7unVy7/Tzz3yASxQD4d4v8buQKJ7smRpjxkhNG8D3yVQg69YBAwfKB+8LL5Rlce369JHpSGfOJMdNQk40fbpvIOrXX5379kAUANx1l0wZsy9P/NNPvktiN2kC7N1rBaIAqfOQE/+t7X9XR49KgOnsWeCee5znuU13zU51SyjHUEqlK6WWK6X8rOdOlISy24f+M2fkgVCogahgBgwAOnSQtta+U/fWrrXa998f+Fq7dknGNOAM0AChrXBn5MolWUTGc8+F/tp469TJub/Gz+dfM11y8WIJjubE+yaiJJPNfjsQJaGhQ+Vp1H/+A+zZY/V36iTz+QGgVy/ZFijgnMblxqRWFyki+2XKOI8PGAC8+KIUDL355uj8GSh0mZlAy5bWfpMmcsNjbg4B4JprfF+XJ48U72zWzOq77jqZgjZnjtU3Z46sPOPN3xLLye7gQWDQoPDH7/aEd+NGSdcfO1b2O3WSOhb274P//U/+PewFdYlSRy9IaQOi1DJtGrBsWaJHER25czun3oUjUGDu3DnJjvKeumfPhOrXz2rPmSP3kSVLOq/zyy+y9a6JmJ4OvPBC6GNdvtxqm9qWN95o9X32WejXiiXvFffsdbAMrX0LvJsg3/z5vg8MiSguGIwiiqVly4Du3aX99tvOmwjj8cet9rZt7oEGAHj0UVlN78EHnf1u6dqDBsn2hx/CHjJl0aOPWu3+/Z3ZO9u2yY2gPbgUCkl3Dey668K7ZiL98YfcxGot/6efew4oVw7o3VuCTJdcEngagr+b6QcecNaKePll38K5VapkffxECaCUqgCgNYARiR4LUdhatZKpaDldoN9t559vrShXsKAU3AYk4xcAnnzSWQz9hhukBql3HdIpnvWg3AJfr7zi2/fAA1Kn8qOPgo+/QgWr7Z2FnCj2vxMA2LfP95z58337GjaUbePGElxkphRR3DEYRRRLs2cHP2fIEKtdvLhsDx+2+oYPl2yO9993X3XNPqffTU6sJRRrGzcCDz3kzHQDpMC4mYo5erTUgbDfDFaoALz6avgrCwUq/moKi27ZEt41E0VroEYNoGtX+bsZYftc/cYbsl2/3v3G0ejf32q/+aZMlwBk+qKdPfC0fr0UZq1ePWvjJ0qcdwE8AyDAp1kiSkqrVwc/5+BBq33ihEzfB6ygVIUKQLFivq/zzowyTJ0uO7es4pEjZVEPU3jc/rr333ee++GHVjtZV0msWdO3z22hl2PHnPtPPBH82hMnWiU2QpWRAXzyifXvSET/j8Eoolj58EPJ+giVvQ5A4cLy4XnYMAl63Hyz/9TumjUlG2fYMPfj7drJNjNTMmy8awhQYGZ1GECCgUrJVMkRI6zplYBk+5hllQHg7rujNwbvp37GN99I4U5j0SJ50vfHH9F772gzT2yDcXuyCUgdLUNrmf7qNl1i1Srn/sUXSwCMKAUppdoA2KO1zibznIhymEgWDZg6VbaHDsm2SBH3AJO/aef+7hvN79ELL3QGm266Se4nly61+u691/naQoXk4ddffwUdfsJoLfVVzeyAzEzn6tPe5xr2h8P+tGtnldgIVf/+QLdu4U2RJMohciV6AETZzrFjMg+9Rw/34zVqyC9Jb59/7px/f/HFvsWr3ShlPamqUAFo08Z5/KGHZLtrlxR1XLMGeO01/wEOcipZ0r3+ACC1ie64Q/7e7QXFp0yJbsFW82+clgY88oj0VatmFTw1rr5atjVqJGe6+bZtvjUsAKmh9fPPzr5du6z24MFSe6tOHaBRI+mrUcP/+/z5Z+irUxKlhmsB3KqUuhlAPgCFlVKjtdb3BnkdEaU6M/3c3LfNm+c73c/8zrevMuud+WNcd537PUJ6ujPzCXDPzPZexTnZzJxpZUetXx84I3rx4tCva8+uOnhQst8HDHDPVrMzJTreeUdKdhDR/2NmFFE0TZggT43sgQlA5vkbs2a5102Ixofn1q2tdu/esu3ZU1Z+sRfQ5tOZ4F56SYJA/gJRRvv2zn/vQYOAW26J/ngefRT497+t/S5dAp//99/RH0NWmSkAdj17AgsX+vZv2CDbNWvk+6duXfk3MczUPOPVV2Xbti0DUZTtaK2f01pX0FpXAtARwGwGoohSzPff+/YVKiRbe2Fwu+PHZSEOAMiXT7aNGkm9KDe5opxnkCePtVCOfUXoVDFjRuDj5iGeEaim18aNVrtHD5mRYL+/N6pVk/tHU3rA7sSJwOMhymEYjCKKpgce8O1r2FCehOzcKU+3ypYFFiyQVfN+/NE6b8yY6IyhUCF56tW3r9V35ZXOTJNJk3yXDs6pMjPlpu6bbyQzbfduKRZqghve5swJnHVkgoCx8vPPEvz6z3+svvPP9z0v2Z5cfv211e7bF+jcWdpm6ehRo5znm9oKZlUgwPlvYp8SCUiAdcYM4L//jc54iYiIosk74HTJJVbphDvvdH/NgQNWMCqUVWBNsXO394vUzp1y39OtW3SuFwtuWdeAb3Bu8ODA1/nf//wfy8iw2qYeq73GKyB/TyZoZRZlseM9CpEDg1FE0XL2LHD0qG//3LmyLVPGupHIn19WzWvaVFKiL788/Dno/hw5IvUA7NPwfv/dec7mzRIkc5sumF398INkrtmdPStp6fPmyY1g167y7+RdV+u116RuwqlT1tNItyWq4zE17uqrpTaU/abUHrCJt2CZY3v2SPCpY0fZ79dPvoYNA7780grgdu4sgUEzHWHXLnmtmWZq5y+tvnnzwMXeibIBrfVcrXWb4GcSUVKx/95u317uwcwKuw8/LPVBjT59ZHv8uDW1K5RglP0hZ07yzTeSdTR0qLPfe5Gf+++Xe3Xv+0HDXkTemz3QZ+5DvO/7g2U+hROM2rtXamL++mvoryFKMQxGEUXL+vW+fW3bBr95ePRRCWxEO7UaAF580f+xX3+VOfXmiVt2s369PJHq2BGoWlWWle7QwXqyNWKE/5VgTEHP0aMlwNSnjwRO7P+Wl19u1edq1iyxN4D2VeNee81qu60eE0333AOUKBE4G2zkSOdS0iZjr0ABCfDZnxoqZf2bTJ0KlC7tfk23guVERESpwtR1Sk+Xh1xKOQMnJvv32DGZrg5Y0/QCiUWZgFSQK5c8hL3oImf/J59Y7X/+AYoWlb9bs7iPt6pV/b/Hddf59nnf+7k9lLabMyfwcbuPP5Z79WguiEOUZBiMIgrHrl3yFMusbGJMnQpceqm1/+yzkp307bfxHZ8379o548b5roziXQQ7O3jhBUl/B2R6mEmnBuRm7+GH3TNuvHXqFPj4t99KwGfmTMlyS6RJk4DvvnPWL7CvPBdtZ85YU0vd6iIAkun03HPW/k03Bb+u27LTdrlzBz+HiIgombk9LJo82WqXLCnbnTutviJFgl930iR5AGS/78lJihZ17psMpqeekjIZwWzfHt77eRdHDxaMspdYCMbc6+zeHd6YiFIIg1FE4ejcWZZofestZ799yfjp04GBA+UJSjRXVIuE94f2tm0lw8fuu++sqVGArA5y9dVSl+jMGeCrr+Q6a9fGfrxuMjMl7TlQUUm73bvl3yiQ4cOd+5s2SY2iM2fCG1vu3Fbx0URr21YK2NufnIbyFDVS3hl/bqv2eNerCOVGOhj7/1UiIqJUctll/o9dcYXVNhk+9sVIatcOfv20NMmK984QyimKF3fvd5vCX7iwb5+9LlQoTH3OWbPkIaf3PbZhpgWuWBH6tc2Yjx6Vh54PPhg82EWUYhiMIgpVZqaVjjtihPPYvn1W2zzNSgZt2zr3zRSo7duBWrWs/q1bZVuzpgTSFi2S1creftvKpLKfHy9ffCEp7OedJ9tbb5Xik1oDs2cDr7/uDCDt3QsMGWLt25co/vNP3+sfOybXuugiCdzkzi3vCQDbtsXmzxRr9gCkd+2raFxbKfeV+uwFygHJIpw/39pv397/TVo4Eh3gJSIiitTy5XKfsnmz77Hp06We6PDh1oOu776L7/hSXYkS7v3Ll/v2uS0cFO7iPtOny7ZZM/ls4Lb4TZ8+wO23S/vHH521p9ysXi0LHdkDYy1aSNmDQAXWiVJQDIrUEGUjo0dLDZ5hw6w5+4AzZXbqVOdr/P0iTATvFceM8uXll12ePPJL8Ysv5M/pXdD8+eed+7feCkyZEpuxejt9WgpN2k2dKl/2qWgLF8qY7r1XsriMmTPl5qBLF3mSVKaMZNWYbKHGjSXI5e2+++QrO3CrYxYpe5Dv889l27EjMHastFetkpu4OXMkU9AezMvMzNrUujx55N851Ow4IiKiZJSWBjz2mPux4sWt+0tzz2kKYntPByN33tP0DLcFZtzuASNZadrt/ubqq2X1YzdHjgT+rGAv++EtWCCLKMXwETORP5Mny7S89etlulGPHs7jZjnXBQusvkWLgAsvjN8YgwkWAPjmG9muWxdaAe6pUyVAFw9uT5fcTJ0K1K/vDEQBUmAckJuNMmWknTcv8OmnwEsvWascZmdZndKmtazEqBTw+ONWf79+sh02zOobMkQKizdv7gxEtW6d9RpPtWvL9IUrr8zadYiIiFKByYwytR979kzcWFJJWhowfrzvisdutS3tmdYtWsg2kmCUG3N/7SacIubeElUygyhGGIwi8ue229z7zz9ftkWLSqaGmb89bZrUWUo2Zkqh28ohjRrJduJE6xdx377OIpreOneWYE4saW3VfRo2DPj++8Dn//abb5+/ugFduwIvv5y18SW7bt1k27hx5NfIzJQbtbp1/Z9TpIjUMDDc0uAjmWLw22/ARx9Z0yy9C/ETERFlZxUrOvfDrWWUk7Vvbz2QNGrW9D3PXjPKlDUIFIwy9/+hKF/e/zHvurPhGDQo8tcSJSEGo4jcuBVjNvbutdoffigfmgHJCElGDz4o6d5uGU1uxbdvuUWm49nrGXg/kQs1aykSZ886n1Y9/DDQsiXwxBMSXLFPobOvMgPI1MMbbpDlcHMyc1N1zTWRvf7YManR5c2+rHHnzrL1zhi0u/XWyN6/Xj3g3/+WrxEjfAvOExERZWfeGcWzZydmHNlBqVLu/XXqyP3F5s3WPc/Ikf6vU6CAs8h8oPsfN3fcIdvFi521ZsPFkgWUjUQUjFJKjVRK7VFKrbb1FVdKzVRKbfBsi3n6lVLqPaXURqXUSqXU5bbXdPGcv0Ep1SXrfxyiKDGrfrVpI4WYjx6VgMzkyVKDyLDP+8+VxCXYatYE8uf37c+Vy3dlF/Nnr1xZAlhdusgUrFdeie0YMzIk6GSKrAPydMt45x2ZWvf555I5c/q0TL8zNwZ58kiR9TlzrMygnMrUTDh4MLLXf/aZb5/WzqmcJghbo4b/61x/fWTvb6SlSTDVbcUbIiKinIK1gsLXvbtsJ070f85DD8n9rilrsHix+3mbNsniLUoBl1wiff5mQ/grTXDXXVY71Cwrt1WR9+wJ7bVEKSDSzKjPAbT06nsWwCytdTUAszz7ANAKQDXPVzcAHwESvALQF8BVAK4E0NcEsIgS6sgR66lDkyZA6dJSCPy99yTT4/PPpTC23WuvxX2YUVOlitUeMwaoWtXa79RJ/rxKAS+84HzdgAHRG8Ott8pKdmZVEsN7hTZAxlKvnhW0+uknWWGPy91azHLAJ0+G/9rjx32Lq5qVFPPmle+D//zHKvyZNy+wcqX7tVq1Cv/9iYiIyBl0ePHFxI0jVX3wgTxICyVL/PTpwMdvukm2S5fKfefSpTKToJjto+vDD8vWrVg64B5Y8mbPeurd23kf16mTbOfMAQ4dAnbsCH49Sl3r1smq5h06OBfRymYiCkZprecDOODV3RaAZ010fAHgNlv/KC0WASiqlCoL4CYAM7XWB7TWBwHMhG+Aiyj+TGYQ4D8Ft2lT534yFS2PVNGisjqaP0rJL1jz99OnT+TvtX49cM89QK9eslKM94qEgPyid5sq5i1fPimubc+oyunM38Wff/oW8QwkM9N3BcaWLZ01u3r2BN5803nOpZcCGzZIu3ZteYJ77JgVxCIiIqLw2LNnkrEmaXYSbMGXTZusdsmSkpVfpAhwwPZx2NT58rfYyl9/BR+HyYC7916rPpTJxDIr8N1zj6yuWKGC/8AXpb6aNeXh74QJcm+dTUWzZlRprfVOAPBszQTd8gBsSythu6fPXz9R/Pz1l/wgP37c95fEvn2SrePGe9qQyURJRaZYY6hZLPZsJbPkcLguuUSysN57z3dp3cOH5d8zQIMvAAAgAElEQVTEPi+fwmP+3/7yS3h/j961wDZulECUdyFVN1WrSrHyuXNl+qfbkslEREQUvjSW+Y2prEyDHD5cFgl65hlZ4Mdf3akOHZz73jMOAODMGdnaH7AuWAAsWeJ8wGey5iJZJIYoicTjJ5vbxFkdoJ8oPsaPl3niaWmSDVK5snOet3kC4cb7g/bFF8dmjPFgprd5Z8T4Y1KVAfnle/BgeKu8+CsOX66cFJlkfaCs81evIJh+/az20KHOKZyhaN068PcNERERha5gQWZ+J0JGhmSXe3ObCfHQQ5K9kju3rNbsLyu8dGlZeMdM7evfX6bb2ZnpgvZ/8xIlgAYN3Ouhrl0b/M9CyWv/frln934Y7FYXLJtmwUUzGLXbM/0Onq35W9wOwP5YvQKAfwL0E8XOwoXyTf/SS9aqFm7q1Al8nXbtnPtly2Z9bIliphx6Tz0MxfTpQPHizkLjwXivzAfI06IdO4Ddu8MfA2XdtGkyLdL49FPgkUcSNx4iIiKS+6ID3pVRKOrMZwKTWX7nnTIVbsoU599/VjORypSRaXaGdz0rUyPK30NFM3XPmDw5a+OJtUcekRpb5K5/f9m+9JKz36yKbTdwYOzHkwDRDEZNAWCWGesCYLKt/z7PqnoNARz2TOObDqCFUqqYp3B5C08fUWycPm0tTe8dgfbmVjjbrlAhiVD/9ptMNUvlbJBnn5W6QvZVPoLxLnA9ZYpsT5+WX6BKyep7V1/tLMY4Y4YURAck5Vhr4OefZcoexdZFF8nTO7tz56QuWuvWVo2Ddu2Arl3jPz4iIiJyKlCA097joUABoFIla4VpswJf27bOe/xo1O7Zu9dqr1vnPDZ4sGzNisXevB+k//KL/xkH8XTmjNzLm9IfgEwvHDYMaNTI+VmAxMqV1r83AKxYIZ+blALmz5e+tDRr1sI/2TNnJ6JglFJqDIBfAFRXSm1XSj0IYBCA5kqpDQCae/YBYBqAzQA2AvgEwKMAoLU+AOBVAEs9X694+ohi49lnAx8v7ylZduml8jQkFPXquWf6pJL0dODyy8N7jduqLgcOAM2bW/t9+wKLFllPRLR2TvEzv/CvvlpqDFHs5M8PbNkCjBjh7B8yBPjwQ2dfpUpxGxYRERFRUsid26rZFEvTpvk/9umngV+bN69v3+HDWRtPNHTvLhlf9tUFJ02y2sePx39Myer99yVQt3q1s79ePfncBABbt8p2/34rASCSFbJTQESfALXWd/s55DPPR2utAXT3c52RAPxUeSOKoi+/BN59N/A5W7bI0wr7anrkrmRJ3z5/2WHbtkm0/8EHrb6BA91/oVJs+Fslxq0eQoUKsR0LERERUbLJk8eq2RRLW7Y4V0o0tm4FjhyRtttDX0AenFeoAGzfbvWZ2q+JorX1sNM+lrffttq//27NTsnJli71nV0SSNGiVq2okSNlNevixWMztgTh0gyUM9x3n9WePRu44AKJPl96qfQ1by5PRMqVYzp0tHXuLIUXf/vN6guWpUZZ568GWLt28uRPa+Djj32Ph1OMnoiIiCg7yJ8/cPbJM89E531KlgRWrbL2zQNDezFyM3vAzcaNzv1EB6NmzfLtW77cuX/99bLdv19WK8+pTEmMcNjrh9n/32QTDEZR9meeMgDypOHGG4G//wauukpWv2jZEhg7NnHjS1Xp6e791av7phnbAxy//BK7MZHl6afd+ydOBEaNAu62JbiOGWOlU//rX7EfGxEREVEyyZ9fsvn96dQpeu9VuzbQpIn1vk8/7cx4CfRgMG9eWcnazPiwf85JhC1brHaBArJioFv5D6UkEOeWFUa+7IGniy6SbdeuwNSpiRlPjDAYRdnbuXPOaXevvOI8Xq0a8P332S7lMS78FSNct05+WPo73rBh7MZElpo1/R/77jtnkf6OHaVIp9bO+f5EREREOYGpcTpunPvxWrWi+37XXmu133oL6NLF2g+04jcg07dMyYxEZkZNmgQMHWrtnzghs0yMN95wf93KlbEdVyq55BLZvvWWLPQ0c6YEGu3F8p98UrabNwO33iqBPfv/lxTGYBRlP1WryjfpnDnA/fdb/cFWyKPw+MuMMumkSvnW3zp0KLZjIkvFis6pkYUKWW37UsD2ovNEREREOdk337j3+7vvjZT9vgwA/vhDtlWrhvZe5vWJyoyaPx+4/XapC+vPPfe499epE5/6XMnEXr916VLZTp4sxcwXLACeekruyZs1A3r1cr62Wzff640aFbuxxhGDUZS9zJ8PbNok7SZNgD17pD1kCHDnnYkbV3ZkflF+/rmzOLndP/8ApUpZ+ywOH19VqljtAQPcz5k+PT5jISIiIkp248f79tlrz0ZLwYLu/aGumla4sGwTlRkVygp5ZqVyN/nyyYNrpYCzZ2VGxQcfWJ/dktXhw5GNccwY2VauDFxxhcxGuPVWWQDKniXnJndu9/5z58IfR5JhMIqyj82bgcaNnX0zZsjWX7CEIjd7tkTv27eXZUrdFCgA7N4tabr+0p4pdnLZFkzt3l1WlfRmL4xIRERERE4jY7D4+8SJ7v0vvxza6wsUkO3WrdEZT7i+/965f+ONzv3//U+2gcpGGE89BfTrB/TsCZQuHZXhRc2wYRI0MooWjWyMEybINpIi5v7kygU8/nj0rpcADEZR6hs+XD5Q27NATFFAgyvkRd8118i85oIFpfgiIHWH3Dz9dPD57xR99mCUUsC99zqPz58f3/EQERERpYLq1a12tKfoAVKv083VV4f2+j//lK2/ukyx5v0g+tNPgdatrf2bb5btjBlAnz7y8PrXX52lIuzXevXV2I01Kx55RIqGDx7sXPHw7NnwrmOCc2++mbXxTJ3qDEANGQJ88knWrplADEZRatu9G3j4YWff+PHuy4xSbGltrchGycGk9dav737cLLVLRERElJN5B0n694/t+3Xt6t5fuXJor0+mOqwdO8q43VZyLl8eeO01+XxWv74zy8ifffuCn6O11KS6+GJZXTDWnnzSWcQ+nPe0r9puL/AejrVrgQ8/BNq0AXr3dh5zqymVIhiMotR16pTvD7R27STyDkhht3LlgO3b4z82omSgFLB/P/DLL1bf7bcnbjxEREREych7QZe8eeUhqz2QEGuzZ1uzDYLxDlppDWzYINt4MyvqNWokQZtVq0J7XZ487v27dgV/7ZEjUodpwwZZFd3fKt5ZsW6d/2O//SZTJP1lSM2YIffh8+cDd98tfY88EnmWXY0awKOPSttM0bRL0YLwDEZRajp5Un5YL1ki+++8I3ONzXxcAOjcGdixI3DxPKLsrnhxZ+HDvXsTNxYiIiKiZOQdJMibV8pP3HVX7N5zzx5nyYQbbgj9taZGU5s2sv3kE8kSGjHC99wffgBGj454mK7q1ZP7y8xMoFgx6VMKePttoHbtwK/dvFn+vidMcK8pW6eOTO0LxDtQtGBB6GMPVaASI61aARdeKDN0tm4FXngBOHHCOn7TTbK11zMOpX5WKNyK37/0UnSuHWcMRlFyO3pUVhlQCnjiCYn6/vabMyJcvboc69s3ceMkShXMjCIiIiJystfZBOLzMPv886VkwsSJUgsonEVl8uaVrflM9OOPsv3hB99zW7WSh/TRdOyYfAaLZCGcypWBjAwJpLkFfDIzZRVot4V3jD/+cO63a2e19+8HSpaUVRBXrgQOHAh/jACwZk3wcz77TIJv/ftbNYs/+MD93Gj9G6SlybXsq/D9/Xd0rh1nDEZRcune3Vrms0kTiTibHyDvvivLgNrr3xw86PvDiIj8MzUKXnklseMgIiIiShZpXh+LI63tE4nbbrMynEJlMrnGjZOsd5MFH6iwtimiHQ3Hj7tn6ETiscdk26WLs/+++2QanrezZ31XONy/X6Y53n03sGyZ7H/5pWRZlSgR/pjCmfZ39KhsFy8GnntOVgX09uGHQJEi4Y/Dn1GjJBvMBOxikRkWB7mCn0IUJxs2WHOOAWDOnMDnf/mlLK9JRKErWlR+wUbyJIuIiIgoJ7CXOEh29esD27ZJ2wRG3LRpE52aUgcPAv/8A5w7l/VrAbIi3JAhct0vvnAeu/hiCT4dPAi8955M37vuOgk4eWvaVLb2QuPG0aNAoUKhj+nUKat94oQEt06dkkLsZcsC99/v/rpBg5z79esDL7/sXGkwmsxK5hddFJvrxxiDUZR49evL1Dt/evWSrCjz4blIEeDZZ4FOneIzPqLshoEoIiIiIv/8FddORiYQBQBz58b+/d54Q7a7d0f3uv4yh9avlxX5xo6V6ZRugSi7YcN8+5YtC68mlz0jK39+oEIFaT/7bOgZZsePuxcbj6ZChYDSpQNnxCUxTtOjxNmyRT4Ueweidu+WwuOLFgGHD0sgCpDUy/R04M8/5QcBP1ATEVEOoZSqqJSao5Rap5Rao5TqlegxERFlSy+8kFqZUXbewY9YrK7nnf0TLd5TJY3Nm61VDZcvdx6bMsX3/B07fPteey28sZhruJW1qFdPtt4rGto99VTsA1HG4cPyufn1152LeaUABqMo/l59VQJJbumEEyYApUrJPO2rrgIKF7aO3XijFLsrVSp+YyUiIkoOGQCe0lrXANAQQHelVJSW5iEiov8XznSuZHPihHzOOnZMprTt2WMd8xfsCSYz071AdrSLogOyKty778pK6cbrr1vtyZOd59evD8ybF/y6wbKpvJmaxZde6nusXDkJVq1da/U9+KAEhYxwa4BlhZlS+OyzQIcOkpGVIqIejFJK/aWUWqWUWqGU+tXTV1wpNVMptcGzLebpV0qp95RSG5VSK5VSl0d7PJQEzp4F2re3CpN7Lz05dqxE7TMznSshEBEREQBAa71Ta/2bp30UwDoAcVjuiYgoh3ErQJ2M7r3X/7FChWRFujJlrL7MzPAKc585I5/d0tOBSpVkZbozZ6zjsVgM5+WXpUTLrbdafQsXOs8pWxaoVg2YOVMCQ40auV/rxAlgxQppHzoU3p89I0O2/jLkypWThbXMZ9gRI5xJFPFYjdEf78/aSSxWmVE3aq3raq2v8Ow/C2CW1roagFmefQBoBaCa56sbgI9iNB5KlIMHZc71t986+5cuBY4ckUjuXXdJH6fdERERBaWUqgSgHoDFiR0JEVE2sn+/fD7Jnz/RIwnNBx+E/xqzCl8ovIt0jx/vrElVqVL47x+qKlWcC1vZ7dwp9aWaNQt8jfz5gUsusfaXLQMmTQotKGVqMIUyXdP+GXbCBKlrHM+C4ps3B95PYvGaptcWgCmN/wWA22z9o7RYBKCoUqpsnMZEsfbOO0Dx4tZ+gwbA779LCuMVV0jEPm/exI2PiIgoxSilCgKYAOBxrfWRRI+HiCjbKF48tabo+Sv4HQ2HDllZRcarrwI33RS79/Rmz47y9uuvzv3ffgMGD5Zi3oBVZNz+WfPKK4Hbb5epbH37AqdP+7++yYzKFeZ6b+3aAaNHhxf0yyrv2lX24vtbtki9rN27JbgX6M+cALEIRmkAM5RSy5RS3Tx9pbXWOwFJMwdgiv6UB2Ar/4/tYMp5atMa+OQTiRA/9ZTVv3QpsGQJcNllzhRGIiIiColSKjckEPWV1vrbYOcTEVE298wzVrtFC//n2esZnTjhPLZ7N7BggbOve3dg3Tr/12vYMPQxRiqcqW716gGPPw7s2iWfR2++2TpmVv8zJk6UKYb33us/OGMyo8INRiXK0aNSM8q0H35Yirs//TTw4osyXbN7d6Bo0cSO00ssglHXaq0vh0zB666U8jOJEwDgNi8rBiX/yUFr58oKu3cDDz0E1K4NbN8uBe/8+e474M03Jb1x1SpnmuPIkVIYr5snBlmzpgSgtJZMKCIiIoqIUkoB+BTAOq31O8HOJyKiHMC+SpxZ5c3bggWSDHDeebL/9tvWsYULJVBx/fVWfd8zZ4D//jfw+/brl6VhZ9n06aGf26GDe//48VL3yU0vz4K1qbKqYsGCwMCBkhm2dSswfDjQtq3v6nqnTiVVgfOoB6O01v94tnsATARwJYDdZvqdZ2vK+m8HUNH28goA/on2mHKMffuAUaMkrVJrCQRt3iw/UDIyZNqcUhIwSkuzfuCUKSNF19asASpWlPTUMWPkP2/jxkDHjsCwYXLuLbdIBD49XbKc0tNltYAyZWQVAWP8eLlegwaJ+/sgIiLKPq4F0BlAE88iMSuUUjcHexEREWVj9mBJ/vzu9ZCuvVa2X3iq5tin3113ne/5AwY49z/91PeceE7XM06eBAYNkkBZoCwwb2bqXqjshdlTbUZPoUISCwjEBNqSQFTzzpRS5wFI01of9bRbAHgFwBQAXQAM8mzNmoxTAPRQSo0FcBWAw2Y6H4VgyRLguecksPTjj1m7Vlqa84fXPfc4j3/9tf/Xmjm5gERhH3ooa2MhIiIiB631ArhnlBMREck0LKWAxYulnlSxYs5i7BdcINtvv5XPfWl+8lJeftlqZ2bKNRcsAD77LHZjD0W+fEDv3uG/LlhB+nHjgDvvlPbixVJPyqhSJfz3S6SNG4Of07177McRomhnRpUGsEAp9TuAJQD+p7X+ARKEaq6U2gCguWcfAKYB2AxgI4BPADwa5fEkt9OngebN5Rv8/vuB1aslu+n114F//Uumu/3yi0xxq1XLymTq0EG2V10FzJ4deiDq8svlm23MGEnP27FDsqa0Bs6ds5amPP9899e/8IKk9h05IlPyjh+XlEAAWLtWXs9AFBERERERUXyVLCnbK68EqlcHSpVyFmS3Zwg1bSqf6YIxK8VVrx69cYZj1aqsXyPYiu1mZffMTGctrB9+8D+NLxW98op8Xvc3nTMBlNapXaJJKVULwOrVq1ejVq1aiR6OO62BadNkLm7evMAff0j63NKlUlQsKy65RNIrr7oKOHAAeOIJCRh9/z3QqpX8ANI6+Deh25iB8F9HRESUzaxZswa1a9cGgNpa6zWJHk8kUuJ+iYiIwjd3rgSeatYMfN65c+EV5F62TJIZACn5YqYEFi7sLIgeS5mZUhamTh3f1f3CYT7TLlkCPP880KkT8MAD1nGtJfB12WWy366db72lVFC7tpTKsatYUbK97r8/5qv8hXu/lCLl4VPA7Nkyv3bWrNhc/8EH5QfAxIkSdHr6aand5LakZ+7cVqohEFlAiUEoIiIiIiKi5HbDDaGdl54uM2zGjw/tfPuDi1y5JDA0aBBw661hDzFiaWnAli3ODK+saNAAmDlT2uXKWbWvvD/75s0bnfeLt8aNfYNRW7cmZiwhYDAqq44ezVphs/btnT8Qli6V+b1Vq1rT5uwRzI8+iizTiYiIiIiIiHKus2fd+xs1kuSKcuWAPZ61xrwDMkpJveJ4q1Qp69c4cMC3uHug6WrhZJAlk+HDEz2CsER9Nb0cRWugc2f3Y48/brVXrwZ+/VW+AZYtkzTH55+X7KZvvnG+rkEDCUQB8g3vlkrHQBQRERERERGF49gx374RI6SkTHo6sH49sH27VbIluyhWDChRwtnnr07yZZcBb74Z+zHFwiOPJHoEYWEwKpiZM63C4ZMmSdHvCy6Q/bQ0YLJnYcDDh+Wb1nwNHmy1a9UC6teX11x+uXyj9+8PvPEGA0tEREREREQUezVqyNYUOwekHMx550m7aFGgfPn4jytZHDoE/P67s9h7KnnrLav90kvAzp2JG0sIGIwKxp6id/vtQIUKwLZtznMaNcraVD0iIiIiIiKiWHrzTVlZ3UzFswelcqKXXrLaK1a412NOJXnyAL/8AvTqBfTrB5Qpk+gRBZSikyHj6IYbZFW677939r/zjkyn+/hjYNy4hAyNiIiIiIiIKCT58gEdO0p7507Zz8muuMJq16mTuHFEU8OG8pUCGIwKRimZQ6s1MH06sG4d0KOHtbTlLbckdnxERERERERE4UjyrJm4aNNGpik+8USiR5IjMRgVKqWAli3li4iIiIiIiIhSl1JSwJ0SgjWjiIiIiIiIiIgobhiMIiIiIiIiIiKiuGEwioiIiIiIiIiI4obBKCIiIiIiIiIiipvsUMA8DwBs3Lgx0eMgIiKibMh2j5EnkePIIt4vERERUcyEe7+ktNaxG00cKKVuBTA50eMgIiKibK+t1npKogcRCd4vERERUZyEdL+UHYJRRQA0BrANwJkED4eIiIiynzwAKgKYp7U+nOjBRIL3S0RERBRjYd0vpXwwioiIiIiIiIiIUgcLmBMRERERERERUdwwGEVERERERERERHHDYBQREREREREREcUNg1FERERERPR/7d1brFxVHcfx7x9KNRVrWw2VUMolKsqDSFEDRGnRiFCjNTEmJqhg5QkewKTGJvpiwIhECRKMSiqNJl4SEC9ECaKpqaGFcNGW2gNt6YMcrVS5iEgiEv8+rHUyAxbKzNmz99nl+0kms8/ae9bZ6z8ze35Zs2dGkqTWOBklSZIkSZKk1jgZJUmSJEmSpNY4GSVJkiRJkqTWOBklSZIkSZKk1jgZJUmSJEmSpNY4GTUBEXFDROyPiB1DbadExNaIuD8ibomIhbV9fkRsrO3bImJVbV8QEb+IiAci4o8RcWVHwxlbE3UYWnd9ROyq9fhIB8OZlYg4NiI2RcRUvT8vre1LIuL2iNhdrxfX9oiIayNiT0Rsj4gVQ31dULffHREXdDWmcTVZi7p+YUT8OSKu62I842r4MXFV7WOqbhNdjWscY9TizfU48u+IWHewfvqiqTrUdYsi4qZ6zJyKiDO6GNO4xqjF+fV5sT0itkTEKUN9nRsRD9bnzvquxqT/F+YlwLw0rOHXxt7mpSbrUNf3MiuBeWnYGLUwL2FeirmclzLTS8MX4CxgBbBjqO1uYGVdXgtcXpcvATbW5aOAeymThAuAs2v7fOB3wHldj63tOtS/vwhcUZcPA17X9djGqMXRwIq6/GpgF3AycBWwvravB75Sl1cDtwIBnA7cVduXAHvr9eK6vLjr8XVRi6H+vg78ALiu67F19Jg4E7gDOLxetgKruh7fhGtxFPAO4EvAuoP10/X42q5DXfdd4KK6PB9Y1PX4JlyLM2eOhcB5Q8+Pw4GHgBNrHbb16TFxqF8wLzVWh/q3eekQyUtN1WGov15mpYYfE+alg/TT9fjarkNdZ17K7vKSZ0ZNQGZuBh57XvNJwOa6fDsw827VycBv6u32A08Ab8/MpzNzU21/BrgPWDbhXW9UE3Wo69YCX67r/puZf5/gbk9EZu7LzPvq8j+BKeAYYA3lIEi9/nBdXgN8L4s7gUURcTTwfuD2zHwsMx+n1PDcFocyaw3Wgog4DVgK/KrFITSiwTok8ErKC8crgCOAR1obSANGrUVm7s/Mu4H/vMR+eqGpOkQ5g+Is4Dt1u2cy84lWBtGQMWqxpR4TAe5k8Hr5TmBPZu6tr6U/qn1oDjAvFealAfNSYVYaMC8NmJcK89JA3/OSk1Ht2QF8qC5/FDi2Lm8D1kTEvIg4AThtaB1QTh8EPkgNHz03Uh3q2AEuj4j7IuLGiFja7i43KyKOB04F7gKWZuY+KAcTysw9lIPIw0M3m65tL9TeS7OpRUQcBnwN+Gxb+zsps6lDZm4FNgH76uW2zJxqZ8+b9xJrMWo/vTPLOpwI/A3YGBG/j4gNEfGqCe7uRI1Ri09T3hWHQ+yY+TJhXirMS+YlwKw0zLw0YF4qzEsDfcxLTka1Zy1wSUTcSzmF7pnafgPlzr4HuAbYAjw7c6OImAf8ELg2M/e2useTMWod5lFmbO/IzBWUU2q/2vZONyUijgR+DFyWmU++2KYHaMsXae+dBmpxMfDLzHz4AOt7Y7Z1iIg3AG+hPE+OAd4TEWc1v6eTN0ItWumnKw3s/zzKR36+mZmnAv+inKLdO6PWIiLOpoSrz800HWCzXh4zX0bMS4V5ybxkVhpiXhowLxXmpYG+5qV5k/4HKjLzAeAcgIh4E/CB2v4s8JmZ7SJiC7B76KbXA7sz85r29nZyxqjDo8DTwE/qqhspT5zeiYgjKAeJ72fmzbX5kYg4OjP31VOI99f2aZ77ju8y4C+1fdXz2n87yf2ehIZqcQbw7oi4GDgSmB8RT2Vmb15EGqrDx4E7M/Op2uetlO9I2EyPjFiLUfvpjYbqMA1MZ+bMu5w30cNwNWotIuKtwAbK9wU9Wptf6HmjOcq8VJiXzEtmpQHz0oB5qTAvDfQ5L3lmVEsi4qh6fRjwBeBb9e8FM6cDRsT7gGczc2f9+wrgNcBlnez0BIxah8xM4BYGgeK9wM6293u2IiIon0eeysyrh1b9HJj5hZcLgJ8NtX8yitOBf9RTLG8DzomIxVF+FeGc2tYbTdUiM8/PzOWZeTywjvL9AL15AWnwMfEnYGWUj2wcAaykfF68N8aoxaj99EJTdcjMvwIPR8RJtal3x81RaxERy4GbgU9k5q6h7e8G3hgRJ0TEfOBjtQ/NUealwrz08s5LZqUB89KAeakwLw30Pi/lHPgW+EPtQjlNfB/lS9KmKe9MXUr5dvtdwJVA1G2PBx6kHAx/DRxX25dRTo2bAv5QLxd1Pba261DXHUd512I75Xsglnc9tjFq8a56f24fuj9XA6+tY9pdr5fU7QP4BuVXDe6nfEnrTF9rgT318qmux9ZlLYb6vJCe/UJMU3Wg/PrFt+tzZydwdddja6EWr6/HlCcpX947DSx8oX66Hl/bdajr3kb5GM924Kf06FekxqzFBuDxoW3vGeprNeU15yHg812Pzctz7mfzUkN1qOvMS4dIXmqyDkN9XkjPslKTtcC8ZF4yL8Ecy0szL2ySJEmSJEnSxPkxPUmSJEmSJLXGyShJkiRJkiS1xskoSZIkSZIktcbJKEmSJEmSJLXGyShJkiRJkiS1xskoSZIkSZIktcbJKEmSJEmSJLXGyShJkiRJkiS1xskoSZIkSZIktcbJKEmSJEmSJLXGyShJkiRJkiS1xskoSZIkSZIktcbJKEmSJEmSJLXmf502+K1RQ7QAAAABSURBVH6fhSHTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1200x720 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# importing the necessary module\n",
    "from pandas.plotting import register_matplotlib_converters\n",
    "register_matplotlib_converters()\n",
    "\n",
    "# Plot\n",
    "fig, axes = plt.subplots(nrows=3, ncols=2, dpi=120, figsize=(10,6))\n",
    "for i, ax in enumerate(axes.flatten()):\n",
    "    data = df[df.columns[i]]\n",
    "    ax.plot(data, color='red', linewidth=1)\n",
    "    # Decorations\n",
    "    ax.set_title(df.columns[i])\n",
    "    ax.xaxis.set_ticks_position('none')\n",
    "    ax.yaxis.set_ticks_position('none')\n",
    "    ax.spines['top'].set_alpha(0)\n",
    "    ax.tick_params(labelsize=6)\n",
    "    plt.tight_layout();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we can see different trends for six of our variables. It would be helpful if we established whether or not our time series followed a normal (or Gaussian) distribution. We will do this based on the test for normality based on the Jarque-Bera test.\n",
    "\n",
    "### Jarque-Bera Test\n",
    "\n",
    "There are actually three test that we could have implemented for testing normality; however, we will focus on just one: the Jarque-Bera Test.\n",
    "\n",
    "The Jarque-Bera goodness-of-fit test determines whether a sample data have the skewness and kurtosis matching a normal distribution.\n",
    "\n",
    "$$k_{3}=\\frac{\\sum^{n}_{i=1}(x_{i}-\\bar{x})^{3}}{ns^{3}} \\,\\,\\,\\,\\,\\,\\, k_{4}=\\frac{\\sum^{n}_{i=1}(x_{i}-\\bar{x})^{4}}{ns^{4}}-3  $$\n",
    "\n",
    "\n",
    "$$JB = n \\Bigg(\\frac{(k_{3})^{2}}{6}+\\frac{(k_{4})^{2}}{24}\\Bigg) $$\n",
    "\n",
    "where $x$ is each observation, $n$ is the sample size, $s$ is the standard deviation, $k_{3}$ is skewness, and $k_{4}$ is kurtosis. The null hypothesis, $H_{0}$, follows that the data is normally distributed; the alternative hypothesis, $H_{A}$, follows that the data is not normally distributed.\n",
    "\n",
    "There is a simple script we can use in python to determine the distribution of the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics=8355.792, p=0.000\n",
      "Data does not look Gaussian (reject H0)\n"
     ]
    }
   ],
   "source": [
    "# imports the necessary module for statistics\n",
    "from scipy import stats\n",
    "\n",
    "# unpacks the test statistic and p-value from the normaltest of gold\n",
    "stat, p = stats.normaltest(df.Gold)\n",
    "\n",
    "# prints both the test statistic and p-value\n",
    "print('Statistics=%.3f, p=%.3f' % (stat, p))\n",
    "\n",
    "# chooses an alpha of 0.05 and assigns to variable 'alpha'\n",
    "alpha = 0.05\n",
    "\n",
    "# creates an if statement for the hypothesis using the p-value test\n",
    "if p > alpha:\n",
    "    print('Data looks Gaussian (fail to reject H0)')\n",
    "else:\n",
    "    print('Data does not look Gaussian (reject H0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, we recieve a p-value and a test statistic in return. While we don't have a Chi-Square chart to determine the critical region, we do have a p-value, which is basically zero.\n",
    "\n",
    "A p-value less than 0.05 basically means our test statistic falls within the critical region (inside the tail); therefore, we can reject the null hypothesis. The dataset is not normally distributed, which we probably could have assumed by looking at the time series plots from before.\n",
    "\n",
    "Next, we can look for a fat-tail distribution and asymmetry by looking for kurtosis and skewness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kurtosis of normal distribution: -1.226141169366336\n",
      "Skewness of normal distribution: 0.5693979892107541\n"
     ]
    }
   ],
   "source": [
    "print('Kurtosis of normal distribution: {}'.format(stats.kurtosis(df.Gold)))\n",
    "print('Skewness of normal distribution: {}'.format(stats.skew(df.Gold)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kurtosis of normal distribution: -0.7778459997868463\n",
      "Skewness of normal distribution: 0.6148674871988418\n"
     ]
    }
   ],
   "source": [
    "print('Kurtosis of normal distribution: {}'.format(stats.kurtosis(df.Oil)))\n",
    "print('Skewness of normal distribution: {}'.format(stats.skew(df.Oil)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These two distributions can provide us with some intuition about the distribution of our data. A value close to 0 for kurtosis indicates a normal distribution where asymmetrical nature is signified by a value between -0.5 and +0.5 for skewness. The tails are heavier for kurtosis greater than 0 and vice versa. Moderate skewness refers to the value between -1 and -0.5 or 0.5 and 1.\n",
    "\n",
    "We can also use a normal probability plot to assess the probability distribution of a randomly selected variable inside of our dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    7193.000000\n",
       "mean      749.122744\n",
       "std       471.580302\n",
       "min       252.900000\n",
       "25%       350.750000\n",
       "50%       433.600000\n",
       "75%      1230.250000\n",
       "max      1891.000000\n",
       "Name: Gold, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14,6))\n",
    "plt.subplot(1,2,1)\n",
    "df['Gold'].hist(bins=50)\n",
    "plt.title('Gold')\n",
    "plt.subplot(1,2,2)\n",
    "stats.probplot(df['Gold'], plot=plt);\n",
    "df.Gold.describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability plot is basically a visualization that plots the Cumulative Density Function (CDF) of two specific distributions: empirical and theorical. Assuming that we have two distributions ($f$ and $g$) and a point of evaluation $z$ (any value), the point on the plot indicates what percentage of data lies at or below $z$ in both $f$ and $g$ (as per definition of CDF).\n",
    "\n",
    "To compare the distribution, we check if the points lie on a 45-degree line ($x=y$). In case they deviate, the distribution differ. However, as we can see from the probability plot, the dataset does not appear to be normally distributed.\n",
    "\n",
    "## The VAR Model\n",
    "\n",
    "Considering that our dataset isn't normally distributed, we can use this information to build a VAR model. The construction of the model will be based on the following steps:\n",
    "\n",
    "1. Testing for autocorrelation\n",
    "2. Testing for stationarity\n",
    "3. Testing for causation using granger causality\n",
    "4. Conducting a forecast evaluation\n",
    "\n",
    "### Testing for autocorrlation\n",
    "\n",
    "An autoregressive, or $AR(p)$, model is created by regressing a time series on its past values, its lags. The simplest form of an autoregressive model is an $AR(1)$ model, signifying using only one lag term. A first order autocorrelation model like this for a time series $x_{t}$ is:\n",
    "\n",
    "$$x_{t}=b_{0}+b_{1}x_{t-1}+\\varepsilon_{t}$$\n",
    "\n",
    "Where $x_{t-1}$ represents the value of the time series at ($t-1$) and $\\varepsilon_{t}$ is the error term. We can extend this to an $AR(p)$ model, denoted:\n",
    "\n",
    "$$x_{t}=b_{0}+b_{1}x_{t-1}+b_{2}x_{t-2}+\\ldots+b_{p}x_{t-p}+\\varepsilon_{t}$$\n",
    "\n",
    "For an AR model to function properly, we must require that the time series is covariance stationary. This means that it follows three conditions:\n",
    "\n",
    "1. The expected value of the time series is constant and finite at all times, i.e. $E[y_{t}]=\\mu$ and $\\mu <\\infty$ for all values of $t$.\n",
    "2. The variance of the time series is constant and finite for all time periods.\n",
    "3. The covariance of the time series with itself for a fixed number of periods in either the future or the past is constant and finite for all time periods, or in other words\n",
    "\n",
    "$$Cov(y_{t},y_{t-s})=\\lambda, |\\lambda|<\\infty,\\lambda\\ constant, t=1,2,\\ldots,T;s=0,\\pm1,\\pm2,\\ldots,\\pm T$$\n",
    "\n",
    "Note that this mathematical representation includes condition 2. If these conditions are not satisfied, our estimation results will not have real-world meaning.\n",
    "\n",
    "In python, we can test to see if our time series is autocorrelated using the `plot_acf` and `plot_pacf` tools in the `statsmodels` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "\n",
    "fig, ax = plt.subplots(2, figsize=(10,6))\n",
    "ax[0] = plot_acf(df.Gold, ax=ax[0])\n",
    "ax[1] = plot_pacf(df.Gold, ax=ax[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plot shows the autocorrelation for the Gold time series. As we can see, each value is highly correlated with the previous value. We have an autocorrelation of +1, which represents a perfect positive correlation. An increase seen in one time series leads to a proportionate increase in the other time series.\n",
    "\n",
    "We can check the same for the silver variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2, figsize=(10, 6))\n",
    "ax[0] = plot_acf(df.Silver, ax=ax[0])\n",
    "ax[1] = plot_pacf(df.Silver, ax=ax[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the silver variable is also autocorrelated. Now that we understand that our variables may have some autocorrelation, we need to also test for stationarity.\n",
    "\n",
    "### Testing for stationarity\n",
    "\n",
    "Stationarity can be defined as a constant mean, variance or autocovariances for each given lag. There are several reasons why the concept of non-stationarity is important and why it is essential that variables that are non-stationary should be treated differently from variables that are stationary. These reasons are givena as follows:\n",
    "\n",
    "* The stationarity or otherwise of a series can strongly influence its behavior or properties. To offer one illustration, the word 'shock' usually used to denote a change or an unexpected change in a variable or prehaps simply the value of the error term during a particular time period. For a stationary series, 'shocks' to the system will gradually die away. This can be constrasted with the case of non-stationary data, where the persistence of shocks will always be infinite.\n",
    "\n",
    "* The use of non-stationarity data can lead to spurious regressions. If two stationary variables are generated as independnent random series, when one of those variables is regressed on the other, the $t$-ratio on the slope coefficient would be expected not to be signficiantly different from zero, and the value of $R^{2}$ would be expected to be very low. So, if standard regression techniques are applied to non-stationary data, the end result could be a regression that 'looks' good under standards measures, but which is really valueless. Such a model would be termed a 'spurious' regression.\n",
    "\n",
    "### Augmented Dickey-Fuller test\n",
    "\n",
    "The Dickey-Fuller test is testing if $\\phi=0$ in this model of the data:\n",
    "\n",
    "$$y_{t}=\\alpha+\\beta_{t}+\\phi y_{t-1}+\\varepsilon_{t}$$\n",
    "\n",
    "which is written as the following:\n",
    "\n",
    "$$\\Delta y_{t}=y_{t}-y_{t-1}=\\alpha+\\beta_{t}+\\gamma y_{t-1}+\\varepsilon_{t}$$\n",
    "\n",
    "where $y_{t}$ is your data. It is written this way so we can do a linear regression of $\\Delta y_{t}$ against $t$ and $y_{t-1}$ and test if $\\gamma$ is different from 0. If $\\gamma=0$, then we have a random walk process. IF not and $-1 < 1 + \\gamma < 1$, then we have a stationary process.\n",
    "\n",
    "The Augmented Dickey-Fuller test allows for higher-order autoregressive processes by including $\\Delta y_{t-p}$ in the model. But our test is still if $\\gamma=0$.\n",
    "\n",
    "$$\\Delta y_{t}=\\alpha+\\beta_{t}+\\gamma y_{t-1}+\\delta_{1}\\Delta y_{t-1}+\\delta_{2}\\Delta y_{t-2}+\\ldots$$\n",
    "The null hypothesis for both tests is that the data are non-stationary. We went to REJECT the null hypothesis for this test, so we want a p-value less than 0.05 (or smaller).\n",
    "\n",
    "We can create a function that will allow us to test whether a time series is stationary or non-stationary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def adfuller_test(series, signif=0.05, name='', verbose=False):\n",
    "    \"\"\" Perform ADFuller to test for Stationarity of given series and print report\"\"\"\n",
    "    r = adfuller(series, autolag = 'AIC')\n",
    "    output = {'test_statistics':round(r[0], 4), 'pvalue':round(r[1], 4), 'n_lags':round(r[2], 4), 'n_obs':r[3]}\n",
    "    p_value = output['pvalue']\n",
    "    def adjust(val, length=6): return str(val).ljust(length)\n",
    "    \n",
    "    # Print Summary\n",
    "    print(f'   Augmented Dickey-Fuller Test on \"{name}\"', \"\\n  \", '-'*47)\n",
    "    print(f' Null Hypothesis: Data has unit root. Non-Stationary.')\n",
    "    print(f' Significance level   = {signif}')\n",
    "    print(f' Test Statistics      = {output[\"test_statistics\"]}')\n",
    "    print(f' No. Lags Chosen      = {output[\"n_lags\"]}')\n",
    "          \n",
    "    for key, val in r[4].items():\n",
    "          print(f' Critical value {adjust(key)} = {round(val, 3)}')\n",
    "          \n",
    "    if p_value <= signif:\n",
    "          print(f\" => P-Value = {p_value}. Rejecting Null Hypothesis.\")\n",
    "          print(f\" => Series is Stationary.\")\n",
    "          \n",
    "    else:\n",
    "          print(f\" => P-Value = {p_value}. Weak evidence to reject the Null Hypothesis.\")\n",
    "          print(f\" => Series in Non-Stationary.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From there, we can use the function to test all of the variables in our original dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Test on \"Gold\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = 0.0946\n",
      " No. Lags Chosen      = 34\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.9657. Weak evidence to reject the Null Hypothesis.\n",
      " => Series in Non-Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Silver\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -1.4796\n",
      " No. Lags Chosen      = 34\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.5436. Weak evidence to reject the Null Hypothesis.\n",
      " => Series in Non-Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Oil\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -1.6308\n",
      " No. Lags Chosen      = 28\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.4671. Weak evidence to reject the Null Hypothesis.\n",
      " => Series in Non-Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Dollar\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -1.9758\n",
      " No. Lags Chosen      = 1\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.2973. Weak evidence to reject the Null Hypothesis.\n",
      " => Series in Non-Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"S&P 500\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = 1.6595\n",
      " No. Lags Chosen      = 31\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.998. Weak evidence to reject the Null Hypothesis.\n",
      " => Series in Non-Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Value\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -2.0941\n",
      " No. Lags Chosen      = 5\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.2469. Weak evidence to reject the Null Hypothesis.\n",
      " => Series in Non-Stationary.\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for name, column in df.iteritems():\n",
    "          adfuller_test(column, name=column.name)\n",
    "          print('\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can, when tested for stationarity, the p-values for all of the variables are greater than 0.05, which suggest very little evidence of stationarity. In order for us to process further, we would need to transform our time series into a stationary time series.\n",
    "\n",
    "However, before we do this, we're going to take the opportunity to seperate our time series into a testing set and a training set. We will do this to assess the predictive capabilities of the model we will eventually create."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7178, 6)\n",
      "(15, 6)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# assigned the integer 15 to the variable 'nobs'\n",
    "nobs = 15\n",
    "\n",
    "# assigning the last 15 observations to the variable 'X_test', while the rest will be assigned to the variable 'X_train'\n",
    "X_train, X_test = df[0:-nobs], df[-nobs:]\n",
    "\n",
    "#check size\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training set is the set we will use to build the model, while the testing set is what will be used to test the accuracy of the model. In order to make the time series stationary, we need to apply a differencing function on the training set. However, this is an iterative process where we after first differencing, the series may still be non-stationary. We may have to apply a second difference or log transformation to standardize the series in such cases.\n",
    "\n",
    "The following demonstrates what time series would generate with our differencing technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gold</th>\n",
       "      <th>Silver</th>\n",
       "      <th>Oil</th>\n",
       "      <th>Dollar</th>\n",
       "      <th>S&amp;P 500</th>\n",
       "      <th>Value</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1990-08-20</td>\n",
       "      <td>0.40</td>\n",
       "      <td>-0.0090</td>\n",
       "      <td>11.50</td>\n",
       "      <td>0.66</td>\n",
       "      <td>0.680023</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-21</td>\n",
       "      <td>-3.05</td>\n",
       "      <td>-0.0410</td>\n",
       "      <td>12.00</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-6.650025</td>\n",
       "      <td>0.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-22</td>\n",
       "      <td>2.15</td>\n",
       "      <td>-0.0435</td>\n",
       "      <td>7.00</td>\n",
       "      <td>-0.45</td>\n",
       "      <td>-5.309997</td>\n",
       "      <td>0.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-23</td>\n",
       "      <td>5.70</td>\n",
       "      <td>0.0995</td>\n",
       "      <td>17.00</td>\n",
       "      <td>-0.74</td>\n",
       "      <td>-9.489990</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1990-08-24</td>\n",
       "      <td>-3.70</td>\n",
       "      <td>-0.0820</td>\n",
       "      <td>-4.25</td>\n",
       "      <td>0.74</td>\n",
       "      <td>4.450012</td>\n",
       "      <td>0.05</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Gold  Silver    Oil  Dollar   S&P 500  Value\n",
       "Date                                                    \n",
       "1990-08-20  0.40 -0.0090  11.50    0.66  0.680023   0.01\n",
       "1990-08-21 -3.05 -0.0410  12.00   -0.01 -6.650025   0.03\n",
       "1990-08-22  2.15 -0.0435   7.00   -0.45 -5.309997   0.07\n",
       "1990-08-23  5.70  0.0995  17.00   -0.74 -9.489990   0.09\n",
       "1990-08-24 -3.70 -0.0820  -4.25    0.74  4.450012   0.05"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transform_data = X_train.diff().dropna()\n",
    "transform_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values in our training dataset appears different from the original dataframe. We can use `adfuller_test` function on the training set to confirm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Test on \"Gold\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -16.372\n",
      " No. Lags Chosen      = 33\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.0. Rejecting Null Hypothesis.\n",
      " => Series is Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Silver\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -13.8087\n",
      " No. Lags Chosen      = 35\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.0. Rejecting Null Hypothesis.\n",
      " => Series is Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Oil\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -13.5267\n",
      " No. Lags Chosen      = 27\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.0. Rejecting Null Hypothesis.\n",
      " => Series is Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Dollar\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -87.3033\n",
      " No. Lags Chosen      = 0\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.0. Rejecting Null Hypothesis.\n",
      " => Series is Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"S&P 500\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -16.6794\n",
      " No. Lags Chosen      = 27\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.0. Rejecting Null Hypothesis.\n",
      " => Series is Stationary.\n",
      "\n",
      "\n",
      "   Augmented Dickey-Fuller Test on \"Value\" \n",
      "   -----------------------------------------------\n",
      " Null Hypothesis: Data has unit root. Non-Stationary.\n",
      " Significance level   = 0.05\n",
      " Test Statistics      = -40.028\n",
      " No. Lags Chosen      = 4\n",
      " Critical value 1%     = -3.431\n",
      " Critical value 5%     = -2.862\n",
      " Critical value 10%    = -2.567\n",
      " => P-Value = 0.0. Rejecting Null Hypothesis.\n",
      " => Series is Stationary.\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for name, column in transform_data.iteritems():\n",
    "          adfuller_test(column, name=column.name)\n",
    "          print('\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the values to see the obvious different between a stationary and a non-stationary time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=3, ncols=2, dpi=120, figsize=(12, 6))\n",
    "for i, ax in enumerate(axes.flatten()):\n",
    "    data = transform_data[transform_data.columns[i]]\n",
    "    ax.plot(data, color='red', linewidth=1)\n",
    "    # Decorations\n",
    "    ax.set_title(transform_data.columns[i])\n",
    "    ax.xaxis.set_ticks_position('none')\n",
    "    ax.yaxis.set_ticks_position('none')\n",
    "    ax.spines['top'].set_alpha(0)\n",
    "    ax.tick_params(labelsize=6)\n",
    "    \n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have transformed the time series, we can test for what is known as **Granger Causality**.\n",
    "\n",
    "### Testing Causation using Granger's Causality Test\n",
    "\n",
    "The question of what event caused another, or what brought about a certain change in a phenomenon, is a common one. While a naive interpretation of the problem may suggest simple approaches like equating causality with high correlation, or to infer the degree to which $x$ causes $y$ from the degree of $x$'s goodness as a predictor of $y$, the problem is much more complex. As a result, rigorous ways to approach this question were developed in several fields of science.\n",
    "\n",
    "This can be done one of two different ways:\n",
    "\n",
    "1. Casual inference over random variables, representing different events. The most common example are two variables, each representing one alternative of an A/B test, and each with a set of samples/observations associated with it.\n",
    "2. Casual inference over time series data (and thus over stochastic processes). Examples include determining wehther (and to what degree) aggregate daily stock prices drive (and are driven by) daily trading volume, or causal relatioons between volumns of Pacific sardine catches, northern anchovy catches, and sea suface temperature.\n",
    "\n",
    "#### Granger Causality\n",
    "\n",
    "Granger Causality is based on contrasting the ability to predict a stochastic process $Y$ using *all the information in the universe,* denoted with $U$, with doing the same using all information in $U$ except for some stochastic process $X$; this is denoted with $U | X$. The core idea is that if discarding $X$ reduces the predictive power regarding $Y$, the $X$ contains some unique information regarding $Y$, and we thus say that *Granger-cause* $Y$.\n",
    "\n",
    "Given two sets of time series data, $X$ and $Y$, Granger causality is a method which attempts to determine whether one series is likely to influence change in the other. This is accomplished by taking different lags of one series and using that to model the change in the second series.\n",
    "\n",
    "We create two models which predict $Y$, one with only past values of $Y(\\Omega)$, and the other with past values of $Y$ and $X(\\pi)$. The models are given below where $k$ is the number of lags in the time series:\n",
    "\n",
    "$Let\\,\\Omega = y_{t} = \\beta_{0} + \\beta_{1}y_{t-1}+\\ldots+\\beta_{k}y_{t-k}+\\varepsilon $\n",
    "\n",
    "$And\\,\\pi = y_{t}=\\beta_{0}+\\beta_{1}y_{t-1}+\\ldots+\\beta_{k}y_{t-k}+\\alpha_{1}x_{t-1}+\\ldots+\\alpha_{k}x_{t-k}+\\varepsilon $\n",
    "\n",
    "The residual sum of squared errors are then compared and a test is used to determine whether the nested model ($\\Omega$) is adequate to explain the future values of $Y$ or if the full model ($\\pi$) is better. The F-test or t-test are calculated to test the following null and alternative hypothesis:\n",
    "\n",
    "$$H_{0}: \\alpha_{i} = 0 $$\n",
    "\n",
    "$$H_{A}: \\alpha_{i} \\neq 0 $$\n",
    "\n",
    "Essentially, we are trying to determine whether we can say that statistically $X$ provides more information about future values of $Y$ than past values of $Y$ alone. Under this definition, it is clear that we are not trying to prove actual causation, only that two values are related by some phenomenon. Along those lines, we must also run this model in reverse to verify that $Y$ does not provide inforamtion about future value of $X$. \n",
    "\n",
    "If we find that this is the case, it is likely that there is some exogenous variable, $Z$, which needs to be controlled or could be a better candidate for Granger causation.\n",
    "\n",
    "#### Granger Casuality Test Results\n",
    "\n",
    "Granger's causlity tests the null hypothesis, $H_{0}$, that the coefficients of past values in the regression equation is zero. In simplier term, the past values of time series, $X$, do not cause other series, $Y$. If the p-value obtained from the test is lesser than the significance level of 0.05, then, you can safely reject the null hypothesis. \n",
    "\n",
    "The following code was performed on the training dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# importing the granger causality test from statsmodels\n",
    "from statsmodels.tsa.stattools import grangercausalitytests\n",
    "\n",
    "# creating a variable named 'maxlag' and assigning the integer 5\n",
    "maxlag = 5\n",
    "\n",
    "# assigning the string 'ssr_chi2test' to the variable 'test'\n",
    "test = 'ssr_chi2test'\n",
    "\n",
    "# creating a function named 'granger_causation_matrix' with the arguments 'data', 'variables', 'test', and 'verbose'\n",
    "def granger_causation_matrix(data, variables, test='ssr_chi2test', verbose=False):\n",
    "    \n",
    "    # creating a dataframe with the same dimensions as number of variables entered, assigned to the variable 'X_train'\n",
    "    X_train = pd.DataFrame(np.zeros((len(variables), len(variables))), columns=variables, index=variables)\n",
    "    \n",
    "    # loops through the columns and the indexes\n",
    "    for c in X_train.columns:\n",
    "        for r in X_train.index:\n",
    "            \n",
    "            # conducts a granger causality test on a variable row and column using the 'maxlag' variable; assigns to \n",
    "            # variable test_result\n",
    "            test_result = grangercausalitytests(data[[r, c]], maxlag=maxlag, verbose=False)\n",
    "            \n",
    "            # locates the test result in the tuple 'test_result' and rounds the number by 4 digits; assigns to 'p_values'\n",
    "            p_values = [round(test_result[i+1][0][test][1], 4) for i in range(maxlag)]\n",
    "            \n",
    "            # if the variable is 'verbose', print the y and x variables and the associated p-value\n",
    "            if verbose: \n",
    "                print(f'Y = {r}, X = {c}, P Values = {p_values}')\n",
    "            \n",
    "            # find the smallest p-value and assign to variable 'min_p_value'\n",
    "            min_p_value = np.min(p_values)\n",
    "            \n",
    "            # find the smallest p-value and assign to its respective row and column\n",
    "            X_train.loc[r, c] = min_p_value\n",
    "            \n",
    "    # remane the row and column names based on the relationship\n",
    "    X_train.columns = [var + '_x' for var in variables]\n",
    "    X_train.index = [var + '_y' for var in variables]\n",
    "    return X_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Beside the scenes, what this code is doing is creating a matrix of equal rows and columns, based on the number of variables. From there, we will conduct a granger causality test based on the row/column pair relationship and the number of chosen lags for the model. From there, the code assigns the p-value based on the tested relationship.\n",
    "\n",
    "The code outputs the following code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gold_x</th>\n",
       "      <th>Silver_x</th>\n",
       "      <th>Oil_x</th>\n",
       "      <th>Dollar_x</th>\n",
       "      <th>S&amp;P 500_x</th>\n",
       "      <th>Value_x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Gold_y</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0178</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Silver_y</td>\n",
       "      <td>0.0575</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Oil_y</td>\n",
       "      <td>0.0009</td>\n",
       "      <td>0.0006</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.0479</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Dollar_y</td>\n",
       "      <td>0.2988</td>\n",
       "      <td>0.5818</td>\n",
       "      <td>0.6116</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>S&amp;P 500_y</td>\n",
       "      <td>0.0289</td>\n",
       "      <td>0.4068</td>\n",
       "      <td>0.0446</td>\n",
       "      <td>0.3913</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.0524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Value_y</td>\n",
       "      <td>0.0148</td>\n",
       "      <td>0.0435</td>\n",
       "      <td>0.0231</td>\n",
       "      <td>0.8580</td>\n",
       "      <td>0.0085</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Gold_x  Silver_x   Oil_x  Dollar_x  S&P 500_x  Value_x\n",
       "Gold_y     1.0000    0.0000  0.0000    0.0000     0.0178   0.0000\n",
       "Silver_y   0.0575    1.0000  0.0000    0.0000     0.0000   0.0529\n",
       "Oil_y      0.0009    0.0006  1.0000    0.0479     0.0000   0.0001\n",
       "Dollar_y   0.2988    0.5818  0.6116    1.0000     0.0000   0.0319\n",
       "S&P 500_y  0.0289    0.4068  0.0446    0.3913     1.0000   0.0524\n",
       "Value_y    0.0148    0.0435  0.0231    0.8580     0.0085   1.0000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "granger_causation_matrix(X_train, variables = X_train.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The row are the responses $Y$ and the columns are the predictors $X$.\n",
    "\n",
    "* If we take the value 0.0000 in (row 1, column 2), it refers to the p-value of the Granger's Causality test for `Silver_x` causing `Gold_Y`. The 0.0000 in row 2, column 1 refers to the p-value of `Gold_y` causing `Silver_x`. \n",
    "\n",
    "* As we can see, `Gold_x` isn't typically caused by any of the other variables. However, movements in the variable `Gold_x` only appears to be caused by the variable `USD_y` This intuitively makes sense, as the value of gold is often tied to the US Dollar and some in the investment community consider gold as a hedge against inflation (the same for the variables `Silver_x` and `USD_y`).\n",
    "\n",
    "* The `Interest_x` variable only seems to cause movements in `Silver_y`; however, `Interest_y` does appear to cause movements in the `USD_x`, which also makes sense.\n",
    "\n",
    "* The `S&P 500_y` variable appears to cause movements in the variables `Silver_x`, `Oil_x`, and `USD_x`.\n",
    "\n",
    "So, looking at the p-values, we can assume that (except Oil) most of the variables (time series) in the system are interchangeably causing each other. This justifies the VAR modeling approach for this system of multi time-series to forecast.\n",
    "\n",
    "#### Testing for Co-integration\n",
    "\n",
    "Regression errors are a linear combination of two unit root series ($X$ and $Y$) of the following equation:\n",
    "\n",
    "$$\\varepsilon=Y_{t}-\\alpha-\\beta X_{t} $$\n",
    "\n",
    "If $X_{t}$ and $X_{t}$ have a unit root, this usually means $\\varepsilon_{t}$ also has a unit root. This is the cause of a spurious regression problem.\n",
    "\n",
    "However, there are some cases when the unit root in $Y$ and $X$ cancel each other out and $\\varepsilon_{t}$ does not have any unit root. In this special case, the spurious regression problem vanishes. This phenomenon is referred to as cointegration, which measures the equilibrium spread between two non-stationary time series measured by constant terms $\\alpha$. If the error term is stationary then we can say that cointegration and an equalibrium spread exist.\n",
    "\n",
    "For testing co-integration, we used the Johansen method to test for co-integration using the following python function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name   :: Test Stat > C(95%)       => Signif   \n",
      " ----------------------------------------\n",
      "Gold   :: 7126.33   > 83.9383    =>   True\n",
      "Silver :: 5795.0    > 60.0627    =>   True\n",
      "Oil    :: 4503.39   > 40.1749    =>   True\n",
      "Dollar :: 3229.9    > 24.2761    =>   True\n",
      "S&P 500 :: 2055.99   > 12.3212    =>   True\n",
      "Value  :: 1007.48   > 4.1296     =>   True\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.vector_ar.vecm import coint_johansen\n",
    "\n",
    "def cointegration_test(transfrom_data, alpha=0.05):\n",
    "    \"\"\"Perform Johanson's Cointegration Test and Report Summary\"\"\"\n",
    "    out = coint_johansen(transform_data, -1, 5)\n",
    "    d = {'0.90':0, '0.95':1, '0.99':2}\n",
    "    traces = out.lr1\n",
    "    cvts = out.cvt[:, d[str(1-alpha)]]\n",
    "    def adjust(val, length=6):\n",
    "        return str(val).ljust(length)\n",
    "    \n",
    "    # Summary\n",
    "    print('Name   :: Test Stat > C(95%)       => Signif   \\n', '--'*20)\n",
    "    for col, trace, cvt in zip(transform_data.columns, traces, cvts):\n",
    "        print(adjust(col), '::', adjust(round(trace, 2), 9), \">\", adjust(cvt, 8), '  =>  ', trace >cvt)\n",
    "        \n",
    "\n",
    "cointegration_test(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So as we can see, there is no cointegration in any of our variables. We can now conduct **Vector Autoregression** or VAR.\n",
    "\n",
    "#### What is VAR?\n",
    "\n",
    "Vector Autoregression (or VAR) is a multivariate forecasting algorithm that is used when two or more time series influence one another. In order to use VAR, there needs to be at least two time series for our variables and the time series needs to influence one another.\n",
    "\n",
    "VAR is considered a 'autoregressive' model because each variable is modeled as a function of past values. That is, predictors are nothing but lags (time delayed values) of the series.\n",
    "\n",
    "#### Deriving VAR\n",
    "\n",
    "A time series is modeled as a linear combination of it's own lags. That is, the past values of the series are used for forecast the present and future.\n",
    "\n",
    "A typical $AR(p)$ model equation looks something like this:\n",
    "\n",
    "$$Y_{t}=\\alpha+\\beta_{1}Y_{t-1}+\\beta_{2}Y_{t-1}+\\ldots+\\beta_{p}Y_{t-p}+\\varepsilon_{t}$$\n",
    "\n",
    "where $\\alpha$ is the intercept and from $\\beta_{1}$ to $\\beta_{p}$ are the coefficients of the lags of $Y$, up to the order of $p$.\n",
    "\n",
    "\n",
    "The order $p$ means, up to $p$ lags of $Y$ is used and they are the predictors in the equation. The $\\varepsilon_{t}$ is the error, which is considered as white noise.\n",
    "\n",
    "In the VAR model, each variable is modeled as a **linear combination of past values of itself and the past values of other variables in the system**. Since you have multiple time series that influence one another, it is modeled as a system of equations with one equation per variable (time series).\n",
    "\n",
    "That is, if you have 5 time series that influence each other, we will have a system of 5 equations.\n",
    "\n",
    "Suppose we have two variables, $Y_{1,t}$ and $Y_{2,t}$, and you need to forecast the values of these variables at the $t$. To calculate $Y_{1,t}$, VAR will use the past values of both $Y_{1}$ and well as $Y_{2}$. Likewise, to compute $Y_{2,t}$, the past values of both $Y_{1}$ and $Y_{2}$ need to be used.\n",
    "\n",
    "For example, the system of equations for a VAR model with two time series are as follows:\n",
    "\n",
    "$$\n",
    "Y_{1,t}=\\alpha_{1}+\\beta_{11,1}Y_{1,t-1}+\\beta_{12,1}Y_{2,t-1}+\\varepsilon_{1,t}\n",
    "$$\n",
    "$$\n",
    "Y_{2,t}=\\alpha_{2}+\\beta_{21,1}Y_{1,t-1}+\\beta_{22,1}Y_{2,t-1}+\\varepsilon_{2,t}\n",
    "$$\n",
    "\n",
    "Where $Y_{1,t-1}$ and $Y_{2,t-1}$ and the first lag of time series $Y_{1}$ and $Y_{2}$ respectively.\n",
    "\n",
    "The above equation is referred to as a $VAR(1)$ model, because each equation is of order 1. That is, it contains up to one lag of each of the predictors ($Y_{1}$ and $Y_{2}$).\n",
    "\n",
    "$$\n",
    "Y_{1,t}=\\alpha_{1}+\\beta_{11,1}Y_{1,t-1}+\\beta_{12,1}Y_{2,t-1}+\\beta_{11,2}Y_{1,t-2}+\\beta_{12,2}Y_{2,t-2}+\\varepsilon_{1,t}\n",
    "$$\n",
    "$$\n",
    "Y_{2,t}=\\alpha_{2}+\\beta_{21,1}Y_{1,t-1}+\\beta_{22,1}Y_{2,t-1}+\\beta_{21,2}Y_{1,t-2}+\\beta_{22,2}Y_{2,t-2}+\\varepsilon_{2,t}\n",
    "$$\n",
    "\n",
    "And a second order $VAR(2)$ model with three variables ($Y_{1}$, $Y_{2}$, and $Y_{3}$) would look like?\n",
    "\n",
    "$$\n",
    "Y_{1,t}=\\alpha_{1}+\\beta_{11,1}Y_{1,t-1}+\\beta_{12,1}Y_{2,t-1}+\\beta_{13,1}Y_{3,t-1}+\\beta_{11,2}Y_{1,t-2}+\\beta_{12,2}Y_{2,t-2}+\\beta_{13,2}Y_{3,t-2}+\\varepsilon_{1,t}\n",
    "$$\n",
    "$$\n",
    "Y_{2,t}=\\alpha_{2}+\\beta_{21,1}Y_{1,t-1}+\\beta_{22,1}Y_{2,t-1}+\\beta_{23,1}Y_{3,t-1}+\\beta_{21,2}Y_{1,t-2}+\\beta_{22,2}Y_{2,t-2}+\\beta_{23,2}Y_{3,t-2}+\\varepsilon_{1,t}\n",
    "$$\n",
    "$$\n",
    "Y_{3,t}=\\alpha_{3}+\\beta_{31,1}Y_{1,t-1}+\\beta_{32,1}Y_{2,t-1}+\\beta_{33,1}Y_{3,t-1}+\\beta_{31,2}Y_{1,t-2}+\\beta_{32,2}Y_{2,t-2}+\\beta_{33,2}Y_{3,t-2}+\\varepsilon_{1,t}\n",
    "$$\n",
    "\n",
    "As you increase the number of time series in the model, the system of equations become larger. What we will attempt to do is fit the VAR model on the training set and then use the fitted model to forecast the next 15 observations. These forecasts will be compared to the observations in the testing dataset. We have tekn the maximum lag of 15 to identify the required lags in the VAR model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Andre\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
      "  ' ignored when e.g. forecasting.', ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Summary of Regression Results   \n",
      "==================================\n",
      "Model:                         VAR\n",
      "Method:                        OLS\n",
      "Date:           Sat, 18, Jan, 2020\n",
      "Time:                     21:05:35\n",
      "--------------------------------------------------------------------\n",
      "No. of Equations:         6.00000    BIC:                    3.85246\n",
      "Nobs:                     7176.00    HQIC:                   3.82605\n",
      "Log likelihood:          -74730.0    FPE:                    45.2498\n",
      "AIC:                      3.81220    Det(Omega_mle):         44.9859\n",
      "--------------------------------------------------------------------\n",
      "Results for equation Gold\n",
      "=============================================================================\n",
      "                coefficient       std. error           t-stat            prob\n",
      "-----------------------------------------------------------------------------\n",
      "const              0.150339         0.111137            1.353           0.176\n",
      "L1.Gold           -0.106090         0.016064           -6.604           0.000\n",
      "L1.Silver          1.741683         0.447254            3.894           0.000\n",
      "L1.Oil             0.094939         0.014576            6.514           0.000\n",
      "L1.Dollar         -3.314005         0.230103          -14.402           0.000\n",
      "L1.S&P 500        -0.009409         0.008014           -1.174           0.240\n",
      "L1.Value         -17.006782         2.008228           -8.469           0.000\n",
      "=============================================================================\n",
      "\n",
      "Results for equation Silver\n",
      "=============================================================================\n",
      "                coefficient       std. error           t-stat            prob\n",
      "-----------------------------------------------------------------------------\n",
      "const              0.001053         0.004007            0.263           0.793\n",
      "L1.Gold           -0.001048         0.000579           -1.810           0.070\n",
      "L1.Silver         -0.138992         0.016125           -8.620           0.000\n",
      "L1.Oil             0.005197         0.000525            9.890           0.000\n",
      "L1.Dollar         -0.101748         0.008296          -12.265           0.000\n",
      "L1.S&P 500         0.001772         0.000289            6.132           0.000\n",
      "L1.Value          -0.218746         0.072402           -3.021           0.003\n",
      "=============================================================================\n",
      "\n",
      "Results for equation Oil\n",
      "=============================================================================\n",
      "                coefficient       std. error           t-stat            prob\n",
      "-----------------------------------------------------------------------------\n",
      "const              0.027735         0.093504            0.297           0.767\n",
      "L1.Gold            0.029424         0.013516            2.177           0.029\n",
      "L1.Silver          0.262844         0.376294            0.699           0.485\n",
      "L1.Oil             0.003524         0.012263            0.287           0.774\n",
      "L1.Dollar         -0.347773         0.193595           -1.796           0.072\n",
      "L1.S&P 500         0.054297         0.006742            8.053           0.000\n",
      "L1.Value           4.457899         1.689605            2.638           0.008\n",
      "=============================================================================\n",
      "\n",
      "Results for equation Dollar\n",
      "=============================================================================\n",
      "                coefficient       std. error           t-stat            prob\n",
      "-----------------------------------------------------------------------------\n",
      "const              0.002986         0.005811            0.514           0.607\n",
      "L1.Gold           -0.000963         0.000840           -1.147           0.252\n",
      "L1.Silver          0.018003         0.023384            0.770           0.441\n",
      "L1.Oil            -0.000203         0.000762           -0.266           0.790\n",
      "L1.Dollar         -0.035641         0.012031           -2.962           0.003\n",
      "L1.S&P 500        -0.002265         0.000419           -5.404           0.000\n",
      "L1.Value           0.405582         0.104999            3.863           0.000\n",
      "=============================================================================\n",
      "\n",
      "Results for equation S&P 500\n",
      "=============================================================================\n",
      "                coefficient       std. error           t-stat            prob\n",
      "-----------------------------------------------------------------------------\n",
      "const              0.412731         0.169770            2.431           0.015\n",
      "L1.Gold            0.054784         0.024539            2.233           0.026\n",
      "L1.Silver         -0.570538         0.683211           -0.835           0.404\n",
      "L1.Oil            -0.017721         0.022265           -0.796           0.426\n",
      "L1.Dollar         -0.038930         0.351498           -0.111           0.912\n",
      "L1.S&P 500        -0.049301         0.012242           -4.027           0.000\n",
      "L1.Value          -4.607433         3.067704           -1.502           0.133\n",
      "=============================================================================\n",
      "\n",
      "Results for equation Value\n",
      "=============================================================================\n",
      "                coefficient       std. error           t-stat            prob\n",
      "-----------------------------------------------------------------------------\n",
      "const             -0.000887         0.000682           -1.301           0.193\n",
      "L1.Gold            0.000144         0.000099            1.458           0.145\n",
      "L1.Silver         -0.001172         0.002743           -0.427           0.669\n",
      "L1.Oil            -0.000020         0.000089           -0.225           0.822\n",
      "L1.Dollar         -0.000512         0.001411           -0.363           0.717\n",
      "L1.S&P 500        -0.000132         0.000049           -2.693           0.007\n",
      "L1.Value           0.037574         0.012317            3.051           0.002\n",
      "=============================================================================\n",
      "\n",
      "Correlation matrix of residuals\n",
      "               Gold    Silver       Oil    Dollar   S&P 500     Value\n",
      "Gold       1.000000  0.700682  0.157692 -0.114290 -0.003904 -0.007193\n",
      "Silver     0.700682  1.000000  0.199357 -0.102306  0.027667  0.024748\n",
      "Oil        0.157692  0.199357  1.000000 -0.146603  0.147270  0.130940\n",
      "Dollar    -0.114290 -0.102306 -0.146603  1.000000  0.001448  0.092021\n",
      "S&P 500   -0.003904  0.027667  0.147270  0.001448  1.000000  0.246468\n",
      "Value     -0.007193  0.024748  0.130940  0.092021  0.246468  1.000000\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.tsa.api as smt\n",
    "from statsmodels.tsa.api import VAR\n",
    "mod = smt.VAR(transform_data)\n",
    "res = mod.fit(maxlags= 15, ic = 'aic')\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've created models for predicting all six of our variables, which has provided the coefficients, residuals, and the AIC for the particular model. We can now begin with the forecasting.\n",
    "\n",
    "\n",
    "#### Conducting a forecast evaluation\n",
    "\n",
    "In order to forecast, the VAR model expects up to the lag order number of obvservations from the past data. This is because, the terms in the VAR model are essentially the lags of the various time series in the dataset, so we need to provide as many previous obversations as indicated by the lag order used in the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gold</th>\n",
       "      <th>Silver</th>\n",
       "      <th>Oil</th>\n",
       "      <th>Dollar</th>\n",
       "      <th>S&amp;P 500</th>\n",
       "      <th>Value</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-12-24</td>\n",
       "      <td>-0.096234</td>\n",
       "      <td>-0.048171</td>\n",
       "      <td>0.533292</td>\n",
       "      <td>0.001496</td>\n",
       "      <td>0.427299</td>\n",
       "      <td>-0.000241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-12-27</td>\n",
       "      <td>0.122406</td>\n",
       "      <td>0.011278</td>\n",
       "      <td>0.035726</td>\n",
       "      <td>0.000984</td>\n",
       "      <td>0.405479</td>\n",
       "      <td>-0.000921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-12-30</td>\n",
       "      <td>0.168982</td>\n",
       "      <td>0.000362</td>\n",
       "      <td>0.051993</td>\n",
       "      <td>0.001737</td>\n",
       "      <td>0.396586</td>\n",
       "      <td>-0.000972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-12-31</td>\n",
       "      <td>0.145024</td>\n",
       "      <td>0.001834</td>\n",
       "      <td>0.049582</td>\n",
       "      <td>0.001465</td>\n",
       "      <td>0.405720</td>\n",
       "      <td>-0.000954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-02</td>\n",
       "      <td>0.150408</td>\n",
       "      <td>0.001682</td>\n",
       "      <td>0.049926</td>\n",
       "      <td>0.001511</td>\n",
       "      <td>0.403087</td>\n",
       "      <td>-0.000960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-03</td>\n",
       "      <td>0.149569</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049862</td>\n",
       "      <td>0.001505</td>\n",
       "      <td>0.403616</td>\n",
       "      <td>-0.000958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-06</td>\n",
       "      <td>0.149665</td>\n",
       "      <td>0.001692</td>\n",
       "      <td>0.049875</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403536</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-07</td>\n",
       "      <td>0.149659</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403545</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-08</td>\n",
       "      <td>0.149658</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403544</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-09</td>\n",
       "      <td>0.149659</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403544</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-10</td>\n",
       "      <td>0.149659</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403544</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-13</td>\n",
       "      <td>0.149659</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403544</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-14</td>\n",
       "      <td>0.149659</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403544</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-15</td>\n",
       "      <td>0.149659</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403544</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2020-01-16</td>\n",
       "      <td>0.149659</td>\n",
       "      <td>0.001691</td>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.001506</td>\n",
       "      <td>0.403544</td>\n",
       "      <td>-0.000959</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Gold    Silver       Oil    Dollar   S&P 500     Value\n",
       "Date                                                                  \n",
       "2019-12-24 -0.096234 -0.048171  0.533292  0.001496  0.427299 -0.000241\n",
       "2019-12-27  0.122406  0.011278  0.035726  0.000984  0.405479 -0.000921\n",
       "2019-12-30  0.168982  0.000362  0.051993  0.001737  0.396586 -0.000972\n",
       "2019-12-31  0.145024  0.001834  0.049582  0.001465  0.405720 -0.000954\n",
       "2020-01-02  0.150408  0.001682  0.049926  0.001511  0.403087 -0.000960\n",
       "2020-01-03  0.149569  0.001691  0.049862  0.001505  0.403616 -0.000958\n",
       "2020-01-06  0.149665  0.001692  0.049875  0.001506  0.403536 -0.000959\n",
       "2020-01-07  0.149659  0.001691  0.049873  0.001506  0.403545 -0.000959\n",
       "2020-01-08  0.149658  0.001691  0.049873  0.001506  0.403544 -0.000959\n",
       "2020-01-09  0.149659  0.001691  0.049873  0.001506  0.403544 -0.000959\n",
       "2020-01-10  0.149659  0.001691  0.049873  0.001506  0.403544 -0.000959\n",
       "2020-01-13  0.149659  0.001691  0.049873  0.001506  0.403544 -0.000959\n",
       "2020-01-14  0.149659  0.001691  0.049873  0.001506  0.403544 -0.000959\n",
       "2020-01-15  0.149659  0.001691  0.049873  0.001506  0.403544 -0.000959\n",
       "2020-01-16  0.149659  0.001691  0.049873  0.001506  0.403544 -0.000959"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = res.forecast(transform_data.values[-3:], 15)\n",
    "pred_df = pd.DataFrame(pred, index=df.index[-15:], columns = df.columns)\n",
    "pred_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The forecast are generated but it is on the scale of the training data used by the model. In order to bring it back to original scale, we need to limit the difference.\n",
    "\n",
    "We convert the differencing by adding the differences consecutively to the base number. An easy way to do it is to first determine the cumulative sum at index and add it to the base number.\n",
    "\n",
    "This process can be reversed by adding the observation at the prior time step to the difference value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   Gold     Silver         Oil     Dollar      S&P 500  \\\n",
      "Date                                                                     \n",
      "2019-12-24  1490.753766  17.536829  592.033292  97.252496  3223.807182   \n",
      "2019-12-27  1510.626171  17.788108  600.819019  96.548480  3240.852799   \n",
      "2019-12-30  1511.695153  17.788470  599.121012  96.411217  3222.519403   \n",
      "2019-12-31  1523.340177  18.010304  590.920593  96.063682  3232.415113   \n",
      "2020-01-02  1521.040585  17.891986  593.720519  96.532193  3259.888269   \n",
      "2020-01-03  1548.040155  18.178677  603.520381  96.529698  3237.291886   \n",
      "2020-01-06  1577.639819  18.410369  603.570256  96.360204  3249.125352   \n",
      "2020-01-07  1567.439478  18.117060  602.120129  96.713709  3240.428800   \n",
      "2020-01-08  1583.939137  18.393752  592.920002  97.009215  3256.702461   \n",
      "2020-01-09  1549.088796  17.885443  581.719875  97.176721  3278.755907   \n",
      "2020-01-10  1550.188454  17.892135  581.269748  97.094226  3269.809599   \n",
      "2020-01-13  1551.888113  17.963826  569.069621  97.077732  3292.992928   \n",
      "2020-01-14  1546.637771  17.750518  570.619494  97.113238  3288.416491   \n",
      "2020-01-15  1553.737430  17.832209  566.419367  96.980743  3294.960172   \n",
      "2020-01-16  1557.187089  17.993901  567.969240  97.084249  3322.883737   \n",
      "\n",
      "               Value  \n",
      "Date                  \n",
      "2019-12-24  1.899759  \n",
      "2019-12-27  1.878837  \n",
      "2019-12-30  1.897865  \n",
      "2019-12-31  1.916911  \n",
      "2020-01-02  1.875952  \n",
      "2020-01-03  1.794993  \n",
      "2020-01-06  1.804035  \n",
      "2020-01-07  1.823076  \n",
      "2020-01-08  1.862117  \n",
      "2020-01-09  1.841159  \n",
      "2020-01-10  1.820200  \n",
      "2020-01-13  1.839241  \n",
      "2020-01-14  1.808283  \n",
      "2020-01-15  1.777324  \n",
      "2020-01-16  1.796366  \n"
     ]
    }
   ],
   "source": [
    "# reversing the difference and assigning to variable 'pred_inverse'\n",
    "pred_inverse = pred_df.cumsum() \n",
    "\n",
    "# inverse the difference values and assigning to variable 'f'\n",
    "f = pred_inverse + X_test\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Forecast vs. Historical\n",
    "\n",
    "Now we can plot the historical observations along with the forecasted observations back to their original scale. Let us assess the differences between the two time series plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,5))\n",
    "plt.xlabel('Date')\n",
    "\n",
    "ax1 = X_test.Gold.plot(color='blue', grid=True, label='Actual Gold Price')\n",
    "ax2 = f.Gold.plot(color='red', grid=True, secondary_y=True, label='Predicted Gold Price')\n",
    "\n",
    "ax1.legend(loc=1)\n",
    "ax2.legend(loc=2)\n",
    "plt.title('Prediction vs Actual Gold Price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the forecasted observations are pretty much in line with the historical observations used for forecasting Gold prices. There is a very slight deviation between the historical and forecasted observations started from Janurary 9th, however, this divergence is very slight.\n",
    "\n",
    "We can also see how this deviation occurs in the Oil time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,5))\n",
    "plt.xlabel('Date')\n",
    "\n",
    "ax1 = X_test.Oil.plot(color='blue', grid=True, label='Actual Oil Price')\n",
    "ax2 = f.Oil.plot(color='red', grid=True, secondary_y=True, label='Predicted Oil Price')\n",
    "\n",
    "ax1.legend(loc=1)\n",
    "ax2.legend(loc=2)\n",
    "plt.title('Prediction vs Actual Oil Price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same with the Gold time series, much of the forecast is in line with the historical data. The only difference is that the divergence occurs during the first 15 days of our time series.\n",
    "\n",
    "\n",
    "### Evaluating the forecast\n",
    "\n",
    "To evaluate the forecast in a more comprehensive manner, we will use mean absolute error, mean squared error, and root mean squared error. What are the difference between these three accuracy metrics\n",
    "\n",
    "**Mean Absolute Error** (MAE) measures the average magnitude of the rrors in a set of predictions, without considering their direction. It's the average over the test sample of the absolute differences between prediction and actual observation where all individual differences have equal weight.\n",
    "\n",
    "$$MAE=\\frac{1}{n}\\sum^{n}_{i=1}|y_{i}-\\hat{y}_{i}|$$\n",
    "\n",
    "**Mean Squared Error** (MSE) is an estimator which measures the average squared difference between the estimated values and what is estimated. MSE is a risk functino, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.\n",
    "\n",
    "$$MSE=\\frac{1}{n}\\sum^{n}_{i=1}(y_{i}-\\hat{y}_{i})^{2}$$\n",
    "\n",
    "As you can see, the main difference between MAE and MSE is the squaring of the deviation.\n",
    "\n",
    "**Root Mean Squared Error** (RMSE) is a quadratic scoring rule that also measures the average magnitude of the error. It's the squared root of the average of squared differences between prediction and actual observation.\n",
    "\n",
    "$$RMSE= \\sqrt{\\frac{1}{n}\\sum^{n}_{i=1}(y_{i}-\\hat{y}_{i})^{2}} $$\n",
    "\n",
    "Taking the square root of the average squared errors has some interesting implications for RSME. Since the errors are squared before they are averaged, the RMSE gives a relatively high weight to large errors. **This means the RMSE sould be more useful when large errors are particularly undesirable.**\n",
    "\n",
    "The following code chunk will calculate the MAE, MSE, and RMSE for the Gold variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bias: -0.939473\n",
      "MAE: 0.952304\n",
      "MSE: 1.300555\n",
      "RMSE: 1.140419\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_absolute_error\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "forecast_errors = [X_test.Gold[i]-f.Gold[i] for i in range(len(X_test.Gold))]\n",
    "bias = sum(forecast_errors) * 1.0/len(X_test.Gold)\n",
    "print('Bias: %f' % bias)\n",
    "\n",
    "mae = mean_absolute_error(X_test.Gold, f.Gold)\n",
    "print('MAE: %f' % mae)\n",
    "\n",
    "mse = mean_squared_error(X_test.Gold, f.Gold)\n",
    "print('MSE: %f' % mse)\n",
    "\n",
    "rmse = sqrt(mse)\n",
    "print('RMSE: %f' % rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the evaluation metric with the smallest error is the MAE; however, this is mostly liked due to the lack of squaring in this technique, which makes it less suspetible to outliers. On the other hand, the MSE and RMSE are more robust in the since that it punishes the model for making predictions that differ greatly from the corresponding actual value.\n",
    "\n",
    "As such considering that there isn't a significant difference between MAE, MSE, and RMSE, there isn't a particualr technique that we would recommend using over another.\n",
    "\n",
    "## Conclusion\n",
    "\n",
    "There are many different variables that can account for the changes in different financial markets. These changes may or may not always occur in financial markets. Nonetheless, this tutorial can demonstrate how we can use the relationship in certain financial markets to create models for forecasting."
   ]
  }
 ],
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