{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "from scipy import stats\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "def r_scatter(r):\n",
    "    plt.figure(figsize=(5,5))\n",
    "    \"Generate a scatter plot with a correlation approximately r\"\n",
    "    x = np.random.normal(0, 1, 1000)\n",
    "    z = np.random.normal(0, 1, 1000)\n",
    "    y = r*x + (np.sqrt(1-r**2))*z\n",
    "    plt.scatter(x, y)\n",
    "    plt.xlim(-4, 4)\n",
    "    plt.ylim(-4, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation\n",
    "\n",
    "In this section we will develop a measure of how tightly clustered a scatter diagram is about a straight line. Formally, this is called measuring *linear association*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table `hybrid` contains data on hybrid passenger cars sold in the United States from 1997 to 2013. The data were adapted from the online data archive of [Prof. Larry Winner](http://www.stat.ufl.edu/%7Ewinner/) of the University of Florida. The columns:\n",
    "\n",
    "- `vehicle`: model of the car\n",
    "- `year`: year of manufacture\n",
    "- `msrp`: manufacturer's suggested retail price in 2013 dollars\n",
    "- `acceleration`: acceleration rate in km per hour per second\n",
    "- `mpg`: fuel econonmy in miles per gallon\n",
    "- `class`: the model's class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "hybrid = pd.read_csv(path_data + 'hybrid.csv')"
   ]
  },
  {
   "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>vehicle</th>\n",
       "      <th>year</th>\n",
       "      <th>msrp</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>mpg</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Prius (1st Gen)</td>\n",
       "      <td>1997</td>\n",
       "      <td>24509.74</td>\n",
       "      <td>7.46</td>\n",
       "      <td>41.26</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Tino</td>\n",
       "      <td>2000</td>\n",
       "      <td>35354.97</td>\n",
       "      <td>8.20</td>\n",
       "      <td>54.10</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Prius (2nd Gen)</td>\n",
       "      <td>2000</td>\n",
       "      <td>26832.25</td>\n",
       "      <td>7.97</td>\n",
       "      <td>45.23</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Insight</td>\n",
       "      <td>2000</td>\n",
       "      <td>18936.41</td>\n",
       "      <td>9.52</td>\n",
       "      <td>53.00</td>\n",
       "      <td>Two Seater</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Civic (1st Gen)</td>\n",
       "      <td>2001</td>\n",
       "      <td>25833.38</td>\n",
       "      <td>7.04</td>\n",
       "      <td>47.04</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>S400</td>\n",
       "      <td>2013</td>\n",
       "      <td>92350.00</td>\n",
       "      <td>13.89</td>\n",
       "      <td>21.00</td>\n",
       "      <td>Large</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>Prius Plug-in</td>\n",
       "      <td>2013</td>\n",
       "      <td>32000.00</td>\n",
       "      <td>9.17</td>\n",
       "      <td>50.00</td>\n",
       "      <td>Midsize</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>C-Max Energi Plug-in</td>\n",
       "      <td>2013</td>\n",
       "      <td>32950.00</td>\n",
       "      <td>11.76</td>\n",
       "      <td>43.00</td>\n",
       "      <td>Midsize</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>151</th>\n",
       "      <td>Fusion Energi Plug-in</td>\n",
       "      <td>2013</td>\n",
       "      <td>38700.00</td>\n",
       "      <td>11.76</td>\n",
       "      <td>43.00</td>\n",
       "      <td>Midsize</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>152</th>\n",
       "      <td>Chevrolet Volt</td>\n",
       "      <td>2013</td>\n",
       "      <td>39145.00</td>\n",
       "      <td>11.11</td>\n",
       "      <td>37.00</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>153 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   vehicle  year      msrp  acceleration    mpg       class\n",
       "0          Prius (1st Gen)  1997  24509.74          7.46  41.26     Compact\n",
       "1                     Tino  2000  35354.97          8.20  54.10     Compact\n",
       "2          Prius (2nd Gen)  2000  26832.25          7.97  45.23     Compact\n",
       "3                  Insight  2000  18936.41          9.52  53.00  Two Seater\n",
       "4          Civic (1st Gen)  2001  25833.38          7.04  47.04     Compact\n",
       "..                     ...   ...       ...           ...    ...         ...\n",
       "148                   S400  2013  92350.00         13.89  21.00       Large\n",
       "149          Prius Plug-in  2013  32000.00          9.17  50.00     Midsize\n",
       "150   C-Max Energi Plug-in  2013  32950.00         11.76  43.00     Midsize\n",
       "151  Fusion Energi Plug-in  2013  38700.00         11.76  43.00     Midsize\n",
       "152         Chevrolet Volt  2013  39145.00         11.11  37.00     Compact\n",
       "\n",
       "[153 rows x 6 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hybrid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph below is a scatter plot of `msrp` *versus* `acceleration`. That means `msrp` is plotted on the vertical axis and `accelaration` on the horizontal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.plot.scatter('acceleration', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the positive association. The scatter of points is sloping upwards, indicating that cars with greater acceleration tended to cost more, on average; conversely, the cars that cost more tended to have greater acceleration on average. \n",
    "\n",
    "The scatter diagram of MSRP versus mileage shows a negative association. Hybrid cars with higher mileage tended to cost less, on average. This seems surprising till you consider that cars that accelerate fast tend to be less fuel efficient and have lower mileage. As the previous scatter plot showed, those were also the cars that tended to cost more. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.plot.scatter('mpg', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Along with the negative association, the scatter diagram of price versus efficiency shows a non-linear relation between the two variables. The points appear to be clustered around a curve, not around a straight line. \n",
    "\n",
    "If we restrict the data just to the SUV class, however, the association between price and efficiency is still negative but the relation appears to be more linear. The relation between the price and acceleration of SUV's also shows a linear trend, but with a positive slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv = hybrid[hybrid['class'] == 'SUV']\n",
    "suv.plot.scatter('mpg', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv.plot.scatter('acceleration', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will have noticed that we can derive useful information from the general orientation and shape of a scatter diagram even without paying attention to the units in which the variables were measured.\n",
    "\n",
    "Indeed, we could plot all the variables in standard units and the plots would look the same. This gives us a way to compare the degree of linearity in two scatter diagrams.\n",
    "\n",
    "Recall that in an earlier section we defined the function `standard_units` to convert an array of numbers to standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standard_units(any_numbers):\n",
    "    \"Convert any array of numbers to standard units.\"\n",
    "    return (any_numbers - np.mean(any_numbers))/np.std(any_numbers)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use this function to re-draw the two scatter diagrams for SUVs, with all the variables measured in standard units.  \n",
    "\n",
    "(*employing Pandas plotting function instead of matplotlib*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SUVs = pd.DataFrame(\n",
    "    {'mpg (standard units)':standard_units(suv['mpg']), \n",
    "    'msrp (standard units)':standard_units(suv['msrp'])}\n",
    ").plot.scatter(0, 1)\n",
    "\n",
    "plt.xlim(-3, 3)\n",
    "\n",
    "plt.ylim(-3, 3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(\n",
    "    {'acceleration (standard units)':standard_units(suv['acceleration']), \n",
    "    'msrp (standard units)':standard_units(suv['msrp'])}).plot.scatter(0, 1)\n",
    "\n",
    "plt.xlim(-3, 3)\n",
    "\n",
    "plt.ylim(-3, 3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The associations that we see in these figures are the same as those we saw before. Also, because the two scatter diagrams are now drawn on exactly the same scale, we can see that the linear relation in the second diagram is a little more fuzzy than in the first.\n",
    "\n",
    "We will now define a measure that uses standard units to quantify the kinds of association that we have seen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The correlation coefficient\n",
    "The *correlation coefficient* measures the strength of the linear relationship between two variables. Graphically, it measures how clustered the scatter diagram is around a straight line.\n",
    "\n",
    "The term *correlation coefficient* isn't easy to say, so it is usually shortened to *correlation* and denoted by $r$.\n",
    "\n",
    "Here are some mathematical facts about $r$ that we will just observe by simulation.\n",
    "\n",
    "- The correlation coefficient $r$ is a number between $-1$ and 1.\n",
    "- $r$ measures the extent to which the scatter plot clusters around a straight line.\n",
    "- $r = 1$ if the scatter diagram is a perfect straight line sloping upwards, and $r = -1$ if the scatter diagram is a perfect straight line sloping downwards."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function ``r_scatter`` takes a value of $r$ as its argument and simulates a scatter plot with a correlation very close to $r$. Because of randomness in the simulation, the correlation is not expected to be exactly equal to $r$.\n",
    "\n",
    "Call ``r_scatter`` a few times, with different values of $r$ as the argument, and see how the scatter plot changes. \n",
    "\n",
    "When $r=1$ the scatter plot is perfectly linear and slopes upward. When $r=-1$, the scatter plot is perfectly linear and slopes downward. When $r=0$, the scatter plot is a formless cloud around the horizontal axis, and the variables are said to be *uncorrelated*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(-0.55)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating $r$\n",
    "\n",
    "The formula for $r$ is not apparent from our observations so far. It has a mathematical basis that is outside the scope of this class. However, as you will see, the calculation is straightforward and helps us understand several of the properties of $r$.\n",
    "\n",
    "**Formula for $r$**:\n",
    "\n",
    "**$r$ is the average of the products of the two variables, when both variables are measured in standard units.**\n",
    "\n",
    "Here are the steps in the calculation. We will apply the steps to a simple table of values of $x$ and $y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x  y\n",
       "0  1  2\n",
       "1  2  3\n",
       "2  3  1\n",
       "3  4  5\n",
       "4  5  2\n",
       "5  6  7"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 7, 1)\n",
    "y = np.array([2, 3, 1, 5, 2, 7])\n",
    "t = pd.DataFrame({'x':x,\n",
    "        'y':y})\n",
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the scatter diagram, we expect that $r$ will be positive but not equal to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.plot.scatter(0, 1, s=30, color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 1.** Convert each variable to standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x (standard units)</th>\n",
       "      <th>y (standard units)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.46385</td>\n",
       "      <td>-0.648886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.87831</td>\n",
       "      <td>-0.162221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.29277</td>\n",
       "      <td>-1.135550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0.29277</td>\n",
       "      <td>0.811107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>0.87831</td>\n",
       "      <td>-0.648886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1.46385</td>\n",
       "      <td>1.784436</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x  y  x (standard units)  y (standard units)\n",
       "0  1  2            -1.46385           -0.648886\n",
       "1  2  3            -0.87831           -0.162221\n",
       "2  3  1            -0.29277           -1.135550\n",
       "3  4  5             0.29277            0.811107\n",
       "4  5  2             0.87831           -0.648886\n",
       "5  6  7             1.46385            1.784436"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_su = t.copy()\n",
    "\n",
    "t_su['x (standard units)'] = standard_units(x)\n",
    "\n",
    "t_su['y (standard units)'] = standard_units(y)\n",
    "\n",
    "t_su"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 2.** Multiply each pair of standard units."
   ]
  },
  {
   "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>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x (standard units)</th>\n",
       "      <th>y (standard units)</th>\n",
       "      <th>product of standard units</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.46385</td>\n",
       "      <td>-0.648886</td>\n",
       "      <td>0.949871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.87831</td>\n",
       "      <td>-0.162221</td>\n",
       "      <td>0.142481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.29277</td>\n",
       "      <td>-1.135550</td>\n",
       "      <td>0.332455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0.29277</td>\n",
       "      <td>0.811107</td>\n",
       "      <td>0.237468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>0.87831</td>\n",
       "      <td>-0.648886</td>\n",
       "      <td>-0.569923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1.46385</td>\n",
       "      <td>1.784436</td>\n",
       "      <td>2.612146</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x  y  x (standard units)  y (standard units)  product of standard units\n",
       "0  1  2            -1.46385           -0.648886                   0.949871\n",
       "1  2  3            -0.87831           -0.162221                   0.142481\n",
       "2  3  1            -0.29277           -1.135550                   0.332455\n",
       "3  4  5             0.29277            0.811107                   0.237468\n",
       "4  5  2             0.87831           -0.648886                  -0.569923\n",
       "5  6  7             1.46385            1.784436                   2.612146"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_product = t_su.copy()\n",
    "\n",
    "t_product['product of standard units'] = t_su.iloc[:,2] * t_su.iloc[:,3]\n",
    "\n",
    "t_product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 3.** $r$ is the average of the products computed in Step 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# r is the average of the products of standard units\n",
    "\n",
    "r = np.mean(t_product.iloc[:,4])\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, $r$ is positive but not equal to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties of $r$\n",
    "The calculation shows that:\n",
    "\n",
    "- $r$ is a pure number. It has no units. This is because $r$ is based on standard units.\n",
    "- $r$ is unaffected by changing the units on either axis. This too is because $r$ is based on standard units.\n",
    "- $r$ is unaffected by switching the axes. Algebraically, this is because the product of standard units does not depend on which variable is called $x$ and which $y$. Geometrically, switching axes reflects the scatter plot about the line $y=x$, but does not change the amount of clustering nor the sign of the association."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEfCAYAAAAUfVINAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAXbElEQVR4nO3dX2zV9f3H8VcP39WuRXcQsEZoQ6wHaBFmgQiyA8woBxm0h0BWaJzZRJE/6oIGRmESpRfWDeRCDIQCZh1/Ns6g26GH8i8EHAfS0WVb2CDZDmsKIQhMsjLbemSHc34XzP5AFAacs8/nHJ6PhIvzPZx+3h+P9Nnv9xw4WW1tbQkBAGAZl+kBAAD4MgQKAGAlAgUAsBKBAgBYiUABAKxEoAAAViJQAAArESgAgJXuqkBFIhHTI6Qce0x/mb4/iT1milTv8a4KFAAgfRAoAICVCBQAwEpGA3X27FnNnj1bRUVFys/P14gRIxQOh02OBACwhGNq4ba2No0fP14jR45UIBBQz549dfLkSfXu3dvUSAAAixgL1HvvvacHH3xQa9as6TrWr18/U+MAAP5b8bichgYVBoNy/H7FysokV/IvyBm7xLdjxw4NGzZMzz//vB555BF5vV7V1tYqkeDjqQDAWvG4cisqlDtrlh6or1furFnKraiQ4vGkL2UsUK2trVq/fr369eunbdu2afbs2Vq6dKnWrl1raiQAwE04DQ1ywmFlRaOSpKxoVE44LCcUSvpaWaY+Ubd3794qLS3Vnj17uo5VV1crFArpyJEjX/m4u+EvvwGArQpravRAff11x89PnapTVVW39LU8Hs8N7zf2GlR+fr4GDBhwzbH+/fvr9OnTN3zczTZ0I5FI5I4enw7YY/rL9P1J7DGdOX6/Eo2NXWdQkpTIyVGe35/0/Rq7xDdy5EidOHHimmMnTpxQQUGBoYkAADcTKytTzOtVIidH0pU4xbxexSZNSvpaxgI1d+5cNTc3a/ny5WppadFvfvMb1dbW6sUXXzQ1EgDgZlwudQYC6qyt1fmpU9VZW6vOQCAl7+Izdolv6NCh2rRpk6qrq7Vs2TL17dtXixcvJlAAYDuXS7Hycp0qLk7pZUxjgZKk8ePHa/z48SZHAABYin+LDwBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwErGAlVTUyO3233Nr/79+5saBwBgGcfk4h6PR6FQqOt2t27dDE6T5uJxOQ0NKgwG5fj9ipWVSS5OkAGkL6OBchxH+fn5JkfIDPG4cisq5ITDyotGlWhsVGzDBnUGAkQKQNoy+t2rtbVVxcXFGjJkiGbMmKHW1laT46Qtp6FBTjisrGhUkpQVjcoJh+VcdXYKAOkmq62tLWFi4b1796q9vV0ej0cff/yxli1bpkgkoqamJt1///1f+bhIJPI/nDI9FNbU6IH6+uuOn586VaeqqgxMBAA35/F4bni/sUB9UXt7ux577DHNmzdPr7zySkrWiEQiN/0Pko6cYFC5s2Z1nUFJUiInR521tYqVlxucLDUy9Xn8XKbvT2KPmSLVe7TmBYru3btr4MCBamlpMT1K2omVlSnm9SqRkyPpSpxiXq9ikyYZngwAbp/RN0lcLRqNKhKJaPTo0aZHST8ulzoDATmhkDqCQeX5/VfixBskAKQxY4F644039Mwzz6hv375dr0F1dnaqsrLS1EjpzeVSrLxcp4qLM/6yAoC7g7FAnTlzRi+++KIuXLigXr16afjw4dq7d68KCwtNjQQAsIixQH3wwQemlgYApAFepAAAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJWsC9e6778rtdmvBggWmRwEAWMCKQDU3N6uurk6DBg0yPQqAVIrH5QSDKqypkRMMSvG46YlgMeOBunjxombOnKmVK1fK7XabHgdAqsTjyq2oUO6sWXqgvl65s2Ypt6KCSOErGQ/UvHnz5Pf7NXbsWNOjAEghp6FBTjisrGhUkpQVjcoJh+WEQoYng60ck4vX1dWppaVFa9as+a8fE4lE7mjNO318OmCP6S8T91cYDCrvP3H6XFY0qo5gUKeKiw1NlVqZ+Dx+0Z3s0ePx3PB+Y4GKRCKqrq7Wzp07lZ2d/V8/7mYbutmad/L4dMAe01+m7s/x+5VobOw6g5KkRE6O8vz+jNxvpj6PV0v1Ho1d4jty5IguXLigJ554Qj179lTPnj116NAhrVu3Tj179tRnn31majQAKRArK1PM61UiJ0fSlTjFvF7FJk0yPBlsZewMauLEiSotLb3m2Msvv6yioiK9/vrrt3RWBSANuFzqDATkhELqCAaV5/dfiZPL+EvhsJSxQLnd7uvetZebm6sePXqopKTEzFAAUsvlUqy8XKeKizP+8hfuHD+6AACsZPRdfF+0Y8cO0yMAACzBGRQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALDSLQXq0qVLN/09H3300W0PAwDA524pUGPGjNGf/vSnr7z/l7/8pUaNGnWnMwEAcGuB+uyzz+Tz+fSTn/xEly9f7jp+4cIFPffcc5ozZ851H0IIAMDtuKVAHTp0SN/73vf0zjvvaNy4cfrb3/6mhoYGjRw5Uvv379fy5ctVX1+fqlkBAHeRW/o8qNzcXK1YsUKTJk3Sq6++Kq/Xq1gsphEjRmj16tXq169fisYEANxtbusDC10ul7KysvTvf/9bktS3b9/rPr4dAIA7cUuX+D799FMtWLBAU6ZMUe/evXXo0CFVV1eroaFB3/rWt7Rv375UzQkAuMvcUqC8Xq9+9rOfaf78+dq7d69KSkr06quv6sCBA+rdu7e++93v6rXXXkvVrACAu8gtBcpxHO3Zs0eLFy+W4/z/1cGBAwdq3759+tGPfqTNmzcnfUgAwN3nll6D+vDDD5WTk/Ol93Xr1k1VVVX6zne+k5TBAAB3t1s6g/qqOF1tyJAhtz0MAACf49/iAwBYiUABAKxEoAAAViJQAAArESgAgJUIFADASgQKAGAlAgUAsBKBAgBYiUABAKxkLFBr167VqFGjVFBQoIKCAo0bN067d+82NQ4AwDLGAvXQQw9p6dKl+vDDD7V//36NGTNGzz77rP7yl78kf7F4XE4wqMKaGjnBoBSPJ38NAEBS3dYn6ibDxIkTr7m9ZMkSrV+/Xs3NzXr00UeTt1A8rtyKCjnhsPKiUSUaGxXbsEGdgYDk4gonANjKiu/Qly9f1rZt29TR0aHHH388qV/baWiQEw4rKxqVJGVFo3LCYTmhUFLXAQAkV1ZbW1vC1OLHjh2Tz+dTNBpVXl6e1q5dq/Hjx9/wMZFI5JbWKKyp0QP19dcdPz91qk5VVd3S1wIAJI/H47nh/UYDdenSJZ0+fVoXL17U9u3bVVdXp1AopJKSkqSt4QSDyp01q+sMSpISOTnqrK1VrLw8aevYIhKJ3PRJT3eZvsdM35/EHjNFqvdo9BJfdna2Hn74YZWWlurNN9/U4MGDtWrVqqSuESsrU8zrVeI/H7aYyMlRzOtVbNKkpK4DAEguY2+S+DLxeFyXLl1K7hd1udQZCMgJhdQRDCrP778SJ94gAQBWMxaot956Sz6fT3369FF7e7u2bt2qcDisQCCQ/MVcLsXKy3WquDjjT7kBIFMYC9S5c+f00ksv6fz587rvvvs0aNAgbd26VU899ZSpkQAAFjEWqNWrV5taGgCQBnghBgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVCBQAwEoECgBgJQIFALASgQIAWIlAAQCsRKAAAFYiUAAAKxEoAICVjAVqxYoVevLJJ1VQUKCioiJNmzZNx48fNzUOAMAyxgIVDof1wgsvaPfu3dq+fbscx9HkyZP1z3/+09RIsF08LicYVGFNjZxgUIrHTU8EIIUcUwvX19dfc3vNmjUqLCxUU1OTJkyYYGgqWCseV25FhZxwWHnRqBKNjYpt2KDOQEBycaUayETW/Mlub29XPB6X2+02PQos5DQ0yAmHlRWNSpKyolE54bCcUMjwZABSJautrS1heghJ+sEPfqC///3vOnDggLp16/aVvy8SifwPp4ItCmtq9MAXzrol6fzUqTpVVWVgIgB3yuPx3PB+Y5f4rrZ48WI1NTVp165dN4yTdPMN3UgkErmjx6eDTN2j4/cr0djYdQYlSYmcHOX5/Rm330x9Dq/GHjNDqvdo/BLfokWLtG3bNm3fvl39+vUzPQ4sFSsrU8zrVSInR9KVOMW8XsUmTTI8GYBUMXoGtXDhQtXX1ysUCql///4mR4HtXC51BgJyQiF1BIPK8/uvxIk3SAAZy1ig5s+fry1btmjjxo1yu906d+6cJCkvL0/du3c3NRZs5nIpVl6uU8XFGX/pBIDBS3zr1q3TJ598Ir/frwEDBnT9WrlypamRAAAWMXYG1dbWZmppAEAa4AI+AMBKBAoAYCUCBQCwEoECAFiJQAEArESgAABWIlAAACsRKACAlQgUAMBKBAoAYCUCBQCwEoECAFiJQAEArESgAABWIlAAACsRKACAlQgUAMBKBAoAYCUCBQCwEoECAFiJQAEArESgAABWIlAAACsRKACAlQgUAMBKBAoAYCUCBQCwEoECAFiJQAEArESgAABWIlAAACsZDdShQ4c0ffp0FRcXy+12a9OmTSbHAQBYxGigOjo6VFJSonfeeUdf//rXTY4CALCMY3Jxn88nn88nSZo7d67JUdJfPC6noUGFwaAcv1+xsjLJxRVcAOnLaKCQJPG4cisq5ITDyotGlWhsVGzDBnUGAkQKQNriu1cGcBoa5ITDyopGJUlZ0aiccFhOKGR4MgC4fWl3BhWJRIw+3kaFwaDy/hOnz2VFo+oIBnWquNjQVKmVic/j1TJ9fxJ7zBR3skePx3PD+9MuUDfb0I1EIpE7erytHL9ficbGrjMoSUrk5CjP78/I/Wbq8/i5TN+fxB4zRar3yCW+DBArK1PM61UiJ0fSlTjFvF7FJk0yPBkA3D6jZ1Dt7e1qaWmRJMXjcZ0+fVpHjx5Vjx49VFBQYHK09OJyqTMQkBMKqSMYVJ7ffyVOvEECQBoz+h3sj3/8o8aMGaMxY8bo008/VU1NjcaMGaO3337b5FjpyeVSrLxcp6qqFCsvJ04A0p7RM6jRo0erra3N5AgAAEvxYzYAwEoECgBgJQIFALBSVltbW8L0EAAAfBFnUAAAKxEoAICVCBQAwEoECgBgJQIFALBSxgfq0KFDmj59uoqLi+V2u7Vp0ybTIyXVihUr9OSTT6qgoEBFRUWaNm2ajh8/bnqspFq7dq1GjRqlgoICFRQUaNy4cdq9e7fpsVLq3Xffldvt1oIFC0yPkjQ1NTVyu93X/Orfv7/psZLu7Nmzmj17toqKipSfn68RI0YoHA6bHitpBg8efN3z6Ha7VVFRkfS10u7jNm5VR0eHSkpKVFlZqdmzZ5seJ+nC4bBeeOEFDR06VIlEQm+//bYmT56s3/3ud+rRo4fp8ZLioYce0tKlS1VUVKR4PK5f/OIXevbZZ3XgwAE9+uijpsdLuubmZtXV1WnQoEGmR0k6j8ej0FUfpNmtWzeD0yRfW1ubxo8fr5EjRyoQCKhnz546efKkevfubXq0pNm/f78uX77cdfvs2bP69re/rcmTJyd9rYwPlM/nk8/nkyTNnTvX8DTJV19ff83tNWvWqLCwUE1NTZowYYKhqZJr4sSJ19xesmSJ1q9fr+bm5owL1MWLFzVz5kytXLlSP/3pT02Pk3SO4yg/P9/0GCnz3nvv6cEHH9SaNWu6jvXr18/cQCnQq1eva25v2LBB9957b0oClfGX+O427e3tisfjcrvdpkdJicuXL2vbtm3q6OjQ448/bnqcpJs3b578fr/Gjh1repSUaG1tVXFxsYYMGaIZM2aotbXV9EhJtWPHDg0bNkzPP/+8HnnkEXm9XtXW1iqRyMx/DyGRSGjDhg2aNm2acnNzk/71M/4M6m5TVVWlwYMHZ9w372PHjsnn8ykajSovL08bN27MuEtgdXV1amlpuean70wyfPhwrVq1Sh6PRx9//LGWLVsmn8+npqYm3X///abHS4rW1latX79ec+fO1bx58/TnP/9ZCxculCS99NJLhqdLvv379+vkyZN67rnnUvL1CVQGWbx4sZqamrRr166Mu7bv8Xh08OBBXbx4Udu3b9ecOXMUCoVUUlJierSkiEQiqq6u1s6dO5WdnW16nJQYN27cNbeHDx+uxx57TJs3b9Yrr7xiaKrkisfjKi0t1ZtvvilJ+uY3v6mWlhatW7cuIwNVV1enoUOHasiQISn5+gQqQyxatEj19fVqaGjIuGvekpSdna2HH35YklRaWqo//OEPWrVqld5//33DkyXHkSNHdOHCBT3xxBNdxy5fvqzDhw/rgw8+0JkzZ3TPPfcYnDD5unfvroEDB3Z9qnYmyM/P14ABA6451r9/f50+fdrQRKnzj3/8Q42NjVq+fHnK1iBQGWDhwoWqr69XKBTKyLftfpl4PK5Lly6ZHiNpJk6cqNLS0muOvfzyyyoqKtLrr7+ekWdV0WhUkUhEo0ePNj1K0owcOVInTpy45tiJEydUUFBgaKLU2bx5s+655x5NmTIlZWtkfKDa29u7fkKLx+M6ffq0jh49qh49emTE/zTz58/Xli1btHHjRrndbp07d06SlJeXp+7duxueLjneeust+Xw+9enTR+3t7dq6davC4bACgYDp0ZLm879LcrXc3Fz16NEjYy5jvvHGG3rmmWfUt2/frtegOjs7VVlZaXq0pJk7d658Pp+WL1+uKVOm6OjRo6qtrdWSJUtMj5ZUiURCP//5zzVlyhTde++9KVsn4z9u4+DBgyorK7vueGVlpVavXm1gouT6qnfrLVy4UIsWLfrfDpMic+bM0cGDB3X+/Hndd999GjRokH74wx/qqaeeMj1aSk2cOFElJSVatmyZ6VGSYsaMGTp8+LAuXLigXr16afjw4frxj3+sgQMHmh4tqXbv3q3q6mqdOHFCffv21cyZMzVr1ixlZWWZHi1pfvvb36q8vFz79u3TsGHDUrZOxgcKAJCe+HtQAAArESgAgJUIFADASgQKAGAlAgUAsBKBAgBYiUABAKxEoAAAViJQAAArESgAgJUIFGDY/v375Xa71dDQcN19u3fvltvt1q5duwxMBphFoADDxo4dqz59+mjLli3X3RcIBNSrVy89/fTTBiYDzCJQgGEul0vTpk3Tnj171NbW1nX8k08+0c6dOzVlyhQ5TsZ/Mg5wHQIFWKCyslKXLl3Sr3/9665j27dvV2dnp6ZPn25wMsAcPm4DsMTTTz+tr33ta9q5c6ckye/368yZM2pubjY8GWAGZ1CAJSorK9XU1KSTJ0/qo48+0sGDBzVt2jTTYwHGECjAElOnTlV2drYCgYB+9atfKZFIqKKiwvRYgDFc4gMs8v3vf1/Hjx9Xdna23G63duzYYXokwBjOoACLVFZWKhKJ6NixY1zew12PMyjAIrFYTCUlJfrXv/6lv/71r/rGN75heiTAGM6gAIu4XC45jqMJEyYQJ9z1CBRgkT179ujMmTOqrKw0PQpgHJf4AAv8/ve/1/Hjx7V8+XLl5ubq8OHDcrn4+RF3N/4EABZYv369XnvtNbndbtXW1hInQJxBAQAsxY9pAAArESgAgJUIFADASgQKAGAlAgUAsBKBAgBY6f8A8jyMh9RWBeQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.plot.scatter('y', 'x', s=30, color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The `correlation` function\n",
    "We are going to be calculating correlations repeatedly, so it will help to define a function that computes it by performing all the steps described above. Let's define a function ``correlation`` that takes a table and the labels of two columns in the table. The function returns $r$, the mean of the products of those column values in standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def correlation(t, x, y):\n",
    "    return np.mean(standard_units(t[x])*standard_units(t[y]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's call the function on the ``x`` and ``y`` columns of ``t``. The function returns the same answer to the correlation between $x$ and $y$ as we got by direct application of the formula for $r$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(t, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we noticed, the order in which the variables are specified doesn't matter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(t, 'y', 'x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calling ``correlation`` on columns of the table ``suv`` gives us the correlation between price and mileage as well as the correlation between price and acceleration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6667143635709919"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(suv, 'mpg', 'msrp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4869979927995918"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(suv, 'acceleration', 'msrp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These values confirm what we had observed: \n",
    "\n",
    "- There is a negative association between price and efficiency, whereas the association between price and acceleration is positive.\n",
    "- The linear relation between price and acceleration is a little weaker (correlation about 0.5) than between price and mileage (correlation about -0.67). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation is a simple and powerful concept, but it is sometimes misused. Before using $r$, it is important to be aware of what correlation does and does not measure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Association is not Causation\n",
    "Correlation only measures association. Correlation does not imply causation. Though the correlation between the weight and the math ability of children in a school district may be positive, that does not mean that doing math makes children heavier or that putting on weight improves the children's math skills. Age is a confounding variable: older children are both heavier and better at math than younger children, on average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation Measures *Linear* Association\n",
    "Correlation measures only one kind of association – linear. Variables that have strong non-linear association might have very low correlation. Here is an example of variables that have a perfect quadratic relation $y = x^2$ but have correlation equal to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_x = np.arange(-4, 4.1, 0.5)\n",
    "nonlinear = pd.DataFrame(\n",
    "        {'x':new_x,\n",
    "        'y':new_x**2}\n",
    "    )\n",
    "nonlinear.plot.scatter('x', 'y', s=30, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(nonlinear, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation is Affected by Outliers\n",
    "Outliers can have a big effect on correlation. Here is an example where a scatter plot for which $r$ is equal to 1 is turned into a plot for which $r$ is equal to 0, by the addition of just one outlying point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line = pd.DataFrame(\n",
    "        {'x':np.array([1, 2, 3, 4]),\n",
    "        'y':np.array([1, 2, 3, 4])}\n",
    "    )\n",
    "line.plot.scatter('x', 'y', s=30, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(line, 'x', 'y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outlier = pd.DataFrame(\n",
    "        {'x':np.array([1, 2, 3, 4, 5]),\n",
    "        'y':np.array([1, 2, 3, 4, 0])}\n",
    "    )\n",
    "outlier.plot.scatter('x', 'y', s=30, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(outlier, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ecological Correlations Should be Interpreted with Care\n",
    "Correlations based on aggregated data can be misleading. As an example, here are data on the Critical Reading and Math SAT scores in 2014. There is one point for each of the 50 states and one for Washington, D.C. The column ``Participation Rate`` contains the percent of high school seniors who took the test. The next three columns show the average score in the state on each portion of the test, and the final column is the average of the total scores on the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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>State</th>\n",
       "      <th>Participation Rate</th>\n",
       "      <th>Critical Reading</th>\n",
       "      <th>Math</th>\n",
       "      <th>Writing</th>\n",
       "      <th>Combined</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Alabama</td>\n",
       "      <td>6.7</td>\n",
       "      <td>547</td>\n",
       "      <td>538</td>\n",
       "      <td>532</td>\n",
       "      <td>1617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>Alaska</td>\n",
       "      <td>54.2</td>\n",
       "      <td>507</td>\n",
       "      <td>503</td>\n",
       "      <td>475</td>\n",
       "      <td>1485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Arizona</td>\n",
       "      <td>36.4</td>\n",
       "      <td>522</td>\n",
       "      <td>525</td>\n",
       "      <td>500</td>\n",
       "      <td>1547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Arkansas</td>\n",
       "      <td>4.2</td>\n",
       "      <td>573</td>\n",
       "      <td>571</td>\n",
       "      <td>554</td>\n",
       "      <td>1698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>California</td>\n",
       "      <td>60.3</td>\n",
       "      <td>498</td>\n",
       "      <td>510</td>\n",
       "      <td>496</td>\n",
       "      <td>1504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Colorado</td>\n",
       "      <td>14.3</td>\n",
       "      <td>582</td>\n",
       "      <td>586</td>\n",
       "      <td>567</td>\n",
       "      <td>1735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>Connecticut</td>\n",
       "      <td>88.4</td>\n",
       "      <td>507</td>\n",
       "      <td>510</td>\n",
       "      <td>508</td>\n",
       "      <td>1525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>Delaware</td>\n",
       "      <td>100.0</td>\n",
       "      <td>456</td>\n",
       "      <td>459</td>\n",
       "      <td>444</td>\n",
       "      <td>1359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>District of Columbia</td>\n",
       "      <td>100.0</td>\n",
       "      <td>440</td>\n",
       "      <td>438</td>\n",
       "      <td>431</td>\n",
       "      <td>1309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>Florida</td>\n",
       "      <td>72.2</td>\n",
       "      <td>491</td>\n",
       "      <td>485</td>\n",
       "      <td>472</td>\n",
       "      <td>1448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>Georgia</td>\n",
       "      <td>77.2</td>\n",
       "      <td>488</td>\n",
       "      <td>485</td>\n",
       "      <td>472</td>\n",
       "      <td>1445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>Hawaii</td>\n",
       "      <td>62.6</td>\n",
       "      <td>484</td>\n",
       "      <td>504</td>\n",
       "      <td>472</td>\n",
       "      <td>1460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>Idaho</td>\n",
       "      <td>100.0</td>\n",
       "      <td>458</td>\n",
       "      <td>456</td>\n",
       "      <td>450</td>\n",
       "      <td>1364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Illinois</td>\n",
       "      <td>4.6</td>\n",
       "      <td>599</td>\n",
       "      <td>616</td>\n",
       "      <td>587</td>\n",
       "      <td>1802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>Indiana</td>\n",
       "      <td>70.5</td>\n",
       "      <td>497</td>\n",
       "      <td>500</td>\n",
       "      <td>477</td>\n",
       "      <td>1474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Iowa</td>\n",
       "      <td>3.1</td>\n",
       "      <td>605</td>\n",
       "      <td>611</td>\n",
       "      <td>578</td>\n",
       "      <td>1794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Kansas</td>\n",
       "      <td>5.3</td>\n",
       "      <td>591</td>\n",
       "      <td>596</td>\n",
       "      <td>566</td>\n",
       "      <td>1753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Kentucky</td>\n",
       "      <td>4.6</td>\n",
       "      <td>589</td>\n",
       "      <td>585</td>\n",
       "      <td>572</td>\n",
       "      <td>1746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Louisiana</td>\n",
       "      <td>4.6</td>\n",
       "      <td>561</td>\n",
       "      <td>556</td>\n",
       "      <td>550</td>\n",
       "      <td>1667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>Maine</td>\n",
       "      <td>95.6</td>\n",
       "      <td>467</td>\n",
       "      <td>471</td>\n",
       "      <td>449</td>\n",
       "      <td>1387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>Maryland</td>\n",
       "      <td>78.5</td>\n",
       "      <td>492</td>\n",
       "      <td>495</td>\n",
       "      <td>481</td>\n",
       "      <td>1468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Massachusetts</td>\n",
       "      <td>84.1</td>\n",
       "      <td>516</td>\n",
       "      <td>531</td>\n",
       "      <td>509</td>\n",
       "      <td>1556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Michigan</td>\n",
       "      <td>3.8</td>\n",
       "      <td>593</td>\n",
       "      <td>610</td>\n",
       "      <td>581</td>\n",
       "      <td>1784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Minnesota</td>\n",
       "      <td>5.9</td>\n",
       "      <td>598</td>\n",
       "      <td>610</td>\n",
       "      <td>578</td>\n",
       "      <td>1786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Mississippi</td>\n",
       "      <td>3.2</td>\n",
       "      <td>583</td>\n",
       "      <td>566</td>\n",
       "      <td>565</td>\n",
       "      <td>1714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Missouri</td>\n",
       "      <td>4.2</td>\n",
       "      <td>595</td>\n",
       "      <td>597</td>\n",
       "      <td>579</td>\n",
       "      <td>1771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Montana</td>\n",
       "      <td>17.9</td>\n",
       "      <td>555</td>\n",
       "      <td>552</td>\n",
       "      <td>530</td>\n",
       "      <td>1637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Nebraska</td>\n",
       "      <td>3.7</td>\n",
       "      <td>589</td>\n",
       "      <td>587</td>\n",
       "      <td>569</td>\n",
       "      <td>1745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>Nevada</td>\n",
       "      <td>54.2</td>\n",
       "      <td>495</td>\n",
       "      <td>494</td>\n",
       "      <td>469</td>\n",
       "      <td>1458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>New Hampshire</td>\n",
       "      <td>70.3</td>\n",
       "      <td>524</td>\n",
       "      <td>530</td>\n",
       "      <td>512</td>\n",
       "      <td>1566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>New Jersey</td>\n",
       "      <td>79.3</td>\n",
       "      <td>501</td>\n",
       "      <td>523</td>\n",
       "      <td>502</td>\n",
       "      <td>1526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>New Mexico</td>\n",
       "      <td>12.3</td>\n",
       "      <td>548</td>\n",
       "      <td>543</td>\n",
       "      <td>526</td>\n",
       "      <td>1617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>New York</td>\n",
       "      <td>76.3</td>\n",
       "      <td>488</td>\n",
       "      <td>502</td>\n",
       "      <td>478</td>\n",
       "      <td>1468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>North Carolina</td>\n",
       "      <td>63.8</td>\n",
       "      <td>499</td>\n",
       "      <td>507</td>\n",
       "      <td>477</td>\n",
       "      <td>1483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>North Dakota</td>\n",
       "      <td>2.3</td>\n",
       "      <td>612</td>\n",
       "      <td>620</td>\n",
       "      <td>584</td>\n",
       "      <td>1816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>15.1</td>\n",
       "      <td>555</td>\n",
       "      <td>562</td>\n",
       "      <td>535</td>\n",
       "      <td>1652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Oklahoma</td>\n",
       "      <td>4.5</td>\n",
       "      <td>576</td>\n",
       "      <td>571</td>\n",
       "      <td>550</td>\n",
       "      <td>1697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>Oregon</td>\n",
       "      <td>47.9</td>\n",
       "      <td>523</td>\n",
       "      <td>522</td>\n",
       "      <td>499</td>\n",
       "      <td>1544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>Pennsylvania</td>\n",
       "      <td>71.4</td>\n",
       "      <td>497</td>\n",
       "      <td>504</td>\n",
       "      <td>480</td>\n",
       "      <td>1481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>Rhode Island</td>\n",
       "      <td>73.0</td>\n",
       "      <td>497</td>\n",
       "      <td>496</td>\n",
       "      <td>487</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>South Carolina</td>\n",
       "      <td>64.9</td>\n",
       "      <td>488</td>\n",
       "      <td>490</td>\n",
       "      <td>465</td>\n",
       "      <td>1443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>South Dakota</td>\n",
       "      <td>2.9</td>\n",
       "      <td>604</td>\n",
       "      <td>609</td>\n",
       "      <td>579</td>\n",
       "      <td>1792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Tennessee</td>\n",
       "      <td>7.9</td>\n",
       "      <td>578</td>\n",
       "      <td>570</td>\n",
       "      <td>566</td>\n",
       "      <td>1714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>Texas</td>\n",
       "      <td>62.0</td>\n",
       "      <td>476</td>\n",
       "      <td>495</td>\n",
       "      <td>461</td>\n",
       "      <td>1432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Utah</td>\n",
       "      <td>5.2</td>\n",
       "      <td>571</td>\n",
       "      <td>568</td>\n",
       "      <td>551</td>\n",
       "      <td>1690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Vermont</td>\n",
       "      <td>63.1</td>\n",
       "      <td>522</td>\n",
       "      <td>525</td>\n",
       "      <td>507</td>\n",
       "      <td>1554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>Virginia</td>\n",
       "      <td>73.1</td>\n",
       "      <td>518</td>\n",
       "      <td>515</td>\n",
       "      <td>497</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>Washington</td>\n",
       "      <td>63.1</td>\n",
       "      <td>510</td>\n",
       "      <td>518</td>\n",
       "      <td>491</td>\n",
       "      <td>1519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>West Virginia</td>\n",
       "      <td>14.8</td>\n",
       "      <td>517</td>\n",
       "      <td>505</td>\n",
       "      <td>500</td>\n",
       "      <td>1522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Wisconsin</td>\n",
       "      <td>3.9</td>\n",
       "      <td>596</td>\n",
       "      <td>608</td>\n",
       "      <td>578</td>\n",
       "      <td>1782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Wyoming</td>\n",
       "      <td>3.3</td>\n",
       "      <td>590</td>\n",
       "      <td>599</td>\n",
       "      <td>573</td>\n",
       "      <td>1762</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   State  Participation Rate  Critical Reading  Math  Writing  \\\n",
       "21               Alabama                 6.7               547   538      532   \n",
       "34                Alaska                54.2               507   503      475   \n",
       "26               Arizona                36.4               522   525      500   \n",
       "15              Arkansas                 4.2               573   571      554   \n",
       "33            California                60.3               498   510      496   \n",
       "12              Colorado                14.3               582   586      567   \n",
       "30           Connecticut                88.4               507   510      508   \n",
       "49              Delaware               100.0               456   459      444   \n",
       "50  District of Columbia               100.0               440   438      431   \n",
       "43               Florida                72.2               491   485      472   \n",
       "44               Georgia                77.2               488   485      472   \n",
       "41                Hawaii                62.6               484   504      472   \n",
       "48                 Idaho               100.0               458   456      450   \n",
       "1               Illinois                 4.6               599   616      587   \n",
       "38               Indiana                70.5               497   500      477   \n",
       "2                   Iowa                 3.1               605   611      578   \n",
       "9                 Kansas                 5.3               591   596      566   \n",
       "10              Kentucky                 4.6               589   585      572   \n",
       "18             Louisiana                 4.6               561   556      550   \n",
       "47                 Maine                95.6               467   471      449   \n",
       "39              Maryland                78.5               492   495      481   \n",
       "24         Massachusetts                84.1               516   531      509   \n",
       "5               Michigan                 3.8               593   610      581   \n",
       "4              Minnesota                 5.9               598   610      578   \n",
       "13           Mississippi                 3.2               583   566      565   \n",
       "7               Missouri                 4.2               595   597      579   \n",
       "20               Montana                17.9               555   552      530   \n",
       "11              Nebraska                 3.7               589   587      569   \n",
       "42                Nevada                54.2               495   494      469   \n",
       "23         New Hampshire                70.3               524   530      512   \n",
       "29            New Jersey                79.3               501   523      502   \n",
       "22            New Mexico                12.3               548   543      526   \n",
       "40              New York                76.3               488   502      478   \n",
       "35        North Carolina                63.8               499   507      477   \n",
       "0           North Dakota                 2.3               612   620      584   \n",
       "19                  Ohio                15.1               555   562      535   \n",
       "16              Oklahoma                 4.5               576   571      550   \n",
       "27                Oregon                47.9               523   522      499   \n",
       "36          Pennsylvania                71.4               497   504      480   \n",
       "37          Rhode Island                73.0               497   496      487   \n",
       "45        South Carolina                64.9               488   490      465   \n",
       "3           South Dakota                 2.9               604   609      579   \n",
       "14             Tennessee                 7.9               578   570      566   \n",
       "46                 Texas                62.0               476   495      461   \n",
       "17                  Utah                 5.2               571   568      551   \n",
       "25               Vermont                63.1               522   525      507   \n",
       "28              Virginia                73.1               518   515      497   \n",
       "32            Washington                63.1               510   518      491   \n",
       "31         West Virginia                14.8               517   505      500   \n",
       "6              Wisconsin                 3.9               596   608      578   \n",
       "8                Wyoming                 3.3               590   599      573   \n",
       "\n",
       "    Combined  \n",
       "21      1617  \n",
       "34      1485  \n",
       "26      1547  \n",
       "15      1698  \n",
       "33      1504  \n",
       "12      1735  \n",
       "30      1525  \n",
       "49      1359  \n",
       "50      1309  \n",
       "43      1448  \n",
       "44      1445  \n",
       "41      1460  \n",
       "48      1364  \n",
       "1       1802  \n",
       "38      1474  \n",
       "2       1794  \n",
       "9       1753  \n",
       "10      1746  \n",
       "18      1667  \n",
       "47      1387  \n",
       "39      1468  \n",
       "24      1556  \n",
       "5       1784  \n",
       "4       1786  \n",
       "13      1714  \n",
       "7       1771  \n",
       "20      1637  \n",
       "11      1745  \n",
       "42      1458  \n",
       "23      1566  \n",
       "29      1526  \n",
       "22      1617  \n",
       "40      1468  \n",
       "35      1483  \n",
       "0       1816  \n",
       "19      1652  \n",
       "16      1697  \n",
       "27      1544  \n",
       "36      1481  \n",
       "37      1480  \n",
       "45      1443  \n",
       "3       1792  \n",
       "14      1714  \n",
       "46      1432  \n",
       "17      1690  \n",
       "25      1554  \n",
       "28      1530  \n",
       "32      1519  \n",
       "31      1522  \n",
       "6       1782  \n",
       "8       1762  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sat2014 = pd.read_csv(path_data + 'sat2014.csv').sort_values(by=['State'])\n",
    "sat2014"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter diagram of Math scores versus Critical Reading scores is very tightly clustered around a straight line; the correlation is close to 0.985. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAboAAAEfCAYAAAA3JgPYAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAuwUlEQVR4nO3deVRTZ94H8G8MqxUNS4wiigUiWl4UBevWKm7YGQVfiwrWOi2O0uL0WN9WTosiVrTqSJ22toziWmurjgut1dpRZxTc7TJqrToYSxFFlKUGoRJkyfsHh1vDGmJCkpvv5xzO4d775N7nyfX647nPJlGr1VoQERGJVDtzZ4CIiMiUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOjMTKVSmTsLRsFyWA4xlAFgOSyJtZeBgY6IiESNgY6IiESNgY6IiESNgY6IiESNgY6IiESNgY6IiETNztwZICIi25RzvxKxx9UoqqiGh6MUG0bI4O1ib/TrsEZHRERmEXtcjW8LHyL7fjW+LXyI2Zlqk1yHgY6IiMyiqKK62W1jYaAjIiKz8HCUNrttLGyjIyIiHfXbzhb0kEBpgutsGCHD7EzdNjpTYKAjIiIddW1nAJCNaiRpHHC8r/Gv4+1ij8MT5MY/cT18dUlERDrqt5Xdq5SYKSfGwUBHREQ66reVyey1ZsqJcTDQERGRjg0jZHha7gCfjlI8LXfA0l4PzZ2lx8I2OiIi0lG/7UylUpsvM0bAQEdERI+lrWY4MRQDHRGRyOkbiAwNWPV7ac7OVLdJb0p9sY2OiEjk9J1qq7VTcuXcr0TYgUL8p0i3Dc9UM5wYijU6IiKR03eqrdZOyfVoTe5RpprhxFAMdEREIufhKEU2qnW2gYavKjtIJQ0+15z6gdBOAgzwcDDZDCeGYqAjIhK5pqbaqt+21s/NDk/LHfSekqt+AB3g4WBRbXN1GOiIiESuqam26tfISqu0yJyof6Bqq7kqHxcDHRGRjWrqlaa+2mquysfFXpdERDaq/gwolloje1ys0RER2ShrqZE9LtboiIhI1Mwa6O7cuYNXX30Vvr6+UCgUGDRoEE6ePCkc12q1WLFiBXr37o0uXbpg/PjxuHr1qs45KioqEB8fDx8fH3h6eiI6Ohp5eXltXRQiIrJQZgt0arUa48aNg1arxa5du3Du3DmsWrUKcvnv1egPP/wQqamp+Otf/4qjR49CLpdj0qRJKC0tFdIkJCRg//792LRpEw4ePIjS0lJERUWhutqyRuYTEZF5mK2Nbs2aNejSpQvS0tKEfT179hR+12q1WLt2LebNm4eJEycCANauXQulUok9e/YgJiYGJSUl2LZtG1JTUzFy5EgAQFpaGgIDA5GRkYHRo0e3aZmIiMjymK1G9/XXXyM4OBgxMTHw8/PDM888g/Xr10OrrV3g78aNG7h79y5GjRolfMbZ2RlDhw7FuXPnAAAXLlxAZWWlThovLy/4+/sLaYiIbEXd3JMD9t5B2IFC3CitNHeWLILZanQ5OTnYtGkT5syZg3nz5uHSpUt46623AACxsbG4e/cuAOi8yqzbzs/PBwAUFBRAKpXC3d29QZqCgoImr61SqYxZlMdmafkxFMthOcRQBoDlaK2ZFx1xqbR2LFw2qjHjUD429aswyrkt+V4olcpmj5st0NXU1KB///5YvHgxAKBfv37Izs7Gxo0bERsbK6STSHTnXtNqtQ321ddSmpa+lLakUqksKj+GYjkshxjKALAchvjtxzvAIwPAyyQOUCp7NEjX2uV4rP1emO3VpUKhgL+/v86+Xr164datW8JxAA1qZkVFRUItr3PnzqiurkZxcXGTaYiIbEX9mU2amumktcvxWDuzBbrBgwfj+vXrOvuuX7+O7t27AwC8vb2hUChw7Ngx4bhGo8GZM2cwaNAgAEBQUBDs7e110uTl5SErK0tIQ0RkK+pmOunxRDt0sJPg9oPKRtvqWrscj7UzW6CbM2cOvvvuO7z33nvIzs7Gl19+ifXr12PWrFkAal9ZxsXF4YMPPsBXX32FK1euYM6cOXjiiScwefJkAECnTp0wY8YMJCUlISMjAxcvXsQrr7yCgIAAhIaGmqtoRERmUTfTSZf2diir0uLWb9pGa2z61vzEwmxtdAMGDMDnn3+O5ORkpKSkwMvLCwsWLBACHQC8/vrrKC8vR3x8PNRqNYKDg5Geng4XFxchzfLlyyGVShETEwONRoPhw4dj3bp1kErFfeOIiJrSUo3NWlYdMBaJWq3WmjsTtszaG3nrsByWQwxlAFiOxxF2oFBn5e+n5Y+3Tpy13wvOdUlEJDK2siqBvrh6ARGRyNjKqgT6Yo2OiIhEjYGOiIhEjYGOiIhEjYGOiIhEjZ1RiIisXGvnrrQ1rNEREVkIQ5fZsbW5K1uLgY6IyEIYGrDuPKjS3S6vaiKlbWKgIyKyEIZOtvxrhe4EV79qOOHVoxjoiIgshKGTLcscm9+2dQx0REQWwtCpuzzb2ze7bevY65KIyEIYOnWXra1G0FoMdEREVo5zWzaPry6JiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUGOiIiEjUONclEZER5NyvROxx3YmVvV3scatcgr8cKGywn9oOAx0RkRHUrQ4OANmoxuxMNQ5PkCPpmgMulf6+f8a/f4WTXTsGvjbEV5dEREbQ1Org6kqJzv6s+1X4tvAhsu9X49vCh5idqW6rLNos1uiIiAxQ/1VlB6luQKtbHVxmr8VNzSMHtLrnqR8gyfgY6IiIDFD/VWU/Nzs8LXdosPjp0l4PsTy3k7C/oroGF3+tEs5TFxDJdBjoiIgMUL8mVlqlRebEhoufdnPW6iyKeqO0kquBtzEGOiIiA3g4SpGNap1tfeizGnhTPTjJMOyMQkRkgA0jZHha7gCfjlI8LXcwas2s7rUoO6wYB2t0REQG0KdmZqimenCSYVijIyKyMPVfg7LDyuNhjY6IrJKY27E2jJCxw4oRMdARkVVqaiYSMTDla1FbxFeXRGSV2I5F+mKgIyKrxHYs0hcDHRFZJVN27ydxYRsdEVkltmORvlijIyIiUWONjohsgpiHI1DzWKMjIpvAabVsFwMdEdkEDkewXQx0RGQTOBzBdjHQEZFN4HAE22W2QLdixQrIZDKdn169egnH4+LiGhwfM2aMzjkqKioQHx8PHx8feHp6Ijo6Gnl5eW1dFCIyg5z7lQg7UIgBe+8g7EAhbpRWNpu+bjjCfyK74PAEOTui2BCz9rpUKpU4cOCAsC2V6r5KCA0NRVpamrDt4OCgczwhIQEHDx7Epk2b4OrqioULFyIqKgqZmZkNzkVE4iLmuS7JuMwa6Ozs7KBQKJo87ujo2OTxkpISbNu2DampqRg5ciQAIC0tDYGBgcjIyMDo0aNNkmcisgzsXEL6MmsbXU5ODvr06YO+ffti5syZyMnJ0Tl+5swZ+Pn5ITg4GHPnzkVhYaFw7MKFC6isrMSoUaOEfV5eXvD398e5c+faqghEZCbsXEL6kqjVaq05LnzkyBGUlZVBqVSiqKgIKSkpUKlUOHv2LNzc3LB37144OzvD29sbubm5WLZsGWpqapCRkQFHR0fs3r0br776KoqKiiCRSITzhoeHw9fXFx988EGT11apVG1QQiIypbxyCZKuOeBepQQyey2W9nqIbs5m+e+MzEypVDZ73GyvLseOHauzHRISgqCgIGzfvh2vvfYaIiMjhWMBAQEICgpCYGAgDh06hIiIiCbPq9VqdQJfY1r6UtqSSqWyqPwYiuWwHGIoA9ByOZQAjvdtu/wYSgz3w9rLYDHDCzp06IDevXsjOzu70eNdu3aFp6encLxz586orq5GcXGxTrqioiLI5WyQJiKiWhYT6DQaDVQqVZOdT4qLi5Gfny8cDwoKgr29PY4dOyakycvLQ1ZWFgYNGtQmeSYiIstntleXiYmJeO655+Dl5SW00T148ADTpk1DWVkZVq5ciYiICCgUCuTm5iI5ORlyuRwTJkwAAHTq1AkzZsxAUlIS5HK5MLwgICAAoaGh5ioWERFZGLMFutu3b2PWrFkoLi6Gh4cHQkJCcOTIEfTo0QPl5eW4cuUKdu7ciZKSEigUCjz77LPYsmULXFxchHMsX74cUqkUMTEx0Gg0GD58ONatW8cxdEREJDBboNu8eXOTx5ydnZGent7iOZycnJCSkoKUlBRjZo2I2hCXzyFTs5g2OiKyTVw+h0zNoBqdWq3G3r17kZOTg3v37kGr1R27IpFI8PHHHxslg0QkbpzhhEyt1YEuMzMTM2bMQGlpKVxcXCCTyRqkaWkcGxFRHQ9HKbJRrbNNZEytDnQLFiyAq6srvv76awQGBpoiT0RkQzaMkGF2pm4bHZExtTrQXb9+HUuWLGGQIyKjqFs+h8hUWh3ovL29odFoTJEXIrIh7G1JbaXVvS7feOMNbNmyBffu3TNFfojIRrC3JbWVFmt0H374YYN9bm5uGDBgACZNmgQvL68GA7QlEgnmzp1rvFwSkeiwtyW1lRYD3TvvvNPksS1btjS6n4GOiFrC3pbUVloMdBcvXmyLfBCRjWFvS2orLQa6Hj16tEU+iMjGsLcltZVWd0Zxc3PD7t27mzyenp4ONze3x8oUERGRsbQ60NWf7qu+mpoazoxCREQWw6C5LpsLZN9//32j04IRUeM4nozItPQKdGvXrsW6deuE7YSEBCxdurRBupKSEty/fx9RUVHGyyGRyNWNJwOAbFRjdqa6VW1X9QPlgh4SKE2VWSIrpFegc3d3h1JZ++jk5uZCoVCgS5cuOmkkEgnat2+P/v37IzY21vg5JRKpxx1PVj9QJmkccLyv0bJHZPX0CnRTp07F1KlTAQATJkxAfHw8RowYYdKMEdmKxx1PVj8w3qtkGznRo1rdRnfgwAFT5IPIZj3ueLL6gVJm33yHMSJbY1BnFACorKyESqVCSUkJampqGhwfNmzYY2WMyFY87niy+oFyQY8SI+aOyPq1OtBptVq8++67SEtLw2+//dZkul9//fWxMkZE+qkfKFUqtfkyQ2SBWj2Obs2aNVi9ejUmTZqEtWvXQqvV4p133sH777+PPn36IDAwEF988YUp8kpEAE7ml8Nr2214fJIHr223cSq/3NxZIrJorQ5027Ztw4QJE7BmzRqMHTsWANCvXz+89NJLOHr0KKqrq3Hy5EmjZ5SIakX/6x7KqrSo0gJlVVpE/YtLZhE1p9WB7ubNmxg5cmTth9vVfvzhw9quzY6OjoiKisKOHTuMmEUiepSmWtvsNhHpanUbnUwmw4MHDwAAHTt2hIODA/Ly8oTjjo6ObJ8jq3WrXIK/HCi06FlKnKQSlFVpdbaJqGmtrtH16dMHP/74Y+2H27XDgAEDsHHjRuTl5eHmzZv45JNPhMHlRNYm6ZqDxa96/Y8xruhgJ4FUUvsAu9hrEXagEDdKK82dNSKL1OpAN2XKFKhUKmg0GgBAUlISfv75ZwQGBqJfv374+eefkZSUZPSMErUFdb3B1pa46vWwrs64NcMTwR4OqAGQXw6LDcpElqDVry6nT5+O6dOnC9tDhgzBmTNncPDgQdjZ2WH06NHw9fU1aiaJ2orMXoubmt+3LXnV68edOozIVhg8YPxRPXv2xJw5c4xxKiKzWtrrIZbndrKKVa8fd+owIluhV6AbNGhQq04qkUhw9uxZgzJEZE7dnLWPvep1Wy2787hThxHZCr0C3bVr1+Ds7IygoCBhSAERNe5xl93R1+NOHUZkK/QKdP3798f58+eRnZ2N559/HlOnTkVQUJCJs0Zkndh2RmRZ9KqeHT16FD/88ANeeuklHDp0CKNGjcLAgQORkpKCnJwcE2eRyLrUbytj2xmReen9HtLHxwcJCQn44YcfcPjwYYSGhmLDhg0YMGAAxo4diw0bNnCgOBFq286eljvAp6MUT8sdWt12lnO/EmEHCjFg7x2OjyMyAoMa3EJCQpCSkoKrV69i165dcHR0xFtvvYUNGzYYO39EVqeu7ew/kV1weIK81R1R6tr4LHnQOpE1MXh4QUlJCfbt24fdu3fj9OnT6NixI2dEITICtvERGVerAl1lZSX++c9/Yvfu3Th8+DAAICwsDFu3bsW4cePg4OBgkkwS2RKOjyMyLr0C3cmTJ7F7927s27cPpaWlGDZsGFJSUjBx4kR07NjR1HkksikcH0dkXHoFuvDwcDg7OyMsLAyRkZHw9PQEAKhUqiY/ExwcbJwcEtkYjo8jMi69X12Wl5dj3759+Oqrr5pNp9VqIZFI2AOTLJqxZi9pq1lQiMhwegW61NRUU+eDqE0Za/aStpoFhYgMp1ege+GFF0ydD6I2ZayejewhSWT5OHEl2aT6PRnzyqoRdqAQeeWtW62bs6AQWT4GOrJJdbOX1MWlipraxUuTrrVuiMzjzoJCRKZnlPXoiKxNXc/GAXvvIPv+768b71W2rkbHHpJElo+Bjmxa/cHZMnut2fLCHpxEpsFARxahrf6Tr3+dxcEdsOSHMmF7QY8So19TX+zBSWQaDHRkEdrqP/n611nyQ5nOdVQqdavOZ8wAzR6cRKZhts4oK1asgEwm0/np1auXcFyr1WLFihXo3bs3unTpgvHjx+Pq1as656ioqEB8fDx8fHzg6emJ6Oho5OXltXVRyAha+k/eWEvXGDuYGHOlAfbgJDINs/a6VCqVyMrKEn5Onz4tHPvwww+RmpqKv/71rzh69CjkcjkmTZqE0tJSIU1CQgL279+PTZs24eDBgygtLUVUVBSqq/mXsLVp6T95YwUUYwcTYwZO9uAkMg2zvrq0s7ODQqFosF+r1WLt2rWYN28eJk6cCABYu3YtlEol9uzZg5iYGJSUlGDbtm1ITU3FyJEjAQBpaWkIDAxERkYGRo8e3aZlocfT0kTGxgooScEdEP2ve9BUa+EklWBxcAdDswzAuCsNsAcnkWmYtUaXk5ODPn36oG/fvpg5cyZycnIAADdu3MDdu3cxatQoIa2zszOGDh2Kc+fOAQAuXLiAyspKnTReXl7w9/cX0pD1aGmxUmPVxJJ/KENZlRZVWqCsSoslP5QZnGeAtTAia2C2Gl1ISAj+/ve/Q6lUoqioCCkpKQgLC8PZs2dx9+5dAIBcrvvXrVwuR35+PgCgoKAAUqkU7u7uDdIUFBQ0e+3mVl0wB0vLj6FMWY4FPSRI0jjgXqUEMnstFvQoaXXHEQDIL3XCo3/f5ZdqGuS7teVI9f/994d31FDdaXW2jI7/piyLGMphyWVoadFvswW6sWPH6myHhIQgKCgI27dvx8CBAwEAEonu4N26lRGao08aS1oJXaVSWVR+DGXqcigBHO/7+OfpmlWIm5qHv2+7OEGp7C5si+F+iKEMAMthSay9DBYzBViHDh3Qu3dvZGdnC+129WtmRUVFQi2vc+fOqK6uRnFxcZNpiOrjq0Yi22MxgU6jqX2FpFAo4O3tDYVCgWPHjukcP3PmDAYNGgQACAoKgr29vU6avLw8ZGVlCWmI6tOab+ITIjITs726TExMxHPPPQcvLy+hje7BgweYNm0aJBIJ4uLisHr1aiiVSvj5+eG9997DE088gcmTJwMAOnXqhBkzZiApKQlyuRyurq5YuHAhAgICEBoaaq5i2axb5RL85UCh2aav0nfgNmcfIbI9Zgt0t2/fxqxZs1BcXAwPDw+EhITgyJEj6NGjBwDg9ddfR3l5OeLj46FWqxEcHIz09HS4uLgI51i+fDmkUiliYmKg0WgwfPhwrFu3DlIpB9q2taRrDrhUar4A0lQAqx8A75RX6XyOs48QiZ/ZAt3mzZubPS6RSJCQkICEhIQm0zg5OSElJQUpKSnGzh61krrerP9tHUCaGmdXPwB2sNPNJ2cfIRI/znVJRiGz1+Km5vfttg4gTQ3crh8AZY7AU64OTQ5MJyLxYaAjo1ja6yGW53YyWwBpamaV+gHQsz1nHyGyNQx0ZBTdnLVmDSBNTZ/V0tRiRCR+DHRkFQxdDofzRxKRxYyjI2qOMZfDISLbwkBHVoGLkhKRoRjoyCpwUVIiMhQDHVkFzlFJRIZiZxSyCuxUQkSGYqAjq9BUr0tDe2MSke3gq0uyCk31umRvTCJqCQMdWYWmel2yNyYRtYSBjqxCU70u2RuTiFrCQEdWoalel+yNSUQtYWcUsgpN9bpkb0wiaglrdEREJGoMdEREJGoMdEREJGoMdEREJGoMdEREJGoMdEREJGoMdEREJGoMdEREJGoMdEREJGoMdEREJGqcAszGcT03IhI71uhsHNdzIyKxY6CzcVzPjYjEjoHOxnE9NyISOwY6G8f13IhI7NgZxcZxPTciEjvW6IiISNQY6IiISNQY6IiISNQY6IiISNQY6IiISNQY6IiISNQY6IiISNQY6IiISNQ4YNxKcJUBIiLDsEZnJbjKABGRYRjorARXGSAiMgwDnZXgKgNERIZhG52V2DBChtmZv7fRJQV3QNiBQrbZERG1gIHOStRfZSDsQCG+LXwIAMhGNWZnqrkKARFRI/jq0kqxzY6ISD8MdFaKbXZERPqxmEC3evVqyGQyxMfHC/vi4uIgk8l0fsaMGaPzuYqKCsTHx8PHxweenp6Ijo5GXl5eW2e/zXFlcCIi/VhEG913332HrVu3IiAgoMGx0NBQpKWlCdsODg46xxMSEnDw4EFs2rQJrq6uWLhwIaKiopCZmQmpVLy1HK4MTkSkH7PX6EpKSjB79mx89NFHkMlkDY47OjpCoVAIP66urjqf3bZtG5KTkzFy5EgEBQUhLS0Nly9fRkZGRtsVgoiILJbZA928efMwceJEjBgxotHjZ86cgZ+fH4KDgzF37lwUFhYKxy5cuIDKykqMGjVK2Ofl5QV/f3+cO3fO5HknIiLLZ9ZXl1u3bkV2drbOq8lHjRkzBuHh4fD29kZubi6WLVuGiIgIZGRkwNHREQUFBZBKpXB3d9f5nFwuR0FBQVsUgYiILJzZAp1KpUJycjK++eabBu1udSIjI4XfAwICEBQUhMDAQBw6dAgRERFNnlur1UIikTR7bUtiafkxFMthOcRQBoDlsCSWXAalUtnscbMFum+//RbFxcUYMmSIsK+6uhqnT5/G5s2bcfv2bTg6Oup8pmvXrvD09ER2djYAoHPnzqiurkZxcTE8PDyEdEVFRRg6dGiT127pS2lLKpXKovJjKJbDcoihDADLYUmsvQxmC3Tjx49H//79dfb95S9/ga+vL954441Ga3nFxcXIz8+HQqEAAAQFBcHe3h7Hjh3DlClTAAB5eXnIysrCoEGDTF8IIiKyeGYLdHXj4h7Vvn17uLq64qmnnkJZWRlWrlyJiIgIKBQK5ObmIjk5GXK5HBMmTAAAdOrUCTNmzEBSUhLkcrkwvCAgIAChoaFtXygiIrI4FjGOrjFSqRRXrlzBzp07UVJSAoVCgWeffRZbtmyBi4uLkG758uWQSqWIiYmBRqPB8OHDsW7dOlGPoSMiIv1ZVKD7+uuvhd+dnZ2Rnp7e4mecnJyQkpKClJQUU2aNiIislNnH0REREZkSAx0REYkaAx0REYkaAx0REYkaAx0REYkaAx0REYmaRQ0vsGQ59ysRe1yNoopqeDhKsWGEDN4u9ubOFhERtYA1Oj3FHlfj28KHyL5fjW8LH2J2ptrcWSIiIj0w0OmpqKK62W0iIrJMDHR68nCUNrtNRESWiYFOTxtGyPC03AE+HaV4Wu6ADSNk5s4SERHpgZ1R9OTtYo/DE+TmzgYREbUSa3RERCRqDHRERCRqDHRERCRqDHRERCRqDHRERCRqErVarTV3JoiIiEyFNToiIhI1BjoiIhI1BjoiIhI1BjoiIhI1BjoiIhI1BjoTW716NWQyGeLj44V9cXFxkMlkOj9jxozR+VxFRQXi4+Ph4+MDT09PREdHIy8vr62zD6DxMtTPf93P/PnzhTTjx49vcHzmzJltlu8VK1Y0uH6vXr2E41qtFitWrEDv3r3RpUsXjB8/HlevXtU5hyXch+bKUVlZicWLF2Po0KHw9PSEv78/Zs2ahZs3b+qcw9z3oqVyANbxXLRUBmt4LurcuXMHr776Knx9faFQKDBo0CCcPHlSOG4tz4c+OKmzCX333XfYunUrAgICGhwLDQ1FWlqasO3g4KBzPCEhAQcPHsSmTZvg6uqKhQsXIioqCpmZmZBK226JoKbKkJWVpbN9/vx5REdH43//93919k+fPh1JSUnCtpOTk8ny2hilUokDBw4I249+dx9++CFSU1ORmpoKpVKJVatWYdKkSfjuu+/g4uICwHLuQ1PlePDgAS5evIj58+cjMDAQ9+/fR2JiIiZPnoxTp07Bzu73R9zc9wJo/n4A1vFcNFcGa3ku1Go1xo0bh8GDB2PXrl1wd3fHjRs3IJf/PnG9NT0fLWGgM5GSkhLMnj0bH330EVatWtXguKOjIxQKRZOf3bZtG1JTUzFy5EgAQFpaGgIDA5GRkYHRo0ebNO+P5qOpMtTP+8GDB+Hn54dnnnlGZ3/79u2bLGdbsLOza/T6Wq0Wa9euxbx58zBx4kQAwNq1a6FUKrFnzx7ExMRYzH1orhydOnXCl19+qbPv/fffx+DBg5GVlaXzB4q57wXQdDnqWMNz0VwZrOW5WLNmDbp06aLzR0XPnj2F363t+WgJX12aSN0/kBEjRjR6/MyZM/Dz80NwcDDmzp2LwsJC4diFCxdQWVmJUaNGCfu8vLzg7++Pc+fOmTzvdVoqQ52ysjKkp6fjpZdeanBs79698PHxweDBg5GYmIjS0lJTZbdROTk56NOnD/r27YuZM2ciJycHAHDjxg3cvXtX5zt2dnbG0KFDhe/YUu5Dc+VoTN13LJPJdPab+14ALZfDGp4Lfe+FJT8XX3/9NYKDgxETEyME4vXr10OrrZ0/xNqej5awRmcCW7duRXZ2ts5fS48aM2YMwsPD4e3tjdzcXCxbtgwRERHIyMiAo6MjCgoKIJVK4e7urvM5uVyOgoKCtihCi2V41J49e1BRUYFp06bp7J8yZQq6d++OLl264L///S+WLFmCn376qUENxFRCQkLw97//HUqlEkVFRUhJSUFYWBjOnj2Lu3fvAoDOq5q67fz8fACwiPsANF8ONzc3nbQPHz5EYmIinnvuOXTr1k3Yb+57oU85rOG5aM29sNTnAqgN1ps2bcKcOXMwb948XLp0CW+99RYAIDY21qqeD30w0BmZSqVCcnIyvvnmmwbtC3UiIyOF3wMCAhAUFITAwEAcOnQIERERTZ5bq9VCIpEYPc/16VOGR23duhXjx4+Hh4eHzv6XX35Z+D0gIAA9e/bE6NGjceHCBQQFBRk51w2NHTtWZzskJARBQUHYvn07Bg4cCAANvk99vuO2ug91mivHa6+9JuyvqqpCbGwsSkpKsGPHDp3PmPteAC2Xw9KfC0D/ewFY7nMBADU1Nejfvz8WL14MAOjXrx+ys7OxceNGxMbGCums4fnQB19dGtm3336L4uJiDBkyBO7u7nB3d8epU6ewceNGuLu7o6KiosFnunbtCk9PT2RnZwMAOnfujOrqahQXF+ukKyoqavAXlrnL8OOPP+L8+fONvp6pr3///pBKpUI521qHDh3Qu3dvZGdnC+0j9f/yfPQ7Nvd9aMqj5ahTVVWFP//5z7h8+TL27dvXoHZRn7nvBdB4OR5lac9FY5oqg6U/FwqFAv7+/jr7evXqhVu3bgnHAet8PhrDQGdk48ePx+nTp3HixAnhp3///oiMjMSJEycarSEVFxcjPz9f+McVFBQEe3t7HDt2TEiTl5eHrKwsDBo0yKLKsHXrVvTo0QOhoaEtnvfy5cuorq42WyO8RqOBSqWCQqGAt7c3FAqFznes0Whw5swZ4Ts2931oyqPlAGqHGMTExODy5cvYv3+/Xt+vue8F0LAc9Vnac9GYpspg6c/F4MGDcf36dZ19169fR/fu3QHAqp+PxvDVpZHVjYt5VPv27eHq6oqnnnoKZWVlWLlyJSIiIqBQKJCbm4vk5GTI5XJMmDABQG1PuhkzZiApKQlyuVzothsQEKDXg2PqMtR58OABdu/ejblz5zZ4VfHLL79g165dCAsLg5ubG7KyspCYmIi+ffti8ODBJi8DAKGtysvLS2hPefDgAaZNmwaJRIK4uDisXr0aSqUSfn5+eO+99/DEE09g8uTJAMx/H/QpR1VVFV566SWcP38eO3bsgEQiEdpXOnbsCGdnZ4u4Fy2Vwxqei5bKUMfSnwsAmDNnDsLCwvDee+/h+eefx48//oj169dj0aJFAGBVz4c+GOjamFQqxZUrV7Bz506UlJRAoVDg2WefxZYtW4SxKQCwfPlySKVSxMTEQKPRYPjw4Vi3bp1FjU1JT0/Hb7/9hunTpzc4Zm9vj8zMTKxbtw6//fYbunXrhrCwMLz99tttVobbt29j1qxZKC4uhoeHB0JCQnDkyBH06NEDAPD666+jvLwc8fHxUKvVCA4ORnp6usXdh+bKcePGDRw8eBAAGvznkpqaiunTp1vEvWipHOXl5VbxXLT0bwqw/OcCAAYMGIDPP/8cycnJSElJgZeXFxYsWIBZs2YJaazl+dAH16MjIiJRYxsdERGJGgMdERGJGgMdERGJGgMdERGJGgMdERGJGgMdERGJGgMdUQvi4uIQGBioV9oTJ05AJpPhxIkTJsnLjRs3IJPJ8Pnnn5vk/KZWt3DpowIDAxEXF2eeDJFNYKAjUSssLMQ777yDwYMHw9PTE127dsXQoUPxzjvv4M6dOwafNyUlRWfxTUtUfxXr7t27449//CMOHTpk7qwRtSnOjEKidf78eUyZMgWlpaWIjIzE7Nmz0a5dO1y+fBlbt27F/v378cMPP7R4njVr1qCmpkZnX93USXXTU9UZNmwY7ty5o9eqD21h+PDhmD59OrRaLW7evInNmzcjOjoae/bssZiFMb///nu0a8e/ucl0GOhIlNRqNaZPnw6JRIKMjAz06dNH5/iiRYvwwQcfNHuOBw8eoH379rC3t9f7uu3atYOTk5MhWTYJX19fREVFCdsREREYNGgQ1q1bZzGBztHR0dxZIJHjn1EkSp988glu376NZcuWNQhyQO2EtHVrcQG1KzYMHDgQP/30E8LDw+Hp6Yk333wTQMM2OplMhoqKCuzYsUN4LTh+/HgATbfRXb9+HX/+85/h5+cHhUKBAQMG4O233xaO5+bm4s0338TAgQPRtWtX9OjRA1FRUbh69apRvxd/f3+4u7vjl19+0dn/8OFDrFq1CiEhIejcuTN69eqF//u//4NardZJd/DgQURFRaFPnz7o3Lkz/ud//geLFy9udPmpQ4cOYdiwYVAoFAgODsann37aaJ7qt9HVfYd79uzBxx9/jMDAQCgUCowdOxYXL15s8PkDBw5g6NChUCgUCAkJwWeffdZoWyDZLtboSJS++eYbODk5YdKkSXp/pqSkBM8//zzCw8MRGRmJTp06NZouLS0Nr732GkJCQoRFNDt37tzkea9evYpx48YBAGJiYvDkk08iNzcX6enpWLlyJYDa16ynTp1CeHg4evTogfz8fGzZsgV//OMfcfbsWaMt4VJSUgK1Wg0fHx9hn1arxYsvvojjx49jxowZCAgIwC+//IINGzbgwoULOHz4sFCr/eyzzyCVShEbGwuZTIZz587ho48+Ql5eHjZu3CicMzMzEy+88AJ8fHywcOFCaDQaLF26tFXl+Pjjj1FZWYnY2FhUVVVhzZo1mD59Os6fPy/k51//+hf+9Kc/QalUIjExEeXl5UhOTjbr8kNkeRjoSJSysrLg5+fXqraygoICrFy5Eq+++mqz6aKiojB37lz07NlT57VgU+bPn4/KykqcPHkSvr6+wv7ExETh97Fjx2LixIkNrjNkyBBs27YN8+fP17scj9JoNCguLoZWq8WtW7ewbNkyVFdX6/wBsGfPHhw5cgT79u3D8OHDhf3Dhg3D1KlTsXfvXkRHRwMANm7ciPbt2wtpYmJi4Ovri+XLl2PJkiXo1q0bACApKQkymQyHDx+Gq6srAGDixIkYOnSo3nm/f/8+Tp8+LbwKViqVePHFF3H06FHhD4fFixfDw8MDhw8fFv4wmTRpEoYMGWLI10UixVeXJEqlpaU6y4now87OTqihGUtRURFOnTqFF154QSfIAdDpgPFo8Hjw4AF+/fVXdOrUCb6+vrhw4YLB19+xYwd8fX3h5+eH0NBQHD9+HPPnz9d5VfjFF1/Az88PAQEBKC4uFn6Cg4PRoUMHHD9+vEE+a2pqUFJSguLiYgwdOhRarVZ4rXj37l1cvHgR0dHRQpADal+btqZdcPr06Trtnc888wwAICcnBwCQn5+Py5cvIzo6Wqf2rVQqLab9kSwDa3QkSi4uLigtLW3VZ7p06WL0jiR1/yk/umBtYzQaDZYvX45du3Y1GPbg7u5u8PXHjRuHuLg4VFZW4vvvv8f777+P+/fv6ywI+vPPP0OlUjUIxHWKioqE369evYqkpCScPHkS5eXlOulKSkoA1LY3ArUBpz4/Pz8cPnxYr7zXrXZdp67N7d69ewCAmzdvAkCj+W6qLGSbGOhIlPz9/XHx4kU8fPhQ79eXzs7ORs+HVlu73GP9labre/vtt/Hpp58iNjYWgwcPRseOHdGuXTskJCQ0GNrQGp6ensKCrGPHjkXnzp3x5ptv4tlnn0V4eDiA2tpZ7969hfbC+tzc3ADUBrLw8HA4Oztj0aJFePLJJ+Hs7Izbt29jzpw5Qj6bK3PdMX00tXinPudozXVI/BjoSJT+8Ic/4Ny5c/jyyy8xdepUo5+/pcBVp67Tx5UrV5pNl56ejujo6AbBRq1WC4HGGF5++WWsXbsWS5cuxfjx49GuXTs8+eSTuHDhAoYPH97seLYTJ06gqKgIBw4cEF4jAsCxY8d00nl7ewMArl271uAcP//8s5FK8nuNr7FzZmdnG+06ZP3YRkei9PLLL8PT0xOJiYnIyspqcPz+/ftITk42+Pzt27dv0PW+Me7u7hg2bBi2b9/eoEv/o7UOqVTaoBayZ88e5OfnG5zHxkilUrz22mu4du0a9u/fDwB4/vnnUVBQgPXr1zdIX1VVJZSzrob1aD5ramqQmpqq8xmFQoG+ffti586dwmtGoLaD0L///W+jlaVr164ICAjAP/7xD+G1KQCoVCqjXoesH2t0JEp180FOmTIFI0aMwOTJkzFgwABhZpS9e/fCzc0NSUlJBp2/f//+yMzMxEcffQRPT094eHhgxIgRjaZdtWoV/vCHPyA0NFQYXnDz5k2kp6fjP//5D4DaGujOnTvh4uKCp556CpcuXUJ6ejp69uxp6FfQpOjoaLz77rv429/+hokTJ2Lq1KnYv38/3n77bZw6dQrDhg2DRCJBdnY2vvrqKyxbtgyRkZEYPHgw3NzcEBcXh1deeQV2dnb46quvUFZW1uAaS5YsQWRkJMLCwvCnP/0J5eXl2LBhA/r06YOffvrJaGVZvHgxoqKiEBYWhhdffBEajUa4zqVLl4x2HbJuDHQkWv3798eZM2fw8ccf45///Cf27t0LrVYLHx8fxMTE4JVXXjH43CtXrsQbb7yBlStX4rfffsOwYcOaDHQBAQE4cuQI3n33XXzyySfQaDTo1q0bnnvuOZ3z2dvb44svvsBnn32GoKAg7N27F4sWLTI4j01xcnLCrFmzsGLFCvz73//G6NGj8emnnyItLQ3bt2/HkSNH4ODggO7du2Pq1KlCV31XV1fs2rULiYmJWLFiBZ544glERERg5syZGDZsmM41Ro4cic8//xxLly7F0qVL0b17dyxatAh5eXlGDXRhYWHYunUrVqxYIVwnKSkJ//3vf6FSqYx2HbJuErVazVZbIhKVadOmISsrS6gxk21jGx0RWa3KykpUVVXp7Lt27RqOHDmiM/idbBtrdERktW7cuIHw8HBMmTIF3bt3x40bN7B582bU1NTg+PHjePLJJ82dRbIAbKMjIqslk8kQEhKCnTt3orCwEE5OThgyZIgwzo8IYI2OiIhEjm10REQkagx0REQkagx0REQkagx0REQkagx0REQkagx0REQkav8PQuAA9uzgozEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sat2014.plot.scatter('Critical Reading', 'Math')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9847558411067431"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(sat2014, 'Critical Reading', 'Math')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's an extremely high correlation. But it's important to note that this does not reflect the strength of the relation between the Math and Critical Reading scores of *students*. \n",
    "\n",
    "The data consist of average scores in each state. But states don't take tests – students do. The data in the table have been created by lumping all the students in each state into a single point at the average values of the two variables in that state. But not all students in the state will be at that point, as students vary in their performance. If you plot a point for each student instead of just one for each state, there will be a cloud of points around each point in the figure above. The overall picture will be more fuzzy. The correlation between the Math and Critical Reading scores of the students will be *lower* than the value calculated based on state averages.\n",
    "\n",
    "Correlations based on aggregates and averages are called *ecological correlations* and are frequently reported. As we have just seen, they must be interpreted with care."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Serious or tongue-in-cheek?\n",
    "In 2012, a [paper](http://www.biostat.jhsph.edu/courses/bio621/misc/Chocolate%20consumption%20cognitive%20function%20and%20nobel%20laurates%20%28NEJM%29.pdf) in the respected New England Journal of Medicine examined the relation between chocolate consumption and Nobel Prizes in a group of countries. The [Scientific American](http://blogs.scientificamerican.com/the-curious-wavefunction/chocolate-consumption-and-nobel-prizes-a-bizarre-juxtaposition-if-there-ever-was-one/) responded seriously whereas\n",
    "[others](http://www.reuters.com/article/2012/10/10/us-eat-chocolate-win-the-nobel-prize-idUSBRE8991MS20121010#vFdfFkbPVlilSjsB.97) were more relaxed. You are welcome to make your own decision! The following graph, provided in the paper, should motivate you to go and take a look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAJ7CAYAAAAspW31AAAYHmlDQ1BJQ0MgUHJvZmlsZQAAWIWVeQVYVc23/uy9T3Ho7pIG6VbpbqRBEA7dcehWRJQQEKUVlDAQAYuSRkQRFQPFQAlRMWkVibsJ/X7/7/7vc587zzNz3rNmrbXfmTWx1zkAcLKRQkMDYToAgoIjyFYG2nwOjk58+LcAD3gABeAAkiSP8FAtS0tT8D+WpWcA2vh8Irnh63/W+/8Wek+vcA8AIEsUu3uGewSh+DoAGA6PUHIEANghVC4QHRG6gRdQzERGCQKAI2xgny3MtYHdt7DMpo6NlQ6KdQEgUJFIZB8AaDb880V5+KB+aELRPoZgT79gVDUVxeoeviRPADhuoTo7g4JCNvAMikXd/8OPz//j0/2vTxLJ5y/eGstmIej6hYcGkmL/j9Pxv5egwMg/z9iBVipfsqHVxpjRebsQEGKygalQ3Bbsbm6BYgYU3/Hz3NTfwC99Iw1tt/W/eITroHMGWACAgSdJ1wTF6FzCLJEBtlrbWI5E3rRF9WFzvwgjm23sTg6x2vYPR3mF61n/wb5eRqbbPo8GB5r/wWXefvpGKEZXGnw9ztfGfosnfCvKz84cxTQoHgoPsDbZ1n8T56tj/keHHGm1wVkQxQveZH2rLR2ELSj8z7gQKQ/SJgc2FGtG+NoYbtkiDl7hDqZ/uHl66eptcUA8vYJttzkj6OrSttq2TQsNtNzWR8q8Ag2stuYZaQiPsv5j+zgCXWBb84BM+JOMLbf4I0uhEZY2W9wwGGAKdIAu4AORaHUHIcAf+D340vQF/bbVow9IgAx8gBeQ3Jb8sbDf7AlGW2sQB76iyAuE/7XT3uz1AlGofPWvdKuVBN6bvVGbFgHgPYqDMBwYdcxujCnaaqJVDqOCUf1jx0f756k4PZwuzhCnjxP7y8MDZR2IVjLw+++yfyyx77GPsBPYYewY9gUwQXu90DFvMAz+OzI78G7Ty/Z3V78U8r+Y8wEzMIba6W+Pzh21nv6jgxFGWStitDFqKH+UO4YFg55MGAV0JFoYDXRsiqj0PxlG/mXxz1z++3kb/P5zjNtyGnEaxW0W7n/56/zV+rcXnf+YI0/00+TfmshR5BrSj3Qjd5E2pAnwIZ1IMzKItG/gvyvh3eZK+PM0q01uAagfvz86MpdkpmVW/tvTSdsMyJvxBhFeMREbG0InJDSW7OfjG8GnhZ7IXnxGwR5SO/nkZGQVAdg437eOj3mrzXMbYnn4j4yErmsVZgCIy//IQmoAqF9Gj7dD/8iEXgLAOgvA+QaPSHLUlgyz0WABEdCiO4MdvT8EgCg6JjmgBHYDTaAHjIEFsAGOYD86674gCGUdDRLAQZAGMkEuyAcloBxUggvgMrgKmkAb6Aa3wT0wBIbBK3RtTIHPYAYsgd8QBOEhaogRYod4ISFIApKDVCB1SA8yhawgR8gN8oGCoUgoAToEZUJ5UAl0FroIXYFaoG7oLvQIegGNQ9PQHLQMIzAVzARzw8KwNKwCa8EmsA3sAvvAYXAcnApnw0VwBVwLN8Ld8D14GB6DP8OLCEAoERaEH5FEVBAdxAJxQrwRMpKEZCAFSAVSh7SisX6CjCFfkF8YHIYRw4eRRNenIcYW44EJwyRhsjAlmAuYRswtzBPMOGYGs4alxnJhJbC7sEZYB6wPNhqbhi3AnsPewPahO2oKu4TD4VhwIjhldG864vxx8bgs3GlcPa4L9wg3iVvE4/HseAm8Gt4CT8JH4NPwxfhafCf+MX4K/5NASeAlyBH0CU6EYEIKoYBQQ+ggPCZ8IPymoKMQothFYUHhSRFLkUNRRdFK8ZBiiuI3kZ4oQlQj2hD9iQeJRcQ6Yh/xNXGekpJyB6Uq5V5KP8oDlEWUDZR3KMcpf1ExUIlT6VA5U0VSZVOdp+qiekE1T01NLUytSe1EHUGdTX2Rupf6DfVPGkYaKRojGk+aZJpSmkaaxzTfaClohWi1aPfTxtEW0F6jfUj7hY6CTphOh45El0RXStdC95xukZ6RXpbegj6IPou+hv4u/UcGPIMwgx6DJ0MqQyVDL8MkI8IowKjD6MF4iLGKsY9xignHJMJkxOTPlMl0mekB0wwzA7MCsx1zDHMpczvzGAvCIsxixBLIksNyleUZyzIrN6sWqxdrOmsd62PWH2ycbJpsXmwZbPVsw2zL7HzseuwB7MfZm9hHOTAc4hx7OaI5yjj6OL5wMnHu5vTgzOC8yvmSC+YS57Liiueq5BrkWuTm4TbgDuUu5u7l/sLDwqPJ489zkqeDZ5qXkVed14/3JG8n7yc+Zj4tvkC+Ir5bfDP8XPyG/JH8Z/kf8P/eIbLDdkfKjvodowJEARUBb4GTAj0CM4K8gmaCCYKXBF8KUQipCPkKFQr1C/0QFhG2Fz4i3CT8UYRNxEgkTuSSyGtRalEN0TDRCtGnYjgxFbEAsdNiQ+KwuKK4r3ip+EMJWEJJwk/itMSjndidqjuDd1bsfC5JJaklGSV5SXJcikXKVCpFqknqm7SgtJP0cel+6TUZRZlAmSqZV7IMssayKbKtsnNy4nIecqVyT+Wp5fXlk+Wb5WcVJBS8FMoURhQZFc0Ujyj2KK4qKSuRleqUppUFld2UTyk/V2FSsVTJUrmjilXVVk1WbVP9tUtpV8Suq7u+75bcHbC7ZvfHPSJ7vPZU7ZlU26FGUjurNqbOp+6mfkZ9TINfg6RRoTGhKaDpqXlO84OWmJa/Vq3WN20ZbbL2De0fOrt0EnW6dBFdA90M3Qd6DHq2eiV6b/R36PvoX9KfMVA0iDfoMsQamhgeN3xuxG3kYXTRaMZY2TjR+JYJlYm1SYnJhKm4Kdm01Qw2MzY7YfbaXMg82LzJAlgYWZywGLUUsQyzvLkXt9dyb+ne91ayVglW/daM1q7WNdZLNto2OTavbEVtI2177GjtnO0u2v2w17XPsx9zkHZIdLjnyOHo59jshHeyczrntLhPb1/+vilnRec052cuIi4xLnf3c+wP3N/uSutKcr3mhnWzd6txWyFZkCpIi+5G7qfcZzx0PAo9Pntqep70nPZS88rz+uCt5p3n/dFHzeeEz7Svhm+B7xc/Hb8Sv1l/Q/9y/x8BFgHnA9YD7QPrgwhBbkEtwQzBAcG3QnhCYkIehUqEpoWOhe0Kyw+bIZuQz4VD4S7hzRFM6KvOYKRo5OHI8Sj1qNKon9F20ddi6GOCYwZjxWPTYz/E6cdVx2PiPeJ7EvgTDiaMJ2olnk2CktyTepIFklOTpw4YHLhwkHgw4OD9FJmUvJSFQ/aHWlO5Uw+kTh42OHwpjSaNnPb8yO4j5UcxR/2OPkiXTy9OX8vwzBjIlMksyFzJ8sgaOCZ7rOjYerZ39oMcpZyyXFxucO6z4xrHL+TR58XlTZ4wO9F4ku9kxsmFfNf8uwUKBeWFxMLIwrEi06LmYsHi3OKVEt+S4VLt0vpTXKfST/047Xn6cZlmWV05d3lm+fIZvzMjZw3ONlYIVxRU4iqjKt9X2VX1V6tUXzzHcS7z3Or54PNjF6wu3LqofPFiDVdNziX4UuSl6Vrn2qHLupeb6yTrztaz1Gc2gIbIhk9X3K48u2pyteeayrW660LXT91gvJHRCDXGNs40+TaNNTs2P2oxbulp3d1646bUzfNt/G2l7cztOR3EjtSO9c64zsWu0K4v3T7dkz2uPa96HXqf3tp760GfSd+d2/q3e/u1+jvvqN1pu7vrbsuAykDTPaV7jYOKgzfuK96/8UDpQeND5YfNQ6pDrY/2POp4rPG4+4nuk9tPjZ7eGzYffvTM9tnIc+fnYyOeIx9fBL6YfRn18verA6+xrzNG6UYL3nC9qXgr9rZ+TGmsfVx3fHDCeuLVpMfk53fh71amUt9Tvy/4wPvh4ke5j23T+tNDn/Z9mvoc+vn3l7Sv9F9PfRP9dv275vfBGYeZqVny7Ppc1jz7/PkFhYWeRcvFN0tBS79/ZPxk/3nhl8qv/mX75Q+/o1fwK0WrYqutayZrr9eD1tdDSWTS5qsAglbY2xuAufMAUDsCwIjmcUSarfxruyDQRtoBgB2UDochehgdrDROEE9L4KRgJ/JRqlPZUEfRFNNO0CswJDE+Y5ZlSWP9wG7KcYOLkzuHF/BF8s8JBAouCCeL0omVSojvbJLSln4s6y03r5CqxKFco6q6a3CPvdqYhrfmZ+0gnRm9IP33hq5GT0wMTK+b81tkW85Z7bFOtGmz/Wkv7xDoWOH0zJngorLf2zXPrZ007cHgKetl4R3gc8i3yO+Sf1vAQOBI0Lvg2ZCVMDyZMZwrgjOSKYoYtRL9KeZpbHNccXxUgkWicOLvpIfJVQdiDu5LUT+0IxWf+u3ws7SuI7VHS9IzMpIyyVn+x9yz7XN25bLn/jr+Kq/9RPnJQ/l+BRaFykV8xcTihZK3pYOnek+3ll0uLz+TdTaqwrlSs2pHNVw9ca7r/JkLyRc9a2wuGdVqXlapk60Xa+C/wnaV6uratS/Xn9/obKxqSmsOaLFsVb7J10bRttA+3jHU2d11vftCT1lv/q1jfQduk/r33GG7s3T36cCNe4WD8ffdHhg+lB3ifIR7NP/47ZPOp+XDCc/sn0uPICOPXxS9dHzF/Ore65hRgdGBN5FvRd++Gzsz7jLBOTEyWfDOeopu6v779A+6H9Y/tkyTPsGfSj/v/jz5peCr2Tf8t87v4TN8M92zlrPP5oznmud3zp9b4F8oX+RfrF3SWhr/Ufoz4JfzcsLv56tV6+ub8deDZREMMo3pxubjIvBuBAcKa6IxpTHVXmoPmizabrqfDDKMvkyVzB9YZdni2Hs5WbkCuDt5udE1MCqgJ3hDWEAkR3RZPEDitaSpVIuMpGyJPI1CsuKMsqtK/y7p3cV71tQ9Nfq0BLSTdEb0pPXTDEaMxI1jTOpMR80pLVQs3femW9VZP7T5bkdtL+Gg7+jmFLsv17nKpXH/bddht0nSd/dfnsAL503pQ+NL58fgzxTAFMgQRBtMDIFDfoZ+DntF7g+/ElEYGR+1L1o1hiVmLnYoriE+NyEk0SJJNpkxeenAq4PdKecP5aTGHHZPMz4ihp6N4+mdGacy47Mcj6lms2f/zhnN7TxekXf4RMBJx3zDAsVC/iJi0VzxSElbafmplNPuZTrlgmewZ6bPPqu4U9laVV9dda7k/PELRy7G14Rccqu1vKxWJ1bPUL/S8P7Ko6sd6Hl19kZBY05TZnNmy7HWvJvFbRXtNR2FnYe6Qrpdesx6NW4p9kneFusXuyN5V2FA/Z7xoPV9iwf6D/cMyT4Sfsz5hOYp9HR++N2z4ed9IzdeVL88/iryte2o4hvmN4tvn45dG8+bCJu0fCc9RTv17f3DD/Ufs6eDPhl/Fv689uXJ16pv5O9qM5iZO7Ppc4bzuPnOBZeFmcWoxbWlkz/kfoz+LPtFXnb8bb/iu5q11rkdfwGoAXZE6JGrmH1YIrYFR8YrEjCEOxS5RE9KfSpZagEaLloGOhp6NgZeRnkmM2YySxnrY3aIQ43TmyuPu5vnKx8Hv/aOAIE8wWahtyJAlF9MQ3yfBHnnIcl8qQvSLTIDsq/kvsqvKlIqcSqLqiir6u2y2L13j6WambqhhoamnBa/NpX2gs4L3Va9Yv0YA1tDGSOi0ahxvUmKqZ2ZpDnOfMKi07Jsb5KVm7W2jYAtxvadXa99uUOCo4OT/D7qfR+cu1yK9oe46rtxuc2Q+tyLPfw8lb1wXsPeVT4Rvjp+jH6T/tcD0gIdgsSCVoLvhGSGGoZhwrrICeFK4bMRNZEeUZxRj6MzYjRjlmJr40jxrPEPE44maieuJt1Mjj2gemD5YFtK0iGtVCS19/CBNNW0+SOXj/qmC6VPZlRmemaJZc0ca8k+nGOVy5f79XgruoYsTrKefJNfWeBTKFb4qaim2K9EtORD6cVTmadDyqzKFc4wn5k/O1RRU3mwyqZauHrp3K3zuRe8L9rV7L1kWqt/WaNOqV68gesK8crS1TfXeq9X3zjcGNIU05zdUtXadvNp27cOQqdAl3q3U09074lbDX2Dtz/fYb9rPJCM3mBzD+Qfxgz1PmZ+EvT07jPx59kjSy+9Xn0ZzXqrPPZtould0fuTH69/Wv2aNmM+H7y08Jt9I/5bv8NtFJwSAHm9ANguAWB9EIDM2wCIrKB5JhEAS2oAbFQBPG4A4JNxADpr8Pf+gNAWh2addIAVzYbFgAKaa5oCJzTDjAFHQSE4D1rAABgFMxAWzRil0TzRGQqHsqAqqAMageZhGlgcNoA94YNwOdwOv4ZXEG5EHXFDDiHnkXvIDIYZswfN3TIx1zCvsTisLNYFm45txE7hmHF6uGhcDW4Uz4A3wCfhG/HfCeIEL0IFYYyCl8KNooJiiihGDCY2UxIonSjrqBCqfVTXqWmpA6nv0eykyaFZoN1He4tOmq6UnoI+jn6WwY/hHaM74ySTD9NX5mg0Y8ljFWBtZDNlm2RP4ODg6OEM5uLlGubO47Hj5eed5xvkr9mRLRAp6CakLswjAolMiQ6INYgXSiTt9EJPQQVpLhmszJIckKdS4FAUU9qtbK5CUo3edWx39Z5OtVfqvzSptXZoq+u46qbrtejPGcoaRRt3m9KZkcxvWCJ7Na0SrW/aLNvttj/gcMeJZZ+/8+394q4FJEr3I56QV6L3L98ov/mAsMCvwX4hU2Ek8miEU+TzaM9YrrjhhJwk4wPIwfZDUYel0t4fPZ1hl0V7bCDnzPGEE6T8vYUWxW6lWaeHz6hVDFRHXaCviat9X29z5fb1PY0tLXtu9nc4dS32LvfLDIgMzjy88Nh32Ggk/rXDOMdU3HTH1+pZhvmfS6E/U5cNfj9apV+TXGfZPD8g9G0DD6gAI+ACwkAWqAETNPr+IB5kgdOgHvSAZ+AzBEFsaOwNIDcoDsqHGqBBaBrGw0KwHhr5VLgavg1/RDN7acQGiUPOoDn8dwwbRhsThCnC9GHmsHxYC2wytgE7gebiJriDuCbcDF4M74Evx78mcBL2EU4T3lIIUvhRNFD8IuoQs4ljlEqU2ZQf0fz4LDVE7UF9h0aapogWQxtGO05nTddPr0bfxCDPcJVRnrGJSY2pn9maeZIlkpXIWsGmxvaSPZaDC413ABcb113uZB5Vnl+8HXzp/E47ZASoBL4KDgldEy4WSRENEnMSN5JQ3SkuySPFIE2QATKrcpTyXApSijpKTsoRKjmqtbvu7f6iRqeupOGsGaNVrN2hM63Hrm9hkGk4aExv4mx60eyXhanlib3D1mw2+2zP2L13kHKMcxpw5nWJ2//STYtU58HnedKbwifJd9bfPeBxkEZwTShDWCz5bYReZE00Y0xtnH78RGJiMtuBhhT9QyOHfdLmjsZnwJlHjlFmn801P75+4np+YKFY0aeS+lOxZfpn2M5+rbxdXXk+82LOpYLLFfVXr/RdG73xs5m1VaXNpeNwV13Pqz7qfv27R+4NP5AdKnvCNVw7YvkKHu0dK3mn+lHh8/1vK7M9C2pLST/zl7NWgtbUtuOPBZSACd37UkAdWAAPEAtywDnQAZ6DOYgGEocMIW/oMLrfb0HvYCwsChvDoXAh3IlGnBHRQIKQU8h9ZB0jj/HFnMG8wDJh92JzsU9wrDgXXBXuG14Vn4Z/ShAixBAGKQQo4imGiXLEk8RflCTKQardVHXUQtRnafhpztHK0LbTmdNN0icw8DD0Mvox0TE1M5NYKFmaWD3ZmNj62RM5lDmWOFu4krkNeVh4PvC28xXyR+ywE9gjKCTEKkwjQhDFieHEiRJ0O9klhaTkpfVkHGQPy3UrIIrGSoXK06o6uyr24NXC1Sc192k91THXvauvY9BptMu42VTFrM1C1/KNVYqNmO0T+0RHYacHzuT9TK7XSdbui55l3ma+GL/egKwglxCVMPZwOGImaiImI04ufizxRLLZQbqU16nX0vKPHsyIzorKds3FHq894ZBPKGgvii1RO0U8PV7ec/ZyZWV1xfkjF8Vq7tUG1zHUN11xuYa5Xtto2wxaLt10bKfouNkV0iPU29fnfnvtTtGA7L3++44PPg5FPFp5kvx07VnC8x8vQl6+f+08+uit3ljtBDxp/C5naugD5Ufd6fBPZz53f3nzdfbb+gyYWZv9Ovdm/uZC4aL/ktzS8o/rP31+cfzqXnZdXv1duiKwUruquNq+JrdWvc62nrUR/3BvebnN6wOi0gYA+2Z9fV4YAHweAKvH19d/V6yvr1aiycZrALoCt/7b2bxr6AA4NbeBBsSHD/z7P5b/Apmqv/gBUfQ5AAABnWlUWHRYTUw6Y29tLmFkb2JlLnhtcAAAAAAAPHg6eG1wbWV0YSB4bWxuczp4PSJhZG9iZTpuczptZXRhLyIgeDp4bXB0az0iWE1QIENvcmUgNS40LjAiPgogICA8cmRmOlJERiB4bWxuczpyZGY9Imh0dHA6Ly93d3cudzMub3JnLzE5OTkvMDIvMjItcmRmLXN5bnRheC1ucyMiPgogICAgICA8cmRmOkRlc2NyaXB0aW9uIHJkZjphYm91dD0iIgogICAgICAgICAgICB4bWxuczpleGlmPSJodHRwOi8vbnMuYWRvYmUuY29tL2V4aWYvMS4wLyI+CiAgICAgICAgIDxleGlmOlBpeGVsWERpbWVuc2lvbj43MjU8L2V4aWY6UGl4ZWxYRGltZW5zaW9uPgogICAgICAgICA8ZXhpZjpQaXhlbFlEaW1lbnNpb24+NjM1PC9leGlmOlBpeGVsWURpbWVuc2lvbj4KICAgICAgPC9yZGY6RGVzY3JpcHRpb24+CiAgIDwvcmRmOlJERj4KPC94OnhtcG1ldGE+CjBYLUAAAEAASURBVHgB7N0LXBVl+gfwH3C4g4jEGhqGhElxNLxAISlYoimuS+aippahla3ZVmqlla2Wl7x08ZK6q+ZumWZq/k0zw11voYWVVlBohCSZGSGCILcD/J93zjlwuAiCCAq/6XM4M++8887M9xg8vDzzvlalsoALBShAAQpQgAIUoAAFKFBvAd2ePXvx25nf690AD6QABShAAQpQgAIUoEBLFOgf0Q8eHm20W9cdPPQ5TpxIha+vd0u04D1TgAIUoAAFKEABClCgTgIGQzFOnvwVt98eVB5U29vbI7RXd4wcPqhOjbEyBShAAQpQgAIUoAAFWqJAZmYWXvzHkgq3bl1hixsUoAAFKEABClCAAhSgQJ0FGFTXmYwHUIACFKAABShAAQpQoKIAg+qKHtyiAAUoQAEKUIACFKBAnQUYVNeZjAdQgAIUoAAFKEABClCgogCD6ooe3KIABShAAQpQgAIUoECdBRhU15mMB1CAAhSgAAUoQAEKUKCiAIPqih7cogAFKEABClCAAhSgQJ0FGFTXmYwHUIACFKAABShAAQpQoKIAg+qKHtyiAAUoQAEKUIACFKBAnQUYVNeZjAdQgAIUoAAFKEABClCgogCD6ooe3KIABShAAQpQgAIUoECdBRhU15mMB1CAAhSgAAUoQAEKUKCigK7iZjPaMuQi7afTuGDript828J8o/nnMpCZZyi7UQf3tnB3KNvkCgUoQAEKUIACFKAABeos0Cx7qg2n4zDAzR83d++LwC49MfKtI2UwSe89Bl+/nmWvt7/LKtvHFQpQgAIUoAAFKEABCtRHoFkG1TpPP0xZtxnpuWk4vDgE26d+jkyTjs5eVgJm4lfZdz7rBJ4IcquPG4+hAAUoQAEKUIACFKBAmUCzDKqha4uIqGC4IAtHDh6CfkpXuJbdsqwl/o4f0zIAna4sLaRsN1coQAEKUIACFKAABShQR4HmGVQrBEMq5gbr8cgGYOhgfVnwbOvaQXYuQ5h/IFzveQMp+XUUY3UKUIACFKAABShAAQpUEjA/v1epuDlsOqLnlEV4fNNkzAqfgT9nvAm9PJDYOfol5Mkr/3Q8/uZ3H57ddA8+GO2v3fAzz81C5tlzFW4+/Y8/MP25JxEc3L1COTcoQAEKUIACFKAABShgFmi+QbVKAYmORsQgH+xtex9+TJ8PvbdKqDYuDl7BeOIVfzycnmcuQtSQgcgvqNh1/e9/v4/U1DQG1WVKXKEABShAAQpQgAIUqCzQTIPqAmTm2MDdRYfMHxKQgBB0dDcG1OmnM+Du5SHpIKew84UktFnsWGbSq1dQ2bp5Zffu/eZVvlOAAhSgAAUoQAEKUKBagWYZVKfvex0dBi1Dn97+2H8gCSMX70Sgi9x/fhJG+0Vgf0AI9ImHJNgej6OjjKkf1eqwkAIUoAAFKEABClCAApcg0CyDas/QSUiMuws/nbqAV9/qgkBfDyOFgz82JMXim29/kiH2/o477g6Fl+RZc6EABShAAQpQgAIUoMDlCDTLoBo6Z/gGBsurKo27tz/C5cWFAhSgAAUoQAEKUIACDSXQfIfUayghtkMBClCAAhSgAAUoQIFaBBhU1wLE3RSgAAUoQAEKUIACFKhNgEF1bULcTwEKUIACFKAABShAgVoEGFTXAsTdFKAABShAAQpQgAIUqE2AQXVtQtxPAQpQgAIUoAAFKECBWgQYVNcCxN0UoAAFKEABClCAAhSoTYBBdW1C3E8BClCAAhSgAAUoQIFaBBhU1wLE3RSgAAUoQAEKUIACFKhNgEF1bULcTwEKUIACFKAABShAgVoEGFTXAsTdFKAABShAAQpQgAIUqE2AQXVtQtxPAQpQgAIUoAAFKECBWgQYVNcCxN0UoAAFKEABClCAAhSoTYBBdW1C3E8BClCAAhSgAAUoQIFaBBhU1wLE3RSgAAUoQAEKUIACFKhNgEF1bULcTwEKUIACFKAABShAgVoEdLXs524KUIACFKAABSjQaAJF9w+G3enfgNIrfEoroKjdn6Bb9/EVPhGbbykCDKpbyifN+6QABShAAQpcAwIOv6fDNuUMUHKFL1b+Vm9tW4riK3yaK9m84Vwqvk4Fugf6oEEDOkMWEuJT4HRrF/i2btCWryRHk7fN9I8m/wh4ARSgAAUoQAEKlAmUShf1le6lLj9Z2VrFlVwkHIzFO+9uxPsbYxGXeAqGihVq3so/g/h9CcisudZl781P3Ymw0Ifxdc5lN1WxgfwUPBQxBFt/zK1Yzq0aBfjrR4083EkBClCAAhSgwFUrYCNX9tBw4JbOxks8mQKJhIGzl3HFhlOYO/gOzDpQsY0+i2Oxa5x/xcKLbOUkbUHYoDl4L+kE7vXWIed0MpKzXaHv3LZhe5RtXeUK3GF3keuod7HOFj5ysL1tvVtokQcyqG6RHztvmgIUoAAFKNA8BIpCh8I68j7tZkoPfwLdB+tlvf5JHTkJu7SA+p9xRzEm0EPaKkDCvv0w3Ox3yWAu+mgciouAnwTUakn98DGETB2JzNyYhg2qL/mK6lhR51DHA1hdCTCo5r8DClCAAhSgAAWuWQFrayvYWBuzWQ2lkohdWv+A2hLBxdEcWNpDHxah7cpJOYJDv7miby8/CaAMSDv8BU620iO0s5txf5rsT3FF71BP4MJ55EnOiEP+KSSmyu6ANPx3XxxaX9cJ12X9iJNFgGVHcJFtW/SWdtVZ04/F4f8+/hbZ9h6488+RCPZ21tpPOxyPCz6dkRf3Eb607YlhPlpx+RfJhT66Zw/+91Uq7D07od+QfujsaV9+7C3BaP/7EXz4yefSdgcMvG9Aec60HBu3fRe+OJGDVvZp2C5HhZe3zLVLEGBO9SUgsQoFKEABClCAAleJgOoOVNGoesl6iVWpMQVbRvOAlYQ1NvIy7zdHrWrfJS4uPt0wUure390fU1fHIdMimfrUwaUYEjEXSfnGxpI+GIF+f/8IxpRmA/bNH4IhyxKQk7AZIRHP4ITUS9q6BGOXJQGJqzBs0AjsSs1A/BsjMETWBw76h7zUu2yvPqb1dKbsmIcO3Udg0q4kHFo7GWH+UYhNUxeRi20T70Ogjx4ho6Zh0pakKnneCf9+GCFRk3DOsxW+emKC1F2DdO1S5dhwOTZmHDy7DMEja/dgiuwf/vZ3xhvJT8YMNz36jZqM9YfiMGnqKq3cGI4bq/Br7QIMqms3Yg0KUIACFKAABa4GAcmhzn/sURTMnC2vV5A/4xUY/G7Vrkw931jcTnpx/z5H26f2Fz3znPFv8nUIqtG6G9acisXCGH8sfWIE2rlFY9XBVO0cnQeMkfdPsS8pS9vWgukD2/DNOdk0pGLzGmDGk73hYKuynI25zvrR83B0cX/pqZ4r6R9pmBV5C8ZsTEOerOflbsI/I1VTE3F8ZSR0hmS8Fr0MiFmBXz95E+s/3YlxSMLCjyQol6WVj/raH7uTk5G3Okrr1VYl5sXtlgex9uMDmDUuBmu+nivFeyAdz9rSSp1nx6dY+PHnyIvfiMOLQ5CwPlH7hSB+zXQskHY3fZeEwxtXIy91M/RSvcB4KL9eogDTPy4RitUoQAEKUIACFGh6AV3kCKBbb+h06inFiot9Bz8JSJ8tLzxzClgwr+7D87X2x8QlsYh+fC/m/30MJkX0BuKTMD6gGxYGAFM+ScFEf1uskPgXOIRdhzPQo8PnWC+B6eHukof9U/klqLUinNcK8uSrOalEFcS9/jAe2eGPnclToKVf5+TjgtqxZgLaSYBuXvqYVgpSgXEbZyHUq/o+ZO9ekbgrJQEfrl6Ojz6YI0f1L3uI0Xjs55gY1t7crOk9C99uOyRx/TuI9HU2lrk6wadSLW7WLsCgunYj1qAABShAAQpQ4KoRUOkepSgpKZF0DyuoTmgreVdLSdlwfMYx+axKSiHZIfVePDuHY8Gmbfi27RDs+vyEBNWSIjFlKLBwH2J9f8P+EYuws28cBm7YiW6dtklA/zD8JWrOv8gZzdkoavfp2DfQ74VDmB17FOFe5eGY/BqAGVI2LdgF+ZL1YfzlQe3P1XqOfdu3VodXsxTgw0l+uH+N7Oo9CjO6hgAWI5ioXufqjzWeW+9lzAvXGtaVX081J2LRRQSY/nERGBZTgAIUoAAFKHD1CRSdSEZRgqQwfHMQeUcPoSgzXR5ONOZVF2adQ9538cZ9sr/ghyN1voHMo1vx2sb4slzqnN//MI3QZww0b+p9L/SJizDkoXWYMW4AwgfcC2yYhvtflgD5ge7VjgBhUBFtGyAvPwvpOQbkp+yAb9QiDF68E0/3UiOMmBYHF3SS1S1bP0emzh4ODvbIPJladi3G/mmLJG/zceo950eskIB69t4E5H0yD0N7dTfuNcXHFz9WBw85acIL7yPBlCpybNce7UFFy+a5XrsAfxWp3Yg1KECBFiDgOD9R+8Fc/awTVujhnol9/d6Cs40BRSVOmPZtBBYl3VY/GRmtIG+qyljkQgEK1ElAOqdtF72KUgcH6aGWQFr1UM9cBPTpLz3SpbBJ/RY2sybBKsM4AoiVQd7Vah16q7/8cBmeX5iE5x+yvLJR+Ndwf61A59UFIyUF5PnEofhzd+nddZCUkN6SEnJgKPp3MQXIRSrd4xAKTU207SQB7oFp6OAxDfpX1+D2Zydoe7Y/MRCOT5gq9Z4pedQxeHbrZNwcJekfy/wxuHcStktv8+y4JDwdCGTLt6kCGTWkbLE8j4sXBsiO58OHSRpKEhJMldZ9korAKM8qxxoKMuXhyfOSmmKPPz+zBvo1MQhquw56ubcEOY9aKpzLWMSvNQgwqK4Bh7soQAEKmAW0Py6XNqM/7nEaYvNHy/drSUCCY13yT+VXLGnVxeezy7at8rKhO/6d5FaUFdV5JWJmLE4+eASfffkjMs4XwvX6m3HX3cHwLEuG9sBf31iCVpn+0Gtlbhj68hLglJ+W+qFO6OAzEDs/vgOdTMd49X0Y21begN/cAzB4wK34/fbNMsKILWyLiiSoNS62bjfKo43yeGPEk/j1617Y/tlxFNi74Mk3Q3B7Z5XrbEDU3s0o6qTWjUvF83jgb6mx6LjtS+R4dER4uB9OfroPRT28pLJNlWNvvGc+dga5Q00fo/OOwIHkWBnG7yDO27fFHWEBMKT9Do9bys9lOiXfahBgUF0DDndRgAIU0ATq0Mt1eWJqauSDOJKSCTs7d9wQcCtuD2hf7Z+TL+88crRpGuKR8qfip4Okt40LBShQJuDp2w33yutii3evKIy32OkVFIWJQeUFutY+CA/zsSjwQMTo0WXb7kHB6Fy2VXXFvXMwxsir4qKDrxxnuVQ+j4OnP+61mPXROzq6rHrlY93l/sJ9y3bDwcsfwy2OhbdP+U6uXZIAg+pLYmIlClCAAldYoAGmRq7TFXIa4jpxsfLVK2D1xy/Az99rF2h1Jq3uI31cvbfGK7vGBBhUX2MfGC+XAhRongINMTVynWQ4DXGduFj5KhWQjCzr91YCOz+QIUAkyeG8DBhtetjuKr1iXlYzFmBQ3Yw/XN4aBShQFwGV4yEvLXm68nEyLJcqMg3bVf6ujqn2gMoNXPL2ZU2NHKamOC7A0did+F/CaZmm+BYMHRYOL3MuaC3TENc4NXJN0xtf8t2xIgUaWEANhHH0mLF3Wv2vqF7yMCMXCjSFAIPqplDnOSlAgatO4K/tfjWN/lH9pd3kkgWdKX62koFvu7Y6h2Fep+sXUmvtVBz9w3Jq5McXb8D0B0PhbvoOrU2N/ChwOGO19mCUmhp5yLdzkf7JaLjIw0tqauRhZ5YgM8wT74zT45ENwOAR/bF9wxxMeXeujCgwGu5qGmKPvjJrGqCP7I8EmVlNLfbaV0BNjRygZnLrPRSDz27B81P/hW1JOxHhXaBNbzxFjlGzsSEgREYMOIS12dtw+KmL55yamuUbBa6sgPq9Vo3uoRa1zoUCTSjAoLoJ8XlqClDg6hF4o8c2uRj5qawmj6i8yBB4tlYlsNNJt5j0gtnIQFl/8T6CftdLHmc11SsfXmVbC6oHVCw2TY3c48VJmCJTIy99IgRLYudjfC8fGKdGHqNNjawPdDb+dVubGnk0Ql1MUyPHyphex3ZpAfUMGeN2WkR7nH5gOXwHTcPmxHvRdZ95GuLFxlnT0uMR5HOfcRpiy6mRl0TC9dzDeLL9QG1q5Ii/dYTl9MZqNraE1dEIWinTG0tQ7VLxLrhFgcsWuHCbHvYd/yS9zvX5n6tupy9q/ScZg4MLBRpGgEF1wziyFQpQ4BoXaOd0pvY7MP1Z2Up6h91ss+VV+yEXq1HtjGuXOTVy8qY47XSzou7ArAonzq55GuL8S5kaubrpjSuchBsUaBAB+9fWNEg7l9LIZfwvfCnNs04LE2BQ3cI+cN4uBShQvcAFg1MNnc5WsJFJXxyspae6VP7WLLnVRcUOKCwx5YNU3+RFS9VRNY14Xd+pkZO0Mw7FoTOLoNcVS+hvnOJYpyvAKlmvaRriU7K/flMjayflFwpQgAItXoBBdYv/J0AAClBACcxMGILSkov9udkKNzrl4GH/3bCT/I+SUjvEnr4Ve8/cJEfWMbCW6momuJnqUItFTY389vF2eGhosJZLbZ4auZVplGptauSHxsjUyCr4nYbwTvLn8UfH4H5pY/be5Votv6BQ2ZqM/x16CoERPlKWi2OJf+CmgOvKpyF+uBv0krNhnoY4XF2DxdTIE3pFaudPT0kG2vnBU35KqLzrAi1EV5W5UIACFKBAdQIMqqtTYRkFKNDiBOYfu0V6oS82bIBMU97mLMZ2krxqm1IUl+rwv/QbsOi4HFOfRbqpZ1Y6riGmRnboHIm1MZMxNqo3nu/dH/oDn8pUxSHygOPGmqch1vnUaWrk8umNK90ENylAAQq0YAEG1S34w+etU4AClgLmXmrzu8U+KdKemTLvKnuY0VxgUfeSVqv2bjfE1MiAM4YvSUbAsN34PDET9hPGIDQ0BL5qSL1apiH2rsPUyJbTG1/S7bISBShAgRYgwKC6BXzIvEUKUODaELjcqZGNd2kPfVikvKrec23TEF/q1MiVpzeueiaWUIACFGh5AjU9K9PyNHjHFKAABShAAQpQgAIUqIcAg+p6oPEQClCAAhSgAAUoQAEKWAowqLbU4DoFKECB6gS0ETtkR9VU6Opqs4wCFKAABVqgAHOqW+CHzlumAAWqCuQ9E1C1sEpJb5gnbXmlI/DKX6pUYAEFKEABCrRQAfZUt9APnrdNAQpQgAIUoAAFKNBwAgyqG86SLVGAAhSgAAUoQAEKtFABBtUt9IPnbVOAAhSgAAUoQAEKNJwAg+qGs2RLFKAABShAAQpQgAItVIBBdQv94HnbFKAABShAAQpQgAINJ8CguuEs2RIFKEABClCAAhSgQAsVYFDdQj943jYFKEABClCAAhSgQMMJMKhuOEu2RAEKUIACFKAABSjQQgUYVLfQD563TQEKUIACFKAABSjQcALNN6g25CLtWDKOpZyBoZJX+rF4fLhxB+ISz1Taw00KUIACFKAABShAAQrUXaBZBtWG03EY4OaPm7v3RWCXnhj51pEymdP7lqND9/tw/8IJ6BfcEzN2nCrbxxUKUIACFKAABShAAQrUR6BZBtU6Tz9MWbcZ6blpOLw4BNunfo5MTecUXhs0B30WbENevOxbORQLopfgWOWu7PpI8hgKUIACFKAABShAgRYr0CyDaujaIiIqGC7IwpGDh6Cf0hWu8hHnH4vDUvjj5Qe6aR+4ftjD6IN12J2Q22L/AfDGKUABClCAAhSgAAUuX6B5BtXKxZCKucF6PLIBGDpYD50qMhTKV3fYqf3aokMr7Z1d1SYQvlGAAhSgAAUoQAEK1ENAxZrNdHFEzymL8PimyZgVPgN/zngTPrXcaZI82FhYqALv8iXjrDFxpLyEaxSgAAUoQAEKUIACFKgo0HyDapUCEh2NiEE+2Nv2PvyYPh9+OmMftWXYnK15GBkWLlyGjIyzFYR+/vkX3N23d4UyblCAAhSgAAUoQAEKUMBSoJkG1QXIzLGBu4sOmT8kIAEh6OhuDwfvUDyOyVjwfgI+GKfHsW1rsR9DsdjfWTNZ9a/XLW209enPz65SxgIKUIACFKAABShAAQpYCjTLoDp93+voMGgZ+vT2x/4DSRi5eCcCXdRtt8fTWyfDN2oggnb5I2FHEh7feACdHSxJuE4BClCAAhSgAAUoQIG6CTTLoNozdBIS4+7CT6cu4NW3uiDQ16NMxSviSaTEB2H3kVO4fnooIgLbl+3jCgUoQAEKUIACFKAABeoj0CyDauic4RsYLK/qSbwCQjEmoPp9LKUABShAAQpQgAIUoEBdBZrvkHp1lWB9ClCAAhSgAAUoQAEK1FOAQXU94XgYBShAAQpQgAIUoAAFzAIMqs0SfKcABShAAQpQgAIUoEA9BRhU1xOOh1GAAhSgAAUoQAEKUMAswKDaLMF3ClCAAhSgAAUoQAEK1FOAQXU94XjYRQTyc5F5Lgs5+YaLVGAxBShAAQpQgAIUaH4CzXNIveb3OV0Td5SyYzkCoueUXevjK7dhwehuZdtVVzLw/ksLcOCsIxwdLfbm5SGv/d2Y91wEtDl7DGfw4ZIVeG9XIrLhhQETxuJvUd1QPmePAfHvLsSKL87BSdq5kHcjnl3wGCf1sSDlKgUoQAEKUIACV1aAQfWV9W0xracfLA+oR04che+WrcPSR4cgz24Plkb7Ve+QcxJrFq6TqeKrWSK7Y55WfApze92BWYnldfYf2IJdL27AjudCYfwHXIATX3yN736UOgcOybT0/TFhbnl9rlGAAhSgAAUoQIErLcD0jyst3CLaP4NVEcYe6tkff4k18+dhT/wi7c5XP7QECfkXQXDphv/LSEam6XU+9wQOLe6vVR45pKvWS522Y5UWUOtjFiElKw2Z361BH6mx/+UR+CjNnGLijOFLNuLwJxvxrul4u4ucksUUoAAFKEABClDgSggwqL4SqtdQm4b8AhhD01ykpZxCjjlOrcM95KccwixVP3IuHglrqx3pEhCNbRP9ZX0LPvrijFZW3RcHB3uYXzpk4X8rP5VqIRg3WB1bgG/3fSbv/vjH9Gh4Sbe0g28EVq0brzX10afJ2rvllyLLDa5TgAIUoAAFKECBRhJgUN1I0FflaXISMNLDD67j5mHqPf64ucsd6Lskoc6Xej4tVTtm8ICexhxoUwv6yEhtbW9iuqmk5recxJ14XqV5THwYt7dWdfNx+tskeb8VN7qrbePi2ekmbeV8QT1+AzA3wncKUIACFKAABSjQgAIMqhsQ85prSnp+XdVFb1iGpQf8MThyKKYM6ljn2ziV+J12THgPrwrHul93nbbdqkLpxTYM2LdimrZzyYO9TLnSDvDopIq24NOvM8oONMCY3JGaerqsjCsUoAAFKEABClCgKQUkrOLSkgXOm27+n3FbMSbQ2bSVi/cnRWHsF0CfNhZdxBZQZ+WBwNtXxmLpaH/o7LUxOmBvCoXN1erUj5z+Gf6xRo4MmI6/BJivwx53DpsMrFmE5yMCcShmFFx//ArrD6jea1kcnYzv/EoBClCAAhSgAAWaWIBBdRN/AFfD6fVTNlgE1OqKnBE0bCJm33JWAuWLLEP6opV3+aB2qlZ6Vo58NQfEFznuIsVx774lo3YAU2cPhadFHc+wx7B7cRb6PbEK29esk6C7P/RI0up26eBmUZOrFKAABShAAQpQoOkEGFQ3nf1Vc2afKsGpAbbX+aN/WA2XWKRDe72PVsGnx23yvgV7D/2MaaYHFdWOU4mm/OyLRuba4UDOEbzxwiHZGI+xfY0POpr2yJs9Qse9hLwHn5cMa3lQUafD6R3z4Bu9DOcr9YyXH8M1ClCAAhSgAAUo0LgCDKob1/uqPFt2QeXLKsbBmREYu6NyecVt/Ss7cfgpPVzadzYNc7cTKVOC4av9q8rADtWzLMuwO7XE6IoHW2zF/2cptsv2yJWjTMda7DSvSjCt9YsbUrF85jIpDcHEIWqEEC4UoAAFKEABClCg6QUYVDf9Z9DkV1D1QUJ7DH8vGf1lqnHbmq5OZ+qC9uyJmBEydvSGVRj+ck98+mI/fP/PWXj+gBwsOdJ3dVb1jLMeLtgGPLlsCkI9Tf/0zsXjxalqGL2heHqYX7VnMxgMMMj05z//8BmWTJyA1TJCiP7FKQi3zBOROpDA25zHXai21YaUcaEABShAAQpQgAJXWoARx5UWvprbNxTJtN/A2YJqRneWgNndpba8DfPNSRC+aBt2bRiC9QsnoN1Cc7k/Nm2IMeVI5+Lw4mXYLgFxyNTHJKg25kMnvLdQm1Fx8OLHoK+Yom1sRFJDItsOqTDropoI5tPngs0nkfdcLOvljynStnkJa69GMQnBvjMbEWx8jtK8i+8UoAAFKEABClCgwQUYVDc46TXUoEMHTHt7CWx73nz5F926G9ac2oNer6/CwV/y4OThjweeikGwlzkwd0bo9OkYdxC4y6f8YUb9A/Pxz+yd6Db8IqkcLr6Y8OIotJIpyG/ppEfve/qib2D7StnUOoTNXoG1uTANtme8nUK0RsfqAvXLv1u2QAEKUIACFKAABSoIMKiuwNHCNnQeCI+Oaribbu2H8TPnyeOG1S06BEY9hqWVT+figzHPPVbdAaYyN9z73DzcW0MN9TCjPiJSRgXhQgEKUIACFKAABZpGgJO/NI07z0oBClCAAhSgAAUo0IwEGFQ3ow+Tt0IBClCAAhSgAAUo0DQCDKqbxp1npQAFKEABClCAAhRoRgIMqpvRh8lboQAFKEABClCAAhRoGgEG1U3jzrNSgAIUoAAFKEABCjQjAQbVzejDvOpuRSZsyTyXhRyZRKYuS44ck3kut2wil+qObag61bXNMgpQgAIUoAAFKFBXAQ6pV1exZlb/2I41ePWT4/BwdNTuLC8vD2hzI4bdfz/COxsnaKnPLafsWI6A6Dllhz6+chsWjO5Wtl3tSn4yXnugL57fYdobMB77djyPYPPsi6q4QeoYZ3dc8cU5OMltX8i7Ec8ueAydOaZ1tR8LCylAAQpQgAIUqF2AQXXtRs24RhYOLHkJ69V04pWW1QvnYOrWzzEron2lPbVvph8sD6hHThyF75atw9JHhyDPbg+WRvtdpIEzeC1KAmp1Lb1HYVyrr7B6xyqE+QBHM14yBbwNVacAJ774Gt/JhDI4cAgJ6I8Jcy9yWSymAAUoQAEKUIAClyDA9I9LQGq+VXSwb6Xurr9M552GvFz1SsbhdRO1W14QtQopdcvckOPOYFWEsYd69sdfYs38edgTv0hrb/VDS5CQr61W+ZK+b70poJ6OlE/mYenGrVgbo6qtwqubkrX6DVUHcMbwJRtx+JONeHdxf61tO+0rv1CAAhSgAAUoQIH6CTCorp9bszuqPKiU2Qll5sOFvdUtnkX2RYLgCgCGDBw9nAxVNT/lEGapnZFz8UhYW62aS0A0tk1U05BvwUdfnNHKKn4pwGebjIH3wnkPwEvbKYHv9DXaLInrF8fiNBqqTsUzF1Xc5BYFKEABClCAAhSolwCD6nqxNfeDzD3YNd+n4dwp7Fg9D0FugQgJ3w7Jxsb5tFTtoMEDesLF4nB9ZKS2tTcx3aLUvHpO0jHU+lCE+jubCwGvrhgaIJuJXyItp6HqlDfPNQpQgAIUoAAFKNBQAgyqG0ryGm9HZ/GQXubRDzFJe1jQCx6WkbHpHjPTErDqpb/Dtf0dGPbEMrSJmY6dX4+Bu+w/lfidViu8h7G/2czift112qqWbWIuNL/npONQomxEBuFGi+uAhOU3+Bgr2eU2UB3zOflOAQpQgAIUoAAFGlCADyo2IOa129RJ/HvJu+jqaYf0H+Pw/MIt2q08vnEEvMtuyoC0o5/hX0tmY8GGJK103CtLMGlEBDp7lfcu6+yNUbg9Kv7TqjE1W6q6ms5jW3a+SisNVadSs9ykAAVaoIAhCwnxKXC6tQt8W1f8XtUCNXjLFKBAAwnwu0kDQV7bzSRh6QvTLG4hBAs3zsHESB9jmSEZM3r1xQLVmywpGv/cOh/39O4Gzwq9ysaq5q/pWTmyWh5sm8trfE89j/NSoZrOcRSaD2yoOub2+E4BCtRLIDMlAd//VgRb7TfhIhTBCR06dYJ3a/t6tdeoB+Wn4KGIIRi5NwFPB9V/6NBGvWaejAIUuOoFmP5x1X9EjXGB/bEzKQG/ph5FSmoCMnM3SkDtV35igwFntYBaFTnCxdkVjhcJqH163KYdt/fQz+XHy9qpxATjdnU/bx280Us9GJm4B8fOWRxmSMMXWhoKYGffQHUsmucqBShQf4GfP5mFfhKYhoWr133oFz4QN7f3Q8zre5FZ/2Yb50idLXzkTPYX/dNY41wGz0IBCjQvAQbVzevzrPfdtHZ3g7unB7w83VAlXnbwx9LcJBz+eAnG9V6H+yP6wtM5GnPf3SsPEFZM7HBp3xl95Cr2v7zTYji+DOxYs067tmF3dqrmGt1wS3iIlB/Cpr2pZfsz4/dgtdoa8Wf4uzRUnbLmuUIBClyGgE79ghwwE79qQ3Gm4fyZL7HplaFY/8IYtHsmtsYZUS/jtA12aHaDtcSGKEABChgFGFTzX8IlCjhDHxaFpZ+kISV+A2bHALMeHYOb23ZEzEsbcTQt19iOZ0/EjFCrqzD85R3INBQg7q1ZxjGoA6bjrs7qJ7Ga0XAe/ho9D3HpxqC8x733a8evHvUMPjyWhfzT8ZhsGu96xrjeWqDfUHW0E0nvu1rMvxIUqm1TmbaDXyhAgUsQsIO5s1fn0haRT72JfQuGAstisDmlwHR8AY7GbsVrry/HMvlF/LR5mE4ZijN+3xHp1S7AsX07sEz2v7MjSRuaUx2YeSwesYdPwZB/BrEb35Xj1yBWvjeo/2sTpD2tfmxS2f/D6pjTiXFYJe3Mff1dxB4tH75TtbVXhv1MS9yLZW9tRYrp25U6Ri2G9CTE7ohF3LEMYwG/UoACFKiHAIPqeqA1p0MKtO6a8+U5y5dwc14BoXhaJk9JT47F2ldGYf3CyQjx/4/pT772GL5oG0ZKOwkLJ6Cdmx/6TVUPPvpj04YYeGrt5+Lw4mXYvmMZvkg1/nRz6ByFfYvlh7H0Vt/fXQ93v/uwXrb0U9bgqV4e2lENVQfIxbJeHeHo7I2QJz6Vtj9FWHvZdrsf8SoVnAsFKFBvgeC/vYn27b1QdGib1sar8/+JyJgZSE/PwMbVr2PSmBhkZcvTEzoPRI16APOnL8CQCa/gj/M5eOnvo/Hptk+04363aoOH7huEx59agJcWv4fs7D8wsncw/rVqPe574lX8nnUe854ej/+8/Z5WPzPzHLreNQ5/FBbht5+/xwOD7sLZs8ZElC9SczAxZiwiR72Eb789gOsdb0KPJyfgty3LtWMnz/4P5i9eiR43VvdEh1aFXyhAAQrUKsAHFWslas4VdLhj8gr8M8YZ3lVyPmq/bxcvfwx/ah7ue2gSks44aEPqaUe17oY1p/ag1+urcPCXPDh5+OOBp2IQ7KV6qdXijNDp0zHuIHCXT/nDjMHj3sTRDkFYsuEwLkjutn7AcPwtuluFdJSGqaND2OwVWCvxfPmkN5BfLFqjYz0cjPfErxSggFnA0/M6ZEnQe+FCHhYtegtbNq9F19sCUFJcjE6db8fmzR8h5iHjX6eOH/8JR776H5ycHJGW9it+TE4xN4OMjLNo1+56rFi+UCvbJMet3/AhvjwcC1cXFxQUFODHH431HR0dcShuJ/z8Omp1/7fnM6i277ijp7Z98qSMq7/9PfTprVLNype5895E/OGj2CUzrDo4mL9Hle/nGgUoQIFLFWBQfalSzbKezJ4YEanNWng5t6dr3R761pVaaO2H8TPnYXylYuOmDoEya+PSqKo7O0eMxlJ51bRcfp2Gue+arpH7KNBSBfLy8iWYTdaC2x9+OI6S0hLMnvN6GUfPHoHofHP5g9DzX30JjvLkc2lpKaytraDT6bR12cR113ngxRcma9uqAWsra8x5Zbo8LO2slVlZWcnoI8b69vZ2cHNzxWp5fuPgwcP45Zdfy86pVgID9VUC6kOfH0Z8/Nf4IfEgWrmyl7oCGDcoQIE6CzCorjMZD6AABShAgYsJrFi5Fm3auKNv+J34KSVV62ne+fGGssDYfJwKorXFCmX7VJEq1/bJu8TMZfvMx6lC87FSU9aNdVQA/6D81WxA/74YMTwKcQe/kL2m46WStXXVbMfbg3vA2clJC/rfWja/7BRcoQAFKFAfgarfZerTCo+hAAUoQIEWKFAo41Mbl+8lqJ367EzMenkhXnl5GuzsbKVH+iZYyX+PPPo0siVnWi0qvaMscJZtbV0Fx8YQWKtj3DIG3eb16t61yqZjV/7rP+gW2AUvz3oO3t7tJQc7pyz4NtarGqCrQHvN6jcRu3sf1phys811+U4BClCgrgLsqa6rGOtTgAIUoABkYB8ZW/4ltHN+CW6tXOFxXRv8efAAfLx9PW6/vYcmpNIzVq96AzHj/o5b5QHnNu6t0fZ6Ty232cbG+OOnpKQExcUlKuLVgmBt21AsZcVaG8WybrmovGxzWWlJKUrkpbYffGA4HnhwIkJ6DdRSTnr06Ip16zbhDrkW1ZttXlQQr67LvHh4tMG7/3kLg4eMQhf9LQgK6mbexXcKUIACdRKwWrDwtVKPNs4YOXxQnQ5sKZWnPz8bgbfpER39l5Zyy7xPClCAArUK5JxOwjcntOGDcNNNPnCwd4SdoxOc7G20Y1XPslpKS4uRe+4csnOLYGVnL7nLrrC3kxSOojxkyTj3Lm4uMB+RL73LJU4ucNJZoTj/Ai4U28LV2ThoX6khH1m5JXB1c6q2vhpqL+uPTOQZrODSuhVsDReQbXDE9R5OKCkwttXKxfxocinUuaycXOEg55Jx+2REkkIZAcgVdjblAbd2A/xCAQpQoBqBzMwsvPiPJZg+/Vn4duyo1WBPdTVQLKIABShAgZoF1Og/oV7V1ynLeda6iK3h5OYOB1fVq1wiQXYJDEVqXQdHJxsUFxbCYOpJtrK3h7WhEPnaAPI2sLUpQX6+6hJXi5UE7jYokm1zyonkmMCmuAgF0pmtOp8dW7nBUVas5WVlK73n8m6Q8eetbR3grAJ56dU29lJLWxLcl/VY6xzg1oZD/xid+ZUCFKivAIPq+srxOApQgAIUqFWgxJzWIWkbal2leqjgWqVtqABblan8jLIMjbKVWps2VjB1LGtvMjqICq5tJFdaBczWNtbaiCGqogq0S6RcPUhUFkwbW+BXClCAAg0iwKC6QRjZCAUoQAEKKAHLXmoVKqttlR/d+m6/2oHuvgcl87bDukimXVz9srxerf2Y6mpIYP7LR99BV2INGxsb7VFGFWirNBPLwLpyfnV1TbGMAhSgwKUKMKi+VCnWowAFKECBOgmo3mhjr7Q8iNjIS6HMrFiis4FOgnpdqQ2s5Ked1nutesWlN1uNSsKFAhSgQEMKMKhuSE22RQEKUKAFC1TXS62N5qFG92jkpaCgUHrJjQ85qlOrgFp7yXqplbH3mmkgjfyh8HQUaOYCDKqb+QfM26MABSjQFALSIaylfqhAW82q2NhLgTwAaQ7yVZ61GpPaWtJB5E3L4ZYIu7EvieejAAWauQCD6mb+AfP2KEABCjSFgApotYBapYA0QU91UVGR9nCijTysaCPTn2u51RLcl5Zaaw9FqnxvlQKirpE91k3xL4TnpEDzE2BQ3fw+U94RBShAgSYVUAFrWVAtgWyxBNaNvRQVylB66uFElVctw/cZh/MzPUiputGZU93YHwnPR4FmL8Bpypv9R8wbpAAFKNA0Aip0VfGrGjqvsZciGZ/aIDMtql5yLaA2PTSpXY+6mMaP8xubgOejAAUaWYBBdSOD83QUoAAFmrOA6qEuW4wRtUy6UlZy8RXtMOPwe1oly3YuflT1eyRdWg3jV1IiU5qbxsQ2j5etetG5UIACFLgSAs06/SPz9CnkGHTw9G4L81xZ+ecykJmnTdeleTq4t4W7eeeVEGabFKAABVqAQIVgWu7XmP5hfpdgefSjNSqoxwZLOwSoYTpk9hZJ1+gShJLRj2h5zzUeeJGd2lB+xRJCm2ZxtOya1q7tIsexmAIUoEB9BZplUG1IT8CsMQOx4ICJpfd0HN/+GLzlbpPeewwhUw+Vec3em4Cng9zKtrlCAQpQgAINL2Dz9IpLalRN0KIW67Bh2su4Vfevpbu3qsxurV/a2GEuDyXWvRkeQQEKUOCSBZouqM5PxTtzV2DPL3kVL/Z8Dm4YNg2zov0qltdhK/373VjQaiYSz8TANy8ef/W5D7uOPYDxAc7Q2UtDATPxa3wMXCXnDrqmI6jDLbEqBShAgWtWQIW2hhOJtV6/laMLrP7krU0lXpyZjtLsDDmmfqGwuefc/F7ryVmBAhSgwGUKNFlEmfLJCjyycF21l68PeRyzqt1zaYVeYU8iL8xU16U9fGQ1+4I55cMVSPwdP6ZloLu3B5oM4NJuhbUoQAEKXLMCamrwEknlsNPJsHUvPVLzfUjsbNX9DhQ9Mg/2pQZY7f0Q2PGuFNYvqMaIKVoKijEmt2jjcnK1a74D7qUABVq4QJPFlNm/pmv0M7bGYqy/g0XQC9i28mqwjyX94AdYiv7Yd4sxxcPWtYO0vQxh/suA3pORuPVJ+DKnusG82RAFKEABo4AVip99FNmnfoFtQQlsMo/XDuPRCjoZUxqGElj/lgocjav9mOpqqBh6RHU7WEYBClDgygk0WVDtf89Q6Kd+iq8TsjEtwh8NF0ZbYKXHYVDEIox8ew+CXYzlnaNfQp688k/H429+9+HZTffgg9H+2s4xD/4Nf6SftWgAOPXraQTepq9Qxg0KUIACFKhdwCb9V1idPoHSHBn+Q/5IeClLw03EYpyW3DgctXoM0rRwJkWzBN8pQIEGFmiyoFrnaIcEuZmEF+7DgITxCL/BHlp2dV4B2oY9iImRPpd5q2cw12cEEmJW4EA1+dkOXsF44hV/PJxentM96x/Pybim5jQR4+nfeHPlZV4HD6cABSjQcAIpsWvwWiwwaVYMOjfWX9nyzyD+i3R0CtPDvQ634lCQB6ecAlipvopLDKrr0HyNVVXsrGZMVEE64+gaqbiTAhRoIIEmC6rzzySX3cL+Dauwv2xLVtoMucyg2oAdz/SUvOyJOL4ksmw4PXWK9NMZcPdSudSnsPOFJLRZ7Fh25o4dVWpIxcXNrVXFAm5RgAIUaDKBM3g/6iWslvO3iYjErIi2l38lhlwcO5aOGwN8KnyvtGw4J2kLwgbNwXtJJ3CvGkap0mIMXK20SVYq7JJxoiGd1KUWHcUV9l/BDTWbooqmtZ5vU2DdBJdxBe+QTVOAAlebQNXvjo10hS7+Q7EvtockUNtWPGNREeyu961YVsetlK0vYJikTKvc6ZudtRX0WbATu2J0GO0Xgf0BIdAnHpKe8vE4OsqY+lHHU7A6BShAgUYXyD+2r+wh7gUb9uGZiGiYMtsu41pOIDB4IPZlpCH4Ij3fLvpoHIqLgF81AXXlE6sgVo24od6LZXy8QjXiUhP0TVhLbraNjZU2Vbm1CqotLlT7JcBim6sUoAAFGkKgyYJqOLRFcK8G6GWpRsG9x3j5ATAWOlO8bigywNGjI+DgjA1Jsfjm25+Qib/jjrtD4XWRHyLVNMsiClCAAk0q8NWH/5IhQadj9+wC9Iv6F76cF41wT+Ml5aQl4JtsL4QGeBgLJGVj74GfEdA3GJ7qO70hA/G7/ovPjmeglWcHdO11B4I7OOBY/FHo4Y/D/92LC+434M5efjh9OB4XfDojL+4jfGnbE2MHyFMvF85DzZvlorWVhaN79uB/X6XC3rMTHh8/uFqX3LY3Iq9YB5tiCWnP/lRtnStVqJPhUm1sbKBGIFG91lbm9wrh9ZU6O9ulAAVaooD8fazpFsO5JCybNA6OzhEIcvbGgEnLcTS9Yk5zfa7O3dsPgYH+0AcYX4GBenT2dtaacvf2R3hkJO6NZEBdH1seQwEKNJGAIRnrX05Cn0f7IrTvPRiMJPxnT3kaXfKmgej30cmyi8tJ2oGBUc/jRL4qKsCHTwUiLPpfOH36d3zw6ASEPXcAfxzbgcCIafJXuyRMmTkGA1d/jXzkYtvE+xDoo0fIqGmYtCUJ5xI2IyTiGVNb8izMvx9GSNQknPNsha+emIAjR78rO695RfUGt3rgSXhNno/rn5prLm6cd4nhVVBtDqxVUK31Vss1qR5srdda+9I4l8OzUIACLUOg6Xqq85PwSPsIrDc5q4cWsWYOQtZ8iX2nViO4dcv4AHiXFKAABS5FIPNIrJZLvW2QpKzJd+5HpgBDFsbiVXkQW3VW6+wlrQ0W6XS2dlLqDvUVEir/+oW8xUzES/Oj4DJfRkCS/gsHaScvqysGuM3Aq/s3IlD7y10uWvlI3cT+2J38FkK97JGT+K4UmNsC3G55EGs/no/hYVLxTjs49RiEvNw0qWNcjGFrKQq694GDtR1KCg04t+2UPAhegoLiYlzIL0BRfiEMeUVQadcf/N+H+M/G92H1f6fQ5asBkjOSBztXJ+xK0CGkTy88OHYsfDvcCCvJz7YqVX1BalBrNUOiFQymriEZERuef3JC+h9nJZi2hZ2dTrILTb3V0mNt7K0uz7E2XyvfKUABCjSUQJP1VB/btFwLqPtMXITDSV/iZPIerH2xv9zXp1jwnhZiN9Q9sh0KUIAC17iAAQc/2KLdw5CHovHX6GgJqGUzcQ4+SynQymv+G58zgh4dJR0Xk+ApfxmcsXovzptFTCMeSdxbthSkAuM2ztIC6rJCixXvXpG4yzsHH65ejpi/T9P2VJ65UPVU51rbINfGGhckqM2XnuMCOzvJsZYg20ESrR0dUWqvg7WDHbIu5EgQ7YwLJQa0lqca7/TrhCP7PkOv7l2lmj3OGwpQ4GSHIjcXGNxcYWjljiLXNihwayPvHtrL2sEJtnIOe3t7OEibdnIuWwmubXWSAiLXoF4q2Fcd1MacamNXtVrnQgEKUKAhBJosqC4qyJHrD8Grc6Kh924LTy8/DH9uqvxJU2Y/bIg7YxsUoAAFmotAzndYu0xSPyZOxsIh9yAk5B4sXDAZfeT+VnzyfbV3mZf1h0W5DsHj5iFdnilZ++KtWPDEGHS4fyPUd+HqFhWm+7a/2J8LJZVkkjc6dBmI+z/4GZ26hlRpQgtaJVa1ll5pG+lPttVZwc7eRl7yblsKe+lQd3awgpurPTzaOOD2nnrccbseXbr6on94KHrcegseGnovXORBw9u73Ybb/P3h6ugEF3k5STDuJO/OalsCaRd5VsbVUV4uraRn2haODg6wl4Da3k71VktQbWsDnQTU1qbAWvVwM46u8pGxgAIUaACBpkv/sHeRy/8UsxfuwKsTwvEnnMO+t5dju5SqHxRcKEABClDAKJC2b5t8b/THzqlPlj2YqPYEnJG86am7kPa3bpL+IbnO276H4Sk9zidu1Sa+gswma15yTp8C5JmS4c+9ic6tchAyNQ6p+dKpoVXIRFFeLtLPG6SDQ3p7pawAFl3X5kbUe86PWLEGmL03AU8HueHY1nl4+a3PtRoqmDb3WKv+X9eSIthbSW+0BNXFpSUoLilBYWkxDLoiSdEohY0E1xdystGujZ08AJkv05OfxzffH8H3khZSrLOGh6sr3KWSfV4+vDz/JEPzSYgu6R+lVvLS0kCk1xmqB1qWUpkO3a5U66XWHlBUDylKIG0r7VhLj7n2wKJcnzGn2pQGol01v1CAAhRoGIEmC6r1UWMx+NEt2P7yBHlZ3kwIpv1Vcga5UIACFKCACGRh28xVQO+56Gka6cPM0jP6QWDhNHxw+DFE2nsBByYj8p5/Yf+BJHlQW2olnkShVjkX//a7A1NkfeSIoVi/4VMgchH8VA611l2dhH4+6vvudPya+wCyEyWoLtIONH4pUskih4xtuXhBsp7xfPgwSeFL0ibxUsF0VvZ5uLVy1VIrzIG1k6EQVgUS8kqPtXVRAWwlKdpOkqhLJc1DZURbS5BtqyvGTa3t0OfWjjh51gnnfs2UPOlS+N90E3TSbnuP1mhbXITr5VViJRcl6SHGtGo1F7lxsZIymdgcOZLuoVI/rCTo1oJoU++05QgglukeluvmtvhOAQpQoL4CTRZUw6Ub3knehtdfeAazNiRp16+PnIg3Fk1CqDb+U31vicdRgAIUaE4CDuj3xgbsu15fZUxql4A/49DHHeF4gwM6B83CbrsgHJWsjynzItDX34AvvvgdnVTgDGeMSz2AgPhEJP92Bn3/HI1+94QaJ3tx8cfyj1dgZzIQNqSfPI5og6i9m1HUyThikjrawWcgdn58h6ktD/wtNRYdt32JHBmqNDzcDzs/2IXtH+3CqFHDVHVtUQFr4vbtWj9yYUEB8ovyJAXDBla2Kq9ZAmIJrPNzzsPVtRV+zzoDNyl3kLTAn39LxfnsC5LOYY9bbvCB1flz+O2br/H7kS8BSQdRDykWW5cYg3IZD1stKqg2OLTGzSOiJL3E1vhQoqlXumzkD/MIIHIkg2mNjV8oQIEGFrBasPC1Uo82zhg5fFADN121uYQd72Jj/HncNT4Gd+q+x9oPj0AS31Ai40hLP4bkvkmKd0Ehbgz7CyLMY61WbaZRS6Y/PxuBt+kRHf2XRj0vT0YBClDgWhZQvdW294ehMOUE7M9JPJwudyPJ2iXybb5Usv8KZWIYWw+gqATI/MMKrp1dkGuwws6cHJzJL0GPDr7o4uYB29RkOJ3NhL2a6ly63SV+ltQQaUcNdCLHWsnoISq2zgpyhdPOb2CQXnG1qMDZ/NJG/pDjVDhvDqjtAzrAWuW5yHVomS4qPpf1ktBeyB09BSM+KMbnP/yBYbe5Sx67Dq7zHgN+k5tQcX0dl2Jpu+jztDoexeoUoMDVLJCZmYUX/7EE06c/C9+OHbVLbbyeakMqVkRP04aEWtC6LzIHHcGkqS9V7/ViN+RdJUF19RfIUgpQgAIUqFVA0j1kWGhYqwBYBa/Sa26tUrVlXQb+kNQQ9TCjDNEnDy/aXsiXGNkGXVxd0MEpH+0Ks2H/23lYn86EVaYWP0Mn4wOWOsq6BMPS8Swb8q7yW6RNW9Psieo0ajEH1BJba8G0uUzbqfarjng13qA6QMXhKqiWNq3kgh2dnCRolxFHrGxhIyklLq5y4TZSoZ4/Ma1U21woQIFmL1DPbxH1cNH54Nm9K3DL4VyE/dUPDvJNdtM6edpFfbO1XCRlzrPrzZYlXKcABShAgWtMQOsRluH6SlUatAS+Kh26LHjNk/hVBbNZxnIn+UlUaiiSUT2K4O9cgFIJYO3P/QE7lcp9QV6qd1gFpqpnWYJqKxUMqzLpqTYHxfLoojZropYhIsVqUT3T2ruKrC0W7drUzx71UrtUgG5uS1bVogJh1aZWwRwUmza1CvxCAQpQoJJA4wXVcmLvoEhMDDJfgR/uvqejPFSivkuaFkMuUo6lo51veS6feRffKUABClDgGhNQ0a8KntVPGgmGtRhV9SxL+ocWzKqgWfbJoB6wkuBZ9T7bFElwLIepXmxI8K0dp46V3mSV9iGDiKBU7ZNFBepaT7UExtYyyocphDbuVPurC6bNe1WQrw5QLxVQVw6q5WLNsbTsvSLL6WNHkJLtih5B0tFkeYZ8mVL+69PoFKyHe6P+lLa8CK5TgAJ1FVC/nzfJYji2Ae4eY5Cg/hRoWlK2TEdAcG+8dTDDXMR3ClCAAhS4RgWKbR2QL+NR50s/SYHkTxe3lfd28pJRTPLdJc+4vcSy10v2hpvs+5Nst5JtlWftKunT8p4n+3KkLEeGzM65To6TOoVtZL9sG6S8WNowSHnhn6xQaGcceaQ87cMYYis6c9lFGc3BdfkhF63acDtysWXMEPQL74sXd6TO3xN3AABAAElEQVRWaDYn6f8QFjEQP2pTzFfYxQ0KUOAqFmj034Hz0+Lx1qYE4HScsGTi30vWwEd1VssDiwXHcjSqXUdP4ule8h2VCwUoQAEKXLMCui494eLRDrpiGa1DhtdTo3fI3IoypLQkVhTLsHoyBrVVkQyxJ/nUNi4SScsY1lalBhQV5MHRVSJnmdil5HyudEPL+NIycojWrayeTFSLys/QkpXVcHoqD1qia1VcqXdaK6zmS6EE+mqcbBl9z9j7rR1r7FivpvoVKWrVRZqV4QuXRr+MqFOrESq3rC3aFPMhpinmTWV8owAFrnqBRg+qDRlf4fkX5pTBLH3hpbL18hWV6MaFAhSgAAWuZYGiZ43f601hcI23orIxzIvqMK5rJ60Kueuy/OblDp2tE4plCvTi4gKZjMZRAnJrtG8jwbl6IrLsCiQNxNYeVtdJF7uVJGnUpzf7InkkBadksrMpk9F+4SL0m7wVmaujKqaBWN6QIQNx2/+LL05kwPPmOzA4spsMf2hcMo/F45vsNrjJ6Rds25eOmzp74vqbgxDoLb85qOP2JKFDSCi8VdqNPNWZcvAznHTrgnAZEOB0Yhx2fPot0uGKnn0jEBHYFpkpR/Dlb67o28tPy9wxnEvFnrjfETggGBzx1oTONwpUI9DoQbWDzxDs29sbF469i4GPrsM/P94pwybJn++076jyxdYVnfR+1VwqiyhAAQpQgAINI3DjPaOAVpJDovWAS5uqh7uoCAb/u1B6Y2fJp5ZxsU1LyQ3+KJ4wV4bvK6pXTG0e5s/cXoX3ToPx6l57rA+fhDkjQjArQnJkKi/5yZjh0RcLpHxkTH+sVx1TAZNx/OCT8Jaf4j//d6HMrHnIdFQQxuEwVseswfklEdAZ0vFG1Ai4rvsca6Lay+8KyXgsYgy6bv0SdzhuhG+wTHc/ZSYG5G3DkNBpeC8pGT2/fR9DRq3DztQ0bQbPpM3PYMgTATieG1z5yrhNAQpYCDR6UK1r3R7BQfI/9i2TsE8/Ad0DfbTfhI3XVIC0lD+qDAhicb1cpQAFKEABCly2wNjjfWW4PNUjXWn5RvWRf40fUs9JAG2FuJ/O45FXv9aeY7SWnmzziCKVjqpxUyaOxPLbL1IlOx+eQQ9jbcwcjI2ajqEZq01Tx5fXj18+XQLq/jJBz0qEyzTybz2zF3/xH4OnNwzGB6OlN1nNpinL1I0HMCvSBylbn8PqUf/FT69HoLOMwCKJNVj/XhzeiopG3nd7sF/aWtRbgvd0Hyx5ezNGRwdLD/ldOLSsN05k5OPeweMxEuuwbFsywsd54qMnDmHwylnw1s7CLxSgwMUEGj2oLrsQBx3SD76DR5achpOTerRbRk468xXW75DpdV/ZhsNPdSuryhUKUIACFKBAQwp8dPR3GGQc6ostMhig5H9b4acsA058/XtZtfpkf6is7+VlLVS3osPwlzdjzZr7EDI3DicftAz2s/DtLumFnrJBC6jV0Q7ed2LCCOD+bV8jR4Jqba75gJl4SgJqtfjefo98HYP4kzPRJm27TCcvy45N+DZ/KIq2Sy+39GL7SyaLzjsYY11T8cWOjdj1icyKKdXCVV2dHya8EoKwJ2KR0tcPs6Ro2wB/tYcLBShQg0CTBdVp21dg2NRV1V7a7R3NmWLV7mYhBShAAQpQ4LIEAm+0l9kdbSV0rm4QrFIcO52Pc4WluF76fHzaOsisjdXVu7RLsFbjANa2tA7Gqo3jcXP0CMx3lNQUrX+5toPM+8/Lil35X3m9umFhgATCn+xHwd5leHzdBnjNGYEPtu0BFgIzYrtrfyFOi30DN0ctkmND8PhEY2+3ucXgEQ9D/0IMAtTDlJGL0FtGbOFCAQrULNBkQXVGxkm5slHY+fVoJL44EFNSp8ufnjwQEj4Zt/gwqK75Y+NeClCAAhS4HIFtj7TV5klQU5xXWOwcUNLOF1Ez4/FZwh8Y6O+GN6f3hlXaMXnGr6hC1UvdKJap0yufprpjvSOfxJIRqzDp5XWye6ipiht6DgmR3I412Du+J8K97ZGfsgcrNkh+9dvdtSG/q7blhn5TRmHKQzHS+9wfh98LhVPhKATItvq5e7i7cXStjB8PAiNWIG91JAxpsdi7bIs812QKC7z6YIpUH7tGTj0x7OIPUFY9OUso0GIFmiyoNoqnw7aNHkMflP/5o3/GuSLjb8rbDqZhYqA8vciFAhSgAAUocAUEnBY+pU1JXqXpdh1Q+NB0GWdPhcHqZQ2btCRYL5sGnD1bpfqlFKgZzgve2V2lasEBYP8Ay0DdDeNfeQcrN8gcDjgNGYRQWwIfmY8Za3tLgO8no36EYPsOSQfpPR3Hh/pp+w3ZMo97YiEsW7qp992yT4LzmBHwl5/0ut4qJUS2J96tpX6oA3X2km29YQKCvgMSZGg/tUx5LRYPyigkLjJ95V3DJgJrTiP69moenjRW51cKUMBCoMmC6hu79pTLmIN+Yzbi1w1D5cGM+zAwQv12Lg9k22tv/EIBClCAAhS4IgJWycclqqym6RIZK7uwQBvv2ty7bFUgY2Wn/Qj89kcDDqlnj4F7NyPshlsrXoRXOLbtfQef/+6ETtoQeLJb54Np8Qm4e8ceHP75LIY9PAOREfqyXmq/YUuwr79n2RB7qkGdVy9sWzwTtn17GW/TKwS7V87EhV6mbamjH/cadnvswg8ZdujaNwTXZXyLuHMdTe0W4H//Wablcusl/5oLBShQu0B131JqP6oBargHxWDf2wX4T4o7XCWX7F8rJ+Lhxf9Fmy5D8dJwfQOcgU1QgAIUoAAF6i5Q8WHEilt1b83Y3131OB18g6ofos4rKBz3VjnADcGRUajuCBdv/2rKnRExTqV7mBd7hI623FblbgiVEUFCzVV8I+BrWs9J/D+MlRSTf34daN7LdwpQoBaBxguqZQD6vVsO4EyFC/JBb99cbN64VZ6x8MeUKf6ytxA//3AG+iD+uakCFTcoQAEKUIACjSGQk4TnZPxqjFiCv3aWCWS4UIAClyTQeEF1/klMfWiS5IldwvLiNuQxqL4EKFahAAUoQAEKNKyA4fxv+FEecNy9qIYZHhv2lGyNAs1CoPGCaod2+MfKRcixsxx/s6phYWEhvIPMf4Cqup8lFKAABShAAQpcOQGd5HXvyg2/cidgyxRopgKNF1Tr2iJydHQzZeRtUYACFKDAtSRQJENHWxdVveJSQyny8/IAmZLcrtSAEkMhLsimY4k1ZLNeS3G9juJBFKDAtSbQeEF1JZn8lFhMmf1fOHoYZ1M0787LyEPgA5MwPqy9uYjvFKAABShAgQYVKI5Pw8WCXfWDcXOlJwILP/yqQc/PxihAgeYn0GRBtSE7Gas3GIfQq8yq7zScQXVlFG5TgAIUoAAFKEABCly1Ak0WVLv4R+Pw3t4w2CobuYysb/HsoMnYL1v/iL75qgXjhVGAAhSgAAUoQAEKUKCyQJMF1XDwkGHzjFOlGi/KH5vjcuAZ+hL2/pCOSF8O41P5w+I2BShAAQpQgAIUoMDVKdBkQXV+WhxeX3UY9q3N0yfK+7lvNKVvj8uUq5E+V6cYr4oCFKAABShAAQpQgAKVBJosqDbIdKizFi6qdDnGzdu7t6u2nIUUoAAFKEABClCAAhS4GgWaLKh28InAzq1dAZt8nM8r1p7CdnVxhsN1Prg9gLMpXo3/WHhNFKAABShAAQpQgALVCzRZUK1r7YPWmdsR8pBFb3XAULz3zxnqsUUuFKAABShAAQpQgAIUuGYErJvqStMPLq0YUKsLSdyC+0MD8WFKblNdFs9LAQpQgAIUoAAFKECBOgs0WVB96uh32sXO2BiLzNw05GUlYPfK8VrZiv87Xucb4QEUoAAFKEABClCAAhRoKoEmC6odW3nKPYcgJNQfDurudW4IHT0Kg2W1laerKuFCAQpQgAIUoAAFKECBa0KgydKXbwrSC9A6DOz/dyx5oi/s7YDsxD3YrtgeXYX3Xe5AYU4O7LzvxPAwH1XKhQIUoAAFKEABClCAAlelQJMF1fl5hUYQyaOe9OiWSjjrMHaUeQrz6eif+xjcK9XgJgUoQAEKUIACFKAABa4WgSYLqh3aBmPtyiWA9FDXuDj7wbHGCtxJAQpQgAIUoAAFKECBphVosqBa56XH8NEqBYQLBShAAQpQgAIUoAAFrm2BJntQUbEZziVh2aRxcHSOQJCzNwZMWo6j6YZrW5RXTwEKUIACFKAABSjQ4gSarKca+Ul4pH0E1pvIE9T7mjkIWfMl9p1ajeDWLe6z4A1TgAIUoAAFKEABClyjAk3WU31s03ItoO4zcREOJ32Jk8l7sPbF/sL4KRa8p4XY1ygpL5sCFKAABShAAQpQoKUJNFlQXVSQI9YheHVONPTebeHp5Yfhz03VxqnObmmfAu+XAhSgAAUoQAEKUOCaFmiyoBr2LgJ3CLMX7kDKuVzknDuFHa8vN45TfU2T8uIpQAEKUIACFKAABVqaQJPlVOujxmKwjE+9/eUJ8rJkD8G0v/pbFnCdAhSgAAUoQAEKUIACV7VA0/VUu3TDO8nbMGNEeQCtj5yI3UlvI9yzyWL9q/rD4sVRgAIUoAAFKEABClydAo0fvRoyEPvvd7D+4AnAqQ36jliOzGXeomMDB4fGv5yr82PhVVGAAhSgAAUoQAEKXEsCjRzF5uL9RwMxdkM50fo1q/DuK5ux66ng8kKuUYACFKAABShAAQpQ4BoSaNz0j/wT2KQF1P6Y8fY72LRyoka1/4WViFeDgXChAAUoQAEKUIACFKDANSjQqD3VhvTTSBWkPq/Mx7TobrIWjn3pPyLshU9xODkXwYHO1yAhL5kCFKAABShAAQpQoKULNGpPdX7GGRindSmCwfSfcWg9IDtLdVUbkJ/Pacpb+j9K3j8FKEABClCAAhS41gQaNaiGrZFn/wv3wdW5o/YKm7pFK5w1qCccpczdoyMe35h8rTnyeilAAQpQgAIUoAAFWrBA4wbVRYWXRP3jqfOXVK+2SpmnTyEt7QzyK1VMPxaPDzfuQFzimUp7uEkBClCAAhSgAAUoQIG6CzRqTrWLfhTSzwyv/Sp19rXXqaGGIT0Bs8YMxIIDpkq9p+P49sfgLXd7et9y+A6aAwTIvkRg6sbPMSuyfQ2tcRcFKEABClCAAhSgAAVqFmjcnmoJll1cnGt/XeZ41enf78aCVjOReCYNeambMfjAHOw6lisSp/CaBNR9FmxDXnwaDq8cigXRS3CMadw1/yvhXgpQgAIUoAAFKECBGgUaN6iu8VIabqdX2JPI2xgDXxdp07M9fOQt+4I8BHksDkvhj5cfUCOPAPphD6MP1mF3ggq4uVCAAhSgAAUoQAEKUKB+As0yqLakSD/4gQTS/XHnLW4wGFROtzvsyiro0EpbZ1d1GQlXKEABClCAAhSgAAXqLNCoOdV1vrrLPSA9DoMiFmHk23sQLL3Wtc0v8789B2RIv4IKZ/355C8IvE1foYwbFKAABShAAQpQgAIUsBRouqA6PxXvzF2BPb/kWV4PcD4HNwybhlnRfhXL67x1BnN9RiAhZgUOmNrS6Yx91JZjkGRr7RoZ9u49iHPnsiqcKe3kqQrb3KAABShAAQpQgAIUoEBlgSYLqlM+WYFHFq6rfD3atj7kccyqds+lFhqw45me0sZEHF8SCQfTYQ6dQ/E4JmPB+wn4YJwex7atxX4MxWJ/40yOs2Y+W+UE05+fXaWMBRSgAAUoQAEKUIACFLAUaLKgOvvXdO06ZmyNxVh/B+1BQvOF2bbyMq/W6z1l6wsYtkwdugw3O2srMuLHTuz6mx5Pb50M36iBCNrlj4QdSTLRzAF0Nkfd9TobD6IABShAAQpQgAIUaOkCTRZU+98zFPqpn+LrhGxMi/DH5YXRFT9G9x7jcShuLHSmGRwNRQY4ykyNavGKeBIp8UHYfeQUrp8eiohAjlFdUY9bFKAABShAAQpQgAJ1FWiyoFrnaIcEudoEmbJ8QMJ4hN9gDy27Oq8AbcMexMRIn7reS1l9d28/uHuXbVZZ8QoIxRg1+QsXClCAAhSgAAUoQAEKNIBAkwXV+WeSyy5//4ZVkttssbQZcllBtUVLXKUABShAAQpQgAIUoMAVF2iyoNrFfyj2xfYAbE05GuZbLSqC3fW+5i2+U4ACFKAABShAAQpQ4KoXaLKgGg5t0f3WTKx8cQGmrDkJPZLQJmY6Xp3xMAI9m+6yrvpPjBdIAQpQgAKNLvDb3H+jVY+ucOp6M07+dh4bdxzCkcRc/HK2CEU2OhTYWSO/pBB2pUXo5JCLBTFhcNjzDuyOJyC3RyTcBo7DX19YIfMlXI9SgwtsrO1gZWWAg20ObrTPRkRHW/RpZwXnjJ/wU6dg+N9yC+yDOzf6ffKEFKBA/QWaLnrNT8Ij7SOw3nTtKr8aa+YgZM2X2HdqNYJb1/+meCQFKEABClCgIQUMjs5I/CwOrVKPo1PonZgwfCC+PvorNv3vKxw8/jMuFDjBUGwLW2sbGEqAkiIrlGbnovT0SZRkZcG19XW4cKEY6YYclFoXwcG+CG6GDIR1bI8727WD84UzyCm1x5/6DETXHv2RfT4P9g15A1egLcO5U/j6+0x0CtbDvemiiSp3drVeV5ULZUGzE2iyacqPbVquBdR9Ji7C4aQvcTJ5D9a+2F+AP8WC97QQu9lh84YoQAEKUODaFNh29Gec13miMLsYyR/vguHbg4jodj1emDICj9zfD75/coXNhQLY5lmjNN8KsLKBLscGrlklaGUlEaeVNc5lnoONrhTOToW4zdcOE6O64i7vQnjkpaBT4K3o/Jf7YRf4/+ydD0CT5fbHv+Bg47+Iy5BQJAyUWWiCIinYFZUwIjXU1DL/lGV6NbVSU8vKvGn1u5q3LDW75dWozEhERBM0xKCUDAoMEcX/qAgM2GDI77zvBmz8VcAN7Dy67X2fv+f5bGznfd5zzjMS//n+Z7y5MaoOqLzMY0jONtygTKiUn52GxNQcaOq0qCdDdQnJCWnIr6foVrNUOVEIDA7BX6r6W15IP4ZUA3kLkHo4EcmZV4FWlKP26E3JVbs+nzOB1iJgMqW6XC1sGu6Pf62MgMK1C+TOHhj36kKMolztLoetNUXuhwkwASbABJhAywh8fcUBr8dk4dsTaly1dEZG6p849NVncLzyJ2Y+ORT/mjceo4N9YCUpgUUHDaSWFjCT2UB1xRIF54sA0qs7OwDudio8/cA9eL67E7rm/I677M1w/5QI2D/yKGKzShH+/EfYvuMXJKZcqCVwMSL7hSHw++xa+cDpPfMwLCAGNEqTSZmxA4GPhCA+V6uCKy9kITXz0s0p5LV7t7CjHH9o9yquXViMHX5h8K+WV4P4VWPhHzwemRoJastRu3WLzhuVq0U9c2Mm0CgB092wkdqSYHvx9ppo/GtmEO7CdSR89hF2Ue6QRkXmQibABJgAE2ACxiVwXmYPjU0pvj6WgfN5ZxAxyAv25kWIifwSHmQ37RUYgiXzwvH1vU44cewnlJVdh7mqGJ273g2rbl1RdvZP9PPsiL7eXvAwM4NjyXV4BvjBzP8BnCjrgM+3bEdM9HGoC8h5n/536dylzgSlg+n3UVrLuZ9qSaSOgLed0KzJZKuIoH0cguHhqv35z/nuefgvnID84qmC3n9LSdZEA315s6PXIOTNDCzb+QuFtKWrC42hHLc0cBOVm5KrieZczASaTaCJP4lm99tkQ0X4FIx6bgd2vTmTHvrV/bHoCS/9DD5mAkyACTABJmBSAsMHOJEiaAebG26wKi5E+rUi9HJ2wD/G0MrriVRk/bIfHn4PYfrkQSgM9YDFtSwUydRQFp8kRfkknPt0xexJ/0DepTx0tpDg3gdHwsKlK86cOofEpGNkd12Mh/t5wMHaESVlJbCWWjV7vrkpySjp5QeXy8fw3Z4jKJR2Q8iYEXDvKPzk06OkCKW0UC1TnUN6DmV552J/QiI6dvZCgDfNU5mD6J0/IpM2Pu4xYAgeHeRRrXCr8jIQE3UYp9S2kKtTqLGwWt1IksqgyY2Gd8R6DHnrW9rsrepioUYOWzrMz0zGL4UuGNpHggNRcfj9HNCPVtSDPEkeIZH9eeKuGPx8qgwu9yng7WaPgiuluC+gL4TYBk3JlZsSh6ifKJSvfTcEho2AoiogAvWbnHgGPQN743LCPuw7egb29w3GhFAFikimXft/JX4eCBs3FK6CoJyYQCMETPcJse2LL7Ki8MFrL2PF9gxRREXoLPzfe7MRUPVhb0RwLmICTIAJMAEmYCwCq/07QWpuAWklmXWob8BMQ1ppGRkTFxRikLwzaXXXaTezQ0BWGjqZm6PscjYqL16GrEMFbJUXYfbTj/Asq4CnDUksKQNOpgJnT+KeCitMvbsLOnS9h6KBkIejhrZBsybFs5K6bNbkihEVNAYLQslHKXovKcz+QHoSthRGIWVeXyjTviUTjG1IuBSHSzvXYcp64fc3A2Mf2YiFkYcQcNdJPOE2hu4ae5FiCSx5bTmmfXYAH0Z4ID81El0D5otSjQr1wq5ooa3gC9VwupYZh7kbVgLj38P2eX7VFfXlkNON69P71yBsYZKu3AtDvDNo7DSkF6yCu+QS3hnUHyvS/bFsqTumRCzX1ZuIlKt9IUlrTC4NEj94DsNe2wtF6Gh0il6JBXOALckZGOdtA2Xm92QOQ/15U5fpdCdgsBcOvrYSX04djYObdwCDid+hlcQvhvgpquXnAyZQHwHTKdUkjcy5LxZtisPC9Wqy5+oAGd+zqe894jwmwASYABMwMQHNf1fRAm8hKq8XwqrCnKJ3dESZuT1UKiUsblwhhVsNipKH4hsdUCmxhGWZErIzRbAgj8DCfbQSffEiKmw6Uvg9DTSVpbhRWQGNxoZsrzvDnH7/1AUXIblRiM5OGlw0t4GVtBNkQ75p1qztSRkWFOo1u49gVqAL0jZFwHdDOpSkVMOChISjaAetmLQKqeo8+GwYivzkSaA1ZcQtH0wK9XAk5PwHfnINxrzshbFrDuLNCCt8ICjU499B9oZJcCbt4ULC/8H9kcMNyih1oeuM9SvF3ZOXfRJKo+olPTmEXInUWSwcsnQztr8aDLvML2HXLwpX6MqiW/5xUqiB/2X8D4+T2cqUBzvCPfwokq6ugkJ2DssakUuTvUtUqIULhhXiTs3LsDHCB1P8PsWQ4rm0zi7woJQ+nea8hOZcjPdHKrCEFOo1ccRvEPH7TwSeUWur8TMTaIyAUZXqtOgvEZlchIenT8VDkj+w5btjoG8UQ/nUZege+BiChVtQnJgAE2ACTIAJtAECjhcKcD0nHbIiwIZWmysu0oMUPseuAEXRgznFvyun1WULCvxhS8bNksu02Cz449O5QymtPidmQ+1KefST50AP8ytUJtS5hxan5bQ4Tb/GlpRndhSw6tUB9g4FoPXsm0yGJhjqHGBapFahbqqDcp17I0lISrUap/8UWuxFoJtHTdPBJLAyHz9TztuzHxUVaqHQrjOt0DeS1GTCMWTpOxgQvwgrAtZg9NXl8JQ11ECAtVhUqAXlW0k3AoQkaAiaEroy0R2LB+ITzVmo04RcJw8foEqjEfEPN7EV4IQxcxdjdvQB5CrnoreY64WYnOWkUAsnEtjT84sCP1KohaQTRTzmJybQGAHjKdWaHHwcsQibSJrVHemq+JFjmL2w6hZOLRGX9kUpK9W1oPApE2ACTIAJmIpAYSd3qC1sUFyai+JKDSxczaChDV/Uko4Uk7oSZRXkmEgKo5nUCaXXi2BHEa6sNCXoUKpGubUlyjrZoawX2UtrzFCk0sCS8i27VeCGyw2obagfsvewtq6E/b0dUCjrTG3salkra1W7g4UldRCUFJ6hvDKU60qERVV3l1vb7KHayVEIv7XgC+S/8RDZn1SQjkmhASlLQntLCMme7MGrkqTmsCqr7qt8IJl4khOmy3j4zOqF87RqbrBiXd2CrlYacLaUef4Da8hJc6zXc2T+0Q0r3twIzNoMhS01FnRxSg3KJWjlVZWEQzHVXnZ2REc9E3b1NcD5FvlV9cyvf28CN/Mn0TqEJG54Jf5j9EopRuATHrSLFPDN1s2il7PBAPStIKcdqzgxASbABJgAE2grBG48Oh621lKUkY00bihhaa6BhJanleoKWFNMagvzCnS4QUvXFh1QQbbT5pcuonTrDsj+SEdF0AOwGT8BZrSBjERqA7PScjL1uCGugJrf0MCKFOoKimNdYWGBCnMJrOl30LxD7Yi3Dug1wh94bQm+Grkd43y0d3PzUndi1msZULxFG7DoYAmbxghGlTeTNIJ+2QkoVRWQ86IU3QfQ+Zo9OP7iQ7RyK4WwkcrJ0s7wpN1dXKhoQ+RhTHojGDJy8Pv+f1GUY7hKThmGSU1MOgZgd9xidAuej2cf7ImvX+hrWKfJMwe43S9U6ga5vBe+iTuE0EFu2lak2Tcm173+w6neTETuyYIi3IOWnS/hf//3Hinwi8nxUNtF7edb4Ve7LZ//vQkYT6mmP8CTp8rRubMl0g/sEvwBtKnO/S3KuEqXnu50f40TE2ACTIAJMIE2QOAziiFdWFSAG+bWZNGhIUfF6/Du3R0PP/QgHDpZ48bpE7icSpEiKiWQ9/TCjR59UfwjOd6dzSDzDjdIR0RAXVQMR+cuKE3/E2cSDuKujp2g6mCNX89cwu9XVSgys8ONG1JYkWLdgZTF+SMMJx4wYwVefC0YUwJ8sIac7vrgD2wTnQWnI2VGjRNgIf3Aqkkxr0oaNZlPpBeJK9kW5bQijKRq05IuPfuRI94idHNaBMVqwRnvW4xaM4bMP7ZiSKg/DtJ27Ahdh/zIcLy0YSJ8n5sKxzVChC7tyrUQp7rOz7huYDX5bR4coRVEPuh5JKz+BYELw7Cw+yEsdzGUQ1MoyFiz2g49OVWZOzB2PXU63gF2pMNf+/MnrE9NRsDjj8HH2atRuSSuI7Bv9WgMmzgUqwcPh+LQXrLx9sL/jj4FZ+pSqTeOTmzU5gd1EtL0gVZV5FcmUIuA8ZRq1RksfGa26LBQS4a6p0ujUOrbpW4+5zABJsAEmAATMAGBzT/+gRtlUpSXyOBEphxDh/aHu98DcLjLEnkJB3D5UBycydj6hpkMO/Zvw+DHHoNVB3I2NO8IpZktLDMu4o2dOzD+icfxoOs9cL2vF1QxB3CmvAPMu/XB2XI14o+dQ1m5NWxopdva1gbza8/T1guri9MwMe4Afvw1g3Z38MInTw/EqNC+1avU5KiE8PhvUd6zZmGq+8h3EePrqF1TdgtBzO6B6KmzbXYeOgNRG+7BRUdvjBqhEEyK8fWlI4jbfQAnSO+dOWsFggK8yN4aEBwbT5ApRmxKLqTd+2KYnyNyczS4v94VXylCSI7Ae7RWy8JU/F5YixSfVBRYW0BWSw6PseuQMFxePQ+xPG4oelPfMk8/TKD2234/jFhrd1jT8aWft2JBVBny9kxqQi4JAl74N7IHRWDf4UyoJ43H4FFD4SmGF6S+a8lRL7/HopBQ7i5MgRMTaJSA2eo171c6dbLBhHGPNFqxxYV0yyV6ewKUlqKBU4PdlZWVwdV3BMWmdGiwjjELFi95Gz4PKBAR8Zgxh+WxmAATYAJMoA0ReHRsNK5eOAH3rhLMefEJDPIlJevsXyj48r8Uz7kQ5Q88jJ1nNNhz6Cy6WWqwYU4ApDvWQZa+B0WDxuKuZ97FINotsUMnJ4x+zB9jwh6Eh4sV8g59jazvIuHp5IK/bjjh84PH8GtFP1hQdIwfYya1IQKmE0WVHQ3HPjMp+kcuRf/QypG785+4b+IDOE+b1lSZvZhOQh7570ggP78AS19fh8WLX4F7jx4iAuOtVEu6IHRSxN+RO8+ZCTABJsAE2jkBR8sSjH16OMbQVuQ2ZoU4szcGV3+j1esbd+FqF098v/8v/HyxnEwhHFEhrUR5hRqyMjN0qKCHdQfc6KBGB3JszCdHw8+3fY8/T/yOiJCB8O89BAOm3ouc+L0wK1Bi+mOD0f2PcqhLBGNnTgIBTeElEcRh2qCmZ19r/JXwFZ5cuAMvbp3HCjV/RNoUAeMp1WRTHb/jELR/Go0xKINtj0CEsvlHY5C4jAkwASbABIxI4K154+BxrwXyjx/EX78dRWmxGYopEPOBnHwcOnUel8usyTnQETcoTKwGpSijCCGVlhWopODVKnNSks1LUHFDTY6KFKv6hhkO/XwKx1NP4bGH/fHo0D7o9fjTsD/5K86Qze+ou20pTrVeOAojzrMtDmWreAzfvHUCY58bjw8FAb2HY93uQ5ge6NYWxWWZ/sYEjKdUs0313/hjxlNnAkyACbRvAvdV5iB7ZwpKLuVAbeuEjBuWOHA0BxdVdrgusYNVRztYlGsgpf2/XSytYEN10LkLKu92h7kD7cboYAcZhafrQFE+JDIbCr9nRSH0pIhPykTmyWyyW74Xjz/8ALzHuqIo+3fkZVQ5ArZvbq0ivcQJofNWoZQenJhAWyZgPKVa1hWvb3jvJm2q2SGgLX9oWDYmwASYwN+NgMqvG7rSoyr1oYNxVScNvY5YKZYIUSaE9GP8XO1Bo89y2Pd8GPYjHm60FhcyASbQ9giYG00ksqnu7liG9PQL6OIfgjGDu6PoyjUUFSkNHupCJco1Nxdf02iy80BMgAkwASbABJgAE2ACTKARAsZbqdbwjoqNvA9cxASYABNgAkyACTABJtCOCRhPqeYdFdvxx4RFZwJMgAkwASbABJgAE2iMgPGUapLC1TcUs3yrxPFCaLiwKxMnJsAEmAATYAJMgAkwASbQvgkYVakWUKmUBSDn6EaTBXlG28qMLlqjMnEhE2ACTIAJMAEmwASYABNoiIBRNVdV9k7aFWl2Q7JU5yveikLKvL7V53zABJgAE2ACTIAJMAEmwATaMgGjKtWawmt1WQz2xyjKzbmWj7R0oTgDfewt6tbjHCbABJgAE2ACTIAJMAEm0EYJGFWptnUbgnULRmP2mh16ONwRNn8cRg7uC7lML5sPmQATYAJMgAkwASbABJhAOyFgvDjVApCOHpj+xr9RejUVSTvfw7RQclQ8tBXPhoehm5MrXlz+JRIzL9EWr5yYABNgAkyACTABJsAEmED7IWBcpbqKi8wJPsER+DAyDnlZB/DNhvlQUNmmNYswrF9/TNiUVlWTX5kAE2ACTIAJMAEmwASYQJsnYBqlWg+LsHtimVovgw5zCg3P+YwJMAEmwASYABNgAkyACbRlAka1qa4Cobp+DkfiY/HflcuxTXRO1JYMGT8LU58aheEDhHVrTkyACTABJsAEmAATYAJMoH0QMKpSrck7htWvvoMV25Nq6HiPxtsLHkf4UF+4y21q8vmICTABJsAEmAATYAJMgAm0EwJGNf9QnTtmqFCLkC4gdvN/MM7NC1Y2ruLjCbapbicfHxaTCTABJsAEmAATYAJMQCBg1JVqWFjWpZ6ehIO1c2vZWNcu5nMmwASYABNgAkyACTABJtCWCBhVqbb1noTS4kltaf4sCxNgAkyACTABJsAEmAATaDEBo5p/tFha7oAJMAEmwASYABNgAkyACbRBAqxUt8E3hUViAkyACTABJsAEmAATaF8EWKluX+8XS8sEmAATYAJMgAkwASbQBgkY1aa6av552cfwfWQUYuPTod3nxQ49B/THY4+HYaiPi5G9J6uk4lcmwASYABNgAkyACTABJtA8AkZWqtWI++AFhL22t460Bw/tpW3KVwLj38GZTZMgr1ODM5gAE2ACTIAJMAEmwASYQNskYFSlWpm6tVqhnrDgDYx5WAG5tQVQXoDMnxOw9rWNSNu+CC8M7Y+vJ3m1TWIsFRNgAkyACTABJsAEmAATqEXAqEp11uFEcfgJaw9g8zQPA1H8BgVhFO1O3jV8I1CoMSjjEybABJgAE2ACTIAJMAEm0JYJGFWp7u7Tn1jsxbY5i6GQzsDDvj3RpZMdNEV5OHn8F/x3JSnUlLR21uIhPzEBJsAEmAATYAJMgAkwgTZPwKhKteOgCHwyfiWe3Z6EJc8l1Q/HexbWTqUla05MgAkwASbABJgAE2ACTKCdEDBySD0nTN6UhdTd6/DieH8DRIrQiViz9VucT34VnjKDIj5hAkyACTABJsAEmAATYAJtmoBRV6q1JKTwDAzHauGxqU2zYeGYABNgAkyACTABJsAEmMBNETDySnVTMmmgUqrBbopNceJyJsAEmAATYAJMgAkwgbZEoG0p1ZosPNbFAxM2ZbQlRiwLE2ACTIAJMAEmwASYABNolIBRzT80eRk4kJwLWFJs6vpScTauUb69mteq68PDeUyACTABJsAEmAATYAJtk4BRlWrVucMIi1jeJAm3JmtwBSbABJgAE2ACTIAJMAEm0HYIGFWphoWlbub+eHttGKTqMkMS6lxsoV0VOTEBJsAEmAATYAJMgAkwgfZEwLhKdblWiR614V28NMmtLidNBqJIqc5Rl9ct4xwmwASYABNgAkyACTABJtBGCRhVqbb1GoMTGaFwdO5SPw5JD3yUGIVCe/f6yzmXCTABJsAEmAATYAJMgAm0QQJGVaohc4Crq0MjGKRw9+nbSPnNF+XnXYKK/B0lVh0h7yitbqi6fhX5pTWOkDLHLnDkzWaq+fABE2ACTIAJMAEmwASYwK0TaFsh9W5d/gZaFGPXrP5w9+iPbsO3QqlXK+N/z4v5Qpnw+Oz3Ar1SPmQCTIAJMAEmwASYABNgArdOwLgr1bcuXzNb2GByZC6eSN8MRz/DLiTCorX3G7Qd+lTYaYSl7DsUgeG0+YwJMAEmwASYABNgAkzgNhIw2Up1fsqXGDHyVXyRkHXbdlDU1OvvaAekX8ZfuVdFhZpV6tv46eKumQATYAJMgAkwASbwNyFgOqX63EkcPLQVzz6yC0W3C3Y9e8xY2HWj0dYj0MsHdiP/D9mq2zU498sEmAATYAJMgAkwASbwdyFgsoVa92FjoMBGpOE9DJ+mwpwRXhCiWJdR1D3Pf4TAz7nGubA13wxP2nymlB6qC8l4wWMMXvlmJL6e5CUO8fCw0bh06bLBcKWlKvg8oDDI4xMmwASYABNgAkyACTABJqBPwGRKtTLrECnU2pS2fT2e3a4n1tIolL7aClFAdOYf9VmByJz9MOctL8zIK60eeM/ur1BZWVl9LhwsW/4vg3M+YQJMgAkwASbABJgAE2ACtQmYTKmWdRmMLRvWQVyeNpCqDLY9uhrkNPdEZkUtvS0hvFSlvAtXKU62EyQ4h5jXMtBpbU2ppWVde5EOHUxmIVMlMr8yASbABJgAE2ACTIAJtHECJlOqJc4KjCOzi9z033HySjnufdAPrrZqZGdeQTfPBjaHuWmYxYhe9Sa2xG8lp0TgsYgUzHxzJR7vnotJHsE46O0PRXoSrZRPR+pErenHTXfNFZkAE2ACTIAJMAEmwASYQC0CJlOqgUtYP60/FujMPtYkp8Lnh/EY9mYGPjmagcmeNrVEvZVTKfo9PgkuIydhuYUEmhINnFzIRlvmhe0Zcfjt+Enk458Y+I8AOMtupV+uywSYABNgAkyACTABJsAE6hIwmVKdHfmBqFAPCR2Og9F7STJbBDz9MvDmVETtP0VKdUucAyVwpvbOdecLR1cvBNGDExNgAkyACTABJsAEmAATaC0CJjMYLinKozn4Y23kBmwZDKgFb0LnHphAL4WtNTvuhwkwASbABJgAE2ACTIAJGIGAyZRqSG1peknYF3cU564JSvUVZO78BtuESYsathFmz0MwASbABJgAE2ACTIAJMIFWIGAy8w9F+AxMeG4HFoSP0U4jaCBW6CY0afh9rTA17oIJMAEmwASYABNgAkyACRiHgOlWqm0V+CQnBm+P86uZqfdwfBJ3BJO9W+KkWNMdHzEBJsAEmAATYAJMgAkwAWMQMJ1SDQ3SDuzDkq+S9eZpC1trDsehB4QPmQATYAJMgAkwASbABNoBAZMp1XmHP4T/M+8ZIkrfgScDfPBddrFhPp8xASbABJgAE2ACTIAJMIE2TMBkSvW51N9FLMsi45BfnIvSgjTs2zBdzPv4+xNtGBmLxgSYABNgAkyACTABJsAEDAmYTKm2speTJP7wD/CCaPAhcUDApIkYRbn2cjtDKfmMCTABJsAEmAATYAJMgAm0YQImi/5xr6+wuctWhAz/J9bNGQqpJcWnTj+AXQKs5zbiK9uBKFMqYen6EMYFugm5nJgAE2ACTIAJMAEmwASYQJskYDKlWlVapgVCdtSzKbSeYdqKKRO36rIWY3jx83A0rMBnTIAJMAEmwASYABNgAkygzRAwmVIt6+KHLRvWAbRC3Wiy8YBVoxW4kAkwASbABJgAE2ACTIAJmJaAyZRqibMC4yYJJiCcmAATYAJMgAkwASbABJhA+yZgMkfF9o2NpWcCTIAJMAEmwASYABNgAjUEWKmuYcFHTIAJ3AEE8rMzkHaBY93fAW8lT4EJMAEm0K4IsFLdrt4uFpYJtDECmgKkHk5G9nWNoWC6/NTsAsP8Bs5UFzKQmH6pgdJbyz79fTB8P+dY97dGjWszASbABJhASwmYzKYaeYl4cdY+hCyfi1BvG6RGfoqNsafhPmIcXojoq41d3dLZcXsmwARuLwFVNmYEj8GE+DS85OtQM5YuH29FIWVe35r8Bo5i/hmMJ6Pn43zxXDhqipGZmYfu3m7N+x6Q+kMBiwZG4mwmYAQCdFGZlpwN69594N6xdX9mhTsx56xcoXC2McJEWj6ElY1ryzu5xR5KaUM5TkzAFARa96/9FmaQfeAHbIreCpdZL2JQyqe0ZflKbevtW3G9yy9YEdjlFnrjqkyACZiEgMQCbjSwtLYOq8uvW1C/lCHrDyDpTUdd6MxT8PELQcLVXPiJO0PV36ahXCsplagbKuX89kBg3O6pUNI/8xuVDYo74K4BmP3gQnSxc2mwDkrygZjFwM8fN1xHV6J6vZYiJtxtSc5Fdz8FHG/1l5IuKp8JDqt7sdmkFE1XEO7E+KujUPpq0xerTffGNZgAE2hNArf6VdFqY5cU5VFfo2ljF1vsitAq1G9/9h7SnpmPn9OpjJXqVmPNHTGB20mgsJHOq8ryM5PxS6ELhvaR4EBUHH4/B/R7JARBnk5i69KiIlwvlECjkeFkciqtNHshZX88ShzvwUODPCB8UeVlJuL73cdRKHXCQ4+Gws+1ZqUuNyUesSl/Qm3vDHVsEjoFNSIUF7V5AhU3ylFuVgGzBnRqM5qB5kYFKisbqFA9QyqvoEct66Tq4kYOlJnfwj94ORIu0cWdbSMV6ytq6GKzvrq3msd3Ym6VGNdnAkYjYDKbao24knQBiTu3Ym00zdf7HTwb4We0ifNATIAJGI/A6f1rEBY0EHZO/RH2zOeI3bYIIf1WI1un7Jze8zJCgmJwMTMaPsGLkIYMLHhjMkI2HYWKxMyOXoVu/cZjdmwGkrbMR6BXOOJyhcYaxH8wDfcFTcbsLb8gfu1sLKHvE3vjTY1Hul0ESBcWVOaGHmLB7Rpb7FfYRMG/ya0UGhKh6oKyofLm5ot3YprbmNsxASZwWwmYbKXaxacPTew9PDsxSZzgsv8LQenhSGyjs2mdm3HP97Zi4s6ZABNoDoEq5VYidRabD1m6GdtfDYZd5pew6xeFK6Qxu9MqoERKe6Z626GjdwRKC+7HCIdl+NfBSPgIXwWaLLwasR6Y+jHOrwuF3fUZmOsSgjU/ZGDoo6cR8tpevPhZHFZHeFHlAmwcqcDXzRGW2zCBRggId1t+K+yEe63PIirhOkKeChc/u43dQanuTjAlOXAAP/6aA6m8J4aFDYOnXLBTAnJTklHSyw8ul4/huz1H6E5MN4SMGWFgi813YqpJtuxAtHU/hvTsyyiztEQnx67wUHjDs53Yp7ds8tzaGARMplTLBz2PpM+kWPvNL3AKmoqFg5yQFilECvDHY4PdjDF3HoMJMIHbTKAQ5boRlPS6WFSoSX2GUrdCXe+GqhptYZmuDlQqlAi9bJ6JrpuFA20aQi9nfj1Ez6Px9GhBoRaSAwaG+WMD21RrcfBzqxEQ7raELNQuAgm/U95PjAIS1sBbuOAbPBqjru3AkoWfIiojBsFyw2HTPp8B/zlJWLj2DZydMxML5izGmeLnIUcxooLGYEHocCB6L11Y+gPpSdhSWOXgK9yJeU68cIT3cIzCXuxKB0YFGfbPZ00TyE+PxrN+M7FLrOpFJmYUelPXbMvvWRjnrr3IabonrsEEGiZgMqWaXJvgEzEDb3gPxMkr5bhAv7k+EfOQ/sAVdHM2oVgNs+ISJsAEahPQKb5q0epZr1Ci/RsO8u6qyywSV6Jr+zPqtWj0kEywsSwuFYvIuFVFY0okHShHgrTPBd8MOawbbc2FTKDlBKrutiyMPIQVoW7iHZQXG7iDEjzVcDyHXk9jy+53yYeI2j1kiW10l+aUkpRquktjH0p1SaFes/sIZgW6IG1TBHw3pENJUXNkubHt/k6Mue67wJCIcc80udHoSgo1vKcjZvtcBLlrIxVpVFdx9OcL6M0KtXHfkDt4NBNqr5ewflp/LNiupbuGnJN8fhiPYW9m4JOjGZjsWeOEdAfz56kxgfZNQCZDT5rBklf/i9Bvnoen6NClRuInH4krQmF3ixnNmGM+ykuLkVekgZw0D2GMHTuPYOagUDESQ152FtDVAx4PBlDJcsQkz8OsQV2gyk3G+7Sa2Gl1M4bkJkygUQK08uP9BuYJCrWQGrmDoq1Q8+xKn9uHs9Pw3aaP8MPXgmP+8GpbbXUOmTxGahXqmhbaozvhTkyUS0XtaRn5XI0f3iWFmu5oJfy43MDpVCJzgl+g1lm6SqiGzHlEMx03T5Qm/oBfLPpjSqgXLtRjuhM2MRSuOIfob2KRmWdp4JCtysvC/tiDOH5WjXv6DMSoEX21kWU0V5GceAY9A3vjcsI+7Dt6Bvb3DcUTNEZp9jH8ctEOQ3UO25rrOTiQeBk+I/wgN6EGV8WLXw0JmOwtyY78QFSoh9Btr4PCbS/YIuDpl4E3pyJq/ylSqhWGkvIZE2ACbY+AxAPL49/BpqBF8OmyEqOmTkTh5q04SJIOWfoFntBdHGsKKbRZelm1MQjKaeUaSSjTzcigXFz9zsAwN8GkYzHFrn4er+ycj/vCyfxjvRdGDc7ALrL6eDsxAy/5hGLN4OVYEEwX6N5UPz1D7FGhrjI70Q3AL0ygxQSEz6ylQQT0hu6gQFNlWCAMqsZ3sz3wpGC6NHgilt1PJh6C1ZIuCZZK7i4dq04NXguvtv87MaGdBFdT4ybBubk6qU7hB2I/5K0pBgp1dbnegeAQXa85j6saUbPITIdMb8Q0fh0mhbrWa7qzIHYiRlG44F0UwWiIdwaWvHYWJ4pfFRXtpW5D8SGtlq+bIqXADGEYtTYOX0/zgjLzewQ+spwu2qh3GmPIYC8cfG0lCuk7LiznK4RN3IqYnFwEkVlRxrcvI2yON/XJgR1070abejGZUq0NqeePtZEbkDqyB84Jv4HOPTCBXoQvKk5MgAm0DwJy30koyhmIWGEF5q/LwFvvYNHwYAR518Sa9xi7DgnD5bo41IDMLQQxcUPRW7eQbVBu64WPdn+MGFqMDiSHLsEG2zF4Ls4fHYRdP52AWmqLuf/2xwBRYbfBrD1p8NkZi9TzZbhv0FD42OfjVLnxN5xoH+8WS9lqBGQN30Eh3acmKf/Cx6TUva3bIClz5yqsWP+XYL0kJsGSV91AzD++E1ODsdlH5KMhXA65yK0Mu6BNpvLyteq3lZ0TbCVZeL8hc54XesDejZqnD8e+rP8gwFl414rrMd35J3znbEUhOWTnkUO2TOeQLZi3ukrK0X/1OqSSg6twR6+/ej9mFIorCNSXzrskfToScpbAT16Ad2x8xM+F66jppBdtxfqoLARNk+MHss0ftWEFKemc2iIBkynVoB9GkNPFvrijUF+jL5XyK8jc+Y0Y/WMIrzK1xc8Ky8QEGiQgkXsgdBI9Gqhh6+oF/XUVSUc3BA2qqWxYLoF7YCjZl9aUC0eOnn50B0u/l6pyBwSER0AwBNEmF7Ky5sQEWkigsbspQtcSt4bvoNBNE/pZQ6GwWGTrjBH0siRoLP2+1TjHbd2TA59wOQppZVL/J0+jFu7qFIl3dRz5TgyRa2Eim2476uL3vFKDjpRp/0W3AMEUR3fB06thh2ihjtZMZ4VOoRZyqvL0TXdIe9Y5ZAsajoFDtswN416QI+1wPDYeTMDXZOrqZmCm5kWr0WSeIn55ySCnVWsxLCPdDZz5lj8C58Qhe6gHVlC/USOEu3ic2iIBkynVivAZmPDcDiwIH6PlQjFshQ+LkCYNv097wM9MgAkwASbABExAQLybsnsgesq0gxvcTdHJ49rgHRQvfBX/LdDThmpK8EJOHHpE/QKlUw8EBXngzN4ElD/oTGUdEE71ysV62k67j3wXMb6OoiIIdOE7MTrWzX6ReeBRchzd9to7iBsfiWABOyVbxVSc//1+jO8zvnrj1wbNeWhVuj4znbp5tCZOoUEttEMYPl8/hqkuYeLC4ahZizGAViB+NqjhiI56i+lC31XJb/wMKF6bCm8hEnHoexjMqwZVaNrcq8mUatAt3rVkR6RYvgpLtidpwfT+B96e+zye8Ba+iDgxASbABJgAEzANAfFuSqBb9eCGd1Oqsxu4g0J3W3xr7qrI5F54nGxnq5JrRETVoUE9IdPRvS9Fp6gupgO+E6NP49aPJXh08RdQbJ6MMI9p2BK/AmN8XSiCkBSOd2mjgIh9NmbOQ5pSfWY69eU1JJ8y5xgp1P60Q2ck2XYX4ItpK2sp1YYttX3r8pyHYAFdGEwhM6KFdAtPd51n2IDP2gQBc1NJocncDrnnKgzfEImiq1nIp0f6QgcseXYs/nP4qqnE4nGZABNoIQHN9XOI37kTX3wZie+iE5F5obiFPXJzJsAE2iuBStIyjP2ozUriHIS9RzeLcb6nCDu72rjC1y8YVl1CRKdqeytSU3XmPGnrySHaJhhPjHRFtz5D8UWG9vurtpmOMEbtPH3THVEG0YQoX3TIltkLPiZJCHyYxrVR4NntwEGKa54mmHXXMjUS2hr2LcXDY2dR7mhEDKjxVRHqcWpbBIy+Ui2EvPrPN+QZfSGRSOTj83Wb4SZckkktoc4U7JGA2NQzeIk2g+HEBJhA+yKgzNwJeb/ZdYT+5GgWJt+rQWZmHrp7u93ESosGFzKzUGjvyrud1aHJGUyg/RAomNJMWc302t1iAJH6VnIdPYPxdTHZtB8+jGN/XiJzDkvYOd0Fz169oPAUlBByJmzQnEdTx0xHWLtu3HRH65C9jxyy7ycDa4ltKE7Ef4HY42fh3Gsg/Hpo8OPuk3AgLay2qVHdvtX48b/rIYRMU9Q3OT1UfGhaAmar17xf6dTJBhPGPWIUSZSpH0Gucw5oaMAhq2MQ+4KioWKj5i9e8jZ8HlAgIuIxo47LgzGB9kdAja+meWDK9ulIubQcCvoh0SjP4cC+HPQPD4AjhRmzcghBwtVc+DX5w6DGehsPLHgrBqXz2sZ3Qft7P1hiJmB6ArIM48epUHnlmn7irSiBMj0Scr/5vIdHKzJtja7y8wuw9PV1WLz4Fbj36CF2afSVaplbGBLiB6OEQs2EPLcVn+yOQR8yayoTvKQFf2cLO/RUeLTGfLkPJvC3IyB7yAQ/YD9V/YBVhYcCrHVKs8TWBcHhLqRdFyOTNnhSUOzWlP3xKHG8Bw8JmxloCpB64AB+/DUHUnlPDKMQep5yKfJzf0OON6C4kIr4hAJ07t0fCspvaGMG5YUMxO0+jFPkLi/v4UnOYAPg2tHoX29/u88bT5gJNEngRpM1uEJjBJQZeJUUalBs7Kq4/41V5zLTEjC6TbWkowv8fBUICp+NhMRDmBCogI+PQszz8+0NZ3ur+j1nTcuJVPGSXAAAQABJREFUR2cCTKBJAjYY8tRiqrUR3g7/xHcpgi+9Nikzo+ETvAhpFFJswRuTEbLpKARTwrTPZ8Cfvguuy+3x65yZ8HGj+K7kab/r9SX4MJ3K1y9CyCORuKLpAGFjhm79xmN2bAaStsxHoFc44nJJkVdl4BmPYDz59W+4cOE3PDtxPP6VeKlqaH5lAkyACbRbApqii/iLduDc9174TZjNtdtp3jGCm24pRyZB3uEv8Oy6C7C21saRKbn0K7ZFZ0DxVhRS5vW9YyD/HSciOKsd/SMfPf0U2m1Y2xiE1pRP2Db2aA7Qz8etaj+H1pktreKmJWfDuncfuLeTVVfnwOeRneiMOQGz8WTQDgr/NB9J/34ePt4RKC24HyMcluFfByPho1vJduj1NLbsfhfjhCgLD1liW78onFI+j8mbdtEuUB5YGxaHlBe8aKU7Cy82sDGDf2CquCX6i7PnYXWoG1avfBca8uznxASYABNo7wQEJ8vY4qD2Po2/jfwmU6pzd32MsQs31gt6QA9hDzVObZaAcMs+ORNlFvVE4ywvh+XdnvAojEJg8EoKH0T2s2Rb25J0IfMYsgvt8KCvh+GVuuoqko9eaJbirsppPflUOTEIDNhBc41r8VwNOKmy8UxwGCbodmIzKGvDJ84+4eQQFIzU6P9iRsRK+EcXIL14OdxpZzMhldVYicB1UCgezk7Dd5s+wg9fCxsxDNftLaYR48J2qtppTtXwxgy23kPx9mDaXCNiMD6kbaC3LJuJcYPchKE4MQEmwASYABMwGgGjm39Uzezq1TN0OBExR2OwhoKgw3sxkuLfE4t7ubFSXcWpbb7mYWPwGAQGhdV9UP4r35ONLdnGg2Jy6jZfbcE0irFjchiGBQ3F0ugcg36UGd+T4h6Cv7Q7zRqUGZ4IkSQyDEO7tZp8NJLYl2MrzNVQakgs4EZZ0nquXWrVbIOnNvAJfR5747TmIL9l629lUCWuGt/NFsJWhZDpxmn0vN+/qqDeV8GYZFlcKq14a0NwFhWcQvSzghOjC17acwrpiZvxIm3nOyV4MF6MzKq3D85kAkyACTABJnC7CJhspVo7oTxYdFJg9NMTsSDiNK6XO4vZUYdzMctHLyj77Zo999s8ArRt6ofFufhQbF2AjWTisWGCocmOMj21eX3X08q+D2WSfe2HEW8i/NwmBHTUVbIQVPabUdwrsKNfcPuLJCFpMkRGPbRMmaVB4qZPcfnB0XjUp4toCnPu7GkSyAuOdlXmGPkoLy1GXpEGcrtcfEybGbytW4nP3LkKK9b/JWxAV5OomfL6VQpHZYuelLtj5xHMpNVtR6qTl02Kc1cPyCV00ZRbAHefYKzekwpnGx9sO0c7m3FiAkzA5ARUvascmU0uCgvABG47Af2fr9s+mP4A3e/vT6crMWxyJM5vH01RAcYgJHirWMW+6vdXvwEft1EC9BHqRP/rXU61I/2omMwAovHjiatwIcV2TCBFfNDNpKFIDrUnqqYlyiEL5sNlzXsYNn8n8jc17LBRX5/1RZJwEwdpnny5KckocfNEaeIP+MWiP8ZqO6sWW5WXhf2xB3H8rBr39BmIUSP6VtuVi217+cHl8jF8t+cICqXdEDJmRI3NNJnWJO6Kxc+nlLCX5oq2wkFVPWvI3CV2P34ilvbybrh/EMU6dW9D8dw1Z7Fzzkq62BLMOGqSYtZmDJTTuRiGPgPD3MhGGotxvjgCI+hoSdBY2mmM4sfqmmzdkwOfcDmk9rQ5wpwQyOcA/8s4hVd2zsd94bQxw3ovjBqcgV2HSCFPzMAc+zi496HY2N7DMcGtSNwGeBqbkOlo8gsTYAJMgAkYi0CVfmOs8arHcfSdioTP1PhvtiPsOvrh0w2zMGPtfnTqMxrLx3Fc2mpQ7fpgL3y7CAoUKcVk83rwtZXolHUKwc4SMZKDt+B4Nng0Rl3bgSW0s1RURgyCXRv4SPYchX/FS7EtaDZWjvfHiuC6u0oJ0SHq9vkNLuoiSSCdIkmsH42YrAGiWQXQHPnUiJo1Bgto5VxMFOYo/CXdsfhyDkvdhuJD7+lYN0WKZyPCMGptHL4WtyguRlQQtQ0dDkTvJSWQzB3Sk7CF7M9Fx1xVFpY5DcVq6kdBddKEOpS015hkKjHPB09u9sKLsx5CLLGcHboO+ZGGFxgVh/JhRv+E/8ZLulVhCTkJ0uYK0w+nIPnPs+LmCt3v98NQX50Dp60XPtr9MfEHAil0niPN7IWcOPSI+gVKpx4UBs8DZ/YmoPxB4Y6VFE/8OwrqoHR0HzRU+7lwnYvzRwdh108noJbaYu6//THA04Yu0kYh+2h3HPntL5y/UoYxc1fiH2xTbby3n0diAkyACTABkUADGowx6EjhF/EinNN/x08Jybg3/FWkTJqH7Mwr6NZCxzZjSM9j3CSB0MVI3/w83GUZFPkhGL9fKkawPA/vNxDJIbihTX8KVZD7zsCWqSsxJXwxRl/dRHc39BJFh6i/z1zE1o4kQc2U13Rtb1m+HrB3o7bpFOIo6z8IcJZCmf6lrjN6UZWj/+p1SH0qHJ70Oe6v3o8ZhTWeefaC/wApy2t2H8GsQBekbYqA74Z0KCnazR+bF5NCPRzf/L4Woe42ZN+QDF+3MaLDHnWM8z9T26mzsPzdcNi+uxwq6ra2gUilzA7m5uYwMzOiVl2ib2phA89BQfSoQVJzJIF7YCjNuyZHJvfC4+IFhzbPNSKiulDm3BfTXzCMAuTo6YfJ9DBMEjh79sXj9ODEBJgAE2ACTMBUBEzmqAhcwvppPXCfXxjFoR2DqNNXkbhqFLz7DcS2zGJT8eBxW5WAFxIEhVq4SCINkO7ma1dd9SM52LjCziUEm25qXAnGvfkthtAKs/87ici30nODbLTPWpEkqsdqnnzqHGBa5ApRoa7uqupA5oZxLwSj/Hg8Nq56A6+8lgE3PXMmbVutQl3VRPtagONRScCsyVqFWsi0s9atqAsnNvB9biKweTbkNsFYtike+qqsUIMTE2ACTIAJMAEmYDoCJlOqsyM/ELaxxxDhVriYbBHw9MviUdT+U7o8fmnfBPQiYtA9EdrsrjqRmXQDkRyqq9R/QKZCGyOnA2vG493Io1RHiDKiTbfeZ/PkU9Nw7i5V3pJVo+terx/DVBsv+AZPRuy1uzCAVqb1591wW+1NI4WznoOuRJun7VkCv2mrkJcRhy1Le2P1nMno9mSk1ky5lgh8ygSYABNgAkyACRifgP6vtlFHLynKo/H8sTZyA1JH9sC5cjp17oEJ9CIoR5zuPALCSrWYZI1Fcqiq1PCra+hcrBu/EbPf3EqVRmsr3kyftGIsRpLoWL9z383KJyw8q6viJ9cSU5lzjBzl/ClmdSTFrC7AF9NWQrDaqEoNt5XAqSftIPjaV0ib0RcKWt3PjD1g4KiovEB/Ga5eGPfqv+Fpr4T/wkTkqCKgqG0DUjWYiV495+1FIQWjLihSo2snG1wuVsHeQoJSVKKkuAzunW2Rfb0EcnJuVVNeIeX16WIH/2vnsAHNu6BWbXzdRLPlYZkAE2ACTIAJaAmYTKkGORoJjmL74o5CfY2UlPIryNz5jei5P0QtaNic2gsBNUVhODii1ntWLhgn5KOsahKacuTQsfjWStwajOTwkg/ZEtdKdft3wPS3vsCG7ZMpYsQF7RiN9klmJ6Qx60eSCG62fLTyTE6KBh9Rsa8kUQ6ZveBAmYTAh4PJ7jpDO5PtnyJt6r9F5bd2W406n+oVoZwMYx59eTMUm6eSc+dWKLxJwdY5Q2rHKsbnHgOxgHqcMH40tm0nJ8bQ9+DRxhRqYcJXCkpRXlmJ0Qpn7M64hLvtLeFAGwX9eU2JMK8u2J+Vh7ttLNBFZon0/BIMc5cjOfcq7vH0ROUzTxnXHlz7DvEzE2ACTIAJMIEWEzBbveb9SidaTZow7pEWd3ZLHSjTMLVLiKhE1273SXIGJnvXVa5q1zPG+eIlb8PnAQUiIh4zxnDtcAwNslOOouQebyica94zjTIHP/+pwQDaBVF75VaMtMMn4NSvL5x1imB+ZnJ1JIdevkIkB21sY0MIVf0/QP0L67w16UJKPI5ctkZQqB9FktCmhvpUXTiGL7/TRZLwcUHz5dPKU96zHzx1W4cL25T/9Fs+HgjQhs7LJblij5+Fcy8KeddDgx93n8Sgp0PhSvGUBVb6bfOzj+G3q454SBchQ3UhA9/vPowiaRcMDPSGJvcynO7vB1dbCVR5OTiSnI6si5cgdfLEsJEB1SyrqKSdtTK6o2IvZ2XV8OJr+PKDOK1U46/LSgT1kOOXvAJ0s7bEZVK0L18txqieXfDDmau4394a1ysqkEt5Tz7gAlnRNWwcKFxs33pSjXzo1htxCybABJgAE2ACzSSQn1+Apa+vw+LFr8C9Rw+xF9Mp1TS8Ji8Na19dgSXbk7RT8h6OT/5vBSYPcmnmFFu/GSvVrc+Ue7x9BKxGH759nTfQc+kOw1AfVs/sFGsOIbvzg+evo7OVBWQdzHG2WI0BXRzw88UCdJRZwJZsxs+WqPCAkx3SrhTS/qpF+FxCJi5kEnKrSbVh0a024fpMgAkwASbABJpNoD6l2mTmH/kpX2L80jRMWrQS+etdxUnJZIYrkc2eKTdkAkzAZAQ628lQWK7BL1eL4GgrQz7Zr9hTmD9Lsqs+nl+Mu+ytcIWUaXOJOawsOuD49WK4drSF6m452bbQHSFjhgM0GSUemAkwASbABO40AqZTqs+dxMFDW+lxN0YVz62+fX+nAeb5MIG/G4EbpeWoJFOPQd07ISU3H51pVdrJsgOyKIb3ABdH/H6hAI7kpOhCjxOU53eXPc6SCYjF5VLgx2autD818u+GmefLBJgAE2ACbYyAyZRq92FjaPOOjeRo9h6GT1NhzggvCFGHy8izzfMfIfCrZT/bxrixOEyACTRAoJfcDrklZTh6Nh+eTvY4UVAMiaUE9hRX/LfzBXjgbnskXiqEi8wMHa2k+PNyEQJdnWB7+gRw4GQzjD9IEFaqG3g3OJsJMAEmwASMRcBkSrUy6xAp1NqUtn09nt2uN+WlUSh9lXdH0yPCh0yg3RBIPEcRTTqYYbhrZ+w9nYcutlIUqjWiyceQux0RT06KTjYyFFHeRbKzFlaqf8i+jGH9fID5rzYv+of6QqN88rPT8MfFclAQkupUXm5Bm08pIDfZt2C1KHzABJgAE2ACdwABk/2cyLoMxpYN6yAuTxuALINtj64GOXzCBJhA+yFgS3bU5WRTnXqlADbWMhRQzOpySzNIyFkxk2yq7am8qIxCMJpbwFJihgyyqe5sL4P8PDkpfrG1eRMd949G253eswLDFuocoqtrTkTq1VWsVFfz4AMmwASYABNoCQGTKdWa0gs4dOAIrJysDOQvvVoKn6cCDPL4hAkwgZsjUDsSx821at1aj7jJodTcQCGZgNxNynKesEU9rVyTxTRKyd66e0crnKYNXzpLOoibvxRRXi8nG3gUXETl75nNE6YJpVoi+EB7v4HzyVPZf6N5hLkVE2ACTIAJNEHAdEp1YRY2ba9/VUrRcxymB7adsHpNMORiJsAE9Agsn0QXxWaUcYuR8ew7VAASYSP325UsoWf9UT2IENv8t8JOuNf6LKISriPkqXC4ywqQeuAAfvw1B1J5TwwLGwZPuTY6UW5KMkp6+cHl8jF8t+cICqXdEDJmBNx1ccuhKUBybCx+OqGE3MUVfQcP0sVwVyM1LgY/pl2gPnth9NigOnHGq4XiAybABJgAE2h3BEymVNt6RSAlfjA04q8ciVFwHK88Mh8HCeHrEfe1GGR+3iXQAhkkVh0h76j9MazqNI9+RH/6LQ93efdHgLewAx4nJsAEWotA7y8+bq2ubr6fl59poq4d7Vx5FueuF6ATmabQNwMc5Q7ixkSn969BSLVpiD+8nxiFkq9mwH9OEhaufQNn58zEgjmLcab4echRjKigMVgQOhyI3kur3/7UbxK2FEYhZR75gaiysNBpKD6kEUbRzpc5ry1HWug65EcOxdfTFKLvyKjxw7Fr+0os+PIdnN8ziVfOm3jnuJgJMAEm0F4ImEyphswJCl8nPU5e+DaRVnYCliP+zzyEutfszqdX6SYPi7FrVn88G03V6ZZvHt3yrdqn7ULCR3B/ZCXlUxltA70w8ghWhPKq+E2C5WpMoEkCFamnmqxj/ArCN8B6+Lisrx56TWIGZvnYQCJ1FvMWRh6i7wI38Ti319PYsvtdjAuk84cssa1fFE4pSammbuxDqQop1Gt2H8EsuqOWtikCvhvSoSSl+rePFpNCPRwxWRsQ5Exfr+uXIU9D33OZkaJCvWznESwKdsGFp4TvoUX4Nv1xTG8ju8eKE+cnJsAEmAATaDYBkynVqtxEfLAxBdLqVWRaTb7+mziR4ycoeoDux615M7PB5MhcPJG+GY5++j2cw/ukUA9ZHYXYF/oi7ct/wjdiHSYWrIKnyUjoy8fHTKD9E+jw+XtGn0Q5rSA3nmgrde/FSN/7JOzElWrAyq7qwl0oewPz9L5zXAeF4mGKGPLdpo/ww9d0EU6KsqVuAHUOMI0uxgWF2jAV4M/YJGDBdq1CLRTS4oGcXtJSEsWqK8IHYoV4xE9MgAkwASZwpxEwmSqpuXocK9bU/+M7oF/rRP/QlBu+XarMRFpF8kLCU9pwfYqxMzDkuRDsS1sKT1qx4sQEmEArEPj0y1bo5Ba7eOHxJhoUUbkd7uroUH3XqqaBUKZvb63Gd7M98ORmyh48EcvuJxOPQzW1Batvd9qCvW5q6ut0NJIuvQeFpAKiAQo5akpoq3ZOTIAJMAEmcGcQMNk3uswtGDE7768TUs+isxsGtJadcy2vJI2mjN41x+oVJ8Gu0l58H4WfOE5MgAm0BoFK5fXW6MZ0fSj/wsekUL8dn4aXfB2QuXMVVqz/S/i6EJPgoaEW1eLaIkrhMcALWLMZ8dP7I8iVapLT4oV8GTx8A6jyfPyYNA8+wW7UVTEy06/gXm+Xqm5rd8bnTIAJMAEm0M4ImEyplnT0QFCwRy1cauRmXxEdDG1NINmXW7+GUlliIFN6egZ8HlAY5PEJE2ACDRMwW/hSw4W3rYRMxhpJmkIqTy9CrZtXYgttWVlNma0zRlDJkqCx2IaM6k2qtu7JgU+4HIXppFTrdaRRV/UtQdDCDzBtTQhCvDyg0DkzpoH8OorHYcvU+ZgSPhhLBg+H4tBe6tcfKVcjoZA1IjgXMQEmwASYQLshYALVVcdGcwnRn3yGb3+9AGtrbazqkku/Ylt0BhRv6TzpW4pR98NX9fsnkWitIoX16qpUKB5oMQgKtVJJ9pV6qVzDq9h6OPiQCTRJ4Mai15qs0+oVVs1vtEuP8esQ85CMDEDqJo+x65AwXK4XhcMJL+TEoUfUL1A69UBQkAfO7E1A+YOCQ2MHhMd/i/KeNeZi3Ue+ixhfR23ftgp8WJCKCbGH8OdpJaRPTkVAQH8yOZFi3LoseI/dhyPp+ZDOnEz5/hS6r648nMMEmAATYALtk4DJlOrcXR9j7MKN9VIb0MOx3vxbzZQJurq3Jaq2l5F5BuBFugW7+qs0MbxVZtQWCuE3Gmu9tD+QM597us4Q166181vZdWbEGUzg9hIw//3c7R2gGb3bOnuR82D9DW1dvWDgz0zVZHIvPD6NTDl0yTUiouoQ7r6GtR3d+yLIvbqYzEScEBAajgC9LO2hFIrAUHrUKeAMJsAEmAATuAMImEypvnr1DOGbiJijk5C+NAQLchYjab0T/IPmo5dbS5XqYkSvehNb4reKYfMei0jBzDdX4nFPF7y0cz7cw0PgG+uFNFoVf5HCaHnyatEd8FHmKbQVAqro99uKKCwHE2ACTIAJMAGjETCZUq2dYR4sOikw+umJWBBxGtfLtUtJUYdzKX6sQwsgSNHv8UlwGTkJyy0k0JRo4OQiuBcBzsFzkZ3si33HzuHuxQEI9nFpwTjclAkwASbABJgAE2ACTIAJVPuzGx9F9/v706ArMWxyJM5vHw0FxiAkmFaWKdlr9V/xuHlPEjh7KtDA3V44ewdgsnfzeuZWTIAJ3BkE+vh/AphLaDf1GzC7UamdlLm5uL16pbDNOqUP3hwKP1/BDERXLubWPJkJ+SXFsB/VGzJz8tYQqgltde3FmjcAwVNDkpwrnvITE2ACTIAJ3JkETLZS7eg7FQmfqfHfbHLw6eiHTzfMwoy1+9Gpz2gsH8fRNu7MjxvPigm0HQKVpFALSrWYBCWYFOJKs0qYicekCaMCNtbW6HIXbd8iZmqrGj5XouL6NZh3oNxGvk3NhO44MQEmwASYwB1NoJGfgds9byn8IuZWOwj5THoVB/q6Q+43H+8PGorNek5Ct1sS7p8JMIG/IwFSoCt1K9C6pWnSqSkJirWwBq1dtW6KTCX1ITTXX5xuqg2XMwEmwASYwJ1HgH412lLSBrsrUnMYu7b0rrAsTOBOJGBWpQbrFGmt7YYw0yr1uOr1Jmav081voiZXYQJMgAkwgTuUgAlXqu9QojwtJmBEAlY2ro2OZk42wi8+a4Ynn6hA1aJsfQ0E9fGuvYDDt6jZBKW+ipTncJxtgxtAw9lMgAkwASbwNyZgZKVaA5Wqol7cEokUpSXalep6K3AmE2ACzSBgBrmjGby6U9MmVlMtncgsmJyEm6hGbn2cmAATYAJMgAkwgdoEjKpUK1O3Qx6wqLYMfM4E2hcBTQHSkrNh3bsP3Dsa9U/o1jmRbbBUZg4Ha2pa//Wstk/BEEzYA0l4bUKrVmlb8DMTYAJMgAkwASagR8DIGsFNrkS3OKSe3gz5kAk0QCA/Ow1/XCyHhYVQgTazt7gL9/u4ocm9gFTZeCY4DBPi0/CSbxPx1FWXkPxzHnoGKvS2wW5AoNuRLdh8VNLa8s14TwhL0E0o1LdDRO6TCTABJsAEmMCdQMCoSrWtYiLyLo1rkpvMVrtteJMVuQITaAGB03tWYNjCJMMevBfjRPLzaNRSWWIBN2olFZVxw+a1z5QZOxD4yEr8L+MUHnc16p9bbVH4vA4BvoKog4QzmAATYAJMoNkEbmb9qtmd12lIBpu2pDA39WDVow45zrgNBAT7YXi/gfPFuSilx4mdi2lb+5WITS9ucrTCJmtoK9gqIpCUeADBrFDfJDFjVruF6B7GFIvHYgJMgAkwgXZJgPXXdvm2sdCtR8ASVrrOXBUe4lEhbWtflfIyE/H97uMolDrhoUdD4eda/10U1YU0fP/dIZyDHfr4+MDZoRxXCuww0I82DikpQil1aUt/bcrcNPxW6IwAb/IKFBKZh8QfOg3voX6QU3luSjJKevnB5fIxfLfnCI3bDWETQ2nl/Byiv4lFZp4l+j0SgiBPXXttL/zMBJgAE2ACTIAJmJiAcVeqTTxZHp4JGBKwo5Xps/g1PQtpqYl4559TqXgWQvto7aSzo1ehW7/xmB2bgaQt8xHoFY643BqFu6ovTW40HD1CMCX+Mq7/+TnCgkPg6xeGhbGnoEz7Fv7BL+OUzrsv65sQDPvhTFVTKDOiERK+RFdejKigMfCZOg3yPmF4dssBLJgzE/c99SqecBqIsc9tQ+y2RQjp9yk4qF01Qj5gAkyACTABJtAmCPBKdZt4G1gI0xCwpWHXY5jf+prhx3vBRfBU1GTh/QjKn/oxzq8Lhd31GZjrEoI1P2QgWNC99VLG3h10thhnIp+HHGr0vOSBZ+3WIemNYKjSv6QyR1jq6kuk/lBAzxjbQiipKbcPpdPovViz+whmBbogbdM/4TtnKwqXbkbeq8GQZX4Ju35RuKAEXAXxOTEBJsAEmAATYAJtgoDxlGrNVcTvOIRLTU67DLY9AhHq26XJmlyBCbSMAGmmZFOdffgpOGrUOP3zd5j0yGw8M8gLX4/ToETofPNMdN1cM8qQmsPqI426qPq45sACdde0SVevqVDvkToHmBapVai1FUhGUti3k0It6NBKXQdVSrq2Dj8zASbABJgAE2ACpiZgPKVadQYLn5mNtJuZ8dIolLJSfTOkuE6LCAjKsCXsJBLI6OEZ+DgmYBGWZOZCBWeyYgaWxaVikZ8tVKTMSiQdKIf+ZDSGn2KvR2dAsXAquk0rwDLr/VgRLbTrL4bmE1TixlJpwRWDYjWdubt01MsjGb3t9Ne29cr4sGUEOPpHy/hxaybABJgAE9AnYDylWtYVr294D0rLxtfYysrK4Orrri8jHzOB20igrHpbbmVuKoQAe0OcO0Mms0VPOt6x8whmDgqFI/2l5GVnAV09yMTDMMnkrmKIPbd77oK85ywkvBxCDo31B1sXIo6kRf0BzTwFitJ34pHg96iz4dUdCq3UTa5nV1fngxYR4OgfLcLHjZkAE2ACTMCAgPGUakkXhE6KMBhcuBmem/47Tl4px70P+pGNqBrZmVfQzbOJDTVq9cKnTKA5BMjigxwVl6OrzXK95l7432P30YK0DV7ZOR/3hZP5x3ovjBqcgV2HgLcTM/CSF3CNWhTSfjFCStu8GrvodWEXW4r9UYbjP2zF8c6eeCwsAFblwmp4EuVqk4XUGTg0H6EjP8XBQxlQeFN++pnq8sJ0Uqp1/QotNOp8Ki+qVvwh9pdfXV/bKz8zASbABJgAE2ACpiZgPKW6zkwvYf20/liwXVuwJjkVPj+Mx7A3M/DJ0QxM9qw/dFmdbjiDCTSTgMfjK7DPRz/itDXc71fAWecA6Bo8F+ePDsKun05ALbXF3H/7Y4D4ufTCV/HfAj21n1G3wKEkwV6sjkrEtJ5CgL5SbNq8HKlkG/1/ASGI2T0QPXXbNHpOojEtfZFKVh8LVgVjqJcGP/98WVcuRTj1W67rV5hW95HvIsbXkZR1bZK5hWBf3FDcr5NRl80vdyiB9ZuEy7WG08FfivDrnyWo1Ft0L6ItQp8ItEfvu5v39T5r2qiGB+QSJsAEmAATaJBA8751G+zu5guyIz8QFeohocNxkKIdUBRfBDz9MvDmVETtP0VKteLmO+OaTKAZBGydvRBAC8eNJUdPP/os+tWqIoG7b01e1pEDZPe8GOf3PK/bilyNXpt3IOpiESQdvRAU6KbX3gEBEZMQoJcTQFE+tMmwXyHP0b0vgvSsoSQd3RAwSFedX1pEoJL2ZBd1UbN6bKtFLfUGIJSZ6Wms9Yxo1kR5PU1uOuvpJ2vf3TNsmoNMxFw5ZaBUW9hIMSLEBw/3cjSsfNNnJTddkysyASbABJhADQGTKdUlRXkkhT/WRm5A6sgeOCfc8nbuQY5iEB3EakTkIybQlgmokXmYLgrT5Th8OA3dLa7gh48nYwV9tveFkZ0IpzZLwKyygpRRc1Fv1gopKNeCAi2o24LCbYaKCkDw82goVVZW4ka5RnBfBR02mCqoTHBzvdXU2alTo00sbWxRbqG7DaKrKbGUwsHBAU21bahjVcntUao113NwNAfo5+Mm8mpo/FvO1xQgLTkb1r37wL2jyX7SbllsbsAEmMCdR8B030B0O124Zb4v7ijUZKCqLr+CzJ3fYBvlDtE3Kr3zmPOM7igCUjz21rdYiCUYG7xVnNmQ8YuRkDUVwmaKnNougYobxaRQW4oKdB0pK2+Qwm2G6wVXceZ0zWY9tesJi9Q3iovEcIcyUsBJTwfp6dokKNl0TF2hhI47127cTs7zs9Pwx8VykFVJdSovt8B9fgrY5WXg12uOtENo0yFQVTkxCAzYgYRLcaCAOq2XVNl4JjgME+LT8JIv++O0HljuiQkwgVslYDKlWhE+AxOe24EF4WO0MgcNpNU9bZo0nBzFODGBdkJA5uyHFZvi6NFOBGYxRQJ/HJnXSiRopfjIyUb7sm60tG0Xnt6zAsMWJtUSciJSr67CT/8MxpPR83G+eK7O9KlWNf1TC8EzoGajI/2iFh1LLOBGHUj1lP4W9ceNmQATYALNJFC1ptLM5i1oZqvAJ7Ry8fZ4/5pOvIfjk7gjmOzNToo1UPiICTABJmA6AkIYSGGTpPPFuSitfqyCJ11LhKw/gKSjk5tWqG+n+BJD85fbORT3zQSYABNojIDJVqoFoc6kUlzg7TUrIEMGBKBv76ZvIzY2IS5jAkyACTCB1iZgWe8GRKVFRbheKKHgqE6inXRuSjJKevnB5fIxfLfnCAql3RAyZkS9ts6qvCzsjz2I42fVuKfPQIwa0VeMBy9I3mQ/ZEeduCsWP59Swl6aK4a0DGrtKXN/TIAJMIFbJGAypTo/ZTO8w5cbiHuQwpD5bj6BFLqtqODFBwM2fMIE6iMgrBw2lPKzM3DOyhUKZxvaIfIm0jSqIzw4tRkClwvUjcpSoiYj7lpJcJi8XlyGptrWalZ9al/HjILMNtLP4tz1AnQip0xhV1FHuYOoRJ/e8zJCFo6mVWwh8k0xooLGYAFFdIIQ0cmb7kKmJ2FLYRRS5vWt7l97cA5L3YbiQ+/pWDdFimcjwjBqbRy+nuZFxU30o8rCMqehWE01FTRWmhg9isw/ao3Ap0yACTABYxMwmVJ9OiVRnOu01V9gyZO+kJXSasMHq/Hs+q14/5sp2DxJ+HLlxATaLwFlbgYSko7jAgWPcHJ0Qe9+PvAkBddY6fT3wfBXR6H01doKjbEk4HFaSqDL07Tn/S0mtVKN8auO3GKrmuql/6sJF6nNFbwK18PHZX11pTW0CdIsHxtIpI6kPNtVr2Lbh1IVUnLX7D6CWRQqMm1TBHw3pENZW6lWlaP/6nVIfSocntR9f/V+zCgUFHZtaqyfPzYvJoV6OL75fS1C3envKS8Zvm5jaCdSTkyACTAB0xIwmVJtZS98UQ/H7BeC4CwwoHi+k99dgePr9+K43perafHw6EygOQSKEffBYoS9tkNsLOyamEY7JQppXXIGphvLZ0DqD0W1uqMdn5//n73vAIyqSr8/SSYzk06AABEDIYAECRgQIqEZlICIiwiI2BW7LKwKWGDVde3Cuiqy6n8Vdf2pCBZEkao0AaULQUMRAqGHkN4nyf98983LTCqhhZL7wZt33+3vzCQ575tzv6sROHEEslUc9q0Lb0GA8lQDPgFVPxwWJPHLDm56JIS6RrOH46aHQ5CwaineX74Ms7jpV/hkV4vq+8nA5jmUDI7+xCDU0iTAVy1UdLXWKY2ARkAjcHYQqDtS7UjF3BnzcBBW2KzA5reEcETi0//MRNtA580XpGIzk+bl2YFEj6oRODUENv1nLAn1Qtw8eQb+dX9PQyeafxhL529G69ZVk5FTG7Hq1j7yfbh231UNjs49AQSyWDcATRoEqdCBNTWUj1tE8wY1VTHK0jdiVPPBKoTqdaMn4opBwK9urarvx/iTFRXqFjrPUnd/xtymqJMaAY2ARqASAnX32yh/L/7xwFNIKDeFREyeMK5cjlz0qZSjMzQC5wkCKSvxxISFiBr/CaY/7LZvor0p4obEl93Ewa0r+S35ZqSQrHTtG4/4aOcCXT58rlm5F22vvBRHli3G4g17EXhJX9w4KBJ2ac0FWpuWLMFP65NgC2mLfoP7oV2IS02avHYpFqz9AwWBoShYsBoN48qGRLVjuqrolEbglBAwnuNcMo7qOstO2khCHcuY1TMZszoDn9zzUjlSXX0/FjRqy29+/v4FEu7rjCh+4bltwRK9ULE6oHW+RkAjUKcI1B2ptl+EyZ++izRvK33V1VshF9i06qv11NUjpEvOZQSy92/Dck7woztjq51m/q6ZiIgZhz7jn8OAvDkY3PMpfJa4EzeE2ZC97VtceS0X8HZgc0pG+vSOxPK/v4RMp4Y14eP7EDt2NSa89Rz2jX0Q48dOxF4uEgth/IWl/34AA+khB0NTXseNlb5n++vijGnUNGa1E9UFZx2BiKY1f7ORmlWIjFzZjtZlHp4eaBpkg6/1ZPZwdPVjphyZafwsZqH8KEapUVZYVpbJz5z73l2OAldb7yLxeK+G7E9pD5SHyNW48io+aG5NNDqb8V8kjHpTLVKvvh8b/vL4dERNH4VuTT+Fu7TKfVyjQ/2qEdAIaATqFoG6I9UW8dTxOz5tGoELGQE+NMpagQ4XubzHlW7XOxxTP/wKt42Ioff5Kqye1hu7Uxmfg6Qa5iPn1nuxLGkSd2XMwMt+0VRxGN6/oPZ34qMfXsNNV4YDvaz4vMsc7M5m5IW0BYpQ//XDRZg8Qh5KM/D+NVGYZQ5e45hmJX0+1xD4870BNU5p3PQteH3OjnJ1bH5WfPRYDAZ0PLk9HPNz95Xrr83IqZjXy87vVCpbm+FTsax/iDNOtQ1Dln6ForauB4GW17yGed2CjbbhAzHvh+5oy69cLBGDsH3pJ1iweR9C23dHTCsHfvrhTwSpv0g192MJi8eKnYvw7Q+rkGVriu5XdoAj+QgatXeNW3mmOkcjoBHQCJx5BNSvsDM/TNUjONIT8d7TkzF++l4uqEpEw1ET8eoz9yE65KxOq+rJ6lyNQG0QKBI/3EJs/DOHXrSq/8jbw2JwV0ASfp07EwvmL6jiq+tIzEt61rnNuR0hHYBM59hhPQbhKm4b/c0H7+C7WS8xt7+i4XvXr2B6KO4can7LE4Tug2PxnlNTffwxnQPok0agAgL+oZGIC62Q6bz0D4uEK1aIBRHdXFdSJTiiM+IinJUbhCNOHgadFtYtDvd2M6+Am1Q4Pbk+Tj+sYeecXPWZERbOF20aAY2ARuDsInD2dlTMT8T9zeNJqPl1NQm1aK2XT38JseEPYE362QVFj64ROFkE/JtHqTUB93+8yulbrtxT8qI3ENC8N/qN+BJ5PhIFp6IFo4GPK8/Ji5lRgG/GhKFFx4G4ZdYetO3kkphkpqaw3AfVbYd9/DFd4+mURkAjoBHQCGgENAInjsBZI9XbvnxHrfzuM/pfWJu4Dnt3LsFHT/fnHSzE5M/KL2c88dvSLTQCZwmBkBg8P5mf42mjcPMrc3GwbNcVB1KS96tNWFJ3rAJGvsstn2fi5THX8Vsamnf1386UCUmyd+Dd6cCLSxOQN/8VDO3RxbhJNm1zuSyK/BTz1hxWefnJa/D6BC5UdDY+0TGNjvWrRkAjoBHQCGgENAK1ReCskeqigmzOMRavvjQCUWFNERLaBjc9OYELrFxfddf2JnQ9jcC5hEDMw29hzgtD8f3zDyKiURh8YuLh49cKLSK749tdBdwwg+rUGQ+iW0wYAiJHqW9pxr++CPITAbfFXOY9lS3a8g+FKGwnxQ1HN78wRN86jVcL8en8JPhHD8KU3sD4+K5qvODIYeqh9Zhz9VaNY5oD6bNGQCOgEdAIaAQ0AieNQPXusZPuspYNbfK190K8OGUuXn0wDk2QjmUfvqP0pTqkXi0x1NXOUQT8EP/om0gZ/pCxoyIjNNgCmqLjZZ0QFWHjIq3XsbjRAvyRakWnvrFonLoZK9NbqRjADrfFXMbNuS/asuDhpEVoNWcdshu1QlxcG+xduAxFl4vg1YbR8xMQPXsBNh0oxCU9+iI6MA27i8JUN1H3VD/mOQqinpZGQCOgEdAIaATOKwQ8Jk95vbRRQz/cfNO1dTvx7I24selgRaLLDxzLRVqfIe4cWaw4cdKLiL4sCiNGXF9+mvpKI6AR0AhoBDQCGgGNgEagXiKQlpaBp/8xFRMnPoGIVq0UBmdN/gH/zvhk5xw8M9KMVgBEDRqNxYkfnjOEul5+SvRNawQ0AhoBjYBGQCOgEdAInDACdSz/4G5wqxIo9PDmP8P63PMiFtxeiGJ4wSqbFezahDW5UYhp57YN7Qnflm6gETg3EbDHUo7hUcXcOscg76n/oqR56yoKjSwPlKLIUVJWXlpaipLSYgQPbQWPNDPoXlkxwKr5vySXZUj902UeHlXdxOnqXfejEdAIaAQ0AhqB8w+BOiXV2Zu+Qmw8d4s7jkW9MAdr23U+Ti1drBE4DxHgc2OV5ukJm48vPP0qx7Y2yXBFIltSWoLioiJ4SJ8Vv3MS/sy80pISUvHTb+acpOeK86p4ffpH1z1qBDQCGgGNgEbg3EOgTkm1pVE7PDN+HGwNyoKEwRYYgIJtH2PSNOdWtcSooc30Y597gOkZaQTODAJCfaumv4WF3CDa4YDNr4oo1Mpj7OY1rtCF0auReRod1QoC01ktBNvD6X4XQm0Sbk2uz8wnRfeqEdAIaAQ0AucmAnVKqu1hPfHUcxJP12UH187GpPdchPqv732FZ29TkXtdlXRKI3ChICD81o0Du9+WSUbNvBLxMrO+54HtlEX9DseVQ+Hl5VXJMywyj3J8XPo3eLQiuMXsR3XkyjaHOKlz2fRJoIU4KyLNARXJdo5rkmtNrE8KYt1II6AR0AhoBM5DBOqUVLvj40hJxFtPjsGkGU5C3ZuLFP/7KHqGubzY7vV1WiNQ3xAoSj+KEosV9i+4HXniTuS37YxCn0DYGzWBp6dBbRURr+CClssSHsJvi4uL4eAhVlKhnso8yRfxTAuJFtLsaSQ4J09nHjvl4JpYnyS4uplGQCOgEdAInJcInAVSXYBNM99B7N3/KgNswodzMHFEZ9jLcnRCI6ARsG5dDse86fD4aTHd1R6wv8ytkW58Bh59bzHAEZIsR5nr2CDTJbwW53Uxi4RQFxY5qK0uJc/lPzdi7ZY8LtjKC+2sZRBqw0Mt5N6Dh6eHJ73opYpge5BcOzm/JtbHRVZX0AhoBDQCGoELBYG6JdXpCQyhNxCTV5jw3Yp5W55CXEQQHPkFagtnMAqI3V630zJno88agbONQElBHhceeqM0PwceQU3gnfgnyIrVtDx+3Y7SB5uj+PAeeIZcjBIuUizlYkWTVCsizZpCps2jiIS6oKAQJSTVIicRU21Uyo2Nq+uaXtgpzZBzkEQ7ibQQai8vEmoS6ZISL1gsXsaaSZNYC+d3Z+Q1DaHLNAIaAY2ARkAjcB4jUKfsNTtpjRuhFtQ+xcCOn1aC754Pl+DtEW0q5esMjcCFjkD+j1/AkpsJy64tKO4QAy+7j8mZ1a079u+C57tPo6j/cJTYG6P48jhYndxYKPPeXgOBq27CimOt8NwXu3Bg5GqUkNQ+1tUL41Y8ieKRt6DHvE7YR6JOxzJGtLTiWZ9ZSGnaCcNWt8HhIoM81wZn6TfIkY/1H8UoMm1xesMt1H2LedB7bRJq8ZCb6dr0retoBDQCGgGNgEbgfEOgTkk1vK21wmfH0fxa1dOVNAIXDgJCZkvhe+APFL//GjzJkEs3/QocOVDuFr0+ngzPndvg8dvPKI6/HcXdrpZmjPNueKeXFPRA7JLlGNzlMFo8PRQvf/QHFidnwe5rhZ83ZRkBNuR5+yDE24b7L07BHYE/o/mwB/Hten8c8jyAEu/ak2qZWAbJcl5eAWPM07vOH2+RmAjHFwKtDmHu/K8JtaClTSOgEdAIaAQuZATqlFT7d7gNeTm3Xch46nvTCJwkAqVwiJwjk17qQqMLz8Qt5bzUkuu5w1jY68nnTkduFhx52a5FiSSvjyW3Qlu/CDzrlYieiRMx/b6/4oNfgnFx6TF4UWxN5zG6NynBQyEsjyjCvuhH8cCne/DlThJqpQ4pLwmR8NeXNPRGdkEJ9ucUCz92WSnD57HDPEq3TK22koLQUy2LFqUtRyShNpqcdW+1IwMJa3bB99KOiGhQp7/6XJjplEZAI6AR0AhcsAjI3z1tGgGNwFlHwBMWb8Zn73ktEGJMpjy9rTBB/yB4dusJi38wCa2xQFG81S+3O4gHWh7GUe9GSA2/AiHrvsFjHfZjWMsj3MW0ENajuzD1ir248hJuHNO6C3b8tBK9rLvwRKtU+HuQVQuxdjt8PUoxuGtDDGofAO+K5corXYr8vHzkk1hLPG1ZsJiTk0MddwGKuEjyodGP48OPZigyLoRcIpCczigkFVCp+TJ/F+6OH4zZO3JUvfyDiVi59XDNbXSpRkAjoBHQCGgEaomAdtfUEihd7cJBIG1XAvZ7t0JUWOXdC0/lLh3p+7Hh9zS0jYlC8En9ZHnA0fka4LXl8HpjDDx+3wruS155SiFNUfz46yjoPoRRPeg9JglW8g/WHLV9GqwWicbBC2e0Stuib+FRwsWOOceA+XMQ5verIuI2fALGE1E7L+4saoaPSx9AtgdDWrq5o3Pp3Z69/ihJcwmKSqt+Bs8ngZaFi7JIUUL4GfG1S7Fu3SZ88slMLF3yM+68c+RpkIA4cHDbTmQGhqFd6Em8dxZvhPN2zb2l5v0tHrfMHYcDOY8gWHDQphHQCGgENAIagVNA4KT+9J/CeLqpRuC0IHBwWwJ2ZRbR+0reSdmEX7PWiI5oVKu+93w7ELEFc5D3ZOda1a9tpfykObgy/iUsO5yMGP/atipfzybe6qgecNz7HLz/PRY4lgYEkPLlZ5H8UrSccgRFk96BR8/B8JZweQUk1STQ4q2WiB9FfeJh8fGGFwmukmQwj85mIDcb+PZr4FJurNS2i5FHaYYooD0o4C5J90XRSi4wFHYuhFza8CzxrrcfZabKk5B5gJ+XB7LcuL5EF5HFid6ce0kxPeAk+kKuZ876FiNH3oCFC5di1aq16Nkzhp2eihXj6y7xGP/CPOQ9yvs4Cct0azNw2hKsfj5YE2o3THRSI6AR0AhoBE4eAU2qTx473fKsIZCDr28fiPF05Lpbn/HT8e1z8cePd26LRZSi4+6tT0PaO4CdxKJ2y3GrHk/pj0lQvVpfBtz7LEo9SVT9AuC1ZSnQ4UpgZwJKWebFiqLSEOIs/NdUbFyxug/JN8NSMiTI+OGtcX2rDGR8MwNZrXohwnMxvLr1xeJGwxBbuBZHfk/E8/u7YM1BC/LIzPcKoRZ2LiZSD9MzLVkq2wODwn3RtWMjTPlhL7IkIDZNHmqKHN4qJnYx2wuhlryvv56L/308Df7+/pgx4+typHrloqVoHN0L7UKMX0HZyRvxW2YL9OwgD0YOJG/6GQuW/IECWwDCo7vj6h5tkJf8G5I68Jnj4CYsXZaBxpd2RfNjv7FdQ7T23Yc5y9Ix8I4hiLBnYNOSJfhpfRJsIW3Rb3A/jlN5U6m8rCykZ1o4WiPILPJTduLHBcuxeV8BLu7YHdcN6HyS3zgIKto0AhoBjYBGoL4hUPX3ufUNBX2/5x0CtoZAn8n0WOYk89iJZW/diuVTRmHWtoKzdi+nM7y6Z9MWQP874dH/dpRExQGtyCZ73wDcMRGWkObl7lE81cqrzFMJvdTd2wTiv3eE4qr0H7Fo2lcYuS0WX+wPQjEjcRQ5SvC36bvw9NY2yAjvhn+12oRHLj4EP49cLiwkc+ZvhMsaWfHqdS3hZzNIc9lgLPO0eKJIpB6MTW2aKfkoppe6lKsdRf7x008r4GO3ITa2K0beNIQE+3sVL9ts88iQ2zE3ydA2S97OLwej33d7VXHKsrdxSc/bsWDXEfyx9CkMj5+IRMbt/v4fk/A2H6QSpj2FgdfOxFGHF/b8OAUD4/rikpjbMX7CZ9ib50DCx/chdsgYpIcEYv3YBxEdPh0p5sBu5z3zH2fbeeB3ALT9eDq8L4a/lYyQwAzcP2Iw7v/YqZ9xa6OTGgGNgEZAI6ARqA4B7amuDhmdfx4hYEPMtdQij/0UmVw0R9UsnZ2pWPn9j/h1dypCLqHXcRC9jtXc0cGtKzF34WYSrwB07RuP+OimqmbatjVYl9kcfTtasGTOImzZD3S5diDi2rlkJvkpiZg3ZxV2F/gjpGAt24m3+jSYhOkwOW36IUMPLd1KDGgznAYvlZ/adFOTEz/eKxjtrGnIXfITnj/UDF+n9WHsaQ90zi7FHms4StL8kcJIHtOWH8bKnT4Y1WMQul+0Gk9w66VHt7fAsRJPBNq90KSpD3zYe47MQXmpSaiZXpCUjcVJWcgpNidHxYhIPoRQU9wtjm7xnn/9zVwMHXqd0lF369YZQQ2CMG/+Ygy5ngsxaXwmKtM2qwy3bw/2b1jFrFsx4flnEdPgWbzBRZAWEvToD74n922DtwYvwtqHI1WzBFuoOk+YuQL/HBSu0snt78RHP7yGm67kdS8rPu8yB7uzH4LTKa7qyIvFxk9EBy7AlIv8InSdPBWb6OluR+lO14IfcV+mm8ZF6mjTCGgENAIaAY1ADQhoUl0DOLroHEfA5vr4puz+Q03W5s28/J14plFfTGbOzaP64/O/v0TyNA7bVz2CMFcTVT9/10xExIxDn/HPYUDeHAzu+RQ+S9yJG8Jsygs6eMJqJwiR6NMhEZP+noCtGa8ggv2kbZqJi3qOU+XXDYrE93PFs9nfWf/0nUr8guFof6WSKByv13dWHIaVYfYyvaKxNVs2YTHI77c7S7DR60aU/NoAmYWie/bA+n35SPo2H61CO6P06CHkCTmnbTiSj90zduKobOToJNSNGb/62uhG+N+6VIPUS76TVxtkmvSeZFr+ZWZmY9GiZWjUqCEWUuYhMarTqA2fMeObMlIt47ib+9vS5to7EfX3B3Fl809x3ejnMOnRWxGtuDN3h2SjhhRsuIxa8Q7P4VEnoZb8MD4oXMXFqN988A6+m8X3nu+J1dWg6pQ9HDc9HIKEVUvx/vJlmPV8IsLlA6RNI6AR0AhoBDQCtUTA/W9ZLZuc39Xy01ORxq+ITbMHN0Ww3bzS5/MJgeWbVmHRslRk71yLW8b+i+RqIq7v4Ic1/55IQt0f83a+h7hQC/7z+FJcH3k7HptxHWbd1qb8LXqHY+qHX+G2ETHUYl+F1dN6Y3cqvd0k1RanF7TP09Mx48l4BGz7PwTQ6yl7E0X478e/hVCPfBm73rsNHAYHl72BiGtXle//NFxZG9FzLsdxTHju+hQyY68gplzyDEnuzS3F3lL2cYy1PHkIIeYplSw1NSmDFz48DMvhropylBnrZpEw791LoYR4yd2KpI5cKkKt8ou5MHEJLr74Irzx7xcYEcRC57oXDh1Kwb33/Q1paekIDm5Q1rWRYFSPJD68hBtX/u0GYW3qJqycPxOP3PosYqfNx7ykmYgLqdBMXXJOpMzK26yuC/DNmDa4ZTovet+KZzrFAitUQc0v6RsxqvlgfM5a142eiCsGAdx6R5tGQCOgEdAIaARqjYDbX95atzmvKyZ+9hAi2nQtOz7cIoRC2/mGgC2QM57+LAZfO1IR6pufnoqtP/ErfmRg8wIStPGjFKGW+7KH9cKDI4Hv52wA/ZrlzB4Wg7v6N8H6uTPxzJjnQYGBiEecJrUnKkIt0pF857OY8npmpynS9eKYvyhCLQ0CGjeW0/FNsVBWK3em99jhYKznQmPhnyz+cx4ORxHkkGuJ/1zAOuZZ8sh3XX1VHJ0cWKJ/+FILfV+Xxgiwe5Zta16xarXXbF/g8MTSw3RdizdbxqvOijIx57sFGHrDIFxxxeXo3r0rddXdMHz4X9CmTQS++koQBkQVXlAkz/QOrPlgHAZPK+PUBDoVB/OD0HPIQ1ibKOx4Nbbud/s55RuUzYdjPttUtuwdeJdNXlyagLz5r2Bojy5GHRmqBstO2khCHasit8x67Ra0PU0qnhqG1EUaAY2ARkAjcIEhcJw/NRfY3fJ2LMKY+HXxgTWjEEASQ1fahXeT9eCOCjIZBYILFdc+fHKh1UyIkhe9gUuG0MtNQvXX0UpjYBbxTC+oqbl1y3VPBorcxGm1+Sjlr0w2q1d9dhypOr9crsFqvchwrd4lKPh2Pcm4A0Uk27hjY7macmHlo/Md3RrjoWHt0DvhEN74djc2HHN9W1OpQcUMEvOaiLQUm9uQZ6fsx/r1m/H6v56v2AtG3Hi9igJy7723oUdvYEzcEBLZRCQgUsXL/r5A9CZciPjpQ+g2djX6jByKwC0MA8jy6Obifc+BPEwtHzsQIWNBmc5utMpMA7byQUQaivmHYgBPk+KGO/tWufh0fhKiKbs/xktGYlTmcGsbECjfBKzGlVfFs79Eo8KM/yJh1JuI0t9kGXjoV42ARkAjoBGoEQEXI6ix2oVUSBfU1iPYkZyKLmFGKK0L6e7q073IYrfKFoSug/mV/4TpWLaUTIEAAEAASURBVHpvV8RRxpG/awnenUF99YddwDVo5Sx1B+UaI99F3geD4EhehKXTSOLciHK5yu4XZNDibX1v5ircJmH8uDDy28/mMKcOXJxOT7F4qEsYSFoWCTqUl7tqohzAKB6hwVa0aNkAvr4e+GApV1yeAKkO8PYAZdj0VjsHdsdBpWUrcm44w5WMHn6tsGnzajRuxDCAjJXtwe3KpUx014/+9S6MHv0AFzx64LYPFyHgm1U4amuKfsMGoGVWIjbnhqneom79L9a234itu/Yhq0dfTOofj2gl/fDDjW/OQUHcVrRkfjwF8tnDp2JZ/xC3RaiN8HDSIrSasw7ZjVohLq4N9i5chqLL+cDEBZhfLP2Kcbr91Dht3NtGDML2pZ9gweZ9CG3fHTGtHPjphz8RVA9/Q1Z6e3WGRkAjoBHQCNQKgXr3J8M7oAWBmYYrI/l9c+9x2Dr7Eca1rRVWutI5hEABdbLLB5T5J8vNLPr+1/DMR70xMLINo37EcgHhar7XE7F9aBujXsFqJDi9ohbGQcaMB9FtCz2kW43i8a8vwp0fDIG7J1OVFIl+dzU3+6bZI/HYe7ei2wOjEDwlkhlO7yY93qpc6tSBmR5i0Trzf2UjD84hTBt2ZGDpiiRkZJdgh6xArI4fV+jBn78h7uzVFDlZhfh0QxoKZYeZCubJ8HqKUMscSKLtdI0XO7izIvO9qN8WvTVL4O3jT+mJMUl7aCQXBgpuTmsQhbKtYexB3P8mTvbAqWR2Lqq89+HOZfn+YZGuds5ce0gkbrjH1XfYiBFl9SO6lY2Cim3DusXh3m5lVXGTWx+uXJ3SCGgENAIaAY1A1QjUO1LdbsSzyOORf3ANHm4zDE98eQ0Xrxl/gHv1uQ4HDx4uh5R4AKMvOzWJQbkO9cVpQMCGgfQ4XnnxpVX3ZQnHU2sScPXcJVi75xiG3/cMBsVHlXmpW14/B8uKIlTbqHte52YoC/BHqhWd+saicepmrExvpeqW82Sytj18IOYt6otLne7uqNtewfZ2V2PB2mTYWnZGv5hgJCc50KmiO7zqWZ6+XCGz8q8qUs1R8rjocNvhXIx69zdE+HjiQKYQ42oqV5hVAT3hRzNycPRoLiOG0F1dRTvZTdGTG8548RBSLZ7o6uZSoXt9qRHQCGgENAIagQsGgXpHqs13zh4ag7EvROK+lDwzCz8vNxZRlWUwMXHSi+6XOn1OIGCBu8ex6ikFIWbQkEpeTKkbHNHZLV8WxI1AT7OTiHgYdJvy3ApeUEuDcMRV8J6GdYsv590MVTIFs7MzczbkFC6PsUmoPRjb2ov7jJcw3IfaEMZt+MQMIcSMDsIY1crU3uVGsqZXCQIyY0M6Pdsk4cLDK7TzpKxDtif3pmRG5B5eymttSD6U97ymznWZRkAjoBHQCGgELiAE6l30j5SDqc4ot/sx7++JaBjoCiV2Ab2v+lZOAIHEbTvx6mtTT6DFOVLV5Lk8e9JD7MUjoDgf3kW5DKpRw1FcQ1mV7fjgWWUbLhwsKYDVypB2JNWKWNNbreQgdFWLx1oRayHj2jQCGgGNgEZAI3CBI1C/PNX5ibitTTyWd4hF1FbqanEvNt3q0l5e4O+1vr1qEGgV3gKrV6/FP557Df949vFqap2j2UpqYSwSFDK7/qPuyM8vRF5+PvLyCphmCD6G4ZPQeyJlMnc+FE21LHSUzVqOZ+IJV/8VR/ZQcaeFxAuZlsPO3Q5tNhJrLt60iLdaJCCci3jUyzTfxxtEl2sENAIaAY2ARuA8R6B+kWouLpuRuAi/bf4Tafgbul/dE6H28/wd1NM/ZQSEEH4x433cNPLe84pYu2QfQl4NT7VstuLNMHslJVZjgSCJsBBdIdXFxZSGUCNtbNTCOopUHx8+cTTLYWilOZZ4xUmaTdmHEGubItjeZZu9eHI+Jqk25ik9aNMIaAQ0AhoBjcCFi0D9ItV8H4Opk43joe3cQSBl20b8/NsOZDNshtW/CVq1bYtOHZpzh8O6M3di/ew/XsNz/zg/PNaK8IrUguHsZOdCC93PpSXeCjghtRYvC4rU5jFWw0vNxYYGqa6Nj7o8/i5SzbGEWJOse1sMPbXV6s2Y2Uy76arFm+1u2mvtjoZOawQ0AhoBjcCFhkC9I9UX2ht4Xt9PfhKmjb4P42cY4eiiOrjC2vV5axEW1HFIs/OJWBsEVSh1qSLUhj5DQtsZUTgssnCQ3mTxXFuLLYpQl5BQlyjNh3irT/yTQ47u1EiLXtrwVisiTyIt3nCRf4iuWtJCqA1PtTTRXuoTR1u30AhoBDQCGoHzDQFNqs+3d+yCmW8qXu/TG5MYG/rF2YvwcHyk0zNdgF2bfkNReJuzcqfnNLF2ktMyT7N4pZ3s2IgT7QUHr8VBbJXwdhDvMfddLLG4vNMsF221n18AsnNya02uTV5sEmQ5K+20eMidJFpItRn9Q86KVCvhiCbWZ+XDrAfVCGgENAIagTpFQJPqOoVbD2YikDz3bUWon/lhHR67UraINs2GiOgY80Kdk9euQW54O+St/A7rvLvirkGRsGQnYe7sn7AtBWh1RR/8pUcbmB/mlG0r8e0Pm5Fpa4RefxmEmDBjBz3pLHnTUixY8gcKAkPR4fJu6BXdXLWr2MbUWNdGCmIS23KTPgMXyt9rslv2r0grr13jG15rU3Yh0o8ST5fcQzzVYqKFttm8GXfapq5P5EX00WIeJNOmN1rItVwbJFu85QahNuUiJ9K/rqsR0AhoBDQCGoHzFYHyosfz9S70vM87BA5ul+0LJ+LecoS6qtvIwZzRwxAdHoXYW5/CmK8T4UhZgxub9sbwBz5HwurPcUt8Xzwyc6dqvGvuK2jRZSTGLEjE6o/GcefMIViULNt3O7D0lRG4pOftqmzpe2MwsOczSMwHqmqz/IinWrz4228JEGJdlZke44plZn5V5xLGda7tUak9I1BLXkUzybWchdAakgxKMUiczQgdajGhTaJ02Bitw6601rK4sLaHXdqp9mzDhZ3mwkSlo5ZweuKl5tgyvpBpd0It89KmEdAIaAQ0AhqBCx0BTaov9Hf4LN5f2q4EJCTnVDGDDGxewK3DBzVC+SjhDqSlpCKFR7bwYKcFhkuiPxbv3Im8D67DireH4XteL0v6HtNnzsaXo4EPpixHmmMnXh8xDdw6EAfmv4nPF87DPdw+fMp3JOK7vsfA51fjmZlLkMeyWWt2Ym/SW4iyVN/GlIJUJNYm2ZVZmWnzbOqWRbtc5cGQGxKBozaH7GBYrg86mlX/bosNZQ5iJnGVs+ioFbH2MqJxGFE6XARbrkWeoRYXygLDWhxmHGo5S311zXHKQug5yXzZduWaSBtvjH7VCGgENAIagXqDgPmNeb254fPxRoWc/n6oiESGs2dotCLvhrisW5uybbfP1Xva8+1AxBbMQd6TnStMMQhdB8cCE3YhiyVlu3pnb8FF4YNV3T6T52HBw8b28AVJwD0z/4meoSJXyMGeP6TKQlzprrvubQWDMiNXiqY/iIumS8KwPjz9uW4JX4fiL1ebWm0bQkLYX3b1baS1Sawl3N6z/3i1LI61ItHOGM/iPDZJtbQRk2vTXElXnll2/LOEyzNqeXFxIH3V6kLIsxwyjkmozTHFWywmBFxC7Zlmlsu1xJG2nLID2SkGcfYjV+ZczDErXpv5+qwR0AhoBDQCGoELDQFNqs+Dd3TP/H+i3wR6dsvZrVh9+BVElzHScoU1XmQf3ImdmQGIate0TIdcY4OTLbRxkx0ulqvKGrXswuxpeHHmcLw9wkl0/TsiZf8K/L/+vbHArVEB0xHNG7hyMpkc/wnSnutFIl3MQMyMPsEsCzf32c/zM4s24akYf+TT2y2eVL4icQZP1Vh1bczqQqxnfP5f3HTzfXjzrf9izJh7SGZZyhfxJJeK55iXQmIl3yiiW1kSfFF1VXWmVZZ6lVSNpggpiTPlysq8KdcwO5My8xCyLETanTRXRWbNPKkrXUoEj5M2duCk1JW6MMepVKAzNAIaAY2ARkAjcAEjcAp/VS9gVM6xW7OIg7bDcziQk4w8HgfWvEuy+ime+CLhpGaa9M1DiO0y17ld+0l1ccqNwgbdhym9Kdu4uy8mfLASKdQ2C/n1bxCCwIblu5fbF020YTa0vIKpKfOxmYsUZTc/S/Zh/JlCcm33R1sWfT37F6QRNClL25tEWQjQpltPKcHMH3ca3fA1JfkwHDW0MSsKWVXE+rP/hw8/+gyjRv0NJdxIxSGHo5hxoItRKN8gFDm4e2Gh2sGwoKAI+UzLroa5efSGO488dZa8mo887oQobaS+sTNiIYoKjb4LeTZ3SDTPEtFD5mkeMneTdMtZaZ1Jpk0vtnvZSaWdCxYrjiN9adMIaAQ0AhoBjUB9REB7qs+bd53bQDvnGtwhDncxvdTmevuS1y7CnJ9JGANb4MrBAxAVYpSlbVuD3zIborXvPsxZlo7+w7phaxIbd0jGj8tWokHjSPRs7cDKFXtwSd8YqGaOVKxcsgWNo3uhnZGB5LVLjP5DWqBbVGtYc/MQ2KkjIvwtOLh1JeYu3IwUBKBr33jER7tH8+BYVVojjCb5tU24C2PGjsTbY4GoDpFI2OqMWT3A1SiTaxrJUZ1mQfyjX+G6KcMo//gUfQbFYvlcevEHTUXazCF4YvY4XDKE8o9pkbiudyK+X8GQfSsT8Vj09fhy/H8xfERfTOY29ddhNb5nv3N27q6hjStqiJBVKxf+rVjxPXr0GIh773sM06a9qrzTslOhbP9dTK10/PNDzYlWeW7m2xzXh9+MvOK8KsvNzJLSfLR8b5J5We352tW/K6IspFp01GLiMRddtcFvXZIMk/DKvYiZ1+pCv2gENAIaAY2ARkAjcEoIuFjZKXWjG9cFAmVvVn4yRFaclCLEjIT43w+g398XImrQUDSc+xLGk6B+tCYRN3Xww54fp2BgmXQkFu94rMJD04S4JmL4te9jwswVuKzoJ/Qb8jmWHV6EEJGT5O/FI0Nux81LE0iqg7Dpg3GIHfs1bh4/Dvj7gxjPKmL/j2Nc5PM1ImLGoc/45zAgbw4G93wKnyXuxA1hhn/ZqFnNq7057p26CNf/lTsqrt2KVOo8bAHBCGvVDh06hjsb2TBk6VcoausiuGgQg1mHf8GiH5ZgO0XZD47+J+J6GnGuw+IfwYENPfD9z9tRYPPHI2/G4op2RttBzy3C9huWYun6fSy7BY90Y1koF9uFVt/GJKBCQ2VxoQ+93z//PBeXX94PL7/8Bp54nGCzUPFUvrTg4sua7NKGbTE+7qGaqhhle3cAnx+fVB8goffi+EKolX6ajmKRdci85doQehhdmj5kTaaPD7+uoRHQCGgENAIagRNFoIynnWhDXb8uEQgAtq7Ft4taoWHhfnz73Dh8wOE/u/5SFdVCCLWQ438OCmfuM3h/RDTuivkv+uQ8AostVE3UVQ7EWlMR/V5fpK25TW24kr2VWl0EQ16VcetpUWDQMUvLwbr3voYsHJwuCwcf7YbPm4/EFBLq20na85PDMfXDr3DbiBj2dRVWT+uN3anUctSGVKvBgJB2nXEDj6rNgohu5eNWq3r+zRE/4jbEV9EouF0MbudRlYVFx+H26MolNbVRxJokVc6lDInnxY1VFi1ahGZNmyky7eVdCouK6EEddR1bVlau8kqLZ9rb4gynJ7splkqsaD4I8MWj1OWtruPp6eE0AhoBjYBGQCNQbxDQmurz4q0W9/HXuGvISAweMQ6/ho/GnA0JuCHChj9XLWHZUIy4Otx5J40w7JGJTK9CcrZk8YV67EcV4TaqFKmYG0BNAoRAoypfqRMuS0vCm3pukWMYGmd7WAzu6t8E6+fOxDNjnmeoO5JxqVbHtnzFauRSknI6zfRSS59qQSJJtXirRUft7x+ABsHBCG4YrM4NGjRAYJALtdM5j5r6Er11QUEBCgup6ea8RIpSQimKSECKi435mu3d78fM02eNgEZAI6AR0AhoBE4PAppUnx4cz3AvB0mMX0aKc6Hi2plPIr5dkDGmci8r9uw2B3caLEHrXHpst0plGm33PJV2FCGzLDMIPccOxfIJA/HXV97AqObDkEASf1UbY/zkRW8goHlv9BvxJfJ8hPyXN9kEpC5MNmhJTU09I0MZHmohqIzuQWe0bN7ibqVOL/XZIK0GoXaorceF7CttN4m1uKlF5iE7HcqaQhV3pDZvhSMDCas2Yle68dDkfp86rRHQCGgENAIaAY1A9QhoUl09NudFSevY/pznQsyc74xq4TiMz974F0l4X4RV5rjqnhzCuanvyMvPQIrsslJUyBjYa9GyKF0RsdVbHFjv5wv7BvE7A9G3vYkRI67HwXW/odNLf8ehA8+jc4BB2lYeC8dVV/VGbvYXmDL5LfTseQVCd3F1IC3nsvFw/B81x3VgSUl7kZOrQoic1tEUoVZh8Vzyj2KSVyM2nmipRW1tlAnprmuTKCH5PCTqiBEJhMSa81j58zr8tmkLSpxz5btVFgKvRk11/i7cHT8Ys3dUtWlPXd+dHk8joBHQCGgENALnDwJaU30evFeOzDRqqrNQFgDDbc6WsAFYPHko+t3KqBa9+yNqxUJ6kiPx2YY7IGrqw6otCZdbm6ZtuwArnkKLRk8hilrptTe2Q8uWYXjiqecVqf711/Xo1KlDWYvPPv8KmzYm4OOPpqryg4eOIDAwQKVDQhphw4bNePW1qfhpyQqsX78Jq39ZhxtuGKS8o4pyKuJZ1l21iRrJXrWt6qZAyLOxC2IJQ+kxuoYRaENxayUNkbulx7quTULuyZcBspOh7JLoyQWLXsWe+Pjjz/ieXozLLuugiH9Cwh98zwIRHh5W8xSppw9nDUNPX3NVXaoR0AhoBDQCGgGNgAsBTapdWJyzqTYjp2JeLzsD1lVlFvR8+E3s6jECi1dtQ8FtI9H7ur5o18B4a9sMn4pl/UO4DNFloX3vw5z3Lsah4A64bgAV0hYHflr8Nf77/v+hVXgLvD7ln1jx8y9o0eJi1eiKmMuRkZmJBx+eoBbFiWe0Ccn09A/ewtX0Us+c8T5+/Gk5Jj71CMJbtsDatRsV4W4dEY4J40e7Bj5Oqir5xLlAtM1nAuW1VuSaHmknqVa3RC6tSHcFWchxbve0FBcwZrVscCMLFS3Uucv24cXFFrWA0pyvnKe+/T46dbyUG9fcd9xxXdKf41bVFTQCGgGNgEZAI6ARcCKgSfV58FHwD41EnLida7DQ6J6MatGzUg3/sEhUioNhaYT4225zq2tBkyYhmDTxUZUni94GXnN1Wfm27TuV53r21x+rPCFp993/GDZu3IIBA/pS8hGjDrOB6Q0NDW2Km0cOVVpks+xEzkKoZSzTzjbBNj3S5WQezvm5z9Ocb12cRfJRVOQNBwl1sdXYkMYq2m/5x7nJXHfs2IVdu/ZQHpMHm92Om24agiDfEmxasgQ/rU+CLaQt+g3ux/CJFZaYZu/H0tVJaNe7J0Ltcjc52LRoLSzR3CmzYt26uFk9hkZAI6AR0AhoBM5hBLSm+hx+c87G1LKystE9dgC2bXNqtDmJd9/9SBG01NRj2E3t8oTH/4EdO3ehd+/uKtqEsfmJEXlC0rIRifshGt/aHrII0DhICJl2J6uSdr8+k/hUHMe4lvFNHbUxetm1mtuZnFHVfRuLE0moZfMZZ9QPIf/O2Sm8tlD6kZ2Tg5ycXBw7lqZ2g0z4+D7EDhmD9JBArB/7IKLDp3PzngqWl4SBjDgzaX6SKnAkL2Wb27HxWIV6+lIjoBHQCGgENAIaAe4NoU0j4IZAQIA/3nzjJQwdflcZsf736y+o3Q6viL0GNwy9U+mp//fR20p2UJFQy7XhPRUPqnG4E+ya0rIA0IxgIR5WpWEWki2eV0VaDbJYkfC6Tf/MJ52k2jM3ndEKj8GDhzrnUPeezaOOTbZLl9B5xSUMpUdNdxnJd5vHsKHXoWNUeyXVefKJsWjIMIBB7e/ERz8wtvk9ozB9w8usvQS7KwaRCbkCc6je+fyleZA7+3Ph13ydiGvaVfBou42lkxoBjYBGQCOgEaivCGj5R3195yvctztR7dXrCvxn2msYOuwufDlrOtpcEoHnn38S//znE+UIrnifFYlTUoMKHZZdGkSv7LKGhMg7VAQ4niXt4cmFdypP0lJm7hRoyELOlhxE7rnJ+xPgabXAk/JqTxJ/Oolly0WgVw03eAaKZHGkbEgjc5IoJJJQ76WcmaMwJY4KT6nBfEmH9RiEq3Yl4JsP3sF3s15iSX/X5j+8MsyC3vdMBaaNwdJtA3HgvYW4+cOnEWIW67NGQCOgEdAIaAQ0AmUIaFJdBoVOmAgI8erdqzumTXsVw24chZlfvI82bVopQl0mMVCeZJFqkKgJmaQZNE6IG8NR1NI8PBQbNMK9CYEmeRbS5yWEWg5GtFBp+VKFDFaI9VkzY6ocvhTWxQtd03Dmq1Ovbq78OkgJ5sYDEUfn+1Zb+2ZMGG6Zztq9b8UznWIZDabqlvZ2fTGlN3BLF74gFov7h1ddUedqBDQCGgGNgEagniNwFhlKPUf+HL99IWrisX576isYcdM9SEzcobS4htxANNMi1aCHlvrpoiKRfPAoZJqHg7KP2h5GG6O99CUSEDkK2YccRVw0aUpMTDmIQSKFQ9aeRJ5puM/uTI5PqEVCk8+dF1NSjA1y3iWhfnFpAvLmv4KhPRhiUazKR+wgDB03zigfeScub2Ak9atGQCOgEdAIaAQ0AuURqPLPaPkq+qq+IiCctUePbnjjjRdxy60PYNdDjYCIIMJRTF0BD8oODL2GPJuVonWBAzfsycagLfvRek86/Lh/iDiiT5Rw5vFTWTJrs9rQxJuh4qS9laHixP9NHzZKvShhUFfMOEdM7pMO9rNkxx948OBrMOqev+GTT2ZhxYrvMYAznRQ3HJ8jkXHNDft0fhKirwFkHWKmW2Dz0G7RqsKL93SHCgLirK9PGgGNgEZAI6AR0Ai4ENCk2oWFThEB8f6qQ8kKjEWC3a/oqoj14AcY4/iFzkAYqRWlGaS+BpNUaTo68zzh4+cNXx9P+LOKP4mZF7n3ibJqK2NAH2b8ZfFUK2c0OaOijd7e1FaTUMsc+U9kInVqZcOVJep0+BoHU1i45vXaa8/Bx+768R78l2uwYd1PkDCHNpsVDyctQqs565DdqBXi4tpg78JlKLqccRvtXvhi6VdAW7+y4Q6u/YXpoRgUw4cqbRoBjYBGQCOgEdAIVImA669ulcU6sz4iIGRVkVlxETMt1z27x+C6Z0fA4emFps1bkiiTMXvIx4cMWDzWrOPDcyfvNDS0HYOlVSE8uGt4aZ4bgsL55JBmJv9jU3F8qzg07Eq6k2IZ39RXi1daFiq6SDQbO9vLA4Arnw3PtMnQvNeqzCkPr6rojOXJXDyUztzExJibzWbjRjDl1V2yw6IpmbGHROKGeyLL5hU2YkRZOqKbe2TzJLw+ZBqiXpiDdvq3RRlGOqER0AhoBDQCGoGKCOg/kxUR0ddGnGiuQJR4x6JzLqCuWWQYc5vtRmkgw6kd2U1m6STVJSRuJQ6ABK5Dfh7CduxDxMYDaLSvFF6MOifEWpFm02MtJNqbpJnNPHhWZWwOHxtKghuqshLywqP97+W4hbDbbbBZbbBy32yr1RveXtw50JvMm0RSIoUEBPips2iGCwsKkZlFzUktTfoWWUmtTBFpIaxC4su3qHBZvvAMX3lxW3J5+Ch7AOFkqiP9Jz6VAix69j68zQWKy+7mNxTaNAIaAY2ARkAjoBGoFoFaMopq2+uCCxUBEuqyWNGysYgHw7ZR0oFSMmA5lFi6kOli7nKehbb0LHfKOYjQ4mxYvTxQ4lOKbBYHiLPU9FYLoTZ4Kdid8FOlIOEr8i6Lhc/apZKkhxWYsfAIeXspbrkhEgdTSvHJov1IzSoiYeRH1sOLnFpYuSesFm/k5pdyEV4pPluYig3JwtBrZ59MuhhNm5DIV2FCTE2vrhTLtIVMG4ckmCHzl7OYnOXBoY7NQ6KjkFirg5io0INOOc6pTyUd239NxISZvyBGL1A8dTh1DxoBjYBGQCNwQSOgSfUF/fae5M2RLApfFFIpxFriUXsx7UUXcgkJdal4pknmPIoLEEgZSCwdx11Ydok1HDHNfNAyZzcs1oMo5prG4n1gJBBKOqSJ+WkTAipkW0zOMphpTEtxfgH13PlkqQzPJ2H7svNKkJZdSq80PcVs08DfG42DfBHiX4j8whKso7e2SQMLIopqz/7Eu3sipmQonJ0Q2KqMXB9fP7sWnDrI85EnB2+hkGfJk3NxyVrMK50ut6VUM2Y/NUUhlOeXoJvuwJHYfti1Jxl2SjvEy+7j4wMfPoF409tusZjEmp5rMn/Rnnvx2wV5+GDzsgeEig8L5vhVn5ti9Pzkqot0rkZAI6AR0AhoBDQC5RAwaU65TH1RPxEQEm38M+7fINWUgMj2114lCCR5zSQRLVbi4RL4klRfwUgcQ+xBCNh+ED6M1paW4w3PTD8EFlsR0qKQG6PQGU0C6WBICbVoURzJ4tG18jA5rZyFXJsEm+dSesAlfJ+DBzk9Cai8sDPVphTRrYMx/OpW8PFn/2Sk3SL+gxguqLR4Vu15Zu9V2N4q8ipnKe80sw0SLlILTxR16UHmnE9pOd3xNHVbnKKDUxQSK554QmPcpqR5KLULz1JBMBGTusrKEmaGcVbViEf273/g2DfzYR/3OOyUwwixtlEOY7NaSaq9SaotJNFCrJ3xveXJg42V5rp8l/pKI6AR0AhoBDQCGoEzgIAm1WcA1PO1S5fcgdRaCLaQP5JZFR+a5zyS6VJxN5PEetB9HOIoQGebHe1LfZF6yAO+dupuG16EQp8MZOz7Do3tB+BxURN45B2Bg1Jnb+qrPck+uaO2WuNYKixTzEkw5azG5LgNfLxQwAsh1uIZvijQCh+WG95XC0KD7QjwY7g9v0A280T3+Bvha8mHpUhYa+2shB702pl4fumZ53z4CguJa9JTb8Lj3y8i/fvZoBNdHfk8F/DexCst0xDPNENug7uIq0M87uZhsmlmKTMhUBfkw/IwIioOcaaTK8Ob58BmTeDl66u05aa3WunCSayt4rEWYq2kIEKsBRWZrUGsjVH0q0ZAI6AR0AhoBDQCZwoBTarPFLLnWb8moRaSZ5Bpp6aaET1MYk2/LBkemV6xFyzFhWhCGUgYSXYDah0OpZbCfmkUfBu1h2fOEWTtX4aSwgMo9W+AIu8jKOInjbt6w1MOMr1SrncUh7WYbPUt8gchn0xCuO7AKy9CTi43fiGZb97MD4/fz75JKH3sduWVXbjiEMa+vhYBHvuRR42FB1c+Rkc1xI+/i/C7dvbFsxcdt6Lp6TXOnCRvXzzClmJuUU4Xtl3uhXnizaaUXNZrwiqkmjdHSTiKeC1EWjzYcm+CrdyrnCsRa+YrFsyTYCLOZhGaiNrEwjJfPoRY/f0UqbbK4k3xVDM8nhxWIdaykNPprRZyrSKmCDOXfrVpBDQCGgGNgEZAI3BGEdCk+ozCe/51LuS6yMENVkokqoQ3ZQZ2EjVuD06W92TL6w1STWmGF5nxxcX5iPahBzmNHutrBiLd0QyZjkLYAn3Q+KpbkVNyFF5NW8LSbh9KjjKKCD3VDgmzR1jYNWUkTMixazscLCT9M6QirJCekY9skmp/f39uAlOMrNxcRv0o5nwYiYRe2UK6gls09YO/d1OWU2fNNk1C/NH6IqGhZ8aU/IPjWEhYSwSThgwjSF4uMg9vkmAbD/FOi5daCLUQaW46qeQr8gChvNQyNebzvzLz7LxUJxMW5almjtyReKt9GnmgkHiIhlo800KiDTLNayUDEW01yT4bylwl1J75MCBnbRoBjYBGQCOgEdAInDkENKk+c9ieNz27vNTC9kRVbYd/oOyc6GYMOP1cw0fcMtySLYx0S7csM0lOqUihj5nhdlYkmp7opH3JaPLqfdz2nMSTmeLVXrH+CPJzitA8tCEOpeRh9tI9XKgoXltqtukd73FZKMbdeik8/QM5X0PmYKP8Y+gJyT/+dJtN5aQQUcFGkVymFTHlhZBW8Vbb+5NMt+d8xSvt8FQEWqX5tEDVCq89KP/gQkuyadF9l/KQMIVCpE3MK4/K5wwnAZZFmXJnnrLokG5wH38L0nwMT72EApSHC2+GFwwk0faifz/t2DElPbHZ/dGgUTAa2MRbLSMYhPpEaXX+wUSsPxaMnh2aVjVNnacR0AhoBDQCGgGNgBsCmlS7gaGT4k2VCBueagGcOx7F9EB7MXzd6TaRlgiJFI+u6EE4vPLwZuRyR0WSauU5J1E+nJmPI5mcmyelHvQUtzyaiyNH86jTdpC0GnQx0LcYRbLHeS2tcYXnhqqamQRXRhDvr1BsWQxI3zFs4ZRjNOG0hUDTLa3003wqkHMJtSwFjiAc46JN8aI38M1kS7rpOdcSIc3ME3JdlamxpJRkWiQmcs/itbZSa1Js8VO6cvGWmxE/CgvzcMddY7B27SZ0jGIIwkNHUMgY30tXLkREc05Q+mI/Mp6BVFWjVs6b97d43DJ3HA7kPILgysU6RyOgEdAIaAQ0AhoBNwRqz0DcGunkhYeAkFd1kORWy/bO4G0XkoiKplroqiLYTJfNqYoJ/botFb/tzkRThtTLk5WBtMvaBeLn3yUOR+3s/ceFcNbOFBklMRWCrPTKTIv3WDTiVMpQnsEoKZxGCVdhyoNBAaUwR5ccBo6lK+97bmgQLuoic2NP0hnryFOE4beWtGTL3fNwlnMIcmESahmXA1tsxSi0crMb8ZST2HuJzIPnL2fNw++/b8ePi75EVFR7Nb/1639Dy+Yhqt+TfRk4bQlWPx+sCfXJAqjbaQQ0AhoBjUC9QkCT6nr1dle+WSGuYkLuJGnQ08r1qs05lARs+QXYt5caCIaXaxoKRHUDIjoKI6y2WcUCU3ssHlkHm9mtTNh40ES/HejnTa0yiSy95SL/4AsXBgqpZAxt6r2F7EpsZqv19GuqTW+1IsKcm5BccR3TWcz5CJGWOcpDgHGkpbC89BA8CcfRDGqcrQFoTulGfkYpAhvT40xteNUmXvvy74ABoXjoeX/UcftyoaahlxYPtminPZGensFFnD645JLWSlMt842J6cK+ZB7A9u1/ohHlIFncbXLLlt/Rv39feIuMxDmJg1tXYu7CzUhBALr2jUd8tCH3yMvKQnqmheECG6m6yWvXILd9DJof2Yhv5v+CTFsLDBw2ABGMD65NI6AR0AhoBDQC9R0B/dewvn8C3O7f8FRT4EAudlwrpJRh8UxgyltA4m6ACwkVu7RTPS3bjY8eDtz7NENWBBy3K6lQTCdusex8zrHF4xvfvRmyKf8QC23mi8duuRR2H0b/YHxmb28rySzlD2S0hV528kZhtCSr1FQ/oFY/qmbHfcnP3X7cOu4VDJIqBFeUzsRJFgMKsXYSaqkrxDq3sA2KshwI3LebG8C04IPGcBST1KYe/RL+DfbCHnDEvdtq0/I2qLeCL+rMsex2BvgmSOqf5DN9150j8dnnX2PQdbfgP9NeU95qNVeWy3s66e8vYd/+g0hLS0eb1q3w+JP/xE3PvoFnRl4Bx66ZiIgZhz7jn8OAvDkY3PMpfJa4EzeE2bBn/uMYOGEo5R8P0VudgzlxwzB+EIXkcxcCHWKBravxUeYcrH1Ub2Fe7ZuoCzQCGgGNgEag3iCgSXW9eauPf6Om3OK4pFq2SPz+A+Cxx4A9dMe6WxavUzKAv00G/vwDeP5jBlg+/oYswoVlo0aJCiJRMjK4JfnBw7lIo6fUL6CUnlgHw+kVM3xcIaOAeNNLzEgXdBWXWvLUYkA2R4OAYuRksXEtrcUJrL8Tkqq8+orQcgAZRgYVxzgfAiQpJh5z36zWyD/KvWHykpEd0oiZwfDJ90UDR1d4p2VRh117Ul3WsXTOsSS6h8xFjed8oxo3bkTpx1eYOOkl9L7yL7j/vjvw7DMT4OvnWh7aPrItpn/wpnogmP7hZ/jiow+x4bor0Mk7HFM//Aq3jYjh8tSrsHpab+xO5QMTSbXFRiV1hwC1aY0MHziILyTUU374BaOvbI6ED0ag23tbkU1SzT14tGkENAIaAY2ARqBeI6BJdb1++103Lx5WcbMq4qgYo6usUip5J/DCa5UJdcWK/7cU6PgecPd4EsLqFzmK4iGHhFHiOzMstjrWJabh199S4W1Ph7fNl9ue+9I7baPcw5B/eFD+ISHjQq3Fhqaa84+K9MfPOwzvdsWpVHU97VES3hMw5f1lfcHI9ASXEWuzH87DMyOd4e+CkdmEoQdzUxFwYAaaFxxEYXg/eOXnKR22Wb3Gs8nUnZUkHrbSc8u1SaxV0oPyjoZ4790pGDv2Ptx99xhs2LgZ38+fCZsR/gNXX91HEWppOuruW/Dll99h2/4cxLSLwV0BSfh17kwsmL8A37M8TipVYQVJwD0zDUJdRbHO0ghoBDQCGgGNQL1GgH+mtWkEXAi4L5xz5VZILf4K2LS3QmYVl+nZwIIlFBbvr6LQlVVKJi2e6gISa4ntLPIPK0mzDzea8aU3Wg4/Si78KLfwo9bCV6Xl2hOBtoMIsh1AEHdv9PM+Bn/Wqe3hmsGJpZSnWLzE6mBbIb/mwZ+owqhmyGEMbQbqoMN3D0K9ErgpzGFkXMxwI20bu+qabWo6y0+oebCe6KmVllpItfMwtdVy7siFirO/+R9Wr15HLfUeg4SznrHY0dVGpu7PsHzJi95AQPPe6DfiS+TJnu81WAHLIpo3qKGGLtIIaAQ0AhoBjUD9RUB7quvve+/0StPz6vRMk8+KG7ZKRDy9fOlBphc4K42LEjOBSyOrrFcpM4BbJ+aJ3rpqD3IpV/mVMgb25rgb4XnVnZR32ODDRXS9KDro3zsMgQEBCFCHP/XEdh6UJVACIYd4bXM53VKnN9azJB+jLbXfUTF575ZK0z0dGYfyc7g5jR/a9bHj8NEuDK+XDb/mv2NPTgrsRZSBCEmurQnhNo1pp/BD5Zie802/JaBBUBDCw8NU/qrVaxXhbtzYJbtJPcb3jZaXl4/Hn3iO+F2Ky1rYkDp/FTDyXeR9MAiO5EVYOu1rBt+u+tcC30kUcNmiNo2ARkAjoBHQCGgEKiNQ9V/PyvV0zgWOgCH7qP4mRWrBlXk86E4+ksJFaonVV3YvaUYqJuExRCxdhTFqM8k6IzjnkVhvy4SVpNpu54JEXz/qqIt4LuZRyJ0Uc1WZbHgiZFoigCjvqzdpHrsXaxzohYwMLuSrpUWF17JiNdU8M0hIq7DLmywqy2148cqy9LWYZaTzyrJOKOGBdHj4u7NsNi/NxNJnX8XMo6llXmkHd9EZNnEaQptQE13qQOtmAfjq6++x4fdtOJSUTM16CR544Q1E8Kc/wcaFpDMeRDc+XyRsNaYz/vVFuPODIXBkkohvLVTbxktJJssL3J6NHAVSnlVWbrTWrxoBjYBGQCOgEaifCGhSXT/f95O/a99AILI1EMRFcBm1YIfhbbnCjeSuBhOPqyw+XLr+MKXX9ER7c0tyaza8rD5M25nHMHJeVmqRqaf24EeWMgdzC+4Q33zkOuNUR0cGYeXW6sLVVZ7A9IknsFKxcnOU3FCzrKWKJqeYRQFGRR7vEYi/ffMOrlm1Fmv+2EdPshUtO8Wgb7dw2TuG30Hko+2Or5Fy27v4iy0NqT37ovvV/RAVKn5n6tDveR2LGy3AH6lWdOobi8apm7EyvZVaeNhm+FQs6x/ijFNtw5ClX6GoLTUtTmt5zWuY1y2Ygfi0aQQ0AhoBjYBGQCOgSbX+DJwYArKrYv/+jAJBr+tPmymArqF5S5LWawYyLEfNm6yIpMHCBYheVhsJNM+UH3hx+21Phs0rpa66lOywlGE1iilNKWZMalFPiCaY7Bp5VCPkFRmSlQKe82Sv81paqYQZOQWTsNznhlFq0iOOR9WzKThG8ty9H27oYBDp8rWC0HPICPQ0MyPiEeFM+4dFIsbMZ6TqiG6uK8kOjuiMOLNyWT2d0AhoBDQCGgGNQP1EQJPq+vm+H+euK0gMKtZu2xl46hng0L3c+CW9YqlxHcxFb4/cDQy4gXHgSMSrNYaq4+K7YkoSnri7BTXVVsajpq6a8a595Ex9tZVE22r1ptSXkg8uVPSkBEVItXi4GwaLn9SYr4P7g4/JrYX33DkXX/Z9KkaHeZ2bU+ly4uMWMUweqiLVJ96VbqER0AhoBDQCGgGNQGUENKmujInOOR4CQpL7DmOs6vbAy48CHy6UFWyGCdHsQ0L95DR6tG83Xco19ijaaJvVApuPFb4+PvDj7oB+jLHs5+urFibK4kSbjcRakWp6sEnC1T+2MxfryQCydbfUqyurZk1nXQ1f63EaX9EfhdUsPqx1J7qiRkAjoBHQCGgENAI1IqBJdY3w1MNCcQHX1lpcCvxnHjBpBzd6oRSkkMw6tBUjg8Qq3XNtu5Ehrdwl0UaPtI0eaeWVZtpC+Yd4py0ky17iFnaSaCHU54KVrk0+F6ZxnDn44aapHxynji7WCGgENAIaAY2ARuBUEdCk+lQRrO/tJSLIxe2M4ySxEJJsoYbam95UOVTIPEb3kCgf4n1W24KTUBtnYxDxULt7qU9yaN1MI6AR0AhoBDQCGgGNwGlBQJPq0wKj7uSUEKDj2RV7Wki1QaZlG3JzsxN3Au2eNsf1+ewmlYxq0MLMOuPntddOPuNj6AE0AhoBjYBGQCOgETg/ENCk+gy/T/ZeYWd4hPLd5/9ce0mCkFO15bYolMXz6/yXTxnHsTRjs5DyvZ+BK4noUVxcRqoNQu30UHuZ3mnn/MRbLZ5xWlXEWvIT0vfKqdYW7FWCglIP5DJWtjaNgEZAI6AR0AhoBDQCJ4uAJtUni9zpbCd8ri2PFB51xGVrmr4HMpCTnYoC7vSRX1CAgvxCFBQWopBku6jIAdlcpKS4VG0iIqT8eBvHlBuL96oIvJMgG1tse1BHbXXKPkiouUW5SD88JMqH2pbbJNXlejqlC3aLWP9sPNL8GLbk2DD9cEPsL/R27i15Sl3rxhoBjYBGQCOgEdAI1EMENKmu6zc9nAPK7tEb3AaWSGeX81jG4yyRaonAIaHtUJSHnAIP+Nr50SBh9mB8aAsXCVqpeXbYvUmoi1HMo4RlJbLFuHkbvK6NlXmYFak2PNFCoL0p+Shm3Ggh0d4So5pjqrWJ9J6Thju7Ns+1Gan6Oo25KeTwJgfwaPgRXBKUi/hCCy7xT8e0PS3wa54P7636trpEI6AR0AhoBDQCGgGNQFUIaFJdFSqnO09Is+yeLZzwSh4Sfm4nD7FsHhJCeDaP2odYZuXTaeJ1FkLriT/3Hkb32AE4sH8rSTO90AyMLOdiRykK8x30VhcaZJr1TS+16ak2r2VmQoormllP8oVcSx1jMSIJNYl1aPMmyMziTopMW7jpi5ylDquq+qeDUrf0ZjzsFvswosUBNLKW4MCB9nxgyMHwi/aiMwn2c3+0x8xM7hZZy4eEiveorzUCGgGNgEZAI6ARqJ8I1EtSnbJtDX7+LQVNOnRFzw5Nz/w7T44G2e2uFY82PGTTv8Y8dvFYwkPItBDt5jzES3rQeeapTkzplJ1bIzqZq0l4hVsacg2SW/4Toqs81Mch1WUe6SpuwOjPINUyjjmW6KnNcHomoVYxqcmqhVifqoVbi/FOmz2Ia3wIn825H//vxygkZdrgzR0buzTPxSNDVuHTK2YjcksE/nkoRBPrUwVct9cIaAQ0AhoBjUA9QqCyO/ECv/mDy95Biy7DcMuUB9Evpiuembv/zN9xFodYx8OPh2wA2ICH7FHyOw8h02LyeCOBK4RY1/WjDgmyxIEWCYjJXVWMaBXmzgsZmen44YcFWPbzSnhwbjZfK6zcqOVwagp2Ju1GavoxfMfyA4cPwe5nV4fNl2TVbsWfSUmYM3eeKpM8m6+dhw1rN25EYUkRCosLsWDxj9i9NwkFlJV4O+NTC6mWOXmQ8CsSLpS+BmY9qeNwAle1+fKmugRm48uOv6OD1ReP/Wcinp7dFbvS7XxA8OC4nli1JwA3v9Ufr334OP7W5gj+1zYBHe2F8DYBqbprnasR0AhoBDQCGgGNgEZAIVDPSPV+vH7tS+gzeQ7y1iRj7XtDMXnEVGwTz/GZNHECH+EhZxmrkMchHgd4UF6hTPLW8BCtdZHKqZOXikRVPMNiQmi96Dk+dPgI+vUbhn37D+CHuQtw550PK8+yL8nxml/XY/y4v+OBBx7Djh07eX4U7733kfI2+3JXxHffnY4pU6aqhY1jxjyBxYuXqp0SpeyF56fgy1mzMXToHdi6NVG1/W1HMtsaIfVUOD0Vo9og0+7zdE8fD6TmlhL8NTQF3122GZf4Av+3oDfm/hZOQm/cJ0UvZV2IlvqtxeH4dtEwjGyZgWntd+IvDbI1sS5DSCc0AhoBjYBGQCOgEagOgbr2iVY3jzrJz9+2Em8jEsvu6KzGixp+H/o8MBCLE55Gu2hxI59BC2TfIu14zzlGG57FYy1kW4yED814CNF2KjGYqlMTsmr6qj1lF0OOLluGz579P1zStrWSfYS1uIwbJxYgIMBfbdQSEtIYs2Z9pLYT37uXWuURdyMoKACjR9+L668fiEcffQj+/n4quse6dRtx0003qHsSp/OqVWswb94XaNy4kcpLO5ZGfXMbRdrV+KxkyENcxPdEAGlvL8LjLQ5i2MUHEEBN+96UZoxrchUG9OF7TclHI1tjpB7Lw+7kdKRlFuJwtgMFxSX4eHkkruneDr2bbUNz3yJcsqcx3th/MfK1zvpE4Nd1NQIaAY2ARkAjUK8QqFek2uEQd3CwWjNovMsWCNc13MdGzhl7FYb6OQ/RS8v3A3t4yAJF04RUd+QhU9xnZtbNWci0+yJCGVXIrFDZZs2awJNSjNmzf8Avv6xTxNput8FuM7YRj4xsiwZB/up5oW3bVoiL64WMjAzYWN6tWzQ2bPiN5Hkt5syZh44dL1XtZMWm/Hvt1Wdx0UXNlKxD7abILcpFdqLGdiPUqrawcFptvNRSp5NvLl5vuxu9QjJhZSzq0lILcvL7wN8viHMt5lvghYY+hejYtSHi+3szbCCwdnUO5v6aioMZftiY2AGhJNURATmYFJmHzgFpeHpnB2wvOjmCryavXzQCGgGNgEZAI6ARuGARqFek+njv4muTp5IQigDaZUl7DqDL5d2wJ1mCSDMaXgN/emll5SGw/0AqHPRsmhbg74OGwf7mZfmze6g8aXLMrVic5Ok8fuaR45Z/GpIpRzORm2cKt4EmjYPgQz202Pad4haX9XgSOs9DlZmk1Qix54m16zZh7N8molfPGMTHx+Hj/32hPNSyoNBcTChp00oZLkTIs4We7vET/oF9+w6gb1xPdO0aDQdjXBt1SUz532ajNpvbksuYQqRFaL57bwqvDULfskUI7Oy7mDGx/0w6WI5QX9SsIQL87eawrjP7Guyfg6mdNiFM9OtOKy72xI/Lm2Dm0jQczHLAxuHyuemLhU83wb4WdG3rix5xdlw9IBzfzUrBoTTX++hPCcmNLTLRzj8BY35vh59zrOohwuzb/Xw0NRM5uS685f5CmwWrKukZOdSn55ZVF6lNWHNZscogMNn5SE0r/9kLu7ix0rnnM0744ZSMsnaSkD6lbwlxuP+g+4cJCGkcCF8fm6pvfm7NxsH8/AbW4vN7+Eg6Y5S7dEg+1Mc3CQlS3aQey0J2juuJUMIhXhQqcSKh7k/u0zR5BGkRxkWfNMFF8HG3iy9qxM+RJ+OgF1FqJD8ELmvWpIF6OCvmz9g+/qy5W+OGAZQSGe//3n1Hyz0UNgj05bclxjdPBw4dY2x111c//mzTiG3FjhDTPGJrmjwoNuWYYsfSspGV7QrHI5/n5pyrWFZWHo6lS9gel7V03mNeXiGOHC3/XjUnNvKwKDHeDxxy/0UANCWmdmIrP4NyH+4mv0vkd4rYvv2pDDnp+l0TGOCL4AbGPR46nEb8XBo2ee/lMyBW8fNoo7yqWVP9eRRs9OdRfx7Pm9+P/F18iL+T3U3/fnT9fnTH5Wyn6xWptlgMMun6MwoYf+INGNpHXkIC6vpDKm9OVnYByZwX8pzEtMj5R07K8vOLUMSNUEyTP8onbJexRSce4sUuzxtOuKuqGhSSrJhzl3IHdy8Ukz/iZaRBZClkP/LAYJpJrl959S3ccvNQjB17P7Zv/1MVq0WEznB3KSlH1aYtQhj+9fp/8OOPy/HKy89g587dmDHjaxw+9Iciw2PGPqViUMt25GLifZZ+zGsh8ZKbk1NYRp5LSKZkHqUeJch2I6rS3rwPSVe0mOBjsHkL4XIRP6mTz4WRKbncvZFktkmAF5IzixEWaFOSjx9/y8LyLdno2bEA117jg8uburCQtuTf8LPmo1NgGtbnNkWuYFaFFZLcuONd6hb0WjByLzMeJIxO5H7cy1SuyE14/xK/u2KZhDkUk/exYpmQUNMqlrk/iAhpljmZJt8umCYb/7i3NbX2Ul7xHovdHqqE5Lu3Mz9H0k52znQvkzyZv5jcT8Uy8x6lvGKZo9gglGaZ2Y9c+3EhrGnyMyo/A6bJg4hpFe9DPoGmVXyvhBSbVlThHiXf+VbxHksqzdW8j6ru0STK0r7iPRbz4cA0If+Cn2nykGOavI/y4GWaPACYVvEe9efR9S7rz2Plnzn9eXQ5as6p349V/J43f6/Iz3rF3x3n6u/Hqv7OSThfsVP5/ag6OEdePCZPeb20UUM/3HzTtefIlM7kNPZjgl93JL01D7PuicK2mU8i+u48bEp9E+1cP0vlJjBx0ouIviyKWuHry+XX9uK425R3ZE/yt/PX2vZYc70T2aa8qp4SuGiwW0w8crP3quJvKdsQT3Vku7b0QmYik578hx8exeNuvPPOh3j8iX+iTZtW/KOezx/sfC5OnIJrBlxFL1Aubr/9YRw5chQZ6Zm4pF1rrFv3G37//WeSHl+0aRuD7+b8H9q3v0SN88gjf8dV1w/B9X27qWt3MiYZFa9VJbeXF7bMwotbvlQ5dnKKOxun4+FWe9EhiHGveV1S4om5P8dj3PQbIY7L7KJSeoEZ4TDYG2kFpTiaI+SyFCH+3ohqXoKX7l+I1s2/UP3Jz/zigyF4Y28wlmY0LiPUebcY5W7T0EmNgEZAI6AR0AhoBOoBAmlpGXj6H1MxceITiGjVSt2xy21TDwCQeHWPzR6HiCED0W1BJBLmJuKvM1dUS6jrBJItdTJKrQfZtGkLv1b3NTzEZJPXDyZWXTsjNfUYoqLaIzMzi97kXOVpFs/yjcMH4/EJf1WbtsjDh0g6xPx9/fD/2TsXuJ7u/4+/bN8ulLAYuaaFUqyZGrVcRkJmYYyx/4htNrPfbGxjLnMZ27Cbsc1cHzQWxpqQmEsTCmsURRQJLZEuKn23/u9z+976fr8Vqeh9PPQ953N5f96f5/tzPud9PufzOWfLptU4TnOq2zg7oX79euRQJ4rhQvy+vdvg4NCYHFtpVG3WzMl41FoqV4jX3UpzqHXTCvsFNFC79np9nM23xKRW5+HfNAeWj/yHti3PoUWD24hLr4OW9S1xOauQvh75H4Qn58JItFCfx2heiFWtf9DQZp8QgCwa7F6b0hpLyak+V1jDTheRAP9hAkyACTABJsAEykKgxnkJDn7v4kK0J/b8lYYm03zg5yG8GJo3gUA8Ob3CdI9RI6V3PivOrLCYUPgvbPXq2Yn/hX0hXpjC0b59O+GwxCbEeXl20oS7ublo9lu1aq7ZF3bs7aU5uUqZepF3cSA41gdy6uBEgium0Xu0P2ifhFYO6Rjc9QjO/94d17Lpi5AkN/22GnUsHkFzm0dpbvWjSKf51lOeTUC9+v8g4WYdfHyuNXZn2SFXfgXfXajCWZgAE2ACTIAJMIEaQKDM9pVOAABAAElEQVTGOdWCTR3cfPCKWw2wblmrSCPSnWnKR0JiEl4aFojZsz/Sy1mao1tavJ6wSjwQZhbfUqvw4eXHEZtdF/M7xuHF56JwOdMBW6KfwK0CWiRJ//6jYerbRf/Re2HuYKJ/Avr0XIOIKw3xwTknxObXyFOkEq3ERTEBJsAEmAATeDgIsMfwcNjxnmrxX/51zJj2EVw7P4k29BYD7VIe82J92z+OWvaDxBHfsuYxL/H+xf6SXRspJ9zwvlMy/jfiZzzl5E3vJ2+IrNxWtHDxXzR97CoGeKbgCbf9WHyuMX663BoX1dW9VvePF0tmAkyACTABJsAEykeAnery8XooUz9SpxFeGNS73HXr2GOA+OKScmesggzCqPXh23Xw/rm2GO+QiaBuoRjck94GctOVFjLeQV27NBzPssGkeEdsvVmfRq+rQEkukgkwASbABJgAE3hgCbBT/cCajhW/GwIXCy3weWpj/J1dB7Oc4+DS5Iy0GPFSE3x/pQVO5VuYfAf13ZTHeZgAE2ACTIAJMIGaQYCd6pphZ66lDoGsf2sh5IYdfjveBUtbXMPBXBsEZ9pBTXOreYBaBxTvMgEmwASYABNgAmUmwE51mVHdXcJ7fW/03ZXKuUojIEwHyaevLAalNC0tKcczASbABJgAE2ACTKBUAuxUl4ro/iS4eSEBabVbw91B+/W3+1NSzZDqad8GE9r1qxmV5VoyASbABJgAE2AC1Y4AO9X31SRqXIg9ipi4NHpZmyWaODnDo5M7GtHXGy/+5oeuhaHI/+gpIxpQvpgTKHLshHaN2ERGAJUI8m/qQR958SgRzgFMgAkwASbABJgAE6gMAuyx3S/KWQlYMNwPcyKlAtzpJ07cHYwY+iw6rLrCHRbGSy9IwEs9hiBuHjndk4w53cazcWglElDfQlz0BdRp3wFO9fk0qkTyXBQTYAJMgAkwgWpJgL2B+2KWNCxoRg41umL5/q8wwrMZBNC5V+MQEaeCC41USw62icKtXfBr9E4UNdN+gdBESg4mAjcvxOH0tSJYiPcoRYDF4+jo4QjCXKFbwdUEHL/RAD5ujelb6Bcwxm8gRuyPw3ue9Sq0HBbGBJgAE2ACTIAJPHgE2Km+Dza7sG0FOdTAov0/4RUdh8vWwR2DHLQFPmZH+AtSsHXzH0jOtsWzzwfAq4UNJVDRvyL6yp+cVp2J6EOX0KZ7e/xzYA/2nLgEu7Y9MTTARXIcadQ0dt8+/HE8BVaN2qD3wN40baTmzNW+uGsOek85rAUr7LlNw9noN9FCP/Sejnb+zw8vh72PK3nvooHKAo4kzcrEw4Z7KogzMwEmwASYABNgAg8cgUceOI0fAIWvJ8eTUzcbL+s41IZqq6zq4uA7M+Fp74uX39iF8Cnvo/uQX3BTTJiHDV4D8WtKnniUm/gbuvcfiKZeNCe7/3iEhv+K14f5YWWsFB+39jV0DZyIrEZ2OP7OeHg4rkKGYYEP8bFKuH8g3lfyUpFP/89umwbEz0d4vMSnoqreb+k+HD7xCn3OXNqyK0owy2ECTIAJMAEmwAQeeAI8Ul3hJryFk+E0avrYQFMzpuUSbel3Nzp8uwWHx3pBHb8KDbxo5oIca+cGZCsHtMhR3OLH4UDKx/BqdAsLbDxQCLUYXM/1VazZ8QVe6u4IPGuJDZ1CkZz7JhoJRdSYzRK15bq2cHcW97JvS3xuJkbTx14ewxN1LiP0QBb6/V8gmuYnYW/4QZy8XIjmHbpggP9TNPpMU0kS/8KxS7dhISMXBBXdsYBHTy+ocnKQla0i6vbidB65OP5hAkyACTABJsAEmAD7BhXfBuqh88CuwJTryCfhJv3awqvAhHVYRQ61sBWIf7V/CrW78p4LdqbMIodaOLRGI8HplmNaeAfgOZpXvHXl9/h903wK7aO44XKKh/2nLo1MX8bx+CTUK0rH7/ODqMITENBBmut8ce8i9NNMD+kKt6FP4XvHnvjObRyWjLaiUf+BGPBtBDaNdUHan2sw8J1fRWD6i0vpxmfXByRnMI2Iv6kZrX7YyXL9mAATYAJMgAkwgbIR4OkfZeNUrlR2TcnjxWKsOJBpMp8whuru0NBkfMmIBqivDMVSpNbpLsTWiS3QskM/vLzpItp0JIe+xm3CrctS9PbqCU+f4ZgTRofDXdBMXqmosnIQiUwJiaTpISHoUbcYnRcuQewfszDurY9weJ4LUrKlUW33sd+IU0iEaSS/BI8T8y2Png93kqWyookfbnU1TxPESP7DBJgAE2ACTIAJMAEiwE71fWgGToHjMIXkzuk/HEsPJMmTNCig4BZSr94qU4nCNGFzmyY+9xx+WAV8Sm+hyN/1GQZ7d5Ky1aiJPbninOoLt5JxMzMBsTsWwH3jRIxZmSAjlOInBThKx9aOeOktPxSd3I8Vn83Gh9MT4KgBKiXJjQ+B28gVGBu8D6+42chy+IcJMAEmwASYABNgAsYJsFNtnMs9hjbDnLSdmOKbgMn9e6KuTQt4erVAbXt3tHX+WVqMWHgYcYXK6z2ouCJhMkchvfND2rLj6Ug5KMqhwMP0ARntpom3dYA/BX/c40V4UjkeI5fS0W4E70rRJn7o9wQ+lqirUsHa2gbtug/CCArZnpgqT6uR4jVT1LP+QpCNCzz9XkH4jcfxTIB2Ko2IiuLHeL0PTF6HrwOl+dkPPUKuIBNgAkyACTABJnBPBGrUeOY9kSpv5vrumLMrGaPpi4qHjieTu2wJ+5aO6OzxpDQf94VQHChy0ki1dgzEnv0AzQ6mzQqB+7egqI00Qmrt2A87d3RBG82Ll3XjVXgrJQKtQ48h1741evRwxqXdB1D0tDTlQRRXI/7c0dyQ5KbG0i0I0I2m12iQ6TDITfkLG+gd4gfSQ+Blewvrxs7HUU18Or7sMxDb6ZV8F2b34EUHGi68wwSYABNgAkyACZgjwE61OTr3HKeCk4eP+N9QVAOnpyAtUZRiVPUd4eOppKJ8ntpYIa6H8GYPzaYfb93IBYNokZ2ytRg2TNmtEb/qQqpm/Cw0tZmlU18X/PxCW/FYnU0vKozXOt3WdvTxFnK7uz/nR+HyFJGNPyEu6BsgeCI+pqcEwHw42QiLPoWtDzngK2FpIOcGxWQrTxPEdPyHCTABJsAEmAATqKkE2KmuqZZ/iOrtPGgO9ngo70IRKlYHTh3d4SC/esX5xSU40KeR5o0dKqcAnN2/DuEnL8PBtQu8Wqvxx47zqEdng23PmdgZcRt1aK5IkcZhroPWNORdW1cOffXyF3qaAPlpwkOEk6vCBJgAE2ACTIAJ3AUBdqrvAhpnqV4EbB1c4GNmtottCxe9pwKC9i08e2Cc5skA8JIy0u/kjh7aWTn6FdWTo/+0QD8hHzEBJsAEmAATYAI1jQAvVKxpFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AXaqKxwpC2QCTIAJMAEmwASYABOoaQTYqa5pFuf6MgEmwASYABNgAkyACVQ4AVWFS3zIBBYVFeFWdg7++ef6Q1Yzrg4TYAJMgAkwASbABB4OAnXr2qJ2besqrQw71aXgP3LkOLZt24nVa34uJWXVRRcUFCA39zYaNnys6pQoQ8mXL19B8+ZNy5Cy6pKkp2fgscfqw8LCouqUKKXkbLrJEzY7u7qlpKy66Dt3ipCVdQuPP96w6pQoQ8kPQpu8fj0Ttra2sLa2KkONqiZJbm4eiorUaNCgXtUoUIZS//33X3FwxMGhcRlSV12SK1euoUmTx/HII9X3QfLNm1mwtLSEjU2dqgNVSsn5+QW4ffs27O35ulgKqlKj09P/oeviY3RdrL4u461b2Rj24kDMmvVBqfW5nwmqL6H7WetyyPb17QKPJ90xbNgL5chVuUn3/hGJkJBt+PGHxZVbcDlLc27rhag/d5QzV+UmH/D8y1i0aA5c2jlXbsHlKO3rb36ESqXC2xPGliNX5SY9FXeGOrfP8euWNZVbcDlLe6KNZ7Vvk2OC3kHQmJch9EXVdQv+eTPOnr2A2Z9U7QXNHJ9r1/7Bi8OC8OfB7eaSVXlcZ8/eCN8Zgnr17KpcF1MKfPDRHHTx6oTBgweYSlLl4bsj9tOA2A4sW/pFletiSoH//vsPLu29q30f1K//cHz7zXy0aeNkqipVHr74y2WoU6fqb/Kq761wlZuIFWACTIAJMAEmwASYABNgAmUjwE512ThxKibABJgAE2ACTIAJMAEmYJIAT/8wiebBiXBr3w5jRo+o9gov+uKTaq/je++9ieo+59Lf/zmab1mr2rN8EBRcvHB2tVfztXGvwNm5dbXW07urFzq4u1ZrHYXpFNM/fq9a6/igKDd8WGC1X8MjtMd61XjdiWBrYd78ws9nVXuzT548AY1pnj9vpRNgp7p0RtU+hbCoRfhf3bfAwP7VXUU819O32uvo6tKm2uv4oCj4ILRJb2/Pao+zdeuW1V5H4a0AfemGlLd7J9CpU8d7F3KfJQiDI9V9gERA8MIL/e4ziXsX3+u56n9dvPdaVowEdqpL4fg+jVxaWlmWkoqjmQAT0CXQrq0zln73uW4Q7zMBJlAGAsLiXuHVYLwxASZQdgJjg0aiVq2qf4LLTnUpNqvur+MpRX2OZgJVQsDS0uKBGCWqEjhcKBMwQ6Bly+ZmYjmKCTABYwTq168er/Nkp9qYdZSw3BRE7InHHZtW6O7nDh47UMDwLxMwTeBmRjoK1Eq8Cg0c7FG1r+NXdOFfJlDNCBTcwtWMAtA7MkucJxmJ0fjz7ww87tYZPm7V+93a1Ywqq/PQEyhExtUsCJcZVe36aFRfeYe/NlxAoB9XOVD47R+mOOfGIaixLwaO/BovBvZDo7HbkGsqLYczASYgE8jDzwGd4eSs/P8ASeQz8MYEmEBJAombF8DJRThXhuOkzgXm6oHv0bLTELy8aDx6e3XGzLC0kpk5hAnUVAIF5/ChfI3pv/q0lkLuOYzSXHs6o//qc9q4Stpjp9oE6OifJmGD2zRcyItAftI6uG+ciLWxt0yk5mAmwAQUAsKYwaf745Cfl4ycWyvhzsPUChr+ZQJ6BNqN+gz5mTvRDQ10wtPwZf/56LYwFPnRqYj5cTAWDluCRM3TH52kvMsEaiIBa3esyqNzY2FXqr3O14/FuRcu2JOWivxbyTg8yb3S6bBTbRR5Hk5uSMCIyf3gIMQ7dMU7tPh1TVSq0dQcyASYgD6BC8kXcDXrX+GpNm9MgAmUg0BB4iF8BxfM/b+nxFzuL75GTncw9sTllUMKJ2UCDz8B4/eZCbickkIzC1T0r/I3dqqNMS9IRng88LRbIznWCh0GdkVc9m1jqTmMCTABHQJ1n+mKlWMGwqmZM4KWRYvz3nSieZcJMAEzBNTqOxTbANp3TqkgfbDcuAthRhRHMYEaRkCFjm7AaB9fNKrnh1/iK392ATvVNazJcXWZwP0lYIOXloTQ1I9UxO+YjQ1TPsafGfe3RJbOBJgAE2ACTADWLlhIU6byb8Vi82Ryrsf8Xulr4dipNtYOrVugB93tHI9XvIFCnAo9DHe7OsZScxgTYAJGCDj5eNFj6wTEp/FjayN4OIgJGCWgUklj1MJ4tbJliztV8TBb0YB/mcADREBlD/9XXwXi76CoktVmp9oo8HrwGOyCDav+gOhWZxzD+khghGcLo6k5kAkwAYVAHr0irFA8KLh0EQdpz62ZjRLJv0yACRgSsJacZUt5Qa91Ox+8jcNY+EucmDIxdA2dR4PR24XPI0N0fFyzCdQWVsVbaW821VmZuCnPkorbt48uPpa6yxgrBZZWm0op7sEpxGf8FxgwdyBaeu2iu53DwPDF2OhZPV4u/uBQZE1rGoGrEYvgFLgC7r60BiGSnu7M2IhnlaUJNQ0G15cJlELgatR6vDNnLTnNCfjw5bF45uWpmBPojPe2vU/nUT94hrsgLiwBb4dEoh2/RacUmhxdYwgUJGHBhAWYs5F8M8zE0OPemLX0TcS/7oHRYUA3N+BgPLDo0JeV/n2RWgsXfVls/5gNRrzUv8bYo6wVVWclIXz3CeTaOKJPgJfeS4/KKoPTMYGaRaAQqfF/4+S5K8Dj7vD3dq6SFdg1iznX9kElcDM1Aecy1ahjoYK6KB8qeye4t5AGb67GH8Kev9LQxN0Hfh7NHtQqst5MoOIJqG8hLu4C1Ba1oSpS4zZdZdq4u6BuQTrijp9BcnoemnV+Fl5O93cg9ObNW5jxyRJMm/YhnFq3FuvJI9VmzK2q74yAYc5mUnAUE2AC+gSs0MLNi/7rh/IRE2ACJQk0aOECLxOzCh3cfPAKn0cloXEIE1DVg7uH9MpJPRi2jeHRnf7rBVbuAc+prlzeXBoTYAJMgAkwASbABJjAQ0iAneqH0KhcJSbABJgAE2ACTIAJMIHKJcBOdeXy5tKYABNgAkyACTABJsAEHkIC7FQ/hEblKjEBJsAEmAATYAJMgAlULgF2qiuXN5fGBJgAE2ACTIAJMAEm8BASYKf6ITQqV4kJMAEmwASYABNgAkygcgmwU125vLk0JsAEmAATYAJMgAkwgYeQADvVD6FRuUpMgAkwASbABJgAE2AClUuAnerK5c2lMQEmwASYABNgAkyACTyEBNipfgiNylViAkyACTABJsAEmAATqFwC7FRXLm8ujQk8fATUtxAXE43YC5mVVjd1Vhqio/5C4tW8Siuz5hSkRm5WZXBVIzX+LxyKScBN9cNMt7J4PswMuW5M4MEgwE71g2En1pIJVDmB3NQEhIWEYMXKEKxbvw2H4tMh+kIFF/B+jyHoOvw33KwkLQtSwtHdbyBGbTx7/0ssSEd0RBjVez3VOwRhB+KQUXD/i62qEhJD3kejZi5YcCD9PqhAjnQsOdJRxFBdiNAxA9G7x0Scu1ueucLNlXBDd+vuda0IGWZKv1ueBRlJOHQgGheyHuo7DjPkOIoJPHgEVA+eyqwxE2AClUsgDxFfTcPA6b+WLDboB9xc2ArNhBhHS1iUTHF/QiwsRbmOVqWVmImIlb/hbF13jB3mBetyanM1aj0G+k1FXIl8gxGT+Q3cyyuwhJyqDijJJ//6VVGpE0l0i9S9ccUqmHEUbX2GA26zcSW6NewcSXx8S0jWLH9Ridu+QPc3fkW3hTsR/la98gugHBUhw1zB+jxVZW6P+WkH0bv/LGDCOuR/0cNcERzHBJhANSHAI9XVxBCsBhOorgSil72jcajdAyZgTcgq/PzjNHQjhWe+2FnrqGZXwxqoM7D8nVmYvKr8I9oFidvgpHGo++DTH3/A5pAlmBJA9QzqA+cH3qGmehjh4/7yfGwO3ohvX3WpcIPGhoaIMqd86o8GOtLv6OyXfTcP0fukG72gXm3Knk0vZUXI0BNY4kCPpxHeJTLIAQ08AjDTjQ6WrkN0lqlUHM4EmEB1IsAj1dXJGqwLE6huBK7ux4Qpu0WtRnwbilVjn5I19MOg4a9BraIupCBDCqPh6rTEaISt/BUX8pvghbfHwK+dNHqYEb8fK37YihO3aUC7jQ/GjR+GdvWVyhYidlswVvx+CLfRCPZt2iJw2EvwcbKB+XxKfuDmhWhsCdmJqBOXgLqN0PP/xuMVn7qIWLsNKUKyG/vw1Vd30O3FkfBpAU156VTeQCFtd0chlc6Wh9++mCgd+07D2e1vooXcWwYEBGIaPZGXfGpF979J99pw938Jrw97CraUsyA1GiuDj6Nh155od+cYgkNpvLtZF7zzbiBaUOZcil++JBiHT9LIcDMndO3ZFyNe7AEHVRp+WbIJOW37YlwAObZqOl4eiut2T2PsKC/AhNz3Jg9ANjmZK0JPAI+549VJw+Fe/18cCgnG0ZzG6NQyD5s3huN2nQ4Y+8Fr8HEoMMrH6VoiUq7koRlNdHZoRJXOTcEvP61FeNwNoI4DhowdgwAPYQS7UJbdAkMHtsGx9Rux90IWXHu9hLGBT2lvtjRUM/HHJsEJ7gN/T+HZhnbetqXA9mo0lm48jkI7V4wZ2wNqvTbzJDq7PIYcmrbvOyRQaju5yQjdKAgfB89m17Huq1BkwB6Bbw6Dk3Uhoqnee9MeQ+DzTfHH5uNo2s0XDS7sQViGGz6Y5EeWp01XxhNWQghuJu7HD99RW6XZL40dHfCM3wAM9XPBxQPbEbx5H86k56KuY2eMnxQELwcryc4kH1Z1YYfr2Lf/FOy7DsZ7EwPIlkDGOZlnRjridpRsj+2L/i7ZdsX22Bi9RvTBnOm78efpTHh524v68R8mwASqL4FaCxd9WWz/mA1GvNS/+mrJmjEBJlAlBHJjV6GRDz2CdnsfZ6PfBfmjJbeCOATZ98MGwxjxEX8Q1FHfo6XffIPYPjiQthJe9Qux9YMBeHlpgl78gNX7sKx5hMl87dPWo5HXVAygx/6bXrfFlHq++I4kdAvog4Nhwk1AVxy4NAcLW/phu47kT/fHosP24Ri4SCiPHFZI5U4JOYI5AeIkFik11Wko1UnIu+hQAiZ42Ejhen8LEUa6v2igO4KWIGNJIHnuMju9PMCAbyOw6VUV3q7XEysprltAV9L5sJhq+akkvPL4OQxtTGXL/Brkki46xxYm5BoUA/d5oYiZ1BYr+rpgYqRhbFfsTJyDpe0M+cThuZj30JVupD7dH4f3XFMRRGUb2nbKNuLlV9+EbCA0KRl+gkepuyn1CFiAjJBRdOORh3XDXPB6GE2lSf8Au5/rgo/jgbGrI7Co83k06DBezO1Oo7VxFK5sol6e9XAzZhWa9hCmR6xCzhfe2CDKovwhx/Cd/00MrSfUbSSi9rWFd09Kp9nG4WzeLLEt68vwQ8aB7+HU37CtTsOZE/Zw7fQ+SXDBgABgexi1m4DFVI9hJu2sxCctGyvx3L0Vh/sM0m+Pe3bgau/+Jdtuegi86M4sN16nnb/lrqkB7zABJlD1BG7evIUZnyzBtGkfwql1a1Ehnv5R9XZhDZhA9SUgz12GY1NpZK8UTbtN+AEXkrZggJBOmGOtTsEXskM9MyQS+Xlx+HlCV4rcjRmro1GQuFN2qLti+f5jFJ+AmIhQLBuoMptPT42CXBq+HIxPV9O82pCVWDNciD2MmFQHbEoPlXTxnY1Leal4x/6I7FCPI0duJ64cWiyKWrhkn4lFln3g6WzMoaaRaNJdcqgHYw85kfkpoRghSFs1EVsTaRRWYUdBn26LxIX9s8WyUEjD3AU5kJYBjsRceryffysOe0K2YJATjZaSL1pXSKnMUTc8NiWXsrxNDqlSTodGtcXyrOzEH8wM2SfyXz5cuJk4jKXhKMHnPXJWVVbCODsNvNJ09bhfvhIdavegxbhC/M7umCbGLQxcgkSqhiIb5LweSDqC5SJ74Gw61d/Uln0HRXpxp/HD/yaJDrX75HX4mpzjhF3CiDZtEzYiJjoVPwcJOtN0o4hjEHQUttN/7hJ/p/h1JGQ2GDRtgXi8cm0EYg/tE53XbvMGo42Ndsa2e8BgzFz9kubmUE8GtdUvZYd6xMKNyKD6XjkRigMJQWiotsSI4ROwOXobNtEUILF9K/XQ2GMwdlI7yKH2L7aDsPepHRRqedq0Kcm7Qy3jbTdJXnipgKJmwRsTYALVnwA71dXfRqwhE6g6AkXybNewE7hY2ksI3KZh/Rf0yLtBHckpFLQmhzdF1H4kBvs70l49+L3cVww5GB6H62pyiGlzn/AWXvEUphTYwN37KTSi8BQhgpw1Y/n0ppjaumPh5g/QyeY0pgzzw+iNYkbpj8pC0sXOkiZn0KP9azQ9RNxWwLNxazT1EUYfabsh11M6Ev+Kji05/3tPZuqEanfVsu7d5o2mqRTk+TZ6Cu8s7CMmOHdJqpdw0I1GjN/zc0SDOlrnDtaPo5OYMhjdHZ3h+fL3KHJtJ04bEYPlP5JPRbKNbIZyu83YiIXkkCrl5GTrGmwwnu/lTFLqoe9YGmoVNsG5N+AjRSh/b+NIuDDqD7wxPkCcA92i+0BMEUMycKtA3KE/LticMI+mQjTDU96DlcASv7kXYyVH1/8pvfnUwtOClRsPU/rBWD+7h3BPAbumjaT8mWm4mpWE5HMJ4rFdHWspnG5JDm4Q8nTFc+JUFMDWox8+pVFthE1FV9k5HtX/STk9/dDTltCQbzCVGEmbgQxNW+2Dd4J8RFs0aPcUvFpYwdYtEIs/HoA7R36Cv5d2dF9vmWyAD7pQO1A5PImeGsS6NqBSDXmba7uU3JbaqLB2YXv4aWhblKQ9/2UCTKD6EWCnuvrZhDViAtWGgG2zduJFHQjGO4v2Q+NHGdPQsa7ouBqLAvJRJPsXWheRnEx5JC4uXxmSM8xtIp9usoIkvN24C/oNex8nGwdgijgSS6OoonumJLQUj9R58gggTUGITYhEzIl9iKX/MesCtDcCQhbrNvAfLuWd4/cd4vS8eFmmrPKNq7JMCs7LzhEja4uThKV0dvIbSvTcK1UzTKVR+z2rp2EAOYJxYUvRr8N7iDUALNwIqK+cxylJlN5fQ7l2jaQRXL1yNDlypdcf0nHO5WtiaLYCXzyS+GiSyzs0TVjcsm8rUvNBM6sNtpZo1kBrVYPIEod2dtIIeokI/IqwKOkGxslnsNTuNr4Pp2Y98bEwfYXmtg90l+qIq2fwa7wQ1hNusv8Nmk89dNY4rVhyonu3s9IcdxvsDQfNEe0YlSElMLzFyhCmmnToh5ffCUObHvKNA92o6W93ZMZqmm0ubYVKo9dPSEcy79LabgN76c06dQ3LKiGQA5gAE6gGBNiprgZGYBWYQLUl0MgHc+XR14NzX0GDvh9hxbYIhG0LwcyxY7EiVutQGq2DrQN6+Aoxv2L29/txNSMBX30kzW8dMaozmtg3kLKtCsKCbX8h9UIcVsyajYibj5nNp1njSLlzEw6Kc5MFp+v7uUPRUpKIjAwdTzjlBOZ/8BlO1GkrxYbFICm7Npo9psLpHSvwe1K+ngsuuOQvfLBElkSj2s38MHPZNkSE0fuqP/sIQZ/th6pxcwizXOOWfooVUWlIjQnBu3OF0VOgo5Ps/IlHRv4UJNCo+te4/eQwbPgjAmPFJLuReEVwx1SoIxxnX8aRqG0IoLnFceKx8MfMpnhyRpNcwqlTachI3I95Y4LFFD08FFJ0KPOJSFWcZyFJHfg8P1JM+/GE7xF7NR37l62QWLt1QAtplogYX5Y/qtpShpTEVI2DL+UbiZ0RS0SWH/vNQSwNyRYU3Jacd9+RWPLjYvy8jabq7NIuFk09cUBkMmBgF71pSS38R8osae76G331nGi7RiJVjaolZNg2gKsYS1OTZoYgLjWFFmJ+jwUhCUiLOSTGjPj2C8wa30dy+OnpzekMHegpl5GSkYlYmh4yMUxIPhLdXUy0A5l36IH9ZttuwcWT0vSb5vWNLPwUVeI/TIAJVCMCZR9eqEZKsypMgAlUHgGvt77E5uz38OJcmgoQGUyL3iSnTNDA3T0V45yLkCYcpMhzZdW6x/YYu2wVQjsEYfv0V+i/kJA2coBn04iySuWMPfP6oDe94WDOyIGYI8XSWyuGINJMPsRFiSlTCotg6+guOjkHI+fDrdl8WQIw56dDmOTbXtItPhgLaWRzrPdebJ7gQnOhf8WLXvK8XSGHrzsmBjjqTb+wbhdIc4hvoK3wrmCaorBwykQs1EhvhcUfvYnVq+nNE2NWYKJfF02M8JaUAHpVSG6sNN4p6Chu8lQa4Tj3fCy+C1sh/tdkxAR4C3OqabSaXpJCrGn02k8bK0xRESRZ6MgRY0s7FhMl4PUeWh3dae77ROFtEgVX9fjc8B6OcYVXxRyC2k6Bk7AoIBiTaSS9q/NSMVyY7vHzutdEhzU7RQi6BGVkV62TV06s+bFu6iLONd5wMl184iG42FL+C6jv9Rm+nrEUvef+iq5BPbG3x+/SjUTkcWzCBZqecxMvByZgLLH9emx7HNu1QpTr7y3fJCmlqBrBVbiJi3TB6D7OUqjCJ1u2gxhaaERGM0yiOfYLaUrQwaXvw1OpLm6hT4h0A7LhnYE6izaDsSl2EmY1lQuPXwpPR00mzNwxUXyPeawBE/FcUdrjk0tNt10/WgSplsg6Nm5ocNMnl8k/TIAJVCsC7FRXK3OwMkygOhKoh4CPVuLKyAREHT6Jqzl3YEWL2Zq0c0fnpwTH5RY+j9iIvDrNpCkU1k56xyonP4SnH0HEjkO4SHntW3rAz89ddmBV8Jm0Ehf6HMKeI8kotLKEg1NHeHdygbW1u+l8Li/gwI52sGzhBNSvh42nQrF7XzzuNHFD3+5NcXbPYRS18SUZ9vg+4gfsPJOHtk/7oKdHM6gCdyI+kKZ8/EMP4e/kwba1O7pSPYwNvLboHoT89AD6st1hnLlGQ6ikn31jRzzp8aQ4L7jBsFm48mQ/7P7zLHLokb7rs73g046cVdqsHZ/DHtKxYfv2esc2pLOt01O4ktAZx44n4FpmLiybtEW3Xl7SyKq1C5Yl7cTzkUmwbOwM72daIO1EHG5ZyHzNyBUKstVlI5Ys/Zny7WK0LCT+bl3wfHdnyUkjxoZ81FfnY6fbDbRsY0MZ62FCSBK6H9iDI/QxGKu6zeHT51k41RcuHWr0W74FbrfroI081blV35mU97acV6dw3d0bOTQZiPSkpwFi/iI7OJM423fX40C3i3RDUQctLTpQit1w96WpJc0aoU6bDByMp7nX76zB+CFvYu8qQeBgdHERdNRuBYn7MFmcKvIqvOV3INq667QVJWlBslEZDTyGISfNC+G7o8V2XrdJa3h6ecCJXi0Yu6MzIpPy0IraUefGN7E/8iLae5KtRS9ZEvwpjarbFVqiYx8/most6eYySIenEd45XVsYb7sk8uqV66Lgxg2VueRKBfiXCTCB6kiAX6lXHa3COjEBJsAEKoSAzmvrbtEXIKt0GEXRBVhDrw58SRiVN7FFzBpGb2k5jDUnkvFSOxr1vxCBIfS04yC9kzrmsCs8u74PDF+CmysDdaZFpONLr87iW0Rm7jiGqWa+BpkbH0KvZDQmw4RCZoKV194Jr9C7Sa/Yqzj3txC/jHUWF94uiU7AODf9GwgzKnEUE2AClUCAX6lXCZC5CCbABJhAdSJQKH7pMhe3DRZBVr6ONug9gRxZ2jbvSzZb/J38w2L86E79MLQvfahFdKjplYHBI6H+M1yMG/u8h44Dq0bEB5JDDVqEOt6MQy1kTjpgTIYotvx/5OkloFfsCSPwFbblnqaP9ZA0eqvOC+xQVxhWFsQE7icBXqh4P+mybCbABJhAlRJQwXnoBIwI6ox6VTpKLUFw8BmAt2l3+4+7kGqGi/+0fVg+bxwG+DZANk20GTFhGkKjj2FhYAskp+RQzj544ZnmOhJUcH/5B3p/dB+EfjPc4JV9OsnE3UITMgzTle3Y1tELM4NG4m3/xrAoW5YypbqwJ1R8BeHb0/rpLcYsU2ZOxASYQJUQ4OkfVYKdC2UCTIAJMAEmwASYABN4UAnw9I8H1XKsNxNgAkyACTABJsAEmEC1JsDTP6q1eVg5JsAEmAATYAJMgAkwgQeBADvVD4KVWEcmwASYABNgAkyACTCBak2AnepqbR5WjgkwASbABJgAE2ACTOBBIMBO9YNgJdaRCTABJsAEmAATYAJMoFoTYKe6WpuHlWMCTIAJMAEmwASYABN4EAiwU/0gWIl1ZAJMgAkwASbABJgAE6jWBNiprtbmYeWYABNgAkyACTABJsAEHgQCqitXriAl+Q7i4s4+CPqyjkyACTABJsAEmAATYAJMoEoJ/FdcjFq1aiEv77ZGD5VKZQGXNk5o3rSJJpB3mAATYAJMgAkwASbABJgAEzBOIO92Po4e+wvFxf9pEqju3LkD8qzR49kumkDeYQJMgAkwASbABJgAE2ACTMA4gQsplxC+96BeJM+p1sPBB0yACTABJsAEmAATYAJMoPwE2KkuPzPOwQSYABNgAkyACTABJsAE9AiwU62Hgw+YABNgAkyACTABJsAEmED5CbBTXX5mnIMJMAEmwASYABNgAkyACegRYKdaDwcfMAEmwASYABNgAkyACTCB8hNgp7r8zDgHE2ACTIAJMAEmwASYABPQI8BOtR4OPmACTIAJMAEmwASYABNgAuUnUOFOdXHeLRSXXw/OoUNAnZWGmCMnkHgtTye07LsFZIOCsicvc0pFr/jLd6dXmQvihKYJqPOQlac2Hf8Qx2RdPoMoOi9Ssx6++t+vc9ZYc5DO46OIv3zLWPR9ClMj9fQJxJxOw8NnvfuErLxiH4C+QTiHY46dKHPbq5q2Wl7w5tNL/dYpXL0fF2XzRcuxaiQe2Y31a35BSOhuxCZnVvg5eC++wcPWrz9Sv369MplFk4gcvjtHjuIOnRia/3RclEwd9OXdyG7piuz3tle5Y/1f8ikUCnoK/6kjL/+mxoWTf1JDXIf1G4TGuO+undzyll1waSd6BAzAK5sSy5sVarKBPdnAnmxQ0eewopfXiA3ILbdmD0qGqrN76YRuYeXgNmjWchLi79a46nRsW7IAH8xdgdjr5tybW4incyfqZEqFd8Cl19N4ipSwGfCj82JzkrGbOnLaTp5AFPVLwkU7RtD92Blk3C0n4yoABemI+WM7Vsr9QljkqXsu436ds7nkwIRt+YV0/YX6sK2IOp0u2lI6jwdhzNbzpmp5H8IL8fsbA9DD93/4y5j5KrzE6nweV3hlSWAF9A33Qy0DmcI53MN/QJnbXoW2VeHclfsFveuX+hZi72NfJ/Vb/tgYV5k3sQr4QoTN9UengNF44/1JGDNmNHw6f4LzStev1J3qf0FvsELuT2kQQz9ckav/ey++gfl+Xb+c6nrUoH4DjWoqW1tbzUFZdop++R/yp0WVTDp1O+z6XJLCY66VjK/kEPUWfxQskAttPweqyHEo87B81inM+j9/LDpUUulvI89hbHubkhEVGaKyEqU5WlqUKrXg2lGsWn8KHsNfgXdzKxTc0NpAOW9KFVLWBLJeaGVVbkfLUM+yFlmp6arQ7mXio85AlNgmr+L2v3dLJgd7P1mCVZTdod9QeDQ0flOde3ITvAJmioVsi78CvyZ3W17F5bOwchCFWVkak0lO24QBmHLaMM4bwcfWIrD1vZ+zV4+swwsBHyLesAgMQXTaErhZl4goU4DhOVumtmBWch4ilnyEwE+2lEz16nJcGlf2/qWkgLsPsWtFeU/XRWm92j3XvwrP47unU76cJRhVSN9QPh3uJrVyDhu/thUiZksI/rxuixdfHYQWwvlUjmthafrknv2dBqukPi1odRSWDHSUshSex0cBgxBJfkIa+Qn1SxNUznilzsb7rXIKK2dy9bUozP76DOWifnDfIrjejsMZlSfaqWRBSt2Fw36fI339K5A8Qm1/Oi/8DCZ1Nn6dkKVo7HQ3vkFV8tHof487dnZ1NRLK7GdqcsgXNgydDqvg5bBaTf+XL4V1/1ao1fEV1Nm0BrU3jEAtTYaq2VEN2Yvamz6X9CAnsOz6pGHWE1qHOmjq5wihOn07dRRVxB8dW937xbkiiahyzmLKgpmIzZak2pINDpG++8kG5btdKo9WluWWbahneUqrnLRVa/cy8VE547MjIQjZNhcd7rYZkozx3w0RkdrVUXpWQ8JqHP5lgyZw4z6hU67+m+i0kZrDP1mKkNVfIcjHlY6iMHLG9nt+slJwbiucNQ61P+Z9txwhwUsxuR8V8ao/nrhLh1qganjOlqktCBlNbDE/vq1xqN36TcTq4DUI/m46fCn9jEGekFxqE5mrQfC91b9qz+PKwleCUUX0DZWgvDIuY6qoxLUfYvq0YGSa6ppMZSxLuE7hq8bMRlSWnOlRCzQTdslPuB/FKqpZ1b6HTkIRUt7fnMviIIDvJ9MQ2NER7boMQGDnxlopSt2FkJ0fYs6uNE2c0p+W72ag/L6BpsCHZOeu21CtLn1g3ddZD0PxZZoGcikduBkHi+bPkCNbiKLQdSjY8Telq41HunTFo3Xv4D+L9qjT/zHkfx+C4jZ9UacvXfzUachf+RuK7Z5G7RHP4L8jW1EQYwGroU/gzpKNqPX8W6jdpTH+O7eP8v2Kf/8BHvF9HnXG9sEjRmrxSGtXWLYAaYByTUW5EPoNFom1csXqI6EY1kb2Xp7rg1ffVkMlnxcZp/dh5YpfceI24Oj8LMaOewntxFvcQkRtWIlYmy7o1fQiVv6cgqHTXkdRxFqDsInwbPgvYonPyh2HkI5GGDjyLYzydRRL1/tTkIaIrb8h9MAZpNNzK1ffwZj0Rk/YXj+DtWv+EJOGrviSnhQEItA9G8dlG3QgGwjqmtV1yzoczWmJFwe0xfENG7A3+SZcewxH0MBOYl49PZSDnZPw8nvHUfeffDTvTbqM7qm5u88i+/xA9jlB9nEl+7xN9mmQZahnfzyRF4MjV4BOA0age2sVogQ96PiZoaPh3USFxD9+wdb4O+g7YgSNpprjVGiCIdmhHHW7Z7tT+w2h9pxD7Xms3J5DqD1fp/YcRO0ZdG6s2ngcDZ/pibZFx/Dz9lNA066Y+PYgOOQa8gnE8L5OiDbSjnAmGdeKaBYC2UJsinkpCFm1GuFH6QlFK0+Mf3MsPOmJhTBNIWzjKqzdc5xSOsDRwwtDhw+mOBsUFQoPP4egi5MJzzzvDH76QetIb1y2D5+NcKUWKmylcS0lvhRO1ibaenlGj7x79UdAeyv0cr6DVb4fAtl3pCcrJlgVyLZp+qwvGiTvQdh1N0yZ2Eeur1DnPIQuniDsAD7TkfDrW2gh9zkBfQdhKj0SEmyRlXwUW7bsQFQs2cK2EXpqzmeFSRN0apmHzSG7cLtOR4x973V6umSDgsuxmnPW1doOvxic08OpPeWalC1qpf1zbR8mTAsXj4cvpmkqozvJcX0QOPR1qFUqFGhG8+mx9x/r9NqiODpIOUz3GYI47Tl3myjZO7dF4JAR8KanAebzyaoIPybsbKxPE+qv0inTXF9ZtvNY0f9v3KbrkrvfcLw2pJM0UKC0T7e+6N8ik/rXUKTlO2Dgm0Hwa0OjdSbPK6kPO3jFHiNfE0ZZZZtft8cLowbByUruH3Tl0nn54rjX8YxFHL5fvQMXblqj18tBotOTSte/zTGZaO32BK7s/RX7L9ZGj6DX8dZzzlAb6feF/iLFoG8wbQulPZa136c5uZG/4+etf+DMP7moK/QzE6mfaUJPRs30a9q2tBsLv/0dmXVqI2etkacnYrMQytiGfTeFg5v4+ftlOOv5AvrbiZH0x3RbNXbNaWTEJ1AkSb/h8JuzHZlfDoC14VM/pQ2Y6Mutlfgy2lIp953ZM5D4eD4yb9fW6RuEWKU9GvoBZKcS1wDBbzConNKvxd8A6jTF4NFBCOjYGGrhurtR8g8iQzbiK8uL2icAilIGv0tHTsfQ86vhSR2u4DsZbqbblJyynL5B6XYy1OABOF646MvilT8tL87LvFKm/1mLhxST71N85dU5xTfCQopvbAqm34Ni3tx9c6S49nOKc0jezfn+0rGQXu8/xV8KL74qhMlp8wyOswzyXp0fXpwTLssX88kyhy4tzjWle1p48TUhbb/PTafRy3upeMdUb2GdZbHv1K0meaSETRfTCOm0//2L958XGJ4r/tZHNxzFPx6JNRJ2pnjbu65yfuUXxZODY4rTIz8XwwOozoJdIqbK8e39i2m0SYwbvvxgcTrx1pZP4cQyUQmj/TTKW15dFXnb4i+VqL+il5JG8/vqmuJMoSyyjxLm1l5mQPa5oOik8CLdDi0fJaZ1kznvkFkErY6hck8VTxbTuhbvSLxkklNeprm4knZQdCtZtwqwO7XfAEFnmbvQnnWPS9hKZhGweK9RO6aZbUfexfsvUVu7tLc4SMNUaUPexRHUDrVtxrvYV7aF7/y9xXnpUWIet6khJeyr9AFJmyZKbWx+cPHq8ZLc1UeS5fSlcS0l3oCLISet3vptXdAtmvoewYYL950xovu54h/7SW3u20hJV03b96FzwQyrkrZ5rTiBylN45FE/ItpSLPucNlw3DXElt1vUz7efv/hLj1wlOxmxpdQWval9X9Han9rOWSPnSppZ2Tp6kj6aurSfol8HHV1NncdCWxTqrOGmtC3xV+nfkouD5TahnE/CbwD1R+bzKfbxLz5EbdeUnTX6K2WL55O581y3/mU5j5OLQ4zoj1eXFqcLjJT2qZSv/MrntVZvg/NKY+OSNqfH56blKvI1vxNFux2i658uX2V/wuoorY2VPKJuynknlV+aLQyvUYr8kn3jleLMI1/JurgWB/ST+5l+X4m8SthL1klpS2k61wSlDOFXubZpzjHit1C5Zsgy3D7ZrrkW6uYV8yttVUe+7jVHtKVOmxfKUdq9m49/sZtcxoxtZJv0vdL5TX6CXhuQba5pE4bHsgxD3bTHki2VfksbLvUTM7b9Reebubat2FRKL+T/8YhB/0PtdbgRPSZvIj/CsC/R9Ec65wz1bWJ+n1HFE+T+E3Q9z8tM1vSnSn9rrk0pbA3rKMgy5xsIvBU+SjnaNqGjp4Etq0uaU8ePFI8d90ZxVlZWsbKVf/oHURO3tTNREDAMBUNH0u9u/CcEKo9XGgjTLW5BHSaNmFgeu4R6l7ZK+Whuj3UizW9+FNKUDGVqhuGxlXbywiOvvgbLPja47S/Nh7IIP4V6EVF4tD2J3BSMIuUxjlzC3f/kIf5glJjdrqHmFllfnDoFCwPmiWEzgqOQl3kGweO96TgcM9YdFcOtNFm9EfTuV+hFo92GYT1UkQgU5zq9huhL4Ujb95WYd9GyP4ic7paHC1daImjqUiRFrsa2fXPEyJzr+fTYeBzIkRWPFxKTPGE+mI4NVOXSdRT2x8fgx6FS2ef+MbOayIfmnmVeQXrkUlDnBKzdgFN5afhOto+gSzTZZ7Jsn0stS+rp0X2gmDf+t1PIQiYOiyyAVUeTUUB32DsFuUPfxtM5u0xyup5sOk5oElrmpdWtAuxO7VecVaU8QjQ8VuxCes3bFIUk2W4oVBu3o57+hu1Impcav2kZVlE6t6n0uDRyB7ZNFdphFFbujEHsQWmkecbsRdgVeQUJ4cFYPKQNnaPNsTAtGdGTn6W0xrY87A1ZIkb4B/RE/+cHiPurdmlnEpfG1Wy8IRe9Y9Nt3ZimpsI2rZiPWe+NgaN8ngYEdEKaSVbEScc2bv2GYMby4aCHXEY2f3g+YWMknIIKc2gUewjmLQ/HrvWrsVo8j6IQc146mxUmM4IPin3Gj0Pp6RzZaul2nfKp36xn7JwuRbaeQkpdWjXVGWnXS6F3YNgWUUqfUXBuB0aKTzG88WP4X1SXc4gO246lAapS+0VtwabtbKxPsy3lPNeVW1r/Leg/TNR/CCLiLyEvcTvIqaA+bAK2naM+T2mPFOQ7fjmS4rciQIgXz2saLTV1XlESycbaOeOKzcXH56bkCrKHfo6ExHDQDTJtZyG89MlCvv65vfoVUqivPbF6ohi7dMUeqI21EYrVlF+KDQVBim5AaX0jPUQussTwoRMREhmKkPXfSTyUpz9KeyOZJdoSPX/9YZJ0zZ6wfC+1lWRse1foo4xtNniLFv0u9BHi/LH//CVET1SeskjpS8o3fc05Y8Yn6PDqB1i3+jVR6NzAL5FIaRtLRUh/FVuZ6suVeEqt10aE3EZsKQklPmF0jc68hP2LhamkwNyFu+npVlmvYdprgCJP+I3f9CU20q/QToRrcsK26WL0oqHfIK39OPIrJP8gYP52KnszPE10X8JT0ymLQuTr+WisPHkVto+LoqQ/ZWhTYsJy+gbm7KRT+gO1+8hda/vqHFiHhcCanFrrMJqCUUIQPaKQncv/ElPw30UaqxY3Bzyi9ZfFEOE2mK5s4l/DP7Xmh6Pul7Nh/Xie5LhTgiL/DrjVzBv/io8xo1CUpO+GGsoo+3E9ePhJJ31KKo1xG9voApciho/CoN6OtFcPvV/qK4ZERggOorK50gKpjVgy4yV6yKds2jCr9Ety4E/watkSzXpOko5vGj50scGoL3/A28/Wx9a5E2HfU+qkFIm168gzJC2N8CuHriF/z6fHec3wVBdpvq0i3+ivnTT3zLb9cxgtdoJ0Eci7AcmNA6aQfWzIPotk+/xJ9imhZ8MOUt7Th3DoyGHsVwo6FYPIg5HiPLAJgV7IN8Pplpk4RRxNQkHpdatIu9NFSCzciD0o3PeT7Zj0nCMaKHaTFS3BR1MBbZvRtiMhMg9H9kiPUuMXjIS9fWsELpBuCE9dfxSeAf6ihLlDvWFj/yJ+v94ET4iPDVWwtpbbjKYMnZ3rf2H9Jul4zIgxCJq/UDyI/OQ3XJAqJicujWtp8cY4mW/rOlqa3Y1c+xMWrZVu6Id/sgbL32hnhlW+Vlb7Kfht/RJ8NERwePU38YaJbpz3nsrUj1CObDrgiw0foZPNaXwwqhfGyAyVaOl3CJ7v4Uy79eA/WrpZEW6qDLcSbaFMsmUparn/2HkcF0uK1ivKaFsspc/ILJLem+A2fgJGiXMzbeDWpRMa/VvWflFQwbydDet/s0znuSC39PNYLevv+8kYcZoZGnbCxPnSuXIuVaqbIAntp2PdpwPgUL+OdLMsBtYzc16JCUr/Yyi3/UQk/PAKWjRsi2f6SdktdKS8MW6AeHPUrs8AcU48DqUineZ+GTLSySLe4KWIAaVfo0rvG2kmU/tBWPzhABRFL0df314IkwvT7eGMtqW8f3BCvAb44+UA4ZyyQtMW+r2YLEr+sYad7DNYWOhKN9FvlnLN0ZetPcq5DrQb+B7mideun/C/6atxThutt2euLy/RRkqxpZW4hkWFDl5tpTLsLJFVprZt7hog9XNCO6lPUlv4vgB6yktbBrKpK1Bpbnp0W5WYQP/PFZrW0+RZrJPX27wzYTLmr9VJUkq/oPHA7sI30CnlodjVb7nlqFKtjj6w6lLy4qMVQaOzoyaiaOcSqEd2A43jiNsji1+HhTXtUsegbOIiwqvnNU6zEi78qro66R7S/hBYH3kfjxZRc69Nh/lFqGVy8aDp6hUXFKKWEeeiSSuhvCjEfz0Sy/z+wls0j9v4lg+1cMZREdpSdJ2VlnB00MZIMrRh6ttyM6QVtyc+84U6n+ZrUyI1deE2Rbt1ilTjwKL+6L+AXFafUZhMo+KLfiDnSbcoSm2lTPbWyandLV3XZg0MddXmNrlHK86PH5JiizSJhmAH2aeJjn3sBPtclBJo9ayHXiNGAYfWY1iA0DF402gIsHHTQgSKMr0R0LkZ1CdNc7JKFcZpaTPCUHvfRjcsZahbxdldml+rpvZ8StJO76+d/EYXqbPWixIPtHyUOG2bUUIMf4OWk6PeyQ4CchQV0bS6NmhRfzUSnt6OJV9/haU7ozBlZC9kbzuFj3ztDbPrHScea9aGmAAAIBdJREFUCEWkEnI6XHMBBX7Crtj38FZnpZ2UxrW0eGOcytbWFfVM/QbRqNjM7o/BorY96tsI+tLQn7wZY4Ur8WKs7wveOjfASg76tW4Lf7Ft0uhSwLd4/vxsuAlXMN2tIAkTW3YTnxz4vjoFkyn9ok1n6DRVeAmJc6GcJzlpV8Xc2ZoQXWHSvqYtlEm2lMe2qYvofEViPf73dT9sm9zT5NoI823RRJ8hN9x46neNbyby6SUum52V+pvrK7XnuVRAqeexrP+Naxo3ALdzpKtTbV1HrlVd8fKipzYdeL5h6ryy1s5BFfvmLFyW+zw9GYZyWzVHAzGBqR5Bzp17CzeE3fb1YSdcP+VNYaQc6/+WZovSz1FBXsaxFXAUn0K6Imj8EESeppt5cgh1N/NtSZtS92zQhpbcszC4vpmXb+KaU1KsHCKwroeJy9Zg+pOjEblpvcmUAmpTfTnKbUup9qLfIJSYnYNCM36Atm2bvgYoD/SzbyvtJ19qJyZrZCKCbmYEl6zdiE8wb8MWTD9EPpDRpKW1KTlTOXyDG3FGC3pgA0sOMJe1KkZGWDRZ5bvN4jzJc6717nRYfkdvCIn8C3VHd5CTyadX9mV6l/RWZHd+XQrP1kiRd+TGYlVXHg3fgqJjN/BIqwYoTj6M/OAEPCJeOPXz/XctDf9eSBUnI+HiZXp/Mx1fp1s32u78OAbZzVojZ4MytqrN6zTwf/KdHo24BjyFYR8vw7Y/9mHbhmUYNnAW4h9tih4+QvotmP3TPlylRSNfT5dGj4eP6KxZsCdKNFwAIQTKYQ1au4hJsDMaSdm1RcfvzK7l+P18vt5lmBRHmOBQ04hr8DcfYlgnNzFfSup13fsSCI+8P5j7C65LUqWnBDbl0FXJV5ZfugXOoQ8NRHz/jfjoCe090fyxunAU825BGNmnMdlHTfb5guxTV8c+ip4ZlPYJ397S4yYhn88L+Pj90cKetPV7AU82BMxxalhWhopMM7/3bncV6gjyqT0fpfY8gNqz2CmVaM9mlKAoXT6alMbaEY32dXxGeqpy9FA8iuo2ogdDmdj67WoaUVYjYtFEBF9vhZm00CriE39R1P7TVzQije9kYsda6QIzL4we7acn4xY9roxePkpMPmXr0XK/SrFkOWY4lbGtl5SpH+Lh2hKNGjaWHWohzhwrbV67hqIFtQGaPSsMfH+pfERPlp7ohVk/bkXELloIuOgDjF20D1ln94sOtbCQcdnMYWgpp864rn12BVxCXFwaMmgx76evS5x7PNlKU4ryZE8JUNpCSplky7kaPou58shrpPAEY+AHWEkffAgL/QWzxo+hx7paZ1IpR++3lD6j8WOSC4i1o/FZKH2Ih74HsHLuLETctC97v1hGOyv1/7cc53lp5/GFes2laWc/zMPKI2lIPfYL3pWf8HRoTQsRzW7mzisV7MXH5WTjw0exbLwn5oqjtGYFlhoZvjcaGVkpWD+frj1C6m4eetN6FEZCf6rZSrGh4f2gJp+JnTR55GT44oWYOc5fGjGnJyFn5OupiWw00qNcE8KxkvqOVGr3360kh9zMJl2hL2Ht17OofSWZSUlRGvnmrzmmhKia90G0PDIrptH01Wb6KFPCyhBeeCuXFg/SFJcJir/gg1ZlbdsmrgHe/aW+efqkZYi9lo4DPy6X+qH2HUFroMu1SR6ZvXizUSJjKW1Kc+bcg29QoswHNaDcCxXne0uLDmkRgeFk8dxInYWK6QelRYI0if5Ke+/iqz6UjxYiXKHFdtcjaXFA2l5tvJBG+U+LAYRFjllyOf8IizzkSerZ26Zr0ynpafL9TXGBoO6k9jPF/2jidWRPFXQ+V5xBCwnF8l41vkDzVuL24gkGiybIvuJijR9pwVbmsTWaBYNKOF1MixPSBR2UBRfKghVTYSYWzPh8rlnYJyzUEBYMrFYWEMg6SGW6FkfQgh/9xQiuxaE75MWC8qKKsunqKi+oulJ8iLgL8sXFNQaLA/TLUhZPeBeHHJMWhiWRfTQ8NLpKC+f085Luos1OFc+Q07mJtonRLLwTFmJKdjfNKZ3YGF10RAzTNXYoW92Esu7J7tSeh2vqrLChX9kOSv0lm2rtZnisse15c+1IrtN544tUgpavM6pLiUUuBvbVLkgaUnxCbMvyOZUYLNtVsKWilymupcSb5WS+rZtrm9rzTljIaLCYR6inKVY6C78UWyj9jeFvwjbtQlz9dj69OO381pJ9gtAeaEFXJrVFZRGlbj638culxV7Ub4rhBm1F0xZOmJMt20jPlmeKQ6YaX+jm9km4ps9Q6mvYNs33GZeK6SatxHkuyDWfT7ddmLezoo+m/ufNnecl61/aeRy9/LUS+tObUqT+5tJ2yY6yLfJ0j020Xem8ogVn43XOe52+QFqoaEauaDuFj3TdUBZv6bYXekorL4bX9h9aRkp+6bwsuy0kfubOrYTgkryEcids+qvUtpS0aUoJ1kJeX3kRvv45RotgX9VhWOJaqK230nbNXXP0ZZfMK8X/VTxPudYrNjdhZ6Uv12sTgu1024gRWyps9Ww59PPiJDGtubat2FTXlzBs738VLyzhH7gWB8sLGpVzSeFlyKSk7pJ8utnQ2E3xBcy1KaUcvTqSb1YW30Dho5RTQkeRk2G9q8exsYWKtQSn+rF6thg+eADxKH0TvlRYRJ+3faR5B1gY3tnT13mKDp9CcRN6nV0bexSMb4rCTbQgcegQ1KLX6SBpPf6jR/u1aF6pHS1CKL5GXz08RHejjzvD0rMl/o2lvLSQyrKzI6RybuPRDk9DVV8e1Sb1ii9TnshY/FdoiUdaOsKi09N4VCdeqcF/505BnXlbORR/azV3p1f92ZCME8gPOwfVC4GwpNcCGd8KceFYDKLikumxniXq0ghNW9cn4d6msTSSTAvzInb9iUs5d+gLhh7o/VwH+d3Nwpe8jiP1jj2e6ewM6UmdsTChVAo/8geO0R2AZVEebFp1QFcPZ9iqMxETc4Z07QAPgTG9xikibD8u3bFBl56+qE2vMTqW3QIDn3OFtRC3dTeNgTWguJ5wa6hGLNmgiGzgSTYQt9J0vV0HT3buQIschdeCncLfl2+jBXF3MuRakInYmJM4e/kyrtMdqR3p26vHM3DQeRyZS/bZQ/bJJPvYk32eJvu0EOQY6tlEuo3OIDudvnYbTVyfRjua85t6kr7sRINp+uWb4CQ2C1NxMvOy1k0iRX/v1u5URWrPu6g9W1B79qH2nEbt+Ra1Zy9qz6DRpuhTl2HvSi/eb0gfz5GP6+jaWNeO1C5NtiOdOlEjR9SOPThz4w4N3DSGO/H2aG0PdV46/jrxN5Ivp9PUqwZ42tcXHs014wma2uruKDqhXmt4dWym88SkEInHYnFNbYG2Hh2Rf5bat44O+m0Gkt4m4+mVbmY4qcy0dTW1rePJt+FEbVNsU7rK07mUevokLmRboD21ZaOvajLBSmAYc1jnfNOTa3BAXKMio3DmGs2/pRVo9o0d0bGjB5zIplnJJ7D7QDzuNHGDv28znNtL6z2cu6F7e2usH9UGb+wEJi/+Ci0Lqc9o3xUDfJ0lxsJXzXTPWSPnimnZ8jluoKZwKHz+99DRk7hGfZQVPSdu3KYDPIX+JbeUtihkNtlnCJHA1dN/Ym809Y3EoEnrjvDxcEV9oR8wmc/gfKQve5a5TxP7ClPnuaiOkT/mz+Osc0ex+9BZOjcs4erTG95KXynY4tgpeuUhnbcdHaEyOKbHN6bPK+ofo/YfxmXqp5/s5o1muWfF9ir2ZbZ5ZuWqhGuBznXj/JqJ8Hp/CwLoOwkvNgNyLJujPy0c1vS1JdqI3F/onHdltkVp/T71iYmREfjzfB5adnoWno/fwP5DF+Haqy+ewGXz/RpZJoPaSii1lbp0Xvh6PIbkc+nUD0r9vaHhhL5h82+xsGzVFj3p2tKgoPS2avKaYyBc6d80fa4cr6Yyw6Nprk6DJ9DLl66pFG62jzJoE4ZtxNCWuJ6Eo9SmUqnPyKb21sb9GfSka4J4+RJ1MNW29duEzmXWoGaFiCf7HDl/k64BzeHdy1dz7TZVZ60AWqR/5C/NdUqr0y1E7TqKf+4Abby7k18h+0mmzu978A0E+5nu17WaVse9CymX8PX3q7F40eeoV0+6vpbbqS5zxdRJyG3cDf/S4h/byEnComoUUUdxmzoKxakusyxOyASYABN4YAnkyU41fXkxnb68qL1yPbA1YsXvL4F42amm10PSF3xNDfzcXx1YOhNgAuYJGHOq71/3ri4Sn+Pg9ELk+h5CrdNR0jEtSLMa5GZeU45lAkyACTxEBArF+Zq5uC1MGr1/ve5DRKymV4WehNBWqBbWJbFTLcLgP0zgASBw/7p3a1fY7FuD/DW/49+kq7QQzR+PBtCbO+j1c7rTOR4ARqwiE2ACTOAeCKjgPHgihjvXg53wyI43JlAKgdpNfOhtSC3pBRP37xJdigoczQSYwF0QuK9n7CMd+8Dmyz53oRZnYQJMgAk8LASs0H30VHR/WKrD9bjvBJz6jsPKvve9GC6ACTCBCiZw96/Uq2BFWBwTYAJMgAkwASbABJgAE3hQCbBT/aBajvVmAkyACTABJsAEmAATqDYE2KmuNqaoKkXUyM3KEwtXZ6Uh5sgJJF6TjoVXckXRcWqWWowvyLul98GZqtK4Iss1rGP5ZGvZlS8fp2YCTIAJMAEmwAQeNgLldqolx+soYpNL+TLXw0bqPtdHeNfvgSNHyYk9ipjTaQalFSImdAU++HgWZi3ZjlTpQ5UGaYRDelfvyROIOkYy6F2gJTbhXZJiGSdwQXaUE7dMQuMn2uCzyHQUXNqJHgED8MqmRDFrStgM+NHx5qQ8+rDjbnrvtCvs39te8Y618N5Pod7HToj/BQaxpL/kypeoRYUG6NaxvIJ12ZU3L6dnAkyACTABJsAEHi4C5V6oGPfL/9BjWhToCz2Ipg+4VL8tExFrtuJc3Q4IGvKM/PGV6qeloUbntvij/wI5tP0cpEWOkz95rsaBRSMpLkqO/AmLPpmIU+lT4VTCeoX4fcIATBE/jzuK0nyhlyZ19+fwGbNelENfL8KkzvWQf53ezELbifM3AC/p1U2OlhZimIWVg/hL33dAwY1L4j5irlW8s1t4Hh8FDEKkVIL2b785SFozDg4l6qlNcq97unU0L6tku9Jj59vYfHaOZQJMgAkwASbABB5qAuUeqVacEMXxqnZ01P/gp/dnYsras9VONXMKtRmyFxGbPoevkKiVleZVturk32WH2hU/bgvBDB8hwRJ8uumMsFNis2ulBK3Hb7GZygH93sLvKySHWggUHGVhc3/pM4SsDsE3o1ylABN/bTu+gkOb1mD/hhHylyNNJLyb4EctQB8NA9qPwo/Ba7B68USIbzLfORPTf6MvblaHzUi7Kiu76qA+68AEmAATYAJMgAncXwIVOwZYQJ/u3vobQg+cQTq9u97VdzAmvdFTHHFNPbIVwX9mouuQEeje2gYF9KntVRuj0PCZYRjm2xBRG1Yi1qYLejW9iJU/p2DotInwbPgvYkPXYeWOQ0hHIwwc+RZG+TqKRLKSj2LLlh2IiqURVNtG6CnEda2LiPXbkCKkuPkHvl5SiG6DXoF3c/qE8Ll9+OH7X3GCPgnu6vs83h7bR/yUcS7p8dP363H4FI3YNnVC1+79MHyQzudgxdIAQf/NMZlo7fYEruz9Ffsv1kaPoNfx1nPOcgr6LLCJMsS6x1hg2NAnsGvJRtg9T7p20R/ZrN/aFd4tIDmXGonAefqMubD5Tp1PdX8GWbWnY67/PGzccAzfjHA16+BO//kwJnYeIDro6uQ/MIU+EW+4ZSQl4OLVPDSj6SB1DSN1jgsux+L4JZpScjMOHZpLTwAyTu/DyhXElL4G7+j8LMaOewnt6lMmdRpCvg9Bjltf9G+RibVrQpGW74CBbwbBr42ZT2W3ehov9u1DTxf6kFN9RfxMb05OvqiFybLoE7pRW9bhaE4TdGqZh80hu+gTwx0x9r3Xye70KXRFlzZ9MbYv3TgIxyt/w3W7pxE04hmdGkq75WlXra9p2TnQJ9aFT5xL7fVv3EZtuPsNx2tDOok2ktr7cWrvPdG26Bh+3n6K2ltXTHx7EFqY/v5sCf04gAkwASbABJgAE6ieBCrUqY767v8QuIBGUNv7w/d0OBbt3ILLDQ9i5RBnZP4dirkLwuFr1QndadqI+sYpTFmwEL7ze5NTXR9nNszTc/o6vjkWWd8PQuDXJA/CKGo4wjatx7ngGMzuXYT5nQdhKYX69vNHJIVv3HQB7c7NpVHqJYgXWFP5cz8Jx7yuQ9Hm2jo4+s8UQuHWHggjvRb9tRTp33XA1CcHYRWF+/bzFuUIZTTqkoxRraWpEGIm+iPoP53k6W5hO9cjZXUUvhjoiIxjK4yX8cMgqe6Ud+4nUm7fli+WcKrFGLXhLGI1kuLEuRzo6N5YTFLfsaM4mh15KBoXC16BmzmHbO0WRM8cAG9ydKO3BEuFG/xNP74FU6YRp6f7wrmOQaTOoWCvd+gJAGhqyhCaVpNzZBkcA+bppNiCpQt2Yf/51fC0uIHNnyxEGBbiHZ0Uq2Lq6kxr0YkosavGlVS6yaEtm75Al2GurPpqnFlLI9p6Nwzh2Lj2EHYkbkb32rIu7etiCDnV9QvpeNo8hFE9XjZ0qtUp5WpXdXTYeTS0RtjH/THsB6G9yhu1pemHqJ19OQgQ27vAS5cZtZ+GLggZbf4pgSKOf5kAE2ACTIAJMIHqS6Dc0z9MVyUPF660RNDUpUiKXI1t++aISXOu54u/Fla24q+dPF8XKslptZMFWik79BnzoHe/Qg/VQdmhfg3Rl8KRtu8rMeWiZX8gqzCHvtA4BPOWh2PX+tVYPVSIikLM5aYIubQdAcKhzxykZF6hecO5+E52qBeGn0J0RBQmk2ONTcE4k55NI+DCNgpzvw5GXvoZRARvRaCBQy2kUPR3e/UrUe6J1ROFYCxdsQdZSDNdRpY2r5B++KuvYWKftsJuGbY8XDslOWntWjaS0tvSV9nEPfrk8b+mRBCbqUMoMhwbDqbRbxI2CHOyfSZi9fxRepmUeinTQfQidQ9ke6EBTU0h53Oh7FDPCI5CXuYZBI/3ptThmLHuKEBfjVNGvX3HL0dS/FbJJjrTWnRFa/Z3bsLMuQswcaA/2Z70pW18LyvzZVEape3MCP7/9u4HKIrrjgP413gIgooWTSEgoMEaIKcWASNEBXViVJKY2CipzMQ/CXam0omNttWSxkyM1vgnJI6pCaOmDdbUDFMnhQBap7aKUUGGiIj18B9/Rg1KFfkPan+7e3+3x8nZxpH0+2a4u7f7dt/bzy4zv3339t0/1LZ89KISpB7Glhyxs7TFUrc+r1RiSW5dV77Wa0KxazV9aQ6oZ2NfeRWa/pmDZGW/v/8p9pia5KepbTdpqz8/jMoC7f9DfofYUjvfKUABClCAAhTowQL/w6DaBymbtmLJkwPx57fT4Jeo9Qx3ZWPwkEjkP1I4dhZ/hs1vzIXnlSrz2kzEBgcjMHGplv+XdF36GPHurl8hyucUfpEyBQs+t9uRjM9VA7oBnvIFvKSmelj6DpdPM8InMA4b1M7fwzhU0xfao5ZZSBg5DLHzP0THyMdcDqlY/EqSDEQBRj6VpI1/LqzGlWsu6qi0zZIyc00Btm16CzOdBO12R2D30QdhMUqwCpRW1mnLG2+gQf00BN4SIDpPfTFuxjNq+7bvPoTyI3vV3vjkl2dh9GDnW7i1VILPC+oGKXh+aqh88sVU+fl5JR3cVyY3GeYUkY5P30lCwEBva5BtWeX8XQLhjM3YXqicsTh8sKcIswLaulcXZuOZhDDZzhfT5idpu9cFrFr4anBetbLUnetKt5fODhnvJGnCqgWI85c6Bkchbc00dZmpWlunrc/B0smhGORtC7LVQnyhAAUoQAEKUKBHC7iIMO5yXJ5qyGpXSJmlYoY8VCcBUXwKlknP5Yat0tuojx08tSrPFh+329byMRih5qkeOpvNwej0dSj57QR0tnRqY4MlPOvXWom04InasI2Xl2OZ9FRvkAf3bI/3KfvrY33YT9v7bHx55HX4d0hopTS9pQMDQkYgQHpZJ8rQiIwMGRKQtxkz8s6gsHYHxrgaVqHsUILbeuU9YiAGWMs6q8MH9SeVgsC08cO1D12+6k+HAf5h2gwcR7+uAZRhJhVF2iwZ08cixFqvfoct8B0+DinTJcjNW4rYPGV9OJKnhMMjr0Vf+L/It0AdsSLNtrXc7oSH9NdubLpbQ3w6SrbPxQA5RYP8/bSZW+SmSEt3qQuN6DCXvFl7Sf3UoC7xMC+Fur/OS2cho5mdp3u6rsy7Mnc411+23UQ135RvVCT19bDpWL6pMRc3b6y9tba2wcvLzs9hLTMUoAAFKEABCjzIAvfcU5277VPsyd+LPV/kYHd2DkprzyFXCagleNv5/i8xJypSPe4L1Vcd5jVuuHoW+3a9idglWc5dzEMaBg17TFufdwyVDX0ROMiAivyP8ZezLWg9c0ANqCFB2Ie/mYNg857qrlr7SIGLx7H212uxr84boer6bOQW1+P7IYPQef4rvLvzNPr3NklP9yY0jZqLP+bvx0K1XAHOXJLe8C5Swf5jqLt+AVlr3tTGbk8cgyGe/buuw8cWULW5mIyu7nItqs9VQw3DLtagsqYWl6624VF5qFJJ5Rlz8J5Yr1+5Xs0vnDPORY+6BJgGX0yZ86paVn2ZngoZuo6Wrg/NVtbVJ2Xsic8jSIhXCmXjrcy/STsrkJGufTOR/FK0eSpAVzvpYt2A/ggc7IcAS0CtFOt2XVU4ebIWdfKw6Dup2rWVMFqZCsUAdah4Qw2OysOmSdGp2nnTuvsdGtLoznVV4xgWez0cpM5YUr51NbYdkXNZ/Ce8Zp4G0TjMxcOZ5hYUfbQAfoHDsGiX8j/ERAEKUIACFKBATxOwRXzdbHlHm9YLiFOZmDcv07rVGwWliJaeUeRVYF600bq8XHqAS36eiFFRo2VZNg6uTXWYj/hCu9a/2HBR2eSmtbfRa9gM7P5JuIxTzZYHGbOt+0O8EUv+YDQ/rLcaxkdXW9e9vf0QXouLkBHOkk5lqcM86se9hJV70rFl1mpsWZIkf5bicfjxs89hS16m+mdZCqRhvIvhGbmr5iF3laX0bBxYngiDKC7too5Fy5+Ht9msrd2ynf79BrIiY5BuWXxqM+JHbwZW5KBp2VM4sHE2El7PRvqCVK2EjBdfKb3WzpLmWIUOCZ4DJs6QQC9TDSKXLU5Qe2ot58/SFse8FnFbzonDOoM5Gr+o3Br4YeH7n+CL6PliYechNzmrlPHMbSXaOVDLSitvdTjm9Q13uf4udUHGK6upAounxVj3HCljuZc84SeDnb+RmTgkFcq3EDOtq2UWE+0Wx/4Y+4W5d10tsjuvBv9E7Pj4VcSmZuJnM23tSN4oY/yDDGg84WiLTvt8E07kFqiN+6zoLLbJrC5MFKAABShAAQr0LIFe6zdsuvM9335IfsE8DvUu7Vd++e/rK82wfakuG0hc7G8ci+Fe8gMZuQdQ1e6DJxInoK9MV1fcMBTPTg6XgK4T54oPovhiE4LCxyM2pBXHSs7Dd8QPEenviXMnjqO63Q/josPU4E9rhmwjU8oVfyODOTqa4BNixPgxYegnQez18yXY+/dytPtHYtqEQJj2H0ZH2ERMivCTbXKQf7oJI6KeROKoQHVoQmNNGf56sBTX2vrILwOGYmzUWAwdaIDyM9VFJadxpb4Rffx/gAkJ4xDgZFhF+Sdp6hRvM1esw48CJfzvEyRBmuPUe13WoZjVNGOoYiR1Okt1pjKYrqnhn3W1b9DjiFSmhZOkHlNRFTwfGSWzbzzZZW9wnakEpy57YPR4IwYaxE9xbfZGhNzoDFHdHNvSerkSR03XtLZ53UBRUQU8gowYI72ryvEcP9+M4dLuof2aUPpVGTr8wxEzQoJVJTXJFIr5h1B1s11Mx2DqZKPWe678QmJxmUxtF4TYUaHyYKMur21te73beld1SVCdlTICi/OAZRvfQ7DcLfhFjEfShDDrkJTWy2XIL6yEx8NhiI8JRm1pGW4YpG3RoTK1o90xKteDG9dVp72d+bxeNx3F3sIzcnvYB+HxUxFntuqUbzeOldXALzwGIwd7wpL3Nlu31pRgZ64Jo56bhRj5f2CiAAUoQAEKUODBFTh3oQoZv9uBjRvWwddX+0ba7aD6wT28b7dllqD6g4PnsSiCQc+3q+3O3i1B9Wwcu7IZkc7vWdzZIctSgAIUoAAFKEABlwLOgup7HlPtsqbv5EptBoe2ztbv5NH15INqU8dHyxSD5hEqPflY2HYKUIACFKAABXqmAPv1unne+vrHI/nFYIT0J1k3ye5TMQPCXkhDcpjM393lFIP3qSmshgIUoAAFKECB/1sBRojdPPXDn34F257uZmEWu48Cnpg0fwUm3ccaWRUFKEABClCAAhTQC3D4h16EeQpQgAIUoAAFKEABCrgpwKDaTTAWpwAFKEABClCAAhSggF6AQbVehHkKUIACFKAABShAAQq4KcCg2k0wFqcABShAAQpQgAIUoIBegEG1XoR5ClCAAhSgAAUoQAEKuCnAoNpNMBanAAUoQAEKUIACFKCAXoBBtV6EeQpQgAIUoAAFKEABCrgpwKDaTTAWpwAFKEABClCAAhSggF6AQbVehHkKUIACFKAABShAAQq4KcCg2k0wFqcABShAAQpQgAIUoIBegEG1XoR5ClCAAhSgAAUoQAEKuCnAoNpNMBanAAUoQAEKUIACFKCAXsDwUK+H0EuW3rp1W7+OeQpQgAIUoAAFKEABClBAJ3D79h307t3bYanh9p3bKDx6XP1zWMMMBShAAQpQgAIUoAAFKNAtgV5nTKY7N282dqswC1GAAhSgAAUoQAEKUIACmoDx8Uh4eHiomV53JBGGAhSgAAUoQAEKUIACFLh3gX8DxRd86eP5+A4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from IPython.display import Image\n",
    "Image(\"chocoNobel.png\")"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}