jmharkins/mock-random-walk-poisson.ipynb

## mock-random-walk-poisson.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing out a model with random walk Poisson parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import theano.tensor as tt\n",
    "import pymc3 as pm\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read in basic mock data\n",
    "Each row has:\n",
    "- a pair of individual IDs for an \"A\" and \"B\" individual\n",
    "- a column for how many rows so far have contained this individual (e.g. a representation of \"time\" in the sample)\n",
    "- an \"interval\" representing a period of observations for each individual (basically make 10 total intervals over the 38 total observations for each individual)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('mock_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n_a</th>\n",
       "      <th>n_b</th>\n",
       "      <th>interval_a</th>\n",
       "      <th>interval_b</th>\n",
       "      <th>id_a</th>\n",
       "      <th>id_b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   n_a  n_b  interval_a  interval_b  id_a  id_b\n",
       "0    0    0           0           0     0     3\n",
       "1    0    0           0           0     8    16\n",
       "2    0    0           0           0     7    17\n",
       "3    0    0           0           0    10    19\n",
       "4    0    0           0           0    18     4"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(380, 6)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(My basic definition for interval below:)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#data['interval_a'] = (data.n_a // 4)\n",
    "#data['interval_b'] = (data.n_b // 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.interval_a.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating mock data  \n",
    "I want to model a process where each row has two values, one for each individual, that come from a Poisson process.\n",
    "Furthermore, each individual has two parameters The Poisson distribution is parameterized such that:\n",
    "$$X_a \\sim Poisson(\\theta_a)$$\n",
    "$$X_b \\sim Poisson(\\theta_b)$$\n",
    "Where:\n",
    "$$log(\\theta_a) = add_a + sub_b$$\n",
    "$$log(\\theta_b) = add_b + sub_a$$\n",
    "\n",
    "That is, each individual has a true \"add\" rate and \"sub(tract)\" rate that contributes to their own count value and that of their paired individual. In this example, I'd like these parameters to vary over time according to a random walk. Thus, the add/subtract rates will be unique to each combination of (individual, interval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create \"True\" starting  Poisson rates for each individual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "true_add_rates = np.random.gamma(10, 1/8., size=(20,1))\n",
    "true_sub_rates = np.random.gamma(10, 1/8., size=(20,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, add a random walk to these parameters for each individual over the 10 total intervals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "att_rw = np.random.normal(0, 0.05, size=(20,9))\n",
    "def_rw = np.random.normal(0, 0.05, size=(20,9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "interval_add_rates = np.concatenate((true_add_rates, att_rw), axis=1).cumsum(axis=1)\n",
    "interval_sub_rates = np.concatenate((true_sub_rates, def_rw), axis=1).cumsum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example of true \"add\" rate for individual 0, varying over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.7330871 ,  0.62427348,  0.71040413,  0.71312737,  0.76179902,\n",
       "        0.76833135,  0.80889259,  0.76476117,  0.71151382,  0.61701864])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interval_add_rates[0,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I also impose a sum-to-zero constraint here on each of the add/subtract rates across all of the individuals, for each interval. This is achieved by subtracting the mean from each of the individual parameters. I add the mean back in later when taking poisson draws "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "true_add_rates = (interval_add_rates - interval_add_rates.mean(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "true_sub_rates = (interval_sub_rates - interval_sub_rates.mean(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 10)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "true_add_rates.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Join these true rates for each individual-interval back to the original data with pairs of individuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "full_add_rates = pd.DataFrame(true_add_rates)\n",
    "full_sub_rates = pd.DataFrame(true_sub_rates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "full_add_rates = full_add_rates.stack()\n",
    "full_add_rates.index.names = ['full_id', 'interval']\n",
    "full_add_rates.name = 'true_add'\n",
    "full_sub_rates = full_sub_rates.stack()\n",
    "full_sub_rates.index.names = ['full_id', 'interval']\n",
    "full_sub_rates.name = 'true_sub'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = pd.merge(data, full_add_rates.to_frame(),\n",
    "                    how='left', left_on=['id_a','interval_a'],\n",
    "                    right_index=True)\n",
    "data = pd.merge(data, full_add_rates.to_frame(),\n",
    "                    how='left', left_on=['id_b', 'interval_b'],\n",
    "                    right_index=True)\n",
    "data = data.rename(columns={'true_add_x': 'true_add_a', 'true_add_y': 'true_add_b'})\n",
    "data = pd.merge(data, full_sub_rates.to_frame(),\n",
    "                    how='left', left_on=['id_a','interval_a'],\n",
    "                    right_index=True)\n",
    "data = pd.merge(data, full_sub_rates.to_frame(),\n",
    "                    how='left', left_on=['id_b', 'interval_b'],\n",
    "                    right_index=True)\n",
    "data = data.rename(columns={'true_sub_x': 'true_sub_a', 'true_sub_y': 'true_sub_b'})\n",
    "data = data[[i for i in data.columns if 'full_id' not in i]].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.55518725,  0.06094377,  0.28350138, -0.09583855, -0.44010963,\n",
       "        0.13159133, -0.01521144, -0.47137044, -0.162909  ,  0.38012936,\n",
       "        0.97410712,  0.5041915 , -0.75094072,  0.42809228, -0.10629827,\n",
       "       -0.03211416, -0.82190344,  0.58301241,  0.1797391 , -0.07342536])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "true_add_rates.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>n_a</th>\n",
       "      <th>n_b</th>\n",
       "      <th>interval_a</th>\n",
       "      <th>interval_b</th>\n",
       "      <th>id_a</th>\n",
       "      <th>id_b</th>\n",
       "      <th>true_add_a</th>\n",
       "      <th>true_add_b</th>\n",
       "      <th>true_sub_a</th>\n",
       "      <th>true_sub_b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.565807</td>\n",
       "      <td>-0.090804</td>\n",
       "      <td>1.028134</td>\n",
       "      <td>-0.025533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>16</td>\n",
       "      <td>-0.235958</td>\n",
       "      <td>-0.730789</td>\n",
       "      <td>0.909008</td>\n",
       "      <td>0.095859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>17</td>\n",
       "      <td>-0.576231</td>\n",
       "      <td>0.663638</td>\n",
       "      <td>-0.317331</td>\n",
       "      <td>0.147703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>19</td>\n",
       "      <td>0.960896</td>\n",
       "      <td>-0.070490</td>\n",
       "      <td>-0.323154</td>\n",
       "      <td>0.155722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>4</td>\n",
       "      <td>0.087794</td>\n",
       "      <td>-0.389996</td>\n",
       "      <td>-0.388655</td>\n",
       "      <td>0.190206</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   n_a  n_b  interval_a  interval_b  id_a  id_b  true_add_a  true_add_b  \\\n",
       "0    0    0           0           0     0     3   -0.565807   -0.090804   \n",
       "1    0    0           0           0     8    16   -0.235958   -0.730789   \n",
       "2    0    0           0           0     7    17   -0.576231    0.663638   \n",
       "3    0    0           0           0    10    19    0.960896   -0.070490   \n",
       "4    0    0           0           0    18     4    0.087794   -0.389996   \n",
       "\n",
       "   true_sub_a  true_sub_b  \n",
       "0    1.028134   -0.025533  \n",
       "1    0.909008    0.095859  \n",
       "2   -0.317331    0.147703  \n",
       "3   -0.323154    0.155722  \n",
       "4   -0.388655    0.190206  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute some sample counts to build the model from by combining the true rates in the way described above to get a unique poisson parameter for each combination of teams and intervals. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data['rate_a'] = np.exp(np.log(1.25) + data.true_add_a + data.true_sub_b)\n",
    "data['rate_b'] = np.exp(np.log(1.25) + data.true_add_b + data.true_sub_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data['value_a'] = data.apply(lambda x: np.random.poisson(x.rate_a), axis=1)\n",
    "data['value_b'] = data.apply(lambda x: np.random.poisson(x.rate_b), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>n_a</th>\n",
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       "      <th>interval_a</th>\n",
       "      <th>interval_b</th>\n",
       "      <th>id_a</th>\n",
       "      <th>id_b</th>\n",
       "      <th>true_add_a</th>\n",
       "      <th>true_add_b</th>\n",
       "      <th>true_sub_a</th>\n",
       "      <th>true_sub_b</th>\n",
       "      <th>rate_a</th>\n",
       "      <th>rate_b</th>\n",
       "      <th>value_a</th>\n",
       "      <th>value_b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <td>-0.565807</td>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
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       "      <td>-0.235958</td>\n",
       "      <td>-0.730789</td>\n",
       "      <td>0.909008</td>\n",
       "      <td>0.095859</td>\n",
       "      <td>1.086591</td>\n",
       "      <td>1.493859</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>17</td>\n",
       "      <td>-0.576231</td>\n",
       "      <td>0.663638</td>\n",
       "      <td>-0.317331</td>\n",
       "      <td>0.147703</td>\n",
       "      <td>0.814335</td>\n",
       "      <td>1.767295</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>19</td>\n",
       "      <td>0.960896</td>\n",
       "      <td>-0.070490</td>\n",
       "      <td>-0.323154</td>\n",
       "      <td>0.155722</td>\n",
       "      <td>3.818134</td>\n",
       "      <td>0.843243</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>4</td>\n",
       "      <td>0.087794</td>\n",
       "      <td>-0.389996</td>\n",
       "      <td>-0.388655</td>\n",
       "      <td>0.190206</td>\n",
       "      <td>1.650608</td>\n",
       "      <td>0.573781</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   n_a  n_b  interval_a  interval_b  id_a  id_b  true_add_a  true_add_b  \\\n",
       "0    0    0           0           0     0     3   -0.565807   -0.090804   \n",
       "1    0    0           0           0     8    16   -0.235958   -0.730789   \n",
       "2    0    0           0           0     7    17   -0.576231    0.663638   \n",
       "3    0    0           0           0    10    19    0.960896   -0.070490   \n",
       "4    0    0           0           0    18     4    0.087794   -0.389996   \n",
       "\n",
       "   true_sub_a  true_sub_b    rate_a    rate_b  value_a  value_b  \n",
       "0    1.028134   -0.025533  0.691981  3.191444        1        1  \n",
       "1    0.909008    0.095859  1.086591  1.493859        0        1  \n",
       "2   -0.317331    0.147703  0.814335  1.767295        1        1  \n",
       "3   -0.323154    0.155722  3.818134  0.843243        2        0  \n",
       "4   -0.388655    0.190206  1.650608  0.573781        1        0  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "id_a = data.id_a.values\n",
    "id_b = data.id_b.values\n",
    "interval_a = data.interval_a.values\n",
    "interval_b = data.interval_b.values\n",
    "obs_value_a = data.value_a.astype('int').values\n",
    "obs_value_b = data.value_b.astype('int').values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rename_map = {i:i.split('_')[0] for i in data.columns if ('_a' in i) or ('_b' in i)}\n",
    "add_values_1 = data[['interval_b','id_b', 'value_b']].rename(columns=rename_map)\n",
    "add_values_2 = data[['interval_a','id_a', 'value_a']].rename(columns=rename_map)\n",
    "sub_values_1 = data[['interval_b','id_b', 'value_a']].rename(columns=rename_map)\n",
    "sub_values_2 = data[['interval_a','id_a', 'value_b']].rename(columns=rename_map)\n",
    "full_add_vals = pd.concat([add_values_1, add_values_2],axis=0)\n",
    "full_sub_vals = pd.concat([sub_values_1, sub_values_2],axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "add_estimate = full_add_vals.groupby(['interval','id']).value.mean().unstack()\n",
    "sub_estimate = full_sub_vals.groupby(['interval','id']).value.mean().unstack()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 20)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "add_estimate.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Functions for doing log transformation of thetas for poisson RVs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def a_theta_fn(id_a,\n",
    "               id_b,\n",
    "               interval_a,\n",
    "               interval_b,                                    \n",
    "               adds_est,\n",
    "               subs_est,\n",
    "               intercept):\n",
    "    log_theta = intercept + \\\n",
    "                adds_est[interval_a, id_a] + \\\n",
    "                subs_est[interval_b, id_b]\n",
    "    return tt.exp(log_theta)\n",
    "\n",
    "\n",
    "def b_theta_fn(id_a,\n",
    "               id_b,\n",
    "               interval_a,\n",
    "               interval_b,                                    \n",
    "               adds_est,\n",
    "               subs_est,\n",
    "               intercept):\n",
    "    log_theta = intercept + \\\n",
    "                adds_est[interval_b, id_b] + \\\n",
    "                subs_est[interval_a, id_a]\n",
    "    return tt.exp(log_theta)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model Specification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construct model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_intervals = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    intercept = pm.Normal('intercept', mu=0, sd=1, testval=0.25)\n",
    "    adds_star = pm.GaussianRandomWalk(\"adds_star\",\n",
    "                          sd=0.0001,\n",
    "                          shape=(n_intervals, add_estimate.shape[1]),\n",
    "                          testval=add_estimate)\n",
    "    subs_star = pm.GaussianRandomWalk(\"subs_star\",\n",
    "                          sd=0.0001,\n",
    "                          shape=(n_intervals, sub_estimate.shape[1]),\n",
    "                          testval=sub_estimate)\n",
    "    \n",
    "    # normalize parameters -sum to zero constraint\n",
    "    adds_est = pm.Deterministic(\"adds\", adds_star - tt.tile(adds_star.mean(axis=1), (adds_star.shape[1], 1)).T)\n",
    "    subs_est = pm.Deterministic(\"subs\", subs_star - tt.tile(subs_star.mean(axis=1), (subs_star.shape[1], 1)).T)\n",
    "\n",
    "    a_dtistic = a_theta_fn(id_a,\n",
    "                           id_b,\n",
    "                           interval_a,\n",
    "                           interval_b,                                    \n",
    "                           adds_est,\n",
    "                           subs_est,\n",
    "                           intercept)\n",
    "\n",
    "    b_dtistic = b_theta_fn(id_a,\n",
    "                           id_b,\n",
    "                           interval_a,\n",
    "                           interval_b,                                    \n",
    "                           adds_est,\n",
    "                           subs_est,\n",
    "                           intercept)\n",
    "\n",
    "    a_theta = pm.Deterministic(\"home_theta\", a_dtistic)\n",
    "    b_theta = pm.Deterministic(\"away_theta\", b_dtistic)\n",
    "\n",
    "    a_counts = pm.Poisson('a_counts',\n",
    "                            mu=a_theta,\n",
    "                            observed=obs_value_a)\n",
    "    b_counts = pm.Poisson('b_counts',\n",
    "                            mu=b_theta,\n",
    "                            observed=obs_value_b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MCMC sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10500/10500 [00:12<00:00, 860.50it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    step1 = pm.Metropolis()\n",
    "    trace = pm.sample(10000, step=step1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This should be "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x127864f50>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x127918090>]], dtype=object)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UPB1cTgeuuTE4ZEHLN8G6HgiqagxARByAV1UDqnrPjEVnjFlUev1hHtvTya2X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\nABGBBQAAEBFYAAAAkQFvAE33pw4lmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f061dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['intercept'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x12accac50>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x12ad39c10>]], dtype=object)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cB851HroqpVQz6feZf3O1hSZ2XbQ9ypJyGERxO3iyrHYrXhRtnUXpQWoE7eCp\nrmlgd4KnUGXcU5RDZGXUQ6uzXMYysPVM+F3qrFv4W8BlKeX/dr/H20nSNjnVO0Jltpdqpc5wPMQR\nvcX80Gk+e/Uy49lHGU3AoplHlzHXAo9Ir5Hqt3jDS+P26TzUajCUSBCHkjiKaVo2RTGIFT7NNXOG\n0fQw5CWu65Jr9WCNSOojDq+/o2EXQZrQyB+hkqzQax5huW+OaqnErcYN4rrAEDGeOUto6lijOWQK\nQtdGapt7lDLlOv3ZPNlEChHDwPB5Ev3demkkoTiNMCSO26C8sIQvNVKZFBKfTN6gXmuhH2lfI5Kh\nS+xMcKz3GJq1OdWy4we8VZmmYs4ijNXKaGC4SFtH8xdx6rOkwhwyBhFm0bGJvdXrqS8KxHYe8pt/\njdxGg5oOTW+OYtXFcDaWoXuXx04dIVEUERkS1+8nmWi/nxO3L1OtLWAmrhIGEfmcTTrTHm4X+AHV\n6RbTbxfpMTPrz7HhZIutMlIHabY3iFgw1N/HU48927UsbrVO8dZtgqDcdfuekDHN1hyp7IaMf1GE\nVg2gsqZKueH1WIsNehoGg0P3tzbS3dbtBRbZs2fIPPHUtvtJKbn8UoJMOiST3SE9f7YPOXSGXN9T\n+zLPOywW0Wo1Nr5ae3wcyiDqC3tyHhlGgAFWD4lj50g8tv08vLvljE8SPf8aTNRwZYR4+OzOZdrn\nVPtr7XqRXOADwInOc54WQiCl/N19KZUCQDC32v0bzs9jnThxcIXZY3eG7XVS3kbhwSdmiOLoTsKI\nltDaCSNgdc0nRVEOg88JIXqAfwG8Rruq9X/vwXE/DPw94G0hxBudx35RSvn5PTj2JkIIPngkxdde\nT1J49AT64mvcZgB3/goBAhFYLBSGiIwkTmOWQqoB0uR4psJCYxzNMFjsPcmZ4VMsjdfQqstcI4kT\np5nrE+ixQCbrfHfP+3hzqUI2ypIveYhGCd9/k7jPgR4dfQCG3V7SiRbZdBanP0vkBVgkMY0+9IyP\nYRgUTp5ChjEDYgBLXz8HV8YS//oiSVNDT+i4lyahsozXqGz52pNPnCE1dIz4ym2ygwMgJHEcMVI6\nj20nSZ5uDzsKZq5SFjFWIoGe7bLOk/RpjNfw9fX9HtOuhkjHhI1Zas4UNQANbO0ICfMck/aaxsg4\nJNY9LGvtxIr20SKrge2GJKIlhJ7BsLfr9RGd/+XGhzbd9cIqiw2Dhcnn0To9RPWGQNcNTDNF6Ds0\nahGxbDf6uATZAAAgAElEQVQsxkGMCziyQi3ePn22pgty6T5y6fb71QqauKHGzetbTRyRmKkCRx/P\n71vGssWXvkl9cZnmDKx7UyIN08l0Cr6+J2ZlL1umSSf76X1offC339nV3KtXiSd8XLYfigeQWhhD\nLmnsdgyN1l9F7Evaex07O4i5YY0140gSobXQ7D3s7dINvFyG6ZvX4NVv7t1xgVapSbVUxAJwPTKj\n53Z6CtHmdbL3zW4Xyf0McBp4A1hpdpG018RQ9kkwP7fm9sJ7K3gK2xeEw9TztBI4JTSTpvSRdg4B\n1N0yqXgEfYcUpIqi7D8p5a90bv6REOJztBMa7bz4zc7H/ToPcjY6cO3KJWrFmzhvv8ntVAo7b5Ia\nfwlZ8UmaWeJmiCWa2KFkNJ7nYXOOo9Ygt40iF+0cju5y6dUUbhThamXiMCLpJ3lkAd6IYT5lk44v\nEffCazWP89518MCwBb0jg2i5PEUmMHpa5DJD6MIh8hxkzgLTIBEf58RDwyRzNiS3Ho4kY4nb1JBh\nu1JvHg0RpoOe6lZRkwTz88jWDPFyjULKQ1bGiVst9DimOVGkuFxHu9BuvHL9Bl7gER4ZgqDLd7BM\nkkw+Qo4CGqsVxoHUZfr7A9LPPkndN8FMEvs+lbcv4LhvIb3VsjnSINB6kO7mno04EngGmFEC03fQ\nmmvStHeb5tN12+qdlbBHj2KyYUi+/xF0s12WnnzIUOE4w8NjvHBxjkq9SStaWZAqRtozHMsv0Dcw\nu/nEd0bbSRqVFjYNEnr7mnZjeYmFlsPc1JXNzwNiLyQOYKgUou/XOlZVSV9YoG9gw9wVCVqvSfLM\n4JarnMooJnQ8Ss483f5Eu8ZQax5ct1l2PUTXg3jhMvFCC+avdzvSuod8X5Ao9GGumb/Wje+D15QE\net+O2fbuRVirEwY+2oaFoLUI8meHKZzqJFTYOLVt7QMb5q/JLr/LQRTw5889j5yvkK1KktkNa7/d\npyiIiMUQPWMhlZvjLI1/Y8f3q/e4Tn7gwcx72m3P0zPAI/JBL+/8LS5aKqLl88TVKlGlewveu9VK\nz5PVyYxyGIKnlflOg1aeSbeIa6dxNY2P/sXf5Scf/0l++umfPuASKooihHgL+H3gD6SUN4HtZ88f\nUjKKuT01R6+cZSE1RkSE0/IYqN7iCa2Xt3MFwkSGMI55tBpiyyS6naS4rJPSBU/qc0Saw2DuQ1yt\n3WAxt4hTCThS1jhihbxoDlA3I0oiRLgzxOkMyUwaQxgkkud58pmPEwQON80/wnDrDKRTaGWHhiXR\ndRdXzrJcvMntbw5jiAQnTo+hZbIE+VNgZza/oFNpklY7eEmKfoS+dQv39Ff/Jf7ya7AUolUrmPqT\n6KaNmUpQqi8Q6A3ssD28SGghRkoyIFJosnvWWc3WyfZl12UvawxEkG0R5AwGjnyQRP48cRSSMHRa\nZQdLrmZFqyzN47fmse3Nx5/MLLNoxvQvDlDzW+jNCCFWgyDEnVlN636sJ9r/xOr9KHDQvBrnemxS\nvUeQUlJtBJRCjdulRTThMXokQz7d7iFzGk3mbgvMioa/JrmSWJlpJNq3JJLF0gRxXMG22j0mFa8G\nGGSsQtf3z3Ugqieo+DsMObsPQRgxKxtI9/aGLRJkxNO9AZbZvUoa+jFuK0I3u5RPrp8Dt+3mLfbp\n/pBEJlKkMgZ2Ut9qp845JK2ZBaqNJnaw/TpgsevhNALsSnJfes4WqlUakcDqX9/YYc1JtKtXiT63\neejrvYiJseOAhJ0G06BVuL8hlZuO34jR/RQVr0lSt0lXne3n1AFJ78GNEtpt8HSRdpKIuZ12VPZO\nVKthjY7iVqtEtftuWD1UVofttXuewsMQPHXmOw2aWSbdIi0zybjZ/kL43Uu/q4InRTkcPkU7YdFn\nhRAx8AfAZ6WUkwdbrLvj+SFy4TIXE/1kdJuZvkc47YTk0zcxoxBfG6Jeg6fK85w/VcAXknemjjKb\nTdCTv01J9wi1mPDITfLGZc5qRQpGi/OZHhLvf5LMzYvMRwnebDXIBR45AbfPfpJPDY6Q6CxG2mr5\neN4jXLnx5xTjJs1IZ9DKM5pOcb43AG2ammER1Wr01k386Ut42ttEZnpNNabTEu0LCiefId0zSHFu\nBj/eoiIjJdXgJHryCYRTQ8Q3IG5gCQvDtWEoh9SzDHxHe2J73Goxd/0K5lGD1MhWQ+YkidQpNG21\nAudWfKJQEsUO5dZtaLUr7eJkltTpPAl7tQfEL6WJKyc4duzpTUc+GksSAm698Q6N+qbki5te25q3\npHOze6W7WVmkOjvF517490SdRW9F1ENSH8YwEhixQaz7mIn2tXEx8mmJGjMZQZouFdU1p4mzOm6v\noFVoX2fFYoPhouB0pvtaOZFmUQ5y+EeOIrdo3e/6OrazIWqZrRYpGy2M9Pqg2nUjms2Y1xfL6xY5\nXiuMJX5ocvrozvNe9lJTC0gPJjj68PZrDAlg4k+/ie40d0wBEWgtms1LaE6EEHvfHxE0Awz7CL63\nfr5hrfcyebPBnRG328YhuwnqJMQxXl+emn2UxNj5eyxxd1FxkejqGywVPWzd5APH7R2LZezQ67eX\ndhs89QOXhBAvs6aVT0r5A/tSKgWAqF4n+fjjuJcuEdcPRza6vbLS02QdojlPzaBdpsHOgngtM8FS\n58tcEwezzlPTaw+jSOxDSlNFeTeSUk4A/xz450KIh4D/HvhntBf5edeQgYu5cIVY7+eFxz7MsAzp\n6zWY0ZdYmJojuXSRUv08C9KmTongWA8Xa3kWGln8dI4B9x0MvcrJ2jWamuCadQbPWEazW+jjXycf\nuASRjd1q4Bo9WJHBtcotXk7ZPKJZZMkSRDGXZ1/mUpgizA1R0TO8GQviUJJfOMrfHMhjE9J0W7xT\nX0C0lrCCYRKdBAcCAUIQx7A8Wac69SKmYRAEswhDx8p0b4224pj+whHMZIIFO8A4M8CCWECaEcv1\nOmXd5M3Ogq7VqIfm4HFGzR4Klc2t5jEhRC6J8uvr6lZXSg61IIlGH7Zs3Rnx40uXk1qJQW01/bQn\nQ0Jh4Fsf6nw4688xkjBJffADxN66qGiXH3T3Havztym9NUkhituBiQCiMobWxM4lkWGIm7SY6fTm\nSb+CU69RSI4SDp9rn16uFEOuOY8kv3SRk0KS79TWfC2JljdIGPmNxQCgFQZo6TKLmRbxPg1P1zOS\nx4f7ODOyvvdrstjgKxeu42s68RYJFKY8l3ekASXxQBfJ7S02GJ6K6H1j596aSd+DZIhtb7+vb0eE\n6TSj/RbGDtd1uSEU201PVVBaRA/rWNbb6x53/GuYA3kePbbz3KHdiKOIa9dn8P0WvvsWur+3gYsV\nTZHUJ6iHA5RDg88unN7x9X+yrtM9Jcre223w9Mv7WQilu7hWwzwyDLpOVN2hxetdJoraCbNMsxch\n9MMxbK/T8zTUWZukaVhUOsNADHE3uVX2hpSSJ//JF3n/8QJ/8Pc/9MDPryiHlRDiOO3epx+iPQ/3\nHx1sie6eH3vU0gJDBrjlAKE5vFj1eaJQpNmsUZT9xJaDb/bwF7U0wa2IK9WIVqpOcyHNbHCUtJZl\ndLmBE9nM5sZYaGosGC7Gkk8UV3kiXKaZ1BFRwIc8h29OnuLC8gwvLbuM1mcw9ZiXjAJSCB7K5pF6\nkkYIZV9jKgjxFgRPDJiE6JxvlakHIegeIlqfgTQWEtE3TUUOkkjmKIVN9PQASbv7mkiT1SoZt4Eu\nKrwWJpm52UNaDzhRiKnEBinTp7/VzvwWRAFhUGMwcY6+XPfW7bpfI4zXzxYvluYpaxZV2WJIkxwz\nfNxY8FozxXRyjA/2rvYmtBqv4zvvMHXzNzcdO5SCWFi4oodUYpDeRN+mfe5F0WpQPf0Mvt2D1Qka\nlmdvYLsTDERFXBySIoOVaZ9PhhYJX6fv2KfoPflweyBgpzIpOiMCV+6X/sKlFJnMBu2hW7GcIDI1\nkn3dhz226g5wk1FTR1tXQd3DQCWOsZoFNGd95rpUc5y+xCS+l2arvLYtTHQtQ741zz501mzJMfOM\nk2Bmi/XK1prM9kBKkE1sn8zDi8ENBNNGBv1uX8tW+6/Nv5Eehtjb9MkZZoqRiktUbCC3mbvVPs3m\n1OR3tq3Nbk4/fbXbpI1pcrff2s0ruCtGL+j5U8wt15DxyvG3/p3s8f4GcHLPy9G1bLvZSUr5XOdi\n9ZCU8stCiBTvsla+dxsZhsTNJlouh57LdR22d7Pl8qNv3+bXzh3loTfKpJ4YwOh9d6QzXwmWdD2F\nrqcO1bC9gc6CuE3doNwZt6/tw0rgO5mruoSx5KXb3dfmUJRvRUKIlwAT+Czwn0gpbx1wke6JE0re\nHH4Ys+ljOE1e83TGGlUuNd/Ht7sXKETLLKSOohlzOJVeoqag11xmvjePLZLUSGC3Bnj6ke/k8nIZ\nDZ9XknlqCfhbuSXChbcYMOZ4u+cYl41HueQGLEqbmZqJr1kUcWjqKZqmoKL1sFBpYcd1BoVHzuzh\ndZnmOj0sN/tZMoc5HoScSL7GBwcbnO5Zn7UtimO+/rpBHIdons+MPIedGeTU6KlNrzuIY25deJ5k\noGPGSYbqUNAaeIZkWQcvTGDpBmeT7SF6fnMGf/JNxqo1zhzvPgIjFCbG0WdAX63SLFx8BdfQmM7m\nMbUehJ1HjwLyYZF8RlKi2Z7XIiUNvUCCYb47tbmSfLFc5qZvMBvUSUdFptm+crxrEkIvoBkUiDuJ\nLqajPKH+AaykSW7xCplGk56yA0j8SKccjlAofh39wtrcJuvn/AhAlz66fYzAOA7AfLMHoZcZ2CI6\nicgRWgWePdnbpXV/80wTwVZV2A37rpnmdeX62wQ1h+SN9T0iTXSahRHsniG0LXq9UkGT0+4yn0o5\ndzITPghXqzNMxoP4evceu7Xmg16G0zYDie3nPDU9n2WtRUqWt8qPAewQtm4Motbc18yAoYzFcG61\nh08AF5b6aPk6t+RWgaDcpje129DTGKImTjZDIjpDYc36VmJdgLVZl1WjNu0TRnXcuEgoDKKqzald\n/N0lu/z97pfdZtv7SeCngF7aWfdGgX8FfHz/ivatLW60K/J6NoeWzRLXNl80vrxc43rL4/euzPFz\nX5jHH6/R/6OPPuii3pMoaqFpFppmoOvpO3OgDlLT7wzbE+3WuaauU+18mTuBs+Xz9stsZfWcfhhj\nGQczdFBRDpkfllJePehC3C/dNFjKj3DEmWSkfIly6hQtoZNoOYSDPiebl7ntPsOiHCVI1OmNJZGm\nczzXwgkhmA3BMqj1JUklQ/TmDHa1Qiqq8cJSjBEe4WjGIGU0CIXPJSsLkUNZSzOvDTGRP8WYETDr\nOozoER8YGmVh6RZ1F4phiGUGSDMm8KepRynGTZMbPMXVmuDRcH3VIZAQyQnSQhAJHaMVkrs6jXPt\n5qbXLaTkSS8gmerFtDNMUeekXsb2BH65j0o1wgvh8U4vyfRylq9OnuGdOYdjV57fdLxQRswREyW/\nRrwmScWYP0eP4VAMz1E2zqFbPlLGLPpVbuk1ejPt4VUS8BwPx8/zmr65SlSNEvRaAYU8JKVHn9yb\nCfdO4EFYJhkKVvIkDHllhrIaw0aKC24NTXikOjXRWqwjpEEtadOXTCA6dV0p2j1Oq6MDBcuuT0Kr\n09N6GQBbs4nMBHaqS5VPwnIUMBWZjE+E3E1v025yMazwwjNosU+vv3kunKl5vH95AkN0GxYpCYWk\nmsrhn/jkrsu2F7zqNIVgd1Mm3t9cZlh69LHD74fRJGw0yBtpNPa+sbvaqkOYJRmur7Oc1Hrw0kdI\nGGuG160LcrbIqc/W+0y7MZaRQFQXcAO51QjVDXMAt9y05jFBq6WxsFTFlzoBgyT6d67bnk0/uDlx\nux2L9A+AZ4GXAKSU14UQg/tWKoWoM8dJy2XR0mliZ3PlfdlvD1MInPbPcOngA5DdCqMWut6eW9QO\nng5Pz9NQ58+ipRtUOhdjP/bxIg9b3z4bkZRyzzLozNdWLzIVx2cw++7oVVSU/fReCJwAkprJt7VK\nLJgWoWfxH0y+wJXCeZJag2Zk8Vz6GQadIh/2nkMA1/qf4FKyn4afIxPOU80lCY0WU9Ftqo1XCIOA\nvlaAZo/SP/Z+XnvnAlLTOJudxfIjym6WMW2Rk9lbzBstEiLB+wo9TDqCKP0Ix3syHOsb4nKjSdCq\nYvo1hNvgIT0gH7q8zw54vjiEdCzernep8iRHOJ+OGDxm8PL1MnhpNg5QufOsWEI2i2km0OUQubxJ\noapzNp3n4psvUvUdPv9au3dLyIjTosGMUaHSbfi0lOQ9Dz1qYq8JfootnZpI8lg0wah1ibGcQSDh\nL5uDXNfGKPnthBQCQQuTlmkwm9k8byOqlZBND78ZECVzmAObe9Puhab7nGi+xY98aLUq5VbmaVTa\nc7HGRtN4vc9gjL2vXQ5nmclrn6d/KKQ6fHTbYz8/4RIGMaWVubpxiNQt4nWp41evU7l6lXP1Zb7L\nzmPqm+epba7wrs8suL7vq3sNutSskg1ceox43ROa6Lyk51iSnQWKu1w/ZRzhOyFfu17bVXbvvcoL\nXQxqJM2QnL5zwNxbHseOq3g7pYyQkPYyjEXHMbq81/drypmm7C4goqV17/OxwMPThgnsdo/UXb9H\nG/Z3IgO31M8tNyIRuOhm+/f2rms/WzzB93S0AILsGIsJg3Ej3vGzr8TB9jvsod0GT56U0l8dXysM\ndj9dUrkHUa09x0nP5dBSKeLW5sCoErb/oGteO3iKmg9whbD7FEVNdL3dxarrqUMVPA3E7V/tpozu\nzHkCqPt17OTWwdOf3fozfv21X+e3PvlbHM1uf3HbjUorWHf7IIKn2RsV3nl+ho//8MNo26QeVhTl\n7gROjVR2gaPpmOQVjbGoxGPlF3mrb5QGNkebc/SISyRTAq2VYFyG1JZ8iiLETWo8lXuDwWSRyekX\nCCMdXxtlIF2nPx8wZk1xQ/pMLj/EybTFQ26ZY3WNZsrkw70VEnKZZa1A3HiScxhcGX+L6YRkyddp\nhDr5dIH/6tGjfOHtKUzfJCpNElohn1yYJuwvkOhZPzwmjuBiJcZtaVxcACeVwxooUEi3G8jaNYdO\nlUEI6q6DEXnk45BHbn6e4w24YhR4R/Sx1LtILa1hxO0xZokIehM9nEoNU8gc2/Q+Oq7LCxMlGqTv\nPCaQLNCA2OGEvkRo5XGEQQD0iSp57Tb9p3pXK25Bi2GvyMku2bq+VA+4wBA34iwG0O/uTdJh363z\njSjLKcfGSndSj/cOcHbMpmCZhMs1ilEC/PaQfU3TOWL2E9aTZMLuc5dW/LWWjZUfwzDb14ypVoWi\nvozVrecJqMVwzTP5osiAvIvv+buoBca5Pkb6j/LQsfXBZyRhzA85YZuYWzQ8zt5+nps3/pTCzKu7\nPt+9NmGuDf7GgKSV5Wjm9A5PkrQaPlr2CFYys2HT+jcpdCMIqrj27R1Tb9+LMG6SlRLdWb+CQ9Jr\nIoxLCGdvruNmJBjQn4DEEcJUHwOZlUQU9zIWcXOvlxu6CIp8z2MpXli4gZRTO5bJ14eB+6977cZu\ng6fnhBC/CCSFEN8N/BfAn+5fsZR4JXjKZtFSqa7rPK0ET/XOT+mGyDBG7MHwriiKuHbtGqdPn8ay\ntv+i3o3KYgvT1kl3Vr2OImc1eBIJ3OmbRKeb6Jn0lseo/dUkes4m/czQlvvcj4bfIG2myYTtoKUp\nQ2prgqdm0KQ/ufVCcL918beYa87xpYkv8eOP/fh9l6furgbDawOpB+nP/uVb+E7Iox8ZZeShrRfJ\nVBTl7miazaniEH5yBnPkBqIS0Owx6RPLpIsZ4oyBIUJ8z6SSSmDqDprRYDiu8knzORKiwkzUT8J+\ngvGogmH62DQ4W3+dUf82V8JBboUptMZ5DC7Qk7qBG6eZKj5GT3yTZEJHT5zidvXzaLKMu1RA1rPE\nJpT8JX73xYtYLY+jo2Ms+wUWTIsnl9/kVPUi+dr6hpw4DLFKVWw7Sc+RXoLQpXDkKOk4jezMaFj5\nB3Dpyqu4YUwcSEqxjucKKlmTQn2JXjcggU7+ziI6MUWjl+X0CPpIz+pROj9KTpLJVsQz0RS9lgMI\nhJS84SeQRkhkp7mYHiNMthMvDJs3+Fj0DoX5F++U3wyqxELiaCObPqd+0+SjacFgDELExOHeJA9y\ngxi9WuPTLx7F1tut9nrkczSf4u8cy/CFW0WWjASG0a5YNiONclNnIHIYkBOrB9qUQUHSCpaJ5TdY\n6QS5ldCZTaXoSXa/vtbjmDIa9Wx+3xbJbYUxt6sLzF5bWvd4FMUQx0yLYMtEejKqkO1L02+fW61m\nbxO47VXLfqbxNlm/heFsHn66joBEysUxDVxjp6xzEV4Ak5k0gXH/datNYpdM8zhD4sT6IsZXyckl\nEnvUBhqLgEQ8RSXdoNHK0ufu7Wup6xHzusF4K0tvbpT+zBl2ComPZzf//e6X3X4L/DzwE8DbwN8H\nPg9sTkuj7JmotjJsr93zFMxuXlG8GnSCpzVfFVEzwMjf/0J3r7zyCl/4whd49tln+d7v/d77Opbv\nhvyb/+GbHDmd5wf/2/e3yxk17wzbi2dLeOUZKn/4h/T92I92PUbcCqh9sX3B+OSX3+GXf+BRPvHI\n5iAqXhqn+qv/Gbkf/hn0Jz+1btubX/o8c9ev8cn//Ge6Dq1rBk3SRppU0B4u5yCp6BrJOMbRNFrB\n1sMipZTM1Nsrz9+s7PBFu0s1d23P01Z5iPaX3xkSWlloqeBJORQ6CYt+Djgm5f/P3ptHSXJd552/\nF3vkXll7dVcv6AYaBEAABAgSJEVTlEiKEq1lLMlaLJ+RNaPF4ow8I411ZjwayZKsGY7HGssaWhu1\nWKuthdIhKS7gIoqbCILYCaD3pbr2yj0jM/Z4b/6I7K6q7qpegGpagvCdU6cyM17EexGZEe9+7977\nXfWDI7nyY0qpv/yvPLSbQtExmdcMgr4grGywODFDX2gkWcJaOk5VbRBpFutZnWY4R5RqVAKPetJH\njxQ9fZxEm+QgVdwwYMI4R3nlJLru8Pyr30ZdW8ITivdHE7wrldT1DZSM8MkIM4P2ULIWfoya9RTT\ncUI1MImlw1DBBb3Myfh2JoyItHsRW0UUtBKBWOCFTBCvXlrVzuceQ0uo1l5A72t4jxdYKo4jzi/v\nKrRjxAkbYpJVe4rz1Un6ssJYt8WUTJBiiG3pHJjO57EgjfEaHqcbiyz3OqNeN8PGwkwjTQv0nQqW\nUbxsOc9MpQRC4oolvtY6yf6SjpQZrWgZ00+ws81Csxcim9WshDe8Ojxekx5le4PXuR7FeIi95ZRe\nii7dmm/yhLiN8WEPhxQUbOgFTiVj/MvOJIGrGDPaVEbeIivxMBOfiurwYGmweSB1dc9/FDp0DBc5\nuv5plDHebzG1tHN0yqSICbUh36bO4+5Sa+ml4lwc0yuO0zP3b98gQBka9YqLtYthr3p9iu0mwpNX\n7LqbbMUelDECIuFhKI2StnNx4a2H04dVqmqeWjq5fcMVkEmKv7pMvTfJdYtCvQg81sxYsUucvcJe\niXoaQkzg7lHudKyBU+qhGQGZWkHtqn6xC5W9jjhFFJusa0c5/fSABJ8jw9Z1xzT/0JB9b/ja67bb\nC9yo2p4E3jf6e8kQQlwAPHKJ2VQp9dq9OO7LCdLb7nnaKWyvk+YPwoFQaGUL6cVIL4Y9IE/Hjx8H\n4OzZl04EOmv52FfPbioGZpl/2fOEn6FsRXJq9xqXSWNzUht0Q37z8+d2JE/t//BzND68THTuf2bm\nT94G5qbyzSd/81cAePgffRfF2hjPfOIj3P3Wt+OO4tyHyZCiVcSMAwwFgcroajqzacY5S7tcB2on\ndKMu/qhW1epwb8I6+sH2sL0rEaUZf/HkMt/x4H6MWxBStzXcwGt/9Sp3v4JXcB38DvAEcEm/fxn4\nU+DvFHlKhE4jjTDTKs20wpcq8xyKNvA6YywNa5To0TSn6MsSL1jzSC2hbq2hkoALjQNQCUmSEqea\nfQQlimGBumlyxFxhcObL2GmEU1hjjdcwFSyhqxhhDNnfO0VoKISZcEDotFMLv+mSiohMRRTNgDsr\na4xZQ6YmTpPoikDLUENJUrbo6xUS7YrQJPKcqnRCZ1BxMZRPYd1ltj0q/nrZWzQqqKsErWqZTqlG\n6nmMq4toTofKlEZLj4lMwdL0mwAI4pRzPRgPYtZ3WN2WSEJrQLfoEV3WfhZs+HXKQYgX1PAocGot\nQpMZoVek3A4B+3LbvmYwsGxqpXTERUaBhgI6vs1AZFhGRlLUMarXV167EQylTnu8xsAqIUV+hdxk\ngCljJuRFDJky028ys5HbAjEGJwoHeFrs49ne7qabQNEwe1QzyRE3Pw+/1cToJFSu8irl71uxxTCx\n+KQzxLhFnqcwzhgTQ169f7sAQyQThskGqlgh2sX1FPkDFgMfpV2/UOpeQkgB8RjFtHTdtvVkg/2N\ndQrX0VLP0oTEH6INZxC3IOdJ+RlhbGOk2z1gQRpjUUealV32vDloScLyBUiFgW9MsXzfA3v63WR+\nSrnV55Cm02CJQtnc/fCjBYRC8aXbvjeKG1XbO89OwipKvZTMybcqpZrXb/b3E5uep+ruOU8jz9NA\nA3O6QOTFZIPtRna7/QV6vSc5dOjdiBss9KqUYm1tbbR/myzL0PUXvxrltTYN7yyT6LpGlvmYZr6a\nI7wENQHJ+sZuh0AONj0vb58f468bQ84/9TgIweH7H7y8zX/mhfz/CnDqEbj72646Vm9jnbNPPMZn\n/uC3aS5e5J0/+j8BMExzzxODIS4CP/HxdI17o4hzlomf+mQy45ELj/C1819LwdyM+18Z5p5BS7NY\nG+bXbiGI+JO1Nj+0f5KqefOhHl6YMlGyaQ4iusHVnqc/ePQiP/+XL5Bkkn/6hkMArK2t4TgOtdpL\n9xJd8joBBINbHzYYxy00zcK4btjDK/h7jiNKqe8SQnwPgFLKF3ul0vJVRCcMeCYacii1CHrfQsFd\n44wBePkAACAASURBVKweorQyNb3BqqwyG7dQIuWB4bM8lR3EjhWJsOmlOmGnhOHEMHWGbjrJCjUs\n+Xq+a/A5DvQD3OQUQeAyNVjGHUb4aobH7ddwyGyQuRmTlSZ9rcr6sEC/NcfYVAOGHhMK9hk9yhNL\n+HpKL3TwiwJVrpAICc2USn/r1J0XyR1M6NjVCQ7MVekOFjHGekQYOyqyBX5ImWew5LNMpAGajKhF\nZSbP15myA1rAyYVc0nqYmSTSplNxmJ9oXHk0UJLxbsBYI2GrKeq2+hQzi4tj4wwjj0gvkUrIsho9\n3Sesb5KgitejmIX8g+jq5+x6P6EdW5iWSaSX0XcJfbtZNByLLFLc13weW2WAomm4ZK5BZrhYG12M\nbkqi8gXANAoopCfxqpNs1DfHkHvhtl9lFZeJUoNFlYdXerKGYQUY+3bOm017IQWvyXg6YMd1uBuO\ng9u9YcOXrMcmqxtbvXsC3YgoFSFNfFK0kYG8/XZWUkdkY+jSAqHdzIBeRAzf5g5+Nk5guhjO9XnB\ntEpoIjCuY1ZHmDQdE4wU7XrKfC8C63qVQBaxkivEWhKF0COKqsu2uk0vsh+pSWLDRDgpqTBxvrK3\nFSMsK6Rgxxw7UmOiIxkzXa7nqhu7jkz8XuJGLbqtniEH+E5y2fJXcIuQeX3QNLRiYVfy1BvlOg0M\ngTHpEp3pIq8wcp959geRMqI29jBjtYduqO9+v08URczOzrK6ukqv16Nev/mve9AJ8fsxgbc5IQX9\nhNKYvU0wQvVj1D5IN3YnT4POJgF7w1SFP73Y4s/f868B+PH/8qE8DE8p4tX8wRD1DeSZv0Ybkacs\n3bwuw16HlVO5Z235xPOXP/cTPydEcQdX0+iNEnXnRh4+P+zz/tPv5+cf/Xl+5L4f4d33v/vyvquD\n3Nv0wPQDPLn+JFJJ/tdTS3y67dFNMn7hjitCFW4A/TBhrubQ9WM6O3ie1kdqfJdU+cIw5Nd+7deY\nnZ3lh3/4h2+6vysRDjf7jIa3ljxJGfO5z78O1znAG9/46Vva1yv4O49YCOEymveFEEeA6Nq7/O1D\n0u1zJimjCQtknWIYI7wJ1kSDfcYap9MpBvo4X5OdRGqSVCYUrAwhBKtWHaENKduLvGo8I+2v4MsC\nRhLz3NgBDmoBK53bqRFQChM2jAqf1F9L257lhDhIUQWYfsQUBgwFr7I9XL9Mw0pYczKamsRCRwiL\nO/UKi70hBatIJ0ux7ASxb7TCO4qPiqOE9V4ZIy4xGJQJVRFpZ8hti0ZbzDRLIrUES4KlJRSCceqa\nQ70cUk8lblAmWWsBipI0CSkhWn1ay1cY1YCuoBjrlKMIZ8siX9UaEDo268YYmTmOEGBlGYmZUbcC\nxu+9//IpPD3o0ciGHFfp5c/yDhSO8iirNsVVk4FeJkp2WNx5MRZolqJEQnlNxzJzj5r0e6RkuJri\nWW2aQLOJrfychKZw/ZCj3QUO9w22m/PbB3DOvp3ALuIVc2OzZHjMFLvM7iLMpMyEojmENRfk1TRB\nXOMdcE2FWTXao1CM2DB1slHI4aURK6URZWVSX4DcqeIPZNJEiwQHRQ/46gljnaWGoxRo1yc562KW\nkyWXgXPtWkNSKbIUMqVzK8qlGlnKVDZkXtv+SAyiCM+BMLyeGuC1f8xb743SULA/mUJaHmqXAswv\nFmmiEQxNTnymx6FoAeeKiCpxxX+AzsQxDt6xvQjzrcKNhu1dGWz4S0KIJ4CffpH9KuCTQogM+HWl\n1G9c2UAI8UPktaU4cOBqhZ2XC5RS/NtHTvLWY1O87vAmQZF9D71cRgiBVixAkqDiGDESb8iUopdm\nCCA0BNp4vqIkt4R6JUkHKfMbyOs/e8PkqdHIV/fuuOMOVldX6Xa7L4o8/cFPP0qWSB74hoOXP/P7\n0Yg8bQpG4MUoB5LmDquKIzQ3hlyasvYZBqbaYtj7Q5xiCbl2kmQA1mydeLVN8vzj2N+atwlGAhwA\nfrdDe2UJgO76KpE/xC4UGSZD5kpzEA8puDr9ON9n7uBboPMkftjm6c4JAE60Tmwb36VQvfsmHuCL\nK4+y7rf5fCefJP54rc2/OjJL8Sa9d/0goeKYlB0DL7yavFwSlLgU0nfpe1tdXd0TyfSt3qbwFpOn\nwSC/nkF4kTT1XvE+vYJr4WeAjwHzQog/BN4EfP9/1RG9CKQypanFHFRTWKLEYFilEnWoWT5dUcKV\nEiMZ0BE17sue51C6St/Ueda6jWOlDm21zp0s8WC3yEA5rOr7OCkEMXCCaQIX1iKXutnnUf1V+LqD\nMFIS16aVSG5L1nEHHmOqy8XpkNQQhELRsnwSETCTOuyP4RwD0qyM2zxEUTqkWop+hXSzRUaZgKGl\n0daKREGNkhYzbmz1BW0aZelGAVOaCE2xQZ1mXGQtNjikP0daKBOFRSZGfQiRklgDxuwe2jbOkPtc\nUkzWs2kasrRNcGBJ6ZAmuP02KBuhHDJg3TXYKFeotx693DaTUDcE+80ti5SjY53UJItKUB/TKNJn\nXO0+T90MpJLEiY482GcocnmMC70ag6iMylyQfWw9ZEbkhCfFRo47GOY0++xrq9Om3pBD2UUOhHkE\nS2IV8OIi3soui3gqRWWKoVW+ZWFxbjTgNmNAFl+dqaSlBmQTyF1CBhMZswp0zVuTj7UbShI0leCo\nGwhb93pMhi5Y283qK89IKQiFRWfyIYR5HU/Jlp3Vrl/M9s+LzSc4Gp6jLrf/RvbpGjULZHFvrmEq\nNZ6O5+kMFVJUObzU3pPjXkIGDITFurI5JefRDcH1tMq19ZCvDnW68bC9B7a81cg9US9FcuZrlFLL\no1pRnxBCnFBKfXZrgxGh+g2A1772tS9bWfSzjSG/+tdn+f0vLvDcz24WgMv6fbRKHpuqjaomS99H\nH5Gn/sjrNGvorKQZ0VgeCyz9zVWZwfDM5dfDLa+vh42RB+j222/nM5/5DN0dlP6uh3CQkCV5cmdr\nZTO51e/F+HFKnAwxRoIRopcTvNTv7Hq82IvJlEIXgooAN9t0/XvNBk6xRPzYxwBB6U0P0/6zj5As\nL2ErBULg9zfzrYa9LoNWk+r0DL31NdbPneXAPffmOU9mEeIhbtHEi/OJZ668f0SeOhxv5x6rdX99\n2/iaQRPCw/z7PzuAMflGXuh3SJTie2fr/NFqm0+1PN5Rd/jAmQ/wrtveRcm6fgx1P0yZqTqUHINB\nePVq2yVBic5ITKLZ3AylOb1+ml85/iv8xGt/4mrZ9PY5aJ2F29/Of15tcci1eUPt6vGEI/Lklk0i\nPyVNEnoba4zv23sp0KG/6fL3/fNUKvfueR+v4OUBpdQnhBBPAg+TWw7/4u9iCLhWdFmpeVSDZUTo\nctS3cKVGOZ2kqoe0ZIUVfQFLCzkfHGDcWCDQA/ZpPRxxlLtVHzdWnKkfoe4vo8smhpohSgWoPjWp\ncHSfWCtzr36ax83bKJXXYHCeVjJJImP0ifM8b9iMVXoUhMa4sqj7JZzY4IAzJM5cegoMSyGtZYx4\nMg+d0i77DQAwFNwubFShS+r6mENB1qkg2jsXZTWkhWaGKAWN0MFOdfTQY0XWKAlFFbinni9eRUoS\nCklbmwVhb+k1N6RsFK6h6JkDMNLLFM3sxThRgJ1eILIhNkCTOuPJEYJUEDaDyzWFdDJqDCkUR9EP\nW2y0Y/EszeFBDBGBSgnU9pyRK6nApu9EbBEuUFu254gzgWHEnKdOTc/ndVsPmXQTDhgDiGNcLUWM\nvFJxCl+JC/iRzbnOtRVnrSSikloUR8fV45DxocfAW7iiZT6uWBf0a0W6Mwe5yty/fu3Ua2DzvBtC\nx4gLxGK7h6IapUwNBJbydxWAMDWHmmbRLH51ZKhzKAwkqRbTcK4WEtkKAUwHi2jRED2+9hUy4pBy\nlmK2Pr6HY91yfFyUPQNX1Cyrq9NATBrujTktVMartfO0HJOurBBdpwbmzUJHYAsbTc2TypSevnwN\neZAczRsQldgr3CgB+sUtr1PgAvCPX2ynSqnl0f8NIcRfkBfg/ey193r54GdOL7MRJ/zq3YdYbOcr\nXYNou3Es+330cv7jF4UCj73qXvYPhpRHuSyXyFMpVqDBUpoy4xrILXkqcZQb+KY5xtC/cfLUaDQo\nFArMzs4ihHhR5Km7sbmC57UDDFsnjTL8fsy7//BxvvdAwCA2UXEMIyNdqhAZBGju1asxSatPkPYo\nGGWKUlCSg3wCl4J+s8Gk1iB55JcBm8Jb3kn7zz5C3I0YfPY0qbdO533/jhIxA8di2G4RDgcce9Nb\neObjH6axcJ4D99yLn/h5zlPi42oTdEaep6OVwwC0/Q3OdXMjvxVuv0m7URfhPUwmQXVfxwvDASD4\nvrlxPtHq88GNDn77S/zCl36BBW+Bn3zoJ697Db1w5HmyzU3Z8rAPv/V2qB2kH/xEPpZBzOnOaVqt\nzTF99MRH+dTFT3Gsfox/ft8/337g3/5GGKwR/cij/PTphG+arO1MnkbepupkgWEv4qPv/UVOPfp5\nvuOn/g0HX7236zthuHz5dRStX6PlK/j7iisW8QAuKbMcEEIcUEo9+dUe00uBkWTM9AcEZJhymfXI\n4K2axarRYV3L0FQTlRmcEWM8pAq0RJ2JbIWStInNDUQiqGVHaK/eS5zOUrHgQFjkiWANU+tTKsRY\n+hQqLCJqA+4qrtEq65TtDn4KrbSAVvKpihChJPNpRj2tMhPtx0UwpMNS4JKoWTK6xLUzzAkXYWaE\nW4rRIkBTCj0aQ3lVtK7E8w2qaoDQdjI6BaHSabOO1CICdRt2tpSHLdoaRqCj7JSPN+4EwBJDxvQh\n40abfZVk01TSRqa5lEx0YwZWB7UlWf+JYJJI04iSCkYEpcwgE4pxoegWJeYW8fQ4HUNmMxTaB7kS\nXiGlrA8p0CWOx0iiUZHRyy12KgurdvQUXGqpAEMpfCwCq8fFUVjYvrROWfqUEw0hq4TUaBplEAqp\n+xjWRRbdRazCLp6Q0UAMIvqphpL5WKfiacbLZWpzO0cQqFSh4grzDY+dA+deOhLTJizoZMWQbTk3\njmBQDegVfQxN31E9MEx9hMyInL2Rib9RvL5VoyYjtOENeGtqKR01Q7glaWynK2lnBgXfwhTxLi12\nwM18JSpG01Mia/uYM2WzLqqsyL1RzdWFoqb16Bo+mfIpW2s3MNwbp95GYmCqi5gsY8R1/HD3MjGX\n0O5+9X4fNxq299a96lAIUQQ0pZQ3ev0O4Of26vh/29FNUn59KXf7/+9HYpa7m5NLlGbYI5nQzPPQ\nKhU+dPZD/NnFv+SRH/vfOLXa5Rf27wM2853oxTBm8NcrXb63YG4jT1Gc91OrPUS3+wQNv8FkYYuM\n5i5oNBpMTU2h6zrFYhHP865qEy8tk66vUXhwU6xhox/y+EKHb7xnhsbqphdp2IsYnyuyfr7P55Y6\nfGJC4xvEBGEPXt3rIUahucqBrNPZkTzR7RNJH0OauEmfH3vL+xgze5z+wEG8VhOefS9pLwBsgmMH\nCFyNyJ/E/+g6/hd/Gbl+ivmJKmdu289gJHc7eeAgbrlCczFfjdvmedLmWPBz0niwMo+pFE83TyCR\nFJMi7aC9LTSuHbZJg/xayGiSE14IuBwrOnzTRJU/WWtz0M6J1/HW8avPL43hUz8Lt70Vbn8bAP0g\npewYlBwD7xK5fvaPoXECGifoV/97ABa6Lf7RB3+Id5ubOVi9Xu5pa/iNq/sZ5A+5p88+jpe9mm+c\n2Fk96pLnqTbl0lxco3Hm8/n4P/fXt4w8mRcErZ/7acq/sg/nrrv2tI9X8Hcev3iNbQr4uq/WQPYC\nahgz52cMLImteuwzFIk5Rd/yGGDywGKBaavKc9MpZ3SIbJ2hKvJwuMHAVHhWGVd08ZynWO+ZaKmN\nnbocTidYLkLdblPQBvTDWeaMJstmkwe7A2q+zgOB5DPZGHX1ECpLOKj6VCpFavokCIkvNPy4Tj0p\nY5mrSFkgGb6RQPXpmWt0tQbb6IMSNLz7iGMTJQ0yIjRbULZ2Ntb7URU9PowmwExSDvsmY90Nguk6\nC0OTVljGN88D4MoYK4PJcIPGMLvKMBNKMaSMTE2E2DRpjgQ2seki3CLFRKGRAhmZFnF/dxZpbLb1\nIpsVDM5ni9vOCwUqtijaffaLdeinyOzaXohtO3OlIbnVA2XguFVkGqEuCwfEkLXQjAUCt0ZgCuyR\ntHQoUnzNpCqKTMRT1+y5Z/VwTXCy/Bx9LaVt94nEzuF+lnQoxYrD0a0Llw7TEJmuYHZHv4kRSdK0\nCN1qgmGgdhEEKJIhM1DZi8urub7JvnOL4/Y6CnPXcW1FAYkl26itsiXqSq8kCKVh2C4LdocUef2x\n7cBErlVc92hjCcsfYG4L9VdsJCaRM4Vp30gtpBtga1LjolXGiy0ENs24fGP73SAyO6Rkt0BfRhTW\nKMXRDYh23L1n/V8PNxq29+PX2q6U+n9vos9p4C9GRqcB/JFS6mM3sf/faTzjbT54n+z7rGwhTxv9\niPn6KETP62MeOswvP/XLpG6+Avf8lpvhkuep4KcwZvB4w+M7TY3Hn1+m+yWT73v9EeKogRAmxeId\nbGx8nH/459/Ie9/2qzw0s3vuk1KKRqPBvffmYVPlcpnBYLCtjYxjzr7jHSAlhz/4AZw77gDgf/jP\nT/HY+Tb//rvuo7CQhz9IkZKEUBqz6azqfGm1R3qfy9OL383BcweI611EmN8S0laknQ7m3ByRlPzg\nU+eYi+A9bzyKGWdEWYAlXML0k0xO5vG1Y3f0CHpdWH6SdPxhEKd412e/j9oPGPzmh8poMiNrngSg\nPgyp75snGBGLQqXGxPxBWosLJDIhlvFIMGKAq1v0vCblyCAJFEUpOTvMDfzxaJyL5kX6cZ+qnROP\nTtAlCmuMlwxaAzjjpcxYJkVd51umavzuSovjvdyjcqZ75uqcpK/8CXzxvfDY++BfrZCgESQZFcek\n4hisdEcrjWc+BZoJMqE/8AGTnp9iAB2vQ7FYZDgcEgzy39WV5CneeIJL08+FXgtcOFbcWYEpHCQI\nTVCecAkHuWR9eXyS9XOnd/39XA/JxgbDz3+B6rd9K2JLDZgwXKFUugvxzCnUWpfeX374FfL0CrZh\nLxfxdoMQ4p3AfyDP5P5NpdR7blVfRsXGLcVEvgAjQqgKntYgcmKydkhR1ijHBoQ1NMNgQbWoJRO0\ns5SxuEOiajxeVnS0gHZmIZXGfUlCo6BR0Gt0M42+bTDrtFnRa8wGMfVMYkQah5Skk2p05ThTWQWh\ndIx1gw7gaQHnDI8xp8y4FBSoQiqwfJ2QMXpJRqxqgLhsc6ZAs9jGdFdwNUmqDAxh4u2g8KoA4XgU\nYoNqpOF2Mgo9jTSZRwzKlHQN9CEPTi0C0FYOg4HF2nAfFV+BGnU7EplLhCAWJkZsom/pr6gUkwgc\nLWS1kNIxNZAKLVnCzRoca22uZE9qGlNGkbXy1dGfiTTJspiWrpOOdRH0t2zdnra+k7CCumrLqK2K\nqIcpRXcdIfJwv+dFibaZYCLRWEMgcFRujCulUUprTMUVDjjXFjB4KioSCZ1gFOaYKompfKrGzmTW\nM3pkTo9zWsaulWpfIqxAYqUG9pVKekqhZIaHS6bt7OHREokWgbpBxeC9gkRAmlGV14++6VkGysyF\nvq4JpXCGKXYosG/BtfaGgkSO0bC3y6DXhwmur1OUuwtz3Qyk0Cg6XfRSkchV+JXtxPzFndkm+dJS\nHT+uMzUsMyh16MjgmkcVQN26dj2uvcTNqO09BHxw9P6bgceAm7ailFLngPtudr+XA55d6vLuR56D\n2/IQqeODgLXepvu96yfMj3QZsr6HKpisDdewS28BQGSbD8xLnqeil/9/rj3kjB9hpw7/10eP5+Qp\nbmBZEwyVhRBgEvBjf/Vj/PE//GMOVHYW4ej1ekRRxNRUvrJVKpWu8jz5jz4KMs9nWv+Lj2F9+xT6\ntMNj53NC89lTTR5uDFAopOUj4zJu2UIrmVjrEfanu8w37kUCG+faXBKFUTZknfwh9emWx8f7OWn7\ncS8k1kx8TaNuFhlmp1CBTjAwKU6FBK0VSAPS2CaZrhNmPdYqEA917GEDsgRlOxSjiNrUNEsnczlz\nt1plfP4gz3/mU/hxHmZY1CxQEkuzSXXF/IZLp9WjIBUrowTMaW2ai1zE22hTmS2Dgm99/s2kmcvU\n0XE++PQ6zVgwVctvr4drJcZNg4vtnDx1oy7tsM34qOI9ACc/OvriI2icwCvnhLTimpRsAy9K8mu+\n8AV4zT+B05+k186/gzA2KCpw2xtUswRfTBIHMZiwEWx/ULZP/x4zQKYJLoQpmgv7nM2H7O9/8QLV\ngsW33DdHOExwiga2ayCTBQrVMe78mrfwxF/+BVJmaLtMdNfCxnv+b/of+QhawaXyznde/jwMVykW\nbyPNLgIxaWNvkrJfwcsPQggH+FHga8hn288Bv6bUjWR1X/O4OvAfgbcDS8CXhRAfVEq98BKHvCNs\nLaXubnCXTAjMGqthRL2k2C9sSmYPZboY+hjTqkJb36CajuElkjgqM0wUcTGmlgak4ZCaI+h401w4\nmrFcqJHqFkV/DmkpLH2V2ztFPMMl6syjiYA7ShVeW7IYmBkrPY+mr7EUdUCmZJqB0C02Mp/UMvEM\nRV3p6EEJDZ0JUcNAZ6tnRQpJOdsgHpq4aUiaGrjSxsquNjEUiuV6BzNrk2QRw4JNOZgkHJ9GTtcZ\n76UciHQmFmcBmFSKNVFmo7hAb0t08SUzSmbgenM4EaA2+xsUN1g1VkmjPiodQ5glFIo4UwzTHgvu\n8LJnYJxZqmaFjKtziUwKGJnJOfMMsfBHUtkvHZEmOWHqKHkIa7Sk1aWDFbuU0jKmlTJu6LijvKWC\nHDIb9YizhGbnWuqtgmmR5N/RKHSrnDQZt4bYxi6CDInOGhZdYaJuEXkSHhihQrD9Nk0TjVjOUbD1\nXa+tyhQig6I22HH7jWKnAMtroRdXEURoQl637XiU0ncq+Pbu+cwCMKOYWrNFVetcn2Gobf+uPtgV\nbRXgxxN47jymsz3KaLm2jKm10MTeqBVqKqXqBxRVh9IgoFTYm/pnl5CqgMnmWUy7zLR/O2dGNtG1\nsDF1aE/HcC3cKHnaDzyglPIAhBD/GviwUur7btXAXo543+fO00EhlGLetTnth0SDTTnJS4n/kIft\nDaz8R16p556n9S1y25fI00SU39SdNGM5gNsRBLEizSRR3MC2JlkNfQzg37z+f+EnHn0vv/fC7/FT\nD/8Ufpzy/b/zZe6cKfOz33I3QgjW13MDf3o6n0RKpRKrq5tFX5v/6XnihTZoGs7dd/PFkzVa/+5J\nat+Zx4ofKGvMnv8zgvgNoOuYrkBFArdsETkapbUUUdp8FPQ3hleF7QE87W3mTH38f/wx3vNdP4Ke\nFPieJz7Lm90NjME4cSegOBPiL+bjS30I5sbQsz5vfmacC6bkbiMPkZP778Q4+zRF0yIa5g/gZ/+q\nSZaUSMKA9Y28QG9xFPbRS2MQML/h0t1oU1D5ddaVzoHaATq9NfiPS7TuCii+boY3tF/FG4BHvHyF\noS917rJyUqILwYOVAs9cbFE0c1W/RW9xkzwpBRc+BwfeCBf/BtaepW/keVZlx6DsmLlgRO8iRH2Y\nvR/VWaS/YWAbGlEqIbMxo5QCHQruHJ0wy8mTv508ZRvP5N9j3WQhM5hzTKzRStnFls//8YFcuv3N\nRycIBwlOycJ0NGS6xOzt91OdnEJmGcNuh3L9+jHIVyJ4/jkA/Cee3EaeomiNev2NMLSAmHR1bwoN\nv4KXJX6PvMj6/zd6/73A75OX0HgpeB1wZrTAhxDivwDfCtwS8mRg0l+6i/n0OOFMTL3SoitdxqRA\nRBGyvkxo94jq61RWDlJUGt4wYDHuI+otikWBSQXzgkbl4BiVCThXrSEKNr2sRz8touIMwyiS6CFv\nWE1w7SO0gZNRRC07T6Z7lNMyS1aF1I6wMxsjtjANhV/ucCr1UEi8NKUamqAXwC6Dtb3WkRKKqdhm\nuj9JZaiQgyaZGsIOxrpSglJ/Gk3ZDN2I1UmdeGqMSlZDi136pWWaY+dYzfL5L1UQaA5BNo++gw2r\nhCAo+ozrAiPbNMxbDvhijoIcY5IB426EyiSqN0FFzJPZtcvGtC5DVBaQ+Rc2jdKRZHNqlRG2QVkM\nyboBxfSlFjbNj+trir5rURBTKC2/npO41LQU2zAollpoTojYUguoXzaJVxXSuvbzURBgs0yJ3uj8\nbDyvztIuQhOZXqalH8GncMvU9jIhMUyfmrZ9MTYzIAsUettHqZ0Ne69o0a4VOTWz79YMbhdUuhHV\nfojF+HXb3hEu4fZ8HLW9jtVVyARxZrBYPLCDp22Xi7/Lx1eTKoFPQr/YJXO2L0BWAReDgnZthb+b\nKeml9BoiHOB4HhVvbzxaW8fhW1MkIiWOzjM2OD/akD8ErvblKuyJI8BXh5bcKHmaBrZWj4tHn72C\nG4QXJjzy3Brq7ipGJLlzwuGMH+EOYg6NF7jQ8i+TJ5UkKN+nbeasolCaAQmtLT+X/qhA7uwl5RRd\n0EgMHgSk1DjfHBLHDRxnP16wxhggsh5vmX8Ln13KtTl+9skLfMHO+NIXF/i6O6f42mNTl8lTaUmh\n5hWlUonhcIiUEsKM8EQbGEcevo1PFQW+8tCBZ082eZsw+e8mP8UbVn6NP+jfjmZPYrsmYRdKNZue\nrihIgbnl7uw/dxpTujz91Jt4Vf15Do7I04UggkSCIfi33/w9NB0NnDLLJZfQbuL2Z4m8VapHPbxu\nA4qQ9kPCQxVmWjaH1oq8MCm4q38aEKipO+Hs0xSSlDTOB3DuGR+V5a9XlvKwtMIotnnYaUEBpoYV\n1r74GIVX5e2qepWp6hRff/FhAMIXWvm1GWHurIfQQgJhMLVFsvTIM0/yhOpyT/lOvpQ8zUXvIvdP\njfKGhg0Ie3DsG+HiF6GzQH8iJ8oVx8xznsIUtfZc/guYvgd/9SQpOreNFzi1PqAQjeHjUCCgE71q\nTAAAIABJREFUaCjU6BzbYZtMZuiaTqPRYNBpkWkavYrJgjXJIWtzpe+Ji5tSo4+ea+XkqWiQxj1Q\nQybm76A8nq9mec3mTZMnmWUki7lEfHx2U8AkTQdk2QDHniEZ5ONJ1l8RjXgFu+IepdTWmM5PCyH2\nguDsAxa3vF8CXn9lo70qo5FaLmUrpjWpk4iEAIvU7rPWMzhaFpTCBCNoIL1xVrQNRNDCTQxmtBpN\n/QyGdZAl+whrR48iHY/M7mM7CWU95Db/OCI7StCZ4oRlEJUVTbGOOzTIsgkWg4ucy1YpOjEH5pa4\nLZ3i+Q0dzxhSsJuUBxqFocmYUSYyZ2lYy/RM0IMuIhM44RWhV0JR3VfEHCug0hJ27JE0E6L46qKz\nAEeKEmFVyDSXtLpMliQMtPMERprXM1Ix1dE8kcmEr1TvpKeVSLF2FGeQSNpRA0dsEo1BNoUbV7DM\nMj1dEIxyh5QFDaVRjfKvWgBRlkLSpjkqKpuHBubneMhsMFZWzEtBogWkYY89gaYjLItCuIo2iirp\nV20SS5GaBm2jRDubYDjK89G0jLKRcKDuEQXXzv0ZWBVWswnUaLLNEosssDCSnT0oiTAhUYg05Aac\nLC8OxQRV6rOsbb9+Oha2puEHatcaQ0KlWFrM29fWr1Hd6mawE+3YAXEflQVgXl1n86q9Zyy6unM5\nVHI3pAj6WoFmzURXe3+xDw/HOOgXKLGd5Geygpk46DeQv3UjUEqQKEHH3mBjrouy7ry05To73tjx\nE01jKEzadhtLaRj6pnYlAOJqaZPXF7565WdvlDz9HvDYSBkP4NuA3701Q3p54nOnm8SZpFhzGA5j\njrg2f932mB5E3Le/yoWWT29Uoykb1SRqaD5Fs4hu1yBI6WvmZbnuSzWeZuNL5EnjXBnSUEdLYLHj\nY0QNKpX72Vh8P2Mu/Pnx3+ahYz/JJxY+wYq3wu8GAzhYYrqf8t6/OsNb7phk8dwCQgk+/ZFP8U77\nXZRKJZRS+L6Psbrp+fL23Uavdxa0L6Dbr+LNyyH3Kxex/KpcMj3RMasatmsQAqYjaCCZUYIZffMn\n33vuFMHEYTxvkuOT9/NQNydP61GC4yVMSI2lic041laxgnJ62K37CQZDhNYgTptgFgl6Hv74DOP9\nfGJJdIN4YwGtNoNu54Z+97SGbt9HFj0FWAgtX1FaXb0AgCsFn+v/AH7tK1AIeNfk93Pq/G9TvDN/\nyI2ZNaaqU8wPpmmYEZOJTXxiUxzDnopxOz6BblDZEl4++4kPon19SK3topkaF/sXNze2RkRi6i6o\nzEF34bK6XsXN6zylUpGun8gfh1N30i/dBsCBisGpdZgYTBLg4BJS0iJEJNCEhlSSU16DOyrTfPSj\nH+LCyj/mu52P4xdWWHBm+Qa1Gaf89MUumgCp4OS6x/QwoTrp0t/IhS7G5o5SHs9ler1WA7iTm8HZ\nv/rk5XDP4NRmxO8ldT3bnmHYH632rq3tSa2qV/CyxJNCiIeVUo8CCCFeDzz+1ep8r8potNsBbnWZ\nFIHUDXANIs/EHJYYFEJ8d4hGl2KaIMf7XGzozIgDVEOHieI8F4r7WJN3Ybk6SJe12ML0U/R6n9vV\nLKmtaBQXecjfz9kxk1S3Ec4qw6+cR01qqHJCs5JRdD2GToYYs9iXxNixTiGTdESd0pJNeeEc0W1z\ndMsFsjEoaWBdEV4ldcGJqoZu6GTKxLLGODpznrHw6khKgYaFQLYLaJnOa6XPMEmJ0gLrahGlNJKk\nyiDInzVSSCpFF4cuKrr6ckvNxLD2Yybbi5MWUokUsL+9Qc/U0HSXFEW3PMWG7nPW2prrKTCKJlNb\ny2WMcqraNUXXENjJNIekR1V78Sb7VkQiY6BHZHZGNjIKzQiGQzC8dZr1WYKoRDYK6QsNg2hS0Csa\nzBnhNW3QwPQppD2iIDfkC5pGwSki9cqO7U3RpVhdIPPP7Kna3tYjxW6RRDOIryhyq2tDDDL2mz7a\nLuRJSwRKTBN6sy/NM6a27n79A8WiRmxKoi0Oot3kshMNBEMK15mzUkMg91VHMvJ7P7+F4wVOyDJx\ndkUuc6ZhdwwKw72pJ64BZRy61SKeZRHvQGZeCvRYUupm3LnQIXLr6Iax69W61G9hZmYPR3Bt3Kja\n3i8IIT4KvHn00T9TSj1164b18sPnTjcpOwaBqyNaGdO6TqwULZVxZLLEJ49v0BlJQ18KXVsxBhwo\nH6ATDQAHJTQ6ScaEZdBPM1whmBw9h159sMYnRcxHHAvnMZ/l9oC5pI2uF3gmUBx1wBERByt5eN0f\nn32KfKEVHn7NLB/58Bk+fWKN8xcvoITiK8ZFHv6bRcpfn6vvDAYDSp0tRQ4LdeidBelT0iX3Z6Ok\n1ugIiTVPkhVxSjpFNaBHhfSDv8S6/U0cVnBQD4F8okvMEp1SvlowNMok7dz70YhSJqKIBxc0Nuoa\n/+TkOr97bIZeqYQwYsxojFDP3c+pPmSx9ADvf9P9qGCD6qVVOZUwaIYUpo8hrDoZ4C/5yHIDhEu5\n7jDoCFyzwsrxUzAP3nLGgv/NOH4GY+vEpsn85DsoyDzcrJg1mZZl9iUFft05zj8Vd1OIJU8aizyQ\nztNNG9yl1/i8ENz7f/4ip5efpv6e92COhBtST2d2fpaL3g7kafwI1A7mnqcRkS47BmU7v02TzkVM\ndwzSGH39WRwmOFjIH4RTURGJToGAghxgpiZHakd4YRDz9U+u8QP7U/7Zmw7TvvAMjyRfwz3Fz9K0\n6hyMN8M/Tqx5PHBgjOYg4vT6gOogYeZwhfbyacBCLDSQa3kxW+8aBY13w/EPf4Dbga5rU2s2kb6P\nVigQRbn6n21PI7x09NUlSM9Dr+w82b+Cv9d4EPgbIcSlm+gAcFII8RVAKaVebJGwZWBrIZn9o89u\nCWJvhZSYdjmimlj0z9mYicX+oUnTrZNZGj2lc7TQwpMSc0axFrYQ7hQlNcmqY9GPGhz2vowdHaUY\ndllzZnB6NhflMepjS8xaKVp4lrZxkEbtEOPdBYb3Zlwc348lQ/RgmScKD1JCcTR5gdQos+bMMdDL\neGaBat0junsKEwNTWMxFHYqqjWFs9yhJBavxOFYzJjYcsvocG2aJWN8pDU2xbg2p6WcQaYeiBqJo\noremKQ9dzlYPsFA+hHTzHAojkcxkNkcGi1TjpauOpqOj9Jih2UcTm+PylEmZJvpwwFiooUvIsGjW\njxK7GqazGT42rBk0x6uEO5hnA22KKCmQdMdp0GV+cPOlO3ZCoBk0jHHKWQnBqCZitYrUJHLMwwkM\njsY++7r5M14JxfN6mWHWZFnLr+Mmto9b1ouklomy8jYFzaKgJDPB2avaIkApnVBVsYJjSHlrFqyM\npEaUzeJcQXKFktjmAKN3bjfHE3ZRUC6nCKe+a5srDrr7pm3vdtNCzOEZDr4oIrWdiz1v23dshaEJ\nmXbtgvKJLWi6LiKzQO29AIbUJZI+ltxetDbUHYaaRksWd9nz5qABolKgatjcrnW5fWNpU1xwD1iU\nFDayopNUDRLRhfT6Xrqx7G8ZeRqhAPSVUr8jhJgUQhxWSp2/VQN7ueHsxoDbZ8v8DQojSKmNogsS\n12C64lC2jcthe9mortK64TNduJ3FoIduGGS6QTNOmLAMOmmGrWBqRJ6+7p46T336N3hi/tsJ7yiz\n3ltlzlaAYCnR8bKMqq6IsghTM1lb/xBvNW/j0+IdTE4XOTJZ5Jfe/zkekJthDxfWLrLPzkur/Nbn\nf4s5o8bbye0SqV26AVMOaH1gkkfudviG50PWs7cSyiqTpRir0wIqOPGXGTjvRENwSI3OE0lilhkW\n8gRLKXS8Xu51WxsOOTJoc/+iy78MejzmPEPNfyODUcFgPaoxPbgfeA5VSPlCeCeZboA+i9u7AOQP\nST/OqE7PYdhT+EBReKh0AaFPITRBvWQiw3EW20swD5f0FZw0P78/FRf40dq9VGT+NKjrPmMv9Mlw\neNq+gOnew3eWFccXFniAedJ+iLlvg30bBnc+9XEiTeN3PvxhBve8nvEwYBhZzJfnWexviQ5qnckV\n9GoHYOwgnP/s5QK4uedp9ODuLkJ1P3z2/2HqxO/z3+gWB803AxZTiQUaeNLBTdvY2X6OVo/ylKoh\ngT9cafPuO/q8znyCj0dv44yeRyPNeuf4F8cv8kR/SNrxef2hOmNFi5Nrfe4ZKpySyfknTqEZs6y/\n7z/BxhOYDx7L5eFvAmmSMDiTe5uSA/vh5Fl6p/6Gsfvfdpk8WeYU9CLSMYXREWTt9ivk6RXshHde\nv8mLwpeB24UQh8lJ03eT51PdGtiK52KNw74NF2wq0RBHpjiJw7AiWauOk2YatUUTV9QZnwho1UJa\nmU952CLu3s3A7NENTe7sNJhQCVNxhuv3WXdTSoNZzMkLCNfAURleUuV4/Rhp2kVqKcnGGANxG2GW\nIjTB+fRutFgRF3TWdQelIvYZC4zrKUpBdQ2svksW7efKtWuhJLOZB8rGL1U4ZySsjuafK6EEuLbO\nmKFTDi2kU0ZpVZifIGOGDWccB50DvXxRyRYWZc1kvmXjcLVQQgIsuSbdJENuyecw5JCWXsUYd9ER\nGLokUwakMZV6A9veDMUquZJSVKA1uFoCXAlBHHs0hOL8mM3ZiRuRer4BqAxNRZSyzmVj35FdCpnD\nwU4XPYwo+33ikdy7KeGhRYNYBxnvrJB6Cd0Nl8R20UalT7q2jVeMOGVemt+3W7dCK1JWhxhzKxjy\n1tR56jh5t+kVnieBiWCOgvMqrF1EBHWnSbd6ltLE0lVjv5VIBLi+gRZcJxxMwfGpMeJ0mjTZPScu\nd2ZKjDCj0s0w9ka7YRsMJSnGHdxsZdvnZ2+bJXYN5IGrS8/sJD6xI7a2kwpNrKMJjYbSKZt7rHQn\nFKaeYEkLO5PU2tcmpQBmsjcLGzeCG5Uq/xlyxb1jwO8AJvAHwJtu3dBeXjjXHPDau6YAhQgyrDBn\n0apoMF6yqBbMy96GS+Rp2ehzh2bjCZO55jqL0/toNM5zZ+ku1qKEghRMSoFQii98+Unmeht8Bwm/\neZvDavM0r7EBBeuJRqwEVV1xoXua11SmeIf5CQBa7j9gKU74b+8UnHzsBJYwSUmxLIvz2Qb1tTw+\n+YtrX2ShvMAbjV/E669RNmYZt+doRStUZEwDSak+wBDLbGR5PlDN7hON4sMzZWLLNjDGVL+CQtHR\nU/TaOMNCG8fpE4YVOsMhi08+wUDTKPTOMW9pOPGDtJ0e43GXljsqUBi61MN9SCkwywmrq/cx4c/g\nly5iyoTIeAY7FSSahKlpZGoSG0XqpTDX1RUmg07I0QkH36gyGKVMNBbzZE83ycnT465g0GvjynwS\neo18LbXzM7y//kkGWocPD4fMzX6GQBgkSErKwXAbfPtffQypa3z8jd/Bn6tjvEFe4HD/MD1R5Z5C\njUdan9z8cbTOQv020jTDKM+Ct0Z/RKTLjkFp5HkS/RWYPAwj6fU7xFJee+T/Z++9gyW77vvOzzk3\n9+3c/fLMmzcRgwEGIEAQBAEQJCVSIilRpETZkiWXVvJaqpJr5Sq77LK0a3t3JW+pLO9qt7S1jlyt\nRSWKChbFIJKgGEBAyGkiJs+bl0O/zn3zOftHv0mYNzMIA7JE4Vs19d5037597r3nnfOL3y/bqSlF\nIGFe19kdr2PqGabyU6SD4f0KlOJUb507OcUzpYOc6uyDGgwuPMcf2w+htMbrREyUPLTWPPnKGipz\nMMyU5vI8pvMeVF7i+Dtx4pRe64rylteA5TMnMTdLeJx33g4nznD8G7/Euw++eKlsz4p8yBTpxNB5\nSjc2sGdmXtf3vI3vfWitZ4UQFYZZIvOK19+USK7WOhVC/A/AVxhSlf+21vromxrsDVCpjWP3XIzz\nElvaSBGikczWBb1yCW1Aamkyt0vY6uBY+yinh8hHCbP9EQalAdtaXd4xVyWz2gQ5l0KcMBV47G8t\ns+F5pOFtJNteYl/zBGuD2zhWniKwy6QJ7On3iMyEKARbCmbLU4SGwVhXM768hmkmGHo3howoyBVs\na4UgP0pY8K/SU4KhrZVslIlEH6Uzti/MY4g+9hZJDI3m+I5JZnO3kToCY5AnEyUKSQVpSIx+TF62\n2dUetlVnVkCaa3J8yoB+7trz6QzbW6KYZthklwy8vmGiDQtEQrfnEyYuAs3oyBqhG9N2L0b9BU6Y\nYDY7jMxfa83GmUZEMGGfoTPik7hvTGvo1TB0RmJLCsYYsKmvlPZxuwG9KKPEKrbbw9gsE4wziyw3\nwiAXEZa21mvavCPke02sXg0zGt6vYtCg21ylLLfu10r9ORbGmoTF16A79AaRZVBt9ZkYXPENGlIt\nOD+2j9g3rpMwEiS2QBmS0PjAliK6bxRbCRlf/dVzyKJAuBed8usV7YGvmoy3U2qdrZynKz6nMqww\noBJItLz1d9sMNI5Q+MbV7Hdjoku7bKCdrWj1t8DNWpe0JgwFqTI5kx/nJSv/JqoQr/2yyNYkRkwp\nMhiNXajKq+bHRZKIK1+bHLm1jH83wmvNPP0ocA/wAoDWelEI8dapqX2PoRsmrPdi/IoLBIggo9eL\nqRiSjm9SzzuUcxatTecp3Szbm5cdHuo16Hk+uxsXmBub4uzCId67c+g8OYnCR2ArRV2c4MP7n8Y7\n/SCfEvewzrCsqhl3ibQgFh5lY8DLq89zh77snd8nT/BCJ8+FFx+nrT32KI+WHzGzaycvHzvE6UeH\nbW7uZv3sF8LPsq1b4qGxT/Dw+I/zudnfouRVeUx22ZZ2cORh8ulHEChyapEgGEb3Al1mXJ0DKhjx\nZsmekGTSJrFtav4sy2GRVjDg7P/4K/AvfgM/6FG2hjXbndimGvY5W95OhqQTKHJWjkaQwyqBdWYS\ngcDv7QR20iq40HyG2DRY0wVEqsnsAnkuRhsNtAIpwDc9AmO4aQYNcAEnG45xPpM82/gaP1VUrAuT\n99s/TGj2+fTI59nWOci59ZjzvecxxbtpioyCdrEjwYef/BYrt4/z2eoBllWeV0Kfu80JnhndzlTW\noRN3aEftoU5U4zQvtKb51s/+HX704+9kRmdE3XVMKfAtRWFTVd3qL8Luh+HYnwMwI5appueAKcqi\nTwCs6BL3ZsOI7ZS9jdSqMCGbLKkKJ3sDqjstDo5+lVeCYXr7vc3n+Op9+/jNEwt8XWkmSg4gMJLh\nihT25kBrhDmJsa9K5Z77sD/7aXorr48Nb+H4UdxkqCHiPzQKfwByNWV19YsEwRyWVUW3h88mndBw\nDLKNjZuc9W38bYQQ4teAnwXOcHnXvSUiuVrrLwFferPneU2QBWYa29EmOPEiUQ5izyEpCEqJTyIU\nbrICsoOb5Bk7sUzgT9KSLkmphqNsJjspI/1FMBzW/RprukfgRFjliDOFEXK9gMLyGDI3wFEZ7222\naYqARmQi0JhhiCeqoGGms4SQGUoKIpmRpgaW6IO3Tld2mDHmOJFzUVrDFSxhAhBK4JoOZhZj6zZp\nUsEReVzj2mix0Jp7z7Tojjh0PZ8F06ASreGIPutej+qGojyAQ+YwkGXHmgmnjWMk6NK1zo3QAiO1\nMJwqWuYvlUIZCcjExLePMZY7hxAJQkMDH9VwGD99ubFfaoHOMqIS15AWxMIlzRdQmFQGkIa3psnf\nlCmFvMWoNLGs4Tlb2qRfdMmwEOSJVIaxSYKhkoyVsINhSdL0RsVn0Cy10V4I6fAaTbuPTBJGzK1N\nvjiJKTVPE3X8tyyxI2SMznzSeOya1/dlz1EohpjXcSaCJKWHC63Zt2Zw10G/pMhyAse51mm/ClqT\nza8yeqaFE776Gl71rDJFpCVNz0FcT+3jRk7ITZ6PEiZ2KYfcNnXVoenKArnmBsYtqhTUgCMslkbH\nsII+Revi39OtcQiTzGRAiSyts2z3MXJXD3zoQ8srNgDBnt0Tt+S7Xwteq/MUa621EEMfTwhxa4om\n/5ZgvbdZpuZKCEGGKWvdiPGcSatoUcvblD2b1iAmjTPC9WF0qOdBtTFLuMNhqjN0eM4059BasxQl\nzESKkvlf+OrzL/PMHTVyXh977POY6UG0NTzHfL8BgDLrFNUsFxpP8YMjAV/ih/koX2BazPPMyjhp\nmiCtAyTxHPl8ng/+4AdRh1qM7J3k6xeeuuQ8ndKneST/3wHgSo9Rdweu6XF07E/5xvo5HpYGtvhh\nyoZG/+6X6O7/KJiaflZlT3YSuPfSfTGVRG8yIJXMdVbYzfrMgLVsmC3JBX0KxhR9d5EYg1o/IZMG\nDV1HJi7TVoFDRkixbiIQzJz/NM/dt5/yxl5cvR8YOk8X2g5FS+PaRezOBWTOwjFjNBCnmhGrQbxZ\nzmDHNSQJphouBKHIOBlv8NHM4B+tGdg6j6sfJ5/6CDUsMRz065TjBNldp+6YPPDEEbw44tBtZZaz\nYUnioqryLtVEuSW2b5JBPDV3hHtG7mF04yzHl3egsozDx1eZAZLOChMFzVNPfwin8ov4mJhxB9wC\nDIYlczvECoPBWZD3kd/ke19VRfxNBzFMfbSR573Z7/FZ8fc50e2yc9QBZdL2crhZyK7BBTBCdgmL\nrwNWzmLEtvA2V6RBa9jyYcg61DP8Bw/g/P5v01u9TEuqU0X3W/N4B+tYo1tvMnPHDjNiuxi1Gta0\nSeRrzDWH+YU/BJ2Rz99GtjGcq8nkJmlE423n6W1sib8L7NZab03l9jcE7V6Aa2mOTO0kL3yspM9i\naYy7LrzCIFthZeddjLUzzCxCJJqetpHhNFY+R+yNIQ2LQtZkbWocaXhoDBJi5vyEXmUSI4jIzAhn\nUEFEVQzpkmgDR2lSu42hS4i0TKoGQIl6ktK2BG2zT2ZamGlKW0aMtdfpZJI5ZxeGNInMgGtsXAV+\nWqWYmrjmFDElEDYBWzGPaQqtBQodG1emFAvzhNUezVyFQTlPS6VkuQgxMlxLokYHcSLBUzkM41qT\nRQhBqk2ifA2MywOLModMKIqqR2bnkEaOREpaVgnRd5Bmf3M0YCqB4Zl43uXo+UWjLBMpSkhMaWAW\nwMjdGuOw10lo923OpglKb5ZSSQvTGGBLgyhTDDLNxSo6ocEWOVTiY6srnUh9zW9F38c2TBy5uY8F\nip6KSPNbR+ajVNBpO2i3+paJ5ObSUwgrQnmvosrWKWnsstrYhnoVQ9zF6xFxl1x/GU/fjPXu1iK3\nEmMoAdy8vk4In35uhnbtxrTmKtWkwYCWm97KJNolmBkY2QC5enUJmxnXEOYkjnlrnH+tIdEp/SDE\nVppy5fXrPt4QoYXZMtGuRS8aoVq8uWN0YGrnrR3DDfBanafPCiH+E1AWQvw88A+A//LWDet7Cxd7\nmQamwBKCEctitROx27U5XrRpSyjlLObW+/zXX34COahzn+0QWSn5xgXYAZNhH6EVF8IBs2FMoBR3\nNl6hYH6OfQHMO8ONICqfZqTbwfOGi/GZ3tDIdd0JcuEsjcRiybybz6Y/zQ/Ix6mzSml9BdMyeVfR\norkWUy/XKZSKPJi7AydX4avmNygoB6Ghm0sZmC7/zX6aDyZ3MZHbDcBJd5bz5hLKaEMCdVNgddpE\n8QgPlkwS+QAz+jPMqhgpbYRKMYUgkxloja0GOPaAdtlndTDcNP0gpehuY948gknEdvMC8A6W9SQF\ncuRwKfSnGKldIBg9zsizp2j6BbzBCLnBDiJMEkOyGlYJUUz7JeLV06iZnczkEtZLBr0wY6e1RGgp\nvAxkVqKenmAhG246QsZsWCUCJA4uJDYR7+TTZ97Pfyw8xkvAemsf733pGYoFD3PyXh5+5nm+cv97\nOS7GsUh5sP0K3yoeINECP0vZuTE89z/93Bcwu12+lOVZ3RhGWRfm19BTQG+Nh6bOE4YLjBb28T+b\n/8twMi0PiSuWCgeZ6Jzg1OA8Qsa4DCO8S7qCz+a5NpmpdquTVGSD86lHsZNQLvwMK4xTzjYX15Wj\n5JNhL0HqGEyVPNzNVb2zNkuxWEYpjSpWsffswbVs1vqX66a7316g8+gsvaeXmPiV+69hyFNZxuKJ\n4+y2HMx8mTBZJKkKxJxLuzPknZne/t+TboospxOb9LrNDbTWPPPMMxw5coRKpcLHPvYxLOvN6qy8\njb/hOAKUgVsrLPIdRpa26YzUUH6OZbeG6pVIZYUXJ99NqjO0kqyUpimvdWnmKti2SbPqM5Y4GJiY\nooYu7+JwwSCO59HxBiM9FyEz1jy4q2uS6QjDdcFykcohl7lo4TMTxQheoWXXGSQ1QhYRnkOickiZ\nx0EOWcHShNlsF7soD/ux/Cp9kTEwrux6Egil8SOQOo+pi0jdxSBCiuDaCxeadl4gZIidZZSaip5d\nxUxcDqwOGNgZqWczslkabPe7FHREzuwC12rUKA0Ny6U5yNDauDgkCrQo6iYa6KYTDOQ0oSmYK40z\noddpFy4bxMIMEVaHxLx2vAYhyjBI6iZpvoQ0b9xvdCVulCRoLynMWcnioHjJX6kNEsqRgWFAnRKW\n5SI2sx52nGCkGUInyBuzYaN6ClBEm1IUWWqA6RL1trbWLRSFgiK3zwPzrUk9tV4wkKJL6lwtdCtT\njRkVcGMLtnCOASxlU7aLqDdVGvb6IdME34Kqd/OmoHZaol3YhnSvl1sYfkZEArcF42Z6S5kNLyHY\nIM366PDquZwNYtKoi+Y6jWVvAKYApyOwVEr+eg1rbxCpDknJcMY2GBnY6NZpbvbw5/PrHLjtRgLS\ntw6vlW3vfxdCfAjoMOx7+tda60ff0pF9D6HZHzpPbTTbXItqwWG1GzKeM8DVPNbrU/YsNroR0QBU\n2uP49AHgMP5m5K4sBP6gy5Kw+fdn5zAF/ODK19Fa8qXxB3CNk6yGNqNunwONc5RLHYQscK7dwBMa\nwxwy6wnpMjv5ayRzHVKjQD5bptZrk8utMrXvXzHf+DEmLpIylB2SVpdA9vAzl0JoYOTz5Ft5plSN\nY8Y8O51JElLm7KEd86VBmQMqoG7a5IwWu6tjjFgS2EVOJywnPRKnihes4Tmgen+KG/ms1jdGAAAg\nAElEQVS4KsTx+8SBz0Z+SBIwpgtY5GiGTXYeeB5nfAP4ERay7ZQ3heh2Lj1Cv/Z7TL//NxkcHqdH\ni9QOEAOJsioM7HVSK0crgz1Fn0Fz+MdXlPdxeuUInrsfK79IZCucxAQM3MV5zNLtw/slYpLCPp5t\nb+c9hb8mBZQu0lEZve79QMqJYCd7z32Gjfs/xLhT4A8+9nf59Ls/iPNcg13GBge7p/lW6U6WrIyJ\nToMwkPjlOi1rjn6Y8Sn1YfJqjh133cPsoRfppxYyWGPX2Gk8d5p6+Q4+Zjw1nEynHwXD5nj+3Xxf\n9zDBYBm0gbXJ1rRq1cgzdKTnox5Q4y8PfwB5W5dlZ5J3HOnAj93L8rLHtN4krVh4Dp0Oy/h6FkyV\nPXKbzlNz6Tx1N0erG5J5RYQQFCenSDvrxGGA7XoELw9LRFUnJl0Lrsk+rZw7TRKFuEpj1usMgllE\nzUG8cjlxUKk8QPb8cA5lZQ05m7SxwYsvvshf/uVfMjIywqFDhxgbG+Ohh95utfxbjl8HXhRCHIHL\n3AVa6x/57g3p9cO2BKpmkrg2TVXAzClsLQmKk8jeAoYGLSVH99wB0sFIBZgpK0aOHX2L1Ig5lU+o\nBH3SbkCHPEam0GjuXJeoZB1hmMR+gpGZdCwLy1DkM4ucnGQidEEJ+sKnbRTpugPGgxxSedS1RzEz\nOJMfQ3ogMxORBJQTj+k0I/8qvSAlBCs5l1bWoUeDfq5G301JtrJ1BHiDNUIiTBz2tpeobqRksk85\niogzRaYyUrlZrqY1HVlkdvc2yupa/bfElKxRwPL72Ffo1qXzijC12bBHaYwcJCxOkSCYtxNUpU8u\nOXTpWEsb2EmeJC1fc35ptoiNNlYLyht9zFuU8KwR4bkz5DwbjGEflREpcsKkZHnIlqRHjv6m82QZ\ninwcsWxlNOXl+y+u4uUY/jIedrHQOJdkIAMKaY+82nrsQmWILCA71HorCOAAqPYTBqJAKF/lfKYJ\nXtLHLV5AXCMaO0SWWKRZneVa5U27G6/H9yquLpGkAzbim5vKRr+HqZbJkosdLdcZqVa4VoQ2VxE3\n6nnaglbw1a9s9WmVeJhGnoGz66rXC8kSmaGInK0YMF8fBKCTFNGXZN2UolXHzW7txFEalFb0VmIc\nFWLLm1OsZwvnb+kYboSbzgghhAF8TWv9AeBth+kNYGPTeVrPMra7Nn7BYbUbYZuSXAm+sN7mo45J\nL1Xsq7/MoVPfZN7P2LPg4/zor8MKFAxJadDjQn4PR1a7/OxknQeix1jXt/F0bR/v4yRPBJofdWFS\nP8ZYcoKeLLAQ9igamifCaX4EsEUH1v+Eu1OXtjAYF4uUwi5uqYW2Olj+Kr1suIAZRZtW/wX6RsBI\nPIbft3gke4gxXeZ4tc6J5CgHwyJzzgph6x3Y5We5sDjFaLXPTs8lm55k0rFZHgwYz+UYz3bjRh0M\nmVJpnaRVjlA6weq1qHwxpXR/wPpkhY49LC3YZQ1L3gatJrXaHCYxjg5ZUtuZnRnhLyoe/+7F7+O4\nucD0/m9w4vunyTcKZBfLMcwyPc9g+vt+jf7yPRT6IY3NsgDf7CDUgFjfzle6/4p4/N9gb2Zq9pW/\nTT3/GH8KCKPLweR9LCaSvtfBAZYTzYuB5khx2JzcUMPFclCcICTh3J47MOf6xFjcbixzT3gc+ARr\npuYdnSZzcR/lTOMVznHfaMAXlh/kJ/gj7nj/B5k99CKtxMMOG4w5s+QL95JP1rCuoOBl8l4uJENW\nqFjFWNW/RnZAkNKxfdx0uMhcyBQVGiw2xwk7sDwygZVq+v44G8LiIZ4gKY1hzT1Lr/CDIAXLKqPo\nmZSlRKuAXnuN3cU6PZGRbNbZF3fugpfXaZ8+RXXHfpLlPv794/SfWSY6277GeZo/Puy5NwYBZr1O\nFJ3AHSvhvLTKnqnfxMwH1GofYH3jPwyfW8GAkkPaaPCtb32L7du383M/93N86lOf4ujRo287T2/j\nd4B/CxwG3ipJz7ccZqTouoKEPm0DEk9RzyymN85j9Nus+3V0BsIqIzHxszZ9qSAdMOcbmEELvzFL\nPVxAxmVGcuMMhIsbzyOzHqkAZUhkFhJaGdqwuEBIEUlqKDrSZExAJfVwiUn9iJIZYgQOXhzja4eD\n/YC+ZXHKtTnmGDgiYUz1GOOK7IHWZMKkmd9OYJmkboliP6ZgmZhXJYkvm3ppvk6ztESWhYRhnkIj\nQcYZWDlyWhFYGWozySQyRWyXEc4Uq8UtqIgzA6VsSDYQg+hifJ+F6i4u5H3sYpUdacJe1UOpjKmB\nxFAVqvH7LtmnOomJQ4VU15YdG7So2T3aVswCddSryDJuZIxv7TsOXy0kBuiEirNBullKlUiFcjus\nl2J6FZMVMUnL3wYIemnCSncFM83wRTq0pLdgWNBo7EoLV6SXqgDGVvtMbvTIJVszltnaoizr9HTy\nVlXtIQ2bpGgjRl4lrh6HJLaJMmzkde6mJsWMZ9mZnfyOav9tZBYtUaTr3lx89UC7zUTnPDK48fhU\nltEP2wi6b0l7WZRlYOYoFq4OBFhyhMzPDUszbwGEVnh2F60EqbTp28M5fONuvNeO/MDAi0KczCXR\nKXLEu/S3c3kQV/93+u7Xpz35ZnBT50lrnQkhlBCipLW+RdLaf7vQGiRo4HwU855anqTgcnSxg9Iw\n7ed4pR/yga4Y1r+2vwybBv7dpyswfi+snKMgJZVel4WR4eSIDv8ydVZ4Vr+PyBs6Oy8HBh8vJ+A/\nRY2MucBlIRJM25oT6dDYLhqK/Z3/zP0GzCYjZOkGuSjGcYeb4fjkCaqlb3DotGJ7/g6a8Ut0ZcRY\nYjGelfnA4EE+V+/zfPNx6o0VZOEnOOvOI+R2drdfRiQGC0nKnpzAuP1XUVpzqtsg7zhYyT5Ct0ah\negT7wioqWUXbNUTcoJ2z8RsDFop1+uN5DJWyw8kTxn0GVp8RK0ZrwZhYZpadnN47jKo8UbfoHf4k\nau9juIUe6+sbvOfgMTz1GMf+6l56jsFX4iZ3z3yBO+arvBBuaia5i1TtmBYakMSOjRNpHNFl796j\nrJoSmMITA+SmIneUHcCRsJo2ODT+dWYHH2EMWBEm50tT7PXLfMV+CT1nkaU+9xjnmTFW2JYfUoYO\nlMTQipe1ptnYgTvxAu+vvsTjq+9hfeIOfmvuSUxvmkZ8mkfOfIXldw7Ie3ux2kM5G4VA3v/zcPff\nY+G/PQMMK7HL1b8i7d6OlAnCjtnIChg64jRFptQcp+MRKnGbJTnDhlnkmM4DETvlKTbKI4zNPc3y\nZICZM7kQxQghGLUtMjXUVMkvrmBPS+LNXq3ygTvg5WfYeO458mJI25u7d5TBS2ukq9fWpF84/BLV\niSmyY09i1mvEcYPC9J1IVgmOp+z/xE8CkDU2kMUilgcUTTpzc7SLBT7ykY8gpWTfvn1885vfJAxD\nXPe1l868je85DLTWv/XdHsSbhZl3kJ2zhO4Uu9qQc3fiBQn5pAWJT763hJYVbOniZD0SuYzWA5bL\nIyQqId+NyQ96NByPaiTwU0EmeziGiTFaI+6nxN0mfR1SyeVpOTFhFtAXBQaG5oKfJycVB9IeJY6R\n5Hxsu4ntSJwm9EWOXsFn0cuTX2txQBg083k6ecnK+Kv6OrRmLG2Tz2WYBYe+aBKKBiHXZjqkFkyo\nKsZA0jUlK5U6qqARKmYkjhlTJWzPJbgYhAkVadAjNEFzLR2yIQSFKMG3tuEYl31pS1sUMoNuqshk\nzBkzG9pyKqURu3RLhUu2XdJYwQq7GMa1NM5uZOPFNSJS2gWLQcG7xiS8oYl4HVu6qBXVVBCOmKS5\nTacmjsi0S2Z6tGXCIFklDYblizIO2NEJyTDwEaCvMSUvYWp1AScVGJv6RIES9Jwc3ZGtS5qc/oBO\ndwMT//oDfpNIZUoW9ZALV5ftoTVWL8DOwGDr7IVOY4JsANG1mUF468jLdRajiiamd6U0x5b5HhZq\nIcg+m23OW0MIiFKctomf34kph9d7c9a/1/6GGnSwDYFrOVfdF521sZwmuVuQeYKhk27lbLQ5Siuo\nEdi3tgU1sAKKqzE6XccWGQVbbu3YX3GRZe++WzqGG+G19jz1gMNCiEeBSxyZWut//JaM6nsMG4MY\nI2fSV4r9vsdK0WG9F9ENUx7aU+YVMua6w2xB15DDxcT/CIXBlzl39DmgRmHpWSYtjyM79zOSNjgw\n9y0yJKfYR9U6RpjBzpaiX/OYsGIqpuD8ICHWNo4QvMIw2lOUmr/KHuAD4gjjYp0oyiEAd9N5Gh05\nj2FmnD7zG+wo/AHz0VHCbg6hJT8V/ARCaRbO/DH7W2tExXFc4bCeLaP8Pdw2O3TilvHZSAZUrRxn\nI8Vq0WcjE+T07USygSGPI50EdIQqHMRotlia8qmnfUSaMPB8ClmfmhxjPVwgnRr+UTaO/RBjdyzz\nrPPApXv7Uslgj3YY9Iv4XgupMuojw9IOu3Avg8DgeJbyfPpjPPbwXsq5z3D/cfj86An2tYbkXAe8\nr/C7dkClV2OX8xRSaFb7dwJNpsRlZ0CpMbTQjNlfZM1dRwUwHTdZsSscnbgdYR9mRXR4Pn0HY6LL\nQXONcaNJNp5RC9oYwkA5ivO5Cml/uImZPImv7uKkN8LLL+0jGz/IgfYSHy49B9Im7+2D1fMA9M0K\nhY/+OwDORcc3RyWoZRkBLtJUCKPHoq6hLcWSqLE3eIFdIzMY6SxLwNncdr7aG861neZZXg4dfmCw\nTrZxFt+vs7ipL1WWBolaQwC52TmcAy5xMCyjKR+8C/4Q2sePEY99AAyBPVXAHPVI1gYkqwMGL6+R\nv38c5cH8sSPc/fD74cuPIasllArI7d1Nwss0X34JPvFJYNjjZFarWBaoQpdgdonqex9m3759AExO\nDh21lZUVDnslDnUH/ML2Uer265GrexvfA/i2EOLXgb/g6rK9N0VV/p2Gg8W29RW2V3qkg9vo97oI\nDAJZRwiBZXtYwqEaGkSGTeJUEP2M6sIiSimaGPj5KQydEnoWodhgJOrhS8gZf0U7vp9+arFmd4nD\nVQxyOCohMj0SW+OQkpkZp52QncpmpO+jjQ5B9wINJErGhNh4oxXOVEcQyiYLE1zVZmqLxn2VGiSt\nMfIbJdxBi0pWoDC6fdO2ucLCUZpWI6NS8EhEGxUfYb5iELgV+nIMAgdXeQTlTcHsVJNtSFq5AKd2\nrWUaKEW3nTDYsQv8y/0mpScPUxp0KQximm4O5Q+dsXSjQSWaJ70iayMySKRBYXzmGnu0l0FoW4jV\nZfJaUU1vDVV5Mw1ppIpmq4jc7EVK04jU0ChD4qUXGEtW8Df3IJEpDK2pyBFs+8ZjcDEw6uPEtz0M\nQHvxKCt5i+Lt+6467uKlhueWCU4mjCbRFfxlbwQ3cAKSGLuv8dKr1+tMZ0QiwTS25qrQQCA1TbvA\nibr8jvY8FWIXP4txubmuYeikBEaKoQOuX7IHmaXo122KexJs17n8xlaH3/RRbEHxHRhos4thXe3M\nFNYnyKkSzi0jys6QsktRTlKOfEZ33FpNxvXOMt9oP0UmMvxOzFhp5lVH6Gsyr8XCLdaaugFeq9Xx\nZ5v/3sYbQLMfk6t7DIDbfRdVcFAagiRjjzCBjJVgONGXrD340QkG4wV6U3fzzRdegbsewuuvcufp\nE3z1Xe8l6T3LR/sR82I36wLqYoXVVLI/Dak2D5KrnsOQA5rpZvmdVaJFCaWhaGgeVQfZvXCUd0wr\nWuHmZuTYCOFjmH2a0e1UnOP07VdY8mfZlrwPgCk9xe+Hn6a2sUH3rh9naXIXnID8fBe5o8ZEy6Bn\nZRS1w7fXn0eZMdJ6kPMzVW5bytCuR9z7c+JuRMsHhIe0qxjSpCtsJu9eZYe5wcB7kIps4SZ1lsOX\nkLXhvdk4+UEm9z0PNthpwvgg5VRBMpE/zyAsUMw1yNX2AEPnyasERKsGsXsn/cpP8jLw/eIwqXGK\n88lexsUDbLNeYL//Jfq2oJA+wB7ncfpYHOn/PeDfc7s+c+k5GsIhULDf+wbKHIoFT69/k+cnPs5T\nlRnK+XOsdncQYvEJ4yw7meMueYS1KcH4yw1Cq0ijprD6CZXQZCI/zZ81G/wH8Zs84hznc+I9/JPB\nP+JrznvYt/MC0KJQPQgnPo0GVuUYOa0xhODs5nOTaMaUJsQFE5RsMa/qtIvDBdJqB9w/U2Wps8Bh\n4Iy/g6d7IVJb1FllzdkDwGjzJSpTP8R8tKkvhSTJNij5eaw0wynnGWxmnvIjwyxm5/xZotkO9mQe\nYUmskRzh6Sbrv32ErBURHFkneESRJjHT22eIAF0abhbuzE4SoH/y5KX7mzY2MKpVbAuSXBPZjXjg\ngQeQm9G58fFhyc7n51f4N/EwGvtkq89f3LvnO1rK8Ta+67hn8+cDV7x2S6jKv5MwpE9V3oN2l4j8\ndViaop8l2CrFMfJokSCloDWuCS3IwhJuopFZxpLuIqQgyhvUdo6xtjZAmRbmqsZunmXpdICvz+Np\ng4I5IHKKWJlgZn1AsZIiqh650Zhl0+ZoIyMOHCpJhQs9iyWzzMABRIxFgtutYQK1Qg4pY4q6hG9f\nTdqilGL9lReYMF/BreZZ7Q4445dI4ouSBhdj60Nj57bAZSJzKUrFas9nlzLZ8CwsIyDqNRnQZ8wc\nGkIqUzQ6XaaDOlbzWo6QLEtohG3yWQ87f9m5aoctTMumVCox7uXJlQqE0YDj/WVCw8Edn7k4NAIV\nEeVdcvs2jdkr1hN7tUm106E938Eih3udvpzXCzPrsKKb7Aj1JZLAQZSSWibkbArdBVy3jbA3DUQ7\nIzNN2gOFEd048+7ZkFnrZL0vA5A6imqSUDp3bsvjlzBZ3F2gZQjE1mJLbxrOAIoqZqJ0tdkZp5LF\nTg5RryDFdfpmwgy3l/KIU3tNztOb2Q2u3EqazXWUEaGcm1cHh4nAVlNgX8vmceV44kShMkXWLBC8\nBfuWVpq84TJevVrwedE9TiJiTHsLkdw39EWgIkHHCWlbG4jw9QcVbjTTAhUQGpNUy7sZiBWavnPT\n5xqa1xLKvFW4ofMkhJjWWl/QWv/Od2pA34toDmLM0nBi3ea7NIqXF77WF+exP16n525mbUKXfVHC\navE82rRoucNo2VdnPsT7v/Yo+Y3f5X3rX+Wv6h/iK/lPcNupE0yJJU6ngtvSCNnMYYwPI1Xr9of5\nh/Uv8bh+J1oYZMqkaGgm2+fY1ljl2EiO6qYR3vFHmBQraN2nb/5DSvqfMZd8jsWBw3t77+AIS/ye\n8XlGlzd47q4H+QdiL8urMWCStpu8c/EU7lyezPOQCFJh0h88T7H4Hk6MWTw0n7IWzIGO8McjBks2\nhvceEukMm6QzA+5qEzyxncGMz3hveL/mWaXoBKjUQqUOj5iP8vXgI9y1cILAqXFqZIT78hcIowK1\n+jy7nMvRDy8f080Mgvz3I7IOucaL5AMb15rhXbOfIMs9z/+7/7f5LQMQJsWwyrhzkrPxXTSTvZha\nUzSGDHCes4IjpuhkHXJGCwbDTF456VBK2swV6gzkOVq6jAB+Lr2Pqvg8ZrbEi5M5xp/c4MXybjZy\nffZ0l/nwthSn+27+xPpjBvV1or7JD+un+ULnHr5ZuB/pxWS4uO4UtGbJMPjfZn6Grz92iN/YM8ZS\n7lF+xR5hd5IwmWoCHFYjQXswymeS78OpOkidoRsp97+3yktHZzF0xrnCPi5ECoFCokktSYjNvuQ4\nJ0qf5JUko59luJkmTjfIb0ZyvdEyKyf7m/e1gBSC/voG8XyX/APDjJA5mkO9uEn6sFvCmQHLXz2L\n4/vUixUWAMrDeW5PzKBMk3RhAa0UQkqyjQ3smR1YNgyco+SjmAMHD156noVCgVwux+8Emt15h5/f\nPsIvn5zn0UaHH6h/58Tx3sZ3F5v9t3/joR0bOd0nURYmGcXxp8kd2Q4izyC/SJwd5/xEmYo3Tjy6\nwlJ6B8lgCmM+oysqFGiji4pmqkl92CEiIrpccCrYtbuor62SSIOwJsnLCYqNAGGkBP0G7rkWq8YM\njj8J/SZLmUnJFqwKgyxXpLx3H6XuBZY6AwJDYkhJvT5JM4gI8wWEc7WhlEZ9rOeeRWcGaiPBDSNG\njCVU3gQ2S9I3TR+hNBu9GGFpmr5DQ4xgygIeAmSXTLZJs4QLXWPz+IwszlAqJLWudRqyJMXs9ZFH\nT2JeEapXpk3fKzFRrzMqunjRcP2SXkrjwG7qe25Db5pvs/2Y1fYazfQiY5i+FPZ3LzyP7Cwykpg0\nvWl6u267Jc9f9QPGW/Pky5czATXRxDIDck6epL6KsPI4uWGPSpi2MOfPY2cbFJ3LDtxWBuh82aFf\nKcGmrpNpdkEKjNLWhrOtfPpWldTcjsGtpJy+PLr2Ro+BBv9VRn0rSZjNhaiCh76OMyFVjFePuK+8\nxncy9TSYH9BNHLS8Mf04aIyogdAllC686p2rYVuacpbQHYdbeqs3IVoNLGMd37tai3HaCbA8A8ss\nbjmui3itrnOawukLKfP9jCW1ge7dWsKIYUOFpNtfwkBhpVv0O74Kkb6JHtctxM0yT3/OpjCPEOJP\ntdaffOuH9L2HZj9BTVhsd23ypsHBbZcNvfFMUusr0uJmadogwY9iYivESzyyeFiVkgnN3N4d/Mts\nie0Dh79/9z9j90aHHcZRSkaH9dTkB5IE1Tcu1bEc8T7Ez4gv8qfZI/hRimEpSgZ8uP0YE8Vp/nOr\nzU+FPqA452zjNnUIpSTjo+/g1KmddM/kmLMO8neiaY44SxQbAR3f4cl3vp9ffWqFqeUWyh3BCFrc\nfeQ5erbNeK9OqwTIPI7q4wzO8shfH6Vr/QiNZNj7s/PD52n+3+M0SweIWd1kRhWELYfuSokoV2aq\nZdPVfbpGwogzIAyLaGvAuFjmFx5/kkCGPD8jabtTRKZFFOQxpOKh4HG6mYUhMlw3Ymrs/cTePfjt\nL1LsPk2htw28dwEZ/98dnyG9QjRwR2Rg+yELwXtYzs/iKImwekRodlLBlgJTnSGwfZLWGAYp21WO\natxkxRshV1xhtS3ZQRefIg31APuyF2jYPoW0yYZRpnDuFQzfZH/v63x+9IcZ73+Gfz5aZ19uN398\n9Jt8zH+aR+XDHEvv4A67hxASmuc5423jSxMPgtL8TyeOYVUe44/q/5zYrLJn6d/yIeFxPNlGGo/z\nJONMlwZMc54P9Q5z73SF5bOrTEZLnM7P0M5sNJBlJoaRsmjO8E51ipfLHhCxGCbISGFkG4i0giyV\ncKoF4nCoayWkxMv5GH4BUo29YzPLNTqM+kQ65PPf/H/42P5fotaoc+d7P4RuDz+bFYEOOHYNMTqC\n22uzsbRAbWo76cYG3j33IEhI8xFSgxVFsKkLIoQgmdrBnOHw69tH+OmJGv/n+WX+cGnjbefpbxmE\nED8E3MFQ0xoArfWvfvdG9PqRRk3mjXXy7YgyIZ4OSCZ6JFGFJH8aP9enGKzwUuAyEmqK3TVqy4dJ\ng5BMmBhhysmK5BP5HGpjkYN7J3gqWme9WccbmSH0q8wbhyj3csjWIUragmKR9rYecSegH4C+5110\nXvw6E+ef5ryZgDbIOR67o7P4t9/GWDhPVTk4rQW8RsxiL0KohNRyryopUpmioSWN0gRxbQZj0GdX\nrcqO8WvLaFKd8vTSMyzVLKRpEy4vs2z5SCfPZCHF7Lk4WlMd3QsamkFMM4wpVAUTpWvpkNNU0zgZ\noZVFdgVDhfPiUWKVsnLhMKpkUSh4EEW01hYZXDjDsbFjl8xwQzQZz61jm1d2nwwvsJiso8ua0Azw\nogsw9+wtef6mGWEYEXs6k8hNK7qXWyYtCWS5B+sh5YFHcTCc4guhyQXbp79DEtRuJNeg0YQU82MU\nStPD83Y2iIME7Du3/ERZJ9yZtLhrZhTzLfJNvniky0ovY3l97erRakUse0yPTGGbW1/XUtRhQ3V5\nXsfItygzthWSWh83S8iZN6fhHiSniIWDkDeW0hAKkjAjcQtoeeupDZvuOj1h0jSvLnHVnRZxX2HI\nhVv2XcqFTr5Aw3TJ+duvfnOLefR6ppbK0iGZiAkqWWOmVrmqwmRLMpbczRn5bhVu5jxdOb5d1z3q\nbVwXR7+9wPxSj2BXnbv94SI4UfL46XdPs/T4Mve+fztHZzQvLQ4j9oGwsbXE1A7+XkW2FiK0Zqaf\n8sntj5I/NuB/3fWLGFrx8CtPkHc6CAFrqWRXkrLS6dDvj3HIqLLsTrLGGD92doIPrZ5n+SFFxRCc\nzJUZr9zFavMJoqCC4ww4qicJSLG0YMdogSefnIEgzw57QFF7oDVCmnzjgYcppH2WJr/MjuVH6EXr\n7Fptc8SxQQjM3LCmeq+/g1OdjHce+k8oofjWAx8hF6/jGnnsDHQisJI2RuagNjeO/pKHGqR0XQ8v\nDnjRXMQ2bGy7TxzUUMaw0VH7a3gb+6gOhlG03fa99MIhqUJ4t0bMmYQjeWy3y2O3PQjC4IOPP8mu\nRYmplqCyDdd/hbwIkBn8WKfH4+H93NF/AnxYsWIWCiewMpvU7FIzGlSNYbSsYL5Cp6Dor1bxrC5j\nrXW2eSucy+9gZteLbMx9nIfkEfq6Sqh3IoFBoEncGIRgdPk8etceBpWUfzz/f3Fnb5mfGT3AgrXM\nS+5+3s0ZtgfLPLRygrr04WFg4yxfrX8QgB/Xf8CfiJ/CTf8JoT+sXmrnHybVDs1s2EyrgfPeNI/o\nb/CuZJZtFY/R3DozwQJfK92DEiZ+0CPKcrhOn3P+Ad6ffI79BcWDg28z35SoQRdDR4SDFHf/fhzP\nJEsUWaowTEm+PkJuk5LV2ax1NupDJ8efrlFOJ/nr03/GByZ+kru27Sdd+DYAaSGFDlhWFXfPHopP\nPsnKmVNDQolmE6NWpdGYwyqlgEm60cQoX24SPjcyidCaj9WLWFLw8dEK/3VhnXaS4mnFyy+/zK5d\nu6jdRKjwbfzNhRDiPwI54APAp4AfB575rg7qDcCSFmd7iu0LE4RqjYmZNrG/QulIGr8AACAASURB\nVK3QoeWuYyQ5tJeQa0tKUZ+aXiIWHUqhYEDCildgxK6yvHsnSdog63XJY7G9soKdO8v5xdOU4nXi\n1COT63R9FzG2wuBgEfvlAc3BSU4u/RF7TzxLaNjM7bmdXqHAZHeB0uJxsudPkYqYnihgDdrY0saO\nIsykRP5VjHNaa7pC0x0pkY57VNQyiR/TLMSXsjvDA0HrDHugEUIRaomqFRk1YFu0ghMlpGZGG4/1\nzVJ2IULGc7Pcva2G60+A1iituejchGkPJWaJjauFTGe6i9idNbq6TCNX5EJlBKUVXtCmGmfsTLhk\n4fTMJnHcIevVrhEubSdlgnwds7RKxUqoFt4IWY1+1U+I1loEHU2nbCE3M3lxa4TkdJ20vw+V9OiW\nUrLp4Tqb2nUsZWCM1EFcP8KugbRzBkKbtDWsnAjiJuuGIhJLW34mU320Djm93LoJ294b96wm801q\nXoRwrg50ZfEAFXaoxaeQ6WVn4spvKqSKlTglTPdeK9D8evA6PiuApCcxjRT7BgmNi6fsJSV8YSCv\na1ZfzLwmFJMO2yggjVvTP3clnk0z5lWJTFzNatgaNNBotLn1+C4JEt/gvasgNNLt4NgK15B8bKx/\nTeABhmvD9c6jb5DnaoYhi0GZXtQkszbQvafgCkKRrT7Z79SAA9c9563EzZwnfZ3f38ZrQJpkfPP3\nT9AsxfRM2O+7JMvLdP7yy/yLj36S3/3KGpXxHLvT83zJG8UUy4TSIa2PMNAmu4sJumvgJjE/ZH0O\nITStvT/P16Z+hIcaL7A7yhMUzwKwmuXxi9MU+kt4T/wf/ML9GXiChWyKnziXoz9yBGMNKiXNqu0y\nMXU/NJ8gbe7Czc9zL88xxwR75Cna87/INlOxIMapZ2VQCpHGGF6Vk7sfZnv7OK3zMTsLEzxR7XPn\nMylmpkgNiVm9Aw+4y89hd0p40Xl+6Z/+aw4cFpT6LQpWnvpCxjIgsw4yG2WQ24uln6N5ukRiWaSG\nQacfEjnzpDkfx+7T39iOlkMyA9dZR/a/j+nVUwAczruMdy5HWYpnI85VJ/H9BnPpPO9YnWLPvEQi\nkOYOTGy6xnkcNPcEEQf6JeT5n2Ai9y9JlWBx8o+Iw49iZjn6ssle5wwJBSCPI+boSU2XMqbRptJc\nY+fOBt/C4Fx7B62kRKepCCrrSIYOV68rccQwIrJhVihpxf/P3puH2XWdZb6/PZ95PjXPVarSLMuy\nbMvyHDtxPCTgGBJuwpBAAxcIF+h05zI0DZcLFxoCNEkDMU0gwSGdwQ5JHNtRJtmWLNkaLFlDlaSa\n56ozz+fsad0/jmRLliwlsR2StN7nqafO2XvtddY6w17ft77ve99a2c9N1Zf49soAb9ffxscCn+NQ\nLsG13jzf8vwnNNshVdVZPvwx2iopdq3ZSZ+YZIezi0eVd+NNtGMJl7iZoU1Zjy2WyDlhtOhz1O1b\nsWSDeC1LKzkkp0TUU2Bj6gzPRm8AwD1WoTwYJBJIM6H28RZJsKH+afr4LPKJv8O1PowqaawP3YES\naccabS7CT//rGN3r41QqHqKxzQi3iBJq5ngLs5kXrgYM3vsnf8nMsaNoRzzU9q6gGKugaZQaTcLO\nwopOeOdOGs88y8qLhxhevxlcFzWeYHX1NO3Bs0K52QwMvKIafswI0JbNoFQrYOj8WGuEh+dTPJkq\nIO/5JidPniSRSPCrv/qrV+ugfnRxkxBisyRJLwkh/lCSpI8AT/57D+q7heoL07HagskEuhojp1VR\nZImxiEbe76d9VlBDpy8+SofeQDIMGoqNcN+CzzlOfc4kmF6mcsyL3WjwIgbtS+DXi7iVfZRoICiT\niAc42BbEDYGi2aipFHUHrLrC4OhJ3JCM4jrs9EQp1b1IRFDlIjUMVrwmGcPA1heIuX6MhISIGOiR\n5m/y3C9MEg5u+hSd0SyGUiddWGS+pDE/v3phO5rVT3mCVOR+NK/AE9iNqq1QCkRItm/gW6VVpq0y\nQX/znmM2KtjlBotLeTqkzKXfSzrYGN9BKJx8+djowJ9RNbOU7Bo5t0GlaiEJgdlZQ/FIiIDMObPG\nrAdwGwkCzUSbC5CqFrEcmxQxCvFByq39F7X5XnDGPYNW2MMx3wCGp+lQaOVFFMkGbx5ZF0ixduL+\nZlq0bZYJ5TL0ZVtwQonX6LU5H7ssUK0qztk3PlezyMkN5FD+gtbnRFpN20YXFepISOLyu/uXw+VE\nXw1FQQsOgKf3whG7FZTlMYTpw3m153oWda1CwV+joKYvzSrxJsG1Hcr4oHGhk3PRLAXUrQRRrY+g\nEbno3PkPPU6epDuD1TAQF9V4XVgbeA7Sy2dBSNKr3ucL27pKjJjWQJEv/K30hCuERBRdb3ljrHnX\nRak7+IVOxFuht9HzBnT6CpxGhWJtmlnLy7TikJUuH9EDsC8hNfBm4UrO0xZJkoo0Pzvv2cecfS6E\nEG8svcaPGFKzZQSCWkBFSBLrAl7Sf/vfyX/2s+DEAT/Rdj/9s6M46nY8PoVGzmCyfZAvNLYwO76C\nErfYUjhBhzrFV7mDSEHjTIePe3MTdDgbWfQ2oy9LUifPMcq1epbfH/DS8Dc/2jm3DwUZ5+g38S7J\nOPe41Ko23vbNXH/aomZDq9ZCN7v4Om9ljXSGvy5tJ1pQ6PHNEjV7OFl+AdlbwwnEQdaQrEk88zZS\nh8bJhI4ysIb23CJz8RAF4SBLgqrj0L46SzrgpYHDtz0W/XaOgUAfnZkykw2LGlUU18BS1hJKPENh\nIkgl3HSCvGUd2chSc73oRoNCCTQkhICIOk8JCaWs4K+5nJZzdFVfuWFp8xL2Og05sMim0VHclQVk\nJEajLfS7O7All91WmBVFZVOjxJJ1G5IcpMNbpGQbFBUZRa6gWmEK2jJRcYgFsR0hBFUcSst+SmoA\nn5oiVCzS0VGEKuw6dQ8AHZ4VKuVWWgIbcCQJZzpG2GqyGc6Eerm+OE1eTlJBI2W1sqO2lY/xOZZy\nWY7EhhmpTvH/+H+C2zd8A/J/RT0c41BoPe/kUZ7K2gwkJ0gHkqwRRTblXuDJ+G0MiAJhT5EPb3mM\nJx2NJ/kx0mqMJZJ4l/eBENyf3sPf9bwPbBc3Z3MyN8jtsQXSKLhCQtS/BjrYWgM1MMmAdiM9oQEk\n3aY7VaVoyHxy8X+SHO1hSz1BMtlJcekgcB8A5kzz9iBcQX7FYnkqRuudSQr/cIza2ARSopVjz40R\nGVT5tz8f5Z63rwGgdugw1lvuBUBOJkhN1Gg56wvb2SxCCLKPjDKxUmJmm8GO9BKrq6tEo1G2Bn10\n6yp/+9Iod548STweJ51Os7KyQltbGyXbwRaCqHaVke9HCLWz/6uSJHUAGaD933E83xMUWWK4Lpiz\nXBrDQ6y2Z5C9RawGuJLO6a4QSt1kTdFGJEPUfS66Kgh5GxTScdJVP12VMnfKOUYzGabLATJ6KwfD\nAazrh5mYO02LPMO2gAKuTElPIqUW6M7WkYVOmysREDL1gIccQToXF8lUJYq+GKmeIUqaQ8Aaw5KL\njIba0BpxXKOOXzbwlDLn9tGb/4VLOFrCVE/hKhoiJJOuttFwPVy8BytQGin82iJtdoWcMPG6MnUE\nOZFH1nL0yiY7Ek1DqNioc8xZoO4qTL2GOa82ZKTs8/hyrxSMr0hdVJUeMmqBuh5F1QyEEOStEF5n\nhZJ5ntCsraGJCBsS5Yv6DvsEFUfmgNtBqiqRnVl+nZ98E3Xbw2zLMEFvBENp3p/0liTxdptoMMzK\n/ARh9xRybRwA124whcUZN45RT1zwTpzLZDt3bMpTx/HaqPrZI3mF3kaeOy8p8SChNhRsu4WAvwXp\nArrwyzgqV/BhXm2fNyqr1AoKxYb37Pmzilx1C8f04hoy7muElSKWRqxQIag2tRXfNGryVz3PNKo4\nikLedyWHTSJSrYAyiiRffq2RhIOhl5n0DeFcZIK/SiVJXObcJcYA0Fqbp9/K0OXzXXDcsXJ4lVWU\n+pkrzOU7gyNscrUyliHjLXtZrr/1su0vHb167XaSnEFSZfxRDVFfi8P6S19wHiLBS1Pxvxm47Kcs\nhHgTytn+90EhVcUEnGDTYx7xGdReaqqaZ04vA4NE23z0v7Afuraj+SUsyeBgoBdXyOzPtLOxI8eD\nK0/hCIV9YhMt+eZuQrAewpUEfn+OkiNRUns4rJzmVqXIV7pMaqqOz62w6HYjrDryi7NId6kgm2wa\nLXD0mr/gPUmHvacsUiWdNtNgozgJBowzzO2NUYohjc5SK8eLX8Hyt2HLNorjoNSO0pFOQAdUlRrH\nB0b4qadOMhcPUaqfQPKtI1VeJFbPkRpYyw1H9vK4/y5ct4FfbSfacOg0S2TkOrKrM1g9ihgsUJgI\nUvY1UxSCNWhE6uiOQJIFZrGED5maqRFLL2FXl4kzSFvOJh/QCFgatulB1euIKQUj76DHmjZWw2nq\nFc0Z29jSaOWFoGA23FwgtjQafM3dQlS2iBtVJspRzug6O7MjPKkfI6t7iHhmKTU0Ki6UlCjz6SSV\nkJ8esxmmbuldRhoVHC02nYGO9UWKh8v0YlAwfPinwthKGdWxseQARjFPPZLgTLSNsD9NaeCj/K7f\n4mvdMp9t/Q0GZz+B0tp0ihUbvjB4J66kMGgf4hPz97AjdpInlHdwq5RiR+E4n2+7jxlPHLOuMduI\nkAq2EhJ5XpCu58lQmp9LH0a3BNtKo7zlpW/z7cQNKJLgaG4dt/MMHmWJMbmDqpZjqmLQ7zcJt04w\nkn8/o2KMvgeGWP1Gng1E+EDtBqKEiSX9VO0Sh+woQ4uL6B0dTedJlXEKDZ7+l1HSc2UkCdZd20pq\n9yxFLYQ3VMEw4kTb/ex+tsF2rxfPmQnMpWY9XE5RqNU9uG3nIk9ZGuN5ihOn+FZ7HDDozzSdp5GR\nESzLontugn0tPXz4rru5cd1aPvrRj7KwsMAhxcOvnpzBdAW/1dfGh/qvXHB6FT8UeFySpAjw58Bh\nmuvtP/z7Dum7h1eWGEyoZFcEOfcwi404jtrJjQGTcEuUXSdbiHgOUoj42bTlV6iVj2GX9tLRHuR4\noY+gdxICLSz1hMjNSWjlLBm1xkL3IL++/n78+mdRLB+Ok2XNcgprpkzBDFFQ/XgMD4nWODdqUzyv\nqEyE21gRDicKMUzNRWg6ruVgq1sRjQDIdQLd7ejyGRLuAoaoXmjHuDZKpYhdCxC0WmjoJu0JF9mo\nv9LsLGmE6zhMza3SotrofgOrXCZotxEJCgLdgtGawOMaKIVpANRakeRqHdnuIaRfSDYAUKXBlLTI\ndNDEMF4x/LNuAFNpZQ6HhKrRqvpxRJN6/FBNwWe9MoUaEq5iMYFz3ljPnvO4qJ4ICwUF13TxuW+M\nLrNj2sRsD7/oF2hnqcdlJ4RXU5BUg4PhYVakIOmzYvHCsajox6n7osjy5R04uVLBo3iIyk1nyfL0\nExA67a/BiFZ3HE5aAiXe9aZFdqxyGp0GMtMXHvdIOFqIysbbkZSmrfSyoS1JIAQNq4xITyFJ1sXR\nrcuO9/KiqlcyxgOZSTy2yRql9prNzx1qmC6KlED1xC/dgOZWg+rW8bs5tmg+hPTaJviF05IuevGL\nTp9FOmMiC52a58LYRi1nsagmEd7LCVF953AsF4oFQkoRSRTpyL6xwX/XcZB0i2OtAzQkl0Rw7yUj\nbi9H6gR4ndv4fu2jXd2OfRNRTNWoyQI3oCO5gthqmfypUwDkUw30iIrPL9O/8Cx0fRDZAw1JJyPF\nXr57FJ0QO8tHOeau4RHrBu5sb1JnH1CW+Mehz/O7YYc5U0ITMYY2/DQ886dsKE+wP7KFCDlWaKO2\nchjZEoiBHmCcaxfrrGQPkC80F6JKw2J6aYg1vSewLI24yOA36xxXAjxQaNCwyhS6vERzEn3Zefpm\n5/B61iGES9iyOda3hkDDIiBFqDReIhePYc49AYC0bQOdU4folWYACKoxTNFGrUMhG5LxWiBaXMJ9\nJSLRMqcHmjceX6NBXQh8cjPNwCw38NrLqCmJzqdqVHsmqfnaGFxY5hvbOmF8gRPH7yBZO4SomShl\nF1W1qFPFSwhX1UiKXmQkjnbKNOwUPldirWnyQs5Lt3sASYLlWpCKBDdXt/Ft/yRZWSOpT1K0LfKu\nxnSwl4llB8ISA7kyQhH4OmaJjJfIWSHafct42utIUlMXYqwyjLemcag9RGsth1A1lHqTDXGadryb\nJ6lrOZJAdL3KHx77DV5cGyUZyVNKRdlSWuCvB7YSETlsu8zuW3+Tx+b/jK9GZFQMtpSa36fFQAIz\nGeQjwf+BkGSkmoWoOjwb3UbvycfoDzUX/MBKDnfEIKzWOVUYRAgIe5b5u0GVH5Mkvl0SdGgGibY8\nalHnrwY+x9zxZbq8w/zW4gcZSQywkM0xXR1nPrULN/Aenn3kOHd8qI3GdAE1amCnaqQzzXqFmeMZ\nbvj1a1j5oxRq67Uk+mrIWpKbf3KYL/3Vi1RHtpA8+jz5Q4ea82iY1GtB3PMiT5lT+5m8+cPskv+Y\nwbKfbl1laamZu79v3z66ZscRrb0s9Q0Ti8XweDzsWUrxV2WVEb+HHo/BX0wvsznovUos8SMAIcQf\nnX34qCRJjwOeH0YBd9njZfDu68h++QTlRpGy6qGzZT33r7uNel3wzOQUDTFPCo1dc2PgCmK2n4mZ\nBVq678LMFVmUZ1laLuIOhNFlP2NulC63ymrqAJPpPhDdyCJIcvKLGI0GrredZf9WVhwDR/cheetY\n+W+iBcOcDLXgmnmCjTJ9lRVmrXVMtHXT1hInoZWJBULYxOiSLJI0U97OaTi5joNVmmJAWkPvtiHG\nXzqJmWsgKRcXxAsh6LP7CSaGUZJxXjjwFdotC3l2BW9XlPajVSrVKjMvEwOEMEpeApIfzXux8a8I\nBcvQKVY1VM8r+72jRZWKR0YyvHTLBsPhdmoClgpLhJ08Sbv2ctua5YBrUstdLMJaVVVyhomjGnQ7\nFv2BN8b4zNo2lm1y0NRQ3VfGElEMeiSJmUgrNS2G8J11GM0yRdVmB2Oo6jlx1XO4MNmrmikSFBrG\nWfbZE47MGdXHJ17DWcjW69QKq8SsBbQ3Ka4j1epERZnuV7HtNawKVilF++zHXtOVqcg62UAbpqwj\nv8lse+dnDmbqPmKNAH7HuuJ1udowg4ZM8BJU5edDEhJBsYy3kUd5E9g5/I6PgtyJZV7oxFmVKD5P\nAH+w8w15HVeyyVWnQA5RcCYxjTxvJBOiIVwMU6CKWXyeMDecPn5FcsJAuBfWbH/DxnA5XHWe3kQU\n03WksIYIqgTLDmN/8k+0uS5aTw9F00O0zYeUHSdRXyGIgzAEOT1K1g3QFhwnXepDLZuMNGb5c/cn\nAYkT8bX0anDU8xyqYhP21HihqNJeidC544GzztMZ9ke24JWqrCjt1Ob/CTku8GibKDNOyCtIzyYo\nVm4CIBM5w1eUKX6x5KNbg/v0OhnAcetMFg4jVIOAsRWXUdaklth4pooU6aEqN1ib13h0Y9PTD8sD\nlJ3DVDiJm5qiEWsldNvnaWsLseH5pqhrQIuScwdYCYLjVcECOyxAyNjiN6B0AgCvXaZa99BJ0+my\nKgZy5QzaMQWt7PDFm9rxOw6RxiKu3MNKrAuyyxiZ7fi9h6ngJwpsn6pwrN9HEIP3nPgy493Xc3N6\nkd3ts0TrMQwxg2yF6JK/iitgphJlQ3WAOH5020tZEaiSRUSZZM7sZdJeQ0o0o39rUjlW12koikWb\nmiNnhdgcGCNqpMkFmnndE7MbyAbPMBfuJdFIk1UiOFkX1TUp5hME1ElcV6bWMLjGX+ff+gaJJ/IE\n5CrHssPck57kpYFruc59nvds+RjWP84SHZAwwnXSZQ/D1Wk01yITi9DoCNJTX2TW24nwashVh3pU\nR2qkUcpeIM+y1wOGgl/JUwmdImvqhEJphhQZ1xZ8fHyZr2zaSXssT9Ga5z2ZVfzv+gNG5E08/Rfz\n9NzSzYlHq5xST9PmlNCcDGOTfTgfe4xYSqC095F0BEGPwsid3Rx8YprFqRSYFUKhJBnlGLqeoHM4\nQktvkBl7GxvFfiqf/wKyYTCTzxEKdaIYAfAL7HSGhdZnyfmCjDLA+0qzdIXamZicJJ/Ps2fPHnYO\nDXEy4OWRxQwf6Ezg7e7lo0aMFl3j05sHCasKYwdq/PHkEnfHQ1droX5IIUnSdmBOCLF89vnPAO8C\nZiRJ+gMhRPbfdYDfJVzTZGr6KHa7xqwZIF9LkFkIMxyGlC3RyDSIeGSkhI/lYhZfoYhXzyEbGu08\nSiw0T0R1GRnZQsbVcZQWGqdnKZZCHE114tcEwVkbt1QmRJxisJVg305+oT2IP1lhoTxNrZKnkRK4\ngTUM9e4k1p7FzmUIaCrFusM6TefGoV5E9gViSo0Dlp+KvpaGct4mhNTcUS/pNzAjScQdFTOxkQQN\nEt5L5+VIqSq6LwQ1iQ3tt1JfnqLmevA+MY/t8YAaZM1gs4bCrjWoqzm0liiR/sGLzLNCtYoz2UbZ\ndOE8XdCSWgTTJlLMItdjLCgCGzB8FVrUBg/0Dp4bPqnlcZZyBVT9YrauWqVBpRKiErqWgUgbHeE3\nRojzTOEYi7k804lWhNbMuEibBk5ZAQka1Qoed464PY4ASq5O2pY5Zraxo+/yDlxer5Hy+1F9zRS5\nymIBqyxw/ZeulVJsgVvXeGu/hqFd3vj/XpGaPYxkFvFUL2R7CwLCJzHQO4wi65dUhm04EkEzieFN\nXl459gqqslcUnX1Vg8N5g0I0yrTn8rU0AsiVihCEcOjyDHp2rUYu1UVYE6/WeH1DUPU41IVN4FUb\nFxW/SnfUIND2ipD0Bamfr+rntVbJ84+H2zdidnVSSc8TEfZrXPG9wc7XyU1nqAUjSKpOx413n127\nz6uglC6cQWx4+BI9vTm46jy9TqRMi49Mr/BT7TG2BC/8gRVSNaSQhghoJFerLJUCtAHhd76DysEY\nyZgGy8eRgF5NYs6rkDob8m2PLxMrq6wpNCMYz7kbAFgNhNlIhWnZ4l6nA1ma4FRDYV1KoD9doyJH\nePfCGEe8dYpRgVpx0FYmKb/NJZrZBOLfsJICz+EAdm8MsPBOneJtKXA7r8VYu4fB6jdQWv38uDHB\nci1GtWsza6fKHIz6aSvkuXFMwK39LMo5JuunqHruJxuOIuQ+cE8Szi/QtmyzequFYntZPPMO2hpN\nMiy/GmbMvpNqt06DEgFA+BXMUhu2FGIluhPFcZDJUbN8+MJNMVTLHMCszuM7BuWwh6e3buU9+3eR\nLOXwNa7leEuUjVkIyUlSQT8NNUYXYEZkFMvEoxgMLjxLpDTJXc8vsO9DOp5KLw1UGiJBwj/BghNm\npR7kxuKNpLU8urtMXbFwAEMZwy54cawKpbMUoEMr86zeI4gDW+QVEkqWe5P78Kpp9nUZ3LIMUszg\nSP8KP+t5kT3mVsZXemgdKbJcqLLqb6X1LGmUbtTolOHT/hoP2QqG7tKRK3MwuJmq5OP+41vxjcs0\nqjZPuR2s4wQT2kYs4aO7vMxkogMd6eV8dT3TwIwZjIpeAnqB6ukQBzxZFlvGCa9+hELvcQzZZqzi\nZ2dskRhAKcAX7vx9pNOHcHq+RqpxhJ+qz1FtfQsePcDTzJNbqtAoOvhamnaqsFfR7DLH9u4CoNP8\nIMmQj3WJKgnjrJDtI4fZDCi+JGY5RTC4FkmS2PrWXp76eIEBj4GvUsHYtInZuTnWrVuHz9eHm5yj\nfuYM5ZsOc0z+MEIo7DS+SVv+AU7UT/Hxj38cIQR33303qgm/OjrLfx1f4Im2IUwXPrWxj4TevMX9\nnz0t/NbYHAcKFa6PvDE7x1fxfcfHgbsAJEm6FfhT4IPANcDDNFn3fmjgyi5po8IJfYQWJYzu2Kza\nEl+criJsG82pEqOVgllFkRz6fAEmsv20eU9jmgeQBcyow9jpbgoiRyAi8BsWjt1AK45hWzJr7Rjr\nWyTkRgi7r4NGYJLYQByBzUA8gm2GmKmdIiSep7M4zZjaQbazn4IUJ50ZR0WQW1pFp8iGodt4VyVP\nqb4KXChW6wo4Igscby+qqlLpjlOKGtS0S+8V16oWyw2bgCzTaAnR39dJ48RefJLDnBTClH3cYTTX\n04YOL3haUXv6UM7JFvCKCeV4QfF20+E4nL8C++em6ZRMrmce7BSQAqtBbWUZRfWgbHrPy21bQzfQ\ngU3obJ3V+cGXwotfwCnOI7kv4NQHkEtvDJPnUH2RuFnFDYygJroRQrAyX6BQLyNrEtWKi1G28crN\naFtZlsgqOnPhIazy5cVA3XqdCBp+p/n+u5ZJn77KNcn6JdsvGg3GZZVoxyDeS0QL3wjE23rw+wLo\n0QsjH5IEqAaEzyMceJXlPjmV5akzqYuYEN9sFP2CVr9BsPXKa4aoW5S9CrJ+ebPadlysfIaE4vJm\nvNP7snWyjUtQq7fATCRCMvbGUBUIIchVLbDAl9jA7d2RNzQmmCmWmEzMISxImDKtPWuueI0e+v7R\nMFx1nl4n/mUxwz8vpDlSrPLUdRd6vcV0DaUng/D1cn/1Sez4Rvzvejfy4DrMYxDSarD8EigG7bLE\neNDHua2ztfEVmDPZWJuionh5SQwgVIm61wMzBzBcjU0eB9OWcTLrSZYLiNPL4K5hvX2Mjx80eay7\ng1PLe5AEFK+T6DwRQWtEya/JE/+7JQ4mGygu/OyuKrIQ1Lb1MBYdoLX1KCMjMPbotSC5xMq3sPm5\n30feMMT48BoiIoGu+ViVZllvtRKtljjd04/paUU11xMoH8ZSFKTrVvEu3k2Xto15ngcVXM3EoZ1J\ndQz17I1dVmTquR5UXwaGU4TdtVh60ziXkjqurSH0XhxpHjNr8M0bb6Ent0TIqtPwedmynGZfTyv9\nkx4wNPKxKLLV3F0x2jqJz0yy0trKbNcddM/v5tvX3YWt7oZ0BytaB5pdIqovs5s1aLIfueHlq8ZB\nMJupFKsiSkgeY0GJYidtcoVmpK07v8KJQZNs3YvHkbg7/AhZfR090hI3E8Vh1AAAIABJREFUb/wy\nYvkdzHca3CQX6OupMfFSHxXLT3R9nsXn6igdLiDz8Rd/lt8TnyG3vY4hC2ZqKn0NwX3mYX639zfQ\nHZNNORuzUWR1fZTjaj+3sYdHPNu49dq/JyfFwVB4IBTgUdqQhUtissBSOIGjqox5BrimmOLpxFZW\nW29Cq5/CKmjY+Z18U2uwc8dHABidu5Y1198F+xagz6HgHkKTHJZP7mX4xntRNJn5U02H6HppikOG\nTESeolKrvPyd93QuQ2mA6P4nqXxxL2z/b9RSzYwqz+YRLJFDU5uij/1bEgTCBs7GdyIOfQHprruo\nLy3S29uL13ctleQZ5IkxXNlmt7aVtSJDOPI07UcfpLevl+WVZR588EFisRg/LgRPpYv8w3war6zy\ntmN7adu+Bs6aU+9MRvi9Mwt8Zjl71Xn64YVyXnTp3cDDQohHaabvHXk9HUuS9OfAAzRvwBPA+4UQ\n+ctf9fogyTqOr5MCFp2dOrVlB1Gp43NzhOw6qmeZFtVmBQ+O5JD3b8Ct7CMj++kTGZalOD41icfn\ngWqIkUKRJb2K7aj4GyGm3TNo0VF6ugZJC5uKliecaENIDghQFT+JlutZVo9z0PFysBzAdHIomQw+\nLHpw2RF2ITJCYfIMmcMmiqTjCoH16roO4bKukaOjrxNfSyv7RicpzK1cshxFCFhxBRU9SlqAVDjF\nqlnCjATx6TK65aLqOodbm5pEJeFSEC5xr07A10wqE+Ic9UTTyxmJeLje78V31vAXArROQYu9hMdu\nx3VaQPOBgPzxM9TsTnw94XOdYGezMD+Fr3bxeOs1qJdtDCcF1TxSIXhxo+8BcrWMr1Fj+dn9IB9E\nAtqEoN+vEmnz49RyTRHVc3NyXEJSiIzkw+d5jejQuXT/hsCwTDhbth7SY5QjcQ52XjpqVk26pBKC\no270Ara918T3EDGpC0HZFPCqX5Vju1jFOiHGX/PatORSVAVv29SO/Lq4yr97jER99PquTE9/ulqn\nZF9ZDypnOdQiXi4tV/z6sbZLEJUVhnwXfkdOLZcQr3KqLvcxXkyu/ypIIHwqVQlGKzWenX1jM6dd\nAaYnSYtPIuL1oK6LXdE5+35+N646T68Te3JNdp4jpSoLdZNOT3OXyDIdqsUGSfUp4Je4u/YM/bHH\nyb3jK7i1IkKs4rcysHwMWtbRU85TD0Qx9CJeq8IWuYKj1bjRPclRdT0OCoFgUwC36L7ESK2bWOcp\njLSXmNwUnfvS2kVyzq38xZmP8MTQAXqy19Pz/LNkOkLMB3xslBfRyu2Ijiqxsks8tYKj+3jsZpXr\nJ7voHP0Gy/0PkFlew35tH9emayieG5Akg9F1d1LwZBCyzLGtG7kFWAqf4u1ikM5sluODWxnIe9Ht\nQWwOc6Y9TKx/mRMHtnKzHGBeksF1KVEn6ga4I71AXyjK45KLaXrxl3qIDDxDSr6FdnkeWy8hOwLJ\niWLVS0QCXrIpQTrg5Ss33s1DmZN4MzmE3+Sh0CfYz+9wumOA9ZUFXH87duNs4alaoGNxhSPXdnC6\nez09899GN5vRvDuOphgzhtl57L8wo8dZvSOE272eQ9oUjmMjB1uBOXLKWmKcYL7jepAkir4Em+xJ\nBm5dZXDO4sV8NweVKkf8FoeDP8Vpfo+oyPBHYZukFWEo5mDrDv0rBdAg5w3gU7LEojX+8fj7OJzd\nyoNs5a/Lf8QW1aXbn2F1Ishnovfy1eRt7Ewd4r7+Tdy/vpXNFVhMd7LOPQEKzAe7oN68Ia6LBaBY\nZqgyze3FZ/jH2Qdx+gPssW5hg/JVPjX0X2hoARrebehn0myIGowulfjcofcyoqQoFlu5Pe8glwdZ\nAgztrEbI1PNIO+7DF9JZmWoy6t0cV9idt/AvN1MwNP/9OPXnWFx8FMf/8yjhbpTxKioZLDFPPRQg\n+M4NiHkLVnQYBkWVub7TT0i5C9FxO8ecZhF0T08PjrODfOsjeA+UGC3fwSlJ4vc7PLgLVerBMd69\n/SfwbIgjnxUZlCWJhzf0crzcgkiv8tjTaVZXV4mc1YjyqwrvbInwpdU8/++aTvzKVS6cH0IokiSp\nQggbeAvwi+ede71r2deB3xZC2JIk/Rnw28CHX2efl4XtSpysvQXLO43iW2G9bxHvisK7fNN47BTf\n9klIssTmYA+NcgbFPIYRCeGR+5iwXQquzKAr895r7mZ+fB67USfRkAklHHSpjZVUmhUpwmc1iVtU\nhZbOPmIdbweg0VhFVYPYss7cuvfhM10CkkF6ZZGOxhxJyebaiE1IknAbgtPqEEVfD44WQIS7m5GC\n8yBsC+PMVzh18FvAt/AAflki4b+0kb9FAq+tIEsSY16NBV0nFWhD8bTQKM0Q1EDraG6AxYBWWeYd\nrVG078Y4qmTBrkOoE7l1PXibjkPQcwbt1Gl48dmXm5778ijRjovSeltjOxHGW1ArE6g+gfwaQq7f\nLVzbZunkLIZn6OVjTqFE0CNhGBpE4hhDQ2itrc329Tr9Y2Poqk4z97F5zcvjPe9/LexF6u5DCTZ3\n4ucWSyw2zFd4Kl+FAoKI12ZENtDfpLTmF+0GVdu52BhXQER19KAHz8vO74WtFCFIGjL39sSRf0DT\nrtcHLh8NPAchBDN1E/uKOYTfO9p0jYB64RrXM/S96JNdGVXTZni1jPsmTEeVJeqWw0K+xhPHLq1R\ndj52DMRpCb0583w1rjpPrwM1x+VgocKt0QDP5MrszZf5ybbmrnoxXaPPOMDeQBLVsenSbiKuPUx2\n14f40mlwnAB65jpQjsOat9Fy6Dm48T6GE3kC9WfYmF+hmuhiML3EZ+t34rfLBCKtZICMOMgOx4+q\nWgSzGjcpMxwPhPEspHhq4838f2f+mm31T/Ofk/18bHaKr73rBsysxXg4zXQhQHuizuSgD0fz0ZCq\nfOru6zkxu43/+j//hpFMgQNSnE0zA0iSSovSRb26wkTfDp65IcmNL32dTPsIrumyfsvjzKsWWzK/\nzGJyIwN5iJWWCZerzMUimEsVvljo4q2ShCJpOK5JRjToEyF6At9GKOtw9FuxqjE6bYPFTZ9glYfY\nzvP4/HncdCu6P03NUgmYNm6lzmIsTEtsifvNRwikAxSumaF3os7TPTfxRNetbF5aJSagnrcRroSr\nZwmWmjVKKxEbIv0MzZ3GY3q459Qotu5HaArCtel6qcTErbCu3sL43Fdx+wKQhJzUiyHtI6FkyOcc\n4v4Qf+/9CLoH6prELalp5tSD/K3Xw6zezT3icXZzJx/a5uO/HGnFbTPQCy7D9hxosFxtobNrAcvr\n5YXR6wCIUGJPajNv7/8mAE8E1vC8+T7qWoCfXv0Kh1Y6+HKnjxlTQpmoIkYcwsEsFSmKfbZI+l9X\nms7O3bkD/JLyGP8yfRf1Xj8HrBsob2rDOquToFoO7lCAnw37+L+XSpxyB2mvNBet4nNLdDfaWTBV\nXrxjHUMv1vCuNMkcAlGDUqaOT84SHL6WhO8M9moZvz+G7Okg2FolN2NjWsuo8TUsdHSRihzFbpFZ\n7biFO1MncF0Z+5RA3ORip2uEVivMNByCcobVxTS+oJe87uGx1Y3QeS/3sYsnc29jqNXg/QMj7F/y\nUu48SuX5W/BuvDB/X5IkNgV9VM8KGqdSKYbPy4H+idYYn1nKsitd5Mdb35i6hav4vuIzwNNSk42l\nBjwLIEnSEPC6tj2FELvOe7qf70MKoKzKlDp8zNBCrGjgLboM+pYJ1kscCCSRlCIi2cPd+Syuu8Ie\nXxwsASJD2tiI7toEDRVJluge7m7OY74I2UkkaZV3RJI86Zjgi7HX7eCu4BbOVC1cBAt1P4YsEKKC\n0Hz0+1VujgZpdMcpVNfi0RVCHg0yE8iOxdoOFWIDIF860UgIwTHzegy3jleXAYnWtg6M12L2Ki6B\n2yzC3yHJkFz3ct/ObJFccQWkV1IDPZoXTY5dui/XhaUjTUdJuK/81XLgb4G+nRc013p6QFEuqm9R\nwmHUxGvpJwGsvcy57x4y0Pnd6nm2fWdMYv5XPQ8nvYxcKpXrLGYaJkfKVfKaesWi/HO4ZO3oZfya\noOWhW1XYGrzQyai5gpcqNaQrOMYhVfmBdZy+G0iSRJ/3zakr+/eAT1fZ3HUx0cobBdN2ifr1K9er\nAX7j++fSXHWeXgcOFiqYQvALXUmOl2s8myu97DxNz+TYFPwMv534S7TVCv7N9zJzaIU15S/R7d3O\nVKHO5Kn9DPemcCPDeA7twrj2Lsykj0Z+hv7l06R7eiANz9nrSIgK5YgHuVpFEmWGwxEcR6HYDmui\nCl+bTbJlehypLnEg2ctNqQk+/Y3fIC0HeeL62/ngxDi7Kiqp9mt4iOd59P3b6ToeYDy0QqK6mcHA\nRsoeL8HMCcJmAqfRQA28A0/+FJrwUCrfzJAzTV1oOFhUAwvYQsIzu4XOnn1kpncgO0U2nfgkpiqT\nbe1g6YlOfKH9fD2wFcdt4I8PkJFLDLsdFNhASDqE5MthV+P4vDWcQJmSFKZFLBMMZCitbEY1MtRL\nbYQWxmgrVBgNePnE3t+nRanACDAHluvlAyctvnGTy+c3beHHjxRoL08gqgayr8431pfw4GKHFjB6\ndtD20r+yeXYNkjSO1ywTuFGjXFJpO5FnQ05Hq60g0BgPNn8eo3aQzZKC5nuBxEyEv448gYPMbmkQ\n9ZplRvaoPGgf4W+kdlxnhR3ybm4oPMcfR/6Ex4ej/IpH0DFRpTt4Em+tzvjsGq6//kU+PfoQMi4P\nmbv5nH4nU5U1VN3nWLbhqGzRGIrQU13gbbl9jIi3szgZ40RAQc2bLDe6eK//n3lY/k3kdB03ZjBZ\na6Z8bl53Hw+P5dnWEWT/aAF7Y5RRd5CHUsf4X61b8WUaFNv96Lu+Srt9DVosRY/Sw+zsLMrpKpYQ\nVPMG4ZYcp4x17CwdBCGIdwZYGi/Qoo1zpBghEZ7mo3fX+XmzynbPl0jllshORinkTjM+IjN2606k\nRh2tUMf26Xzt68+jaQ+SEQ7KIwcIFzRkj0ou5qOwXGRVqXAo0MLf7D+Jo6gMtL2N+9jF5oVF3v/Q\nA3g1D/H4LeTdw9S/nib/xXECN3eitVxYa+jz+QgEAqRSqQuO3xjx02FoPLqSu+o8/RBCCPHHkiR9\nkyYX7S7xyva0TLP26Y3CB4DPvoH9XRKScBkI5Yhl5pFlyHYHUOwETw8MUXYT2CsT3CB8qDTwBIe4\nYWQDzy+PYRXztBld+F2VhM+CwgLIKsgqUm4KNA+svZ824N21Bb6UKmAYbbxQkzk/9OA/u8uf0FR2\nnE1lNVSFltB55nN88DubiySxedM13/nkPa/Neql4wyQKs5A5eeGJ0hyol9hVdiwoLYHuB0UDqem8\n4Y1BtPei5rJhYAwMfOdj/RGAJEvo3tc29zo0iWXXwXk5EfLK+G4DDRFFZcBrEH4VY2IYaHuNCOVV\nXIWuygwmf/BS7a86T68De/JlFAluigS4ORpkb66MEAJJkti9+1Nsamln1YjTNzHGSVHn6GmLh+I+\n7m4Z5zO125gop3GEROa5JaqSYFNumSPJTm7xDbGj/z/yhzP/QAQ/J0Uf9yddHg/rKKVJJAHJlkWK\nxSTRaDPVqdCqUZ/XuGP8EPMbLL6l30Ls8Tnm17RyIriBeqPI6bYAT3du4R73EdYFylRQKGtV/vOC\nQbcl8cyW60iujuNKabTIJhSpm86ZT3JyzTWoLgzVjlJWDAquTTV+jNJLAcqnkwy3HiObcbClIhIC\nMxhg6F3T7H6mnevnD7FSOIoGePVW0nIz7etJ3wC/5u5GjSzhLveR7vwyS24XKJB0UvgDOep2EMVb\nIXGsQtvMPla0psE7VY4we6uKK0N4l4Y0dg3uHRF+fs9e/sftt/G1DdfzpzzDEbGFIW8Jy3MrplZC\nFyrZ7mvQT8C79hQxVZ2qL8Ha3gPsqt5M5+g0m8/M8svveIlM+u00SkPo7S/xnDtLMTDEP7VWedie\nQW8o/KHzH7hp3efx1QP8m3MzvyZ/mneVyvx97Tirtsn2yCzXpcd4rmUdd5eHuDOzH1TYVjnNc/J1\ndM7Ps2fhRjq8RZ5Y91YYtZmK9fNL8j/hXX4KOx5GeDTedfJxviFdyzWBKY7NDKAAblAj19LBvTzK\nyd33sd8MkLglzrzPw3q/h7du3sh/fKzAr/WnuevUI+w4NMuRwFo+3fEQuIL6qSJqi5d/GNjJ+w45\nHJppYes7tzI7O0teWaZezeHUJHrFNMd97+Te/DdxMpMoLQWsyAQxdT/PzKxl07YMG/Ie/k1Lcd/8\nh/H864c4tqOfryd1GsoCA46f1cmDeML/Ac/UJ8m1eDHWBzhV9DE2+STHutZwYON6RhQd76kYU203\nkApGGZ4f58ETe/k/1n2ArBHkg/lFOv1No6mj/SdJpXZRveUQ0h6NyuFVkh/YiDFwoTGWTCYvcp5k\nSeLHWqI8PL9KxrSJX6Gw9yp+8CCE2H+JY6e/k2slSfoGcCmxr98VQnzpbJvfBWzg05fp5xc5mzLY\n09PzWs2uCB2XnfYcTylN8W/F8IDRhhPsprpscotbIYQHuq4jFC0TaVtHa8RDvnSaBe9OlrJpBsun\nYHbfhR075sspXD5fF/d0tLE7+0qFxfqAl26P/nJ90A8ckiOQOK9+uDAHcy9AebXpIF0KnjD03Qza\nd5Y6dRUXwq8q3BJ7Y2q5ruIq/nfAVevhdWBvrsQ1QR8BVeHmSIAvr+aZrDXo0WTe3vhf/MLGP0aq\n2mw6fYZ6XweRrn52Z7bwY5E/457OCT4/FeH4civlo9/C7W3hmvwiB1t6mPbdTUqJcmPmAHu9m9Ed\nlVvW9vA5w8KXHWW9FMRnrGDV/Li2TmbsbWzduI99g3dwx6kXWZ24jvC4iVE2Wbg5hCNpPNIS50jP\nCG2FPDPuWq4Jv8jz6gAb1Ttor/QQd0xyPgkR8tEth7Hl7ZRci2B5iae3/Dib5yG2FGawZYrDK13M\nFhdZfilBv3Gc0pHbacs7nBxKMFh/G8u3Fmnz7+PJzVmGW3vYfrQINqTzJwkYa7FwkCrX8JXGw0Qi\nL2DGZGqdx0lnfh0S0FFYxR8oIexFJBni42nqbpD0Xe0Ez+QYzbfQLqmowQreiQ4KlTSnJnJ4qnv4\nzcQGPrK5hZ/Z+WcAvEV7hvtrFU5yBuF08Jcdf8+W6yTe8fwKpqJS3tp0yEb9w8Q7vSizz1FSXIJm\nnKITRHM1TgRVpkNekmad1cIGflv+KXrlEpGkw+pqFzc3nsfxws8UK/xreS8HpAI3yvCTkY9ykP/O\nI9Z7+GX2k66p/I78CO+1fo9PnXwPPlHjJmeS4xWbUSVBNhdCajep9D4AQLg4Si3Vyj5aGVYncT0K\nkulibY7yohjmXgnqoWmk9Hp+x+8w1t3Cu9tjeHWVoaSfLan/xm3FF5mmh4c3vJcJTzuJukmjL0gA\nhRcHQxQ9DXac6WPfJ1PEI1EOaBOEcqfpsCQMqcGxeBvFvJ9HPvU5VosN8MDXuAalbjI/v45tWZnH\nw2U+G30Gz/t/jlqlglqr8IBnJ6Gswmn/DGXdT2/3g3g0hfhKBw3J5gV1AhbOsMXvYe+ajbzY78Pf\nqPA7o0XeuWOIx5/8PHUpiz60kdpZDSiAePx2YrFbWMz/M9v+r/up/kuZ7GdP0fafrkNSXzEGk8kk\nR44ceXkz4xwebI3wt3OrPJ7K87Odl0vRuYofNQgh7rrceUmSfg64H3iLeHXRxYX9PEyT3Y/rrrvu\ne8/0VzTa4538jDTDs2o7kykvVGZwzhzndqdMWDhUA4N0X/dKbldQ30gwtJFuwArH0cx2QECjBLYJ\nK8eh75YLXiaqqfR7DQTQ7dFfZqD8gcb56VmBVoj2N6NIr0G1fRVXcRVX8f3ED8Fd9AcTZdvhxVKV\nX+tpFnPeEm3u2uzOljBPPcOXtv4Ok4EetMMZbtAq3PbTPw/Ayb2LnH5mkbXSJ9lkDLF/uYdoXCDp\nBurKCq3Jk8xE1/KW/CEea7mLT/a8m3+87jqe2vcEsBbD3s0Wr8B1FYKhVQoTt1M+vZ17Nv4Bg7ML\nOC0dpFe62brv6ywnknRsGSVpr/L8wAYM2+WOU4f4+sg9bJAP0d5xmr2euwnMWOxLf4lIeYHBlSz+\nxgpjG12C5TPUNY2Dw+vobKgYM9vZ2gsvCYfpGR+jXRupSEHk1R0EgYcKOgdvfA9PJjQm+RXc5CmW\nlI9iz/SgZUycWpHy9PO8lNwOdjdzuEjjd4LssvzP25i5aQRf0MRbcgh05JE6m8QO6ppfJNjRznv4\nNb4a2Mx00UPj82vp2baBOd8cU9456tU9ANy3nGHArXHAt5fn+vr+//buOzyO6l74+Pc3s12rsuqW\nZFuyZbnijgs4BuwABkIJScBwCSRAeiEJqTf3uQlpN/clJC/JJcALF0ICgdBMDcHEBGywwb1LltUs\nyeptV9L2nfP+sQvYxhCDFcuyzud55vHu7M74d36rMztn58w5vOxawnU5d7E0tp/XGUdjuqL+TJP6\nyKX4M73cnX8HW+LTSFiZ5JTOJNy0h3N2mKzzFlKBSW8klwFfE0FHHzMPlLBp4nga6sbwqc4XsNli\nVATqme1up9njoiQY5oK+Kl52FlIfiVDm7GT54D5ezJrJQZuPrOAA0/Kb+Xrr09i3DFA3pYBE8Vg6\nI15MrxDtVYyLNtHjr0VCW1nS5SNqFJAmCQZDXmRxJqorhvLa2a9OI6FsTM6pxt+dy/yGTVw+/2uQ\nGhXoq+5VnFO/jWZfBX/qvZAFzTU0Tcily+WAUgcSU2AK9QU2aktcXFUzwBdqp/GYuYG+oiK84XZ8\n9CPpg9ytribSH+ITFy5n8l8v52+eT1JtuKivS96vtTQEISyCOQEKWpoJt3TyWl43l3iuZlb+lQAo\nxjGYaGZP33pagrW4nRlMLpjMvupd3Dp9Eq/t2kZPbzsfjy3BN7+AJdOvgADI/OnEHthAZP9+nJMm\nISJMnfpLNm68mMoDNzPj4nvpvb+Gwc1teBcVvV0/8/LyiEajBAIBMjOTV6WamppY++xzFJTO5tGG\nDq4rziUej1NfX09JSQlut/7VerQSkRXAd4GzlFLBE/SfQvF8TMPG2bkVFA36cST6cfbX4HDbiIYg\n4XjvewnspgHu1OupwRDILT/qe2dnvP88NSc1mxNK5g13FJqmaW87Sa/bn8TiUeg9wCsdHSQULPUl\n+2KWuh2UuR38cP9BbjEm0m7LZmWr4ra//p4Lxr1zUjbtzCLGf/1bhMZM4eySeqw0oTMzh/y5i0DB\nLHMPFgavZs3hpxO/RIsjm6t21vEH9wRKYvV4aGemr5tYzIEIZKzrZ2r9/UT7PEwv3saMoheYYb1G\ndp+f7lkZeGxhLq1fQ+ZggH/bXUV2OEKTTKSneywlJXuJ2nup795I60AtoIh4MsmK2DDMbHJ7a+n2\nOrnimXspi6/CVDYyuxbhxUt3Xj5Pn381vz3vYoIOB50ZJlctT+e2qS7i9n7ObVUknNMIZPyc9D4D\nV1o+oSlT8Y4dz8G4nWK7hSvnLsSMYEU8JKJLqXLFGN/SiD+ah80eoWBsLVgG4egcvK67aTJdbC0c\nR9SykZcepGbPJNpTt7ee5m9natEiVsXTWNieTUP/XioCD6PE4JGii1HbfUycuJFSy8v3At38d2kd\nt/nKCUT/TFbiv7hILeGAbTt+j52Pv+6gTTlYGg9TpMIYjuTYqtOdYTYGnIiySJtWjWUpcl0B1s3L\nYuc8H3s9ZdzYZzFo7+fuTidP7D2L67eVYRkmf/BeTlpODKXg2TGX8ZPFN+D1hHhq9kdomj0RwysY\nwTi/uO02Fg88SE79TIoGi2nPtJM7Lpc28vnc/ieI+jwsbNxKDDvKNYXZObt5wvEjxjXcTuNd53L2\nMxuY/OuX+a7rAs5e/P/4gfvLxMRkTdF0rnD08fiOb7A7r5tvPdPHnEELw7KY2B7i4XIvr8wvZGFF\nGZbNwcHe07EsYVn/eqLiYGXkKab3vYaDOK0xizlzn2NZfpAs0jjXeB2j8FnW5PwdX81mnPEY8c4O\nHjP+xK/GPMBjri28EIiyevLv2DXvETpvKOXly/qIqmYKrEyeWrWKnsFWHPFcgk4bfU/WkNOfT1O8\nmtW7XkOJ0PvMszTv6+WVh6pY+6cunP6bGBiooi76c8xSG/2vNqMS71wEyMvLA6CjI3nTeSKR4Mkn\nn6Svs4fxrQ1siUZZs6eSe++9l4ceeog77riDQCBwAg4g2knqf0jO1/mSiGwXkbtOyP9qGFA8F5xe\nCsp8RDOm4J0whZyi5PeKadO/b2qapp1sdOPpWCkFb9wJt5bD7TP569oH8cUHWPjS1+C13yC1L3NX\nQYxPDGzj3t3/ScnaOlZGQpx2cC/eeXMBiEQ62brtGta/uZz1k7rYP8PNyulNXDzhS/QNmATNIGfP\nuIiKYAMf6d3MLdENfCT0eyS0F6ca4KPRV7nKF8NlJnA6Q0SbvYzdvJPQEhuOtEHiRQp7g8XkpzrY\nN1bwrwgxGE/nde8CFu3ZiBmopTSRx421A9TVzcE041wW/h3V/W9ioFheMJXtZy6kPz3Z3zy3u4pN\nyxYScbrwV+9nsvRgsznIjTdiivD5F3fyrRf8FPgTONNj5IV7cKtBZnaspbz9Za7r/iNGKEg0PkBO\nWx0XbXgeb3gCYsSZ4XaQs1Mxb+0vGdv8Mv3p46grLsEpLgYGkoNuhIs3EguWsz3vCVpslawc6+PJ\n0u20+8JUBywcPf+HBXvXsqyykYzuKFta95DX+jgA13ZfwHW15zFF7WFXaQ6eq6IUFe/j8tw+Fm4v\npFN9is3OJnbN/hkve1pwKztZzkXUFmfhC4VY0biJ0/Y/wmceDaIsE0fPPB7J62KgrYSSgU5KKgZJ\n70rwE28WryonfxmYxp1jVzIh3sd/7LqcYn8eWw9MJXcwwRmNXdw35ZO86J7Bf8SvZWs4nfNztnPf\nBTfS50ln+fZ1nLE9OcpepTmRb92juLj3AAZCVUsRv24qR5TFnK6PbFpQAAAVKElEQVT9fKPjz+S2\ntjEp2Mim0DzyvV1E0yweNK5l3EA91268B6MjxGerha9vSWdiSyOlmbms3/QNflVeyBLVRe/zq8hF\n8b0eO5bdzuS4jUm9nfwkJ86GpoNkV++kPK+EQCCfnIJGmnIL8GzzU/PtB2gKlTNYZLGWsykvPo+5\nS8fSkWXj+z0NrPeezsKWCCti7VxUXMW3zhrHF1deT8OE54lZBttbl/JHp8WjDY8zQIjVi2sZH3Hh\nthzE4mG8k+280jlItNiLY2EeOZ9eiDl5OlVl46j9y19Y9fP72b+xlbQ//4KMb/+czFsKGHhiNfW+\nbxMMNRLa9c49Tvn5yRH3WlpaANi6dSu9vb2cHZnGzUWTMBMJfryrhkAgwLnnnkskEmHVqlXvGiJX\nGx2UUuVKqbFKqdmp5YsnOobMPA8VpxeSPnMJAL4xXsZNH5oJWTVN07Sho3/W+if8sTiZKgLP3gS7\nHoNJ59E4+XKe7Z/MNcEd2Fq2wN5VAMwC7jCd/JivMBAvRe76KUZaGt5zzmFgcD87dtxANNpD+cTv\n8sTue1AFPQx4g2T4Hybeo1iQPYC99WFu3/8Ca90e/hzzEYyHWGJ/nSuyw3hTPS9eql3OJLOVmffX\n0p5tsuDLD/DKkyswXsxlR+EMxs08QP3lQeam7eeJ+JUsaq5nQqiaT7OKOtciGnouZqM9k4N7KiiZ\nsQ/3FQ4m1Bmkdd5MZbmbKQcOkBbuxsrq4bfLf8E1m+tYtGsH4zLyaYom8PfPxcxvwXA2YfSb+Gw+\nBvyvce+PVtOZkcOe+WVkFXQwY3c9xZVVxBXk+YO05M2jLz6HMQefpzFeS15vO0EHtLtqqRkzn5hN\nKBxoxt4xC/gbAI6eGInIc3yusIDMqI/Lt62EnK1EBw/S4yni3z/TgyfiJCMAOYEuot0Oqvu3MjN9\nLsHeXj4Sf4F7XNPZ7YTSYBaZ2Z20TLuJDaFa0ite5rX8hbg666gczOFmVwnz5n6Zxra7uWnbowB0\nZgiTq65nq1SwsL+HnWoCi5zbEZeQvVdR7InxaJqbaTKNZ8aczW07bmW5axXWy1fyo/JJVAab+HrT\nBP6txM3Pyr9DoutWrg7EeHbmFfSbXmY21DAh0MsLUxZAt+LRBeey5NXtpFkeGBjEsmyEcNPhSmdH\ndBrfb7iTLiOTuk1jSPc66Zit2FA8g//YtQKfvYqV5nOY2eVMNbLY1mVDTDizrRzLdgbRnU+TWHQz\n1Y+0k+1WVDQNcrUID5Y4mVjXQnq6nXvmLuNL7W189YtfYP36fiLRu8ku38Omc0rIS3QQsYfpGWeS\nRwfVvu+QiAdwzHDytKqgsHEddjOTiRdeR0HuVth2HxUfuYlLSj7PgZLNzGs+n/lWBuPeXMe0smxy\nL7uMAxdZ5D4/yD+clbQ3NOAv2UFdrwt3twt2ANhoXrAIACPeQ3bwWTq9g3iXn49t81bSHjGBHkK+\nH1Ff83EaT89iwSeuJKdkLEVFRdTU1LB48WJe+ccrFKosykrHk/fR07iuqp77zRKWLDuTM/KzcTgc\nPP/882zZsoX58+ef0GOMpr1L2VJcdg849XxkmqZpJxsZjl9aU/3Lbyc5f/a9Sqlfvt/758+frzZv\n3nxCYjtUdzTO9Nd3Uxbt4GNtL/GJ0glkLLiez+xuoDYU4dUFUyhxOYgHuuje+gaDB2roy1vI5Wt7\nOGsgwS+8b+C76lMMjOmgsup7GIaT0vHfpLVD0bjtH+wyNrO0pA9sqZtjVXLG9JgSnuxzYGYt5eqi\ncURa72MgYfJIn4d5VUv5ffB8Lul5havfWEPdjWeQXeeiZPULtBQWUj1tCl25eYwpqiF97EbqNn0K\nLINM1ccU8yAliV5WcQaOsMJ2oJLM0n7KF3UTzQjgqrqS8Y0XvF3+gA16JUZJMI5pd9MU7mdLXyXi\nmoNl9NLr2otFgkG3QUumh+bcEqpLK1CSGgK3u43z1q2mtH8KXfmT8PXHCGTUoxwtHDn1/CsVs6nJ\nL+GG15/BIoh77D7GZ9bzoD9Os2mnLFDM6a3n4IxlMM22iea2ZvxRJ5KwWDeri4aiIFn9dla8UUDU\nbpHmHY+7rYe0M9q5ZdatzA5Vcu3aXtKW3UPQX8T+tqmsmTGXnTKXpZVbyN6ym/PTZnG6ZyKN0S5a\netaz17WBg0VTcMXLeTp6GnmhHjrd2Xxzxp3MzdiLJxZl1u5+KqWQa067nZLBDp7d9zUME14Nn8tn\nuY55effwBUcxfy0s58+5yzFjrVhmDjmxBOfvOEDI8pAf2YrfWUZ1Xz6tovg1YV5x7WTsgQgF7RaD\nxUX0FHhotx3En1PAjaF7mB6sJYHBY9OXkJezl73tc1m/fxF/TPycRxNn8xv1Sa7KXYcjs5dxOe0k\ndl+Jt38yu6wEq6woZRLjd4vG0pubwyX7G+kqS0MdMoeLQyw+6h1kQdtdTPIkBzgLB104I1Fq0idy\n0DWTJsdidseLaI4dPsysHcUEhzC1eQ2+uNDe7WJGoZNC/wHitma6+5wMdvsoaO1gIN2LzTuGZZHp\nVDu76BQ/BiCmImaLIKKwWXayA0I4NkirI0zAk5yvygz24+7uZGywlbG9rQT9btpzc2l3GUw6Yxn2\nsgqq16zG68skkN3JbF+AYPoObJ4YYYebf+dXhEjjJtdePjvnMlY99gIHDhxg3umn02lBVTBEcyTG\nYMLCQigsLSOnsIiYZTEQiuMMW2QNJBgXEiZikp3lIjPfja8gjbQsx9HnQdEAEJEtSqkR30odru8m\nTdM0bWh9kO+lE954EhETqAbOBZqBTcBVSqm977XNkHxBKQVWHBIxVDxKLBwm3u/HCgYg2o+KBIkO\nhgh1dRPvbMAZakRZ9TyRPYsNvtN5NWsuidTJkKEsvty6kznxdqxEP+FQL+4xu8CIsrO/mKpAGRcX\nryMvI0yCEJDAwmR3ENYP2qgOG9gExjhclBgFnB2sx4r187R4aHHZuD4HxjnDhJQHF0EEMPpPIywJ\nSm6rpy/kIZ6w4bKiZIUHSRjC6gmn88CkC/nZ+bfQ3jyN5uYZJLBQURO7JFA2450ZyeNxPA2VOCyT\nvNzzUWYOGfMewFO0k9Duy6FuOg4zglIJqv1uHBLFbgYxbIOIUqwrzuO5Mxa9K8Xe8CCTWw8wsfMg\n3d5M3pwwgwGXh8ltbUxs78QV7wMSuC0HUYkCFu5ohC5vJn+bsYjsvi3IwG8P22feYCaz2yaTHckh\nYbODYUOZgighK+iAtt3Eo37cjkzCsX6UzaS09CwWxueRUAm2dq/mwdNzeL1iOWdue52C4m5UXpjX\nOItucvn4ljfJG2jHCAVxtTdS6qhgRuZivLY0wsToVX4GVJCo4cIlXnzYyHQM0htLI6RstCiLZhQt\nWEQJMy1RxxLHmxSYrTQn8vFbXroMJ1OjvdRkVhBxZpMTiVI40IUr0Qaqh7gjRMIWJhR30mXYGUMC\nHzZcqpeERAhYGQxamXTbLfySwZqS2QQNOwdzx9ATz+WboZ9SWHyQWMSOFXRj2BKYaSEMwyJhGTT1\nFvNS5TJquieCgjQVYgJdFFqCoVx4lSJqs6hPj+DPTqOtbAIBl4dutw+bijMh1ExBpBN3LIJd4thU\nAgGi4oB4nFgoQHrQyZzBXQxOgT7TR2ushA3pc+iwvzMy9G/V58khOWFxIuZFOh3kxvy4VZRQIp2+\n4CSs/kJcwRJcVjam007M20sorQ3l6sJpi2IaJlGJ0tZUyv5+N2F7sm57IhaeuOCNm7giUfIjnaS3\nBTCCQVomxth4JvRHHYQjDkgYYAlxMfA704gYNkTFMVQUQ4EowcBi0BYg5AhgV25sRjYJM4OQLZ2Q\nmU7cyCTkzCZhT8eVUKTFFPkDcfIH4qRFYmAaZLsrMDMdGFkOcJnYDMGuwIwrPBZ4ohamYaDsJq6o\nhSuqSEOwGwaGIYgIYpD6VzAMASH5miGIgBJIiGAZioQhJIC4ISREkRCIixC3LELRBJFYglDUImqD\nvKk+gpZFzFLYRLCJYIpgk+T8LWFLEbYswgkLU4Q000gtJhVpLiZ4jm9eFt140jRN004mJ3vjaTHw\nY6XU+annPwBQSv3Xe21z3F9Qv5sH3TUfaJOg8tERnUBjZC5VoXPodXioGucgc/aTLJQN5NP+9nuV\nJSDqsIsploL2uFAfMaiLGGwL2kggpJsmOZ4inGqQtlAv/kNucs+3WVyYGWOWO/HOvhSYoSxULIDl\ntsi+10bMNOlRmdQMlNHgLmJt8SyM3CgTsxrIdPhZ3rIMw+pjh63h7X24B8diJlwQ78fw78UgG5tr\nPmJ4sCSO5fBTvOABfGMqqXq0jHDvUSYjBCybnQOzl9KQW4hpJbDFLXwRG/k9A3gDXaCCyTM6ewZB\nb5xNZeVUFY4nYnccdX9vyQtG+PyOTaQlovisNDJVGhmJNApjhw9Nq1B0Sz/VZiu1ZhsRFSW724/H\n70dhkOkej2nPQWyZKJeBskUYiHTxwOwpVJYk52QRZTE+1MDiyirG9AtKWYQk9r6zox/KVO9coXlr\nSsG3PkUl765PpjK4KDqXfPXeE0MmJeCQ+d0PGqvpN9eRKwFyxU8hPdjEOmyL1XyE9czDl32Q3NxG\n3K4AZhzMkI3J/hbszylCjUf/LI/m9YtO48b0FwGo8pTyq9LP8kLuEhLy/j185/t389z2rxy27ql5\npdhM6EqMIRxJ59KW18juD9GXZaelwEUgw0bcdmy3XVpxIR42sWFgiIOsmovJbz+PHhmg1mynzeil\nT4JEJX7MZf1n5sbKmJv4106m+WSJnV9MP/bP52TwndJCbi472nRJx043njRN07STycneePoksEIp\ndWPq+aeBhUqprx7xvrcnIgQmA/tOaKDHJhfoGu4g/gV0uUaOU7FMoMs1knyYMo1XSuX9K4I5kUSk\nEzhwnLs5Ff8mPiydi8PpfBxO5+NwOh+HO958HPP30kk7YMShExGerERk86nw6+mRdLlGjlOxTKDL\nNZKcimU6VkPRABzN+TuSzsXhdD4Op/NxOJ2Pw53IfAzHUOUHgbGHPC9JrdM0TdM0TdM0TTtpDUfj\naRMwSUTKRMQBrASeGYY4NE3TNE3TNE3TjtkJ77anlIqLyFeBF0neHX+fUmrPiY5jiJzU3QqPgy7X\nyHEqlgl0uUaSU7FMJ5LO3zt0Lg6n83E4nY/D6Xwc7oTlY1jmedI0TdM0TdM0TRtphqPbnqZpmqZp\nmqZp2oijG0+apmmapmmapmnHQDeejpOI3CoiVSKyU0RWiUjWcMc0FETkUyKyR0QsERnRQ2GKyAoR\n2SciNSLy/eGOZyiIyH0i0iEiu4c7lqEiImNF5B8isjf1t3fTcMc0FETEJSIbRWRHqly3DHdMQ0VE\nTBHZJiLPDXcsI82peFw60nvVaRHJFpGXRGR/6l/fIdv8IJWTfSJy/iHr54nIrtRrvxWRY5zW/ORz\nZL0ZzfkQkSwReTx1HlUpIotHeT6+maoru0Xk4dT3x6jJx9HObYay/CLiFJG/pNa/KSKlHyZO3Xg6\nfi8BM5RSM4Fq4AfDHM9Q2Q1cDqwd7kCOh4iYwB3ABcA04CoRmTa8UQ2JPwArhjuIIRYHblZKTQMW\nAV85RT6rCLBMKTULmA2sEJFFwxzTULkJqBzuIEaaU/i4dKT3qtPfB9YopSYBa1LPSb22EphO8vj2\n+1SuAO4EPgdMSi0j+fh3ZL0Zzfm4HfibUmoKMItkXkZlPkSkGPg6MF8pNYPkoGorGV35+APvjnUo\ny38D0KuUKgd+A/z3hwlSN56Ok1JqtVIqnnr6Bsl5q0Y8pVSlUmrfcMcxBBYANUqpOqVUFHgEuHSY\nYzpuSqm1QM9wxzGUlFKtSqmtqcf9JL9Ei4c3quOnkgZST+2pZcSP1CMiJcBFwL3DHcsIdEoel470\nPnX6UuCB1NseAC5LPb4UeEQpFVFK1QM1wAIRGQNkKKXeUMlRrv54yDYjynvUm1GZDxHJBJYC/wug\nlIoqpfoYpflIsQFuEbEBHqCFUZSP9zi3GcryH7qvx4HlH+aqnG48Da3rgReGOwjtMMVA0yHPmzkF\nTshPdalL6XOAN4c3kqGR6qazHegAXlJKnQrl+r/AdwFruAMZgUbdcemIOl2glGpNvdQGFKQev1de\nilOPj1w/Eh2t3ozWfJQBncD9qW6M94pIGqM0H0qpg8CvgEagFfArpVYzSvNxiKEs/9vbpC58+IGc\nDxqQbjwdAxH5e6r/6ZHLpYe854ckuyg8NHyRfjDHUi5NO9FExAs8AXxDKRUY7niGglIqoZSaTfLK\n9AIRmTHcMR0PEfkY0KGU2jLcsWgnv/er06lfhkf8ldhjcSz1ZjTlg+RVlrnAnUqpOcAgqS5ZbxlN\n+Ujdy3MpyUZlEZAmItcc+p7RlI+jOVnKf8InyR2JlFIffb/XReQzwMeA5WoETZz1z8p1ijgIjD3k\neUlqnXYSEhE7yZOsh5RSTw53PENNKdUnIv8g2f96JA/2cSZwiYhcCLiADBF5UCl1zT/ZTksaNcel\n96jT7SIyRinVmupi05Fa/155OcjhXeJHar6OWm8YvfloBpoPuRL/OMnG02jNx0eBeqVUJ4CIPAmc\nwejNx1uGsvxvbdOc6hqZCXR/0ID0lafjJCIrSF6Cv0QpFRzueLR32QRMEpEyEXGQvLnwmWGOSTuK\nVL/j/wUqlVK/Hu54hoqI5ElqFE4RcQPnAlXDG9XxUUr9QClVopQqJVmnXtYNpw9kVByX3qdOPwNc\nl3p8HfD0IetXpkbEKiN5o/fGVJedgIgsSu3z2kO2GTHep96M1ny0AU0iMjm1ajmwl1GaD5Ld9RaJ\niCdVjuUk7xMcrfl4y1CW/9B9fZJkHfzgFz2UUno5joXkDWpNwPbUctdwxzRE5fo4yV+FIkA78OJw\nx3QcZbmQ5EiItcAPhzueISrTwyT7RMdSn9MNwx3TEJRpCcnL8TsPqU8XDndcQ1CumcC2VLl2A/85\n3DENcfnOBp4b7jhG2nIqHpeOUsaj1mmS9xisAfYDfweyD9nmh6mc7AMuOGT9/FT9qQX+B5DhLt9x\n5ubtejOa80FyBNLNqb+RpwDfKM/HLSR/XNsN/AlwjqZ8HO3cZijLT/KK72Mkz903AhM+TJxv7UzT\nNE3TNE3TNE17H7rbnqZpmqZpmqZp2jHQjSdN0zRN0zRN07RjoBtPmqZpmqZpmqZpx0A3njRN0zRN\n0zRN046BbjxpmqZpmqZpmqYdA9140jRN0zRN0zRNOwa68aRpmqZpmqZpmnYM/j9ygAPp9daaNwAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12ab0e810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['subs'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examining individual/interval rates from the posteriors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "add_samples = pd.DataFrame(trace['adds'].mean(axis=0))\n",
    "sub_samples = pd.DataFrame(trace['subs'].mean(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "add_posterior_means = add_samples.stack().swaplevel()\n",
    "add_posterior_means.index.names = ['full_id', 'interval'] \n",
    "sub_posterior_means = sub_samples.stack().swaplevel()\n",
    "sub_posterior_means.index.names = ['full_id', 'interval'] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# make a DF with team attacking and defensive strength, indexed by the 0...n-1 team IDs, with the team name added\n",
    "indiv_params = pd.DataFrame({'add':add_posterior_means,\n",
    "                               'sub':sub_posterior_means})                \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style>\n",
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       "    .dataframe thead th {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>add</th>\n",
       "      <th>sub</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>full_id</th>\n",
       "      <th>interval</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.805894</td>\n",
       "      <td>0.902967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>0</th>\n",
       "      <td>-1.407112</td>\n",
       "      <td>-1.091009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>0</th>\n",
       "      <td>0.456462</td>\n",
       "      <td>-0.310513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.282786</td>\n",
       "      <td>-0.542787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.689741</td>\n",
       "      <td>1.088295</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       add       sub\n",
       "full_id interval                    \n",
       "0       0        -0.805894  0.902967\n",
       "1       0        -1.407112 -1.091009\n",
       "2       0         0.456462 -0.310513\n",
       "3       0        -0.282786 -0.542787\n",
       "4       0        -0.689741  1.088295"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indiv_params.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Join these to the true rates to compare"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "indiv_params = indiv_params.join(full_add_rates, how='left').join(full_sub_rates, how='left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>add</th>\n",
       "      <th>sub</th>\n",
       "      <th>true_add</th>\n",
       "      <th>true_sub</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>full_id</th>\n",
       "      <th>interval</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.805894</td>\n",
       "      <td>0.902967</td>\n",
       "      <td>-0.565807</td>\n",
       "      <td>1.028134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>0</th>\n",
       "      <td>-1.407112</td>\n",
       "      <td>-1.091009</td>\n",
       "      <td>0.054584</td>\n",
       "      <td>-0.094828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>0</th>\n",
       "      <td>0.456462</td>\n",
       "      <td>-0.310513</td>\n",
       "      <td>0.374870</td>\n",
       "      <td>-0.290390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.282786</td>\n",
       "      <td>-0.542787</td>\n",
       "      <td>-0.090804</td>\n",
       "      <td>-0.025533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.689741</td>\n",
       "      <td>1.088295</td>\n",
       "      <td>-0.389996</td>\n",
       "      <td>0.190206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <th>0</th>\n",
       "      <td>0.351690</td>\n",
       "      <td>0.317567</td>\n",
       "      <td>0.075837</td>\n",
       "      <td>-0.131558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <th>0</th>\n",
       "      <td>0.037281</td>\n",
       "      <td>-0.018126</td>\n",
       "      <td>-0.026505</td>\n",
       "      <td>0.170707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.189041</td>\n",
       "      <td>-0.607342</td>\n",
       "      <td>-0.576231</td>\n",
       "      <td>-0.317331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>0</th>\n",
       "      <td>0.087373</td>\n",
       "      <td>1.281420</td>\n",
       "      <td>-0.235958</td>\n",
       "      <td>0.909008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <th>0</th>\n",
       "      <td>0.588528</td>\n",
       "      <td>-1.247383</td>\n",
       "      <td>0.285583</td>\n",
       "      <td>-0.457500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <th>0</th>\n",
       "      <td>2.413115</td>\n",
       "      <td>-0.264217</td>\n",
       "      <td>0.960896</td>\n",
       "      <td>-0.323154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <th>0</th>\n",
       "      <td>0.968850</td>\n",
       "      <td>0.522531</td>\n",
       "      <td>0.465336</td>\n",
       "      <td>-0.226733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.690888</td>\n",
       "      <td>-0.245011</td>\n",
       "      <td>-0.646994</td>\n",
       "      <td>0.097898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <th>0</th>\n",
       "      <td>1.123418</td>\n",
       "      <td>0.571917</td>\n",
       "      <td>0.585964</td>\n",
       "      <td>-0.343051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <th>0</th>\n",
       "      <td>0.418854</td>\n",
       "      <td>-0.639930</td>\n",
       "      <td>-0.143498</td>\n",
       "      <td>-0.300226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <th>0</th>\n",
       "      <td>0.168723</td>\n",
       "      <td>0.550106</td>\n",
       "      <td>-0.077431</td>\n",
       "      <td>0.103723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <th>0</th>\n",
       "      <td>-1.620531</td>\n",
       "      <td>0.180240</td>\n",
       "      <td>-0.730789</td>\n",
       "      <td>0.095859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <th>0</th>\n",
       "      <td>0.419834</td>\n",
       "      <td>0.733785</td>\n",
       "      <td>0.663638</td>\n",
       "      <td>0.147703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.527102</td>\n",
       "      <td>-1.670057</td>\n",
       "      <td>0.087794</td>\n",
       "      <td>-0.388655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <th>0</th>\n",
       "      <td>-0.821030</td>\n",
       "      <td>0.487545</td>\n",
       "      <td>-0.070490</td>\n",
       "      <td>0.155722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <td>-0.606227</td>\n",
       "      <td>0.959402</td>\n",
       "      <td>-0.665534</td>\n",
       "      <td>0.950566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>1</th>\n",
       "      <td>-1.363702</td>\n",
       "      <td>-1.311365</td>\n",
       "      <td>0.002954</td>\n",
       "      <td>-0.039217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>1</th>\n",
       "      <td>0.401234</td>\n",
       "      <td>-0.105006</td>\n",
       "      <td>0.375661</td>\n",
       "      <td>-0.254806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <td>-0.333873</td>\n",
       "      <td>-0.464025</td>\n",
       "      <td>-0.072599</td>\n",
       "      <td>0.005820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>1</th>\n",
       "      <td>-0.717721</td>\n",
       "      <td>0.986254</td>\n",
       "      <td>-0.412512</td>\n",
       "      <td>0.251428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <th>1</th>\n",
       "      <td>0.243136</td>\n",
       "      <td>0.631411</td>\n",
       "      <td>0.140119</td>\n",
       "      <td>-0.052155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <th>1</th>\n",
       "      <td>-0.037464</td>\n",
       "      <td>-0.014632</td>\n",
       "      <td>0.049241</td>\n",
       "      <td>0.140423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <th>1</th>\n",
       "      <td>-0.454430</td>\n",
       "      <td>-0.479509</td>\n",
       "      <td>-0.521713</td>\n",
       "      <td>-0.358751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>1</th>\n",
       "      <td>-0.065603</td>\n",
       "      <td>1.379056</td>\n",
       "      <td>-0.227301</td>\n",
       "      <td>0.922936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <th>1</th>\n",
       "      <td>0.598591</td>\n",
       "      <td>-1.482881</td>\n",
       "      <td>0.387853</td>\n",
       "      <td>-0.398188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <th>1</th>\n",
       "      <td>2.584978</td>\n",
       "      <td>0.158012</td>\n",
       "      <td>0.906381</td>\n",
       "      <td>-0.296287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <th>1</th>\n",
       "      <td>0.973978</td>\n",
       "      <td>0.181813</td>\n",
       "      <td>0.446687</td>\n",
       "      <td>-0.229846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <th>1</th>\n",
       "      <td>-0.680517</td>\n",
       "      <td>0.001374</td>\n",
       "      <td>-0.626138</td>\n",
       "      <td>0.080671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <th>1</th>\n",
       "      <td>1.039724</td>\n",
       "      <td>0.590670</td>\n",
       "      <td>0.493274</td>\n",
       "      <td>-0.411890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <th>1</th>\n",
       "      <td>0.154029</td>\n",
       "      <td>-0.683559</td>\n",
       "      <td>-0.080896</td>\n",
       "      <td>-0.316528</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       add       sub  true_add  true_sub\n",
       "full_id interval                                        \n",
       "0       0        -0.805894  0.902967 -0.565807  1.028134\n",
       "1       0        -1.407112 -1.091009  0.054584 -0.094828\n",
       "2       0         0.456462 -0.310513  0.374870 -0.290390\n",
       "3       0        -0.282786 -0.542787 -0.090804 -0.025533\n",
       "4       0        -0.689741  1.088295 -0.389996  0.190206\n",
       "5       0         0.351690  0.317567  0.075837 -0.131558\n",
       "6       0         0.037281 -0.018126 -0.026505  0.170707\n",
       "7       0        -0.189041 -0.607342 -0.576231 -0.317331\n",
       "8       0         0.087373  1.281420 -0.235958  0.909008\n",
       "9       0         0.588528 -1.247383  0.285583 -0.457500\n",
       "10      0         2.413115 -0.264217  0.960896 -0.323154\n",
       "11      0         0.968850  0.522531  0.465336 -0.226733\n",
       "12      0        -0.690888 -0.245011 -0.646994  0.097898\n",
       "13      0         1.123418  0.571917  0.585964 -0.343051\n",
       "14      0         0.418854 -0.639930 -0.143498 -0.300226\n",
       "15      0         0.168723  0.550106 -0.077431  0.103723\n",
       "16      0        -1.620531  0.180240 -0.730789  0.095859\n",
       "17      0         0.419834  0.733785  0.663638  0.147703\n",
       "18      0        -0.527102 -1.670057  0.087794 -0.388655\n",
       "19      0        -0.821030  0.487545 -0.070490  0.155722\n",
       "0       1        -0.606227  0.959402 -0.665534  0.950566\n",
       "1       1        -1.363702 -1.311365  0.002954 -0.039217\n",
       "2       1         0.401234 -0.105006  0.375661 -0.254806\n",
       "3       1        -0.333873 -0.464025 -0.072599  0.005820\n",
       "4       1        -0.717721  0.986254 -0.412512  0.251428\n",
       "5       1         0.243136  0.631411  0.140119 -0.052155\n",
       "6       1        -0.037464 -0.014632  0.049241  0.140423\n",
       "7       1        -0.454430 -0.479509 -0.521713 -0.358751\n",
       "8       1        -0.065603  1.379056 -0.227301  0.922936\n",
       "9       1         0.598591 -1.482881  0.387853 -0.398188\n",
       "10      1         2.584978  0.158012  0.906381 -0.296287\n",
       "11      1         0.973978  0.181813  0.446687 -0.229846\n",
       "12      1        -0.680517  0.001374 -0.626138  0.080671\n",
       "13      1         1.039724  0.590670  0.493274 -0.411890\n",
       "14      1         0.154029 -0.683559 -0.080896 -0.316528"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indiv_params.head(35)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>add</th>\n",
       "      <th>true_add</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>add</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.752817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>true_add</th>\n",
       "      <td>0.752817</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               add  true_add\n",
       "add       1.000000  0.752817\n",
       "true_add  0.752817  1.000000"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indiv_params[['add','true_add']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sub</th>\n",
       "      <th>true_sub</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sub</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.767598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>true_sub</th>\n",
       "      <td>0.767598</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               sub  true_sub\n",
       "sub       1.000000  0.767598\n",
       "true_sub  0.767598  1.000000"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indiv_params[['sub','true_sub']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "interval\n",
       "0   -0.821030\n",
       "1   -0.659618\n",
       "2   -0.405675\n",
       "3   -0.197921\n",
       "4    0.334409\n",
       "5    0.372244\n",
       "6    0.082320\n",
       "7   -0.208276\n",
       "8   -0.080617\n",
       "9    0.035490\n",
       "Name: add, dtype: float64"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indiv_params.loc[19]['add']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare estimated and true add/sub rates for two different individuals "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12f1ca950>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xuSISC3xjjOnRwHz+wMfA58aY/5zs5+s1gd2bMYY/fbCRt1bs5q5zuvDQ+T1a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\nBoBSSnmp/wfAXl/X//9skQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f1a6fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(0,10),indiv_params.loc[19]['add'])\n",
    "plt.plot(range(0,10),indiv_params.loc[19]['true_add'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12f20fc90>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gf6RtbVC+qb2h37nCuW7ceo+KBuVARj5knAbp+TB0vDP0blMdVO90vtOqYqja4X3u/akr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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e6d7a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(0,10),indiv_params.loc[19]['sub'])\n",
    "plt.plot(range(0,10),indiv_params.loc[19]['true_sub'])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:pred-clean]",
   "language": "python",
   "name": "conda-env-pred-clean-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

## mock_data.csv

          
            n_a
            n_b
            interval_a
            interval_b
            id_a
            id_b

            
              0
              0
              0
              0
              0
              3

            
              0
              0
              0
              0
              8
              16

            
              0
              0
              0
              0
              7
              17

            
              0
              0
              0
              0
              10
              19

            
              0
              0
              0
              0
              18
              4

            
              0
              0
              0
              0
              5
              11

            
              0
              0
              0
              0
              2
              14

            
              0
              0
              0
              0
              1
              15

            
              0
              0
              0
              0
              9
              6

            
              0
              0
              0
              0
              13
              12

            
              1
              1
              0
              0
              4
              0

            
              1
              1
              0
              0
              14
              7

            
              1
              1
              0
              0
              17
              13

            
              1
              1
              0
              0
              3
              9

            
              1
              1
              0
              0
              16
              10

            
              1
              1
              0
              0
              15
              8

            
              1
              1
              0
              0
              11
              2

            
              1
              1
              0
              0
              19
              1

            
              1
              1
              0
              0
              12
              5

            
              1
              1
              0
              0
              6
              18

            
              2
              2
              0
              0
              0
              2

            
              2
              2
              0
              0
              10
              9

            
              2
              2
              0
              0
              16
              11

            
              2
              2
              0
              0
              15
              18

            
              2
              2
              0
              0
              19
              4

            
              2
              2
              0
              0
              8
              3

            
              2
              2
              0
              0
              13
              5

            
              2
              2
              0
              0
              7
              12

            
              2
              2
              0
              0
              17
              14

            
              2
              2
              0
              0
              1
              6

            
              3
              3
              0
              0
              2
              1

            
              3
              3
              0
              0
              4
              16

            
              3
              3
              0
              0
              12
              17

            
              3
              3
              0
              0
              18
              8

            
              3
              3
              0
              0
              5
              19

            
              3
              3
              0
              0
              6
              15

            
              3
              3
              0
              0
              9
              13

            
              3
              3
              0
              0
              3
              7

            
              3
              3
              0
              0
              14
              10

            
              3
              3
              0
              0
              11
              0

            
              4
              4
              1
              1
              7
              5

            
              4
              4
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              4
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              4
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              4
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              4
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              4
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              5
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              6
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              6
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              18
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              18
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              18
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              19
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              19
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              20
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              20
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              20
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              20
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              20
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              20
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              21
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              21
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              22
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              22
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              23
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              23
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              24
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              24
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              24
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              24
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              24
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              24
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              24
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              6
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              24
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              24
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              24
              24
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              25
              25
              6
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              25
              25
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              25
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              25
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              25
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              25
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              25
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              25
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              26
              26
              6
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              26
              26
              6
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              26
              26
              6
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              26
              26
              6
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              26
              26
              6
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              26
              26
              6
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              26
              26
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              26
              26
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              27
              27
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              27
              27
              6
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              27
              26
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              27
              27
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              27
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              27
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              27
              26
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              27
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              26
              26
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              27
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              28
              28
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              28
              28
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              28
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              27
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              27
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              28
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              27
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              28
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              28
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              28
              28
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              29
              28
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              29
              29
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              29
              29
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              29
              29
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              29
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              29
              30
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              29
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              29
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              29
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              30
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              30
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              29
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              30
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              29
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              31
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              30
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              30
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              31
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              31
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              31
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              30
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              29
              31
              7
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              31
              31
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              30
              29
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              31
              31
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              32
              32
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              31
              32
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              32
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              32
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              31
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              31
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              30
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              32
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              32
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              33
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              32
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              32
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              32
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              32
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              33
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              32
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              33
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              33
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              33
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              33
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              32
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              33
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              34
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              33
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              34
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              34
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              33
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              34
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              34
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              35
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              34
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              35
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              34
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              8
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              5
              3

            
              35
              35
              8
              8
              10
              0

            
              36
              36
              9
              9
              18
              13

            
              36
              36
              9
              9
              4
              2

            
              36
              36
              9
              9
              19
              9

            
              35
              36
              8
              9
              15
              11

            
              35
              35
              8
              8
              16
              5

            
              36
              35
              9
              8
              8
              7

            
              36
              36
              9
              9
              3
              14

            
              35
              35
              8
              8
              6
              17

            
              36
              36
              9
              9
              12
              1

            
              36
              36
              9
              9
              15
              0

            
              36
              36
              9
              9
              16
              7

            
              36
              36
              9
              9
              10
              17

            
              36
              36
              9
              9
              6
              5

            
              37
              37
              9
              9
              17
              16

            
              37
              37
              9
              9
              14
              19

            
              37
              37
              9
              9
              2
              3

            
              37
              37
              9
              9
              11
              12

            
              37
              37
              9
              9
              5
              8

            
              37
              37
              9
              9
              7
              10

            
              37
              37
              9
              9
              9
              15

            
              37
              37
              9
              9
              13
              6

            
              37
              37
              9
              9
              1
              4

            
              37
              37
              9
              9
              0
              18
n_a	n_b	interval_a	interval_b	id_a	id_b
0	0	0	0	0	3
0	0	0	0	8	16
0	0	0	0	7	17
0	0	0	0	10	19
0	0	0	0	18	4
0	0	0	0	5	11
0	0	0	0	2	14
0	0	0	0	1	15
0	0	0	0	9	6
0	0	0	0	13	12
1	1	0	0	4	0
1	1	0	0	14	7
1	1	0	0	17	13
1	1	0	0	3	9
1	1	0	0	16	10
1	1	0	0	15	8
1	1	0	0	11	2
1	1	0	0	19	1
1	1	0	0	12	5
1	1	0	0	6	18
2	2	0	0	0	2
2	2	0	0	10	9
2	2	0	0	16	11
2	2	0	0	15	18
2	2	0	0	19	4
2	2	0	0	8	3
2	2	0	0	13	5
2	2	0	0	7	12
2	2	0	0	17	14
2	2	0	0	1	6
3	3	0	0	2	1
3	3	0	0	4	16
3	3	0	0	12	17
3	3	0	0	18	8
3	3	0	0	5	19
3	3	0	0	6	15
3	3	0	0	9	13
3	3	0	0	3	7
3	3	0	0	14	10
3	3	0	0	11	0
4	4	1	1	7	5
4	4	1	1	10	18
4	4	1	1	1	9
4	4	1	1	19	12
4	4	1	1	17	11
4	4	1	1	13	14
4	4	1	1	0	6
4	4	1	1	16	3
4	4	1	1	8	4
4	4	1	1	15	2
5	5	1	1	5	1
5	5	1	1	4	13
5	5	1	1	18	16
5	5	1	1	9	8
5	5	1	1	2	17
5	5	1	1	11	7
5	5	1	1	12	15
5	5	1	1	3	19
5	5	1	1	14	0
5	5	1	1	6	10
6	6	1	1	3	12
6	6	1	1	6	4
6	6	1	1	8	1
6	6	1	1	9	18
6	6	1	1	14	11
6	6	1	1	0	16
6	6	1	1	15	10
6	6	1	1	2	5
6	6	1	1	17	19
6	6	1	1	13	7
7	7	1	1	19	13
7	7	1	1	12	2
7	7	1	1	16	15
7	7	1	1	18	17
7	7	1	1	4	9
7	7	1	1	10	8
7	7	1	1	5	14
7	7	1	1	7	6
7	7	1	1	1	0
7	7	1	1	11	3
8	8	2	2	3	6
8	8	2	2	12	18
8	8	2	2	5	4
8	8	2	2	14	8
8	8	2	2	7	0
8	8	2	2	19	15
8	8	2	2	13	16
8	8	2	2	17	1
8	8	2	2	2	10
8	8	2	2	11	9
9	9	2	2	8	19
9	9	2	2	4	11
9	9	2	2	15	5
9	9	2	2	10	13
9	9	2	2	9	17
9	9	2	2	1	7
9	9	2	2	16	2
9	9	2	2	18	3
9	9	2	2	0	12
9	9	2	2	6	14
10	10	2	2	5	6
10	10	2	2	19	0
10	10	2	2	2	9
10	10	2	2	17	15
10	10	2	2	11	1
10	10	2	2	12	10
10	10	2	2	13	8
10	10	2	2	7	16
10	10	2	2	14	18
10	10	2	2	3	4
11	11	2	2	18	2
11	11	2	2	15	7
11	11	2	2	16	14
11	11	2	2	8	17
11	11	2	2	0	13
11	11	2	2	10	11
11	11	2	2	9	5
11	11	2	2	4	12
11	11	2	2	6	19
11	11	2	2	1	3
12	12	3	3	17	0
12	12	3	3	2	8
12	12	3	3	5	10
12	12	3	3	11	18
12	12	3	3	14	9
12	12	3	3	7	4
12	12	3	3	13	1
12	12	3	3	12	6
12	12	3	3	3	15
12	12	3	3	19	16
13	13	3	3	19	2
13	13	3	3	4	17
13	13	3	3	12	14
13	13	3	3	16	9
13	13	3	3	18	7
13	13	3	3	8	0
13	13	3	3	3	5
13	13	3	3	15	13
13	13	3	3	6	11
13	13	3	3	10	1
14	14	3	3	9	12
14	14	3	3	11	8
14	14	3	3	0	15
14	14	3	3	1	16
14	14	3	3	14	4
14	14	3	3	17	10
14	14	3	3	13	3
14	14	3	3	5	18
14	14	3	3	2	6
14	14	3	3	7	19
15	15	3	3	10	7
15	15	3	3	15	9
15	15	3	3	12	11
15	15	3	3	19	14
15	15	3	3	16	17
15	15	3	3	18	0
15	15	3	3	4	1
15	15	3	3	6	13
15	15	3	3	3	2
15	15	3	3	8	5
16	16	4	4	13	18
16	16	4	4	0	10
16	16	4	4	9	19
16	16	4	4	7	8
16	16	4	4	5	16
16	16	4	4	14	3
16	16	4	4	2	4
16	16	4	4	17	6
16	16	4	4	11	15
16	16	4	4	1	12
17	17	4	4	9	0
17	17	4	4	18	19
17	17	4	4	6	8
17	17	4	4	12	16
17	17	4	4	4	15
17	17	4	4	11	13
17	17	4	4	5	17
17	17	4	4	3	10
17	17	4	4	2	7
17	17	4	4	14	1
18	18	4	4	10	4
18	18	4	4	7	9
18	18	4	4	19	11
18	18	4	4	13	2
18	18	4	4	17	3
18	18	4	4	15	14
18	18	4	4	0	5
18	18	4	4	1	18
18	18	4	4	8	12
18	18	4	4	16	6
19	19	4	4	15	6
19	19	4	4	13	9
19	19	4	4	1	2
19	19	4	4	8	18
19	19	4	4	16	4
19	19	4	4	0	11
19	19	4	4	10	14
19	19	4	4	17	12
19	19	4	4	19	5
19	19	4	4	7	3
20	20	5	5	18	15
20	20	5	5	4	19
20	20	5	5	2	0
20	20	5	5	12	7
20	20	5	5	5	13
20	20	5	5	9	10
20	20	5	5	14	17
20	20	5	5	11	16
20	20	5	5	3	8
20	20	5	5	6	1
21	21	5	5	3	16
21	21	5	5	12	19
21	21	5	5	5	7
21	21	5	5	14	13
21	21	5	5	18	10
21	21	5	5	2	15
21	21	5	5	4	8
21	21	5	5	6	0
21	21	5	5	9	1
21	21	5	5	11	17
22	22	5	5	10	6
22	22	5	5	13	4
22	22	5	5	0	14
22	22	5	5	8	9
22	22	5	5	19	3
22	22	5	5	17	2
22	22	5	5	16	18
22	22	5	5	15	12
22	22	5	5	7	11
22	22	5	5	1	5
23	23	5	5	10	3
23	23	5	5	15	4
23	23	5	5	8	6
23	23	5	5	16	12
23	23	5	5	1	14
23	23	5	5	19	18
23	23	5	5	0	9
23	23	5	5	13	11
23	23	5	5	7	2
23	23	5	5	17	5
24	24	6	6	12	8
24	24	6	6	9	7
24	24	6	6	3	17
24	24	6	6	2	13
24	24	6	6	4	10
24	24	6	6	6	16
24	24	6	6	11	19
24	24	6	6	14	15
24	24	6	6	18	1
24	24	6	6	5	0
25	25	6	6	16	0
25	25	6	6	11	14
25	25	6	6	10	15
25	25	6	6	18	9
25	25	6	6	7	13
25	25	6	6	19	17
25	25	6	6	5	2
25	25	6	6	1	8
25	25	6	6	4	6
25	25	6	6	12	3
26	26	6	6	15	16
26	26	6	6	14	5
26	26	6	6	9	4
26	26	6	6	8	10
26	26	6	6	17	18
26	26	6	6	13	19
26	26	6	6	0	1
26	26	6	6	3	11
27	27	6	6	18	14
27	27	6	6	8	13
27	26	6	6	4	7
27	27	6	6	10	5
27	27	6	6	16	19
27	27	6	6	15	3
27	26	6	6	9	2
27	27	6	6	1	11
26	26	6	6	6	12
27	27	6	6	0	17
28	28	7	7	3	1
28	28	7	7	5	9
28	28	7	7	11	10
27	28	6	7	2	18
27	28	6	7	12	4
28	28	7	7	14	16
27	28	6	7	7	15
28	28	7	7	17	8
28	27	7	6	19	6
28	28	7	7	13	0
29	28	7	7	10	12
29	29	7	7	18	11
29	29	7	7	9	14
29	29	7	7	4	3
29	28	7	7	8	2
28	29	7	7	7	1
29	30	7	7	19	8
29	30	7	7	17	9
29	29	7	7	5	15
29	30	7	7	13	10
30	30	7	7	11	4
30	28	7	7	14	6
29	29	7	7	2	16
30	30	7	7	3	18
29	29	7	7	12	0
31	30	7	7	4	5
30	30	7	7	16	13
30	30	7	7	1	17
31	31	7	7	9	11
31	30	7	7	18	12
31	30	7	7	10	2
30	30	7	7	15	19
29	31	7	7	6	3
31	31	7	7	8	14
30	29	7	7	0	7
31	31	7	7	15	1
31	30	7	7	17	7
32	32	8	8	4	18
31	32	7	8	19	10
32	31	8	7	11	5
32	31	8	7	14	2
31	31	7	7	12	13
31	32	7	8	16	8
30	32	7	8	6	9
32	31	8	7	3	0
32	31	8	7	19	7
33	32	8	8	10	16
32	33	8	8	0	4
32	33	8	8	7	14
32	32	8	8	13	17
32	33	8	8	2	11
32	32	8	8	5	12
33	32	8	8	8	15
33	31	8	7	18	6
32	33	8	8	1	19
33	33	8	8	9	3
33	33	8	8	2	12
33	33	8	8	15	17
33	34	8	8	0	19
32	33	8	8	6	7
33	33	8	8	1	13
34	34	8	8	12	9
33	34	8	8	6	2
34	34	8	8	4	14
34	33	8	8	18	5
33	34	8	8	16	1
34	34	8	8	8	11
34	34	8	8	3	13
35	35	8	8	2	19
35	34	8	8	9	16
34	35	8	8	7	18
35	34	8	8	13	15
34	35	8	8	17	4
35	34	8	8	1	10
35	34	8	8	11	6
34	35	8	8	0	8
35	35	8	8	14	12
34	35	8	8	5	3
35	35	8	8	10	0
36	36	9	9	18	13
36	36	9	9	4	2
36	36	9	9	19	9
35	36	8	9	15	11
35	35	8	8	16	5
36	35	9	8	8	7
36	36	9	9	3	14
35	35	8	8	6	17
36	36	9	9	12	1
36	36	9	9	15	0
36	36	9	9	16	7
36	36	9	9	10	17
36	36	9	9	6	5
37	37	9	9	17	16
37	37	9	9	14	19
37	37	9	9	2	3
37	37	9	9	11	12
37	37	9	9	5	8
37	37	9	9	7	10
37	37	9	9	9	15
37	37	9	9	13	6
37	37	9	9	1	4
37	37	9	9	0	18