apc/vignettes/vignette_over_dispersed_apc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Over-dispersed Age-Period-Cohort Models\n",
    "\n",
    "We replicate the data example in [Harnau and Nielsen (2017)](https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1366908) in Section 6.\n",
    "\n",
    "*The work on this vignette was supported by the European Research Council, grant AdG 694262.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we import the package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import apc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Turn off a FutureWarnings\n",
    "import warnings\n",
    "warnings.simplefilter('ignore', FutureWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create a model and attach the Taylor and Ashe (1983) data to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = apc.Model()\n",
    "model.data_from_df(apc.loss_TA(), data_format='CL')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deviance Analysis (Table 2)\n",
    "\n",
    "We first consider a deviance analysis. We start with an over-dispersed Poisson model with an age-period-cohort predictor and look for reductions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>deviance</th>\n",
       "      <th>df_resid</th>\n",
       "      <th>P&gt;chi_sq</th>\n",
       "      <th>LR_vs_APC</th>\n",
       "      <th>df_vs_APC</th>\n",
       "      <th>F_vs_APC</th>\n",
       "      <th>P&gt;F</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>APC</th>\n",
       "      <td>1.39552e+06</td>\n",
       "      <td>28</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AP</th>\n",
       "      <td>1.78058e+06</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>385058</td>\n",
       "      <td>8</td>\n",
       "      <td>0.965737</td>\n",
       "      <td>0.481777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AC</th>\n",
       "      <td>1.90301e+06</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>507496</td>\n",
       "      <td>8</td>\n",
       "      <td>1.27281</td>\n",
       "      <td>0.296797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC</th>\n",
       "      <td>6.86273e+06</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.46721e+06</td>\n",
       "      <td>8</td>\n",
       "      <td>13.7119</td>\n",
       "      <td>7.48102e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ad</th>\n",
       "      <td>2.26976e+06</td>\n",
       "      <td>44</td>\n",
       "      <td>NaN</td>\n",
       "      <td>874238</td>\n",
       "      <td>16</td>\n",
       "      <td>1.09631</td>\n",
       "      <td>0.402678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pd</th>\n",
       "      <td>7.99075e+06</td>\n",
       "      <td>44</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.59523e+06</td>\n",
       "      <td>16</td>\n",
       "      <td>8.27051</td>\n",
       "      <td>8.24632e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cd</th>\n",
       "      <td>7.80787e+06</td>\n",
       "      <td>44</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.41235e+06</td>\n",
       "      <td>16</td>\n",
       "      <td>8.04118</td>\n",
       "      <td>1.10465e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>2.47405e+06</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.07853e+06</td>\n",
       "      <td>17</td>\n",
       "      <td>1.27294</td>\n",
       "      <td>0.277883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P</th>\n",
       "      <td>9.7658e+06</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.37028e+06</td>\n",
       "      <td>17</td>\n",
       "      <td>9.87901</td>\n",
       "      <td>9.8804e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>8.59758e+06</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.20206e+06</td>\n",
       "      <td>17</td>\n",
       "      <td>8.50022</td>\n",
       "      <td>5.02329e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t</th>\n",
       "      <td>8.89773e+06</td>\n",
       "      <td>52</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.50221e+06</td>\n",
       "      <td>24</td>\n",
       "      <td>6.27192</td>\n",
       "      <td>4.29218e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tA</th>\n",
       "      <td>9.09618e+06</td>\n",
       "      <td>53</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.70066e+06</td>\n",
       "      <td>25</td>\n",
       "      <td>6.18031</td>\n",
       "      <td>4.50108e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tP</th>\n",
       "      <td>1.06557e+07</td>\n",
       "      <td>53</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.26014e+06</td>\n",
       "      <td>25</td>\n",
       "      <td>7.4319</td>\n",
       "      <td>6.4688e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tC</th>\n",
       "      <td>9.67492e+06</td>\n",
       "      <td>53</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.27941e+06</td>\n",
       "      <td>25</td>\n",
       "      <td>6.6448</td>\n",
       "      <td>2.12562e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06995e+07</td>\n",
       "      <td>54</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.30395e+06</td>\n",
       "      <td>26</td>\n",
       "      <td>7.17987</td>\n",
       "      <td>8.43731e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        deviance df_resid P>chi_sq    LR_vs_APC df_vs_APC  F_vs_APC  \\\n",
       "APC  1.39552e+06       28        0          NaN       NaN       NaN   \n",
       "AP   1.78058e+06       36      NaN       385058         8  0.965737   \n",
       "AC   1.90301e+06       36      NaN       507496         8   1.27281   \n",
       "PC   6.86273e+06       36      NaN  5.46721e+06         8   13.7119   \n",
       "Ad   2.26976e+06       44      NaN       874238        16   1.09631   \n",
       "Pd   7.99075e+06       44      NaN  6.59523e+06        16   8.27051   \n",
       "Cd   7.80787e+06       44      NaN  6.41235e+06        16   8.04118   \n",
       "A    2.47405e+06       45      NaN  1.07853e+06        17   1.27294   \n",
       "P     9.7658e+06       45      NaN  8.37028e+06        17   9.87901   \n",
       "C    8.59758e+06       45      NaN  7.20206e+06        17   8.50022   \n",
       "t    8.89773e+06       52      NaN  7.50221e+06        24   6.27192   \n",
       "tA   9.09618e+06       53      NaN  7.70066e+06        25   6.18031   \n",
       "tP   1.06557e+07       53      NaN  9.26014e+06        25    7.4319   \n",
       "tC   9.67492e+06       53      NaN  8.27941e+06        25    6.6448   \n",
       "1    1.06995e+07       54      NaN  9.30395e+06        26   7.17987   \n",
       "\n",
       "             P>F  \n",
       "APC          NaN  \n",
       "AP      0.481777  \n",
       "AC      0.296797  \n",
       "PC   7.48102e-08  \n",
       "Ad      0.402678  \n",
       "Pd   8.24632e-07  \n",
       "Cd   1.10465e-06  \n",
       "A       0.277883  \n",
       "P     9.8804e-08  \n",
       "C    5.02329e-07  \n",
       "t    4.29218e-06  \n",
       "tA   4.50108e-06  \n",
       "tP    6.4688e-07  \n",
       "tC   2.12562e-06  \n",
       "1    8.43731e-07  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit_table('od_poisson_response')\n",
    "model.deviance_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we see that the age-period-cohort deviance is an extremely unlikely draw from a $\\chi^2_{28}$ so a Poisson model is clearly rejected. Thus, we look at the $F$-tests in the column ``F_vs_APC`` and the corresponding p-values. We limit ourselves to nested models that cannot be rejected at the 5% level.\n",
    "\n",
    "*Remark:\n",
    "The nesting is nicely illustrated in the following figure, taken from [Nielsen (2014, Figure 5)](http://www.nuffield.ox.ac.uk/economics/papers/2014/apc_deviance.pdf):*\n",
    "\n",
    "<img src=\"https://user-images.githubusercontent.com/25103918/42902938-3fc5c6bc-8a9e-11e8-94b6-7406f9a42c29.png\" alt=\"Nested Sub-Models\" width=\"400\"/>\n",
    "\n",
    "*Nielsen (2014) also discusses the individual sub-models and provides their specific parameterizations.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AP</th>\n",
       "      <td>1.78058e+06</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>385058</td>\n",
       "      <td>8</td>\n",
       "      <td>0.965737</td>\n",
       "      <td>0.481777</td>\n",
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       "      <th>AC</th>\n",
       "      <td>1.90301e+06</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>507496</td>\n",
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       "      <th>Ad</th>\n",
       "      <td>2.26976e+06</td>\n",
       "      <td>44</td>\n",
       "      <td>NaN</td>\n",
       "      <td>874238</td>\n",
       "      <td>16</td>\n",
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       "      <th>A</th>\n",
       "      <td>2.47405e+06</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.07853e+06</td>\n",
       "      <td>17</td>\n",
       "      <td>1.27294</td>\n",
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      ],
      "text/plain": [
       "       deviance df_resid P>chi_sq    LR_vs_APC df_vs_APC  F_vs_APC       P>F\n",
       "AP  1.78058e+06       36      NaN       385058         8  0.965737  0.481777\n",
       "AC  1.90301e+06       36      NaN       507496         8   1.27281  0.296797\n",
       "Ad  2.26976e+06       44      NaN       874238        16   1.09631  0.402678\n",
       "A   2.47405e+06       45      NaN  1.07853e+06        17   1.27294  0.277883"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.deviance_table[model.deviance_table['P>F'] > 0.05]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The models not rejected at the 5% level include the age-period (AP), age-cohort (AC), age-drift (Ad) and age (A) model. Only the AP and AC model are immediately nested in the APC model with the Ad and A model nested in both of them.\n",
    "\n",
    "When it comes to forecasting, the age-cohort model has several advantages over the age-period model. Since is does not include a period effect, it does not require parameter extrapolation. Further, in a run-off triangle, the situation we have here, the age-cohort model replicates the chain-ladder point forecasts. Thus, we now take the age-cohort model as the primary model. We can then see what models we can reduce the age-cohort model to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>deviance</th>\n",
       "      <th>df_resid</th>\n",
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       "      <th>LR_vs_AC</th>\n",
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       "      <th>Ad</th>\n",
       "      <td>2.26976e+06</td>\n",
       "      <td>44</td>\n",
       "      <td>NaN</td>\n",
       "      <td>366742</td>\n",
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       "      <td>0.867225</td>\n",
       "      <td>0.552461</td>\n",
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       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>2.47405e+06</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>9</td>\n",
       "      <td>1.20028</td>\n",
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      "text/plain": [
       "       deviance df_resid P>chi_sq LR_vs_AC df_vs_AC   F_vs_AC       P>F\n",
       "Ad  2.26976e+06       44      NaN   366742        8  0.867225  0.552461\n",
       "A   2.47405e+06       45      NaN   571039        9   1.20028   0.32489"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit_table('od_poisson_response', reference_predictor='AC')\n",
    "model.deviance_table\n",
    "model.deviance_table[model.deviance_table['P>F'] > 0.05]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Age-drift and age model are (still) the only feasible reductions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Remark (not in paper): we can also consider the age-period model as the new primary model and see what reductions are feasible. This yields the same reductions:*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Ad</th>\n",
       "      <td>2.26976e+06</td>\n",
       "      <td>44</td>\n",
       "      <td>NaN</td>\n",
       "      <td>489180</td>\n",
       "      <td>8</td>\n",
       "      <td>1.23629</td>\n",
       "      <td>0.306831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>2.47405e+06</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
       "      <td>693476</td>\n",
       "      <td>9</td>\n",
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      "text/plain": [
       "       deviance df_resid P>chi_sq LR_vs_AP df_vs_AP  F_vs_AP       P>F\n",
       "Ad  2.26976e+06       44      NaN   489180        8  1.23629  0.306831\n",
       "A   2.47405e+06       45      NaN   693476        9  1.55787  0.165612"
      ]
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     "execution_count": 7,
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   ],
   "source": [
    "model.fit_table('od_poisson_response', reference_predictor='AP')\n",
    "model.deviance_table\n",
    "model.deviance_table[model.deviance_table['P>F'] > 0.05]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we take the age-drift model as the primary model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>deviance</th>\n",
       "      <th>df_resid</th>\n",
       "      <th>P&gt;chi_sq</th>\n",
       "      <th>LR_vs_Ad</th>\n",
       "      <th>df_vs_Ad</th>\n",
       "      <th>F_vs_Ad</th>\n",
       "      <th>P&gt;F</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>2.47405e+06</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
       "      <td>204296</td>\n",
       "      <td>1</td>\n",
       "      <td>3.96035</td>\n",
       "      <td>0.0528199</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      deviance df_resid P>chi_sq LR_vs_Ad df_vs_Ad  F_vs_Ad        P>F\n",
       "A  2.47405e+06       45      NaN   204296        1  3.96035  0.0528199"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit_table('od_poisson_response', reference_predictor='Ad')\n",
    "model.deviance_table\n",
    "model.deviance_table[model.deviance_table['P>F'] > 0.05]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can still just about not reject the age model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taken together, these results replicate Table 2 in the paper."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter Estimation and Uncertainty (Table 3, Figure 1)\n",
    "\n",
    "We move on look at the parameter uncertainty of both Poisson and over-dispersed Poisson models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we fit an over-dispersed Poisson age-period-cohort model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.fit('od_poisson_response', 'APC')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As part of the estimation, the package attaches a parameter table to the model. This includes parameter estimates, standard errors, $t$ statistics and p-values compared to a $t$ distribution. We take a look at the first couple rows before recreating Table 3 from the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>std_err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>level</th>\n",
       "      <td>12.787864</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>slope_age</th>\n",
       "      <td>0.697764</td>\n",
       "      <td>0.435277</td>\n",
       "      <td>1.603033</td>\n",
       "      <td>0.120150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>slope_coh</th>\n",
       "      <td>0.111482</td>\n",
       "      <td>0.449524</td>\n",
       "      <td>0.247999</td>\n",
       "      <td>0.805945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_3</th>\n",
       "      <td>-0.895632</td>\n",
       "      <td>0.220082</td>\n",
       "      <td>-4.069533</td>\n",
       "      <td>0.000349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_4</th>\n",
       "      <td>0.013571</td>\n",
       "      <td>0.203554</td>\n",
       "      <td>0.066668</td>\n",
       "      <td>0.947320</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                coef   std_err         t     P>|t|\n",
       "level      12.787864       NaN       NaN       NaN\n",
       "slope_age   0.697764  0.435277  1.603033  0.120150\n",
       "slope_coh   0.111482  0.449524  0.247999  0.805945\n",
       "dd_age_3   -0.895632  0.220082 -4.069533  0.000349\n",
       "dd_age_4    0.013571  0.203554  0.066668  0.947320"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.parameters.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To recreate Table 3, we further need to estimate an over-dispersed Poisson age-cohort model, and a Poisson age-period-cohort and age-cohort model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_ac = model.clone() # this creates a model object with the data already attached\n",
    "model_ac.fit('od_poisson_response', 'AC')\n",
    "\n",
    "model_apc_pois = model.clone()\n",
    "model_apc_pois.fit('poisson_response', 'APC')\n",
    "\n",
    "model_ac_pois = model.clone()\n",
    "model_ac_pois.fit('poisson_response', 'AC')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a Poisson model, the parameter table includes $z$ scores and p-values compared to a normal rather than a $t$ distribution. We look at the first couple rows of the Poisson age-period-cohort model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>std_err</th>\n",
       "      <th>z</th>\n",
       "      <th>P&gt;|z|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>level</th>\n",
       "      <td>12.787864</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>slope_age</th>\n",
       "      <td>0.697764</td>\n",
       "      <td>0.001950</td>\n",
       "      <td>357.874970</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>slope_coh</th>\n",
       "      <td>0.111482</td>\n",
       "      <td>0.002014</td>\n",
       "      <td>55.365525</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_3</th>\n",
       "      <td>-0.895632</td>\n",
       "      <td>0.000986</td>\n",
       "      <td>-908.517521</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_4</th>\n",
       "      <td>0.013571</td>\n",
       "      <td>0.000912</td>\n",
       "      <td>14.883527</td>\n",
       "      <td>4.216704e-50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                coef   std_err           z         P>|z|\n",
       "level      12.787864       NaN         NaN           NaN\n",
       "slope_age   0.697764  0.001950  357.874970  0.000000e+00\n",
       "slope_coh   0.111482  0.002014   55.365525  0.000000e+00\n",
       "dd_age_3   -0.895632  0.000986 -908.517521  0.000000e+00\n",
       "dd_age_4    0.013571  0.000912   14.883527  4.216704e-50"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_apc_pois.parameters.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can combine the resulting parameter tables. We recall that the parameter estimates are identical for over-dispersed Poisson and Poisson model.\n",
    "\n",
    "*Remark: The standard errors do not exactly match those in the paper but give the same impression. This is due to a former bug in the software.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"3\" halign=\"left\">apc model</th>\n",
       "      <th colspan=\"3\" halign=\"left\">ac model</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>se N</th>\n",
       "      <th>se t</th>\n",
       "      <th>coef</th>\n",
       "      <th>se N</th>\n",
       "      <th>se t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>level</th>\n",
       "      <td>12.787864</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>12.506405</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>slope_age</th>\n",
       "      <td>0.697764</td>\n",
       "      <td>0.001950</td>\n",
       "      <td>0.435277</td>\n",
       "      <td>0.912526</td>\n",
       "      <td>0.000649</td>\n",
       "      <td>0.149217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>slope_coh</th>\n",
       "      <td>0.111482</td>\n",
       "      <td>0.002014</td>\n",
       "      <td>0.449524</td>\n",
       "      <td>0.331272</td>\n",
       "      <td>0.000669</td>\n",
       "      <td>0.153916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_3</th>\n",
       "      <td>-0.895632</td>\n",
       "      <td>0.000986</td>\n",
       "      <td>0.220082</td>\n",
       "      <td>-0.866222</td>\n",
       "      <td>0.000962</td>\n",
       "      <td>0.221149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_4</th>\n",
       "      <td>0.013571</td>\n",
       "      <td>0.000912</td>\n",
       "      <td>0.203554</td>\n",
       "      <td>0.020862</td>\n",
       "      <td>0.000900</td>\n",
       "      <td>0.206944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_5</th>\n",
       "      <td>-0.642054</td>\n",
       "      <td>0.001030</td>\n",
       "      <td>0.229913</td>\n",
       "      <td>-0.657887</td>\n",
       "      <td>0.001021</td>\n",
       "      <td>0.234774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_6</th>\n",
       "      <td>0.258904</td>\n",
       "      <td>0.001403</td>\n",
       "      <td>0.313113</td>\n",
       "      <td>0.235501</td>\n",
       "      <td>0.001395</td>\n",
       "      <td>0.320795</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_7</th>\n",
       "      <td>0.256459</td>\n",
       "      <td>0.001797</td>\n",
       "      <td>0.401251</td>\n",
       "      <td>0.268782</td>\n",
       "      <td>0.001790</td>\n",
       "      <td>0.411596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_8</th>\n",
       "      <td>-0.294147</td>\n",
       "      <td>0.002228</td>\n",
       "      <td>0.497467</td>\n",
       "      <td>-0.301633</td>\n",
       "      <td>0.002221</td>\n",
       "      <td>0.510595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_9</th>\n",
       "      <td>0.705788</td>\n",
       "      <td>0.002865</td>\n",
       "      <td>0.639509</td>\n",
       "      <td>0.791901</td>\n",
       "      <td>0.002855</td>\n",
       "      <td>0.656359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_age_10</th>\n",
       "      <td>-1.759462</td>\n",
       "      <td>0.004753</td>\n",
       "      <td>1.061198</td>\n",
       "      <td>-1.793115</td>\n",
       "      <td>0.004744</td>\n",
       "      <td>1.090610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_3</th>\n",
       "      <td>0.046443</td>\n",
       "      <td>0.002669</td>\n",
       "      <td>0.595830</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_4</th>\n",
       "      <td>0.213822</td>\n",
       "      <td>0.001888</td>\n",
       "      <td>0.421402</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_5</th>\n",
       "      <td>0.211836</td>\n",
       "      <td>0.001513</td>\n",
       "      <td>0.337735</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_6</th>\n",
       "      <td>-0.405308</td>\n",
       "      <td>0.001264</td>\n",
       "      <td>0.282186</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_7</th>\n",
       "      <td>0.354415</td>\n",
       "      <td>0.001215</td>\n",
       "      <td>0.271149</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_8</th>\n",
       "      <td>-0.559004</td>\n",
       "      <td>0.001142</td>\n",
       "      <td>0.255047</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_9</th>\n",
       "      <td>0.556712</td>\n",
       "      <td>0.001195</td>\n",
       "      <td>0.266889</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_per_10</th>\n",
       "      <td>-0.075721</td>\n",
       "      <td>0.001102</td>\n",
       "      <td>0.246125</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_3</th>\n",
       "      <td>-0.365437</td>\n",
       "      <td>0.001127</td>\n",
       "      <td>0.251676</td>\n",
       "      <td>-0.341426</td>\n",
       "      <td>0.001105</td>\n",
       "      <td>0.254168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_4</th>\n",
       "      <td>-0.025435</td>\n",
       "      <td>0.001120</td>\n",
       "      <td>0.250134</td>\n",
       "      <td>-0.005005</td>\n",
       "      <td>0.001110</td>\n",
       "      <td>0.255236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_5</th>\n",
       "      <td>-0.009241</td>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.260439</td>\n",
       "      <td>-0.071485</td>\n",
       "      <td>0.001159</td>\n",
       "      <td>0.266410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_6</th>\n",
       "      <td>0.114695</td>\n",
       "      <td>0.001245</td>\n",
       "      <td>0.278036</td>\n",
       "      <td>0.137404</td>\n",
       "      <td>0.001238</td>\n",
       "      <td>0.284553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_7</th>\n",
       "      <td>0.053027</td>\n",
       "      <td>0.001291</td>\n",
       "      <td>0.288247</td>\n",
       "      <td>0.051371</td>\n",
       "      <td>0.001281</td>\n",
       "      <td>0.294620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_8</th>\n",
       "      <td>0.050816</td>\n",
       "      <td>0.001350</td>\n",
       "      <td>0.301344</td>\n",
       "      <td>0.078993</td>\n",
       "      <td>0.001341</td>\n",
       "      <td>0.308230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_9</th>\n",
       "      <td>-0.408218</td>\n",
       "      <td>0.001589</td>\n",
       "      <td>0.354779</td>\n",
       "      <td>-0.365524</td>\n",
       "      <td>0.001575</td>\n",
       "      <td>0.362043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dd_coh_10</th>\n",
       "      <td>0.101509</td>\n",
       "      <td>0.002549</td>\n",
       "      <td>0.568956</td>\n",
       "      <td>0.057498</td>\n",
       "      <td>0.002539</td>\n",
       "      <td>0.583742</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           apc model                       ac model                    \n",
       "                coef      se N      se t       coef      se N      se t\n",
       "level      12.787864       NaN       NaN  12.506405       NaN       NaN\n",
       "slope_age   0.697764  0.001950  0.435277   0.912526  0.000649  0.149217\n",
       "slope_coh   0.111482  0.002014  0.449524   0.331272  0.000669  0.153916\n",
       "dd_age_3   -0.895632  0.000986  0.220082  -0.866222  0.000962  0.221149\n",
       "dd_age_4    0.013571  0.000912  0.203554   0.020862  0.000900  0.206944\n",
       "dd_age_5   -0.642054  0.001030  0.229913  -0.657887  0.001021  0.234774\n",
       "dd_age_6    0.258904  0.001403  0.313113   0.235501  0.001395  0.320795\n",
       "dd_age_7    0.256459  0.001797  0.401251   0.268782  0.001790  0.411596\n",
       "dd_age_8   -0.294147  0.002228  0.497467  -0.301633  0.002221  0.510595\n",
       "dd_age_9    0.705788  0.002865  0.639509   0.791901  0.002855  0.656359\n",
       "dd_age_10  -1.759462  0.004753  1.061198  -1.793115  0.004744  1.090610\n",
       "dd_per_3    0.046443  0.002669  0.595830        NaN       NaN       NaN\n",
       "dd_per_4    0.213822  0.001888  0.421402        NaN       NaN       NaN\n",
       "dd_per_5    0.211836  0.001513  0.337735        NaN       NaN       NaN\n",
       "dd_per_6   -0.405308  0.001264  0.282186        NaN       NaN       NaN\n",
       "dd_per_7    0.354415  0.001215  0.271149        NaN       NaN       NaN\n",
       "dd_per_8   -0.559004  0.001142  0.255047        NaN       NaN       NaN\n",
       "dd_per_9    0.556712  0.001195  0.266889        NaN       NaN       NaN\n",
       "dd_per_10  -0.075721  0.001102  0.246125        NaN       NaN       NaN\n",
       "dd_coh_3   -0.365437  0.001127  0.251676  -0.341426  0.001105  0.254168\n",
       "dd_coh_4   -0.025435  0.001120  0.250134  -0.005005  0.001110  0.255236\n",
       "dd_coh_5   -0.009241  0.001167  0.260439  -0.071485  0.001159  0.266410\n",
       "dd_coh_6    0.114695  0.001245  0.278036   0.137404  0.001238  0.284553\n",
       "dd_coh_7    0.053027  0.001291  0.288247   0.051371  0.001281  0.294620\n",
       "dd_coh_8    0.050816  0.001350  0.301344   0.078993  0.001341  0.308230\n",
       "dd_coh_9   -0.408218  0.001589  0.354779  -0.365524  0.001575  0.362043\n",
       "dd_coh_10   0.101509  0.002549  0.568956   0.057498  0.002539  0.583742"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.concat([\n",
    "    pd.concat([\n",
    "        model.parameters['coef'],\n",
    "        model_apc_pois.parameters['std_err'].rename('se N'),\n",
    "        model.parameters['std_err'].rename('se t')\n",
    "    ], axis=1),\n",
    "    pd.concat([\n",
    "        model_ac.parameters['coef'],\n",
    "        model_ac_pois.parameters['std_err'].rename('se N'),\n",
    "        model_ac.parameters['std_err'].rename('se t')\n",
    "    ], axis=1)\n",
    "], axis=1, keys=['apc model', 'ac model'], sort=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the parameter estimates, replicating Figure 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0OvsBywEdeMLlcs2rtn0IsBDICqxa6XK5nmhWIw9zTGmGQg/CRahhGpawxQyJV5P9ohU4ULgeZB0SpJAIKZDCErhCCIJ/mtAOmttdIPZvqyX9e0vo/SpxG+TkCXp2gUiku2/5rZcirjClSZm3LDTATmIJjPAJIGIRw5Dsy/NTmJeEzd+WTu07AHlRtSlaDaz0JuMoT2X3T+UYtjISW3lo196kdbIekZtWPCBE1fg8U5pWSJC3DCAUnuHQHaT4UvAa3iqNXmj5cPnA6sCvv/7KqFGjmDx5Mr169Yq2OU2K0+nUgYeAPsBu4DOn0/mKy+X6rtquL7hcrjub3cAWRNBDGxSzhml5ZP3SH/LOBgVrcDnorS2zlVFQVmAVJLDEK5ZHtj51WQTUa13FrGI/hiHZm2dQlJeI5svgiDYdgPyIlN1sAtnpdA4HhgO4XC4yMzOb69QHxWazxYQdjSVer8OUJl6/NxQy4TN87HHvQUvWaKO1ibZ5dcLjNdiVZVJakEhre1syjwwM8DL1qH4n0W5gbTZB24RkIBnTkOz7pZKdopTE5EratjVIb62jaYdXK1CTaC73lbPXvZfC8kJrZZi3iFBbeWAjW31d+KsmNDS0kGdJQ0PTtNDAmuBrvInvJUuW8OWXXzJ06FBefvllunbtGm2TmpKzgZ9dLtevAE6ncx1wBVC9/h6WHBA+ELZsmvu9tYY08Et/FYFrShNg/3Ig5CBYbqjO1OCZDdabYA+QQ3fEtOOmJeOu8JOdrVNZ2opUezrtEm2QSETblWYTyC6X6zHgscBbmZcXXe8aQGZmJrFgR2OJh+uonjw8OCo2PEUMQEZGBkVFRVG2tnZK3QZZWRpGeWvSk1qTZNPwedwUeaztrVql1fqddOzYsSlNjJkGVtME6SlJQBJSQsHOSvbIMuxJFWS09ZORrqPr8SXWIkWwZ6QhIUNVYgprWH9Ad23Aw1XduxWse+HCOSikg703utBDIltDq3JcfWwNdjtXETPh3jtp1Gj7jt928PLLL9P3sr58+tGn3HjTjTzjeoa2mW1DdtpEYDyCph9U4MQRnYBdYe93A+fUsN/VTqfzfOBHYIzL5dpVfYf6OqeKK4utTEAHIejtBKp8vuHrw98fIDKFoNwox5ZsC33vNX3nUtYcdhBcH/57DsbTBj24QZFrEzaSRNIhr7cx2Gw2MjIymqz85iQersU0JfvyfOTl2JGVaXRKSUFPq/r78ngs55QWgSg2FWKhiDg1iuFqycPDc8/GC1JCTr6P/NxEhCeDNsmt0FJjtgGOWAML9WtkKyvB4xHYDnJ3aRPWOVBW7mN3cRGOVpW0aWvQrq2O3Va330U83NDrQqxeR3Wvmx9/FdEjpazild5Xvg8jwThA0AQ9dlWoJmZs2A7ZFT1n6hzsDjuz5s9i185dDLxyIOPvHs+al9aQkJiw30bpx4dvv51Bj7rYL+qD/8EBlcGBvuHbYqBXrqYbS7VHIV4F1rpcLo/T6RwBPANcWP2g+jqn9pTtqdPDT0io1mhozduCx2RkZFBYWBiXPRnhZGRkUFBQEG0zIkIsX0ul1yB7L5QVtSJZSyclyQEYlJYWH7Cvw2E5pw4lkOvqnIpUmre1QG8g0+l07gamuVyuJyNRtiK2MaWJx2/NpBMUw37pR0hRVQzH8aAkn99kz15JaWESSbQns1UCxH6vWsQaWKhfI5ufr1FcrKPXccxHEnZw29mb7+dnbxl6Ugmp6V7at9Vw2A/+u4nlG3p9UNdxaLJ2ZbHRtZFrb7wW3a5zzPHHMHPBTCaMmsBdt93FnKVz0BrgLgqPJw33RgIc1+E4fGUH96JCk/cA7Qa6hL3vDOwJ38HlcoUHWj4OzG9Kg6pTl5jaGjYAhB5IFIpDkV/oJzfHjlmZQVpiCkckN+9vJlJZLAZGohxFbGOYBl7DGxLDoTnWq4nhljJbXanbz549Gr6y1qQltaZ9q7ga5RvzDWx1WiXaaJWYDqRTUWDw074ytAQ3yake2rcTJDri6vNXRIinH3saTdMYPGxwaF2fS/uwZ/ceVixcQeejOnPnuPqH0WtCs0K8qqWIDMauRpnPgBOcTuexWINorwduCN/B6XR2cLlc2YG3lwPbm9dEhSLy+Pwme/eZFBckkWC2IyMlEVKiY4sKsVAcQHAWnaBn2JBGKEwiXAy31Fnq8gr95O5zICszadMqBb11XHYBxnUDm5Sgk5SQBqThKTX4JdeNcFhiOTNTkpykbl2HA3uz9/LKS69w5bVX0v7I9lW23TzsZnbt2MVT/3iKTl06McA5IEpWRh6Xy+V3Op13AluwstCscrlc3zqdzpnA5y6X6xXgbqfTeTngBwqAIVEzWKFoJCVug+wsDZ87dhxSqpU5zAnGC1cJkQjMohM+e05LEcNffPoFqampnNjjxCrr/YYke59BcX4SibIdbZMTIXZTLddKS2pgE+w67eytgdb4yk12/OBG2ty0P9Kg0uMnORmSkiwPcxyHMypq4NnHn0VKyZDbhhywTQjBfdPuI3tPNnOnzaVDpw70+nPLSf/mcrleB16vtm5q2PJEYGJz26VQRArDkGTnGhTnJ6L72pKenIQWQw4pJZAPE2rzCgdjwlryLDqbN23m/nvup8vRXdiweYM1mrrST9YeDU9JCqmO9Jh4ao0ULbGBtds0MlNTgVTSRDreshQKC/zsNTyYeNHtPnSHgW73k9zKtMRzoo7tMM2SEc/k5uSy0bWRy668jA6dOtS4j91uZ/6K+QwdOJTxd41n1bpVdD2xRad/UyjinlCKtpJkUh1poRRtsYYSyC0QwzTwmb7DxitcF97e8jZT751KRmYGO37bwXvvfkaHTudgVrYlPTGVtNjNRqE4BHabht3mILXaqEnph8o8PyXZPnzSA7oPm8OPZvPhSDBJTjZplSRISrC1eK/z9m3b2ZO1h4v6XhRtU+rFc088h2EY3DLilkPul5KSwvLHljP42sGMGj6Kp11P0659u2ayUqFQHArDkHh8Bl4fuMuhuMABHit8sXWMt7tKIMcxQa9wqaeUvIq8kEe4eqxwS/YK14bPMHlny/vcP24iXbudzJgpSxg7bAAb12xhyqSroxb8r2hahICkBBtJCTagah5Un9ukuNBPTjWvs2bz06qVQUqKIClRwx5naQhrIndfLnfcegelJaU899JzdD+pe7RNqhMF+QWsX7eefpf1o8tRXWrd/8gOR7LsH8sYdsMwxowYw+OrHyepVdPlv1UoDndMU+L1m3h9Ek8lVFSCx6MhTQ3TryMNHcOvg2lDFzbsmsPqAUywxUMWKEAJ5LggKISDscKGaYVHBBPsZyZkhjzEh5NXOIhhSCo8fsoroNyt4fVomIYdv9fGN19uZdmCSRx73CnMmv4iqalpXHjhNWzZ8jylpYWkpsbHjH2KyHFQr7MBlfl+9u7d73XW7X403URoBja7SaskiT1BkmAXJDhiO3TDNE2mjp+Kx+OhdVpr5s+Yz5Nrn2xQSrTmZvWq1Xg93lq9x+H0OLkHc5fOZdzIcUweN5mFKxei1zXXoEKhCOH1mXh9JpUeicejUVEBpqEhDRumoWEEBLBNs2HDgc2m47DppNmszDDYiesxPEGUQI4x/KYlhD2GJ5RGzW/6Q0n5daEfkFs4GDLRkjFNSYXHoKJC4i4PiGC/HcNnw/TZ0YWdRLuDRLuNVroADb769kNWLLqDo446kTkPuEhNTQOgX79BbNr0FO+8s54rrrgtylemiBUO5XUGMCollWUGJT6JX3ow8SOFH0030O0mQjfQNBO7wyQpySQhQWC3WYMMozFT4OpVq/n040+5/4H70XWd6ROms+mfm7j8qsub3Zb6UFRYxIvPv0ifS/tw7PHH1uvY8y88n3GTxrFw9kKWzlvKPZPvaSIrFYrIY5oSKcEMzJBpmtaUK6YpMQPz7ZjSmrTKMALrpMAfWJZSwzAkUgqkCYYJpmn1IsvAcZaCFSAF0rTWCyFITREUFiZg+nR0zY4mbdh1Gw67TqotMADaFvhPiM7n09y0fGUVowRzCntMT9U44UCyeps4/MIjTFNSXumnoMhPmRs8lbolgP02DJ8Nm3CQYEsgwa6TZNP2V9YaelK3bdvK9Ok30aHDMcyZ8yKpqemhbccffwonnHAamzev5vLLh8X1TE6K5kPXBUm6jaQEOKh7RFohHBUlJkVeAz9eTGmA5ke3GZaIthkIzSQhwSQpETSbl7JyPyCtOi+s6bkF1isCNPavrwvfffMdK5es5KJ+F3HFNVcgpeSlF15ixYIVXHDxBaS2To3QpxJ51j67lnJ3OUNHDm3Q8dfffD27d+1m7TNr6dylM9fffH2ELVTEO1KCYVqzPRqmDIhKiSmFJTwNERCh4DPANEBKgd9vCU6kVQ/Tck2KigPvpbVPUHBKiSVCJYEpmgRSisDr/m37xatVpiZ0rHtBoKdHisDEK9b02SIw1XvoPiFAE4HtGugiWI4IbQ9RfTmsMyk9MR1bUlGN7enhihLITUhwliaf6cNjePCaXitO2DQwpRkaMNfShbBhhMUqeSSVlaJarJKGYVhdNhnpGVSUJpGUYLO6a4JdNfWotNu3f87UqQNp164jc+euJy2t7QH79Os3iAcfvIfvv/+CHj3+GLFrVSisEA4t4Ik+iKtFgq/MpKzIwCxNpbg4ETMwNbM1Ua9EiMA7aQLCEtqAEBJEYFJEIa0GUEirCRWSygo3U+6ZQnp6O667eTo//mhHSsn1gycyeeyNzJ35CENG3IsQ7D9WSGw263hdFwhhWu8B3WY1vJoGWuAYTRNooVdxgHA3jKDtAY+YlCHvmDXdsMAwLaES8o5JQWlpKWufWce5f+lNYuqx7MzyV/GGWSJCouug6xJNB5su0TXLTl0HXYPho+5i184sFs9ZzJEdO9L74vMj/TW3WIqLodLj3//7CBA+fXRNUTr7pyEPOyZsOurwifMMPBQW+K3fvCkCYlXDNAOe02rfebiQtMq1zhj0hB5UnJrWfmbAW2rtawlVa/pxK3OTJUI1dKEBWuD3bv22hRDogeXEaoIzXUsHkVrzvKWKuCdmBXJ+ZT5SypB4FOwPK9DQAl4VDU3TQvO5h/6ECKus9fvlykAjJaXExAw8YVqC1pAGJtZr+H6SwHSl7J++VAa6SIJTmIanUWspIRHB0ak+P3g8Ek+loPIgQfqa0LHhwG7XDhmrlN46lSKz4bNY/fTT19x///Wkp7dj7twNtGnTvsb9eve+iscfn8qWLWuUQI5DKirK0DRJWVlJoI6LkFel6vtg/d//vvr2aPUgBIV0emoiwoic22bpI6PZl72TefM20qVNt9D6jG4d+Wv/wby+6Rmu6DeCY489mYAet4SqV1pCNiBmfVhetqCwBRNDmgH5boII3ANN633rNAclxa2wpIwWEN/778sEvGfWvVyA1MK+M+t7e2n9ctxlZVxz5SRkcZeDesMMn2WnYUo8gddQ93TgPj3k1ofI2jGQiWMmMWn6ao49/iTrYUCzHgiEMBEaCM36EIQmQZgIAemtdJI0M2LfSTxRlt0l1J7VRkiwVpvFXsoadg6nNI2SktSAAAWCPSSB93pYj0mN1fNgXlGFIoLErFIr95VX8ahWF6QhAQqhChJ6WhUgpAitD4rm6sveBC/57vwDRG6wbOtJ9ECRXlODGhTkutDjusJKaU31aAXpQ2WlxOfT8Hk1TFNDGjqmXztA+DrsOnabFtUg/V9/3cbkyU6Sk9OYN+8lMjNrzp0K0KpVCn/5ywDef38jw4fPolUrlc4ilpFSsmPH93z88WY++WQLP/zwZcTPUV0822x2brzxHq699q6In6up+PDDV3jzzee5/voxnHrqnw7YfvPNE/ngg1d46KEJLFz4yv77orBCSPRG3LzS09JJkg2v9OXlZWx69XHOPvsSTup+2iH3Ddp6yLOlJjN71lrGjLmUFQtHsmzZZtq161SrHaYJvrI0klrn1e8CWgg2XUNv4gwurZMdmL6W2WOqaDnErECuTsgrHGHxGS6YW2r2BynB6zPw+WVI9Ho8GobfEr2mX6sS5qBrNjRpw6bZLC+XrpNkC3z2wbjfGGPHjh+YNMlJQkIS8+ZtoH37zrUe06/fILZsWcN7771E//43N4MEW9IQAAAgAElEQVSVivpgGH6+/fYTPv54M1u3bmbv3h0AdOt2BjfcMI7MzCOpqCgPdOMHn5ZllffBZRkIBKx5mQP2B8nPP/+PVatmkZ7ejj59Yj+ONSdnNytWjKNbtzO58caaB6elpqZz661TWLZsDO++u54LL7y2ma08OJs2raK0tJAbbhgbsTIzMo5gxow1jBt3GVOn3sCiRZtITo7d+GuFQhE7xKDUUdSFYA5Cv1+C5mXPPl8V0Wt5esVBRW+iLTCyvgWkZNm9+xcmTrwaTdOYN+8lOnQ4pk7Hdet2Bscc04PNm1crgRwjlJeX8cUX77B162Y+/fQtysqKsNsTOO2087j22js555y+tG17JADp6ekUFRU1mS0+n5dp025g+fKxZGQcwZlnXtBk52oshmGwcOFIDMPgvvsewWY7eIXu02cgb7zxHE88MYNzzukXE4KxstLNSy89yhln9KZbtzMiWvYxx/Rg8uQnmTr1BubOHcb06asP+fkoFAoFKIEcM0gJfsPE4zXx+SU+H1RWCrxeDdMQYOoBb69u5SM0dWyazgfvbOSfG1bg9XkCI1nD467DQktqiMe01lOnfe12B/363UT//jfHVOOSnf07EyZchWmazJ+/kU6djqvzsUII+vUbxKOPTuaXX77h+ONPaTI7FQcnLy+brVut0Imvvvo3fr+X1NQ2nHPOJZx7bj/OOKM3SUnNHwJjtzuYPPkp7r33bzzwwK0sWPAKXbvG5m/E5VrOtm1bueeelbU+IGqaxsiR8xg9ui9r1ixg+PBZzWPkIXjjjecoLs5j4MDIeY/DOeOM3tx55wKWLx/Lww9P4K67FqnsNQqF4pAogRxBQiOykUjTGrltGBLDBE+lxOvTqKwMJNw2LZG738uroWt2hNSxCTsOu4ZN10jVA4Nd9MB/mDZdv34lTz45k549e9GlywmBgRHVu4oJdRnvXz5wXfWu5urrc3J28cgjE9m06Sluu20GZ50V/Wlrc3J2M2HC1Xi9lcyf/xJHH92t9oOqceGF1/DkkzPZvHk1d9wxvwmsVFRHSslvv33L1q1b2Lp1Mz/99DUAHTsey+WXD6VXr36cdNJZ6Hr0b0/JyanMnLmWsWP7M3XqQJYufYMjjqh9ZrfmZPv2z1m9eiG9e19V55CJE088jX79BvHyy09wySU3cMwxPZrYyoPj9Vayfv1DnHrqn+nZs1eTnadfv0FkZ/+Oy7WCDh2OiavYckXs4HaX8N13n/Htt1vZtesnWrVKpX37zrRv35l27TrRvn0X2rXrSEKCypfW3JimyY4d2znxxMhMNR/9Fugg/PJdGgZGKHWRNWrO2rY/NRGBQXTBfQhkfgmKPxnykAoRPtJWomlQWOKjoMAIJdI2w/IVIrVAom4RShtjpYmxtpvBdDFmcISglTpGoCG0qiO3dezYbJbgTbZpVkokK5tMg74BKSVPP/0ALtcKzj//SmbPXo3bXV7/gup5zq1bN/PEE9OZOnUgZ555AbfdNoOjj47O1LV5edlMmHAVbncx8+a9ZI3IbwCpqW34v/+7jHff3cDQodNITGwVYUsVAH6/j2+++ZhPPtnC1q1b2LdvJ0IIunU7g1tumcI55/TlqKNOjEmvXmZmB2bNWsu4cZdx//0DWbz41ZiZgdHtLmXBghG0a9eJO+9cUK/Pb8iQyfz735t45JFJzJv3UtQ++y1b1lBQsI977324yc81ePAk9u7dyapVszjyyGM477y/Nfk5FfFNQcE+vv32E7Zt28q2bVv5/ffvME0TTdM55pjuFBcXUFCwt4pzCSAtLTMgnDvRrl3nA5bT0trG5P0uXjEMg6VLR/Gf/7zGe++9S5cutQ/IrY2YFcitRFsSEyNYYLW0M9IPiZVppBrpVTeIaq8xNm7PMAweemg8b7zxHP37D2bkyHnY7Q6gaQWyEIJzz72UP/7xIjZtWsXzzy9m5MgLuPTSmxg0aDzp6ZlNev5wCgr2MXHi1RQV5TJnznq6dj21UeX163cT7767gX//+1Uuvvi6CFmpcLtL+PxzK574s8/ewu0uweFI5PTT/8L114/m7LP7kJFxRLTNrBNHH92dqVOfYfLk65g5czAPPODC4YjkDaphPPzwfeTkZLFo0SskJ7eu17GtW2cwZMgkHnzwXt5//5/07j2giaw8OD6flxdfXMlJJ53NH/7wf01+Pk3TGDduBXl5WSxadAeZmR1UmkdFCCkle/b8xrZtW/n2W0sQZ2f/DkBCQiu6dz+TgQPHcvLJvejR40yOPLITRUVF+P0+8vOz2bdvN7m5u8nJySInx1reufMnPv/8XTyeqm20w5EY8DiHe5/3L7dr1ynQtitqwzD8LFp0J++99xJDhkyjU6fGi2OIkEB2Op39gOVYcvIJl8s1LxLlNiXBtEbxhM/nZeHCkXz44Stcd91oBg+e2OxPoHa7gwEDRnDhhdeyZs0iXnvtad577yUGDhzL3/42FIejaeegLC7OZ9Kka8nN3cPs2evo3v3MRpd5yinn0qnT8WzevLpFCeTa6qXT6UwAngXOBPKB61wu1++NOWd2djYvvvgmb721hW+++Qi/30daWiZ/+tNfOffcfpx++vkkJiY35hRR49RT/8y4cQ8yf/7fWbToTiZMeAytphkTmol33nmRd95Zz6BB4+nR46wGldG37yA2b17NE09M4+yz+zR7usO33nqB3NwsRo1a3Gz3Mocjkfvvf4axY/szY8bNLF36ep0H9jYn0ai/hxuGYfDbb9+FxPC3335CYWEOYD1Annzy2fTvP5iePXvRteupBx1/Y7PZOeKIozjiiKNq3C6lpLS0kJycrICA3h0Q0Fnk5GTx6af/Cp03iBCCNm3a065dJxyOxGppKA/M9y6ERvVUlcE841XzwlfNAR887pJLnJx++oWR+mibDb/fx4IFt/Phh69wyy1TGDRoEhCZFI2NFshOp1MHHgL6ALuBz5xO5ysul+u7xpat2E9lpZvZs2/liy/eZdiw6Vx99cio2pOW1paRI+dy2WW38MQT03niiem89trTDB06jT/9qX+TNHalpYVMmnQt2dm/M2PGmojFK1qD9W7kySdnsnPnjxx11IkRKTea1LFeDgUKXS5XV6fTeT0wH2jUE8Ibb7zBwoX307lzV668cji9evWje/c/ousx1hXTQHr3HkB+fjZPPDGdzMwOURvglp39OytX3sfJJ5/D9dePbnA5uq5z++1zGTu2P2vXLmbo0GkRs7E2/H4fL7ywnBNPPJ0zzmjeDCHp6ZnMnPk8Y8b0Z+rUG1iy5LWYCZuB6NXflo7XW8mPP34V8hB/991nlJeXAtC+fWdOO+08evbsxcknW+N6IvUALISgdesMWrfOOOhAX6/XQ17enoBo3i+gc3Oz8Ho9yOAkZNXSVFqzU5o1rK85naX1X7Ws8vKygPd1Mk7n3XET+uHzeZk3bzgfffQ6t902g6uuuj2i5UfCg3w28LPL5foVwOl0rgOuAGJaIH/88RukpKRwyinnRduUWiktLWLatBv44YcvGT16GX373hBtk0IcddSJzJz5PF988Q6PPTaN2bNv4ZRT/sTw4bMiOuLf7S5h8uTr2LnzR6ZPf5bTTovs93bxxdfx9NNz2LJlNbfdNjOiZUeJutTLK4DpgeX1wEqn0ylcLldt82AdlCuvvJLu3XuTlNSNFqKJD+Cqq24nNzeLjRv/Qbt2nRgwYESznt8w/CxYcDuapnHvvQ83ejBjjx5/5JJLbmDjxn/Qp8/AZntAfPfdDezbt5MRIx6ISoPcuXNXpk59hkmTrmXWrFt44AFXLHVpR6X+tjTc7hK+/fZTvvvOiiH+4Yf/4vd7ATjqqG707j2Ak0/uRc+eveqUO78pcTgS6NjxWDp2PLbZz+31enjooXt5+ukHyMnZzciRc2NikPSh8Ho9zJkzjE8+2cKIEXO44ophET9HJD6BTsCusPe7gXMiUG6TsWHDwzzxxHQAzj//CkaOnEdaWtvoGnUQCgr2MXmyk927f2HSpCf4858vi7ZJNXLmmRfy8MPn88Ybz/Hccwu4++6Lufji6xkyZFKj40zLy8u4//7r+fXXbUyZ8hRnnhn5bqD09Hb06tWPt95yMXjw5CYPFWkG6lIvQ/u4XC6/0+ksBtrSiP6pjIwMjj46k5yc2veNV4QQ3HbbTPLy9vD449PIzOzIeedd3mznX7NmEd9//wUTJz4esYwat9wyhY8+eo1HHpnInDnrm1ywGobBCy8s47jjenLOOZc06bkOxSmnnMuYMctYuHAky5ePYdy4lcTIVKhRqb/NiZQSn8+D1+vB662ssuz1eqpt8x6wz/7lA4/3+Tzk5+/l99+3I6VE12107foHrrhiGD179uKkk86mdeuMaH8EMYPDkcC0aU+Tnt4el2sFeXnZTJz4j5gNh/N4Kpg9+xY+//wd7rxzAX/965AmOU8kBHJNd5MDnmCdTudwYDiAy+WKWBB1Y/ngg5f54IOXo21GnZg9+9Zom1Av/vWvtfzrX2sjWuaMGTdFtLyauOKK5knjVX3Uc4SpS72sU92F2K2/scCcOZH3XNSFuXNvY+7c2yJa5ldffUj//s07cLK5z3cw3n77Rd5++8U67x8v9VfVXavX5YcfvuCHH75gw4amz5YS73z66ZsMGND8nuyGsHLleFauHF+vY+padyMhkHcD4YqiM7Cn+k4ul+sx4LHAW5mVlXXIQj/91B7RLBamafLoo5N59dUn6dv3Ru66axFt27blv//9D4sW3cWvv27jwguvYcSIOaSmptdeYBPz22/fMWXKdfh8XmbNWnvI2aWaekaxhrJnz688+eRMPvroddq378wtt0zhL38ZcEjvVPi1eL2VTJ8+iK+//jf33vtIk4+yN02TW245i44dj2Hu3A2NKqtVqzS6do2qI6cu9TK4z26n02kD0oCCmgqrT/3NytLIydGbPMQiFn73JSUFjBt3GUVFuSxatKlBubjreh2lpUXccccF2O0OHnzw7YgPqDMMg7vv7kNJSQGPP/6fenuP6nodpmly++1/QQjBww+/F9WBjkGklCxZcjdvvfUC48atZNiw22jdumXU3/q2vf/9rz3iddc0TV5//RlWrZqJaUouv/wWHI4kHI5E7PYEHI6EGpYdOBwJ2O2JgXVV97HbE6L+24mFe1CkCL+Wjz9+g/nzR9CmTXtmz36hXhNwNSUVFWVMn34T27Z9zJgxy2scVO9wpHHiiXlE4qcRCYH8GXCC0+k8FsgCrgdiJ0gW6+lxyZK7eeed9Vx11e0MGzY9JNKOPfZkli3bzLp1S1m3bhlff/1vRo1aGtWJMLZv/4ypU28gIaEVCxe+0qBGNxbo2PE47r//af73v//w2GNTmT9/BC+//DjDh8+qNbWS1+th9uxb+eqrDxkzZnmzpKDSNI2+fW/guefmk539e0yObK8HdamXrwCDgY+Ba4B3VPxi/WjdOoNZs/ZPJLJkyeuhqbAjiZSSlSvvpaBgH4sXv9Yk2SZ0XWfkyLncc8/fWLduGUOGTI74OQD+85/X2LnzB+6779GoC5wgQgjuvnsxublZLF8+hlNP7cbFF58UTZNaTP3ds+dXli0byzfffMRpp53HqFFL6N79Dy1GWLZEzj33UubNe4lp0wYxdmx/pk9/rsGZciJFeXkZU6cOZPv2z7nnnoe44IKrm/ycjb47uVwuP3AnsAXYbq1yfdvYciOF11vJAw/cyjvvrOfmmydWEcdB7HYHN910H8uWbSYlJZ2pUweybNkY3O7SZrf3iy/eZeLEa2ndOoPFi1+NW3Eczqmn/pnly99kzJjl7Nu3i7Fj+zN//ghycnbXuL/f72PevNv47LO3uOuuRfTpc32z2dqnz0A0TWPLlueb7ZxNwcHqpdPpnOl0OoMBs08CbZ1O58/AWGBCdKyNb4488mhmzHiekpICpk69gfLysoif41//WscHH7zMzTdPoFu30yNefpCTTz6Hiy5ysmHDw+ze/UvEy5dSsm7dEjp1Op7zzrsi4uU3Bmtq8VV06XICe/fWfG9qLlpC/TUMgw0bHmbkyAv49ddtjB69lDlz1nPkkUdH2zRFHeje/UyWLn2N5OTWTJhwNR999HrUbLEG6V/L999/wYQJ/2gWcQwgmjiO6mDIPXsOiMKoQiRCLMrLy5g5czBff/0ht98+l8svH1ple03dI16vhzVrFrJ+/UoyMzsyevQyTj/9/MYZUkc+/PAVFiy4naOO6sbs2eto06Z9nY6Lp26eiooyXnxxZSgO7KqrbsfpvIukJMsjlpKSwqRJ1/Phh6/U+J01B9OmDeLnn7/m2Wf/2+CRvHUJsejYsSPEyIigenLI+ns4hViE89lnbzN9+iBOO+08ZsxYc9CcqdWp7Tp27/6Fu+66iG7dzmDOnPVN7nUtLMxh2LBz6dHjj8yata7OA/bq8n1s3bqZGTNuZty4B2M257jP5+eEE9rWGmIRp/W31rY3EiEWO3Z8z9Klo/nhhy/p1asfd9wxn8zMDqHtsVZ3G0pLuQ44+LUUFeUxffpN/Pjjl4wYMafZ2+TS0iKmTLmOX3/dxoQJj/HnP//1kPvXJcSirnVXnz59ev2sjQzTS0sP7Z39/rcyyjxu3J4Kyr0VuH3luL3luH1uyv3llPvdVPjdlPvLqDDcVPjLqDDKqDTLqDBLySvJYvr9g/jh+/8yYvRMzu/bn0pKqaSESoqppBgSPBRV7LPWm6VUmGV4qaD7qWdwyml/4svP3uflfz7G3ryddDnhJDzSh9tbgdtTQZmngnKPl3JvJRU+LxVeD+UeLxVeP5VeP16fgcdr4vUZmIGHEF07+PfxxhvPsXjxXfTo8UceeMBVr6waiYmJVFZW1nn/aGK3O/jDH/6Piy66lvz8bDZteoo331xLamobjj66O4sW3ck772xg2LDpDBjw96jYmJTUis2bV9O166l06XJCg8qw2xPJyDj07IapqakAMxp0guhyyPpbWipwu7WIxIAdilj73XfqdByZmR3ZuPFRcnOzOPfcS+skLg91HT6fl2nTbqCiws3s2S5SUuo3W15DSEpKJiEhiVdfXcWxx55c57RvtX0fUkoWLhyJw5HIqFGLYya8ojpCaLRpk0hCQousv7W2vXv36g2uuz6fl3XrlrJgwe14PJWMHr2MwYMnkpycWmW/WKu7DaWlXAcc/FoSE1vRu/dV/P779/zzn//A4ynntNPOb5bUjCUlBUyadA2//76dKVOe4txzL631GF1PpG3bcg5lXl3rbswmujvx1Hzset08MNXJzcll6j13sPO3nSxcuYDeF/cGzGp7CTIydAoKBNbA36qe9O7dT6JPvzU8vORhnn/meb7/7t9MnzedM87aP1jONCWmtG78hikxzWDSbjAlmKb17/VKfF5BsUdDmgJp6EhTxzQ0TEPjtY2rcD2/iNNOv4Bx9z6GzZGCYci4m+mvPrRv35n77nuUyy8fxmOP3c/SpaN46qlZFBXlMXjwpKhOhHLWWReTkXEEmzevrlOFVCiC9O17A3l5WaxevZB27Tpx882N6/V+7rn5/PTT10yZ8hTt2nWMkJW187e/3cqWLWt47LH7OfPMC0hMbNXoMj///B1++ulrRo1aEvM5VhX158cfv2LZstH89tt39O59FX//+2zS0zOjbZYiAiQmtmLKlKd49NFJrF//ELm5exg7dkWTpkMtKspj0qRr2L37F6ZNe5Y//rH5Z/mL3btUA7Vh1q4sbh9yOwX5Bax4fAVn/+nsBpuQmJjI2EljuaDPBUybMI3hg4YzcPBARo4ZSVJSEpomAkHcgvpJeROwZrJZsXAFruefpc9f+3LftKkYMh+vN59Kj4bh1zBNDdOvIU0N09CRhgZSRxc2dOzY7RpJPgMpOeQTU6zSo8cfWbLkdd5/fyPPP78Ep/NOBgyI7iyBum6jT5+BvPjiCnJz9zSrMFHEPzfccA85OVmsXbuEdu06cemlDUtN+N//fsD69Svp3//mWrsVI42u2xg5ch7jx1+By7Wi0UJfSsnatYtp374zF13kjJCViljA46lg9eqFvPTSw6Snt2PatGfp1atftM1SRBhrEO882rfvzKpVsygo2Mf99z/dJFm/CgtzmDjxGvbu3cGMGas5/fS/RPwcdSF2BXID+PXnXxk5ZCQej4dHnnmEU/4QmZncTj/rdNa9so4VC1fw/NPP85/3/8P0edM59fRTG1ymYRg8cP8DvLz+ZZw3Orn3/nsP0uUoASPw7wPAZ5h4vSZ+A7weIKmMsspiTENDGnpAVFseakwbmtCx4cBm07DbNOy6hnaIcI/mRghB795X0bv3VTET09W37w288MIy3nzzeW688Z5om6OII4QQ3HXXQgoK9rJy5Xjatj2Ss8/uU68yiovzWbz4Tjp37hq1mR1POeVcLrjgatavf4iLL76uUTN8ffXVh2zf/jl33DEvlmarUzSSbdu2smzZGLKyfqFv3xsZNmw6KSlp0TZL0UQIIbj22rvIzOzIkiV3c889f2PWrLURnYUwP38vEydeTW5uFjNnPs+pp/45YmXXl9gMAmsA3/7vW4bdMAxTmjy+5vGIieMgrZJbMWH6BB55+hE8Hg9DBw5lxcIVeDyeepfl9XqZOHoiL69/mWF3DGP81PH1isez6xrJSTbSUmy0a2vj6M4Ojj9G54TjBSeeaNK9u5+Tenro+YcKepxawrE98jnyhD2kdtgFrXfitu+gmJ0UGVkU+LLJq8ghpyyPnJIi8kpLKS6rpKzCh8dnYJoxlzWoWejQ4RhOP/183nzzeQzDiLY5ijjDZrMzadITHHfcycyZcxs//PDfOh8rpWT58jEUFxcwfvyjEQlvaChDh07DZrPxj39MaVQ5a9cuISPjCC65JKYygCoaSEVFGQ8/PJHx46/A7/cxZ86LjB69VInjw4QLLria2bNfID8/mzFjLuWXX76JSLm5uVmMH38FeXl7mDVrXVTFMcSpQJZSIqXElCaGafDJx58w4uYRJKck8+jqRzmq61H4TB8+w4fX8OI1vfgMn7XO9OE3/RjSwDAN/KZ//76B/cL395t+TGmGZl45+09n88KmF7j86st55vFnGDRgEN99812dbS93lzN6+Gje3vI24yaN4/ZRtzdpsLuuC5ISdFon22jX1k6XjrZaxfQRXbOriOkidlJkVhXTuWXF5Je6KXF7qfD4MYyWJ6T79buJnJzdfPXV+9E2RRGHJCWlMGPGGtLTM5k27Ub27PmtTse9/vozfPzxZm69dQpdu0b2Qb++tG17JDfeeC+ffvovtm7d0qAytm3byjfffMQ119yJwxHB2Z8UUeHLL99jxIi/sGnTKv72t6E88sh7UesCV0SPP/zh/1i06FV03ca9917OF1+826jy9u3bxfjxV1BUlMcDD7jo2bNXhCxtODGb5i2nPAeJRCBCAjK4LBBoQkND47133mPUyFEcdfRRPLP6GTp06FBlvyrL1YRoZmYmeXlWKh8pJRJLdAdfDdOwBuBJA0MamJiY0gzt/+F7HzJr8iwK8gsYPHwwt9x+C3aHPbRdCGHNAy90dE2nqLCIUcNHsX3bdqbOmcplAy6LyIeZkZFBQUGNE6A1GcEwD49X4qkUVHoEfp+2f/BhIMRDSBsaNmzCgcOuYdd1bLa6zaQXbbxeDzfddBqnnHIuU6asqtexKs3b4Zfm7WDs3v0zY8f+ldat27B48WsHZKgJv44dO35g1KhL6NmzFzNnro1apgcpg4OQJV6flzGjLsbrrWTxsndwOBIxTYGUJiYGgTsnaWlplJQUIWXwzqshEMydPYidO7bz4MMfk5iYhBACTYjAmAnrNZjhJ7i+PiFgphkYJC1lyGbTlJgmSAwMaSIxQUjLZmkihAQhEZpECIkQJggQmjVg+6xTupDsOHR2gjitv3VK8xb82YXrg9LSIp54YhpvvbWOzp27cvfdSznppLMD+4WdoObZ6quQlpZOcXFRg77vWCJe7kF1oaHXkpeXzdSpA9m580dGjVrSoHkLsrN/Z8KEqykvL2H2bFejcr1HMs1bzMYgt29Vew7gjRs3Mnr0aE4++WRWr15NRkZGg88XLrxD1NLAX93/ai7600VMmzaNVY+sYuv7W1m2bBk9TuphebgDA/G8hpcdWTsYMWQEu3fuZu6Dczn/wvMxpVn1fHGEXdewJ2kkJ2FNcBrCDPz7AfAbEo/XwOOTeD3g8WiUe63Bh9LQMf0ahl8PCWlha4XHZ5Bgb2J1VQccjgQuvtjJyy8/TmFhTp3zUisU4XTu3JVp055l4sRrmD59EHPnbgiFTfj8Ju4KP+5KHx5PJXPn/Z2EhFbc9vfFlLh9IEzMwMM7ASkqxP53yEDmHExAWqIzKP4CywIsQYhEaIHtgX2FJgPvLYGoCatcTZdoGth0iU3AiHtGMXnUHWx5ez433TYMTbey7GjCGhwsBGS2lRQUFoTEtZSSb/+3jW/+9yHDR91Jh275SENY29if5UdKzQrlkuAzBYZhrQ+4RELiy3oNOEvCrs9ml+i6RNMFdk2i66DroOmga5Ztui7QNWENrK5FkEkpSW3jxXRH/KcQF4i0XZRVVA0r++Lj93lsxXyKCwsZcP1grr15GA5HApXsOKgQ0cR+oVxdMpupxZhGEX4pkCYYJkhpfdc1f+cCTBHIEhX87gL7VTtOIkLrkMHlwAObZj22ITUEmiXQsdLaCWH9RoIPcJoQaFr8ivfmIjOzAwsXvsoDD9zCkiV3k5ubxcCBY+vcM56V9SsTJlyFx1PB3Lkb6Nq14WO7Ik3MCuTaeOaZZ5g8eTK9evXiqaeeCua1a3bS09NZvnw5/fv357777uOvf/0ro0eP5o477sBut7zJWTuzGDpwKIWFhaxZs4Ze5/bCZ/jwGB48picU6mFiIqRA1/S4Fc7VsekCW5LNEtJVkARFNOwX0skpXnbtKqakUsfw6Zh+G36vDV04cGgJJC/r6dIAACAASURBVCXYsNua77Pp128QL730CG+99QLXXntXs51XEd8YhsTrN/D5TXymj/ZHdePvd8/noSVjeGD+LYyZvACbXWBPNkk6Ih1fUgFrli1jx+/fMXvpYrqe4UXT9oQEKBDytAkR8LRqWD7aiHjgxEGWLbp07MX7Wy7B9dyzXDvwb3Tq0umAfRITdBIdVR9s1zz5FGnpadw05DpaJTcsbeeh7VXiJdK0b2+iCet7LCwoZMHMBbz5+puc0O0EHnx8GT169mj0OTIyHBQk10d+HJiKtT6E94gEU7Ja7y0hbRhg+CVG4KHNMAQ+U+D3BwS5FJjB50gtkK7VFBheNyW+0oAYB0u0i5CwDxfwhK0XaIEHvGBvC6Gel+CDoSYCQj7Myx6s+zX1vEQzLWxyciozZjzP8uVjee65+eTmZnHHHfNrnSxp166fmDDhKvx+P/PmbeC443o2k8V1Iy4F8sqVK5k7dy4XX3wxjz76KElJB6ivZqdv376cddZZTJ48mYULF7JlyxaWLVuG3+/nxhtvxDAMXnzxRU491Xo6SrAlkGCrmkPQMA18po9Ko3J/rLRpBLoEBTZha5bk3NEgKKQz0hLACP4sTcCLlF4qPCVUVkKZG8ordQyfDdNvw/DZsIkEEmwOEux6xMVzly4n0LNnL7ZsWcM119zZYj9/Rd0wTYnXb+LzG/gMP4bwIaUfYTPQdAPdZiI0A1uiSWKCJDVJkmAXOBwaJ592HolJ41g0exH/XLuA+6bdhxA6GRl2vvz4Mza+sI7rbrqOS//aO9qXWSOjJ4zmw/c+ZPGcxSx5ZEmt+2/ftp3/vP8fRo4ZSavk6A00VNQfKSWbN21m4ayFuN1uRowawZDbhoRCCOONUC9CvVOy1sR+sZ6RAQUFvvodHexhITieCquXKNTzErZf2DrTBKTAb8hQz4thSEuQB7zwprm/1yUk2oVmifOAB14IESorKOpNKfDoHopK3Ng0K4WsTbfVq0212x2MG/cg7dt3Zu3aJeTlZTNp0uOhWXKrs2PH90ycaE0ZvWDBRo4+unu9PsfmIK4EspSSuXPn8tBDDzFgwACWLl0a8tLGAhkZGTzyyCP079+fiRMn0q9fPxISEkhJSWH9+vV07dr1kMf/P3v3HWdJVSZ8/Heq6oZO02F6Ug9JggpiRJKgohjQRQZ88QjCAi5BVlF0DYAomF8QdRcFURTEBUTOKmkVUYJEUUHXBOi7SJAJzExP7Hv7pgrvH1W35/bt2/nmfr6fT3+m7626Vad6+vR56tR5zrGtcKxy0hmfyOL5HnkvT9bL4gYurh9+lY5zbmdKQWfSoTMJA2NTLoZT3/l+lkxuG6OjAaMZi3TWIvBiuHmHwI1hEycZj5GMOXO+w37rW0/gq1/9IH/+868anlUrasv3A7J5j2whjxvkUU4BOwp+le1hxXwSPQH9HRCPBSTilRoQxWTjs44/6XieX/s81119HStWruDk009m44aNXHjOhezxwj04+xNn1/wa52rZ8mWc9v7T+MZXvsFD9z3EIa+fui5895vfpWdRD/pEmfe4lWxYv4GLLryIB375APu+fF8u+NIF7LHXHo0uVtsoBuvRqzqccWa97wMDLsPDKfKuTz4aEjmagdFctA6DaxN4Np5rj5s+NhG3cexwClmlFCeddC6Dg0Ncfvk5fOITR/PZz17PwMCyced6+unHOO+8d2HbNhdddNOcV6yttZYJkD3P45Of/CTXXXcdJ510El/84hebdqnSd7zjHRx00EGcf/75PPvss1x99dWsXDnxkeRM2ZZNh9VBR2x8T7nru+S8HAkngaWssRk3fHxswmC73VmWomvCEA4XcPG8DJmcG1bytEU+Z+F7MdxcjJ5YHx2Jmf36H3roO/jWt87nZz+7VgLkNpEv+GRyLi5ZPPLYMRc77mLHXHoGfAY7wtlfxt9UTR74zsbZnzibDc9v4OuXfJ0ly5Zw9x13k06lueL7V5BI1G5lqmo44ZQTuO3Ht3HJFy5h/4P3Jx6vPKfx//71f7n3rns5/QOnN2z4m5idIAj4wQ9+wGc/91lc1+Uj536E408+HrvW2baiaViWIhm3ScaBrvKtxfUYwiFkuYJHwYVMJiCXs8jkrbE1GA54wxE4XV1c/u//xoc//DbO+9R17LbrC4k7Nk8//Rc++cljSSQ6uOiim1i5cvc6X+XMtUSAXCgUOPvss7n11ls566yzOPfcc5v+UfeSJUu48sora3oOx3JwLIfBzkGInmAGQRAO03Cz48c3L4BhGuVsW9HdGaO7ExibOMDF8wo8PzzCho1JYl4v/d1TP/5NJjt54xuP5Y47rmdkZAs9Pf21LrqoguIf8UwhhxfkUbECthMGwclFHou7A7qSFolx42ZtqhEET8WyLD775c+yaXgTn/7YpwE454Jz2POFUz9hagaxeIxPXPAJPvDeD3DtVddy6r+eWnG/q664is6uTo4/+fg6l1DMleu6XHPNNbx4nxfz6S9+mp133bnRRRJNyrYVndFy8b3jRlAUc4tc9tn3AF6237f4t/d9mAs/fRTn/98v43lJvnjeB+nsWMSXv3wzK1bsVv/Cz0LTB8iZTIYzzjiDe+65h/PPP5/3v7+xyxA3O6UUcTtO3B7fs+P5XpgU6OXGze+8kHqbi2xbsXKZw8plLpu3rWfD8zH87CL6kj2TTkF3xBEn8t//fTX33PMjVq06vc4lFlPJFTyyOZcCOfyS3uBY0qVrsc9gB3QknLLHmo390xePx/nK5V/h/e99P3vsuQfvOuFdDS3PbBx0yEEc/tbDueqKq3j7UW9nxcoV47Y//eTT3HXHXZx8+sn09snCEa0iFotxww03kI1nceymDw1EC3jZy/flGnMNHzr9Q1zwkQ8Ri8fo7+/jS1//Bk7MYePIdvo6uuuaeD8bTV0LRkZGOOWUU/jNb37DxRdfzIknntjoIrUs27LptDrpjO3oLZXeZhjodRjoDcjkNrNm7Ray27rpiffRkRh/w7D77vvywhe+kjvuuI6jjjqtqX8uWusB4EZgN+AZQBtjtlTYzwOKSyD9wxhzVL3KOFdBACOjObLBCF5nmhSbGtobPB+Lehdx7Y+vZWBggC1bJvz3NLWPnPcRHrr/Ib72f7/GJZddMm7b1d+6mkQywYn/In+vW83g4CBrU1PPkyzEbOy0y05c/cOr+dgHPsbmTZv55jXfZPmK5UBANr+Z1Ws2s3mkky6rj+6O5lqGvmkD5E2bNnHCCSfwxBNPcPnll7Nq1apGF6ntzKW32VFO20xBV6ojYbPnC8D10qxbv50NmzpIBn0s6tqRMHnEESfy9a9/lL/+9XfsvferG1jaaZ0L3G2MuUhrfW70+pwK+2WMMa+ob9Fmz/cDRkZz5NQIia4M/Tt5DPTZDA52sHlz43uD5yOcwql5b7Yms2JoBaeeeSqX//vlPPzgwxx86MEAPPfsc9zxkzt4zynvoX9AhiIJIaCvv4/vXP8dfN8fN6Y9GQ/bXd/PsmHTaoaHk5Drob+zu6HT1hU1Zcuydu1ajj/+eFavXs3VV1/N4Ycf3ugiLSgz6W0em0mDoK2GaDi2Yuchh52HCgxvWcfG9XGC7CL6O7t5/euP4corP80dd1zX7AHyKuCw6PvvA/dSOUBuWp4XsD2ToWCNkOzKsWR3n95uOwomm/LP1oJz4qkncttNt3HJ5y/hxv++EQh7j2OxGP986j83uHStq52fAImFSyk1acKnZSmWL4mxfInHSHqY55/fQm6ki55474yT6WthXmfWWr8L+AywN3CAMebR+RZoeHiYY445hq1bt4aLahzU+PW4ReXe5nYPmgf7HQb7fVKjw6xbt4Ws282hhx7NfffdwhlnfJ6urqbNzl9mjFkHYIxZp7WebAnApNb6UcKsiouMMbfUrYQVFFyf7ZlRfCdFsjvH0Eqfni6Has0eIaorHo/z8U99nA+d/iGuv+Z69Hs0P731pxx7/LEMLhlsdPFmzI+Wnw7C5djC6TMbuwBJWz0BEmI2erocevYAz0uzbuN2NgyHyfR9XZ3U+2HbfEPzvwDvBL5dhbIAsHjxYo488khWrVo1tqiGaE6TBc1u4JIpZMYFzQAWVksGzd2dDnvtAQV3hDcd8ybuuusH/PxOwzuPrpzBXw9a67uA5RU2nT+Lw+xijFmrtd4duEdr/WdjzN8nOd8ZwBkAxhgGBycPgLJZyOUUzgz+uuQLPlszIwROiu4lBXZfpujq6AGmv/lwHGdey8s3i1a4jmIAWRxqBeF6X2896q0c/uPDueqbV/G3J/6GZVl84KMfoLt34uIAAQHFdcOUmvjvfBXLFxDgBd5YkFs8vqUsLGWN+97CGpsNyFb22Cqm8Vgcr8Ob5ow10/JPgISYL9tW7LTcYaflLttSG1i31sJNL6K3o4dErD5xhKrGIhNa63uBj82iBzlYu7bxiQCDg4MMDw83uhjz1uzXUQyas242XOxkiqB5YGCAzZs3N6qo0wqCgOPecRzKjnHBRTegcovo7+qasNRvZ2cve+459f/J0NAQ1GCmeK3134DDot7jFcC9xpgXTfOZa4CfGGN+NINTTFl/16yx2LDBZrLpU7N5j5F8ChVP07Mox5IlasISxTPR7L8rM1XL6wiCgIAgDB7xIYBABahAhf9SXKrWGhdIlgavlrLC4FGFwWMxiCxuW/3cat7whjeQzWY58cQTufjiiyecO2BH8Or7/ligXey99fHH9oMdAXnxdemxxspbGvRGZXGUg23ZOJYzFgAX952NmfxNrWH93WqM6St5vcUYM2FAt9baBf7ANE+Aym5u98vn81Oef9PoJgp+uDrcZD+3qXrYZ/IZx3YoeIUJvyPF/9/J3g/XZGasp7/4ulY3XdNxHAfXdWt+nnpohWspuD6r17lsHU7QwQB93ckJ++RyNgce6DLVMhnR/O3T/oLIYD5Rc0opYipGLB6jJ+oZLAbNOTdHxsuMBc15Lz+2QmAzUkpxjD6GS75wCXbwOEN77cHaNZtxR3ro6+htlulqbgNOBi6K/r21fAetdT8waozJaa0HgUOAL9eqQJmcy0guhd2Rpqcvz16DFvGYhfwJYmz2mIBgrPEHxn8fqRQAVHqvNGgsBomVgttqBBK77LILH/3oR7nssss466yzdpQ1KtOEZqj1HiJVXT2fABljrgSKk/IHM+lMcWpcL/sG+xgeHp7VUJYJQXPxxq9kiIyHV/Gmq/ge7BhSMy7QJvx9tdhx4zUT7XKTDq1zLb1d0NuVYtOW9Ty9IYaXXURvcsdUcfF4L8PDw1MGyNHN7bSmrQVTVWRjzISGd4rjzPgRbb04jtMU5ZivdrkOAF/5bE1sJVPIUPALYa+Q1VxB1AmnnMDXv/J1br/tdj7/5c+z687hUIF/rN7OyOYkPc5Ao/9PLgKM1vpU4B/AuwC01q8GzjTGnEaYN/BtrbUPWIQ9UI9XqwBBAKlMnnRhhHhnht7BAkOLLWL2wg6KPd8bG6JQfLS/KLEIP+GP6xUdC3jr3CM2V+9///v5+Mc/TjqdbnRRWoIx5k2TbdNar9daryh5ArRhkmOsjf59KnqK+0qg4hCpdjDpDdcclQ7J8QN/bLYmN3DxAm9CQF0abIf3sgF5L0/ey4+Vq5XqbKtb3O+wuD+cKm7d85vZvDWcKm6gijPFTdtSTVWRZ2Mud7G11uxDE2aqXa4Dwmvx0z4JEsSCGKOFUbYUtlDwCwQETTM38+FvOZxb/usWzjz7TDo6wnWuB3qhr2c7z29cS8AQw8NTd5XN9C52towxm4AJU79EQ6BOi77/FfDSWpw/sEfZzlYWr3DZta+4XPPCC4o938MjHAtbDIa7Yl0kneS43+PeZC+FeKHBpZ2/jo4OCZCro+meALUjpRS22vE3uny606kUg+uBngHiufi4IHqqoUPlveCTvVc6FKr8iVKxl1sC8FAybvOCXcDfKcvwltWM5vIolajKsRdeqyVahqUsuuPddMe7CYKAnJcjVUiR9/K4vjuWVNMIx7z7GG6/7Xbu+tldvOOd79hRZksxtCxGb18eCh0NKVujLerP88JuH0stnD8vfuCPJYYVx8B2Op0knSQxKyYNmZiNhj8BElMrBtcxOzarwHomphtKUvxbUx6Aj+vhZnwPuUKN5SAopcZmaikNtKuRj9ZIlqVYujhGT68LhTjVeNQw32nejgG+ASwBfqq1/oMx5q3zLpUQZZRSJJ0kSScclO/5HulCmoybIe/nIYCYHatbeV756ley6wt25WZz87gAWbS/YgNFECYbOZZDh9VBh9MhwbCYt0Y/ARKNVe2hJDAxWbcYPHuBF47dDjwSTgKlFK7v4vnegllNdyrzCpCNMTcDN1epLELMmG3ZLEosYlFiEUEQkHEzpN00eTePF3hjWey1opTi6HcdzaVfvpSnnnyK3ffcvWbnEo0TBMHYjCvFnuGkkyRpJ0nYiQXdeAghWkNp0G1PkiU72DkI0dpgxdV0M16GgrdjNd1mzAmqpaZIuRdiPpRSdMY6WdKxhJU9K1nRvYIOpwMCKHiFsSmLqu3IY47EiTnc8l8NXV9DVJnruxS8AgSQdJIs6Qx/r4a6h1jauZS+RB9JJynBsRCiLdmWTWesk8XJxSzvWs5OPTsx1D1Ef6J/LEAu+IWx4Y7tauHcCogFI2bF6E+G04b6gU+mEPUue3l8fGKqOo/BBxYP8PrDX89Pbv4JZ330rOLciqIFFadZi1tx+hJ9dMY6a/oEQgghWoljOThxhy66xt5z/XB9g9KpWttlJV2QAFm0OUtZdMW76IqHlTrn5tiW30bey1flUdEx+hjuvuNu7r3zXt7yT2+Z9/FEfRTn4VYoEk6CRfFFdDgd0isshBAz5FhOmEhPuHJmpZV0i1NbOqq2wx5rQQJksaAknARLnaVszW1lJD9CzJpfYt+BrzmQoZ2GuNncLAFykyvOdepYDgknwYAzQMKpznRAQgix0I0tCpbY0a4GQUDBL5BxM2TdLAW/0DLjmFsrnBeiSvoSfQwkBsIZMObBsixWHbuK3z78W577x3NVKp2oltLxxF2xLoa6hxjqHmJxcrEEx0IIUWNKKeJ2nN5EL8u6ltEd7w7/JrcACZDFgtUV72JJx5J5J/Ed9c6jsCyLW/9rxgtLihpyfZeCX0Ch6E/0s7JnJcu7l9Ob6G2ZngshhGhHfYk+FncsrlnyfDVJgCwWtA6ng+Wdy8OV+uY4UfrS5Us59LBDue2m2ygUmr/St5viI7zi8InBjkF26t6JZV3L6Ip3tdy4NyGEaGedsU6WdS4Lk/qaeIESaTnEghezY6zsXgkwtgrRbB39rqPZtHETD933UDWLJibhBz55L08QBCSd5NhURIMdgzIFmxBCNLm4HWeoe2hscZJmJAGyEISzXSzvWo5jOXOqrIe8/hCWLF3CzUbWzam1YpLHzot2ZkX3CvqT/fNOthRCCFFflrJY1rmMjlhHUwbJEiALEVFKsbRz6Zwqq+M4HPV/juJX9/+K9c+vr1EJFzbP9/B8j8GOQZZ2Lm2LeTaFEGIhU0qxOLmY3kRv041LlgBZiDKLk4tZFF8060zbVceuwvd9bv2RJOtVW97Lk4wlGeoeCldJFEII0TZ64j0MdgyODZ1rBhIgC1HBosQiBpIDswqSV+68kgMPOZBbf3QrnufVsHQLh+u7+IHPss5lLE4ulrHFQgjRpjqcDlZ2ryQgmHM+UDXJnEdCTKIr3oVjOWwY3YBjOTMKzo7Rx3Du2efy4H0PcsRrj6hDKSfSWr8L+AywN3CAMebRSfY7ArgUsIHvGmMuqlshpxEEAa7v0pPooTfeK4GxEEIsALZls6JrBRszG8n7eRzVuDBVepCFmELCSTDUPYSPP6M72sMOP4z+gX7MtaYOpZvUX4B3AvdPtoPW2gYuB94G7AMcr7Xepz7Fm5rruyilWN61nL5EnwTHQgixgBTzgbqcroaOS5YeZCGmUbyj3TC6Ac/3pkwOi8VjHHnMkTzwywfI5/PE4/E6ljRkjHkCQGs91W4HAE8aY56K9v0hsAp4vOYFnEQQBLiBS1+ij554T6OKIURDtcMTICGqoT/ZT9yKszm7mZhd/5mKJEAWYgaK09EMZ4bJ+bkpH/u874Pv49Nf/DRxr/7B8SysBErXxl4NHDjZzlrrM4AzAIwxDA4OTnrgWDZGPB+f1QIdBb9Awk6wpHPJjGencBxnynK0CrmO5tPgayk+Afr2ZDuUPAF6M2HdfURrfZsxpmE3uELUQle8i5gdY8PoBmxl1/WJogTIQsyQUoolnUvYkt1CqpCadO7djs4OLMuCGubpaa3vApZX2HS+MWYm02hU+iszaeqwMeZK4MrifsPDw5MeeHtuO6lCakYBsh+EQ1cGkgM4MYct2S3TfqZocHCQqcrRKuQ6ms9MrmVoaKgm527VJ0BC1Ercjs/4KW41zStA1lpfArwDyAN/B95rjNlajYIJ0az6k/04lsPW3NaGLVBhjHnTPA+xGti55PVOwNp5HnNWCl6BjlgHA8kBWQ5aiNmZ8ROg2Tz9qZd2edrQLtcBrXEtS4OlbBzdSMbNTNr2BipgsHewKj3N8+1BvhM4zxjjaq0vBs4Dzpl3qYRocj3xHhzLYTgz3KqruD0C7KW1fgGwBjgOeE89Tuz5HihY2rmUhJOoxymFaCr1fAI0m6c/9dIuTxva5Tqgda7FwsLNuWzOVR6X3NPbw/Dw8JQB8kyf/swrQDbG/KLk5a+BY+dzPCFaSYfTwbLOZawfXY+jZjYNXD1orY8BvgEsAX6qtf6DMeatWushwmSet0c3tWcBPydM8rnaGPNYrcuW9/P0xHpkdgqxoLXDEyAhGqU30UvMirEpu6mmHVTVHIP8L8CNk22Uxzy10y7XAa15Lcv8ZaxLrQPYMVTAgsHexlyHMeZm4OYK768F3l7y+nbg9nqUyQ1cbGyWdy4nbjd18qIQraBhT4CEaAadsU5iVoz1o+uxlFWTYXrTBsgzeRSktT4fcIHrJzuOPOapnXa5Dmjda0kEiXBicy+PYzn09vU2LMmnmQRBgBd4LIovYlFiUaOLI0TTa+YnQEI0k5gdY6h7iI2jGyn4BRyruvNOTHu06R4Faa1PBo4EDjfGNMcC2kLUWXFi803ZTWQKmUYXpym4vkvMirG0c2ndso6FaHXN+ARIiGZlKYulnUvZnNtc9bZ3vrNYHEGYlPd6Y8xodYokROtanFzMNrUNL6jhHG8twPVdFicX0xXvanRRhBBCtDGlFIuTixmxRnADt2rHnW9/9GVAArgzmrPx18aYM+ddKiFaWG+il96eXrZt2dboojREV6yL7ni3TN0mhBCibnriPfQuql7bO99ZLPasSimEaDONWBazWchwCiGEEI1QzbZXuniEEEIIIYQoIQGyEEIIIYQQJSRAFkIIIYQQooQKgobMzCbTwQkRasXl5KT+ChFqtfordVeI0LR1t1E9yKoZvrTWv2t0GeQ62vNaZnEdrajhP18W5u9KU3+1y3XM8lpaTcN/trTR70q7XEc7XUs1664MsRBCCCGEEKKEBMhCCCGEEEKUWOgB8pWNLkCVtMt1QPtcS7tcRzNrl5+xXEfzaadraUbt8vNtl+uA9rmWql1Ho5L0hBBCCCGEaEoLvQdZCCGEEEKIcSRAFkIIIYQQooTT6AI0itbaBh4F1hhjjmx0eeZKa90HfBfYl3COy38xxjzc2FLNntb6I8BphNfwZ+C9xphsY0s1M1rrq4EjgQ3GmH2j9waAG4HdgGcAbYzZ0qgytpt2qL/tUndB6q+YuXaou9A+9Vfq7uQWcg/y2cATjS5EFVwK3GGMeTHwclrwmrTWK4EPAa+Ofslt4LjGlmpWrgGOKHvvXOBuY8xewN3Ra1E97VB/W77ugtRfMWvtUHehDeqv1N2pLcgAWWu9E/BPhHd/LUtrvQh4HXAVgDEmb4zZ2thSzZkDdGitHaATWNvg8syYMeZ+YHPZ26uA70fffx84uq6FamPtUH/brO6C1F8xA+1Qd6Ht6q/U3UksyAAZ+A/gE4Df6ILM0+7ARuB7Wuv/0Vp/V2vd1ehCzZYxZg3wFeAfwDpgmzHmF40t1bwtM8asA4j+Xdrg8rSTdqi/bVF3QeqvmJV2qLvQJvVX6u7UFlyArLUujlf5XaPLUgUO8CrgCmPMK4E0LfgoUGvdT3jX9wJgCOjSWp/Y2FKJZtRG9bct6i5I/RUz00Z1F9qk/krdndqCC5CBQ4CjtNbPAD8E3qi1vq6xRZqz1cBqY8xvotc/Iqy0reZNwNPGmI3GmAJwE/CaBpdpvtZrrVcARP9uaHB52kW71N92qbsg9VfMTLvUXWif+it1dwoLLkA2xpxnjNnJGLMb4WD0e4wxLXnHZIx5HnhOa/2i6K3DgccbWKS5+gdwkNa6U2utCK+j5RIeytwGnBx9fzJwawPL0jbapf62Ud0Fqb9iBtql7kJb1V+pu1NYsNO8tZEPAtdrrePAU8B7G1yeWTPG/EZr/SPg94AL/A8ttOyl1voG4DBgUGu9GrgQuAgwWutTCf8IvatxJRRNquXrLkj9FQtWy9dfqbtTk6WmhRBCCCGEKLHghlgIIYQQQggxFQmQhRBCCCGEKCEBshBCCCGEECUkQBZCCCGEEKKEBMhCCCGEEEKUkGnehBCiBWmtHwM+YIy5dw6fDYC9jDFPVr1gQggAtNa7AU8DMWOM2+DiiFmSAFkIIVqQMeYljS6DEKJ+tNaHAdcZY3ZqdFkWAhliIYQQLURrLR0bQiwwUu/rTxYKaTNa63OB04GlwHPA+caYm7XWNvBlwqUXR4CvAt8gevSjte4Fvga8HfCB7wEXGmO8BlyGEG1Ja/0M8G3gn4EVwC3AvxpjslrrI4EvALsRLlt7pjHmTyWfuwI4AXgR0AU8CZxmjLlLa50ALgZ0dCoDnGOMyUWf/zjwb0AAfAq4ChliIcSsaK13Bi4F+xyaMwAAIABJREFUXkvYwXgD8CHgk4TtbgdwB/BBY8y2kiEWpwCfBzqBfzfGfDE63qT1tthbTNhOfwR4ADgSSACj0f4vNMasrd0VL2zSg9x+/k5YeXuBzwLXaa1XEFbetwGvAF4FHF32ue8TLjW5J/BK4C3AaXUqsxALyQnAW4E9gBcCn9Javwq4GngfsJgwiL4takCLjgf+CeirMJ7xfOAgwvr9cuAAwkAYrfURwMeANwN7AW+qzWUJ0b6iTqafAM8S3sSuBH5IGPyeArwB2B3oBi4r+/ihhDe2hwMXaK33jt6ftN5GlgMDwK7ASYRt+FpjTHf0JcFxDUmXfZsxxvxXycsbtdbnEVY6DVxqjFkNoLW+iLCyorVeRljx+owxGSCttf534AzChloIUT2XGWOeA9Baf5Gwh2gx8G1jzG+ifb6vtf4kYeN5X/Te14ufq+AEwl6rDdFxP0tYdz9NWPe/Z4z5S7TtM4TBthBi5g4AhoCPl9ygPhjVta8ZY54CiNrcv2it31vy2c9GbesftdZ/JAyGn2Dqegvh09wLS54E1fQCxXgSILcZrfVJhI9Sd4ve6gYGCSt2aeNa+v2uQAxYV1IBrbJ9hBDVUVqvniWsm7sCJ2utP1iyLR5tq/S5ckPRscqPW9z2u7JtQojZ2Rl4tsLTm0p1zwGWlbz3fMn3o4Tt8mSfLa3zG40x2fkUWsydBMhtRGu9K/Adwp7hh40xntb6D4AC1gGlma87l3z/HJADBmUqGiFqrrTu7QKsJayDXyyOTZzEVAkjawmD7MfKjgth3S8/pxBidp4DdtFaO2XtZLHuFe1COFxxPePb3Eqmqrcwsc5L0lgdSYDcXroIK9BGgOgRz77RNgOcrbX+KZAGzil+yBizTmv9C+CrWutPAyngBcBOxpj7EEJU0we01j8h7En6JHAjcBNws9b6LuC3hMk8hwH3G2NGZnDMGwjHMj9C+DfgAsIEHwjr/ve01v8JPANcWL1LEWLB+C3hzeZFWusLAQ/Yj7DunaO1/hlh2/sl4MYo+X26Y05VbytZDyzWWvcaY7bN62rEtCRJr40YYx4nnJ3iYcKK9FLgoWjzd4BfAH8C/ge4nfAutzhLxUmEj3QfB7YAPyLMshdCVNcPCOviU9HXF4wxjxIm0l5GWP+eJEz8makvAI8S1u8/A7+P3sMY8zPgP4B7ouPeU42LEGIhiWZ0egdhIvs/gNXAuwmTa68F7iecsSILfHCSw5SbtN5OUoa/EgbVT2mtt2qthybbV8yfTPO2QGmt3wZ8yxiz67Q7CyGqIpqu7TRjzF2NLosQQojJyRCLBUJr3UE4Dc0vCJMHLgRubmihhBBCCCGakAyxWDgU4bzIWwiHWDxBON5JCCGEEEKUkCEWQgghhBBClJAeZCGEEEIIIUpIgCyEEEIIIUQJCZCFEEIIIYQoIQGyEEIIIYQQJSRAFkIIIYQQooQEyEIIIYQQQpSQAFkIIYQQQogSEiALIYQQQghRQgJkIYQQQgghSkiALIQQQgghRAkJkIUQQgghhCghAbIQQgghhBAlJEAWQgghhBCihATIQgghhBBClJAAWQghhBBCiBISIAshhBBCCFFCAuQKlFJfUkqtV0oFSqlTlFKfUUo9WcfzX6OUuqvkdV3P3+rk5yWaXXkdr9M5D4v+pu1Uz/MK0YpmUl+krZ6fZv95SYBcRil1IHAecAawArgR+ApwUBWO7SqlTpnDR6ty/lpSSh0a/THZrdFlEUIIIRpA2uo24jS6AE1oL8APguDWsvdTk31AKWUBKggCrxYFCoIgNdX560kpFQ+CID+Pz8cANwiCoIrFEkIIIRpK2ur2Ij3IJZRS1wDXAlZ0hxVE7497DFB8rZR6t1Lqr0Ae2Fsp9RKl1M+VUluVUmml1BNKqX+OPvMMYAPfKz32DMs12flXKaX+Gp3rl0qpPco+t59S6hdKqZRSaqNS6ial1K4l218QvbdWKTWqlPpzsbwl+9yrlLpKKfV5pdQ6YE2F8u0GPBC9fDq6vnuLP1Ol1F1KqQ9GP4Mc0BVt+2BU/qxS6n+VUucrpZyS4z6jlPqcUupSpdTmaNjLV5RSdsk+CaXUFUqpbUqpLUqpK4DETH+2QjQDpdRxSqk/RHXhGaXU15RSxXpyevT73VH2mXOUUmuiG3SUUnsqpX4c/f3ZEtX9lzbieoSAsd7Kh5RSI9HXH5VSby3ZvixqIzZG2x9SSr2u7Bh7KKX+K2oDRpVSf1JKHVmy/e1Kqd8ppXJKqQ1KqW8W6060vdgGnaGUelYptV0pdatSaknZeT6olFodnePnwC5zuF5pq9uorZYAebyzgQ8DHuHwihVT7DsEvB84BdgHeBa4AdgEvAZ4KfBvwJZo//2j4354BseeiRXAvwInROfrA64ublRK7QPcBzwMvBp4Y3T+O5VSyWi3buBu4IiovFcSBvBvKDuXBpYAh0fHKfccsCr6/oCobO8s2X5A9LmjgZcDWaXUZ4CPEQ5n2ZvwZ/8+4MKyY38QWAccCHyI8Od3Usn2i4D/E713MJAGPlChjEI0JRUOu7oC+Crh35KTgDcB34p2MUCcsP6U+mfguiAIfKXUMuBBYAPwWsLHvH8D7i0PBISohyg4ug34DfCq6OszwGi0vQP4JdADvA14JXA7YRu1d7TPcuBXQD9wFGE79WnAj7a/LDrH/cArgJOBI9lRd4r2B94A/BNhe/cKwuEQxbKuAv4d+Fq0zQCXVOcnIW11pPXa6iAI5KvkizDgdcve+wzwZNlrH9ilbL9twClTHNudanvJftcAd01zfhdYUvLecVGZkiXH+GHZcROEf5yOnuLctwLfKXl9L/D/AGuaMh8KBMBuFa5lK9Bd8l5nVI4jyvY9Cdha8voZ4Layfe4Aboi+7wKywOll+zxa+vOSL/lqtq/SOh79np9Ztv11UX3qj17/EPhZyfZXRdtfEr3+DPDrsmMo4O/Ah6PXh0Wf2anR1y9f7f9FGNQGwGGTbD8FWA04Ze/fA/xH9P3ngeeBrkmOcS3w27L3VkVt4a7R62uAjUCiZJ9zgXUlrx8Eri87zlemqy9IW118/Qxt2FbLGOS5Wx8EwT/K3vsK8N2oR+hewl+Y39fo/GuDINhY8noNYYO4FPgH4R3znkqp8vFQScJx1iilOoELgHcQ3knGCSvmL8s+87sgCPx5lPWJIBybVfQSoAP4sRo/1MQGkkqpJSXX9oeyY60BXhB9v0dU3l+V7fMgYS+CEE0t6t3dFfiaUuorpZuif/cEHgH+E7hNKbU8CILnCXuPfxcEwWPRfvsD+1Wo7x1E9V2IegqCYItS6rvAz5VS9xD2kt4cBMHfol32B5YDW5VSpR9NAJno+/2AXwVBkJ7kNC8hDKhL3UdYf4pPdiFsg3Il+6wBlpW83ofwCXCpB4GPTn6FMyZtdYu21RIgz92EChsEweeVUtcTPgZ5I/BJpdSXgyD4VA3OXz74vvjLa5X8ey3hY41ym6J/LyG82/4o8FfCa/oq0Fu2/2R/nGaq/PPFMr6L8I633OaS7ytdZ/HzquQ9IVpR8Xf5bCY2dhD2sAH8nLAX7ASl1KXA8cCXyo5zN3BWhWNsq05RhZidIAhOj35f3wK8Gfi8UuqsIAi+Tfg7+wRwTIWPjpYeZrrTzOD9Su2IqvBeLUhb3aJttQTIVRYEwVPAN4FvKqXOBT4OFAPkPOGdVz08CrwM+HsQPcuo4HWEj5VuhLHZOF4IrJ/D+YqVYybX9xjh45bdgyC4fQ7nKnoyOu8hwOMl779mHscUom6CIFivlHoOeFEQBN+ZYj9PKfUDwkebTwADjO/xepTwkfWaIAgyE48gRGMEQfAX4C+ET0m+RTiF6rcJf2dPArYHQbBhko//DjhdKdU1SS/yY8Dry957PWEg9vjE3Sf1OGE78s2S9w6ZxefnQ9rqJiVJelWilOpWSl2ulHpjlHH6SsKe5NJfhqeBNyilhpRSgzUu0pcIB9Rfp5Q6ICrTG6Is092jff4GrIq270M48H9ojud7lnBc1duVUkuVUuV3tmOiRzhfAr6klDpLKfUiFc4AcpxS6uKZnjD6g/kt4AtKqaOi43wZePEcr0GIRjgf+JBS6lNKqX2j3+OjlVLfLtvv+4QN6RcJxyOXPra9jLDBu0Up9Vql1G4qnEHgi0qppm6ERHtS4awqF0e/h7sqpQ4mTCAttonXE7aJP1VKvSX6nT1QKXWeUqqYkPpNwjjlVqXUIVE7dqRS6m3R9kuAV6lw1pcXK6WOAL5BGEyWD4GcyleBdyulzlZK7aWUei/hMKZ6kLa6SUmAXD0uYVLCVYQ9PD8nvLt7T8k+HyUcU/U04ePSmgmC4AnCu7PuqCyPA98hHE+0NdrtI4SV5ZeEj2fXAD+a4/nWE2a5nkuYyVo+j3T5/p+Pzn8a8EfCsUgfIRzsPxvnArcQJWsQZghfPstjCNEwQRBcS5h9/k+Ev8OPECb3rCnb70+E4/xeQTgmuXTbesLM8GHgJsIG9XrC8c3ranoBQlSWJhxD+0PCx/M/JhyDehZAEARZwt7eR4HvRfvcRDiTwrPRPusIk8pGCGe4eIzwBlFF2/9EOLvF6wnbkWuBnwJnzqagQRDcTNg+fwL4E+GME+fM5aJnS9rq5qUm79EXQgghhBBi4ZEeZCGEEEIIIUpIgCyEEEIIIUSJec9iobXemXA83HLCgd9XGmMune9xhRBCCCGEaIRq9CC7wEeNMXsTLm/6Aa31PlU4rhBCCCGEEHVX9SQ9rfWtwGXGmDun2E0yA4UIlU9W3wqk/goRarX6K3VXiNC0dbeqC4VorXcDXgn8psK2MwgnCMcYQz5fvuhK7TiOg+u6dTvfbDVz+aRsczOTssXj8TqVpvrWrl3b6CII0VBDQ3Odhrax6ll3BwcHGR4ertv5ZquZyydlm5uZlG2mdbdqAbLWuptwnsMPG2O2l283xlxJOLk1QFDPH24z/2dCc5dPyjY31aykQgghhKivqsxiobWOEQbH1xtjbqrGMYUQQgghhGiEasxioYhWjzPGfG3+RRJCtKoLLriAxx9/fPodhWhi++yzD5/73OcaXQwhRANVY4jFIYRrlv9Za/2H6L1PGmNur8KxhWg5fuCTKWTqci6t9dXAkcAGY8y+0XuXAO8A8sDfgfcaY7ZW+OwzhEu4eoBrjHl1XQothBBCVFkQBFVte+cdIBtjHqT1MnmFqCrP90gVUmQKGQp+gX6nn26663Hqa4DLCOciL7oTOM8Y42qtLwbOA86Z5PNvMMZUbSC39LoJMX+VbnzLtivgUuDtwChwijHm9/UtpRCN5wc+6UKa0cIoBb9Aj9PDomARSs0/LK3qLBZCLCQFv0AqnyLrZin4BRzLwVIWMTuGbdlhv2yNGWPuj2aPKX3vFyUvfw0cW/uSCCGq6Bom3viWehuwV/R1IHBF9K8Qbc/1XVKFFNlClnyQx8bGtmwcy8FR1QtrJUAWYoaCICDn5UgVUuTcHF7gEbNiKKWI2007Zdu/ADdOsi0AfqG1DoBvRzPNVFQ+TePg4GDVCyqECFW68S2zCvhPY0wA/Fpr3ae1XmGMWVefEgpRX3kvz0hhhJybw/XdsQ6puKpd2ysBshBTCIKAjJshVUiR9/IEBDjKwbZsbOxGF29KWuvzCVe6vH6SXQ4xxqzVWi8F7tRa/9UYc3+lHRs5TaMQzajB0zSuBJ4reb06em9CgNzIm1vHcZr6ZrqZy7fQyxYEATk3x/b8drKFLL7j093RTY/qmfpzKmCwd1CGWAhRC37gM1oYJV1Ik/fDBW1iVgzHap3qorU+mXAM4+FRL9MExpi10b8btNY3AwcAFQNkIURTqdT6T1bPZQ2CSTRz+RZi2fzAJ+NmwrbXC9ve2ba7Pb09DA8PTxkg132hECFameu7pAvpsSQ7pRSO5RCzYo0u2qxprY8gTMp7vTFmdJJ9ugDLGDMSff8WQDLshGgNq4GdS17vBMjylqLleL4Xtr1u2PYGBE3TIdX4EgjRIAW/wPb89gljmmJ26wTFWusbgMOAQa31auBCwlkrEoTDJgB+bYw5U2s9BHzXGPN2YBlwc7TdAX5gjLmjAZcghJi924CztNY/JEzO2ybjj0WrKCbZZQoZCkFhXJJdM2mu0ghRQ5Ml2VnKauYkuykZY46v8PZVk+y7lnBaKIwxTwEvr2HRhBBzNMmNbwzAGPMt4HbCuvwk4TRv721MSYWYmZybI+Wm6ppkN18SIIu21spJdkKIhWmSG9/S7QHwgToVR4hZK3ZIFWeeKLa9rdQhJQGyaDvtkGQnhBBCtJLJkuxate1tzVILUaZ04vBWT7ITQgghWkEzJ9nNV+tfgViwCl6BTdlNLZ1kJ4QQQrQS13fZkt0SriLbxEl289VeVyPaWnmSXcpJkXfzLTWmSQghhGg1pUl2KSdFxs00fZLdfEmALJpaEASMuqNjY5pKk+zidrwqq+UIIYQQYofpkuwsZTW6iDUnAbJoOqVJdu02pkkIIYRoRsUku1Q+Rd7Po1AtnWQ3XwvzqkXTGZdkFxQWfMUUQgghaq08yQ6QBPeIRB+iYSZdyU5JxRRCCCFqwfVdRvIjbZ9kN1/y0xB1U5pkl3WzLTlxuBBCCNFqSpPsPN/Dtuy2T7KbLwmQRU1VSrKT8cRCCCFE7QRBQNbNMlIYoeAX8AN/rEPKsts/wa4aJEoRVSdJdkIIIUR9+YFPppAhVRifZGcrG1vZjS5ey5GIRVRFaZJdPsjLmKY60lpfDRwJbDDG7Bu9NwDcCOwGPANoY8yWCp89GfhU9PILxpjv16PMQggh5k+S7GpH+tnFnOW9PJuym1ibWsva1FpGC6OgIG7FsS25W62ja4Ajyt47F7jbGLMXcHf0epwoiL4QOBA4ALhQa91f26IKIYSYj+JKdutS61iTXsNIfiTM6ZGZn6qqKj/JSj1Yov1MN3G4aAxjzP1a693K3l4FHBZ9/33gXuCcsn3eCtxpjNkMoLW+kzDQvqFWZRVCCDF7xSS7bCGLH/iSZFcH1brVuAa4DPjPKh1PNIkgCEgX0mNJdoDcpbaGZcaYdQDGmHVa66UV9lkJPFfyenX03gRa6zOAM6LjMTg4WOXiCiGEKAqCgEwhM5Zk5wUeMRXDtmxs5AltPVQlypmkB0u0qNIxTWknzebsZkmya0+V1ukOKu1ojLkSuLK4z/DwcM0KJUQrGBoaanQRRJspTbJLO2m2ZLdIkl0D1S3iaWQPlOM4Td3j1Qzlc32XkdwImUKGvJ8nloiRtJI4jsOywWUNLdtkHMdhYGCg0cWozILB3ob+n67XWq+Ieo9XABsq7LOaHcMwAHYiHIohhGgwrfURwKWADXzXGHNR2fZTgEuANdFblxljvlvXQop5K+2Qynt5lApnnojZ0inVaHX76TeyB2pwcJBm7vFqVPlKJw4vXcmu1MDAAJs3b6572WaimcvW29c77f9pjXugbgNOBi6K/r21wj4/B75Ukpj3FuC8WhZKCDE9rbUNXA68mfBG9hGt9W3GmMfLdr3RGHNW3Qso5qXgF0jlUxNWsovZMvNEM5HbkwVEkuxqo+D6pDM+6bQiM2rhFRwW93aw7x71Ob/W+gbCnuBBrfVqwpkpLgKM1vpU4B/Au6J9Xw2caYw5zRizWWv9eeCR6FCfKybsCSEa6gDgSWPMUwBa6x8SJt6WB8iiReTcHW2vF3hjHVKSZDd3Bc8nk/VJpQLSaZvAdehMJtnvxZVGD86eBMhtzg/8cCyxJNnNSxBAJucymglIpy1yWQvfjeHmHawggRMkSCYcFsVtcCAZ9AL1eSpgjDl+kk2HV9j3UeC0ktdXA1fXqGhCiLmplEB7YIX9/o/W+nXA/wM+Yox5rsI+ogGCICDjhuOJS1eykyS72cvmPUZHA9JpyGbtsbYXL0ZMJUjE4iyK2ygb4qqXIBhGVSFGrtY0bxN6sIwxV1Xj2GL2yicOl5XsZs71AjJZj1QK0qMWfsHBKzi4eQdHJUg4CZIxhw5HQYzwSwghqmsmCbT/DdxgjMlprc8knM7xjeUfkvyfyVW7fH7gk86nSeVTYYdUHPqsvjmXrVlzbGpRNs8LSGddRkbCQNjNO7h5G68QwyZJwk7Qn3CI9029fEcuZzM4OIhVhVU+qjWLxWQ9WKJOXN9lJD8yYUyTBMWVZfMeo5mAVApyFe9IY/TEHZRNmCKTbHSJhRALyGpg55LXOwFrS3cwxmwqefkd4OJKB5L8n8lVo3yTJdnNVzPn2MynbPmCTyrjkU4pshkbr+DguQ5BIY6j4nTE4yRiNpal2DH4xCNwRxl1YXSa48fjYf7PVAHyTPN/JHpqYaVJdp7vycThZTwviIZFwMiIhec6ePmwR9gmTkwl6Ug49DpWWBOkNgghmsMjwF5a6xcQzlJxHPCe0h2Ks9REL48CnqhvERcuSbKbmu8HZHIemQykUop83sYvREMSiRMjHJLYG7N3PIntaHSpJ5KQoIUEQUDWzZJyw8c3xTFNlrKw7IW7anilJDmv4OAXYtgqTkcsQWfMxrYVJAi/hBCiSRljXK31WYQzzdjA1caYx7TWnwMeNcbcBnxIa30U4AKbgVMaVuAFQJLsJipNkhsdtcuGJCZJOHE64g6dtoI40GI/KgmQm1wxyS6VT5H38yjUgpw4vHhHOjoakEpbFHIW3V2weWPHuDvSRTF7R29wE96RCiHETBhjbgduL3vvgpLvz0OmZayZ0iS7vJcfm/VpoSXZBcGOJLlUWpHLWvR0waaNSfBiJKwk8ViMnihJrp2GJEqA3ITKk+wgnHkiZrX/45up70h3JMl1OYq+RB9O99ZGF1kIIUQb8AOf0cJoOOuTn4eABbNgRzgk0SOVDqdM8woOXpQkZxEnYSdIxh06HIu+eB92V/u3ve3/v94iFlqS3fTTtkiSnBBCiNryfI9UIUWmEHZIja1k16YdUrm8x2g2TFCfLEmuK0qSI8mCbnvbM/pqEcUku+y2LBtTG9suyW7qJLkEMZWQJDkhhBB1VUyyy23PsSG9AQurrZLspkuSi6skybhDb8xq6iS5RpOQpI7Kk+y8wCOmYvRYPS1dMfMFn3TWJzUygztSSZITQghRZ1k3S6qQGkuyi1kxulRXS/cUF1yf0azPSAoyJfP2e4UYjkqQjMVJxlo3Sa7RJECuMT/wyRSigf4tnGTXLtO2CCGEaH/tkmRXTJJLj/oTVnFVQZw4CRLxGL1xSVCvNgmQa6CVk+zK1zbveT5gy6b4uCS5Vp62RQghRHuakGQHLbOKbDFJLp2GVNpi/fqAzcOxiklysoprfTT/b02LaLUkux1JcopMpuSO1I8RV+G0LYviNv2xPqzk1gU9UF8IIURzarUku8mS5HBjOCRJxmN0xWz6e/pR0vY2VHNGby1iLMmukG3KicNLp21JpcIguNK0LX1yRyqEEKJFFJPsMm4G13fH2t5myeXx/YDRbDQkMa0o5Mev4hq3oiQ5aXubmgTIs1Ac05R20+OS7Bo9pimX90hn/SnXNu+WaVsWFK31i4AbS97aHbjAGPMfJfscBtwKPB29dZMx5nN1K6QQQsxAEATkvNyEJDtLWcTtxnVIlSbJZUftsVVcvYIzLkmuS1ZxbUkSIE+jWZLsZpIk15GIybQtAgBjzN+AVwBorW1gDXBzhV0fMMYcWc+yCSHEdJolyS4IiKYrDSomycWCZLiKqyTJtR0JkCsoTbLLe/m6jmkquD6ZnM9IKmA0bY+ftoUEiVhrr20uGuJw4O/GmGcbXRAhhJhMI5PsXC8gW5IkV7qSnM2OVVw7HCXDIhYICZAjxTFN5Ul2tRjTVD5ty4aNHps3OTJti6iV44AbJtl2sNb6j8Ba4GPGmMcq7aS1PgM4A8AYw+DgYE0KKoRYWFzfJVUIc3nqkWSXzXuMZsIkuQ3DLluitrd0FdfuuIOykCGJC9yCDpBzbo6RwsjYmKZqJ9nNdG3zvo4BiG2VO1JRdVrrOHAUcF6Fzb8HdjXGpLTWbwduAfaqdBxjzJXAldHLYHh4uBbFFaJlDA0NNboILavgF9ie307OzdUkyW7qVVx3JMn1JQfA2brAIyExmQX1a1E6pqngF/ADvypjmqZa2zymEmPTtkiSnGiAtwG/N8asL99gjNle8v3tWutvaq0HjTES/QohqqY8yc4nbHvnm2RXcH3SGT+crnTUqpgk1xlzsCVJTsxB2wfIfuAzkhthfXr9vJLsSqdtSacV+ZJpW1QQJ2HJ2uaiKR3PJMMrtNbLgfXGmEBrfQBgAZvqWTghRHsKgoB0Ps2G0Q3zSrIbS5IbDUiPWuQyFp4bwy/EUEEcJ0hIkpyoibYMkItJdqOFUQp+gcXxxQQEMxrTNHFt89iOO9LyJDm5IxVNTGvdCbwZeF/Je2cCGGO+BRwL/KvW2gUywHHGmKARZRVCtL7SJLuCX6A/1h8+qZ1Bkl3pKq6jozsS1EtXcR1LkpMEdVEHbRMgT5VkV145p5u2RZLkRDswxowCi8ve+1bJ95cBl9W7XEKI9jEuyS4ojD2ldSyn4pji0iS5XNYea3tLk+R64g7KBmxkSKJomKoEyFrrI4BLCX+dv2uMuagax53OdEl2xWlbsoUCa9b4kybJydrmQgghmsl07arWOgH8J7Af4dCodxtjnqlH2SZNslNhI1pMksu5eVav9iYkycVUko5EtJJcsRNKiCYz71/LaBGCywkf5a4GHtFa32aMeXy+xy432cThBRdGMxaplE82q6JHMzECN05MxVk6uISuQq8kyQkhhGh6M2xXTwW2GGP21FofB1wMvLsW5SlNssu62bG213VhNGuRSgVkRoNxCeq2irF8cBmd+T5JkhMtqRr3bQcATxpjngLQWv8QWAXMOUC+6aabePGLX8zee+9NQMBoYZSRXJptmVFGRyE7GsctxCpP21KhN7irw6GQU/O7SiGEEKI+ZtKurgI+E33/I+AyrbWaTx6P2sYhAAAgAElEQVTBL37xC0ZHR7EsC8uycHHJBwWyhQL5gsIrJPE9B4gTuDFsKxG2vck4yXgMy7KxLBvbtrEsi212nlQqHb1vlWzb8XrHl4VS0k6L5lGNAHkl8FzJ69XAgeU7lS80sHLlyiqcWojWFQSSDyeEqGgm7erYPsYYV2u9jTDnYNw0jdL2CjHeTNveagTIlW75Jpy9fKGBNWvWTHrAtWvX8rOf38U9997LI795mPTIdpRS7Lb7vrzs5a/jVa88nJfuuz8dyZk9r+nr62Pr1q0z2rcRmrl8Ura56ezsZc89ZTphIcSczKRdrXrb+9xzz7F5a4rhrWk2bR9lZDRP4Dp4eYvAt7F8m5gNlgoIAh/f9/F9D9/38Dxv3Gvf90gmk6RSI9G2idt93y/ZFr4OAn9W+5du97yJ+1faViw7BBQKhVkfK/xsaynv3S/vva+0TSmrwv4W8XgC3w9mcKzK24vblLKm2X/mxyoeL5Ho4eSTDyIWm/vaFkXVCJBXAzuXvN6JcNnaORsaGuLU957Eqe89Cc/z+P0ffs+d99zJA/c9wH/fcgW33nQ5nV1dvOTlB/CyVxzCPi99HUsW7xZlwMZJxm3kSY0QQogWNZN2tbjPaq21A/QCm+dz0p133pmdS87q+R6pQopMIUMqnyObhUzanrAglqPidMTjJIoLYkWauRMD5l6+IAgqBu/FG4WZ3DxMF+x3dHSwffv2SYJ9LyrDTG8OKp9/um0T/w33tyyLfD6H6xYqHGu6a610rtKbl/k/WX3Pe/7eNAHyI8BeWusXAGuA44D3VOG4ANi2zf777c/+++0PH4fNWzZzz333cO999/Lwgw/zyK9+CcAuu+3CfgcdxEtfeSC7v2h/Ek7P2ByKruWQzRToiEcr6gghhBDNaybt6m3AycDDhHOa31Ptecxty6Y30UtvonfHHMe9afJ+HgKXmB3D87Jkch6pdEA6bY+bLapg2WRH8yTjDjHHqmbRGkophW2HPZu10sw3F7UsWzHwn9tTBB/b7iQer84k2fMOkKOxT2cBPyecjuZqY8xj8y7ZJAb6Bzj26GM59uhj8XyPx/72GHf/8m4eeuAhbr/lVm7+oSEWi/GK/V7Bwa89mIMOPZjd9t6PNWs2k0pbFHIWvhvHzTtYxIkRrsKTqMLdhhBCCDFfk7WrWuvPAY8aY24DrgKu1Vo/SdhzfFwty2Qpi+54N93x7nEzSrkqTyIZ0NXhoJYowAd8gqBAR9dmVq/ZRDptkZ5kvYFkXNpesUN48+Fg23MLT+PxXiyrOsMbVYMShYK1a+c1CmPiAYOAramtPPDrB3jgvgf49YO/5qn/fQqAJUuXcMBrDggD5kMOon+gH4B8wSed9UmNMOGRkU34yCgZH//IqBYW6p3ifDVz2WYyBnloaAgqjyNsdlWvv0K0mhatvzWpu1k3S6qQGluTIGbFUEoxMDDA5s0TR31MXLHWiVasjY1bsbbWT3ybuQ2Rss1NPN7LC184jDXFA4uZ1t22mZ5bKUV/Tz9HvfkojnrzUeTcHH9f/Xfuv+9+fvfb3/HgvQ/y01t+ilKKvV+yNwe/9mAOPvRg9n3FvvT3FOeE8wAvemTkMpqBkRGrbJLzBDGVoCPRXo+MhBBCiLlIOkmSTrjAQOmqtjkvh+d72Nb4XuKYY9HbbdHbXXzHB/L4fo5MbhuZDKRSinzexi/E5ImvaIi2CZDLJZwE++y2D/vstg99H+njyeee5H/++D889MBD/PbB33LNlddw1RVX0dXVxf4H7z8WMK/ceSW2rejujNHdCUsXQ5gYXAAKZPMpRkcD0mnYNskymcm4I0mCQgghFpyYFaM/GT6l7V/UzzPpZ8gUMhT8AkqFy1BPxrIUXR0OXR0wOFB8N2x7c/kU6axPOqXYNsMkQSHmo20D5FKO5TDYNcibX/Nm3njQG0l/OM2GzRt4+FcP8+sHf81vHvoN9951LxAm+x186MEc9NqDePUBr6azq3Pcsf4/e/cdJ1V1NnD8d6Ztp+yuhSo2FEQF6QJRIyogYktOYproq1iiiSYao4kxGkPUWIIViV2TyIlgx4jEqFRj776vJiogKGUpO7vT733/uHeGYdm+szOzs8/385nP7szc8szunLlnzjnPOcUBL8UBqOyVfCQOxIkl6gmFLYJBm9p6b6rLKB714VNFFPmKKPb78Pmk8AohhCh8jSb5xZJJfuD3+ls+iKso4KUo4KWyR/KR9B5fJ0kwGHTGOSeTBD0EKPIWFVySoMiOblFBTuf1eOlR1IMefXqwzyn7cMoJp1AbreXT/3zKq8te5dXlr/LkgieZ/8h8fH6fk+w30WldHjxkcJMr/fi9HvxlHnqUJR9J7zLaTn29TbDOQzDiIRH3k4j6UbbbZVSayNbLF92I1vpzoBbnShI3xoxq8LwC5gDTgHpgpjHmzWzHKYQofE0l+UUT0dTS1e1ZSc/p8fVRXgrsBulJguForXvtVTslCZLwE/AUUVRSgW0jPb6iUd2ugpzOozyUBcooC5SxxyF7MOqgUfzozB9RW1/LW2+8xWvLXmPVslXcduNt3HbjbVRVVzFuwjjGTRrHuAnjqKyqbPkcaV1Gu1UlH3VbneN11IUsPL56todq3SQF5+ZTRRT7AxT7ZWo60SFHGWOayhacCuzv3sYCd9HIKphCCJFJSilK/aWU+p0e2kg8Qm2sNpXk5/P48KiOtfgqBSVFXkqKoKp38tGde3x9vjAbwtudxVAa9PjKtLCiW1eQ0ymlUokGu5XsRr9v9uPIbxxJJB7h66++5rWVTmV52cvLePbJZwE48KADndblSeM5ZMQh+P2t7y4CJ1GhV4WHysoA5SWKnbuMtjaRJBjAr4olSVBkwonAQ+7cqau01r201n2MMetzHZgQovso8jmVUtg5yS9mx/Di3SXJr6OSPb6VlQFKizw01uNbV+eRJMFuTirITUgvsLvvszuD+g/ihJNPIJKI8MkHn/Dq8ldZuXQlD93zEPfffT+lZaWMHrcj2a//wP7tPneLSYIhm2AQ6sJebEkSFE2zgcVaaxu4211yNl0/YE3a/bXuY7tUkLXWs4BZAMYYqqurOydiIUS3lp7kl7AS1MXqqI/VtyrJr6Ma7/F1rr3RWB3BUKLRJMFsTgsrskcqyK3g8/h2KrCVIys55NBDmHnuTGpra3nr1bdYtWwVK5et5OV/vgzAgL0GpFqXR43dNdmvvVJJgj2TjzhdRvFEiFA4QW0jSYJeJYkK3dQEY8w6rfXuwAta64+NMa+kPd/YJ3mjE6O7letkBdvetCkzE7EL0VW5c6mKTpTKGSrq0eEkv44K+D1U+j1NJAnGCdbhJgk6113LTRIMeGRa2K5KKsht1LDAhopDVB1XxTcmfwPbtlm3eh0rl65k5bKVPLXwKcxfDD6/j0MPOzRVYR584GA8zc1i3Q4+r6KizEdFgyRB2446XUYhe5fVjDx2ET7b6TKS1YwKjzFmnftzg9b6cWAMkF5BXgsMSLvfH5AVQIQQeaexJL+6eB3RRBTLttqd5NdR6T2+TpJgeo9vrUwL24VJBbkDPMpDmb+MMn8Ztm0TSUQo3reYfnv149QfnIoVs3jnzXec1uWlK7n9ptu5/abbqaquYuzhY92lsMdRWdlysl97KQWlxT5Ki6G6YaJCvJ66kEVdnWJ7vafRJMGKRE5WWhQdpLUuAzzGmFr392OBaxps9hRwgdb6UZzkvG0y/lgIke+ykeSXCa2ZFnZ7nbfRJMHycrn25ppUkDMkPckPnAIb9AcZNW4Uw8cM54JLLmDzxs2poRgrlq5g0VOLABh2yLDUYiWHDD8EfyA73UbJJMFeFclH0ruMtlEfsgn56ti6PbhTkmDAUyzDNfLfHsDjWmtwyvlfjTH/0FqfC2CMmQsswpni7VOcad7OyFGsQgjRbtlO8uuo1kwLG/YF2bq9FiseIB717ZgWVnp8s0bZdk6+pXTKevBNqa6uJpdjJuNWnGAsSDgWJmpH8eJFofj4g49ZuWwlr618jTdff5NEPJFK9hs3cRzjJ41nwMABLZ+gE1VWVlJTU5O6H44mUkmC4XByrLMfOx7ArwIUB7LXZZTP68GXlvZkv/2af8+1dj34PJTV8itEPuqi5bdbXXuTSX6heIhoIrpLkl/D61s+aRhbLG5RF7IIBhUht8fXijtjnVPTwmYpSTCfr72BQE8GD95Ec6NYW1t2pQU5C3weH72KekHRzgV28EGD2f+g/bn0V5eyevVqXlv5GiuXrWTV0lWpZL/+A/vvlOxXVl7Wwtk6165Jgk6rczwRIhxJUFcHwTp3uIasZiSEECJHdskZirmLk7hJfl1J8z2+W2Ra2E4gFeQsSy+wtm1TH6/HozwUlxYz8eiJHHXMUdi2zZov1rDilRWsXLaSpx9/mr//9e9ZSfZrL1/aakZ7NFjNqKkkQWUHCFBEUcAvXUZCCCE6TfrCYMkkP5/HR8JOkLAT+JU/J0l+HdXitLD1NsE6qJckwTaTCnIOKaUo85dRXV6NN+Qlkog4QzHiYfoM7MN3fvgdvvuj7xKNRnn7jbd3SfarrKpk3IRxO5L9WrGyX7a1lCRYH7aoDcK2eg9WzC8rCQohhOhUySS/6rJqPCGPkzMUd4ZB5lOSX0c1lSSYnBY2GITaes9O08ImkwSL/T58vu597ZUKcp5oNMkvHiQSj4AXRo0bxZjxY/jJpT9h08ZNjSb7HTD0gFTr8qEjDs1asl97+X0eepZ76FmefMTpMrIsN0mwHoJ1ilh0R5eRsgME3C4jIYQQoqNSSX7FTs5QbbQ2r5P8OqrFaWHrberqPQSbmBa2u+g+r7SLSc/KbZjk17uqN9NPns70k6djWRb/++H/snKpU1l++L6HeWDeA5SWlTJq7KhUhXnAXrlN9muLXVcz2tFlFIkGqQtbzmpG1FITq0utZuRTzmpGRX5ZzUgIIUTbNVwYLJkzFLNiqecL1U49vqkO6UamhVVBtsTrCr7Ht3D/0wWkYZJffbw+tfSmjc2QYUMYMmwIZ553JsFgcKdkv1dedNaF6DegX2oZ7NHjRuc82a+9igJeigJeKntAZaWPmqr0RIUEwTqbujqvJAkKIbokrXUlMB8YBHwOaGPMlka2SwDvuXdXG2NmZCvG7qK5JD9F5y57nW/SkwQrK33UVO46LWxdnWenHt+uPi1s9/nvFgivx0tFoIKKQEUqya8u5qwmZGNTXl7OUccctVOyX3Jlv2efeJbH/voYXp+XQ0fsSPY7YOgBeZPs117etCRBGiQJhqO11NVbkiQohOgKfgn80xhzndb6l+79yxrZLmSMGZ7d0LqvxpL8kiv5deUkv47a6drbWJKgOy1sXdq0sF0lSVAqyF1YMskvfSW/ZJKfjY1P+Rg4aCADBw3kOz/8DtFolHfefIeVS1eyatkq7rjlDu645Q56V/Z25l2e6CT7VVVX5fqlZYxSUFLkpaTI22iSYChiURu02V7vbZCoUEyRL0BJoLC6jIQQee9E4Ej39weBl2i8gixypLGV/JI5QwkrgdfjLYgkv47q6tPCykIheaAz4osmoqmlN+NWvNGs3E0bN/Hq8led4RjLVrGlxunFO2DIAamFSo6afBTBYDCjsWVKZ03yblk2oUiCUAiCQUU06sWKuYkK7FjNqMjfdKuzLBQiRGHrrPKrtd5qjOmVdn+LMaZ3I9vFgbdxvvFfZ4x5oonjzQJmARhjRkaj0UyH3CSfz0c8Hs/a+dqqM+KLW3G2R7YTijnjlr2qfUl++fy366zYbBtCkTh19QlqaxXRsJd4zEsiuZKgKqGkqPke30jEy9ix8WYXCgkEAtDZC4Vorb8N/BYYAowxxrzekeOJzAl4A1R5nZbg9CS/mB3Dgwevx0v1btUcf9LxHH/S8U6y30f/m2pdfuT+R3jwzw9SWlbKyDEjd0r2K/RupPQkwR2JCo0kCYbcsc6NJAkKIURTtNZLgD0beepXbTjMQGPMOq31PsCLWuv3jDH/abiRMWYeMM+9a2ezsag7Nk4lFVGEz/JRF6tje3x7KmfI72nd7FJdaZW/TPOCsyBKxY7HYnGL+rDF9iBs2OZNJQg2TBIsKenFpk2tWkmvRR0dYvE+cApwdwePIzpRepKfZVvUx5xxy+kF1uPxMOSgIQw5aAhnnnsmdcE6Xn/1dd587U1eWvISS/+1FIB+/fsxbpIzHGP0+NGUl5e3cPbCkp4k6Ng1STAY9FBcEgLye5o9IURuGGMmN/Wc1vprrXUfY8x6rXUfYEMTx1jn/vyv1volYASwSwVZ5E5jSX518ToiiUi3S/LrqOamha0Pb3N6fOsUnuJaoJhMdO506L9jjPkIQGvd4UBEdniUh/JAOeWB8kaT/HzK54xtLi/jiKOP4ORvn0xNTc1OyX6LnlzEgr8twOvzcsjwQxg/aTyHTzq8IJL92qthkmDPXnGISQVZCNFmTwGnA9e5P59suIHWujdQb4yJaK2rgQnADVmNUrRJwyS/SCKSGgZpYXXbJL+O8nh2XHt3q4KKnhYqlpljZ+3rS4NxUFRXV2fr1Ph8vqyer63yIT7btonEnQKbXE3I7/Hj8/morKyksrKSQ0ccyrk/OZdoNMqb/36TV/71Cq+8+Ap33nInd95yJ1XVVUw8YiKTvjmJbxz5DXZz1pzuNMnY8pIHqnvm73tOCJG3rgOM1vp/gNXAtwG01qOAc40xZ+EMa7xba20BHpwxyB/mKmDRNs0tDJZM8hO512KSXnNjpYwxT7rbvARc0oYxyJKklyYf44tZMbZHt1NWUcaGzRuaXXpz86bNTrLf0pWsWr6Kms3O2KTBBw5OLYM9fOTw5MD4jMnnMVo9e/WkJFbS7DadmaSntR4APIRTdi1gnjFmToNtjsRpnfrMfWihMeaaVhxekvREt9dFk2zl2psmH+NLruRX2qOUrzd/nZcr+eXztbeiZwWlsdJmW+NbW3ZbbEFubqyUKFx+j5+q4iqqe1bji/h2JPlZMZTaeexUVXUV006cxrQTp2FZFv/38f85wzGWrkwl+5WUluyU7Ddw0EDpTupcceDnxpg3tdYVwBta6xcaaWVaaoyZnoP4hBBCNJBcya+6RzW+sG+nlfzakuQnOk5GiIsWNZXkF7Wc6YLSC6zH4+HAoQdy4NADOeOcM1LJfsnxy8teWgZA3/59U/Mujzl8TLdL9utsxpj1wHr391qt9UdAP0C6YYUQogvYJckvHkrlDEFhL3udDzo6zdvJwG04a5c9q7V+2xhzXEYiE3mpYZJfKO4uvdkgyS8pmex3xNFHALBm9ZrUVHLPPf0cCx5dgNfr5eDhB6eWwh4ybEi3TfbrDFrrQTgZ7q828vR4rfU7wDqcYVIfNHGMnOUQCCFEd+dRnl0WBksm+TV27RUdJwuF5IF8jq+1saWv5BeJR1JJfs0V2Fg0xrtvv5tqXf74g48BZ/xu+sp+u+3eeLJfPo+DyvUY5CStdTnwMvB7Y8zCBs/1ACxjTFBrPQ2YY4zZvxWHlTHIotuTMcgty+drG+R3fG2JLT3Jr6mFwTIpn6+9mRyDLBXkPJDP8bU3tpgVIxgNEoqHWl1gazbXsGr5KlYtXcWq5avYvGkzAPsfsH+qdXn4qB3JfvlcSPOhgqy19gPPAM8bY25uxfafA6OMMS39w6WCLLo9qSC3LJ+vbZDf8bU3tvSFwaJ2tFOS/PL52pvVJD0h2sPv8dO7uDe96U3CShCMBVNLbzZM8kuqrKpk2oxpTJvhJPt98vEnrFzmtC7/9cG/8tA9D1FcUuwk+00az5Tjp9Crspd0KzVCa62Ae4GPmqoca633BL42xtha6zE400VtzmKYQgghMig9ZyhhJaiP11Mfq5ckv3aQCrLodF6Pl55FPelZ1LPFJL8kj8fDAUMP4IChBzBz1kzq6+p5/d+vs2rpKlYuW8nyl5dz47U30qdfH2dmjInjGX34aCoqKnY5Vjc1Afgh8J7W+m33sSuAgQDGmLnAt4DztNZxIAR81xiTky4lIYQQmeX1eKkIVFARqGh0YTCpLDdPhljkgXyOrzNja02SX1PWrl7Le2+9x5Lnl/Dayteoq6vD6/Uy7NBhqZX9DjzoQLze3MwfmQ9DLDqRDLEQ3V4XLb9y7U2Tz/F19rU3mTMUjofbnOQnQyyE6GRKKUr9pZT6SwEIx8OtTvLrP7A/hww/hKknTiUWi/He2++lkv3mzpnL3DlznWS/CeMYN2kc4yeM7/SV/YQQQoh819xKftlI8usqpIIs8kZ6gU0m+YXjzuIkzRVYv9/PYaMP47DRh/Hjn/2YLTVbWLV8VWplv+effR6A/Q7YLzUcY/io4RQVFWXttQkhhBD5qMhXRJHPuR6mJ/nF7BgePHm3kl+2SAVZ5KVkkh/Q6iS/pN6VvZl6wlSmnjAV27Z3JPstXcmjDz3Kw/c+TFFxEaPGjHJalyeOZ9A+gyTZTwghRLfWcGGwulhdt03ykwqyyHtNJfnFEjFiiRh+b9MFVinF4CGDGTxkMKeffTqh+tBOK/st//1yAPr068O4CeMYP2k8Y8aPoaKHJPsJIYTovjzK02iSX9yKE7NiBV9Zlgqy6FLSV/Kr6lmFCqk2JfmVlJYw6ahJTDpqEgBfrvky1bq8+NnFPG4e3ynZL7myX66S/YQQQohcU0qlVvKr6lGFJ+Rpd5JfVyEVZNFlNUzyi8R3LL3ZmpX8APoN6Me3TvsW3zrtW8RiMd5/+/1UhfnuW+9OJfuNPXxsqsIsyX5CCCG6q4ZJftFENHXtLaQkP6kgi4KRnmiwU5KfHWvVakJ+v58Ro0cwYvQIzr/4fLbUbOHVFa+mhmMsXrQYgH0H7+sk+00az4hRIyTZTwghRLcV8Aao8lYBuyb5KZrPGcpnXTNqIVrQMMkvPdGgpSS/pN6VvZkyfQpTpk/ZJdlv/sPzeeS+RygqLmLk6JGp1uVB+0qynxBCiO6pYZJfKmeoCyb5SQVZFDyvx0uPoh70KOqx60p+Ns0m+SU1mey3bCWrlq3iptk3AbBn3z0ZN2Eck6dMZsYxM2TsshBCiG4pPWeosZX88n3cslSQRbfSsMAmV/KLWTEs22p1gW2Y7Ldu7bpU6/ILz73AquWrOOm4kzr75QghCozW+tvAb4EhwBhjzOtNbDcFmAN4gXuMMddlLUgh2ig9yS99Jb9IPIJF66+92SQVZNFttZTk15ZEg779+3Lqd0/l1O+eSiwWoy5Yl3eFXQjRJbwPnALc3dQGWmsvcAdwDLAWeE1r/ZQx5sPshChE+zVM8otZMbZHt+ddkp9UkIVwdTTJL8nv97PX3ntBrDOjFUIUImPMRwBa6+Y2GwN8aoz5r7vto8CJgFSQRZfj9/ipKm4kya8NOUOdQSrIQjSisSS/UDxENBHNaYFti5a6YLXWRcBDwEhgM/AdY8zn2Y5TCNFm/YA1affXAmMb21BrPQuYBWCMobq6uvOjc/l8vqyer63yOT6JzV3JL1pHMOqsdQAt5wzZyqa6Z3VGenDz/yovRI41TPILxZxxy21J8su2VnbB/g+wxRizn9b6u8D1wHeyH60Q3YvWegmwZyNP/coY82QrDtHY1d9ubENjzDxgXnKbTZs2tS7IDKiuriab52urfI5PYtvBjx+f7SMUD7E1trXZJL+KnhVs2rSp2Qpy3759W3VeqSAL0QYe5aEsUEZZoGynJL9oIoqFhV+1vDhJlrSmC/ZEnGQggMeA27XWyhjT6IVWCJEZxpjJHTzEWmBA2v3+wLoOHlOIvJWeM9Qwya+1C4O1lVSQhWinxpL8gnFn7FTCTuQ4ulZ1waa2McbEtdbbgCpgl6aBht20/fr164yYhegybDun3yNfA/bXWu8NfAl8F/heLgMSIlsaS/Krje5YyS9TOlRB1lr/ETgBiAL/Ac4wxmzNRGBCdDWpJL9i6N2jN1tqtuQynNZ0wba7m/bLL7/sQGhCiKZorU8GbgN2A57VWr9tjDlOa90XJ5dgmvuF9gLgeZwcg/uMMR/kMGwhcsbv8VNZXAlA716Zu/Z2tAX5BeByt7BeD1wOXNbxsITo2lo740Unak0XbHKbtVprH9ATqMlOeEKIxhhjHgceb+TxdcC0tPuLgEVZDE2IvJfJa2+HKsjGmMVpd1cB3+pYOEKIDGlNF+xTwOnASpyy+6KMPxZCCCEyOwb5TGB+U0/KVDNNy+f4JLb2yXVsTXXBaq2vAV43xjwF3As8rLX+FKfl+Ls5C1gIIYTII6qlRIPWTEejtf4VMAo4pZUtUPa6ddlLuM3n6VIgv+OT2NqnNbG5U83kxZQXbZTV8itEPuqi5VeuvWnyOT6JrX0yee1tsYLcEq316cC5wNHGmPpW7ibduEI4utoFFqT8CpHU1cqvlF0hHC2W3Q4tdu2u1HUZMKMNlWNwAsvaTWv9RrbPWSjxSWydHltXlPO/r9zklie3riarf598/ozO9/gktk6PrUUdqiADtwMVwAta67e11nM7eDwhhBBCCCFyqqOzWOyXqUCEEEIIIYTIBx1tQe4q5rW8SU7lc3wSW/vkc2xCCJEN+f45mM/xSWztk7HYOpykJ4QQovNorZ8DHjXGPNiOfT8HzjLGLMlgPDawvzHm00wdUwgh8k0m50EWQgiRYcaYqbmOobNorQcBnwF+Y0w8x+EIIURKdxliIYQQXYrWWmmtC/Yz2l3eXAgh8lJBf0BprQcAD+EsdGIB84wxc3Ib1c601l7gdeBLY8z0XMeTpLXuBdwDDMOZO/NMY8zK3Ebl0FpfDJyFE9d7wBnGmHAO47kPmA5sMMYMcx+rxFlZchDwOaCNMVtyFWN3pLX+JXA2sDuwBmdxo8fd57zADThLbdcCNwG34bZkaq17AjcD03A+O+4HrjLGJFpx3pdwlu8+GjgAeAnnPVrjPj/OPfZQ4Avgp8aYl9L2XQ4cCRwGHKy1vgd4xBhzj1thvsJ9XSXAP4ALjTHb3P1/CJwm3DoAACAASURBVFwLlLvnaC7OSvd1H+ce62VjzEnuc2fjTOFZCSwDzjXGpK8wMdkd+lEN/BW4wBhjNxdfWmvxWcBVOOVikHu8rVprgGPy5XNGtJ9ce9svn6+9kF/X386+9hZs64QrDvzcGDMEGAf8WGs9NMcxNfRT4KNcB9GIOcA/jDEHAoeSJzFqrfsBPwFGuQXCS+6XSH4AmNLgsV8C/zTG7A/8070vsus/wCSgJ3A18IjWuo/73NnAVGA4TkX0pAb7Pojz+bEfMAI4Fuei0Fo/As4E+rrHuRVS799ncSqxlcAlwAKt9W5p+/4QmIUzheYXDY47070dBeyDUxG+3T32UOAud/++QBXQv5kYHwZKgYNwvkTc4h7nm8AfAA30cWN4tMG+04HROJ8NGqeS3Wx8aY4Ahrj7fMN9rJcxpjyfKgKiQ+Ta2355ee2FvLz+PkAnXnsLugXZGLMeWO/+Xqu1/gjoB3yY08BcWuv+wPHA74Gf5TicFK11D5wL10wAY0wUiOYypgZ8QInWOoZzgc/pusfGmFfc1rF0J+K0AoJT2XoJp0VOZIkx5u9pd+drrS8HxgBP4lTq5hhj1gJora/DafFFa70HTuW5lzEmBNRprW/BqbTe3crTP2yMed893pXA2+6qoz8AFhljFrnbvaC1fh2npTqZhPeAMeaD5IHcltWk7wM3G2P+6z53OfC+1voM4FvAM8aYV9LOe0FjwblfFKYCVWmtKy+nneM+Y8ybaefYorUeZIz53N3mOmPMVpyW33/hfNH4RwvxJf3WGFPXyGsTBUKuve3TBa69kEfX386+9hZ0BTmd+0ccAbya41DS/Qn4BU5LUT7ZB9gI3K+1PhR4A6cbuC63YYEx5kut9Y3AaiAELDbGLM5xWI3Zw71IYIxZr7XePdcBdTda6x/hXPwGuQ+V4wwJAKeFdU3a5um/7wX4gfVpFThPg21akr7tF+7xqt1jf1trfULa837gX03s21Bfdm5V/gLnc3wPGrwmY0yd1npzE8cZANQ00fXYF3gz7ThB9zj9cLosAb5K274e52/bUnxJbfk7ii5Orr1tkrfXXugy19+MXXsLfYgFAFrrcmABcJExZnuu4wHQWifHzbyR61ga4cPpdr7LGDMCqCNPhghorXvjfEPcG+diXKa1/kFuoxL5Rmu9F/BnnBbUKmNML+B9diwxup6dhx8MSPt9DRABqo0xvdxbD2PMQW0IIf14A4EYsMk99sNpx+1ljCkzxlyXtn1zc2+uw6lkpx87DnztvqbUebXWpTjDLBqzBqh0xzs2ew6tdZl7nC+bias18SXZTfwuCoxce9ssb6+90P2uvwVfQdZa+3EK6F+MMQtzHU+aCcAMd57SR4Fvaq0fyW1IKWuBtcaY5Df+x3AKbT6YDHxmjNlojIkBC4HDcxxTY75Ojnd1f27IcTzdTRlO5WsjgNvFPyzteQP8VGvdz60kprrg3NaHxcBNWuseWmuP1npfrfUR7rEGaa3tRrr20v1Aaz3UraReAzzmJvg9ApygtT5Oa+3VWhdrrY90u3xb42/AxVrrvd3Kx2xgvjtF2mPAdK31RK11wD1v6jPePY+d9hqfA+7UWvfWWvu11snxwH8FztBaD9daF7nneDVteEV742vMRpwkrn1a+fpFFyHX3nbJ52svdI3rb8auvQVdQdZaK+Be4CNjTLMZ3dlmjLncGNPfGDMIZ5D7i8aYvPgmZoz5ClijtT7Afeho8mTsGE7Xzjitdan7/z2aPEpiSPMUzgwJuD+fzGEs3Y4x5kOcGRpW4rReHowzO0TSn3Eqwe8CbwGLcFo6k7NU/AgI4Lzvt+BcqJIJfgNwhg4016L6ME4CyVdAMU5iC8aYNTgtMFfgVA7XAJfS+s/i+9xjv4IzI0QYuNA99gfAj3EquOvduNem7TsA5++R9EOclu2PcS4iF7nH+SdwJU7lZj2wL61PxGkyvsYYY+pxxoEu11pvdWf4EF2cXHvbJ8+vvdA1rr8Zu/YW9Ep6WuuJwFKcqUgs9+Er0hJk8oLW+kjgkjybamY4zlQzAeC/OFO55MU0ZVrrq4Hv4FRo3sJZKSySw3j+hpMUUI1TGbsKeAKnlXIgzofKt5PTfIn8o7WeCsw1xuzVim1/DWw0xjSasKedqdoeMcbck9koO0Y708X93RjzfK5jEYVNrr3tl8/XXsiv629nX3sLuoIshBCN0VqX4ExFthgngWwBsMoYc1EGjv0SeVhBFkII0XoFPcRCCCGaoHDmRt6C0wryEfCbnEYkhBAib0gLshBCCCGEEGmkBVkIIYQQQog0UkEWQgghhBAijVSQhRBCCCGESNNtlpoWQgghhMgWdzGhzwB/M4vliDwlLchCCCGEEHnOXQ1zbctbikyQCrIQQgghRB7TWkuPf5bJNG8FRmv9S+BsYHecZWx/ZYx5XGvtBW7AWXqxFmcZ3ttwu3601j2Bm4FpOCsf3Q9cZYxJNHIaIYQQolvRWg8A5gCTcBoY/4azjPwVONfdEuAfwIXGmG1pQyxmAr8DSoFbjDG/d49XBFwPaPcUBrjMGBNxV/l7BOc6fTHOyoTTgSKg3t1+sDFmXee94u5NvpEUnv/gFN6vgG8Dj2it9wNOBKYCw4E64O8N9nsQZ6nG/YAy4BmcCnajy+kKIYQQ3YXbyPQM8CLwQyABjMKp/M7EWZlzA/AQcLu7TdJE4ABgMPBvrfVCY8xHwK+AcTjXZRt4Evg1cKW7355AJbAXToV8LM4qnf076WWKNFJBLjDGmPSK73yt9eXAGJxvqHOMMWsBtNbXAUe7v++BU3nuZYwJAXVa61uAWUgFWQghhBgD9AUuTUu4W6a1vhq42RjzXwD3mvu+1vqMtH2vdq+t72it3wEOxVm98/s4rc0b3H2vxrnmJivIFk5PbsR9vlNfoNiZVJALjNb6R8DPgEHuQ+VANU7BXpO2afrvewF+YH1aAfQ02EYIIYTorgYAXzQyG0Vf4Iu0+1/g1K32SHvsq7Tf63Guy03t2zft/kZjTLgjQYv2kwpyAdFa7wX8GadleKUxJqG1fhtQwHogvVtmQNrva4AIUC1T0QghhBC7WAMM1Fr7Glwn1+E0MiUNBOI4QxZbGgqR3PeDtH3TxxQ3TBKTpLEskgpyYSnDKUAbAdwunmHucwb4qdb6WZwxyJcldzLGrNdaLwZu0lpfCQSBvYH+xpiXsxi/EEIIkY/+jdPQdJ3W+iqcMcgjcRL1LtNaP4dz7Z0NzHeT31s65t+AX2utX8O5dv8GJzGvKV8DVVrrnsaYbR16NaJFMs1bATHGfIgzO8VKnIJ0MLDcffrPwGLgXeAtYBHOt9zkLBU/AgLAh8AW4DGgT7ZiF0IIIfKVO6PTCTiJ7KuBtcB3gPuAh4FXcGasCAMXtvKw1wKv41yX3wPedB9rKoaPcSrV/9Vab9Va921qW9FxMs1bN6W1ngrMNcbs1eLGQgghhBDdiAyx6Ca01iU409AsxkkeuAp4PKdBCSGEEELkIRli0X0o4Gqc4RNv4Uwx85ucRiSEEEIIkYdkiIUQQgghhBBppAVZCCGEEEKINFJBFkIIIYQQIo1UkIUQQgghhEgjFWQhhBBCCCHSSAVZCCGEEEKINFJBFkIIIYQQIo1UkIUQQgghhEgjFWQhhBBCCCHSSAVZCCGEEEKINFJBFkIIIYQQIo1UkIUQQgghhEjjy3UAomtSSp0PXNPG3faybbuuM+IRQrSelF8huiYpu9kjFWTRXkVAVRv3UUqpAcBDwJ5AAphr2/btbThAh/YXQgBSfoXoqqTsZomybTvXMYguSClVAbwIjAJWAxNs217biv36AH1s235TKVUOvAGcZNv2R608b4f2F0JI+RWiq5Kymz0yBlm0i23btcBU4H+BgcDzSqnKVuy33rbtN93fg+7+/dtw3g7tL4SQ8itEVyVlN3ukgtwIpdRvlVKf5jqO9shU7K05jm3bm4BjgDXAUOBZpVRZG86xN3AY8O92xtih/UVhkvLb9cuvUmqaUuo1pVRQKbVGKXVVe84huhYpu12/7BYSqSBngFJqiVLqgVzHkQu2ba8BjgU2A+OABUopf0v7ud1EC4CLbNve1uC5PZVSMaXUV00dq7n9hWgLKb/5VX6VUhOAx4FHgEOBK4DfKqUOafMLFAVNym5+ld1CIxXkLFJKBXIdQ2ewbftjnC6fIHAc8JBSqsn3llvwFgB/s237sUY2ORN4GYgAJ7ZjfyEyTsqvIwvl9xL3uTm2bf8HeNR9vEfrX5UQO0jZdci1t226fQVZKVWklLpLKbVNKbVFKXUXTpZow+0uVEp9rJQKK6U+UUr9Sinlc7+9Hg2crpSy3duR7j4vKaXuVUr9Tim1HviypeOlPf+SUuoepdSV7re5GqXUA+ndKB2Nva3HaY5t268BJ+EUrO8Ctzbx91bAvcCHtm3/sZHnPcDZwAM4LUiz2rK/u81QpdTTSqk6pdR6pdQPlVL7KaU2q1aM1RJdh5Tfwiq/7v7HAE+nPTwViALvteU1ifwmZbfgyu47Sqn3lVK7N3j8Ovfxrjdrmm3b3foG3AJswPm2dCBwI7Ad+DRtm98CXwAnA3sD03CyR38H9AReAebjTH+yJxBw93sJqAXm4owTOril46Wd8yVgqxvfgcAU9/7VmYq9Lcdpw9/zVCAO2MBVjTw/0X3uXeBt9zYj7fkp7t+sFDgAZzqZfdqw/8Fu7Le4+1+L0wX1AHBlrt9vcsvsTcpvwZXfoe7zewEBnFaxdcDNuX6vyS2zNym7BVd2h7h/p7PSHtsfp+J+VK7fb+16j+Y6gJy+eCgDwsDZDR5/PfkGdd8s9cCUBtv8CNjq/r4EeKCR478E/B/gSXusxeOl7ftug23mAiszHHuLx2nj39QLvOoWpNVAWRv3fzz9b+kea3Yb9l8M/DPt/j5uLOuB8ly/5+SWuZuU34Isvz/A+ULbB+cCbbv/g8pcv9/klrmblN3CK7vuPs8AN6XdXwTMz/X7rb23rtfknVn74nRnrGjw+DJguvv7QUAJzgD49EmjvUCxUmq3Fs7xhm3bVtr9Fo9n2/ZG97G3GxzrS5xB+ZmMvU8rjtMWtwNjcL5JTrXbsHqPcuZZnM6O1wjwIHClUuo3tm3HW9i/CpiM8006Ker+vM52pqYRhUPKbwGVX9dhOPOrbnHjOAj4Dc6F9/DWxiLynpTdwiu7AB/jtCSjlJoBHIHTMt4ldfcKsnJ/2s1skxyn/W2cb6QN1bRwjoZv0rYcL9rgOTtt/0zF3rcVx2kVpdSvgHNxB/jbtv1BGw/xPzjdqS+lPfYoTjfUDGBhC/sPxfm7vJr22AHuz3ltjEXkPym/hVV+wakgr7JtO4xTUX5DKZXAST5SttssJbo8KbuFV3bBmRv5ZKVUkbvvbNuZbaNL6u4V5E9xCsIE4MO0x9NbKj7A6QbZx7btRY0dRCkVxflm2BotHq+VMhV7a47TIqXU6TjjfS3gB7Ztv9LG/T3AWcAj6RdB27ZrlFLP4iQMtFRIe7k/4+4xvcD17mPhtsQjugQpvwVUft0koOHAfQ2eOgxYJpXjgiJlt4DKbpqPgUE4vT7gjKnusrp1Bdm27Tql1FzgWqXU1zjffv4Hp0tgg7tNUCk1G5jtfH7zAs7f7WBghG3blwGfAUcppfYFtgHbbNuONXHO1hwva7G35jgtUUodB9zj3r3Ybt/0L1NwEnPeUEoNa/DcCuB6pdQg27Y/b+YYb7o/L1dK3QlcmvbcMUqpfzX1fxFdj5Tfgiu/++IkXv3CrTx8hZPYdD5OK5YoEFJ2C67sJv0vTuv5L3GWoY60I578ketB0Lm+4YwTuhu3cOF0xf+BBoPkcd64b+N8K9yC041/nvvcPjjZtEGc7pIj3cdfAu5p4rxNHq+pfYFfA59nMva2HKeJ1zESJ/PVBm7owP/hSfcYzd2ubcVxfoZzYY0AzwO9gb/gJPzsm+v3m9wye5PyWzjlF9Bu/E+4P2vcv+MxuX6fyS3zNym7hVN2GxyvBngu1++vTNyU+4KEaDPlLDe5EtgD+CtO9468oYToAvKt/CqlrgPG27Z9RK5iEKIryLeym+QO19gOnGHb9t9zHU9HdfuFQkT7KKWqgX/gFNB/AjPzoYAKIVqWp+X3MOCtHMcgRF7L07KbtD/O9HUFUY6lgiza6y5gsPv70UBU7VjNqKnbSTmMVwixQz6W3xHsOr2WEGJn+Vh2k0bgDPv4T5bO16m6dZKe6BAv8HUb95GZJITID3lXfm3bbmleWyFEHpbdJNu2H8WZHq4gyBhkIYQQQggh0sgQCyGEEEIIIdLkaoiFNFsL4VAtb5J3pPwK4ehq5VfKrhCOFstuzsYgr1u3Lmvnqq6uZtOmTVk7X1vlc3wSW/u0Jra+ffs2+3w+k/LrkNjaL5/jK+TyK2V3h3yOT2Jrn0yWXRliIYQQQgghRBqpIAshhBBCCJFGKshCCCGEEEKkkQqy6PYSVoLtke3ErXiuQxGN2B7eTiQeyXUYQgghMsi2bepj9Xn7+S4LhYhuKWbFCEaDhONhYnYM27bxe/z4PFIk8s32yHY2hjbiwUOxv5gegR74Pf5chyWEEKIdElaC7dHt1MXqsLDoGehJka8o12HtQmoDoluwbZtIIkIwFiQSj5CwE/g9fpRSBFSAmBXLdYiiCUqpVIU4Go+yProer/JKZVkIIbqQcDzMtsg2IlYEn/Lh8/iwbCvXYTVJKsg5Fo1Gcx1CwbJsi1A8RF2sjmgiio2NT/nwerx48eY6PNEOSikC3gCwo7Ls8/go8ZVQEaiQHgAhhMgjlm05rcVRp7XY7/ET8ARyHVaryBjkHKipqeGBBx7ghBNOYO+99+a8884jFArlOqyCkBxP/HXd16wLrqMmXINlW/g8vlSLsSgMycqyR3kIxUOsC65jfXA9W8JbZDy5EELkUDgeZkP9Br6s/ZL6WD1ej7fL9fZJc0uWhMNhlixZwoIFC3jxxReJx+MMGTKEU089lfvuu48VK1Ywd+5c9t9//1yH2uU0HE/sxYvX45XWxG7EozypluVQPERttBa/x0+Jv4QKfwVej/QYCCFEZ7Jsi2A0SDAWTA1j9Hu7VqU4ndQgOpFlWfz73/9mwYIFPPPMM2zfvp099tiDs846i1NPPZWhQ4cCMHPmTGbOnMnUqVOZPXs2WuscR57/YlaMjfUbWVe7DgsLn/KlxhOL7i29slwfq2d7dDsBFaDUX0qZv0wqy0IIkUGReIRt0W1EE1EUCq/Hi0d1/QEKUkHuBJ9++imPPfYYjz/+OGvXrqW0tJRp06Zx6qmnMmHCBLzenS/Qxx57LIsXL+aCCy7g4osvZvny5cyePZuysrIcvYL8ZNs2dbE6aqO1xKwYexTvIeOJRbM8ypP60lQbrWVrdCsBFaA8UE6pv7QgPsSFECLb0q/HcTueSrorJIX1anJo06ZNPPHEEyxYsIB3330Xj8fDEUccwWWXXcaUKVMoLS1tdv8999yT+fPn86c//YlbbrmFt99+m7vuuivVytydxawY2yLbCMVDKBQ+j4+ANyDjiUWbpH+Z2hrZytbIVvweP+V+p7Is7ychhGhacjaor4NOjk/yeuxXXXcYRXOkgtwBoVCI559/ngULFvDyyy+TSCQYNmwYV111FSeddBK77757m47n9Xr5+c9/ztixY7nwwgs54YQTuPrqq/n+97/f7S7eyW+nwWiQmBVLJdkJkQnJlg4bm5pIDTWRGoq8RZT7yynxlXS78iaEEI2xbItQLEQwFiRqOUModi/bvVtcj6WC3EaJRIIVK1awcOFCFi1aRDAYpG/fvpx33nmccsopHHDAAR0+x8SJE3nhhRf4yU9+wmWXXcaKFSu4/vrrqaioyMAryG9xK87WyFbC8TDgVGS68iB/kf+SH/SWbVETrgEg4A3QI9CDYl9xLkMTQoisi1tx6mJ1hGIhYlYMpVS3bKSSCnIrWJbFG2+8wdNPP82zzz7LV199RXl5OdOnT+eUU05h/PjxeDyZHctYXV3NI488wp133skNN9zAO++8w9y5czn44IMzep58kFxusjZaS9SK5mRFu2BtkOri6qyeU+Sf5PvOsi02hjaiUBT7iqnwV+TlSk9CCJEJ0USU2lgtkXiEuBXH5/HhUZ5u3UAlFeQm2LbNO++8w1NPPcXTTz/NunXrKCoq4qijjmLGjBkce+yxlJSUdGoMHo+HCy64gDFjxnD++eczY8YMrrzySs4444yC6AKOW3G2RbcRioWwcZZ6Ts4+kC22bTP31rnce+e93Dn3TmZMn5HV84v8lWwtiSVibIhvkKWuhRAFw7ZtwvEwwXiQaCLqrBegfDvNAtTdSQU5jW3bfPDBB6lK8erVq/H7/XzjG9/gsssu47jjjsvJMIcxY8awePFiLr74Yq688kpWrFjBjTfeSK9evbIeS0fZtk19vJ5gNEgkEclJa3FSJBLh6l9ezfPPPk8gEOCO2+/ghONPKIgvHyJzlFKpJJSGq/f1srpeGRRCdE+WbVEfq3dWl3XHE/s8PrzKi1fJbFANdfsKsm3bfPzxx6lK8WeffYbX62XSpElcdNFFHHfccXlREa2srOSBBx5g3rx5zJ49m+OOO44777yTkSNH5jq0VonEIwTjzmIeySWfc/ktdUvNFn523s949613ufCSCyktL+X6317PihUrmDBhQs7iEvktfanrUDzE2u1rqQ3WUuwrpjxQLi3LQoi8Yds20USU+ng9kXikW48nbo9uW0H+5JNPePrpp3nqqaf45JNP8Hg8HH744Zx33nlMnTqVysrKXIe4C6UU55xzDmPGjEklBV5++eXMmjUr42OgMyFmxdge3U44Fk4t5pEP31L/++l/uWjWRWzauInrb72eyVMmEwwFuef2e5g7d65UkEWrJLsilVKE42Fqo7V4lZciX5GMWRZCZF1yGrb6eD3RRJSYFQNILaTVnccTt0e3qiB/9tlnqZbijz76CKUU48aNY+bMmRx//PHstttuuQ6xVUaMGMHzzz/PJZdcwu9+9zuWL1/OnDlz8qJS32ilOI8W83h1+av84ie/oKioiHmPzGPYocMAKCoq4vSZp3PzjTfz0UcfMWTIkBxHKrqS9Jbl1Jhl5cHv8VPhr6DYVyxDd4QQGZWsENfF64glYrtWiKWVuEPyr9kxw8LhMDfddBNTpkxh4sSJ3HDDDZSVlXHNNdfw+uuv89hjjzFz5swuUzlO6tmzJ/PmzeP3v/89y5Yt45hjjmHVqlU5iSVmxdgc3syXtV+yPrieaDyK1+PF7/HnVaVg4fyFXHjWhezRZw8e/PuDqcpx0vd+8D1KS0uZO3dujiIUhSB5YfIqL5ZtsTm8mbXBtWyo30BdrA7LtnIdohCiC0rOSbw5vJn1dev5Mvglm0KbiMajgJNYnG/X3a4sIy3IWuv7gOnABmPMsJa2z6brr7+eefPmMWLECH7zm98wffp0+vXrl+uwMkIpxcyZMxk1ahTnnnsu3/72tznnnHM4+eSTGTp0aKcWkmRLcXJKGL/Hn1ctxeksy+K2G2/joXse4vBJh/OHOX+gvLx8l+169erFaaedxoMPPsgvfvGLLv8+0VpPAeYAXuAeY8x1DZ6fCfwR+NJ96HZjzD1ZDbIbSJ86riZcg8KpQJf4Sijzl+H15F+ZEbkn5VdYtkU4HqY+Xk/MihFPxAHnMyU5llh0nkz9dR8AbgceytDxMuLLL7/kwQcf5PTTT2f27Nm5DqfTDBs2jH/84x9cccUV3HXXXdx111306dOHyZMnM3nyZCZMmJCRKeniVtwZPhEPpyrF+T4lTCgU4spLruRfL/yLb33vW1z660vx+Zp+28+aNYsHHniAe+65h6uuuiqLkWaW1toL3AEcA6wFXtNaP2WM+bDBpvONMRdkPcBuKtnlaWNTG61la3QrARWg2F9Mub9cLngCkPLbXVm2RSgeIhQPEdkeYUNwA+B8bihkDHG2ZWSIhTHmFaAmE8fKpJtvvhnbtvn1r3+d61A6XXl5ObfeeitvvfUWN998MyNGjGDhwoWcfvrpDBs2jNNPP52HH36Y9evXt+m4cSvOlvAW1gXXsT64nnA8vFNyUj7buGEjs74/i5eWvMTPf/VzfnnVL5utHAP079+fE088kb/85S9s27YtS5F2ijHAp8aY/xpjosCjwIk5jkmk8Xq8BDwBUFAfq2ddcB3rguvYUL+BYDRIwkrkOkSRO1J+uwHLtqiL1bExtJH1detZG1xLTbiGuBVPDdWSccS5k7XmCq31LGAWgDGG6urOXbXso48+whjDBRdcwD777EM8Hu/U83WEz+fL2N+jurqaoUOH8uMf/5hIJMLSpUt59tlnWbRoEUuWLAFg+PDhTJs2jWnTpjFy5MhdZsBIWAm2R7ZTH6tnfd16SnqUUKbK2hxLLBZjzRdr+Py/n/PFZ19QW1vL5CmTGTpsaEZeq8/nazIx8cP3P+Ss753Ftm3bmPfwPCZPmdx8rIkY1WXVlPhLuPzyy1m4cCELFy7k0ksvbXdsnf0eb0E/YE3a/bXA2Ea2O1Vr/Q3g/4CLjTFrGtkm6+U33Vf1X+VFAmpjmnsPdkTcihOyQ3iVF7/XGY5R6i9tUwtSHrwHm5XP8eVBbBkrv7ksu3nwd2xWtuNLjiGui+1IqlN+RU9vz0Zj6w6fe5ZtUe4vp1dJZqbTzeT/NGsVZGPMPGCee9fetGlTp57viiuuoLS0lLPOOot4PE5nn68jqqurOy2+4cOHM3z4cK644go++eQTlixZwpIlS7juuuuYPXs21dXVHH300Rx99NEcNu4wVJEiakdTK+pUVlZSs6XpzoF4PM76detZ8/kaVn++mtVfrHZ+/2I1679cTyKxcyvYLdfdwn4H7Me0GdOYcsIU9thzj3a/tsrKSmpqdo1t2UvLuPziyykvL+fPf/kzBw49sNHt0sWsGJ6QhxJ/CX379uWII47g1ltvFMS9XAAAIABJREFU5Xvf+x5FRW2frqs1/9O+ffu2+bht0Fjzvt3g/tPA34wxEa31ucCDwDcbO1i2y2+6RCDBli1bsna+tmjqPZhpCStBwk6kln4NeAKU+cuaTcjpzM+VTMjn+Aqp/Oay7Obz/xg6P76ElSCccMYQx624UyGmdbNLZOuzpT0yGZtlW0T8EeJFmWnEzGTZLcgBb2+99RaLFi3ikksuoaqqKtfh5AWlFIMHD2bw4MGcf/75bNmyhRf/9SLPL36eRc8tYv78+fj9fkaOHcmkIycx8ciJ9B/YH4BEIsFX677aqfK7+vPVrPliDV+u/ZJEfEcluLSslAF7DWDIQUM47vjjGLDXAAYOGsiAvQaglOKFRS+w6KlF3PrHW7ntxtsYPW40U0+cytHHHk1ZedtbqRua//B8bvz9jex/4P78ae6f2H3P3dt1nHPPPZfTTjuNhQsXctppp3U4rhxYCwxIu98fWJe+gTFmc9rdPwPXZyEu0Q7pCbC2bROKhwjGgoCbue71U+YrI+AN4FEFPzlRdyDltwtqrELsweMk1aGcIVWiyyi4CrJt28yePZuqqirOPvvsXIeTd5JLPUcDUcYeM5axx4zFTti8+9a7LP3XUpb+ayl/vPaP/PHaPzJon0F4vV5Wf76aWCyWOkZxSTED9xrI/gfuz9HHHe1UgAcOYMCgAVRVVzU7Nln/QKN/oFn9+WoWPbmIRU8t4upfXs11v72OIycfyfEnHs/YCWNbHCvcUCKR4KbZNzH/4fkccfQRXHvjtZSWlbb77zRp0iSGDRvGXXfdxXe+8528XIilBa8B+2ut98bJcv8u8L30DbTWfYwxyUHpM4CPshuiaC+P8uxUEY7Go9RH61FKpaZYLImWYNmWVJi7Jim/XUDCSjhJdYmQVIgLUKamefsbcCRQrbVeC1xljLk3E8duq1deeYUVK1ZwzTXXNDqVV3eUnEx8e3Q7kUQEcFqdUhnzHhg5ZiQjx4zkossuYs0Xa1j60lJWLVtFRUUFE4+cmGoJHrjXQKp3r+5wgt7AQQM596fncs5PzuHdt97l2Sef5YVFL/D8M89TWVXJcdOP4/gTj+fAgw5s8Vx1wTqu+NkVLHtpGd8/4/v89Bc/xevt2NRZSinOP/98zj//fJYsWcKxxx7boeNlmzEmrrW+AHgeZ5qo+4wxH2itrwFeN8Y8BfxEaz0DiOMk2c7MWcCiQxqukhW34myq30RNbQ0+j49iXzFl/rK8nnFG7CDlNz/FrTj1sXoiVoRoIkrCcoY9dZcKcSgU4vH5jxMIBDj1tFPzPlG/o5RtNxzWlBX2unXrWt6qjSzLYtq0aWzdupWXX345NXa0u46DisQj1MZqCcfDAO2aQiqb46Ci0SjLX17OoicXsfRfS4nFYuy9795MmzGNqTOm0qdfn11i+/CDD7lo1kX899P/8ovf/IJvnfatdp07ZsWoLnaS9JLi8TgTJ05kzz335IknnmjT8dowDqorfsJ0SvltSiQQ6fZjkNsjPTbbtonb8dTqfmX+Mkp8JTltXc7nz+UCLr9ZLbv5/D+G5uOzbZuYFUst2xxNRLFsC6/yZmXu8nz6bAmHwyz42wIe/PODbN7kjOyZceoMfvW7X7W5t7chy7Yo85fRs2jXRMX2yGTZLaghFs888wzvvfcec+bMaVdiVSFIX+o5QQK/8neZuVUDgQBHHXMURx1zFNu2bmPJP5aw6MlF3HHLHdxxyx2MHDOSqTOmMnnKZCp6VPDuW+9y5vfOJBwKM+fPcxg/cXxG4/H5fMyaNYsrr7yS1157jdGjR2f0+EJki1IKv3JamC3bYkt4CzW2tC4LkZTsaQ3FQ0Qtp0JsY6cS1rvKdTSTwuEwC+cv5IF5D7B542bGjB/D9bdez/tvv8+fbvgT27Zu4w9/+kPB1rcKpgU5Fotx1FFHUVRUxOLFi3fqYu/K32JbY6dKsZ3I6FKT+fAtdu3qtTz39HMsenIRqz9fTSAQYPyk8by64lV6V/bmT3f/if0G79eqY8UTNuFIgmCdTTDowYr7ScS8REI+Rh9cQVXvnVvU6uvrGT16NOPGjePee1s/aqiAW6Agy61Q738SYEPN13j9cbyBGBXlFmVlNiVFPrze3P758qF8NKW1se3Suuwro8Tf+a3L+fy5XMDlV1qQXQkrQY/ePVj99erUlGsAPuXLi6EDufxsiUQiPD7/ce6fdz+bNmxi1LhRnHPhORw2+rBUbHNvncsNv7uBw0Yfxk133URFRUXrjh1NUBu02LrNQyIaIBr2s3//cgYNzMwXEGlBbsT8+fP57LPPuP/++zs8/rQr6EpLPXdU/4H9OfvHZ3PW+Wfx/rvv89yTz7F40WIOGX4I1950LVXVu85UEo4mqA/ZBIMQCXux4n7iUR8kAnjxUxIIUO734vEoKIKwDR7iNJxJqbS0lJkzZzJnzhw+/fRT9tuvdRVxkTnl/h5YJc7/xU5AeGOcmrVR4oTxBWJ4A3E8vhg9eliUlSpKitz/q2iVXVqXI1uoCUvrsigMlm0Rt+KE42GiVpS4FSdhO9MmhgIhovFoalGO7i4ajfKEeYL7776fDV9v4LDRh/H7m37PqLGjdtlW/0DTo1cPfvOL33DOD8/h9ntvp7Jq57mRY3GL7bUW22sVsbCfWCSAsooo9pZQFvDh9SkSJeDzJAArS6+y9QqighwKhbjlllsYNWoUxxxzTK7D6TSNVYrzfannTFJKcfChB3PwoQdz6ZWX0rNnJeu+2sjXG+ME6zwkYj4SUS+JmB+vCuBXRZQU+ejp8zjv9Ha+28844wzmzp3L3XffzR//+MeMvibRNkpBSZGPkiIfsGOWEituU/dVnM2xKHHbrTgXxfEH4pSXWZSVKUqKfORBw1DeS+9KDsfDBGPBVOtycvW/ZJKvV3nzorVNiGRPSDQeJWyFnYqwlXBWpFTgwZMaO+xVXrzK2yVWhM2GaDTKk489yf1z7+frr75m+MjhXH3D1YweN7rZv8+U6VPo0aMHl1xwCWd+93+YPWcOpeX9iEb8xCJ+VKKYYm8xJQE/ZV6V/pHdJRREBfn+++/nq6++4s477yy4N3vMihGMBgnFQ92yUpwUT9gE6y22bYNI2EciEqCspITQ9j0pDvgpS7YGF+PcMqi6uhqtNY8++iiXXnopu+/evrmVRefxeBRlxX7Kiv3Ajvm0E2Gb2u1xNsbDWETxBmJ4AzGKihNUlNuUlSqKAoXX65IpDVuXrYRFOBbGsi1sbGdaOeXFo5zKh1c5FeiAN5C1ZCbR/cStONFElHAinGoRjlvOQhMKlfqS51EePF6Z5rApsWiMpxY+xb133cvX67/m0MMO5ao/XMWYw8c0W5eKxS22bI+zfbuius8ELrvqXm669sf85Mxz+d01hn33HQQlTe7eZXT5CvLWrVu5/fbb+eY3v8nYsY2txNn1xK04tdHablspTvw/e3ceH1V1Pn78c9eZrCQhYUdQgUpVcMPdStXi8rPaolzEKggubG4oCKjIpggIiFZBUFnEjVtbq6hVq7ZVqm2/bRWX2lYrIquyZzLr3X5/3EwIGCAkk8yS8/bFyywzd55J8sx95txznuN4hCIOoUqIRjWcuIZr6WjkU5CnkafKEISSViXs8nY1S0w33HADK1as4Mknn2TixInN8phC4ymKRGGeRiF7Xz61wi47dthsdmN4UgI1YKFoFsE8h6IiKMiX0cSJtU77m8rluA62ZxPxIni1piolC2VZklElFV3xR6BdL/MuqQqp8+9//5sZM2ag6zpdunShS5cudO3ala5du9KhQ4cDdj9wPdcveh2bhJvAcq09X3NtPM9/c5acL1zf3ekEn2VZrPrNKpY8toTNGzdz7HHHMum+SZx6xqk1hbHnVU9VjHhEIhCrNVWxuKCAWEgnP+ifj087rhNz5rzMXXcZTJhwKdOmPUPPntm/qD3rC+SFCxdSWVnJhAkT0h1Ko9Quih3XQZXVFlEU710M+yPDTiJAQA6SH9QpqS6GUz0qfKgOP/xwLrroIlasWMFNN90kemxnOU2V0VQd2Du/4pUOW7dabPRiSKqFrPojzgUFDsVF/vzmdC8MzGTJomVfnuf5xY1nE7bCeHgkdieorKpElf2iOagExU6AOWLz5s1cddVVJBIJSktLeeedd4jH4zXfV1WVTp06cViXw+h4WEc6du7o//+wjrTt0NbvilCdZskrFIAohBvJsixe/e2rPLnwSTZt2MTRvY7mjskT6H3SKUTCEl+t83AspWaqooxOQAkQ1PeeqljX4FTXrj2ZO/cV7rrLYOLEAdx99xJOOul7O59nlawukLds2cITTzzBz3/+c44++uh0h3NIPM8j4SSosquI7Y6xtWprzShLrl4SchyPcMxh1y6IRVWcuIaTCGZcMbw/o0aN4tVXX+XZZ5/lhhtuSHc4QhMIaAoBTaH2H6HnQmy7zYbNCWwvjqInUHQbRbNIOAmshC0WBtZT7QI6WQy7nkvEihBKhMDzR6hF0Zy9QqEQV199NaFQiLffeZvC8kLidpwtW7bwzbpv+Obrb9jwzQY2rN/Axm828o9//INwVXivY7Rp24ZOh3Wic5fOdOrciU6H+f+6HN6FgsKC/TyysD9WwuK3v3mF5YuWsnnjRo7o/kPGTb6TY47ti+TqfPu/AAFNo1BXkWQafB5u164Lc+as4u67r2DKlKsYO/YR+vbtn+qn02yyukCeP38+tm0zduzYdIdSL47rELbCRO0olmvV9Fgskov22gUr2zmORzTuEA5DZUjGtTQcS8W1dHQ5QH4gQImW2cVwXY477jhOO+00Hn/8cYYOHYqm5c7vTNi//S4MtDyqNhXy7TYdm7i/MFCzkVSbggKHwkKJvKCYqlEf+26dLYrm7JRIJLj++uv54osvWLFiBT2P7sln33yGrui0bdeWtu3a0ueUvS+9e57Hrp272LB+g184f7OB9evWs+GbDaz+02q2b91ec1tZlunWoxu9TuhF7+N70+v4XnTs3DHn1h4dKtf1iCUcYnGIRCEek7EtifVr1/GX995m9R9XsfXb9RxxZC8mTbqf0047v8l+ZqWlbZg9+7dMmXI1s2ePJBTayU9/em2TPFZTy9oC+auvvuLZZ5/l6quvpkuXLukOp06e5xGzY4TtMAnHby+TnI+XC03H/ULYpioM4bCCk1CxExqupaFKAfJ0nWJdRUp2kMiBSfsjR45k8ODBvPzyy1x22WXpDkdII1mWKMzXsIsLqL0w0B9xdtiyJYHlxUGxUKtb0QWCDoWFkJ8nERSLAw+oPkWzpmhoskaekkdAzc3NCrKF53mMGzeO9957j3nz5vGjH/2oXveTJInSslJKy0o5tvex3/t+NBJlw3q/aP7i31+w5sM1/O6l3/HCsy8A0Lq8Nb2O71VTNB919FE5t3GF41QXwDG/AI7FZDxXwbVUHFvBtRVUSUeVNDZu+Jy//eV3/PnPq9iw4UskSeLoo09h1Ij7OOWUpiuMaysoKObee59n5szhLFgwkcrKHVx55diseyOTtVXanDlz0HWdW265Jd2h7MVyLcJWmLgd90eJPQ9Nye5Fdq7rEYnZhCNQVeUXwo7lF8OqFCBfD/hdJBTJL4JzoBDen3POOYejjjqKhQsX0r9//6xLeKHp+SPOCnmB7yeDVeWyY7vNt14Mh0T15ifJdnQeeXkegYAiRp33Y9+i2XEdLMfv9NOpqFMaIxPmzJnDCy+8wNixYxk4cGDKjpuXn0f3H3Sn+w+6c04/f06r4zh89cVXrPlwDR//82PWfLiGP/z+DwBomkbPY3rS63i/YD72+GOpaFORsniagr+Ble2PAEckEnGFom89dmzXcGwFHA1F0tAVDV1TaKUp/hxtHTzN47///ZDVq1exevUrbNmyDlmWOfbYM7j00us5/fSLKCtr2+zPKRDI4+67l/DQQ7fx9NMPsHv3DkaMuA9Zzp7XtqwskD/99FNeeuklbr755rS33HI9l6gdJWyFsVxrrwV22TZK7HkQjdtEIhCqkrDiGvlBmZ3bClClIHlagAK9uhDee5pmiyFJEsOHD2fMmDH88Y9/5Mc//nG6QxKyyP4WBzoxj6qQzTYrgYuFJ9koqo2susiqjaa5BPNc8vIkArpEQFNET+dqYqpF+j377LPMnz+fQYMGceuttzb54ymKQvejutP9qO5cPuhyAHZs38HHH37Mxx9+zJp/rsF82uTpJU8D0KFTh5qCudcJvejWo9sBu2ikWl0FsGsrONX/JFdDRiOg6gQ0hWJVpkQtQQrsgjoGw13X5fPP/4/Vq1/h/fdf5bvvNqAoKscddxYDB97CqadeQElJebM9v/1RFJUxYx6iuLiMX/96AaHQTm677WE0LTsGC7Orgqs2c+ZMSkpKGDlyZLM/du3FdQnbnzYhSVJN0/xs2cUvnnAIRz1CIYl4VMaxdFxLQ/J0gmqQPF2lQJEoyS9BL26eVmrZ4mc/+xmzZs1i4cKFokAWUkJRJAqUZB/n73NiHvEqh8qEgyPFsV0LWXNQVAdZ9f8fDFaPQOuI6RtCs3nnnXeYMGECffv25f7770/bVbWy1mX0Pa8vfc/rC/jzof/z+X9qRpj//te/8/qq1wF/VPqYXsdw5tlncnTvozmm1zFoesPXlFiOSzyenAKxdwHs2iq46vcKYBT8f/WcDeI4Dp999hdWr17Fn//8Kjt2fIuq6px44o+56qo7OPXUCygqKmnwc2gqkiRx3XVTaNWqNUuWTKeqahd33fUkwWDmL7bMugL5/fff5w9/+AOTJk2iuLi4yR/PcR1iTqxmYV2yGXmy/2KmL66zHY9w1KGqSiISlnFtDSuuInt+K7Wgrvp9hQPUO1FbOl3Xuf7665k+fTpr1qyhd+/e6Q5JyHGKIpGnJBcKfj9RPRsSuxx2fOf4V7I8i02lKuGohqzZyIpNUaFHXj7kBWQ0VYy6Co33ySefMHz4cHr27MmiRYsyauGyrus1O6/+Yugv8DyPLZu21EzL+OgfHzF/9nw8zyMvP4/jTzyePqf1oc+pfejRs8deg13xhEPc8ohEPKJRGduScW0V15ZxbBXJU1HQ0VWtwQVwXWzb4uOP/8zq1av44IPfsWvXNgKBPE466RzOOONiTj65HwUFRY3+WTWHAQNuoqiolF/+cix33jmAqVOfoaioNN1hHVBWFcie5zFjxgzat2/PkCFDmuT4CSdBxI5guVbNlInkdIlM7sFYu3NEqErGSWjYlgq2ji4FCegarXSlUVsuC3v84he/YP78+SxcuJDHHnss3eEILZwk1W5R51++LCkqYZfjn51d2yO21WG3ZWGRwKN64WB18VxY4JFfIIpnof7Wr1/P4MGDKS0t5amnnsr43vCSJNG+Y3vad2zPBRdf4H8Nid//7i3++sHf+Ptf/877sx8CoKCwmB8eexI9jz6Vo354Gp06HYUuBdA1laBa3Qu9Cc6lkUgVmzevZcOG//HJJ3/m3XdfJhTaSTCYz8kn9+PMM39Knz7nZMXoa10uuOAqiopKmDlzBOPGXcq9966ktLR9usPar6wqld544w0+/PBD5syZQ15e41eC2a5NzI4RdaI1+7Z7eHu2Ts3AKRN1d47wW6gpBMgP6BTV7hwhNImioiIGDx7MwoULWbduXcZ2UhEE8Dtu7GlVt/drp2t7xLc5hDbbJIjvt3gO6jKqIol+zwK7du3i6quvJh6Ps3LlStq2bf5FYAfiuh4J28W2PeJxiCc84nEZx5ZxXQnXVvBcmcL8Utq2u4T+/S9n4OU6VaFtfP7Zn/n44z/z0Ufv8X8fvAP4rct69z6T4447i969z6Rdu4a/3ofDlWzatLbWv6/YtGktmzevZefOrTW3Kygo5pRT/KL4hBP6Egjkxur3M864mOnTn2PatMGMHftTpk0zqajIzPNn1pRQjuMwc+ZMjjzySAYMGHDI9/c8j7gTJ2pHSbiJmoK49uhwJi2qE50jMt+wYcN4/PHHWbx4Mffdd1+6wxGEBtm7eN575W3t4tkigePaSLKLJHvIsoOkeEiSh6S4SJKLrHioqoemueiahKJ6aKqEqkooiiS6c+SAeDzOtddey7p163j22Wfp0aNHkz+m43jYjovteNgOxOMe8bhEPC7huTKeo+C6Mq4t4zoKnqugygqyp6EqCqqiEFRlf+RXguTO8yVFJQScPWtsigs60KHdAM49168xtmxZx0cfvceaNatZs+Y9/vjH3wDQtu1hexXM+3aJCIV21RS+yeJ306a1bNy4lsrK7XvdtnXrdnTocAQnn9yPDh0Op337w+nQoSvHHnsykUi06X6oaXTccWcxc+aLTJo0iPHjL2b69Efp1OnMdIf1PZlTER7ECy+8wBdffMHixYsPefVpxIqwPrR+r73bM2V02HE8qiI23223CIUUHEut6SesSgHROSKDtWvXjv79+/P8889z++23U1ZWlu6QBCGlDlQ818kBK+5iux4xx8VxPBzPxsXBw8H1HCTZL6hLSyWqwjKS4iArLoGgRzDgEQxIBHQx1SMTua7Lrbfeyl/+8hcWLFjAaaedVq/72ckC1/ZwXLAsD8eWiCfAsiRcV8JzJfAUXEcCT8Z1JFxXBlcGT0GWZSRPQZM1FEVCVxWKFNnv5pKc75viGZDt2nXhggu6cMEFV+F5Ht9881/WrFnNRx+9y/vvv8qbbz4LQOfOPejS5Qds3bqRTZvWEgrt3Os4FRUd6dDhcE4//SI6dOhKhw5HVBfDXfY7XULXAzlbIAP06HEcc+eu4p57ruSmmwby0kvnMWnSJLp165bu0GpkRYEci8WYO3cuvXv35qKLLjrk+zuuU7NBRzokp0VEoxJVYQkrIeM5GrblN/ouLyknHinwC2FZyrod5lqyESNG8Pzzz7Ns2TJuu+22dIcjCGmnqXJ1nZJ8va27pVNJsAQ15u9M6FoeiajLbtthm2PjSjaOa6FoLrLiICtOHYU0BHRFFNLNaMaMGbz88svcfffdXHrppQe9fTyq8uk/Swho/rRFPAVV8gtcRZZQFRldrp62I+H/y9BfpyRJdOnyA7p0+QGXXHKt34v5q09Zs+Y9PvroPb788mPatTuMs866hA4dDq/5165dl5yZHpFqnTp149FH3+WddxazbNl8zj33XIYMGcKYMWMoLU3/Ar6sKJBXrFjBxo0bmTt3bsZuzGDZLrG4SzjiEQ7LNe1dHEvFszUUdIK6RkBVKVBrTfDPg5LiAna5VrqfgtAA3bt3p1+/fixZsoSRI0emZG68ILQ0suzvLOi3p9t/j9T9FdIFBRIdjm++eFuiZcuWsXDhQq655hpGjBhRr/tIKJQFy8nP95o4uuanKArdu/eme/feXH75jekOJ2vpepCrrx7N9dcP4IEHHmDp0qX8+te/ZsyYMQwZMiStnVEy9L3aHqFQiIcffpizzjqLs846K21xOI5HOGqzo9Ji07cW//va5b9fSvz7c41P1+Tx389K2PxlO+JbDyM/0YUSqTNlWnsq8itoU1xC6+J8CoIaqpqZBb7QcCNHjmTnzp2sXLky3aEIQk5LFtJF+TplRfmUFxbTtrg1QU9Mb2pKb7zxBpMmTeL8889n2rRpGTtQJWSv8vJyZs2axZtvvkmvXr2YPHky55xzDm+++Sael543WBk/grx48WJ27NjBxIkTm+wxkvucxxMQjXnEov5qV8/Z0+cQV0WRVFQpgK7JFGiyf1no+5tiCS1Mnz59OPHEE1m8eDFXXXVVs+7QJAiC0JT+8Y9/MGrUKHr37s2jjz6aEWt3hNzVs2dPnn32Wd5++22mTZvG0KFDOfPMM5k8eTI//OEPmzWWjD6Tb9u2jUWLFnHxxRc3ajMGx4Gdu23icYhGwXX8Jt+eU73No6ciexpa9T7nBWp18StapQn1IEkSI0eO5LrrruO1117jkksuSXdIgiAIjbZ27VquueYa2rVrx/Lly8UUMqFZSJLEeeedx9lnn82KFSuYO3cu559/PoMGDWLcuHFUVFQ0SxwZPcXi4YcfJhaLMW7cuEYdp2pnAdu/7oKzszOFdhdKpMMo0zrQOtiWNoXlVBSV0Lq4gOICnWByoZwgHIJ+/fpxxBFHsHDhwrRdDhIEQUiV7du3c9VVVwH+OqDWrVunOSKhpdE0jWHDhrF69WqGDRvGypUrOfPMM3nkkUeIxWJN/vgZWyCvX7+ep556iiuuuKLRbT9kSaYwTxPFr9BkFEVhxIgRfPzxx7z//vvpDkcQBKHBotEoQ4YMYcuWLSxbtowjjjgi3SEJLVhpaSlTp07lnXfe4fTTT+f++++nb9++vPzyy006IJWSCQSGYVwAPITf1+cJ0zRnNvaYc+bMQVEUbr311kbHJwjN4bLLLuOBBx7gscceq1cLpKZ2sLw0DCMAPAWcCGwHBpqm+XVzxykIwvelK38dx2H06NF89NFHPP7445x44omNPaQgpMSRRx7J0qVLee+995g6dSojR47kySefZMqUKRx/fOrb2DR6BNkwDAV4FLgQ+CEwyDCMRs2k/ve//82vf/1rhg4dSocOHRoboiA0i2AwyLBhw3jnnXf45JNP0hpLPfPyWmCnaZrdgAeBWc0bpSAIdUlX/nqex+TJk3njjTeYNm0aF154YWMPKQgpd9ZZZ/HGG2/wwAMPsG7dOi6++GJuuukmNm7cmNLHScUUi5OBL03T/Mo0zQTwPNCo4bNZs2ZRVFTE6NGjUxCeIDSfwYMHk5+fz4MPPpjuUOqTl5cCy6s/fgE41zCMRs1BWr9+PdOmTWuW+WFC89iyZR0TJ17GggUTcn5+/Y4dO3jwwQf58MMP0x1KWvJ30aJFLF26lOHDhzNs2LDGHEoQmpSiKFx55ZWsXr2aG2+8kVdffZUf/ehHTJ06lUgkkpLHSMUUi47A+lqfbwBO2fdGhmHcANwAYJomHTt2POiBjznmmBSEJwjN75lnnuGZZ5454G2auNj8VfH0AAAgAElEQVSoT17W3MY0TdswjN1Aa2Dbvgc71PxdtGhRgwMXMtNHH73HqlVL0h1Gs5gzZ85Bb5Mt+duQc++iRYtEDgtZacaMGcyYMeOAt6lv7qaiQK7rHev3Ht00zcXA4uT3DzQUHolEkCQpZS1lEolyPvlkN2nckOWASkpK2LVrV7rDqFNLiS0Wg+7dbUpLG3/SC4VCdOrUid27d6cgsgarT17WK3fh0PL37bffZsyYMYTDYaZPn86gQYMatbHA11+XU1mZ1p/lfuVqfsRiYRYtmsTrrz9Nz54ncccdC1myZDqrV6/innue4tRTz09rfPuybTjhhEPfjfTTTz9l4cKFrFq1ClmW6d+/PyNGjOD0009n27bvvU9sTinL30PJ3crKSnRdJxgM1jfOAwoEyvnTnyozdie9XM3fppbK2BwHKiocOnVyU3K8VErFFIsNQOdan3cCNjXmgPn5+aLfopC1ioqK0ro9ZrX65GXNbQzDUIFWwI7GPvC5557L73//e0466STGjRvHiBEj0v1mQTgEa9d+xs039+ONN55h4MBbmD37Jdq168Jttz3MkUcey+zZI/j668/THWaDeZ7Hu+++y6BBgzj//PN56623uOGGG/jggw+YN28ePXr0SHeIkKb8LS4uTllxLAjpUF5enrJjpWIE+f+A7oZhHA5sBK4ArkzBcQVBaLj65OXLwBDgA+By4B3TNFMy1NO2bVuee+45FixYwOzZs/noo4945JFH6NOnTyoOn5P+859/0q5dF1q1Sk+/Wc/zePXVpSxePJnCwlbcd9+vOP74H9V8PxjM5557nuKWW/oxZcrVzJ//OiUlqTsZNTXbtnnllVdYuHAhn376KW3btuWuu+7iqquuori4ON3h7Sut+SsIQgpGkE3TtIEbgTeAz/0vmZ819riCIDTc/vLSMIxphmEkt/p7EmhtGMaXwG3AhFTGIMsyN954Iy+++CKyLHPZZZfx0EMP4ThOKh8m63mex3PPPcitt17ANdecyJNPTmPXrua9vB8K7eTee4fy6KMT6N37TBYs+MNexXFSRUUH7rlnOTt2fMt99w3DshLNGmdDRCIRli5dyplnnsno0aOJxWLMnTuXDz74gFGjRmVicZwR+SsILZ2UplXJ3qZNjZqFcUjEHOSGaymxpXIOMviXeQ42h7G6hWE27lxzyPlbWVnJhAkTeOmllzj99NN5+OGHad++fb3um8tzkB3HYdGiu1m16knOPvvnyLLMn/70IpoW5OKLr+Gyy0ZRWtqmSWP79NO/MHv2SHbu/I6hQ+/mZz8bjiwfeOzkD3/4NbNnj+T883/BLbfMa9Ac86aeg7x9+3aWLl3KsmXL2LlzJ3369GHUqFGcd955B31+OZy/zXruFXOQG66lxJbqOcipzN2UbBSS6eRAlEo24UVVXFtBklQUT0NXNTRVJqAp6Q5REHJacXExjz76KGeffTZ33XUXP/nJT5g3bx79+vVLd2hpk0jEmTv3Rt599yUuu2wUw4bdgyzLXHnl7Tz33DxefPExXnllKf/v/w3hsstGU1bWNqWP7zgOzz//IM8+O4d27bowd+6r9OhxXL3u++MfX8a6df9h5cr5dOlyFD//+fCUxtYY69atY9GiRaxcuZJYLMYFF1zAiBEjxPQeQRAOSYsokAsKbXr0SKDI/qVdy3aJJ1xicY9oVCKUkHFsGc9RcW0Zx1aQ0FA8DU1R0TUFXVVoxEJ8QWjxJEli4MCBnHjiiYwaNYqhQ4cybNgw7rrrrha3MCgcDjF9+jWsWfMe1147mcsv39PzvVOnbowbt4BBg27n+ecf5Le/fZxXXlnGRRcNYcCAG1NSKG/duokHHhjFJ5+8zznnXM7o0bPJzy88pGMMHjyBb775D088MZlOnbrRp8+5jY6rMT7++GMWLFjAq6++iqqqXH755QwfPpxu3bqlNS5BELJTiyiQ96WpMpoqU5gPlNb+jl3zkeWEiccdYnGIx2WqYhKOJeE6Kp6j4FgqiqShSUF0TSGoi1FoQaiPbt26sWrVKmbMmMETTzzBBx98wMKFC+nevXu6Q2sWO3d+xz33XMnatf9i7NhHOPdco87bdep0JGPHPsKVV97G88/P5+WXn+C115Zz4YVXM2DATbRu3a5Bj/+Xv7zOvHm3YFlxbr/9l5x33sAGHUeWZcaNe5SxY3/KzJk38OCDv+Oww5q/A8Tnn/8fy5bN5OOP36O4uJhRo0YxbNgw2rZN7Yi7IAgtSyravOUkTZEpzNcoL9Xo2E7hyK4yPbpLHHWUQ8+jExzdO8LhPXdQ1nUDSul6dkvr2OVsZFtsC99VbWNbVSW7QnGicYcc33xKEA5ZIBBg6tSpLF++nG+//ZYLL7yQ5557Lud3atu0aS23334x69d/yeTJK/ZbHNfWocMR3Hbbwzz++Pv07dufVauWMHRoHxYsmMjWrfWfT5pIxFi48E6mTh1Mmzad+OUv325wcZyUl1fI5Mkr0PUAU6ZcRWVlo7sE1pvj2DzzzAOMHftTNmz4gkmTJvG3v/2NiRMniuJYEIRGa5EjyKkgSRDUq0eOaxZBu9X/LBJWmGjcJRz2qIoqOLaCa6nYCRUJDQ2dgKahq2LkWWi5zjvvPH7/+99z8803M3bsWN59911mzpxJq1at0h1ayn355Sfcc88V2LbN/fe/QM+eJx3S/Tt0OJwxY+YzaNAYVq58iNdeW87vfreCCy74BYZxMxUV+98hbcOGL7n//hv46qtPufTSGxg2bBK6HmjsUwKgTZtOTJq0jPHj+zNjxnXce+9KVLXxK6Jt28NyHBKWi+0lcLHxJBtZcdmxcwML5k3gP599xNk/uZBbJ9zByUdlRP9iYR+um9tveoXcJQrkJqJrMrom06pmWp8HWICFZYeJxV3CEY9oVGanU8WOeBgnoSGjE1SD5OkqiiImPQu5r127djz33HMsXLiQ2bNn8+GHH/LII49w0kmHVkBmsjVrVjN16mAKC1sxc+aLjZqK0K5dF265ZR5XXHErK1c+xOuvP83rrz9Nv35XMnDgLbRp06nmtp7n8dZbK1mwYAK6HmTKlKc55ZTUL4z84Q9P5pZb5jJ37k0sXHgnN944u87OFo7jYbuuXzSFEmwPVe1V+Mqqg6w4yIqLVuASDHgUBTwCmkRAV1AVibdef4t7774X13GZPmc6F11yEa6XebtwCaDoCSj7kt2WhudJ4Ml4joznSXiOhOsqeK6E58rIsoLkySioyJKKqoIiyyiyhKaKi91C82sRBXKemkdQC2K7NpZj4XouiqSgyOkZvU3OgS4q8D8vK5PZscPC8yyi8UrCYY9wWCaRUHESKk5CQyFAQA2IwlnISYqicOONN3LaaacxevRo+vfvz9ixYxk9evTB75zh3ntvFbNnj6RjxyOYPv15Kio6pOS4bdsexs03z2XgwFsxzYd5881nefPNZ/nJT65g4MBb0TSZ2bNH8sc//oZevc5g3LgFlJfXr7Xe/riuh+N62I6L7bg4joeDjYtDr5PP56JLruW1l5+komNH+l18BUgusuIiyS6S7KFoHpoGebpLmzYlFFTtril89yYBe78+RyNR7r9vDr/91W85utfR3DfvPjof1hkhcymKR6cOErqSLHA9oHYfdL81n+eB7brYtofjeFi2h2NLxC0P15apTIDnJgtrBdeRcV0Zz1aQUJBRUdDQNBlVkdEUGVkW50mhcVpEgawqKq2De3ansl2bqB0l5sSwXRvb8RfnqbLaoH6eqSJJkB9UyQ9CRWtIjjrXVTjbcRXXEoWzkFtOPPFE3nzzTcaPH8+sWbN47733uOOOpwkEDq3DQqZ45ZUlLFgwkZ49+zBlytMUFZWk/DHatu3MTTc9wBVX+IXy668/w5tvPkdpaQU7dnzL4METMIxbUJT6DQjEEg4Jy8HyYjiehaJZKJqDpDjImoumeQR1UFQPTZNQFVAVCVWRmdJrOKHQf3l6ySxOPr0jp55xavVRJfZuO6pQ1ioATv1OQf/513+487Y7Wbd2HUOHD2X4zcMzYTt3IUUkyV/3U7+Oqw61i2zb8fy/VxusBERjEE5IOI4Mrl9Me46M48h4joIiq8ieiiqrBPIcXNcTxbRQpxZRIO9LlVWK9CKKKALA9VwSToKoHSXhJrAcC8/zkCQJVU7/j+hAhXMkVkk0CqEqCSuh4sRV7ISGSpA8PUBQV0TyC1mluLiYBQsW0LdvX+666y4GDTqWAQNupn//EQQCeekOr148z2PFilk899w8TjnlfCZMWEQwmN+kj1lR0ZHRo2dhGLfwq189zH//+yHjxy/imGNO/d5t91sEqzb5pR5l+S75QXmf7jzfH9X9PoX75t7H0CuGMuGWCSz/1XK6HN6lwc/J8zyeW/4cDz/wMK1KW7Fg2QJOPu3kBh9PyD3+m7P9naeT64KqP3M9LNvFsj0SFmjBMNsSu3FsGdfe06FKljRUNDRVJaCqqKo4h7ZE6a/+MoAsyQTVIEF1Ty9W27WJ2TGiThTbtXFcBw8PVUrvKHNtkgQFeSoFeVBeBsnC2XUTRGKVRKIeoZCCk/CLZtfS0eUAQV0XbemEjJbsmXzKKacwceJsnnrqfl5/fQVDh97N2Wf/PGNysC6O4/Doo3fwu9+toF+/K7n55jko+z2Bp15FRQdGjpxJXkER323dzvaqykMogpOXwhv++lBQWMCDCx9k8OWDGTNiDMvMZRS3OvTtnHds38GU8VP487t/5kfn/Ih7ZtxDaVnpwe8oCPshy/5c9oDuf15WppMfSP6tJ0emEyQsl1jCJRbz1wmF4/7os2P7BbTkqcho6IqGrilis7EcJQrk/VBllUK9kEL8S7ue5xF34jWjzAkn4d8ugwrmJFmWKMxXKcyHNq3Bfwcdx3FihGMOlSHYHfYT3bE0JDeARoD8oCYWQwgZpWvXrtx/v8nq1a+xePE9zJo1gpdeepwbbph+yF0gmkMiEWPWrBG8//5rDBx4C0OG3Nkkrw+O4xG3HCzbxiKB61nIqlM9FcJGUV0KS4spK9jZJEXwwXTs3JEHHnmAkdeMZMKtE3j48YdR1fqfbj5Y/QGT75hMqDLE+HvGM+AXAzLudVbIXclF9sUFtb+6p0uV7XjE4k7NZmO7YzKeq+BYCq7t79irSjqarNcU0OLPN/uIArmeJEnaa5Q5WTCH7TAJO4HlWcjIGTElY38URaK4QK2V9P47ZsuOUBVxCYUgHFVwLR07oSJ7ARStAMfxxPxmIa169TqDhx56k7ffNlm27D5uu+0i+vbtz9Chd+/VtSGdqqp2M3XqYD799ANGjLiPSy+9vsHHilv+FIiEY+Fi+V0eVBtFdZBUh0C+S36eSzAo1XR42JtMWZnOjh3pm6d7Qp8TmDhlItPvms68++dxx6Q7DnofK2HxyLxHeHrJ0xzZ/UgeXfoo3X/QMjaQEbKHquwZhNqz2ZiHv9mYXfMGNhbH3603KuE6Cm71CLQooLND5lZzGW7fgtlxHaJ2lIgdwXL9ThmZOLpcF02VKS2WKa25Cuq3o4vGq9B0iw3rK/fqqCFa0QnpoCgK/foN4qyzfopp/pLf/GYh77//Gv37j8QwbiIvL30L+bZv38Lddw9kw4YvGT9+EX37/vyg97Fsl1jCJuHGcEigaDaKbiPJDsFil1Z5HsGARDCwb5eH5FzgzL+s+7MBP+OrL77imWXPcGT3I7nsisv2e9t1a9dx52138u/P/s3lV17OmAljWtwW5EJuUBSJfMVfN0RNS/c9BbTresQSBy6gLVkhUmUR0GVRQKeJKJBTRJEVf0qG7p+kLdeiKlFF3I5jezYeHpqcXauu8wIKZWUBVElBdNQQMkVeXiFDhkzkwguvZunSe3n++Qd5441nGDLkTs47b2C9uzWkyoYN/+Puuweye/c2pk59hhNO6FvzPc+DWMImbllYXhwUC1W3kVSLYKFDaSHk50l1TIHInalON99xM2v/t5ZZ02ZxWNfD6HNqn72+73keq15cxexps9F1nTmPzuHHP/nxAY/peZ7/uup5KLKCLutN+RQEIaVkWapZeL+/Ajq/UGHTlu1EIhJVMRnHlvEcFdtScC0FVdZQvIA/p1oTi/GbgiiQm4gma5QG/WsvrucSs2M10zEcz0GVVWQp+06CDeqoIQUJajp5uiqSWEiZNm06MX78Y1xyyXUsXjyJ+fNv5eWXn2D48On06nVGs8Twr3/9ndtv/ymSBFOmvUCnrkfxbeV2VN1G0WxkzSa/tUNpoURe0O/P6pNoKS+/qqoyY/4MrhlwDeNvHs/yF5bX9C8OhULcf8/9vPHqG5x48olMnzOdtu323ia6djEsSzKaoqEpGq2UVgSUQNr62QtCU0kW0GXFGmV7rW/1C2jP86dhxRMekTCEo1JNJw7X9udBy5K/Y6+uqeiqIgatGqBlvEKnmSzJ5Gv55Gt+myfbtQlbYWJ2zG8r51ppjrDxDtRRIxqvJBzxCIVknISGldCQnCABOUh+QBOJKzRKz54nMW/ea/zpTy+yZMl0xo//OaeffhHXXnsPHTockdLHsm2XjZvX8+Xaj/n664955cXHKWpVwj2zHqbHUa3Jy9tKXqD2aE5ujQY3VFFREfMXzWfIgCGMGT6GpeZSvv7f19x0/U18u/lbRo0ZxTU3XIMsy1iuJYrhHCFLMh6e3zoVDwkJRVaycnAok0gSBHWFoE6t3XqhdieOeMIhbnlEqnfstRIyrq1hJ1QkV0OTAgQ0jaCuiukb+yEK5DRQZZVWgVa0CrTC8zwK8gsI7w7v6YyRwQv9DpUsSzWFc+2OGgkrSmWVw+7dMnZcw07oSG5AFM1Cg0iSRN++/TnttAv5zW8ewzQf4m9/+z2XXHIdgwbdRmFhq4MfpBbPg63bt/LF/z5h3Tf/YtPGf7NhwxdsWPcl4apQze2OO/E4Zj40k4o2Fal+Sjmnc5fOzHp4FqOHjWbYwGGsW7uONu3asHDFQnqf0BtV8TdvKFaKCSpBUQznAE3R6FLcBc/zcDwHy7GwXIuEm8D1XBzPwfVcPM/D9VwkJGRJFr/7FEi2s9u7E4c/Am05EaIxl6oqj1BEwbVUHEvBsfw1RgElQFBXW3xXq9ypxLKUJEnka/m0yW+D53lE7ShVVhVxJw6e/wKTi3RNprxUprwU/KI5RjwRpjLksrtSxkno2AkNnAB5ah75ATE9Qzi4QCCPQYPGcP75V7J8+f28+OJjvPWWydVXj+PCCwfX2Y94dyjEV199ztpvPmXDhs/ZuOEL1q/7gp3bt9bcprCokG49unHBT/vRrUc3uvXoxpHdj+TwIw5nx44dzfkUs0rN9Ijq0cPjTz6ecZPGMXPyTH522c+YNHkSFaUVoiDKcZIkoUr+G6A8vr/ZT7KAtl2bhON3hXI9F9u1cT0X13P9i5IgRqBTQFNktILabez8FnbJNUaRqL/GKBLfM+qMs2fUuZWXxuCbkSiQM0iyWM7X8ltUsZwU0BUqWivVc5v9S0WxRJhQyKUypGDHNax49cIEJY/i4haSpcIhKytry5gx8/npT6/l8cfv4dFHJ/Dyy0swrhhL3Imxfv3nbNrwH9Z/8yXfblqP5/l/S7quc3i3wzn9rJP3FMI9jqRN2zZZ0ZGmuSULG6/6PwmpZn2FLMlosoYu62iKhiL5hc1N193EFZdewVFHHcX27dvT/RSEDFC7gK69YVdS7QI67sRJuImaDbxcz625v8jRxqm9xqi8pn3d3qPO4SoIyVXssCLYCQ3FC9Z0tcq1QSxRIGeoll4sJwV1hWAdRXNVlUdYCrPLDeMk9lwa0uUAeQFxaagls22PaMIi4cYpbteeO6Yt4J9//z3PLpnP3AduAECWZTp36czRx3Tnkp9fQLcf+CPCnbt0bvYuGNnAcR0cz0GSJBRJqRnFUyUVXdHRZO2QFh5XVFSIYkaotwMV0I7rEHfixB2/Y5Tt+v+S89hzacpiOtUedS4r0ygv23M+rgy5VFb6g1h2XEf2AuRreeQFsnt+s/jLyQIHLJYh69rHNVZQVwiW+UnaunTPpaFYIkQk4hGJwO6YstelIZUAQV0T7XByiON4RBP+lvAuCRTdQtEt9HyHVm1cCgv27CDX84c/xrjiTP76/l8pb1NO1yO6ih67B5CcGiEhockarQKtyFPzxFQIIeMoskK+vGcRPOwZcY47cWJOrGa02XEdPMlDQRF/yymSHMRqUzOIFSUSC1EZ8giF/N16rZg/0pyvB8kLZE/ZmT2RCoAolvdHkvy+zXkBaL3PpSHbiRKNOUQiUBWW/S229xl1lryW+XPLBq7rEYnZRBNxbGKouoUSsNGCNkWtXdoVSPuMVNS9iYama5zZ98zmDD2rOK6Dg4MqqQTUAKVqKQElIEZ6haxTe8S5QNuzSs3zPH+RoJMg5sQAarpIiSkaqVPT47kCkufhcDREKAS7Q/65147pKATrnFKTKUSBnMX2LZYjdoSqRBUJN1EzF1DwtwUtKlApKoC2FZBckAB7Rp0rq1wkrQ2QucnaUqllm8hXv6MiX9qnhVp27CaXqcQosdDSSJKErujoik4hhZQXlaPFNBJOgogd8duuVrekS86ZF1Ij2c2qXRvweznbhKO72V3poRSUAkVpjvD7RAWVIyRJokAroEAr8ItlK0KVVUXCSYi2OQeQ7CVZVGwRCIhFf5mobRvQNTHCnwpilFgQ9iZJEgHV3wU2yXItIlaEuBPHci1c1xXn0RSTJCjM18jPc8nX3HSHUydRIOcgSZIo0Aso0AtwPZeqRBURK0LCS6BK2bmDnyAIh06MEgvCoUvmSpLt2kTtKDEnhuVY/oJVcZU25zXqt2sYxgBgCtATONk0zb+nIighdWRJpjhQTHGgGMd1CFkholYUy7Wydrtr4cAMwygDVgJdga8BwzTNnXXczgE+qf70G9M0L2muGIWm4XketmvXjAjrqk6ZWoau6GKUOEuI/M08qqxSpBdRVD0NwHEdYnaMiBOp6ZoBLXcNUK5q7NufT4H+wKIUxCI0MUVWKAmUUBIowXZtQokQUTuK7dposiZOoLljAvC2aZozDcOYUP35+DpuFzVN87jmDU1IJddz9xoh1lW9ZtpERVEF2+Lb0h2icOhE/mY4RVb8q7T4CwBdz/ULZjuC5VrYjg2SKJizXaMKZNM0PwcwDCM10QjNRpVVSoOllFKK5VpUJiqJWTEcHDRJFMtZ7lKgb/XHy4E/UvcJVsgyyX7EsiSjKRr5aj75ar54g5tbRP5mGVmSaxbMw34KZlrO/gW5otkm0BiGcQNwA4BpmpSXlzfXQ6OqarM+3qHKhPja0x6AuB2nMlFJ1Iri4qKqKmVlZWmNbX9SGZvlWJQXlJOnfX8b1IZI8++0rWmamwFM09xsGEab/dwuaBjG3/H78Mw0TfO3+ztgOvN3S2RLi/gbrEtyq11VVtEUjaASpEAvqNfcx0x4XTmQTI4vl/JXnHv3r7niSxbMYSuM5fht5gB0RT9gbC3hdc/1XAq1QkrySlJyvFT+Tg/6KmsYxltAuzq+dZdpmi/V94FM01wMLK7+1Nu2rfku/ZWXl9Ocj3eoMi0+CYk8L4+YE8NVXL7b9h1Axi1IKCsrY8eOHSk5luVayFE5ZQVyfX6nHTp0aPDxD5SXh3CYw0zT3GQYxhHAO4ZhfGKa5v/qumE689fRHXbu/N4UzIyQyr9BqNWTVfZ7uOYr+XstqrOw2MWueh0r015X9pXJ8eVS/opz7/41d3wSEjo6qqcSs2NU2pV7jTCr8p5ezKl+bUmlVMbmei5xLY4dsFNyvFTm7kErHtM0z6tfWEIukSSJPDWP8sJylKjSYre6zlQHykvDML41DKN99ehTe+C7/RxjU/X/vzIM44/A8UCdBbLQNJJdJmRJRld0ivVigmpQLJ7NcSJ/W7b6TMlIOAk8zxNTp9JIvAoLB5XckKRNfhs6FXaidV5rZEnGci0sx0p3eML3vQwMqf54CPC9Kz2GYZQahhGo/rgcOAP4V7NF2IJ5nkfCSeC4Dpqi0SavDR0LO1KRV0G+li+KY0HkbwuTLJjL88ppX9CejkUdaVvQFl3V8fA701iOheeJXv3NqbFt3n4O/BJ/Q8FXDcP4yDTN81MSmZCRxFbXWWEmYBqGcS3wDTAAwDCMk4ARpmleh9+acZFhGC7+G+WZpmmKE2wTcT23pltMUA1SrpeLXBH2R+RvCydL/nS/1sHWgP+mOu7ECdv+HGaxPXbzkNL0jsTbtGlTsz2YmAfVcPWNLbnVddgKN1uxnOo5yOXB1C3SO4R5UNn46tas+RvX41k5B9lxHVxcNEkjT8ujUCts1g06Mvl1BTI7vhzOX3HurSWT4ztQbMmCOWpHa3b7g+YrmFM9B7lAK9hrY5bGSGXuZtaqKyFrfW+raztCVaKKhOuv1hWjZUJLYLlWTU/i4kAxBVqBmDIhCEJKSZJEUA0SVIPAnmlbETtCwk3485fxxM65jSQKZCHl9lcs116hLwi5wnZtPDwCSoCyYBn5ar647CkIQrORJImAGiCgBgC/YLZci4gdIW77I8zJq1nitan+RKUiNKl9i+Uqq6qmWBabGwjZKrm1rCqrlOeVE1AC4m9ZEISMIEkSuqL7fZb9mpm4HafKriJux7FdG1UWo8sHIwpkodlIkuTvZ68XEbfj7E7sJu7EkZGbdW6mIDRE8gpIcqQ4T82joqCCbdHMnMMoCIKQVHuE2XZtqqwqYlbMnxYmSeLKbh3ET0RIi4AaoI3aBtdzqUpUEbbC2J4t5ioLGSU5UqzJmpg+IQhCTlBllZJACQT8RXIRy19gn3ATYp+DWkSBLKSVLMkUB4opDhTXjConnAQSkhhVFtIi2X1Cl3VKAiWiN7EgCDlLlmQK9UIK9cKa1q1hO0zcjtcs9GupgwKiQBYyxr6jylVWFY7niFFlockl+xTrsk6RXkSBViDeoAmC0KLU3ucAxLxlUSALGUeMKgvNwRvA6K4AAAvWSURBVPP8HaoUWSFPzaNYLxZ/X4IgCNX2nbcctsJErWjNTqC5/nopCmQho9UeVQ4lQoStsBhVFhrM8zxsz0ZGJqgFqdArxOIUQRCEg1BllVaBVrQKtKKsVRlfhb8inAj77eNy9HwszgxCVpAluSY5Y3aMykQllmPVXPYRhP3xPA/Ls/yiWA1SppXVjIoIgiAIh0aWZEoCJZQESojZMXbHd5NwEyiSklNTMERlIWSd5A5CZa3KIAJVlr9jn4RoVSPskdzVThTFgiAITSN5PnZch8pEJWErDOTGhmDZ/wyEFkuWZAr0Agr0gpq96UNWSKy+bcGSbdkCaoCSQEnNVqyCIAhC01FkhdJgKaXBUiJWhFAiRNyNZ/V216JAFnLCvnvTW65FVaKKmO03QlckJecXFLRUyaJYV3Sxq50gCEKaJTthOK7DrsQuYnYM18u+ucqiQBZykiZrlAZLAb+vbdgKE7WjNbuh5cLln5asrl3tRFEsCIKQORRZoXWwNZ7n1YwqJ9wEmqxlxeu1qBKEnKfISk3bONdziVp+I/SEk8DDy7p3tS1VsijWZV3saicIgpAlJEmqmQ5puza74v6oMpDR0y9EgSy0KHXNW66yqmqKLyHzSJKEhERZoIx8TRTFgiAI2UqVVcrzyvE8j7AVJpQIIZGZr+miQBZarH3nLQuZqUNRB/S4nu4wBEEQhBSRJKlmi+tMlblj24IgCIIgCIKQBqJAFgRBEARBEIRaRIEsCIIgCIIgCLWIAlkQBEEQBEEQapE8z0vH46blQQUhA2Xm8t0DE/krCL5sy1+Ru4LgO2jupmsEWWrOf4Zh/KO5HzNX4hOxNXls2ShTf5aZ/HsWsWVRfDmcv5n6c8z037OILfdiOygxxUIQBEEQBEEQahEFsiAIgiAIgiDU0lIK5MXpDuAgMjk+EVvDZHJs2SaTf5YitobL5PgyObZskuk/x0yOT8TWMCmLLV2L9ARBEARBEAQhI7WUEWRBEARBEARBqBdRIAuCIAiCIAhCLWq6A2hKhmF0Bp4C2gEusNg0zYfSG9XeDMNQgL8DG03TvDjd8SQZhlECPAEcg987c5hpmh+kNyqfYRhjgOvw4/oEGGqaZiyN8SwBLga+M03zmOqvlQErga7A14BhmubOdMWYbUTuNo7I30OKR+Rvion8bbhMzl3IrPxt6tzN9RFkG7jdNM2ewKnAaMMwfpjmmPZ1C/B5uoOow0PA66ZpHgX0JkNiNAyjI3AzcFJ1QijAFemNimXABft8bQLwtmma3YG3qz8X6k/kbuOI/K2/ZYj8TTWRvw2XkbkLGZm/y2jC3M3pAtk0zc2maf6z+uMQ/h9ax/RGtYdhGJ2A/4f/bjFjGIZRDPwIeBLANM2EaZq70hvVXlQgzzAMFcgHNqUzGNM03wV27PPlS4Hl1R8vB37WrEFlOZG7DSfy99CI/E09kb8NkwW5CxmUv02duzldINdmGEZX4Hjgr2kOpbb5wB34l6AyyRHAVmCpYRgfGobxhGEYBekOCsA0zY3AHOAbYDOw2zTNN9MbVZ3amqa5GfyTBdAmzfFkLZG7h0zkb+OJ/E0Rkb+HJGNzF7Imf1OWuy2iQDYMoxD4NXCraZqV6Y4HwDCM5LyZf6Q7ljqowAnAQtM0jwfCZMglRsMwSvHfIR4OdAAKDMO4Kr1RCU1F5G6DiPwVMoLI30OWsbkLLS9/c75ANgxDw0/QZ0zT/E2646nlDOASwzC+Bp4HzjEM4+n0hlRjA7DBNM3kO/4X8JM2E5wHrDVNc6tpmhbwG+D0NMdUl28Nw2gPUP3/79IcT9YRudtgIn8bT+RvI4n8bZBMzl3IjvxNWe7mdIFsGIaEP5fnc9M056U7ntpM05xommYn0zS74k9yf8c0zYx4J2aa5hZgvWEYP6j+0rnAv9IYUm3fAKcahpFf/fs9lwxaxFDLy8CQ6o+HAC+lMZasI3K34UT+poTI30YQ+dswGZ67kB35m7Lczek2b/jvFK8GPjEM46Pqr91pmuZraYwpW9wEPGMYhg58BQxNczwAmKb5V8MwXgD+ib9S+kPSvO2lYRjPAX2BcsMwNgCTgZmAaRjGtfgvKgPSF2FWErnbOCJ/60nkb5MQ+dtwGZm7kHn529S5K7aaFgRBEARBEIRacnqKhSAIgiAIgiAcKlEgC4IgCIIgCEItokAWBEEQBEEQhFpEgSwIgiAIgiAItYgCWRAEQRAEQRBqyfU2b4IgCDnJMIzPgNGmaf6xAff1gO6maX6Z8sAEQQBqttleC2imadppDkc4RKJAFgRByEKmaR6d7hgEQWg+hmH0BZ42TbNTumNpCcQUC0EQhCxiGIYY2BCEFkbkffMTG4XkGMMwJgDXA22A9cBdpmm+aBiGAszG33oxBMwFfkn1pR/DMFoB84CLABdYCkw2TdNJw9MQhJxkGMbXwCL8XcbaA78FRpqmGTMM42LgXqAr/vayI0zT/LjW/RYCvwB+ABQAXwLXmab5lmEYAWAWYFQ/lAmMN00zXn3/ccBtgAfcjb8NsJhiIQiHwDCMzsBDwFn4A4zPATcDd+Kfd/OA14GbTNPcXWuKxTXAdCAfeNA0zfuqj7ffvE2OFuOfp8cA7wEXAwEgUn37HqZpbmq6Z9yyiRHk3PM//ORtBUwFnjYMoz1+8l4IHAecAPxsn/stx986shtwPNAPuK6ZYhaEluQXwPnAkUAP4G7DME4AlgDDgdb4RfTL1SfQpEHA/wNK6pjPeBdwKn5+9wZOxi+EMQzjAmAs8BOgO3Be0zwtQchd1YNMrwDr8N/EdgSexy9+rwF+DBwBFAKP7HP3M/Hf2J4L3GMYRs/qr+83b6u1A8qALsBg/HP4JtM0C6v/ieK4CYkh+xxjmuavan260jCMifhJZwAPmaa5AcAwjJn4yYphGG3xE6/ENM0oEDYM40HgBvwTtSAIqfOIaZrrAQzDuA9/hKg1sMg0zb9W32a5YRh34p88/1T9tYeT96vDL/BHrb6rPu5U/NydhJ/7S03T/LT6e1Pwi21BEOrvZKADMK7WG9TV1bk2zzTNrwCqz7mfGoYxtNZ9p1afW9cYhrEGvxj+nAPnLfhXcyfXuhLUpE9Q2JsokHOMYRiD8S+ldq3+UiFQjp/YtU+utT/uAmjA5loJKO9zG0EQUqN2Xq3Dz80uwBDDMG6q9T29+nt13W9fHaqPte9xk9/7xz7fEwTh0HQG1tVx9aau3FOBtrW+tqXWxxH88/L+7ls757eaphlrTNBCw4kCOYcYhtEFeBx/ZPgD0zQdwzA+AiRgM1B75WvnWh+vB+JAuWhFIwhNrnbuHQZsws/B+5JzE/fjQAtGNuEX2Z/tc1zwc3/fxxQE4dCsBw4zDEPd5zyZzL2kw/CnK37L3ufcuhwob+H7OS8WjTUjUSDnlgL8BNoKUH2J55jq75nALYZhvAqEgfHJO5mmudkwjDeBuYZhTAKqgMOBTqZp/glBEFJptGEYr+CPJN0JrAR+A7xoGMZbwN/wF/P0Bd41TTNUj2M+hz+X+f/wXwPuwV/gA37uLzUM4ynga2By6p6KILQYf8N/sznTMIzJgAOciJ974w3D+B3+uXcGsLJ68fvBjnmgvK3Lt0BrwzBamaa5u1HPRjgosUgvh5im+S/87hQf4CfSscCfq7/9OP+/nTtUiSAMAjj+N/oKFp/HYB2byeozWO4BDAa7YBgEm8IhF8yHwglqkAtiP6PRMCt8CIuCCyfs/wdblo+Pb8PA7O7MwBRYAPfAFfWW+zWlYp/6pfsIrIALqste0rDOqVhcdtckM+dUI+0JFX8vVOPPb02AORXfD8Bdd4/MvAaOgVm372yIh5DGpJvotEs1sr8Cb8Ae1Vx7BtxSEys+gMOebb7rjdueMzxTSfUyIt4jYqtvrf7OMW8jFRE7wGlmbv+4WNIgunFtB5l5s+6zSJL6WWIxEhGxSY2hmVLNA0fA5VoPJUmS9A9ZYjEeG9Rc5BVVYvFE1TtJkiSpYYmFJEmS1PALsiRJktQwQZYkSZIaJsiSJElSwwRZkiRJapggS5IkSY1Pn6ZFEExY4ooAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x576 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot_parameters(around_coef=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Besides plots for the double differences and the detrended version, the plots also include the level, for which there is no confidence band given the sampling scheme, and the trends. We point out that these trends related to the detrended parameterization. Thus, they cannot be interpreted separately, in contrast to the detrended parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Remark (not in paper): instead, we can also plot the double sums of double differences as shown in equation (3) in the paper. To do this, we merely need to add the argument ``plot_style='sum_sum'`` to ``plot_parameters``. In this case, the trends are de-coupled and can be interpreted separately. However, the interpretation of the double sums is difficult.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forecasting (Table 4)\n",
    "\n",
    "Finally, we replicate the forecasting results. The package has both the $t$ and the bootstrap forecasts included.\n",
    "\n",
    "*Remark: The quantiles of the $t$ forecast do not exactly match those in the paper but give the same impression. This is due to a former bug in the software.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we look at the $t$ forecast. If we do not supply the argument ``method`` to ``get_distribution_fc``, $t$ forecasts will be generated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_ac.forecast()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forecast by cell, cohort, age, period, and total are automatically generated. First, we look at the forecasts by period (calendar year). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point_forecast</th>\n",
       "      <th>se_total</th>\n",
       "      <th>se_process</th>\n",
       "      <th>se_estimation_xi2</th>\n",
       "      <th>se_estimation_tau</th>\n",
       "      <th>q_0.75</th>\n",
       "      <th>q_0.9</th>\n",
       "      <th>q_0.95</th>\n",
       "      <th>q_0.99</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Period</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5226536.0</td>\n",
       "      <td>749213.0</td>\n",
       "      <td>525626.0</td>\n",
       "      <td>492961.0</td>\n",
       "      <td>205007.0</td>\n",
       "      <td>5737024.0</td>\n",
       "      <td>6204644.0</td>\n",
       "      <td>6491431.0</td>\n",
       "      <td>7050492.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4179394.0</td>\n",
       "      <td>711896.0</td>\n",
       "      <td>470031.0</td>\n",
       "      <td>508914.0</td>\n",
       "      <td>163934.0</td>\n",
       "      <td>4664456.0</td>\n",
       "      <td>5108785.0</td>\n",
       "      <td>5381288.0</td>\n",
       "      <td>5912502.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3131668.0</td>\n",
       "      <td>645728.0</td>\n",
       "      <td>406872.0</td>\n",
       "      <td>486139.0</td>\n",
       "      <td>122837.0</td>\n",
       "      <td>3571645.0</td>\n",
       "      <td>3974675.0</td>\n",
       "      <td>4221849.0</td>\n",
       "      <td>4703690.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2127272.0</td>\n",
       "      <td>480308.0</td>\n",
       "      <td>335337.0</td>\n",
       "      <td>333590.0</td>\n",
       "      <td>83441.0</td>\n",
       "      <td>2454537.0</td>\n",
       "      <td>2754320.0</td>\n",
       "      <td>2938174.0</td>\n",
       "      <td>3296578.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1561879.0</td>\n",
       "      <td>405967.0</td>\n",
       "      <td>287338.0</td>\n",
       "      <td>280166.0</td>\n",
       "      <td>61264.0</td>\n",
       "      <td>1838491.0</td>\n",
       "      <td>2091875.0</td>\n",
       "      <td>2247272.0</td>\n",
       "      <td>2550203.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1177744.0</td>\n",
       "      <td>365194.0</td>\n",
       "      <td>249514.0</td>\n",
       "      <td>262631.0</td>\n",
       "      <td>46196.0</td>\n",
       "      <td>1426574.0</td>\n",
       "      <td>1654509.0</td>\n",
       "      <td>1794299.0</td>\n",
       "      <td>2066805.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>744287.0</td>\n",
       "      <td>295151.0</td>\n",
       "      <td>198354.0</td>\n",
       "      <td>216605.0</td>\n",
       "      <td>29194.0</td>\n",
       "      <td>945393.0</td>\n",
       "      <td>1129611.0</td>\n",
       "      <td>1242590.0</td>\n",
       "      <td>1462830.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>445521.0</td>\n",
       "      <td>251606.0</td>\n",
       "      <td>153463.0</td>\n",
       "      <td>198618.0</td>\n",
       "      <td>17475.0</td>\n",
       "      <td>616957.0</td>\n",
       "      <td>773996.0</td>\n",
       "      <td>870307.0</td>\n",
       "      <td>1058054.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>86555.0</td>\n",
       "      <td>108536.0</td>\n",
       "      <td>67642.0</td>\n",
       "      <td>84812.0</td>\n",
       "      <td>3395.0</td>\n",
       "      <td>160507.0</td>\n",
       "      <td>228250.0</td>\n",
       "      <td>269795.0</td>\n",
       "      <td>350785.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        point_forecast  se_total  se_process  se_estimation_xi2  \\\n",
       "Period                                                            \n",
       "11           5226536.0  749213.0    525626.0           492961.0   \n",
       "12           4179394.0  711896.0    470031.0           508914.0   \n",
       "13           3131668.0  645728.0    406872.0           486139.0   \n",
       "14           2127272.0  480308.0    335337.0           333590.0   \n",
       "15           1561879.0  405967.0    287338.0           280166.0   \n",
       "16           1177744.0  365194.0    249514.0           262631.0   \n",
       "17            744287.0  295151.0    198354.0           216605.0   \n",
       "18            445521.0  251606.0    153463.0           198618.0   \n",
       "19             86555.0  108536.0     67642.0            84812.0   \n",
       "\n",
       "        se_estimation_tau     q_0.75      q_0.9     q_0.95     q_0.99  \n",
       "Period                                                                 \n",
       "11               205007.0  5737024.0  6204644.0  6491431.0  7050492.0  \n",
       "12               163934.0  4664456.0  5108785.0  5381288.0  5912502.0  \n",
       "13               122837.0  3571645.0  3974675.0  4221849.0  4703690.0  \n",
       "14                83441.0  2454537.0  2754320.0  2938174.0  3296578.0  \n",
       "15                61264.0  1838491.0  2091875.0  2247272.0  2550203.0  \n",
       "16                46196.0  1426574.0  1654509.0  1794299.0  2066805.0  \n",
       "17                29194.0   945393.0  1129611.0  1242590.0  1462830.0  \n",
       "18                17475.0   616957.0   773996.0   870307.0  1058054.0  \n",
       "19                 3395.0   160507.0   228250.0   269795.0   350785.0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ac.forecasts['Period'].round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The point-forecast corresponds to the cash-flow by calendar year. Besides, the output includes quantile forecasts, and the standard error and its components:\n",
    "* ``se_total``: $[\\hat{\\tau} \\{D_1/(n-q)\\}\\{\\hat{\\pi}_\\mathcal{A} + \\hat{s}^2_\\mathcal{A} + (\\hat{\\pi})^2\\}]^{1/2}$\n",
    "* ``se_process``: $[\\hat{\\tau} \\{D_1/(n-q)\\}\\hat{\\pi}_\\mathcal{A}]^{1/2}$\n",
    "* ``se_estimation_xi``: $[\\hat{\\tau} \\{D_1/(n-q)\\} \\hat{s}^2_\\mathcal{A}]^{1/2}$\n",
    "* ``se_estimation_tau``: $[\\hat{\\tau} \\{D_1/(n-q)\\} (\\hat{\\pi}_\\mathcal{A})^2]^{1/2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can look at forecasts by cohort"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point_forecast</th>\n",
       "      <th>se_total</th>\n",
       "      <th>se_process</th>\n",
       "      <th>se_estimation_xi2</th>\n",
       "      <th>se_estimation_tau</th>\n",
       "      <th>q_0.75</th>\n",
       "      <th>q_0.9</th>\n",
       "      <th>q_0.95</th>\n",
       "      <th>q_0.99</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cohort</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>94634.0</td>\n",
       "      <td>110371.0</td>\n",
       "      <td>70728.0</td>\n",
       "      <td>84649.0</td>\n",
       "      <td>3712.0</td>\n",
       "      <td>169837.0</td>\n",
       "      <td>238725.0</td>\n",
       "      <td>280973.0</td>\n",
       "      <td>363332.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>469511.0</td>\n",
       "      <td>216576.0</td>\n",
       "      <td>157541.0</td>\n",
       "      <td>147468.0</td>\n",
       "      <td>18416.0</td>\n",
       "      <td>617079.0</td>\n",
       "      <td>752254.0</td>\n",
       "      <td>835156.0</td>\n",
       "      <td>996764.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>709638.0</td>\n",
       "      <td>261515.0</td>\n",
       "      <td>193681.0</td>\n",
       "      <td>173502.0</td>\n",
       "      <td>27835.0</td>\n",
       "      <td>887825.0</td>\n",
       "      <td>1051049.0</td>\n",
       "      <td>1151153.0</td>\n",
       "      <td>1346295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>984889.0</td>\n",
       "      <td>304298.0</td>\n",
       "      <td>228173.0</td>\n",
       "      <td>197591.0</td>\n",
       "      <td>38632.0</td>\n",
       "      <td>1192227.0</td>\n",
       "      <td>1382154.0</td>\n",
       "      <td>1498635.0</td>\n",
       "      <td>1725701.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1419459.0</td>\n",
       "      <td>375938.0</td>\n",
       "      <td>273925.0</td>\n",
       "      <td>251386.0</td>\n",
       "      <td>55677.0</td>\n",
       "      <td>1675611.0</td>\n",
       "      <td>1910252.0</td>\n",
       "      <td>2054155.0</td>\n",
       "      <td>2334679.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2177641.0</td>\n",
       "      <td>496599.0</td>\n",
       "      <td>339284.0</td>\n",
       "      <td>352422.0</td>\n",
       "      <td>85416.0</td>\n",
       "      <td>2516006.0</td>\n",
       "      <td>2825958.0</td>\n",
       "      <td>3016048.0</td>\n",
       "      <td>3386608.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3920301.0</td>\n",
       "      <td>791908.0</td>\n",
       "      <td>455229.0</td>\n",
       "      <td>629476.0</td>\n",
       "      <td>153771.0</td>\n",
       "      <td>4459880.0</td>\n",
       "      <td>4954148.0</td>\n",
       "      <td>5257277.0</td>\n",
       "      <td>5848196.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4278972.0</td>\n",
       "      <td>1049093.0</td>\n",
       "      <td>475597.0</td>\n",
       "      <td>919909.0</td>\n",
       "      <td>167840.0</td>\n",
       "      <td>4993788.0</td>\n",
       "      <td>5648578.0</td>\n",
       "      <td>6050153.0</td>\n",
       "      <td>6832983.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>4625811.0</td>\n",
       "      <td>1984981.0</td>\n",
       "      <td>494497.0</td>\n",
       "      <td>1913818.0</td>\n",
       "      <td>181444.0</td>\n",
       "      <td>5978309.0</td>\n",
       "      <td>7217231.0</td>\n",
       "      <td>7977049.0</td>\n",
       "      <td>9458235.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        point_forecast   se_total  se_process  se_estimation_xi2  \\\n",
       "Cohort                                                             \n",
       "2              94634.0   110371.0     70728.0            84649.0   \n",
       "3             469511.0   216576.0    157541.0           147468.0   \n",
       "4             709638.0   261515.0    193681.0           173502.0   \n",
       "5             984889.0   304298.0    228173.0           197591.0   \n",
       "6            1419459.0   375938.0    273925.0           251386.0   \n",
       "7            2177641.0   496599.0    339284.0           352422.0   \n",
       "8            3920301.0   791908.0    455229.0           629476.0   \n",
       "9            4278972.0  1049093.0    475597.0           919909.0   \n",
       "10           4625811.0  1984981.0    494497.0          1913818.0   \n",
       "\n",
       "        se_estimation_tau     q_0.75      q_0.9     q_0.95     q_0.99  \n",
       "Cohort                                                                 \n",
       "2                  3712.0   169837.0   238725.0   280973.0   363332.0  \n",
       "3                 18416.0   617079.0   752254.0   835156.0   996764.0  \n",
       "4                 27835.0   887825.0  1051049.0  1151153.0  1346295.0  \n",
       "5                 38632.0  1192227.0  1382154.0  1498635.0  1725701.0  \n",
       "6                 55677.0  1675611.0  1910252.0  2054155.0  2334679.0  \n",
       "7                 85416.0  2516006.0  2825958.0  3016048.0  3386608.0  \n",
       "8                153771.0  4459880.0  4954148.0  5257277.0  5848196.0  \n",
       "9                167840.0  4993788.0  5648578.0  6050153.0  6832983.0  \n",
       "10               181444.0  5978309.0  7217231.0  7977049.0  9458235.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ac.forecasts['Cohort'].round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and for the total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point_forecast</th>\n",
       "      <th>se_total</th>\n",
       "      <th>se_process</th>\n",
       "      <th>se_estimation_xi2</th>\n",
       "      <th>se_estimation_tau</th>\n",
       "      <th>q_0.75</th>\n",
       "      <th>q_0.9</th>\n",
       "      <th>q_0.95</th>\n",
       "      <th>q_0.99</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Total</th>\n",
       "      <td>18680856.0</td>\n",
       "      <td>2952921.0</td>\n",
       "      <td>993729.0</td>\n",
       "      <td>2682412.0</td>\n",
       "      <td>732744.0</td>\n",
       "      <td>20692875.0</td>\n",
       "      <td>22535935.0</td>\n",
       "      <td>23666265.0</td>\n",
       "      <td>25869724.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       point_forecast   se_total  se_process  se_estimation_xi2  \\\n",
       "Total      18680856.0  2952921.0    993729.0          2682412.0   \n",
       "\n",
       "       se_estimation_tau      q_0.75       q_0.9      q_0.95      q_0.99  \n",
       "Total           732744.0  20692875.0  22535935.0  23666265.0  25869724.0  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ac.forecasts['Total'].round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we compute distribution forecasts based on the bootstrap by England and Verrall (1999) and England (2002). Since bootstrapping requires random sampling, the results differ somewhat from those in the paper. We note that the bootstrap does not have a solid theoretical foundation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "fc_bootstrap = apc.bootstrap_forecast(apc.loss_TA(), seed=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just as for the $t$ forecast, this automatically computes forecasts by cell, age, period, cohort and for the total. The output for the bootstrap forecasts contains descriptive statistics over bootstrap draws:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>90%</th>\n",
       "      <th>95%</th>\n",
       "      <th>99%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Period</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>999.0</td>\n",
       "      <td>5203999.0</td>\n",
       "      <td>829641.0</td>\n",
       "      <td>2926417.0</td>\n",
       "      <td>5144427.0</td>\n",
       "      <td>5762222.0</td>\n",
       "      <td>6254180.0</td>\n",
       "      <td>6590469.0</td>\n",
       "      <td>7262189.0</td>\n",
       "      <td>8319387.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>999.0</td>\n",
       "      <td>4153410.0</td>\n",
       "      <td>759793.0</td>\n",
       "      <td>2021208.0</td>\n",
       "      <td>4139537.0</td>\n",
       "      <td>4624053.0</td>\n",
       "      <td>5168286.0</td>\n",
       "      <td>5440464.0</td>\n",
       "      <td>6056917.0</td>\n",
       "      <td>7456182.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>999.0</td>\n",
       "      <td>3142845.0</td>\n",
       "      <td>713375.0</td>\n",
       "      <td>1311819.0</td>\n",
       "      <td>3101645.0</td>\n",
       "      <td>3608460.0</td>\n",
       "      <td>4085611.0</td>\n",
       "      <td>4416031.0</td>\n",
       "      <td>4909628.0</td>\n",
       "      <td>5911036.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>999.0</td>\n",
       "      <td>2119326.0</td>\n",
       "      <td>508279.0</td>\n",
       "      <td>913750.0</td>\n",
       "      <td>2083975.0</td>\n",
       "      <td>2445325.0</td>\n",
       "      <td>2785607.0</td>\n",
       "      <td>3003399.0</td>\n",
       "      <td>3453377.0</td>\n",
       "      <td>3976919.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>999.0</td>\n",
       "      <td>1545178.0</td>\n",
       "      <td>455274.0</td>\n",
       "      <td>507736.0</td>\n",
       "      <td>1511352.0</td>\n",
       "      <td>1825142.0</td>\n",
       "      <td>2136125.0</td>\n",
       "      <td>2332187.0</td>\n",
       "      <td>2847346.0</td>\n",
       "      <td>3155313.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>999.0</td>\n",
       "      <td>1170091.0</td>\n",
       "      <td>394602.0</td>\n",
       "      <td>245565.0</td>\n",
       "      <td>1125245.0</td>\n",
       "      <td>1424747.0</td>\n",
       "      <td>1716499.0</td>\n",
       "      <td>1858683.0</td>\n",
       "      <td>2204893.0</td>\n",
       "      <td>2653666.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>999.0</td>\n",
       "      <td>746713.0</td>\n",
       "      <td>348868.0</td>\n",
       "      <td>-100513.0</td>\n",
       "      <td>697799.0</td>\n",
       "      <td>957036.0</td>\n",
       "      <td>1217316.0</td>\n",
       "      <td>1399849.0</td>\n",
       "      <td>1679438.0</td>\n",
       "      <td>2560591.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>999.0</td>\n",
       "      <td>446096.0</td>\n",
       "      <td>280466.0</td>\n",
       "      <td>-114902.0</td>\n",
       "      <td>392203.0</td>\n",
       "      <td>578785.0</td>\n",
       "      <td>820631.0</td>\n",
       "      <td>986236.0</td>\n",
       "      <td>1278147.0</td>\n",
       "      <td>1775041.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>999.0</td>\n",
       "      <td>87893.0</td>\n",
       "      <td>134991.0</td>\n",
       "      <td>-430840.0</td>\n",
       "      <td>45298.0</td>\n",
       "      <td>120367.0</td>\n",
       "      <td>270958.0</td>\n",
       "      <td>365589.0</td>\n",
       "      <td>562607.0</td>\n",
       "      <td>1140665.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        count       mean       std        min        50%        75%  \\\n",
       "Period                                                                \n",
       "11      999.0  5203999.0  829641.0  2926417.0  5144427.0  5762222.0   \n",
       "12      999.0  4153410.0  759793.0  2021208.0  4139537.0  4624053.0   \n",
       "13      999.0  3142845.0  713375.0  1311819.0  3101645.0  3608460.0   \n",
       "14      999.0  2119326.0  508279.0   913750.0  2083975.0  2445325.0   \n",
       "15      999.0  1545178.0  455274.0   507736.0  1511352.0  1825142.0   \n",
       "16      999.0  1170091.0  394602.0   245565.0  1125245.0  1424747.0   \n",
       "17      999.0   746713.0  348868.0  -100513.0   697799.0   957036.0   \n",
       "18      999.0   446096.0  280466.0  -114902.0   392203.0   578785.0   \n",
       "19      999.0    87893.0  134991.0  -430840.0    45298.0   120367.0   \n",
       "\n",
       "              90%        95%        99%        max  \n",
       "Period                                              \n",
       "11      6254180.0  6590469.0  7262189.0  8319387.0  \n",
       "12      5168286.0  5440464.0  6056917.0  7456182.0  \n",
       "13      4085611.0  4416031.0  4909628.0  5911036.0  \n",
       "14      2785607.0  3003399.0  3453377.0  3976919.0  \n",
       "15      2136125.0  2332187.0  2847346.0  3155313.0  \n",
       "16      1716499.0  1858683.0  2204893.0  2653666.0  \n",
       "17      1217316.0  1399849.0  1679438.0  2560591.0  \n",
       "18       820631.0   986236.0  1278147.0  1775041.0  \n",
       "19       270958.0   365589.0   562607.0  1140665.0  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fc_bootstrap['Period'].round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In contrast to the $t$ forecast, the bootstrap comes with a mean forecast that differs from the chain-ladder point forecast. Also, the reported bootstrap standard deviation differs from the bootstrapped chain-ladder standard error since it is computed around the bootstrap mean, not the chain-ladder point forecast."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just as before, we can look at forecasts aggregated by cohort and for the total."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>90%</th>\n",
       "      <th>95%</th>\n",
       "      <th>99%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cohort</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>999.0</td>\n",
       "      <td>99932.0</td>\n",
       "      <td>133943.0</td>\n",
       "      <td>-353238.0</td>\n",
       "      <td>60208.0</td>\n",
       "      <td>147604.0</td>\n",
       "      <td>268642.0</td>\n",
       "      <td>374220.0</td>\n",
       "      <td>611144.0</td>\n",
       "      <td>786161.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>999.0</td>\n",
       "      <td>469351.0</td>\n",
       "      <td>254392.0</td>\n",
       "      <td>-118315.0</td>\n",
       "      <td>428713.0</td>\n",
       "      <td>627686.0</td>\n",
       "      <td>798055.0</td>\n",
       "      <td>911724.0</td>\n",
       "      <td>1244976.0</td>\n",
       "      <td>2232640.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>999.0</td>\n",
       "      <td>700233.0</td>\n",
       "      <td>302688.0</td>\n",
       "      <td>93328.0</td>\n",
       "      <td>661154.0</td>\n",
       "      <td>879059.0</td>\n",
       "      <td>1089169.0</td>\n",
       "      <td>1243316.0</td>\n",
       "      <td>1634851.0</td>\n",
       "      <td>1902108.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>999.0</td>\n",
       "      <td>1001183.0</td>\n",
       "      <td>352004.0</td>\n",
       "      <td>246163.0</td>\n",
       "      <td>954864.0</td>\n",
       "      <td>1202015.0</td>\n",
       "      <td>1462714.0</td>\n",
       "      <td>1645972.0</td>\n",
       "      <td>2002757.0</td>\n",
       "      <td>2314298.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>999.0</td>\n",
       "      <td>1411220.0</td>\n",
       "      <td>427463.0</td>\n",
       "      <td>399122.0</td>\n",
       "      <td>1367368.0</td>\n",
       "      <td>1695548.0</td>\n",
       "      <td>1946368.0</td>\n",
       "      <td>2147654.0</td>\n",
       "      <td>2525025.0</td>\n",
       "      <td>3483236.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>999.0</td>\n",
       "      <td>2160578.0</td>\n",
       "      <td>541155.0</td>\n",
       "      <td>839328.0</td>\n",
       "      <td>2116195.0</td>\n",
       "      <td>2492633.0</td>\n",
       "      <td>2906799.0</td>\n",
       "      <td>3139106.0</td>\n",
       "      <td>3604324.0</td>\n",
       "      <td>3993580.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>999.0</td>\n",
       "      <td>3886857.0</td>\n",
       "      <td>852271.0</td>\n",
       "      <td>1708823.0</td>\n",
       "      <td>3801465.0</td>\n",
       "      <td>4444893.0</td>\n",
       "      <td>5032850.0</td>\n",
       "      <td>5424910.0</td>\n",
       "      <td>6016739.0</td>\n",
       "      <td>8124079.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>999.0</td>\n",
       "      <td>4268894.0</td>\n",
       "      <td>1092751.0</td>\n",
       "      <td>1077711.0</td>\n",
       "      <td>4184782.0</td>\n",
       "      <td>4935941.0</td>\n",
       "      <td>5701416.0</td>\n",
       "      <td>6277549.0</td>\n",
       "      <td>7211547.0</td>\n",
       "      <td>8344057.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>999.0</td>\n",
       "      <td>4617302.0</td>\n",
       "      <td>1998469.0</td>\n",
       "      <td>300744.0</td>\n",
       "      <td>4408087.0</td>\n",
       "      <td>5795458.0</td>\n",
       "      <td>7334020.0</td>\n",
       "      <td>8224876.0</td>\n",
       "      <td>9951241.0</td>\n",
       "      <td>13342088.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        count       mean        std        min        50%        75%  \\\n",
       "Cohort                                                                 \n",
       "2       999.0    99932.0   133943.0  -353238.0    60208.0   147604.0   \n",
       "3       999.0   469351.0   254392.0  -118315.0   428713.0   627686.0   \n",
       "4       999.0   700233.0   302688.0    93328.0   661154.0   879059.0   \n",
       "5       999.0  1001183.0   352004.0   246163.0   954864.0  1202015.0   \n",
       "6       999.0  1411220.0   427463.0   399122.0  1367368.0  1695548.0   \n",
       "7       999.0  2160578.0   541155.0   839328.0  2116195.0  2492633.0   \n",
       "8       999.0  3886857.0   852271.0  1708823.0  3801465.0  4444893.0   \n",
       "9       999.0  4268894.0  1092751.0  1077711.0  4184782.0  4935941.0   \n",
       "10      999.0  4617302.0  1998469.0   300744.0  4408087.0  5795458.0   \n",
       "\n",
       "              90%        95%        99%         max  \n",
       "Cohort                                               \n",
       "2        268642.0   374220.0   611144.0    786161.0  \n",
       "3        798055.0   911724.0  1244976.0   2232640.0  \n",
       "4       1089169.0  1243316.0  1634851.0   1902108.0  \n",
       "5       1462714.0  1645972.0  2002757.0   2314298.0  \n",
       "6       1946368.0  2147654.0  2525025.0   3483236.0  \n",
       "7       2906799.0  3139106.0  3604324.0   3993580.0  \n",
       "8       5032850.0  5424910.0  6016739.0   8124079.0  \n",
       "9       5701416.0  6277549.0  7211547.0   8344057.0  \n",
       "10      7334020.0  8224876.0  9951241.0  13342088.0  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fc_bootstrap['Cohort'].round()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>90%</th>\n",
       "      <th>95%</th>\n",
       "      <th>99%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Total</th>\n",
       "      <td>999.0</td>\n",
       "      <td>18615551.0</td>\n",
       "      <td>2980270.0</td>\n",
       "      <td>10971577.0</td>\n",
       "      <td>18503493.0</td>\n",
       "      <td>20384311.0</td>\n",
       "      <td>22654087.0</td>\n",
       "      <td>23854419.0</td>\n",
       "      <td>26481398.0</td>\n",
       "      <td>29652589.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       count        mean        std         min         50%         75%  \\\n",
       "Total  999.0  18615551.0  2980270.0  10971577.0  18503493.0  20384311.0   \n",
       "\n",
       "              90%         95%         99%         max  \n",
       "Total  22654087.0  23854419.0  26481398.0  29652589.0  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fc_bootstrap['Total'].round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taken together, this replicates Table 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecasting with smaller models (not in paper)\n",
    "\n",
    "In the deviance analysis we found that we cannot reject a reduction to an age-drift or even an age model. Since the age-cohort model replicates the chain-ladder point forecasts we have so far not considered forecasts resulting from the smaller models. However, this is easily done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_ad = model.clone()\n",
    "model_ad.fit('od_poisson_response', 'Ad')\n",
    "model_ad.forecast()\n",
    "\n",
    "model_a = model.clone()\n",
    "model_a.fit('od_poisson_response', 'A')\n",
    "model_a.forecast()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now compare the forecasts of the three models. We look at the forecasts for the total, but we could just as easily look at other aggregates or forecasts by cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Age-Cohort Model\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point_forecast</th>\n",
       "      <th>se_total</th>\n",
       "      <th>se_process</th>\n",
       "      <th>se_estimation_xi2</th>\n",
       "      <th>se_estimation_tau</th>\n",
       "      <th>q_0.75</th>\n",
       "      <th>q_0.9</th>\n",
       "      <th>q_0.95</th>\n",
       "      <th>q_0.99</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Total</th>\n",
       "      <td>18680856.0</td>\n",
       "      <td>2952921.0</td>\n",
       "      <td>993729.0</td>\n",
       "      <td>2682412.0</td>\n",
       "      <td>732744.0</td>\n",
       "      <td>20692875.0</td>\n",
       "      <td>22535935.0</td>\n",
       "      <td>23666265.0</td>\n",
       "      <td>25869724.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       point_forecast   se_total  se_process  se_estimation_xi2  \\\n",
       "Total      18680856.0  2952921.0    993729.0          2682412.0   \n",
       "\n",
       "       se_estimation_tau      q_0.75       q_0.9      q_0.95      q_0.99  \n",
       "Total           732744.0  20692875.0  22535935.0  23666265.0  25869724.0  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Age-Cohort Model')\n",
    "model_ac.forecasts['Total'].round()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Age-Drift Model\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point_forecast</th>\n",
       "      <th>se_total</th>\n",
       "      <th>se_process</th>\n",
       "      <th>se_estimation_xi2</th>\n",
       "      <th>se_estimation_tau</th>\n",
       "      <th>q_0.75</th>\n",
       "      <th>q_0.9</th>\n",
       "      <th>q_0.95</th>\n",
       "      <th>q_0.99</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Total</th>\n",
       "      <td>19846937.0</td>\n",
       "      <td>2467485.0</td>\n",
       "      <td>1011836.0</td>\n",
       "      <td>2115010.0</td>\n",
       "      <td>769028.0</td>\n",
       "      <td>21525090.0</td>\n",
       "      <td>23057357.0</td>\n",
       "      <td>23992879.0</td>\n",
       "      <td>25803777.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       point_forecast   se_total  se_process  se_estimation_xi2  \\\n",
       "Total      19846937.0  2467485.0   1011836.0          2115010.0   \n",
       "\n",
       "       se_estimation_tau      q_0.75       q_0.9      q_0.95      q_0.99  \n",
       "Total           769028.0  21525090.0  23057357.0  23992879.0  25803777.0  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Age-Drift Model')\n",
    "model_ad.forecasts['Total'].round()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Age Model\n"
     ]
    },
    {
     "data": {
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point_forecast</th>\n",
       "      <th>se_total</th>\n",
       "      <th>se_process</th>\n",
       "      <th>se_estimation_xi2</th>\n",
       "      <th>se_estimation_tau</th>\n",
       "      <th>q_0.75</th>\n",
       "      <th>q_0.9</th>\n",
       "      <th>q_0.95</th>\n",
       "      <th>q_0.99</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Total</th>\n",
       "      <td>16676254.0</td>\n",
       "      <td>1565677.0</td>\n",
       "      <td>957519.0</td>\n",
       "      <td>1043789.0</td>\n",
       "      <td>667087.0</td>\n",
       "      <td>17740884.0</td>\n",
       "      <td>18712650.0</td>\n",
       "      <td>19305694.0</td>\n",
       "      <td>20452847.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       point_forecast   se_total  se_process  se_estimation_xi2  \\\n",
       "Total      16676254.0  1565677.0    957519.0          1043789.0   \n",
       "\n",
       "       se_estimation_tau      q_0.75       q_0.9      q_0.95      q_0.99  \n",
       "Total           667087.0  17740884.0  18712650.0  19305694.0  20452847.0  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Age Model')\n",
    "model_a.forecasts['Total'].round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that age-cohort and age-drift model yield quite similar results, especially when we look at the higher quantiles. In contrast, the age model produces substantially lower forecasts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "* England, P., & Verrall, R. (1999). Analytic and bootstrap estimates of prediction errors in claims reserving. *Insurance: Mathematics and Economics*, 25(3), 281–293. \n",
    "* England, P. D. (2002). Addendum to “Analytic and bootstrap estimates of prediction errors in claims reserving.” *Insurance: Mathematics and Economics*, 31(3), 461–466. \n",
    "* Harnau, J., & Nielsen, B. (2017). Over-Dispersed Age-Period-Cohort Models. *Journal of the American Statistical Association.* [Published online](https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1366908)\n",
    "* Nielsen, B. (2014). Deviance analysis of age-period-cohort models. Nuffield Discussion Paper, (W03). [Download](http://www.nuffield.ox.ac.uk/economics/papers/2014/apc_deviance.pdf)\n",
    "* Taylor, G. C., & Ashe, F. R. (1983). Second moments of estimates of outstanding claims. *Journal of Econometrics*, 23(1), 37–61. "
   ]
  }
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