censored.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Censored data\n",
    "## Bayesian networks vs standard AFT models\n",
    "\n",
    "We will examine data with censored values: for some observations we know the time that passed before the event, for others we know that event didn't ocurred before that time, but could have occurred later. \n",
    "\n",
    "The traditional way of doing analysis with such data is Survival Analysis: in particular we can use Kaplan Meier curves, the best non-parametric estimate of survival function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt; plt.style.use(\"fivethirtyeight\")\n",
    "import seaborn as sns\n",
    "import pymc3 as pm\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from lifelines import KaplanMeierFitter, WeibullAFTFitter, LogNormalAFTFitter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>intens</th>\n",
       "      <th>time</th>\n",
       "      <th>vomit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   intens  time  vomit\n",
       "0     1.0  30.0    1.0\n",
       "1     1.0  50.0    1.0\n",
       "2     1.0  50.0    0.0\n",
       "3     1.0  51.0    1.0\n",
       "4     1.0  66.0    0.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_stata(\"data/seasick_eng_data.dta\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f3b0fc63160>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmf = KaplanMeierFitter()\n",
    "kmf.fit(data.time, data.vomit)\n",
    "kmf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.085631</td>\n",
       "      <td>-3.005719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.997345</td>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.282978</td>\n",
       "      <td>2.567086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.506295</td>\n",
       "      <td>-4.518265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.578600</td>\n",
       "      <td>-0.260902</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y\n",
       "0 -1.085631 -3.005719\n",
       "1  0.997345  4.000000\n",
       "2  0.282978  2.567086\n",
       "3 -1.506295 -4.518265\n",
       "4 -0.578600 -0.260902"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"data/censored_dat.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Censored data with constant censoring threshold \n",
    "\n",
    "Now consider a case when we have some **observed variable** (like age) and the outcome $y$ which could be censored. In this case we will consider censoring all observations higher than $4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cens = pd.read_csv(\"data/censored_dat.csv\")\n",
    "x_obs = cens[\"x\"].values\n",
    "y_obs = cens[\"y\"].values\n",
    "\n",
    "ln = LinearRegression()\n",
    "ln.fit(x_obs.reshape(-1, 1), y_obs)\n",
    "y_pred = ln.predict(x_obs.reshape(-1, 1))\n",
    "\n",
    "plt.scatter(x_obs, y_obs)\n",
    "plt.plot(x_obs, y_pred, color=\"red\", label=\"Simple linear regression\")\n",
    "plt.legend()\n",
    "plt.title(\"Data\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We clearly see the bias in the data. Observations with $y$ higher than $4$ are censored and set to $4$ automatically. This could be for example a sensor that measures some value only to a certain point. Obviosuly if we know that such mechanism occurrs in our data there is no point in ignoring that. These observations could have been much larger than 4. One way to solve this problem would be to simply ignore these observations. That would probably work here (especially for simple linear regression), but it would be stupid for more general types of censoring. In the most extreme case, we could have a clinical trial with a group in which one patient died very quickly, but the rest of them lived so the are censored. If we threw away their observation we would be doing reasoning about quality of the drug based only on one patient who died right away. Alsoif the relationship wasn't linear but was some more complicated function where $y$ could be bigger than $4$ in multiple intervals, we wouldn't be able to reason about some intervals of $x$ after throwing away parts of the data.\n",
    "\n",
    "## Bayesian model\n",
    "Since we know that the mechanism of censoring occurs, and also know how, we can model that with random variables. The universal tool for that is a bayesian network in which we describe the process how data is generated, condition on observed data and then reason about unknown variables. In our case these unknown variables are the balues of $y$ for $y>4$ and coefficients of a linear regression (since we are using baesian model we say that coefficient are random variables as well and follow some prior distribution)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "</g>\n",
       "<!-- b&#45;&gt;z -->\n",
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       "<title>b&#45;&gt;z</title>\n",
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       "</g>\n",
       "<!-- a&#45;&gt;z -->\n",
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       "<title>a&#45;&gt;z</title>\n",
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       "<!-- x&#45;&gt;z -->\n",
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       "<title>x&#45;&gt;z</title>\n",
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       "<text text-anchor=\"middle\" x=\"215.7935\" y=\"-53.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">y ~ Normal</text>\n",
       "</g>\n",
       "<!-- z&#45;&gt;y -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>z&#45;&gt;y</title>\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x7f3b087924a8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_obs = x_obs.size\n",
    "theta = 4\n",
    "with pm.Model() as censored_linear_regression:\n",
    "  a = pm.distributions.Normal(\"a\", 1, sd=100)\n",
    "  b = pm.distributions.Normal(\"b\", 1, sd=100)\n",
    "  # useless distribution (could be constant, because this is something we observe anyway)\n",
    "  x = pm.distributions.Normal(\"x\", 0, sd=1, \n",
    "                              shape=n_obs,\n",
    "                              observed=x_obs)\n",
    "  sigma = pm.distributions.Uniform(\"sigma\", 0, 100)\n",
    "  z = pm.distributions.Normal(\"z\", a * x + b, sigma, shape=n_obs)\n",
    "  y = pm.math.switch(z < theta, z, theta)\n",
    "  # Just some random noise needed for a sampling to work\n",
    "  y_ = pm.distributions.Normal(\"y\", y, 1e-2, observed=y_obs)\n",
    "\n",
    "pm.model_to_graphviz(censored_linear_regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this model we have some initial data $x$ that we observe. Then this $x$, combined with the knowledge of parameters of linear regression (which we also model as random variables) tells us what is the value of $z$. But there is also the mechanism of censoring, so we don't observe $z$, but a truncated $y$ instead. \n",
    "\n",
    "Let's see how this works in practice and what are the estimated values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [z, sigma, b, a]\n",
      "Sampling 4 chains, 0 divergences: 100%|██████████| 10000/10000 [05:13<00:00, 31.94draws/s]\n"
     ]
    }
   ],
   "source": [
    "with censored_linear_regression:\n",
    "  sample = pm.sample(draws=2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd_3%</th>\n",
       "      <th>hpd_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_mean</th>\n",
       "      <th>ess_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>2.987</td>\n",
       "      <td>0.038</td>\n",
       "      <td>2.918</td>\n",
       "      <td>3.060</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8042.0</td>\n",
       "      <td>8034.0</td>\n",
       "      <td>8044.0</td>\n",
       "      <td>6472.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>1.018</td>\n",
       "      <td>0.033</td>\n",
       "      <td>0.956</td>\n",
       "      <td>1.081</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9434.0</td>\n",
       "      <td>9434.0</td>\n",
       "      <td>9448.0</td>\n",
       "      <td>5880.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.959</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.917</td>\n",
       "      <td>1.005</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8327.0</td>\n",
       "      <td>8317.0</td>\n",
       "      <td>8337.0</td>\n",
       "      <td>6063.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hpd_3%  hpd_97%  mcse_mean  mcse_sd  ess_mean  ess_sd  \\\n",
       "a      2.987  0.038   2.918    3.060        0.0      0.0    8042.0  8034.0   \n",
       "b      1.018  0.033   0.956    1.081        0.0      0.0    9434.0  9434.0   \n",
       "sigma  0.959  0.023   0.917    1.005        0.0      0.0    8327.0  8317.0   \n",
       "\n",
       "       ess_bulk  ess_tail  r_hat  \n",
       "a        8044.0    6472.0    1.0  \n",
       "b        9448.0    5880.0    1.0  \n",
       "sigma    8337.0    6063.0    1.0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_censored_regression = pm.summary(sample)\n",
    "df_censored_regression.loc[[\"a\", \"b\", \"sigma\"], :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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t6oMllPpNTk7mwYMHXLx4kblz5xqW606cOEFaWlqB+ABQrVo1nJycOHbsmOH1TExM5J9//jH8bKntatWqKb63goKCCAoKYvz48bzwwgusWLHCsExatmxZXnrpJV566SU6duzI0KFD+fLLL3MIWe3atblz5w7h4eGGWc+1a9e4c+cOderUsfLVEEoGetzdX8XJab1Zi/T0IOLjd1DUPuqLXXBBUebBgwf06NGDlStXcubMGa5du8a6deuYP38+bdq0oVSpUnbvc+7cuezYsYNz584xZswYnJ2deeGFF0zajhs3jmPHjvH2228bloc2b97M+PHj7e6XLf16e3tTtmxZfv75Z65cucKePXt455137HrWyZIPnp6evPzyy4YAifPnz/PWW2+h1+st5h/LbHvChAkm27527RofffQRBw8e5Pr16+zatYuzZ89Su3ZtAD755BP+/vtvLl++zIULF1i/fj1Vq1bNIToAbdu2pV69eowYMYLjx49z/Phxhg8fTsOGDQ2iLZR81OqdeHmVVhSduLhdxMfvpqiJDhRFj4oxHh4eNG3alMWLF3PlyhVSU1Px8/PjhRdeyLdMBdOmTWPy5MlcunSJOnXqsHLlSrPLUfXr12fjxo3MnDmT559/nvT0dKpWraoYHWYPLPXr4ODA0qVLmThxIi1atKB69erMnDnTZIBEfvkAMGPGDBISEhg4cCAeHh6MHj2ae/fuWZwhZ7b98ccfm2zb3d2dS5cuMWTIEKKioihfvjz9+/c3CJOLiwszZ84kPDwcFxcXmjZtym+//WayL5VKxfLly/nggw/o0aMHAG3atOHTTz+VBJ2PBQmUKlUblSrerEVKyliSk4t2BKMqOjpab9nsEXv37uXrr7/m5MmT3Llzh4ULFzJ48GDDfb1ez+zZs/npp5+Ijo6mSZMmzJ07l7p169rkWExMjNHmqL0ojKW2/CAkJIR+/fpx+fLlYp1FoCj/PlJSUggKCmLs2LFG0XDmKMpjsYW8jiO//nZtJSwsjMDAwMJ2I89kjsPF5XNcXZUFJSbmGmDbMZDCwOaltoSEBJ544glmz56Nm5tbjvtfffUVCxcuZM6cOWzfvh0fHx/69OlDXFycXRwWhPzi5MmTrFq1iitXrnDy5EmCg4OJj4+nb9++he2a8Bjj4hKOl5e3ougkJPxCTEw0xUF0IBdLbZ06daJTp04AOSKE9Ho9ixYtYvz48YazFosWLSIwMJDVq1fz+uuv28FlQcg/Fi5cyKVLl1Cr1QQFBbFx40YqVapU2G4JjyU6PDx6ExS0y6xFWtozJCT8RXHbrrfrHk94eDgRERE899xzhmtubm60bNmSgwcPivDYkVatWhGdxwg/wZiGDRuyc+fOwnZDEHB0/DtHYbbsxMUdQaerWUAe2Re7Ck9ERARAjoOIPj4+3Llzx+xzYWFhOa65urqajOqxB7amsymqyDiKHiVlLHkZR2xsLPfu3bOjN7nH1GdLUUatjuXJJ9sr2ty6FcydO28AeqBojs/S3lqRiGoz5WRMTEy+bNTKBnDRoqSMA0rOWPI6jlKlShmyMhQmxS24wNV1Ki4u883e1+s9iY09j6enJ/kyLJ0Ot+BgnFeuBCB52jRS3n47Hzqy88JgZrr87GldIiMjDSlfBEEQhEc4OJzGy8tbUXQSEv4gNvYm4Gl/B/R6XKdOxatMGYPoALhOnw7ZMofYC7sKT5UqVahQoQI7duwwXEtOTmb//v00a9bMnl0JgiAUc9Lw9HzGYjXQI0cOkZbWLl88cP76a7xKl8ZlvhnRs6LeVW6weaktPj6eK1euABiSOJ46dYrSpUsTEBBAcHAwX3zxBYGBgdSsWZO5c+fi4eFh9jS9IAjC44Zt1UDtv4/jtHw57ibyFmYlrUkTyKdDyTYLz/Hjxw0npiGj6NSsWbMYOHAgixYtYty4cSQlJfH+++8bDpCuXbsWjUZjV8cFQRCKG4VdDdRx82Y8zORyzErCTz+RZkX5kdxi81Jb69atiY6OzvFv0aJFQEZKj0mTJnHhwgUiIiLYuHGjydTyQsni66+/JihIOUOut7c3f/75p9HP69ebzzUl2JfslW+FgqUwq4GqDxzAy9vbougkffklMdHR+So6UESi2koa9+7d4/PPP2fLli3cvn2bsmXLGhI7Zh6+FTJqy5SEKLDiwrJly+yaeFWwDrX6EJ6eyn/38fFbSE+3/z64w9mzaFq1smiX/H//R8qECXbv3xzyLrQz4eHhdOnSBU9PT6ZNm0b9+vXR6XSEhobyzjvvcObMmcJ20Sypqal2L9ugRIUKFYrEuRdrx52fr09BvPaZtY+EgqLwqoGqwsMp1bChRbuU4cNJ/vTTfNvLMUfxyrNQDHjvvfcA2LFjB3369CEwMJDatWszYsQI9uzZY7CLiYlh3Lhx1KxZE39/f7p168bx48cN93/99VcqVapEaGgoLVq0oGLFijz//PNcu3bNYHPz5k0GDhxoqEDZtGlT1qxZY7h/9uxZevXqha+vL1WrViU4OJiYmBjD/eDgYAYMGMC8efN44oknDEuit2/f5o033qBKlSpUqVKFF198kcuXLxuN86uvvqJWrVpUqlSJkSNHEh9vPluuObIutYWHhxuW4nr37o2fnx/NmjUzipAEOH/+PC+++CL+/v7UrFmToUOHGg4uAxw7dow+ffpQvXp1AgIC6NKlC4cOHcrR75IlS3j55ZepWLEiH3/8sUn/unfvzjvvvMOUKVOoUaMGnTt3tsqHtLQ0Jk2aZHj9Jk2axDvvvGOUCTu3bZ89e5aePXsSEBBApUqVaNWqFbt2ZaRU0Wq1TJgwgTp16lC+fHnq1avHRx99ZNRn1qW26OhoRo0aRZUqVfD19aVXr16cO3fOcN+a96BgGmfnJXh5VVAUndjYi3YXHVVkJKUCAiyKTmrv3sRERZH82WcFLjpQDIXHy8s7T/8qVPC1yd4WHj58yLZt2xg2bBienjnj7b29M9rT6/UMGDCAO3fusHLlSnbt2kXLli3p2bMnd+/eNdinpKTwxRdfsGDBAv73v/8RExPDO++8Y7j/7rvvkpSUxPr169m/fz+zZs0yZAVOSEigX79+eHh4EBISwrJlyzh06BBjxowx8mnv3r2cPXuW1atX8+eff5KYmEiPHj1wcXFhw4YNbN26lQoVKtCrVy8SExMB+OOPP5g5cyaTJk0iNDSUwMBAm6tlmmPmzJmMHDmSPXv28OSTT/LGG28YRO3u3bt069aNunXrEhISwrp164iPj2fQoEGG6ppxcXEMGDCATZs2ERISQlBQEP379+fBgwdG/cyZM4dOnTqxb98+hg0bZtaf33//Hb1ez6ZNm1i8eLFVPnz99dcsX76c+fPns23bNnQ6HatXr7ZL28OHD8fX15eQkBB2797NxIkTDcuVixcvZsOGDfzwww8cPXqUpUuXUrOm+ZQqwcHBHD16lOXLlxMSEoKbmxsvvPACSUlJBhtL70HBGJXqBl5e3oolqBMTFxETE23fEtRxcXg2aUKpwEBUCgmZ01q0ICYigqQffwS12n7924gstdmRK1euoNfrqVVLOWpl165dnD59mkuXLhkyfE+ZMoXNmzezcuVKxo0bB2R8c547d67h9PXYsWMZM2aMoaT0jRs36Nmzp2FTP2ulzNWrV5OYmMi3335riCicN28ePXr04MqVK4ZKnC4uLixYsMCQnuiXX35Br9fzzTffGOq7zJs3j5o1a7Jlyxb69OnDokWLGDhwoCH33nvvvcfu3bsNYfZ5YfTo0XTt2hWAqVOn8ttvv3H69GlatGjBDz/8QP369Zk+fbrB/ttvv6Vq1aocP36cJk2a0KZNG6P2Pv30U/766y+2bt3KgAEDDNf79OljVb2fypUr88knnxh+/uSTT8z6cOLECVq2bMnixYuNEuXOnj2bkJCQPLWdOb4bN24wZswYw3ssa0XVGzduUKNGDVq2bIlKpSIgIMDs+bnLly+zadMmNmzYQKt/9wC+/fZbgoKCWLt2LUOHDgWU34NS/ycrhVQNNCUFj969cdy/X9EsvUYN4nfsgHwoRpkbRHjsSKYgWOLkyZMkJibm+DaanJzM1atXDT+7uLgYpfzw9fUlNTWV6Oho3NzcGDVqFO+88w4hISG0adOG559/nkaNGgEZG/f16tUzCmNv1qwZDg4OnD9/3vCBVbduXaOceCdPniQ8PBx/f38j3xITEw2+XbhwgVdeecXoftOmTe0iPPXq1TP838/PD3iUCePkyZPs27fPZLboq1ev0qRJEyIjI/nkk0/YvXs3kZGRpKenk5SUxM2bxkseTz75pFX+ZL6emSj5EB4eTr169YiIiKBx48aG6yqVisaNG3Pr1q1ct505vtGjR/PWW2+xYsUK2rRpQ8+ePQ0iNGjQIPr06UOTJk147rnn6NixIx07dsTBIefCxoULF3BwcODpp582XPPy8uKJJ57g4sWLhmtK70HZM8pArd6Jp2dvRZu4uF3odA3s12l6Om5Dh+K8bp2imV6jIe7YMfTZ8mcWNiI8dqRGjRqoVCqjP1xT6HQ6ypcvz6ZNm3LcyyoU2SOQMr9hZi67vPrqq7Rv356tW7eyc+dOOnXqxNtvv82kSZMU+8/6TTV7tVKdTkdQUBBLly7N8VxBfNA4ZTkpnelnpqDrdDo6derEzJkzczyXmZg2ODiYe/fu8Z///IfKlSvj4uJCz549Sc2W+sNcldbsmHp9zPlga2lzW9rOHN+kSZN48cUX2bp1K9u3b2fOnDl88cUXvPLKKzRq1IhTp06xfft2QkNDCQ4Opn79+qxbt86k+FiDpffg400hVAPV63GdMAGXJUssmsaePIm+ShX79W1Hip3wZBQ7yj35mcixdOnStG/fniVLljBy5Mgc+zzR0dF4e3vTsGFD7t27h4ODg9HyWG6oVKkSQ4YMYciQIcybN4/FixczadIkateuzbJly4iLizOI2cGDB9HpdNSuXdtsew0bNmT16tWUKVPGsCeVndq1a3PkyBGjWc+RI0fyNA5raNiwIX/88QcBAQFGApWVAwcOMHv2bMNm/b1794w25/PTh8z3VoUKFTh+/Lhh2U+v13P8+HGL+QqtGR9kfMGpUaOGYcb7yy+/GH4XGo2GXr160atXLwYNGkSHDh24cuVKjtl17dq10el0HDp0yLDUFhsbyz///MOLL75o8+vyuFEY1UBdPvsM1yxLs+aI27sXXZaVg6JIsQsuKOrMnTsXvV5Pu3btWLduHWFhYVy8eJEffviBZ555BoC2bdvSvHlzBg0axNatW7l27RqHDh3iP//5D/v27bO6rw8++IBt27Zx7do1Tp06xbZt2wyi0r9/f9zd3Rk1ahRnz55l7969vP322/To0cNoXyA7/fv3p3z58gwaNIg9e/Zw7do19u7dy+TJkw2RbaNGjWLFihX89NNPXL58mS+++IKjR4/m4VWzjmHDhhEbG8vrr7/OkSNHuHbtGjt37mTcuHGGCrc1atTg999/5/z58xw7dow33njDrmHKSj5kBkGMGjWKr776ivXr1xMWFsbkyZOJiIiwuCdiaXxJSUmG/bTw8HCOHDnCgQMHDL/zBQsWsHr1ai5cuMCVK1dYtWoVpUqVomLFijn6qlGjBt26dePtt99m3759nD17lhEjRqDRaOjTp4/dXq+ShoPDpQKvBlpu7Vq8vL0tik78pk3EREcXedGBYjjjKepUrVqV0NBQPv/8c6ZNm8adO3coU6YM9evXZ968eUDGcsXvv//OzJkzGTdunCF7d7NmzRg4cKDVfel0OiZMmMCtW7fw9PSkTZs2hmUad3d31qxZw6RJk2jfvj0uLi5069aN2bNnK7bp7u7Oxo0b+eijjxgyZAixsbH4+vrSunVrwwyob9++XLt2jRkzZpCUlETXrl0ZPXo0y5cvz+WrZh1+fn5s2bKF6dOn069fP1JSUvD396ddu3aGfaoFCxYwfvx42rZti6+vLxMnTiQqKqpAfMgUuLFjxxIREcGbb76JSqVi8ODBdO/ePUfW9tyMLzo6mtGjRxMREUGZMmXo3LkzM2ZkfAhqNBrmz5/PlStXUKlUBAUFsWrVKtzd3U3298033zBx4kQGDhxISkoKzZo1Y/Xq1SZL2ojtcZoAACAASURBVAsZ1UAdHZWqgbYmIeFP7PV93vHPP/F47TW8LNglrFhB2r8BOcUFVXR0tHU74gVMTEyMITTYnkjNlKJFSRkHKI+ldevWNG/enM8++6yAvbKdvP5O8utv11bsVY+noKuBqnftwrNnT4t2iQsXoh082C59FjQy4xEEO3P9+nW2b99Oq1at0Gq1/PTTT5w9e5b55lLPC0WUaLy8qipaJCdPISXlPbv05nDiBJq2bS3aJc2YQerYsXbps7AQ4REEO+Pg4MBvv/3G1KlTDcEcq1evtjqEWyh8rK0Gao/CbA6XL6Np0sSiXcpbb5E8fXqhZBqwNyI8gmBn/P392bx5c2G7IeQCB4fTioXZIKMaqD0Ks6nu3kUTFIRKq1W0u9+tG07LlkEuQ+KLIiI8giAIpOHp2Ra12nwSX622J4mJPwF5nHFER6N55hkcbprP4wagbdeOxJUruRYeTmAJEh0Q4REE4THHtmqgeSApCY+uXXE8cULRLP2JJ4jfuhWsPORcHCnSwiP5oASheGFt2qiiQIFVA01Lw33wYJy2bFE00/n4EH/wIPoyZfLWXzGgyAqPh4eH4aS/iI8gFH30ej3R0dHFosy9m9tbODv/bPa+TudPXNxRwMWsjUX0etzeegvnX36xaBp75gz6bPkRSzJFVngcHR3RaDTExsbatd3Y2Fibc2oVRWQcRY+SMpa8jEOj0RTpKqcFVQ3UZeZMXOfOtWgXd/AgOoUUViWVovsOIUN87H0Q7d69ewQE5HGttggg4yh6lJSxlJRxGFMw1UCdFy/GbeJEi3bx27aR/tRTeeqrOFOkhUcQBCGvODsvUSzMBhnVQPNSmM1p1Srchw+3aJewdi1pzz2X635KCiI8giCUSJyd7+Ll1VTRJjFxEVqt9fkRs+O4bRseL7xg0S7xhx/Q9uuX635KGiI8giCUMDKqgTZokH/VQNWHD+PZsaNFu6Q5c0gdOTJXfZRkRHgEQSgxWFcNdDc6XVCu2ne4cAGNmXLiWUl+7z1SpkzJVR+PAyI8giCUAPK3Gqjqxg1KBVkWq9TXXiNp3rwSkU8tPxHhEQShWJOf1UBVUVF4Nm2Kw4MHinbarl1J/OUXKMKh5EUJeZUEQSiWODhcQqNRDklOSPiFtLQetjceH49nx46oz51TNEt76ikS1q8HKZ5nEyI8giAUM3R4ePTC0XG3WYu0tNacODGXwEAbD2empuLRvz+OoaHKHgQEELd7N3jbp7z144YIjyAIxQbbqoGGWd+wTofbyJE4r1qlaKZ3cSHu5En0vr7Wty3kQIRHEIRiQD5VA9XrcZ08GZdvvrFoGnfsGLrq1W1rXzCJCI8gCEWa/KoG6jxvHm4ffWTRLi40FF3Dhja1LSgjwiMIQpEkv6qBOi1bhvuYMRbt4tevJ721cv9C7hDhEQShiJE/1UAdN27EY9Agi3YJP/9MWs+eVrcr2I4IjyAIRYb8qAaq3rsXz+7dLdolfvUV2tdes7pdIfeI8AiCUOhYVw30M1JTLWeAzsTt4kW8mionCQVInjKFlPdsDEoQ8oQIjyAIhYq9q4Gqrl2jVKNGWKrklTJyJMmzZ0t6m0JAhEcQhELB3tVAVffuoXnySVQJCYp2qX37krRkCajVVvsq2BcRHkEQChg7VwONjcWzTRvUV68qmqW1akXC2rXgYt3MScg/RHgEQSgw7FoNNDkZj549cTx0SNEsPTCQ+O3bQaOxxVUhHxHhEQQh31GpblCqlHJZgcTExWi1L1luLD0d99dew+nvvxXN0jQaEo8fR1+unC2uCgWACI8gCPlIRjVQJyc7VAPV63F97z1cfvjBYq+xp05xMSWFQBGdIomDvRucNWsW3t7eRv9q1VIOkxQEoeShVu/Ey6u0oujExe0mPn43lkTHZc4cvEqXtig6cfv2ERMdjb5y5dy4LBQQ+TLjCQwM5O8s02C1RI8IwmOE/aqBOn//PW5WnLGJ37yZ9ObNbfJSKDzyRXgcHR2pUKFCfjQtCEIRxl7VQB3XrcNjyBCL/SWsXEla587WOygUCfJFeK5du0adOnVwdnbmqaeeYurUqVStWjU/uhIEoQhgXTXQZaSlPa9oo965E8/evS32l7hoEdqBA23yUSg6qKKjo/X2bHDr1q3Ex8cTGBjI/fv3+eyzzwgLC+PAgQOUKVPG5DNhYTYUbBIEoQiho1atNylV6ohZi9jYp7h4cSFKW8ru//zDE1bkSbsxfjwRgwfnxlGhAAkMDFS8b3fhyU58fDyNGjVi/PjxjLEiFXl+ExYWZvFFKQ7IOIoeJWUs1o7DtmqgpnEIC0NjTT618eNJmTbNpvQ2j9vvoziR7+HUnp6e1KlThytXruR3V4IgFAh5rwaqun0bTb16qPTK33tTBw4kaeFCcLB7AK5QiOS78CQnJxMWFkZrKagkCMWevFYDVT18iGeLFjjcvavYj7Z9exJ/+w2cnPLirlBEsbvwTJkyhS5duuDv72/Y40lMTGSgbAQKQrElz9VAExPx7NIF9alTim2kBwURv3kzeHjk1lWhGGB34bl9+zbDhg0jKiqKcuXK8dRTT7F161Yqy4EuQSiGpOHp2Qa1+qxZC8VqoFot7gMH4rRtm2IvOl9f4vfvR1+6dB79FYoDdheepUuX2rtJQRAKgTxVA9XpcHvzTZxXrFB8Xq9SEXfmDPpKlfLiqlDMkFxtgiAY4egYhZeXcqSZ2Wqgej0u06fjOm+exX7iDh9GV8KitQTrEOERhEIiPE7LzGNx3ElMx89dzZTGGqponMxeV3p2SC03Pj4Wy6F7aWSNE3MAyrk6UNVDxaV4HQlaPU4OEJ9m2qfv2k9leKM15n2O9aPWTxtJTXcGbhndG7/zJ77881OL42769m8cqRwEe4A9tyzam0IFRuN0BvQq0Ga5WMbRlc8c4th8U8vVuDTuJenwcVVRvZQTUxprOHIvmbH74khO06MHPB3B1VFFUx9n3qznwY8Xk7iTmE4pJxV6PcSl6U3+PjJ/F6b6sPR7s8ZmcGkVBSXP1vhnD/L9HE9Ro6TExMs4ih62jCU8TkvvLVFcjUs3XHNxgBYVnLkUo+Vm4qM/S393FQ3KOhOr1RtEZuTuaG4m6Aw2DoCO3NPc7wT7BygfzGyx8lcO3GmU4/rgI+tZ9utEi310HLWEbbVb5tpHe1LOBe6nmL+vVkG6mU/Gaho16zqXNXxJyP57NGUHpn/n1tj4u+rY8LxvvghAVqzxz15IcLwgFAIZ35CNP6xSdLDzTqqR6ADcTNSz8UYKe+6msupKEi9sfWAkOpB70XFWp3LtjQ6KorPkdD9U887mEJ2u/+xC/3Y9i6Iz4NW5qL48W2REB5RFB8yLDsDVuHRmHosDTP8eTdmZs7XG5mayg5FNfmGNf/ZCltoEoRC4k2j6w8oaknL/qBGjGyxn4XOfKNpU+C6Ue4nGNW1aXD3OvvnKGQsA3uw3mW+eGZQnH4sqd//9/Vn6Pd7Nct+cra02+UVB9i3CIwiFgMbR+tQv9iZAc5vrQzsq2ryyeRbLzvc0uvbEnUuc/bSXxfandwrmo66Fnx4rP/F1zyj14ueuXPLFN8t9c7a22uQXBdm3CI8gFBBZN24vRmsLwQM9q7uPp1+g+TM1x+/VoemKlaTrH300VH5wm/AZykIFsKjlAEa/8KFN+dQKi7zu8UxprAHICFKITDW7x5NpZ87WGht/V52RTX5hjX/2QoRHECxgj0gfpU3ogqB9wH629RumaNNw2RpO3a9j+Llc/AMuzOpOmcRYxefWBnXgxdc+J11dcB8n1kW16fispTebb2q5FpdGRJKO8q4qqtkQ1XY3MR3Nv1Ft8Wl6fLP9/qtonFjXuSwzj8WZ7CPr+ySr7d3E9BxtmbMZXPpBvgcWWOufvZCotmKKjKNgsCXSR2ksw0MfsOpKUp79cXHICEKwFg+nBO4Ob4Ons/m+PzvyOhP2PEro6ZmcwKEvX6LuPeXEvvuqNuK50UtJcXIBoKu/Cys6ljNr//ymSPbcTc1xvbWvM+u7+lgais0U9feWtZSUcWRFZjyCoIBSpM+SNqbrS5kiL8EEWbFFdP6v6bd80sp8Qk+A0ov2EZ3iBYBzWipbFo+g7eXDis9cKePPk++tJtbt0RJMNY2a2c29FJ8rzP0LoWghwiMICtgr0sfSJrQ9CfS+xsUh3RVteq+fz5+X2wPgoEvn12Uf8NLxTYrPJDq5si/kIN891FArVsu9ZD1eThCjhbKuGSG/SkszBbmHIBRtRHgEQQFrv6WHx2n58IIT8ZciTe4DKW1C2wsVOrb1G8pzAYfM2my/8TQd1vyAHgfQ6/ly3WzG71pmse0akzdRuX4N1jUoT2YyncxlyOvx6VyPT+dIpJYjkalmDxwW5B6CULQR4REEBaz5lv5oH8gJyNjDyP4BXEXjxIJWXgzZ8YBIC4cXc0OvGiGs6/GWok2tHzcQFl0VgInbljBrg+V8ao3eW83JSnUBqKxSMTz0gSHIIkGrs3kZsorGyaYlSqFkIsIjCApY+pYeHqelx+aMb/1ZuRqXztNr79G+kguzmmXsfYzZG2N30fF2ieFhsHJGgP/bO45Zh0cAMPTAar5fOc1iu23e/JFdNY0ThR6ISCU5yx6Ti5m8JwVx2FEo3ojwCIIFzH1Lz7rUZIoUHWy8kcKpB/cJKu1k92W2Oc/MZcJT/zV7Py7VHb8lO0nQetD71Db++O84i232fmM+fwa1N3kvOVtgg7lABwkWECwhwiMIuUQpT1dWbiboSEm334HRBuXOc/Llfoo2HdZ8T8iNFjx76TChC4dYbHPogI9Z2ly5TVM4qyA1y4EMf3eVBAsIFhHhEYRcYkuIdGxqXnJHZ6BWpXF0UH8a+lw0a7PqYide3PgFDW+dRz+3nsU2J3Yfz5wOJurqWImDA5D1ZSgGWQuEwkeER3isyUtWAltCpG05f2OKV+r+yc+d/0/RpvIPW3G6mob+k/oW2/uizau822tCnoUiOZv23kzQ2XzGSXj8EOERHlvC47R03xhpVIZg/91kNnTzMVuc60qslshkPeXdHPBxccDfwyFHiQJ7Ut79PhEj2ijavLl9Mmv2dOTajE64puXMDJCV5Y278fLgOegd8q8iigQXCJYQ4REeWyYeiDFZ+2bigRij1C+m0uZkBhRUcAEfF/IlRPq79lMZHqRcDfSpxSs5PPslFj5ULm+wvebTdBn5LVpH51z746rOOcMxhQQXCJYQ4REeW47cN73hn/26UhBBRD4IjjXVQNsu+y+zp3xJZPizinZnK9Sg2dsrSHDxyLU/Pq4q2lZ0JT5Vx6abygOWTASCNYjwCI8VWfd0zG/4G8+CrsQWTAkDZ3UqF1/rRpVSd8zafH+qL+UGR7PzzOuKbUW5e1Fn0t/c97TPXkummJzPNvOr4AJqtQMJWj1eLg4saOUlmQgEi4jwCI8N1pYmaOrzaDlq750kTkal5bdrVlUD/bl7D4ZtXGuxrcpTt3KjdEWb+vdwhAQzw4xM1tN7SxTrOpc1Okzr6aji9EOtYY8rRpvOmL0xrOvsKOIjKJJ/O4yCUMSw5tyNGkjU6nh+UyQDt97nha0PSMvHwiEBmtvox9dTFJ0/Pn0OVPDqxvWKbdWb8CeqL8/aLDrVNGp+71CGbgEuOJv5RMhMhZN5mHZ9Vx88nXMGVmTaCYISMuMRHhusOXeTDuy8WxBLa5argd64UoGAWhH0Sd+u2FKLcb9yoGqjXHlR2fNRbaFWfm4M3Hrf7D5O9mg1e2XuFh4/RHiEx4b8L02gJ6M2pjLWVAOlIQScilA06TpiMZvrtrbBP2OcHaB+aeOPgDiF6V32aDWpryPkFhEe4bFhSmMN++8m5wihth/KomNNNVA+BT5Q7uXlwbP59aketruXjdR/c8mdi44yzHo0jqbH4OGYMxWO1NcRcosIj/DYcDM+jagUY9FRqyC9AIq/W1MNlNJAtPnb43t/wFdtXrWqPzXGmWyUyNyXmdJYw+mHOZcZXR3g9w6lcwQMSH0dIbeI8AiPBeFxWl7c9pCkbJ/G+S061lQDpTfwp/nb/+kwnMndxwMZQumuhjgTEWjOKuBfIdXZOK67iRniYyoLw3OVXGjl52byOamvI+QGER7hsWDSwRgS8jM8LRsqdIT0e4N2AYfNG20HOpD92JCBpU/3YdiAjw3pbVwdYE2nMsw6Ec+euzlT46TqzbdlCV93tdlggThtwb1uwuOBCI9Q4gmP0xJyKx9SDJjBmmqg1ALCTN/aWLc1vYZ+TZo6Y8nK2QHaV3RhdvOMw5l+FxX2iHJB5r6MuTBoCRYQ7I0Ij1BiMJdpeuaxuDxnh7YGa6qB8n/ALNO3jvo/QeuxP5PkbLys1ay8M7ObexnGpnFU2SU5aWYqnMzXSYIFhIJChEcoEZjKSnAkMpV1ncvaVDcnt1iqBkoc4Ack5Lx106sCQRP+INrdy+Sjno6qHGPzd1fRLcCFOK0eX3c1664kYevpozrexvszmcECH4TeIkHtIcECQr4hwiMUCyzVzTGVlSAzWis/z+9YUw2UDkBIzstpDmqqfLiV294VzD7q7JBRMif72G4m6mnh68DyDhnCcS/hHqEROaWnlCN4u6pNluc2tYRWRePEjNpaAgN9lMckCHlAhEco8ijNZiBDdLbcSDb57N3EdBY8481f15LsutxmTTVQVgEvmr5Va9IGwspXtdhPy/JOHI40PZfJmiFgfuvSdFp/zyhbdgUX+F+P8gA5Xj9ZQhMKExEeochjbjYz8UAM52PSFPOv+bqrqaJxon0lFzbeyBlg4Kz6NxrMBqypBkpl4EbOy0+9vZKjlS1XCAVwAvbd02IuiXbWGUsVjRP/61He7JkaOW8jFCVEeIQij7k9miP3tUQmK09jrsdpqb78NnGpelQYRxursE10rKkGypvANzkvtw/+ge21mlvfGWTs2ZgZnqkZi9KZGjlvIxQlRHiEIo/5PRrLqnEw0nxJA1smOpaqgRJORoh0tuM1/V/7gtWNOtvQk2V8XFWGFDeCUBwR4RGKLJkBBVfj0vBwVBkdAK2mUVPX29Hk8pk9aeF3nH0DXrZgBBwwvhT8wocsbvVSvvjUtqKriI5QrBHhEYokpgIKPByhrrcj1Uo5GZaZQu9E5ktGAhd1Chdf60blUnfNGy0BRhhfmtrlTWZ0Hm13fzKRoAChJCCF4IRCIzxOy4cXnHh+UyTDQx8QHvcoestUQEFCGlQrlbFXUUXjRBWNE793KI2bnaOlRzdYTvLYxsqiUwEj0VnY6iVUX5zJV9FxVUMZFxUzj8UZvVaCUNzItxnP999/z/z584mIiKBOnTrMmjWLli0tnOoWHhsezWicyNwYyQyRrqJxUiwylrkEdyFaS1hMWo7En7klQHOb60M7Khu9Aix79OPqBh0Z8Nrn6Bxyp37+7ipqejlxICIVC3ESJKfD0ftpHL2fZvRaCUJxI19mPGvXrmXixIm8++677Nq1i6effpr+/ftz44aJ+FLhsUTpwCeYDyg48yCVluvusepKEqce2Et09KzuPk5ZdI6T8TXtX9HZU+1JXD89Rv/X5+VKdEo5Qf/qbmzo5sO6Lj4c7Fue/tXdaO3rTGVPy+1JiWmhOJMvM56FCxcyaNAgXnvtNQA+++wzQkJCWLp0KdOmTcuPLoVihrkZzdVYLcNDH5gMKAB4mDMpc56wthoopzL+G1auMk3eXUWcq2ee+k3KFmyXNdzZ1P6WKaTEtFBcsbvwpKamcuLECcaOHWt0/bnnnuPgwYP27k4oppib0ZyLTuPI/Uefyh6OGWlj7C04tlYDjXNxp+bkTdzTlLNL/1o9rLqSZHLJLHuBtfD4dKtT3ghCccDuwhMVFUV6ejo+Psa5nnx8fLh37569uxOKKaYyIZua4SSkgburA2ZPUuYCW6uBVp+8mavlAuzWf1Yyl8yyH+60NAOS6DahOFMkwqnDwswUJikh/eUXxX0cX9ZSsfi6I5GpDvg467iZ5MCZ+Jzf4lO1adhjO9LWaqAN3l/L6Yq189yvJa5ExRMWFqVok/21GlU5idS7cYQpBN7lheL+3spExlE4BAYGKt63u/CULVsWtVpNZGSk0fXIyEjKly9v8hlLTtqTsLCwAu0vvygJ4wgEKrk9Gsfw0Aecic+59BWvy5vo2FoNtPWYn9lTo0me+rSF6mU9CQysrGgTCLRtUDD+lIT3Fsg4ijJ2j2pzdnamUaNG7Nixw+j6jh07aNasmb27E4oA4XEZAQGmzuPYYjOlsYZqmpwznvQ8nA/tXWMbuvFByqJTC2gPPd/4GtWXZwtUdGTJTHgcyZeltjfffJORI0fSpEkTmjVrxtKlS7l79y6vv/56fnQnFCJKJQsyN8wtlTXIJOum+oVoLacemM+zZglbqoG+/tJMfhzdJ9d92YK/u4oGZZ0NBdwkS7TwOJIvwtO3b18ePHjAZ599RkREBHXr1uX333+ncmXl5QSh+KF0Hidzc1zJZkJF0+1eiM696PzUcCKvtltv3uDfaqAT2r3DZ18OzXU/tlLZU836LnLoUxDyLbhg2LBhDBtm4XyEUOxRyjBgiw1Yf37FHM+rd7B+7Bhlow4wN30I7894L6O0ZwFSxVMtoiMIFJGoNqH4Yu48TtYzJtbYgOmZkTVUir3D9V4dcGioYLQKls3pzquDZqN3KJwUhXLuRhAyEOER8oSp8zjZN8zN2Qyp5caHR52IvxSJn7uaK7G2Jb70SorlcngXyi6OUbTb3eZJ2vdYivZlZ5vatycSRCAIjxDhEfJE9lP2pjbMTdkMqeXGmL0xRklCrV34ck1NZv+KQTQ6fkHR7tb/+VDbawMJfTxyOTrr8XCEqq7pVCntjl4Pkcnp3EvWU8HNgaoaRwkiEIQsiPAIecaassrZbTLysRkvq1mKmlanp7Fu6Vs8Pz40I2mnGdKvOxDw6zbulK9gyXW7kBk0kHr3msXzOIIgiPAIBURmKYM7ien4uau5GmdD1Jpez5KV0xjmsAbOKpv2WjKfvxLag1ve/LWWahq1IXQ8v7IICEJJQ4RHyDXZxSRzOSn79UfLasZ52axhxsavmLLrO7gIKEwmVh3qyIv75uVxRLZR2VMtNXEEIReI8Ai5wtyh0AWtvHKIzMbrySaSf+pxVIG5qtVjdy1j/h+z4E3gf8q+VPgulHuJ9skabS1ZZzqCINiGCI9gFdlnMfGpOpOHQoeFPuROUk6RMUXGZT1ZwwoGHv2b5cs+gAAsbvq8snkWy873tH0wucBNDe0qukjGAUGwAyI8gkVMzW5czRxJuZtka2K1DNHpfG43m78blXFpNdDP/BPH79Wh6YqVpOsL7u1bv4wTyzsU7KxKEEoqIjyCRUwd7Ew2c87TVtlpdu0kB74alPFDB2Crsn3DZWs4db+Ojb3knaoa+VMRBHshf02CRcylvMmOiwOkWFmvrU7EZc7N/neZzAO4CyhUk/70yOt8sOc96xq3M0qHP7MuQXqmOzHHVytLcIJgAREewSLmUt5kpa2vE6hU7LyjXKM64OFtrn/c8dGF/wM+UW679KJ9RKd4WeGp/VGKXMu5BOnEhS1REnQgCBYonKRVQrHCXJ2crBy+r0WvM7/Q5paaxJnZPR+JTiAZ63IKotN7/XxU885aFB0HwNUB3B1VuCha2kY1jXI2aaWs24IgmEdmPIJVVHZ3UEzgmZAG/8TkvO+RksD+rwZT6941XNK1GbEEIUA7832FXG9Gx7Xfo7fye5GOjETTqzqUJnhPDNfjc5fdGjLEq0k5J6si16zNui0IgjEiPI8B5g56Wvus9aUKHs14nNJS2fhdMB3CDjy63Rv4Q7mFWj9uICy6qlW+ZSUpHV7Y+oBAL0euW2Fv7gzRE95q1nf1sapPa7NuC4JgjAhPCcdShVBLomRLqYKmPs7supXM4p8+YPCxDY9uuAMTgQ/NP/t/e8cx6/AIG0dnTFI6XIq1zteKHmqTM6N7yXrC46wLELAmM7cgCDkR4SnhKO1DTGmssVi22tqINl9XFcP++wkbNvzX+MYcYIL552JTPPBbspPENHer+rFEoomMCNl/rqZRm8ywAHA9Pp3eVgYIZM+67ZGewJw25SWwQBAsIMJTwlHah7CmbLU1EW3vh/zAp39/YXyxAXBS+bkOa74n5EYLi+3bSpo+IxqtiqfaUILhx4tJOco2rOvsSI/NUTlmPtlfAyWyZt0OC4s2iE5eljcFoaQjwlPCMSccno4qtt1MMnlv5+0Uw3LTlMYa1l9LItnE+ZwhB//gv79NMb6oBo4AjUz7E5FQlg3XnmXo1hlYX4HHdqp4Gu/VtPLLma66isaJyp6ml9zyEiBgaXlTEB53JJy6hDOklluOTND+7iqO3U/hoZkjN5HJOnpviSI8LqMiaPZDoT3ObEf/dr2covMykIZZ0QGo9dMGhm6dSX6KDli/wZ8fAQISZi0IysiMpwQTHqdlzN4YoySdHo5Qs5QjO+8ql5nO+kGZ+fQzl4+ye8GrOY3LAxHKvry5fTLfnBpkg/e5J3OD35rlrvwIEJAwa0FQRoSnBGPqm3dCGpyNtu4D8G5iOnqgwa3znJxrJmvnd8Bw822Ex/pR66eNpKY7W+d0FlSAswNodRlndawhM9MAYNVylzWlu21FwqwFQRkRnhKM+Yg061J5Bj64wQ9vPmf6ZnNgv/LzLVb+yoE7CutuFtCTscyXGYW28GwC22+lmNxvgowlxMxMA6ZKa5sLGrCmdLctSJi1ICgjwlOCMffNu6mPM6eiUrmZaFqAysfd58onXfFIScx505mMaqBVzPf7/Zl+DN/2se0Om+FqXDo/XkxieYdyhMdpTUaiATQo62wxDLwglrvyYxYlCCUJEZ4SjLlv3m/W82DhWUhISyExLaMMdaCXmgeRsWz+pC/V798w3eBoYKFyn/lVDTRTMJQi0eK0j4S0sJe77D2LEoSShAhPCcbUN+8htdxyHJz0JJXBCAAAF3FJREFU16fw9bQ3aHr5uOmGAsBSHpq8VAN1cYD2lVwUZ2FZBcMaUZHlLkEouojwFEPC47R8eMGJ+EuRFg8nZv/mnXXvw0GXzqof36Hv6W3mO8vnaqAq9NT2dsLDyYFvny1tch8nu2BYIyqy3CUIRRcRnmLGo8OJTkDGQRxbDifeSUwHvZ6Fa2Yweu9K84btAQU9grxXA1WrIF2v4tSDNE49SDOMA1AUDGtFRZa7BKFoIsJTzLAmzU0mps6xjPlrIbtXzDPfgTsZ1UAVVqQ+O/I6EyxUA1UBTipINRNA50jO7NBZx2FJMERUBKH4IsJTzLA2Wit72pZRe3+jQa8ZNFBqfBLwH+X+ra0Gqkf57E2ametyyFIQSj4iPMUMpdxrw0MfGGY3CVodV+PSeeHEFlb99I5yo4FkhEgr0Hv9fP683N4mX03Vu7GEHLIUhJKPCE8xw9TGur+7itMPtdxMeDTH6BJ2AP03Q5UbU8G509WoW++qWZPtN56mw5ofjKqBOmB9JoHsmCvABhJ1JgiPCyI8xYzMjfUPQm+RoPbA99/ZzcYbKQA0uX6GI18OsNhOysqBuLy4grqYF52s1UDdHVU84a2mWikno/5sxVwBtsxUN7ZURpWyA4JQPBHhKYZU0Tgxo7aWwEAfwuO0dPj7PoH3rnFxVneLz37VYxDj/lqOCyvM2kze+xb/OTzS6Fpimp6oFD0//DsjORdtbTnsR3g4QimnjAOrWROXVtPYLjpSdkAQii8iPMWE7N/wB5dW4RynZejys9yd2A4HvfKGyk9P9eTeN2V5v+l/zdrEpbrjt2QnCVoPk/ezRp2t61yWJmvuKe7jBGqgkY8b1+LS+OdhGglpes48zBALD0eo6+1IOVWS1VU7M1+DnbdTiMyWsM2W4m2CIBQuIjzFAFPf8P9JT2Znr3ocfnhP8dnNdVoxedJbHH1Vefmt49olbLve0qIv/7uRzPDQB0xprDG7bJZJIx83lrQpw8Ct941mOJCRJbtaKScmVIy1WnSyvwbZkYg4QSgeSCG4YkDWsztuqUkcnfsCZ957hnIKonOiYm1KzdmP7677iqKz/3ZXNp6/jbO+HS5WvBtitHpWXUmi95YopjU2PTMCcHXIKEI3aNt9Nt80vR9ki1CYOr+UHYmIE4Tigcx4igF3EtNxTNfy1/dj6Hp+j6LtXU1ZnvjgL7o32UVslxaKtpV/2MqNuIr4e8QQVNqJoLJOnPt3ScwSV+PSmX4sgWY+jhyMzHkqR+MEI3dHG0XaZccWoTBf4iEDiYgThOKDCE9RR6djxpKJtN2+xqKp/7QQtBUdeTCilaJd9mqgNxN03Ex4NCvJSGVj2bXr8enodCr8PRxyCExkCjlrZmfB1SEjNDz1bpTljjB/fsnHVUXbiq4S1SYIxQgRnqKKXo/L9Om4zptHWwumdSau50KF6nzXfirDg8wL1I04P57+dRN3k5U/oK0RnUxuJurp6u+MgypNcb8nO89VcqGKxomwu9bZm0sMKpFsglD8EOEpgjgvXIjb5MkW7d6etYZ5rnVo7ncC/YB6iraZ1UA9HFVYW4HUWuLT9GZr5JjCVQ2zmllOu5MVyTYtCCUHuwtP9+7d2bt3r9G1vn37snTpUnt3VeJwWrkS95EjLdp1HLWEbbVbUt1Ty40BHfDX3DFru+R0P0aEPKoGmpCmz1PmAVPYuqnfzs8lV4IhiUEFoWSQLzOewYMHM3XqVMPPrq6u+dFNiSA8TsuG7/5i0gwL6W2Al175jJWNuwHwZsNfWdBOOaOnuWqg9hSdrJv62ZfCKrhAbBokpRvbz25u22xHEISSRb4Ij7u7OxUqVMiPpksUkTv30aB3N+WM0cCtGbN5qWY/9txNJUBzm+tDOyra56UaqDW4OEBQGUeqlXIyWu4ytRQGyrV1BEF4/MgX4VmzZg1r1qyhfPnydOjQgQ8++ACNRkJdM3E4dw5NixZY+t4/vVMwH3UdQ//qbvihZ3X3cfQLNF+dLa/VQLPj4mA6MK1nVTeTS17mlsJkeUwQhKzYXXj69+9PQEAAvr6+nD9/nunTp3P27Fn++OMPe3dVpDGVxLLqwzuUamBpfgOLW7xIcP+poFIBkKLfzp+9hik+k9dqoNmpplGzoJUXY/bGKJaYFgRBsBVVdHS0xRCnmTNnMnfuXEWb9evX07p16xzXjx49Svv27dm5cyeNGjUy+WxYWJiV7hYPbiWpGHPWhZvJGakAysU/IGxWd7wTYxWfW1f/OV4Y8iXp6ozvA+6Oidwd0QaNc6LZZ6ypBmotziodtT30VHLTMapyGpXc9NxKUrH4uiORqQ74OD+6LgiCYI7AwEDF+1YJT1RUFFFRygf9/P39cXd3z3Fdp9Ph4+PDkiVL6Nu3r6Wu8p2wsDCLL0peGR76gFVXkvBMTuDQly9R994VRfv9VRrS7s3/kuLkYrg2qel3/KfVV4rPNfrlICejPBVt3B1V1CvtyJkHWqNNflP0r256CS0/KYjfR0FRUsYi4yhalJRxZMWqpbayZctStmzZXHVw9uxZ0tPTH6tgg/sxiexY8DptLx9WtIuoEECtcauIdXu0dBXofY2LQ5TLGyQkLOPcudr83K6qYeP+ZFQqsdqcttU9VWx9vjzhcVomHojhyH0t6To9Sen6HNFmsoQmCEJBYNc9nqtXr/L777/TqVMnypQpw4ULF5gyZQoNGjSgefPm9uyqaJKejtvw4Wxfu1bRTO/mRtyJE0S4l6Hslihi49JRoSOk3xu0CzAvViHXm/HdiV/5rk05IMxoMz9zlpWdq/E6wuO0VNE4saLjo9DqzD0oiTYTBKGgsavwODk5ERoayuLFi0lISKBSpUp06tSJiRMnolaX4MzBej2ukybhsnixRdO448fRVasGQBUyQpC33F7D+0+PUnyu1o8bSEuvwYJWHgwPfcCV+y5Uv/3AIBhTGmvYeD3ZZPmBrHVqsgc9LHjGWwRHEIQCxa7C4+/vz8aNG+3ZZJHH5YsvcP34Y4t2u9dupcFzTbNdjaaBf1Ua+Jt/7v/2jmPW4RG4qWFBK48sUWZqjsYmGVXerFvakSOROdfbMssPSOVOQRCKAlKPJ5c4/fwzXt7eFkWnzZs/ovryLK89CCA87pEouLpOxcurqtnn4lLd8Vx4iFmHRwAZp/8/PBKfoyZNZuVNgGoa098jfN3VhMdp6bE5ZyG1zOfD47QMD33A85siGR76wMhXQRAEeyJJQm3Ecf16PF55xaJd7zfm82dQe8PPmR/wP7S7hUaTM+w8K/3//p7Vl3LW0rmXZDrZTeaMxlwG5yG13Oi9JcpsEs+rsTITEgSh4JAZj5Wo9+zBy9vbouhMfHUGTZddNBId+P/27j0oynqNA/gXFna579IeEJVFhMCUsSE92knFCwamk8rUoBAdujCdDmPZxUz01KCFt5ypNLOLTGMn8RwJzOA4jd04ilJOhWbqHC9RJIlAIuteuCzsnj8MAnb3ZXdZ9mWX72fGGXn3fV+eHZ332d9lnweQeHViU9IiwaRjMCyFWn0dR+os99OReFm+rrtIZ3cF5/QYfyRFSJEe44+DC5TYc6FVsHtnY5tJcCRFRORMHPH003/xvUD2M+LvSR7wunWLnsLmlJvTYlH9RiYP3laGD+5ZK3j9jRs/wGRSAQAmySU40mY+uvlLmC9+0RsFKwlYKlsj1L1zfLAESj9vi6Mhe1pTExHZiomnl96L77FNtajctGjAa16f/SCeScvrKW8DAOF+XjAavdCBJjT8bY7g9a2t29DR8VifGH60kARGyYAdSaEAbu5Sq7mmRYwyyOI26P7JM9jH8lApKkjSU9jT0qYEe9sdEBHZgomnl4JqDVrrrqK1IBV+nR2C53bcfz/+mrUFxbXm540P8cXLM1/EPeOLrV5vNEZCo/kOgKzP8YJqjVkbaQCYGv5HD5vdc27BxYvXEBcXZXaepZ1rkYHeiAzwQp3+j63Wvbt3Wlsb4hdKiWgoMPF0U6uxPScJo3/7VfC0zqQk6EpKAJkM/9AY8E1z34f8fbGnUbw4U/AeWu2n6OqabvE1a9NiGoNt9dEKqjVm6zV1OiMWqWS4K8Lb4hdG2d2TiFyJiae1FYGLF8Pn228F2xR0TZgA7eefA8F911O6H9jX2vT4972pCAu4YvUeu3+4HwcvbMW+u82bs3UbbWV6y9ZpL6HEte9u63XY2N2TiFxl5Caezk4EZGfDd4AvvDYHhKD6s+OYlqCy+Pq4YF+8n1ICf//nBe/T3Q10ocCXRQHhLdGPHWnuWbfJCvWCpbKBg01cRERDbeQlHpMJ/k89Ben77w946rgXP8Mvt4xB+m/+6F1zoHvxvguXUbpEePNA/26g2k7hKTNL014Px/ub9cX5yk+GQ+MNZtNhXK8houFuRCUe2caN+PO2bQOel/D8xzg3+taen3tvK765eP8bts1+UrAb6E/qSYjb8y+zbqC2jDz6T3s9dqTZfN2mzbtPDbbe13K9hoiGsxGReKTvvgv/54WnwgDghS0fYqNsktnx3sni418+QU1OtuB9NJpKaDS3ISromlNGHtbWbax9z4brNUQ0nHl04vE9cAABjz464Hm64mJ0pqZimcaAfYetJQsdQkIm4MUZWqv3aW9/Em1tLwMAxgVjwJGHpfbYlkYmXLchIk/ikYnH58svEWhDt1P922/DkJHR87O1aar4P+2An9/Lgvd65JOTeH3G+D7HhEYe9lSKtrRuE+ln5LoNEbklj0o8ku++Q9D8+QOe17pxIzpWrLD4Wu9k4e19CcHBMYL3SivfgdONqTi4wL4OrZa+b9NdH82WdZus0OYhWbexdRRGROQot008vR+QU5t/xusrUga8pu2ZZ3AmMxNx8fEDnGlEYOAS+Pgcs3rGD0134Ykv9mBUgC8OLrD/4TzYdZuLF6/Z9ftswX49ROQKbpl4uh+QHZd/Rd2GgUc4HVlZaH3jDcDbG7h4UfBcH5//IDDwQcFzNJpvESW9FWUL7Qq7j+G4bmPPKIyIyFFumXgKqjU2JR1DSgr0+/YBvrZ8Wm8RbMwGAG1tL6K9fZXtgQqwtG4T6AM8HO/vlPs7wt5RGBGRI9yyH0+9vgsPfltu9fWamAT8cKEW+g8/tCnpDNQN1GQKglpd57SkA9ycOts5U47AXpWjdZ3AE8fVonX/HI6jMCLyPG6ZeEYHSFAfEmZ2/Fd5OG4pOI7YJ4ux9GjrgA9wb+/TkMsVkMl2WD1Hqz2IGzfqAAQNNmwzey60QtevkoGYDdhemBKM8cF9kwyrHhCRs7nlVNsLU4Jx/9WleKHlKmb9VI2o6/VI+XshrihG9ZwjvDbRiaCgOZBIzlr9HQbDUuj1ewBYafvpBPZMbfXfbWatVttgsOoBEbmCWyaeccG+KF00CgURz+Covgv/azGgqc28BpqlB7hSeQhy+XrB+/fuBjqUbJ3asrTbzFqttsFi1QMiGmpuOdUG/PGALF8Yhrlj/Cye0/sB7uXVCLlcgfHj11u9Z2vrNqjVLS5JOoDtU1sWe+z8XquNiMjduOWIp7+BKjL7+6+EVPpPq9db6wY61Gyd2uJuMyLyJB6ReKw9wGMUJxEUlCp4rVA3UFewZWqLu82IyJN4ROIB+j/A2xEcfAe8veusnt/RkY3WVuu72YYT1mojIk/iMYmnm1T67oDdQG/cuACTKdxFEQ2eK2u1ERENNY9JPF5elxESMlnwHL3+bZw7NxVxccJJZzgWynRFrTYiIlfwgMRjQkBANnx9rVcy6OqaDK22AjffrnCtNhbKJCIaWm67nRoAJJL/Qi4PFUw6Gk0ltNpK2JpjhQplEhHR4Llt4vH2/hFBQWlWX29vfxJqdQuMRuHpt/64dZmIaGi57VSbr2+p1dfU6p8BKBy6L7cuExENLbcd8XR1TTA7ptPthVrdAkeTDsBCmUREQ81tRzydnUug1++Cj89XMBpHo709D87IoyyUSUQ0tNw28QBeMBgegMHwgNPvzEKZRERDx22n2oiIyD0x8RARkUsx8RARkUsx8RARkUsx8RARkUsx8RARkUt5tbS0mMQOgoiIRg6OeIiIyKWYeIiIyKWYeIiIyKWYeIiIyKWYeIiIyKVGbOJZuXIlEhMTERERgdjYWGRmZuL8+fNih2WX69evY/Xq1Zg2bRoiIiKQkJCAZ599Fs3NzWKH5pA9e/bg3nvvRVRUFBQKBWpra8UOySaFhYW4/fbbMWrUKMyZMwdVVVVih2S348ePIyMjAxMnToRCoUBRUZHYITnk1Vdfxbx586BSqRAbG4vly5fj3LlzYodlt927d2PGjBlQqVRQqVRISUnB4cOHxQ7LaUZs4rnjjjuwa9cunDhxAqWlpTCZTEhLS4PBYBA7NJvV19ejvr4eGzZsQFVVFd555x1UVVUhJydH7NAcotfrkZycjLy8PLFDsdmBAweQl5eHVatW4ejRo5g+fTrS09Nx+fJlsUOzi06nw6RJk7Blyxb4+/uLHY7Djh07hpycHBw+fBhlZWXw8fFBWloarl+/LnZodhkzZgw2bNiAI0eOoKKiArNnz0ZWVhbOnDkjdmhOwe/x/O7MmTOYNWsWvvnmG8TFxYkdjsM+/fRTLF++HLW1tQgJCRE7HIecPHkS8+bNw/fff49x48aJHY6g+fPnIyEhATt27Og5NmXKFCxduhT5+fkiRua4sWPH4pVXXkFWVpbYoQyaVqtFVFQUioqKsHDhQrHDGZTo6Gjk5+fjkUceETuUQRuxI57edDodioqKEBkZiaioKLHDGRSNRgOZTIaAgACxQ/F4HR0dOHXqFJKTk/scT05OxokTJ0SKinrTarUwGo1QKBzvSiy2rq4ulJaWQqfTYfr06WKH4xRu3Ahu8AoLC5Gfnw+dToe4uDiUlZVBJpOJHZbDWlpasHHjRmRnZ8PHZ0T/07rEtWvX0NXVhbCwsD7Hw8LC0NjYKFJU1FteXh4mT57slg/ss2fPIjU1FW1tbQgMDMTevXuRkJAgdlhO4VEjnoKCAigUCsE/lZWVPeenp6fj6NGjOHToEGJjY/HQQw9Br9eL+A5usvd9ADc/2WVmZmL06NF46aWXRIrcnCPvhcgZ1q1bh6+//hoffPABJBKJ2OHYLS4uDpWVlfjiiy+Qk5OD3Nxct9woYYlHfSzOzc3FsmXLBM+JjIzs+btcLodcLkdsbCymTZuG6OholJWVISMjY6hDFWTv+9BqtUhPTwcA7N+/H35+fkManz3sfS/uRKlUQiKRoKmpqc/xpqYmhIeHixQVAcDatWtx4MABlJeXIzo6WuxwHCKVShETEwMASExMRHV1NXbt2oWdO3eKHNngeVTiUSqVUCqVDl1rMplgMpnQ0dHh5KjsZ8/70Gg0SE9Ph8lkQklJCYKCgoY4OvsM5t9kuJNKpUhMTERFRQXS0tJ6jldUVGDJkiUiRjayrVmzBh999BHKy8sRHx8vdjhOYzQah8XzyRk8KvHYqqamBmVlZZg7dy6USiWuXLmC1157DVKpFAsWLBA7PJtpNBrcd9990Gg0KCoqgl6v75kqDA0NhVQqFTlC+zQ0NKChoQGXLl0CAJw/fx5qtRoqlQqhoaEiR2fZihUr8Pjjj2Pq1Km488478d577+Hq1atut/NIq9WipqYGwM0HXF1dHU6fPo3Q0FCoVCqRo7Pdc889h/3792Pv3r1QKBRoaGgAAAQGBg67D2VC1q9fj9TUVIwdOxZarRYlJSU4duwYiouLxQ7NKUbkduq6ujo8/fTTOHXqFNRqNcLDwzFjxgysXr3arT4hVVZWYvHixRZfKy8vR1JSkosjGpzNmzdj69atZsfffPPNYb21t7CwENu3b0dDQwMmTpyITZs2YebMmWKHZRdr/5cyMzPx1ltviRCRY6ztXluzZg3Wrl3r4mgcl5ubi8rKSjQ2NiIkJAQJCQlYuXIl5s+fL3ZoTjEiEw8REYnHo3a1ERHR8MfEQ0RELsXEQ0RELsXEQ0RELsXEQ0RELsXEQ0RELsXEQ0RELsXEQ0RELsXEQ0RELvV/E2+0TGxjqYEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_hat = df_censored_regression.loc[\"a\", \"mean\"]\n",
    "b_hat = df_censored_regression.loc[\"b\", \"mean\"]\n",
    "y_bayesian_pred = a_hat*x_obs + b_hat\n",
    "\n",
    "plt.scatter(x_obs, y_obs)\n",
    "plt.plot(x_obs, y_pred, color=\"red\", label=\"Simple linear regression\")\n",
    "plt.plot(x_obs, y_bayesian_pred, color=\"yellow\", label=\"Censored linear regression\")\n",
    "plt.legend()\n",
    "plt.title(\"Data\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see clear improvement - the line isn't skewed towards these censored outliers. BUT, it took 5 minutes to calculate all of these values and it was only simple regression (with censored data). Such procedures in R take a fraction of seconds (but the underlying models are a little bit different: either Cox model or parametric models with some assumption on the hazard function (or on distribution in other words). In the latter models we simply maximize likelihood of the censored data (the contribution of the single observation is the density for non-censored observation or survival function for censored observation). This is very fast to compute and without a need for sampling like in Bayesian or Monte Carlo methods. \n",
    "\n",
    "This is example how we pay for a generality of the framweork. With bayesian probabilistic modeling framework we simply specify the process of generation of data and let sampler do the rest. There is no need for writing custom functions, calculating likelihood or expectations, optimizing the model etc. One way to maybe speed up the computations, but without changing the probabilistic formulation of the model would be to change the way we calculate these samples. We could do it with EM Expectation Maximization, which requires calculating expected likelihood based on the conditional distribution of hidden variables and then iteratively change the parameters to maximize it. It takes some time to calculate all of this, but it would be interesting to see if it's worth it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accelerated failure time model\n",
    "\n",
    "Finally, let's try to fit a standard Accelerated Failure Time model. One issue is that the values of y are sometimes below y: this means that it can't be interpreted as time to survival (because time is never negative). To deal with it I exponeniated the $y$, fitted the model and then took logarithm of a prediction.\n",
    "\n",
    "More details about the parametric censored regression and python lifelines package can be found here:\n",
    "https://lifelines.readthedocs.io/en/latest/Survival%20Regression.html."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>observed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.085631</td>\n",
       "      <td>0.049503</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.997345</td>\n",
       "      <td>54.598150</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.282978</td>\n",
       "      <td>13.027807</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.506295</td>\n",
       "      <td>0.010908</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.578600</td>\n",
       "      <td>0.770356</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x          y  observed\n",
       "0 -1.085631   0.049503         1\n",
       "1  0.997345  54.598150         0\n",
       "2  0.282978  13.027807         1\n",
       "3 -1.506295   0.010908         1\n",
       "4 -0.578600   0.770356         1"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observed_indicator = [0 if y == 4 else 1 for y in y_obs]\n",
    "df = pd.DataFrame({\"x\": x_obs, \"y\": np.exp(y_obs), \"observed\": observed_indicator})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lifelines.LogNormalAFTFitter: fitted with 1000 total observations, 162 right-censored observations>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aft = LogNormalAFTFitter()\n",
    "aft.fit(df, duration_col='y', event_col='observed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_aft_pred = aft.predict_expectation(df[[\"x\"]]).values\n",
    "y_aft_pred = np.log(y_aft_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OnSTnPDkhbfSAjH6f8vO7Iyj6TPl7CkvOLpHYgnyCqF66OjLZA2xsqknKVKp2xMf7A4UfdaLYCU9xxN3dHbVaTWJiosE9oE6fPo2rqyuQek5y9epVevfunWHd6tWrc+3aNSpUqGDQMWRHVv0mJiby7Nkzbty4wbx583TbdefPn0etVhfKGADKly+PsbExZ8+e1b2e8fHxXL16Vfdzdm2XL18+yy81np6eeHp6Mm7cOLp3786GDRt026SlSpWid+/e9O7dmxYtWjB48GB++OEHPSFzd3cnLCyMu3fv6lY9oaGhhIWFUbly5Ry+GoI3idNhp2mxqYXENqHeBL5q8BWgwcKiJ8bGf0nKo6OvoNU6FeIopQjnAgPy7NkzOnTowKZNm7h8+TKhoaFs27aNRYsW4eXlhY2NjcH7nDdvHocOHeLatWuMGjUKExMTunfvnmHdsWPHcvbsWT799FPd9tCePXsYN26cwceVm36VSiWlSpVi7dq13Llzh6NHjzJ+/HiD3nXKbgxWVlb069dP5yBx/fp1xowZg1arzTYO2cu2J0yYkGHboaGhTJ8+nVOnTnHv3j3+/vtvrly5gru7OwCzZ89m165d3L59m+DgYHbu3Imrq6ue6AA0bdoUDw8Phg0bxrlz5zh37hxDhw6levXqOtEWvB3Eq+Jx/9FdIjolzUry8JOHfNXgKxSKHdjalpSITnz8CqKiIl+r6IBY8RgUS0tL3n//fVasWMGdO3dITk7G0dGR7t27F1ikgmnTpjF58mRu3bpF5cqV2bRpU6bbUdWqVSMwMJBZs2bRvn17UlJScHV1zdI7zBBk16+RkRGrV6/myy+/pEGDBlSoUIFZs2Zl6CBRUGMAmDlzJnFxcfTp0wdLS0tGjhzJ48ePs92afdn2//73vwzbtrCw4NatWwwcOJCIiAhKly5Njx49dMJkamrKrFmzuHv3Lqamprz//vts3Lgxw75kMhm//fYbEydOpEOHDgB4eXkxd+5cEajzLeK7U98x+8RsiW1Pzz3UL1MfmewJNjZSYVGrGxAXtwuQF+IoM0cWGRmpzb5a4RMVFSU5HDUUhXHGUxgcOHCAbt26cfv27WIdRaAovx9JSUl4enoyevRoiTdcZhTlueSGvM6joP5m88rNmzdxc3N73cPIN2nncfnJZT5YL3U8GVZjGHObzgW0mJuPwMRkk6Q8JuYsGk3hbq9nh1jxCAQvuHDhAjdu3KB27drExMSwcOFCYmNj6dq16+semuAtJzklmQ/8P+DG8xs6mwwZISNCUJopUSgOYmkp/T1NSJhLcvKw9E0VCYTwCARpWLp0Kbdu3UIul+Pp6UlgYCBOTq93P1zwdrMpZBPz/pwnsQV0CaBZuWZAJDY2JZHJXnkspqRUJjb2bwoy8kB+EcJTTGnUqBGR+XQtF0ipXr06hw8fft3DEAgAuP38NrV/rS2x9a7Sm+UtlyOTyTAzm4Sp6XJJeUzMMTQaD4o6ufZqO3bsGL1796ZKlSoolUq929BarRY/Pz8qV66Mg4MD7dq149q1awYbsEAgELzJpGhSaLWplZ7o3Bx2kxWtVqBQnMbWVikRncTEyURFRRYL0YE8CE9cXBxVq1bl22+/xdzcXK984cKFLF26lDlz5nDw4EHs7Ozo0qULMTExBhmwQCAQvKn8dvU3Si0qxamwUzrbnFpziBwXiZ2FJdbWFbGyaqkr02jsiYr6j6Skgs/vZUhyLTwtW7bk66+/plOnThgZSR/XarUsX76ccePG0alTJ6pWrcry5cuJjY1ly5YtBhu0QCAQvEk8iHmAcoGSkX+9iqzRqnwrno99TjPHZpiazsHWtgxGRq/CHsXG7iMmJhgofrmaDHrGc/fuXcLDw2nWrJnOZm5uTsOGDTl16hSDBg0yZHcCgUBQrNFqtfTe0Zu9IXsl9suDL+Ns7YyR0SXq1GksKUtKGkli4jeFOUyDY1DhCQ8PB9ALNmlnZ0dYWFimz928eVPPZmZmluHNbUOQ25QFRRUxj6LHmzKXvMwjOjqax48fF8Bo8k5Gny1FhYNhB5l4dqLENq36NNo7tycxPBqTUjUwNw/VlWk0Ci5c2EdKihVQdOcFZHt/qkh4tWU0yKioqAK5jPe2X/Irarwp84A3Zy55nYeNjY0u4nZRoKheIH0S/wS3H6XjqudYj8AegciN5JiYrMTcXCpIsbHbSElpSiGHWSwwDBqr7WVK5PSh+588eaIL6y8oGqTPJFpY/RRWv4JXpM9gKng9aLVahu0Zpic6/w74l7299mKsS8z2SnSSk304c+YfUlKaFsoY5SdPYqtU5jvvWXYYVHjKlSuHvb09hw4d0tkSExM5ceIE9erVM2RXRRZfX1+USqXuX4UKFejVqxc3btzI/uFCxNnZmeDgYDw9Pd+Kft9mDh06xODBg1/3MN5qDt49SImFJdh8fbPO9q3Xt0SOi+TdEq5YWrbC2lrqPh0dfYuEhGUURtoCo/PnsVUqsWrd+pXRgNHh05PrrbbY2Fju3LkDoEvUdfHiRUqUKIGLiwu+vr58//33uLm5UbFiRebNm4elpWWmEZPfRJo2bcrKlSsBCAsL4+uvv6Zfv378888/r3lkr5DL5boV6tvQb0aoVCq9vDUZkZycbPB0FoXR9kveeeedAm1fkDmRiZG4rnCV2NxLunOk7xFM5CYYG2/AwsJXUh4Xtw61ukOhjM/o6lWsGzbUs8dt3gwGjA6v129uHzh37hxNmjShSZMmJCQk4OfnR5MmTfjmm1Qvi7Fjx+Lr68sXX3yBt7c3jx49IiAgAGtra4MPvqhiamqKvb099vb21KhRg5EjR3Ljxg0SEhJ0daZPn06dOnVwcHDA09OTr7/+Wnege/fuXUqUKKG3HfXrr79SoUIFXXK069ev07NnT5ydnalYsSKDBw/WOXgAXLlyhY4dO+Li4oKTkxONGjXi77//1vWRdssrJSWFUaNG8d577+Hg4ECtWrVYuHChJHmYr68vvXr1Yvny5VSpUoVy5coxcuRI4uPjc/zapO/32LFjKJVKgoKCaN68OY6OjjRt2pTz589Lnjt16hRt27bF0dGRKlWqMH78eKKjo3Xl+/fvp02bNpQrVw5XV1e6du1KcHCwXr9btmyhQ4cOODg48Msvv2Q4Rk9PT/z8/Pjkk08oW7YsQ4cOzdEY4uLiGD58OE5OTri5ufH999/Tq1cvfH198932sWPH+PDDD3FycqJs2bI0a9aMq1evAqnnocOGDaNixYrY29tTvXp1SRK59Ftt9+/fp2/fvjg7O+Ps7Ey/fv14+PChrvy7776jQYMGbN26lRo1auDs7IyPjw8RERHZvb2CNEw8PFFPdI72Pcqp/qcwVTzB1lYpER2VqjVRUc8LRXSMbt/GVqnUE534n38mKjISdcuWmTxpoP5z+0Djxo2JjIzU+7d8eeotWplMxqRJkwgODiY8PJzAwMAM0we/LcTExBAQEEDVqlUlF24tLCxYsmQJp06dYv78+QQEBDBvXmo8pnLlyuHt7Y2/v7+kLX9/f3r16oWJiQnh4eG0bduWKlWqcODAAbZt20ZsbCw+Pj46sRg6dCgODg4cOHCAI0eO8OWXX2Z6aKzRaHB0dGTNmjWcOnWKqVOnMn/+fL0xnDhxgmvXrrFt2zZ++eUXdu3axYoVK/L9Os2YMUOXC6dkyZIMGzZMl8H0ypUrdO3alTZt2nD06FHWrVvHpUuXGDVqlO75uLg4RowYwcGDB9m1axc2Njb07t1bL4PpjBkzGDJkCCdPnswyHcSyZcuoVKkShw8f5uuvv87RGGbMmMGxY8fw9/dnx44dXL58mRMnTuS7bbVajY+PD/Xr1+fo0aPs378fX19f5PLUEPezZs3i6tWrbNq0idOnT7NkyRLKlCmT4bw0Gg0+Pj48efKEnTt3snPnTh49ekTfvn11rzfAvXv3CAgIwN/fn4CAAC5evMjMmTOzexsFwKn/TqFcoGTl+ZU62+QGk4kcF0k1Ow8sLHpjYyONMBAdfZn4+I0U9Laa7N69VMGpLd3Wi1+yhKjISFTduhVo/y8pEl5tucHWNn+HXrmN2h4Vlft4aPv379cFloyLi8PZ2ZnNmzdL6kyYMEH3/3LlyjF+/HgWL17MlClTABgwYABjxoxh9uzZmJmZERwczOnTp1m4cCEAa9asoVq1asyYMUPXzsqVK3F1deXcuXPUrl2b+/fvM2rUKCpVqgSQZeZRY2NjJk+eLBnThQsX2Lp1qyQvjrW1NT/88ANyuRx3d3c6d+5MUFAQ48ePz/XrlJbJkyfrEplNmDCB1q1b899//+Hk5MSiRYvo0qWLJDXB/PnzadKkCU+ePMHOzo5OnTpJ2lu6dCkuLi78+++/NGjQQGcfNmyYXt2MaNiwIWPHjtX9PHz48CzHYG5uzoYNG1ixYgXe3t4ALF68OMMvXbltW6FQEBUVRevWrSlfvjyA7j2F1BVM9erVqf3iw6Rs2bKZzisoKIgrV65w7tw5XQbTVatWUbNmTYKCgmjatCmQKnbLli3TpTkYOHCgXngsgZQ4VRzVfq7G88TnOpu9hT3nBp3DwtgChWInlpYfSZ6Jj1+GSuVT4GOThYVhXbMmsnRu8gnffUfyi1V3YVLshKc40LBhQ51AREZGsmrVKrp27cr+/ftxdnYGYPv27Sxfvpw7d+4QFxdHSkoKKSkpujbatm3L559/zs6dO+nRowf+/v7Url1b90F28eJFjh8/nmHk5JCQEGrXrs3IkSMZM2YMGzZswMvLi44dO0o+sNKzevVq1q5dy/3790lMTESlUum5x7q7u+u+aQM4ODhw5syZvL9YL/DwePUN0MHBAUj1hnRyctJl9fzjjz90dV5+Ow8JCcHOzo6QkBBmz57NmTNniIiIQKPR6M4g01KzZs0cjSd9vezGYG5ujkql0n34Q2piwIyEJ7dt161bFx8fH7p164aXlxdNmjShU6dOuvdm8ODBDBgwgPPnz+Pt7U3r1q354ANpzpaXBAcH4+joqBMdAFdXVxwdHbl+/bpOeFxcXCS5dRwcHHj69Gn65gQv8Dvhx5xTcyS2fb328b7j+8hkT7Gxka5A1ep6xMUFUtCJ2WRPn2JVrx5G6bZJE6ZPJ7mAMw9nRbETnrysQNJSGHctLCwsJKuLxYsXU7ZsWdasWcOUKVM4ffo0H3/8MRMnTuSbb77B1taWwMBApk6dqnvG2NiY3r174+/vT5cuXdi0aRNfffWVrlyj0dCyZUtmzZql1//LC7yTJk2iZ8+e7Nu3j4MHDzJnzhy+//57PvroI71nAgICmDRpEjNnzqRu3brY2Njw008/sWvXLkm99IfxMplMskWTV9K2+zKT5st2NRoN/fv3Z+TIkXrPOTo6AtCrVy/KlCnDggULcHR0RKFQUK9ePb2ttsyys6Ynfb3sxnDr1q0ctZuXtiF1e87X15cDBw6we/duZs2axfr162nevDktWrTg0qVL7Nu3j6CgIHr16kWnTp0k5zw5IW0G04ze57TnfYJULjy+gNdvXhLbJ7U+YXaT2aQmZhuJiclvkvKYmDNoNBULdmCRkVg3aYLRvXsSc+Lnn5P0YlfldVLshKc4IpPJMDIy0jkXnDx5EkdHR8l22/379/We69+/P/Xq1WPVqlV6Ccnee+89du7ciYuLS5aeWe+++y7vvvsuI0aMYPz48axbty5D4Tlx4gS1a9dm2LBXiaNCQkLyNF9DU716da5du5bpVuGzZ8+4ceMG8+bN023XnT9/HrUB3UGzG0P58uUxNjbm7NmzuLq6AhAfH8/Vq1d1P+e17Zd4enri6enJuHHj6N69Oxs2bKB58+YAlCpVit69e9O7d29atGjB4MGD+eGHH/Sif7i7uxMWFsbdu3d1q57Q0FDCwsKoXLlyDl4JAUCSOokG/g24E3lHZzORm3Bz2E1sTW2Ry4OwspJu6SYk+JGc7Ju+KcMSG4tVy5bIXzie6MY7ciSJs2dDEUmPbtB7PIJUkpKSCA8PJzw8nODgYCZMmEBsbCytX/jIV6xYkbCwMDZv3kxoaCg///wzW7du1WvHzc2N+vXr8/XXX9OxY0dsbGx0ZYMGDSI6OppBgwZx5swZQkNDOXz4MGPHjiUmJoaEhAQ+//xzjuDJ9RAAACAASURBVBw5wt27dzlz5gwnT57E3d09wzFXrFiRixcvsm/fPm7fvs3cuXM5fvx4wbxAuWTs2LGcPXuWTz/9VLcttWfPHsa92CpQKpWUKlWKtWvXcufOHY4ePcr48eNRGNAdNLsxWFlZ0adPH52DxPXr1xkzZgxarVaykshL26GhoUyfPp1Tp05x7949/v77b65cuaJ7L2fPns2uXbu4ffs2wcHB7Ny5E1dX1wxDTjVt2hQPDw+GDRvGuXPnOHfuHEOHDqV69eo60RZkzZKzS7BfYi8Rne1dt/N49GNsTcHGxk4iOikpbkRFPS5Y0UlIwLJFC2ydnSWikzRwIFHPn5P4zTdFRnRArHgKhMOHD+s+FKytrXFzc2PNmjU0bpwa7K9NmzaMGTOGSZMmkZiYiLe3N1999RWfffaZXlsfffQRx48f11ulODg4sHfvXmbMmEG3bt1ISkrC2dkZb29v3QdOZGQkI0eOJDw8nJIlS9KqVatMPZMGDRrEpUuXGDJkCFqtlo4dO/LJJ5/oebW9DqpVq0ZgYCCzZs2iffv2pKSk4OrqqvNKMzIyYvXq1Xz55Zc0aNCAChUqMGvWLIlTREGPAWDatGkkJibSp08fLC0tGTlyJI8fP852aze7ti0sLLh16xYDBw4kIiKC0qVL06NHD50wmZqaMmvWLO7evYupqSnvv/8+GzduzLAvmUzGb7/9xsSJE+nQIdVt18vLi7lz52YrkG87N5/d5P2170ts/Tz6sfjDxS8Ss03B1HSJpDwm5ggaTQFelk5OxqJnT4zTJTBM7tGDhBUrQF6wZ0h5RRYZGZn/DfoCICoqSnK4aSiKWzytBQsWsG7dOv7991+JvbjNIzPelHmA/lySkpLw9PRk9OjREo+1ok5e35OC+pvNK4aK1abWqGm5qSVnw89K7LeH36aUeSnk8tNYWbWQlCUmfklS0pf57hsymYdajcXAgRinO4NVtWpFvL8/5OBi9OtErHiKKLGxsdy/f58VK1ZkuBISFD0uXbpEaGgotWvXJiYmhoULF+qdzQmKF2svr2XM/jES2/oO62n3bjsgHmtrd4yMXl3a1mhKERNzEciZE0uu0WgwHzkSk3QrWvUHHxC3dSsUUER/QyOEp4jyxRdfsHXrVtq0aSPyGBUjli5dyq1bt5DL5Xh6ehIYGJihy7ugaHMv+h7vrX5PYmv/bnvWtV+HTCbD1HQeZmZSj9LY2L2kpBRQTEqtFrPPPsN09WqJWV2rFnG7doFF8UoGJ7baiiliHkWPN2Uub/NWm0aroce2Hhy4e0BivzrkKmWsymBkdAVr60aSsqSkESQmfpvv8WaIVkvC6NE4pDtrTXF3J3bfPkjjcFScECsegUAgALbd2MbAwIES24+tf6Rn5Z5AMlZWDZDLr+nKtFojoqPvAAWTQsB07lzMvvmGtFKucXIi9uhRtCVKFEifhYUQHoFA8FYTHheO+0/SawaNnBqxo9uOF4nZfsLc/AtJeVxcAGp1swIZj8mSJZinu+SptbUl5vRptG9IXjMhPAKB4K1Eq9UyZPcQtt6Q3qE7N/Ac5ZXlMTIKwdpaGt4oObkXCQkrKIhgnia//IL5p59Kx6hQcHHbNlwzCYFUXBHCIxAI3jr2heyjx/YeEtt87/kMrj4YSMHSsi0KhfQCdXT0TbRaO4OPxXjjRixGjNCzR58/j9bVFdXNmwbv83UjhEcgELw1ZJSYzeMdDw73OYyx3Bhj401YWAyXlMfF/YpanX1E89yi2L4dywED9Owx//yDJotgvm8CQngEAsFbwecHP2fVxVUS24mPTlClVBVksv+wsZFGElepWr7IkWPYyGKKv/7CsmdPPXvMkSNo3pKU8CJWmyDXREREoFQqOXLkSI6f8fPzk+TFEQgKi2MPjqFcoJSIzrRG04gcF0mVUpWxsOirJzrR0ZeIj9+MIT8i5X//ja1SqSc6sfv3ExUZ+daIDogVT4Fx/vx5mjVrxvvvv8/evXv1ypVKfRfMatWq4enpyYYNG7JsOzIyf6khBIK3gXh1PGWXlSU6+VUKcWdrZ04POI25whyFIhBLS2kStvj4xahU+tHb84P8n3+wyiCVdOyff5LSqFEGT7z5COEpINatW8fgwYPZtGkTwcHBGUaFXrRoEa1atdL9bGxsjFwuZ/r06TpbzZo1mTp1qgi7IhDkgpnHZjL/9HyJ7WDvg9RyqIVMFoGNjaOkTK2uQ1zcHgz5kWh04QLWXl569ritW1G/SGfxtiK22gqAhIQEfv/9dwYOHEjHjh1Zt25dhvVsbW2xt7fX/StZsqSeTSaTYWNjI7FlxJEjR1Aqlezbtw8vLy8cHBxo06YNDx8+5OjRozRq1AgnJyd69erFs2fPdM9pNBrmzp2Lh4cHpUuXpmHDhvz555+Sts+ePYuXlxf29vY0btw4w4yj169fp2fPnjg7O1OxYkUGDx5MeHi4Xj2BoCA5H34e5QKlRHTG1RlH5LhIajnUwtx8NDY270qeiYk5TVzcfgwlOkbXr2OrVOqJTpy/P1GRkW+96IAQngJh+/btuLi44OHhQa9evdi4cSMqlapQ+vbz88PPz4/9+/cTGRnJxx9/zNy5c1m4cCG7du3i2rVr+Pn56eovX76cxYsXM336dI4fP067du346KOPuHjxIpAarLRnz564urpy6NAhpk+fLsmUCvDo0SPatm1LlSpVOHDgANu2bSM2NhYfHx+RtVJQKCSqE/H82ZOmG5rqbOZyc+6PvM/0D6Yjlwdha6vExOTVl8CEhNlERUWi0eQ/gjWA0Z07qYJTv77EHv/TT6mC0769Qfp5Eyh2W23KBQUTniIzIsfl/jxl3bp19O7dG4APPvgAc3NzAgMD6dRJ6pI5fPhwSbrjH374gZ4ZeLvkhsmTJ9OwYUMgNcfOhAkTOHz4MDVq1ACgT58+7NixQ1d/yZIljBo1ih49euieP378OEuWLOHHH39ky5YtJCcns3TpUqysrKhatSqfffYZw4e/cjn9+eefqVatGjNmzNDZVq5ciaurK+fOnaN27dr5mpNAkBULzyxk2tFpEtuu7ruwT7DH2kSLjY0jMlmCriwlpQKxsScAw0Rylt2/j00GjgHxixahMmBOqDeJYic8RZ07d+5w8uRJVq1K9aCRyWT07NmTdevW6QnP//73Pz788EPdz3Z2+b+c5uHhoft/6RfhNdLbnjx5AkB0dDRhYWHUT/cNrUGDBvz1118ABAcH4+HhgZWVla68bt26kvoXLlzg+PHjGUZhDgkJEcIjKBCuR1yn/jrp7+7AagNZ8OECAOLjx2Bru1ZSHhMThEZT3SD9y8LDsa5dG1lsrMSe4OdHsm8Bp7gu5hQ74cnLCiQtBR1BeO3ataSkpFCtWjWdTatNDQD+4MEDnJ2ddXZ7e3sqVKhg0P6N0ySAeplRMr0tJ9tfuclGqdFoaNmyJbNmzdIrM4SYCgRpUaWoaL6xORefXJTYQ0aEUMKsBHL5WaysmpE2UHZi4hckJU02SP+yZ8+watAAo3RnmIlTp5IkcmfliGInPEUZtVrNhg0bmDZtmsRbDVK31davX8/EiRNf0+j0sbGxwdHRkZMnT+KV5iD0xIkTOi88d3d3fvvtN+Li4rC0TE1udfr0aUk71atX548//sDFxUUicgKBoVlzaQ3jDoyT2DZ12kSr8q2ABKytq2Jk9J+uTKNREhNzBYMkZouKwsrbG/mdOxJz4mefkTRlCojU4TlGOBcYkL179xIREcGAAQOoWrWq5F+3bt1Yv369bvVTVBg9ejRLlixhy5Yt3Lp1i9mzZ3PixAldqubu3bujUCgYNWoU165d49ChQ8yfL3VTHTJkCNHR0QwaNIgzZ84QGhrK4cOHGTt2LDExMa9jWoI3jNCoUJQLlBLR6eLWhedjn9OqfCtMTX/A1tZRIjrXr/9ETEwo+RaduDisGjfGtlw5iegkDR9O1PPnJE2dKkQnl4gVjwFZt24djRs3pmTJknplnTt3Zvr06Rw6dIhmzQomnHpeGDFiBLGxsUybNo3Hjx/j5ubG2rVr8XxxWGplZcWmTZsYP348Xl5euLm5MX36dPr06aNrw9HRkb179zJjxgy6detGUlISzs7OeHt7Y1pMUvEKiiYarYbOAZ35+/7fEvv1oddxsHTAyOga1tbSiBhJSUNJTPyO2Nh8BtdMTMSySxcUJ05IzMn9+pGwaBEYie/teUVkIC2miHkUPd6UuRSVDKRbrm9hyJ4hEtvqNqvp6t4VUGFl1RS5/Eq6MYTyMjFbXjKQApCcjIWPD8b790vNXbqQsGoVyOW5bzMf5HkeRRix4hEIBEWKsNgwqqyqIrE1LduUgC4BGMmMMDFZjbn5eEl5XNwW1OoPyRcpKVh8/DHG27dLzKqWLYlfvx7E+aXBEMIjEAiKBFqtlgF/DmDHrR0S+4VBFyhnWw6ZLBQbmxqSsuTk7iQk/ES+ErNpNJiPGoXJb79JzOqGDYkLCIA3YBVb1BDCIxAIXju77+ymz44+EtvC5gsZ4DkA0GBp2QGFQhoNPTo6GK024xBSOUKrxWzCBEx/+kliTqlendjAQLA0gCecIEOE8AgEgtfGs4RnVFgpvctWo3QN9vfej8JIgbHxFiwspOc88fG/oFJ1yXunWi2m//sfZj/8IDGnVKxI7IEDUABnywIpQngEAsFrYez+sfx6+VeJ7VT/U7iXdEcmC8PGRnrOo1I1Iz5+C/m5BWI6bx5m6S46axwdiT12DG0G3qiCgqFIC49Wq83VDXqBQPB6yM39tL/v/03HrR0ltpmNZzK69mhAi4XFAIyNpQf80dEX0WrL5nl8JsuWYf7VV9Ix29gQc/o02kwivgsKjiIrPJaWlkRGRqJUKoX4CARFGK1WS2RkJNbW1lnWi06Kxv0ndxLUrwJ2utq6cvKjk5gpzFAo9mBp2VvyTHz8IlSqvAfaNP71VyzGjpWO18iImIsX0aYJXyUoXIqs8CgUCqytrYmOjs6+ci6Ijo7GxsbGoG2+DsQ8ih5vylzyMg9ra2sUisw/TqYdmcbCfxdKbId9DlOjdA1ksmfY2DhIytTqmsTF7SOvH1HGmzdTZ9gwPXvMuXNoypfPU5sCw1FkhQdSxcfQl0gfP36Mi4uLQdt8HYh5FD3elLkYch7/PvqX5hulic8+r/s5UxpOAcDMbBympmsk5TExp9Bo9DP25gTFzp1YfqSfujrm5Ek0lSvnqU2B4SnSwiMQCIonCeoEav1Si7C4MJ3N1tSWK4OvYGVihVx+FCsraWK0hISZJCePzlN/iv37sezeXc8eExSEprph0iAIDIcQHoFAYFDm/zOfmcdnSmyBPQJp6NQQiMHGxhmZ7FUOG42mHDExp4DcX9SUHz2KVQaZPWP37eO6UvnGhZp5UxDCIxAIDMLVp1dp6N9QYhtafSjfeX8HgKnpDMzMpHdnYmIOo9FIoxHkBPmZM1h9qB8iJ3bnTlIaN0794WY+g4QKCgyDC4+fnx9z5syR2EqXLs2NGzcM3ZVAICgCqFJUNPmtCdcirknsoSNCUZopkcvPYWXlLSlLTPyMpKSpue7L6OJFrJs00bPH/f476hYtct2e4PVQICseNzc3du3apftZXsjRXAUCQeGw6sIqPj/0ucS2tfNWmrs2BxKxtq6GkdEDXZlWa0N09FXAitxgFByMdb16eva4tWtRd+yYwROCokyBCI9CocBeXMoSCN5YQiJDqLmmpsTWs3JPVrZaiUwmw8RkIebm0yTlsbF/kpLSKFf9yEJDsamhvxUXv3Ilql69cj9wQZGgQIQnNDSUypUrY2JiQp06dfj6669xdXUtiK4EAkEhkqJJof3W9px4KE2OdmPoDUpblsbIKBhra+nKJCnpYxITv89VP7KHD7F+7z1kKSkSe/yCBagGDszT2AVFB4Mngtu3bx+xsbG4ubnx9OlTvvvuO27evMnJkyczzMwJqYmOBAJB0SbwQSDTLkhXMd/W+pbmjs2RydRUrjwQS8tgSfm5c/tJScn5XTxFRATVunVDERcnsd//9FPCfXzyPnhBoZKdN2GBZyCNjY2lRo0ajBs3jlGjRhVkVzniTcnmJ+ZR9HhT5pJ+Hg9jHuLxs4ekTgvXFmzqtAkjmRHGxmuwsBgnKY+L24xa3TLHfcqeP8eqYUOMwsIk9sSvviJpwoTcT4I39/14Eyhwd2orKysqV67MnTt3CrorgUBgQLRaLT47fdh9Z7fEfunjS7jYuGSSmK0rCQk/k+PEbNHRWDVvjjzdrkfiuHEkTZsGIk7jG0mBC09iYiI3b96k8UvfeoFAUOTZdWsX/Xb1k9iWtFhCP49+gAYLi84YGx+WlEdHX0erlcZcy5S4OCzbtUNx/rzEnDR0KIlz5wrBecMxuPBMmTKF1q1b4+zsrDvjiY+Pp0+fPtk/LBAIXitP45/y/p/vS2zvO7zP7p67XyRmC8DC4mNJeXz8z6hU3XLWQVISll27ojh2TGJO9vEhYckSMMp7rh1B8cHgwvPff/8xZMgQIiIieOedd6hTpw779u2jbNm859IQCAQFi1ar5ZN9n/Db1d8k9jMDzlCxREVksnBsbKSBO1WqpsTHB5CjxGwqFRZ9+2L8119Sc8eOxK9eDVlEtha8eRj83V69erWhmxQIBAVI0L0gOgV0ktj8vPzwrekLaDE3H4SJyR+S8ujo82i1rtk3npKC+bBhmGzdKjGrmjcnfsMGMDHJ5+gFxRHxNUMgeEuJSori3ZXvotaodTa3Em78Wv9XqrpXRaH4C0vLnpJn4uMXoFINzL5xjQbzsWMxWbdOYlbXr0/cH3+AubkhpiAopgjhEQheE3djVMw6G0NYfAqOFnKm1LKmnLWxnn1gJXPW3EiQ1AP06vzvbDT/PFaT9n6EEfCOmRGuljJuxWqIU2kxNoLYmG8hWSoKWG3lpqYy7f6N5FldpaTo7OMq1Nu4AbXGGHiY+aS0Wn7Y9i3j/vaXmM85Vabx6LXEmVrCxmd5f9FeIAPJPE0ArQxUaYwlFWZ8ZxTDngcqQmLUPE7QYGcmo4KNMVNqWXPmcSKjj8eQqNaiBawUYKaQ8b6dCZ94WOpecxtjGVotxKi1kvfpJS/fr4z6SFsvbd3073lWdfqWkFFYztQ5GZ8hKPB7PEWNN8UnXsyj6JGbudyNUdF5bwQhMa9u5psaQQN7E25FqXgQ/+rPMv2HrLOlEaoUDeGJr2xGgCYnHavPQ1xfqc30EzAbCcAS75l8Un2jpLjq2u1ce1Yx26ZnBi5kyr4fJbbbpVyo/dlmosyLVmbWd0zhaVLm5XIZpGTyyVjeWs62VqV0XxLSv48Z1YOM3/Oc1HE20/Bne4cCEYC05GR8hkK4kAgEr4HUb8jSD6skDRwOS5aIDkhFB+BBnFR0IAeio02A6MZS0ZGVBJszYDaSD8r8i3ach0R0JhwZj2zBlWxFZ+L+n9B+6iERnXCrUrwz8ygVp+wpcqIDWYsOZC46ACExKcw6GwNk/D5mVC+zujmp8yDRSFKnoMjJ+AyF2GoTCF4DYfEZf1gVCInLIGmp1GbpD4qaWBrH8WBIfZSmrz5c7kY74v7rnySlmGbZ7Ki/17P4j28ktlgTc9y+2s0jWzuDDb8o8ujF+5fd+/goTXlmdXNbp6AozL6F8AgEhUTa/fPbUaqC7zDlOsSmu19j8hGYfwnA/xosYmq9lZLiOr9t4t/H1bJsdtCpAFZv1M+lU/brfdwvUSZ/Yy4mOFikpnpxtMg65YtDmvLM6ua2TkFRmH0L4REICoGszgIMjjYZYruCJiSNUQE2R0FmTU27q5zt20PyiN/pIXx17NMsm+11NpCN677Qs7t9Fcgtu3KGGHmhkd8znpcOHlNqWXPmSXKmZzwv62VWNyd1nM00kjoFRU7GZyiE8AgE2WAIT5+szgJyio0C4lNAnZU7UNI6SPxWarNcBYoGmMiTuda/FRVsXyVmi002x/GnIGJVlpk22eHyQXb8PFrPXm3CNq44vh7HkJx5tWn4rqGSPQ9UhMaoCU/QUNpMRvlceLU9ik/B+oVXW6xai0O697+ctTHbWpVi1tmYDPtI+3uStu6j+BS9tjKr07fEswJ3LMjp+AyF8Gorpoh5FA658fTJai7tdz/h6KPkfI3FTA42xjIeJ2bwJ5sSCrHtpDbjzmA+C2Qyxtdaw/wm30mKm275haAHdTPt78Pg4+xbMVTPXmv875xzqapn71HBnJ+8Mk59Apm/Bo0dTNjZxvBnQkX9dyunvCnzSItY8QgEWZCVp09WH7Lpye4sICckpkBi+v0frRri+kPKBand+ggYlcS9xB2uD+ggKfrxUneGH5iRaT8f3P6XI0v669kbjvHn3/I1yUg+c7Il8zrPLwRFCyE8AkEW5NTT526MiqnBxsTeepLhdlxWZwF5JvkPSJgitVksAuPmyGVqTvTqyfsOVyTFpVYc41mi9HLoS+rcu8TpH3rr2Zv7/szBSvV5386Y014lUsU4WsXjRC22xhClglJmqS6/WW3NFOYZgqBoI4RHIMiCnHxLf7UdZwwv1gNnniRLtuNe7p932BPBvdh8io/mP4hpIbUpmqWKjkzGxx5b+bnF15LiDtuXsCvEO8PmPP8L5uJ3XfXs7Ycs5U+Pprqf3zE1opy1sW6l93Le92JTuBebwpknKr15p6UwzxAERRshPAJBFuTkW3pm23F1Ax7T3MkUv3q2ug/XClZGeRcerQbiR4L6iNRufQCMHChr/R93B0sF6fcbLekZ+D0ZJWar9DiEYL/2evbuA75na41WevaEFC1Dg57pnCziVJpcb0OmFS7B24sQHoEgC7L7ln43RsXh/zL2y03SQOD9JC4+e8rKxkpGHYvK+1ab6i+IT+fubP4NmHRChobAzsNo7SrNcVPmp0OExZXWa8o14gEhs/SFZUCf2ayt2znTIRwPTyY5TYgE00zinhTGZUdB8UYIj0CQDZl9S3+51fQkMeuANQ/iNPgejcrbSkfzFGK8pDZ5bbD8BWRyurvt5fd24yXFPrvnsCFYfyVTJjKcO7NaYZoivbzq230qKxrpn+2kJzndNJMymbZwFhBkhxAegSCP5OZuzn9xuRQdrRYSvgTVLqndKhDk5Sht8ZTwYVJBOni/Li0CVqHRSj/47WIiuPZtB0rFR0nsn3f8nPneg3I3rmxQyGBgJZHyQJA1QngEgjySm3hrWV76TI/qKMQPl9rMJoOpD6DFv/UE+lb+U1JcYfUeQqJdJDZlfBTn53Wj3PMwiX16q5HMaP1JLgaUc9RaWHMjgUaOQnwEmSOER/BWcywsAd+jUUQmaVCaGrH8A9ssPzTTRjHIt3daerRREN1QajNyA6vfQWZMy3JH2dtFKki+B6ey4qJ0m8wqMY6TC/rgEX5bYv/OexBfdvgMjUzf0cCQiDMeQXYI4RG8tRwLS6DT3me61Ui0KoVOe5+xvVVJPfG5G6Piy5NRHApLIjHN52pWMb1yRcJsSP5NarPaBnI3lKZRPPeVCtKFJ5Wos2Hzi8RsqZgnJ3Bo6SDq3bskqbu8YS9Gdp8K+RQcEyP9c56MEGc8guwQwiN4a/E9GqW3BabWptov9nglPFkF+My36Kj/TY08kBbTsWA2DICFXt8wpuZ6SXG1ddu4EvEqhIqJOpnAH0fQ/OYpSb11tTswwOcbtEb5S7tlZyajaRkzYpM17H6QdSIbcSFUkBOE8AjeWiIzccuKSmf/8mQ+3KAzQxsP0c2B6Fc2WWmw3g0yMxo6nuVYr48kj0w6No5vT7+KnSZPUbN1zTg6XT4kqfeHZ3N6DPieFLnh/rxfisn19NkxLWS8V8qEGJV+AE2BIDOE8AjeKtKe0WR24G+b5oLKsbAE9mbzLT/XJC6GpBVSm+UGULyHhSKee4MbUsr8lQfagxh73NYEkphiBoCRJoW16yfR96zUwWBfpQa0H7qMZIWJQYf7JFFL570RbGtVSu9O08BK5qy5kUC0SpzrCHKOEB7BW0NOc+I4mstov/sJ1goZh8OSsk8rnVNSrkKsNA8OJoPA/HMAptdfwrT6yyXFdTds4HT4e6k/aLWs+H0Gw0/8Lqlzolx1mo1cTaKJWZ6HZqmAOHXm5WkjEqQPmZP29cwqZI5A8BIhPIK3hpzeuzn1JItP4LygTYbYjqC5n8ZoBjZBILOiut01zvftLnlk7plBTDz6+Yvntczb8R2fHf5VUueSoxsNx6wn1izzXDo5oby1nCWNbFlzI4EDDxJ5lpzxUjC9t5qhIncL3j6E8AjeGnJz7yZvaNGLiZa0BhKleXCwXA2KepjIk7ncrw1uJe7pihLUptj/+DcxyVYATN+9hGl/SVdBISWdqPXZ70Ra2OZrtCYyaO5kyrf1U2PJNXI0zzJvUHpvtZxG7hYI0iOER/DWYIicOFmTRnRS7kCsNA8Oxt3A4n8AjK25lgVecyTFzbb8zKEH9QH4/OBqvts5X1L+xLIEVb/cwVMrw6wmrIxlWJlIPd4ye40sFTI9bzWRX0eQV4TwCN4aWjsbs+VOAgWaclerhjgfSJHmwcH6GBgpcVOGcmOgNFPoqsvdGLo/VZB8j25g2dZZkvIEY1PenbyHMFv9gJ/54Vmylt/vJEjOZQZWMmdXaBwJmleCZKmAzR+W0Du3Efl1BHlFCI/greBujIoxx2MyFJ2cXozMluTfIWG61GaxBIy9kcvUHO3Zh/qOFyXF76w4SkRiCQb88wdrNqRL6ga4Tv2LuyWdJDaFLJcheLLh5bnMlFrWjDoWlYHo6F+oBZFfR5B3hPAI3gpmnY0hLpNP63yLjuYhxLSU2hQtweJ7kMkYWPUPfmkpFZWOOxaz804zup/fy++/SqNLA1Sa9Cc3S7vq2Z0tZDhYKjjzRKVXJoM8r+Yexadk6CwQp8469prIryPIC0J4BG8FITEG9lSDF4nZhoP6uNRufQiMSuNi/R/30iVm++NWc7ruWki7K0FoV3noNen58Bls7AAAIABJREFUxR9cLlNJz24ENLY3ZlHj1NTTGQlPfhZBDhZy4SwgKDSE8AjeeO7GqLj23MDCk7wbEj6X2szngEl7ZGjY2cmXduX/lhQ7/XSQKmfvoF1RTa+5Op9u4t+y+naAkqYy1nmXYM2NBD45Gom1QoazpREP4gxzw+jlucysszEZlgtnAYGhEcIjeGNIG5XAMc15Q1bbbLlG8wRimkpt8npguQpkRnR5dx8BHcZJij/a48edQGceLm6m19wHo9dyrELtLLusZ2eil73U2UJGWxdTXaiarXcScn3R1dZYRksXM93rJJwFBIWFEB7BG0FWt+gNcn9Hq01d4aj2SO3We8DIBTvzCB4PbyIpCnpQh88XfM7p+frZPT8csYoD7g2y7daI1KDS6c9eHsRraeBgxG8fpp6vHA0LIyxBX3pMjFJXLBmlcGjpYiY5n3npLDAx6CFxckvhLCAoMITwCIoFma1mXtoP/5fIk0Tpqualt1a+7++o/oZ4X6nNbBqY9gS0rG31JR9V2SkpbjN3Obsn+nIaqeh0GLyEXdW8c9z1+3YKTmdwngPSs5dVXko67n0miZYtl8EfLUvibKXQE+XMVjLlrI2Z6a7Czc0ux2MUCHKLEB5BkSez1cySRrZ6W1DpeRSfwpIPlATeS8xwu00BZHr6o4mEmEZSm1EVsNoAMmNalD3GX12HSYqn7/Bleqfl7EYqVL36z2NzzTZZTVMPpTE8jNfwJDHjTbS0Zy+NHM3Z0aokvkejiErSYJsuqZ1wexYUJYTwCIo8mcUE8z0alW0W0FtRKrx3PiE5g8Q58qzuwyT8D5I3SW1W20FeEVvTaCKG10Ju9EoQgsNdcXcJZbpKGt5mUO9ZrKnXJcsxZkaiBiIzcSDIaMXSyNFckkcoLcLtWVCUEMIjKPJkdkaTPm9Ohs8mZO5UkGESN/VpiBsotZl9BqYfA/B9k2/5tNY6SXFCLRPcz4VKbJ90m8yyD3yyHV9WJGaiqXZmMhEBWlCsEcIjKLK8PL8Jjsz4jMPW1IgoQ+WB0cZBdFMg/pVN5gTWO0FmSgPHcxzv1U/ySOz/zLGaloA5r4JqTmg/nu+aDzbMmDKhaRkzITqCYo0QHkGRJLvcOS9D+ffc/zz/rtKJP0DSKqnNajPIPTBXJBD6cWNKWzzTFakfGaGooMEqIUFnm9liOF+3HZO/ceQA4d4seBPIXzJ2gSAf3I1RMTXYmPa7nzA06Bl3Y16tbDLLnWNnZkSPCuZsa1WKRo7mbP6wBOZ5dVpTX4YoD6nomA4D2ysg92BqvWXEj6ojER3qg8JRAy8053uv/si+v1wooiOXpV4mnXU2RvJaCQTFjQJb8axatYpFixYRHh5O5cqV8fPzo2HDhgXVnaCY8WpFYwwvtqrSRknO7FynslKhu2UfHKniZpSahNzutmmTIKYtaB+lMVqBzUGQWfLeO9e50K+b9Jn5QJpABSsb9GBEj2mpl2zygbOFjIq2xpwMTyYT5zUdKVr496maf5+qRaZPQbGmQIQnICCAL7/8kvnz51O/fn1WrVpFjx49OHnyJC4uLgXRpaCYkV32yszu3lx+lkzDbY+zTNOcJUmrUrfW0mL5KyjqYGyUzMV+7alcMuRVWTJgB0Sn/ri+Vjv69/VDY5S/u0E2xtDKxVzvPtKj+BTuxqZk660nMn0KijMFstW2dOlSfHx8GDBgAO7u7nz33XfY29uzevXqguhOUAzJbEUTEq1iaNAzQmLUWCr0VxPPk8mb6KTcSt1WSys6Jr1St9UUdRhdw5/kMTWlovMhYApEww6PphjPO0+/j+bmW3QAEtLN4aW78842duxsXYry1tn3IYJ3CoorBl/xJCcnc/78eUaPHi2xN2vWjFOnThm6O0ExJbMVzbVI9f/bu/Pwpqr0gePfLG3SphuUsnZhsShWmAKiDIggIAgIIgLC4KgIDIM4Do4yoDIDOCpuM26oKIuowE92BGQREcruhoLsVbBQsaVQ2ibplib5/VHa5mZp0zWkvJ/n8XnsOfcm5xbIm7O9h+8uln0qG7TFaV8uuz+NuWJ2C5hGgu2UsvzKwWzXRaSQ/PBAZd2HQPHqab667hYGTHyfQm1gFRvgnsWOyyFsJZzPufHUA5LkncJf1XjguXTpElarlagoZcqNqKgoLly4UNNvJ/yUu4SUBq3KZYWauQiC9WqodApMoGA55D+nLAueBwE9UKus7Boxhu7Nf1TWRwEX4ZvYm+g1eTF5ge43ZNYUT0Nmjhs+3a3wk9Vtwp9dFcupk5OT6/X71RZ/f47X26qYd1ZLRqGaqEAbqXlqjphcv8UXWoqo1Kiw7RwY71KWBQyEoFdApeLP7T7j4/7PKOvvBdbBsSat6Trn/zDqQyr9PFV1+pKJ5ORL5V7j/Lv6a2wehWlGktPKva3K/P3vVgl5Dt+Ij48vt77GA09kZCQajYaMjAxFeUZGBo0buz8zvqJG1qTk5OQ6fb/aUh+eIx5oEVT2HBOSMjliynO5LtvqZdCx28D8CFi/VZaH7gR1FC1C0kgd30dZtx64B85GNCXx+dVcNkRU+jmqq3VkCPHxseVeEw/06lA37akPf7dAnuNqVuOBJzAwkMTERHbs2MHQoUNLy3fs2MGQIUNq+u3EVcBT5ujKXuNu+M1rhRshb5qyLPh/ENAfsPPZ4MkMabNTWR8DmZlhtHtuAxdCG1X+PWuADJmJa1GtDLVNnjyZiRMn0rlzZ2699VYWLVpEWloaY8eOrY23Ez5U3jk4JYGlvGscxYUGMLd7OJP2ZHPebPWcwNORLR2MTgesabsXz+Wo1Axt8yVrB/9dWf8QFC7V0nrGVn6LaFqp562u6GAVHSIDSw9wkyzR4lpUK4Fn2LBhZGZm8uqrr5Kenk67du1YsWIFsbHlDycI/1PRfpyKrvln87KyFKOFx/ZWnHEaKD6YLXcKFH2pLA/dBurmNArKJGNiD2XdHqAntH56C2deq/v9ZLEhGjbcJZs+hai1xQXjx49n/PjxtfXy4irhaT+O4x4Tb64Bz2lyXFi+glzlcn2CnoPA+wA72zuPpXePb5T18XDD8A2c/G/ril+/lsSFaCToCMFVsqpN+C9P+3Ec95h4cw14DlClbJfBeJuyTNMeDEtApWW6fT5znnhDWf84/EG3msOTbyj/teuA7LsRopgEHlEt7hYEOE+Ye7rm4bZB/Ov7AEw/Z9AsWEOom0wFpXL/DZbVyrKQjaBpxaBzO9g45zFw3ON5HLot/IT9rTtV9xFrhCwiEKKMBB5RLc677N1NmLu75uG2QVeOrS5LEuq2P1B0AMxO59vo/wm6h+j664/sj0koTuDpYOxL/2GxfhhE1+ijlsughZZ6K3ENgrHbISPfyoV8O02C1LQM1coiAiEcSOAR1VaZY5VLFqq9c9TsMp+j+Mlugpwe4HDIGuo4CFlH4m+/8MOeBDigfO2P1g/h4dNzQF/ZJ6iekkUDhWm/VrgfRwghgUfUAuc9O2W9m7LQoitvT2jea1D4obIsZBXtMgI4Nqcj/AK8VlaVlRNCi493kFsUXKPP4Y1WoZrSpeO1lUVAiPpGAo+oMnebQgGXPTubzua75GArcJd6regwmEcry3SP0sZ4Nz8/NRCeQXEyNUC35UvY/3vHGniayosN0ciZOEJUgQQeUSWeNoXeEK51GULzdDR1aepPe15xbjX7xbJKVQQtrB+T+vQQuOndsjG6K9744QGeSHq6Zh6mChx7OkKIypHAI7zi3LsxFdrcbgrNKvA+3Y0NIH8eFLytKG/AXFJe/CehtiHwE3BTWZ3Vpiby/b1kF4RV/WGqIEgDdzTXScYBIWqABB5RIXe9G72HLSnZ3p6bYz0FpnsVRTrVCM68toNmxsfgUeAd5S391nzAtrPdvW94DbqpYQDL+vomn5sQ9Y0EHlEhdxkF8j10bCo8NcdeCKbhYPvFoVDFdx+0oPP5ldCa0mOmS3x8bAgPffEiUM4+n1rWMlT+qQhRU+Rfk6hQhRkFrtCpPSwaKGHZCrn/UBS9symGR785B+pUSAJuV97S+P1dZOQpk4nWtfI2fzoOQYZYA3i5qUWG4ISogAQeUSFPKW8cBWmgQ0MtX2cUuVZaU4oTejocP93/54ZsXpKJinMwBliivOW+ja+z5ud+XrVPTfHx2Gq1Ci12ctw0oarKW7nmOgQZwMmtl2TRgRAVqMSxjuJa9XDbIIIqiD15Vjhrcuru2K1gGgOmgaVBp2tqQ9JfhS1LMlE1p3i1mkPQ+fzM7ajf+MnroAPFw3sqFazs24D4iIq/S2m8HLFrFVp+Nunysm4LITyTHs81wJtD2Mq797G92eR5MdqW67hsunAd5D2rqF+5IpjhxzKLf1hD8XHTDmIXbuOcsTlVkWeF4dsyiQis+LuU1V68OMLdPFWzIDXXhWu9WrnmbdZtIYSSBJ56zpuD2srj9VEFQLhOTXZBKhj7KsoHnYINy0BFLgym+LhpB2O/eJ7Fx5yiUBXkWcFa7iRTGZ1aRb7VdX9Rkd3O3NsivPrdeJt1WwihJENt9VxFw0EpRgsTkjK5e3MGE5IySTFaFNd6u7CgkQ7MWZNcgk7K67BxGaiC4PjOVoqgc+D3DmjfPFQjQadEoXdxh3APOXsy8u0M3XrJ5ffgzoxOobQKVQYZyUItRMWkx1PPlTcc5E1vyJuFBVi+5GK28njpD9fBwz8W/3/WJyFEPGCiHWdK66//aCOnLreq5NNUjVaF4hjtVqEa5nYPd8kfV8L5BFVPnLNuG6xmXu7ZmLjQgGoNbwpR30ngqec8BY4QrYq7Ps/g9zzlcJPzh+6MTqFs+DWPfHc9CdslMCrXP3c7C7s+BI0dMgZHELU+iwhMAOQXBdJ3zQL2nu9c/QerQJRezQ0R2tIjGBafynM5tmFdfy19N14kw83DeTtP45iZOzk5qzToVGd4U4j6TgJPPefuELboYBUHLxaQnu/+np3nC0gxlu1HcZk2sdsh7xmwKCdrTr0F8ZmQHWVAd76QKG1WaV3y5VhuWvIZhdZA6kKv5jpFj6V7syCXa+JCA+jVXMfK03kuddWZpylveNPb4yOEqM9kjuca0C5CS5ReRZRezYBoHR0iAz0GHYCMfFvpPMfzB43K/JyWvZBzkyLovLkZ7LOg9WU17+0eSfgFM3pt2RxJx6WraPvR5joLOiXzLBXNX0HtzNPIajchyic9nnrMdcjHzonsIhrqKt7IUvINvfRD1J4DOd1xTIpzQwYcmgeBVrj33TdYO2kKk1hRWv/cgb8y88DfqvUMgVfmZ7xcM0CUXsW6/sWZDrwZ7vLmBNXKktVuQpRPAk895mnIx2r37gMw7crEOHlzoFCZWuDQe9AhHRJnrOTzaZNZGzKltC4zP4zYhV9ithiq/QyF9rLFAO8cNfPVbwXu55uu6NVcT1xoABOSMr0e7qrMCarecDe8KavdhCgjgace8zTk0yRIjc1mIzXX/Tk5JYosP7Dyh5GKsue+gn/tgsSnVjFg6B5+7D5CUX/bio9rfPHAGaOVxafyWNa3ESlGC9MPZPPV+QKXuafoYFXph7svh7tqoxclRH0igace8zTk00inJkofiLmogNyi4uSeFjtl2QnsuQRm92J/trn0niYmOP0m9H50GcvHB3Pkz0MVrzn3x9H8beeM2nqU0oARFxpASKDabTLSDpGBFS4Dr6vhrpruRQlRn0jgqcc8rWj76bKFVHPZJ3dzg4YZHQ3MPmhGfeZZfg1cTaHDNND+BTD9ng8Jf60j348eSYeoU45vQ4P39pFVEF7ldmqA/jE6Dl8q9NgLcwwYnnozRkvZvTLcJcTVSwKPH0oxWvjXyQBMP2eUuznR3ZCP2WJj07kCxXVnjFbeWPkpZ/VTwWHh2RP74XjcPP74ZA/+2uFTdvYeq7hvwLp5bPm1R7WfR6sGQ4Ca929v4HYexzlgeNObkeEuIa5eEnj8TNlKtQCg+LjP8jYnOg/53L05Q1HfNv0EdvN9/ORw5E1gEfQ7P4fX7xpCq7Bz2B9JUNyz7MRAxmx5hZo6mK3ABitP55U+B1BuwPC2NyPDXUJcnSTw+JnKbE50l7alpLfQ+uJZ/rZ9AE/cBejL7umTOp7tCU+wqZGVr4Y9zB0x3ypes+kHO0nPjaqVZ3N8jvIChvRmhPBvEnj8jLertdylbdl0Np+FrY3MeqErCY/Zi4POFW0vJ3IqbgnbE1SMvn4jywZMU7zeyM//y8rku6gMFVD+urmKn8MT6c0I4b8k8PgZb1drOfeMGhsvcmzOQAaOMfPNY043h+7mVHhDmhkucH7CHYqqrSndGLD2fexVSHJR2aADsslSiGuBBB4/42l+4+G2QUxIyiwdVjtjLD7/uaE5i8Ov3suW1hdopOzEEBb+Njn0BuysHDSF4fHbFPVxC7dx1s3BbGq8zyTgzDlTtCNZdSbEtUECj58pmd+YlvQbZo2hNPuyc4r/phYzJ14dib7wV6KfUL5GpKEvP49fSdtP07i72XY23KPsAo3fNpuFR4cryoK1Km6M0NAqLMDtyjhvNTdoOGtyHU6LDdFUKnuzHDsghP+SwOOH4kID+M/1FuLjo0gxWhi85VLph3lwQS675j5Ex9+OMXAMbL3O6ebQr2jfIga1+jIX/tpOUfVtWgJ/XL4Mq931r0VukZ1LBXYWXumRHM+65PYsm/IYtBAWAAatCrNDt6dVaOWDjhw7IIT/ksDjJ5y/4Y9poCLQaGHQ5oukmm3oLAVsff8v9PzlO1beCDePd3qBoJcgcDAAY258hrCwlYrqdh+t58TlNuW2wXHV2br+kXRefcHjsBlAfCgkRgXxq7GIY5eLMBfZOXK5OFgYtMVZsxup8koPT/P2d7DzfIHLGTpy7IAQ/kMCjx9w9w1/v17HdeezSMspYOPCxxl0fBfpBlDNcrpZ0wUMC0GloWf0N+wcrtwEevzCv+m8/P6ydDkV+OJcPhOSMpnRKdTjsFmJxKgg5vdsyOhtFxU9HABzEbQKC+CfzXO8DjrOvwNncuyAEP5BAo8fcLd353yunf9+8Dg7ftiMHfjTffB/7Z1uDNkMmlhCAsyk/aUnhoCyA89ScqJ5ZMsWIvXBrLoziHeOmtn+m2viTWfZFnvpZs+ZnQyM25Xj9jq9Gh5uG8SfvrzIllT380GVCRTufgfOZEWcEP5BAo8fcNy7o7LZmL9iJuO+XgPA5utg4ANON+hngG40AHO6v870LgsU1Z2XreDghZJsBHnsTy+gfYMA2kcGcPzKkFhFzhitzD5o5tYoLV9nFLnUhwbAxN1ZipxwzioTKDztXyohK+KE8B8SePxAs2AN2O28sfYl/r67+Fycy3poON3pQnVbCFkBqgA6Nz7Cd3+6X1H9wjd/Yca+v7u8fqrZRqq5rFeiUYHVi004Z01WbDYV0Qa1S4DJKMDNmdll9OripeGFaZcqfiM871+K0qvo1Vwvq9qE8CMSeK52djtvb3uLFXPfKC2aPBDevcXpupDPQHMdOk0Bpx7qQ2xYWmlVTkEICR99RYEthIaBkFlYflTxJuiUSM21MyA6ELWqqNz5Hme9W+iICw0gOa3ia8Hz/iVZySaE/5HAcxXTvf46+tmzKTlwYFcc9BzrfNEU0E8AYGrnhbzS43+K6p4rF7Prty5XfrJj0NZMYk9HpiI7sSHlLzRwpNfAnFsrd4yC5GcTov6o8cAzaNAg9u7dqygbNmwYixYtqum3qpdSjBa+n/02Yxc8V1pmCoQWT0KOzuFCVVNaNNmESh1EqO4Uxx68R/E67x2+n0e/+rfL65uL7NXKPOBOZSf172imq1LAkPxsQtQPtdLjGTNmDP/+d9mHnl6vL+fqa5vj/pz7klYyZd4zdHCon9EbXrjd6SbDp6BtT3qBhR/+NIybGh1XVDd8by+XCyI8vmdNBh3HSX3nobAmOsgpQrFUu1Wohpe6Vv3QOCGE/6uVwBMcHEyTJk1q46XrlRSjhUGbMrhtz0Z2f/JPRd3BZtB5otMNunGg/wcAE25awQd9ZyuqB657j82/OkepmqdTQ/uGWlqFBSiGu9wNhUH5Z+sIIa49tRJ4Vq9ezerVq2ncuDF9+/Zl2rRphIZeW0tdvckltu7tVZx7ZZKiLF8LYc80xqK+UFqmVgUzpP0B1qVoaBmWyplH+ivuWX7qLkZteo2aOpithE7tfmHakJZBboe8PA2FyfCYEMJRjQeeESNGEBMTQ9OmTTlx4gSzZ8/m6NGjrF27tqbf6qpVUS4x7VdfYRg2DOcZmBbTH+C8fglQFnQwfEhkSFcsNg27hj9Ij+gDinuafbCTtFo4mK1VqIa53cNdko/KfhkhRHWpsrKyKlw8+/zzz/Paa6+Ve82GDRvo0aOHS/n3339Pnz592LlzJ4mJiW7vTU5O9rK5/uFfJwPYkuE6nPTUpQO8+vw4l/LEKS9zKMLpzILAERA0C4D7227i04FTFdWPbnuJ944OrrE2AwSqbFxvsNMiyMZfY4toEWTntzwV885qyShUExVYVi6EEJ7Ex8eXW+9V4Ll06RKXLpW/0S86Oprg4GCXcpvNRlRUFPPnz2fYsGEVvVWtS05OrvCXUl13b85gT1ph6c83n/2Jb18f5XLdtH8v4hXtq2BTLg4gdC+oI2ganMHvf+mlqDqc0Y24wI3sPHyaJ06FVJhGJlirIqGBliOZlgrzsY1o7X4IrTbVxZ9HXakvzyLPcXWpL8/hyKuhtsjISCIjI6v0BkePHsVqtV5Tiw1Kdtm3P3+Sw6+6Blvzp5+yoEUar2x/RLnELPhdCOgJ2Pl04JPc33aL4r5Wi7YSE9yaDQPUtAiyKybzD10qJMfi2pbWISq23d2YFKOF6Qey+e6iBavNTp7V7rLaTIbQhBB1oUbneM6cOcOKFSvo168fDRs25OTJk8yYMYMOHTrQtWvXmnyrq9p/wtNZ8cQfXcpT3ltA1sCbSfwwEU6UlUdHDKRl4zcIC1TTuclOnrtNeabBxO0z+eCnkQC0C1MxISmT0xd1tD5vLF20MCEpk5Wn83B2xmQjxWghLjSA/7uzUemih9M5FjLy7TQJUtMyVCurzYQQdaZGA09AQABJSUnMmzcPs9lMixYt6NevH9OnT0ejqf+Zg1W//kpYYiLOu1Te+furdH/yQaZsG0nSh8qgcmLCCZoamqJSXSYsrJWi7ocLN3DLp59SZCsOCE308NNly5W8aBq+z8krXbQwo1Mom87muz1+oOScGneLHjQqWNBTgo4Qou7UaOCJjo5m06ZNNfmSfkF1/jyhiYmoCgsV5fP/+hwf9xyNpWATjy1SDjUuuGsBw28oPl5ar/8HOp0ys8ONH3/G8Uzl8aF2VC7JOB0PQGvXQMt3Ga7jbWm5VpeTSt3dL4QQdUFytVWDKiOD4C63oM26rCg//+wsbms1ijPZaXBSOSnYK7YXa+5dg1qlRqPZS0jIIEV9Xt4s4j4aSUa+65qPzAL360BKzrVpFeo+8IRoVQzd6hp0HO/3Zt+REELUBAk8VZGVRehtt6FOTVUUz+r/KB+PeJwbwjWcOTkZir5Q1A+8cRfL+nUATISFtUOlMpbW2WzRGI3fAXrgd8A1yGhUuD1quiRXmqcMzioV5a5+KwlMnvYdCSFETVL7ugF+xWgk5NZbCW/ZUhF0Xr1jLKr/HWH2XZM5k7mdzUfjlUEnaCaEH8VobYZO9x/Cw6MVQcdk+gqj8QjFQQdubuT+w75rVACtQpVzZY6r0UoyOI9oHUSPpoGMaB3Euv6R5Fg8r5j3FJhKhuCEEKKmSY/HidshJ40Fw+DBaL//XnHtur6juXfgs6BSgS0LcrorX0yTAIZloNLSqfFRdo0aqajOz59CQcEslzY8dpOBHecLyHeYzokOVvFWjwZA8WKB05dMtI4McRkSiwstzp9W8gzPHzQS6uEohNiQ4vNsJu/JcltfmaOphRDCWxJ4HDiv+gosKmTKtD8RfkKZpqZw5Ejy5s1j2e4sOJ0HuTPBskpxTZNGG0i3tEanKeD4gwNpFf5baZ3dbiAn5wTgum8mxWjhsb3ZiqBj0ML7tzcoDTDzezYkOfkS8fGxFT4DQLRBTXSwitTcsp6P4yFqnk73rOxxB0II4Q0ZanPw/EEjZ4xWNNYi1i18jIKpHenmEHQsgwaRffEieR98AGo1/ZoeguwERdBpGD6VQ+My6Ny0HU92+pD8v3VSBJ1Ze5eRk/Mb7oKOYxscmYtg8SnXPTre3p9qttEhMtBlCK4kkM3oFFruEJ4QQtQk6fE4SDcVsuSTfzLm4OeK8m9v6kbb7WtBV3wSm7HQSNsP2pJXVBYM9AHRDLxxGzNvbkSr8DN8fp/ybOoPfhrOxO2z6dE0kCdu8tyG3z0Mb3k77OXpfqPFzrK+7pdMy+meQoi6JIEHwG5H/8QTJC1erCjeH/cHej+6iME3NGD+laAza88s3vjuDcV1O0fvJLFJIlCEwdAXrfZHRX3kvL1k5hcfzBYaUP7RBZ6GvUK0xRkLSuaexjRQ4S57U1WHzeR0TyFEXbm2A4/djn7GDHTvvKMo/qlZPN0eX4pJb0CrgofbBnEw7SC9P+2tuC6m4SS6xk2lQXAoAQEfExz8uKJ+8Gdz2XjmDue3LJe7JdHRwSqHjAXF9ut1fN7K4tIr8bSkWobNhBBXi2s28OhefBH9K68oyi40jub6v68gK7gs6U2RLZ/hazqSZ0krLVOrwrCFfsk5qwH1xZ/pEN1P8ToWy2B6r/4ve9JcN3Oa3G3EceBu2MtssbHpXIHiutR8tduMAzJsJoS42l1zgafJJ58Q/tZbijJbZCSmr7/mvm/tZDkcZ0D+fCh4A8dp/V7xn7LzQntU2Nh87wT6x+1TvFZOznHs9mY0C84EXAOPNyvFnIe97t6c4fY6T/M+MmwmhLiaXTOr2gLnzyc8IoIYh6Bj1+vJOXYM4y+/YG/UqGx+xJpcvFqtoGwuZ8IfJpA1JYsidWeGx28WHCpaAAALKUlEQVTFNqW9Iuj8Z/9rZGdnYbc3A7xbKZZitDAhKZO7N2cwISmTFKObcw2o+ryNEEJcjep9jydg6VKCJ092Kc85dAh7XJyibFqinnU/9cdSpDwRdfcDybRvFIVKlc7uUdcr6nac60LfNQu5r1WIoryiIa+Kjsd25HbeR2+TeRshhF+qt4EnYO1agseOdSn/adUqYvv2dSlfcGgBT+14SlHWo82HzO11N3GhWoKCxhMYqNwk2ubDzZzOjvU4eV/ekJe7/TaeMkW7C2JjGmTWyryNJAsVQtS2ehd4tFu2YBjlesy0ce9ebAkJFCQrezNnss7QcXFHRdnIG0byfv/3UalUaLVfYjAMV9T/dvllntg9ghZBVjpHVu3DubL7dZyDWHJy+UeRV0VlemFCCFFVfht4nL+Zv2Q+SOs/DXe5zrRjB9aOHV3KrTYrg1cPZt9vysUBpyacorGhMZBFeHhL5T3WGzGZkghRBzC/Z/XafzXO21SmFyaEEFXll4HH8Zt5t9MHWfH2n12uMW3ejPWPrsdPAyw/vpyJWycqyhYPXMzQtkMB0OunotPNV9Qbjfuw2W6soSdwP29j0BbvGfKV6mZNEEIIb/hl4Cn5Zj7o6E42LlAuHDCtW4e1Vy+39503nafL510UZXe2vJPl9yy/cjDbfkJCBijq8/P/RUHBkzXafigeOpvbPZyRX14uPa7aXASP7c1mXX+tT4a2rsZemBCi/vHLwFPyzbyRuezkz8Hj5vL1zX24Pk9Ls6RMxbyL3W5nzIYxbDqtPJb78COHiQ2LBcyEhd2ISpVdWmezNcNoPAjUXg9k8am80qBTwpdDW5L1QAhRF/wy8JR8M//olnv55OYh2NRXvpHn28i4sgG0ZFL8yIUvGLNhjOL+t+98mz8nFA/P6XQvoNe/qqg3mb7Ear25lp+ickNbznNannK1VYdkPRBC1AW/DDyO38xLg46TM9kZ/GHhDYqyLk278FbHt2h3fTvU6kOEhipXCBQU/I38/P/UWrudeTu05W61madcbdUlWQ+EELXNLzMXOB/xHKV3yPhst0Pus2Dsobjn2we/ZduobQRobISEdFQEHbtdR3b22ToNOuD9OThuz9i5kqtNCCH8jV/2eED5zXxCUiYrT+dB0QEwj1Nc9+LtL/Jop0cBCAycS+fOMxT1JtNnWK3VXBtdRd4ObclqMyFEfeK3gcfR32+ys/KHRByTcgZoW7H/gT1cF2FArU4mNFS5mq2w8AHy8t4Gyj8fp7Z5M7Qlq82EEPWJXw61OXp217Pc9kkbHIPOndd/zncPfcN1EToMhj4uQScn5xfy8ubi66DjLXdDcpKrTQjhr/y6x3PP6ntIOpdU+vP0rtOZ3nU6AAEBnxAc/DfF9WbzEo4fv574+Mg6bWd11WWuNiGEqG1+HXhahrck6VwSkUGRHH7kMIYAAyrVOcLC2iuus1gGkpu7lOIeTrLb13J0NSbKrItcbUIIURf8OvC82fdN3uz75pWfbAQHjyAgYJvimpyco9jtLbx+TUmUKYQQtcvv53gAtNrPCA9vqAg6ubnzrhzM5n3QgfITZQohhKg+v+7xuMsgXVT0R8zmjUDVVnzJ0mUhhKhdfh14QkMTFT8bjQex2VpX6zVl6bIQQtQuvx5qy8//LwB5eS+TnZ1V7aAD3mcTEEIIUTV+3eOxWO4jO/u+Gn1NSZQphBC1y68DT22RRJlCCFF7/HqoTQghhP+RwCOEEKJOSeARQghRpyTwCCGEqFMSeIQQQtQpCTxCCCHqlCorK8vu60YIIYS4dkiPRwghRJ2SwCOEEKJOSeARQghRpyTwCCGEqFMSeIQQQtSpazbwPP744yQmJtK0aVPatGnD6NGjOXnypK+bVSmXL19m6tSpdOnShaZNm5KQkMA//vEPMjMzfd20Klm8eDF33303sbGxREREkJKS4usmeWXBggV06NCBJk2a0LNnT/bt2+frJlXa3r17GTVqFO3atSMiIoKlS5f6uklV8r///Y877riDmJgY2rRpw/3338+xY8d83axKmz9/Pt26dSMmJoaYmBjuvPNOtm7d6utm1ZhrNvB07NiRd999l6+//prVq1djt9sZOnQoFovF103z2u+//87vv//O7Nmz2bdvH++//z779u1j3Lhxvm5aleTm5tK7d2+mT5/u66Z4bc2aNUyfPp0nn3ySXbt2ccsttzBixAjOnTvn66ZVitls5sYbb+Sll14iKCjI182psj179jBu3Di2bt3K+vXr0Wq1DB06lMuXL/u6aZXSvHlzZs+eTVJSEjt27OD2229nzJgxHDlyxNdNqxGyj+eKI0eOcNttt/Htt98SHx/v6+ZU2RdffMH9999PSkoKYWFhvm5Olfzwww/ccccdHDp0iLi4OF83p1x9+vQhISGBt956q7SsU6dO3HPPPcycOdOHLau6Fi1a8MorrzBmzBhfN6XaTCYTsbGxLF26lAEDBvi6OdXSsmVLZs6cydixY33dlGq7Zns8jsxmM0uXLiU6OprY2FhfN6dajEYjOp2O4OBgXzel3issLOTHH3+kd+/eivLevXvz9ddf+6hVwpHJZMJmsxEREeHrplSZ1Wpl9erVmM1mbrnlFl83p0Zc0wfBLViwgJkzZ2I2m4mPj2f9+vXodDpfN6vKsrKyeOGFF3jwwQfRaq/pP9o6cenSJaxWK1FRUYryqKgoLly44KNWCUfTp0+nffv2fvmBffToUfr160d+fj4Gg4ElS5aQkJDg62bViHrV43n++eeJiIgo97/du3eXXj9ixAh27drF559/Tps2bXjooYfIzc314RMUq+xzQPE3u9GjR9OsWTOee+45H7XcVVWeRYia8Mwzz3DgwAE++eQTNBqNr5tTafHx8ezevZvt27czbtw4Jk2a5JcLJdypV1+LJ02axMiRI8u9Jjo6uvT/w8PDCQ8Pp02bNnTp0oWWLVuyfv16Ro0aVdtNLVdln8NkMjFixAgAli9fjl6vr9X2VUZln8WfREZGotFoyMjIUJRnZGTQuHFjH7VKADz99NOsWbOGDRs20LJlS183p0oCAwNp3bo1AImJiRw8eJB3332XuXPn+rhl1VevAk9kZCSRkZFVutdut2O32yksLKzhVlVeZZ7DaDQyYsQI7HY7q1atIiQkpJZbVznV+TO52gUGBpKYmMiOHTsYOnRoafmOHTsYMmSID1t2bZs2bRpr165lw4YNtG3b1tfNqTE2m+2q+HyqCfUq8Hjr9OnTrF+/nl69ehEZGcn58+d5/fXXCQwMpH///r5unteMRiPDhg3DaDSydOlScnNzS4cKGzRoQGBgoI9bWDnp6emkp6fz888/A3Dy5Emys7OJiYmhQYMGPm6de5MnT2bixIl07tyZW2+9lUWLFpGWluZ3K49MJhOnT58Gij/gUlNTOXz4MA0aNCAmJsbHrfPeU089xfLly1myZAkRERGkp6cDYDAYrrovZeWZNWsW/fr1o0WLFphMJlatWsWePXtYsWKFr5tWI67J5dSpqalMmTKFH3/8kezsbBo3bky3bt2YOnWqX31D2r17N4MHD3Zbt2HDBnr06FHHLaqeOXPm8PLLL7uUv/POO1f10t4FCxbw5ptvkp6eTrt27XjxxRfp3r27r5tVKZ7+Lo0ePZr33nvPBy2qGk+r16ZNm8bTTz9dx62pukmTJrF7924uXLhAWFgYCQkJPP744/Tp08fXTasR12TgEUII4Tv1alWbEEKIq58EHiGEEHVKAo8QQog6JYFHCCFEnZLAI4QQok5J4BFCCFGnJPAIIYSoUxJ4hBBC1CkJPEIIIerU/wPZIRnrirsK4QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_hat = df_censored_regression.loc[\"a\", \"mean\"]\n",
    "b_hat = df_censored_regression.loc[\"b\", \"mean\"]\n",
    "y_bayesian_pred = a_hat*x_obs + b_hat\n",
    "\n",
    "plt.scatter(x_obs, y_obs)\n",
    "plt.plot(x_obs, y_pred, color=\"red\", linewidth=2, label=\"Simple linear regression\")\n",
    "plt.plot(x_obs, y_bayesian_pred, color=\"yellow\", linewidth=2, label=\"Bayesian linear regression\")\n",
    "plt.plot(df[[\"x\"]], y_aft_pred, color=\"green\", linewidth=2, label=\"AFT model\")\n",
    "plt.legend()\n",
    "plt.title(\"Data\");\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "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",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model</th>\n",
       "      <td>lifelines.LogNormalAFTFitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>duration col</th>\n",
       "      <td>'y'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event col</th>\n",
       "      <td>'observed'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of observations</th>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of events observed</th>\n",
       "      <td>838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood</th>\n",
       "      <td>-1198.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time fit was run</th>\n",
       "      <td>2020-03-12 19:42:22 UTC</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>exp(coef)</th>\n",
       "      <th>se(coef)</th>\n",
       "      <th>coef lower 95%</th>\n",
       "      <th>coef upper 95%</th>\n",
       "      <th>exp(coef) lower 95%</th>\n",
       "      <th>exp(coef) upper 95%</th>\n",
       "      <th>z</th>\n",
       "      <th>p</th>\n",
       "      <th>-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">mu_</th>\n",
       "      <th>x</th>\n",
       "      <td>2.98</td>\n",
       "      <td>19.77</td>\n",
       "      <td>0.04</td>\n",
       "      <td>2.91</td>\n",
       "      <td>3.06</td>\n",
       "      <td>18.38</td>\n",
       "      <td>21.27</td>\n",
       "      <td>79.96</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>_intercept</th>\n",
       "      <td>1.02</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.95</td>\n",
       "      <td>1.08</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.95</td>\n",
       "      <td>30.55</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>678.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma_</th>\n",
       "      <th>_intercept</th>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.91</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-1.82</td>\n",
       "      <td>0.07</td>\n",
       "      <td>3.85</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table><div>\n",
       "<style scoped>\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",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Log-likelihood ratio test</th>\n",
       "      <td>2224.03 on 1 df, -log2(p)=inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aft.print_summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that both Bayesian linear regression and AFT model worked pretty much the same. (coefficients of $2.98$ and $1.02$). The question now would be how to do reasoning about the quality of the model, uncertainty and hypotheses testing. For AFT there are standard sets of procedures to diagnose the model and test hypotheses, for custom baeysian model I would have to think about how to do it."
   ]
  }
 ],
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