{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Markov switching dynamic regression models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook provides an example of the use of Markov switching models in statsmodels to estimate dynamic regression models with changes in regime. It follows the examples in the Stata Markov switching documentation, which can be found at http://www.stata.com/manuals14/tsmswitch.pdf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "from datetime import datetime\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Federal funds rate with switching intercept\n",
    "\n",
    "The first example models the federal funds rate as noise around a constant intercept, but where the intercept changes during different regimes. The model is simply:\n",
    "\n",
    "$$r_t = \\mu_{S_t} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\sigma^2)$$\n",
    "\n",
    "where $S_t \\in \\{0, 1\\}$, and the regime transitions according to\n",
    "\n",
    "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n",
    "\\begin{bmatrix}\n",
    "p_{00} & p_{10} \\\\\n",
    "1 - p_{00} & 1 - p_{10}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "We will estimate the parameters of this model by maximum likelihood: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\sigma^2$.\n",
    "\n",
    "The data used in this example can be found at https://www.stata-press.com/data/r14/usmacro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the federal funds rate data\n",
    "from statsmodels.tsa.regime_switching.tests.test_markov_regression import fedfunds\n",
    "dta_fedfunds = pd.Series(fedfunds, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n",
    "\n",
    "# Plot the data\n",
    "dta_fedfunds.plot(title='Federal funds rate', figsize=(12,3))\n",
    "\n",
    "# Fit the model\n",
    "# (a switching mean is the default of the MarkovRegession model)\n",
    "mod_fedfunds = sm.tsa.MarkovRegression(dta_fedfunds, k_regimes=2)\n",
    "res_fedfunds = mod_fedfunds.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>226</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-508.636</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 24 Feb 2020</td> <th>  AIC                </th> <td>1027.272</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>22:49:06</td>     <th>  BIC                </th> <td>1044.375</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>07-01-1954</td>    <th>  HQIC               </th> <td>1034.174</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    3.7088</td> <td>    0.177</td> <td>   20.988</td> <td> 0.000</td> <td>    3.362</td> <td>    4.055</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    9.5568</td> <td>    0.300</td> <td>   31.857</td> <td> 0.000</td> <td>    8.969</td> <td>   10.145</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    4.4418</td> <td>    0.425</td> <td>   10.447</td> <td> 0.000</td> <td>    3.608</td> <td>    5.275</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.9821</td> <td>    0.010</td> <td>   94.443</td> <td> 0.000</td> <td>    0.962</td> <td>    1.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.0504</td> <td>    0.027</td> <td>    1.876</td> <td> 0.061</td> <td>   -0.002</td> <td>    0.103</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  226\n",
       "Model:               MarkovRegression   Log Likelihood                -508.636\n",
       "Date:                Mon, 24 Feb 2020   AIC                           1027.272\n",
       "Time:                        22:49:06   BIC                           1044.375\n",
       "Sample:                    07-01-1954   HQIC                          1034.174\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          3.7088      0.177     20.988      0.000       3.362       4.055\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          9.5568      0.300     31.857      0.000       8.969      10.145\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         4.4418      0.425     10.447      0.000       3.608       5.275\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.9821      0.010     94.443      0.000       0.962       1.002\n",
       "p[1->0]        0.0504      0.027      1.876      0.061      -0.002       0.103\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the summary output, the mean federal funds rate in the first regime (the \"low regime\") is estimated to be $3.7$ whereas in the \"high regime\" it is $9.6$. Below we plot the smoothed probabilities of being in the high regime. The model suggests that the 1980's was a time-period in which a high federal funds rate existed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_fedfunds.smoothed_marginal_probabilities[1].plot(\n",
    "    title='Probability of being in the high regime', figsize=(12,3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the estimated transition matrix we can calculate the expected duration of a low regime versus a high regime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[55.85400626 19.85506546]\n"
     ]
    }
   ],
   "source": [
    "print(res_fedfunds.expected_durations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A low regime is expected to persist for about fourteen years, whereas the high regime is expected to persist for only about five years."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Federal funds rate with switching intercept and lagged dependent variable\n",
    "\n",
    "The second example augments the previous model to include the lagged value of the federal funds rate.\n",
    "\n",
    "$$r_t = \\mu_{S_t} + r_{t-1} \\beta_{S_t} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\sigma^2)$$\n",
    "\n",
    "where $S_t \\in \\{0, 1\\}$, and the regime transitions according to\n",
    "\n",
    "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n",
    "\\begin{bmatrix}\n",
    "p_{00} & p_{10} \\\\\n",
    "1 - p_{00} & 1 - p_{10}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "We will estimate the parameters of this model by maximum likelihood: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\beta_0, \\beta_1, \\sigma^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Fit the model\n",
    "mod_fedfunds2 = sm.tsa.MarkovRegression(\n",
    "    dta_fedfunds.iloc[1:], k_regimes=2, exog=dta_fedfunds.iloc[:-1])\n",
    "res_fedfunds2 = mod_fedfunds2.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>225</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-264.711</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 24 Feb 2020</td> <th>  AIC                </th>  <td>543.421</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>22:49:06</td>     <th>  BIC                </th>  <td>567.334</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>10-01-1954</td>    <th>  HQIC               </th>  <td>553.073</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.7245</td> <td>    0.289</td> <td>    2.510</td> <td> 0.012</td> <td>    0.159</td> <td>    1.290</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.7631</td> <td>    0.034</td> <td>   22.629</td> <td> 0.000</td> <td>    0.697</td> <td>    0.829</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.0989</td> <td>    0.118</td> <td>   -0.835</td> <td> 0.404</td> <td>   -0.331</td> <td>    0.133</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    1.0612</td> <td>    0.019</td> <td>   57.351</td> <td> 0.000</td> <td>    1.025</td> <td>    1.097</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.4783</td> <td>    0.050</td> <td>    9.642</td> <td> 0.000</td> <td>    0.381</td> <td>    0.576</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.6378</td> <td>    0.120</td> <td>    5.304</td> <td> 0.000</td> <td>    0.402</td> <td>    0.874</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.1306</td> <td>    0.050</td> <td>    2.634</td> <td> 0.008</td> <td>    0.033</td> <td>    0.228</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  225\n",
       "Model:               MarkovRegression   Log Likelihood                -264.711\n",
       "Date:                Mon, 24 Feb 2020   AIC                            543.421\n",
       "Time:                        22:49:06   BIC                            567.334\n",
       "Sample:                    10-01-1954   HQIC                           553.073\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.7245      0.289      2.510      0.012       0.159       1.290\n",
       "x1             0.7631      0.034     22.629      0.000       0.697       0.829\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0989      0.118     -0.835      0.404      -0.331       0.133\n",
       "x1             1.0612      0.019     57.351      0.000       1.025       1.097\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.4783      0.050      9.642      0.000       0.381       0.576\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.6378      0.120      5.304      0.000       0.402       0.874\n",
       "p[1->0]        0.1306      0.050      2.634      0.008       0.033       0.228\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several things to notice from the summary output:\n",
    "\n",
    "1. The information criteria have decreased substantially, indicating that this model has a better fit than the previous model.\n",
    "2. The interpretation of the regimes, in terms of the intercept, have switched. Now the first regime has the higher intercept and the second regime has a lower intercept.\n",
    "\n",
    "Examining the smoothed probabilities of the high regime state, we now see quite a bit more variability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_fedfunds2.smoothed_marginal_probabilities[0].plot(\n",
    "    title='Probability of being in the high regime', figsize=(12,3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the expected durations of each regime have decreased quite a bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.76105188 7.65529154]\n"
     ]
    }
   ],
   "source": [
    "print(res_fedfunds2.expected_durations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Taylor rule with 2 or 3 regimes\n",
    "\n",
    "We now include two additional exogenous variables - a measure of the output gap and a measure of inflation - to estimate a switching Taylor-type rule with both 2 and 3 regimes to see which fits the data better.\n",
    "\n",
    "Because the models can be often difficult to estimate, for the 3-regime model we employ a search over starting parameters to improve results, specifying 20 random search repetitions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Get the additional data\n",
    "from statsmodels.tsa.regime_switching.tests.test_markov_regression import ogap, inf\n",
    "dta_ogap = pd.Series(ogap, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n",
    "dta_inf = pd.Series(inf, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n",
    "\n",
    "exog = pd.concat((dta_fedfunds.shift(), dta_ogap, dta_inf), axis=1).iloc[4:]\n",
    "\n",
    "# Fit the 2-regime model\n",
    "mod_fedfunds3 = sm.tsa.MarkovRegression(\n",
    "    dta_fedfunds.iloc[4:], k_regimes=2, exog=exog)\n",
    "res_fedfunds3 = mod_fedfunds3.fit()\n",
    "\n",
    "# Fit the 3-regime model\n",
    "np.random.seed(12345)\n",
    "mod_fedfunds4 = sm.tsa.MarkovRegression(\n",
    "    dta_fedfunds.iloc[4:], k_regimes=3, exog=exog)\n",
    "res_fedfunds4 = mod_fedfunds4.fit(search_reps=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>222</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-229.256</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 24 Feb 2020</td> <th>  AIC                </th>  <td>480.512</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>22:49:06</td>     <th>  BIC                </th>  <td>517.942</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>07-01-1955</td>    <th>  HQIC               </th>  <td>495.624</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.6555</td> <td>    0.137</td> <td>    4.771</td> <td> 0.000</td> <td>    0.386</td> <td>    0.925</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.8314</td> <td>    0.033</td> <td>   24.951</td> <td> 0.000</td> <td>    0.766</td> <td>    0.897</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.1355</td> <td>    0.029</td> <td>    4.609</td> <td> 0.000</td> <td>    0.078</td> <td>    0.193</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>   -0.0274</td> <td>    0.041</td> <td>   -0.671</td> <td> 0.502</td> <td>   -0.107</td> <td>    0.053</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.0945</td> <td>    0.128</td> <td>   -0.739</td> <td> 0.460</td> <td>   -0.345</td> <td>    0.156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.9293</td> <td>    0.027</td> <td>   34.309</td> <td> 0.000</td> <td>    0.876</td> <td>    0.982</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0343</td> <td>    0.024</td> <td>    1.429</td> <td> 0.153</td> <td>   -0.013</td> <td>    0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.2125</td> <td>    0.030</td> <td>    7.147</td> <td> 0.000</td> <td>    0.154</td> <td>    0.271</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.3323</td> <td>    0.035</td> <td>    9.526</td> <td> 0.000</td> <td>    0.264</td> <td>    0.401</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7279</td> <td>    0.093</td> <td>    7.828</td> <td> 0.000</td> <td>    0.546</td> <td>    0.910</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.2115</td> <td>    0.064</td> <td>    3.298</td> <td> 0.001</td> <td>    0.086</td> <td>    0.337</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  222\n",
       "Model:               MarkovRegression   Log Likelihood                -229.256\n",
       "Date:                Mon, 24 Feb 2020   AIC                            480.512\n",
       "Time:                        22:49:06   BIC                            517.942\n",
       "Sample:                    07-01-1955   HQIC                           495.624\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.6555      0.137      4.771      0.000       0.386       0.925\n",
       "x1             0.8314      0.033     24.951      0.000       0.766       0.897\n",
       "x2             0.1355      0.029      4.609      0.000       0.078       0.193\n",
       "x3            -0.0274      0.041     -0.671      0.502      -0.107       0.053\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0945      0.128     -0.739      0.460      -0.345       0.156\n",
       "x1             0.9293      0.027     34.309      0.000       0.876       0.982\n",
       "x2             0.0343      0.024      1.429      0.153      -0.013       0.081\n",
       "x3             0.2125      0.030      7.147      0.000       0.154       0.271\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.3323      0.035      9.526      0.000       0.264       0.401\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7279      0.093      7.828      0.000       0.546       0.910\n",
       "p[1->0]        0.2115      0.064      3.298      0.001       0.086       0.337\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/statsmodels/base/model.py:1354: RuntimeWarning: invalid value encountered in sqrt\n",
      "  bse_ = np.sqrt(np.diag(self.cov_params()))\n",
      "/usr/lib/python3/dist-packages/scipy/stats/_distn_infrastructure.py:901: RuntimeWarning: invalid value encountered in greater\n",
      "  return (a < x) & (x < b)\n",
      "/usr/lib/python3/dist-packages/scipy/stats/_distn_infrastructure.py:901: RuntimeWarning: invalid value encountered in less\n",
      "  return (a < x) & (x < b)\n",
      "/usr/lib/python3/dist-packages/scipy/stats/_distn_infrastructure.py:1892: RuntimeWarning: invalid value encountered in less_equal\n",
      "  cond2 = cond0 & (x <= _a)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>222</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-180.806</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 24 Feb 2020</td> <th>  AIC                </th>  <td>399.611</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>22:49:06</td>     <th>  BIC                </th>  <td>464.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>07-01-1955</td>    <th>  HQIC               </th>  <td>425.713</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -1.0250</td> <td>    0.290</td> <td>   -3.531</td> <td> 0.000</td> <td>   -1.594</td> <td>   -0.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.3277</td> <td>    0.086</td> <td>    3.812</td> <td> 0.000</td> <td>    0.159</td> <td>    0.496</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.2036</td> <td>    0.049</td> <td>    4.152</td> <td> 0.000</td> <td>    0.107</td> <td>    0.300</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    1.1381</td> <td>    0.081</td> <td>   13.977</td> <td> 0.000</td> <td>    0.978</td> <td>    1.298</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.0259</td> <td>    0.087</td> <td>   -0.298</td> <td> 0.765</td> <td>   -0.196</td> <td>    0.144</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.9737</td> <td>    0.019</td> <td>   50.265</td> <td> 0.000</td> <td>    0.936</td> <td>    1.012</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0341</td> <td>    0.017</td> <td>    2.030</td> <td> 0.042</td> <td>    0.001</td> <td>    0.067</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.1215</td> <td>    0.022</td> <td>    5.606</td> <td> 0.000</td> <td>    0.079</td> <td>    0.164</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 2 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.7346</td> <td>    0.130</td> <td>    5.632</td> <td> 0.000</td> <td>    0.479</td> <td>    0.990</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.8436</td> <td>    0.024</td> <td>   35.198</td> <td> 0.000</td> <td>    0.797</td> <td>    0.891</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.1633</td> <td>    0.025</td> <td>    6.515</td> <td> 0.000</td> <td>    0.114</td> <td>    0.212</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>   -0.0499</td> <td>    0.027</td> <td>   -1.835</td> <td> 0.067</td> <td>   -0.103</td> <td>    0.003</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.1660</td> <td>    0.018</td> <td>    9.240</td> <td> 0.000</td> <td>    0.131</td> <td>    0.201</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7214</td> <td>    0.117</td> <td>    6.177</td> <td> 0.000</td> <td>    0.493</td> <td>    0.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td> 4.001e-08</td> <td>      nan</td> <td>      nan</td> <td>   nan</td> <td>      nan</td> <td>      nan</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[2->0]</th> <td>    0.0783</td> <td>    0.038</td> <td>    2.079</td> <td> 0.038</td> <td>    0.004</td> <td>    0.152</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->1]</th> <td>    0.1044</td> <td>    0.095</td> <td>    1.103</td> <td> 0.270</td> <td>   -0.081</td> <td>    0.290</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->1]</th> <td>    0.8259</td> <td>    0.054</td> <td>   15.208</td> <td> 0.000</td> <td>    0.719</td> <td>    0.932</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[2->1]</th> <td>    0.2288</td> <td>    0.073</td> <td>    3.150</td> <td> 0.002</td> <td>    0.086</td> <td>    0.371</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  222\n",
       "Model:               MarkovRegression   Log Likelihood                -180.806\n",
       "Date:                Mon, 24 Feb 2020   AIC                            399.611\n",
       "Time:                        22:49:06   BIC                            464.262\n",
       "Sample:                    07-01-1955   HQIC                           425.713\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -1.0250      0.290     -3.531      0.000      -1.594      -0.456\n",
       "x1             0.3277      0.086      3.812      0.000       0.159       0.496\n",
       "x2             0.2036      0.049      4.152      0.000       0.107       0.300\n",
       "x3             1.1381      0.081     13.977      0.000       0.978       1.298\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0259      0.087     -0.298      0.765      -0.196       0.144\n",
       "x1             0.9737      0.019     50.265      0.000       0.936       1.012\n",
       "x2             0.0341      0.017      2.030      0.042       0.001       0.067\n",
       "x3             0.1215      0.022      5.606      0.000       0.079       0.164\n",
       "                             Regime 2 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.7346      0.130      5.632      0.000       0.479       0.990\n",
       "x1             0.8436      0.024     35.198      0.000       0.797       0.891\n",
       "x2             0.1633      0.025      6.515      0.000       0.114       0.212\n",
       "x3            -0.0499      0.027     -1.835      0.067      -0.103       0.003\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.1660      0.018      9.240      0.000       0.131       0.201\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7214      0.117      6.177      0.000       0.493       0.950\n",
       "p[1->0]     4.001e-08        nan        nan        nan         nan         nan\n",
       "p[2->0]        0.0783      0.038      2.079      0.038       0.004       0.152\n",
       "p[0->1]        0.1044      0.095      1.103      0.270      -0.081       0.290\n",
       "p[1->1]        0.8259      0.054     15.208      0.000       0.719       0.932\n",
       "p[2->1]        0.2288      0.073      3.150      0.002       0.086       0.371\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds4.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to lower information criteria, we might prefer the 3-state model, with an interpretation of low-, medium-, and high-interest rate regimes. The smoothed probabilities of each regime are plotted below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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N9SG5qDUEWNnRmaQ/EmdwJKEZ4QobzQhrIKzUZOmLxMeUfIH12aalEaoQDYTVjDAYTdBYa2eE26xAcNcMqxN2nm+uQFhrhMsXS9cIa9ZJqcnSH47lLo3wezUQVgVpIKxmhMGROA12Rrg+6KMtFGBXz/Ak71V1ORlw54dApoBPSyPK5WSEtbOcUpOnL1KgNCKuP1JVfhoIqxlhMKNGGKxgcKZmhBe25MoIC/GEDu1djnjSOm46fJpSk2MkkSQcS+bpLKelEaowDYTVtGeMGRsIt9bNuBrh3T1h2usDhIJj+8gGfF5GNCNclpjdEUczwkpNjv5wHICmHDXCQZ+WRqjCNBBW014kniSZMunSCIDFrXXs7YtUtIPYf96/mW/+4eWKba/SdvXkHjoNIOAV4vplURYnI6yd5ZSaHH0RKxDOWRrh11EjVGEaCKtpbzBqBSiZGeGFrXWkDOzti1TscR7e3MWPHtvOYDResW1WUr4xhEFrhMdDO8spNbn67IxwS86MsEfHEVYFaSCspj0nMD0sI9xmD6FWwTrhkXiSkUSK+zYeqNg2KyWWSLGvP5I3ENZRI8rnnFVwzjwopaqrLxwDyD+hhp7tUgVoIKymvYEcGWEnIKxkhznnw/Y3z++p2DYrZW9fhJSxMuG5BLweLY0oU+YPCC2PUKr6nNKIXDOF6oQaqhgNhNW055RGNGYEwrMbggR9HnZ1V24Itag9RM/jHYc4OBit2HYrwQn4nUx4Nr+WRpQts85cyyOUqj6ns1zucYR11AhVmAbCatrLVRrh8QgLWys7hFo0nuSspW2kDPxu/b6KbbcSdhaYTAPsKZb1y6IsmRnhYc0IK1V1fZEYXo9Qn2NEnKDPSyyRwhgtW1K5aSCspr1cneXAGjmikkOoReMpTpjfyIq5jfz6+b0V226mp7Z10x8pvTPe7p4wAZ+H2Q3BnMu1s1z5Mo9bWDPCSlVdX9iaTENExiwL+qwwRz/fVD4aCKtpL1dGGEhnhCuRKTDGEE0kqfF7eeup83hhdx87DlV25rqBaJz3/s9TfO2eTSXfd1d3mIUttXg8Y78owJ5QI6kZk3LEMiYiGdKxhJWqur5wnKYcZREwGghreYTKx1UgLCIXisgrItIhIp/NsbxJRH4rIi+IyEYR+VDld1Wp8gxGE3gEQgHvYbcvbqsjHEvSPRwb92PEkwZjrA/dvzl5HgC/37B/3NvNtOXAECkDv3l+L12DIyXdd1dPOG99MEDA6yWZMjrqQRli2llOqUnVF4nlHDoNIOi3Pvd1CDWVT9FAWES8wPeAi4AVwKUisiJrtY8Dm4wxJwPnAd8WkdyvSqWqbDCaoD7oG3PabHGbVS9bifKIqN0rucbvZW5TLYta69iwp3/c28205cAgYAVeP35qp+v7GWMKTqYB4PdZx0aHUCtdPJHCZ2fadZplparPKY3IZTQjrO9NlZubjPAaoMMYs80YEwPuAC7OWscADWJFGvVAD6CpETUlDETiY8oiYLTj2O4KdJhzRoxwsg8r5zWycW9lA+HNB4ao8Xt43fGz+clTO9OPWUxvOM7QSCLv0GlgdZYDPX1Yjlgyle6trtMsK1V9WhqhxsNNIDwf2J1xvdO+LdMNwKuAvcCLwCeNMWNedSJypYisFZG1XV1dZe6yUqUZiCbGdJQDWNBiBYZ7KjC7nHParcb+0F0xt5Ed3eGK1oxuOTjIstn1XHHOUnqGY/zqOXfjFW/tGgKszoH5BOz91oxw6eLJFM32aVkNhJWqvv5InObaPKURPi2NUIWNjQ7GytW7JruQ8ALgeeC1wDHA/SLyqDFm4LA7GXMTcBPAqlWrtBhRVcVgNE5jjoxwjd9LKOCle2j8NcJOdrbGyQjPbwTgpX0DrF7SOu7tg1Uj/Opj2jhzaSsr5zXyw0e34RXhud19DI0kuPzVSzh9ccuY+z3ecQgRci5zOBlhHUKtdCOJVPq0rI4jrFR1xZMphkYSOccQBmscYdDSCJWfm4xwJ7Aw4/oCrMxvpg8BdxlLB7AdOL4yu6jU+AzmyQgDtNYH6BkureNZLs5pN+c03Mp5TQBsrFCdcH8kzv6BKMvm1CMiXHHO0WztGubTd67nnvV7eWRzF+/4wRNcdvNfeGX/4GH3fWzLIU6a30RLKH/Zvt+rGeFyxZMpagNegj6PdpZTqsqc4STzBsJaGqGKcJMRfgZYLiJHA3uAS4D3Zq2zC3gd8KiIzAGOA7ZVckeVKtfgSJxja+pzLmsNBSsyakR2Rnh2Q5C2UIBN+wYK3c21joNWcHvs7AYALj55Ps11ARa21LG0PUQknuQnT+3kxoe38tEfr+XBfzoPEWEgGue53X1cde7Sgtt3SiM0I1y6WCJFoM5DKOjTCTWUqrK+cP7plSGjNEI/21QeRQNhY0xCRK4G7gO8wM3GmI0icpW9/Ebgq8CtIvIiVinFZ4wxhyZwv5VyzcoI5/6QbAsFODAw/umQo06NsB0Iiwgr5jWycW9lAuHNB6w632PnWIGwxyOcf9zs9PJQ0MdHzz2G9vogn/q/F1i7s5fVS1p5cms3yZThnOWzCm7fyQjroPOliydTBHwe6gJeLY1Qqsr6wlYiI+/waU5G2GXnYjXzuBpH2BhzrzHmWGPMMcaYr9u33WgHwRhj9hpj3miMOdEYc4Ix5icTudNKuWWMKVwaEQrQU9GM8OhbasW8RrYcGKpIlnXzgUFq/V4WtNQWXO/CE46iLuDlznWdgFUWURfwctqi/PXBkDH7kmZNShZLpPB7PdQHfdpZTqkqczLC+UojavxaGqEK05nl1LQWiSdJpkzBjHD3cGzcs8tljiPsWDmviVgyRcfBoXFtG6Dj4BDLZtfnnRnOEQr6uOiEufxu/T6i8SSPbunizKVt6dKHfEZrhLUPa6niSZPOCId1HGGlqqrPqREuNmqEBsIqDw2E1bQ2GLUydIUywrFEatzDnDlD8wQzAs6V86yRIyoxnvDmA4Msn5O7zjnbO06fz+BIgh89tp0d3WHOWd5e9D5aI1y+ETsjHAr6dIplparMKY0oPo6w/khVuWkgrKa1waiVLcgXCLfVBwHGXR6RKyO8pC1Erd877g5z/ZE4BwZGWG53lCvmzKPbmN9cy3cf2ALgKhD2e3VmuXLFkymCPg+hgE9HjVCqyvojcTwCDcHcn/E6jrAqRgNhNa0N2BnhXOMIg1UaAYx75Ih0ZznfaCDs9Qivmtsw7g5zztTKx7rMCHs8wttPm08skWJuUw3HzCp+v4AOMVQ2q0ZYqAtqZzmlqq0vHKep1p+3bCyoNcKqCA2E1bTmpjQCoGeck2qMTrF8+FtqxbxGXto7MK4a5C0HDx8xwo13nLYAgLOXtWPNfF5YQMcRLls8mdFZTjPCSlVVXySentkxl9Hp4/VHqspNA2E1rTmlEY15xphMB8LjzAhnT6jhWDmvicGRBLt7yp/G2RkxYn5z4REjMi1pD3H9pafyidctd7W+TqhRnlTKkEg5neV8hDUjrFRV9YVjeUeMAOsMWcDr0YywyksDYTWtFcsIt9VXpjRiJJ4k6POMyb4um22VJWzvHi57225HjMj2lpPnsbC1ztW62lmuPM64y1ZG2EssmdJjqFQV9YXj6SnO8wn6PFojrPLSQFhNa6Od5XJ/UNYFfNT4PeOeZjkaTx7WUc7hDPLu9Gwux0Akns5cTxTNCJfHOV5BOyMMaIc5paqoLxIrWBoBVsmalkaofDQQVtPaYDSBRyAUGBukOtoqMM1yNJ46bDINh3PKrt8e67LcbdfmCLIrSTvLlcfJ/lrDp1ltpEOoKVU9Tme5QoI+r362qbw0EFbT2mA0QX3QV7DDWFt9gO7xdpZL5M4IOx/QzuxH5YjEkzmD7EoK6IQaZXGOV8BnjSMM6KQaSlVJIpliMJooWCMMdmmEBsIqDw2E1bQ2EI3nLYtwVGKa5ZF46rCh0xx+r4eGoI/ecZRG5Cu7qCStES7PYRlhuzRCp1lWqjqc4TGL1QgHfB5G4voDVeWmgbCa1gajibwd5RyVCISjieSYodMcTXV++seREa5GIOz1CB7RGuFSOZ3lnCmWAR1LWKkqcfpeFK8R1tIIlZ8GwmpaG4zG806m4WgLBeiuRGe5HBlhsOqE+8ZTI5xITXggDFYwF9NAuCRORjjglXRphI4lrFR1OJ+r+aZXdlilEfoDVeXmKhAWkQtF5BUR6RCRz+ZZ5zwReV5ENorIw5XdTaXK4y4jHCQaT42rt380nsqbEW6uDZQ9akQyZYglcnfEqzS/16OlESWKZ2SER2uENRBWqhqccbudsqR8tEZYFVL021VEvMD3gIuAFcClIrIia51m4PvAW4wxK4F3TcC+KlUyN4FweprlcXSYK1S+0DSOjLCTxahGRjioGeGSZY4jPDpqhGaelKoG50dnXYFRgcAeNULHEVZ5uEkzrQE6jDHbjDEx4A7g4qx13gvcZYzZBWCMOVjZ3VSqPIMuO8vB+GaXiyVSY2aVczTX+sseNSJqf3hP9PBpYAVzcc2alCSeLo0Y7SwX1s5ySlVFxO4AV1ssENZxhFUBbgLh+cDujOud9m2ZjgVaROQhEVknIpfl2pCIXCkia0VkbVdXV3l7rJRLxhh3GeH68QfChTLCLXVWaUQqVfrQZM4HfTVKI7RGuHQjTkbY50n/WNFRI5Sqjog9VGHxjLCWRqj83Hy75hqANfsb3QecDrwZuAD4VxE5dsydjLnJGLPKGLNq1qxZJe+sUqWIxJMkUqZoRrgtFATg0FD5HeaiBep4m+v8pAwMlVE7Go1XrzTC7/XoqBElyswIezxCKOBlWMcRVqoqnDG7i50x0wk1VCFuAuFOYGHG9QXA3hzr/MEYM2yMOQQ8ApxcmV1UqjyD9hiTRTvLVSojnGfUCGdSjXKGUHMC4WCebVdSQDvLlSxz+DSAuqBPO8spVSWuSyN0HGFVgJtA+BlguYgcLSIB4BLg7qx1fgOcIyI+EakDzgBequyuKlWawagVeBYLhEMBLwGfp+xA2BhTsDTCGeOynDrhqMsP+krw+zzEdGa5kqRHjbBn5gsFvNpZTqkqCccSeD2Sfv/lY9UI6498lVvhCAEwxiRE5GrgPsAL3GyM2SgiV9nLbzTGvCQifwDWAyngh8aYDRO540oV48w6VGwcYRGxxxIuLxBOpAwpQ/7OcvYYl32R0rfvdJarybPtSgp6PcS0Q0lJ0jPL2e0TCvq0s5xSVRKOJanzexHJVcE5yimNMMYUXVfNPEUDYQBjzL3AvVm33Zh1/VvAtyq3a0qNj9vSCBjf7HLF6nhb7EC4dxwZ4arUCPskHXgrd5wM+mhG2KcTaihVJdF40tXZMidJEUumqlJmpo4sOrOcmrZ67NninOHRCmkdR0Y4nbXNN8VyrfX4/WVMqpEePq0apRFaI1yyWCKrNCLo1SmWlaqScKy0QFjLI1QuGgiracuZIMMZFaKQ9vpgOnAuVbpDW74JNezOcuXUCKeHT6tSZzkdNaI08fTwadbp1rqgZoSVqpZwLOlqjPV0IKxnvFQOGgiraatnOIbPIzTWuiyNKHNmuWKzvwV8HkIBb1mzy0WrOI6wX8cRLlk8OyMc8Oo4wkpVSSSWLDqGMIyOuqOTaqhcNBBW01b3UIzWUMBV54jWUIDhWDIdeJbCKV/I11kOrJEjxjNqRE0VSiOCWhpRslgyhQh4PdZrzOosp1+2SlVDOJagLlA80RH0a2mEyk8DYTVtdQ/HXNUHA7TZ65VTJ1wsIwxWeURfWTXC1SuN0Ak1ShdLpgh4PekfW05nOWN0GDqlJlokniqtRlhLI1QOGgiraatneCQ9fXIxTsBcTnmEmyHOWkL+MksjUngE/N6JH/In4NOMcKliidRhY5jWBb2kDDr6hlJVEIklXNYIW+to6ZfKRQNhNW31DMdoddFRDmBWg7Ve11C05MdxM8RZc22g7IxwjYtxMivByghrJrMU8WQqPascQH3QOk2rHeaUmnhh1zXCTkZYy5bUWBoIq2mreyiWLnkoZk5jDQAHBkofOcKpOytYGlHnp7+cjHDCXa/oStCMcOliiRT+zIywXa+oHeaUmngRt8OnaY2wKkADYTUtjSSSDI4kXAfCTkb4wED5GeGCneVq/fSF4yXXjhT87vcAACAASURBVEZiqapMpgEQ8AqxZErrW0sQT5qcGeEhDYSVmlDGGMLxUkeN0EBYjaWBsJqWeoet7Guryxphv9dDe32grIzw6IQaBUoj6vwkUqbkACmaSKazGRPNCei0PMI9KyM8WraSDoSjGggrNZHiSUMyZdyNGpGeUENLI9RYGgiraenQkBXQus0IA8xuqOHgODLChcb6ba6z9qPUIdRG4tUrjXBO8evIEe7FkikCGSN6hILWZa0RVmpiRWLup59PZ4S1E6vKQQNhNS312MOgtdW76ywHMKcxyMHBMjLCLoZPa7Znlyu1Tjhid5arBicjrHXC7lmjRuTICOtYwkpNqHDc+rHpqjRCa4RVAa4CYRG5UEReEZEOEflsgfVWi0hSRN5ZuV1UqnROIOx2HGGwMsLl1AiPuJxQA0rPCEfjqarMKgeaES7HmFEjarSznFLVELYzwiWNGqGlESqHot+wIuIFvgdcBKwALhWRFXnWuwa4r9I7qVSpnIkxSimNmNMY5NDQCIkSA8FoIknA5yk4xFlznZUR7ouUNoRaNJ6symQaMJoR1qyJe9mjRoS0RlipqnBKI0oZR1g/21QublJNa4AOY8w2Y0wMuAO4OMd6fw/cCRys4P4pVZbuoRF8HqGxxu/6PrMba0iZ0meXG4mnCk6mAaOlEb0lZoQj8WRVplcG0hNDaEbYveyMcCigo0YoVQ2jGeHineUCOrOcKsBNIDwf2J1xvdO+LU1E5gNvA26s3K4pVb6e4RgtoQAej/uJKEbHEi6tPCLqoo63yc4I95c4qYYVZFe3s5zOvuTeSFZG2OsR6gJeLY1QaoJF7E7KtYHiYYzXI/i9oqURKic3gXCuSCJ7fKXrgM8YYwq+ykTkShFZKyJru7q63O6jUiXrHnY/mYZjTqMzlnBpHebcBMJBn5e6gLeMGuFk1WqE08OnJXT4NLeyM8JglUfoqBFKTayI/R6r9RfPCIP1GaylESoXN6+gTmBhxvUFwN6sdVYBd9g1ku3Am0QkYYz5deZKxpibgJsAVq1apd+2asJY0yuXGgiXlxEeSbjr0NZc66evxFEjolUdPs36zRtLatbErVgylS4pcdQHfQxqjbBSE6qUznJgdZjTjLDKxU0g/AywXESOBvYAlwDvzVzBGHO0c1lEbgXuyQ6Claqm7qERTlzQXNJ92kIBRCh5LOFoPJnujFFIU12gpIywMWaShk/T36huxRNmTCAcCmpphFITraxAWGuEVQ5FA2FjTEJErsYaDcIL3GyM2SgiV9nLtS5YTTnllEb4vB7a64NllEa4zwj3lzBqRDxpSJnCE3VUUkBrhEsWS6bw+w6vHqsP+hjWcYSVmlDpUSPcBsJ+LY1QubkqrjHG3Avcm3VbzgDYGHP5+HdLqfLFEikGo4mSSyPAmVSjxIxwIpmeSKGQ5jo/Ww4OlbRdcDdzUiWM1gjrl4Vb8USKgPfw9qkP+tjTV/p41Eop99Kd5Vx+PmpphMpHZ5ZT0045k2k45jTUlJURdlMa0VznL6k0IlrCFKKVoBNqlC5XRjgU9GlphFITLBxLEvB68HndhTFWIKyfbWosDYTVtNM9bAWy7fWlB8KzG2tKzgiPJNyN7NBcF6A/EsMYdzW4Ubuereo1whoIu2KMydtZTgNhpSZWJJZwXRYB9qgRWiOsctBAWE07oxnhYMn3tWaXi5WUFR1xmRFuqfMTTxrXky2MlkZUuUZYsyauJFMGY8gZCOuEGkpNrHAs6bqjHEDQr6URbg1G4zPqzKAGwmraGVdphD2EWteg+/IIt2P9ttdbgfmhIXcd5qIl1sCNl2aES+McJ3+OcYRHEqkZ9UWiVLWF48kSM8JaGuHWm69/jB88tHWyd6NqNBBW044TaJZVGtHgTKrhvjzCzYQa1v5Y23YbZEcmq0ZYvyxccSYeGTt8mtVxUssjlJo40VhpY6zrhBruxJMpdvWE2dblvmP3kU4DYTXt9AyP4PUIjTX+ku87OqlGCRlhlxNqzGpwMsLuth1NODXC1Z1ZTjPC7ozYE49kZ4Qb7EBYyyOUmjgll0boqBGu9IatRFJPibOgHsk0EFbTTs9wjJa6AB5PrtnBC5ttT7PstsNcIpkimTLUuKgRHi2NcBkI26URbuqPK8GZWS6e1Ak13HCOUzBPRlgDYaUmjlUa4W56ZbBrhLWzXFG9w3H7v/sx7490GgiraefQUOmTaTjaQkG8HnFdGuFkbYMusratoQAecV8aka4RLiHrMR7OKX49feiO06lw7PBpVntpaYRSEycSS1CnpREV54y61KOBsFJHrp7hGG1l1AcDeD3CrBJml3OCVTd1vF6P0BoKlpwRrlaNsIjg94p28nLJOU7ZE2o01DgZYT0Nq9RECcfK6Syn78linIywBsJKHcF6hmNljRjhsGaXKzFYdVm+0F4foGvQ7agRdo2wr3pvU7/Xo8OnuZTOCHvHTqgBmhFWaiJFyxw1wu047jNVj10jHIkn0x22pzsNhNW00z00UnZpBNiTargsjRgpoTQCrA5zXS4zwpEql0aA1WFOM8LuOJ0KA9nDp9l1i0NRDYSVmijhWLK00gi/F2O0D0QxPRnDezpB8XSngbCaVmKJFAPRRFmTaThmNwTZ1x91lTkotXxhVn2QQxOUba4EzQi75xyn7OHTRksjNBBWaiIYY4jESx81AtDyiCJ6M4LfmdJhTgNhNa3s6B4GYGFrbdnbOHF+E/2ROJ+44/l0MJqPU74QdFm+0N5g1Qi7C7Kt6XvLGf2iXAGvR4dPcymeLyOspRFKTahoPIUxlDZqhE87A7uRWRs8U+qEXX17i8iFIvKKiHSIyGdzLH+fiKy3/54QkZMrv6tKFbdp7wAAK+c1lb2N96xeyGcuPJ571u/lPTc9VbBMYqTEjHB7fYCRRIpBF0GS2xnrKing04ywW6M1woe3kd/rIeDzaEZYqQkSjlnvrdoSPh+dYSg1EC6sZzhGU60/fXkmKPoqEhEv8D3gImAFcKmIrMhabTtwrjHmJOCrwE2V3lGl3Ni4t5+Az8PSWaGytyEifOy8Y7jx/aezef8gn//VhrzrRhMllkY4k2q4KI9wO2NdJQW8WiPsVr6MMEB90KeBsFITJGx34qorcRxhGE1eqNx6hmMsm12fvjwTuPk5tQboMMZsM8bEgDuAizNXMMY8YYzpta8+BSyo7G4q5c6mfQMcN6dhTJauHBesPIo3rJjD5gODeddxBmh3m7kdnVSj+AfMZATCfp9oRtilkTwZYbACYS2NUGpilDPGupZGuNMbjrG4rQ6PHF4vPJ25+faeD+zOuN5p35bPR4Dfj2enlCqHMYZNewdYMbexYttc0FLL3r4IyVTumt50Rtj18GlWIOxmUo1o3N3UzZVkZYS1V7Ub6ZnlcmSEQ0GfjiOs1AQZzQiXNqEGaCBciDGG7uEYs+qDNNcF6NaMcFqunjo5vylF5HysQPgzeZZfKSJrRWRtV1eX+71UyoX9A1F6w3FWzq9kIFxHImXyzjSX7ixXwvBp4G6a5Ug8SW21M8I6aoRr+WqEAeqDXoZG4tXeJaVmBCcQLisjrKUReYVjSWKJFK2hAK2hgI4akaETWJhxfQGwN3slETkJ+CFwsTGmO9eGjDE3GWNWGWNWzZo1q5z9VSovp6NcJTPCzugTu3vCOZeXOsRZS501zbKbQDgaTxKsdo2wT0eNcKtYjfCwZoSVmhCRuNNZzv3nY40dNIdnyCQR5XBqgltCAVrrAlojnOEZYLmIHC0iAeAS4O7MFURkEXAX8AFjzObK76ZSxTmB8PEVLY2oA6CzN5JzeXr2N5cfyM40y65KIxIp7Sw3hTnHKXtmObBKI7RGeGrafGCQbV1Dk70bahzK6Sy3oNlKauzKk9RQo4Fwa12AlpB/xgTCRV9FxpiEiFwN3Ad4gZuNMRtF5Cp7+Y3AF4E24PsiApAwxqyauN1WaqxN+wZY0lZHfdD9h2Mx85prEMkfCHf2hmms8ZVUy9teH3CVER6JJ6ltLH9ikHLo8GnuFess52aIPFV9H7rlGfb1R3jHaQv4f284lvnN5Y85riZHpIwa4VkNQUIBL9sPDU/Ubh3xnJnkWusDtIaCrNvZW+Qe04OriMEYcy9wb9ZtN2ZcvgK4orK7plRpNu0bYOW8ymWDwepgMaehht29ubMIHQeHWDa7HvsHoCvWNMvFf2lHJmPUCM0Iu5YujcgRCGtGeGrqj8TZ0xdh5bxGfvPCXn7z/F6ufffJvOXkeRV7jGg8yd3P76U1FGDN0lYaa/wV27aylDP9vIiwpD2UnnRJjdWbkRFuDfnpDcdJpUxVJ3WaDJVLnSk1iQajcXZ2h3nX6ZUfuW9BSy2deQLhrV1DvPb42SVtb1Z9kG1dxT+Mo/FkVadXBs0IlyKWSOHzSM4vifqgj3AsOSO+RI4kHQetkoh/fMOxHD+3kX+443n+6RcvcFRjDWuObh339h/Z3MUXf7OBHd3W54XXI5y+uIXrLzmVo5pqxr19ZSln1AiAJe0hNuzpn4hdmhYya4Rb6gIkU4bBaIKmuun9Y06nWFbTwsv7rbF+V1Q4IwxOIDy2NKIvHOPQ0Ojg4261NwTpcjHN8mQMn+b3eojp8GmuxJOpnB3lgHR5znBMs8JTScdB63Ni+ewG5jfX8j+XrWJBay1X/ngt27qGMMawrWuIPX25S6EK+bffbuKym/+CR4TbPryGn//tmfzdecfwYmc/n7lzvatp1ZU7TiBcaqJgaXuIzt6InvXKo2c4hs8jNNb4aKsPANA9XLyM70inGWE1LWy0f+WPZ2rlfBa21vHb9ftIJFP4Mk6DO9mlUgPhWfVBYvY0y4VOm0biyXRP52oJeIVYQntVuxFLpPJO3BKyA+GhkQQNemp8ythyYIgav4f5LVZdcFOdn1svX8Pbvv8477zxSZIpQ38kzpzGIE997nWuS5729kW49YntvP20+Xzj7Semx6w965g22uuDfOnujfxi7W7es3rRhD23mSQSS1Dj95R8tmVJW4hkyrC7J8zSWaV9bs8EveEYLaEAIkJLXSB923SnGWE1LWzaN0BbKMDshsp3LlvQUksyZdjXf/hYwulAeFZDSdtrb7A+YAqNHJFKGWKJ1KSURuiEGu7EkiZ/RrjGzghrnfCUsuXgEMfMqsebEUAtaqvjhx9cxcp5jbzpxKN4x2kLODAwUlKnqv9b20nKwD+8/th0EOz4wJmLOWtpG1+956WyMs1qrEg8WdKIEY4l7SEA7TCXR89wjFY7AG4NBezbpv946BoIqyNeKmV4ensPK+Y1ltRpza18Q6h1HBwi6BvNLrmVnma5QCDsjEgwGZ3ldBxhd2KJVM6OcmBNqAHo7HJTTMfBIZbnOINz6qIWfvyRM/jG20/iY+ctBWDtDnc95pMpwy/W7ubsZe0sbK0bs9zjEb75zpMwxvBZLZGoiHCsvMmGlmogXFDPcIyWkHUGazQQnv6lERoIqyPeAy8fZGd3mHdOQEc5sDLCwJiRIzq6hlialV1yY3R2ufynnNK9oqs9xbLPQzJl8k4prUYVqhEOBTQjPNUMjSTY0xdh+ZzCZ3COmVVPS52ftTt7XG33sY5D7OmLcMmahXnXWdhax6feeByPbjnEk9tyzjelShCJJUvuKAdWJ7CmWr8Gwnn0DMdoC1nfT5oRVuoIctMjW5nfXMubT5w7Iduf21SLJ8dYws7QaaVyMsJdg7mnbYaMGesmISMMaGcSF6wa4dw/gpwa4cGoBsJTxVaXNf0i1kgPbjPC//vMLlrq/LxhxZyC6733jEXMbgjy3T9tcbfDKq9wLFnS0GmZdAi1/HrD8XRGuNbvJejzaI2wUlPds7t6eWZHLx8+++jDOrJVUsDn4ajGGjozZiSKxJLs6YuwrIwOF6PTLOf/gJmsQDhoZzi1PKK4QhnhBq0RnnK22IFwrtKIbKcvbmXboWG6i0x8c2hohPs3HeDtpy0YUxucrcbv5apzj+Hp7T08pVnhcYmUWRoBVnnEjkM6u1y2ZMrQGx6tERYR2kIBul2MeX+k00BYHdF++Og2Gmt8vGd1/tOSlbCgpe6wjPDWriGMKX3ECLDGFm2rDxacXW506ubqD58G6FjCLsSSxUeN0OHTpo4tBwcJeD0sylHHm231khYA1haZWevOdZ3Ek4ZLXH7+vPeMRcxqCHL9A5oVHg+rs1yZGeG2EHv6Iulkg7L0R+IYY5WPOFpCAc0IKzWV7ewe5g8b9vO+MxdXdFrlXBa0Hj6pxtau8oZOc7TXBzkwkL80IjJJGWEnw6mlEcUV7iynpRFTTceBIZbOCrk6c3TC/CYCXk/BKWZHEklufnw7Zy5tLVp37Kjxe/noa5byxNZuntnhrgZZjRWOJcoaNQJgSbv1Q2hnt2aFMzmTabRmBMKtoUD69ulMA+EqiydT/OChrezUGqVxu+HPHfg8Hi5/9ZIJf6wFLXXsG4imM6UdB4fwyOiHaqlOWdjEU9t66A/n7ogwMsk1wpoRLi5WoDQi6PPg84iWRkwhW0qo6a/xezlpQRNrCwSrdz27hwMDI3z8/GUl7cf7zlhMe32Af/nVi3nf/6qwyDhqhJe2W68B7TB3OA2EVdXcua6Ta/7wMpfd/JcZ8QKbKBv29PPLZzu5/K+WMKdx4qcuXdBSizGwr98qj+g4OMTitlDRusB8PnDmEiLxJL9Yuzvn8mhCM8JTXTyZPyMsIoSCPg2EJ1F/OM4tj28nEksSiSXZ3Rtm+Wz3Y36fvqSFF/f05zyFnrATGictaOLsZe0l7VdtwMt3LzmVHYfCfOS2Z4jE9BR9qcLx8muEneSFBsKHS0+vXJdRGlEXoHcGxCkaCFfRSCLJ9Q9sYWl7iP39Ua68fa3WKZXBGMNX79lES12Aq19bWjamXAuzxhLusAfmL9eKeY2sWdLK7U/tyDlUWSRmBaLlftiXK2CPgjCiGeGiCs0sB1Z5hI4jPHk+/+sX+cpvN3Hlj9fy0v4BjIHlc9y/Z1ctbiWeNKzv7B+z7Hcv7mNXT5iPn7+srLHL/2pZO995zyms29XL1T97Vn94lihc5vBpAA01ftrrA+zQQPgwTi2wM7UyWBnhwZHEtD9D6KrIRkQuBL4LeIEfGmP+I2u52MvfBISBy40xz1Z4X494d/xlN3v7o/z4I2sYiCT4+M+e5dO/XM933nNKyWPRzmT3bdzP09t7+OpbTyg4RXElOWMJP7Ojh9MXt7Cje5jXvmr2uLZ52asXc/XPnuPBlw/y+qyhl0ZHjaj+OMKAzi7nQrzAzHIAoaCXoRE99T0Z7tu4n9+t38fZy9p5dMuh9NBpbkaMcJy+2Oow9/S2btYc3Zq+PZUyfO/BDo6dU88bXlV4yLRC3nzSXHrCJ/Cvv97Ax37yLP916alln+6fSX7w0FZiiRSL20Jlb+Po9hDbs8oTjTHs6gkzp7HmsDNxf9y4n7ue3UNdwEt9jQ9jYDAaZ2gkyZzGIMcf1cCKeU2ctqh5QiZ0qpZcGWGnTKI3HKvKmdfJUjQQFhEv8D3gDUAn8IyI3G2M2ZSx2kXAcvvvDOAH9v8Z5cBAlGt+/zJ/eukAl6xZxNWvXZYO1CKxJDc82MGao1s5e1k7IsLOnuP45h9eoTcc47uXnHpYbY7KrXc4xr/f+zLHzqnn0gkeKSLT3KYa5jQGue5PW/jRo9uJJ01ZQ6dlumDlURzVWMNtT+4YGwhPUmmE1gi75yYjPKwZ4arrD8f5wq83sGJuI7d8aDU/fnIn/3bPJnweKSl4ag0FOHVRM//15w7aG4JcumYR/eE4X/vdJjYfGOK695yCZ5wJjA+cuRhjDF+6eyPv++FT/OiDqw/rta8O97Ond3HNH17m4lPmuR6pI5clbSHu27ifnz69k2PnNPDK/kF+/pddbNw7wIKWWv79bSdy9rJ2vvvAFr77wBbmNAbxez0MRhOIWMMjhgI+nt7ezU+ftsqfXv+qOXzznSe5+h6PxpO8sLuPQ0Mxzljamh5bvuPgEPdt3M+OQ8N0DY3QF47TVOtnVkOQo9tDvPXU+cxvLm0mU7d6hmPUBbyHfeeMTqpROBBOpQwvdPbxxNZujmqsYcW8RpbNri/4+TiVuMkIrwE6jDHbAETkDuBiIDMQvhi43VhzRz4lIs0iMtcYs6/iezwO0XiSF/eMPc2VyRjoC8fY1x9l/0CUoWiCcCxJyhgWttSydFY9RzXV4BHBGEM4nqQ/HKfj4BA3P76dRNJwxtJW/ufRbfxyXSeXnbWYeU21bNzbT9fgCDdcemr6V+PfnbeM1roAX7x7I399/aN8+S0rD/sQzJ6JM3tqzlw5uzH3yV6r8NUx98+1jbGPkb2N4vs5dj8KP0YknuT3G/Zz/8YDxFMpbv/wmgkbNzgXn9fDQ/90Pg9v7uIPG/bx4p5+zlzaNq5t+r0e3nfGIr59/2buXNdJayiA1yN4PcLm/YMA1JRZg1wup+Z1w55+9CRFYeFYokhG2MeBgWjO0QFyvs/yTL3r5n1urZcni59z3TyrlrDd3Ovm2+7YJW4+FwrtQ76Ziu96dg89wzFuuXw1fq+HD599NAbYcWi4YHvlcvMHV/OJO57jc3e9yCObu1i7s5fuoRE+eu5S/ubkeSVtK5/LzlrC7IYgn7jjed76/ce56IS5HDunnvnNtTkzjKW8Tqz189xewuulktvPvz4MRRP0RWIMRhMEvB7qAl58Xg+RWIJ9/VF+8PBWzj9uFte+6+Rx/Qg5//jZ3PviPv7lVxvStx1/VAOfvvA463v75r+wbHY9HQeHeOfpC/jaW0/ImZQwxrCvP8o96/dy7X2bufC6R/jcm46nPugnEk9ijKEu4KPG72FPb4RN+wbYsKefDXsG0mO1i8BJ85sYSaR4ef8gIjCnoYb2hgDNtdbwZa/sH+TOZzv59h9f4bzjZnP+8bNprQvQUucv+Jo2WLXQT23tZu3OXtrqA5xxdBurl7SkR7ZxXmMdB4cOywbDaHb46W3dh/V3MFhJqR3dw2zrGuahV7rYnzUKUo3fw6rFrZx1TBuL2+qIxlNE4kmOm9Nw2BmWqUCKzXsuIu8ELjTGXGFf/wBwhjHm6ox17gH+wxjzmH39AeAzxpi1+ba7atUqs3Zt3sUTYsehYc679iHX6/u9Qn3Qlx6mZV9/hEIzz75xxRy+8OYVLGqrY8Oefr56zyae3j76JfiaY2dx+4fXjLnfi539fOyn68bMXKYO11zn522nzuc9qxdy/FGNk707FXFoaIRzrnkwPVxapoDPw4YvX1Dyl/d4vLx/gAuve7Rqj3eku+rcY/jsRcfnXPaPv3ieu57dU+U9UgBXn7+Mf7rguIpsK5kyfOf+zdzwYAcr5jZyzTtO4sQFTRXZdqZndvTw5bs3svnAoJYm5fFXy9r44WWrK1JCkkoZ9vRF2HJwkLZQkJMWNCEiRONJvv9gB7c8sYNPvm45Hzn7aFclD5v2DvDJO55LT9ySS33Qx/FHNXD64hZWLWmlrT7AY1sO8fDmLrwiXHTiUVx0wlyOahqbfd3dE+Z/n9nN/67dTddg4YlesrWFAqxa0sKhoRgv7O4jkSeQWbOklV9cdVb6+q7uMK/51oMFt91c52fV4lYuOuEozj9+Nj3DI2zcO8Bzu/p4als3L9tJHcflr17Cl9+ysqT9rwQRWWeMWZVzmYtA+F3ABVmB8BpjzN9nrPM74BtZgfCnjTHrsrZ1JXAlwKJFi07fuXNn+c+qDJFYsuC4kI6mWj9HNdXQFgoc9qtzJJFkZ3f4sBdhbcBLc62f1lCA5rqxp0SGRhL0hWP0heMsaQ/lHe92MBpnfWf/mF/L2e+/MW/HHO9Pybqx2Day3+S53vNj71N4jaL7netxCzyGR4Tlc+rLHqVhKtvfH6VrcISkMSRTKRJJQzJlmN0YZFkJvdwrwRjDC539DEa1trUYQTh1UXN68oxs/eE46/f0jXk/Qu73mLVNtzeOfZ+Xut18X+5u3v+FH68S283x3FzuQ9Dn5dg59RWv19zdE2ZuU82En4mKJ1Ps7B5mf/9Iaa+TAgtyvVagxNchpb1mCm8n9+31QT8tdX7qa3zEEinCsSSJpKE24KXO/qtWHa4xpuTHisaTbNzbT8DrpTZgvU7C9qglc5tqWdBSO+5ymmTK0D00Qk84Ru9wnESqcBnbnMYals8efT+EYwk27h0gnkilc/ZO3LF8Tv2YEogXO/vpi4wdOaKhxs/RbSGa6gr30+kZjnFoaMSastnvoSHon5Ra+PEGwmcBXzbGXGBf/xyAMeYbGev8N/CQMebn9vVXgPMKlUZMRkZYKaWUUkrNLIUCYTc/bZ8BlovI0SISAC4B7s5a527gMrGcCfRPtfpgpZRSSimlMhXtLGeMSYjI1cB9WMOn3WyM2SgiV9nLbwTuxRo6rQNr+LQPTdwuK6WUUkopNX6uxhE2xtyLFexm3nZjxmUDfLyyu6aUUkoppdTEKVojPGEPLNIFVLe33PTSDhya7J1QJdN2OzJpux2ZtN2OTNpuR66p2naLjTGzci2YtEBYjY+IrM1X+K2mLm23I5O225FJ2+3IpO125DoS2+7ImPZDKaWUUkqpCtNAWCmllFJKzUgaCB+5bprsHVBl0XY7Mmm7HZm03Y5M2m5HriOu7bRGWCmllFJKzUiaEVZKKaWUUjOSBsJKKaWUUmpG0kB4ChGRm0XkoIhsyLjtZBF5UkReFJHfikhjxrKT7GUb7eU19u2n29c7ROR6EZHJeD4zRSntJiLvE5HnM/5SInKKvUzbrYpKbDe/iNxm3/6SiHwu4z7ablVUYrsFROQW+/YXROS8jPtou1WJiCwUkQft985GEfmkfXuriNwvIlvs/y0Z9/mc3TaviMgFGbdru1VRqW0nIm32+kMickPWtqZm2xlj9G+K/AGvAU4DNmTc9gxwrn35w8BX7cs+YD1wsn29DfDal/8CnAUI8Hvgosl+btP5r5R2y7rficC2Rd+5LAAAIABJREFUjOvablO03YD3AnfYl+uAHcASbbcp324fB26xL88G1gEebbeqt9lc4DT7cgOwGVgBfBP4rH37Z4Fr7MsrgBeAIHA0sFW/346YtgsBZwNXATdkbWtKtp1mhKcQY8wjQE/WzccBj9iX7wfeYV9+I7DeGPOCfd9uY0xSROYCjcaYJ431yrsdeOvE7/3MVWK7ZboU+DmAtlv1ldhuBgiJiA+oBWLAgLZb9ZXYbiuAB+z7HQT6gFXabtVljNlnjHnWvjwIvATMBy4GbrNXu43RNrgY64fniDFmO9ABrNF2q75S284YM2yMeQyIZm5nKredBsJT3wbgLfbldwEL7cvHAkZE7hORZ0Xk0/bt84HOjPt32rep6srXbpnegx0Io+02VeRrt18Cw8A+YBdwrTGmB223qSJfu70AXCwiPhE5GjjdXqbtNklEZAlwKvA0MMcYsw+sgAsraw9WW+zOuJvTPtpuk8hl2+UzZdtOA+Gp78PAx0VkHdZpiZh9uw/r9MP77P9vE5HXYZ1yyKZj5FVfvnYDQETOAMLGGKfOUdttasjXbmuAJDAP61Ttp0RkKdpuU0W+drsZ6wt3LXAd8ASQQNttUohIPXAn8P+MMQOFVs1xmylwu5pgJbRd3k3kuG1KtJ1vsndAFWaMeRmrDAIRORZ4s72oE3jYGHPIXnYvVt3cT4AFGZtYAOyt2g4roGC7OS5hNBsMVntqu02yAu32XuAPxpg4cFBEHgdWAY+i7Tbp8rWbMSYB/IOznog8AWwBetF2qyoR8WMFUj81xtxl33xAROYaY/bZp84P2rd3cvhZNKd99HNyEpTYdvlM2bbTjPAUJyKz7f8e4AvAjfai+4CTRKTOrls8F9hkn6IYFJEz7R6ZlwG/mYRdn9EKtJtz27uAO5zbtN2mhgLttgt4rVhCwJnAy9puU0O+drM/H0P25TcACWOMfk5WmX2MfwS8ZIz5z4xFdwMftC9/kNE2uBu4RESCdknLcuAv2m7VV0bb5TSl226ye+vp3+gfVoZwHxDH+vX0EeCTWL00NwP/gT0boL3++4GNWPVx38y4fZV921bghsz76N+UaLfzgKdybEfbbYq2G1AP/J/9ftsE/LO22xHRbkuAV7A6+PwJWKztNiltdjbWafD1wPP235uwRjt6ACtL/wDQmnGff7Hb5hUyRhfQdjsi2m4HVofWIfs9umIqt51OsayUUkoppWYkLY1QSimllFIzkgbCSimllFJqRtJAWCmllFJKzUgaCCullFJKqRlJA2GllFJKKTUjaSCslFJKKaVmJA2ElVJKKaXUjKSBsFJKKaWUmpE0EFZKKaWUUjOSBsJKKaWUUmpG0kBYKaWUUkrNSBoIK6WUUkqpGUkDYaWOICJyuYg8VqFtLRERIyK+SmzPxeMZEVlW5n13iMjr8yw7R0ReybWuiHxeRH5Y3h6XvI9vE5HdIjIkIqdW4zHLISLniUhnxvWNInJelR779yLywWo8lipM20IpiwbCSuUgImeLyBMi0i8iPSLyuIisrvI+VDVQPVIZYx41xhyXZ9m/G2OugKocz2uBq40x9caY5yboMSrOGLPSGPNQlR7rImPMbW7WFZGHROSKid6nPI+d94fXOLY5ac8nl1LaQqnpTL9glcoiIo3APcDHgF8AAeAcYGQy92sqExGfMSYx2fsxyRYDGyd7J5RFRLzGmGSVHquqr38REUCMMalqPaZS05VmhJUa61gAY8zPjTFJY0zEGPNHY8x6SJcnPC4i3xGRPhHZJiKvtm/fLSIHM085ikiTiNwuIl0islNEviAiHnuZx76+077f7SLSZN/1Eft/n326/ayMbV4rIr0isl1ELsp6rB+JyD4R2SMiXxMRr73Ma9/vkIhsA95c6CDYWbHPicgm+7FuEZEae9l5ItIpIp8Rkf3ALfbtfysiHXYW/W4RmZe12TfZx+uQiHwr4zgcIyJ/FpFue9lPRaQ5676rC+1LnufwZRH5SZ7jea69nydmrD9bRCIiMivHtnK2lYgERWQI8AIviMjWPPvyXfv1MSAi60TknALH/lYR+b59+nrIfr0dJSLX2c//ZckovxCReSJyp/0a2y4in8hYVmtvr1dENgGrsx4rs5TkVhH5Wsay7DKKHSLyzyKyXkSG7dfaHHs/B0XkTyLSUuB5pbOi9vvlsVyvZRH5OtaPzxvs53+DffvxInK/3W6viMi7s47ZD0TkXhEZBs632+ZaEdklIgdE5EYRqbXXbxeRe8R6D/eIyKN2G/8YWAT81n7sT+d4HmNe/yLSYm+vy34+94jIgnKfT55j93UReRwIA0ul+Pv922K9n7aLyNWScUYkR1uU8pmW97gqdcQxxuif/ulfxh/QCHQDtwEXAS1Zyy8HEsCHsIKfrwG7gO8BQeCNwCBQb69/O/AboAFYAmwGPmIv+zDQASwF6oG7gB/by5YABvBlPXYc+Fv7sT8G7MXKDgH8GvhvIATMBv4CfNRedhXwMrAQaAUezN5+1vPcAWzIWP9x4Gv2svPsY3CN/ZxrgdcCh4DT7Nv+C3gkY3vGfsxWrEBjM3CFvWwZ8Ab7frOwgtbrStiXzqx1X29f/jLwkwLH8/vANRnXPwn8Ns/xyNtWGc9vWYHX1fuBNqwzcZ8C9gM1eda91T6WpwM1wJ+B7cBljL7mHrTX9QDrgC9inb1YCmwDLrCX/wfwqH3cFtrHMd/xutU5rgWO7VPAHGA+cBB4FjjVbrs/A18qcAweymjzyyn8Wk6va18PAbux3nc+rNfZIWBlxr73A39lH5Ma4Drgbvu5NwC/Bb5hr/8N4EbAb/+dk/HY6WOS53mcx9jXfxvwDqDOfqz/A36d67m7eT55jt0uYKW9vp/i7/dNwAKgBfgTGa//HG1Rymda3uOqf/p3pP1N+g7on/5NxT/gVfYXa6f9BXE3MMdedjmwJWPdE+0vmDkZt3UDp9hfKiPAioxlHwUesi8/APxdxrL/z955h7l1lun7/lSn92J73Mu4xnYcJ05IcRokgZAElpJsgIUFQug/YHcJZVk6S1k29JBAQmCBhBJIgPRiOz0ucWLHvc/Y4+lFMxr17/fH0dFoNOdIR5qjNnPu6/J1WdKR9KnM0Xue87zPuxSlOHCgXwgfirtcFt1mBkpx4gdK426/gbGC6Ung5rjb3pD4+AnvwbGE7d8IHI7+/2IgQFwhB/wS+E7c5Yroa5kfvSyBK+Nu/wjwhM5zXwe8nMZaMi2EN6AUI7bo5W3AO3TWpPtZxb0+3UJY4/H6gTU6t/0KuCPu8seBvQnfuYG413Ai4f6fA+6K/v9Iwvt+U5L361ekLoRvjLv8Z+BnCev8q9Zrit6+ifHFl+Z3OXHb6OV3Ak8nPN7PiRbe0bX/Ou42AYwAi+KuOw84Gv3/V1EOUCd8ZhgrhMd9/zW2WQv0a712I69H5737atxlI3/vH4q77XKSF8JG92lJ31frn/Wv2P5ZHmELCw2klHtRfhwQQiwD/g9FBbkhukln3Oaj0fskXlcBNKCodMfjbjuOoqYBzNK4zYHyI6fH6bh1eoUQRJ+rDkUl6oheB4oy1hb3XG1jDzPuefVI3D7e6tAtpfTFXZ6Fog6qaxsWQvSivNZjyR5PCNEE/BBFlauMrrs/jbVkhJTyxehp9I1CiA4UZfoBnc2TfVYnUz2XEOIzwAeijyNRzjw0JLlL4vdJ6/sFijd5lhBiIO52O4oKrK473c89GYbWJYS4DUUFB/imlPKbGo+l913WYh6wIeF1OoDfxF2Of52NKMX19ri/B4Hy3gB8F+VA6dHo7bdLKf9b57m1GPf9F0KUAf8LXImiwAJUCn2vspHXk0j865tHen/v8f/Xwug+LdX7amFRVFiFsIVFCqSU+4QQv0JRctOlB0U1nIdymhIUW4BaOJ2K3kbcbSGUH6UW0qMNRSFqkNqNOx0op8bjnysVidufirssE7Yd91qEEOUop4vji8Q5jDWUxT/et6KPt1pK2SuEuA74cRprMULielXuRinYTgN/Siju40n2WSVFKH7gzwKXAa9JKSNCiH6UAmKytKGocUt0blc/9/j3XY8RlCJHZUami5JS3oxyej7jh0i43AZsllK+3uB9elCKt5VSygkHKlJKD4pF5TNCiJXAU0KIrVLKJzSe28j6PoNylmCDlPK0EGIt8DJjn3EmryfZcxr5e58dd3mOxjaZkPR9tbAoNqxmOQuLBKINLJ+Ja3SZg6IEv5DuY0WVoD8A3xBCVAoh5gGfRlGYAX4PfEoIsUAIUQF8E7g3+sPWDURQPJ9GnqsDeBT4HyFEVbTxZ5EQYmN0kz8AnxBCzBZKQ9MtBh72o9Ht64DPA/cm2fZ3wPuEEGuFEO7oa3lRSnksbpt/jzYVzUHx46qPVwkMozSytQD/Psm1aKH3fv4GeAtKMfzrJPdP9lmlohKlaO4GHEKIL6EowmbwEjAUbdwqjTZJrRJjcX9/AD4Xfd9no9gX9NiJ0tBYJ4SYAfw/k9aYCZ2M/6z+DrQKId4thHBG/50thFiudWepJCrcAfxv9IwDQogWIcQV0f9fLYRYLBRZcwgIR/9pPbcRKlEKxIHod/S/zHw9Gq/PyN/7J6OvuQblQGzSpHpfLSyKDasQtrCYiAfFd6meNn8BpcHoMxk+3sdRlLYjwDMoBeOd0dvuRCnEtqA0Q/mi2yOl9ALfAJ6NdnKfa+C53oNixdiDYi34EzAzetsdwCPAKygWhvsMPN7vUH5sj0T/fV1vw6iS9p8ovtEOYBFwfcJm96M0du0E/oHiKwb4Ckqz0GD0eq21GV6Lzvo0308pZTvK+yEZsxNooftZGeAR4CGUBsHj0fumOlVtiOjB1ptR/JtHURS7XwBq+shXos95FOX9S3bq/Tco349j0W3TPdgwkx8AbxNKAsMPowruG1C+U6dQFHy1WU2Pz6I0OL4ghBhCaRhTM6eXRC8PA88DP5VjecrfAr4Y/Z78m8H13orSNNeDss94OAuvJ5FUf++PAq+iKNMPohyMmREpl+x9tbAoKtQOWQsLC4txCCGOoTTTPJ7vtWQbIcSdwCkp5RfzvRYLi2wglGi626SU81JubGExjbA8whYWFtMaIcR84K0oEWAWFlOCaK7vJSiqcDOKVeMveV2UhUUBYlkjLCwspi1CiK+h2F6+K6U8mu/1WFiYiECxxfSjWCP2omRNW1hYxGFZIywsLCwsLCwsLKYlliJsYWFhYWFhYWExLcmbR7ihoUHOnz8/X09vYWFhYWFhYWExDdi+fXuPlLJR67a8FcLz589n27Zt+Xp6CwsLCwsLCwuLaYAQQneiZkprhBDiTiFElxBit87tQgjxQyHEISHEq0KIdZNZrIWFhYWFhYWFhUUuMOIR/hXK7HQ9rkIJJl8C3AT8bPLLsrCwsLCwsLCwsMguKa0RUsot0ZxNPa4Ffi2V+IkXhBA1QoiZ0fGPFhYWU4DdJwfZcrAbAJsQXLe2hRnVJSnv9+yhHlqbK2msTGdYVnLCEckLR3o5NTCKLxQhEIrgdtgoc9mj/xyUuewEw5LuYT/dHj+BUCTpY0qSp+fMqCrhretmp7XOA50eHt/bCYBAcPXqmcypK4vdPuQL8oetbQTCytrOmlvLhoX12uuTkt0nhzg5MEq3x4fHb2Sq83gEgqtWzWB+Q3na9801kYhk84FuOod8lLrslDrtjAbDeHwh5ft35izKXFYMvoWFxeQxY0/SwvhRoe3R6yYUwkKIm1BUY+bOnWvCU1tYWOSCbz+8j6cP9sQue/0hPv2G5BNVpZS8766tfPjiRXzq9a2TXkPfSIDfvnCce7a2cXJgdNKPly4bWxuprzBe0N/6+AEe3HU6drlzyMeXr1kZu/zI7tN8/R97Y5eXNlfyyKcu0nysh3ef5sO/3ZHBqsdzos/Lt956xqQfJx1eaRvgmUM9rGqpZs3samrKXLrbBkIR7tvRzu1bjnCkZ0R3u9u3HOa7b1/D2fPrsrHkgqV32M8Te7t4dE8ne04N8sYzZvKvFyxgVk1pvpdmYVG0mFEIC43rNOUVKeXtwO0A69evtwKMLSyKBF8wzIYFddz9r+ew9quPMhoMp7xPKCIJhCN4A+mrl1p88a+7eHDXaS5Y3MAX3rScM1qqKXHacTls+ENhvP4w3kAYbyCENxDGbhM0VbppqHBT6rJn/Lz37TjJ5/+yy9BrjmdwNMjaOTXcc9O5XPSdp/Al3F+9/Owtl/Lth/axs21A97F6RwIA/Ob957B0RiVVJc40XwVc/v3NE9aQC77+jz1sPdYfu/yJSxfrHkR995F93PH0UVa1VPGjG87krHm1eANhfMEwJU47VSUODnUN89n7XuUdP3+e/7hiGR++eFGuXkpekFKy9Vg/dz9/jEd2nyYUkbTUlLJ0RiV3PXeMXz13jA9cuJBbrlqW76VaWBQlZhTC7cCcuMuzgVMmPG7OODUwSiAUKYpThhYW+SAQltSUOpTC024jGE59HBuMnvI3sq0ROgZ9XLC4gf/7wAaNW51QacrTTKAsWkSn+zqG/WGqS52xYl21QKgEoo9X4XZQ4rTF3i8tVGvHqlnV1JbrK6rJcGusIdv0jwTYfryfD1ywgEuXNXH388f48VOHeMPKGaxqqZ6w/ZYDPVywuIHfvP8chNDSWKCpqoSHP3kR//qrrfzymaNTuhAOhSO8/+5tbD7QTVWJg/e+bj5vWdfCiplVCCFo7/fy9b/v5bbNh/nX8+fTVJXarmRhYTEeMwZqPAC8J5oecS4wWAz+YH8ozO9ePME7bnue1/33k7zxh0/T3u/N97IsLAqSYCiC067sLhQFNnVBFQwphV6ybb2BEIOjQUNr6B8JZFwETgb1dScrVLUY8YeocCtFtMtum+BTVi+77Dac9uSFsHqby5H5LtupsQYjPLG3k9FAZkrypgNdRCRcvWYWr1vcwHfetoa6chdf+OtuIpHxBxbD/hAHujysn1+rWwSrlLsdLJ9ZRSCUe4U7l9z6+EE2H+jms1cu48XPX84Xr17BylnVsfdndm0Zn7x8CQBP7e/K51ItLIoWI/FpvweeB5YKIdqFEO8XQtwshLg5usmDwBHgEHAH8JGsrdYkwhHJ/7tnJ5//yy56R/x84tLFAHzhL7uxRk5bWEwkEI7gcig/vq4URZuKP6wUKcmKr8/dt4vL/mcTBzs9KR+vbyRAXVn6loDJohaf6RaRI/4Q5dGGLpdj4nsWX9ymOrhQn1styjPBrbGGVLzaPsD7797G317J7CTfE3u7aKhwszqq/laXOvnCm5bzStsAv996YvxztQ0gJaydU2Posd0GD8iKlacPdvOTTYd45/o5fPjiRbr2nmUzKplVXcKT+6xC2MIiE4ykRtyQ4nYJfNS0FWUZKSVf/dtrPLT7NF9803Lef8EChBDUlrv4yt/2cP/OU1x3Zku+l2lhUVAEwxFc0SLM6TCmLKpWgmTFV+9wgJ7hANff/gK/++C5LJ2h7W8IhSMM+UJ5UoSVA4B0bQXDvhDlbkf0MbQVYZsAu02kPLhQb1PXkgmZKMKb9itJIaeHfGk/XzAcYfOBbq5aNQObbWzd161t4Q9b2/n2Q/u4YuUMGqINiC9HPdJGC2HVbiKlTKkgFxtdHh+funcnixsrxjVYaiGE4JJlTfzl5ZP4Q2Hcjsz98BYW0xEzrBFFxc+3HOHu54/zwQsX8IELF8Z2oO85bz5nzq3hK397jd5hf55XaWFRWIyzRhhUhNWiK1nxFQhFWNBQjt0muOGOFzjUpa0MD0TtE7VJEgeyhXoAkE4RKaVkJBCisiReER5/tikYjsTU5lRFqj+67WQKPi1VOhWbDyiFcLcn/X3i1mN9eHwhLl3WPO56IQRfu24lHn+I374wpgq/fGKAhY3lSVMl4nHZbUipNGVONW59/CAeX4if3LjOUKPnZcub8AbCvHS0Lwers7CYWkyrQviVtgH++6F9vHnNLD531fJxt9ltgm//02qG/SG+/fC+PK3QwqIwCYQjOA0WbSpjzXLJC7zZtaXc+6HzGPaH+P1LbZrb9UdTE/KhCKvFajpF5GgwTEQSpwiLCe+ZP8F3HZGKbUuLYEjGCvJMSVcRHvAGePmEkvbQk4E48OTeLlx2GxcuaZhw2+KmSjYsqOP+V04ipURKyc62fsNqMIDbqbwfU80eEYlIHn2tk8tXNNPabKwD9LyFDbgdNp7Ya9kjLCzSZVoVwqtnV/OD69fyvbevHneqTqW1uZJ3nTuPP+84yYleq3HOwkIlEBqzRmglIOjdB5JbCtRhGAsaymmqdMcK3kT6vYoiXJcHRdiZgSI87FMi49RC2OWwT3gfgmHltcc/h16xHQiHJ9Uop6zBFkuqMMIzh3qISKgscWSkCD+5r4tzF9XH3oNErlnTwpHuEV47NUR7/yg9wwHOnFtr+PEzUeqLgZfbBugZ9vOGFc2pN45S6rJz/uIGntzXZfW5WFikybQqhIUQXLu2JamH6uaNi7DbBD/ddCiHK7OwKGyCYRkrxLQSELRQC79k28bbA2rKnPR7tQvhvmiBXJPHZrl0FOHh6OS3SrUQ1lCEAwmKMOirm8GQnJQ/WFmDLa2Uhc37u6kudXLRksa0FeEj3cMc6Rnh8uVNuttctWoGTrvggVdOxfzBZ6ahCLui+/GpVgg/tqcTh01w8VL9906LS5Y1caLPy+Fu/UEkFhYWE5lWhbARmqtKuP7sOfx5R7sVp2ZhESUQjsQKMaNe06BBRVhV9mrLXDEvcCJqgVyXx/i0dNTUEb9ScI4pwtqpEWMHFyJ2nRaBuG0zRcunrIeUyojjC5c00FTlTlsRfv5ILwAXLWnU3aa23MXG1kYe2HmKHcf7KXHadJsltXDHDh6mVoTaY3tOc+7CeqpL0zvou3SZUjg/ua8zG8uysJiyWIWwBjdvVALab9t8OM8rsbDIP+GIJByRuOyKAue0C0MFlRFFOBAaK/CqS50MeLULYVURLpZmOVURLner75nWQI0xRTiV/SJ+20xRPjdjr2Fvh4cuj5+NrY00VroZiU7sM8qeU0NUljiYV1+WdLtr1rZwesjHn7e3s7qlJq3XmGmsXSFzpHuYw90jvD4NW4RKS00pZ7RUc9ezxwxnc1sUBx2Dozy0q2NC9raFOViFsAazakp5+/o5/GFrOx2Do/lezrRHSskft7Xx1P6utLveLSZPLLrLMaYIm9UsF0iwRgzoWCMGvAFKnLZJjUrOlMlYIypi1ghbTCFXCcQ1wKV6jnjlPFOMfm4wlhaxsbUxFm/W49H+bLTY2zHE8hlVKVMuLl/eRKnTjscfYu1c47YIiFeEp84+4bE9ipp7eQaFMMDXrltFl8fPVx54zcxlWeSRl0/08+YfPcuHf7uD9/1qa0aNqxbJsQphHT68cRESyY+ftLzC+ebV9kH+/U+v8r67tnLONx7nK397zSqIc4iqZLri1Esz49NUpbm2zMXgaFBT9egbCealUQ7icoTTKLhGEgphp0ajWjAhiUO9TougCdYILVVaj037u1gxs4qmqhIaK5VCuNvgD3AkItl32sOKWVUpty1zOXjDSqXoS8cfDKl91cXIo3s6WTmripaa0ozuv3ZODR+9ZDH3vXySh3YV/IBXixT8/dVTXH/7C5S6bHzm9a08f6SXq37wNFuPFV5M3pAvyMd+t4Ofbz6cUXNtPrEKYR3m1JVx/dlzuXdrG8d7reaDfHLP1jZKnXZ+8s/r2LCgnruePWbFBOUQVcmM+VkNTvQKxAZq6J/OS7RGRCR4fBNPwfd78zNeGcxThBMb1ZSDgDGVHfSLOlMU4TTi0w53D7MmWpg2qoqwwUL4RJ8XbyDM8pnG/L7vOW8eCxvL2bCw3tD2KlPNGtHt8bPjRH9Gtoh4Pn7pYlbPrubzf9lFVwaDUCzyz8FODzf9ehsf+93LnNFSzV8/cj4fv2wJ93/0fNwOG1+6v/AU/3teOsHfX+3gWw/t47xvPcGn/7CTUJEIVlYhnISPX7oYh11w6+MH872UacuIP8QDO09y9eqZvGn1TH5ww1rcDltBHhFPVdRCNt2BGmoBrVfcSSnHWSNU/+/A6MRT8P3eQF78wRDfLJeJR9jYQA1XTBHWyRE2wSOczkANbyBMRdTfHFOEDao8ezqGAFg+M7UiDHDWvDqe/MzFaTdCquk/U6VZ7rnDPUgJly2bXCHstNv4/jvWMjAa5J6t2rncFoWJlJIv3b+bK27dwnOHe/n061v5vw9soD56MLp8ZhVvO2s2+04P4fEVjg88FI5w93PH2bCgjsc/vZF3nj2H+3ac5B9FclbCKoST0FRVwntft4C/7jzJvtND+V7OtOQfr3YwEghz/TlzAOXHb82cGrZZhXDOUBU3Z7o5wrFmOe1CRb3dHecRBjQb5vpH8qgIZ9AsN+IPIQSUucYaDCfVLBcyxxoRkaRUaaSUjAbDlLqUIl4tUI0qwns7hrDbhOFhEJninmKK8Pbj/ZS77IYsJalY3FTBosYKdkZj6SyKg9+/1Mavnz/O9efMZct/XMInLltCiXN8X8S6ubVICa+0DeZplRN5bE8nJwdG+dcLFrC4qYKvXbuK1uYKfvLUoaJo8LMK4RTcvHEhFS4H//PogXwvZVpyz9YTLG6qYF1c0P458+vYfWoo5sO0yC4xj3CcnzWx8UuLsWY57R2hWsCohaZaCGtlCfeNBKjLQ4YwgM0mcNiMJy6AoghXuByxZjGX3R5L31BJHFICyeLTpCmKsPIcyX+YfMEIUsYX8Tbqyl2GFeG9HUMsbCif8ANuNjFrRJGcfk3F9uP9rJ1bg11j2FMmrJ1TwyttA9aAjSLh5MAo33xwL+ctrOfr167SPUOydm4NQsCO6NTHQuDOZ48yp66Uy5crZzNsNsFHL1nMgc5hHt1T+HF+ViGcgpoyFx+8aCGP7enkUNdwvpczrTjQ6WHHiQGuP3vOuO7zsxfUEY5IS+3IEcFYs1xcaoRTFYiZAAAgAElEQVQJk+UCCd7jmqj1ITH6KRSOMOQL5U0RhvTHEw/7QuMmqqmJG/GF7vix1SJ2nRaBUDimgGaK0Ql5akxaWVxCR0OFy7AivOfUkGFbxGSIpUYEi78QHvGH2Hfaw1lpTNZLxZo5NfSOBGjv104+2nKgm8f2dOoWyp1DPus3L0dIKfncfbsIRyTf/iftybcqVSVOWpsq2X68MArhXe2DbD3Wz7+cN3/cQdzVq2exoKGcHz91sOAPxgztWYUQVwoh9gshDgkhbtG4vVoI8TchxCtCiNeEEO8zf6n5463rWoCxSCGL3HDv1jacdsFbzmwZd/26uTXYBLx01LJH5IJEa4SSGiFT7tzUoi5RCU28PVYIRwcIJI5ZVods5MsjDOkNowAYCYRiGcIQZ6+IK3SD4QjuBEVYr0gNhk2YLGdQQfUGFCtLaZyi21hpbKjGgDfAqUGfKaf3UzGVFOFX2gcIRyTr5plXCKspHFqCwbA/xEd+u4MP/nob77nzJY72jBAKRzjaM8L9O0/yL3e+xHnfeoKrf/Q0vVZcV9b50/Z2thzo5parljE3RfY2wLp5Nbx8or8gbAd3PXuUcpedd5w9Z9z1dpvgwxcvYvfJITbtL+zaKWUhLISwAz8BrgJWADcIIVYkbPZRYI+Ucg1wMfA/Qoj8/WqZzOzaMhY2lvP0wcL+MKcSkYjkgVdOcemyplijgEpliZPlM6ushrkcEUwoWF0p1MvY/UJjO2mtU/6J1gh1klbidDm1MM67IpyWNSJMRcmYlUOr0B03YjlFfJoZHmGjn9toUCmEy1xjinZDhZue4dQ5wns7PIDxRrnJkIl3u1DZEVX3zjRREV46oxK3w6ZZCN+3o51hf4j3nT+fnScGeP33N7P8Sw9zyfc28cl7dnKw08N7zpuPLxixGu6yTDgi+d/HDrBubg3vPneeofucObeWIV+Iw935VezDEcmDuzu4Zm0LVSUTrWtvObOFlppSfrapsIeTOVJvwjnAISnlEQAhxD3AtcCeuG0kUCmU89cVQB8wpQycFy1p5J6tJ/CHwrFuZYvssbN9gG6Pn6tWzdS8/ez5ddy7tc2UbnqL5KiFk3OCn1XiTrIHCYTDcf+PTPCMJlojHHYblSWOCc1y/dHL+coRBqWITLdZrkJDEQ6OU4TlON81JFOEzUmNAFL6u1VFON4a0VhhTBHeG0uMyG6jHIDbOXVSI7Yf72dJU0XaY5WT4bTbWNVSzSsJhbCUkrufO8bq2dV86eoVfHjjIu54+gh2m41FjeUsaa5kdUs1NpvgQKeH375wnA9dtBCHtZ/NCpsPdHFq0McXr16R1BIRz1nRMwc7TvSzJMtNqck41juCLxhhnc4wHKfdxrvOnce3H97Hke5hFjZW5HiFxjDyzW4B4g8J26PXxfNjYDlwCtgFfFJKOWFvK4S4SQixTQixrbu7uNTVC5c04AtG2H6sMHw5U53H9nRitwkuWdqkefvZ8+sYDYZ57ZSV5pFttKwR8dfrEW8l0NrWn1AIg/Z0OXW8ck2emuUgvegxiHqE4xRVrfdsnCJsZLKcWR7hlNYIRcOIn+LXUOlmNBhO2aC6p2OIhgoXTZUlk1qrEaaKIhyJSHacGIgVN2ayZnYNu04OjvtePXOoh8PdI7z3dfMRQtBUVcIX3rSCW65axtvXz2HtnJpYQfYvr5vPqUFfbOKdhfn87sU2GircaeVHL2wop6bMyY7j+e2T2Rc9A7Rshv4ZoH9a14LdJvjT9vZcLSttjOxZtQ5REo0pVwA7gVnAWuDHQogJ74yU8nYp5Xop5frGxsa0F5tPzl1Yj9Mu2HKwJ99LmRJIKXlqf9eExiiVx/Z0smFBHdU6xc/Z85UfDStGLfuoBa3anGR0wERi0Tfh9oSJdaD4gCdYI6KFcbo5s2aSdrOcP0RFyVghrPWexWcop4xPC5szUCPZc6iM6ijCkDpLeG9HbhrlILOJf4XIkZ4RBkeDpvqDVdbOrcEfirD/tCd23d3PHaOhwsWbVmufbYvn8uXNtNSU8qvnjpm+NgvoGBzlyX2dvH397LTO+AghOHNODdvznByx//QQNgFLmvWV3qaqEja2NvLnHe2avSKFgJF3vh2Id0HPRlF+43kfcJ9UOAQcBZaZs8TCoNztYN3cWrZYDXOTZnA0yId+s5333bWVm369bUKu6ZHuYQ51DSc9Qm6qKmFefZnVMJcDguHMFOHExrAJt2sowtWlzpgVQkVVhPPfLJeGNSIQik2Vg7H3TFXBpZSak+USxzCrmDJiOc1mubIERRiSZwkHwxEOdg6zIkeFsBACt8Eph4WM6g/OhiKsNsy90q4ohyd6vTyxr4sbzplryOJntwnec948XjzaF7O9WJjHvVvbiEi44ey5ad/3rHm1HOoaZlAjdz1X7DvtYX596qjEd6yfTeeQny0F2mdlZM+6FVgihFgQbYC7HnggYZsTwGUAQohmYClwxMyFFgIXtTayp2Oo6OZoFxK7Tw7y5h89w5P7urh27SxePNrH9x8bn9GsnoZLdaro7Pl1bDveX/DRLMXOmDVCKdrcBguqVIpwYhMeKBFqgwnWiAFvgBKnbdyp+lyjNMsZ+55JKSfEp7njfNUAoagyMnGy3MT3KRSOEJFM2iOsJlSk8girinD8j5sRRbhjwEcgHGFRU+58gEbHfRcy24/3U1PmZGFDuemPPbu2lLpyFztPDBAIRfjy317DJgQ3bjDWlAXwzrPnUOK08fPNhd3wVGyEwhHu3drGhUsaDCVFJKJm67/clj9VeH+nh2UG+gEuXdZMXbmLP24rzMbLlHtWKWUI+BjwCLAX+IOU8jUhxM1CiJujm30NeJ0QYhfwBPBZKeWU8xBcuKQBgGcPTbmXlhOO9oxw4y9eJBiOcO+HzuUH15/JDefM4aebDvPE3jEP2mN7Olkxs4rZtcl3DkubK+kbCeCxBmtkFa2BGmDEIzzeBjDhcUNa1gjnBGtE30gwr41yoKxRb0JeIv5QhFBEairCsWxljWl98dfHoxbPuVOE1RzhuNSIytTT5YaiI1/NbPhKhdthL/r4tO0n+lk3t3ZcVrpZCCFYGz2F/pHf7uDJfV18+c0rmFFt3MNdU+bi/Rcs4K87T/Hw7tOmr3G68tT+bjoGfdy4IX01GJScaJuAbXnqW/IGQpzo87K0OfUZIJfDxnVrW3hsT2fsDF8hYWjPKqV8UErZKqVcJKX8RvS626SUt0X/f0pK+QYp5RlSylVSyv/L5qLzxapZ1dSWOQtW3i9kBkeDvP/urdgE/OFD53HWvDoA/uvNK1k5q4pP3buTXzx9hH2nh9h+ot9Q40BTlaJSdQ1ZCn02CSZ4eVNFfSXeD3Q8wlrNcqVOBkeD47xk/d78jVdWSSdHWG0oiy+EEz3CiWq43SawieQWkkmnRhj83LzBidaI+nI3NpFcEfb4lNddWWIkjMgc3A5bUQ/UaOvzcqhrOCu2CJU1s2s40j3C43s7+dq1K3n3efPTfoxPXtbKGS3V3HLfq5we9Jm/yGmGPxTmWw/tZU5dKZctN94kF0+528Hq2TU8ezg/wtyBzmGkVGL6jPD29bMJhiX37zyZ5ZWlj5WHkgY2m+D8xQ2WIpwmoXCEj/1uByd6vdz2rrOYUzem9JY47fzsxrNY1FTB1/+xlytvfRopU9siAJqrFFWja8jaMWeTxILVmUS91LofaI/1TVSaQVGfpASPb0wV7vcG8uoPBsUWYrQpa8SvFJLjJsslNHZpFbd6DXla71MmGFXyRwNhhGDcJDu7TShjlpNkCaufWaU7d4qw0SmHhcpPnjqEy2Hjn9bNztpzXNTagMtu42vXrcqoCAblfb71+rX4gxE+88edBTHIoZj56VOHOdI9wtevO2NSB7gXLWnglbaBvPiE959WPOPLDBbCy2dWcdmyJhwmjRA3E6sQTpO1c2roHPIXpLxfqNy2+TBPH+zh69etYsPC+gm3z60v4y8fOZ/HP30RN29cxLvOnctKA5OpmqINPJ0eqxDOJonNclpT0rQIGI1Ps8cXwtGhGnE79v6RQlGEjRVcHr+y9nE5wgm2BK3iVq+oG0vXMGuyXPIixhsIU+a0TzhV35AiS3jYny9FuDhzhNv6vPxpezs3nD0nLatCupw5t5bdX7nC8LAGPRY1VvClN6/g2UO9fO6+XfiK9H3PN4e6PPx00yGuXTuLja2TS8+6sLWRiITnj+RenNvb4aHUaWdunXF/8y/fe3bGB2PZJHd7rCmCGl59oNPDuRpFncV4hv0h7nj6KJcvb+b6c5J7oRY3VXLLVcbDRppiirBljcgmqpo75mc1FlsVCIWV4i4UGTdcY+x25f5ux8RCuN8bYD5K81DfSIC6PGYIQ3rxaaoiXBGnjCZGl2n5o1127WI7qGEhyQSj8WneQJhS18SfhsZKd1KPsGqNqMhhIVzMivBPNx3CJgQfvnhx1p9rst8dlevPnsOJPi8/23SYV9oH+MmN61ikMyRhx4l+vvGPvQyNBil3O2iucvOfV69I2ftRbOw5NcSPnjzIFStn8OY1s7AnUTz9oTCfu28XZS4H/3l14oDe9Fk7p4YKt4MtB3u4Umf4VLbYf9pD64xKw0NAChlLEU6T1mhe3sFOT4otLQB+/+IJBkeDfPSSRaY/doXbQYXbQadVCGcVf+w0fjTqy64onak8s8HwWMNYIKRhjdAcqKEov2rDXCgcYcgXil2fL1xpjFhWPcLlGorwmEd4YgOcetCQSOJkv0wxmv88GgiN8werpJoulw9F2JVmvnOh0Nbn5Y/b2rnhnOyqwWYjhOCzVy7jrvedTZfHz9U/fIav/m0PJ3q9sW18wTDffHAvb/vZc3QMjLK4qYLKEgfPHurl/b/aNs72VOz87ZVTvPVnz/LYnk7+3707ef33N3P/zpMTkox8wTC/fv4YG7+zia3H+vnim5bTEE1imQxOu41zF9bzdI77lqSUSmJEHqfamYmlCKfJjKoSKksc7LcK4ZT4Q2F+8cwRzltYz5lzs9MM0lTptqwRWSYYHeagnip3RhVhI81y5W47fSM6qRFaHuFS1RqhWI/UgjifwzQgXWvExGa5VKkR6v81vdQa6nEmqAcyKZvlAmHNQrghqghLKTUTDoZ8QVx2W05H0LudNnxF2Cz3002HsQnBzRebLxDkgkuWNvHgJy7kvx/ay6+fP8Zdzx1l2YwqBr0Buof9BMOSG86Zy+ffuIzKEuVv+tlDPbznzpf4+O9f5hfvWV/0I5v/59H9/OjJQ6yfV8tPb1zH9uP9/OCJg3zynp38aXs733zLGTRWurl3axs/3XSIziE/Z8+v5XtvX8MF0QQqM7iotYHH93ZyvHeEefXmR/Bp0T2s2EONNsoVOlYhnCZCCFqbKznQOZzvpRQ8f9lxks4hP997+5qsPUdTlZtuSxHOKsFQJFZEgfFT7IFQJDZmWCu7Vjs+LaoIRz3C/eowjTwXwulZI1RFeGIhHEzwCMe/r3oNebFtzYpPS9UsFwxrZjY3VrjxhyJ4/CGqSiZaVYZ9oZyqwaB8d4ZGiys+UUrJI6+d5k2rZzKzujTfy8mYGdUl3Hr9mXzujcv5zfPHefXkIMtnVtJcVcJFSxo5b9F46+D5ixv42rWr+PxfdvH1f+zly9eszNPKJ8+r7QP86MlD/NO62XzrrWfgcti46oyZXLFyBr976QTfenAvV9y6hQq3gy6Pn3Pm1/G/71jLeYvqTY/Ju2CxUlRvOdjDu3NUCKuTCo02yhU6ViGcAa3NFTy8+7SuMmIB4Yjk51uOcEZLdewPNRs0VZbEpiZZZIf4UcAQp26mbJaLxPJ/9XKEbYJxylBV6fhmOXXKXG2ePcIZxadpjFhWG9W0hom4dDJx1YMI92StEQY/Nz1FuL5C+Sx7hwPahXDCWOlcoGcnKWRODozSNxLIykjlfNBcVcK/XbHU0Lb/vGEuh7uH+eUzR5lVU8JNFxWnIn7b5sNUljj48jUrxv0N22yCd507j4uXNvL1v+9lJBDi1uvXct5C8wtglQUN5bTUlPL0ge5JN0QaRS2ELUV4GrOkqZLfe9voHvbTVFk8/q5ccv/OkxztGeFnN67L6sFCc5WbziGfdVCSRYLhyLhT+G6DymIgFImponpKZ2ITj90mqCpxxKwRhTBeGdJThFWvbHlcw5mxZjmhnSNskiKcTrOc1vutFr96Hk9PHhRht8OO3+Cgk0Jh98lBAM5oqc7zSvLDF964nNNDPr754D7qy93801nZi47LBkd7Rnho92k+vHFRzPaRyOzaMm5791k5WY8QgotaG/j7Kx2EwpGcWE72nfbQWOmm3gSfcyFQ3CadPKEeBR207BGajPhDfPvhfayZXc0VK2dk9bmaq0rwBSPWdLksEgjJCV5WMOYRVn2yeoMitHyvteWumDe4O5pSkG9rhMsuCIQjhsZ5D/tClDrt47rHUw3UUP+fdBT1JH/gbDaBw6ZdbMej1yynFrlqOkQiw77QOF90LihGRXjXyUEcNjFlTiuni80m+P471nD+4nr+48+v8tieztR3KiBu33IEp93G+85fkO+lxLhgcSMefyhnZ0dfPtHPKgMRp8WCVQhnwJJocsQBq2FOE7Ux4EtvXpn1aJXGSnW6nNUwly0C4ci4iLNk44DH3S8UiSUn+DW29YciuDQaq2pKnTFLxAuHe2mqdDOzKr9nXtTXHDIwSGAkEBrnD4axyXGpm+WyN1lOfQwjirBWIVyRohAe8gV1FbJsUYzxabtODrGkuZISZ+6aCgsNt8POz9+9npWzqrjpN9v43iP7CRXB59jl8fHnHe287azZsd+eQmD9fMVms/vkUNafq9vj53D3iOZMgGLFKoQzoLHCTU2Z02qY0+BEr5c7nj7KW85syerYUBV1upwVoZY9lGa5TBRhGSsI9Qo8t8bp/uoyF4PeAP5QmM0HurlseXPesyqNTmUDGPaHNS0C8ckTWokZ+pPlJkatZYoRr/NoQLtZTp0YN6xz9mXYH6Iyx4pwsY1YllKy++QgZ7RMHTUtUyrcDu696TzecdYcfvzUIW6444WCFzTuevYYwXCED164MN9LGUdTpZuqEkdOxLmXjvYBsGFBXdafK1dYHuEMEELQ2lQ57RXhziEfm/d3s/lAN4FwhIWN5bzSNoA9mjWZC2Jjlq0ItawRDEdikWkwcVywHoqSbMdh009D0CruasucHO8d4cUjfQz7Q7x+RdMkX8HkMZrBCzDsC47LEFZx2m0xZVzTI+ywaU59Mys+LXENWkgp8Qa1FeExa0TheIRdDhv+IlASVU4N+ugbCUxbf3AipS47337bal63uJ7P3beLf7lrK3+8+bycW2yMEApH+OO2Nl6/vJkFDblJZzCKEIKlM3JTk7x4tJcyl51VU+g7XHjftiKhdUYF9+88NS2btLo8Pr7ywB7+sasDGMtW3rxfKYj/48qlOQuJj41ZthThrBEIj/fyCiGiAyb0lUUpZdQDLHRP+Qd1PMI1pU76RwI8vreTEqeN1y3KXuqIUdJRhEf84XGNciruOEVYc6CG3vukoR5nSvwatAiEI4QjkjKN9avq/rCGNUJKmZfUCLfDTiAUKZr98K52pVFuKhURZnDt2hZqylz866+28vHf7eCOAswZfu5wLz3DAd66rjCb+1qbK/nbK9mvSV480sdZ82pNsWoVCob2WkKIK4EfAHbgF1LK/9bY5mLgVsAJ9EgpN5q4zoKjtbkSjy9E55C/qCYDTQYpJX/c1s7X/7EHXyjCRy9ZxNWrZ7FsRiVCCMIRSZfHx4wc+jnLY9PlLEU4WwQSrBGQuklJ9dK6HLakE9PilWaVmjIXQ74Qj+3p5MIljQXhpTQaPQaKRWBWzcS/gXjrQyCadOBMVIST5C3HZw5nil5WscpoQFlXqcZ77nLYcDtsmtaI0WCYcETm3CMcSzCJnn0odHadHMBuEyyfaVkjEtnY2shXrlnJF/+6m6/9fQ9fuXZVvpc0jr/uPElliYOLlzbmeymatDZXMuQL0eXxx86Umk3fSID9nR6uWTsrK4+fL1IWwkIIO/AT4PVAO7BVCPGAlHJP3DY1wE+BK6WUJ4QQ+T+XmWWWNCkdvwc6PdOmEP7JU4f43qMHOGdBHd966xkTZszbbSIvAfFNVW66kox+tZgcyoS48bsKp07Ul0p8g5dTZzyxXmpETTQzuGPQx6cub53M0k1jzBphIDXCP7FZTn2MZIqw3ntqpiKcakKeN1oIa1kjACpLnJoJLapKnPPUiDilvjgK4SFap3mjXDLede48jvWM8ItnjnLlqpkThnLkC18wzCO7T3P16lkF+9m1Rscd7z/tyVohPBX9wWCsWe4c4JCU8oiUMgDcA1ybsM0/A/dJKU8ASCm7zF1m4dE6zZIjntrfxf88doBr187ing+eO6EIzidNle6Cb7IoZhKtEZBaEY4v3twOG4GQtvdVq7hTC2Eh4JJlhXFMnZ41QrsQjj8g0J4sp/2e+nOYGqEWwlrNcqD4hLVSI4ai1+U8R9ipvCfJfM+FgtUoZ4zPvGEppU47/9h1Kt9LifHE3i5GAmGuLWAlNBc1yYtHeylx2lg9uyZrz5EPjOxZW4C2uMvt0eviaQVqhRCbhBDbhRDv0XogIcRNQohtQoht3d3dma24QKivcNNQ4YpNWJnKHO8d4ZO/f5llM6r477euznsHfyLNVSWWRziLBBNyhEE/6ktlrNCz6UZc+cM68WnRYQ5nzqkpmIiitJrl/Np5ui772AGBfrNc9nKEkz2HymhMEdYuaCvcDoY1muVUu0Q+RiyDsQOUfGM1yhmj1GXn4qWNPPJaJxEDcYW54P6dJ2mqdBd0ZJhak2S1ED7Sx7q5taacnSokjLwaraon8dvpAM4C3gRcAfynEGLCOU0p5e1SyvVSyvWNjYXps0mHZTOq2Hs6+7l9+WTIF+RDv9mOEIKfv+ssXaUonzRXldDl8RkadmCRPkpqxERFOFm3fnyh57SL2JjgxG30muUALl/RPJllm4qq3KZSHoPhCP5QRLMQdjrGK8JOuxjX1KLXLBcIRXDYhCkHoKkVYaWg1bdGODQ9wmqSRIU79znCUByFsNUoZ5wrV82g2+Pn5bb+fC+FQW+QTfu7efOaWeOG5BQirc2V7M9SrOugN8je00NsWFC4BwOZYqQQbgfmxF2eDSSes2gHHpZSjkgpe4AtwBpzlli4rJxVxYHTw4ZUomLE4wvynl++xOHuYX50w5nMrS/L95I0aap04wtGYqdnLczFr1Gwuuw2zeJWJd4Dq6dCBkJhzRzhVS3VfPSSRVx/9txJrtw81Nef6m99RB2vrFEIu+PeM63EjGST5cxSYFKlRniDya0RFW5ta8RwvqwRDv2BLYXG7pODVqOcQS5Z1oTTLnh49+l8L4WHX+sgEI4UtC1CpbW5kkOdnqwo6VuP9SElbFg4tfzBYKwQ3gosEUIsEEK4gOuBBxK2uR+4UAjhEEKUARuAveYutfBYMauKQDjCoa6pN1hj2B/iX+58id0nB/nxP6/jotbCVfCb1CxhyyecFZRCbLwSotcAp5LYLKepdOoUeE67jX+/Yhl1eR6rHI9Ra4SqllZo5Qg7xHhF2DHRbhKREE74EdNK7ciUVJ/baIpmuQodj7AnX81yRaQIv3ZqkMWNFQXbbFVIVJU4OX9xAw/tPp33M30P7jrN3LqyorC0tDZXMhIIc3Jg1PTH3nVyECFg7Zyp5Q8GA4WwlDIEfAx4BKW4/YOU8jUhxM1CiJuj2+wFHgZeBV5CiVjbnb1lFwYro7O295yaevaIj/52B6+0D/KjG87kipUz8r2cpDSrY5at5IisoJzGn6heJisK45vlXDpDHPSsEYWI0Wa5Eb9SSGpZBOKtD0GdBkSt5wiEpWmKsKLk6xcWsdQIp3ZBW+nWsUZEr6vKw4hlgEA4nNPnzYS9HZ7Yb4ZFaq5aNYP2/lFey+Pv65AvyHOHe7hiZXNR5FQvnZG9hrnjvSPMqi6dkgdyhvauUsoHpZStUspFUspvRK+7TUp5W9w235VSrpBSrpJS3pqtBRcSCxoqKHHa8vqHmg2eP9zL5gPd3HLlMq46Y2a+l5OSptiYZUsRzgZap/FT5dGOJR2IpPm4xdJ0YVwRVryyepPl1PfBr6HyxorthOcw84DBmbJZTilo9VMjnAz7QxNUOtUjrPW6s4lqrSn0Mcu9w35OD/lYYRXChrl8eTM2AY+8lj97xFP7ugiGZcGLQSpLmtVYV/PPUh/r9TK/oTDtkZOlOH6FChS7TbBsRhV7OgbzvRRT+cETB2iqdPPu8+bleymGsKbLZZdgWGo0y9mTTpaLTzpI1gRWLIWwWqSm8qIOxxTh5M1yQQ2V1xVtyEt8r8z0CKccqBFMbY0IR2RsO5VhX4gylz3n08DU96XQxyzv7VAUuhWWP9gw9RVuzllQx0NZ8gn3jwTY2zHEpv1dtPd7Nbd59LVOGircrJtbm5U1mE1ViZOZ1SVZU4Tn1RfWaGmzsEYsT5KVs6pyMtYwV7xwpJcXjvTxpatXFM0pEHW6XJfHUoTNRkqpbY3QSYJQGWeNSDJZrlgK4bFmueR+xVTNcvGT5QxbI0IRU6bKgYFmuSST5WCswFcK37HX6PFpR8ZlG/U9LHRFWBVLrEa59LiotZHvPLyfwdEg1aXm2W7ufu4Y//XAa7HLs2tLeexTG8edCfEFw2za38U1a1sKLjI0Ga3NlabHug6OBun3BplXZynCFhqsnFXNkC9Ee7/55vR88IPHD9JY6eafNxROx74RmqrcljUiC6iFX2K6Q6o82lTNcpGIVFTRIvEIG23KGmuW0x6oET9ZLnG8tNOubb8wVxFO3SxX4rTp/vCrqRCJCS3D/lDOEyMASpzGRl//6tmjrP7yI1z4nSe59sfP8I9XO3KxvBh7Tg0xs7qE2gJqAC0GFkcHNx3pNvdU/6N7TjOvvoyf3riO775tNT5MKhgAACAASURBVO39o/zoyYPjtnnucA8jgTBXrCycGEcjLJ1RyaHu4QlNt5PhRK+imE9VRbg4foUKGNXzNRV8wi8e6eX5I73cvHFR0ajBKg0VbnqHA/lexpRDLcoSFclUAzVSKcKBuNuLAaeObSGRZIqw0mAoY49jvFnOvNSIVLF33kBYVw2GsUI4sWFuyBekIseNcgAuu7LWVAcoW4/3I4TgrLm1HOkZ4YFXTuZieTH2dAxZtogMWNSkFMKHu0dMe8xAKML24/1csrSJN54xk7evn8PbzprN7VuOjLMUPLK7k0q3g9ctajDtuXPBnLoyAqEIPcPmWQWP9Srvv+URttBk2YxKbAL2nCp+n/Bfd56kssTBjUWmBgPUl7vo91qFsNnEK7vxuFIMZvAnKMITGsCil7VyhAsRo81yqrWgWJvlvIGw7lQ5GEvDGNZQhKvyoAiPjVhOnhox6A2yqLGcW68/k5Wzqugbyd2+whcMc7h7xGqUy4C5dWU4bMJURXjXyQF8wQgbFozl4X7+jcupKHHwhb/sIhKRDHqDPL63k0uWNRXNwbrKrGqlebxj0LwzpCf6FEV4rmWNsNCixGlnUWMFezqKXxF++cQAZ86tLTo1GKC23JXTH7fpQlBHuXWmjE+LDtSw23BrKcKhYlOEjTXLjfhDOGxCs3B1jWuWm2h30PMhm+mlVhoXpW4262gwlHR6pKoIexLGLA/n2SOcShEeGA3ERnfX5XhfcbBTOU1tKcLp47TbmFdfxmETC+EXjvQBcE5cIVxX7uLzVy1n67F+Vv7XI6z56qP0jgS4clVxpEXEMyNaCJ8eNM+ueaxnhKZKd9KD5GJmar6qHLNyVhUvHu3L2fO92j7AgDdo6pCLEX+IA52eoomJSaSuzEW/N0gkIouqsaHQCYT1FeFkReEEa4SG71V9nGIgnclyZS67ZuOsK5rYIKVUVN4yY9YILRtFpozl7kZiU9niURRh/UJYLXY9CdYIjy8/HmGj3u0Bb5DWJiVaKteFsNooZynCmbGwscJUa8SLR/tY0lRBfYV73PVvXz+b430jjPjDtNSUMr+hnMuWNZn2vLliZnUpYK4ifLzXy/wp6g8GqxA2hZWzqvnrzlP0jQSyOg3raM8I331kHw/uOo3DJnjpC5eb9nyvtg8SkbB2bnFOjaktdxGOSDy+ENVlufcqTlViym2aAzXGLBUCp11MVDmLTBG22QQOW/LoMYCRQFhXGVVfaygiNRVhvWY5MyfLxavOWss07BHWsEZoDRHJNrEc4RSfy6A3OKYIl7kYGA0SjkjsOTho3nNqiAq3gzm1U/O0crZZ1FjBpv1dhMKRScfzhcIRth/r4y3rWibcJoTg369YNqnHLwRqy5y4HTZzC+G+ES5cUrjTZSdLcfwKFTgrcjBhbmfbAK///mY27e/mnzfMJRSRPLjLvM7nl9v6AVg7uzgL4bpy5Ue4z/IJm0rM4qBxGj9ZUTh+spydcESO62IutkIYUjcIQlQR1imE46fTaRW3+oqweZPl1KY/vc9u1KAiHN8sF47IvKVGOOw2bCK5IhwMR/D4Q9RED5Dryl1IqURC5YI9HUNKL4l1piojFjWWEwxL2kxIZtp9aoiRQJgNC+pNWFlhIoRgZnWJaYWwNxCic8jP/PqpeyBXPL9CBYyaDbk/CyHWKo/tUULFn/q3i/nGdatY3FTBA6+cMu3xd54YYEFDedHG+9RG1R7LJ2wuQR1rhNNuIyLRjegZ1yznmJi44Ndpwitk4lMf9BgJhDUTI9T7g/I+aBW3sSI1m4pw1A6hV9B7A6GkPkCH3Uap0z7OIzwSnUaXj0IYUkf5qQWvWgir+7i+kewP4IlEJHs7PJYtYhLEkiO6Ju8TfvFILwAbFtal2LK4mVFdYppHWG2Um6rRaWAVwqZQW+akqsTB8V7zfEyJ7Dg+wPKZVTRXlSCE4Jo1s3jpaB+nBox/2QdHg/xxWxs3/Xobq7/8CH9/VSmkpZS83DbA2jnFqQYDMYtIv1UIm0r8qOR4UnkzEyfLxT8WFF98GihFe6pT8F5/iHIdRTVeEdZKjdDzIZvZLGdEEU7WLAfKdLl4Rdjjy28h7HbY8Qf1UyMGvEohrA5kqIsVwtlXhNv7Rxn2h6xGuUmwqEGNUJt8IfzS0T4WNpTTVFky6ccqZGZWl5qmCB+PZQhbirBFEoQQzG8o51iv9pjGyRIKR3ilfYB1cf7da9bMAogVs6mIRCTv/Pnz/PufXmXXyUFKnHZ+/OQhpJScGvTR7fFzZpH6gyFOEbasEaaimxqho16qBEIRHDaBzSZiPs744kv9v7uYFGG7SGmNGPbrK6rxjWrBcERzSAloT5ZzmTRZLn4NWniDya0RoBS8njiPsOoXzodHGIwowso+IT41AnKjCKtnCZfOqMz6c01VqsucNFS4ODLJhrlwRPLSsb4prwaDogh3DvmImDBUQxX45tVZirBFCubVl3OsJzuK8P5OD95AmDPj5p3Pbyhnzexqw/aIZw/3sO+0h69du5LnbrmUf7tiKftOe3j+SC87TwwAWIqwxQT00h20itvE+6mKp1YTWDF6hPVGRcfjDYSp0MgQhvFRX1pjk3MxWS5V3JjXgCJc6R5fCKs2ibxZI+y2pCOWVUW4tiz3inDbNDitnAuU5IjJKcIHuzx4fKFxsWlTlVnVJQTDkh4TDvaO9XqpLXNO6SZ0Q3tXIcSVQoj9QohDQohbkmx3thAiLIR4m3lLLA4W1JfR3u9N+UOZCTuiheq6uEIY4M1rZrH75JChHcSvnz9OfbmLd5w9J2atqC93ceczx9jZ1o/LYWPZjOI9fVfmsuNy2CxF2GT0BmroFW0q8R5YLaWzGAthI81y3oB+s9yYR1g7NSKZImyeR1j/cwtHlFi3MmfygnaCNUIdK50va4TThj/J59IfLYRrSpUCWD17lIsBPO39o5S77LEi3CIzFplQCHcNKUXhdEjvmBGNUDttgj3iRK+XuVP8QC7l3lUIYQd+AlwFrABuEEKs0Nnu28AjZi+yGJhXX05EQnu/+faIl4/301DhYk5d6bjr37xmFkLAAzuTq8InB0Z5Ym8n7zx7Tiw7tMRp58YNc3liXycPv3aaM1qqi6ooSUQIQX25iz5rzLKp6FkjUnmE4z2wmopwEXqEU0XGgRojljw1whcME4rIJJPlxk5nRiKSUMTM1Aj9z80bbXpLaY1wO8fFp6nqcD4my0HqBJOBaMGrKlolTjvlLntORrK39XuZXVummSttYZxFjeX0e4OTaoYe87JP/YOSmdGhGqcGJl8IH+sdmdKJEWBMET4HOCSlPCKlDAD3ANdqbPdx4M9Al4nrKxrUGdzHs+ATfrlNmfiWuDNtrirh7Hl1PLanM+n9f/vCcQBuPHfeuOvfde48HDZBW99oUdsiVGrLrDHLZqMWZekrwmO+VrWI82spwkXkEU7VLBeOSHzBiG4hqb4PasqC/mS5iQcMZivCWp7a0eh4aCPNcvGpEfn2CLsdyT+XwdEgNqFYOlTqKnKzr2jvH2V2bWnqDS2SsqhRaZibzKjlfFt4colZ0+UCoQinBkanvLXHyN61BWiLu9wevS6GEKIFeAtwW7IHEkLcJITYJoTY1t3dne5aCxp16spRk33CfSMBjvaMTLBFqGxc2siejiG6PdpeIF8wzD1b27hseTMtNeN3yE1VJVy9Wmm6mwqFcK4nRk0Hkg3UAP1BBoHQ2Kl/zQKvCK0RrhTWCLXALddpllM9wSP+cOzxxj2+hsquPl9iY12mJFeElXWlUoQr3I5xk+XyXWC4HXYCoeSpEdWlznE5vnVlLnpzsK9o7/dahbAJqIXwZOwR+U43ySX15S5cdhsdQ5NThE8OjBKRMLfOUoS1zukktiLeCnxWSqm/NwKklLdLKddLKdc3Nk6tKSV15S4q3eZHqL18Qhl0sU4n0eGi6LSXpw9qH1g8tLuDvpEA/3LefM3bP3rJIs5bWM8Fixsmv9g8U1vuivkBLcxB1xphQBFWiy6tAs9fpNaIZKfgvdECVy9HWC1mR/zairDdJrAJ7QMGsxRhd5xPORGjhXBV1CMspfIYw/4QNpH6ftki1ecyMBqM+YJVastdWW+sHfQG8fhCzJniRUQuaKktxeWwTWrU8pAviBD6B6pTCSFENEt4coWwKiw1VBTnfAGjGNm7tgNz4i7PBhJNqeuBe4QQx4C3AT8VQlxnygqLBCEE8xrKTI9Q23GiH7tNsFpn4tvKWVXUl7vYckCnEN51mpaaUs5frD1JZ3FTJb+/6dyiHaQRT12Z01KETWZsoEb6OcITmuU0Cjy3PT/FUyZojYqOJ6YI66RGqMWs2mimVdwmFnV6k/0yJZkiPBpU1lWaolCoKHEgpTI8BBSlrcLtyJsPNpU1YsAbmNDxnouzR23RfhFLEZ48dptgQX35pIZqqN/T6TLhb0Z1CR2T9Air0YNqBvdUxcjedSuwRAixQAjhAq4HHojfQEq5QEo5X0o5H/gT8BEp5V9NX22BM7++nGMmK8LKII1KXd+ezSa4cEkDTx/smZAZGAhFeO5wLxcvbZwWzRq15S4GR4OEUjQ0WRgnpkhOyBHWVxbBQLNcMVojUjTLqUqvXo6w+j6MJCmEnXab5gGDWYqwekCj9TqMWyOUH0XVG+zxhfLagJRSEfYGqUn4Ia8ry34h3B4dCTx7GqQU5IKZNSV06VgAjTDkC1I1DRrlVGZWl9AxNDmP8NhUxuIXypKRcu8qpQwBH0NJg9gL/EFK+ZoQ4mYhxM3ZXmAxMb++nPb+0ZSd5UYZG6Sh7Q9Wuai1kd6RAHs6hsZdv/14P8P+EBtbp5YNRQ81H3Rg1LJHmEUs3UHHz5q8WW68R3gqxKclK7hGYtaIFM1yOtYIUNTNbKZrJGuWUwvhUmfqgRoAw37l78zjC+bVd5lqoMbAaGDCD3ldhYvRYDjWIJgN2i1F2FTqy930DGdeCCsHbFPfFqEys7qUzkH/pIZqDCZMZZyqGPpWSCkfBB5MuE6zMU5K+d7JL6s4md9QTjgiae8fZUHD5LssXzs1hDcQ5qx5yQvhC6M+4c0HulnVUh27fvOBbhw2weumgP/XCLF80JEADRXuPK9mahAMRU/NT0iNUJTFZM1yqjLqcqhT6MZ2yIFwGLtNYC+i05Que/KCy5uiWc4Vs0aozXITX3tisT3WrGjSZLlk1gijinC0mBiKKsLJIuNygduReqBG4g95XdwkyhZXdgrV9v5RKt2OKV9E5IqGShe9wwGklBmd4fRMQ0U4EI7QOxKgsTKz30NVVMpXNGKuKB45pghQs/bMskeovt9UjWyNlW5WzKxic4JPePOBbtbPr83rj1QuURXhXHSDTxcC4XBsVHI87pSKsIwVy66oDzjR+1pM0WmQ+hS86v3Va5YzoggrQzvGDhj0mhUzJZmSP2aNSL6/UGPIxlsjClMRDoUjeHwhzWY5yO4kyvZ+Ly21pdPClpYLGivcBMKR2AFYuuT7e5prxiLUMvcJD44GqXQ7cBTZvjpdpvaryzFq1p5Zo5afPtjDqpYq6g2omxe1NrLjeH8syqhzyMfejiEuXtpkylqKAWvMsvkoBa12wQbpNcsleoSLyRYBqSfLqYVkyma5gPFmuTFrijlNhUYGaqQcsRxV1dTCf9gfoiKfHmG7HX9Q2+KgFk01Cc1y9Tk4aG7rG7X8wSZSH00uyNQeMd0KYXWoRscksoQHR4NUTYMzGsX1S1TgNFS4qHA7TBmq4fEF2XGiPxaPloqLWhsIRSRP7FXmmahq8nTxB8NYIWyNWTYPZbzvREUrlUc4MK5ZTsSuU/EXYSGcShFO1Synvl6vqggbaJYLxprlTLJGJPnc0rVGeHxBfMEwHYOjNObRiuR26ivC6tCMxEI424qwlJL2fu+EaaAWmaPa3TKdCKh42ad+UacyUx2zPIks4UENW9FUZPocHuUAIQTz6stMGarx/OFeQhEZ8/+mYv28OpY2V/L5v+xiTl0pmw5001TpZtmMykmvpVhQf+wsRdg8AuEILsfEwmhsHLBOIRzfLKcRtRYIRYrOGpFoW0gk1iynU0gmDtRITOKAickUZuctO2wTD0pUvMEwTrtImVChWq08vhBPH+zBF4xwybL8HXC7op9LJCInWHgGdJp9VEU4W8kRA94gI4GwpQibSH25UghnoghLKaedIlxf7sJpF5Maszw4GpxwEDkVKa5foiJgfn25KUM1thzsptxlT9kop+Jy2PjN+8+huaqE9965lc37u9nYOj1i01TcDjsVbgd9I1ZqhFkEQxHdpi7Qt0bEWx+0iuZAOGLatLRc4bILAuFIbJBEIt5ACLfDpuunG2uW01eEXXYx3kttcnyaECLqqZ34GkYD4ZSJETBWCA/7Qzz62mkqSxxsWKCdU54LkiVhqDmoiakRVSVO7DaRtUJ4LDrNUoTNoqEyamfJoBD2BSOEInJaKcI2m6C5qmRSY5YHR6eHIlxcv0RFwPyGMlMi1J4+2MN5i+rTUoKaqkr47Qc2UFXqVGLTlk4fW4RKbbkzdjrUYvIEwxFN5dKdpPiI3S9pfFrYtOIuV4zZCrQL4WF/SLdRDpQi1GkXscEb+s1yEz3CZh40uHRi4LyBUMpGOVCGG5S77Ax4gzy+t5NLlzXl1eaivjdaCSaqIlyboGrZbILaMmfWbFTWMA3zqStzIQR0Z2CNGMrzGPB8MbO6hFOTbJazCmGLtJlXX04oIjk1kPlR2PHeEY73eg3bIuKZVVPK7z94Lp+4dDGXL2/OeA3FSi6C8qcT8RaHeGJDMkLaRWG8ImyzCRw2MSWa5UDfF+0NhHUb5VRcdttYaoShyXLmKsLqc2i9hsFR43nAFSUOthzopt8b5A0rZpi2tkxwa1hvVNRCuKZ04kCA2jIXfRn6TVMxliFsWSPMwmG3UVvmysga4ZmmhXBzVQndkxhCMjAanDCVcSpSXL9ERcCMKqVTs3MovS9fKByJ/UBuOdgDKEkQmTC3voxPv2EpJQZOc041astdk1aEpZSx09fTnUBIOzVCzQAOhLW79RPTJrTSEIqtEE41VnrEH9LNEFZxOmxjI5Z1FOFxectZGDziTLBfqHR5/DRH91+pqHA7ONIzgstuy/uZJ1dMEZ74XRzwBhBCuwCqLXdlTRFu7x+lqsTKEDabhgpXRtYINT1kOuUIAzRVltCZYbOcLxgmEIpMi+/w9Do8ygFqZ6uRo9Yuj48fP3mIV9oH2dcxhD8UYWFDOf5QhNm1pbFcYgvj1JW5ONiZ+Tx6gO8/doDbtxzhu29fwzVrZpm0suJEzxoBSkGlZROQUkaV5DFvcWLWa7E2y4G+IjwSSG6NAEUFVlVKfUV4rKBTi+JcKMJdQ342LDA2CEj1Wp6/uD7vOeVux8ScapWB6KndxCY6UJqJDnZNbl+hR1uf11KDs4AyXS79gxePWgiXTq+Sp7nKjTcQzmjojTpeeToUwsX1S1QEqIb+VIWwxxfkPb98iXu2tlHmtPPuc+fx6de3sripAoB3rp8zrRrdzGKyivCgN8idzxwF4BO/f5nvP3ZgUiMqi51AKII7SfOXVvGhFsfxKuYE72sRWiNcGk1/8Yz4wymjx8ap5JrNcuOTKbKjCNtiaRQqUkq6PX4aq4zFoKkK6xtW5tcWAcmb5Qa8QWp0fshry11ZS5hp7x+1/MFZoKHSnZEiPGaNmPpFXTxN0b/nTFRhvcSVqcj0OjzKAaqhP9lRayAU4eb/286hrmHufO/ZGVsgLCZSV+7CGwjjC4Yzsobc/fwxRgJhHvjY+fzm+eP88ImDDI0G+fI1K81fbBEQDEdwO3UKYZ2JXlq+VpfdNq6ZqVhzhCG5NWJGCmtBfNObdrPceC91bLKcmYqw3RZLo1AZ8AYJhCM0VRq3RggBly3P/8Ae9b3RGrM8MBqckBihUh89aNaKXZsMSobwqLVfzwL15a5JKcLTziMc/XvuGvKzqLEirfuqirCWv36qMb2+FTkglaFfSsktf36VZw/18r23r7F2liYTmy7nDcQCxY3iDYS469mjXLqsidWza/jO26pxOmz85oXjvP+CBcypm36nOoPhSGyAQiJ6irCWiqmcjo9TOovQIzxmjdCLTwuntEbEHxzoDSpJzFtWrzcLrQOYrmhDTbNBRfgNK5tpqSk1XDhnE/VATTM+zRuIDc9IpLbMRUQqP/h622RCl8fPaDDMHEsRNp3GSjfD/lDaQsf0VYSjhbAnfUXYskZYTIqGChc9Op2a7f2j3PfySW7euIi3nTU7xyub+tSWZR6Uf89LbfR7g3zk4kWAEnf1iUuXYBNwx9NHTF1nseBP4uV16nhN9RThcd7XJJaLQiWlIhwIpU6NUJM0BJp5wxMmy4Uj2ITSnGgWLo1R0eqpU6OF7VvOnM0Xr15h2pomg1Y8n0p/EmuEOrLX7Ia5PR1DACybWWXq41oov62Q/lANjy+ETegPu5mqTM4aofxdWIVwFCHElUKI/UKIQ0KIWzRuv1EI8Wr033NCiDXmL7V4aKhw6/6hqvmSFy1pyOWSpg0xRTjNoRqBUIQ7nj7COQvqWD+/Lnb9jOoS3nrmbO7d2japGJpiJVmznK4irDENbYIiXITWiNioaF2PcOpmOfUx9JrftBRhs98np8bnpirCTZX5G5WcKe6oMqiXGqFnjZjMQXMy9kYL4eUzrELYbMamy6X3mXl8oaidZ3r13VS6HZQ67XSlmWIFcYqwFZ8GQgg78BPgKmAFcIMQIlEKOApslFKuBr4G3G72QosJpRDW/kNVxx3OrLFOm2WDunLljzZdlWfT/i46Bn3cvHHhhNs+tHEhgXCEXz131JQ1FhPBsNRXhDWURYg7nZ9gAyj6+LQkqRGBUIRgWKZUnNTXrPfaE9XaQNxgErPQmiynnjptMmiNKCT0FOFwRDLkC+kqWnUGxiw/e6iHg52etNazt8Pz/9k77zBJrupuv6fj5N2JO5vzarVa5VWOICEQwQLbBBFENIhsG/sz+DPBH2CMDRibaIIIBiMTZBAgEEISWmWxypvDbJ7ZyTu58/3+qKqemurq7uqZnunp6fs+Tz/TXXWr6lbdnupT5/7OOSxfXF0RBsRc02I+qBUaMDcciVecLAKMWc0lDWG6p+HEGZ6IG6kHS5wVZi7wcoe9GDiolOpQSsWA24Gb7A2UUo8opQbNj48BFT3nn8sj3GUW2li6qPTauoVI2stT4I3y0Y5+wgEfV2zI9NSva63jxq3tfP/Ro2mtWaWQK81ZKOBzreYVd0n5lVEoogzTp+WSRlg5wPNVZnNW23Nbn1KGEWcdq9ilqF09wsNR6sMBT5Xl5huTeYSnntPwhHtVOQvLEO7P4V384O3P8Pnf7S+oP3u6hjlzaX1B22i80Vw7fWlEpQXKWbTVV9EzDWnE0ESchir31IMLDS932OXAcdvnE+aybLwd+I3bChF5p4jsEJEdvb293ntZZrTUG5kLxmOZRRk6hyZorg1VZLGLuaCxJkQo4Cu4rOTjHQNcuLoxnZPUyXuu3cBIJMHtTxx3Xb9QMaQR7jdCN60puAd4ObWv5egRzpVH2CqbnC9Xp2UA55JGwOQ1jM+KR1gyzqFnJOI5ddp8I1uJ5dNW1HsWaURbfRi/Tzg15F4FdGgiTt9olMN9Y577Eokn6egdZYvWB88KrfXTk0YMm0ZdJdLWEE5LnwrByLhSGdfMyx3W7VfQNWxaRF6AYQj/ndt6pdQ3lFLblFLbWlsXbraEdFGNkcx/1s7TEZZpWcSs4fMJKxurOdrv/cdraDzOnlPDXLK2OWubrcsXceHqRv5nx3GUqpy8wrmm5p1eXvs2MDUrQtjWNpVShuSizAzhXB7h8ZihT63xGCyX7dyta21dw9nQCLtpu3uGo2WpD4bsJZatfOLZJAoBv4/2hipODLobwh29RrGNI/1jnnOJ7+8eIaXgTG0IzwpVQT914YD2CBfATDzClRAoB94M4RPAStvnFUCns5GInAN8C7hJKdVfnO6VJ62mIdzr8s/aeXpCyyJmmdXNtRztH/fc/okjAygFl65rytnuNdtWcLBnlGeOn55pF8uGXIZYtspy2TzClhfSLZiuHHAaqXasssl5SyynPcJZvOwZHmH3EtczwU3bXUh55flGNmmEFfWeLWsEwIrG6hyG8Fh6v6c8GhLpQDltCM8azXWF5xIeicYr1hBe0hBmzKwuVwjaEJ7KH4GNIrJWRELA64A77Q1EZBVwB/AmpVRhgqoFiJWWxynoV0rReXpCe4RnmVVNNRwbGPfsuX28o59QwMe5KxfnbPeyc5ZRHfTz4x0ncrYbiyZ4yRe3860FkHItnsytEc6VPi3k1Ag7DeFy0wjnyCM8HjU8wnlLLKc9wu6eY6sstXUNc6Wvmy7OcVNK0T0cKWOPsHuJ5R1HBvH7hHUt2QsJrGis4cSg+0NzR99k+eUjHuURuzuHqQ35WVWBOcfnipa6wqvLjUQSNFSIUefEesAtNIXa0Lg2hNMopRLA+4C7gT3Aj5VSu0TkVhG51Wz2MaAZ+KqIPCMiO2atx2VAWhrheGodjiQYiyVZtrg8PS/lwurmGsZjSfo9pkV67HA/F6xanFe3XRcO8NKzl/LLZzuZiGWmarL42VMn2HtqhH+6aw+PHOwrqO+5mIgl+dETxzhVoP55uiRTipTKrmd1C7qC7HmErWpm1jbFDgKbbXIGy8WsYDlvJZZDeTzC1jXMlb5uugQdVf6GIwmiCe9V5eYb2cblnt3dXLK2KWf2hhWN1ZwajriOaUfvWDpi/ojHGaY9XSOc0V5fEQFGpcKoLufdEFZKVbg0wrBHCk2hpj3CDpRSdymlNiml1iulPm0u+7pS6uvm+3copRqVUueZr22z2en5TnOWpN9dZlCG9gjPLqubDW+MF3nEcCTO7s7c+mA7r9m2gtFogt/s7HJdn0opvvPwEbYub2Bdax0fuP3paSUzt6OU4rc7mTIFiAAAIABJREFUu7j+Cw/wkTue57aH5yaNW76qZtlKLLtKI+we4VmoljYXBB3eWjtW1oh8wXJhrxph20NDsQuPhB0e4d4yTp0GRrERv0+m5BE+0jfGgZ5RXrRlSc5tVzRWk1K4Plx29I5x0domwgEfRzzEHCil2HNqWMsiZpmW+nDOTB9OJuJJkilVkenTYHrV5ZRS2hDWzIxwwE9DVaagvzOdOk0bwrPJqqZaAI4N5P/x2nFkgJSCS/Logy0uXtvE6uYafpJFHnH/vh4O943xzqvX87U3XMBYNMn7//tpElmKMHjh07/ew60/eIr6qgDLF1endYizTczFs2snX0ENp0c4mihvQzi3R9hbsFy+ghpOHXKurB3TxenJ7x62immUp0cYpgZjguENBjwYwsZDs1MekUwpDvePsaGtjtXNNZ4yR5wYnGAkktCG8CzTUhdmYDzm+Z46EjEeUivWI9xQuEd4LJYkkVLaENbMjJb6zFzCVjGN5dojPKusaKxGxJtH+LGOAUJ+HxesavS0bxHh1Reu4NGO/nRUuZ1vP3SYpYuquHFrOxuX1PP/bjqLJ44McN/enoLPw+LXz3fxws1t/Or9V3LZ+mb2nioswf90mSyMkX0aP1f6NLv0wd42n4E9X8kVLDfmMVgub0ENh7Edy6HRni6hwNRcxeVcTMPCOTtxz+5uzlzakDZ0s7Gi0bgXOwPmOk9PEEukWNdSy+rmWk8aYesBdcsybQjPJi11IZQyymd7wcr9XqkeYau6XCEzk0Pp1IOVcc3K65eojGipC2ekT+s8PUHAJ+lciJrZoSrop72himMeDOHHO/o5b2V+fbCd12xbSV04wMfv3DUlIG9P1zCPHOrnzZevSRtNN523nOqgn4enqRU+PR6jayjCpeuaCPh9bG6vp3ckWnD6oOkQz5PdIbtG2KWghq2tW+W5ciBbBTOA8WgCEajO8z2azBqR3csOk9cwlih+HmGn/KJnuHzLK1uE/D6iceN8BsZi7Dg6kNcbDEZhI79PMjzCh8yH3HWtdaxtqeXowHjeFGp7ukYQgc3tupjGbDIZg+PtHjhc4R7h6VSXGzIfMrRHWDMjWl2qy3UNRVjSYNx4NbPLqqYajg7kNoRHInGePznkWRZh0dZQxd+++AwePNDHz585CUAimeKLv99PddDPzRetSrcNBXxcvLaJhw9NL6Pgni7D+7u53fAyWdOu++bAK+wW9GbH8PJmGgeT28mUtpYXMlqm0gifTwj4MotRgDGVWBP05w2S8uoRtnvPi55HODDVs909HKUm5M+rb57PNNaEeOhgH4f7xrhvbw8pBTd4MIStXMLHHR5hK3XautZa1jTXEkuk6MrhUVNK8fzJ06xpri3L6nzlRKHV5SxpREOFGsJQeC5hyyNcKZk2yuuXqIxoqQtl5BE+eXpCZ4yYI1Y3GynUcvF4h6EPvmy9t0A5O2+8dDXnr1rMJ3+1hxOD47zrv57k7l3dvP+6DRlR6lduaOFgz+i0sj3sPWVMt242S7Za3qa50AlbHsOcWSOSqYw0ddnyCFvrylUjDO45eMGQRuRLnQaTHt9cJZZhamW5oksjzAeUtEd4xEidJlK+D+if+bOzmYgn+dOvPsx3HznMskVVnOVRomDkEp56r+joG6WhKkBzbYg1LYa8wk0eMRKJ85X7D3Ld5x/g93t6uGRtYQ/VmsJpMWcuvAbMWaW2K1UaAYVXlxuasHJwu1dlXGiU3y9RmdBcF2YkkiASn4xk7hrSOYTnitXNtfSORF3LXFs8cqifcMC7PtiO3yd85k/PZngizvVfeID79/XwyVdu5T3Xbshoe/mGZvN4hcsj9naN0FwbShdpaa4L01ofnhOdcL7CF+HA1Gl853ZTpBE27au1vtzSp0H2anpjsaQ3QziQzxA2jdTZrCzn8Dr3jETLOlAO4IJVjdzx7stZVB1k58lhrt+yxLNhb+QSzvQIr22tQ0RY22IE37oFzP3jL3fzr3fvo6UuzGf/7Gw+/oqzZn4ympwUKo2o9GA5MHIJT8cjnCv14EKi/H6JygTrn3XAzGWbSilODUV0xog5wkpon8sr/MihPi5a01SQPtjO5vYGPnDdRgI+H9968zbedOlq13ZntjfQVGtM3RbK3lPDbF5aP+VHfXN7fdpTPJtYBq5Xo83CTQMcsrWdXD+9615KDC+4W0GNRN4cwtb2QNZMEM5ywbNVWc5+jN6RaFkHylmsaanljvdcwVuvWMPbr1zreTu3XMKH+8ZYbxrAS+qrjBRqDkM4Ek/y252nePWFK/jxrZfx2otWUe3hO6CZGQ1VARbXBNOysXxUerAcGPr/QqrLpQ1hLY3QzIQWRy7hvtEo8aRiuZZGzAn5cgn3jUbZe2ok7a2dLh+4biNPffRFvHBzdj2izydctr6ZRw72e652B4aedl/3SFofbHHm0gb2d4/OKCWbF/JJI9KBXQ4PaTyZIuCTKXpZuy61nKURIb+4eoRHC5ZGuBtMQf9Ub+1ceISNqnIL477UVBvi4684i9XNtZ63WdFYjVKTed7HYwm6hiKsazX24fMJa5prM3IJb9/fy2g0wcvPXVa8E9DkRUS4amMrD+zvzRvACIZH2CdQW8EPKVZ1Oa9e4dPjcQI+qZhrVn6/RGWCpWOyDOGTp3Uxjbkk7RHOYgg/YgavXb6+ZcbH8mKoXLmhhVPDEQ71eivVCnC0f4xIPJURhb65vZ5YIuUpyf9MyJs1whF0ZeGW6SBoM5pjyWTO/c5nsqWMG48lPf1oWNcsm0fYLVhutjzC0USK0WiC8VhyQXiEp8tkLmHjHj0ZKDdZmnlNS2Yu4V8/30VjTZDLpxFjoJkZLzijlb7RKLs688+MjUTi1FcFy1oDP1OsjDDdHnMJW8U0KuWald8vUZlgaTqtFGpdZqCUlkbMDYtrQjRUBTiapajGIwf7qK8KcPbyRXPSnytMg7uQNGqWDtiZoN/yEHudGpwuMZfsD3aypROLu2Q6sHuE4wk1ZVk5kStYrqYAj3C2anF22YJSatY9wpaHqJxTp82UyVzCxkNzR99kxgiLNS21HB+YSOdejsST/H53Ny/Z2l52+bAXAldvagXgD/vy52ev5PLKFoVWl6ukqnKgDeFZw9IIW5kjrKpyupjG3LG6uZZjAxOu6x4+1Mel65rnLJXdquYaVjZVF2YIdw3j9wkb2uqmLF/fVkvAJ7OuE84rjcjmEXbRtdqN5mgyU0NcLmQPlktQ5yFtVijgtbKcIpGyNNrF/Y7ax8LyEFlTp5XIZC5hyyM8igissckr1jTXEkum0vfxP+zrZSyW5GVna1lEKWipC3POikX8YX9v3rbDkURF64MBlhRYXW5oIl4xgXKgDeFZozrkpzbkT0sjOk9HqAn5aaiu7CfTuWRVcw3HXOQDxwfGOT4wwRVzPKV5xfoWHj3Unw7eyMfurhHWtdRmBPOFA37Wt9ax1+ERVkrx/365myv++T5e/G/bec1/PurJY5KNeJ7sDk49q0UskcrYxpIETMSTPHSg1yg+UYb6MytlnJPxaDJveWWY1Abny8Qxm2nmJj3CimeOnwagfVHlGsJWLuETgxPEkyl+/VwXm9rqp/zfWUaxJUf69fNdNNWGuLTAHOSa4nHtplaePjbI6fHcadQMaURl/+7WhQO01IW4Z0+3pzgV7RHWFA2jzLLxT9p52kidVimam/nA6iYjLZIzqMxKY3bFhpnrgwvhtRetZCyW4KM/3+mpvZExwj0X6ual9Rkp1O546iS3PXyYda21rG6uoWtogvf88Cn2d09PQpG3oEYOaYRTTmFJAf7up89x965u/uaGM8qygIO9Qp6FUsrwCHs4H+u65PMIx5OpvNd/ulj7O9w3ypfuO8ALzmhlXYv34LKFiJVL+HuPHOFAzyh/8+Izpqzf0FZH0C+8/0dP84k7d3HvHkMWESjDWY2FwrWb20gp2H4g9yzbSCRR0cU0wAgw/NANZ/DE4QHueOqka5v93SP87MkTPHqon/7RmDaEnYjIS0Rkn4gcFJEPu6wXEfkPc/1zInJB8btafjTXhugbiTIaTXCgZ4SlFex1KQWrm2tIpBTfeLCD3+7s4r693XzvkSP84LFjtNaHMyQHs835qxr54HWb+Pkzndzx1ImcbYcjcU4MTmQt17q5vYGTpyfSaW6O9o/xsV/s5OK1TXz3rRfzjVu28dNbL6cmFOBd//Vkul0hpKUReYLl3DzCGcFyZtvD/WN88qazeO8LMvMtlwNuwXKReIqUwlNFsclgOfdr6vcJfrN63Wx5hC1j/F/v3gfAp151dsU/oK9orOFAzyj//vsDXLOplevPbJuyvrU+zI/+4lKu3NDCfz9+jPFYkleco2URpeTcFYtprAnmnfUaicYrXhoB8NptK7lg1WI+fdeeDC/6Xc938fIvPcSHfvIsN3/zMU6enqC5tnLiBvLeuUXED3wFeBFwAvijiNyplNpta3YjsNF8XQJ8zfxb0bTUhdlxdJDrP/8Ap4YjvPUK77ktNTPnvJWNVAV9/Mtv901ZXhX08c6r15fkx/99L9zAw4f6+OjPd7J1+SI2ttW59mN/OlDO3RDeutzwFN9y2xO8dttKfvLkcXw+4d9ee15a97ykoYqvvfECbv7GY/zV/zzDJ15xFssWV3n2YsXy5BEO2bIP2HELllvZWMOqpho+dMMmbjpvuafjz0eCfskoIDJmFm2p9SSNyB0sZx3DXnik2B5hS34xHEnw8Vds0XELGB7h0+Nxgn7h46/Y4vo/uW1NE9vWNHF6PMaerpFpVaTUFA+/z0ijtt1Mo5atvPnwhA6WAyMN4KdfdTYv/9JDfPa3+/jMn56NUopvPtjBP921lwtXN/LJm7YyOB7j1FCEKzfO7YxpKfHy7bgYOKiU6gAQkduBmwC7IXwT8H1liE8eE5HFIrJUKdVV9B6XEUsaqhgYi3HWsga++sYLplXBTDN9zmivZ+cnXszAeIzekSiReIqVTdW01pWunKzfJ3zxtedx478/yA3/tp1wwEdbQ5hwYKoRZemInTmELa7c0MLHXr6FHz1xjL//3+cB+NLN52cYNRetaeLjr9jCR3+xi/v29hDwCUsajOAgn4BPBMy/qZQRoJVMKRKpFKNmRaZsHkkr8Ouv/ucZAj4fiVSKRFIxNBHn7BVTs3G0L6pi+/95QYFXa/4RCvjY1z3Ci77wQHqZFdTmxSMczpM+DQzD93uPHuG7jxwBoHqaBV9y7R/gvJWLueWyNUXdd7liZY5425Vrp6RNc2NxTUgbwfOEa89o5c5nO7nis/eZ97TJ+1osmWI8lqw4vWsuzlzawNuuWMM3HzzMr57tZCyWIKXgZWcv5fOvOXfaxaXKHS+G8HLguO3zCTK9vW5tlgNTDGEReSfwToBVq1YV2tey49Zr13PZ+mZefFb7nGUn0Ewl4PfRVl81rwoGLFtczc/efRl/2NdLz0iUnuFIhpcRYGVTTVY5jYjwtivX8tYr1vDciSG6hiZ4ydalrm3fdNkazl25mL1dIxzpH+PUUISUUiggpTDeK4VPhKDfh98nBMwp+lVNNVl/RLYsXcRrt61kIp4k4BeCPh9+vxD0CS/Y3Oa6TbnzuotWuf4vn7dyMVd60Jyva63j3deu5+qNrVnbfOCFG9nXPUJTbYi2+nDRr+WKxhreefU6Xn+x+7lUIi/c3Ma7rl7HB164sdRd0RTAS7a289yJIUajCfM+ZtzPkilFKOCjNhSgNhzgNdtWlrqr84a/etEmwgE/Y7EEtaEAq5pr+PMLVmT1qFcCki+CUEReDbxYKfUO8/ObgIuVUu+3tfk18Bml1EPm53uB/6OUejLbfrdt26Z27NhRhFPQaDQajUaj0WjcEZEnlVLb3NZ5EZ+dAOyPUyuAzmm00Wg0Go1Go9Fo5g1eDOE/AhtFZK2IhIDXAXc62twJ3GJmj7gUGKp0fbBGo9FoNBqNZn6TVyOslEqIyPuAuwE/cJtSapeI3Gqu/zpwF/BS4CAwDrx19rqs0Wg0Go1Go9HMnLwa4Vk7sEgvcLQkB18YtADe6/Vq5gt63MoTPW7liR638kSPW/kyX8dutVLKNUq5ZIawZmaIyI5swm/N/EWPW3mix6080eNWnuhxK1/Kcex0fUiNRqPRaDQaTUWiDWGNRqPRaDQaTUWiDeHy5Rul7oBmWuhxK0/0uJUnetzKEz1u5UvZjZ3WCGs0Go1Go9FoKhLtEdZoNBqNRqPRVCTaENZoNBqNRqPRVCTaEJ5HiMhtItIjIjtty84VkUdF5HkR+aWINNjWnWOu22WurzKXX2h+Pigi/yEiUorzqRQKGTcReYOIPGN7pUTkPHOdHrc5pMBxC4rI98zle0TkI7Zt9LjNIQWOW0hEvmMuf1ZErrVto8dtjhCRlSJyv/m/s0tEPmgubxKRe0TkgPm30bbNR8yx2SciL7Yt1+M2hxQ6diLSbLYfFZEvO/Y1P8dOKaVf8+QFXA1cAOy0LfsjcI35/m3AJ833AeA54FzzczPgN98/AVwGCPAb4MZSn9tCfhUybo7tzgY6bJ/1uM3TcQNeD9xuvq8BjgBr9LjN+3F7L/Ad830b8CTg0+M252O2FLjAfF8P7Ae2AP8CfNhc/mHgs+b7LcCzQBhYCxzSv29lM3a1wJXArcCXHfual2OnPcLzCKXUdmDAsfgMYLv5/h7gz8z3NwDPKaWeNbftV0olRWQp0KCUelQZ37zvA6+c/d5XLgWOm52bgR8B6HGbewocNwXUikgAqAZiwLAet7mnwHHbAtxrbtcDnAa26XGbW5RSXUqpp8z3I8AeYDlwE/A9s9n3mByDmzAePKNKqcPAQeBiPW5zT6Fjp5QaU0o9BETs+5nPY6cN4fnPTuBPzPevBlaa7zcBSkTuFpGnROT/mMuXAyds258wl2nmlmzjZue1mIYwetzmC9nG7afAGNAFHAM+p5QaQI/bfCHbuD0L3CQiARFZC1xortPjViJEZA1wPvA4sEQp1QWGwYXhtQdjLI7bNrPGR49bCfE4dtmYt2OnDeH5z9uA94rIkxjTEjFzeQBj+uEN5t9Xich1GFMOTnSOvLkn27gBICKXAONKKUvnqMdtfpBt3C4GksAyjKnaD4nIOvS4zReyjdttGD+4O4AvAo8ACfS4lQQRqQN+BvylUmo4V1OXZSrHcs0sU8DYZd2Fy7J5MXaBUndAkxul1F4MGQQisgl4mbnqBPCAUqrPXHcXhm7uB8AK2y5WAJ1z1mENkHPcLF7HpDcYjPHU41Zicozb64HfKqXiQI+IPAxsAx5Ej1vJyTZuSqkE8FdWOxF5BDgADKLHbU4RkSCGIfVDpdQd5uJuEVmqlOoyp857zOUnmDqLZo2Pvk+WgALHLhvzduy0R3ieIyJt5l8f8A/A181VdwPniEiNqVu8BthtTlGMiMilZkTmLcAvStD1iibHuFnLXg3cbi3T4zY/yDFux4AXikEtcCmwV4/b/CDbuJn3x1rz/YuAhFJK3yfnGPMafxvYo5T6gm3VncCbzfdvZnIM7gReJyJhU9KyEXhCj9vcM42xc2Vej12po/X0a/KF4SHsAuIYT09vBz6IEaW5H/hnzGqAZvs3Arsw9HH/Ylu+zVx2CPiyfRv9mhfjdi3wmMt+9LjN03ED6oCfmP9vu4G/1eNWFuO2BtiHEeDze2C1HreSjNmVGNPgzwHPmK+XYmQ7uhfDS38v0GTb5v+aY7MPW3YBPW5lMXZHMAJaR83/0S3zeex0iWWNRqPRaDQaTUWipREajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IajUaj0Wg0mopEG8IazQJGRN4iIg8VaV9rRESJSKAY+/NwPCUiG6a57RERuT7LuqtEZJ9bWxH5exH51vR6XHAfXyUix0VkVETOn+G+visin8qxflRE1nncV0HXvZB9a2YXPRYaTeFoQ1ijKQIicqWIPCIiQyIyICIPi8hFc9yHOTVUyxWl1INKqTOyrPsnpdQ7YE6u5+eA9yml6pRST8/SMQAwj9FR6n3P5OFmJszWWJbqfLIxm+Os0SxUtCGs0cwQEWkAfgV8CWgClgP/CERL2a/5jDbWAVgN7Cp1J8qFuf7OLPTjaTQaA20IazQzZxOAUupHSqmkUmpCKfU7pdRzkJYnPCwi/yYip0WkQ0QuN5cfF5EeEXmztTMRWSQi3xeRXhE5KiL/ICI+c53P/HzU3O77IrLI3HS7+fe0OUV6mW2fnxORQRE5LCI3Oo71bRHpEpGTIvIpEfGb6/zmdn0i0gG8LNdFMCUGHxGR3eaxviMiVea6a0XkhIj8nYicAr5jLv8LETloetHvFJFljt2+1LxefSLyr7brsF5E7hORfnPdD0VksWPbi3L1Jcs5fEJEfpDlel5j9vNsW/s2EZkQkVaXfbmOlYiERWQU8APPisihLH35d/P7MSwiT4rIVTkuP0CjiPxaREZE5HERWW/bV9pzKSLNIvJLc79/NMfcKZ+5XkQOmNfuKyIi2Q7q2Pd3zfYZ/RAR63o+a17P15rLXy4iz5j/G4+IyDm2fR8xvzPPAWMiEhCRZSLyM/P/47CIfMDW/mIR2WGeW7eIfMFclfV/w7btJ0TkpyLyAxEZBt5i7u9Rs29dIvJlEQlN93yyXLv3isgB4IC5bLOI3GN+1/aJyGts7XOOnctYfFVEfmP272ERaReRL5rjuldskpxc11WjWdAopfRLv/RrBi+gAegHvgfcCDQ61r8FSABvxTB+PgUcA74ChIEbgBGgzmz/feAXQD2wBtgPvN1c9zbgILAOqAPuAP7LXLcGUEDAcew48Bfmsd8NdAJirv858J9ALdAGPAG8y1x3K7AXWInh6b7fuX/HeR4BdtraPwx8ylx3rXkNPmueczXwQqAPuMBc9iVgu21/yjxmE7DKvA7vMNdtAF5kbteKYeh8sYC+nHC0vd58/wngBzmu51eBz9o+fxD4ZZbrkXWsbOe3Icf36o1AMxAAPgScAqqytP0uMABcbLb/IXC727GA281XDbAFOA485Gj7K2Cxed17gZfk6Kd93577YX6+AOgBLsH4fr7ZHI+wbWyeMcexGsN58yTwMSBkXtsO4MVm+0eBN5nv64BLs42ly3l8AuN/5ZXmcaqBC4FLzXNZA+wB/nK655Pl2t2D8R2txvg/PI5xrwiY++sDzipg7Oxj0WeeQxVwH3AYuIXJ+9D9Ztuc11W/9Gshv0reAf3Sr4XwAs40f3hOYBh8dwJLzHVvAQ7Y2p5t/mAtsS3rB84zf6CiwBbbuncBfzDf3wu8x7buDPPH2/qhdjOED9o+15ht2oEl5rGqbetvtv043gfcalt3Qy5jwvzBt7d/KXDIfH8tEMNmyAHfBv7F9rnOPJc15meFzQAD3gPcm+XYrwSeLqAv0zWEL8EwPnzm5x3Aa7L0KetY2c4vqyHssr9B4Nws674LfMtxvnttnxXGw4Pf7MMZtnWfItOYutL2+cfAh3P0y2l85e2H7fPXgE869rcPuMY2Nm9zXP9jjvYfAb5jvt+OIUtqcbTJGEuX8/gEtgexLG3+Evjf6Z5Plmv3Qtvn1wIPOtr8J/DxAsbOPhbftK17P7DH9vls4LSX66pf+rWQX1oaodEUAaXUHqXUW5RSK4CtwDLgi7Ym3bb3E+Y2zmV1QAuGR+aobd1RDN0x5n6d6wIYRm02Ttn6OW6+rcPQqAaBLnMa9zTGj26b7VjHHcfKh7O9XerQq5SK2D5PORel1CjGA8FyWxvX/ZmShNvFkHMMAz/AuHZe+zItlFKPA2PANSKyGcO4vDNL8+mMVRoR+ZCI7BEjAPM0sIjMc7RzyvZ+HGOMnbSafbBfm+Mu7Vz3JSK7zGn20RxSDS/9sFgNfMj6/pnnuZKpY3Xc0X6Zo/3fM3lN344hVdprSgdenuPYbky5FiKySUR+JSKnzO/ZP5F7DLycT65jrgYucWz/BowHV69jZ8d5j3G751jHzXVdNZoFixbnazRFRim1V0S+i+HJLZQ+DK/PamC3uWwVcNJ832muw7YugfEDZzcgvXAcwyPcopRKuKzvwvgRtx8rH872nbbPytF2yrmISC2GFOCkrc1KJgPK7Pv7jLm/c5RS/SLySuDLBfTFC87+WnwPQ7ZwCvipw7i3k2uscmIamX8HXAfsUkqlRGQQyKrV9Uiv2YcVGFITmHqdcqKUOmuGx3dyHPi0UurTuQ7raH9YKbXRtaFSB4CbxdCS/ynwUxFpJvtY5joWGB7ep4GblVIjIvKXwJ/n2N7L+eQ65nHgAaXUi5yNxNDuT3vs8pDzumo0CxntEdZoZogZ3PIhEVlhfl6JITF4rNB9KaWSGFPRnxaRehFZDfw1hscT4EfAX4nIWhGpw/BQ/Y9pyPYCKQx9n5djdQG/Az4vIg1iBHetF5FrzCY/Bj4gIitEpBH4sIfdvtds34ThUfqfHG3/G3iriJwnImHzXB5XSh2xtflbEWk0r+kHbfurB0Yxgp+WA387w764ke16/hfwKgxj+Ps5ts81VvmoxzB6eoGAiHwMQ4s+I8zv1x3AJ0SkxvRq3zLT/RZAN1Ov5zeBW0XkEjGoFZGXiUh9lu2fAIbFCKCrFiOgc6uYqQpF5I0i0qqUSgGnzW2SFPi/YaMeGAZGzWv17iKfj5NfAZtE5E0iEjRfF4nImbM8djmvq0azkNGGsEYzc0YwNHaPi8gYhgG8EyPAaTq8H2P6vQN4CMNgvM1cdxuGIbYdI/AlYra3ZA+fBh42pzcv9XCsWzCkGLsxNKg/BZaa674J3A08CzyF8SOcj//GMK47zFfWIg9KqXuBjwI/w/A+rwde52hRPOzRAAAgAElEQVT2C4wgnmeAX2PoisHQgV4ADJnL3frmuS9Z+ud6PZVSJzCuhwIezLGLrGPlgbuB32B4/o6a2+abBvfK+zBkFqfM/v2IuUv19wnge+b1fI1SagdGIOeXMb5/BzF07a6YxuArMPT0hzFmUL6FcT4ALwF2iZGV49+B1ymlItP83wD4G+D1GP/j3yTzYWpG5+NyfiMYWvzXYcwonGIywBRmaew8XFeNZsFiRY5rNBrNjBCRIxhZHX5f6r7MNiJyG9CplPqHUvdlpojIZ4F2pdSbS90XTWHosdNoZo7WCGs0Gk0BiMgaDP3pjMoilwpzSj0EPA9chBFg9o6SdkrjCT12Gk3x0YawRqPReEREPgn8FfAZpdThUvdnmtRjTKkvw8h5+3kMCYpm/qPHTqMpMloaodFoNBqNRqOpSHSwnEaj0Wg0Go2mIimZNKKlpUWtWbOmVIfXaDQajUaj0VQATz75ZJ9SqtVtXckM4TVr1rBjx45SHV6j0Wg0Go1GUwGISNbKqHmlESJym4j0iMjOLOtFRP5DRA6KyHMicsFMOqvRaDQajUaj0cwFXjTC38VIUp6NG4GN5uudGCUpNRqNRqPRaDSaeU1eaYRSaruZNzMbNwHfV0b6icdEZLGILDXLt2o0Gg8opUgpSKRSpFLG33DATygwv+NZI/EkiZQi4BOCfh8+AREpdbdmDaUUwxNmhWSBRdXBoh8jkUyRUszq2CdTCr9v4Y6TRqPReKUYGuHlTC39ecJcVvGG8M6TQ9yzu5s3XLqKtvqqUndHMw+ZiCW58d+3c6R/PGNdW32YRz9y3ZwaLJ2nJ3jxF7czGk3gE2FlYzX3/PU1BP2ZRtnxgXGu+/wDxJKpKcuDfuF1F63ik6/cOlfdnjM+9es9fPuhyfTBH75xM7des97z9oNjMa793B+47S0XceHqRtc2N33lYXZ1DlMXDtBWH+Zrb7yQM9rrZ9x3i+FInCv/+T7+4eVbeM22lUXbr0ajmf/s7x7hz776CPFUitpQgFXNNXz+1eeyrrWu1F0rGcUwhN1+pV2TE4vIOzHkE6xataoIh57f/PDxo/zoieN8Y3sHb79yLbdeu566sK5hopnkl891cqR/nFsuW01zbZiAX/CJ8OTRAX6/p4eJeHJOvzMnBicYiSR45XnLGBiPs31/L6ORBI21oYy2p4YjxJIpbr54FSubqkkkFYlkil8828lzJ05PaauU4pFD/Vy0pmnee7lzcbR/nCUNYd519Xq+cM9+jg1kPsDkonskwtBEnCN9Y1kN4aP945y/ajEb2+r48Y4T7OocKqoh3D8aYziS4JO/3M3VG1tpX6Qf0jWaSuGzv9kLArdctoaxaILf7jzFn37tEb55yzYuWtNU6u6VhGL8Ip0A7G6FFUCnW0Ol1DeUUtuUUttaW12zWCwo+kZjrGis5roz2/jy/QeNL6BGY+OHjx9jQ1sd//gnZ/HB6zfy3hds4N3Xrueqjcb/RzSenNP+xE3v7s0Xr+IlZ7UDZHh8LWIJY/krz1vGe67dwAeu28hf33AGm5bUE01M3WZX5zBv+NbjvOP7OxiPJWbxDGaXeDJFe0MVb7tyLQ1VgfQ18IrVPts1tdZduq6Zv7x+U/qYxcTqw0g0wUd/sRNdVEmjqQz+eGSAe/f2cOs16/n7l57Jp191Nne853KaakK84ZuPc/euU6XuYkkohiF8J3CLmT3iUmBI64MN+kejrG6u4cuvv4Btqxs51Dta6i5p5hE7Tw7x7PHTvOGSVRm62rDpNXUalLONZSQFAz6CfpmyLKOtaaA5Pbwhvy/DeBuLGsbv9v29vOnbTzA0Hi9qv+eKWCKVPt9QIPM882G1z7adUopYIkXQ70sfp1Bj22sfLlrTyD27u/ntzsr88SuEVErxhXv2860HO9jVOUQqpR8eNOWFUorP/mYvbfVh3nbF2vTy1c21/Ozdl7O6uYb/uPdACXtYOrykT/sR8ChwhoicEJG3i8itInKr2eQuoAM4CHwTeM+s9bbM6B+L0VwbBqC1PkzvSLTEPdLMJ374+FGqgj7+9IIVGevCwdkxgvKRNm5thlg2oy1tNDv0w0G/ZHg8rc/vuHItz58Y4g3ffqwsjYl4MpU+36DfV/D4WA822bZLmNckHPCljxNLFvc6WX249Zr1nLWsgY/duausvfRzwZH+Mf7j3gN86td7eNl/PMSln7mXnpFIqbul0Xjm3j097Dg6yAeu20h1yD9lXWNtiPNXLaZ/NFai3pUWL1kjbs6zXgHvLVqPFhD9ozGa6wxtZWt9mEc7+kvcI818YTgS5xfPdPIn5y5zzTwQDhg3qlJ5hEMBH6G0IebeB8tADjs9wgEf8YRybfuKc5fRWBviX+/ex9BE3FV7PJ+JJVPUmprt6XmEVXo/rvtPP1xI+rrOlke4OujnfS/YwLt/+BQHe0Y5Z8Xioh5nIXF8cAKAL918Pt3DET716z3sODLIS89eWuKeaTTe+Pw9+1nbUstrL3IPkG2qDTMwFkMptaAz/7hRvlEr85xIPMloNEFLnekRrgtzejxONDG3mk/N/OTnT59kPJbkjZeudl1vGaFz/X2J2zzClkfSadRaZPcIZxqI9raLawzDP5dOdr5il0YE/b6CH1RieTzC1nUL2q//LGmEQwEfSxdXA9AzrGercnHcDIrctqaRN122mqBfeP7kUIl7pdF4IxJPsqdrmFedv9w1AxBAU22QWDLFWKzybBRtCM8SA2PGFENz7aRHGIwAOo3mrue72Nxen9ULVzJphF0jHPDmEQ66eISd/Y66eZrn+NyKQTyZSvd/NjTCdiPV7xP8Ppk1j3DQ72NJg3Ff6tbT/Dk5PjhOyO9jSX0V4YCfTUvq2akNYU2ZYD3o5soQ02TKOAcq0EbRhvAsYWltmhyGsNYJa8C4Ma3PkbexVNIIu0c4n8GaNtr8mcFyTuPZkgTYtcdzfW7FIJa0Bcv5fenz8sqkIZzFy56c6mUP+qXoHuH0GAd8tNSFEdEe4XycGJhgeWM1PjOn99Zli9h5ckhn3NCUBdaDbntDLkPYmKkbGNeGsKZI9I0ZPyzNpjTCKqihDWENGIGUTTn0sZNZI+Z2mio2xWA1fvSzei9tbe0ETUPYbiTYPZ2zpX2dC+IJlc6mEfQX7q3NFyxnGchhm7Fd7AeGqE2mEvT7aKoJ0aPvSzk5PjjOisbq9OetKxYxOB7n5OmJEvZKo/FG97BhCC/JaQibHuGxyrsXaEN4lrA8wi112iOsmUoimWJoIp7TEE57TeOlC5bLp1G1t7UTCvhQyijja2H3QobySC7mMzFb1oiZSCPyB8tN/xj5+zDV2G5rqKJ3gUgj7tvbzSX/9Hv+sK+nqPs9PjDOyqaa9OetyxoA2HlyuKjH0Whmg25zxseSQrnRVGP8Hg2MlWdqy5mgDeFZYsDhEbayR2hDWDNo5tC1vhNuhEtkLE7qRyVvHlt7WzuTBnSmRzjoF0J+f879zmfijmC5aRfU8BAsB6bMpMjXyWlst9WH0z+U5YpSitseOsw7vreD7uEo9+zuLtq+RyJxBsfjrGycNITPXNqA3ydaJ6wpC7qHI4QCPtcMRRZNdZYhXN73gumg6/3OEv2jMUIBH7Vmvr6g30dTbYje0YXhedFMHyuQsrEmhyEcNDXCJfAIi4DfJ7Y8ttmNNp9AwKkRthnQVr7KmItHuNiezrkg5giWK/RBJV+wXNThZQ/Oikd46jHa6sPsPVXens0v3LOfL913kBu2LKF/LMZzJ4pnoB4fMOQPK5smpRFVQT8b2+rY2akN4VJQiSm+ZkL3cIT2hqqc16w25Cfk92mPsKZ49I3GaKkNTfnitdbpohoa6LdmC+ahRtjKiiAiaYMva2BXIuWaiidkVaSzGXBpL6Rv9iqmzTZKqYxgudnzCMvkMWYpfZp1jCUNVfSNxqZIWcqNO546yVUbW/j6Gy/k4rVN7OkaJlJAefKhiThfvu+A6zbHB43UaXaPMMDW5TpgrhSkUoor/vk+bn/iWKm7UjZ0D0dyyiIARITG2mBFeoS1ITxL9I9F07IIC11dTgMwaD5xN+WQRpQqs0I0MdXjCblLLDv1wVO2sxvCyRRBv+DziS1HcnkZwsmUQqmZ6XetAMNs2zmLlBjyi+IaWs7S2G0NYZIplX5AK0eiiRQrGmvw+YRzVywikVLs6fLu5b5vbzef+91+vvfIkYx1Vg5hu0YY4Ozli+gbjXFqWM/yzSUD4zE6hyJ09I2VuitlQ89wlLYcgXIWRlEN7RHWFImBsViGBrS1PqyjsxcAPSMR3vVfO6b9UGM9cXvLGjH3GmG7BtZa5kbMZjTbmSzEMbldPDE1yAzKL1guM7XZ9D3C2cbVLVhu1jzCvklpBJR3CrVoIpn+nzl3pZGb+9njpz1v3zVkGLNfe+AQw5GphsCJwQlqQ34aa6bqK7cu1wFzpcD6no5GdVlwLyilODUcYUm9F0NYe4Q1RaR/NDM9luUR1lNp5c1Pdpzg7l3d3Ld3egE5/R40wqXymtrlDtbUea5pfDePsJsBbfcel2v6NKvCXloaEZhJHmHvwXLxIl+nuM07D6Q9ReU8WxVLpNLfq/aGKtrqwzxbgE741FCEoF84PR7nWw8enrLOyhjh1FduWboIn6ArzM0xPWaGk3FtCHtiNJpgPJakfVFuaQQYHmErmLuS0IbwLKCUom80mi6vbNFaFyaaSDGi/4HLml891wXAM8en9wM4MBajoSqQtdQlGHqtcMBXGo1wwJvnNqtG2MWb7azIZm1fTqQlBek8wpn5kvPuI49G2BksN1seYfu4pT3CZZpCTSllSHrMayYinLNiMc+eKMwjvL61jpee3c63H+ygf3TyoeD44HiGLAKgOuRnQ1udzhwxx1izqqPRyisFPB0mU6d58AjXBKd89ysFbQjPAmOxJNFEKiMYSucSLn8O9Y6yp2sYn8AzBUy92jFkM/mfzkMB39xnjTC9hTA5dZ7de6ncNcIuHuGoXRqRrlhXXj9kTm2t5YEsxCucr7Jc3FGkZLYqy9nHzbovlWsKNWdeZIDzVi6io3eMoQlv3q1TQxHaF1Xx1y/axEQ8ydf+cAgwjOzjAxMZgXIWW5ct4rkTp0mVcaBhuWH9fo5ph5InekwNe5snaUSY4UiiLDP6zARPhrCIvERE9onIQRH5sMv6RSLySxF5VkR2ichbi9/V8sF6onIaO23aEC57fv1cFyLwZxesYN+pYcZjhd+MB/JUlbMIB/xzrqONJRQhs7yzzycEfNmrp0XzeITt29mnrstVIxx36HeDLtkx8uE1a8QUj3Cx8wgnp45bOOBncU2wbD3CzgcUmNQJP+9RHtE1FGHpoio2tNXzqvNX8IPHjzI4FqN/LMZEPDkldZqda85opW80xo6jgzM8C41XLMNuOvfeSuRUuqqcF2mEoYMfrLAyy3kNYRHxA18BbgS2ADeLyBZHs/cCu5VS5wLXAp8Xkfy/9AsUSwOqPcILj18918lFq5t4ydZ2Usr7D62dgbFYTn2wRbhEHuGQrUBGrswI+TXCUyvL2YPMoHylEU7PdiEa3lgejbAzWM6SXxSTWEJlBDkuqa8q22C5qJnyzH5O5yw3A+Y8yCNiiRR9o1HaGwxj951XryMST/HfTxybzBiRxSN8/ZlLqAr6+OWznTM6B413JqUR2hD2QkHSCLPM8mCFZY7w4hG+GDiolOpQSsWA24GbHG0UUC9GNEEdMABU7LfUKq/sljUCtCFcruzvHmF/9ygvP3cp5630/kPrZGAsljOHsEVJNMKJqcZt0J89IMzIGpGZoN3ylE4JlptSkS13EN58xVlSOjgNz3a+rBEZeYRnySPsfIBpawjTXab3Jev6W0VoABbVBFnbUuspc0S36TFbusgwFM5or+eqjS18/9EjHDZTdLlphAFqwwGu27yEu57vIlFmMxzlSk9aGlFe0qpS0T0coT4coDacv35ao+kRLudUitPBiyG8HDhu+3zCXGbny8CZQCfwPPBBpVTF3hWySSMWVQcJ+oXeChSjLwR+9WwnPoEbty6luS7MyqbqgnXCSikGx2M5cwhbzIYRlA/ntHnQ78tptOXKIzw1WE6ljTsRo3xztMwMh7RsIUPr7P08Cq0sF/LPQmU5l7R3rfVhess0H276AcVxTuesWOTpQdWaOm5fNOkxe9sVa+kejvKN7R0ArGh0l0YAvPycpfSPxXisY6DgvmsKx5LwaI2wN7qHI7R5kEUANGuPcFbcavI5XUQvBp4BlgHnAV8WkYaMHYm8U0R2iMiO3t7egjtbLmSTRoiIri5Xpiil+NVzXVy6rjnt2T93xWKeOVaYIWwEIihvHuGgv6R5hMHwSmedxk9mqyznkj7N4WkOTyMHb6lxeoSno3W22uYqWw2TgYqzphEOTL2tL2moone0PFM7Oh8eLM5dsZju4Wja45sNK4fwUpshfM2mVta11rL31AjNtaGc3rQXbG6jNuTX8og5QCmVlvCMxRJl+X2da7qHI1Me8nJheYQrLZewF0P4BLDS9nkFhufXzluBO5TBQeAwsNm5I6XUN5RS25RS21pbW6fb53lP/2iM2pCfKttUnYUuqlGejEQTdPSNcfWmye/teSsX0zkUSQdveGHAQw5hi1JII5yptXJlLchWUMMtWC6aTKWD8Kw25WYIWxKRDI1wAYawlYs4m67YmeN3OkU78vYhmTlubfVh4klVljlEresTdhjC61prAaMgRi5ODRnr7caCzye89Yq1AKzIIouwqAr6ueGsdn6761TZfafLjeFIgmgiRUtdiJSCyBzHUJQj3cNRT8U0YPJ3qdKqy3kxhP8IbBSRtWYA3OuAOx1tjgHXAYjIEuAMoKOYHS0n3MorW+gyy+VJz3Cm1+j8VYZOuBB5hGUIe5FGGIZwCYLlHBrhXCWWgzmD5aZWlnMG4ZWb0RBLmkFZjsp7hZxHNI9H2PkgMp2iHXn74JLtw0qtlM97Oh/J5hG2MrMMjuWOgO8ailAXDlBfNbVy3J9dsJzGmiDrTYM6Fy8/ZylDE3EeOrhwZzrnA72mLGJNszEmOmAuN0opekYinsorg3FPa6gKaI+wE6VUAngfcDewB/ixUmqXiNwqIreazT4JXC4izwP3An+nlOqbrU7Pd/pHM8srW2hDuDyxpuPsuRjPWraIgE+mZQh7DZaba2PR6S3MmzUih0c4W2U5q025pU+LJSyP8GQgGxTqEZ7MI+w2rWtoqR0PIgUW7cjbBxdtt5Vayets1XgsMW8S71uzJs5zSnu38qSCsnIIO6kJBbjjPVfwf196Zt4+XLWxlYaqAHc9f8prtzXTwLoPr20xDGGdQi03A2Mx4knlKXWaRXNdmIEynBmaCfnDCAGl1F3AXY5lX7e97wRuKG7Xype+0SgrsqTbaa0LMzAWJZlS+H1u8mvNfKTb9ETYgw6qgn42L60v0BA2buRe8wiXosRyKMMQy5U1IrtH2FlZboqnsww1ws5guUmPcOEFNYz3ipBDqxt1aqltRTucbaeLuzTCMAS9ynz++Td7uX9fDw/8zQvSMo5SMSmNmCpFazT/x07nMYStHMJuWAZXPkIBH+evamR357Cn9prpYT2orW3VHmEvWKnT2j16hAEaa4LaI6yZOf1jMVpyeIRTKnt6kt6RKH/Y18OpofKbolzI9GTJxXjeysU8d2LIc2UpK5DSmyFcihLLakoglWGwuvfB2da+jbXewmk0l6U0IiNYbhoFNRxecidOI3U6RTvy9sFNGlGgR7jzdITjAxM8Pw/KC2fTCNeG/IT8vrx6x1NDkYIMhWxsbKvjUO8oSV1lbtawMkasNaUROoVabiYdON6/30214YrTCHvyCGu8k0opBnNUDms1PS+9I9G0F2Y0muCr9x/kf58+mY5gvm5zG99+y0Vz02lNXrqHo9SE/NQ5osdXNtYwGk0wEU96ytM4OBajKuijJpS/bUlKLCdShPxTg9om4u4/Ns629m2s9RZxh564HKURkzl+rWA549wLKahhbxtPpMAxY+nMrjGlaIf32c3cfXApjV0V9FNfFfDsER6JGD+Uv9t9Kl3FrVRk0wiLCItrgjk1wolkip6R7B7hQti4pI5oIsXxgXHWePQkawqjZzhKVdDHEnO8xrQ0Iic9BVSVs2iqDfL8ycLz45cz2hAuMsOROImUyhksB7Cna4SQ38fTx0/zubv30TMS5UVblvD2K9ey48ggD+zvJZpIZkz3aUpDz0jEtTKPlRkkmkhR6+Fe0z8WS+dqzEe4BMaiM7VW0C8MR3IFy2V6hP0+wSdTZQBRp0e4DKURzlK+wWl6hEVAqewe4aAtqHA6RTvy9iFLaewlDVWePcLWlPTvdnXzty/OSBA0p2TzCIMx85JLI9w7GiWloH1R9jzBXtm4pB6AAz2j2hCeJXpMB5LlkNC5hHNzaigztiUfTbVhBsfiKKUwaqQtfLQhXGT6zKpy2aQRVlDG3/zk2fSyc1cu5j/fdCHnr2oEYE1zN7/ddYonjwxy+YaWafWjkr7Ec0HPcDT9EGPH+vGNZPGaOhnIMVuQse+gf049wkopYokUYadG2MVgdWtrxxlkF0ukphgqoYCv7PR9zvLH00mfFkukqAsFGIkmXK+rm5bafuxi4FZZDowUaoUYwn6fcKBnlI7eUda11hWtf4WSzSMMRsBcLo2wWw7h6bKhzbgGB3pGeNGWJTPenyaTnpEIbfXh9OybNoRz0z0Sobk25Pq/kY2m2iCxZIrRaCIjk8pCRRvCRSZdVS6L12/54mq+/sYLGY7EqQn5aa4Nc8napikBJ5etbyboF7Yf6JuWIfxfjx3l339/gDvefTmrmnPnwNR4o2ckwtkrMqeA7R5hLwyOxdJBPPmYa41wIjU1Ty5klzC4tbXjrEjnNPDCAR8DY+XlEbY0z85guUICGmPJFIurQ4Yh7HJdncFy0ynakbcPWUpjt9aHedpjgZiRSIKrN7Zw/75e7tndzbuuKZ0hbGnY3WbPGmuD7Ds1knVbKxbDa8GBXDRUBWlvqOJA9+iM96Vxp2ckyub2empDxlhrjXBueoa9p06zaLJVl6sUQ1gHyxUZyyOcy+v3kq3tvGbbSl5+zjIuW9+cEXVdGw5wwapGtu8vPCflT3Yc56M/30nfaJTf7dapfIqBUoru4ShtRfAIG9IIb4ZwyO8jpQwd41zgDAaz+uDm8XRra8e+XSKZIqXITJ9WbtIIxzlPZnQopMSyojbsz7pdNo9wMcssZyuNXRsOeE5HNRpJcEZ7A2cta+B3u7uL1rfp4JSs2GmsCeUsElJMjzAYOuEDPdkNb83M6B02pBHaI+yNrqFIQfpgMDzCkD2gfyGiDeEic6R/DGDGntirN7Wyu2u4oJzDv3y2k7/72XNctbGF9a21PDANQ1qTiRUM53ZDKdQjXJg0onCP40xwBoNZ77NN4Tvb2rEbus6KbGBqhMswWM4npNMeFlpQI5lSJFMqrW90284pIZlO0Y58ZNMI1wT9jMfyP9BFE0liyRT1VQFu2NLOU8cG09H8pcCSD7ml8muqNaQR2bK6nBqaoCroY1F1cTxfG9vqOdgz6jmLjMY7E7EkI9EErfVhgn6fIa/SwXI5OTUUYWmB+ve0RzhP2sGFhDaEi8yh3lHaG6oysgsUytUbjVK+XisV9Y1G+esfP8OFqxv5zzddyAs3t/F4x4BOOF4Eul2KaVgU4hGOxJOMx5LeDeFAYUb2TElrYB2eW7fKZvk8wkGbR9jV01yOHmGXoiDg3VtrtbO8We4eYZUhTSnkGPlIpRSJVGbWCICakJ+JeDJv8Y6RiHFPqa8KcMNZS1AK7t3TU5T+TQcrADHoIvdYXGOU4h2OuHuFu0xDoVjxFBuX1BGJpzh5OndZZ03hWA9b1sxcXTjAuJZGZCUST9I/FmNZgbMdTWYhmv5RbQhrpsmh3rF0jfuZcNayBppqQzy431uBvu37e4knFR97+VnUhAJcs6mNWDLFYx39M+5LpdPjUkzDImx6hL0YwgMF5BCGSSNornTClofWGSznlh4sPR2dM1jOMKiiyczKX7lKN89XnJ7UQr211gONZQi7PeBkZI2Yhg45F7EcnvzqUAClIJInQHPUNITrwgE2t9fTUhfmqaODRenfdLByVLsZs9Y070CWFGrFyiFssWmJoZXe363lEcXGCuS0NK81Ib+WRuTAKpdeqP69yQz01x5hzbRQStHRO8r6IkRQ+3zClRta2H6gz9M02/b9vTTXhjhrWQMA29Y0Uh3088A+LY+YKW7llS2qCpAvFGoIW97muTIYJz3C9vRdQnQaGmF7sNxkkJmtUEcZeoSzF7vwNg1ueXXr0h5hd097KDA1j3O2ttPB6oNbqrEaMwAp3yySle2jLhxARGiqDaa9xKXAGWBoxyqznE0nnKuq3HTY0DqZQk1TXCbvw5Me4XLLPDOXTOrfC5NGWIVorJnQSkAbwkWkdzTKSCTB+iJ4hMHQCfeNRtmbI+oZjOnOBw/0cdXGlnTgXVXQz2Xrm7VOuAhYHmE3jbAlX/DiEbaqynkNlptracSkwTppiIVNiYNzutxN92vHnj4tmzTCzcCezziLXYhIQfmQY2mPsH/K5yltHB7hYqdPc6aAs1OdNoRzf5ctmYEVUV5qgySaSGXNt542hF08wqmUons4UpSMERaLaoK01Yd15ohZwCmNMII7tTQiG9PNiCIiXLKuiV8+2znnlU1LhTaEi8ihHiNQrlg5Na80U6c9cii3PGJ31zD9YzGu3tQ6Zfm1Z7RypH+cI31jRelPpdI9HKU6mFlVDgr1CBtP2IV6hOcql/CkkTR1al4pMsrG5s8aIbZguUzjK2wakPn0qPMJZ0YHyMyXnG97yK0Rdsu3nK3tdEg/7LiMW7Up88lWSdBi1KYRNv4G05XmSoHzmtmx/tfcimr0j8VIpJRroZyZsGlJvc4cMQv0jEQJ+CT9cFMT8obwuhEAACAASURBVGuPcA5mkhHlL65aR89IlF8801nsbs1LtCFcRDr6DC/A+rbiGMLti6pYvrg6b25Py+t71caphvA1pmG8/YD2Cs+EnpEoSxrCrhrEtNfWk0bYMBbmu0bYSx7bSa2pe5CRa7CcaxBY+RjCboUogjaDP+/2lkc4lD1rhNPYTssv5sAjXOPRI2yXRgDUVRkFQkpFNJHMLo0w/9fcimpYGsjmLMWPpsuGtjqdOWIWsIoaWbOedeGA1gjnoGtogoaqQPrBuxCu2tjCmUsb+Mb2jor4HnsyhEXkJSKyT0QOisiHs7S5VkSeEZFdIvJAcbtZHhzqGaM66GdpET0MF6xu5KljuQNRHtjfy5alDRmVz1Y317KmuYY/aJ3wjOgejmQtUVmIR3hoIo6IkXjfC6XSCIdcAsLiCac0Io9H2C6NsIzmWS4UMdvEEmpGHuGYwyPsXmJZuT4wFOs65cq5a0kjJjwawpZHuKEqUFKNcC6PcG3IT9Av6YdQO5Zm3/IwFouNS+oYjyXpHNKZI4qJVVXOolYbwjnpmkbqNAsR4V1Xr+Ngzyj37ytdRpi5Iq8hLCJ+4CvAjcAW4GYR2eJosxj4KvAnSqmzgFfPQl/nPYd6R1nXWptRIGMmXLBqMV1DEbqy3FRHInGeOjqYIYuwuPaMNh451MfQhPvUpVKKw1o6kZPekahrxggoTCM8GklQFwp4/n6EC8xRPFPcjNtgNo+wi9Fsxx4sZ7W1Z6OYjdLBs41bIYpCsl9Y7epyaYQTqakPDLOkEXarLFdjeqon4rmNC8vorTMN4bpwIC2XKAXZSkaD8YPeWBNy1QhbXuJiG8KblpgBc1onXFRODk6wbPGkYVcb8jOmNcJZOTUUYeni6TvlXnbOUpYtquI/H+goYq/mJ148whcDB5VSHUqpGHA7cJOjzeuBO5RSxwCUUgv/EcKFjr7RoumDLS5Y1QjAU0fd5RGPHuonkVJcvcm9FPOfX7iCSDzFz5484br+f58+yQs+9wd2dQ4Vp8MLkFwe4aBf8Ik3Y3UkEk8bD14Iz7U0wmXa3DJenYZwQR5h12C57MbgfMWtNHG2EtRuWDKQbBphpZQZLDebGuHs4+ZVGjESSRDy+9IPgfVVQSbiyaJWvyuEaDy7RxgMKZJbKqhCpUpe2WD+BhzUmSOKRiyR4ujAOBtsskPLI1xOcQZzyUwzogT9Pt5+1TqeODLAcye8lV4vV7wYwsuB47bPJ8xldjYBjSLyBxF5UkRuKVYHy4VIPMmJwYmiZYywOHNpA+GAL6s8YvuBXmpCfratbnJdv3X5Is5ftZgfPHY0Q+ujlOKbDx4G4I+HB4ra74XCaDTBeMy9qhwYHqdwwO/NIxxNFFRoZVIjXEqPsGH4OXMJ59KawtTKcW7BcqE5ln0UA9dguWlljXDXCFuG8mxWlsuZRzjoVSMcT8siYFIrXKpp6lweYYDFNUFXQ9hatrimOFXlLBprQ9RXBTg+OF7U/VYyxwbGSKbUlNSkteEAiZSas/tjORFNJOkbjdLeMD1phMUrzlkKkDdOqdzxYgi7zeM6H8ECwIXAy4AXAx8VkU0ZOxJ5p4jsEJEdvb0LS7d6pH8MpShKDmE7oYCPs5cvcjWEUynF/Xt7uXx9c84fglsuW01H3xgPO7JPPH54gD1dwwA8c3xhf9Gni5WUPJs0AgydsJeb8Wg0McWAyEd4jg1hNyMprRHOGiyXTRohaV1xtvRpxn7KZ2rTzeCaTtaIuiwe4ckHhqn5lt3aTpd4jgeYGo8a4ZFIYsrMhvWdLpVOOJpIZpXogOHxdSuoMTgWoybkT5dJLyarmmo4NqAN4WJx0MzINMUQ9jiDUYlYOZdnmiO7tT5MTcjP0f6F/V32YgifAFbaPq8AnDk1TgC/VUqNKaX6gO3Auc4dKaW+oZTappTa1trqrmktVyZTpxXXIwxGwNyuk8MZU+RPHRvk5OkJXmY+tWXjpWcvpbk2xPcfPTpl+W0PHaaxJsg1m1p5WhvCrlg3lCVZpBGAZ4/wcCRBncdAOWu/MPcllsMuGlVnH9za2rFLBtyM5mz7nc84K8uBlR3D29SsdR0sz6uzEEfaI287RsBX5KwROaURhkGb1yMcmTqzUWpDOJYjjzAYGuDTLgU1BsZjRdcHW6xsrOG4NoSLxqFeQ2Zi/32tLfFMxHwmnTptBhphMGY8VzXVcLR/YccReTGE/whsFJG1IhICXgfc6WjzC+AqEQmISA1wCbCnuF2d36T/UVuK6xEGI2Aulkyxq3N4yvJfPNNJOODjRVvac24fDvh53cUruXdPNyfM6brjA+Pcs6eb11+yisvWN3O0fzxrGdJKJld5ZQvPHuFInPoCpBFhKyOFByO7GLgVyQhm8UjmK6hhL83sZjTPdUaMYuAeLFd4+rRwwOcqqZis7Oco2hHwea5e57UPbh7UqqAPEZjIU1luxDGzYRXWKFUuYWehEyeNNYZG2CkNOz0ep7G2uLIIi5VN1RwfnKiI1FNzwaHeUdobqqakArMexnQu4Uys4PpiVE1c01zLkUo3hJVSCeB9wN0Yxu2PlVK7RORWEbnVbLMH+C3wHPAE8C2l1M7Z6/b8o6N3lOWLq9MpiIrJZMDcpDwikUxx1/NdXH/mEk+609dfshqAj9zxPPfv6+FbD3bgF+FNl67hvJWLAXh2gXiFf7+72zVv6HRIl/XMkRKvEI1wIdKIUJZAtdkiZs44hFw8wk6vp1tbO3k9wuWaRzgjfZq/gGC5SW+sm6Qim9ykEB1y/j5kL6ghIlQH/Z6C5erCkwZkqQ2SXCWWwdDsptRkRTyLgbHZ8wivaqohlkjRO1o5ZWpnk0O9Y6xvmzrbWhO2ZjC0IeykK11VbmYaYYDVLTUcH5jIKKq0kPCUR1gpdZdSapNSar1S6tPmsq8rpb5ua/OvSqktSqmtSqkvzlaH5yuHesdmRRYBhhHmLKzx8KF++sdi/Ml5yzztY/niav7y+k08dXSQt37nj3zv0aO89OyltC+q4uzli/AJPJ0nX3E50D8a5R3f38G3HzpclP11D0eoCvpyenKrgj4iHqq/jUQKC5ab68pyk17eTI1qtsCubAU1rGA5pVTaM+yqES4nj3BCZZxv6P+3997hcZTn+v/9zlatepcsS7Ik94Yb7jaYDk5iSCCUHBJIAU4g9ZzkkF/aOSEJCclJAklOCMk3QAihJfRmwBAbcO+4yrZsNav31Upb398fM7Ma7U7dvtL7uS5dlndnV6N9V7PP3HM/9xOBImwxcbJKspLdxIgPWXMfBE+2kpLvsJrg0posF9oslxLWCDWPMF+094XYI/rjaI2YWuAAAGaPiAGUUjR0OsP6b8QYQqebeYRDaR8YRbbdbOjzRonqgkx4/AG0C/0yExE2WS4GUErR0BX+hxpLQgdrvHzwPLLtZlw8S7/X+quXzsD+H1yOR2+/EF9aV4P/vGIWAN5rNassZ0L4hBuFD55YNf/xU+XsslPlRGwWk2bEmT9A4fL4DcWniZfFE90sNy41QqNZTkmJk45mlp1YF1S70+dDLFbNckqKsJLdxIj9QnMffMqKMMAP1dAcqDEaao0QCuFkpUZoKMJ5QrEbav3qHfbEPDpNpEoohFnDXPR0Dbkx5PaFfb4yj7AybQMjMbFFAMC0Qv693DiB5w2wQjgGtA2MYtjjj9loZTnEwRp/3HoGAyNebD7ajqvmlak2ichhM5uwYVYJvrtxLqqENzgALKrMw6Hm/rT3tDX1jBXC0f4ugQDFifZBlGpMCrSZtRXhsWlcxjyJNjOX+BxhTmbEr8JADem2UqQT0YwozamMV6FZTq81wj1OEVb2CIfbL2KnCLs1RmM7LGbVS82U0rArG9m25HqEtawRBUIhLB2q4fMHMDjqi3l0mkiFMPihuZdNl4uW00L/TVghbGWFsBLtA6MxsUUAQHURf6X73AROjmCFcAw4JjSxzS3PjtvP+OTiqVg3owj3v3ECa3/+LpxuHzYtCo1zjpzFlXkYHPWhIc3P+kQFZmjUh7NRGvyf29eM+g4nbrqwUnU7u8WkqdqKRYKRZjmAL4QTNmLZH+AHhEgm3yk1tcltK0U6mtktU+BZ0jE1Qk4RljQFaiHNCZYbxCE3ihoQpvTFOD7NZpI/gc6wqnuE3b4AfAE67sqG3cLBzJGkTJcTh5CoCQKi6tsr6RvoH4nPMA0Ru8WE0hwbU4RjwJkuITotxCPMFGFlzg+MolxDwNFLWY4dVhOHxt70rg3UYIVwDDhyfgCEALPLcuL2M3IdFjzxhRX42xdWYFphJmqLMrGyVn6IRiQsruIb5tI9T7ixxxWMnDoYRQh4v8uDn795EhdOy8d1i9VPOGxmTjPZQVSEjVgj+OfWLrJjhZLiCcikRshsK2W8IswXzVJ7SbqlRogFV6haazEwWU7qEZZrgJPLEQaMFdua+xAsthUUYQ1rhOgDll7ZIIQgy25OikdY/H3UPMKi6ittoBXV4bw4eYQB3h7BhmpEz5lOJxxWE8pCCrtMwSPMxiyPx+MLoNvpjjo6TcTEEVQWZKCxe+K+l1khHAOOnh9ETVHmuGiXeLF2RhFe+cpabPmPi2BWKUSMUlechWybGQeb07thrql3GIur8pBpNeFQFGMh//etegyMePGjTfNV/cGAPkXYGSwgjCvCifQIh8eDKXuE1S5HWyWWCn40cfjlfvH+dMAfoKA0ukQHrz8AE0dg4oh8aoRKs1ysXievgv1CxKGhCCtd2ci2m5OSGuFWeM2kZNnMsJhIcKQyMNY4VxDHQrgy34EWpghHzRmh/yb0OGwzm2Axkbgowt1ON57b25y0seHR0Dk0CkpjE50mMtEj1OJfuU0Cjp0fxNLq/IT+TK3izCgcR7CwMjftRyk29bqwfkYxTByJWN0+0jqAJ3c14rOrpmFOubbKz3uEtSOnABju4rXqUJtjhewIYcXUCH2KsNcXkG1mCjbLpYkirNQcaKRIFe0kgLy3WG4UNSAowjFLjQiAEF7lkSPDasaIyvsteGUj5H2cZbMkRxGWSSQJhRDCZwlLPMJi41y8coQBoLLAgRcOtsLt8xvu5WCM0dA1jAunyX++OqzmmBbC/S4PHtnWgMe2n4PL44fVzMXUgpgI2mMYnSZSVejAjoYeUEpjXnukAkwRjpK+YQ9a+0cwb0r8bBGJYvm0QhxrGwwOB0k3Rr1+dAy6UVXgwKLKfBxvG9SV7xvKK4fOw8xx+MblYVPCZdHlEXZHrggnSjV1yyi3YlEWOtBBblv5xwUMFdipipi2IF+k6pwsJ3nNeLtDaDazfFEn11gXKaK9Q+nDzGExqTbLKV3ZyLabk9IspzYgRIo4VENE/D5e8WkAXwhTCpzvn7ixU/HG5fGhtX9EMZEpy2aOWXxac68Ll/1qK/6w9Qwum1OKbLsZO870xOS5E8l5capcjBVhl8c/YXOxWSEcJeK0t3lTcpO8J9HzmZVVsJtN+N27p5O9KxEhNqZUFTqwqDIPXj/FsbZBjUeF09znwtSCDORm6FOL9CjCThlvpb7nNiU0R1ivciu3rRSL5HGyinCaFcJKirDFxMEfoLrC5qV2Eos5vAFOcaBGjCfLqRWNWs1yg6PyXvdsW5KtERaNQjjTkvhCOJ9X5FjDXOQ0BBvl5AvhTJv6iZtenG4fvvj4Xnj9FK/csxYP3bwYK2oKsLMh/Qrhtn4+qaQshoVwtRihNkGTI1ghHCVHzw8AwIRQhIuybLh1VTVeOtiKhjRUhcXoNF4RjnxaXkvfCKbmO7Q3FLBbTPAFKHwqyq2olhm1RtgsiYxP84c3aimMWPb4/KoFlfRxck1mZo6AkPTxCAcLYZ2vjxzeMEVYPkdYTpWP3WQ5dW+3VrNcMAbQNv6ELjtZzXJBRVjdelCQaR2XI9w37IHdwsVlEqiIGE/JhmpEzhmF6DQRhzX6E7BAgOLrTx/E6S4nfn/LEsyv4EWtlbWFONfjCo4rThfOdDlRlGVFjkHRRY3qQj6xgxXCDFmOnh9ERV4G8uMUw5NovrSuFlYzl5aqsDhMo7owE2W5dpTl2CPyCTf3ujA1X7+/KjgBTqVYcbp94AhfaBjBKuMljRdyKq+JI+CITGqEnyomDwDjlWQ5RZgQEtPRwfFGLFrlhl0A+mLgPP5AMBrNaiaK2cyhr5UtlpPlNNI+HFb+pE5pXZziCV2IIpyVpGY5PR5hACjOsqFj0A1K+ZONPpc3ro1yAFCazcdOseSIyDneNgSOjCmSoWTZIvMIN/e68Ku3TuL7Lx7BZ/+yG+8c78D3N87B2hlFwW1W1hYCQNqpwvUdTswsjW2Ua0VeBkwcQeMEbZhjhXCUHD0/gLkTQA0WKc624daV1XjxYCvOplmmcHOvC9k2M/KFuKQLKnMNK8JOtw99Li8qDSrCgHoxJA4hMNpoYLNwCbNGKBVJSsMf9CnCVGgSC982kVPzokXJGmEzogj7QxRhnc1yMZ0sp2FpyRCGFCipwkpNn9l2C4ZGvcFCM1GIV0vUUiMAYHpJFpxuH9oE/2TfsCfu4gXHEVTkZzBFOAq2HO/A8pqC4DE2FN4aYfyK2S82n8RD757GK4fPo7nPhXs2TMfnVk8bt82c8hzk2M3YeaY3kl1PCoEAxamOoZgXwlYzh4q8jAk7VIMVwlEw7OYHUEwEW4SUO9bXwWrm8MOXj6aNYgcAjT3DqCxwBIvNRZX5ONfjGtctrkVrH38ZLBJFWM0nPDTqM+wP5p87cTnCchYGQD4ZQam4FRlrlvMrXo5PZCNgtHgUFWH9XmfpiYbqZLkoxjjr2wflkzHxioXLK6+yOd2+4EAQKVk2M7x+mvATG72K8AyhMDjVyV9q73V54uoPFqkscLDpchHS0OXEqU4nrpxXprhNZgTWCKfbh7eOteMzK6pw8AdXYOu3NuA/r5wVJlKYOIIVtYXYeTZ9FOHW/hEMe/wxL4QBXpVvYoowI5QT7YOgdGI0ykkpzrbh+x+bi231XfjKU/vTJkuxsdc17hKaqNSfNuB3FtUbI4WwqFaoFcJOt9ewPxhI7IhlpYJVTr2UsztICY5m9lFF9TitrBEq8WnS+9Xw+GnQGmGRyxFWGKgR89QIlSivYCGspAi7fbLJJznCbYn2Cbt1FsJiYXCqYwgA0O/yJsTOVpmfwZrlImTz0Q4AwBVqhXAE1oi3jrZj1BvQHJQE8PaIxh4Xzvenx8nMqU7+/T2rTN5THQ3VhY7JrQgTQq4ihJwkhJwmhNyrst2FhBA/IeT62O1i6iImRsyvmFiKMAB8ZkU1fvjxudh8tANffepAyhfDgQBFS+8IqgrGCuE8IfVhcER/rFOL4OerLDBijdDnETYanQYIamyiFGGFglWuEPMqqMciUsuAtACUksjfLVqUYrqMKcJ+2CTWiND3S9AawcVvoAa/xsqKcIZwUqdmjZC7siF6hhPtE9YzUAPgm+UKM6041SEowsOeoIUqnlQVODAw4sWAgWMQg2fz0XYsqMhFRZ6yKMEXwsaEghcOtGJqfoau7H9xemu6+IRPtvPv7+klsVeEa4uyMDDiRcfgxIsD1CyECSEmAL8HcDWAuQBuJoTMVdju5wA2x3onU5UjrQMoyLSGjX6cKNy+pgbf/9hcvHGkHT965Viyd0eV9sFRePyBYKc2MJZ1akSlaukbgd3CodCAWiSG5WtZI4yOV+afO3E+WqUhGfyl+fDMW0PxaUqWC5nfrXNoFEvvexv7GlPHmxdMdFCKgdPlER5rMFSaLGcxEXBc+IjlWKZGqDfL8e9RJUXYOSp/ZUNMkUh0lrCeEcsiM0qzUN85BJ8/gMFRb0KsEeKJ+URtMooX7QOjONjcjyvnlapul2k1BadX6qFzaBQfnu7GdYsrdPVrzCnLQW6GJW0K4fqOIZTn2nVHfxphmTDUZNfZ1Dkuxwo9ivByAKcppQ2UUg+ApwFsktnuKwD+CaAzhvuX0hxrG8S8KTkTctKKyBfW1uDO9bV4YmcjntvbnOzdUSSYIVwgLYSNfziL0WlG1tSmRxEWmuWMklCPsEJxazGFJxzoniwnDNSwyiRMKCmdZ7uG0TPswfP7W43+CnHD4+cLQ7mBGgDCThTkCG+Wo2H3K5+IJCY+LSNojVD2CMu9j4OKcKKtEV6xWU47jWVGSTZOdzjRP+IFpUiIIrxQiHHcey69R9cnmreOtQOAqj8Y4BVhQPn9Gsorh9oQoNA9LY7jCFbUFASnqqU69XFolBOZW56DLJsZu9LkpMAIegrhCgDSCqhFuC0IIaQCwHUAHlZ7IkLIHYSQvYSQvV1dXUb3NaXwByjqO5yYXRafN10q8a0rZ2HN9EJ898UjONySmiOYxQzh6oLM4G2iIjxo4MO5uc9YdBqgUxF2R9osxw9sUMsojhVePzWUGqGvWU5FEVYYHdzn4k9c3jnekTIfPp7gZLlw/y5/v/FmudBBHMonIhwCFDF5D+iJTwO0rBEyinAEf2uxQCnNQ46ZpVkYcvtwXBiykwiPcEVeBqYVOrA9DSeUJZPNR9tRW5SJ6QqDNETEkzK9lpwXD7RiQUWu5vNKWTezGM29IzjeNqT7McnAH6A41enEzNLY+4MBwGzisGxa/qRVhOWksdBPp98A+C9KqapZh1L6CKV0GaV0WXFxsd59TEkae4bh8QWC3cgTGbOJw29vXoLiLBvuemJf8IMklWjsHYaJIyjPG7Op2C0mWE2cYWuEkeg0/udoK8JDo96IPcJAYgZPuBUKMbkcW49GDJd0cpxaLJvcazYwwqd8dAy6caQ1Nd5rXoVL8Maa5cZeX7nHeRRORKRRdNGitW6azXIKFh/RGpFoj7DeEcvAWHLEbuGDvCBB2e+r6oqwq6EnISezE4F+lwc7G3px5fwyzStzDpv6+1XKue5hfNQ6gE2Lphjan40LymHmCF48mDpXqOQQa5J4KcIAsKKmEKc7neieYKOW9RTCLQAqJf+fCuB8yDbLADxNCDkH4HoA/0cIuTYme5ii1AtNF7MmQSEM8B8af7x1Kdy+AD7+2w/wi80nNMcKJ5Km3hFU5GWEFRL8xCt91ojBUb6pJdaKsNcfwKg3EHFqBICEZAnzl+7DP3gssqkRftWmK6llQDGNQsEj3O8aW6+3j3fo3v94ohyfRsbdr/Uc1qAiHD6IQ6kB0YjqrL0P6hMBRWvEiMJ72en2IVvFGpFoj7DeEcsAMENQAUVFKxEeYQBYXVeIIbcv2FzNUMbrD+DrzxwEpRQfX6hdsGYaUIRF+5w4dVQvBZlWXDyrGC8dbNU1Sj1ZBGuSOF6lXiE0D+6eYKqwnkJ4D4AZhJAaQogVwE0AXpZuQCmtoZROo5ROA/APAF+mlL4Y871NIcQYHiOXWNKd+RW5eOebF+HaxRX4/XtncPEv/oXvv3gE757owJ5zvXhmTxN+9dZJtCYhaqapZ3icP1jEyOjXll4xQzi2irAY7xOJImzTMawjVqhdmg9PjVBXFsOa5ZRyhGV+rz6XFxYTwbLqfLxzLDUKYa34NH3NcmOvg9wgDqXXKZZXBbTWzaEyUINSKqSfyKRG2JLjETaiCBdm2VCYaQ1Om0zUNFBxQtmHZ7oT8vPSlUCA4tv/OIx/nezCT65boGtQlZH3nZjcEUkj2bWLK9Ax6E7pprn6BNQkCypy4bCaJpxPWPPoQSn1AbgHfBrEcQDPUkqPEkLuIoTcFe8dTFXqO52Ymp8RPCOdLORnWvHLGy7Ak19cgfkVOfjHvhZ8/rG9uOHhHfivf36Eh949je++8FHC96u5b0Q28izbbsGgTpVqLDotMkXYraCiKU3j0oP4AZ+ILGG1Zi2PzsYuERNHYOKIEJ+mf1AHwFsj8hxWXD63FMfaBpNyYhXKWMavfLNcJB7h0Mfxr6lMU6GoOsfMI6wdnyZ3qXnE64c/QGWtEVYzB5uZw1ASrBEc4e1bephekhV8zRPRLAfwueyzSrOxg/mEFQkEKH782nG8cKAV/3H5TNy8vErX48SiVs8xPppC+LI5pciymfHCgdS1R5zsGEJVgSN4MhsPLCYOS6snnk9Y1ytGKX0dwOsht8k2xlFKb4t+t1Kf+vb4dWemA2umF2HN9CKMev3Ye64P3kAAdUVZeONIG+5/4wTeO9GJDbNLErIvw24feoc9sgVsToYBRbgvPoqw+PMjU4Rjd1lcjUCAwheQVwstJg5eyc9X23b84/i0CY+SNUIhFqzf5UVehgWXzS3F/W+cwJbjHfjsqmnGf6kYomSNMOIRlqqxsh5hDUXYG4P3gFZqhIkjsJk52clyTo0TOn7McqJzhP26EiNEZpZmY9fZXtjMXLDoTwSr6grx9J4mw/s7GegacuM/njuEbfVduG31NNxzyXTdjxWz4qV2KiXEQjgngkLYbjHh6vlleONIO+7bND9oIUol4jFaWY4VNQX45Vv1CRlTnijYZLkI8PoDaOh2TupCWMRuMWHtjCJsmFWCqkIHbl9Tg9riTNz36rGEDUto7hOnwckowjaLbt9ic58LDqvJsFKk5RF2Bq0RkY1YBuJvjVBSPAHAah4fn6a27bjHmTi4PD5QqvS8StYID/IcFtQVZ6G2KBNvp4A9QmxUC22WiyY1IvRxSmOrpQkc0aKVGgHwDXNy1oghDYuPET9+rNDKsw5F7KgvyLQmNPZydV0hRr0BHGxKzdSdZPHh6W5c/eA27GrowY+vnY8ffnyuoXXJFY7VegaWDI54YTNzwUmgRrlucQWcbh/eSZG+BSkeXwANXcNxS4yQskKw+uw+N3FUYVYIR0BjzzC8fpqQN126YTVz+P7H5qKhexh/3XEuIT+zWfD2Vso0uRnyCAuJEUY/IC0mAo6oKcL8QTqqZrk4WyPUBhOExpzpHWJgNXNwCVOfFJvlZIq7fpcXeUIj06VzSrCzoUd3Tmi8iFYRppTKpkZ4QhRh2ROGWDbLaSjCAO8TlrNGaF3ZyLabE58aoeP3kSJO3MpLUKOcyIra+9LYkgAAIABJREFUQnAELEZNws6GHtz+2B7kO6x4+Z61+LeV1YaPvTazCQ6rCX3DHs1tB0a8EanBIitqC1GWY8c/9rVE/Bzx4nSnE74AjWujnMjCqbmwmTnsamCF8KRG7M5kirA8G2aVYMOsYjz4zin0JCBmRW0sspHLtfwwDWP+YAAghMBmNmkqwpFMlrMGC+H4KsJehUJPvE16WV5t29DHib+7fI6wSdUaAQBzynPg9VN0DCY3rsfrDwR9z1IsJn3rE5xMJ/hz5Ypbrz8ge3JhkSmaIyFYjGusm93CySrCY9YI+WIiy6b/pDNWuL3yr5kSY4pwYvzBIrkZFiyoyGU+YYFj5wfxpcf3oqrAgefuWhVVAZeXYUG/DkV4YMQb1cQ1E0dw8/IqbK3vCjbLpwo7hOa1ZdMK4v6zbGYTFlflYW8KTf6MFlYIR8DJ9iEQMrkSI4zy3Y1z4PT48Nj2c3H/Wc29I8iwmGTHIosqlZ7Ym5YIhmmI2C0cRhUizqLyCCeoEFYbTGAJUW71DjGwmjkMC0quRUkRliuER8a8Z+K/vToUn3jiUWhkG0t/UH9/haZOyGUDKw00sYlRdFG+B/wBCkq1ExZ4RVjGI+zmiw1VRTjRhbBBRVhMjijItMVxr+RZO6MI+5r6dKmXE5nmXhdue3Q3suxm/PXzy6NW53MdVt0e4WhHD9+6qho2M4c/v39Wc9sRjz+YGBRv3j/VhdriTFTkRfb5ZZR5U3JR3zGU0nFyRmCFcASc6hxCdYEjYq/RZGB6STaunFuGx7efi7tvsLnPhcqCDNnLauKHttYl2wGXF0OjPsONciJ2i0nRvhAshBWUNDXGEinirQiLk9O0m9rUtpXCK8LCCFyV1Ajp9LhRrx+j3kDwA0vMek128aA2FES8X+vx0u1lPcIKE/hipQgHvd0ahWOG1SRrjRAn/ikVE1kG/PixgleEjR2Hf3vLYnztUv0NWbHi6vnl8AdocHzwRMLrD6C1f0QzW35w1IvPP7YHo14/Hv/8ckyJQeGWl2EJDuFRIxaFcEGmFTcsm4oXDrSic2hUdptAgOKZPU1Y9bMtWPbjd/A/rxzF+Tgm37h9fuxs6MH6GYkbUjarNBuj3gCahWzmdIcVwhFQ3+GcFBPlouXLG+owOOrD33c1xfXnNPe6FKfB5QgNalof0M0RRqeJ2MzKirDT7YWJI8F0CUPPG0ykiLdHWN3LK1Uu1bYd9zgTF1RELGZlNVVa4InKTp7QBFMgFsKu5BbCSrYFaUyc1uMBOUU4JD5NwaMdum0kiCcw2oqwSXagRtcQb08pzJJX8LLt5sTHpxlUhAFgdV1R0CucSOZNyUF1oQOvHm5L+M+OFz1ON3675RTW/OxdrPnZu5j9/Tex8L8346tPHQibPubzB3D3k/txtnsYD9+6NGbWwjyHJWGKMAB8YW0tvIEAntjRGHZfc68LNz7CR4nOKMnC1QvK8MSORqx/4D38+NVjcRlCta+xD6PeANZOL4r5cysxU7CynEwxi0iksELYIG6fH+e6E9Odme4snJqHtdOL8OcPzsZtCh2llG9yk/EHA2OK8OCI+gd0pNFpImqKsHPUh2y7OaIu9Vg2Sqnh8Y33sEoRY9D0bDvuceaxQthqClft5H63fkHZEZXgfMHLmexCWC1tIfT1kcMdpgiHT5ZzK2T8xmqynFs4gdFShB0KinC3043cDIuiAivakAIJvFzq8fllrzakIoQQbFxQju1nepJu9YkWSike+/AsVv/sXfzv2/WYVZaN+66dj/+8Yiaunl+ON4+044pfb8Nrh9vQN+xBc68LP3z5KN4/1Y2fXDcfq+tiV7TlOfR5hAdjVAjXFGXiirmleGJn4zgL0cCIF5/7y26cbB/CA9cvxDN3rMKvPr0IW7+9ATcsm4o/f3AW1zz4PvY19kW9D1LeP9UNM0ewsq4wps+rhjilsb6dFcKTkrPdw/AFKGuU08mXL65D15Ab/9wfn07bfpcXTrdP0dsrdglrKcItwQi22CvCQ6O+iBIjAKkiHGdrhIrv12oywR+gQT+YXo+wTdIsJzsowhxe4PUNC4qwsG5ZNjPMHEHvcGIvuYeilr+rlIcc+nhgTAWXmyynpDqPJUxEV2AGI+A0CscMi1m2Wa5ryI3ibGVvbbbdDEoBVwJHr7t9AV3jlVOFjQt5e8Tmo+lrjxhweXHnE/vw368cw+q6QrzzzfV44gsrcOvKatxzyQz8/PqFeOUrazE1PwN3/30/Ft/3NtY98B6e3NWEO9fX4sYL9Q3L0Euew4p+l2ecxSqUQIBiyO2LKjVCypfW1aLf5cX3XzyKoVEvfP4AvvLUATT1uvCnzy7Dp5dVghMaayvyMnD/Jxfi719cAbcvgOsf3o5t9V0x2Q+A9wcvqcqP+DMmEjJtZlQWZEwYRXhyjUWLASwxwhir6gpxQWUe/u+9M/j4BVOCVgUlvP4ARrx+ze1E1DKEgTFFWKubvaVvBNk2c8SKgU3NI+yOohCOIkd4Z0MPZpRkoTBLuzFILRtYtDXwyQmmYPGm6RE2kzFFWOfoYNHrJ+aDEkKQn8l/0CUTpYxfQDkGLvTxgLpHWHGyX4wU4aBPWcamIoVXhMP/XrqdbhQp2CKAsTSJoVFvwj6UPb4ArI70KYTnluegpigTr3/Upnt6WirRN+zBpt9/iPP9I/jexjn4wtoa2Stds8qy8fy/r8aLB89jaNSLTJsZpTl2rIvD5fu8DAu8fgqXx6846XVolM8zj4UiDABLq/Nx5/paPPJ+Az443YXFlfnYVt+Fn31yQTBnN5TV04uw+Rvr8bGH3sePXzuG1+vW6Z6IqESP042j5wfxzctmRvU8kTCrNDs41jndSZ8jSIpQ3z4EE0dQW5yZ7F1JCwgh+O41c9AxOIqvPnVAscv02PlB/OiVY1j50y1Y/8B7unNjgxnCCt5ecYjFkFtbEa7Il2+404OqR3jUp7uwl3tewLhHuH1gFLf8aSfue/WYru3VItGChZhQzIkFlZbX1GLiIC630mQ56fMBYx7hfEkneYHDmvRLyR6ffKIDIOQsaynCIf5cxclyCk2FodtGQlD1l7GpSFGyRvCKsF3xccHG1AQmRxgdqJFsCCG4ZkEZtp/pSUi0JMAfO57a3RR1ggGlFPc+fxhtAyN46o6V+OK6WtXjpdnE4fqlU3H7mhp8elklLppZHFRJY4nYT6Bmj4hmvLIchBB855o5eOHLa1CQacObR9tx2+ppuEnj5CbLZsa3r5qN+g5nTPKIPzzTA0qBdTMT1ygnMrM0Gw1dw4ZO0BOVomGU9DmCpAi7z/ViTnk2G5NpgOU1BfifTfPwr5NduP/142H3/2NfC6556H38bWcj6oqz0O/y4v1T3bqeu1klQxgwpghH6g8GRI+wgjXC7Y0oQxiIXA188WArAhR4/aN2XR+4bjVrRMiIX73pA9KiTq3AG2eNCGmWA3ifcLI9wmrWiNB4OTk8If5cuWlxXj+VfU1FW0nMFGENb3eGlX8vh560djs96oqw6MdPYCHs9hnLEU4FNi6YAn+A4s0E2SNeO9yG7zz/EW5/dE9Uhcize5ux+WgHvnXlLFyYgLxaveRm8O9JtatGsS6ERRZV5uGVe9bgmTtW4vsfm6vrMVfPL8OSqjz86u36qAcFvV/fFcyoTjSzyrLhC1A0dDt1bR8IUFz14Db8VKYGSDbpdQRJMi6PDwea+rAmgd2ZE4XPrKjGbaun4c8fnB03ce542yC++8JHWF1XiN3fvRRPfmkFcuxmvHVU3xjLlj4XcjMsioqrnkKYUorm3sgzhAFeuXUrDdSIwiPMcQRWE2fIGkEpxQv7WzE1PwMefwDP7tVWHrwqKq9YtIkeU92KsKRAkc0nlikG+0c8sJo5ZEiiCfMd1mCBnCx4tVa+gAydvCf/eDFyjgj/jj8JEIddKI2iBqJXhPV6ux1W/rWXJkeMePxwun2qHuEcnVGFsSTdFGEAmFOejZmlWfjft+pxuCX+I5cPNvfDauKwr6kPtz26O6L1aehy4r9f5j3BX1xbG4e9jBzxpHlA5RgRr0IY4JXvFbWFYcN2lCCE4Lsb56BzyK0rj1gJSik+ON2NNdP1/+xYIg5BOamzYW77mR40945g3pSceO5WRKTXESTJ7DnXB6+fYk0MO14nE9/bOAcbZhXjBy8dxb3/PIyuITe+/OR+5DkseOjmxchzWGExcbhkdgnePdEBn44P/ubeEdXIM5vZBKuZw6BKs1y/y4thj19RVdaDmiLsdPsiGqYhwhfZ+ougY22DONkxhDvX12JlbQGe3NWoGXyuViSFqtJqjXXj9ltS1MkOipBRhAeEqXLSS675mdak5wirKsImLljoqj0ekGuWo+P+lZ0sp3N6nRZqJztSMqz8e1WqVolRWEUqfnOpRzhRRBKflmwIIfjjrcvgsJpw8yM78YHOq1+Rcqi5H0uq8/DQTYuxv6kfX3x8j2pjmRz3Pv8RbBYOv/r0orjYG6IhGdaIaFlaXYCr5pXhj1vPRNz/0No/graBUaxU8CTHm9qiLJg5otsn/MzeZuRmWHDlvLI475lxdB1BCCFXEUJOEkJOE0Lulbn/M4SQw8LXdkLIBbHf1eTz4eluWE1cSl0WSifMJg5/+uwy3L2hDk/vaca6B95FU68Lv7tlybgP2MvnlqHP5dUVM9Pcp5whLJJjVx/9OhadFp0irBQRNzjqi9gaAfDJEeKl9VAGXF7sa+zFweYxZemF/a2wmAg+tnAKbl05DS19I9ha36n6M9Qa4EIHOoQOh1BCer9qs9w4a4RnnC0C4D3CfS5PQmO5QlFrltNljdAYqDH2+suka8QoR1ivpcUhqPHS5IhOIUNYTREuEKYAdiZwHLbb609Lm1pNUSb++e+rUVngwO2P7cauhviMXh71+nGsbRCLKvOxcWE5fvjxudjZ0Gto1PPhln7sPtuLr1wyA2W5yh7xZJGXoZ01nmqFMAB87bIZGPb48WSEOfsHmvhj/pKq/Fjulm6sZg41RZk42a5tjeh3ebD5aDuuXTQlJQeRaRbChBATgN8DuBrAXAA3E0JCzTBnAVxEKV0I4D4Aj8R6R1OBD093Y0l1HjKsqbeQ6YLZxOFbV87Go7ddiAKHFd/bOCfsxOKiWcWwmji8fUzdHhEIqGcIi2TbLRhUUQuao4xOA5QVYbfPD48vgOwouuitpnBFuKXPhTU/excX/OgtfOoPO3Dt7z/Eb96ph88fwEuHzuPiWSXIz7TiinmlKM624W871Q+2QbuDrCI8lhoh/VdLiZOmE6h6hEMGaoSOXM1zWBCg2j7veKLUyAbwyrdms1zIaxY6iEPNbsJxBGaORO0RHmuW02eNkDbMiYpwsYoiXJRlRWGmFSfaB6PaTyOkoyIsUppjxzN3rkKmzazLvhQJx9sG4fVTLKrkPaSfXlaJfIcFj20/p/s5Htt+Dg6rCTcsmxqXfYyWoCKcJGtEpMwpz8H6mcV49MNzEQ1M2t/UB7uFC1oUksHMMn3JES8dPA+PL4BPX1iZgL0yjp4jyHIApymlDZRSD4CnAWySbkAp3U4pFeW7nQBS8y8mCvqGPTjWNshsETFiw+wSbP/Opbh9TU3YfVk2M1bVFeLt4x2ql/C6nG54fAFUahSw2oqwegSbHpQUYbGDPjvC1AhAjGYbXwQdbO5Ha/8I7rqoDv/vc8tw/dKp+M07p/CZP+9C15Abn1xcAYBXHm++sBLvnexUHYcpZtTqyfvV23QlTScwkhqRF/JhJSqNvUlsmFOa+gbwBb/R+DT++7HHeTXUWn66X6ya5bSsEeGFcJcORZgQgjnlOTjelphIpUCAwuunadcsJyU3w4J1M4qxtb4rLlc8xCtFiyp51dBuMeGm5VV453hH8LinRrfTjVcPteFTS6ZGnHwTb+wWE+wWLljsyjEw4oXVxEU03TOe3LGuFt1ON146cN7wYw809WNhRZ7m33M8mVWajaZel2bT3zN7mjG/IgfzpiS+qU8Pel7BCgDNkv+3CLcp8QUAb8jdQQi5gxCylxCyt6srdoHSiWBHAx9Tspo1yiWEK+aVorHHFcxtlkMs7LQK2Gy7RdW32NI3ghx75BnCAH8w9gVomK9ZbEyJJlfVZubCFAMxNu7uDXW4dE4pfnH9Qnz54jrsOtuLHLsZl8wpCW67ceEUUApVq4lYJNlkorUsIZfmPcHBDOpXRnQrwiGT5fJDFOF8sRBOok/Y41dWhPU1y4WrsdJBHKGT50Kx6BjaoYW4btrNcvx7dURGERZPSpSYU56Nkx1Duvz90aK3+S/VuWhmMbqdbhxri72Sfqi5H6U5tnGWhn9bWQ0AeGLn2IhgJcHh6d1N8PgD+Nzq6pjvWyzJy1DPGh8Y8SInI7LpnvFkzfRCzCnPwSPvNxg6EXL7/Dh2fhCLq/PiuHfaiPMUTql8Th9pHcCxtkF8ellqqsGAvkJY7p0ju2KEkA3gC+H/krufUvoIpXQZpXRZcXHic++i4YPT3ciymXHB1NQ8o5loXDanFADw9jHliKGx6DR1RThbh0c4GjUYQFBpCFVuxZ8bjUfYag4vglr6XMhzWIJKMyEE375qNh68aRF+/qmF43yT1YX879bYo6wAjSmSKiN+Qz3CGoMZxjXL6RyowVsjxp+QiIVxModqeH1UsRDWU6TKFW3SQRyhzXSh8NtGpxjqTfsYs0aM/c10DblRkGnVVJ/mlOfA4wugoXs4qn3Vg1vn75PqrJ/JiytbYzhtTORgcz8WVY4vliryMnDF3DI8s6cZTrcPf91xDkvuextL73sb1/9hO+7952G8d6ITo14//razCetmFGF6SWoPkMpzWFStEYMj3phNlYslhBDcsb4Gpzudhtb/SOsgPP4AFlcmxx8sEkyOULFHPLOnGVYzh00XqOmnyUXPEaQFgLSUnwogTMcnhCwE8GcAmyil8XH+J5Htp7uxsrYg6kkwDH2U5tixuCoPrx5uU1QrTnfyZ6HairB6Idzc69IsprUQC89Qe4R4uS6ay4oZFlNY5FFz34hsk+CmRRW4ekH5uNvsFhPKcuxo7FUuTtSKpFDlVq/X1BKifoY9b0gawojHD7cvEJwqJ1LgSA1FWKnw1zNZTi6xQTqIQ22yn7htzDzCGgpqhkx8mtZUOZG5QjTS8Tiom6GIV0lsKdh8Y4SSbDvmTcmJeSHc7/LgXI8LF1SGq4afWz0N/S4vLv7Fv/CDl45idlkOrphXChNH8PpHbbj9sT248MfvoH1wFJ9bNS2m+xUPcjMsmqkRqeQPlvKxhVNQlmPH//3rtO40jwNN/NW9JVXJVYSrChywWzjFGMDBUS+e39+Cjy0oDzuupxJ6qro9AGYQQmoIIVYANwF4WboBIaQKwPMAbqWU1sd+N5NLa/8IzvW4sJr5gxPKp5ZMxYn2IRxuGQi7zx+gePHAeaydXqTZhapmjaCUxlURPisoY6IqGwlVBY4wNbfFYPFeVeBAk4YiTAhk8yjHUgvGcoSVth33OEnBJecnDo1P6xfGK4dbI/gDaDKHanh9AcWJbHqKVLnEBmnaROjkubCfEVOPsPaIZSDcI6wWnSZSV5wFq4mLy2X+UMbsPOkvTlw0sxj7G/tUYx6NMuYPDi+WVtYW4ILKPFhMBL+/ZQn+/qUVuP+TC/HMnauw93uX4+F/W4qVdYW4aGYxNswuCXt8qsErwsrHh8HR1C2ELSYOd18yHXvO9eG9k+rpPiIHmvtRkZeBkpzkpniYOIJLZ5fitcNtsg1//9jbgmGPX7YXKJXQPIJQSn0A7gGwGcBxAM9SSo8SQu4ihNwlbPYDAIUA/o8QcpAQsjdue5wEXjzQCgBYN4MVwonkE4umwG7h8Mze5rD7ttZ3orV/BJ9ZoT7SEuAV4WGPXzZLt3fYgxGvP6rECEBZEW7oGkaGoMhGSk1xJjqH3MFiPpiWYaB4ryp0oFGtWU5IRZDz0IV6hL1+5W3lHqe0bajS3DcsTJUL+cDKsplh5khSh2poKcJaRap4EhGmCPtDFGHFrOIYpkZoxqeJOcJSRdij2ignYjFxmF6ShWPnE1cIp7tHGAAunlUCX4Bi++nYZQofah4AIZCdOkYIwTN3rMS2b2/AxoXl4/4+rWYOV80vw58+uwyPf355UoY1GCXfYdVMjUjVQhgAbrqwEtMKHfj5Gyc1M98B4EBjHxYnWQ0WuWHZVPS5vNhyfHwR7w9QPL7jHJZW52NBiltKdR1BKKWvU0pnUkrrKKU/EW57mFL6sPD9Fyml+ZTSRcLXsnjudCIZcHnxx61ncMnsEswoTW2f1EQjx27BNQvK8fLB82FdqU/ubEJxtg2XzS3VfB7RR+uUsUc0BzOE46MIN3Q7UVOUGVUIfW1RFoAxdbnL6YbHHzBUvFcXONA15B7XACVFtRkspGB1q0SJSRGLOqVCJdQjLCrCoZfQCCFJHaohTn2LxiPsllFjpY/TUmv12C+00GrIEwlaI0I8wnoUYYC3RyQiOUL8fdI5NUJkcVUesm3mmNojDjb3YXpxlmJijd1iSmriQCzJdfDWCCVrQaoXwhYhVvRkxxCe368epdc+MIrzA6NJyw8OZd2MYpTl2PFsiGD1r5OdaOxx4fY105KzYwaYGH8FceThbWcw5PbhW1fOSvauTEpuXFYJp9uH1z8aa5pr6XPh3ZOduHFZpa4DuTjVTe6yY4vOhjst1BThmuLMqJ67Tnh8QxdfCAfTMgxMwqsSrBlNCqqw2qhasTiTNnbpUeHES9aKxV1IfJo4IjXUGgHwPuFkeYT9AQpKtWwL2pPlQpVxaQOcVrOcRUcyhRZ6vd1WMwczR4KK8LDbhxGvX5ciDPANc91ONzqHRqPaXy0mkiJsMXFYM70IW092GZ76JgelFIdaBmRtERORvAwrPL4ARmUmcAYCFIMpXggDwDULynBBZR5+9Xa94nAmYMwfnCqKsIkjuH7pVGyr70L7wNjf/KMfnkNZjj0lJ8mFkv5HkDjSOTiKRz88i09cMAVzylNvPvZkYHlNAWqKMvHsnrGzzWeE729ari+OJUe1EOYV4Yq8KAthGUXY7fOjpc+FuqLoCuGqQgc4AjR08c2BwbQMAyp2dSG/D4098g1zXpXJaaGTzTw+5W2liFYCpULFbOLAEYk1QiiEQ1MjAN4nrHbpM55o2xZ0eIR9gbATAt5b7A/eLz6XHFYTF/WIZY8vADNHdF2dyLCagoWwmCGsVxGeU85fOdOrCvv8Aexr7NW1rZSJEp8mcvGsYpwfGFWNjNTL03ua0TvswZpJEvc5NmY5/GTZ6fEhQFNrmIYchBDce9VstA2M4tv/OKzoeT7Q3A+rmUupTN7rl05FgAL/FNTsI60D+OB0N25dVZ0WVx1Sfw+TyG/fPQ2fn+Kbl89M9q5MWggh+PSySuw+14sXD7Ri+5luPL2nGRfPLNZtZxATG+SSI0JjyCJFThFu7HEhQIHa4qyon7uywIEz3aIibHwkdHVB5IqwXGqEnuJDbC5TOxBKL/krNcuJtyVroIaeRjaPP6Cq5Mm9ZlIlWcu/G4tmOb3rBvB/M2J2cHCqnE5FeG65seSIv+9uwqf+sMPwRDpx2mI6jliW45LZJSAEePOIcmSkHhp7hnHfq8ewZnohPnHBlBjtXWoj9hXInSyLV5pSMT4tlFV1hfjapTPw2kdtuPR/t+KFAy3jjivn+0fw4oFWLJqal1IngNOKMrGipgDP7W3Gr9+ux/UPb0eO3Yybl2v38KQCqfNKphiNPcN4ancTbrywMqimMZLDp5ZWwGbm8PVnDuKWP/GT08RQeD1kqxTCzb3Gms6UkPMIi1aG2iitEQBQW5QZfL6WPheKs22GZrbzxb5ZMUvY66eKFobwgRrh6qb849QVYWB84sKAywubmZP9vZLpEdZShMdGUCsXwnIqurQBLhHxaXqVfIC/ErP9TA8CASpRhLXj0wAgz2HFlFy77kL4BaEZee855YEvcnj8/ElnKhUE0VCSY8ey6ny8caQt4ufwByi++ewhmDiCX1x/QVS9CemE2FcglyyTiuOV1fjG5TPxyj1rUVngwDeeOYS7/74fg6NeDIx4cdujuzHi8eNH185L9m6GccOySpzrceHBLadw2ZxSvPH19ZoDeFKFyFP+Jzi/frseZhPBVy+dkexdmfSUZNvxr29djI5BvtnLxBFcOE1/o4DoEZaLUGvpcwWn40SDnCLc0M1f4qyJ0hoB8Kryjga+MOGLd2NWDkIIqlWSIzz+AKwKytpYISzGp1HFbcc9TmyW01CE3UFrhEfWFgHwHuH+ES8CAZrwD/fgJXiVRjZAXXH1KCrC45vl1Bryoo5P81PdRePFs4rxwoFWHDk/YFgRBiCMWtYuhJt6XDjQxMd8HWjqN3SCq3dASDpx9fxy/OjVYzjbPRzRceOP285gX2MffnPjIkyJ0u6VTuRl8AXXgIwiPJhmhTDAN5w+/++r8af3G/DA5pM40voBirNtONs9jMdvX47ZZaln1fzYwnKc7nTiktklWF5TkOzdMcTEOYLEkBPtg3jp0HnctroGpUnO6WPwlOdmYFFlHlbVFWJ5TYGhUZljhfB4RXgsQzj6DwwlRbgk2xa17QLgVeVRbwBtg6No7nOh0kCjnEh1QSaaFDzCfHyakiLM3+6WWiN0KMJis5xeRbjf5ZW1RQC8ou0PUNXBKPHCq9GUZQlp+pNDjKcLfdyY3UR9/LHcdEGjyO2DEmunF4EQ4F8nu9A15AYhY4NN9DCnPAdnuoZVm34A4JXD/GymeVNycKDZmCIcTI2wTJyPsavm841FkajC/gDFI9sacOnsEmxaNDksESJi1rjcUI10U4RFOI7gzovq8OydK+H1B7CvsQ8PXL8Qq1PU9223mHDv1bPTrggGWCEsyy83n0SWzYx/v6gu2bvCiAFj1ojxB8kzXU64fQHURenhBcYUYbdUEe5yxsQWAYxFqNV3DKFtYDQiO0dVoQNVhJiEAAASUklEQVQtfSPwySiLamomIWR85q2Kn1iKXkU46BF2KXd2i5fYkuET1rQtmMdbR+RQ8giPja32q/4MXhGOLk3AiEe4MMuGhRW52FrfhS6nB4WZVkNTNRdMzYU/QHGoWX7iFMCfiL54oBUXTsvHNQvK0dA1LKvoKTFRRixLmZLHn/C/8ZFxn/CBpj70u7y4bkmFIaFgIiAqwrIe4TQthEWWVhfgza+txwtfXo3rFk9N9u5MSCbOEUQnWtE0e8/14p3jnbjrorqUHgnI0I/VzMFm5sLUxK31fHh9LDqrZRXh7mHUFEVfZANjEWrbT3fDH6ARqdjVBQ74AhRtA+GxVlr+UamfVS1hQopYoGg1y4mKa/+IsjUiPzN5Y5b12BaA8Azp0OcIfR2sBhXhWKRG6PF2i1w0qwQHmvpwptOpOzFCZHVdISwmgndPKE/KOtE+hFOdTnxiUQUWCzFfBxVGtcrhmYCKMABcPb8MH7UOBGMS9bLlRCfMHMG6GcVx2rPUxW7hYDVzsqkR6V4IA7wHenGK5AZPRCbWEUSDzsFR3PTITsWpR4EAxc/fPIGiLFtahEAz9JNtt4TFp22t70JtcWZENoNQxAYv8VJw77AH/S5vsICNluJsG7JsZmwTivdI9lktS1iruB3nZ9WpLFr0WCNCFGEla4R4u9oY1Xjh1WiWs+lShMP9uaGvKaCWuUwSmhoB8GN/AxTYfa7XkD8Y4P/eVtQUYotKIfzSwfMwcwQbF5RjYWUeCBnLSNVD0BqhMPo6Xbl6fjkA4+kR7x7vxIXTCtK64IsUQgjyMiyyVxQGRrwwcyQ4OpzBCGVSFcK+AEVjjwu3Pbo7OEhByjN7m7HnXB++deVMOKysj3AikWM3Y1CiCI96/djV0IOLZsZGPTFzBBxBMNBdzPyNlTWCEILa4kyc7OCzWSOxRoxlCYe/990adgdLiDVClyIs5AirFtiCKvrn9xvQOeTGNIUGIdGfmsqKsGpqhEzShtTuoPUzYuIR1qnkiyyqzAsWVUYVYYCPAzvd6ZTNrg4EKF45dB7rZhShINOKLJsZs0qzg41zephIAzWkVBU6MG9KDl49fF73cI2WPhdOdgzhktklcd671CXPYVFMjcjJsEw6uwhDPxPrCKLBlLwMPP755Rjx+nHbo3vGqUsdg6P46evHsaq2EJ9epm9QAyN9yM6wjLNG7DrbC7cvgPUxKoQJIbBbTHALXs9gdFqMrBHAWPoER4DyPONNnGU5dlhNHBp7wwsTcfKZEhbJQAe1ccNSxBxhtRG4VjOHfY19+PFrx3HNgjJ8YW2N7HZiM4zcB1280bIt6G2WC49P40LsJkTxwzomqREG4tMAfmLUuhm8bcioIgwAl87hi7Itx8NV4RcOtKK1fwSfXDLmeVxUmYeDzf26iz/xb22iFcIAcPPyKhxqGcBfdzTq2v49QXm/ZM4kLoQzrIoe4cmokjP0M/GOIBrMKsvGnz67DE09Ltz+2B7sEiKpfvDSEXh8Adz/yQXszHECkmM3j2uW21bfBauZw8qawpj9DJuZCyrCZ7qdsJhITBIpRMSiujw3I6JpPSaOYGpBBppkFGEtu4MtZPiDvmY5URFW/nuymk0Y8fqxcWE5HrxpseLvlWUzw8yR4PS5RCLm1Wo1y3k0muVCTwikgzi0ilSrmYMvQBEIRN4wJ7cPWohXTPRmCEupLszE9JKsMJ9wv8uDn75+HEuq8rBxQXnw9sVVeRgY8eJst3yySSjipDzTBMzKvWV5FS6ZXYKfvHYcR1oHNLd/90QnphU6UBuDqMZ0JddhCfqBpQyO+tJimAYjeUy6QhgAVtYW4sGbFuFE2xBufGQnVty/BZuPduCbl89UvDTLSG+y7eZxivDW+i6sqClARgx9Y6GKcHVhpqFOey1Em0U0xXV1gUPWGuH1KQ/UAARF0ie1RmgXH1YdHuGr5pXhttXT8OCNi1QLQUJI0oZqeDQmy4mvhVFFWDqIQ+vkIqg6R6EKG7VGAMCG2SUozbFhfkVk41wvnV2CXWd7xp2E/vzNk+gf8eLH1y4YlwktNgPptUfoTS9JRziO4Jc3XICCTCvu+ft+ON3KsYEjHj+2n+nBhtklk1rEyXfIj2FnijBDC11HEULIVYSQk4SQ04SQe2XuJ4SQh4T7DxNClsR+V2PL1QvKsfd7l+HBmxZhQUUuLptTqnhZlpH+ZNsswQ/j1v4RnO50xswfLCJVhM92D8dcnREL4Wia+6oLM9HU6wq7/KylCFvMJFiEyTV+yT9GuxC+ZUUV/vsT83SdMBQ4rEnxCI+NP5YvMvQ1y8nHp4n3efxUtUi16VCdtfD6qOGosaIsG3b9f5dhdV1kySqXzimF10/x/im+yXNfYx+e2t2E21dPw9wp44cCTC/OQrbNjIMqkWtS3D7jCnc6UZBpxUM3L0ZTrwvX/2E7/rGvRTaXefuZbrh9AVw6uzQJe5k65Dms6Ha68eiHZ8cpw4OsEGZooNkRRggxAfg9gMsBtADYQwh5mVJ6TLLZ1QBmCF8rAPxB+DelybSZsWlRBTYtqkj2rjDiTLbdjH6XFyfaB7G/kf+gjXUhbLeYMOz24Ykd53CuexiXzYntB1NtURbsFg4zSiL3HS+oyMVj28/hlj/twv2fXBC8AuLVujQfSbOcjvg0I+RnWnC6y4lz3cMJvXIz1simPnkvEo+weJ/WsItgQ14UDXMef0Ax+SJeLKniG+4e2daA1z5qw44zPSjLsePrl88M25bjCC6ozMN7JztxuKUfC6fmKT7vm0fa8fpHbRE18aUTy2sK8Nubl+DX79TjP587hJ+8dgxXLyjH5XNLMbssG0/tbsZfd5xDjt2cloMMYsmmRVOw62wv/ueVY3jgzZO4bG4p1s8oQu+wB7kZrPmdoYyed8dyAKcppQ0AQAh5GsAmANJCeBOAv1JeZtpJCMkjhJRTSiMfms5gxJA55Tlw+wK46jfvw8QRlOfaMT2KglIOm5nDlhOd2HKiEytqCnDb6mkxff4MqwlvfG09ynMjn3Z43eIKuH0B3P/6cVz5m23YtGgKirJsGPH6NS/NN/W68JcPzmJUY1vpY4DYNTNtmFWCBzafxMW//BfWTC/Egoq8YH6o2xuAy+ODy+MXvnwwmzgUZ9lQnG3TVA7VLimLkV4WBUVY/P02H22XjaYDeJ+ikiL8xM5GnOwY1IyZA4CfvHYclQUOvgtecWt5eoc9CR8+YTZxuGpeGZ7Z24yuITdW1RbiS+trkWWT/+i5bfU0fOPZg/jE7z7EqtpCLK3Oh8vjx4jXjwyLCdl2M053OfHa4TbMm5KDX9+4KKG/TzLYuLAc1ywow44zPXhydxNeOtCKv+9qAgAQAlw+pxRfvXTGhLWJ6GXelFy8dPcafNQygL/vbsTbxzrxyiF+cqFSLCODAegrhCsANEv+34JwtVdumwoA4wphQsgdAO4AgKqqKqP7ymBEzKeWTsXq6YXYVt+Fbae6saauKOZ+unkVuRj1BvCtK2fh0jnx8evVRKmEchzBLSv4Rpz7Xj2GLcc70T/ihT9AUV2g/NzVhQ7sOtuLH73Kn/9W6bBnmDiCmaVZMZncBwB3XlSHaxdX4Nk9zXhuXwt2n+0dF1mWYTHBYTXBYTPBYTHD6w9gm9Mdk7HMOXaz4uXV4iwb7BYOz+1rUX2O0NesMt8BQoBfvV0PAKoJJkuq8rGgIhfbTnWh2xm5PUTPusWaH183H/919ezgdEA1Lptbiu33XoKndzfjLx+exa6zPXBYzbBbeNuR0+2DxUTw9ctm4O4N02N2tSHVIYRg9fQirJ5ehFGvHzsaenC0dQBXzS+P+Ql9urNgai7un7oQP72O4kT7EPY29uHyGF+dY0wsiFZUDSHkBgBXUkq/KPz/VgDLKaVfkWzzGoD7KaUfCP/fAuDblNJ9Ss+7bNkyunfv3hj8CgwGIxoopRj1BlQbBwMBGiwoCQfk2FPDc+cP0GDTlFJ6wKjXr+mt1Ursspm54NAUpZ/h9qr8DCI/2crp9sEvFPNZdrOuBASvPwCXO9wrqgnhC/p0aagSP5uk++sPUPgCgeBIcwaDwdADIWQfpXSZ3H16FOEWANJg3akAzkewDYPBSEEIIZrpGRxHUnLkuInT3ne7xaRaxMaCSH+GkkVADYuJQ65j4iuhcgW7iSMwcawIZjAYsUPP0XQPgBmEkBpCiBXATQBeDtnmZQCfFdIjVgIYYP5gBoPBYDAYDEYqoylHUEp9hJB7AGwGYALwF0rpUULIXcL9DwN4HcA1AE4DcAG4PX67zGAwGAwGg8FgRI+u63KU0tfBF7vS2x6WfE8B3B3bXWMwGAwGg8FgMOKHZrNc3H4wIV0A9A1SZ8hRBKA72TvBMAxbt/SErVt6wtYtPWHrlr6k6tpVU0plo3mSVggzooMQslepA5KRurB1S0/YuqUnbN3SE7Zu6Us6rt3Ebz1mMBgMBoPBYDBkYIUwg8FgMBgMBmNSwgrh9OWRZO8AIyLYuqUnbN3SE7Zu6Qlbt/Ql7daOeYQZDAaDwWAwGJMSpggzGAwGg8FgMCYlrBBmMBgMBoPBYExKWCGcQhBC/kII6SSEHJHcdgEhZAch5CNCyCuEkBzJfQuF+44K99uF25cK/z9NCHmIEEKS8ftMFoysGyHkM4SQg5KvACFkkXAfW7cEYnDdLISQx4XbjxNCviN5DFu3BGJw3ayEkEeF2w8RQi6WPIatW4IghFQSQt4T/naOEkK+JtxeQAh5mxBySvg3X/KY7whrc5IQcqXkdrZuCcTo2hFCCoXtnYSQ34U8V2quHaWUfaXIF4D1AJYAOCK5bQ+Ai4TvPw/gPuF7M4DDAC4Q/l8IwCR8vxvAKgAEwBsArk727zaRv4ysW8jjFgBokPyfrVuKrhuAWwA8LXzvAHAOwDS2bim/bncDeFT4vgTAPgAcW7eEr1k5gCXC99kA6gHMBfAAgHuF2+8F8HPh+7kADgGwAagBcIZ9vqXN2mUCWAvgLgC/C3mulFw7pginEJTSbQB6Q26eBWCb8P3bAD4lfH8FgMOU0kPCY3sopX5CSDmAHErpDsq/8/4K4Nr47/3kxeC6SbkZwFMAwNYt8RhcNwogkxBiBpABwANgkK1b4jG4bnMBbBEe1wmgH8Aytm6JhVLaRindL3w/BOA4gAoAmwA8Lmz2OMbWYBP4E083pfQsgNMAlrN1SzxG145SOkwp/QDAqPR5UnntWCGc+hwB8Anh+xsAVArfzwRACSGbCSH7CSHfFm6vANAieXyLcBsjsSitm5QbIRTCYOuWKiit2z8ADANoA9AE4JeU0l6wdUsVlNbtEIBNhBAzIaQGwFLhPrZuSYIQMg3AYgC7AJRSStsAvuACr9oD/Fo0Sx4mrg9btySic+2USNm1Y4Vw6vN5AHcTQvaBvyzhEW43g7/88Bnh3+sIIZeCv+QQCsvISzxK6wYAIISsAOCilIo+R7ZuqYHSui0H4AcwBfyl2v8ghNSCrVuqoLRufwH/gbsXwG8AbAfgA1u3pEAIyQLwTwBfp5QOqm0qcxtVuZ0RZwysneJTyNyWEmtnTvYOMNShlJ4Ab4MAIWQmgI3CXS0AtlJKu4X7Xgfvm/sbgKmSp5gK4HzCdpgBQHXdRG7CmBoM8OvJ1i3JqKzbLQDepJR6AXQSQj4EsAzA+2DrlnSU1o1S6gPwDXE7Qsh2AKcA9IGtW0IhhFjAF1JPUkqfF27uIISUU0rbhEvnncLtLRh/FU1cH3acTAIG106JlF07pginOISQEuFfDsD3ADws3LUZwEJCiEPwLV4E4JhwiWKIELJS6Mj8LICXkrDrkxqVdRNvuwHA0+JtbN1SA5V1awJwCeHJBLASwAm2bqmB0roJx8dM4fvLAfgopew4mWCE1/j/AThOKf2V5K6XAXxO+P5zGFuDlwHcRAixCZaWGQB2s3VLPBGsnSwpvXbJ7tZjX2Nf4BXCNgBe8GdPXwDwNfBdmvUAfgZhGqCw/b8BOAreH/eA5PZlwm1nAPxO+hj2lRLrdjGAnTLPw9YtRdcNQBaA54S/t2MAvsXWLS3WbRqAk+AbfN4BUM3WLSlrthb8ZfDDAA4KX9eATzvaAl6l3wKgQPKY7wprcxKSdAG2bmmxdufAN7Q6hb/Ruam8dmzEMoPBYDAYDAZjUsKsEQwGg8FgMBiMSQkrhBkMBoPBYDAYkxJWCDMYDAaDwWAwJiWsEGYwGAwGg8FgTEpYIcxgMBgMBoPBmJSwQpjBYDAYDAaDMSlhhTCDwWAwGAwGY1Ly/wPae+W6AprSngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, figsize=(10,7))\n",
    "\n",
    "ax = axes[0]\n",
    "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[0])\n",
    "ax.set(title='Smoothed probability of a low-interest rate regime')\n",
    "\n",
    "ax = axes[1]\n",
    "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[1])\n",
    "ax.set(title='Smoothed probability of a medium-interest rate regime')\n",
    "\n",
    "ax = axes[2]\n",
    "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[2])\n",
    "ax.set(title='Smoothed probability of a high-interest rate regime')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Switching variances\n",
    "\n",
    "We can also accommodate switching variances. In particular, we consider the model\n",
    "\n",
    "$$\n",
    "y_t = \\mu_{S_t} + y_{t-1} \\beta_{S_t} + \\varepsilon_t \\quad \\varepsilon_t \\sim N(0, \\sigma_{S_t}^2)\n",
    "$$\n",
    "\n",
    "We use maximum likelihood to estimate the parameters of this model: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\beta_0, \\beta_1, \\sigma_0^2, \\sigma_1^2$.\n",
    "\n",
    "The application is to absolute returns on stocks, where the data can be found at https://www.stata-press.com/data/r14/snp500."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the federal funds rate data\n",
    "from statsmodels.tsa.regime_switching.tests.test_markov_regression import areturns\n",
    "dta_areturns = pd.Series(areturns, index=pd.date_range('2004-05-04', '2014-5-03', freq='W'))\n",
    "\n",
    "# Plot the data\n",
    "dta_areturns.plot(title='Absolute returns, S&P500', figsize=(12,3))\n",
    "\n",
    "# Fit the model\n",
    "mod_areturns = sm.tsa.MarkovRegression(\n",
    "    dta_areturns.iloc[1:], k_regimes=2, exog=dta_areturns.iloc[:-1], switching_variance=True)\n",
    "res_areturns = mod_areturns.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>520</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-745.798</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 24 Feb 2020</td> <th>  AIC                </th> <td>1507.595</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>22:49:06</td>     <th>  BIC                </th> <td>1541.626</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>05-16-2004</td>    <th>  HQIC               </th> <td>1520.926</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 04-27-2014</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.7641</td> <td>    0.078</td> <td>    9.761</td> <td> 0.000</td> <td>    0.611</td> <td>    0.918</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>     <td>    0.0791</td> <td>    0.030</td> <td>    2.620</td> <td> 0.009</td> <td>    0.020</td> <td>    0.138</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.3476</td> <td>    0.061</td> <td>    5.694</td> <td> 0.000</td> <td>    0.228</td> <td>    0.467</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    1.9728</td> <td>    0.278</td> <td>    7.086</td> <td> 0.000</td> <td>    1.427</td> <td>    2.518</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>     <td>    0.5280</td> <td>    0.086</td> <td>    6.155</td> <td> 0.000</td> <td>    0.360</td> <td>    0.696</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    2.5771</td> <td>    0.405</td> <td>    6.357</td> <td> 0.000</td> <td>    1.783</td> <td>    3.372</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7531</td> <td>    0.063</td> <td>   11.871</td> <td> 0.000</td> <td>    0.629</td> <td>    0.877</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.6825</td> <td>    0.066</td> <td>   10.301</td> <td> 0.000</td> <td>    0.553</td> <td>    0.812</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  520\n",
       "Model:               MarkovRegression   Log Likelihood                -745.798\n",
       "Date:                Mon, 24 Feb 2020   AIC                           1507.595\n",
       "Time:                        22:49:06   BIC                           1541.626\n",
       "Sample:                    05-16-2004   HQIC                          1520.926\n",
       "                         - 04-27-2014                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.7641      0.078      9.761      0.000       0.611       0.918\n",
       "x1             0.0791      0.030      2.620      0.009       0.020       0.138\n",
       "sigma2         0.3476      0.061      5.694      0.000       0.228       0.467\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          1.9728      0.278      7.086      0.000       1.427       2.518\n",
       "x1             0.5280      0.086      6.155      0.000       0.360       0.696\n",
       "sigma2         2.5771      0.405      6.357      0.000       1.783       3.372\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7531      0.063     11.871      0.000       0.629       0.877\n",
       "p[1->0]        0.6825      0.066     10.301      0.000       0.553       0.812\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_areturns.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first regime is a low-variance regime and the second regime is a high-variance regime. Below we plot the probabilities of being in the low-variance regime. Between 2008 and 2012 there does not appear to be a clear indication of one regime guiding the economy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KPLBwH+ZvrI3bplOzfo40VtlS04Ele5qO7CAOHHzO6M+qEd+mlBZTSj2U0uGU0mcppU9QSp8wtlNK6U8opeMopdMppU741wsWljVh+l0LsbWmc7CL8pWCplOh0H1Vcc9HZXhrU/zA83kgENXgj6hfyLkGAjFN/1zub3N3OKHq1R9wMtCXT3h3Qzcm/eETfLwjcSJsaFYKK0s/rRH/WLwf722tS7itoSuEV9fX4OJHVlg+H/3bj3DX+7v6dXw7dJ1+oW0lGNUQjulo80cH9LhcvexNaZYJXkTV0Oo/Ou0qmaluAMC+pp64bRo1+9ojDRj0XuxFuxu6EVGTB5BfJI7U/uTgq41Be7Oc3Fk1d4dR3RY8pO+HYxoiqgZKKT7d1Qg1yWAX0/QBUWIOB5TSuAe9oiUAAHhzU03c/qvKW4/6lB3HY8vK8cyKCvH/uDsW4OaXNw9iiY4cT684iNvmbxvQYybrwHWdDnjq+fPExY+swNPS/QaAq59agyv+tfqwj0kpxSn3LsFNL206rO9zEtDXGLnfUGc/3J6YCBdkMCLc1NW/fuidLbVYVNa7ihZR9bj7+/zqyn4df29jDy76xwq0BxgR/eeycky781N0hb6YTBWlA0OyOD7e0YD3ttYJ9ZLXSzimxaX/BRHWKW57YxtOuntxvwIw+z5fdeLEsxSVbYG4bcwaMUBEWDcDj/LmHpEN7QnHcOE/VuDW17Ym/B6lFLUdh8YJDheVrQGMuX0Blu879JWsni6twMHW+DrsDcv3tSQNACpa/PjNm9sRVQ8veB9ILC5rwi/eSHx/vgyoaQ9i2d7mATnWoBHhfU094iG56JEVmHP/skPqXG55dQtuf3sH1lS04aaXNuHBRfsQjmnoDFpVhrc21eLsBz5DKDrwkWcgouIvH5ahI5BY2XhlfTVOvXeJ8AgCwLAc1gGtOdAWt/93n1mHuQ8uH5Cy7W/qwYtrKuPqVNcp7nhnB/Y2xisBAFDfGcKv5m/rVSGilCYMXPZL9/RIcf+ne3G3LbX/ya5G8fdr66vR2E9iISMQUQddhehNoXx+1UEs29O/h7u8uQczkmQXdEqh6jqCURW3v709aRsdSPgjKs68fxk2VXWguTuMX83fhhP/sghVbQF8srMBL66pTPrd+s4wamwD39qKdmys6gAAVLUFDpl8qEZbXGrUZyCi4sonVmNLdUe/vt9fMpCd5gGApESSELawTmM/A3I5NW2H/PHhTvjaXtuJsoZurK1gfRC3EvS3Xg4VdiGCK+zqAPUV/1lXhedXVwoCzI+7/mA7Hli4D9trzedDtrss38uIT31X797t6rYgpt/1KUoNorSpqh0TfvcxNvejvp4urcDOuq5Dvqa+sP5ge692nP6iMgGJY+2P/S23t8PJrMjP0LkPlWL6XQuh6xSqxj7/eGdjwu99srMRZ/x9GT7rJ9F5ftVB/OXDsqTbV5e3ojnJ83fQCAb+uuDQrGSBiIp7FuzG2Q981ue+pfta8OmuRtR2BPH959bjx0mC84cW7cPrG2v6DIQ5dtR2YU9j96EUGx9ur7c8E8lw6+tb8fbmOlQkEOfmb6xBV9Da3933yR6s2B8fTKwub8WPX9pkCdw1nWJ3Q/Jy94RjqGnvPRB6duVB3PDCRgSjR57NGjQirOoUO4wOotVIkVXZyFVzTxhXPbEm4U1r6g6jvjMEYqzetmJ/C+7+qAzffNyqILX0RBCMaoekClNK+9XJrCpvxbMrD+LFNVUAgFBUw2KpAe9v8qMjGMMf3t0Vp4IcaAkkVbH7QjCqJn2oD7T4oWo6XlxThT++twvvb7P68NoCUbyyrhoXPFxq+XxdRRvqOkNYd7AN8zfVJk3NAsD72+ox5/5lWFVuevGq2gI4/+FSLCxL3LH5IyqWHoZXzE5+KGVp3N++vQMfbOvdY/jq+uq4jv6qJ9fgtjesquxd7+/C//xnU9y59jb24MS/LEJZfTc0nULVmAr38OJ9vT6kMU3HFf9anVRhKKtnHcC+ph5LO9N1ivs/3YsnSw8AQNJ7zLGtpgs9ERWPJ5jRrVOmCC/Y0YhX19fg75/swbtb6nDPR8kHiyNFuz+KqrYgDrT48dyqSszfVIu2QBTbarvw/OpKPLhwX3IFm5qDox2l+1pw5v2fHbJiI5PJ5p4wDrT4saGyA48tOxC3b1VbQNwX8/vW38ng87oAIOnaqzw4bOiDcHEwG5D5fzimiUFEHkwWJLFiyKjtCOKdLVY7TsAIcrcZ/er04dns/5qBJ2y7G7ox894l2FRlkna7csvx7pY6cQ80neL65zfg3S1mPxTTdFz73Hr8e9VBy/d03Ro82OtK7mblfUYXpAMws3QA0BGI4snlByzttKyhC4Gohj99sAsxTce2mi6oOsV1z62PC6ofXLhX3JeoquOeBbvxtUdX4vHPyvG3j/egvLknaaamrL4bN7+8qdfJfgCwbE8zrnpyDR5duh8A0OaP4PJ/rcamqg48vHgfbn7ZSjo6g1G8t7UO22o648ahygSChk5pQptJf6091mOZx+R4bUONxW5EpfNxtBmB+wurK7G2oi0hwZJx1wdleHblwaR1+6MXN4px2o5UN3t+9zT2iHLENB1XPbkG722tQ3NPGG9sqEHpvhaL0BOS+u6+JsI+s/IgHl9Wjoih9C7b25KwrGONNrmzvgt7G3uwq773Z/KOd3bgjrd39LqPjKiq45fzt+GhRfv63Pf4kTmirDIau8L41Zvb8d1n14rPKKV4qrQC93y0O+5ePrBwLz7Z1WjhC4vKGnHhP1ZgdXm8n98fUXHFv9bgokdW9CrI9YRVqDrF5qpO3PDiRny4vR4xTe+zzhJh0IgwACzZzYhRcTZTSVfYKmVbTRfWV7bjhhc3ximQGqWIaRTUWLK4vNmPVeVtqGgNWJYp4lFsoodY1yluf3sHfjV/m+Xm/f7dnZh57xJsrelERYs/rrPb29iDmvYgKgyS9fqGamgGifnRixvFRBb+MC/e3YS1FWwgkDvlHUmUgt4m0721qRaz/roUZ97/WVyAUFbfjXMfWo53t9aj2iBqd76/Cw8t2ie8cPJ1yg/izS9vxlPLDyASYwVMNImCg9+L0n0tqO8MoaY9iLL6blAK1LRbO4SKFj/CMQ1vbKjBD5/fGEc2+kKnLeps6YmIACLaSyARimq4/e0dOOuBzwTZDMc07G7oxkc7GsQ92lXPSNrHOxvx6S4rUX9vax0LHNZX4RdvbMXl/1qN1Qda8fDi/Rbbhh2t/gg2VnXgjQ3x9hcA2FTVgaiq4/z/K8X1L2wQn9d1hhCIathR24XSfS2Y+dcl2N3QjT9/UIYbX4y33nMFddHuprionVIWbOZneAEAtR0hvLmpFk+vOIh1FfHZCAB4aU1lv1SuZOCDm65TRFUdirHCeF1HCLUdIXSFYqjtMNvHpqoOocLoxvOcCE8sZ8SVE7WuUAwPLdzbZyApk8nle1vQ3M2egaV7muLSrvd9uhe/eWu77ft9e04BUzVLpghzEtDQzwwGpdb1iyf94RP80rDUyITi/W31fQbsb2+uwy/e2Ga5Bj64bDfqMyuVKdq8P2kPRPHokv348Uub+jWxt6Y9mLQcvB9aJ6nXIl2uW8nQra9vxUWG97mhK4Qle5rxv29sFUH5E58dQOm+ljgLCiduvGq4IpxI0ZftLqPyfQBgeXYWlTXhrx/vsbRT/veBlgDe3FQL1WhY3WEVL9nI1aNLy4WFSz7vfZ/sxVOlB3DuQ6UYd8cC3J1AvVy+rwULdjTikkdXxWU2n1t5EDvruhCKavjDe+wlL6+tr0FE1XCgJYBNVR24/F+r8fDi/ViwoxEvSDaZNzbW4OevbcU3HluFxbubjbo3j21Pw2uSrUq+hsPJwInj6ECahxHO51YdtBx3/sZanPa3pZY2yvddtrcFP3phI77/3Po4D34y33EihGNa0jYql2VfE2sLHcEo1h9sx89f24pL/7kKv35rO659br1FWJKP11u2C2BtXbXNc7nknyvx9UdXWj7LN2xUO2q7cO1z63DxIyvxP//ZlHTpxYauMHY3JA+u7NhR14lwTMe2mk7UdgTx45c2xSm7HEWGfcaeoeScamedWdfhmA5Vp9jT2IMttgzlCSNzAQBvbTY5xX6jnp8ojR9Hf//ODuxt6kFPWMX7W5OLXTygf2xZORaVNeGu98vwq/nbcPEjKxMu9zfPJv7JGDQinO51YYlRwUUGEV5pi/r48k8dwRjOfGAZbnvDJKy6zh5g/hCHY7rw6sipqKgxuCaKsv+5rByvrq/G/E21eGtzHR5bVo7nVh7Ey+uqEYyquPSxVTjnweX40Qsb0RWMCTvBLa9uwR3v7BAdaH1XGE+WHsB/1rJOkZejPRDB5OIseF2KUEPlh27Znma8uKYSZ96/zNKQ99hsC1SavPDQon0oykpFfoYX331mHc7/v+V4ZR17DexLa6tAKSPENe1BTC/JRlFWKh5duh+/e2eHcX7zuJz0UErREYzCHzE7i601nQknUgBASW6auM5fvLEVN7+8WfgkWwMRbKnuwF3v78If3t2Jcx5cjsc/OyCOtWR3E7ZUd6B0XwsqWwNYsKOh19SG3cO2u9F86O2puseWlYvgSh7AeZR6sDUgJm/8+s1tuOXVLfjl/O3ISnVjXGE6/vbxbsugwNNTb2+uw3tb67GttkusxPDxzkboOhUPo4yOADv3yvJWy33NTGETVDZVdwirzqpyk5Tub2Z1FIhqeGxZOSgFtlR3YsmeJiwsa4pLgdW0h5CV6oZCCN7ZYlXwNUMR9rrYI17fGRLt8oGFe8VztKisCZf/azXe21qHP7y3C797J/Gb1CKqht+/u6PXzIo8EUmnFBkpbuT4PKhuDwgSKD+bS3Y3CV+wrsffTz7JbLVhI9rbxK5/5f5WPLK0HHsae/DWplrM35g44JDJ5Gf7WtBk9AE6Rdyrk4MRNW6gNElT74MM388etJnb2e/GrnC/7B2sjVr34/eXH+vbp4xAVyiGj3f2Tg5UTQe1WS16jDa7s66LecmNbdtqmWL4yJL9eHDRPnyyq1EEH+GYljAF64+ouODhUjyyZL/4LKJqqGkPIqrqYpCV7zsvipagTBycdHldCp4qrUBTdxiPLN0Pr0vBzrquON+vplNJ7dWN3/GEW141Ii+dBYkVUtaI90VyfdV2hJDudaEwMwVbqjvQHVKhEODY4dl4a3PyzBk/xq3nTsDK35yN9b87F3d+fQpOH5+PF9dUxY1JvNyN3WE8/tkBS9l5RmdhWSNqO0K46cyxaAtEsWBHg6WPmVaShTOPKcT9n+4Vxw9F2XHTPC5h75Cvr9qW3aKSNUIeL/qTVd1S3YFv/HOlyI7ICjQXrSKqZiHin+xqRENXGN1SIKlKO0Q1HVOGZeHW17eKfvOZFRX42qMrxfF5ULOhMt4upOtsObhkVhy5/j4yyDYXhACm/L5yw0yMzPPhTWmyc0QaK54qrcAd7+zAvIdLRR1bymC0UbkMuxu6saOuC1tqTPGBl2VleSuauiM4b8pQLN3TjLMf+Ayn3rvEIq6omo62QAShmIaDrX5RF5RSrDnQhkeW7I8jyDwg7QjG8JDxjC/enThTy8u67mAbuoIx6Dq1+McBZs8DrOPty2utfavLxRSRT3Y2inZR1W6KaXZxbPWBNlx63DBMKsrEf9ZWJe0zA8azuqaiDR4XQas/gne31mN4bhru/3Qvbn1ti2UybEUvXu5BI8KZqR7squ9GQ1dIkI/V5W2Yv7FGKBb1nSF43QoW/e8cfOeUkXhrcy0+MTxFTEHSE6pIstLKO0x7RKXrFI8u3Y/zpgzF2MJ0/HL+Ntz/6V78+cMyDMtOxSe3zsFNc8bih6ePwYr9rTjpnkW48B+laOoOo6o9gK3Vndjf7MeJo3IxOt+H+z4x11msMshbmz+Kkpw0nDgqFysMHx6/qeOHZOCtzXX443u7UNUWtJDBbTWd+HRXoyj7gh2NOOHuRQhFNXSHY5g1Lh8v/PAUnDYuH25Fwe/e3YEnlx8QacT9zT2o7QjhtPH5+OTWObj+9DFYsrsZbf6IZfD5yFBWglENOgXCqoawcS8UgqQEgx+ivMWPrTWd2FXfhW1GFNjaE8Wr66vx/OpKvLS2CiluBVAOnhoAACAASURBVFuqO4QC++7WOnzvmXW49rn1OOuBz3Dzy5tx8SMrxQNlh90us7ex2/QCahSl+1pw2eOrsKW6A/d/uhe3v70D4ZgmBtbCzBS8tLYKf/9kryjD7AkF2FLTiU1VHahqC+DWc4/B7y+egsq2IJ5ffRDXPMvKt7/Zj7MmFiIY1ZCZ6kZmqht7GntQmJmC5p4ILnt8FU7/+1K0B6KoaQ8KUtwZYmpOVygm0s+AOfhsr+1EWMoy8E5kb6OpTPEOa3N1h6gDHmhx1HQEcczQTGSnecTEJ/lcqmZ2vBWtAdR3hVCYmYINlR1C5fpoez02VXXg58aklbGF6ajvDOHGF63eq/e31uM/a6vx8OL9SAZ5prlOKVwKQUlOGjZVdYh7tlNKW2mUSgMutQx+AJCT5rX8zwNE/lyEYxpeXV+N16TB4bY3tgl1Ru6wy+q70dwdASHAnGMK8damOssgEdOsHTz7vvV3X9edTBHmz3wwqqE71LefjQcx8nfNMrH/TxtXgNH5Pry6rsayTyBqJ/PW7wGAP8zK0BNRUdFqeq9b/VHUdoQsGTCedXh/az2+/ujKuFRl6b4WBKMaVhnBSmVrALP+uhSz71uGO97ZIZ6F7bXW+w7YJ0yz/jnFzYYkHjidMiYPB1r82FzVgZhGcc2sUYiouiVI555Wu0c40f2TVwLhf8vWiJBBgOTv1HaEMDzXhzyfF12hGHrCMWSmenDZ8SXY3dCdMEBo9UdEedK9bgzP9aEgIwU/OH0M7r50OmK6judXVULVdGyobEdPOIZAVIPXpeCSY4fhlXXVuPa59TjfULF0I0sQiLB7c91pozE8Nw0f72gUz83dl07Dy9efij98bTJCMQ3vbam3XPPMsXlYdYCPQ2ZZ7dkkXaobOYjojyK8tqId24yMllyPuvys69b2yG0PnaEYFpc1oby5RwhYAPDzuRNw/RljEFF14edmtoFuEdwPzWRi2sbK+IyW6UlPnEHi2/PTvfj3yoNoD0TFM/C7iybj01vn4LRxBbjs+BKsOtAqBDoeOD/8reNw+rgCvLKuGnUdIfzklc2oaPFD0yl21XexDI9OLUr7X74xFct+eRY8LmLJRMr1kuJW8PC3jsOHPzsD86YVQacUb0qqalsgKu7je1vrMf2uhfjZq1tw1ZNr8O2n1+KhRfviFPJ1Fe3CysX5wqoE9gTAzLiqOsW8f5Ti5HsW44YXrbYbXvZuo0/JSHFjyZ4ma+ZZ4wGQjocWMktGdXsQk4oy4fO64iZJqzpFeoob3z11FMoaui3Ks4yg1NfNm1aMK04cjlNG52HxL87Ez84Zj492NOBeQ7iilPY6AXHQiHCacTMOtgYQVXVkp3kQ03X86s3tuOgfK1BW3436rjCGZadiVH46/nTJVEwqysTdH+1GRGWeOVkRBgC3MfDKRJhvt1sjuLViRkk27rt8Bs6dPBTv//R0PPLt4/HsdSdjXGEGbr9oMv749Sn4zbxJOH5ELnTKIs5wTEdPRMX22i4cMzQTC34+G49/9wQ8e91JyEp1C+LSFoiiIMOLMyYUYE9jD1p6IsIacfXJIyy+Ik2ncBu55Ps/3YubXtqEm17ahHBMw/qDbegMxtDcE4Y/oiIrzYNxhRl48pqT8PbNp+Hk0Xn468d7EIppGD8kg6XeNR0j81iUfOVJI6DqFO9urbd0bJys8sEtHDUV4bmTh+KdLXUJJ0jwDqWiJYBwTIdOIfybrf4IGrrCmFaShQ2/OxeXHDsMuxu6Ud7ih8dFcKAlgIiq42/fnI4/XTIVT3zvRLT5I/jHEmsqg8+054qwy6ibPQ09ouOK6To+2FaPLdWduPbZ9XApBM09Eby8rloM9n+9bDq+ddIIPLH8AJbsbgIhwNPXnoTdf56HVb89B2V/nocfnjEGZ00sxOnj83Hvgj1Ysb9VZCf+dMlUHDs8Gz+fOwGXnzBcfOZ1KdhW24XOYAx/+mAXzn1oOa5+ai1CUc2Salou+at41feEVcvkTa5i7GvqwdCsFLG0EQB8agR+RVmpeGdznUW1rG0PYkSeD+kpLkunALDBhnW85v2jFDh2OPN9ycr/6HwfcnwsPe5WCLZUd2JhWZOFINQYxLkgw0pOLee0DHoUCiEYnpsm0o2EADukTo2KgZEmtEbIQduU4ixUtgYQjmmigw7FNASjmsUisbaiTUwi4209xa2griOExq4w8tO9uPrkEWjsDlsGgJihnFqvh1p+93XdALMr2P138sDR0N23T1h+oYGdhPOyuBWC86YMxZaaDku52/zx/RxgTYX7I6roa7bVdFrKV9bAAs3CzBS4FSIsJN3hGGIaRdBGhLmatKuuC8Goirs/KkMkpmFMQTqq2gJCJa/tCIkJm3YvL2Bm7Phzz0nX7AkFCMd0LN3TDEKAK04cbpTb7OO5NYIfjnvNE61OIVsj+P4yEeTPhVy2us4QhuemITvNg65QDN1hFZmpbnzt2GFwKQTvbolP3+5t7BHHV7hHyMCYgnTMm1qExz87gOl3LcSVT6zBC6srEYyo8KW4cOOcsfBHVJTuaxHBOyf6/Hn2uBQUZKQgFNME8Z86LAvZPg/GD8nEsSNyRCpapxSEAKePK0BFSwCNXWHLs1WegAhT6Vnm6M9kz0aDqNqVZ123Bsr2IBRgXuZfvbkNz62qRMwYt9f/bi5+cvZ4FGWlGcc3VG7jPvFsEb+eDZXtccGjLJwkAi/XHRdNRjCm4ZEl+xE2AqJR+T4MMSwC3zyhBJQy0glA7JPt8+C5607G4l/MwYKfz4bHpeDyf63GzHuX4OJHVmJ/sx+UWi0nJblpGJWfjlnjCvDprsaEnuyzJhYiPcWNCUMz8cCVx+LS40uwtbpTtFFZoX9yeQUiqoZFRsbg6pPZy37leQuqpmNTVQcuOXYYUj0KdMr6kVUHWhOqrqqmY1JRJubfNAsj83yIaTpq2oOWNrGlmgk9XMw5dWw+OoMxi0VSoxSZqW784PTReH51JZbtaUZ1WxBTh2Xj6pNH4oNt9Xh7cy0eWsjExJimw+NS8PUZxXArRKj0dgQiqiD13zh2GO6/YgZev+lUpHpcuO38iThhZK4QfHqzUQKDSIQVYyZ1RNUR1XScPbEQu/40D6/8aCaCURX3LtiN+s4QirPZA+B2Kfjh6WNQ1xlCfWcYOqWIqLqFqE0ZloWTR+diR228ItzcHUGbPxKX+lIUgpNG5+GZ75+EGcNzcMmxwzC5OMtS1v85axwevOpYAOaDB7BGO64wHT6vGxdNL8bsCYUYlZ+OqvYgsxsEoshL92L2hAIALPLi5503rUiQD1ZOU72LqDpOGpWLpXua8ezKg6KjqusMgVIgSyJKqR4XXr3hVCy4ZTbm/3gWLp5eLEgRJ8ITizIxvSQbH2yrF+f/6zenY/aEAvz5g13oMPxoYZWt7+l1KfjWSSPQ6o8mXMEgkQrPy94WiKCxK4ySnDQUZqZgyrAstPqj6AzGcNnxJQCAa2aNwtWnjMT3TxuNedOKcO7koaxupE7AyOiLyW68g9gjWSNUjQp/eU9ExTePL8HMMXl4aU2lIPeZqW789JzxAIAPtjdgZJ4PqR4XUg0PGgchBHdcNBlet4KfnTMeL/5wJv7wtSkYlZ+O9356Bn40eyx+es54/P7iybhgahFumTsev7pgIs6fMhTvba1nKdv6Ltz5/k50GIN/QUaKxXPLO+tQVLMowtwesa+pBxOLsjDDmLx0+vh8oWxfedJwBKKaUH6jqo6G7jBG5KYh3euGP6KirL4b33l6LcIxTSis9ns1fkiGKEtHIIrKtiCuOnkENv/+PIwtTIeqm8qsnMarMzoU/jzKqO8MobI1YFGRNJ3VaUmOT+x38ug87Krriuv0uTJsD7r48bxuBdfOGgWdMm8ZH9BCRuAmX6OmU9H++fHHFKQjqunYXteFwsxUzJ08BNlpHotnLabpcesFJyIDiSBvv+XVLRabANtu/t3Q2TeZ4NYS+RoAGOlJ9jchBCluFxtcpfO3+uMzA/Yy+sOq6Bta/BFL+WIaC2y9LgXFOaliIOHflwcUTadYtqcZxdmpUHWKBxfuw+Ldzbhl7gRMKc5Cmz9qeVUvzwaI+y+ViWfsuKe9oSuMdK8Lxxv+wk93NWJkng+TijKR4/NYV4IwCAY/rqpbjy+fx1QlTbtZfVdYjAucZMjEoLYjiJLcNGSledAZZIpwVqoHBRkpmFaSnXAy9+6GbnF8Gw8GAPz9ihm46+tTcNkJJUj1KGj1RxGIakj3ujGtJBvXzhoFACJg4Wl13h5chMDjIizro/HgyBzOLz+hBHsae1BW3y2C0lnj8gEAayrMcSjFrVjGS1Y3kq1Eahv9UYS5kl+6rzVuGTa5TSd6pFr9UXQEY4jEdNEH+bxsrOP9PD8+FxLWGPMd+D1v7onEZcf4tmRzEPi1TizKxLmTh2DpnmahCKdI48So/HQUZqagup2NSXyfVLcLXreC8UMyMSLPhzd/PAtF2WkiLR+IqELRV0WbYPf1gqlDUdUWxO4GluHgbbUkJw3fO3WUpZyzxuYjapBZwMyieN0KopqOedOKsfWP56P012fjGqP9yBmoxbub4I+oOGNCAaaXsDHm2lmj0dQdSbhsa0yjcLsYP3r9plmYPaHQyFaZ+/A66DGEJ851tkrPBBf5fnvhJAzPTcPTKyrQ2B3GyDwfrp89BhTAL97YhkeWliMYVaFqbP8cnxezxuXj450NCYl6IKri/ClD8fqNp2Lu5CEghIgVegAgL90ruE2kj+XoBpEIs9+RmI5ITIfXrcClEJw2vgDnTSnCjrou1HeGMCzHHHhTPKy4mm4OnFzxzfF5cM6kIZhWko3G7rDoWHnH3dwTxol3L8Y1z64HYCokCknQSyXAsJw0uBUSt+zZ2MJ0y/+j8n2oagugO8RmNOalezF1WDbSvS5sqe4QNzTV48LfvjkDZ00sZPVgNKgcnwfHjcjBS9fPxDFDmbp7oJk9eHxQ4pNbOFwKMYKAPEt5+GAHAKML0tEViomHPs3jwtxJQxDTqJTq0RGOaUhxKzhrYiEKM1Nwz4LdeODTvfjh8xuEz08enPPSvcKfleJW0NoTRWN3WBjt5aDi4hnD8OoNp+I38yZZyj/nmEK0B6LYJXmF+Dkq24IWgtwVMsmAqumIGdvOnTwU/3PWOBw7IgeN3WHxYGakujEiz4eJQzOh6RTjCzOQDFOHZWPzH87DbedPxBkTCnD9GWMs2wsyUvCj2WPhUgh+es4E/OTs8bhl7gQUZKTgwauOxWXHlWDJ7maRDh5T4BPlAMzBNaLqFgX39Q012FDZjvJmPyYOzcClx5Vg3tQizJtaBICReU5guRJSbwRFw/N8yEhxIxBRsaGyHasPtKHVHxGqi90jNs5oH5pORWd13IgcKAqBR1FYnWp84DA7D95G3K745+W0vy3FWQ98Zhk8KaVwKaafnBDg3MlD0BaICrJmJ3t2xUbXKS6YOhSf/Hw2Th6TBwDY09gtBkmuCNv9omawyz7j7XNvYzeGZKYgxe3C+VOG4jNJrVf1eGuEPNGnN/T1wg35uMlWlrCfNxGBrWo3gw2FsCBeJs1AvCKciMz3GFklfi77BFpdp1AUYHiOTyLCbLucgdtR14WOYAy3zJ0AhbDljCYMycAPTh+D/Awv2gJRdAajKMxkKu8GI23Nb5cm3W+ubnHfbkNXCMU5aZhgtPvusIqJQzNBCMGM4TmWJQN5HZirRFjtDfL1JbJGAOa8Dk6E+XeZFULF8Nw05Pg86A7F0B1SRdYmxa0ktLHsbugRx3clYMJZqR5cd/oY3HvZdOT5vAhEVASjqsiU/vkb0/Czc8YzAsmvSxJLXC4Ct6JYVGL52eR9x5qKNmg6I85TirOQmeLG5qpOcX0njMyNW35RJq3yNcmK8IEWf0Ji3NgdBiHs974mv8WTLWc5EgWXB1sZGYtKfZDHuCY+j4i3E94Prqtos8yhASDsfRy8nWlJHmTzmSLIS2cqO1d7U91WiuRRiOinuI841WPdZ2xhBj746el47DsniONrlAUsZkaHfefCacXwuhS8YdgQ+XUs++VZmD2h0HLck8fkwaUQrDbsLTzLPWssC3C+ffIIpHpc8LgUwRG4UhuOafjLh7sxcWgm5k0twoXTinHauHxcd9poAEzgo9Su1DNllkNRSNz69LwO+Dh34qhcpLgVbJfalKozm1yK24WzJw4RYuKofB9KctJw69wJ0jmZEOMx6v3i6cWoaguiLMEkyGBEQ3qKGzPH5lsIMEeuTIRjX1IiTIQizFKdKW4z8po6LAtdoRgausJi3V3A7FD4DYtquiC6C/93Dn4+d4KIdDhp4w8Uj7h4NGV2Uv0rr0thaV7eYXKCN7bASqxG5ftQ1xESE3MKMlLgUgh8KW5ENWtEP29aES6eXgzA7IBvnDMW7/7kdKR5XZhekoONle2iA+KDkpw6t2OcQfRcCrEEES5iBhAAa9Q5Pjbo8DQGe0mJjhSPC26XggevPBZuheCfy8qx5kAbrvv3BtS0By3E47gROTh+BEu3nzgqF809jIQWGcqhTITHD8nArHH5cWrs6eNZFFm630pMAGaNsKc2ORGK6RQxVYfP68Iz3z8JYwszkJ3mQTimi2icdwhzJw8RZegNGSnJ6zYRppVkY/0dc3H+1CKMyk9HWyCK5u4IUtwKcn1eiwWCK20AxKzwh646FrnpHlz5xBpEVB2TirJw5Ukj8MQ1J2JiEau7yUVZYhY1Px73bo7I9cFnEGHe6fHlpFTdOjkjL90riIamU2yt7gQhwAzDLuF2EcvAKt9nbuOxR+b1kr1HJl2azlSoEqMNFmWlIi89xXINfH9TsbErwkwRGluYgdH56UhxK9jX1CNNkNUsqWF+bh5k8HYzOj9dHI9PwMtN91pIXUyjcYS3v9aIvibAydv7Uib4+RK9CrhaSksqhAgxQR6Y2mxqWCIy7w+bRNg++FGDpHBbC7dGmBNUzX15Gz5maCYmF2dBIcB9V8yA160gPz0FXaEYWnoiGJnnw5nHFOLp0gpUtPgtZJSDq1s81dnQFUZxdipyfF5hl5hUlAkAmDg0A5XSutI8la/b2pOe4NrlFzzIzY1bOEI2awTPhJTk+CRrREzUn4sQcT1y3exu6BbXl2iQlpGewjI6gYiGdK/ZNxLCAh153WVeLrdC4HYRxKSsj1si3OlGP8YmSzJrhKIQpKe4jclq7DsnjMpBQ1fYkmaXrRHyPZInBt/62lbc98meuGtp6Arj1DGMmG2p7kiY2eDEkGOsbRm7mJTp9RiEMdXjQo7PI5Yg5M94qz+KAy0By/HtXlB5vEgE3g5cCkGax2VZYcI+VrmMPhIwx2yZu3C4XYpYX1ynJvnnJJqL93npXsybVoS3NtciFNUsZbEjI8WNGcOzxQpU3E5081njcO2sUTjVIMQARPvk3t23NteirjOEOy+ZwrLrZ4zBKzecihF5rH9uD0SxsKwJJ969SFxXTNNF/QMGh7AFkKYizJ6f3HQvpg7Lss6NMYgwYI71ADDCEOp+NncC/vyNqeKcMY3CY+x/3pShACDmWMnwR1TRzhMh1+dBRzDG/MFfVmsEsSjCGrxS5DV1mEmerGTOSBMZNyMmeYRTXC4QQjC1JBuEmJMzuNeIE6NhRmSpSQNKfzHSGFAzU9w4b/IQZKW6MTzXmioelcfSyzzdxImHQszZq/J5ecTFZ/bKndmM4dmiIQPMEwqYjTwRxhidyrCcVGs0Z3TYsqLEH1Q+2IVjGiIxTUS4c44pxKL/PRPb7zofH/zsdPgjMTxVWiEGGrdCcOrYPJw9aQhyfB7MGpsvro+nsrLTPBiemwaf1yXq3o7CzBRMKc6yrBWpCd9YzEJ0ZOVO1diSLXKd8WvixI0TW/5ATSrOTFp3hwvuAeQkq7zZj1yfFz6vy7LWpKZT+FJYp8lXlhhdkI43bpqFOy6ahAevPBYXzygW+080Bv7JxZlCKeLH48HLyHwfMlJc8EdUEZVzz6TdIzw63yfKqukU22s7MWFIhqgjt0IQ06ikCJv1zuvT3p/wyavMc2YSE51CkCkAGJ6bJtSdmG1WP/f42omwplPRT7gUglxjshJvD8EoI8JWRRhx1ojheT5BGocYk2oIsQ7yzBJgHSj7a43oazlw+Tz9eWMUlciPPMBXtQXF8+VSiOhD5PuUaNKk/BtgKcVsoQhb0988WHYRguG5PjR1RxCOaZb1VeVyAqwv+eUFE/H3y2cIKwO3OBxsDSDX58HfL5+BFI+CO9/fZbHQcHB1i19vY5eZVRo/hPVpPDAsyk5DOKaLyYncHiIsF5r1mpNZIxItJWlOlmP/876Re4S5PYmLEYoiE3Czblr8EVE/rj7GmIxURoSDUVVYAeTvyUq3UIQVArehTqpCEbb29/x6+cRV/j1NmqzGl7ZKpLDL9SWXA2CkOGBb7SeqMgGCiw2y3Ugmobp0r245ZzyevOZEABIR1hgRdinE4q8uykpFYxdrJ2FpnOoOxyxlsy93KuovmTVCEsXSvIoQhAAzC83hVhSLhRGIV4Q55EBVLJ9mU4QB4DszR6InrLIVQKTxORGmFGcJT3tzTwR56V7MHJuPP39jmqWuMlPcIARiJY4mI9DkQQoHD9J0naK2I4TOYEx8RzWsEeJ6FGJZ+cLjIqIO+NiTmerGjOE52FnXLfp1Nkaz6501Nl9cG8/UyfXBSThvy7mGWGdf0UfVdERUHene3oiwF5pO0R1WEeljmclDk78GEEqcImw2jElFTF3QqZUIy4O4bijCInJ0s20ZKW6MKUgXE+bsg+skQ6Gkh2iNAIBRRgRTkpuGm88ej2/PHGnpfADz5nJvKCfCLhsRJcbXeEPjnlH5AeEL3XMks0bISE9xozg7FSNyfZbPeVpDKOGEINvHibBkjVA1SxSsKARZqR5kpXowJDMV/ogqGviK35yNQkPx/tqMYfhwuzlphL/CE2CNn6XMktf12MJ0S/pDHrwsip9uepRUjcalb3Js18QjxuNH5uL1G0/FCaNyk5bhSMGveU9jDwoyvEjzugUp4x1/uteNzmBMpGxS3S4UZ6fhxjnj4o6XnebBw986TijtgKmmljezyYdFWalIN87Dgya+6gAh1gloowvSLZ7DjmDMcp/cLpZqFR0YX69Zep2vnRTyt/2Nzk83J2ZRdr2KAokI+8R9Um1EhZfRvrwRpdRCIjxuRtR5uQIRFVHbPAFNNyd08TKnuBUMy0lDbUdIBCsKIRYipCYgwvLEqt7Qn8l0Hhcre38VYXmZSI7qtiBmjeMqo6kayZMFW/3xq+PYy+gPq2KegV3h4WodIea9q+8MCUIkl19ktxSCsycOsZw33+j3Wv1RZKd5UZSdijPGF4j1xvm5OXj75u2vuScsgukJQzKxtqJdBIbDJL9ojs8rVGz7G+t6s0bYVUn+uWmNMBRhIwAsMawRrKwR0QcrxFQI5WdN7muTkRqODEMRjsR0DMsx+3berXE1S6NmnbsVBW6XgpimSx5hmbSY16Xp5jhHiHUy5vSSbLgVgq01nbhgapFpw0gQrNjbiV1gbe4Jg0pjtuwFlkmoJvXhE4uyMGFoJrJS3aiQrBGqRkXgzFGUnYrGblMRzkjxIByLiEAoxa2wOUd2a4RoF0msEbopiqW6XYhpVMwxSbWpvS4lXhG2q8YcnK/wcV8mkTJtmDkmD16Xgn3NPfC6FCgkeRZhWE4aOoIxhKIamrsjGGLYjhKdO8PrFlasQERFutcVN3GTX5NOzXrgz3hM0y2Kq4tYrRFcPQeYIkwIkOF1Y0pxFkIxDfWdYYzM97HsoHG92T4Ppg/Pwf6mHtFHAKYFxiTCxFqHtsYWNPZLT0lc94DJvToC0T4V4UEkwuw38/hRiyKc5nVh/JAM7GvyW1REEeUaKoY8sHilljWjxEwf2CuAE24zCjwEImyQ3JKcNKR6XAknDvG3FfGZ61wZIYRYBh0+wHPiywmO/PBPKc6CWyHgTYCnw3uzRgDAH782RdgeOFzG+XkjJoQgJ81KGiPGZLlkEa7bRSxL1hVlpYoH1kXMGd+AqQgDbGJeH1yCPYw25ZcjJnVscnowplO4bURYVrlT3IqlXc0ca42GBxpDDJLV6o8YkyhdCEWtpIw/uIIIJ6lrjkuNCYa8QwsZbxn7aEc9Zk8ohMtId/ojqui8+UAne4R/PW8izpk0BO2GP5dvkwdPl8Lur92qINsf5MGQUoqNle3iePIkOM1Ir2eneTDV8K/zc/Hj6rYBKtGqEXKg6jEGfr60UnvAVC7k8vFOUlbkRuQyv2uhoQi7JALDz23vK00lrvfW2x9rRKrHhZim9ksRlu+bTNaq2gOWQZtXjcUaETdZDnHH6YmoyEz1SKRIvqdGECOp+bUdIYnsWf3YvCx25Et9ASeQbMClCeuVWyM0naK5h03gKzYI1QVTi1DTEcRoo//lftHGrjAmF2cJK4m4Vk6EbYRYLjNPV9s/t3uE11W0oyDDi/x0r+hbAHPCshxQqba60fTk9SMjI8WNpu4wYhq1KMK8b+XtW1aEFcLGCplcyeqdi5gEglldjM8VYlHP07wuTCrOFFZCuxIsN225T5aPwcE9w3xegKwsxyQSSqXPeded4/OK9YxjhuVRTssDbEzh5eRLWrb6I1ANy6HP60pIhNUkgba4Fimg45m3TtE/W4mWWyGivxKqsTuZIsytnBD9sS7OZX6HECLGP43QXtuLOWkwhJaesPDfJ0JWmkdMlgv0YiNQbJYHrqjHbMGISyEWVZvZbFgddIdVZHjdUKQ6jGpmZk4W+G4+axzKm/0Wss/HcC4cWSwZRpuVwW06vj4UYQBoD0b7zMoMukeYS+p2n83UYUwNLZatEXKUa1RMIKpa1BEAYsJcc0844Vtz+DGAvqN1GSMkRTgZhmSmYERemnjBhFCEFWLxsZnWCPabp7zlByTV48IxQzMxKp/507hXuDdrBABcOL1Y2GWnVAAAIABJREFUzBDmUBSWBhXkQPIIm9YIPlkucZTl5QqEztJW9qg1X1paqyjbqjR6+jBjc6LOIZM0uROVI1LVUA7kAYCvPVvXEUJmL8r55wFZXc31eZHmcSFopJX5fecPLl9ZIs2bPKKVIXuES/e3oKk7gqtOYktJZdg8wjz1KZPaK08cwTItkiKs6dTS3uwDKyem8oL7MnmRPeeyQsSvVzFm8X50y2x8Z+ZIUxEWRIXtzweqeGuEdekp0f6M/doDkbjvUcomUQCS/UkxJ46airCVCMUML6UM+dp6g51Ae20Do6ZTMaDa07aJIPcTcn13BmMWawTv3OUBvi1gU4RtqnZE1RBVdWSkuEQwYLmnlLcLguFGndV2hETdyP1p70TY7At4wK3YxAALETasEapOxcoAvA85Y0IBnv/BKSL7xgUIvh8/phlYWft4iz9VnryV4HNZEe4MRrF0TzMuObYEhBBLvys8wtIgzc/rNTIrvM4TqXAy0lPc8IdVy3JQ/NgApAwNszq5jb7XZaTpTatavDWC1w0vg8J9xxJJz0nzCmJhV9EtqrmtvuwBIh+fSox5PXKfoMYpwqYgAyB+BSWNiglTHEOzUtHqjyKqsnGKC0I86OB9qz3rkmwyrtgutWP+nPL+2U5yD0kRtlkjLIqw7ZnhlhVNuleJILf95p6IsHolQmaqW4wJ/oiadP4Lt03yeuATBVXdKjLZA1keeACMx/H7wb8TVc3nT+ZnF0wtwk/OHm8pg50IWywZxAwk2sRKHH0rwrkG9+oMRr+8q0YQsAvkSpd98LjqpBG47rTRlptnebiNmxGIqPC6FAspkyfMxTTdstyY3Z/WVyclQ1aEk14XMdOEmSluQSoVMVmNdwBsf96521MCHLdfNAl3XDgZ2Wke0bH2pQgnAlcuzA7QVDU6pIkisvfKDreLiE7KnaDeuCKc4/Mk7RySlk8hIn3Gy2lPpXtcLCIVvjONIqZTSzZATl8eTj0dCfJ8XlEvOT4P0rwuUMo6Zn7feXvulKwR/QHv5EMxDW9urEVeuhfnTGK+5/QUN3RqLkHFB3lNp9A0q/dcWCME4THP4VIUxGTF3fhujfQ6Ynnss3sv5VUjZBWKg7dtflw7gbC/MpmvPMHBFGFzMGk32q19+TRumZIH+5HGs8vXBLWn3BJ7hOMVxUSwf8/+bOiUzTZ3K6RfinCyWfsWaxUx+0N5gI9XhK1kkA8gGSlMvZFfamKeg/VjPO3aKr2Ix+7HBsw0vIyC9HhFWCHEptyy38Gomc3QKUWzQaiGJhnkCzOZHYuvWcsVRjMjYV01wp7SB6zWBcBsi1yQ0HWKD7c3IKrp+OYJLCuTIxHhTEkR5tfB68brVsS6sWyfhJchwK0RwaiW0CMsrBEGkeKkwsMzOLZnHLC2b52aFiNGKsx7zn249rqy/3YbaiAHpfHWCKEIG0smysEGV1H5+eVsDQCL2s49wvbnqFhaOSIYNYkdzxIKJTJuslziQJvDVGmJEBz45MnEirCVMCZVhBNYI2T1WQYnmbpOe1Uv+eIBdZ0htPRERBYyEbLSPFZrRG9EWArcTGsEtVg/eRDA68vndVusEVx48rqt/byq630qsm6bIGj3u+s6xQfb6jHnvmUIRTWxMlDvHmFWnvZArM9+d9CIMMBUYG7MthPhWePycdclUy2fuWwPN8A6dq9NbZxsTLbb3+RHTKM4fmQubjvvGIzM88WlHA/FIzxhSCZunDMWF00v7nU/viRanqSKKFJDl6+Fz47kDcrui5o9oRDnThkqFIg0Y3mUQ4VLsaoxikLgdinitb8A62gDES0pOeOpaZYyiS9Drs8LhZjvKD8UuCVlhd8j3iZMIqxY7B0xTUdM1S3Bg6zaHOoKEEcKRTHJQ44xWQ5gKi6vd/4ZnyzX34BBVoR31nfhtHH5on4yjKiYD0RcqZXVIpfNc8XXC5ZVJI9CoOmm55b/lpeAk1Uh+0xwmXTpenyKj58rzhqhmR2vjHhrBLEsmcgVYdn7x48ZjJoTvFwKwTdPKMHvLposrFbmZCJTLbIrXInIaCLYiXCi4ygKYet99scaIdelLUuSyBohZ0zsyod99Qm/WFbQA4UYJFLKvvBJZC7FuoYtvyS7HxtIPBksK80tvp/tkyYMS9fGf3NbBMDuAyd+ybIlLuM5q+/ir8zmViDjGLY+Xr49cr3abT6AaVHTKfDxzgaMH5IhJm9nW4gwJ/eSemqcN8WtWG1wfTBhToQDUdWicPFqlVP7miRCuI11hIVv2DZ2mEqaqbxyUmENqOKJL69Lfm1ul9W6Zq8/gKmUPq9LBD7ypDzhY3YpljbAux/Zyhc13i1gH2P4SkRs9RSzf9d0XVgjgF4myyWJaGWbJG9zXcYSmL0pwhFVM1bv6N0akYgI2+8VP66m995eeNZxa00nVJ32OtZmpbola4RmyTbEnxuW6wL48mmyMkuE7Q1gz2ciRdjrconvA+jzmgDJIyysEdbz6pSi1R9BIKqhJxITgbOv34pw75m4QSXCqR5FTPBJFlXJEIqw1KD8ETWORGcYUQJfYzTVo+BncycgN90LPtaKiPgQiLBLYS9dGJHn63W/WWMLjCWEJCIsJstZr8UliLBu/J+4HngnnJV2eOSON2K7RznbZ7UPdIViScmZRzGtEYnWk3UpBHnpXos/uN/lU0jcQMbvKx8YPS7F0omruh5H5jJT3EKB+aKJMGAqjjk+j+h4gjFN3HcelXOPcH/aPQCkeg0veUyDP6xaBmWuIvGls7hCZvEP2hRhvoKJ3EG5FOsC/ZyY2gkvh90mwTdx36m98+OdnZgsp1vPE7d8mh7vEY6q5mL7PJiIadLkMonQyMFucXYabpgz1vS0S8o4wNqYne/yvuJQ1glm14+4/xVCxGSe3kANtUystWupe6nfUoiUOjf3sU8IslsjeiKszjJS3MIaoVPTXsSVfW5rIZy8ikEyPuhINLGHECJsYTlpVo+wqRKy3+1BU8XWKU04+cuOouxUa+CnWwMxds3J2y+vY5Pss+28H9Z0is5gDKPyfOL6rB5hyRpha8det5Xs9bV8WkYqy+hQavU8ivsrrbIiK8JuF7NGmMunJSBtlFoyK/Z7oBBiWQKOV5VZd+x/LkKY9Rjf7vlKH3YCyK7BEDMU65JwwhphU4QTTpYz+la+hCkPRrilIE3Yj+yKsBFo24hwOMZsQpbJckY2tCMQYxPXbG3QrSiifbL5NMmJmOnThiFM6JIybg9aTKGqN86Y6nEhP92LhcYkZfuEehlZqZIiHE1ujRDPOLU+43HLpylWW026l73QR9V09ERikjXCyGSovN0m5gsy4q0RdiUalucsKGW2kiEzhQXj7YHoV0cRPhQiLA8IgYgaFzkqCoHXZc4g5dtdRJpAoZsR8UAjzevC92aOssykdom0IH/o2Od2a4QnyVPAO+HD9b0ya4TZsSkJOncA6AxF45aM4fC4ibFSA43rdDm+d+ooMcHrUCB3xkIRdlkVRI/R8ctELWbzkimK6eX7oq0RgLROrc+DNG5niKpxinBnMIYUd3xHmwxeF3vhTCiqoSeiIkO6NnvKyzJLWaRNWR3JwST3enNwxd+eSrQrQeI8Ut8ip4L582knAKZH2Jq6Fh6+OCUVcURYniUv+2HtKwUEomqvk5X4R/xyZMuNeU28r4j7urWcxvYXfngKvnfqyIQKsULQL0VYDibs57YoaZI1wqLSJnlNtd0akZnqtngD+YDH1V+LgiidV1btRXo7SRvmE+b4pBUe7PJ7JMh1zEztW96e1qtXMlWsKcsDv7g3y4k2Ed9m+f5mAMDJjbnKi06t1rnsJNYIOTAH2FgmW0D6Elvk51dWhPn1c6+laiiffMzgE7cSvVAD4OsQm2t68880W9n4Z3I92H9z3zOH/cUKALNmFWamiLFNXi5U9EPCP00tdWP3CNtXA5L34fed3wNNZ2TWVIQTe4TtL9S46aVNuPP9XZb2xoltZyiWcBy0eITV5DZCwOxjTA+7WRZ7kOdS2LNr99MmQnEO80p7XYplqVk72GS5vq0R9uCIP4/Mp20TSnRdGstMTzZThNn98dgELDVBdtAOsWhAgsw4z1gI0ULVxdJ9vU2WI4TNg+roh0d40FaNANgafTxi6Q8RFtYIqWMORLU4RZgfjy/NxgmV3Ij7m7Y6XPzx61Ms/xNiepsJMQca+2S5ZGkW7ufNOkxy51KsHmUzJWUlwuGYnnSynMelwB9my6fZo3WOW8895jDLRyzrDgLx1ggvVxT5K4A1HTGFxAUPOcarUDMGgQhz1SI7zfQLB6PmAva8M2oPRoWC0R8Qwvxr3WHmd5ItLfaoWPZ9cuIlp1MBI6ui0ThFWCbPYra6JYVsnkdWH+W2xdt5co+w9bg8tZ/oFctWjzDzqPMONiy9LYgpSOZAI7/IJNEzLq/Rygd1O4G1k4Fk4NcxtiCdrV2Z4DhMEXb1maKzE1d5XVE5LUkIsdhc+HXGL0FnvRa/pAjzJRUphYUQMk8p+57LRpxkIt+XB7bAsIaZHmHrKhX2VGya1yXWWwX6UISz0vDZ3hZxPF0K8s11hK11INcDr0uPoiAMc3CXV42wt2G3SxE2Bh5sy/5aVVKELTa0PoYY+VmWB3bhAU+mCBvqZKIXagDmcldyQOlSrPeATTQ3gxIqCLG1vtwuEjdR0tbU0BqIYHJRllWwsgW59qyQIoiwmT1NZr/jgQhfS9i0RrDj87pL5hG2T5ar7wzBpRCx7rGLyB7haEK11+0ior1GehkrgfgXgPFrk7eJfQ1FWEuQSbOjODsNO+u6MbUkq9fzZxnrU+s6hd94C1si2LPV/PqimjXbyj3+/DnjNpJwTLNZI7iAZfafvT3LgMSDxOpZVnFLJupRVe/XZDkAyEv3oOPL7hFOdbuEhyURmbWD141sjWCKcHwlp3hcCMeY35Efm6cf+DHYMT8fImwHWzXC2ikB8ZFQsgZjWiMOUxHmHmGbSsZXWZADtqST5RRFvB1voOvNJQ0ovIz8gRLWCB5pqiZhtq8aAUjq+SBaI3KNyXKAQYSNa0uXOutDIcIAS4vxCXEZSVQkwDrQRVRdvFUKsL6URrN1UGIyJO9wEinCOkVzTxjbazvj1mGVSVdia4Q1sDGXnbIOEvK5elOEZURtqz4Eo5r0jMftbknfxmwKtbgm4ZOM/74M2YvMMy9yWaihLHrdSp/rWSadrORSLMe1vlmOZ0xMdZJDVukBWF49zlPnssrI7x2vH0VJPJDLZUum9nBrGLdf8cHe7n/mas3/s/e2sbY0WXnYquq99zn33Pt+v/edz3deZoZhhjF4BjPMABMwAxjGEOx8EBksO4HY2CjGDolAthQ5+eEfkeVIcRITIWQ5KJYtYimWgxEyyh/s/DNjC7CxNdZkkPFkbDzDAPN+3HvO3t2VH9Wr6lmrVnVX769zbsKSrs49+/Suru6urlr1rGc96/5mNSLCY/h4BhF+Y4yOaGoEj19T+SDkn4PaAIQQcmW5ilPyjIo28QYF783FqktILFFbZTk25HHqgin9eG86AFE4KdRS8Un6sCHruPIayNXmnHMC1db6wXzrOBrHhnx1ts+/ek0vPthkZZpQPhNe75IMHAMyRrKcXtcv1x1tVj5pCTPQsRsR4csKNaIWceLo1wB94Tn7N9+4McE5jQjXoqdEGH3L95HXLj2uks5/A3rKeQ5cDKVmT99b0xBidOz1613KJbH6yfQSonz/dkrWdgXzBRGlKoiPd4NIllurSO6un/cXUmExww/KFK74+81uyMlyM2v8c1cb+sKxOMLOuY875z7pnPuUc+7PGX9/xjn3d51zv+Sc+xXn3Pe3tCsR4XmnwMEizgPr9esdbYzvMiKMO0vUquWbOjdJHcuQo4tjgl/2FB6sIK3HoUbIbGGivEg9DzvyGu9ps4qo7Xawk+UOMZxgSkQ4UyOI8mTC6GCBHIzXchuIMPOjX3iwydXgwClDp3VOQ1jb1QYcYRgHBSIME+/1TmZfJ27suJlEZ2PFiPCQJzAiSgUWiOKi+hN//9P0A//rJ8RmEhf+YQjUh/Ld0jrC+XnL87FxkhnbenQkLWH8WBAj//76zW6yxG3Oqi85y3h+/Fkz/pp3TqBh4jrcOCfN1LzPmwkSfVp7ztiOn3cuy6exo6SdFesaOMmEufTsKHFUJaJ4+f7wvGVVlsvRJXvOevjUBa07l3I2HCCURIgIxzavmHPYgAi/CbSE+Roy2ivHl6BGgKM3wAagH+JmCpHQIYRi7GhHGCldOG+FkDdSLclybFI+Lf7E9wUTj7gk+nYoFRaIxijkoFUjMkc3b3YyQFQmzWVQAt+PEOR9vd7Fgj6sHJTR//j3nUJC+ZoyIpw515wHYK0xz95bJ9m8jAiHERG2VSPSPKM2obGseo6yoGpEjf+LqhHX23pieWwv/rT4t3pMoJM5T42ISYNf9Y5nJ4/jMfpbb2zp0XYKES7BEyIqlDu4shwfx9S/Lz7a0rYPGRFWgFXLNWnViBIRzs/xpu8TInw1AyY9d7Wh33z9CNQI51xHRD9GRL+PiD5DRL/gnPvpEMI/g8P+FBH9sxDCdznnHhLRJ51zfyOEcGM0mexy1SVydBMi7CDUABO7VV3lYh05wlvkCBsv/JJkuUMsPcwgd3w8EXNIoMa9TYjwvtQIlfHJ45LbffjURUq2qr3cK591XOdCHUvNQutTGC39rrhH/UCdp2oI7dw6wkRE3/GVb6F15+ndDx/QJ3/9VSKKLzc7Epfrbixk0K4YwXZv3dHnXrMQYTkmcMJ/vO0L+gNRXjwkIuxjQodCaDmpiBeON7a9QFwjEomLKBdlkP3XSEFeJLMjEcD5GIJ8P1lHmDmT4poHyVl8dNOniID1jiceYwgihIemUbKaIUUAF7+O8r32rg0R1s4bn1tn2ztXyqdtupKDjCg9EapGrISCACLCPTw7DNkS6WS5fIxl3//Rd9LXv/vFHI3wcpz04FAQxQxwrGI4tXherXNYlh0u7ZAi+pv7nO+v2AAMQVBtQrClrJ65t6aLlc+ymACuZER4HOcgGTZltXdZP19Gy9lpSDrCFTlLjkJiZMW7zN1F51iPk0H9rpPl4pjI5+LS3swL75TTlDdr8pr4GbMj/PDBBf32oy1td2Wkjyjefy7wkznCcXzem1GN0Ko016PDjbkEOCdbQIVUjRgmEeE8jwVw4uqIcD8EGvy8ktUHX36Wnr1a00feOV0gihM6Wd+5JjWmZdGux3dqpwCvvPHOG1eiXM3yaZ0sBzKZc47wRvtBmiM8SEf99ZsdXax8lUrK9tz9Df3mv9weRUf4w0T0qRDCp0fH9qeI6A+qYwIRPeXik39ARF8goh3NGA6iJRxhzCC0kuWIojN3vY0cYSZ888Qf25AO4amNCd8haGqE3AnNIcKHUCMi2pNfeqIcksKqcDWkknVctb7gMYw5zEQZIdSqEcwR1tQIHULja7oN1YjLdUff9YG3knOOrtZZvQSReEYdljrCl5suSU1hIqCe4DA7+npXZv4SZccRJyhGO1Ky3PgcuNJYkuAbpBTQ2nsRuso8U4V6qI2N1hglKjWBdfRkuwsmInyzkzrAr1/viugHGqpGZEdYHsO/t1SOI4rvWIpaQWNDiIvipptHhLWTmDcbSnbKZfm0XaJGlIhwRunj769d78i7uKnKC6BUE+HnTURp08bNWvJptTn0rc/eo4+9LycM8xyoyz4nRHi9qhaI0CYiG6OjzteoNxODehb8U1NCmB8c27AX8GfurcUczKg6UXbuLlRuw1xCLEauTGpEhSOM0pvWfJxpEJn6hsmP/FnnUGmD7498Jxh9ZsPkRCKiz78aHeEXoZKqtenhfu7U2Pldb32GvvfDL9PH3vcwUiMqiPAz99b0+k1O+OS2WQJw3ZVa3Tp5km3bDzGpETZeOCdbUeqVz+/Y4xlEWKpnxM/4/S8KakDEeM5p/Np3vUC/+F9/22RVOaLsKzCCPs0Rzs86bhDkxoUob/JvdtIR5ihl0hFWgEcbIsyqEdFtxHdfU6q2fRipHvPr+7NX66MV1HgbEf0r+P0z42dof4WIvpyIPktE/4SI/vMQwvSZSTq/LYhwysIcJCphJsutPT3eDmWynEKElxTUOMQ4hKYTMPhlf9zIEd5XCcGnRbOyE4eXqrYpYU5aDFsd97513heLP1NeuMSyRoS5FKdeBA69V8eyTI3YCSQ+O8ILqRHrLm2YapnmRPL9uN71SUOYSGpx9wrx4uSbpOurKgN1LoeohCOs5KK4bY1sZI4wI8KjIwzO7/Wup0/+m1eFc4nfZ/6gNiz9SZRLURPZyjCI1ohwv1rs48/y+2j8d94sEEleMctXXaw7up7lCPN3uD/xZ0bd4++WfNp6VZYi1aHuVx/HBSRzQ6PDp+XTuG2NFskqfnx/2+aCHFol0W9eWDlZrgURzsUKsvNeIMLKIcY+MyiRkkeVIzyMjrW+tO/43W+hP/Shl9PvsrKc3MDzOJ9D+PD9vW/Ip21h498PqCPMa4cdoUvcT3ieHp4nUiO0w5o5wtmBlaoR0rH8/Kjg8uK4juT1jsS94X5qGbHLdUf/7X/wu+nNT9+j3RDoelt3hNkeXKzTfeHoVkxI1dQIvn/yc6ZgJGoEJMvFPs1whLfD5ByO8mmpMiMjwlUd4Wn5tCXGiPC/HhH0WmKZ9xK1vt726T0XhS0SrSUex8mJjAjrynJp3FYiFmiYWB7byMdn9ZP4e+QI95MawmwPLuLm+tXH20kfs2Ultq5ALw3fTkS/SERvJaIPEtFfcc4Vuh7OuT/hnPuEc+4Tn/vc5+hiZvelrVMPgq2GCL9xs6MQ8t+xChC/E0sKahxiKEYteJkT3Bi0pxM1Yj9EWIc1tHzaiw/mOcKYrHRsakSeNDIitFHogeYeseZtoRpxdXuIMNoVJssN2Wm43BMRxgIDeG2rzovNC74f12qRxLK8uyGICXnVuVHrUi7s/YjuOsf8X6mysO6kSD87bPrVYmQ6q0ZQ6gvb3/un/4Y+/j/8g1QswUqW0+8/kcERvs5FTKzQfaZZSUdc8knHnzOeMCKjSLnANn1ChKeTNnTECrP28Z57pEawA6acFXEN4/dQRokXwBCyHCI7qqi3jJscSzWiNXGWQ/DVZLmLTlBcpuYYvM+MWPMt1wmCeEvwvkZqhE/HPEJHeLCjGn/gA2+lH/n296bf3Zh7QZTHNa9lHJmZo989dYGa4IAIQ/SG+x4R4djnVIRg15uRROR+IjWC71dyjp0rNg2DupebcSOGGwm8r58fUUGuKKjD2VgUCX8vNsurvB5aYIt0hMdkOV7TvF20BqklaNt+oD5AlHRElPm+WGgvS9YRxU37lN+SgDugFqVkOXXdKGV4LHCOaw5oTrU2PneA93GrnhdRmeORqRExGqDl05ByNkuNWClAUOkI41i62Q302vVusqocG1/zF163kx/ZWhzhzxDRy/D72ykiv2jfT0R/O0T7FBH9KhG9TzcUQviJEMKHQggfevjw4WJEuFMT/9R3L9Y+ZUjz32P4XaJRR47wVy0uOlRQI3giTiGTyoB5+fkr+pIXrugr3lYX0J4+f80Rjg4wIsJTjvBu1Hg8BTWCiERWqi7VWGSjDsMo5Sb78vQtcoTR+D7GKmfxs87l6kWt5ZXZEK3QaDdOchJhlVrBQoJwUBxhrwtqjO/KECdn1JvEEHYM20snIxiTX6ZGZMoFnocolk8NgZL+JbaxWY0llg1U9aYfhBOI2s3WO8UfcbIRm9RJDsVnlmF0CcvA5zajw3SxXq4awe2svReoDcqn4aKFiW2inbS5CQIY4DZR6imELJ/GaAzf2q3YNNDYzuQlJUshToU6Mqfzcp3l05ybjtah/B3PGbpkt1ZAwD7z8QkJH4KQ3BsCCQdy8pr43oJ8Wvy9jSN8ufbpmCvBEY4/cb5DRJif2fW2N2kkyNPFAk4cZs7UiKzYU6NG8Jjp4d7ifWVn6MWnQDNaoPQyGVyvQ2wMftQoj0hL4TkwoazOpSR5NP18iDLg0o+IMN9LlqkkorqOsCioMU/fCXCvaqoRaaM7TJdYXmK8/n02IcIVjrDKH4qOMK+5uS9at7ykRkj5NNQRnqVGaIqoWrN6WF9u+lhieU4xAq/5GI7wLxDRe5xz73TObYjoe4jop9Uxv0ZE30JE5Jx7ExG9l4g+Pdew5OPMdyVN/CpZRpdY5vY4Q5pfqBWG3xeG9Q413nXr0EdXIMJ1asTP/+jH6IMvT2eK1kyHUXnefP9bn6Zveu9D+rp3vZiOrXOE3Zi1X/JyD7UkuQOIkNYjXKvfo2pEyVd+14v3qfMu1WW/Let8nJgfbaHKmc8Oba2EbM1qiDCRnORwo/hYLZI4DnaDpkYwRzirchBlrmSW2YnH83u4GRNpcBG1qBGFjrCxQL06vrM82WITTM2xEWHpAL4OyXyWQyXk00S4Px/Di/iMHyx4u9wuEsPYsbwwktnKtmSbSTVizNpPGyrvhDPPx+Dvoh1wAD04QIwA80aH0avkODkneJRWZblWBCtxhLkvsPBuOk+bkePcV1QQRFtA8Sl51XKjZalGMCoqOcLy2vph/tqk2o1Kluvb1hjnXHp/cbOrVUH6XukIg+SUjQhnOg3Kp+lcFe9h06DGC9/DNLbGjRIi+0REv/HaNV1tuhQuz+g/jfcmb+jwd+2/Y4WxeWqE1A3uugoirJ4PESRyDfEfzoO8/pmIcJdVIx5v+8mo3pR8mh7fkc/dxqdttWfurWndOfr0WIlvqrJcCJSi5de7vkDwifLawfeOx2xJjRiPE6oR0/7dCp47kQQ3XZo38mZiqmQ0GkvGRUe4fvysSx1C2DnnfoiIfo6IOiL6ayGEX3HO/eD49x8nor9ARD/pnPsnFKkUfzaE8Pm5tpciwjp5YOq7l+suZUhzkhWKn+vKNqc2DDHqBCUi5AifBqLOHGEZmnnm3pp+8vs/TK91eUQ4AAAgAElEQVSOMnZEJCgraLmy20CrI9MOVpYjrJAVRoizzmHUyNVO+Ye+5Hn6x3/+9xVV827DrjYdPbrphbOUJtqFHGFeJJ2jYhJAR3irEGFcJHOyHCMTEPoaJyOUzyGKEyTr1mKy002f6TzI0eSqWnVqhOIIw/vM7+y2l+OUzxNLylocYUmNeEPdc22WfBr2Kf6//MwyPq5z4Jwq58uPiPBc0kYtNM38X6RGaLpTel+GQDzn5ySo7OgkaTSYk5jWMQQaubE5lC4TVQxHeAFHOIR8bzInMWq9c39aECSryqjeWFkcb6QADENIa1A/GBzhIAu6WMZOBJEssUyE79j8/XnqYlXorSZqBCBruEnIyXIVjjBwP4V82iCjACytyfeBr58IIhKwyRogesf2+deu6QWg12nViFQ2u5PXVMsjeOPGrg/Ac/q6yxQzpBtYZcytDXee24bxncjHXyZEuFwHC9WIKZRx/BNTHuJ3+tRO2e5AQ3DN79Ocdd7R25+7ok9/7jUimkCEvZRIvN5mRNiS3mQA5F4lWc45l0ALIhJRjJoVqhGKzsdyh0TsCO9S8aop42v+zddvqn4NUWNluRDCzxLRz6rPfhz+/1ki+raWttDQQ29SjWBqRMERLm/yxcrTazcSEcbsWJ7Pz1VQw407vuggyMWdKCPCp+qPFmfXSEcLOs/hm+vd8ZPlMKSs5dI0NSLpCA+BaDefVHGbdrVZCY4wSvS08OLReOLhZCe0++AYI3XgemfLpyVkwnCS2SFAfd3OZ8cJFwKi6KS1UCP8iGLmdsf+gqfyWkKESydL16NHu9lJ+bQ3bnb5Hbcc4fGjIQRBV8A2guFIWcaLvXOSepL+Pm4kLHmzWls6crXykn4SVSN4U8PvS3lu/i8+mw6cXC773nHy3CAdQJYHS1EAca/iz1YwIcuB5QWSiLmWPpdYnijhzoZUKp3Ip+d4a3PDThqP/xAURzhISkG1Hw6S5aCgRvw9b1rm7P7FqqDNZOAnPzt0lnOyXIUa4fJGBzc2mfaRz1PyquXvPLbQucX94edfuxHKQ3rTrCuq8ftdFt3JGxyLfsfz+r11lxzNa2h7GhHO8oyIVuqk4USNMNbBQjWiAREWaGY/kHdllCDRE46ICBMRvfLCFf3qiAjfryCoSJEiktQIBBn5ehgAuZ+S5SItBhFnzucgyvKRU8bv4WMjVwr50/H8ISbLNSDC7Aj/xus39M4X71ePOxND1jZExCx6gzYe+BoRskssd6IqTvx+WWL5TIAwdS5zhQQ1wsckJGsAHPX8FY4w27rzOUlgAhEmqk+8x+jfMOTKUhsVYtSOMBf3qEnO3QW7t+no0TZLeXngoC2mRozfsyrmSWqEQoQNR5idWOloZoSJSOlAOpcWVp3klLmplI7Xetn5HB4quZVIjUaEpWpE/P8bo4Zk7D9fc1lZLofui24I+TSJCOdjdAZ9zXCTk9Qo4DtckORiPV9iWTsiARwRpEbwpoKo1NnG528hzIgEMr+WaR3aAcTPiGSy3NI5VNOzNLLGDtkiRBhRx0G2mzYylfvRD5kvrVUjWG1hbgFHxQV2WDM1ohzDNXtwuSrmg1RQQ6tGjO8BRhNr1Ah+L1EFhOkpmBBZu2c5ITYjwlrdhygiwtIRltzycoza/Glcyy2fIDnCmy6tQci7tVQjdGVMIl2tTyaopRyOCUQ4hDDqCE8U1MAxCooHZs6Cj5vSPrRTjVrsleev0v+XlFjOZbtLakRWjWDawTU9uFiJ61rDpr8FEdaqEUJH2Jdl3q93PV02USNW4zUNB6tGnMx457xZ+Sau7iLVCHSyOVnO5UkraQeekSPMu2l9zrX3yfk4lVOnxdmt675c1blRRBC+qEy8hxjq2+qkk1qy3BDi/9cnopMcw642nXDKOk/7J8sxImzIwn34nc+nSkO4QMWCGjCZ8a7e4KrxcRkRlslyaULixUTJ2vXgvDEKqo0TLvF43NhqjjAOM0SEdULkrg8iVPvGza7QzEbj+SaEFvm0GUd4/DNKmqHvzOg4I8JTusQ6kSwrKGgdYXQsx40jPwelxcx9iL/n+5GzseNCzAUv0DHgRBWzshzPoY0LNz+GXPACHOF1lyobtiycIulTod7aIdbPgr8XAugnh1AgwiHM0z78yKEmQgqX4sE2rDEPLlZFFrxOTsoc4THnBTauNjVipKIA+OJcTsrKn5UVDUP6GcS5cMOL70VEhDM1gu+LjnCs1Bpeo0bgsWhcCfVqs0r9R0fYirrgxjCVj2cnLZR0RZ6XLeoaq0awsz1JjUhRTjnWa7rmHN045tL6ygsRBbXodKmfPkcJuI9WspyOJvJ6NIQyeTsWD8rvo5aL08Z0ikcGRbTzipK3G2KiYsP6ic7/oclyJzPu2EUjCqonBrYaIswmKsupkOO5dIRTQYtQhkVWYgCcyBHmQWwkIbFlWa86NYIo8niOLp8mEOERWVGOry6oQURCHu8u2uW6E1XYMCt5X46wlfTwpz72pfSXvvsDRCTfD01j0Yiw3MWPC+uIWpbJchKBu1EOGOoDY+gVbdU5OC5+JqgRjxU1QqEMRHEjxhMvSwRheVyi6Cxj6VRtWXXA5r0Slc5BzSz5NMkRjnPXxSrSG7SME1qB4DIiN34361G7YnNrIcJBtYOLfkKCRuTTuezoiEpkBh0G+9jKadSqP1iq9mLl0/y8BBHGa9XUCH0P5d9YNWJMlhvKynIRPZ++Jr4/RFZBjZLnXrMf+IZ30Z/5lvdMXmMqgjM2x87Co2pBjUxlwOTHECRFBukdBUd4vCUb2Ozihpfti4+29OyV4gjDJkWDGVX5NLiOtbGuIzXCubjxFIjw2lKNyM81OcKwudDUCEYaLeoaj1FWeZqkRozdx/yJm91gyzmmokTHp0YQRRpDDWzEYh5EkiM8VVluSsWIq4ASxfvf8g6svE8cYa1WgXPQTd/To21P9zbz6+cD4QhPPKvZlk5olxMyJZZpjhlbTTUi/Z0ry0EYa+kkfqihE6EBzBU46MeWJWPT/GrrZZvTt1130xPvMfpnc4Tl75pLd5epEZwsF2C8XR6oGvGgIgunQ+VEcVLDZx0LKdilPtPCeqOT5TQ1IrdNlCctDDfW+JUr7zPn0QixvqYQYWyD3/MQsp7204AII5r7xnU/+Y4jR9iSBOO/4c+aYWEJDNmz9UOkRmgdbMv4a4VqBFM50oYqbxKYasKOwxAC/e1//Bn6wus3JjUCk+UYrWI0mxdtfqUybzj+LjjCgE63mM5TQCUKdISbVCMMUCTrxUrqjZSTyz+HkNVv+oHMynJNqhGJGiFRwqwaMdkEERF945c9pO/4yrcUbeM15k3CiAgjNcJChF1OsNQKEQjIyHVRAkUWNUKjvMMQefaI0DknUbwiWW4o3+94Htj4Gtf0LFAj+B6hfNqmK5PlBCLcq7mN7w9SIyaSmZnH/jhJ/jUgwvD+3PQVRNgBTeOIPgkjwrViGkRW7kdfrMFEJSLMqkhEpVSpTpZrce7XoMghCnkwf3ocdwwsNSHCsMbeYWpEPH0LP5gIJgaFqFjfR2cuJ8s58fIStU/ih5pQjVgYDjqGIZcy/l6ehzckU5XliOIEf1L5tHHA6+zrdcWRaB0/t2FXm1gN7ijUiAmOMJG9UXy8KxfJlfdiMsufj2jxlhHh7FBw+WBMTrrRKE+SrYqOhjX5xTLJ0lFBZ2bKEWaxfSLUil6lc6PD+sZ2Nxm6x/G2qyDCOUw87QjjtSb5NPgKlyzm92pKOaJwSAbpQGyB2pTQ57RRjB98/rVr+i//1i/Rz/zyZwstXenkUkqEYye+kE/zurIcos3RwV9SWY4IkuVCXngvVl1yKndDmwMa2wInp6BElBsZ3GCEkOlAQ9A6wrLUdPWaRoQ1hACI8Jgst0A1otY2kdYRzpsETDCqcYTD6PTqKEAAQAbpHSVFQo4/HAs6MoSAli6CoMtm54iP7DPO5VM6whzm71xGhL13dLHuivUBN9oFNWKoJ8vZHGEfEyvHsTKJMhpRCw1M5HbbSywvsZefv0fO1fnB3E+mAhFJaoTm6hLJxMfsCMv2dbJci19T84M6z+9Y/P2Lj+Ia0VKQatX5tFm5s9SIKZkSyxI0rwa6FULBl9KiRmTH5DyecHIiQumE4mA7NTWiNgERITdqGhEmOr7MmxDIr+gGP4mI8L31ih5BmH5OsH26rTo1gsjm0AfDIfXe5givFDUCHYvOuTQh9Wox0c+JkSDLh0AdTkvWKFEjdnnjwIbjL1EjRiTiZpepEfc3Hb1xDTrCRj/QYcWNNTpNWn2gZj3QQPi10NSImNEu5Z4sy04GiZ+rhMjlDUKaD8eD2InghBO8J+hYp8QpcIo6B4oCQ3ZuY0ENcHpUZbklORY6YsHOV+QI++RUbhsqV/KfJSIsKRc6vE8kC0bwAs3oJSLCiRrR4AjH9vL51ys11+6J8GlnP54j8y35fRiCPR9nhD2/i0k+DakRvtw0aMWUjUCESRzLkSF0NLwaN3xvUonlWtI2tGGt65frji5WPq1RK6BGrHwLIiw33/H+yDkyJ8sZiPB473nDPokI81wA54+IsEVjyajsMRHhi1VHb3n6crIKG2uFcz8fb/tizeXj+Br4d/bdNCKM6h0tVCciuY5L1QiZpPnFUeq1JVmOKK+X/59BhN14mObYmYiwwRHml5NIyhCdwxI3y3AQrMzMU5yfaJq3NpUtSyTDFcd2PhFx0CWVedK6qCDCp6KTHMNistwuLSxCNWJhieWriWQ5IkxGUhtFdX865xKPzqudN1FewDNqklUKELHPjrBcsKeoEWufkQJ2SnZqoSDKYWZLapAIqBEjQoSleS/WsVTvEOrvOMpvbQ3ea+xfiShaplUW9HeYL72EGqE37Lq4jJBPU8g8OyYYmhbUCAiJYzjWkk9jJ8mST7M29VOmHbtUqnY7JPm0eH/62XlQlx/G//e9vGZE9DHkP4yINjshj7Z9RtkHBi3mrikfvx1ipExzt/ed0rOzD4giqMDoqpDF930uiyxVI+Sz40gAEd6ffF1EtmoEH8MbZ0RHvSPBEc4hb/ncSvm0+ejos1frjAh3TtC8LK1uiQjHv6GTpumKfB01jjBRrHxHNB3VsyJ0Nzub9pM2LeH4eUtf9Y7n6EsmpMNcelbjxmY3wJxSrg83OwbTsia+hQjfADDSRo1gP02OC4xUEeWqo5cTji0ao+FTiPBxqyIstBSKb0TGNFmbbQ4R5hvQ+TKR4pwc4VroY5V2+K45zLjU5uTTiOLuFmuta9tUdmzHMHQg+BlpRzgvlJoacXcRYVaNQM3Vy5kNR834e1PC6ETlRtESb7cQYf1MEVlDHWFdGnet0EpeaG1qRKkaYZVMZucUN2y44X3m3po67+iF+zFBZ9tnNYZ150Y0tB71cTDecONgleOd5whT6QhDOxGRQ2pEXUJNJuvldyEjaTmig05bvO7YPiObUXJIou+RF5sXHC5+wuWhc6JjiRoT6UTVMt9hyrLucd5g8f24WHU5oXc3zOsIG06GTsLTIXz8P1fLY+575AgPdH+zolevd1D5bHpuEeOoj/326jr3dWx0KJpIckxFJNGkRuSkQO6Tg3UIUWKmd9QKa2T0uTymhghjkliitykalV6G0PGqIXj/1Xe+n15+7h4R8aY+r2lRNUK+X4I+w5t8gQgrasQUIjzee466TPkuOmJDNCWfdhrVCCKiv/w9H6SpJjsf+byWaoQtn5avgTcLZrIcbDaWUCM0sOWdE/KYvz06wq05NoyG3/lkuaUcYV1Qw1KdwJdS6AgrlOdc1AhZxUk5wrBbP5XxKbcTE/zlqpvc4Z6Sy5x0XYc8Saakk52cjPVG6FTV+I5hl+tO7LC9m+agTVk7R1i+H/pZiQQTAxFmqyfL8WIyPhd+TkMOq2I4VvSlc0Uyk6WiYAnua2rEX/9PP0x/5GtfScdjFazIp5T3RdwDcFhv+tJRwv/P+MFCnsqWTyOBCE9xhHvlQCdHRPHlvXOwMMmNI7c/ACKHzovg/4YspRVRqewYE4HcluKD6rZaTJcMxoVXIMKVhCLRlkED0vrEc9QIRkW9j/fn8a5Pi2tCLGeuD2Xctn3U+NV925saoRxqosjfz4jwNFUtFdQY5EaNHd4yilFGRPh+IZKr11De2GmOsJVYpzd0+v5uuulrIiL6Ax94K33VO55L58FNvY0Il5sloSOs1uQ0P08gwpkaUZ/DU4SuspFBQ+nAY/sB685PRk2ztGv8/RqoERvIy0i61n1WgeA1+mmdLLcanethVKFpcoRHQNBYrzAS8erjeTQe7YmhRrQiwsmZKxDh8iZfiGQ5QDfUJHkmPzhzs4YyuYQX+FPq4WrNUeu6L9fd5LOQ1IjTIMLRgVHhYFVg40niCCfnBMT195VP452t3n2z1VRVSkTYTpbTCZBYqpYRQ0yW4Ta0fFof6olGq84XqgGaykGE1Ij8mcgo7xx9/Ze+SM+PiPCuHxLndNP5UZw+o6faLG4nkXRE9SJeM8w61ygt/x0TS6YcYXS6hwBor+FcaYQ1F0RhRLikRqCTK7TNR66sLvrDSb7cD02N2IsjzFzePoepL9a5oM+NKgtumUUD2irKBXdVbG6YPsFIKYzrXZ9F93fwvrZcU6R0xSqX+jr31arXKhtErEPLyNkcIpyfb3qeHGYekC4R/4bRnvh7Sc0RHOEUGWLgAlUjXOKb4zWsEphhbxKEfFrDvI4cYe8dXXSebnqp1Y0b7cfbgf75v/6iSJZjnXS2qRwO7n8LNYIVevD51RDhTjyr865nTKFBiUQLEcbkTf54Klnuph+gMmbLs6wgwql/8XdGhFuBJFbMuPPJcs2IsBFqiN8vb4iFCKPUTeIIn8kT7hzyteTfUqWgEzp0Go2xXsY3P3NJb36mXr97TtrmEEvC9oNRhaiXk/GTpBqhoxjeOfq6d79Af/RrX6H3vvmpRW29/Pw9+m++6/308a94s/n3xClU74dGVjo/XVCD7UYhwmlCUkiQlk9L1AiTI5xldRJ/UCHYRJgsB2MO3mm+JowSpEV75UUozSyxjNxO5dzp/89yhId5jrBzrpEjLL/HfVh12kErUdHEEcZFvuB+Smm0MDqErMmqo1ZIn9B9x/B6i2leb0KgdkNSjeDf90GEBTVnyCF8myPMah55bu4Hm4s9eU1iQxVDwFotYF+/xqqkihzhueRlLJSA8mn8fmJCJJHk/8dryhsgUWK5eH7MEUZEmKRqhOKc1mgja2PdnjLvXZG8FYIaF3BNf/eXPkvf+T/+X/Svf/tR+ptWcprSEeZ7//pIjZhCGYlyWJ9tihrBGvrnilKnc7vMmSeK45Y1tdfimXLEJpdAv1zXqRE3uwxqWQmC2tZAEZ3qH6PxLTrCRFludOpZ3S5HmJPlGknPGtVks3aOOIi5feRCTSXSnMKyfqNFjWBH/XQOnYPdHJF93T/67e9NfC/L1idEhBM1AlCJUj4tI0ZodzlZLldSykj88/c39Bf+va9Y3JZzjr7/o++s/j3dQ02N6MrxZpZYVhPwDhxhTpbjqAZRqRqR5dMYbSv7GAtqyM2orhQZPyv7tzHQInTCkc/Ijolugy2rRkgd4aAcgfhZeR1oMcSu29V/d2lOmuIIa0ck6QirYhneQYnlXkZMGBFGGgtSIzBxqh/D31GOLeoKi4Q6JyXzpObyskVby4GhbinrCBPFcVWLerBpXXQiuQHE5B+t4MH3g6/TwUKrx/Lc1JKoEUMYZSV9cZ37OjY1KiA+P7aajvCuH8Qz58gkbwLENQAVgig+n0yNQERY3te6akQpn1YCA7LPMuozP68jItx1LoMlgO7jfPjrX3xMQyD63KvXRES58p6BCNdKLBPld2zWEfZOPL+bvlJQg9+zEM4Gzolzw3Mlyog3rglYlZQ/TojwhaZGxKTo/Nzn+5E4whq4MfoXz91KjahvbNhumRox30E0N05aLZXlLivyaUS8q41/O2eJ5eggWNQIeyd0TLOQSW2X6y6VsLRsadhqiQldV7X43yiOsKZGnPK+HWp6UTzlJJc2O4pqYMqnGTqRJUcYUURADBU1YqWQ+35caK3Ez3XnU/9CWiQNaoThCFvyOoxkRh1h/tv8PUcu766CHlnJVpahQ2jLp0Wno6Z6gibQywF5zwpJcxl51MlyiAhzc1kKTqK9/ZA5zoy8hFBySmvyactUI1RfRgoNFtTg/s85j5oWQlRSXPixIsqPG4IhxHHA43o3hMyFXYwIR2oEcoRb25hru8yJGNcL5AgbcyBudLgLKNOVnWMar0Ena5bUCESJ+V4magQ4jryp0lEfneeh743gCDfM68gRjojw+A6AFJ6oXDk6eL/1xjZ9FsdbbvOb3/cS/fC3vofeZSgt5GS52M48IjyfvExEuXx9OJ9PwsY0lt64T1ZBjeZkuT4sQoRrkXGrf0T7JMvdWWrEMkSYKL44GkGyK8uViDCijlnXdVmf9zXma7FmJ9rK4Hwd2/gWHSLybkmpHMuEjrBChHW5R+1I3OUSy8dKnFlyrrlkOVlQo47y68pAjhFDdooYiVSSSBzSN6kRpmqEhQiXiFEtIhGrGIXCIZxC5BK3MyhqBAwtnnf7BkfYgePIn+HfO9daUEP+X18TImnJUeL3RXOEwYFFmgeig+zkJtWIQcunOeFUIv8Sw+stpjmv/YiihhCdKEScZlUjTGpE/j/K5+nNBfedpSyR+641sWcdYVhTEjWC+5Y2LZNN1NuuOMKd4TDUEGGmMlnyaXrMIv+XSEYUOBq36/MxiOgTaURYqlDwupOS5RRCzIbveAvlDRN/WUeYqEzqZONEK+aZEsnkL6IYsfvhb/2yyQ00q0bM9ZFReasN+Vmk9twGNSLTWPJnjAhbQAk6wlk+za4sp5MkpyzlSmm5T0WzYWvnCN/5ZLl5ErO2zrk9EGG1SA15cjzXoMsTkEGN4InthNQIPudNJSTVYmehRgAifKGoEdYkR3S6IiTHMC2BdMquJueuQCB8cRyiKGz6PuYypPE6OidpRbnEsuSvsgNnXevKGxzhCUQY30+LGkGUtYn5ndZcXMshR9krRNBNqa1pP5iGIZ/Dkk/jAhUtHGGRZAeTP1aWc25MxOHNrdYRZtUI2FRi4p8HpyglC7ksn4ZZ9KhFy4byZEumAS0r1g9BOFEZEZ7XEbbk04RT3JcyX/E+UOo7b1CwxGyJvM9dU/wZeak6WW6caw+lRuj32RmOsPEgmMqEa44Tn/FxbrwGnSwHHPVxsFmbq5wsJ9FDBDV06Vx+v/WriWt5C8CBib+xshwjwhApgGt6fURyf+vRTfrsZjc0PyO+D4kaMdPHzrkiZ8NWjfDpfp09Wc7JSB+RjQijvCH3sYYIr0eO8BIJwUyNkMfmSKQ8vlVH+EGDjvAtO8J7IMK+TJ6yXhhEhNeJgxt/j1mzY3tnGnQ8AVkDvTYAjmmoKMAL6VIT1IhjI8LAU+Okl4QIa2pEQ2XBu2IlR/j0z7hQVZngCAueIWp4jjxbdpQ6Jx0nPE9C0cBBqnHdorSZROpsRLicQCU1R4ZQd4AI87xwXVlsiaR8Go8vopp82jwiXPIty7/znKQ3crot/H/iCPu8KUSNX6IyWQ51hAM4ftwvdNoRvcfwbEYLZaIKUX7/lma4W/J+j4BridSI2cpyKcJVQ4QHgf6yYZGUYdzgRYcxI6eRftcGlGAki6kVWvZsf2pE/FnkRPgSOKkVadDyaVkXGj5DyqCgBuX7hQU1tApH4givtWoEFNRQZcBr8mlWpcspExxh71LivESE8/+5ciVSI7Z9e4XEAhGeWXucK3OaptB7jMacy5KGMTxXkxoB60uiRowbDy2ftllF1Qi+9W2qEbzBkzeAq/LqyFwzNeKuI8LeO3r+/oZefHDR/J24w4p3d4pawQ8IQ1UyBMS79f37v8Q6mBj0OWsD4Kjnh7D5vhOznKSOjQjHn4gIa/k0zf1kO6Xs3KGG4V6i8zjCc5w0D4uHDK/m+8jvFoe3mBohdYRlZnFGhDPKqG3VZUQ4JcsZkKsVml5XQsFc156bSY65oTyR7kFChCUirakJRBLdtYxVF4iy063l0zwgwshf1IZzfR8yJQG5q3w5OdtfPgepIyydQcEN9Tl0zgU6GBVM1AjHyF7uV44U7McRxvf30Y2FCM9zhK1N31Y4P2UpYPw/It9aUqyDcPa8fFpeU7ZjQY2cmGw7e61Wf59LKp3lNKIGdEJ/PVwroP5EWU2CTSZrwto5yGNM1QjnRrURuWlewYYOrxH7PAVwaROqER7oRxVEmB28LwI1YhkiLB3hufwUBg90n8vj6FYR4RCIEI947XpH3sm5E99P7iPTE3S1003HyXL1qJw2nr90gSyWvdXzcKuO8P2GZLlbVY0gIvrpH/oovXC/3RH2QI24XHf0xcc784Xhm2SRvTHkeLZkOc+JC4G8ctwyNeL0TlIta7XFZNjquH3FBYWzfLOmJ/PUJH+P7S7rCGvJqFP67Dx8ask1bJ3PTmwtGe3eJr5bqQQpOwywEPJis1EoDy+oNjXCi+OIJGLDlqgR6Ajj+FMhVKEaobjlS+TTcNEKyomsWQiQyQ9hZjZGHlOy3AQiLM9P4Ijka9JIXt44jgsV6Aib1AhAezlvwTuXkqtkKL2kRvAmKhib+ilzhmP3+nUuz7tER9jiw+tyywkFF6hx/MnX5F1GL/neRMmrciNmGb/fIcS+YGVOdqbdnu98TSUpVSJtKKgRgtr8APLIl8bvqUb+B9iIYWU5PKYPwaRGeD8quQx53MV+yk2CHTVydNO36wjj9Wat+bzZtDjCvzXBEZ4y5mc/HstxzwFCVk5TrRz27alG5HlgM+r/vn69Myu8EUlE+Fve99K4cZZ95jk5J8s1OMIVQDBGpWSuxmblm+9TCzXi1h3htz93teh4lCPh3Yh1gbFcsZ3ghXJAZ5NPcznz8UIVADlHslzirQ3D3s6YrKrwTDQAACAASURBVG1/XI8ucdAAEV4pBLjGx7rbyXLx56Hi+m3nypsJ+blOPvBmEgP+nyWEtruMCEe1iTy5MfVAS3sNExP6GhBhS5KLzeJUC46wR0eYVSMkesUOm3XLW+TTtBNZM+RDI7rGxgUqNgZapW1Q5+fJHwsaoCNLVFJUHu8wWU62K2gcygFMRRBE2LxMVNH60q3WGY7wo210TPQc3qrWgPxuTZOwON4CEWYE2GOSoFQmmq8sN54vjKoRHjjC7AQciAjf9Pp9ZofBfnfT930eA4LqMgRz86Z5orgBwmRNrSxhFdRIsnvjoVs1p0eKj33d65UnuunbOMJwb1sQYe4rI7r8WWuuECLCLZRO76WOMPdTG6OeS9+pYxgqiVyuoyP86uNdsd5ingJfw0fe9QJ95F0vFG2uOy9AhiaaS4Ui6pmSB69BKz+YiOgtz8Ry3A+fqgOud9eDqFjnERGuh1Cciy/FRr2cRCNXd7yp59p98QTE6BCatcM/th2DGiEKGhxdPi3+zIhUdo5v1EJf9OsOI8JduoY44PbhZrdaQtzmSizDr5IjnO/vvVFyZjs6mElVAKkRFR3h5AhXqBHoMMf+1hHhGkdYJwohNQKRV0b8tOGmGM9vUiOaOMIZceN29d9Xo5M1hQgH5bQVyXLodEMUhQiS5bZ5o5EcP7jnghoxgIyYy+g8os4aBURZvUUcYbUpJMoOCVaWI5qPjiVnU5RYls6P9fy0fBpX/2KQYjU6xrv0vs5cEziRXGK5TJDd0xE27hcRcoTtdxf7NoxRSFQB4XcYUWIiWzVCby5RPo2/c73tC9AJkWe8BpRarN2XrB4wf9906F5X8iSiUQ2k3laslNaICI/HPWp01L0rN/p2slycF2+loAbMA1fjvP/a9a5Y43GczHWRVUYe3bS/A1XVCFcm87UqRhARvf+tT9M/+NGP0Ve87ZnqMU+cI4yhhlSZrrI7uFx3gm9iI8Kn7G02noBQyJwtJ/OdEBGGyXlvasQJdYSRtrIbYuUaLZqPz9mqHHgXDRMMiE6vUtJ5V+gIWwU18Pj8OSLCmYYyBEoFF5CrdVOrLDfUqRHM5yUC+TSDe2BxhDufi0jIqlpOhGFRb7p2v3M42Jbg0tSGKQuwucUwM36fHfKLlZ+RT4PvDdmBTdn2wGfM77RyhM3Kcnx9sq88Fzon51a+Dk5UCSGPD5Est2A8W8lyyREGagRRGcXQlmkh4PyqKnOI/rJlOk5Ga5E3m6kRbe8rgitcYlnPW/vufS0EHfvEGtpEE8lyg1QBQU3WRI0AekeRrKmoEbjB4GNYBxo3nIg8E8FmDdah2thZwhHW8l6paI1ChKf4oZEuOHuqeL5xXD7a9k1qV8g3x8+0oY7++TnCI51tCHQ1JqC9dr0zKpKWvlTN+BlyMmybfNo4lg0HXG/AWhPl2N7xwjTzoMmDcM593Dn3Sefcp5xzf65yzDc5537ROfcrzrm/v6iXC8y7vLtkR7jmlF2svCwRKHa+7dyVY1iagEIZ+jhHiWXU8Nz3PTslNQInfQzFE2HoN58fd4R3mSOsqRGnHm7x/ZhGhPHRVakR40SDlalYAjCXWI4KJOy0iGQ5Y5wTSR3hFDadoEbotdBCizYrT7seqRHgNFYGOzowyBG2eMGLqBHQLn6fFzouPTrVFn6Pu7Y2FkqkOxERbUYURugIK8cenwtKOvJGRyeJpZBtCOmdy9SWZePZojNwYQJMliOaXzhzcSVAhAeNCOeNGZvefHnHXNo872C7rY6w0BFO13nYGoOcaTTrnbXmwERPgDGDNAg9jgpFiFBGG6xjuES27jtGj7YaEZ5AFbND1IK4OvH/jcHD55B/zbYLqBFZNcLOTdLGCYtWG+IzWJ/PjetgbsDVmFj22uOdmbTGNues6yqXLfc3UUS13KdnNRtAhBsT5Vpt9pY75zoi+jEi+v1E9H4i+l7n3PvVMc8S0f9MRH8ghPC7iOg/OmovwaKAdhsifLHqTB08lsohOh9HGFGCsrJc+w748PO3v/RFG+MiQXR85xPl03hB0aL5iEgLRPgOq0boIgKnHm+YTMqm0bU6IgzUCHB6GD3yTiZgxSx5KPU75LBzCDYlQegIp+NLDnhG02QbfIyWjrIKatz0DY5wUMlyEDpnm1ONQKfClE8DR+Ri3U2WWMbvoWRQQoSBW6mRR80RRpF8TJYTiVOMGI4bT50kltCikJ2JhDgvpEZYHPYqItwSFldom0iW63NSp0WNQIffOy4aEu9D5zMiPEdl4iE7DKAjXGx+93vnrep58ZxlNKxKjUjRGen0bkF9RERKgxz3WZs7vy+Deje4RLbuOzrNOu9jNyFZtoQaoTcFmSMsK8vNIcKtz4jP96iZI9xGjUgavQtoGscyxxvBEOjNT0c+bZQC1A5p/v+cD7FWiHBTstw4xvRz77zUryciulyICM9ZiwfxYSL6VAjh0yGEGyL6KSL6g+qYP0xEfzuE8GtERCGEf3vUXoJh2OqDLz9LH37n89Ukqsu1V6oR8SeH+ri9cxg6C3pM8Mt1WmpE/Lk9IPTinEtO57Gddlwk+2GgrsvICj9vPOcFFky5yzrCDeV+j2mY8Z76UCDC4HDgQmIg7qzGkKgRAakRcQHRIfpeOVOiL6OOME5sFvUlSSLpTWPSHsd+S47wBu557Z2yCrgQ2bzgOWoEOhrcXV3EgbsREeF6g0E5bZxolyMLMsxNlJ0MzRHuAzrAY18GyWfmhCamBGQkNB6fElWGnAzFYzksdIT5UHQMHu3JEeb+a+eXDRMNNd0Ej+Xxy6FhRnRbpc+wMAvrCGsKyL6vvKWMQaSUEiaoEXETIysFJhUbeDf4GuJ4y99HakSSPetDwX+/3g5iPibKvE4+NG3WDD1sbTyOWyvL4f8tZZZ+KPuHhslfred7tO3b+ucak+XwOs5MjchqQJEa8eKDDRHZ+vPpO42O8BJEmMeGpVbB1CW2JclyLdbS2tuI6F/B758ZP0P7MiJ6zjn38865f+Sc+4+thpxzf8I59wnn3Cc+97nP7ddhn1+qb3v/m+hv/cmvq+7aL1adWFyFRNeZOcLWBMS2WrAD3tcyunrYjjOFrY584/DZ7IboeKU+c1KW4AgDNeLMO+glpvVOT91VS7eyGG8NjrBGhDM1IghqRAehYEZ2t4lfWfaPQ/zINeTjEVWqcaqtYgKb5AgrRHhXz0znKSOEeBzPE9yGTlqbskh9INHfoJwFrOY21V6vHPCsZFC+v1peK4UjBSIsncFeJ04N6Gy7AsX0LpdhvgBtaSKJLreYVQ3uDdQRdva4rFlE2xARluiwRXNJoXqoHOddzk0oKCIz3UCqQYxkZYd+O+xfvAjb1smVeG+m5uP0vg5lMuduyJHJTBksN4BJXQaS5YK6nxY1AqML8XxSPWDX1/nlPM+3UCNKR9jgCPdhNpTerCMM+RBtyXKu2MhMUSNqfz+l5ahPPPdbn42osL6+JYgwz0W80W2hUqZIgAZunKEasSBZrsVaHGHrivVMviKiryai7ySibyeiP++c+7LiSyH8RAjhQyGEDz18+HBxZ4nigLmpLJLaLtde3FQMv5+bI4whcr0TzpPZ6ZBNRCkO2XGmSerYHGGBCGdhe6LMtZMc4SckWU6hpaeOQER+o1w49QZLaAdXtEiZI8yIMIaQeUK6GR1hHaKv0RqI8uKGvEc+Hh3hWqJRDgVLBx45oeuECtUXW6EaMYR0blRXYJtHhKE4AXBG2QIgxpwdXm8r/59RTeccOCvIR44/twptS4jwkBE+VEvge+Jc6Wyz44NOEqMx7EzkZLmFHGHYBLEhNWJODkxb56RGq1YzsOTvdBQCN3jDwOMcdb+n+4HzVqRGAFXowLnWQTtoVhGcekENO5kT5cv4p6UjHEIYFSEyt1drXVvUCO0AljrC9U0qR3QOUY3QHOEpRJioHYXFcdkqn6aTl+cQ4bMny/ks3eYc0dsqjrBw1uc4wuOzY2pEi7uQ1LMMRDgE+R7fO7Ij3KIj/Bkiehl+fzsRfdY45vMhhNeJ6HXn3D8gog8Q0b84Si/BvIFa1OyPf8O7xO5VJMuND/2UclZoWDlNn3IqvHUsQ2TykNOcSvOYr50XXZaaIpJViZyLky+HpRjJuqumVSNOPcmh9FP+THOEYdJVu3y+vwUiPIaQQ8jO4m7csCSHbJzwp4oRaI1fPH7TgAjzMRiWXHkuqEHibze7ukKK5ghfrDp6lXZZVUBxJaesB3Qttwt/D6qyl1FAhE0jyQOglERMrXKpLT4/UebYiWQ5TY3AZDnY2ERnG9B86O8Q4pi4VIjwvqoRsrJcTpaTCiGNaBvcaJ04l56lctzi37PDH5UxciIzOnHz1Ij4cwhkUCPauaeWWcoYRKTuUx1EYW4ljj+kWySuOIwjHLdB0WaIZJSBv8OqEbqPiPzzs8FkuZojmZHB+TGwUg6kpdW9G8Ks49ROjZCRqDnzbj55WZ///IgwyOy5jAjrNV44683UiLx2z1lNNQKr7kUd+unkx32spbVfIKL3OOfe6ZzbENH3ENFPq2P+DyL6Bufcyjl3RUQfIaJ/ftSejha5R+P/Z3r/7b/rzfTxr3hz+l2/8OfceSHfVQ90C+U6tuVJ9bDKNUt260ssJzKOiHDnksZn5nPnhanzUZf1lGWpj2FISSE6h2rEPEe4liCHx3LoadeDioeTCVx8vIfFNf6coEYoiS88HsOrVuW7+H2eLGFBWsUEvCSfBpXlamNdqkYAIszUCMWVnLIAyCj/LKgRgAhr6gqaTNKLDqxWUCnD3DLZMJVYNniySGdAGo12ABFB5KQpHhNYwnmRjrCBcO6rI8x9FMlyCgXkZzBFc+lc/BfnnZikh8lyc+s3Rhm5xHKmRuyv0BP7xnNH/X2epEa4rAbAbWH5Z02N0KgbUyW8A6BiKFHj662tGiH52+wQ5bmiBkKtOz+O+bYxwMYJ1ivvispyFiKMp1+aLEfUiAgb8/FUslz8TlNXjmasGsHJrzVEWOSWzNyvlCw3bnSbOMIV0QAPERuOSi2VT5uz2ScZQtgR0Q8R0c9RdG7/VgjhV5xzP+ic+8HxmH9ORH+PiH6ZiP4hEf3VEMI/PWpPucPwAJaiuYgIWzJmp7QpakSWwDklNSL+PFSnMFd/OTI1Ap4N6wgT5ReI0XtcxFeda9qV36admxoRw7rTobhashxRfq5Xm4wI86aREUT0JRAt2ipqhJ0sFz9D5YREjVhntLeGoJvUCC/l0zaAOtcR4fhzCHGR5nPvTY1IjqNEacPIqURViSlHeFBOGzsiSD/hV6+gRqykI4xJwSEEgfARxfdJcGW9K8YpLpJvffYedd7R//1vXxvv1bLEHtyMs7EjvOmkI9yycHZeKqToxDkrWU7fe1EoZojjJdKL2t5XkdswllhGRPgQdK92asnrr/NpnXPU91LBhV+bHpLVZDGj/H3OB3AONruDSqgbIiddO5rOaY4w09vGTepUZbnON0dHZXQr/v9i5QUiHJFEX5wPecOtywje+2ZHeILjnT5z5XWcyzJFKp47c4QVgGJEImq2j2pEtbKc46I+WS1iSgVkH2sqsRxC+Fki+ln12Y+r3/8SEf2l43XNtiW7Em1CJubA3fpSy2jIUJy3NgCOe/5li0zNauGLQw0nWi3xRCS1T/nn2vsmmaXbtKLK1IknOWviLQtqTDnC8fd7G50sFxdTK8yXFA1aqBFeOmt4/GZcrC5WHpxp9X0jo3zV2fJpUzQgdGC2/ZAq6fHabUlu1QypEVo+LUcz8t+nOcLgtDGah6j7MNCFW4k2U7KcWs0FRxOcnNwX6J9nbmyZLMebgwcXK/rytzxF/+jXfjO1uWQO1Qg2UdRj5cjOXqoRfels8f/5NBY1AttgZYwc+XDNVCak2OyGgVadFxGSQza+WPUOzeJSW/MxjjVNp9n1yDXP16D1r0MgkbiMybL8e0SESz6ptUnhfnK7lm1W7QAHUhW4j5uVLzjCK+9o5ePnzNO/t+kWOWpENho/3T+DqmZcN17ubahGYNLs25+rcISNTUfNso6wjARM2TqN5XIsMXjJlIjbSJa7UyYGzEKnAsPviOKcwzBcVkhCnSFZTpLx92/nVJrHK5hod8NQSMppnVbvIiJ8ynt2DCs5wqc9Hy7iPMwKgXIYf3qC4oUK5dOyvmqZiOd9VjToGREe6te6ArSWjY+/WHu6XHfkfT0hdmNsGhlB5vVZOMKVG+5hvCE1IqOI+dgWakQOPY/fGRvIeuWUrmcSER6kA47VzuI1lYl5yclQ14rOwABh76QagSjUeI5ebUC8cxktco6++h3P0S/+2m/Rrh/G0r3tA1rLihFFRPhiVT7Tlg2ud7I4B26gsbLcFDXCA/0qRT7AeZm7vhRZGEYlAS8584e+73ZildwEEtXl03KFPP6M16GhGEea/8v5AN4BpQEoJ0SsGtGXqhHOTpZD3u8UNaJVEhOXIe7jxapTHOE4D/C9eu5+lAdD3nDrhkUiwvPOmB6jsY3y2o4FVO1jGXENQjVisrLcTBd1Zbll1Ah5LG8GBTXi//eOsKBGLPsu8pz64bwc4aT5aSRQ8IA7pXyaV4vevrY+EXqdFzBJ30iTtZfHdSOKpKvf3DXD5BT8/ZTn08hoDfW1/saTNE80u2FICVs6FM3f72BxJYKwsnGtvNtHagQff7Hq6HLdiaIbBTVi5cZqduDMj6oR7HRugCJQu9/8cQg0Jsv58XcrnG42kcyST9OyZXwv5jjCIsmOOZoelQhyRElTDVgBgQ2fFXPvsS9OLL4kMtyzRJukaPyeV56j1296+uSvv7qYZqX58kRjqdpxrAlnoKFdC23jOVRUllMIpmwD6B9jshuG9eeuLwMcLA/mFY3lsPe9VpQm/79OVUOqi07mRI4uRjHk+LOT5fB9CCEmy+nkJe9L/VwiucGpvZubzjevhXjd3McaIszne2F0hLHP7Yhw/k5LH72FCBteFyL6t6IaEfK6+9zVmu6tO6HVTrSQGjF+dxk1gudIm5vMKD4RHT1ZrokacZfMLXgY2lDaiCf2cxlONnrO4gFwSidpiQbglC0pf7nEZIgxpHuSFn3lGK+8o7V/EpPlTjvocBG/6GI538mCGpXoBDvCN7th1J6NyK9VJclC+ojsa+WNy7VRZvhi5ely5Wk78i11X2P/PK29F/PAWukIo2pE7X4jTQoz2FucJ21YYU3Lp2lqhJU8g6bP28MmhEipRoyXhpJnuBHC5yEkI10537Czo/ndLJnHx3/1K88REdE/+pe/OapNTN4aYbq/RESvX+/MaoEtc5R3rhhH687T4+0gFBD6iU2Nc8ARHp8jFkGY60aqCLbLOrlY6OTQMLcdRsexz/NxeZyFMmYaU17/HDyXQrVk3IhlEKncJJo6ws4unb4WY668XiKiP/K1r9BHv/RF+48N13ix8jIHYYwUMDDw3NWICG/2QIThPms6SK1/ZbLcXUOE4092hJ1z9FXveJbe8fx9eZyaL6YsqUbctDvCaR6ocJN3/ZAilcdOlnviHGE9ee/z3QGQlnMZnqolE/7YJpH0/a/7VMU/EDnVme1ENWqEP6nSxjGM+3uTkJnznI9oTJ66LsPMvKg5Vzqa/H3UEeZkL7NKksuKBnrCN5PlDI4w2ysv3KffemNLv/r51zPKWbwr5TPPjnD+PfZ9niM8hEBbWMizzFg+do4jjAlouV3+m6QarDonwrZlW+CIjOib2GyAIxylv0ZqBr8vcL+2ihqBDi32ifvdOUSXx899dBIdxQXybc/eo4dPXdAvf+a3F9PLLB3hRzc50Qr9gzbViDIx9GLl6VXiEsslzUU/y1QxMXGER3rRrk2rnp8Fj+e1l1znQ+U5rfPbiLDhMIsoYNkfPWaYisPGdBoP8wRSTuIxga63pY5w7b7hGldbfz/w8rP0gZefNf9Wtlde42blBfUqc4TjAc8b1Ij9OMItjnD5mfW1JfzbYxvq9fOp/8Yf/4g5dnmjPXe/NDWi5X2u+RYpz2bIyjVzBVKW2t2G0wzTvLZF3xXZsbejGqH/TwTUiBO+ADIje/92LPTmGJZ2pSHrCBPBoq1+f1JUI3RC06nHHI4tnlC0HiffQ2ty4smdHWFGVroxPD+FCJd9KT9LqhHKGfSO6M9+/L30N3/gI5N89hg2ldezGsOPST4tVcGqL3AY6t1CCdaECCuHYMqGAROP4k8sYIHn67yfRoTVecNIu8DkPguZSY42/G2rwsPsM+rEKf6+NUd5h0U3oiP1zL01Pdr2e8inlce+sUWOMCDCreVrC2rEyPUGaoRGOUWfRmoEbxSSagSg7HN9IJKIsOWA7mv8/XWFUlALJxPZCJ4FiCQnV6lGcEVBrSBi6ghrasRMJGbqmCWG6wFfT0SEZaJe533hCF/u4QgLjnBjZbmyjfJ7S4pVHNumym5r64y5w7JUWY4LajRc01RBDaI4n73j+Xv09e9+gb7qHW0bpVZ74hDhQ0L8mud0XkS4PjnyJHdKBQRnLHL72FRyxiHGYd1U6lQhwXw6dIzX/u4jwlhJiej01Ah8LDwZlTxgeW+tvzFawlm/qFygj686whOONoYuuS95Ya63se5cgRisOy8qXlll1Yu+jR8PIaKHF2O/LPm0fhYRNqgRCo3MFJ9Swku2lf+P2p7injj5/55AHgvuDTrcXFiByEaP9fMVleWGqA7B1xY3HsPiPAtrgX/juqeL50aO8GJEuOSsYwW0RI2Y2NRwslxGwv3IPW5DhPmSeDyvOk/uSDQ0ojz+Y9SjLFc7pRphRSGtcYRjVju5/QBjwY9cfLjl234YKzOWyXLanNOOsH3NS0xT5oji+3+9G+jv/tJn6Wd++bMZEWZqxCHJcuo8c2ZHxYxndSSgah/DKFZTJcV+3lnPOsL8Xszf30yN0MBN/BkC0f3Niv7mD3ztbFtL7W7DaYZNOZRzlhOyIhfqnBGIqdBHlxDhc6lG7H/hrMd4ik0ElnPVOsL658o/IaoRyRE+DzVCIsIVztUEIpzk09YSEcaEGd1WbeKeWgRudhoRthER3caDyxU9uJD791StblyhEVGY5QiPG6+MCJP4SdRIjVCRC/5+0M6n9zOOcIUjXLknGukTiPDOpkbkYhnS8cXhoAswMD2Gr2WfOdR6FDeQqLiUIxypOvJesnPSD0OxGYn/L+k73mWHmqkR/J25BZ/7yRGOta8/q32M20KnSyLCdaqaldxUQ/2J4jOW6DmNyiC5Pa0swYhfWVnOvpZj3huicl2IfenoejfQP/zVL9D/+c9+nbYj0pkQ4as1EUmeaavziYmrLdQIW/Vj+lmdO1muq2yy7WPL+20Z69C/+ri9oAY/Hx0ZF2P2RE7bE4cIH8KlwUQWXmDOZXiqghpxIm1etCUZn1O27k6XoOZ9dkxKRFg5xI5VI+62I4w6wt6dvqS3FbqrIcIm/5CT5TYaEa5P6rVrsoZZVo3QMmz4f9spJiL6M9/8HvojX/uK3ebY15rTgJYTmqTzbCbLzalGGNSIJJ+mqBHzqhGSI5xUIyrznnZmcG7ZwnkwpG2FN7XihI7A6GvQet8tVjuWNyH4rFt1hPW9REQ4V5aboEYoRxgdHaL5jSvfE96ErTqvFu7Zy5huHxBhNlwnUjRxlhoh+xu/I+cBRoDZNDUijl1J33lccYStZ+1H2gn+fqhpCh1R5ghH+g7Ra9e7BJwQET3/4IKIFEd4QV9Yj7gFEbaaNefRBjWNU1kNhLCPLb9jWSyZTvTq421Tu0T14jBL+revPXGO8BTXds5yslyumHMumwoJrScSHo5lcgLav52YtX+afibhbChDXSTLwSL+8MFFIfFy1wypEefY6Ws1BSKDI6w2FWiMynEywiwirFAe8Tej/YTeTiDCslqU/P5LT1/SS09fqj6zM9KP55hPyOH+cT+0IzzlPGnDpLE0xyg9YnQsLVmp3Jb8P2/Ya5Ew/X7gvcPCKpgIlTVlczt6k6Y5+foaOIx+KEeYKFeJWkp7s54tq5KwAD///1/8+qv06KYvNjW8wUvJcc4VG4Qp43uZEOFO01gOe+cT+uhzYqR0Zutrh4WkyUQ+eRwqi8TfVSKod2OyXD5HLpEtqRHW2qqpEcdw+KzrYtUIDsuHQGPp7Hivnr8qOcJLQDWmB7SAMCJ5eSz8YyqB3CIirCNDUzYVTURzztH9zYpeu96Nx8/fq00luiHmqd9BhKOJF2lPR5hLj55z5zUF72dE+MmgRpyqn7zA7npEhPPfxE/n6L//Qx84ST+OaTlZ7rAqU62Gj6bGEc6LR/kckXO47pzkCFfQjdp1WZPquoYIz4T+p0zTLXAinXrFvcvfSfJpZjh9+vwDbKox6kSUHWrkWU61pzmaTLuoLZT8X/6JyNJWFTRAmTXuC7YpHWMn2iXK42bVxcp/LZxCNM0BTjJ/BjWiZeG0piGLIzyEQP/dz32Sfv2Lj02Hzbms6qLHc6tqxA3wd4+JYOHGv3OOdiEIJ2QN72vZt7Kf9mfZEdbFMrACKyfLIWeenc0SETauxdc3dPvaFCL8xs1OHMfzwnP3DWrEIkTYpfPMmdzgR573HF3i3KoR1sa6Zjp5fcquLjp6dXSEWyIj9y/i87jaSLf02Lxyy+52XNkwuTtY+l1AC4bzcoSnFvdcWe50HTrWjvP+pqP7R9bwY0OkaaVeuKKgRufoqcs1PXW5PklfjmXc35t+ODhM2mKWakStxLLJEYbvrLwXqhG1Cbx2XdZw5j6VyXKyTev/NeONGTt+ghoxMda9cwWv2E6wWi6fFkL+G17Hag4RVgluTLvAy7De5dx+vnYtn1ZQI1Q7ltqBda6VR0S4eimFWfx1ouxELUaEjWebOcJIjSB6vBvo8XYw5dM6jxzhZaoP3AdGhLVqxKF7X+RzW5SmKdUICzQy5dNSFKPkU+toh9YaztSI+WS5YrN1hPXO4j4zR5jRaqKRSjce+8oL9+mDLz9LH3j7rGkpQAAAIABJREFUM3v1hTebSx3hTGOx7w329Zy2xNHMY2G+3fvg0LZsbN/18AH9L9/3NfRN730oPp+iyh3LnjhE+CjUCBAKP5fpMCRa0oI8ZWW5I4Wk/rOPfSn9h1/99mN0qTBGHJAjrBdtK+P9LhuWWD52fXTLLGrEIo4wVKpag+YtqjrotqoJacbnNR3h2vhsecy8wHGbm0ZqhHeObnYSldynoEaUYuQ2x8+YI6x0hL3PZYzttvL/GX3TmxDhFCtHAC9XOsKhcMo18mlRI+Qx+djH235xnkWnnIJHkT6YnChLDWHKrHGXEOE+I+B9CLTrB9qqsD4RJWk6dIQFCt4YKr7eITXiOKADfp+Tva5JrhOJVznjXCVU1/iMv4p0EiLmCEtaGkYWiIAaUSTLlf1xTmpfHzNZDq//AjjC+ThPq1ER5MHFiv7On/oo/cZr10U7LZaSuhbqCNcidPqzc6e9WO99zSyVjppdXSyXp/vY+14qPvudZDnDDqJGJERYSh6dw6b6PbWrP6Z5R4urQWl709OX9CbF0TyWeZeF7XXIS/Naz51QsK8xejCE8zjvuJfKIecFjnCXSxivO4UIVxzhuYQ03T7RNEd4KTqSUHfF9537fuczIrwpOML5uDlqhCgJPvaFHQp2iPlerMbNXs00R5PbrlNHSLXvxffT/8GBwfLJbPzM9Tksp45pDSEsS/6sIsJcUAMd/AZQwN7IxfGLXFauVqnlwbhP3jlRAn0J2MJ/TjrCPl/LcAT6HVLETESYHcEZakQOaePf5TMuOMID035yG3HtzG0k1YgGHWGcy3dH0vG3qBGaI0w0Rrg6R5eVRNpFG7rxe8sR4TZH+PyqEe3n1uo4U4YUh0Peg3Pwp59AasT+uwOeBIYhisvfVkENvXi88sJ9+sg7n6evfNsz+mtHtbvuRHLINXKEeUGRL54V1r3LdswwaYtZE2+hywgOjbZYupqTFnzmCLsKR9i56nXZyXKMCJc6wtb3Wp4zt5kz93GOqH/PuSwxxmHLXFmuHRFGh5B/Zvk0eR0cXq6ZKKgx5NC0VNWA/6d2KbVvtjtDjdAc8Iz8WOfyUAGyeimFCY6wUaqWtcSJ2hBha/7mcsA7cHqHISYOYtEVvCbv8tjBctZE83NlRoSlXip/fmhCdookOAfob8mlttBJc2NjbKIkRzh/XxeeimN3EPeQHWGdOGaNC92HY8yHaZ1QuRE3mhoxbtilZNp+vgTf883CzVqrI3zu9dl672u2JCJ7X5Sw3q9vRDoCtn87U/bEIcI5ZLf8u4jW9LDTPYdNhcseXKzof/uTX3f6PjhHROeVjVti3ufQW1FZDlAJotPSSI5pU8UhTnM+wxGuIMJWfzh8SBTvcVKN8PWCGrXxZF1uXUcY2ly42c2IcE/eSUdhypFGjvBmDM+z89Qrh3TKuOpabrcszIGO6mRlOc3RHHgTYs8f2rmovResSYx90e2YclvGZ5Ij3D6m6xxhmbTUU5ssm3VqRk5jJb38DKIsY0mN0BEN7xU1ojFUrLnmjufaQ+XTwAm1gIwp3uks1UWFuQcljRbG8Sc2cUFuDDM3Wl6otQHIoAYR9ceiRsSf+M5frDwNIUt3xb/HCJcYawIRXnLOePBS+bSpXKClc94xzaLQ1GxKcUjb1aj3HqM0+1/TOdDyJw4R5gG7z64pUyPCKBR+vgEnw1RnO63qw3FQilOZ4Ah30lnToecnERE+xwYEx9lcZblashw7UxtEhH0dyag9C5PDuWpQjTDkvaYMJdkKZHOikc67QjWCE4GmijBoQ2oEt5sc6sQRRlStjRrBnE3n6uFB/T7UEWGgRhjHFvQL4z1LUZnOjU7lsjwLPN+mk46LPmYJJQbNu5jkqVUjdmOkST9L56TjMSVVZxnPpckhPHLkCp+vleQ6VenTSoKSXHNeD+LvWhGCowiSGjGIY1IUpjLHoGkE+hjrbwdUFDZ+l7/4eAfHxft3uS7H2tK+JNWIbj7noxURFomiZ17bFqmkTIAo2q7WLIt4nHdA//+Y9sQiwvs4c8iFWioGf6hZNd7PbRlRuJXTz5rQEU4LCY0/5eR5V69Bm7XwnOt8c4hwjWOJFemkjrB9vtpEZ5ZY5mS5rXSEJe+xvmBYxovhtg9jMo5LDuc0IlxKrjE1QlfYmjItI+acq8qnzRXUkMlKEaHbrHzVOeOPk6pK5XqZ70mEYfv8d19xti30eZ0Q4WWROTyfoEYYzklLxMd2KPKz72FTs+uDcI7T8WpcrzpFjWgMFWtE+FgbdkRRrff2Y+99iV6/7isIbNmOMz7j9oYhKG68RP15fsZjEjd6Qvu1ON9RqRH8E8bTqnRQV97R9330S+gLr9/AZ21JteU5x/egYYzi829Pljuvf7AEcdUbvSm7D4jwIeaMOejY9uQ5wq79QWhDRLhfmOhxqJ3jYc6ZdirvmjGSZqlG6EXgrtI7tHHp2qVOw77WItcz6Qh3HiZ6nwTRa8ivRmBlX8rPeMHUHGErHN06TpFuIfmMc45wPVkOHaa5Esu61HDnXCGflt49P02N0I4Iq0bUpMW0w1pbRPtgJcvJxVc6Tvw5fsbf87my3IL3UFaOq1AjfD7HnNXC7yxRl9D9kRax64eC5qKpPdoxnlsj+FiUT4vfk3/f13CDYyHCH/qS5+lDX/J8pW/lOJEVRuXfkEeef5fzha4sZyWo6nPn88l7c0xEGMeLRVnovKevf/eLqo/w9yXjmBHhfZPlrHtzi/6BNffWzEqirRmXWT70OZ+DNvLEOcJLOCra+CYmasQZx5tcdM53XrQlYY3bsM67lNBS6gjLRaBlobwr1nlHQ3+eCAQiP7VEmilH+Jvf9xK98CBWXlp1Pi3wOmSc2qp8jn1By1Xg6tSILEXW6Aizcz2Wsebz3ND0u+adA0TLk3M2R3gKwSWKTqZGbPk7OkFt5d0k5xj/xgUNvNPyaSV6NMcR5nK52Be9+FqcUnkuStfANIO9VSNW6AgbiHDDu2Jdqnd5E1RQI0zViPJ+Wve3ek1ebux0NONgagQ4HlPvrfldL8ck9pcoXzdPpViGmwhKfIPjWlAjdjY1wrpu7QAfw+HL60H+TEu5Wf2L/WmLHBVtdRkomDM87RSf23pW57J9IiBLEOGDHeEz0EaeOEc4T9DLv5tCQCEsHvyHmhWmOrct0QC8DfMOEOFO9lWj2U8KNYKI+3ye8ZYWLefMsCH/jcheHL7jK99C3/GVbyGimBX9GJLlpDNGqTpjbaKzF8NRD3WCGrHvgr/dDQXaOXXPO+8Ex5HHH9FCaoSaS7x3hUOdq7n5UXrMdiJLjmZ8prPUiORk2C9GlGLL14194j5bSLNF6Yoc4bBYCxadsE2FGrGEP1rnCDuhI8zUiJp8mr7uJbx+7u+1otgsQc4m24dxzImsrZuPKS45/p+vMZbhzt9n7WkH19IH+T7k98febFv9sWg3+5o1Tm1E2D4XJ2cuo0bE9i2He+q8d1c1ot0Jt6QXa8aI8DGpEada958gdyLanEzQ5HfHG5p0hM844Kyd+LntEMWNc1ji9jXoCN9VVNsyvpZzPHZc8FLYUJ24FZFZeY0I579tYFKvNVN7RKvOFYiwCM+5ZfeLF+Gbfigcqalx4lwuOsEVwTKKmI9bUlmO+89fyfJp8WfK0K80KagRQ85lqCW0FAVnKpcrSyyX7URnOx9vRd4S6szI4EL5ND5PbANC2ZB0NFX1sGzLdrbYUWdL1IgWjrCXNBQ3c31JNWIn1ROyszd7GU3ts6zbEhDDUiqSgIz8m64aNwTe5MXf+blj1ELLxum2xbWod/IYU7itI2xwhCsvxj45J0tKLONav5lwhK2k1HPZknOnaF1DH7my3DGpEafynZoev3Pu4865TzrnPuWc+3MTx32Nc653zn338boo7ZDdZNIRTrIwx+zZzLmN0O+5DcNsd9E671IIM+tDyj4/aRxhorLvpzTMBH/xwYaeu1oXz7s1IWm98gkR1klxOKlX5dMq17sGBzsdazh6rfcLi3Tgok00PU46n6kR7NBr2TMi6ZxapksNe2dQI9Q9r9EtMEsfk5UkCmw5OHzPaoiwQY1QIUe5WZc/8Xh+T/cpSmSNPVM1Ym9HODrZKM+Hihk3u0EkOelxXWw65hDhsesJEVZO3qHvvE6WW9KeGJPGfdWOackRViWWnStQ9VqynOWw6OjFMRDhzqAboIP67NV68lz70DQwh2LO8Bk0I8JnXtvk3DV97lx5dL6PXFnu0Os5h6LG7JN0znVE9GNE9PuJ6P1E9L3OufdXjvuLRPRzx+4k2iGOMCbL4Qt+DrtNncB03iNOQKewzudSp9mRiX/TC8u5w0eH2DE5cbPnAiTvj37dK/RzP/yNe/dn7TOy6ZWDgBnQSzjCRNHB1oiw9X7slSynN0wT48Q7HG8x7KxLLK/gs5rpuUS2k8+F/ak5wv0QkrJGD4iwhcwSlRvF2gIVQumUo7MSkzrLc9QR4f3K1PM5hXyapRrRkANQQ9bWoHZCNFIj2BHuB9G2c+X9tO5DzTQ1YqWcnYNVIyChrfNuUZhZcsBlf4mA8sAbL6UEwhxhB2NhGKjCEW6nRhyS56PNags3Vm966nLs37QjvKQvSxBhQY14AlQj5nx7HI9zlhDhA5G/WjTsmNaCCH+YiD4VQvh0COGGiH6KiP6gcdyfJqL/nYj+7RH7V9g+oQz9XZbWOadDiKe6bWrEXUVTOycROqJyQX4iHeEjhUlbDCeqi1VHLxnlsFsTknSpYouHpxE10ZdK85EjXFeNWKlnP2d8PTf9UJQanmrCu+zAsEOPCVb8+Vyy3DCUTmXJER77Ov5nN8iNQGoLsvRDGBPxvEpkEwiO/FlbdJAaYc0DGtmf4pSuuqzTu3RM8zmqBTW4by3SVJaz5SOXFnWq+xBSCeVtP4hxX1y3Qt/n/HH+rqYIHIsHi/PdyrtFToVT16X7o8GFIXCiMiuoSLWbGAkYRITkukE+LX0/Rav4Z/OlVM2iRqCD+tLTF8Xf0faJMC5DhMERTprP5feWbL6ObUvOvWT9zRzhwxi4eK5T3ZqWHr6NiP4V/P6Z8bNkzrm3EdG/T0Q/PtWQc+5POOc+4Zz7xOc+97mlfSWiw3baUWM0v/DnHHC3GfrQfbirggveRy1YojJsdwo04Vx2TkS4ZZHJ93B6IOhSxVbVuiknv4oId144oPpYK3Q/ZdyXLcinzenq8jkx6905oDQMue0WaoSmGfD3mXOpN3QVP5hCCJk+EWRCmrVoF9QIA3HlPk6VWPau1BUuj8kbqIRWLxzTlsO+r2qEPeaiw5G47d5RCCFtPG52gxzXrizAogtsTBn/OcmIqZK/h05T+HwXI8LCgSjnfv3usWoE3x9eJ3Eu7oOMZujr1v0mKjelxwQzrPkDx9NLjAjPcISXlVh2xXlqJqJoKVpQbxP7dC6bqnpbHLtg/WXViGO9A63n3escDcdYZ9ZLw18moj8bQuiNY/OXQviJEMKHQggfevjwYWsfZWeMCXqJZZ7TeQfckszMU/fhrlIjkNtXq9CkEZcnwW6DGjGplpB4ddNtoTOlHQYtDm85MLX3a9W58jnjZLwnIizl0+aLcnQeVCPGQgpBUyO6eWqEKZ+mqBGaG1tDhPshJMc+Ff5Jc178aZfO5esuF2nnRnRZqUbo8t8W5cIKmyJKvjS6hc+W2xbUiAULLTqpqNYQN1osZ+aSagQRO8JqXKsxuwQhY51wjYwea8OOSW662MecdRNOL/cdPwsjAsxjiCX3cAPEdAk2vaHV/SayUPLymH3NmncENSIhwvZkt4+SEre1lCOcxoaFCBvv2blMovfT92HJWnYsRHgJZ39fa5FP+wwRvQy/v52IPquO+RAR/dT4Yr1IRN/hnNuFEP7OUXoJphGfpRZ3tSyfdsSOzZglTH9u06Gwu2beZ25fjQqBk/KTYjnh5fR9bnnGWT6tHRHWPFWd+BHf/TCGTyUdoGjXO5CbiuiwQOUWbtgYjbox5NOmHDXnMgd65WP1Nu3AznGEw4jaaue0Ro3ADH3L0BFh1Qi5MSgT8/iceN0Xa0+vXse/rb2XBTWMxR8dUzwGz+WMd2/pXILqFuxQW9SIJkRY9WM7anWvOkevXeeNFtIkdqBIE/ujKSLKMWhCpvPz1rSeQ2lwOP91wS9yKiw6jQXI8E/mffNGgQEjdJh3Q5AFNVJFPXmdOC70ZnfpRnfKLHQZx9Obnj4NR1jPh3P9I5opqLEAlT22WUVW5o5to0YcRzVi6fu4j7U4wr9ARO9xzr2TiP4fIvoeIvrDeEAI4Z38f+fcTxLRz5zCCSbaj9Mjvu8cCIWfb8BZKM657ZzI5D7WOaLHW5l0UkO87qryhWWduoZTWos0kYXCWrZWyJmUAlIblfFvFu3BaheRWKIKytm45ncq1E1kC+0X31OIWZUjPAEIs4+sncosnyadT+5XX3GuQ0BEeKRdaGoEOoCViAmi+d3omOtkOU0BmHKw8RyIaC0d0zgHcd/3VY3AUr34/3XnlZyZDFTqDZ6+xqXvq/eOaKQQoObukjaqbYMDu/LLnAo7AbX8O+bOYOLnEGTVxIwI5zY4QVU7/PhrlpTL16L7sq/xxsBK5CVCRHjaEV6kI9y5gnpUM2f0y+qLxc8/l+n8hilb4n8l1YgDr+ccm4RZRziEsHPO/RBFNYiOiP5aCOFXnHM/OP59khd8bNMTzVKLKASd3RG2MnjPbXedGtF5R68+3hIR0X0uz6gnzwM3QrdhS5O/DrEWJKpVzm2tnKlaslw8b/xc8y/n2rWc8hSCb7xfGuHDc89xhLEN76ikRng/WWK5T45u/gypAzXViF3Fu+6RIwyqEdiGLZ8mf79YgzZv5xK6HPtQXr9zttMr+Xlje3jcYkSYzwfUCJMj3BB2huvA/uJmTCOVRJLPit/l8zpXjskpswrU8H+PR42IBXKWRMIsioflVPD1hlFWNEUkuMQ3fHc3VpbjMX69680+yfdZnueYeR78KC05PueIvvHLHtIPfexL6YMvP2t+v0Vm0fqONa4sQ395CoAQNKVzI8LGxnru2KYSy+vjOMLnoI00VZYLIfwsEf2s+sx0gEMI33d4t+q2NGyqLW7eb5sjfDtO3DF34qewzjt6/SaiN5loLyePJzFZ7pylrVs4b+2IsJwg8fDkCKsNiuUMFOeHdjOiU15D63tiOWaJlzhxjZrH6F3pwK5nOML8N63Bq2XYdCGgKWoEVvqSoWkSP+N55bVYHOF154VGrOUUFdxYw0GwHMSlc1k+d74OdNot/vJsW84JxDPKp9WjEjj+nCvv59Lxx9/XEZTY/mHvPCLkF52ny3VZLKLaL0N/VW9+8Dw6WS4EqYgSKT9jQufoCG/7QJdG0hieZ63mG/7TMdSTphDhe+uOrjYr+pFvf2/1+0ujT0TxOjZG0Q6zfXhnuom8hduUV7Xmk+qx6VnOt7vqPF2s/ME0xnP4Tk9cieWlaFH5/birHYZAJ7qnpunElNuwffhQ5zTsF2sQFqoRE/Xa76rdjnza1DGl02qZSCpSqhEpA1olwqx86QxoQ0TOokboYipzZp2zhQaEzWcd4fh7ABpBTeEhHifPy/9PHOEgk8qSI1xxrrmgBjomCcE13l+N3FrlX5kakRHhcjwiVYHIHrOZ/lIe12rYXx5foq/GOKoZOlZpk+BjuzlZrmwHqR2a69n5vOFrdoTV5gv7dnAxAXBCf+Tb3kuvPt4t/i4RcNQrmxiuqjiE/H7y+EvRHp/VQhh174cg5gmrbU2NOCZVzKo0y3MTJ2tN2T6I8Je96Sn6/Gs3TcfiJnYKxFmCyh7blqhGLN0k3r9YHezvnIM28sQ5wh4mv30MqRG3hwif7bSyD2dEJvcxvEf3VVUajVA9SY7wOekcLUhUa4XBKWqETvzoDGegNlniMVYCydLNbmc4Zi2ot1cTrHO5shw7jSvvJxHhnIAG/XF1+TR2zGqIcAghOWPDKFWlUX4LIdEhYuRJrsGBEd9R9xxvNzqW+lzoSC4d0hgm92OUwUq+a3m98Trw/5sZasRKXZPW211KjZjaBB46TSHS/fLzV4u+a9ETxDjVUYyCIyxzaThiMgT9DpcXKTeZck6yIhL7moWyrrq4qW1Bz/fpyw/+3nfTD/7ed7f1D+ZjvmcWAMHqI0NYhk4fw5YgrkvBtKtNdzAiLOel06yhZ77lh9uhL5F3I1/u3BzhA8KJxzIrtHqXTCDCFxIR5rn2nHzbY9ltcISn3o/Mw5xxhBVKgRN0lSPcMM4RQcrJj3ANCze7K7Wg47knEWFcPD0ny5WyZy3UCO1UJPWJgftD4rgqR3jgkspjYhKoRlga0TpikjjCK+QIe1FZzsraR84unkvMWwZHeOk8nJ9PdL4vVp2KBrhR03m+XRzr6DCufFmYB01v1tCPQ4S49dL4eHQIjwU6cJP7bKJNjrCBEhPlcY6OMMup4XzRD7LoBn+36LdwTOW5j6kaUUN0L1a+DRFuoFAdYh6en85z0XasKMJSW4K4tuReoN3frA7e8NyJZLm7ZociginkOJzXmTrHrmbO9tFMPKdZjrBO7GlN9LpLdmgUY4m1LOKtu/o1oIpTJZaJQFpL0SnMdhV6E/srne6W/qU2DMcsa5fWvyfQsVGjVatGrDtHNxPq6OzoamdOJ93pDUrNuWZOMDvlMllpbN+ILk1xhFkLOTn3xv3FhRr/hvdoKuGq1XDsdc4JDeH0eeNz5/vhnHQ41oofrU0my0nHRFAjmhHh+FM62PzzsJd+znlq6RcR3iv72UW0d6RGsGpJKrFMqQ+78bO1wfO3+o1/17StY6yDFi2FKM5P9zbz7s1Sx26p6Q0aUR2AiH05b6SaSIEQM/dhqWrTB19+lp65Wu/dNyI7snFse+IcYY2OLLXI+ZPcu3PYnVCNOPDendrwHmXVCPnizU0md9ESqnOGPmtE1LJWXpxwMJWjlKskybZaEGF0TtaKY4xtti6UlmM2lZhifW/tvUBy2ZFddZ6GUOdlZkc3fxadWP13eX92k9QISeEqUF/1XPD8fE3oYK69p+0wQIllPlb2WW7W8+d4DJFy+BaOaUSuu87RRSgd4dZ3WxTngBC03GiVbRXyaeoalzpHfDw62MfKCzhEhm0O4ZfvTRxr05UNWUmigRphPAN9X48xHdaibRcrn1QLWr5/qrlZjPeZc+VE0TM7wgt8k6U0v7/43b97736lcxrz0rHtiaNG5FDRnt/3WFDjfAPOWujPbXqxvGs2RY3QKM1d5TlbZmU2n8oyR3jiGJ7MZl6ijUq4EgkpB8inSdWIclFcioI554p2Wugo+p3sHCK5+fOpwnIWNcJ7Qz6tUI2oV5Zjp3RQkSvr2WoHh69b6wgjNQKdxtzn8hrwnLEdeQ3x7+ZlVI2Pdy7240Jl3y9BhBGhRv6p5LZbyXLSQdTjYClgMMWPPzgsfEA7Jpe84lRwERjkpCeOehpbPmkNy4RXCxGGa9AbuSPdG2xDt7VppEYck6ZhGSa6vvfNT9F73/QUPXVp44+3Ro1YgLimOWBfB2wPE+P4VBuWk7R6Qjs0NI4lls/pTC3JzDyVHTNb9xTG92iz8mkx05PmPlm+t228ZpyTGjH1frSi6iL5x0vEcKOS3Dwslvk7drtSR9igRuwxTjWa0nIfZPiWebnx95ws56qJbUSlKgT3W8un6XHcV5QomBrBnM0eIlcWUq5D3nz96GCuO5ksZy243pXIKB6L59CRgiWGqKD3TlA4+HPLsbIMkUVEufH7a+P5F0mgSus1AwZN3QC0vxz7h0bfDnHULLqRN54n/x2T47zLJZYxysQcYcEBNu6xSKxVEonHujd4Hv2ev+WZe/T25+7Nfv98iDDRR7/0Rfq5/+Ibi80f29JEtGMZnm62oMaJqSTmOQ+Yb1rtyaNGGGjGou97fOGP2bOZ84rBdr7zyj6Uk+FdMp6U7m8MXVGFJpw7s/YQO+cE10KNaA39apkssbitpMRZCg+3IMK4iBrJKvsgI7lUs/zu1C1HdJIdfZsaMVViWbYV/18m3WnHcldBhGMludwGInTJQZtA+hJHeC0RO5RPs9Fe7QhTeYzl8C2czHDD0jknog5ElLjaLYbILaLcm64cX2ha61pXNVy62PPtWCvKxZI2qm03vM9z/SKy5wWdLMkcYe/z+ENqxKpzCRFmLrVWkMD22FKyXDGXL76kwpKcpro/P/n9X9M0jvLcfHhfLFuCfh9aI2FfWxKtvo0cnXNE0584R/jQCSYjwuH2djW35IjeVuil1XjAMy0CPyuR4SfHE9bXcEqzwt7a8sI0fQ9FgQAVOmdEWCMqLU6SUI1QGqPY1qKyp2psd4aDXfsOXoOmRqx9IzVCo2ujn8tybNpRrRfUyKoRheNqIOX6veCfLdQI7ShZ7VqJNBgWXTqkUfmiqyHCrY4wbAzwHVsZEQe0UjVCPjvX8A7JfrCjeHz5tEM20ZYagCVTyP8fhsgR9t6P9B4SgBGPyX6QCZ22VnN5bk3jOcY6WEN0rxoS5fB7p5qb82Z7vv3bSgRfwhG+DdUmXazoJOc4TbOnM2sSX2L8gvdDOGvSWG0nfk47p0O2j/EEcB8mMR0WzhPfeft2iFk82FMZJrbULCF7MzwvEUJ2UtKqVI2gos3ahguRs7Uxse6TTLPS/WjY9OVQf6ZnZG4vFNRo0hGWk3WST1PUCJ7Uq47wwDQFom1v6/5qBFNeS/wpkuW67MDwNeFPohHxF0hpef+OIZ+GyhfREZZh4qtNR/caq6fhOMmIp+Kgm4iwdFg1N3oph3UqUfTQ6Nshc7ZFx8NmtIIERw2QGoEc4c5zAl2k60wV5sGP1mqzu3SjMXmNC5+VtlPr0i+heZ2z8JI4rzFOanY7iHD+/+8gwqNZIZ4lxpmv4RZLLN+WH3rXqRHJEb4AaoRaCE6d3HAKOzXqgNZyf1r7o7PrLURYI01C07fijK9Eok05JveZbHUpHFVLAAAgAElEQVT4teUadZ851EsEHOFumiOcqBHKOdyOXqemRrQgwoyW7nqphWst2ojW4d+EjvBYFKRwypUjZIUgLbmtJQunNnyfn7+/oefvb8Tf//S3vIe+0Fi1S1Aj4Ll3BI7wLCIs5+OVz5zh1uHH35cllvnnsRzh/b9LlDcxNUDGO65kyNGBLLmXkdyYLNeH7CwT2ZsNrdEdv8/jmMafh8+Hh3J8Tz03p3vX0H5M+jy/qhOebu4+aCnHc5iO2JzCnjhH+NCwClMj4s73mD2bNrGruSUnbukEf27LjjBQI9SO+tTJDaewcyLxLaE4ja7XbCOoEU6Mm7Xi5lnh4SoivIJF0tQRpuKzOdNJdy3V81KCFTjj7Cyyg9t5TxN+sFlZzkKWtWpETT4tarR68s7RVqHNiHqylfJp8UQXK4kIswIAHquzsSWCKPuLx+skyiWGJWf/p+/9quL7b3v2Hr3t2fkkJ+wb8psjXzgfY41xjWjrML5OPGzth1Vi+dBpylLqaP7uzCZGUydCwMqGccwEoEbw8bs+03eIbK1mHFu6jPpROcLe0YsPLuilpy/3/j7+PLYtyWnqvLsV32CZasT51jI2CyQ5tj2xjvC+DyLJxIA+5zlMh99uww4NI53aeBIQ1AjV57t+DZadM1muJbz21OWavvXLX6Lf88pzk21pmgO+c2stn+Z5UbQRJzSUXmJqhK7uNfV9y2oUjSn2h0ZpZZJbSP0LE9QIjbIS8Rwz/l05s9zPoeoIj+isJ9qm6mj6GvO5NOKU5NOwoIaXyXLWePROjhlnjKNjyKfhNTx7tZk5etqyQy/7u16VEQc03Kxp+TR08JbqCOMGYakzXW3b798Odt+aF/T/k5rSiPYi+kuU7+VNP5B3dhRIn48ob86KqN4R5kPnHP38j35TM51G26nn5iUbmU5tRs9lSzjCt7H+noNW+sQ5woeia4wIhzMny2l5pduwu15Qg/t3BdQIPWnqEPiTYNpJO6W1CJ533tFf/U++ZrYtLTOFSI5G5jUiSVS/XsnhLBHhfYoI1KgRU+NEOzAiyS3kdqdLLMs+c7910p12uqcQYQ5N7wabyiARnPiT32l+dx5AVKXrWAEgiNCrdHJtbqykdJWOz3L5tHy+Qw3vCzocYqNlVpbTYxfGo0dqxDJHWKusLGljru19bpf1HJ2L4fcQ1JrkkSMcfw9hLPGtrmXbD2MZbD5PeY/xsvVm14pIHGI41pfauagRLc8PNxfnNGvurdltIMK/Q40w7NCwCovdn7ugBlEcRLdx3nT+hUjHuY379cBUjYi/s9PyJKlGnJUjfKQFmKhEdwUPM5VNlU4F6rbWnB2pI1xuzvahv+hsZh4fLRQR3KjoJDfmRdbMqizXOWcky/E5Y7/qyXIhhUiZZ1zy4/Px+v34fe9/E/31P/Zh8X6sec5Tm3+dTGXNrVYoHTcySzfVxw6LE5FIcHPOSeqNhVZqXVu8n7jha+xkpkb44rND59pD5myLI8yf90o+NHOCAyhCUFFZjihSI9adz++8gbrjuCkqy3nZ3m3ayRHhBfOxpumcy6z5pGbnjG6yYa7JqZb9OzAUl9khnCkiAuHw81MUjr0T3vf8d2ECsownzCtLNWK8Zx9730v05//d99O7H94/e//2tVNnJqPxKY4xxGqFB7zLElfakW2qLGcskrrcL7bZYkX4teGec/O4UCckFwpqtMinaeQ0I8tSAo3HQj1ZLrblXHQ48Bos7rSWpLpYdfQN73moHBFPIcQiHrXCPpj8NJVQRSQ3oUvH9D7Pdq4t7yTyZiVjoumy3rUEy9ZL4+NwE+ic/Nu+dkgUz5K+I7LnI46GhMA0KCr09vkd2/aDoErZleVwQyw3pZorfJt2anAoJSk2DAR8B89pNd741LHndIQtrvux7Y66RHVbulvX1nkMOR6tW012zqQp8/wHTKrnML4vD5AaoSbPBxcr+mP/zjvv7DVYlu/76c91zIlKykxJp0s7dhY1otYFS+dVLpzLF6fs3PA55tuwHKHE7W2lRgyyLe7DoBzqdK5uzhGOjgcqT2glEFERrFKlS1dLY6emFmbkcxbXYqAxx+AIH4UaAf1FJQKrciGaRiiLBMs0ltv6qGlb+N3D5dOW9QXN0hEmyvOQ5JrTqBoRREGNPoRiI3bTD/EYtRkW54bbvlab3Rat83NZVq05TftLNlW3hQjrUutTdhtFP5Yk8+1rT64jvOeD8LDAnJsikJ34s5422Z2nRoz3BVUjbmMHemw7pwj5MdGWzSpP4li9C4seaKeVFz3n6gvdpsN2Zb9FmwueeY0bPHUbdLKPc1SoPazAObbMpEZ4q7IciXPVOMJZxzWrRmgFDAQ5awutztpnOphM2pV9/n/b+9ZgS67qvG91n3Nfc++dezVvzUMSozfiJU0kHkokIUCWnJRcGMfCjiCOCQXBiW2q7ICppJwyLttK7LIJjmUVOBVXxWA7YEeUBSRRGTtYYPQwyEiyxEgiaATCCAlpxGhm7r1n50f37r32o8/px+7HuXd/VafOOf3Yj9W7u9de69trufiMboswL6PcOPNlKQX0lzJ/Lwxjve8mMk64oaya/8tyhN0JNep1tI43SfccsDIj+zonUSMSxTejRoxUym9ALUI8tTbSrJcuRVinOpneGtm30l3yjqYXf5UZB4OOFOG8NQEudBFHmDcpWIRTmLPT0ueTcjm2TY3ogmjurL+nV13KRU+oMf2KcJEFbN7qyhTL+mVZCgNTyPLcyS4Lr1Uui0HsikupLJ/F2zo06i3CM1YJIlR7JDVCLizjIdVc4Ik3ePvt8Gm6nDZyypSczIjIihqRURccLy6znxo9IJLUCJsXKsFj8WoxkR2KcJkXpwmfz8BMLpE+ZlwcdA4z+YppdS1LjcgmgQ651H1s1fEmlb2OySJynRrBw6fNpbGpT5xeT63w9gTAVZ8VPs2TtdwHmjZSlBnvnJ/eJswJ0Tj4jAFdFHmeDZ/oqUqUj7oJFeKIcNpYhNIW1IO3mwdAn7hZLsiHErcI85Ss04q62RBL1eVx4iAtQKYnI46URVi91JJ9A4Oi4ALnFbvu5zoWYfMeKxQ1grnKs4QaLNVx2cxyyYr75LfJIc4Sasg0bwYy13QErKe8C5MH7EpyYd7TfKwNY0aNcChHpoUwlyNsXGNeRlH4pIfx5xlPGOGKSsIRx3q/TUpEWSuhkosjoUbN+7DOort8y75jW+r5kNQcIvlfHTc3lIrwhuZBcGeWcyne+v8+vIeatnCqcTD5WDO7Y1vI8xy4kI3HFs35dahYRVHo1UxEP0BEDxPRUSJ6n2P/jxPR/ennLiJ6hf+mJigSKH8cIiJlEW55zHW9WrbuQsOmIdu14Mgs11c6RxG4FJim4HOykxdmKiLCpYdW8U+PHMBFe5e1fUUsLNJixxfcuF6cZfpghk8r0g5T4YmIUyOS/4llLL9euU933yGXGiFfIOPCp0lrW7ZYzpCHbiGx6+d9Sn5H2BAuasRkBdC14KrOi8mXpRRwUyPiiLREMENHRab3wJxoKK9KQUXYmFDpZdXrqGmtLgPXtea/XWM2G38RC6cWSUU4pUasp3GEI7vfqg5kdZgKcBc80zwUScVeB2Uyy3VnES4+sd02OwARKsdtrgJXSnnfmBg+jYhiAL8N4I0AjgG4m4huF0I8yA57HMBVQohnieh6ALcBuKKJBmcPhhoW4TUjdWlbcC12aRN9egC5IAe5FgO158p7EfgKpVSoLo+KBldYAX0it7ptBre8Rc131UuxCDVCtdFlnarirjTPiePJZbiUZp5QQ4WRGpdi2aZGuMOn6WMgr0wVNYKwNtKfUy4l0qUcm/+HcWKhlkoOR3IN8st3WZB5nN6yLyZfllLeNt4HImMxpsPqYHot1Lg2QgIWHH/yfJdc6t7zdd4ZeZMO13tAxtcfjWSSETsT4dxQX8Qst4/LLBcTWfUpz1LpLnlH0zSNMgsDY+bZaBNlqE43vGwfztqxzUqN3jTiKBmfjUX3KHDM5QCOCiEeE0KcBvBxADfyA4QQdwkhnk3/fhHAAb/NVDBdsVXON+NztoWuXUJ9p0bIQb4wkx81YhrhWpzSFMpas8ZBrajWLUiu8WO6ScdTI5TCMU75KiMvM3ya4gjnnyO7wXnNPMWytFjL1LMuuKgRPHyayCzC+mRivEU46fvauskv1suSdfFjJPh/2b+1DVsRjvk1cESgcLq4C4TIy4NP7wgfj5xiM3GxnDFZiw3FrCw1wh06UG9jVdRZE5P3vjEt4AAyLnxCn0nOMce2tAjLbeOjRqi67dTK/XmmL80OaiXkmARF2Zl8LF8z0Sa0ifWEhs4NY1w2ISNpE6jjGSmCIiNgP4An2P9jGG/t/UkAn67TqHGo63JKAtV3FT5NtaELtKmQVcFC+kBaZalX6y6O7AOiHGWlkbo8Wp+HbFEbL9N178nrYyrP7nJVOS6LTBXenqmAm4qxC2aCiChSVIYsw1ZmwXWPwUnUCNOqpjjCYxThKHFNS46wxeXVaA92/fwc7ppe3xhZMuWL5Fw0JCdH2FF/UeRZsKuAy4O/KPMWy80NI5xcG1neA9N9XVaJleNCi7tdUpnOQ1mlXGtXjrXTXHwpfydRIkSqvIIZjJJjZgeMssYmUO6oEerbnOz6HAN18bbXno1rL9rTWPllrl8cdZNimWcb7KtukMhRNLZWqIgi7Kra+RQnomuQKMJX5ux/J4B3AsChQ4cKNlFHXatql9SIIiGd2qi/rzSD6166B3/wL6/AmSvz2ba+t7kIyqZsrQPTulcHQ8tyln8t5DEm/3JcuXHkTuJQZR2Alb3KUa7VZqM/JjWCu39HQiB2PAozagRvf6SXo7VLKsJ51IiRsqKZE/Zx4c0saoTDIrc2Eta4iImY0uIq31EX21g6s5zHyThXXLmypSVsYR2eG8aaImxN8MztBRvpUgh9ed9qJdQg/Vttt8uMI8L6xigLl5ZMxHSPBKdGEPGJZD41gt9Ddpi60l3yjuW5IZb3DRsrv4z1uyuLMJB6AIzFtH1C0/TCIkPxGICD7P8BAN80DyKilwP4CIAbhRDfdRUkhLhNCHFECHFk165dVdpb20TOF8u17Zpp0zLoAncl9hGzgxivPbxT29YnN1pVmCldm60r+fYhL6mommU6FeESSgTnaLo4zWXciVmZhvUrNqzZLrgW+MkEGEIgC58G5HN6pUIbGUrQRpZZTm5T+yIqkFCDEsVE65NDucozDPBz5L71NCMYRxw5QuFpFl+7Lj3RSklF2OMziNMh+HOCW2Y5TWI2jYIi95vPQzNLYtGXrkqowSzCnhT+OpZlaekz++GaPElFaMQ8IesGNWJ+RrcIy9Nd9BPebjshjN6OzYwy42AQkXNS0QZ6v37Ik4clD0UswncDOI+IzgHwJICbAPwYP4CIDgH4JICbhRCPeG8lQ21qRIQsfFrri+WMzDpto27EjS7Q9A3QBtqUu2+34yCOcsNs6fUm32aGNxe4pdkZPq1CH8zJhqkYu2BOqhNLbrJNhhqT7cpbLzcyOMBJOdDiEUdkJxgYxxFOlAdkFmFT/lwskxZEEZvIrG0ISx7jXNfJfuY2dUxQyo4zn/cCfzZk19JQhOW4GERkxcU2LZPmhKPoZNJMJqOXXa+fvF/VzrcjEfBQc/w4GT5NhkbbGOnUiLmBPgEyF5ua9QLu8dV3pcsnZBeLvL/effVhPH9yveEWudH3yYnpFfONiYqwEGKdiH4KwGcBxAB+TwjxABG9K91/K4B/D2AHgP+SNnRdCHGkiQbnPfiLoo2YdHmo2/a6aDN6gS+4+GzThk6oEZ6qmokjy53teqibUSPGPbC4BTZ7ADuskGUeekMzNmwBS4zdZp3by926uRZcR7p2aV3j5XBEkTrPxEa2at+OGuF6qea9IHjMZ1n/Wo5F2LQqm9dX9odbXQep67zskHbRL6qCeyq4UutaLBdHKr6wyRE2J49qnBdrh5mYJWkTtLKrom569phs3qlpmU22JWNSRi2JCIyakxxoR42Q8nRQIyJ+XNoWY3LQV6XLJ8oo/a861P4iNIm+rx/iSZyaQKHlkkKIOwDcYWy7lf1+B4B3+G2aG3U5o9xa0PaN2HWO9a4V8SqoywnvA3zyIifW5Vleg9hWlFxlm1Ejxk22OEfYRY2oco+bnqIiVmU70oWiRkiupFosl2/B5fW6yjHlNc4iLIRyTWcRJyzlntWVIyv+Apb9XN+wOYAyixgvyxRZTIQN6KGLBnGiCJd9DvucFPLnmaakO6gRwzjSvATJObJNugzL8nszhdCRaKSu0aHuojsi+7njsspLXvsozagow1UBeYqwOn/ooEbwSVWeXPsQPq1pTIvS33fPKw/D1wSmbijW5dlun1fE+LYHZxk3SRPomqNcBZthsVzTQds5YsPNWxeDKLKVzDGu0EKZ5bKUq27luop1wlzYVyR6hRUfmRQ1QlEakv95STXkdpNLK1g5lmLJlAy7PJXQQJWnyuX/87bx9hAhWzi4tjGynnmaNdWoRx2jfwPFUmm74LJGVgWf9HALLE+owekQvM3copmnEBe9h2Q5w5isbXX7yS37VcAVUYnsPcQal1AhJEc4mTytG1EjkogcSkZyuzN7HxtTphegaTd3n2D2ua+Qz7q+XpMoajbG8tQpwnVd5SuO0FxtoWv3Q5suel+Ylhn1OLS54M+n6xkAZmLbtemkRsiXYjSZGsEtwq7JYZUJm3lvFZlAZS9y5lbniTC4sjQpjrDpZubUCMsKO0YRNikZgO1eNfnISf16HdxSLH+vOdsy2YoulR4zygCvvyh8prTllkY+meGW2SGjQ2iJXCI+ATAUYIeiWKQd2iJCT/2s++yImUcg2+Z4D8Ukk66o621GjQCAuTSEGjELnauPavJEljynkaJXFdPi0ewqq11RcK9PI+U3VnJDqLsYaHWBWYRb1kjbVIic9Vd8eXWJaVzgZ6LuAs8y8E+NiKwXp6ts0yo2TgHgIdZcC8CqvCjNxXFFEnuo+0Ep70IoSgO3puVZhIWDGiHdzPI8U148NJVdnrJYmu10yT/PSu+mRoycfFEzkYYpdteCKzPCQlGMG0Nl4aJGRGTGOU4Xy8VkUSPyEj2UpZDJrugWYb2NVVFXaUw8AvY1T/bxMZZM3iQ1IiIVXYn3YTalR/AJlIsa4QxtZ4yZPoRPaxrT4oVtmnpQF4EaYaCuMsmTNbQ9Nrvm4UzL7JRjM1gPimQ58wWf4dOA5CXH7zmiHGqEoVSOG+J6imV7TFaZOJhxhIuMdUt5JxY1YiQVguR/PpVBbzOgZ5YbOagRg0ityLfL0xN5yON5HVyBmESNiNgLJKFG6MdxJTfPiu6yxlS9L32mAOft5RbIJIRaOiHKLMKRllEumYTZ5QBs4lGwkVk8XXZheNSOOqjLp+UUBrtMfUI1GolsIhaTSujCr73MLhcRC5/mWizHDFYm97zrtTJtomsvcFEQu559BJG96NMnpk4RrssZXWEW4baVqyrxUX1iGsPWyKb2/UEyDnWC4pcF1XxxmhgyizCQPzPPaAbx5DHGj3FlwqtGjdAV8Jfs2oY9y7PYz5Kz5LWZv6w2Rjo1QsozlxqRWYR5W9QiOiEcUSNIxRl2lWfyOncszgJwL+LKszzq1tJk2/qGsK6da8GiS+k1dR0z8kJR+Ezzzttrut0l/WbILML8OvP4yvZiRFVuEajoI+y69IQawe8x1Ta5T22TXowNxo1XcYTVcXLBHPfmOMOnsWeeSY0oSz2ZZmTKf89fYHHU7za6uO4+0VyS7YZQ9wHDLcJtz0i7VkR98vPawqagRrToCfA9xoZxZMWtdRWdKSBSIS1AjeDWKl5mFSuKaTU9d/cS/voX3jD2HPNFHlmUBiXHMtSIiFj4NEe2pkE8ziJsW2f2Ls+l7VXlZ3XlKKTcIiyPOe2kRrDJZo7cXdSImKWlLgOfNCFuaTQt41b2uIjAU3sT2Xx6kyNdVFGT5bgiEnVNjXBxP10WWTlmR0JkkwQXNWKeKcJye14SiIiS8WF5aTyOgb7DjJjRV8SOe7xPcHk2fGLqFOG6LqfVDhfL+bSGVIE0WPR4vFvYDNSIaQ+fxo2hUY7lwMw6V4QawcOTOakAJfrAyywK1Wbl7h1xi3Ck3Oe5meVGbkVYiERJlgo1x3iOcJpZLj1pZWGYZfQan1lOL4dbu+UxGyPbIuxaNGZbEG0vQJFU2i5k1lYPHgs9e1myTV7TmSyLnJqgxQY3XT4P7YQl5Sbfcozo3GRkddWBSd8oCz6WJPJSdY9GMqNiIs+MGsEOlNSIOFLbXZnlZJu5B0l596pNoqYR00JH5Jb7PoJPdpvA1A3Fum6VpTml+7d94bvmC02lRXgK22yiqhu5ClxZo+rApEZwlyhHxpMsQI1QUSPc1vKyHE2gmvIs3988Gx7PLMepEZM4wi7lVCrD1qp9orGKNVdepTUYyFdgAFtW8sWWvECSbWu5cYR12dk0C0ds4Yr3pU9rIFcyTN7rIKNEKO/DkD1/+Tmm4quoEeXaMXBahMv3iyNvAWNR8NBy2TbHtYsIGic4oe+Mp0bI7cMcjVZOdGX9ZqSRviuHPqDurY4bMgE8ukwfEee8d3xh6izCdR+k/GK3HzVCfncz4KZldspxyf7t+Olrz8MVLzmj66ZURjdRI/yUd8MlezXrZZ4LjSsPXJFzgcf8JXYer0PuL4pBgUV6VpsNhUCjRox0akR+imUZYoq1P/29IURWDkccKbezXZ5uKd+7fU47j7eb1+WSlbwO8ry1vKgRhrJl8YgdLyFXtI8i8PkMUlZge9wPB1IhTr6HnCMckbb4xqTIlFXyzUWXfFvdl3ddWpXLmu96D/ExKce9mVkOAGbT8Gm83Ly2SSXcokZ4ks00oOt3flFE1G+v66R3Sl1MnSLcRK76tlBlEZBPtKmQ+cIwjvCzbzy/62bUgm/ldBxcylId/PPXnaP9z0t1aS6OGef2lKv8uZJmhnICysmrSAINq83SksfuC8UR1uP55maWc1AjZF/k4iPzBZNwhO3yhOCKSLJtH1OEXS/VcXQrKV8ePs20TPFA9aZCrB3j6ANQ/uXpk8POaVOmbPgiOXmsmoClrn1jEmZZiAu20RlH2JMCVJsj7Ji4uq4zEWFtQ1EhIoJKqOGgRiReAnsCoNeT1m/cz20+D7tG3cWObSGK7HjTfQKxcdQEpo4asbIwxHuuOYxrL9xdu6zWo0ZQtzycjFayFZ5APYJv5XQcZBVNDW1uJdW3c6VkcszHYRRpZZmRKcxtk1BlkqfqjrJ6FTWiaIplvSz+ezSS4dP0NsWkFtO5yoqZW3rvsop64eKajwtHpiYcyX9XQg1uCcqTIaeIqLJrcoQ9jE+uVJshunjYNPmtLSAksu5LM1lT0b5lVmieYrmixdzEzsVZEAE7l2Yrne9yeZtUmOQ4ne8eEY2NGpF4CZJtuYvl0kmzvUhOb8dmhkkH6Ssidj37CE6jawJTZxEmIvzcdRfWKmNpdoDjp9ZbJ+s3bd6fXH9593FAfXRBjWjqoZGEsXFvl/W7FCcTMpwVZS9FtU8udJLfRTCsMLbNRU4RQbMI8wVB+YpwPjViJNK4rEY34shtEc4UkYjwnRdOATAtwvaEKrO2OTouFyrpcYRNhZZgco9dNAjzmpsJTIqiCv87DzwxgzmhktZf2U4toQaZKZb1c8sqL2rRmP/MchfsXcI9H3hDFkKvLPhESLUt/TYmb2tM8Y0ici4ElRZhPkl0hU+T57kWxE6jZ7Iq1POt333te9QIPtltAlOnCPvA8vwwUYRbvvBE3dEiAODqC3bh37z+XBxcXeisDVsRbYbNa5oHztPZ6tvT+iPdtZ+HQaqAuagRS3ND3HbzZbjinB2F21Vl8Zask0ecUNEeTGqEu4xMEXZYhDdYORyDKHJyhGVZRMB3jieK8B7OEXZc23HXW1IaVCxkWz4mPYXItmImypStHCfnW9WOhc/xqU++9PKlUsqpEXr8anvSaFq5i1uEbYXQZz+rKsGAW8FxUSMiIkWFICPFMrcID2RmOWITAHcfZcgrkwrRdfSkNtGmN7AOXPd4n+Ci+Hgtv7GSe4zl+SSpRtsUgaZj4U3CzsVZvPdNF/T+ptxsaDNaSNP8uzzLgemmnnRvDWODGmGU+aaX7sV2lvxmEqqET4sNBUa2eSRKUCNSZcGVEESM8kKWwUmNEIwa8e3nTwLI4wizssZcb2lxd0Xk4GWa5Y2LLCFRJJW2Cz7vBRc1QpY7I8OmycQaMQufFunKs+xanMm3nPIi28HjCHcdM17CZUmLSI+jLLdlNB/Dc8l/y1B+/N51ZZaTx3BvgmUR3gLax7TwoXkIwj5ChuJrCj3uenPYPp8Ywk+v56R3aghNz2oC+gmf7uDJdel1ei+f3MoPt4AVoUbIsGxK6ajXrkHG8y1+jqzTpAxtjEQWzzezCOdmgkvL0hSH9JyUGmGKYhBFbmoEsy4/e2INgB41whUxZ6xFmMiafLssu3xbngXRpndU4wgrz0H98anczrYcsvHAJjk8oQaPhGFa7cou1pTHccsob1uXiCLb+OJSKjgNhMsz+a9+Z+HTIhWHOX+xHGUpr3k5pvV+M6NpD50vFFnX0SUkXacpbE1qxFxiaXr+xbVW6+37YAtoBq3GEW74wbs4N8DirP3YUPzSgtSIWPI05fn12lvFBWm6tHm0B55hS25zQUZ6II0jnJyTR43IS6jBqRGvPbwDdz36XSwxWbusjPGYiU+cWT65oqsf86P/4BD4JnJcO2fUiExmVrVj0UTUCK7syXKHA50jrIVPIzOznD4OyvLspex5PN2+xD93LTIyFV1AHz9SPmqf+j07UBMg08JrQt7f5mR30nmbCdOi9EeR7TnoE5JJfXPlb0lFeP9qshLb5Z5sEhFNV1a3AD9QD/7m62qahvG7Nx/RktJI8PBpcWFqhDuzXBWYymwRKK0A6nMAABGsSURBVD6p/mIWIrEK8/ZNWizHlQ1LoTapBpHKYMchRmr/R95+BN87sWaElbOt564kG1k9qVt8XOz0t1x2wGqbrbjbylTVsF4+XcVcsTUV7KHkp2YKaaSFTxvGkbZI0iwPKE+NGDjiCHcdksrlhTQVXbkt+23cv7wPPGpENgHIebDJsWQqg9NCF/CBaVkY6Joc9QlNe9O3pCL889ddiD3Lc7j+kn2t1ltEQQjYfGg3akT63dA4O2fntpx6ubVt8kNrkCoqvmRTJa6t5RpPT91IUyMTKaUzb7Fcur7I6UoejZL9dugx3SJ819GncXJ9A688uJqdvzAzwMKM/nh2TRrGWVilpZQPhUnyKao4VfVyNJNZzs7AZk60hpEeLu39N1yElXStSBb7uqLrfmVhiIWZWIty0mZa9XFw0VryeOBqv3uMAUoR5p6DvKgRRLrCbFvrNz8zc9xEtU/g0WX6iJBQowHMz8R411WHW683cIS3JqTBpA3rUFecNDO5waS+Ls4lih5lSke9+itllste5DrfNeH2CsRRpFl3XeB0Bgk9fJqw2jSICBuMdPzLdzyE515cw5++53Vj++BS0Mal1FYWOdK2jQORfYxTcapARUnKym9vWfBJn+luH8RkZT8bMoXsqvN3GWWRNSkrarT4kSMHcdX5u52L5bo2fLiMLy6lgh9iUSM0RVhxr12JRMx6iOxn0rUX7savvvllOGvH5o9e1BeKzCS4Jrt9wk+87mycanBN15ZUhLtC37O3BDQDnrChaXTldpRdk1agSYvW/uNbXoG5YYTHn/4+gPoW7CqZ5chQVpQlN7EI80VFYgJH2OVK3hi5OcI8RuvJtQ08/NRxrI8Enk5jB+f1wUV7mUSNMBe/TZIPj+2cnUO24iot+mXhM2KARo0wJgQzaVQS2ewkbnX+ZInTAcomw5gbxjhkKHU+Ff46eM81h7N+SxDZfdM5wqaHQx0nw6dJzw+QHz5NTsIU9ST53jY7wE2XH6rSnamD7Hvf3/tR1G9l/dqL9jRaflCEW0TiCu66FQFtY1z2L+91dcRJ46nPi1Ajzt29CAD4f989kZxXlxpRod9m+DR5fUYpR5hbszZyjBHfO7HmjLwApFxjYSufA6YIP/it5zOaxFee+N7YPrjir06iRnAXNgCcsTDj7og8x3HtXBbEQRxVenH6jCHL6QfmhGAQ65OAQRRpcYRNcNew3F1n4nrOrm3YtTSrRf3oAq+/0FYg3BZh0n5rVAl2nfWoEZMUYWjxmvuuDDaBNteH1MFW91YXujxE9ANE9DARHSWi9zn2ExF9KN1/PxFd6r+p04++Z28JaAar24aIqF5g/KJQVIN2xxlfaR9FxV96vqgRVVKZSkOZuVhOURp4Qg1HlIeRwKe/+hSuPHenEas3+d7IoUZwjrBUfgHgb74hFeGcPmaWNV1pMbep40lLfAAA10xITe+iQbh4pjIhSln4jBrBx5xJ1ZAcYW7lHZcN7xd+8CK8+dID2bH8uwou3LuMuz/wBuxs4Z4vi3FUF7mfX28XNSJiE6z8OMI6NafPHNSm0BVVrSzM58RWw0SLMBHFAH4bwBsBHANwNxHdLoR4kB12PYDz0s8VAH4n/Q5gWJ4fYvt88SQBAZsDB1YX8IX3X4vdS82/FNtM3sHBrXMxFQ91wy3JdaAiAhQvh1sLARbtIaVGcEujSxG+++vP4MnvvYifu+4CZ7mjvPBppKJG3H/sOexamsX2+SG+nCrFeQqmiszBt8Haxo83LT2vOrjiLFu13eE2z7ESV1FsFGWg9KkWlAXXjkywY3EWK+kEFEjCpw3ifGrEza8+i7Vxc1sw+QRPwhxTerINtc+MGkGUP2Gwokb03CraBKaFGnH9Jftw4vR6183oDEWoEZcDOCqEeAwAiOjjAG4EwBXhGwH8vkgIc18kohUi2ieE+Jb3Fk8x3vum8/H9U1t3sG1l7Flux0VaNvSTv3qTb0mLKKqQ+ooi4ErVPLFuw5oqvz/6V4/jme+fxu6l2axff/nI03jquSTb28m1Eb7xzAnc9ejTWJiJ8aaX7nGW+9kHnsK3nz+FVSND3iAmHD+1jk/edwxfevwZvOLACpbnB/iTv3kyaUeeIuywLo2zOMVRouBIGsbe5bmJ42JmEGHGmMU4qREVOcJeo0YwXrDJjX/3VYfxz644xHjgUWH6jKJG1G5iL8EneBJmZkQXDx1g1IhU5sMx2m0WjaPCvblZEEeE8/cs4vAud7SdvuDHrtganO08FFGE9wN4gv0/Btva6zpmPwBNESaidwJ4JwAcOrT1BL88N8ySeQQENIHF2QGWZgfYt32+1XoPri5g+/wQi7MDnLkyX7j+i/ct4y2XHcArD4y3VE7Cvu1zOHTGQqkXzlk7FrBzcRYHz0jaes0Fu3H1Bbvwu3/xGADgynN3ZnSWW//iUe3cmTjC9oUhfvLKc6wwZ9IdfstnHgYAXH/JXm3/rsVZHD+5jvf+0VcAJCuit88P8cn7nsTy3CDjT5s4c2UO22ZiLY7z3uU5DCLSUjFLnL1jG1YWhti5mPCC/+31F1jHmPi1H365xWv9wZfvw4unN7Rth3cv4vy9SxPLM7F/ZR7zwxgrJdJn52EYRTiwOo+zdixgZhBh+/wwU9TmZ+IsHfD+lXnsX53HvuU5LM26E8JwLM0OsTw3wP7VzRnVYP/qPM5c0e/PXcxbtWPbbHb/EgE7tile+a7FWcwPY+xbmcPxU+tZTH5nPStz2L08hz1L+WN0s4OI8L9+9qqumxEwAZS3Gjo7gOhHAFwnhHhH+v9mAJcLIf41O+bPAPyKEOLz6f87Afy8EOLevHKPHDki7rnnHg9dCAgI4Di5toHZQdSqBSbLsEaEtY2Rk4c4LfjO8VM4cXod+1fmMYij7L/EMI6wZ3lubP+eeu4kTq0nyuO+7fNajNnRSODYsy9CIKFNHEiViWdPrGF1YZh73YQQOLU+ypQ9iVPrG5gdxM5zJF48vZEphl1CCIHTG6OJ7fVZ7un1UcppRuG6k4Qqm9OKOUqjmQyY5V8IgW8+dxIxEfZun4MQAt9+/hSGMVlrG+TzRQhgfSS0sc2xtjECIVlYeXJtwxq3AQFtg4juFUIcMbcXsQgfA3CQ/T8A4JsVjgkICGgBXbxwuMKQl2lqWpBYx2Zz/xfBuGgBUURWuC0AOGPb+IgOROS8tkUUuz4owUDSB99K8KRyuaJWtO5pncQVQRQRIuj9IyLsZ1ZiShViF3hSjZkxcuLPgaAEB/QZRd5YdwM4j4jOIaIZADcBuN045nYAb0ujR7wawHOBHxwQEBAQEBAQENBnTLQICyHWieinAHwWQAzg94QQDxDRu9L9twK4A8ANAI4COAHgJ5prckBAQEBAQEBAQEB9FEqoIYS4A4myy7fdyn4LAO/x27SAgICAgICAgICA5jDdZL6AgICAgICAgICAigiKcEBAQEBAQEBAwJbExPBpjVVMdBzAwxMO2w7guZpV+ShjJ4CnO25HkIW/832VAdSXRx9k4ausPoyNvpQRZKGj6/ukT2UEWShsFln4KmezPDf6KosLhBB2AHQhRCcfAPcUOOY2D/X4KGNiW5tuR5BF/2ThQx59kIXHtnQ+NvpSRpCFX3n0qB9BFkEWvZVHX2TSV1nkldl3asSnelKGD9RtR5CFv/N9leEDfZBFE2VVRV+ubZCF3zLqoi/9CLLwW0Zd9KkffZAH0A+ZTJUsuqRG3CMcGT76iGlqa9MIstAR5KEQZKEQZKEjyEMhyEIhyEJHkIdCE7LIK7NLi/BtHdZdFtPU1qYRZKEjyEMhyEIhyEJHkIdCkIVCkIWOIA+FJmThLLMzi3BAQEBAQEBAQEBAl+g7RzggICAgICAgICCgEWxJRZiIDhLRnxPRQ0T0ABH9dLr9DCL630T0tfR7lZ3zfiI6SkQPE9F1bPvn0m1fTj+7u+hTVXiWxQwR3UZEjxDR3xHRD3fRpzrwJQ8iWmJj4stE9DQR/WZX/aoCz2PjrUT0t0R0PxF9hoh2dtGnqvAsix9N5fAAEd3SRX/qoqw8iGhHevwLRPRho6zL0rFxlIg+RETURZ+qwrMsfpmIniCiF7roS134kgURLRDRn6XvkQeI6Fe76lMdeB4bnyGir6Tl3EpEcRd9qgqfsmBl3k5EX63duLrhKabxA2AfgEvT30sAHgFwMYBbALwv3f4+AL+W/r4YwFcAzAI4B8CjAOJ03+cAHOm6Tz2RxX8A8MH0dwRgZ9f961IeRrn3AvhHXfevC1kgSeX+93I8pOf/Ytf960gWOwB8A8Cu9Lj/BuDarvvXgjy2AbgSwLsAfNgo60sAXgOAAHwawPVd969DWbw6Le+FrvvVpSwALAC4Jv09A+D/Ttu4aGBsLKffBOATAG7qun9dySLd/2YAfwDgq3XbtiUtwkKIbwkh7kt/HwfwEID9AG5E8mJC+v1D6e8bAXxcCHFKCPE4gKMALm+31c3Asyz+BYBfScsaCSHqBsNuHU2MDSI6D8BuJA/zqYFHWVD62ZZa+5YBfLO1jniAR1m8BMAjQojvpMf9HwBT5zkpKw8hxPeFEJ8HcJKXQ0T7kLzgvyCSt9vvQ8lwKuBLFum+LwohvtVKwxuAL1kIIU4IIf48/X0awH0ADrTSCY/wPDaeT38OkEwOpmqBl09ZENEigPcC+KCPtm1JRZiDiM4G8CoAfw1gj3wIpd+S5rAfwBPstGPpNon/Son7+99Nm1uPo44siGgl/f9LRHQfEf0xEe1ppeENwdPYAIC3AvjD9EU/lagjCyHEGoB3A/hbJArwxQA+2krDG0DNcXEUwIVEdDYRDZA89A+20/JmUFAeediPRDYSrvtnalBTFpsKvmSRvlv+CYA7/beyPfiQBxF9Fol37TiA/9FIQ1uAB1n8EoBfB3DCR3u2tCKczio+AeBn2GzLeahjm1RqflwI8TIA/zD93Oy3le3AgywGSGbsfyWEuBTAFwD8J+8NbQmexobETQA+5qttbaOuLIhoiEQRfhWAMwHcD+D93hvaAurKQgjxLBJZ/CESD8HXAaz7bmdbKCGP3CIc26ZywuhBFpsGvmSRThY/BuBDQojHfLWvbfiShxDiOiQUg1kAr/fUvFZRVxZE9EoA5woh/sRXm7asIpy+nD8B4L8LIT6Zbv526qqTLru/T7cfg261OYDUtSuEeDL9Po6ErzJ1lAlPsvguktmZHJx/DODShpveCHyNjfTYVwAYCCHubbzhDcCTLF4JAEKIR1Or+B8BeG0LzfcKj8+MTwkhrhBCvAbAwwC+1kb7faOkPPJwDLrLW7t/pgWeZLEp4FkWtwH4mhBiqhYac/geG0KIkwBuR0IpmCp4ksVrAFxGRF8H8HkA5xPR5+q0a0sqwil94aMAHhJC/AbbdTuAt6e/3w7gf7LtNxHRLBGdA+A8AF8iogGlq9/TC/yPAdRfwdgifMkiVXA+BeDq9LhrATzYcPO9w5c82HlvxZRagz3K4kkAFxPRrvS4NyLhh00NfI4LSiPLpKuj/xWAjzTfA7+oIA8nUlfocSJ6dVrm2yad0zf4ksVmgE9ZENEHAWwH8DO+29kWfMmDiBaZsjgAcAOAv/Pf4ubg8ZnxO0KIM4UQZyNZTPeIEOLqWo0TPVhN2PYnFZ5A4qL9cvq5AcmK7juRWGjuBHAGO+cDSFZ+P4x09SqSVY33puU8AOC34IgY0OePL1mk288C8JdpWXcCONR1/7qUR7rvMQAXdt2vrmWBZOXvQ2lZnwKwo+v+dSiLjyGZJD6IKVv5XVMeXwfwDIAXkFiCL063H0FiQHgUwIeRJnqalo9nWdyS/h+l37/Ydf+6kAUSz4BInxmynHd03b8O5bEHwN1QusZ/RuJp7LyPbcvCKPNseIgaETLLBQQEBAQEBAQEbElsSWpEQEBAQEBAQEBAQFCEAwICAgICAgICtiSCIhwQEBAQEBAQELAlERThgICAgICAgICALYmgCAcEBAQEBAQEBGxJBEU4ICAgICAgICBgSyIowgEBAQEBAQEBAVsSQREOCAgICAgICAjYkvj/bNAKX6hNIyQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_areturns.smoothed_marginal_probabilities[0].plot(\n",
    "    title='Probability of being in a low-variance regime', figsize=(12,3));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2rc2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
