{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Robust Linear Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.sandbox.regression.predstd import wls_prediction_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimation\n",
    "\n",
    "Load data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = sm.datasets.stackloss.load(as_pandas=False)\n",
    "data.exog = sm.add_constant(data.exog)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Huber's T norm with the (default) median absolute deviation scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-41.02649835   0.82938433   0.92606597  -0.12784672]\n",
      "[9.79189854 0.11100521 0.30293016 0.12864961]\n",
      "                    Robust linear Model Regression Results                    \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   No. Observations:                   21\n",
      "Model:                            RLM   Df Residuals:                       17\n",
      "Method:                          IRLS   Df Model:                            3\n",
      "Norm:                          HuberT                                         \n",
      "Scale Est.:                       mad                                         \n",
      "Cov Type:                          H1                                         \n",
      "Date:                Fri, 24 Apr 2020                                         \n",
      "Time:                        14:17:04                                         \n",
      "No. Iterations:                    19                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "var_0        -41.0265      9.792     -4.190      0.000     -60.218     -21.835\n",
      "var_1          0.8294      0.111      7.472      0.000       0.612       1.047\n",
      "var_2          0.9261      0.303      3.057      0.002       0.332       1.520\n",
      "var_3         -0.1278      0.129     -0.994      0.320      -0.380       0.124\n",
      "==============================================================================\n",
      "\n",
      "If the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .\n"
     ]
    }
   ],
   "source": [
    "huber_t = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())\n",
    "hub_results = huber_t.fit()\n",
    "print(hub_results.params)\n",
    "print(hub_results.bse)\n",
    "print(hub_results.summary(yname='y',\n",
    "            xname=['var_%d' % i for i in range(len(hub_results.params))]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Huber's T norm with 'H2' covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-41.02649835   0.82938433   0.92606597  -0.12784672]\n",
      "[9.08950419 0.11945975 0.32235497 0.11796313]\n"
     ]
    }
   ],
   "source": [
    "hub_results2 = huber_t.fit(cov=\"H2\")\n",
    "print(hub_results2.params)\n",
    "print(hub_results2.bse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Andrew's Wave norm with Huber's Proposal 2 scaling and 'H3' covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters:  [-40.8817957    0.79276138   1.04857556  -0.13360865]\n"
     ]
    }
   ],
   "source": [
    "andrew_mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.AndrewWave())\n",
    "andrew_results = andrew_mod.fit(scale_est=sm.robust.scale.HuberScale(), cov=\"H3\")\n",
    "print('Parameters: ', andrew_results.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See ``help(sm.RLM.fit)`` for more options and ``module sm.robust.scale`` for scale options\n",
    "\n",
    "## Comparing OLS and RLM\n",
    "\n",
    "Artificial data with outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "x1 = np.linspace(0, 20, nsample)\n",
    "X = np.column_stack((x1, (x1-5)**2))\n",
    "X = sm.add_constant(X)\n",
    "sig = 0.3   # smaller error variance makes OLS<->RLM contrast bigger\n",
    "beta = [5, 0.5, -0.0]\n",
    "y_true2 = np.dot(X, beta)\n",
    "y2 = y_true2 + sig*1. * np.random.normal(size=nsample)\n",
    "y2[[39,41,43,45,48]] -= 5   # add some outliers (10% of nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 1: quadratic function with linear truth\n",
    "\n",
    "Note that the quadratic term in OLS regression will capture outlier effects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.13655226  0.52332656 -0.01396673]\n",
      "[0.48429453 0.07476854 0.00661586]\n",
      "[ 4.78738395  5.05566688  5.31929617  5.57827182  5.83259383  6.08226221\n",
      "  6.32727694  6.56763804  6.8033455   7.03439932  7.2607995   7.48254605\n",
      "  7.69963895  7.91207822  8.11986385  8.32299584  8.52147419  8.71529891\n",
      "  8.90446998  9.08898742  9.26885122  9.44406138  9.6146179   9.78052078\n",
      "  9.94177003 10.09836563 10.2503076  10.39759593 10.54023063 10.67821168\n",
      " 10.81153909 10.94021287 11.06423301 11.18359951 11.29831237 11.40837159\n",
      " 11.51377718 11.61452912 11.71062743 11.8020721  11.88886313 11.97100053\n",
      " 12.04848428 12.1213144  12.18949088 12.25301371 12.31188292 12.36609848\n",
      " 12.4156604  12.46056869]\n"
     ]
    }
   ],
   "source": [
    "res = sm.OLS(y2, X).fit()\n",
    "print(res.params)\n",
    "print(res.bse)\n",
    "print(res.predict())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimate RLM:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.08903521e+00  5.01749981e-01 -2.16892662e-03]\n",
      "[0.1499114  0.0231443  0.00204791]\n"
     ]
    }
   ],
   "source": [
    "resrlm = sm.RLM(y2, X).fit()\n",
    "print(resrlm.params)\n",
    "print(resrlm.bse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare OLS estimates to the robust estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f09cce96fd0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xCaZZs2ZERt5/KaFJkyaZMSyllFIq8yR0UwCZqZ03T65/Jxx//HEJvwB//QVFi2bP1U45UHJlDEmJiYFFi2DMGDh0CDw9YdIk6SKXxIXvFLsSeYV5e+bx+abPiY6PlveKjyHgRICGX6WUUkrZUFSUlCZs3iy3nTvlGreLi6xucneXBWoNGsjMboECic8tXtx241aP5MYNmDEDxo2DsDCpRvnuO9mGOK1bEJumybawbUwLmsbSA0uJiouibD5vDMIxTSsmjhgx1dL3G3kEGn6VUkope3DpkrQPc3WVWd1+/WT6D2THtDZtJBm5uMCIEbYdaw6Smg0oMtL58zBhgmyKFx4uu7LNng2tW6e9c8ON6BssCl7EtKBp7D2/l7zOeXnR50Uq5unKjHXxFI/fT5RDMC7WGswLcKZyoTCbfO/30vCrlFJK5TSmCYcPy4zupk1yf/iwbCDx5JMy3Td4MDRqBA0bSgmDSnep3YAiIxw9KruvzZ0rn3W6d4d335Uuc6kVeDqQgBMBuOdzJzA0kEXBi7gZcxOfEj5M7zidntV7ki9XPhqNWk9kbAy5qEIuaxUAIq0P7j2c2TT8KqWUUtldfDzs2yeztlWqSBFntf8uMxcqJCH3pZcSj/n4yE1lqNRuQJGedu6URWw//ijlDH37yv4hCV3oUivgeABtFrYhxipXC5wtzjxf43le83uNuu5179obIT22UM5IGn6VUkqp7MY0ZTb3779h40bYskU6M7zyiuxIULmyXNNu0EB2TdOFaTaR2SHQNOHPPyX0rlsH+fPLLO/gwVCiRNpeM+RSCNOCpjFt57TbwdcBB4Y2GsrI5iOTfM6jbKGcGTT8KqWUUlndjRsScK9ckR0HDAP69IFjx2Q297nnoEkTaNpUzndwkJleZVOZFQLj4mSG98svZTO9kiUlAPfvf/c6xZSKiY9h5T8rmRo0lQ0nNuDk4MTjHo+z6dQm4qxxOFucaVeh3QOfn5YtlDOThl/AYrFQo0YN4uLiKFeuHAsWLMDNzY0TJ07QsWNH9u/ff9f5ffv2ZdmyZZw/f558+fIBMHjwYCZMmMDFixcpcuc2jUoppVRabN4sNbp//SVdGeLjoVQp6NFDwu8PP0CZMndvDayylIwOgZGRUsv71VfyOcjbG2bNgl69IFeu1L/eyfCTzNw1k1m7ZnH+1nk8CnjweYvPecn3JYrnLX675reZZ7OHti171N7DGU3DL+Dq6sqePXsA6NOnD5MnT2b48OEPfU6FChVYuXIlvXr1wmq1smHDBkqVyhp/qUoppbKZ69dlYdrGjfDJJ+DkJOF28mTZPOK996TPbsOGiUvzfX1tO2aVrIwKgVevSteGCRNkr5H69SUAd+oEFkvyz4fExWtNPJpwLeoa03ZO47cjv2GaJh0qdWCA3wDaeLXB4pD4gg3KNEhxr9609B7OLNky/Kb0k0daNGjQgH379iV7Xs+ePVm6dCm9evUiICCARo0asXr16nQdi1JKqRzsn3+kLjcgQK5VW60Senv1km2Dhw+Hzz57tB0HlM2lZwgMDZX+vDNmwM2b0K4dDB0qn4tS064s8HQgLea3IDpONqEwMSmepzjDGg/j1dqv4uHmkS7jzaqyVPh96/e32HNuz0PPuRZ9jX3n92E1rTgYDtQsXpMCuR5c0OJTwofxbcen6P3j4+NZt24dL7/8crLnVqxYkZUrV3L16lUWL15Mr169NPwqpZRKWkSElDGsXw9du8ps7tmzMnX32GMSdJs1k68Twq6WM6j/HDok9byLFslnpB49ZCFbzZqpex3TNNl4ciNvrH6DqLio28d7Vu/JvC7zcLI4pfPIs6YsFX5T4lrUNaymFQCraeVa1LWHht+UiIyMxMfHhxMnTlCnTh2eeOKJFD2vW7duLFmyhG3btjF9+vRHGoNSSqkc5tYtuRa9fj0EBkJsrPScKltWwm+TJrLbgGvWWAGvsp4tW2Th2qpV8mPy2mvwf/8nWxGnRnhUOAv2LmDazmkcvHiQvM55cXRwxDRNnC3OvFHvDbsJvpDFwm9KZmgDTwfScn5LYuJjcLY4s6jbokcufUio+b127RodO3Zk8uTJvPnmm8k+r0ePHtSuXZs+ffrgoG1klFLKfsXHw+7dEnTz5YMBA2TF0TffgJcXvP02tGgh/Xbz5pXnODqmfT9ZlWNZrfDbbxJ6N22SNs0ffgivv576iwE7z+xkatBUFu9fTERsBPVK1ePbTt/ybPVn2Xtub4aVkGZ12e5fXYMyDVj3wroM+QsrUKAAEyZMoHPnzgwYMCDZ88uWLctnn31Gq1at0m0MSimlspGFC6XH1IYNcO2aHOvSRcKvoyOEhenMrkqR2FhYvFjKGw4ckAsE33wDL78su1KnVERsBEv3L2Vq0FR2nNmBq6Pr7c0o6rjXuX1eahav5TTZLvxCxv6F+fr6UqtWLZYsWUKTJk0ICQmhdOnStx8fN27cXef3798/Q8ahlFIqi7l4UXYOCAqCMWNkhdHq1bBnDzz9NLRsCc2bQ/Hiic/R4KuScfOmtCcbOxZOn4YaNWDBAnj2WVn/mFJL9i9h4raJ7Luwj5sxN6lSpAoT2k6gd63euLm4Zdw3kA0Zpmk+/ATD+BboCFwwTbP6PY8NAcYARU3TvJTcm/n5+ZlBQUF3HTt06BBVqlRJ7bizHXv5PpVSKkfZvx/mz4c//pCQC+DmJp0aiheXRqsuLqlbaq8U0qJs4kTpZnf1qnRsGDpUOjik9McpNj6WVSGrGLVpFEFnJV9ZDAsT2k5gQN0Bd205bI8Mw9hpmqbfvcdTUqg6F2ibxAuWAZ4ATj3y6JRSSilbM00JuKNHw5EjcuzgQRg/XgLvp5/Ctm1w6VLi7K6rqwZflSrHjsGgQeDhIT9STZvKesi//oL27VP24xR2PYyPAj7CY7wHT33/FEeuHMEg8YnXoq/ZffB9mGTLHkzT3GgYhmcSD40D3gVWpvOYlFJKqcwRGQk//QRr1sDatXDunBwvUgQqVpRdA65eTV3RpVJJ2L1b6nmXLZONKHr3Bn9/qFw5Zc+3mlbWH1/PlB1TWBWyCqtppW2Ftkz3m05B14K0XtD6djOAZp7NMvR7ye7SVPNrGEYnIMw0zb3JfbIwDKMf0A9kgZhSSillM7GxMnsbHy9TbrGx0KcP5M8PrVtDmzZy7+4u57u42Ha8KlszTVkLOXq0fLbKl09alb31luxUnRJXIq8wd89cpgVN48iVIxTJXYR3GrxDf7/+lC9Y/vZ5GdUMICdKdfg1DCM3MBxonZLzTdOcAcwAqfl9wDk5eno+ubpqpZRSGejECZnZXbNGFqxdvy7BNyBAQu/eveDtnfJ9YZVKRnw8LF8uM71BQVIl8/nn0gTELQVrzwJPB7Jw30JOXDvB+uPriYqLomGZhnzQ9AOeqvoULo73fyiz5+4NqZWWmV8voByQMOtbGthlGEY90zTPpfbFXFxcuHz5MoULF86RAdg0TS5fvoyLzh4opVTmiImRQFu3rvy5Xz9ZsFa2rGyN1aaN9NxNULWqbcapcpyoKJg3T/Y2OXoUKlSAadPk4kJKYkBEbASfbvyUUZtGYSITZ529O/Nxs4+pVaJWBo/efqQ6/JqmGQwUS/izYRgnAL+UdHtISunSpQkNDeXixYtpeXq24OLicle7NKWUUuksLEzajv32mwTdW7dkOX2RInLNecIEmd3NgZMsyvbCw2HqVOnLe/48+PnB99/LTtYpuaBw+PJhpgVNY86eOYRHhd8+bjEs1C9VX4NvOks2/BqGsRhoBhQxDCMU+NA0zdnpNQAnJyfKlSuXXi+nlFLKHsTFybXlXLlko4neveV4mTLw/POybD5hJzVfX9uNU2VpK3aHMWZNCGfCI3F3c8W/jTddfFNYjIt85ho/HqZPhxs3pFx86FBp95zc56w4axw/h/zMlKAp/HnsTxwdHOlepTuPezzOkLVDdPFaBkpJt4eeyTzumW6jUUoppR7k0iWZ2f31V1k99M038MIL0KSJFFe2by8lDDq7q1Jgxe4whi0PJjI2HoCw8EiGLQ8GSDYA//OP7HOyYIF8BnvmGXj33ZR9zjp74yyzds1i+s7phN0Io0z+Mnza/FNerv0yJfKWAMC3hK8uXstAyW5ykZ6S2uRCKaWUeqhbt6RONzAQrFZZPdS+vdTyPvaYrUensqlGo9YTFh553/FSbq5sfq9FEs+ArVulimblSrno8PLL0r2hfPkkT79ty6ktzNk7h2NXjrHx1EbirHG09mrNQL+BdKjUAUeHbLnhbpb3oE0u9P9tpZRSWUdMDGzcCD//DA4OMG6c9Nh1d4f334cnn4TateUxpR7BmSSCb1LHTVPKyUePlh/NggXlR/GNN6Bo0Ye/x7Woa4z8ayTjto67vYCtZ/WefNzsYyoWrpgu34dKPQ2/SimlbO+XX2SZ/Jo1Ujzp4iKrhRIsW2a7sakcyd3NNcmZX3c3V0BaQC9dKhU1wcFSTj5uHLzySmI5+YPsO7+PKTumsHDfQm7F3rp93GJYqFGshgZfG9OPzkoppTLf4cPw9dcy0wuwaRNs3iytyFauhMuX4bvvbDtGlaP5t/HG1enuVgyuThbeeLwyEyZIm7LevaXSZt48+Pdf2ZziQcE3Jj6GxcGLaTKnCbWm1WLe3nk8U+0ZZj05C1dHVyyGRRewZRFa86uUUirjWa2wY4cE2xUr4NAhOb5pEzRqBBERMtur5QwqE93Z7aGoU37KX6jFnz/m5/JlaNxYOje0b//wH8tT104xY+cMZu6ayYVbF/Aq6MUAvwG86PsihVwLAbJphS5gy3wPqvnV8KuUUipjREfLYrVChWDLFgm5FovsrtalC3TqBB4eth6lsnMnT8pFiFmzIDJSfiyHDoWGDR/8nM2nNjN792yOXjnK5tObAehYqSMD/QbyhNcTOBj6IS4r0AVvSimlMt61a9KObOVKuX/xRWlJVr8+LFoEbdtKGFbKxvbtk3reJUtkZvf558Hf/+Eb/l2NvMpHAR8xcfvE2wvYXqj5AiObj8TDTT/IZRcafpVSSqWP556DH36QlULFi0v9bsKiNYtFHlfKhkxTOjaMHi0dHPLmhcGD4e234WEbse4+u5vJOybzXfB3RMYlLpKzGBYqF6mswTeb0fCrlFIq9U6fhp9+ksanixbJxhLly8uKoK5dZaZX63dVFmG1ysWI0aNh2zZpUfbppzBwoLQuS0p0XDTfH/yeKTumEBgaSG6n3PSq2YtGZRox4NcBugNbNqbhVymlVMqcPi0dGJYvh+3b5ViNGtKZoUgRSRNKZSHR0bL79ZgxEBIin8+mTIG+fcHVNennnAw/yfSd05m1axYXIy5SqXAlxrcZTx+fPri5uAFQqXAlXcCWjWn4VUoplTTThP37ZZqsRAmZ5X3vPahbF0aNkhneSpVsPUql7nP9OkyfLn15z56VbYeXLIHu3cHxnuQTeDqQDSc2kNspNxtObOCXw78A0Mm7E4PqDqJFuRb3LWBrUKaBht5sTMOvUkqpRKYJe/fC99/L7cgR+PxzGDYMOnaUpfFly9p6lMoO3NmGzN3NFf823nTxLfXQ55w7J+srp06VtZctW0qP3latpDLnXmuOruHJxU8Sa40FoKBLQYY1Hka/Ov0oW0B/znMqDb9KKaVEXBz4+MCBA7JArXlz+L//S1y05uqqwVdlihW7wxi2PJjI2HgAwsIjGbY8GCDJAHzkCHz1lQTd2FiZ4R06FOrUSfr195zbw+Ttk5m7dy5x1jgAHHDg7cfeZkTTERnzTaksQ8OvUkrZoztneE+fhvnz5Xpwly7w5psSeIsWtfUolZ0asybkdvBNEBkbz5g1IXeF3x07ZBHb8uXg7Cy1vEOGyO5s94qJj+GHgz8wecdktpzegqujK+0qtGPtv2uJs8bhbHGmVflWGfydqaxAw69SStmTkBAJugklDQ4Ock04NhacnHTRmsoSzoRHPvC4acLatRJ6N2yAAgWkFP3NN6U0/V6nr51m+s7pt3dgq1CoAmNbj6WvT18KuhbU3dfskIZfpZTK6Q4elCam+fNLahg1Clq0kCkyneFVWZC7myth9wRg02rgfMqD2rVhzx5wd5cuDv36yY92goQFbPmc87HhxAZWhQp+IOYAACAASURBVKzCalrpWKkjg+oOum8HNl28Zn80/CqlVE507Jgsb1+yBIKDYfZseOkleOEF2XxCA6/KwvzbeN+u+bXGOnAruAw3dpQnNjw3lSvLj/Pzz0OuXHc/789jf9J+UfvbC9jyO+dnSMMhvOb3Gp5unpn/jagsScOvUkrlJLduyaxuQh/ehg1h4kTo0EH+XKCA7camVAp18S3F9XAH3v88krDNpbBG5sK7ZjSj58KTT96/f8rBiweZvH0ys3bPuh18HXBgSMMhuoBN3UfDr1JKZWcXL8KPP8r9iBGQJw94e8NTT8Ezz4CHbruqspdTp2DsWJg1qyS3bsnntqFDoXHjXHe1K4uzxrHyn5VM3jGZDSc2kMuSi5blWrL++HpdwKYeSsOvUkplNzduyNbCixfDH39AfDzUrg3Dh8uU2Pz5th6hUqm2fz98+aX8WAP07An+/rKJ4J3O3zzPzF0zmRY0jbAbYXgU8GBUy1G8XPtliuQuogvYVLI0/CqlVHYQGyvB1mKRBWuffy6zukOGSEqoWTPpLv5KZWGmCZs2SeeGX3+F3Llh0CBpL31nS2nTNAkMDWTyjsl8f+B7Yq2xtPZqzZQOU+hQsQMWB8vtc3UBm0qOhl+llMqqTBMCA2HhQli2TGZ027eH/v3lvmFDDbwqXaRlN7VHYbXCzz9L6A0MhCJFYORIGDgQChdOPG/D8Q1M2j6J/Rf2c/jKYfLnys/AugMZWHcglQrr1toqbTT8KqVUVhMRITO7330Hx4/LzmqdO0Px4vJ42bK605pKN6ndTe1RxMTAokXSouzQIfD0hEmT4MUXZdY3wbGrxxixfgTf7f8OAAODdxu+y4imI8jrnDddx6Tsj4ZfpZTKCs6cgcOHoVkzcHGRhFCpEnz8sey6li+frUeocqiU7qb2KG7cgBkzYNw4CAuDWrXks93TT8vGggBW08raf9cyafskfjvy213PdzAccHNx0+Cr0oWGX6WUspVbt2DFCiln+PNP6b0bFiZ1vYcOSQhWKoM9bDe1R3X+PEyYAFOmQHg4NG8uPXpbt06s2AmPCmfunrlM3jGZo1eOUjxPcUY8PoI6JevQ48cexMTH4Gxxpplns0cej1Kg4VcppWxj9mx46y24eVOu/f7vf9CrlwRf0OCrMk1Su6klHH+Q5GqEjx6Fr76CuXOl1KFbN2lXVrdu4msEnw9m8o7JLNi3gIjYCBqWacjIZiPpXrU7zhZnANa9sE47N6h0p+FXKaUyQ0gILFggu6tVry4lDc8+KzuuNW58f9d+pTLJnbupJXB1suDfxjvJ8x9WI1zWLMXo0fDDD1LO0KePNCSp9N/atL9P/s20oGkcvHSQPef24OLownPVn2NQvUHULln7vvfSzg0qI2j4VUqpjHLlCixdCvPmwbZtEnBLl5bw26SJ3JSysYQZ25R2e7i3Rtg04coRN/o+48q1o5A/v/TnHTwYSpaUc87fPM+IDSOYtWsWJiYGBoP8BvFx848pnLtwku+jVEbR8KuUUhkhNhYqVpQAXL26LG9/7jlwd7f1yJS6TxffUile3JZQC2xaISKkJNe3eRFzvgCWvFGMHi2d+AoUkN6820K3M3H7RJYdWHZ722GQBWyl8pfS4KtsQsOvUkqlhwMHYM4cCA6G338HJyeYOBGqVpWl7dqPV+UQxfPk4cimwlzfXp648Dw4FrpJobb7qNToMu++25youCjm7VnKpB2TCDoTRD7nfAzwG0CDMg14aeVLuoBN2ZyGX6WUSqvwcFiyRELv9u1S5Nixo/TpzZNHZnqVyiGuXpWuDf+Mb8K1KxacS16laLN/cK14jty5LLzUvBD/W/c/Zu6ayaWIS1QpUoXJ7SfTu2Zv8uWSVn0eBTx0AZuyOQ2/SimVGlarLF93cZEtqgYMgBo1YOxYeP55KFbM1iNUKl2Fhkp/3hkzpDlJ27YWGnW7yNILSwiNDCKvS37civ3La+vWANDZuzOv13ud5p7NMe654qEL2FRWoOFXKaVS4tgx6ds0d66s5HnnHejeXcoaatfWsgaV4xw6JKXqCxfKZ75nn4V335UqnnXH9jFy0TvEOsUSHg+XL+fn3Ybv8prfa3i4edh66Eo9lIZfpZR6mMWLZcorIEACbuvWsoANZD/WOnVsOjyl0tuWLTB6NKxaJTtr9+8vn/U8PeHolaO8/ftkpgZNvb2AzQEHhjQcwoimI2w7cKVSSMOvUkrd6/hxKFdOvp4zB06fhk8/lZ68ZcrYdmzK7iS3oUR6sFrht98k9G7aBIUKwQcfwOuvQ+EiVtYcXcPARRNZfXQ1jg6ONPdszsaTG4mzxuFscaZV+VbpOh6lMpKGX6WUArh+Hb77DmbNgt274dQpKFVKZn4LFtRNKJRNPGxDifQIwLGx8iP+5ZfSsKRMGRg/Hl55BeIs12Tb4SWTOXLlCCXyluCjph/Rr04/SuYrSeDpQF28prIlDb9KKft24gR8/DEsWyZdGmrUkN/++WR1OoW1D6mynXs3lACIjI1nzJqQRwq/N2/K57yxY+XCRvXq8MHMQJwqBlC0kAf+AZuYv3c+t2Jv0aB0Az5u9vFd2w6DLl5T2ZeGX6WU/bl4ES5fhsqVpR/vihXQq5dMd/n56eI1lWUkbCiR0uPJuXgRJkyAyZOlddnjj8O0aZCv2iZaLWhJTFgMAE4OTjxf83ler/s6ddy1rl09QGQknDlz/y0sLPFrNzdpBZmFaPhVStkHq1UWrU2fDj/9BM2awdq1Utpw/jw4Oyf3CkplOnc3V8KSCLrubq6pep1jx+Drr+HbbyEqCrp0gaFDoVKtK8zeNZvPF39OTLwEXwODdxu9y6ctPk2X70FlU9euyWWBO2+hoXcH26tX73+ei4vsZFmqlHTCqVgx88eeDA2/Sqmcb/58WbB25IjU7w4aJLO8CTT4qizKv433XTW/AK5OFvzbeKfo+bt3Sz3vsmVgsUDv3uDvDzEF9zFx20QWjV1EZFwkPiV8OHjxIPHWeJwtznSo2CGjviWVFURFybqGkyfvD7gJIffGjbuf4+AAJUtC6dJQqZJMILi7JwbdhK/d3LL81TMNv0qpnMc04a+/oH596dV04QIULy7L1596SmYmlMoGEup6U9PtwTRhwwbp3LB2rZSv/9//wetvxrHjxgr6b53IxpMbcXV0pVfNXrxe73VqFq+pC9hykogICbYnTsgt4euE+3Pn7n9OiRKy4rFKFXjiCfn6zlvJkrKLZQ5gmKaZaW/m5+dnBgUFZdr7KaXszOXLMG+e9OUNCZEZ3969peRBuzWoHC4+HpYvl5neoCD5vDd4MDzT9xLLjs5katBUTl8/jaebJ4PqDuIl35co5FrI1sNWaREXJzO0x47Bv//K/bFjiWH34sW7z3dyAg8PuXl6yi3hz2XKyMxtDrwCZhjGTtM0/e49njMivFLKvkVEQL9+8MMPEB0NDRrITmxPPSWPa/BVOVhUlHzOGzMGjh6FChVkEZvhO5fpeyby4axgYq2xtCzXkontJtKxUkcsDhZbD1sl59q1xFB7Z8A9dkxmcOPiEs9NCLfly4Ov7/0ht2RJ/e/gHTT8KqWyp+vXYdcuqTtzdZVZkFdeke2oatSw9eiUynDh4RJyx4+XNZt16sB3S2Oh8nK+2PwZwaulH7Cj4ciibot4rsZzNh6xus+NG/KJ5cgROHxY7hNuly7dfW7hwhJu/fxkr+ny5eXm5SUztxb9QJNSGn6VUtnL3r0wdSosXCh/PncO8uZN3H5YqRzuzBkJvNOmSXZq3Rr6vX2Bg64zGLJzKmcOnaGgS0EMDMz//ncy/KSth22/oqIk4IaE3B1ujxy5v/bW3V26I3TpIvdeXokht0AB24w/B9Lwq5TKHrZtk1U7W7bIgrXnnoMBAyT4ggZfleP984+UNixYIPW9zzwDHfvt5I9rE3kuaDEx8TG09mrNjI4zcHNx44kFTxATH4OzxZlmns1sPfyczTSlzvaff+QWEpL49fHj8niC4sUl2LZrJ/cJtwoVIE8e230PdkTDr1Iq6zpxQn7Le3lJacPFi7IlVZ8+UEgX6ij7sHWrLGJbsQJy5YKXXo2lSrcfWXZyIr02biGPUx5erf0qr9d7ncpFKt9+3roX1mn3hvQWHy81twcPJobbhLB7Z89bV1fw9oZ69WTRbeXK0h6sQgXIn99241dACro9GIbxLdARuGCaZvX/jo0BngRigH+BF03TDE/uzbTbg1IqWfHxsGYNTJkCv/0mM7wJJQ6mqTO8yi6YJqxeLe3KNm6EfFUCqfHUL5SvfoH1ob9x5sYZvAp68Ua9N+jr05cCLnpJPF3Fxckis4MH4cABuU8IvNHRieeVLCnB9s6bt7d0UNAFZjb3oG4PKQm/jwM3gfl3hN/WwHrTNOMMwxgNYJrm0OQGoeFXKfVQ06fLb/vjx+XSYL9+8Oqr8otEqRxixe6wB/btjY2FpUtlpjc4WPYTaPT6HH6IfpV4Uza6qF+qPiMeH0G7iu1wMJIOWA97D3WH+Hipx92//+6gGxICMTGJ53l4QLVqULWq3FepIjedxc3S0tzqzDTNjYZheN5zbO0df9wKPPWoA1RK2angYPll4uAgMy2lS8OoUbLgIwf2nVT2bcXusLt2bAsLj2TY8mCiIg0uBLkzdqx0sapSLZYBk5ezx3kCS8O23H6+xbDQ2bszHSo9eAe2B70HYL8B2DSlJUZwsNz27ZP7gwdlQVqCcuUk4LZrJ/dVq0rITVhboHKE9Kj5fQlYmg6vo5SyF7Gx8NNPMHEibNok13fbtoUvvtB2PSpHG7Mm5K6tiuMjnDi7y5PeY4sQFwH1ml2kyf9msP7mFKZelNKGwfUHM2PnjBQvXrv3PQAiY+MZsybEPsLvrVsyg3tv0L2zdViJEtISceBAua9eXUKuLjizC48Ufg3DGA7EAYseck4/oB9A2bJlH+XtlFLZXUQEfP219Gg6c0ZmWb76SrYhBg2+Ksc7Ex4JQNw1V67vKMfNfWUwYx3JVfcPWr/yHesuLGb72ejbXRsSShuerfZsihevJbxHSo9nW6YprcL27JHb3r1yf/hwYneF3Lkl2HbuLCG3Zk35c9Gith27sqk0h1/DMPogC+Famg8pHDZNcwYwA6TmN63vp5TKxs6flxpeZ2eYOVN++UyfLpcWNfAqO1IgsghH/yzNrRsnoNwinDpdg0priM4VzF+X8vCy78u8Xu91qhStctfzGpRpkOKODe5uroQlEXTd3VzT41uwjbg4CbUJATfhduFC4jnlyoGPD/TsCbVqSdgtV04Xnqn7pCn8GobRFhgKNDVNMyJ9h6SUyhGio2HZMiltOH1aChmdnWVhiS4SUXbENKVjw+jRsHd1faj8C7zYFYw4Yg2wmIV4sdqHjO34Fm4ubo/8fv5tvO+q+QVwdbLg38b7kV87U0RHy38ndu6UXRx37ZKyhYTaXGdn+QDdsaOE3Vq1ZEbX7dH/v1P2IdnwaxjGYqAZUMQwjFDgQ2AYkAv4w5C2Q1tN03wtA8eplMouLlyQHdimTpUZ38qV4f33wWqVxzX4KjthtcLKlRJ6t22DgpX3UefjCexmHlYz7r+zDJ6t8grfPvVRur1vQl1vtuj2EBUlNbkJQXfnTgm+sbHyuJsb+PpKba6Pj9wqVwYnJ9uOW2VrybY6S0/a6kypHCwuDhwd4c8/4YknoH17GDxYvtbevMqOREdLa+oxYyDkcDzFH19F/tYTOBIbQG6n3LQu35rf//2d2PhYnC3OrHthnX1sQhEVJaUKQUGJQffAAWk3BrJxTZ06cqtdW+7LldP/fqg0S3OrM6WUeqD4eJna+uYb+UU1diy0bCl71leoYOvRKZWprl+XUvbx4+HMlau4d5xNkd6TOB93EpfcHoypN4aXfV+moGtBAk8H5uzd1+LipI3Yjh2wfbvcBwfLcZAFZ3XqwJNPJgbdsmU16KpMoeFXKZV6V6/C7NkwaZLU8np6yiITkF9eGnyVnVixO4zPfjjOkfUluLnHg/h8RyjVbSK5Ss3njDWCpqWaMrj+OJ70fhJHh8RfualZwJblmab06N6xIzHs7t4t3V1AShf8/ODdd6FuXfm6VCkNuspmNPwqpVLP31/Cb9OmMG4cdOqkXRuU3Zmy8hzDP7YSftmE2iMxXgmGInu44JCL3jWf5836b1KrRC1bDzP9Xb4sRczbtsHWrRJ4r16Vx1xcZCb31Vcl6NarB15e2nFBZSla86uUejjThPXrpaTh009l8cnRo3Dzpiw+USqTZJUte3fskO2Hf/j5GjT/AOpPBMMEE/LGt6NK7lfZPqxrpo8rQ8TGSrnC1q2JtyNH5DEHB+m6UK+e3OrWld0adTGayiK05lcplTrR0bBkiYTeffugWDEpcfD11bIGlelsvWWvacLatdK5YcPeozg3mQj+s8HxFtyeQ3LA0SzKxWvZeFvuM2fuDrpBQRD5X8/gYsWgQQN46SV47DEpX9Btf1U2pOFXKXU/q1V6Z4aEyEzO7Nnw3HNySVMpG7DVlr1xcfD99zD6S5O91/8kV9MJGE1/xXRwpChNiY+sylXnaZhmHAaOuFhrZJ/NJOLiZFZ3yxbYvFlup07JY05OUr7Qr58E3cceAw8PrdNVOYKGX6WUOHwYFi+GDz6Qy5n+/lCmjLYqU1lCZm/ZGxEBc+bAmPERnCywAOfmE6DAQQrkLsZrfiN4ze81th21Mmx5MM4xZYhyCMbFWgM3S/Wsu5nE9esym7t5swTerVulfAnA3R0aNYK33pLZXR8f/bCrciwNv0rZM9OEgAApbfjlF8iVC555BqpUgZdftvXolLots7bsvXwZ3pscyMKgFUQ5hmF55jdwvkq1Er4Mrj+XHtV7kMsxFwBdfOU5Y9Y4cya8StbaTMI0pUwpYUZ3yxaZ5bVa5cNtzZrwwgsSeBs10jZjyq7ogjel7NWxY9C9uzSdL1pUdlAaMACKF7f1yJS6z701vyBb9n7RrcYDw2ZqFsidOgVfjzWZtmM6Ma1eByMeDGju0ZyRLUbSqEwjjKwcDq1WOHQI/v5b9lL++28IDZXH8uWTsoWGDSXo1q+vOy0qu6AL3pRSctnz8GFZqFK6NBQpArNmwfPP6yVOlaWldsvelC6Q278fvvgymiX7l2GtNx5a77r9mMWw8ITXEzQu2zijvq20i4uTXroJYXfTJpm2BihZEpo0kVvjxlCjhrYiVOoOGn6VsgehobIL24wZMuNz/Dg4O8Mff9h6ZEqlWBffUikuKXjYArnOPqXYtAlGfn2eP8OnQd2p4HWeCgWq0K3au0zcPpGY+BicLc4082yWAd9JGkRFSV/dhLAbGJhYr+vlJTulPf64BF4vLy1hUOohNPwqlZOFhMBnn8lCNtOEp5+GIUPAUf/pq5wtqYVwpglHd+SnVttdBOf+BmouAUsMrTza499kME+UfwLDMOhSuYvttx5OCLsbNkhd/tat0n4QZCa3T5/E2V13d9uMUalsSn8DKpXTmCbExMjitWPHYPlyGDRIVnF7etp6dEplioQFctEOh4hkP9ajTYk46UR8tdFcqPk3zuThRd9XebvhG3gXSezOIHXCkZwJr8kvbpH4twnLnAVsCWE3IEBugYESdg1DWo69/rrM7DZuDIUKZfx4lMrBdMGbUjlFbCwsXQpffQVt28KoURKEw8OhYEFbj06pTLVidxhvLP2BUOeh4BAjBw2T/JTl/VaDebXOS7i5uN33nNQuqkuz6Oi7Z3bvDLu+vtCsmdyaNAE3t2ReTCmVFF3wplROdfMmzJwJ48bB6dPSpqxWLXnMMDT4Krtz/jz8/sNNzlxdDCWjwQBMeLxUV9a/9D0Wh6QXf2XoRhrx8bBzJ6xbJ7fNm2W2NyHsDhqkYVepTKLhV6ns7o03YO5caNoUpk6Fdu2kj6dSduboUZO3Jv7B6qvjsXqtxijhiIODBQNwdnRmVBv/BwZfSOeNNExTWo8lhN2AALh2TR6rUQNeew1atJAyBv2AqlSm0vCrVHZz7Bh8/bX05a1WDYYOhf79pY+nUnZo8/YIBs9ewE7HCVDsIK4FivNKjY8Z3ro/x64eS/HitUfeSOPUqcSwu349nD0rx8uVk8WmLVtC8+baS1spG9Pwq1R2sXs3fPklLFsmPTv9/CT8Vq5s65EplelME5b8Fsr/fprMicIzwP0Kxa21Gd5sPv0aPXN7F7bieYunuGODfxvvJGt+H7hdcXi41Oz+8Yfcjh6V48WKyaxuy5ZyK1fukb5XpVT60vCrVFZnmtCtG6xYITs1vfOOdG7Q9kbKDm06GcjHK+az7cgRbhQOgFIm1R27Mqb7W7Sp8mi7sCW7kUZsLGzfLkF37VpZsGa1Qt68Uq87aJCE3erVtc+uUlmYdntQKiuKj5dfsG3ayC/RTz6RTSleew0KFLD16JTKdNdvxvL8tC/45ebHYFjBhHq5n2N+n8/wLu6ZMW9qmjKbmxB2N2yQXRIdHKBuXXjiCWjdWrYLdnbOmDEopdJMuz0olR1ER8OCBTB6tPzS3bhRVn+PGGHrkSllE/+euczA2TP58/okrHnDbh+3OFjo0qB6+gff8HCp2V2zRkLviRNy3NMTevSQsNuihS5SUyob0/CrVFYQGSmdGr7+Gs6cgTp14IcfoGFDW49MKZsI2H+IwYu/YZ8xH5wiKRzXiqfLv8W8Ux+k79bDVivs2QOrV8Pvv0u/3fh42Qa8RQt4912Z4dUtg5XKMTT8KmVLVmtiW7LRo6FqVZgzR37Z6i9aZWesppVZG9Yycu14wlzXgEMuvG71ZnTXwXRvUh2AF043evSthy9dklnd1atlhvfCBTlepw68955sEvPYY7oNuFI5lP7LVsoWwsJg7Fj4809pfO/qCvv2aQskZXcCTwey9thaDh+/xaqQn7np8g/EleSxW58y6aV+1Klc9K7zG5RpkPrQGx8PO3bIzO7q1fK1aULhwlJX37atlDPovz+l7IKGX6Uy09Gj0q5s3jz5hdyjhyygKVRIf/Equ/PToZU8vewp4s04MMAhohJdnBcwacgzlCrxiAvILl+WsPvrrzK7e+WKXGWpVw8++kgCb5060jZQKWVXNPwqlVm2b4cGDcDJCV5+Gfz9tf+nsktbTm7n/74fx7YbS8EwwQADB0Z06sNHLXul7UVNU66e/Pqr3LZulbKiokWhY0do3x5atZLZXqWUXdPwq1RG2rpVVov36CGbUnz+OfTpAyVK2HpkSmWqOGsci3f/xAerx3MifgtE5Sf/hWeJ9FiBlVicLc60qdQ8dS9665Z0Zvj1V/jtNwgNleN16sD770OHDvLvTrf7VkrdQfv8KpXeTBMCAuDTT2WL0woVICREfwEruxQeFc74jbMYv2Ui14xTcKU8XpcGM6rHi3TvmI+toYGpW8B2/Dj88osE3oAAaQ+YN6/U7HboAO3aQcmSGf59KaWyPu3zq1Rm2L4d3n4btmyR2d2vvoL+/TX4KptasTvswbuWZZCjV44ycu03LP5nDnHGLTjZlPrWCXz9WkcaNUiss012AZvVKgvUVq2S2/79crxSJRg4UAJvkya6yYRSKsU0/Cr1qKxWufyaL598HRYGkyfDSy+Bi4utR6fs3IrdYQxbHkxkbDwAYeGRDFseDJDuAXjLqS3M2TOHoJOH2HN5C1gdMQ70pHPRtxg11JfKle8fW5KhPCJCOqGsWiWzvOfPy8K0Jk2kS0rHjlCxYrqOXSllPzT8KpVWcXGweDF88QU0bgwzZkhv0KNHtT+oyjLGrAm5HXwTRMbGM2ZNSLqF3+i4aEb+9QlfbPocExNMcNz/Iq96fc77E0vg7n7/c+4N5TGhYex6fyWP3ThIiR2bICpKNppo1w46dZJ73VVNKZUO9De0UqkVHS2tykaPhmPHoEYNqTdMoMFXZSFnwiNTdTw1Lt66yOTtUxm/ZQrX4s6DiXRuMCwM61+RkU88eGHnmN//ocyZf2l9ZCutjm7D5+wRGVfBEtCvnwReLWdQSmUA/S2tVGq9/77U8tarB+PGySVYrelVWZS7mythSQRddzfXNL/m/gv7+XrzeBbuW0gc0XCkHUXC23Ct7jCshmw93K5ys/ufaLXK9sErVrBw9iLKXT0LwO6S3nz5+Ausq1CPw0U8OD66Y5rHppRSydHwq1RyIiJg+nQpbahbF15/XbYf1i2IVTbg38b7rvICAFcnC/5tvFP1OlbTypqjaxizaRwbTv0Bsa6wty/Vbg7mo0FV6NoVtp+pd3/nhuho6Xry009Sw3v+PDg5cd7Th5n1uvFHhfpczFvo9vuUeoRQrpRSKaHhV6kHuXEDpk6VWd6LF+F//5Pw6+EhN6WygYS63rR0e0jYevhWzC1+OvgzR8P/wbhZErZ9RrN8/RnxTmGaN0/8DHi7c8P167BkCaxYIf13b9yQdmTt20OXLtC+PeeO3eSndAjlSimVWhp+lUrKhAnw8ceyJWrr1jBihMz8KpUNdfEtlerFbatCVtF9WXfirHFy4FIljL8X8FSVZxj2jTO+vvc84eJFCbvLl8vGE7GxUKyYbPDSpQu0bAm5ct0xpgJA2kK5Uko9Cg2/SiW4ehUKFJD63fBwaNhQ6nvr17f1yJTKNLvO7mLc1nF8t+87rKYVDMDqQH2XPny3vBfly99x8pkzEnZ//BE2bpSa3vLl4c03oWtX6X5isTzordIUypVS6lFp+FXq0iVZuDZxIsyZA927y0yv1vMqO2E1rfxy+BfGBo7lr5N/YYnLi/Wf7lD5ZwxLLLmcnRn3SnPKl0G26/7xR7kFBsoLVKkiZUFPPQU1a+q/HaVUlqbhV9mvixelnnfyZFnU9vTT8ksc9Je3sgs3Y24yd89cvtn6DUevHsUpogxsGkPxc68w5HU3anYIZPv5AJpZytNgYQD8+Abs3ClP9vGBTz6RD4sJ/26UUiob0PCr7JNpQqtWEBwsNYnvvw9Vq9p6VEqlyKNulLGOzQAAIABJREFUVxx6PZSJ2yYyY+cMwqPDcb5QH/76lAp0Z6i/Iz17gvPRg7B4LS1/+CFxS+H69eHLL6FbN/DyStcxKaVUZtHwq+zH+fMyyztsGLi6yqK2YsV01kplK2ndrjjwdCALgxdy5PIRNpzYQLzVitOR7vDX29T1aMDQL6CD1z84/LAMai+DAwfkCkjjxjB+vATeMmXSdUxKKWULGn5VznfuHIwZI23LoqNlIVvbttC0qa1HplSqpXa74nhrPGM2j2H4huGygM0Ey6EemGu/oO3jnnz4ZQi1//0Uhi+TKyEJgXfiRClpKFky3ceklFK2pOFX5VwxMfDeexJ6Y2KgVy8YPhwqVbL1yJRKs5RuV3wz5iZzds9h/LbxHLt67PbWw1gtNCrozvcvLKJYwDJ4bp88oXFjuRrSvTu4u2fImJRSKivQ8KtynshIKWtwcpLFOc8+K6G3YkVbj0ypR5bcdsWnr51m0vZJTN85nWvR13C70RC2vYzR9BMMSzS5TCujfh1LsVDkKsj48RJ4S5fOsDEppVRWouFX5RznzsHo0TB/Phw8CMWLS7N9R/0xVznHg7Yr7lo/iud+fI5lB5ZhmuB2tjuFf+3FgKtHea3gEk6diCLAE5rlrU6D/3tJ2pI9oIY3vcaku7UppbIiTQUq+zt/XlagJ5Q3vPCCNNsHDb4qW0hNp4SE4x+sXs7piB3kd8mFQ4Fg/Dduw9XIT9ED/Wm+phRvRv9B/ejOGKYJlXwp1fNLGjzzTIZszf0oWygrpVRm02SgsrfLl6FCBenT27u3tCyrUMHWo1IqxdLSKSFfgX/4J/4dYp1iCY+HfFeK0zjgOQYHXqBz9AyciMP09sbo+aG08vNO/QxsaluX6W5tSqnsQsOvyn4uXYI1a+D556FwYZn1bdVKa3pVtpSaTgkJ/XknbJ9ArDUWAMMK/7fhEh/9/R2RxT1w7PMO9OyBUatWmjdr0dZlSqmcLNnwaxjGt0BH4IJpmtX/O1YIWAp4AieAZ0zTvJpxw1QKmeX96itpwRQVBc2aQalSMGCArUemVJqlpFPCrrO7GBs4lqUHlmK1WvE9W4z9Rc8RZ4CzFep6dYXR/4frY4+ly+6E2rpMKZWTpWTmdy4wCZh/x7H3gHWmaY4yDOO9//48NP2HpxRw7Zr06f3mG7h1S7o3fPCBBF+lsrkHdUooWSAXq0JWMTZwLH+d/Iu88c7025kL/y23KBgewZKGHTj+THE6d3mRBh6N03VM2rpMKZWTJRt+TdPcaBiG5z2HOwPN/vt6HhCAhl+VUaKipB1Thw4SeqtVs/WIlEo393ZKsBJFjPMGThmr6LzkNGVuOvL1Zui9y8r2+FZsebIXLb7uQP9yGddGTFuXKaVysrTW/BY3TfMsgGmaZw3DKPagEw3D6Af0Ayhbtmwa307ZlevXpdn+1q3w88/SsuzECShSxNYjUyrdJZQRDPttDqER3xHr8C/RlhjqHoOvt0CRQw1Yk68XS//3FC+8VYj8+TN+TNq6TCmVk2X4gjfTNGcAMwD8/PzMjH4/lY3dvAmTJkmJw5Ur0KmTHMuXT4OvyrH2ntrOjHX9+Sd2DziBxYSPfitJxPY3mOH1HM/P9OCT5yFXrswbk7YuU0rlZGkNv+cNwyj536xvSeD/2bvzOJvrL47jr++MGTsjS7KFlAglIyZLY18qeyFJGy1aMbSX7AahhFL2NVlClmxlmWQt+76OPTtjtvv9/XHCj1SY5c7yfva4DzPfe2fuuT3u3Hvu53s+5xyNz6AkFVqzBmrXhmPHoG5d6NwZAgO9HZVIgnA9HubM6Ee/Ff2ZnzYcvxhwfMF1INbjy7dFXmPge+/S43Hw8fFOjGpdJiIp1a2+rP4AtPrr61bA9PgJR1KVyEjYvNm+LlYMqlWD5cth1iwlvpIiXdy+mWGd61GifTrqrgthU9RB2v5emtKTe+DGpAfXl7R+/ozvUYX69b2X+IqIpGSO6/57JYLjOOOxzW05gCPAx8A0YBJQANgHPOG67on/urPAwEB31apVcQxZkr2oKBg+HLp2tQls27aBn5+3oxJJGKdOcWzCtwxePoBBt+/jaCYodSYTZfY+xfc/9OCCexvNm0PN58PY77uY4ILBBOUP8nbUIiLJnuM4q13X/dtq2o10e2j+D1dVi3NUkrrExMCoUdCli21gCwqyrzWCWJKwm510BhC2ewmLFwyj4IqtLD62klElPFy8C6pcLErpPz5h7pSm7Mjg0PpVaNcObC9w0F8XERFJSMo6JPHMng0vvGAlDYMHQ61a8dKQXySh3PSks40bWT6yK1XTTiDSF8gHfnl9qOXXgAOLu7FofnFy5LCS9rZtbUChiIgkLiW/knBcF6ZNs8lsL75ofXrnzbNRxEp6JRm4oUlnJ0/C+PFEj/yWSRGr6VgDIi+/sjpk3fwOMyd1o2BBG074/POQIUNiPgoREfl/Sn4l/rmurfJ++KF1cXjoIVvx9fGBGjW8HZ3IDfuniWaHT5yDOXNgxAhOz57KVyWiGBjsx4EMkD9jPnzPHyHW44FYfwKOPcaAsfDkk6rwERFJCvRSLPFr9Wp44w3r2lCoEIwcCU89pZVeSZaunXRW6EQ4TdbP54lNi9jz9XEGPJKWYW+7nHOgQp6KPLyvPXO71SE20woKVV3M648F81aXID39RUSSECW/Ej+io61jQ2ws7NsHQ4fCc8+pi4MkKTe7eS2kVlG6jF9B9fWLeWL9fALDN7M8r0Prp3IyK7cPjk8sdQs0xW9VO2b1fJDlkdCoEXTsGMRDD2nzmohIUvSfrc7ik1qdpUCrV1t5Q548MGyYHbuUCIskIdduXgMb2dujUcm/J8CuC2FhMGwYMRMm8muOC4RWyMDq/OkIz3iCLGmz0CDfS5yY/QY/TshHmjTQqhV06AD33JPID0xERK7rlludiVzXpk2W9E6ZArfdBu+9d+U6Jb6SBN3Q5rWjR60d3zffwJYtXAjIyMev3EXfLBtwuYBDBA3veJOTU7owam5msmSBkBB480244w4vPCgREblpSn7l5n37rXVvyJQJPv4Y3n4bsmb1dlQi/+pfN6/Nnm1nLn74AWJiOBIcyKA2j/Nl1DL+vLj+8m1djw9TR99O7h2Z6dULXnrp70/9W+kLLCIiiUfJr9yYAwfgwgU7p1u9ui13deyoRqWSbFy7eS3fqcM8+cdPNN20EEKPQc6cbH77afqVOMfofTOIOrOaR4vUI9ORWkw82R7XicJx/enULJhPXoS0af9+HzfdF1hERBKdan7l3x07Bj16wJdfQtWq8OOP3o5I5JZMWxvOR5NWU3nTMpr9PpeKe3/Hg8ORCo+wtXUwfXxXMGvnbNKlSUfzYs8SsPltxg68h6NHoVjNMB5suJiX6wRT8c5/3shWoefCqxLsS/IGpGfZO1UT8uGJiMg1VPMrN+fUKejbFz77DCIi4JlnrMRBJDnato0G476mzrBvWZPpBNOLZmR6mTr4NnyYny5MZc2eT8iZISftH+zMhV9eYXSrnJw7B7VrQ6dO8MgjQTjOf3dv+KfSin86LiIiiU/Jr1zf4MHQtat15u/cGe6919sRidycyEiYOhW++goWLQJfX9Y0r0i1u8O46F4A5uDunE3R7EXpXOYrtk95moHvp8fjgaZNrarn/vtv7i6vLa34/+MiIpI0+Hg7AEkiIiNt9uqsWfb9a6/ZdLaJE5X4SvKydav1HMubF5o3hz17oHt39m/+lU5VPUS4Ubh//Vf7jme456dNfPx4a76fkJ6XXoIdO2Ds2JtPfMH6Aqf3873qWHo/X0JqFY2fxyYiInGmld/ULiYGRo+GTz6x4RStW8Ojj0LmzFC6tLejE7kxkZHWdm/oUPj5Z5sjXL8+tGnDuhI56LviMyZM+AiPx4Ov44vHBSfWnzldXua2Cz589JF93suZM25hXNrUpm4PIpKsuC5ERVmf/kyZ7Ni6dXDyJJw7B+fP279580KdOnZ9t25WIhkVZZfISAgKsjwC4PHH7ecmTYIcObzzuP6Bkt/UbM4ca1O2ZQuULWu9TatV83ZUIjdu+3YYMsTGaP/5JxQuDD164LZqxdzzv9M3LJT5YfPJ6JeRV8u8RoFDbzJo5CF2u4vJGRHMex2CeOGFK6/18aFB6bxKdkUk8V28CGfPXvkUv2QJ7N5tCeylS86c8MEHdn39+jao6lJiGxNj3Zx++smub9wYdu26+j7q1buS/A4aZMmvv7+1v/H3v7r34+nTllTHxCTs474FSn5TG9cFjwd8fa2hv4+PrZg1aACO4+3oRP5bdLT14x0yBObPt1XeBg3gpZeIrFyB8Zsm0ndaTTYc3UCezHnoXKknaX5vw5CXs7F/P5QoUZBRHYNo1kzzWEQkCYuJgePH7b362DH79/x567MP0KWL9Sg/etQuZ8/aAsDOnXZ9586wYMGV35clCzz00JXk9777rF1ppkx2yZgRihS5cvvhwy1n+Ou6OXvO0nfFEXa8M8vOas1a+e8f9H/5JX7/f8QjtTpLTZYutUls9etD+/YQ+9e0K1/ff/85kaTgwAH4+mu7HDoEBQpAmzaEPVqK2SdXcuzCMaZvmc6hc4comaskbUp04NBPzRj8hT8nT0KlSta5oW5dfc4TkSRg/37YuBHCw+HgQfv38GHbqOs4luR+883VP5MunfXcdxz46CMbw54rl11y5rSyhFat7LY7d1rymi2brcimufX1zpsaD5+EqNVZarZ2Lbz/vn1CzJ37yikRJb2S1Hk8dgpuyBCYMcO+r13banvr1mXKtuk0ndyIGI+dViubpyw9y49gxfgadGzvEBFhn/U6dbJSNBGRRLNtm6287t1rl/37LckNC4Pbb7fEtnPnK7fPkcOS17NnbZW2RQt48MErye2lBPeSTz/99/u/6654eyg3NB4+GVHym9J9+qn1582WDXr1sl09GTJ4OyqRf3f8uJ1yGzrUVi9y5rSpgm3aQKFCrDq4ij5TWzBp4yRc7OyVD75E/t6Q51+piY8PtGxpTR+KFfPyYxGRlMV1beV1zx6YPv1KcnvpMneuJa1LlsCrr1p9Vf78dgkKunLW9ZlnoEYNS3jvuOPvYyOrVLFLEpDSepgr+U2J9u+H9OntU2RwsNX3tG8PAQHejkzkn7ku/PqrTRP87jvbOVypktW1NWqEx9+P2dtn02fk8yzes5gsabPQvERzJm+aQlRsNJ4Yf3b8FMzbb8Nbb9n7iYjILTt50qaa7txpPRAv/fv117bxa9s2e7FJnx7uvNMugYFWOwvQpImdqcqd+/pnWgsXtksykNJ6mCv5TUn+fxTxSy/BgAFQubJdRJKqiAgYP952Dq9ZY6f7WreGl1+G++4jMiaSsevH0jesL5uObSJflnz0rt6H2w+05oteWYg6FEamEot5umIwPVYE6TOeiNyY6Gh7zdmyxRLZSwnuq6/C889b/e3TT9tt8+WzzWD16lkyC/bh/OhRW2i63kaCrFmv7n6QjIXUKnrdmt/k2sNcyW9KcPYs9OsHffpYIXyrVtCunbejEvl3u3bZJMFvv4UTJ6BECfv+6achUyZORpxkyJIeDPxtIIfPHeb+2+/n28dGc3F1Uz57zo/t2+29aMgHQbRqFUS6dN5+QCKS5Hg81sN+yxa7bN1qq7MvvGCtwcqXt9v5+kKhQlYneylhLVLENqQVKmSru9dKn/76x1OglNbDXMlvStCuHQwbZj35unRRkaMkXR4PzJsHX3xhpxN9fKBRI2jbFipXJuzAr0wN+5S9p/Yya/sszkefp9ZdtRhSczSbZ1XjvcccDh+GMmWsb3qjRtq3KSJYW7Dt22HDBntRaNTIjufLZ91hLsmW7UoJYObM9jp0112W4F7b+9DPD4oXT5z4k4GU1MNcrc6So5gYa+pfvrz16du92zYIlS3r7chEru/kSRgxwkpyduywnc5t2lh5zl/FucPXDqf1jNbEunZarU6ROrQr1ZN5o0sxZIid4KhZ0zo3VKmidmUiqZLHY6UGl0oP3nnHOhlt2WJTxsB62a5YYV8PGGA1uEWLwr33/nOJgqRIanWWEng88P338OGHduomJAR697ZPrIUKeTs6katMWxvOlBE/Uufn72m4aTHpoiOhQgXrQNK4Mfj747ouc7bPJnR5KIv2LLr8sz74cmxVJR59vhQxMfDkk9CxoyZui6Q6q1bZyPING6wEYeNGK0s4eNCuP3/euijUrm2lUyVKWJJ7yZtveiduSdKU/CYXCxbYu/+aNXYaZupUa2AqktTExrKi/3DyDBzIqH3riUiTlmnFH2HSQ4/zzKsNaVA6L1GxUYxbN4I+y/uw8dhG8mbOS9uybRm2+lsiY6PwxPjzxw/BvPiiNSr5pw3R09aGp5gaNJFUy+OxM0Lr1sHvv8Mff9hCj78/jBljq7e5c1ti27q1/evxWNnU5597O3pJhpT8Jhfz59umoJEjrfG1Ch0lqTlxwpq2DxpEub17OZAlJ92Dn2NiqZqcTp8ZgPA5q9l6fgwDfxvIwbMHKZmrJCMbjCLgQFP69fYncmcL0hVbTLNywfQKCyJXrn++u2snDoWfiuDdKesBlACLJFXnz8P69baIkyULjB4Nr7xix8GmkBUrBkeO2IruO+9Yu84cObwb9//Rh+7kTzW/SdWmTTaVrU0bqFPHXhjSpPl7E2wRb9u40VZfRo2ytmWPPMLL2Srw093luJBmGxd91pPGk59In42cSzMX14mgeuHqtCsXwp+/1SA01OGPP2xfSrt2trCTKdN/322Fnguv23cyb0B6lr1TNQEeqIjctCNHbHfqqlWwejVs3myrtj/+aO9tK1fa6u4DD9ilePEk/T6XXMf8plaq+U0u9u6FTz6xRCJTJuspCFeaZoskBbGx9uY1YICV5KRLZ2ckXn8d7r+f9T0XcuHMGg77vwdE//VDDjl8qzK9RSirZ5XmlZr2dC9e3PbCNW9uZzlvVEqbOCSSrEVEWMnCpSS3YUN7/zp6FN54wza5liljXRhKl7ZNaWAbtZPRZu2UNuY3tVLym5R062abgRwH3n7bTvckoVM9Ipw+bX15v/jC+vTmzQvdu9ty7V/PVdd1qVH6CN2X9wPnr8TXhYCoJ6h+4mvqPZSFP/+0vW+ffw6PPmqlezcrpU0cEkk2oqPttSBHDustX768na28NLY3V64rCW3x4jZ1NG/eFNFlQR+6UwYlv9529qytmvn52QtGy5bw8cdW6ySSVOzYAQMHwvDhcO6cZa49e0KDBpd7Y0bHRjNp4yT6hPVh3eF1ZE6bjZhoX1zXBY8/5ye+wYRdWXj8cWtXVqHC1Xdxs3V0KW3ikEiStW+fjR5fscIua9ZA3boweTJkyGDlCvXr28puYODVia6vr9U0pRCJ8aFbNcUJTzW/3nLxIgwZYqu9XbrYKFeRpMR1rcXQZ5/BjBlWc96smbUOKlPm8s3ORp5l2Jph9F/Rn32n91EsRzE6PNyB+50WvD9oDfO2LcZnbzBPBwcREmKtqa91q3V0epMQiWdnzlgdbng4PPOMHStb1soZ0qaFBx+EcuWgWjV47DHvxuoFCV3zq5ri+PVPNb9KfhNbbKztbv34Y/s0Xb26raD9XzIh4lVRUTBhAvTvD2vXQvbs9uGsbVu4447LNzt87jADVwxk8KrBnLp4ikoFKhHycEcyHapLaG8fZs+2UvU2bayK599OZmjzmogXzZ8P330Hy5ZZ+YLr2h/v6dO2cvvLL7bCW6rUzRXmp1AJ+aFbr4XxSxvekooWLWDiRDs19M03lvyKxNHNvhhf9/b509rZiEGD4PBhazc0dKiV4vw1vz5sfxjfbfqO7Se2M2/nPKJjo2lUrBHtg0I4vKoc3VrZWdGcOe2Exquvwm23/Xf8qqMTSQQXL9oK7vLldhk50gZGLF9uHRmCgmyiTLlytiHtUkvNypW9G3cSk5BjfvVamDiU/CaGxYvh/vttpvgrr8ATT9iO1xRQ/C/ed7P9bq+9ffodW4maFErspkX4RkZCrVpW21ur1uXnqOu6DF09lLY/tsXjegBoeG9Duj7Sm7BZRXiuhg0dLFTIcufnnrucL98QbV4TSQCua3/Dy5ZBhw7WhSH6r02od99tG9GyZrVpoR98cGs7TyVe6bUwceiZnpDWrrWRi1WqXJlC88gjNtpVia/Ek39rvfOPt4+KodLuNYyc9BHzv3mVeusXMrNUdRshOmeOPW8dB4/rYermqVT4tgKvzHrlcuLr6/gSsbMsNcoU4cUXLdEdPx62bbPV3ptJfME2r6X3u3pwizavidwE14WdO61v4PPPW3I7YYJdlzmz1ey//TZMn27tx7Zts0lpYH+wSnyTBL0WJg6t/CaEHTvgww/thSdbNggNtXpJkQRwU6fJoqIov3QmL/42lWLH9nAsYwB9K7ZgbOm6nMyQlfp/7Ua7GHORUb+Pom9YX7b9uY1CAYVoV74dX64cTGRMFLHR/sz5Opiq99oicY0acfs8d2mFWpvXRG6Qx2PdgrJmtemKJUvCwYN2XfbsULEil0cklioFS5Z4L1a5YXotTBxKfhNCSAjMm2cT2jp0gIAAb0ckKdgNnSY7dcrqdwcOpO/Bg2zNUYCQOm8yvXgwUWmsVVnegPScjDjJ4FWDGbhiIEfOH6HMHWWY2GQiJdM0on+/NMTOb4KbdzFVCgbTe2oQgX/bRnDrErKOTiTZi462FmNLltgGtKVLrTRp/HgrrG/QwBLgSpWsXl8rucmWXgsTnro9xIdTp6B3byt0vPtuG1uVNi3kzu3tyCQV+NfWONmirWvDN99Yf95q1Vje4FleOJydiBjP5dun8fuT4vcsYeH+8ZyPPk/tIrXp+HBHMh4LJjTU4fvvbZN3q1b2ee7uu73xSEVSkZgY2L37yh9b+fK2mxTsWOXKNiGmYUPvxSiSxKnbQ0KIiLBa3p494eRJa+x9991w553ejkxSkeudJuuWL4LgXu2tfZGPj/Xnbd8eHniAh4Eea8P5aPYU9lyYh4//Yc6ylr17HJqXaE77oA4c/r0UXV6ARYvsrOo779iEUn2eE0kgsbGwbp390S1adKVM4cQJq9dt397qeitX1h+iSBwp+b1VI0daWUN4ONSpYyNeH3jA21FJKtWgdF4a3H8HzJoFfTrbadEsWewN8403rpqw5Lou+6OnsDHmLTx+HnCh6X1N6V6lNyvmFeDZOvYenCePlau3aWO/atracEJHqA5NJF54PPD771aikC6d9Qbs3NmuK1oUnnrKNkt7/jpD88QT3otVJIVR8nszLrWNAWsZU6AAjB1rHRxEvCUyEsaMgT59YMsWe1726wcvvGBZ619iPDF8v+l7ei/vzZpDay4f93V8ubD7fqp3LMDu3XDvvVYl0aKFVe/AzbdTE5FruK5thl6wwIZKLFpkq7rz59u0tCeftKT3kUfsk6eIJBglvzdq4UI79xsaai9OvXtbZqCWZeItp0/bJrb+/eHQIShdGsaNgyZNwM/v8s0uRF9g+Nrh9A3ry+5Tu7kn+z10qtCJASsGWueGKH9mfB1MUH6bZPz443/fK/Nv7dSU/Ir8gyNHbKNavny2YFK2rB3Pnx/q14eqVa0HPEDx4nYRkQSn5Pe/rF4N774LP/1kL1jnz9vxdOm8G5ekXgcPWsI7ZIi1OqpRA0aNstWj//sw9ueFPxm0chCf//Y5xy8cp1zecvSt2ZfSGeoxoL8vzKqPe/tiHs4TTM9xQVSs+M+f5TR1SOQGnD0LP/98ZXV3wwYrOxowwMriBg+2v9MiRbRwkkAScvSwpBxKfv/Nq6/ai1X27HYa+ZVXlPSK92zebKUNo0fb5pgnn7S2eg8+eNXNdp/cTb+wfny77lsuRF/gsXseo+PDHcl2tiKhPR2eHGe3a948iJCQIEqW/O+71tQhkeuIiYEDB6BgQStrKF7cvk+XzvrsPv20dWQA27T28steDTelU3mW3Cglv9c6dMgag/v62vSbDz6w3k5Zs3o7Mkmtli+3Mpvp020SU5s20K4dFC581c1GrBvBZ79+xvoj60njk4YWpVrQIagDJ7fdR6/XYOZMyJDB5q20a2elwTcqpFbR67ZT09QhSXX27YO5c62X+/z59t6we7et5IaG2vvHww9rocQLVJ4lN0rJ7yWnTkGvXnZ6auhQaNnSVn5FvMHjsc4NvXrBsmXWxP6jj+C11yBnzss3c12XBbsX8N6C91h5cCUAaXzSMLHJd/hur0+bhpY758hhG8nbtrUTGTdLU4ck1Tp/3j41Og689x706GHH8+aFRo1s0MSlzdDNmnk31lRO5Vlyo+KU/DqO8zbwIuAC64HnXNe9GB+BJZr/79V76pS1l6lQwdtRSWoVE2NjsXv2hI0brWf0wIHw/POQMeOVm13TuSGTfyYcHFxcPB6Xlz/YxNEp9SlY0J7ezz9v799xoalDkiq4rrUgmzvXLkuXwqpVNiK4Th1b2a1Z01qUqW73piR0Pa7Ks+RG3XLy6zhOXuANoLjruhGO40wCmgEj4im2xPH447Y5oW5d69V7aeetSGKKiIDhw+206Z497Ly9EJ8/1p415WvSruJ9NPgr8b0QfYER60bQN6wvu07u4p7s9/D141+TJ10RGnxXl2hPFJ5YfzKfCOazsVYWnEbnd0RuzLp19l5w6JB9X6oUvPkmZM5s31eqZBe5aYlRj6vyLLlRcX1bTAOkdxwnGsgAHIx7SAnMdWHqVNshnzmzDar46CObmiOS2E6ftk2V/fvDkSP8WaoMHzzZijkFy+A6PnA2mnenrOdM1En2XpzKwN8GXu7c0KdGH8oF1OPLQb6EDILoTAsoVHUxrz8WzFtdgrQoJfJPXBf++ANmz7bLo49Cx47WhaFyZahd28oZ7rjD25GmGIlRj6vyLLlRt5z8uq4b7jhOH2AfEAHMc113XrxFlhAu9epdudJqe994wyboiCS2o0ftOThokCXAtWrBu+9Sb3kb/m0QAAAgAElEQVQM4acvEumzmYs+60njyccJ1vPcnJ/wcJFH736UjhU6kie6En37Ojw1wmZcNGwInToF8dBDQd5+ZCJJ2+uv2wJIeLh9/8ADVlMPkCmTlR1JvEuselyVZ8mNiEvZQzagPlAIOAV85zjO067rjrnmdm2ANgAFbmZ7eXxas8Z69c6bZ716hw+3DW0iiW3vXmtXNmyYZa2NG9sHsjJlADg4exaRPps57P8eEP3XD/mQMSaYsNf6Ex1ekl4dYfJkK2d45hlrRlJUZ/VErua6NvFw5kzrxvDll3b86FEICrLyhtq1tbqbSFSPK0lJXMoeqgO7Xdc9BuA4zhTgYeCq5Nd13a+ArwACAwPdONzfrevUCdauVa9e8Z7Nm20T27hxtkmmZUs7zfp/WavrumTMspUDkZ+B81fi60LmmIbkP/w+7Z4uyfz5NrG4Qwd46y29b4v8zZo1NvRlxgzYtcuOPfCAfdhMmxYmTvRufKmU6nElKYlL8rsPKO84Tgas7KEasCpeoopvX38N2bKpV68kvnXroFs3+P5769H72mvWZDd//ss3ifXEMn3rdHot68XG6N/wcTKC6wu44PoROeslNq0rzYnclj+//LKeyiKXHTlypW43Z0749VdrV1mtmg2BqVv35ppaS4JQPa4kJY7r3vpirOM4nYGmQAywFnjRdd3If7p9YGCgu2pV0syPRW7EDbfq+fVX6NrVevVmyWJ1hm+9ZQ13/xIZE8noP0YTujyUbX9uo3C2wnQI6kDmqBp0+nIlh49tw7O5Jnf4lKXzB2lo2VInLUQutyKbOdMuv/1mx0aPtolq586Bj0/ce/uJSLLnOM5q13UD/3Y8LsnvzVLyK8nZta16wE7b9WhU0hJg14Wff7akd8ECmybx9ts2WSIg4PLPnL54miGrhtB/RX8OnztM6dyl6VShE9XyNOarIWkYMMDKEsuWtYqdBg1s4KBIqhUVBSdOQO7cNmHtzjvt+EMPWbvKxx6zNpVqcSIi/+efkl91ABW5Qf/YqmfOFhoc/sOS3uXL7Q26Tx946SXbPQ6E7Q9jxrYZ7Du9jxnbZnAm8gzVC1dndMPR3Otfjf79HV4caotWtWtbOXBwsN7LJRU7edLKGaZPt3+rV4cpU6yEYfJkqFgRbr/d21GKSDKk5FfkBl3bksdxPdTc/iuvLZ8IR3ZaHe8XX9g4tfRXdjBP3DCRFlNaEOta4ly1UFV6V+9NhtNlCO0KY8bYNOOmTS3p1ZwVSfVeecU6osTEWILbtCk0aXLl+saNvRebiCR7Sn5FbtClVj0+nlge27KUtmETKXp8HwduywPffGP1hv7+l2+/MnwlvZb14vvN318+5uv4crdvdT59pQw//GA58ksv2R64QoW88ahEvMh1rTvDtGkwfz4sWmSF7aVKWUuT+vWttMHHx9uRikgKouRX5AZ1rHYXYV0/p/XSCdx1Ipxt2QvQoUFHKr33KvnKWg2i67r8tOsnei7tyaI9iwhIF8AzpZ5h0qZJRMVE48b4M/SdYLKdhw8/tH1wOXN6+YGJJLYdO+Dzzy3p3bfPktuKFa1zw5132sqviEgCUfIr8l+io2HMGOp360b9nTvZnrswrzR4l/Vlq9KhTjHql85LjCeGyZsm03tZb9YeXkuezHnoU6MPz5VqQ+fPonEnP4Mny2+kOR7Es82KMeDjy+XAIinfxYu2snvnnVCyJPz5J3z1FdSsCZ0724a1/+uEIiKSkJT8ivyTqChrlt+9u02IKl0apk7l7nr1GPzXadiI6AgGrxxMn7A+7Dq5i6LZi/JNvW+oX6gFo0ekpWjjGI4fzoxfjofInj87GcsfZHm6X5m/vaT6W0rKduaMtfqbOtU2rJ07ZyPlBwywVibHjukToIh4hZJfkWtFRdkI7B49bBxxYKC9YT/2GDgOYfvDmL1jNkfOHWHa1mkcPX+UcnnL0bdmX4Juq8egL3y4+wvbrJ6l4DlyNtlO+sJHL3duiIiOJXTuViW/kvJcmqLmulCiBOzfbxvWWrSAhg2hShW7nY+PEl8R8RolvyKXREbaxrWePe1Nu1w5GDzYeo/9lbn+sOUHGn/XmBhPDADl8pZjUpNJ5PdUpl8/h6e+hYgI26fTqRM8NX0Z1+ukfW3nCJFk69AhW92dPNk+LO7YYX8vfftCnjxQvrwaVYtIkqLkV+TiRRuB3asXhIfDww9bm6UaNS4nvVuPbyV0eSjD1w3H43oA69xQNkt9hr73CJMm2WJWy5a2Sb1YMfvVeX62DhHXyhOQ/m/HRJKVefOgSxdYtsxWeu+911Z4IyOtY8MTT3g7QhGR61LyK6nXxYuW5HbvbqtXlSrByJFQterlpHdl+Ep6LuvJ1M1TSZsmLQ3vbcis7bMud274on0wmU7ZILe33oK811QyhNQqet2pcCG1iibmIxWJu9274fvvoV49uOceO8Vx5gx88on14C1e3NsRiojcECW/kvpcKm/o3h3Cw1lXsCS9mr3OvlIPEXLbvdQHfto5j17LerFw90IC0gXwfqX3eTXwdZbNy8Wmn8PYHLGYbGeCCXk1iFdeuWp68VUu1fWGzt3KwVMR5AlIT0itoqr3leRh+3ZLeCdPhtWr7VjGjJb81qtn9T0iIsmM47rXq0hMGIGBge6qVasS7f5ErnJpI1u3brB/P38+UJYO9zVkUd6S4Di4xBLj/yvpbpvBrtMbyJM5D+3Kt+OZ+9owbVJmQkMtFyhSxEobWrWys7siKcqFC5AhA5w/D9mz24fFcuVsdbdxY01jEZFkw3Gc1a7rBl57XCu/kvJFR1s5Q9eutiGnfHkYNox6q30JP32Riz7rOeM7nSif7cT6/En6M/n5pt43PFagBcOHpaVUYzh8GMqUgUmToFEj7d+RFGbvXvjuO5g40Z7cv/5qK7wTJ1qLvwIFvB2hiEi8UfIrKVd0NIwebUnv7t02JnXIEKhVCxyHAwsnccJvJOd8fwQHcB0Cop4h46kWbBlfk7eGwNmztu9tzJirSoFFUoYpU6B3b1ixwr4PDLTVXde1J7vKGkQkBVLyKylPTAyMHWs70XfutCXbzz+HunXBcTh87jADfh1AePrPieU8V3qROVzYlpvTU6vT17XN6h07woMPevPBiMSj8HCr323eHHLlguPHrRyoRw948kkoXNjbEYqIJDglv5JyxMbaadpPPrHi3NKl4YcfLg+n2HliJ32W92H4uuFEe6IJyvMoO/fdzWGfQeDGQKw/USsfp3ajC3zRIxN33eXtByQSD44ft4R3/HhYssRWdXPmhKeegtatoU0bb0coIpKolPxK8ue61mT/o49g40YoVcq+r18fHIffD/9Or2W9mLhxIml80vDs/c/SPqgDO1feTcjQSA4faYJTZAE5shaj9zd38Ww1TZ6SZO5S2cKxY9Z/Lzra+vB+/DE0bWpfg+p4RCRVUvIryZfrwuzZ8MEHsHatvaFPnEhY+bws2vszAasOMnPbTGbvmE1m/8x0COrAa4Fv8cuPd/BENfjjD8ibNy192wXRunUQmTN7+wGJxEFEBPz4o63wpkkDEybYCm+/flCxItx/v5JdERGU/EpytXChJb1hYVanOGoUPPUUy8J/peqoqkTFRgGQLV02ulftTqv7XuH7sQFUam0b24sVs65nTz0F/v5efiwicbF0qU0onDrVdmjmymWjBi+t/r72mrcjFBFJUpT8SqKZtjY87sMeli2zpHfxYsiXD776Cp59lmgfmLBhHB1+6nA58fXBhzal3iJq4buUagh//mmTiwcOtDJgH5/4f4wiCc7jgeXLrTNDunT2QXD6dNuh2bw5BAfbyq+IiFyXhlxIopi2Nvy6Y357NCp5YwnwqlXw4YcwZw7cfju8/z60bs0FXw/frv2WPsv7sPf0XgpnK8yBMweI9cTiePzxHbuAyB1BPP44dOoEFSok4IMUSUibN1vPvXHjYM8em7zWqJGNGE6b1i4iInKZhlyIV4XO3XpV4gsQER1L6Nyt/578bthgSe+0aTZtqndvaNuWk04kg37rw4AVAzh+4TgV8ldgUN1BbF9bhs7TVnEq5g/Y+wiV7i/F59PgvvsS+AGKJJSjR6F2batr9/GxxtOffmr/AmTJ4t34RESSGSW/kigOnoq4qePs2mXdG8aNg8yZ7c3+zTc55Jyn39KPGbJ6COeizvHo3Y/SqcI7uHsr0u6Fi6xemg7HrzaZ7y9Olkd3cyj7ErZHleQ+brK8QsRbTp+24RPnzsHrr9umtcKFbZ5206aQO7e3IxQRSdaU/EqiyBOQnvDrJLp5AtJffeDgQZvI9vXX4OdH2DtPszj4TorkvZf5P4cw4vcRxHhiaFaiGSFBndizohQdm9k01jQZfchaaSuZS+/FN300ABHR/Pfqsoi3RUVZ55IxY2DGDIiMtImEr71mm9YmT/Z2hCIiKYaSX0kUIbWKXrfmN6RWUfvmxAno1csmsUVHQ5s2hLWuTZWZTxAZFgmAn48fLz74Iq8HdmD5zMI0qwJbt0KhQjBoEPTauQDHz/O3+/7H1WURb7q038JxbJTggAG2ytu6NTz9tCW/ak0mIhLvlPxKori08vq3bg93Z7WV3tBQa9PUogXuJ5+wJE04L/7wIpGxlvg6OLxepgO5N3anehtbIH7gAWtp2qSJbW4f2zPtja0ui3jT3r22wjtqFIwcCeXL25S1mjWtjtfPz9sRioikaEp+JdE0KJ33SvlBZCQMHQq1u9mGnvr1cbt0YVbavfT4+RmW719OQNoA/Hz88LgeHI8/Q9s/zvktULWq9eitUePqhbH/XF0W8ZbISKtfHzXK2vQBVK5sI7kBihe3i4iIJDglv5K4YmJg9Gj45BPYtw+qVCFm6vdMyryPnktbsP7oeu7Meidf1PmCypmf58NB65i5cTExO4NpUC6IjqOgbNnr/+p/XF1Wva94Q0wM7N9vdTmuC+3aWVlDly5W1lCwoLcjFBFJlZT8SuJwXWtX9v771q+0bFkufj2YEdn2EhrWil0nd1E8Z3FGNRjF3ZHN6Bvqx+vfg79/EC+0CqLDV3D33f99N1etLot4w4YNVs4wZox1Ktm61YZRrFsHBQqojldExMuU/ErC+/lneOcd+PVXwircyZwvn+B4gRxMWf8Ch88dplzecvSt2Y90ex8ntJ0PCxdC1qz2I2+8oc5Okkz8+CN8/LENZEmTBh591NqTXRozfOed3o5QRERQ8isJ6Y8/4N13LSnIm5cfP3+T+icHEXP0OzgKZfOUZXT9cRxbGcynTzmsXQt58tjetzZt1LtfkriYGJg3D+6/H/LmhQsX7Fj//vDUU1biICIiSY6SX4l/e/bYgIoxYyBrVvb1eIe+Jc7w5dpBxHhiAPBxfLnjdEPa1KzC7t1QtCh88w20aKEprZLEbdoEI0ZY7frhw9Cjh52maNzYWo+IiEiSpuRX4s+xY9CtGwweDD4+bOn4PL0evMCYrX1gLdS8qyYLdi0kKjYaT5Q/P3wdTPl80K8f1Ktnk1tFkqyYGHjkEVi+/EpZw3PPQZ06dr1qeUVEkgUlvxJ3587BZ59ZvcL586x+qR49ykUxZc+3pNuejlcDX6V5wfZM/KoAC2eF4d6+mKA8wfQcG0SlSsoZJInyeGDhQhsf+MEHlvAGBcETT1hZQ65c3o5QRERugeNemjKUCAIDA91Vq1Yl2v1JAouOtjHEn36Ke+QIvzxdie4VPMw7soysabPy2kOvUSvgTYYNyMm4cbbvp3lzG2ZVsqS3gxf5B/v2WSPp4cNtIMVtt8GuXbYLU0REkg3HcVa7rht47XGt/KZQ09aGJ1y/W9flt75fEz7ifTZnO87RwNzMr1iUjZFLuP3c7fSs1pMHYl7hi75Z6DYTMmSAtm3h7be14V2SuMmT4ckn7ZNa9epWz9uwobUqExGRFEHJbwo0bW34VZPOwk9F8O6U9QBxT4CXLuXEq28SeXoNTVtBtA/gHMb3YiStS3ajhu/b9O+UnneWQ/bs0LmzJb7Zs8fxQYkkhD/+sJ2WFStaOUNwMHz4odXyagiFiEiKpOQ3BQqdu/WqEb8AEdGxhM7deuvJ75Yt8O67RM6YxohyGXmvXlqifSPtOtfBP7w5Ywa/wddH01OwIHz+OTz/vK36iiQpp0/bqOFvv7WevP7+Vz6d5chhn9hERCTFUvKbAh08FXFTx//V4cPQuTPnRnzF0PJ+9PswMwc5SxpPPnAP2+nhWH8i5jyNn+th7Fg7a5xGzyxJqurWtY4NpUrBgAHWX0+nJkREUg2lKClQnoD0hF8n0c0TkP7Gf8m5c9CvHycG9uLzUhcZ2NGPEz6RVC1UgUzbH+fQgrqcO3IEN89S/CJKky3Il7tKr+Kpp6rG4yMRiaMTJ6wf77hxNpAia1bo3t1OSQQGqtWIiEgqpOQ3BQqpVfSqml+A9H6+hNQq+t8/HBMD337LwV4f0K/IMYa86st5Xw/1i9bmmULvMn9kOZZ+6xIVCRnuyUyWQj6kzXOK9H4n6FhbLRwkCXBdG6n99dfw/fcQGQkPPQQHD1ry+8gj3o5QRES8SMlvCnSprvemuj24LmETQpkyvSfbOcnspx1ifX1pVqIZ9bO/w/eDS/DEd1bO8MwzDg/UPcK4rZsTppuEyK1wXVvJ3bIFqlSxRLd1a7uUKuXt6EREJIlQn1+B1asZ0/tpnr13C7EO4ED9ovVpnLkfowcU5qefIEsWePllePNNyJPH2wGL/MXjgQUL4KuvIGNGGzsMMHMmVK2qHZciIqmY+vwmYwnWs3f/fn779CW6n5vN9OJXDvvgy8pp5Zg+sTC5c0PPnpb4JnaP/wTtVSzJ27FjlugOHQo7d9qGtdatr1z/2GNeC01ERJI2Jb9JXEL07HXPnGFx6Kt03z+e+YU8ZHPT8ey9TzB2y2SiPVF4Yv3x2RfMV19By5be6e+foL2KJXm6dJbKcaBvX+jVCypXhi5doFEjSJvWu/GJiEiy4OPtAOTf/VvP3pvlRkczY2BbHu6Ug6ppxrIhvz9dSrzLG/5Hmf3mKKKHLSDvti50K7qAPUuCaN3ae4Ot4vNxSzJ36hQMHAj33Qdz5tixN96ADRtsY1vz5kp8RUTkhmnlN4mLj569sbExTBr/Pj1WD2B9QCQFs6ald4FOhG/8hF7PpuPcOahVCzp1CiI4OChJdH+K117Fkvy4LqxcCUOGwIQJEBFhHRv8/e36PHlUfC4iIrdEyW8SF5eevT/v+ZkB8z7ltz1LCU8bRTH86J/hddbu6cP7/fyJjYWmTaFjR3jggYSI/tbFS69iSX48HvDxsX+bNLE+vS1bwksvwYMPejs6ERFJAeJU9uA4ToDjOJMdx9niOM5mx3GC4iswMSG1ipLez/eqY//Vs/d81Hne+r41VUYEM/XQQg76RxFy4VGK7TzDWx0HMmmiP23awI4d1vs/qSW+cGuPW5KxzZutlKF4cYiKAl9fmDrVevMOHarEV0RE4k1cV34HAHNc123iOI4/oL5C8exmevaeuniKL5cP4LMlvTnOhcvHXdeX0OUVyLYxHR9+CK+/DjlzJtpDuCW31KtYkpeYGJg+Hb78EhYutJKGJ56A06ftCVqmjLcjFBGRFOiW+/w6jpMF+B0o7N7gL1Gf34Rx7Pwx+v/6GV8s788ZTwR1tkPFC/fz4X1b8TjROK4/bwQsoOtLQWTK5O1oJdW7NIxi0SLrxVuggPXSe+EFyJXL29GJiEgKkRB9fgsDx4DhjuPcD6wG3nRd93wcfqfchANnDtBneR++WjmEi7GRNN4Er2y5m6GHh/L+sSoUOh5GYJPFvP54MJUKqSJFvMh1YckSGDQICha0NmXBwda9oXp1K3MQERFJBHFJftMADwKvu667wnGcAcA7wIf/fyPHcdoAbQAKFCgQh7uTS3ac2EHvZb0ZsW4EntgYnv7d5fXV2Rn1Z09qXHiOCpV8mTkc6tYNQmXY4lVnz8KYMVbasGEDBATAW2/ZdY5jbUZEREQSUVyS3wPAAdd1V/z1/WQs+b2K67pfAV+BlT3E4f5StbD9YUzcOJFNxzaxYPcC/FyHF1fD28v8mHamHVVi3qVq/Sws7QRBt5DvapqaJIj27eHrr23D2jffQLNmGjksIiJedcvJr+u6hx3H2e84TlHXdbcC1YBN8Rda8pAYSeM3a76hzcw2eFwPAM22pqffjAiWnn+CR317UbFlIVaEQLFit/b7NU1N4oXHA3PnwuefQ9eulvB26ADPPw/lypEkGkiLiEiqF9duD68DY//q9LALeC7uISUfCZk0uq7LL3t/oduSbvy066fLx31j4bb9t9EqdgL3t6/IwjchX7443dW/TlNT8iv/6fRpGDHC6nm3b4fcuWH/fkt+77nH29GJiIhcJU7Jr+u664C/7aJLLRIiaXRdlzk75tBtSTeW7V9GrnQ5aLn/bibn3k6UDzgefzy1JjJpRgUCAuLjUWiamsRBTIyNHQ4Pt3qbzp2hceMrk9hERESSGE14i4P4TBo9roepm6fSfWl31hxaQ75M+QjZ/yidRi0kY/RZchZrxZ5WBXm9SS2C74rfTWyapiY3LDYWZs+GH36w4RNp0kBoqK3wqi+viIgkA0p+4yA+ksYYTwwTNkyg+5LubD6+mcJZi9D2yCu81e1HikTPYkFAYy52DaX3y4USrBtUSK2iV5VvgKapyTXOnIHhw2HgQNi1C/LkgQMHIH9+aN7c29GJiIjcMCW/cRCXpPHnPT/Tf0V/fgv/jYNnD3JvthK0PNaT57rOpkrMYHZlKsma7guo2r5qgu8T0jQ1+VerVtkwirNnoUIF6NEDGjYEPz9vRyYiInLTlPzGwa0kjReiL9B0/BvM3P2NHXAd7tvfidc+PUVrz3tc8A9g3ztfUrhLazulnEgalM6rZFeM68Ivv8DJk9CgAZQqBS1aWNeGsmW9HZ2IiEic3PJ441uRmscbn4k8w6DfBtFzaV/ORP0JLuCAE+vDB4v8+XhZNGdbvkrAZ5/Abbd5O1xJjSIjYcIE6N8f1q2D0qVh9Wq1KBMRkWTpn8Yb+3gjmNTkzwt/8tGij7iz/528t/A9Yk8VxXdZKD4xafGNhXQeD7kjCtDqza8IGDlQia94x7hxUKAAPPssREfbYIply5T4iohIiqOyhwRy+Nxh+i7vy+BVgzkffZ6yGRtxatF7xPycjc983yTX5kim3puZzbmb0LtaIxwlGZLYfv8dcuWCO+6wD11ly9ro4WrVlPSKiEiKpeQ3nu07vY/ey3ozbM0woj3RPOjXnIPT3mXDukL0ydGTF3x6EePjwxd3tWLa/Q2ISmObhtRWTBKF68KcOdC3LyxYAO+8YxvYate2i4iISAqn5DcehO0PY/KmyWz7cxtzds7BwaGkpxW7R3di1c67eO+e73k/Z10yHNvH/tr1aXlPY/akv1LeoLZikihGjoTevWHTJmtV1rMntGnj7ahEREQSlZLfOBr7x1haTWtFrGvtzopENuHAt/1YcyQ/rwZvpFtAdQJWL7Qd85NHk79yZd5aG662YpI4zpyBLFns6zlzrD3ZqFHQtKmmsImISKqk5PcWrT64mm5LujF1y9QrBz2+7Fr2IC9VzUyXNG+Tfdznlnh88QW89NLl1mVqKyYJbts2+OwzW+397TcoUcI2sWXMqHpeERFJ1ZT83qTl+5fT9ZeuzN4xm0xpAsh77HnCA8aDTxRpfPyZWfcstfoVhWPHoHVr6NYNcuTwdtiSGlzqz9uvH8yYYSu7LVtCpkx2/aV/RUREUjElvzfAdV0W7VlE11+6smjPIrL45iD/1h7sn/Iq6bNkofXrL3JHvtHUnrCYoHk9ICgIfvwRypTxduiSmpw5A48+CunTw4cfwquvwu23ezsqERGRJEXJ779wXZcft/9ItyXdCDsQRoBvHnKt+Yyjs1uTPV9GBvWDZx87ToYu38JHwyB3bqunbNECfNRCWRJYRASMGAELF8KkSZA1K8ydCw8+aAmwiIiI/I2S3+tYtm8ZX678klUHV7HtxDayOQXJumQwp35+lgdKpGPAKGjSMJY0w7+GB96Ds2ehfXv46KMrm4tEEsqff8KgQfD553D8ODz0EJw4AdmzQ4UK3o5OREQkSVPy+39iPDF0/bkrn/7yKS4uuA7+Kz7g5LyPqBrsR6dZUKMGOL+tgAptbfRrcLBtaLvvPm+HL6lBWBhUrw4XLsBjj0FICFSqpE1sIiIiN0jJLxAVG8WYP8bQY2kPdpzYAS7gAB4fcuf2Y/KvfpQti62ytXkXhg2zqVjjx1vLKCUekpDWroWjR6FWLShdGp5/Hl5+WR+4REREbkGqLky9GHORL1d+yd2f380LP7zAob2Z4aceEJMePL7gpMHJl5lwZx8MHQr33GM1lu3bw9at0KyZEl9JGK4L8+dDzZpWwxsSYsfSpbNyByW+IiIityRVrvyejzrPV6u/InR5KIfOHSLL6SCYMYSI/dXJUnovac9lIDrTatJ5SnL/AZd7G9SA8G0qcZDEsWgRdOgAa9bYGYZevaxPtD5oiYiIxFmqSn7PRJ5h0G+D6PdrP45fOE6mY1XgxzFkuFiFD952+OLgXJy0McBdZDuTg5BfRtHs93kcy5QNxo3TSq8knKgou2TKBOfO2SbKYcPg6achbVpvRyciIpJipPjkN2x/GD/u+JGDZw4yZfMUTkWeIv2B2jD3A/JmqEDHD6wzWdq0MK2nHwdPRtH897mE/DyKzJHnGVa2Ad/VfY6fmj/u7YciKdH58zZ5rW9feOYZG4ry2GNQty74+no7OhERkRQnRSe/YfvDCB4ZTFRsFABpwivBrH7cXyCQTgOhXr2r2/F2LRDFbZ+HcP/BrYQVKMlH1V/mQJ7C9Khf0kuPQFKsEyeshGbgQGtd9sgjUK2aXec4SnxFREQSSIpOfhfvWUx0bIx94/GlsKcOX48P/HtnqNOn4cMPqTJoEBezZafzk+8youDD5MmWgS+UPxUAABLfSURBVB61itKgdF6vxC8pWNu2MGGCrfK++y48/LC3IxIREUkVHNd1E+3OAgMD3VWrViXa/YXtD6PqyGpExkSRNo0/C1stICh/0JUbuK4lIO3awZEjNg62a1cICEi0GCWV2LEDeve259q991q3kKgoKKmzCiIiIgnBcZzVrusGXns8Ra/8BuUPYmGrBSzes5jggsFXJ75bt9rq24IFEBgIM2dCmTLeC1ZSpk2boHt36wnt5weVK1vyW7SotyMTERFJlVJ08jttbTihcyM4eKoUMwMiCKkVToOi2SwZ6d0bMmSAL7+ENm1UYynxy3VtA9vYsfY8a9fOLnfc4e3IREREUrUUm/xOWxvOu1PWExEdC0D4qQjm9hpGjSXfkPHgfmjZEkJD4fbbvRyppCgbNkCJElZUnj8/vP8+vPkm5Mjh7chERESEFJz8hs7dejnxzXPmKB/P/4pa239ld64CFFq82HbXi8SXX36xevGffoJLz6/u3b0dlYiIiFwjxSa/B09FAFBny1L6/vgZAD0feZZvy9ZnmxJfiQ+ua8lu166wZImdRQgNVe24iIhIEpZik988AekJPxXB5lyFWFQ4kO5VXiA8ay7yBqT3dmiSUkREXJmQMnAgvPgipNfzS0REJCnz+e+bJE8htYqS3s+XPbflpW2DdwnPmov0fr6E1NIue7lFrgvTp8MTT0BsrG1k++kn2LkTXn9dia+IiEgykGKT3wal89KjUUnyBqTHAfIGpKdHo5IaWCE3z3Vh2jR48EFo0ADWroV9++y6Bx6wlV8RERFJFlJs2QNYAqxkV+IkPNymsK1bB0WKwIgRVuqQJkX/6YiIiKRYKXblV+SWeTw2kQ0gd27Ilw9GjoTNm6FVKyW+IiIiyZjexUUu8XisvKFzZ1vx3bMHMmWCGTO8HZmIiIjEE638ing88P33Vr/buDFcvAj9+0O6dN6OTEREROKZVn5FVq6EJk3gnntgzBho1kzjrkVERFIoJb+S+rguzJkDW7fCW29BuXL2ffXqSnpFRERSOJU9SOrhurBgAVSsCHXrwpAhEB1t19WqpcRXREQkFVDyK6nDxo1QpYqt7u7bZ4nvH3+An5+3IxMREZFEpLIHSdmiosDf3wZR7NwJAwZAmzbazCYiIpJKKfmVlGntWvjoI/DxsZHERYrA7t3q0SsiIpLKqexBUpbNm61zw4MPwrJlUL681fqCEl8RERHRyq+kIN99Z23KMmaEjz+Gt9+GrFm9HZWIiIgkIUp+JXk7cgSOHoWSJW0zW0gIdOgAOXJ4OzIRERFJglT2IMnTqVPw/vtQuDA8/7yVNmTLBj17KvEVERGRf6TkV5KXCxegVy9Lert3h8cfh7FjwXG8HZmIiIgkA3FOfh3H8XUcZ63jODPjIyCRfzVuHLzzDgQFwZo1MGGCjSUWERERuQHxUfP7JrAZyBIPv0vkah4PjB9vnRqaNoVWraB4cXj4YW9HJiIiIslQnFZ+HcfJBzwKDIufcET+4rowZw6ULg1PPw0jR9pxPz8lviIiInLL4lr20B/oCHjiIRYR8/vvUK0a1KkD585ZqcNMVdWIiIhI3N1y8us4zmPAUdd1V//H7do4jrPKcZxVx44du9W7k9QkPBzWr4eBA21oRfPmNqlNREREJI4c99L0q5v9QcfpAbQEYoB0WM3vFNd1n/6nnwkMDHRXrVp1S/cnKdjRo9Cli7Uq+/RTK3k4fx4yZfJ2ZCIiIpJMOY6z2nXdwGuP3/Jymuu677qum8913YJAM2DhvyW+In9z7pwlvXfdBYMHw9mzdtxxlPiKiIhIgtCEN/GOOXPg2WdtQlujRtazt2hRb0clIiIiKVy8JL+u6y4GFsfH75IUzHVtSEXGjJAvH9x7L0ydaj17RURERBKBdhFJ4vjtN6hcGV54wb4vUQIWL1biKyIiIolKya8krD17rFtDuXKwfbu1MBMRERHxEtX8SsKZNg2aNbM2ZR9+CCEhkDmzt6MSERGRVEzJr8Sv6GhrXZY3r01ia9XKEt98+bwdmYiIiIjKHiSeuC5Mn261vE2a2Pe5csHQoUp8RUREJMlQ8itxt3o1VKkCDRpYj9733vN2RCIiIiLXpbIHiZuZM+HxxyFnTvjyS3jxRfDz83ZUIiIiItellV+5eRcuwIYN9nX16tCtm3VyeOUVJb4iIiKSpCn5lRvnujBhgg2nePRRiIqCdOmszCFrVm9HJyIiIvKflPzKjVm5EipWtJ69OXLA6NHg7+/tqERERERuimp+5b+tWAHly1v3hmHD4NlnwdfX21GJiIiI3DSt/Mr1XbwIYWH29UMPwRdfWF3vCy8o8RUREZFkS8mvXM11YfJkKFYMataEkyetfVnbtpAli7ejExEREYkTJb9yxbp1EBwMTzxhY4inT4ds2bwdlYiIiEi8Uc2vmL17ITDQkt0hQ6y8IY2eHiIiIpKyaOU3NYuNhV9+sa/vvBNGjrS63pdeUuIrIiIiKZKS39Rq+XIoW9bKHLZssWMtWkBAgFfDEhEREUlISn5Tm0OH4JlnoEIFOHbMhlYULertqEREREQShc5tpyYREfDAA3DqlE1le+89yJjR21GJiIiIJBolv6nBqlVQpgykTw8DB9rXRYp4OyoRERGRRKeyh5Rszx5o3Nhqe2fPtmNNmyrxFRERkVRLyW9KFBkJXbvaoIo5c6BbN6ha1dtRicj/2rv7WDvmNIDj3yfUH1bjpV2rW7W2tVl2CepqLK1IbaSEWiSoxjYhhCyhWpYIERFJySIroiGkFvGyXpYIWTQSWa97VVutqurS6LZba5uU1Xq57W//mGn2Ovec23t6b8/MOfP9JJMzd+Z3nMeTZ6ZP5vxmjiSpcE576DQpZb/M9uqr2VXf22+HMWOKjkqSJKkUvPLbKdauhZ6e7KeIZ83Kpjk88YSNryRJUi82v+2upwfuuCN7XNmdd2bbpk6FKVOKjUuSJKmEbH7b2euvZ09umDkze27v1KlFRyRJklRqNr/t6uabs4Z3/Xp48kl4/nkYN67oqCRJkkrN5redbNkCX3+drR97LMyeDcuWwemnZ3N9JUmS1C+b33axaFF2pfeqq7K/J06EW2+F3XYrNi5JkqQ2YvNbdl99BVdemc3tXbkSJkwoOiJJkqS25XN+y+yNN2DaNFi1Ci64AObMgT33LDoqSZKktmXzW2Z77w0jRsCDD8KkSUVHI0mS1PZsfstkyxa491547TV44IHs6Q3d3d7MJkmSNESc81sWS5ZkV3cvughWr87m+oKNryRJ0hCy+S3apk1w7bVw+OGwfDnMmwfz5/sUB0mSpB3A5rdoX38N990H06fDBx/AjBle7ZUkSdpBbH6L8PnncN110NOTPb1h6dLsiu/IkUVHJkmS1NFsflspJXjkETjooOyxZW+/nW0fMaLYuCRJkirC5rdVPv0UTjkFzjkHxo6FBQvg6KOLjkqSJKlSfNRZK6QEZ54JixfD7bfDpZfCTjsVHZUkSVLl2PzuSCtWwD77wPDhMHdu9jp2bNFRSZIkVZbTHnaEnp5sTu8hh8ANN2TbDj3UxleSJKlgXvkdau++C+efn72edhrMnl10RJIkScp55XcozZsHRx4Ja9bAE0/AU0/BqFFFRyVJkqScze9Q2Lw5e500Cc47D95/H844o9iYJEmS1IfN72Bs3AgzZ2aNbkowbhzccw/stVfRkUmSJKkOm9/t9dprcNhhcMcdMHp0dpObJEmSSs3mt1kbN8IVV2RTHL77DubPh7vugmHDio5MkiRJ27DdzW9EjImIVyJiWUQsjYjLhjKw0tq0CR59FC6+GN57DyZPLjoiSZIkDdBgHnXWA8xKKS2IiOHAOxHxUkrp/SGKrTw2boS774bLLoMRI7Ib2vbYo+ioJEmS1KTtvvKbUlqbUlqQr38JLANGD1VgpfH669nc3tmz4eWXs202vpIkSW1pSOb8RsT+wOHAW0Px3yuFTZtg1iyYOBG+/Tab2ztlStFRSZIkaRAG/QtvEbEb8CRweUrpizr7LwQuBNhvv/0G+3GtM20aPPNMNrd3zhwYPrzoiCRJkjRIkVLa/jdHDAOeA/6aUrptW+O7urpSd3f3dn/eDvfNN9kPVuy6K3R3w4YNcPzxRUclSZKkJkXEOymlrtrtg3naQwD3AcsG0viW3uLFMGFC9hgzgK4uG19JkqQOM5g5v8cA5wKTI2Jhvpw0RHG1zubN2bSGri5Ytw5OPrnoiCRJkrSDbPec35TS34AYwlha7+OP4dxzs19rO+MMmDsXRo4sOipJkiTtIIO+4a2tpQSrVsFDD8E550C0dy8vSZKk/lXv543XroWbb84a37FjYeVKmD7dxleSJKkCqtX8Pv44HHww3HQTLF+ebdtll2JjkiRJUstUo/ldvz6b1nDWWXDAAfDuu3DggUVHJUmSpBbr/Dm/KcEJJ8CiRXDjjXDNNbBz5/9vS5Ikqa/O7wIj4JZbYPfd4Ygjio5GkiRJBer85hdg8uSiI5AkSVIJVGPOryRJkoTNryRJkirE5leSJEmVYfMrSZKkyrD5lSRJUmXY/EqSJKkybH4lSZJUGTa/kiRJqgybX0mSJFWGza8kSZIqw+ZXkiRJlWHzK0mSpMqw+ZUkSVJl2PxKkiSpMmx+JUmSVBk2v5IkSaoMm19JkiRVhs2vJEmSKiNSSq37sIh/A6ta9oH/NxL4vIDPbVfmq3nmrDnmqznmqznmqznmqznmqzlF5usnKaUf1m5safNblIjoTil1FR1HuzBfzTNnzTFfzTFfzTFfzTFfzTFfzSljvpz2IEmSpMqw+ZUkSVJlVKX5vafoANqM+WqeOWuO+WqO+WqO+WqO+WqO+WpO6fJViTm/kiRJElTnyq8kSZLUWc1vREyJiOUR8VFEXF1nf0TEH/P9iyNifBFxlkFEjImIVyJiWUQsjYjL6ow5LiI2RMTCfLm+iFjLIiI+iYj38lx019lvfeUi4ue96mZhRHwREZfXjKl8fUXE/RHxWUQs6bVtr4h4KSJW5K97Nnhvv+e7TtQgX7dGxAf5Mfd0ROzR4L39Hr+dqEG+boiIf/Y67k5q8F7rK9v2WK9cfRIRCxu8t4r1VbePaItzWEqpIxZgJ2AlMBbYBVgE/KJmzEnAC0AARwFvFR13gfkaBYzP14cDH9bJ13HAc0XHWpYF+AQY2c9+66t+XnYC/kX2vMXe2ytfX8CxwHhgSa9ttwBX5+tXA3Ma5LTf810nLg3ydQKwc74+p16+8n39Hr+duDTI1w3A7G28z/qqv/8PwPUN9lWxvur2Ee1wDuukK78TgI9SSv9IKX0LPAqcWjPmVOBPKfMmsEdEjGp1oGWQUlqbUlqQr38JLANGFxtV27O+6jseWJlSKuIHbkotpfQqsL5m86nAA/n6A8Bv6rx1IOe7jlMvXymlF1NKPfmfbwL7tjywkmpQXwNhfdWIiADOBB5paVAl1k8fUfpzWCc1v6OBT3v9vZq+zdxAxlROROwPHA68VWf3ryJiUUS8EBG/bGlg5ZOAFyPinYi4sM5+66u+s2n8D4b11dePUkprIfvHBdi7zhhrrb7zyL59qWdbx2+VXJJPE7m/wVfS1ldfk4B1KaUVDfZXur5q+ojSn8M6qfmNOttqH2UxkDGVEhG7AU8Cl6eUvqjZvYDsq+pDgTuBv7Q6vpI5JqU0HjgR+F1EHFuz3/qqERG7AFOBP9fZbX1tP2utRkRcC/QADzcYsq3jtyruBsYBhwFryb7Kr2V99TWN/q/6Vra+ttFHNHxbnW0tq7FOan5XA2N6/b0vsGY7xlRGRAwjK9iHU0pP1e5PKX2RUvpvvv48MCwiRrY4zNJIKa3JXz8Dnib72qY366uvE4EFKaV1tTusr4bWbZ0uk79+VmeMtdZLRMwATgamp3xCYa0BHL+VkFJal1LanFLaAtxL/TxYX71ExM7A6cBjjcZUtb4a9BGlP4d1UvP7d+BnEfHT/GrT2cCzNWOeBX6b35V/FLBh66X5qsnnL90HLEsp3dZgzD75OCJiAlm9/Kd1UZZHRPwgIoZvXSe7yWZJzTDrq6+GV0usr4aeBWbk6zOAZ+qMGcj5rhIiYgrwe2BqSmljgzEDOX4roeY+hNOonwfr6/t+DXyQUlpdb2dV66ufPqL857BW3VnXioXsbvsPye4gvDbfdhFwUb4ewF35/veArqJjLjBXE8m+YlgMLMyXk2rydQmwlOwuzDeBo4uOu8B8jc3zsCjPifW17ZztStbM7t5rm/X1/Rw9QvbV83dkV0LOB0YA84EV+ete+dgfA8/3em+f812nLw3y9RHZ3MGt57G5tflqdPx2+tIgXw/m56fFZM3GKOurcb7y7fO2nrd6jbW+GvcRpT+H+QtvkiRJqoxOmvYgSZIk9cvmV5IkSZVh8ytJkqTKsPmVJElSZdj8SpIkqTJsfiVJklQZNr+SJEmqDJtfSZIkVcb/ANqe3SNTINz+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(x1, y2, 'o',label=\"data\")\n",
    "ax.plot(x1, y_true2, 'b-', label=\"True\")\n",
    "prstd, iv_l, iv_u = wls_prediction_std(res)\n",
    "ax.plot(x1, res.fittedvalues, 'r-', label=\"OLS\")\n",
    "ax.plot(x1, iv_u, 'r--')\n",
    "ax.plot(x1, iv_l, 'r--')\n",
    "ax.plot(x1, resrlm.fittedvalues, 'g.-', label=\"RLM\")\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2: linear function with linear truth\n",
    "\n",
    "Fit a new OLS model using only the linear term and the constant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.69949707 0.38365924]\n",
      "[0.41857319 0.03606596]\n"
     ]
    }
   ],
   "source": [
    "X2 = X[:,[0,1]]\n",
    "res2 = sm.OLS(y2, X2).fit()\n",
    "print(res2.params)\n",
    "print(res2.bse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimate RLM:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.15324293 0.48432707]\n",
      "[0.1160125  0.00999611]\n"
     ]
    }
   ],
   "source": [
    "resrlm2 = sm.RLM(y2, X2).fit()\n",
    "print(resrlm2.params)\n",
    "print(resrlm2.bse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare OLS estimates to the robust estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prstd, iv_l, iv_u = wls_prediction_std(res2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,6))\n",
    "ax.plot(x1, y2, 'o', label=\"data\")\n",
    "ax.plot(x1, y_true2, 'b-', label=\"True\")\n",
    "ax.plot(x1, res2.fittedvalues, 'r-', label=\"OLS\")\n",
    "ax.plot(x1, iv_u, 'r--')\n",
    "ax.plot(x1, iv_l, 'r--')\n",
    "ax.plot(x1, resrlm2.fittedvalues, 'g.-', label=\"RLM\")\n",
    "legend = ax.legend(loc=\"best\")"
   ]
  }
 ],
 "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
