{
 "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:                Mon, 24 Feb 2020                                         \n",
      "Time:                        22:49:06                                         \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": [
      "[ 4.98937229  0.53607174 -0.01435181]\n",
      "[0.4821492  0.07443733 0.00658655]\n",
      "[ 4.63057699  4.90556963  5.17578033  5.44120909  5.7018559   5.95772077\n",
      "  6.20880369  6.45510467  6.6966237   6.93336079  7.16531593  7.39248913\n",
      "  7.61488038  7.83248969  8.04531705  8.25336247  8.45662594  8.65510747\n",
      "  8.84880705  9.03772469  9.22186038  9.40121413  9.57578593  9.74557579\n",
      "  9.91058371 10.07080968 10.2262537  10.37691578 10.52279591 10.6638941\n",
      " 10.80021034 10.93174464 11.058497   11.18046741 11.29765587 11.41006239\n",
      " 11.51768697 11.6205296  11.71859028 11.81186902 11.90036582 11.98408067\n",
      " 12.06301357 12.13716453 12.20653355 12.27112062 12.33092574 12.38594892\n",
      " 12.43619016 12.48164945]\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": [
      "[ 4.93135487e+00  5.15380256e-01 -2.30780247e-03]\n",
      "[0.12270896 0.01894461 0.00167631]\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 0x7f36320ea510>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\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": [
      "[5.56783819 0.39255362]\n",
      "[0.41789611 0.03600762]\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": [
      "[5.00775204 0.49586454]\n",
      "[0.10336252 0.00890613]\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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vnlyUm7yEf+I2UT5neRbcu4AHaz2Il82LduXbse7wOlqWbUmTUk3cPezMGYCDjwW77B+xSZMm7NixI9nX9evXj08//ZT+/fuzbt06mjVrxrfffpuuY1FKZUHx8RJkP/xQZrfe3tC3r2xa2mxw333uHmGmERIC48bBNzuCYXAr8LrCRcDXuwizOsxicN3BeNu9r72+SakmHhF4E3hUAH7yuyfZdvL27QgvXrnIjlM7cBonNstG7aK1yeubN8nX1y1Wl+kdU9bkweFwsHbtWoYOHZrsaytVqsSXX37JhQsXWLp0Kf3799cArJRK3vTpMGYMlCoFkydL+7+iRd09qkzlr78kueqLLyB31U0UGDaQ81wBwIaNxxs+zvC7hrt5lMnLdHvAF2Mu4jROAJzGycWYi2n+ntHR0dStW5eCBQty/vx52rVrl6K/17NnT5YtW8amTZu0PKVS6t+MgfXrZYa7YoU81r8/rFwp7f9efFGDbwqsDAmj2dSfCHjkZ4rUO0nNmoZvQkKoNKELEX0b4/A9g7fNG7tlx9fLl7bl27p7yCniUTPglMxUg48F02ZhG2IdsfjYfVjcc3GalxQS9oAvXrxI586dmTFjBqNGjUr27/Xt25f69eszaNAgbLZMdy+jlHKVS5fgk09kf3fXLsiX73pjhGLFoFs3944vE1kZEsaz8/ZzfFc40fF/gwnF+5ElRBf7jrN++ZnSdApPNHqCnad2etT+bkp4VABOiSalmrB24FqX/EPnzZuX9957j27duvHoo48m+/rSpUszefJk2rbNHHdbSqkM0ro1bN0qpSLnzIF+/a733lUpduoUPPa4kxOhXjDgIfCS9opx+BBgH8iu0e+R10+2ID1tfzclMl0ABtf+Q9erV486deqwbNkymjdvzt69ewm4oWfmO++8c9PrH3nkEZeMQymVScTGypLywoXw2WcSaKdMkVlvgwZaqSoVzp+XJgnvvQdRvrHYBj6K0ysGLMBAnvgeeMX0vhZ8M6tMGYDTW2Rk5E1f39iaMC4u7l+v79WrV6Lf5/Dhw+k6LqWUBzt2TJrbz5kDJ09Kdf+DB6U+c/v27h5dpnTpkuSovf02XCKUiiNe40DeOUjWjw0MWHiRwxno8jrNGUEDsFJK3an9+6U4hjFw773wn/9Ahw5yjCiLWRkSlmyjg7SKipJTWVOnwrkrJyk/6HViis7kCE46lu7P/gNtuew4maF1mjOCBmCllErOhQtSkzkiQs6/VKwo07Tu3aFsWXePzmVWhoTxwvKdRMc5AAgLj+aF5TuB9GlUf+UKzJ4tp7FO5vqWfAOn4p1vI0dwMLjOYMa1GEfZfGVvuAnIuDrNGSHZAGxZ1lygM3DaGFPzlueeBaYBhY0xWoNRKZW1bN0qU7OlSyE6Gtq2vd6d6Mkn3T06l5u2Zu+14JsgOs7BtDV70xQA4+Ol8Ncrr8DR0+EUHfgUlJhPOGDHztL7l9KrxvWtPnfUac4IKVkvmQ90vPVBy7JKAe2Ao2kdhDEmrd/C42WHn1GpLOWNNyAwEJYtgwEDpOzSDz9kq6SqpBrSp7ZRvdMJS5ZA9eow7LEIHM1eI9dL5ThVYv5Nrztw/kCqvn9mk2wANsasB84n8tQ7wHNAmiKLn58f586dy9IByhjDuXPn8PPzc/dQlFJJOXAAnn0WNmyQr7t3lzTc48dh5kyoW9e943ODpBKd7jQByhipQ1KnDjw0OIqI2tPI/XI5wqq8TOuKLZjfbb7HNUrICKnaA7YsqysQZozZbiVzN2hZ1ghgBMi52VsFBAQQGhrKmTNnUjOUTMPPz++m40xKKQ8QHw9ffy0FM77/Hry8pERk06ZQpYr8ysbGdKhy0x4wgL+3PcUJUMbAmjVSr3nr2XXkbP82OXv/zknnBTqW68grLV+hQckGAFQuWDnTFdJIKyslM0/LssoCXxtjalqWlQP4GWhvjLloWdZhIDAle8CBgYFmy5YtaRuxUkqlB2OgYUPYsgUCAmDECBg2DIoXd/fIPEpqs6DXr4eXXoLfgmPJ0+1lLtWeBhhslo0P7/2QRwKzRw0Fy7K2GmMCE3suNTPgCkA5IGH2GwD8aVlWQ2PMydQPUymlXMgY+OUXKZbx/vtgt8Pjj0PevNC5s8x+1b/caQLUH3/IjPeHtfHka/EJBSdM4pzz8LXnLSzORye2q5n93PGhNWPMTmNMEWNMWWNMWSAUqK/BVynlkS5ehA8+gBo1pB7zsmWwb588N2iQ7PVq8E2zHTukxHWjxk42Ri6l8IQahLccQtmiBRlc/WVs+IKxYYwXVmwNdw/XI6TkGNJSoCVQyLKsUGCCMeZjVw9MKaXSbOdOaNIELl+WspDz5kGfPuCf+asoeYq9e+HxqcH8eOBnfP0sikxYzGl2U7ZwLWa1WoGJCuTFFbso4njtWiGNBet8qFogLEseLboTyQZgY0y/ZJ4vm26jUUqptIiJgc8/l/rMQ4fKeZcRI+DBB+VIkUo3hw/LOd55azfAwFZQJpYrFvjlKc2ydsvoVaMXNstGs6k/ER3nwJdq+DqrARDtTPtZ4qwg69VNU0plPwcPSpP7gAAYOFCqPIDs8/73vxp809Hx4/DYY1CpsuGTDT+Qa1Af8IoFC2zYGHHXCPrU7IPNkvCS3meJsxINwEqpzO3116U05DvvQMuW8OOPkmyl0tWZM3JMukIFmLVmPYXHtCSuX3ty5I7F2+aN3bLj6+VL63Ktb/p76XWWOCvSzAOlVOZy8qR0IHrgAWmI0LIlTJokR4hKlHD36LKc8HB46u1glmxYR+zFQhQf/Rkn/H+EXMV5v/n7DK8/nD9P/JnkGd60niXOyjQAK6U8nzGwbp0UzFixQgpo5MsnAbhJE/ml0lVkpBQCe/2TYCJ7toLmV8CCKN+8vH3P2zwa+Cj+3jKLvV2P9oR9Xld3VMqMNAArpTyb0ykFM7Zuhfz5YdQoGDkSKlVy98iypOhoCAqSlf0z1i5yDRkO3lcAOcP7ZOMnebrJ03f0PbNqM4W00gCslPI8W7fC6tXS+s9mg1694IknoHdvPULkIrGxMHcuvPYahMXso2ifiVhFluH08sfL6YUxBh+7Dx0qdHD3UF3jyhVYvlxaTz72WIa8ZYpKUaYXLUWplEpSVBR8+qksM2/eDDlywJ49kEgNeZVyyZWSdDjgk09kG/2fC/9QuNcrnCu5ED9vP0Y1HMWzTZ9l37l9WbdO86FD0mxj7lw4exbuuks+f+nU9Sq9S1EqpVT62rQJOnWS2Ue1arL5OHCglIlUqbYyJOymBKiw8GheWL4TgK51SvK//8GECfC3+ZIcXadgy7+VS3YvRjcYzdi7x1IkZxEAmuRIeo83U0powhEUJN0i7HYp4zVyJLRpk2EtJzUAK6UyXlwcfPWVXPi6d4dataBrVxgyBFq0yFY9d11p2pq9N2UfA0TFOnhh+lkmbi/J9oMnyd17FJT+nCjAy/Liswc+o2vVru4ZsKuFhkoG/ezZcqA5IECqiQwd6pYMeg3ASqmMc+yYXPzmzIETJ6BdOwnAOXLA/PnuHl2Wc2OxC2Mg5khBwtdXIfaig3z3Po9Pz/eJNDFYWJir/9t9ZnfWCsBOp7SaDAqCVavkH6JTJ/m6Uye31gHXAKyUyhgTJkiGT8IFcNYs+V25TIl8/oSFRxMTmp/w9VW4csaOdc9UrIbvc9EeTf9a/elSuQuDVg4i1hGLj92HlmVbunvY6ePUKan9PWsW/PMPFCkCzz8Pw4dDuXLuHh2gAVgp5SpnzsgFcOBAKFZMykE+95zUZvaQC2BW17NUTSbMsbjs3A6te0OpjRivKJqV6MLs7m9QrbDUZg7IE5A1kqwSWk4GBUlGc1ycdMCaOlVWWnx83D3Cm2gWtFIq/RgDv/8uF8CEpgjz5sHgwe4eWbaye7ec4Fq+Kgqve8cQX/dDsABsjKr7X97tNtrdQ0xf58/DwoWSzfz333JefPBgudmrWtWtQ9MsaKWU6125Ao0awfbtkCePXPxGjpQ+vCpDHDgAEyfC4k9j8G06i5wvTeEyp649b7csihWIct8A05Mxkj0fFCTH12JioHFjacTRq1emOC+uAVgplXohIfDrr1KdytcX2reHxx+Hfv0gZ053jy7TS+4Mb4KjR+HVV2Hugljsd80j94uvEWELpUnZlvStMYmn1jyVdfZ4IyJg8WIJvNu3Q65ckj3/yCNQp467R3dHNAArpe5MdLTMOIKCZAaSMycMGCDLfm++6e7RZRm3O8ObEIRPnoQn3gxmechP4BVFrrFLuGQ/TINSTXm11YJrnYlqF62d+fd4t22Tz9zixVKouk4d+frBByF3bnePLlU0ACulUm7tWulCFB4ue2vTp0uSVf787h5ZlpPYGd7oOGlk37x0Sd58E6Yv/43Yvm3gHunHW7xgFZZ1+IaOFTti3XCW+nbNEjxaVBR89tn1mz0/P+jbV7Y2GjbM9OfFNQArpZIWGwtffgkFCkiFoJo1oWNHWe67555MfwH0ZIk1rHde8eKvrwMo97qTiIAV+PZ9DLxiAbBZNgbWGUinSlngaNeePZJQtWBBlr7Z0wCslPq3I0fk/OTHH8t5yt69JQAXLQpLl7p7dNlCwhleAGesnYiQMlzcWB5T+gfyPtoH/LdRNE9pTl72weF04GP3oVXZVm4edRrExkqryaAgaT3p7Q333y+z3SxaHU0DsFLqZk8+KbWYAe67Dx59FDpk0Q44HmxMhyo8/9kuTuw9S8TFgxC1F9vQRZjCWymYvzzv3bOAB2s9yOawzZl7f/eff+Rmb+5cOH1azohPnSqJVUWKuHt0LqUBWKns7uRJKQP5+OOSUVq/Prz4olQMKlPG3aPLluLi4OzWkpz69hARXYaC/QpYkNunENPaz2Jw3cF4272BTLq/Gx8v7SYTmiFYFnTpIrPd9u2lBWU2oAFYqezIGPj5Z7kArlghF8QaNeQiOHCgu0eXJaT0CNGNHA5YtkzO8h6I2YhvvyHgdQUAGzaeaTqK4XcNz4DRu0hY2PVmCGFh0gBh/HgYNkwaI2QzGoCVym4uXJCCBfv2SXLV6NFSNKNyZXePLMtIyRGiGxkj90Hjx8PucyHk7vYyFF+Nn29enHHeOI0TH7sPbcu3zdCfI104nfDjj3Kz99VXcpfRoQN88AF07uzWZgjuln1/cqWyC2Ng40apTzhsmGSRtmwJ48bJkaJMUDEos7ndEaIbA/CKP8N46f0zHPyuLLHOUPzufRnKrsTLLz9Tmk7hiUZPsPPUzsy5x5tQC3zmTGl6X6gQPPusbG1UqODu0XkEDcBKZVWXLl2vGLRjhyS0DBggFatmznT36LK0xI4Q3fr4a3POMOUVf6Lz7IWeA6DwLmLJQZ/KTzGzxwTy+uUFMtkerzFSGS0oCP73P9nMvucemDwZevSQz566RgOwUlnR559LFunly1CvngTcfv30AphBbjxCdOvjmzbJ4sOPWyKhy2NQ/rurz9opGPscx440vxZ8M43wcGmGEBQkZ3jz5oXHHpPz4tWquXt0Hit7pJopldVFRcly36ZN8nXt2nJ2d9Mm2LpV9ngzabm+zGhMhyr4e9tvesw6l4+4b5vQuP0xfss3EkZVhvLfX30SwBBnO5Tk7NnjGAN//AEPPyzJVKNHy2ds7lw4flwKZ2jwvS2dASuVme3eLbPbhQvh4kVpitCoEVSpIhdClWqpyWJOkPC6aWv2cvigjSubqnHuH8PxNmOxPx2Ew2Yoxr3ER9fmnM+bGBOPhRd+zlqUyOfhe/KRkbBkicx2Q0Ku1wJ/5BE5wqZSTAOwUplVnz5SJ9fHR5KpRo6Eu+9296iyhDvNYk5M7bwlyfvPUY4fWo292my8eq7AYYtlSN0hjGsxjpB/vHhh+U68YicTY9uJn7MW+ew1GdOhist+rjTZsUOC7iefSEeiWrXgww/hoYek/aS6YxqAlcosDhyQi9+4cXJ0o0ULCAyUxuOFC7t7dFlKSrOYExMaKjlHs9auwdm3MxSPx2FBxwodef/e96lYoCIAZeolvJcPx8Or3fEsO0NER0syVVAQbNggOQR9+sjNXuPGWbI8ZEbSAKyUJ4uLk2YIM2fKWUq7He69VzrB/Oc/7h5dlpWSLOZbnT4tFRRnzLlEfOaMoiQAACAASURBVOC7WP0mgy0eALtlp0WZFteCb4Lu9Up6VsBNsG+ffObmz4fz56FSJXj7bRg0CAoWdPfosgwNwEp5qoMHZUn55EkoXVo6rickvCiXul0W860uXIC33oLpM6KIrjkDnyffwGk/R/PSzfkj7A/infH42H1oWbZlBow8DRI6XwUFwU8/ySpLjx4y223VSme7LqABWClP4XDAN9/AuXOyrFyunDRD6NFDWgDa7cl+C5U+xnSoctMeMIC/t/2m/dmICHhmejALf/uRK9Y5/J5YhvE6RauKHXml5Ss0KNmA4GPBnl9E49bOV2XKyBr6ww9DsWLuHl2WZhljbv8Cy5oLdAZOG2NqXn1sGtAFiAUOAkOMMeHJvVlgYKDZsmVLmgetVJYSFiYXv9mzZQOxVi3Yvl1nHG6WVBZ0dLTkHr2yYD2XurcFWxxYUK9YPd7v9D7NSjdz99CT53DAt9/CRx/J75YlWxsJna/0Zi/dWJa11RgTmNhzKZkBzwc+ABbe8NgPwAvGmHjLst4AXgCeT+tAlcp23n0XnnlGLojt20sbwM6dNfh6gFv3Z2NjJfC+Ojmek0UWYe/yNNjjrj5rUSN/B88PvidOyM3erFlw7BgULy5JfcOGyTaHylDJBmBjzHrLssre8tj3N3y5EXggfYelVBZ16pScz+3aVboPNWqk9XE9XHy8JJ9PfMXBkVyf4vfQRMi5H7sJwGEiAScWXvy6swgrK4V5XlKV0yl7ukFBsscbHw/t2kmhjC5dpPG9cov02AN+GPg0qSctyxoBjAAorXdYKjtKrPWfn58E4MaN5ZfyOE4nTF4YzHtf/czZMxZ+PRZDnt1UKlKLuPOvEBVRj1jb39fO8OKsnKJjShnm7FnJYp45U46wFSwITz0lVdEqVkz2ryvXS1MAtizrJSAeWJzUa4wxs4BZIHvAaXk/pTIdY+Ss7p9/Suu/UaPkAljFQ4stKIyBVavgqXc2cOjuVlA7FiwomrcMb7RdRq8avajwwrdYgK+zGr7O6+UW3V5G0hj4/Xe52fv8c1k3b95cGgzff7/c+CmPkeoAbFnWICQ5q41JLpNLqewioRvMN9/A66/LXu5DD8nM44EH9AKYTtJSJjIpxshR65fGGTaf/RF7z4fBKxYAGzaG1x9On5p9gDs7ppQhLl6ERYsk8O7eLZWpHnlEftWo4Z4xqWSlKgBbltURSbq6xxgTlb5DUioTOn9e6jHPmnVzN5jSpeHpp909uiwlPcpE3uq33yQX6ZfD6/HtNA6K/UqhHEU5H+ON0zjxsfvQulzra69PyTGlDLFliwTdpUulIUdgoCRZ9ekjNZqVR0s2AFuWtRRoCRSyLCsUmIBkPfsCP1iSrbnRGDPSheNUynP9/ju0bQsxMZJUNXeuXABz5HD3yLKktJSJvNXWrRJ4v9u1EZ+OL0OrHymQqzgvNf+AYfWH8eeJPxM9x3tjs4X0nIWnyOXLEnCDguQHyJFDWk2OHCkBWGUayZ4DTk96DlhlCQnLffnzy/JydDS88IL0361Tx92jy/LKjV1NYlctC/hn6n0p+h67dsH48bDin/nYWkzFWWAvhXIU5oW7x/Jo4KP4e3tgR6JduyToLloEly5BzZoSdPv3lxUX5ZHSeg5YKZXQ+3TmTFi2TIJu794SgP395UiHyhBp2X/dv1/ykZb8uAt7l8ehzi84AW+bN8vuX0qb8m3Sf8BpERMDX3whBTN+/12aIfTqJYG3aVM9L57J2dw9AKUyhf/8R44LffaZzDi2bIFPkzx9p1wosWb3ye2/Hj0qtSaq3r2XTx394NHa2MsEYyEBzGmc/BH2h0vHfUf274cxYyAgQD5vp05JwenQUJkBN2umwTcL0BmwUonZskVmuxMnQsmSksFcuzY8+KD2PnWzO9l/PXECpkyBmZ8dwnH3K5hHF+Hr7cfoRs9zT5l76PlZT2IdsZ7RLCEuDr76SpaZf/xRmiF07369GYJN50tZjQZgpRJERMjyclCQnNv195eykCVLQuvW8kt5hOTa+J07B6OmBfPp9pU48u3FenQ1Pl52HmswmuebPU/RXEVZGRJGResNjsVuoVSOQE6dLQ2lMvCHSHD0qNQBnzPneuer116TZgjFi7thQCqjaABWCiAyUi584eHSDOGDDzS5xY1Se8734kX473/hzZVfE9OtBzSKBwt6VO3Je53eo2Sekte+vxwjKk9eynPpEmk+ynRHHA5Ys0Zu9lavlhyDe++V2W6nTtoMIZvQAKyyp8hIme3u2iUJVLlywaRJ0KCB7PXq/prbpOac7+XL8P77MPW9s1ys+SZW93fAFg+A3bITWCLwWvCF9D3KdEdOnpRjarNmSRvAokVh7FipjlamjOveV3kkDcAqe9m2TfZ2Fy+WJedataSAQY4cUiZSud2dBMeYGPnP+drbFzhb6W3sw97Fsl+mbuF72HZmA8bEY/DCir25GlRSJSNdUkoysVrgbdpIUlW3btoMIRvTAKyyj4ULYdAgKQfZu7eU6WvSRGe7HiYlwTEuDsbNDOaj778jwhzHa9Dn4HWR+2v05u4ij/LhDzEUdey61ihhwTofqha43qkoQ0pJnjsHCxbIHcK+fVILfPRome1Wrpx+76MyLQ3AKuvavl2W+lq2lLOT994ry80DB0oRDeUWye3v3i44OhywZAk8F/QTJ9t0hPpxYEGT0s15v9P71ClWh2ZTfyI6zoEv1xslRDtvnkG7rJSkMRAcLLPdzz6DK1fkJm/hQsmk9/fAAh/KbTQAq6zl8mU5nztrFmzaJIULAgLkuUKFZAai3CYl+7uJBUc/LzvN7HWoUSeGvblmYms7DuxxgOzxdqrYiTrFpApZSmbQ6V5K8tIlaRocFAQ7d0Lu3DB0qKyy1K6duu+psjwNwCpr6dRJuhFVqyaz3QEDZOlPeYSU7O/eGBzDLkST41QAMZsrMC3HJ3jd9xrkCKNesbvYdWYX8c74f53hTenycnJHmVLkzz8l6C5ZIjd/9erJzV+/fpLYp9RtaABWmdfly7LMt2gRrFwpBTLGj5dZ7913696um9xuiTmlyU/d65Uk9OhRpn0ezJ7jG/DqtARyH6ZhQDNea72IVuVaEXwsONFGCS7vVBQVJassH30EmzfLsvKNzRD0c6dSSAOwynx27JDElk8+kaW/qlXlSEetWtKVSLlNckvMKZmdbtwIj7/xG1trtoGKsVAJKhSsyvSO39KhQgeudmCjSakmNwXeBC7rVPTXX/K5W7BADhxXqwbvviurLJpToFJBA7DKXPbvl45DCUXpR4zQ2a4HSW6J+Xaz023b4KVxTr45tAKry2PgFQuAzbIxsM4AOlbsmOJxpMvyMkgS1fLlssy8fr0cGXrgAZntNm+unzuVJhqAlWdLyGQ2Bj78ECpVkplvx45QsKC7R6dukdwSc2Kz076VarD49SL8b/vX2Nu+DA22EZC7DKeifHA4HfjYfWhVtlWG/QwAHDwon7u5c+HsWShfHt54AwYPhiJFMnYsKsvSAKw8T2KZzAMGSBC2LGkBqNzmdnu8KVliTpidHjoEEycZRn/8A1br8fDgJkrnrcCkVgt5sNaD/BH2R6J7vC4THw+rVsls9/vvpRxk166SydyunTZDUOlOA7DyHAkBdvJkeP11zWT2QMnt8aYkASo0FB5/I5ivjs7DlPwD+m+nRK5STGw1m0F1BuFtl8pQSe3xprvQUGmEMHs2HD8ux9YmTZJjRCUzoC60yrY0ACv3ioy8PtudNEmWlkeOlKIZ2vPU4yS3x3u7BKjTp+W+6v0Ns3F0HAmFnAA83fhpprSZgq+Xb8b9IE6nzHKDgmTWa4x89j76SD57XnppVK6nnzLlHiEhEnQTajJXry4dYkC6EpUu7d7xqUSltMjFjQlQFy7ASy/Bf5f+SUyT8XDv6mvP2S07hXIUyrjge/r09WYI//wj+7nPPw/Dh0O5chkzBqWu0gCsMo7TKftoDofsrZ09KzWZR4yApk11tpsJ3EkN5YgIOaXzxrxdRAZOgEHLyeuTn361RrJg+wJiHbH/KqLhEsZIBvNHH0lGc1ycNLifOlUa3vv4uPb9lUqCBmDlelu3yoxj3Tpp/+ftDf/7nxSk1/OTmUpK9nijo+G594OZs+FzYvLshAFryeWdm2eaTeCpxk+R1y8vA+sMdH2C1YULUoM5KAj+/ls+a48/Ljd8Vau65j2VugMagJVrXLoES5dK4P3zT6kW1KePTIsKFIBGjdw9QpUKt9vjjY2VXKaXFn9BeNs+UNcBFgyoPYDpHadTwP96Ip3LEqyMkcz5oCDJLYiJkWYICxbIuXFthqA8iAZglX6MgdhYOTa0ebMkU9WuDTNmyNGhvHndPUKVDm7d442Ph3nz4OW3jhFW/jVoOwdskmBlt+xUK1TtpuDrEhERkk8QFCRnx3PlgiFD5AhRnTqufW+lUkkDsEq7ixfl4jdrFrRuDf/9r+yxbd4Md92le7tZlNMppbhfev0Eh0q+jnX/TLy8DF2r9uCb/auJc8S5fo932zYJuosXS0Z9nTry9YMPSkcipTyYBmCVejcu9UVHSyeYevXkOZtNCtOrLMcYeHNpMG9/tZozcf9gdV2BzSuWIfWG8HKLcZTJVybJRgnpIipKIn9QkHwG/fygb19ZcWnYUG/4VKahAVjdmYsXry8lBwVJMtWAAXKMQwNulmaMHJ19Yvoa9jfoDFXjwYL25TvywX3vU7FAxWuvdcke754915shhIdLItU778CgQZrMpzIlDcAqecbAb79JpaDPP4cNG2SmO2UKvP++9j3NBn79FZ4ff4lg57vQYjLY4wHZ472nbIubgm+6io2FFSvkZm/dOsmgv/9+me22aKGzXZWpaQBWSYuMlH3d2bPlGEeePPDww5AvnzxfvLh7x6dc4sZaz7kjisD28uzkY6zmb4DfeZoFNGfLiT+Id8a7bo/3n3/ks/fxx3DmjBTJmDpVEqu0GYLKIjQAq5sZAydPSnC1LJg4EWrWlOpBvXtDzpzuHqFyoYRaz2fOHuLiqcPER8dC06WQ8zRty3VkcptXaFCygWv2eOPjYfVqme2uWSOfvy5dZLbbvr02Q1BZjmWMybA3CwwMNFu2bMmw91N34NQpmD9fDnL6+sLOnXIBPHUKihZ19+hUBqn/TDC7Nx8ntmU/sMWBBd7xFani/wQ7XxzlmjcNC7veDCEsDEqUkJyCYcOkMYJSGWXyZHjxxXTd2rAsa6sxJtEEGb2lzO7++EMajAcEwNixcvEbO1bOmIAG32zi8GEYMjSekJ//IrbpMLBL8MVY5DRNibxUIX3f0OmUWW6PHlCmzPWVlhUr4MgR+VqDr3K18HDJqE9w6JBst2UQXYLOjsLCIEcOyRw9eFCSW0aNklmHlujLVo4fh1cnO5i9YRnOFpOg237s8aVwmEjAiYUXfs5aidZ6TpUzZ6Rqx8yZcrErVAiefVY+exXSOcgrlZiE2uBz5sgpjpgYOT9epYo8loGJfRqAs4v4ePjuO1nm+/pryWB+/nmZ/fbsKcvOKstLSLA6djye+G2VOHNxK/HNJ0D3v6hWoDbdKnzMiuDiXIzdTYxtJ37OWuSz17yp1vMdM0bSqBOOrcXFSQbzq69KRrN+9lRG2b5dSpLu3y9JpYMHy1ZH5cryfAZn1ScbgC3Lmgt0Bk4bY2pefawA8ClQFjgM9DbGXHDdMFWqGQOvvHJ9f61oUXjuOfkQghzrUNnCypAwnluyh7Dd54jy/xrqbIJC+ynqW5H3unzKA9UfwGbZaFQ8jGlrfDkeXu2mWs93LDz8ejOEPXvk/Pijj0p5yOrV0/8HVOpW8fGy1WGzQadOkk1ftiyMGyeTjxw53Dq8ZJOwLMtqAUQCC28IwG8C540xUy3LGgvkN8Y8n9ybaRJWBomLkwpBd98tX3fuLC0AR4yQP2vQzXYuX4Zq9x/gWORKaPO81Go2kCe+HzVyDmHDC+3S542MkRKkQUGwbJlUSGvYUDKZ+/Rx+wVPZROHDsnJjXnzZJ+lXTupIuMGt0vCSnYGbIxZb1lW2Vse7ga0vPrnBcA6INkArFzswAHZw5g3T/baDh+WxvYrV4KX7jZkRzExEgsnLfiF8HovQ5lf4do9tw0b3py4GJv2N4qMhCVL5M1CQuS4Wv/+Enjr10/791cqpZ55RurR22zQsSN88IFMPDxQaq/KRY0xJwCMMScsy0ryZLxlWSOAEQClS5dO5dup29q9G554An7+Gex2uO8+me2WvLpsqME324mLk/uwcTODOVPzZei+Fi9HYfzjehDptRpj4tMnwWrHDkmoWrRIOhLVqgUffijdr/LkSb8fSKmk7NolBVtefBEKF4bmzaVY0ODBUKqUu0d3Wy6/MhtjZgGzQJagXf1+2caePVKU/q67oGBB2d997TWpFFSihLtHp9zE4YBJc4N5d+1iLuX8E7oGk8+7MONb/ZcS3l2Y+OUBwmObpi3BKjpakqmCgqQsqa+vLC+PHAmNG2t5SOV6kZHSBGbOHNi4EXx8pBNbly7Qvbv8ygRSG4BPWZZV/OrstzhwOj0HpZIQFSW1mGfPht9/v76vUayYnF3TC1+Wd2OZyBsTpJxOWL4cRn38CScaDoZqDgBG3jWSae2nkctH6nX72v2ZtsYndQlW+/bJbHf+fDh/HipVgrfflmYIBQu65gdW6lYXLsjZ8YgISeZ75x3Z7ihUyN0ju2OpDcBfAYOAqVd//zLdRqQS98YbcnTo0iVJmZ82DQYOvP68Bt8sL6FMZHScBNew8GjGfrGTLb/68sXn5/i76ERotEwKaCCNEkrnLX0t+AJ0r1fyzjKaY2Phyy9ltvvTT7Kd0aOHzHZbtdLPnXK9c+fgk0/g2DF46y2pX/Dyy5JkmslXXFJyDGkpknBVyLKsUGACEng/syxrKHAU6OXKQWZLly7B0qVyZ5czpxzh6NpVChY0b56pP3Qqdaat2Xst+AJEHynIiRBfJld7FlovwtfuT6+aA/hiz/+IdcSmrVHCkSPXmyGcOiUzjilTZIujWLH0+YGUSorTKQWCZs+WpZ3YWGjaVI4VeXnBmDHuHmG6SEkWdL8knmqTzmNRxsh+xuzZsr8RFQUFCsiZ3ZEj5ZfKto6HRwNw6WwYly7swuF9FHqvBsvOk42f5IUWz7NhXxzb/27AsdgtlMoRyKmzpSGleSgOB3z7LXz0kfxuWZI9mtAMwW533Q+n1I3efReeflpmuyNHwtChULu2u0eV7jQ91lNcuCAz2927Zcb74IMy223QwN0jUxkkqf3dBHkuF+bv7fuIbfkfCJB+vP7xzaiRcxTvdOp9wxJ1efJSnkuX4IXlOwFuv+x84oTMdGfNkmW+4sWlUMHw4R6fRaqygPh4+OYbSagaMkS2OHr3lqJBPXuCn5+7R+gyGoDdxemEX36RkmgjRsidXoMGMHo09O0LuXO7e4QqAyW2v5sQPCv7luT5SWfYceFzaDkdbPFXGyXYyGWrxEsdmwH/XqIGiI5zMG3N3n8HYKdT9nSDgmSPNz5ekvqmT5dMUi3Wolzt0CG58Zs3T24CixaV0qQgRygffNC948sAGoAz2okTsGCB3O0dPCgftCFD5II3b567R6fcJLHgeem0L8MeieBc7nHQeDqWdzS1CrRg54UNGBOPzfLm6Xt6XAuuCUvUt7rp8bNnJYt55kwp3FKwIDz1lNwEVqzoqh9PKWGMbG0YA/feKxOQTp2kHvN992W7Gz8NwBlp7ly50DkcUox+4kS548tmHzr1bwlB8optD1Gxe4jd3pqYuK3Q5r/gd5FuFXvzevuJVCtcjeBjwaw7vI6WZVvSpFSTa9+jRD5/whIJwiXy+sFvv8ls9/PPJaHl7rth0iRthqAyxl9/yaTj66+lIYK/v1wPS5fO1m0nNQC70pEj8iHr0EEy+Jo0kcSCG7tvqGzjdnu8JfL5s//UTs7kfhm8r0CzuWBBPkdzfhn5AbWLXk9AaVKqyU2BN8GYDlVuWsbOfeUyvfesY/SBn+DFvVKZ6pFH5FeNGhnzQ6vs6/Jl6bU7Z44UbPH2hm7dJN/F31+uidmcBuD0FhsLX30lmcw//CCPJXzYqlWDN9907/iUW9xuj7dFmZIU3leLDbFvQd6Yq/u7kM/RmXk9gqhdNGXndhOC+aqPv6L9ryvpumc9/nExEBgoe219+kiCn1KuFBMjiVO7dsHDD0uf3YS6BUWSrFqcLWkATk/GSCLVjh2SPTp+vOzvlinj7pEpN0tsj/dypMUTz0dwNvojYhpOhjxhYCwwYLN8eP6e4SkvmnH5MixdSvegILpv3Spdhwb1l9luYKKNWJRKPxcvwuLFMtsNDJSM+oYN5Vhlw4YeUbcguVMG7qABOC2iouCLL2TGu2yZnJN8/nnJaNZzk+oGNyZCOeNsXAoJ4NLlYEzTRyDfEeoVbMbb9y3Cz8sv0f3dJO3aJXu7ixZJ8ZaaNaX7S//+UrxFKVfatEnOjX/2mdQIr1tXttpAgm6jRu4d31W3W4FyZxDWAJwaISFyp7d4sdz5Vaok5yfLls0WqfPqzpXI50/o2SucP3SGSJ+voO5GyBuGf1w1Vjz0He0rtMe6OktINvDGxFxvhvD775JElVCspWlTj5htqCzs3DkpEGRZcuO3fLksLw8bJs1hPPDzd0dH9DKQBuA7tX493HOP7HE88IB86Fq08MgPnfIM8fFQN7oOwds/wDSbBJYBY1HI8TCzek6iQ8UUZoHu3y9Le/PmyUWwYkWpjTtoUKYsRK8ykYRz47Nnw4oVsHatFA6aMAGmToVcuZL/Hm6UoiN6bqAB+HaMkRnGnDlQrpx82Jo1kzOUvXrJUrNSSXA6YelSw5g5X3Oi6stw93ZIaMhpWXSsWYQe9ZMJvnFxssURFAQ//ih1cLt3l73d1q2l6bhSrnL5spSF/PhjKZyRPz889tj1o0OFC7t3fCmU5BG9tPTCTgf6/97EnDkjbdaqV5e7vIRi4CD7ugmVq5RKhDGwfLmhfPs19F/XmBMtu1KsdCQvtxiPv7c/dsuOv5cvjzXpmvQ3OXpUOr6ULi0rLfv2Sb/no0flLG/bthp8lWs4HBJsQW74pk+Xz+HixXD8uHxdrpx7x3iHxnSogr/3zTk5/t72O++Fnc50BpzA6bx+QXvqKfmwNW0q53h799bjGyrZLEpjYPoXwUz5Zh5nfTZB8x0U8irNlI5zGFx3IN52bzpV7Jh0kpXDAWvWSFLLN99crxY0cqRUC9KkPuVKR47ITHfuXGlwf+CA5Bfs2wf58rl7dGmS8P9TT8uCtowxyb8qnQQGBpotW7Zk2PulyNGjsqc2dy6sXi1ZpHv3ysWwenV3j055iFuzKEHuoF/vWYvu9Uqyfj0MnTGLA1UfBZsTgKcaPcPrbSfj65VMpamTJ+XzN2uWXASLFpXcguHD9Qibcr0NG+DVV+XmD6Rw0PDhUjRDb/rSzLKsrcaYRM8CZs8ZcMK+2pw51z907dpdX2au4t5lCeV5ksqiHD/nOFOPn2RTjvFQ/Ztrz9ktO4VzFkw6+BoDP/8se7srVkimVps2klTVrZuWJ1WudeCANHwpWlS23Hbtki2Phx/Wm74MlL0CcGSkZOtFR0vafIEC0nbt4YflCJFSSbg1WzL2dG7O73RwpMLrUHcF/uTnobojWbxrAbGOWHzsPrQs2/Lf3+jcOWnGMXOmLO0VKCAdsEaM0PKkyrViYuRmb/ZsufkbN05mvp07SyMEr+wVDjxB1v8Xv3xZklbmzJE///mn1MTduFGWmHWJRaVAQhbl5YjDhJ/fTrz3P3DfWixHTsY2mcjzLZ4kr19eHq4/8N97vMZAcLDMdj/7DK5ckfyCceMkwcrfvZmYKoszBl54QQLv+fOSQDV5MgweLM/rNdBtsm4A3r0b3n8fliyBiAiZXQwbJnu7Xl5Qq5a7R6gykYE1q/P0jC+JajgaCl9tdhDXjhld/8uARjWBhCStaI6H1+brfNG80OxvOu+82nN3505Z8hs6VI4Q1a59u7dTKm2iomSWe999UqMgNFS2OIYPl981g94jZK0AfP68BNc8eWDLFli4UDKYhw2T87taLEPdoePHYeyUYyw+9hrOhnPAckqzBGx0q3PXTcE3IUmrxskDPPTdt7Qa/wvExUC9epJg1a+fxxcsUJnc9u0y0/3kE6nSt2+fVOpbtEivfx4o8wdgpxPWrZMl5uXLYcoUafnXp48ks2Ty9HnlHmfOwLg3TvDx3tdx1J2JrRDcW64HP4WuJs4Rh4/d56ZzvO+t2k7nrd/z0LZvqHtiP9FevnxVrQXfN+/Oxx88qhc/5Vq7d0vjl82b5ejQAw9IXkHFivK8fv48UuYNwMZICbQ5c+TQeL58srzSoYM87+cnv5RKoeBjwXz79zr2ra/D8pCfias7A+uuWPpWfpg37htH6bylCT4WfPMe719/wcyZrJz5MXmuXGZ/wVJMbDOC5TVbc8kvl0yW9eKnXGHrVkkovftuKFFCronvviuNOAoUyLBheGKXocwi8wZgy5LapGXKSCZfjx6azKJSbdLqr5i0qTfGFgt2A4EW3coN4O0u46lQoMK11zUp1YQmRerLakvQWKkN7uPDxmrNmV2jHZsDatwUcN1d6k5lMRcvSl7L7NnSFKZFC/jlF6nMt3lzhg8nvboMZdcgnnkDMMDXX8tyi1KpFB0Nw8cdZfG5d6HsFdnfNZDf2Z3BtadQocANF4GDB2Uvd+5cOHsWKlSAN9+EwYOJCo1l1/KdcEuhDneXulNZyNSpMtmIioI6dWDGjHTpvpaW4JceXYY8tVVgRsjcAViDr0qhWy8yT7auwvGt+Rj/9QdcqvkmlDsPxgYGLLzwjW8qF5FaRWHVKslk/v57ObLRrZuUh7whm7T71Zr02fEuXrnIhQuSTNW/v8xwAwLgoYdkqy0wMF22NtIa/NKjy5CntgrMCJk7ACuVAjdeZIwT/v4tVlCBQAAAIABJREFUJ32/X4zzrreh4Wl8IptQIKY3WPHE2Hbi56xFmfDC9Fo/B94fIKnQAQHwyityjKhEiUTfp3u9kln+gqFcLKED26xZUr8gJkb2cx96SAJx//7p+nZpDX7p0WXIU1sFZgQNwCrLm7ZmL1GxDsKPnSDCayWm+ibIeZYc0Q35fsgKnlsSQ1h4NJbTSfsDUTy07QvaHPgDCyNNEIKC5HetFKRcKTISGjWSxL7cuSWrefhwOcbmImkNfmM6VEm0RvqdbL14aqvAjKBXFJUlJLWPZQzs3+LPuSurcd71DlgGjEX+KyPJS2ealW7KuMBt/DXlPXr9+Q2lL57iTI58zG7ai/IvPEn7+xq7+0dTWZUxksS3Ywc88YScEW/dGp55Ro5RZkAHtrQGv/ToMpQeQTyz0m5IKtNLrFORn5edviXrsfiHHzkQMBEKHgDD1SQrG/ni+vPQmTp8cOkPyWiOi2Nr+brMq9menQ1a89R9NXU5WbnGmTNSD3z2bCmUUbiwdMFywymO5Lp8ZeQ4smr+xO26IWkAVples6k/3XQXHx2al/PH9hNf8y0o8hcFTQ0sRyPO2T/BEI+X02Lp8gI8sPuMJLcMHixFC6pWdd8PobKHTz+FAQOkI1uzZvK5e+AByJHDbUPKysHPE2g7QpWlJexXXbpwhIvR63AWCIFKB7BFlWdht8/oV7snvy5azZZFu4iK20rbQw4qFygNC96CXr30/LhynVOnYP58aNgQWrWSPd7HHpO93Ro13D06QJMH3UkDsMr08l4pyF8H1hBX/xWwOcFY5I55kIY5evPQxhMw+C7u2b6de3Llgv7D4b2Rco5SKVdwOmHtWslkXrlSej2PHSsBuGxZmD7d3SNUHkIDsMq0DhyAR9/4he2OcRD4m+zxAmBx76EtLPr6S4i6DHXrSv/dfv0ku1QpV2rfXgJwgQIwapTMdnV7QyVCA7Byuzvdgzp6FB5/I5hVkS9D+bXkcpagRbFhfH98PsbE4+Nw8viWf/Du/ZAUzGjYUOsxK9dwOuGHH2DpUrnJ8/WVs+JDh0p5XK1Hr24jTQHYsqyngGHI3GMnMMQYE5MeA1PZQ0or8QQfC2bVrnX8sbYYP536H6biN/gXKsKLFcfyzOYI/N9bTHCueNY1KEzLZg/SZMsESbBSyhVOnJCSpHPmwOHDUKgQ/P23bG306+fu0alMItUB2LKsksAooLoxJtqyrM+AvsD8dBqbygZSUonnu13BdP5faxzEQG7wzpGbsTn68fx3oeR8ZSp4e8P999Nk5EiatGihs13lWn/9BbVrg8Mh+7qvvy6zXS2Nq+5QWpegvQB/y7LigBzA8bQPSWUnt6vEc/EivPTOXj46MxJn4RiwpI7GC1sdTPpmKZQrJwXqhwyBIkUyeOQq2zh+HObNkz+/9BJUqwavvQY9e0Llym4dmh4hytxSHYCNMWGWZb0FHAWige+NMd/f+jrLskYAIwBKly6d2rdTWVRilXicsXYch3woMmIwsVUX4VXAC5uxME6DjxM65guE716Edu2uNUNQKl05HLK3O3OmNONwOCTggqywjB3r3vGRvbsIZRWpvnpZlpUf6AaUA0oAOS3L+lelcGPMLGNMoDEmsHDhwqkfqcqSxnSogr+3nSu2PYTbPufsPwcJPfw5x2t3wFRezJM7cnD8v7F8+WluOh6qTaDzFU49uwQ6dNDgq1xn7Fip//3771Iacv9++OILd4/qJrfbvlGZQ1qWoNsC/xhjzgBYlrUcaAp8kh4DU9lD93ol2X16Ky9vGIexYqHaAuwOi5Fb4cVfDfaadzHpvhZ8WzYQh80OTvQuX6WvG2e7Y8dKsYwhQ6BBA+jeHXx83D3CRGXnLkJZRVqmEEeBxpZl5bAsywLaAHvSZ1gqO3A44KOFZ5j65RSMdQUsgwU8vd2XD2o9R4mQA/TsOp6vyzeS4HuV3uWrdHH8OEyeDBUqXJ/tHjsmz1WvDr17e2zwhaQbJmSHLkJZRVr2gDdZlvU/4E8gHggBZqXXwJRncEWShzGw8LNzvP3pk+yrtozYwvHYDWDAx+5Dj+nfQfl7ADge/nei30Pv8lWaxMdLgZYzZ6BtW5g2Dbp18+iAe6vs3EUoq0hTFrQxZgIwIZ3GojxMeid5GANffnqUD5eMJLjGGiLrOOm1x5tJxfoTfn8n1nGElmVb0qRUk2t/Jzv3ClXpKOHc7vr18N130tt5zhyZ6Vas6O7RpUp6tAJU7qWVsFSSUnJGN0WMIei9j5i9fTL7ix4n4i7odDQ/kwOfpN6YZ691gmmSyF/Vu3yVaglVqmbN+n97dx6nc7n/cfx1zWZnCi1EDi1UEo1CKdEqScupFNpR2rejhZZTv0qdThSGVKRSKUSlToc8iuaoiexFMhljT/Zllvv6/fG5GU0zYzZzL/N+Ph7zMHN/v/fM9fW97+/nvq7vdX0+MHmy9Xo7doRNm6B2bejaNdQtLDUVUohsCsBSoFJP8ti+nSXPjOHZBU8wNmkjHA0uAPfVuYd/Pf7vIv0KfcqXEpsyxSZR1akD995rOZmPPTbUrRLZRwFYClTi4d/581n9zDDGp41m0Jl7WN2afYUSvIth7LrNtJ+bUeQgqk/5ckCBAPz3v9bbTUqy2cydO1v93UsvVZYqCUtaSCkF2rtGd38FDv/u2gVjx7L11Ha8cUML2tYbwT2d97A7+3gSd/bFkQA+BkccsdknahazlI116ywb2rHH2trwGTNy14fHx9tMZgVfCVPqAUuBijT8u3QpjBjB11NfY+iJ2/j67FjW1oL6OS35sNuz3D8uC3BUzmzC7pgFVA40p1KgmWYxS8l5n5vv+7bbYOJEOPtsSw+pCkQSQZz3/sB7lZGkpCSfmppabn9PDpLMTPj4Y0hOJvDVdP7vTMfAjh7vAO8Y0PY5njz/QZxznPHc9HyHsesnVmFW/47l33aJXBs2wOjRNnv5s89s/e6iRRAbq3q7Eraccz9475Py26YhaCm6tDRLRt+wIf6qq3hn0wLq9TmSAZ383lu8xMbEUKVqDi7YQynWMLZIXt7DV1/BNddA/frw0ENw+OGwZYttP/FEBV+JWBqClsLl5MDUqTB8OEydSsDB62eezkOX1mJzvaXUyDqGu04eyGuLXyAzJ5OE2AQ6NOqw7+maxSwlEgjYvdzff4cLL7SlarffDr1729pdkSigIWjJ3+rV8Prr8NprpPh0vmpeg/WHnMnIahvYVT+VqlkNefSMx3nogl7ExcSRkp7CjLQZf0mkIVJk3sM331hO5nXrbFYzWPKM1q2hipKvSOQpbAhaPWDJFQjAtGmQnGz3eHNymNmtNR1PXkuW2wZuKglZdXikxVAGdrmZSnG5s0vbNmirwCsls2kTvPWWLSFasgRq1YKePS1xRlwcnHVWqFsoclAoAFdwk+ZmMHLCd7SfOYWe87/gqE2roXZtcu6+j/+r0Y4nt/yDnJgsABwxPHrenQw8+/YQt1oinvf2gS82FsaNs0QZp59u6SKvvnpfdjSRaKYAXFF5zzdvTCT2368w8aeZVMrJZvZRJ/Jy+56sO+kCPlo9hF01XyC2Wg1iXTwQICE2gfManxfqlksk27IF3n7bhpn79YM+fay3e8YZVhxBpAJRAK5oNm+GsWMhOZn2ixezNaEqT51zOu+feCjrNrVhR84cfNwgYurVoOdRT/LKdfeweMOiQu/vHoyKSRJlUlPt1sa4cbBzJ7RqZbOZAWrWVPCVCkmTsCqKvBfA1q15qE5b3j/hcFZWexJcpu2XXZmqm7qz8sUXqV310AP+2rwVk8CWGT17eXMF4YouK8uyUQG0bQvz58O111qvNynfOSkiUUfrgCuqHTssaUFSks0iHTfOLoCpqfjZ3zHpqAtI3/WhBV8H4Kjpu3JKwx5FCr5QeMUkqaDmzoW+fW3d7u+/22Nvvmkz6197TcFXJEhD0NFo4ULr7Y4dC1u3wkknwSuv2L22WrWYNG0N/W69k9VHjgQCQCx4jyOOQ2LaFCtJRqkrJkl02LnTCh8kJ8N331k6yKuvthzhoGQZIvlQAI4Wu3fDhx/aBXDWLEhIsET0fftCu3bgHF/O2kDvtx4gre5QqJdNu6o30qPNLQz/djbpO1NpUDWJpy66vFhDxyWumCTRYc8eK3aQkQE33QTNmsHgwfZh75BDQt06kbCmABzpli2z9ZNvvmnDfcccAy++CNdfb3VQgRH//YLHPn+OjZX/B0dkcmp8D0bfOJCT6jcB4LYOp5X4zz94wfH53gNWqskotns3fPSRfdg77DD7/thjbei5RYvcQgkiUigF4EiUlQWTJ9sF8L//tbWU3bpZb7djx33l2OYu3sqVr93Pr7VGQQ1wxDLqore56bTuZdYUpZqsQJYts+VDo0fnfti74orc7ZrJLFIsCsCRZOVKm8QyahSsXQsNG1oJtptugiOP3Lfbkl920Gvoq6QmDILETeytlBDjYN2etDJvVreW9RVwo1Vmpn2gi4uz9buDB9uHvT59/vRhT0SKT++ecJeTA59+CpdcAn/7GzzzDJx6KkyZAr/+atWJgsF3Rfpu2j/4MieMbExqYn8axbfhpbPfoEp8FWJd7F8KJYgUaMUKeOQR+5A3ZYo9dtddkJ4O48fDuecq+IqUknrA4WrtWkvLN3Ik/PabJS14+GG49VY4+uh9u6WkpzBl0TS+/GYLqXvehRqrqb+nE692+SfdTrWkGW2aNFWhBDmwQAA++cRubXz+ud3L7dIF6tWz7bVrh7Z9IlFGiTjCyd7ap8nJMHGiJaPv1MmG+7p1y01qEDR10Td0Gd+JAFngIHHPybx68WCuO6NDaNovkWnnTsu9HAjAccfZ0qFbbrGvBg1C3TqRiKZqSOHu999hzBib4LJ0KRx6KNx9t9U+Pe64v+y+dVsOtw4Zx/htd+OrWKGEGGJ48KKrFXylaAIB+PJL+7CXkgJpabZ29/PPoVEju+crIgeV3mWh4r1d+JKT4YMPbD1lu3YwYABceaVdDPPYuStAv1c/Yuyqx8k5dAlV3TFkue0EyCEhNoFzGp3zl+coT7P8ycaNVud55EibQ1C3rk3i27PHXnPHHBPqFopUGArA5W3rVptNmpwMCxZAjRp2AezbF04++S+7p6SnMG35V8ydE8eUtHfJqj2PqpWa8fDJH3DC0W144vNJ+5JorNvYEPYbMcybpzlj8y4enrAAQEG4IvHehpWrVrURlv79rcbuM8/AZZdZIg0RKXcKwOVlzhwLuu++azmaW7a0Xkj37lC9er5P+SbtWzqO6Ui23wMO4qvWp//xY3n6qu5Mmbc2GFwbU4vGbN3KX4JrYXmaFYArgD/+2Ff5irPPhuHDrSjC0qWWOENEQkoB+GDamx93+HD4/nuoUsUCbt++lpC+gIxBgQD8c+wMnl54A9nVLfg6Yhh4UV8eO7sHULTgqjzNFVRqKgwbBu+9Zz3fNm0sAIO95hR8RcKCAvDBsHixTagaM8YKkJ9wghVD6NEDEhMLfJr38K8PvuXJbwawve50YuPqEEs8uAAJsQl0atxp375FCa7K01yB7NhhQ8zO2T3eDz6AXr1sBn3LlqFunYjkQwG4AMWevLRnD0yYYMN9X39txRCuvNIugO3bF9jbTUlPYUbaDDavOoKRs8azue5UYqsfxrW1/82IW/qwYMOP+a7hLUpwVZ7mCmD+fHvNvf22zWBu1w6eeAKef94K3YtI2FIAzkexJi8tX273ct94w2aYNmkCgwbBDTfYDNNCPDdtMo9883c8wXq8NWtwWY3neOOBO0isVg2Atg3a5ps8oyjBVXmao1RmZm7pv2+/tUlUV1+dW33o8MND2z4RKRIF4Hwc8P5qdral50tOhv/8x4ohXHqp3dvt1KlIKfr6j5nFoLn98YnB4Osdh8Z0pdc5PfYF38IUNbgqT3MU2bEDqlWzSQL33muZqV56ySpfHXpoqFsnIsWkAJyPgu6v+pUr4fHHrRjC6tVw1FHw5JOWMWhvur4D+OL75fR59yl+q/k2VE8AHwt4HHEkBE4p1gxlBdcKYP/KV2lp8PPPtl73u+8sN7hK/4lErFIFYOdcIjAKOAmruXOT9z6lLBoWSvvfX40J5HDWirlc9+NUOi7/HvBw4YV2QbzooiJnDJq5YCU3jX6aZdXehGpxJKy8gTqJ5xOoks7umAVUDjSnUqCZZiiLyciwiXyjRsGaNZYSsndvG36uXBkaNw51C0WklErbAx4MfO69v9I5lwBULYM2hdyDFxzPi299Tdc5n9N93hc02LKOjdUS+eWG2zl+wH3W8yiiN2ZN5uHPnmV9TCpUjaFlTl/e6v0IfcYtsSAfaEalQLN9+2uGcgUWCNhkvipVbNna00/bh7wRI6BzZ7vVISJRo8QB2DlXEzgLuAHAe58JZJZNs0LEe5gxg27JyXSdMJGY7CxSGjZnZOfeJN1zI5eeVvTAuyhtA+e/cjura3wI8YCPpV/TYbza/WYAHrwgoBnKYtavhzfftEDbs6fd1ujSxSb4FePDnohEltL0gBsDG4A3nXMtgB+Au733O/bfyTnXG+gN0LBhw1L8uYNo06bcYgg//wyHHELMnXdA7960bdqU4hTwW756Ez2Hv0hKYAhU32kPOgDPB0tmcu7cC/9071YzlCuwmTMtYcaHH9q93g4doHVr2xYXp+ArEuVKXI7QOZcE/A84w3s/2zk3GNjqvR9Q0HPCqhyh9zB7tt3Lff992L3b0vT17Qt//7sNAxZDxsat9Bz2b77a/RJU2kpCejeqVmvOlkOex5ONI47DM5+hcc1WzOrf8SAdlIS9vaX/AK64AqZNsyVrffpAs2aFPlVEIs/BKke4CljlvZ8d/PlDoH8pfl/52LYN3nnHAu+8eZaH+cYb7QLYokWRf82kuRkMnDqB37bNJrDZs73W51BlE0fuuoxXLnqSBz5diQcqZz6jSVZiucCHD4dx4+z7446DIUNs7W7VqJg6ISLFVOIA7L1f65xLd84d773/GegELC67ppWxH3+0oPvOO7B9O5xyig05d+9uFYmKYdLcDO788B1WxT0KlbLhCIhZn8Qdx77H4MfPA+ClWRvI2LyLSppkVXHt3m35mIcNy80Ffu21EB9v2+vrdoNIRVbaWdB3Au8EZ0D/CtxY+iaVoZ07LSducrINN1eunFsMoXXrEq2h3Lknk1uHj2BjnZchJtse9DHUPOQEUjfkzlJVGsgKbNcuC7Y7dthrrXFjGDzYcjMXkgtcRCqWUgVg7/2PQL5j2yH100/Wux09GjZvhqZN4eWX7QK4N11fMe3JyuKu19/ijeX/JLv+b7DxRIhfCi4HRxyVA83/NLxcFpOsip2PWkInKws+/tiGmXfuhJQUy1Q1b54NNythhojkET2ZsDIzYeJE6+3OmGHDfFdcYfd2zz67RBfAlPQUpq+YzvzFmUxa/i6Z1X+hSmZrjlj9D1xiA7KyfvrT/d28w8ulyVRVrHzUEjqrVlku8L0JM44+2hJm5OTYut3jNeIhIvmL/AC8YkVuMYT1623pxnPP2cSqww4r8a+duXIW54zuSHbAcjXHBY7h/nqTef6xLkyZvzoYHHPv75b18HJR6v1KiAQCFmDj4+HTT3MTZowcaf8qYYaIFEHkBuDp0+GFF+CLL6x327Wr3W8777wiFUMoiPee5yZO4fHUPmRXsuDriOHxrjfy2NmXAOVTZago9X6lnG3caB/0RoyA+++H22+3Gs/nn681uyJSbJEbgOfOhQULrDjCzTdbYYT9FPf+qfeeV6Z+wYCvBrK1+vfEZNUntlICuBwSYhPo1PicP+1/sAshFKXer5STb7+1e7sffGC3Otq3z83FXK2agq+IlEiJE3GURJkm4ti1y4YA8ymGkPf+KdgQ8bOXN/9T0ExJT2FG2gy2/V6DEbPeY1P1WcRsPZor6gxk1J29WPTH98xIm0GHRh3yrcl7MBX1GOQgycrKXS505plW+L5XLxtlOemk0LZNRCJGYYk4IjcAF+KM56bn23usn1hlXxaqlPQUOow+h8ycPZYqcmcdulR7itF33UztxISD3sai0CzoEFi4MLe3u2iRzSNYtgyOPNKStoiIFMPByoQVtg50/3RyairdP+pFZuVg8PWOy5tdz0c33FaOrTww1fstJ3v2wIQJljBj5kyoVAmuusoSaQAce2xo2yciUanks5XCWEH3SavGbqDxI5dx6aet2ck6CMSBj8ERzw/L6zNpbkY5t1RCKic4vL9qFVx3nS0jGjTIfn7rLQjX4iEiEhWisgecNwvV7j1r+GPXJDKP/BR216Ta0vupmXgWvtbSfet4CRynJT4VQU6OzZwfNgwSEqzn26QJfPcdtGpVqhn0IiLFEZUBeG8QfWDSKFZsf59AzZ+galWa//EIo/vczxVjUvAAefI0a4lPFFu/PncJUVoaHHGEJWnx3paxJYVfQjcRiW5RGYB/WrOSh6fcwXI3BWqAI47hHT+gT6fOgJb4VBje21dMjAXegQOt5u6gQdCtW+4sZxGREIiq8bZfN6ym/bN30Gz4sfyU/RnBLBrExHg2Jczbt9+DFxxPlfg/ZytSoYQosm2bpSRt0cKGmAFuu81mNX/1ldV7VvAVkRCLigCcsXk9571wP02GNGHmrhHUW38Dz7YaT5X4ysS6WBJiE+jQqMO+/bu1rM+zlzenfmIVHLY8Setro8DChdCvn5X5u+02Swm5t9ZunTpwwgmhbZ+IyH4ich3wpLkZDJw6gd92zMLv2MX26tPwsbuou6Yn/+42kOs6W5aivYk2QpFIQ8rJ3nu43kOzZnZ/9+qrLQCffrqqEIlISEXVOuBJczO4Z8IH/BbzEMRnQyK4VR3oe9L/MeyJtn+63rZt0FaBN1qtXGnFDyZMgNRU6+m+/TY0amS9XRGRMBdxAfiFL35mi/8RXE4wiUYMNQ9vyPzdu9TZiXaBAHz5pS0h+uQT6/VefDH8/rsFYM1kFpEIEnEBePXmXVSOaY4jHu+zccRRxTfXEqKKYM4cuPBCqFsX/vEPq7vbqFGoWyUiUiIRF4BtCVEzDs98Zl8SjUqBZlpCFI2+/956uzVqwJAhcOqpMGWKlZysVCnUrRMRKZWImwW9dwlRpUAzamVfRaVAMy0hiiY7d1rCjKQkOO00GD8+d8mQc9Cli4KviESFiOsB710qpCpBUWrAAHjpJVsy9Oqr0LMn1KwZ6laJiJS5iFyGJFEiO9smUw0bBo89BmedBStWQHq6Fb3XrDoRiXBRtQxJosC6dTBqlKWHTE+Ho46ymcwAf/ubfYmIRDkFYClfgYBNpsrIsMlUQ4bYfd04vRRFpGLRVU8Orm3bLEHGJ5/A5MmWHnLECDjmGDheE+dEpOJSAJaDY9EiGD7cCttv2wYtW8LatZan+eKLQ906EZGQUwCWsvfNNzahKiHB8jLffrvyMouI5KEALKWXkWF5mRMT4d57oV07GDwYune3rFUiIvIXCsBSMt5bbd1hw2DSJJtc1auXbYuNhbvuCm37RETCXMRlwpIwce+90KmTBeH77oNly2D06FC3SkQkYqgHLEWzYAEMHQr33ANNm0KPHjax6qqroIrycIuIFJcCsBQsM9Pq7Q4dCjNnQuXKlqGqaVPL1azyfyIiJaYALPnLzrZAu2IFNG4ML7wAN94ItWuHumUiIlFBAViM9zB9OnzxBQwaZJmp7rsPmjSBCy6AGE0XEBEpS6UOwM65WCAVyPDedyl9k6RcbdkCY8bYbOaff7Ye7j33QL16cMcdoW6diEjUKotuzd3AkjL4PVLeZs2yzFR33w21alkgXrXKgq+IiBxUpQrAzrmjgIuBUWXTHDmoMjPh/fdh4kT7uWVLq7ebmgqzZ9s63sqVQ9tGEZEKorRD0C8DDwE1CtrBOdcb6A3QsGHDUv45KZGMDCuA8Nprlo/5wgvhssugalXL1ywiIuWuxD1g51wXYL33/ofC9vPej/TeJ3nvk+oqLWH5e+opOPpoePppKwP42Wfw6aehbpWISIVXmiHoM4Cuzrk04D2go3Pu7TJplZTc1q22bnfdOvu5ZUvLWvXLL1YS8KKLNKNZRCQMlHgI2nv/MPAwgHOuA/CA975HGbVLimvxYgu8b70F27fbMqI+feCSS+xLRETCitYBR7qsLOvVTpuWW/6vXz847bRQt0xERApRJgHYez8DmFEWv0uKYO1aS5px7bUQHw/HHQfnngs336zyfyIiEUI94Ejhva3bHToUPvoIcnKgY0c44ghLoiEiIhFFs3Eiwdy5cMopVghh6lQbYl6yxIKviIhEJPWAw9WyZbBtG7RqZZmpEhJsLe9110G1aqFunYiIlJICcDjJybF1ukOHWlGEDh2s4P3hh8P334e6dSIiUoY0BB0uxoyBY46Brl1hwQJ48kl4991Qt0pERA4S9YBDKTUVmjWzIeVt2yxj1aBB0K2bzW4WEZGopR5weduzB95+G9q0gdat4Z137PF+/WDGDPj73xV8RUQqAAXg8pKdDY89Bg0aWAWiP/6AIUMscQaAc6Ftn4iIlCsNQR9M3luR+6ZNLTXk9OnQrp31djt1Uk5mEZEKTAH4YNi2zXIyv/oqpKVZkfvatW2IOSEh1K0TEZEwoC5YWUpPhzvvhPr14Y47oEYNSE6G6tVtu4KviIgEqQdcWtnZsHkz1KkDO3ZY0XsVRBARkQNQAC6pDRvg9ddh+HALtOPH273edeugVq1Qt05ERMKcAnBxzZkDgwfDe+9BZqYVROjZM3e7gq+IiBSBAnBR7N5ta3NjY2HSJJgwAW691YaZmzULdetERCQCaRJWYdLT4dFHoWFD+OQTe+y++yAjw2Y4K/iKiEgJqQecl/dWAOHVV+Hjj+2xSy6xmc0AiYmha5uIiEQNBeC9AgFLjBEIwC23wNat8NBD0Lev5WgWEREpQwrAP/9s5f8++wwWLoTKlW24uXFj+15EROQgqJgBeG/d3Ve5j19fAAAHEUlEQVRegS+/tAlWV10FW7ZY0D3hhFC3UEREolzFDMCzZ1vd3fr14amnoHdvK3ovIiJSTipGAJ43zyZV1aoFL74IbdvCp5/Ceeep9J+IiIRE9C5DysqC99+H9u3hlFPg3XdthjNY6b/OnRV8RUQkZKI3APfvD9dcA2vWwEsvWUWif/0r1K0SEREBoiUAew8pKXDddXZ/F6BPH5vNvHQp3HsvHHJIaNsoIiKyn8gOwLt3w+jRkJRkhe4/+QR++cW2HXccXHyxit6LiEhYitxJWN5DixbWwz3xRKtK1KNHbu1dERGRMBa5Adg5GDDAlhJ16GA/i4iIRIjIDcBgPV4REZEIpBukIiIiIaAALCIiEgIKwCIiIiGgACwiIhICJQ7AzrkGzrmvnHNLnHOLnHN3l2XDREREollpZkFnA/d77+c452oAPzjnvvTeLy6jtomIiEStEveAvfdrvPdzgt9vA5YA9cuqYSIiItGsTO4BO+caAS2B2fls6+2cS3XOpW7YsKEs/pyIiEjEK3UAds5VBz4C7vHeb8273Xs/0nuf5L1Pqlu3bmn/nIiISFQoVQB2zsVjwfcd7/2EsmmSiIhI9CvNLGgHvA4s8d6/VHZNEhERiX6l6QGfAfQEOjrnfgx+dS6jdomIiES1Ei9D8t7PBFSCSEREpASc9778/phzG4DfyvBX1gE2luHvCyUdS/iJluMAHUu4ipZjiZbjgLI/lqO99/nOQC7XAFzWnHOp3vukULejLOhYwk+0HAfoWMJVtBxLtBwHlO+xKBe0iIhICCgAi4iIhECkB+CRoW5AGdKxhJ9oOQ7QsYSraDmWaDkOKMdjieh7wCIiIpEq0nvAIiIiESkiArBz7kLn3M/OuV+cc/3z2e6cc0OC2+c751qFop0HUpQays65Ds65LfslNxkYirYWhXMuzTm3INjO1Hy2h/15cc4dv9//9Y/Oua3OuXvy7BO258Q594Zzbr1zbuF+jx3qnPvSObcs+O8hBTy30PdVeSvgWF5wzv0UfP1MdM4lFvDcQl+L5a2AY3nCOZdxoMRF4XReCjiO9/c7hjTn3I8FPDfczkm+19+Qvl+892H9BcQCy4HGQAIwDzghzz6dgalYYpA2wOxQt7uAYzkSaBX8vgawNJ9j6QB8Euq2FvF40oA6hWyPiPOyX3tjgbXYur2IOCfAWUArYOF+jw0C+ge/7w88X8CxFvq+CpNjOR+IC37/fH7HEtxW6GsxTI7lCeCBAzwvrM5LfseRZ/u/gIERck7yvf6G8v0SCT3g04BfvPe/eu8zgfeAS/Pscynwljf/AxKdc0eWd0MPxFe8GsoRcV720wlY7r0vy2QxB5X3/mtgU56HLwXGBL8fA3TL56lFeV+Vq/yOxXv/H+99dvDH/wFHlXvDSqCA81IUYXVeCjuOYD2Aq4Bx5dqoEirk+huy90skBOD6QPp+P6/ir0GrKPuEFVdIDWWgrXNunnNuqnPuxHJtWPF44D/OuR+cc73z2R5p5+UaCr6YRMo5ATjce78G7KIDHJbPPpF2bgBuwkZU8nOg12K4uCM4nP5GAUOdkXRe2gPrvPfLCtgetuckz/U3ZO+XSAjA+eWbzjt1uyj7hA1XeA3lOdgQaAvgFWBSebevGM7w3rcCLgL6OefOyrM9Ys6Lcy4B6AqMz2dzJJ2TooqYcwPgnHsUyAbeKWCXA70Ww8FwoAlwCrAGG77NK5LOS3cK7/2G5Tk5wPW3wKfl81ipz0skBOBVQIP9fj4KWF2CfcKCO0ANZe/9Vu/99uD3nwHxzrk65dzMIvHerw7+ux6YiA3T7C9izgt2kZjjvV+Xd0MknZOgdXuH+oP/rs9nn4g5N86564EuwHU+eEMuryK8FkPOe7/Oe5/jvQ8Ar5F/GyPivDjn4oDLgfcL2iccz0kB19+QvV8iIQB/DxzrnPtbsJdyDTA5zz6TgV7BWbdtgC17hxTCSfCeSaE1lJ1zRwT3wzl3GnaOfi+/VhaNc66ac67G3u+xyTIL8+wWEeclqMBP85FyTvYzGbg++P31wMf57FOU91XIOecuBP4BdPXe7yxgn6K8FkMuz/yHy8i/jRFxXoBzgZ+896vy2xiO56SQ62/o3i+hnplWlC9sNu1SbBbao8HH+gJ9g987YGhw+wIgKdRtLuA4zsSGLeYDPwa/Ouc5ljuARdgsu/8B7ULd7gKOpXGwjfOC7Y3k81IVC6i19nssIs4J9qFhDZCFfUq/GagNTAOWBf89NLhvPeCz/Z77l/dVGB7LL9i9t73vl+S8x1LQazEMj2Vs8H0wH7t4Hxnu5yW/4wg+Pnrv+2O/fcP9nBR0/Q3Z+0WZsEREREIgEoagRUREoo4CsIiISAgoAIuIiISAArCIiEgIKACLiIiEgAKwiIhICCgAi4iIhIACsIiISAj8P+xrw9ReWPpRAAAAAElFTkSuQmCC\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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
