{
 "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:                Sun, 16 Aug 2020                                         \n",
      "Time:                        18:00:44                                         \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": [
      "[ 5.10536296  0.50471967 -0.01094475]\n",
      "[0.46491098 0.07177598 0.00635107]\n",
      "[ 4.83174413  5.08060125  5.32581165  5.56737531  5.80529224  6.03956244\n",
      "  6.2701859   6.49716264  6.72049264  6.94017591  7.15621245  7.36860226\n",
      "  7.57734534  7.78244169  7.9838913   8.18169418  8.37585033  8.56635975\n",
      "  8.75322244  8.9364384   9.11600762  9.29193011  9.46420588  9.6328349\n",
      "  9.7978172   9.95915277 10.1168416  10.27088371 10.42127908 10.56802772\n",
      " 10.71112963 10.8505848  10.98639325 11.11855496 11.24706995 11.3719382\n",
      " 11.49315971 11.6107345  11.72466256 11.83494388 11.94157847 12.04456633\n",
      " 12.14390746 12.23960186 12.33164953 12.42005046 12.50480467 12.58591214\n",
      " 12.66337288 12.73718688]\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": [
      "[ 5.05151558e+00  4.88800321e-01 -6.26818270e-04]\n",
      "[0.16126063 0.02489646 0.00220295]\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 0x7fbe37a8fe20>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Nv0oppZSKW3fvwi+/SODdtAn8/xptW6SIhNzu3aXfrh4Yt4t/1uMGBsLQodK94cYNKF9eanubN498PxJVNx7dYKrvVEbtGkWoLRSAUGsoWy5u0fCrlFJKqWTi5k05nFawoOzanj0rdbsZM0oPrFq1oHZtiGghmi2bfderAOnLO26ctEZ++BDq1YNPPpH3J9Gd6nzo+iHG7xnP/CPzCbWGUjl7ZQ5cO0C4LRxnizM1cteIh1cQMxp+lVJKKRU9Viv89pv0t9q0CY5In1j69JHwW7asHGIrXhx0Amqic+qUTGKbO1faJrdtCwMHRr/axGqzsvbMWsbtHsfmi5txd3Ln/TLv07NiTwplLKQ1v0oppZRKokJCpNfu3bvQooUE2i5dZLxX1aoyRa1WLQm9IL2wSpa075rVv+zZIwfXVq2SGt7334d+/aT0Ojoehjzkp4M/MWHPBM7dO0fOtDkZUWcE75d9n3Ru6Z4+r3KOyokq9EbQ8AtYLBZKlChBeHg4efLkYe7cuXh6enLx4kUaN27M0aNHn3l+586dWbJkCTdu3MDDwwOAXr16MWHCBG7dukXGjBnt8TKUUkqpuHPsmHRk+PNP2L4dnjyBPHkk/BqGlDnkyQOurvZeqfoPpgnr10vo3boV0qWDzz6Djz+Ofpvk5ceXM3b3WPyu+/Ek7AlVclRhWJ1hNC/cHEeHpBMp9VoE4ObmxsGDBzl69Cjp06dn0qRJL/2c/Pnzs3r1agBsNhubN2/GyytxNnNWSimlXur8eZg1C2w2+Xj8eGnqevkyvPeebBceOBD5/CJFNPgmYuHhMhOkTBlo2FDKsMeMgUuXYPDgqAdf0zTZdmkbr/38Gq2XtmbnlZ2EhIcws8lMdry7g9ZFWyep4AtJNPz6XPFh6Pah+FzxifOvXblyZfwjTqX+h/bt27N48WIAtmzZQpUqVXB0TFr/85VSSqVgDx5IM9cPP5SDaPnySciNuNr5v/9Jl4bjx2HCBOnB6+lp1yWrl3vyBCZOlDZlb70FoaHw00/y3qZPH/jrgvVLhYSHMOfQHMpNL8drP7+Gr78vBpGn4G4+vhlPryD+Jaq01nt9bw5eP/ifz7kfcp/DNw5jM204GA6UzFyStC4v7rhcOktpxtUfF6Xvb7Va2bhxI++9995Ln1ugQAFWr17NvXv3WLhwIW+//Tbr1q2L0vdRSimlElxoqNTt5solt23boFUrSUM1a0oyqlMHCv017CB3brsuV0XPnTswaRL88APcvg2vviqb940bR+/M4c3HN5nqO5XJ+yZz4/ENimYqyvTG08mfPj+NFjQi1Bqa6Lo3RFeiCr9RcT/4PjZTLsnYTBv3g+//Z/iNiqCgIEqXLs3FixcpV64cr7/+epQ+r2XLlixatIg9e/Ywbdq0WK1BKaWUilOmCSdOwB9/yG3LFnj8GL79Fr74QgLv9u1QsSI4Odl7tcnWKj//5w6UiCuXL0s5w4wZsuvbuLG0K6taNXpf5/CNw4zfLa3KQqwhNMjfgD6V+lAnbx2Mv/qebey4MVF2b4iuRBV+o7JD63PFh9pzaj995zG/5fxY/w+IqPm9f/8+jRs3ZtKkSfTs2fOln9euXTvKli1Lp06dcNBWLkoppeztzh1p3lqihHRo8PaGoCC5Bt6pE7z+uoRegFSpop+QVLSs8vN/ZpSwf2AQg1ZIW7jYBuCjR2HECFi4UD5u317alRUvHrXP97niw+aLm3FycGL9ufVsurAJdyd33i3zLj0r9qRwxsL/+pzE2r0huhJV+I2Kyjkqx9s7j7Rp0zJhwgSaNWtGt27dXvr8nDlz8t1331GnTp04W4NSSikVZWFhUsqwYQP8/jv4+kK5crBvnxxGW7YMihXTSWp2MnLDqafBN0JQmJWRG07FOPzu2CGdG9asAXd3GZbXty/kzBn1r7Hx/EYazG9AmC0MgEzumRheZzjvl32f9G7pY7SupCTJhV+I33ceZcqUoVSpUixatIhq1apx6tQpsmfP/vTxsWPHPvP8Dz74IF7WoZRSSj3X5cuRSadDB1i8WGbQVqoEX38N9etHPrdhQ7ssUYmAwKBo3f8iNpuE3eHDYdcuyJABvvlGgm+GDLLD3H7By0srLgZeZOLeiUzcO/Fp8HXAgZ4VezKwysDov8AkKkmG37j26NGjZz7+9ddfn/4+LCzsX89v06bNc7/OxYsX43RdSimlFI8eSU/d9etlh/fcObh6Fby8oFs3Gc9Vq5Z2YkiEsnm64f+coJvN0y1Knx8aKmUNI0ZI041cueRA27vvyq4vvLy0wjRNdl3ZxdjdY1l5ciUGBjVy12DH5R1PRw/XzlM7bl5wEqHhVymllEpMTFPGBzs6wtq10LKlpCB3d6nX7dUL3P4KT6+9Zt+1qv80oF6hZ4IpgJuThQH1Cv3n5z16JAfYxoyR9zklSsC8efI+559nE19UWjF8/VGeOG5l7O6x+Ab4ks41HQNeHUD38t3JkTZHoh09nBA0/CqllFL2dv8+bNwoE9XWr4fPP4cPPpAJBb16SSlDlSoyk1YlGRGlB1Ht9nDzpuzsTpoE9+7Je5vp0+V/v2E891P+VUJh5T6PHDdwNWQNb624S6EMhZjSaAodSnYglXOqp89LLofXYkLDr1JKKWUvoaFQt66cYrJaIU0a6ciQN688ni2bXPNWSVbzMl4vPdx2/jyMHi0D9kJCoHlz6dxQqdLLv35EacUjhy08dFxNqMMFMMLxNLxZ0H4e9fLXw8HQjlR/99LwaxjGLKAxcNM0zeL/eKw/MBLIZJrm7ZguwjTNpz3kkiPTNO29BKWUUvZ2/7702/3tN/l41ixwdoYcOaQxa/36kna0526KcfCgHGJbskTOLHbsKBOlC/13VcRTNtNG7TIBjNw1mGCH02ACOJA1fCCTW/akQYG46yecnERl5/dnYCIw5+93GoaRA3gduBybBbi6unLnzh0yZMiQLAOwaZrcuXMHV51/rpRSKdOCBVLAuWMHhIfLwbQWLSIfnzvXbktTCc805fzi8OHSnc7DQ1qV9e4tZxij4knYE+Yemsu4PeM4efskrk6pwWqAIZtttUs4xOkgjeTmpeHXNM1thmHkfs5DY4GBwOrYLCB79uxcvXqVW7duxebLJGqurq7PtEtTSimVTD15Islm3TopV3B3hzNn4O5d2dJr2FB2dx216jClsVph1SoJvfv2QebM8P330rAjqo06/B/4M3HvRKYfmM7doLuUy1qOeS3mkSNtDurPq/90ANhHlZvG50tJ8mL0t88wjKaAv2mah2K7W+vk5ESePHli9TWUUkopu7l1CxYtknKGzZulaDNVKpmoVr68jBL+6it7r1LZSXCwbO6PHCnvg/Llg6lT5Y9HVC8K7/Xfy7jd41h6fCk200aLwi3oXak3VXJUSXajhxNCtMOvYRjuwGdA3Sg+vyvQFWQimlJKKZWkhYeDjw+kSyezZK9cgZ49oWBB2cZr1AiqVYvszOCgh41Sovv3JeSOGwfXr0PZsjKPpFUrqe/9Lz5XfNh0YRMAv539jV1XdpHGJQ09K/SkR4Ue5En3703DlNy9IbpisvObD8gDROz6ZgcOGIZRwTTN6/98smma04HpAN7e3nrySymlVNJz754MmFizRkoa7t6FLl2kD1WZMrKllz+/vVepommVn3+U25BF1bVrEninToUHD6BOHdn5rV37xe3K/u73c7/TeEHjpxPYsnlkY3z98bxT+h08XDxitTYloh1+TdM8ArwS8bFhGBcB79h0e1BKKaUSndu3IWNGOaFUtixcvCgfN24MTZpISzKQRKPBN8l52WS06Dp9Wkob5syRiwOtW0u7snLlovb5Z+6cYcKeCUzbPy1y9LDhwEfeH9GzYs9or0e9WFRanS0EagAZDcO4CnxlmuaP8b0wpZRSKkGFh0tHhl9/ldujRzJey8EBxo6VE0oVKrz8mrVKEl40GW3khlPRCr/79skhthUrpHPdu+9Cv35Rez9kmiZbLm5h7O6xrDm9BkcHR+rkrcOmC5uejh6uladWdF+aeomodHto/5LHc8fZapRSSil7mDUL+veX8gZnZ6hVS3Z3w8Pl4+bN7b1CFcf+ORntZff/nWlKm7Lhw+WMo6cnDBokpd+ZM7/8eweHB7Po6CLG7R7HoRuHyOiekc+rf85H5T8iS+osKXr0cELQXitKKaVSlitXZGf3l1+k11TZspArl4Tdpk2hXj1Indreq1TxLGIy2vPuf5HwcFi6VLrYHTwofXlHjYKuXaVf74tEhNmSmUviG+DLZN/J3Hx8k+KvFGdmk5m8VfItXB0jWz/o4bX4peFXKaVU8nf/vpxC+uUXOHBA7itQQNqUgZxGql3bbstTCW9AvULP1PwCuDlZGFDv3+PVnjyBn36SEcQXLkDhwnKx4K235MLAf/G54kPN2TUJtYZiygg2GhZoSJ9Kfaidp3ayHPCV2Gn4VUoplfyEhcH27dJzt0EDSSijRkHJknKtumlTSTAqxYqo6/2vbg9378LkyTBhgrxPqlQJxoyRPz4v62BnM22sPb2W3ht6E2INAcDAoHel3oypNybeXpd6OQ2/SimlkofHj6UQc+VKaUl27x5UrCjh180NAgL++9q0SnGal/F67uG2K1fkjOP06fLHqmFD+OQTad/8so3aR6GPmH1wNuP3jOfM3TNkdM+Ik4MTNtOGs8WZNkXbxNOrUVGl4VcppVTSdf8+pE0rv+/QQYJvunRSv9u8OdT92zwmDb7qJY4fl3re+fPlUFv79tKurESJl3/ulftX+GHvD8w4MIPA4EAqeFVgYauFtCrSCt8AXz3AlogYpplwcye8vb1NX1/fBPt+SimlkqFLl2DVKrnt2CFFmNmzy9S1oCDZnnNysvcqVRKya5dUw/zyi1wkeP996NsXcud++efuvrqbcbvHsez4MkxMWhVpRZ9KfaiUvZLW89qZYRj7TdP0/uf9uvOrlFIqafDzk1QScWCtWDH49FNw/OtHWWXdUVNRZ7PBb79J6N2xA9Knh6++gh49ZJbJf9l+eTuT903myI0jHLt1jLQuaelTqQ89KvQgl2euhHkBKsY0/CqllEp8TBMOHZLJAWXKQIsWkDUruLjIdenmzaVbg7KL+BgLnFDCwmDhQvljdOwY5MwJ48fDe+9BqlT//bmBwYF8vvFzJvtOxsTEwKBvpb58XeNrHT2chGj4VUoplXjs2QPLl8vt/Hk5Ut+/v4TfLFnk+rSyq7geC5xQHj+GmTOlW8Ply1C8OMydC2+88fIqmTN3zjB+z3h+Pvgzj8MeP73fwXAgo3tGDb5JzEsadSillFLxyGqFo0cjP+7RQ/rxFiwIM2bAtWtyXVolGv81Fjgxun1byhly5oTevWWeydq1cPgwvP32i4OvaZpsvrCZpgubUmhiIWYcmEHroq35udnPuDm6YTEsOFucqZG7RkK+HBUHdOdXKaVUwgoPhy1bZFTWypXw8KE0UU2dGn7+WcZmeXraeZHqRWIzFjghXbwoQyl+/FHOQTZrJu3KXlYaHhIewsKjC5+OHs7knokvqn9Bt/LdyJI6CwAFMxTU7g1JmIZfpZRSCWf1aimuvHNHCiwbN4bWrSO334oVs+/61EvFZCxwQjp8WOp5Fy2Sqpm334YBA6BIkec//+no4Swl8fWPHD1cLFOx544eBh0/nNRp+FVKKRU/wsJg0ybZ4W3XDurUgfz5pfdumzZQv770lVJJSnTGAicU04Rt26RCZt06uYjQu7fcsmd/8ef5XPGh1uxahFhDdPRwCqLhVymlVNyx2WTK2tKl0of37l0ZLlG+vITfYsVgwQJ7r1LFQlTGAicUm00uJgwfLmclM2WCIUPgo49k1skLP8+0se7MOnqt70WwNRjQ0cMpiYZfpZRSsRMWBufOQeHCMvu1a1eZvNa0qezw1q0Lrq4v/zoqyXjRWOCEEhIC8+bByJFw6hTkzQuTJ0Pnzv99MeFx6GPmHJrD+D3jOXXnlI4eTqE0/CqllIo+q1WuMy9eDMuWgcUC/v4ycGL9esiXT3ryKhWHHjyA6dNh7FgICJAW0IsWQatWkbNOnsf/gT8T905k2v5p3Au+h3c2b+a3nE+bom109HAKpOFXKaVU9CxaBH36wPXr4O4uO7xvvBH5eNGi9lubSpZu3JBBFJMny0WF2rWlMUidOnKx4UV8A3wZu3ssS44twWbaaF64OX0q9aFKjipP63n18FrKo+FXKaXUi5km7NsnO7wdO0KpUjJs4tVXJfA2avTysVhKxcAqP3++nX+ZMxuz8fhodrA60KqVwSefgLf3iz9vx+UdTPWdypGbRzh84zAezh58XOFjPq7wMXnS5Um4F6ASLQ2/SimlnmWacOSIzIBdvBguXJBWZMWKSfitUUNuSsWT0fNv8s13Djw8WQkcbKQufpVXqlzirffz4f2CWuMHIQ/4cvOXTNgz4eno4V4Ve/FtzW9J45ImgV+BSsw0/CqllBKPH8subnAwVKkikwHq1IEvvoDmzf/7+LxSsWSasHEjDBsGGze+guEcRpqK50hT7iKW1CFYkQ4T/zxod+HeBSbsmcCPfj/yMPTh0/sdDAcyp8qswVf9i4ZfpZRKya5dgyVLZJf38WPZ8XVzk8lrpUpJ7yil4pHVCsuXS7uyAwcga1ZIV+MEqUtfxsEl/JnnRkyRM02TXVd2MXb3WFaeXImD4UDbYm2pnac2PX7rQag1VEcPqxfS8KuUUinRH39I2ti8WZqlli4NHTrI6GFHR9nxVSoeBQfLobVRo6RTXsGCMGOG/DGsNfYa/oHh//qcLGmdWHhkIWN3j2VfwD7SuaZj4KsD6V6hO9nTyDSLIhmLaPcG9Z80/CqlVErw5An8+itUry5bazduwKVL8Nln0L79i2e/KhXHAgNhyhQYNw5u3oQKFWQccbNm0jEPIqfIBVqPEuxwBCdbfnC8wBmH9by54hoFMxRkcsPJdCzVkVTOzx641O4N6mU0/CqlVHJltcrO7rx5cl350SOYMAE+/lgC71tv/XefKKXikL+/BN5p0+DhQ6hXDz75RM5O/vOPYfMyXpy8u5//7fgM0wyFvx6vnbU2fSrNoEGBBjgYDgn9ElQyoeFXKaWSo6AgKFQIrlyBNGmgbVsJu6+9Jo9HbLEpFc9OnpRJbHPnyvuxN96AgQOl0uZ5TNNk88XNzD75CSYSfA0MPq7wMeMbjE/QtavkScOvUkolB5cvw4IFEnYnTZJDa+++K+3JGjf+75mvSsWD3bulrHz1ahn217Ur9OsHeV7QajckPISFRxcybvc4Dt04hKeLJ44OjpimibPFmXbF2yXsC1DJloZfpZRKqu7dk9HC8+bJqGGQmt6wMOnL+/XXdl2eSnlMU6ZbDx8OW7dKd7zPP5dKmxc1Drn1+BZTfKcwed9kbjy+QbFMxZjZZCZvlXwLv2t+enhNxTkNv0oplZSEhsqvzs4wc6ZcPy5UCIYMgTfffPG2mlLxKDxc5qGMGAGHD0P27DBmDHTpAqlTP/9zjt08xrjd45h7eC4h1hAa5G9An0p9qJO3jo4eVvFKw69SSiV2pgn798OcOdKPd9w4qd/t3Blq1YKyZfXgmrKLJ09g1ixpV3bpEhQtKu3L2reX92f/tOvyLmYcmMHx28fZ678XV0dXOpfuTK+KvSiSSTuOqISh4VcppRKr8HBJFXPmwIkTUjjZrBnkyyePZ8qkQyiUXdy5I6XlP/wAt2/LQMAffoBGjcDhOU0YgsKC+Hrr14zcORITE4CuZbvyXe3vyOieMYFXr+KdacL163DsmLT2aNHC3it6hoZfpZRKTB49gkOHJE1YLDB/PqRPL/2h2rYFT097r1ClYJcvSznDjBmy69u4sbQrq1r1+c+//ug6k/ZOYur+qdx+cvvp/RbDQm7P3Bp8k4ObNyXkRtyOHpVf792Tx728NPwqpZT6B5tN+vHOmSP9eA1Ddk1SpZIj86lSvfxrKBWPjh6Vet6FC+XjN9+EAQOgePHnP//g9YOM3T2WhUcWEm4Lp0mhJtTNW5cBfwzQ0cNJ1b17Mv787wH32DHZ+o/g6SkdZtq0kV8jbomMhl+llLKn336Dbt1kSy1NGkkVHTuCu7s8rsFX2dGOHTBsGKxdK38Ue/SAPn0gZ85/P9dm2lh7ei1jd49l88XNpHJKxQflPqBnxZ4UyFAAgLJZy2r3hsQuJESaMx85IrfDh+VXf//I56RJI6G2efNnQ27WrEni/IGGX6WUSkiPHsHSpVCqlBxUy5ZNRgsPHy71vNqPV9mZzQZr1sgfyV27IGNG+OYb6N4dMmSIfJ7PFR+2XNxCRa+KnLh9gvF7xnPm7hmyp8nO8DrD6VK2C+nc0j3ztbV7QyJimvKmOyLcRtxOnZLzBiCnFosUgZo1oWRJKFFCtvu9vJJEyH0RDb9KKRXfbDbYvh1++kn68j5+DP37S/gtXVoaoyplZ6GhMidl5Eg4fhxy55ZDbO++G3khIoLPFR9qzalFSHjI0wNsFbwqsLDVQloVaYWTxSnhX4B6saAgKVE4dEhuBw9K6L1/P/I5uXJJwG3WTEJuyZJQoID0DE9mNPwqpVR8q1JFanc9PKQH1DvvQGXd/VKJw8OHcoBt7Fi4elUyz/z5cr7S8TkpwTfAl25ruxEcHvz0vg/KfcCURlOe9udVdnT9+rMh99Ah2c21WuXxVKnkf3L79nIFqmRJ2c1Nk8auy05IGn6VUiouBQXBihVSJDlvnvR9eucduWbcsuW/t9CUspObN2HCBJg8Wc4yvfYaTJ8O9ev/+4q21Wbll1O/MHb3WLZf3o67o/szo4c7leqkwTeh2Wxw/jwcOAB+fvLroUNw40bkc3LmlIDbsqX8Wro05M37/H50KYiGX6WUii3TlB88P/4o143v35dJa1evyg+frl3tvUKlnjp/XtpH//STnG1q3lzalVWs+O/nPgx5yE8Hf2L8nvGcv3ee3J65GVN3DO+VfY9jN4/p4bWEEh4uvb4jQq6fn9wePpTHnZzkwFnDhhJyI3Z006e377oTKQ2/SikVW5s2QZ064OoKrVrBe+/JNloK311RiYufnxxiW7pUWkh37CjtygoV+vdzL9+/zA97fmDGgRncD7nPqzleZXid4TQv3BxHB4kOengtnoSEyMGz/fsjw+6RIxD8V5mJm5vs4HboIOcGypSR4OviYtdlJyUafpVSKjpsNti4UXZ5ixWDL76IvF7cpo0OoVCJwio/f0ZuOIX/vSBS382G09EiHNztiocH9OsHvXtLo5G/87niw9zDczl95zRbLm4BoHXR1vSp1IeK2Z+zLaxiLzRUeubu3w++vnI7cgTCwuRxT08Jt927y69ly0LBgvLuRcWYhl+llIqKy5flOvFPP8GlS5AuXWSHf0dH6NLFvutT6i+r/Pz5dNkR7hzLxIM9ZQm97oklVQhvf3yfH75N+6/3Z+G2cDot/YwFJ0fCX50bqns1Z26b8eRM+5yGvipmwsKk44Kvb2TYPXxYAjBI0C1XDvr2lV/LlZPyKa2ljnMafpVS6kXCwyOPu/fvL23K6tSRrv/Nm0uZg1KJSHAw9Bv8kMtbqhJ+LzWOno9JX+8IqYtf5XxGFzw9az197oOQB/x44EeGbh/DraCrknsNwHTgxGVPDpy3kLOM3V5K0mazwZkzsHcv7Nsnvx48KCUNAGnTSrjt1Qu8veX3efNq0E0gGn6VUuqfTp+GmTNh9mzYuhUKF4YhQ2S+a+7c9l6dikcR5QIBgUFk83RjQL1CNC/jZe9lvdT9+zBlCowfD9evF8Y5SyAZm+3HveB1jL9KzwMCgwC4GHiRCXsmMPPATB6GPiSNUQLP0Nrcd1qIaYZj4IglvBgjN5xKEq89UQgIkIAbEXb37YvsoZsqlQTcHj3kV29v7bhgZxp+lVIKZEdm+XKp3d26VWrqmjSJ7I1ZsKB916fi3So/fwatOEJQmPw/9w8MYtCKIwCJNgReuwbjxsHUqfDgAbz+OqRv5MejDAH/2kT0SHOeNkvbsOLEChwMB9oWa0ufSn1oM+EGJuBqFifY4QiuthK42Io8DcvqHx48iNzNjQi7EaN/HR2ly0K7dlChgtyKFNEa3URGw69SKmV79AhSp4YnT6RLQ7Zs8P330LmzzKlXKcbIDaeeBt8IQWHWRLkDevq0TGKbM0eqc9q0gYED5TzUKr9XGLTiBoHWowQ5HAZshDj6cinsFFfOezLg1QH0qNCD7GmyA5DNcxP+gUG42IrgYivy9Htk89RR21it0mJs9+7I2/Hj0t4QZALaa69FBt3SpXVEeRKg4VcplfI8fgxLlshYq/Bw2b1Jl04OoRQurJcjU6gX7XQmph3QvXulXdnKldLZ6r33pHtDvnyRz2lexouDN7fy7e5PMU0rGJDBNQujak6kU+lOpHZO/czXHFCv0DM73gBuThYG1HtOD7Tk7uZN2LNHQu6ePfIfPKKXbrp0UKmSjL6rWBHKl9c+ukmUhl+lVMpx8iT88INMXnvwQBqcdukiuzsWCxQtau8VKjvK5umG/3OCrr13QE0Tfv9dQu/mzdIU4H//g48/hsyZn33u+XvnmbBnAlN8p2AiwdfBcKDvqx/TvUL35379iF3tpFjrHCvh4dJtYdcu8PGRwHv+vDxmscigiA4dJOhWqiS7vHogLVnQ8KuUSt6CgiQ9uLvDjh3Sn7dNG5m6VrWq/jBTTyXUDmhUD9WFh8tAiuHDZWqtlxeMHi3v1zw8Ip9nmiY7r+xk7O6xrDq5CgfDgdp5arPl4hbCbeE4W5ypmbvmf66peRmv5B92796VgLtrl9z27JFyJ5Byp0qV4MMP5ddy5XQUeTL20vBrGMYsoDFw0zTN4n/dNxJoAoQC54B3TNMMjMd1KqVU9Jw8CdOmSceGb76RbbI334QWLSBDBnuvTiVCCbEDGpVDdU+eSDvp0aPhwgWpxJk1C956C5ydI79WmDWMZceXMXb3WPYF7COdazo+qfIJ3ct3xyuNFz5XfFLu+GHThFOnIoPurl1Suwuyq1u6tNSMvPqq3HLk0DfCKYhhRhRtv+gJhlEdeATM+Vv4rQtsMk0z3DCM4QCmaX7ysm/m7e1t+vr6xn7VSin1PKYJixfL0fetW2XefcuW0KePXLpUys6qDNv03NIKL083fu1ai0mTYMIEuH0bKleGTz6RpiN/L0MPDA5kxv4ZTNg7gasPrlIwQ0F6V+xNx1IdSeWcKgFfTSISHCxDI3bskJuPj+z0gtTlVq4cGXTLl5f2YyrZMwxjv2ma3v+8/6U7v6ZpbjMMI/c/7vv9bx/uBlrHeoVKKRVTt25BpkyyczNlCly5IoMo3nkHXnnF3qtT6qnnHZ4Lf+DK0Y25yTlEzmI2bAiffvpsVY7PFR+Wn1jOpcBLrDu7jsdhj6mZuyZTGk2hYYGGOBgp7JDmvXuym7tjB2zfLu3GIialFS4sV3giwm7BgnqIVT0jLmp+3wUWv+hBwzC6Al0BcubUMYlKqTgSHg5r1sDkybLLe/mynP5ZuhQyZtQfdipR+vuhutDbqXmwJy+Pj0u5w9tvSruyEiUin2+aJlN9p9JjXQ9spg2ABvkb8H3t7ymdpXRCL98+TFP+fkfs6u7YAUePymOOjjI0omdPebfw6qvyRlip/xCr8GsYxmdAODD/Rc8xTXM6MB2k7CE2308ppbhzRwLv9Olw9arU6n3+eWQxpO70qkRsQL1C9Bp/hVs78xB0NjOGUzjpyl1m2FeudG2U5enzIup5x+weg29AZLmgxbBQLWe15B18TVNq9rdti7xdvSqPeXhIwG3XTsJu+fJ6ME1FW4zDr2EYnZCDcLXNlxUOK6VUbJimjAr19JSem998A7Vrw8SJ0KiR7P4olYjZbPDbbzB6uBeXd3jh6BZG2iqnKVjzBv9rmZfmZST43gu6x4wDM/hh7w9cfXCVQhkK0Szfh/x6bhY2MxwTR4zQYnZ+NXHMaoUjR54Nu7duyWNZskD16lCtmoTdEiV0WpqKtRj9xDAMoz7wCfCaaZpP4nZJSin1l/v3ZYTVlCmQN6+UOeTOLTW9On1NJQFhYbBwIYwYAceOQc6cMH48vPeeE6lSFQRkbPbZu2cZv3s8Px38icdhj6mVpxZTG00l5FFJPlt5jFes+Z6OHp69xZnC6f2TbmuysDA4cCAy6O7YAYGB8liuXNCggQTe6tUhf37twqDiXFRanS0EagAZDcO4CnwFDAJcgD8M+UO52zTND+NxnUqplOToURlGMX++nACqUAHeeCPycQ2+KpF4Uc/eR49g5kwYM0beq5UoAXPnyh9jJyc5wLb5wGbSuabj9/O/s/rkahwdHHmzxJv0qdSHUllKAdIdIijMiguRo4eDbIlz5PILhYVJJ4YtW+S2c6f8vQYZNNOmTeTubq5c9lypSiGi0u2h/XPu/jEe1qKUSslCQ+WQmqMjrF4tO75vvgndusmBFqUSmef17B0w9yQLpnjw57I03LsnmW7qVNnMjNjA3H5pO3Xm1iHUKt0J0jin4X/V/kf38t3J6vHsG7ukMHL5X8LCZFR4RNjdsSMy7BYvDp07w2uvSdjNkuU/vpBS8UML5ZRS9uXvL8Mopk+XBqdt20KPHvDRR5Aunb1Xp9QLjdxw6mnwDQt04+G+vDw6nIOz4RaaN5cevZUqRT4/op73u23fPQ2+DjjQ99W+fPXaV8/9Hol15PIzwsOljGHLFpm/vGMHPHokjxUrJmG3Zk15J6CdGFQioOFXKZXwTFN6c06cCCtWyGmgRo2kIBIgbVr7rk+pKAgIDCL0pgf39+TjyYmsYECqYv6krXCelTNfe/q8c3fPMX7PeGb5zeJx2GPKZS3HkZtHsNqsOFucqZu37gu/R0KNXI4Wm03mLW/aJLft2+UgKkDRotCxI9SoIbu72n1FJUIafpVSCcdqjTyp3bUr3LwJfftKaUOePPZdm1JRZJrSWjpwZSUCT2fAcA4njfdFPLwv4JgmGC9PN0zTZMflHYzZPeZpPW/7Eu3pU6kPpbOUjvLo4YQYufxSpgmnT8PGjRJ2N2+OnJ5WqJDMXa5ZU8Ju5swJty6lYuil443jko43ViqFOnNGevOuXClH3lOlghMn5HCL9uhUSYTNJuXow4bB3r2QNr0Vp5LncC11AYtrOACuTiaNKlxi2/Wf8Q3wJb1berp5d3tuPW+iduVKZNjdtEnKk0D6ateuLbeaNcEriRy6UylSjMcbK6VUjNhssG6dlDasXy9H3Fu3lvZlqVJBkSL2XqFSURISAvPmwciRcOqUdN2bMgU6dbKw4WQqvlx3mstPduHmEsQj572MOXCNghkKMqXRFDqW6oi7UxJ4g3fnjoTcjRvldvas3J8xI9SqJWG3Vi3Il09bj6kkT8OvUip++PlB48aQLRt8+y106aInu1WS8uCBnMUcNw4CAqBMGVi8GFq1iqzeCXfx4YS1L+FO4dy3QVnPsvxcczoNCzTEwUjEI7aDg2HXLvjjD7kdOCDlDR4eUr7w0UcSeIsX11HhKtnR8KuUihunT8sur8UCY8dCuXIy0qpOHdn1VSqJuH5dBlFMmSIXKmrXhp9/lj/KhgGmabLz8i7G7B7DihMrnn6exbDQumhrGhdsbL/Fv4jNBocPS9D98085pBYUJK0FK1WCr7+WF1i+vP59Vcmehl+lVMzZbPD779KibN06cHaGd96RHSTDkOamSiURZ89KacPs2dJ2unVrGDgwss10uC2c5ceWM2b3GPb67yWdazo6lOzA0uNLCbOG4WxxpkbuGnZ9Dc+4ciVyZ3fjxsiRwUWLypWY11+XXV4PD/uuU6kEpuFXKRVzgwfLjlHWrFLa0LWrnvZWSc7+/TB8OCxbJu/fOnWC/v2hQAF5/H7wfWYemMmEvRO4fP8yBdIXYHLDyXQs1ZFUzqno5t0tSp0b4t2TJ9KGYsMGuZ08KfdnyQL16snObp06ekhNpXja7UEpFXVnz0ppQ+vWULUqnDsnx95btZLUoFQSYZpy9X/4cNkUTZNGylx79YILYdKGrGCGguy4vIOZfjN5FPqIGrlr0LdSXxoVbJQ46nlNE44ciQy727fLlrWrqwyUqFdPdneLF9dDaipF0m4PSqmYMU3p6zl2LKxdKzWCefNK+M2XT25KJRFWq+zwjhghZ7yyZpXff/CBBGCfKz7UnF2TEGsIIHW8Ef15y2Yta+fVI6ULf/whYff336VAGSTg9ughgbdaNXBLRBPglEpkNPwqpf5b3bqyRZYpE3zxBXz4oSQGpZKQoCCp5R01Si5YFCwIM2ZAhw7g4iL1vEuPraTf7/2eBl8DgwGvDmBonaH2W3h4OOzeLe0C16+P7MqQIYPs6tatKzctZVAqyjT8KqWede0azJkjRY8WC7zxBrz5JrRvL5dTlUpCAgNlvsr48TJQsEIF2elt1kz+eD8IecBknx8Zv2c8l+5fwsvDCycHJ2ymDWeLM00LNU34RV+7JkF33TrZ5Q0MlMVWriy19fXqQdmykf3WlFLRouFXKSUOHJCGposWyW5TtWrw6qvw/vv2XplS0ebvD90HPeTXxW7YQh3xLHiHwUNsfPZ+JgwDLgVeYsKeCcw4MIOHoQ+plrMa4+uPp3HBxuz135uwB9jCw8HHR8LuunVw8KDcny0btGwpXVPq1AFPz/hfi1IpgIZfpVK6GzegbVvYtk0mr334IfTsCfnz23tlSj1jlZ8/IzecIiAwiGyebgyoV4jmZZ693H/ypLQrmzPHJNyaGvfCAaSteB7nzA+Yf9mC8+ZwDtydx7LjywBoW6wtfSr1obxX+adfo3KOyvEfegMCIsPun39KQ2FHR6hSReYn168PJUvqQTWl4oGGX6VSogcP4NgxuYyaMaM0tR89Gt59V3eXVKK0ys+fQSuOEBRmBcA/MIhBK44A0LyMF7t3S+eG1aulhjejtz8OpU5jS3+AJw6HCTINrhu+fLL9OGld0tK3cl8+rvAxOdLmSJgXYLVKZ5S1a+UWsbvr5QVt2sjubu3akDZtwqxHqRRMW50plZJcugQ//CAnfZyc5Nqwi4u9V6XUS1UZtgn/wKBn7jNNSHUjO5kulGLbNkiXThoefPwxVBi9licOB7np/BVgBQMstnSkDW/DxS9H4eGSAIMd7t2Trgxr10oN7+3bUqf76qvQqBE0bKhtyJSKR9rqTKmU7PhxOSizTC718sYb0KePBl+VZAT8LfiaNoPHJ7LyYE8+wm6l4WF2GDNGhpalTg1XH1wlNPVcboavAMP61ycZpLY2prDHG/EXfE1TrqhE7O7u2iU7vhkyyM5uo0ZyWC1duvj5/kqpKNHwq1RyZbXC48fSvPTuXdl56ttXtsVyJNClXqXiSDZPN67cCuHR4Zw82JsH6wN3nDI8JH/r4xybXxRnZ9gfsJ8xv49hybEl2Gw23M2SPOEYYMXAEU+jDAPqFYrbhQUHSx/sNWsk8F66JPeXLg2ffiqBt0IF7cygVCKi4Vep5ObhQ/jpJ+ncUL++9HmqUkVKHFKlsvfqlIq2O3cg50Vv9sxxxRrkjIvXXdK/foz0he/wfctirL/wC2N8xrD10lY8nD3oWaEnH1f8mIMXnPhy3QquPPElh7s33zZo+a8DcjFy44YE3V9/lVZkjx/L3606deCzz6ScQfvuKpVoafhVKrm4ckXqeadPl5Pjr74q4RekplCDr0piLl2ScoaZM+HJkzSUrx7EnZI/cTftFjK5laBqkVA+3dmTM3fPkDNtTkbXHc37Zd8njUsaAHKXgeZlPo79QkwTjh6VsPvrr7Bnj9yXPTt07AhNmkDNmtoHW6kkQsOvUsnFkCGSElq3lnreSpXsvSKlYuTIERlEsXChvG97800YOBAepDlIrTkfERIeQmC4yfEjUMGrAotbL6ZlkZY4OsThj7SQENi6NTLwRpQzlC8P33wjgbdUKT2splQSpN0elEqKTFNqeEePhsGDpWXZ1avSLD93bnuvTqloM03Yvl3alf32m1yo6NJF3sflzAmHrh/indXv4Hfd7+nnfFDuA6Y0moIRVwH03j0pZ1i9Wro0PHwIbm5SztCkCTRurKO9lUpCtNuDUslBSAgsWCCh99gxqSu8dUsey57dvmtTKgZsNvjlFwm9u3dL2+lvv4Xu3cEznY31Z9fz7pwxbLywEVeLK44OjpimibPFmU6lOsU++F66JGF39WrZ6bVaIUsWGefdpIn03nVzi5sXq5RKFDT8KpVUmCaUKyeht2RJmDNHWpY5O9t7ZUpFW2gozJsn09hOnpQLFhMnwjvvgOEUxLzD8xi7cCwnbp/Ay8OL4XWG06VsF07ePhm70cOmKQMmIgJvxLCJokWltqJZMyltcHCIw1erlEpMNPwqlZhduCAh94sv5IfxJ5/IrlSdOlprqJKkhw/lTOaYMTLht2RJuZjRpg3cDbnJiL2TmbxvMree3KJMljLMazGPNsXa4GyRN3kxGj0cFibjuyMC7+XL8venShVJ382aQYEC8fBqlVKJkYZfpRIjX1/5obxsmYTeJk2gbFno0MHeK1MqRm7cgAkTpPNeYCDUqAE//ghpivqw5PhiFiw9xx/n/iDEGkKTgk3oW7kvr+V6LeZlDY8fS93uypXSgzcwUMoXXn8dvv5a6nczZYq7F6iUSjI0/CqVmFy7Bm+9JU3z06aF/v1lKIXW86ok6tw5GDVKWk+HhkKLFnIBo3x5kwl7JtD3577YTBsAzQs1Z1idYRTKGMNBFPfuSdBdsUKCb1AQpE8PzZvL7fXXwd09zl6bUipp0vCrlL2FhsLp01C8uOxEhYfLgbYuXcAjnsawKhXP/PzkENvSpeDoKO1w+/eH3PlCWHh0Ie9PHcORm0eePt9iWKjgVSH6wffaNVi1SnZ4N2+Wvz9eXvDee5K0q1eXBSil1F/0XwSl7OXhQ5gxA8aOlQB86ZI0yd+2zd4rUypGTBM2bZLQ+8cfMlm7f3/o1QtcPO8w1XcqE9dM5Pqj6xR/pTj/q/o/xu4eS6g1FGeLMzVy14jaNzp7VsLuypXSIsI0oWBB+WYtWoC3tx5YU0q9kIZfpRLajRswfrwUP96/L8WPAweCi4u9V6bUU6v8/Bm54RQBgUFk83RjQL1CLxwNbLVKpcGIEVKuniULDBsGH34IN8PP8N3ucfx08CeCwoOol68es5vP5vW8r2MYBo0LNo5a94bjx2H5cqmDP3xY7itbVvqitWwJRYroIVClVJRo+FUqodhssht1/LhsjbVqBQMGSFslpRKRVX7+DFpxhKAwKwD+gUEMWiElCn8PwMHB0oxk5EjZjM2fH6ZNgw4dTPbd3E6ndWP45dQvOFmceLvE2/Sp3IfirxR/5nu9sHuDaUrIXbZMQu+JE5EdGsaOlRpeHeiilIoBDb9KxTcfHwm7efLID+0aNeD8eciVy94rU+q5Rm449TT4RggKszJywymal/Hi/n2YMgXGjZMLGd7eUtubsex2ph6YxNhZhzh5+yQZ3DLwefXP6V6+O5lTZ/7X9/nX7nLdgjS3Xovc4T13Tt4w1qgBPXpISYNOWFNKxZKGX6Xig2nCunVy7Xf7djlxXqmSPGYYGnxVohYQGPTc+y9fsTFwIEydKiXrdetK54ayle/z5pLerJv781/PNGierxsL3hiNm9Pzp6NF7C4Hh4ZRxv8UDTfuoMJQH3hwUw6o1a4tX7x5c21JppSKUxp+lYoPn30GQ4dCjhyyPfbee5A6tb1XpVKo6NTvAmTzdMP/bwE47G4qHuzJy+Nj2RltQtu2UqaeLs9Fxu8eT6PRMwi2PgYTMADTYOfpIDYcvfv872OzsWHaMgb6bqTBqZ1keXSXEIsj23OXYVbdznw+/VNIly7u/0MopRQafpWKG48fS8f+116DUqWkr1PhwtC+PTg52Xt1KpmJTpiNav3u3w2oV4hBK44QeCk1D/bk48npLBiONuq1fMLEoam57bKHoT6jWf7rchwMBzx5DfeQ4txznoJphmPgiCW82NMyCUBq3n18pD5i2TKm+PsTYnFiS95yfF+4KpvyVeCRizsG8LkGX6VUPNLwq1Rs3LkDEyfCDz/I77/8UsJv4cJyUyqORTfMvqx+959ME1xveOG4PiPXfV1wcAkje81LfPM/Rzy99tJp6xh2XtlJWpe09K/cn48rfky17w9hAs6h2Ql2OIKrrQQutiJcu/cYdu2CJUukhtffX7qaNGjAV1U7syxrKR67PDt0Ipvn88sklFIqrmj4VSqmvvgCxoyBJ09k/PAnn8hJdKXiUXTD7Ivqd/95f3i4ZNQRI+DQIfDycuHjET6kLrmBYPMB3x1fzfmd58njmYfx9cfzbpl3Se0spTzZPE/jHxiEi60IrtZClAk4RaOTM2hyeieMuA3OztCggXzxxo0hTRrK+PmzZMUR+NtrcXOyMKBeDKe7KaVUFGn4VSo6zpyRfk4R/URbt5bix2LF7LsulWJENcxG+Gf97t/vB3nvNmuWDBW8eFHa5f70E3h4/0K7la0I3x0OQPFMxVnWZhnNCzfH4mB55msNqFuQ+ZOWU/fIFhqd3EG2h7cJtThyp2ot6NJR3hymSfPM50QE9ejUIiulVFzQ8KtUVOzZI50bVq2C336TXazBg+29KpUCvSzM/lNE/W7QP3ZYP6xUmMGDYcIEuH0bKleWs5k5yh9k7J7RLFixAJtpA8DBcODNEm/SqmiryC9smnDkCCxeTPNFi2h+/jxhFke25S7DjAbvU657RxpXL/Kfr6V5GS8Nu0qpBKfhV6kXMU3480/p2rB5s5w+//JLHUqh7OpFYfZF5QL/3GHNgCfZzpei29jUPH4MjRrBgIE2HmVZz5jdo9k0YxOpnFLRqnArfj3zK2HWsGdHD586BYsXw6JFMnjCYpG2ZJ99hlOLFtROl47a8f0fQSmlYsEwTTPBvpm3t7fp6+ubYN9PqVgJDYV8+eSUer9+0KULeHjYe1VKRbt1GcCxY1Jyu2CBfNy+PXzcN4iD1nmM3T2WE7dP4OXhRc+KPelariuerp74XPGR0cMuhai8+YyEXj8/KfupVg3atZNJha+8kgCvWimloscwjP2maXr/634Nv0r9JTQU5s2D+fOltMHFRRJD/vzye6WSoB07ZMDgmjXg7i7v4Tp2u8kv1yYzed9kbj25RekspelXuR9ti7XF2eIsn3jtmpyAW7QIdu+W+ypWlMDbpg14abmCUipxe1H41bIHpR4/hhkz5MTP1atQpgwEBMg4Yj3IppIgmw3WrpXQu3MnZMgA733tg1OpJVwIOs+rSzcQYg2hUYFG9Kvcjxq5a2AYBty/Dyvmy/bwpk3yhUqVktKfN96QvxNKKZXEafhVKduFC1LDe+eODKiYOVNmtkZ0c1AqCQkNhYULpbzh+HGZoj1+vElomYl8srk3tkNygK1ZwWYMe30YhTMWhqAgWLFCAu/atRASIuU+n30mtRFF/vvQmlJKJTUaflXKc/261C02aAC5c8Pbb8uuVuXK9l6ZUjHy6JFcvBgzRi5elCgBP88Nwyy2mPF7R3Nw08Gnz7UYFipmK09hvyuwYLgE3wcPIHNm+PBDePNNeUOobwCVUsmU1vyqlOPSJdkS+/FHcHOT0gY3nSalkq5bt2S44MSJcO8eVK8OPfoHcj7ddH7YOwH/h/4UyViEZoWaMX7PeELDQ3A2Hdi40oPKh+9J791WrSTw1qgBjrofopRKPmJc82sYxiygMXDTNM3if92XHlgM5AYuAm1N07wXlwtWKs5cuADffCMH2QwDOnWSwRQafFUSdeGClKjPmiVVC82bQ4ePL7A1ZBzv+P3I47DH1MpTi+lNplPfzIfD/AU03ZCeLU7+1AiwULlMLfjqTWjYEFxd7f1ylFIqQb1059cwjOrAI2DO38LvCOCuaZrDDMP4FEhnmuYnL/tmuvOrElRYGDg5SYlD1apyzL1fP8iRw94rUypGDh2SQ2xLlgA5fCjdbAtNX8/IkSe/s+LEChwMB9oXb0/fwp0pvfG4dC/Zs0fe9NWqBW+9BS1bQtq09n4pSikV72LV6swwjNzAmr+F31NADdM0rxmGkRXYYprmSweya/hVCWL7dvj+e+k9Onu23Hf/vv7AV0mSacLWrRJ616+H1KmhUbcdrPCoTZgtFIDUzqnpXrorH9/Oh9fi3+SJVqt0anj7bTm4pq3JlFIpTFy3OstsmuY1gL8CsHY4V/ZlmvD77/DddxJ+M2WS0oYIGnxVEmOzyTTt4cNh7155L/fVkMe4V/mJ4Xu+IixYgq8DBv1u5OPrttPl5Fv27NC/v+zylihh3xehlEo2YjJcJ7GK99MNhmF0BboC5MyZM76/nUqpRo2SsJs9O4wfD++/Lx39lUpiQkJg7lwYORJOn4a8eWHoxADu5J/IhINTubf1HsU98vMoKBCracPZalJv/Rl4o73s8lavDg4O9n4ZSqlkZJWf/zNj1f0Dgxi04ghAkgzAMQ2/NwzDyPq3soebL3qiaZrTgekgZQ8x/H5KPSs8XAof8+aFSpXksm66dNCxIzg723t1SkXbgwcwbRqMHSvD1cqUgRGzD3Mk9Wi+PLYQ6x4rLSzF6bc1I5U3n8Enl4UtdQtTo8rbVPbrqwc4lVLxZuSGU0+Db4SgMCsjN5xKUeH3F6ATMOyvX1fH2YqU+i+hobItNnQonDsH770n4Td7dtntVSqJuX5dLlZMmSKl6bVqm/QYt4HNwaMZeOFPUhkufHjdi15LL5Pv9mHpwfvDD1Ru147KGTPae/lKqRQgIDAoWvcndlFpdbYQqAFkNAzjKvAVEnqXGIbxHnAZaBOfi1QKgDlz4PPP4coVKFdOmvM3a2bvVSkVI2fPSmnD7NnSmKRah604VJ7AhWA/PjtxgaxWd4b6uPDBjhDSZQyH9wfKlQ2duKaUSmDZPN3wf07QzeaZNK84vTT8mqbZ/gUP1Y7jtSj1bw8fyuVcR0e5FpwrF0yfDvXq6QQqlSTt3y+H2JYtkwqddu/cIajKIJacmwHXwTDh823whS84t3gD1nSUARQWi72XrpRKoQbUK/RMzS+Am5OFAfVe2ugrUdJxPipxundPRleNGye/vvWWnGD/5KXtpJVKdEwT/vxTQu/GjdJ8pOugMwQXG86Ss3MJOhcKJmCAgwnuzdvg/Mss6WumlFJ2FlHXq90elIoPt25J4J04UU4ANW0KxYrJY7rzpZIYq1V2eEeMgAMHIEtWk27fb+eK+/+Yfm8nTifgrSNQ60kWula5Q6hhw9nZmRot+mjwVUolKs3LeCXZsPtPGn5V4tKoEfj6QuvW8L//QenS9l6RUtEWFCS1vKNGybnMgoXD6TVkKrtChzEl1J/0gfC/w870yN2WLJ98BJUqke/qbrZc3EKN3DWonKOyvV+CUkpFXXAw3LgBt2/LmRyARYtkQs/IkYnuzXyUJrzFFZ3wpv7l8mU56v711+DhATt2QPr0ULSovVemVLTduwcff3GfRb8fwpp5J57BeWjqvYytaddwyS2E/HegT2BhOtUdQKqW7bQXtVIqcQsNhYAAOWh+5QpcvQp9+8o5nLFj5QzO9esQGCjPt1ikWbnFAh9+CMuXw759kDu3XZYfq/HGcUXDr3rq/HlpVxYxfnj1amjQwL5rUiqG/P3l58CkKTaC0+/GoXMNbJYwedCAytddGJitFU06DMGSO499F6uUUiB1Wf7+zwbbK1ekq1KmTPKPWr9+cmjh7wICIGtW+PlnWLsWsmR59lavnoRj07T7wXQNvypxCAmBLl1gwQL5y/H++zKZTaf/qQQQ1+M5T5yQK3rz5kFmawBNi3zBlupzOP5KOBiACXnvVyLLK0PYOUgb5CilEpBpyjmaCxeevfXtC4ULS3h9551nPyd1ati+XUoOd+2CP/6QPvo5csgte3a5SptEvCj8as2vShg3bkDmzODiIteGe/WS7g1Zs9p7ZSqFiMvxnD4+0rnht9WhtHD+lXEVhrM8/z4m5wGXMAMDA9M0MHDkiVsrAu4Hx/nrUUopwsPh4kU4c0bmoZ8/D+3aQeXKsHkz1P7Hm+5XXoE2bST8Vq8uZQsRoTZHDmlFE+HVV+WWDGn4VfHrwAEYMgR++026+mfPDr/8YvdLISrlie14TtOUP8bDh8Pt7cfp6j6N1yvOYpL3I5ZkAi/Tg5LBDblntiDMdoVghyO42krgYiuSZBvBK6USAZtNyhNOn5aQW7w4VK0qQbdQIQnAEVKnltnolStDiRJypiZPnshbqlSRz82bV24pkIZfFT/27IHBg6UeKG1a6c8bcdpTg6+yg5iO5wwLk0PLk4Y+oMSJxXyVdiq7qh9gaAW4mRpKu+dlbp0vaVuyPb8dvvXX7nJqXGwyiS0qjeDjuhxDKZUEPXkCp06BgwOUKiWHzby9JfAG/+3qUa9eEn6zZ5crqAULyq1AAanVjfgZmykT9Oxpn9eSyGn4VXEvIACqVJHQO2QI9Ojx7KUUpewguuM5Hz+GmTNMtg3dSRHn76lY9Hcul7DSpKBBkCM0zFmHfjUGUTN3TYy/ftjEpBF8XJZjKKWSgNBQGe8I8O23sHcvHD8u5QumCc2bw8qV8pzSpeH11yPDbcGCkC2bfK6zsxwcV9GmB95U7Jmm1BZt3QrffCP3rVkjI1kTWW8/lXL9M2SC7MoObVnimZB5+zbMGn6Lh5Pm0D5oBlvLnaJHI7AZgAGNCzZmeJ3hFM0UN+34qgzb9NxQ7uXpxs5Pa8XJ91BK2cmRI9Lq6/BhOHZMTslmyyaBF6BmTbh7V9p7Fikiv5YqJUFXxZoeeFNxzzRhwwYpb9i1S/5C9+kDnp7QuLG9V6fUM162K3vpgo01fTaSZc0MepgrWVMknA61U3EgfeTXsBgWXs3+apwFX4h5OYZSKpGw2aSLwuHDEnYvX4aZM+Wxb76RXrfu7hJua9WKHAIBsGmTlgLagYZfFTMnTkCnTvKONkcOmDQJ3n0XXF3tvTKlXuh54zmP/+HPsf4/4X34Rzo6X2RyZXcKv+bGFaeHFEifjf6FmjFp3yRCraE4W5ypkbtGnK4puuUYSik7evgQDh2CSpWkXefo0fDVV1InBRJk8+WT+l13dyn9GzZMDpY5OPz762nwtQsNvyrqbDa4eVOaWGfOLD17p02Dzp0j65eUSgLMsHCOjfqNx2Nn4H3rN9J62Pi6ZS6WlHLngfmEqjmrMqFyP5oUbILFwULLIi3jbfTwgHqFnluO8bJDckqpBHDuHCxbBn5+0r3o7Fm56nn4sHRTKFIE3nsPSpaUj4sVe7ajQuHC0f6WegA2/mnNr3o5mw1WrJDyBosF9u+Xd6uJYHqLUtFhO3+RM5/MJP3qWWQKu8amLBkY0SwrG7OdxIaN1kVb069yPyp4VUjQdekPO6XsyDRlsllEwPXzgwEDoFo16W/YqJGM5y1TRm5ly0qP3HgY9hDVswkqarTmV0Wf1QpLlshlm+PHpZ/g559Hhl4NviopCA8nbOUabnw7jWxHN3Azu0nPJl5cKJyfM85nSeUUTPey3elVsRd50tln9PDzyjGUUvHkxg35+ZYtm+zsVqokJ11BShMKFYLAQPm4Vi24cwfSp3/hl4tLse1HrqJGw696sYULoUMHOX26cKFMhbFY7L0qpaLm0iVCJs0kbNqPpH5wjRBLNho3rsJ6752Y+APQzbsb39X6jnRu6ey8WKVUvDBN2LhRzqdE3K5elV6548bJmZVmzSJ3dEuWfLZswdU1Qc+y6AHYhKHhV0UKC4N58+Qvevv2EnZTpZJ/GJ5XqK9UYhMeDmvXEjJhGk6b1uMErHSrzbTWtTlc5k/uhu14+lSLYSFHmhwafJVKLkJCpGRh9245jNajh9zfoQNcvw7580spg7e37OiCnFeJ6MyQCOgB2ISh4VdJw+05c+D776VdS5MmEn5dXKBFC3uvTqmX+6u1UPj0H3G8EcBtsjEq3Uf88cZDznktI9j6hHo569GwwCA+/fPTaHVu0HpcpRK50aNh6VIJvqGhcl+1ahJ+DQPWrYNcuSBd4n+jqwdgE4aG35Ru9WoZf3j5MpQvL3PAtUevSgqsVli/HqZMwVy3DtNm8gf1GZnrYy6+sZeL7pNxdHDkrRJv0bdSX0pkLgFA+Wzlo9y5QaevKZVIPH4sh61375bbiRMyNMLBQQ6rOTtLKUPlylCxYuQUNJApaUlETKZEqujTbg8pUXCwlDh4eMhJ1sGDpU9hvXp6iE0lfjduwI8/Yk6fjnHpEuvzpGdU9hIccaqAY5UdBFh8SOeajg+9P6RHhR5k88j28q/5Ajp9TSk7uXJFWmo6O8MPP8gAJetfu6H588shtYkTIW1a+65TJWra7UFBUBDMmAHDh0PHjjITvEEDuWnoVYmZacK2bbLLu2IFRlgY+zxq0T93J7a/PRQsW4GtZE2dlQlVJ/BOmXdI7Rz70dp6+ESpBGC1wtGjsHMn7Nghv16+DFu3Sksxb2/49FMJvJUqQcaM9l6xSuI0/KYET57IMIoRI6To/7XXoH59eUxDr0rMAgNh7lyYOhWOHyfE3ZMF7t0ZYm3FvXrreVR8JBAGgAMOdC/fnY8rfhxn314PnygVD548gb17ZWBS4cKwZw9UqSKPZcsGVatCv34yKQ2klKFy3A6XiQ09B5D0afhNCbp3h59/hpo1YdEiCb9KRVOC/oO/fz9MmSIt9p48ISB7BUakmcVUlxJ4NJ1CYM7aWM0wquWqxp6rewi3heNscaZWnrgtRdDDJ0rFAatVDp1t2ya3/fulM0u/fjBqFJQrJ4euq1aVYRKJeFNGzwEkD1rzmxw9fAiTJkHz5vKu+sQJaeBdrZq9V6aSqASZOhQUBIsXw+TJsG8fNjd39hV4k/5nP2BH5vtkbDqa2+nW4eboxjul36F3pd4UyFAAnys+8TZ6GHSXR6lou31bQm5oKLRrJ2VLr7wCDx5AhQrys6hqVdnNTQIdGP5OzwEkLVrzmxI8eCAHAEaPhrt3ZSBF4cIye1ypWIjXqUMXLsgu748/wt27hOQrwvJKE+h5oB13+Z20PbuA60EcUr3C4AqD+dD7QzK6R9b8Vc5ROV5CbwSdvqZUFKxbB7/+KnW6x4/LfSVKSPg1DNiyBfLmBbekXTKk5wCSBw2/ycWoUdKn9949aNgQvvxS2r0oFQfi/B98m03alE2aJD80HRy4W705/d1r8NPjm1hSn8L1k7KYlqtkzViEUZVn8lbJt3B1TLhJS0qpF7h+HTZvllrdsWMl3C5dKreqVWWoRMRBtQjFitlvvXFIzwEkDxp+k7KHDyF1avmH58oV+Ufnyy+f/QdHqTgQZ//g370Ls2bJTu/585iZM3Ou3ecMutCVZdf2Qdu2YIRjNaBQlrIMrjWN+vnr42DohEGl7OrgQZmEtmmTlNKBtBnr3x+yZ5crjtOny2S1ZEzPASQP+hMlKbp7V0Ju9uxyKQlgzBj45RcNvipeDKhXCDcnyzP3Resf/P374d13wcsLBgzAzJqNnT0WUv6VyxTY0py1+QditGsFDuFgyOjh1kVb07BAQw2+SiW0+/elhKFPHzh8WO67dEkOTufKJZ2D9u2DO3fk5xBI7W4yD74gZVBDW5bAy9MNA6n1jdOzDypBJP8/qcnJnTtyiWnCBNn1bdFCmoCD1PcqFU9iNHUoJEQug06cKJdH3d0Je7MjyzJ9xKDFJbh0cz3udepD5s04OnvwRoE3WHVqFWHWMB09rFRCu3tXQu2mTfJm1WYDV1fZUClZUsrp7t0DJyd7r9Tu9BxA0qfdHpIKmw0KFoRz56B1a/jiC/kHSanEJiBA+vJOmwY3b0LBgjzu9BETH3Zi5E+u3Mk2H7faowlKfQIvDy96V+pNl7JdSOuaNlqdGxKkA4VSyZHNJmUMf/4pvXY7dpRuK6+8IqOAa9WS1piVKkkAViqJelG3Bw2/idmtW1JjNWCAXE769VfIkweKF7f3ypR6lmnCrl0yhnT5cunr2agRa5vVZujZJ/iuKUtIBl9cqk0kxOkGpbOUpn/l/rQt1hYnS8x2krTlkFLRNHeu/BzZuFF2egHeegvmzZPfh4SAi4v91qdUHNNWZ0nJzZswcqT0Ow0Kksk31atDkyb2XplKJuKsXCAoSAan/PAD+PnJAZiePTld5yN6r7zJuou1wDUEWptgQK38DehXuR+18tTCiGUje205pNR/uHtXQu6xY/D113LfkiXy97RpU6hTR3Z4s2aN/BwNviqF0PCbmDx5IuUMU6bIO/D27eHzz6VXr1JxJE4mFF2+LH9OZ8yQWvRixWDqVHblfZuhE1KxZokPRrMu4BgMBhgY9KzYk3H1x8XZ69CWQ0r9w4kT8mZ0wwY5kGazyRvSfv3AwwMWLIjsEKRUCqbHqBODkBD51cUF/vhDanqPH5dLURp8VRz7r4EV/8k0pbtIq1ZSfjNiBFSrhu2Pjfz6/RGqzH2fKj1/Z322KvD+q6TKdhlHiyMWw4KroytvFHsjTl9HrDtQKJXUXbwo7cUCAuTjHTtgyBAJt59/Djt3yrQ1Dw953MNDg69S6M6vffn7w/DhsGKFvGP38JB363rpScWjaJcLBAfLjtH48dL2KH166N+f0Pc/YuGuXAzr+4STrlNwrDYW0pwle9o89K08gXfKvMORG0fibfRwjDpQKJWUBQdLKcOGDXI7fVru//ln6NRJpqm1aiV/R5VSL6Th1x6uXpXQO2MGhIfLP1pBQRJ+NfiqeBblcoGAAKk7nzZNdo+KF4cZM3jU7C1mzHNjZKMbXMv+JZbGk8HlDmWyVWBglaW0KNwCi4PsyOroYaViwTTh5Em5Oli6NAQGQuPGMiL4tdegWzeoVy/yCmHEDq9S6j9p+E1oFy9CoUJSi9W5M/zvf3IJWakE8tIJRXv3yi7vkiXStaFJE+jVi1vFa/LJxN0seP8zQtzPYbTbgGEJpXGhpvR/tT9VclSJ9SE2pVK8x4+l1+66dXK7eBEaNYI1a6Qt2c6dULastiBTKhY0/CaES5fkH6w334TcuWHYMGjZUiblKJXAnlcuMLBWXpqd2g4fjYfdu2UHqUcP6NGDCw75GDXaZPrnUwh//WMoawOgaaFmDK8znEIZ46bGVgdWqBTJNOUqi9dff9br1ZOfF6lSSUeGTz+FBg0in//qq/ZZp1LJiIbf+HThAnz/vdRjubnJ5ao0aWRkpFJ29LRc4M4dOTDTsqPUoOfLJ7u+nTtz6EIahn4RzpKji6HyKMx6kT26LYaFil4V4zT4xroDhVJJxZMnsHkz/Pab7O4GBEhrMnd36fjj6AhVq2oZXAzom2gVFdrtIT5cvQrvvScT2ebMgQ8+kO4NadLYe2VKiePHoWtXyJ5dSm8KF4Zff8U8dZrNJXpSp51B6Q/GsyRLfsxW7chd+D4DXx2Im6MbFsMS5fHDURXjDhRKJRURA6UWLIAMGWQz5OefpZZ+7NjIx+vVg9q1NfjGQMSbaP/AIEwi30Sv8vO399JUIqM7v3HJZgMHBzmcsGQJfPQRDBwYeTlLKXsyTWmlN3YsrF8vNYNvvw29emEtUpzVq+HbGgEccvkBo/xUcA2kYraqfFptPE0KNcHBcKB54ebx0r1BB1aoZMdqlfr5NWvkNniwDJcoWVLeeDZqJIfWNOTGmf96E627v+rvNPzGhdOn4bvv4MEDWLlSLh0HBOjJW5U4BAfD/PkSeo8dg8yZ5QfxBx8QkiYTc+fCkHePcMlrNNRcgGGx0rxQSwZW7Uel7JWe+VLx1b1BB1aoZOPhQ6mX/+036ZJisciUzoiQW7y4lBapOKdvolVUafiNjZMnpaH4woXyD9tHH0Xu/mrwVQnouXVu2RxlCtvkyXDrFpQqJZdZ27XjfrALgybv4udDnxLkcQwa7cHFcOf9ch/Qp3Jv8qXPl6Drf2kHCqUSq3Pn4Jdf5Pd9+sgEtUOHpHyhcWP5NV06+64xhdA30SqqNPzG1JIl0lDczQ369oX+/WVHTakE9s/DYqnPnMC6aBjW41uxhIXKD+A+faBmTa5dNxjzVRgTDn5FaKXBUETqDLuW/YChdb4nvZt9muPrwAqVpBw4AEuXSug9flzue/11+XtmGODnp5PU7EDfRKuo0vAbHUeOSA/GSpWkBc2gQdC7N2TKZO+VqRRs5IZTBIWGU+P8ft7bt4pqlw4S5OjC6nL1aTl7BBQqxJkz8N2H95l3YgZW7/FQ+erTz7cYFnJ75rJb8I2gAytUovXkifTebdhQruzNmAEzZ0rN7gcfSC/sv/dr1+BrF/omWkWVYUacME0A3t7epq+v78ufmNgcOgTffitjiKtXh61b7b0ipURwMJ+0+IT39q2i4J3LXE+dntnlmrCgVH0euHmwtHUjvhpzhd/uTIBy08DlIRUz16BNycZ8sfkLQq2hOFuc2dhxY7xOYlMqybl+XQ6q/fKLHBQNDpYDbOXLy5kONzctZ1AqkTMMY79pmt7/vF93fv/LoUPw9dewapW0KfviC9npVcre7tyRet6JExl+4wbHXslL78b9WFu4KqEOTgRfzMiT88GUP90Bii/CKGjSLH8bPqvVD+9s8u/AqzlejZfODUolWeHh0mN3+3bZ6AAZTNS1q3RqKFVK7suWzW5LVErFXqzCr2EYfYD3ARM4ArxjmmZwXCzMrkxTLlvt2QNbtkgA7tULPD3tvDCV4p09K10bfvoJgoKgQQN2NO1El6tpuBd+nId3/yTkghfWrJug8Z84k4r3y/RgQPVe5PbM/cyXiq/ODUolGTYb7NsnGxyrVsEbb8i/9+XLSwefJk2kO4OWMSiVrMS47MEwDC9gB1DUNM0gwzCWAL+Zpvnziz4n0Zc97Nkj5Q0NGkirmtBQCRhp09p7ZSql27ULRo2SH9BOTtKft29fKFaMoCB4Y8hafrW0AIcwMMDFTM8XNQfyUYWupHPTS7NK/Uv//tKpJyBAdntr1JAd3jZt7L0ypVQceVHZQ2wnvDkCboZhOALuQEAsv5597Nol7WgqVZIA7OQk9zs7a/BV9mO1wrJlULmy9AndskWmsV26BD/+yL1sxfh8SCCZmo/gV1t7sEjwdcCBz2v14bPXPtHgqxRI792lS+GzzyLvu35d/m7NnQs3b0pdrwZfpVKEGJc9mKbpbxjGKOAyEAT8bprm73G2soTSt69cRs6UCYYPl169qVPbe1UqGYn2rPnHj6WsYexYOH9ehqZMnAidO0OqVFy9Ct/0v8TsU+MJKzEDXn1EwdTeXAw6gtUWjrPFmdp5aifY61MqUbp7Vw6rLV8uwTYkRP6dHzhQNjXmzbP3CpVSdhLj8GsYRjqgGZAHCASWGobxtmma8/7xvK5AV4CcOXPGfKVxxTRh82YoUUL+IWzUCLJnl3Y1qVLZe3UqmflnD96IWfPAvwPwrVswaZIE3Tt35ErEyJHQrBlYLJw4AZ+MO8Cau6Mxiy7GKAcNc7RjSMN+lMlaBp8rPnqATaVs166Bu7uE2+XLpYwhVy7o1g1atJArKBaLvVeplLKz2NT8tgHqm6b53l8fdwQqmab50Ys+x641v6YJf/4pNb07dsihhq++ss9aVIpRZdim504c8vJ0Y+enteSDc+dgzBiYNUvaKTVtKrtTVaoAsGuXSb+p69ltjIK8m3CyedCpeFe+qNuTnGkTwRtKpezpwgUZK798Ofj4yBvIbt3g3j25clK2rB5YUyqFio9WZ5eBSoZhuCNlD7WBxHmabcMG+OYb+Ycxe3bZWXvvPXuvSqUA/zlrft8+2dldvlwO3HToAP36QZEi7Lrsw5QZg9m6M4QrqVZBvmN4mF70rTySPtW7kNZVa9FVChccLG8QDxyQj0uXls2NunXl43TpoFw5uy1P/Vu0S8CUiiexqfndYxjGMuAAEA74AdPjamFxasYM8PeXvqjvvAMuLvZekUoh/jVr3jSpcX4/PQ+shOGH5PLswIHQsydkzUpYGHw27XdGBjQGIwzyQEYjH9/Xn0Oncm/gbHG234tRyl5ME44elQOggYEwfjy4ukq4bd8eWraEvHntvUr1H6JVAqZUPEsZE95u3ZKQ4azBQSWsiH/ww4ODaXJiG133rKDw7Us8yZwV94H9oUsX8PDg8WMYOf0SY3aN42HhyeAYCoCD4cDgmoP5X7X/2fmVKGUHx4/DggXSqeH0aRkt/Prr8Ntv8nuVZESpBEypOJayJ7xlymTvFagUqnmBtOR7sptXfpxM5vu3OJc5D/u/HUe5Tz8CJydu34b/jd7P7DOjCM2/FKOoQdm0dTj2ZDPhf3VuqJm7pr1fRozoJU4VbaYJfn5QpIiMD16+HIYOhZo1oU8fObSWObO9V6li4D9LwJRKYCkj/CqV0G7fhh9+gB9+oMS9e9JAf+BA8tWvD4bBhYs2ev3wG2vvjcKWazOO+dLwZp6+DG/Zk+xpsif5zg16iVNFmWmCr6+UNCxbJofUVqyQoPvRR/Dhh7qBkQz8qwTsb/crldA0/CoVly5dgtGjYeZMmQ7YvDl88om0LQN8/UL4eMZ8djuMhkzHcXfPTveSo/iswfvPHGJL6qOHR2449TT4RggKszJywykNvyrStWsyaOLSJTn0WaeODKJ47TV5PEMG+65PxZkB9Qo984YYwM3JwoB6hey4KpVSafhVKi4cPSpDUhYulLZKHTrAgAFQpAimCaNXbGD49jHcdvKFzHfJZC3F56/NpVu1N3CyOD3zpZJDuYBe4lT/Yppw6BAsXiyHjr/+GrJkgVq1oHp16WedTicSJlcR/4Yl9X/bVPKg4Vep2Ni5E4YNgzVrZEhKz55Sm5gjBzYbzFh8kUGbB3Ivy1LwBAMHvqs2nk9rfozxnN6jyaVcQC9xqqeOH5c3hUuWyKE1iyVyjLBhSH9rlSI0L+OVpP4dU8mXHpdVKrpMU8JutWpQtar0j/72W7h8GcaMIeSVHHw5dT+e77fjw+P5uJd5OfyVcx0MA5wePzf4wn+XCyQlA+oVws3p2UlaeokzBTl5Emw2+f2kSfD995AjB0yfDtevSxhWSik70fCrVFSFh8sP7VKloEkTCbsTJki94hdfEGjx5L1hv5GmZ00G3/DmcbZ1NM7Qj+VtV+Dm6IbFsOBscaZG7hov/BbJpVygeRkvhrYsgZenGwbSzmhoyxK665OcnT0LQ4bI6PgiRWDPHrl/0CCp7f3zT2ntlzGjfdeplErxtOxBqZcJCYE5c6Sm99w5+cE+e7Y013dy4nJACB8N/Yl1D0Zhy3Acl/TZ6ZJzFCPavY+nmxxi25hmY5S6NySncgG9xJlCXLgAbdtKxwaQqyE//AAFCsjH2bPbb21KKfUcGn6VepFHj2Q64KhREBAA3t6wciU+ZTOx5dI2svhsYupqP/YaE8DjGmndS9G31FwGNfn3Ibaodm/QE9Eq0bt1S1qSubtDp06QLRt4eMjfk7ZtpbxBKaUSMQ2/Sv3T3bswcaKMUL17Vxrsz54NtWszbNOv/G9WLUzCABPSgFdwXQbXmE3n6nVeWMsbVXoiWiVK9+/DypWwaJGUL1it0LixhF8XF9i0yd4rVEqpKNPwq1SEa9dg7FiYMkV2fZs0kXrFypUxTfhw4kZmnB2EmS5UDrCZkDa4BRPb/hCn4VTLBVSiEBIiwRbg/fdltzd3bhg4ENq1k9pepZRKgvTAm1IXLsgkqTx5ZEBF06Zw+DD88gvh5SsxaNY60n5cm+l362CmvgimBUwHDJxxM15Ncp0YlHqh8HDYsEF2dDNlkmlrAP/7H+zeLR9//z2ULCltypRSKgnSnV+Vcp06BUOHwrx50nu0c2fZ1cqXjwePQ/l47M8sujSa0HRHcUzlhfulvqRPX5lw8yLBDkdwtZXAxVYkyXViUOpfrl2TvwuLF8PNm5A2rdTvmqY8XqaMfdenlFJxSMOvSnkOH5bdqyVLwNVVBlP06wdeXly6EciHQ0bw+/3x2FIH4GYpwcfZ5zC8wxvUGbMD/8AgLLYiuNiKPP1ySbETg1KcOAEPH0KFCuDsDD//DPXqwZtvQsOGkSUPSimVzGj4VSnHvn3w3XewerWcTv/0U+jdG5+Qc8zbO4GN+y9zyrYWXB6SIbwOA4v/RP8Wr+PgIJd3tRODSvKuXpVe1QsWwMGDMlZ461bIkEF2fF1d7b1CpZSKdxp+VfK3Y4c039+wAdKlg2++gY8/hnTpGLZ+Nv/b/R4mVnCELI/rMqbuMNrX+PdlXu3EoJK0nj2li4lpym7v+PFS2hBBg69SKoXQ8KuSJ9OEjRsl9G7dCq+8IkMqunXDTJ2aH377gyGbR3LL4095vgEOWOjZtAbtq724vlE7MagkITQU1q+XHd6pU8HTE6pUkR3eN9+MHEChlFIpkIZflbyYJqxdK6F3zx5pwD9uHHTpQoizI58tXMzUw6N4nPowhpGVctZuHHP+mTBb6EtHDyuVqJmmdGSYN08Ort25I6OEjx+HV1+FN96w9wqVUipR0PCrkgebDX75Bb79Fvz8pB/p1KnQuTN3w0PoMWsyy66OI8zNH8fQYrRz/YmJvd4kg6czPlc6RGn0sFKJUmioHFg7e1ZCrqsrNG8Ob78NdeuCk9NLv4RSSqUkGn5V0mazwYoVMHiwdHHInx9mzYK33+bM3Rt0G/c5mx5Mx3R+gPuDmvTINYOhn9bHxSWyR2lURw8rlWjcuSO7u3PnQs6c8vsCBWQKW61akCaNvVeolFKJlg65UEmT1SqjVkuUgDZtZBrV3Llw4gSTCzqS9fsKFJyUm41PxpLhTkNGF/Ll4cRNjOnW4Jngq1SS8uef0LIlZM0K3bvD48dSyxuheXMNvkop9RK686uSlvBwCb1DhsiQiqJFYeFCzNatWei7hX7fVOW64x4wwXBwZHDJxXzWsqW9V61UzJgm+PrKkAlHR9i8GXbtkm4lHTtCqVL2XqFSSiU5Gn5VorXKz/9pW7EcHk6MCz9G2XmTpbaxRAlYupSwZk0Y88dyRnxZgbsufmBNDRYDDBMHw8Qhk44eVknQ5cswfz7MmQMnT8KaNdCoEQwaJK36HPWfbqWUiin9F1QlSqv8/Bm04gjhwcG0ObqZ7ruXkCvwOoGFi+O5ciUP69Xks5U/MfOrggS5XMZ4VJjaYTPp0jo/7/zZgFCrdm9QSdDNm9C+vezwmiZUqybTB6tWlcdTp7bv+pRSKhnQ8KsSpbFrj9LU9zd6+Cwhx/0bHMpSgG9bdeFQ6eLkvr6HVd+9g9UpEMfb1XnTayLjvmxEpoxSwp4z28Yod2/4++6yDq1QCc5mkz7U169L6M2YUe776ivo0AHy5rX3CpVSKtkxTNNMsG/m7e1t+vr6Jtj3U0lQWBjMns2V/p+T4/4NZpfOwYRKBbiUthyPHp0hJP1vYITjfqkl3Ur159sPKuLuHrNvFbG7/M9xxUNbltAArOLXuXNS0jB7Nly6JF1KTp8GQw9jKqVUXDEMY79pmt7/vF93flXi8Ffo5bvv4OJFHmYvRMOmjViXdy5wBYxN4OSM44lODG/0CR9/ni/W7UtHbjj1TPAFCAqzMnLDKQ2/Kv58/z189pkE3Tp15OPmzTX4KqVUAtHwq+wrLEx2wIYMgYsXoXx5rBMnMOlhAOsPfQ1GmDzPNPAIfJvZg76iRdm4CaYBgUHRul+paLPZYNs2+Pln6NNHujPUri2PdegAOXLYdXlKKZUSafhVgB1qX58Tep9MGM1ISwBjdvfmgeU8hHiBsxMYVhwMJ/7XvFmcBV+AbJ5u+D8n6GbzdIuz76FSqAsX5ErG7Nny5ztNGmjQQMJvxYpyU0opZRcaftW/al/9A4MYtOIIQJwG4FV+/oz57RiVdq6l1+6leN27Bt7e3Br3PZ8/OcHPe7sS6ngH41olaruOZMJHzbifem+8jR4eUK/Qc2t+B9QrFKffR6UQpimlC8HBEnIfPZKyhu++k7KGmBanK6WUilMaflWC1L6u3neJPYMnMG/bfHL+1b2h39s9OVfiPgf2v4vNEozjxaa0yzaAkV9VIXv2iPrH+Bs9HPHatNuDirGIIRQ//gjHjkmJg6ur9OgtVUpGDyullEpUNPyq+K19tVph4ULK9v6UZnf8mVfSi8GvleO8s43w1D/AQyfcTnfkg1L9+OqHwnh6xv5bRkfzMl4adlX03boF8+bBrFlw9Ci4uUHr1hAUJDu8TZrYe4VKKaVeQMOvip/aV5sNli6Fr7+Gkyd5kCkX5bvUwjfbZjD8wQROvEm6J+8TsLQmrq4x/1ZKJYjwcKlVd3OD33+Hvn2ldnfaNHjjDUib1t4rVEopFQUO9l6Asr8B9Qrh5mR55r4Y177abLBihVzybdeOYEeY+MMHlH7XAV+vTUjqBXAgbX5HilQxNfiqxO3MGRkrnDMnTJwo97VsKTu+u3dD164afJVSKgnR8KtoXsaLoS1L4OXphgF4ebpFf9CDacKvv0K5ctCqFXcJ4vMRbcnY8h4f35lGeKAnjn4DwXQB0wEDRzwdSsf54bJVfv5UGbaJPJ+upcqwTazy84/Tr69SkAULoEYNKFgQRo4Eb2/58w2y+1usmF2Xp5RSKmZ0wpuKHdOE9evhyy/B15eLJXIwpG1hZoftItzhMZytx2tOAxj1US2uWgL4ct0KrjzxJYe7N982aBnn3SR0YpuKlfPnI0cK16snk9jefx86dYKsWe27NqWUUtHyoglvGn5VzG3cCF98AT4+HCibha8a52StsR/TZuBwvD2tsvbn+14lyZ8/YZZTZdim59Yue3m6sfPTWgmzCJX03L8PCxfCzJng5weXL4OXF9y5A+nSgYNeIFNKqaRIxxuruLNrF7d6DeDM9V2Mr+jC9j5ZuJb2OoQ8xvlIb7qU6MUXk3KQOXPCLksntqlouXhRDmQuWSJdGkqWhPHjwcNDHs+QwZ6rU0opFU80/KqoO3AAPv+csA3rGF7LhdGNACMEzOsYfh/QLs//mDo/J2nS2Gd5OrFNvdStW7KjW7gwODtLnXrHjlLaUK6cDKlQSimVrOn1PPVyx45B69Y8eLUco0K2kKl/akZXDfnbEyykKRrMpcxn7RZ8IY67Vqjkw2aDTZugXTspZ+jRQ+7Plg2uXYOpU+UwmwZfpZRKETT8qhc7exbefpuAysX55MmveA1wYUD1IO7f8MbiM/hvnRssuFHc7uUFcdK1QiUvs2dDoUJQu7b05u3eHSZMiHzc2dl+a1NKKWUXWvag/u3yZRgyhOO//MjIKgbz+jgQTjgcb82rxgDup3PgYalrhIYNIdjhCK62ErjYiiSK8gKd2JbC2WxyELNKFZm0dueO7PB+/TW0aoU2lVZKKaXhVz3lc3ANmxd+j+fWvfyW38babiZGmCvsf49mmfoy+Mu8lCgR0VLsJkZYEVxsRQAtL1B2dv06/PQTzJgBFy7AnDnQoQP06SOT2JRSSqm/aPhVcO8eO0b1pLbDPELdgAZgBHngtKM/nYp+xGcTM5I7d+TTI3ZWR244RUBgENk83RhQr5DuuKqE9+iR9OD95RcZP1yzJnz3HbRoIY9rHa9SSql/0PCbkj1+TND40fy0YRhfVAoi1P2v+20OvObWj6ULvyRjxud/qpYXKLu5dQv274f69SFVKnj4EHr3hi5dZBqbUkop9R80/KZEoaHcnjaWiRsGM6noY27XAuebecHlKg4WKy7Oznzfse4Lg69SCc40Yds2mDYNli8HJye4cUPC7++/23t1SimlkhANvymJ1cr5n8cy+o9v+Sn/Q4LKQ7pTVchz7Xu+ebcauavuZsfVLdTIXYPKOSrbe7VKiS1boFs3OHkS0qaFDz+EDz6Q4KuUUkpFk4bflMA02bdgJCM2fceK7A9wKGjwyqF6FAkZzeCexWjQIKI0sjLV8mjoVXZmmrBvH6RODUWLQsaMkCYNzJoFb7whXRyUUkqpGIpV+DUMwxOYCRQHTOBd0zR94mBdydoqP/8EOSy26/Iupq/5mkOnd3Iw3RM8XnEg/65m5E47ia8/9aKy5lyVmDx+DAsWwJQp4Ocnk9dmz4bixWHPHnuvTimlVDIR253f8cB60zRbG4bhDOiWzEtIm7AjBIVZAfAPDGLQiiMAcRaAQ62hDF7wId+d+wnTADyhyJ7aeGdewqAJ6SlSJE6+jVJx55tvYOxYuH8fSpaUAPzmm/ZelVJKqWQoxuHXMIw0QHWgM4BpmqFAaNwsK/kaueHU0+AbISjMysgNp2Idfu8H32fauiGM2zuJa66R09YMLDTtXpthjdLH6usrFWfCwmDdOmjUCCwWsFrl9927Q+XK2qJMKaVUvInNzm9e4Bbwk2EYpYD9QC/TNB///UmGYXQFugLkzJkzFt8ueXjRCODYjAb2f+DPuD+GMO3gjzx0DOO1AAvlLtRlQ63t2IxQnB2daVayRoy/vlJxxt9fBlHMmAEBAbB+PdSrB99+a++VKaWUSiFiE34dgbLAx6Zp7jEMYzzwKfDF359kmuZ0YDqAt7e3GYvvlyxk83TD/zlBNyajgY/dPMbwjd+x8ORibNhoddKBIgfbkbvLBNpNzcTB2z5suajdG1QicPu2dGlYtUpGENevL23L6tSx98qUUkqlMLEJv1eBq6ZpRpxEWYaEX/UfBtQr9EzNL0RvNLBpmmy7tI2hm4ex4fJ63MLggwNQ6kQLsvQdQ4OFuXH86/9q5RyVNfQq+3nwAE6cgIoVIV06OH9eRg1/8AHky2fv1SmllEqhYhx+TdO8bhjGFcMwCpmmeQqoDRyPu6UlDdHt3BDT0cA7Lu9gyr4p7LtygDP3T5LhsQPf7oHy5+uS9otRVFpbQsskVeJw/DhMmgRz5kgv3itXZCjF/v1ay6uUUsruYtvt4WNg/l+dHs4D78R+SUlHTDs3RGc0cFBYEF9u/pLRPqMxMTFMGLAT3jxcAdfvRlL4/aqxfyFKxQUfH/j8c9i0CVxcoF07OcDm5CSPa/BVSimVCMQq/JqmeRDwjpulJD3x2bnhzpM7TNo3ibG7fiAw9LZ0UTbAwQRL/Q6U/n22hgllf7duSQ1v5swQHAxnz8LQofDee5Apk71Xp5RSSv2LTniLhfjo3HDh3gVG+4xh5v4fCbEFUeFUJjqdgf71DEKdDJydXWjatpsGX2Vf+/bBxImwaJEcZBs/HmrUgHPneFp0rpRSSiVC+lMqFuKyc8P+gP2M2DmSpceXgs1C1UM5mbzrHPkfhWH+byRl2nuzJcBHOzco+1qyBMaMkYlrqVNDly4SfkHekGnwVUoplcjpT6pYiE3nBp8rPmy+uBk3Rzd+ObWGLZc24RDqwWt7y/Hj3kPkfHIVeg7A8fNBkC4dlYHK+WpEeW0JNUJZpQC3b0PGjPL79eshMBB++EHGD6dJY9elKaWUUtGl4TcWYtq5Yful7dSZW4dQqwzEc3iSgdd2NGLuwR1kD/LF7NARh8HfQgyHgiTECGWVAuzdCxMmyG7vrl3g7S3lDalTa9mNUkqpJEvDbyxFp3PDw5CHzDwwk682f/M0+GIzGLAvjGG71mI2aIAxbBhGyZKxWlN8HsRTyVxYGCxbJqF3927w8IBu3eCVV+RxDw/7rk8ppZSKJQ2/CeD6o+v8sOcHJu6ZzIOwQLhWGiPTURwcwnG2mjRz9IJNqzBq1oyT7xcfB/FUMme1gsUCISGRYXfCBOjUSUsblFJKJSsafuPRqdunGO0zmp/9ZhNmC4MTLSm2twnLw+Zw1whnS7n01Gjeh8qDP4vTy8hxeRBPJXN+flLKcOgQHDggJQ179kCBAuDgYO/VKaWUUnFOw2888Lniw4idI1h9ajVYnTEPvEuBo+1YkmYmpS92hgwZ4MvxVP7wQ3B2funXi+7htdiOUFbJnNUKv/wCY8fC9u0yha1zZ3jyRH5fSP+cKKWUSr40/P5DTLokRHRucHRwZPXJX9h1dSeW0HSYPp9R8HIH5uX8Ee/r9TBuGPDpp3JLmzbK64nu4bWYHsRTKcSqVdC6NeTODaNHw7vvgqennRellFJKJQzDNM0E+2be3t6mr69vgn2/6Ppn0ATZMR3assQLg+PWi1t5fe7rUtYAODzOgm3bIIo/eZsfS8yl/IbBGHfvQocOMHhwtDs4VBm26bklDF6ebuz8tFa0vpZKoc6fl/rdvHmhZ0851Pbbb9C4sdT5KqWUUsmQYRj7TdP81yRiLer7m//qkvBPgcGBDN8xnMYLmjwNvtgcyB7QnX2vZeXwkwpUWNAbo3Rp2L8fZs+OUesyPbymYsQ0Yds2aNEC8ueHSZPg0iV5zMkJmjXT4KuUUipF0rKHv4lK0Lz64Crjd49nqu80HoU9xAgoD68cBks4Lg6OLLqzCO/5x6B4cdldq18/VofZ9PCaipHevWW3N316KbPp3h28tOxFKaWU0vD7N/8VNI/ePMqoXaOYf3g+VpsJx9pi8RnAW7XL0Kj4Ys5t/pYaa49T2XoXZs6UA0RxsLOmh9dUlNy5A1OnwttvQ65c0LYtFC0q5Tbu7vZenVJKKZVoaPj9m38GTRMTnI4TkvZ3SkzZiMXqjnXfR7gd6sMHb+Sm39o7ZJ/VC96eDK6uMPBb6NtXTszHET28pv7TmTPSteHnnyEoSMYQf/ABVKkiN6WUUko9Q8Pv30QEyi9+W8aF4JXYHC8SxCUCrmaEHd+S9vxH9O6age6zQki/YDTUGAIPHsD778O330LmzPG2Lg276hk2G7RrJ9PYnJxkx7dvXyhWzN4rU0oppRI1Db9/ExQWhM/tCRwLH4npaIJpwM4BZLvwDQP7uPFOZxP335ZC1U/lBH39+jBypNT3KhXfwsNh61aoXVsGUGTLBp99JvW8WbLYe3VKKaVUkqDhF7gbdJcp+6Ywfs8Ebj25CSZgAKYDbZulY/6Hbjj67oa6/WDXLihRAjZsgLp17b10lRI8fCh15OPHS8eGQ4egZEkYN87eK1NKKaWSnBQdfi8FXmLs7rHM2D+TJ+GPcbzQEI43xKH+ALCE4uLsTO8KhXDs0B4WLZLdtRkz4J13tE2Uin9378LQoTB9upTXVKsmAVivNCillFIxliLD76Hrhxi5aySLji7CtBlw9E3Y0Z8mr5bgkx/Alq0sW06up8amc1Su/qZcYv7iCxg4EFKntvfyVXL3+LEcmrRY4McfoUED6NcPype398qUUkqpJC9Zh9+/jyrOmtaV+uXusOvmLDac24CjNTXWvb1x3NeLTi1yMGArFCqE1FVO96PyV5OlfVTHjjBkCGTPbu+Xo5Iz04TNm2HECLh+Hfz8ZAT2pUvg4WHv1SmllFLJRrINvxGjiu9ZD/PQaS1Xgs/h4+OPY0hm2D4U15Mf0u0dT3rPknNDAKxfLyfmT5yAGjVg9GgoW9aeL0Mld+Hh0rFh5Eg4cEA6hkSMIHZ21uCrlFJKxbFkG35HbjhFoPUoN5z/B4ZVOjds/xR8P2Xop2n58Ffw9PzrycePy2Xl9etlFOyqVdC0aawmsykVJUuWwFtvQcGCUtvboYP0jFZKKaVUvEi24TcgMIhgxyNI6wbAdMAt5xMyld7Fp582kPtu34avvoJp06SWd8wYaRvl7Gy3datk7tYtmDhRymi6dIHWrWV3t1EjqS1XSimlVLxKtj9ts3m64WorgYETmBYMw0LaLDnIntEFQkMl6ObPL8H3ww/h7Fno00eDr4of587BRx9BzpwyEMXPT+53doYmTTT4KqWUUgkk2e78yqjiUAgdQrDDEVxtJfB0KMYY5wtQ7AMJu/XrS11v0aL2Xq5Kzr77Dr78Ehwd5QBlv35QuLC9V6WUUkqlSMk2/EaMAx65wZmAwCK89sSfkT5DyOS7C4oUgXXrJPwqFddMUyaxFS4svaErVYIBA6BXL8ia1d6rU0oppVK0ZH2ttXkZL3Z2LsqF2yv5eeKHZLpwSuotDx/W4Kvins0mhyUrV4aaNWHyZLm/dm0YNkyDr1JKKZUIJOvwC0gHhzlzpJ73zBk50OaYbDe8lb3MmyeT11q0kENtU6bAoEH2XpVSSiml/iH5p8COHaF6dcib194rUclNaGjkAck1a+T3CxdKBwd9g6WUUkolSsl/59fBQYOvilt378I334CXFxw9KvfNmCEdHNq10+CrlFJKJWL6U1qpqLp+XVrkTZkCjx5JizKLRR7TSWxKKaVUkqDhV6moCA6Wmt579+CNN6Set0QJe69KKaWUUtGk4VepFzl1ChYvhi++kJHDkydD2bIyHEUppZRSSVLyr/lVKroOHoS2baUf9NChMhAF5D4NvkoppVSSpuFXqQgBAVLHW6aMtMj75BO4dAkKFLD3ypRSSikVR7TsQaVspgk3b0LmzJA+PVy8CN9+Cz16QLp09l6dUkoppeKYhl+VMpkm/PGHBF1/fzh9Wup6Dx8Gw7D36pRSSikVT7TsQaUspgm//SYjiOvVk7KG/v3lftDgq5RSSiVzuvOrUpY//4RGjSBXLpg2DTp1AhcXe69KKaWUUglEw69K3mw2WLlSprJ16QK1a8OiRdCyJTg52Xt1SimllEpgWvagkierVUJuyZLQurWMHzZNGXf9xhsafJVSSqkUSsOvSn62bJFpbO3by87vggXg46P1vEoppZTSsgeVTFit8PgxpEkD7u7g7AxLlkCrVrLbq5RSSimF7vyqpM5qhYULZae3b1+5r0IFmdLWpo0GX6WUUko9Q5OBSppsNli8GEqUgDffBIsFGjaMfFxLHJRSSin1HBp+VdL09dfQrp2E3MWLZThFy5b2XpVSSimlEjmt+VVJQ0TLsty5oVw5eP99KFpUShssFnuvTimllFJJRKx3fg3DsBiG4WcYxpq4WJBSz7DZYPlyKF1aWpZNmSL358wpO78afJVSSikVDXFR9tALOBEHX0epZ23YILu8rVtDSAjMmydT2ZRSSimlYihW4dcwjOxAI2Bm3CxHpXimKTeAffvgwQOYPRuOHYO33tKdXqWUUkrFSmx3fscBAwFb7JeiUrydO6FWLVi2TD7u3x9OnoSOHcFRy9OVUkopFXsxDr+GYTQGbpqmuf8lz+tqGIavYRi+t27dium3U8mZry80aABVq8KJE9K7F8DVVccQK6WUUipOxWbntwrQ1DCMi8AioJZhGPP++STTNKebpultmqZ3pkyZYvHtVLLUuzeULy8lDiNGwPnzcpBNKaWUUioexPhasmmag4BBAIZh1AD6m6b5dtwsSyVrp09D9uwyhrhKFciQAXr1ktHESimllFLxSIdcqIRz6RK88w4UKQKTJ8t9bdrAF19o8FVKKaVUgoiTU0SmaW4BtsTF11LJ0M2b8P330qPXMKBnTznEppRSSimVwPQIvYp/HTrAn3/Cu+/Cl19Cjhz2XpFSSimlUigNvyruBQfLLm/79pAlC4wcCc7OULiwvVemlFJKqRROw6+KO+HhMpDi66/h6lVpU9ajB5Qsae+VKaWUUkoBeuBNxZXly6F4cXj/fciWDTZulOCrlFJKKZWI6M6vihsrVoCDA6xcCc2aycE2pZRSSqlERnd+VcwcOAB168Lhw/LxpElw5Aj8v737j5WqPBM4/n0WaBtXuqzKKnsLuKXb26xNEYvICmrL9qc1ovxhQerSuNHaqFmbJYX+0FobsWppwppmKbRNqSFqtlqXNrSxbWgMUuhWChYFRS1U1NVdbcu1WxXk3T/eQ/Y6zFzucIc5c+d8P8nJPfecd5gnD++c++Sd97znggssfCVJUsey+FVzfvMbuPhiePe7cwG8a1c+PmYMjBhRZmSSJEmHZfGrwfvsZ6G3F+69N+8/8QScf37ZUUmSJA2ac341sD/9Cd70pjyVYcQIWLAgr+bQ01N2ZJIkSU1z5Ff17d8P3/gGvO1tsHZtPnbDDbBypYWvJEkatix+9XopwZo1MHkyXHYZTJgAY8fmc97IJkmShjmLX73evHl5qbJ9++C734UNG2DatLKjkiRJagnn/Cqv2NDTk5/INns2nHNOfljFqFFlRyZJktRSjvxW2e9/D5/+dF7B4etfz8fmzYNPftLCV5IkdSVHfqto3z5Yvhy++EV48cW8gsOFF5YdlSRJ0lFn8VtF8+bB3XfDrFnwla/AlCllRyRJktQWTnuoigcfhN/9Lu9/6lPw/e/DT35i4StJkirF4rfbPfUUXHIJTJ2aR3kBZsyA885z6TJJklQ5TnvoVn19cPPNsHRpXrt38WJYtKjsqCRJkkpl8dutrr4aVq2Ciy+GJUtg4sSyI5IkSSqd0x66yfr18OSTef/aa2HjRli92sJXkiSpYPHbDXbvho9+FM46K4/yAkyaBGecUW5ckiRJHcbidzh76aU8wvuOd+TVG77wBVi2rOyoJEmSOpZzfoezJUvgppvyvN4vfxnGjy87IkmSpI5m8Tvc/PznMHIknH46LFyYlyw788yyo5IkSRoWnPYwXOzZA/Pn50L3+uvzseOOs/CVJElqgsVvp3v5ZbjxRujthXvugc9/Hu66q+yoJEmShiWnPXS6VatywTtnTn5gxcknlx2RJEnSsGXx24keeyxPc5g1Cy69NK/mcM45ZUclSZI07DntoZP09eVHEL/znXDllXDgAIwaZeErSZLUIha/nSCl/CS23l645ZZ8Y9u6dfBn/vdIkiS1ktMeOsG6dfCxj8HUqfmmtunTy45IkiSpKzm0WJYXXoC1a/P+e9+bn9C2aZOFryRJ0lFk8dtuBw7AihXw9rfD3Lmwdy9E5IdVOM1BkiTpqLLaaqfNm/NDKT7xiXxT2wMPwJvfXHZUkiRJleGc33Z5+mk44ww4/ni4/fZ8U1tE2VFJkiRViiO/R1NKsGFD3u/pySs67NiRb26z8JUkSWo7i9+jZdu2vD7vjBnwq1/lYxddBGPGlBqWJElSlVn8tlpfHyxcCKeeCg8/DCtXwuTJZUclSZIknPPbWvv3w+mnw6OPwmWXwU035Tm+kiRJ6ggWv63w29/C+PEwciRcey1MmuR6vZIkSR3IaQ9D8corcMMNec3eO+/Mx+bPt/CVJEnqUI78Hqmf/QyuuCJPcZg7Nz+lTZIkSR3Nkd8jsWhRLnZffRV+9CO44w446aSyo5IkSdJhWPwOVkr5hjbID6v4zGfycmYf/GC5cUmSJGnQLH4HY8eOPNJ766359zlzYMkSOOaYcuOSJElSUyx+B/Lyy3DddfCud8HWrTBuXNkRSZIkaQi84a2RDRvg4x+HnTvzCg5Ll8KJJ5YdlSRJkobgiIvfiBgPfAc4CTgArEgpLWtVYKUbORIi4L774P3vLzsaSZIktcBQRn73A/+SUtocEaOBByPixymlR1oUW3ullFdt2LYtz+edNg0eeQRGjCg7MkmSJLXIEc/5TSk9m1LaXOz3AduBnlYF1la7d8NHPpKnN6xblx9eARa+kiRJXaYlN7xFxMnAFGBTK/69tnntNbjtNjjlFLj/fli2DNavhze+sezIJEmSdBQM+Ya3iDgWuBu4JqW0t875y4HLASZMmDDUt2utZ56BxYvh7LNh+XKYOLHsiCRJknQUDWnkNyJGkQvf1Smle+q1SSmtSClNTSlNHTt27FDerjVeeQVWrcpzfMePh82bYe1aC19JkqQKOOLiNyIC+CawPaX01daFdBRt2ABTpuQlzB54IB/r7c2rOkiSJKnrDWXkdwZwCTArIrYU27ktiqu1+vrgqqtg5kz44x/zSO/MmWVHJUmSpDY74jm/KaX1QOcPmaaU1+n9xS/g6qvhxhvh2GPLjkqSJEkl6P4nvEXAl74Eo0fD9OllRyNJkqQSdX/xCz6hTZIkSUCL1vmVJEmShgOLX0mSJFWGxa8kSZIqw+JXkiRJlWHxK0mSpMqw+JUkSVJlWPxKkiSpMix+JUmSVBkWv5IkSaoMi19JkiRVhsWvJEmSKsPiV5IkSZVh8StJkqTKsPiVJElSZVj8SpIkqTIsfiVJklQZFr+SJEmqDItfSZIkVUaklNr3ZhH/Dexu2xv+vxOA/ynhfYcr89U8c9Yc89Uc89Uc89Uc89Uc89WcMvM1MaU0tvZgW4vfskTEL1NKU8uOY7gwX80zZ80xX80xX80xX80xX80xX83pxHw57UGSJEmVYfErSZKkyqhK8bui7ACGGfPVPHPWHPPVHPPVHPPVHPPVHPPVnI7LVyXm/EqSJElQnZFfSZIkqbuK34j4UEQ8GhGPR8TiOucjIv61OP9QRJxWRpydICLGR8S6iNgeEQ9HxD/XafOeiPhDRGwptuvKiLVTRMSuiPh1kYtf1jlv/ypERG+/frMlIvZGxDU1bSrfvyLiWxHxfERs63fsuIj4cUTsLH7+ZYPXDni960YN8nVrROwoPnPfi4gxDV474Oe3GzXI1/UR8XS/z925DV5r/8rH7uqXq10RsaXBa6vYv+rWEcPiGpZS6ooNGAE8AbwVeAOwFfi7mjbnAj8EApgObCo77hLzNQ44rdgfDTxWJ1/vAX5QdqydsgG7gBMGOG//qp+XEcB/kddb7H+88v0LOBs4DdjW79gtwOJifzFwc4OcDni968atQb4+AIws9m+ul6/i3ICf327cGuTremDhYV5n/6p/filwXYNzVexfdeuI4XAN66aR32nA4ymlJ1NKrwJ3ArNr2swGvpOyjcCYiBjX7kA7QUrp2ZTS5mK/D9gO9JQb1bBn/6rvH4AnUkplPOCmo6WU7gderDk8G1hV7K8CLqjz0sFc77pOvXyllO5LKe0vft0IvKXtgXWoBv1rMOxfNSIigIuAO9oaVAcboI7o+GtYNxW/PcBT/X7fw6HF3GDaVE5EnAxMATbVOf33EbE1In4YEae0N7KOk4D7IuLBiLi8znn7V31zafwHw/51qBNTSs9C/uMC/FWdNva1+i4lf/tSz+E+v1VyVTFN5FsNvpK2fx3qLOC5lNLOBucr3b9q6oiOv4Z1U/EbdY7VLmUxmDaVEhHHAncD16SU9tac3kz+qnoycBtwb5vD6zQzUkqnAR8GroyIs2vO279qRMQbgPOBf69z2v515OxrNSLic8B+YHWDJof7/FbFvwGTgFOBZ8lf5deyfx1qHgOP+la2fx2mjmj4sjrH2tbHuqn43QOM7/f7W4BnjqBNZUTEKHKHXZ1Suqf2fEppb0rppWJ/LTAqIk5oc5gdI6X0TPHzeeB75K9t+rN/HerDwOaU0nO1J+xfDT13cLpM8fP5Om3sa/1ExALgPGB+KiYU1hrE57cSUkrPpZReSykdAFZSPw/2r34iYiQwB7irUZuq9q8GdUTHX8O6qfj9T+BvI+JvitGmucCamjZrgH8s7sqfDvzh4NB81RTzl74JbE8pfbVBm5OKdkTENHJ/eaF9UXaOiPjziBh9cJ98k822mmb2r0M1HC2xfzW0BlhQ7C8A/qNOm8Fc7yohIj4ELALOTyn9b4M2g/n8VkLNfQgXUj8P9q/Xex+wI6W0p97JqvavAeqIzr+GtevOunZs5LvtHyPfQfi54tgVwBXFfgBfK87/Gphadswl5mom+SuGh4AtxXZuTb6uAh4m34W5ETiz7LhLzNdbizxsLXJi/zp8zo4hF7N/0e+Y/ev1ObqD/NXzPvJIyD8BxwM/BXYWP48r2v41sLbfaw+53nX71iBfj5PnDh68ji2vzVejz2+3bw3ydXtxfXqIXGyMs381zldx/NsHr1v92tq/GtcRHX8N8wlvkiRJqoxumvYgSZIkDcjiV5IkSZVh8StJkqTKsPiVJElSZVj8SpIkqTIsfiVJklQZFr+SJEmqDItfSZIkVcb/AaPT4ImufGjZAAAAAElFTkSuQmCC\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": [
      "[5.54650352 0.39527214]\n",
      "[0.39597165 0.03411852]\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": [
      "[5.07327213 0.48301984]\n",
      "[0.13186014 0.0113616 ]\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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
