lp06_quantile-regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>Quantile methods</center>\n",
    "### <center>Alfred Galichon (NYU & Sciences Po)</center>\n",
    "## <center>'math+econ+code' masterclass series</center>\n",
    "#### <center>With python code examples</center>\n",
    "© 2018-2023 by Alfred Galichon. Past and present support from NSF grant DMS-1716489, ERC grant CoG-866274 are acknowledged, as well as inputs from contributors listed [here](http://www.math-econ-code.org/team).\n",
    "\n",
    "**If you reuse material from this masterclass, please cite as:**<br>\n",
    "Alfred Galichon, 'math+econ+code' masterclass series. https://www.math-econ-code.org/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "* Koneker and Bassett (1978). `Regression quantile'. Econometrica.\n",
    "* Koenker (2005). Quantile Regression. Cambridge University Press.\n",
    "* Koenker, Roger and Kevin F. Hallock. “Quantile Regression”. Journal of Economic Perspectives, Volume 15, Number 4, Fall 2001, Pages 143–156"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is the right definition of a quantile?\n",
    "\n",
    "\n",
    "In dimension one, the following statements equivalently define quantiles of a\n",
    "distribution $Y\\sim\\nu$:\n",
    "\n",
    "* The quantile map is the (generalized) inverse of the cdf of $\\nu$:\n",
    "$F_{\\nu}^{-1}$.\n",
    "\n",
    "* The quantile map is the nondecreasing map $T$ such that if\n",
    "$U\\sim\\mathcal{U}\\left(  \\left[  0,1\\right]  \\right)  $, then $T\\left(\n",
    "U\\right)  \\sim\\nu$.\n",
    "\n",
    "* The quantile at $t$ $F_{\\nu}^{-1}\\left(  t\\right)  $ is the solution of\n",
    "$\\min_{q}\\mathbb{E}\\left[  \\rho_{t}\\left(  Y-q\\right)  \\right]  $, where\n",
    "$\\rho_{t}\\left(  z\\right)  =tz^{+}+\\left(  1-t\\right)  z^{-}$.\n",
    "\n",
    "* The quantile map is the solution to the Monge problem between\n",
    "distribution $\\mathcal{U}\\left(  \\left[  0,1\\right]  \\right)  $ and $\\nu$\n",
    "relative to cost $\\Phi\\left(  u,y\\right)  =uy$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile: properties\n",
    "\n",
    "\n",
    "\n",
    "Quantiles have a number of enjoyable properties that make them easy to work with.\n",
    "\n",
    "* They fully characterize the distribution $\\nu$.\n",
    "\n",
    "* They allow to construct a representation of $\\nu$: $F_{\\nu}^{-1}\\left(\n",
    "U\\right)  $, $U\\sim\\mu:=\\mathcal{U}\\left(  \\left[  0,1\\right]  \\right)  $ has\n",
    "distribution $\\nu$.\n",
    "\n",
    "* They embed the median ($F_{\\nu}^{-1}\\left(  1/2\\right)  $) and the\n",
    "extreme values ($F_{\\nu}^{-1}\\left(  0\\right)  $ and $F_{\\nu}^{-1}\\left(\n",
    "1\\right)  $).\n",
    "\n",
    "* They allow to provide a construction of distance between distributions:\n",
    "for $p\\geq1$,<br>\n",
    "$\n",
    "\\left(  \\int\\left\\vert F_{\\nu}^{-1}\\left(  t\\right)  -F_{\\nu}^{-1}\\left(\n",
    "t\\right)  \\right\\vert ^{p}dt\\right)  ^{1/p}\n",
    "$<br>\n",
    "is the $p$-Wasserstein distance between $\\mu$ and $\\nu$.\n",
    "\n",
    "* They allow for a natural construction of robust statistics by trimming\n",
    "the interval $\\left[  0,1\\right]  $.\n",
    "\n",
    "* **They lend themselves to a natural notion of regression: quantile\n",
    "regression (Koenker and Bassett, 1978; Koenker 2005).**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###     Quantile/quantile regression: applications\n",
    "\n",
    "Quantiles are widely used in economics, finance and statistics.\n",
    "\n",
    "* Comonotonicity: $\\left(  F_{\\nu_{1}}^{-1}\\left(  U\\right)  ,F_{\\nu_{2}%\n",
    "}^{-1}\\left(  U\\right)  \\right)  $ for $U\\sim\\mu:=\\mathcal{U}\\left(  \\left[\n",
    "0,1\\right]  \\right)  $ is a comonotone representation of $\\nu_{1}$ and\n",
    "$\\nu_{2}$.\n",
    "\n",
    "* Mesures of risk: Value-at-risk $F_{\\nu}^{-1}\\left(  1-\\alpha\\right)  $;\n",
    "CVaR $\\int_{1-\\alpha}^{1}F_{\\nu}^{-1}\\left(  t\\right)  dt$.\n",
    "\n",
    "* Non-expected utility: Yaari's rank-dependent EU (Choquet integral)\n",
    "$\\int_{0}^{1}F_{\\nu}^{-1}\\left(  t\\right)  w\\left(  t\\right)  dt$.\n",
    "\n",
    "* Demand theory: Matzkin's identication of hedonic models.\n",
    "\n",
    "* Income and inequality: Chamberlain (1994)'s study of the effect of\n",
    "unionization on wages.\n",
    "\n",
    "* Biometrics: growth charts.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is quantile regression?\n",
    "\n",
    "* Quantile regression therefore adopts a parameterization of the\n",
    "conditional quantile which is linear in $Z$. That is<br>\n",
    "$\n",
    "Q_{Y|X}\\left(  \\tau|x\\right)  =x^{\\intercal}\\beta_{\\tau}\n",
    "$<br>\n",
    "(note that one can always augment $x$ with nonlinear functions of $x$, so this\n",
    "parameterization is quite general).\n",
    "\n",
    "* In order to estimate $\\beta_{\\tau}$, first note that<br>\n",
    "$\n",
    "Q_{Y|X}\\left(  \\tau|x\\right)  =\\arg\\min_{q}\\mathbb{E}\\left[  \\rho_{\\tau\n",
    "}\\left(  Y-q\\right)  |X=x\\right]\n",
    "$<br>\n",
    "where $\\rho_{\\tau}\\left(  w\\right)  =\\tau w^{+}+\\left(  1-\\tau\\right)  w^{-}$.\n",
    "\n",
    "* Therefore, if the conditional quantile has the specified form,\n",
    "$\\beta_{u}$ is the solution to<br>\n",
    "$\n",
    "\\min_{\\beta\\in\\mathbb{R}^{k}}\\mathbb{E}\\left[  \\rho_{\\tau}\\left(\n",
    "Y-X^{\\intercal}\\beta\\right)  |X=x\\right]$<br>\n",
    "for each $x$, and therefore it is the solution to the quantile regression\n",
    "problem introduced by Koenker and Bassett (1978)<br>\n",
    "$\n",
    "\\min_{\\beta\\in\\mathbb{R}^{k}}\\mathbb{E}\\left[  \\rho_{\\tau}\\left(\n",
    "Y-X^{\\intercal}\\beta\\right)  \\right]  .\n",
    "$<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile regression as linear programming\n",
    "\n",
    "* Koenker and Bassett showed that this problem has a linear programming formulation. Indeed, consider its sample version<br>\n",
    "$\\min_{\\beta\\in\\mathbb{R}^{k}}\\sum_{i=1}^{n}\\rho_{\\tau}\\left(  Y_{i}%\n",
    "-X_{i}^{\\intercal}\\beta\\right)$\n",
    "\n",
    "\n",
    "* Introducing $Y_{i}-X_{i}^{\\intercal}\\beta=P_{i}-N_{i}$ with $P_{i},N_{i}\\geq0$, we have<br>\n",
    "$\n",
    "\\begin{array}\n",
    "~ \\min_{\\substack{\\beta\\in\\mathbb{R}^{k}\\\\P_{i}\\geq0,N_{i}\\geq0}} &  \\sum\n",
    "_{i=1}^{n}\\tau P_{i}+\\left(  1-\\tau\\right)  N_{i}\\\\\n",
    "s.t.~ &  P_{i}-N_{i}=Y_{i}-X_{i}^{\\intercal}\\beta\n",
    "\\end{array}$<br>\n",
    "therefore $\\beta$ can be obtained by simple linear programming.\n",
    "\n",
    "* The above can be simplified to<br>\n",
    "$\n",
    "\\begin{array}\n",
    "~ \\min_{\\substack{\\beta\\in\\mathbb{R}^{k}\\\\P_{i}\\geq0}} &  \\sum\n",
    "_{i=1}^{n} P_{i}+\\left(  1-\\tau\\right)  X_{i}^{\\intercal}\\beta\\\\\n",
    "s.t.~ &  P_{i} + X_{i}^{\\intercal}\\beta\\geq Y_{i}~\\left[  V_i\\geq 0\\right]\n",
    "\\end{array}$<br>\n",
    "\n",
    "* The dual of the latter is<br>\n",
    "$\\begin{array}\n",
    "&  \\max_{V\\geq 0} & \\sum_i  Y_iV_i  \\\\\n",
    "s.t.~ &   V_i\\leq1~\\left[  P_i\\geq0\\right]  \\\\\n",
    "&  \\frac{1}{I}\\sum_i  V_i X_{ik}  =\\left(  1-\\tau\\right)  \\bar{x}_k  ~\\left[  \\beta_k\\right]\n",
    "\\end{array}$<br>\n",
    "where $\\bar{x}_k:=\\frac{1}{I}\\sum_i X_{ik}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import the libraries we shall need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import gurobipy as grb\n",
    "import scipy.sparse as spr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "base\n"
     ]
    }
   ],
   "source": [
    "import os \n",
    "print(os.environ['CONDA_DEFAULT_ENV'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the data\n",
    "\n",
    "We shall use a historical dataset by Engle on food expenditures as a function of the household's income."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>income</th>\n",
       "      <th>food</th>\n",
       "      <th>clothing</th>\n",
       "      <th>housing</th>\n",
       "      <th>heating/lightening</th>\n",
       "      <th>tools</th>\n",
       "      <th>Education</th>\n",
       "      <th>Public safety</th>\n",
       "      <th>health</th>\n",
       "      <th>Services</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>835.94</td>\n",
       "      <td>576.28</td>\n",
       "      <td>129.34</td>\n",
       "      <td>78.32</td>\n",
       "      <td>46.80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>873.44</td>\n",
       "      <td>631.80</td>\n",
       "      <td>83.00</td>\n",
       "      <td>79.80</td>\n",
       "      <td>73.84</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>951.44</td>\n",
       "      <td>608.64</td>\n",
       "      <td>134.00</td>\n",
       "      <td>108.00</td>\n",
       "      <td>78.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>473.00</td>\n",
       "      <td>301.00</td>\n",
       "      <td>40.00</td>\n",
       "      <td>76.00</td>\n",
       "      <td>46.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>601.00</td>\n",
       "      <td>378.00</td>\n",
       "      <td>65.00</td>\n",
       "      <td>84.00</td>\n",
       "      <td>50.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   income    food  clothing  housing  heating/lightening  tools  Education  \\\n",
       "0  835.94  576.28    129.34    78.32               46.80    0.0        0.0   \n",
       "1  873.44  631.80     83.00    79.80               73.84    0.0        5.0   \n",
       "2  951.44  608.64    134.00   108.00               78.00    0.0        5.0   \n",
       "3  473.00  301.00     40.00    76.00               46.00    0.0        0.0   \n",
       "4  601.00  378.00     65.00    84.00               50.00    0.0        0.0   \n",
       "\n",
       "   Public safety  health  Services  \n",
       "0            0.0     5.2       NaN  \n",
       "1            0.0     0.0       NaN  \n",
       "2            0.0    17.8       NaN  \n",
       "3            2.0     8.0       NaN  \n",
       "4            6.0    18.0       NaN  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "engle_path = 'https://raw.githubusercontent.com/alfredgalichon/VQR/master/engle-data/'\n",
    "engle_data = pd.read_csv(engle_path+ 'engel.csv')\n",
    "\n",
    "engle_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "income = np.array(engle_data['income'])\n",
    "food = np.array(engle_data['food'])\n",
    "housing = np.array(engle_data['housing'])\n",
    "nbi=len(income)\n",
    "X_i_k = np.array([np.ones(nbi),income]).T\n",
    "#Y = np.array([food,housing]).T\n",
    "_,nbk = X_i_k.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-01-12\n",
      "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "Optimize a model with 235 rows, 237 columns and 705 nonzeros\n",
      "Model fingerprint: 0x2e1ba335\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 5e+03]\n",
      "  Objective range  [1e+00, 1e+05]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [2e+02, 2e+03]\n",
      "Presolve time: 0.01s\n",
      "Presolved: 235 rows, 237 columns, 705 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0      handle free variables                          0s\n",
      "     223    8.2118037e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 223 iterations and 0.02 seconds (0.00 work units)\n",
      "Optimal objective  8.211803659e+04\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[81.48614818083601, 0.560174688436782]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr_lp=grb.Model()\n",
    "τ = 0.5\n",
    "P = qr_lp.addMVar(shape=nbi, name=\"P\")\n",
    "β = qr_lp.addMVar(shape=nbk, name=\"β\", lb=-grb.GRB.INFINITY )\n",
    "qr_lp.setObjective(np.ones(nbi) @ P + (1-τ) * (np.ones(nbi) @ X_i_k) @ β, grb.GRB.MINIMIZE)\n",
    "qr_lp.addConstr(P  + X_i_k @ β >= food)\n",
    "qr_lp.optimize()\n",
    "\n",
    "βhat = qr_lp.getAttr('x')[-nbk:]\n",
    "βhat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can recover the result using the `quantreg` package of `statsmodel` library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit using:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                         QuantReg Regression Results                          \n",
      "==============================================================================\n",
      "Dep. Variable:                   food   Pseudo R-squared:               0.6205\n",
      "Model:                       QuantReg   Bandwidth:                       64.51\n",
      "Method:                 Least Squares   Sparsity:                        209.3\n",
      "Date:                Fri, 14 Apr 2023   No. Observations:                  235\n",
      "Time:                        12:29:50   Df Residuals:                      233\n",
      "                                        Df Model:                            1\n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     81.4862     14.635      5.568      0.000      52.652     110.321\n",
      "income         0.5602      0.013     42.513      0.000       0.534       0.586\n",
      "==============================================================================\n",
      "\n",
      "The condition number is large, 2.38e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.quantreg('food ~ income', engle_data)\n",
    "print(model.fit(q=τ).summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      q           a         b        lb        ub\n",
      "0  0.05  124.879058  0.343360  0.268630  0.418090\n",
      "1  0.15  111.687464  0.423713  0.382779  0.464648\n",
      "2  0.25   95.473330  0.474120  0.439914  0.508325\n",
      "3  0.35  105.834881  0.488907  0.457761  0.520053\n",
      "4  0.45   81.087627  0.552422  0.525015  0.579830\n",
      "5  0.55   89.655957  0.565608  0.540962  0.590253\n",
      "6  0.65   74.032619  0.604577  0.582173  0.626980\n",
      "7  0.75   62.384896  0.644028  0.622428  0.665628\n",
      "8  0.85   52.275717  0.677601  0.657384  0.697817\n",
      "9  0.95   64.103547  0.709066  0.687835  0.730297\n",
      "{'a': 147.48419855663224, 'b': 0.48517267413692045, 'lb': 0.45686794285854737, 'ub': 0.5134774054152935}\n"
     ]
    }
   ],
   "source": [
    "# code taken from statsmodel documentation: \n",
    "# https://www.statsmodels.org/dev/examples/notebooks/generated/quantile_regression.html\n",
    "\n",
    "quantiles = np.arange(0.05, 0.96, 0.1)\n",
    "\n",
    "\n",
    "def fit_model(q):\n",
    "    res = model.fit(q=q)\n",
    "    return [q, res.params[\"Intercept\"], res.params[\"income\"]] + res.conf_int().loc[\n",
    "        \"income\"\n",
    "    ].tolist()\n",
    "\n",
    "\n",
    "models = [fit_model(x) for x in quantiles]\n",
    "models = pd.DataFrame(models, columns=[\"q\", \"a\", \"b\", \"lb\", \"ub\"])\n",
    "\n",
    "ols = smf.ols(\"food ~ income\", engle_data).fit()\n",
    "ols_ci = ols.conf_int().loc[\"income\"].tolist()\n",
    "ols = dict(\n",
    "    a=ols.params[\"Intercept\"], b=ols.params[\"income\"], lb=ols_ci[0], ub=ols_ci[1]\n",
    ")\n",
    "\n",
    "print(models)\n",
    "print(ols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Food expenditure')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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/hw8fZvHixeTn5wNgMBha7V4t5WYQQr4FrFMU5c+oQcyI2uMJwN465+XVHrPXfn/tcYlEIpHcArjdEoODg3nllVcICgpq8Zjl5eWcPn2aYcOGERkZyaOPPtrssaxWK2vWrGH48OF06NChVeyZhRCYTCZCQkIYMGAAkZGRrd43wh/cDELIV4B/EkIkAf8EfFZ7vL5ckmjkeL0oijJbUZSDiqIcvN06WUokEsmtRmFhIR999BEHDhwA8EvAAHDo0CG2bt1KVVVVi8dyuVzk5ORQUFDgh5nVz4oVK/jyyy+x2+0EBATccGfH5nIzZBqeAd6s/X4x8Gnt93lAXTePRNSti7za7689Xi9CiLnAXFB7T/hnyhKJRCJpDjExMYwdO5bevXu3eCwhBGazmeDgYMaOHcuAAQMICQlp9lgZGRmkpqZiNBp57bXXWsWoCdQKjn79+pGcnIxW23rLcGZmpt/HvBkyDZeAMbXfjweyar9fCTymKEqQoigpqILH/UKIy0CVoijDFFXZ8jSw4kZPWiKRSCTeYbFYWL58OSaTCUVRuOuuu/ziPbBixQq++uorHA4HAQEBRERENHusjIwMFi9e7Flo/R0w2O12lixZwv79+wFVnNnaRk3+NseCG19y+R0wFohWFCUP+C3wIvCuoihawIpaFYEQ4pSiKIuAn1BLMV8TQrh7ob7CzyWXa2u/JBKJRHITUlFRwZkzZ0hNTaVHjx5+G7dPnz4kJCS0qPzRZrMRGBhIamoqjz/+ON26dfPb/Oqi1WpxuVweS+jWQAjBiRMniIuLo3379owfP97v95CtsSUSiUTSKtRtFW21Wv3SM+Hw4cNoNBr69+/f4rEOHDjAzp07mT17NsHBwS0e71psNhvbtm1j5MiRGI1GT3Or1sJqtfL++++TmprKAw88AMjW2BKJRCK5BTh9+vRVraL9ETAIITh16hQZGRn444E3KSmJLl26+H0rwk1ZWRn79u0jK0vddW+NgEEIwZkzZxBCoNfree6555g8ebLf7+NGZhokEolE4nfsdju7du1i5MiRLV6Uy8rKMBgM6PV6ampq0Ol0zbZvzszMpLi4mBEjRjR9cjNwOp1kZ2d7qiGqqqqaLc70hpMnT7J06VKefPJJunbtet3rMtMgkUgkkpuSsrIyVq5cicPhQKfT+aVVdE1NDZ999pmnJ0VQUFCL+j1kZGRw8uRJT+8If7Nr1y7mz59PSUkJQKsEDC6Xy9ObIi0tjUcfffSGlWzeDCWXEolEIrkNuHz5MhkZGQwdOpTY2Fi/jBkUFMQ999xDYmJi0yc3QGlpKQEBAYSFhTF58mQURfFr7wghBFarFYPB4Hnv/rDDbohly5aRn5/Pa6+9hlarpWfPnq12r2uRQYNEIpFImo0QgvLyciIiIkhLSyMlJaXFNsjuEs277rqLpKSkFlk4OxwOvvzyS2JjY3niiSdaRb+wePFiTCYTzz77LEFBQX6tEHHjcDg8wc7QoUOpqqpqVY+HhpDbExKJRCJpNrt27eIf//gHZWVlgH/6JiiKQllZmWfM5uAubdRqtUyZMqVVxYFpaWn069ev1SojLBYL//jHP9i9ezegCjjT0tIavUYIwZEjR/w+F5lpkEgkEkmz6du3L0IIwsPDWzSOEILMzEy6deuGXq/npZdeavYWQmVlJfPnz2fs2LGkpqbWKxBsCTU1NaxatYpevXqRmprqF3fL+nCXaBoMBrp27epTb4qKigpWr17t9znJTINEIpFIfCI/P5+NGzcihCA0NJRRo0a1+Ck7OzubBQsWcOLECYAWaQ6Cg4MJCwvzW1+La9FqtVRUVFBZWdkq4wPk5uby8ccfe3pp3HfffXTu3LnRa5xOp6e8Mzw8nFmzZvl9XjJokEgkEolPZGZmcurUKSwWS4vHcm8jdOrUiUceeYQ+ffo0a5yamho2btzoaQD1xBNPNLnI+oLbqMk9/nPPPcfQoUP9Nv61GI1GNBqNT5/xnj17+Pbbb3E3Z4yLi/P7vGTQIJFIJJImcblcnifrsWPHMnv27Bb3jzh//jwffvghlZWVKIpCampqs8sp8/Pz2bNnDxcvXmzRnBri0qVLbNu2jXPnzgG0qOyzIU6dOsWmTZsAiIqK4sUXX6R9+/aNXmO1WikvLwdgyJAhPPnkk8TExPh9bm5k0CCRSCSSJlmxYgXz5s3Dbrd79tlbSmhoKO3atWt2PwYhBIWFhQB07tyZN954w6/6BafTSV5eHqBmQl5//fVWLW/Mz8/n/PnzOBwOoGkHSSEE8+bNY9myZQghCAwM9Lt+41qkI6REIpFImiQ3N5eioiIGDBjQonGqq6vJzMwkPT29xXPatm0bO3fu5NVXX21Rh8uGWLduHQcPHmTOnDmtYtIkhODw4cMkJiYSGxuLw+FAo9E0mcWorq7GaDSiKApZWVkYjcYGRZLSEVIikUgkN4TTp0/jftBKSkpqccAAsHfvXtasWUNFRUWzx3A/7A4cOJB77rmnxZUb145tt9sBGDFiBDNnzmw1G2ir1crmzZs5fPgwoAosmwoYrly5wnvvvcfJkycB6Natm09VFS1FZhokEolEch1CCBYtWoTJZOK5555r0R6+EAKbzUZQUBAOh4OSkpJmO0bu3LmTK1euMHPmTL/7Iggh+O6779DpdDz00EOt4rvgcrnIyMggLS0NRVEoLS0lIiKiyXs5HA5Pe+0NGzYwZMgQr7IrMtMgkUgkklbDZrNhsVhQFIUZM2bw9NNPt1j0t3btWubNm+dZ+FpqMa0oSrN1EE2N27lzZ1JSUvw+tpuTJ0+yZMkST/fPyMjIJgOG/fv389FHH2Gz2dBoNNx7772tsh3jDdLcSSKRSCSA+hT85ZdfYjAYePLJJwkMDPTLuF27diU4OLjZ3gtnz55Fr9eTmJjIyJEjAf+1mbZaraxevZohQ4aQlJTEsGHD/DJuXRwOB+Xl5URHR9O7d2+MRqNXgYnb3Ck2Npbk5ORWCZR8RWYaJBKJRAKoZYRDhw5l+PDhLV6UT58+7dl37969O2PGjGnWmE6nkzVr1rBjxw5ADRb8uW2gKAqXL1/2VGG0BkuXLuWbb77xCB27du3a6HtwOp2sWLGCXbt2AdCxY0emTZuGXq9vtTl6i8w0SCQSyR2MEIL9+/cTExND586dW9Qcqu6Ye/fuBaBXr17NWuSrqqpo164dAQEBPPnkk4SGhrZ4Xm7sdjsHDx5k6NChBAUF8fLLL/u9+ZPNZiMgIICAgABGjhyJxWLx+h4BAQE4HI5Wa9/dEmSmQSKRSO5gHA4Hhw4d8tg3t4Tq6mpsNhuKovDII4/w1FNPNStgKC8v58MPP/Q0aIqKivJrd8rMzEzWr1/vMYLyd8BgNpv56KOPPJmCxMREunXr1ug15eXlLFq0yGMbPXPmTMaMGePXefkDmWmQSCSSO5Dq6moMBgM6nY5nnnmmxe6OdrudTz75hE6dOjF9+vQWjRcWFsbQoUOb7OToC06nk9LSUmJiYkhLS+Oll17yu82yW4NgNBpJS0ujY8eOPs3v4sWLXLlyhZCQkFbrmNlSZKZBIpFI7jAsFgsff/yxx7I4ODi4xYuUTqdj1KhRzRYSlpSU8PXXX1NVVYWiKIwdO9avFQKrV69m3rx5WK1WFEXxe8CQnZ3tscQGmDhxYpNBQ35+vicbERUVxVtvvdXqjo4tRQYNEolEcodhMBgYPHhwi/ULNpuNFStWkJ+fD6hmS81djF0uFyUlJZSVlbVoTnURQnh0AcOHD2fy5MmtJiYMDQ3FYDBgs9m8vubUqVPs27cPq9UK4NctmNZCmjtJJBLJHYDL5WLLli2kp6cTGRnplzHNZjOffPIJI0aMYPDgwT5fb7PZyMrKolevXoCaom9JS+y6OJ1OvvvuO2JiYrj33nv9Mua1HDt2jMLCQiZOnOj1NZmZmYSFhREbG4vNZsPlcrVqVYQ0d5JIJBKJz5hMJg4dOkRGRkaLx8rJyUEIgdFo5NVXX21WwACwe/duli5dSmlpKYDfAgb3WLGxsURFRfltzGu5cuUKeXl5ngZTTeHOzLgFnoGBgTdFGaUvyEyDRCKR3MaYTCbatWt33ffNJScnhy+++IKpU6c2q+mUEIKamhr0ej0Oh4PLly+TlJTUojm5sVgsrF+/nrvuuqtVggWXy8WBAwfo1KkTsbGxOJ1ONBpNo3oQIQSZmZl0794dRVG4cuUK0dHRfg2QGkNmGiQSiUTiFVeuXOH999/n2LFjAC0KGNwPmElJSUydOpU+ffo0a5xVq1bx1Vdf4XQ60Wq1fgsYQC0fzcrKIjc3129j1qWmpoYdO3Z4Ps+AgIAmBaSnTp1iwYIFnDt3DoDY2NgbFjC0BjLTIJFIJLcp7uZGw4cPb5E5Ul5eHmvXruXxxx9vcabi9OnTlJaW+sV1EtRSz1OnTtG/f39A3QLwl/01qNqIkydP0rdvXxRFoaKigtDQ0Ebn7nA4qKioICoqCpfLxZkzZ+jZs2eblFHKTINEIpFIGsRms7Fu3Tpqamo8zY1a6qao0+lwOp0elb8vCCHYuXOnxzyqZ8+ejBgxwm8L6JEjR1ixYgWXLl0C8GvAAGqDqeXLl3uMoMLCwpqc+7W20ampqTet74Kv3NCgQVGUzxVFKVQU5eQ1x99QFOWMoiinFEX5Y53jv1YU5Wzta/fWOT5QUZQTta+9p9wu/xoSiUTSQgoKCjhw4ICni2JzsdlsnDp1ClBT6i+99BLR0dE+jyOEICsri/Pnz7doPnVxuVyUl5cDMGjQIJ5//nni4+P9Nr7dbqeoqAiAvn378vTTT9OpU6dGr7FarZ7yzhEjRjB58mS/O03eDNzoTMM84L66BxRFGQdMA/oKIXoBf649ngY8BvSqveZDRVHcG0EfAbOBbrVfV40pkUgkdxrV1dUAJCcnM2fOHHr27Nmi8Xbu3MmyZcs8vgm+PptdvHjR08r5iSeeYOrUqS2aT12WLVvG119/7XmS96cuAmDJkiXMnz8fp9OJoihNdqQ0mUz8/e9/91RFJCUlNWkbfatyQ8MgIcR2RVE6XXP4FeD3Qoia2nPcrcamAQtqj19QFOUsMERRlGwgVAixB0BRlK+A6cDa1n8HEolEcvNx+vRpli5dyjPPPENiYmKLtiMcDgdarZZRo0bRtWvXZrkylpeX89VXXzFixAgmTJhAUFBQs+fjxq2/UxSFwYMHYzKZ/Pokb7Va0el0BAQEMHr0aE/DqcZw+0q0a9eO9PT0m8vNUQhYvtzvw94MmobuwChFUfYpirJNURR3wW8CUFcCm1d7LKH2+2uPSyQSyR1Jx44dSU9PJyYmpkXjbNmyhXnz5uFwONDpdCQnJ/t0vduvIDw8nIcffphRo0a1aD5ubDYb8+fP93TO7Nixo8cQyh9UV1fz4YcfsnPnTgASEhKazC6cPn2ad99919Ngavz48XTo0MFvc2oR+/fD6NEwc6bfh74ZggYtEAEMA/4FWFSrUagvFyYaOV4viqLMVhTloKIoB917VBKJRHKrU1VVxaZNm3C5XBgMBiZPntziJ/q4uDji4+ObJdrLzc3lvffe4/Lly4AqePSXKFGn02E0Gv0ucnS5XIDae6N///5ebSm4Mx7t27cnISGBm6oCMTsbHn8chg6FzEz4xz/8foubIWjIA5YJlf2AC4iuPV53oyoRuFR7PLGe4/UihJgrhBgkhBjU0ihcIpFIbhaysrLYt28fLX0YunjxIqdPnwYgNTWVyZMnN8tHICoqiri4OL8t7BaLhdWrV1NdXY2iKMycOZOBAwf6ZWyAc+fO8cEHH3gaTI0fP75JMeXmzZtZs2YNAJGRkTz66KMtrkzxC+Xl8H/+D/ToAStWwH/8B5w9Cy+95Pdb3QzSzuXAeGCroijdgUCgGFgJfKsoyl+BeFTB434hhFNRlCpFUYYB+4CngffbZOYSiURygzGbzRiNRtLT0+nSpQthYWHNHksIwebNm7Hb7fTo0QNFUSg327hQXE2lxU6oQUdKdDDhxvoDgdLSUg4dOsTdd9+N0WjkiSeeaPZcrqWqqorjx4/TqVMnv25FuImIiCA8PNxrC2hQt1+cTqenBXabY7PBxx/Df/4nlJbC00/Df/83JCY2fW0zuaHmToqifAeMRc0kXAF+C3wNfA70B2zAPwshNtee/xvgecABvCWEWFt7fBBqJYYBVQD5hvDijUhzJ4lEciuze/dudu/ezUsvvURISEizx3F7OOh0OkwmEzqdjqCgIMrNNo7klGEM1GLQBWCxOzHbHKQnR9QbOOzfv58tW7bw4osv+qUJlt1u59y5c57KD3eA5C8OHjxISUmJ1w2sLBYL69atY/jw4cTGxt48wYJb5Piv/wpZWTB+PPz5z1CPrbe/zZ1udPXE4w289FQD5/8O+F09xw8Cvf04NYlEIrnp6d69OyaTqUULqcPh4NNPPyUxMZFp06Zd5fB4obgaY6AWY6C6NLj/e6G4mvRkNWiw2+2UlZXRvn17Bg8eTFpaWotdIt3s2rWL7du38/rrrxMZGenXgAGgrKyMoqIir7tpCiE4f/48ycnJxMbG3hwBw4ED8KtfwY4dkJoKP/wAkyfDNXOrrKxk/fr1fr/9zbA9IZFIJJIGKCws5Ny5cwwfPpzo6GjuueeeFo2n1WoZMGBAvUr/SoudiGsyCgZdAGVmm+fnZcuWcenSJd544w20Wm2LAwaXy4XFYiE4OJgRI0bQsWNHv7Xudjqd7N69m27duhEXF8f48eObbDBVWlrK0aNHGTduHEajkTfeeAOdTueX+bSI7Gz4zW/g228hJgY++ghmzYIGyk41Go3HxdKf3AxCSIlEIpE0wOHDh9m9ezcWi6XZYzidTtatW0dBQQEAw4cPr9fhMNSgw2J3XnXMYncSotd6qgTGjBnDtGnT/OaR8N1337FgwQJcLheBgYFNljr6gs1mY9++ffz000+Adw2mzp49y/79+z2mVm0eMJSXq9sQPXvCsmXw7/+uihxffvm6gOHQoUOsWLECUJuTvfnmm36fjsw0SCQSyU2GEAKr1YrBYGDixImMHDkSg8HQ7PGsViunTp0iODiYuLi4Bs9LiQ7mSI66WLo1DSZrDYUndlJxPoZx48Y1er231NUGpKen43K50Gj88wxrt9s5ceIE6enpGAwGr/QfeXl5OJ1OOnbsyKBBg/y65dJs7HZV5Pj221BS8rPI8Rr3y7qfpdlsprKyErvdjk6naxUba5lpkEgkkpuMlStX8tVXX+FwOAgICGi26PHKlSsIIQgODuaVV17hrrvuavT8cGMg6ckRBGo1lJltBGo1DOwUTbBB77cnbqvVyrfffsvJk2oLorS0NHr39p9E7dSpU6xatcrTHrupz04IwcqVK9m8eTOgpvXbNGBwixx79YI33oC+feHQIfjyy+sChsrKSr788kuys7MBGDlyJE899VSrZkdkpkEikUhuMtLS0mjfvn2z/BLc5Ofn89lnn/HAAw8wYMAArzMV4cZA+ifp2L9/P53jehJmDGTKlCl+EwEGBgbicDiw2+1+GQ/UapDy8nJiY2Pp168fUVFRTfajOHv2LCkpKQQEBPDII4+0qBrFbxw8qIoct29XtyNWrYL7779O5OjOLhgMBmw2m2fryl/ZmsaQmQaJRCK5Cbhw4YJn771bt24MHz68RQt1fHw8EydObJbHQWVlJZs3b+bw4cOA782qrsVqtbJhwwZPA6unn36a9HrKA5vL4sWLWbBggafBVFMBQ35+PvPnz/e8v+joaL/0x2g2Fy/CU0/B4MGQkQEffggnTsADD1wXMOzbt48vvvgCIQQ6nY4XX3yR1NTUGzZVmWmQSCSSNkYIwY4dO6ipqSE1NbXZi3RhYSE//vgjDz74IMHBwQwfPtyn60tLS4mMjCQsLIzZs2f7rYqhoKCAvXv30qlTJ7p16+aXrIXZbCYoKIiAgADGjx+Py+VqNDMjhKC4uJiYmBgSEhJ4+OGH6dGjR4vn0SIqKuB//xfeeUcNDv7931XR4zUuky6XC0VRUBQFo9FIWFgYNpuNoKCgG14GKjMNEolE0ka40/SKovDQQw/x9NNPt2gRcDqdlJWVeayRfcFtq5yZmQmottAtmYvdbvfstXfq1Ik333zTb+2i3a2o3Q2m4uPjSWzCBXH9+vV89tlnnhbiaWlpLdr+aRF2O/z979C1K/zhD/Doo2qviN/97rqAwWQy8fHHH3Ps2DEA+vTpw4MPPthmmREZNEgkEkkr4HZX3HamkCM5ZZTX8ToA9enxq6++8pTIGY3GZi0ETqeTs2fPAtChQwdef/31ZnVb7NSpE6NHj6Zjx44+X1sfGzduZP78+ZhMJgC/9GhwOtVy0Hbt2jF48GCPc2RDOBwOampqABg8eDD33Xef3w2jfEIItTdE797w+uvQp0+DIke35iM4OJj27du37bzrIIMGiUQi8TPugMHmcBFhDMTmcF0XOGg0GtLS0khLS2vRvXbu3Mm3335LSUkJgE9Pz+fOneOrr77CbrcTEBDA2LFjGw1cvAmE3Iv0qFGjeOyxx/xWiZCZmcl7773nyaKMHTuW2NjYBs93OBzMnTvX44oYGRlJ//79287V8eBBGDcOpk8HjUYVOW7aBAMGXHfqnj17+OCDD7DZbCiKwoMPPkj37t19up3FYuHChQt+mvzPSE2DRCKR+JnG7Jg1ZRnExMQQHx/PsGHDmn0Pt7fB8OHD6dChA1FRUT6PIYTAbDZjNpubbHxVty9FhDEQi93JkZwyT18KIQRff/01er2eRx55hHbt2vm1dDE6OprY2FhPO+uGcFtEa7Va+vfv32hgcUPIyVG1CvPnq06OH34IL754nTGTO7Og0+lITEykZ8+eTb7Xxli7di1ZWVktmnp93NCGVW2NbFglkUhuBNvOFBJhDLzqqVYIQXFlNcc3LKZjx47MmDGj2ePv2bOHM2fO8Itf/MLnffmysjIKCws9IkBvjZXcmRN3AARgtjkI1GpIT44A4MCBAxgMBr/5LuzZs4fy8nImTZrk1fl5eXksWrSIJ598su2DhYoK+P3v4W9/U0WOv/xlvSJHUKtL/vGPf9CvXz/GjRvXrNsJITh+/DhdunShXbt2lJaWYrPZ6NChw63bsEoikUjuBNx2zO4F1m6rwSY0RIQYefbZZ1vsCdCuXTtCQkKarBiojw0bNpCbm0vnzp3R6XRe1/bX15dC47Sxa9M6IiaOpVOnTgwePNinuTSFyWSioqKiycDG7VsQFRVFXFxc2zaWstvhk0/gt7+F4mL4xS9UgWM9ZaCVlZWEhoai1+vp169fiyy0y8rKWLFiBePGjWPUqFF+q3y5FplpkEgkEj9TN5WvcdSw9YdFtO/Ug2n3Tai3xbQ3FBQUYDKZ6Nq1K4BPbZrtdjsul4ugoCBMJhN2u52IiAif7l9fpqGy2sy+dUuZMGYU/fr182m8+nA4HOzYsYPU1FTi4uKuKjVsiIMHD3L+/Hkefvjhtg0WhFB1Cv/n/8CZMzB2LPzlL/VqFkD1W9i4cSNvvPFGs0Wily9fJicnh6FDhwJw6dIlOnTocNXn4O/W2FIIKZFIJH6mrh1ztSuAuKQUhvTp0eyAQQjB2rVrWb9+vWef29sF0uVy8cUXX7Bq1SpAzVL4GjCA2pfCbHNQYaom48g+qq02bELDs8/P8kvAAGpwc+jQIU/ZZ1MdKUF9f06n068Okz5z6BCMHw/Tpqk/r1wJmzdfFzBYLBZPyWePHj2466670Ov1zb7t0aNH2bFjBzabKkiNj49v9cBJZhokEonEzwgh2LNnD3379m2RGNDhcABqO+uKigoCAgKaNd7+/fuJiIhosU9CudnGrgNHObjtR0beN5NBvbs3OxByY7PZOHr0KIMHD0ZRFMxmc6PlhXa7nS1btpCSkkK3bt083TfbJMuQk6O2q/7mG1Xk+J//qbarrqf3g8Ph4L333iMlJaXZehar1crWrVtJT08nNjYWq9UK0Gjg4e9Mg9eaBkX9F5kCjAaigLeFEBcVRRkDZAkhLvlrUhKJRHIrU1ZWxtatW3G5XE02iWoIp9PJvHnziIuL44EHHmiyuqEuNpuNtWvXMnDgQBITExkyZEiz5uDG4XBQVFREhw4dmDx6MMN6d2lWtUZ9nDx5krVr13oMmpryI1AUhbNnz6LT6fzmLukzlZU/ixwBfv1rVeR4zb+REILLly8THx+PVqtl/PjxLeoS6hY7RkZGEhsb26IsRXPxKtOgKEoEsAYYClQCIcBgIcRhRVG+AUqFEHNadaZ+QGYaJBJJa1JTU+PxOSgpKSEyMrJFi9r27duJiYnxubeA1Wpl7ty5DBs2rMUBA8D3339PVlYWb775pl+cCC0WC+Xl5XTo0AEhBAUFBY0aUlVXV7N7927Gjx9PQECAp/XzDcctcnz7bSgqUvtF/O53kJxc7+kHDx5k9erVzJ49u1mGWwAnTpzg3LlzTJ8+Hbj6d8wb2krT8CcgCRgJRAN1/y/YCEzw14QkEonkVuTKlSu89957nDlzBmieDbO7B0VhYSEAo0eP9jpgEEKQkZGBEAK9Xs8rr7zSooDB5XJ5tkdGjRrFzJkz/WZdvHjxYhYvXuwROja1oObn57Nv3z7y8vIAbnzA4BY59u0Lr70GaWmqWdPXX18XMFRWVlJcXAyols/3338/7du39/F2wrPtYjKZKCkp8ZhmtWljLbwPGqYBvxFC7AGuTU3koAYUEolEcscSGRlJ165diYmJafYYZrOZffv2ceLECZ+vPXfuHIsWLeLUqVNAyxZW99aI200xOjraU7XRXEwmk8cGeuLEiTzyyCONllGWlJR4ArDu3bszZ84cv1lc+8ThwzBhAkydqgYPy5fDli0wcOB1p7pFp2vWrAHUBX7QoEE+lcVWVVUxb948jzX40KFDef7559s8WHDjbdDQDshv4DU9V2ceJBKJ5I7AXSLocDjQ6XTMmDGjWfXxZWVlCCEIDg5m9uzZjB8/3utr3cr5Ll268NhjjzWrFfa1BAQEkJKS0mSLaW+pqqq6qsFUhw4dmtzbX7duHWvXrvUEGv7oXeETubnw9NNqcHDihNpg6sQJtUKiTgbJ5XJx+vRphBBoNBqmTJnC1KlTfb6d+30ajUaEEJ5qEG8qSG4k3gYNZ4B7GnhtDOB7WCyRSCS3OBcvXmTz5s2ep8LmUFBQwIcffsiRI0cAdXH0dpE4cuQIH3zwAVVVVSiKQo8ePZq9wJhMJhYtWkRRUREA48aNo0+fPs0ay417eyMkJIQRI0Y06RSZm5uLxWIB4P777+eFF1648Z0oKytV2+fu3WHRIvi3f4OzZ+HVV+utijh16hQLFy7k/PnzAHTu3Jnw8HCfbrlz507mzp3rMet67rnnWtyTpLXwNmj4O/CWoii/AdwbOOGKojwHvF77ukQikdwR1H26f/XVV5vsttgYsbGxjBw50mPr7AuJiYkeZ0d/kJ+f79FTtJTTp0/z7rvvehpMjRo1qtGKC3dafseOHQCEhYW12DnTJxwO+OgjtV31//4vPPSQatL0v/97XVVEUVERFy9eBKBXr148/vjjdO7c2afb1dTUeLILMTExJCcne4KsmymzcC1e+zQoivJ74J9RtyIUVG2DC/ijEOI3rTZDPyKrJyQSSUvJzMxkxYoVPPPMMz4L3NyUl5ezfv16pkyZgsFg8Ona8+fPk5+fz6hRo5p177pYrVaOHz/u8UhwOBxotf7pLlBWVsaGDRuYNGlSo4t/UVGRRwdy5swZOnXqdGP374WAH35QnRxPn4bRo1Unx0H1FxwIIZg7dy4As2fPbtYCX1lZydy5cxkzZozfrbevpc0cIYUQ/wZ0AV4C/gN4FehxqwQMEolE4g86dOhA586dW2TaZDKZuHjxomcrwBcyMjI4ceKEXxwQjx8/zo8//siVK1cAWhww7Nixg9WrVwMQERHBI4884gkY6murvX//fj766CNPdqNHjx43NmCoK3J0uWDFCti69bqAweFwsG/fPhwOB4qiMGPGDH7xi1/4FDAIISgrKwPU7Zo+ffoQHx/vz3dzQ2gy06AoSiBQADwrhFh5Q2bVSshMg0QiaQ4Wi4WjR48ybNiwZqeOhRDk5uaSXFui54vXgLtpU0REBA6HAyFEs7ckHA4HFRUVREVF4XK5KCwsbJHhUF02btxIZWUl06dPv6oyom4vDr1WQ1W1GbuiJTVGz4XMnxgyZMiN1S7k5qpOjl9/DdHRqu/C7Nn1ahYALly4wFdffcXDDz/cbK3Bjz/+yPHjx5kzZ84NNWW64ZkGIYQNcABWf91UIpFIbiWOHj3Kpk2bmpUZcLNr1y7mzZvnGcPbRd/lcvHll196ekdotdoWaRiWLFnCN998g9PpRKPRtChgsNvtrF+/nsuXLwMwYcIEZs6ceV0p5YXiaoyBWgy6AHavX86Jnesx6AK4XO1i+PDhNy5gqKxUgwW3yPFf/1UVOb722nUBQ25uLidPngQgJSWF2bNn+xwwFBUVeYSd/fv3Z+LEiQQGtsx2u63xNhe1HHgIWN96U5FIJJKbC3c2YNiwYc32YHB3oxw8eDChoaFER0d7dZ27HbRGo+GBBx7wWZF/7Viglu+NHDmSmpoavyzUDoeDEydOEBwcfF13xbqUV1uJamdAURSSOvdA0Wgw6AIot9ygJlMOB3z6qdquurAQnnxSdXJsxPdhx44dlJWVkZaWhkaj8dnRsaqqin/84x+MGDGCCRMmEBcX57eMTlvirY30DOA9YB9qAHGZa0yehBCbvRjnc+ABoFAI0fua1/4Z1XkyRghRXHvs18ALgBOYI4RYV3t8IDAPMKDaW78pvHgjcntCIpF4y969e9m/fz+zZs1qsh9CQxw5coSffvqJxx9/vFEjo2sxmUzMnz+fESNGtLjs0Waz8c0339C9e/dm98Goi9Vq5ciRI56tGqvV2mi6vbS0lM/nfUXPwaPomPKzQZTZ5iBQqyE92feOm14jBKxeDf/yL6rIcdQoVeRYj/jQarWyc+dOhg8fTnBwMFVVVQQFBfmUGbBareTk5NC9e3dAtYDu0qVLs39//EFbCSGXAgnATOArYAOqfXTd/3rDPOC+aw8qipIETER1l3QfSwMeA3rVXvOhoiju0PgjYDbQrfbrujElEomkJSQmJtKpU6cWpZMVRbnKqMdbjEYjYWFhfhEF6nQ6oqOjfWp41RinTp1iw4YNni2JhgIG93NcWFgY7dvHYBcazDZVj2G2OTDbHKREB/tlTvVy5AjcfTdMmQJOJ3z/PWzbVm/AAGpmYM+ePZw7dw5QxYq+/ttv2bKFRYsWYTabAdVGui0DhtbA20zDmKbOEUJs8+qGitIJ+KFupkFRlCXA/wesAAYJIYprswwIIf639px1wNtANrBFCNGz9vjjwFghxEtN3VtmGiQSSWOUlZWRm5tL3759WzRGRUUFnTp1An7enmgKm83Gjh07GDVqVIv3vU0mExs2bODuu+/2i9eByWSioqKChIQEhBAUFRU1Wm56+vRp9u3bx1NPPeXZBik327hQXE2lxU6oQUdKdHCL22rXS24u/Md/qCLHyEhV5PjSS/WKHDMzM7ly5YqnfLWqqsqnz0sIwcmTJ4mPjycqKoqqqipMJlOzm1O1Bm2SaRBCbGvqq7kTUBRlKpAvhDh2zUsJQG6dn/NqjyXUfn/tcYlEImkR27dvZ926dZ7mQM1h5cqVrFy50qMj8LbaoqCggN27d3uedFuC1WolMzOT/PyG3P99Y8mSJSxdutTTYKopfwqNRoPdbvc8cQOEGwNJT45gTI/2pCdH+D9gqKpSg4Xu3WHhQnVL4uxZeP31Bqsizp49y8mTJ69yrvQFs9nMqlWrOHTokOf6mylgaA28Nnfy2w3rZBoURTECW4B7hBAViqJk83Om4e/AHiHEN7XXfYaqX8gB/lcIcXft8VHA/xFCTGngfrNRtzJITk4e6HbxkkgkElCfFt29I2w2G9XV1URE+LbP7nK5EEIQEBBAaWkpiqJ4Nca1T+3l5eXNFjzW1NSQmZnp0UD42kL5WioqKmjXrh0BAQEUFBQQEBDQoBDU5XKxd+9e9Ho9AwYMALzPsLSYa0WOjz8O//M/UJvpqUt1dTUbN25kxIgRxMTEYLPZCAgI8EkUWlBQQGZmJqNHjwbU7qbt27e/aV0c2yTToCjK5ia+NjXz/l2AFOBYbcCQCBxWFCUONYNQt1tKInCp9nhiPcfrRQgxVwgxSAgxqCXd5yQSye3JmjVr+Pbbb3E6nQQGBvocMDidTr799ltPR8jIyEivx9izZw9z5871tFJuSYXE7t27Wb58ucdAqCUBQ2VlJR9++KGnwVRcXFyjlSOKonD27FnqPpS1+iLqFjn27QuvvKJmGPbtg2+/rTdgcM8pKyvLk4EJDAz0uYokMzOTvXv3Ul1dDag24DdrwNAaeFtyqeH6lthRQA+gCMhszs2FECcAT57rmkzDSuBbRVH+CsSjCh73CyGciqJUKYoyDLWa42ng/ebcXyKRSBITEzEajT5VN9QlICCAuLg4n4IN91N4//79CQgIaLQnQ2M4HA7MZjOhoaHcdddddO/e3eegpy42m43AwEBCQ0MZM2ZMo74ENpvNU21gMBh47LHH/NYDo0mOHoVf/Qo2b1Z7RSxbBtOnX9V90s2JEyc4f/4806ZNw2g08uabb/o0z5qaGrZt20b37t3p1KkTw4cPZ8iQITfUoKk5NFXV0ly81TSMFUKMu+arL5AGlAH/4804iqJ8B+wBeiiKkqcoyguN3PMUsAj4CfgReE0I4ax9+RXgU+AscA5Y6839JRKJBNTGTO6uhP369WPcuHE+WwIfOnSIkpISAO6++24GDhzo1bV79+5l8eLFCCEwGo0MHTq0WU+qQgjmz5/PwoULPQ6RCQnNl3edPHmSd999l4qKCgBGjBjRaOajtLSUXbt2kZWVBahP7a3+xJ2XB88+CwMGwLFj8N57cOoUzJhRb8AAqoizuLjYo1PxNbDRaDT89NNP5OXlea6/2QOGc+fO8Ze//MVT4eJPWmQ0LoQ4V9vI6k9AuhfnP97E652u+fl3wO/qOe8g0HiPVYlEIqkHIQRr167F5XLx4osvNmuhs1gsbNq0iT59+jBp0iSfrnWXYbp1FL7iFiMqisKwYcPQaDQtWqzdWY+EhAS6dOnSaP8Jk8lEdnY2vXv3Ji4ujjlz5vitlLNRqqrgj39UPRacTvjnf1bbV9cT1FRXV7NixQqGDBlC165dGTp0qM/23xkZGRw7doxHH30UnU7Hq6++etM7OZaXl2O324mJiSEhIYG+ffv63AzNG/zRzqwI6O6HcSQSiaTVqCtWfPjhh9HpdD4vttXV1QQHB2M0Gpk1a5bXWwHZ2dloNBqSk5MZMmQIQ4YMadZCbzabWbBgAYMGDaJv377Naqddl82bN1NdXc2UKVOIiIhg5syZjZ6/fft2jh49SufOnT1eEq2KwwGffQb/7/+pIsdHH1VbVaekXHeqO/gJCgrCZDJ5NAfebju5iwIURcFut1NVVUV1dTXt2rW76QMGl8vFvHnziI6O5qmnnkKv1zNlSr21AS2meZt4tSiKEgn8EnWLQCKRSG5KnE4n8+fPZ926dYBqOOSr6U5RURHvv/8+R48eBVTBozcLv8vlYvXq1WzduhXAkyVoDnq9Hr1e32z9xbUIIRBCeMpD66O4uJjy8nIAxo0bx+zZs1vfsEgIWLMG+vWDl19WRY5798KCBfUGDEeOHOGLL77A5XKh1Wp58cUX6devn9e3s1gsfPXVVxw7plb+9+nTh1mzZrWok2lrU1RUxMaNGxFCoNFomDZtGlOnTm31+3qVaVAU5QLXCyEDgdja7x/056QkEonEnwQEBBAfH09kZGSzx4iKiqJ///4e06amMJlMHoHl448/3uwFyGQysXXrViZOnEhQUBCPP/54s4OOmpoaNm7cyIABA+jQoQPjx49vdCy73c4XX3xBx44deeSRRzAYDK2S8r6Ko0fV7YdNmxoVOboDHo1Gg16vx2AwYLVaMRqNXn8+DocDrVaLXq9Hp9N5grFboRoiLy+PAwcOkJ6eTlRUFCn1BFOtgbeOkPO4PmiwAheBxUKIWyLTIB0hJZI7i9OnTxMTE9Ps6oTq6mo2bdrEPffc45P4zd2saMiQIYwZ06ShbqPk5OTwzTff8Nhjj9G5c+cWjWWxWPjoo48YOXIkQ4cObfC84uJiT2Otc+fOERsb2/pP3fn5qjnTl1+qTo6//a3q5FjP1oDFYuHbb7+lX79+DBrUPAuC/fv3s3v37ltCrwDqe/7+++/p3bs3ffv2xel0UlNT02TWx98+DV5lGoQQz/rrhhKJRHIjqKmpYdWqVXTt2pUZM2Y0a4ySkhJOnTpF7969fVqwQ0JCGDJkCL169WrWfWtqasjNzaVr164kJyfz1ltvNXtLoLq6miNHjjBy5EgMBgOvvfZaox4OmZmZfPfddzz55JN07dqVLl26NOu+XlNVBX/6E/z5z02KHOtmBsLCwnyuYrDZbCiKgk6nIy4uji5duuB0Opu+sI0QQnh0FXq9Hrvd7plvQEBA2/S1cKd4GvsCPgdSGnitI/C5N+O09dfAgQOFRCK5vbHb7Z7vCwoKrvrZG1wulygoKPD8bDabvbqutLRUfP3116K8vNyn+9XHDz/8IP77v/9bmEymFo918OBB8V//9V/i0qVLDZ7jcrk879PhcIjt27eLmpqaFt+7Uex2IebOFSI2VggQ4vHHhbhwocHTDx06JP76178Ki8XSrNuZzWbx5z//WWzZsqV5820D1qxZI/761796foddLpfPYwAHhR/XUW/VNM8CDdmBRQPPtCx0kUgkkpZTXV3NJ5984ukFEBsb22gJYX3s37+fuXPncuXKFQCv9/BdLhfFxcWUlpb6NulaHA4HFosFUAWHTz/9NMHBzesCWVlZ6fEVGDBgAK+++mqjPRHWrFnDF198gdPpJCAgwC9NsxpECFi7Fvr3h9mzoVs3VeRYj5Oj0+n0dAiNi4sjJSWlUdHm9bcSHrdNg8HAwIEDWz9z0gKEEJw+fdrjKZGamsrIkSM9GoubQWvhy/9NDYkf4gCLH+YikUgkLcJgMNC+ffsW2TG7VfdNNWUCVSh45swZevfuTVRUFG+88YbPtsSgLhbz5s0jODiYxx57DKPR2KLU85IlS6gyVTNq2pNUWR2EGnQEGGxXNYmq6/fgdpJs9UXp2DF1+2HjxiadHO12O5988gndunVj4sSJxMfHM336dJ9ut23bNnbt2sWcOXMICQlh7NixfnkbrcWVK1dYuHAhkyZNYsiQIXTq1Mlr4e2NosGgQVGUGUDdjcD/VBSl+JrTDMAo4FArzE0ikUiaRAjB0aNHSU1NRa/X8+CDvhdznT59mpMnTzJz5kz0en2jIsG67N+/n40bN9K+fXvat2/vc8Agar0FFEVh4MCBtGvXrtkLd2lpKaGhoWi1WkZPuIfMIgt2pyDCGIjF7uRITpmnu6TFYmH+/Pn069ePwYMH061bN7p169as+3pFfj783/8L8+ZBRAS8+65aSllPNsPthaHT6UhNTfXZ5bK4uNhjhd2vXz9CQkKanbG5ERw/fhyLxcLQoUOJi4vjqaeeumGVEM2hsUxDMmpAAGqWoT9wbb/YGmA38Gu/z0wikUi8oKSkhB9++AGTycSoUaOavqAeTCYTZWVlnpK9hig32zhfZKKssprIsHb07DuAxMREr7IS9d1zyZIljBkzhpSUFNLTmzTVbXhe5eV89NFHjBo1itGjR1OlBBMVacAYqP6Jd//3QnE16cmB6PV6IiMjW38xNZl+Fjk6HPDLX8JvfqMGDvVw5MgR1qxZw6uvvkpERATjxo3z6XZWq5W5c+fSp08fj2GVt/beNxJ3sAiq8LSqqspj+HUzb5+A9yWXF4DpQohjrT+l1kOWXEoktw/u/XdQe0nEx8f79JRuMpmoqKggISHBY3DUWKag3GzjSE4ZF4/tpuxKPkPve5gaF56nd1+x2+3MmzePkSNHNtoYqjHqtr/et28faWlphISEsO1MIRHGq3tBFBfkc3TfDl5+/unW91pwOuHzz1Unx4ICeOwxtV11PU/QNpsNu91OcHAwlZWV7Nu3j74Dh3LJ5KTSYifUoCMlOrjBz7impoazZ896KlVOnz5NUlLSTZtdyM7OZuXKlTz77LOEhoZSU1PTqn072qQ1thAi5VYPGCQSye1DYWEh77//vqcVc0JCgs9/dL///nsWL16M0+lEUZQmtxYuFFdjDNSS0LEziSndaacPxBio5UJxtdf3rK6uZuPGjbhcLnQ6HbNmzWp2wHD8+PGrGkwNHTqUkJAQAEINOiz2q0sJHWhw2Wuoqqpq1v28Qgj48cefRY5duqgix+++qzdgcLlcfPzxx6xZs0add2gog0eO4adCCzaHiwhjIDaHiyM5ZZSbbfXecu/evSxZssTjWtmzZ8+bLmCw2WyYTCZAbX8eFhaG1WoF1BbmN4PA0Vsa0zSMBg4LIUy13zeKEGK7X2cmkUgkDRAaGkpMTIzPdfqesjGNhkmTJuFwOJoMFoQQ7N+/nwulNaT17osxsRNxiZ0AMOgUyhpYzOrj4sWL7N27l549e5KYmNjs7paKopCUlETPnj3rrXJIiQ7mSE4Z+edP47RWk5w2EG27CJ5/8SUighv2aGgRx4+rIscNG1SR49KlDXafvHLlCrGxsWg0GkaNGnWV+ZY7OGtoa0UIwU8//URkZCQdOnRg6NChdO3atUXi19bE6XTy4Ycf0rFjR2bMmEF4eDjPPHPrFhw2pmnYCgwD9td+39A+hlL7mu+SYYlEIvESl8vFkSNHSE9PR6/X8+STT/p8/ffff09oaCgTJ070OB42hRCCM2fOUCO0WOy9PIsYgMXuJNTQeKfKmpoaCgsLSUpKIi0tjcTEREJDQ32au5t169ZRU1PD1KlTiYiIaLDXQLgxkPTkCL4/fImK8jI69x7Y7G2UJrl0SRU5fvGFasj0zjvwyiv1ihwBTpw4wbJly3j++edJSkqif//+V71eabETcc08DboAT3Bmt9tZu3Yt3bt3Z+rUqej1+ha1BG8NzGYzWVlZ9OvXj4CAAMaMGUNMTEOuBbcWjQUN44Cf6nwvkUgkbUZmZiY//PAD7dq1a1Z3R41Gg9Fo9Ho/Pzc315PNePTRRzE74GhuOaAuYha7E7PNQY+4xjtd/vDDD5w7d4633nrLo+pvLjqdztOts74shdPpZO/evaSmphIZGclTD09Hq9W2TvrbB5Gj2WzGbDYTHR1Njx49uPfeexv0jXBvrdQNzgoLC7mSnYnofj+BgYE8++yzLeoj0tocPHiQLVu2kJycTERERItErjcbXgkhbxekEFIiufWoK3jMyckhOTnZp+szMjKIi4sjIiKiwcX2WkwmE++88w6DBg3ivvvu8xwvN9u4UFzdpEDP4XAghECn01FaWkp1dTVJSUk+zRvUaoB169YxZMgQOnTo0OT8q6qq+OCDDxg5ciSjRze5q9w8rhU5PvqoKnJswGZbCMFHH31EUFAQL7zwQpPDuwWnxkCtJzg7l3GcnBP7mT37xZsyWLBarWzZsoW0tDQ6duyI1WqlsrKyWVU1/qZNek9IJBJJW3D27FnWrFnD008/TXh4uM8Bg9VqZeXKlaSmpjJ16tQmAwZ3b4N27drx8MMPX2eso6b9G0/xOxwOPvvsMxISEnjggQeIjIxs0UJ34cIFEhIS6NChQ73zr6mpISMjg/79+xMSEsKrr75KWFhYs+/XKD/+CP/yL3DyJIwYAd9/D8OGXXeaEIKzZ8/StWtXFEXhvvvu84g0myLcGEifDu1Yt3ELQeHRdOnWg/vGDMcwfljrV334iDug1Wq1nDlzhvDwcDp27OhpYX470pgQcrMP4wghxAQ/zEcikUg8hIeHExkZ6bNpkrsUUa/X88wzz3i1n3zp0iUWLFjAI488QmJiYrO2QAC0Wi1paWnExsY26/qqqioOHz7M6NGj0ev1vPbaa+h0DesmDh06xIYNG4iPj6d9+/atEzAcP64GC+vXqxURS5bAzJn1ihxB3Upyf5apqak+d+eMDDFQVZRHXLiB9OTGt3/aii1btnDu3DleeOEFtFotr7/+us+W5bcijZVcalBFju6vnsBYoBOqE2Sn2p971L4ukUgkLaampobjx48DEB0dzVNPPeX1UyqozogffPCBZ4y4uDivgo7IyEji4uIa7QDZEJWVlXzzzTeefhWjRo2ie/fuPo8D6oK7c+dOCgsLAeoNGKqqqjyvDx06lFmzZrVOKvzSJXjhBbWE8sAB+Otf4aef4MEHrwsYysvLPSWw3bt356GHHvIp8MrKymLevHk4HA40Gg2zZs1iwoSb61m0sLDQ0/siOjqapKQkT9fJOyFggEaCBiHEWCHEOCHEOOBdwA4ME0J0FkIMF0J0BobXHn/3xkxXIpHc7uzbt4/ly5dTUlLSrOvDw8Pp2rWrV0/65eXlbNiwASEEer2eJ554olkq94CAAMrKyigvL/fsyW87U9iov0BdysrKyMnJAdQGU6+99lqD8xdCMH/+fJYvX44QgoCAAP9XD5hM8PbbajOpr7+Gf/onOHdO/W8DVRHLli1j1apVHt1Fr1690GiatgJy6+o0Gs1VfgY32yKcm5vLRx99xMmTJwHo06cP99577003z9bGW0fIE8CfhBBf1fPas8CvhBB9/D89/yKFkBLJzYvL5UKj0eB0Orl06ZJPwsGamhq2bdvG2LFjferOePjwYdatW8esWbN8Dhaqq6s5cuSIpwuhy+Wi0uq4TsRntjkaLXcUQvDZZ59RU1PDq6++2qDuoqSkhMjISBRFITc3F6PReJW/gV9wOtXSyf/7f1WR4yOPwP/+b70iR5fLxdGjR+nTpw86nY7CwkL0er3X1SF2u50FCxbQuXNnRo4cCeC1UPVGkZOTg9VqpXv37h6/jr59+9502orGaBNHSKAbUNTAa4VAV/9MRyKR3IkcPHiQTz/9FJvNRkBAgM+VBgUFBezfv5/s7Owmz3U4HJ7Ufnp6Oq+//nqzsgunTp1i69atFBWpfxo1Gs1VxkSKoni+r881sqioCIfDgaIoTJ06lV/84hcNLphXrlzhww8/9LT8TkpK8n/AsG6dug3x4ouqe+Pu3bBwYYNVEfn5+axatcrz5N2+fXuvAgZ3q2udTkdISMhVC/DNFDAAbNq0ia1bt3qCmaFDh95SAUNr4G2mIQM4I4SYXs9rK4DuQohU/0/Pv8hMg0Ryc5KVlcWRI0eYNm2aT5qC8vJyjxNgZWWlV4vWsmXLOH/+PHPmzPEpKwFqRqOiooL27dsjhKC0tPSqxbu+ng9CCMrMNsb0+FlzUFZWxgcffMCYMWMaLY20WCwYDAaEEOzatYv09HT/WySfOKE6Oa5frwYIf/hDvZoFUIOzoqIi+vRRE8t5eXk+WXgfPXqUDRs28Nprr7Wo9XdrkZ+fz9atW3nooYcICgqirKyM4OBgn39PbibaKtPwn8AURVFOKorytqIor9T+9yRwP/C2vyYkkUjuDKqqqsjKygKgW7duPPLIIz4FDIcPH+aDDz7wiA+bChjcD0ijRo1iypQpzVoIlixZwnfffefpV3Ht0359PR/qukZaLBYAIiIimDRpUqMdGHft2sWHH36IxWJBURTuuusu/wYMly7BrFnXixwfeqjBqogdO3awadMmj/jPGytsu93u6bOQkJBAjx498OZh9UYhhMDhcHh+LioqorS0FFD/nW7lgKE18NrcSVGUu1GDh0GADlUAeQD4rRBiU6vN0I/ITINEcvOwdOlSzp8/z5tvvtmsP8xms5n9+/czatSoRqsjXC4Xq1atwmg0MnHiRJ/v41bzazQaLl26hMPhaNAvoj5jIrem4fzpk6xfv55XXnmlwbLIur0xCgoKOHHiBGPHjm205NJnqqtVF8c//hHsdnj9dfiP/4B6vCRsNht79uxhwIABhISEUFVVhVar9TpF73A4+Pvf/07Xrl25//77/fce/ITD4eDTTz+la9eu3H333cDP2prbhTYzdxJCbAQ2KoqiAaKBYiGEy18TkUgkdwbuP8r33XcfJpPJp4AhOzub48ePM2XKFIxGI2PHjm3yGo1Gg06nQ6vV+iy0q6mp4YsvviAtLY3Ro0cTHx/f6Pnung8XiqspM9sINejo1j6McGMgnTt3pl+/fg2a/rhcLhYuXEh0dDQTJ04kLi6OuLg4r+faJE4nzJunihwvX4aHH1ZFjl26NHhJdXU1O3bsIDg4mEGDBnlV+iqEoLCwkNjYWLRaLUOHDm3QMrotqCu01Wq1dOvW7ar53U4BQ2vg86cjhHAJIQplwCCRSHxl/fr1LF26FCEEwcHBPhsgXblyhZycHKqrG29HLYTg4MGDnjTzpEmTGDdunM9Cu6CgIDp27OjTPN2Bw+juMeQf38WOTevU4+HhTJo0qcEtGI1GQ0RERIt6UzTI+vWQnq5uR3TsCLt2waJF9QYM2dnZ7NixA1DT82+88QaDBnn/oLpv3z4+/vhjj0B02LBhdOzY0T/vww9s2bKFefPmeVqET5gwodntye9EvM40KIrSGXgESAauDZWFEKJpU3GJRHJH065du0YbLtVHTU0N5eXlxMbGMmTIEAYMGNBkur66uppNmzZRWlrKPffc41OwUFFRwY8//sikSZMIDQ1l0qRJXl9bF0VRCA4Oxul0Nvh+i4uLWbVqFdOmTSMyMvKqPhd+4eRJVeS4bp1aEbFwoZphaOTzyMzMJCMjg6FDhxIYGOiVw6TbUyMqKoq+ffui1Wpvmh4RdrudQ4cO0bVrV6Kjoxk8eDDJycm0a9eurad2S+JV0KAoyjRgMWpmohCoueYUr4QRiqJ8DjwAFAohetce+xMwBbAB54DnhBDlta/9GngBcAJzhBDrao8PBOahOlOuAd4UN5OyRiKReCgsLMThcBAfH8/w4cN9ftpftmwZBQUFvPHGG2i12kYDhrKyMiIiImjXrh2zZs1q1sLlcDjIy8ujsLDQ56d+s9nMmjVrGDFiBPHx8Ywb13iD4MDAQKqrq6moqPDvInv5stpQ6vPPITQU/vIXeO01qCfLYbVa2bx5M+np6XTo0IGxY8cybtw4r3UUDoeDzz//nOTkZB599FGMRqNPmYnWxmazsXnzZmw2G6NHjyYsLKz1enPcCbiFN419ASeA9UCMN+c3Ms5oYABwss6xewBt7fd/AP5Q+30acAwIAlJQA4qA2tf2o7pRKsBaYJI39x84cKCQSCQ3DpfLJT788EMxd+5c4XK5fL5WCCEKCgpEdnZ2k+dnZ2eL//qv/xKnTp3yeZ4mk0kcOnTI87Pdbvd5DCGEsFgs4p133hFHjhxp8JyzZ8+KH3/80fOzr59Lo5hMQrz9thDBwULodEK89ZYQJSWNXmKxWMSf/vQnsW/fPq9vU1NTc9V7PHv2rKiqqmrurP3O3r17xffff+/5uaysrM3m0tYAB0UL1u1rv7zVNHQG/iyEaMjgydsAZTtQes2x9UIId73LXiCx9vtpwAIhRI0Q4gJwFhiiKEoHIFQIsaf2A/kKmN6SeUkkEv/i/gOjKAoPPvggjz76qNcZBpfLxZo1a9iyZQsAsbGxXu2JJyUlMWrUKJ+bIwHs37+fNWvWUFFRAfhmYVxeXs6mTZs8VtSvvfYa/fv3b/D8/Px8srKyPGWIfjE0crer7tZNtX+eNEktn/zb3+qtijhz5gwrVqzwzHnOnDkMGTLE69sdPXqUFStWUFBQAECXLl3aPN1vsVg8pZw1NTVYrVZPaajby0PScrz9P+M04Gf7sXp5HlhY+30CahDhJq/2mL32+2uPSySSmwCHw8HSpUuJi4tjzJgxPjdS0mg0OBwOHA5Hk9qH7Oxstm3bxuOPP05gYKBX1RRubDYbZrOZ8PBwRo0aRa9evZqVtj537hz79u2jb9++xMTEXBdwCCE4evSop8HRyJEjGTFihP96FmzYoOoWjh+HoUNh8WKotWVuiIqKCi5duoTFYsFoNDZZwSKEICMjA4PBQEpKCgMGDCAhIcG/1R0tIDc3l6+//ponnniCTp06MWrUqJvOXfJ2wdvf2v8DvKMoyj4hxPnWmIiiKL8BHMB896F6ThONHG9o3NnAbKDB2mqJROI/AgIC0Ov1PneLvHDhApGRkYSFhTFlyhSv/ugLIaiurqa6utqn0k0hBF9//TVOp5MXX3wRrVbrU3BTXFxMdXU1HTt2ZMCAAXTr1q1B/YPdbmfbtm2kpKSQlJTkc5vvBjl5Um1X/eOPTYocrVYrq1evplevXvTs2ZNBgwYxaNAgr8sLXS4XmzZtIi4ujpSUFLRarf+bZPlIRUUFZrOZDh060KFDB/r16+f5N5ABQ+vhbdDwNmqmIUNRlCyu2WJArZ4Y09xJKIryDKpAcoJw55fUDEJdA/pE4FLt8cR6jteLEGIuMBdUc6fmzlEikTTOhQsXiI6OJiQkhKlTp/rsh7Bo0SK6d+/OjBkzGr22srKS/Px8UlNTSUlJ4eWXX/Z68XM6nWg0GhRFYcyYMeh0Op8XGCEE33//PQ6Hg5dffhlFUa4LGJxOJ8eOHSM9PZ3AwECee+45/5VSFhSoIsfPPlNFjn/+s2rQVE+Q5s7UBAYGUlJS4ikz9ObzKi4uZt++fUyaNImAgACeeuqpm0ZAKGo7fQYGBjJr1iy0Wu1NaR51O+Jt0OAEzrTGBBRFuQ/4V2CMEMJc56WVwLeKovwViEdtmrVfCOFUFKVKUZRhwD7gaeD91pibRCLxDqvVysKFC+nZsyfTp0/3eiF2OBxotVqCgoJ44oknvPJD2LRpE1lZWXTu3JmgoCCvA4bq6mq++eYbhgwZQnp6Ol27+tZn7/Lly57th+nTp2MwGBp8n5mZmaxatYqQkBC6devmn8W2ulqtgvjjH6GmBt54QzVqaqBx1alTp9i3bx/PPPMMAQEBzJo1yyfjouLiYk6cOMHAgQOJi4sjIiKi5e+hBZSUlHDw4EEmTpyIRqNhypQpreNpIWkcf6oqm/oCvgMu87Mu4QVUgWMucLT26x91zv8NatXEGepUSKBaWZ+sfe0Dau2wm/qS1RMSiX+pq/y/ePGisFqtXl9bVlYm3nvvPXHy5Mkmz3U4HMJisQghhKiurhZFRUXNmuuiRYvEmTNnfL62uLhY/Od//qfYvn17g+dYrVaRl5fnudfFixd9vk+9OBxCfP65EPHxQoAQDz4oRGZmvae6XC7Pv0lmZqb44osvRGVlpZe3cYiNGzd6qkhcLpcwm83+eQ8twP1+MjIyxO9+9ztx6dKlNp7RrQV+rp7wuvfE7YDsPSGR+Ea52caF4moqLXZCDTpSooMJN6ragerqahYsWMCIESNITfW9ya3T6WTp0qUMGzasUb2REIIvvvgCo9HoUxUGqPvemzdvZvLkyT5rLEB9j8HBwR4xY2pqaoM20AsWLCA/P58333zTfyLHjRtVkeOxYzBkiJppuOuuek+12WwsXLiQbt26MWzYME8lgbeflxCCr776ivbt2zfb0Mqf2Gw2li5dSpcuXRgyZAhCCI9wU+I9bdXlEkVREhRF+auiKAcVRbmgKIrbnOktRVGG+mtCEonk5sDdfMnmcBFhDMTmcHEkp4xysw1QLZZ9baTkcDjYvn07drudgIAAHnnkkSYFyoqi0K9fP/r16+ez/qCqqorMzExPaaAvHDhwgPfee4/y8nIA0tPTrwsYKisrsdnUz2P8+PE89thj/gkYTp2CyZNh4kSoqIAFC2Dv3noDBndZoU6nu6oSQlGUJj+vCxcu8Mknn2C1WlEUhaeeeqrNAwa37iIw8OoW44qiyIDhJsCroEFRlF6oBk+/QBUdJgNuqXJH4M1WmZ1EImkzLhRXYwzUYgzUqn+wa7/ffei4R4vwi1/8wqcsQ35+Plu3biUzM7PR8+x2O6tWrSI7OxuAgQMHen0fs9lMRkYGoLZufuutt3zqfeByqW11unXrxqBBgzAajfUuvtXV1Xz44Yds374dgPbt27e8oqCgAF56Cfr2hT17VJHj6dPw6KP1VkWcPHmS9957z9M++8EHH2TAgAFev0e9Xo/L5cJkMgH4r7KjmWzatIkPP/yQmhrVdPixxx7zyT9C0vp4GxL/BcgA7gWsqJbPbnajOjlKJJLbiEqLnQjj1WWMtqoyDmxeTZimhpEjR3r95O9O83fs2JFXX32V6OjoRs93uVxcvHiRqKgoOnXq1OB59W2f7Ny8mePHj9OxY0eMRqPX2xJCCFasWAHAtGnTCAsLq7eVttVqRa/XExwczLhx4+jWrZtX4zeK2Qx//Sv84Q+qyHHOHLVddT0iRyEEDocDnU5HTEwMiYmJOByOega9HpfLxXfffUdMTAz33HMPHTp0YPbs2W1WoiiEICsri4SEBIKDg0lNTaVdu3ZtHrzcDogmPE6ai7fbE3cBvxdCmLjeE+EKcHM4fEgkEr8RatBhsaupb/f+eGBIBMPumcbw4cPrvca9pbHtTKFnK+PEiRO8++67XLlyBaDBgEEIwenTp3G5XAQFBfHSSy8xYsSIBudXd/skRAcmUzVHcsoYNHwUL7zwgs+pbEVRiIiI8FQJ1PcH9+TJk7zzzjue7plDhw5tWc8Id7vqbt3USoh77vnZybGegMHpdPLpp5+yadMmQHXLfPjhh5tsWe1+ctdoNERFRV1VzdGWngZlZWV89913HDp0CID4+HiGDh3qP03IHcrhw4f57LPPaA3NordBQ2NtsKMBix/mIpFIbiJSooMx2xwUFhWx6fv5XLlSgNnmYGi/tHpL9xrSQETFJZKent5kyV5OTg4LFy7k2LFjAE3qJdzbJwathu2rF3NqzyaMgVouV7u8bmVtMplYsGABly6pVi9jxoxhzJgx1y2k7nR+x44d6dWrV4NiSJ/YtAkGDYLnnoOkJNi5E5YuhXpKQS0W9U9sQEAA3bp1IzEx8bpzGuKnn37ir3/9K2VlZQDcd999DB3adjK0U6dOeVpvR0ZG8vTTTzOyCQdLSePY7XaOHTvmCQ71ej2hoaEeq3J/4m3QsB94roHXHgF2+Wc6EonkZiHcGEh6cgRGgx6hKGhwkZ4c4ameuJa6GoiK0iLOHt6FQRfAFQtMmjSpQcdGt5CwY8eOPPbYY432bahLhdmGQReAotHQrc8gevQdhEEXQKXF7vV71Gq1FBUVeVo718fq1atZtmwZACEhIUyZMqVlgrxTp+D+++Huu6G8XBU57tnToPXzqVOn+Otf/+qZ49ixY+ndu3ejt7Db7VRXVwNqT45evXq16dN73SfeCxcukJGR4QnEUlJS5HZEM3F/hleuXGH58uWcOaPaKaWlpfHII49gMBj8fk9vg4b/D5iiKMp6VDGkAO5WFOVLYAbwO7/PTCKRtBmittdAmEHH8J6J/NPrrzB+YGqDAQOoGgiDTv3jX3Qpl7wLWSh2a6OL+IkTJ3j//fc9jaJ69OjhVbq8oqKCoxuXknvxAgDJXXsS3SERi91JqKHxDEVJSQnr16/3NGt69dVX6dOnT4Pnh4WFER4e3vJU75Ur8PLLqshx1y74058aFDk6HA7Pot+pU6d6KzcawuVyMXfuXNasWQPgcehsagujtcjLy+O9996jqEjtd3jPPffw4osv+mQ0Jbka9zbV1q1bAUhISOD5559v9PfYX3j1ryaE2IbaSTIF+By1/8PvgVHAdCHEvtaaoEQiufGcOnWKRYsWce7cOcC7fe9gnUJxSTEAXXsP4O6ZT0GgodFFPD4+npSUFJ/6RgAYjUZCjAasdgdmm9rYymxTv0+JDm702uzsbA4fPux5cr/2KddkMjF//nxycnIAuOuuu7j77rubv/dvNsPvfqduO3z2merkeO6c6r/QgPXzZ599xsqVKwEIDg5m8uTJBAc3/L6EEOTn5wOqbmHEiBEMGuS30nyfsdlsVFZWAnh0Im6x5rWllBLvyM/P5/Dhw4D6O5uYmEhUre5FURSSkpJuyOfqs7mToihdgfZAiRCiVaylWwtp7iSRNI5bcS2EIDMzk+7du3v9h2j+dwvJzctj9LSnaGcIwmJ3YrY5rtvSuHjxItnZ2YwZ41u7moqKCnbt2sW9995LQEAAQggqLPYGzafqUlBQgMViISUlRQ0wzOYGF2GbzcZnn33GXXfd1bInN5cLvv4afvMbyM+HmTPh979XRY/1UFxc7BGJHj16lHbt2nltdX3s2DGWL1/O888/T1JSUtMXtCJCCD788EMiIyN5/PHH23Qutzo1NTWe6p/Vq1fz008/8U//9E8+bTW1mbmTGyHEWSHE7lstYJBIJI3jNvoxm80oiuL1VoGb8WNHM/GeezHoAykz2wjUaurVQJw+fZrjx497RFvecvnyZY4dO+apwlAUxaO7GNOjfYN6CyEEq1atYsOGDZ6g6NqA4fLly6xcuRKXy0VgYCAvvfRSywKGTZtg4EB49llISIAdO1SRYwMBw5kzZ/j73//OhQvqdkv//v2bDBhKS0s9plVpaWncf//9xMfHN3/OLcBisXDo0CHP5ztmzBgpbmwhZ86c4c9//jPFxWr2buzYscyZM6fNK0u8vruiKN2A/wCGAwlAPqpHw38LIc62zvQkEsmNwp02ttlsXgn9hBBs374djUbDqFGjPC2K66Oqqgq73U5kZCR33303Y8eO9co/wWw2c+XKFVJSUujZsydz5sxpNE1fl7y8POLi4tBqtcycObNBkyaAoqIisrKyKC8vJzIysvn77T/9pLarXrMGOnaE776DRx6BesarqamhqqqK6OhounTpwoQJE7xe9IUQfPPNN4SGhvLss8+i0+nadDvi5MmTrFmzhsTERGJjY5sUakqux2azceDAAZKSkkhOTiYhIYH09HRPkODt731r49X2hKIoY4E1qKWVq1G9GWKB+wEjcF+t7uGmRm5PSCRX43A4yM7O9jzV+mIII2pbRAcEBDTaClsIwUcffURQUBDPP/+8T9mLxYsXk52dzVtvveWTZXVxcTF///vfmTBhAnc10KshKysLl8tFjx49EEJgs9ma1Z8CUEWOv/0tfPIJhISoWxJvvAGNiBc//fRTnE6n1+ZKNpuNY8eOMWjQIBRFITc3l/Dw8DYRONpsNrZs2UKnTp3o0aMHDoeDkpISr0tdJSoul4vq6mpCQkJwOBz87W9/Y9CgQYwbN85v9/D39oQvjpBHgHtrDZ7ckwkB1te+3nZhrkQiaRY7duxgx44dvPHGG0RERHi1eF2+fJl27doREhLCtGnT0Gg09V7ncrk8/Q/cQj5vF0dQMx8TJ07EarV6HTBUVlYSGhpKdHQ0M2bMoGfPnvWeJ4Rg27Zt6HQ6j26jWQFDXSdHqxVeew3+3/+DegyshBBkZ2fTsWNHNBoNEyZMICgoyOsgKjMzkzVr1hAdHU1KSkqbaBecTicBAQFotVrOnj2LwWCgR48eaLVaGTA0g++++w6z2cyLL76IVqvl9ddfb5UySb/iTStM1AzD1AZemw5Y/Nl6s7W+ZGtsiUTF3W64pqZGZGVleX1dTU2N+MMf/iAWL17c6HnV1dXi008/9bRZ9ha73S7ef/99sXz5cp+uE0KIPXv2iN/97neirKys3tddLpc4duyYqKmpEUIIUVFRIex2u8/3EUII4XQKMW+eEAkJarvqGTOEaKLl9vnz58Xbb78tjh075tUtXC6XyMjIEBkZGZ6f8/PzmzdfP7Bjxw7xwQcfCKfTKYQQzf/s7mBycnLE0qVLPZ9hRkaGOHny5FUt5v0Nfm6N7e3GXR4/N6i6lkBUfYNEIrkFOHbsGPPnz8fpdBIYGOiVQt/lciGEIDAwkIceeojJkyc3er5eryckJMRrbwFRu02q1WoZOHAg/fr18/o6d5fH1NRURowYQbt27eo9t6CggO+//56jR48CEBoa2jxR2ebNP4sc4+Nh+3ZYtgy6d7/uVJPJxMWLFwHVb2HGjBn06tXL61vt3LmTAwcOAKrw80YLHQsLC7HbVZ+N9u3b07lzZ8/PbS3Iu1UoLS31ODNWV1eTnZ3tsSHv2bMnvXr1urVKUL2JLIBZwCkg4ZrjCbXHn/dnJNNaXzLTIJEIcezYMfHll18Ki8Xi1fmVlZXi448/9jzxNoTdbhebNm3yelw3paWl4tNPPxWXL1/26TqXyyUWLVokli1b1uA5DodDXLx40fNzdnZ285/qTp0S4v771cxCx45CfPutmnFohK+//lr87W9/8zxZNkVJSYlYvnz5VdkQb6/1N1euXBFvv/222LdvX5vc/3aguLhYvP3222Lv3r1CCCGcTucN//fEz5kGb0PFMUAIcE5RlL38LIQcVvv92FqxZG0cIp7xT0gjkUj8gdlspqSkhKSkJPr27UufPn28froxGAzoAoPILrFw5Uxhg34IV65cYdeuXcTExPhUrhgUFHSV7bG3KIpCXFwcGo0GIeoXcG7cuJGDBw/y5ptv0q5dO59aZHu4cgXeflsVOQYHq/qFOXPqFTkKIThx4gQ9evQgKCiIe+65B61We101Rn3dOcONgVRXV/PTTz+Rnp5OcnIyoaGhvs+3BeTl5VFRUUGvXr2IiYnh/vvvJy0t7YbO4VZGCMHGjRsJCgpi9OjRREVF8cADD9C9Ngt1O7hgels9ccGHMYUQonPzp9R6yOoJyZ3KwoULyc3N5c033/RKVOhyuTh06BDp6emYbC4OXywlOEiHQRdwnWlTUVERMTExAJSXlxMeHt7k+BUVFRw+fJixY8d6zKS8CWKqqqpYsWIF48aNIyEhod5zrFYrTqeT4OBgqqqqKCgoaF77arNZ7Tb5+9+rIseXX1YrJBpp611QUMDHH3/caFMod2MvY6AWvVbDiUN7cKFh6r3jCTcGXmXoc6P57rvvKC4u5vXXX7+1UuZtiM1mIy8vj86d1WVv2bJlBAUFcf/997fxzFTapHpCCJHirxtKJJIbh3sxvvfeezGZTF5XIeTl5bFmzRoCAwNxRSQTHKTDGKj+uXD/90JxNY4rx/jxxx+ZPXs2sbGxXgUMoFYC7Nmzh969exMTE+P1AqXT6aisrKSioqLeoMHpdDJ37lzi4+N56KGHCAkJ8b0k0eWCb75Ryybz8mD6dDVw6NGj3tNLSkq4dOkSffr0IS4ujmeffZbk5OQGh79QXI1BF+D5HK1V5aDRcqG4mvTkwBsaMBQUFLBhwwZmzpxJcHAw999/P3q9XgYMPrBt2zb27t3LL3/5S4KDg5kxY8Zt/flJJYtEchsihFpSaDabmTx5MuHh4V4t6O6n3OTkZGbNmkV8fDzbM4uIuGYrQq/VUG6xM7RPHxwOhyfT0Bhms5mKigo6dOjAoEGD6N69O2FhYU1eV1hYyKFDh7jvvvvQ6/W8/PLL16V5rVYrer2egIAARo8eTfv27Zsct162bIFf/QqOHFHbVs+fD6NHN3rJ9u3bOXv2LD179kSn0zW5BZKbm8u5Q9sZee8MDMHtGDx2EoqiUGa2NW/OPiKEwG63ExgYiFarpaSkhNLSUoKDg2/4dsitiLuj5LRp04iLi2Pw4MH06NHDY4h2OwcM4KWNtKIof1AUpd4AQ1GUGEVRfvDvtCQSSUtQFAW73Y7NZvO0z70Wd5p825lCjuSUcejYSd59910KCwsBtXOeoiiEGnRY7E7PdRdOn2D3hlWE6LXo9XqGDx/u1V7tkiVLWLRokce/wZuAAdSsx8mTJykrKwOu3xe+ePEi77zzjqfBVP/+/X2vMsjIgClTYPx4KClRg4V9++oNGJxOJ3v27KG8vByAiRMn8sorrzSZxXFXeUSGh4KiocZi9rwfb7pz+gOXy8Vnn33G+vXrAYiOjmbOnDlt3q/iZkYIQU5ODpcuXQJ+rrpx26CHh4eTnJx82wcLbrzNNLyBKnZ8Qghxzn1QUZR7gC+B+v8qSSSSG0ppaSlCCKKiorj77ruB+p986u6rRxgDsdidlLmMdEzpfF3JYkp0MEdy1AXboAvA5nBidzpIDGt6kbPZbAQEBBAQEMA999wDeCcGy8vLw2az0blzZ9LT00lNTb3O9MblcqHRaOjQoQOpqanNc0YsLFRFjnPnqiLH3/8e3nyzUSdHk8nE5s2bcTqd3HXXXQ2WeLoRQrB48WICAwOZPn06vVPisd09k8AgHUIIj0akR1yE7/P3ApfLRU5ODp06dUKj0dCjR4+rsk63gzivNXD/frn//ZKTk3n44YcxGAy88MILbT29NsNbIWQfYAGQBLwOfAf8AXgT1V76OSFEcSvO0y9IIaTkdsblcvHhhx9iMBiatGs+klOGzeHCZTWRczaD1PRhWOxOT5Opa8nIOk9eqYnA8DhC9FpSooOJCG58791qtfLJJ5/Qu3dvn2xxhRB88sknaDQaXnjhhXrfx65du8jMzOSZZ55p3qJnsfwscjSb4ZVXVCfHBrZZ8vPzOX/+PKNGjQLU4CwyMrKJW1g8gc727dvRarUMHz4cRVEarJ5oDXbu3MmmTZt4/fXXPa2UJY2zZcsWzp49y6xZs1AUhcuXLxMVFeVzC/ebgbYSQp5QFGUg8B7wBWrAEAa8JYR431+TkUgkvuMWO2o0GqZNm+aVXXOlxU6EMZDMjCzOnTpKp269MLQLqXdfXQjB9s0b0Gq1PvWO0Ov1pKam0qlTJ6/Oz87OJjExEa1Wy0MPPdTo+wgNDSUyMhKHw+HbH3KXS916+Pd/V0WO06apJZR1RI71Lehnzpzh8OHDDBo0CIPB0GTAcO7cORYsWMBzzz1HfHw8o6/Z5lC7c7bOAuRwODh8+DCJiYnEx8eTnp5OdHR0k3O+kzGZTBw7doyhQ4ei1WqJjo6mpqYGp9OJVqttsBHbnYhXmQbPyYryLPAREAScAKYJIbJbZWatgMw0SG43nE4nP/zwAwkJCV53OXS5XOw9nUeAPhiDLgCruRpDcDvMNsdVmYbq6mqPuLCsrAyDwdCkw2NJSQmrV69m2rRpXmsWQBU7fvTRR9x99931tlS22WysWbOGLl26NL9ldV2R48CB8Je/wJgxV53i3rYJVAQ5Px0mMr4jgWHR9I4LJtSga7SyweFwYDabCQ0NxWq1snHjRkaNGuXT5+APbDYb77zzDgMGDPBsUUmux+Vy4XQ60el0nD17lvnz5/OLX/zCUzp5u+DvTIO3QsgQRVG+BT5DzTSMQLWPPqooyuP+moxEIqmfa0WL5bUZAUVRqK6uxmw2ez3WqlWr2Ld+GVVmCxa7E70xGLPNgdnmICVabb9rNpv5xz/+wZYtWwCIiIjwyhJao9FQVlbmES02+b5qxYTt27fnoYceYsiQIfWep9VqKSsro7Ky0qtxryIjA6ZOVUWOxcVqOeX+/dcFDKCWQxoDtRgDA8g5+xNVxZcwBmrJq7Q3GjAIIZg3bx7Lli1DCIFer+eBBx64YQHDoUOHWLBggcfq++WXX2bChAk35N63IlarlXfeeYf9+/cD0KVLF954443bLmBoDXwxdwoBZgkhltceM6BuV7wAfH0ruEDKTIPkVqSuaNFtrnTl8iWGpnYkNjLUI9jylry8PAoLC+ncs3ej++o7duyge/fuTXYvrKysJCMjw2Nm5O18du3axbZt23j11VfrLQctKytj27ZtTJ48WfWL8PF9XiVyNBrVLYk334QGugheuHCB9Tv2MWzsvWg0Guy2GnSBQQghKDPbGNPj+jLO3NxcEhMTURSFjIwMgoKCbtjCY7FYPJ4K+/fv5+zZszz00EO35L77jeD06dNUVVUxePBgADZs2ECXLl1u+0ChTTINQDbQzx0wAAghLEKIF4GHgQf8NSGJRHI1Pz/9alEUhQCXneNbV7F2nVo219RCKoTgwIED7NmzB4DExEQGDBhQu68ewZge7UlPjkDjsPLtt996mumMGjXKq3bHhw4dYtOmTZ4sQGPzcXsEAPTu3ZvRo0c3WPVQWVnJ6dOnKSgo8Op9erBY4H//F7p2VQOGl1+Gc+fg3/6twYAB1CClsriA8tr3oQtUMwsNlUOeOXOGzz//nMzMTEBtmHWjFqCCggLeeecdTp8+DcDgwYN54oknZMBwDXUzUz/99BOHDh3yNEebOHHibR8wtAbeZhoU0ciJiqIkCiHy/DqzVkBmGiS3ItvOFHrMldzCwEsXzxEQEs3dfRt2HnQjhGDJkiU4HA4ee+yxBsWF5eXlzJs3j/vvv79J22WLxYLFYvGIEauqqoiIaLxkUAjBggUL0Ov1zJgxo95z8vPzKSoqon///sDPpk1e4RY5/uY3kJurbkn84Q/Qs2e9p9tsNtatW0fnzp3p1asXLpeLsuoajudXXpXVqWuZXVZWhslkIikpCZfLxdGjR+nbt+8N6fjodsJ033v9+vUMGjSI6EZsre9kDh48yJo1a3jrrbcIDQ3FYrEQFBR0x5WYtkmmwR0wKIrSV1GU1xVF+a2iKHG1x7oCFd6MoyjK54qiFCqKcrLOsUhFUTYoipJV+9+IOq/9WlGUs4qinFEU5d46xwcqinKi9rX3lDvFVUNyRxJq0FFhqmb3+uUUXVZj8/AOHYkKb9yXoKSkBJPJhKIoTJ8+vd6AweFwcPKk+r9jeHg4b7zxRpMBgxCCr7/+miVLlqhd77TaRgMG9/OGoigkJSWRmJhIQ88gu3fvZvv27R4jJK8Dhq1bYcgQePpptWxyyxZYsaLBgAFUnURBQcFVplFRIQbSkyMI1GooM9s8wtBwY6An+Prhhx8QQqDRaBgwYMANaxG9ZMkSVq5c6bn3fffdJwOGOlRXV7NmzRry8/MBVacwYcIEj+mWwWC44wKGVsGbVpio1RKLASeqkZMTGFD72jLg916OMxoYAJysc+yPwL/Vfv9vwB9qv08DjtXeOwU4BwTUvrYfGA4owFpgkjf3l62xJbciZdU1Yv2xi+Iv734gftiyV+w9Vyw2ZxSIsuqaBq+x2Wziz3/+s1i4cGGjY+/du1e8/fbbIj8/v8l52Gw2T1vp8+fPi0uXLjV5TXl5ufj8889FXl5eg+ecOXNGVFZWCiGEMJlMvrXWzsgQYupUtV11UpIQX38thNMpyqprxOGLpWLr6Svi8MVSz2eVmZkpPv/8c2G324UQosk2xTabTezdu9dz/uXLl0VFRYX382sBpaWlYvXq1cJmswkhhLh06ZIoLS29Ife+VbBaraKkpMTz/R/+8Adx8ODBNp7VzQV+bo3tbdj1O+Bu4BeoLbHrPq6sBe6t76J6ApTtQOk1h6ehukpS+9/pdY4vEELUCCEuAGeBIYqidABChRB7aj+Qr+pcI5HcVly8eJFQvZbBXeMYM/Ux2nVIuerp91pE7RO8TqfjgQce8LgwXovVagXUvfCnn366SdvlqqoqPv74Yw4fPgxASkqKV7Xrer2empqaBtteV1VVsXjxYnbv3g1AcHCwd9mFoiJ47TXo3VvNKvzP/8CZM/DUU5RbHR7zqghjIDaH2qWz3GxDq9Vit9sxmUxA0zqJ3NxcfvzxR7KysgCIi4tr9f4M7n/DiooKjhw54rEv7tChQ5NbQHcan332GT/8oHYxCAoK4pe//CUDBw5s41nd3niracgH/kcI8XdFUQIAOzBICHFYUZS7gcVCCK9+mxVF6QT8IIToXftzuRAivM7rZUKICEVRPgD2CiG+qT3+GWqAko2a2bi79vgo4F+FEPWKMRVFmQ3MBkhOTh548eJFb6YpkbQ5ly9fZu7cuY22Wa6L2WxmyZIlDB8+vNEthk2bNpGRkcHs2bO9Fs4JIVi5ciV9+/YlJaXxpreXLl3i8OHD3H///fW2vRa1Xv7uxk65ubnEx8cTEBDQ9EQsFnj3XTVIMJvhpZfUdtV1GlS5AwZjoBan08GeTWtw6MMxJvdiQHIEnaKMjbpZZmZmYrFY6NevH6CKDuPi4pqeWwtxOp0sXbqUuLg4Ro8ejRACq9V6nX32nUxGRgbHjh3j0UcfRVEUMjMzMRqNJCYmtvXUblraqnoiCshoZIzW6OVan05BNHK8XoQQc4UQg4QQg7zpxCeR3Cx06NCBGTNmeP3kpNPpsNvtnixCQ3Tu3JnU1NQm9+KLi4tZuHAhV0orOZpbTnjP4ZQHhHs8IhqioKCAzMxMKipUqdO1Oor9+/czb948Ll++DEBSUlLTAYNb5NizJ/z61zBuHJw8CX//+1UBA6hul0EB6j3NdoHJJtBoAtAANoeLo7nljb6HgwcPcuDAAc8Tf2sHDO7PKSAgwNN5EtTP7U4PGIQQZGdneypubDYbVVVVHl+S7t27y4DhBuNt0HABVUNQH0OAMy2Yw5XaLQdq/1tYezwPtdeFm0TgUu3xxHqOSyS3PGVlZXz55Zce06OmlPlCCE6ePOlxtnv++eevc0wUQnDo0CHclUMpKSlMmDChydR8TU0NOTm57P0p+6pUf11zKTfZ2dmcPXsWgPT0dF577bWrvBccDoen/C09PZ0ZM2Z4vxhv2wZDh8JTT0F0dJMiR3NxHusWz8NqqeZSuYXE9LFEpvQiRK/zlK5eKP55u6S8vJzvv//es4Uybdo0nnvuuRvStXDnzp188MEHnntPnz6dESNGtPp9bxVyc3P58ssv+emnnwD1/4cXX3yR4ODgNp7ZnYu3QcNXwL8pivIkqhMkgFAUZRzwT8DnLZjDSsBtDPUMsKLO8ccURQlSFCUF6AbsF0JcBqoURRlWWzXxdJ1rJJJbGpfLRUVFhdfOh3l5eSxdupSjR48C9Xe0BNVTICsrq8GqBTeVlZWcOHECUFtjj3vwGeLiEzweEfUtukII1q1bx44dOzxzqOueKITgm2++YdGiRR7Hwr59+za9KJ85A9Onw9ixcOUKfPUVHDig/nwNQggcDgcAPTt2wBgagclcg8nqQAgXVruT+HD1qd2gC6DSYvdca7fbOXPmjEc7EBwcXG/moyFXTl8QQpCVleUJCnv27Mn48eOlv0ItLpeLxYsXe36XkpKSeOihh0hLSwMa/v2W3Di81TQEAPOBR4Aa1O0IC6BHFSs+6dXNFOU7YCwQDVwBfgssBxYByUAO8LAQorT2/N8AzwMO1OZYa2uPDwLmAQZUncMbwos3In0aJDcj1+7xe+N8WFxpJre8hkqLnZqyywzu0/O6ffpLly4RHh6O0WjEZrOh0+ma/KP7ww8/cPLkSd58800MBoPHI+JaTUKZ2UZCQCWdOnVCq9VSXl5OcHCwp7wN1ExFYKB67ZkzZwgICKBr165NfyBFRfCf/wn/+Ifq5PjrX8NbbzVozORyufjmm2+IiIhgypQpwM9Np47klBIYEEDnmHaE6NW5mW0OLv50iIgghYkTJwJq2ruxhbs+V866/g3eYjKZeOeddxg6dKjn3nc6FRUVXL58mZ61maNly5YRFxcnMy5+wt+aBl8bVo1CrZRoD5QAPwohtvlrMq2NDBokNyPHjx/n+++/5+mnn25SZAhw/KczrP5hFUMmTicmOrreBcxisfDOO+/Qu3dvz0LaEBaLBYfDQUhICFarFbPZ7OmIWFdU6MZsc2CpLGXbim+55557GD78+p3LkpISvvjiC+69917vG0xZrT+LHKur6xU5Xn36z8ZP27Zto127dtfpP+ou9nqtBqvDhdnmoCLzAE57DTNnzvTq6bWhz6GhVuJ1OX36NPn5+Z5eEDk5OSQkJHgn/LxNqRsYr1y5klOnTvHP//zPVwWdEv/QJq2x3QghdgA7/HVziUQCvXr1wul0et1CugoDYZHRtDPoPVsGoNpN94nXoNVqMRgMPPjggyQlJTU6lsvl4rPPPiMiIoInn3wSvV5/VcljSnQwR3JU8yO9VkNJaQmKPoT07h2Je/TR66o03ItBREQEPXr08M58yOWCBQvUjEJODkyZAn/8Y6PGTFlZWSxevJgXXniB2NhYxtTTfArwWGUfPZPN9q0/MnTCZNK7JhPafbJPRj/uVuJ1MegC6m0lrr6lnxfF/Px8zpw5w+jRo9HpdCQnN+3ieTtz4cIFli1bxnPPPUdkZCSjR4/2fDaSmx9pjyWRtAF5eXl888032Gw2AgICSE9Pb/SJ12QyeXpHOAL03HXvdIztfnaENOgCuHS5gA8++IDs7GxAVZY3pL53Oy5qNBrGjx/P+PHj6z3PvegGajUcPbCH3asX0iVcQ7gxkJ49e171tHzixAk+/vhjbDYbGo2GKVOmNO3lsH27KnJ88klV5Lh5M6xcWW/A4HK5PILBxMREevfu3WR1gcPhINwYyJAeiUSGBpMSEUS4MdBnZ8BQgw6L3XnVsYZ6UhQUFPD++++Tl6e6d44ePZpXXnnljl0UnU4nJ06c8GhGoqKiSEhI8PwOhoeH19uwTHJzIoMGiaQNqKmp8fQx8IYjR46wefNmSktLG1zA2kdHEhsb26Q5UllZGR999JGn0VJaWlqDi7sQAqMW0pMjmH73SCbefTeJ7aPqPTc0NJSwsDBsNi8EgpmZMGOG2p66oOBnkeO4cQ3O46uvvvK0njYYDEydOrVRo6Xly5ezcOFCAIxGIy+88EKTmZeGSIn+uX24EOK6VuJ2u90jboyMjCQq6ufPyBstye2I+/fA5XKxevVqjh07Bqi/J4899hiyBP7WxCdNw62O1DRI2hKXy8Xly5dJSEig3GzjXGElphpXvW2pQV0ozWYzwcHBajOlsjKioqKu2qfHbuH08cMk9RrMgE5RXonyHA4HixYtYsSIEY1uiYjaHhPt2rVj5syZ9b6fTZs2YTQaGTlypHcfQnHxzyJHg6FJkWNZWRnh4eEoisKxY8fQ6XSkpqY2uAhXV1djNBpRFIUDBw5gtVq56667/LJou8WV9bUS/+STTwgICLhhpZo3O99//z1lZWU8//zzgKpxiYyMlJ9NG9BW5k4SiaSFbNmyhS+++IKcgiKO5JThcCmNeh/8+OOPfP7559TU1KjNlGqfXutuGVzMziY38wSJBjvhxsAGywKLi4tZvnw5DocDrVbLE0880WDA4H6QUBSFrl27NijO1Gg0lJeXe8yJGsVqVXUKXbrARx/Biy/C2bNq0NBAwHDhwgXef/99j/9Dv379SEtLa3Dhyc3N5Z133uHcuXOAapE9atQovy1UdVuJp7Y3kHnyqOezGj16NOPHj79jF8WioiLWr1+Py+UCfjYQc38+UVFRd+xnc7txY9qzSSR3KHWfToOTUpkYHkWJTYsx8Gclfl0hY3ryz5mCXr16ERIScl0poNPppKaqjPTkWNKT76JqRD9CQkKuykBEGAOx2J0cySkjPTmC0tJSMjMzKS4ubtRUqaysjCVLljBp0iQSExOvK3urrq5m8+bNjB07lpCQEB588MHG9QEuFyxcqAYHFy/CAw+owUNqar2n2+12KisriYqKIjk5mdGjR5OQkNDg8HXbcnfo0IEBAwZctTXQWmRlZbF27Vri4uJITk6mR48erX7Pmw2r1UpAQAA6nY7CwkIOHDhAv379iI2N9VhwS24/ZKZBImklys02Nuw+zMFt6wg36FC0QZiDO3Cp3IJBd3W5ndtw6NSpUx7nxuTk5HpT66tXr2bevHlYLBYAQkJUQeSF4mqP+ZKiKCh2K9VF+VworqZ79+7MmTOnSRdGo9EIqJqL+qipqeHUqVPk5OQATTR82r4dhg2DJ56AyEjYtAlWrWowYABYsGABCxYswOVyERAQwNixYz1zauj87777DpfLhVarZdKkSa3S1MnhcLB+/XqOHz8OqAHdyy+/fMdWQpSXl/OXv/zFo1Po2bMnv/rVr4iNjW3jmUlamwYzDYqiXKCRng7XIoTo7JcZSSS3CReKq3FZq7FUVeCw2zAGqQLFwsoaLHbnVTX/FruTEL2WE3tOYLVaGThw4HXBgrvx01133UXXrl2vqxy4tizw2N6tlBTkY4x8CohoUCCZk5PDkSNHmDp1KkFBQcyaNeuqe5eWlpKVlcXQoUOJjIzkrbfealxsmZkJ//qvsHw5JCTAl1+qFtANBBh1G1a5g6TGgpGLFy+SlJSERqNhxIgRuFyuZqW+G9MouHFv5wQEBJCTk+OZl0ajueMWyL1796LRaBgyZAhhYWGMHDnSEzQFBATc0b4TdxKNbU9s4+qgYQJqW+xdqG6OscBIoADY1FoTlEhuNWpqalQraAv07DuAnn3S0QQEUGW1k19mJqe0mqoaBylRwcSEBFFWUUmNUzCkWwd6zZiBVqu9zoFxzZo1KIrC5MmTiYyM9Jgv1SXUoKPSVI0xSIcuMIi+Q8dQba0hIqTxssSSkhKys7OprKwkLCzsugX40KFDHD58mD59+mA0GhsOGOqKHPV6+N3vVJFjI5mC/Px8Pv/8cx544AEGDhzYpLlVTk4O8+bNY+rUqaSnp9O5c/OeVRrbynEHDvv27WPPnj289tpr6HQ6nnvuuTtqYRRCUFRURPtac60LFy54ggZFURhbj5235PanwaBBCPGs+/va9tJDgRFCiLw6x5OAdcCeVpyjRHJLsWzZMgoKChg17SmstS6CVVY7ZwoqUYBOUcFEBgdxocSEucZGxuYlxHeIJ7zfY/WOpyiKp2zv2jbTdUkKC+TThZ8T3SGRIWPuhUADCjpPWWBdsrKyAOjWrRvp6en07t37Kh+BvLw8AgMDad++PWPGjGHYsGENbxNYrfDee2qQYDLB7Nnw9tvQwJO4xWKhqKiI5ORk4uPjmTZtGr169Wrw86yoqKCkpITOnTuTlJTEjBkzPL0ImkvdrRz4WVdy/GwuQ7onoNfriYuLo1u3bjgcDnQ63R0VMIAq3N29eze//OUvMRqNPPzww012RpXc/nj7G/AvwL/XDRgAhBC5iqK8DfwP8Imf5yaR3JJMmDABk8lEZFyYx00xv8yMAggUEiKMhOh1tNNrCdRqSLn3Hs/TnBshBMeOHSMhIYGYmBgmTpzYYLDgDiSiw4IZMXIkTn04ZWYboQYdPeKu740ghGDz5s0YDAaPo2PdgMHhcLBw4UISExN59NFHCQwMrL8vw7Uix8mT4U9/giYW9JUrV5Kbm8tbb72FVqulf//+jZ6/atUqiouLmTNnDhqNhr59+zZ6vjfU5/AoaqrZsnw+YswYxowZQ8eOHT39QO4ESktLWbduHXfffTcxMTH07duX9u3be/7tZcAgAe+DhkTA2sBrNUDD8maJ5DZHCMG+ffuoqalhzJgxtG/f3hMEpCdHcKG4miuVVmJD9SREGNFrBPs2r6ZTj97owuMY07v3dWNarVY2bNhAWloa999/f4MBQ3FxMYsXL2batGnEx8czesQwz2s/79mXE6LXIsov0TetBzqdjscee+y69sIXL14kOTkZrVbLY4891rgF9I4d8KtfqYZM/fvDZ59BbW+F+j6fM2fO0KlTJ/R6PePHj/cIF+vD4XBw4MAB0tPT0ev13Hfffeh0Op9dHBvDbZBVU1FCZVkxHbv3QgkKpv/Iuxk06M5R/peVleF0OomOjiYoKIgrV65QVlZGTEwM0dHR3tmAS+4ovP2/8CfgXxRFuWozU1EUA2oW4id/T0wiuZW4cuUKBQUF17Wedtf2j+wWQ3JUMCF6HYoCpooyymrdHetSVlbmcTx8/vnnmTRpUqP3DQ4OJjAwELvdftVx9569zeEiwhhISVEhPyxfys69+wEICwu7atHOzMxk3rx5nD59GlDbYtdtb13nRJg5E0aPhkuXYN48OHSowYABVM3EwoULPVUhMTExjYoIi4uLWb9+PRkZGQBER0cTFhbW6OfgK26HxzMnD3Pq0B5MlhrMNgdjhg+6Lpi6XXH3Hdm8eTOg/i69+eabdO/evY1nJrmZ8bY19gRgNVAJrOFnIeRkIAyYJP7/9u47PK6rXPT/d03vmlHvvdhykXt3nOY4vQfSSAKhhxAC3AP8uJx7zgHuPQU4h0OAQxIgIaQQ0nviFNuxE9uRu+Uuy+pdM5pe9/79MdJEsmVHjuWa9XkePxrvaXuWxt7vXvtd76uq757E/ZwQsiKkNJF8Ph+qquJwOEgkEmg0mqPOCHiCUd7ZsJ38ohKsRj2BSJRwXB2VeNfe3s6f//xnrrrqqmOuc+/v76e+vp5LLrnkqHkOW1rcRGIJEkEvDleybkFzUyN5RSXMLk3+XVVVBgcHcTqdKIrCtm3bmD59+pjX7gdbOoj80z+T+difUI0mot//X5j/4fupJMfDVyJkGhIM9nUxdWgWpampiZKSkqPOFhw4cID+/n7mz58PJIsFnYwyw729vbz++utcddVVCKOV3a29BGNqsi/FGKsnzjUbNmzgwIED3HbbbQA0NjaelKBMOnOcloqQqqq+A8wEVgJLgXuHfr4F1J0NAYMkTSRFUXj00Ud54YUXgOSSs2Mt+wt6+ti55lU6DzTgDkYxGfSjAgaAvLw8lixZckTnyMM1NTWxdetWBgYGAMZ8X28oxqGdH/HeS08S9PsAKC4txx/5uGfFSy+9xCOPPEIsFkOj0TBz5swjA4ZwmNDP/x+WqZPJevRh3J+/nW3vbGD9zV/DM3R18/BZjWhc4bWV7/Lyy6+k6j2UlZUd8/JCQ0MDmzZtSjUxmsiAQVXV1H4YjUbcbneyPLXFwMKaAi6aWnjE7+JcEYvF2L59e2pch4sxDc9MVVRUyIBBOi6y94QkfUr79+8nLS3tiCTGkUa2SN61axc1NTWjDsxtbW288847fP7znz9m7QOfz8fg4CCFhYWjelKM9X6xWIxd3cHkss/uNkprpiKEIBiNo0VhZkk6Wq2W1tZWBgYGmD59+pGBh6p+nOR46BDu8y+m93//lEhNsjBTMBrHoNMws9iVnNWIxulp3kdWXiE2hxP3oBetUFhcO3Yiodfr5e233+aCCy7A5XIRDodPygqF4UZXVquVG2+8MbXtXC9pPPwZ9+3bx5NPPsktt9wiLzt8Rp3W3hMiaYoQYqkQYrI41//lSdIIiqLwxhtvsGtXMoWnqqrqmAFDa2srv/vd73C7kysoamtrjzgoqqqKz+f7xG6Xzz77LM8991yqkNHRAoZHHnmEV155hbJMK6reTE75xwf5QX+Ada88xbp16wAoKiqirq7uyAPo2rXJSo633AJpaWz709O0/uXvqYABPq5gCclZDU0iyvb1q2nelxwbp8OOJ64fsw8GJGdHGhsbU+2STSbThAUMiqJw8ODB1PtMmjSJysrKUe99ropEIjz00ENs2LABgMrKSu66665PnL06Gx2tz4p0co17DY0Q4svAz4CR84Y9Qoj/rarqHyd8zyTpDKMoCi2tbQyEEvRqM49aRXCYzWbDYrGkpoaH+f1+WlpaqK2tpaioiG9+85tjTt2PPPu+/PLL0Wq1Yz5u+KxSo9FQW1uLzWZLJWA29QUY8IdJsxqZV5mL2llNYWHh2B9w/3744Q/hueeSlRwfeQRuvx2l3Ut0jAqWIuLl/ff34iiZSjSu5cJrbsGWlizh3OuL0DkYItNmTBVPennlakwJPzddfx12u53777//pCzj27RpE6+99hpf+cpXyM/PT+VJnKva2trweDxMnToVo9FIVlYWNpsNSFauPBeXjY6nOJd0coxrpkEIcRvwILAD+BLJBMgvDf39QSHELSdtDyXpNOvt7SUWi+GPKlQsuoyKugVH7U4ZDofZvHkzAC6Xiy9+8YtHLFt77733eOmll1K9I8YKBEKhEL///e9ZtWoVANnZ2WM2Yurv7+d//ud/aGtLllBZsGBBKvnQaTHgTHjY8fbfqXTpcFoMrFix4sgqiv39ycqNtbXw5pvw058mV0nceSdotamVBsFoPHlpZOh2uLeVdevWkW1KbtNaHEByVqOpP0BZhg2zPpnrYTHo0ChxBgb9qSBqogKGRCJBfX09hw4dApLdMD/3uc+Rl5c3Ia9/Jhq5WubDDz/k7bffTq3cufbaa1PfgXPV4X1Whm839QVO966d88b7r/YfgMdVVf3CYdsfFUI8BvwAeHJC90ySzgCBQICHH36YmTNnklM7H5vZdMzulPX19bz33nsUFxeTmZmZmgpXFIVoNIrJZGL58uXMnz//iN4R8PGsgdlsZtasWZ84rWyz2TAajcTj8THvT0tLw263E42OMXUbDsMDD8DPfgY+H3z5y8ky0Ic1tRqetTjQNcjW+o/ILyhkztRqrBVLWLJwPhaLBastuXpiuKhUXpoJkxLk7eeeZubii8jMLWDq7AV4QrGTUlnx/fffp7q6mtLSUgwGA5OP0RTrbLdjxw5efvllvv3tb2Oz2VixYgVGo/GcvuxyuLGKc5n1WtzyEsVJN96goYZk4DCWvwIvTMjeSNIZxmq1ctlll1FRUcHmjtBR/6OKRCIYjUYWLVpERUXFqNkFVVV5/PHHAbj99tsxmUxjJj329PTw0ksvccMNN+ByuVi2bNmY+zS8euLaa6/FaDTyxS9+cdQBY/369Xg8Hi699FLS09O56667Rr/AYUmOXHZZspLjMUo5Oy0G6oqcvP/ibvLtOpyW5JnscCXJZGCRHJvhs+BQWIPJbEVVFQDCceWIuhSf1rZt29i2bRtf+MIX0Gq1fPnLX05NyZ9rwuEw9fX1VFVVkZOTQ35+PjNmzEjNLDgcjtO8h6fecHGuwy+ZTdT3Szq68SZC+khWhRxL4dD9knROiEQiPPvss3R1dQEwY8YM7HZ76j+qkUKxBB2763n44YeJRqNoNJojpsWFEEybNo0ZM2Yc82zQYDAQjUYJBI49xerxeGhvb8fn86VefySv14vb7UZRlCOfvHYtLFyYTHJ0OOCtt+C1144IGIavGb/8wQ7+/MTfcQci6PV6vva1r3HxxRcfdd9ef/11HnnkEUozLEQUweyLryEztzB1SWOsPhjjFQqFUpc2NBoNGo1mVHvwc+lMW1GU1PdAVVVWr15NY2MjABkZGVx++eWpluifRUe7ZHYi3y9pfMZb3OkvwArgRlVV3x+xfSHwHPCWqqp3nrS9nCByyaU0Hn6/n4cffphly5Yxc+bM1PaRyVdmvZZQLEGPL4wy2E1/Zwt185dQke3AaTEQj8dZuXIl1dXVVFRUHPW9+vv72b17N0uWLAE+vjxxeLGkxEAbDouR6upqVFUlkUikcgKi0SirVq1i+vTp5ObmplZYjDqIHjiQbFf93HOQn5+8JHHHHTDGpYKRn7OvZT87PlrL9AuuYVFtyZhJZn6/H6vVihCCnTt30t/fz5IlS/BFEp/Yenq8+vv7efDBB1mxYgWzZs066rLJ8bS7Phv88Y9/xGQypYowBQKBz0ylyvE6V37XJ9tEL7k8npyGBcAqIUQ70AnkkpxlOMDRL11I0lmju7ub7OxsbDZbqh3ySCNXJBw8eJBoOIAlt5zcwhLKyspHZXBb9YJDhw5hsViOGTTs2LGDDRs2UFdXlzpbPjwzPBiJsW7NGjKcDqqrqxFCjEoiTCQSbN++HZvNRm5u7ujEyv7+ZGLj734HBgP8y7/Ad78LRzkAxeNxXnntDazOTDInTaGoYhL5pZVEFTEqd2NYT08PDz/8MFdccQV1dXWjEvCcFu0Rjz8ePp+P/v5+SktLSU9PZ+7cuamVH0cLGM7WjPpDhw6xY8cOrrzySoQQzJ07d9T3TwYMRxp5SUw6dcYVNKiq2iWEmEFyxcRSIB04BKwGHlFVNXiydlCSjmWizjba29v54x//yJVXXsmsWbOOCBgOf5/Bll24B70sqJg0KjGyp7WJRqOW2WWZfPnLXz7idSB5MAyHw2RlZbF06VJmz549aqq5qS+AWa+lv7WR/JIKrCYDcy68Epvt4wOH3+9n69atLF68GLPZzD333DM6sTIS+TjJ0euFu+9OJjl+wooCrVZLb1dHKlkxGaDo0apqKskskUgwMDBAVlYWWVlZzJs3j6KiouMb8HF46aWX6O7u5jvf+Q4ajeaYl0Xg6O2uxwp2zgT9/f2pHiADAwPs378fn8+Hw+GYkE6eknQyjLu4k6qqQVVVH1BV9fOqqi4f+vk7GTBIp8tY5Ys/bZGX/Px8LrnkkjGXqg2/TyAYwqZTicYV8urOo3zRFViMHwcFA71dbF71KnsbtgOMGTAMJ0W+8MILqKqKVqs94tq0NxQj4u3no1Wvc2hfAwCutDT8kY9zFHbv3s2qVavo6ekB+DhgGE5ynDwZvv/9ZP7Ctm3w4INHDRgOHTrEo48+Sq/Hz9ZWD47pF5LInYIv/PGyvpFJZs8//zyPPfYY8XgcIQQXX3wx6enpnzjGn2RwcJBXX301laewfPly7rrrrnF3t/SGYpj1oy+3jCxCdSZpb2/ngQceSDXlqqur4zvf+c5nMqlROrsc10JpIcRUYBnJmYY+4H1VVXeejB2TpE9yomeWPp+PN954g8svvxyr1cqk6bNo6Eq2kh6etQB4bnMrzT1+NPvfweJwsXj5VaTZrLj7AoRiCQwaFZ1OT3pWLpMXX4piy2H13p5RMx+RSASDwYAQgvMuvIT+CKzZ1zvqMYqi0N3djcNsIqrPZMllN5CVl5yOD8USaKJ+WlsjFBUVMXv2bCoqKkYfrNetS7ar3rABpk9PJjkuX37Uzz+yKJTX52PjvjYyM7OYlOdie/sg29vcTCtwotNq6GhrYcn05PLPBQsWUFdXN2FLJ4f3IxQKsXXrVqqrqz+x2uZYzuSMekVReOutt0hPT2fevHnk5+ezYsUKysrKAE7KMlRJOhnGW9xJJ4T4K7AN+A3wz8BvgW1CiMeEEPIbL51yJ3pm6fP5OHToEL29vWPOWqzd38ubOzvZ0+nFatZjyJ+MP62MrS1u4gkFm0lHy8H9vPG3P+Mf9NDjDdOpOslymNFpBA3tg/zlg0O8tfUgD/z2t9TX1+MJRulWrBisaUfMjrz77rv86U9/IsuoEIzGsWUmZwaC0TiBSIwda9/i1VdfRVVVNBrNxwFDYyPceCMsWQKtrfCnP8HmzUcNGBRF4YUXXmDNmjUAFBcXs/iqW8nMzMJi0OEwG6grdGIz6dnT7SPid7P9vZfY17ANgMLCQqqqqk54tYKqqjz77LOsXLkSgNzcXL73ve996pLHZ1pGfTQapaWlBUiu9ujr68Pj8QDJyz4LFiw4Z5eJSueu8c40/B/gc8A/kqzL0EUyEfL2ofsODv381IQQ9wNfBlSSlSa/CFiAvwGlJHMoPqeqqnvo8T8C7gYSwLdVVX3zRN5fOvt82jPLnp4esrOzyc/P57777sNgMKQS6EbOWrj9YQ5t+xBXZjEaYcGUV4k+ruCPxGnqCzClII2MrAo87Qfxx1UGIhGmFjgxG7Ts7fJi0muxGrTUt4fQWHPojpsItXlGvY9JK4iRXGUwb948srOzKchOx2aP0dQXoLm1jfy8XGaVpDP1huuxWCwfH6wHBpJJjr/9bTLJ8Z//OTnTcJSkuZEzC8N/H+YLx0fVoNAmwmTG+zFnFXFeTTaZupsmrH+Bx+PB6XQmK/lZLKNqVhyradcnGZmoOlxkqib39CVBvvHGGzQ0NPC9730Pg8HAbbfddk4tC5U+m8ab03A78FNVVX+uqmqzqqqRoZ8/J9mP4o4T2QkhRAHwbWCOqqpTAS1wM/BD4B1VVauAd4b+jhCiduj+KcClwO/kbMdnz6c5s9y2bRu///3vaW1tBZK1EWDsWYtoLEZisBtbfJBIPEE0rqDTQtDdS/uuesoyrRTnZfGVO29leV0puWkmsuxGOjwhRGiQ1o/epKN/kGgCiusW48GemqUAUBWFVa88zd6Nq5MJlkMJcEIInBYDBaYYm1c+S7RrP06LAYPNyf6BGGt2tNL2k5+hVFTAf/833HVXsm/EP/7jUQOGpqYmfvOb3+D1egG45pprOP/881P3H16DouGjdWx+fyWWofirtrZ2zByN4/XRRx/xm9/8JtXE67LLLuO888474dcdNhw4LKvJPuWrJtrb23nwwQcZHBwEYOHChdx+++2pcZMBg3QuGG/QkA98eJT7Phi6/0TpALMQQkdyhqEDuAZ4dOj+R4Frh25fAzw1FLw0kVz2OW8C9kE6iwwfIAw6De5gNNWq+VgHismTJ7N8+XIKCgpGbR950Bzo6URVFIxGE4Ypy8msmE5JphWdFjzBOFp/F7hbMBAf8zX8kTh6rSDs96KJhkgz6THpdcQVlXSbkYO9Q0WZNBpKqiaTXVKVmh1RVTU1hZ2dnc0111zD7Nmzk5dPmgewvfgc869YSuHPfoJ72iy86+uPmeQ4XAzJ6XSSlpaWKid9+AGsyGlk345NDLg9qKpKed18Zl5yA1W5znH8Jo5OVVUaGxvp6+sDoKamhgsvvPCcWEKoqirNzc309vYCHy+LHO5YmpWVRVFRkQwWpHPKeIOGDmDxUe5bNHT/p6aqajvwC6CFZA2IQVVV3wJyVFXtHHpMJzCcGVUAtI54ibahbUcQQnxVCFEvhKgf/sctnTvGc2bZ3d3N888/TyKRwGAwsGjRoiMy8odnLbq6ulj18t/YvWMLToueitw0BkNRlGgIpyZCTpqRurkLuetLX8ZisYx6DZc2QuOeHeg0AmFxokxagWp1kWU3EoknsBl1ZOkiHHr/BdrbW1FVlbzKqdhyilKzI2vWrOF//ud/UtUeZ8yYgcFgoOeNd5lz21VUffvLKDYbTY8/z4FHnqYxp3TMcVFVlb/97W+8/PLLyX1zubjzzjuPaJ41TKdEad6xkd7WA7iDUdLS0lg4eexiTscjEonw9NNPs379eiBZ8njx4sWpGZ6z0fBlnVgsxhNPPMGHHybPp5xOJ1/96lePCEgl6Vwy3pyGx4EfCyGUodvDxZ1uBn4M/NuJ7IQQwkVy9qAM8AB/F0LcfqynjLFtzNKWqqo+SLJDJ3PmzPnk8pfSOae3t5empiY8Hs+YnSIB0sz6oevhBmrmXUB59SSq8pwAbGt1s+7Vv4OqsPjKz1NXNHZwsnNLPW27djHn8gp2dgUxGrRk2YxoNRCOJSjJsKImdFjtdro8YQ74e8iym5hXliwGBTBt2jR0Ot3HZ+KNjfCjH1H9978Ty86l7RcP4L7xFtBqMY+onTAsGo2mVmnk5eWh0+mOWj3x4MGDtLa2smzZMpxOJ9/85jcnZOnk/v37OXDgAJdddhkmk4k77riDnJycE37dM8Gbb75Jb28vt99+OwaDgdtvv/2c+WySNB7jDRr+CSgnuWrin0ZsFyS7W/7zCe7HxUCTqqq9AEKI50jOYHQLIfJUVe0UQuQBPUOPbwNGVpMp5ARnO6Rzi6qqHGrvwqOY8OqzWXrNbWjNY9fq7+7u5uWXX+amm25iZrGLmcXJa+zD5ZiX1eRQZr4ag8FAbu7oA4TP50NRFNLS0pi7eBnpFdOJaYzMKDbij8Q50O0n2N9GpLuJSHwxsQQUzFlBaaYVs15LIBLjhaefoDg/lxuuu4b09HQWL16cTHL82c+SBZoMBjrv/wFtX/omJmda6r0PT/o8dOgQTz31FHfccQf5+fnHzBXwBKN8uGUXbU37sRROpirPeUIBw8jS1T09PTQ2NhIOhzGZTGf1mbfP56OhoYH58+cjhMDlcgHJz6vRaE5KUStJOpON6/KEqqpxVVVvBaYD3yK5iuJbwFRVVW9TVTVxzBf4ZC3AAiGERSRPiS4CdgMvAcM9Le4EXhy6/RJwsxDCKIQoA6qAjSe4D9I55NU33uLxvzyC1+vFZTGgCN1RCz/pdDqi0SjB4Md1yiKRCH/5y1/46KOPgOSyxNzDWkYnEgn+9Kc/8fyLL7FmXw9/29TBwUEFnUZg1Gkx67VcMCkbNRYh6h8kTZfAqNPgDkaIJ5IHWZvJQE5hKQZn9vAbw3/+J1RWwq9/DXfeCfv3Y/7Zv+DXGY9I+izNsKSKIeXm5lJTU3PUFQiBQIDnnnuOvQeb2dLipnTqHC658QsoQvupi2JBsrLhAw88kGqoNH/+fL75zW+e0EqI00lRlFQuSFNTE2+++SadnZ0AzJs3jxUrVoy74JQknWuOOtMghLgQ2Kiqqn9421Ahpwkv5qSq6gYhxDPAZiAObCF5ScEGPC2EuJtkYHHT0OMbhBBPA7uGHn/PBAQu0jnEVTKZGoy40tKSS/sOK/wUj8fZu3cvU6ZMISMjg2984xujpvANBgM2m23MA18sFkOv16PVall6wcV0hrW09AfJtBkRQsPeLh9p4U4SQsdH8TQc2eXkl9ZQkG5lX7cfNehlzYuvsmT5lTgzspg6az7uQASeeSbZVOrgQbj0Uvj3f4dp0wBwwpjLCd946TnC4TB33nknJpOJ66677qhjotPpaGlpQZuWQ27Zx+Wvh/8TOJ5yy/F4nMHBQTIyMnA6nWRnZ6dWCYzsi3G28Xq9PPTQQ1x44YXMnDmT2tpaCgsLJ+SyjSSdC471r3slsJChM3ghhAZYBdytqur+id4RVVX/D0fWeoiQnHUY6/E/B34+0fshTaxT2Ynu4MGDHDhwgOXLlxPXmqiZOroVtVmvTeUAbNiwgbfffpusrCyys7MRQpBIJFi7di3z5s3DbDZz4403HvEe/f39PPbYY1x66aVMmjQJ4cwnM67Q2+nFYdIjhEBVFPbt2IzWZKU/exYVmRlEEyp7u3xoNSCMVoTOgJJIrr7QbljP7H/9P7BpYzJIePNNuOSSI957uEHP4OAgDocDIQRTpkwhHo8f8dhh9fX17N+/n5tvvhmj0ci9997L2gP9YxbFOjw/4lieeOIJ/H4/3/jGN9Bqtdx8883jfu6ZZteuXcTjcaZPn47dbqempiYVJOh0OhkwSNIIx5pjOzxzSgBLgM9uE3fpuExkb4jxaGpqorGxkWg0ekTdAUjmAFgNyS6Spvwa6i64mvawPrU/fX19vP/++6l+AGNxOp0UFham+kUM13ewGrT0HNqDkohjMuiIly0ia9p5ZNvNRBMK4d5m3LvWoqoqfkVD4fzLyQmGyf/anUy56TIsbS3w8MOwZcuYAcOwtrY2fvOb37Bnzx4gmTg5c+bMUcGRoiipDP/hn8NLLbVa7VHH5lhFsSKRCOvXr09N2y9ZsoTLLrvsqI8/0wUCgdTtzZs3U19fDySXol555ZWUlJScrl2TpDOaGFkVbtQdyZUSC1RVHZ5p0AIxkgWYNp+6XZw4c+bMUYf/c5BOvuGAYWTFxmA0nqqnMBHi8Th+vx+n04miKMTjcQwGw6g2yWa9llAswd7t9Qy2H2TysquwW8yp7X19vSyeWo7TYsDtdqeS3YZ1dnaydu1arrvuuiOm3oc/40BPFxvffIbsKQtJK6xhT5eX0gwLhelW2t1Bwp378XU0Yp9yPmUGhamP/Jb8v/4RVafHd+93aL7r63g0xjFnYxKJBIODg6Snp6MoCu+99x7z5s07otEVJJs+Pf7441xwwQVMnjx5zJUTY41NMBo/Zo2L/fv388QTT3DrrbdOWGXI02XdunWsXr2a7373u5hMJgKBAGazWeYpSOckIcQmVVXnTNTryX8l0klzKroO/v3vf+evf/0riUQCjUaTWv8/VuGn6VXFWJ0ZKKqgdSDI5hYP27dto/71p9m8O5nEd3jAAMmz0tbW1lQVw2GJRAJzbJBgNE56di5zll+HLb+KPn+E0nQz2r4DCF83NbkOMksn45x8HgtefYpLrj2Pwkf+gOaOO/DvaGDLF79N2Gg56mzMM888M+ozXnTRRUcEDJFIBAC73Y7L5TpmFcLxFMVSFIW33347lQhaWVnJ17/+9bMyYPB6vbz66qv09/cDyc+ybNmy1NhYrVYZMEjSOH1SxlKBEKJ86LZ2xDbP4Q9UVfXgRO6YdPY7FV0HFy9eTDAYHNUlcGQehRIYwCYizKypA1y0J9JoGwxj0mlxmHSEsktIq/AT0I4+CA8MDNDT08OkSZOorKzk3nvvPaKM8ttvv019fT13feUb9IQFtoxc8odmCgb8YZ78yyv09A1QWudk0rqVVP7nzzC3NicvP/zHf8D06RxscWMRCod36ty69xBLppWj0+lYsGABkUjkqAe2d955h4aGBu655x60Wi233HLLJ47bcH7E4YaTPDUaDV1dXcRiyQBPCHFW1SOIRCJEIpFU7sf27dspKSkhIyODnJycs+qzSNKZ5JOChmfG2PbCUR4rez9Io5RlWtnSkjw7HzkNXpM7vksTR0ui3LJlC4lEgjlz5lBcXHzEc4an3l0WA++vWU/AN0h5ZTUZdjP+cJxg50E8vc2UzrsEi9mEs3Qqwagy6nVWrlxJe3s7lZWV6HS6VMAQi8VIJBKYTCYWLlxIcXExBdnpFJDMG9iwYQMJ1xyaB0LMufh6dJs2MeVL15HbsIXo5Fp44w1YsSL1Pt5QbFSjKICY383ql57EFFnBggULxry+HggEMBqN6HQ6SktL0Wg0KIpyQi2WN2/ezDvvvMO9996LyWTi1ltvPSvPwFVV5Xe/+x1FRUXceOON2O12vv/9709I7wxJ+qw7VtDwxVO2F9I56US6Dh5+8A/FEmxpcTOjyMmePXtQFIXZs2cfMf3e1BfAqAGDUBBCx/zzVxCKJWhxh8mwm7GZdPSoKvFEgkQsSlyjQ1FVbCYdfr8frVaL2Wzm8ssvR1GUUTkMiqLw8MMPk5WVxY033ojD4cDhcKTub2lp4d133yWgtZEbVSj95c9wvvICsewcDv7f/2Tw5tuZWTa6jPPwbIxBKAwO9JGRk4/e5qJu0YXMmDFjzLEZHBzkd7/7Heeffz4LFy6koqKCioqK4/jNfKy/vx+TyYTVaiU/P5/Jkyenkh2PN2A4lStlDrdjxw4aGxu59tprEUKwfPnyUZeaZMAgSRPjqImQ5yKZCHn2ODyJMhIOEY4lsFotTMm1otPpxjyovbe7i+3vPo/Vnsb8C68AkmeeLW3tTM424dWnM+CPMhCIEIgm+0G4LAYcRsGaFx6joqKCa6+9dtRrJhKJ1Bl8fX096enplJcnr9r5/X66u7tTB+3+/fsJ/t9fUfD4H0Gnp/fr99L3tXtJWKy4g1GW1WSPeu3h4OjAR+/R23aIZdffSVQ9MscgkUjQ29ubKjC1Zs0aamtrj9pLYjyCwSC/+tWvmDdvHpccY8XGeHya5MoTMdwsqri4GI1Gw4cffsjOnTu54447MBqNE/5+knS2muhEyLO3Cot0Ths5ba8oCVa/8jS2NBeTFq04ZrMjp9VIXvkknGkfn2UGo3EObllLm0bl81/4Ip5glOKMj8s4h+MKVXlO9BdddETJ4+7ubp588kluuOEGioqKmDNn9L+91157jZaWFr7zzW+i+8MfyPjpT0n3eOi98Vb6/9ePieclG8CGovFRuRyeYJSN2/cgLGkYTWaKJs8kp7wWi9nElDHO0F9//XV27tzJfffdh9ls/tTtpDs7O2lra2Pu3LlYLBauvfZaSktLP9VrjdTUF8Bi0B2Rm3E8BaOOx/79+3nyySe55ZZbqK6uZsGCBSxcuHDC30eSpNFk0CCdkUYmUWo0WibNmI/OYh8ziVJRFFavXk1VVRVlmdl4ympRFNjZ3E2XP85gRKFq6lIqc50IIVKXTFo7Otm17g2uuvpawIWaXsKugRiOkDs1te50OsnKyhqVK9DX14fVasVsNnPJ8uVoX3gB3fTpyeZSy5fj++n/oyGtMHnWrapH5HJ4glE+3N3CR2+9QPX0OZRNn0/C5mRB7eiz8paWFjIyMrBarcyfP5+qqqoTLs28bds2duzYQV1dHQaDgalTp57Q6w0bKzfjeAtGHUs0GuX555+nsrKS2bNnU1FRwfXXX09ZWRkw9ioRSZIm3tmX5SR9JpRmWNi1+UNamw+hqiqZxZUYHBmpFtLDPMEo9Y09bNy0hTUfbQOgPMtGY7eb/WtexNu4mWy7kYjGhD+uTSVmzix2cVFdGblZmQiNZlQRqtaD+/nrE0/iDkQwGo3cdttt5OcnZwyCwSAPPvggq1atgvXrcV55JfYvfQlMJnj9dXjzTRzzZ4+5pFGvxmhoaKCpL0C6y8WiFdcyacb81Bl6U9/HBYe8Xi+PPPJIqu1yVlYWNTU1xzw4Dl8iWL23J7Vsc2BggL/85S90d3cDsGzZMu69994Jb039aQpGfZLBwcFUPwuDwZBKQoVkkapp06bJXAVJOsXkTIN0RrLqBf6uQ+hIYM3MG5VEOZxw19jSgVsxUZ5p48JrbkHRGtjS4karEdSVZKH0TMHoysGZZiEcS+AORkkjwAsvrePOz1+HyWTiC1/4QvJaPB/nT2jUBPFwkL3tfSyoTl6uGBwcJC0tDYvFwg2zZlH8P3+AF18gkpVN97/+F45vfAWnw5La/7GWNL7xxrvU19cz/6ovkJOehqXg41URZr2Wrn43OwbbmDZtGg6Hg1tuuWXclQlH5hQ4zXp8wRBbWqLJPA6vl8HBQXJycjCbzSf6qxnTia6UGTayGNUbb7xBW1sb999/PxqNhttvv33C91uSpOMjEyGlM0Jzf4D1jf109faTk+FiYVUW2RYNJpNp1Nn18MExERzkg1f/hrNiJvbiWmpyHejVKPVr3kYUTmNRbRmbW9wf94NQVbzhOOnhNhrqP+TrX/1yKrt+1Z5uBlv3YTJbyC+tRFVVVEXBE46zrCab7du38+KLL/LVm24i5+GHUX/zGxSNls6v3IPnm/cRMJjHTPpTVZWGhgZyc3PJzMwkGAwSCARoC+nGrJS5b9NaWvc38J3vfAeL5eMAZDxGJo5+8NaLKIkEsy66GoNOw4wi54RM33/S6ogTXT2xd+9eXnvtNb72ta9hsVjo6+tDp9PhdDpPeN8l6bNKJkJK55zm/gAvbG7Dqonh2/YGSkE1L/imcu2sQkrMRy6ptBh0mK3ZOCtmkVs2iYRGS4cnRLFdg8/dh8XlIRRLroyIxBOIaJCA30daVh7ZuZPILakctRzPbtKxZc8OHE4X+aWVCCEIxhUsQ/86qkpK+HxXF9mLF4PbzcBNt9J83w/RFxcBYBmxbyNnF8LhMK+88gp1dXVcdtllWCwWLBYL+qHAR0kk6GrchT07H60ljYsvWIbp4vOOO2BQFIWmxgNUVFQCpAIfk06DJxSbsIBhrCWwIwOloxWMOpp4PM6uXbvIz88nMzMTl8tFXl4e4XAYi8VyQitDJEk6OWTQIJ0WI89KNzQNYDNoyXC6SFTOIC2vlLDQs76xn5KMj3MYBgYGeP+15ymbvYx9A3H2J7I51OyhRONGl1kCmHDMvhKDXkuPL4zLYqC530/PplUkYmFKLr+ZUCzBzOJkD4dNmzYxY8YMKrLt9J93OQ6bDXUocXHL+29hVKPM2WLD/MMfUt3YCBdfDL/4BTtNeUdN+nO73TQ0NLBkyRLMZjNf+tKXjjj4Ddev2NvWR8PmD6moreOySy7+1EsTGxoa2LHmNUyGaykqKaW0egqQnL2YqOqbE7k6Ih6Po9PpiEajvPTSSyxevJgLLriA7Ozss7pbpiR9FsigQTrlRp61OgwavPs3EsmrwWE2kF05HQC9otA5GBr1vHg8TsDrYe2uQ6Rl5FOSYaWnaQ+evh0ESsBaWY5Bp6Uk3YbX50VjsJKTZkY3fQl2i5EMuyk1Zd7a2sprr72GTqdj5syZzKvK52CvP1WEamEiQvl//xdi+3aYMgVeew0uvRSEwNHiPmp57N27d7N69WqmTp2K0+kkO3t0XYbm5mb27NnDihUrmF+dT803v0FaWtpxzQYoisKWLVuw2+1UV1dTW1tLJAGdONnW6iaWUNBrNTgtepZUZZ3Ab+pjE7U64qmnngLg5ptvxmKx8NWvfpWsrInZR0mSTj4ZNEin3Miz1oBvEL23nYTFSa/DhdWY/Er6wjGy7CYUReHgwYNUVlZisDmJ1lxMd1+YhC9IptNKenE1B+M6tNixmfTkO80YiLPxvecprqrlthuuBJIrH+LxOB0dHTiLiykqKuIrX/kKeXl5AGjiYTa99SwXlZdT/tBD8Le/QU4OPPggfPGLMKIy5MikP6NWsG/XNnSWNC6cOxVb/jymTp06qlLkSO3t7ezevZslS5ZgtVqP63r9cJKgEIINGzaQl5dHdXU1Wq2WyuoaOvf3gkggECBgIrOVPm0fke7ubnbv3p1qEFVeXs7IPKrDgypJks5scsmldMp5QzHUSHJ5odWexpzLbyGSVky/P4SiKAwGIwyGYiyoyGDjxo08/vjj7G9qZUuLm2AMKpVWrE3v0dwziF6roaiklByHieocO3aTHqPJTPX02biKKke978qVK3nssccIBJLvnZ+f/3Gnw2iURc8/T+lll8FLL8FPfoJnWwNbVtzI6saBUZ0nR3WJDERo3r0V3G04LQZ0Ot2ogCEUCvHCCy9w4MABAObNm8e3vvUtrNbRS0c/SUNDA3/84x9JJBIIIbjzzjtHVa5s6guQbTdRV+hidmk6dYUusu2mUcs4T0RZppVgNE4wGkdV1dTtw5fAQjKXY3hpZEtLC+vWrWNwcBBIfv758+dPyD5JknTqyZkG6ZQYmcPQdKiFlo2vM3fZCgrLayjOcrFQ6NnT5aNzMESW3cSymixKMqwUpM0hLS0Nv9aGxaCQbTcSiudgJkF5lgO9Xks8oSCig7zz3F9ZsPwqbA4nhZNmYNBpiEajyRbWZjOLFy+mqqoqdcA+dOgQG95/n5v6+9H+9KdMcbvhrrvgpz/F48o6auJfxOdm48aNXHHFFWg0LuYWf+WIIGB4VsBgMNDR0ZGq8zCyl8UnCYfDaLVa9Ho9BoMBo9FIZ7+H3rBmaIVCNHW55WQXVxpvH5Hu7m4efvhhrrvuOmpra5kxYwbTpk074aJUkiSdGeRMg3TSDecwDBdPKiwowJA3CeHIwRuKsq3VzaG+AAvK07l9YSlVuj7efenpVMLc5MmT2bdrJx37djCtwElQ70DJm4ZOp6HXH0Wv1VCSk47QaolFI6mz4GKXiQcffJBXX30VAIfDQWXl0OyDqmJ45RVWfO97aO6/H2bOhM2b4U9/goKCUZdQhBCjCjD19/eze/du+vr6ALDZbKNyErZt28YjjzyS6jr59a9/nXnz5h3XmPl8Pv7rv/6Ljz76CICqqiquuuHz7B+Ip8YxGldSMyAno7jS4YYDh2U12alVE6qq8sEHH7BtW7KwVlZWFvPmzUtddtDr9TJgkKRziJxpkE66pr4AOjXG3o/WMW3eUnKcFuYuOo/mAT/+vgHSbUZml7jQaZOVGR1aAxaLJRU0qKrKYHcL0XCY86bMYG5pBh809nKwtY8spY/Lr7mMonQLB0tz8IXjaFFSB7WFCxemEu1UVWX79u2Yd+yg+g9/IH/tWtTaWnj00VSS47DDe1/s2boRi82Bo6CS8yZPpqKiYlRjJEVJttbWaDSpmYHhpYPj7Rbp9/vp6uqisrISu93OggULUo2xhsfxaCsYJqq40nioqsrAwAAZGRkIIdi9ezcZGRnU1dWh0WhYvnz5hL+nJElnBjnTIJ103lCMqM9Ny4HdDPQmyxln2ZMH3PnlmdQVuhDRAINdrcleE64Cbr75ZjweD36/HyEE115zDbVLL6fXF8EdijIlP40pVj92fxsdfcmD5aySdKodCVY//xe8fV14glE0WeU0hUxsaXHj3b0Px9e/TvUXvoC6bx/84Q+IbdvgsstGBQwwuiyyEBp6O9ro6+7CYU4WixoZMAyXlt68eTMAkydP5rbbbjvuegtvvvkmzz77LPF4HIDzzz8/1dVyeBzNeu2o55j1Wryh2Og8ixGlq09Gh8nXX3+dhx9+mFgsBsAXvvCFIzqDSpJ0bpIzDdJJNTg4iMOsJ6rP59LPfQmjOXkgTZ4JK7T0BwhEFfq3vUM8OMiKG+9kMBQjGo3yyCOPklVYQuXcC3GY9VTkOFiz4xDBQJDcnFwqFyzGpFlIQqNP1QvIyMigsLCQqJqctTDpBIPb11P+xuvYH/sTDp0W9cc/RvzgB2C3H3W/zbFB3n/7HWYvuxy71cysi64ikmBU4l/XwCCdfoXBYBS9zYXGkCzRPN7lkz6fj9WrV7Ns2TLsdjsXXHAB559//lHzHj5pBcPxFlcar56eHt59912uuOIK7HY7M2bMSLWkBia8j4UkSWcuGTRIJ822bdt4+eWXmXnxdTT69aRbDZRl6tBpNfT4wgQjMbYN+PFFVVTLJBwZWpr6A5Rm2QklBFXzLyQ7J4+0oUTE7a1umj9aiVanIyf7ajQaDVE07Nqxg57m/ahXX095tp3Pf/7zbGlxYyVMxkO/p+43v8AcDtN33efp/ocfM3X+J3d2dJgNJEI+YiEfbqHFYTZQO6Is8tvvrWbjhg0su/YLpFvNmBddzGA0jicY/cSz++EkyXg8zvbt2ykvL6e2tpb09PRjPu9UXoJwu90IIXA6neh0Otrb2+nr68Nut5Ofn59K7JQk6bNF9p6QTprOfg8vvrkKS8k0/FGFwVAMjYCFFZn4wzHq334Jv6IjWjAbnVbgH3ST07uJFZddjjkjP9VLIRIOEVG17Gj30N/TTWGWC4PFhjsQBQFKXzOhzgMsWH4lcaFnSo6Zxt/8nlmPPISxqZH+uQvYct8/0lpSgwLcMKvwiAO7qqq88cYbGI1GLrzwQiCZpzAyHyEQCKDT6TAajby3eQ9tTY1MnTUPnT75WsFoPHVZ4GhefPFFhBBcffXVAEQikVGXOj7JifZ3GI9YLMZ//Md/MG3aNK666irgyLGQJOnsIHtPSGe0gYEB6uvrWb58Ofv7o4SyJuP1RoklVPRagV6XPPB0eiOo9myUhA5PMIYKOMw2VJOdsKIhNpSIGPR5ee+lJ3GVT8dRNIl2fRor93sxD24jpjGSlldKXVEZVZOn0B2Io6lfS+w/f8LCfbsJlFdy8MHHWT9pPiaDDqMKCuqongkjCyZFo9FRB8aRt0OhEL/5zW+YPXs2y5cvR2NNp25e7qhLEUdb4jgwMJCaRbAPXRIZft/jCRjg5F2CWLduHd3d3Vx//fXo9XpuuOGGVOErQAYMkiQBMmiQJlhjYyNbt25lzpw5bG8bxB1IJuX5w3H84ThGz0Gi3gJsrkxa9EVkWFWKBg4Qya4lGFNQSheitWVgN+kIxRKYbXaKq2rpM2Syt9nNtlY3mRY9RbFuBlUz29tdTC1wMrBtOwv+9N+UvfsaQWcGH93//9Fz21dxR1WMAkAQiSeoybWj1Qia+gJkaXp48cUXue2223A6nVx99dWjggBFUejo6KCwsBCz2cwFF1yQWs0w3gqJ27Zt44UXXuDrX/86OTk5qVmM0y0Wi7Fv3z5qa2sRQqAoColEIjWjUFNTc7p3UZKkM5A8fZBOmKqq+Hw+AObMmcM999xDeno6A/4oqqrS54+iqOAwgtVzkN7mvSAEWiEg0I924CCakId4QkGr1ZDw9/PRm8/i8foIxRKUTJtPb1SPu6kBl0mDIjTsttTRYZ9MkYhQ8G//h5vuupLC999m5xfv5a0X3kf51nex281EEwmi8eQsR03uUMVIrUhO7zscmEwmQqFkj4vDExjfe+89HnnkEbxeLwA102bSFtKxem8PvnAsmZdxWIXE0gwLTU1NdHZ2AlBdXc1FF110xrR3Hr4c2dDQwDPPPENbWxsAS5cu5aabbpIzCpIkHZOcaZBO2LvvvsvWrVv5+te/jtVqTVVHTLcZ2NXhwaRG0OntxBUdvsKFWCxWYv4BqnIcNPVrCBdfgN5sJU0jsBp1FGXY2ROPUeHS4xMaGjo85OiD6CKNNGkNBO0FGLRalr/3NJ9/63FsQS8HL1jBlq9+D39BBTW5dsx6LeGhjpbDuREAm95fSSQSZd6Fl+FwOLj77rtHfZbW1lZsNhsul4u5c+eSn5+P3W4fszW0IEYkniA8NMNQk+vCZtDwx2efpaysjBtuuAGz2cySJUtO+e/kcH6/nyeeeIIFCxYwffp0amtrcblcFBYWnu5dkyTpLHLGBA1CCCfwMDCVZK+dLwF7gb8BpcAh4HOqqrqHHv8j4G4gAXxbVdU3T/lOSwBMmzYNvV5/RF2C6YVpNLZ24mhZQyhjEkpmBVZbGtnePXj3NTL38lvJdphoHQgS9rnRevuwpE/Br7Fyy513YzNoaG9vpyLLjqskg/9q89EXM7J0yxrufP4Bcns72Fs9nQevv4/qS5eRYTVQ4zRjN+lTbaHLMq3UH+wFTJj1WoxWB6o+SmnGkTUUwuEwjz32WCoB0OFwpPpIjFVYKctuwqDTkBZ3s2PLDmYMXd64/fbbj2iHfTq0tbURDAaprq7GarXicDhSyyMNBgMlJSWneQ8lSTrbnDFBA/Br4A1VVW8UQhgAC/D/Ae+oqvqvQogfAj8EfiCEqAVuBqaQbGH4thCiWlXVxNFeXJpYra2ttLa2smjRIrKzs8fsVji90MnWglw8kWocmaXoTCbsJj0lJbMJFBZgspiZ5NRRmWVj3XtbifS3M23RXKJxha2tHrobPuTA7gZyFl2L2Wxlnr+fpQ/+G1MObKMjr5Q/fOl+Ppx3DfOq86nOsWEx6DDrtalLBTW5LgLuXja//gSzz7+CsCOTSTPmjlpx0N4zwMZtDaQX1+Aw67n6+puoLj/yYHp4bwdVUTBpBZ5QDDXgobm5Gb/fj91uH1WQ6VQbrqIJyRmgQCBAdXU1Qghuvvnm07ZfkiSdG86IoEEI4QDOA+4CUFU1CkSFENcA5w897FFgFfAD4BrgKVVVI0CTEOIAMA/48JTu+GfYtm3baGpqYs6cOUcU9/H5fLz55pssXHYR+U4T2w0l2Jt2YtKohMrn0uNXqc0rJhr0EQ1CW1BDbu08ip3JHgVNXQN0BRS6Y7nkT8vC2N3LtP/5B+rWvIbfZuOR27/PC7MvpyTbwSXlmUzOd1CWaU01U7KbdNRmm3FaDFh0WZSXlTGtJPOIwMYTjPL22vU0N2ziksISonEtHhwUxiEYH720UQhSiY9Bv4+1bzxHxbS5lFRNoq5qBjNmzDjt+QCbNm3inXfe4Tvf+Q4Gg4Err7zyuLtpSpIkHcsZETQA5UAv8GchRB2wCbgPyFFVtRNAVdVOIcTw//oFwPoRz28b2nYEIcRXga8CFBcXn5y9/4xIJBJEIhEsFguXXnopsVhszGqAgUCAgwcPEk0rwqtPtmluGdQTikXp6PVRV5yOLxTh4PqXsDhdVCy4lCKXhQ53gA0vP4FqSceTNRN/r48rVj/JwlcfR0Xw7pU3s+a8iyhfdAH/K9uBTqtJtWceuRTx+eefZ3N/P3fffTcGg4Ebb7xx1GfYtGkTeXl59Kk2KqfMorqmFqs9LfWY7W0eEoo6Kn/B4w8TDngpKcjDZLFic2agaJOXP05XsBAKhaivr2fatGk4nU5yc3OZNm1a6vfyScWiJEmSjteZEjTogFnAvaqqbhBC/JrkpYijGatO75hVqlRVfRB4EJLFnU50R89F4y0Y9Mwzz+D1ern77rvR6XSjyh2rqsqeA02EjS68IQ1FS26gp72JNKcBd8yEmjuZPl8EjaIQiSewGM3kTltMaUEOnYEwvTotHzV70OZNwWp1UPLsX7nh1T9hD3jZufgC2n/0rwykZ5EZjDKtKB1vKIbFqEm1Z/b7/VitVoQQVFVVkZ+fn6qFMJKiKKxdu5bJkydjKZ+Ny2JCCHPqfrNeS0OHhyn5zlH5Cx3bVuPp6yH7qltp6Aiiq1xIZrbtJP1Gjk5RFCKRCGazmWg0ynvvvYfFYmH27NkUFBRQUDBm7CxJkjQhzpSgoQ1oU1V1w9DfnyEZNHQLIfKGZhnygJ4Rjy8a8fxCoOOU7e05ZKxVASOLH400Y8YMwuHwmGfW73+wgffefpOCBVegs2bQ1DMI++qJZBTQbJ2E3ajHHA+S27uB7sRUCl3TwZEL8TAHV73IwNTzCMcszG8+xJKH/oP09kPsqZ3DuytW0D99PlNz8yEax2LQHlFxsbu7mz/+8Y9cddVVTJs2jalTR5eJbm1tZcuWLVx11VXo9Xq+8pWvYLPZ2NrqGbPWgopAR4L9O7ZTNmkqOr2Bmulz6HL7UVTBlHxnqozz0cbqZFBVlT/84Q/k5uZy3XXXkZaWxv33358qGCVJknSynRFBg6qqXUKIViFEjaqqe4GLgF1Df+4E/nXo54tDT3kJeEII8SuSiZBVwMZTv+dnv2O1W55ZbGDXrl0A1NbWjlnwZ/hsPuEqwl49H73ehM2kw2q20JSzAK3Ris2oSz7GYCVkysZgc9LhDlKRbUdvTSO7oIjynlau/vUvKNrxEb05eTz+o//iw8mLiasKNbkOwrEEg+EYU/Idqff1eDwIo5X2sJ7ciikMCtuYvR8GBgY4cOAAg4ODOJ3O1EH2aL0cqrJt9PX2smPjGsxWK4XlNVhc2WgSVqxG/VHH6mRobGzk4MGDLF++HCEEc+bMSa3oAGTAIEnSKXVGBA1D7gUeH1o5cRD4IsniU08LIe4GWoCbAFRVbRBCPE0yqIgD98iVE8cvOcswgAYNNpOO/KHlisPlkFVVZf369eh0OiZPnnzEVP+uXbvYtGkTt956K00DYVyZuTSve4H8qQvJz61kIOCipaWNGtFKb+YsQNCfMZXiaB/B3Q04S65FtHdw52uvYPjbk0TTM1hzzw9Zm59G9sxFGH1a4mEVo15LQlUodJmZXugEkj0cGg82UXfJ57BbTMxZtCx15j8118oHq9+hrKyM6dOnp+oS6PWjqzUOt5Nu6gswEIjQuWczWWkWZs5fyBZFZclVt5KVlZVajWEz6cZsTT1W6egTMTAwgMvlQghBZ2cnO3fuZOnSpZhMJubOnTuh7yVJknQ8zpigQVXVrcBYTTUuOsrjfw78/GTu07ls+LKEQatFIyCWUNnb5aMm146aiGHRa1PL9AwGw1HbPcdiMSKRCCoCoy2NrMrpOHKK0Rt1VGZbCfQJVLcfpz5OnisNs15HsMeNOR6l9tc/J+8vD6MCh27/Ai33/SMxi51KXwh3OE6pQaEi24bVoMNh1uPUhLHqk/sxa9YsdM48bGZj6ox/+IDeOhilv7+fjIwMIFnp8fCAYZhFR+pyxzM7AwR9sRHBhAF3MJoq3NTUFxhX6egT0djYyF//+lduv/12KioqmD9/PosWLTrtKzMkSZJAdrn8zNrS4iYaV0goKnu7vJj0WlQVEkqc7o2vUVSQz+dvuuGI5/l8Pvr6+igrKwOgo6ODlStXUjjrArZ3hYgmFOI+DyLqxZxdyqRcB3qh0NO4E5crnYycItL++meqfv8rNP19cMcdvLZkKXtCYarOu4ZgVE3NeoxMyHS73TzwwAOcf/75LF26FIDVe3twWZIBTVvTPvZu3ch5V34OX1RlaVXmJx5od+7cySuvvMI999yD3W7/xE6OI/M/Rl7OOJGchng8nhy/wkKmTZtGPB5nw4YN1NXVYbOd+kRLSZLOLbLLpTQhhosVCSGoyXXQ4QnhC8dQEMyZPYvigrwxn/fKK6/Q0dHBfffdl1o9MTg4yHSDQjSWIJpQUdp3QsiDJi2f2nwHdqOWx1YdJHP1O0x/8XlMBw/gmzMH5e9Po85fjL6xm4UmI1aTIXUgLsu0YjNo2H2gibDBSYcnRNbk+fSb8tnS4qYs04rdpCMQjmIzGzGZrRhNFnyBIA6H46gH/4GBAbRaLWlpaRQUFFBbW5u675OCjJGXM0bOQBxvwBCNRunr6yM/Px+tVktraytmc3IFh06nY/Hixcf1epIkSaeKnGn4jBqeabAYdKiqSmPDFmyZeWRm56Sm64eXYg4Go9iNWipyHIhYiMHBQXw+H1OmTAGSywA/3N2KL6riT2gZ9Pkx6yDac4gpM2czd6AF5bvfRfP++1BTQ/inP+W/Dhxg1uzZZE2aO6o3BEAwGseg09C0+X0aGnYw94rb6fDF0QiBApSkW1GVGLvXvIw9p5jJMxdg1mvp9UVo6g+Ql2Y6YqYCkgfrX/7yl0yZMoWrr776lI73SE8//TRtbW185zvfQaPRfOIMhyRJ0qclZxqkCTFy5YBWibNvx2bS80uZW5ts/Tw8FW/Wa9m/4W2EVo93zjJmFrtoaPiAzZs3U1JSgs1mIx6Ps/rlp8gtKmPushWQ66C/u4Ota98i+3f/Be++hcjKovMnPyHvJz/BpNdzd28vmZmZrNnXO6o880BPJ2arHW9MT3blNIyZRfjjGswGHSa9jkAgeZZflG4hLTOPyeWF6HQaWt1BOgdDlGXYyLIbU0mRReYYPe0tLFq0CIPBwHXXXTchtQzGW9sC4NChQ7z99tvcdtttqQZWiUQilSciAwZJks4WMmj4jHJaDEzKNNIZUPDFBEuvvInJxTmpA9/IpZhprky0Oh06JUZTX4ALL7yQmTNnYjIlyz4bDAamLzgfk91Fd1szeQ4ntX9+iKUP/Q4hNPCjH7Hp4ot59f33ubm1g6DOgTek4gh5RpVnDoeCrHn1GYqqp1K3cBlerBSVuNjc4sZh0tN3aBdduz4ib9G1VOfYKalbRFWRk6a+AF3eMCa9FrMhmcA5PHNRv3ULh3ZvZcaMGVgsFiZNmnTCY/dJtS1UVaWlpYW0tDScTidGo5FEIoHP58NsNpOfn3/C+yBJknQ6yMsTn1Fer5eHHnqIhQsXsmjRoiPuf/rNteTl5qK1OtnX7aVp40oS0Sih0iVcM7OAXH2Yl5/7OzfddBPFxcV4glH+/rdnKHzuKS5etw69e4COK68n/r9/SPH8uSQSCXbuPcCAxjkqkbBzwIuvp53qSZMx67W0HDqI0ZnF3IocmvoC+AMB2geCqDojIhqkp2k3OVV1lOY46Q9E6PCESCjQ4w2Rl2ZGjYaIHNzIlJnzycgtoHfQz6KKjFTOwEQYeWlnWDAaR68VzCpJJxAI8Ktf/YqFCxdy8cUXT9j7SpIkHS95eUKaEHa7nWnTplFZWXnEfZFIhIPb1tPfWYBaMoeWgSBRUx7CpBCKxtl0aIDydCPZuXmoqkrA70f3+pvc+i8/wXroIJ0z5tP58E+p728msbmer8+bg1arRbFlYxlxsLUYdPiaG2hq2ExFaTHumImCkrLUVH9RWowHn3wIe3YRXWm19PmjqGohqj+BqvXT64tgN+pwWfV4vD5a3UEK04z4/X4i4RChWIJ0h3VCAwY4suMlwJ6NqwiGI8y661asViu33367LOksSdI5R15M/QxJJBK89957BAIBhBBccsklozo/BoNBVFUllBBMv+BKOvwKjfv244/EUF1FCKOdXE8D0XgCX0wweeFy1v761/jnz8f2uRvRaDTs+92faH76JQZrp7PovPO5+uqrU9fuvaEYJp2GrtYmBgf6AJhcN4dJy67BbEtWNlQVhbbWFgAy06zMW7yMeEYF/kgCi1FHutVIXyBCy0CIhAoOs4G2ratRD6wFRWUgGCdn7pW4CspSqzAmmsOsxz04SNOeHaltOpMVh8PB8MxdWVnZmM28JEmSzmZypuEzZGBggA8++AC73c6cOR/PVnmCUXY2dbDm5b9ROnUO9qJJZDrTMUUGiCRUOuNpFGdaSNfHSAT6iAW8GEJuiv7118x56RmiLhdN//zvdF99Le+89gxTmvaQVzmFmC6DgoKP+0Q4zHr8oTD1q98kt7icOeddwmBU4NXYiMYVXBYDu7Z+xN7NH2D+4leoKM4no7iaLN0guUKDaah4UygaY+++fYisQiLxBI7cUqzpYQw5Nhp7AqhCxaDTHLEc8niSF8eiKAqQTCJ9ZWs9jVs+IDOvEK3ZTv6kmcwsdh21CJYkSdK5QAYNnwGhUAiz2UxWVhb33HMPTqcTSB5Et7d52NrixmU1kFdagyeUwNPvJ8OaQdWSKznY1k3CM4gQNqy55STiCnMf+BEL169HI4Af/pAPr7kDV0EeiXAMV0ktvcJJrD+AxahjZrELn8/Hjh07mFw3m62tUeZcfC1ZmZkEo3Ga+gNkigAxP1jSM6mqnY7Z5mBQTSZZekMx4nEVi/njSbHoQAeapg/BuISwvQxTVhFGnRZvKEpRhoXrZxUdEQwcT2OusfT19fHoo49y5ZVXUlNTw/Kl8ymtqCKms2AeI0CRJEk6F8mg4RzX1tbGY489xo033khVVdWogOGjA11s3fA+8ZxaBgJxNJps1F0rSasI82GsGpNeS+jgR1jjUbriVsrffprzn/o9dp+b3Rdcjv1Xv6BHCbH+nVepW34TnX4FV+VMjDoN3lCUwXAcTzDKvt27eeedd6iqqkqVZx4cOtvPsenY+dYbmJw5uKYuw2bUkldYji8cB5KzE1ot9Bzai9FowJlfjiE9H9eU8zBnF1GcbmUgEKHXH0ar0bC8NnfMg/cnNeY6nKqqNDQ0oNPpmDRpEi6Xi7KyMiwWCwA5Lgc5LscRz5MkSTqXyaDhHJeTk8PUqVPJzc0dtb2pL0DQ5yXQdQijJQtXTikBrYuunNmEhBNTKEpZZjq66Usxv/Ak3/rPG8nu7aaxdjarvvu/MS9YgFYrKDRFKSsvp2UggMFgwqjTEI7F8XU2kpfhoqnPxezZs6msrCQ9PR2A6owY27fvYcaCBfjCMayTzyMjIwuzSUckrrC9fZAp+cn8gLJMK60DAVpb9mAwWTBmFuENxyivqmZaoZOBQBSdVlCZYz/m5YaxkhfHajY1PCsjhOCDDz7AZrMxadIktFot119//QT+ZiRJks4+Mmg4B0UiEdatW8eyZcvQ6/VcddVVo+7v6enBG4KowYG+bA7RQ5sx2dOxmh1EDGm4Glejz6nAGUhj8X/+lJxNHzKQncPu3/6Z2JXX0L/2bQx768mZNJfNPSq5U5fQ0+7BIMAbjmHVawi37WIwnIO3oBitVpsKGAB2797NypUrKS8vBwQGRwaaoZLUwWicDk+IUG8rm97YxW133Ml51dlYtFfS7IkRiivU5qcxvdCJ02KgJGN8iY4Os/4Tm029++67bNq0ifvvvx+dTsctt9wi+z9IkiSNIIOGc9ChQ4dYt24dmXmFJKxZoxL/Du3bxUsvvcSSK25iIKinoKCIlv5WoqrA5wvT7lexhezc9vBvmFX/ARFnOo0/+b+8segqlk4pRAiBVqcjrgqa+/3EFJic58CihunZtZNFyy4izWKi5PIbUXRGjHotiqKwefNm0tLSkpcoZs6krKyMjIwM9nh6mFbgpHMwTKfbR38gQkm6nYTPStRgpP5AJ4tqS7h4WskJjcnICpjDNSIG3AOE2/ZQnXEhVquVyspKTCZTagWE3W4/4d+FJEnSuUQuuTyHhEIhAGpqarjj7q/SL9JSqxKicYUtLW7ySyuZN28ewZ4WNEKA3kRe9XRCDe/SvHc/d7/6MP/vl//A9K0bWXPxlax77UNab7qFcNNG+vr7AahbeAGWkulohCDDmmx6laGLEu5uYs/BVlRVRdWbCMUSqSWPGzdupKGhAQCtVptqW+0w69FpNZS5DAxsfBFNzz7a3GH8OgezL76WjPR0mvoCJzw2w82mhBKje8CTXF2RbWXXzu20t7cDUFxczKJFi47aRluSJOmzTs40nIXGWjrY2riX1157jbvvvpvMzEwG4gYshmQhpZ72Fg7u2c7UxZfQ7o1hsVior6/nshtnsq7ZRxw9s+rr+f7Kn2Lz+9h23hWs/+K36cssROOOM9OkQwl66O/vxepwYtZr6fOHiXTsxZLugNw6ysorScvI4aAnijsYRQkM0LV/O/aqG9BoNNx5552pJMJhgUAAxd1O0JiFokA0oxKjIxedVuC0GNjb5aM6x0Y4lpiQcbMZNKx67i9MnTqVmXWXAy6+//3vYzQaJ+T1JUmSznUyaDjLeIJR1u7vxROMEUsoxBSFtft7KbQZySmuQNF9vFRxOPEvHAri8wwQHOgimpbD0iVLyM/P5+DuLdzsC6L74Q8wNe7nUEkJj3/v5wzMuwglMECifQf+rEksqKlk+fT78EUSqbbQTrOB7sEu/EoAqEMIgdliodJgxG7S09Tpp7m5haa2LipLCrBaj8w9WLVqFVu3buXL37yXVfs9aHJqMBh15DstWI06wrEETf0BpuSnferx2rp1K11dXVx66aXodDouvvjiUUmhMmCQJEkaPxk0nGW2t3locwdJMxuIh0O0799DPKMCh8nB5PkX0NAVwGAwYNIk6Ohoo6CgiOLKSezftY0Na94me/5VOMx6Im+/y+Rf/ge2AwdIVFby5P/3a/ZOm4srMwN9XCHk6UIMNDO1dkZqRULE18fute9w3XXXESlyUm+9FLvFnCwlHYmyae27mB0ups6YQ0V5Bbn5RbSGIDMYxWkxEAgEWLVqFQsWLCAjI4OlS5cyf/58Ml0OctPCFLrM7Ov2odUklzyqqsKAP3JcVR1VVaW1tZWioiKEEPT399PR0UEikUCr1TJr1qyT9auRJEk658mchrPM9jYPnlCMpr4g+/fsQtO9B4c2Rqs7lKpD0NQXYP9Hq9n83mt4A0G8oSiawumYi6ZSMXCIwvu+zoJvfI3s7m7euuoqNr/4LpYbbyAe9uHr60GnFSQyqvCXX8iS2sJR79/V1UVfXx9Oi4E55dnotQJ3MIrJoId4GCPJFQoajQa7xYTFoONgrx9IHtB37NhBa2srAA6Hg8zMzOTtodyGmlwHeq0GbziGosKMcRZfSo3P9u38+c9/TuUpXHDBBXzpS19Cq9VOxPBLkiR9pskul2cRTzDKv72+G6sO7FYz+7t8GJQQTpcLjYBrZhSiKAqeUIxJTpXnX3iRjMJyfGllWEIBSv/9+8xZvQqN0ND1xa/RdvfXKC5KZ++gBodRw5t/f5S4yUm4cB5mvcCg05Dpa8SgFVxx6SU4LYbUGTvAvn37ePPNN7n77ruxWCys2tNNutU4qpTy1g/ew+vzcc/dXwAgGo2O2ZNhZMXG4dUNwWj8Eys2BoNBXn75ZaZNm0ZtbS2RSIS9e/cyefJkmdAoSdJnnuxy+Rk0nPi4pWUAQ+9eYu4WotNWYDNp8UcsdA+GmFqQxso3XmUgGMeTMYWaXDtCbyUajlL21mMs/OtvMQ300TBjBjvv+BKTb/wCwUCEgYF+7JYcogrMvuga3HEdvf4YXb4wWQ4DGk+UUCTB5uYBZpWkk2bWE4vF0Ov1OJ1OnE4nkUgEi8VC2lB55kTQi92ZrMugN1tJ02pRVRUhxFGbOA2vbhjOmXCY9UctzezxePB6vRQXF2M2m/H5fITDYSCZozB9+vST98uQJEn6DJMzDWe4kWfguzu8BNzdtB86gLF4Oooq6PFFAKjItjGwrx41MICubD4xjYHyD1Zy3eO/IKu3l666eXx0z4+IleWQl5dHUJg51NRIW/1KpixeTtxRgDsYwxT10bp1Nb682RhtaeQ7zWTbTbgsBpwWHVvfeYG8vDwuv/zyMfd15Qeb2bXuTZZefiPWjNxxzRaMx3DQAfDII4/g9/u55557EEKMuk+SJEn6mJxp+Ixp6guQCHjo7RzAZi/EmJ2PyZmNJxgjw2YgQ3XjjmnxhoxEHcXY3U2U7PuQxU8/SdXOjfRn5/LULbey78ovEzFn4IxqifV56YpGmFJaTpHrahw5RWxs6sOk16HojCgqmDQJhBAc6gvQ0+9BYzAzKc9BRUXFqOqOAM3NzQghKC4u5vy501AjfhSTY8xOk5/Gzp07WbVqFV/72tfQ6/VceumlmEymVKAgAwZJkqRTQwYNZzhvKEbzri30d3ew8MpbONAXxqzXorFCVaaZ1WvX43Bk4Jp2IV5PLxe+8z5T3n+bgNXBM3f+LzZfcgPxzga0GjOJWAL3oY8IBHuZfsnN5KSZIa2c7etXE+zuI2/exUzKy8IdXYE3HMcbjqH1tCF6tqFUX8TWlgSXTqvFrcKWFjdlmVYcJh0vvvgimZmZ3HrrrWSlWfncFRcf8zN9UovqeDzOrl27KC0txeFwYLfbycrKIhQKodfrj+ijIUmSJJ0aMmg4Q6mqSiyWPKhOmrcMvVAxWyzU6PQc6HKTUDVYzEbmzV/AR2+9QeXKVcx79e8IVeWDpct474IVdJRfiNsfJyd3CqVOO8G4IJhTTTRSyM4OL4rQku80Y7LasNqi9AeSlzrMWoW2wUHiWjMmZy56TZiQ1kAgmqClP0i+LsDGD7fhnncBs0ozuPnmm3G5XOP6XMdqUW03atFqtfh8Pp5//nkuueQSFi5cSElJCSUlJ1ZGWpIkSTpxMmg4A7kDEZ555llCoRB151+BN6KQbU/2RIiFAnSsf5lFixYxM78E33NbWfTb32Lxevlg3iU8cfVXwQGOuBt/OIpOSeBqfp9goJRwdi0Jo4NoLIGh4Q0G9efhC2dTUzUdZ0mCpn4/gXCUwS1vYNdaGcyfi9FswZJRRywYJc+sIa6oDPr89Pd0Em/potcfY8XU3HGvVBirRbWqqjz+179SmJPBNddcg8vl4qtf/aqcUZAkSTrDyKDhDOMJRtna6iE9vxiNEseo1yEiCSLxBOFYArvDTla6i+BTT6B+5W7su3bRWlnDE7fcRueCK4iQxUAwhsZVTLZBhy8cwx8rxeUqxKxVsRsNDCgOhMWFRqfHqNPQ2OPFEh1g+bTJDASiFE9bQOMgTMpxkOswEwwG8WxaialkEiJ9Mm59JqVLr8eo19EXiKZmCsaTuzBcqdLT10NvZytV02ZjMeiwZeZRUJCVelxeXt7JHGZJkiTpU5BBwxlkW8MeNrV4iFkyyXCVkOM0YzXqURIJmnZu5PrLLsK8dy/VDz2Ibf164mVlrPr572mcv5SeLe9AJEBtWRXKYAe+vWsoWXgFit5Bi9tCtG0rqr8PT+FSwnGVmTMuQGvQEo2reDv2c3D3euaWZzOzuJiZxYs52OPlzfp99Go0uMxGLK4shCHZO8Js0GHSJ8s8Z1gNqYJSM4uPHTSEw2HsJh2hWILO1ib2ba+npHoKcaFj+pwFzCwe3yUOSZIk6fQ4o4IGIYQWqAfaVVW9UgiRDvwNKAUOAZ9TVdU99NgfAXcDCeDbqqq+eVp2eoIM+MOsXPk2MaGjatHlxBIKW1vc2Ew6Qp4+AutW0fv7/6b4nbexpqfz9jXXsG3xUjqLZhPsDJFXdQF2s4G4onLIr8NlzSTfYaA9DFk2Awe1abgTCYKDIRZWZWGMegkG4lSVlZCWPwvL1CKKiopS+7Pjw/fw7t3LhTfcRTAOuReswBuK0e4JYTMkA4ZwLEFJhp14QqGhw3PUxEaAlpYWHnvsMa654XMM4iC/aioVtXXEhY5gNE5NrgwYJEmSznRnVNAA3AfsBhxDf/8h8I6qqv8qhPjh0N9/IISoBW4GpgD5wNtCiGpVVSemHeIpFI/H0Wg0NA+EmHPRlXQHFGIKJBTo7h8gqtFy8St/oebxPyAUhdC3v0P0H35IV/12/Fs+QPH20BFJQ9e9h4Q+iq16MX5FR27RVDa9/QLF0xbQrmYSseWhM+VSZjPgCUQI7l+FxmihyZHBjbOLsOjSWL9+PXV1dUTRkVY8maq0ArQ6HXV5NpwWA55glDd3dtEXiJJhNVCSYQdge/sgduPoxMbpBQ727thCRkYGNTU15OXlMXv2bPKy0ik020esnpiYZZmSJEnSyXfGBA1CiELgCuDnwHeHNl8DnD90+1FgFfCDoe1PqaoaAZqEEAeAecCHp3CXT1gsFuORRx6hqKgIc9ks0p1ODOY4e7t8dDXuYc6zv+f81Wuxe91snXc+qxbNwjRnEfPjevIqpxGy5BAeVMgNRVF7BZ5QAuF3U+CyYLUZyK6egmpNp9JiJxGLYvI0UZA/iw5vmGjJfMoLc7DbzDgtBnp7e3nrrbdICC0xZwmWtAwqM7NHrW5wWgysmJo7qtzz9nYPApXyLBsAaiSAxWhlZ4eX+o31OLILCJqzKcu0cumll6Y++yddypAkSZLOPGdM0AD8F/APgH3EthxVVTsBVFXtFEJkD20vANaPeFzb0LYjCCG+CnwVoLi4eIJ3+fiMVZ+gvLycgoICQmY9oVgCu1HH/D3ryfyXH5Pd2kRjaSVP/vg3BGbMwrvldTyNu9lbXgeqir9pGxnppVidLvzGWuKt2xD7VlO77Ab294ewZNbS4w2Rp42jCfQRaW1AFJVSlZWD125C6d3HYHccT2UmbSEd8y6/hXbVRKaSXNXgC8fo8IToD0Tp8UZYMTX3iHLPkbjCtAIndpOej1a9QV9XO4uuuo1trYMsuPQm7FbzEYGHJEmSdHY6I4IGIcSVQI+qqpuEEOeP5yljbBuzHraqqg8CD0KyjPSn3ccTNbI+gbf9AEpGLluCUWYvXJqa+t/69IsU/uKnFDTswFtYyl/uvIeDNWWkTZ6MVqPDPPlCvIEAG1t96NUEtoEeLAYb6Ow4zCaUggqCXif1zR5KsmxEuw8QD8RpVoqZOXkyfTk5CIuNcCyOTiPw+7yYNAqbmwewGvUU5GbTcrCPQDROQlFp94Qw6bVkWg30BSKjDvwziw10dnay98MPIPMiwEBpzVTyisto6g+QbjXgsCUTJ4eXV44nWVKSJEk6c50prbEXA1cLIQ4BTwEXCiH+CnQLIfIAhn72DD2+DSga8fxCoOPU7e7xG65PoFVi7Nz4PgcbttDuCfHs5jZ2bmzA/LWvsOxLn8d18ADbvvU9tr3+PpsXXoGIBgg2bcIbitHS5yXYuZ8+bwSdTk+idCH+5p0Y+vcTjMXoVawE7cVMKXSRbTcR6DxIRryPgjQTwXiCbH2Uxveeoru3l+IMCzdddzXTllyC1ajHYtAhhCDDakQD7Gj3YNJrMem1RBMKGVYjFoOOnQfb8fuTra4TiQTevm76+/sIRuNk5haQXliBOxijLNM66vOb9Vq8odhpGHlJkiRpopwRQYOqqj9SVbVQVdVSkgmO76qqejvwEnDn0MPuBF4cuv0ScLMQwiiEKAOqgI2neLePi9sXxKzXYjSZmbP8ekThDAyBALMe+iWTz5uD/m9PEfjGPfzxRz/i4IWLWTq1kOlTqqFsHpHc6fT6w5iibuz+dvKUXtJtJuJ6C4m8KZBZRnG6hUp7gpy+LaQZBGaDnsJZF5FRPYcKhyASV7CmZ1FUXs0Nc0s5rzobl9WINxTDrNem9jPfaUZRVXp8EQxaQTgWJxxLkO80o0lEefe5v7JhwwYACgoK+O537+e8mTUYdBrcwSgGnYYZxS502tFfrVAsgcMsW1VLkiSdzc6IyxPH8K/A00KIu4EW4CYAVVUbhBBPA7uAOHDPmbxyYnBwkE1vPE35tDlU107HG9Mx9fWnmfbgLzAP9NEwfTrBX/4BXXUNxjefZfv27Yj0EnLTc+ky2dBEvWQ48tg1mEWmIZfMrq3Yy8vIynVgLprNof4AXd4QaapCzNtHX38fuXkFmExGdr/9PL7cAuZfdEWyDkJd6ah9cwzlUgxfQrCb9JRk2OgLxOgLREi078Ik4thLLyIYFcw8bzlzZ9UCyUZRQojU5Yphw5diIDnDEIol5LJKSZKkc8AZFzSoqrqK5CoJVFXtBy46yuN+TnKlxRnPbrdTUlKMzuJA/9YbXPizf8TVtI/uabNZ86OfsD7gZo4O8IQomnU+WstW8vNyULQGdJ3bCQdDtKfrMBosOEunYFJK6Q5ChjZOuGkzmhiU18xGI+wYZlxER/NBDI5MzHoNOVOXUFyQe8TlgmFlmVa2tLjxh+MMBCL0+ULEB7u4bG4dff4Izd0KSjRGIBIjFEuwdN4sHJ+QzHh4sqTDrJfLKiVJks4BZ1zQcK5QVZUNGzYwc+ZMjEYjn6uqJHb/d9G/9y7u7Fz+/pX76LvlHlxGgXjnSbatX03O4usx6vREbbkcGohQmGlk5pKL+ODVv1Or6SCndgnNfX60WgfBcIJ9XT7sfV7S7FayHSba3UFUXy/6/v1095Vjs9uZUVPF9ELnUQ/YTouB8iwbbzV0oagqoreRgT0f0VKQw9SKItLmn4cvHMeo1zIpzzHuA//hsw+SJEnS2U8GDSdJd3c3b731Fqb+fmY8+yw88gh6l4vgv/+CP+uM+PweyjQJFI0Jc3412kSU3sEQuaYAPVvfIZRfTmDyYqpz0jFWLcSRm49WCBwxN73b1tFgnoEr3UV++QzUlk3s37eXquoaPPpJGLJLEXojN8wq/MSDvNvt5vknn6SybgEl5RVECmz4KkoxuzIZCESZVZJ+ikZMkiRJOtPJoGGCxWIx9Ho9uTYb3/V4sN50EyQS+L7yFeI/+AGHdC6KGraxa+MavC27sJXPIrd2HkFPP9kuB1qhwVVYibvtABkVdTT1aSgtryTdrKXLH6MrqkcY7NRm6bFn2gnH4uijEXRqAm8oxuSCdILROAadZsyAQVVV2traiMfjlJWV4XA4EFoDhqHERaPJjDG3AFVVcQejp3r4JEmSpDOYDBomUFtbG397/HG+CDh/9Z/YerrpWHE19V++n+37PsT88qtMuuAGyqsmc2D7RpxmHXUlLrZsWEtnwyZM1UtoV5zYHZNw1RYR11nx+COYWz5gQOhx1C5hSkku+3ptiPYt5FWWEY2rtFcsw55txxeOEYzGx0w6TCQSaLXJVRKvvvoqJpOJsrIytFot511xA9G4MurxcrWDJEmSdDgZNEwUVSWrvp4vP/AAaW1tDM6cy95fPcTO4lo0QiCat+Mf9NDa68aUl8mKm+5CVVV84RiD1gIQWwl3NuIqnY8nFEcVerz9ARZWZpJun0xXbz99kRharRZzVjGmjCyseh1WgyCaUFBQUQCD7sheDu+uXkt9/UbmXn4LTquJS664msKczNT9w8mQIFc7SJIkSUd3RtRpOJvFYjG2P/YY6iWXYLzuOtKMRg7+/hG2/eUZ3uk4QKh9L2kWI/asIlAV0qIDHOzz8t7LT7Pm1Wdo7PWhN1mxTrmQnozpuINxzKFuTPtWkqUJYDPqyM/PZ9vmerLiPdTmp7F09lQcRTVEEgrhWAK7SUeB08wNswqZWexCr8Z4//33CQaDeIJR3KqJ7MIyHAYN0bhCc0BLMP7xZxhe7TCy1oIs+SxJkiQdTs40nIhwGN8ttzDthRdQ0tLQ/ud/wje/SWuTBzUeIxry0XdwB9H0SjKrZmLOrWDK5GJa3UG0GVm0Nu7B5O6jvLiQNb1ecswxPHFBR8xGlj4Dm68PX7iEoqoibrnlFjLzi9nWNojFoKM6J9kpciAQZUaxk6n5DszaZJVsv9/Pu+++i8vlIuYooLC4DEtlFQDDYcDhJZ3lagdJkiTpk8ig4UQYjbgiEQJf+xq2//f/UNLSWLduHYn0Mvb0hEDoIBYmFo1woKkLXdM6GiJzmFQ3h8tuvYn+/n7aQjp2tnswHlqLKjSoBYvJdNqx+LX4e1rpHJzCYChGdXU1ADOLNTT1BQjHEkwpSKMs04rdqOW3v/0tNTU1rFixgpycHO677z6cTier9/bgOmzGwKzXyiRHSZIk6bjJoOFECIF45RVsmuRVnv179/Luu++SU1KFpnQu2bOW0+MP449DX1RHtqJwqPEAixYtQgjBwMAApYWlvL+vB1tOCe7WfSSiEbRGI4aKeUQUDWUZVra3ebCb9KO6Y/a2N9PV3IWzeCkAs2bNIicnJ7VrTqcTOLLiI8gkR0mSJOnTkTkNJ0qjIRgMApCenqxp4O7pxKTX0tvZinLgA3rcfhw2K9raS5h78bUc7PXzfv02nnrqKd5a+xE2kw5jVhHCYMGiTZBmNmAymanJS8Ok17C1xU00rmBIhIjGFba0uNm7v5EtW7YQjyeTE5YsWUJVVdURu1eWaU2tqFBVNXX7aBUiJUmSJOloZNBwgnbs2MEvf/lLmpubycrKom7WHNKmngcqZJoEmniYXK2fqhw7pU49BHpRFNjjN6EzGPD1dRFPwK5+lb68BWhMNqwGHTajnsrsZN6CSa9jZ0MDb/39EfY1taAokFMzk29961vodMeeLJJJjpIkSdJEkZcnTtC+fftQFIVdu3aRn59Pe1cPGoMf1ZGJs3IW/ZZiNIZkiWfboQ/oikUoWXo9qkZPZd0C3KoVvUZgM+nwBGJ0DIbRajWYtQo7N6ymT+MiLbsQiyuXnElzEAYLzf1+ctLMaDTji/lkkqMkSZI0EeRMwwm68MILSUtLo66uDq1Wi7u3C3d3O8FonI5+D/GeA2hVhUy7iYzsHIJ+H30eL+kWPdrsStIyc/GFY2TaTBS7DCzM1+OyGNDrdfS1N2NVAliNOqwWKzlVM7BabWiEwB+Of/LOSZIkSdIEkjMNJygQCKDRaDCbzXjDcbLmX4PBYCTNYqQ/0EOgew+YzDgyp1MzayGF1dNpCmhJtxppdYdwmHQEowp6LaiNH+BRouTMv5rZJS76c28hGFPp9oYJxxIYdRoicQUFsJnkr06SJEk6teSR5wR4glE272vF7Xazcl09udV12CN99Pb4MJVPxZmVR6fOiFanpTjDQlCF9MxMKksMHOz1E3W3c+DgDjSVSwhEVApqZqHVaLEZk1UZnVYTTsCkSy6R9Ibj2Ixasu1W0m3ycoMkSZJ0asmg4VPyBKNsaXGTU1rNJbkFaExWNhzsJ7JnC9FIiPzKaQSigpoLb8JmNXNedTaqqtLc3EymKYu0YheD3SZ6ojHStTHsJit6gxUFSLcaR5Vx9gSjFKVbRpV4lqsfJEmSpFNNBg2fUlNfAItBRyLoZfPat5l7wWWkWw30ZldgSoTwh2PYzQZcFgMuqx5PMMqOg+28++xfmDxnMZdccB7XnDeL8+dOo6kvQIcnhD8cx2bSkW4zUJZpTa1wmFnsoqkvgDsYxWHWH9FbQpIkSZJOBRk0fEreUAyXxUBrXzf93R0079tFVtk06nX5zCh1DhVjirJv47sUZzkZnLYAi8XBwuVXY8vMY0uLO7X0cWZxclnk0cjVD5IkSdKZQAYNn9JwpcXC8hrCwQClNVPZ3ROixqUj3tdMj7OIYCSO0BloHoyRp4DFoMNSXA6ANho/ov+DJEmSJJ3J5JLLT2m40mI4rlAxZSYxtAwEolj9rXRsfx+9EiHfaaZ61hK8ziqa+/34wjF84Rh7u7zs7vCypWUAj+wBIUmSJJ0l5EzDpzRcaXHLnibefutFNBWL6Fes+I35pM/Nx2q1YdLrCMcSZNuNaITgQI+PhAImvRaDTqCo2lGXKSRJkiTpTCZnGk6A02KgKC8bYc0g3WqkrshJIKFhfVsYbyhGOJYgHEswrcCJAhzo8WPUaQCVSFyhPMuGxaCjqS9wuj+KJEmSJH0iOdNwgja1+sifeQFpFiMAk/OdeMMJtrZ5uGhSDiUZduwmPVqNoG0gRCSewG7SU5JhxW7So6qqbFMtSZIknRVk0HCCen1h8tLMqb9bjTrmlbnY3OJO1VYIRuNoNHD+pCyMOq1sUy1JkiSdlYSqqqd7H04ZIUQv0DyRr6mxpGUgNBqUROLjjVotgBoLB4TQ6FRViavxaARAozdbVVVRUBUFodEIodEosVBg1PMhE+ibyP38DJJjeGLk+J04OYYnTo7hiatRVdU+US/2mZppUFU163Tvw3gIIepVVZ1zuvfjbCbH8MTI8TtxcgxPnBzDEyeEqJ/I15OJkJIkSZIkjYsMGiRJkiRJGhcZNJyZHjzdO3AOkGN4YuT4nTg5hidOjuGJm9Ax/EwlQkqSJEmS9OnJmQZJkiRJksZFBg2ngRDikBBihxBi63BmqxAiXQixUgixf+ina8TjfySEOCCE2CuEWHH69vz0EUL8SQjRI4TYOWLbcY+ZEGL20NgfEEL8txBCnOrPcrocZQz/SQjRPvRd3CqEuHzEfXIMRxBCFAkh3hNC7BZCNAgh7hvaLr+H43SMMZTfw3ESQpiEEBuFENuGxvCfh7afmu+hqqryzyn+AxwCMg/b9u/AD4du/xD4t6HbtcA2wAiUAY2A9nR/htMwZucBs4CdJzJmwEZgISCA14HLTvdnO81j+E/A98d4rBzDI8ckD5g1dNsO7BsaJ/k9PPExlN/D8Y+hAGxDt/XABmDBqfoeypmGM8c1wKNDtx8Frh2x/SlVVSOqqjYBB4B5p373Ti9VVdcAA4dtPq4xE0LkAQ5VVT9Uk/9i/jLiOee8o4zh0cgxPIyqqp2qqm4euu0DdgMFyO/huB1jDI9GjuFh1CT/0F/1Q39UTtH3UAYNp4cKvCWE2CSE+OrQthxVVTsh+Q8LyB7aXgC0jnhuG8f+R/ZZcrxjVjB0+/Dtn3XfEkJsH7p8MTylKcfwGIQQpcBMkmd58nv4KRw2hiC/h+MmhNAKIbYCPcBKVVVP2fdQBg2nx2JVVWcBlwH3CCHOO8Zjx7rGJJe8HNvRxkyO5ZF+D1QAM4BO4JdD2+UYHoUQwgY8C3xHVVXvsR46xjY5how5hvJ7eBxUVU2oqjoDKCQ5azD1GA+f0DGUQcNpoKpqx9DPHuB5kpcbuoemixj62TP08DagaMTTC4GOU7e3Z7TjHbO2oduHb//MUlW1e+g/IAV4iI8vfckxHIMQQk/yYPe4qqrPDW2W38PjMNYYyu/hp6OqqgdYBVzKKfoeyqDhFBNCWIUQ9uHbwCXATuAl4M6hh90JvDh0+yXgZiGEUQhRBlSRTF6RjnPMhqbsfEKIBUNZwneMeM5n0vB/MkOuI/ldBDmGRxj6vH8Edquq+qsRd8nv4TgdbQzl93D8hBBZQgjn0G0zcDGwh1P1PTzdmaCftT9AOclM1m1AA/Djoe0ZwDvA/qGf6SOe82OSGa97+YxkCI8xbk+SnLaMkYyQ7/40YwbMIfkfUiPwAEMFzj4Lf44yho8BO4DtQ/+55MkxPOr4LSE5fbsd2Dr053L5PZyQMZTfw/GP4XRgy9BY7QT+cWj7KfkeyoqQkiRJkiSNi7w8IUmSJEnSuMigQZIkSZKkcZFBgyRJkiRJ4yKDBkmSJEmSxkUGDZIkSZIkjYsMGiTpM0gIcZcQQhVCVJ7ufZEk6ewhgwZJkiRJksZFBg2SJEmSJI2LDBokSUIIsUoIsVYIcbEQYrMQIiiE2CmEuHaMx9YJIZ4XQvQLIUJCiL1CiB+NuF8IIe4f2h4VQnQKIR4QQjgOex1VCPEzIcT3hBDNQoiAEOJVIUT20J+nhRCDQohWIcQPxtiPMiHE40KIXiFERAixVQhx3UkZIEmSABk0SJL0sQrg18CvgOtJlpx+ZmTegxBiHvDh0GPvB64YevzIxjc/H9q2ErgK+HfgLuBVIcTh/+d8AbgQ+CZwL7AU+AvJRm7bgRuA14B/FUJcPmI/iki2VK4b2o+rgc3As0KIq09sGCRJOhpZRlqSPoOEEHcBfwaqVFU9IIRYBSwGalVV3T/0mGySgcNPVFX9v0Pb1gBlQI2qqsExXjedZKe8p1RVvWvE9ttJ9he4RlXVl4a2qSTr5Neqqhof2vYrkkHAT1RV/dnQNt3Qa76qquoXh7b9kWSgMElV1f4R77MSyFKTbYMlSZpgcqZBkqRh+4cDBki1bu8BigGEEBaSgcXjYwUMQxYARuCvh21/CogDyw7bvnI4YBiyZ+jnmyP2Iw4cYHR730tJzkAMCiF0w3+Gnld3+KUQSZImhu5074AkSWeMgTG2RQDT0G0XyRONtmO8RvrQz86RG1VVjQsh+kfcP8x92N+jx9huGvH3bJKtfO84yn5kAN5j7KckSZ+CDBokSRovN6AABcd4zHDgkUuy9TuQusSQAfSP9aRPoR94H/i3o9zfMUHvI0nSCDJokCRpXFRVDQoh1gK3CyH+RVXV0BgPW09yduJm4J0R2z9P8v+b1RO0O28AC4GGo+yHJEkngQwaJEk6Ht8neeD/UAjxS5KXKsqBGaqq3quq6sBQMuOPhBABknkHk4GfAWuBVydoP/4R2AisEUI8ABwieflkKlCuquqXJuh9JEkaQQYNkiSNm6qqHwkhFgP/AvyGZNJjM8mVGMN+DPQCXye5lLKf5DLKH6mqqkzQfrQIIeYA/wT8XyBr6H12Ao9OxHtIknQkueRSkiRJkqRxkUsuJUmSJEkaFxk0SJIkSZI0LjJokCRJkiRpXGTQIEmSJEnSuMigQZIkSZKkcZFBgyRJkiRJ4yKDBkmSJEmSxkUGDZIkSZIkjYsMGiRJkiRJGpf/H2rJ0u1Q8pQRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# code taken from statsmodel documentation: \n",
    "# https://www.statsmodels.org/dev/examples/notebooks/generated/quantile_regression.html\n",
    "\n",
    "x = np.arange(engle_data.income.min(), engle_data.income.max(), 50)\n",
    "get_y = lambda a, b: a + b * x\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "for i in range(models.shape[0]):\n",
    "    y = get_y(models.a[i], models.b[i])\n",
    "    ax.plot(x, y, linestyle=\"dotted\", color=\"grey\")\n",
    "\n",
    "y = get_y(ols[\"a\"], ols[\"b\"])\n",
    "\n",
    "ax.plot(x, y, color=\"red\", label=\"OLS\")\n",
    "ax.scatter(engle_data.income, engle_data.food, alpha=0.2)\n",
    "ax.set_xlim((240, 3000))\n",
    "ax.set_ylim((240, 2000))\n",
    "legend = ax.legend()\n",
    "ax.set_xlabel(\"Income\", fontsize=16)\n",
    "ax.set_ylabel(\"Food expenditure\", fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 3: vector quantile regression\n",
    "\n",
    "## References\n",
    "* Ekeland, Galichon and Henry (2012). Comonotonic measures of multivariate risks. *Mathematical Finance*.\n",
    "* Carlier, Galichon and Chernozhukov (2016). Vector quantile regression: an optimal transport approach. *Annals of Statistics*.\n",
    "* Carlier, Galichon and Chernozhukov (2017). Vector quantile regression beyond correct specification. *Journal of Multivariate Analysis*.\n",
    "* Chernozhukov, Galichon, Hallin and Henry (2017). Monge-Kantorovich Depth, Quantiles, Ranks and Signs. *Annals of Statistics*.\n",
    "* Carlier, Chernozhukov, De Bie, and G (2021). Vector quantile regression and optimal transport, from theory to numerics. Forthcoming, *Empirical Economics*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classical quantile regression and duality\n",
    "\n",
    "\n",
    "* Recall<br>\n",
    "$\\begin{array}\n",
    "\\min_{P\\geq0,N\\geq0,\\beta} &  \\mathbb{E}\\left[  \\tau P+\\left(  1-\\tau\\right)\n",
    "N\\right]  \\\\\n",
    "s.t.~ &  P-N=Y-X^{\\top}\\beta~\\left[  V\\right]\n",
    "\\end{array}$<br>\n",
    "where<br>\n",
    "$P=\\left(  Y-X^{\\top}\\beta\\right)  ^{+}$ and $N=\\left(  Y-X^{\\top}\n",
    "\\beta\\right)  ^{-}$,<br>\n",
    "\n",
    "\n",
    "* Eliminate $N$ and rewrite<br>\n",
    "$\\begin{array}\n",
    "~\\min_{P\\geq0,\\beta} &  \\mathbb{E}\\left[  P+\\left(  1-\\tau\\right)\n",
    "X^{\\top}\n",
    "\\beta \\right]  \\\\\n",
    "s.t.~ &  P + X^{\\top}\\beta\\geq Y ~\\left[  V\\right]\n",
    "\\end{array}$<br>\n",
    "which we call the *dual* problem.\n",
    "\n",
    "* The corresponding primal problem is<br>\n",
    "$\\begin{array}\n",
    "&  \\max_{V\\geq 0} & \\mathbb{E}\\left[  YV\\right]  \\\\\n",
    "s.t.~ &   V\\leq1~\\left[  P\\geq0\\right]  \\\\\n",
    "&  \\mathbb{E}\\left[  VX\\right]  =\\left(  1-\\tau\\right)  \\mathbb{E}\\left[\n",
    "X\\right]  ~\\left[  \\beta\\right]\n",
    "\\end{array}$<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Complementary slackness\n",
    "\n",
    "* Let $V\\left(  \\tau\\right)  $ and $\\beta\\left(  \\tau\\right)  $ be\n",
    "solutions to the above program. Complementary slackness yields<br>\n",
    "$\\left\\{\\begin{array}\n",
    "~Y-X^{\\top}\\beta\\left(  \\tau\\right)   &  <0\\implies V\\left(  \\tau\\right)  =0\\\\\n",
    "Y-X^{\\top}\\beta\\left(  \\tau\\right)   &  >0\\implies V\\left(  \\tau\\right)  =1\n",
    "\\end{array}\\right.$<br>\n",
    "therefore<br>\n",
    "$1\\left\\{  Y>X^{\\top}\\beta\\left(  \\tau\\right)  \\right\\}  \\leq V\\left(\n",
    "\\tau\\right)  \\leq1\\left\\{  Y\\geq X^{\\top}\\beta\\left(  \\tau\\right)  \\right\\}.$\n",
    "\n",
    "* Assume $\\left(  X,Y\\right)  $ has a continuous distribution,. Then for\n",
    "any $\\beta$, $\\Pr\\left(  Y-X^{\\top}\\beta=0\\right)  =0$, and therefore one has\n",
    "almost surely<br>\n",
    "$V\\left(  \\tau\\right)  =1\\left\\{  Y\\geq X^{\\top}\\beta\\left(  \\tau\\right)\n",
    "\\right\\}.$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile curve regression\n",
    "\n",
    "* Consider now solving the problems above for all values of $\\tau$ *all at once*. We can write:<br>\n",
    "$\\max_{V\\left(  .\\right) \\geq 0 }\\int_{0}^{1}\\mathbb{E}\\left[  YV\\left(\n",
    "\\tau\\right)  \\right]  d\\tau$<br>\n",
    "s.t.<br>\n",
    "$V\\left(  \\tau\\right)  \\leq1~\\left[  P\\left(  \\tau\\right)  \\geq0\\right] $<br>\n",
    "$ \\mathbb{E}\\left[  V\\left(  \\tau\\right)  X\\right]  =\\left(  1-\\tau\\right)\n",
    "\\mathbb{E}\\left[  X\\right]  ~\\left[  \\beta\\left(  \\tau\\right)  \\right]$<br>\n",
    "\n",
    "\n",
    "* The problem has dual<br>\n",
    "$\\begin{array}\n",
    "~\\min_{P\\geq0,\\beta}  &  \\int_{0}^{1}\\mathbb{E}\\left[  P\\left(\n",
    "\\tau\\right)  +\\left(  1-\\tau\\right)  X^{\\top}\\beta\\left(  \\tau\\right)\n",
    "\\right]  d\\tau\\\\\n",
    "s.t.~  &  P\\left(  \\tau\\right)  \\geq Y-X^{\\top}\\beta\\left(\n",
    "\\tau\\right)  ~\\left[  V\\left(  \\tau\\right)  \\right]\n",
    "\\end{array}$\n",
    "\n",
    "\n",
    "* The solution to these problems are the same as the solutions to each of the previous problem -- the contraints don't interfere."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Sample version:<br>\n",
    "$\\begin{array}\n",
    "~\\max_{V_{ti}\\geq 0}  &  \\frac{1}{I}\\sum_{t,i} V_{ti}Y_{i}\\\\\n",
    "s.t.~  &  V_{ti}\\leq 1\\\\\n",
    "& \\frac{1}{I}\\left( VX\\right) _{tk}=\\left( 1-\\tau _{t}\\right) \\bar{x}_{k}%\n",
    "\\left[ \\beta \\right] \n",
    "\\end{array}$\n",
    "\n",
    "* In matrix terms, this is<br>\n",
    "$\\begin{array}\n",
    "~\\max_{V \\geq 0}  &  \\frac{1}{I}1^\\top_T V Y\\\\\n",
    "s.t.~  &  V\\leq 1\\\\\n",
    "& \\frac{1}{I}\\left( VX\\right) =\\left( 1-\\tau \\right) \\bar{x}^\\top\n",
    "\\left[ \\beta \\right] \n",
    "\\end{array}$\n",
    "\n",
    "* After vectorization $v=vec(V)$<br>\n",
    "$\\begin{array}\n",
    "~\\max_{v \\geq 0}  &   \\frac{1}{I}\\left( 1_{T}\\otimes Y\\right) ^{\\top }v\\\\\n",
    "s.t.~  &  V\\leq 1\\\\\n",
    "& \\frac{1}{I}\\left( I_{T}\\otimes X^{\\top }\\right) v=vec\\left( \\left( 1-\\tau \\right) \\bar{%\n",
    "x}^{\\top }\\right) \n",
    "\\end{array}$\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code this as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([81.48614818,  0.56017469])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_i_1 = food.reshape((-1,1))\n",
    "nbt=21\n",
    "τ_t_1 = np.linspace(0,1,nbt).reshape((-1,1))\n",
    "A = spr.kron(spr.identity(nbt),X_i_k.T) / nbi\n",
    "obj = np.kron(np.ones((nbt,1)),Y_i_1).T / nbi\n",
    "xbar_1_k = X_i_k.mean(axis = 0).reshape((1,-1))\n",
    "rhs = ((1-τ_t_1) * xbar_1_k).flatten()\n",
    "qrs_lp=grb.Model()\n",
    "qrs_lp.setParam( 'OutputFlag', False )\n",
    "v = qrs_lp.addMVar(shape=nbi*nbt, name=\"v\",lb=0,ub=1)\n",
    "qrs_lp.setObjective(obj @ v , grb.GRB.MAXIMIZE)\n",
    "qrs_lp.addConstr(A @ v == rhs)\n",
    "qrs_lp.optimize()\n",
    "\n",
    "βqrs_t_k = np.array(qrs_lp.getAttr('pi')).reshape((nbt,nbk))\n",
    "βqrs_t_k[10,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile curve regression under dual monotonicity constraint\n",
    "\n",
    "* Koenker and Ng (2005) consider imposing the monotonicity constraint of\n",
    "the estimated quantile curves. Thus, they impose a constraint on the dual,\n",
    "namely:<br> $X^{\\top}\\beta\\left(  \\tau\\right)  \\geq X^{\\top}\\beta\\left(\n",
    "\\tau^{\\prime}\\right)  $ for $\\tau\\geq\\tau^{\\prime}$,<br>\n",
    "that is<br>\n",
    "$\\begin{array}\n",
    "~\\min_{P\\geq0,N\\geq0,\\beta}  &  \\int_{0}^{1}\\mathbb{E}\\left[  P\\left(\n",
    "\\tau\\right)  +\\left(  1-\\tau\\right)  X^{\\top}\\beta\\left(  \\tau\\right)\n",
    "\\right]  d\\tau\\\\\n",
    "s.t.~  &  P\\left(  \\tau\\right)  -N\\left(  \\tau\\right)  =Y-X^{\\top}\\beta\\left(\n",
    "\\tau\\right)  ~\\left[  V\\left(  \\tau\\right)  \\right] \\\\\n",
    "&  X^{\\top}\\beta\\left(  \\tau\\right)  \\geq X^{\\top}\\beta\\left(  \\tau^{\\prime\n",
    "}\\right)  ,~\\tau\\geq\\tau^{\\prime}%\n",
    "\\end{array}$\n",
    "\n",
    "* This is the most natural approach to solve the non-monotonicity problem. However, it does not leads to a simple duality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile curve regression under primal monotonicity constraint\n",
    "\n",
    "* By contrast, [CCG]'s vector quantile regression approach imposes the constraint that the primal variable<br>\n",
    "$\\tau\\rightarrow V\\left(  \\tau\\right)  $<br> \n",
    "should be nonincreasing. This is justified by the fact that<br> \n",
    "$V\\left(  \\tau\\right)  =1\\left\\{  Y\\geq X^{\\top}\\beta\\left(  \\tau\\right)  \\right\\}  $,<br>\n",
    "so<br> \n",
    "$ X^{\\top} \\beta\\left(  \\tau\\right) \\text{ nondecreasing in } \\tau \\implies V\\left(  \\tau\\right)  $ nonincreasing.\n",
    "\n",
    "* Therefore, we let consider the program\n",
    "\\begin{align*}\n",
    "&  \\max_{V\\left(  \\tau\\right)  }\\int_{0}^{1}\\mathbb{E}\\left[  YV\\left(\n",
    "\\tau\\right)  \\right]  d\\tau\\\\\n",
    "s.t.~  &  V\\left(  \\tau\\right)  \\geq0~\\left[  N\\left(  \\tau\\right)\n",
    "\\geq0\\right] \\\\\n",
    "&  V\\left(  \\tau\\right)  \\leq1~\\left[  P\\left(  \\tau\\right)  \\geq0\\right] \\\\\n",
    "&  \\mathbb{E}\\left[  V\\left(  \\tau\\right)  X\\right]  =\\left(  1-\\tau\\right)\n",
    "\\mathbb{E}\\left[  X\\right]  ~\\left[  \\beta\\left(  \\tau\\right)  \\right] \\\\\n",
    "&  V\\left(  \\tau\\right)  \\leq V\\left(  \\tau^{\\prime}\\right)  ,~\\tau\\geq\n",
    "\\tau^{\\prime}%\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Primal monotonicity constraint, sample version\n",
    "\n",
    "* Consider $\\tau_{1}=0<...<\\tau_{T}\\leq1$ and let $\\bar{x}$ be the\n",
    "$1\\times K$ row vector whose $k$-th entry is $\\mathbb{E}\\left[  X_{k}\\right]\n",
    "$.<br>One has\n",
    "\\begin{align*}\n",
    "&  \\max_{V_{ti}\\geq0}\\frac{1}{I}\\sum_{\\substack{1\\leq i\\leq I\\\\1\\leq t\\leq T}}V_{ti}%\n",
    "Y_{i}\\\\\n",
    "&  V_{ti}\\leq1\\\\\n",
    "&  \\frac{1}{I}\\sum_{1\\leq i\\leq I}V_{ti}X_{ik}=\\left(  1-\\tau_{t}\\right)\n",
    "\\bar{x}_{k}\\\\\n",
    "&  V_{\\left(  t+1\\right)  i}\\leq V_{ti}\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "* As $\\tau_{1}=0$, one has necessarly $V_{1i}=1$ and the program becomes\n",
    "\\begin{align*}\n",
    "&  \\max_{V_{ti}}\\frac{1}{I}\\sum_{\\substack{1\\leq i\\leq I\\\\1\\leq t\\leq T}}V_{ti}Y_{i}\\\\\n",
    "&  V_{1i}=1\\\\\n",
    "&  \\frac{1}{I}\\sum_{1\\leq i\\leq I}V_{ti}X_{ik}=\\left(  1-\\tau_{t}\\right)\n",
    "\\bar{x}_{k}\\\\\n",
    "&  V_{t1}\\geq V_{t2}\\geq...\\geq V_{t\\left(  m-1\\right)  }\\geq V_{T,i}\\geq0.\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix notations\n",
    "\n",
    "* Let $\\tau$ be the $T\\times1$ row matrix with entries $\\tau_{k}$.\n",
    "\n",
    "* Let $D$ be a $T\\times T$ matrix defined as\n",
    "$$\n",
    "D=\n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & \\cdots & 0 & 0\\\\\n",
    "-1 & 1 & 0 & \\ddots & \\vdots & \\vdots\\\\\n",
    "0 & -1 & 1 & \\ddots & 0 & 0\\\\\n",
    "\\vdots & \\ddots & \\ddots & \\ddots & 0 & 0\\\\\n",
    "\\vdots &  & 0 & -1 & 1 & 0\\\\\n",
    "0 &  & 0 & 0 & -1 & 1\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "we have $V^{\\top}D\\geq0$ if and only if $$V_{1i}\\geq V_{2i}\\geq...\\geq\n",
    "V_{\\left(  T-1\\right)  i}\\geq V_{Ti}\\geq0.$$\n",
    "\n",
    "* One can write\n",
    "\\begin{align*}\n",
    "&  \\frac{1}{I}\\max_{V}1_{T}^{\\top}VY\\\\\n",
    "&  \\frac{1}{I}VX=\\left(  1_{T}-\\tau\\right)  \\bar{x}\\\\\n",
    "&  V^{\\top}D1_{T}=1_{I}\\\\\n",
    "&  V^{\\top}D\\geq0\n",
    "\\end{align*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "* Thus, setting<br> $\\pi=D^{\\top}V/I$, and $U=D^{-1}1_{I}$, $\\mu=D^{\\top}\\left(\n",
    "1_{T}-\\tau\\right)  $, and $p=1_{I}/I$,<br>one has<br>\n",
    "\\begin{align*}\n",
    "&  \\max_{\\pi}U^{\\top}\\pi Y\\\\\n",
    "&  \\pi X=\\mu\\bar{x}\\\\\n",
    "&  \\pi^{\\top}1_{T}=p\\\\\n",
    "&  \\pi\\geq0\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "* Assume that the first entry of $X$ is one. One has that if $\\pi$ satisfies the constraints, then\n",
    "$$\\sum_{i=1}^{I}\\pi_{ti}=\\mu_{t}\\text{ and }\\sum_{t=1}^{T}\\pi_{ti}=p_{i}$$\n",
    "thus $\\pi$ can be thought of as a joint probability on $\\tau$ and $X$.\n",
    "\n",
    "* One has\n",
    "\\begin{align*}\n",
    "&  \\max_{\\pi\\geq0}\\sum_{\\substack{1\\leq t\\leq T\\\\1\\leq i\\leq I}}\\pi_{ti}\n",
    "U_{t}Y_{i}\\\\\n",
    "&  \\sum_{1\\leq i\\leq I}\\pi_{ti}X_{ik}=\\mu_{t}\\bar{x}_{k}\\\\\n",
    "&  \\sum_{1\\leq t\\leq T}\\pi_{ti}=p_{i}%\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computation\n",
    "\n",
    "* Recall the problem to compute\n",
    "\\begin{align*}\n",
    "&  \\max_{\\pi\\geq0}U^{\\top}\\pi Y\\\\\n",
    "&  \\pi X=\\mu\\bar{x}\\\\\n",
    "&  \\pi^{\\top}1_{T}=p\n",
    "\\end{align*}\n",
    "which we sill vectorize using $vec\\left(  A\\pi B\\right)  =\\left(  A \\otimes B^{\\top\n",
    "}\\right)  vec\\left(  \\pi\\right)  $ so that the constraint becomes\n",
    "$$\n",
    "\\begin{pmatrix}\n",
    " I_{T}\\otimes X^{\\top}\\\\\n",
    "1_{T}^{\\top} \\otimes I_{I}\n",
    "\\end{pmatrix}\n",
    "vec\\left(  \\pi\\right)  =\\binom{vec\\left(  \\mu\\bar{x}\\right)  }{p}%\n",
    "$$\n",
    "\n",
    "\n",
    "* There are $IT$ primal variables and $KT+I$ constraints.\n",
    "\n",
    "* Computation is done with a linear programming solver like Gurobi. Large-scale linear programming solvers make use of sparsity of constraint matrix. However, if dimension of $Y$ is larger, $T$ will need to be large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recovering the $\\beta$\n",
    "\n",
    "* $\\beta$ is the vector of Lagrange multipliers of the constraint $ \\frac{1}{I}V X= \\left( 1_{T}-\\tau \\right) \\bar{x} $ in the former problem.\n",
    "\n",
    "* Let $\\psi$ be the vector of Lagrange multipliers of the constraint $\\pi X-\\mu \\bar{x}$ in the latter problem.\n",
    "\n",
    "* We have $\\beta = D \\psi$. Indeed:<br>\n",
    "$\\left( \\pi X-\\mu \\bar{x}\\right) ^{\\top }\\psi =0$<br>\n",
    "thus<br>\n",
    "$\\left( \\frac{1}{I}D^{\\top }V X-D^{\\top }\\left( 1_{T}-\\tau \\right) \\bar{x}%\n",
    "\\right) ^{\\top }\\psi =0$<br>\n",
    "and therefore<br>\n",
    "$\\left( \\frac{1}{I}V X-\\left( 1_{T}-\\tau \\right) \\bar{x}\\right) ^{\\top }D\\psi\n",
    "=0$\n",
    "\n",
    "* Compute in the following manner:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([81.48614818,  0.56017469])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D_t_t = spr.diags([1, -1], [ 0, -1], shape=(nbt, nbt))\n",
    "\n",
    "U_t_1 = np.linalg.inv(D_t_t.toarray()) @ np.ones( (nbt,1)) \n",
    "μ_t_1 = D_t_t.T @ (np.ones((nbt,1)) - τ_t_1)\n",
    "\n",
    "A1 = spr.kron(spr.identity(nbt),X_i_k.T)\n",
    "A2 = spr.kron(np.array(np.repeat(1,nbt)),spr.identity(nbi))\n",
    "A = spr.vstack([A1, A2])\n",
    "rhs = np.concatenate( [(μ_t_1 * xbar_1_k).flatten(), np.ones(nbi)/nbi]) \n",
    "obj = np.kron(U_t_1, Y_i_1).T\n",
    "vqr_lp=grb.Model()\n",
    "pi = vqr_lp.addMVar(shape=nbi*nbt, name=\"pi\")\n",
    "vqr_lp.setParam( 'OutputFlag', False )\n",
    "vqr_lp.setObjective( obj @ pi, grb.GRB.MAXIMIZE)\n",
    "vqr_lp.addConstr(A @ pi == rhs)\n",
    "vqr_lp.optimize()\n",
    "\n",
    "ϕ_t_k = np.array(vqr_lp.getAttr('pi'))[0:(nbt*nbk)].reshape((nbt,nbk))\n",
    "\n",
    "βvqr_t_k = D_t_t.toarray() @ ϕ_t_k\n",
    "\n",
    "βvqr_t_k[10,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vector quantile regression in the continuous case\n",
    "\n",
    "* This rewrites as a *Vector quantile regression* (yet for now in the scalar case), introduced in [CCG16]\n",
    "\\begin{align*}\n",
    "\\max_{\\pi}  &  \\mathbb{E}_{\\pi}\\left[  UY\\right] \\\\\n",
    "s.t.  &  U\\sim\\mu\\\\\n",
    "&  \\left(  X,Y\\right)  \\sim P\\\\\n",
    "&  \\mathbb{E}\\left[  X|U\\right]  =\\mathbb{E}\\left[  X\\right]\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "* This is an extension of the optimal transport problem of Monge-Kantorovich. As a matter of fact, when $X$ is restricted to the constant, this is *exactly* an optimal transport problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vector quantile regression, primal problem\n",
    "\n",
    "* Recall our previous problem\n",
    "\\begin{align*}\n",
    "\\max_{\\pi}  &  \\mathbb{E}_{\\pi}\\left[  UY\\right] \\\\\n",
    "s.t.  &  U\\sim\\mu\\\\\n",
    "&  \\left(  X,Y\\right)  \\sim P\\\\\n",
    "&  \\mathbb{E}\\left[  X|U\\right]  \\sim\\mathbb{E}\\left[  X\\right]\n",
    "\\end{align*}\n",
    "and replace mean-independence by independence; one has\n",
    "\\begin{align*}\n",
    "\\max_{\\pi}  &  \\mathbb{E}_{\\pi}\\left[  UY\\right] \\\\\n",
    "s.t.  &  U\\sim\\mu\\\\\n",
    "&  \\left(  X,Y\\right)  \\sim P\\\\\n",
    "&  X {\\perp\\!\\!\\!\\perp}U\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "* The solution to the latter problem is simply<br>\n",
    "$U=F_{Y|X}\\left(  Y|X\\right)$<br>\n",
    "which yields the nonparametric conditional quantile representation<br>\n",
    "$Y=F_{Y|X}^{-1}\\left(  U|X\\right).$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vector quantile regression, dual problem\n",
    "\n",
    "* The dual problem yields\n",
    "\\begin{align*}\n",
    "\\min_{\\psi,b}  &  \\mathbb{E}_{P}\\left[  \\psi\\left(  X,Y\\right)  \\right]\n",
    "+\\bar{x}^{\\top}\\mathbb{E}_{\\mu}\\left[  b\\left(  U\\right)  \\right] \\\\\n",
    "s.t.~  &  \\psi\\left(  x,y\\right)  +x^{\\top}b\\left(  \\tau\\right)  \\geq\\tau\n",
    "y,~\\forall x,y,\\tau\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "* Optimality of $\\left(  \\psi,b\\right)  $ yields\n",
    "$$\n",
    "\\psi\\left(  x,y\\right)  =\\sup_{\\tau\\in\\left[  0,1\\right]  }\\left\\{  \\tau\n",
    "y-x^{\\top}b\\left(  \\tau\\right)  \\right\\}\n",
    "$$\n",
    "which yields, if $b$ is differentiable,\n",
    "$$\n",
    "Y=X^{\\top}\\beta\\left(  U\\right)\n",
    "$$\n",
    "where $(U,X,Y)$ are the solutions to the primal problem and $\\beta\\left(\n",
    "\\tau\\right)  =b^{\\prime}\\left(  \\tau\\right)  $.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multivariate case\n",
    "\n",
    "* Vector quantile regression yields a natural way to extend classical\n",
    "quantile regression to the case when the dependent variable is multivariate.\n",
    "If $Y$ is valued in $\\mathbb{R}^{d}$, one may take $\\tau$ in $\\mathbb{R}^{d}$,\n",
    "$\\mu=\\mathcal{U}\\left(  \\left[  0,1\\right]  ^{d}\\right)  $. We replace the\n",
    "product $\\tau$ by the scalar product $\\tau^{\\top}\\beta\\left(  U\\right)  $, and\n",
    "the analysis goes unmodified.\n",
    "\n",
    "* We get a nice tensorization of vector quantile regression that way: when\n",
    "the components of $Y$ are independent, the previous propal amounts to running\n",
    "the scalar version component by component."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
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