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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import matplotlib.pylab as plt\n",
      "\n",
      "from pandas.io.data import DataReader\n",
      "from datetime import datetime\n",
      "from custom_functions_iversity import graphicalComparisonPdf, multivariateGaussianRand"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Week 9 -- Modeling and quantifying financial risk "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This week of lectures looks at how we can model and quantify financial risk. It discusses concepts such as VaR, copulas and model calibration using techniques such as maximum likelihood.\n",
      "\n",
      "Our approach is as follows: we first discuss the concept of maximum likelihood. This a statistical technique for parameter estimation of a distribution on a given dataset. In particular, we apply this technique to estimate the parameters of the student t distribution.\n",
      "\n",
      "Next we consider a portfolio of assets (stocks). We model the historical data using a student t distribution"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Maxmimum Likelihood"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Maximum likelihood is a technique used to estimate parameters of a distribution which we are fitting to given a dataset $\\lbrace x_i\\rbrace_{i=1}^N$. Recall that when we fit a Gaussian distribution to a dataset we need to estimate two parameters: the mean and the variance. These are easily extracted from the dataset using the estimators $\\hat{\\mu} = \\sum_{i=1}^N x_i / n$ and $\\hat{\\sigma}^2 = \\sum_{i=1}^N (x_i - \\hat{\\mu})^2 / n$. These two parameters uniquely fix the Gaussian distribution fitted to the data.\n",
      "\n",
      "However, many distributions are characterized by other parameters, which we collectively write by $\\lbrace\\theta_i\\rbrace_{i=1}^p$ with $p$ the number of free parameters. For instance, a student t distribution has the so-called degrees of freedom parameter. Fitting a distribution to a dataset requires us to fix these parameters in a way that generates the 'best fit'. Although 'best fit' is somehwat subjective, the maxmimum likelihood is a\n",
      "\n",
      "Given a dataset $\\lbrace x_i\\rbrace_{i=1}^N$ and a distribution $f(x | \\theta)$ characterized by a parameter $\\theta$ we construct the likelihood function as\n",
      "\n",
      "$$ \\mathcal{L}(\\theta | x_1 , \\ldots, x_n) = \\prod_{i=1}^n f(x_i|\\theta)$$\n",
      "\n",
      "The dataset is given to us, so this expression is really only a function of $\\theta$. As this parameter is varied we fit different distributions $f(\\cdot | \\theta)$ to the dataset. As the name suggests, the maximum likelihood fit is obtained by picking the $\\theta$ which maximizes the likelihood function.\n",
      "\n",
      "First, however, we note that the likelihood function almost always leads to a very small number. This can cause computational problem. Instead, we therefore consider the log-likelihood function given by\n",
      "\n",
      "$$ \\log \\mathcal{L}(\\theta | x_1 , \\ldots, x_n) = \\log\\big(\\prod_{i=1}^n f(x_i|\\theta) \\big) = \\sum_{i=1}^n \\log(f(x_i|\\theta)$$\n",
      "\n",
      "Since the logarithm is convex it will map maximum points to maximum points. So to obtain the maximum likelihood estimate of $\\theta$ we can simply optimize the log-likelihood instead. It also common to consider the minus log likelihood function. Optimization corresponds to finding the minimum of this function.\n",
      "\n",
      "\n",
      "If the log-likelihood function is not too complicated then we can use analytical tools to obtain the MLE of theta (maximum likelihood estimator). See for instance wikipedia for a derivation of the MLE's for a Gaussian distribution. However, for more complicated expressions we need to resort to numerical optimization techniques to optimize the LL function.\n",
      "\n",
      "Here we use the most straightforward way of optimization (using `fmin`). We can do better using for instance explicit implementation of the first and second derivatives, but this requires knowledge of the pdf."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We define a generic handle to the minus Log Likelihood function for a given pdf. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def minusLogLikelihood(pdf, X, parameters):\n",
      "    \"\"\"\n",
      "    minusLogLikelihood: minus the likelihood of a model pdf, given the data sample X\n",
      "\n",
      "    INPUT:\n",
      "    parameters : Parameters of the model pdf\n",
      "           pdf : Model pdf\n",
      "             X : Sample\n",
      "\n",
      "    OUTPUT:\n",
      "           mLL : value of minus the loglikelihood, normalized by the sample size\n",
      "    \"\"\"\n",
      "    # Compute minus the log likelihood\n",
      "    return -np.sum(np.log(pdf(X, parameters)))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then the fit function is given by"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fit2pdf(X, pdf, parameterseed):\n",
      "    \"\"\"\n",
      "    Maximum likelihood fit to a PDF\n",
      "    INPUT:\n",
      "                  X : Sample\n",
      "                pdf : Model pdf\n",
      "      parameterlist : Seed for the parameters\n",
      "    OUTPUT:\n",
      "      logLikelihood : value of the loglikelihood\n",
      "         varargaout : list of parameters that maximize the likelihood\n",
      "    \"\"\"\n",
      "\n",
      "    def mLL(parameterlist):\n",
      "        return minusLogLikelihood(pdf, X, parameterlist)\n",
      "\n",
      "    varargout = fmin(mLL, parameterseed, xtol=1e-8, disp=0)\n",
      "\n",
      "    logLikelihood = -mLL(varargout)\n",
      "    return logLikelihood, varargout\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For example, we create a dataset of 1000 samples drawn from a normal distribution, and scale this to a $N(\\mu=10, \\sigma=3)$ distribution. The `fit2pdf` then generates the following estimates"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = 3 * np.random.randn(1000) + 10\n",
      "def gaussPDF(x, args):\n",
      "    mu = args[0]\n",
      "    sigma = args[1]\n",
      "    return np.exp(-(x-mu)**2/(2 * sigma**2)) / (np.sqrt(2 * np.pi) * sigma)\n",
      "finalLL, param = fit2pdf(X, gaussPDF, [1, 2])\n",
      "print \"Estimated parameters (mu, sigma): \", param[0], \",\", param[1]\n",
      "print \"Sample mean and variance:\", X.mean(), X.std()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Estimated parameters (mu, sigma):  9.98795784087 , 3.01609796942\n",
        "Sample mean and variance: 9.98795786912 3.01609814296\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sometimes the optimization procedure leads to unrealistic parameter estimates due to runaway solutions. We can therefore also use a bounded optimzation procedure using `fminbound`. In SciPy this particular implementation can only handle scalar functions. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fminbound\n",
      "\n",
      "def fit2pdf_con(X, pdf, lb, ub):\n",
      "    \"\"\"\n",
      "    fit2pdf_con: ML fit to a pdf, considering lower and upper bound constraints\n",
      "\n",
      "    INPUT:\n",
      "                 X : Sample\n",
      "               pdf : Model pdf\n",
      "                lb : lower bound constraints for the parameters\n",
      "                ub : upper bound constraints for the parameters\n",
      "\n",
      "    OUTPUT:\n",
      "     logLikelihood : value of the loglikelihood\n",
      "        varargaout : list of parameters than maximize the likelihood\n",
      "    \"\"\"\n",
      "    \n",
      "    def mLL(parameterlist):\n",
      "        return minusLogLikelihood(pdf, X, parameterlist)\n",
      "\n",
      "    varargout = fminbound(mLL, lb, ub, xtol=1e-8, disp=0)\n",
      "\n",
      "    logLikelihood = -mLL(varargout)\n",
      "    return logLikelihood, varargout"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "X = np.random.randn(1000) + 10\n",
      "def gaussPDF2(x, mu):\n",
      "    sigma = 1\n",
      "    return np.exp(-(x-mu)**2/(2 * sigma**2)) / (np.sqrt(2 * np.pi) * sigma)\n",
      "\n",
      "\n",
      "finalLL, param = fit2pdf_con(X, gaussPDF2, 0, 15)\n",
      "print \"Estimated parameter mu:\", param\n",
      "print \"True mean:\", X.mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Estimated parameter mu: 10.0582928857\n",
        "True mean: 10.0582928857\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Example: GOOGLE stock"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider now the log returns of the Google stock. In week 1 we already saw that a simply, but primitive fit of the log returns is generated by the normal distribution. We show this result here using the MLE method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S = DataReader(\"GOOGL\",  \"yahoo\", datetime(2007,7,1), datetime(2013,6,30))['Adj Close']\n",
      "logReturn = np.log(S / S.shift(1))\n",
      "logReturn.dropna(inplace=True)\n",
      "logReturn.plot()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.axes.AxesSubplot at 0xea22080>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6dq224le6fIQ1Lq51662AYioSP9RdcukA/JVzixZSpy81N1PLlvwZ79qlfS3B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\nkJeXV1X7durUCYWFhaioqMDAgQPRrVu3qk+zqVO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       "text": [
        "<matplotlib.figure.Figure at 0xea06ba8>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The PDF we use is the normal distribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def gaussPDF(x, args):\n",
      "    mu, sigma = args     \n",
      "    return np.exp(-(x-mu)**2/(2 * sigma**2)) / (np.sqrt(2 * np.pi) * sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we obtain the MLE and compare it to the sample estimates of the mean and standard deviation. For the Gaussian the parameters mu and sigma coincide with the sample mean and standard deviation, so we should obtain the same values. We use then use the graphicalComparisonPdf function to estimate the goodness of our fit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fitReturns():\n",
      "    LL, (mu, sigma) =  fit2pdf(logReturn, gaussPDF, [0, 1])\n",
      "    print \"Estimated parameters:\", mu, sigma\n",
      "    print \"Sample estimates:\", logReturn.mean(), logReturn.std()\n",
      "    \n",
      "    def modelPDF(x):\n",
      "        return gaussPDF(x, (mu, sigma))\n",
      "    graphicalComparisonPdf(logReturn, modelPDF)\n",
      "fitReturns()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Estimated parameters: 0.000335811350516 0.0209772909183\n",
        "Sample estimates: 0.000335812691068 0.0209842419645\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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C9UjNXjjOli2GRE9UFFnOjeY6Pmg0msqPRo1YXZHoQUo5wiNJshd1y6WHSCih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\nC0iyF0IILyDJXgghvMD/A1NaBQ8zipwWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xea13c18>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Student-t distribution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From the above fit we notice that the normal distribution does not produce high quality fits of stock data. In particular, it underestimates the tail events. Here we take a look at the student t distribution as an alternative model.\n",
      "\n",
      "We first define some handles to the distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import t as tdist\n",
      "\n",
      "## Define the \n",
      "\n",
      "def locationScaleTcdf(x, mu, sigma, nu):\n",
      "    return tdist.cdf((x - mu)/sigma, nu)\n",
      "\n",
      "\n",
      "def locationScaleTinv(p, mu, sigma, nu):\n",
      "    return mu + sigma * tdist.ppf(p, nu)\n",
      "\n",
      "def locationScaleTpdf(x, mu, sigma, nu):\n",
      "    return tdist.pdf((x - mu)/sigma, nu) / sigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def demo_studentT():\n",
      "    mu = 0\n",
      "    sigma = 1\n",
      "    nu = [1, 2, 5, 30]\n",
      "    alpha = 6 \n",
      "    xMin = mu - alpha * sigma\n",
      "    xMax = mu + alpha * sigma\n",
      "    nPlot = 1000\n",
      "    xPlot = np.linspace(xMin, xMax, nPlot)\n",
      "    fig = plt.figure(figsize=(10,8))\n",
      "    ax_pdf = fig.add_subplot(211)\n",
      "    ax_cdf = fig.add_subplot(212)\n",
      "    for n in nu:\n",
      "        ax_pdf.plot(xPlot, locationScaleTpdf(xPlot, mu, sigma, n), label=r'$\\nu$ = {}'.format(n))\n",
      "        ax_cdf.plot(xPlot, locationScaleTcdf(xPlot, mu, sigma, n), label=r'$\\nu$ = {}'.format(n))\n",
      "    ax_pdf.set_title('Student t distribution -- PDF ($\\mu$ = {}, $\\sigma$ = {})'.format(mu,sigma), fontsize=19)\n",
      "    ax_pdf.legend(fontsize=15)\n",
      "    ax_cdf.set_title('Student t distribution -- CDF ($\\mu$ = {}, $\\sigma$ = {})'.format(mu,sigma), fontsize=19)\n",
      "    ax_cdf.legend(fontsize=15, loc='lower right')\n",
      "    fig.tight_layout()\n",
      "demo_studentT()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Y2Fh+++03AGbMmEFUVBTjx48H4L333iNv3rwZvkZGxyCbTJC1Wi3ly5fnzz//\nxNPTk1q1arFu3Tr8/Px0daKjo3FycgLg3LlztG/fnmvXrgHg6+vLX3/9hauJRe9zwxtMCCGSffD3\n39RydubLkiX1D8TEQLVq8O238OGH6T7/g+gHXH50mWdxz8hnlw/fQr6ULFAy/b28Fy6om4gEBUGZ\nMnqHDkRG0v3iRS7Xro1jnjzpjlmI3Cg35C8XL16kadOmjBw5kvbt21Pmpc+AzBISEkKpUqWAf9dE\nVhQFjUbDzZs3jQ7vSItMnaQXHBxMmTJl8PHxAaBLly5s3bpVL0FOTo4Bnj9/jru7u945XvU3jxBC\nWOpwZCQnoqJYk+IzUmfCBKhZM13J8YPoByw+sZj159cT9iyMioUrUtCxINEJ0Vx5fAUbjQ0dK3Zk\nQM0BVHCvkLaTV6yojoceMAD27NEbatGoYEH88+dn/t27jDK2RbYQ4pXl5+dHeDbsoOnj40NSUlKW\nXzctTE7SCwsLo0SKD0UvLy/CDGxV+uuvv+Ln50fLli2ZM2eOrlyj0dCsWTNq1qzJDz/8YMWwhRAi\nZ1EUhVHXrzPZ15e8L/e2njkDy5fD99+n6ZwxCTF8s+8b/Ob7cefZHZa1XUbE6AiO9D7C711/50CP\nA9wdeZd93ffhbO/MW8vf4tNfP+VhdBrXMR4+HB4/hjVrUh2aXKoU027f5mkuWPhfCCEsZbIH2dKv\n7Nq1a0e7du04dOgQ3bp14/Lly4A68Lt48eI8fPiQ5s2bU6FCBRo2bJiqffK4E4DGjRsbXZxaCCFy\nqo0PH5KoKHz88o55Wi307w+TJ4Oh3fSMOHv/LF1+7kKVolU43f80JQoY7sHVaDSUdy/P/zX9P754\n8wvGB4yn6qKqLGi1gPZ+7S27mK0tLFkCbdpAq1bg5qY7VMnJiffc3Jh++zaT/vlKVAghXiUBAQEE\nBASkqY3JMchBQUGMHz+eXbt2AfDtt99iY2NjcgB36dKlCQ4Oxi3FByzAhAkTyJ8/P6NGjdIPIBeM\n4RFCvN4SkpKoEBzM0vLlaVKokP7B+fNh3To4eBBsLFtZc+25tQzbNYyZ78ykW7VuaY7nSOgRPt78\nMT2r92Rso7GWj08eOhSeP4cff9Qrvv3iBf4nTvB3rVoUd3BIczxC5EaSv+RsGR2DbPLTumbNmly9\nepWQkBDi4+PZsGEDbdu21atz/fp13UVOnjwJgJubGzExMURFRQHqRL4//viDKlWqWHZXQgjxCll1\n/z6+jo41wO/jAAAgAElEQVSpk+NHj2D8eFi82OLkeM6xOYz+czT7P92fruQYoH6J+gT1CeL3a7/T\nY2sPtElayxpOmgS7d6urbaTg7ehIj2LFmHTrVrriEUKIV43JT2xbW1vmzZtHixYtqFixIp07d8bP\nz4/FixezePFiADZv3kyVKlXw9/dn2LBhrF+/HoB79+7RsGFDqlevTp06dWjdujXvvLRjkxBCvOri\nk5L4v5AQJvj6pj44fjx06QKVKll0rumB05l/fD6Hex6mcpHKGYqrWP5i7P90P+FR4fTa1oskxYIJ\nMS4u6lCQ4cNTbf/1dcmSbHjwgGsxMRmKSwghXgVm10HO9ADkKwohxCts8d27bHn4kN3VqukfOH9e\n3Yzj0iW9Mb3GLD+1nAkHJnC412G8XLysFl9MQgwtf2qJn7sfC99baH64RVIS1KoFo0bBxx/rHZoY\nEsLNFy9YXiGNK2UIkQtJ/pKzZeoQCyGEEMbFJSUx+dYtJvyzFKaOosCIEfDf/1qUHO+6touv933N\n7k92WzU5Bshnl48dH+0g6E4QM4/ONN/AxkZdbePLL9W1m1MY6unJ9kePuBEba9UYhRAip5EEWQgh\n0mlZeDhVnJyoW6CA/oGdO+H2bXWHOjOuRVzj018/5eeOP1PevXymxOns4My2j7Yx4+gMfr/6u/kG\nDRtC3brwv//pFRe0s2OQpyff3r6dKXEKIUROIUMshBAiHV5otZQ5doxfK1empovLvweSksDfX90Y\npF07k+eIjo+m3rJ6DKg5gEG1zCfTGXUk9Ajt1rfjWJ9j+BYyMGY6pRs3oHZtdYhIig2gIhISKHvs\nGCdr1qSko2MmRyxEziX5S84mQyyEECIbLL93j+r58+snxwAbN4KjI7z/vtlzDN81nOrFqjOw5sBM\nilJf/RL1+bLBl3y0+SMStAmmK5cqBZ06wbRpesWudnb09/BgqvQiCyFyMUmQhRAijRKTkpgeGspX\nJUvqH0hIgG++gSlT9LZsNmT75e3svbmXea3mWb5OsRUMrzsct3xufLP/G/OV//tfdU3kl3ZQHenl\nxYYHDwh98SKTohRC5GYbN27kvffew8PDA2dnZ2rWrKlbBS2nkARZCCHSaMPDh3g5OPDmy2OPV64E\nb294+22T7R9EP6Dfjn6sbLcSFwcXk3WtzUZjw4r3V7DyzEqC7gSZruzhAb17q+sjp+Bub0+f4sWZ\nJr3IQoh0+P777ylUqBBz5sxh+/btNGnShI8//ph58+Zld2g6MgZZCCHSIElRqHbiBN+VKkXLlCtU\nvHgB5cqpQyzq1jXaXlEU2m9oT3m38kxrPs1ovcy28fxGxgeM51T/UzjYmtgd7/FjKF9e3TykdGld\n8b24OPyOH+dK7doUtrfPgoiFyFkkf0m/iIgIXF1d9cq6du3K0aNHuXHjhlWuIWOQhRAiC/32+DG2\nGg3vvvThzqJF6uQ8E8kxwM8XfuZqxFUmNpmYiVGa17FiR8q7l2fyocmmK7q5qVtQjx+vV1zMwYEP\nCxdm/kvDL4QQwpyXk2OA6tWrc/fu3WyIxjDpQRZCCAspisKbp04x3MuLTkWK/HsgNlad1LZ7N1St\narR9VFwUfvP9WPfBOhqWbJgFEZt2N+ou1RdVZ0+3PVQrVs14xagotff44EFIsUnIpeho3jp9mpC6\ndcmXJ08WRCxEzvE65y+JiYlm69ja2qbpnB06dOD69eucOXMmvWHpkR5kIYTIIgefPuVRQgIfFC6s\nf2DpUqhTx2RyDDAuYBzNSzfPEckxgIezB5ObTmbgbwNN/7JwdlZ7kadM0Suu4OREfRcXVty7l8mR\nCiEyy7Bhw7C3t2f//v26sr///pvGjRsbrL9ixQrs7e3NPtJi7969bN26lVGjRmXkVqxKepCFEMJC\nbc6do42bG/08PP4tjI9Xe1e3bFG3aDbizL0zvLPmHf4e+DeFnQobrZfVkpQk6iytw7A6w/ik6ifG\nK0ZGQpkyqcYiBz59SveLF7lSpw55snA1DiGym6X5i2ZC5vy/UMZZJ3eKiorC3d2dJ0+ekC9fPgC+\n/vpr4uLimDFjRqr6ERERhISEmD1vjRo1LLp+SEgIderUoUGDBmzevDlNsZuS0R5kSZCFEMICl2Ni\neOvUKULq1iVvyuEES5fCzz/Drl1G2yqKQsPlDelerTv93uiXBdGmzdHQo3Tc1JGLgy/i7OBsvOI3\n38D9+7BkiV7xmydPMtzLi44ph50Ikcvllvxlz549jB49mpMnTwIQExNDhQoVOHz4MN7e3gbbWGuI\nRUREBG+++SYFChQgICAARytuPiRDLIQQIgt8f+cOAzw89JPjxET49lsYM8Zk280XN/M8/jm9/Xtn\ncpTpU69EPZr6NmXKoSmmKw4bpv4x8NLybp+XKMF3oaG5IlkQ4nUTGBhIgwYNdD+PGzeOwYMHG02O\nrTXEIiYmhtatW5OYmMiOHTusmhxbQ9pGUAshxGvoUXw86x884FLt2voH1q8HLy9oaHxMcbw2ntF/\njmZJ6yXkscn4RLY7d+DcOYiIACcnqFRJHfmQ0dENU5tNperCqvSp0YfSrqUNV3J3V9dFnj4d5s7V\nFbd1d2f0jRsciIykcaFCGQtECJGlAgMD6d1b/eN948aNREZGMn36dKP127Zty4kTJzJ0zcTERDp2\n7Mj169c5cuQI7im2s88pZIiFEEKYMfnWLa7HxvJjihUcSEqCypVh9mxo3txo21lHZ7H35l52fLwj\n3dePi4NVq2DBAggNhRo11Fw1KgrOngUbG+jZU51HV7Bgui/DpIOTOP/wPOs+WGe80r17ULEinD8P\nxYvrin+4e5dfHz3iNzMTFYXILXJD/qLVanF1deX06dNs376d2NhYRo8enenX7devH0uXLmX27NnU\nemnuRo0aNdI8yc8QGYMshBCZKC4pCZ+gIP6oWpUq+fP/e2DzZpg2TZ20ZqT7NiI2ggrzKnCgxwH8\nCvul6/r790P//uoqcp9/Do0bQ8pRHooCZ87AnDmwYwd89x18+mn6epSj46MpO7csOz7eQY3iJibY\nDBmidl9PnaoritVqKRkUxGF/f8r9M9FHiNwsN+QvFy9epGnTpowcOZL27dtTpkyZLLmur68vt2/f\nTvX8aTQabt68aXR4R1pIgiyEEJlo5b17/HT/Pn9US7FOsKJAzZowdiy8/77Rtl/s+YJncc9Y1HpR\nmq+blAQTJqhzABcvhtatzbc5cwa6d1eXKl6+HNKTpy48vpBfL//K7k92G69086Z6/yEh6hJw/xhz\n4wZRWi1zypZN+4WFeMVI/pKzySQ9IYTIJIqiMCs0lJFeXvoHAgIgJgbatDHa9t7zeyw7tYxv3vom\nzddNTFSH+v7xB/z1l2XJMUC1amqHtoMDNGoET56k+dL0qdGHG09usPfGXuOVfH2hWTP44Qe94oEe\nHqy5f5+nFsxwF0KInEwSZCGEMGJ/ZCQJikKLl7dF/d//YORIdfCvEd8e+pbuVbvj6eKZpmsmJkKX\nLnD3Lvz5JxQrlraYHR1h5Up13mDz5uryxWlhl8eOSU0m8eXeL033sHz+OXz/PSQk6Iq8HB15p1Ah\nloeHp+2iQgiRw0iCLIQQRsy+c4dhXl5oUg7ovXBB7dbt1s1ou9Cnoaw5t4YvG3yZpuspCgweDM+f\nw7Zt6jDf9NBoYMYMNUlu0ULt7E6LjpU6kqBNYMcVExMLa9ZUl8/YsEGveJiXF3PDwtDKV89CiFeY\nJMhCCGFASGwsh58+pWvRovoHZs6EQYPUrlojJh+aTN8afSmav6jROoZMmwbBwbBpkzpMIiM0GjXU\nsmWhVy81+baUjcaGcY3GMf7AePO9yNOn6528rosLbnZ2/Pb4cQaiF0KI7GU2Qd61axcVKlSgbNmy\nTJs2LdXxrVu3Uq1aNfz9/XnjjTfYt2+fxW2FECKnWnT3Lp8WK4ZTyiUj7t1TV68YNMhouxtPbrDp\nwiY+r/95mq63cyfMmwe//aY37y1DNBp1kt/NmzB5ctravl/hfRKTEvnt6m/GK737rjqbcM+eFNfU\nMMzLi9l37qQzaiGEyH4mV7HQarWUL1+eP//8E09PT2rVqsW6devw8/t3uaLo6Gic/vke8Ny5c7Rv\n355r165Z1BZkFqgQIud5odXiHRREoL8/ZVMuBfHNN/DoESxcaLRtz6098XbxZkKTCRZf784ddcTC\npk0m9xxJt/BweOMNWLdOnbxnqS0XtzDl0BSO9z2uP8wkpZUrYc0avSQ5PimJkkFB7Klalcopl8YT\nIheR/CVny9RVLIKDgylTpgw+Pj7Y2dnRpUsXtm7dqlfHKcUguefPn+t2Q7GkrRBC5EQbHj7kDWdn\n/eQ4JkZdb23ECKPtQiJD2HZ5G8PrDrf4WlotfPSRuslHZiTHoO7n8eOP6rDpiAjL27Wr0I6EpAR+\nv/q78UoffQQXL8KpU7oiexsbBnp4MCcsLANRCyFE9jGZIIeFhVGiRAndz15eXoQZ+MD79ddf8fPz\no2XLlsyZMydNbYUQIqeZHxbGYA8P/cIVK6B+fShXzmi77wK/o1+NfhTKa/l2yzNngq0tfJm2+Xxp\n9u670KGDuumIpZ1eNhobxr411vRYZHt7deOQ77/XK+7v4cGmhw+JTLHKhRBCvCpsTR00+pXaS9q1\na0e7du04dOgQ3bp149KlS2kKYvz48bp/N27cmMaNG6epvRBCWEvws2c8SkigpZvbv4VaLcyapXbD\nGhEeFc66v9dxabDln3+XLv07Mc/EinFWM3Uq+PvDli3wwQeWtWnv154JByaw89pOWpVtZbhS375Q\nujTcvw//TGosam9Pi0KFWHX/PkNfXkdaCCGyUEBAAAEBAWlqYzJB9vT0JDQ0VPdzaGgoXiY+6Bo2\nbEhiYiIRERF4eXlZ3DZlgiyEENlpflgYAz08yJOyg2DbNnB1hQYNjLabFTSLT6p8YvHKFUlJ6mYg\n48er20hnBUdHdW+Pzp2haVMoZEFHt43Ghq8afMXUw1ONJ8iurtCpEyxaBOPG6YoHeXrS/8oVhnh6\nWtzhIoQQ1vZy5+uECebniJjss6hZsyZXr14lJCSE+Ph4NmzYQNu2bfXqXL9+XffV28mTJwFwc3Oz\nqK0QQuQkD+Pj2fb4Mb2KF9c/MHu2OvbYSJIXERvB0pNL+fxNy1eu+PFHdaiDiQUxMkWDBuru2F98\nYXmbjpU6cufZHY6EHjFeaehQNUGOi9MVNSxQgDxAQFp3KxFCiGxmMkG2tbVl3rx5tGjRgooVK9K5\nc2f8/PxYvHgxixcvBmDz5s1UqVIFf39/hg0bxvr16022FUKInGpZeDjt3d1xs7P7t/DsWbh61eSY\nhLnH5tKuQju8C3hbdJ2ICBgzBubPz5qhFS/79lt1ObngYMvq29rY8nn9z5kWaGK5zkqVoHJl2LhR\nV6TRaBjo6cmCu3czGLEQIjdZsWIFNjY2qR5LlizJ7tB0TC7zliUByDIpQogcQKsolAoK4pfKlamR\nciHivn3B21td4s2AqLgoSs0pxeGehynvXt6ia332mTrEYsECa0SePsuXw5IlcOSI0Y5xPbEJsfjO\n9mVv971UKlLJcKUdO9QxI8eP6076LDGRkkFBnK9VC4+M7n4iRA4i+Uv6rVixgl69erF//37y5s2r\nK/f19aVw4cJWuUamLvMmhBCvix2PH+Ph4KCfHEdEwM8/Q79+Rtst+WsJTX2bWpwcnz6trnc8aVJG\nI86YTz+FhARYu9ay+nnt8jKszjC+O/Kd8UqtWsHTp2rW/Q8XW1s6Fy7M0vDwDEYshMhtatWqRe3a\ntXUPayXH1iAJshBCAPPCwvjM01O/cNkyaNNGtzLDy+K18cwKmsWXb1q2RpuiwLBhMHGiOq8tO9nY\nwJw5MHo0PH9uWZuBtQay48oObkXeMn7SIUPUMdsp23l6suTuXRKTkjIYtRAiN8nJPfCSIAshXnvX\nYmI48/w5H6bsvdBq1UHCQ4YYbbfx/EbKu5fHv7i/Rdf5/Xd1I77evTMasXXUr6/urPediU7hlAo6\nFqS3f29mHp1pvFKPHvDnn5BiFaNq+fNT0tGR7Y8fZyxgIUSOkJiYaPZhidKlS2NnZ0eFChVy1Phj\nkARZCCFYGh7Op8WK4ZByxtz27eoWdLVqGWyjKAqzgmYxsu5Ii66h1aqbgXz7rboxSE4xZYr6d8D9\n+5bVH153OKvPruZRzCPDFVxcoHt39aQpDJLJekLkSMOGDcPe3p79+/fryv7++2+je1KsWLECe3t7\nsw9TPDw8mDRpEmvWrGHHjh3UrVuXAQMG8P1LGw5lJ5mkJ4R4rcUnJeF99CgH/f0pl3Jr6aZN1Ql6\nH31ksN2BkAP039GfC4MvYKMx39ewcqW6BvGhQ5ZNistKw4erkwb/2QjVrL7b+uLl4sW4xuMMV7h+\nHerWhVu34J/nNC4piRJHj3L45edZiFeUxflLZv2Ht1LuFBUVhbu7O0+ePCHfP/83v/76a+Li4pgx\nY0aq+hEREYSEhJg9b40aNdIUR5cuXdi7dy8PHz5MUztjMjpJTxJkIcRrbdODByy4e5f91av/W/j3\n3/DOOxASom6lbMD769+nZZmWDKg5wOw1XrxQd6hetw7efNNKgVvRgwfg5wd//QU+PubrX3h4gaYr\nmxIyPARHW0fDldq2hdat9SY4fnn9OvGKwswyZawTuBDZKLfkL3v27GH06NG6vSxiYmKoUKEChw8f\nxtvb8NKVlgyhsE3jV2WbNm2ic+fO3Lx5k5IlS6aprSGyioUQQmTAkvBw+r28Mci8edC/v9Hk+Orj\nqxwJPUL3at0tusaiReoWzzkxOQYoUkRdem6ckQ7hl1UsXJEaxWuw9pyJJTCGDVO7pFP8Eurv4cGq\ne/eI0WozGLEQwloCAwNpkGKX0HHjxjF48GCjybE1hlgYktN228xBI+GEECJrXY+N5fTz57R3d/+3\n8MkT2LABLl402m72sdn0f6M/+ezMDxWIjVUnwf3+uzUizjyjRkHZsnD+vLrnhzkj641k+K7h9Kze\n0/AvtqZN1YHXBw+qMwEB37x5qe3iws8PH9K9WDEr34EQIj0CAwPp/c/M4Y0bNxIZGcn06dON1m/b\nti0nTpywehw///wz7u7uVuk9tgZJkIUQr62l4eF0L1oUxzx5/i388Ud47z0wksBFxEbw07mfuDDo\ngkXXWLwYateGlCM4ciIXFzVJnjRJHQpiztu+b2OjseGP63/QokyL1BU0GnUf7fnzdQkyQL/ixflf\naKgkyELkAFqtluDgYJYsWcKcOXOIjY3lhx9+MNnG1dUV1wyuU/nhhx9Sr149KlWqRGJiIhs2bGDj\nxo3MnTs3Q+e1JkmQhRCvpfikJJaHhxOQMnNNXtpt/Xqj7Zb8tYS25dtS3Lm40TrJknuPf/vNGhFn\nvkGDoFQpuHQJKlQwXVej0TCy3khmBs00nCCDuhvJuHEQFgb/rDH9npsbg65e5Xx0NJWcnKx8B0KI\ntLhy5Qr58uXj559/pn379pTJovkB5cuX54cffiA0NBRFUahUqRKrV6+ma9euWXJ9S8gkPSHEa2nz\nw4fMuXOHA/4p1jDetg0mT4Zjxwy2idfGU2p2KXZ8vIPqxcx3Cc+ZA3v3wtat1oo6802ZAhcuwJo1\n5uvGJcbhO9uXP7r9QeUilQ1XGjQICheGCRN0RWNu3CBaq+X7smWtFLUQWU/yl5xNJukJIUQ6LLl7\nl34eHvqFc+fC0KFG22w6v4ny7uUtSo5fvIBp02Ds2IxGmrU++wx274YrV8zXdbB1YHCtwcw6Ost4\npcGD1fXt4uN1RX2KF2fN/fvEymQ9IUQOJQmyEOK1czM2lr+iovgg5eS8ixfV5d06djTYRlEUZgbN\nZETdERZdY+lSqFED3njDGhFnHRcX9W+EKVMsq9+/Zn+2XNrC/edGdhqpVEld4+6XX3RFvnnz8oaz\nM5uttN6pEEJYmyTIQojXztLwcLoVK6Y/OW/+fHVjECPLEx28dZDn8c9pVbaV2fPHxam9x5Yum5bT\nDBkCO3ao+32Y457PnS6VurDg+ALjlQYPTrWzXj8PD34ID89gpEIIkTkkQRZCvFYSkpL48d49/bWP\no6Jg7Vp17WMjZgXNYkTdERbtmrd8OVStCjVrWiPirFewoJrTfvutZfWH1x3OwhMLiU2INVyhXTs1\n2z57VlfU1s2NyzExXIqOtkLEQghhXZIgCyFeKzseP6Zs3rz4pVxBYfVqdd3ef1ZaeFlaNgbRamH6\ndPj6a2tFnD2GDoUtW9QFKMwp716eOl51WH12teEKdnbqHx8pepHtbGzoWby49CILIXIkSZCFEK+V\nxXfv6vceK4qauH32mdE2s4/Npm+NvhZtDLJli7qEck7dNc9Sbm7QvTt8/71l9UfWHcmsoFkkKUmG\nK/TtCxs3QmSkrqhP8eKsun+fFzJZTwiRw0iCLIR4bdyMjeVEVBQfFC78b2FAgLqpRYrNLFJK3hhk\ncO3BZs+vKOrY49GjrRRwNhs5EpYtUzcXNKexT2Py2uZl59WdhisULw4tWsDKlbqi0nnzUj1/fn55\n9MhKEQshhHVIgiyEeG0sCw/nk6JFyfvy5LxBg9Qk2YAf/vqBtuXb4uHsYfB4SgEBEB0NrVtbKeBs\n5u0NbdrAAhPz75JpNBpG1B3BrCATS7599pl6sqR/e5n7FS/OEhlmIYTIYSRBFkK8FpIn5/VNufbx\nnTuwbx9062awTbw2nrnBcy1e2m3aNPj8c7DJRZ+sX3yhLg8da2T+XUqdK3fm4qOLnL1/1nCFN98E\nR0d195R/vO/uzoXoaK7ExFgpYiGEyDizH+O7du2iQoUKlC1blmnTpqU6/tNPP1GtWjWqVq3Km2++\nydkUs5R9fHyoWrUq/v7+1K5d27qRCyFEGvz2+DGlHB31tzdesgQ+/hicnQ22ScvGIGfOwLlzkIN2\nSrWKSpWgdm11ZQ5z7PPYqxuHGOtF1mjU5THmzfu3jY0NPYoVk8l6QoicRTEhMTFRKV26tHLz5k0l\nPj5eqVatmnLhwgW9OkeOHFEiIyMVRVGUnTt3KnXq1NEd8/HxUR4/fmzqEoqZEIQQwipanjmjrAwP\n/7cgLk5RihVTlJc+05IlJSUpNRbXULZf3m7R+bt2VZRp06wRac4TGKgovr6KkpBgvu6j6EdKwakF\nlfCocMMVnj9XFFdXRQkJ0RVdiY5WCh8+rLzQaq0UsRCZT/KX9Nu0aZNSr149xc3NTXF0dFTKly+v\nTJo0SYmPj09V9/z580rTpk2VfPnyKR4eHsrYsWMVrQWfFaZeH0teO5M9yMHBwZQpUwYfHx/s7Ozo\n0qULW7du1atTr149ChQoAECdOnW4c+fOywm4FdN5IYRIu1svXnDs2TM6ppyct3kzVKwIfn4G2xy6\nfcjijUFu3YKdO00uo/xKq19fXQFv0ybzdd3yudGlUhcWHl9ouIKTk7o8xqJFuqKy+fJRxcmJX2Wy\nnhCvhYiICJo1a8ayZcvYtWsXvXr1YvLkyYwcOVKv3pMnT2jWrBl58uRh27ZtjB07lhkzZjAuC3Zh\nsjV1MCwsjBIlSuh+9vLy4tixY0brL1u2jFat/v1lotFodDfWv39/+vbta4WQhRAibZaFh9PV0OS8\nlz6MU5p5dKbFG4PMmgW9e8M/fQW50pdfwpgx0KWL0fmMOsPrDuetFW/xZYMvyWuXN3WFQYOgQQN1\nq0FHR0DdWW/J3bt0LlIkE6IXQuQk/fr10/u5UaNGPHv2jPnz5zN37lxd+aJFi4iLi2PLli3kz5+f\nt99+m2fPnjF+/Hi++OILnI0Mj7MGk5/8GnOfgins37+fH3/8UW+ccmBgIKdOnWLnzp3Mnz+fQ4cO\npT9SIYRIh8SkJJaFh9M35drHp0+r3b5t2xpscy3imsUbgzx+DKtWwbBh1oo4Z2rVSt0EZfdu83XL\nu5enlkctfjr3k+EKZctC9ep6XdLt3N05Fx3NNZmsJ8RrydXVlYSEBL2ynTt30qJFC/Lnz68r69y5\nM7GxsRw4cCBT4zHZg+zp6UloaKju59DQULy8vFLVO3v2LH379mXXrl0UKlRIV178n19IhQsXpn37\n9gQHB9OwYcNU7cePH6/7d+PGjWncuHFa70MIIQz6PSKCko6OVEnxAcv8+TBgANga/gicHWT5xiAL\nF0L79kY34cs1NBp1RYvvvoN33zVff0TdEQzdNZTe/r0Nd7YMHgyTJ+tWEHGwseHTYsVYGh7O1NKl\nrRy9EMKaEhMTzdaxNfL5mpJWqyUuLo6TJ08yd+5cBgwYoHf88uXLNGvWTK/M29ubfPnycfnyZVpb\nuKZmQEAAAQEBFtXVMTVAOSEhQSlVqpRy8+ZNJS4uzuAkvVu3bimlS5dWjh49qlceHR2tPHv2TFEU\nRXn+/LlSv359Zffu3ekaKC2EEOn13pkzyvK7d/8tiIhQlIIFFeXePYP1I2IilEJTCylhz8LMnjsm\nRlGKFjU6zy/XiY9XlBIlFCU42HzdpKQkperCqsquq7sMV0hMVJSSJRXl+HFd0aXoaKXI4cNKnEzW\nE6+A3JK/DB06VLGzs1P27dunKzt37pzSqFEjg/WXL1+uaDQasw9LODg46Op37do11eQ7Ozs7Zfbs\n2anaeXl5KWPGjDF5blOvjyWvncn03tbWlnnz5tGiRQu0Wi29e/fGz8+PxYsXA9C/f38mTpzIkydP\nGDhwIAB2dnYEBwdz7949OnToAKh/aXTt2pV33nknbdm7EEJkwO0XLzj67BkbK1X6t3DFCnW8QNGi\nBtss+WsJbcq3sWhjkJUroU4do/P8ch07O3XY9nffmZ+wl7xxyMygmbQo0yJ1hTx5YOBAtTf/nzXk\nyufLh1++fGx79IgPZSyyyCU0ae25tJBipW/bJ02axKJFi6hTp46ubO3atbzxxhsG67dt25YTJ05Y\n5dpBQUHExMRw7NgxJk6cyMCBA3U5ZrYzm0JnshwQghAilxp744by2ZUr/xZotYpSpoy6bpkB8Ynx\niqdOH7oAACAASURBVOcMT+VU+Cmz505MVJTSpRXl8GFrRftqiIpSFDc3Rbl61XzdFwkvlGL/K6b8\nff9vwxUePlR78x8+1BWtvXdPaXb6tJWiFSLz5Jb85Y8//lD8/f11P0dHRyslSpRQbt26ZbRNQkKC\n2UdarVq1StFoNMq1a9d0ZUWKFFEmTpyYqq6Tk5Pyv//9z+T5TL0+lrx2uWi/JyGE+Ffy5Lx+KSfn\n/fEH5M8P9eoZbLPpwibKuZWzaGOQLVvUTug337RWxK+G/PnV4dszZpiv62DrwKCag/g+6HvDFdzd\n4f33YdkyXVF7d3dOP3/OdUu27hNCZFhgYCANGjTQ/Txu3DgGDx6Mt7e3wforVqzA3t7e7COt/P39\nAbh165aurEKFCly8eFGvXmhoKDExMVSoUCHN10gL8yOohRDiFbQzIoIShibnffaZwXXKFEVhxtEZ\nTGg8wey5FUXdVvqbb6wZ8atj6FAoXx7Gjzc6UkVnQM0BlJtXjslvT6aIk4FhE0OGQIcOMGoU2Nri\nmCcP3YsWZWl4ON+WKpUp8Qsh/hUYGEjv3r0B2LhxI5GRkUyfPt1ofWsOsXg5DgBfX19dWcuWLZk+\nfTrPnz/XrWSxYcMG8uXLR6NGjaweQ0qaf7qas41Go5HNRIQQVtfm3Dk6uLvTM7kH+eZNqFULbt+G\nfKlXpzh46yB9t/fl4uCLZtc+3r9fHT574QLYvKbfww0cCG5uMGmS+br9tvfDy8WLsY3GGq5Qv766\nREa7dgBcio6m8enT3K5XD/vX9QkWOV5uyF+0Wi2urq6cPn2a7du3Exsby+jRozP9uu+++y7Nmzen\nYsWK5MmTh8DAQGbOnEmbNm1Yu3atrl5kZCQVK1akcuXKjB49muvXrzNq1ChGjBjBxIkTTV7D1Otj\nyWsnCbIQItcJffGCaidOEFqvHk7Jm4OMHg2JiUbHBry//n1almnJgJoDDB5PqWVL+PBDdXOQ19W1\na+pIlZs31WEXplx4eIGmK5sSMjwER1vH1BXWrlWHWezdqytqdOoUQ728+CDl7odC5CC5IX+5ePEi\nTZs2ZeTIkbRv354yZcpkyXXHjh3LL7/8QkhICLa2tpQuXZqePXsyYMAA8qTc0OmfGD/77DOOHj1K\noUKF6NOnD+PHjze7V4ckyEII8ZIJISE8iI9nfrlyakFsLHh7w9GjYOAXwJXHV2jwYwNChoeYXfv4\n7Fk1Qb5xAxwcMiP6V0enTmqSPGKE+botf2pJp4qd6OnfM/XB+HgoWRL+/BP+WXHkp/v3WXnvHn9U\nq2blqIWwDslfcraMJsjy3ZUQIldJTEpiaXg4/TxSLNO2YQPUrGkwOQaYdXQWA2oOsGhjkOnT1V3z\nXvfkGODzz9Vttl/a/MqgEXVHMCtoluFfSvb20L8/zJunK/rA3Z1Tz59zQybrCSGygSTIQohcZVdE\nBJ729lQzNDnPgEcxj1h/fj2Dag0ye+5bt+D339VcTqhDusuUgfXrzddtXqo5SUoSe2/uNVyhf3/1\nRJGRADjmyUO3fybrCSFEVpMEWQiRqyx+ufc4OBgePza6P/KiE4voUKEDxfIXM3vuWbPUcccFClgr\n2lff6NHqxiHmvmlO3jhkVtAswxWKF1dfoxUrdEV9ixdn+b17JCQlWS9gIYSwgCTIQohcI/TFCwKf\nPqVzyl3Y5s1Tl1x4aeIHwIvEF8w/Pp+R9UaaPffjx7BqFQwfbs2IX33vvKOu5LFzp/m6Xat25cTd\nE1x8eNFwhSFD1N7+fxJiPycnyubNy/bHj60YsRBCmCcJshAi11gWHs5HRYr8u3LFgwewfTv06mWw\n/tpza6lerDqVilQyeDylBQugfXvwML8D9WtFo1FXaPvuO/N1HW0dGVhzILOPzTZcoV49cHGBXbt0\nRf2KF2fJ3btWilYIISwjCbIQIldInpzXP2UGu2SJuh6bm1uq+oqiMPPoTEbWNd97HBurdkT/5z/W\njDj36NQJQkLg2DHzdQfWHMiG8xt4FPMo9UGNRu1FnjtXV/Rh4cL89fw5N2WynhAiC0mCLITIFZJ3\nzquaPDkvPh4WLlS3fTNg9/Xd5LHJQ7NSzcyee/lyqFsX/PysGXHuYWcHI0da1otcNH9ROlTowOIT\niw1X6NIF/voLrlwB1Ml6n8hkPSFEFpMEWQiRKyy+e5d+ybvmAWzerO6HXKWKwfrJvcfmFptP3lsk\nCzaXeqX17g0HD+ryWpOG1x3O/OPziUuMS33Q0VE92YIFuqK+xYvzo0zWE0JkIUmQhRCvvNsvXnD0\n2TP9yXmzZxvtPT57/yx/P/ibj6p8ZPbcW7aoCyzUr2+taHMnJycYNMjoRoV6qhStQqUildhwfoPh\nCgMHwurV8Pw5ABWdnCiTNy87ZLKeyEEKFSqERqORx/+zd9/hUVRdAId/6b2RhPQQEAgdUXqRiBQB\nRbAAyqeoiCiCBVREkWKjCYIgCtIsiIgioAJKi3RCD70G0kghPaTvzvfHZVNIBdMg532eeWZ25s7k\nbsrsyZlbquni5OT0n36+EiALIe54hs551obOefv3qw56jz5aZPnZe2czqu0ozE3MS7yupsH06aoT\nmijdqFHwyy8QFVV62THtxzBr76yiJw7x9YWAADVsyA0ve3iwSJpZiGokPj4eTdNkqaZLfHz8f/r5\nSoAshLij5ej1LLm5c96XX6porYih3SJTIll3dh2vtH6l1Gtv26Y66D3ySHnW+O7l6grPPKO+/aV5\nuP7D6DU9f1/8u+gCo0ernpE3AugnXV05kJzMZemsJ4SoBBIgCyHuaBvi4/G1tKS5oXNeZKQalLeY\nod3m7pvL/5r/j1pWtUq99vTpajplY7lTltnYsWrwkJSUkssZGRkxrtM4pu+eXnSBrl3VPzhb1cx7\nVtJZTwhRieS2L4S4oxXqnPfNN/D00+DoWKhsYkYii48sZmzHsaVe98gROHVKZURF2dWrB927qyC5\nNIOaDiIkIYT94UWMD2dkpJ4CzJ+fu2u4p6d01hNCVAoJkIUQd6zQjAz2JScz0NA5LyMDFi5Uj+eL\n8M3Bb+jToA9+jn6lXnvGDDVrnoVFOVa4hnjnHTUtd1ZWyeXMTMwY02FM8Vnk//0Pdu2CkBAAmtrY\nUM/Skr+ks54QooJJgCyEuGMtvnqVZ9zc8jrnrVoFrVpBo0aFymbkZDB3/1ze7Vh6j7sLF2DzZnj5\n5fKucc1w//3qR7ByZellh7Uaxq7QXZy9drbwQRsb1VQm38QhL3t6Smc9IUSFkwBZCHFHyu2cZ2he\noWlqaLc33iiy/HdHv+N+j/tp7lb0uMj5TZsGr72mZj0Wt2fcOJg5E0prDWFjbsNrbV5j5p6ZRRcY\nPRq++w6SkgB4ytWVoORkrmRklHONhRAiT6kB8qZNm2jUqBENGjRg+vTCj8FWrFhBy5YtadGiBZ06\ndSI4OLjM5wohxO36Kz4eP0tLmhk65+3eDdevQ69ehcrm6HOYsWcG73V+r9TrhoaqsY+LGUJZlFH3\n7mqGvQ0bSi87qu0o1pxeQ0RyROGDPj7QsycsWQKoznpDpLOeEKKClRgg63Q6Ro0axaZNmzh16hQr\nV67k9OnTBcrUq1ePHTt2EBwczIcffsjLN55JluVcIYS4XQsjI3k5/9Buc+eqbGMRQ078duo33G3d\n6ezbudTrzpgBw4eDs3N51rbmMTJS40eXZfppZ2tnnmv5HHP2zSm6wFtvqZ9vTg5wY2a9q1fJkc56\nQogKUmKAHBQURP369fHz88PMzIzBgwezbt26AmU6dOiAg4MDAO3atSM8PLzM5wohxO24nJ5OUHIy\nT7m63thxWQ1aPHRoobKapjF993Te61R69jgqCn76CcaMKecK11BPPQXh4bBzZ+llx3QYw9KjS0lI\nTyh8sG1bNXnI778D0MzWFj9LS/6QznpCiApSYoAcERGBj49P7mtvb28iIop4BHbDkiVL6NOnz22d\nK4QQZbXw6lWec3fP65w3dy4MGwZ2doXKbr60mSxdFn0b9i31urNmwbPPgptbede4ZjI1hfffh48+\nKr2sr4MvfRv05euDXxddYMwYmD079+VILy8WREaWU02FEKIg05IOGhkZlflC27dvZ+nSpezevfuW\nz508eXLudkBAAAEBAWU+VwhRs2TodCy9epVdrVqpHYmJqhNXvv4P+U3bNY13O72LsVHJXS6uXVPN\nXIu5jLhNzz0Hn3wCe/ZAx44ll32307t0/747b7V/Cyszq4IH+/WDt9+GvXuhQweedHVlzIULnE1L\nw9/auuLegBDijhcYGEhgYOAtnVNigOzl5UVYWFju67CwMLy9vQuVCw4OZvjw4WzatAknJ6dbOhcK\nBshCCFGSX2NjudfWlgaGoOjbb6FPHyji/rInbA+XEi7xdLOnS73u3Lnw5JNFXkb8B+bmeVnkTZtK\nLtusdjPaebdjyZEljGo7quBBExM1QskXX0CHDlgYGzPMw4OvIyKY06BBxb0BIcQd7+bk65QpU0o9\nx0jTbkx0X4ScnBz8/f3ZunUrnp6etG3blpUrV9K4cePcMqGhoXTr1o0ff/yR9u3b39K5oDLNJVRB\nCCEK6Hj4MON8fXnMxUXNRFGvHvzxhxr/+Ca9V/RmQKMBvHx/yQMaJyXBPfdAUJC6nChfWVlQvz6s\nXg3t2pVc9mDkQQasGsCF0RewML1plpaUFKhbFw4eBD8/rmRkcN/Bg4R26ICNobmNEEKUoiyxZ4nP\nHE1NTZk/fz69evWiSZMmDBo0iMaNG7Nw4UIWLlwIwEcffURCQgKvvvoqrVq1om3btiWeK4QQt+tI\nSgrhmZn0rVVL7fjlF/D3LzI4DooI4mTMSYa2LNxx72bz50Pv3hIcVxRzcxg/HsqQtKG1Z2tauLVg\n2dFlhQ/a2cELL8CXXwJQx9KSzg4O/BQdXc41FkLUdCVmkCulApJBFkKU0fCzZ/GztOSDOnXUxCCt\nWsHUqSq6vcmjKx+ld/3ejGwzssRrJiWp7OauXSrWFhUjM1N9n9esgTZtSi67L3wfg34dxPnR5zE3\nMS94MDQU7r1XjVxib88/8fG8e/EiR1q3vqW+L0KImus/Z5CFEKK6SMzO5tfYWF4yzJy3bRtkZ8PD\nDxcqe/jqYY5cPcKLrV4s9bpz5qgmzBIcVywLCzW7XllGtGjv3Z5GLo34/tj3hQ/6+qrJYBYvBqC7\nkxNpej17k5PLucZCiJpMMshCiDvC3PBw9icn81OTJmpH795qoN0XCwfBA1YN4EG/B3m9XcnT4cXH\nQ8OGsH+/aoMsKlZGhsoir1sH999fctndobt59vdnOTvqLGYmZgUPHjoE/fvDxYtgbs4XYWEcTElh\nheF3QwghSiAZZCHEXUHTNBZERDDSMHPeiRNw9CgMGVKo7LGoY+wP38/w+4aXet3Zs1WcJcFx5bC0\nVLPrlaUtciffTtR1qsuK4ysKH7z/fmjUSM3qAjzv7s6G+HhisrLKucZCiJpKAmQhRLW3NSEBS2Nj\nOt2YtZPZs+G119Rz+5t8svMT3u74duFxdG9y7Rp8/TVMmFARNRbFefllOHJEZe1LM/GBiXy681Ny\n9DmFD44bp+ax1utxMjPjCRcXFl+9Wv4VFkLUSBIgCyGqvQWRkYz08lKdsMLCYO1aGFm4892JmBPs\nvLKTEfePKPWaM2fCwIHg51cBFRbFsrSEiRPV2Mil6erXFU87T34+8XPhgw89BNbWaog/1Mx630RG\nopMme0KIciABshCiWgvPyCAwMZEhtWurHbNmqXbHhqHe8vlkxye81f4tbMxtSrxmdLSaX+SDDyqi\nxqI0zz+vBqPYurX0shMfmMjHOz4unEU2MlJZ5GnTQNO4z84OLwsL/oyLq5A6CyFqFgmQhRDV2jeR\nkQxxc8PW1BRiY+H772HMmELljkUd498r/xaega0IU6fC//4ns+ZVFTMz+PhjlUUuLeHbrW43PGw9\n+DH4x8IHH39ctZXZuROA1zw9WRARUQE1FkLUNBIgCyGqrXSdjkVXrzLay0vt+PJLNXKFobNePhO2\nT2B85/GlZo9DQuCHHyR7XNUGDlRjI69bV3I5IyMjPu32KZMDJ5OZk1nwoIkJvPMOTJ8OwFO1a3M0\nNZVzaWkVVGshRE0hAbIQotr6KSaGNnZ2NLS2huRk1avu3XcLldsbtpfg6OAytT3+8EMYPRrc3Cqi\nxqKsjI3h009VJ0mdruSynXw70bR2UxYfXlz44HPPqV5/wcFYGBsz3MOD+ZJFFkL8RxIgCyGqJU3T\nmBsezhuGdhDffAM9exY5JtsH2z5g4gMTsTAtPKpFfkeOqHavY8dWRI3FrerTBxwcckdrK9EnD37C\npzs/JS37puywpSW88YYa0QLVWe/H6GgSs7MroMZCiJpCAmQhRLUUmJhIjqbRw8lJzTAxZw68916h\nclsvbSU8OZyh9w4t9ZrvvacylnZ2FVFjcauMjFR78IkT1Y+4JK08WtHJtxPzg+YXPvjKK7BxI4SE\n4GlhQe9atVgaFVUxlRZC1AgSIAshqqW54eG8bhjabflyNTlEixYFymiaxvvb3uejBz/C1Ni0xOtt\n2QKXLqlxeEX18cAD6sc6b17pZT8K+IjP93xOUkZSwQMODipInjYNgDe8vfkyPJwcvb4CaiyEqAkk\nQBZCVDuX0tPZlZTEs+7ukJOjHp+PH1+o3B/n/iAjJ4OBTQeWeD29XjVd/vRTNYKCqF5mzFDLtWsl\nl2vs2pg+Dfowe+/swgffegt+/RVCQ2lrb4+XhQXrZcg3IcRtkgBZCFHtzI+IYJiHBzYmJvDzz+Dj\nAx07FiiTo8/h/a3v88mDn2BsVPKt7OefwdRUDYAhqh9/fxg8uGxTUE/qOomvDnxFdGp0wQMuLjB8\neIEs8tzw8AqorRCiJjDStKqddsjIyIgqroIQohpJycnBb98+jrRuja+pKTRtCgsWqJnT8ll8eDE/\nBv/I9qHbVTOMYqSlQePGavjkrl0ruvbidl27pn5OO3dCo0Yllx3791jSstP4+pGvCx6IjVXRdnAw\nOZ6e1Nu/n7XNmnGfNDoXQuRTlthTMshCiGpleVQU3Zyc8LW0VKnf2rWhW7cCZVKzUpm4fSKf9/y8\nxOAY4PPPoV07CY6rOxcXNTFeEaP4FfLBAx/w6+lfORV7quABV1cYNgymTcPU2JhRXl6SRRZC3BbJ\nIAshqg29ptEoKIil/v50trWFJk3U8G43BciTAydzPv48Kx5fUeL1wsLg3nvh0CHw86vAiotykZmp\nsshLlsCDD5Zcdvbe2Wy/vJ0/nv6j4IHoaHWR48eJr12b+vv3c6pNG9wtSh4CUAhRc0gGWQhxR/kz\nLg57ExM6OTjAypXg7l4oUrqacpV5QfP4tNunpV7v3XfhtdckOL5TWFioJsRjxpQ+echrbV7jZMxJ\ntodsL3jAzQ1eeAFmzKCWmRmDa9fm68jIiqu0EOKuJBlkIUS10eXIEUZ5eTGoVi2VPV64sFCAPHz9\ncJysnJjRY0aJ19q5E555Bs6cAZuSZ58W1YimqR/5wIEwcmTJZVedWMWMPTM4MPxAwY6aUVHq9+fk\nSc7Y29P16FEut2+PlYlJxVZeCHFHkAyyEOKOsS8pifDMTJ5wcVFTq3l4QEBAgTInYk6w/tx63u/y\nfonX0unyJleT4PjOYmQE8+fD5MkQE1Ny2YFNB2JmbMZPx2+ais/dXU1BPXMmjWxsaGtvz/fR0UVf\nRAghiiAZZCFEtfDEiRMEODoy2t1dtSFdtKhA9ljTNHqv6E3v+r15o/0bJV5r8WI1t8jOnSrgEnee\nsWMhIQGWLi253K7QXQxZM4TTr53G2sw678DVq2oElBMn2GltzYtnz3KmbVtM5BdCiBqvXDLImzZt\nolGjRjRo0IDp06cXOn7mzBk6dOiApaUls2bNKnDMz8+PFi1a0KpVK9q2bXuL1RdC1BTn09LYkZTE\nix4esGIFeHoWalqx/ux6QpNCGdmm5Ofu166p6aS//FKC4zvZpEnw99+wd2/J5Tr7dqaDdwem7ZpW\n8ICHB7z4InzyCZ0dHHAxM2NtaTORCCHEDSVmkHU6Hf7+/mzZsgUvLy/atGnDypUrady4cW6Z2NhY\nrly5wtq1a3FycmLs2LG5x+rWrcuhQ4eoVatW8RWQDLIQNd6r587hYmbGx56eahzbH3+Ezp1zj6dn\np9N0QVMWPbqI7vW6l3itF14AR0f44ouKrrWoaD/9BDNnwsGDUFLz4fDkcO795l6ChgdRz6le3oFr\n19SgykFB/G5nx9TQUPbfd1+pQwMKIe5u/zmDHBQURP369fHz88PMzIzBgwezbt26AmVcXV1p3bo1\nZsXM3yrBrxCiJDFZWayKiWGUl5fqlNesWYHgGODzPZ/TyqNVqcFxYCBs3QoffVSBFRaV5umnwcFB\njfRXEm97b8Z0GMOYv8cUPODiAqNHw6RJ9HNxISknhx1JSRVXYSHEXaPEADkiIgIfH5/c197e3kRE\nRJT54kZGRnTv3p3WrVvz7bff3n4thRB3ra8iInjK1RW3zEz47DO15HMl8Qpz9s9hVs9ZxVxBycyE\nV15RTStk4rS7g5ERfPWV6rBX2khtYzuM5UTMCf6+8HfBA2PGwObNmJw4wds+PswIDa2w+goh7h6m\nJR38r4+hdu/ejYeHB7GxsfTo0YNGjRrRpUuXQuUmT56cux0QEEDATT3XhRB3pzSdjq8jI9nVqpWa\n8q57d2jRokCZtze/zettX8fP0a/Ea82YoVpn9O9fgRUWla5pU3j1VTXk2++/F9+u3MLUgjkPz+H1\nTa9z/NXjmJuYqwN2dmqKvg8/5NnffmPi5cscT02lua1t5b0JIUSVCgwMJDAw8JbOKTFA9vLyIiws\nLPd1WFgY3t7eZb64h4cHoJphDBgwgKCgoFIDZCFEzbEsKopODg40vH4d5s6FAwcKHN96aSsHIw/y\nff/vS7zO+fPq9MOHK7K2oqp88AG0agW//gpPPVV8uUcaPsLXB79m7r65vNPpnbwDr74Ks2djeeAA\nr3t58XlYGN/l60sjhLi73Zx8nTJlSqnnlNjEonXr1pw/f57Lly+TlZXFqlWr6NevX5Flb25rnJaW\nRkpKCgDXr1/nn3/+oXnz5qVWSAhRM2Tr9cwKC+MdHx+YOlU1OK2X18EqMyeTURtH8UWvL7Aysyr2\nOno9jBgB778Pvr6VUXNR2Sws1NB9r78OcXEll53Taw7Td08nNClfUwpLSzUsxvvv84qHB3/ExRGW\nkVGxlRZC3NFKHQd548aNvPnmm+h0OoYNG8b48eNZuHAhACNGjCAqKoo2bdqQnJyMsbExdnZ2nDp1\nipiYGB5//HEAcnJyGDJkCOPHjy9cARnFQoga6fuoKJZFRbG9Vi2VHjx5Uk3wcMOUwCkciTrC74N+\nL7G514IF8P33sHt3ySMdiDvfG29AUpIa47okH//7MUGRQawfvD7vdycnR3UAnT2bsQ0bogGz69ev\n6CoLIaqhssSeMlGIEKLS6TSNpkFBfNWwIQ+98YZK/X7ySe7x07Gn6bKsC0dfOYq3ffHNui5dgrZt\nYdcuNZqXuLulpqoYd+FC6NWr+HJZuixaLWzFlIApPNnkybwDf/wB48YRceAAzY8c4Wzbtriam1d8\nxYUQ1YpMNS2EqJZ+i43FycyMbufPw5YtqhPVDXpNz4g/RzA5YHKJwbFer+aBeO89CY5rCltbFRy/\n/LLKJBfH3MScRY8s4o1Nb5CYkZh34JFHwN0drx9+YFDt2swOD6/4Sgsh7kgSIAshKpVe0/jkyhUm\n+PpiNHYsfPxxgXHZlhxeQpYui1dbv1ridRYsgKwseOutiq6xqE569YLevdXwxiXp5NuJfg378d6W\n9/J2GhnBrFkwZQrvOTmxKDKS+Ozsiq2wEOKOJAGyEKJS/RkXh4mREX0CA9Uz8+efzz12NeUqH2z7\ngG8f/RYT4+IbFJ87p8bGXbZM2h3XRLNmwb59sHp1yeWmdZ/Gn+f+ZFforrydrVrBww9TZ/ZsBri4\nMEeyyEKIIkgbZCFEpdE0jXaHDzPO3Z0nunSBJUvgwQdzjz+1+ika1mrIpw99Wuw1srKgY0c1pfRr\nr1VGrUV1FBQEjz6qhvbz8iq+3JrTa/hg2wccGXEES1NLtTMiAlq04OL+/bSLiuJCu3Y4FjMbrBDi\n7iNtkIUQ1crmhARSdToGrFihJgTJFxyvOrGKkzEnmfDAhBKvMXEieHioiSNEzdW2rfoH6fnnVXv0\n4gxoNIBmtZsxcfvEvJ1eXjB6NPdMmkQfZ2fm3cIMsUKImkEyyEKISqFpGg8cPcoIGxv+17Ej7NkD\nDRsCqmnFvQvv5c+n/6SNV5tir7F9OwwZAkePQu3alVVzUV3l5ECXLjB4sBoCrjix12Np+U1Lfnnq\nFzr7dlY7r1+HRo04u3IlnY2MuNSuHXamJc6dJYS4S0gGWQhRbWxOSCA2K4unZ86EZ5/NDY41TWP4\nH8MZcf+IEoPj+Hh47jnV7liCYwFgago//KBGCCxpFkVXG1cW9F3A82ufJzUrVe20sYGZM/EfNYru\nDg58JVlkIUQ+EiALISqcpmlMCAlhSnY2Jhs2qB52Nyw7uozIlMgSm1bo9TB0qJpmuKTxb0XNU78+\nzJ8PAweWPPRb/0b96eTbiXGb84YUZNAgqFWLD/fuZXZ4OMk5ORVfYSHEHUECZCFEhfszLo4MnY6n\nXn8dZs4EBwcALideZtyWcXzX/zvMTYqfsGHmTLh2DaZNq6waizvJoEHw8MOq42ZJT03nPjyXP879\nweaLm9UOIyOYN48m779PLysrvpARLYQQN0iALISoUHpN48OQED4+dQpjR0d4+mkAdHodL6x7gbc7\nvE1zt+bFnh8YCF98Ab/8AjLpmSjOrFkQFgZz5hRfxtHSkcX9FjNs/TDi0+PVzqZNYehQJi9fzrzw\ncOJkXGQhBBIgCyEq2G+xsZjpdPR75x31LNzICICpu6aiaRpvd3y72HOjolSnvO++Ax+fyqqxWi5L\n6QAAIABJREFUuBNZWKh/oqZOhb17iy/X856ePNH4CYatH5bXSWfSJO757Tee0OuZERpaORUWQlRr\nEiALISqMTtOYePkyn6xdi9GwYdCkCQA7r+xkftB8Vjy+otgJQbKy1KPzl16SdseibOrWhcWL1e9N\ndHTx5aZ1n0ZoUihfHfhK7bCzg5kz+XDiRBZfvcrVzMzKqbAQotqSAFkIUWF+io7GOS2NnitXwocf\nAhCXFseQNUNY0m8JXvZFz/CgaWoqYQcHmDSpMmss7nT9+qm2yAMGQHFxroWpBaueXMWUf6dwNOqo\n2vn003ibmDA0PJzPJIssRI0nAbIQokJk6fVMDgnhk1mzMJo7F2xs0DSNF9e/yFNNnqJvw77FnvvV\nV2qY5BUrwFjuUuIWTZoEnp7wyivFd9qrX6s+cx+ey6BfB6mh34yMYNEi3nv/fX66epUrGRmVW2kh\nRLUiHz1CiArxdWQk/uHhBFhbQ//+AMwLmkdkSiRTu08t9rwtW9S4tuvXqyffQtwqY2PVbv3oUZg9\nu/hyzzR/hs4+nXltw405y++5h9ojRzLy33+ZcvlypdRVCFE9yUx6Qohyl5idjf+ePWwdO5Zmf/0F\nbm7sCdtD/5/7s3fYXu6pdU+R550/D507q85WXbtWcqXFXSc0FNq3hyVLoHfvostcz7pO28VteaPd\nG7x8/8uQk0NSQAD+kyfzT/v2tLC1rdxKCyEqnMykJ4SoElNDQnh0zx6avfkmuLlxNeUqA1cPZNlj\ny4oNjq9dg0cegY8+kuBYlA9fX/j1VzXJzLFjRZexMbdh7aC1TNg2gb1he8HUFIf58/lw+XLePnVK\nEjhC1FASIAshytWVjAwWX7nCR0eOwJAhZOmyeHL1k4y4f0Sx7Y6vX1fB8RNPwIgRlVxhcVfr2FGN\nLti3LxTXaqKBcwOWPraUp1Y/xdWUq3Dvvbxcpw6hERFsio+v1PoKIaoHaWIhhChXz+7dS90VK/ho\n3Djw8WHkXyOJTIlkzaA1GBsV/p88O1s1UXZ1hWXLcodJFqJczZunOn/u2gUuLkWX+ejfj/jn4j9s\nG7oN82w964cOZfxLL3HsoYcwld6iQtw1pImFEKJSHY6PZ2tMDO+0aAE+Piw9spRtIdv4fsD3RQbH\nmqYyxpoG334rwbGoOKNHq6HfHnlEPbEoyoQHJuBs7cxbm94CS0seffttap89y5LTpyu3skKIKldq\ngLxp0yYaNWpEgwYNmD59eqHjZ86coUOHDlhaWjJr1qxbOlcIcffQNI13tm9nUlAQdsOHs+PKDt7b\n8h6/D/odewv7Is+ZMAFOnIDVq8HMrJIrLGqczz4Df381kUhRM0obGxnzff/v2XZ5GwsOLMCoTRs+\nz85m8qVLpGRlVX6FhRBVpsQmFjqdDn9/f7Zs2YKXlxdt2rRh5cqVNG7cOLdMbGwsV65cYe3atTg5\nOTF27NgynwvSxEKIu8VvO3Yw+fJljvTqxUWTRB5Y/gArHl9B93rdiyz/ySfw00/w77+qeYUQlSE7\nGx5/HCwtYeVKMDUtXOZSwiU6Le3Ekn5L6FO3J899+SU+Xl58OmhQ5VdYCFHu/nMTi6CgIOrXr4+f\nnx9mZmYMHjyYdevWFSjj6upK69atMbsp/VOWc4UQd4e0hATGxsQwz9WVBFtj+v7Ul8+6fVZscDxj\nBvzwA2zdKsGxqFxmZmpki9RUeO450OkKl6nnVI/fB/3O82uf5+i1E3zWpw8Lray4GBxc+RUWQlSJ\nEgPkiIgIfHx8cl97e3sTERFRpgv/l3OFEHeW6cuW0S4tjfY9HqT/qv4MbDqQYfcNK7LsF1/AokWw\nbRt4eFRyRYUALCxgzRqIjYUXXyw6SG7v3Z6v+nzFoysfBU9b3snM5PVdu9CKm79aCHFXKTFANvoP\nPWb+y7lCiDtHyOrVfNWwITMe6cvQtUPxsffhk26fFFl2/nw1msC2beDlVckVFSIfKytYt05NJvLy\ny6DXFy7zVNOnGN12NI/89Agv9nmIi+7u/DFnTuVXVghR6YpofZXHy8uLsLCw3NdhYWF4e3uX6cK3\ncu7kyZNztwMCAggICCjT1xBCVLFz5xgTEsKbnTszbc8EolOj2fS/TUWOWDFjBnzzjWpW4etbBXUV\n4ibW1vDHH2pki+eeU8MM3txZ9J2O7xCaFMoTv/Tn866LGa3T0X3tWqxvTJ8uhKj+AgMDCQwMvKVz\nSuykl5OTg7+/P1u3bsXT05O2bdsW2dEOVJBrZ2eX20mvrOdKJz0h7lDp6Wx6/nleGzaMx43/JTDk\nH7Y+t7XQiBWaBh98AGvXwubNkjkW1U96Ojz5pOqwt2qV6sCXn17T89zvz5GQkYC197s0/mU1H40d\nC3XrVk2FhRD/SVliz1InCtm4cSNvvvkmOp2OYcOGMX78eBYuXAjAiBEjiIqKok2bNiQnJ2NsbIyd\nnR2nTp3C1ta2yHNvp5JCiOrn+iuv0KxPH7o5RrL3+JfseGEHLtYFZ2DQ69X4s/v3w6ZNxU/QIERV\ny8pSWeTYWPXPnJ1dwePZumye+OUJjCxrs9tuMPs+/5z669apBs1CiDtKuQTIFU0CZCHuQN9/z7tn\nzrCzZxuijo1h1wu78LIvmBrOyoJhw+DKFfUY28GhiuoqRBnpdPDqqxAcDH/+WfgfuoycDHqv6E26\nWz8co5zYeOQIRnPnVk1lhRC3TWbSE0KUv6NHOTpvHgu7B3A5+AM2P7u5UHCckAAPPwwpKSpzLMGx\nuBOYmMDChfDQQ9ChA5w7V/C4pakl6wevRxf+C4e9HFgRG6sG8xZC3HUkgyyEKLvYWHRt29J03kxi\n4tay/5FJNHBuUKBISAj06aMC5M8/V0GHEHeaJUtU2/nVq6FLl4LHkjKS6Lz6RS67D+PCK6NxW7UK\nWreumooKIW6ZNLEQQpSfrCzo0YO3+3RmflMfTnToTn3n+gWK7N8PAwbA++/DqFFVVE8hysnmzTBk\niBq7e8iQgseSM5NpsnEu7um1OPDuNIyCgmRgbyHuENLEQghRft58k62ORnxxf3s2tH6oUHD83Xdq\nuKxFiyQ4FneHHj3UmN0ffADvvVdwQhF7C3sO93qdky7uvP+/rmiPDwCZRESIu4YEyEKIUmnz5xO1\n4Tcee2kIE+rUoZt7XrOKrCwVEH/6KQQGqiBZiLtFs2Zw4IBaeveGuLi8Y7WtHFhzb0e+eGggmy3i\nyHl5uBrXUAhxx5MAWQhRIt26tSRNGsdDkwbT0rMlk+o3zz0WFQXduqmRKoKCoGnTKqyoEBXE1RX+\n/htatlRNjY8ezTvW29WD530a8Mo7YwkJ/J30jz6suooKIcqNBMhCiGJl7N1J6rODGDnuQaIbPMUP\nTZpjfGMa+W3bVLDQo4eastfRsYorK0QFMjWFmTNh2jT1O//tt3nJ4tn1G2Lm0opxs98mft4MEr75\nomorK4T4z0qcaloIUXMlnDqMrnd3loxsz/luk/nEw4N6VlZkZ8PkybB8uZqat2fPqq6pEJVn0CBo\n0QIGD1ad+BYtAkdHE35s3JhHcnL44csMXhrxNqGO1vgOHlHV1RVC3CbJIAshCjl74l8SA9qze0gX\nEocvxdXcnBGenly+DF27wqFDcPiwBMeiZmrcWI3Y4uYGrVrB3r3Qxt6e17y82N50MPvmjcf6pVfZ\nvUYmERHiTiUBshCigM0HVqHr8RBJT/TF9pPVfB8dzTL/RixfbkTbtvDEE7BhgwoOhKipLC1h3jyY\nMwf694cPP4S3PXxJzMnhUvdXiP3iU+55YQzLVo2XoUyFuAPJOMhCCAA0TWP+1ql0enEy7g8/gdm8\n5dx76BCzXBvxw5u1iIxUzSpatqzqmgpRvVy9CiNGwOXL8PHSdIZnHmZD8+bU/e4bsiZN4Mup/Zk8\n7AcsTC2quqpCCGQcZCFEGaVkpvDcT0/R/rXPaNDtSdy/WcHzZ89yb4w7ozvWol07NUqFBMdCFObh\noTqqvvsuDO9jxQOHGzDw5ClMXnkLpynTeWvCnwyc1Y4riVequqpCiDKSDLIQNdyJmBMM+fFxflyR\nTuOGnTD9cQXjgiNYeCoWv9mt+G6psQTGQpSRIZu8+/7zNA/IZPsDTWHuXJJmfkzAC0ZMHfoDvRv0\nrupqClGjyVTTQogS/XDsByb8+RZ719fGs34r0r/5jpeXpLCizineC72fKSMtMTOr6loKcWfRNPhp\ntZ4Xrh+mVYw7f7zgTe3vPydtwVweeDaHh7sOY0rAFEyMTaq6qkLUSBIgCyGKlJSRxKiNozh5YS87\nf7XDpmkrNgz4llc/yiZm8mGW1W/MYH+nqq6mEHe0Y9fS6XjoMGafNmXq046MSJqBfuFXvPCaNyG1\njPhhwA/Udapb1dUUosaRNshCiEJ2XNlBy29aUjvTjAOrncis24FHoxcz+l2wmH6Sj5t7S3AsRDlo\n6WLFmjaNMfv4FMs2ZHD/qne58Nh4vp9zhZfM29N2cVu+O/qdJImEqIYkgyxEDZGZk8nkwMl8d+w7\nvm87la6vzCbQ+CGGRM1i/AdwtMdZ0tGxqkkTjG7MlieE+O9mhYWxIjqasZdbMek9E162/YkxYW9x\n6cdZPB4yjUYujfjmkW9wsXap6qoKUSNIBlkIAcDu0N3cu/BezsSdYf/9K2n96EQ+u/wM//Saxdlz\nRmQOCOV4eipL/f0lOBainI3x9qapjQ1/ND7DyZMaFi88wwu6xXg8/hb/2EyljkMdmi1oxk/Hf5KE\nkRDVhGSQhbiLJWcmM37LeH4/8zvTA+ZhtMCJXssGs7rjHPr8+Ax+frA6JoYxFy+y77778LKQcVqF\nqAjpOh1djx6ld61aTKlbl8REWDlqF4//9CTbH5iMzRf38f6+Yfg6+PJ136/xdfCt6ioLcdeSDLIQ\nNZSmaaw/u55mC5qRkpHJsIyT7Hkwg34rBpO+bBUjd6ngeF9SEiPPn+ePZs0kOBaiAlmZmPBH8+b8\nGB3N4shIHB3h1R87Y7p3Fw8Ff0Foh1V0OR5EU/uO3LfwPr7c/yU5+pyqrrYQNZZkkIW4y5y9dpY3\n/36T89cu0SlxAX/PD2Cx63h6Jq/GfON6aN4cgAtpaTxw9CiLGjbkERdp+yhEZTiXlsYDR46wtFEj\n+jg7q53x8WQ9+gTnYhzofe1HOg0JJ6TpK2QYJTD34bkE+AVUaZ2FuNuUSwZ506ZNNGrUiAYNGjB9\n+vQiy7z++us0aNCAli1bcuTIkdz9fn5+tGjRglatWtG2bdtbrL4Q4lYkZybz9j9v0/7bTiQe7s61\nj47jdLEVFxv25hHPw5gfO5gbHEdkZtIjOJgpfn4SHAtRiRpaW/N7s2YMPXOGg8nJametWphv/5tm\nXV0IcWtHB70RFydux2LfBAavGsrA1QMJTQqt2ooLUcOUGCDrdDpGjRrFpk2bOHXqFCtXruT06dMF\nymzYsIELFy5w/vx5Fi1axKuvvpp7zMjIiMDAQI4cOUJQUFDFvAMhargcfQ6LDn1LvdmNWP1HIibf\nnKSn7Vgu/nqGObvbYNOhBWzaBDeyVdeysuhx7Bivenoy3NOzimsvRM3TwcGBxf7+PHL8OCdSU9VO\nc3P49ltMx77JG792IXzOGp5v+xTWS0+zZ11Tms27jwlbJ5GcmVy1lReihigxQA4KCqJ+/fr4+flh\nZmbG4MGDWbduXYEy69evZ+jQoQC0a9eOxMREoqOjc49L8wkhKoZe07P8wC94ftqEMUtWYfvHesY3\nXUzoqdpM8VqE88CH4KOP4PPPwdQUgJScHPocP04/Z2fe9ZVOQEJUlcdcXPiifn16BgdzNi1N7TQy\nguHDYcMGLD8Yy8iQdzgfbM68JybhH3iY2Usv4zm1AZM2fkFGTkbVvgEh7nIlBsgRERH4+Pjkvvb2\n9iYiIqLMZYyMjOjevTutW7fm22+/Lc96C1FjaZrGvI2bqD2hNS8tnUmTkAX8OXALIbtb88qgBKyf\nHwgLFsDOnTBkSO55yTk5PBwczH22tkytV68K34EQAuBpNzc+q1uX7seOcSk9Pe9A69Zw6BCcPIlJ\n184MaH6BA1t8CRr/HY8mbGXqyn+pNakhb32/hKwc6cgnREUoMUAu63ioxWWJd+3axZEjR9i4cSNf\nffUVO3fuvPUaCiEAiIjU8+L09di+2YGx/4yhl9UEwicFEbi0OwEBYLRnN7RqBR4esG8fNGqUe25i\ndjY9jx2jpa0tCxo2lLGOhagmnvfw4ANfX7odPcrF/EGyszP8+Sc88wx06ABLl9KsqcbKuc2IX7CW\nNzx/YXHQCqzH+dN7wkKCT2ZW3ZsQ4i5kWtJBLy8vwsLCcl+HhYXh7e1dYpnw8HC8vLwA8LzRvtHV\n1ZUBAwYQFBREly5dCn2dyZMn524HBAQQEBBwy29EiLtRejr89nsOMzf8wgmnqTjZmfNu5/f54PEB\nmJoY5xX68EP48UdYtAj69StwjYTsbHoGB9PB3p659etLcCxENfOKlxfGRkZ0PXKEv1u2pKmNjTpg\nbAyvvw7duqmnQX/9BQsXYuviwtTX2jOVbXy3fTdTtn1Gq+8+wuvKWN7s8jJDn7Y1dDkQQgCBgYEE\nBgbe2klaCbKzs7V69eppISEhWmZmptayZUvt1KlTBcr89ddfWu/evTVN07S9e/dq7dq10zRN065f\nv64lJydrmqZpqampWseOHbW///670NcopQpC1Djp6Zq2bp2mDX4uRbN+YIFmNe4ezX9aF23tiU2a\nXq8vWHjXLk1r2FDTBg3StJiYQteKzMjQWgYFaW+dP1/4XCFEtfJjVJTmtmuXdvDGZ2cB6ema9vbb\nmubmpmkrVmjaTX/PB8KOaA98OVCzmOCqmfeapHXvf1VbvlzTEhIqqfJC3EHKEnuWOg7yxo0befPN\nN9HpdAwbNozx48ezcOFCAEaMGAGQO9KFjY0Ny5Yt47777uPSpUs8/vjjAOTk5DBkyBDGjx9f6Poy\nDrIQKgm8aRP8+ius33URh+5fkVDnO7rW6cr4gLfoUuemJy/JyTBxIvzyC8yfDzf+1vI7m5bGw8HB\nDHN354M6dSRzLMQdYN21aww/e5ZVTZrwoJNT4QIHDsBLL4GXF3z9NdSpU+Dw2Wtnmb7jC1adXEWt\na48Qv3E0Xeu35amn4LHHoFatSnojQlRjZYk9ZaIQIapIdDRs2KCaGW7ZqqfuQ1vRt55HhPFeXrrv\nRUa2GUkdx4IffmgarFwJ77wDvXrBzJkU9Sx1X1IS/U+c4NN69Rjm4VFJ70gIUR62JyQw+NQpZtxz\nD0Pd3QsXyM5Wo9PMng3jxqlmGObmBYokpCew9MhS5u2fj1mWG47nRnNmzRO0u9+SRx6Bvn2hQYNK\nekNCVDMSIAtRjej1cOSIakb4559w7hx07HMFi3bLOaRbhrONE6+1eY1nmj+DtZl14QucOAGjRkFS\nkhqlokOHIr/O6pgYRp4/z/JGjegrDRGFuCOdvn6dvseP8z83N6b4+RX9BOj8eXjrLXUz+eILFfXe\nRKfX8df5v5gXNI/DkUfoYPsMZideZN/ae7G3JzdY7ty5UIwtxF1LAmQhqlhYGGzdmrfY2UGvvunY\nt13HvsylHIk+xNPNnmZYq2G08mhV9EUiImDyZFi7Vq1feQVMTAoV02saE0NC+DE6mt+bNaOVnV2F\nvjchRMWKzsqi3/Hj1LW0ZEmjRtgU8XcPwMaN8OabcM89KrPcpEmRxS4nXmb50eUsO7oMZytnergM\nw+jE02z7qxbnzkHXrvDQQ9C9OzRurIZlFuJuJAGyEJUsLg62b88LiOPjVQf0rt2yMG+8mR3xP/PH\n2T9o49WGF+99kf6N+mNlZlX0xRITYfp0NTLF8OHqUWpRbRJRYxz/7/RpEnNy+LVpU2pLKkiIu0K6\nTser585xKDWVNU2b0sC6iKdLAFlZqj/CtGnQpw9MmgR16xZZVKfXsS1kG0uOLGHjhY108e1Cb5/B\nWIU+xp7tdmzZoi7XrZsKmB96CGReIXE3kQBZiAqkaXDlCuzenbeEhKhHlQ89BF0fzCHRYQe/nPqZ\nNafX0MilEYObDebJJk/ibltEu0KDlBTV+ebzz9WQbZMnw03DK+Z3MDmZwadO0atWLb6oXx9z4xKH\nNxdC3GE0TWPR1at8GBLCt/7+PObiUnzhpCTVNnn+fBg8GCZMUGOjFyMlM4X1Z9fz88mf2XFlBz3q\n9WBQ08E0Nu3Dnn+t2boVtm0De3vo1ClvadJEjUInxJ1IAmQhylF2NgQH5wXDu3aBTlfwQ6NB01S2\nh/7N+nPr+evcX/g5+jG42WAGNh2Ir0MpKZj4eJg3T32wde+uPtiaNi22uKZpzA0P57PQUOY3aMDA\n2rXL+R0LIaqT/cnJDDx5kn4uLsyoVw+r4ppcAMTGqmzysmVqspGxY4vNKBvEp8fz++nf+fnkz+wP\n38+DdR/kMf/H6H1PX+LD3AokA+LioGPHvHtfmzZQXHJbiOpGAmQhbpNOB2fOwMGDeUtwMPj5FQyI\n77kHwpJD2XB+A+vPrmdX6C46+HSgX8N+POr/aOlBMUBkJHz5JXz7LfTvD++9V2r38sjMTIafPcu1\n7Gx+btKEulbFNNMQQtxVErKzGXn+PMdSU1nRuHHpfQ2uXoW5c9X95eGH4d13oWXLUr9OfHo8G89v\nZN3Zdfxz8R+auDbhMf/H6NuwL01dmxIdbVQgYD5+XN22WrdWy/33Q4sWYGlZTm9ciHIkAbIQZZCV\nBWfPwrFjcOiQCoaPHlVPJQ03+tat1SzO9vaQnJlM4OVANl/czD+X/iE+PZ6e9/TkMf/H6HVPLxws\nHUr/opoGe/eqjPHff6tZst5+u9CYpoVP0/ghOpq3L17kFU9PJtSpI00qhKhhNE3jp5gY3rxwgTe8\nvHjX17f0+0BSEixcCHPmQPPmakScPn2K7PB7s8ycTP698i/rzqxj44WNZORk0OOeHvSo14Pu9brj\nbutOZqYKkvMnFc6dUzPeG4Lme+9VD8UMEwUKUVUkQBYiH01To0ocP66W4GC1vnBBZYabN8+7kd93\nHzg6qvPSs9MJigji3yv/svnSZo5GHaWdVzt61OtBz3t60tK9JcZGZQxS09Jg9WoVGCckwOjR8MIL\n4FB6UB2akcFr588TlpHBskaNZJQKIWq40IwMXj13jtDMTL5t2JD2ZbiPkJkJP/+s+jlERalRcYYN\nA1fXMn/di/EX+efiP2y+tJntl7fj6+BLz3o9CfALoJNvJxwt1c0zPV3dZw0B87Fj6smcp6e637Zo\nodbNm0P9+mWK1YUoFxIgixpJp4PLl1VW+MwZtT55Ug0jbG2dd0M23KAbNy74GDAhPYHdYbvZFbqL\nnaE7ORZ1jKa1m/KA7wN0r9edLnW6FD1OcXEM2eJly9RUeR06wMiR0Lt32bI3ej2zwsKYHRbGG97e\njCtLtkgIUSNomsaqmBjeuniRx11c+KhuXZzNzMp28qFDakz1NWvUxEPPPQc9e4KpaZm/fo4+hwMR\nB9h8aTM7ruxgf8R+6jnVo7NPZ7rU6UIX3y542Xvllc9RSQlDgsKwREWpbHOzZuDvr7b9/VXgbGFx\nq98VIUomAbK4a2ma6tN2/nxeEGxYLl0CNzd1czXcaBs3VgHxzZ2/c/Q5nIw5ycHIgxyIPMCesD2E\nJIbQzqsdXXy70KVOF9p5tcPG/DaeCYaGwk8/wfLlqsIvvADPPqumiC3Te9T4My6OsRcv0sTami/q\n15e2xkKIIsVnZzMxJIRVsbG87+vLa15eZf9HOiEBVq2C779XN9Cnn1bB8r333vJgyNm6bI5EHWHn\nlZ3sDN3JrtBd2FvY08m3E20829DGsw33ut9baHjL1NS8REb++/nly+qWmf9+7u8PDRuqZnAyVrO4\nHRIgiztaZqYaRu3SpbwlJCRvG1SnkPw3TX9/ta+o3tR6Tc+F+AsciDjAgUi1HIs6ho+DT+6Nu513\nO1q5t8LMpIwZmJtdvqyyxKtXw8WL8Pjj8PzzKmt8C3fynYmJjL90icScHGbecw+9ZUY8IUQZnLp+\nnbEXL3IxPZ3p9erR38Wl6Fn4inP+PPzwg1qsreHJJ9V9rEWL24pGNU3jzLUz7Anbw4HIAxyMPMjp\na6dp6NyQ1h6taeOl7r3Najcr8r6bna3u94aA2ZAQOXdOBdV+flCvXuGlbl1p6yyKJwGyqLY0TfUZ\nCQ9X7YLDwtR2aGheEBwTAz4+6kZ3842vXj01Z0Zx9+uE9ASOxxwnODqY49HHCY4J5mTMSWpZ1cq9\nIbfxbMP9nvdjb2H/397IiROwYQP89puqfP/+8NRT8OCDUNZHnTccTknhw5AQTqWlMcXPjyFubphI\nikQIcYs2xcXx3qVLGBkZMbFOHR5zccH4Vu4lej3s2we//67ubUZGKlAeMADatftPDYYzcjIIjg4u\nkKwISQihoXNDWri1oHnt5rRwa0ELtxa427oXG+CnphZMmuRfLl9WXTvq1VN9n3191edJ/sXFRTLQ\nNZUEyKJKaJp6Ynf1qgp68wfBhkA4LEyVNdyovL3ztg1BsLd36U3hEtITOBt3lrPXznL62uncoDgx\nI5FmtZvRora6yTZ3a07z2s1xsip6JrpbkpICW7ao6V03bgRzc9WeuH9/CAi4pfZ7oDIs2xITmR4a\nyqnr13nX15cRnp5YSDtjIcR/oGka6+PimHL5MjpNY0KdOgxwccH0Vu8tmqYaDa9Zo5arV6FHD9Vu\nuWdP1evuP0rLTuNU7CmCo4NVYiPmOMeijgHkBs1NXJvg7+KPv7N/iYEzqPg+Kko9yLtypeBnkGFJ\nS1OfMzcHz97e4O6umnDUri2dB+9GEiCLcpWeDtHR6t4YFVV4MeyPjlZP5tzcCga++bd9fNSQaWX5\n7z1bl82lhEu5gfDZuLO52+k56TR0boi/sz+NXRrT3E1lHvwc/co+skRpMjJUJiUwUC2HDqkmE336\nqMC4YcPbSkNk6vWsiY1lVlgY1/V63vXx4Rk3NwmMhRDlytCfYVpoKBGZmbzm5cVLHh6OSEdIAAAg\nAElEQVQ43eITrlxhYfDPP2qIyi1b1M29Vy81N3XHjmUalaes9Y5KjcpNfJyKPZV778/WZ+fe+/2d\n/XMD5wbODcrcifr69aID54iIvM+z+Hhwds4LmA3rorZlopQ7hwTIoliaph5PxcbCtWt5S/7Xhu3Y\nWBX0pqWpm0D+G0VRr93c4Fb6kuk1PVdTrhKSGEJIQoha59u+mnIVHwefQjdCfxd/PGw9bq19XVkk\nJcGBA7BjB/z7rwqImzVT2eGuXaFLF7C1ve3LX0xPZ1FkJMujomhuY8Nob28edXa+tcefQghxGw4m\nJzM3IoI/4+IY6OrKix4etLWzu/37aE6Oul/+/be6Xx44oDqCdOkCDzyg1m5u5fsmgLi0uCKTJpcS\nLuFk5URdx7rUdapLPcd61HWqm/va294bU+NbGKUjRzX3MwTMV68W3ja8NjVVzTZcXYtf8h8va5JI\nlD8JkGsAvR6Sk1WThoQESEzM287/Oj6+cOBrapr3B2tY8r/Ov+3uXnKb3+JomkZSZhLhyeFEJEeo\ndYpahyaFEpIYQmhSKA4WDnk3Mce6+Dn65b72dfC9/U5zpcnKUoNzBgXlLeHhalaQzp1VUNyx438K\niEH1MP8tNpaVMTGcuH6doe7uvOzhQQNJOQghqsDVzEyWRkWxPCoKMyMjnnd3539ubnj+1zHVsrJU\nUmHHDti5U02z5+io5qLOP81eOWWZb6bX9ESmRHIp4VKRCZeY6zF423vj5+iHj70P3vbeeNl54W3v\nnbu4WN9ix0YKJp1uXgyfuzcvWVl5n7G1aqnPWCen0rcdHKTZx38lAXI1p2mq2UJyslpSUgquk5NV\nMrOk4Dc5WfXUdXTM+yPKv53/df7/YJ2d/9vjIEPgG50aTfT16Nx1ZEpkgSA4IjkCYyNjdROy9ypw\nM/Kx96GukwqGb2lc4dsVE5M3+KZhffq0GmizbVvV8aRtW2jS5JbbERclKSeHP+PiWBkdzc6kJHrW\nqsXTtWvT19lZmlEIIaoFTdPYnZTE8qgofrt2jWY2Njzu4sLjrq7UKY95ovV6NTLGgQNqtpADB1RS\nwstLBcstWqgndM2aqcbAFZxSzczJzE3OGJI24cnhhKeE535mpWal4mnnWSBodrd1x83GDTdbt9y1\ni7XLf2rKl5GRFzzn/2yPjy+4vnlfSorKPucPnB0dVeBsb6+Worbz77O1rdnZawmQy5lOp5oZXL9e\ncDHsS00tOsgtbl9KiurfZfiFtbMrvHZwKDrwNWw7OJRLLIemaaRmpRKfHk9cehxxaXHEpsUSnRpN\nzPUYFQTnC4RjrsdgYWJR4GbhZuOWe1MxBMFe9l7/bZSIW6XXqwZk58+rcYDOnlWjTAQHq/GC8k/f\nZFiX01hAmqZxJi2Nv+Li+Cs+noMpKTzg4MDTtWvzmIsLduXxgxJCiAqSqdezJSGBNbGxrLt2jbpW\nVvRzdqaHkxOt7exuvXNfcXJyVHLi4EF1fzYsKSlqLmpDwNy4sUpg+PqWzwddGaVnp+cmeQxLVGoU\nUalRBT4HkzOTcbF2KRg459t2tnbG2co5d+1g6VAufWN0OpU8yx9AJyTkxReG5FpJ2+npebHGzcG0\nnZ36WLS1VUtR20Xtu5M+4mpMgKxp6lFFerpaMjIKrvNvFxXg3hzoFncsM1NlXW1sil9uDnaLCnwN\n23Z25f8LlaPPITkzmaSMJJIyk0jMSFRBb1occelxudvxGQX3xafHY2psSi2rWjhbOVPLqhauNq6F\n/uBr29TO3b55oPdKk5WlmkFcuaIWQzB87pyaosneXnWca9hQtYUzTJvn5VXu/zJfTk9nR1IS/yYm\nsj0xkWxNo2+tWvR1dqabkxM28hxMCHEHytHr+TcpiQ1xcfyTkEBEZiYPOjrSw8mJro6O+Ftbl3+/\nifj4vNlCjh9XCY4LF1QnmDp11P28fv28db16qsd3eWS6b0OWLovY67EFgubo1OjcQNqQbDIknq5n\nXcfJyin3MzY3gM4XRDtbO+No6YiDhQMOlg44WDjgaOmIhWn5TieYk6OSejcHz0lJar8h6Xcr26am\nJQfTVlYqhrKyKn67tH0WFuXzMX7HBMgzZmhFBrOlBbuG7YwMNdyspaX6BhrW+bcN65IC3NKCX0vL\ninkkoWkaWbosUrNSSc1K5Xr29dxtQ6CblJGkAt8b20mZSQW2DUFxRk4GdhZ2Bf64DH94huDX2dq5\nQCBseG1pWjU3mQLy94i4elV1KTYEwleuqIGSY2JUr8A6dfJumoaAuH59FSBXgOs6HUdSUjh4Y9mZ\nlESGXk9XR0e6OjoS4OhIE2vr8u80KIQQVSwyM5MtCQlsTkhgd1ISiTk5tLe3p4O9PR0dHGhjZ4d9\nRaUQ09PVgMfnz6vlwgW1vnxZJUscHVWW+ebFx0cNQVe7tnpcW8WyddkFntLmT1rl35eYkVjwsz4j\nCWMj4wIBs2Hb8FmfP6i2M7fD1twWW3Nb7Czytm3NbbEytaqQzyhNU0nEkgJpQ9yWllZwfSvbOTkF\n47mbA2hLy7Itr79+hwTIY8dqpQa2Je2ztKzYBut6TU96djrpOemkZ6eTkZORu33zOi07rUCAez3r\nOqnZ+bZvCoAN+4yNjHN/gW3MbdTazKbQH0FRa3sL+9xtW3Pb6hegpadDXFzecu1a3nhxN3cHNoyp\nYxgWw8cnLxA2LJ6eFfosR69pXM7I4HRaGqeuX+fE9escSknhUkYGzWxsaG1nx/12dnSyt8dfAmIh\nRA0UlZnJ3uRk9iYnsycpiSOpqbiZm9PS1paWNja0sLWlhY0Nda2sKnayI71efZ6EhqolLCxvOzRU\nfa7ExqrESf6hl25eDD3lDB10qtF9XdM00nPSCwTMhifERe0zxBdFLZm6TGzMbAoEzSUtVqZWWJlZ\nYW1mnbtd0j4rUytMjCsuINPpVFK0uCDakDQtbZk/vxwC5E2bNvHmm2+i0+l46aWXGDduXKEyr7/+\nOhs3bsTa2prly5fTqlWrMp9bXJpb0zSy9dlk5mSSpcsiU3djXQ6v03NUQJuRk1FkkHvzsWxdNpam\nlliZWal1Eb8QhuOGX7zctXneL2Jx+2zMbTA3qfr/boul16t///I3YLqxDjxwgAB3d9VjMH8QnD8Y\n1uvVTSf/4uZW9GCSrq6V0pApS68nLDOTyxkZucvF9HROp6VxLi0NZzMzGltb08TGhibW1txvZ0cz\nGxvM77LOdYGBgQQEBFR1NcRtkp/fnetu+9npNI0L6ekcS00lODWVY9evczw1laisLPwsLWlgbU1D\nKysaWFlR38oKX0tLfCwssKqMZmh6vfo8KmoAf8Ny7ZoqEx+vyhuCZcM6/7aTE4FhYQR06FCwAa+h\n/WQ1blqn0+sKJOmKWgyJu5SslNzEnyFuKvD6RoyUlp1WIIYyMzErNYi2MLXAwuTGYlpwbW5iXmjf\n7axLau9dliYWJUYiOp2OUaNGsWXLFry8vGjTpg39+vWjcePGuWU2bNjAhQsXOH/+PPv37+fVV19l\n3759ZTrXoO7cuoUC2SxdFmbGZrnfKHMT8wLfuJJeF3fMwcIBCxuL3B9SacGuYZ+FiUX1zxLm5Kjn\nG5mZ6t+o/I2qb3Wdv2GSoUGStXWR3WEDL15UN3kHB9W54uZA2NlZtU+ppO9fuk5HXHY20dnZRGVl\nFVquZmZyJTOT6KwsPM3NqWtlhZ+lJX6WljxcqxZveXvTyNq6xnSou9s+pGsa+fndue62n52JkRH+\n1tb4W1szsHbt3P3pOh2XMjI4l5bG+fR0DqWmsio2ltCMDCIyM7E1McHnRrDsY2GBl4UFrmZmajE3\nz912NDW9/c9hY+O8YZyaNy+9vOGpZ3x8XrLHsB0bC2fPErhvHwFBQQV7xhl64FtZFQyaDYuhLaeh\nPadhO/9S3H5DA1xT0//0eWpibIK9hX2FdZ7XNI1MXWahJ+s3JyIzdZlk5mQWuU7MSCy4/6Yyhlix\nuPMNaxMjk9yY0MzELHe7rAnJEqOAoKAg6tevj5+fHwCDBw9m3bp1BYLc9evXM3ToUADatWtHYmIi\nUVFRhISElHquwbbnthUKZs1MzMpvJrTiaJr6T1GnK7jW6yFbB+nZkH2j0Ut2tlrn3755fbvHDIFt\nWZaMjKL3g2prYmGh/pDyN6r+P3v3HdbU+bcB/E5I2EtQUAFFARXcq0qtFaw4sO5RR22t27ZWrV12\nqq911LbWn6t2qXVbbau2iuJAxa1YcSCigAIu9oaQ5Lx/HBOJhD0CeH+u61wnOTkn+R4S5ebJc57n\n2X94+dd2dgX30wyfkf+S1sL+Ip43T1zK/BYIyBMEZKlUyFSrkalSIUOlQqZmebIt//ZkpfLpkpen\nc18tCLCXy1Hf2Fhn8TAzQ3cbGzgaG6Pxk/+E5bWsNZiIqLoxMzJCSwsLtNQzWpBaEBCfl4fY3FzE\n5OQgJjcXcbm5uJOdjfi8PHFRKBCfl4dstRp15XLYy+WwMTKCjUwGa5mswG1rmQw2MhnMpVKYGxnB\nTCp9uhgZwfzJ7SJH5DAzE2cHdHYufJ/Cfvep1WJj07PBOTVV3J5/ycgQr6nR3Nc0VOm7n50t/q5X\nq8Xf8/kXze/+ki7GxuKFWzKZ7ro8256sJXI5TI2MYGpkhDpGxoDUFDCtK2YIqbTgupIIggClWok8\ndZ620TVP9fR2ixktin2OIgNyXFwcXFxctPednZ1x7ty5YveJi4vD/fv3iz1W4+rn3wJqtdjc/SS0\nCprwKgi6t5+sC91f3zHP3tYcA4hvkEQCwchI/KtMKoXwZBuMjAAjIwgymbifTCbul//2k/uCTKZ7\n+8kHQLtP/ttyue59mUw85smHTOe25oOnb598i5Dvg5b/S4Nnb6sFASpBgAriV2Lqom4rlVAlJEAd\nH1/oPiHx8bh14wbUT4KuQhCQq1ZDoVY/vS0IUKjVurefrBWCAJlEAnOpFBZGRuLy5Lal5v4z21xN\nTdFeJkMduRx2MhnqPLldRyaDmVRa/Vv7iYgIUokEjsbGcDQ2RkcrqyL3zVWrEa9QIFGpRKpSiTSl\nEqkqlc7t+7m5SH1yO0ulQrZaLS75bmu2SyUSbXA2lUohl0ggf7I2zndbuzzz2LWEBDwID4dMIoFU\nIoH0yflIIbamSwFIjY0hrVsX0nr1nm7LtzZ65r7mWAmg/T0mebJobkMQIHnSwCZRKiF50tCWfxue\nbNfZ9sxaolIBKpW4Ta2G5MlQYBKVSnxM3z6a19Fse/K4dnmyn05jY77Mln+RqNVPTkrMXQUWzXZN\nFsu/TfN7Pv+++TKcdlv+58i/lDCYFxmQSxo0ynOdn5ubGwatWVPm48nwrpbz/VMCSHuyUNWbP3++\noUugcuD7V3PxvTMcNYD0J0tZ/bd6dQVVQ1XNzc2t2H2KDMhOTk6IiYnR3o+JiYHzM185PLtPbGws\nnJ2dkZeXV+yxAHD79u1iiyQiIiIiqipFtjN36tQJERERiI6OhkKhwI4dOzBw4ECdfQYOHIjff/8d\nAHD27FnY2trC0dGxRMcSEREREVU3RbYgy2QyrFq1Cn369IFKpcLEiRPh6emJdevWAQCmTp0Kf39/\n7N+/H+7u7rCwsMD69euLPJaIiIiIqDoz+EQhRERERETVSbUZ52rlypXw9PREq1at9E4oQtXfd999\nB6lUiqSkJEOXQiX04YcfwtPTE23btsXQoUORmppq6JKoBAICAtCiRQt4eHhg6dKlhi6HSiEmJga+\nvr5o2bIlWrVqhf/973+GLonKQKVSoX379hgwYIChS6FSSklJwfDhw+Hp6QkvLy+cPXtW737VIiAf\nO3YMe/fuRWhoKK5du4YPPvjA0CVRKcXExCAwMBCNGzc2dClUCr1798b169dx5coVNGvWDIsXLzZ0\nSVQMzSRMAQEBuHHjBrZt24awsDBDl0UlJJfLsXz5cly/fh1nz57F6tWr+f7VQCtWrICXlxeHFa2B\nZs6cCX9/f4SFhSE0NLTQ7r/VIiCvXbsWc+fOhVwuBwDUq1fPwBVRab3//vv45ptvDF0GlZKfnx+k\nT8aE7NKlC2JjYw1cERUn/wROcrlcOwkT1Qz169dHu3btAACWlpbw9PTE/fv3DVwVlUZsbCz279+P\nSZMmlWuYW6p6qampOHnyJCZMmABAvF7OxsZG777VIiBHRETgxIkT6Nq1K3x8fHDx4kVDl0SlsGfP\nHjg7O6NNmzaGLoXK4bfffoO/v7+hy6BiFDY5E9U80dHRuHz5Mrp06WLoUqgUZs+ejWXLlmkbF6jm\niIqKQr169fDWW2+hQ4cOmDx5MrKysvTuW+QoFhXJz88PDx8+LLD966+/hlKpRHJyMs6ePYsLFy5g\n5MiRiIyMrKrSqASKev8WL16MQ4cOabfxL+rqpbD3btGiRdr+c19//TWMjY0xZsyYqi6PSolf6dYO\nGRkZGD58OFasWAFLS0tDl0Ml9M8//8DBwQHt27dHUFCQocuhUlIqlQgJCcGqVavQuXNnzJo1C0uW\nLMGCBQsK7FtlATkwMLDQx9auXYuhQ4cCADp37gypVIrExETY29tXVXlUjMLev2vXriEqKgpt27YF\nIH711LFjR5w/fx4ODg5VWSIVoqh/ewCwYcMG7N+/H0eOHKmiiqg8SjKBE1VveXl5GDZsGF5//XUM\nHjzY0OVQKZw+fRp79+7F/v37kZOTg7S0NLzxxhva+SCoenN2doazszM6d+4MABg+fDiWLFmid99q\n8f3A4MGDcfToUQDArVu3oFAoGI5riFatWuHRo0eIiopCVFQUnJ2dERISwnBcQwQEBGDZsmXYs2cP\nTE1NDV0OlQAnYarZBEHAxIkT4eXlhVmzZhm6HCqlRYsWISYmBlFRUdi+fTt69uzJcFyD1K9fHy4u\nLrh16xYA4PDhw2jZsqXefausBbkoEyZMwIQJE9C6dWsYGxvzw1aD8evfmmXGjBlQKBTw8/MDAHh7\ne2PNmjUGroqKwkmYarZTp05h8+bNaNOmDdq3bw8AWLx4Mfr27Wvgyqgs+Duv5lm5ciXGjh0LhUIB\nNzc37QR3z+JEIURERERE+VSLLhZERERERNUFAzIRERERUT4MyERERERE+TAgExERERHlw4BMRERE\nRJQPAzIRERERUT4MyERERERE+TAgExERERHlw4BMRERERJQPAzIRERERUT4MyERERERE+TAgExER\nERHlw4BMVAbz5s2DVCrFiRMnDF1KldN37kFBQZBKpZg/f36V1lLY6xqqHkO/NhVOqVSiWbNmGD9+\nvKFLoUpw7tw5SKVS7N+/39ClUC3BgEzVXlpaGr788ku0bt0aFhYWsLCwQJMmTdC3b18sWbIEWVlZ\n2n1rczgpy7lV9c9DIpGU+piKqLGw1y1LPSVRkpor67Wri+DgYIwbNw5NmjSBubk5LC0t0bp1a8ya\nNQs3btzQ7hcdHQ2pVKqzWFlZoVGjRvD398d3332HhIQEva+h79j8S/v27Utc72+//YY7d+5g7ty5\n5T73qhYcHAw/Pz/Y2NjA2toaPXv2xLFjxwxdVqXbtGkTJk+ejPbt28PY2BhSqRTHjx/Xu2+XLl3Q\ns2dPfP7551VcJdVWMkMXQFSUlJQUeHt7Izw8HF5eXnjrrbdQp04dxMbG4uTJkwgMDMTIkSPRtGlT\nneNqczgpy7lV9s+jS5cuuHnzJurWrVvm5yhLjRXxuuWhr2ZD11TZVCoV3n33Xaxbtw5mZmbo1asX\nWrRoAQC4efMmfvnlF6xatQpHjhxBjx49tMd5eXlh5MiRAIDs7GzExcUhODgYAQEBWLBgAdauXYsx\nY8bofc38x+ZXv379EtWsVqvx9ddfo2/fvmjevHlpT9mgDh48iP79+8Pa2hqvv/46TExMsH37dvj5\n+eGvv/7CgAEDDF1ipfniiy9w7949ODo6wtHREXFxcUX+PzF79mwMGDAAe/bswaBBg6qwUqqNGJCp\nWvvhhx8QHh6O6dOnY/Xq1QUev3DhAuzt7QtsFwShKsoziLKcW2X/PMzMzNCsWbNyPUdZaqyI1y0P\nfTUbuqbK9sknn2DdunV48cUXsXPnTjRs2FDn8aSkJHzxxRdIS0vT2e7l5YUvv/yywPNt3boV06ZN\nwxtvvIE6deqgX79+BfYp7NiSOnToEGJiYrBw4cIyP4chKBQKTJ06Faampjh16hQ8PT0BAB999BHa\ntWuHadOmwc/PD6ampgautHKsX78ezZo1g5OTEz744AN8//33Re7fp08f1KlTB7/++isDMpWfQFSN\n9evXT5BIJMKVK1eK3ferr74SJBKJ3kUQBGH9+vWCRCIRNmzYUODYwh5LS0sTZsyYITg6Ogrm5uaC\nt7e3cOTIEe1rHT9+vMBzbd26VXjppZcEKysrwcLCQujSpYuwc+fOAvsdO3ZMkEgkwrx584QzZ84I\nPj4+gqWlpWBnZyeMHTtWiI+PL/G5leXnUZzSnHv+c8lv27Ztgre3t2Bvby+YmZkJLi4uwpAhQ4RL\nly6VuMb8z33kyBHh5ZdfFqysrIR27doJQUFBel9Xc8z8+fOFwMBAwdvbWzA3NxccHR2F6dOnCykp\nKTr7l+SzsXHjxhLVXNjPIjc3V1i0aJHg5eUlmJqaCnZ2dsKrr74qnD9/vsBrluazUZXCw8MFqVQq\n1K9fX0hOTi5yX4VCIQiCIERFRQkSiUQYMWJEoftu2bJFkEgkgqenp872khxbEqNHjxbkcrmQlpZW\nruepav/++68gkUiEKVOmFHhs4cKFgkQiEXbv3m2AyqrenDlzCv0/N7/x48cLMpnMYP9GqPZgCzJV\na3Z2dgCAiIgItGnTpsh9fX19cffuXWzcuBE+Pj7w8fHRu19RX9Hlf0ylUsHf3x+nTp1C165d4evr\nizt37sDf31/nq+P8Zs+ejRUrVsDd3R3jxo2DTCbDv//+i9deew0xMTF4//33Cxxz/vx5LF26FL17\n98b06dMRHByMrVu3IjIyEqdPny7VuZXl56FPWc4d0P35rVy5EjNnzoS7uzvGjh0LCwsLxMbGIigo\nCGfPnkWHDh1KVWNwcDAWLVqEfv364Z133oFSqdT7uvmdOnUKixYtwuDBg+Hr64sTJ07gxx9/xMWL\nF3Hq1CnI5fJC6y9MWT5narUagwYNwsGDB9GmTRvMmjUL8fHx2L59OwIDA7F371707t27wHOU5LNR\nlTZu3AhBEDB16lTY2toWue+zP9uijBkzBp9//jlu3ryJ0NDQYv+tl9bRo0fh6ekJKyurCn3eyqa5\nENbPz6/AY35+fvjiiy9w4sQJDB06tKpLq7a6dOmCjRs38udC5caATNXa8OHDsXXrVrz11ls4e/Ys\n+vTpgxdeeAHW1tYF9u3RowcEQdAGl/J8JQuIF/WcOnUKo0aNwtatW7XbN23ahDfffLNAmDpw4ABW\nrFiBkSNHYvPmzZDJxH9eS5YswSuvvIK5c+di1KhRBb6SPnDgAHbv3o0hQ4YAEL+29/Pzw9GjR3H2\n7Fl07dq1TOdWnp9Hac9dn/Xr18PJyQmhoaE6XwELgoDU1NRS13jkyBFs27YNr732mnZbUFBQkTUE\nBgZi06ZNGDt2rHbbpEmT8Ntvv2Ht2rV47733ij2PZ5Xl57phwwYcPHgQAwcOxF9//aX9+c2YMQNd\nunTBhAkTEB0drf3MaJTks1GVNKG8NH9sldRLL72E6OhohISEFAjI169fx7x58woc89Zbb6Fx48ZF\nPm9kZCQeP34Mf3//QveZO3cuUlJSsHbtWu22Xbt24X//+1+JR6rRV19h6tSpg5kzZxa73+3btwEA\n7u7uBR5zc3PT2ac8tm7diiVLliAsLAwqlUrnsbfffhurVq0q8vjKOPey6tSpEwDxs8qATOXBgEzV\n2uDBg/H1119j4cKF+O677/Ddd98BEPskDh06FDNnztTbB7kibNmyBVKpFP/3f/+ns33cuHFYvHgx\nbt68qbN9zZo1kMlkWLt2rU7QMTMzw2effYYBAwbgzz//xLvvvqtznK+vrzYAAWLL4xtvvIGjR4/i\n0qVLVR6CgNKfuz4SiQTGxsYwMjIqsL241kd9OnfurBOOS8LT01MnHAPA/PnzsXHjRmzevLlMAbks\nNm3aBIlEgqVLl+r8cdG2bVuMHTsW69evR2BgYIH+t9Xts/Hw4UNIJBI4OTlV+HNr/nDUN6JFWFgY\nFixYoLNNIpGgZ8+exQbkqKgoACiy5i1btmDy5Mk623bu3Kn9BqskFixYAIlEUqK+9K6uriUKiZp+\n3PoaBDTbNH9sltVnn32GX3/9FZ9++ikaN26sve5j8+bNAIB27doV+xyVce5lpfkcRUdHV9pr0POB\nAZmqvblz52L69On4999/cebMGZw7dw4hISFYuHAhfvnlF5w7dw4uLi4V/rqhoaFwcHDQttTk5+3t\nXSAknj9/HlZWVlixYkWB/ePj4wEA4eHhBR7TN1SV5j/5lJSUMtVeXqU9d31ee+01fPLJJ2jdujVG\njRoFX19fdOnSpcwXFGlahkqjW7duBbY5OTmhUaNGuHr1apnqKIsrV66gXr16ekdQePnll7F+/XqE\nhoYWCMjl+WykpqZi+fLlOts0rXdFPVYdDR8+HDt37izTsYmJiQDE89Pn7t27iI2Nxcsvv6yz/cyZ\nM6X6eajV6jLVZ0j79u3DmjVrEBISgiZNmgAQP3Ourq5o0qSJdltxqtO5a/6oKWzoQKKSYkCmGsHW\n1hZjx47Vtgbeu3cP48ePR1BQEObMmVPmX55FSUtLKzR4Ozg4FNiWlJQElUpVoKVLQyKR6IzZrKGv\ndUjTAv3s151VpbTnrs9HH30EW1tbrF27FgsWLMCCBQtgbm6OcePGYdmyZbC0tCxVTSV93fzq1atX\n6HNFR0cjLy+vVH1lyyotLQ0tW7bU+5ijo6N2n2eV57ORnJxcoGVP03pX1GNFqV+/PsLDwxEbGwsP\nD48i9y2tBw8eACj8PassJ06cgLGxsU5r/L179xAXF6f3D6yqpHn/9X02NNtsbB96ahEAACAASURB\nVGzK/Pwff/wxPvjgA50grPn5P378uMQBuTrRfJ5r81CfVDUYkKlGatSoEX777Tc0bdoUJ0+eLNEx\nUqk4L07+i7s0CgsnmpbfZz1+/Fjv/jY2NoiMjCxRPdVZac+9MFOmTMGUKVPw6NEjHDt2DD///DPW\nrVuHrKwsbNy4sVQ1leUXXlHnYGxsrA3Hpf1slJa1tTUePXqk9zHNdn1huDxcXV0Lbdkr6rGidOvW\nDcePH8fx48fh6+tb3hK1BEHAyZMnIZFI0LFjxwp7XgDa8aiTk5P1Pn7y5El07twZJiYm2m2nTp2C\niYlJqb61qIx+uJq+xxEREQW6OhTVP7kkrly5gps3b2L06NE62yMiIgCgVN/KVac+yJr3ubaOQ05V\nhwGZaiwLCwsAQGZmpnabpr+rvtY1Tb/XuLi4Ao9dvny5wLa2bdvixIkTuH37ts4vIUEQ9I4g0KVL\nFxw8eBAPHz4s8QQGpVHUuVXkMUDpz704jo6OGDVqFEaMGIHGjRvjn3/+KXeNJXHq1KkC22JjY3H3\n7l2dIFbaz0Zpa27Xrh2CgoIQHh5eoJuF5g+8kvT1NLQ33ngDS5Yswbp16zBr1qwi+5IrFAoYGxuX\n6Hm3bduG6OhoeHl5oVWrVhVVLgDxjwFA/3sLiD//ZyfbOH36NDp37gy5XI7r168X2vqfX2X0w+3R\nowe++eYbBAYGYsSIETqPBQYGAkCBriElFRYWBisrqwKTLO3fvx/t27cvcDFxUapTH2TN+6x534nK\nilNNU7X2008/4cqVK3of++abbwCIV79raPqfxcbGFti/U6dOkEgk2LFjBxQKhXb7+fPnsWXLlgL7\njx07FoIg4IsvvtDZvmnTJoSHhxdo0Xz33XchCAImTZqEjIyMAs9348aNQls0S6Koc6vIY4DSn7s+\n+qaETU9PR1ZWlk5rXVlrLImbN29qLzbS+Oqrr6BWq3Uu3ivtZ6O0NY8bNw6AOMlG/hARGhqKTZs2\nwcnJCb169Sr5iRlIs2bN8P777+PRo0cYOHCgtltEfgkJCZg2bRoCAgKKfT5BELB161ZMnToVRkZG\n2otwK1LTpk1Rv359XLx4scBj8fHxCA8P1wmJgiDg2LFj8Pb2BiCOxlISarUaKpUKarW62KWk3zL1\n6tULjRo1wpYtW3Sm737w4AFWrlyJhg0bon///jrH+Pj4FDkls0adOnW0jQwaOTk5+PHHH0s9AlBl\nnHthigvhly5dAgC8+OKL5XodIrYgU7V24MABTJs2DZ6envD29oajoyOSk5Nx/PhxhIWFwc7ODsuW\nLdPu36JFCzRo0ADbtm2DiYmJthXk888/R8OGDTFixAjs3LkTnTt3Rq9evRAXF4e9e/fi1Vdfxd9/\n/63z2hMmTMDvv/+OHTt2IDo6Gj4+PoiMjMSePXvg5+enbcHR8Pf3x4cffohly5bBw8MDfn5+aNiw\nIR4+fIirV6/i8uXLOHv2bJn7WOo7N4lEgs8++6xCjynLueszaNAg2NnZoWvXrnBxcUFmZib27t2L\n1NRUzJ07t8gaAfE9K69evXph0qRJ2LdvH9zc3HDixAlt6+Dbb7+t3a+0n43S/lzHjx+PP/74A3v2\n7EHHjh3Ru3dvJCQkYPv27ZBKpfj1118LjPZRXS1evBgZGRn48ccf4ebmht69e6N58+YQBAE3b97E\nkSNHkJeXV2D0kPxDteXk5OD+/fs4efIk7t69C2tra/z+++/o06dPpdTs6+uLnTt3Ii0tTacri6b1\n/v79+9pt33//PZKTk+Hq6oo7d+4YtB+uXC7HunXr8Oqrr6Jbt24YPXo0jI2NsWPHDiQlJeHPP//U\n+WMTEMOqRCIptm99jx49IJfLcevWLTRr1gwqlQrTp0/H0KFDq80sdL/88guCg4MBQPsHzpIlS7R/\ntEyePLlAP/GzZ89CJpOVuWWdSKuKJiQhKpPw8HBh6dKlQq9evQRXV1fBxMREsLS0FFq1aiXMnj1b\niIuLK3DM6dOnhe7duwuWlpaCRCIRpFKp9rGsrCzhnXfeERwcHAQzMzOha9euwsGDB4UNGzYIUqlU\nO1uaRnp6ujBjxgzBwcFBMDc3F1588UXh6NGjwrx58wSpVKp3Vqd9+/YJffv2Fezt7QUTExOhcePG\nQp8+fYQff/xRyMzM1O6Xf7a3ZxX2WFHnVpiyHFPac9dX79q1a4UBAwYIjRo1EkxNTYX69esLPXv2\nFP7+++9S1ViWn1P+7YcPH9bOpOfg4CBMnz5dSE1NLfBcpf1sFFZzYTUpFAph0aJFgqenp2BiYqKd\nSe/ChQslPq/iHqtKwcHBwuuvvy64uroKZmZmgrm5udCyZUvhvffeE8LCwrT7aWbDk0ql2hkHLSws\nhEaNGgn+/v7Cd999JyQkJOh9jYqaSS8gIEBnNkSNWbNmCW5ubsKAAQOEmTNnCjNmzBDOnDkj7N+/\nX/Dz8xOmTp0qZGRklOu1K0JwcLDQq1cvwcrKSrCyshJ8fX2FY8eOFdhPrVYL9vb2QtOmTQWVSlXs\n8165ckUYNmyYMHPmTGHs2LEFfj6GNn78eO1nJ/+i2fZsvQqFQqhTp44wcOBAA1VMtYlEEErQaUiP\nCRMm4N9//4WDg0OhwyW99957OHDgAMzNzbFhwwa9QxYRERFVJkEQ0KRJE3h5eWH//v3a7R07dkT3\n7t3xww8/GLC6inPjxg20atUKa9aswbRp0wxdTpX7559/MHDgQPz9998YOHCgocuhGq7MfZDfeuut\nIvuY7d+/H7dv30ZERAR++uknTJ8+vawvRUREVGaa7i8HDx7UjuGdnp6O0NDQWvVVfHBwMOrXr48J\nEyYYuhSDWL58Odq3b89wTBWizAG5e/fuhQ68DgB79+7Fm2++CUC8uj8lJaXQYY6IiIgq04QJE+Dm\n5oYlS5YAEEeqUKlUtSogT5kyBffv3y/x6CG1yblz53Ds2DEsXLjQ0KVQLVFpF+nFxcXpjKPo7OyM\n2NhY7aD4REREVcXIyAi3bt3S3n/w4AFeeeUVjpdbS3Tp0qVazehHNV+ljmLxbPdmfUNDubu7486d\nO5VZBhERkV6ccY3o+ePm5qadbKcwlRaQnZycEBMTo70fGxsLJyenAvvduXOnRIOLU/U0b968Us2i\nRNUL37+aje9fzVVV750gCEhSKpGQl4eEvDzEKxTiWnM/Lw+JeXlIVSqRplIhValEqlKJdJUKZlIp\nbGQyWMtksDYygqWREcykUpg/u5ZKYWZkBPN820ylUhhLJJBr1hIJjKVS3fUzj8ufbJdLJJBKJJBC\nzx8wggDk5gJZWUBmZsnWubnikpPz9La++8XtIwiAXA7I5ZinVGKelZX2PuRyQCYr/H5Rj2nuGxkV\nXKTSou+XZ1v++1KpuEgkha9Luq0yHqtgJfnDuNIC8sCBA7Fq1SqMGjUKZ8+eha2tLbtXEBERVaCk\nvDzczs7GvZwcxCkUiM3NRVxuLmKfLPdzc2EqlcLB2Bh15XLUk8u16wbGxmhjaQl7mQw2TxZrIyPY\nyGSwMjKCTFqBc4kplUBSEpCcDKSlPV1SUwu/r7mdkaEbeGUywNwcsLAofm1mBpiaAnXqiGsTk6fL\ns/f1bct/X5YvMs2bJy5UbanUKuSp85CnytNZK9XKEh1f5oA8evRoHD9+HAkJCXBxccH8+fORl5cH\nAJg6dSr8/f2xf/9+uLu7w8LCosSzEREREdFTGUolrmdlISwzE3dycnA7Oxu3s7NxJzsbKkGAm5kZ\nXE1N4WRiAmcTE7S1sICziQmcnizmFT0JjVoNJCYCDx+KS3y8GH4TE3WX/NsyMgBbWzGo2tgA1tbi\nkv+2vT3QtKnuY1ZW4pI/+Mo4x5khqdQq5ChzkKvKRY4yR7ytfHpboVIUWPLUefq3qwrZXtj+JXge\nTRgGALmRHHKpvMC6JMr8Kdu2bVux+6xataqsT081hI+Pj6FLoHLg+1ez8f2rufS9d2pBwO3sbISk\np+NqZiauZWbiamYmHioUaGFuDi9zc7ibmaG/nR3czczgZmaGunJ5xfWjVqvFsHvvnrg8eCAGYM06\nfyC2tgbq1wccHYF69cRwqwm4nTs/vW9vD9jZieG4IlukDaw6/NvLU+UhKy9LZ8lWZhfYlpWXhey8\n7KdhNn+wLSTkFrVdLahhKjOFqcwUJkYmT2/LxNvGRsYwMTKBsZEx5EZyGBsZi4vUuOA2I2NYGFvA\nVmqrs03ffsZGxpBL9WzLt1/+EGwkLfwPQ8ns4v/NlHmikIoikUjYB5mIiJ478QoFzqal4Xx6Os6l\npeFCejpsjIzQ0coKrS0s0MrCAq0tLeFuZgajigjBajUQGwvcvg1ERT0NwpolJkZsrW3UCHBxAZyc\nxBCcf2nQAHBwAJ7DoeTKQqFSIEORgfTcdHGtENeFbdMXbgsLvxJIYCY3g7ncvMjFTGYGM5mZNsjm\nD7OFhdyitsukNb8FvyTZkwGZiIioCsQrFDiekoKglBQcS0lBXG4uulhb4wVra3SxskJna2s4ljd4\nCoLY4nvzphiEIyLE5fZtIDJSbMn18ACaNAEaNxbDsGZxcRG7MDznBEFAjjIHqbmpSMlJQWrOk7We\n+2m5aToh99nQq1KrYGViBStjK1iZWMHS2BJWxk/WJlawlFtqt1saW8JCblHi0Cs3KllXASqIAZmI\niMhAlGo1Tqel4d/ERBxISsLdnBy8ZGMDX1tb+Napg3aWluVrGU5KAq5fB65eBa5de7oYGQGenmIQ\n9vAA3N3FtZsbYGlZcSdYzeUqc5GYnYjErESddVJ2EhKzEpGck4yUnBRt2M0ffAHA1tQWNiY24trU\nRve+iQ1sTG1gY2LzNOw+G36NLWFiZMKhBKshBmQiIqIqlKFUYl9iIvYlJuJgUhIam5riVXt7+NvZ\noZOVVdlHhoiPBy5efLpcuiSO8NCqVcHFwaFiT6oaEAQByTnJeJTxCI8yH+Fx5mM8yhDXidn6A7BC\npYCdmR3sze1hb2avXduZ2cHezB51zOqgjmmdguHX1AamMlNDnzJVIgZkIiKiSpatUmF/UhK2P36M\nQ0lJ6GZjgyF168Lf3h5OJialf0KFQgzBwcHAuXPi7dRUoFMn3aVx40oZI7YqpeemIzYtFnHpcXiY\n8VAbeh9likFYE4jjM+NhLjeHo6UjHC0c4WjpCAdzBzhYOBQIwJq1pbElW29JLwZkIiKiSiAIAk6n\npeGXBw/wd0ICOlpaYpSDA4bUqwd7eSn7hqanA6dPAydPiqH44kWgWTOge3ega1cxDLu51ahRIFRq\nFR5nPkZcepwYgNPiEJf+ZEl7ulYJKjhZOcHJ2gkNLBvA0cIRDhYOOkFYs81EVoY/Noj0YEAmIiKq\nQAkKBX5/9Ai/PHgAtSBgUoMGeN3REfVL01KsUgEhIcDBg8ChQ8Dly0CHDmIgfukl4MUXxWHUqjG1\noMaD9AeISolCdEp0gSUmLQY2JjZwtnaGk7WTGIKfBGHN2tnaGTYmNmzlpSrHgExERFQBQjMy8F1M\nDPYkJGBQ3bqY1KABXrIpRbiLjwf++QcICAAOHxaHTOvTB+jdG3j55Wo5eoRCpUBUchRuJd7CrcRb\niEiKwJ3kO2IATo2BnZkdXG1d9S6NbBqxHy9VCLUayM4WJ1EsbtFMtljccuECAzIREVGZCIKAg0lJ\n+C42FjcyM/GukxOmNmwIu5J2oYiOBv7+G/jrL+C//wA/P8DfXwzFzs6VWntJCYKAmLQY3Ey4iYjE\nCDEMJ91CRGIEYtNi4WLjgmb2zeBh54Fm9s3QtE5TNLFtgkY2jWAmNzN0+VSNKJViQM3IKH4par9n\nw2xOjjjjt7n500UzqWJhS3GPd+nCgExERFQqakHA7vh4LLh7FxIAc1xcMNrBAcYl6QN87x6wbRuw\nfbs4KcfAgcCQIcArrwBmhguUgiDgUeYjXHt8DdceX8P1x9dxLf4absTfgIXcAp71PNHMrpkYhu3F\nMNzEtgnH2q3F1GoxqKalPV1SU3Xva5aShN68PHEUwcIWC4viH8+/aMKsqWnFd79nFwsiIqISUgsC\n/k5IwLzoaJhKpZjn6op+dnbFd6NITgZ27QI2bxbHIR42DBgzRuxPLKv6WceUaiXC4sMQ8iAEIQ9C\n8N+j/3Dt8TVIIEErh1Zo5dAKLeu1FNcOLWFnZlflNVL5KBTixy4lRVxrgm1hAVdfAM7IEAOotbXu\nYmOje9/KSlwXF3BNTGrOoCoMyERERCVwOCkJH0ZGQgpgvqsr+tvbFx2M1Wrg2DFg3TrxYjs/P+D1\n14F+/cSkUEUUKgWuPrqqDcMhD0Nw7fE1uFi7oEODDujQoAPa1W+H1g6t4WDhwAviqglBEAOqJuDm\nD7v6tj37uEIhTopYp464trF5ujwbePWFXk3wNTIy9E/CMBiQiYiIihCWmYkP79zBzawsLHVzw9C6\ndYsOkQkJwIYNYjA2MwOmTRNbi21tq6Te++n3cSbmDM7Eist/D/9D0zpN0bFBR20gbuvYFlYmVlVS\nD4l9b5OSxI9GYqK4aG4Xtk5JEf+O0gTcOnV0b+vblv+2hUXNaa2tjhiQiYiI9EjOy8MXUVHYER+P\nuY0a4R0nJ5gU1dExJAT4/ntxJIpBg8Rg3LVrpaYUtaDG9cfXERQdhFMxp3Am9gwyFZno6twV3s7e\n8HbxRueGnRmGK1h2NvDokbg8fvx0XVjYTU8XQ6u9vbjUrat/rbltZyfub2xs6DN9fjEgExER5SMI\nArY+fowP7tzBkLp18X9NmhQ+sYcgiMOyffstcOsW8N57wMSJYsKppNrCEsJwLOoYjkUfw/G7x2Fr\nagufxj54qdFL8HbxhoedB7tJlJIgiC22+cPuswE4/+28PMDRUZyxW7N2cADq1dMfgm1ta9QcLgQG\nZCIiIq2IrCy8HRGBeIUC65o3R5fCJuNQKsWRKJYuFTtpfvghMHJkpTT5PUh/gIDbATh45yCORR+D\nhdwCPq4+8HX1hY+rD1xsXCr8NWuT9HQgLg64f7/gotn+4IHYnUETePOHX323ra3ZfaG2Y0AmIqLn\nnkoQ8ENsLBbfvYtPGzfGe05OkOlr8lOpxOHZ5s8XJ/L4/HPx4rsKTEtKtRJnYs7gwO0DOHD7AO6m\n3EWvpr3Q170vXmnyChrbNq6w16rJBEHswnDv3tMlLq5gGFarAScnoGHDp+tnlwYNquU8LGRADMhE\nRPRci8zOxvibNwEAG1q0QFN9YxGr1cDOnWIwtrcX1z17VlgwTstNw/6I/fjr5l84dOcQmtg2QT/3\nfujn0Q9dnbtCJq36oeAMLScHiInRDcD5l5gY8RrIRo2eLs7OBUOwlRVbe6n0GJCJiOi5JAgCfnnw\nAJ9GReGTRo0wy9kZRvqS1LFjwJw5YveJBQsqrMU4MSsRe8P3YnfYbpy4ewLdG3fHkBZD0N+jPxpY\nNSj381d3arXYwhsZ+XS5c+fp7ZQUMfDmD8D5FxcXcWxdosrAgExERM+dVKUSE2/exJ2cHGzx9ISX\nhUXBncLDgY8+Aq5eBZYsAUaMKHcwTs1JxZ9hf2LL1S24cP8C/Jr6YZjnMPh7+MPG1KZcz10dKRRi\n2L11Szf8RkaKs2zb2gJNmwJubuI6/1K/Pi9sI8NhQCYioufKpfR0vHb9Ovra2eFbNzeYPjsTQkoK\n8OWX4kV4H30EzJghzmVbRgqVAgG3A7Dl6hYcvH0Qvk18Mbb1WPh7+MNcXvM7vgqCOLJDeLjucuuW\n2BXC2Rlo1gxwd9cNwE2aiGP1ElVHJcmez1/HJyIiqnUEQcCa+/cxPzoaqz08MMLB4dkdxAvw5swB\nBgwAbtwQx+0qo8sPLuOXkF+w88ZOeNb1xOttXsfa/mtr7LTNajVw9644U/a1a+KPRxOGZTKgefOn\ny0sviWs3tyqdNJCoSrEFmYiIarQclQpTb93ClYwM7GrZEu7PDllw+zbwzjvieF/r1gHe3mV6nfTc\ndGy/th0/hfyEx5mPMan9JIxrOw6utq7lP4kqomkR1gThq1efBmJbW6BVK3Hx8noaiO3tDV01UcVi\nFwsiIqrV7ufmYui1a2hkaor1LVrAIn+XCqUSWLYM+O474OOPgVmzgMImBSlC6KNQrD6/Gjtv7ISP\nqw+mdJiC3m69YSQ1Kv5gA1KpxK4QISHA5cviOjRUDMmtWz8Nw61bAy1bVtls2UQGxy4WRERUa11I\nS8PQ69cxrWFDfNqoke4Mc+HhwJtviuOAXbwIuLqW6rnVghr7I/Zj+dnlCIsPw/RO03H97etoaNWw\nYk+igigUYitwSMjTQHzlingxXIcOQPv24t8IbdqI2zg0GlHR2IJMREQ1zq7HjzE9IgK/NG+OQXXr\nPn1ArQZWrxbHMp4/H5g+vVTDJWQqMrHxykasOLcClsaWmN11Nka2HAljo4qfRa+sBEHsL3zuHHD2\nrLiEhooXxrVvLwbiDh2Adu0Am9o3eAZRubGLBRER1Tr/i43F0nv38E/r1mhvZfX0gdhYYPx4IDMT\n2LhRHF6hhFJzUrH6wmqsOLcCL7q8iNldZ6N7o+66rdIGkpEhNoJrwvDZs2ILsLc30KUL0LUr0LEj\nxw0mKikGZCIiqjXUgoBPIiOxNyEBAW3awDX/rHj//gtMnCgO2/bxx+LQCyWQlJ2EFWdXYPWF1ejn\n0Q+fvvQpPOt5VtIZlExKChAcDJw4ARw/Dly/LnaN6Nr16eLiwm4SRGXFPshERFQrKNRqvHXzJqJz\ncnCqQwfYay62y8sDPv8c2LoV2LVLHIOsBJKzk7Hs9DKsu7QOg5sPxtlJZ+Fu516JZ1C4hAQxDGsC\n8e3bYsvwyy8D33wDvPCCOO0yEVUdBmQiIqrWclQqDL9+HUYSCQ63bQszzUgVsbHAa6+JHW0vXwby\n90UuRFZeFlaeW4lvz3yLwc0H49KUS1U+TFtuLnDqFBAYCBw6JAbibt3EQLxmjdhdwrj6dHkmei4x\nIBMRUbWVqVJh0NWrqCuXY5OnJ+SaC+6Cg4GRI592qSjmQjylWon1l9dj/vH56OrcFSffOokWdVtU\nwRmIF9XduCGG4cBAsXQvL6B3b+CHH8QuE2UYfY6IKhH7IBMRUbWUplTCPzQUHubm+KV5cxhpOt2u\nWwd88QXw++9A377FPs/hyMOYGTATDhYOWPLKEnRx7lLJlYvDrp04AezdKy4A0KePGIp79gTq1Kn0\nEoioEOyDTERENVJyXh76hIais5UVVnp4QCqRiKlz5kyxo+6pU4CHR5HPEZUchTmH5uC/h/9heZ/l\nGNh8YKWOSpGUBBw4IAbiQ4eAFi3EWa3/+UeciIMX1RHVHAzIRERUraQplegbGooXra2x3N1dDLUp\nKcDQoeJYZmfPAtbWhR6flZeFpcFLsfrCaszuOhtbh22Fqcy0UmqNjwf++gvYuRO4cAHw9QUGDgT+\n9z/A0bFSXpKIqgADMhERVRsZT7pVdLSyehqO790D/P2BV14Bvv8eMCp8iucjkUcw5Z8p6NSwEy5P\nvQwXG5cKrzExEfj7b2DHDuD8eaBfP+Cdd8TeHhxtgqh2YB9kIiKqFrJVKvS/ehWupqb4pXlzsVvF\nf/8Br74KzJkDzJ5d6LFJ2Un44NAHOBJ1BGv816B/s/4VWltWlthSvHkzcPq02Jf4tdfE3G5uXqEv\nRUSVjH2QiYioRshVqzHk2jU0NDbGz5pwHBgIjB0rjn02fLje4wRBwK4buzAzYCaGew3HtenXYGVi\npXff0hIEccSJDRuAP/8UR5t44w3gjz84ax1RbceATEREBqUSBIwLC4OFkRE2tGghjlaxezfw9tti\nMi1k8o/k7GRM/3c6Qh+FYvfI3fB28a6QemJigPXrxdmqTU2BN98UZ7Nr2LBCnp6IaoCiB44sRkBA\nAFq0aAEPDw8sXbq0wOMJCQno27cv2rVrh1atWmHDhg3leTkiIqplBEHArNu38VihwBZPT8ikUjGZ\nzpgBBAQUGo6PRB5B2x/bor5lfVyacqnc4VitBg4eBAYPBtq2BR4+FPsYX7sGfPQRwzHR86bMfZBV\nKhWaN2+Ow4cPw8nJCZ07d8a2bdvg6fl0Dvt58+YhNzcXixcvRkJCApo3b45Hjx5BJnvacM0+yERE\nz69Fd+9ix+PHONG+PWxkMmDVKnF+Zc04ac/IUeZg7uG52BW2C78N/A1+bn7lev3ERLG1+McfASsr\nYPp0YMwYdqEgqs1Kkj3L3IJ8/vx5uLu7w9XVFXK5HKNGjcKePXt09mnQoAHS0tIAAGlpabC3t9cJ\nx0RE9Pz65f59/PzgAQ60aSOG46VLxanlTpzQG47DE8Lxws8v4H7GfVyZdqVc4fjGDWDSJMDdHbh6\nVbz4LiQEmDKF4ZiIytEHOS4uDi4uT4fPcXZ2xrlz53T2mTx5Mnr27ImGDRsiPT0dO3fuLHulRERU\na+xPTMQX0dE43q4dGpqYiK3Gv/4qhmM9/Rl2XNuBdw+8i0U9F2FSh0llmvBDEICgIODbb4FLl8Sh\n2SIigLp1K+CEiKhWKXNALsl/TosWLUK7du0QFBSEO3fuwM/PD1euXIGVVcVcYUxERDXP1YwMjL95\nE3+3aoVm5ubAd98BP/8sptdnwnGuMhdzDs1BwO0AHHr9ENo3aF/q11OpgF27xAyemSmOGLd7t3gB\nHhGRPmUOyE5OToiJidHej4mJgbOzs84+p0+fxmeffQYAcHNzQ5MmTRAeHo5OnTrp7Ddv3jztbR8f\nH/j4+JS1LCIiqsYeKRQYcPUqfnB3x4s2NsDy5cDatWI4dnLS2fduyl2M+GMEnKydcHHKRdia2pbq\ntVQqYPt2YOFCwNYW+OorcUhlabkuTyeimiYoKAhBQUGlOqbMF+kplUo0b94cR44cQcOGDfHCCy8U\nuEjv/fffh42NDb766is8evQIHTt2RGhoKOzs7J4WwIv0iIieC9kqFXpeuYLedepgfpMm4gV5y5eL\n4dhFd8a74HvBGPHHCMzxnoM53nNK1aVCqQS2bRODcb16YjDu1QsoQ68M3TsXOQAAIABJREFUIqqF\nKnWiEJlMhlWrVqFPnz5QqVSYOHEiPD09sW7dOgDA1KlT8emnn+Ktt95C27ZtoVar8c033+iEYyIi\nej4IgoAJ4eFwNTXFPFdXYMsW8aK8kycLhOMN/23AR4Ef4fchv6Ove99SvIY4icfnnwP164vzi/Ts\nyWBMRKXHqaaJiKjSzY+OxoHERBxr1w5mAQHAxInA0aOAl5d2H5VahY8Pf4w94Xuwd9ReeNbzLOIZ\ndR0/Lo5XrFSKufuVVxiMiUg/TjVNREQG93d8PH598ADnO3SA2ZkzwPjxwD//6ITj9Nx0jN49GtnK\nbJybdA52ZiX7tvHaNeCTT8SZ7r7+Ghg1in2Miaj8+N8IERFVmpuZmZhy6xZ2t2yJ+uHhwLBhYveK\nLl20+zzKeATfjb5oYNkAAWMDShSOExOBadPELhSvvALcvClO8MFwTEQVgf+VEBFRpUhXKjHk+nUs\nbtoUnRMTAX9/YOVKoHdv7T53ku6g22/d8GqzV/HTgJ8gN5IX+ZwqlTjrnacnYGwMhIcDs2cDJiaV\nfTZE9DxhFwsiIqpwgiBg/M2beNnGBhNNTcWm3k8+AUaO1O4T8iAEr259FV/2+BLTOk0r9jnPnBEn\n97C0BA4fBtq0qcwzIKLnGQMyERFVuKX37iE2Nxdb3d2B/v2BPn2Ad9/VPn448jDG7B6Dda+uwxDP\nIUU+V1oa8PHHwN694mQfY8bwAjwiqlzsYkFERBUqMCkJK+LisLtlS5i8/TZgYSHOlvfEnpt7MGb3\nGOwauavYcLxvH9Cypdi14vp1YOxYhmMiqnxsQSYiogoTl5uLcWFh2OblBefvvweuXBHHYDMyAgDs\nvrEbb+9/G/vH7kenhp0KfZ7Hj4GZM4ELF4Dffwd8favqDIiI2IJMREQVRKlWY8yNG3jHyQm+hw6J\nV9Pt2yd2Ggaw7eo2vHvgXRx8/WCR4XjPHrF/sbMzEBrKcExEVY8tyEREVCH+7+5dyCQSfBofL/Y3\nPnwYaNgQAPD7ld/xyeFPEDguEK0cWuk9PiNDHJHiyBFg926gW7eqrJ6I6Cm2IBMRUbkdTU7Gzw8e\nYEu9ejAaNgz46SegbVsAwPrL6/HpkU9x5I0jhYbjc+eA9u3FmfD++4/hmIgMiy3IRERULo8UCowL\nC8Pv7u6oP2yYOFPeEPHiu+3XtuPzY5/j6BtH0bxu8wLHqtXAkiXAihXA6tXA8OFVXDwRkR4SobjJ\nqCu7gBLMh01ERNWTWhDQJzQUXa2t8X/ffgvcuyd2IpZKsTd8L6bsm4LAcYFo7di6wLGJicC4cUB6\nOrB9O+DkZIATIKLnTkmyJ7tYEBFRmS2LiUGuWo2vjh4VOw9v3gxIpTgceRiT9k7CvtH79Ibj8+eB\njh3FIdyOHmU4JqLqhV0siIioTELS0/FdTAwuSqWQzZ0LnDgB2Njg1L1TGL17NP4c+Sc6O3XWOUYQ\ngDVrgPnzgXXrtD0xiIiqFQZkIiIqtSyVCmPDwvCDgwMavfIK8PPPQIsW+O/hfxiyYwg2D9mM7o27\n6xyTmwtMnQpcvgycPg24uxuoeCKiYrCLBRERldrHkZFob2GBMTNmAKNHA4MGITolGv239sea/mvQ\nx72Pzv6PHwM9e4r9jRmOiai6Y0AmIqJSOZCYiL0JCVi9bx+QmQksXIik7CT029IPH3f7GMO9dIei\nCA0FXngBeOUV4I8/xJmniYiqM45iQUREJRavUKDdxYvYnJsL3zFjgIsXkeNoD79Nfujq1BXLei/T\n2X/PHmDyZGDlSuC11wxUNBFRPiXJngzIRERUIoIgYOj16/BQq/FNv37Ahg1QvdITr+16DXIjObYM\n3QKp5OkXk6tXA4sXA3/9BXTuXMQTExFVoZJkT16kR0REJfLbw4eIys7G9rlzxWZhPz+8f2AmErMT\nETA2QBuOBQH44guxO0VwMODqati6iYhKiwGZiIiKdTcnB59ERuLY6dMweZKAV59fjcNRh3FqwimY\nyEwAiFNFT50KXLsmhuN69QxcOBFRGbCLBRERFUkQBPQODUXP1FTMHTkSuHwZh7Ov4/U/X8fpiafR\ntE5TAEBWFjBypDh9NC/GI6LqijPpERFRuf304AFSc3Px4fjxwE8/4ZZxOsb+ORbbh2/XhuPUVKB3\nb8DOTrwwj+GYiGoydrEgIqJCRWdn4/OoKBzfvBmyfv2Q7NcdA37tioW+C+Hj6gMASE4G+vQBOnUC\nVq0CpGx6IaIajgGZiIj0EgQBk8LDMSc+Hl4nTkB5/ixG7hqKfu79MLnjZABAQoLYctyjB/D994BE\nYuCiiYgqAAMyERHpte7+faRnZuKDqVOBwEDMOfE5jCRG+Lb3twDE2fF69QL8/cXh3BiOiai2YEAm\nIqICop50rTixdClkn32GLbiKfyP+xcUpFyGTyvDggTgz3ogRwLx5DMdEVLswIBMRkQ71k64VH4aF\nwUulQujIHpi1qReOvHEEtqa2SEgQW45HjQK+/NLQ1RIRVTwGZCIi0vHbgwdIT03FnK++QuqZIAz7\noz+W91mONo5tkJIi9jkeOFCcDISIqDbiOMhERKT1IDcXbS5cwOEvv0Tr6dMwWLkZjW0aY6X/SmRk\niKNVdOwIrFjBbhVEVDNxqmkiIiqV927fxuTr19G2QQMsqn8bCbcSsGvkLmRnA4MGAS1aAD/8wHBM\nRLUbAzIREQEA9iYk4L/Hj/H7kiU4umsZVgW9hwuTL0CiNsaIEYCjI/DTTxznmIhqPwZkIiJCmlKJ\nd8LD8fvSpcj4Zh7GHHsX24dvR0MrJ4wfL+6zcSNgZGTQMomIqgQDMhER4dPISPQJC0MPZyf0yPgF\nM7vMhI+rDz77DAgPB44cAeRyQ1dJRFQ1+EUZEdFz7kxqKv6MjcWy77/HokH2MJOZ4eOXPsaaNcCu\nXcA//wAWFoaukoio6nAUCyKi55hCrUb7c+fw1bffwn3oixjw6HuETAnBqUOOmDEDCA4GmjQxdJVE\nRBWHo1gQEVGRlty7h6a3bsG/vj2aP/oeGwdvRMR/jpg2DTh4kOGYiJ5PDMhERM+psMxMrIyMxKVV\nqzBmmg3Gu46Hq7oXXhoObNkCtG9v6AqJiAyDXSyIiJ5DgiDA59IljFi9GnYd5FhjcQN/DQpC924y\nzJ4NTJ1q6AqJiCpHSbJnmS/SCwgIQIsWLeDh4YGlS5fq3ScoKAjt27dHq1at4OPjU9aXIiKiCrb5\n0SNk3r2LIcpUzM7dg98HbcOYUTL07ctwTERUphZklUqF5s2b4/Dhw3ByckLnzp2xbds2eHp6avdJ\nSUlBt27dcPDgQTg7OyMhIQF169YtWABbkImIqlRKXh68goPx51dfYWr/GMwftByBKwcjKgrYuxeQ\nsfMdEdVildaCfP78ebi7u8PV1RVyuRyjRo3Cnj17dPbZunUrhg0bBmdnZwDQG46JiKjqfRURgQHH\nj+PcyyZ4wbMXYg8PRlAQsG0bwzEREVDGgBwXFwcXFxftfWdnZ8TFxensExERgaSkJPj6+qJTp07Y\ntGlT+SolIqJyu5KRge0xMXj72mmscoxGf9lyLFwI7NsH2NgYujoiouqhTG0FEomk2H3y8vIQEhKC\nI0eOICsrC97e3ujatSs8PDwK7Dtv3jztbR8fH/ZXJiKqBGpBwDshIViwYQNGt7qMrzv+gymDLbF7\nN9C0qaGrIyKqHEFBQQgKCirVMWUKyE5OToiJidHej4mJ0Xal0HBxcUHdunVhZmYGMzMzvPzyy7hy\n5UqxAZmIiCrHpthY5EVGIt7uBoa8OAPzJnXBwoVA9+6GroyIqPI82/g6f/78Yo8pUxeLTp06ISIi\nAtHR0VAoFNixYwcGDhyos8+gQYMQHBwMlUqFrKwsnDt3Dl5eXmV5OSIiKqeUvDx8cuMG5h7YiX/b\nmeHGuk/RrRswZYqhKyMiqn7K1IIsk8mwatUq9OnTByqVChMnToSnpyfWrVsHAJg6dSpatGiBvn37\nok2bNpBKpZg8eTIDMhGRgXxx6RIGBh3D5+5n0C/hIk7EyrB9q6GrIiKqnjhRCBFRLXc5LQ39jh/H\nm399AGXPj7H1wwk4fx7Id601EdFzoyTZkwGZiKgWUwsCuh04gEF/bUFQ1yxc/uxP7NwhQY8ehq6M\niMgwSpI9OeIlEVEttuHmTahjY7Df5hCSf7qBuZ8wHBMRFafMU00TEVH1lpSXh08jI9Ez+GdIMn9E\nG/d6mDnT0FUREVV/7GJBRFRLvR0YiJxjgbhlFoW0P/7AmTOAhYWhqyIiMix2sSAiek5devwYf2Vm\noHPydoRtuowzRxiOiYhKil0siIhqGbUgYPqpUxgRsBEXwlZi1Tf2aNbM0FUREdUcDMhERLXMbxcu\nQPrwAU4KcgxqMQijRxu6IiKimoVdLIiIapHEnBx8+ugheob8jOtXjuCHE4auiIio5mFAJiKqRT75\nZx98Lp9GwOX5uLjdDqamhq6IiKjmYUAmIqolLkRGYp/UCPXD7+PnjwfC3d3QFRER1UwMyEREtYBK\nEDD53Bm8fOoP2DTYgBEjDF0REVHNxYBMRFQLrNm/D/LkJFy/NQEh+2wNXQ4RUY3GUSyIiGq4hJQU\nzFeqYRJ0Cft+HAgTE0NXRERUs7EFmYiohnt7xxZ0iruNcSP/h6ZNDV0NEVHNxxZkIqIa7MjpEzhR\n1xH2qd0wdri1ocshIqoV2IJMRFRDqZRKvBd+G+0u/of1y/9n6HKIiGoNBmQiohpqzg8/QG5hgmUz\nFsLY2NDVEBHVHuxiQURUA/0XEoot7m7on2uP1i3YtYKIqCJJBEEQDFqARAIDl0BEVKMIAtDn6/lQ\nCxIc/uJLQ5dDRFSjlCR7sosFEVEN88Gn3yC0U0ucffFlQ5dCRFQrsYsFEVENEhQUhQAPO0xMz4Br\nAwdDl0NEVCsxIBMR1RAZGcDqnUsgV6ux8M03DV0OEVGtxS4WREQ1gCAAU6Yvx7Hh/RDQpiUkEomh\nSyIiqrXYgkxEVAOs+uUB0tzjMSgjBZ2aeBi6HCKiWo0tyERE1dz16wJOBL6Di6NfR0T/Vw1dDhFR\nrceATERUjWVlAW/MWIvc1/vjW2cnWHFGECKiSscuFkRE1djk2Q/QrsVx2FqaY2ynFwxdDhHRc4Et\nyERE1dSWLQJS48fi4PiZCH6pOy/MIyKqImxBJiKqhiIigPdX/wTTNt54y9wcLezsDF0SEdFzgwGZ\niKiayc4GBr0Rg9ea/IqzHbvgKx9fQ5dERPRcYRcLIqJq5t0ZAhxbjMbRHtPxg6cXLGX8r5qIqCqx\nBZmIqBpZvx4IePgjOhm7okE9BwxzczN0SUREzx2JIAiCQQuQSGDgEoiIqoUrVwDfIVEY0dUHu8au\nwZkePdDM0tLQZRGRHnZ2dkhOTjZ0GVSIOnXqICkpSe9jJcme/N6OiKgaSE0Fhg1Xo/WYMUg0nYi3\n69VjOCaqxpKTk9nAV42Vd9QfdrEgIjIwQQAmTAAaDFoF/yhzhHTohE87djR0WUREzy0GZCIiA1u+\nHLiVeAsNkufhlwGT8b927WBmZGTosoiInlsMyEREBhQcDCz5RgnbgePQ3HgYWjo64tWGDQ1dFhHR\nc419kImIDOT+feC114A+Cxeje0AePp00DJe8vQ1dFhHRc6/MLcgBAQFo0aIFPDw8sHTp0kL3u3Dh\nAmQyGf7888+yvhQRUa2TmwsMGwYMnH4eyZe/x17vsZjj6orGpqaGLo3+v737jqu67P84/mLKUoa4\nGIqCIoh7kGXm1jS5c1Rm3Q01R1qaWpR1/zRvS0vzzlFqlpmZpFm5xVyUori3pKmgCE6mzMM55/v7\n4yv7IEPgAH6ej8f1+K7rfM91OoZvL67vdQkhHnmlCsg6nY4JEyYQHBzM+fPnCQoKIjw83GC9wMBA\n+vXrJ096CiHEfYoC48dDXdcU/rIZzss3nuRy69ZMadbM2E0TQohyd+nSJcaMGUOrVq0wMzOje/fK\nt1poqQLy4cOH8fLywsPDAwsLC4YNG8bGjRsL1Fu0aBFDhw6lTp06D91QIYSoLpYuhbAwqPPSVD46\n5sj7r43iq3btsDSVx0KEENXf+fPn2b59Oz4+Pnh7ez/0lGzloVQ/jaOjo3F3d88+dnNzIzo6ukCd\njRs3Mm7cOODh56MTQojqYN8+mDEDJn61lWthGzlduzOPu7jQw8nJ2E0TQogKMXDgQK5du8batWvx\n9fU1dnMMKtVDesUJu5MmTWLOnDnZq5XIEAshxKPu+nX1obwF395m6uFRbDjpQ793AzjTsqWxmyaE\nEBWmKnSaliogu7q6EhUVlX0cFRWFm5tbnjrHjh1j2LBhANy9e5ft27djYWFBQEBAgfvNmDEje79b\nt25069atNM0SQohKKy0NBg+Gt99WCEp5g68jWhD4wnD+4+1Ngxo1jN08IYQoNq1WW2Qdc/PKM1Fa\nSEgIISEhJXqNiVKKrl2tVou3tze7d+/GxcWFTp06ERQUhI+Pj8H6r7/+OgMHDmTw4MEFG1CM9bCF\nEKIq0+vhxRfBzAy6TVnOhuD/8eJRb+ZPmcKRxx/HXMYeC1HlVJf8MnHiRJYsWcKOHTuyH5Y7e/Ys\nEyZMMBgqV65cyYgRI4q8r16vL9b7Dx06lLi4OPbs2VOidhflQd9Pcb67UsV7c3NzFi9eTN++fdHp\ndIwcORIfHx+WLVsGwJgxY0pzWyGEqJamT4eoKPh6XTi913zA0YPt8H97HJtbtZJwLIQwqlmzZrF0\n6VL8/f2zz61Zs4b2hSx3HxAQwNGjRyuqeUZTqh7kMm1ANfkXmBBCGLJqlfpQ3t79aQzc6M+iW+35\nwbo5NZ99lgXe3sZunhCilIqbX8pruG1ZRaedO3cSGBjI8ePHAUhNTaV58+bs37+fhg0bGnxNWQ6x\nqKw9yNJ1IYQQ5WTfPpg6FbZsgc9OTKGLqQf6kAh2PfYYszw9jd08IUQFUJTyKWUlNDSULl26ZB9P\nnz6d8ePHFxqOV65ciaWlZZGlqqs8I6iFEKIauXQJnnsOVq+GcH5lx6VgTgY3pcN777GoRQtqVqIH\nWIQQj67Q0FBGjhwJwLp160hISGDu3LmF1n9UhljIT2ghhChjd+7AgAHq0IpmnSLptHwcYSajmdtW\nj5+7O/9ydjZ2E4UQAp1Ox+HDh/nmm29YuHAhaWlpLF++/IGvcXJywukh521PS0tj69atgLpuxr17\n91i/fj0AAwYMwNra+qHuXxZkDLIQQpShlBTo0QN69YIZMzN5auVTvOrYnSf/u42nvvySk489hqtM\n6yZElVcd8kt4eDg9evRg8uTJDBo0CC8vrwp538jISJo0aQLkzImsKAomJiZEREQUOryjJB52DLIE\nZCGEKCOZmfCvf0GDBvDtt/DhnmmcuHGcLat0dJvwFsPat2e8q6uxmymEKAOSXyo3o0zzJoQQIi9F\ngTfeAFNTWLYMdlwO5odTPxBu8Q4rmkaQ6erKWBcXYzdTCCFEMUhAFkKIMvDBB3DhAuzeDdHJV3l1\nw6ts6ryI1Nc+5MNvv2WXtzdmVWB5VSGEEBKQhRDioc2fDxs2QGgomFlmMPSnobz32FT8Zyxn2OzZ\njHBzo5WdnbGbKYQQopgkIAshxENYsgQWL4Y//4TateHNre/Q0L4hk4/XYIO7O8fd3Fjh4WHsZgoh\nhCgBCchCCFFK338Ps2dDSAi4u8OPp35kd8Rujj2xioT3XmD8qlX83Lw5NmZmxm6qEEKIEpCALIQQ\npRAUBB9+CHv3QpMmcObWGSb/MZm9LwRj969RvL5wIYMbNOBJBwdjN1UIIUQJSUAWQogS+v13eOcd\n2LULvL0hPi2eIeuGML/PfPy+Wkdw166E1K3LmcaNjd1UIYQQpWBq7AYIIURVsmEDjB0L27aBnx9o\n9VqG/TqMAU0H8O94d5LWr2f088/zrbc3drKctBBCVEny01sIIYpp7VqYOFENx+3aqecCdwaiKApz\nO30Ibdvz3nff0c/ZmZ6OjsZtrBBCiFKTgCyEEMWwciVMmwY7d0LLluq5VadWseniJg6NOoT5qLfY\nM2IEW21tOevpadS2CiGEeDgyxEIIIYqwZAn85z/qA3lZ4fjQ9UNM/WMqG4dtxOm37SSfO8eoPn1Y\n2qwZ9jK0QgghqjQJyEII8QDz58Pnn6vzHHt7q+di7sUwZN0Qvgv4Dt8EC5g0ialff01XBwcG1K5t\n3AYLIUQlt27dOgYMGICLiws1a9akQ4cO/Pzzz8ZuVh7SzSGEEAbo9fD++7BpkxqOGzZUzydrkhkY\nNJDxHccz0KMPdO7M9i++INjEhFNNmxq30UIIUQV8+eWXNGnShIULF+Ls7MzWrVsZPnw4d+/eZcKE\nCcZuHgAmiqIoRm2AiQlGboIQQuSh0cDrr0NkpBqQszqFtXotz/78LPXt6rN84HJMJk4kNi6OVm++\nyWofH7rLg3lCPDIkv5ReXFwcTk5Oec699NJLHDx4kCtXrpTJezzo+ynOdydDLIQQIpfEROjfH1JT\n1XmOs8Kxoii8vf1tNDoNSwYswWTDBpTNm3lz6lReqFtXwrEQQhRT/nAM0KZNG2JiYozQGsNkiIUQ\nQtwXEwNPPw1dusDChZB7heh5B+ax/9p+9o/Yj8X1GBgzhp9//50zGg0rZUEQIcQjRKvVFlnHvIQP\nKx88eBDvrAc9KgHpQRZCCODIEfD3h2HDYPHivOH4l3O/sPDwQra9tI1aptYwbBjXP/yQicCPPj5Y\n564shBBVyMSJE7G0tGTv3r3Z586ePUu3bt0M1l+5ciWWlpZFlpLYvXs3GzduZMqUKQ/zUcqUjEEW\nQjzy1qxRFwD55hsYNCjvtb+u/sWQdUPY+e+dtKnfBiZNQrl0ib6zZvGkgwP/8fAwSpuFEMZV3Pxi\n8rFJuby/Mr1sstO9e/dwdnYmPj4eGxsbAKZNm0ZGRgZffPFFgfpxcXFERkYWed92WaspFSEyMhJ/\nf3+6dOnCr7/+WqK2P8jDjkGWIRZCiEeWXg8ffQRBQbB7N7Rqlff68RvHGbpuKD8P+VkNx0FBsHkz\nXwUHk5iUxAdZU1sIIUQhyirIlpewsDBatGiRHY5TU1NZvXo1+/fvN1jfycmJWrVqlcl7x8XF8fTT\nT9O4cWN++umnMrlnWZGALIR4JCUlwcsvq9vDh6FOnbzX/777NwPWDGDZM8vo2aQnnDkDb7/N6eBg\nPr59mwNt22JuKqPUhBBVW2hoKF26dMk+nj59OuPHj6dhIR0AK1euZMSIEUXeV6/XP/B6amoqzzzz\nDFqtli1btmBlZVWyhpczCchCiEfOyZPw3HPQpw/873+Qf7jctcRr9F3dl9k9ZzPIZ5A6tcXgwaR+\n+SXDdDq+8PSk6f3eFiGEqMpCQ0MZOXIkoC7gkZCQwNy5cwutHxAQwNGjRx/qPbVaLc899xyXL1/m\nwIEDODs7P9T9yoOMQRZCPDIURR1n/NFHsGiR+kBefrdTbvPk908yrsM4Jj02SR2HMWgQuLsz5q23\nSNHp+NHHBxOT8hlXKISoGqpDftHpdDg5OXHy5Ek2b95MWloagYGB5f6+o0eP5ttvv2XBggV07Ngx\nz7V27dqV+CE/Q2QMshBCFENyMowZo46U2L8/Z9no3OLS4ui7ui/DWgxTwzHA7Nlw5w7rlyxh17Vr\nnOjQQcKxEKJauHjxIjY2Nqxfv55Bgwbh5eVVIe+7c+dOTExMmDhxYp7zJiYmREREFDq8oyJJD7IQ\noto7dgxeeilnfmNDoyNiU2Pp9WMvejXuxee9P1dD8KZN8OabXN2/n47R0Wxp2ZJOZfRwihCiapP8\nUrk9bA+yBGQhRLWl1cKcOWooXrAAXnzRcL2scNy7SW8+6/WZGo5Pn4aePdFu2UI3CwsCnJ15rxL0\nagghKgfJL5WbDLEQQggDLl2CV15Re4uPHwc3N8P1ssJxnyZ9mNNrjhqOb92CgABYtIiPnJ2xTU5m\nqrt7xX4AIYQQRiNzFAkhqhW9HpYuhc6d1Yfw/vjjweG456qeecNxRgYMHgyvvMKmXr1Yc/s2P/n4\nYCrjjoUQ4pEhPchCiGrj779h9GjQaODPP8HXt/C6Mfdi6Lu6L/29+ueEY0VRb9CgAZcDAxl18iSb\n/PxwLoMnqoUQQlQd0oMshKjyNBqYNUt9CO+55yA09MHh+FLcJbqs6MJwv+E54RjUActnz5L2/fcM\nDQ/no0aNeMzevmI+hBBCiEpDepCFEFVaaCiMHQsNG6pjjYt6ju7kzZP0/6k/M7rNYHT70TkXfvwR\nli2D0FDeio6mmbU1b7m6lm/jhRBCVEoSkIUQVVJMDAQGQkgIzJsHzz8PRQ0T3nd1H0PWDeHrAV8z\n1HdozoUdO2DqVAgJ4XtTU0KTkjjcrp3MdyyEEI8oGWIhhKhSMjLgs8+gVStwd4fwcHjhhaLD8Ya/\nNzBk3RDWDFmTNxwfOwYvvwy//cYRV1feu3KF9S1aUNNc+g+EEOJRJX8DCCGqBEWB33+H999XV8EL\nC4PiLPqkKApfHPyCL8O+ZPtL22nv0j7n4pUrMHAgfPMNMR06MOjYMb5p1owWtrbl90GEEEJUehKQ\nhRCVXkiIGozT02HRIujbt3ivy9Rl8ubWNzkSc4SwUWG41co139vt29CvH/znP6QHBDDo5EnGuLgw\nqE6dcvkMQgghqo6HGmIRHBxM8+bNadq0KZ999lmB6z/99BOtW7emVatWPPHEE5w+ffph3k4I8Yg5\ndQr694cRI+Dtt9WH8IobjuPT4nn6p6e5mXKT/SP25w3HcXHQpw+8+CLK2LGMvniRRlZWfNSoUfl8\nECGEENlWrlyJqalpgfLNN98Yu2nZSt2DrNPpmDBhArt27cLV1ZWOHTsSEBCAj49Pdp0mTZrw119/\nYW9vT3BwMKNHjyYsLKxMGi6EqL7OnVOnbdu7Fz78EDZsgJJMRfz33b8ZtHYQ/Tz7Ma/PPMxMzXIu\nJiXB009Dz54wYwZfREVxJiWF/W3bykN5QghRgfbu3Yu1tXX2cePxD7NdAAAgAElEQVTGjY3YmrxK\nHZAPHz6Ml5cXHh4eAAwbNoyNGzfmCcidO3fO3vf39+f69eulb6kQoto7eVINxvv2weTJ8M03ULNm\nye7x6/lfGbd1HLN7zmZku5F5L6amwjPPQNu2MG8e2+Li+OL6dQ61a4etmZnhGwohhCgXHTt2xMbG\nxtjNMKjUATk6Ohp3d/fsYzc3Nw4dOlRo/e+++47+/fuX9u2EENXY0aNqMD58WJ1t7YcfoKTPyWn1\nWqbtnsYv538p+DAeqNNfDBoEHh7w9decTE7m1b//ZoOfHw2trMrsswghhCgeRVGM3YRClTogl+RX\nkXv37mXFihWEhoYavD5jxozs/W7dutGtW7fSNksIUUXodLBlC8yfDxER8O67EBQEuX7bVmy3U27z\nwvoXsDSz5OgbR6ltUztvhbQ0GDwY7O1hxQquaTQ8c+YMXzdtyhOyUp4QQpSIVqstso55MabK9PT0\nJDY2Fk9PTyZPnszo0aOLfE1phISEEBISUqLXlDogu7q6EhUVlX0cFRWFm5tbgXqnT5/mjTfeIDg4\nGEdHR4P3yh2QhRDVW3IyrFwJCxaAoyNMmaJmVwuL0t1v15VdvLbhNV5r8xofd/s473hjUIdVBARA\n3bqwahUJikL/06d5x92d5+rWfejPI4QQVdnEiRNZsmQJO3bsoHv37gCcPXuWCRMmGAyVK1euZMSI\nEUXeV6/XF3rNxcWFWbNm0alTJ3Q6HUFBQYwdO5bU1FQmTZpU6s9SmPydrx9//HGRrzFRStm/rdVq\n8fb2Zvfu3bi4uNCpUyeCgoLyjEG+du0aPXr0YPXq1Tz22GOGG2BiUqm72IUQZePyZXVM8XffwVNP\nqWOMH3+86AU+CqPRafhw94cEnQ3ih2d/oGeTngUrJSerY44bNYIVK9CYmPD06dO0sLVlgZeXPJQn\nhCi16pJf7t27h7OzM/Hx8dnjgadNm0ZGRgZffPFFgfpxcXFERkYWed927dqVqB3Dhg1j9+7d3Llz\np0SvK8yDvp/ifHel7kE2Nzdn8eLF9O3bF51Ox8iRI/Hx8WHZsmUAjBkzhpkzZxIfH8+4ceMAsLCw\n4PDhw6V9SyFEFZOZCZs2wbJlcOIEvPIKHDoEnp4Pd98Ldy/w4q8v0sihEafGnio4pALU2Sr69wcf\nH1i2DL2JCa+Hh1PTzIz/STgWQlSU8vpZU0bhPCwsjBYtWmSH49TUVFavXs3+/fsN1ndycqJWrVpl\n8t65DRkyhHXr1nH16lUaVYIpN0vdg1xmDagm/wITQuSIjITly2HFCmjaFMaMgSFD4GGfhdMrepYe\nXcr0kOnM6j6L0e1HGw66N2+qU7k98QQsXIhiYsKEf/7hbEoK21u1wkZmrBBCPKTqkl9mzJhBXFwc\nCxcuBODdd9/F2dmZwMBAg/XLYoiFIevXr+f5558nIiKiTAKy0XqQhRAit8REWL8eVq1S5zF++WXY\nvRt8fcvm/pfiLjFq0ygydBnse30fzZ2bG654+bK6CMirr8J//gMmJnx05QphSUnsbdNGwrEQQuQS\nGhrKyJHqlJjr1q0jISGBuXPnFlo/ICCAo0ePlnk71q9fj7Ozc6XoPQbpQRZCPITMTAgOhtWrYccO\n6NED/v1vdWRDjRpl8x46vY6Fhxbyyb5P+PDJD3nb/+2CD+JlOXECBgyA6dPVbmtg7rVrrLh5k7/a\ntKFOSVYbEUKIB6gO+UWn0+Hk5MTJkyfZvHkzaWlphfYcl6WhQ4fSuXNnWrRogVarZe3atfz0008s\nWrSI8ePHl8l7SA+yEKJCabXqQh7r18Mvv0CzZmooXrIEnJzK9r1O3zrN2C1jsTSzJGxUGF5OXoVX\n3rULhg+HpUvVaTGAb2Ji+Domhn0SjoUQooCLFy9iY2PD+vXrGTRoEF5eD/gZW4a8vb1Zvnw5UVFR\nKIpCixYt+PHHH3nppZcq5P2LQ3qQhRBFysxUl33+9Vf4/Xdwd4ehQ+H55x/+gTtDEtMTmR4ynTVn\n1vDf7v/ljfZvYGpiWvgLli6FGTNg3Tro2hWA5TExzLx6lb2tW+NVSVdqEkJUXZJfKjfpQRZClIvk\nZHUM8caN6kwUXl5qKD50CBo3Lp/3VBSFn878xHs732NA0wGcH38eZxvnwl+g06kTKQcHw/79aiNR\ne45nSTgWQghRShKQhRDZLl+GrVvVcvAgdOoEAwfCxx+rvcbl6Uj0Eab8MYWUzBR+e+E3HnMzPHd6\ntqQkePFF0GjUxt5fiGhZTAyfXL3KHgnHQgghSkmGWAjxCEtPhwMHYNs2NRTHx6sP2A0YAL17QzlM\ndVnAlfgrTNs9jX3X9vFxt495vc3rhT+El+XcOXWccc+e6pJ895fhWxIdzexr1yQcCyHKneSXyk2G\nWAghik2nUyd62LVLHT4RFgYtWkC/fur0bO3bg+kDhvqWpdjUWD7Z9wk/nPqBSf6T+C7gO2wtbYt+\n4dq1MGECzJ0Lr70GqEMz5ly7xvIbN9jbpg2e1tbl23ghhBDVmgRkIaoxRYELF2DPHjUQ790LDRqo\nHa9vvaXORGFvX7Ftik2NZf7B+Sw9tpTnfZ/n/JvnqWdXr+gXZmZCYKA6KHrnTmjTBlDD8buXL7Mj\nPp79bdviUlbzywkhhHhkSUAWohrRaNQe4v37c4qtLXTvDoMGwaJF4OJinLblDsZDfIZwbPQxPBw8\nivfiK1fUKdycneHo0ezxxlq9njcuXuRCaip/tmmD0/2hFkIIIcTDkDHIQlRhCQnqrBJZYfjoUXUi\nhy5d1PLEE+DmZtw23ky+ycJDC1l2bBlDfIYw7clpxQ/GoK5C8s478NFHarf3/TEgKTodw8+fJ0Ov\n51c/P2xlhTwhRAWS/FK5yRhkIR4RaWlq7/CRIzklOlodN/zkk+rog86dK37IRGHO3T7H/IPz+e3v\n33jR78WS9RiDunb1+PFw/Lg6aLp16+xL0RkZDDxzhjZ2dixt1gzLiho4LYQQ4pEgAVmISigjA86f\nV3uEDx9Ww/DFi+Djo0691qOHGoh9fMC8Ev1frCgKeyP3Mu/API7fOM6EThP4561/HjyXsSHbt6tL\nRQ8YoP5HyDUjxYl79/jX2bO86eJCYMOGmJiYlPGnEEII8aiTIRZCGNnt23DqVN7yzz/QpAl06AAd\nO6qldWuwsjJ2aw1LTE9k1alVLD22FEVRmNx5Mi+3ehkr8xI2OD5eHU7x55+wfDn06pXn8qa7dxl5\n4QJLmjZlaN26ZfgJhBCiZCS/VG4PO8RCArIQFSQtTZ1R4vz5vGE4PV0Nv7mLry9UhZnKjsUcY8nR\nJfwa/it9PPswrsM4nmr0VOl6dTduhDffVOc3nj0b7OyyL+kUhZmRkXx34wa/+vnhXxETNAshxANI\nfqncZAyyEJVMUhKEh6tBOPc2JgY8PdVhEa1aqVmwTRt1hbqqNErgdsptgs4Eser0KmJTYxndfjTh\n48Opb1e/dDe8ckXtNQ4Ph6Ag6No1z+W4zExeCg8nVafjaPv21Jdp3IQQokpbv3498+fP5+LFi6Sk\npNCoUSP+/e9/895772GRbzai8+fP89ZbbxEWFoaDgwOjRo1i+vTpmJbzsycSkIUoBa0Wrl1Th0Jc\nuqT2DGeF4YQEaN5c7QX28YFRo9RtkybZC75VOenadLZc3MIPp35g39V9DPQeyJyec+jRuEfRq94V\nJjUVPvsMFi+GqVNh3TrIF35P3LvHkHPnGOTszJwmTbCQh/GEEKLKi4uLo1evXgQGBuLg4MChQ4eY\nMWMGN2/eZNGiRdn14uPj6dWrF35+fmzatIlLly4xZcoU9Ho9//3vf8u1jTLEQohCZGbC1atqAM4K\nwln7V69C/frqlGpNm6olKxA3bFhxq9GVp0xdJnsj9/LLuV/47e/faFO/Da+0eoXBPoOpWaNm6W+s\nKPD77zB5Mvj7w7x5ajd6LnpFYeH163xy7RqLmzblBRlvLISoZCS/lK2PPvqIr776ivj4+Oxzs2fP\nZt68eVy9ehW7+8Pu5s6dmx2ma9Ys/O8iGWIhRCnp9XDjBkRGqoE3MjJn/8oViIpSF9Xw8sopPXuq\nYbhx48r7wNzD0Og07Lqyi/Xn17PxwkaaOjVlqO9QTow5QUP7hg//Bn/9Be+/D8nJsGKFOh1HPrc0\nGl77+2/iMzMJa9dOlo0WQohHgJOTE5mZmXnObd++nb59+2aHY4AXXniBwMBA/vzzT5555plya48E\nZFFtZWaqATh/+M3av35dXZDNw0MtjRpBu3bqM2IeHmoIfhSGu8alxbHj0g62/rOVbf9sw7eOL0N9\nhzKj24yyCcUAZ87ABx/AuXMwc6a6Kp6BhT22xsYy6sIFRtavz3QPDxlSIYQQlZBWqy2yjnkx5iDV\n6XRkZGRw/PhxFi1axNixY/Ncv3DhAr3yzWbUsGFDbGxsuHDhggRkIfJLSVEDbnR0wW3Wfmws1K2r\nBt+sENypEzz/vLrfsGH17AUuiqIonLtzjq0Xt7L1n62cvHmSro26MqDpAD7r9RmutVzL7s3OnYNP\nP1UX+pg2DX791eC/OmIzM3nn0iX2JSay1teXrg4OZdcGIYQQhZo4cSJLlixhx44ddO/eHYCzZ88y\nYcIEQkJCCtRfuXIlI0aMKPK+er2+yDq2trZoNBoAhg8fzueff57nenx8PA4G/j5wdHTMMxSjPEhA\nFpVKcjLcugU3b+aUW7cKBuGMDHB1VZdRzto2b64Ogcg6V69e5VpEw5huJd9ib+Re9kTsYcflHZhg\nwoCmA3i/y/t09+iOtUUZD2M4dgw++QQOHIBJk2DJEihkarb1t2/z9qVLPFenDmc6dMBOvjQhRDVi\nYiBklgWlW7cyuc+sWbNYunQp/v7+2efWrFlD+/btDdYPCAjg6NGjZfLeYWFhpKamcujQIWbOnMm4\nceNYtmxZmdz7YcnfRKLcZWTkhF5D4Tf3sU4HDRqoD8DVq5ezfeyxvIHYyalqTY1W0RLSE/gz8k/2\nROxhT+Qeriddp2ujrvTw6MFE/4n41vEt+xXoFAX27FEfujtzBt59F1avzrMKXm5X09N559Ilzqek\n8EuLFjxRWdbIFkKIMlRWQba8hIWF0aJFC2zu/6xOTU1l9erV7N+/32B9JycnapXRXPRt2rQB4PHH\nH8fZ2ZlXX32V9957D09PT0DtKU5MTCzwuvj4eBwdHcukDYWRgCxKRFEgMRHu3oU7d9Rt7n1D51JT\n1aEO9evnLc2bQ7duOcf16kHNmhJ8SyMqMYoDUQc4EHWA0KhQLsZepLN7Z3p49GBFwAraNmiLuWk5\n/e+elqYG4YUL1ScfJ02CDRsKHcCdptMxNyqKBdev87abG2t8fLAyMB5ZCCFE+QsNDaVLly7Zx9On\nT2f8+PE0bGj4GZSyHGKRW9u2bQG4evVqdkBu3rw54eHheepFRUWRmppK8+bNS3T/kpKA/AhLT1dX\n9s0qcXF59w2F3dhYdYU3Z2eoU0fd5t739s7Zz9ra21ePac8qC41Ow+lbp/ME4gxtBk80fILH3R5n\nQb8FdHDpQA3zcn7C8PJl+PZb+O47dXD3/Pnq0tCF/AtHURQ23r3L5MuXaWtnx7H27fGQGSqEEMKo\nQkNDGTlyJADr1q0jISGBuXPnFlq/LIdY5G8HQOPGjbPPPf3008ydO5fk5OTsmSzWrl2LjY0NTz31\nVJm3ITeZB7mK02jUHt3c4dZQ2DW0r9WqQxUcHdWSf99QAHZ2BktLY3/qR4dGp+HMrTMcu3GMYzHH\nOHbjGOfvnMfLyYvH3R/PLp6OnmU/ZMKQtDT1QbvvvlMfwHv5ZRg3Tp377gH2JyTw/pUrJOp0/M/T\nk15OTuXfViGEKEfVIb/odDqcnJw4efIkmzdvJi0tjcDAwHJ/3379+tG7d298fX0xMzMjNDSU+fPn\nM3DgQNasWZNdLyEhAV9fX/z8/AgMDOTy5ctMmTKFd955h5kzZz7wPR52HmQJyEaiKOoDaUlJasDN\nKrmPi7Ov1ao9tFnh9kGBN/++jY0MZ6hM4tLiOHPrDGdvn+XUrVMcu3GM8DvheDp50r5Be9o3aE8H\nlw60rt8aGwvD43rLhaJAWBj8+COsXav2Fo8cCQEBRf5r6XRyMtOuXOFcaiozPTwYXq8eZvKHTghR\nDVSH/BIeHk6PHj2YPHkygwYNwsvLq0Le9//+7//4/fffiYyMxNzcHE9PT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       "text": [
        "<matplotlib.figure.Figure at 0xeb63c18>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we write a function which fits the student t distribution to a dataset, using moment estimates for the mean and standard deviation as input."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fit2StudentT(X, nu0):\n",
      "    \"\"\"\n",
      "    fit2StudentT: ML fit to a Student's t distribution\n",
      "    INPUT:\n",
      "             X : Sample\n",
      "           nu0 : Seed for the degrees of freedom\n",
      "\n",
      "    OUTPUT:\n",
      "     [mu,sigma,nu] : Parameters of the Student's t distribution from ML fit\n",
      "          modelPdf : Fitted pdf\n",
      "          modelPdf : Fitted cdf\n",
      "          modelPdf : Fitted inv\n",
      "    \"\"\"\n",
      "\n",
      "    ## Seed for mu,sigma determined from moment matching\n",
      "    mu0    = np.mean(X);                        # match first moment\n",
      "    sigma0 = np.sqrt(np.var(X) * (nu0 - 2)/nu0) # match second moment\n",
      "\n",
      "    ## ML fit \n",
      "    def PDFhandle(X, args):\n",
      "        _mu, _sigma, _nu = args\n",
      "        return locationScaleTpdf(X, _mu, _sigma, _nu)\n",
      "        \n",
      "    LL, argsout = fit2pdf(X, PDFhandle, [mu0, sigma0, nu0])\n",
      "    mu, sigma, nu = argsout\n",
      "    \n",
      "    ## Model pdf, cdf and inv\n",
      "    modelPdf = lambda x: locationScaleTpdf(x, mu, sigma, nu)\n",
      "    modelCdf = lambda x: locationScaleTcdf(x, mu, sigma, nu)\n",
      "    modelInv = lambda p: locationScaleTinv(p, mu, sigma, nu)\n",
      "    return [mu, sigma, nu], modelPdf, modelCdf, modelInv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An example"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def studentFitExample():\n",
      "    mu = 3\n",
      "    sigma = 2\n",
      "    nu = 2.5\n",
      "    M = 1e5\n",
      "    ## Draw M samples\n",
      "    X = mu + sigma * tdist.rvs(nu, size=(1e5))\n",
      "    \n",
      "    nu0 = 5\n",
      "    \n",
      "    mle_args, mle_pdf, mle_cdf, mle_inv = fit2StudentT(X, nu0)\n",
      "    mle_mu, mle_sigma, mle_nu = mle_args\n",
      "    graphicalComparisonPdf(X, mle_pdf, xMin=-15, xMax=25, nBins=1000)\n",
      "    print \"Estimated parameters (MLE) vs True parameters\"\n",
      "    print \"Mean:\", np.round(mle_mu, 5), mu\n",
      "    print \"Std: \", np.round(mle_sigma, 5), sigma\n",
      "    print \"DF:  \", np.round(mle_nu, 5), nu\n",
      "studentFitExample()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Estimated parameters (MLE) vs True parameters\n",
        "Mean: 3.00505 3\n",
        "Std:  1.98921 2\n",
        "DF:   2.48078 2.5\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h3V1Po0ePZtcu7Qr77N69W456Es7FbCAbpzmD32Cx+8lZqhKiK9rtUXz11VdM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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x17986240>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Copulas"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recall that in Week 8 we encountered the multivariate Gaussian distribution. These multivariate distributions are characterized by (1) the marginal distribution of the random variables which are also Gaussian, and (2) a linear correlation between the different random variables which is completely captured by the covariance matrix $\\Sigma$.\n",
      "\n",
      "The multivariate Gaussian can only deal with linear correlations among its random variables. For more complex dependencies we make use of a more sophisticated object: copulas. Using copulas we can seperate the process of (1) modelling the individual assets and (2) modeling the dependencies between these assets. For an exact definition of the copula we refer to the lecture.\n",
      "\n",
      "Here we look at two different copulas: the Gaussian and the student t copulas. For simplicity we assume that in both cases the  marginal distributions are all Gaussians. \n",
      "\n",
      "We first implement a random number generator from a Gaussian copula."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.linalg import cholesky\n",
      "from scipy.stats import norm\n",
      "\n",
      "\n",
      "\n",
      "def gaussianCopulaRand(M, rho):\n",
      "    \"\"\"\n",
      "    gaussianCopulaRand: Generates random numbers from a Gaussian copula\n",
      "    INPUT:\n",
      "         M : size of the sample\n",
      "       rho : corelation matrix [D,D]\n",
      "\n",
      "    OUTPUT:\n",
      "         U : Sample from the copula [M,D]  \n",
      "    \"\"\"\n",
      "    \n",
      "    rho = np.asarray(rho)\n",
      "    \n",
      "    ## Dimensionality of the copula\n",
      "    D = rho.shape[0]\n",
      "    \n",
      "    ## Cholesky decomposition\n",
      "    L = cholesky(rho).T\n",
      "    \n",
      "    ## Sample from N(0, I)   [independent components]\n",
      "    X = np.random.randn(D, M)     \n",
      "    \n",
      "    ## Sample from N(0, rho) [linearly dependent components]\n",
      "    Z = np.dot(L, X)                          \n",
      "    \n",
      "    ## Gaussian copula (U[0, 1] marginals)\n",
      "    U = norm.cdf(Z)   # Matrix [D, M]\n",
      "    U = U.T           # Matrix [M, D]\n",
      "    return U\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For example"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def exampleGaussCopula():\n",
      "    rho = [[1, 0.8], [0.8, 1]]\n",
      "    M = 2e3\n",
      "    U = gaussianCopulaRand(M, rho)\n",
      "    Uinv = norm.ppf(U).T\n",
      "    fig = plt.figure(figsize=(8, 8))\n",
      "    ax = fig.add_subplot(121)\n",
      "    ax.scatter(Uinv[0], Uinv[1])\n",
      "    ax.set_xlim(-4, 4)\n",
      "    ax.set_ylim(-3, 3)\n",
      "    ax.set_aspect(1)\n",
      "    ax.set_title('Multivariate Gaussian', fontsize=18)\n",
      "    ax2 = fig.add_subplot(122)\n",
      "    ax2.scatter(U.T[0], U.T[1])\n",
      "    \n",
      "    ax2.set_aspect(1)\n",
      "    ax2.set_xlim(0,1)\n",
      "    ax2.set_ylim(0,1)\n",
      "    ax2.set_title('Gaussian copula', fontsize=18)\n",
      "exampleGaussCopula()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jSlGLVey5efMmkpKS0LDh69BquwCIhVL5MbTak4/cAWry5KmYPn0DLl36Bhcv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MuW3Rk7diyOkyq0/B2PJ04s1op4fBjRaA4zZ84kEinFtfbdi9ApMOYdPJ6YNrF5vHYcj+dKhg49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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xeb6c9e8>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is clear linear correlation between the X and Y components of the sample points. To introduce non-linear correlations using copulas we need a more sophisticated construct, for instance by using a student t distribution.\n",
      "\n",
      "Here we implement such a coopula. To emphasize, the marginal distributions are still assumed to be Gaussians. It's the correlation among the different components which is described by the student t distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import t as tdist\n",
      "from scipy.stats import chi2\n",
      "\n",
      "\n",
      "\n",
      "def studentTCopulaRand(M, rho, nu):\n",
      "    \"\"\"\n",
      "    studentTCopulaRand: Generates random numbers from a Student's t copula\n",
      "\n",
      "    INPUT:\n",
      "         M : size of the sample\n",
      "       rho : corelation matrix [D,D]\n",
      "        nu : degrees of freedom\n",
      "\n",
      "    OUTPUT:\n",
      "         U : Sample from the copula [M,D]  \n",
      "%\n",
      "%% EXAMPLE:   \n",
      "%        rho = [1 0.8; 0.8 1];\n",
      "%        M = 1e4;\n",
      "%        U = studentTCopulaRand(M,rho);\n",
      "%        figure(1);\n",
      "%        plot(U(1,:),U(2,:),'.');\n",
      "    \"\"\"\n",
      "    rho = np.asarray(rho)\n",
      "    \n",
      "    ## Dimensionality of the copula\n",
      "    D = rho.shape[0] \n",
      "    \n",
      "    ## Cholesky decomposition\n",
      "    L = cholesky(rho).T\n",
      "    \n",
      "    ## Sample from N(0,I)   [independent components]\n",
      "    X = np.random.randn(D, M)\n",
      "    \n",
      "    ## Sample from N(0,rho) [linearly dependent components]\n",
      "    Z = np.dot(L, X)                       \n",
      "    \n",
      "    ## Sample from Chi2 with nu degrees of freedom\n",
      "    xi = chi2.rvs(nu, size=M)[np.newaxis, :]\n",
      "    \n",
      "    ## Student t copula (U[0,1] marginals)\n",
      "    U  = tdist.cdf(sqrt(nu) * Z / sqrt(xi), nu) # Matrix [D,M]\n",
      "    U = U.T                                     # Matrix [M,D]\n",
      "    return U\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def exampleStudentCopula():\n",
      "    rho = [[1, 0.8], [0.8, 1]]\n",
      "    M = 2e3\n",
      "    U = studentTCopulaRand(M, rho, 2).T\n",
      "    \n",
      "    fig = plt.figure(figsize=(5, 5))\n",
      "    ax = fig.add_subplot(111)\n",
      "    ax.scatter(U[0], U[1])\n",
      "    ax.set_xlim(0, 1)\n",
      "    ax.set_ylim(0, 1)\n",
      "    ax.set_aspect(1)\n",
      "    ax.set_title('Student T Copula', fontsize=18)\n",
      "exampleStudentCopula()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oCCKBlpQyzXQiUI6VKtWixWLh9u3bKTk5/ySPd0n+/YP8gZpOJ6dXOLZ369at\n1OvtqVC4EBDp6xv0RH+sLVu2UBSdaTK1ocFQkm3adMozBnjx4kXu2bMnxzGbNjwb69evpygWl/VG\nCdRourBdu9A8mctisfDSpUs8ffr0ExORxsfH88yZM7xx40a25hg9ehzVaj2VSg3r1GmW4yQbycnJ\n7N//c4qiAw0GJw4e/GWef/i///57mkxtrT5IyVSpRKs6HCkW9D6cNm0ao6Oj+cEHPQiMsupzipJT\nsyelNFbFCXxKvd6bx48fZ61azWWjh0gpjM2Z6ZMdkAZD4VeT+cXExFAUHWUxdzaBfwl8TXf3IoyP\nj8/Q3t7eg8BvTAmENhrLMDw8PDfIT4eRI7+mTudMO7tgGgzO/OWXX3J9DhvS478MI79UIefOnaOX\nlz+NxiLUau346adDn6u/xMhLUArVyh1GPn78ZIpiMIHLBCIoiuVzJX/g07B161YajeUJJDGliJFa\nrWeVKvWpUHxCyWXlOHU619TY9DFjxlKhqCFLefYEasvGjBRXp7sEnGk0luXevXtZoUIdWdLrQ+Bt\nmUlah3/eoFJpeDWZ34ULF6jTuVHy9Unj9lqtN6tUacCAgGD27v0pY2NjmZiYSEFQWN0MUhQ/4Ny5\nT/YTzA6OHDlCUfSiFJFAAjtpMrkU6GpcBQXJycn5vlUsW7YaBWGafO/v0GAo+cQP7I0bN3j27Nl0\nEmTfvp8QmEDrLbybW9Ec0SSljNpsNeZq1qvXOkdjPguJiYmsVq0hRbEOFYohFEU/Tpw4lWPGfCXH\nYqsIGKnRmFKzLq1evZqS0/JfBG4SqEylsli6dxsIJKBnmzadWLt2IwIVKbm9fEwggEALAqUpRXf4\nsFixN7LN/F6Kur1PgoeHBwQhDsC/SCtUch7x8Xdx6FAjnD49Cd99dwEdOnSFSqVCiRLloVB8A4CQ\n0lxvybFF8L84d+4clMrKANzlI7WRkJCIu3fv5uo8NmSEQqGAVpuDOq25gDNnjoMMlX85IT6+GY4f\nP56uDUn06vUJfH1Loly5hihWrCwuX74MAChUyANa7R+QnlEA+APu7h5PnG/VqtXw9Q2Cq2sR9O//\nOZKSkjK0cXV1hCCcTv2tVJ6Bm5tjTpb5TKhUKuzcuRmzZoVg5Eg9NmyYj88+G4B585bDYtkCIAbA\nQyQl9cSCBYswbtx4jBkzEVLltbIAXAHMgsVyA8AyAAkAVgK4DGAlwsOJkycjIBUsqgpgOoC6AOwB\njAbgDY2HEqEWAAAgAElEQVTGDaGhHbK/iFz8GDwV2Z0qPDxcDn4uQ2AYlUovqlRNrL4UMVQqNYyL\ni+OFCxdYpEhpajRmajQGzp+/KJdXQR4/fpyi6C4rX0lgMx0cPF7pGFwb0uDvX47AUqZk3TEYyvPH\nH39M12bNmjU0GMoQuEcp6cYYVq3aiCQZHR3NwMBKNBpr0GjsQKPR5Ykpy3bs2EFR9KQU93qaolg7\n0232mTNnaDa7Uad7nzpdZ9rbe2QrTjkhIYGXL19mbGxs6rG//vqL7dt3YdOmHbKUNs7LqySlzMv/\nynR3o6OjD7Xadyj56HW0enfX0tPTn35+QRQEpbylXUxgAYF5BJRUq/0oOTin5O+rTsCOKpUDmzZ9\nmwkJCa/mtjcFt2/f5qhRo9ivX38OGDCARmN9qwt4h0qlJnVrYbFYGBUVladVs775Zha1WjuaTAE0\nm924d+/ePJvLhrzHnj17WKJERTo5+fDttzs/1QBx9OhR2tt70M6uKkWxEN999/0MxoWhQ4dTCsZP\neUav0Gx2Tz0fGxvLdevWcenSpU912O7Vq/9/tshHWahQqUzbXrlyhTNmzODMmTOzFZ+8b98+2tt7\nUBQ9qNfb88cf1/LEiRM0GJwJTCawhKLoy7CwpSTJR48e8fLlyxnUPZMmTaNa7U3JqluRgIFqdQAl\nN6U3KIWotZW3rXYsUSKIly5d4vz582Xm50YpiWlFAiIVCg0BDYFvKenzaxDQs1mzFqxWrTGLF69U\nMJhfREREjsd59OgRCxcOpEbzIYHvKIqV2KfPpzkn8Dlx69YtHj9+/IVkws0qDh8+zJo132JgYFUO\nGzbqpSub+DJCSq7gTCmI/jy12hA2bPh0fdm9e/e4a9cuHj9+PFOralhYGA2GapSyD5OCMDdbfolD\nh35BlaqPFfPbyICAys89zrMQFxdHOzt3ApvkeQ5TFJ3ZpUv3/zDxX1m8eCWOHz9FjoZxo8HgzkKF\ngli9ehMeP36cd+/epVptInBc7nOCgJ7AOgJvElhLKTnpZAIfUhDK02x2k+eqQqAc0/J0rpN1hO6U\nrL6BBHpQ0m/qCcwlsL9gMD+93plLlizL8VhRUVH85JPP2bp1COfMmWfz56P0Ekt+V/MI7KIo1mKv\nXgPym6yXHvPmzaModmF6NYo6RwaspKQkNm/egQZDYdrZVaWTkzdPnjz53ONcu3aNzs6FqFb3oCB8\nQVF05datW7NN15Nw7tw52WUkzfAgCJWoUhkppY5KOb6HXl4BFEUfSm5H7xJoTuAQBWEOzWY3/vrr\nrzSZAuT21ykZKQIoubEUo+SuMp9SMgNnAqeoUIymp2egvCX+2Gq+aEp1eR8wLZdfUUq5/6xjgQsA\n8wNOUaez4717917UtK8EEhMTuXXrVn7//fe8fPlypm2mTJlCjeajdFstg8HpBVP6dERERLB1606s\nUKEuP/tseKbuSi8aK1eupMFQj2nRI2ep19vl+INqsVh49OhR7tq1K0d+fNevX+dXX33NoUOH50o5\ng2vXrjE4uD7VapEeHsX4yy+/8NGjR9Tp7CillpJcSCSJa5YscS0isJGiWIJt27ajVtubkiuLhpKz\ncYoXxtucPXs2DQYnSglJQ5mWfy9Z3u4WpuS69hbTCpgvpb//G9RoKsuM7Zp8fCql9FakpOtbK9+n\n/nK7AsX8SJOpeLa+gq8rEhISWK1aQxqN5WkytaXR6JKpjnHGjBn/ybpxmnZ2HvlAceaIioqis7MP\nlcrRBP5Hvb4J27XrnK5NbGzsCzccxcTEsGTJCnL43BiKYmF+883MF0pDZkhMTGS/foPo7FyY3t4B\nXLZsOcPDwzl69GguXbo025Jp2bJVqVINkaWpbRRFZ164cIFLly6nXu9Mjaa2zPi+lp+j76jVurFy\n5YZcsGAR169fT4OhrCyVaawYlcSgRo0axfDwcNk/14npS3guo6QLFCk5N08gcISiWJyLFy9h48Zt\nZOOmlpJ7izelMpv7KfkFXmbKthywpyD0knc6BYL5bafJ5PJS6cledixcuJCiWJdp/ovrWKRImQzt\n0vKtfUZgIUWxJMePn5wPFGeOVatW0WhsZvUiPE610t+6dYuVKtWhUqmhRiNy6tSsF+bJDURHR3Pq\n1KkcOPDzPNlWZgeffTacoliLUoaj36hSOVKrLUKFYggNhqps0qTtc38ooqOjqVRqZSlMug9G4ztc\ntkxSRf3222+sUqUqFYoOVvdpHRUKJwYHN+D58+etiocVoeSAHERJh9eNgAeHDBlCkvz9998pOTB3\nkp/dWAK1CDgS6C1LdS40Gl05dep0WiwWbt26lWPGjGFYWBgXLFggM0mt/K80U7LtSIWLyhGoQZXK\noWAwP5PJhTt27HhRU74SGDVqFAVhiNXDeOOJ29mrV6+yV6/+bNOmM1esWPmCKX06fvjhBxqNDa3W\ncZ9KpYbx8fGsV68l1ep+8ktykaLoy+3bt+c3yfkKX9/SsoRDSpXN9JS2oyQQT6OxBPft2/dcYyYl\nJVGjMcjSFAkkUq8vwy1btnDnzp00GJxpNDYiYKIgdCIwUJa4llGhmEx39yJ8/PgxLRYLDx48SCen\nwpSKincjMJxabUtOmTKFEydOZpEiQZQMGF4ywzPJ/7/JNBXD73R19SNJdu/elwZDSer1PajXF+KY\nMePZpEkbAnUo5e+rTsCVglCU0tb5X0q6yaEFg/lZ+w/ZkDVs27aNougni/zJVKk+Ze3azdK12b17\nN4sVK0d7e082b/7OS6lTffjwIb28/KlW9yfwPUWxOj/4oDdJyjqilBebVCgGc/To0XlKz927d/nz\nzz9z7969L2V0jptbcaYV+r4qbwPT0v2bzQ2yFbr57bdzqdG4U6qMVoEKhSPff783PTyKEdjCFH2x\nSuVNpdLEtGwspF5fihMnTkx9jzds2EBRdKVK9Sn1+jb08ipOOztvCkJdSuGo1WS6nSnp6dZQis0d\nRKn40ACKooPsO+tFKeqjM6WkpVpqtfaUkhhEy9LqRzQanSglRkj5iE4sGMzPhuxh4sSpVKv1VKlE\nlitXnTdv3kw9l+aqsZ5AJDWaD1inTrOnjJZ/uHnzJnv0+JgNG77NSZOmpTKdwoWDCGxgimJcFOtz\nwYIFuTKnxWLJYLw4ceIEHRw8aWdXl0ZjAGvVasqEhIRcmS83sHLl99RqC8lMYyiBrhQEE5XKETKD\nWEmz2Y23bt167rGTkpKo1RopWVVXErhLg6FohoQEGk0fqlQGq2MxBJwpiuVZsmSF1FrEhw8f5tdf\nf82JEyfSZHImUMhqexpLScfX1IpZRcpSYC0Cg6hSebFbt560s6tJoB+lDC/3ZWnPWx7Pl8AZajSd\n2bRpM1nnuJPAj9TrXV8P5hcfH88xY8bxrbfe4aBBw/jo0aNcoKxgIDExMdPi1wsWLKAohlo9XHFU\nKNQZfPx27tzJokXfoL29J1u16pjniQEeP37MSZMms2/fT7h27dqntt29e7e85XqHRuObrFy5bq5Y\ngseOnUC93o4qlY7t23dJlVjKl69FQZibuvUTxQacPTtvEwE8D9599wNKerQ/CXxBoCe9vUuySpUG\nFEUH+vuXz7bl9969e1SrjVbPC2kytWfhwkFUKsfI0uUlimIh1q//Fg2GypTcXcpR0sG9QbW6GUeP\nHsvjx49z06ZNvHTpkpywIZjps65YKDktW6s7VhLwZ5oO+zIFQUNJf1iUUgr7lLbTZQl1BgXBm97e\nxRkVFcVJk6YxICCY5cvX4datW1995mexWNi06dvU65sQWEattiPfeKPaS/XFzg+sXr2aRmMtqy3R\nOep0Jn777Vw2bPg2O3f+kDt37pSLgG+QpcOurF8/79Kzx8XFMSiosmxBnUCDIYBffjnmqX0iIiK4\ndOlSbty4MVfu6erVqymKJSklyrxPna45e/X6hCTp5ORD4ILVS/Y1Bwz4LMdz5hY++eRzqtXWzs0L\nU8PjcgqLxUIvL39K7iskcJKi6Mrt27ezePFy1GjsqFLpOXXqDCYnJ3Pq1KmUDA6fUUoqOp2AF4OC\n3qQoetLOrjFF0ZlDhgyl0ViJkk/fF5T0lX0o6fnsCIyj5JxchILQyGptyZT0mdMo6ReXWJ37gJKT\n9XVqNE92kXvlmd+VK1eo0zkTiEu9aEZjEPfv359LFBZMxMXFsXTpYOr1zQmMoCj6skGDt2gwlCPw\nPRWKLyiK9tTru1o9VLE5duS1xunTp9mjR1+GhPTgjh07+NNPP9ForGbFkK9RpdJlKeIkOTn5iVbM\nS5cucfz48Rw3btwzY1c7d/6QwEyrNf9BP783SJINGrSmSvWZTF8UDYayXLUq56UYcws3b96kh0cR\niuLb1Om60Wh0ztWKdidOnKCHR1HqdE7Uak2pgQcPHjxgvXrNqVRqqNfbcdq0GVy/fj3V6nrpJEXA\nRLXahcAd+fdcKpU6urkVolLZmJJRw4VSPH5tWYrtRKARgbZUKEyUojduUtIFlpbvxV6ZEb5DoB6B\nEgTuUqGYxoCANxkUVIUGgxMrVarDQ4cOMSIiIkc1PAoM84uIiKBe72ElLltoNlfknj17conCgouY\nmBjOnDmTQ4cO57Zt22QDQkTqw6pWV6NWW8OKGZ3JFUdeUmJ8RqMLBWEkgenU6935ySef0Gh82+pl\nSaBSqX1qKcikpCR269aHKpWOKpWOH37YLx1zPn36NE0mV6rVvahS9aHR6MK///77ieMNHjycanUP\nKxoWMTi4AUkp1VRgYCXq9a7UaIzs23dgrjg13759O9cct+/evcv58+dz5syZeVJMPTk5mTdu3EhH\n7zvvvE+t9j1KjsvnKIp+nDJlCkWxKNOcmS9QodDSZEpJLjKfkl5uFDWa9jSZ3KlU2lPS042lShVI\npbIcJaPNZYpiRXbp8j4lvZ+OkrNyCQJdZWaqJDCGknXXSL2+ON3citBkcqLkHG2g5EIjUq/3YJky\nVV595mexWFipUm1qtV0I7KRa/Rl9fQNttVUzgV5vLz9sKZ73nenuXpR6fUtZOvTJtWSXH33Uj4Iw\nworJ/MSAgDflspBhBE5To+nKWrWaPnWcsWMnyPUzogjcoShW54QJU1LPt2sXSkFIS2UvCFPYosW7\nTxzvzp079PYuToOhBfX6LjQaXdJJT8nJybx69WquWMbPnz9PX99AarX21GgMnDs368Yai8XCUaO+\nptnsRoPBif36Dcp16/Ply5dZsWJtqlQ6enr6c+fOnZm2c3YuTOCs1b38mgMGDOS7775PozGIotiV\noujJkSPHUK93phSh4ca0OF4LJdeUqpTcXExs3rwV+/b9lHq9HfV6ew4cOJSffvoppXx/PzPF51Ny\nXylBKXdnbfnY53znnRBu27aNgmBHyUI8S2aMjwkkU6PpXTCYX06/rg8ePOD77/dm6dLV2a5daJ7V\nVyjo6Nt3IEWxGoGtFIQpNJvdePbsWc6YMYNDhw7PVubpO3fu8NChQxmueZcuPSk5rKa8MLtYsmRl\nHj58mOXK1aSbWzG2axf6TANL1apNCGy0Gmcda9Zsnnq+Tp2WlFwl0phstWpPZqjXrl3jb7/9xjlz\n5nDOnDm8dOnSU+e/cuUKBw8exl69+nPXrl1ZuCJpKF68vFWC07MURQ8ePnw4S30XLvyOBkNpmelE\nUhSrcsyY8c81/9NgsVhYokR5KpWjCDwisIUGg3OmYZKBgZWtrrGFOl17Tpo0KdUBed68eamGluXL\nV1KnM1MqJ3nP6r40phTZMZPABAqCIV3Kr2rVGlCyYteltDVeLvdrSClpwTBZ+tNSEHw4duxX3LFj\nhywpkkB3Sm40KfP9WTCYnyjaP9dX0YbsISkpiWPHTmClSvX51lsdeOrUqRyNt379TxRFJ5rN5anT\nOXDBgu9Sz+3atYt6vRslHc5OimIQp06d/txztG/fRX5BpYdaqfyC773XLfX83LkLKIqlKWUJOU1R\nfIMzZnyb6Vhffz2JWq09zeYg2tm5P1MvfOXKFTo4eFKplFJIiaLHMy3UKUhISJBz0aVFTYhiV86f\nPz9L/Zs27UAp7CvlZf4fy5evk6W+WUFUVBQ1GjOtfQRNplZcs2ZNhrZ79+6lweBMvb4rDYYGLF68\n3FM9KmJiYtiwYWvqdB0ouaZsoOTXZ/2Rmkil0o7Hjx9neHi4zBjvyudOUApz+5WSYaSvzBCLU7L8\nvsG2bUMYGxtLhUJHKfZ4PKVszknyczKmYDA/6aH1zhU9XVxcHPfu3ct9+/a9FAHyBQUnT55kr179\n2b17Hx44cOCZ7R8+fCjHaf6eKtno9U6MjIxMbbN582aWK1ebAQHBnDp1RrYk/IiICDo5edNgeJsG\nQxs6OxdKJ51YLBaOGTOejo6F6ODgzS+/HJPpPH/++afsMPuvTO8GOjl5p2ubEqWQguHDv6RSaZ1N\nZBuLFSufZdrt7d2ZVrEshgZDUJbD5Lp06UmFYnjq3IIwg40atc3Q7uHDh+zd+xNWq9aUffsOzLKb\nV3x8PNVqkWk64AQajaWeGGl1/vx5zp07lytWrODjx4+fOX50dDTfffcDOjv70tOzBAXBiUC41bWc\nQ6Aya9duyvHjxxOoaXWOMvPTyZJdIUrb6P0yY6xEk0nKg7h48RJqNE5Uq9+iIDhQpSpCszmYHh5F\n8475bd26lSVKlGCxYsU4fnxGcfz27dts1KgRy5Yty1KlSnHx4sWZTwQpsYFC8TnHjh2bLWJTEBUV\nxeLFy9FkKkuTqQwDAytx3bp1fPvtUL73XjcePXo0R+O/qjh+/DgNBmfZODGBoujyzDCyU6dO0WTy\nT/fA2tnVyJMwxdu3b3Px4sUMCwvjnTt3sjXGsGHDqFD4UYoumMyUqmIPHjzg4cOH6e5ehEqlhg4O\nnqnb2/79BxIYa7XGv+jlVTLLc0oVBp2oUjWiIBSir28pRkVFZanvpUuX6ODgSZ0ulBrNhzSZXDMY\ncpKSkliuXHVqtaEENlCrDWHFirWeqhu8du0aGzVqQ3d3fxYpEkSdzpsaTT8aDJXZuHGbPEsg0aNH\nT0ohbVspZWFxJ/AZNRpXHj58mJLB4k+m+fz5UEp1NYSS0WOO1X3YRZ3Ok6SUduvLL7/kRx99xP/9\n7388cOAAd+3axUePHuUN80tKSmLRokUZERHBhIQEli1bNsMWasSIERw8eDBJ6eF1dHTM1KVBYn7J\nFMVGOfbef//93nL6Jgul4tINqFI5yxduEg0G59eeAVosFt68eTOdY3SnTt3TGQ2A5axatfFTx0mT\n/A4xzVLs9MTUWvmJv/76Sy6QvYzADgIVCITSwcGDjx8/pqOjF6Xi2BYC/6PR6MLbt29z//79FEU3\nSsk8/6QoVuPnn3+R5Xnj4+Pp6xtApfItAjOpVvdg6dLBWTZcXL9+ndOnT+fUqVMzTfh77NgxGgxF\nrbbWSTQY/HjixIlMx0tMTKS//xtUqQZTypc3gY6OHuzXrx+//PLLLEeGxMTEsFOn7jSb3ejpWZyr\nV2fcKmeGihUry9vXypQst74EFIyPj+fQocMo+Q0aKVVj+0ze8h6gFHViHce+jEFBVTly5EiqVCLV\n6poUxYb0938jneSbJ8xv//79bNQozbly3LhxHDduXLo2c+fOZa9evUhK1db8/f0znwig0ViD5cvX\nyHEFrozVqsoxLQ6SBMazS5eejIiI4PHjx1+7bfGdO3dYvnwNarUOVKtF9unzKS0WC1u3DqHkmpBy\nnbayXLnazxxv48ZNss7vDep0Dly0KOwFrOL5MWjQEALDaS3BCYId9+zZw5MnT9JkKv4fCbZqqvS3\nadMmBgRUpo9PEIcMGfFcFtdDhw5Rr/ehVGuiN4F/aDAU5unTp3NlXX/99VemzO9Jrj7//POPnJw0\nRc9noVpdiFqtO+3sqtFsdsuSyqNz5w+p07WiFFe+h6LonppM4d69e5w3bx6nT5/Oc+fOpeu3f/9+\nqtUOlGp2VCDQlnZ2hahUaqhUavjWW61YtWodSoaPlpTKUvYgcJBSFMlHlDK3GFi6dCUKgj+BLylZ\nkd+hVvs2p0xJ8wTIE+b3ww8/sFu3NKXzsmXL2KdPn3RtkpOTWatWLXp4eNBoNHLLli2ZTwRwzZo1\nucKI+vUbJCtZEwkkUBB8mGY2J4EZLFy4NHU6F5pMJVioUIlcSaFfUNCyZUeq1b3llyWKoliOy5Yt\nk/Osectbkt0UxQDOnj0vS2NGRUXxjz/+SBdX/LLhiy9GyEaLlOdgL729A0lKuxKt1kwpAzEJRFGv\nd0stq5gTjBgxkoArpdxyIwi4UadzzcAUsov/bnt1uhBWqFDziQxaCghwomTdpSzR+lLK4SdZ0j09\nMxdSYmNjGRkZyYSEBDo4eFOKkEnRR37BYcO+4O3bt+npWYx6fQsqlVWoVotcunRp6hhXr16lp2dR\nmZGpqVI5UqOpQSl5xZsEilGpLE1BMFJycv6HkqFEQ6CVLC1+IX+o9ZSsyQ8pJV5wJ/ARBw78PHW+\nPGF+P/744zOZ35gxY9ivXz+SkrLUz88v0xjU3Exs8PjxY1av3oh6vfSQFS9ehqLoT0nRuooajTN1\nuhKpN1+p/JrVquVOeFBBgLu7P4FTVkxgMj/6SLpHq1atZmBgFRYvXokzZnz7SpUAiIiIoNnsRkH4\nksA8iqIvFy1anHp+/PgpFEUvGgydaDD4Zang+N27d3n+/Pmnhtz5+ARRKq6Tcr0/ZuHCJXL12j54\n8CDLBo+EhAQ2aNCcglCCUsLQIpSyKqc5nQuCIoPeb9Wq1VSrRarVJhoMjnRz86NkiU2xwLfn5MmT\nOXjwcKpUoZQssu8R+JSCYOaAAQPYrFlz6vVmStvew5Qsu20pRXcMl9unSLCfUzJ0CHJ7f0oW3xQ6\nf5WPX6DkDF2NQGEKgj03btyYSnd2eYvqaWUtvby8cOXKldTfV65cgbe3d7o2+/fvx7BhwwAARYsW\nhZ+fH/755x9UrFgxw3gjR45M/bt27dooU6YMIiMj4evrC0fHrNcZFUURe/ZsRWRkJARBgI+PD777\nLgzffjsZWq0a3t518eOPpQEYAQDJye/i1KnZWR6/oMPX1xc3b+4EGQAgGTrdbhQrVgcA0KFDe3To\n0D5/CcwlREdHY+XKlXjw4AEaNGiAN954A4cP78XEidNx//5ldOo0Ay1atEht//nnn6BevZr4+++/\n4e//IapXr/7U8UePHo+vvvoaarUjzGYVdu4MR4kSJTK0S0pKRMqzJsGMNm1aQBCEXFopYDabMWvW\nlGe2u3//PmrUaIyzZ2+DjAcwB0BTAD8BuAnADYKwBEWKlIZCkVa2OzIyEh079oDFUhpALSQm/oDY\n2NsAWgNIBqBBcnICbt8ujlu3opCUdAdALQCLAABkbUyb1hlALwBHAIQCKC+PPg1SrV4nAI0ApMzb\nFMAaSDV+qwCYAKCG3K8oVKphcp3iVgB6ABgMIBlkFUydOg2HDx9+7uuYDk/jjImJiSxSpAgjIiIY\nHx+fqcFjwIABHDlyJEkpbMjLyytTS9d/p1q1ag31egeazaWp1zvwhx+y5leVFSxevJgGQ1WmVIFS\nKKaycuV6uTb+y45Tp07R0dGLZnMDGo1l+eabdV65XIoPHz5ksWJlKIotqVb3p17vws2bN+fa+FIy\niMJMSdMuCLNYsmTFTNuOHPkVRbECpTxzyyiKuWtwS0pK4unTp1MzKT8N3br1oUbTg5K+L5lACKX8\neR8S0NNoLEpXV98MxpIpU6ZQsrzGy1LXdUqW2dYEblOqxetMOztXrl27liqVE9MXNzpFKUqDlJIU\nNGWazvFnSi4tJSiVnoyh5Kf3jryN9aWUFJWU9H61CTiwdev2svTqTOu8gsDMdNnMn8HGnohn9tqy\nZQuLFy/OokWL8uuvvyYpGTnmzp1LUtKlNGvWjGXKlGFQUBBXrFiR+URWBN66dYt6vSOBv+TFHKEo\nOmbbveG/SE5OZps2nSiKXjSby9HdvUiu6V8KCqKiorh582bu2LHjlShhGRcXx7Nnz6ZGikyfPl3O\nGpPyQvzCQoUCc22+b775Ri7UkzJ+LBUKVabMJzk5mRMmTGFQUDVWqdKIu3fvzjU6oqKiWLp0MA0G\nX+r17mzYsFUGvfnVq1cZGtqT9eq1ZqFCpZmWlJSUSnK2oEbzEdu0eY9nzpzJ1OA4e/ZsSiFpKf0s\nMvO7ZHVsGAFHtm8fQldXP6ZZaSMphbWZKGV/figzrHoEusuJDDSUEo/WpJTlxUTJJcZMKROMgZJz\n9EMCbdmqVUfGxcXJx+0pGUGSKamygmlnl1YHOc+YX27BmsCDBw/SbK5gdVFJs7lsrlSnSoHFYuHJ\nkyd56NChLDlrvsywWCycN28B3333Aw4fPjJTnWp+4dGjRzx//nyOLfhPwx9//EFHRy8ajX7Uas2c\nNWsOR4wYKacwT3mG0hcGzyk2btwoh52lJPNcTy+v4una3L9/nx06dKWXV0lWrlz/qYkWsoorV67w\nt99+Sw0j7Nixm+zWlUwgnnp9U371VZq/bVRUFF1dfalUDiawhkqlDxWKjnL7REqlJe3o6Vn0qb6H\nN27coGSgWEMpwcCXMpOyNiS2o6Sn01MyRoyWGaCRQE9KUnIpSvo9M6VoDjX79u1LyeqbMs51pkVy\npBhhlsgMUcUyZaowLGwJHRw8KYW6ecuM0l2mqS7Ll6+VSnuBYn43btyQJb+UUnl/U6934O3bt/Oc\njujoaK5YsYILFixIF6XwMqNnz/4UxUoE5lKrfY8BARUzbGMtFgsfPHjwQg0YixaFUas102DwpYOD\nJw8dOpTrc1gsFrq4+FBKZ05KYVRmtmnTjqLoQWmbdIta7Tts374LSSklVM+e/di0aQd+883MVMX+\n48ePuXnzZm7YsOGZscYWi4UhIT0oij60s6tNk8k1NUwuIiKCNWo0oUrlKNe6+JuCMJd2du68ceNG\nttc6e/Z86nSOtLMLpig6cc2aHxkQEMz0xpTFbNWqU2ofqUB6a6vzEZSyofjIzCeAwGqKYplnxgxX\nq3BGtR4AACAASURBVFafUuYUEyW3ksry3x9RCikrQymxgPV8KVXcUrItDZUZ1HICIwnoGRYWJktw\n/8ht9lOK6uiZbhxBUHH79u08cuQIdTpXSr6l0ZRciBwIVCTQJEOSigLF/EhyyZJl1OsdaTZXol7v\nyOXL877gzv3791m0aGkajY0oip0yXMSXEY8fP6ZKpWNaPKSFJlOVdPUb9u/fTycnb6pUIh0cPF9I\nmq9//vmHer0LgdOpkpGjo1euZyRJi021DolqQ43Gg/37D6Czsy/1enu2adOJjx494oMHD+jl5U+V\nqh+B5RTFYPbqNYBRUVEsUqQ0TabqNJnq083N75mO2im1d3/55ZfUD3NsbCy9vPypUIyQJaDEVLpM\nppaZxsxmBZGRkdTrnWTmTgJHqdc7sGXLd6lWD6S0DU2iTteGX36ZVt9E0m+3S302gG8IGOnnV0xm\nOBpZwvqRrq5FMl3j9u3buWLFCu7atUv2z3uTUkbmKtRoylGjESnpDi9QEN5h+hC1K/J1sFBKW1+W\n6XWBH7BKlers2rW7zPCKENBTEEQqFD6UsviQwDwqlfZMTExk69ZvU0pkOoFAIKV8fwq+9VYLzpw5\nM8N9K3DMj5Q82/ft25ejr+XzYNSoMdRoOlvdmDBWrJh7QeR5gfv371OlEplWF4E0mZpw3bp1JCXF\nv9nsxrQaGFtpMrnmeRGjtWvX0mxukY4p6XQuvHbtWq7Ok5SUJBet2SvPc4eSYr43P/740wztv//+\nexqNTazoiqJKpWWvXgOo0XzIFCW8UjmCrVq998z5U5jDt99+y6ZN36afXzmqVO6UUoZpCdxK91Ha\ntGlTtta5c+dO2tlVT3c9Tabi3L17t8y0S9NgKMYqVeqnS+N269YtOjp6UaH4ikB7SqUkp8iMb7e8\n3sUEvKnRONPPryyrV2/Mrl178P33e7FGjQY0GAJoMrWnXu/MKVOm0M7OlaJYiqJYlPXrt+DRo0dZ\nqlQwDQYnlitXjQqFmVIo2ixKoWl2lAIN3Cltg63drPqwTJmKfPToEc1mF5mJ/kYpnFAvS3SB8j0t\nxD59+lCp1FMynrxBydCyi4ALly9fniVjalaRr8zvRaN79z6ULFEpN+ZYqhPsy4xatZpSq+1E4BAV\niil0dPRKNQ4d+T975x0mRbWt/V0dq6vDpJ7EzABDDgNDkpwEyTlIjiIoEhQQBEEkCCooKAIqQQSU\nJMmEIiAIqBgYUPHIQUBRJAgSBAkT+vf9sXcnZ4BR4dzD/e56Hh6d7qpdu6prr73Cu96VkYHHUy5s\n0Xg8lfOF4P8nsmfPHkUg4F/8n2MYUXni4X766ScyMjL+duz1vffew2RyIV2xBIQYi66355lncvcl\nfu2113C5Qt2yC5jNNpo06YgQr4d8voX09LrXva7P56Nbt3sxjJJoWiKyCmE70l2rgIx/lUeIGdjt\nHUlLq/a3Y59Hjx5Vlt8+Nb+PcTpjuHDhAleuXGHXrl1kZGTkaVkfOnSItm27ITnyTiETHn9mX45G\n0yoj62onIhMSU5TyWRb4DV2uGM6fP8+2bdv44osvwrCAv/zyC0WLlkfG6wyl6F5DeiWbEMKFpiUo\nZfaeUo4GL774oorzV0JaenWQSQw70nL8CpkBbkG9evWQrnacGtM//3loWgQ2m5uWLTuFJX1ua+W3\na9cu5s6dy4YNG25pzGr16tUYRklkBusPdP1u+vZ94JZd72bJ77//Tp8+AylatBINGrTmwIEDge9+\n+eUX1eLPz2JyAl2PuSF/3c2QMWMm4HAkEBHRAMPwsm7d+lzHDB8+Bl2PxuNJIyYmha+//vovXcPn\n83Hx4kVFHhCJYTTB5apNWlq1PJXpqVOniIlJxmR6EiE243A0o1On3jz99LOqCfgFhLiCrrdnyJDr\n9+3Yvn07TmcJZOypGKHlYtJSGYLNVoLU1DSmTn2Sixcv5jn/VatW8fjjE1ixYsV13++lS19H1yNx\nuUrjcESxcuXKfD+nzMxM1YHtDyQsJJlgMuEQ0v09F6JMaiFBxO8jCUTlfZlM1mvCoqpUqYOmtURa\n4ReU4l+kzr2KzRZFSkppda1IzOZoxo6VNdIHDhxQ1GddkTHEbISohKzlPYcsUHAycuRIZHKjMUIs\nCZnv40ig9mUcjhaMGfN4YF63rfKbMWMWhpGEw9EfpzONbt363VIFOHnyU9jtLsxmG61adf7HmeAf\nfviBfv0G0bJlF159NVjic/r0aX744Qeys7PZu3cvy5cvzzfB5V+VKVOmYRhJuFxdMIwUxo//Z6w5\nf0X+9a9/sXHjRo4ePZrru40bNyrl4Y/rvELRoun5Hnv16jUYRiQWi05qahrbt2/ntddeY926dde1\nsA4ePEirVl2oUKEeI0eO4+rVq2RnZ9Ojx71YLA7MZge6HovJZKVs2WrXhEGtWLECt7sDMq4Z2pIx\nC5stme7de7Nw4cLrMqT07fsATmcFNG0sTmdlevYccN17XrhwEXa7G7e79F/Gv7Zt202xde9AQk8K\nYBjdcDgSMJmcBMvdspHu8U6kW1kKIXxo2rOUKFExz7EnTnxSWYvdkbg8yQwkx1mNw9EGjycZs3kM\nMtP8bwyjQJgH0rfvA2haNEHm56PI7LAVIdy0bduJn3/+GYvFraxTJzLrPAKZPW6qzltP7dotAuPe\nlsrv4sWLqoO8H0v0B05nkVuSNQwVn893UwLzv/zyC5GRich4hxUhLNSs2YBBg4Zjs7kxjAJ4vYXR\n9Tjc7o4YRhITJz5544H/hnzxxRcsWbLklj+7vyIzZ87Ebg/tQnbpmli5P8uBAwcwjFikm+ZD016g\nUKEy/3hjPHz4MC6XF0m++gea9hzJySXyxEJ+//33iq79C4RogRDNEOJVHI621KnT9Ia0UIcPH0bX\nY5HYNZnRdDgSrllP/Ouvv2KzuZVCKYAQ5dC0aKpXb5wvCrHLly8zZMhISpeuTqNG7ViyZAmLFi1i\nz549dOvWD7u9BpIFuTkyMbEDk6kcJpMdISKw2RIYM2Zcrmf8yy+/oOtRSIgKyFCHF5utGnfcUYM7\n72zDmDGPq8TchcDvbbMNYcaMGYFxcnJyiIgoiIxJghA5aFpThDATG1uINWvWUL58Dcxml1pPFZGh\nhbHIDLFXnTeQvn0HBsa9LZXfzz//rExhvysBERFNw+r2/pvl2WefxWSqpBbGRWS8pSxWawoyDuJT\nP95d+PFNuh7zX0OysHfvXpYtW3ZT8ZWhsmHDBpzOUgTdrddITS2Xr3OXLVuG2303QcUJVqvrHydy\n3n//fSIiGoSN63AksXv37jyV2Zo1azGMKMxmO5GRiTRs2IYJE57IV8VMRkYGbnfZsGt5PBX4/PPP\n8zx+3bp1ytpZjWz1WBhJSrAEw4gNs6I2b95MuXK1KFSoHCNGPHpDIHt2djb16jVEApl7q/+m4XDE\nqLamCxBiI4ZRiQkTpuS6jz/HlYUogckUicNRgKpV61CqVFWVCFmrrMPSmEwFmDp1Kr169aFkyYpU\nqFAZu70s0q1tgKz48CKTWBvQNA9m80BkV7enkVAdP2X9e8gYYzpCGGFJ0ttS+WVnZxMXVxAZnzAh\nRDEcjih++eWX/9S0/pE8/bS/aHxryEuxGIlH8v/9o9rFUcq9aoAW6H9SnnnmeQwjEbf7bgwj+Za4\nyj6fjwceGI7DEYfHU5moqAJkZGTk69xt27Ypl9nfNewbdN39jy32L7/8UtE9+cd9HSF0bLZIoqOT\n2LVrV573kVc870Zy+fJlEhKKoGnPIcRxNG02cXGFrznW888/j8TTgRDVkeVy/vdoOvfcI+PTe/bs\nURbpGoTYjWHcyeDBuTPff5aJEydjtd4bMuZ6YmKS0bRHQj77ivj4YmHnrV+/HpngWKM29LeRbuhv\nyAoPDxJtMAeZrBiAdG2nKeYWNzJG6kBatf9CJmWWIAkLTuPv1iavE4Msfeur/m4a8vndlCwZzrJ9\n2yi/y5cvM3r0eO68sw0DBgzB5YpFosqvIsRCPJ6E26Yj2/fff4/JFKV2KfnyaNpALJZUgjWSLxLs\nYr8Zlys23yy/t0p+/fVX7PYIZFkSCHESXfdy6NChW3K9gwcPsmvXrmtWpuzbt4/hw0cxbNjIQJWE\nrCWvgdmcis3WAYcj7qZgQX0+H1269MXlqoDV2k8tKj+MZh2RkYnXteoOHz5M8+adKFOmBgMHDrth\nzPjAgQNUqlQXl8tLenpt9u/ff81j165di91eVSmYWoSWqWnaZAYMGAKgqltGE1RY3xMdnXLDez91\n6pTq19sNs3kEhhFLz569MZsfDBlrVxiL9alTp3A6vQjxEtIStaln5k9GjCdYl3tUKaickPEqIa3Z\nB5C8fdXUZyBL4YooxfeAOm8QktTUf/6LxMSkYrHo2O0xFCpUhoMHD4bd122h/I4cOUJsbBE0rTlC\nrMZqbYbJVCbkRsHtLp0rI3j27Fn69BlI+fJ16d69/3+kEiS/sn79eiwWD5rWDJutIUlJxalfvxlO\nZ3EiIurhdsfj8Xix2Tx4PHE3pI2/VZKVlcWHH37IW2+9xUcffYTbXTrsuUdEVGfHjh3/8Xnt3r1b\nLa7HEGI8TqeXzz//nJYtO+Fw3IUQI7BYylO2bJWbBqD2+XysX7+e+++/XxFgBJ+Dy1X0mgrqzJkz\neL0FFaZuO7rekSZN2t2UOYFU+BUq1ELXWyhFEYN0R5/B6fQG1sXTTz+tFLd/3p9QoECJG4wu5bff\nfuO5555jypQp7N27N0ADZjJNRIhFGEZR5sx5KXD8jh078HiqIcHT3RHiYTTNi9k8TinpJ5DYPZQl\n6CKYZc5WCrMwMn43Xyk2A5utiDo2CQl78SdBeqvj/Pe2g9Klq3Pp0iWOHTuWZ2jitlB+MTFJ6gf1\nZ832IwGS/pjQr9jtkQGg7Pvvv8/YseNITi6C1XoPQmzBZhtCiRIV/6vYmU+ePMnSpUtZvnw558+f\nJycnh127drFp0ybOnj1LTk4Op0+fvmV9E24kly9fplq1Brhc6Xg8jYmMTFAWtx8YvQWn03vTiCX+\nirRq1RUhZoW87LNp2LCNShTsQ2Yi4xHCxtChw//WNS5dusT58+dzfS6rVOIIYhUPYrd7rhlXXLt2\nLW53k5C5yuZAf7XW+uTJkxw+fDhPZX7p0iVmz57NmDFjmThxIm3adKdLl3vCWGJOnjyJ15uCxTIE\nIZ7FMFJYtGjxX5pDqBw4cIBeve6jTZvuuajqf/jhB0ymCCTG8lWE6IUQLpKTS+B2l8HhSMBi8SDE\nvcjOah4slgoI8Ry63kopOLNSgCZktckdWCwuZALpC2UJPqOe6RJlDR5AiBMYRkNGjbp+S4HbQvk5\nnXWRtYP+OkAfFksBHI7i6PpAnM6ijB79OIDCZRVBZnrqIFP3WUgkfZlbFqT/3ygzZz6Hw9Ey8Nw1\n7UVKl65MdHQSNpv7f9Qilf14V4YolDeoWrURhpGCLLPy9wQ+gq4nsXPnznyP7fP5GDRoOBaLjsVi\nUK9e81yK6tFHJ2IYybjd7XE44pkz59rM1m+//TZud22CeL9zWCx6vuFSPp+PAQOGYrdHYBhJlChR\n8W9XxPz888/Ur9+IAgVK0rhxy5teWXP27Fl2797NJ598gnR1LwTWrM1WkbfffpuMjAxmzJihDJhC\nyMTfLGw2Jz179mf69Gd48803kbG+dUi3dpk63qR+99HIemAnQhTEai1MUlJxXC4vuu7h3nsHX5dI\nFm4b5dcQmfnsjsze9KdYsXTefvttZsyYQYcOXShR4g5VNK4TjEnlIIGY7yD7FxTLd+D8/wQGDRqG\npBPyK5jviI8vhs/n47fffvsfs0gBlix5DcMohsSm7cQwirNo0auUK1ddLZArgXnr+v3MmjUr32PP\nn78Qw6iCzLxnYrf3pFev+3Idt3v3blauXHnNhkB+uXTpEsWKpWOz9UO6iLW4554H2LlzJ4sXL77h\nO/n666/jdFZSno4Pi2UM6em12LRp01/2ZPr3H4Jh1EaIVVgso0hIKHLDTLgf4nX27Fl8Ph9fffUV\nw4ePYuTIMezfv58NGzZQunQ1vN6CWK0ePJ7yaJpbKaZgeaXVWpN33nmHrVu3YrfHKoW2DpnY642u\nJwUy0x9//DFWa1rIuwcSM2lHJjsmKwswEpnkiGLatBnMmzePqVOn5qtS6bZQfsnJJTCbByFEazQt\nmaJF0wOuVteu9+BwNEeIj5ElaNYQCxGEaIkQD6Drnaha9c5/FP/x+Xy3lILpv03mzZunGn7/hhA5\nWK1DaNWqy//0tAIyd+7LFClSgdTUdGbPfhGQ8TXZh8If9L+E05nOm2++me9xu3W7lyBUAoT4gtTU\nCv9ormfPnuX++4dQuvQdNGzYhE6deuF0puJydcMwEpk584Vrnjts2EiEmBoyn4MIEYnbXYXy5Wvk\nO6OclZWFxWInSHYBLlfLa3JpfvrppyQnl0QIE5qmY7E4iY8vrMrpxqNpo7HbI1UN+ZPIkjd/EqgG\n0uXtiqwVnoDNFsW5c+fo2LE3MsMLQnygzuuDELUoUKA4hw4d4uDBgyqE4Qe6n8BicWM26wR7CfuQ\n3t0bCHEYTbPjcDTCYnkYhyOBpUvzvi+/3BbK7+TJk9x772AaNmzH1KnTAgosJydHWXpnAz+mphVS\nivIoMjkSQf36LRk9+rF/VJXx1ltv4XZ7MZkslChRMVfm6GbKM888R0xMQSIiEhk+fPRNZzy5kVy4\ncIH69VtgtbrQNDua5sRmi6RSpTr/I/G9vyrbtm3D5YolIqIpTmdROnXq85dAzuPHT8Ru747fTdW0\nmdSv3/IfzenkyZPExRVSkJEHlMXiV0I/YrO5OXPmTJ7nvvjiixhGgxAr6gUk3u0CZnM6lSrVZNmy\nZbz33nskJBTFZnNSp04zDh8+zMaNG9m6dStXr14lKytLlbL9TlD5teW1117Ldc1Tp07hdsepa8US\nZESuQnhi4Skk/VUisq7W//kYJBdfApKVJYb77hvEihUrSUwsjcxK70NCWPwblQ8hmmKzOdm1axeD\nB49A0wooBZqA1RqBplkIIiJAeoOL1P9HITvGgRBfEhmZeN3f5LZQfl9++SVNm3akRo2mzJ37cuBF\nPnDggCpcb40slAbDaErZstXweOIpVqziTcHGHTx4UAE6P0Wiy2eSmpp2S8rpli1bjmGUQBZtv4TJ\nlEJaWvX/aD/hfv0Go+vd1GI7j2HUZMqUJ2+rpkXHjh3j7bffZteuXX953r///julS1fB7a6B292c\n6Oik60JN8iOTJk3Gau2PH7okF39otrjINSs4srKyuOuu1jidxdG0CkrRfIWMbXZAiJk4HGWxWCLU\n2Ocwm/tjtUbi8dTB7a5IuXLVuXDhAt2734thNEKIDZjNk/B6U/Lc0DZt2kRERD0knrFTyFwbI8Rb\nIX8vUd//gIzxbVOfb0JCW95FiNNo2jBSUkqrePwSZSlGIuN4P4eMNw4hOlK4cBrPPPOs6t72EtKi\nfAGJ/euL7A63Sim8Q0gyhFgkWeodCFEFTbNeNyxwWyg/CWmYgxBv4nSmMXXqNEaOfBSz2Y0sXF6K\nEMUwmepQoECxm07LtHz5ctzujmEv6/V26n8ibdv2QIiFCLEcGeN4hT9DFm61lCxZFRlG8N/vQtq3\n7/UfufZ/i1y5coV33nmHNWvW3BRrd8SIR5AMxtKFk+iFD5W1s5yYmGSuXLmCz+fLM5aak5PDZ599\nxl13tcBm64aMldVAEgwUUdaVrpTVVaWQ/L2Ifdjt3RkzZjyZmZmMHTuRxMQSWCwRuN1xjBs3MdcG\nsXfvXhWXq6KUytNqruOQMbddyHhrEYKJp2iE0HE40rFandjtoSw5OUj2mBYEgeIjkJUandQzaasU\nZgoWi87QoSOQlqV/jAVI6Et3tTbKIISOpplJTi6FxeJEZoc/RIYt3Giambi4wnnGAG8L5ReOJP8S\nw0jAai2MbK7i/3wvDkdsvrvKh0pWVhZDh47E6y1MSkoZXn89HBS7detWnM6SSNJFEOJf2O2uXKVB\nGRkZ9Os3iL59B/7tWtn+/QdjMj0a8mL73fmJgTaSt1qaNu2IpDEvihCFMZsrM2rU2FtyLZ/Px/z5\nC2nduhv33//gDbOPt2vcdefOnRhGAtIy+w6brRI2WwQWi05CQhF2797Nww8/is1mYLHY6dGjf57Z\nyvPnz1OzZiPFXVdDKY8lShnUVgqhBpI5ZWfI+niFdu16AjBr1hwMoyISFnIAw6hIp07daNSoA927\n38vhw4f57LPPMJsj1Cb8IbIsrRy67qVHjz4kJZVG0yKVAstBiNk4nXGsXr2aTz/9lMWLF+NyVSYY\nfz+kFFsbhLhHfTYW2X/XhUyOtEKGq7ajaRE89dRTqszxF4TIwmJpi9kcTzCD/DM2mzuA3y1btgYy\n/ncRmURZpRT2ejye+Fws3LeF8jOZHg75ET9Dmr7+BxfMROYHrZ6XjBjxKIZRH4kf3I5hJLF58+bA\n9z6fj44de+FypeF09sbhiM+Fj/rss8+Ua/wkQkzD4fD+rYY0P/74o+pBUFC9dMHYSv/+g288wE2Q\nGTNmqsWUgRDfommleeKJ61OZ/1159NEJGEY6QryKxTKcuLjC16xkWbhwEbruwWSyUqFC7b8N08jM\nzGTq1Gm0aSOtob9TgvZ3ZM2aNaSklMJq9WKzRZGeXpvPP/8cn8/HSy/NwzAqIUkAzuFwNL4mTs3f\nZ0bXPUhQcxuEmE4wbtYeTXNisfRAwrwuYhj1efbZ5wCoU6clspbW/26tRVqi5dG0PkRGJtKv3/3I\njKr/mM9xOhMpUaIqVavexYYNG9i0aRPR0UlomplixdLDQgNZWVnUrt0Eq7UmQgxT79NcZL+OKKR7\naiDxewXV/x8NXM9kGsWkSZMZP34ymmZFiAhiY4vQvHkHnM4y6Hp/NC0WIazExKQwY8YMypatrJRx\nBjKWGPTUIiKq5LL+bgvl53LFomnTEGIZhlFcPYzP1a43FyHew2arEMbV5ZcVK1aSlFSK6OgUBgwY\nmmcMICWlrHpg/oc1jQceeCjsGJ/Px/vvv8+CBQv46quvco3Rtm13wkG3C6lfvyX/+te/AjvOnj17\n6Nt3ID17DrhuVcQvv/xCu3YdsFpTkfGVxRhGLLt27eLMmTOsX7+e9957jytXrrBkyWvUrduKZs3u\nzrO+9O9IixZdCOdEe4/KlRvclLH9smXLFpo374ym6QSD1GC3t2PBggW5jpebSyKyf0s2ZvMIYmOL\nULhweapXb8TevXvzdV2fz6eqQBojxKvoemcqVarzH+lUl5WVReHCZTGbJyLEETRtLjExKZw/f56W\nLbuqd/kDJBPJZsqVq33d8ebMmYPJVJogc7H/95pLgwYtqVHjLnQ9BpvNQ6dOvQOJs/bte6JpT4cc\nPxXpji5HCC9Wa1saNGiEyTQq5JjNaJoXITYixCoMIz6wuX/zzTc0adKBcuVq8/DDYwNr7Ntvv8Vq\n1ZEJkY/UOJ9gMkVgtXqVwluLjKVHhRxzFrM5jfr172LIkAcxjKIIsQRNexqn08v8+fOJi0tG0wYg\nXfz+COFVxL3xyHiqG+lKgxCn0HUvhw8fDnt+t4Xy++abb7j77t40atSBJUteU1ilOkiKm/KYzbE8\n/vjkXLGSjz76SC2YjxDiIA5HEx54IDfav0yZ6gixPvBDWyyDGTNm3F+ap2T8DVUYEzCZXLjdxdH1\nCCZNmqxil08ixEwMI45NmzblGicrK4vPPvuMjz/+mBdffJlSpapTpEgFJk2axIEDB/B6C+LxNMbt\nrk5CQioOR1Gkqf/STev72rPnAEymSSH38hING7YNO2bnzp08+ug4nnnmmb8cY928eTOGEa92fx1Z\noO6/1t1Mnz491zm5aa46IimWdiPEfNzuOH7++ecbXvunn35SvG+dEWIIQhzB5SpzyxmsQSbonM5C\nBMHOEBFRk23bttG5c09kzKwekrWkPA0btr7ueJJxpTlmc0GE8Ft55zCM6rz4okwMHjt2LFfMcv/+\n/Xg88apPb29kTG8//jicyVSFsWPH4nbHoWmPI8RcpfhCu97NpFev+zh+/DiRkYlo2gyE2IrD0YRu\n3foB0Lp1VzRtglJ+XZHxwkhkBrgXQcvyXSTY2Y0Qg9W1OiPEk2haPLJ/cNAiHDZsBFarUz3HY2pM\nP23WaVVZ4kGWwPVEiASaNctdTnhbKL8/S3Z2NlOmTKN27RZ07XoPBw4cyDM+Mnz4KMJN929zMU+A\nJM80jFg0bRxWa3+83pS/7FKtW7dOVRdsQIKqDWR8R17XbPYgXXX/XF6ndu3mYWNcvHiRSpXq4HKV\nxu1OJzq6IA5HCjbbUJzOysTFFUXT/AFgH5qWTDgzzORcFuvfkQMHDuDxxGOxDMZkGoHT6Q1r2LR8\n+QocjgQ07THs9m4ULFjqhl3NQkVuFK+oOQ9UC34rQjyPEE6WLFmSi6Ri+fLlqp42S/3zsw/Le3c6\nu7Jw4cIbXnvw4GFIduXFSNqwFFyu9JvevCkzM5PTp0+HJRKOHz+u2LP90KwrOJ2pZGRkUKRIOjJj\nCTLLXoPq1Wvd8DpZWVksXLiQQoXKYLV6sFoN+vUbRE5ODjk5OYwePZ6oqGS83kI8/fSzgfkcOXKE\n6dOnYzI5kGwr/neoF3a7ix9//JF///vf9O8/mM6d7yE1NY1gWaMkTOjffzALFy7E6ewScv55hLAQ\nGZlE8eJVkEUJ55CGSgel4J5TinAYMnESp+awFE2LQmaU/eN9TTiEZiwPPjhC8XkeQPbwDqf/MpvL\nIqn2P0bCciZx551tcj2721L5+eXSpUu0bNkJs9mGxWLnwQdHhb1skyc/8Scqng0UK1Ypz7G+/PJL\nxo59jClTpv7txkivv76MtLRaFC9eCbs9KewHsVhqIEQoC8bbVKlyV9j5o0aNQ9e7IgPIPoQYjESv\ngxCX0bQkwjFWJQiPC068ofLLL+zjxx9/5IknpjBhwsRcMI+EhGKEBtN1vRPPP/98vp9To0YdD4v2\nKgAAIABJREFUlPLxL/QOyJhQSzTNjdlsx2LRA4sY5CKvV685LlcVDKM7EswejBG5XI1ZtuzG7C2G\nEU0QJCstyOjov8cI9Prry3A6Y9E0G4mJJQMbxPz5r2C3u7DZIihUqEwY4/N99z2I01kBISZiGLVp\n2bITPp9PAbMPhcxrCk5nbL7n4vP5OHXqVFgt8rRpM1Tr0v0I8TWGUSqMNfzHH39U8JhCauMZhBBO\n5s6dm2v89evXKy9qDpo2BafTy759+1iyZAlOZ2hDquNIa74uMpFxB5Kv8jjSPW+krjcSaelWQyI2\n/Oc/guzAtgxpLfZRv/U7SE/BTcOGzXnppfkYRiJ2+z3qOivVmnlL1QyHZoln5tl06rZWfgMHDkPX\n2yOzsKcxjMrMmxeMF/3666/Ex6dis/VB0x7FMOJ45513bvmcL168iMMRiXTJ/FkpL3Z7HHL33Ihh\nFOOVV14NO69588748Yry34dIBLv822qth8VSXymMc1itxbDZCiJjNS9gGN5rxr7eeGM1kZGJmM1W\natZs/Ley4n6R4NcgNstsHsXkyfnn9duwYYNaSK+rf5Hoel0slkTM5nLIOM45HI4atGvXiWLFKlO6\ndHWWL1/BW2+9xSuvvMKgQQ9hGGUQ4gVstr6kppbNV+JCJglOBOZuMvXgiSfC5+7z+fjggw9YsmTJ\nNfF9n376qYpbfY605HpisUTxzjvvqKyudCM1bSYlSgQ33N9//53GjVsRH1+S6tXvDHgYqanllELw\nIcHP5ShQILeX4p9ffkoLK1dugAyJzENCxWbSvHnnwPc//PADDkcCMuRzP0KMwuksfU1s7KZNm+jc\n+R769Lk/ALs6e/YsiYlFMZuHqg2tMhLgfB5JTNAFWaPrRHpDUep7f0tKP4+fD1nN8ZI6vgiSEOFx\n9XdtJBRmG2azjatXr/L5558ze/ZsnnnmGRITi2IyWYiNLaR6EnvRtNFo2iM4nXmvi9ta+eXGo83n\n7rv7hB1z6tQppk2bxrhx46/JhHsrRPaRiCEiog4Oh5dp02ayZs0aKlSoR7lytZk/P7eLNmHCE4pI\n4CrS+uuulN8FJMYxlho1GmK1urBYHPTrN4hly5bRoEFbWrXqek3Shr1792IY/mbOl7BYHqJWrSb5\nuo+NGzdSokRl3O54qle/ix9//JFu3e5F19sigaYfYBhxf7mP8bvvvkv9+q2pV68Vzz//PEuWLKFw\n4TRkl7OgC2Y2F1OfvYdhJLFhwwZAKoDly5fTu/f9PPbYhHzHHQcMGKoy+1vQtFm43XFh/VxzcnJo\n06YrLlcaLldXDCOWtWvX5Rpn6tSpSLfNP9eTCOGkTZu2GEbfkM9z0DQzmZmZ+Hw+atZspADkH2C1\nDiM1NY3Lly/z1VdfYTZHKmvIwGyOCNyrX3w+H48+OgGbzYnZbOPuu3uRkZHBV199lWfCpm7dZsgE\nwN1IYHAELVt2DBuvdu0m6HpnhHgbm+1+SpWqnGdS8LfffuOll14iPf0OkpPL0qxZh0CM9cSJEzRq\n1AKJsXtZKbJzSvllqr99ai5rQp7NYKSVVwCJHXQirbyoEMMBJKTtCfX/v2EyWShQoCQeTwLduvUL\nVG6FQqC+++47Ro8ey6OPjrvmBnZbK7+GDdugaf6Wkj5stnsZOfLR/9TUbijHjh3jww8/zJVlupZc\nuXKFxo3boutxGEYSaWnVSEurhsWik5xcMsBMcubMGS5cuJDvecyaNQtdD+1yfwmz2XpdF9jn89G9\nez/1Qs5BiKOYTFMoWLA058+fp1ev+4iKSqZgwbJ/u+fsn6V5806K8w61WAojs4vBxEvHjr3/0TWy\nsrJ47LHJpKfXpVGjdgESVL9s2LABl6s8QWKEz3G7vbme1csvv4wsMfMnL7YiRDw9evTE6UxDtlSU\nWVKHw8Nzzz3Hpk2b0PU4gg3LfbjdlQNZ0+PHjzN69GiGD384z81k0aLFqtb6KEJ8g4SneDGbY/F4\nkujb974Asezp06epW7eBUnz+Ob5A9eqNwsb8448/eOihR6hRoyn9+w/JE7j/888/4/UWRLqrDZBx\n7VFERycFYr1nz57F40lAEo2uRTJKO5FAaJCxuQikpez/PWcgLc72SEswG+kiRyCz+v7jHsJkqoYQ\nS7Dby2KxRCOTmD+h6+3p1KkPffs+QOHC5alVq+kNiSb8ctsqv+zsbB57bDw2WwQ2W3Ncrgakpqbd\nkqqL/6T4fD5++OEHDh48eNNYU2RD7joEmXI/C9Q9+nw+Fi9eSseOvRkyZATHjx8HYNWqVeh6MWRM\nJhi7dLmK/ONSr2vJ4cOHVdVOA6TFG4d06f1B9il5sqvcTFmwYAFOZ+8wy81ksuQCVv/xxx/ExhZG\nJmsGIUQUNpubxx+fSFRUEUymOByOmmiaG7u9EXb7A+h6DFarJ0Sx+nC5yofBnq5cucLTT0+nd+/7\nmTv3xbB3oFOnvkgX9iIyY/qQUkRtkfHfqng88bzzzjtERCRgsVRFYuj8ceSPKFOmZr6fhc/nw+fz\n0aNHfyR+zk5okknTarN69erA8UePHqVRo1akpKTRrFlrypW7QymyEsiMbEVkSd53SinGIStICqrP\n/M+8GZpWBgnyfxldj6Z+/UY0aNCKZs1aYDKFslF/oq7hQgK7HyUiIiHwHl9Pblvld/fdvTCMugjx\nJFZrRUqVSs+TePKfSGZmJtOnT6dMmQoUL57Oww8/mq8GNP9tkpmZSfXqDXE666DrA3E44li16g0A\nJk6cimGURYj5WCwPER+fym+//cbEiRORLkkhgpUtZ8NIY/8sH3zwAUlJJdB1D/Xrt8wVVzx37hzH\njh27psWZnZ2NEBqyEc9byCB3BDJR1Bpdj2Dfvn388ccfdOrUB4cjgqioJBYseOWmPauvv/5aEZV+\ng+xH+zSlSlXJ89g//viDzp27kpJSnBo1GjBixCgVh3wXIRZjNjuw2VqFWF7vo+txKrSxEru9L2XL\nVg24mdnZ2dSq1Rhdb4mM4daia9d7AtcbPvwRrNaByAxqZYIW5BVk7Kw6ZvMwoqMLIUs+Ub9dNYR4\nCV1vQIUKtUlKKkXZsjXYunVr2P38+uuvTJs2jfHjH6dXr3ux291YrQbR0UXUJmQntMuaplVn7dq1\ngfN9Ph9PPPE0UVFJREQkkJhYXJ33LdINfhUJPk5GQlEmIeN/8QRZdHKQ9HVmrNY4UlLKYrdHEhHR\nEIfDS5cu3ZWbDtJSLIaMCx5HEhwk4nSGM9UcO3aMjz76iCNHjoTd722p/I4ePYrdHh2yC2XhcpUI\ni3nt27ePHj3606ZNd958803OnTvHp59+GnBBs7OzmTNnLv36DeK5557PBZXJzs6mZs1GaFoNJFV6\nUSyWsrRocfetveFbJJmZmSxfvpxZs2aFYQENw18YLl9ow7ibefPmsWrVKgyjArLuUj4Dk6kE99+f\ndzZZtoz0g2B/w2p9iGrVGgJyUQwdOhKr1YmueylXrvo1Ey6ypae/OP4yFks8JlMUFksHHI5UBg0a\nQa9e96lE168IkYFhJIdV5ORXfvnlF7744otcMB3ZBNyDxaJTokTFfIUtMjIyiIlJJbyk7E61uP1/\n/4zbHc9jj03irrvaM3ToyLANe9OmTar5kr8k7CJ2e1Rgszl16pSidyuGTAKYkVnVQ+rv3ggxQbEd\n/xpy3YcRwobZHInV2ghJirAaw/AGXMSTJ08SH18Yq7U3MitbCpkVb4QsJrgDiZm7E5lEGYJhxIaR\nvC5cuEhtpP9CiIPYbJWwWgsgQcwfIcMYs3E4GtCiRTscjmg8nopomk3Nv5a6bgWkZfsC0nX2t6jd\nj65HkpxcHF3vhKbdj4yRBnGTQtRD18uzZo3sW7xy5Rsq9l4ThyOGWbOCmezbUvl9//33ClMXvGmP\np2oAq7V//35VFTIVIRZgt8erB10ZXfcycuQ4WrXqjK7XRWKOamI2R7J8+YrANTZv3oyulwnZXY8j\nhAOLxfhLmLZ/KsuXr6Bdu5707z/4lrSutNvDF4qu38Ps2bPZuHGjgl9oaJoLXZdxq2tZbRLv1TPk\nJczCZJKsGhKjl06QF3AYzZp1DDv/yJEjlC9fE00zI4QDh6MahlEMk0lH8teBBPAmq/K/f4dcaxJN\nmjT/S8SeTz31LLoehcdTAbc7LlcpYk5OTr7jqhLjGYd03zaHzKsnFksssnroHHZ7T9q165Hr/KtX\nr9K6dRfFVRfam8aHYSSFKd8dO3Zgs8UgKaaykNAQP53UAgwjlrJlq6nYqU/9tgWRcdtoQuFBFstD\nPP300wCMHz8Bi+V+ZGIhEQk1eQkhGiIty8FIYgKZkEhJKZ2rcVXDhm0JQrGyEWIDKSnlKFSoHF5v\nUdzuOCIjCzBw4DAyMzM5deoUCxcuxGqNRbqva5CbbX11ne38GcPndpdh586dPP/884wa9QhWq4sg\nSP4KQiSRklKCS5cu8fvvvyvUhZ+O6wccDm9gHd2Wyi87O5syZe7Aan0IIfZgNk+mQIFiAajD8OGj\n0LRQQHESkgUDhDiF2VxA7Sh+d+4qQiRjt0cHrKK1a9diGKF9F3wIEYnF4rjp7vW1ZObMWRhGcYRY\niMk0lsjIRI4ePXpTr9G370AcjkbIGMyLuFyx7NixQ1lxmxHiCibTZIoVq3DdBMnatWtxOMoi0fwO\nhKiG3e5UVt+f2TkOEBubGnZ+6dJVMJsnqwX9MTZbFM899xyGkRz28kdENCIpqRihgFshOmO1FuOO\nO+pfl7r80KFD7NmzJ6RUzq8I3icyMuFvx1jj44uohfqaUjQLEeJJnE4vU6ZMJSIiAavVQbNmHcnI\nyMhViTJmzOPoenMkBMfPUrwHq3UoaWnVwuY1Z84cdH1AyL1fRQgTxYtXplKl+mzevJmDBw/idicq\nZWdHogZQcwtmUXW9Ky+8IElUhwwZjixz81uQo5Bx1+JIyrivEWIOFouX5s0788knnwDSSo6MLKCs\nNzcSfF5cKS8HxYqlX/fZzZgxA6t1UMj9XFDnpiBjeA6CSZJtuFzeMGtz+PAxOJ1lEOJRLJZKlChR\nMWCcfPfdd7hcxf70/tQNtF64LZUfyPhEmzbdKFgwjbvuahvmzw8ePJxgavwq0j0INY07I3fK0M/K\nY7O1D9CdnzhxArc7HolDO4oQI9C0eDp0yL1z3yqRAfW9gTlarf2ZNm3aTb1GZmYmI0eOo3Tp6tSs\n2ZgOHbpTpEhFLJaSBFl0fTds/H3kyBHFrfgmkixzIrGxhfH5fLzwwgs4HE0J7QVSuXL9wLkXL17E\nbLaH/R4uV1deeeUVYmMLIssGfQixHafTy4oVK5RyHoAs6i+NEGdwuWqGBeD94vP56N37fhyOONzu\nskRGJuF0hm5sYLdH/u3ufg5HBDJLCUKsR9PSqVChRlgm+dSpU5QtWxXDSEHXY2jfvkeg1rZIkTSl\nOCxIl68gFksUbdt2zzWn1atX43RWI+iR7MLp9BIZmYDZbCcxsSh33tkIkykF6aJWQMJPQFJCJSLE\ndKzW/iQmFg2QSGzZsgWHo4BSPN8jM8l1kO7qbGSMLkGtB1lKuXDhQoUT/AIZ0+uDdFvbIbPdR9D1\n4gEXNC9ZtmwZTmctgq7+VqRhsgAhdmIylcFsNpCut45hRIbFKn0+H2+++SaPPz6BpUuXhhH/Xrx4\nEaczhiB8ah8OR0xg87ltld/15IsvvlCLYzFCvIemeQhyjp1ABlyLIEGlXyPEBIQohWHUYMWKFWHj\nFC9eCas1gsjIQjz88Jg8LQt/hvajjz7KV31pfiUqKglZwiMXqNn8EFOmTL1p44dKTk4OlSvXxW7v\ng8yy9UMG1TOR8RvjusX/69evx+NpFqJQfOi6l+PHj3P16lVq1WqMy5WGx3MXUVEF2LdvHz6fj2nT\nZlCsWGU0zU4Q3nAVl6s8Gzdu5KuvviIpqTgWi47bHcv7778PSJIITTMh3TnZ8tAwejNv3rxcc1ux\nYoXqgbEA2Qs5WSkbP1D7AyIi4q9r+R0/fpyMjIw8XeEWLTphs/VFgpN34XDE58KUtm/fE6t1qFLi\nlzCM+sya9QJbtmxRNE37kW5bb4QoidkcGUhKhYq/ntflqoph9EXXvdjtHmSjch/SXXWq/y5SSsyF\nEMORpYQ6Hk8CjzwyJpdiXbLkNcXh1wZpcYXWXBdCJnL8f0+jZMl0NG04QSzfSXXe18g4XVeEKEXZ\nsnfkWUGzZcsW4uIKI4QTk6kMhtENqzUSs7lpyHV+QVqvC5VC3YTLFZtvVMfGjRtxuby43aXQ9ciw\nHs7/K5UfSFKD2rWbU6nSnYwc+QiRkYl4PGmYTC40rT6yILo2MptYHMOoTM2ajf4yu8e6devR9Uhk\n05wYhNCJiyt8U7rEPfzwoxhGdfViz8fp9LJr1y5effVVFi1axMmTJ//xNfyyf/9+DKMgQTiMxNlZ\nrR0wjCTmzr12dzKQsSjJeeiHcfyM1WoEAKjZ2dl89NFHvPvuuwFrQ5ZfpSNd7ocQIgK7vS8uVyWa\nN+8YpowuXLiQy+2uWbMRVusQtUg/wDC8ebIhP/bYeLUQ/bXQGQhRBrPZjcdTCZcrNpc1MXbsBAwj\nCrvdTbVq9bHZIvB40oiISOCTTz7h3LlzvP3227z//vucOHGCZs06Yre78HoLsmLFylxzKFw4HSG+\nDFnUc+nevT/jxz/+pxDNUWT283M8nnhef/11+vZ9gIkTJwfcvezsbNatW8fLL7/MggULFOMyIf8K\nEoyJPo+MmxVEutM/YLN1p337Trz66qu54nYXL16kRYuOSuH8GDJmMqHN0IV4Bk3z98+1IC3DEUhX\ne65SlhMRYisWSyuaNesQdp0jR44ooo+NCHEBTetBfHwK48ePx+HoFnKd/UqZh7quuemprie///47\n33zzTS7P5X+t8vuzXLx4kYyMDL788ksSE4vidjfG7W5EbGwKTz31FG+88cZfVnyyf6sXWZydg4xr\npSGEE8OI/kclZODHMk6iQIEiFCxYgieffJK4uMI4ne1wOjsRFVXgpvUSkdnaJILuVA66XoSRI0fm\niyrLTxXldFbFan0IwyjMk08+k+t+FixYwIgRo1i8eDElStxBeEXHcGrUqMubb76Zr/jbqVOnaNCg\nNQ5HBAUKlGDjxo15Hrds2TLM5iSCxAEgxHaKFq3MZ599lmtRSG69dLX4jyOxaH5C3beIjEwgLq4w\nHk9D3O5qlCpV+YZx4CZNOigqK5kMcjha8dRT05g7dy4ORwuCLv/byFjXFYSwK1Dz89jt3SlRomIu\nC+rbb7/F4UjE32lOZsoNguQJzyKtXH/M+ypClMdkSsNq7YDNFpmLXcjn81G+fHUkme1ChBiE3e7B\n4SiEECsQYj4mkxsZbrhPXXc/sjIjRinOuiHP+goWiyMsVrdq1Src7rYhx/iw2TwcOHCAuLhCmM0D\nEaI5ZnO88gp+Ur/FF9jt0blgK3v37qVt2+40aNCWRYsW56uG/f8b5Rcq58+fZ/Xq1axZs+YfJS+W\nLl2KYdwd9gPKesWyCOG6bqwjP3Lp0iVKlaqMrrdDiPHqRQi6libT1DwLtv+O+Hw+6tRpiq53QIhV\n2O098uS58/l8rFq1irFjx/Hqq6+GxVhycnJYuXIl06dPz4Uh8/l8tGnTVbVNnILTWZXIyFTCmULG\nMWjQsJtyP3++dvHiFZC9Xv2/1QqqVMmbo7BZs04EcXLSLZYZSP88PZjNkwK/ud3eJ4zp2ufzMWHC\nFOLiChMXl8qsWbP56aefSEoqjsdTBaezOLVqNebKlStcunSJ8uVr4HDUQWY6oxHifczm4cqiOhG4\njstVLwxX55ehQ0fhcKQoKqhY9Q62R4g5WK2R3HlnE0ymskoh1UZWX/gt/HfR9djAZpORkUGbNt2o\nX781TZo0Iz29Ju3adeb48eOsXLlKfd6RokXTkdZeKKRmOELUwemMRNerhyj085jNNgYNepCJEyfz\n66+/8uGHH6pEhb8Z0WE0zcbZs2c5ePAgHk8imtYbIeZhsaSp0JULITwkJ5cKW7f79+9XVuRMhFiJ\nYZTk+edn3/C9+P9S+d0s+eCDD3A6yxJ09fapHygKIUowZ86cwLGXL1/m2Wdn8MADD7F8+fJ87UyS\nMaNxyEv0DRIp73/Z3uOOO+664Tj5lUuXLvHII4/RsGE7hg8fnWd8a+DAYQq28jhOZy1at+6S6162\nbdvGvHnzAhlBkISXEp7kz7BfwGr1qHKvZ9G0cbjdsdds4vNP5eDBg7hcsZhMDyLE4xhGbFjD9R07\ndtC6dTeaN+9M48atMZkeUdbGUSRWr6ZSRBsxmWIIlm2BEIto27YHly9fZtasWdSp0xCTKRHpEtZA\nCAOPJwaTyU5sbIFcgfkrV66wcuVKBgy4D5dLdgisWvVO1Wkt2KnM5epwzTaTqanlQko9T2I2p1C9\nen127Nihehl3RMJWPITXJJ9CCJ3PPvuMb7/9VimR5xFiBYZRjDlzXsrzerNmzVE09v5WCzlInF4d\nbDYvBQuWxma7DyGWYrWWxGz2IsQUrNYBxMcX5uTJk2pDKovsZicVt657qVnzLpzOeiHv/eNq7EsI\nkY3d3od77hmEz+djwYJXSEkpgYzf++9pFykpZW74Tvyf8stDMjMz+fbbb3OZ1n8Wn89H69ZdsNvL\nIGsoI5DxiZWYzSmBPh6ZmZlUqVIPXW+FENMxjPI89NAjN5zH7Nmz/wRruKCsgZMIcQbDaMDjj+ef\nTeXPcuHCBR5++FFatOjCE088dcMO9ydOnPgTH91lnM7CYaDpYcNG43QWwTD6YhgFmTjxSUCyoHg8\nlULuBVyu4rz66qv06zeIwYOHc+DAgb99L6dPn2bo0Idp3bobzz8/O0+3+YcffmDs2McYMeKRsNrZ\njz/+GMOIRcaqFmK3exXJQCTSZXQj8XdOHA5JDiCpxzIR4mvs9nQmTZpCpUp1VPVGAbWoL6p7XaXG\nGIcQfTGZ3GFVMj6fj5kzX6BSpTupV68lTz31FA899DDFi1fAbu+GEHvQtJdylW39/vvv7N69WyV/\nXAjRBBnXy8RqfYjp06fz7bffYhiFkAm+iUqReJHYyWyEGIbJFMf48ePp2bMPwaZHIMROChcun+fz\n9vl83HffA+q6HZBZZVleJoTB119/zYMPjqRFiy5ERCQTGt6w2fowbdo06tVrhWR96aMMhvUIcQiL\npTNmc5GQeXQinCj4I8qWrcn06TMxjNLq+qGs05+TnFz6hu/M/ym/P8lPP/1EoUJlcLmKq2Yt/a8b\nf8rJyeHdd9+lcuXqWCzFEOJJbLZG1KnTNHDepk2bcLkqEnQ1TmGxOHL1Ec7KyuL48eMBV/O7775T\nWet3EOIIdnsvChYsi9XqwGKx06fP/YFjs7Ky/pILn5mZSfnyNVR/2qVYrQ2pVavRdc+RTMSFCYWk\n+JmI/d/L0jA/REaSd544cYKLFy8SH5+KyfQsQhzCbJ5MwYKluXr1KufPn6dt2+54PAkULlyODz74\nIN/3AVKJSzLPgUjK/xoMGDA03+e3b9+T8HhgKzStIzL+eQVJ8T4JIT7BMKI5c+YMtWs3RsbWXGha\nSXQ9GoejjPqNSyLrff3jXVSb1lqlCHswfPiIwPWnTJmmrOn3kSSvToQYis3WloiIZFJSylKjRuOw\n7n07d+7E7ZbQHXn8cGQIoTFC9MDprMDatWvZv38/drsXWYOMUngpSNfYhj/z7Xa3xmKJQ1qH/o12\nCB5PfCDDnpf8+9//Vr105+PvK2yzdQjLukdHpxAEqoOmPcpDDw3D7U5Axg1TkdUffjKI35HwtGeQ\n1SEllYKT68diGUP79j0pUKAk0gJ/ExkueB4h1mAYpZkx48b8kreF8rtVZAXfffcd8+fPZ926dQEl\nUqdOMzRtfOAFsNsrs3jx4huMJJXgvHnz6NdvEDNmzAyrNsgNA8nBZvOE0Ytv27aNiIh4dN2L2x0b\nCEJv3ryZIkXSiYwsQLt2PXjzzTdZsGABGRkZgXNnzZqjun45SE1NY+3atXz//fds3779mgXecvGU\nD1HIlxHCyYQJ17Yks7KyKFSoDGbzEwjxM5r2EjExyQGlu2PHDiIiqofcJ7jdpQOL9vvvv6datbuI\njk6hTp1mAcu6SZP22O29kdCTDRiGl3/961/XnEdmZiZvvfUWM2bMID29FjabgaaFXvcsFos93xUf\nsl3oSyHnV0TG+fx/r0TG0MDhiOenn36iaNE0pIUXxPcFQxIzkXg6f7zuOfVdQ6VIvXTv3idw/aSk\n0oRngsch45MnMYyqLF++PGy+OTk5REUlIqEna0IUVlDR3n13rwDvX1paFaQl6t+0/o0QHkVTryNx\nfdJdlhZqEaR73AQh7sJk8tKlS7c8QzWHDh1SSvRkYA4OR9cwctv77nsQXb8LGRZ6F4cjjjvuqKtC\nC36F7N9gQEKedCQhQkkk/MeDxBCWRtNcuN2xGEYMEntYUn2fQkpKGgsWvPK/J+Hh9RbMlZLPS7Kz\ns9m7dy979uzJs63k3LlzWbduHTk5Obz11ls4HF4MozcuV1Xq1GlKVlYWuu53Cfwv01Q6dOh8jSvm\nT06dOqX6HLyEEPuxWh+gSpV6gR/o/PnzuN2xIQtuK06nN6yLmc/no1ev+3A6S+F09sQwEpg//xW2\nb9+uYmmH1cs9Gk2LRdM8eDx3YBgxrFmTO0i+bds2DKNyyH1mI0QkJpPtuuQNR44coWbNJng8CaSn\n1+bbb78NfHfmzBk8nngkKYHEnNlsUZQqVZW2bbvnWZ2yePFStctfDMxF1wcEKg/+LFevXlUkDXeg\naXFIN24eQoRiwy5hNtvzTULx4Ycf4nDEI5McqzCbYzCbHyTIQ9cHGVN6n4iIeL7//ntstgj1eWiy\ny4TE1h1C08ojhK5qW10EG39fQIhHqFmzceD6BQumEV4TPAKZmPAgRCJRUclh7/9vv/2GzeZRx65B\n1t8GlZ/ZbA/zKt5//31kBjYeGYdMoHr1unz88ce4XEVDzgVJglBJKeuCyIKA2QhRhoFXFhCRAAAg\nAElEQVQDg3XdJ06c4KmnniImpgAyG14bmamejBAOzGadJk3a8ccffzBv3gIVRvCqce1oWgyypM1/\n3QVIkoKJ6ncthoxNRiM3kspK+cUrZZikFPXr6vxjCOGlatW6+eaWvC2Un8n0NI0bt+fs2bOsX7+e\nd999N9eLfeHCBSpVqoPTWQyXqwTlylUPlLksXrwUhyMeh6M/TmdlmjZtT3R0MsGgdTYuVy1WrFih\n6gz9bQAvI0RVatWqQ6tWXYiISKRYsYp/qyXlN998Q5UqdxIfX5TWrbuGKbbdu3fj8ZQPewn/jGX6\n9NNPcTqLKCVxBdkgyUbv3r2xWkMD2OeQbtA9ahHtxjCiciUvJCVTIXXMVmQJVDpCJDFlypN/+f78\n8vHHHxMbWwhNM2O1RmG1tkSI7Vgs40hOLhHGtrxr1y5VIRCNTOZIJeJ0NmLJkiV5jr9gwQIMoyES\nhpKglM5ppCv3BLKJThtat+4Sdt6JEycYMmQE7dv3yhMKsXHjRurVa0WtWs1ZsGAhqalpuN1VsNvL\noGlunM6iOJ1e3nnnHY4dO4bV6kZi2fzW3SqkJVgFIVy0bNmZAwcOcODAARo1ao+MWQ1AgoANXK4C\nAQU1b94CDCMV6fJOUsqyMH6Qscn0NJUq1Q3MNScnh4iIeORmeR7pNg5DiPU4HI3p1Kl32L3JuuMI\nZFzsC4QYgqZ5cTq9uFyxyM0KJHO4bCIkyTzKEbQWz2A260yfPp13330XrzcFq7UfkjQhBgl5aYq0\n1h5DiKvo+t0MGDAEu92NpKzKUUprLRJEf5/67DJC3IWmOWjUqClWa2l1X2eRVqC/r28sQVaZQ8jN\nJrRKqztCdMp3I6/bQvkJ8QmpqeWJjS2k8Hk1w2r4AB58cJRqXZeDEDnY7ffSv/8QcnJyFHX5PvWA\nMnG50jGZzIRyk9ntg3juuecoUqS8eolLIneqOEwmD1ZrV4Q4ghDrcDq9YTvxvn37WLRoERs3bsx3\nj4xQOX78uAJK+0GlR9H16LBqkbVr1+LxtELGVeqrF20cVmscNtsdBPF576kXcBWS501y8OWVRd29\nezea5kbiuQYjYy2fkpJSNuy4zMxM3n33XYoUKY/d7qJixTo3ZDo5fPiwsqKzA8/Y46kRlmF96qmn\nsFiGI3f9ZGSDp8aULl3lmj01Jk+erPjc/Erer3y+w2yOo2jRSjz44KiwzfHMmTMkJBTBYhmKLP4v\nx2OPTbru/C9dusS2bdvYsWMHL774Mna7B7c7DYcjilWrVtO5cx8V4/Ug3UQ3Eu95GqvVEfYezJjx\nPFZrUaR19DtCXMVkak69enfx8ssvc/z4cd54YzVt2nSna9d7KF68DHJT8i/q05hMjrANbOvWrbhc\nsXg8lbHbI0lPr0nt2i14/PEnwhJXp0+fRpashbq9PqUwZxIfX1gRRTiVkqmqvl+HdHv9c8hCCB2T\nqScWixdNaxQy1mDkRjBavUujlULdTIkSlRUDk4x1B0MDZ5CZ8Djk5tcai8VgxowZaFpZ5CbhT+KY\nkTHTKoQaCHLOb4eMVxSJc3yC9u278Omnn+aKq4fKbaH87PZuJCWVwWSaGnjgNls4tqp+/daEU2S/\nS9Wqjbh06ZKCDITWjXajaNEyWCyPqMX5DYaRwBdffMHGjRsxm11I83+POm8csl5Rnm8YPQOdwl5/\nfTmGEYfT2QOXK4327Xv8LQU4c+YLGEYCHk8bDCORp556Nuz7H3/8USU/pqsX1B+r+wEhXFitpfDH\nk2TgvAUyu7cdpzPmmi9B587dCMe/7QpTflu2bFH1kQaSm+0sJtM0ChYsHQbX+LOcPHlSuYb+IHYO\nbnd6mNUsmWD8UJ6tCNEbt9t73Rd2y5YtKnt5COnyFkKIe7BYUkhOLhVIvoTKwoULMYz2Ifd4BJNJ\nJy6uKBUq1GDcuHG89dZbuX63kydPMmnSJEVA+pU6dw+GEc3JkyeZPXsOzZq1V20UJyCrTO7knnse\nCBsnJyeHlJQ0gk2bpNWqaW1xOLoREZHA9u3bA6GaFStWYLNVCHl2i9G0AvTpMzBs3DNnzrBr164A\nDf+xY8eYNm0aTzwxhe+++w6QGW5p9RXCn5CQnkM8QmRgsxlkZ2czaNAwbLbCSOoqqXCllfYMkgyh\nK8Guav9GxuQyke0/SyLEi0gCBAMhWiGhQak0atSWhISiyJhqFjKr63fxTyJENJrWELM5mlq16jN4\n8BBk1vicGr8z0rKMV7XjG9Q4cxHCgWF4MZnKIa3C0Wo9V8JiScDjqURiYtEwQ+XEiRNs2bKFAwcO\n3B7Kr379FqoaIDQuspD27XsFjhs+fDS63kXdfA52e+8A91zZslUVuj4TIT7B4fCyc+dOKleuh8lk\nwTAiWbx4aWCs5s07ECRXRP34fqohHy5XXd54440Qq9K/MC7jcpXJsx9vfmTfvn2sXr06LKsXKmvX\nrsVudyJhBQOVUj6B2Wxn5cqVlCxZHrs9Gqs1EpPJg8tVEpfLe83KB4DXX38dkykKycTRFYejJDNn\nSnKHc+fOKbfoaWSRfHDXNYzkG1JstW/fHcO4CyFexW7vTvnyNcKsksuXL1OhQi2czjvR9ftxOLz5\nosSfOfMFbDYDs9lGoUIllJIdhxDP4nDE52pS9eKLL6qstn/+Z5AxsHuRVtsgnM40+vUbHDjn6NGj\nipa9MeE0U+DxVAgrX9y/fz/Nm3eiUqU7GTduEpmZmSxdupSBAx9kxoyZXLlyheHDH1GdxnzquqGQ\nksmYTDHEx6eyb98+cnJySE4urZRPHWTMaylFi1bC5/OxadMmlixZElBwIGOxUVEFsNnuxWweFiiF\nzM7OJjm5pLqHZkpJ1UZmtJ+kYsU6gIwpz58/H6czDmnJvY1k1I5Cxv5K4a+hlvdgVWNGqmP6qGf1\nQsgx7Rg+fAR79uzBZotSSlhXCrIiQngwm52qj/JoNG0UZnMUQSIGuRlLr6AQVquHiIhEhDARHV2Q\n9957j99++42RIx9B1wsik059kApcYm9NpmnUqtUU8DfO8vfVibs9lB/w/9h77+iqqq39f52zT9v7\nlPRKSCAEQgmEFnqR3puCKEiR3pRepVvoXQREEEVQmiDYsKCXq1e8AgrIjQpYKAoIIi1ISM7n98da\np5HQfK/vGL7f3xyDoUl2WXvvteaa5ZnPpG/fx7BaOykFdhHDqO1HcX/77bfUrdsCuz0GTYvHMIpR\nuXJdfznN8ePHycysjdmsER4ezxtvvOG/vq+xTLAsWrRENbm5ihBeNG0IZnO0mohuNM3DjBlzuHz5\nMhaLg1Cr8qFbxqv+J/Lss8tU4xon0i1fjIyZxFCpUh1ATuATJ05w6tQpzp07x4EDB24Lf5EYsGhk\nPOoTzOYsGjdu5X8fe/fuxePJRFIKpRIAKJ/BbNbvmAW/ceMGs2bNo23browbN6lQ0PQff/zBjBkz\niItLw+EIp0qV+neV3MrPzycnJ4cBA4aqxtq+xfI6lSrVDzmuadN2SBdpCTLOWw8ZH4ogAMu5hK7H\n+8MDDz7YFWnVnFHH+UgXDqHrEbdlgBk0aLgiUpiLrreiRo1G/Prrr6SlVUDXK6p+y5uCxrwDGcZY\nRdGipQGYMGEyVmsLJK3Yb5jNc2nYsC0PPNANl6usv7mSj/xg4MBhaNrYoGuu9i/648ePU62abHxl\ns8lWmw5HLMWKlQvZwD788ENSUyso8HImcoMNR1q10Ujr/A+EmKTgMwPU3L+i1kYKwSxEQizi0UcH\n0rRpe3S9HUJsRdP6qW8xEkl6WhkJd0lX92uE2dw5aE3NRoZv6iIJECKYNy/gFd24cYPjx48zePBj\nhIcXV6D5YJiRpE+7ceMGTmckoVbnX6T83nnnHdLT00lLS2PmzJmFHvPRRx9RsWJFypUrR/369Qu/\nkRB4vV46d+6B2RyHjAXYKFmyIvn5+Zw/f57IyCTVMf7fWK1tqVy5TqEuWfDvzp07x+jRE+jSpQ+v\nvLIuRAHm5eVx//1dFWNGDA5HIuHhxTCZ0pAuy9cYRinWr3+VtLRMzOa56mPtwzBi/us9LiT/XCLS\n1YvB1xZR7mytmT9//p+67pNPPqXKqL5BuhMfERFRxP93GYuMQGaSH0Fm3IaqSd4Ww0hj3ry779db\nmPz+++9ERhZB1pCewWyeQ1JSqdsCrq9fv87ixYsZNGgYtWs3RkJJfJP9Y8qUqeE/dsuWLTidVZBQ\nkjbI2msXEj9WJug8CAvL8lelyNivz/p/RSmBdHQ9knXrXi10XJcvX2b16tWKnstHLJCHy1We5557\nDqs1TCkRO9Ka6YC0uBORyQgvmmbj6tWrXLp0iTJlquJ218Dtbk5UVBIvvviiqijybUL7MYxwvF4v\nnTr1RGa9fc/zD8qWrVnoOC9dusSJEydC8Ktff/212gjfUHMhDJOpGHKD9fXf9SCTDEl4PIlIggjf\n/Z5V86Iz0kD5FcPIZMmSJSrm56tU8SKtyI+QqAoDuSkdRFah1MQw4pBWZVNkIuso0lqVMVuz2cXx\n48f54osviIwsgs0Wq97pACTWz6WUnBdNm0yDBm04c+ZMUOzR9+8vUH55eXmUKFGCH374gdzcXDIz\nMwvgti5cuEDZsmX9Qf1b7aRCCEUgEI/cYS4gxCFstjA+/vhjtm7ditsdjKG7cUfuuYsXL5KUVAqr\ndQBCLMMwyjJ16tMFjlu3bh0ORxyyp8RbyAycD2m+ko4de3Ds2DFKlaqEptkwjAg2bSrIJxcs98I2\n7BNZ/N5X3ddFAFsGdnu/e2oYHixz5szBbPYFnZsgRCQuV2zIMQMHPoZ0V1ohXZYKBEqaviY8PPFP\n3dsn//jHP3C7s5DwhWIIUQNdTyywgZw7d46ff/7ZT+mk680QYg52eyk0LRIZYN+NYZRn7tyF/vPm\nz5+PzfZY0Pw4hxAaul5fPfdzyCTEGiIiivgt5SZNWiLdva+QG151wsISOX36NJ9++imrVq0KKd87\nf/48xYqVxelshAzSxyMtG3A6a2CxOJHxM5CbjQtZ3fA1Mo6bghDv4PHE+jfia9eu0b9/f8LDixET\nk8b99z+AyxXsvgeU5caNmzCMNGSc+iiGUfueqn/mzZuHzTYk6NrZKhn2LNLqn4NMglxFiDkkJZVR\neE+55kymJiQnlyQr6z4sFgnCHzlyPCdPnlSM4DcrvzVqLvnadT6AtMItvPDCamrUqK8SeVuQ2eMk\nZLgCTKb2rFy5kqioYAv6IIHKlZnIBFQSJpObnTt3kpeXpxI7vlryo3+N8vvXv/5Fs2aBvrAzZsxg\nxoxQ+MTSpUuZNGnSnW8kBJ9//jkeT0U16J3qIStgt0fTpUtP3O7gIurfsFgctw2av/TSSzidbYI+\n9E/Y7e4C7u/993cnFPy6gwCgdCTp6ZX8LlpOTs5tEx27du3C7Y7G15u0dOmqd93S8s0338TpLI8M\ngPdRi2svQryM0xnNkSNHCj3v22+/Zdy4JxgzZnyh7fw+++wzNUl8jMaHsVhcIa6ytJzuUxN/FNIS\n8L2Pk5jNzntmwwmWAwcOYDZHKuX3HTKpYvj58PLy8ujSpTc2mxuHI4py5arhdKYRyG7/jsWiU6ZM\ndUqVymLOnAUh3yGAg/xGLTAbQlioX78pnTp1JT6+JFarTlpaxZDG1gcPHlSJjhiEiMRiieTVV1/j\niSemYRgpOJ3dMYxkpkyRm+aoUeOx2foEvZsFyJhZd6Xo6iFjeI2R2fpkdYxPIScihIcmTVr4LbK5\nc+equb5aKR9DhT2+QjZXmkfJkhX9Y1606FliYoop/rpEHI5IKlas46c+y8nJ4eDBg5w+fbrAd1ix\nYgWG0SFo/P9Wib8oZGa4uVJ832MYaTz//PMkJJTA46mOy5VOrVpN/B3uLl++7N/kvV4vjRq1UYQZ\nO7DZHiMqKlnF9u4ntIpmOFarC6/Xq+Kk40lLq0rAUpfK02qtx9KlS1XcLtiSa4WM+81HJmi+Rojx\nOJ1JVK7cgMcfH47HE4fLlaY4EP8C5bdp0yb69Onj/3nt2rUMGTIk5Jhhw4YxePBg7rvvPqpUqXLL\nOJkQgitXrihM2mL1MXx1gqcxjCKkppbDbn8YIZ7DMLJCwJg++fXXX+natS+ZmfXIyqqLyRT8oS9i\nsdgLlLE9+GBPJCWQ77jX8CUGhIjBZBpKWFh8SNPrwuSXX35RaPQopUQuIcTTFCtW7q6om7xeLw8+\n2AOnMw23uwUWSxhxcSXJymrorx++WQ4dOqT6mIzFZHoCpzO6wLEffPABbnfdkAnkcqWFBNJPnz6t\ngMsvq11TR+7a/0KIRlgsiQUYXO5Frl+/joQx/OEfg9XakdWrZUe2xYufxTB8jdvzsFp7YrGkBI3Z\ni2Ek3jb5MmfOAlWD2lbd5xyGUZXnn38BgO3bt9OtWz+GDRsdAsT+6quv6NKlNx06dOOtt97ixx9/\nVFaMj8nkNHZ7BCdPngxqK+kb178UAYKdQA+Js8j44UpkLCsaWV1RFol7W4sQlejevS8AUVGphPYt\nnoLdHomuh6FpdtLSMgtQmp06dUolgF5DVswMJiIiRTVYSsLtLo3dHs7kyaFW4aVLlyhWrKxKDE1H\nWmS1kTHH2Uir34QQGn36DAAkTdzHH3/sT6zcSnJychgxYjw1azbn0UcH8euvv1K6dHVCq2hew2yO\nY/bsgiGcBx/sqlzwhZjNXUhNzeD8+fOKQdv3bs8hre3p6h1/iozTRqnv8g6GUYmJE6eRnZ3Nb7/9\n9tcov82bN99R+Q0ePJiaNWuSk5PDuXPnKFmyZKGF7UIIpkyZwuDBg4mJKaImU2Cxut0deOmll5gy\nZTpdu/bl+edfKGCBXb9+nfT0ysr9+RCTqTvS4lmGEJ8jROMCZIsg3U2568xGMgbHqIU6Eh++zGIZ\nWMCqvVneeecd1QkttCeIwxF718zPXq+XTz/9lNdff/2OyhagU6cemExzgu63jGbNQp/x1KlTSin7\n+jq8h8cTW8Bq3rdvHxkZNQkLS8BkMpDWSxWE6ITZXJRKlar6m0fdq3i9Xmy24A5dXlyu+9i4caN6\njp4EmuLI7J/ZHIXZvBAhsrFaR1G2bNYdN5ESJSoTsB5AiBV07tyLFStWYhjFEGIJmjaCqKgk3njj\nDUaOHMv06U+GWEnSAwklZ/B4KrBv3z5WrlyFYVRSCi4Hi6UNKSll1HyxI13ca0jP4R11voxxSYop\n3zV/91enREQUR8bGfH+bgdMpGad9YPGNGzdRrFgF4uJKMGzYWFauXKm+j++cfISwERtbnEDI5jSa\nlkBWVn3efvtt//P9/vvvTJo0WR0bjkwcXEFS2buRccl+aJr7jqQfIKuqatduTlpaFYYNGxsS8unS\npTdW6wh8VTSa9gitWt1/y2tt2LCBXr0GMXXqdD++97XXNmIY0Xg8LbDZ4khISKdcuZo4HCnIhMZE\nQtleXsDpjGDKlClMmTLlr1F+n332WYjb+8wzzxRIesycOZMpU6b4f+7duzebNhWk7Q4eYKCm0Qds\n/B5dj7tjh/YvvvgCl6ssAdc4HxlIrYMQ5TGbU3j88ccL7F7btm3D6ayF7Cb/qNoFXUi3YxQSdFma\nQYMG3/b+X375JXa7r2THF6w+hdXqvGOHsA0bNtKuXVd69hxwS/e2MGnatCMyUO/78G9Qo0azAsdt\n3rwFXQ/H6SyKxxNbKE7OJ16vlypV6mGzDVDvo5RaEBUxm8PZvn37XY8vWGbNmodhlECIZ3A4HqBs\n2Sw/SHnSpGnY7Z3x4Ro17Snq1WtBzZpNiYsrQYsWHQt147Zt20axYuWJji5G//5Due++1kGUT15s\ntkcZN24icXElCDTIAU3rqXpGTMNs7k1MTLL/+r///ruygrepufQ6YWHxfpbpIUNGKmVnwWSKQ0KS\nziEzzHWQSaNIfIB7q7U9JpP1JmV1zR+2eeKJyWqebkda2y4eeyzg1cgSxQQk0/dhDKM+zZq1QsbU\nfODyk2pMgmDAuYSEdMcwEhgxYiQlSlQiKaks4eFFMJuHIa2yh5DubiMkLb7v3BH07/8Y8+fPZ8KE\nibz99tv8+OOPIeGPH3/8UcGknkeIz9D15nTtGjCIzpw5Q5EiJbHby6Jp8eh6ImPGPHFHZqGb5fvv\nv+ell17iySef5NVXX+XixYuMHTsJi0VXnf+C472fk5iY7j/3L1F+N27cIDU1lR9++IHr168XmvDI\nzs6mUaNG5OXlcfXqVTIyMkLqRAsb4NmzZ4mLS1G7kGSmmDatYKLiZtm/f7+KE/k+fi4SO7UJGfRu\nhMNRjjp1moW8/LNnzxIWFo/MRB7Fah1KbGxxxQrcEmlJLMXpjL6jBde79xA0LRaZbRyIzZbEU0/N\nuu05S5cuV0phNWbzNDyeuLtuXynB12lI9/TfGEa5W1LRX716lWPHjvljNreT3377jdatOyHdXx9M\nJAchilCiROH0R3cjO3bsYPjw0cybNy+kBO7KlStkZtbC7a6Ix1OPuLji/Pjjj7e91meffaYyhu8j\nxLfoenMefLAbERGJuFxtcbnqk5ZWgWPHjilmEV9hv1zYoTW7PZk6dVrItWNiUjCbrcTFFQ8JJcyZ\nMxe7vQPStX4YWbnSWG0SFdTGaUFmOEsTHZ3EzJmzkXHg6QixC5utDW3ayFpySac/ibCw4ng8KYwc\nOQav10tOTg5Hjhyhf//HEGJG0Fi/IiEhXdXR1kFaPr7a4mQCbM6/IcM3HyLEOgXj2oVM/gRXgvhA\nycmEYmyfxeVKwOHohBCTESICqzWS2Nhi/qZNko6tV9A557BaDb9X9sor67Hbo9T1ZWmeYTShc+ee\nId/yxo0b7Ny5k02bNoXQgPnk8OHDhIXF43Q+iM3WEE0Lo0iR0ixe/Cx79+5V5A1PIsQaDKMEzz67\nzH/uXwZ1efvttylVqhQlSpTgmWdk053ly5ezfHmAHHHOnDmULVuWjIyMW2YsgwfYv//jqmfDVYQ4\njNk8hgce6HbHwebl5VGtWgPV6X0dVmsrBewtigywgxB5GEZDVq5cGXLuV199RWZmHaKikmnRoiM/\n//yz2q0v+j+sYXQtcN7N4vV6ee+99+jfvz+PP/44u3btuuO4JWXP5/77aNpjTJt2+7KsYFm6dDnJ\nyRkkJZVl9uz5t0zI5OXlMXv2fFq0eJAhQ0aG1B0XJt988w0WS2LQxAYhMoiMLHLb8/6s5Obm8tFH\nH7Fz504uXLjArFnzaNmyM0OHji6U8Wf8+CeQGULf2L4jOjqFzz//nIcffphHHnmEtWvX4nLFYLOl\nIC34zwg0/wluizmVBx54sMA9Ciu/C23RORJZidM+aNMdg0y65GI2P0jnzj0AGVaoV68F5crVKlCa\nd7P4GvI4ncWwWFyYza2CxvqWarjlqziZhGSk8REaxKkxeQjw361HeiQg3dsKQcrvGgGYS3Vkfe5n\nWK1FsNurEfCiNiFDQs/7cYorV668qarmGLoeDsi1IIsD6iLdft8xoaQM169fp1atJrhclfB42uF2\nx/rB5SdPnqRhw7ZYrdGEQp36IC3aVDZs2Mg333zDI4/0pXXrh0P6csNfqPz+WxI8wKZNH0AGcn0P\nupMqVQqnIr9Zrl69yrhxk2jR4kEmTZrOzp07sdnCkd2hfNebxKRJk297nUCM6oT/PKez9V3RXgVL\nbm4uP/30k3+inzt3jg8++IAmTdoRHV2MSpXqqebUB4PGN4pRo8YAEgZx/vz5P1VKd7N069YPw6iH\nEOuw2QZSvHjGLbPlZ8+epWfPAVgs4cg+r2eQ2chYbLaw/0pP41OnTvHRRx/5rdyLFy+yf/9+zpw5\nQ9eufTCM+gjxCjZbX9LSMgsoopkzZ2KzBVtvHxIfXwKXKwaL5TEsloFI6+tdpHXTX1kgDZGuXiNk\nsHwnQoTfMabrE9m8vBTS1fwFGTcLToLsQYJ6QYjPMJsjsVgcNGzY5o4bju89uFzRSkmhNkYDTeuB\nEFPR9VhWr16NwxF/08bUHOnp/AtpZenI5OFaZJLAjYz7XkdahF3VOmuIhB89gRAeHI5oEhPTefDB\nhxQs5g+EaI00IooiiRDsZGU1plOnbsTFFVc9eZdjGGWYPl2+x2vXrqkxVORmOq5g5bd8+XIMoyky\nTPAyQoyndOks5VmWR9MmIsHYwewwzyMt95do1eqh273Ov5fymzlzrlqklxAiB11vzahRT9zm7NtL\ngwZtsFpHqd3rFBZLyi2plIJl4sRpGEYGQizHah1AUlKpe1r0n332GRERiTgcsWiaW2GmdEymEmqn\nXYh0QWzIxMJ7SNfbxbx585gy5SmsVh2bzU1mZq0/1cXt+vXrvPDCC0ycOFGBci/hi4e53fUKjd9d\nuXKFlJQyqln8eGQmLRJpTRzA46nEv//9b7xeL99++y0HDhy45xjOxo2bVQlSHXQ9mkGDhqgC/vLY\n7WEqjnM5aKy1QoL2IDP7ksigBUJkoWkRpKdXQQJg5SKT79Yb9LOOtGx89aoehEjGMMJZuHAh993X\nhPLls2jYsBnTpk3zh3F8sAyfTJ8+A4vFgabZKF68NJpWF2lB5SNZXXxK+WlkyeBFrNaBNGzYptD3\nsW/fPqpWbUCRImVo3bqjIi8NTvhVo3fvPowZM549e/Zw48YNhWfzxXv3ILPKLmy28vhc7gCJwZsI\n0QmTqRlCTEfXo2jbtpPq4RuFdIN7IERDNM3D888/HwSIfhQZ/vG1riyHdPPfwmIZTUJCKkOGDOfh\nh3uzfn0oMFxiM/cgrc6xCPEGmnZfCCONtOA7Ia3KhxGiDFZrJNnZ2TidxdU9RyCt66vIJGRFhFiN\nyTSDLl36cDv5Wym/vLw8evToj6bZ0TQ77dt3uas41a3k9OnTpKVVJMBq2wzDKAgJuVm8Xi8vv7yW\nhx7qxahR40JISe8k169fJzw8ARkPikcW57+kJsFCpKUXiewfoSFjOvURojWGUYOxY8cq6+IXhMjH\nYhlB48bt7+m5b9y4QY0ajVTd7UhknWYAauJ2N2Xr1q0Fznvrrbdwu31duU6ocdnQOD8AACAASURB\nVPpYVU5js0Wwb98+WrSQ7S5drlKkpWUWmpAoTC5fvqzcoRfVO+mmvsvr6h5fIjOngb4WhnFfoYp6\n8+bNWK2RSAtnnuKP8yXKvEhLaCO+pIDVGondHo3b3R5Ni8PlSqBGjSY0bdoOi6WKUlZZSnEkoOtR\nqqbUjdlspXLlen7i2Ly8PK5du8aNGzdo2/YhHI5oDKModns0LldV7Pb71Lvz8UZewmrVCzzDwYMH\n1fsYhyQh6IDZ7CRQ4fNDAfYf8CXYIvExo9hs6VSvXg+rNTzonnuVInwMXU+nY8fOPP74SL9befXq\nVQXM/hoJMB6KEHOxWuNYt249O3fuVF3jfJn4C+p6gRJIXa/A8uXLyc/PZ//+/YwZM446dVrSrFkH\n4uNLqu/xMzKhWJKqVWuSldWQxMR0OnXqwfr169Xa9MFZrqFpqaxfv14932V1v4cIML/UxWQaicsV\nc1tCXPibKT+fXLt27bYg5nuR5s07IpH3vo/2LK1b395c/p/IDz/8gGEkKaU2kMAu/iUSTArSlP8E\nTUtQC2UrFstY4uNTGT58JDKe4zvvOGFhCfc0hh07duByZRFghmmJdI0+RNOmERtbrNAKmTfffBO3\nu37QvachRJTKxkZjsyWiaQY2WwOlTL1YrWNo2rQ9mzdv5t13372tJThjxiy1gIqrjWE+0uooSaBv\nSCJyp9+FEJMxmZyFtu+U/SGCO7B1RNPKIa27Q9jtxTGMaNzudOz2MGbOnEd2djYbN270KwBZWZRA\ngF3lqhpXJaWYI9T18rBYxoQQlPrE6/Xy008/ceTIEd58800GDx5Mx44dFXbRZ3nuITIyyX/8tm3b\nGDNmjCotrEmAlOAiJpMVXY8mLKwRuh7DokVLC9wTZFhl3rx5DBkynNWrV/P+++8TFhbcThKkS1uf\nuLi0QqFCERFFkM2FBgSd8zEpKRn885//VJyGDZGb0QWlqK4iE03RCFEZqzWaokXLYLUmISmnwpEV\nQx5MpjBMphHY7d2JjU3B44nFZFqGEF9js/WhevWGmEyhjExO58O89NJLdOvWD6ezGkLMxDAa0LRp\ne6VgxzNhwsS7Qkb8LZXff1Pq1WtDwAIAIV6lYcN7s6QKk507dzJp0mSWLVsWYp1evXoVq9WFdK2C\nSUizkVm1wwjhxOFoTLVq9zFlylPUqdOKBx7oSt26LfB4imA2F0VaiLkIsY4yZapx5cqVu4r/eb1e\nBg0ahM3WLujeVxHCICOjDu3bdy0Uw/X777+zd+9eEhPTsFhGI8Sb6HprSpUqj6Y5kBbAGqSL8hzS\nlRyNdNtduFzNcLmqkJV1X6EB/WPHjilw7n+QgfnDQeNrj2T6yFYLrAYySdEFt7tGoSw6NWs2J2Ax\nghAvULJkRSIjixIVlczTT89iw4YNTJky5ZYYxX379uF2Z9ykMMqp+7cldPMq3Hq7fPkyzz//PHXr\nNkHXS6DrfdH1YsTFlcDpbIjNNgRdj2Xjxk0KzN4Tl6siJlMqEocKMi7ZFCGexmYzOHbsGO++++49\nQZ+OHz+OrkfhK7mTIOAohPgNuz280NDJiy++hKZ5CGWgOUxsbAnlMW1Q7yEJIYpis0VhtzdRm8JH\n6vjpyIqWXGTs0MdJmYvJ1I4aNeoxZ84cXnzxRdzu4ORNHlari9TU8phM85QC/ApdlxZdfn4+a9as\n4bHHRrB8+fI/VWX0/7zye+WV9QpOsgshPsAwihfICt2ryK5SxRFiErrenKpV64dYPA0aNEMGmV1K\nUexUu3sSQuhkZdVg0aJFfqV5/fp1ihUri6ZNVpN3CjIracFq9RAXl4Km2XG7JdPwtWvXGD36CWrV\nasGjjw701017vV66du2DrmcgY1rbEOI0Vuswqlatf8vnWbt2HQ5HGC5XGk5nNI0bt6JGjWZkZtbA\n4SiJtCDeQQa9HydQwtUJGVPqhwz0X8PhaBWS2T969CirVq1SpX/pauK7Ce0H+yh2e5KqNW2oNo4Y\nhNiAzRbJyJEj2bdvX8iY169/VYGXdyDE6xhGoj82mJeXR5Mm7XC5qmAYPdH1mEJrsq9du0aRIiWR\niZ1jSNc3QX2n0kg32JfJ/ZC4uOIh51+8eJHU1AzVvyIcX22qEGew22Uscf78+f6x//vf/1axrBxk\nrW9oOwWLJYapU59i06ZNjBw5hqVLl95TrfiLL76s6O+LK8X3NkJcw2YL4+zZs4Wes3z5cpXc2ooQ\nezGMegwfPk7hHU8qpZSNEH0ZN248Y8Y8ofqC+Mbdn0BzqNYE4DYgxA4qVJCUWu+88w4uVzBP5a9Y\nLA4OHz5MWlomFosDXQ/jtdc23PXz3kn+n1d+ACtXrqJUqSzS06uxatWLd3XOokXPkpBQiri4Ekyf\nPsNvdeXl5WGzGQQqFvJxuWqE0GgtXLgIu70Osl6zsVpIOppm45lnCmL/Dhw4gMuVTihldwUk2UIi\nMh7jRYhP0fUo6tZthq63R4jtWK2PU7x4Bjk5OXzzzTfKjbuCLBHMQAidWrWa3HLy//TTT+h6NAEm\n7A9wu2M4cuSIirv8pHb6h5C1qqeVgrAhrbRJakJXQGblnsFicTJ79nzmzFmIrsdgNldRCs9XrtQb\n6Yp/hRDrMYwoevbsid0eDJ14EyE8WCx1sNmGYBhxbNiwMWTsL7/8CpUq3UfVqo1CYpjbtm3D5apK\noD74C9zumEKf//vvv6dGjcbY7VFYrTFYLOEqFpaFtMayEOJhTCYX77zzTsi5c+fOxW5/SD13VtDY\nwe0uG1JLDDKs4HLVUu/0fiSQ3osQ57FYSjNs2DBGjZqgmF2eRtebUrt2Uz84/9KlS2zfvp0dO3Zw\n5coV/vjjD7p27YPd7sLlimbWrHmcPHmSokVLYbU+ihCb0fVWtGrV6VbTHJBeTEZGLVJSyjNmzCSu\nX79OhQrVMJsrqm9+CMMoxnvvvYfX6yU2NoUA4cA0JEzmGnJjfJRAb5Q+NGvWDpAbfMWKtXE47keI\neTidmYwYMc4/hsuXL99VKei9yP+v/P6ErF37ClZrMWRlwAEslrJ+JpFr164p5ugAmv5mjr/c3Fwa\nNWqD05mKppVBCCcWi4tWrToVupMfOXJEsdr4Yk9/IK2sw0iXZFLQvRpjsXgIZtFwu6vz/vvvs2fP\nHjyeSndchMHy7rvvEhbWKOQcp7MYb7/9Ni5XSfW7TUhLdDDS2uunnv8M0k3coBTtW8j4XWkcjhRs\nNl9iB6XonEqRlsBkchMdnUrFirLRzuTJUzCZnggax0K1qHwbwuchdFy3EwmhCAbg3sBk0u7adfr6\n669Vc+8lCDEBmy2RMWMmFDhu7NgJSCt9tVLuz6j38gqRkUVC4tYnTpwgLa08MhEShSzSl13UrFYn\njz8+mkuXLmG1GgRYfSRd1q5du/j5558pUqQkbndD3O76pKSUoXfvQeh6S3X8txhGKVasWMGcOXOo\nV68ptWu3YNKk6fdkPf7yyy+UKJGJyVQW6fZLmrlRowKKykc15XKlqRCPoZ4/BmkBV0DCYtxs3bqV\nChVqExGRRMOGbZg4cRL9+z/OunXr/iswrtvJ31L55efnM2PGXKpWbUTz5h39qPL/LcnMrENoE+W3\niI8vzalTp9i+fTsZGTWwWgchM6JbcDqjC1Ql5Ofn07Xro9hs9ZHB4mvoestCe0t4vV7FilwPSbRQ\nGwkQ3YiEK0zDF3cyjKKKN86XvfXidlfjgw8+8BNEmExLEeIXzOYFJCSUuC2oNtCL14dr/BJdD+e3\n334jKakUZvNsZMbuiaBJ/m3Qu5lJgEPPrhRkKkI8hqalI63WachqkVSE+AiHI41XXnklZByffPKJ\nslo/UwolCglo9d1HEsvejRw8eFA9036EyEPTJlOxYh2OHDnCpk2bQliabyVffPEFLVp0olatFowc\nOZq2bbvQps3DIfHH999/X4HpayhFEYEQDmJjU0Ia7OzcuROLxYV0p8ORwOPaxMQk88knn/hrWWXT\n+AgCriEIUZPhw0fQpUtv1ZZB/t5qHYrLlYhsWOQ7diJWaxi63h1df5ioqKS7qhM/deoU48dPpFev\nAbjdkcjYtG9+nUQInXLlqoWcc+3aNbKzs1WnOSeS1r4p0p23IoSNmTNnBlVQ/YDVOoqMjOp/udLz\nyd9S+Y0cOR7DqI4Q72AyLcTtjrnrsq//hiQnl0N2CvNNqmXY7XE4nbLI2jBSSEhIx+OJJy2tEp98\n8kmh16lWrQky7uK7zmYaNJBuwLFjxyhfvgaaZuB2J7JixQpWrFhBmzYdVeyrLEI0wGRyYrdH4nJ1\nweksSa9eg2nWrAO63hYhtmG1DiE1tbwfCJydnU1mZh1crmiqVKnvD5p7vd5bMnPMnr1AZRjrYRhR\nbNy42T/GrKwGuN0xFC9eFoejuJrkL+Bz+SWZQxgyQZODdOU6YjL5eATnIN3cFITQsduj6dfv8UIX\nwEsvrVUlURWRVlck0qWUWLkGDVrf8dv985//pFWrDmiajnTLzXg8RWjSpBl2exQeT3sMI5mhQ8eG\nnJeXl+eP2/7444+MHj2ewYOHsWTJEnQ9Bkl9thJdDzT5fvvtt7HbMwi4198hhI7DEe2vob58+fJN\nwOX9SrHPpXjxzJAxeL1eypevgYx5HlNKIxaHI5ry5esgLWvfXNqC252CTELJ30lrbbb/Z017gp49\nB9z2fZ06dYrIyCJo2uPIdgZuQoHJXoSIQdcjbnmNSZOmKKVeRr3zMCwWnS1btuDxNA25lsMRdVto\n1IULF+jVazBVqjSkV6/BvPbaa2Rk1KJ48YpMnfr0PbnGf0vl53bHItmF5Uuz2QYwd+7c/60h0a1b\nL2TCYCiyTCgcTQsjQNGTg8tVvkAviZvlkUf6qu5l8sPbbAPo338oU6Y8pXZHFzJb+gJCGGzevJlF\nixbhcLQM2v1XkZ5elZdeeomPP/4Yr9fLtWvXGDduMnXqtKJPnyF3xCEuXbpc4ck03O4knnpqRgHl\nc+zYMT788ENOnDjB2rVrmTRpMps2bfIf98wzz6Bpo5Exu3BkwqO0Unyt1aIJR5ZZNcVkchJavdKS\n2Nhknn322duO1TAiCFihWxAiAk2z07Bh2zs+59tvv43DEYO0wN5WC/eg+pYOAu0zL2AYRdm3bx9e\nr5dhw8ZisdjRNBvNm9+PxxOH2TwcIWZgMt3cc2IRlSrV4ezZs7z88su4XA8F/S0faf0+S4sWMs52\n6NAhnM5SQceAz7J3OmM4fvx4CFpANiTy1erWQYgDOJ1dadmyPbreGhlbu4quN6Vv30E4ndHY7X0x\njAewWmMJMMqAEK/StGnHAu/pwoULfP3111y+fJmpU6djsQwKOscX4tiGj5pNiKSQ1po3y/bt2zGM\nGkp5voQQuRhGAhs2bMDlCt4cfsVqNfztJ26WGzduUL58DWy2vgixE6u1NSZTGJL4YQ+GUe2eCFz/\nlspPNjEJULnb7b1YsGDB/9aQ+OWXX4iKKoLFUg6zubJakKagjwi63o+lSwvHYPnkzJkzpKSUwe2u\nictVhRIlyrNhwwZFSPAzvibkPhxe6dKVGDZsFKHF7EeIji72p59l165dOBxF1Pv8AyF6YTYnMnny\nkwWO9bnfTmcNhJiE01mB/v2HcvToUZYtW6ZwV2uQ8ZyXlIIZo5ReC2Ss53FkdtiOjAn6nmMAQnTH\nak2gffv7+frrr/F6vcydu5ASJSqRnl6N9etfVZ3kfvCf53B0v6PC9Enlyg2Q8JGb65JrKiUdHAtt\nydatW1m+/HnV3P0sMlHUhFAKqgbImB5IazQMTSuHYUSpHsPRSDagy8jQQE2EWEvjxpK+6cKFC5hM\nOoGE0o9KuSRjMhkYRgIuVxTvvvsuv/76K7t371Y8dj53dj82WzxjxoyhVatOWK0GFotOx47dyM3N\n5dixYyxevJjnn3+e8eMnK3zhaYQ4jmFUZunS5SHv6OWXX8HhCMftls2vOnbsTCiu9Gtk7C4VuUGH\nExdXrFCspU92796t6o0nqXdUAbM5ipdffpm6dZtjGE0Q4kmcznKMGjWBd999l+HDRzNr1uwQRfjV\nV1+pOLMvzjvsprXwBcnJGXc1F+BvqvymT39GlZetw2yeQnh4AqdOnfL//fz58zz33HPMnz+/UI7A\n/4acP3+e5cuXs3jxYn744QfS06tgMi3yT2DDSAppOn4rOXXqFGXLZqFpOhaLg1q16mEyTQj6oL8g\nAaNlSUvLZPPmzTidZZXiyMNqHUzr1p3/9HN0794dIYLvdwIhYoiOTilw7IEDB3A6UwgAwrMRwo2u\nJ2G3h5OcXAaLJUpZA77rHUO6cSWQ9aPRyAqOdsgY0AFkQiRaXW87QpTCMKIZMWKU+s6fINtCJtG5\ncxfFjfgqZvNkIiIS/ZUVd5KyZWsi63kjgpTHz0jLL5EAbdN+rNZwvv/+ezp06Bak3EBmyYMttUVK\nuc9DuuG+LP9nOJ2R7Nixg/DwIsjqg0oI8TyGUYTt27dz7tw5zp07p4C84Uh33o0MB+hI+BUI8U8c\nDo8q+6uBzRaBxRKOrtdGCBea1h2Xqz6VKtXh119/vaXllJeXx4ABw7DbXeh6GKNGTWDLli0sXbqU\nffv2BWEBfYr4H+h6pHLrdyBd8trq+csQGSljl7dLmBw4cAC3O1Zll9sqxb4OId7CMIqyefNmli1b\nxujR45Rn86yCKD2N3d6ZtLRMP8uPtJKLI8lI+quxDAv6Fu+Qnp51V3MB/qbKT7bZW0WzZh155JG+\nIXTwp0+fJj6+OLr+EDbbwEIZjP8KOXLkCEWLpqPrcdhsThYsuHON8Mcff0xycjkFGfgaIc5gsxVR\nMBifFfkaQsRgNsewaNGzeL1exo2bjMXiwGp1UbVq/QLu3pkzZ5g6dTrDho26LT9fbm4udrtLKSHf\nbroDIUoTG5ta4Pjdu3cTFhZs9bRDApm9CHERp7MqrVu3RiZhfNnmJQhRCoslHlkP7OusdQ0Z6wtD\n4vt87NzbkFi+F3A6kwhl+13OAw/0YOnS5TRp8gDduvXzx3pzc3M5depUCJ7S6/WyYMESatVqQbt2\nXRg7doJSpk8HKRsPAZKDFKXAdAYOlD1yhw4djaYFU/fPU+e+rRRoNYRogdUaiabVDjpOtvf0zc3X\nX3+d6tWbUqNGM1atWkW5ctWw2TxYrbpq3RiHrDT6nkC3PN+18tQYP/YrbIcjAZcrFmlVyrCJYTTh\nhRdeuOO8A5lwa9asAy5XVXS9H4YRz6hRYwgLuy/kGVyuEqxYsYKwsBRkQmYiMju+hCZNOtzxPg0a\ntCW0DezwIIX1Ei1aBBhz8vLyFFLBB3uagGE095OGyDacpZA4xSUI8SBCGJjNoxBiLoaRwOuvv35X\nzw9/U+V3Oxk1arxiksD/gqtXb/yn7r1t2zbatevKI4/0vSNhKsgJdfLkyduW3h07doyJEyfTseOD\nqs3efKQ7EKkW00wSE9NxucpjszVGCIOwsDhmzZoXEoe7du1aoSVoZ8+eJTa2GFZrfyQWLOGWwNBT\np06pGFgVJA7tESQ3W2JIEyCfXLx4kaioJEymFUg2nFhCufBm8thjwylVqhIS61cJIcKxWp307TsQ\nq1VHshf7jj+EyxWtcITLkBn0BCTMozu6XgRpJfiOn06xYhkFaKwkzVMUuh6LxxPrp9V/4ompGEZl\npVCH43B46NGjl8J0VmXq1KnMmzcftzsBac2sRtP6Exub4mdZ+fXXX4mMLIqsr+5AoMg+Qp3zOA5H\ndTIyKmE2e4Lex8e4XNGFZtLr1GmOpk1AbhonsdtTkLWpV9W5Z5BxvWMEkiDGTYq1jcKTBppZWSyj\n/PRxdxIJVcok0Mj8MHa7S9H0/+i/r83m5siRIxw/fpyoqCQcjkew2/vidsfcsr90sJQrVztIaYO0\norup/19Mhw6P+I99+ulZyA3pFBICVQWLpY4/fCSpsMIIjvc7HI1o1qwV/fo9ds/tFP7PKb/u3fsT\naJwMQnxOamqle77vmjUvYxgpCLEKk2kGLpdsSXnx4sU/3bDnP//5D253LGbzCCTe7XX1kTPVYrKj\naeWZNWs2u3bt4vXXX78rl86X4frtt98YM2YMNtujQc//MUlJZQAZqzx06JB/Qebm5qpM4/tIsGoW\nJlM4zzxTeKtRkOSRFSrUxuWKwelMDGJHzsUwGtGz56NqgjqQGL8ROBwpzJo1j7NnzxITk4ymDUeI\nZVitKZQvX50ePXpRsWIdRT4QjcxIdsPpjMLhiEbi4yYgRCSaVofSpSuSl5fHlStX+OabbxTmzmc5\nvo/bHcPFixdVbPg7JCYwASHaYzbHEhdXkpYtH/T3KvF6vTz//Au0a9eVgQOHFSDNPH78OC6Xr+l2\nMkI4SE0tS1JSGWJiimMYMfhYYIRwoGmpuFzRrFmzhkOHDhWoZ5Yx4kAFi9k8lvj4NMzmccikyDd+\nogWPp4Wf/SeQzf0BIcIoX7666kB4DSEOousJfPrpp3c1F9esWYPL1SVonnjRNDuzZ8/H4YhC0yoi\nhBObLQO73U3v3r3ZsWMHS5YsYeHChXeNrhg/fgqG0RAZvjmKtNoeRtbkRvsbVQFUr94UCV73jWkj\nZnOUP3Tl9XpVn+zf/cfo+qMsW7bsVre/rfyfU35btmxRCYP/IMQv6HpThg4dwz//+U+2bt0aEhu8\nnaSlVSYQcwGTaTyRkYlYLAY2m1EgUHwryc7OZv369Xz66ad06dIHWevoawf4EdLFm66sgJ8xmRLZ\nsmXLHa979uxZBgwYgGFEYTJpxMamYrW6sVjCkO6lbwJ9itsdQ7duvbDZwnC704mOTubgwYNMnfo0\nLpcEqVossVitYTRt2prOnXuxaNGS2zalAVn4Hx2djMdTC6czjerVGyhrdgmy9tYH9D6OxeLgxo0b\nnDp1ikce6YnZHI60dqLQtMq4XIkqA3wgaGJ3pFOnTlitKcjKgFhkgqEoRYqko2nS9TebywY9L3g8\nGXz55ZeEhycicYFhyKoJkJZSNELIEq3ghkWFidfr5fz588THlyAAGzmBYSSxZ88eli5dqq7nY7fZ\ngBB2GjVqha7H43KlkZaWGbKJyZ7AW9TxN3A667Fw4UIyM2ujaTbsdhcvvLCab7/9ljfeeIPs7Gxc\nriik1VlGPU9Txo4dR/36LTGbLbhcUaxevcY/5s8++4wtW7bcskPgd999p5IxnyDEdTRtqh+r99RT\nT2G3V0XGX6ORHsF9mEwe6tdvcU80Zbm5uaq3sgMZLmiK2RxGixYdCpQktmvXBZPJRwYLQkykSZO2\nIcd07twTXW+D9JJW4XLF+DG069atJyKiCFarQfPmD/jxkbeS/3PKD2Du3IWEhcWj6+H07DmA1q0f\nxOlMx+NphcsVc1fNdooXv5kkcRoSWuBF9kUtwr/+9S+ys7OZNm06Tz31dAFCgKlTp6Fp4VgsrXA4\nilG0aFkk4LclEv7h4+87H3SfESQmFrvtBDt16pTqZeJB9ofw1dX+gowXRSorYS1CuLBYfG0TOyjL\nYhXR0ckYRgWlfIsjRFnMZjc2WzOEWIFh1KdTp+53fE+XLl3i448/5osvvmDBggXY7YOQiYO2SBBy\nFYRoh9ls4/Lly+Tk5ODxxCPhITnqWEONT0daBz2Q8bdkOnTogMtVAdn60QcpyUVmXCshWZddyIzk\nMwjxNg6HLNSfMuUpHI5S6j0T9K8WMpjfneeee+6Wz3bhwgVq1GikqhTM/m8vxGys1qrMmTOH0aNH\nI4v1g69vw+GogXRj12E21yUrq67/up9++ikuVwx2e3NMphLY7TEsWLAYkAzRhWHV4uPTkLTzBxHi\nLHZ7d+bNmwcQcrzX66Vnz4E4nal4PG0xjOiQ0spg2bFjBxERiZjNGhUr1vEDnseNm6Dm+32Egvl7\nYrGksXDhvfWJLleuFtK78F1nAd279y90PHIuPIxsfu4sEMO8du0agwaNoHjxitSo0cSvQPfs2YNh\nxKv5fwGb7VFatSrIwB0sfyvl5/V6+fzzz9mxYwcnT55kypSnCAtLICwsnnHjJnP48GFWrlzJG2+8\n4bdaZHa0KgFE+g6KFCl1x/vOnbsQwyinFMsa9VF2+z+g3T6E4cOH43RGo2kjsVgG43bH8sYbb3D+\n/Hl2796NrG/1Zc4uomkJStHkq4X0JDK466uDvI4QNbHbUwsQdAbLkCEjMJtbqEkCEig8NGhybUJC\nLnwF6ajnz0JWhVxXirM3Mtnhi/s8jVTMIMQV7Pbwu86kzp27EF2PRO7wD6nnqoLM7kUjhJujR49y\n4MABNC3lJmVREWnVtEC6jo8oJbMJXY8kIyMLaTX8EHTOU8jyNqf69wASRuP0N/mRCY/FKojus7Q+\nUPf6FcN4iBUrCu9rArJ1qdX6sHpvBtJij0HSPHXF7Y7ltddeQ4YsfL2PdygLdiFCdEEmRMYgRDJj\nxgT6VM+cOQebLQmZDPgXhlGSl19+5ZZjWb36RWy2eISYicXSl7i44n7CimD56KOPFG7QR/j6OU5n\n5G2rJm5Wtm+88QZOZzoyEfVV0DufjxD30bv37Rt23SwVK9YnuDWAyfRUodfo1WsQkth0qXovq6lc\nucFd3UPiTEcFjfUMhnFr4DX8jZSf1+ulS5feOJ3F8XiaqybWGchSqiPYbBUwmVxYLA9jGJVo2LAN\neXl5qhP940Ev5e7KoLxeLw0btsBsjkNaa+nIkrJ8hMjF6axGuXI1CKUpn4TFkoCuR1CxYi21KAKL\n3GxuiMUS3PowT/UD0ZUSSkeIjrhc7diw4dbsFbKd41Akbu4PtbAzCdT+biIlpZyqA70YdL+hSEW5\nEV2PQ1pTwX2JDxOAceSj6/EhZXlnzpzhgw8+4PDhw1y6dIm9e/dy4sQJFWooiYSqnCHQJ6IcsnuZ\nFyEmkJlZm5MnT2I2u9TvUeOLQcJhziBd4a+RiY4P0fXuDB8+HKlMA4X+8tlfQ2ZJ+wY9wxbKlasZ\n8r4+//xzoqOLKhZoJ0I8gaZNIDq66C0JHQCKFCmDtDAnI0MUEQQYSsBszy3mjwAAIABJREFUfoJe\nvQYxZswTmM0uTKZUrNYw+vcfgN1eHYlnnI5U0vXRNIc/kVKrVgtkIsY37lf92L9gycvLY+HCRURH\nF8diScdiqYDF4mT9+vUhx2RnZ/PNN9/w4osvFojlWSyOO3YJDL6WrGCZoJR4SySY+ShClMRmK82y\nZXcX8vHJ1q1bVWniMoSYidMZXWiyRIaFFgeN/X0yMmrf1T1k0/WWan6cRYhZREUl3Vbp/22U31tv\nvYXTmUEgI1aPUB6+7Ui3VMZRdL0KW7Zs4R//+IdKXBxHdrmfQcWKde543wsXLmCzuQhk03IRIgm7\nvT4uV3maNeugdrRgKMaLyN3+K0ymcGSQ/UX1t72YzW4F0n0FmbHqi8lUHJn90pGB/hfxeOJua3Gt\nW7delZIlIN2xMIRwY7MlERbWAI8njs8//5zKlethNs/Al1UUIg6nswxhYfFs2LABu91nnV1WxwxX\nSvTfCPEo5cpV81sFH374oaKTr6fidWGYzTFYrS4yM2sRmmTahrQAJwf97gROZzQA99//MNLNHaSU\nrQdJiPAyEg8XhYQxlEGIIsTFFUEq1Ej1rC6lCHPVsbOD7nOAuLiSrFy5kg0bNvirI7xeLxcuXODZ\nZ5fRvHknHn104B3rWmvVaoa03q8QcJeD3bc1NGnSgfz8fH7++Wf279/PpUuXyM3NJTExFQkNqYH0\nGNYhhJO33noL8JHoLvVfy2SaS8eOoWEGr9dL+/ZdsNnS1dz2VfXsIi5OQpEuXrxI5cp1cTpTMIyi\nZGbWVBtbtjp2BUlJ6SxYsIAxY8azc+fOWz6v5GssgWEkYrO5mDx5Ok2atMPXe1jTPHTq1P2OseDC\nZOfOnXTq1JNu3frdkkhj165dynV9HSHexzDKhHRbu53k5ORQtmyW2nQ8CJGF3Z5Chw5db1ny9rdR\nfkuXLkXX+wVNvB7IXdX38xxknMC3K/fwp8hnz56P1WrgcESRmlr+rjJVP/74o5pEwTRS1bBaIyhZ\nsjyXLl1S/WarIi2mfcgMrmywpOupWK1RagHIov7hw0fwxRdfUK5cDcVoUpmABTQfqzWaChVqs3//\n/kLHdPr0ab777jtu3LhBbGwJJObqOkLsxm6PYNu2bbz33nt+d+jHH3+kePEMHI4YrFadxMR0dD2C\ntLRK7N27l2PHjlGxYk1FWBmNtHBbI0QlLJYSrF27FpCLMDw8HhlzmqAW4n5kZi4Gs9mDxRLM9rsG\nXY8gFO+3kqJFy1K2bE1KlqxK8+YtSE0tS0ZGFosXL1Z4Rx+4d4865xoyMZSAtCJ3qf/WRFrcTZTy\nLqoU9nHs9sZYLGEYRg9crnpkZta6LXHD7SQ7O1vVUfs2uKeQccbv1TdPwWr1UKZM1QKb1bBhI5DW\najAp6xgmTJgISEXjdEZjMo3HZHoMw4jkwIEDIdf4/vvvVQLpaULBvBew2ZwACrTcQynGGzgcD9K8\neRvsdhd2eyQJCamUKFFeUUVNxzCKsWhRaEXMH3/8QevWDyKrbnRk2OIYhpHC7t27yc3NJTs7+64a\nlf9PZceOHVSu3ICMjNo8++yyeyI5yMnJITq6GAGj6BpOZ1U2btxY6PF/G+Une7EmEcAgTcRsdmKz\n9cVk6oN0Z/ojM4wHMJvDQ5gzcnJyOH369B1f5ldffUVychmEMKFp4ZjNTyCtplVqEZ7F4XiIMWMm\nkp+fz8SJ04iKSlYT3Ue59DW6HsGLL75I1aqNyMysy8svrw25jwwCbwia0NupWbN5oWPyNcS228Nw\nOlMoWrS0ajoUUMwu18MhtFk+yc/P58SJE5QsWVF1u/oFIdbh8cT52Xsli7IRZC1cwelM9VeoXL16\nVdF0eZWCD67JnYqmlSUsLAFd74TNNgCnM5p//OMflCpVCU1Lxm6vidMZrRby2wixG6czg8WLl4Y8\n41tvvYXJpBHKWtKdAEGqzwJPV5i6osjESDGEcGOxeBSTiS++50XXW4UkNQ4cOMDDD/emXbuuIbXX\nx44d44svvgjpGfz+++8TEVEUIWyYTMnoemmSk8soenk3MimQj8UylkaN2oW8908++QRppQaSZiZT\nf558MlB7evDgQcqWrYLZbGCzRVCzZuOQRlirVq3CZPIx2SQga49zsVgeo379VgBkZTUmtF5XkmNc\nv36dM2fOqBadjYPmyrfoejhHjx71w3DGjZscVBecg3R1p2G3DwohnvV6vWzevJnhw0ezZMkSv1Wd\nnZ3N/PnzWbFixX+le9//RCSDTAAKY7GMYNaswvtj/22UH8D8+Yux2ZzoehxJSaXYvXs3c+fOpUuX\nrtjtRdSubEEIB927P3rP98rJySEqKgnpfuUhxAtoWoSKUZUnEPxdF4JMP336NBUr1kEmGRKw28NY\nu3bdLe9z6NAhRTtVTlkG32IylWH+/MUFjv3tt9+YMGECDkcxfLWwZvOTmEz2IGWVi91eju7duxcg\n1ATJFSerCEYgLaY8PJ5m7Nixw3/M8uUrMYx4nM7uOJ2l6d69f8hGkZBQAumuZxLq+sk2lu+88w7L\nli1jwYIFfqaY/Px89uzZw86dO2nXrguhSP/3KV8+EH44e/Ys6emVVbhgllqsh5EuTDoyJuo7t7Z6\n/ifVN/kUIV6gadOOCrc4CMl8sguTaSKTJ08Bgnn4ZiPECxhGEuvWradfv8dxOGLweDKJiirKoUOH\nOHr0qIKCvIsQF9C0kaSlZbJ//36V/Q1m9fme8PAivP7666xevZpjx44B0K/fQCQ85zmEGE14eAIn\nTpzgm2++YcuWLYwaNUbRlF1GiBvY7T3p0WOAf6yy1CwNWUXzJNKDMFO9eiO/dd+79xBstn7qfeVj\ntz/C8OEBRhrJXRiM+8xBCA2HIxaXqyTFi2dQpUpDAs2dQCbJmuNyVQhpDjV27CRFpPoMut6CGjUa\n8cEHH2AY0dhsg7Db2xIVVZQ9e/aQm5vL8OHjSE7OICOjFh9++OEt18N/UypVqovZPEs9xy84nSUK\nbXMAfzPlB7J94okTJwrEHfr1G4jDEY/DEcvQoSP/FCfYwYMHcbtLB00CCAurTsuW92O390ZaJNfR\n9bZMnix5927cuEGpUpWwWkcjxEHM5ieJjy9xyyoPr9dLnz590LTOyKLsJGT8y1bAPfvuu++IiiqK\nzVZXKco6yJjnz9hsHgwjAYejP5pWHpMpHiFG4XCkMmnSkyH369jxEaW8ZyJjpZ0wjFIFEPFffvkl\nq1at4oMPPvC/v61bt9KoUQeysuojM56xyqLxNWDSiYoqxogR40PYR7xeL7/88ovf2n700YGYTMEK\nYwPVqgUqb9q0eQhNa42MHRZHxtqcSHhLP0ymGGTWfSCSLWYT0vr6CCE2oOspLF36nMrsjkCGQSIQ\nwuUnvRg0aBgm07SgMbxLZGRxDKMsMvFyGEkVZiMsLBGHI7jUKx9Ns1OvXitkZrkMMjh/DCGWoOtx\nuFw1cTq7YLF4KF26Ct269WP16tWkp1dB12Ujn4EDB2MYsbjdbZAxzHBkeODfCPEppUrJ2tTZs2dj\ntT6OxA92RojSmExhBUI2Fy5coFy5arhcpbFYkjGbPTgccURGFqNWrWZs3boVuz0cGUf7HoulK2Zz\nEaUEvWjaRBISSmGxjAx61sFoWjRduvT2z4OcnBwsFp0AODsPl6siycmlCVjaIEQXLBYnTZq0Rtcb\nIcMjWzCM6AJu/V8h33//PSkpZfxxy9uxvPztlF9hsmbNy9jt8WrHH4XTGe1H79+L/PLLL2qi+ACr\nF9D1WPbu3UulSnVwOpPR9QQaNWoTYvI7ncUIdkE9nip8+OGHHD9+vEA1SM+eAxRotySBeNhezGY9\nJDCbn59P5cp1kLWwl5XibY+kUVpJRkZN9u7dy9ChQzGZopFW4VMI0QuTyeoHeH7//feKuNMXtL+G\nzK4a2GxO1qwp6Cr7ZMOGjRhGUWSwfgVCODGZOiGxeW2UgnoEIT5A19vQrt3DgFwojRu3w26PwG4P\np0WLBxQjRwwm0ySEmI1hxPLee+8B0nKWlGCNkHCXSGTiyAeS/gMhNMVHNwoZJ72BDE14MJkisFgM\nmjZthaYFQ352IkQ6uh7F7t276dNnMNKq9P39Y2Q3tkRkcsaDbOV5EQmJcRFgDzqCzeakdOlqSjnX\nQSYz7AihYbM1IuCub0eINKzWYXg8iTgcdZGtIrep479Tx51BbiZzESIWs3kULVtKqqvnnnsOXQ8u\nBdxPVFTRQr9Tbm4ubdp0wmqtg0zK9EaIg5hMizGbXdjtlTCZiiCEi8TEdEKJJ74mMrIIMTEpuFx1\ncblqExsrKenz8vI4ffo0ubm5ipTUQ3BIwuNpqdqw/ifoejPVnHAQ3IPEbB7N9OkFmYL+jHi9XmU5\njy20j4kvY/3/BMjZ4/F1jG+vFnYHhg8f/afuN3nyUzidxdD1PjidJXnsMXmd/Px8vv32W44ePRpi\nVf7000+qBMuXhc7FZovDanVhtcZgs0XQo0dvLly4wPHjx1Xfi1RkBUR55K7uwmLx+APKN27coGnT\n9mphVlGL7ShCLMFiSSAysoifvXrChAlqEVZWCmMhQqRSu/Z9/Pzzzxw6dEg1aCLoXzoS2X8YiyVS\nhRLCGD36iZBnkxRQbwSdN5+oqOLoehhxcSUwjFpBf8tB0+xcvXqVkSPHo+v3I5X7H+h6G8aPn0J2\ndjZDhoygb98hIWVYvXsPxmQKhiN1UM/jW2hfYRiRShFLLj+T6TnVWMfHuHJUMcoMCbrOPnwlZxZL\nBLGxyepbrUWCwEsjXdKGBPqOBBa32Xw/NlspLJYRGEYSs2bNweEIRxK0RiNxltWUQhsbdN+f1d+9\nSAvRigzH+BAAwd+iPjKM0JSwsFj/HPj9998pWjQdm60HQjyDYRRl5cpV/nf25Zdf0qfPYB54oAsb\nNmxQzDH7kAo876br+yA1a0hOLqXKzf5Q46uB2RyPx3MfDoeHOXPmcOXKFb788ktiY1NwOKLQ9TBe\nfXUDlSrVUdboUYRYTVhYPC1bPoCm+ajyD/5/5J13dFTV+vf3mT5nWnolIY2EHiBIB+m9916lI1JE\nBUEQEWkKgl5ARBRQQBFBBUEUbFfFdr12REDaVZQuJYFkPu8fe58pJAG8v3vfd/l791pZLJIzM2f2\n2fvZT/k+3y8yB7sdCVl6N3AfNtvgW+bcPH/+/A3z8zL8rogQc9D1VtSr1+L/H/W2v//977Ro0ZW6\ndVszffoDyuAZSc5/IoTOmDF3/duf+d577/G3v/0tQP2+detWXn75ZY4cOcL7778f4JoDeQr16DFQ\n8aQ9jt1eH5PJR9BjWI8Qssr82WefoeupyDxOETJRvQYhKmG1egIVw0mTJmG1NiLoGS5AJvyrU736\nbWEn2vz585EVuroEvc9fEcKKz5fAvn37VMVyFrLpfh4yXDS6SrohwavH0PW8sCJE9eqNkV6MsZEW\n06fPMECylHg8oYy+5zGb7Vy5coU6dVoR3qO5hUaNOpQ6382adSEctrQNmT+tj8VyJ05nAmvXrmf+\n/Mew2dy4XCnEx6cXK/o4nb2Vluw2hNiHBCdHYhAEaNpSkpOzsNni1XytUq/vghCDkZ6eQcFfiNtd\nk4kTJzJ//nzef/99unTpjzTKGQSB6X7kIRarjMI1JO6wtfpbDpKCqRDJWaiHzOnHSKjOLISIJCIi\nhSVLlgXW1pkzZ3j44blMmHB3wEsGSaEv84E5yAMyGoslChl+OkOebZG6t10Yh0hycgUlKp+K05mO\npmUSjApeIzExi8LCQiVC9HzgdU5nDJ9++ilt2/YgOjqV3NwGrFy5EqczGpOpHPLgiEWI5ZhM80lI\nyFKH1SIslrHExZW9IabS2EsjR96F1erCbo+kZs3bi5FYXLx4UYXfBhdkIW53Lm+99datbO2w8Zcz\nfl988YVKRK9CiFew27OUGHXoaeoKWyz/7jh16hTp6ZXweBrjcrVA09x4PNXQ9TL07j0kEKZ+8cUX\ndO7chbp1m9CrV2/c7u7X3Y8bt7sumzdvJjk56zrjcwkhYmjWTFbvnnhiuerMCMWu/aBeUytMKAZk\n8UR6Hq1Dri9ACDuaNpXWrTvj8dRAMqWkIb2Wskgg8WW1gQwox4s0axakKdqwYaMy1i8gxCp0PZYP\nP/wQkPTrqanlsVrHIRXWGgYo0QcNGoXVaijK+bFYRtK+fbewnGDomDt3AbreGAmmvYTD0YopU+7n\nueeeY9GiRWGUZOfOnePQoUOcPXtWyV2+r+79Ai5XFvPnzycxsTyaFqU2/oCQeSlE00wMGjQKh6OH\nmvufCZJzLkPmX+9E02rQqFGbsNxyVlYeQSr3n0Petz6yFcyF9PIqIkRtzOahyIjE6C46gfT+dBXm\nO5AA6Axkzm8fTmc2a9Y8d8N12bXrACTMx0gNFKJp3dS6qY/MDy/Bau2kmKZ/RIiLOBzdGTJkDH6/\nn2+++YbJkyfjcIRClPLRNDMHDx5UbD/BNez1dihGF5WWVoUg2cILCOHEZLKRk1ODQ4cOsXPnTkaO\nHM+0aTNuSE1vjGeeeUZBx84iRCE226hi2MfffvtNpabCw++tW7fe9P2vH3854zd27ERk5ct4MO8h\nT3ejEruWyMjk/4jM3bhxk7BaQ4WpZ6kFdwmnU1ZX77rrLpzOWKzWCTidXUlISFNkjGfVa/YhRCRu\nd1teeukljhw5QmJitjJEd2M2V6JatXpcvXqVoqIiVap/RG0KA3x8D0JUxuOJC1QSQ4fbLXN4EkH/\nJTLn0hEh1tOoUTul/Gbcz68I4cTlaofZnIoMmX9DiANo2nT69bsj7L03b36ZJk060apV92I90b//\n/jujR0+gdeseLFy4OGAofvvtN9LTK6uFnKOeTzlSUsqXSMN17do1BgwYgdlsx2y206PHwFIJMv1+\nP61bt1fdB1ZMJjdeb0t0PTVM+2P79u20b98ZiyUD6WH/hBB7AqppHTr0wmSyIT2WOch8cTJCZGG3\nu5k1a1axUKpLl/6YzZOQKYvBSC/PMJ5r1YbMR+IRYxW1WCg4eQtClCc6OpWpU6ciw+0owsXVNxId\nnUXLlt157rl1JU0BrVv3UPcQmpLYRtWqDbn//hn07t2bTp16kZVVSQkjudA0Mx079g4rxL3//vvq\ncDNa85agaT4cDp+qaBskE2fR9VQ+++yzsPsIavca9zCNqVOLq9jd6pDtbUtC3u+flClTsdjzz82t\nh9U6EYm3XIPPl1Ci6PrNxl/O+I0fP5nwzoE9mEyROBxe7PYo4uPT/2NVpTZtehLOJ/c2slr6DjIs\nG46mxRMqHGO396F+/WYKsCvhL0L0IDq6DKdOneKrr76ibdue5OTUoG3b9mzcuDGsoibxdEboFIUQ\nidjtMfTvP7RUVuq2bXtgsQxCnvhGLuozdL0Sq1evYezYybhc2Tidw9H1NMaNm8SGDRtYv349NluE\nMpwJCOEmJqYsmZnVeeGFDWGfcfDgQWbMmMm0adNvSS3v3LlzqvLaA1lk8SPEAFq37ljqa/Lz828K\nSO7Row+yQr4UKZEZSb16jYsBw48ePcqcOXMwm93IVjgvVqsvLCLYuHEjDsdtSI/vI6QMqYv9+/eT\nn5/Pnj17eOuttwIG4+TJk6SnV1ZGMhKZx7MiQ9dcdYhcQBZtxuNyRVOjRkM0rTKS+NWH3R7L6tVr\neOmllxSspzbh3TELkd7i85hMZXE6o2natGMYzdaWLa9gNkcjgf5FSKzhQEaPngjA3LkLVeqlNTIn\n+hgOR3yJdFdz5y5UnUxR6nP3I8TnWK0eHI4YvN6OOBxJJCVJo12vXssAU0yHDr2x2YYiI4hv0fUy\nf5pTL3Q88sh8HI7OgcNC0xbToEGbYtcdPnyY1NRKWCw+oqLSbomopKTxlzN+33zzjcLdPYpMXKeh\naS0ZN24iJ0+e/I94fF988QUtWnQhObkSVms5ZD7xUWROyKkWvwFQTiW0qqVps5gwYRJJSZmYTJUQ\nogVms4dXX32VgwcPKlT/YoR4Fbu9Kg0bNuXZZ58NeE01a96uYAenEWIdDkck+/fvB4LMxHXrtqZ9\n+94BgtVff/2VChVq4nQmYTK5sVq9+HyJPPTQvIBh3bFjB82bt6JSpVr06zeMt956i+eff1715Brw\nhQXIAsvb6HpyQIXshx9+wOOJw2yeiKZNRddj+Pjjj284hz/++KM6AELb/zaiaZG3JA15/Th79iyf\nfPKJMmY/hrxnZ6KiwvV6pQ5FlHpWBsj4Xzgc8QHD7ff7ad68AzL/eod6ph3Jysrl9OnT5OTUwOPJ\nw+OpQ9myFQJhW0FBAdu3b6dFiw7k5ORhsZRBentTMCq/ck1Ux+WKoaCggOeff57u3XswbNiIQG5K\nanfYCVL734uE6OhqnT2h/paOxTKV7OzqFBQUMHPmHCpVqkdGRlUsFh+aloLdnkHVqnU5d+4cn376\nKbqerAxyAhKwLPuMp027v8S5/cc//qGIY4MaND5fM5555hk2btyo8qsPI8RBTKb5JCVlcfnyZc6d\nO0fz5p0wm624XFGsWLEq7H0///xzhgwZzaBBo266XkAe/nl5jXC7q+H1NiM6ukxg7RvD7/dTr14L\nHI7eag8Np2LF2/4UzZYx/nLGDyA1tSIyh9UDmXheQa9eQwGZpzP0O0JlGU+dOnVTceZTp07RvXt/\nZVyfQIidmM1V1emeiMSB/YbklDNEr0eoU/0nhBiF2RxF2bIZyCqukYx/ijp1WtC4cTNk0tvYuN8j\nRAwuVwNat+5KUVERJ0+epFGjtjgcXsqUyQkDh06f/qBiJt6Gpj2GxxMbOIULCws5dOhQie6/3Ogd\ncTi6IMGsIxDCi8lkUypkxv2cVRsPhFjKgAEjABgwYASaFppqWEXjxh346aefePnll4uFQyCT9XIe\neyC7Mi4jiSHKBVq8bnXs3r0btztGCa5bCacAG0JGRjA0On36tKrI7kGSHoTmrdrxyiuvAPDCCy8g\nPUhDj+QQmmbjhx9+YNy4yUohTD4/q/Vu+vYdFphLY6O99dZbeL0NQz7jGtIjXIIQu7HZKrBgwWMl\nfqeioiJ0PUIZuO+U8YxGhs9GKP06stLvR9eTGDx4JA5HTSRMyocQVgYNGsZnn33G3r17KV++Jh5P\nPGZzNhJCY2jKyKJO27YlS3v+8ccfSr3PaMU7idMZz3fffac0OCpcN49Vww6wkhyOffv2qdz8PCTF\nfCzvvvvuTZ/11atX2bNnD9u3b+fMmTMsWrSE2Ng0oqJSmDp1ptKRTgox1H48nkq3ZFyvH39J4zdl\nynR0vRkygfwtup7Npk0v8uuvvxIfL/U77Hap37Ft2zaysnKVXoLOsmUl87dduXKFrKxcTKbayHaq\nYLFBtlKF5iI+V6fqaYTYh8kUpSqq3ZTRvL4j4Qvi48thtUYhQbrG779GegkFuN05YWFJQUEBq1ev\n5uGHHw7ocERGJhMqCG61ji21dSd0/Otf/1IQGwk9kf27sWqDlCfIBvM8MnwDTZtM9+59OHLkCB07\n9iVU/1WInaSlVcPpjFGccSnFdG4B2rTpgEG6IL2wLISIYc6ch2/18YewTe9Vn90dmSv7DKkQ56BL\nl56MGnUXH3/8sQKqV1AGN55g69cBnM7YgCdRoUKN654RWCw+Tp48SfPmXQlvPdxFXl5TFi1agt3u\nxmSy0qRJe37++Wf1TFYhxHE07QFk6GhATT4kI6Naqd9t8+aXcTpjsNnaIA/XUQQPzNuRhZC5CHEG\nm82rJFvrIHF6foQ4gtWaxNq1a1XHUBQyLeNWhvQfId9hWcCAlzTWrl2Prscq3elEHnhAgoMPHjyo\netwNKNdldD35pjjazp37Ec7Q8iAREWmUK1eTsWMn31K/tbwng1brB3T9NqZMmVbM+LndFf8tnZ6/\npPG7evUqw4fLZnCfLyFwuk6efB8Wy50hE/4sup6AyWQsloPoenKJqmrvvPMOHk8ewc6FYNJVbtxh\nIb9bj8eTgt3uxudLYNSoMXg89UMW7imkh3JQGZYO1K7dGLu9vzI4DyMJECphgG59vuYBDr9r166R\nl9cQk6keQkzGZIpjxoxZREaWIRRQarWOYsGCBTedQwnejlTGb64yflfVJq2MyRSPy1UPGXKNQtP6\nIISO252LwxFFly69FFbwI4T4B7peDbNZRwp1D0WIAdjtscU8wIcemoNskl+IhGH8jKa5bpkjEOD4\n8eOqYBOsSFqt2UREpJKaWh6nMwpNm44Qj2C1RtKxYxdVDXxP/cQgRBJ2u4+VK4PEmAkJ5ZSx2K3m\nYgFudwJ+v5+ZM+fgdLZFeoVXsds7EBeXjqYlIZPsBdhsQ+nSpR9ff/01VarUw+uNV4WsUJzhm+Tk\n1Lrh9ztw4ADr1q1TcpSGgd+PxH5mICUdqzF69ET1/O0EoSlgNo+hSZMmyEPmKMFD1Y3M/V5DiNPo\neg3WrHn2hvdy8OBBtm3bFpbT9fv99O49BKezFkLMxWLJISYmi2bNuoS1R14/WrXqTpAI9YQyxjK3\n6nB0pFu3ATd99u3a9SacTHUX1as3oX79ljgcvRBiK3b7MCpVqvX/T9hb2ujXbzihNEFys5oIQg0o\n1qxtjKDxO4L06maqiS+rDFkm0usYhRAeJk+eHHjtiy++iMfTMeRzr6pF6kAIK253Elu3bsXlKo/s\nFa2iFkMVpEc1FLc7OtCv+corr6BpVQhWCX9CCCtTp85A16sgxIto2ly83vhbYtrw+/20bNkZs7kN\nsosiVIrxAxITs3n77bd58803mThxigpXDBLU39D1skyePIXk5PIkJJRj0qR7FTdeNDK570QINwkJ\nWWGGTcKSjPDtEzQtHbs9mkqV6tySrCeU5PkdweGIo0OHnpjNLnUPqwh6rpWx2zOwWDy4XOmYzR4S\nEyvQoUOvAGX9q6++SlpaeTStAjL0NaNpMUyZMoXx4yczdOho6tVrgt0egc0Wid0ejabVQxIZGPN2\niKioFJ57bh1Nm3amU6e+bN26VXWxzEaI5eh6GTZs2HhL3zMY2lfM4KH+AAAgAElEQVTC4Yhg5cpV\nrFixgsmT72HDhg34/X4WLlysRLoNDGUBul6TNm3aIDGNhPzEkZNTA4vFhcXiYNy4f6/lEyTTis3m\nQUYJXiQ2dT1OZ1JY72/o2Lp1K05nCrIYOAaJPjDu7Q/MZttNqbEGDhyJyRSqGbycZs06c+nSJSZO\nvI/69dsyatSEm3ZylDb+Vxm/zZs3qwR+UL9DKoPtDiwWlyuvRI2M/Px8ypWrhs02BiFWYDJlK++u\nPDKP8zHS03kMh6N+GIPKb7/9ptp8HkeGxL2RYju56Ho0H374IX6/n6FDR6sTeQISFyXBsZrWG4cj\nlueeW8fp06dp166dWmifqPsuRAgLO3fuZMWKVTRt2pmePQcXSwbfaFy5coWcnCrqu7RQBtqPEGPo\n3LkvII3klStXMJkshIKHXa5BYXTiXbv2UwfEVCQNliQs1bRJNG/eOexzd+7cSVZWdSyWSDStK7JY\nsSFMewFk3qi0YlVozs/hiKRu3WaKheQXZGiXqg6VN9WcTkUInwL+dkSIt9G0qSQlZTFwoKEF8jAS\n3OzGbHbSs+dA3O4YpZm8EF2P5/nnn+eVV17B681Tz7ZTyLy8RHx8FrqejQyRl6DrUaxfv56hQ0fT\ns+eQEtm4f/nlFzp16ktWVh7dug0IA/6eP3+eL7/8spgUqTGOHz9Os2bN0DQXFkszdD2HDh168c9/\n/hOJMTTgXm9jMrkYP34S3377LZcvX77ldVLSyMjIVfPbh3Dy3o00aNC21Nd1794LTUtRa64BQnRF\nhvc1MJvtNzXGP/30Ez5fAlbrKMzmCbhcMcV0P/4n43+V8QNYuHAxHk8sdrubvLwGJCdno2luHI72\n6Hp52rXrEbbJrl27xjfffMOPP/7IqVOnGDp0LOnp1cnJqcE990wlISEdTWunPIQHMZk6kZ1dPQwv\nVVRUxJYtWxSgtDKyoPAzVmsEH3zwQeA6Gd60D1k8vyO9wyIM6cDExEys1n7I6l80sqI9Bk2L5L33\n3mP8+CnUrt2SIUPGlLpJShubN29WRquJ+j4ZCOFm7969jBkzEZvNhdnsJFhxHIns/CgbyEeeOHFC\n5Q/zEKIf4ZhL6Q2FjitXrtC0aXtk3i8emWe7iMvVlzVr1lBYWMjw4XdisTgwm+3Ur9+EgQNHMn/+\nwjBQtFHtPXHihOpP/Trkc+cjC0wVkKFsCySY20WQoh/s9jpqvg02HD9CNOLxxx9XpAczQt5zC9Wq\nNeKTTz7B7c5BQljqYEhY6noM8fEZyGpyEbIH24HZ7KFu3eYleiP5+flkZFTBYrkHIT7Gap1ATk6N\nQMj222+/MXDgSGrXbsmECfdy+fJl/H4/f/zxBwcPHiQiIhGbbQQm0zDsdg+rVq0KGJBVq57GYnFj\nMiUiPfExCHEXPl/CTUWabjakdOcI9fxWhszRBho0aFfq67p1G4QQTyND8ig1R0cQ4gXMZvctiYkd\nPXqUefPmMWfOw2GH/ZEjR5g2bQYTJ07h448/5vLlyxw8ePBPcTf+rzN+jz/+JA5HJDZbJhLAOhrp\npruwWFzExaUFchqnTp2iUqVauFwZOJ1JNG/eUbWqSbEch6M75cvXoFmzDpQtW4Fy5Spy9913h1GC\nv/LKVnQ9ErPZiaZlhSwM8HqrhOHP1qxZg653C7nmHDI8LlQb0Yym9Q/5+xtqA1vQNAc+Xxns9m4I\nsR2bbSzlylUrtWuitNG37zDM5ng0rRxCOHA662O1xmKxpCM5CzORnvOvCNEYs9nL9OmSwebChQuq\n59iA+0QqQ2okn1eRmxvOki254joj843XkN7DZGy2ukyfPp05c+ar+T6tjGlNhFiG3d6OevValBga\nSfmAzSHzNBBJTjAeCTW5gPQAXQQT9X4FPbKovxuv7UfTps0ZNGgU4UWtd8nJqUVhYSF16jRTlfK/\nYbNVoVq1Whw6dIjU1MrI1MpKZRjPIzsThtKv33D8fn8YUPrTTz/F46lE0Hv043Zn8fXXX3P58mXS\n0yurzpjtOBzdqFGjAZGRSVgsDhyOKDQtlJpqJY0bh7cMfvnll+o7h8KLhjNr1oN/ao1cP3JyaiAr\n9auRB/JqhFiLrifdMO/3yCMLcDpbIyvWOqFdGQ5H21JJRm82fv75ZyIiEjGbJyDEQ9hsPux2Ly5X\nKm53TKkUVteP/1XGb//+/YrBZDbSve6N9HQmIbsfBiLEg8TFlaWoqIjevYcqgXO/2pxN1cY+px7U\nSKR2aRImkxe3OxenM46xY2X+5PDhwyo/9onaUJFIT+0KQjxLZGRywANYvXoNdrsLITR1T+uQrUid\nlPF7GJmcN3Ic/0SetBZkmLYDSdxgJNT9eDzVeP/99295foqKivD7/XzyyScKDmK0hp1GeoLdCAfc\nfkJKSuXA6zt06K2KNv8iqGkRgRBp6HpjIiISiwHMmzTpdJ2h2oHMo5bF6UxXinbbkCFsJMFk/jUc\njqwSIQx79+5F12NUcauDuvctaFq2mq9zSChUXWSOc7169m5kzqonsqiwGSF0oqJSePvtt9H1RGQ+\n7QN0PTdQSLt8+TKzZz9Mjx6DWbjwsYBBW7JkmapGtlTry/iOnxIdnYrT6cNkstCwYWtOnz7NV199\npRiADG+0AKczif3797Nnzx48nlohhrFAGbJ16v9bkd6TIUz0Frm5jQAJc+rTZ6jibJRtkMGOnmmM\nGDH6ltdISSMqKpWgGPvbCFGV9PTcACV/aaOgoIDWrbuqSrQFWfiQaRy3uwZvvPEGfr+fDRs2cP/9\n01m3bt0t4XQnTboHk2mKeq+Tag3uU/+XYvG3Qqr6v8L4/fDDD9x77zS6deuBy9VYLQBD1f2sMoQV\n1eaKRYgIGjVqTU5OLSS7ibFon1EbaTayEFFLGTU/MgztghBncbly2LVrF1u2bMHrNWQLtxPsEbUg\nNS4c6HoEjzzyCFZrBNLo3Y0QLdA0H50798DjiUUWZfKQzf2JSDqlZGTBxY/sKIlRRqIWQeNXNSys\nliDox4mKSsdsdhETk8a2bdu4cuUK3boNwGKxY7e7uffe6SqBHZog74g0rmNCfvcc0dGZrF69mqys\nXKQnfSrk72PJyanMokWLeOyxx0oMr8aOnaS4EP3qZwShvISaZsdkmoZUZksiNNdoMlUptWPg22+/\nZcGCBYwbN44aNW6ncuX6LFq0hCFDRitPcjEy3MpRcxmrNkhfZQANLr0hJCZmc/XqVZYuXUpOzm1k\nZeUxf/6jJeakfvrpJ1q37k6lSvUYN24yy5evJDW1AiZTl8C9a9pITKZYZE92AVbrKFq1kjjOxo3b\nqdTHUzidrWnVqgt+v5+9e/eqgpvUb5aMKDryUDBC9BRkGHkAXa/DnDkS5rR06ROKWOMi8iAdpNbq\nZoRw/+k+96KiIt566y02bdrEkSNHSE4uT6hyoRD90TSNlJTyN4WY+P1+Dh48SO/e/bHZ0hBiJk5n\nS+rUaca1a9cYMmQ0LlcNhJiJy1Wbnj0H3TAXmJ+fT5MmLZEH2AHkAR5e7PF4KpaqExI6/lLG79q1\na6xatYp7753KSy+9hN/v56uvvlIVtvuQIa4LmQAP3dh5avGvRvbJJuNwtKRixVpomtGAf01t/qHI\nvtu+hHO/7VeGDRyOUSxdupR9+/apk/yCuv7pkIW6FZl7+kypqEUgsWnG3+sze/Zszp49q1raDKPy\notqYMdd9h6YIMQhNS0OIgZjNeWRkVAoDbs+bt0h1VfRHnojvIISbjIxKOBwd1H0eweksr7RzDSaV\nnxDCi93eXH12B6RIuBcpauRBtoilENTX8KPr7cnJqYLLlYbHU4WyZSsWy+OcO3eOihVvw+OpitNZ\nRXEPngq8h90epcTg2yMPh1HIIsbDmEwe/vjjjwBI3fC4/H4/Dz44F6czAqtVZ8CAEYF5KCwsZN68\nRTRt2pmMjCoqD3s7QSxjPvKwGYAsUuQwY8YsypatgNudid0exZAho0vcgKdOnSI6uoxiCn4Xh6ML\n7dv35OLFi1StWhePJw+vtxm67sNkMiiu/kCIl3A4vFy7do38/Hzmzp1Pz55DWLBgUSDfl5+fr2j/\nGyONdgVkFPIM8gBvgKEFY7NFcffd0wJeUq9eQwnPxe1DiGg0LY4OHbqVurfefvttsrPziIlJo3//\nEVy6dInCwkJatuyC210Fj6crLlcM06fPQNeTkDCpochI5BhCvITPl1CMeaW08dprrzF16v0sX76c\ngoICfv75Z0UxZqQhLuF0JpWKIbx8+TK5ufVwOusjwfORSBC1myDRxH5sNi+zZs1i9erVN8wB/mWM\nX1FRES1adFLsH7NxuaowfvwUOnToifSmDPqnXsgTcz1Br0lX/xqLYxBC9KFt2+54vUlI8G0GMnxZ\nqDa9BUkMabzvo+rvv+NyZQY6L0aMGI/LlYnJVIbwnNE6ZOgFDkcuEi4TKiM5DLs9Abc7hkaNmuF0\n1kaIlzGb7yc6uozyzAzv9Rwy1+LEanWjaQPQtEk4nTFhqHkpbO1CiDMhn3Mn8jC4I+R3T9K2bRei\no8vgcqVht3vp23cAyckVSUjIoWLFymo+UpH5mnJIWqaNGN6rprUiJqYsJlMm0lvORtM6lSgUXVBQ\nwAcffMBDDz2kNvSLyGLP/aSmSoM5depULBYXssqdgqal0K/fUH744QfFa+fD4fCwdu161q1br+jU\nDyHEKZzOVkyeHN5Qf/78eXXorFbGz/Aov0cIO926DaB58648++xaGjRojdlssExfwOXKC5OGNMam\nTZvweEILVlcwm+1cvnyZgoIC3nrrLbZv386SJUvQ9VZqQ2YiRC00LZ28vEalMnyDZBKXYlJG+95n\nCOHAZMpGhu2FCHEBXa/Pk08GVc1mzXpIsdTInJrJNJvMzKoBB6Gk8e2336qUzTaE+BGHozvdug1g\n48aNuFx1kaH5VoRIRdN0GjRoTu/eA5Qo18nAHJhMVahdu9G/JW5UEnO611ujxFTHhQsXWLRoEU5n\nu5Bn+SpmcyTNm7fD6YzF52uOzRaJ1RqB1ToBXW9F5cq1SzWAfxnj99FHHykxZiNfchqTSVeGLV0t\nsh8RQnZ0eDzxaJoNTdOVQQilIBqNxVKRhx6ay8GDB/H54rHbWyO9t0hkJXEDwQplJTTNhcuVhc0W\nQXZ2DXQ9GqczjipVajN48B0hmLN5ygjGIiE2Z3E6yyhhHcMj24P0sPogRAyaloPTGUVe3u307z+c\nY8eO8fjjT6LriWhaZ4JErS8rw/wvjGpb9eq3B+ZKAneTCOY//Mjm9vvV/Mjvb7UO5777plNQUMCB\nAwd46aWXVD/oawixW7G9xCJhO18jUwYt1Os/QojmVKmSp0LhJkjP8e8IkUhCQkapz7JevdbInGYu\n0ruJR9MsmM02WrbsqFIDvRGiHCZTFMuXr6Bs2YpomqH98Q1OZxwtW3YhHHLx92Jg4pMnTyqw8yXk\nIdYWCYGJJz4+Pexa2aURuj5mc889U4vd/5YtW3C7m4RcJ73269smr1y5QvXqDTCbyxAk4SjC4ejO\nrFmlsxnv3bsXn68BocZA1zOJjExFiE9Dfr88wKsIUmCqRo2GuN1V8XobkJCQEQYjKmksXrwYm20s\nkpVlG0LsxGZzs3DhQqzWCerZxyFzu//Cbu9Hq1ZdFJuzYfwOIyMaM0LYWbKkuAbNjUZ+fj7JyeUw\nmRYgxDE0bSlxcWlhIlJFRUUMGTIaq1VXLDzTQubhOF5vPCB7yXfs2EFkZBLBfm4/ut6KZ555JvBe\noeMvY/x27dqF1xuqqeBXhsqg3VmCENVwOCpgt/twOOooAzMB6W2kIrFaKxDCSfXqdQOV0t9++435\n8+djsejIUvxVpOfzhDIk83G5otmzZw+tWnXBbu+rDNA7SCLJFEymaGSoOACZZHficnVE18ty551T\nOHXqFHl5jRTFULTaFJUIeoNrycioGvbdd+zYgc3mQ9Kc10VWMDMJUhntIz1dtk9t375d0RDFqnmZ\nqAxfDNJ4enE6++JytSM1tXxAPBugU6d+BIHCKCNYPeT/O9RcdkGILthsERw4cACfrwzhSm7zSE+v\nVOqzlOSoO9W185EFn3MIcV6BiDsSxOA9i9WagqYZqnHyM9zuPrRs2Q6LJbQFcQWNGrXj8uXLDBo0\niujoVNLTq5KdXV316H6MxJjZcTi8xYgVatZsjKYZrVhXcLnqs2bNmmL3f/HiRdLTK2GzjUSINeh6\nHUaMGF/idy0oKCA+PpvgQQRCrKRnz9KFtY4dO6ZISg0ozj50PYrGjdthMs0LMaI9ePDBcG2Kq1ev\n8u6777J7924uXLhQ6mcYY9WqVdjt9dT6aIsQaVitkUrnOgWZ4w6Vy/wNu92rPNNkZCQRgywKXkWI\nH7Dbk26pfzd0HDx4kFq1muL1xlOjRiN++OGHsL8vW/akYgw/jyRljUemoAqw2YYXizTsdjehkY/V\nehejR48mPj4dTTNRrly1QFj9lzF+Z86cITIyCU17CiF+xmS6DxluGeXzMwhhIympHDJP0gzJkzZI\nGTIDp1QZh6M+mzZtCnyG3+/nqaeeVl0L3yLb0sLzhj5fU9auXYvd7iPIgmKElZHIPsYxSC/0LRwO\nH8888wz79u3jl19+4fXXX2fBggWUKVMReVrWJjwUvYjZbOfkyZM89thjPPLII3z22WeKtdYITz5H\nQkE6IsRP6Hpj7rlnBr/88gu6Ho30vlYjQ0cpNC2LJv9EiOZUqJDH2rVri22O3r2HIg1saMheOeT/\nTxAfn0358tXp1q1HoLBRvvxthDM9D2Py5HD5gDNnzrBx40ZeffVVHn10MbpeCZmkrk+wiwT1PtnI\nyrzxuw9VR4Ph9VzE5cph8+bNJCRk4HB0xWLpj90ewUcffUTfvsMUJdJPCPEGTmc0LVp0IiWlElWq\n1OWJJ54okVRz//79SiiqCmZzAnXqNC21++D06dNMmHAPnTr1Y9myv92wOtmnzzBlfIsQ4iK63uim\n3tGaNWtxOiPxequi69Fs2/Yqhw4dIi4uDa+3MW53NapXb3DD8BlkEXDUqNEMHz6Kr776qtjfL1y4\ngMnkIdgAcAm7PYcdO3awePEylYduFnLwfKh63HcgI5fFyKgrNAS+hzlzShcM+ndG9+6DkLl0PxKJ\nkIksJppp3LhdsXxjq1ZdsdmGIREMf8fhiFF7YztCXEPT/kZiYibXrl376xg/kKzFubkNiIhIolKl\n2jidlQlCI54jO7sG8fFZSJxaU/WAyhLEep1ACDcuVx6vv/46+/fv59NPP2XatJm4XFWQHHpGB4Qd\nQy9CiD/QtFg0zYtMrgbdakkv3zRkw3bBatVZteppvv/+ewXLiFSJfh3ZgvU1Mh8YTZChZAUuVzyx\nsanY7YOwWCSiPS+vNkE9YBDiWzTNR2RkMuPGTSY/P58ZM2bgcGQgvQyZFpC9t8NDXncSIRyAdP+X\nLFlG8+ZdGTx4FDt37lSSjg8jxKOqncuBLD7chd0eUSKyfufOneh6LCbTfVitg4iLSwtjlZk16yFk\nyuE2TKZaJCVlMXv2w2Rl5eH1pqgDTN6f7KyIUxuuCdJT20hkZCq6HqOS71kMGDACv9/P+vXrsVhc\naNrtOBzNyM6ujssVTRBOARbLZB555JGbrrGjR4/i88Wjaf0Q4j6czjIBYSe/388TTyynWrXbqVev\nNS+//DJff/01LVt2JSoqhapV65daWTx79ix5eY1wOuOw2Xz06jX4pi1dICORzz77jN9//z0gxHP+\n/Hl27tzJ3r17b9rHum/fPsXnl4gURvIV88gKCyWrdajeh9N5B8uXLw/ce1paJTStlTqQvGiak3Dy\n0iSCxBFF6HqLsE6g/8SYOnUGdrssTsnI522E2IzTGVcizOvs2bO0bt0Nu91DbGwa998/HZ8vVG4B\ndL0Mhw4d+msZv9CRn59Pnz5D0fVkfL46REYm8eWXX9KjxyCs1sHqtIhBslwQ8hNL+fLV6NatH05n\nIl5vVSTq3ygufIum1cBuj8BsjsPhuENVWMshW9JqIj23Kcg8XAWktweSTrwn8fEpmM1eXK4MdbpG\nqWsHhtzHH0jvLBKZU4tWSmSh4dxakpMzsVhGhvxuL5GRZZk3bx5fffUVTZq0R9drI8kKDBxhIrKi\n2RAZqjZC4gOd7Ny5k/Hjp6DrtRBiI2bzfcTFleWdd95h2LCxDBw4knLlqmIy3YXs3hiD3R5djCz0\n2rVrPPXUUwwaNITu3Xsyf/78sFatvXv3YjZHIYtRQS95yBCJOTt+/Djx8Wm43e1xuzsSG1uWlJRs\nZD5wF9KTdjFp0j389NNPbNq0iffffx+/38/x48exWCKReUMdIR7B6eyM2x1NsBoNTmcPli1bdtM1\n9sADszCbQwkx3qVsWYlvXLx4qfJWd6qDy+B0zEZKAUghn9L0Kfx+P8eOHfvTTMMHDx4kNbU8up6s\nJBhvnQknI6OqWmtF6jDsQNmyFYtdl51dA00zaK8OY7PFh0FXOnfug8l0u1oHezGZUjCbByEr598g\n8886ZnMvXK561Kx5+58G3d9snD9/ngoVairS4FC4zUKGDRt709fL/vJUgk7SMWw2N+fOnfvvGb83\n3niDnJwcsrKymDdvXqnXSYJKc4n9tlDc+F29elV1Kdgwmax07NiDvXv3BsDEDzzwEJpmqGXpiu78\nVSTE4XHs9kjVwmVBVoYvq8X8KzI8fAchutGtWw/+/ve/M336dEymSIKFlmvKqI5Dkii8rf7/rjqZ\n4pAV0brIfFZH9fMcMrdiPLwD6nMPIzsbqiM9zlBihg9JT69KdHQZzObxyEp0FBZLPSyWu7DbI3E6\nyyHzj7HITpZUZFW6unr/x5G4wVoIUZ2KFetgtYYKwICud2HmzJnUrNmEiIgkZTh/QhI51MBsrhKm\nvFVUVESzZh3Q9SYYlfcJE8IprRo1aoE07KFi2OFCRmfOnOGFF17g+eef58yZMwrzeDhwvdk8nIUL\nFwauv3btGh9//LHa3PciPe8TCJGJpvWkW7fu6HoSmjYLu70fqanlw9rMLly4wNChY6lYsS4dOvTm\n66+/xu/3c889UxEitLXtKxISygGQmVmDIBgcJOvPOGRxTObEvN42bNu27WZb4k+N3Nz6mEwL1WdK\n8e1bFenxetMIF5bfgNebVuy6adNmqLRCNELoWK0xYVoYaWlVkamWoMFJSMjGbLbicEQwYMBAduzY\nwdNPP83mzZv/LWaVWxn5+fnqXoKiWJo2g7FjJ970tX6/n4EDR+JyVcLhGImupzJv3qPAfynnV1hY\nSGZmJocPH+bq1avk5uby3XfflXhdkyZNaNeuHZs3by75g667wZkz56DrzZGe03l0vUkA7PnGG2+g\n6xlIap9CLJax1Kp1O4mJWZhMZuLiMrBaE5AJ5T+QHQ3jkBVGQzy8JkK4sFrdHD58mI0bNyI9qWBL\nkrxuBEKsRtfTadq0DV5vMjJUK0SeuIORRYfHlFH7A5lH66+MWCJlypRD19ORhvgUMgeWgcS5/Yyu\nN+Gee2Zw4sQJ7rvvfmrUqIfJ1C5kMW7CZEpVxu12ZURnq78tI1y85xeE8JCSUgmLxUEw3D6GFDx3\nqJ8HkJ5tinqvfQgxmMzMqgHYxKZNm1SBx4ks2ryJzeYO6HPs3r0bu11qlEiDfxkhLqFpDW8oIu3z\nJRBUvQO7fQiLFy/mm2++UfTxJqTnZSM873oPFouLjz76iHfffZd7753GwoULw/RCDAZgGUJNV/fu\nICWlPFu2bFHsMxuR3R21mTp1JgDly9cmqH6GMpKTkHmvhshuhaphpLP/iSFhOkFolNU68ZboywAa\nNmyJTHn41VrsSrNmxengq1W7HRm2nkCmhlbRrFmngBFr0aILZrPRu12I09mJuXPn/dvsMP+TsWXL\nFpzORIRYhqY9iNsdW6w4Utrw+/3s2LGDJ554Iowz879i/D788ENatWoV+P8jjzxSYu5l8eLFPPnk\nkwwePPiWjV/duq0pzZu4//4ZavN+hfTCzGial3Xr1lGz5u2YzQnIEDML6WH8Q23eNsgigZEbfBaT\nKZa9e/eyevVqxeN2B9LLG4YQbtq27Urnzv3ZvFl6rA0atCVciGY70gObhwxH70JWVJMQohpCVCEl\nJYfMzKpIqICx0P+GEJE4HFGMHj0xAOy9fPkyycnZSLzhRWQ+8jOlA/GMet9GBPs6lyOBoMb9HEII\nncmTp6kuiCZq4ZdH5hQlOabMkQ4lvOBRhNMZHxBhj4kpi6S8/11d68Vq9XD06FEAHnvsMWy2cUiM\nZF9laKxkZVW9oXcwffosbLYchFiHyTSdyMgkfv75Z+Li0tTcFSET7k6CgPKrCFGd5s2b32hJcuLE\nCRwOg+AzDoO1WNOWkpkpjVdeXhOys29j1qy5gUKGVLArg4TWGC2I3yMN+204na1K7UH+s+PgwYNM\nnnwvY8ZMUJhNoy3wCi5XXrE94vf7ixVc/vjjD4YMGY3FEqvuNYHk5JywfnRj1K/fhnC+vAexWOLI\nysrll19+4eeffyYxMROvtzZud3nq1GkWAJ3/vxi7d++mX7/hDB8+7qZkqrcy/ivG76WXXuKOO4Iq\nYOvWrWPcuHFh1xw/fpzGjRvj9/sZPHjwLYe9vXoNwWyeHnhgFsu9Abr15cuX43Q2R3otz6rNtxGZ\nF7qNIK/fw8gc2bOYTHF4PFFIL81YBKcRws6JEyf44IMPVM5gCAarh8cTE7YAPvroI9LTqyDDxCL1\n0xchkrHZInnnnXdITs5E5okGIEOJg0gvZgvSY2yIEDsxmR4mKiq5WA6pT5/BmEwGa4kLWbmOoHHj\nVkRGJiLzX15kweASMmz1qE26FiGyqFWrIdeuXePatWvMnDmHmjWbKSiJoXmMmoc7kF0uRiX9Ijab\nj19//ZVDhw4pTOA1ZLGnDULMQ9OyuOuuewCJ5Jd5MqMP9VmEKIfTGV0qGPbUqVOUKZONzVYNkykH\niyWCbdu2sXz5cuz2MiH3B/Lw8CGLRpUwm8uwcWM4b15RUeFad0MAACAASURBVBFnz54NPKfffvtN\nwYZWIL1v4738mM22G9I+vf7663Ts2AevNxldr4DXW4/o6BRGjRrL3/72t5vKI9zKOHDgAF5vHCbT\nPQgxV6U0ovD5muJyZdCt24CAoTM6XOx2DxaLBGxfuXIFv9+viD77IsQuLJa7SE4uF4abCx0S1mL0\nk09Bevw9MZmkrAJIY/rOO++wa9cuGjZsjclkweHwlMqIHjo+/PBDVq9eHZA7LWkUFBQwZcp0qldv\nTMeOfUpUJ/yfDIO16Ycffvi/g/PbvHnzTY1f9+7dA0juQYMG3dDzmzlzZuBn06ZNxMWl4Xa3w+1u\nS0JCRqClKj8/n8qVb0N6L6GbpTLhDLvfIUQcuh7D+vXr2bJlCw5HOYJtVwvRNB9bt27j0KFDVK9e\nB7M5EperMm53bFiII4XIY5AeWSVkvi8NIapisaSyapUUdUlPr6DuayAyjJ6E9NYM7+VOzOZYOnfu\nV2wBdO3aWxkyTRnyDRjeXUpKBSIiEtG0ZcgQ1Wjut2KzRTBo0Ajat+/D008/U+KJXaZMDkFP+ipC\n5GGzpRMVlYrD0R0hVqLrt9Or12BA5umk2tdmZMubUS08hdWqc+HCBfx+P50791aGuh4GOazZnEy1\nao1KxIJNmTINqzW0sPM4uh6Py1UH6ekZlfcLSM8tAyFGYza3Iy2tYtgGf+2113C5orBa3cTFpVGz\nZqMAEavNVg1ZvLqkjPuLOJ2+MPYVv99f4lwVFBSwZ88edu/eXapBAQmwfvHFF3n11VdvmWJJUmrd\nj6ymPoEQd1C+fB47d+7k008/DbufjRs3ousVkMDsCzgcnRg1agJHjkii13B9i7wbYu8+//xzypev\nrtZNOYx0icUSEfYd27btofCNBQjxI7qeesNQf8aMh9D1VFyugeh6aoAZ6PrRs+cgnM42CLEbk+lh\noqPLBEh9SxobN24iMbEcXm88AwaMuOGhdfr0aSpXro3LlYGulyE3tzb3339/wJb8V4zfRx99FBb2\nzp07t1jRIz09nbS0NNLS0nC73cTFxZWYNC7pBs+cOcOGDRvYuHFjMd60w4cPKxaJ39UCMFrD8tSC\n96NpU8nOrsFjjy2mV6+hTJp0L337DlGbzKjsblF4qzgFyViM3Z7AU0+FK1QNGTKaYA9wIbJg4cFs\nttGxYzdatOhGo0ZtlIi20cN4EJm3Cq1Ev0eZMhWKfVfJweciGPa9gSxunFTfxYLbHVpIuYoQFjIy\nKvP111/fNBx79913cbli8Ho7YbfnkJ5eibVr13Lx4kUefHAOPXsO4fHHl4W9z4wZD2G3JyC91WBo\nbLdHBaqaFy5cUNTsS5GQIwOc/Sy6HlusIb5v3zsIZ0YZi6YZ5KGPIkQimtZPkWM6cLkk+HfKlGlh\nWK8jR46ow+gjjIq5NJb/wGyeSExMCklJ5bFYUjGZUhAiBru9DHl5jTh37hyTJt2HzaZjtToZNmws\nP/74Iz17DqZ+/bbMm7fopqwj3377LRERiXg8HfF46lOx4m0lhpzXjwEDRiC7F+KR+eI+mEweDh8+\nXOzagQNHKgNpzNWnpKfncvz4cdUra0Q4xckvShoLFixCtl/+K/A6s7lBGBZWavSuQToRDyDEJB54\nYGaJ73f06FGlnmcU1U7icEQV8/oLCgoUnjBIy+92d+L5558v8X0/+OADJWnwPkIcxensxKBBo0r9\nXv37D8dmM3RRruJ0dmLmzGCHzX/F+F27do2MjAwOHz5MQUFBqQUPY/yZsPdWxj33zMDlysRmG4EM\ngUciPa4otYkisFjcOBzlEWIFVusYoqNTsFhykQl3Wdk1mRLQtO4hi2w3WVk1Ap9z8eJFOnfuSbDI\nAEK8gckUSYUK1XA6U5E9xk8gQ9wvQq7zYTa7FcRiEbqezNq16ygoKGDs2MkkJJQjO7smeXk1uV6F\nTBY33kSId3C5olUvplGQ+R2Lxc7rr79OdHQZNM1EhQq38dNPP5U6X8eOHeOll15iz549tyz9+fLL\nLyuOuRUI8SNW613k5tYL81B27dqFyxWtMI57Qu5/HsOHh0cCq1c/g9NZEVmsuoDZXE4ZPeM164mI\niGf37t039KZeffVVfL42181XAtJz9KPrKRw4cIBevQZgtXZXB1Yhdvsg6tdvjq7fhiwOncLprIfT\nGYXJNBshtqLr9Rg7dtIN56V+/dZommGY/NjtvZk9++bA3zfffFMVkRYE7lvTptO///Bi106dOgOr\nNRTD+TR16rTA7/fTqlUXxRqzCbt9CJUq1bppWH7p0iVk3vly4D11vSfPPvts4BpJaJqKLOBJveRQ\nBEDo+PTTT/F6q4U9A6+3Gp988knYdVevXlXGL9iR4Xa3LpbCMMa0adMJ1+w+WIw8N3RUrlyf8J7+\ntbRr1zvw9/8a1GXHjh1kZ2eTmZnJ3LlzAVixYgUrVqwodu3/1PgdOnSIPXv2cP/9Mxg5cjyvvPIK\nb7/9NkuXLqVv30FYrW6lJ6AjPagCwpkgwGJpjax2GupoHyA9rgiCwjCfk5Ii27ckBVGsEvZxIBP/\nTyJzUS5laEOrhA8jq8t+ZPI8A7O5B5mZlRk+fFyAdmjUqAk4nS2QOKrtSv4xFHB9HiGicLnq4XLF\n8Nprr1Gx4m3Y7b0RYim6Xo1hw0Yr0PIeJKr9UcqWrRgwTF9++SX9+t1B164DeOONN246v6WNr7/+\nmry8xsTGptOuXc8SsW4XL14kKyuPYFsbaNpsRo++C5Cg1AYNWmE225WUpo7FYqdOnYboemUkBOkZ\nhIjAZLLTrl3PG7Zvff7556o9y8hj/oBMGVxGiD+w2yM5ceIEjRt3RPZKBwtUXm86wZQCCHEXJlPn\nkP//is3mumHCXxKchqqmLQ1gG282MjPzkIUy47WbaN68a7HrTp8+TWpqeVyu9jidA3G7YwM4zIKC\nAmbMmE3z5l0ZP37KLfHagQxrJVHu5wixAo8nLoyizO2OI7SVUdM6lqiFAxKbJyv3r2AwHPl8CYF7\nOXXqFO3b9yImpizR0WmqFfV5rNYJJCeXC7vnq1ev8vLLL/P0009z7733Kj7JoDNi4DFLGpKvcxwG\na5PD0Y37758V+PtfFuQMMjczduxkHI5YxaIcgRCT0fVyzJsXPJWOHz/OokWLcLsNqUK/MlhnQx5m\nLyQkJQJZKfYhPaxRSDzg39H123jggYfIz8/H640jiKX6XklX2pHh9UVkcSQUa2VQ75iRwOhvEeIo\nPl9i2HeSJ+yBkPuaqu41GllEKUNKSg6vvvoqx44dA2RSevbsOQwZMprnnnuOzZs34/WGCsYQCEkl\noWYM0sNYia4n8/TTT7No0SLmzJnDtm3b+OCDD0o1MAUFBSxevISRI8ezZs2aW6r8Pf/8C8ogrUGI\nR3G5YgItV50791MtYFcRYjd2exnWrVuH3+9n6tSZmM1W9Uw+R4iz2O396dKl/w0/b+zYyeh6uoIF\nuZEwplFoWnX69JH6zuPHT1GwF1mgstvvUJRSU0PmrQ0yF9YNGZL/clPj16/fcPW+VxHid3S9Wpje\ny43Gww8vUH2sJ5BQpxo88cTyEq89f/48zz33HCtXrvy3GFWuH5cuXWLo0LGULVuFunVbhpHS+v1+\nRX77S2BubLYxPProo6W+38cff0xsbCpCmPH5YlmyZAkFBQX4/X5yc+uhaQYwvwt2u48mTToxcuT4\nMDB4QUEBt93WGLe7Hi7XQJzOGGJjy+Bw9MZkuhddjytRQOnYsWNs27aN0aPHqYMvDSHiSU4uH5Yj\n/EsZv7Vr19OuXW8GDBjBgQMH2LFjBy5XhRAjtgZZCTyEw+HF7/fz2GNLsVp1VenzIF32dsi8XhNk\nq9pypFc4G4kf+xxZ9RyLEJJiKj4+m/79h1BQUMChQ4dwuVLCjIvT2VgZv4Uh95KGFFVfhaYZHpxb\nfdZahNhKZma4ruv1xJE222BGjRpFTk51oqOT6dt3QFhyvqSxa9cuzOY4JNC5DUK8js3mIj8/nxEj\n7kTT5oTc+2uYzTHYbINVd4kLXS9PdHQK33zzDUePHg0oshUWFtKwYWscjtYIMR2nszpDh465pee4\ndetW2rfvQ8+eg8O6RWJi0pBsPHcoI5WH3R4RuGbGjBnqADDuN8jkcaOxZs0axRIThWTLzkLTvHzz\nzTeAPDAkE0o53O4cKleuzZtvvqka99uoHx0Jpt6AELlYLGmMGzf5hp974cIFGjduh8XixGSy0afP\njck5Q0dhYSHjxk3G6fThdEZw770z/p/BSozx+++/U716A9XX2xiZunkBXY+5Ic5u8+aXcbkiEMKJ\nydQAl6sGubn1OHz4sNqHfZEdMx0wm1PYsmVLsfdYvXq1wvQaqIM3SE7OYcmSJcye/VAxggog0Krp\n8bRB5nr7IqnB9uJwxHLgwIHAtX8Z4/foo48ryvDnMJkexOeLZ8aMGdhsoe1gl5CFhIuYzbYQhoqf\nkd5eTWSSfisSBOpBVl59yvOLQkJaeiLzbE9gt0fhcETgdnfH7c6jXr0WnD9/Hl2PJNhwf1wJO5uQ\nfb4GB2BvZQA7IBPKRi7oO4Tw4XBEBATJjSFxZUkI8TBW6wji49NKbZ26fpw7d45mzToiq70OJMxl\nEUJ4MJnsREYmc/vtrQjPpb1NsD0PJKlBM4RYgtMZj8MRh90eSadOfXjvvffQ9SxlVGOVMXcGVMr+\n+c9/0qZND2rVasHChYtvmD+8fPkyhYWFVKlSD6m9UZ1g4nsdWVnyUFi2bJnSADFymrsQwoPbHcPS\npU8C0gt64IEHGThwJGvWPIvf7+fzzz9XB42R8ylAiJywdrfCwkL+8Y9/8MUXX3D16lVFfjodSdpZ\nXRlNY16OYrG4biknunPnThyOKGy2imhaFF5vCitWrORf//rXLedUrx9+v58PPviADRs2/CnVvv/p\naNeuJ1breGTaYAyaFk1a2o2LKJIrMFbtNYPj0o/D0YM77hhBOCFJAUJEhHnHf/zxB+PG3U1qajaa\nNjnkGfyG0xlR6uf6/X58vnhktxVqPZXHiMB8vgZhzOB/GeMXG5tOaC7FYhnN4MGDlRau4fmtRlZa\nK9KhQy8effTREON4URmES0j3PRvJrJKnjN5JJPD5AYQwExeXRfXqt5OYmEGQfeQEFksm3bt354kn\nnkTXo/H5GuJ0xjB//mPMmPGgquomqknPQFZ2/cjQLZhj1LQ2LFmyJOy7PvvsWrzeeEwmK6mpOUyd\nOu1P9YR26dIfm20wUkPkRyS0phGS2eY8QuxTOrQxyFN3O7Ig1CdkgX2IPCSGqN8XIsRldL0Fw4aN\nxGxORrLXJCC944ewWqNYs2aNYtR+HCFeR9drct99DxS7x7Nnz9KwYWvMZhtWq5PRo+/EZjNA4MY9\nnMNmcwEyZ5iTUwOXqw0m0wgklnEzQnyHrqexdetWcnJqqFzQE7hc1Zkw4V7y8/OR0KCgepumDS61\n1/fXX39VqnRPI1MMmYSDxH/Fbnff9Bn4/X6VEpmCTG98gMy9xmKxeMjMrPqnw9SioiJ69RqMrmfi\n8XRH12PZsGHTzV/4HxjSMz8QMg+PMGHC3Td8zerVq3G5BiKhX1+GvHYZbdt2U0B24zArxGSKCYCW\ni4qKuO22xup5zkV6b/sR4ipW6500a9ap1M/Nz88vJrsqu56eRoj3cLliwvbTX8b4RUenEuQ5A7N5\nIrNnP8S4cXcrlzxHbeQP0LQsVq5cyYsvvojLZehwTEN6hZeQoW94w72kwD+EPJUa43Y3JyUlB5cr\nShnLbWrj1USIXthsEWzcuJE9e/aE4fJ27drFHXfcgfSKnkaG0Q8ivZCPkZWtbgjhwemM5/bbW7N2\n7VqVzI1Chtx/YLMNo23bHgENhG+//bZYuLt9+3amT5/BU089xVtvvYXT6UV6esaGn4UM3U4TPDQm\n0qRJEyVxeDsytC+jPvddZTDrqN+9S3COnqNNmx4qfB+BDAeNv71MYmKOEoMyfvcjERFJnDlzhokT\n76Vjx34sWbKMTp36YrPdgcSiHUPXyzFhwgTs9gwMnKWmPU6VKnUD3/PSpUs888wzirgglELrETp0\n6ILb3ZDrq90FBQVUqlRbCYj7EWI/dnt8sYqjMS5fvqzowyKRB8cJtfHmI8Qb6HoDxoy5eS/p5cuX\nMZmsSAB4aCfSswjRG7N5Drfd1uSW1//JkydJT6+IPFAN0Pg/A7T4/+1RvXojglyPhTidbVm69Ma0\nXK+//jpudzUkZGcY8gA9g67XZOXKlWRl5ape9bexWAZSo0bDgEf83Xff4XKVVa95BVk8tCGEmSpV\n6t4QAwiQnl5ZIRBAAv0lssPjiWHXrl1h1/5ljN+0abPQ9ZrIquFyXK6YgPsv+bpeJxg2PUhmZkWK\niopo27Y7ZnMsUse1MTIsrXXdJnoF6ak1RLZ6fY4Qh7Ba7yQpKVvBUVzIgoixyd4gMbFcifdcWFiI\nDIGrIb3NDPV6HxLYPEQZ2heUUYzAYumtrhupPuMkTmck7dv3xOlMwOXKICenRiAEfvDBubhc5RDi\nAazWCkq7YwISVNxaGZf2SI/TyCFKZtsOHToQ3sg/D4lxdCIPhSVIbzhLGcjB2GxduO++GYrDz6AL\nC3qL0dEZ14GUv8XnS1RVv2yEaITFUgW7PVotSpAHShSaZiY+PhObzYfbnUFSUhY//vhjsXmtUKEW\noUpwNlsfkpLS0LRYZB73IEIUYLE4uHTpEkeOHFE9wXaEsGG1RtOxY+9SsY/jxt2l7tX4Dj9gsSRQ\nsWJdHnpo3i23sJUtWxF5SD4T8l4LkIiAM9jtHkB6KkePHr1hy1+rVl1V4SZU8hRsNm8YIe1/Y/z+\n++9MmjQJu92Dy1UPtzuX2rWblsjccvz4cZo27UhsbDq1azenUaPWuFy5mExpSD1jB2PGTMTv9/P7\n77/Tt+8d5OY2YtiwcWHV3e+//14Zv0PI9rzP1H54gejoMjclT/j+++9JSsrC4YjDanWxdOmTnDp1\nqsR0w1/G+BUVFbFgwWPUqNGEZs06h/HLSQ4/AyBbgBD1AyHKkSNHsNmi1e8LkN5QJCZTM4yGe7PZ\nkKyMQZ6wVTAYbitUqEXa/+HuzONtKtv/f+95r7Wnc5x5cAaHY56OeSYZMhOZMpMMkZAimadUCikl\nZYhKJWVMZIp6KuWRlEpCPEQyD+ec/f79cd97cgaHeL4/z/V69epVZ+217jVd6xo+1+eTko6Pdl1G\niJeQaZAnz3WXKVMdg2EAAUbkb5Hpp5kAAv+Sco4+Z3ABWX/7EiE+xe2OVgXfywjhxWIZRtu2D3Ll\nyhVFTvAH8gupqxcf9d+lMJtL4XLFUrduA2y2SKzWwTgc91KuXA3efPNNbLZiyFGvfQgxTjmI4Prp\nJgJKckOxWAqxadMmxo0bh93uo+naiBDfoOtVeeyxUXg8sQoTtwxdL02xYqWVA12hXv4oZLf7DWTd\nMxJJwHoFk2k0pUtX5ccff8wTlyZrjpHY7Q/hcDTHYgnHZBqE5EechhCJWK0duPfeVv7fZGTUQdLX\nZyLEZXS9dg7OuTNnztCgQQsVsVmR6W42QnyBrkfkK9Bz7do1vv76a7755ht/JLZv3z4KFYpHfvAm\nqONHIqEi75OcXNqv96zrcXg8MWzbti3X/cs56o3q2vlSyPkkJBS7Y82Qv/76i2bN2mM0ujAYumAw\njMJqLcTUqVNzjTYzMzNJSyunxk4PYDQ+T1RUMu+88w6vvPIK27dvz3ciJtiys7OpWrUBFosvUAk4\nfF1PuCE9P8Bbby3HZnNhs4UTF5fm1+m+3u4a55eftWt3v3rQaiAbDGFERiYC0vmZzREEj/yYTMWp\nXbuxoq23IlO9vsi01qcX8TdCpGE0RmAyuZAzuPuRvHzdEKI3derkZMrw2aFDh0hM9MFviiBEBrKG\nYSJACHlEOVWC/qmHxdIUTYukfv37uF4PNjW1vBoxc+FjCJaOKyAIbbO1pUqVWthsHlyukrjdsTz2\n2GO8+eabXLp0ibZtu2I2F0MW9F2q5laFULD2t8ialbxmNlsRbLZodL0nul6SUqUqkZBQksKFSzN2\n7ESys7P5+eef6dq1L40bt2fBgoVYLOFIvKJvnwMRwojDEYnNVpnQmloWRqP5hoDcn376iTlz5jBj\nxgw0LVTq0mAoQ5MmrTh//jxXrlyhWbP2yI+aR53rZYSYzPDhj4fss1WrzpjNvZCTET8jCUDdaFo4\nH32Utyj3mTNnKF26Kk5nCZzOdCpWrO2HCGVlZbF27Vr69x9MampJNC0Ft/s+XC4Jz5DZyr/wZRFu\nd0yuo1oZGfUwGOYjxDvq+dQIC4tn3759+V6nmzWv18vq1auZNWsWJUpUxGisQijT+GrS0yvn+tuf\nfvpJqRgG7oXbXS1Ph34jO3/+PF279lKg78PqfZMoiZdeyn+m+MCBA6rZ4pO3eIO4uLRcPxT/E86v\nZs37VDTxKTJqWkjlyvcAshMoMXidkCnzIxgMHrZs2cLUqVOx2YJBrDrB2D9Z0G9y3UPwJ0JYCQ9P\nom/fvrz//vtkZNTFZLIQE5Pq51z7+++/iYpKRoKbv0GmutGq2RCPJIhspm7qS8p5bcFqDWPs2LEs\nXLiQfv0eRtOaIWt4XszmMbRo0dGPlTKbhytHWhqZ8p5CiDXY7R40LZFgoaP4+KKAnCSQyme/I6dE\n3lWsz32QNa73kE2PsgRS4yvIj4QPAH4Rh6PoDcemJIvKvqBrNwCz2cnhw4cZNmwYdnsFAh+lf6Pr\nYQWOZo4dO4bNFk6gDpaJw1HMX9MbM2aCUvq6jIz42yLEcByOKjlwdx5PnLoevnU+jdkcz5IlS/Jd\nQ79+jyiMoqSOstm6MWTIyBzb+Tq1q1atYuPGjZQtWxWjMSPoeOB0puXKVLJ3717Cw+Nxu+/F4ShF\n9eoNbzthKEDv3oNwOEpjs/maWXXUsxsoY/g4Dn/99VcqVqyDzeYiLa08a9euVffCN755FYejSA4C\n3Ju1ESOewmSKQPJhnkKIb9H1xHxniqXCXruQa2u1ejh16lSObf8nnF/Dhm2U8/Od8AQSE0vStGkH\nZsx4RuG92qgb+hBOZz3WrFnDk0+OwWAYH/S78shUcB1yaN+DJEVoGrTNHuUk45DRhAdJXXUJIT7B\nYnGRkVGfihWroevBSlxZCBGhGg2dEOIJ5Nzri1gshTAazYSFxbJixQqKF8/A5crA6ayEyRSGTLdT\nMRjcNGjQgl9//ZUTJ07QsGFr3O4Y0tLKU6FCbex2N4mJJRgxYgS63jPo2F6MRjNbtmxh1qxZaFpD\nZBrVAMlNaEPTopBNoUrKCSao816GxdJBkcIGHii3uzUrVqzI974MGfIYsoa2Eol/1PyjXpLLsQVO\nZ3Xs9ofRtBgWL15aoGfC6/Wybt06KlWqjs1WGiFmoWn3Ubfuff7aTt26LQmlGFuNwRDhp8EPtrS0\nCkj4E8qRtcJsrs2UKVPyHZyvVq0xoRMZ71O/fqs8t//tt99wOqOQEXYEgY/Tj9jtnhxz6j47deoU\na9asYevWrf+IOuvw4cO0b9+dSpXuYcSIMX4n+v333yumHp/zOhH0jO9AiIPYbPcycOBjZGZmkpRU\nQhGt/oUQy/B4YunUqadqLk5H1xvQtGm7An/I/v77bxYsWMCcOXNykHp4PAmEdpsnMnLkE3nua+fO\nnTgcqUHn8l2ezaH/Cee3efNm9fK+iK/DaTA8jRBL1FxpODJycSPEAFyuaE6cOMHmzZsVV9t3CHEG\no7GRkrp0IXnjfkZGfk4k9m+qchpuAvOIvyJTq7Pq73EEJC/TCKSj5xDCidlcFjk14ruZC6lbtzmL\nFy/mlVdeoWvX3mom2av+aYiMFJPVv8cREZGY65fMZ9u2bcPhKEKgy7saIXTc7srqC60TGDc7ixCx\n9O/fn+LFq6jmwXRkxDQFkymeLl16kJhYXCmcZSMJPyNzHboPNq/Xy5gxTxMdXZy4uOK8+GJolzAr\nK4sVK1YwZ84cvvrqq3wdTbD17fsIDkcp7PaHsVoLU7FiLaZPn0HfvoMpV64O7dt358EH+2C1DvRf\nR7N5KO3adc11f1u2bFFjhJ2RDZ6KCBGGxeLCYtGZNCl3JvIBA4Zhs/n0dDOx2x9g+PCckpc+mzNn\nDjZbT7WmZ9QzUgtNi+L119/M9fqdPn2a7Oxsfv/9d5YsWcKqVatuiULrzJkzREenYDI9jRAb0LQW\ntGnTBfBJZtYK+bjJ6K+8ctIeWrXqwNWrV/nll19wOK4X96rHJ598wqJFixgyZDivvPJKgTvRPioz\nXW+D3d4XhyMyhPSiaNGKBDcnbbbOIezeuZnU0k7F7W6bLyzornd+Fy5coE+fwcTHpxMVVZRSpcpj\ntfZQF2uRunmT1Ev+IULoJCeXJD6+BPfc04rp02fg8cRitTpo3bozY8aMwWgMluw7ppzbKIQYrpxf\nneselGhk0yJGOb/DyFS1DLILOQ8JH6lLeHg8ul4IiSecgqZFkJJSGqezAbreQ9U5fB3NBcgGyMdI\nggQJZXE6W+Y5/O2zwYOHq+3LI5sTxZE0WkfU//+3egkHIIvxJTAanURFJWMyTUWIXzEaZxAfX5RL\nly5x4MABihYtj9Foxu2OZs2aNbftHs+d+zJWqwOTyUrFinVyVVjz2e7du7FaYwh82WXjqVq1Bths\nXRFiM2bzEyQkFCM1tQwuV1VcrhqkpJTKFzO5Y8cO4uOLYDCYEcKKwdAKH02+rhfxz14H27lz56hc\nuR66noSuJ1KzZqM8VdX279+vmhcm5VjWI8Q6bDZXrqQTUqc6EiE0DAYNs9mB09kRp7M6lSrVLTBV\nls/ee+89XC5fBvMpctzPxo8//sjp06cVa8sKhLiMwfAyNlsYZnOaemckumLv3r2cOnVK1Zt9TNqX\ncDhSchW4KoiNGfM0FktwWWkxlSsHoEAbN25E12XDTtdbkZpapkDzyrt27eLdd98Nmei43u5659e4\ncVvs9o4I8SUGwwvY7S4VOYEEmnoIBT3WRqarS5GpD4RZzQAAIABJREFUnYXk5NIMGTKERYsW8eKL\nL6JpvkL8j8hoslDQ7wchI0EffGQZQjiwWgcgGw9llKPcSWDixI0QdiyWCDZu3MjevXupUaMeDkci\nul4Ik6lF0Bo7YTA0QtbZahJgZgbJqNEMp/PePPkPfSY53+oi6X/+QtZMbMgaWz1k8+FDtV5f3Wwx\nNlsEtWs3JSIiiZo1G3Pw4MGQ/V65coWTJ0/mG3nejMkObqL6eGRjNo/Ms5F08eJFUlJKKIce+PhI\nBp8wAvVDcLtrsGbNGjZu3MiGDRs4cuRIgWplFy9exG4PpkQDkylvScbs7Gz279+fK1mmz7KyskhI\nKKbE171I/GQYdnsxJk7MyXB+8eJF1RDx6TN/hmycTUKIp7Baq/PSSy/d8FyCbeXKlbhcDZHkvvFI\nPOgQwsLiOXLkCF9++SWFC5fAaDSTnp5BXFxxJC7Vd02fYsQImW6OGvU0Dkc6JtMIHI7KNGnSll69\nBnD//T344IOVN7WuXr0GqnfMdz93k5xcFpD1eh8Z6fPPP8+rr75aIE3igtpd5/x27txJ06YdSE+v\nQv36jdSX+kLQi9BIUS29iKxhWQgwolxBgndXIaO191UEMQMh4tD1mtx7bysKFy6OyVRZOb3Kytn5\norG3FVeZFZneWklMLMkjjzyCxeJGNkfGI6PAbkjgtXyRjMaZZGTUZeTIMRiNZdU67lHb+27+fkym\nMAV4DicUjzgFIUqRlFTihhxxS5cuxekMLvxeUGs+gIxePQqwPDBom3MIYc5zAuHy5cs0bdoOq9WN\n1eqmRYsHCpyCnTt3jnXr1rFx48YQJzR9+nTVuPGtQeLgjh07xvHjx0PqRrNnz8Zuv09d2/fV/ZxP\nZGSSuvY+SiYvLldFPvvsM44dO0bp0lWxWl1YLBrTpuVOwxRsUiBphdrXNRyOWjdsfuRnf/zxB5oW\nHeKwzeYGDBs2LOT8srKyWLZsGUOGDFHaLL7tz6tn8X5kEyqKFi3yri3mZufPnycpqQTygx+gFzOZ\nBvP00+P92/nWExdXFJl1GJHlm+48/nggpV+7di1Tp05lzpw5uFzRGAzjEOJVdD2F1157vcDrkvop\nxdRz+Rea1ooHH+xDqVJVMJt1rFadl17KyQR1O+yucH7ffvstn332mdLAjUQ2Jd5WjqwYMrW8iBBn\ncDrrMWvWLJo2bU/p0tWR9a1EJIatjHJYHyAR+MGpazxCHMDhSGf+/PlYLFFIOiWQ3Vo7TmcbnM4o\nNmzYoFTOFiHEXxgML+ByxWA0Btfy1iKEDaMxeJLkNHa7W33VfVKZG9Sxf0bW2bpiMIQzc+bzzJkz\nVwG0X0M2DHSEsOB0RjFlyox8C8onT56kUKEEjMYZ6mFvgCwBaMjO806cznDlnH0M1pKSS9Micm0+\njBgxBk1rrZzOZTStOaNHj8/l6KF25MgR4uOL4nLVxeWqQvHiGf7i/sKFC7Fai6r78zpCrMFmi8Rm\nK4TNFk7Tpu38zlLyuY1T1ywCOb7mZNKkybRu3RlNa4wQS7HZelCqVBWuXr1KrVpNMJlGIyOuw+h6\nKhs3bsx3vbt27cLlikbXa2I0RmGzRVGhQi2io4sQH1+8QBTuwXbp0iXFfh3AczocqX4mc5BOp3nz\nDjgc1TEaByPxn75xyGeve16/xuW6MbnD9Xby5Ek1g/7voH2NZ8SIUOU9GXlGIrOabGTDSs9BQAsw\nduw4TKbgMtEOkpJK39S6Zsx4DocjAotFp1OnXgo9MU7ds1/Q9YQQKvxDhw4xevRYhg0bmeuaCmp3\nhfPT9WQ8nlpYreHIYjzqhR2JT8FdRjV27PZof81o7Nhxyvl8ppzHM+qlKaNeel+kcEz9vhVud13G\njRuntEACztFiiWLu3LkcOXKELVu24PHUvO7vCYTqgHyHEBpWa/mg48iBfZvNpbZdoW5wDXV8CzIl\n/xqr1UFWVhYff/wxFkskcrpkNz5wsN2ezrx58wGYN28+CQkliIlJY+zYiSxatIhOnfrQt+/DNGrU\nRuHhaiBT8c0IEYPROIBGjdoSF1dMOdUkJFZyAULsw24PC1E/A6hevQn5SVGC5Jq7PiVu06ZrkO6K\nF6u1F8OGjfJLYBqNtdULnoHB4MJiqYusmV5B01r6Odhk/ccnzfmwuq7/Rtfj2bp1K1OmzKBZs448\n9tgT/rqQZJMOTWGnTJEauHv27GHZsmW5jrzt2rVLNYfeUs6iORJy8SW6XpTly/OvuV5v8+bNR9fj\ncDh64HCUpHv3/iEfr88//xyHI50AKcYU9Vy3QGYewdMzf2K3u2/q+D4bNWqsos36F0KsRNejc5z/\nnj17cLlKhTzfTmelEOWzwP5GK/p937bfEh9f/JbW5jNJcHrRv0+rdTCzZs0CZMfc44nFZBqGEBPR\ntKgcY2sFtbvC+cmICPX1m66+iIWRbCmNkdHcXoTIxGbr5hc0mjBh4nVfpa+Q9bdk9UCVRUYcsUg5\nw56YTOG888476u8+jNpqDAbdn+Lt2bNHscX4btAplXbpyKbIC8imSCUMBiealoTHU4ewsDjateuC\nxVIC6bjLKqfkQkZmPj0ML2azztmzZzl+/LiiJg+OUlshxOPUqdOCpUvfUkpdFRGiKSZTvNr/K1gs\n/YmJSVXnUhM5uvdvhHgQjyeS33//nczMTDVXXJhgQLLLVdxP/+Sz7t37Y7EM86/RYhlM376Skfnq\n1au0bNkRq9WF1eqmWbP2/oitbNnahDI5L6F5807s3r1bdaV9s8jnFSYzWFHsvRD4yNy5LyNrlwGH\nZjaP8BPmBtu//vUvwsKileO4gMQC1lG13ZfQ9Vhcrg7oemGefDI0gp07dy52e3Ah/m9k1OxFiDdp\n0aLzTT/L33zzDQsWLGDjxo05ovbVq1fjdjcOOp4XiyWce+65l6ZNm6syyDqEOITN1om2bXPvXN/I\nsrKyGDNmAqmp5SlbtlauZLYSQxlGIPM5jaZF59qYke9CJDIL+hRdz2D8+IILrOdm8pn1cWFew+Go\nxrvvvgvAI48Mx2gc5b9GQrxHhQp1b+k4d4nz8z0QnyCjk9qEzqY+iaSokilBamp5QDI8u1zRyELx\nEmSKPBeZthkwmeKQEZdHOcDHMZnsLF26FJutuvr/yQgRi8lk86dqXq+XLl364HBkYDYPx2RKCYKQ\n3I/ECKYhRGU0rQxz585l06ZN7Ny5U009+GQqzyNEGA5HhHKAW5UjmEDx4pIu/9q1a2haGHLGEfXS\nJyLEcFq16kxMTDHkR2ArEmpjITBBAnKeuadyypo6HwdPPx1gXDl27JhKxX00+1twOiNz1BVPnDhB\ncnJJXK6auFzVSU0tw59//snly5cZMeLJIFDxFTStFf36DaJPn0EUKVIei6WDOrcL6Po9TJ/+LNu3\nb8ftrhLywpvNcZjN3fFBVKzW/gwY8GjIOuLj04NeDi+63jjHyNqKFe+h6zEYjY8hRCMMhmgcjtI0\naNCCEydOYLO5CQik/4mmRYdQRS1cuBBd913XRcj6bASydjvJ/4G9XXbixAnVcX0HIU5hMk0iLa2c\nv4mybt06UlLKEhYWT8eOvQqkC/JPbODARzGZIjEa07FYonn00byxdTt27KBWrfsoV64Ozzzz/C3T\ndvnM1+F1uTrgdJajceM2fnxjjx4Pq2e5FHJUtASFC5e6pePcJc7vtHroZlCyZAYeTyqhjYAPlAMA\ng+EF6tVr7v/9/v37ad68PbJbNhKZ4vYiKqoIzZu3REJAfkLWYyQRwX33tcZuL4zsQr2DZHEOD7mp\nXq+X9957j/T0MpjN9ZAzrOvUerKRkVYp7PZofvzxR/766y/i44sQyp0HTmd5bLYoZDqZiCwwu4mP\nL0mVKg3Ztm0bH3ywUk1LVEPCUmrhdEoRIIPBQiAyzlIPxPmgY7RHiMkE4DggxBrCwmJDsFjvvvse\nmhaG01kEpzMyz7rYxYsX2bBhAxs2bODixYsMHDgMk8mmJDCrE2g+fYTRGKEK4S9gNIZjNruwWJx0\n6NCdzMxMLly4QGxsEYzGZxBiP2bzk6SmliElpZSCqFQiPb1ijtlaKU4fiab1xeGoR0ZGnRyd3JiY\nIshOty/Vbs7QoUPJzs7mhx9+wOksFnIfrud6O3fuHE5nrLon7ZEfwtKYTENxuaLvCKfel19+SZEi\n5bDb3VSp0uC2MDTfih09ehSPJxaDYQpCrMRuz2DkyDE5trt06RLfffedn1H8dtrBgwdZtmwZGzZs\nCHnvPvjgAwIKhpeRbORRNw39gbvE+dlsHhyOFJKSSnDw4EEmTpyGrtdHjqL9hcFQGas1FZerGYUK\nJfDJJ5/QrdtDNGvWkTffXOxXbA8PT8JsdlO2bHVOnTpFvXqtEOLdoJfgI4QIx2CIwWj0MQDHYTZ7\ncm3hZ2dnB9UnwghOxYQYhsmk07//YLZu3cqoUaOxWLop5zcbiZOaR3h4AnZ7DLLbNQ4Z1VZEIusl\nY+6ePXs4fPgwCxYsYNCgwUyYMJGff/6ZK1euYDLZVHTSG8ldFoXZfB9yoD4KGdn6KMMDL7vdHsWx\nY8e4cuWK33GcP3+en376KU+s2vX2yiuvKsGfv5BRXXt83WOjcQhyWsR3zE9JTS0bwkSye/duihev\njNkchtUaRf36zTl27BiXLl1i06ZNfPbZZ3nCU3744QfmzZvH8uXLc+04S7LZ//iPbzAM86fGly5d\nIiwsjsAEyEsYjeEUKVKRxx8fS2ZmJrt371a6L74o/RdMJp3Ro8fkgP/8r9mLL76I3d4r6N4dwuEo\nFLLN999/T2RkEi5XKez2QgwblndkeDtt+/btaFroaKDLVSJP8oL87K5wfidOnODAgQN+OpvMzEyl\nSm/DbLbRq9cAPvroI95//3327Nmj2EXGI8QSTKYi1K7dMFf6n3r1mhI6zP+ccnjhBMadTmO3x4TM\nXR4/fpxevQZQv35rTCYHEg/YCskLmInkjoujWLGyOJ3FcburKqjDbGSU6aNZchEVlUxSUhoy7R2i\nHFaAt9BoHBUCRbje7r+/E7KmNxPZFQ6nSpWaGAzhyDnnU8hmiY+XEIT4HLvdQ0yMZKsxGEx069Yv\nT1T+n3/+SZs2XUlKKsO997bxM2s88EAvhJgfdP2+wGCIweWqhcslywiBv/2LpKSA2EwgzXsTIX7D\nYnmUChVq3RRTyaVLlxgxYjS1ajWjb9/BIfe4WrV7kCWI/yAxmW4GDRrq//uXX35JZGRhLBaHiiQW\nIcROdL0BDz/8KKtXr8bjaRLykul6/B2Nxs6ePUvLlp2w2z1ERibzzjvv5rv9qVOn6NlzAFWrNmLw\n4BEFZk65kUlI0fXOLyJkm/T0DAI8f6dxOIr/IzGsgtr+/fuVfKXvo/QnNlsYx44du+l93RXOLy/L\nysrKMes4Y8YMTKZgWb9/I4SHlJSSOR6O++5rpxxdd2RRPBrZ5OiGhH34UqI6bN68GZAPaHx8UYVN\new+LpRYmUySyYVIYIWwYDOFERxfBaKyDr4lhMHTAZCqiorQIZHfzFSQhgUf9HuQs7Bf+Y1ss/XMt\n5vusT5+ByLTWd74fEx2dlEP3wmBwYrEUwuOphd1eSDntBcjINwWLpVSuY1xZWVmULl0Vi2UoUvt2\nEnFxaVy4cIEnnxyLzdYDH0DbaHyO8uVrsX79erZv367YNZYhxCZ0vQKTJ8/w73flypW43cF6w9l5\nDqDnZl6vl4YNW6Jp7RBiFVbrAJKSSvjV5KKjiyF5G32szOMpU6ZWjn2MHz8eszlY0P53XK5ojhw5\nogr5O/A1OaKjU+4ogWirVp2V+NGfCLETTYvJE8px5coVihWroAhk12K3d6J27ca3hebqjz/+UAHE\nVIT4AF2vnCPtNZttBONrrdYhOaQsT58+nS8d2K2aHF8rhc02GIejKKNG5WQML4jd1c4vNxs4cCCh\nwN2fkLKHsSGD+LNnv6TEakYoB/gQsot8Sb0svqhlEzabm5o1m9K8eUdF7tggaP/nMBqtDBw4lLJl\nq2K3N0N2Nqci63O+MaCvcTpjMRp9FFoVkalqDDLqm48U2m6EHJF7CZNpJB5PLIcPH87zfGUBOFiT\nYyOxsaloWlsCUyOfkphYgl9++YUtW7bQoUM35Xx9v1mLEOVyHcr/5Zdf1ARGMF1RVbZu3crZs2dJ\nT6+Iy1Ubl6sFhQolhNTCNm3aRLVqjShTphYzZ84KeTE//fRTnM7yBDrcJzCbtQKn3AGBbl+n+BRC\nuNQUxQGMxkeQJQbfupdQo0aTHPt54YUX1Hyu71rsITw8AZC1RZcrErPZTmJiul9xLtjOnj3Lhx9+\nyKpVq/5x5CXHHgOpusmUexcbZJPB5aoQdH6ZaFpMgfjuCmIHDhygQ4ce1KnTguefn53DqUog+BJ1\n7LM4HKVZvXo1gJ9OTHb+XbRq1emW5pHzMq/Xy5o1a5g1a9YNMZv52f+c85swYYJyJnOR85NVVFRV\nnLFjxwK+gnkKsskQiYz8PAhRF4sliQYNmhEdnYLZrGG3e7DZUlWENBeZIlUNelkuYDLZOHv2bA71\neQnDqaL234FixSrSpUsX5Vx9eK7vkU2KKLWWqQjRBoPBhdGoYzJ50LRCzJ07N9fzlSr2UchxvY/R\n9WK8+OIcihWrgK63wGIZiq5H8fHHAV466TBnBq1zNUIUpUePh/3bZGVlMWPGcwok7CYA68nE4Uj3\nY8MuXbrEqlWrWLFixQ0pxoMtMzOTmjUboWlNEGISul4yV82PvOzIkSPK+fmu4xpkbTPQOZbCTf0Q\n4il0PTJXfrmTJ08SFZWkIFHzkKL2NgYNegyv14vX682zs3r06FHi4tJwue7F5apPcnJJTp48idfr\nZd68+RQrVpn09Cq88caiAp1TbGwaAekAL7reMleda5C4QJerXJDzu4amRd+2tPyHH35gyJDhDBz4\naK4qad9++y3h4Ql4PJXRtBj69x/qd5AjRz6FprVCoiouoWnNeOqpCbe8litXrjBz5rP07j2Q+fNf\n/cfdZJ/ddc7vypUrjBkznoYN2/LIIyNyDDmvXbsWuz1ZObN7VFSUjRC1/Txuw4c/TiBV3IekaQ9j\nypQpfP755/6H/ty5c6SlVSRUy2IcMlIcgxCrsVga8sADPbh27ZrqvJ4O2rY2MsorjRBWHnqoP/36\n9SNUFcyLbErEEUzRLuE7PoHmdxHCwYsv5u4AP/30U6pVa0SFCvV4/fU3AEn48OqrrzJz5ky+++67\nkO2/+uorNC1CvexLESIGjyc6pG7Sp88gdL0OQqzAYKignPhcNK0FtWs3+UfUSj67evUq8+bNY8SI\nUblKF+ZnXq+XBg1aYLfLtNdsbo3BkEogkjyN2exg5MhRjBo1mm+//TbPfR07doz09PIYDGXUtT6N\nrldi4cI38l1Dx4691PSIr0QxhH79HmHhwjfVyNYWZMqfzJIlS3nttdd47rnn8izOr1wpQccWyzB0\nvQXFi2fkGQlLjZKq2Gx9EOJ9NK0t5cpV4eGHhzBhwqQCp5u//fYbI0c+yaBBw/xTFHv37sXhiMRg\nGIsQU9D1qBwqgyA74rt27cohOSDB8KuDnuWcYPiCWlZWFrVqNVYwqhcxGCqg67E8++wL/zjFv6uc\nn9frpXHjNuqr8i42Wy9Kl67qD6mPHTvGwIGPkpBQUjm/TkiMWz10PcyvfzFz5kxstgeCvprvU6JE\nFUB2sWbOnEnt2o2pUKEebndSLs4vBllML0mdOg39qvJmczwyKlyMrCG6kBMCHyFEHA0bNmHHjh1I\nrOIu9aJKcSM5hbEt6Dizkam4/KrLbrKdsLB4Zs0KUEOFztu6aNmyY4FSjF27dtG0aXvKlq3F8OEj\nQrjkMjMzVU3HR+yahdVahjp1GjNjxsw7QqZZUDt79qyfsODMmTOMGDGamjXvo3fvgVSv3hBNa4oQ\n03A4KjB4cP4qY8FWuHBpgtUBhZhNr14D8v1NmTI1kPjSl9W1epeGDdsqct2VQftagqbFoestsVoH\no2k5xXR89s033/DMM8/w6quv5lsCWLlyJeXK1aFQoTTS0ytyzz1N0fUiyIi+CxZLOO+//36+6z94\n8KCq7Q1HMgxFs3btWrp27YvBMD1o/YuoU6d5vvsKtm7dHgqa1/ZisTxCnz6DCvz7YNu1axdOZ4mg\nj9o5hHCjaem8/PKrt7RPn91Vzu/w4cPY7VEEUh0vLlc5Pv/8c06dOqVS1ccQ4nWs1hRFwDkaIWZj\nt8fy7ruy5nfu3DmKFauAw9EETeuDwyFTohUr3sNuj8RgiEaOn23EbK6C0ZiIxPvNRaamjyJEOXQ9\ngc8++4yhQx9XknmPIhslnZDR4dygB+gd4uMlGHPOnDmYTE6EMGIyhVOyZFW6d++NrldEdmg3qN/7\nIsGHkLjBowjxPbpe1P9gjxgxGputsYoy/kDTmjF27MQ8r+exY8fo0KEH5crV4aGHhuSa0l27dk2l\n8Of863c6W/PWW2/5t/nrr79Yvnw5y5YtuyNF7dzs0KFDxMSk4nLVx+WqQqlSVUIi/6tXrzJnzhyG\nDBnO8uXLbyoyqFWrqSLDkM+V3d6ByZPzbjRt3boVs9mjPnLtEaIomlaPSZOmc++9bZHNJN+9fx6j\nMVgYaS2pqeVu+TqsX79eaTt/iBAb0PVianZ4f9AxmmG1unIdSfPZ0KEjgqYlQIiVlCtXm9atu163\n/rVUqnRPnvvxer0hmcB//vMfkpJKqFpwTVJTS99USSTYNm3ahNsdPEqajcySFlC9es4a7s3YXeP8\n/vrrLypXroMcTwvocbhcGWzfvp358+ejaQ8QKH43V1/lLsjRsS4ULVrRv9+LFy+yePFi5s2bx4ED\nB/B6vbhcUcp5VQ+62JkYDDYMhnTl1L5Sxzcwf/5rzJ79ksK6LUamt38T6NoG628spGrVe/3Hf+ON\nRWhaEWSz4QM0LZYWLdrgdCbi8SRRqVJ1JDylsXKEu4L29RIPPtgPgMTEUurvVZB1w3F5sglfvHiR\npKQSmM2jEGIzNltXatZs5HcSO3bsICOjPqmp5SlRohKa1ggh1mIyTSAyMsnfiT1y5AjR0Sk4nS1w\nOlsSHZ1yR4Cu11vz5g9gMvmgSV5stm6MGvXUbdn3/v37KVQoAbf7PhyOcoSHF6Z5844sWfJWrtuX\nKVOTUIxoN0qXrkhmZiY7duxQneIpCDFejT4+FLTtb4SHJ97yWtu27UYoxOhjZGYQLMHwEEK0ZODA\nR/PcT+/eA5E0ab7f7CQtLUNpjBRGTtFsR9dL+ufIg83r9TJu3GQ/F2OrVp38hLQXLlxg3bp1rF+/\nvsBNrNzs3LlzREenIAWq9iD1nashxMvce2/bW94v3EXOr0WLjlgsDyHnezsjxHpMpkdISyvH5cuX\nmTNnDnZ7b+QYWAwSdhKJHG37BCGaYDB48mQLzszMxGAwIYkeyyMjxm4I8byaXiiGLOCCENswGHR+\n/vln7rvvAWRq60VGfuEYjamEhcVgsXiQEo8vYrNFhEwQVK7ckFCSgPkYjeHIhsc0dD2SJ554goSE\nokrHYJF/W7N5KMOHj2LPnj3qb3+ov32GEK48U4xNmzbhcoU6drs9kqNHj/LDDz+oF/YthPgXdvs9\nVKxYi6pVG9G+ffeQLmKXLn1Dal0m0xi6dOlz+266suXL36Zz5z4MG/Y4J06coHjxKsgpnSeQkfgs\nWrXqUuD9HTlyhNdee43Fixfnygt36tQpXn/9dZzOKIzG0QjxBrpenGeeeT7HtgkJJQhlR5kZ4mi+\n+eYbBgwYysCBj6pRuQQkO9ApbLaOdOrUO9+1Xrt2jSeeeJqyZWvTuHG7EMGizp37ENqtX0ZERFEM\nhmbIGfflCBGJwdCPxx57PM9jbNq0CV2PQ2YaX6HrVfz8gkuXvkXx4lVIS8vghRfm5BpFS87IUkjK\nuItYLG3weJJIT6/C3Lkv+39zs7W5v//+my+++MLPFP79999ToUIdDAYPcgprBLoeya5du25qv9fb\nXeP8wsMTkbOYF5CMxCUpXbqKv4536NAhpY9QRL3ATxIqfXcBIUx89NFHeR6rQoXaGAyPI7FhXZC6\nq5UVq0p9pJrZ/eorm07ZsjV46KFHQvjoDIYnqFOnMZcuXWLXrl107tyHTp165xD7qVmzqXpIfet7\nllCG6Fe4774OXLx4kWbN2iLrhA9htXYiOjqF48ePs2LFCpzOVkG/ASGc7Nu3j08//ZQpU6ZQvnwt\nUlLKM3DgY3zyySdKTNpX67yMzRbO8ePHFa/e0KD9HMbpjMr1OtWu3ZwACByEWEWtWs1u0x2XNm3a\nTHS9OEK8jNk8mPDwBCIjUxCiFrIkEYYQDkwmjdmzb0wx9d133ymaqgdxOJqTlFQiV0zhc889h9nc\nRH1guyHEWxQqVDjHdg89NARNa4nUu9iDriezdu3aPI//xhuL1DSPm7Ztu94QFtOz58OKWWgzBsMs\n3O4Yjh49CqAIISKR0dALaJpUhLvnnubqupRAiB64XLmTEQSbHNGsTFJSGcaNm3xTnVSJGpgd9Bzs\nRo55bkHXi9OxY1ccjgjMZjtt2nQpUAT4xRdf4PHE4nZXwm6PpEqVepjNGlarm9KlKzN48FAee+xx\n9uzZU+B15mV3jfOTYtnv4Mv7Na05c+bMISsri0WLFjF+/ARmz56N0agjQaKvqxfFd2POIISZDz/8\nMM9j/frrr3g8McihaZ+DOIfBYEPW7z5D8giORYgOGAx2GjZsg8MRiaY1w2Jpg80Wlu8xfLZ+/Xo1\n9TELIWZiNLoIBSu/S/36rXjggZ6qo7kOIXphsTj8jnTv3r3oeiwB5bENuN3RNG/eHl0viUyZnQjR\nG4ulDtWr1yEqKkHNIi9VAuYdAR/e7cGg439LRETOlx5g0iQpUiNR9mfR9XuYMCH3+lhWVhanT5/m\nypUrN/ViSbKHA0HraYFM7zORac8z6v8fRNcTQrjxcrNatZoiQeVyf1brQ4walXNetXv37siMYQFC\nzEGICHS9EIcOHQqJFi9fvkzXrn3RtDDCwuKdu5SYAAAgAElEQVRvK+GmbDjZCfAsgqY9yPz5gdTz\n22+/pVevAXTt2i8EwrNx40a6d+/PwIGP5kvhfjts7NjxWK3BkyCvEeAdXK30YPYjxFns9g50796f\n8+fP88QTY2nZsgtTpszIIUIeG1uEQLPoFLK+9xFCZGOxDKJly063bf13jfOTXZ8onM6OaFo5UlNL\nsH37dpo2bYfDURuDYTQOR3FiY4tiNE5B1t4KIcRg5JRBFTQtKl8a7BYtHsBsroSkeffd0GuYTA6V\nwk4joLxVXOk8LMFma66omJoixHB0PZLt27fneZzs7GweemgIRqMVg8FMUlJpJk+eorCHGxBiI7qe\nyrJlyxUf3UkCL+0jIUj655+fjc0WpqZHNIxGK2ZzAnLou7u6Bo2U44jDYBiNxVKKxMSSTJ483f/w\n/fnnn0RHJ6tphxfR9VTmzn051/VnZmbSo0d/TCYrJpOV7t0fynXy4e2338Vmc2EwuBHChMWiMWXK\nMwW675Lz8GTQfeitoopspA7GNQKO4WHmzJmT7/7S0jKQzSTf/ubRpUvfHNuVK1eHUMjRKEwmD7qe\ngNXq5PnnZ+ey99tna9asweEohCQzLYxMlUHX2/H66wVnSL4d5vV6843Wzpw5Q2pqaZzOJphMPvIQ\nX8d8MZLdyHcd9xMTU5SKFWtjt3dGiEVoWhNatHjAnxZfvXpVlZ6CZSceJFDf/ImoqNTbdn53jfMD\n2e1t3LgVZnMMMkV0KEfk6/6ewGJxkJxcEl2Px2zWiYxMxulMomzZqrkCQA8fPszgwYOpVauuihr/\ng8TmTUaONnUgJiaNL7/8krS0spjNhdC0kkj2ZV/7/Sqy2eBjTXkjX2jAs8++oAglzyDEBTTtPh5/\nfCxvvrmYUqVqULJkdRYufBOA8PAEgiEYmtY2JAIA6NSpJxZLMyTBwFkkoUBvdX188oiHkVHgfxDi\nHHZ7TvW148ePM3Lkk/TqNYBVq1bd8N5cu3Ytx5fbZwHx6NYI0QNZL/0dXS+W675PnjzJuHETGDJk\nOJs2baJnz4exWhsiCVgXIKOxaGT05ivGy9Td6axww/UOHPgYdnsrZAf7CLpemiVLcrJVV6p0D6GM\nQckEhOwPoesJ/4g9OD87evSowl8uQHbv30CIaEymocTEpOQ6n36nbP369bjd0ZhMVgoXLpGD29Fn\n58+fZ9myZYwfPx5NC1dSsNOxWMIwm4MJgd8lNbUcTmdpAoqGl7HbI/zpPEB8fFECGd4JJNWcDwL2\nGhkZ9W7pfLKysjh48GBI1/mucn4SnFuYgGzkbvWFvIqsz7XHZApjy5Yt/P777zmYiIPt7NmzLFq0\nSJE2dkF2cnXkONxvSKnKWISoSuPG7QD5Jfz222+ZO3euuom+L1Q2UhvhR/Xf66lYsX6ex27atAMy\nGr2IbMZMz5OQ8bXXXledt8lYrQ+SnFwyB7C7WLHKhHaDX1MvbfCXF4RI8TtSl6t0vsDff2pvv/02\nLtf9yBrsT0FrmMaQIcNDtv3zzz+JjU1VDa1p6HoCCxe+SZ8+AxVBQ11kI2shRmMYTmckRqMLl6s5\nDkc67do9eMOi+uXLl7n//m6YzTasVgdjx07M9TdLl76lIvAPkKQLhqCXFXS9d46Pz+2yjz76CJMp\nERnhVkeIFIzGQnTp0vOWBvdv1Y4ePapqilvVM/46sbFFbjjX/P333zNgwFD69RvMpk2bKFKkDLre\nHLu9Hw5HJHPmzMHtrhz0LGShaXEhH+Gvv/5aibSXxWYLJz6+GE5nRdzuZoSFxeVa69u7dy9jxoxl\n3LgJuTLuHD58mNTUMuh6Ilari/Lla1K1aqO7y/nNnz8fo7HhdS+0AyHaIut0byHE03g8sezatYsH\nHuhJzZr3MWnS9BAc0t69eylUKAGzOZHQMa/RyNGzj5At9aJoWlE/3OH48eMsWrSIpUuXkppaRmkt\nfIYQPVUnahOS5rxsntMYIIvlJtNDSGhMDYSoiK5H5znUv3HjRh577HGmTZueq0Nv3LgdRqMPlOrF\nbO6MJDV1qzWBhNQ4EGI3BsMLxMYWuSUOtIKahHskE2hAybXZ7e155plQ3dXnnnvuuvnaz4mLKwbA\nwoWLsNvDcLlKhvAMHj58mA8++IDt27ffVDcxKyvrhtsvW7acGjWaUrduC1yuGAJR5nkcjpK5ylje\nDnvyySeRU0G+lH4mBoPnjhOXXm+5M9rE5Ttj7rOsrCz+85//kJmZyfnz51m4cCFz5szhwIEDXLp0\nieTkUgpqtRWbrTeVK9fLcT8uXLjA7t27OXr0KOfOnWPhwoW89dZb/uZmsO3atQtdj8RgeAKT6VHc\n7pxcizVqNFIQKS+yjlgUOfJ6lzi/iROnYTTakanbXnVTlqvoTCdAOQ8WS1903YPJNB4hPkLX6/rp\n1gElbOQrzq4LusnLESIBt7swNlskUVEp/mmKffv24fHE4nR2wOlsjKZFYDSmIUQGQtTHanUTF1cE\nlyuGMmWqM2fOS3kW+E+cOKGaHYPwMRZbLAND1ngz9uuvvxIVlYTb3QiXqxqlSlVhy5YtGAx25QBd\nSBbnGITQKV68Qo6RpNttJ0+eVASsrZG1oNZYLNUpVapKjk7nhAkTrwPbHiQsLN7/99OnT/Pvf//7\ntsoWFtQ2bdqE0xmFx9MYXU+mZ88Bt4U5JTcbMGAooRCW/bjdCXfkWPnZN998o7RSfCD3X7BanTfs\n1u7YsYPw8Djs9giczgjWr1+fY5vjx4/Tvn13SpeuSc+eA/LV4N22bRtudwxOZxp2u4c33licY5t6\n9Vogm5vymhmNE+nevX/INhIFcizouo5BTmrdBc5v/fr1SmaxBjKds6mXOgwhNEUhH+gMmkwDsFjK\nIJseixBiFkaj1R/9yU7if5C4vIrIyYmDSJ49jU2bNtGwYWvsdjdxcUVZs2YN9eu3xGAIbuv3QDLC\ngMTZxSon0wkhFqDrNXLF2+3evZtp06aRnFyO68WAypatlWP7G9n27dsZMmQ4w4eP5I033mD9+vVc\nuXKFhg1bK2qvjsh62QaE+Bwh6mC3x7Jy5c3pq96sPf/884qeaTeydjUMtzs612hz9+7dqj74EULs\nRdOa0K/fI3d0fTdjx44dY82aNbcszF1Qe+ONN9D1asrpeDGbR9Kkyf139Jh5maSNKobD8SC6HnfD\nbvaFCxcUP+Ma9Txvw+GIzDVaK4hdvXpVIS98wckPaFokv/76a8h2FSvWV8+27z16g9atQ/VNSpWq\nhiyLQUAPe/Hd4fwyMuogU1Jffe0BJBlAC8LDC2OxxCPrW2sR4kXs9nDs9gbKUcapqMdFzZoNyM7O\npnLlBoo6fYH6XRiycTIOg8FCzZqNFU/aaYTYjKZFKmcVXFd7VTk6kNMk96uL6qsD/o3ZbA/5Wq5e\nvRpNi8JsfgyTqTSyOyxlIIVogtkcwezZBROj/vXXX5kyZYqSIpyK0TgIi8XDI48MC3oQjyKhNIOR\nnc5I5NTJUnS98E0rkN2MTZw4CTnnXBgJuYlA18Pz3H7Dhg0UL16FuLh0Bg0aflspkPKy7Oxs3n77\nbaZPn/6PqJFu53q6d++PzRaGw1GY4sUz/EqEt9O2bt1KUlIpNM1DnTr3cfz48RzbeL1ePvvsMxYu\nXFig2vDevXtxuUoEvR/g8dRg69att7TG33//XY3wBe+vaQg7EfiahxWRaom70PUi/jFWn+3Zs4fw\n8Hg8nroYjfEYjUWQ0zl3gfNLSSmP7Lz6LsRChJBRmaYlIzUrnkeIOhgMbj755BPs9jAkzONV5cRe\nQggnL7/8MgcPHiQxsTh2exyyUeHTvNihRtyMSNZj6cg0rS916zbGbm+LbFKcwGIpo+Qq5yGj0AUI\nEVwnuYrF4ggJ65OSSiMbHLLTJVlIdPX79kgZxvAbplVPPz1Z0Tm5kcQNH6q1DsRkKkPFirUV0+7b\nyHpVUWSkGpxSfUyFCvXu2H1bsGCBura+1OkzrFbPHUsZb9a8Xi+tWnXC4aiK2TwcXS/C+PF5z/L+\nN+348eP88ssvt4U553r7/fffVTPjI4Q4hdn8OOXL559xHD9+nFatOpOaWp4WLTrm2nw5deoUNpuH\ngB61VB28PlIrqF2+fPk64a5j6HpsyKQL+AhppxAbW4zExJK8/HLuzai//vqLTz/9lO3bt/P4409R\nv36ru8P59ejxMCbTg0hoyQWEqEaXLt1YsWIFbvf12hSRHD9+nNq170U2QUK7nZ06PQhImMb+/fvp\n2LEnDkcqbndzdD2SadOmqUjRiYSzbMfprMvixYtp3bozJpMVs9nOiBFPsmjRYho3bq2c0EsqypmG\nEJ9jNrenYcNQGh8pdH4oaD1jMBrLEND+uIjJZM0XDPz111+jaQnI6YN05LhXaeTUyxSEGI7TWYZX\nX30Vlysat7s1FkthdT7BpKdrKF/+1iT/CmKvvvoqNluXoON5MRrNd7TJcjO2a9cuHI6iBEYWj2Gx\nOP5P6or/TVu2bBkuV/ug+5KN2azled5Xr16laNHymM2PI8TXmM1PUKRI2Vwj8zlzXkbTYnC7W6Pr\n8UyYMO0frfWDD1ai65F4PPXRtGgmTZpx4x/dhN0Vzu/s2bNUr94Qmy0Ci8VN69adyMzMVCwv4erF\nfwshniUpqQTZ2dlMn/4MktbKF3n8jRBOxowJRfV7vV6+/PJLPvzwQ/bs2aOKo77u3scI4aJChVr+\nm33t2jX/F9nr9RIRkYhMLWOQaW8EdnssffoMylHY79y5D3Z7B2S9cRd2e6z6Wn6AEAex2brRpEm7\nfK/H8uXL0fXGyHTeF7GeQabukSp6rcbmzZs5duwYK1as4JNPPmHVqlUqWnwNId5B15NZujT3of1/\naj/++CORkYlqTb5I4HWSkkrekeNduHCBq1evsm/fPtq160b9+q2ZP39BvlGm1MltFOKcNS3mv0LQ\n8N+0uXNfJiGhBLGxxZg4cRpr167F6axIAKP6GxaLlieM5bvvvsPpLE6gnOPF5SrF7t27c91+3759\nrFixIgeH5K3a0aNH2bhx4x1p0N0Vzg+ko/njjz9CCqibN29WzY6OCFEJiyXcf1N27dpFZGSccoDF\nkQDZ8pjNHr766iv+/vtv/vWvf4UALCU8I1QZym6XrMW5vUhHjx5VtPTvIQHOH6NpDXnzzTdzPZeL\nFy/SoUMPdL0QUVEpvPXWMrZu3UqxYhmEhydy//3d8u1+gaxf2GwRyC5zcFSbiBBDMZufIjExPdfZ\n0W3bttG48f3UrdvyhuI4/8TS0zMwGOYiSwJOhChEoUKJeQJlC2per5fp058lMbEkyclleeGF2dSp\n0xSz2Y7JZFNTOM8gxAocjjJMnZr3NMmJEyeUpvN7CHEGo3EqqallbpolODs7m8WLF/PUU2NZsWLF\n/zdpPcDbb7+DrqchNWG+Q9cr8NxzL1CnTlMcjnqYTCPR9eR8p1Z+/PFHRcrgGyS4iq4X5ocffvgv\nnsmN7eDBg9x7bxtSU8vTsWOvAtGs3TXO73o7ffo0hQrFKsf3Pj7NXZNJo337Lio1fFClhvchpx5G\nIUR7HA4PTmcUbndF7PZwpk9/DoCxY8cRmIIAIQ5jtXooUSIDo9FMXFxR/xzl8ePHSUgohuxAN0Ti\n2b5F1wv7Kd7vlE2d+gyyVijrmQbDbOz2SNLTq9C6dZcQh/7ftuzsbAwGIwGs2nkslk688MIL/3jf\nkj6sHJJWbAdGYxRmcw/kvO9/kLVNH83UnhuOQu3atYuUlDJYrQ4yMuretP6F1+ulTZsuOBzVEeJp\nHI5yPPxw3hRS/21r0aIzEqjt+0Cup1Kle7h27RqLFi1i6tSpfmGuvMzr9dK0aTs0rTFCzEPTmtKo\nUev/r5z8uXPniIlJxWSaihBfY7X2JyOjzg3XeFc4v/3797N48WI2btyI1+vlr7/+Uo7nASTJQBiy\n3uVFTjBYCdTWLiAnGxao7cKRNboJSLnJKphMYWzbtk3NVA5TUVQHhCiEwaBjMDyN7MiuxumM4vjx\n4/Ts+TBm84igB+txjMYwxo2b8l+5Ltu2baNIkXLYbG5Kl67G8uXL2bNnz/8XD6XFEk4A8nABIVJZ\ntKhgOhb5maQBWxt0zRMQ4oeg/34GCV8CIfYSGZnC1atXGTRoODExaaSlVczRLfwn9t133+FwJBMQ\njT9zyzKKd8IefLAfBkMwWcZrNGiQO9djfnbt2jWee24WXbv249lnn89zpPF2286dO6lbtwUVK9bP\nl7b+k08+we2uHXSe2Wha9A2DgLvC+el6FE5nZxyOUtx/fzc1EdDVf6Khg+6HkbCV4JSwkXpRJiMZ\nUJ5VEd7zyBGeOhgMTsVefBbZYVqGBOhWQ+L/ZNjva7fXq9eSgOg1CLE635G2O2UHDhwgOjoFt7sK\nup5M8+YdbqpLeOrUKRo3bouuF6Jw4ZL/GPJx+fJlxWodhQSRJ2MyFffrp/wTa9CgFcGAVlnO8GnH\nehGiGUK0RIiV6Ho5Jk6cxsMPP6pIWX9ACMmkcyMGmILatm3b8HiC+RHB6SzCjz/+eFv2/0/tp59+\nwuWKxmR6FIPhCRyOyNt27rnZnj176NSpN82bd+KDD/4ZjvTf//634pdciGSrrujnGrzetm3bhtNZ\nlsAY4nmsVvcN2aPvCufnY7YQ4jIOR2kefLDbdbq0CcgxM5DSk24kHVEWElriUtFcsEMsQUAf908k\nI4oHo7G1elHeRnZ9Y5F4wQoIcRiHI40vvviCiROnoesNkU2Hi2haU8aMKZhCVVZWFmPGTCAtLYOK\nFeuxefNmsrKyePLJcSQnl6VUqeqsWbMmx+9+++03+vUbTLt23f01u2rVGmI0zsIH4NT1uixYsKDA\n17dOnaZYLAORQ+Tr0PXIf1RczsrKwmLRkODmdQjxNQ5HzdsCqt65c6d6IcZiNI5E08JxOqNwudri\ndNagWLEKNG/+ALVrN+ell17B6/UqDsDAbLHBMJbRo28P+/PZs2eJiCiMwfAKQvyByTSVpKQSBY6M\nDh06xIcffpirOtrtsoMHD/L00+MZM2bsP6655mc//PCDgtA8gySBTebNN/P+4Hm9Xp577kXS06tQ\npkytHAJWTzwxBoNhTND7+i1xcem57iszM5PKlesp6rd56HptunbNydhzvd0lzi9AceNwPMjYsWPV\neNgnCPELJlMlNQHSFAn7uA8JOzFgsYQREZGoaJV83dFLyM6oL2U6hGyMuAmkxYkqYswmgKGLp337\n7ni9XjIzM+nSpQ8mkw2TyUb79t0K/NAPHz4aXa+NBE2/g65H0r17X3S9loo6P8oRoRw9epSwsDiM\nxjHICZKivPjiXCIikhDi16CHZArDho0s0DoyMzNVlHbV/3td78lrr712S/fKZ5LvrxhCTMFub0PZ\nstULJHp05coVDh06lO+2e/bsYcSIJ3jiiTH8/PPPHDt2jOXLl/PRRx/l+juJrfzMf35Wa2+mT88p\nzn6rtm/fPsqVq4XLFU316vcWuG4oqeIj8Xiao+vJ9O8/9Lat6f/Chg4dgSxB+Z7DTylWrHKe28+a\nNQddL4NkbFmNpsXx7LPPkp5eiUKFClOiRHlMpmFB+9tJ4cKl8tzfpUuXmDRpKl269GXu3HkFalzd\nUee3bt06ihcvTtGiRXN94JYuXUq5cuUoW7YsNWvWzJWxQQiB0fisckAfYza76NixG08//TRudyJC\nuDCZyipige7IQX4vQuzF4ymMridgMIzHaCyBwVAKISagadVUNDhIhdVFkbg5O0KsUg60PaFMy5+S\nmlohR93h0qVLeVLj52VRUakEi81ILsJIpEZBJkJMR4jylCtXzR+6z5gxQ7Ge+NazG4ulENWqNVAz\nzF6EOIfDUYUlS5bkeezdu3dTrlwtIiKSaNbsAex2FwE2mmycztoh4u63aqtWrWLYsJE8//zzBWLw\n3bBhA05nBLqegMMRmAvdtWsX/fsPYciQ4beUTr777go0LRYhJmGx9CMmJuWWR65ul2VnZ6v6si/z\nOIvDkZYvB+TN2p49eyhevBJ2u5ty5Wre8VnuQYOGEUrGu520tIp5bl+qVE2E2By0/RxMpnAkkemv\nWK1tMJlcGI0TEeJ1dD2V+fP/2Uf5ertjzi8rK4u0tDR+++03rl27Rvny5XO0x3fu3OmXTFy3bh3V\nqlXLdYHFilXAaLQghIbBMAoJJHYhxb57qehsOrI+dxk5F/kUFksEsjMoa0IWS2UaN25KjRr1MBoH\nIJsb3ZC1Kaf65xdkvWoUsuZ3DSGysVp70adP3sQDO3bsoHbtZpQvXzfX4uyuXbsoXLiU4gz0IOds\n5Y03mR4iPDwOqR/SC9k9fhejcSApKaW4cOECkyZNvu5L+BNCRBETk0pSUkmczjRstkJ0794/z8Lw\n8ePH1djbmwjxKxbLYJKTS6PriRiNo9D1xlSqVPe/MloWbGfOnAmiUJIvjsMRyfvvv68E2adhMIzB\n6Yy6JYjFtm3bGD58FBMnTvo/d3wgNSosFkfQvQSXqyNLl+bkF7wVO3v2LIUKJagP+2kMhheJi0sL\niYxv9z3++uuvg2p0H6PrJfNlNsrIaEAwaazBMB6TKZiC7SJGo4UePfrTps2DrFjx3m1dL9xB57dz\n506aNAlIy02bNo1p0/JGfMsObk4GC98CJbfbU0EX5z0koWkNJMFlJmZzDDZbDC5XCVJSSmO3u5G1\nLPkbs7knffv2pUKFOlxPKiDnT9OU0xuKnO5IQohwLJZYMjLq5InB++6779SNfxMhPsHhCC3OHjt2\nTL3cK5DsxI2QTZkXlQN28MADnbDbY5CkDReCXop6fPzxx+zfvx9NK4TsWm9G8r2Nxu2uwI4dO9i/\nf/8NAbrvvfcebnew5kc2FouD1atXM3nyZF577bX/E03er776Cre7QogzcLszKFWqOsHRt8Ewkd69\nB/7X13e7zev1KtLON9S5/Yiux9ywJvf333/z0ksvMWPGjHw1LLZv347HU+0655rO999/z/bt24mK\nSsJgMJGYmB4yt5udnc0XX3zBhg0b8sXJnTx5kmeffZYJEyaGgJm3bdtG/fqtqFKlEa+88lq+yIN1\n69ap0tVMDIansdvD0bTg2fj9BRr1vN7efXcFUVEpaJqHli075YubvWPOb8WKFfTtGyg6LlmyhMGD\n846cZs6cSb9+/XJdYGZmJp0790aIF5AsLY8rJ1VVOb5eCLEYTXMzevRo1qxZw9WrV+nQoQd2+/3I\nmtgjCOHE6ayH2RyG2VweWfu7qBzfZOVQwxDCSWRkEpMnT+aDDz7gp59+yreGMHLkE4TWO74hIaGE\n/+/vv/8+dnvw3O9MpLjSAHUu64mKSmH16tWKtusygYe2oZ+leOXKlRiNhZTDn44Ql9D1JPbu3Zvr\nui5evMiHH37Iiv/X3nmHR1VtbfydPufMTBopJCEQCAGSQBIg9N47KHDpioBSpUoTqVKkXKV/Fxso\nXOAioCIgqJdeBQHxiqAgAWOUjiIQIDPzfn/sM8nEJGQSJk3n9zx5IJkz++x9zsw6e6+91rs2buTN\nmze5c+dOms3Vmb4rdoVarTGDwfv999/ZvXs/BgdXYLVqjbKN5Hcnv/76q5Kp48gGSaTR6MuKFWsx\nPduGBP6P3br1y/f+FAT/+9//GBRUlpIUSIPBwnffXfXY42/dusWwsIqUpH9Qqx392MLnZ86cUQKT\nHQ/RWzQYfBXxgUCKMCQ7gX+zRIlSTElJodVqVUpCRNLLqzF9fUOyNLBXrlxhYGAZ6vXPUa0eT1kO\n4K5du/J0DQ4cOMABA4Zx2LDR/Prrr1mpUnXl+zqDslyGS5fmXJjKmWPHjilCH4cIXKfB8Aw7duyZ\n7fH5Zvw2bdrksvHbvXs3o6KisnzaAKBWa1S0/b0ogpVnU2Q4JFAImWqpVnvRaGxPSepHszmAx48f\n571799inz0D6+oYoBcwdGwM/UK02Ua02UIh+tqLwv8QTmEogiXq9yWURyVdemaJUvadiTPezdOnK\nGcZnNEYxvd7wRAp/o+NLfSFNv65Dh+6UpI4EdlCrncTg4Ii0p5fdbme3bn0VCfz5lOXGbNu2a5ZP\nx1u3brFcuSq0WBrRYmlHf/8wnjt3jjVqNKYktSUwm7IcxUmTpmd4X5Mm7Wkw9KXQR1xJiyWQycnJ\nLl2HJ0HkhQbQ27s1JSmAixcvV5ziVShELXZSlkO5Y8cOksLXunjxYo4bN9GtsXsFidVqZXJyskv5\nzq+9Npd6vXOBqa0Z6lA7Y7fb2bv38zSZqlKjGUeTKZrDh4/j3r176e3tXNSLNJsjeebMGaW8ZgOm\nb369y8qV62Rq+5VXplKrHerUxmZWrlz3ia8FKdIUFy5cyAkTJuVJMPa1117LUEkRuPpYJaF8M35H\njhzJsOydM2dOlpsep0+fZkRERLaVpsRu7wgK6Sk904Nc7xPwY7ly0Rw5cgw1mo7KE+0qgVWsWbNZ\nWhubNm2iSlUxw0338orlvn37+M4779LPrzTTN0DErEiSSrqc5/njjz9Sln0pwmKEb9LfPzhNmdlm\ns7FhwzZUqRKUmV4wRYbGKgL7Kcv1OXLkeFqtVs6YMYelSkWxRIny7NChe6ZATZvNxnfeeYdDh47i\nv/71r2xzMseMmUC9/gU6lhFq9Wts3borHzx4wKVLl3LMmPGZwgtSUlKUWMf04kBmc1euXZs/OcCk\nMGLnz5/n3bt3+f3333Pr1q1pSrx2u50LFixkRERVVqpUi//5zwaSwl8VH19PKR05k7Jc3uXCSMWV\nsWMnUNSgTvf5+vuHZ3u83W7npk2bOHv2bG7dupV2u11xnQQxvQxEMg0GL167do2TJk2mEPh0tP8z\nvbyCMrU7ePBIZlQ/P8WwsJj8HLrLrFixgrLcnulL5/0sWTIi7fU9e/Zw2rRpaT/5ZvxSU1NZrlw5\nJiYm8uHDh1lueFy+fJkRERGPLT4sjF8diri8sAwGDKjA5s2bK8arDIUvLZDAewwPj01rIyampjJr\ndOyuHaTR6MPbt29z/PgplKTSFMGxQW6sllUAACAASURBVATmU6V6g6VLV8oULJycnMw+fV5g/frt\nOH367DTD8/DhQ2o0FgJrlAu/i4CJ7dp1zXA9li9fzgYNGrFp0zacNm0669Ztzaio2pw6dRatViv7\n9RtCWW5EYDO12gkMCiqbpWz9+fPnOWHCJI4ZMz5brbVOnXozY2rTfkZHZ36S//meiZKJ/6MQau1D\nvT4yg5FMTU3liy+OpZ9fGIODI3Ncrj0OUUQ9gCZTOCXJhx984JpT+6OPPqLZ7Owf+ok6nZTpft25\nc6fIqMg8Kbt371aWsscI/EKjsROfe25IrtsZMWI8TaYIyvJzlOWwtIfG5s2baTLFUMi826nRTGOD\nBm0yvf+zzz5TasocJXCRktSco0ZNeOLxuYN79+6xYsVqlOV2imsgMNMD3pl8DXX59NNPWaFCBUZE\nRHDOHKGVtmLFCq5YIVRhBwwYQD8/P8bHxzM+Pp41atTIsoMijS2FIqJ/JoVvaAGBQKrVQQSqMF2a\naCOBAA4alJ5jqdVKBOZQxPCFE7CwXr36DAuLUozijbQvEWBkxYrV0oo9//TTTzx8+DATExNZsmQ5\narUTCXxMSWrOnj37kxSOXrFD7GyYq7FECdclyB89ekSt1kChPuOYdbXj+vXrMxx39uxZms0BVKvH\nE5iWbZnMxYuXUZbrUCi+PKDR2IVDh47JsR/jx09SYiIHE1hFlSqGL76YXnBo3LjJlOXGBM4TOEpZ\nDktbiuaGu3fvKtqJjhojJynLJVxaYq9evZpmc3ena51KjUafZuju3LnDRo3aUquVqdUa+eKLLxWJ\ntL8nZdWq9+nvX4YmUwn26jUg1yFWDvbu3cu33norw6TDbrdz9OiJ1OstlOUQli8fl2162MqV77Fk\nyfL08Qnh4MGjCizdzRXu3bvHt956i/PmzctRebuYBDkvUz7klygKvJiVGZ6BQGMCzuv836hWG5iS\nksINGz5gTExdik2M0hQhJlOo04VTrw8j8DJF6lq60VKpQtM2EGbPnq/M6LwIGJRi345j/6BGI86z\nc+dOpS+OfOLbBPxYuXL2QZ5/5tGjR8qS8w7TjV8Hrlu3Lu2YpKQkVq1alyqV8/LnvSzLZIrawMOp\n0Rio1RrZpk0Xl74s69ato9HoLPV0jVqtMW1WVbZsHNPDh0hgYZZy/Tnx3Xff0WKJzHDtvb0b5Jho\nT4oHkpAeW08REzaQ9eunu1ieeWagIqH/iMBNynJ1rly5Ktd9/Dty8+ZNXrp0KV+EVIsaxcL4GQxV\nKfwUqQR6U0jGU/kSWigUVX6hEMycw2rVGnL9+v8oRVg2Uuj1B1Jo/lno71+OYkm4XHm/Y0dxEwGJ\nV69e5enTp6nT+VD4Gs9RhKU4J08L47dq1fuKarRZmf31UgytJdcxab17P09Zbk5gKzWaqQwMLJNW\nq1XUMTFRpPK949SPx5fJTElJyVLeKjvef/99ms3/cGr/LjUafdrTPS6ugXJNxesazUiOG/dylm09\nePCA27dv5+bNmzPlWf7222/KdXMUnkqiJPlnWXowK44ePcqoqJr08wtjx449M2yWhYfHMj0lkgSW\nZSpq48FDsTB+Q4eOplYrUas1U6UKyLA0FL7AwQQMVKt9GRhYlhcvXlTqci6jCHF5Qfm3LVUqf6pU\nBgqpqw0U8XxBFHm8ITQavWi327lx40ZqNOWcvui/KceOpWPZ26lTDyX27htl1leFgJ6hoZF5qon7\n6NEjTp06k7Vrt2K3bs9lKBVoMgVRSHd9ROHf3EfgGGU5losWLXXb9b5y5Qp9fIKpUr1OYB8lqT27\ndHkm7XXhe/KnWj2Bev0A+vuHZali8scffzAmpiYtltq0WNrR1zeEZ8+ezXDM6tX/VlK8mlKSArhg\nwZPLXpFkw4btqFItVu6bnQZDT06fPtMtbXv461AsjB8pfERDhgynqD3rSMdyFC03UKMJpVbbn7Ic\nz+7d+7FKlboUPr7pBJZQBBUbKDZNIimKDlko/IgBlOXmlKQS/OSTT0iKOCy12pfCV+gwtK9QLJ19\n2aRJa+7ZsyeTqofFEu02FVsHdrudQrnG4ddcRSCUGo0fX3ttgdv9WefOnWPLlp0ZE1OXo0ZNyBT4\n/PXXX3Py5Cls0aIVW7R4iq+8Mj3TknrGjFk0GHrQsSmhUi1hgwZtM53r8uXL/Oyzz7Ld7c9r/319\nQ2ixtKPFUodRUQkFXvvWQ96w2+1ctGgpy5aNY/ny1Z5oQy0nio3xI8kaNZpTSNb7UsT7CaFRvd7C\ndAHS+zSZwlmnjnPFN1KEy5RVDOYJAmKzQ6Px5tSpU/nRRx9lSkqfMOEVZUbYj8AAZVl7hsAKqlQW\nnjhxQpn5OVRDTlOSfF1Skc0tfn5lKJRqSFFcKYT/+Ecvt5/HFex2O5s166CEmqym0diVtWo1zeAn\nevbZQUz31ZLAiQw78PnN9evXuWnTJm7btq1QslY85I0VK96mLEdRBCrvoSyH50tqG1nMjF+nTr2o\nVs9RvvxHqFaPZOfOPWkyZQyB8fZuouwkOscj1WdG/b0PFCP6CseMGZ/t+Y8fP86EhASKAOhE5b1W\nAiq2a9eFrVu3p15vodlchUajL9ev3+DW8T948IA9evSjRmOgiHMUmy8REVUKLYzj/PnzlKQQpscD\nWmkylc+w1F+5cpVSEuAmgVQaDH3Zu3fmDJ7HcfPmTc6dO48TJkziwYMH3T0MDy6SmJjIAwcO5KiP\n5w6Eu8o59fR9tm3bPV/OVayM34ULF+jrG0JZ7k5Z7kxf31CeOXOGfn5hFAKlfxDYSK3Wi0ZjBQpf\n3mYKSaMAivQ4x0WdT6AGtdoXOXXq9GzPb7PZGB9fS1kuOySxPlOW3wuVGaGZBkMI4+PruX15NXz4\nOEpSOwqf4080GqO4YME/3XqOrNi4cRMTEpqxevWmmer7fvfdd5TlcKanydlpscRk0KWz2+0cPnws\ntVojtVqZDRu2ybE+iTMOtW69/lmqVNMpy8FpQc4eCo5Zs+bTaCxBb+/aNJmyT6lzF02bdqKzYK1K\ntYDdu+dPSmOxMn6kcMj36vUMtVqJZnMkLZZA6vVmOmp4AFHU6QKVVJ1PKUJhalGkwJmUZfNoZTlb\nnz4+wVlqsH3++edcsGABX375ZcpyPIVKsL/SlsyMisLdCSyl0fgMhw0bw6tXr+Y5BuvPREYmMGOx\n9BXs2XOAW9rOji1btlCWS1HUA95CWS6dtvSwWq3s0+cFit3t5wjspU43kpGR8VkqhaSkpOTK6Dl4\n4403nNS6RZB2SEjWYpYe8gehphxMIDntHpjNJbLNKnIHhw4dUkRCZlCleoUmk/9jRRyy48SJE4yL\nq09//3B26tQr29TZvFDgxu/69et8++23OW7cOKV62UUKZ/rzijFKX/aazZ0oSd4UEuffUa9/nhUq\nxFKWq1Pk7k5TZoQSjcZABgSU5tKlS1m9ehPGxNRl8+btaTKVp043inp9NDWaysq59lH43fTK0ttx\nzmHKzPM9Go2BNBh8qdNJnDXryeuMNmjQlkK8QZxLpxvCl16a+MTtPo4WLbpQhAc5xvcfNm4saj+8\n/voi5cFymcDzVKnCGBlZ1e1SUdOnz6BaPdGpD5fS8p/dyRdffMF+/YZw+PCXXA6z+buwefPmP6kA\npdfFzk9OnjzJ4cPHcPTocXmSMPvll18UAYf3CZynXj+Ideo0z3RcsTB+SUlJLFEilCpVKcXQ6SjC\nV8ZRCByUpEgtI4FvKUkB3LJlC6tXb8ySJSPZpcsznDdvHo3GQU43MkVpx04R/2emCGvZrMwKr9ER\n5yZ2ijcpy7xpFDu+JZVZ4CTlvaepUpWjSjVJafNnynK5PCVoO/P111/TYgmkJD1Dk6kjQ0Mj8933\n0r59jwwGF3iXLVp0Vl7r+SfDuIdVqtR3ex+OHz9OWQ6kcDGcp9HYPk/pXI9jw4YPKMshBBZSrZ5I\nb+8gJiYmuvUcxZkzZ84oslMOX/dOensHFfkA6A0bNtBiecrpM2qlVitlckkVC+P37LMDKYKNX1AM\n0A0K9WUNRf2Nrylk52VqNEa+//4aJicnc/bsOZwyZRpPnz6taO4FEvhSMXzDKaSsHBfITOGc/54i\nji79aSdJNRVDqaNIj4umkN/+gGIDogwNhmCqVEamp8qRGs04vvrqq098DX766Se++eabXLVqVZr4\na35y8OBBSpI/hU9zMSUpgHv37iVJjho1PoNggkbzKjt06JEv/di6dSvLlo2lv38Z9u8/zO0bPJGR\n1SlKIYj7pVa/xAkTJrn1HMUJh/jBiRMn0nbIlyz5PxqNPrRYommxBKaVbi3KbNu2jWZzLab7pH+l\nVmvMlIZXLIxfYGBFZfbliO97SCFEIFNkXuyj2NBoSoOhAhs0aE1f3xBqtYOoUk2kLPtz7969/OCD\njUodDB3V6hIEflDaO0axgWFV2i5FsTlyh8B6enuXZJUqtanVvkgRF+icPfAq1eo4vvzyywwPr8J0\nddpHBOKp0ei5YkVm+e3Lly9z9+7dGQKZixJHjhxhz54D2KNH/ww7rbdu3WL58rG0WOrTYmnJwMDw\nXNe7LSqEhcVQ1Exx3MtZHDHipSyPvXHjBjt16sXQ0Eps0KCNW+MSiwKpqals27YrZbkULZZolikT\nnZbbe+3aNX799ddFNlbSbrfznXdWsmXLruzT5wWePXuWVavWp9HYkcAcmkxRnDIl8ySkWBg/lUpH\nwI/AvxRr3oZCDHQJhaBpAEXmgzA6Ol0NqlRtnT7U61m9epO0NsVO5DjKcil6ebWh0ViCer2FKtWr\nFBsXAQwLi6JWa2R4eGV+9dVXvHbtGlu0eJoqlS/Tk/FJYDQ1GhO/++47Hj58WBEdaKzMTJ+iUKQN\n4Zdffpl2/vHjJ1IEWOupUnlzwYLXC+pyuoX79+9z27Zt/Pjjj7NUnckJu93Ot99+l23adGPfvoMK\nbak5bdosynINipiyzZTlwCwVhmw2G+Pi6lKnG07gf1SrX6e/f+kCmYXnlosXL3LQoBHs3r0fP/74\nY5fft2TJUqUa4QNlRj+FLVt2zsee5p7du3dzzpw5XLNmTYZNF1EwqzKBdVSrZ9DbuyQvXLjARYsW\ncfTocdkquxQL4ycS/stS+NqqUaSZOYRB7ymztm/SDJJKNVqZGToM1OEsK0mdPHmSCxcu5KBBQzlk\nyDD26NGXvXo9z//+97/Z9mft2nWUpFCKjY+JVKlMXLVqVdrrycnJVKnUFL4qMe02GodwyZIlJMlT\np04pM9YtFOEr06lSWXjlyhW3X7uiyvTpsxWR0n9TrZ5CX9+QfHeiZ4XNZuPMmXMZGZnA+PiG2arT\nJCUlKb4vm9NnrBrLl48tUvGHP/30E729SyoV/lZQlsP51luulTEdMGAYM4aCfcPQ0Kh87rHrLFiw\nkLJchhrNWJpM9dm0aYc036OvbyidC4Lp9c/z9ddznlAUC+M3cOAIajSBin8tmsL/57hJdooQlIHK\n/5NoMJSmwRBI4DBFfYR6nDw547TXbren5akCU6jRjKC3d0mXdvx27NjBPn1e4NCho9Kkr5zx9y/N\n9HKJj2g21+DmzZtJiipsIvzGuf8mzpo1yz0XrBggiij9kHYNDIa+XLx4cWF3K1tu3LihZBH9zvQg\n90oEplKW/fO0I5kfvPrqTGq1zgrhRzKUU3gcS5cuoyw3VWZ+dmo0k9mqVcHM/L799ltWr96Y/v7h\nbNOma6bIgYcPHyq1oC8r40ql2RzLL774giTp7V2SovCYIyJiKOfPz1nctlgYv2vXrlGW/Sg2OG5T\nKLRMp9joGEWRqeGnzAx1nDhxMt95ZyVDQirS3z+cY8a8zAcPHvB///sfz5w5w4EDh1Onk5TldLu0\nJ7paPYlDh6brAH700UccNmw0586dlyt/x44dovi3xdKNZnMVtm7dJa0GyJYtWyhUXxxy4UkEtDQa\nS3PevIJd/l64cIFr1qzhzp07Xapz6i7MZn+my3+Rev1AvvHGGwV2/rzQv/9QynJNik2g9hQV9qzU\nakdw3rwnD2lyB5MnT6VK5Rwe9C0DA8u59N7U1FS2b9+NkhRCiyWK4eEx2er5uZMbN24oZSZWEPiB\nOt0oxsbWyZCvfuvWLep0ZjrX7/byepobNoig9/HjJyvui0+pUi2m2Rzg0iSmWBg/YfgiKUJQ5ivG\nzleZBfakqM3hTeA4JakUL1y4wF9//ZVbt27l/v37efHiRUZFJdBkiqBW60e1ugbFLvE1inCV15WL\nupy9eom6I8KPUIHAfBoM3VipUvVcBS7/+OOPXLt2LT///PMMhsVms7FatfoUCjDDFUM+gMAl6vVy\ngRmhnTt3Upb9aTZ3p9kcx5YtnyqwEIaRI8crQqufUaVaTIslIM3v98MPP7B//6Hs3PlZbt6cvQpv\nQWOz2fjuu+/SYPCjCJR/oLg0eqe5NAobEZTsTxGKtJeyXIsvvzzN5ffb7XaeO3eOp06dKrDypdu2\nbaOXl7N+pI1GY4kMbhC73c6YmJrUaCZRRGRsodkckLZZaLPZOH/+G6xZswXbtPlHtgW9/kyxMH7p\n4pnnKPx7pSl2Xen0U5aAPzUab7Zv34VmcyCNxjiKgGQ9hZ/wRwKtKfxtjvd9SKAJRS2N0ty2bRtt\nNpsyzf4pbWlqNjfmBx984JYxWa1W9u/fn1ptRQLb0pbHarWuwJLwAwLKMH3j5hFNplpuGd/Vq1eZ\nmJj4WCNutVo5a9Y8VqvWhK1adUn7sF68eJFeXoFUq6cTeJuyXNZln1VBsWzZvyjLZQksplY7jEFB\n4Wm1WooCBw4cYO3aLRkdXZczZ87Nt4epzWbjjBlzWKZMFVasmO7WyS179+6l2VxFcSWQwE3qdKZM\nWUHJycmsU6cFjUYvli4d7ZaQm2Ji/JyNXBWKeD8LhYP2V2XmZiKwk0Je3VdZlvhRqLDYKQqd1yDQ\nl86FWlSqyTQaA1m6dAxXrXqfpPAxiCLpD9KOM5l6csWKFVyw4J8cMeKlXO2kZcWlS5eUWr4bKNSI\nn2ejRpkln1xh48ZNjIyszrCwGE6dOjPHD7zdbqdGo6MoAuXwuw3lokV519Oz2Wzs128I9XpvynII\no6Nr8OrVq7lqY8qUaX8qzH6IYWHRee5TfvHJJ5+wf/+hHD9+0t9qo8oZsTJKoAgT20lZDnZJhfvP\nWK1W1qvXkpLUmsBrNJniOGLEuHzocWaKifE7ljbz02q9KKTn9yuG0KQYO0c5vW+V5XErClXl9Chv\n4TM8Q8BClaoa1eqKlGVv/vjjj5nO27x5J0UK/SyBNTSZ/FmhQlWlrqhYEs+cOZf79u3j8uXL+cUX\nX/DevXs8deoUL1++7NLYDh8+zEqVatDXtxRDQ6NYsWIN9ujRP8NM4s0332a5cvEsWzaOS5Ysz6Td\nt2vXLkpSMEWw7gnKck3OmDEnx3NXr96IGs1U5cHwA2U5hEePHnWp31khSh/WpIiNtFOnG8P27XOn\nxjFhwiSqVK843bNTDA7OOZ/3xo0b/OGHH4pULYm/OhER1ShChBz36vU8lTMgxWRj6dKlHDlyLNev\nX++yPmVKSgovXLjAe/fu5em8xcL4ybIfLZZ46vXenDp1OoOCyitLWYkqVTAtFh9qtX2Vm9CfQoB0\nO8WusGP2doSARK3Wn1qtD4We32sEarNGjUaZZkt37txhjx79GRRUnnFx9Tlv3jyazQ2Z7nRNolpt\noCyHU5IGUpLKUJJK0GKJodFYgsOGuVY059GjR6xUqTr1+uEE9lOne5FRUQlMTU3lunX/oSxHKIb+\nEGW5YiZxRxGi8LrTh/AIAwLK5xh/l5SUxMqVa1GrNVKvN2UZiJ0bBg0a8ad+nHHJcDlz+vRpxWf1\nHoEvKMvVOH367Me+Z9q02TQYvGg2l2XJkuUyqUV7yB9iY+tTCF84smMmcuTIsQV2/j179tDLK5Am\nU5lcVf5zplgYvw4d/qHM5vyp0ZRiTExNjho1lrVqNWG3br14/PhxenmVpErVS5kNvkexg9uTwjfY\nniIcZhKDg6Mo4uwcYQsPqVKFZJBjygpR26KH05f7kTKTdGy/V6eoCUICt2kyRbtUTPvUqVM0mys6\nGVU7zeZIfvPNN4rAwFqnc37EevUyLo1HjRqnVHJzHPMxVapSDAkp75LYwN27d93iF1q4cBElqQ0d\n8Zdq9etZlj7MiYMHD7JBg7aMi2vIBQsWPvYBIkKVytIhMqFSLWfFitWfZBgeXGT79u1K7ONrVKvH\n0csrKMsVVH5w7949Ra/TkZooKv/ldne6WBg/rbY8gR7K0tVGtbovy5ePpyyXprd3M+p0XtTrK1Dk\n6hopivzsp6gtGqoYwB8ILGWZMpUpdP7sTgajMvfs2cNLly6xZcvOLFtWSOE7y+AkJSUpFcP+TeB7\n6nR9qdE4l6s00bm2iFb7UpZF2v/Mt99+S1kuw/Sg7UeU5TB+99137Nz5GYrQCsc5VrBVq64Z3p+Y\nmKjEOY0kMJti93g7dbphHDOm4OqpPnz4kA0atKbJVJFeXvUYEFAm2xSwjRs3sU6d1qxXr41LD4js\nWLRoEQ0G57i2FKrV2r9EmcriwMGDBzl06CiOHTuxQBVxzp07R7M5wum+k97ejR6bnJAVxcL4AXWZ\nXkjoOoGXqFaXo1BcIYXyqw8d9TVEKctYAjEEnlX+lkCj0ZcTJ06kSuVNocZygcAi6nQ+TE5OZnBw\nBDWaWQSOU68fzKpV62eYFR07doyxsfUYGFiOTz/dm35+oRT1NFIVA/u20p87NJmquLQpYrPZ2KBB\na0rSUwTepyR1YqNGbWiz2Xjq1CllU2QyHTV6s/LLXbp0SYly70kR2E0Cb7J79/5uvRc5YbVaeeTI\nEe7atStbDb9NmzYrRa83EdhAWQ7mzp0783S+rVu30mSqzHSR2c0sVarikwzBQzHg999/p9HoTeHf\nJ4GfKUkBWSYcPI5iYfxUqpoUgqGDKbI8ZAohTYflf0hArSxFh1IUObdS+PvaE5hCoDz1+kCazRUZ\nGFiWKpWFgIkmk3D079q1i15edZ3atFGSgh4rPHD69GlKUpBy7tIUMlexVKl8+PzzL+bKcTtt2kx2\n7NiL06fPyqBecubMGY4ZM54jR459rKjjyJHjlWXnLQKJlOVo/vvfa12/0AVE/frtKHa4Hdd5Jdu0\n6Zantux2O/v2HUxZDqO3d0N6eQU90aaNh5xJTU3lsGFjaDb709s7mPPnF05w+po1aylJ/vT2bk5J\nCuS8eZn7Ybfb+d57q9muXQ/26zck0+y0WBi/0qUrUaXyovDn/U7ggGJofla+QEspNjDErEvsBntT\nCB60oojtK0mgKoFkGgwDOHDgiAxBy4cOHaLZHMP0/M271Ou9cwzXGDVqPHW6/hTL6D+oVr/Apk3b\n5/dlycSDBw/Yu/fz1OkkSpI3p0+fXSSXf40bd2S69iIJ/IsdOvR8ojZPnz7NXbt2Fal4u78qkye/\nSlluSOHrPkNZrsi1a9cVSl8uXbrEHTt28Pvvv8/y9ddeW6AUQ1pNtXoKfXyCmZycnPZ6sTB+oaFR\nNBod+nK/UOjodSagJeBDrdabwItpMzagI0WZyskU+ntzKUJcxikG8GPWrt0qw3lSU1NZo0ZjGo2d\nCfyLstyAPXrkXDvg9u3bjIyMo8VSjxZLCwYGhrsc6pIf2O32Imn0HHz22WfKbPlNAsspywE8cOBA\nYXfLg4tER9ehkJBzPLzeYZcuzxZ2t7JEuILOpPVVrx/Af/4zvf5NXo2fFgVIcvL7ANYAWAdgJoCq\nAJIBSAAAq/U+zOb/QK3+Gnb7HwgPN2Lp0p3o3LkXbt/2BTBBaWkegLLQ6VYiIaFyhnNotVrs2/cp\nXn99Ec6ePYG6dXtg8OBBOfbNx8cHp08fwZ49e2C1WtGoUSN4e3u7a+i5RqVSFdq5XaFly5bYtm0d\nlixZCY1GjTFjPkK9evUKu1seXMTf3w/A9wAaAgA0mh8QEOBbqH3KDpvNBsCY9jtpVP72hLjLOucE\n0jI8bisbF6ucZnitKLI8kqhSBXHevHncu3cvf//9d+7fv58rVqygJJVleonFPwiYGBtb2yWhgsOH\nDzM6uhb9/cuwS5dniqR+mwcPBcnx48dpNHpRo2lOvf5plihRiklJSYXdrSx56aWXKcu1KeTlltNs\nzrgpklczVsDGr6Ni+Mx0lq4RoR2OGLchbNGiJa9cucLw8BhaLNVpMsXQbA6mJDUn8DolqRbbtevq\nUlxbevrZfwhcoF7fj02bduCuXbtYq1YLVq5cj//856IivcT04MGd2Gw2durUk7JciQZDJ+p0Ply9\nenVhdytbbDYbZ8+ez6pVm7BFi6cz1JUm8278VMqb8x2xjAsAUBPAVQA1ACwFcB1AbQALAbQFUA06\n3c9o2LAR9u+viNTU+QAIrbYZNJqvQQKxsdHYtWsHvLy8cjzvqlWrMHz4Lty792/lL4+gUskwGv2Q\nkrIYQBBkeQymTOmDiRPHun/gHoo1JHHz5k14eXlBr9cXdnfyhN1ux+rVq/Htt2dRpUo0fH190bv3\nVNy9+yUAA4DD8PHpgtu3fy3sruYJlUqFPJmxJ7XKrgKAInD5JeWnKUWoi4FC3KA5Rc0NH2q1PRkS\nEkVgtzIb/IZC3GAngcs0GHrwqad6uXTe999/n0ZjfaYHQ1+iWi0RmOk08/ySZcpUybYNu93O6dNn\n02z2pyT5cPDgUfla89RD0eDChQsMD4+hweDjltTBwsBut7Nr12cU6bHZNJlqs3r1OpTl/k6ffytV\nKk2x/Uzn1YwVsPErqSxxvQjMUHZ9S1KUV+xGIEJ53ZuNG7emwdCXIs5vLkVsoONm3aTBYMnxnFev\nXmWpUpFUqwMpxE5nU5LKsUGDZlSpJji1919GRmafTrVy5XtKbYELBH6hLDfilCkz3Xl5PBRBKlVK\noErlyHM+T1kO5ldffVXg/UhNTeWBAwf4+eef57pw/Llz5xTBDIfyz10aDH40GoMoxD7sVKvnMTq6\nZj71Pv8pJsavH0Vu70CKbA8vmpDB5gAAD8tJREFUAnEEuhIIpihgTmo0ZXngwAHWrNmEklSSWq2J\nGo1zecqv6OsbmuM5n3/+Rep0oygySN4gUI/16zfj+fPnabEEUqWaroTDlHpsIHHHjr0p8owd59/N\n2NgGtFqt3LRpE5ctW8YTJ06483J5KGSsVqtSw8Wadt9leQBXrFhRoP1ISUlhrVpNaTbH0MurAQMC\nyuQqA+L48eO0WKo4fXZJiyWa06fPoMFgpk5nYvnyccW60HsxMX7+BGY53YjVBMpRKLs4qrb9TqPR\nn4mJibTb7bx06RLPnTvHiIhYGo1dqVJNoSSF8L33cnbQNmv2NEUsoeN8O5iQICq+nzt3jgMGDGO3\nbv24ffv2x7YzcOBwajTpM0WVahmbNevEpk070GyuRaNxECUpiKtX/9st18pD0cDXN4TAXjryjc3m\n2Bw/K+5m7tz5SulGYYTV6vls0qSDy++/f/8+Q0LKU62eT+AiNZrXWKpUBaakpNBqtf4lIh+KifEL\nYXrerDBGQsL+NarVgVSpJtNkqsp+/YZmev+xY8c4ePBgjhw5ymX1VxEZ3pgiW+Q+JakdJ0yYkuu+\nJyUl0d8/jEZjLxoMz9NsDuDixYtpNicwXcjgG8qyj2fX+C+Eo0SAl9dTNJkqsGvXZwv8/vbrN4Si\ntKvjO/M1w8JictXGxYsXWbduS/r5hbFevVaFVmLUXTx69CjDfSgmxm8ogTACXxA4SCFZbybQnmq1\nhVOmTOUHH3yQ6QM2YcJUSlJJens3oyz7pymI2Gw2btmyhStWrMgyX9ZqtfKZZwZSozFQozGwc+fe\nea5pcO3aNS5fvpyLFy/mpUuX+M4779BkejaD01it1uZavj4xMZEdOvRglSr1OXz4uAz5wFlx/fp1\n7t27N9tUIA/u5dKlS9y0aRP3799fKA+2t956W4lxu0PARp1uGDt3fqbA+1GYOCo0Ll26lFFRNahW\na2ky+XHt2vUki43x60khJVVDMXyVKIQEKlCtlnn9+vVM7ztx4gRluRSFCgwJHKUs+/Lhw4ds3boL\nzeZqlOUBlOUgrlmTtd8uJSUlV0WLXOHs2bOU5QAKFdwH1GheYXx8/Vy1cevWLQYElFYUaPbQaHya\n7dr9I9vj9+zZQ7M5gN7e9ShJQRw79pUnHYaHIo7NZuNzzw2mXu9FSQpkfHy9v1Xus91uZ8+e/Wky\nVaRaHUaR2molcIqSFKjUzy4Wxs+XQqcuikKLr4wymONUqXyyDFreuHEjvbyeyuCwNRj8uG7dOprN\ncUzP+viGkuRdoE/nLVu20Nc3hGq1lgkJjTMkW7vC5s2babG0cRpbCrVaI+/evZvpWLvdTl9fh8w9\nCdygyRTOQ4cOuWs4Hoow169fZ1JSUoGWJi0K7N69myZTJWXTUsP0UrGkJA3k8uXL82z81E8eYpgb\nngUwEsAlAHaIYOe1AEbDz88XarUaN27cQPv23eHvXwbx8Q2g0WiQmnoYwA9KGx/CbJaRkpICsgoA\nnfL3GDx8eB8PHz7McMbLly+ja9dnkZDQFE2btsTQoaOwZcsWt4ymY8eOuHUrGVbrIxw/vgchISG5\ner9WqwWQ4vSXRyAJjUaT6dj79+/jzp1bAJorfykBlaoezp8/n9fueyhG+Pv7o1SpUlCrC/grW8j8\n8ssvUKniAJggkiROKa9YodGcRsmSJfPeuHvtdPYAoEhhCyDQSAkdeZdAHQKN2Lx5S9rtdlar1oA6\n3QiK8pQr6e1dkq+/vogGgxdNpjL09Q3hsWPHnJadRwlYqdG8ypiYjLFKN27coL9/GNXqyQQqEHia\nwHzKciRnz865Enx+c/fuXZYtG0O9fjCBNZTl+uzXb0iWx9rtdgYFlXXavf6JshxaKHFnHjwUFGfP\nnqUkBRD4msBmZfXYjbJcnU2atKfVai0uy15SFCQKpFAA/llZ/i5l9+7P8fPPP6dOZ2G6Fh/p5dWO\nH374Ie/cucPz589n2FD4+OOP6eUVSJVKwypV6mQSLF27di3N5k4Ueb3N6JzlodebisTO7M2bNzl8\n+Fi2a9eDb7yx+LEFx7/66iv6+YXSYqlAg8GL8+cvLMCeevBQOKxfv0ERYZAIyDQYIqjX+3Ho0DEk\ni01uLwGcA1AHwC8Q0lRHYDA8gI/PZdy9K+PevQsAfgYQCMAGs7kGPvxwHlq0aJFt21arVVlCZmT9\n+vUYOHAd7t59GsAeCDktAHgAjcYLDx7cz/J9RZmUlBQkJiYiMDAQ/v7+hd0dDx4KBJvNBh+fQNy9\nuwVAfQC/wWSqju3bV6Jx48Z5yu0tYON3CcBzAI5B6HOlAngIvd4bdntTWK3rAUwF8B8A/SBJhxAb\n+wAHD36WJyP122+/ISqqOq5fbw6bbSOEkEJ1GAyz0LhxCnbu3OyewXnw4CFfuXPnDkqUCIbVek/5\ny1moVE1AXgdgz5PxK2DvaQyEg9+m/PsOgF/x6NFgWK0nlWNeBdAIOt0imEznEBVVMdMmhqv4+Pjg\n5MmDePZZLRISYhEcPBNBQR3QubMRGze+54bxePDgoSCwWCwICAiG2CC1AWgLchrEBCpvFPDM7wLE\nktcCIATAAeVVAvAB8J3yezSAWQBqw2j8Jxo3tmHHjk0F0U0PHjwUUU6fPo0WLTrijz8e4cGDBwBu\nK6/kTdKqgGd+EQDiAFwB8BOAR8rffwXwAJKUAL2+MtTqugCGA6iBBw9W44svtuZ59ufh78nDhw/R\nr99QeHsHo2TJ8li7dl1hd8nDExIXF4fk5Av46qv/Qq+3QrjR8k4BGz9fAPsBmCF8fo0BjANQF8HB\nZfDtt4ewcOFsGI33IWaDAHAHKpUqy9g3Dx6yY/jwcdiw4SfcufMlrl5dg4EDx2Hfvn2F3S0PT4hO\np4OPjw8kyQwgAUCvPLeVo/HbuXMnKlWqhMjISMybNy/LY0aMGIHIyEjExcXh1KlTWR4jeBOABsDv\n0OvLARgEwBc6XTk8/XQHlCtXDrGxsUhJOQUREL0CQAN069az2O3K/lU4efIk5s2bhzfffBP37t3L\n+Q1FhC1btiMl5Z8ASgOog/v3h2Dbth2F3S0PbmDo0HG4e/d5ADvgKMCUJx4XB2O1WhkREcHExEQ+\nevSIcXFx/O677zIcs337drZp04YkefToUdaqVSvLtpAW59eN0dHRbN26M43GEjQaA1i/fsu0lK72\n7XsQWEBgKoHnCfRhu3bd8xTHU5Ds2bOnsLvgdj7++GPKciC12tE0GOoyMjLepYJRRYHy5aspMaWO\ncofPcfbsOVke+1e8d8781cZXqVItRRjFkRaaD+ltx44dQ/ny5REeHg6dTocePXpkSg375JNP0Ldv\nXwBArVq18Ntvv+Hq1avZmVoAN/D995excOFs/PjjN/jhhxPYv38nTCYTAODu3fsQT+sZAN4G0BH3\n7qVk017RYe/evYXdBbczdOh43L+/AVbrG3j4sDl+/rksVq9eXdjdcoklS2ZBlp+DWj0BBkNv+Psf\nxKBBA7M89q9475z5q42vZs146PUrkR41kjcea/ySk5MRFhaW9nupUqWQnJyc4zE///xzNi12BvAj\nDIYOOHr0KEJCQhAWFpahRu2AAd0hy5MA7AOwD7L8MgYM6J7bcXlwA3fu3AZQQflNhUePKuDWrVuF\n2SWXadOmDQ4e/AzTp1swb15NfPvtMZQoUaKwu+XBDSxZMg9xcRchSaEwGELz3M5jHWmuFs7mn7aZ\ns3+fGUBlqNU/ICCgT5ZH9OnTC/fv38eCBS8BIMaOnYA+ffLu1PSQd1q1ao1t28bh4cNFAJJgMHyK\n5s0/KuxuuUzVqlVRtWrVwu6GBzfj7e2NL7/cjaSkJOj1egQHB+etocetiY8cOcJWrVql/T5nzhzO\nnTs3wzGDBg3i+vXr036vWLEir1y5kqmtiIgIxe/n+fH8eH48P+77iYiIyJPP77Ezv4SEBJw/fx6X\nLl1CSEgINmzYgPXr12c4pmPHjli2bBl69OiBo0ePwsfHB0FBQZnaunDhwuNO5cGDBw8FymONn1ar\nxbJly9CqVSvYbDYMGDAAUVFRePPNNwEAgwYNQtu2bfHpp5+ifPnyMJlMWLVqVYF03IMHDx6ehAJL\nb/PgwYOHooTbMzzcGxRd9MhpfGvXrkVcXBxiY2NRr149fPPNN4XQy7zhyr0DgOPHj0Or1eLDDz8s\nwN49Oa6Mb+/evahatSoqV66Mxo0bF2wHn5Ccxnfjxg20bt0a8fHxqFy5Mt57772C72Qe6d+/P4KC\nglClSpVsj8m1XcmTpzAb3BkUXRRxZXyHDx9Oq4W6Y8eOYjM+V8bmOK5JkyZs164dN23aVAg9zRuu\njO/27duMjo5mUlISSWZZUKuo4sr4pk2bxokTJ5IUY/Pz82NqamphdDfX7N+/nydPnmTlypWzfD0v\ndsWtMz/3B0UXLVwZX506deDt7Q1AjC/7mMeihStjA4ClS5eia9euCAgIKIRe5h1Xxrdu3Tp06dIF\npUqVAoBiJRbryviCg4Nx584dAA59vBLFJm20QYMG8PX1zfb1vNgVtxo/9wdFFy1cGZ8z7777Ltq2\nbVsQXXtiXL13W7ZswZAhQwC4HgdaFHBlfOfPn8etW7fQpEkTJCQkYM2aNX9upsjiyvheeOEFnDlz\nBiEhIYiLi8PixYsLupv5Rl7silvNvvuDoosWuennnj17sHLlShw6dCgfe+Q+XBnbqFGjMHfuXKhU\nQj/tz/exKOPK+FJTU3Hy5Ens2rUL9+/fR506dVC7dm1ERkYWQA+fDFfGN2fOHMTHx2Pv3r348ccf\n0aJFC5w+fRoWi6UAepj/5NauuNX4hYaGIikpKe33pKSktCVEdsf8/PPPCA3Ne4pKQeLK+ADgm2++\nwQsvvICdO3c+dqpelHBlbCdOnECPHj0ACOf5jh07oNPp0LFjxwLta15wZXxhYWHw9/eHJEmQJAkN\nGzbE6dOni4Xxc2V8hw8fxiuvvAIAiIiIQNmyZfH9998jISGhQPuaH+TJrrjNI0kyNTWV5cqVY2Ji\nIh8+fJjjhseRI0eKzYYA6dr4Ll++zIiICB45cqSQepk3XBmbM8899xw3b95cgD18MlwZ39mzZ9ms\nWTNarVbeu3ePlStX5pkzZwqpx7nDlfGNHj2a06dPJ0leuXKFoaGhvHnzZmF0N08kJia6tOHhql1x\n68zvrx4U7cr4Xn31Vdy+fTvNL6bT6XDs2LHC7LZLuDK24owr46tUqRJat26N2NhYqNVqvPDCC4iO\nji7knruGK+ObNGkS+vXrh7i4ONjtdsyfPx9+fn6F3HPX6NmzJ/bt24cbN24gLCwMM2bMQGqqqN+R\nV7viCXL24MHD35IClrH34MGDh6KBx/h58ODhb4nH+Hnw4OFvicf4efDg4W+Jx/h58ODhb4nH+Hnw\n4OFvicf4efDg4W+Jx/h58ODhb8n/A3jTwZzSjeaZAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xeb794a8>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Fitting a copula to a portfolio"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S = DataReader([\"IBM\", \"GOOGL\"],  \"yahoo\", datetime(2007,7,1), datetime(2013,6,30))['Adj Close']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def demo_multivariateModels(portfolio):\n",
      "    \n",
      "    portfolioReturn = np.log(portfolio / portfolio.shift(1))\n",
      "    portfolioReturn.dropna(inplace=True)\n",
      "    portfolioReturn.columns = ['r_' + s  for s in portfolio.columns]\n",
      "    \n",
      "    ## Seed for optimization of degrees of freedom\n",
      "    nu0 = 5\n",
      "    \n",
      "    ## Create a dataframe which stores all fitted parameters and statistical functions\n",
      "    ## Note that the columns PDF, CDF and INV store functions\n",
      "    modelDF = pd.DataFrame(index=portfolioReturn.columns, columns=['mean', 'sigma', 'nu', 'PDF', 'CDF', 'INV'])\n",
      "    param = ['mean', 'sigma', 'nu']\n",
      "    \n",
      "    for s in portfolioReturn.columns:\n",
      "        param_fit, modelDF.loc[s, 'PDF'], modelDF.loc[s, 'CDF'], modelDF.loc[s, 'INV'] = \\\n",
      "            fit2StudentT(portfolioReturn[s], nu0)\n",
      "        modelDF.loc[s, param] = param_fit\n",
      "    \n",
      "    print \"Fitted the Student T distributio to the log returns of each stock in the portfolio.\"\n",
      "    print \"Found the following parameters:\"\n",
      "    print modelDF[param]\n",
      "    print    \n",
      "    print \"=\" * 30\n",
      "    print \n",
      "    print \"Plotting PDF's fitted to asset returns\"\n",
      "    \n",
      "    \n",
      "    fig = plt.figure()\n",
      "    \n",
      "    nSubFigs = len(portfolioReturn.columns)\n",
      "    ## Transform to U[0, 1] marginals\n",
      "    ## And plot fitted PDF's\n",
      "    logReturnColumns = portfolioReturn.columns\n",
      "    for n, s in enumerate(logReturnColumns):\n",
      "        portfolioReturn['u' + s[1:]] = modelDF.loc[s, 'CDF'](portfolioReturn[s])\n",
      "        ax = fig.add_subplot(nSubFigs, 1, n+1)\n",
      "        graphicalComparisonPdf(portfolioReturn[s].values, modelDF.loc[s, 'PDF'],axes_object=ax, nBins=100)\n",
      "        ax.set_title('Fitted PDF to asset: ' + s)\n",
      "    transformedReturnColumns = portfolioReturn.columns[len(logReturnColumns):]\n",
      "    plt.tight_layout()\n",
      "    plt.show()\n",
      "    print\n",
      "    print \"=\" * 30\n",
      "    print\n",
      "    \n",
      "    print \"Joint distribution of the first two assets (historic and simulated).\"\n",
      "\n",
      "    fig = plt.figure(figsize=(10,10))\n",
      "    ax= fig.add_subplot(221)\n",
      "    n1, n2 = portfolioReturn.columns[0], portfolioReturn.columns[1]\n",
      "    print n1 + ' vs ' + n2\n",
      "    print \n",
      "    print\n",
      "    ax.scatter(portfolioReturn[n1], portfolioReturn[n2])\n",
      "    ax.set_xlim(-.15, .15)\n",
      "    ax.set_ylim(-.15, .15)\n",
      "    ax.set_aspect(1)\n",
      "    ax.set_title(\"Historic joint distribution\")\n",
      "        \n",
      "    ## What copula best fits this joint distrubtion? \n",
      "    ## We first try the Gaussian copula, with Gaussian marginal\n",
      "    M = portfolioReturn.shape[0]\n",
      "    \n",
      "    mu = portfolioReturn[logReturnColumns[:2]].mean()\n",
      "    Sigma = portfolioReturn[logReturnColumns[:2]].cov()\n",
      "    Z = multivariateGaussianRand(M, mu, Sigma)\n",
      "    \n",
      "    ax = fig.add_subplot(222)\n",
      "    ax.scatter(Z.T[0], Z.T[1])\n",
      "    ax.set_xlim(-.15, .15)\n",
      "    ax.set_ylim(-.15, .15)\n",
      "    ax.set_aspect(1)\n",
      "    ax.set_title(\"Gaussian copula + Gaussian marginals\")\n",
      "    \n",
      "\n",
      "    ## Next look at a Gaussian copula with student t marginals\n",
      "    _inv = (norm.ppf(portfolioReturn[transformedReturnColumns[:2]]))\n",
      "    _corr = np.corrcoef(_inv.T[0], _inv.T[1])\n",
      "    \n",
      "    # Generate from gaussian copula with implied correlation\n",
      "    Z = gaussianCopulaRand(M, _corr)\n",
      "    \n",
      "    # Generate sample points using implied CDF inverse\n",
      "    z1 = modelDF.loc[n1, 'INV'](Z.T[0])\n",
      "    z2 = modelDF.loc[n2, 'INV'](Z.T[1])\n",
      "    ax = fig.add_subplot(223)\n",
      "    ax.scatter(z1, z2)\n",
      "    ax.set_xlim(-.15, .15)\n",
      "    ax.set_ylim(-.15, .15)\n",
      "    ax.set_aspect(1)\n",
      "    ax.set_title(\"Gaussian copula + Student marginals\")\n",
      "    \n",
      "    ## The final one is a student t copula with student t marginals\n",
      "    ## We did not treat the ML estimates for the parameters of the student t copula\n",
      "    ## so we will use some given estimates instead\n",
      "    \n",
      "    rho = [[1, .55], [.55, 1]]\n",
      "    nu = 2.4\n",
      "    \n",
      "    U = studentTCopulaRand(M, rho, nu)\n",
      "    u1 = modelDF.loc[n1, 'INV'](U.T[0])\n",
      "    u2 = modelDF.loc[n2, 'INV'](U.T[1])\n",
      "    ax = fig.add_subplot(224)\n",
      "    ax.scatter(u1, u2)\n",
      "    ax.set_xlim(-.15, .15)\n",
      "    ax.set_ylim(-.15, .15)\n",
      "    ax.set_aspect(1)\n",
      "    ax.set_title(\"Student copula + Student marginals\")\n",
      "    \n",
      "    \n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "demo_multivariateModels(S)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Fitted the Student T distributio to the log returns of each stock in the portfolio.\n",
        "Found the following parameters:\n",
        "                 mean       sigma        nu\n",
        "r_GOOGL  0.0007592356  0.01231535   2.75534\n",
        "r_IBM     0.000662365  0.01006211  3.131078\n",
        "\n",
        "[2 rows x 3 columns]\n",
        "\n",
        "==============================\n",
        "\n",
        "Plotting PDF's fitted to asset returns\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GDcHVFQyGW38LTs7O5jG9mjQx/y3udZMm5iu2hg3BwcFmCz2b/45b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\nKaWUUnZLg5RSSim7pUFKKaWU3fo/uHimnkAwdlIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xf079ba8>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "==============================\n",
        "\n",
        "Joint distribution of the first two assets (historic and simulated).\n",
        "r_GOOGL vs r_IBM"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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csQrLYDBg+fIv0LPnYEyeHInk5GRLh/TU9Ho9Tp06hRMnTiAnJ8fS4TDGGLMC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E1nA0gBcBIKxVf46afvcerUXty6dQne3t5q04eGhuLkyT+xdKk7Pv20L86fPw5ra+tK5+3n54cp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\nGTIENWvWLPf+K1tmZib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LS0tjjx49zpmGfuTIEfbp06dguaVLl7JRo0Zs0KABp06dWvD5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\nEEIIIYQfkeJMCCGEEMKP/D82GN2TRJ7guQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x17665cc0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A Gaussian model for the stock typically underestimates the fat tails of the asset returns. A Gaussian copula only takes into account linear correlation among the asset, which again underestimates high ''tail'' events in the joint distribution. The student t copula and student t marginals model this much better. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Value-at-Risk"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We finally arrive at a risk measure: the Value-at-Risk (VaR). Imagine we have some portfolio of assets. The VaR is then a method to quantify the level of financial risk of this portfolio due to e.g. changes in the market (market risk). A common definition of VaR is: what is the maximum loss of the portfolio, over a fixed timeframe, at a fixed confidence interval $\\alpha$.\n",
      "\n",
      "So suppose we have some model for the return of the portfolio. This can be based on historical data, or some assumptions on the underlying distribution of returns. Using this model we can estimate the distribution of possible returns for the portfolio over a fixed timeframe (e.g. the distribution of returns 10 days from now). The 5% VaR is then the worst possible return we can expect with 95% confidence. Put differently, it is the return that corresponds to the 5% quantile of the underlying model for that particular time horizon.\n",
      "\n",
      "The VaR is an example of a non-coherent measure: if we have two portfolios with each its own VaR, then the VaR of the combined portfolio is in general not equal to the sum of the individual VaR (or a simple combination thereof).\n",
      "\n",
      "A related risk measure is the Estimated Shortfall (ES). It is the average loss for losses larger larger than the VaR.\n",
      "\n",
      "We now compute the VaR of a portfolio of stocks using two methods: Historical and Monte Carlo."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def simulateLossMC(logReturns, S0, priceEuroCall, priceAsianCall):\n",
      "    nu0 = 5  # seed for estimating d.o.f.\n",
      "    modelDF = pd.DataFrame(index=logReturns.columns, columns=['mean', 'sigma', 'nu', \n",
      "                                                              'PDF', 'CDF', 'INV'])\n",
      "    # Fit student t distribution\n",
      "    for n in logReturns.columns:\n",
      "        params, modelDF.loc[n, 'PDF'], modelDF.loc[n, 'CDF'], modelDF.loc[n, 'INV'] = fit2StudentT(logReturns[n], nu0)\n",
      "        modelDF.loc[n, ['mean', 'sigma', 'nu']] = params\n",
      "        \n",
      "    \n",
      "    # Transform to U[0,1] marginals\n",
      "    u_margin = pd.DataFrame(index=logReturns.index, columns=[], dtype=np.float)\n",
      "    for n in logReturns.columns:\n",
      "        u_margin[n] = modelDF.loc[n, 'CDF'](logReturns[n])\n",
      "        \n",
      "    # Estimate correlation for Gaussin copula\n",
      "    n1, n2 = u_margin.columns[0], u_margin.columns[1]\n",
      "    rho = np.corrcoef(modelDF.loc[n1, 'INV'](u_margin[n1]), modelDF.loc[n2, 'INV'](u_margin[n2]))\n",
      "    \n",
      "    \n",
      "    # Simulation time!\n",
      "    # Generate samples from estimated copula\n",
      "    M = 5e4\n",
      "    U = gaussianCopulaRand(M, rho)\n",
      "    \n",
      "    simulated_price = pd.DataFrame(index=np.arange(M), \n",
      "                             columns=logReturns.columns,\n",
      "                             dtype=np.float)\n",
      "    for i, n in enumerate([n1, n2]):\n",
      "        simulated_price[n] = S0[n] * np.exp( modelDF.loc[n, 'INV'](U[:,i]) )\n",
      "    \n",
      "    # Having generated different simulations we now compute the corresponding option values\n",
      "    simulated_price[\"IBM_call\"] = priceEuroCall(simulated_price[\"IBM\"])\n",
      "    simulated_price[\"GOOGL_asianCallAM\"] = priceEuroCall(simulated_price[\"IBM\"])\n",
      "    \n",
      "    return simulated_price"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 225
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bootstrapindices = np.random.randint(0, 10, size=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def simulateLossHistoric(logReturns, S0, priceEuroCall, priceAsianCall):\n",
      "    M = 1e3\n",
      "    \n",
      "    bootstrapindices = np.random.randint(0, logReturns.shape[0], size=M)\n",
      "\n",
      "    simulated_price = pd.DataFrame(index=np.arange(M), \n",
      "                             columns=logReturns.columns,\n",
      "                             dtype=np.float)\n",
      "    for n in logReturns.columns:\n",
      "        simulated_price[n] = S0[n] * np.exp( logReturn.iloc[bootstrapindices].values )\n",
      "    \n",
      "    \n",
      "    simulated_price[\"IBM_call\"] = priceEuroCall(simulated_price[\"IBM\"])\n",
      "    simulated_price[\"GOOGL_asianCallAM\"] = priceEuroCall(simulated_price[\"IBM\"])\n",
      "    return simulated_price\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we will compute two risk measures of a portfolio consisting of IBM and Google stock, IBM call options and Google Asian call options (arithmetic mean). The functions to compute these options were implemented in week 8, so we will simply import them here.\n",
      "\n",
      "To compute the risk measures we need a distribution of the expected losses (or profits) over a given time horizon. To obtain this distribution we simulate the assets in the portfolio over the given time horizon using either Monte Carlo or the historic approach. With these simulated portfolios we then compute the loss for each simulated portfolio, and from it construct a distribution of potential losses over the given time horizon. Finally, we compute the desired risk measues."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from custom_functions_iversity import (priceEuropeanCall, \n",
      "                                       priceAsianArithmeticMeanCallMC_withControlVariate)\n",
      "\n",
      "def constructPortfolio(N=5, horizon=5, simulateLoss='historic'):\n",
      "\n",
      "    if simulateLoss == 'historic':\n",
      "        simulateLoss = simulateLossHistoric\n",
      "    else:\n",
      "        simulateLoss = simulateLossMC\n",
      "    S = DataReader([\"IBM\", \"GOOGL\"],  \"yahoo\", datetime(2007,7,1), datetime(2013,6,30))['Adj Close']\n",
      "    \n",
      "    ## Select data in recent past -- we don't want to test with data which is too old.\n",
      "    N = 500\n",
      "    \n",
      "    S = S.iloc[-N:]\n",
      "    S0 = S.iloc[-1]\n",
      "    print \"Behavior of stock over last %s days\" % N\n",
      "    S.plot()\n",
      "    plt.show()\n",
      "    ## Compute returns for specified time horizons\n",
      "    # Horizon for the risk measures\n",
      "    horizon = 5\n",
      "    \n",
      "    # Overlapping indices    \n",
      "    logReturns = np.log(S / S.shift(horizon))\n",
      "    logReturns.dropna(inplace=True)\n",
      "    \n",
      "    \n",
      "    ## Portfolio of stocks and options. \n",
      "    ## portfolioComposition holds the number of assets held in the portfolio\n",
      "    wghts = {\"IBM\"               : 500, \n",
      "             \"GOOGL\"             : 200,\n",
      "             \"IBM_call\"          : 5000,\n",
      "             \"GOOGL_asianCallAM\" : 2000}\n",
      "    portfolioComposition = pd.Series(data=wghts.values(), index=wghts.keys(), dtype=np.float)\n",
      "    ## portfolio will hold the value per asset in the portfolio\n",
      "    portfolio = pd.Series(index=portfolioComposition.index, data=0, dtype=np.float)\n",
      "    portfolio[[\"IBM\", \"GOOGL\"]] = S0[[\"IBM\", \"GOOGL\"]]\n",
      "    \n",
      "    \n",
      "    ## Computing value of European call options for IBM in portfolio\n",
      "    r = .01         # interest rate\n",
      "    K_call = 180    # strike price\n",
      "    T_call = 1      # time to maturity\n",
      "    sigma_IBM_implied = .16  # Implied volatility on IBM call options\n",
      "    def priceEur(S):\n",
      "        return priceEuropeanCall(S, K_call, r, T_call, sigma_IBM_implied)\n",
      "    portfolio[\"IBM_call\"] = priceEur(S0[\"IBM\"])\n",
      "\n",
      "    ## Computing value of Asian call options with Arithmetic mean for google using a control variate\n",
      "    N_AM = 6      # Number of monitoring times for the arithmetic mean \n",
      "    T_AM = .5     # Time to maturity\n",
      "    M_AM = 1e3    # Number of simulated trajectories\n",
      "    K_AM = 430    # Strike of the Asian arithmetic mean call option\n",
      "    \n",
      "    \n",
      "    #\n",
      "    ## !!!! K_AM should be changed to 880 if you are using this code for the homework !!!! ###\n",
      "    #\n",
      "    \n",
      "    \n",
      "    # Here we use historical volatility\n",
      "    nDaysInYear = 252\n",
      "    sigma_GOOG   = sqrt(nDaysInYear/horizon)*std(logReturns[\"GOOGL\"])\n",
      "    def priceAsian(S):\n",
      "        return priceAsianArithmeticMeanCallMC_withControlVariate(S, K_AM, r, T_AM, sigma_GOOG, M_AM, N_AM)\n",
      "    price_AM, std_AM = priceAsian(S0[\"GOOGL\"])\n",
      "    portfolio[\"GOOGL_asianCallAM\"] = price_AM\n",
      "    \n",
      "    print \"Current value per asset:\"\n",
      "    print portfolio.head()\n",
      "    print\n",
      "    print \"Weight in portfolio:\"\n",
      "    print portfolioComposition.head()\n",
      "    print\n",
      "    \n",
      "    # Next we simulate the potential returns of the portfolio using either the\n",
      "    # historic method (bootstrapping of historic data)\n",
      "    # Monte Carlo (Fitting a copula to historic data, and simulating new data)\n",
      "    simulated_assets = simulateLoss(logReturns[[\"IBM\", \"GOOGL\"]], S0, priceEur, priceAsian)\n",
      "    \n",
      "    print \"Simulated return histograms\"\n",
      "    simulated_assets.hist(bins=20)\n",
      "    plt.show()\n",
      "    print \"Corresponding simulated returns of weighted portfolio\"\n",
      "    simulated_portfolio = (simulated_assets * portfolioComposition).sum(axis=1)\n",
      "    simulated_portfolio.hist(bins=25)\n",
      "    current_portfolio = (portfolio * portfolioComposition).sum()\n",
      "    plt.show()\n",
      "    \n",
      "    print \"Simulated loss of portfolio\"\n",
      "    loss_simulated = (-(simulated_portfolio - current_portfolio))\n",
      "    \n",
      "    ## Finally, we compute the VaR at 5% and the estimated loss\n",
      "    p = .95\n",
      "    VaR = loss_simulated.quantile(.95)\n",
      "    indexTail = loss_simulated > VaR\n",
      "    ES = np.mean(loss_simulated.ix[indexTail])\n",
      "    \n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    loss_simulated.hist(bins=50, ax=ax, normed=True)\n",
      "    y_lim = ax.get_ylim()\n",
      "    \n",
      "    ax.plot([VaR, VaR], y_lim, 'r', label='VaR 5%')\n",
      "    ax.plot([ES, ES], y_lim, 'g', label='ES 5%')\n",
      "    ax.legend(loc='best')\n",
      "    plt.show()\n",
      "    print \n",
      "    # Print out returns. VaR is the value at risk, and larger is worse.\n",
      "    print \"Value-at-Risk: %.2f\" % VaR\n",
      "    print \"Expected Shortfall: %.2f\" % ES"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First we have the Monte Carlo approach"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "constructPortfolio(simulateLoss='MC')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Behavior of stock over last 500 days\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IYWxc8T6cmocnzypAKP4zrlP9qFvr3r1AaCgwdiwz5O+9B0yfzlwpsltK9vbs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x16dc8f60>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Current value per asset:\n",
        "GOOGL_asianCallAM     27.054184\n",
        "IBM                  188.110000\n",
        "IBM_call              17.288251\n",
        "GOOGL                440.630000\n",
        "dtype: float64\n",
        "\n",
        "Weight in portfolio:\n",
        "GOOGL_asianCallAM    2000\n",
        "IBM                   500\n",
        "IBM_call             5000\n",
        "GOOGL                 200\n",
        "dtype: float64\n",
        "\n",
        "Simulated return histograms"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bJuXZ4/rbugxnly8WBRHJH/yzDQqFAg6mkk1p6foxdr4d7+tK9WQJzmZDUutr3Kacq14Y\n8xFrQ/xFwDAM08XhhsAEarVabhXaoZZbAT0cr44YXdS2lW6H62/rMpxdvli4IWAYhuni8BiBzPAY\ngfQ4mw3xGAEjFpuPEZSWlgrO5kJDQ7Fjxw4AQGpqKlQqFSIjIxEZGYmsrCwhT3p6OoYMGYJhw4bh\nyJEjQvrZs2cRFhaGIUOG4LnnnrNaaYZhGEZCyARarZYKCwuJiKi2tpaGDh1KxcXFlJqaSlu3btU7\nXqxvdjNUsis5OTk2lQ+AADLyM7QvR9jnKNi6jizFkerGHKTWV99ubGsz9rj+ti7D2eWLvbYmvwh8\nfHyEObDu7u4IDg4WXOmSgU8R9s3OMAzjXFg0WFxSUoLCwkKMGTMGALBz506Eh4djyZIlgnO6zuab\nPSYmRm4V2hEjtwJ6OF4dMbrE2Fa6Ha6/rctwdvliMbshqKurw9y5c7F9+3a4u7tj2bJl0Gg0KCoq\ngq+vL9asWWNLPRnGrjQ1NSEyMhLTp08HAFRXVyMuLg5Dhw7FxIkThRcfgMfEGOfHrIbg3r17mDNn\nDhYtWiS40fX29haWsC9duhQFBQUApIlJkJycjNTUVKSmpmLbtm06c3DVarVdt21d/q+p7f7vaHub\nzra968PQ9rZt22Qvv9VekpOTIQXbt29HSEiI4PQvIyMDcXFxuHjxIiZMmICMjAwAQHFxMT744AMU\nFxcjOzsbzzzzjNBlumzZMmRmZuLSpUu4dOkSsrOzJdHNctS2lc7rCGSXLxpTgwjNzc2UkJBAK1eu\n1EmvqKgQ/n/llVdo/vz5RHR/sPju3bv0008/0eDBg4XB4qioKDp9+jQ1NzfzYPGvgAeLJUds3ZSW\nltKECRPo+PHjNG3aNCIiCgoKoitXrhBRywSKoKAgIiJKS0ujjIwMIe+kSZPo1KlTVFFRQcOGDRPS\n9+/fT08//bRN9DUkjweLu5Z8sdfWZISykydP4t1338WIESMQGRkJAEhLS8P+/ftRVFQEhUIBf39/\nvPnmmwAc3ze7pThe316M3Aro4Xh1JI5Vq1Zhy5YtuHnzppDWUbzi1jEz4P6YmJubmwONicXYVjqP\nEcguXywmG4LHH38czc3NeulTpkwxmod9szPOymeffQZvb29ERkYa/Zy3Rbzi5ORkIXhJr169EBER\nITw8WvUwd7sFNe43AGqdsiyVx9uOt11UVCSMU5WUlEA0En2ZSIajqcRdQ6bpTF1DL7zwAqlUKvLz\n8yMfHx/q3r07LVq0iIKCgkir1RJRS7doa9dQeno6paenC/knTZpEp0+fJq1Wq9M19P7773PXkAOX\n4ezyxV5b9jXEMG1IS0tDaWkpNBoNDhw4gPHjx2Pfvn02jdPNMHLDvoZkhn0NSY9UNpSbm4utW7fi\n0KFDqK6uRnx8PC5fvizEK26NOpWWlobdu3fD1dUV27dvx6RJkwC0TB9tOybW6p7FVvq2lce+hroW\nYm2IGwKZ4YZAepzNhrghYMTCgWlsjOPN/1XLrYAejldHjC5q20rndQSyyxcLNwQMwzBdHO4akhnu\nGpIeZ7Mh7hpixMJdQwzDMIworA5M01WccDle355abgX0cLw66vx4evYWFra1/+mjtqkuPEYgv3yx\nmGwI3Nzc8Oqrr+K7777D6dOn8frrr+P8+fNO7oSLYZyb2toatHT/GPoxjGVYPEYwc+ZMLF++HMuX\nL0dubi6USiWuXLmCmJgYXLhwAenp6XBxcUFKSgoAYPLkyUhNTcWgQYMwfvx4nD9/HgBw4MABqNVq\n7Nq1S1chJ+vfFQuPEUiPs9mQNfpaZzfOVS+M+dh1jKA1ME10dHSHTrg6U2AahmGYzo5Jp3Ot1NXV\nYc6cOdi+fTs8PDx09knthEtKB1xit7dt22bT8ltQQ99BmLHtbQAi7ud0EAdYK1eulLV8SR1wdTrU\nsKUHUrVabXPvmrYuw9nli8Ych0QNDQ00ceJEevXVV4U0WznhMlMlu8FO50zTmZzOyYE1+lpmN+x0\nrrPLF3ttrQ5Ms3btWiEgR3p6OqWkpBBR5wtMY2ssbwjIpjd1Z0Bs3dy+fZuioqIoPDycgoODad26\ndUREVFVVRbGxsTRkyBCKi4ujmpoaIU9aWhoFBgZSUFAQff7550L6mTNnKDQ0lAIDA2nFihWS6Wud\n3bDNdFZs3hDk5eWRQqGg8PBwioiIoIiICMrKyqKqqiqaMGGCwZti48aNFBAQQEFBQZSdnS2kt94U\nAQEB9Oyzz9rkhJwNbgikR4q6uXXrFhER3bt3j6KjoykvL4/Wrl1LmzZtIiKijIwMvZefhoYG0mg0\nFBAQILz8jB49mvLz84mIJH354YaAaYvNGwJ742jGyl1DpunMXUO3bt2iUaNG0bfffmuzcJXcNSR/\nGc4uX+y15ZXFDGOA5uZmREREQKlUCgsqeaYc01kxe9ZQV8XxRvpj5FZAD8erI/G4uLigqKgIN27c\nwKRJk5CTk6Oz3xFmyt2ndTumXVr7bXQoT8zMt7azYmw1U8xW+jujfKlnyrHTOZnhBWXSI7UN/d//\n/R8eeugh/P3vf4darYaPjw+0Wi3GjRuHCxcuCKvq161bB6BlEeWGDRswaNAgjBs3TlhEuX//fuTm\n5kqyiJIXlDFtYadzNkb/7Utu1HIroIfj1ZE4rl27Jrxt3b59G0ePHkVkZKQTh6tU21Y6+xqSXb5Y\nuGuIYdqh1WqRlJSE5uZmNDc3IyEhARMmTEBkZCTi4+ORmZkphKsEgJCQEMTHxyMkJASurq544403\nhG6jN954Qydc5eTJk+U8NYYxCHcNyQx3DUmPs9kQdw0xYuGuIYZhGEYUJhuCxYsXQ6lUIiwsTEhL\nTU2FSqVCZGQkIiMjkZWVJezrTLEIAEfs21PLrYAejldHjC5q20rnMQLZ5YvFZEPw1FNP6cUNUCgU\nWL16NQoLC1FYWIgpU6YA4FgEDMMwzojJhmDs2LHw8vLSSzfUH3Xw4EHMnz8fbm5u8PPzQ2BgIPLz\n86HValFbW4uoqCgAQGJiIj755BMJ1Lc9jjdHPkZuBfRwvDpidImxrXQ7XH9bl+Hs8sVi9RjBzp07\nER4ejiVLlghT7XiFJcMwjPNh1fTRZcuW4S9/+QsA4M9//jPWrFmDzMxMyZTieAToYJvjERgqn+MR\ndIQaHI+gc8sXjTkOiTQaDYWGhprcJzYWwa9TWc1RyW6w0znTdGanc/bAGn0tsxt2OtfZ5Yu9tlZ1\nDWm1WuH/f/3rX8KMIsdfYWk5UrTinp69Bd807X9WaCRaH6lx6DcdBjxG0Pnli8Vk19D8+fORm5uL\na9euYeDAgdiwYYPwOa5QKODv748333wTAK+wNEZtbQ06XvzDMAwjH7yy2ARS9O2JWT2sv0+Nljc8\nNwCNRsv08PDCzZvVlqhpNY7W/+loNmQK268sVqPFZmxTLzxGIL98XlncZWlEy81u+NfyFcJYQ2lp\nqRCDIDQ0FDt27AAAVFdXIy4uDkOHDsXEiROFAWqg8y2kZLoYIscoJMcBVRINRISjtG5f56xHcxF7\n7lqtlgoLC4mIqLa2loYOHUrFxcUcqpJxWMReW/4iYJh2+Pj4ICKiZYquu7s7goODUV5ejkOHDiEp\nKQkAkJSUJCyK7IwLKZmuBTcEJnA8HyFquRXQw/HqSDpKSkpQWFiI6OhoJw5VqbatdPY1JLt8sXBD\nwDBGqKurw5w5c7B9+3Z4eHjo7JM6VCXDyAkHpjGBI82GaSFGbgX0cLw6Es+9e/cwZ84cJCQkCGte\nlEolrly5IoSq9Pb2BtDypl9aWirkLSsrg0qlwoABA1BWVqaTPmDAAIPlcczizhVT2NbyOWaxEyLt\n9FFz9rXs72z1aC5ibYiIkJSUhD59+uDVV18V0p9//nn06dMHKSkpyMjIwPXr15GRkYHi4mIsWLAA\nBQUFKC8vR2xsLH744QcoFApER0djx44diIqKwhNPPIEVK1boraHhwDSMWEQ/N02NJj/11FPk7e2t\n42KiqqqKYmNjaciQIRQXF0c1NTXCvrS0NAoMDKSgoCD6/PPPhfQzZ85QaGgoBQYG0ooVK4yWZ4ZK\ndkWKpeGQdGZQjhn57FuPnc3FRF5eHikUCgoPD6eIiAiKiIigrKwsqqqqogkTJhi0+40bN1JAQAAF\nBQVRdna2kN5q9wEBAfTss89Kpq9ldsMuJjq7fLHX1mTuEydO0Llz53QaAltNo5PihKSGGwLTdLaG\nwN5wQyB/Gc4uX+y1NatrqKSkBNOnT8c333wDABg2bBhyc3OFPtOYmBhcuHAB6enpcHFxQUpKCgBg\n8uTJSE1NxaBBgzB+/HicP38eAHDgwAGo1Wrs2rVLryzuGpJiX8v+zlaP5uJsNsRdQ4xYZFlZ7LzT\n6BiGYZj2iJ41ZItpdJ0xHsF9Wrdj2qXFGNnffls3HoHx4yFKX0tnMHA8AkdGDY5H0Lnli8ac/qP2\n8QiCgoJIq9USEVFFRQUFBQUREccjMAZ4jMCuOJoNmcIafS2zGx4j6OzyxV5bq7qGZsyYgb179wIA\n9u7dK8yz5ngE9iBGbgX0cLw6YnSJsa10jkcgu3yxWByP4K9//SvWrVuH+Ph4ZGZmws/PDx9++CEA\njkfAMAzjjPCCMhNI0bdnm3gEjjNryNH6Px3NhkzB8QjkL8PZ5XM8AoZhGEYU/EVgB3gdgX1xNhvi\ndQSMWPiLgGEYhhEFNwQm0F8HIDdquRXQw/HqiNFFbVvpHI9Advli4YaAYdqxePFiKJVKhIWFCWkc\nr5jp1IhahWADHFAl0UDSBWXm7Ouc9WguYs/dGRwtWmcbXdcmOjtiry1/ETBMO8aOHQsvLy+dNI5X\nzHRmRDUEfn5+GDFiBCIjIwWDt+YT2pFxvL49tdwK6OF4dSQ9zu1oUf3rX1fBN1j7n6dnb+ul8xiB\n7PLFIsrpnEKhgFqtRu/e940oIyMDcXFxeP7557Fp0yZkZGQIUZw++OADFBcXC1GcLl68CBcX/ihh\nnAtHcbR4n9btmHZprdtFv/5tRMu00vbHq1FbO+5+Tgsd/xUVFVl0vLWOBVm+rjxJHS2K6Vfy8/Oj\na9eu6aQFBQXRlStXiIhIq9UKDunS0tIoIyNDOG7SpEl06tQpPZkiVXJIwGMEdkWKc3d0R4vW2UbH\neRjnRez1E/U6rlAoEBsbi1GjRuGtt94CYPknNMM4A13J0SLT9RDVNXTy5En4+vri6tWriIuLw7Bh\nw3T2m/qENraP4xGgg22OR2CofCk/kzufo0U1OB5B55YvGmk+TIhSU1Pp5ZdftvgTuj0SqiQJHI/A\nNByPQBzW6GuZ3ZhjM9bXGccjkF++WJu32tdQfX09mpqa4OHhgVu3bmHixIl46aWXcOzYMfTp0wcp\nKSnIyMjA9evXhcHiBQsWoKCgQBgs/uGHH/S+CpzNT0wrnp69UVtb08ERxs7JVr6G3NAyOKiPh4cX\nbt6s7iCvc+NsNmRPX0Md5XGmOmN0EWvzVncNVVZWYtasWQCAxsZGLFy4EBMnTsSoUaMs/oTuDLQ0\nAh3dmPamdYaIPrW1nafeGYYRD3sfNYG5fXv28zCqhrnxCOz19udo/Z+OZkOmsGc8AlvYBI8RyC+f\nvY8yDMMwouAvAomwf8wBx/kicDSczYZ4jIARC38RMAzDMKLghsAE+usA5EYttwJ6OF4dMbqobSud\nfQ3JLl8s3BAwjAPj6dnboJM4hpESHiOQCB4jcByczYY60te4XfEYAXMfHiNgrMA27ogZhnFO7N4Q\nZGdnY9iwYRgyZAg2bdpk7+ItxvH69tQSyGhdbKb/63h1tBGNHK6OHAv5bV5tW+k8RiC7fLHYtSFo\namrC8uXLkZ2djeLiYuzfvx/nz5+3pwoW0+prHTDeX2vfPtsi04fYmbZ1xOjiGDZvzvWx/ivRHtff\n1mU4u3yx2LUhKCgoQGBgIPz8/ODm5oZ58+bh4MGD9lTBYtpGWLvvRsLQz24a2bEs82hbR4wujmHz\n5lwf678S7XH9bV2Gs8sXiyg31JZSXl6OgQMHCtsqlQr5+fn2VIExiavRL5zO7qzOFphr8+vXv6iX\nxrODGHth14bAUsM+f/48QkJCjO5/6qnF2L0702I9OvYU6gbgnk7Khg0bLC7DdpTYWH5HzurcjF7D\nDRvS0L5vjkwhAAAgAElEQVTe7qNfp6109sbFXJtPT99oQy1KROY39nJw/7rq3yOGr7m111uScIyd\nWL5Y7NoQDBgwAKWlpcJ2aWmpTtQyAAgICDD75nn77d14++3dkupo/GHWSke62WvfXjPy2UofY3RU\nb8b31dbWSP7mGxAQIKk8MZhr8z/++GMHUozVjyXX0BybsfQ6WH7NxVzv1ghxtsKZ5Yu1ebuuI2hs\nbERQUBC++OIL9O/fH1FRUdi/fz+Cg4PtpQLD2BW2ecYZsOsXgaurK1577TVMmjQJTU1NWLJkCd8Q\nTKeGbZ5xBhxuZTHDMAxjX+w6ffTOnTuIjo5GREQEQkJC8MILLwAAUlNToVKpEBkZicjISGRlZQl5\n0tPTMWTIEAwbNgxHjhyxiV5NTU2IjIzE9OnTAQDV1dWIi4vD0KFDMXHiRJ2pX3LoI3f9+Pn5YcSI\nEYiMjERUVBQAeevIkD5y15E1SL3QrLS0FOPGjcPw4cMRGhqKHTt2AOj4WlmDJfeLNVy/fh1z585F\ncHAwQkJCkJ+fL2kZ6enpGD58OMLCwrBgwQLcvXtXlPzFixdDqVQiLCxMSJP6/jBUxtq1axEcHIzw\n8HDMnj0bN27csL4MURGPreDWrVtERHTv3j2Kjo6mvLw8Sk1Npa1bt+od+91331F4eDg1NDSQRqOh\ngIAAampqklynrVu30oIFC2j69OlERLR27VratGkTERFlZGRQSkqKrPrIXT9+fn5UVVWlkyZnHRnS\nR+46spTGxkYKCAggjUZDDQ0NFB4eTsXFxaJkarVaKiwsJCKi2tpaGjp0KBUXFxu9VtZi7v1iLYmJ\niZSZmUlELc+J69evS1aGRqMhf39/unPnDhERxcfH0549e0TJP3HiBJ07d45CQ0OFNKnvD0NlHDly\nRMibkpIiqgy7u5jo3r07AKChoQFNTU3w8vJqbZD0jj148CDmz58PNzc3+Pn5ITAwEAUFBZLqU1ZW\nhsOHD2Pp0qWCDocOHUJSUhIAICkpCZ988oms+hCRbPXTSvvy5awjQ/oYS7NnHVmCLRaa+fj4ICIi\nAgDg7u6O4OBglJeXG71W1mDJ/WINN27cQF5eHhYvXgygZYylZ8+ekpXh6ekJNzc31NfXo7GxEfX1\n9ejfv78o+WPHjhWeY61IfX8YKiMuLg4uLi2P8OjoaJSVlVldht0bgubmZkRERECpVAqfsQCwc+dO\nhIeHY8mSJcJnVEVFhc5UO5VKhfLyckn1WbVqFbZs2SJUKABUVlZCqVQCAJRKJSorK2XVR6FQyFY/\nreXHxsZi1KhReOuttwDIW0eG9AHksyFrMLTQTEq9SkpKUFhYiOjoaKPXyhosuV+sQaPRoF+/fnjq\nqafwyCOP4I9//CNu3bolWRm9e/fGmjVr8PDDD6N///7o1asX4uLiJD0HwP73x+7duzF16lSry7B7\nQ+Di4oKioiKUlZXhxIkTUKvVWLZsGTQaDYqKiuDr64s1a9YYzS/lnPPPPvsM3t7eiIyM7NANcEdl\n2kMfueqnlZMnT6KwsBBZWVl4/fXXkZeXp1emverImD5y15Gl2FKHuro6zJkzB9u3b4eHh4deudaW\nLcX9YorGxkacO3cOzzzzDM6dO4cePXogIyNDsjJ+/PFHbNu2DSUlJaioqEBdXR3effddSc+hPba+\nPzZu3IgHHngACxYssLoM2dxQ9+zZE0888QTOnDkDb29vobKWLl0qfMa0X4xTVlaGAQMGSKbDV199\nhUOHDsHf3x/z58/H8ePHkZCQAKVSiStXrgAAtFotvL29ZdMnMTFRtvppxdfXFwDQr18/zJo1CwUF\nBbLVkTF95K4jSzFnoZk13Lt3D3PmzEFCQgJmzpwJAEavlaVYer9Yg0qlgkqlwujRowEAc+fOxblz\n5+Dj4yNJGWfOnMGjjz6KPn36wNXVFbNnz8apU6ckk9+Kve6PPXv24PDhw3jvvfeENKvKMD0UIh1X\nr16lmpoaIiKqr6+nsWPH0rFjx0ir1QrHvPLKKzR//nwiuj/ocffuXfrpp59o8ODB1NzcbBPd1Go1\nTZs2jYhaBnoyMjKIiCg9PV1vEMbe+lRUVAjp9q6fW7du0c2bN4mIqK6ujh599FH6/PPPZasjY/o4\ngg1Zwr1792jw4MGk0Wjo7t27kgwWNzc3U0JCAq1cuVIn3di1EoM594u1jB07lr7//nsiInrppZdo\n7dq1kpVRVFREw4cPp/r6empubqbExER67bXXRMvXaDR6g8VS3x/ty8jKyqKQkBC6evWqznHWlGHX\nhuDrr7+myMhICg8Pp7CwMNq8eTMRESUkJFBYWBiNGDGCfv/739OVK1eEPBs3bqSAgAAKCgqi7Oxs\nm+mmVquFWRBVVVU0YcIEGjJkCMXFxQmNlz31ycnJEfRZtGiRbPXz008/UXh4OIWHh9Pw4cMpLS2N\niOSrI2P6OIINWcrhw4dp6NChFBAQIJyHGPLy8kihUFB4eDhFRERQREQEZWVldXitrMXc+8UaioqK\naNSoUTRixAiaNWsWXb9+XdIyNm3aRCEhIRQaGkqJiYnU0NAgSv68efPI19eX3NzcSKVS0e7duyW/\nP9qXkZmZSYGBgfTwww8L13rZsmVWl8ELyhiGYbo4HKqSYRimi8MNAcMwTBeHGwIHwc/PD1988QX2\n7NmDbt26wcPDAx4eHggICMCuXbuE40pKSuDi4oJHHnlEJ/+1a9fwwAMPwN/f396qM4xT4Ofnh+PH\njwNocUmSkJAgs0aOAzcEDkLbGLGPPfYYamtrUVtbi48//hjPP/+8XszT27dv47vvvhO233//fQwe\nPNgh5sgzXQ9neJFpe2/wfaILNwQOBrVzJxEREYHg4GBcuHBB57iEhASdQBf79u1DYmKi0YU+DGNL\nnO1Fhu8TXbghcHAKCgpw8eJFjBo1Sid94cKFOHDgAIgIxcXFqKurQ3R0tExaMkwL9niRKS0txezZ\ns+Ht7Y2+ffvi2WefBdCyanj8+PHo27cv+vXrh0WLFul45GSMww2BA3L69Gl4eXnB09MTY8aMQWJi\nIgIDA3WOUalUCAoKwtGjR/HOO+8gMTFRJm0ZxjhSv8g0NTVh2rRp8Pf3x88//4zy8nLMmzdP2P+/\n//u/0Gq1OH/+PEpLS5Gamir1KXVKuCFwQMaMGYOamhrcvHkTV65cwbfffov169frHKNQKJCYmIi3\n334bBw4cQEJCAn/uMg6BLV9kCgoKoNVqsWXLFjz00EN48MEH8dhjjwFoids7YcIEuLm5oW/fvli1\nahVyc3MlP7/OCDcEDo63tzdmz56NTz/9VG/f7NmzcfjwYQQEBEjip4ZhpMCWLzKlpaUYNGiQjvfT\nViorKzFv3jyoVCr07NkTCQkJqKqqkuy8OjPcEDgQhm6Eqqoq/Otf/0JoaKjevh49eiAnJwd///vf\n7aEew1iM1C8yAwcOxOXLl9HU1KS3b/369ejWrRu+/fZb3LhxA/v27UNzc7Poc+gKcEPgQLTOujh1\n6pQw/S4kJARKpRI7d+7UOa6VRx55RGfKHU+LY+TCHi8y0dHR8PX1xbp161BfX487d+7gq6++AtDi\nfrtHjx7w9PREeXk5tmzZYv3JdDHMagikiKF79uxZhIWFYciQIXjuueckPg3nR6PRYPz48UhKSkJj\nY6Mw/a6yshLvvfce+vbtC6BlvnZTU5PBT+PY2Fj89NNP9la9UyJVnOauZPf2eJFxcXHBp59+ih9+\n+AEPP/wwBg4ciA8//BAA8NJLL+HcuXPo2bMnpk+fjjlz5hiVJ3XMAafHHM93YmLotro/HT16NOXn\n5xMR0ZQpUygrK8ucohlGFsTGaWa7Z5wJk18EYmPo5ufnQ6vVora2VnizSkxMFBXXlGHsQXsbtyQO\nLds940yYbAikiKHbPn3AgAEOETeWYYwhRZxmtnvruHz5stC11Pbn6ekpBGhnpKXDhkCKGLoM44yI\njdPMWM/DDz8sjJG1/d28eZOnSdsI1452tsYoPXz4MO7cuYObN28iMTER77zzjnDM0qVLhUFkQ7Ey\nVSoVBgwYoNOSdxRDs2/fvjz3lxFFQEAAfvjhB1EyOorT7OPjYzIOrSV2zzbPiEW0zZs7mCA2hm5U\nVBSdPn2ampubOxw0s0AlgyQlJXF+kcitg9j8Ym1IyjjN5ti9WH1NIYVNyCnfHmU4u3yxNtThF0G7\nBkP4FH7++efx3//+FwqFAv7+/njzzTcBACEhIYiPj0dISAhcXV3xxhtvCHneeOMNJCcn4/bt25g6\ndSomT55sfevVAX5+fpxfJHLrIMU5iKGyshKzZs0CADQ2NmLhwoWYOHEiRo0ahfj4eGRmZsLPz0+Y\ntugIdt8Rtq5Pe1wvZz8HuW3aFGY3BDExMYiJiQHQ4inQGOvXr9dbTg4AI0eOxDfffGO5hgxjZ/z9\n/fXcJgNA7969cezYMYN52O4ZZ6bTrSzu1asX5xeJ3DpIcQ7MfWxdn/a4Xs5+Do5u052uIYiIiOD8\nIpFbBynOoSvj6dlbJ1DMqlWroFAo4OnZ2ybl2eN62boMZ5cvFsWvAw0d0tTUhFGjRkGlUuHTTz9F\ndXU1nnzySfz8889CX2lri5eeno7du3ejW7du2LFjByZOnAigZal9cnIy7ty5g6lTp2L79u2GFVIo\n2J0yIwpnsyGp9W0ZnzAkz7nqhTEfsTZk1hfB9u3bERISIgyAZWRkIC4uDhcvXsSECROQkZEBACgu\nLsYHH3yA4uJiZGdn45lnnhGUW7ZsGTIzM3Hp0iVcunQJ2dnZVivNMAzDSIdVLiYceam9Wq3m/CKR\nWwcpzoFpi9q20u1wvWxdhrPLF4tVLiZ4qb11tO+7bf3Zqu+WYRjGHKxyMdEWR1tq3zrFVc78xh74\ntbU1aOm71f21pEtXvljk1kGKc2DaEmNb6Xa4XrYuw9nli8ViFxMJCQk2W2rfSnJysrAAo1evXoiI\niBAqsvUTy5G37z/wgfuf5TEAFO222+6Hw+jvbNtFRUWC48OSkhIwDGMh5i5BbutiwlZL7X+dwWT5\n+ug25OTkyJ4fAAFk4Gc83VH0dwQdxOYXa0P2Rmp99e0sR8/OpEQKm5O7DGeXL/bamr2yGLgfPWjd\nunVOudSeYRiG0cesdQT2xNnmgBuio3ncPL/b9jibDfE6AkYsdllHwDBdjfZxujleMdOZ6XQNgdxz\n2J09vyPo4AhzrjvXIkq1baXzOgLZ5Yulw4bgzp07iI6ORkREBEJCQvDCCy8AAFJTU6FSqRAZGYnI\nyEhkZWUJefjtiHF2nG0RJcOIxtRo8q1bt4iI6N69exQdHU15eXmUmppKW7du1Tu2ddZQQ0MDaTQa\nCggIEGYNjR49mvLz84mIbDpryBGAiFlDjHjE1ufcuXPp3LlzOjPlevXqJexvbm4WtpcvX07vvvuu\nsG/JkiX00Ucf0ZkzZyg2NlZIP3HihCBLan0NyWM761qIvbYmZw11794dANDQ0ICmpiZ4eXm1NiB6\nxxp7Oxo0aJDBtyOeOcQ4Gm0XURr7nLfFIkop1860oAavVem825KvnTHVUjQ1NVF4eDi5u7vT2rVr\niYgoNTWVBg0aRCNGjKDFixdTTU0NETnG25Hcc9h5HYH8+cXY0AsvvEAqlYr8/PzIx8eHunfvTosW\nLaKgoCDSarVE1BKqNSgoiIha1tGkp6cL+SdNmkSnT58mrVZLw4YNE9Lff/99evrppyXX15g8XkfQ\nteSLvbYmB4tdXFxQVFSEsrIynDhxAmq1GsuWLYNGo0FRURF8fX2xZs0a8S1SG5KTk5GamorU1FRs\n27ZN581MrVZ3uF1UVGTR8bbIr4saum9khrbvI7f+rW8bzpR/27Ztgr0kJydDDGlpaSgtLYVGo8GB\nAwcwfvx47Nu3DzNmzMDevXsBAHv37sXMmTMBADNmzMCBAwfQ0NAAjUaDS5cuISoqCj4+PvD09ER+\nfj6ICPv27RPyMIzDYUmr8de//pW2bNmik6bRaCg0NJSIHPPtSA7AYwSyIlV9qtVqmj59OhERVVVV\n0YQJE2jIkCEUFxcnfAUTEW3cuJECAgIoKCiIsrOzhfQzZ85QaGgoBQQE0LPPPmtzfdvKYzvrWoi9\nth3mvnr1qmDw9fX1NHbsWDp27JjwiUxE9Morr9D8+fOJyDFcTDgC3BDIi7PVJzcEjFjEXtsOu4a0\nWi3Gjx+PiIgIREdHY/r06ZgwYQKef/55jBgxAuHh4cjNzcWrr74KQNfFxJQpU/RcTCxduhRDhgxB\nYGCgzQaK23YbcH7n1EGKc2DaoratdF5HILt8sXQ4aygsLAznzp3TS3/nnXeM5lm/fj3Wr1+vlz5y\n5Eh88803VqjIMAzD2BL2NWQD2NeQvDibDbGvIUYs7GuIYRiGEYVVLiYc2QGX3P3Tzp7fEXRw9P5U\nR8BYFDzDC93UNtWFxwjkly+WDhuC3/zmN8jJyUFRURG+/vpr5OTk4Msvv3RyB1wM4/wYC3tquEuI\nYTrG7DGC+vp6/O53v8OePXswZ84c5ObmCiErY2JicOHCBaSnp8PFxQUpKSkAgMmTJyM1NRWDBg3C\n+PHjcf78eQDAgQMHoFarsWvXLn2FnKx/1xA8RiAvzmZD1uhr3MYAtrOuh83HCJqbmxEREQGlUolx\n48Zh+PDhqKyshFKpBAAolUpUVlYCACoqKqBSqYS8KpUK5eXleukDBgxAeXm51UozDMMw0mHS6Vyr\ni4kbN25g0qRJyMnJ0dnvaA64tm3bJsphlxT5dVH/+jfGxDYcQv9WFw8rV650mvwcvN4Uaty3NxtI\nV6vbObxzvjKcXb5oLFl91upiwpEdcMnt8IydzsmfX6wN2Rtr9DVuS+x0rivKF3ttrXIxsXbtWsrI\nyCCilod/SkoKEbGLiVbENASMeMTW5+3btykqKorCw8MpODiY1q1bR0Qt/oZiY2MN+htKS0ujwMBA\nCgoKos8//1xIb/U3FBgYSCtWrJBMX8saArazzo5NG4Kvv/6aIiMjKTw8nMLCwmjz5s1E5FwOuOSA\nGwJ5kaI+DQVkWrt2LW3atImIiDIyMvRegKwNyMQNASMWmzYEcsBdQ/Lq7wg6OFLX0K1bt2jUqFH0\n7bffUlBQEF25coWIiLRardAlmpaWJnwhE7V0iZ46dYoqKip0ukT3799vsEuUu4bkL8PZ5Yu9tryy\nmGEMwLPlmK6EyYagtLRUuBFCQ0OxY8cOAI4bwF7syHxXz+8IOjjC7Ir2AZnsMVvOdsTYVrodrpet\ny3B2+WIxOX3Uzc0Nr776KiIiIlBXV4eRI0ciLi4OCoUCq1evxurVq3WOb7u6uLy8HLGxsbh06RIU\nCoWwujgqKgpTp05FdnY2xy1mHJqePXviiSeewNmzZ4UFlD4+PtBqtfD29gbQ8qZfWloq5CkrK4NK\npcKAAQNQVlamkz5gwACD5VgzZfo+rdsx7dJi2u1Hh/J423m27R6zuD2///3v6ejRo5Samkovv/yy\n3n45+kvbInf/NI8RyJ9frA3Ze7acNfoatyUeI+iK8sVeW4vGCEpKSlBYWIgxY8YAAHbu3Inw8HAs\nWbJEaJ24v5RxdowFZFq3bh2OHj2KoUOH4vjx41i3bh0AxwjIxDBiMNvXUF1dHWJiYvDiiy9i5syZ\n+OWXX9CvXz8AwJ///GdotVpkZmbi2WefxZgxY7Bw4UIAwNKlSzFlyhT4+fkJNxIA5OXlYfPmzfj0\n0091FXIyPzGGYF9D8uJsNsS+hhixiLV5k2MEAHDv3j3MmTMHixYtwsyZMwFA6B8FWh7206dPByBf\nf6mjbd+ndTvGxDYcSn9n2mYXEwwjElN9R83NzZSQkEArV67USa+oqBD+lzKAvRkqdYjc/dM8RiB/\nfrE2ZG+s0de4LfEYQVeUL/bamvwiOHnyJN59912MGDECkZGRAIC0tDTs378fRUVFUCgU8Pf3x5tv\nvglAt7/U1dVVr780OTkZt2/fxtSpU7m/lGEYxgHgmMU2gMcI5MXZbIjHCBixcMxihmEYRhSdriHQ\nH6zl/M6mgxTnwLRFbVvpHLNYdvlisdrFhCMHsGcYhmEswNRoslarpcLCQiIiqq2tpaFDh1JxcbFD\nueR1NCBi1hAjHmerT2v0NW5LbGddEbHX1uQXgY+PDyIiIgAA7u7uCA4ORnl5OQ4dOoSkpCQAQFJS\nEj755BMAwMGDBzF//ny4ubnBz88PgYGByM/Ph1arRW1tLaKiogAAiYmJQh6GYRhGPqxyMREdHe2w\nLnnl7p929vyOoIOj96c6H2rbSucxAtnli8XshqCurg5z5szB9u3b4eHhobPPuVzyMgzDMG2xyMVE\nQkKC4GLC0VzytvX3rVarrXZZIEV+XdS//o0xsd0mh4z6t39zcYb8UruYKC0tRWJiIn755RcoFAr8\nz//8D1asWIHq6mo8+eST+Pnnn+Hn54cPP/wQvXr1AtAyQWL37t3o1q0bduzYgYkTJwJomSCRnJyM\nO3fuYOrUqdi+fbto/SwnxrbSOR6B7PJFY2oQwZiLCUdyyetogAeLZUVsfTrDBAnjtsR21hURe21N\n5s7LyyOFQkHh4eEUERFBERERlJWVZbMA9mJPSG4/N+xrSP78Uj/wWmNwcMxiw7CvIfnli722JruG\nHn/8cTQ3Nxvcd+zYMYPp69evx/r16/XSR44ciW+++cZUkQzjMJg7QaI1Rgdwf4KEm5sbx+BgnAKz\nxgicCbF9cV09vyPo4Cj9qfacIGHbUJVtj5HeFXhrmq1dj9tKf2eUL/W4GDudswHsdE5epLChe/fu\nYdq0aZgyZQpWrlwJABg2bBjUarUwQWLcuHG4cOECMjIyAECIWDZ58mRs2LABgwYNwrhx43D+/HkA\nwP79+5Gbm4tdu3aJ1pedzjFtsbnTucWLF0OpVCIsLExIS01NhUqlQmRkJCIjI5GVlSXsk9u9hNj5\nul09vyPoIMU5iIGIsGTJEoSEhAiNAADMmDEDe/fuBQDs3btXmEE3Y8YMHDhwAA0NDdBoNLh06RKi\noqLg4+MDT09P5Ofng4iwb98+IY99UdtWOq8jkF2+WEw2BE899RSys7N10hQKBVavXo3CwkIUFhZi\nypQpAIDi4mJ88MEHKC4uRnZ2Np555hmhlVq2bBkyMzNx6dIlXLp0SU8mwzgKrTE4cnJyhJed7Oxs\njlnMdFrM6hoqKSnB9OnThYHeDRs2wN3dHWvWrNE5Lj09HS4uLkhJSQHQ8omcmpqKQYMGYfz48cIn\n8oEDB6BWq/U+kQHuGmLE42w2xF1DjFhki0ewc+dOhIeHY8mSJcKghdzuJRiGYRjLsaohWLZsGTQa\nDYqKiuDr66v3ZSCW5ORkpKamIjU1Fdu2bdPpX1Or1R1uW3q8LfLrooZuH62h7fvIrb9ardY5B2fI\nv23bNsFekpOTwbRHbVvpPEYgu3zRmLPYQKPRUGhoqMl96enplJ6eLuybNGkSnT59mrRarc7Cmvff\nf9/gwppfu6nMUckoci9m4gVl8ucXa0P2xhp9jdsSLyjrivLFXlurGoKKigrh/1deeYXmz59PROLd\nSxA5301sCDENASMeZ6tP2zcEbGedHbHX1uSCsvnz5yM3NxfXrl3DwIEDsWHDBqh/XdCgUCjg7++P\nN998E4Du7AlXV1e92RPJycm4ffs2pk6dyrMnGIZhHAWJGiTJEKuS3N0S3DUkf34HNOsOsUZf47bE\nXUNdUb7Ya9vpgtczDMMwlsEuJmwAryOQF2ezIV5HwIhFFhcT1dXViIuLw9ChQzFx4kRhHQEgv4sJ\nhmEYxjKscjGRkZGBuLg4XLx4ERMmTBCcbjmCiwmx83W7en5H0MHh51w7HWrbSud1BLLLF4vJhmDs\n2LHw8vLSSTt06BCSkpIAAElJSfjkk08AAAcPHsT8+fPh5uYGPz8/BAYGIj8/H1qtFrW1tYiKigIA\nJCYmCnkYxtHgr2Cmy2HOiHL7dQS9evUS/m9ubha2ly9fTu+++66wb8mSJfTRRx/RmTNnKDY2Vkg/\nceIETZs2zWBZZqrk0IDXEciK2Po8ceIEnTt3TsfmbRWm0lp9jdsS21lXROy1FR2YRuoAHYC44PWO\nsn2f1u0YE9twKP2daVvqIB1jx47Vk3Po0CHk5uYCaPkKjomJQUZGhtGv4EGDBhn8Cub1M4xDYk5r\n0f6LICgoiLRaLRG1rDJujd3KLiZ4HYEj5BdrQ0SO/xVs3JY6Wkfg+us+/Z+Hh5fFOrTC6wjkly/W\n5q36ImgN0JGSkqIXoGPBggVYvXo1ysvLhQAdCoVCCNARFRWFffv2YcWKFeJaMIaRCUf5Cr5P63ZM\nu7TW7aJf/zai5bnf/ng1amvH3c9p4VdZUVGRRcdb+9XH8nXlSfkVbLIZmTdvHvn6+pKbmxupVCra\nvXs3VVVV0YQJE2jIkCEUFxdHNTU1wvEbN26kgIAACgoKouzsbCH9zJkzFBoaSgEBAfTss8/arGVz\nBGDxF4HhNzUxb2ldGSlsyNG/go3bkjX21znuu66M2OvncFe/Mxik5TciD+5JiS0agrVr11JGRgYR\ntTz82w8W29vRIjcETFu4IWiH3P3T1o4R6PfnWlcXPEYg3oac4SvYsoYgx4T9iaszHiOQX75Ymxc9\na6gr4+nZG7W1NXKrwUjM/v37DaYfO3bMYPr69euxfv16vfSRI0cK4V0ZxpER5WvIz88Pnp6e6Nat\nG9zc3FBQUIDq6mo8+eST+Pnnn+Hn54cPP/wQvXr1AtCy8Gb37t3o1q0bduzYgYkTJ+or5ER+Yqzx\nKWRpurPUhSPhTDYE2NfXUEd5nKnOGF1ki1ncWrharUZhYSEKCgoAWOZ+orm5WUzxDMMwjASIdkPd\nvhWyxP1Ea+MhJWJ9eoj3CSJvfil8mshdh1KcA9MWtW2ls68h2eWLRfQXQWxsLEaNGoW33noLAFBZ\nWQmlUgkAUCqVqKysBABUVFRApVIJeVUqFcrLy8UUzzAMw0iAqMHikydPwtfXF1evXkVcXByGDRum\ns93l1CwAAAsvSURBVN/Uwhtj+8S4mGhNs3axhqX5DS/maUv7/ca22+exj/6mFis5Q37JF9d0OmJs\nK72N7TlrGc4uXyySBabZsGED3N3d8dZbb0GtVsPHxwdarRbjxo3DhQsXhLGCdevWAQAmT56MDRs2\nIDo6WlchJxro48Fix8SZbAjgwWJGPLINFtfX16O2thYAcOvWLRw5cgRhYWGC+wkAeu4nDhw4gIaG\nBmg0GsH9hNTI3z8tb34eI2D0UdtWOo8RyC5fLFZ3DVVWVmLWrFkAgMbGRixcuBATJ07EqFGjEB8f\nj8zMTGH6KACEhIQgPj4eISEhcHV1xRtvvCG5vxaG6WzwWhXGHnDMYhFw15Bj4kw2BHSsr+U21tE+\n7hrqrMi6joBhGIZxfuzeEGRnZ2PYsGEYMmQINm3aJLl8+fun5c3PYwSOh61t3jRq20rnMQLZ5YvF\nrg1BU1MTli9fjuzsbBQXF2P//v04f/68pGW0+kaXK/993+/y5Bevv/x1KMU5OAr2sHnT2LY+7XG9\nbF2Gs8sXi10bgoKCAgQGBsLPzw9ubm6YN28eDh48KGkZbYOKy5EfkDK/q7AWo+3P07O38dyi9Ze/\nDqU4B0fBHjZvGnPq07CtmbI3wD7Xy9ZlOLt8sdjV+2h5eTkGDhwobKtUKuTn59tTBYuRd9ZGa0Qp\nXWprebaVs2Cuzb/77rt6afadVWfY1gC2t66AXRsCqQ37X//6F2bPnq2XvmHDBvz975lYsmSx2bLa\nPvA3bNjQbm9HszPaU2J2mYYxJ7+rwbr08PDC7NkzRJYvfnWu3PkdCXNtPiEhwYZalIjMb9zebt6s\ntsv1snUZzi5fNKKiGVjIqVOnaNKkScJ2WlqaEPWplYCAgF8DaPCPf9b9AgIC7GnWHcI2zz97/MTa\nvF3XETQ2NiIoKAhffPEF+vfvj6ioKOzfvx/BwcH2UoFh7ArbPOMM2LVryNXVFa+99homTZqEpqYm\nLFmyhG8IplPDNs84Aw63sphhGIaxL3adPrp48WIolUqEhYUJaWvXrkVwcDDCw8Mxe/Zs3LhxQ9iX\nnp6OIUOGYNiwYThy5IjB/K1s3boVLi4uqK6utjj/zp07ERwcjNDQUKSkpFiUv6CgAFFRUYiMjMTo\n0aPxn//8x2j+0tJSjBs3DsOHD0doaCh27NgBAKiurkZcXByGDh2KiRMn6kw1M1eGufX47rvvGsxv\nbj12lN+cejSW39x6/OyzzxAdHY2IiAiEhITghRdesLgOHQWpF5pZY1/W0NTUhMjISEyfPt0m8q9f\nv465c+ciODgYISEhyM/Pl7SM9PR0DB8+HGFhYViwYAHu3r0rSr6h54LU9ij22WkSUSMMFnLixAk6\nd+4chYaGCmlHjhyhpqYmIiJKSUmhlJQUIiL67rvvKDw8nBoaGkij0VBAQACp1Wq9/EREly9fpkmT\nJpGfnx9VVVVZlP/48eMUGxtLDQ0NRET0yy+/WJT/d7/7HWVnZxMR0eHDhykmJsZo/vLyciosLCQi\notraWho6dCgVFxfT2rVradOmTURElJGR0WEdGJNhbj0OGjSIzp49q5ff3Ho0lt/cejSW35J6rK2t\nJSKie/fuUXR0NOXl5VlUh631JCeNjY0UEBBAGo2GGhoaKDw8XLgO1qLVai2yL2vZunUrLViwgKZP\nn05EJLn8xMREyszMJKKWa3z9+nXJytBoNOTv70937twhIqL4+Hjas2ePKPmGnmtS26PYZ6epMuz6\nRTB27Fh4eXnppMXFxcHFpUWN6OholJWVATAc2vLBBx/Uyw8Aq1evxubNm3XSzM3/t7/9DS+88ALc\n3NwAAP369bMov6+vr9ASX79+HQMGDDCa//Lly4iIiAAAuLu7Izg4GOXl5RaF9zQko6Kiwux6HDZs\nGBoaGvTym1uPhvKXl5dj165dZtWjsfyW1OO3334LAGhoaEBTUxO8vLxkD5FqKbZYaObj42ORfVlD\nWVkZDh8+jKVLlwpOzqSUf+PGDeTl5WHx4pap366urujZs6dkZXh6esLNzQ319fVobGxEfX09+vfv\nL0q+oeea1PYo9tlpqgyHcjq3e/duTJ06FYD5oS0PHjwIlUqFESNG6KSbm//SpUs4ceIExowZg5iY\nGJw5c8ai/BkZGVizZg0efvhhrF27Funp6WblLykpQWFhIaKjo60O79lWRlvMrce2+a2px7b5L168\naHE9tuYfM2aMRfVYWlqKiIgIKJVKoSvE2UKkGlpoJqVe5tiXNaxatQpbtmwRHkCA8fC01qDRaNCv\nXz889dRTeOSRR/DHP/4Rt27dkqyM3r17C3bWv39/9OrVC3FxcZKeA2D/kL3WPDvb4jANwcaNG/HA\nAw9gwYIFRo9pv6ilvr4eaWlpOgvAqIOxb0OLYhobG1FTU4PTp09jy5YtiI+Ptyj/kiVLsGPHDly+\nfBmvvvqq8CbTUf66ujrMmTMH27dvh4eHh94x5oT3rKurw9y5c7F9+3a4u7sL+82tx7b5XVxcLK7H\ntvk9PDwsrsf2+ltSj926dUNRURHKyspw4sQJ5OTk6Mm3JkSqPbGlDmLsqyM+++wzeHt7IzIyskO3\n2WLOrbGxEefOncMzzzyDc+fOoUePHkJ0QynK+PHHH7Ft2zaUlJSgoqICdXV1equ6xZ5De2xtj9Y8\nO9vjEA3Bnj17cPjwYbz33ntC2oABA1BaWipsl5WVCd0Frfz4448oKSlBeHg4/P39UVZWhpEjR6Ky\nstKs/EBLa9m6Onn06NFwcXHBtWvXzM5fUFAgBOiZO3eu8AlmLP+9e/cwZ84cJCQkCNHblEolrly5\nAgDQarXw9vY2S8aiRYsEGZbUo1Kp1MlvaT22z29pPRrKb2k9AkDPnj3xxBNP4OzZsxbXody016u0\ntFTnLc5aLLEvS/nqq69w6NAh+Pv7Y/78+Th+/DgSEhIkkw+02JFKpcLo0aMBtNjCuXPn4OPjI0kZ\nZ86cwaOPPoo+ffrA1dUVs2fPxqlTpyST34q97NHaZ6ceZo+ISIRGo9EZ8MjKyqKQkBC6evWqznGt\nAx53796ln376iQYPHkzNzc16+dtiaJDTVP5du3bRX/7yFyIi+v7772ngwIEW5Y+MjCS1Wk1ERMeO\nHaNRo0YZzd/U1EQJCQm0cuVKHb3Xrl0rrDZNT0/XG/QxR4a59ejv728wv7n1aCy/ufVoLL+59Tho\n0CCqrq4mIqL6+noaO3YsHTt2zKI6bG5uNnru9uLevXs0ePBg0mg0dPfuXUkGi5ubmy2yLzGo1Wqa\nNm2aTeSPHTuWvv/+eyIieumll2jt2rWSlVFUVETDhw+n+vp6am5upsTERHrttddEy2//XLCFPYp9\ndnaEXRuCefPmka+vL7m5uZFKpaLMzEwKDAykhx9+mCIiIigiIoKWLVsmHL9x40YKCAigoKAgys7O\nFvI/8MADpFKpaPfu3Try/f39hQeYufkbGhpo0aJFFBoaSo888gjl5OSYzN+q/+7du+k///kPRUVF\nUXh4OI0ZM4bOnTtnNH9eXh4pFAoKDw8XzjcrK4uqqqpowoQJNGTIEIqLi6OamhqLZBw+fNjsenz5\n5ZcN5je3Hg3lz8rKMrsejZVvbj3+7W9/o8jISAoPD6ewsDDavHkzEZFFdegoHD58mIYOHUoBAQGU\nlpYmWp419mUtarVamDUktfyioiIaNWoUjRgxgmbNmkXXr1+XtIxNmzZRSEgIhYaGUmJiIjU0NIiS\nb+i5ILU9in12moIXlDEMw3RxHGKMgGEYhpEPbggYhmG6ONwQMAzDdHG4IWAYhunicEPAMAzTxeGG\ngGEYpovDDQHDMEwXhxsChmGYLs7/Bwds9AHdjqxWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xf0a5828>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Corresponding simulated returns of weighted portfolio\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ImYuZtJExk95YOIiIKCHsceiMPQ4iSjb2OIiISGosHBrIOaepGB0giozjJGMm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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xf390860>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Simulated loss of portfolio\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CAJhMJrS0tAAAvF4vzGZz0H31LE9ISFD3VV9fj48//hi33norpk2bhj/84Q8X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\nRc3whuOoEEMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1798d080>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Value-at-Risk: 66374.80\n",
        "Expected Shortfall: 83508.28\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And now using the historic method"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "constructPortfolio(simulateLoss='historic')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Behavior of stock over last 500 days\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IYWxc8T6cmocnzypAKP4zrlP9qFvr3r1AaCgwdiwz5O+9B0yfzlwpsltK9vbs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xf09cfd0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Current value per asset:\n",
        "GOOGL_asianCallAM     27.089735\n",
        "IBM                  188.110000\n",
        "IBM_call              17.288251\n",
        "GOOGL                440.630000\n",
        "dtype: float64\n",
        "\n",
        "Weight in portfolio:\n",
        "GOOGL_asianCallAM    2000\n",
        "IBM                   500\n",
        "IBM_call             5000\n",
        "GOOGL                 200\n",
        "dtype: float64\n",
        "\n",
        "Simulated return histograms\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ISMD48ePxzjvvADCeK55h+gL81Mo4EpJesp44cQK+vr64ceMGEhMTERoaqldu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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xed705f8>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Corresponding simulated returns of weighted portfolio\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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33hKFhYWG5vzkk0/U6z777DMxb948cf78edPVc6icLS0tpqqnP0VRxDe/+U0h\nhPm+P4fKabbvzwcPHoj79+8LIYTo7u4Wc+fOFWfPnjVVPYfKaMbvzXnz5omPPvpICCHEG2+8IbZv\n326qWvoLuSlcvHhRWCwWkZmZKZxOp3A6neLMmTPi7t27YsGCBSI1NVXk5eX1O+EvfvELkZycLKZN\nmyYqKyvVy99//30xc+ZMkZycLH74wx+qlz98+FB8+9vfFikpKSInJ0fU19er1x0/flykpKSIlJQU\nUVpaOqyc7777rigqKhKzZs0SGRkZ4lvf+pZobW01NOc///lPkZWVJTIzM8WsWbPEL3/5SyGEMF09\nh8pptnr6UxRFfVeP2erpr6qqSs25du1aU9Xz1q1bIjMzU2RmZooZM2aIffv2ma6eQ2U04/dmTU2N\neOmll0RGRoZYsWKF6OzsNFUt/fHDa0REpOJ/x0lERCo2BSIiUrEpEBGRik2BiIhUbApERKRiUyAi\nIhWbAhERqdgUiIhI9f+B6vAin7c7WQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x179b02b0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Simulated loss of portfolio\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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37dpl2M8lL1YlIiLdmPLsOCIiig3shIiISDfshIiISDfshIiISDfs\nhIiISDfshIiISDfshIiISDfshIiISDf/D1YGNE1AlAt+AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xf165940>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Value-at-Risk: 64479.93\n",
        "Expected Shortfall: 80451.25\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Expectation Maximizaton of Gaussian Mixtures"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the homework we are given an implementation for an algorithm which finds the maximum likelihood for models with latent variables. This particular algorithm applies to Gaussian mixture models. Here we provide the Python version for this implementation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def expectationMaximizationGM(Z, K, p=None, mu=None, sigma=None):\n",
      "    \"\"\"\n",
      "    expectationMaximizationGM: EM algorithm for a mixture of K Gaussians GM[p,mu,sigma]\n",
      "\n",
      "\n",
      "    INPUT:\n",
      "         Z : Sample with M observations \n",
      "         K : Number of Gaussians in the mixture\n",
      "\n",
      "    OPTIONAL INPUT PARAMETERS (initial seed for EM)\n",
      "         p : vector of probabilitiess  [Kx1]\n",
      "        mu : vector of means           [Kx1]\n",
      "     sigma : vector of stdev's         [Kx1]\n",
      "\n",
      "    OUTPUT:\n",
      "         p : vector of probabilitiess  [Kx1]\n",
      "        mu : vector of means           [Kx1]\n",
      "     sigma : vector of stdev's         [Kx1]\n",
      "\n",
      "%% EXAMPLE:\n",
      "%\n",
      "%   %% Sample matrix (M rows, N columns) \n",
      "%   M = 1000;\n",
      "%   N = 1;\n",
      "%   %% Gaussian components\n",
      "%   p     = [ 1/2 1/3  1/6];  % probability vector \n",
      "%   mu    = [-1.0 4.0 12.0];  % means \n",
      "%   sigma = [ 1.0 3.0  0.5];  % standard deviations\n",
      "%\n",
      "%   %% Generate sample Z ~ GM[p,mu,sigma)\n",
      "%   Z = GMrand(M,N,p,mu,sigma);\n",
      "%\n",
      "%   %% EM for Gaussian mixture\n",
      "%   [p, mu, sigma] = expectationMaximizationGM(Z,3)\n",
      "%\n",
      "%   %% Compare modelPdf and scaled histogram\n",
      "%   modelPdf = @(z)(GMpdf(z,p,mu,sigma));\n",
      "%   figure(1); graphicalComparisonPdf(Z(:),modelPdf)\n",
      "%   title('Z ~ GM[p,\\mu,\\sigma]')\n",
      "    \"\"\"\n",
      "    if K == 1:\n",
      "        # Fit to a single Gaussian  \n",
      "        p = 1\n",
      "        mu = np.mean(Z)\n",
      "        sigma = np.std(Z)\n",
      "        return p, mu, sigma\n",
      "\n",
      "    if mu is None or sigma is None or p is None:\n",
      "        # initialization of parameters\n",
      "        mu0 = np.mean(Z)\n",
      "        sigma0 = np.std(Z)\n",
      "        mu = np.linspace(mu0 - 2 * sigma0, mu0 + 2 * sigma0, K)\n",
      "        sigma = 2 * sigma0 * np.ones_like(mu, dtype=np.float)\n",
      "        p = np.ones(K, dtype=np.float) / K\n",
      "        \n",
      "    p = np.asarray(p).flatten()\n",
      "    sigma = np.asarray(p).flatten()\n",
      "    mu = np.asarray(mu).flatten()\n",
      "\n",
      "    Z = np.asarray(Z).flatten()  # Ensures that Z is a row vector\n",
      "    M = Z.size                   # Size of the sample\n",
      "    \n",
      "    a, b, c, m = 0.0, 0.0, 0.0, 0.0    # standard EM\n",
      "    #a, b, c, m = .2, .2, .1, .0       # Modified EM (Hamilton, 1991)\n",
      "\n",
      "    TOL_MU = 1e-6\n",
      "    TOL_SIGMA = 1e-6\n",
      "    TOL_P  = 1e-6\n",
      "    MAXITER = 5000\n",
      "    \n",
      "    ##  EM Algotrithm \n",
      "    dmu = 10 * TOL_MU\n",
      "    dsigma = 10 * TOL_SIGMA\n",
      "    dp = 10 * TOL_P\n",
      "    nIter = 0\n",
      "    \n",
      "    def gt(vec, tol):\n",
      "        return np.any(np.abs(vec) > tol)\n",
      "    \n",
      "    def weightedNormPDF(Z, mu, sigma, p):\n",
      "        Zsc = (Z[np.newaxis]-mu[:, np.newaxis])/sigma[:, np.newaxis]\n",
      "        return p[:, np.newaxis] * np.exp(- (Zsc**2) /2) / (np.sqrt(2*np.pi) * sigma[:, np.newaxis])\n",
      "    \n",
      "    while ((nIter < MAXITER) & (gt(dmu, TOL_MU) | gt(dsigma, TOL_SIGMA) | gt(dp, TOL_P))):\n",
      "        # increment the iteration counter\n",
      "        nIter = nIter + 1\n",
      "        gamma = np.empty((K, M), dtype=np.float)\n",
      "        \n",
      "        \n",
      "        gamma = weightedNormPDF(Z, mu, sigma, p)\n",
      "        \n",
      "        gNorm = gamma.sum(axis=0)\n",
      "        gamma = gamma / gNorm[np.newaxis, :]\n",
      "        gNorm2 = gamma.sum(axis=1)\n",
      "        \n",
      "        \n",
      "        dp = -p\n",
      "        dmu = -mu\n",
      "        dsigma = -sigma\n",
      "        \n",
      "        \n",
      "        p = gNorm2 / M\n",
      "        mu = (c * m + np.dot(gamma, Z))/(c + gNorm2)\n",
      "        sigma = np.sqrt((b + c * (m - mu))**2 + \n",
      "                        (gamma * (Z[np.newaxis, :] - mu[:, np.newaxis])**2).sum(axis=1) /\n",
      "                        (a + gNorm2))\n",
      "        \n",
      "        # check how much paremeter estimates have changed\n",
      "        dp = dp + p\n",
      "        dsigma = dsigma + sigma\n",
      "        dmu = dmu + mu\n",
      "        \n",
      "    if (nIter >= MAXITER):\n",
      "        print 'Warning: EM for GM has not fully converged. Try a smaller number of Gaussians'\n",
      "\n",
      "    return p,mu,sigma\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 181
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def categoricalRand(M, N, p):\n",
      "    \"\"\"\n",
      "    Random number generator for categorical variables.\n",
      "    \n",
      "    INPUT:\n",
      "    M : size of sample\n",
      "    N : number of samples\n",
      "    p : array of (normalized) probabilities for categorical variables\n",
      "    \n",
      "    OUTPUT:\n",
      "    \n",
      "    k : N samples of size M (MxN array) of randomly drawn categorical variables.\n",
      "        k takes values between 1 and the size of p.\n",
      "    \n",
      "    \"\"\"\n",
      "    p = np.cumsum(np.r_[0, p])\n",
      "\n",
      "    # Sample from U[0,1]\n",
      "    k = np.random.rand(M,N)\n",
      "    # Sample from Categorical[p,K]\n",
      "    k = np.sum(k[:,:,np.newaxis] > p, axis = 2)\n",
      "    return k.astype(np.int)\n",
      "\n",
      "def GMrand(M, N, p, mu, sigma):\n",
      "    \"\"\"\n",
      "    Random number generator for random variables drawn from a Gaussian Mixture.\n",
      "    \n",
      "    INPUT:\n",
      "    M     : size of sample\n",
      "    N     : number of samples\n",
      "    p     : weight for each Gaussian\n",
      "    mu    : mean for each Gaussian\n",
      "    sigma : std for each Gaussian\n",
      "    \n",
      "    OUTPUT:\n",
      "    \n",
      "    Z : N samples of size M (MxN array) of randomly drawn variables from a Gaussian mixture. \n",
      "    \n",
      "    \"\"\"\n",
      "    p  = np.asarray(p)\n",
      "    mu = np.asarray(mu)\n",
      "    sigma = np.asarray(sigma)\n",
      "    \n",
      "    xi = categoricalRand(M,N,p) - 1\n",
      "    \n",
      "    X  = randn(M,N)\n",
      "    Z  = mu[xi] + sigma[xi] * X\n",
      "    return Z\n",
      "\n",
      "def GMpdf(x, p, mu, sigma):\n",
      "    \"\"\"\n",
      "    Exact PDF of a Gaussian Mixture\n",
      "    INPUT:\n",
      "      x     : shape used for shape of output [MxN]\n",
      "      p     : Probability vector  [Kx1]\n",
      "      mu    : Vector of means     [Kx1]\n",
      "      sigma : Vector of stdev's   [Kx1]\n",
      "\n",
      "    OUTPUT:\n",
      "      y : Value of the pdf [same size as x]  \n",
      "    \"\"\"\n",
      "    \n",
      "    # Compute pdf \n",
      "    y = np.zeros_like(x, dtype = np.float);\n",
      "    for k in range(len(p)):\n",
      "        y = y + p[k]*norm.pdf(x,mu[k],sigma[k])\n",
      "    return y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 252
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def example():\n",
      "    ## Sample matrix (M rows, N columns) \n",
      "    M = 1e4;\n",
      "    N = 1;\n",
      "    ## Gaussian components\n",
      "    p     = [ 1/2, 1/3,  1/6]   # probability vector \n",
      "    mu    = [-1.0, 4.0, 12.0]   # means \n",
      "    sigma = [ 1.0, 3.0,  0.5]   # standard deviations\n",
      "\n",
      "    ## Generate sample Z ~ GM[p,mu,sigma)\n",
      "    Z = GMrand(M,N,p,mu,sigma)\n",
      "\n",
      "    ## EM for Gaussian mixture\n",
      "    p_e, mu_e, sigma_e = expectationMaximizationGM(Z, 3)\n",
      "    print \"Estimated vs True parameters:\"\n",
      "    print \"Gaussian weights: {}   {}\".format(np.round(p_e,4), np.round(p, 4))\n",
      "    print \"Gaussian means:   {}   {}\".format(np.round(mu_e,4), mu)\n",
      "    print \"Gaussian std:     {}   {}\".format(np.round(sigma_e,4), sigma)\n",
      "    print\n",
      "    print \"Estimated PDF vs histogram of sampled data\"\n",
      "    def modelPDF(x):\n",
      "        return GMpdf(x, p_e, mu_e, sigma_e)\n",
      "    graphicalComparisonPdf(Z, modelPDF)\n",
      "    plt.show()\n",
      "    \n",
      "example()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Estimated vs True parameters:\n",
        "Gaussian weights: [ 0.4997  0.3298  0.1704]   [ 0.5     0.3333  0.1667]\n",
        "Gaussian means:   [ -1.002    4.1116  12.0065]   [-1.0, 4.0, 12.0]\n",
        "Gaussian std:     [ 1.0123  2.9481  0.491 ]   [1.0, 3.0, 0.5]\n",
        "\n",
        "Estimated PDF vs histogram of sampled data\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nFSWFXjKFtvBd3XC0JxykG5U7axwHbT4xpSA7G4qLtbEMXqLGpGCsMrLZbFVK\nClJ95H+igNDy2Yes6I6q69HD8Y/m8GG4dAlCQqyJRYh66sohfVtLCs5KADp21HrXKaWtMli5MdpC\nNSaFJ554AoDPP/+cnJwc7rzzTpRSLFy4kKioKI8FKDzHWFlkRXdUXYsW0KULHDqkLWO4b59Xr2kr\nhFEcjqVkj1J18C8AnTs7ptU+etQ3ksLw4cMBLTn8YJi4acKECVxlnNRJ+A1jZZFl7QkVkpK0pABa\nu4IkBeEjYsjUtzOJqf6gzp0dU2sfPVr9MRZxOSFeYWGh03QWhw4dorCw0NSghDWqlhQsJI3NwkfV\nKSnExzu2vayx2eWEeK+99hrXXnstXbt2RSnFkSNH+Oc//+mJ2ISHGdOAZY3MFaSxWfioOpcUKvha\nSWHYsGE8+OCDtGnThsDAQKZNm6ZPiCf8i5QUhGg8X08KNuVixZxbbrmFsLAwvaH5o48+4ty5c3zy\nySeeirFGlXtFiUZQioKAAFqX717GKU5zWaWDbLhebMfVMa6fV0ppcx61aaM91KyZNptkkMuCrRCW\nCrTZKCKQIG3CFkK4SBGVe87ZULt2OUrDFZ0qPKi2706XSaFXr17sqlR8r+4xK0hScKPsbK2bHHCW\ncCLIo2rvIw8mBdDiyc7WtvftqzqxmBBeJtpmo/wTSy5taUduNUfZUBcuQKtW2m5QkNbtOjDQU2HW\n+t3psvroyiuvZP369fr+hg0bpPeRP9pv7eyo1ZIqJOFjjJVFNVYdAbRsCZGR2nZpKZw8aWpc9eEy\nKWzevJkhQ4bQuXNn4uPjGTx4MJs3b6Z37970kW6C/uOAF0xvUZk0NgsfU+ekABBjeD4ry5R4GsJl\nJW1qaqon4hBW2+8F01sAEKTPrTUdqJhP8v2nnuLep54CIDQ0gvPnz1gTnhC1qFdS6NgRfvyx/OBM\n8JIaGJdJId7Yn1b4ryrVR1YppaLNYTergREAJNEfSAcgP98LqraEqEaDSwqZmTUf52Euq49EE+E1\nScFhN442hUT24LqRWwhr1S0paKXh5955R3/k+V/8Ql9vISws0tQYXTE1KaSmppKYmEj37t2ZPXt2\nlef37NnDoEGDCAkJYc6cOfU6V7iRUl7ZpnCCKPLQuqWGke/U/1sIb1S3pKCVhjP5h/5IR6ag/ehR\n5WsyWMe0pGC323nkkUdITU1l165dLFy4kN2VepC0bduWuXPnMmPGjHqfK9woOxvKpy7Jow1nsPaX\nioPNqbQsK55sAAAdhElEQVTQC2lsFt6tPtVHxue96QePaUkhPT2dhIQE4uPjCQ4OZtKkSSxevNjp\nmHbt2pGSkkJwcHC9zxVu5I3dUcvtwtEDKQn5YSC8W32SQhYdDec1gaSQmZlJXFycvh8bG0tmHRtT\nGnOuaAAvbE+oYCwpSFIQXq2ggPDyzUs05zRtaz3cmDQ64j1dUk1LCo1ZslOW+/QwQ3uC5RPhVSJJ\nQfgMww9XrRRQ+/fYKdpRjFZLEkkeIVw0M7o6M20ymZiYGDIyHItNZGRkEBsb6/ZzZ86cqW8PHz5c\nXwdC1IOUFIRoPENSOI7r7zpFANlE05ljgFaFdNCkH2VpaWmkpaXV6VjTkkJKSgr79+/nyJEjdOzY\nkUWLFrFw4cJqj608B0d9zjUmBdFAXpwUjtKZQlrQkou05xRtyeW01UEJUZ3MOsyOWkkWHT2SFCr/\nYJ41a1aNx5qWFIKCgpg3bx5jxozBbrczdepUkpKSmD9/PgDTpk0jJyeH/v37c/78eQICAnj99dfZ\ntWsXrVu3rvZcYYJK3VG9rfpIEcAeErmSrYBWWlhrcUxCVKsBScEb2xVMnYt47NixjB071umxadOm\n6dsdOnRwqiZyda4wQVYWXNTqMs8AZ1w0jllhN0l6UriC/0lSEN6pkUnBW3ogyYjmpm7fPn1zfy2H\nWWk7yfp2X7ZZGIkQtZCkIPzCnj2OTQvDqM1W+unb/cpLDEJ4HUkKwi/s3evYtDCM2myjr77dmx/x\n3FIkQtRDAxuaK0Try/NYS5JCU+cDJYVc2nG8/B9ZCy7R0+J4hKjCboecHH3X+GVfG28c1SxJoakz\nlBS8NSlA5SokIbzMiRNaYgBO0o4SmtXpNGNS0HofWT8TsCSFpqywEI4e1bYDAjhobTS1MlYh9a3l\nOCEs0YCqI4ACQjlPKAAhFJWvjW4tSQpN2f792jgFgK5dKbY2mlpJSUF4tePH9c36JAWorrRgLUkK\nTZmh6oie3l1Tb0wKfcGRzITwBg0sKYAkBeFNDI3MJCZaF0cdHCGes+VzULYFqGHQoxCWcFNS8IbG\nZkkKTZmxpODlSQFsTu0KbJXxCsKLSElB+AVjScHLq48AtnClY2fTJusCEaKyRiQFb5v/SJJCU6WU\nj5UUYCMDDTsbrQtEiMqkpCB8XmYmXLigbUdEwGWXWRtPHTglhfR0KCuzLhghjCQpCJ9XuZTgA6vd\nHaUzJ2iv7Zw/7/wahLDK+fNQUADARSCPiHqdLklBeAcf6nnkYHMuLWzYYF0oQlRwKiWAq2U4K8sm\nWt+OJtvyL2Wr7y+sstuwtKUPNDJXkHYF4XWqJIX6KSKE00QCEISddm4Kq6EkKTRV//ufY/vyy62L\no54kKQiv08ikAJWrkKwlSaEpUso5KVxxhXWx1NMm+qM3L//4ozZ/kxBWckNScO6Wai1JCk3RyZNw\n+rS23aoVdOpkbTz1cJ5wx2yudjv88IOV4QghJQXhB3budGxffjkE+NbHwKl5ed06q8IQQuPmpFC/\nDq3u51vfBsI9fLTqqMJ3xp01a6wKQwiNlBSEz/PRRuYKacadtWuhtNSiSIRAkoLwA8bqIx8sKRwB\niIvTdgoKYMsWC6MRTVppqbbqWrmGrrIsSUFYIiwsEpvNxrnvv9cfixkzBpvNhs0HRjQ7GTbMsS1V\nSMIqOTmO6Vbat6ekgZeR3kfCEvn5ecSQUb4qAeTRhizK0NaF9bFFa4YPd2xLUhBWMa7rUVF6bYAT\nRFFWPhI6CqCkoeml8SQpNDFX4GhP2Mnl1HdIvncIIuH++/W9c0uXElRe2rHZbISFRVoYm2hSDMtw\nNiYp2AnihJYONNkNrYhqPEkKTczlONoT/ofvtSdoSjlIGRnEAhAODGAdFSWe/HzrFz8XTYSxpBAb\n26hLGdsVyLJuYjxJCk1MMtv1bd9NCgA2vmaMvncDyyyMRTRZxpKCJAXhi/rhWMbSaXlLH7SMG/Tt\nsSy3MBLRZLmpTQEkKQgLhABJaLOjlmFjO8nWBtRIqxhJCUEAXMUWosixOCLR5LixpOC0OI8kBeEJ\nV6BNzQtwgAQKCLU2oEbKJ4x1DNH3ryfVwmhEk2RW9VFmQ4fBNZ4khSbEWFm0lX6WxeFOxiqkG1lq\nYSSiySktdf5FH9O4WYuk+kh4nDEN+Hp7QoWvGKdv38AyWnLBwmhEk1Jp4BrNmzfqcpIUhMcZk4K/\nlBR204ud9AKgFYWM4yuLIxJNhhu7o4IkBeFpdjt9DLv+khQAFnGbvn0biyyMRDQpbhq4ViGXyygm\nWNs5exYuWFPqlaTQVOzfT6vyzSyiOWkcPenjjEnhBpb5ePO58BluLikoAjiO4TrHjjX6mg1halJI\nTU0lMTGR7t27M3v27GqP+eUvf0n37t1JTk5m61ZHH/r4+Hj69OlDv379GDBggJlhNg1b/Wd8QmX7\n6MnW8tcUQhE3WxyPaCLcXFIAOEpnw85Rt1yzvoLMurDdbueRRx5h1apVxMTE0L9/fyZMmEBSUpJ+\nzLJlyzhw4AD79+9n48aNTJ8+nQ0btHW1bDYbaWlpREbKPDZuYZhe2p+qjip8xB30YxsAD1oci2gi\n3NgdtcIxDEvj+ltJIT09nYSEBOLj4wkODmbSpEksXrzY6ZglS5Zwzz33ADBw4EDOnj3LCcPc5Er5\n2Myd3mzjRn1zMykWBmKO97lHr48dDLBjh6XxiCbA+EveTUnBG0oKpiWFzMxM4gxFqtjYWDIrDcio\n7RibzcbIkSNJSUnhzTffNCvMpqG01GmB+40MtDAYc5yiPZ8z0fHA3/9uXTCiaThyxLHdpYtbLukN\nScG06qO6LtpSU2lg7dq1dOzYkVOnTjFq1CgSExMZOnRoleNmzpypbw8fPpzhxnn2heZ//4PCQgCO\nEUe25ct4mOMfPMRt/Fvbee89mDkTovynQV14kQsX4ORJbTsoqNED1yqYlRTS0tJIS0ur07GmJYWY\nmBgyDK3zGRkZxFYqYlU+5vjx48SUv7kdO2pfXO3atWPixImkp6e7TAqiBoaqI38sJVRIYzibuYoU\nfoBLl+Avf4E//cnqsBosLCzS5TTgoaERnD9/xkMRCZ2xlNCpEwQGuuWyZrUpVP7BPGvWrBqPNa36\nKCUlhf3793PkyBGKi4tZtGgREyZMcDpmwoQJfPDBBwBs2LCBNm3aEBUVRWFhIfn5+QBcuHCBFStW\n0Lt3b7NC9X/ljffg30kBbLzI047dN95w/JrzQVpCULX+ydoRnlWxpO04w9rmqw4dctuStk5JITNT\nq/r1MNNKCkFBQcybN48xY8Zgt9uZOnUqSUlJzJ8/H4Bp06Zxww03sGzZMhISEmjVqhXvvvsuADk5\nOdx8s9axsLS0lMmTJzN69GizQvV/TaSkAPAFN7ETuBwgPx+eeQbKP3OWUwpOndKqBY4dg7w8OH8e\nzp3TSjaBgRAQAMHB0KYNdwCnSeU4sRyiKxdpafUraPIqEnUX5gK/BOAw9wMV7Z6NSwxFhJADdACw\n27XE0Lmzi7Pcy6Z8uIuPzWaTHkqunDsHERGgFKVAGBdq+XKxUftaza6ed8c1Gn+PsdgcS+7YbJCe\nDinu7XHlqmqnOXBNi1BWzH4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       "text": [
        "<matplotlib.figure.Figure at 0x15dfbe10>"
       ]
      }
     ],
     "prompt_number": 255
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}