{ "metadata": { "name": "SSVI", "zanadu": { "authors": [ "Antoine Jacquier" ], "bibliography_data": { "Gatheral": { "author": "Jim Gatheral", "id": "Gatheral", "journal": "Global Derivatives, Madrid", "link": "http://faculty.baruch.cuny.edu/jgatheral/madrid2004.pdf", "title": "A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives", "year": "2004" }, "GatheralJacquier": { "author": "Jim Gatheral and Antoine Jacquier", "id": "GatheralJacquier", "journal": "Quantitative Finance", "pages": "59-71", "title": "Arbitrage-free SVI volatility surfaces", "volume": "14(1)", "year": "2014" } }, "category": "6", "clearance": "Private", "group_name": "Imperial College", "md5": "da73255100e2c9226f3665cc995f1921", "notebook_id": "DCE90286-7E5C-4E1D-8E12-3745665FFDB1", "python_name": null, "reviewer_id": null, "status": "WIP" } }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "SVI, SSVI and local variance\n---------\n*******" }, { "cell_type": "code", "collapsed": false, "input": "from scipy.stats import norm\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.integrate import quad", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 1, "metadata": { "zanadu": { "is_hidden": false } }, "source": "SVI Parameterisation and absence of arbitrage" }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "SVI parameterisation" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "The SVI formula, proposed by Jim Gatheral in 2004 (see \\cite{Gatheral} and \\cite{GatheralJacquier}), is a parameterisation for the total implied variance, and reads as follows:\n$$\nSVI(x) = a+b\\left\\{\\rho(x-m) + \\sqrt{(x-m)^2 + \\sigma^2}\\right\\},\n\\qquad \\text{for all }x\\in\\mathbb{R},\n$$\nwhere $x$ represents the log-moneyness, and $a, b, \\rho, m, \\sigma$ are real parameters satisfying $a, b, \\sigma>0$ and $\\rho \\in [-1,1]$." }, { "cell_type": "code", "collapsed": false, "input": "def SVI(x, sviParams):\n a, b, rho, m, sigma = sviParams\n return a + b*(rho*(x-m) + np.sqrt((x-m)*(x-m) + sigma*sigma))\n\ndef SVI1(x, sviParams):\n ## First derivative with respect to x\n a, b, rho, m, sigma = sviParams\n sig2 = sigma*sigma\n return b*(rho*np.sqrt((x-m)*(x-m)+sig2)+x-m)/(np.sqrt((x-m)*(x-m)+sig2))\n\ndef SVI2(x, sviParams):\n ## Second derivative with respect to x\n a, b, rho, m, sigma = sviParams\n sig2 = sigma*sigma\n return b*sig2/(np.sqrt((x-m)*(x-m)+sig2)*((x-m)*(x-m)+sig2))", "language": "python", "metadata": { "zanadu": { "is_hidden": false } }, "outputs": [], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Numerical example" }, { "cell_type": "code", "collapsed": false, "input": "a, b, rho, m, sigma = 0.030358, 0.0503815, -0.1, 0.3, 0.048922\n\nsviParams = a, b, rho, m, sigma\nsviParams2 = a, b, rho, m, 3.*sigma\n\nxx = np.linspace(-1., 1., 100)", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": "impliedVar = [sqrt(SVI(x, sviParams)) for x in xx]\nimpliedVarpp = [sqrt(SVI(x, sviParams2)) for x in xx]\n\nplt.figure(figsize=(7,3)) # make separate figure\nplt.plot(xx, impliedVar, 'b', linewidth=2, label=\"Standard SVI\")\nplt.plot(xx, impliedVarpp, 'g', linewidth=2, label=\"$\\sigma$ bumped up\")\nplt.title(\"SVI implied volatility smile\")\nplt.xlabel(\"log-moneyness\", fontsize=12)\nplt.legend()\nplt.show()", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAbUAAADkCAYAAAAfD7o7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhBBiMCioEUIIMRj/D52UqBJp7ewqAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Density function under SVI" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "Recall that, given the total implied variance at time $t$, the density of the corresponding stock price process reads\n\\begin{align*}\np_T(x) & = \\mathrm{e}^{x}\\left.\\frac{\\partial^2 C(K,T)}{\\partial K^2}\\right|_{K=S_0 \\mathrm{e}^{x}}\n = \\mathrm{e}^{x}\\left.\\frac{\\partial^2 \\widetilde{C}_{\\mathrm{BS}}(x, \\sqrt{w(x,T)})}{\\partial K^2}\\right|_{K=S_0 \\mathrm{e}^{x}}\\\\\n & = \\frac{g(x,T)}{\\sqrt{2\\pi w(x,T)}}\\exp\\left(-\\frac{d_-(x, w(x,T))^2}{2}\\right)\n\\end{align*}\nwhere\n\\begin{equation}\\label{gFunction}\n\\left.\ng(x,T):=\\left(\\left(1-\\frac{x\\partial_x w}{w}\\right)^2 -\\frac{(\\partial_x w)^2}{4}\\left(\\frac{1}{4}+\\frac{1}{w}\\right) + \\frac{\\partial_{xx}w}{2}\\right)\n\\right|_{(x,T)}.\n\\end{equation}" }, { "cell_type": "code", "collapsed": false, "input": "from math import pi\ndef g(x, sviParams):\n w = SVI(x, sviParams)\n w1 = SVI1(x, sviParams)\n w2 = SVI2(x, sviParams)\n return (1.-0.5*x*w1/w)*(1.0-0.5*x*w1/w) - 0.25*w1*w1*(0.25 + 1./w) + 0.5*w2\n \ndef dminus(x, sviParams):\n vsqrt = np.sqrt(SVI(x, sviParams))\n return -x/vsqrt - 0.5*vsqrt\n \ndef densitySVI(x, sviParams):\n dm = dminus(x, sviParams)\n return g(x, sviParams)*np.exp(-0.5*dm*dm)/np.sqrt(2.*np.pi*SVI(x, sviParams))", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Numerics" }, { "cell_type": "code", "collapsed": false, "input": "def plotDensityandSmile(sviParams, nbPoints, xmin, xmax):\n xx = linspace(xmin, xmax, nbPoints)\n zeroLine = linspace(0., 0., nbPoints)\n densityPlot = [densitySVI(x, sviParams) for x in xx]\n \n plt.figure(figsize=(10,5)) # make separate figure\n \n plt.rcParams[\"figure.figsize\"] = [12, 10]\n plt.subplot(2, 2, 1) # creates the first plot on 2 by 2 table\n plt.plot(xx, densityPlot, 'b', linewidth = 2)\n plt.plot(xx, zeroLine, 'k', linewidth = 2)\n plt.title('SVI implied density')\n plt.xlabel(u'log-moneyness', fontsize=15)\n fill_between(xx, densityPlot, zeroLine, where=densityPlot" } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Arbitrage (the density becomes negative)" }, { "cell_type": "code", "collapsed": false, "input": "sviParams2 = -0.041, 2.1331, 0.306, 0.3586, 0.4153\nxmin, xmax, nbPoints = -2., 2., 100\nplotDensityandSmile(sviParams2, nbPoints, xmin, xmax)", "language": "python", "metadata": { "zanadu": {} }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Check that the density integrates to unity: 0.852190451426\n" }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAl0AAAC+CAYAAAAPzbouAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": "" } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 1, "metadata": { "zanadu": {} }, "source": "Surface SVI and equivalent local volatility" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "We consider the following SSVI parameterisation of the total implied variance surface:\n$$\nw(k,\\theta_t)\n= \\frac{\\theta_t}{2}\\left\\{1+\\rho\\varphi(\\theta_t) k + \\sqrt{\\left(\\varphi(\\theta_t){k}+\\rho\\right)^2\n+1-\\rho^2 }\\right\\},\n$$\nwith $\\theta_t \\equiv \\sigma^2 t$ and \n$$\n\\varphi(\\theta)\\equiv\\frac{1}{\\gamma\\theta}\\left\\{1-\\frac{1-\\mathrm{e}^{-\\gamma\\theta}}{\\gamma\\theta}\\right\\},\n$$\nwhere $\\gamma>0$, $\\rho \\in (-1,1)$.\nWe further need to impose $\\gamma \\geq \\frac{1}{4}\\left(1+|\\rho|\\right)$ in order to prevent arbitrage.\n\nWe then compute the (Dupire) local variance via the following formula:\n$$\n\\sigma_{\\mathrm{loc}}^2(x, T) := \\frac{\\partial_{t}w(k, \\theta_{t})}{g(k, w(k, \\theta_{t}))},\n$$\nfor all $x\\in\\mathbb{R}$ and $t\\geq 0$, where the function $g$ is fined in (\\ref{gFunction})." }, { "cell_type": "code", "collapsed": false, "input": "def phi(theta, gamma):\n return 1./(gamma*theta)*(1.-(1.-np.exp(-gamma*theta))/(gamma*theta))\n\ndef SSVI(x, gamma, sigma, rho, t):\n theta = sigma*sigma*t\n p = phi(theta, gamma)\n return 0.5*theta*(1.+rho*p*x+np.sqrt((p*x+rho)*(p*x+rho)+1.-rho*rho))\n\ndef SSVI1(x, gamma, sigma, rho, t):\n ## First derivative with respect to x\n theta = sigma*sigma*t\n p = phi(theta, gamma)\n return 0.5*theta*p*(p*x+rho*np.sqrt(p*p*x*x+2.*p*rho*x+1.)+rho)/np.sqrt(p*p*x*x+2.*p*rho*x+1.)\n\ndef SSVI2(x, gamma, sigma, rho, t):\n ## Second derivative with respect to x\n theta = sigma*sigma*t\n p = phi(theta, gamma)\n return 0.5*theta*p*p*(1.-rho*rho)/ ((p*p*x*x + 2.*p*rho*x + 1.)*np.sqrt(p*p*x*x+2.*p*rho*x+1.))\n \ndef SSVIt(x, gamma, sigma, rho, t):\n ## First derivative with respect to t, by central difference\n eps = 0.0001\n return (SSVI(x, gamma, sigma, rho, t+eps) - SSVI(x, gamma, sigma, rho, t-eps))/(2.*eps)\n\ndef g(x, gamma, sigma, rho, t):\n w = SSVI(x, gamma, sigma, rho, t)\n w1 = SSVI1(x, gamma, sigma, rho, t)\n w2 = SSVI2(x, gamma, sigma, rho, t)\n return (1.-0.5*x*w1/w)*(1.-0.5*x*w1/w) - 0.25*w1*w1*(0.25 + 1./w) + 0.5*w2\n \ndef dminus(x, gamma, sigma, rho, t):\n vsqrt = np.sqrt(SSVI(x, gamma, sigma, rho, t))\n return -x/vsqrt - 0.5*vsqrt\n \ndef densitySSVI(x, gamma, sigma, rho, t):\n dm = dminus(x, gamma, sigma, rho, t)\n return g(x, gamma, sigma, rho, t)*np.exp(-0.5*dm*dm)/np.sqrt(2.*np.pi*SSVI(x, gamma, sigma, rho, t))\n\ndef SSVI_LocalVarg(x, gamma, sigma, rho, t):\n ## Compute the equivalent SSVI local variance\n return SSVIt(x, gamma, sigma, rho, t) / g(x, gamma, sigma, rho, t)", "language": "python", "metadata": { "zanadu": { "is_hidden": false } }, "outputs": [], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Numerical example of a SSVI local volatility surface" }, { "cell_type": "heading", "level": 4, "metadata": { "zanadu": {} }, "source": "Printing some values" }, { "cell_type": "code", "collapsed": false, "input": "from mpl_toolkits.mplot3d import axes3d\nimport matplotlib.pyplot as plt\nfrom matplotlib import animation\nfrom matplotlib.colors import cnames\nimport pandas\n\nsigma, gamma, rho = 0.2, 0.8, -0.7\nt = 0.1\nxx, TT = np.linspace(-1., 1., 50), np.linspace(0.001, 5., 50)\n\nprint \"Consistency check to avoid static arbitrage: \", (gamma - 0.25*(1.+np.abs(rho))>0.)\n\nlocalVarianceSSVI = [[SSVI_LocalVarg(x, gamma, sigma, rho, t) for x in xx] for t in TT]", "language": "python", "metadata": { "zanadu": {} }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Consistency check to avoid static arbitrage: True\n" } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": "fig = plt.figure(figsize=(8,5))\nax = fig.gca(projection='3d')\nxxx, TTT = np.meshgrid(xx, TT)\nax.plot_surface(xxx, TTT, localVarianceSSVI, cmap=plt.cm.jet, rstride=1, cstride=1, linewidth=0)\nax.set_xlabel(\"Log-moneyness\")\nax.set_ylabel(\"Maturity\")\nax.set_zlabel(\"Local variance\")\nax.set_title(\"SSVI local variance\")\nshow()", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAElCAYAAABpkNLMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvXd0XXeZ7/3Z5fSi3i1LLrIsN1m25aISnNCSQCjDQDIB\nklyYd4C5rFCnXFrCwFrMDBNuLsPcECa8gRTCBBjeEEgPJHGTbdmOe1GxbNmSbEmWjqTT996/9499\n9kGWZVtyJFtW9metrPjo7HrOPvu7n+f3/T2PJIQQ2NjY2NjY2FwS+VofgI2NjY2NzfWALZg2NjY2\nNjYTwBZMGxsbGxubCWALpo2NjY2NzQSwBdPGxsbGxmYC2IJpY2NjY2MzAWzBtLGxsbGxmQC2YNrY\n2NjY2EwAWzBtbGxsbGwmgC2YNjY2NjY2E8AWTBsbGxsbmwlgC6aNjY2Njc0EsAXTxsbGxsZmAtiC\naWNjY2NjMwFswbSxmQSvvfYapaWl07qPe+65h29+85vTug+LW2+9lccff/yq7MvG5nrHFkyb65LN\nmzdTV1dHZmYmOTk5NDQ00NzcDEAikeArX/kKpaWlBAIB5s2bx5e+9CUAbr75Zu67774LtvfMM89Q\nVFSErutXVbDGQ5IkJEm6Kvt67rnn+OQnP3lV9mVjc71jC6bNdcfQ0BDvf//7+cIXvsDAwACnT5/m\nvvvuw+VyAfC9732P3bt3s3PnToaHh3nttddYvXo1YEZvTzzxxAXbfPzxx/nEJz6BoihXVbAuxnT3\ndRdCTPs+bGxmG7Zg2lx3HDt2DEmSuP3225EkCbfbzbvf/W6WL18OQHNzMx/60IcoLCwEoKysjE98\n4hMAfPCDH6S/v59NmzaltzcwMMAf/vAH7rrrrvTfJiomhw8fZuPGjWRlZbFs2TKeffbZ9HvRaJSv\nfOUrlJeXk5mZSWNjI/F4HICPfvSjFBUVkZmZyTve8Q4OHTp02X3F43EyMzM5ePBg+m+9vb14vV76\n+voYGBjg/e9/P/n5+WRnZ3Pbbbdx+vTp9LIbN27kG9/4BvX19fj9ftrb29m4cSM//elPAWhra+Om\nm24iNzeXvLw8PvGJTxAKhdLrl5eX88ADD1BdXU1mZiZ33HFH+nzAjNJXrlxJRkYGCxcu5MUXXwQg\nFArx6U9/muLiYubMmcM3v/lNDMOY0OdrYzOTsAXT5rqjsrISRVG45557eOGFFxgYGDjv/fXr1/OD\nH/yAhx56iP37958nfh6Ph4997GM89thj6b89/fTTVFVVpQV3oiSTSW677TZuvvlment7+fd//3c+\n/vGPc+zYMQC++tWvsmfPHrZt28a5c+f4/ve/n45c3/e+99Ha2kpvby+rVq3i4x//+GX353K5+MhH\nPsJTTz113rFv3LiR3NxchBB8+tOf5uTJk5w8eRKPx8PnP//587bxxBNP8MgjjzA8PExZWdkF0fTX\nv/51uru7OXz4MJ2dndx///3p9yRJ4le/+hUvvvgix48fZ9++ffzsZz8DYMeOHdx999088MADhEIh\n3njjDcrLywEzqnc6nbS1tbFnzx5eeuklHnnkkUl91jY2MwJhY3MdcvjwYXHPPfeIOXPmCFVVxQc+\n8AFx5swZIYQQuq6L//iP/xD19fXC5XKJ4uJi8fOf/zy97ubNm0VmZqaIx+NCCCHq6urEgw8+mH7/\nnnvuEd/4xjfG3e+f/vQnMWfOHCGEEG+88YYoLCw87/2/+qu/Evfff7/QdV14PB6xb9++y57LwMCA\nkCRJDA0NXXb/r7zyiliwYEH6dV1dnXj88cfHXXbPnj0iKysr/Xrjxo3ivvvuO2+ZjRs3ip/+9Kfj\nrv/b3/5W1NTUpF+Xl5eLJ598Mv367//+78VnP/tZIYQQf/M3fyO+/OUvX7CNnp4e4XK5RDQaTf/t\nF7/4hbjxxhvH3aeNzUzGjjBtrksWL17Mo48+SmdnJwcOHKCrq4svfvGLAMiyzN/+7d+yefNmQqEQ\nX//61/nUpz7FkSNHAKivryc3N5ff/va3tLW1sXPnTu68885JH0NXV9cFjtmysjK6urro7+8nFoux\nYMGCC9YzDIN//Md/ZOHChWRkZDBv3jwA+vr6LrvPjRs3EolE2LFjBx0dHezdu5cPf/jDAEQiET7z\nmc9QXl5ORkYG73jHOwiFQudF2Jdy+J45c4Y77riDOXPmkJGRwSc/+Un6+/vPW8ZKc4MZrYfDYQBO\nnTo17rmeOHGCZDJJUVERWVlZZGVl8dnPfpbe3t7LnquNzUzDFkyb657KykruvvtuDhw4cMF7LpeL\nv/3bvyUrK4vDhw+n/37XXXfx2GOP8cQTT3DzzTeTl5c36f0WFxfT2dl5niCdOHGCkpIScnNzcbvd\ntLa2XrDek08+ye9+9zteffVVQqEQx48fByY2bqooCh/72Md46qmneOqpp7jtttvw+XwAPPDAAxw7\ndowdO3YQCoV4/fXXLzD3XMrM9LWvfQ1FUThw4AChUIjHH398wmONpaWl455raWkpLpeL/v5+BgYG\nGBgYIBQKsX///glt18ZmJmELps11x9GjR/nBD36QNrR0dnby1FNPsWHDBgAefPBBXn/9daLRKJqm\n8fOf/5yRkRFqamrS27jrrrt4+eWXeeSRR7j77rvP2/5EhAtg3bp1eL1e/vVf/5VkMslrr73G73//\ne+644w4kSeJTn/oUX/7yl+nu7kbXdbZt20YikWBkZASXy0V2djbhcJivfe1rk9r/nXfeyS9/+Ut+\n8YtfnBcZj4yM4PF4yMjI4Ny5c3z729++YN1LbXtkZASfz0cwGOT06dN8//vfv+xnYG3v05/+NI8+\n+ih//OMfMQyD06dPc/ToUYqKinjPe97Dl7/8ZYaHhzEMg7a2Nt54443LbtvGZqZhC6bNdUcgEGD7\n9u2sW7cOv9/Phg0bWLFiBQ888AAAPp+Pr3zlKxQVFZGXl8dDDz3Eb37zm7QJBWDu3LnU19cTiUS4\n9dZbL4jCLhWJWe85nU6effZZnn/+efLy8vj85z/P448/zqJFiwD4t3/7N5YvX05tbS05OTn8r//1\nvxBCcNddd1FWVkZJSQnLli1jw4YN5+3vcvtfu3Ytfr+f7u5ubrnllvTfv/jFLxKNRsnNzaWuro5b\nbrnlgu1carv33Xcfu3fvJiMjg9tuu42PfOQjl/0crPdra2t59NFH+dKXvkRmZiYbN27k5MmTADz2\n2GMkEgmWLFlCdnY2H/3oR+np6bnodm1sZiqSmOjjtI3NLEAIgWEYaJqGruvEYjFk+fznRqfTiaqq\nyLKMLMszYl6mjY3NtUe91gdgY3M1EEKg6zqapjE0NEQgEECSJBRFQZZlhBBomoamaYBZLWg0iqKk\nl7X+b4mpjY3N2wNbMG1mNZYQ6rqOEAJJktL/jsViaJqWFj/LIKMoygXbMAzjvG1YWAI6WkTtqNTG\nZnZip2RtZiWWwFkRoyVguq4TCoWQJAmHwwH8WRANw0gL4mjxu1g0af10LKEdLabWNhRFsdO7Njaz\nBFswbWYNlmglk8n0dAhLnDRNS0eUQgiCwSCyLJNIJNJjmJqmkUgkcLvdaQEd/R9wUSEdLYJjhXT0\n30cL6djI1BZSG5uZjZ2StbnuGW3kGSuUyWSSaDSKEAK3243f72dwcPACo89oLAEbuw9rP9b/LWEW\nQlwgoKNfj7edZDJJIpG4IL0ry/J5EakdldrYzBxswbS5bhlt5LGiN0tY4vE4sVgMSZLweDw4HI5x\nRWfsdI6LYW17PKEdndIdPdZpGMZF07vjCSlwXhp59L7Hi0ptIbWxubrYgmlz3TGekUeWZQzDSAul\nqqr4fD5UVR13LuJY885bwXLbjmcWGi2muq6fly6+WHp3PDG11h+Lnd61sbl62IJpc90wnpFHluX0\nfMpEIoHD4SAYDF4gXteCi0WlVyO9a7l9nU6nnd61sZkibMG0mdFYomBFlPBnIbKMPMlkEpfLRUZG\nxiXHJmcKk03vXs69O56QRqNRHA7HBbVg7fSujc2VYwumzYzkckaeWCyGYRi43W58Pt+kbvZWSnYm\niuuVpHdHC/BYAb3SOaV2etfG5kJswbSZUVzKyJNIJIjFYgC43W6cTueU3swtIZ2JTCS9a0WilpDG\n43GSyeRFU7zjbSeZTJJMJi/Y98WE1BZTm7cTtmDazAistKs1V9Lj8Vxg5FEUBa/XO66R5+3KxYQ0\nGo2mp6dYYjp6nHQq3LvAuEJqR6U2sxVbMG2uKWONPFaEaY3DxeNxHA4HgUAAVZ2ay3UmR5JTyVSl\ndyfi3rXTuzZvB2zBtLnqXMrIY41bhkIhnE7njHG8ziauJL071r07kfSupml2etdmVmELps1V41JG\nntHpWEmS0qXrbK6MK4mgJ+PenUh692K1d+30rs31ii2YNtPORIw8Vuk6l8s1bo/K6Tgmm4lzpend\n8eaSTja9a10vTqfTTu/aXFNswbSZNi5WkUcIkTbyyLJ8Xum6ZDI57WJ2sRvtbBvbvBqCMtH07tg5\npZOpciSEIBwOnzen1NqGnd61uZrYgmkz5VysIo9hGGkjj6qq+P3+C4w89o1udjCV6V3rmhgd3drp\nXZtrgS2YNlPCpYw8o0vX2UYemyutvRuNRt9yetd279q8FWzBtHlLXMzIY6VXLSPPREvXXY206GxL\nvc4WLhaV6rp+Xqm/t5LeBdLuXUtM7fSuzUSxBdPmiriUkWds6Tq/32/fdGyuGOvaGm8e7pW4d6+0\nOIMlqnZU+vbFFkybSTGekce6cUy0B+WluNrRnxGL0feb3+BbsQLf8uUAU9r6y+atc6nv41Lp3dHd\nYMZz74518L7V9O7F5qXazB5swbSZEJazVdO0824OE+1BOZOQJInYyZN0/eY3dP7Hf6D19qJkZrL0\n179GXrLkWh+ezRRgCelYxnPvWlmSqUjvWvu2xNQqT2ind2cHtmDaXBLrhqLrOvF4HMMw8Pl8F/Sg\nnKrSddMdYZ579VW6fvMbzv7856DreFetQhscRB8c5MAHP8i8Rx/F8+532ym3WcpUF2e4mJBaUWki\nkTjvfVmW0yJqp3evPyRhux9sxnAxI4/V/cIy9LhcLtxu95SmoIQQDAwMkJWVNWU3EW14mDNPP82p\nhx4ifOAAsteLc/58YgcOAOCrqSFy+DAiFkNyu5n3k58QfNe7xp10f73c3CKRCC6Xa1a4ka2HNa/X\ne032Pza9O/q/S6V3x6t0ZP2n6zq6ruN0OoHz07tjr7Xr4Xp7u2BHmDZpRv+QL9WD0uPxTLoH5USZ\nym2Gjx6l5+mnOfXDH6IPD+NduRJcLoxIhHhLC4E1axhubia8Zw++5cuJHj8OQjD8n/9Jhqbh+vCH\nL0jbjb1JXm9Cej1yrceUpyO9a/3WFEW5IL07dt92enfmYEeYNuM6Xi1G96BUVRVd1wkGg9N6POfO\nnbviCFPoOr3PP0/nww/T//LLyB4P3kWLiO3dC4C/uppwaysiHEZSVfyrVjG8YwfusjJyFy5EPXQI\nurtBlsl88EH899xz/vbHuUmOF21cayGdTRGmJSQej+daH8qEudg1MtooJ4TA6XRetvaudc2N/vto\nIbXnlF49bMF8G2M5XkdX5LF+yLFYjHg8jizLuN1uHA4HyWSSeDxOIBCY1uMaGBiY0JzN0ST6+uj5\n9a/peOABYp2d+GtqGDl0COJxJKeTjOpqRnbuBMBTVUX89GmM4WEyVq0iOy8P44UXkAB53jzE8DCi\nrw+AjO9+l8C99152/5MR0tE1Vqfr5mYL5szEukas8VHLODfZ62R0enc89+7osVI7Kp06bMF8GzJe\n6TpJMltrWULpcDhwu93nGXmSySTRaHTaI8zJCObg7t2ceughep5+GhQFT0UFYSuaXLGCSFsbRjiM\npChk1tYy3NSEEgiQu24dnu5uOHgQAGd9PYktWwBQSksRuo7R1QVA4KtfJeNb37qic7mUkAIXjUjf\n6o3NFsyZTSKRQAiBy+UCpu46uVhUClw0KrWFdOLYgvk2wfoBjS41Zv1QrNZayWQSp9OJ2+0e90ar\naRrhcJiMjIxpPdbBwUECgcBFb/Z6PM6ZZ5+l/cEHCTU3k1lbS/jNNyGZRHK58C9fznBzMwD+pUuJ\ndnaiDw3hnT+fgiVLkP/0J6RwGHXePIxoFKOnBwBnQwOJzZsBkAsLkVwuRDRKoGoRwZoViG9/D6bo\nxjL6Bjn2Rnmp8a+J3thmk2Amk0l0Xcftdl/rQ5kyxgrmpbhUencyxrTREelY7PTuxLAFc5ZzKSPP\n6B6UVmutS0V111owI6dOceLhhzn1s59hxOO4S0sZSUWIgZUriR85YjpdVZXg6tWEtm8HWabgpptw\nRyKIrVuRAHd9PXoqmpSLi0GWMU6dAkBZvx69qQlnVRXB/Cy8Q+eQjx0BwPjLOzD+9/+FKZg+cyku\nd4OciJDagjmzicfjSJKUdsleCaOvk7HXjJ3enR5swZylTMTII8Sfe1BO5OLXdZ3h4WEyMzOn89AJ\nhULpAggA/W+8wfEf/Yizf/gDmevWMbBtGwiB7PXiWbCA8P79AARXrCCeSsGqWVkUbdiAvH8/dHbi\nmD8fIxJBT0WTrro6jK1bAZDz8pACAfTOTlw11WTlZODa/Cckw0AEgjBnLtJhcwqK8d5bMX78M7gG\nN+/LGUlG39ASiQQul2tK5sZea2zBnBzXIr1r/Xu2C6ktmLOMSxl5RvegtIw8k7m4DcMgFAqRlZU1\nXYcPmILpFIIzTz3FiYcfJtHfjxIIEG1vBzCng+zZA7qO7HYTWLqU0K5dAOTdcAN+SULeuRMpGsXT\n0EB00yYA1DlzANBS0aS3sZHEpk0o2dkEalbgj4dx7DGNQWJVLex/EymZRLg9iMrFyHv3mJ9DXSPG\nz38J/uk1P02U8VK6Y1urzQTn7pUymfTl9UIsFkNRFBwOx1Xd73Skd0c/kFvRrdXsW1EUksnklM/X\nvlbYgjlLmIiRR1XVtFBe6T6mWzCHjxzhyP/5P5z59a/JXLmSkCV2WVmo2dnE2toAyKytJfTmm4hk\nEtntpvCGG3CdOYOydy+Oigr0gQGMlNPV09iYFk2loADJ60U7fhxnRQU5lQvwbnsdORZF+PwYc8tQ\nDptpXrFiJRw7ihSLIhwOxIoapOEQSlEmiksn9uCvEFk50/ZZvBUikUh6ysJMnwJzOWzBnH7Ge+i6\nkvRuMplMdyeypOVzn/sc3/nOd1i4cOG1OLUpxRbM6xjr6W60Yce6iMf2oLyYkWey+xsYGCA7O3uK\nziC1XV2n+9lnaX/oIaKnTpEYHCTZ3w9A1oYNjGzbBoCakYG7pMScLgJkb9iAy+nE1doKPT341q4l\nnlrWUV6OEYulU7Bp0ZRlfHUbCHgcBLa+BoCxqhbJiiZdLoyqpShv7jaPbfES6O5CqliI4owjZwVQ\n95ipXL18EdH/+P8QhXOm9POYCi41hjmRKTDj3SSvlZjORsG02pXN9JT5ZNO71oP7aEfz7bffzuOP\nP05Ozsx8uJwM13+M/DbEGp9MJBLpguiJRAJZltE0jeHhYYaGhpAkiYyMDHw+35SaP6bqGSt+9ixH\n//mfeXnpUloffJC+118n3NZmlq4rKABgYNs2gg0NCEALhYieOEFuQwOl9fUE3nyT4LlzSKEQ6Drh\npiZcDQ0AJDs6kBQlnYaN791L3gfeT0l5MXnNW3Dt2YWx1OxOIu/eCVVLEW4PUjyOfGAfxpp1CH8A\nKS8Lx+r5uKIdODv2o+7ZirbK3IfScQzvp96D1NEyJZ/H1cISQ1VV0w9TXq8Xn8+X7jJj3fwSiQSR\nSIRwOEwkEkk/hFllE+3n7dnNpa4Vn8+XfiizHPiJRAJd14lEInz/+9/n/vvvJxaL0dbWRjgcvuS+\nXnjhBRYvXkxFRQX/8i//Mu4y9957LxUVFVRXV7Nnz57037/3ve+xdOlSli9fzp133kk8Hp/Sz8HC\njjCvIy5m5Ekmk0QikfRNbjJGnsnyVqrwpLexfTvtDz1E+PhxBt98ExGPgyyTtXYtA01NALiKi5Fk\nmVhqvDGnoQFHIoE/FkNuacFVVUVstxkFuqqqSHZ3YwwOAuBrbCSeSsG6V64kUJSPZ8cW5HAYad16\nRPNO0HVwe5CrFqPsM394omopdJ6EjAzkRWUoARVH8+sAGEWloBvIZ08DoK1qQNm9GQkwsnKJ/N/f\nIhZVX/FnMtVMtUt2Kpy7V8p0GmSuFbPJxTwaS6hUVeWll15i586dPPvsszidTlpaWsjPz+cv//Iv\neeCBB85bT9d1KisreeWVVygpKaG2tpannnqKqqqq9DLPPfccP/rRj3juuefYvn07X/jCF2hqaqKj\no4ObbrqJw4cP43K5uP3227n11lu5++67p/z8ZnY+wAYY38hj1aO0jDxWjVcrLTtdWAaiye5Dj8Xo\n/K//ouPxx0n29RE+Yk7VyKiuZvjYMYxolIHt28mur+fcli3Eu7pwFRYSXLqUQHY23tZWPGVlRA8e\nROg68QMHcK9dS2zHDuKHD+NcuBBdVdH7+ghv3kzO+27B3XsG977dSGeyYE4pHD2C2N4ENasRB/cj\nxaIYBw4gVtWi7t4JioRUV43z9FGUo+a0E211A+quzcjdnRg5+eil81E621F3b0arqQN0JAbxfeNW\nol//BXr1O6b6I78ipvo52KqnerG+k+N1+LhYHdWZOE5qMzUIIdLXyS233MLNN9/M1q1b2bx5M4Zh\n0NHRMW6kuWPHDhYuXEh5eTkAd9xxB88888x5gvm73/0uLYLr1q1jcHCQM2fOEAwGcTgcRCIRFEUh\nEolQUlIyLednp2RnMNYNyJorOVooo9Eog4OD6QookiRNW1T5VggfP86+r32NrbffTvNnPkPf5s2E\nu7rwL10KQGjvXrzz5qH4/SAE57ZsIbOuDn9FBUXz51M0OEhGdzd0dxNtasJdUwNOJyKRILZrF54N\nGwBItLai5OSQdeNGyirKyHr1ebx+LxLAwAB0nYZUCpY9uxAVleDzmYUIHCryh96N99wBPAc2g9uD\nkVcMgLprM9qqegQg959FDp1DW7wSbX09crQdKUNHPteBFB3G8+2/RN3yzNX/kC/C1bgWLCF1OBy4\nXK50Yf7x0nWxWIxwOEw4HCYajaa731jNmd9OXOuC8lcb6zpZsGABK1asuOD906dPU1pamn49Z84c\nTp8+PaFlsrOz+cpXvsLcuXMpLi4mMzOTd73rXdNyHrZgzjCsJ/Z4PJ4en7SE0jAMwuEwoVAIXdcJ\nBAIEAoGr6rSzIsxLIYSg5+WX2fE//gevNjZy7Ac/4MyLL5Lb2AiANjTEcEcHvmXLABg5dAhvaSmO\n7Gzy1q0jODhIWUEBjq1bMU6fRu/rw5V60ow1N+NesgQ8HtB1ok1N+G+6iZwbGino7Saz9RiOlCFB\nbN2MtH4DyDIMD0NbK1LNavM8uk7juKkBz4oSAh3bcG17Ga0mNTbZfRIMHb2kHAB19xb06vUYxXPR\nly1B5hSSYwR5qAflWDPGnEUITwApGcf9r3fjeOHRKf/crzcuJaSjpzRZrbtsIZ0djH0QSCaTEzI2\nTfThYbzroa2tjQcffJCOjg66uroYGRnhySefnPhBTwJbMGcIY408ox2Luq4zMjJynpHH7/enL8SJ\niNhUcal9JQYHafn3f2frRz/K5ttu4+RTT+HMyMCZmwtA36ZNZKxfD4AeDjPS1kawpgZnTg7B3Fzm\nlZcTbG1FPnSI8ObNuFICawwOkuzsxLXcjBBjb76Ja+FCvKtXU1i7mpzNr5EhgzI0hOjuQgtHYZ5p\nYRdN25BWrQGHA2JRCI/g+NDNBIJhPLteRFFljOw8ANTmzSSq6wCQ+88gDYfQ51eiVywFj4axKB/l\n9C7koT7kE4fRKtcCoBzfj5FdiBHMRTIMXP/v11Ff/PE0fQPXN5aQXspwNFZIk8lkuvD/bBHS2Rph\njj2vUCg0oUInJSUldHZ2pl93dnYyZ86cSy5z6tQpSkpKaG5upq6ujpycHFRV5S/+4i/YmipKMtXY\ngnmNscYn4/F42j5vGSaSySRDQ0MMDw+jKAoZGRl4vd6LTgC+VjeRgf372futb/GHBQvY+3d/x5mX\nXyZrtRnJjbS1oXi9OPPzAQg1NZFTVweShL+sjEyPhwUVFTg2bSKxezdKRgZynilgI5s24Uo5ZI2R\nERKtrXjWriVYX0duIkpBLIz7eDuSYWBs3oTcYAosvb1oZ/sQlWZUKnbtRHnXO3HfWEtg5Cju5pfQ\nltQAIJ9sA6cLo9Ac83Du3kpyxXqE6sBYUIHIdUKBgnqyGXV0NKklUFqa0ZaYAqucbkHkFpPccBMU\nyHj+++9x/fLv4Dq/sV8tLuXGtMbExgrpyMiI7dydYYwVzMHBwQmV0lyzZg0tLS10dHSQSCT4r//6\nLz7wgQ+ct8wHPvABHnvsMQCamprIzMykoKCAyspKmpqaiEajCCF45ZVXWLJkydSeWArb9HONsITS\neloePT45ugel2+2+rJHnaj6pWhGmkUzS+cwzdPziF3Q99xwA+fX1nNu6FSMeZ3DfPoKrVzO0axfR\nkyfxlJbiLi4m3tuLahgseec7SfzpT2ZaVVXxrltHZPt2Eu3tqHPmIBUVoXd3M7J5M74NG9A7Osis\nWIiv9Rjq3LkYba0IQJo3H+FwwNkzpmjWN2Bs2QyhQXSHA/et78HZfQx17wsYFUsRgSDS8BDOvU3o\ntY0oOzch95zCyDYNPdK5XnDKaDesR21pQtKTCIcLbdEa1GPNKMf3o5dUIA27kIf6UA9tJVn7biQx\nhNKzC+lcFkZmPsrZIZx/ehhppI/YPQ+DOnscnlcT6+Fx7CT/8eYHTqR580yI6ixBnwnHMt0MDg5O\nqNCJqqr86Ec/4r3vfS+6rvPpT3+aqqoqHn74YQA+85nPcOutt/Lcc8+xcOFCfD4fjz5qDn2sXLmS\nu+66izVr1iDLMqtWreJv/uZvpuV87GklV5mLVeSxChCM7UE50R/VlfSQvBJ6W1o48/vf0/rDHxLt\n7sZXXo4eixFLFQjIWb+eoR07wDCQFIWs2lrONTXhysujqLoa95kzaKnar961a4ns3g2aZhYUWL+e\ncCqVohQxjeinAAAgAElEQVQWIjudOAIBMoMB/DKIXc3msoqCXLsWo8ksUiDNKUUIA1ImAeWd70SV\nE7hP7UPW4hiLlqHsN7uXGOUVEBpAHjCrAGmr61F3bcEoKMGoXIDQBnEc3weAvnAlcvcxpHgEISvo\ni9eiHjL3aeTPxcgvRlIjKGf3oVXUobRsQ0Ig3EH03DLUU+Z5alU3Ev3sk+D2T+t3M5pwOIzH45kV\n5cgmO8n/Wk6BmejxhcNh/P6rdz1cDazz8vl86c/z5ZdfZu/evXz729++xkc3NVz/v6brAOsHPLrQ\nwOiIMhKJMDg4iK7r+P1+gsHgpKeHTPc45tmtW9nyiU/wak0NB++/H0/Kth3u6EB2OHAXFQHQ39RE\ncM0aUBSzp+TICJXvex9FAwPwyitoZ8/imDcPgMiOHXiqq8HlAsMgvG0bvoYGJKcTz9y5FOTmUpyM\n49vZhNjehLyi2ix6rusY25uQ60yTjjjVCZqOvGE9nhvXETj2Gh5HHDkeQYrHkA+/ibHSHDuVO1rA\n40XPM4+X0Dni7303ktqD2vIGSlcr2gJzPqXS+iZGbhnCl4Fk6KiHtqEtvwFt+QZEnoqcbAdMi7za\nshV9fi1CcSDFhlDOtKCVrzG/m6Ee3L/+HFK4b9q+H5s/MxnnbjQaPa8ow9UYJ52t45cWY8cwp7v2\n9NXEjjCnEUsorbEV+HNEqes60Wj0sj0oJ8rYDh9TQTIc5uSvf83RH/6Q0MGD5DU00Gv1i3Q4yKyp\n4dyOHQC4CguRHQ6inZ3ILhfz3vlOlI4OxKFD5nhlfT0jqXXVnBycOTkkjh0DwFNdTaylBcXnI2Px\nYvyyjPS6WTBAyspCLS6Eo4fN18tXII63w8iIeRyNNyBrcdwM4wj1IHLykdtS7biW1iCdOIoUiyAk\nCbG6Hrl5M0JRSNRuAKeOq8WMGBOVa3C0vomkawjVSXLBCpxHzahUL5oHqoQoLEYePIoxpxKlzSxa\nIDxB9OxS1NNm/Vl9bjVyTyskI+jzVyMKcnB0vGgeT/Z8Ip/4LSJr3pR9Rxfj7RxhTpbJdIGZipq7\nhmEQjUbx+XxTeBbXnvHO65FHHiErK4t77rnn2h3YFGIL5jRgOV4jkUi6j5zFZHtQTpShoaG0y/Ct\nEmpp4diPf0zbE0/gKShA6+sjce4cANnr13Nu+3YQAklRyFy1ioGdZoePzCVLyCkuRt6zB/r78a5a\nRfTQIURqPNbf2MiIVQQ9MxN3URHxw4dxL15Mdmkpzt27IVVDlro6sJxufj+OBfPgoJnilKqqECMj\nOCvK8ZxtQVpQgbzT3K7wBxBzypGPmMsai5Yine1EGhlC+AIk6hpQOveghnoQgSyMrAKUk6bA6hUr\nkU4eRY5HEbJMcvFalLOdaHPnoCR6AAP1nOnSSy5Yh3qyGUnoCIcHo6QKpWM3QnWhLb8BSetG7Tdb\ngmllDagnzIcFw5dP9OO/wSia3qpAtmC+dSZSc/dKhNQyLnm93qtwFleP8QTzgQceoKamhg9+8IPX\n8MimDlswp5CxRp5QKERGRkba8Wq5uKajdN1bFUzDMDj9hz9w5KGH6N+5E9/cuQxazZkXLEAPhUik\nun9k1tYyuGuXOU4py5S86124QyGk5mbU7GyUYJB4qquIp7qaWGsrIlXdIy2aqkrW+vVkulwor74K\ngFxZidHbCylxVhob0VMCi8eDY8lipNAArgUluJIDyAO9SP29AOhrGpCbU1Gf24OxcAnKAbPll75y\nLXq2B/VkM3I8jLa8HmX/ltSyPozi+SjtqfHGuYuRz3Uj8koQ2T4IulGPmsdg+LMx/LmoPWZknJhb\njdp7FDkZw/BlkVxci+PcbuR4H0bGXDB05OFUKb25dSgnU2OczgDR259En7/xir6riTCbBHOmlZGb\nrJBaWSXr9z5bBXO88/rWt77Fhz/8YW644YZreGRThy2YU8DFjDwDAwO4XK50YfQr6UE5UYaHh3G5\nXJOutxnr7aXl0UdpeeQR/GVlnLHaafl8BBYsYGCfaYDxlpUhIhGSvaZA5dXX45Ak3D09GG1tZNTV\nEdlilpNTsrJw5OcTO3oUAM/SpcQ7OzGGhlCysshvaMC1cydqTw94vaZQpgopy/PnYwwPQ2o/Sl0d\nelMT6soVeDNVnD4FZe92AIziuUi6hnSmy3y9agPS3h1Iuo5QHeh1NyCSIdSTuzHySpAkA7nPFLDE\n4rU4jjYjCQPhcKHPX47Sshtt0UrIdKCEOpBDZwDQFtWjHEsJrMuHUbAQ5eTe1HsbMPxOHH07kbQI\nibINOE+baV7dm4vhysAxYD48aCVrkAdPYBQvQtbaidd9B23hxyb1fU0UWzCvPhPt7AGkaz7PFOfu\nVKBpWrrymMW9997Ll7/8ZZan5lBf79iCeYVYPw4rooQLe1DGYjFUVZ2yVOmlGBkZSZscJkLv9u0c\n/fGPGTl+nL7duxGJBAD5jY2ctdKmHg/+igpCKdH0zZ2Ly+8nmJWF4+BBfBUVjLz5JiSTAGQ0NhJJ\nrSsHgzhLS4mlotRgYyNeRcHZ1IQci+FoaMDYbEaEOJ0o1dXoqdQupaWmG3ZwENfaGrw5LhzNm5A0\nDaEoiFXrkFMttkReIcLlRj7VAYCxci1CASGGUM4eQ1uyDscBU8BEdgHC60PuNhtRG4trkVr3gqKg\nL1mFyHLhOPJH872sYpBV5P6TAGgL1qEc34VkmGOcWmUdkhJF6W9GZM2FRBR5xHQKa+X1KJ1bkCQw\nnAH0zDLkSB9aYTmSK4o6chw5OYRAIrrmfpLVX5jyG6ctmDOHsUKq6zq6rqeNejPBuTsVWGYpt9ud\n/tvdd9/ND3/4wwuKEFyv2II5SS5n5Bndg1LTNLxe71UpXRcOh1EU5byLdSxaNEr700/T/vTTjBw+\nTLTLjMyyV61i8OBBjFSngbz6enpT0aLscpG1bBmSrpOpqqg9PUiGQTK1rm/1asIHDkBq3bGimbV2\nLe6zZ3Hs24e8YAHG0FA6elTr6hBNTUiGAaqKsmYNelMTUkE+zpVV+OP9qMfMcUBjxWqkIweQEnGE\nJGGsrUfZZY4LiqwcRGEJRmYAKdSOkZWD2t2BFDONQXp1I8re1BhnIAsj1xy3FJl56CtWIffuRw6Z\n55OoqMPZYoqx4c9B+HNResxIWS+vAVkCr448sB997nrUE6llA4UI1YMycNz8rEvXopzZg8gsxcgr\nALdA7TU7seiBeaBFUKJmBBuu/H8YqrkfWVGm7MY5mwQzHA5PST/XmcJoYZnpU2Amw3iC+aEPfYhn\nn3121qSfbcGcIBdrrSVJEpqmEY1G053G3W43sixfcZr0SohEIkiSdF46xGKovZ0j//mf9O3aRc8b\nbwDgLSlBBaKpuYtZK1cSOnoUIxoFIK+hgYE9eyisqcF75gyezEzCqQhQLShAdrtJnDgBgG/lSiJH\njyJS62Zu3Ihb1/G2t6OcO4dSVYWeasUll5Uh4nFEat6mum4dYtcuJE1DWboE79J5uJteRNY0RHYu\nIjMbud0cMzSWrEA60Y4UTgnh+kbkU+3oC8uRzrViZOTgOGE2lzbKqpD6e5BGBszX1Y3IKdE05i0h\nUVqEq3MTkpZAL1yENNKPPGIajhIVdThatqbGOP0YBQsRbjeS1AduB9JwN3LUbCWmlTegdqSE252J\nESxCOXsYvWgZRkE+6rmdSNowAgm9uA71rPkgYngLEaoXZciMduMrPke05j4MyTElN87ZJpiz5Vxg\nfGEZy+WE9GJjpdeS8Rp933zzzWzatGnWfHe2YF6G8SryWKkUqwPDxXpQTjZN+laIRCIA6Sc5IQSn\nXnqJzuee4+h//ifCMFDcbjKXLKE/JV6ewkKcTieRk2baMbh0KeGODjy5ueSWlhJUFCLW9A5Vxbdm\nDSOpfpVqXh5KIEC83bzhe5ctA00jMzcXz+7dOFevRrMMO04nanU1Wkpw5ZIShCwjOjtBUfC+7z14\nB7twtabGBWsbUHemRCiQgSiag3zMTO0aC6uQznYjioox8nwYARXHwW2p8UUPRvkSlKOm2UcUz4do\nBGnAFGe98RaInkXp2oVQnBjza1DaU+OhOXNB15AHzUhTW7gB5fQh9AXLkRMdGJnFqKfMKTRGVjlo\nceThbnPZsg0oJ83t6OVrEVl+HD2vmK8zK5DiA8jRVKGE4gaUM5uRJBDODLTCGmR6UGJH0HIaiK77\nBTj+XHvzSiOQ2SQys+lcYHxhmSjjXQ/W36ZjCsxkGNu3VAjBLbfcwubNm6+5mE8VtmBehEtV5Ekk\nEkSjUSRJumTpuomkSacKy4GrxOO0/vKXHH7oIYZS8xwLGxvpsdKkTifZK1bQ12zOMXTl5eHyeIh2\ndpK3ahU5gQCJ3bvN1CmQ0dDAiDXWqCj4amsJW6KZnY2al4fT7ydgGLhjMeSuLgiFzPfr69FSqV1U\nFXXNGrTUusqC+bgr5+PrPIijvxtjSTVSRytSxHTTJlZvwLkrNfbo8SHmVyAd2Y+xcjVGUEbubUUZ\nMkXIWF6HdKDJNPCoDkTlKuSDKSEsLEPMnYcUO43c14KxcC1Sx5tIWgIhyRiLNqC0pqK+YD6G04ec\nCGOULwJ3EqVnL5IWQ0jy+SlYfwHC6UM5145QXGhLbkSOtaKEWxGSgl6wFrUnVRXIV4KQVZRhMyLX\nijaAAyS5G1nrRs+oRh0wxVgPLCa6/jcI75/bGI3H5YTUMAwcDgdKKs07k1N5l8MWzMszXVNgJkMs\nFjuvhKElmFuse8AswBbMUVzOyGM1a1ZVFbfbjaqql7zoLpUmnWpOb99OyxNP0PbEE+jRKPm1tQzs\n2YNICf55oulwkLFsGQN79uAIBplbW4tveJhoqgiBt6qKeFcXekr4gnV1hLdtQxICJAnvunXEDhwg\na+VK/H19qLKMfshMhSoVFcjnzqXnU6obNqBt3w6GAbKM86YbcYkYvpY9yB43Ii8Pud0cIzQqliCd\nOY00ZO7XWNuItGMT+AMYNTUYPnDsM1PKRv4cUEE+e8p8XVWL1LLXFEJZxqhuRFINpKEWQEP4s5G7\nU6ndsmroaUWOm+KcrKzH0boFo2ABWkEBsjSE2muOneoFS5FDnUgx8wFidArWCJagz12CMvImcqIX\nPXsp8kgnUiK1bFEDandqWVcWRmAueP3ItCF8+cgjx5H0VLo2pw61PyXc7iKi63+NkTF5Z6E1dGBd\np+O5NK+XMTGLkZGR88qtXe+MjcSmk4kK6dh/X8lnPVYwDcPg1ltvtQVztjFRI4/D4UgL5USwor7p\nGvDW43E6fv979v/wh5zdvh3//PloQ0PEUvMl89asYXDvXkTKxZpXV0dvqhhARkUFcyoqSLz2GkQi\nZrSYm0vMqr6zaBGJvj701JzI4Pr1hHfswFVSQnDOHDKcTnQrXev3o8ybl64Rq8ybhxKJIM6YphZ1\n3TpIJvD7ZDzHdiPWNqBsH1VoYG4ZsmXumZeq9XquD1E0B311NcqRTUiRIbOe65Ja1ANmlCqy8hF+\n/59drxUrITKMmFOMfHaPmXI9nNqPJ4DIK0c+aR5jsqACNXwOaaQfrWw5orQItf1lc56kw4NRUIXS\nbaaujewFkBhBHklNM1l4IyhJlOheEEn0nGWoZ1O1aoPzQIsiR1KO2aI65HNHMIqqkEUbhq8EdTA1\nP9S3EEkbRo6ntptTj9K/FeEpwchbQGL+l9Azbrqia2NsVDbeDfN6EVJbMKeeiU6Bmcw1MbbAxPDw\nMPfccw8vvfTSVTmnq8HbWjAvZ+SJxWIkk0lcLtcV2dpjsRi6rk95Cazhzk4O/+QnHPnZzxCahjsv\nj1BK6ALz55McHiaWcqLmrlrFUMoBKykK89/7XpRTpxD79oGiEKitZdhKk2Zm4iwsJHrErHzjXrAA\nLRRC6+8nuHIluXl5SH/6E1JKgB2NjSRTUavk9aJUVqJZ8ylLS1EdDlxzCvGPnMGRnYl09CBS3Kz6\no69r/LNoeryIRZXIB811tfUNaB5wHduKJAySlatR2/YhaUnTIVtdj/KmNcaZhcgvAlkg8oJIjCAN\nnEYKm6YcY3Ej0pFN5hinw41RugylvRkhK4iVN2LII6hd5vlrc9ehdO5CEhpCVtHnrkHtNN8zAkUY\nGcXgd6IMN2PkVSP37Ucy4mYKtnAdancqXZsy9Eh6FCN/Hnh0lKG9SEbMXDZrHeq51LLuQoTsRYm0\nY/gXoOcvQI1tRiKCkBzEyn+IlvvxSV8jE0ljTsdNczqYbYI5NhKbSYy+JsZeG5cbNx87/aezs5P7\n7ruPX/3qV9f4rKaOt6VgXsrIYzleLRfbWyldZxVynqquBKdeeYWDDz/MqZdfJnvFCnpTKVRnZiae\nggJCqUIBgfJykpEIsbNnAchfv56g04nc0oLR3U1mYyNhy5AjywTXr2fI6hISCOCaO5fIwYPIPh95\ndXX4+vrMcneAumoV2sGD6Wkko0UTlwt1+XKMzk78yxYRGOlB0ZLInR3AhS5XY30jctOfRdO4oQFp\nqBP59GH07AKEw4V6xjQkGZV/rgsLoNc0Iu/dgliyCrw6uATyiTfNZQvmI8UjSINmlGcs2oDUugPJ\n0M3ar9UN0PcmaqQLESjAcJhjkQBa0UqU3qNIWhQhSejz6pHiAxB0IcU6EP58lMFUKb2cpcjDo1Kw\nxfWoXVswMuaj5xUhOUZQQ6aRSQ8sQYp1ISdT7tqcBtR+U/S17FWQmYMSfRlJAt2zBCnRhayby8aL\n/4FEydcnda28lXG/mSSk43XAuN6ZyYJ5KSY6bq5pGidOnCAej/PEE0/wk5/85Fof+pTxthJMSxAv\nZuSZTA/KiWB1JwkEAle8jfjgIEcef5wDP/kJ/sLCdCUeSVXJW72as9tNc4sjIwNPQUHa6OOdMwdf\nXh6ZHg9i1y78ixcTaWnBSLlpM+vrGdliVq9BkgjW1zOUKo7uWbiQ7IULkbduRR4aQiktRTEMRGoK\nirR8OaK1FVLTSCzRdFQtJliYjdcNyq5UYYHsXERGJvLxVgCMRVVIPV3pcUq9fiOSrEOoFWnoLMnK\n1TgPmw8CIjMXEcxGPpkae5y/FOlMJ2hJjOWrIcuNfPAVM3pUnRgLVqK0pdbNLkHICnJfSnCX3IBw\nSciDeyERIlG6DtfJVPTozkBklKCcMcdhtbzFyCNnMPLnI7miiGA2Sleq7J7qwchZjNJnPkAYwfmQ\njCBHe9BzlqDnl+AY/COSpCNk13mGHsNbBoaGHDM/x2Txe5HlHhRjL0JyontXooZTyzrnAgZywhyj\nTeTdQ7zsAZAmdpOdDqPMtRDS2dgK61rVxp0urGsiGo2iqirt7e3ceeednD59mmAwSGNjI1VVVSxZ\nsoT3vve95OTkXLCNF154gS9+8Yvous5f//Vf8w//8A8XLHPvvffy/PPP4/V6+dnPfkZNTQ1Hjx7l\njjvuSC/T3t7Od77zHe69995pOde3hWBa45PRaBTDMPB4PGmhtIw801G6zqofGwwGJ71u37597P/x\njwm1tXH6jTcg9TWVjKrEIykKebW1nLVcq34//rlz8fr9+MNhHENDoOvErSIDy5YR7ejASHX6yKyr\nY2SUmSfvPe/Bee4cSnMzstuNungxyVRkqRQVoTgciNQUFHXZMrQTJyASwV27moyiTNxvvGSKiiwj\natcjN6dEM5hpdvo4lpojOa8CHA5EUTZy5x60BUtRW3aZEaAkYayoR9mbSrn6goiCUuT2g4jMPIzq\nGqTBVuTe1Lhl5QakllT0KCuIyvXILabJQARyMQrnI/kdSH07EfmVSAMn0gYefX4DSntqPw4PRv5i\n5J6DaHNrkPwacqwLOZyaOlK4DuXMqHRt4RrUM6lUbmkjwgOOQfN70bNWIYcPIxnRCw09rnz0zCpk\npQdFO4ruq0ZOtiMZKfOPvw51JLWsmoPhKgWXH0Xdj+5eSTTvCZAv38F+ZGQEr9d7VZylVyKkEz0u\nWzCvD8bLBDzzzDPs3LmT+vp6Dh06xOHDh/nmN7/JsmXLzltX13UqKyt55ZVXKCkpoba2lqeeeoqq\nqqr0Ms899xw/+tGPeO6559i+fTtf+MIXaErd9ywMw6CkpIQdO3ZQWnppl/mVMusF0xJFK4q0qu9Y\nve8ma+SZDJqmEQ6Hyci4/A0OQE8kaPvtb2l/5hk6XngBPRUNFq5fT0+qKTNcKJrZq1Yxcvw4+RUV\n+Lq6cAUCZvUdwFlcjKQoxDvNLhu+JUuInTqFnpo2ktnQgFsIvD09yG1tuBobiY9KsTqXLyeRmoIi\n5+WhBgKI9nakjAyCN2zA130c5/GUy7V2A9Ku7UiGYQrf+gaUHamUq9eHKF8AGIhsD1K0F5GIofSn\n5khWrUbuOICUNFO98WUbcKVK2hnzqjAWlKMce9V0weaWgjCQ+s1IzViwBunEfiTNXFdf2ogUG0Bk\nupGHjiFyypG7zPJ+Rm4FUiyENGKmq/XyDcgndoDTi15WjeGXcfaknLjeAoTqSxcX0PNWIg+0IGlh\nhKySXPgulGQrSqwV4chA95aihlLu2uBipORZ5KRpmtJyGkFOIqndyKIXw1OJEjYfRnT3QiSGkbWU\n+cdfhxxrxcioQFaOYDjnoSZSrcYcVUTzf4VQ517yWpoJ434TEVJFUdIOTevfY7cx2wTzei/1Nx7j\nfU9PPvkkQgg+97nPXXLdbdu28e1vf5sXXngBgH/+538G4B//8R/Ty3z2s5/lxhtv5Pbbbwdg8eLF\nvP766xQUFKSXeemll/inf/onNqcyZdPB7JjYdAlG26XBjPpCoRBCCILBIH6/f9qe9Cba1Hnk1Cl2\nfPe7PL1+PS/ffTdt//3fZC5YgJoyC/U0NVG4di2kzuH0pk3k1tcDkFlRQaYsU1VZiWvbNrQTJ4ge\nP45vxQoAEl1diGQSd1kZAOFDh3AVF+OtqKC4sZGcAwfITiaRU1V74ps24WpsNA8sHiexdy/OdesA\nzE4iPi/+m29ijj9J1tYXUNERObkAyDu3IVauQTgcSEKgbNuEvq4RoaqIZcsgKBCFTpT2ncjdHUiY\n8yQBlMO7EHMqER7zB+c6sA298Rb02tVI8cMox15FzKsxP9e+TtA0jML55n7bmhEllQhvJsbitUhS\nP5RkofQ2I8WHkM4eRZ9bay7b1wKqEy04J/W6jWT1uxBFbtSRzTh6NpEorDPfi5xBjvWh5ZhPxErv\nmxgZ89DKb0DMKcA5/ALCn49AQkqGUIZb0LLN/ShDR0Dyo3vnoxXUITtaIGAg691IRgQ5sh8tYO5H\nibWCLqE7F2A4isANRkEZirIHmX6UxG40l/l9K8nDeHveiRzfPZFL8Jpi/fZUVU33fPV6vfh8Prxe\nb3rYwzDM5urhcDjdzNka/7eGT2xmNuM1xQ6FQmRnZ1923dOnT58XEc6ZM4fTqeGfSy1z6tSp85b5\n5S9/yZ133nklhz9hZr1gghnpDQ8Pp4sNZGRk4PP5pv0J73KCefKPf+RP//N/8lhlJTu/+120SARP\nfj4A/fv3kzFvHmrqia2nqYmCNWtAUVBcLmRNY8W7303GkSPo27czuHUrHkvYwmGiLS0EakyBSfT0\noEcieObPJ7B8OTnBIMWyjO/QIaTBQRI7duBcuRJSNvfzRDOZJLFrF4Fb3kNhwypKuw6QfaQZqcxs\ngiwfbwWvH5FfaL7evQNRtQLhciOCGUgqGLfegHxqO/LJ/cit+9GWpMSrvwcpFsaYW2G+btmHyC9H\nX11Pctl8lLbnkQIukGQkLYHUuhNjsSkcUugM0vAARukShNODCAYQyxYhae3I5w4ht27CmFuHkGQk\nLY58ajfGvNS6g6cQ3gy0le+GzEGcZ19EBPIQzgwkBM6erWjF9QhASgyhDLaiFa1HK69H8nYjy8dB\nNW8Oat9WjKzVCMmFZMRRzu1Cy61HOIIYmaWQBZKrH9noQR3ZgeFdhJCDSEJDHd6KFmwwP2fZhQgU\nIvILUeWtqMmdGOocDDkPCQM1vgXNVY9ARtIHcI3ch2I899Yu0GvEpYTU4/GkhVTXdZIpR3Y4HCYa\njaaF1DLsXY+MJy6zkcHBQTIzMy+73EQ/i7Hf9+j1EokEzz77LB/96Ecnd5CT5G0hmNYcSr/fn/6x\nXg3GE8x4KMSBRx/lsepqfnvrrbT87nf455rptaGODlSvF08qzdB/4ADBsjIcKdPQ8MmTVL3znSwI\nBvFu387Qyy+TZQmbEAzv2EGwwbwBG9EoI4cOEVi9GtntJlhRQUEgQEE0irJjB9rRo4iMDOSUQCea\nm3EsXQqpqkTxTZtwveMd+BvrKF02l4KdL+MLeJABeXgIqbMDY6kZxUqdHaAoiBLzCVA6dxbjXTfA\nXCfy8U0ozX8kvmy9KUBaEuXILoxqS7z6zOUXrzILFah9SMlu5KQ5ziof2YpYuAahOpGEgXxkC/qS\n1DnLMiI/H2N1DUr/FuRTO8DtQ2SUmG+3b0UUr0IoLiRDRz6+BX3Je825nPIhlIFtGDnmOInSfwjh\nyUb3mJ+92rUFvXAdhq8Yfe5qFOUQ+AWy1o8c7QQ9ih6oNNcdaMYILESoQYQrB1wS+vyVKGxBSbYj\nJ06i+1aZy0YOIBw5GM5i8/yTPSRL3oOU042qbEFOHkBzbjCX1Y6BpKKrZiStJHahZbwHo6AIJfg6\nbv1OHPqPruzinIGMJ6RWlSyr448lpPF4PB2RzhYhvZ65WISZlZV12XVLSkroTA0ZgTkdZWx3k7HL\nnDp1ipKSkvTr559/ntWrV5OXlzfhYx4aGko/kE2Ut4Vg+v3+dEF0a/zkaiKEoP/QIV79/Of56fz5\nvPHVryKnLOXR3l5iw8ME55s3xeGODlSXC2+hGbGdO3iQglWrqNywgZKzZ9FeeolAWRmk1h/YtInM\nlEgiBOc2byaYElFHVhZ+v5+FtbUEtm6FvXsx+vtxLF4MgNbejuF2I///7L15kF1Xee79W2vtM/fp\neVSPaqkltVqSW+pBLbXaxoCNcYgzFCmSFFW5gFMkhCL5SCWEVEKGqtziIyTUrY/kg4oTA7m5XLgJ\nGT9DHxkAACAASURBVODDBmwGy5qseZ7VUg/qbqnn02fce6/1/bH2aQ2WbcU22Fh5/9t99nx2n2e/\n7/u8zxMcyz18mNCaNai2NsofHKJm+BjVMQiPDSOMQb6wC3/A7ltk0ogL5/A39djliXF0czP+o+8A\nM4Y6/F38ZCU6Yfu3kRN7MRsHMFIhtEYe3YW/eQhT24jeuAnBKISXEKlJ5OQlQKGr7YuEPP8Cpnk9\nJmJL1OL6Fbz7fwYqMqiJHyLHDqBbbXYtZq+A9tDVq+y2Vw5gqteiV/aj12xATX8HEYuCMQh3CTlz\nGq+u3667MIwQ4CXb0KWtEJeYlnqUexThL+LM7MartvdaFmaQmVH88m57XHcer6kHUx/DMc/jpJ7D\nL9mKIYTQWWT66HIJVuaH0dEm3BVvR1VcIGS+iw6tw4hSBC5OYc9yCdaWcJdwSx9G15bgJJ4GFUFT\ni0AT0X9I2P84GP/1eFTflPFKGelPG5C+FTPMlwLMu8kwe3t7OX/+PJcvX6ZQKPC1r32Nxx577JZ1\nHnvsMb7yla8AsHfvXsrLy2/pX371q1/lV37lV+7qXLPZLD/84Q/5xCc+wb/9278BcPjw4VsA+aXi\nLU/6AW6ZuZybm7uruvrrEb7rcjSQq5vcv5/a++5jMhAgDyUSlLW3Mx2o40SrqoiXl7N40ZoNl65e\nTXl9PaHxcfzhYUrWrcObmLghV9fTQ+r48WUfy/LBQeYDCarSDRuoa21FP/00wvfBcYj09JAPRlBE\naSlOczNu4FWpGhtRQuCUJimtLiNeSCPGryACYhB9A6hj+5GBXGC+dxuRA4HOazyBf/8O5MwV5PgZ\nTGklflklzmgwRtK8CpFZRMxbIQXd1Yc4dxTTshpTk0QkI8iTlmRjnEAQ/Zw9T1NWg0mWISftvvzu\nt0PIRY4/j8CgV25HXA40ZIXErNyOLLJeY+WYylaIx0FMQUhZsk/Wkn0Kdb2EZo9Y1isCr2EboYnd\neBVr0eVlyFAaJ2Xvj5/sQBTmkPlAQL1qG2rmBQQ+frIDXbcaJ/0dhNDoUC1GlaFy5+228Y3I3BWE\ntvfSrX4XMjSBEscwIo4OrUMVAkUhZyXoPFIHAvCRIQiDjB5HyDS+7EWJgAhFPYYSFPbeeOJdZNWT\nCGFL+G8G0s/rEUUQ/M+oZb0ZdFVf7tzeanOlcGcHll/+5V/mS1/60l1lfU899dTyWMmHPvQhPvnJ\nT/LFL34RgA9/+MMAfPSjH+Xpp58mkUjw5JNPsmWLrdqk02laW1sZHh5+2RE+3/dRSvHlL3+Z559/\nnuHhYe6//34+9alP8alPfYpoNMof/uEfvux53pOAWVFR8WN9WFNjYxx94glOfPnLJFtamA6ASoZC\n1HR3M1W0yUokKL8JNCOVlVS0tlISjSJOniRSWorR+sZYyJo16OvX8easZVVy82aWTp/G5HLISISa\nBx4gfuUKKhAwiA4NkSsyXpUi0t9Pfo/9wRWJBKH2dgqnT5Po66Hc8YnOTyNGLgNgVq+BmWnEnGV5\nsqUXdeYYMgBof+hBhPQR189B6jp+Vx/OsUCyLp7ENLQiLwZydw0tCO3B7CRmQw+mOoEc3o8ItFz9\n9TuQp4I5R6kwa7ciTwcjKYkKdGc3wr+GnDmJrg5ECVKBKEFLH+LqsRsM2VVDyLHDliCkRzElVajJ\nwL0k2YgRCrloR2Pc6k2o1AWkn8Gt2YRfWUt0zrqMGBnBK+sitBiAWawRhEJmAkPphndCKIVy9wVZ\n6SBOKhhnkSXo6CpUxooW6OgqdLQWEZ1HydN4ka2o/CEELgaFH9mKkw+Uf2QN2llhR0mix9GqFWmu\nIAjEEeQgEmtObUjgsw6twmRis2hVSij7ZYRpuqcB86XizQCkb0XWL9wZMB999FG+//3vv2kEGoqA\n+Vu/9Vu85z3vYXx8nJmZGT7xiU/we7/3e9TX1/O7v/u7L7uPe6Ike7Pk3d0yV19NXPn+9/n3X/5l\nvv2hD7H3059maWKCiRdeoG67LcVp1+X64cPU9dsSoJdOM3/xItWbNlHX3U1LUxPlV66QmJnBLC6S\nC1hg0aCenz53DlldjRMM/qYOH6a8t5fGBx5gZTJJ8rvfJVZRscymze3cSbTY4/R98vv2EQnYtSIc\nJl5bSds7ttFwah+xYwdgaQmzcrX9/MI5KCvHVNseJ4cO4HV04a9aQ2HHVuToXkzCh/lJhO+jju/D\n7Q72nUkhxi+h1wWs1rlp9JpO9LYe5PR+1JkfYmpbMQlbrlGnnsesLZZrfeTp3eTXDeJv2I5pLkVO\n78PErLODnL4EUqErLLtWjtj5ShNJYkpqIAL6vh7E4vPIpcvIa0fRjbYnKFLjUEjjla8BwJk5gW7Z\ngde+mZA4RnTuGdzKrRgUQudx5o9SKB+wx8mOg5siXzOEt2IDjn4GIecxIftdOKldeMltwbZLyOxJ\nvOQ2vLJ+TJlAxi9CyDI+nfy+m0qwPk5+N15khwXLkjXI8jFI5BByEWWOY6hAY58BR+9C048xCVx1\nH6mSNEuJOH54HKNOU4i/By0Pv+Zn+a0Yb4bS7ls1P7lTSVZr/aaaNS2eX21tLTMzM+zfv3955G9y\ncvKu+q33RIZ5s03X/Pw8yWTydWPI5hcXOfk//ydjzz/PuW98Y/nvTUNDjBWzOyFo3r6dyaBkKh2H\n2i1bmD1zhvr164lNTREvLSV11GYkTnk50fp6lgJN10h9PSIcJheIBsRXrSJeVkYyFEIePEi0sxN9\n6RKkbcYW2bqV/IEDEJRQb840Q+3tVNzXSWL391G5LCYSgfUbEYftnJ8pq4C6esS503a5yfpEUlOD\nrHAQqoAYH0ZmLSmn0NVH6PRBRNAb9rcMoQ4Fs5e1jfj3daOu7EJk5zHJSkxZLXLMXpduWGXBdcGW\nSfXqXsTMGKatAzN/EprXoy4EJVYVwrT1IK8EWWyiClNSg5w6g6lsRbd2IFMnERkrNKBXbEVMHkJo\n1woCNA7ijAfOIdFK8o2bifjnkYURdNzOdcpsoMBT1o2TOovQVsnIrdmBkDmILKL0KF50HaFMMEMZ\nasQoiePa/oeX2IzKXsIvXY+MjKOjzTi5IPMUCXS4A+UFEn7OStAFED460Q4xjeIwgjwGiS+24Zhg\nWyrR1CO5QCHUTzou0c5lkLYCILwBjHoBhAYTxZv/v4mr9/5Xhvka4seRkRYVcV5vfek3On6avDDH\nx8f5m7/5G77+9a/zwAMPcOrUKfr7+/njP/5jqqurX3bbewIwtdbLbKiFhQXi8fhrLhNcP3GCM//n\n/3Dob/4GN1DOuQUkb1++CTTLV62isrqapBDL3pIyGiXZ2clCUbO1rIzoihUsnbbAFamrw0kmiVdX\nk1xYIJLLoTMZ/MARJNLVhR4ZgVTKLvf1kT9yBFzXSt89+m5i0xNETxxGAGLHEKqo4+o40N2LOBCA\nUUkSWlrhwjlETw8ykkdkp5ETQSmzpQM1ex25FAicb+hDnDmC8Ow99nY8jNRLiNH9YDRm3Vbk2aDE\nGktiatuQV2wZ2lQFbDgpMM0t4OQQ188h8vY69KpBxMXd1kVESMzq7cjhAPhatmDqapHj37GflzZb\nMk8qsPyq7UbMWqEBALf5AaTjI/2z4M+jq7agpgPfzEg1JlyJSlkZPr90HSI/i65YhQhdxSRWoBZt\n39Kg8Eu34iwGZVSnAh2uQxUuUyjthngOx4yijLU4c8MDOIUDCDwMDn6sD6ewB60a8ZPtiMgMDlYF\nyRfrEWYCiS27e2IQZfYAIfKhATKxCDpij4tuABMBddk+Yv59GHkByOIVtqDNz5J0f/0unuY3b3ie\nh+u6PxGLvLuN1wKkRfejtxpg/rR5YWazWZ5//nkuXLjAli1b6O7uvit/0nsOMFOpFJFI5FVZ6/iu\ny/lvfYvDn/8848GD0LRjB2M3KUvcDpoNg4NM7NqFdBwaNm+mprSUpWefBaxKT1VfHwtF0IxEKOnq\nYvGQ7Zs5ySSxlhby165Rs24diakppOfhXbLKM05LC6ZQwJ+0/TxnzRrE5CQEZJ3I1q2Eo2GSU6OE\nRy/D1u3wwp5lmT0Gh3CKjiFSQu8A4oXdmIpKxJZNyLCLOhrItFXU4CdLCF0dtsuN7TY7nAvIPOs2\ngyMh5iPHj9i+5OldCGOs6k/XjhtWW+EYumU96sJBdEsnpq7SquJcs0QZXbcWUteQGQsauq0fMXoY\n4QduJd3vRngjyIUTGBVB196Hmgg0ZOM1mEgFcs4Cn1fegUBDdQMyfwxT2YWY3r9M9tE1g6jrQRbr\nlOCXtKNS5/Frt0AshdQzyILNPP2Szcj0WYSxCkxe6Q6cxecxKolfuRmT0IQKAZirFRhCKN8KQrjO\nRpR3CUka32nFLVtHJPyM1Zwlhi+6cExgEUYzBoniCoYYmcg7yMXPY5xxMALhD2Ac24vGlIBeCeo4\nGIXvPUhGZMk7NouPuT9DRe7PEbxxVlKvJd6MgPlScTdACvb3qMjaf7NlX682bgdM13X5+Z//eZ57\n7rk3+MxuRLFs/JWvfIUHHniA1kDMpVAocPz4cbq6um7pwd4p7gnALMrigWUPhkKh/5Tb+eL4OEee\neIKj//APpKemaNq+nYnduyk+6o07djD+EqAZraqivbcX9/BhTOAeUrVjBzPB+kIpqvr7WSiSccJh\nSjduZOHgQUo7O6msrCS+tEQhKNfKqipURQXuBcuOdIJZJC9QxgitXk1IKUoaaik5ewzV2gYXz0Mg\ns0ffABzav1yuvQU0V65CdHeiDn0P6eYx4Qj+6i6cUxbATbIcU9eAvGyzXt3QAkJAQyN4UxCPIa6P\nIDIWsPW6AcS5/Qhtj6U3DiFP7cQIgVnXh6mrQJ37jt13rBxT3oicCJipFS0I30MuWsKTbumBWBTM\nBHLpEn7LDuTVXTcyz8ZtyLEA3EMl+MlWlLeIqW1BiEmEySEygZRe5RaYP4PUAfBVD6Kmd0GoFK92\nEzoOkXQAfKFqjFOFyloilR9bi3Cnkd4M2qnArx1AsQ/JrC2jRgdwckE2LcvwnWacgiU/ebHt6JhD\nKLITIQwF00uIYwhRwBiJK7YS5gYLNhvuJpc4hXFmwV8FIgXSPkPC68OoIyBcMGE87+1k1CgFOYnU\nFeBXoEP2xSrkb6Iq+z9Q5uXLTW/G+GkCzJeKm4G0aP5QHHF7o1m7r1fcro87PT3Nxz72Mb75zW++\nwWd2I7TWSCnp7OzkBz/4AfX19biuSygUYseOHXzta1+7ZbbzTnHPAWY6nUYp9YpvEgCXf/ADDn3h\nC5z/1rdY0dfH+E16rk3btzO550a2dnumufrhh5Hz8+jDh8F1qRoaYuamzPOWZSmpHhhgYfduRChE\ndX8/lfE4/ve+B1ivyXBHB/kiaFZUoOrqcIMep2poQIRCqJISysviJNPziIUFmLbZH+s3wMgVWLJl\nTnr64FhQrgXEex7FWZpAXjqMBPyeIdTBAESVg+7qQR0LRj3iJfiNrajpcUzXRvCnwc0ir10GQDeu\nQSzOIFK2HKk7ehGXjyPcPCYUQQ88hJg7iVwYtkDXvh15McjwwnFM3VrkaNEJpB4SlVBehcifx5RU\nIJamELnZ4FhbEddtnxKg0LCd8MRu/MoOqK6CiEHNBOcdrcGEKpBBydUrWWNnKQsz6EgNfmMvKr8H\naeZtz7N0O85ikfWaQMc7UEu29+gnNqKTtThiD0Jk8MP3IQuXENj760UHUTnrBGNEBC8+iIzOI8OH\nMKIOQ3J5HMQXXQgzjiSw8mIIzzEUSi5gnAy+240IBzJ4ugZMGSi7rfC78Ew5S3IOV04R9nooqMNB\nHzNMyO/Edewzo3Qz5Zn/h6hZ9XKP/Jsu7sS+/GmOm18A3gys3dcrbtfHvXjxIn/1V3/FP/7jP77B\nZ/bi6O/v51/+5V9ukdrr7u7mRz/60Svqfqs//dM//dMf8/m9KcIPMqoi+eelepi5hQUOP/EE/9/j\njzO+bx+Xf/AD0JrU2BiNW7eSunoVjGFxdJQV27ezFDBZF0dGaL7/fioaGqiPxTD791Pe1kbu8mUA\nsiMjVA0NkQ2IO7csG4Ofz9Py4IOUz84SPnMGf2SEWF8f/vg4uC56cZHIxo34k5OYXA4KBUKrVuHP\nz1PS1UlNMkpFfoHoudN2FKSqBmIxSC/B9WvQ1g6eB/kcTFyFLb2I1SsJ1YUIX3wBWtsR18atQMHE\nCG73dtTkKMJoxPUJTPd2xOQopqYe3VSLaSpDDe9FpKZBKkxNMyIVAGVFHYSjiNwSYvYqpqMHvbID\nEV9ATh/BNHbC/ITd99wI/uoh5OwIwnchPYNp7ce4OXRLBzI0DREfuTiMyExDSR04MURhCZEaR1dv\nBDdlQTNeYec43f3IwhgiN4Gp2Y7IjCK8DJgCpqwTkZuyQFm2Dl2/ARk+h/LOohNrEX4aYQrI/Che\n6SAiP4YwBYQ7jVcxZG3AYseRahYdakTqaaQ/hXZagBDCpJHeKH6kH+NUYcprUIl96NAqFCMI0ggK\naNGFZBLJdQy1aOophLvIlZ3Dj5SDmkaIHFJdBXcAI8cRMoMhg3E34PstLMocOVHAEMLIRXw5QUh3\nokUGRA4tpwh7fRi9gkVhmA7/BxHdSlS/vHD7mymKfotvJrbla4kiy9ZxnGXWflF43nEcQqHQcqZ2\ncwnX8zwKhcLyC0TxvsAN9v8bGUU1teJ5XL58mUuXLvHoo4++oed1pxgeHmbXrl00NTXheR5PPPEE\n09PTfOADH3jF+3hPZJhgWVzAssXX7U33qWPHOPSFLzB7/jxju3djAoBdsXUrV/fvv+EUMjDwokxz\n6fJl6trbMSdPUrpmDal9+5bLtRXbtzMXmDMDL8o0VzzyCJH5eZyDB8HziA8OkilmqkoR7+ujEPQ4\nRSRCeMMG8gcPoqqqKLtvI6U6T2h/ICJQUYmpqEBeuhjsvNGWTMcDkeJVHYBBtjYQmjoFKxoRIxcR\nWUuKKazvIXT2KMK3LxW6ZwgZZJp67UbMqmbkyadsX1KF0Ku3oM4WM89STE0z8ootqZrKFZiKOihP\nIK4fwlS1IDLXEJkgO2ztRYzfcBjRq4cQF3ZCdRumfgVeFMJXg9JmKIGpWoOctJmnSdShnTgqyFK9\n1W9HqnnUYtADrNmKmD+MMLaqoGuHkNeKvdowun4HvkwR8g9CuBJ9c8k1uhq8eZRnRQr8ZB9485iy\nSpQ4YEuu+SLrNYYf6lp2EtGqHiMS4JRgSnxExNySPXpiG8rcRBwSW5HmFPnIJnLxq0AZOJb8g98O\nIg3Skrrw+vDVWbS/iZSYB92MG7LzpegE0mtCh+01SL8JY3yEWcGiWkKZWjLyEog8GEF94YPUFt7P\nT0O81TLM13I9b+aM9Hb/1WeffZZDhw7x53/+5z+R4/9nIp/P88lPfpJvfetb5PN5HnroIf77f//v\n1AYyoS8X9wxgFgqFZasv13VvGRwe27OHf3rnO28ByYkDB14WNK/u30/9hg2UOQ4Jx2HhhReWy7PV\ng4PMFc2ZgfJt25gPepQA1fffjywUSC4uIk+dIj40ROYmEL1lWUoSAwPkA9CNdHZSsXol4eeeRebz\nEIuj1nQgT9jSmyktQ9SvgGAshNp6qw8bDqGaa1C568hcChHYankr1yGvXUWmg75jVw/i/AlEIY9R\nCv3gI4i5y8u9Rb3J9iEh8L1cO3BDZCASxzStBTeHqS5FLg1j4uXIKVsGNdUrQWcRi4HoQOMmxPQw\nIp9CN3ZhmpqRY88gjAVsr2kQZ6xYFg1hGnqQ4/blwY/VoJs2ovyLyNwVTIk1Z77Rp9yEyAwjvIBt\nWzMI3gKmJILMHcItHyCcDl40ZBwdX3Oj5BpqABkBFcaUliIiOaQ3ijBWZcmLbEPli8An8SPbcPK7\n8KNbMAkfEQFFIFpAC2CQ2LETX3QjzQUMEfKRLnLRMIR2gzCW8epvAscKW9gSbDnIy/h+PykiFOQ4\nRloyVNjbQkEdBeGDcQh5m3CdowjvPlLGx4gwhZAlaYW8JrTI4Cv7wlLmvoPm3O8j3+RkoLcaYBZ/\nh/4zHIpXijcaSO+kXvSNb3yDmZkZPv7xj79ux3k9w/O8V1W1uOcAs1AokM/nXyShdOrrX+ebH/jA\nK4JmKBajpbubcsdhYefOZRCt2raNmX37lpert29nrmjOjCX6pM6cobazk+jZsyTWrn1pkLx92XGo\nfvidRCevEj11DBwHsaUX80JgoBqNorq6kEeCjCOZhOYWOH0KsWULqkyhsrPIK4FcXV0TRmrU9YBQ\n09qBmJ9FLAR9x419mJI4cuE8Yv6qJe+cP7Ccebrrt+Oc2x306AQ6UOoxa3og5mHiEdRwsXdYiqlq\nQY5b4ospa8BEIsjZy3bbDe8EuYi6Hox3NPQirp1A+DkA/OYdyNFABQhBoXEQFTYofR70Erq8EzUT\nKPlEazChcmQqYNuWdiD8BUyyCWIuRCKI1AmEsfv2ynegUs9b1Rzh4Jf04qT24sbXI0oTEMniuIFa\nkdMGxkX6AWM2vBlZOAdk0LFedLIUh+9bEhIhfKcXJyDwFGcoFafQVJON9lCIXQHHMmjxt4A8BcKe\nF952cHZbMo+/jbQpIReyICp1HcJE8FVg5O2vxZNXgQzK30zWVJByjoAwCOMQ8zvJOHaER+lylC7D\nlVModx05Eqxe+i2iVN3yQ/pGl/dujh8HwLyR8ZO8np8UkN5Jvejv//7vKSsr4wMf+MDreUmvObLZ\nLN/85jf53ve+RyaTWRaqaG9v5y/+4i9ecft7BjBd110eL8lms5SWlr5onTuBZjGzLG9ro62zk/Tu\n3ZhAz7Wiv5+5gweXGaeVAwPM3lSurdq2jfm9eylZvZqqqiqSoRD5nTuXM8/4jh03yq+8GDQTD76N\nsOdROn6Z0MQ4YtsgZnewvpSI/gHM3qDcGw4jN25EHTkIsThioI9QiUAd/CEAprQCXV2HuhSIBlTX\nQSyGnLhsP29ciYlGMXXVyMmjmLomxPQ4Im2vVXf0IG4yeHbXDeBc3AdOGLPOyt2pM5akZMk825AX\ng+wwFEOvWI+6EgBbaT26fT0iP4xMD2PKWkG7iFQA4LUbYH4EWbBZb6GuF5UaxTR0oArHMNX3IaeC\nLFc4mJp+5LVi+TaJKVmJmD+BqeuzpVF9HZmz4KRLuhC5qwjPZml++QBy6SACF790M35pNeFC8Toi\n+LFNOAULVlpWY2QVyjuLQeElH0REruNIm036shepTyAIAFntwBEB21Y0kYluxo0/DzJ3I3tUFtzx\n14CYATkDJkzBe5iUuoInp8AIwn4PBceWfoWJo/RKPHUSjEJ5g6SFR9qxmXzU7yAvxjHSsoAT3n2k\n1TEEYcL+RrIkmHMCg3FdwdrF/4tEYeVyX+ylfkjfCCB9qwHm7QP+b0S83kB6JzGGz33uc2zcuJFf\n+IVf+Elc0itGkSG7Z88e3v/+9/PpT3+aysrKZUWnsrIyHn744Vfczz0HmJ7nLd+gO8Wpr32Nb37w\ngxjfR0jJ2kceQUxMUDhsB/7Le3uZP3z4Bkhu3crsTao6lVu3Mrt/P0Ipant6qEwkcAPiEEBi+3by\nN2WedwJN78oVyle2UHLiCKp7M2bXDRAVg0M3loVAbNuO2R0MB69YgerbSOzcPuTSPCYSRa9ejzoZ\n6KHGS9ArWnEuBH3GimpMeTmEHKgrh+xVhNaI6WDwv7EDkZpDLNp+nm7fhLh6CZFbQifKML07kNcO\nIZYCdZ2OIcT5Gy8EfscQ6nyRbRtCr9yKCAtE/hz4GUzVSuT1Y/bzRB0mlEDO21EIr7wdkV8EJwL1\nrYiIi1g4hfBtv1XXbkdc22tnLAG/bgg1tdP2KBu2QmkItfB9u2+nAhNpQKZtf9DE2tB+AVW4aoXX\n6x5COJM4xp5LIbyVUGE/Am0Zs/HtOIViabgMr6QfFTqNVGNoUY8hjjL2vH3RiTBTSGzps+A8iBv1\nKSSO2hEQfwCWZyhj4K8DJ5Cy0824/lpSagxXzuL4HfjiOkbaHmjY20xBHQtKsCGkdz+L6ip5eR1p\nEoT1CnIBADteHUKAq6YQJkzEG2BWTpJVtopQ5q1nQZ0GYZAmzNrcb1Dv3X/HH9IiYa7446mU+on1\nyP4LMH9y8WqB9E6A+Sd/8if83M/9HA888MAbeEU3ojiDuXPnTv71X/+Vv/7rv77j568U9wxLtvgw\nFPuYL9UTqdmwgcqODvzZWSpdl/yhQyQaG3GvXQNjyF29SmVfH9nJSTCG7Pj4Lcs6n2fl295G5cIC\nkTNn0MPDhHt6rCKPMbijo8S2bcO7ehVhDO7ICPHt23HHxojfdx+laKpqq4nsex7pFmB0BDE4BKO2\nBPfi5VHkux4i3FpLbPE84cmLsH4zYnIU4XuIuWncdd2o6xMIt4DIpDEdXTAzhVmzHlMdQSR85Mhh\nm01GYpiKOsTSHCI1C+W1EIkiskuIuSn02h78latQYhQ5cwpTvwYy8wjtIWZHMKu2WQYsBjk7gu4Y\nAi+PXn0fMnccqmqRM6cRfgGy8+iGLcilqwg3bdnC5SuR2Wl0rBK9og1VkkaljyOyVzGlq8FohJ9F\npEcx1T2Qm0UYD5GfwW9/FzI+h9SnEPkr6IpBZG4EoXPgp9HJTcj8BMKbx8gEflUvokLgiIOYUBKE\nZbkqfxwd2YzwFxC4SHcULzqEjjUhkmlU6ATa6UKaUQRLCDy07ESaKSTTGFGFJ9vJx1eTLT+MHyoD\nmbUlVzkG3lbroCIKIK6Bvx1ft7Io8uTVNYRpxpfX0XIWZcqRuiJgwU7i6LUY3c6SKGHRuUTEX4Ur\nZjAijyfmifsbceUUWqYRhIh4PcwLwZwzhkMpysTxRYa8vE5Sr8IXObTIs6jOkRWCKt2BlOoW1mY4\nHH7DWJtFsH6rsGSLM5g/bvP6VxOvhbVbBJzpafty/dRTT/HAAw9QH1gHvtFRPL/h4WH+4z/+A8/z\nqKqqwvd9wuHwXXsk3zMZZtGxRGvN/Pz8y1p8eZ7Hxf/1vzj8m7+5XJ6t7u9n4ebya38/s4cOUP00\n2AAAIABJREFU2VENYMVDDxFNpxEHDiAKBeL9/WRu+vz25cTAAPn9+5GhEMmeLZTHo8gf/XA5E1WD\ng/DC7uVMVGzfcaMci5W2E4UcESdL6PIJ/L6bNFyFwL1vgPCRoIemFGZjP/LIHkwkht7SC+Uh1Mkg\nA4smMCtWIS8F2V6yElNWgxyzrEtTtQJT1wwxEJP70VVtCDeFXApUflZ0IeZGEdmAONTWixg7DhWN\nmPo6TEIhR6zIAIDfOoS6UjxXhW7eigoYsW79ZqipJjQTlEUj1ZhoFXIhOJeSNvALiGxQvq3pg3gJ\nwj+C0HPosq2IBesEAqArhpBzN45lyrZhHAPhYaRYREdWo3KBtquqx4g4yguyxfA6hF5Cx1uR8bMY\nZyVSH79RcpU7ULrYXw3hy16EuUou0UwhPgymARybzaNbAG0BE8DfAGISX3eSkhNI3Y6rjgTZo0L5\nW8g7tjIgTAmObkWbKAsyg0aAcXCVvQdRfzUFMYmWVqIx4d1H3jcshFLkRZpSfw0LjiWBOSZBVNey\npCwZKOGvxOgaxpwRtPCo89YzkP0QYV5Zuu0n0SN7M2dkryZuV8T5aY7i9++6Lp7noZTiM5/5DJ//\n/OcpKytjw4YN9Pb2sn79erq7u9m0adOL9vH0008v23o9/vjjfOITn3jROh/72Md46qmniMfjfOlL\nX2LzZmvqMD8/z+OPP87JkycRQvAP//APDAwM3PFciyXZf//3f+d3fud3AMvsBSuy8PGPf5zPfvaz\nr3jN9xxgvpTFlzEGz/PI5XJ4nkc0GuXaN7/Jnpt6mtX9/SzcBHqVW7cSEoKSVApx8iTx3l4yR48u\nCwK8aLmvj0yg7+rU1VHb10vswH7ktFVvkf1b0QdvlHfltm2Ig/uWhc3FtkHM8aM4Pd1E5i8jWlci\nD9wo13q9gziHb2g3+r1DqOBzU1WL7u9HXtiNSM9ilIPp7EWeCfRjw1F0axfqfNBnjCUxdW0QjUA0\nj8hOYmLly/J1fnkj0pGIOcv+1LUdiMwcYmka3bQB3VCHuvYCwg1Yqo39iInDyyIDfssO5EgANkJS\n6HiH1V9Nn8EIB6+mh9BsQBxySjClq5CzARM4VodJNGISCaR3CBOtt/OThYB9m7wPkbmE8INjl29D\npE5hqjYhQmcxsbXITHBfCOFHe3BywX2QpbiymZAexU9uRMRnQGRR2B6oLblO3tB6lf0ofQQtG8kl\nGihEY5awY28q+N3gWNk+dDnoFaCG8fxeMsLDFym0tCVtx1+PJ0dAWOBzvF5y6gTK38iiKCBNLRnH\nvtTYEmwjOWX7liFdizBhhKliTqbAL8NVs3gBiJZ561hQ5wNAlpR7XRSEYlxNInBI6lrmAiJRia5h\nMPublOoVvJq4WyAtlnZfLiN9qwHm7Yo4b4W4ncnsui6/9Eu/xAc/+EGGh4c5efIkkUiEL33pS7ds\n5/s+a9eu5ZlnnqGxsZG+vj6++tWv0tnZubzOt7/9bT7/+c/z7W9/m3379vHbv/3b7A3G7H7t136N\nBx54gA9+8IOv2GqDG6B5p7hb1uw9A5g3O5bMzc1RVlaGlHL5DSmbzWKMIRaLEQ6Hl/+BR/75n9n9\n3/4bJti2qq+P/MgINWvWEDp3jnhzs1XgCUAx1tND9vhxCJSFbl8uf+gh4tk08QMvIDwP2dOLPn5s\n+XPZ14c+ckOFR27dijhyAFFXT2hdO6ESUId23eQOMog8fCMTzXcPEDm+98Z13/8uhJ9CjB5AeAX8\nTUOoYzeNhXRtQ54O+nNOCLO6B3HxMKazB8QsxGPIK8H8Y6wMU9mEHA96oMkaTKIMef0CRkh019sg\nnEVNBvJu1WsR6WlENmDf1ncjZs7b8itQWLEVHHDUJDJ/BV0/hJjcucyI9eq2EZopysyFMVWbLXBX\nNyH0GUx0BXIpEHEP12NUHJm12aGOdyC8BdAFTNVGTMJF5o8jTCDEHhnAye9HEAhaxHbgZJ9Hywrc\nkk5UUuKYQIGIcnzRhGMCxqxoBgOSUXy5mmxiJW7sBCjba8TrA3XUllwBvG22b2lieH4/WRIUnMDM\n25Qj/Vr8gLCjdDMGDy2mkP5mlkwZS84wRhQJPJtIqxOBmo8k7m8go04Q8TeyKDwgzpKy9yCiq5Am\nRFbZF4mE34onsii9gqvqGuV+MzPqMkb4YATV/mqmnaAHaqL0Z3+dRr/rzv9QryJeCkRfjmhUKBT+\nCzDf5HGn0Z9HHnmE55577mVLz3v27OHP/uzPePrppwH49Kc/DcAf/MEfLK/zG7/xGzz44IO8733v\nA2DdunX86Ec/IhqNsnnzZi4Futp3G9lslqNHj3LlypXlefxwOMzmzZupq6t7xe3vCT/M26PYqM7n\n8ywuLpLNZonFYpSVlRGJRG55221573vZ/pWvIByH8nXrKHccVrW14ezdi5maIn3gAOFNmyD4h84e\nPEhswwYISArZgwcJr19P6cBWWjasp+YH36Mkn0ME/zD64AFE14319f79yI039kd6iejPvoOSyAyx\nMztxDuzEbOzDKLu9OrQLd2OvFU8HIkf24m8eRHd1o7duRl34DpQohGd/vNWxnehN1iNTaI08vgt/\nfeCZGS2BRBi9Yztyejfy+hnE+En89q12/ewC4vowfnO3XU5dR2QW8Tc9hOloQc1+H5m6hK5oB0BO\nn4VIEpNssMuTR9ClzfglDRTatuGEhnHKXYR3Pfh8J6Yu8JTEEJraja6x52aSbZgY6KYWZGEXwptB\nZM7hl1pvUVGYRLiz6JINdtmbR9dsxDQ2INVOVG4vJtSIUdb9PZTfix/ehBHWNkoWzuJWvxtR6xIp\n2Y0yu/DkDrsv5lHmPJ60x5JmFK2qSZc8QrpyBB37EUrHwQ90KJ39oFfbjBJAHaXgvoc508yCc4KC\ns4+Q12uvS8zjq8uEPFtm8sU46JVkvLcz4YyRCp0kZMoIaTtUnXaOEdWrkMZS+H3AeENcVRMsqUmW\n5DBl3noA8nKGgpwn6a1GmSiYchZNFbPCxRMFpp2LJHUtEZ0EYZh2zlPltZP0mxC6lW/Gvsr+8DMY\nXp93aiHEcjkyEokQi8VIJBIkEollWbWbX2DT6fRyua9QKOB53i290p/GuFtyyU9TvNQ1vVJfcHx8\n/BZ5uqamJsYDTeyXW2dsbIzh4WFqamr4wAc+wJYtW/j1X/91MkW97DuEDhKMr3/963zuc5/j8ccf\n5/Of/zwf//jHef/738/58+fv6lrvGcAsfqHFclEqlVr22SstLb0lq7w9Wn7xF3nn179O7cWLyD17\nyOzbR/wmkMwcPEj4ZpA8dIhYZydOQwNVQ0PUTkxQnc0RvmL7RubwIeSatRB4/JnDh5Br11kpO0Af\nO0r4Xe+g5G2bKF88SeSF78Lq9ZiIfYOTR/fhrtmACdnjh4/tx2zsxcQS5Lf0I8wUNEQR40H57vhO\n9IZBTHB98thO9Mah5Z9BOTGM97b3QFUeOfEc6uwP8NcEoOoVkMP70R2BOXQhg7x6ikL7ALprCKoN\ncnY3JKz5qkhPIbJz6Br7oy3mL1syT1kbOlaJX14JzZWE1DDSvYacPoRJtmLCdns5tQdT3Y2Rgdi2\nO4/X8TAicgmV24ea3YkuLQJ+Hrl4AF0eAJs3D34av/lRqF5EmWcR/iQ6YrMkWTgHIowOtQHgFA6j\nYxtxK96GqF0kFH4K7axBE0NgcPTzeHI7Bokgj9L7yYceJpPsJVN1Ej+2C0xvcBNHUWYRvKCcpE6B\nqcZ1H2LO1JEK7UGaKtC2ZOQ6B3C8bjAhEAVcdQzpPsSCXs+Ec5El5wxxz4J/QU6gRZaob3Vgc/Ii\nEb8L3+vhqjPObOgECd2Mo0tAGBacU5QUOhDGwWDQJDDeFq4446TUdbJyjirPvtQsKlsOLvUbKPHr\nSIsI8yRIiQIIw8HID3gq9o/kg77tjyNeDkiLZdsikGYyGdLpNJlM5nUzdf6veG1xO2De7Xdxty8O\nt+9PCIHneRw6dIiPfOQjHDp0iEQisZyhvtw+vvzlL/OZz3yGX/3VX+Wzn/0sFy5c4Gd+5mfuOuO/\nZwCzSH2en7dls2g0Smlp6S36hy8X1Y8+Svs//RMiaNZnDh4kvnHjMkhmDh0i3NkJ0SiRVasoTSRo\nXrGC5MGDOFNT6KNHMW2rMcFwrz52FNHeDjctyw0bCL3zAcq6qik5+hROyGBilnwhTx7Cb+tAxyzI\nhk8fwaxej4nGMKUVUBJBD3UTnjuKvHYBeWovZs0WjGPPV57YhVm3FSNtiUQe34ne+i50/1aIX8U5\n9y3Myp5lEFXndqKLoGk08vwu/DVDmPIG/M4+HP8kJDUidx3hphFTJ9Ergkw0N4eYv4Jfb7MmLRR+\nXRO6vYlwdjdqIVANSq605zJ/GiLlmJhl1InpQ3iN23FXbkGGj+MsfBdTdt8yiMrZnehkMRPVyPnn\n8asfQtdvRyRHkfmnMdE+uy89hyhcxI8Fmag3jvAXcKP9uOUDyMRBVPg8WtgsWOlD+DShsc4ejt6N\nlt24sptMcjP5ih/iheNglJWakwfB325vmphHcR7crXje/cwJj5S6iNB23546hySO9K0HqOccQemV\n4PWzpNdyLXQYx1QhTBgjXDLOCRLefWAEvkiRlyNE3R3kdAdjzgVSziQlvgW+tLqMIkLMt/cwHbpM\niddDVq/kijPOtdA5Kr2VSBPCFwVmnEtUex1gQBHBM5XkTCPj6hrzahoPlyrfnveIc5ZvJP5f5gKn\nlJ9UFHubSqlbgDQejy+/4BYNptPpNOl0mmw2+6YG0nshw7yZLf1y0djYyOjo6PLy6OgoTU1NL7vO\n2NgYjY2NNDU10dTURF+f/T9/73vfy6HAFvHlwnEcXNclnU4zFuiAX7ly5a6/k3sGMMH2MYsgebc0\n4puj4rHHWPW//zfipswyvn49IhoFKXEch6Zt22iYnCS2axfm4EFkezsE80n+8ePoxlZM0oommBMn\nEM0tiHVrib5jB6UzJ0m415GuLS3Is8cxja2YEru+c/Y4prFteVkszqHvH4JmBzmyE3V6F17jakw0\nANkz+zErN2DCAdCc3ovp2Izu7EVv3oga/Q5EAGHvhTy3E7N6G+amZb9jBwbQdasQUQ/T2YEzuwvp\nppAju/DbAlD1C4ix/ejmIBN102g3Q27Dw8jkBOGl51Gpi+hqC6IiO4nIz6Mrgkw0NQxS4bc8iGlb\nRch/FilmMJGgnLtwEBNfiQlZdrOc24NJdKOTXfgNW5HiGYgZbPdTI5eeR0eHMAaEySGzB9DxHZhw\nO6Z8LU7yBERdhPCQZhzhzeMZm4mGOA8ijE8bntpIrkSTrXTxI7YXiNoLegOYhJW0U7vBH8CYcgpm\nG3NyigxxtExh5AK+ukTI2wKAlhMYuYDy1yO9LSziMC9T+NgXm6xzkqiuQwXl3LRzlJheR9jbRE6v\nYjx0GsfUBCCaYUlevqUE64olkm4/Kd3AcOgiriiQDEB01hkmoSuJBlluWk5T5vVyjQijziRTzhXq\nvVaEkeRlllk5RYPXhjIOYV3GV2P/xpmg1/pGRZE05DgO4XCYaDRKPB4nkUgQi8WWX4B/2oD0rRS5\nXO6u7Nh6e3s5f/48ly9fplAo8LWvfY3HHnvslnUee+wxvvKVrwCwd+9eysvLqauro76+nubmZs6d\ns8/jM888Q1fXS/fbi4D4yCOP4DgO73vf+/jCF77Au9/9brTWLwLql9zPvUL6ebUWX3eK+aef5uL7\n3ofJ55ElJdQODRE9fx4n8KiUGzagL1+GJctQZN06uHp12dhZrluHvD6B09ZKpCJMyF9CXp9CLAaG\nye1rEAvTiAU7/O61rkbNzyAWAnWawbeD4yLPP48wBt26DjE/iUjb7Fm3rkdMjyGK+rArNyBmJzAr\n14J7FZJliKkLiHwgAtDWg5g6iXBzwfp9iJEjCN9Ft2yyfcDRZxHaEp/8lkHkyO7lMRHdOoS8coOt\nm+t4B0peJ5Q5ZlV/6rYjJwMCjQxhqnuQ1wJWqhNHV2yASAgpLwNpTKwRmQqIRZF6jEwgs1ZQ3sTa\nQLuYSAUmGUaEswjvGsIPiEWxLYjc2WVyj05sQ+T3YyLtmJJyRDSKcJ8LiEWBB6UpSthFcOVGwvIA\nebGJfMJBhzWyKIiu64E4yIBooFcBSxiRwTU9pIWDqy4ts1xD3mZcdRxE4JDj9eKqQ0i/m5RwEabm\nJtZrnLBuIaesEpOjK8GUAklSGDwctMiRl/aZKPHbycpJ/IAMVOatx0MyLdOkxRKVhZXMRi4F+w5R\n4Tcz49jlpF+Po5u45FxBC01SVyAMLCr7fFX6dWREirzIUe23kTMljDmTeMISpLbl+3hbYRD5E3jf\nfq0kmbth7N4uxPDjzACXlpZu0Vx9K8Tt39H4+Dh/9Ed/xD//8z+/4rZPPfXU8ljJhz70IT75yU/y\nxS9+EYAPf/jDAHz0ox/l6aefJpFI8OSTT7Jli335PHr0KI8//jiFQoFVq1bx5JNPvqI9181x8eJF\nzp8/z+Dg4IukUl8q7knALGoIvhZT2oXvfY/UX/818QMHkKkUcuNG9KVLEMz2yPXr0WNjyyAp1qyx\nBtKZDOGBHhJJCI2cXQZF3bYasTiPmLWDv15TGzKXQs4HQNDWgamvRxSuIyfOoFesQmQWEfPBLGTj\nakRuHrEQqPI0rQm0YTVm7QZw0oiZy4h00UtyPWJuHJEJpO+aNyLmLiNyKct47X4Y4U0gZwIR8cZe\nxORxhG+l8QoNvYSmjiyDqNe8De3nkbE0TvYsumEIMbWT4u+Crh9CThZHOQS6fhA5cwTTsBnBBUyy\nDTlXFEOP4Sc6cVKBcbVThok2I5dOoMs3Y0odhFpA5u3bpQ61IDAINxhxiay1pCB/Gh1bjylvQIr9\nCAKpPdFLyBxDYJ8HTw2ifPsC4IZ6WYpXoBI/Cp6bMMbbhAxZWTqjSzB6JdI5jjFl5HU/GZnHcwJv\nUt2MwUVLm406/lo8MQFiCel3kzWVpJxTywzauHcfGXUsEF+XxP2NZJyjhP31pEwEQ5zFgLka0knC\nuoK0Y8c/oroWjMAxVUzLHMokyYp5CtI+g5XeSubVGFpYxnWt20lOSEbUdTSGer+FCeey3bcJU+7X\nct0ZAyOo91eTJsJlx/Y4K3U5Hh6LwZjKSq+Vn88+Spwfr7Hzj4tV+moYu68HyL0VAfN2L8xTp07x\nd3/3dzzxxBNv8JndiL/927/lIx/5CE8++SSVlZWUlZVRXV1NWVkZsViM6uq7M1e/ZwATbrX4MsYQ\nD0g3rzbcZ58l/Uu/BAE7S3Z1oUdGIGXn/+S6deiJCVhYgMpK4vf3Ebt+AWfUZku6pR2RTiFmLOj5\nja2QzaJmba/INLZiwg40rUDMX4BIGLwCYiaQoqtrQXju8rKpa0XrPGpuElPbjF6zBrFwATkT6KjW\ntiNyacTiVLD9akRmAZEKQLdpA6a6EpG/jEyPoGvXIxbHEbkAVOs3IWaHEYVgvrFhC8xexKtbh1RX\nEaX1yJmjCB3YatVvQ1x/YXl0w6/fgZzcBZFKdP16RIlCzv3QnjsCXbkDNXtDZMBL9hJa3IdBYKoG\nMGUlqFwgaCCTmHA7MhfMZqpqjFONzFvg8kuHICFRwgKfL1eDXkRh760nNyD1CJJFDIJ87BHc2FVM\nNHB58QdAvmDHN8D2KVUw4qIryXiDZMLHMCoLOob02tFhmxULXYHU1fjOeTAS6Q+SNoZ0yJ5bxG/D\nE/P4geRd1F9HXl7BiCxhv5OcbmDaOR3MTArK/U7m1SkQIIxDqb+aBXWWEn8d80IgiC7PUEZ1GY6J\nsqTsd1ziW6q8MtWMqGnKdS2LcpZCIPRe77VyTY2hg2Ot8DqZkhmuqRTKKFb49Yw6lrkYMREqdDmT\naooKXUFE1/Nwvp9mXfUK/ymvPn7SYxg/TiC9k6vHWyFut/batWsXzz77LH/5l3/5Bp+ZDa01n/3s\nZ/n93/99fvZnf5aFhYVbiGNCCC5evHhX+7qnALOoS1kUJ7hZXf/Vhvfccyz94i8ul19vzyydoUFC\nJYqSc/uQbj4AySXEjP3h1o2tmHwONR2AWEOTnbEUAr2mHZGfRLhZxHXboDbVKzDKQU6N3HG50NWP\nqEngXPqhdc6oaMQIhZwN1q9sAgxiNrDBqmqBcAxqahHZUxAvBS+LSAUiAJWrEPkUIh2cbzBbabwc\nbtMmZLyAs3QB4QagWnUfYuEiwrP3Q9f0BBqwWUyiEb9pE2ppF8IE5eKK7Yi5G5qwumIIMRfMYgoH\nf8W7kOIMUl/EIDGJ7ch0UN4VIUy8B5kuig4k0MkBRHQKqU5gRAVaNKC0LalqUQ+iBKlt6dwXK9GR\nZvKJKXRkGPQ6K1UnbBaO3w3yHARlT+MNURAhUs5FtMwGJdYD2JOVKHczfrjoURnF5PtZCk2Td64h\ndYKQbiDv2GM7ugppEhSKQOf1k0Yx49h/3ITfRl5MLwsPlHprSKlhDB4JvYa8qWZSnQsy01tnKJUJ\nkXRXsBSapMRfxTWZJWwSzASM2BJdhjSKxcDqq8KvRf3/7L15rB3neeb5+76v6uzL3feV5OW+L6Io\nSnYc27Id90zDVtrIxOkEbRvjjp12bCAYx0mm0wlmMkaQwE6QBU5i2AkwcdBOAiSdWE5stT0mtVEr\nJS7iTt7L5e7buWer+pb5o+qcS1GURMqSJYt5Af7xourWqapzWE+97/e8z+NSLAuPa2qJXtPNvFyg\nHlfBg7qPK2oSKywFWyBvBnnOm8IJ8Jzkgfp+7g7HbuF/y+3HW2Vu8dU0dq9v676cotHNXD3eDnEj\nYH7rW9/i7Nmz/Pqv//qbfGYvjmq1ytNPP83Bgwdf8zHuSMB8OYuv1xr6kUdY+ff//kWVpWwtkE2E\npM48gxkaRVRLyIWoXer6h3FhHTkdg1J3P+CQU1ex6zfhBjsQyxPIyYvR/q3duFQGeS0eS2ntwqVy\nyGvnm9vt2g0IN4+cOYbNd0KmiJyKHs6u0IlLFZDT8TpgoRuXzCJ0HTs0iggvgyeQi/Hx83045SMX\nL8X7RwviYvkyNtNBMLAVZcfxK7FIQGEtIlhB1GLQb9mAqM0harEJc/87ICuQ1cMIDLawE1E+izAx\nqBb3IpZXbbds60Gs5xD+RRRXMdl7keVVaT2bvQ9Zvq69m7s3kqvLlRDyLNbbj9KxGANJjNqOZyLH\nEScKWLUWIxPU83O4RAVsG8SKOdh+rBVIL5aws+twOEI3yIp3BulGCeVVXEONx2xHy1MRY5ZondJg\nKImAqpwmrbdT9aMqGKdIBhupJ+NK1KVIhNspyypL3lU8m8e37ax4UWv5RuGBgt5NyTlm/Gh7ixli\nRc6gRRWAdr2WeXUJiSAbjBKoIlfU+bgylXSbISbjFqznfNpMD4GoE1BgTtTI2SzTXvSdFW0e6SQL\nKnoR6tO9OJflhLeEEY5B086sXKYat3v3B+t4oL4fn9dXI/XGdt9bKW5XGhAiQsyN5vU/znGzqvmv\n//qvMcbwqU996k0+uygaLN5Lly7xwAMP8OSTT77mY90x4utAs7XSsPl6vRwQ5OAg3k/8BOGDD5Lc\nu4M8i2T9AG9+ElGrIpcWsa0diHQaUVlBlJaw2TwuV0CWS1At43buxm0YQk0+hZwbB8/HtfVEbiG1\nMkiF6xxALM/HucD1rcWOjkG6gqxMQCaDWJlFBBVwDtc5iijNIuoVcDRz19aP6+uBIqiZpxC1RXAS\n1zqMqM5GLVfp4YqDiMocor6MKQ4SDG7BU+fw6+dAJSDTjagvIOoL0VhIshURLCFqc5DuxLWux3b3\nI8NHwfcQykeYFUR9EpcZBQTCVhD1q7j8RhAK17ELkTwNmVQ0AkKIDMdxmX0QziEwiHAcmz0A4Qwu\nvweRncIVWpDumYghaycIxAEUl6P93STWvxdhr2JSu6gVlwjSBUiciKpHUQG7HeQ1EKX4vNbihCFk\nHSVpCKXGqVmcnEW5ToTL4cQKVk6h7AggkXZjJKAu8tTlLIgAraZI661osQBCY7wZ0uF2hMtTc93M\nehP4up/Am8WKACNWyOkx6moeI6o4ocnrbVRp5ap3DSMcWdtBXZaoySVSrohvs4SyQl2UaNNbKZHj\nmj9HSS7QafsJRYARmhW5SI8epiJWyLgi2uUxtDGhpgmlpipqDJg+lmWJuggwwtJn+sjYdk6pgGVh\n6XB5SrLGsqySc2nyNkVFBszIZa6KKgO2lezraEodhuGLhL/fSnG7YuVhrN71RorVvxlx47P08OHD\ndHd3s23btjfxrF4cQgjm5ub4zneiJZ18Pk8Yhret63tHVZi3avH1muP5p0n8wr9DLEatLje0Bq5r\nv5qefpyweDPxGuTgKG7tGuTcKcTcZVxLJy5fRF6NK8N8K66lCznREB5vwXX0IeYnceu3QG0csjnk\nRMwoTeUwXcN4VxsM0yyuay1yImJi2rH9uI4C6lK8DpjI4drWICefW8071iCn4zyZR/fuwHlV/Moz\nkMjjcgPI+fj4iRZctg+5ENtmpdpxqc6oxZs1CKZwKo+sxNeT7MV5SWTtYnQ+6SGEs6BXcO3bILGI\nYAZhoopK+2Mou4AwMZEptRURXAa7givswxU8pH0GQVTthWI3njuOIKr2rHcAoZ8AJCa1j3oujfEO\ngYwr1fAA0m9YbUmw+0E9irXthG47dZkgjD0ocRmUXYtRkRSfcC1getDqLNLupOySBKJGqKLK1Lf9\nOAK0jNaHk2YULRZQrp0qOTRJKvIqNq4OC3ojy+psk1GbCzZRE3UqZFjwZmkP1zCXiDoE0nm0muFm\n+9Z3GQp6jKtqgRVZJm2zJE2aRT+6b3nbgnCSZTVP1hZJ2UGuyWVKMTmox3SxKJeoxVXygO5jVs7R\nZns4r8r0mA7Oq1msAOkEI6aT8170m046n6Gwj9NemSWpyTqfT1R3sdO8Pi4Vb+UK83ZDa029XieZ\nTL6orduogG7W1n2rA+nNrL2++MUvcu+99/KBD3zgTTyz1Wjc39OnT/PRj36UmZkZWlo+X+hvAAAg\nAElEQVRakFIyPz/PO9/5Tv7yL//ylo51RwFmQ4DdGEOpVKKlpeV1/wxx8nn8n/+pJpHH9g/hgjpq\nJmpXuq5eXFcHrrMFefUoJJO4bAF5JW6X5ltx7d3IiYgg4rIFXNcg8sJxXM8wbmQYJ1dQF2MGaSKD\n61uPvBg5bjg/hRnYhDcR678ms9gt9yKqF5BLp3FeCtu9FXUlZn3eLO/dinMBNuvwgzPY1i2o2ViU\nXaWxbZtRM3HuZXEt6xFzR3E9eyFdg4RALsdkHK+ASw8jS7Hmq9+KS0felC7Rie3YivBmI+svwPk9\nOC+LDOP74Q/gkFGVKZLYlnci0pNI4pcAuR5n51HEoKq2IMxVBAvRmEj23YSp06AampP7MPJkZOIM\nCHsAJ54AoXGug5o9SEU9ASoCD0/fhW6IpzuFZ3ajvSfACYTZQ5luSjGo3jgaolwBz3RQ986TMGsI\nXCcVUaHacBmxPVhCAhkxoTNmiEAs4rtWKhQJSVKS0+iYoNMajLDoT0Tar0BbsBYtHHPSUpIr9Jjh\nJutVOkWXGWDSi9rqedtK2gxxyruCFY6MTZOzOaa96HdasHk857Eol+gxAywJxYoIWIxBtde0sShq\nrMhoXXPYdIBTXJWOGRkwptu4oBbQwiEcfCBYxwPBJiQ/3AP/xvWxH+dozIbeSDZ8sxi7r0fcDDC/\n8IUv8HM/93Mv6xzyVgitdVN+UUpJV1fXLf3dHQmY1lqWlpZobW19Qz5HnH0B76PvR85ElZLp7gPn\nEPk8DLQhSuO4RAp5NV6DzLfiWruR4zFIZvK4viHkhVgRZ8NuXF8n8tS/RkSeRBrbvxl1oQFaSezw\ndtS5eJ1O+dixvYikhwjOQ20a17cHOdEgx3i4gX3I8UdflIuJxzGDe3CJZcgX8ecioHDCw3XvQ8ai\n6k54hG27SMw9gZM+tn8/FJKohYfi4yWxhZ2oxdhtRKawhW2oxej8bHYNtnMjqv4QgjpO5nDJdchq\nDPqqiE0NoeoNEO3H5rcg1VGEmMLJLqwqolxEcrGiD0QSaaM1WKvWo5OD6PRxnJoG1gErQCw8wGaM\nnIV4ptGZewhIs+KdABkggq04/2zkXwl4ejdaPRdVf06Afi/LcppqTKLJ6J1U1LNN8k9jNAQgYdai\n7QgzfnRt0qXImgFKTfJPjqTtoOxdJG0GCVwXJRFSilmuWduOAyoxqBZML4Eok7IdzOOQLkNJLRLE\nLwAdQT8L/hQmrlT7wrUEQnFOLaIxDJkBxtVlECCdZMD0Me5dRjhBnxkkcBlO+9F9SrkEHbbAZdWo\nVNNkbAYhfBbxqAmB5wRTKiJF9ZocdaGZj8/lnmCEnw420upee4v27QSYjbbsrY6z/TgA6c1eAn7x\nF3+R3/iN32Djxo0/0nO5lThz5gwTExMopZrKUX19fbeMBXcUYDYcS17O4uuHjYZFWLVaRVw8S9t/\n/g+IqavY7bswLRKvOoOcbBBp2nDFDuRERDZx2QKuexB5Pm53pnPYXXcj6teQ08cjUBzahjofV4LK\nx47uRp2NQUl5uDV74doZzOhGvPpJXPdG5KV4FEJI3PAB5MWYDCMEbvgg8uJhnEqih/dg8glSM9+P\ntiOw/feipq4j1/Tei7oW5dbLYkbfiVd/GqEn47GQg6j5hsOHxLXdg2zkQmE7fwLhVxD2CCBw2buQ\n5cb53cB4FUmC9E78TAKROAGiilWbUTq6fksW66/Dc3ElK1owag0ukSPInAQpgA7ghfjb6QbyQNwe\ndgOEog3rdbMsTiJdL07UcTICKmnWYsUixEClzEaMy7MsAqpq8kWjIABpvYWqOg0xCSYdHqAi6szH\nFV5Rb2FJnWjOWxbNJpZir8y0GcTZES77UWtbuQR5M8Rcc0YyTdZ2sqjGKZphKi5LXTgWVNQWvZH1\nWjBtOAu+a+WSVyJvilRklaqKzrVHd7GgFpss2NFwHddknWsqIq2N6m4uqWlsXC2Omh7Oq0m6bSt1\nl8cjzSkvui8JpxgyBc56kehB2nkM6TampOScCmm1Pr9S28A289qWP+5kwHy5uBFIG0UA3Dpj9/WK\nm13Tz/7sz/LVr371lqu2Nzoatl6HDx/mq1/9Kn//93/fVIW6cuUKX/7yl/nMZz5zS8e6IwETXmzx\n9cPGy1qEXbmE/39/fNU+q6Xzxe3XbBHX2Y+82FgDzGJHNkE2haxfgvL0DSDp4Ub3IBsgKRVu3X7k\n6UdwncO4wUFMBvzxVaNpM3If6uKqCo8ZvQ91IQbBZIFw/UHU0hGUjgUS+u5DXl3d3/bfh5y67u/7\n34XwNYTPI90itv0+5Nx1+98kJ5jGFYtI/QQ2fy9q5brj5e5r5g3Gq6wewxa3IBLP4VLbUUEDhBWh\n2EvCxdePj0vuRdhj6PROgsxZkCPA4/HRM8BmoMGKywFjwCRVNrLiXUOJbrSMQFXYNqRrw6hYscl2\ng0vjaGUJi46fO2EsSpCwA1hqaBlVYEkzisMjcHnmvItkzVpqcgojorZm3oyxIsdx8VphMdxNRTiu\nqXEQ0K7HmFPnmrOf7XoD0+ocCCiaIZzt5oIfdSWU8+g0/c2Wa4P1Oqeu0WZGmKZKQuSZVFHLNWsz\npG2KWS8C1bzOkdUFljzBVa9Mh8mjsSyqxrpmKyuiyoqs0WYLZEwXZ1WZsoxeCNbqVi6rZepxe3i9\nbqMkAix5TsqAzabASbUcr3vC/xYM8ZFgAHGbLdq3E2DezAbr9YofhZn3zeJm1/TBD36Q7373u28Z\nS7aG1+WnP/1p3vGOdzA3N0cqleJjH/sYv/qrv8r+/fv50Ic+dEvH+vH/Fb7GEEL80HqSzrlXtggb\nGCH8rb/EDkQzamJxBrE8jx2KWhWivISYGseu3YYrdmB37EbKy5CtIpYmELqOvPQsdl0sam404twT\n2PWxXqs1UF3EvOOnID2OnD2MP36YcGh1zkhdPISN9V4B1IVD6HXvJhw7iOuyJOYehM5Nq84lVw9h\neu/FxQ82eeUQpusgLt2DGb0PyRHI2eYcpZw7hG2LHD1W84M4JLa4FVIr0NOBNE8ihEOtHMLkDjb3\nj/L487wOSIHt34ZMPYyUy6jgMIG6BwcIDAn3ODYRX4/IYBI+1bZ9BLmHQU4BR4B746upAE9flxep\nyTYWvb2UkidwagEtzuHF1lpOzmPkZUSwNWq9ul5WXDtL5KiqSUI5iRFlkmYdAIG8jMOQNCP4doC6\na2VOQEWEgKCszuO5LMnYmqukzpCy7aT1KL7ewTnvEmWhSbhovGnOO0PRDuC5dJyfoltvJq03cUkt\nM+6foU8PoJzCCM2kd4lePYJwAosFfPJ6E2fULEtemVk5xYiOTKDLssKCWmJQ99Nu2pGijbPJOl6s\n1DOrSlRFQF8QtaYm1QJpm2S4vpZzIsFRf5EEil4TzRCe8xbIuyRdJkOLTVElyRJFpkV06457ywzZ\nDC3Wxwr4f5Pj/EHyHItxq/hW4+0oVv5GxJulsXuz/Y0xt8U8/VFFY6Rnfn6+aSM2MzPD/Pz8LR/j\njqowG+MkAEtLS2Sz2dc0EN2Y5axWq0gpSaVSr+h64uYmUZ97P/74TYg8faO4oQFcooa6sLoG6UZ3\nr1aSQuLGDiBPP9zM7Z73IWoTyPnI1NisuQ81fl1lN3of8sJ1ldzIvYily5jOHrzy0+jO3XjTR1YF\nA3oOIKaOIJyJ87sRU09CfgDX0QcZiyg9hXDR/Qvzu/FWjiNczEht2YdYeg7h6tjWXbjWNmTt4dXZ\nysw+RPX51Ty7D1F+LlrD9Hsx7TtR8hEE0dyf8fYh9dGmfJ3x9yPDpxGEONlKULgHnXoM5EJ8hfcQ\nVZYmzg8CjwIWGKAq9lPyHoe4QvL0PrR6gkbB4+l9TTKPC7dRp4+VxBPxF6hIme2Uvefj3CNtNlH1\nnse3fWjbR50EJS9iM9+4TqlclpTtIhTLYAeZk4skXIGSiv7TRuo8aVbiecuMbce3LdREkqtqmoJt\nx6Apy+jetJguqqJORa5Ea496IzOyxnSsBdtjupkX8wTxtfbpPq6pObIui2dbMSQZVzOYuJJdo3u4\noCZxIuoYrwl7qaI46dexwJqgyNlkpErkOcmILnLWXyDjfHpMBxWSHPeidm7GKQZMmtNexFzOW48B\nm6ZOgmeUpsP5/NfaADvMrc0ivp2k5Bpz4K/XONsPEzerSF8LY/fGa3LO8YEPfIDDhw+/Zb6zxjV9\n/etfZ9u2bSwtLfGnf/qntLa2cuzYMX77t3+b97znPbd0rDsWMJeXl5tvXrcajYqyVqshpSSdTuN5\n3qv+MJxzLI6fo+v/+o/IMxF71W7ei+tpR77wLxFXxEtgR3eizjeINhI3djfy9CPN45hN70AQgptC\nLp9/CSjaNfchLl2n3zp8EHHpEVz3Rkwxg0tJ/Nmnm1J1tvsuxMyzq1J2XXsRc8cQpoZt24DtHkSV\nHkXYWMi8uBNRWxUcMPltyMolhInk5Wzf+xBqEqkjgotNb0XUJxB26aa5yd8LGQ8pDyOExnpbEXqi\nCZqh2IznrqyCaOIAJpUizDwBsgLsAC5ArBELu4AzEI+ZON5FXfgse8dAGny7k1C80CTzyGA71n8h\n0nV1AqHfzYqcpaoiYYC03kFVHYsk6oC03sWKOg7C4tterN7MtH80Qhka65THm+Sfxjqlb1uRdoQ6\nKWZjt49oNGSEuSaoJiiYAeqyhLNdTKkFiraL2XhMJeHS5G0rczHDNm1z5M0A07LGnCqRszmSLsGc\nWm25KuGxqBbJ2RxZ0881WWNeRfem27RQFXWWZbSu2WvaqIo6BdvKCyqg2+aZEZVmC3aNbuGqKlET\nBt9JRus9vOCHLKgIdDeGOc56K8229RZdYEJW6LFFjirDRpPheVXBClAO/lPQxX8MOl61RftvgPmj\njdslGgVBgJSy2X5tAObDDz/8Jl/JS2NmZobW1lY8z+O5557jBz/4Affffz/r16+/5WPcUYB5vQB7\nqVQikUjc0o+3AZTVahXP85oV5e3EwsICRQWJP/wMYuYYcuYkzk9hB7egzsdsV6lwY/uQZxvEF4Fd\nfxA5/hxu3Q5E5TSuZ/2LQXL0PsSFQ83Hjh4+gLryOAKLHdhF2N5KYvZQszK0XXsQc8cRJq70OnYi\nFs8gdASKZuS94JdQMfnG5jcjatcQYeykkt+I0LOIMB7jyG3EZboQ/gTSXsAm1yFMCaFj1Z/kmkic\nIJxs5qgC5FIIdQS8EXBVhI0Yp1oMI1yAIp5VVWtwIoXJtBNmnwLRB1Qh3g5rgTKrDNgxHGlqsoOS\negHFCFYs4kS0RuvZMYyYw8Xyd57dgLYFyqJGVV0ladYRiElcLEmXNOsJrlP2Sem7qJJgRp0F4V6y\nLpnXG1hR53EixLdFfLONK955TLz9peuUY8yps6RdK9L2EpLhmroQg66gx4ww6UXs30itZ5hAhCyR\nYE6u0Gt6uRyrEnlO0W26ueJFoJq3eYp6gGP+LFrYl7BeMy5Jq80yKRfpN71MCYV0istxtdhqU6Sc\nx7UYZDtthlZT4LSyzElDr0lhcUzFIzh9Okkdy7LSjAYFFmWCOWmZU9ELx1qTZF5oFmSU/2RY5L/U\ne2l3N5+xfLtprzZ0S98qa3u3E68EpI2K9Bvf+AaDg4P8wR/8Ad/73vde8Tv79re/3XQp+cQnPsHn\nP//5l+zzmc98hgcffJBMJsPXv/51du2Klk5GRkYoFApN0YEjR4686rkLIfid3/kdCoUC99xzD+vX\nr39NEoV3LGDeisVXQ3e2VqvheV6zonwtsbi4SD6fR4VV/N97AHkidsO4ke0qBG7DPcgzD+NaerAj\nY5BTqPPfbx7rRpC0I/cgLj2GcBYnFfWNP4nnJvDKsRB55y7k/AsIE1UTtn0bYvkSIoz1XNs249JF\nRGIJWT+BzY0hgkVEEBFGXGYNmAqiPhnnwxgpINeL8i6BJ3EympUEcH4fTiSQwcU478GJTKQeVGhB\n+uM4mUOaqLqyogvj8vjEZCjZhRNFnC1h8usIs+Mg0kTVI0AXULwubzBgNVW5hrKaQ5DCyOjzpetG\nuPR1eQ/YJNYWqSgI0AinCOPqTZluBAIdt0h924ewOQJamVaXSLkeLEFzfjJt+jGiQhC3h3N6DO2K\nXPMuY0RIwfRTE0sEMQgXzSAVMU8oyyRtkbQZ44qapiaj8YxOPcCCmkbHLNYuM8ScvEbBdlBxWQQZ\nJtUkJq58B3Q/V9U1bAzCQ+EQVQvnEzXqwryk5dpgvQpg0PSiXYHnvTkQoJxgnWnlVEwO8pxkjWkh\nEHANn1lpWWuynIxBNekkoybDC94K0sFG00rgUjzpR7+1nJX0G49TfnQtBSvp0wkQPk95koJT/D+1\nVu42L/1/+HbTXv1xBsyXi0qlglIKIQSf//znOXbsGEePHiWXy7F161a2bt3Kxz/+cXbu3Nn8G2MM\nGzZs4Lvf/S79/f3s27ePb3zjG2zatKm5z7e+9S3+6I/+iG9961s8/vjj/PIv/zKPPRa9xI+OjvLU\nU0/R1tZ2W+f6L//yL/zFX/wF09PTHDx4kI985CNs2bLltoqfO4r0c/0bzyuRfqy1VCoVFhcXMcaQ\nz+fJ5/M/lAB08/NSOcL/4x8wuyIVDGFC5PknsevviXLnYHESfe8HITeHmj6EOv997OgqcUdeOIQb\nuWfV6PniI7jhuzFj92KHu0ktfge8BM6L1onUzDO44hpcIqL2y7nncdkeXKYbO3AACjVkehJB9JCU\nK2dApXDpweicKucjMfjMCM7L4YpD0OYjUtMIexURXEboMjYZ/eBFeBVhlrCpyNjY+W24tk7oSqK8\nIwg3ibDTaLk1+jw3jSemsd6OaH+RJMz3Um7vJcw9AuIyUUW5K74D08DV6/IMVTnMgreOkn8cKyex\nYgbfRtJcVkxhxSy+3Rrf415W6GSJDBV5BS2nMHKZpIlaM0ZNYcUKSTOGZ7vQdpAp6SjjQDhq8hqW\ngIweAqCqruCwZPVa0nonl1WJGTVPOnbxWFZXkHhN55AlNUHKtVAMdzMlUpzzL+KRJG8iws2Md5mM\ny5GLTaRrVMmZ9UyJJFe9Ba54V2ixRXI2+n4ve1dos23kbZ5ePcILKmBeenguehCc9ybptW1kbBIn\nonxMD5M3QzzjhTzvzzFqW0g5hRGOU948a3UrSafosXmmRYKyKzAnDYGwnPRKbNZ5fCeoC8sL3gq7\nww5abBuPeI4n/So7dAbPwYq0nPIDdugMKScYNBlOeEnqLolGMCstn0zP8ftyjnK99rY2eH47Epga\n1WUikeBLX/oSX/nKV/jQhz7Ec889x6/92q+xdu3al1zzkSNHWLduHSMjI/i+z8/8zM/wD//wDy/a\n5x//8R/5hV/4BQD279/P4uIiU1NTze2v5ffxvve9j29+85v867/+K8VikQ9/+MPs37+fSuw2dStx\nRwHm9XEzwGwA5dLSEs45CoUCuVzudXFKeNHnJVLoz/13zP4Hom3WIM48itn9PszOPQj/HN75f8aN\nrCplyAuHsCMHV9mrFx/BDe7FZTsxG+4F9wI2uYTUMTlj7jlcZhiXiB66cv44Lt0Z/fPSuEIXbqAX\nkRhHBucRlQtNUAQQ1QkwNWwu7u+bGq5tFDu8ASkO4ekzSD2NTW+P9tdziNo4Nh2BmDAL4GUw/fcj\nW06g5OMIfRrj7Yu2u2WUPY3xYwawKwFl6i0fpNo1ic4cRvonwB2I78AK8DzQyMs4ylTFTzPnr1Dx\nj2LlMZJ2LwBOlAnFSRJ2X5yvYEkSmp9iSo5TURcIvfNkbPTma8UKdXmOtI6vhxSB62DFbmHKu0go\nl6moKxR09FKgZYmqukZeb0S5DL4dZVJqyiTQIqQul6jKOdr0GgBqcpGqXKBNj1HUW7ksDePeJG2m\nN7o6uUBNVugwkdD9spzHcyk6wh1ckIbz3iShCOg2EeN2Ts1jsHTqToQT+C5DzXUwi0dFhkz5S0gE\nPSb6/q+qeTwUI2EvRT3IY36ZJWnpiVmvF9QiWZegOybjlGRAj+lhhiznVMgLXolWl6THREsYJ7wS\nnTbJel2gR7fzP31NiEe3jUD6qFeh3ybosh7CQYCg27RxRiVYkoKnE5o11qPLSqyAr2dr/EqhxGWr\nmyzOxoMsCAK01i/SX/23eGvEjS8Bi4uLtLW10dvby3vf+14++9nPsmPHjhf9zZUrVxgcHGzmAwMD\nTdbqrewjhOA973kPe/fu5c///M9v+VwvXrzI4cOH+f73v08ymWTDhg1Ya29rzOeOA8zGl3s9gFlr\nKZfLLwLKbDb7uupXvgSgPR/9X/4K886fx66/C7d5I2ryXyCfabZa5flDmNF7V0c+Lj6MG9ofKfMU\nenHZBHrdEKLyFDKcx59/HlccwfpxJTl/Aue349JRZSOqM9j+nbg1a1H6MHLlWXAhNhuNSURrlUvY\nfFwpBjPgNHr4/dBZR9nvIesnMdk90XZbQtROYXIx6NkyonwM3Xo/tmsLMvskUj+E9eIxGOpI/RSh\nOhDnATI8gk69l7B4N2HbOVzyW0h3d3zPQhCPsjoWooFHsbyPmnwn8/48lcT38dlPNHei0fJxknZf\nMw/EkyhzPxW7gyl5kSX1OFm7O5p9EIaKfJa03tXMA3kFau9iSiSZ8s6z7J2gqLdE7FmhWfZONnOB\nxJDCmF2MqwnqcoV57xwdej04MCJk3jtPu16PcklyZoxxVaFKGo1Gi4AZdYUePQoOQlFnTl6hNxyj\nRW/gvAw57V1h0EQPjpqoMy1nGNQRqFZFFY8U7XoLz3tlrqllptUSo2H0fZdklRm5zKjupt0WSNgO\nnvMMKh4lmZc15mSFMR21tuZkFSscm8IhzgqPo16ZRVljs45AdVLWWJAhG3WeTpsk4XIcUx4qFluf\nUAElYdiio+NfUgHtNsEW3cEjns+znqEsHNt1BKpnlaYqHDvDBDvDDN9zaf6XvOV7uQTZbPZFzMvG\nnHMDSGu1WhNIf1xA9O1YYd54TUtLS68qOXo7/qE3i8OHD/PMM8/w4IMP8sd//MccOnTopvtdH2EY\n8od/+Id88Ytf5Hd/93eRUvJnf/ZnPPvss7c143vHAWYjGjNJDaAUQlAsFl93oLz+817yA5AK/b9/\nBbdjD3IhMi5W526cmzyMGznQbL9SmcHs/ElccRm1dBh/5im4vt06fwKbam2CpFw6h0t2YsbeDV0W\nVfkOIpzC5uLZ0Po0oj6DLcTtynABURnHtB/EDhxEFC+j9Pew2Xi7rSArR9GZRmVYR648gc3diy3c\nheteg0p8B5eMHsICg6w/TJ0GSFp88yg2cV8kYVfchyl8B5vyIxsqHNIdQtkDONv4eR4G7sGxkap8\nBwv+UwQqDSJ68IbyMTy3B2IJNi0fI+l2IO1uqm47U+opoKW5vSyfJm03g4seyFXvGZJ6F0rfzYzw\nmUs9T84MIePtS95x8mYdIs5L6gw5fYCS62fcm2DWe4FWM4qKjz/rnabVRrlyPgYPabYyruapizrX\nvAt02sGoZSock94FuuwgWdtCixnjpLdIlQQKDyccE95l+nQfnlvNh8MxUmaE570KL/jXGNFdeE5h\nhOWCP8VQ0IHnJFkXzUha2815VSMUljPePGO6Dd/JZr4x7GCt7uaiSPCov8wGU2y2XE95S2zRWXwn\nSDqJIUHatnFcaSrCctyrsl1n8B3NfJ/OsUa38IiX4JCv2aMTJBysCMdzXsgenSDlYI1OcsKmqegU\nGsGSgP/s1/m8H1CX0ShDMplsypg1gFQphbWWIAhet5nCf4vbjxvv8eLi4qsCZn9/PxMTE818YmKC\ngYGBV9zn8uXL9Pf3A9DXF80Wd3Z28qEPfehVST8QrZvu2bOHv/u7v+Ohhx7iM5/5zIsq2FuNO4r0\nA9GbRhiGlMtltNakUilSqdQbriTyaiQj9eB/xXvod5u5WXMv8tKqB6TZ9D4QC8iFIwgBum0LqjSO\nCCPyhW1Zh6gvIaoxUSc3gMt0QCGLCJ8Av4hLtCJXYik+r4DLDCOXY71WlY4YsXoRWjoQ7iguuxO5\nEjN2kbjcPciVVRWhMHMPXuVxXHEfpKch3Y+sr77thd49ePrRVR/L5EFE+CgusQGTzWKTPpEKTxj/\nxV3AUYjdRrTZCd5ZnBykJrsJpELL8xAr53h2C1qMx5Zc4NlNaHEV6dawDGhShGIWK6KxlKRdgxYL\nGBGRc7xwCITDmG7mEpdJ6C6MrKBV1NZOmT4CUSeUUZ4xQ2DbmVZz1GSZnOlGizq1eHvOdqEJqckF\npPNo0VuZlwFzsYRdwXZgCJvzlI35ylDUyZth5oWjLgJKssFSbUWjV3PTSsplWMJn3CvRaQqEwjQF\n0q/P0zZBlxlgQobMNCTxTI7gOq3XHpPD4ci5HCdVQKtNUReG2Vhgvd+km3nSSdaZTi4KwbiKvq9B\nkyAQjim5micQeC7NEeUYsj4hjisxS3bYeOg436wThDrNNIJL8X+9YSsQOC7G+e5Q8etLcFf+lVtm\nt6Jyc/1c4ZslXv52cl6Bm7OYv/a1r5HNZvn4xz/+sn+ntWbDhg089NBD9PX1cdddd70i6eexxx7j\ns5/9LI899hiVSqXJKymXy9x///385m/+Jvfff/8tn7cx5jUrHd1xgLm4uEitViORSBCG4RviWHKz\nqFQqCCFeUUdSfe/38f551aXcjhwAEeLSVVTpOGHbNrzlcwgdre3Y1vWI6lzkPwm4/CA4i5FJZGcn\nwl6MjKPLEZvUeXlcdgS5FIOkTGELW1GLT2ILm3DFHCLlIcuxyDoikrIrXTfGkr8PWTqEEz46vwfZ\nkkPq764ydhP3IILHm7Oexr8LGT6LIMAmtqCLfTj/YSIVHnjpLOUWIkLPAtpuoOKvo5Y43xwLUXYU\nK8o4EYGQckNYQpy4hrS7WHF5amKxKV/nu25wilBGDFjPdSFcAkMJF45R8ioIPGoxQ9a3LUiTpe5H\n6yWeKSJtC7gCs6qMEZC0eUpeNNaSsDlStsiyF+2ftAWyZpRrapEVWSbpMmRtkdz8WlwAACAASURB\nVPlYqD1p02RdC/PqGp5L0GrWUkJxJT5eyiUp2iJTMcg28gCNocg1WaPd5rmsYoauS7woL9gM7bqH\nY16JmnSknUePzXEhfglo5ONyiRHTzlUhybokZ68THug3Gc7Eec56rDFtHFWWeenIOMmISXLCq8b7\nS0ZNkguqzqjJcVwqhqzHUS/W1HWCDcbj2TgfMz4tYYbvSBFfH2x3kiMyYvgmHezSkno1wxOVJCHw\n39KaTyc1t/t8u92Zwjf6pfntCpjXs5i//OUvs3nzZh544IFX/NsHH3ywOVby8Y9/nC984Qt85Stf\nAeCTn/wkAL/0S7/Et7/9bbLZLF/72tfYvXs358+f58Mf/jAQAe9HP/pRvvCFL7ziZzXkUJ1zTUbv\na31huuMAs1aL5w+tfcMsvm4WDZ3ZG619bgz5yJ/j/eOv4EZ2g5rCZlpQ88cRNlbUaduMWLmCCKIq\nxRVGQNcQlUls51Zcax5rJvGr0eye8wq4/BCyFCkCOZnCFrehFmLnkNZduPYeVOXB5jmY/H03BUkA\nJ1LYrncjxDPIGIRsYj8ieKapyqPVTpQ5jYhBUWfei0kvQ7Kh8boJmIHYkutGNxEr7qOi8pQTDdus\nXnA+Vo7HeSfC5TEy0lWV5iBlsiyrSDBBuQKe66IuY01YlyPh+qnJU0ibx4WbqUnFit8QEUiRNoOU\nvTNxniCth6l450mbzcyKEM+1sODFn+c88sEgS8nGfKSiVY9ihGBWaFZkhS4zyGQsni6cpMsMMRXn\nnkvQEW7kgjdLRdYRTtBv+pvzlMIJBkw/E95l8vHaY0ia895kc/uo6ea8moza2E6wxnQTIjkrDSvC\nsDZo4WxiMd4O6007p1Q0OjJq2sDmeNZbbo6abDZFTqglXFN4oEhNOK6IJFekZYfOcExVMPH27TrD\nSVXBARtNnjopnlUhQbx9t05wQgXU4vzuMEnZ+TzsFFYI9ljJaWEpNfa3krNYRqsZTq2k6JeOi0Yw\nH68avcszfCUb0PM6YNrLiZe/kZqr8PbSxYWbW3v91m/9Fh/84Ad517ve9Sae2RsXdxxg/qgsvm6M\nWq2GMeZFP66XjRP/ncR3P4Zw0ZuR7diOWDqPCKM5PltciwhKiGpsTD38Tsha1GLDSaSIS/ejSrGo\nu0pjWzajlmKBBOFh+t6NlBNIE+1zM5AUpdVZT1N4B8IHkTiJEDMYby9SH0MQvYCEcgvKjiOJW8Te\nRqxXxGbLuOQxXiowMEi0hH4pzrvRjFH1BRX/FMK14kw7xEo4wuWRbhAjT8R5Fux+SmKBsryCcElS\ndixS5gGES5B2G6nIyDdT2hZcfSfzqdNYEYCTZIP1lJOxm4mTFMzmSBXICdJ6M1U6mPJPNu9Jh17P\nrDrdlNNrD9cz552moNewIMA3Lcwkxpvbu4NhpvzxphJQjx7FILkqI4WdG+cn+3V/c74yYzO0mmFe\n8Oapx/qrw7qTq2qeMJ6/HDKdTMlFukwHE1JQsBmuxWo8ACOmyLQsU4n/fkvYzayQnIqrw1GTZVbU\nKUkd759lQQQUXZIV0hh8FoVmPhYaGDVJVoRhJt5/T1hgSng870Xnf33LFWDQKpJOkDUJHnc+nUgS\nDs7FBt59TpB3cEo6NmtFWMpS04pjJqrAOoWl1xmeI1qr3oLl/0xqfirTkD98/eJWxcsbrd3XUqW8\n3QDTGNPUZ23E5z73OT796U83RQbe7Hjsscf4q7/6KzZs2EBbWxudnZ20t7fT0dFBoVCgtbX1tr6P\nOw4w32iLr5eLBhnhlYawGz/AIAjITX6f7EP/aVWRp20jojyFqMeKO4URXNsQQlxF1s/iEm24ZBey\nFOvVqgy2sBG1EBtNCw/XcRd4BpJzSHv2VUHS5u5GVE/jWrYgks/j/LWI8ASC6IEbyk0oexUZS9dZ\nbwxhS9hEPyZXxSVKROgxHh+xGyiwKjjQCvRhkZT9IlXvKsqNoGUEergkym7CxJUjzsd3OzAYloGy\nmCTrtlOWz8TbBVm7i7J6unlNqWAPgRPMJyYxokbRbmNJHFuVszNbWZLHY9stQU7fzTTzlPzoPrfp\ntSyoS7gYdNrMGhblBFaEFM0ogW1n0rvaFBlo130syzlCGXUEWsNuynKZnOlkRjo8MpRlmWosSddh\nOqiICpVYtKDbdCNtnhe8ZUJh6DQFAqFZire32zwWx4Jcod90UXVZFoVhRjW2p1FOMB3nbTZFi01T\nEQleUHXabIKs85iIt7dYn6L1ueRV6LYpUrZISXicUdHvruAUvdbnVJznnGRMZ7giPU4pyDrBOvPS\nFuwxFbJVpzltEww41Wy5JhzsspLHpY2qXSvpK2V5sJrAIZA47lGWR43EEK1p3ict1CVHKh41J/j5\nXMAX2+vkfgS40wDSxkv2D+NJ+XaS+YObe2F+7GMf4/d+7/cYHh5+E89sNR5++GG+9KUv4Zxjenqa\nxcVFVlZWCIKAa9eu8bnPfY7f//3fv+Xj3bGACa+vxderRRAE1Ot18vn8Tc+pAZTJZLJJQhKXf4D/\nP34aEUTre664BmyIbRtGigvR+qZfQK7EHo9eDpdbi1xseET6uNY9iMWncV17wb+Myw2jyq8CkitP\nglfEtmxGZOoIfRxBrCfrbQI9iSQGbjWCcAHYa9jUXkze4fx54Hx8xDagBzgR53miavNZLNsp+y0E\nMo1WDdDz8NwutGwIn0t8u49QPY6yu1jBYeliRT7bvIas3UVZPNsEwYzZSVWcA72eBW+KrBulJM80\nQS9vN7AiLjbl7HJmHcYlWBSWRTVPXvdTlQvoGKTypo+6KBHE5Jt2vZUyiivxumXBtmMxrDTJP60I\nByW1QLseokyaitAsxOuIWZMh4ZIsxB6SGZsma3IospzzqginaHEZrqqGx2SCNpvnSrxOOWC6wBY5\nGoN60ikGTIFz8fESTtEf5lj06uRsC6dVnTUmz0kv+h15TrDe5DkR5202Qb/u4JBfwwiBdLDdZDiq\nKs2W7Q6TYUqEpFyWZxTsNgmOqqCpHbtbJzimAgIBW3QSEaZ5WkLl+parsCzH+V1GQdXnf65kMEi2\nScuMhcm4BbtRWirW0VtznK0kaFEglOOsjqrPUc/y551V7kpZ3oy4WTVqTFT53ihc3ni+vJ1k/uDm\nXpgPPPAA3/zmNykWX5v/6esZb8QYzx0NmE25uh/BInxjjqxQKLzoXG4GlNeHmHoa/x/+VzB1XP9O\n8OfAriArDRm6Ii49gFyOjadlEp3bgr/8NE5lcF17cIUEqvRQ85i2eB9i5TqR9hgkBRrnd2M7diHF\nk4h4jdF6GxFmFuGi3IhBwKDcVRwSk30HJqvBazBoi8AQkdAA3OhLacUeymoNlUQkD3g9KDbCt3cT\nyoihq+wuqq6XknyiqcGatjtZESebIJi2W6mKMwgUIthEVfpUvKtYEYFe1o5QF3PomFGbtgOEboWk\n6GbZRauvWjgqsbxdyrQi8ajEfpIpWyRtu1kRikk1Q8pmSbscCypSH4nE0VuYi8k9nXqE0LVwzo+o\n8b7z6TQdXI3JPQ3d10k1RafuZ0JqWkyeS4noHksnGAo7uZiI2u7CCdbpARak4JSqvGRdEiJPyrNq\nnrTz6QhbCFWaU2q5ue64SRc4q0qE8YvFZl3E4vOkctQFbNIpJlTASnyP15sUkyKIBBBsjgXhMyMM\nc3FLdY3xqAjLZFw97tFJApPiUPzDGnCClIOz8f49TtBhIR0meHwpSxLBgLA8a6P/f0XhWC8tTxjF\nTmOplSUFLEeCaFwnKRx7U4aHAwVCsEEYPpIM+VxPiPcWwKBXa+s65/B9v9nafbPYuq9X3MwL8/3v\nfz8/+MEP3jLEputfZp566immp6fxfZ9sNks+n2dsbOxFz+RXizsOMF8vi6/bDa015XKZYrGIMYZq\ntUoYhi8LlC+KhVP4j34EWY7so1yiA5doWx0RuaH9av0WdP8B/PBxhIvk7mzhPuTydZVl4QCicmSV\nzVp4J6RAqkcRIrgJSA4ADuWiqsrKbuqJDaj8OM6/SFQ5riEaCwFIAjtZNXNWaPE+Kv4CVS/SjPXN\n3YTqseY5+WY/oTzSrBRd/SepqEVqsUlyym6hJs413UaSdj01MY0RJYRLI+q7KXkL1LwGw7QXiyYQ\nEeglXSfSeVTlNbJ2jFKYRvtQktE1+TZL0naw2BQzT5Gz3WjqhLQxLRdoM71Mew3ykaLTDDAVn59w\nkl49xrw0XFELCCcYNP2Mx8fDwaAZZEJNIBD0mAECV+C0N9kk24zqbi6paWx8D4bCDlZEDWWKnErU\nGNYtXFMr1ON1xWFdZEZF65RJp1irezgrQ6ZV1CIeNBnKQjMfj4r0mTQWR9FlOC4lGTyUg8vxqEin\n9cg4xSVVJ+UEG3SBWeFxzIs+r+gEA1ZxXEUvKjkn2KgTlJzPEadIIdh2Heu10YI9Ii27Qp+zyxmG\nkTyiJTZuuR5QlieNJECwxjrWBPDoikc5fhPYmzScCwUL8VzugaQmVXf8f4seFsGujOHP1tTYkH5z\nqs1XiwaIVqtVfN//odq6b6UIguAlSjnvf//731LWXtZapJT8zd/8Df/0T//E3/7t3zI4OEipVGJ6\nepp//ud/5gMf+MAtH++OBszXYvH1WsMYw/LyMr7v3zpQXh+Vcfwf/DtkqTFHecOIiPCxHQcg6RD2\naSRlTOE+1PUgmT+IKD266oGZ2wssQ74dwRFcYj2CaYSLWn9WDuKsQRGxYZ3siITREy3o3GWcmkOI\n9UDcTsUH9gANEBTAvVhRoewr6t45PHuAujjSrIp8u49QPANxpejZnRgUFQwVOUHCjBHKSVxcGSbs\nCEYsYxpuI2aYIOxnMXGNUFZIuHaUS1GNQdBzeZKunXIsvJ6zmwhcJ9dUVJErl6BgB1lQEYgLp8iH\no8wnLpCxnTjbhSbTdAzBCXrNyKqjCBGZpyJWMLQwruZfQubp031Mq2l0g7wTjjEpNVdU1BLtM20s\nijKVeN2zx7RQFjUs0GK7mBWS2nXzk+0mjXAwG5N32nSKdlPgjG9YlIai9Skaj/GmALpHt0txXq6w\nzrQwKRJkXKI5GpJ0gvUmxfPX5Tt0kacUzMrIjmuXSfCUCpot2t0mwTkZMqwzPOY8dljFUWmpX9eC\nPROzYDcZRWo5w/P1BHPxTduiLAsWrrro979TGDpqgu+VfAyCQc+SFZYXwuhltlNZhpQlHcIzSwol\nYFPK8Hg52p4Sjv82UOcXu8PbHj/5UcTNGKWvNvZyM0/Kt1L8OHhhGmNQSvGe97yHP/mTP+FLX/oS\nn/zkJ9m5cyef+tSn+MQnPsHu3btv+XhvD7rWbcStCrC/nmGMoVKpNP8jFItFMpnM7a2dZoYI3/UQ\ntjX6coUuIUpnMG17cel+3MB+ZOJJyDlkvN6olg9hC/etSuuVHsbl9uBEEpuOXFBoSyDkSYQwyPAk\nzuawMlLUkHYirjY34EhgUxsxLQG6UAVvHCHKwDFW9V1DoooyUiqyYg+lRI3lZM//z96bx9iVXed+\nv733OXe+NY8sTsXiPDVn9iRZeorsGI5fHmS/J8jIcwyPwoMgD4FjS7bhAUas4FmCHhILdhTIimNI\nBhwjsOy4NUutVjfZzebQZHdzaM41z3Xn4Zy9V/44596qZk+k1OyWw6y/eIr37rNP3VvnO2utb30f\nDRP1NEN9gqQcbKvuBPoUnuwEyaHdAUpAEU09ttNqmlfw6MCToehY30Sh8cMxVPMwc0qznJwlQaRs\n1FSLNNUi+VhIPVQlqmqSzvAo2u3jlp5jRl+kz+6IPhvVZFlfpyeMXi/K0jBLdDSOMqFgwptlxrvB\nYLgJLQaUtJV6jPjkXDdVfKr0MRsLCEx4k/S6HtIu6u1MeVN0uDxD4XqSdhOn/SVqytFjo352S+d1\nwEZ9n2VdoccOYdwI570qU6ZMTYWMxrqwi6ZGyTTZGnYzGvZQUTnOJQIGY0m6gg6Y9Grsakbrl3WI\nE8W2cIRnjeGmsbzsrQqkN5RwwauxL8ywM8yQdJ18zYd14pMTsAqe95rsdD7dTuEBVgwdzU5eEZ+G\nUjxnHEOi2BwneWe0Y9RpHi5kOTnfzXcbSVBwMM6MX7Kasige1pbHm8LVhQTfL/scT1lAGA81rwSG\nRxJNPIRRcUwva1wATqBoFc9WPI5mQ7qMoy6Kv5/2+O/Oprhd+9G4Wb9VtITLfd9/lZpRJpMhkUi0\n1cha2ro/ampGb9Qj/FEBy7XRKosXi0VefjniU7z88stt96q7jQcuw7xXi68fJu4svdbr9Xu2pHlN\nBCX8p38GPf89JDuK9A5DWqFLq4atQe4x/PLqscs/jCpFPUqX3Y3rHsLIaZTEs5zeKLh625PSqT7E\n78a4VxCVxmWOYzMhWkU9SsHD6aOgT6zZ2HuAeKxFHaHqbaDufb/dc/TcQUL1MsREG+N2E6gpRJXQ\n7gA16aKmZ7Bx+dSTAbAeYeztaKQLI70EagKCvSybKj49lE1r7MQjL9spxmMniKbT7aGpCjToYl5P\n0ud2sqAutTPDzsYYhcSNVW/KYA815XPTzCBK6LMjFPQCQbznbjtITZWo6ypplydjNzFjyhRjMlCH\n60CLZqVF7nFZUpJCUDTJM6cadEuWydjkOSk+g7aL217cJxWf9cEGXvIqlLV9jdXW2r7lBtdJkSRZ\nSb1pn3Jvs4sVPF5IRMdjQYIFE1LQrVGQBBXlyIqhKWlK2oDAeDwaMug0eVFcjY8PB2nqNsnT8bNe\nXmCbKM7EfcqkwCGraTSTPFVMA4qHPcfToUbiEuyjxnEq1BywwkTZY4PneLlhKMV16QNJy2SgmHea\nHSqkLxTGG4bbzeikmxKOtBYu1aM+2aFESG8gfGMuqhTlPeF/2tXgv9/QUpB69+P1GKX3Enf2R1us\n3XezrFuv19uAD9Gs+Uc+8hG+9a1vvcU73/n49Kc/zYc//GFOnjzJ3/3d39HT08OLL77Il7/85Xti\n9D5wgAnRiAfcnfrODxJrgTKVSpFMJlFKvX1jLLaBufy7mKW/RMU3xjvLr2H2EUzl2Xb51fb+BCSX\nMMSCBd42lCuiXERasWoAURk8dxMAMQPYjkNI4jTKzCP4iDqCllWQbNhH8JKrx4H6t9T8aZrxgL9x\nB7DqUrvnaNwOrJoFFQGKsu+jgqYcz04a6cVInmZcPlUui+dGCLwrKElA8yEqZCkl49lI0XS63RTi\n9wN0uX2sqAukZT2B9GHJsqCvtEGxx21lRd2OZjGBLreJJjVwg9w2i+RdL3Wq1GPT5LzrRojcRAA6\n7QAJN8gr3gxWOVKSosPlmYvJQb749Nk+pr1pOl0X2vUQkuRG3FfVothsB9eIEET+lAGKcQ2LOmB7\n2MM1s4yNP9utYTe3TYGmitxFMq6by16VimpJzmUoqICVWKJunU3hWYXSOc4aS78kSInidtzX7HaG\nbmu47jfpDw2dNktV+7zkR+ulRLHLepyNR0U8gWNhmhvO56LSKIHjojmlXBuojzrNZeXY0UxwqpBl\nm4KrVrMSP53s1Y6FmAW72zo665rZQHE9Zr2uM44e43ixGZVYtxvLaBjy9UI0bpLWwsGM5Zly9P8G\n4T1ZS1CGEwsGh+KR7pALRUM53tSP94f8L3vrDKff/VtcGIY0m80fGDDfKO5WzWjt/OjbFa2ebIsD\nMj09zSc+8Qn+4R/+4W07x9sZYRjieR7f+973uHTpEh/60Ifo6+u7pzUeSMBs1d7vVn3nbuNOoEyl\nUq/6gr6tYyxi8a7+J8zc/9H+ket4D6q4dkTkWAQUuRpavYTzd6HCtT3KdTjx8CRm3KpOrL8Vlczg\nMi+BKSPqEFpWiTlOvQctq8Bs9WOExlL1mzS9W3juIUJ1BVTUDzNuO1YtQNxz1G49TjZRVjWqegIj\nXXjSS0O3eohpkm4L9bjHqCQNjeMs+RM0TQlE0en2UjAX2ntYO0uZcutQMsaUfgWnoht+l9tEWc0T\nxozZvFtHoCqEEpCRMRZVk0AUpXiMI+WyJF2GQpz5JSRFpx3AkeKGWUFQDNgBpuLsV4tmnV3XVurJ\nuzwddiPn34TMsykcYNIsMuR6WUCTJM2MrrVFBkZsnrJqUoj7mlvCbrSkOe1VEKXodQnSYpiIdWI7\nnE+vJJjTDYZtFxc1rHepdp/SF8Uum+a815q/NIyFnTzpW4L4O3oo8Djvhe1Rkf1NQ0ELfpjmee2z\n32nGlWO5xcp1irISpoEDoUexmKVoDVdjcs6gEgaV43zMgt0uji1NxVdLUUaSUsLhlOXpmoF4BvM9\nSYttwOmCoSaKY5kmF+s+JRdnnxnLfKDY7BznFwzDSUfo4HotBt6Uoy8hXClpDict15c0f3iwwc+N\nhbyb8XojGPczXm929O1WM7oTMC9evMhf/uVf8oUvfOHtvpwfOj7/+c/z4Q9/mHw+327FXbx4kV27\ndt3TtT/QgHlP6jtvEmEYUq/X3xAoW3E/xljMzd/Hm/zz9rHLP4oqPUeYewiTr0AigQpvoiSe5fQ2\nIS5Eu5jtqrrBDKHcFC63H5e5BGYLSiJ2q6AQ9firQFLU4yAnacgBahmLM913gOS2iJQT679qWQdi\ngD6KKBqqhJF+mrpVTk2SdNuotzJFMaTcQzStsGTKNEyRTruPgr6wWk51uymoK22yUKc9RF0ZptR1\nUNDhRmioEg0VXXdG+kAUVT2PJ2lybheLtsFyoqU5myLnBlgwrRKwR58dYdFM02U3c1uX6XP9jLcY\nr8CGMGK8tva0MdhEQ3lcMgWsEjaEfcyZlbZSz7DtpqhqVHSdYduLuDxzpsFSLGLQ7dJ44jNjWsCe\noN9lERJcMA18DBtshiuxzqsviq3xfGVCNKO2mwZpTptae0+vJ2kHHmeMpqRgt/WZUiEra0ZFKsrR\nADYEaW6LhxbFjfgr2+tgwMHFmFi+P9Bkyhm+1ojaGkmEw8bxjNW0QVA7bFVzquLREMXDqZAXG4by\nmhLsVKAYw3GtqOnyhKaDm80YBH1Hr+e4UPM47IVUSopOT3h2JdpEUgtHuyzPLEWZ5rFMSCYUnpvz\nqMYX/l+PhPyXh+sMZ96d2907DZivF2819vJ6JKM3A5M7tXFPnDjB1772tXsSAngnwlrL1q1buXHj\nBs5FlaYgCDh69Cjnz5+/p7UeaMC8G/WdN4u7BcpW3K8xFjP5WczNTwAa6TqKzfl47lRbti4qvxZQ\nLpbSU32guzD2KqJ7sPn9uGwDTUt0XSPqUbSsOpOIeg/I9wGFNQ9TTvTQMGdBt8qtd4Lkqv6rdgcp\nkSZE0dCRyo+SBCnZSS2WrkM0aXeAmj6PCfaxbIr4doSif6U9ZtLhdlJS15G4nJpzW3CEWPqYVrfJ\nyABWBdTjbDYlXXiSpqyn28dpu41xM0Vd1dHi0e82MGtamrCaATvKlHcLLYZeO0qdHDfXgOJa+TqA\nITtIWVXIuX5eMWW6XAcVVacc/156XA4EluIS7wbbj3J5zvvRHjPi0++y3Ir7nr4YNthubpsS620f\nl03ARpvnZa/Q/ix2hx1cMkWcIhIZCAd42QjTcV9yR5hiUjcoxyDYkrQbcCmuaA8fgxG4Hfcle52m\nz2kueyFJUewN0lRskpMmen9bnce4+LOFRwPNUjXJiXr0sHlMBbwoHtX4F3VQWyadYmuguFQy9Buh\nJorbYZR9rvccHVp4uWnYpy26Dr4Snl/Dej2UCXim4gOKbZ5l1DqenI9AF+Bol+VqRbEcRGv+WGeA\nrSi+PxutsT7j6E4KF5ajG3pXQvjskRofGnv7pfXeKl5vZvFHJe5FpL41Pwqvlfp74oknuHz5Mn/w\nB3/wbl7Oa6JQKPC+972Ps2fPtn+2vLzMBz7wAc6cOfMm73xtmD/6oz/6o7d5fz/y0foytEZMWrTo\nu43WTGXL9SSXy+H7/lum9s1mE8/z3vahXul4GMlsRyXPof0LGLmNNdtQhCjqKLeEU504utAU0VTB\ndGA7H8F1XkMlXwGmEfUIinEUguJ2BJLcjm+BkzS9/4ZiKkM5dQ1rJiDcHN09VR1RS2i6UdKFqCKi\nyiC7qdn9LJnLBGoJR5m07CFUs6AsIXNk3GECPQ1oxA5QD7axlLiG1TUCM0/OjmFVHVEhDbVARiIG\nr0cOYZhlFHUCAl0hUBU0hqwM0lBFQlXHEtDltpBimFkFc3qBPtlAWS0jylHRKwzZMcpqGZRQVQUG\nm7tZVkkmvRIrusiQG6SpAqyylHSJXtdD5NwpZF0fJXKsKKGsG1R0nYR49NgcZV2nppo4JWy0A6Rc\nFxdNjUXdZIvtYUnXCJSjqOrssH0sqghuuiRPSnq4YKo0lDCvG2y3eaoqJIyPN7ksgy5LjTznPEeX\n+GSdpqwdizok5wxDkmBFRz3MULI0VJIbxlFSQl0J+22CGW2pKaGgHI80M8zYDOeVx4SGY1azoISm\ngkktHHAaI8K2eorvruTJOp8EQgnFJIYhJQwqyxKawYYjVVa4QHHDeiw6TSBwJGWZCDVFp8iI8AiW\n55YN04FmKtAcz4UUQ0VVFOOB4VgqYIc4zs4YrlYMGzPCYMKxGGim6pqsEQ7kLOud48SEx1xNc7zf\nMlFRFAPNfF3x6IAlg9Avwl+eS/L8rOGxdZaOe/uz/6GipQL0Tsx832ustUDzPA/f90kkEvi+3wZI\n51y7D9sC/1ZmWq/XCcOQ8+fP4/s+x44de7cv6VURhiFXr17l5MmTpNNp5ufn+fu//3uazSY/+7M/\ne09rPZAZZhAE7S9AS0zgbiIMQ2q12qt8NO+l/l0qlUgmkyQSiR90628auvpVvLmfQ0ls/+WNIraK\nkYjYI7oH649BOomknwflEHUQLasKO3f2KJ16FKsNpeQKgTcVabuqSYhLncqNAArRLaeNLsQdoKyK\nVPXE62SSiow7RNWcjo8NXvNxls00DS/KTnNuG1U1gYtLvGm3gaaq01TL+NKN53ZQUBVKsVuKLxmy\nMsBKTBbS4tEtW1hS1+h0O5jRVfJukOmYUQswbMeY1tfb2WtfuAGHz4J243nKYAAAIABJREFULOsy\nPWEvFd2gGpdLO10nCBRMIe5ZbqaIx/V4z0nxGbCdjHuR0IMRzUbbz7wu0OX6uGQqbLG9XDEL7Wx1\nW9jLdbOEVYIS2BWOcEtLm5yzwWYoq5DlWHRgwCUxojFoGpJhVit6xeOqifqcadFssUleivuWm22K\nLpfjO34YfzZw2CY4a5rtEu2B0KcpigWX4orS7HGaGeVYjP9/s4seDKYVPNRMcLOYIY3iQiyQnkfY\nZRzPxcfbnTDaFL5e9pH4Qh9JNjnb8KnHx8e9BskmnCwlaIpiR8pSd3BrTQm233Nk647zix5aKXbn\nLCfjEqynhOPdlrPLhkMpy7kZw55uy8UVQzGI5zy7LMVAUagr9mUsEyuarqTwwkK8b1/4k8ca/OLe\nd2Zu886ZxX+tsVZbt9FoYIzhW9/6Fr/4i7/I0NAQ/f39/NRP/RT79+9n3759jI2NveYe+dWvfrVt\n7fXLv/zL/M7v/M5rzvPxj3+cJ554gkwmwxe/+MVXiblbazly5Ajr16/nn/7pn+5q3xMTE3zyk5/k\n9u3bFItFDh06xGc/+9l7ri4+kIDZciyx1t6VxddaoEyn023W671GuVxuz1zdr1D15/Bm/h26pfCj\nh0BnUNLA5jcj6ZdAj6Ekdi553R7lYyDPE5pjFFPLiOrFqltto2YtGxFCREWApaQbLQMIGYooamru\nzUESSNuDBE5YURXq3hJZt5WaWpWyS7kRLHUCHfs+ug042cKkvopTIZ4kybsRluP5TiWGXtnGgr4E\nouiSnTSki3G96i4y6EaZV+O4uKfYFQxR9YrkXT9LGEJlsGsMm7Muiy8ZFttjIEkGgw1MeBWWdA0j\nmvV2kGteS74uYrxeNzOk8Bmwg9RJci0GRYBNtos5Hc1VAgzbPGlJMqd8bpmAPpckIYqpWOw8Lx79\nLsl1U6Hfpci4DpokeDEGxZbu6zlTbV/n4SBLwRmeTyhEKfZZn5s6aFtpbbUeReVIisYP08zhvUrC\nrltgg9Ocj0uwRwIPVcrwzVii7k6BdIAfUxZX0zxdjtR39icsc1YxY6Ny3ajvSIjQGwoXVzQG2JC0\nnG2sEoAeSgc8W/U5ZEIWCpqRhOVM0W+XYI90Wm5WFQuB5kg6hLpipQFXSxEIDqQc67PCmUWDQnis\ny+Jb+O64WQXv4ZAXFwylQNHhCz+9LuB/eKzJ1t77extsMfP/tQNmK+70wmw0GvzZn/1ZO0u9cOEC\nN27c4MKFC6+6V1pr2bFjB9/85jcZGRnh6NGjb2oe/eyzz/Lrv/7rnDy5Sjz8zGc+w+nTpymVSnzl\nK1+56z1PTU1RKBTo7++/Z3ZsKx5owHwri6+3Cyhb8U7Nfbr6RXrKH8HIBOJtIOwYhdQKigjABA9R\nx9DyTPu9UY/yKcAnNI9QTuZomvNtIo92o8ga42YlvYjtAu8a2h2iiIeTPPUWe1UUGXeQ6hrnkLQ7\nSE29iBfuZkXVUHTSMLM4FQ38p9w6nGrSVFGW5rlOPNsHuptJPQMoOt0GlmJVHkTR53awYC6tOT7C\nrFpmOR4DGXCbWFLTbTeRbjdEXZWpqTKdwTpC1U1RN1lpaci6FDmXZyFmyBrxGLBDBApW0MzpKpvt\nIDdiL0qATeEQN80CVgmeGEbDjVwztbYyz7DNU13DeO1xaXwxKBQheSaVY0BSXI/7nL5oxmyOS7E4\nepfz2RD28X1/Vey85UcZJ1TstCmWVUivy3LKwDprqGvaOq9r5yl7nWYkzFC2PmfeoE+pBH4s8LlV\nSXGuEd3kjxrLZaspxhe+WzuqDkaainMlj24j5LVwMc4UO7WwI2F5ru5xQFmqZej3hGdKqwD2aEfI\nuZqhKoqtJmQkcFwsGebiNTalQpIarlSj7HJ/OmQI4esTEdAmtHCs33Ji1rTB+8cHAmaXNS/MR2vs\n6rHUQrhZjI6HM449ecuZ6x5LNUXKE373fU0+/mgT7z5JoDYaDZRS96269E7H6ykXffKTn+QjH/kI\njz766Bu+78SJE/zxH/8xX/3qVwH41Kc+BcDv/u7vtl/z0Y9+lPe///18+MMfBmDnzp08+eSTDA4O\nMjExwS/8wi/we7/3e3zmM5950wyzJaywuLjIl770JZ544glKpehh+EMf+hAf//jH77k99sAp/cCq\nEkWLXnznM0MYhpRKJUqlEr7v09XVdc/l1zc67/14PrHWUi6XKRaLGGPIdB1kqeOfCXt+lrB/EpX6\nHnAFUUejfRCi5Rmces/qIvIsDe+/ZSmzk6XsSzS9ZzGyASQSWnA6IsZoNxq9XC3iXBe18CeZ0RNU\n9U3q+iXSNpaZUkLVnCFjD0YMWVEEzlJvHmPOLFL3Fql510nQQUKip726nkIIyLjNGMli3BgzRiiT\nxKoAq5os6ev02Z3tcyyYS/TZHXS4MUS2cslcx5DDl+ihZE7fIiudZKSlojNDTvrptge57je57c1S\nVRWGgqF4D3WWzCLrmlGvtNv1sIJHUyJvSVHCDW+GDW4AX6Kb+C1vhnWug83hCKH0cspfRqHpt9HN\nZNqUsAgbbKv0r/CkEyt9XDZNyjrkpi6zJ4zKvoFyXPKK7Ak72RH2MqU6+W6iyZhLkY9HNs57VYZc\ngkHn44vCE5+GdDCjPJpKcdNzlJWwP4yAZVY7ZrXj0Uae6SDP9/A4Y4TjNvKobCp41jgOOM1Wq9hT\nzvCPS53UAp8N8QzrKWvIKNhrLIiQb4IpGMKmoiKKiVDzSlPzWDpEIxScYr6h+KANubaouVIzPF3y\n2JNxjCSiNZ8peowax4+bgOszhicXE9Sd5nhXlIHfqntcrxne29ngEa/JS5OGr0/4HO5p0u07mi4i\n+Yx1OA50hRzLhHz9is9UWXFkMFrj4pJhuqJ5fF3Ivs6QXE345ks+W/ssPRlHPVT80TeTvO9/y3Bu\n6v7cEu+Hc8a7Ga93PXfjLzw5OcmGDRvax+vXr2dycvKuX/Obv/mb/Of//J/vajSvxYj9+te/3mbv\nPvXUU3z+85/n1KlTfOYzn3nLNe6MBxIwW9H6wFsgdr+Acu353k7AvBMou7q62qw1qwaxHX8B+rHo\n3NRBTuPU4+33a3kKp95Dw/wYS9lRCpnvI7obJFLvt/oKmhTKrQdA1ByiFlD2/VTdAZYTN6ma02Td\ngfgCHTVzhow9BLFGaFWfww8eoxruZcabpJy8RILuVZBU022QBHAEIAOEcphxb5KmrrCkr70GJHvd\ndpQYOtwoiwoKZCnF2fCCHidFlpyL/ngLeh5HyKDdSt7u5JIucVNPM9gcBqCpmsx4M6xrjICAU46K\nrjLQ2MNVLUx4JW54Mwy7XtKxpN+4maNDMnS5HCN2iDlSXNchWYmysUVdpaDrbAmjB46yblJUDXYE\nm7mhMpz3GlzySuwOOzACTsFLXoGtLkfeeewIe3hR+0yoBDmJnoIvmzpJNJttdI4J3WTQJRkL+3jK\nM9wwjlvacjjwQaCshPNewOEwwYFminqzg39Rhm1i6Iy/hs8axwZRrHeRao+pJ5hb7KJYj85x2WmW\nRPFwzKidEYVqKj5Yh+dXfK4FhmfrHsdTIR1KCFE8XfM47Fv+jQu4Pa/5xrJHhyfsTUcA9mLVUAgV\nj2ZDHk+E3J7XfGvW49Eei6+EYqh4dsXjcEdAv+84lrKcG08wXzOM5qKb4OmlBFrD4Z6AlBZ6bMj1\nKY1xDk8J8zXN87MeR4dCelKObl8ICtAoRPZlAM+Ne4jA8Q3Rvnwn/Mf/Pc0n/+8klcY9/zk+8HE3\ngHm399I775Miwj//8z8zMDDAwYMH7+k+euPGDfbs2dMu++7cuZNjx46xsLBw12u04oEEzLUfmtaa\nIAgolUrtHuPbDZRrz/t2AKa1lkqlQrFYbGvTptPp12TOqE6c/884/TPRz3Fo+T6i3oOQIjDvpZCZ\noprWhDoqB1r9Elp6UBJpszo1BaqCcTvQ7iAVGWNBv4zQG1+Upa5Pk3UHaYnWVs0ZUrILL3yIariD\n6cRLOKNIxNnqaiYZSVIFqkBTLZEJ38sSA9w0t5hXV+gNd8TnaIHkNlSc1QXUSbuDTCrLvF5gUU+S\nIEWHi/ZVUos0VZ1et56c6yEpG7miS1gVzcGFKmQ2MR1lkgIomEpOsiHcTHdzC9eN4mJyhp4wT9ZG\n2eqUWSThPHpt9EDhSwLnelghy6xpUNQNZnSZbWG0h6ayXPeW2Bn0MxoOMaXyPOOX2eLypOIHipe9\nIutchm7XKtUZUq6PCZVkKSYAVZVjZ6wTu6BDJnSDI0EHva6LJz2PE34Eip5AqOC0H7A7MOQFdocJ\nbtgU4y5NMu4FvqAdSWBXLAZwWwkjzQRjS518u5hj3BlesprHjcUgVFCctIb3Y3m0KlxYTvCNis/2\nhGPEiwDs2bpHTgv7EyGPScjlOcNzKx5HcxHQTjY1L9cMj+dDfISdnuX2gqZeV/hKsKL4/pLHprRj\nayZ6T9iAgbqjWYdioLhaNNyqaB4fDDEIiw2NCRVH05Yriz7FpubETIJNHY6tnZFoxQtzhr2pgFEV\n8uwtjysLhquLmsc2haQ8YbmmmV7RvH8oYGZOc2tR879+N8HxT2X52ktvX332/88woxgZGWF8fLx9\nPD4+zvr169/0NRMTE4yMjPDMM8/wla98hdHRUT7ykY/w7W9/m5//+Z9/w3O1stBDhw4xPT3N3/7t\n33Lu3DlOnDjB2bNnGRsbu+vrbcUD2cNsjZO0gLIlj/fD9ijfKn7Yuc9W3+DN/DMh+jK/SoZPHMr+\nNtr+BUKa0DtGJZElNCchnifUbgehWkJU1MtT0o+SPE5fj4ASg5Pcao8SSAQHaPqrRs4p9xBV9Qqe\n3UZBHFZ5WF0h1K0Zw248yVPTLXusJFm3FatSzKgl6tQivVdzsb1mZ7CFone77XvZZ/dRwWPcRGtk\npQsjPkXdkqZL0ukGWDDjZKSDpKynKSlux68HGG6uY8afRmIizpAdpkYNz/Vw1SvQbTtoqpBSLCCQ\nc2kyLsmcF13HQNCNCXu4kI4l/iRivF7xVr0pt4a9jJsVRmwfl7XQK2kWVIOSjq5j0KVQAjMxuWd7\n2ImTLM/6jfg6Xq3Mo2Jyz6IK0WR4wcB+63NdB5Tjc45Zj7KKSq8bQ0MmzLKC4VKcUmUFdoni+fjY\nCLy3nuCFSpobcen2uLGRMPqaPmXgYKCuOFX26PeELu14KZawyylhb9Jysu5xRIXMFzUbko6TRUPY\nsufKWa7VFMtWs82zDDhhpqa4Vo0Aqdd3jGYczxeiNceSlq3G8Y3xiEAEcKwv5HLBUIibto/3Bpgm\nPDke7bsnJYx1WU7NxExaLfxXQyGXxzU34jnMA8MB0yXNbDk63todMpoNefJikqZVpH3h8CbLiWsG\nGz9c/KfHG/zGBwOGun642+Sdqjj/2uONvDDfyqkkDEN27NjBt771LdatW8exY8felPRz8uRJfuM3\nfuNVpB+AJ598kj//8z+/a5bsF77wBb74xS9SrVapVqt87GMf41d/9Vfv+fN4IAEzCAJWVlbaNe6W\nO8D9jmazSaPRIJ/P39P77hYo18bS0tJrdGud/StKyc/iYtancfux6irEzFTt1mOVjrJKQLuHqUsX\nJRPpz0biAgeprWG7JsOHaJgXQVk8u5dS2EXZn8LFGeuddlsRSI5S1tfIuH3M6iIZN7JK3AF63TaW\n1I02SHa4DQiaQHJMmBky0okvCQprQLLLDTIfg2JKcnTaHVwxE4TxA8FIuJ4pM4WoFglmkBVWiIhE\n65hXjhBhJSbepF2CLpdjOhY+N6LZGA5TVoZLpowoxbagl6veYlv+bmOzk1mvTFNZNoa9lMmwYGzb\ni7Lb+eTEZzwG4qRotoWdLGuP88a9LuN1X5jmiqmRFY8+l2NFGRaUa5s4DzlDWhQ3Yn/KTdZjsJnm\nG1ojSuEJHHGak9q11zzqNCUnNMpZztVT7NOO+VjnFWC9cuQUvGIVx0MYrxiGjeO5xqqO68Mpy8l6\nRLTZpiwbQ8epgkcxzlq3pSyhwI1GBE7bEpYx5fj6TASCCSUc67Y8vbRKAHq8K8Q0hGemPAKn2N4R\n0rRwMxYz6E85xrIO3YCTk5HF1/Fhy8kpQ9hi0g5aGk1BVxQvTBk2dzuyvuOluWiNbEJ4aNgS1uHG\npGa+rDm2qcnlOY9CLbr+sb6QjqRgGvD8VZ/OtPD7P9PgVz4Q8IOqWt6pivOvPX4Ya68nnniiPVby\nS7/0S3ziE5/gr/7qrwD4tV/7NQA+9rGP8dWvfpVsNstf//Vfv8aC68knn+TTn/70PbFk18bf/M3f\nsH//fg4cOHBP73sgAbNV0kwkEpTL5fs6G7k2giCgVqvdtcO3c456vU6j0SCRSLxKVeOt4o10axv6\n/6Lq/SbErFHttuLUcluhR0kvzh2grArU9DiIR0r2UderKhlpe5iaPtOeYfSD91KkStGPACspAyCa\nho5k54ykScsGyvoKSjwybh81OplZk0n2uu0sqWtIDHAdbgM1tYRxaZQaZllV0JJ4VSbZ7YaYM7fi\nfSuG3TaaGG7oZZoqZL3bwJSabPtS9tl+KrpMTdUikfRgM/MqZNaP2KgJ59EbdjCdiHVvRbHRDrCg\ni2RtHxe9KlvCHm54q8LoG8JOlnSVSix8vj0YpCAJXk5E/dSsM/SHSW4mIpD0RLEtzDFjGnS7Ts4Y\ny16b5SVTbTNgd9gUU6pJSTsyotkRdnJDa27EfcQup1knhpdj0+eEwEM2QeB8TohHQymOBvCCF5F5\nAPY5xaQSfFEMVNNMVpMYVFv3tUsJW7Xj+Xie8qgVOhrw7arXBrTjqfBVriJHEyH5uvDdpQgEB33H\nUEJ4oRKtkVLC4ayFBrywGImi3ymQvjtvKQewXguX5gwJLQylhXNL0RpJLRzps5yaNxzNWS5MGXb1\nWi4XNCuNaO9buywamClr9mYtl6Y12/scJ29HIKkQHtlkOT9tGM46Eo3IIqwRwPV4LrMnI2wbtJy9\nbTgyFHL+qmHvhpCXJjxK9dizc1PAZ36+ysFRuWf91QcFMJ9++um3eOc7F2vtz6y1EbcjzoofffRR\n/vAP/5Cf+ImfuKc1H0jAXGvx9U7MRrbiboUSfhigbMWb6dYG6ikq/i8iLfEBWQfiE2m9Ql0tkHRb\nV7VdgbQ7Qk0/3z5Oub00rVDCUPZnSNphRAU0dWtwP0dKBqm0RdV9cvZh5s00lditpMftZEFda2d9\nnW4jVbVIoCqkpAfPbmJRKpT8CMwjkBxkLs4klSiG3Bjz+jbdsoWbqkifDL4KJHuCHmqmRm2NAEHO\nDnDNK1FRAQnxGAi7mPAX2mtuDAa45c+SFJ+eYICKSnHbLxDGILkuFkYvxmMiXS5FT5hlWSe46gWk\nRLMxzHLFb82tws6wg5e9ImkxrAs7qUiSq36T+J7P5jBBWVsWdMtWy2fEpjljNMsa0qLYYT3OxQ4i\nLRGC86bJ7jDNC85nVLy2aTPAmFM0ECY05AT2VtMsVFOcjkFxVfd19TvyQSxLZcPpegQ2+xKW+TXz\nlCOeo0878g04G5c692ctJ0prwClvOVM27PMtUwVNX0KYbShm4osdSTm6fceLJY/9aUtYjmTrnpmL\nRNgBHukPubCkKVvNgbwl1RBmKoqbhbiMm3Zs6XacmvMiy7AeixfCyVuGRgzGDw1bFiqKyaKmK+V4\nqMtRqcHzt6K9+kY4ttny/C1DI1QcGrIkRZhY0IwvRnvt73Bs7necuuYx2GHZkLbs3xTyP/77Ip1Z\n7lp/9U4ZuX/tceeYjLWWn/7pn+app556i3e+M/FWPeNjx47xuc99jiNHjtzTug8kYMLqIHGlUkFr\n/Y6IIr+VUMKdQJlKpX7gJ9K30q216mVK/s8hahrlDlMiRYimqa9EL3id8mvKHaCuLuC77RQkQVMM\noSlidQS8vnTiSxdV3cr6PPKyE4tiiTplvUyv28WiurhGRH0zRbVAqFqAtgmRAW7qmzjl8FyCbhlk\n3ozHayqG3BamzbVI79VtpU6W23piFSTDXmqqSi128shJjpRL4UmWCR1QVZZh28PttYIDbpjrehpU\npOe60W7hii63VXYGbY4GASuxqk7OJehwSRrK4ksXV0zIVpvjYjw7CbA7yHPJK+FU1JPcGfRzyYOZ\nGBTXWR8BpuNMMe80g6HBKI9xnWBWK/aHPmf8VV/HQ2GCF02TpoK9YZIgSHNdw3z8+1wniqwTXom/\nNh0Ch2pJvl/OsOjigX7PcSJcFR04ZCwFq+ivaZ6rGDb5ghHhanjHPGXNcFxbJgqazUnHydLq7OOR\nnOV6TbEU9yn7rbDQUFyJs80OT9iVtzy7HH0fNyQcuzzLk5MejbiMu7/bslhXTMal0f35JgPAN29E\nN+WkEY4OWU5MrfYYP7g+ZGkFTk9E627qcuSTjhdjPdmsL7xnJOS5K4alarTu0U2Wm4uK+XJMChkJ\n6fWEb7wQ9UOTnnBkzHLqmqEZKnwjvH9ryI0JzSuTsUhCl+OP/2ON//BjjdfVX70TSKvV6v+nAPNO\nL8zl5WU++tGP8i//8i/v8s5W47d+67dwzrFu3Tr6+vro7++nu7ubnTt3cvjwYb7zne+wZcuWe1rz\ngQXM+2Xx9WbxRkIJzjkajUZbm/aHAcpWFAoFMplM+wv9uvthkjnvTyiYSHRdSYKk7KKuX2i/Ju0O\nU1OnIyCxO6nYQVa8W4iOSoy+68WQpK5bVldRj7KkL5OVPSwTkGSQBfVyGyS73BglNYGNjZkzMhDZ\neEk3t/QcBo8O6WdBvxYko2PNsNvPhCqwHKvy9Ll+KpTbmWRWsqQkzaJaYMhuYFFpkmS5ZWbb17a5\nOchNf3bVbcQOAj7XVciKDhhwWSzCYnytWUnQ6zLcNivkXZJu20NDUrycKLXX3NnMcdUvt8urm8MM\nSUlyVRvmjNBvPdKiuB1nimlRjNrIhmvUpqhKiqz4nPUCYhxhT9Nwy7PE93cONxPUXYqn45vvnco8\nvsCBEBrKMFnIcT3wedhYLlhNJb7YXdpRFFgSxSERxguGbg0vxIIBSSUcSVqerkdZ3y5lWRc6ni14\nlOON7Uxbqla1jZ3v7FP6cZ/y5NIqsD7SFZJswIkpQ8MpNuUcaSNcijPHnCc81G1RNXjutqHpFI+s\nC3lxPlLnAdjRY0kpIRXCs7c8ulLCzn7LyfE1We5GS60OpRXF1TnDjkGLE3hlLgbwlLBvnUU14NTl\nKMM8vjXk2qxmoRRdz8Y+x5bekOs3PG7PaZK+cHSH5fnLhnq8l3/3cJPf+Q8Be8ai3/0b2WpBlI2u\nBdJ3wuT5fsWdJKYbN27wqU99ii996Uvv8s5W40//9E8ZHx9neXmZxcVFVlZWKJVKVKtVFhcXmZ6e\nfkuVtzvjgQfMt8vi626ixV7t6elpH9frder1Or7vk06n37YeR7FYJJ1OvylgAlhKTPm/SVU/F29S\nRSBpVsuvyfC9FKRKIe5R3qnIYyRDSkaoxE4kWbeHhvQzu6ak2+O2sbyGyJNzwwSqhiMg5bYyrSsk\nJc9STA5Sohl0o8y0VH2AIbeFAFhEWNQl+l0/ZVWhFpOWMi5LWlIsmqiEO2jX46SLS950e42NjQFu\nJ+baILne9rOgC/S5XqaUwhGV+OZjkEyLx5DLcyP2ysyIz6ZwhOe9KvU4o91pO7iuSzTjku1ImKaq\nQjpcgkXSFIymxxmue1G26otiZ5jigh+B+5D1GQjzPJ1wq33M0GNeW5Zics+g0/RbTcMmOaV9MiLs\nCBVn449XCRxzitNa2OQUtpBB2wS3rGYpvtiN2pECrjiNQngch6lpvluJFlEIj6Utz9YMQYuIkwgx\nNeHJ5eg1IwlHl3G8VItulC1jZ92Ac2v6lOcLhkoLWHOWuoVhJVyd1ziB0bzj+YWYRKSEh/ujPuXh\nvOWVac1IXpgtw0zMpB3KOoZzwkvzmmM9lgsThr2DlufGDUHLK3PYMl9WWAsbU45bC5oN3a5dgjVa\neHjUcua2YW+/ZXxK05MTGgFcm42BNC3s3WC5OatZlxKev2w4tiPk5qxmbiUuKfc5hrsdKQfPnTdY\nB7/0bwN+/5cadL0On68lI5dMJt9xk+f7FXcC5rlz5/jyl7/M5z73uXd5Z/c3Hki3Elh1LGlpyr5T\nklX1ep1kMkm9XqdcLqOUIpfL3RXz9V6i2Wy2n2jfLDRJOtxPEqgpGrHuaqinYsWeDqp2E3PedZR0\ngnI41SRUJTQ+CTtAqIuICggpkrcPUyPPrJ6joufodTupsQRKqKkl8rIOEKxq4gjJuB2U6WXCTBGo\nBg2qDMpo2zmkrJfpb2ykZor0yiaWMNRJUVF1QhVSVVUSzifrctR1nUAFBCpgJBzF0sVVU2FBlxkN\nhljRZVBQ8CqMuD4CFRIqS1ZyaOljXinmdI2qCnAIG10ny7pOqBwFVWen66dDOphQaa6aBltcnooK\nCJWwoBsMSpqUGKrK0kGCpHRT0RmueyF1JRSVZV+QYtaEOAVzJuShZpoel+WC8bnhwWZn8AUqGha1\nIyWKjdYQAOuDNGckxaB4TGoIlGLGwBGrWFLR/GVTYEchyc1ijqs2yYxocjGZZ1Y0BVGUBP6Ncpiy\n5mwxwc3AcDwVUrSKBpH91pjv6NPCztBxet6wFCj2ZixTTU3JKpZCxWMdlqmG4iHfMrEUqQXVHFSt\nYqKuGUgKm1KWuaZmUDuSVUVa4FJBU7OaqarmWH9IOVDUrCKHMKocy2XFeMkwW9GIwJGhkImSphxo\nRpKOsZRwftJQqCvGC5pNXcJwh2OholmqKfZ3O3o94eR1Q7mhmSpojmy0WAelhsZDGMs6wobilRnD\nfFFTqise3WGZLyhCCyMZwTShWofFomZyUaMUHN1hmVpUbO93TNzWpHxQClZKmtOXDP/nv/h0d8D+\nbe41gu4tC8DXcwMB3tANZG0v7kcJSIMgwPO89j3r0qVLLCws8IEPfOBd3tn9jQc2w2w5lvygox4/\nSLQyTKUUnueRTqfv21zWD0JmWjB/waL3V/huG1WXo+ES1PwpXFx2TDrXAAAgAElEQVQ6jdivhkbs\nL6klQSrcDAbKJFjWM6/bo6yoOcJ2FjhAQjZyW89RU/XIqFnWMxs7jQAMuzGm1bXICDoYRutBJvQ8\nDdXqH+Yx1lDwI/KQJx6DbpCqquGki+umwBa72pMEWBf2smRK1GN28CY7TFOyXPCW42vzWO86uBaP\n3CiB7a6PV/QCm90AN5SiWzJM6ipV1SLmpFDATKwZO+IydLlunjI1REWKMg+5LOd0pT16stummVFN\nhl2GM8bQ6zRWhClP4mtTbLaGF/2QhMDuIEUQpngmUhcE4CGruKGFYny83Sn6awm+U8pSQ5NH2KFC\nnpcoK9QIx1XAlBh664oz5QQHkiETgWbBrZJ5OrRwqaF5WFnGi5qNScczpdXv5yP5kAsVQ9kptvmW\nwUCYqClu1mO/SV/YnrU8F7uKrPMd+33Ld9b0Kfd2W5Ybism4n7gjb9lsHF+/GrFxjRIeXmc5NR2V\nYwHesy5A1eF716Pr6c04tvQ4TsV9S62ED24OuD5p2iXXHYMW5+CVWE92MO84NGj51lmPZkwKOjpm\nub2gmC1Ee3nv1gDVhCfPx783LTy80/LiTUOxqtjY69jY4VgpwovXYvNqXziy23LmkiGbFMb6HEFD\n8T//Tp3jD62WadcKlb9ZrDV5XlvafStvync67iQx/eM//iPT09P89m//9ruyn3cqHnjADIKAarV6\n1xZfP0i0zKpb/dJcLnffM9ofROhdRJiz/w/XMv8F4tJpym2goaoEMbM1Yr8OUNHXSdsxypLCqB4W\n14yIdLutFNRtXAxOUY9S4Uk/k7pME/uquUmAYbeVaXV1FeDsHoo4bplojKTTRZ9PQUdGyr749Ll+\nps0UHa4Dz/VjVfpVIDnc7GHJK9GIRz66XY6sZGiQ5qIpkxSPEdfB9RgkAXbYPi7ryIJrk+3FSgdX\nTZVKDJL9LomHZjrulabEsMXlCEhyWltC4IDL8oKutHuQO2yaKd2gimOXyzNHgqZS3IhFDNKi2OF8\nzsW2Xlrg4XqK88pnQkc3/N0WZjVt260hgS4H2dDjQjFHyRoOaMtJtwbgjOWc1SSAPVYolDUrTjEZ\ns2J7lGOjZzkXRADxECH9ofDtlVXBgENZy+2GYiE2ft6TsoxYxzeno9ektHCo2/LMsqGVVj3aFeI3\n4bkpQ80qRnOOhBEux33KjCccjPuUZyYN1UBxfDjk0pKh0IjWGO105ExIHsWpmx6ehkMjlhO3Da41\nczliqdWFRKg4e8sw3OkY7hDOjEfn8bRwfNTi6vDK7ag3uXNdlG2+MhP3TFPC0dGQ4qLi9JXod3do\nm2V2WTG5ED9M9Dr2rbN8+4RHM66ZH98TcnNaM7uk0Vp4396QZkXx/dNxH1UJ//4nQ/7kNxoM9dvX\nCJXfa9xp8rzWj/JOIH0nyrrlcplsNts+zxe/+EVSqRS/8iu/cl/P+27HA1uSXSu63mg07ouDSAso\nK5UKIkI2myUMQ5LJ5H1nywVBgFLqLXuYa/dZLpdJui30mP0smxNRqVUV8cngSy+hKiGqiS99aPcQ\nk+Y2dV2hphdeVX6tqyWyMoRC4wjJykYKJKmqBAW9jFOWmioy7LZS1hFYldUSg7IZX9L4bj1XzDyK\nJJ71aOomDdXAidAfz1I65RAcg8F2rpgai6bOsi6zLuyloQKscpRNjQ7JkpEUvhgy0scr2pKWDMu6\nhlWOZV1rmzejIg3Y3XYY7bo574XM6iadkqBLEpRUSFVZAhzbXJ6SChh1PZzVmk7JMKMCRMGMDhhz\nKVxs1LyoQ/bYHFnp4IQHi1qoITzkkkxrS6gi5uxhm6TTaTyb44T2GcYjgVBWMK8hJTBmo39vDBTL\nhTyJeorLLlLVmRDNER1SFmigmBXF49ZiSprTlQTzTiMoDqYsk6GmhmLGGd7vN+ivOs6s+FyvG7Yn\nQ1IaSk4zHWhSWtiTtmwRx+U5w5WS5pEey0xd0RTFeE2zP+/QCnYnLDfnNPMVxZYOYaamWWkqCk3F\no4OW6apiX9YyMaMxAiJQaiomy5qOhLC7zzJVUuzMO8ZnNL1pmCtramFUgt3R7+hMCc1AsT7puDGt\nGc4L48uKckMzXdQc2xzSCGA4JzRXFHMLmnW9wsxKBJqFquLR7ZZKDfb1O54945HyYaBLWChqppc0\nQQAP77YM5Rwrc4pzlzx2bnb8v+y9WYxc2XWu+e29T4wZETnPI5kkk0kmx2RyqpJUZfV1yW1Yth98\nZcHWNW5buJYu7LJxBQ+6RtvtNmAZsIH70obbL1cW+qXtbrS7DUil0S5VFYtJJqdMMkkmx+SQ8xSR\nGfM5e+9+OCcig6xSqWZJLi2AQGXUGSNPnn+vtf71/w0Jy/qmZG7F//v9xCGPcBkmLjs8XJCM7NHU\nJy1racn0bcWr45L0qmBkuEQ89u4XyW9m8lzpIVbeJZUEoFwuP+HIVJsTvR9Aaq3FdV3C4XD1eK+8\n8go9PT3s27fvPR//xzk+shnm27X4ejdRmfMsFAoopZ4ovb5dMs57jXw+X5X8ezfXmRP3uRH6MmXh\ns0qljRE1I2SFYSUwi2729rKmbr55+dUKmswhskgWAnEBaRXNdoCFmvJrh9nJkpj1Je5oJ4OlKArk\nAsuviImQ9JKshrfnJHt1PyUUt9UWrtD06TYW5BpukAU2mSQWy4bMErMRmnUXW8J5Q7m1kkkC9OtG\nXKGxNsk1VfJ9KZHMB5lk2EoGTYIbahNpYbdpomzruKzyVTPmQRNlHZeNYGykyTr06ijLIsR1ZXEs\nHDYRLqhtZe8jOswNWabFOsS8GGs2RBnL44BAlLIwaCWXA5uuQSPp2KrjW4VwlXl6UHjMWclaoNTT\ngWGPNdzPOjwqOUSEZTTs8XrJoXLDY2GXOVcy4FomMoqesMURlttBebVO+mLp53IhjsoSixmH3qjm\n2pZDLijj7qrzmaf38oqhqCbm+iSgsys1WW6rx7UNxZYn2BnTdGJZzgpuBzOcdSHLoTbN63MBG7dB\n0+EYJue3x0B66g1NMctUkBWe6vSIGsuZO9vl1f1dmlwJZtcU9RHLwSaNceHMze3ZzrHdmgerguUt\nyWi3R3FTEAtbLsxsZ4Un92luPJakotDkWNbSgtZGy6Wb/rmVtJwY0TxeknQnDOOXFL2dlpZGy6VA\ne1ZKy7NHNdK1vPKqgzGC7k7N//rlMr/yi94b/xDf53g6G61kpO9XNvpmJeY///M/54UXXvhpD/Pf\namit8Tzvjbqr7yFqAagy2/k0MG5tbX0oykJvNS5TWSHm8/kfeJ0AZda4EfoymhJF28qyXKDJ7mZN\nbsvYpco72Qpta73GbRth08aaKJCWaRwbptF0saJmq/u0m93Mi3tYAXGbos4M8lCukReV8Y06IjrC\nulNR3JF0mx4W5QLNupe7Kke7aeaxXEEHTNVmncITmoz0gTZp4rSaTq6qTQrCvClIDuhGluQWYRzq\nTTNzApw3gGSSGypTvfajbhu3lWU2ALCdJkIGzVpQXm2wilYTYlNoEraOKxKOmAgTslQ97yEd5o4s\nkxPQaCU73QT3reRe8P99zVfFhQB4AT6uHbLFMN/fimKQ7FOGtBHMB+XJJgy90pC3kkhecCPncDzs\ncq4cqpZXD4U95jzJhhacwGM1JwkJW2W8hoXlWJ3H2azfT9ztaHqM5cqGZMOtiA5o6h3L9ay/T2dI\nczDi8d3H2wB+tFnzMCdYDRRy9iQ0OxzDd+86aCv8Ummn5vzCNsP1ZIdHTFtevu2fuzFmGGzyuDC3\n/Xfy7wZcNjZElfU60GxIRAzX5v2fo47l+QGPizcUy0Ffcl+vpliGewELdm+HZqDe8O3zTrW0e2SX\nT/h5vCKJhS0ndmq8Epy5prDBNkf3apbWBfMrglN7NI8fSXo6DONXFKbC0t2nyWxCW8py56akXBYc\n2q85f0lRDsZQjh/V/OX/XODY0Q/3tVvbG336nxDibQswwJt7YX7pS1/iC1/4whsk7P6txUceMOHN\ndVffSbwdoKzEh6Us9GbjMhWgLBR8QKhc51uKJVNgwvnfWKwRMHia2JMyvRRFmphtJ4MkK4rU2XrW\ng9lMAkWeRXWneox2s5uyjXE7AL2UTaGsqho/K6voMJ3Mqccoq2jTfRSp455axATZV4uboijLZAMB\n85iN0GSSKKLckS5beD5Iqm0bnx26kQW5SVFo4jZEt+5gXsBDtQ2SO02Cm6pGgEDXkxOago1yS3ns\nMFE2sFWQrLeKdhPiliqSsooek8QlzHlZ3taE1WFmpctWcO39xqHDi3LGKrJCELVw0CrO14DkcaO4\nLTS7SlHOZuJ0S0HJwoPgBZ3CsguPS4RoF5adrkCVBOcKsjoWsj+s2dCC+UCp5yRlwkXDK1m/BSGx\nnEx4nM86VbH0kzGXSMny6rIPti1hQ19McymzTSJ6pllDES4tKXKeYLjeI+vCo8DouT5k2JP0cFzB\njXlFuiQ51eVxdUWRDcBjsMHvbTYJy+RDfzzj6T7l0S7NZgHapGX8lqI5YdnRajj/cDsrPLVDk89D\nfkNwa07R32qoj1umHgS9TGV5Zo/GlmB8yhcj2N2jURJuPgxk/MKW5/Z7XL+peLgQEJIGNMKBm7P+\nNvv7PTqTljMTDoWg17qrXxOLwNVbip1dmoSERNwyfVORCVhZPV2a9lbNVkahPLhxQ/FLn3b5s/+l\nxI6BH+3r9weB6A8SYBBCoLWmVCo9sRj//Oc/z1e+8pV3LATwkxYfWcCs1PvBV6lIpVLveAbyaQCK\nx+M4jvOWAPRuyDjvJp52RqlcpzGmKmjwtr3pMFxV/wd3nZeqnzWaQTLiEUaUSZkdFG09OVFgM5DG\nk1bRavtZkveq+7SbnaTFEnVmgLsyTcKmcIXLlvAH/0MmRJNuYinkl4GFFXQVd/EglCPj+GXMdq+R\nTZGjEBBkEjZGwkRZkhv0mC7mBDTa5BMgOaibeCTTlINstMMkSZkUV5VLVhgiVrLjKZDcr+u5KTO0\n2BgRmyArFGk81mtAstVEmamCteSg18AZZ1uabkSHeVADkh1GkbCChA1xU4dZR3DESs4F2SrAmFFM\nC00RX9VnbTPOppbcC8qgdVj2K8157QNGHMtzBsbTivVgmz1hQ9nCbJAVpqTlaEiT3hRc2fKf8dNJ\nj0tZRTEApl0RD2Ms7Z5laj3k9yNrlHkATja6XM047I16LKYlEenPUN4OmLQxZTnSrHl9WXGwTrOV\nFjRFDLObkrViZZ5S0xa3TK04HGnySKcFXUnLhcfbknZ7W7Uvur4uOdGmeTgv6W82nL27LdQ+2u8x\ntynxNAzG/V7mQJvh/O2a693jcWteMthsePRIIgV0NpsquUcIy8lhzUZGENVw5aaiu83Q0Wy4eGN7\nm48d8ZCe4JVxP5vsaDH0dRvOTwZqQlHLswc8bt5QPHjsf+f1KcvIsObcRUU0DCODLrlNhevCzRn/\nuwiHLZ//n1z+4PdLNL1/HaH3Jd4MRCvZaMU+MBKJkM1mSSaTfOYzn+Ef/uEf3rEQwE9a/BQw+eEy\nck/Hu8nUKvF2eovvR1TGZWKxGPl8HmMMsVjsiUb9O4178ttMOX9f1X5t0gfY8gSLEV9sIGSjpEwr\na2rby67D7GZR3MYhTL3dRZowGyJNIZDCi5kYcR1nLVQRfxf0ml5KGFaQrKgcPbqVZbFBOQCrpI4R\nMor1kO8s0uW2AQ1MBccA2KWbmZXrVf3XNpPAYEnZOu4JSV5Yek0dt54CyRsygxFQb8L0miZuSJe1\nIOurt4o2E+J2AJLSwgGToITilnBYlrBfh3kkXTar51WkrOCO8hjWETZ0hAYTYrwmkxw1ihmhqzZd\np90QuVyMV4p+OTKG5Yhjed3bJoqdlBppBLczihVXsSNkUMCdACTjwnIoapgpSoY9w/iGZCxpmM5J\ntoIMdSBiCAu4VZQcD2tWM4KOiOH19e2+39FUmXt5h7QnGYx4tFrLVlkwHYyOhKTleLPH+IqDRtAV\n1gyFNbdWFXOBjVZj1LC70XB+IZDFi3vsjnlMPAqzFagE9dVrkhFbdRU51OLRhMdrtyO4FaH2Tk0x\nEExXwvJsnwYPXpneBtLDA5qVLcHcmmSgWdMSsoQVvD69fU+jezwW1yXrm4KjfZrb9yS7eg1np7ZL\nsEf2alY3BN1Nhtu3Ja4nODCkOXdF4VX6prs1LQnDzHXF4pIkErYcO6KZvKbI5vxtfuaURzlnee1M\nIA4hLGPHNHNzkoVFwcnjmgf3Jf/pP7l88YtlPuB19HuKSlnXdV08z0NKyZe+9CX+6Z/+idbWVn72\nZ3+WQ4cOcfDgQQ4cOPCGyYNvfvObVZeSz3/+8/zhH/7hG87x4osv8tJLLxGPx/n7v/97jhw5QrFY\n5BOf+ASlUolyucwv/uIv8pWvfOXDuu0n4qeAydsn4rwXoKzEhyXFVygUKBaD7Od99PpcEpNMO/9A\ngRgLcpGIThATCdKBM4mv0LOzWn6V1qHVHOKhTJMWPsAlbRJlHNJqu/zaabp4rB7RpjvJECZE3RM9\nygYvAcKSVn6PMmQder1OloVl1vF/HztLDcyG09Vxjg6doCBcMrLEgG5mgyiSEHcCCy/wQfK6zFRn\nHHfrJCEb4ZLSFIWlwTq0GIc7NSB50CS4IrPsNnUsiShx+2QmWQuSADt1iFavjm/VfP1HreQOpjpL\n2W0FHVqylY8xkY8SwXLMsZypAclR4XLLOuyQlsKWouQK4tJys1bOLmo4U1CEsJzAYEpwPS9JBy/5\n7rCh0bFcCxR09oU0vdaXs6uCToNmviBYDsTSB2OaXY7mO49DGCsQWE40l7m8HqYUfHEj9R4dGF6d\nDVHSgrqQ5UCrx/j8NtHoZIdLVMPr93yyTludoafBcGluW9Lu430lipuCc3f8lsVAsyYesVyf3xZM\nf36Xx+wjya35YOayS2Mt3FoIxmUShhN9Ht+/GCIflE6H+zSegduP/W1O7vaIC8trl51qf3FowO/C\n3pxV7OrWxID6hOXydUWuECwyegwNKcvqqqA1Zpm8Kjl+VHP3vmQlEGxvaTbs263ZWpVcvuyfb2S/\ni+tKZm5VfvZob7VcmHDIZILfTbfhv/7XEr/2a967thH7MOJpL8z19XU++9nP8tnPfparV68yNTXF\nc889x1/+5V9W99FaMzQ0xHe/+126u7sZGxt7Sx/Mc+fO8bu/+7tVH8x8Pk88HsfzPJ599ln++q//\nmmefffbDvXE+woBZ61jyw4g47wdQVuKDluLT2p/5qoyV1NfXv+8zWetinm+H/neygSXYmxF7OvQu\nXCGZEy4ZkafJNFMWZbI15ddm08JiIFvXbFpxdDs3nIUqeLV69eRFiVwAVlEbptmkKAoXa+u5LXPs\nMa3MyJUaqbsUaVEkG4im95cb0SbBZNT/3Qnr9ySnVaa6z06dYE2U6LRJbkhQSBqMw70nMsk6JgOw\n7jNREibFZWWeAMmkFdwNQNKxMKqj5GyI143ECL/8ercGJLusIAGsA735GOe2ohx1eBIkpccdI8kg\n6ReWnqIgXRJMByAZwnIiZnitIKnc0Kccj4ebgusBKLaHLB1hU7XdUlg+ntSUsoLxFYlBsD9lyJTh\ncUDUqQ9Z9iYMjgvXliQZV3CqTXNtXbIVzCIOJDQRaak3hvtLikxJMtpe5txCuEo0OtCqWS9AT8Ry\nd0HiGtjbojn3eHtxOtbj8XBDsrvOcOmOIhW1dDVoLj3czsqOD5RZSkuaFVy8E6KvRdNQR7VPqaTl\n5B6NKcHdWcnyhmSgw5CKW6bubW/z3EGP7Lrg3FSQ7XYYWhoslwMWbCpuOb3f4+KkYmXd/y7amg07\neg3nrijCITg+pCnmYGVV8CCY+ayLWw4f0Fy9rjg4qJk4q+jpsSRSlskpVb2PZ05rwo7l5X/12bOp\nlOXAAc3Fi4piUTAw4LFnT5n/+B8NP//zP56v5nfjhXn27Fn+7M/+jG9+85sAVTD9oz/6o+o2X/jC\nF3j++ef5zGc+A8DevXv5/ve/T3t7e3WbfD7PJz7xCb72ta/9SEZYfozXMR9eVGryT0cFKCuCvdFo\nlFQq9Z7Kmj/oXO81jDHkcjk2NzdRSpFIJD4wcecm28Uvln+fNuM3+D1RZkU+oEPvRlhBs9nFI2FZ\nI0YRv/S4LtfwrEeT2wyAK10W1QL93iANepBb0nA9tECnaSFq/BflipNBSEG79hs8ERtCkwDbwS3l\nq+fMqBUGTCMx678AH6tNFJJBr4V23c2lsOJapMg+z/cgtQKmnQw73TgxIxHWz3DDpoEFQmSEYV14\nPJQlDml/UWMETKocR70ke71mLos4rziaOisZDHqJy1LzUHoc02HqrGDEq+MVHSFnQiQC8LgsDHUI\n9gQrgg0sjaUIvesNvLwVo4DkjCcZVYYG/GfkonFok/CCscytKM5sOcyUJR+LaQQWF8FrBcWhiOGo\n0hwoGr656LBUlhxN+N/9kiuYykmeTWmSwnI6ZDj/ULFWEPTH/fNMb0o2XMHpJn+fwbBhaUXglkAG\nj9DZZUUy7I9sgD8XGspKwp4PlmUjOLsQYXejYUfKXziUioZGVyPLhrW8IFOUnHsc4nCnR0fSrx54\nBUtjyVDOW/JlweKm5NLDEKN9ZVrqDCEJjqswWxKCdu/DVcXUA8WxwTKNdYa+Rk1mCe7NSvra/I1m\nFyVT9xTHhz26mw0nd2peO+Nw96Hk5AEPsDxalFy+qTi2z+NjB1winuWb/xqiVBY8M+rhKMvymuTc\nFYdPHvc4tkPz2msOFy47zC9KTh/3SKUsubwgtynobzS4BSiV4O5dyeRlxaERj8GdHsdHNTenJWde\nczh1SlNfb9ncFJw549Daavi5nyuwtFTm298WfPazik9+UvHKKz8+cng/LN7qXTM3N0dvb2/1556e\nHubm5n7oNo8f+yNsWmsOHz5Me3s7zz///I9s3vOD0WX7CYjaX64QouooUIlaksx77f09fd73EzBr\nLcEikUjVNLrWPPWDiBhJft59ke+a/86j2BQIiys8kmaUGTkXlFKz1Jt6IibCptqkKAu4okyP6SHD\nJmHTymWVps+041iFJzTzapV6XUdcx1hXm2RFASkEO9w9XHbW8eQWsMUu3cwDuYErDLNqg2YTJ2kj\nlDEkbROTqsygiQIltLBcdzafEEm/F86zz2skb0NMhMqAS8gK9pWjXA8X8YRlUuXYr+MsiTKtNsnL\nStBiFX1W8EB4LEpN2MIx7c9WWkBbRW8pwQVhKAi4jKHTCjos3BKWBWFZs/B8Icq5XJRve/6f4Khj\nuO/BOoKLWtKG4ZAyJLVkas3hnhacjhnOFCweglcLigMRw4pnMQbiObiVleyM+s/xmidYyyqeSWku\nbkmKVuAWYY9nWMgLclowk/WVep5p1pxZk+S0YD4n+GTCY3JVsVoUzGahNWoZbdZcXFPM5yWuZ/i5\nRo9X7vsMWYCdDYawNNxcV8xsKDrjhv+xy+U7N53q6Mi+No9sCR5mHK4sOOyqd/nZTpdvXw1TyY4P\n93osbwrmM4qLD8Oc7HWJWcu/XgsBgoeriqM7PRY3JPMbkpm5EIc7PLwynL3ul3+XNiSHdrqsbkrm\nVhW6YImWLXjgaVhNS1bTkv2DmlIZtAulDcHVu4pjhzS5vGAzKzhz0WGgx9DRqNF5wfe+HUIIy4lR\njwePJIvLktfPOwz2a06NGL73bQcv+D6G9mjCEcvVqw4bG9DYYJFC4DhQKvkgmUpZnn3WI5/XrKxo\nXnpJ0N8PbW2GiQnBxITgl39Z8Gu/5vIf/oPg2LEfD/Ppp70mK3aEbxVvm2D41Dursp9SiitXrpDJ\nZHjhhRd4+eWXee65597Zhb8P8ZFV+gGqIFkBl1AohOu65HI5yuUy0Wi0SgZ6vzK1Su/0vY6VVGah\nKqzbitxe7XUWi8UPlFwkUTSnB6kLp1gRhlmZYUOmabEtWMAVnq//KqDVtJGVWWLEUKYBY5u5q1ax\nAjIyR5OXRCIoS4+SdDHC0GNaSdlm7kvBQ5Vnl2lhQ+SxAtZlgTabIGQlReEPRDTZFjQNXAvEBFZk\niX26nnVRwgqqIuntJk7MJrnkGDakZdjEWZa+ndaK8hjxYqSFh0RQ70bYpI4VFGkFW8JSxHBIh1mQ\nGi1gXmqedeso6jgXrMNjYWlF0I4vjJ4VsAWMWUW9kYh0ktfyMYYkFA0UESwYQRJLP5oVJPuEZS3j\nUO8J7pb9sulDT7I/YlFYslawqeGINTSU4fWMomAE82XJ6ZRmrSxwETwqSU7ENYPacGbRYaEoyWo4\n1WR4VBB4gVLPiQbDkGO4uii5u6mISDjYZJjLS/KeYKEgeaZVM+D4Wdn1FUV7naW/3rCcl2wUBRtF\nwbM9hv6I5eGiZHpRMdhsaY5b1vOClZykpAXP9Bn6wpbrdxW3Fh2GOzV1EUOmIFnclHgGTu8o0SJh\n4maI2WXF/l6/l5nJSxY2JNrA80Nl1hcl12cdHq8ohvsNjQnL+pZkaUPRmjAc63OZmAyxsiF5tCgZ\n6NJ0txlWNiT5vGB3myHpwO37fp/y0bykKWUZ2aNZWhUM9xqmLikaGyyRsCWdkcwt+Oc/eUzT12q4\ne01xY9ovwe7apVlYkKytSTIZwf/wSY/NjODGjRCPH0s8D06e1KTTgnDYkEq5PHpk6O+3LCzAxoZg\nfl4wNAQjIy5aF/j+9zVf+5rmyhXD0JCkvf1Hm3VWCD+VqYLV1VVeffVVfvVXf/UH7rO5uck///M/\n8+u//usAfP3rX6e+vv6JPuQrr7xCU1MTIyMjAPzFX/wFL7744hMCCdFolIWFBVZWVjh9+vQHcXtv\nGR/ZHiY8afFVIQBVmtnvF0nm6fA8j1wu9661a9+uJdjTVmIfVGxsbFBfX88t5yZfd/4fXOF/j3Fd\nh2OjbDi+Bm3UxmjxdnLdWakq8nR7zazKDKWA/VoZEVmVm3SaLu7KMp2m8YkeZa+pZ10UyAU6tQ0m\nRodu4YpTIhcQhEZ0PdM1RJ4+E2cTHwAbbJLb0tBtItwMZteb3ywAACAASURBVC8BDuk6rskcWvh9\nzqO6kcfCYTrwmIxZwW5PMRXaVmo5VHbIYinbGFeFQ68VhIB7QV8zbKmOjfQbSSwbR5fD3PEE6eCG\n2oWlBc10UFIeloa+guQ7W6raB9wfMWx4VGcp64XlhONxdU2xELBMTyU1UzlZtdTqixhalCVcgHMr\nEkfAiSbD62tyu7+YMmyUod+xXF+RGAPDjYbx5e3n6Xir5lZGsjNiWF0XuB60JyxXAiEAgeWZHsPF\nBcnelGEjELuti1qml7c1XU/1Gc4/khxuNszOSVJRixSWmUC9J6wso30u0/MOIy2aizMOfa3+QvbO\nol+iDzuWsV0ea2l/3nT6vmJnpyYatlyvsfA6tc9DluHcZYeSK94wKgLw70aLPLyvmAkE3RtShuFd\nmnNX/N7iyKBHIuwD2Myd4D4cy/Gjmms3Fd2tBncTNjOCwUHD+Pg2w3ZkRNPYYJidVTx6JFHKMjbm\nce+eYnlZIoTh4x8vA5pz5wTFYvA767N0dFhu37YMDeUYH3cZGZGA4lrglCcEfPGLlt/4jTDDwx+s\nWtgPiqetvWZmZvibv/kbvvrVr/7AfTzPY2hoiO9973t0dXVx/PjxtyT9jI+P83u/93uMj4+zurqK\n4zg0NDRQKBR44YUX+NM//dMfiarQRxowK7qLuVwOrTXxePwDA8pKaK3Z2tp6x/NKtQLujuMQj8ff\ncm70/VQweqtIp9Mkk0mklDxyH/D/xf8vcgEL1RdI78SzEe6pHAXhMaA7eCiXquIDjSYBCDbkFtIK\nek03RVvHtPPkHOVjmaEUAG2DiVFnQ0SJcUdAWmj2mXqu1SjyDOoES7JIVngkrEOvbmJdyOrcpAic\nRCZrnER2mCgxG2JehLkjIWEFO02IqWDmE2BUh5mSZRqtosmLsWD8IfuA+0HEwgENF4J3c5MV7M/F\nOZONsBFQBjqFpUlapgMAVFg+IQ2FkuJsRgLyjSApLXvDhmwZTFZwIy85ldRczcmqoXNvxJBQlnsF\nyZgyXFuTjKSeBMn9KcOmC48KkkNxjZeFVATOrmw/S2MtmrtbkvWSYCBm6LAWz4MLi9vbnO7WXF2W\nbLmCvrihL2TZzMNUwFSVwnJ6h+HivK8Du6ve0CotmzmYnq8h6uzUXHqgKLiCY10eXsG32Lr28Eky\nz5X7/ijJ/laPuSVJQ51h6r5fBhTCcmJYM/NQsqPFsDgnKbuwo1szMb0NKkf2ehjXQlEyOa2IxyxH\n9msmJreVeA4OlWlNar73cqx67ONHPe4/UCyvSuqTloM7NVbD+LiqlmB37dLUxWFhUdDfZ7hwQTE2\nppmflzwOZjNjMcszz5RZXdVcueLv19ZmGRy0nD8v0Npy6lSJbLZIKASXLm23iQ4dUkgJjlNkYqKI\nlPBLvxTjj/4oxd69Hy5wPg2Y4+PjfOMb3+C//bf/9pb7vfTSS9Wxkt/8zd/ky1/+Mn/3d38HwG/9\n1m8B8Nu//dt885vfpK6ujq9+9ascPXqUq1ev8hu/8RvVWdDPfe5zPzJXlI80YG5sbFAqlQiFQhhj\nSKVSH/g536l27Vvpvf6weK8KRm8n0uk04XC46r9p4pr/N/qPLIkFWk0/s8Kj1TRxr8bEuc1tIKuK\n5OU2+7XL6+KRclkIPtujW7gjV6sjIm0mgYdmXRbYoVtYFmHqbOwJ2bq9OsV9maUUZJrtJkqbSXJZ\neWSFDUZC6rgSsF3988RYkGXqrQM2wayUdBrFDeVWtzmmI1yWJbSApBUMuwlmrOJBcG1xC/utYqJm\ntnLME9iS4nw2yZZVdGFICcPNIJNUWE5IjynjcMTCxLpidxhWPFisAcmhsOF8UdEtDN1lX492Mrud\nSfZGDEllq4zYkxFNnWt5eVlVpeqGk4acBw8L/nF3xwy7lOGl2e3naLRV8yAvWQ3GMPrjhn1Rw3fu\nKLyKfF2X5saa3HYUSRmG4oZ/uaEoa4EQltP9hql5yVY56OW1GgbqDN+dUmgTbDNomHok2QqOc7TH\npdkRfOdKjXrPHsP0I18oHSw/M6RxC/Dq1PY1j+31eLDoGzt3N3l0xjRKCM5Ph7azvV2afBEWViRH\nBjymrjocHPa4Mu2QDzK7nk5DW7MhKmH6mq/QM3rIY2lZ8DhYAMRjhtNHSly7FGYxWDj09mra2iwX\nLzpIaTl1UlMqQTotuBNkpaGQZXTU5dEjycCAy/i4JZmE/fstFy4ISsF3cOyYS1NTge98x6XyRh4e\nloTDMDmpOX3acu1ansFBh3zeMDPjP2tSwuc/H+M3f7OO4eEPZ4gzn88TiUSqC/ZvfetbXL9+nT/5\nkz/5UM7/o4yPNGAWCgWEEHieR6FQ+FAA8+2WSt+u3utbRaVc+kE4o1SuL5vNopSqqhwZY3Cty9dD\nr3EmPFPdvsdtYVGt4wWqNikTJ0IYhcOWjfJQFt4gY/d0+XWnbsGQ5KLaqm5TKzYA0GVieBgabZy7\nQrApLEMmztUakNyn49yXBQrC0mxCtJkUi0JxWwUvIQujT+m/DusQcR3iog2RFoKkhd1WcqlGpee4\nUVwVmmEvxEymjpBRhLHcDhR4QlhGhcu4DSGBMaMxOcUDV7FstkFyT9gwESjjJLB8XHqcXXPY0E9m\nkjcCkHSE5fk635JqKrDQehok48oyWq+xBcH5OZ/RerRF8zgrWA5GSRojlt31hpAHN+Yl60XBiS7N\nrXW/RwnQFjf0piyOC7PzkqUtwal+zfSiZDN4+XckDd0pS9TC9KwknRecGtRcn5dkgnnG9qSmt1ET\n0ZJzN30xgBO7NXcWJWuBVFJz0nKwV7M0L7k+61/j6B7N4vq29VZz0nJ80OP749sAONSvQVhmggXB\n0V0lEgquTIfYzPr7tbcY+gO1nj19HpQhGoGtLNwPyrvhkGXsqMfaqkQVYXpa0d5mGBjwOHfeJyEB\nfOxjJbDw6qs+L0FKy9iY5sEDyeKi5OjRPOvrLt3dgslJRbZyDe2WXbsMUhY4d65EuQyDg5KGBrh4\nMdAq3mnp6nLJZAxXr24v4o4cCVEsGpqaPCYmsriu5dOfTvIHf9DKgQMfLHA+7YX5j//4j+RyOV58\n8cUP9Lw/DvGRJv3UMlY/KIuvN4tisUg0Gn3TzK8CRLlcDs/ziMfjP7BP+cOiwl57vwGzcn2VWc8K\nmFfIU0oohu0OHCO5q+ZBwKbK02zrcaykJFxStg5j6ymT4L7aqlprDepmsqKEEZZNUaLOhunWDYRs\nI5NKsyTK7Df1LEtfKm9Flui3dRigJAxtJk6JOsqEeahctIBl6XJQ17EuAmKPdOmxUfp1iikZ5Z6C\nTWE5Ynwijw2IPPtNiLKw7NFRHuooDwnRYyXLwlIWsCAsJ41iCRuoA0maM0ke5eI80oqMFeQsnHAM\nj4xfFn2M4gVpSOQkFzfDzGtFWFj2Oh6LRlGygnlPcirs0udZMpuCyS2HtrA/S7nmSTa1IO0JTqcM\nJRf2Y3l1XtEc9uXpMp5gtSxwLRxvNDzOC8bihpl5RVxayhpynmAhL3EkHG42zOX8OchsWhC2sF4U\nFDzB3JYkEYJ9LYb5rKQnZjCbgoiFpS1B0RM8zkjqY5bhNsP8pmQgZchnBFEB6zlBwRU83pAko5bh\nDpeFjGSkzTD7wCEZhbIHuZJgbl0SdmB0pyGbF+xtNpy5pOhsssTCkM4JFtZ84sypfYb2hKWwAZem\nHfo7Ld3thuV1yVpGsp4RfPKYpjNhOT8R4sGcQ13ccnCvx/ySJJuXbGXhmYNlttKSW3ccllYkW1nB\nyWMeubzAWkFH0jB3T9LRYVhYkGxlJXNzit27DQMDhh0DhrOvh3jwwGF01MVxLJmMYm5O0tTkMjaW\n5do1w9KS4NEjSCQsR49alpZgxw6XxcUs6bRmzx7F/Lxlfd2ysGAZGREcOeIxOZlndlazvGw4cMCh\nvV2yvGxoabHk8zkcx5JKKVZWNDMzZb761Q3u3i3S3a3o6vpgDB7K5fITBMMzZ87Q2trKwYMHP5Dz\n/TjFRzrD/CAtvt4qflDm9170Xt8s3qnk3w+LSiauta6O2mxtbeE4zhO+fEBVxupefIn/O/kKpYAM\n1KGbidgmLqk1bHBvtabNAB0mQQkPkNTZRm7KMjtN6ony6x6d4qHMUgzKr3t0PcLGOOds9ygPmgRT\nMlvtUfabKEU0LTbOpHQo8aRxM/hOIrdlmbyA3ToMXoxNFDPBeYSFk1ZxTuhqVntCO+hclO/l/QVX\nHMshx3L2KQGCgpFES5JLWw6tytLlGCZL2wuhZ2IeEwXFEJp8VuAZnxF7r+xXFkLCciLhcWbLISxg\nTBlyRVgpiqrgQFxZDjcYXl8LFGVimmZjub4uWQmyzfqwZW+D4VxAyumMGg7UGS7MKdaDLK05ZtlZ\nb5gIyo9NYctYg2ZiVrGe97dpqbPsaDJMBA3ctrjhcIvh4l3FWiAN11Rn2d2uOXfPfwZ3N3v0xOHG\nI8li2r+eZMxysN/w+s2AwLRDU84L1rcE9+b9z8KO5cSw4fxNSWvK0h6xrG4IGlOWKzPb3+GJA5rH\ni4IdLZYLlySRMIwMGcYvS3RFq3bQ0NWsmbyiWFuXQZ/S5e59xep6YCF22CUq4LXXHNygvzkwoGls\nNFy+HOL4mMu9e4qeHkMmI7h/f5sYdPKkh1IlJiY0+bwgmbSMjBiuXJEUCoKmJs3wcBGtLRMTBh1U\n8nfskLS0QLmsWVsr8PixZnjYIRIRXLni//2kUjA2ZllZKTM1tW0Td+hQFK0tiYTl5k0fhJ97Lsl/\n+S8dPPfc+1c5q1h71ZpH/9Vf/RVjY2P8wi/8wvt2nh/X+EgD5gdh8fV2okKUqWSNnue9b3qvtZHJ\nZKrA+16iVj2oIrMH2zOgrutijHnCyLbSb1VKsSQ2+D/D/4ohxrTMIpDs0E3criH29OtGluUWBeGR\nsGHadBsbwnmDjF1t+bXDRInbEIYoV5Q/Rzls4ky9oUdZIothr0myRIQQDtM1PcoKkSd4L3JQh3F0\nlH8JSDohC6NWPaH/ut9K8tbSWIzy6maMuBDsVZbzNSA5JlymrUNUwLAHD7YkDRKulWsYpjHDeEHi\nIegThh2e4VFBci8AwLCwjCU0Z7a2tVA/GS6yuCmZzvoZREJZRlKa8Rqh9I83elCAVx77nzWELUM1\nIAlwqk0TdS3jjxQFT7wBJAFOdWnCruXyfcVmUdBcZxls9oUPKnGyTxMzlvO3FbmSoDFuGeo0jN+t\nAbKBMnVW8PKUb6tVF7UcGTC8PiOrziTP7fUwBXglEDV3lOXkPsOlW5J8SRAJWZ7do8luCs5drSEp\n7dc8WhIsrkqO7tJk1wRtLZbxy7JKyhnsN9TFLdktQZ2Fq9OSE8c0DxcEC0uBsH3ccuKIZmsFJs77\n19DdrWlv97h0yX/m+3o1AzsMiwuSW7e2/S/HxjxmZ/2sslQqsbgIR47A1BRsBSXm1lbLkSNlLl4s\nsRbIHvf0QEcHXLwITU2GnTtd0mlDKiW4eHH7GR0edujqMkxObrG66j+H+/dHcByYnCzR26toaDAY\nYwmF4MqVbQb4xz5Wx2//dguf+lTz+2Jh+LQX5h//8R/zmc98hmeeeeY9HfsnIX4KmO+Txdc7iUrm\nB34f1fO891XvtRLv1ay6MutZLpeJRCLVmc4KWw22B4vL5TLFYrE6n1VrWquUouho/nviMtdDy9Xj\nP03s6TBJ6k0Dl1WRQkDSGTaBjF0QAybBugicS0wDN6Wmx0S5ofLVbQ7oOmZkjoB3wgGdpGRjvO48\n2aO8IEvV7HPQOGChzkQ5axQKwYGniDyHreQehiJwqBzh9macRgRX9DZInlaai1pSQhDB8jEsK1nJ\nZHGb7OMLEGwzV4+GNU0ly/fXFa4VxKTlaMJwZnMbFA7XaaSG0pZgOiNJOZbhp9xEjiTLLBQVO6Xh\n0qJD3LEMpiwTNQzYE22aW2nJnrjh4arA1YKBevMEA/Z4l+b2uqQ/ZsisCTZLgsEmw/lHNSDVq7m/\nJulLGlZXBZsFwXCn7yhSiYPdLmtZQX8KbtxXlFw4utPPJCsgOdRtiDqWOgNnr/mOIif3Ga7ckeSC\nbLer2TDcrZmZUTwOwG10WLO4Jphb9n/e0WnY22n43qvbjNeBHkNjveXytPIBepehXIC5BcFckLnG\nopbRo4ZrNyUHBg0XxiWNDZbePsu5c9tygwcPatpaNa++GqJU8slLo6Mu8/OK+XlFKqU5cKAAaK5e\nhc1A/7ChwbJ3r2ZtzRIKlbh+3dDVJejrk0xM6CC7tPzMzxiKRZfXX98GyV27JKmUZGnJo7W1zJUr\nRfbujRCPCy5d8ispjmN5/vkwmYzL+fP56vXu3h2hocFB6zJzc1mWlsrs2RPnxRd7+dVfbSccfndt\nmjfzwvyd3/kdfv/3f5/9+/e/q2P+JMVHGjCftvj6oAgyT0cmk6n6ykWj0R/Yz3yv8W7Nqq21FAqF\nag80FotV1ZCeBkrP8ygWiwghiEajT5R/K157Wmt/cWI0/xS/wb/WzVa36dYpsqJMi01xV/pg1GOS\nzNQQe2oVeqJWMaibWX1qROSgqeOqzFXBt9dEiFlFkSiXlN+XO2AiXFTbZax9OsSc9CgC+7wYMyZM\nm5VcecJuS3JVGIrBfOZpN0w6G+P1oEwqsDzjWM56ospK3SUNnRbuZxSPy36Pcizqg2TlhXYgYlj3\nYMBYpjd8jdWDdYazW9uAM5rQzBYlylp2GsuttGRXwnB+owbcGjUzW5KMCyfqDBsZSDiGS2s1Wq3N\nZWYyDpueZHedpsFYjBVcrAHJk12am2uSdEnQEzf0ORbXpVpuhW2QXM0L+lKGzrC/qKkFycO9muVN\nmM8ohts8VEnQEOcJkNzTZRDCcntecmrAcOOOZLjfMHlXkq2Qghotfe2GxRVBW8Ry8bpidFizvCF4\ntOj/jUbDluMjBkpw4aIkXxT0dhnami0XazLQT532WHgkmAw+i0QsY0cNV6Yk2Zzg0LCvQZuog/Fx\nWWXY7t1rcByLo2B9XfDwoWRsTLO05P83+BZdzz+f49Ytj/v3Azu1lGVkxHLpks+RGB0tMTvr0d8v\nmJgwBGt0ensF/f2GjY0i09P+h4ODDk1NkomJMkpZTpywbGyUiMUEly5ttw527QrR1SV4/DjLvXul\nYN8ozc0hLlzI09zsMDBgWVoq0tMT5cKFDIF0Njt3RvjCFzr47Gd7qK9/Z4vpN/PC/NznPsff/u3f\n0tnZ+Y6O9ZMYPwXMADDT6TSJROJ96/f9oPPVAlFtH+CDiHdqVl0761kRRZBSvgEoK8ziYrGItbYK\nlG/nXqy1vK4e8LXIRTwMfV4TaRvGFYL50DYA7tUNXFebmOCYPSZOvYlzXRk2hPFl7Ey8KogOsFvH\nWJRlHCtotSmmpaTPhLha06M8osPckOUqAI7pOGkvzPlgnVTpUZ4XvooPwIAVtHiKpVyca8WwL3ju\nWF7zBBUA3IvHBpImCTInuZ9XHIoazha2X9xHo5oHZcmaERwNa4pbkLBwPlsDgEnNzZxk0wiiwnI6\npMkXBePrNWXSJs21jGQruMDjSU3Khe8+rtmmXXNtbVsofVdSsyPk8b374SpwHe8oc3PdYTMQP+hN\nGEaS/phIKdhvrFdzb02yFvQtO5OGwy2af7nqVLc53BtYagU9ye6U5lC75dsXt0dSdncapLTMzAW9\n1W5NR8xyblqxVQOSAx2GczcUkZBlbMBQzMHyuuBhAJKRsGVsv+HCtGSox5BZFngedLRZLkzVfNcj\nGuOBKMLlK4pw2HJ81DB1TbIZlEh37zTs6jV86yXf5xJg925DLGaZmlK0thp27rBoDaurgtmAqes4\nlhMnDOm0xnFKTE5aEgk4fBguX4Zc8EiePFkiGi1z5oy/+ADo7hb09AimpjRHjmgmJgp0dytaWwUX\nLnjVkZJnnpFEIi7/8i/bz/fgYIimJsXNm0VGRuDcuS36+sK0tCguXy7UZKt1eJ7m3LkMpZJ/wNbW\nEENDcUqlMnNzGebniyQSis99rp///J930t//9tyT3gwwP/3pT/ONb3zjA7cs/HGInwLmO7T4erfn\nqdV71VoTDoffszzeD4u3a1b9ZrOelbJqxQOvApRa66rjSjQafdfEpPtina+FbjPpBO4lVrBTJ5lx\ntv0pB8pxFh2XDl3HvAyxKf3MsVahp7b8GrOS3bqBBeFwIxgREUH59ZIsVbPPPuPQrB3mbJhbyDft\nUe61knUMYStJ5eJM5iIcdCzjNT3KI1Jz3wjSSLqEZUfZn6u7UKwpgcY014uSrYrPYkTTWrJ8e3V7\nYXYqqZnMSvLBNl1hw7BjuLEsmQ96mc80ay5tSArBTXRHDV0Rg5MXjC9ILIJn2jWXViWFAEi74obW\nmCVpYGpOslkWnO7WTC1Lsu72mEhXQuOULA8XFcs5xViPy+01RTogCTXFLXtaDbYMs3OSpU3BkT7N\nUkYwnwnIRmHD4V4P6Uomb/sgWMkkKyApheUT+zReDl6b9JVxakGyEi8c9lheElwOPqsFyWJZ0NZo\nGGo3FAuCicma7Ha/Jp0RLCwLxoYMVy5LDh94EiSbmyx7d2vwBFcvSzY3Bbt2GerqLJOT264in3pB\n8+CB4Pr1QEBBWU6eNNy6Jchk4MSJAteuafbvh8lJ2AoKIk1Nln37PDzPZXzczxqfLsEeOKARokQ4\nDBcv6ipI7tzpA6dSJcbHcxgDO3aEaGmRXLhQwloYHXUol0vE44ILF3JVwlB3d4jBwTDpdJ6pKb89\n0dzsMDQU49q1HI4j2LVLMD2d4fDhBmZnc8zN+QvUhgaHf//vO/iVX+njxIkW3io8z6tyGSrxqU99\nildfffVDqc79qOMjDZjvxOLr3UQtUFZKm1LKtw1k7zVyuVx1hvPNota2rDIe4jhOtZRaC5SVe/E8\nr/o9vdfsOE2Zv45MMa3S1c/26QZmZBotoF8n8UwdawLmHH9hIyyMuFGuhopVVu2AiZAyMSaVYk34\nJJ1DJsyFmsxyrw6xJD0SVhH24ty0kmEruVBTfq2136q3gqF8jHQhwoRXk7k5hklPkA9OvkMa9niC\nlzcUJRuAW0xzoeD3MQF6HEObssRcOLssscAzKcO5TYkbbNMXMcSkRXig8oIbGcHpZsO5dYlrt8UE\notIym5OMxQyTC5JDzYbzy/5cJUBfwpAIWa5vKI7U+wDSlbBcWqgB0oShNW6ZXFbsThmiRUiE7BOz\nlM1xw0Cjx8W5MDvrXWKeIKJgPu3rvQLURSwHul3O3Qsx0mHIpQVhBdrA7YVAxUhaTu4xTM1KDnYa\nrs5IYhHoazdM3Nz+Xo/s1mgPQmW4OK3eAJIAfR2G4R7Da68rckHGe3ifJr0pmA3UdI4Na1Jhy4XL\nqtpHbG6y7N1jOHtesnvAQEmgPUgkLVeu1GSlRzUhx5JOS2ZmZFASNdy+LVhZCY5/rER9fZnz520N\nSMLQkOHiRRgddZmeLpFICAYGFOfOeVVQGxkR9PZ6fOtbeSpeDwMD29nlkSOWubk8sZigtVVVQRLg\n4MEQnZ2G7343XT1eZ2eIgYEwU1M5Dh+OcuFCmmTSYe/eOFNTWTY3/Q1Pn44ihMvdu3kWF/3yrVKC\no0friUbh1q0NlpZ88BwdbeKLX9zDL/9yL6HQGwHwaS/Mt2Pt9W8pfgqYAWC+0/LlDzvuW+m95vP5\nKkB9kPFW56kApbW2CpSVDLIWKGu1ditZ8fv5h6ExfDV0m6+HHlU/26+bKBBhIgC8iBXsNjGu1RB7\n9nhR5mSJLh3jkYiQkZJerbgeqiHp6DA3g/Jrk5X0uXWsGodrcvuRP2EUl4WuEoT6rKC/GObVrTgZ\no960R9mHJiIFrVYws6FIe4JTMcPrNUSeXSGDAeY8wZhjmF6RjNQZXsvIqlHz7pjBM3C/JGlThl3G\nogy8tlazTcKgDdzL+y+vk3WaOm15+fG2ks9gyiAF3A6yvYG4YW/M8L37quoU0pcyJMOW6dXtMZET\nTZozt1UVJNsShr4Gy4WgtNsQtZxo97hyX7EUgGQiYtjf6XJu1ncYaU9o9jVqHi4r7i5ty9mdGjJc\nuivJlwUjnZpwGaSCC7dqAGq3L7awmhEcHzBM3ZAc2G2YmJaUgl9Id5uho8VSzkNuQ3DvgeTIfs1G\nWjA7F7CYHcvHxzTFtODM2eD+Gi3DewxnJ6TvO5m0jI1o1ldF1dQZfJBMbwhWVgUHDxgmJiTHjj0J\nkvG45cQJD9ct8tprgaRjI+zbBxMTlnJZMDjo0thYJhwWT4BkX5+ksxOkdLlxo0g6bdixw6GtTXL+\nfBlrob1dMDSkKZU0588XqiDZ1+fQ0SGR0uXatSzZrAlAMsKlS1lKJdi3L4JSLsmk4tq1LJubPhLX\n1UlOnEhQKhU4c8an5ColGB1tIJMps7ZWYmAgxIUL6wwN/f/svXlsJOd55/953+qLzeZ9k8PhOTyH\nHN6cQ4fltR0Hu9kL3iSAgRhxYlsBslnFiWML8P4Ub3adGHHstR3E2CNIAuSPbBDsAQRr2ZatyJoZ\n3ucMjxlySA45vIZsks2jm91d9b6/P6r6GGlGthSNJK/1AAMBre6qYrNZ336e53sECATcTE7uY1lQ\nWOimrS2DK1dK+NVfbaaoKHX/eFQW5rVr1/hZqJ9pwARbLwg/+fjyjeon9XtNAFX6HuBx1MPO8zAt\nJTya+RqNRnG5XPh8vsc6cnnZ2OBv3Mtk6izGpUmOdpOnUyHO8KBBeo3KQKkAe1Ky7Ji3Cw2dpotJ\nl5kcv9aYBgWmh+vCQ1gIDG2nhgwKK9mh1mtJBEWx5WbpIJMt06DXpR8Icm4SJgdasIVBp1SEjySF\nCK6l7SjPexW7adZ2lz0WGRHND9KYrG2Zip04bDl7wzxDc8lj8g8bLsJOB3jeMUVfd8axPqm5kmux\nExRMO/rK5lxFxIQVxzXGLTWXixXqFIbWJDFLUJerMCTcdoKQpdBcqVAQ0UzfNQidCsqzFcUBzeTG\ngzIRt6W5uWywHxbkZGhayh9kwLZVxCl0a4bm3ISj04h0ZgAAIABJREFUAreh6amLMb7kSe42W8ot\nzmZpXryW+vl7mizW9wSbzjX111sEXJofjRrEndedKVEU52vG5wwKszX1RYpYFHb3BKsbKZDs77TZ\nreerFeNjkgwfNJ6zGBhOGaHX1yqqyi2mRl3s7jqs5C6L/T3BsrOTvHjRwuuBmRmZfI7fr+nqUkxN\nCdraoszMxDEMGySHh0kSaM6etWhujvPyy7G0xyRlZYLhYYvqak0gEOPkRFFUJBkaSk096uoM6us1\nAwMhDg/t23B1tZvSUjfDw2Gqqw18vhiHhyZnz3oZHT1KnqOy0qCpSTI0lALJQMDgwoUAd+6Eqasz\nGB/fJR7XdHXlsL8fZ2HhxPl5szk9jeFyCcbH95Ldbmmpj7Y2P3NzO9y7Zz/X45H8i39RzWc+00JP\nT0lyhZUuLfun//SfcvXqVX4W6mceMBPfmMJhu3t5KyD2Zv1eEzvAdGr246j087yRlvK1QBmPxzk9\nPU1+gXgrLkNvpW6LMF/0LrMl7buCSwtaVSZTaVrMditATPu46rI/tl4taFVuxtPGr82Wm/vC5Izy\nMWu5OUbSZMFE2q+kzYJVCSEBjZaBOs5Exl0P6Ci7DcWCBYeOHvO8VFREBd8NpTFQfRa3o5KQc4PO\nkZpOt8XuseCmY1PXG7BYjMiktV2OoWnyK3QU7u0JNk4l3bkWK2FJ0OmsAi7N+WzFwqGk0VAMbkja\n8hXbYcGWs1vMMDRdhYrr25KLeYqFLUmRX9tA6nSbLqm5WK4YXJe05CpO9m1z84BHM7OdZqZebXFz\nU1KZpYgfC4JHgrpixfDygyAZPJGUZEBwV7B9IOg7pxi8JYknbPsKFfmZCr/STM8bnEQk3Q0x1u4b\n3D9wfFl9movNFkcHghGHuXq2TJGfZkIgpebnui3uLEpuO+xTj1vT16GYuCk5iQja6ixkDPwZMDCc\nYiCfq1P4vLbmMsttE3i6uyyCQcHK3RRx5wNP28YC16871+WA5MSE5OREUF8fJyfnFJ9PMzxMkrhT\nVqaprFTE4xbb21E2NjRVVZLSUsHQkN1aejyap57SHB/HGRxMB0kXBQWSvb0YHk+M2dlTams9FBUZ\njIxEUAq8XnjiCTfRaJyhoaPkeYuL3TQ0ZBCLRbl795Dt7SjZ2QZtbdnMz58SDJrU1rrweGJkZ7sI\nBmPcuZOayly5kktGhsVLL20n36vy8gyqqzPZ3g4TCJhMTe3i8xl0dBQSDJ6ysBCioSGHr33tIt3d\nBcnpk2EY/N3f/R2lpaX81//6X/nOd77DG9WLL76YNF7/9V//dT7/+c+/7jm/9Vu/xXe+8x38fj9/\n+Zd/SWdnJ2tra/zKr/wK9+/fRwjBpz/96XfVgu99wEyL+HqzIJYOlG/G7zUajRKPxx8Q/z6OSrjt\nSCmTWsqEhOXNSkTeqTrE5EveFUbSZCXnrUzuixj5OotBCdkYFCuD+TTzgS7Lw00ZIyagxfJyYvqI\nYTAnUjvK145fm01B9pGH70Wzks+5JE3GlEHMuaGUCUW50HjjksF9A4V83Y6yzKUokJodS1KjFIM7\nksvZiokjScQB0hK3psSjmD4xaHJbGGFBlqG5GZIcO2BT4NFU+xVjBwYuNBf9CisKtw7s5BCAbLem\nJS2CqyXLolBoFvckG0636TM0PWWKa/fs0W55hqIhQ7OxL7i9k+o2L1Upxu/ZaSLFfkVjtiJyKhhd\nSRtZVlms78H2kUFFtkWFGzwuGFiQWE4bX1OiyPRobq4ZtJc7xgG5moU1SdDZIwYyNG21cSYWXHRW\nxpm46aG0wCIQgJtLaYbqrRZYmoNtycKyxOfV9LQrxm5IIo4us6FaUV+q+L8vpswcGs8p3G7NzVnD\n1la2KmJh2NoSrK49yG5dXBScq9eMjkpcLujoUIyN2S48AGfOWLS1nfLyyxanzoCjogIqKjQjI1BY\nqKiujrK7qygqsjvJRNXXSyorFcvLEVZWTOcxF3l5tlTE54OeHrh/P0purmRkJDWCrapyU1dnsLx8\nyPKyPfkqLXVTV5fB+PgRgYCkuhpu3z6ivT2bmZkj9vYSDkAGV65kc/v2wQMg2d6ehdaaQEAxOblD\nJGJx9mwmFRUBpqdDhMMmly7lcPv2LufO5bC5GWZlxSHiuSUvvNDDpz/dgs9n39cS9zqtNZ/97GeZ\nmppibm6O6upqLly4wIULF/jkJz9JRUVF8hosy6KxsZGXXnqJiooKent73zDaa2hoiH/37/4dg4OD\nbG1tsbW1RUdHB8fHx3R3d/O///f/fuC172T9zANmwqXmzYBYOlkGSBqP/6S7vcSoMysr68c/+S1W\nwpEj3XTgYUD5j5GIPK5SaP7cvclfu7bxIqlT2Wzh4VDApsNkNTR0vcYgvcf0EVNefuQ84NLQ85Dx\nq9CanKiPV0MZKAQXXYqrZqpDqcMkBtzHoNuymA25Oe/RXDs1krvFxI5yKS7xC023YSEj8GoolWNZ\n7VW4BSw4o9UyQ9HhsvjBhouYA6RnMhQ5Ls1Mmv7y5/NM7uxIbjsyjUKfpiqgGNtNPefpYhOi8Ipj\nFB5wa9qLFdfX01ijRTaYXr1tcGoKO5eySjF4VyZ3m9V5ioYci2tzLk4cUO6rsVi8L9lz7O0KMxV9\nZRY/HHNx6rBrz5UrpEtzyxnllmUrLpQoBm4YhI6dTjpT01qruH7Dfm+7aixkHMIRmE0b7/acj7Oy\nKTEtQWOxyc05Nx2tJiNTrqQJQXmxorJc41Jwc1ISOhS0NNnONvNpe9GPfsBk465g2pGYeDyavj7F\njZt2oPOFdotYTFBQoBkZkcm0kOJiRX29JhaLs7ERY2MDKiuhrMwewQIIofjgB+NEIhbXr6dyURsa\nJIGAYGXFpKHBZHDwlMZGF4GAZGws1V1+8IMutI7x8supiUlNjYfiYoPbtyM0NUkGBkJUVHiorvYy\nOnrsyEI0zzzjR+s4k5OHHBzY587IkHR15WBZJhsbx6yuhhECurpyiccV09OH1Ndn4HKdEospiot9\nTEwEiUbtv//m5gClpW5u3w6xvp6Sr7S3F3D2bCaf/3wnLS0P2oXG4/EHrDCnp6f5q7/6K5577jmm\npqaYmpriN37jN6iqqkq+ZmBggC996Uu8+OKLAPzRH/0RAF/4wheSz3n22Wd55pln+KVf+iUAmpqa\neOWVVygpKXng/P/yX/5L/u2//bfvShYmvA+YScD8SUHstWSZtyKrSBzjcaSjpO9RDcNAa012dvZD\ngfLtkog8rromQ/wnzyErDknnYfmUbZaHQ6HINDMY0JIA4nUpIgmHngjQEfcwH8qkXIgHxq+dhsWy\nZUtEAJ4QCndY8PJJamJw3hVjyzLY1c4IT2iedJlM7RlsRe3XtfqdHMtYytquP6DQERjfkYQt8Toi\njyE0l/IVW8eCQEwzuWNQGVBkuzUzaSYFl0ss5vclLT7F+JokwwW1+YqRtNFqZ4nF5rHgrFeztiU4\niAi6KhTXV1JEoroChcvQ+AXs7QpW9wSX6hQ370kOnS4uN0PRUGqiowbr9wQbe5LWs4pIFJa2UwzY\ny80KGYfRG/aYtCBHU39GMTSTxixutsgUmpeup+K7LrYrbi1L9g5t15wn2y2kgleHjaTna0WJRVGB\nxeSsx04UiQi8bohEYfFOSgLS36MIHUCmAaMjBj6fpqdHMTUlk7Z0tbWKxibFS983kt6wZWWKqirb\n0aekxOLMmVOCQUVhIYyMpD6H9fWKkhKTYDDO/Lz9ha25WeL1wuSk/Tm7eFERi8WxLM3UVGry0dTk\nJicHhDhlcNAGpXPnPOTlGQwP21+4+/vdHB2dkpNjMDJylDQ2KCpy09bmIxQ6ZmzMdrvKzDTo7Mxm\ncTFMJGLR0uJleDhIV1cuJycms7N2d+j1Cp58MptwOMrw8A6maf8N5ed7OX8+F8OwuHZtnVhMIaWg\nvT0frTW3b4f43Ofa+Y3faMHjcWMYRpL8F4vFME3zAYb8//yf/5OrV6/yF3/xF4+8d/zd3/0d3/3u\nd/lv/+2/AfDXf/3XDA0N8a1vfSv5nF/4hV/g+eef5/LlywB86EMf4itf+Qrd3d3J56ysrPD0008z\nMzPz2Kdzj6p3fub2Hq305JKH1dvp9/rjzvVW6rV71KysrKRRQsL+L10iknjc6/Xi9/vfU0CZqCsq\nh29H/Tzn3eWWjHMsNDdkjB7L1lX6ERjKTUh5OAa00BwB40JxURmMCgtTwKRQXIl7CB1n8FLUBsB7\nwBWXYsQUxBBMWAYlQvGUsNg9NrgatslQF30W06eSMIKbpocCqehwm8QUmMfw3WM33RkxwtLFoZLM\nhCXZhqY/y2LoyKDTrVjcFJR4NQGXJmwJFo6lTeQpsLgWlGRJ4Bg8YQg5xJe1Y4khNE+UWgxt29KS\n+CmcsTSHxxCOC8JxCK4b9FdY3DqwXXqOwoIKpTGisOkwW6+tGLSUKMIxzcq+Ha6cp8DngrmQncpx\nfdGgJFtRV2QyseYm16uJBg0kkPhozKxKPC7NEy0Ww7clLWWKtSVBNAbNVYrReYNgSBAMGVyotziO\nCMoyNWPjkpgJT3RaTN+WHJ4IBqYMcrM0H+w12bon+ZFDDKqpVGRnKaZmDda3DY5PJB/qibO4IFm5\nm9pv9vfEWLjj4vBIYFiK+3cNmps1GRmaSERw9apBQYHmyhUTENy4IVn6vy7OnFGUlyuGhw02N+3k\njw9/OEwoZDE0ZP+cy8vQ3AxSWiwvC0pKIgwORmludnH+vOTmTcXcnA2UTz0l8HhivPRSipx2/rwb\nIeDGjTh5eSZzc8eUlrro6spgfDzCwoL9ha+nx0thoeJ730sRb8rK3NTW+piePqapSXLt2iY+n+SJ\nJ/KYnz9mdzfO1av7XLyYhcul2NpKmLjvA9Damk1RkcHdu0FeeslmnhcX+2hoyGF2dp/SUi/37u2x\nunpEV1cx4XCcmzf3mJwM8tRT5QwNfYSamuykO1csFnuAOb+xscErr7xCa2srg4OD/P3f/z2f/exn\n3/Dv+Ce9t7z2npj+uuPjYz72sY/xjW98410DS3i/w0wmlpimycnJCTk5Oa/7/2+336tlWRwdHZGb\nm/uPOg48ejwMJPM0E8bo6R6vHo/nsVnyvd11iuJLnn3+j8v+hu7S0BcPMK9dLDmX79VwQUuG0zrL\nRi3JsAQHx36mTr1pDj2pztIev0q0EFTEBGMhg0sZiquRVEdW7Va4gYW4pMKlqIhrPHEe0FGWuhWF\nLsXNiP3eN8g45ZZi9MDNscOazXVrzgUUI07XaKD5cI7Fwo7kzmHa/rFIcXUrNSK+UmjiicLLy06H\nhuZKpWJ0Q3LqdGO1OYrGLMX3Zo3kbrGzwmLzULB15DByfZpL5Rb/cMMg7HRZZwsUOT7NDWeUG3Br\nnqg0mVww2Np3ZBVeTVed4vqcbW9XmqNoyFccHAmmF9Os/BotNnbtCK6uGovQrqC8SDNyM6WlLMzT\n1J9VzN+RtFQoBkck52o0hlszm3as3nYLv0tzc9IguCdwu+1OcnpGJvWV3W0mORkWr/7Ik+waS0os\nqqoUw8MuGhrs7ikatQ0FxsZSx29uVhQUxNnejrKwYD/W1gamCXNzzs/THcXtjrG/nwpsBujsdHF6\nCoWFcYaH7bHphQte4nHJ7Kz95bSqSlBVZbG/b3LjRgpMGxq85OQIPB6TiYkQ4bDi7FkvZ854GBmx\nCT6trR6EiJKX52Z6+pBQyD6mzye5ciUHpUxefjnlydzRYd+zlpaOOX/ey8DAFhUVfqqqAkxP73F0\nZOL3G3R352BZFjs7pywsHKT9PIV86lOt/MqvND1wP0h8sVZKJe8VMzMzfO1rX2NycpK7d+9SXV1N\nR0cHfX19/O7v/i4Pq8HBQX7/938/OZL9wz/8Q6SUDxB/nn32WT7wgQ/wy7/8y8CDI9l4PM4/+2f/\njJ//+Z/nueeee+g53ql6HzAfEfGVzip9u/1e3644sfSuNz2VJP0bIaR0ofF4/IFEkQSIpv97LwPo\n37iO+D8yworychdBoRYUI5hNI/b0KoObwiIXQeGJn5kTL7USxtIM0rukyaKSHCLJRtOpIB6RXE+T\niLR7LbZNwbbzugKpuShNXrrvIpqwUctQxBWsOONYieYDWRanx4KBHYdw41PkuBRzx6lhTl9uHDMK\n+weS5SPjoUki7QUWkbigWGkG70oMCf3limtrKa3n2RxFjluTLWFmTXIQEVysspjbloSc0WqWV9NW\nZpOH7m4ItkKSxlJ7JLzoGJcLoemvNjFMwe0lg52QsPePlYnILftYzWcUZ7Isro27CDu7v4ut1gPk\nnrpSRUOJ4vtX7VBosPeP5UWa0RkD0FxqVsTDcBASLK6kruFil2JhTZKdofEDi4uC3i7F2KQk7BBy\n8vM055stzGPB9Wv2+1VZqSgt1YyMOKAfUPT0xAkGBTdupIxIzp83iccFm5uCtrYIAwMWHR1weAiL\ni6nP2ZNPmrjdUX74w5TvcG+vi2BQsbSkaGuD4+MIBQWSgwOLxcXUPrO720t+vuJHPzpK2tKdP+/D\nMGBqyt5tam13hYWFbkZGjpLdZW2th8ZGF6++ep/j44SeMjGCPaGuzsvU1B7hsEl3dx7hsMnMjD2C\n7ekJEI+fkpnpYmxsN7mnDARcPPFEEVtbh0xOptKBWlvzCQTcFBb6+M//+UnKy1NdW2JalTBcSTQJ\nkUiEP/qjP2J6epo//dM/pbq6mlu3bjE1NcXW1ha/8zu/w8PKNE0aGxv5wQ9+QHl5OX19fW9I+hkc\nHOS5555jcHAQrTWf+MQnKCgo4Otf//pDj/9O1s88YL424is3NzeZ0PG4jNET58rPz3/L1xwOh9+0\nltLr9SYlIq81Rk/8e6+D6DQWnzbCrAr7Y2to6NMGAw6xJ0tDW9jPUtjLLSstRus15gNnhKJJw/iB\niz2n40wfvwLkSU2dR+FVML9rSz66AxbLp5I9Z3Tql5qOTMXEsaTbUIzvSM76NWETViOpHeXlfMX1\noKTcoyiKa7ZPBDluxWyaRKWvKM78gYvjOFzOUSzfF5zN1gykEXmaCx395YGkLc8ieiwoDmhGViVR\nB6CKMjVV+YrRNYP6XEVGzAbz3XDK79UlNX3VMUbveqjKUXiitoFAZZFidCFNSlKtOArb3WnwvuDe\nfcHlVsXUokx6wOYENG01FkQFY1OSSFRQe0YR8Gum0wg5H+w1iYYE14bT7Oa6FDdv2SSezAxNd7OF\nNgWDIzLVNRZrqqsUw6OSy52Km1OSwgJN1mucetraFIWFitlZg+1tp8vutAiFYGnJkfj0HiFllI0N\ng7W11Ii3u1uxsQHV1XYqSCSi6etzce+exb17CbMCTV+fZn7+lLt3E2sOe7QaDFr4/ZqTkwjLy1E6\nOjKIxwUzM/b41e8XXLniYn8/yuhoimCT6C7j8Sirq0dsb0fJzXXR1pblsGBNamo8ZGWZ+P0udndN\nFhdTr+/tzaWgQPO9760lgTc/30tray7r68cUF7sZHNxECOjsLEJrzcTELoWFPr761Sf4N/+m/oG/\nr0SjACQNV7TWvPrqq7zwwgt8+tOf5ld/9VfftCb7O9/5TlJW8mu/9ms8//zz/Jf/8l8A+MxnPgPA\nb/7mb/Liiy+SmZnJX/zFX9DV1cXVq1d56qmnaG9vT96H/vAP/5CPfvSjb+r8b1e9D5gOYFqWlUwR\nScgvHpdQ/63mbz6s64WHA+VbkYj8OBBNB9N30zcyhOa3ZITvy9Q3+04l8cQMxg4DBJXx0BDnJmES\n0pIyCfuHBmunkovO+JW08asLWIxLOjwWxyFBiaEZOZRJqUmRW1PhUUye2Dfcfo+FJ6a5GTLYd27y\nfkPTkaO47pimZ0nNRb/F8p5k8TAl7bhcYjF830ha213MieGOKV5dSxlodJWYrB2mAqDPZinO5yhe\nnDGSRurVeba0I6GtzPHaxx69bbDjsFb9Hk1ntcX1JZvtm+NVdBcrdvcF02lSkt5zFnd3BPcPJBV5\nigq/xmvA0Kwk5nxRKMnTVJUqhucMOmssgluCgB/iJizcTb3nF9stNncElbmagWGJy4DeDsXYdEom\nkp9ru/BMT8hkNuXZSkVhgWbcAcRzNYqSHM1ekKS/KzgmBPu2AXthoWZyUtLXp7h3T7DuOAEZhuYD\nH4hzehrm2jX778Tlgt5euH1bEgxKGhqiCBEmL0+wuKjYdZoxtxv6+twIEWNu7oRgUGEY0Nvr4969\nOPfuWWRnC9raNPG4RTBocudOipTW3p5BXp5kYeGQjQ378XPnfOTnuxgePqaw0KC6GlZXTzh3LpPJ\nyVCyu7SlIpnMze2zspICyQsX8hwZm2ZmZodQKEZ5uZ/a2iymp/c4PIzT35/P6uo+VVVZhEIx5ub2\nk69/9tlWnn++h8LClINPgiyYYNUnOBp7e3t88YtfJBKJ8I1vfIPS0lJ+lutnHjBN0+To6IhoNJpk\nlL4T+sM3Eyf2WvP2R2kpHyYR+ceayT8KRBPi5fR/7ySIajR/JmJ8RUZptVysHQY4jRvkSc1s2vi1\nT8S5oV1EENRJRX5EQlwwkmaQ3uG1uBeX7CZGrW7FOVPxf3dSn4N6nyMjcSQiAs2HAxZb+4Jpx6Cg\nxKsp8ykmQ2ngk2uRYWpmtgyCp4IMQ9P9mh1lfbYtLREnMOp0k5cqTKa3DU4cgMrxKhpy47jjgvFV\nN6emoKXE4iQmuLufBsBVCn2qmVs22DsR5GdqzpUqhtJkHM1lJqUBzeSci/1jm6V6qVFxc1Vy6Hi0\nFmZr+qpM/mE4NX6tKlXkZGqmnWOV5yuaSxW37shkTqVhaC61qyS5p7/ZYmtNcKZMMzgukwzY8hLF\nmTLN1ragwK+ZmDJoqFd4PLaWMlH93RbZXs0PX0qxZ/v7LdbWBBsbErdbc+mShVKC+fmUU09CTjI/\nL2huDjMyEkMI6O4W3LihCTkRq4WFit5ei+vXI8nHfD7o7JTMziqyshR5eVFu347T3e1lYSHOzk4K\ndD/yETcrK2FmZ52kHQE9PX4ODiz29uLU1xsMDR1y/rwft1swMZEAPs2HPpRJPB7j+vW9pDlBTo6L\n9vYsjo9jhEJHLC0dO5Z2eRwdmczNHVJZmUF+vuDoKEZpacYDI9iqKj+NjZksLBywvJwKMmhszOXs\n2SyeffY8H/1oSvIBKZ5GQkueSCj6X//rf/HNb36Tf//v/z2/8Au/8J6aNL1b9TMPmNFolOPjYzIy\nMjg6OiIrK+sdcbY5ODj4sedK96R9o1zKdImIUgqv1/tYJSLpIJoOpsBDx7mP8w9t2FJ8PORlwwE7\nF/p1usp2qSiJw0v7LjQpg/SRSKprLDQ0dW6FKwaDOxJLO+PXiGTPuVEngp3vnAiqLM3wrqQ+oB+Q\niAg0VwoUw3uSRp/i9Eiwfypep6PsKLDYPBEcxwWdmYrJe5KOEsX1tB3lmSxFnk9zY8egt9BiY0dQ\nlqVY2ZPsOufzujRd5XGGVt005llYx4JIVJCXqZlOy7LsOBtjY9+gwA/qRLC8JehvUAzdTnWNRTma\nmmKFFYPtTcG9+5LmakXchMV7aSHZ5y08SjM8bhA+Ffg8mt7ziqEbMqmbvHDOoixL8+IPU+YCtWcV\nWQHN1Kxtrt7Xojg5gtCh4M5y2pecHovVNcHZEs3dRUkwCP39irk5yd6efSyfT/P00xZ370rm5x0z\n+EzbqWdsTBIOC9rbo8TjYQoKYHRUJ00IcnI0LS0a07RYXY2yva3IyRG0tbkYH48TDtsmB088oVHK\nZGLiNGm07vNBR4eLYNAkMzPO5OSp0636WV83WV21u8jLlz1YVoyjI50EU4DGxgyKigxCoSNu3LAP\nWlLiSXaXABcueJmY2KWjI4+NjTArK7YRgZTw4Q8XcXgYYWho54ERbEtLDlJaTE7e5/DQvoaOjkJc\nLsnExA6f/GQzf/AHF8nKSu1007kN6X7S6+vr/O7v/i6VlZV8+ctffizyt5/W+pkHzHQD9lAo9AB5\n5nFWKBQiMzPzod3sm8mlfBwpIm+lEjFgr+1Egdd1oVLKt/UadxX8+pGL78dTN90OabKlDM4B43v2\n6LLLpx7wfj3nVsSB9big3624uSs5n6EYPJSYzk2+2G0HJU+dGPiEpsdQxGOwcCTZc8DBJzU9eYqr\njs9ruVvRYCjuHabGr2DrKKeC0u4ateapfAsjDi+vpD4D6TtKsI3V6/2KHy0aRBxgy8uw47aGVu3z\nFWUoWrMtVrcFS7sprWNfTZyZdRfHUUmBX9Gcr9EWXJtLG0EXK7IyNDfuGlTmK4o8GqFhMyjY2HX2\nnYbmYqti/JaksVwR3BaEDgXnzymuT6YClytLFaUFGq+CoVF7B9naqIjFYCENED/6hMnmPcHUzbRd\nZo9i9pZk/0BwtkJRnKXxeWF83AY/sIOZ29sVd+4Iqqo0g4O2dKSpSTE0JDGd9+fcOZP6+jDf+17K\nBL2kBGpqbKee4mJNWVmU9XWT+noXQ0PxpPaxsFDQ2Ql374a5fdtu+3JyJG1tHiYnTwmHNZcvG8zO\nHtPU5OXWLVu7af8c8OSTPkwzytWroeTPe+FCAK0lc3MRLl60dZNlZV7Ky32MjOwnu8vLlwN4vRYz\nMyHu3091rF1deXi9gmDwmFu37ONWVPiprs5iejpIXp6HnByYn9+nq6uI4+MYMzP2CLa+Podvf/sD\nXL78YLhzglnvdruTEyvLsvjzP/9z/vZv/5Y//uM/5vLly+93la+p9wHzMUd8Paoelr/5Wqu9hHn7\no+K2Eu5EjyNF5O2qh41ztdYPHee+1eu3pTUmf3wCX7H8KKBPaI6ODKSCm7G0gGafxXxUcujc5C95\nLfwRzQ/2UqDVmKGIWLDqmA8IrflowOTmfYM1Z49Y5NWc8Skm0savfbkWmTGbpHNqCTxS01esuLaV\nkqicyVRUZyj2gpJZx6aut9zizr5kzyHR+FyavjILFRYMLktMJTibq8j2aW5upZ3vrJ1cMnLL4PhU\n4HFp+usUAwsyGdxcmm1xvijO0KyHI+faWyrqTgm5AAAgAElEQVRNwlHBisPKzfBoPtBgMnbT4P5B\nmpSkUTFw07bAK8tT1OVrolEYuZm6hqYaBWjmlw36mixWl+zx6+a2YN0JfZZSc6lbsX1fkOfWjIw6\n9nXdyiYJObvM4gJFT5vFKz90cXKScuCpq9MMDkrAHr8Gg5rcXMHQkAHOxODsWUVxsUr6sx4cQHW1\nDYCjow5BzFA884xJOGw+4NRz5ozkzBmD+fk4LS0mAwNhiosN6uvdDA+fJgGts9NFUZHF9etHHB/b\nx/T5BD09fpaWotTUwOjovmN4nsn+vsmdOzbTtrnZS1aWxrI0Y2OpUWlJiYempkxMM8K1a7ZUxOOR\ndHXlsbMT5d69ML292QwOblFbm0V+vpexMdtU3QboQizLZHX1iLt3Uw5Czc15/Ot/XctnP9uJz5f6\nbKdLRdI9r2dnZ/nc5z7HM888wxe+8IV35B7401jvA+Zjivj6cZUOzm+kpXxY3FZiOZ+41p+24NbX\ngmiic34rIPrane2w9vAHO25ePbLfPwPN5dfoKitciipDcXIimHIMwfuzLOZOJIcO0GRKTXum4uAU\nxIlg9lDSEFDEFKykjV8vFyhG9ySdfsXyfUlc2V3hyE5aikm+Yj8K0bjgnEsxck9ysUIxvJ7KsSzI\n0NTmKkY3JZeKFPPrkvJszWEUVvdT0osr1YqxNUlTnmJ/V7B/IuwkkTQNY22RiUuCVwrCB4I7m5Le\ncxbL24Jdp+P1uDTdtTGiEcHWpsHGrkFBtrJdemZTN9imSkVlnsW1YRdhB9i6mi129gVrDiBWlyrO\nlSpGJwz2Qw7oezW9FxQjUxLTgoutiqXbgpoqm/yjnJ+7rFRReVYTj0JwQ7C6KqmuVhQUPKibfOKJ\nOF6v4gc/SCNxNWncbsmNGy5qa+NkZJw4X8Y0N26kPiMNDZriYlvkv7hoOY8ZZGYKJiZs4Ozv14TD\ndjDz0FBKTlJWZlBX50KIGNevH2JZkJNj0NaWwfR0mMNDRWurG9OMUFjoZmUlwvp6ivTT3x8gO1vz\n0ku7abFdXkpLPUxMHNHVlcGtW3tYlubChVwWF4/Z2rK7y/b2LDIz4fTUYmIimDxmUZGPjo4cgsET\nxsd3nM8GdHQUIQTE4xbf/vYzdHYWJV/zKKnI6ekpX/3qV5POOy0tLbxfj66fecCEtzfi6yetBDgb\nhvFQLWUCRNIB452M23qn62Hj3DcC0fRR9Gtt/YIWfGbDy3dOHtRVbpoCjaBBKUZ3Jf1ZiquHaUDq\nsck3s2GDUkNRZWlQMHcoOUzISAxNZ67iWiJmK8MiNw67EZHMowS4VGJxMyg5MgVuobmSY6Fi8KPV\nFBjV5ipcafFb5/Msil2a8XsGB063meHWdJ9RXFu2r7MiS1HjVRyeiNfsKE22DgRbhwalWYrqgMYl\nYGxREnFMA3L8mtaztrayqkCTb2j2DgVZfvWAAXpbbZz9I0GBH/bvS9a2BBfbFfNLkn3Has7n0fS3\nKXRUMzhkEIsLcnM0LecUA2OpMe0TnSY+AS/9MHX8ulpFZqZm+oZBcaGiulxzciywLM18Wqj0hQsW\n8bgiL08zOAiWJejsVIRCgiXHsSIjQ/H001EWF80HtJQdHRAKKXZ3BW1tMQYGorS3u4hGddLeDuDK\nFYnfH+P7308ZltfXu8nNlYyORunuNtjYOEEI2/d1ePgk2XGWlxtcuGAwOHjA/r4NvC6XoLc3i83N\nKIWFBmtrx2xvR2ltDeD1SsbH7e6yosJNRYXG5YIbN0IcHdnX5HYL+vryychQ/OAHG0mQrakJUFbm\nZ3Z2n/PnMxkcXMcwBJ2dxRwcxJifD+H1GnzhC1389m934Han3sdHSUUGBgb44he/yCc+8Qk+/elP\nv2OpRD/N9T5g8mDE1zsR7Ax2h5kYs/p8vh8btxWNRpFSvqNxW+92PQpEE522y+XC4/E80iz+W3su\n/r8dNzEt8ArNZcMiEhYMHqbdlDMtNmOC+87+M0tqnvSavLLh4sQh+5T57N3edNrrnswzkRH40T1b\novGw8Wu5X9Hot7izabDqgGlXqcW9Q8H9cEoP+dQZi/CRYNCJ0irK1FTlqWSQM0BnuUW+0FybNTiN\n28zWy/WK6VXJkcNizfUrLp+1eGUiZaR+pkBRmKOZdHSIfo/myTqLO6uSxfU0gD9vceuuZO9IUJqr\nOJutcEvNyEzKAD03S9FYbTF0w0X3OYutNYkQUFKkGZtOXWtDra3B9JgwOGg/fqHN4uhYsLScYtN+\n5GmLxduShYU0A4V+xcqKYGtL0tsbZ31dU1WlWVoSSW2lYWj6+21CztpajPV1ezzZ1ydYXtZsbdnX\n0d8fx+MxWV42k1pKsE0IDg5sf9ixsRMiEU17uwfLIqmbLC4WNDdrwmGLkZEUmJaWuqir82KaUVZW\njtnejjnmAgHm50/Y3TUpKnJRU2OD0tGRyfx8ShJy7pyf2lo3165tcHxsg2Qg4OLChVyWlo4pL/ew\ntmbvMFtbs3G7Daam9tEaWlsDKBWloMDH0lKIjY3UcX/xFxv4/Od7aWpKmaE8SioSCoV44YUXCAaD\nfPOb33wgWeRxVHV1NdnZ2RiGgdvtZjjhZv9TWO8DJinATMz2H2dOZWKHkOgUE2bvDyP0JHIp3824\nrfdKJUZKiZxOl8v1AFP3UYYLE6eC/7TtZnpHsn4qbRZrtmI4TVeZ59LUeRVGHO7uCbZO5etCnKUz\nfp3cl3R6FWObtvl5TUAxuvv68atHQ25cM7kpuVKpGNlIGQvkeDVNhYqJTUlfoWJ8RVKRrdHA4m6a\nhrHKYv6+pDFbsbpuj197ahTXF2RSf1mSbVGepyAuCe4KVu9LWioVp3FY2ko7VqOdFLJ817au87hs\nlupwmrayKFfRU6N4ZcBIjl/PlikKcjUTcw6hqdCivshiY1OwuJLav3eeN9kJSta3BJfbbHOB5kbF\nnSXBzm4KJC/2KSIncLQnWFiQSfnH9HTK8q621qKhweTqVcFxQkPq13R3ayYmBJmZirNnT5mZUXR1\nCaanNYfOWtDr1Vy5oolEogwM2K2g2w29vW4WF03u37cZsvH4Kfn5BltbZtKEAKCz00N+vmJ4OMTR\nkf33WF/vJT/fYHg4TGmp5MwZxdpahHPn/IyPHxIO27fQjAzBM88EWFg4YmEhkjzmhQv23/jpaRyt\nT7l9+5CSEh/nzgWYnj7g8NCksNBDXZ0X0IRCdseYqHPnAtTUeBkcXOfwMO68l4KOjkIAfumXGnn2\n2XYMI/X7fphURGvN3//93/PVr36V3/u93+NjH/vYO8J7qKmpYWxs7C0btbyX6n3A5K1FfL3Zeq2W\nMlFer/c9H7f1bpbW+gEThsRI6bXPeSPDhTAGv7eayf/YTREZ0m3tmt0W4sQmpIzvSyLOfi3LpWnJ\nUgw53q99fgt1CnsRwdLRw9mv2S5Nh99CxeHqWuoLTnWuwmdo5p1Rbk+hRYbWzG4aBB0WqNvQ9J+1\n47dMJajNURQJjbJgJC3IuaHUwjQVS7tuzuQoSr0aA1jclASPUse62GjLRspzNTlCs7olaapSDKSR\ndqpKFTkBjTThYEewsi45f04ROYU7a2kd6AWLDKG5PmBwGhVIabv0zNwShJz3orkmTkm2xdCwh0gk\nTepxwWJo1MCfAS31irkZSWurYnAwxWzNz9e0tJgIYUtAIhHhMGA1g4MCyxJIqXj66RhKmVy7ppPM\n1txc2xt2akrQ1RVnbOwUl0vQ0eFiYiLOscOFKSoS9PTYHePuborZ2tvrY33dxO1W+HwxZmcjjlOP\nZmYmwVbVfOhDPk5PY1y7FkqTdLhobc1kZyeC2x3jxo1DXC5BT08eOzsmd+5EHGJQBjs7J+Tmehgd\nDSbZu1lZLp54Ip/FxX0WFlJkoJaWXAIBF5YVY319n62tMJmZbjo6ilhfP2Zl5ZBnnqngT/7kCuXl\nGQ/1i/Z6vcld5dbWFp/73OcoKCjgK1/5yj/alvPNVE1NDaOjoxQUFLxj53xc9T5g8uYjvt5MPUpL\nmbDfS+wxEx1TNBp96F7uZ7HStaVv9ovDw0D0b3c9PL+RzbGyb+ZVLotWqfjOhitltO5XuCUsHKfA\n4sP5JvsHglGHVepzzAeupZkPVGYqGn2K8VUjyXbtKrVYOxTspMV4ffCsRXBPMO7sH/P9mnOFKYkI\nQHupRalL84PplJF6X63FnW1B8MQZHfs0T1ZbvDplJC3qcjM1TWcUg7fsY2V6NBdrFMEgTKaRgtrq\nbLu7lU1pj19zNFLD4ppkd9/RsxqaixcUE3OShjOK4IZgd0/Q3aYYHJfEExKXHM35Rgt1IhgYsMk8\nxUWKmmrF0EhCg6l5+lIMMwrXrqW+LFZVKYqKNKOjBm1tZtLhxjZKT73/1dWaqiqTzc0ot2/bt6vK\nSigthZERDQhaWy3c7ih+PwwOmmmAJmhpMYjF4qyshLl/38LvF3R1ebl5M8rBgcbrhf5+gWlarK3F\nWFtLxXNduJBBRobm8PCE2Vl7BHr2rJeKCi8jIzbAXbrkY27ugKamLG7dOmJnJ0X6+chHCgiHo1y9\nupN8rKzMR11dgO3tCH6/YmpqzzEnKODkxGRm5oD8fA/19R7W1g6pr89hZibI3l7U+Zm8fP3rH+Bj\nHzv3wOc9MYFJ7Pn/7M/+jP/+3/87NTU1LC8v8+yzz/Lxj3+c6urqd/S+UltbS05ODoZh8JnPfIZP\nfepT79i53+56HzBJGbC/nTmVb6SlTNzMTdN84L8AUkrcbjcul+s95+P6TtXj0pZqrVkMa5697UNG\nNBO7LiJK0JUdYyns4sCx0fNITV+eYj4kaJCawU1JSYamKEMzHUzbfxZYbIcFRS7NaUhwZ19w+cyD\n7Ndcn6axQDF3X9IWUAzdkVTna6QLbqeNX3srLZaDkoZsxa0VyWEELtYpBu9I4lZqR9lYqrBigo1N\nwUZQUl2iCHg1N9MAt6PGItutubVgsL1v7zsvtirmVyT7zogz06d5usVicNRgzxmFZmdq2hoUA1M2\n8JXmK+qKNGYMhiZSxz9boSjI00zclFxsUyzMSAry9etcelqaFVl+xcmB4KbT1Z4/b3J6qllctMe5\n+fkWHR0x1tZSu0yAtjZNLKbZ2ID29igDAybNzTb4zsykfqcXLmjKyky++91IkiBTVSUpKZEMD5tU\nVGhKSuKsr8dfJxMJBARXrrhZXT1hbs7uJF0u6OnJZGMjxvZ2nN5eF0ND+zQ1+TEMweRkSrpx6VIm\ngYDJq6/ucnpqn9zrlXR35xIMRsnLEwwO2kDZ1JRNdrab0VGb7Xr5cg63bu3S2JjL8vIJ6+upEe7P\n/Vwxp6enXL++QTyekK8YdHYWU1ubzR/8wRVKSvzJ5z9KKjI/P88LL7xAUVERxcXF3Lx5k8nJSerq\n6njllVd4p2pzc5OysjJ2dnb48Ic/zLe+9S2efPLJd+z8b2e9D5j8+IivN1NvRkuZvpR3uVy43e7X\nEV3e62bob2e9VjLzuOLH4gr+47ybr912JV11ij2KUq9i+siFG02PN8ZpRLIZkWxFUibul0sVI/dt\nQCzzKWqkPTIdTDNIT2e/CjSXChUyBrNbkj1n/OqSmks1ioE1e/zaUmDhjYLH4AEbu5oiC49U3Np2\nU52nyJW2V9HmnmAzTW5yqUlxY0VSlKXJVLC4JuhuVAzOyGRqSH62prFSEQnDwX17/HqmRFGUn9pR\nArTUKipyLa4NuJIpIe3NFscngqVV+5y1ZxRVhYrFRclamgtQf6/F3VXB4ZGgq1UxPCjp7lYOaSel\ny+zvt3C7FVNTEArZoN7TY7K6Ktl2/HD7+k5xu03u3tXcu5f6/XV0KEIhSXGxyeJihGBQ097uwjQ1\ns7MJswzNP/kncHgYZ3Aw5bRTXm5QXe1mYeHU0Xcek5Ul6ejwc+NGmIMD5ZzDQ3a2yb17pywtpV7f\n1OQnO1vidscYGNhFKSgocNPSksWNG4ccHJj092extBSiujrTCXVOjVr7+3PJydFcv77F8bHpXKug\nq8veR1pWlPHxbQCKijJobMzj1q19DEPw9a8/zT//53XJYz1KKhKLxfjGN77Byy+/zDe/+U3a29sf\n+PyHw2H8fj/vRn3pS18iEAg8MtnkvV7vAyYpwLQsi8PDw7c830/kTwJJiUgCAF8LlD+JROSnNVHk\nzVZCh3p6evqOSmau7kp+bczDvUhKV/nRPItbWzK5o8xyK5qyTUaCqf1nU7bJGZfi2pI76b7TW25x\nZ0+y55Bl3FLzwQqTtU2DWYd8U+DX1BUqhtO6wc5yiwK3PX5NSDF6qi1Wg4L7iWvw2uPXqzeMpNdr\npk/TUWNLRLQWZPk03WcswmHBcFqXV1uuyPBqZpaN5Pj1NALHYcFSGtD1nrdY2xIU52gOdwR31wSX\nuhXzC5I9R1vpcmkudytkTHP1VQPTFHi9mt5uxcSk5MS5tks9FhkezcB1g0gknbSjGB2VVFQoPB6L\nlRXo6rKJPAmjAp9Pc+lSnJOTKAkypdttE35u3RLs7wsqKy0KC6N4vbC2ZrG+nrqFdXe7cLtNgsEI\nCwt2K9nU5CYjQzIxYY80L10y2N+POAboJ8ldaCAg6e3NQKkor7yyZ38mBPT0ZBEKmdy+HaGnx8fa\nWojMTIPiYi+jo/vJ19fWZnDunJfp6X02N1Mg29KSTSDgwuOJMzi4iWlqsrLctLcXsLJyxMbGCVeu\nFDIxsUVFRSYFBRmMj28n/WE/+ckW/uN/vEJOTmqc/SipyOjoKM8//zy/+Iu/yG/+5m++60TBRKpS\nVlYWJycnfOQjH+GFF17gIx/5yLt6XW+13gdMXh/x9WbZXI/KpXyURCTB9HwrEpH/10A0weZ7t5jA\nBzH4rSkPE7uS7KhmctegLtv+nd1Js7XrL7aYP5A0+CzWtiXBiKCnNMbQhifZpRZkKKpzFGsHkhqP\nZmjJoKFYYVqwFEzzSq2yWNkVNORqpu5IIjG4WK8YviOJOd1gtk/RUqHQMcHKmmT7QLxOIgLQUqko\nzlTMzBvsHDiA22Rx775gay9lUvChNouJG5JNZwzsdmn62xVjM3YcV3Geoq5QYwgYHE+RcXKyNecb\nbW1lT5Pi7h2JaUJjvWJgOKW3LCnWNNZbnIQEY6P29ZWWKqqqNEND9q43M1PR12cSjWoGBkTytUVF\nmnPnNGNj0NcXY3Q0js8HLS2CkRGN4ytCbq6iv/+UkZF40lPW44HuboOFBYtoVNPeHmdo6JjOzgyC\nQc3SUooBe+WKh8zMON/7XqrjKy93U13tYWTkhK4uN4uLISIRRWdnFrdvh9nZiTvX6KK93cX9+6fc\nuJH+eh81NRkIYZsLnJyYuFyC7u589vaiLCwc094e4ODgCK01Z88GmJy0nwdQV5dJZWUGe3sRpqdT\neZX5+T6eeKKcT32qjQ9+sDL5+KOkIsfHx/yH//AfuHv3Lt/61reorq5+w8/9O1XLy8v8q3/1rwD7\nb/3jH/84zz///Lt8VW+93gdMXg+YP2nsViKX0jRNMjIy3lBL+Vbitn7S+mkE0QShx7Ks9wTB6W8W\nDX77modDR3PoNTS9RSld5blMRb6licVhYjs9n9LiJAarhwYeqenOiaOimrltN4dOsLTH0PRVWQws\nG1ha0FFiYZ5ApgeG0sCvutDC51LMb7mpL7DwWQJDaIKHgntpgHux0eLWuqTAr/GZMH9XcLFVMTov\nOXVMCjIzNB31iuMjONwVLN+TFORqGqoVA5NpZKVSRUul4tp1g2Ony6s+o8jN0UzO2Nd2tlRRXaTY\n3xPcmEldb2ODwmVobi9K+jsVY8OS6mqNEPqBCK6mJkVZmcX8vGZzM+H3qvH7NVNTjmnD+Tg+XxSt\nYWwsdUsqK9NUVkIkYnF0dMzKikV+vqS52c3oqEXU0Zv29Zl4vVGmp2OEQvbrpYTe3gx2dizKy2F0\n9JDTU01rqw+XSzA1ZXdoFRUGZ88qpLSfkwh+9noFPT1ZGIbJ1NQuoZANci0tWWRkSMbGQtTWZuDz\nWWxshDl/Ppf5+UN2d+1ONjvboK8vi/39CGNjKTDMznZz4UIBbrfi2rV7RKP2GLm+PofiYj9TUzt8\n4hOt/P7vXyQzMyXdeZRU5Pvf/z5f/vKXee655/jlX/7l/6cMTd5r9T5gYgNc3GEC/CSxW4kle3rI\ndOLx94pE5L0KounynXfTLP5htXok+NQrHq6m+bX2F1oETM3Ld1LZk1cqLSY2JWGnC8twaZ4qNZm7\nayRt7IoDiooci4n11A2vtzxGJvAPs6nxbk+Nxd1dwY4zfs3zay6esbg6bXDkjHczPJruesX1OVt/\nme3TdJZaxGOC62nAdKZIUZSrmVgwKMlRVAU0BwcCw2PHfSXq/DlFOAJ+t+Z0X7C4Iulqs9gNClY3\n0qQkXRZ+aY9fE8CU2FFuOfvI9laLvIDm1rxkK0332ddnR3BJqSkttRgbE/T2Kra3Baurqd/35csW\nmZlRXnrJSpJ2WltBKc3cnCA3V9HcHGFnxyQnRzA2lmKwlpZKGhvdhMMnjIzY4BcICC5c8HLjRpTD\nQ01TE8RipxQUuNja0qytpTrO8+d9lJdrrl4NEg7bf7dFRW4aG/1MTBxRVGSQlRVnbu6I7u5cdnai\nLC3ZKxePR/DUUzlEInGGh4NJco5N+snHMExu3drl/n37uqqqApw5k8n4+C5VVX5MM8bycoiurmKi\nUSvZXTY35/Ptb3+Q3t5U7uSjUkXu37/PF77wBbxeL3/yJ39CYWEh79fjrfcBkwcB841it95MLuV7\nrYOCdxdE0/e272UPXKXhGzdcfHnMTVdAMX1PojWcL1IMpBF7KrMVOV7NcUSQpzQTqwZt5Yq9E1hP\nt8irtljcETTmaEYXJEpBT3Wc4WV30iA926doLrOQpuDWssHesaCiQFGco5lI60AbyhUVWYrpGwZB\nZ6/Y0WCxd2IbFoAtB/lwq8XMnEyCnxCaS52K2RXJwZGgMEfTUKKQwORNybGze/R6dDLcualasXNP\nENwV9HQpRsYlp/8/e2ceX0ddr//3zNlPlpM9zb60WZt9adJCN/aroCLq5QcIoqDCFYRLy1LWakVA\n2goVuFxFEXh5FeTqVRGQrWxNs6dJszRp0rRJs68nycnZZub3xyRzEtpqC93J819P58z5ZrZnvp/v\n53meGQK3WhRKimRcU7Dj4xkHoZk1ytloLb1e5pxzvIBCTY3AxKw+1KCwbJlCUxOkp3toaXEzPq66\n9HR2+lx6BAEuucTNwYPT1Nf7SC4zU49eD7t3e1ixQqC2dpKQEB0xMXoqKpyanCQmRiQnR6SsbExr\n5NHpoKDASn+/jMmkoChO9u51kppqISBAR3W12gGr18PKlRYkyUtDw7hmeycIkJ9vw2qFgwcn2LdP\nlZlERJhITQ2kvn4Uk0kgMVFPVdUAeXlhKIpCXZ3aGWux6Fi2LBhZlmhvn+/Uk5YWzNVXp3PLLXkY\njb5zfrhUEVmW+d3vfsevfvUrNm3axIUXXnjKny2fFywQJodGfH0ydutYcilPl7ito8WJJtG5DT2f\ndt32VKBxUODbfzGxe9BHfkVREvvG1PXLAINCXoCMIEF5p8/Fx2pUyI9RvV9BYFmUxJRdwGRQqOn0\n/d2Lw70IgsLeAQPp4V5kh5pSMmgX6B31XXulqV5aenRE+CnoHbCnU2B5thq1NevGYzYqFGWq5dfx\nAYF9XSIBfgo5aWr5ddboPCxYoShdoqxcx/gMgUWEySTFK5TXzKw7hsksiVTN0MurfOONjpKJi1Go\nrBFZXijTUCfi768QG6tQUeHbLjJSITvby759Cu3tM2u7nzAgSE72EhQ0hZ+fQGUlGhGbTAqFhTAy\nImM0OqivdyOKsGyZke5uL93d6r2WliYQHu5lZMRLU5NP85iYaCAyUo+iuOnsnGRgwIPNpiMnx8qu\nXVPY7bKmwfR4vAwNeWhv9zXnJCUZiY3V09MzTnv7bBCCjvx8G+3tU0xNecnONlFW1k9Ghg0/PwNV\nVWPazHjVqiAEwUt7u53ubh8ZJicHkpRkZd++ETo6VAcftTNWnV0ajTqeemotWVm+GeKRpCIdHR2s\nW7eO7OxsNm7ceMq6XT+vWCBMjhzxNVdLqdfrsVqt87SUR5KInM5xW0eD40Wic8vRc2/6MwVuCTZ9\naODn5XqkmXJsqFmhMMxLzV49QzOaxsQQGYtBoXnO2uaaJC/eafioZQ75LZZo7hEYn+nKjfCTKYyS\n2F6v1wzSrSaF/GSJshbdTPlVJjvMg9clUD6nlBsVJhMdplDdoiMiSCYpWGFwSMDfolDfOmdWmiQj\nCgqCBNKkQGu7SGaa6nLU1jknPzRTItxf5uOP9Fr+ZHaWzPQ07G1Xt0tbLBEeDP19wjzNZGamej/0\n9wukpXnZuRNSUtSO1/p633YpKTKLFzt5912n1sgTEQFJSQKVlSJ6vcCyZS5aWqZJT9dTU+Nmpukc\ngwGWLzeg13t4//0JzSmnoMDM1JTMnj1uoqIEoqMlRkc9hIerHbCzT7fAQB0rVljp6JigtVUlQ0GA\nwsIAJiclurud5OYaKCsbJDraTGysidpa33pmUZEVk0mir89Je7tPixkXZyU52Z+JCYeWHCKKAoWF\nYTidEvv3T7B0aQBlZQcJCjKRlRVKe/s4vb1TWCx67r+/hFtuyUMU1WN+JKmIx+Ph6aef5u9//ztb\nt26lqKjon126CzhBWCBMDo340uv1iKKIw+GYp6WEw8dtnc0pIrM4FhKdnWWfTuXoz4Kd3SLffc2I\nUVFgUqC5T6QkQaJ1QGR0RjahExWWJ8o094mk22TK94gY9ZCfIPNxm6/JJtRfJjlMNSbf3SoyPiUQ\nHyFjC1BomCM3yYiVWeQns6veZyyQu8SrNgDNOA7pdQrnZ7tpadWzv8f33dI8ibZOkeExgeAAhYwY\nGUFGDWieKeWKosLyYpndbSLxkTJTwwL7DwiULpNpbBIZG/cZna9cLoMEH2xXZ6uqjlKmrU1kaEgA\nZFaskBAEmX37BHp6fOe6oEBmbEzAZjfSSnIAACAASURBVHMzOOigu1th6VI127Kx0ffoWb1aQadz\n8+67vmitsDCRtDQ9FRVucnMFDh50MDoqUVRkprnZNSe4WeGii4x0dTnYvdtnAJCUZCIiQk97+zSL\nF+spLx/H319HXp4/zc1TDA+rpdaiIjM6nQeHQ5rXARsWZmTpUv95WZUAOTmByDI0N9spKQmipmYA\ns1lHVlYIbW1j9Pers9bi4hA8Hjdms46amgHc7tnxClxzTQbr1hWSnOzTfB9OKgKwa9cu7rzzTi67\n7DJuv/32kxJwv4DDY4EwZzAb8TUxMYEkSQiCcMRcylmciaXG44kjkSicfY5FDjc88HcD//WxXpND\nhPkpJIbIVHXpAIUV0TITE+CVoHkOgWVGe5iYFuga1ZMdKTE9IhDsr7CvX2RohpgEQWF5hszubpFo\nmwyTAnsPCJRmyVS3qNIPmCm/ZshM2Ge6X7tE/K0y2aleyusNWvnV5i9TutRLZbmekZlQ6OAghYxU\nibJKVfMZFqKQniAjexXKyn060OAghcx0VTZSnCfT0SridkNWlkx5uU9y4uensHy5l6Ehhbo6X1m1\nuFihvl7AbhcID5dYvHgKUZTZu1dmwMc75OeD260QEOAzF0hP12MyCezapfYUREaqM1NZlikvn9Zm\nlmpp1czEhGoHt2ePSjRFRX6Mj0u0tan7W77cxNjYNDabgcrKSe37FovI8uX+SJKL99/32dZlZATg\n56ejunqM0tIAmpoG8XoV8vNDaG+3a/rKlBQ/goNV56GammG8XvUxajCILF8ehsGg8M47B7T9hoaa\nycgIoa/PwW235fOtb2Vq98SRpCIOh4Of/vSnNDU1sW3bNpYsWXJsF+2nhCRJFBUVERsby1//+teT\n8ptnChYIcwYOh4OpqSkkSUKv12sG7CdbInImYu4sW6fTaeXs06k793jh/b0iN/3ByP5RXxXhoiVe\nhoYEbY1SJyosXyxRtU+Hc4Zc4oJkskJl/lHh84e1WRWWJsjsmHHZCbYqZEfLOB3MMx+IjZjpfm2d\nKb8GKQwOC/hZFBrmlF9TEmT0egWvW0HnhJY2PSnJHkQR9uz1zUoyUiSiw2SqKvSMz8xeU1NkDHqF\nxpmxJMbJxEYq2Mehfk50V2KiTEiIQkuLQEGBWn6NiID4eHWNcnYmHRYmU1TkpLzcyeio+l2LRSXJ\nhgaYmFBYvlymtXWa1FQ9+/d76emRtd/JzdUTHi6zc+eE5jEbF6cnJkZPebkTiwUKCkR2754gK8tK\nY6M6+5zF2rV+CIKHd9/1BS/HxJhISLBSVTVBUZGFxsZhHA6JoqIgentddHaq9V/VK1aYMYIfwu1W\nH5FqyTgUPz94771ujSQjIiykptpobBwhLc2fpqZB7HY3aWk2AgIM1NWphHrJJfH8/OeriY0NnPcs\nOZxUZPv27WzcuJGbb76Za6+99qRWrbZs2UJ1dTUTExP85S9/OWm/eyZggTBRH/jDw8MYDIZ5GZWn\ni0TkdMXcJJF/ltV5ukpcPi0mXbDhrwb+r15Pir/MzjaRMH9IDJPnpYrEhUgE+ykEKgI1TSIOl0Bq\nrIwiQ9sc+UZuskSwSaFut46xmWacwnSJg4MCfTP6S52ocFGeRGOLOE/6UZon0bpPdeMJ9FPIjlfL\np82tIiNjvtlrSaHEnjaR8BAZxamwt11PcaGHjn16huZoPFeUSph0Ch9/oMM9s65aVCQxMCBwYMYW\nr7DQg8GghjPv3es7X2lpMiYTOJ0SojhFS4tMXJxAVJRARYWPDLOzFaKjPWzf7mSmsIPRqDb3NDd7\nCAkBnc5FS4uLggIzk5MSra0+Ocl55xkAD++9Z9fWKP38RPLz/WhtdZCaqqOychSXSzUg8Hhkdu9W\nm3ASE42EhwuYTAK1tWNMTc3e41BcrNrWffhhL06nSr7h4SbS0mw0NIySkGBhbGyKAwcmyc4OwWQS\nqa4eQlEgNtZCRISA2axjYMDJ3r2+0m5aWjB3313ApZcmzIujA7R8V51Oh5+fH8PDw9x77714vV62\nbt1KZGTk0V2Uxwnd3d1861vf4t5772XLli0LM8xPYIEwZ+DxeDQpyKxF22w5cbZkcrasyR0PfPLl\n4VjXVc4GEt3eLHLzb43sn2OiXpjgpmNIz+iUSH6UxNiAQHSIwq4OkUnnnCSQdJnKVpHF4TLeKYED\nvQLFmTJlDT7vVz+LQn6qzPg4TI2oPq6B/qpB+o5an8uOLUChdKmX6ko9Q8MzRu02hcw0mbJKdTtb\ngEJuqozshR07fZ2zAf4yWZleKmsMZKV5GOjVMTYqkp/vpbpar3WwGo0K557rxemU2bFjries2g07\nMCDg7y+Tl+fA6fQyMqLQ0eF7tKSkgL8/+Pl5qKiYxu1WdZTJyXp27nQjy2C1QlGRAkjs2uXUDAhA\njeByuyVMJjcVFRMAJCaaiIz0NfcsXWpElp2Ehhpmwpx9JJuX509kpMj27QOa5ZzNpicnx0Zjo53w\ncD2y7KStzU5WVhBms0hVlWqPFxioJzfXH1mW6epSCXMWCQl+ZGT4U1nZzfCwb/00Ozscs9nA4sUh\nPPbYuYSG+kLpZ72mdTodoihSXl7O1772NWJjYxkbG+NLX/oSV199Nfn5+Sc1hgvg61//Ohs2bMBu\nt/P4448vEOYnsECYM9ixYwcpKSmYTCatnOhwOLQZkyiK80h0dtb5ecNc2czxfnk4E0l00gn3/1HP\nL983aASWHiGR6C/zRrnvJWJRsExMmEJ120ysl79CTpTEyJhAfdscuUmMjNmk0NihI9wmszhEYXRc\nQEChZY4mMz1ZrYRIHgGzBLubRdJTZEChZc7+0lNkosNkdtXqGJ4h0yXJMlarQv1MgsiiCJnURJnJ\nCYGamrkSEYnYWIldu/QsW+airk6NwsrMFGbWMlXitFoVVq1y09LioLNzrssOdHaq3bN5eTIjI9OE\nhIhMT8vs2eMrnyYk6FiyRKG5eZKeHvXzwECR3FwTdXVOJiZkzjlHT2OjnZQUM8PDXjo6fM1BGRkm\nEhNF3nprQPN1NZtFCgsDaW93EBKiw+l00tExRVqaPzabnspKVQ5isYgUF1uRZS+dnVN0dzu0/SYm\n+pGS4kdz86D2uSgKFBSE4nbLOBxu9HonLS0j+PsbyM2NoLt7gv377cTGBvDEE+dzySVJ2v6OJBXp\n6upi/fr1xMbGkpWVRUtLCzU1NTQ0NNDV1XVc0pOOBn/72994/fXXeeqpp9i+fTubN29eIMxPYIEw\nURe5b7/9durr6/F4PCQkJDA9Pc327dt55513WLJkySFrcsAhD/GzsTt2FqdKNnM6k+jcY1J1wMqd\nf/AnVKdQ1aha1BWmzJRVx+aUUNMljIrCrt06xmes6JZnS2r01qy4X69wYZ5Ebb1I74BvNrc8T6ah\nVcQ+qcpH8pLU8mtDs6itRYqiQmmhTHOrSHCgghVo3C1QUiKzt1PUZqAApcUSZoNCRZlOk5Lk50uM\njwt0dKi/u3Sph4AA1Vygudn3d8THy4SFCfT2CkRFTVFTIxEaCunpIuXlskZc0dEKOTledu6cZmzM\nd+yKiw0MDclMTkokJUlUVDhISTEQGKijutqnjczK0hMTI/Pxx+NMTqqPKtUQ3Y+RES/BwdDVZae/\n301cnInYWDOVleN4vaqZen6+GUmSOXhwmv37fTPAhAQLKSlm2tuHNQOC2UxKu93N8LBrxmN2gNBQ\nExkZwbS0jDE05MRoFCkpsTE4OEFwsJmamj5t1qrTCdx1Vwm33lpIQIBRu04OJxWRJIlf/vKXvPrq\nqzz++OOUlpbOu4bnlm5PBjZs2MCLL76IXq/H6XRit9u54ooreOGFF07aGE53LBDmHDgcDrZu3crj\njz9OYWEhS5YsoXEmfG/p0qXk5eVRVFREamoqoigetjv0bCPR01E2c6pJdHbtdrasNtusMe2CH//O\nwC/+otcae/wtCrlJMh83iWTFyrjGBQbHBDISZcoafLO5UJtCSpyMY1Itv7YfEAkLVlgcL1O+y7dd\neIhCQYqXuhod/TOmCqHBCqmLZcqqZkzOLQrFGRKSS+CjHb7SbUCAQm6ezM4qkfQlMtN2VQJSWChT\nUyNqpKnXK6xcKSHLHj74QNG+v2yZmk/Z3S2g08mUlrqYnPTgdMKePb7jExsLUVGg13toalJLq4GB\nArm5BqqrVW2lICicc46AonjZv99Dd7fPzSc93YifH1itXsrLx3G7FYKDdWRlWamtnWRyUiEyUkd8\nvKqFttu9tLb6ZobR0Says9VQ5wMHVJIURSgsDMJu9zAw4CQtzcjOnQMza5SBNDSMMT7uARRWrAjV\n1uWrqwe1dVKTSWTNmkjs9knKyg5qvxcSYiYzMxS3W2LTppWcc06s9n9Hkoo0Njayfv16LrjgAu68\n806MRp/G9nTA+++/v1CSPQwWCHMOenp6WLduHQ899BCpqamAbxbR0NBAZWUlVVVVtLa2YjAYyMrK\nIj8/n8LCQpKTk7W3xlkz91l5yuzD+0yTWMzKZgRBmHezn444WSQ6+wD8Z2YMNW0iNz9lpGGfSmhh\nAQq50RL7ukQ65jTs5CyRGJ8U2N8nEhaosCRMxjkNo+MC++c2BaVLjE8ICDIE6tTZaXamzNQUdOyf\nYyCQJhNhk2nepaO/f9bkXMZkVNg9Y5oeEqyQkyUxYReorp7v0JOUJLNzp8Dy5V727PEiSZCdDRUV\naA1ARqPCeed56elxUV/va+QpLIT+foXuboGkJAmz2YnXK2OxCPO2CwtTLesGBhzs3q2WVQ0GWLbM\nQnu7m74+iZwcHWNjDvz9RYxGgbo6HxkGB+soLTVTWztCX5/P5Sc/PwCXS2Zw0EViokBl5TChoUYy\nMwPZtWsCu119oS0p8UeW3Xi9CrW1I9r3/fz0LF8egtPp5KOP+rXP4+L8SEgIoKVlhLQ0Czt2dKlW\niVlhWCx6qqv7EEWRH/6wkA0bSjGb1evhSFIRp9PJY489RnV1Ndu2bSM9Pf1Il9opxfvvv8/mzZsX\numQ/gQXC/BRQFAWHw0FdXZ1Goh0dHVgsFvLy8sjPz6egoIC4ODWW53QsJ/4zzDY/ybJ8RncDH08S\nnWuAfTSWh14Jtv6vnvcqddQ0iEw4BIwGhZKlMuWNIm6Pz9lndbaX8kq9ljtpMioUZ8tU1KvbWU0K\nRSlq+bWyVmTa6ZsJlhbK1O0WCQlUCDWr6R/LS2SamkVGx3zjK1kmYTYq7KrTMTbzeV6ehN3uK78m\nJ3uJjvYwNqawe7fvu7GxCjEx0NqqkJHhoqzMQ2AgZGeLVFbKWqdrQIDCueeqDTtzJSLZ2To8HoXO\nTon8fC+VlU7CwnQkJuqprHRp2sjISIH8fJHa2gn6++f6x1owGgUmJjyYTG6amiax2fRkZ/vT2Dg5\n4/WqsGKFHy6XE0lSqKsb174fEKBn2bIQXK75ZLhkSQBhYSZqa4cpLg6kqqoHj0emoCACh0OisVHd\nR36+jYmJSSIjrezfb6e7e0Lbx3nnxfPjH68kLy/Cd+6PIBX5+OOPuf/++/n2t7/NjTfeeMorNQs4\ndiwQ5nGCoihMTExQU1NDZWUllZWV2oL9LIEWFBSwaNGiQ9ZDTxcSPdN8cD8NjpVEP6tpfFuXwK2P\nG/mgbo6WMUomwE9B8YBzTGDvfpHEGJnAAIX6Ft928VEyKbESTfU6emfSQaIjZaKjFKpm9mcyKpyT\nK+GaEvh4h++7NptC1lKZsp0iyUkKJj3s2ydQUKCGODvnkO6KFRKi6OHjjxU8M0ReXKzQ34+WLFJa\n6sbtduPxQEODjwwjIyE5WcDplBgcnKa7W8JiESgsNNDQoK59AuTnC1itHvr7vezd6+tejY3VER0t\noihu9u5VtZRqrJYfbW1OBga8mExQXGxkdNSJySRSU+MjLD8/HaWlATgcU5SV+TSXqan+BAUZqa4e\nobTURl3dEB6PTGFhKP3903R0TM5sZ8XfX8Zq1VFfP4Td7htbYWE44eEG3n67Q9NciqJAfr5Kjpdd\ntoTbby9Crxe1a2tuqshs5/jY2BgPPPAA4+PjPPHEE0RHRx/t5bOA0wwLhHkCMZuvWVVVpc1E+/r6\nCA0N1Uq5+fn5hIaGnlISnVs+mpuK8HnBkUh0ljAFQfjMLxAv/F3Hvc8YGbELhAUqpITJoMCeDlGb\nWQKU5Eq0HxCxGtUZY+0uHcX5El09vkgtgPxsCatB4UCbSFfXbIOOjNuN5vPq56ewvFhiaEigbg5h\nR0XJxMcrlJfrKChQSWxyUjmk/GowKKxaJTE56aK83NfVmp8Po6MKnZ0CYWEKixe7GRz0EhIiUlXl\nI5zAQIGCAj0ej5OPP1bLqqre0czgoMS+fR7i4kRCQz2MjnqIjNRTVeXQEkfUCC0T/f0OGhp8ZuYp\nKVaCg/XU1topKbFQWak69RQVBbN/v4PubnXNMDnZSni4gF4vUFU1rDXmqGMIIThY4J13OjUytFr1\n5OeH09U1waJFZtrbBxkedhIZaSUlJYTm5mGGh6dZsSKap566kNTUEO36mZ1Vzr1/FEXhr3/9K5s3\nb+aee+7h8ssv/1zdV2cjFgjzJEM1qe7XSLS6upqhoSGio6M1Es3LyyMwMPCQh7gsy4dtKvq0N+Hc\nJJHTpaHndMBs+7/X69VmCbPn4rO8xAyOweO/NfDCy3rsM8btwTaF9CRfqLPZpGo0JRd8VO5r2LFa\nFQqyZXZWq81AcUFq+XVZsUxNra9hRxQVlpfIKAq0t4naWmZxsURfn6CR66JFEhkZbvr7FZqa5pdf\no6Nh1y6FZcvcVFS4MZkgN1ctvzpnGlj1eoWLLpJpbXWyd6+PTDMy9BgMUF/v4ZxzBHbvnkKvF0hP\nN1JVNT3PqOD88w3s3TtJW5tPIqJqKw20tk6Rnq7GcxmNAvn5/nR1uejpcc/8jhGLxYvRqOolZ7ty\ndTqBkpJg/PwUtm/vw+NRSTI01ERmpo3du8eIizMxNmbnwIEJUlODCA42UV09gNersGiRaryukqDM\nrl0+27zQUDObNq3km99cqp3zI0lFent7Wb9+PRERETzyyCMEBQUd1TWygNMbC4R5GkBRFLq7u7VS\nbk1NDXa7nfj4eAoKCsjPzycvLw+r1XrcSHT2jXjB3s+HfyWdOV5rou+Vi9z+EyNtcxp2lqbIhPjJ\n7GsV6Z5p+EldLKPXKTTN2N/p9QprCyXGRwQqKuc37CQmypSX64iLkQkLVehoF8nOltm50+f9ajQq\nlJRICIKX6mqZqSlf9+vBg3Dw4IzJe64Hs9nN1JTC7t2+8mtEhFp+HR6WMRicNDV5tHJpU5OHkRH1\nUZKcDLGxbgYHZZqbPXPGqWPJEiN2uyrc37vXiU4HxcX+9Pa62b9fJcOSEhOTk9MEBOiprBzX1jj1\neoHS0kBMJhfvvTegzUQXLTKRlGSlrm6c5GQLk5PT7N8/RV5eMIoCu3ap3nyBgWrUl6LIdHVNzDMg\niIiwUFgYQn19HwcP+j5PSrIRHe2HzWZmy5a1xMUFatfCkaQizz//PL/73e949NFHWbly5cKs8izC\nAmGeppBlmX379mkkWldXh8PhYPHixdp6aE5ODkaj8ZhI9HQMtj7VmFtSO9aZ9qclUZcbNv9az+PP\nGQgLVIgKUKhrELUmnskpn61daaGMx6kwclCkY6bztqhQordX4OAMuRqNCmtXSXR3CTQ2Hur9WlOj\nIzPTg8ejuvCkp8POnSBJPtP0FStkPB4XH33ka7gpKIDhYYX9+wUsFoXCQjd9fS6CgvRUVfm28/dX\ny6+C4GTHDjsej/pYKSy0YLdDW5uXgACBnBzo7HSQkGCisnKSmdx2dDpYs0Y1Q9++3de9GhtrIj5e\n1Vbm5lro7h5nYMBJYWEwdruHPXtUcgsI0JGba0GWZZqa7IyN+Yg6JSWAhAQjjY399Pb6SsMFBeF4\nPDJ2uwt/f9i9exCzWUd+fiSDg9Ps3TtKSIiZRx9dzVVXZWr7O5JUpKWlhXXr1nHuueeyYcMGzGbz\nUV1DCzhzsECYZxAkSaK1tVUj0YaGBjweD2lpaRqJZmZmotfrkWVZk7bMTVpRFGVe88rnnSyPRiZy\nrDgWEu04IHLPjw289pbvdyPDFRLjZcqrdYQGKaREybQ0i2RlyvNs7cxmhaJCGYcDhgcE9u8XDxO9\nBTabTEmJi/Z2X6gzQGKiQmgo1NQorFjhYfduF4IAWVkiFRWyllmp08FFF8kcODBFY6OPiDIyDBgM\nIvX1Erm5MDKiGqUvXWqiutrBDKcgCHDJJRb6+pzU1s7VSxpITDRRUzNJUZGJmpoRnE6Z4mIbg4Nu\nOjrUHYSF6UlP1wEyNTWjOBxzTdpthIToaGoa1mK1LBYdBQUh7N8/idPpJT5epKZmkMhIM8nJgTQ2\njmK3e9DpYMWKcIaGpggKMs0zIAC4+eY81q8vISLCqp3Xw0lFXC4XW7du5cMPP+TJJ58kOzv7s15C\n/xJOp5PVq1dr4/nyl7/MT3/60xP+u593LBDmGQ6v10tjY6PWVPRJo4Xs7Gzeeust7HY799xzjxaA\nfbYaLRwtZFnG5XIdtUzks+Jfkehrb5u59ydWDvapx18QFC5eIdHdKWgaSoAlS2QsFoWGBh3h4TLJ\n8QoHDghaE88s/P0V8vNlPB4vbW0Sw8MCOp1CaalqMjBLpkuWeImOdtHfL7Nnj+9REBUF8fECnZ0S\n8fFOKiudmM0CRUVGdu92MzambhsSAgUFCgcPumlunptlqSMtzURXl5OICJmqqomZZpsAhoYkOjpU\nNk5LM+Ln58FiEaistGvJILPhzoGBMtXVQzOmAhAcbCAry0ZDwxgGg0Biokhl5SCpqTaCgsxUVY3M\nlGoVzjknGElyMzHhorFxVBub1apn+fJw7PZJKit9eWPBwaoBwfi4k/vuW8Fll/nitI4kFamoqGDD\nhg1cddVV3HzzzSdVq+xwOLBarXi9Xs4991wef/xxzj333JP2+59HLBDmWYbZt+D6+nqeffZZXn75\nZRYvXkxsbCxJSUlaY9HixYuBQzWicHaT6GeViRzvscwlUfuExONPW9n+vgnvpEBrq17VWpZI1Dfo\nsM+xv7v4QonWFpH29jnGBZkysqzQ0qIjMdFLYKC6rhgTA+XlvpcBf3+FwkIFRXGxY4cHr3e2c1Sg\nu1ump0eYceLxMjbmxGCA2tr53a85OQZk2U1T0xRjY+p1o5ZfJdra3AiCwooVRnp6HERHG6isnNBm\nrIIAy5cH4Ocn8+67w0jSbEyWkdRUK9XV40REGAgM9NDQME5eXhCyLFNfP5sAorBqlQ1B8NLaOk5v\nr8/yLibGSmqqDbt9kupqHxlmZAQTGGhk9+4h8vODKSvrRpYV8vMjkGWFujq1ueeqq1K5//5igoMt\n2vXv9Xrxer1YrVatCWxiYoKNGzdy8OBBnnzySRISEo7TVXHscDgcrF69mt/+9rdkZmb+6y8s4FNj\ngTDPUtx33338/e9/Z/PmzaxZs+aojRbONreiuZjb6HS6OhcpikJLC9x5t5F3t/vM20NDZZYslhgb\nE1C8Aq2tOiwWhaIiVVc5Pa2eD4tFZs0aF/X1itbEA5CZqd7mTU0CRUUuDh50IMsKyckGystlrcxr\nNMKaNQpDQw5qanwzxuxsA7IMjY0ekpIE/Pxc9PZ6SE83UVXl0LpfBQEuuMDC9LSTjz7yRVwtWmRg\n8WIzFRUTZGeb6etz0NvroqgokPFxn7WdXg+rVvkhSR5qa8ew233rpBkZAYSG6hkft9PQMDqzvUBR\nURjDwy46OuwsXx5CVVUfJpOO7OxQ9u4do69PJdScnGAUxYPNphLn2Jjv7zv33Bg2bChl9ep4bU3b\n4/Hg8Xi0pYxHHnmE/v5+wsPDeeutt7jnnnv45je/ecpeuGRZpqCggPb2dm666SYee+yxUzKOzxM+\nV4T5yiuv8NBDD9HS0kJlZSUFBQWH3e6NN97gtttuQ5IkbrjhBu66666TPNLPjvHxcQICAo54M58N\nRgtHi9nWf0mStHXK03Wsc/HXv+m4e4OBzv0igQEKSzO8jI6o425pmbPmGSmTkCDj8cgMDkp0d6sy\nlMJCqK5Gk5xERXlZutRJS4ub7m7fbZ+YCMHBelpbIS/Pzc6dU1gsAnl5RmprXUzNSCBNJli7VqCz\n00lLi2vO7+tZssRIQ4ODnBwdO3eOI8sKRUX+DA15tGSRsDAdGRkiigKVlRO4XL4xFBQEYLEo9PXZ\naW+fbeTRk5sbREuLnbExN6WlAVRW9hIVZSU62kpV1aBWwk1LCyAsTIfD4aG2dkjbr14vsHx5JFYr\n/OMf+zRfWItFT35+BIOD01x8cRIPPrgCq9UnIfqkVGTWqedXv/oVXV1duN1uWlpaiI+P57rrruPu\nu+8+Hqf8U2F8fJyLL76YRx55hDVr1pyycXwe8LkizJaWFkRR5Hvf+x6bN28+LGFKkkRaWhpvv/02\nMTExFBcX8z//8z9kZGScghGfXJwpRgvH8vecioSV4wmnE/7rWT3/9Yxe01AClJZKdHYK9PWJRER4\niYtzMTmpIAjKPDKNiFBYskRBFJ3U1k4zNaV6txYViTQ3y1qCSFGRgk7nYWJCpqnJV34NDRVJTzcw\nNeVidNTJ/v3umfKthYEBL52d6rb5+Xq8XhcBAToqKiY0XaQa8+WP1SpRUzPM+Lh3ZlxGUlICqK2d\nRBQhN9dAWdkgWVk2RJF51nY5Of6Ehiq0t9s5cMBnYBAebiYjw4ZO5+WDDw5qpd3k5EAWLbJSXT1A\ndnYwXV0j9Pc7yMgIJTDQSHV1H16vQmZmKM88cxFFRYuAI0tFZFnmpZde4je/+Q0PP/ww5513HoIg\n4PF4aGlpwe12U1hYeBzP+rHjxz/+MRaLhXXr1h3zdyVJOi2rLacjPleEOYu1a9cekTDLysrYuHEj\nb7zxBgCPPPIIwCl9gzyVOBajhdOFRM9GQ4aDBwXuv9/Ayy/rNDMDPz+Z1avdVFTIWhMPQHGxzMGD\n0NMjkpbmxOt1oCjq2mNdna8LUN/jsQAAIABJREFUNCBAJc7paSc7d/pmjEVFRkZGZDo6vISEQGqq\nzIEDThISjFRUODRdpE4H555rQafz8O67vqaamBgjCQkmyssniIszEBDgYfduO8XFNkZGPOzd6+uU\nPffcQIxGmaqq0Xnl19ncSqPRw44dfciygiiq8VsTEx5aWsbJybExOjrJ8LBTc+iZ1VaGhZlITfVH\np4M9e4YZGPCtc8bG+nPzzQXcfHMeBoNKFEeSirS3t7Nu3Try8vJ46KGHsFh8QdCnEkNDQ+j1eoKC\ngpienubiiy/mwQcf5Pzzz//U+9y3bx9JSUn/esPPMRYI8xP44x//yJtvvskvf/lLAF566SXKy8vZ\ntm3byR7maYtTYbRwtDgRMpHTCeXlIuvXG5iakpEkL21tqnFBcrKqq5wl09BQiWXLnJSVOeflUGZl\nqbPWjg6FkhIv9fUurFaBlBQDFRWuOY45cNFFOvbtm6KlxZcKEh9vICrKQEXFFMuXG2lsHGdqSqa4\nWHXi6e5Wt9XrYfVqC263h507RzS9pap/tCFJMgaDl8pKVXM5t/w6NOQmP9+f/v4x9HqBuDg/qqqG\nNMmHzWagqMjG+LiL6uoBrcyqhjuHY7OJVFf3aGuUBoNIfn4kk5Nu/PwMPP30hWRmhgFHlop4PB5+\n8Ytf8Oabb/LEE0+Qn59/Qs7np0VDQwPXXXcdsiwjyzLf/OY3Wb9+/VF//5NZm5s2bcJoNHLnnXee\n9BzOMwlnHWFeeOGF9PX1HfL5ww8/zGWXXQb8c8J89dVXeeONNxYI8xhxOKOF6elpFi9erK2Jfhqj\nhWP5/VmZyNluyKAo8Ic/wIMPqtmUs0hNVTCbwWJx0dHhYHBQwWYTWLpUoKrKp6tMT1dYtMjL3r1u\nurt9M87YWJGoKJH+fi82m5uGBicGg0BxsYX2dhf9/erUMjFRR1SUjCTJVFT4XHH0eoHiYn8kycPQ\n0CQdHepMMirKxOLFViorx3C5ZFasCKSpaZTERCuyDPX1vvLrokUmcnPNNDePzCu/qtZ2QXi9Hvbu\nHWFwUJ0NxscHEBfnR23tIMHBRsLDRerq+khJCSYszI+amgFcLhmrVc/996/gllsKtOviSFKR2tpa\n7r77br7yla9w2223nXUvXbOa7Nl7xmKx8Mc//pEtW7awY8eOUz280xpn15UAvPXWW5/p+zExMXR1\ndWn/7urqIjY29p98YwEAoiiyePFiFi9ezJVXXgnMN1p49dVXeeihh/6p0cJsZ67L5TpqEv2kTCQg\nIOCsJcpZCAJceSV8+cvw5JMKW7bA5KSaGGK1TuH1KgQECAwOKoyPK+zYoRAdLZCQICCKbsrKpmlp\nUdcyV6ww0dbmYXBQpr9fIiFBwmJxotOpx9DjUdixw4HZLLBypQW93sPHH4/R2Tm7XmgmLExPRcUk\nVquAIDipqxvRZpH79zvp7XXR2+siJ8efqCgdH300yNSUpK1TZmQE4OenR6/30No6zJtvDiKKAsuW\nhWG3q+VXnQ6czmkaG4fJywvDatWxf/8kBw5M0NU1wZo1EUiSm7Y2tTTc1jZKW5vq1HPllRmsX7+M\npCTVz1VRFM0reG6qyNTUFD/5yU9oa2vjhRdeIDk5+WSf2hMGSZJ4++23Wbp0KbGxsXz44Yf8+c9/\nJjY2lptuuokLLriA7du309XVpcUSLuBQnHUzzKPB2rVrefzxxw+7UO/1eklLS+Odd94hOjqaZcuW\nfW6afk4G/pnRwuyaaGpqKjqdbp60ZdataK60ZTZOSafTYTabP7eNC3198MwzXp55xq51tOp0aqhz\nZycMDKhxXQcOTBMYKBAQIFJT4yuzWq0CK1fq6eqaoqnJqX2ekWHCaBTYtcvJ0qUiExPTDA56yMuz\n0NrqYnjYZ7p+/vl+eL1uPvhgeE6JFIqLgxgddRMZqaOiQi2rBgUZyM62sXv3OKOjHmJijISHK4yN\nuYiKUrtfZ631QOGSSxZhtzvZscNXOZq1tjMaFcbHJ2hqGpr5uwUKChbhdHrp6rLz8MNruO66HHVP\n/yRV5L333uNHP/oRP/jBD7jmmmvOqpJkdXU1hYWF/N///R+bNm1i6dKlJCYmUlhYyN/+9jcAbrrp\nJu644w5eeukloqKiFsqyR8DnijD/9Kc/ceuttzI0NITNZiM/P5/XX3+dnp4ebrzxRl577TUAXn/9\ndU1W8p3vfId77rnnFI/87MXsGlJDQ4NGonv27MFoNJKVlXVYo4WhoSFMJpNGkHNJ9GwzWjgWNDV5\nue++Kd5800dkSUmQluZlx45p7D5ZpKarPHjQQ0aGzM6dkwQEiOTkmKmrm2ZyUn0s2GwCxcU6+vtd\nNDT4mnUsFpG8PAv9/U5sNi+1tWpGZWKimchIE5WV48gyZGaacbsdBAUZmZxUaGnxlXD9/XWsWmWj\nqWmIzs65RuhmUlNtDAw4MJkkGhrUnMuEhABiY/2oqRnE65UpLQ2hvLyLhIRAwsKsM9Z26t9+6aVL\neOKJC1m0yB84cqrI0NAQGzZsQBAENm/eTESELwj6bEBVVZWmGf3HP/7BlVdeSW5uLu+99x6g3n8/\n+MEPiI6O5ic/+QlPPPEEN9544yke9emLzxVhLuDMgKIohzVaMBgMGI1GqqqqeOqpp7jsssvmGS18\nXtyKDoe5XZ5VVQYeemgak8lLTY0Dh0MhKEgkK8tAZaVLMxkoLRUAD0ND6nrmLEJCdGRmmvB63bS1\nTTA8rHYCqUkf0NDgmHHyMdPaOk5amh8tLZMMDfnkKEuWmEhK0vHBB/3z9JY5OUEIgo6pKQ96vYuW\nljEMBpHCwlAGB120t9vR6WD58mCamwdITw+hs3OSgwd9ZF1YGEpwsGqW3tfnW+cMDjZTUhLNVVct\n5Yor0oF/LhV55ZVXeOaZZ9i4cSOXXHLJWVXKnysVmZyc5KWXXuLrX/86H374IRs3buSVV15hyRLV\n+m9iYoK2tja++93vcs0113DbbbctzDCPgAXCXMBpD0VR+N3vfsddd91FRkYGq1evpr6+/ohGC+Cz\n/Dvb3Io+idmy9CebnRRF4U9/cvCjH43R1uaTayxapCM9XWR83EFtrUqwn9RVxsSIRERIdHe7SEuz\nHGIysHatP4Lg5t13fQYBZrNIYaGN9nYHMTE6Dh4co6/POWN4bqW2dgynU8ZkEigsDGB01Im/v57q\n6mEtpgvg/PMjkWUX773n6yNQy6wRuFwygYGwY0cXsqyg14sUFCxiaspFY+MwV121lEcfXUtIiCr9\nOJJUZP/+/axbt47U1FR+9KMfERAQcPxPzCnEbFMPwFNPPcUXvvAFCgoK+PWvf83ll1/OAw88QG1t\nLX/9618BlVD9/f35zW9+w+9//3vefPPNUzn80xoLhHmGYmRkhH//939n//79JCYm8vLLLx82pDYx\nMZHAwEB0Oh0Gg4GKiopTMNrPBkVRuP322/na1742z1xaURRGRkaorq4+K4wWjgVHqzX1ehVeeGGS\nhx8eZ3DQy/LlApWVE0RG6omM1FNR4dMnGo1wwQUm2tomaWvzrWVGRBhISbHQ0DBBTo6B8vJhPB6F\n7OwARBF27VLLsWFhBpYsURNTursdHDjgmxUGBxspLrZx4MA4LS2+rtiYGAuxsVb27BknM9NKeXkP\nkqSwZEkQ4eEWqqr68HgU8vJCGBy0ExBgJCjIRHW1Lxw6Li6QZ565mLVrE7VjczipiNfr5dlnn+XP\nf/4zW7ZsYdmyZSf0fHd1dXHttdcyMDCAIAh897vf5dZbbz1hvzd3Vrhr1y6ee+45ent7eeWVV3j5\n5ZfZtGkTO3bsQBAEzjvvPC699FJGRkbIz8/n2muvZfv27fziF7/g+eefx9/f/4SN80zGAmGeobjz\nzjsJCwvjzjvv5NFHH2V0dFQzWZiLpKQkqqurCQkJOQWjPPk4E40WjhWfRms6PS3z4otjbNrUN69Z\nZ8kSI0FBaonU63XS1jatyUPm6ipzckzIsnMmB3MMp9P32MjM9CMmRkdlZb+WQ6nTCRQWhjAy4mZg\nYJqsLCtlZf0zlnQh7Ns3QU+PSta5uYG4XA5CQkzs2TPK8LDPRCEpKYC0tAAqKg4yMuIj8fBwKxkZ\noWRmhrNx40r8/Y3A4aUioOoW169fzyWXXMK6deswGo2f9vAfNfr6+ujr6yMvL4/JyUkKCwv585//\nfEIbCGdnlw888ABbtmyhp6eHwEA19PqrX/0q8fHx/PznP2fXrl08+OCDmiGD0+nkvvvuo6SkhK9/\n/esnbHxnOhYI8wxFeno677//PpGRkfT19bFmzRpaWloO2S4pKYmqqipCQ0NPwShPDxyL0cLpTKJH\nmjkdC+x2iV/8Yoht24aw22X8/QXy8kSGh11YLDpqaubrKs85xx+93s077wxqn4eGGsjI8Ke2dpyw\nMD2BgV4aGsZISQkgJMRIRYWvU7akxIYgSExNeTXD9Nl9L18ejtns5a239mufm0w6CgrC6e93EBpq\noKNjmOHhaUwmHbm54QwPT9PePk5KSjBPPXUx55wTpx2bw0lFpqenefTRR6mrq2Pbtm2kpaUd83E/\nXvjKV77CLbfc8pnceD6J2VmlLMv09PTw/e9/n+eeew6LxcKyZcu44447tCaevr4+CgoK+M1vfsPF\nF1/M9PS05ly0sGZ5dFggzDMUwcHBjI6qDyBFUQgJCdH+PRfJycnYbDZ0Oh3f+973FjrgZnCqjRaO\nFR6Ph+np6eNm9Tcy4uWZZ4b4n//pYd++uVISC2azSG3tFCUlJvbuHWN83EtRkY2eHicHDqjb6vWw\ncqU/suyhrm5My6sEiI+3kpRkxel0UV4+N2LLhr+/gaqqIYqLg9i3b4jBwWlycsLQ6wVqalRSjogw\nk5BgwePxIooitbV9GgHr9SL33lvKd76ThV6PdtwlSdLWps1mM4qi8OGHH/Lggw9y44038u1vf/uU\nEkJnZyerV6+msbHxuJc7XS4XJpMJgC9+8YssXbqUxx57jL/97W/ce++9vPPOO4SFqc5GTz31FOHh\n4XzjG98A1GeHoigLZHmUWCDM0xhHci36yU9+wnXXXTePIENCQhgZGTlk297eXqKiohgcHOTCCy9k\n27ZtrFy58oSO+0zFXKOFyspKGhoa/qXRwokm0SPJIY4XBgc9bN16kF/+sg+HQ10TjInRs3ixwOSk\nh5oanxZFpxMoLrahKBJDQ+Naqoi/v568vCBaWiYYGnJyzjnB1NcPYbHoSE21UV8/rPnEqpmXFhRF\norZ2EIfD15CUmBhAWpqNurqD9Pf71j/j4gKJjw9EkmS2bLmA3NxIwFeanj32iqJw0UUXYbfbCQ4O\nRpIk7r//fi644AJsNttxPW7HgsnJSdasWcN9993HV77ylc+8r3379pGdnQ2opeaXX36ZlStXctFF\nF3HgwAG++MUv8uSTT7J27VpuueUWBgcH+f3vf388/pTPPRYI8wxFeno627dvZ9GiRfT29rJ27drD\nlmTnYuPGjfj7+3PHHXecpFGe+ThWo4XjRaInO2mlv9/N1q0HaWgYo6JiUCPPtDQ/AgL0VFWN4+8v\nkptrYufOAfLzg5mY8LBnz4S2j5QUKwkJBlpb7fMafgICDOTmBqPTSdTW9mC3q+uiNpuJ7OxQWltH\nMZtFgoJE6usHZj4Pp6NjjJ6eScxmPRs2rOCHPyxGrxePKBVRFIX//d//5YUXXiAnJwe32011dTX1\n9fX8x3/8B48++ugJO35Hgsfj4dJLL+Xf/u3fuO222z7z/pqbm/nTn/5EZGQkBw4coLCwkA8//JCQ\nkBC+9a1vERUVxZYtW3jxxRcpKytjYGCA66+/nhdffJGoqCjtGprbSbuAo8cCYZ6huPPOOwkNDeWu\nu+7ikUceYWxs7JCmH4fDgSRJBAQEMDU1xUUXXcSDDz7IRRdddIpGfebjWI0WZFme51YEh2pEBUGY\n9/A6UuPKyUB/v4snn+zkl788wNTUXCcfG5Lk5v33+5n7xMjNDUJRZGw2gYqKHlwueSZVJIyJCYmW\nFjsJCRYCA2VaWkYoKIhgZMRJW9vYzLEQOOecCDweD6OjTlpahrV963QCV121lDvuKCElRW1aO5JU\npKenh3Xr1hETE8PDDz88b0bp9XqZnJw8bBf5iYSiKFx33XWEhoaydevWT70fWZa1a2R4eJgrrriC\npqYmbr31Vu677z7eeecd/vKXv1BSUsJVV13F9PQ0wcHBPPDAA2zYsGEhvus4YoEwz1CMjIzwjW98\ngwMHDsyTlcx1Lero6OCrX/0qoD40rr766gXXohOAIxktWCwW8vLyNBKd9eg8ktGCKIraZ1arVWtc\nORUYHnazbVsnr7xykIgIhYoKVXMZH28lJsZKVZUqLcnM9MPlcmA0ijPrk4Maoep0cMEFixgddVBR\n0T9v/zk5YdhsBgYGxtizx7eUkJkZSkCAidbWYR58cCU33JCnzR4P1/AkSRK//vWv+cMf/sBjjz3G\nOeecc9rMnD766CNWrVpFTk6ONqaf/vSnXHLJJUe9D6/Xq5XhZ4lv06ZNtLW1cf7553PttdciyzLP\nPPMM1dXVrFq1ira2NoaHh7nhhhsoKioCFpp6jhcWCHMBCzgBUBSFiYkJampqtDXRwxktREVF4Xa7\neffddyktLZ03Ezgd3IrGxtw8++xenn66jaEhn9wjMdFKZqaZDz88yMSEbx0yPt6f2Fg/xsam8Xhc\n2kwyMTGQ6Gg1PURRFIqLQ9m5s5voaH/i4gLZtaufyUm1cejii5N58skLiY1V5RBHmnE3Nzezfv16\nVq1axT333KM1vpxtUBSFO+64A1mWWbZsGVdddRWvvfYar776Ktdffz0rV65kaGiIHTt2sHXrVoqL\ni3nsscdO9bDPSiwQ5gIWcJJwOKOFtrY2xsbGiI6O5j//8z9ZsWKFppk9klvRXN/ckzWbcji8/OY3\nHTzxxB4iI/X09o7R2+vAZjOSnR1Cc/OoJk0pLAyitXWY1NRgmppG5uknly2LICBAoKFhgIEB3zqn\nv7+RFSti+MY3Mvh//2+pdrwOJxVxuVxs3ryZHTt2sG3bNpYuXXpSjsHJQHd3Nxs3buSGG26gpKSE\nlpYWrr32Wi655BIuvfRSvvOd7/DAAw9w+eWX8/DDDzM5Ocm3vvUtqqqquOqqq3C5XPj5+QELs8oT\ngQXCXMACTgGmp6e55ZZbeP3117nvvvuIjY2lqqrqtDda8Hgkfv/7dp54ooHmZl8ytdmsY/XqSIaG\nJqiuHpj3eUFBBMPDqq6yrKwLRVFDnQsKFmG3u2huHuZrX0vn8cfPJzzc+k9TRcrLy7n33nu5+uqr\nuemmm866tbn//u//5vvf/z7XXnstv/rVrxgcHKS3t5e4uDiuv/56PB4PbW1t7Ny5E7vdzubNm/nT\nn/7Exo0b+d73vgcsSEVOJBYIcwGnDG+88YaWCnPDDTdw1113HbLNrbfeyuuvv47VauX5558nPz//\nFIz0+EOWZZ588kmuv/76QyQPs0YLFRUVVFVVHWK0UFBQQG5u7ik1WlAUhddf72Lr1nqamkbIyPCn\nrKxnJnYrArfblzJSWBhKT88YkZF+iKJATY1PKhUd7c/TT1/MhRcma8flcDIau93OQw89xMDAAE8+\n+eRZlVE7Pj6uXQMNDQ1s2bKFyclJSktLueOOO5iamuKaa65h1apV3H777Vx88cUEBQXxhz/8Abfb\nzdjY2FmXsnK64qwLkF7AmQFJkvjBD37A22+/TUxMDMXFxXzpS1+aZxv297//nb1799LW1kZ5eTk3\n3XQTO3fuPIWjPn4QRfGIMgNBEIiLiyMuLo4rrrgCmG+08MYbb/DII48c1mjhkyTq8XgOIVG9Xv+Z\nNaKCIPCFL8TzhS/EU1nZxxNP1KLTCUiSos0wCwrCiYw08Pbb+/B4ZHp7Vd1mQoKNuLgAUlND2LRp\nDTab6RCpiNVq1WaVr732Gj/72c+48847+drXvnbaNPUcD9x///385S9/4dlnn6W0tBSDwcDQ0BC3\n3HILzzzzDKtXryY1NRWLxcKVV16JoigsWbKEDz74gH379pGQkEBERIR2js+mY3M6YmGGeZbjlltu\n4YEHHiA8PPxUD2UeysrK2LhxI2+88QaAJom5++67tW2+//3vs3btWv793/8dmG8HuIDTz2ihs9PO\nU0/t4oUXmli6NIjW1gFGR51ERFhJSwuhqUm1uUtODuIXv7iY1avjtb/jcFKRvr4+7rrrLmw2G489\n9thZ6YdcWVlJSUkJV199NV/60pe44oor+OEPf0hCQgImk4m6ujqee+45vvGNbxAcHMw//vEPbr75\nZm655RbMZvOpHv7nDgszzLMYiqLw1FNPsW3btkP+b7aJ5FStcxw8eFCTWQDExsZSXl7+L7fp7u5e\nIMwZ6HQ6MjIyyMjI4NprrwXmGy288MILR2W04PV6cblcn5lEExMD+dnPVnLffcv47W/refbZcUZH\nnQwMOBgYcGC16tm4cSX/8R+FWCyGeVKRudFksizz4osv8vzzz/PII4+wZs2as3bmVFxczPe+9z16\ne3txOp1ce+21fPWrX8XhcFBcXMyOHTv44x//yO9//3veeecdLr/8ck2WsqCvPPlYIMyzGKOjo1oH\n4SdvriPdaCfLAeRof+OTBZCz9cF5vKDX68nNzSU3N5cbbrjhEKOFp59+ep7RwuxMdPHixfPCuD8L\nidpsJm69tZgf/KCI117by9NPVzMy4uSZZy6hoEDNK50rFfH399de3Nra2li3bh1FRUVs375dMwc/\nkfj2t7/Na6+9RkREBA0NDSf89z6JrVu3EhMTw3PPPUdDQwM//OEP+eIXv8g111zDl7/8ZZ5++mnW\nrl3LhRdeCPiaehbI8uRjgTDPYjQ0NFBQUADMJ8yysjLKyso499xzKSwsnPcAnGudNfuwPBGIiYmh\nq8sXEtzV1XVII8cnt+nu7iYmJuaEjOdshSAImM1miouLKS4uBg41WvjZz352VEYLs/mb8K/digBE\nUeCyy1K47LIU7UXsSFIRj8fDk08+ydtv///27jyo6ur/4/iTTfEihMomqXG9KKTIprmMUeakBqMM\nM+IENZPoRbRxQ9tsyhVadMzJghC1rDTRZtJ0HEQySTRUJBhZrrFcRcXlNqQkCgIf7/n+wY/PDxWV\nCoHwPP7R4fPh8zmfO8N9zzmfc17nIOvXr8ff37/dPqMZM2Ywf/58tZfe3mxtbfnyyy+ZNWsWu3bt\nYuLEiVRWNgZFTJw4kaCgoDt2G2rps5bah3yH2YUtXboUnU5HVFSUuqPBmjVrKCgowN7enlOnTjFz\n5kz0ej0A+fn56lBQU6FsqcfZFkNBiqLg5eXFzz//jLu7OyNHjiQlJeWeST8JCQmkpqZy/PhxYmNj\nu8ykn86mNUELw4cPx83NrcWZufDgoIXmG17fvVQkNzeXJUuWEB4ezvz589s8YL41ysvLmTJlSof0\nMJuMHz8evV7Pq6++qmYIN5HZr52DLJhdWGBgICkpKXh5edHQ0ICNjQ0BAQF8+OGHBAcHk5mZyRdf\nfMGWLVvYvn07Bw4coKSkhDFjxnDjxg30ej3jxo1Tr9fSH23T4uh/Mktv//796rISvV7Pu+++S3Jy\nMoC6pmzevHmkpaVhZ2fHli1b1B6z9Oi1FLRw5coV+vTpow7lBgYG3hO00FLkn6IoCCHQaDRqQbxx\n4wbx8fGcOXOGzz//HK1W22HP2hkK5p9//omzszP19fVYW1vLItkJyYLZRQkhcHV15Y8//n8ReXV1\nNb6+vhiNRnW927hx4zh48CBjx45l06ZN6r9Lly5l3759jBgx4o4vv927d+Pi4kL//v0ZMGDAA9vQ\nPDRa6hqEEJhMJnJycjh58uQDgxYUReHo0aMEBgZiadm4y0hcXJw6tJ6RkcHixYuJjo7u8EX2naFg\nAvz+++94e3vLYtlJyXeYXdTVq1eprKzkrbfeQqfTERoaSk1NjboGz9LSkuzsbGxtbVEUhYaGBsaO\nHYuiKIwePRoXFxd8fHyAxkJpNjdu95SUlESPHj0QQpCTk0N6ejplZWVcv36dkJAQnJyc1D/2lr4E\n5RfBf5uFhQVubm5MnjyZyZMnA3cGLRw5coT169dz5coVqqurcXR0ZPny5YwZMwaNRkNkZCRJSUkU\nFhbSq1cv3njjDdauXcvkyZNZt25dBz9dx/P29gbk5LbOShbMLqp379788ssvnDhxgr1797J3717e\nfPNNoqKiiImJwdfXl+zsbGbPnk1FRYUaXG1tbY3RaKRPnz7Y2tqSnp6Ol5cXTz31FDU1NSiKQkhI\nCLNnz+aTTz4hOjqayMhIjhw5Qnp6Ops2baJHjx6UlpZSWlqKj4/PHT3R5l8Eclp819A8aCE0NJSV\nK1eSnJxMbGwsWq2WzMxMPvvsM65evUp1dTWJiYlMnDhRnZVbXFyMyWR6+I0kqaMJ6bFy4cIF8cEH\nHwi9Xi/27NkjhBDi7NmzIjIyUnz77bfi119/Fc8995xYvHixMJvNQq/XCz8/P7F27VpRUlIiJk2a\nJP744w/R0NAgNm/eLF544QUhhBC1tbViwIABQlEUUVhYKCZMmCDCwsJEQECASE5OFkIIUV1dLbKy\nskRVVdV926coilAU5dF/EI/I/v37hZeXl/D09BQff/zxPcczMjKEg4OD8Pf3F/7+/iIuLq4DWvno\n3L59WyxbtkxcunTpnmN1dXXCZDJ1QKseLCIiQvTt21d069ZN9OvXT3z11Vcd3SSpk5IFswu7ffu2\nUBRFNDQ0CLPZ/MBzMzIyxCuvvCLmzp0rgoKCxHfffXfPOVu3bhXR0dHi1q1boqamRqxYsUIsW7ZM\nCCFEamqqiIyMFMXFxWL58uVi3rx5QgghCgoKxDPPPCPq6urEwYMHhY2NjYiJiRE+Pj5ixYoVD32G\nh7W7M1EUReh0OnH27FlRX18v/Pz8hMFguOOcjIwMMWXKlA5qoSRJ/4aMs+/CmvJDra2t1aHQ5hFp\nTY4cOcL58+eJj4/Hx8c2JwrUAAAH1UlEQVSHfv36MXr0aKBxfVxDQ+M+henp6bi7u9O9e3eqq6s5\nf/48Q4YMARqXpGi1WkwmE3V1dYSHhwONWzENHz6csrIyTp8+jY+PD8nJyXz66afk5ORw/fp1amtr\n+emnnxg3bhzTpk3jm2++Abhj7d7dmuLdWjrWUbKzs/H09MTDwwMbGxsiIiLYs2fPPed1pjZLktR6\nsmA+ZpqHcDdxd3enqKiIOXPmcPDgQeLj4xk4sHH3CBsbG3Vx+bx589Rc16qqKsrLy/Hy8gIgNzeX\nfv364enpyalTp9Scy7KyMnr27InZbKasrEz9fTs7O1xdXTGZTOzatYutW7eyb98+Fi5ciMFg4PLl\ny/zwww+8/PLLarG/efMm9fX1AH87tq09tBTld/HixTvOsbCwICsrCz8/P0JCQjAYDO3dTEmS/iE5\n6UdCp9OxevXqh543cuRI9f+DBw9mx44dODk5AeDs7IyXlxd9+/ZFp9Oxb98+7OzsSEhI4LXXXkOr\n1WIwGAgLCwMag7V79OhBz549SU9P58cff6SyspIhQ4aQmprKoEGD8Pb2xtHRUb3nqlWrqK2tZc6c\nOezevZuxY8ei0WgYPnx4i5OH2ntZS2vuExgYyIULF9BoNOzfv5+wsDBKSkraoXWSJP1bsocptVrT\n0pImzXdASUhIYPz48QDExsZy7do1YmNjiYiIICoqimvXrlFYWKgGD5hMJjQaDa6urvz2229kZWWx\nYcMGhgwZwksvvcSzzz6Lv78/N2/exGQysX37dmpra1m8eDGHDx/m+++/58CBA0RFRbFo0SI1sq2q\nqgqj0Qig9kCbD4HePRzdlloT92dvb49GowEgODiYhoYGrl69+kjaI0lS25I9TKnVWlpX2VSQRLMd\n3nU6HQkJCXecZ2Vlxdy5c3FwcKCmpoZz586pa0K9vb0pLi5m6tSpzJw5847fKyoq4tatWyQlJbF0\n6VI8PDw4duwYoaGhxMXFsWrVKqZMmYLRaMTNzY0dO3Zw6NAh8vPziYiI4O2338be3p6qqiocHR1b\n7Ik2D2b4N0aMGEFpaSnl5eW4u7uzc+dOUlJS7jjHZDLh4uKChYUF2dnZCCG65LZVktQVyaQfqc2Z\nzWY1Mu/uItv088uXL/PXX3/h7e1NQUEBs2bNws7OjsGDB/Piiy8ydepU6uvrmT9/PjU1NdTX17Nz\n506gMXNz9erVBAQEoCgKvr6+5OTkkJiYyMmTJ1mzZg2enp6Eh4ezatUq7O3tWbZsGbm5udja2vLe\ne+8RGhpKbW1tm++G8bC4v8TERJKSkrC2tkaj0bBu3Tp1gpUkSZ2bLJhSu7jf+8SmAlpXV0deXh4G\ng4GhQ4cyatQoABITE4mLi+PYsWNotVpKSkpYsGABGzZswMPDg/z8fCIjIykqKmLChAn06tWLc+fO\nYTabMRgM7NmzB6PRyJkzZ3j//fcpKirC0tISX19flixZQmZmJvb29sTExBAeHq4GOEiSJN1NDslK\n7eLunqZoFp8nhKB79+6MHj1a7W2J/wv+NhqN6PV6NZg7NzcXS0tLHBwcADhx4gSDBw/GbDbj5ubG\nokWLCAwMpKqqivPnz+Pi4kLv3r1Zv349Hh4evP766wDk5OSQl5dHVlYWeXl5mEymDtklQ2qdtLQ0\nteceHR3NO++809FNkh5DctKP1CGa9zSbrxFVFAWAr7/+Gn9/f1xcXIiNjQUa3zWGhYWRmJjIE088\nAUBxcTGDBg3C0tISHx8fNm7ciKIoODg44Ovri7OzM4GBgRw+fJjCwkKioqK4fv06PXv2xGQykZyc\nzLBhwwgLC5MxfZ3U7du31V1rDAYDKSkpnD59uqObJT2GZMGUOg1LS0u1lzdjxgzy8vJYuHChOhvX\nysoKW1tbtFqtWtzWrl1LfHw8ANOmTUNRFAICAhg6dCipqalcuHCBtLQ0evfuTUxMDA0NDWRmZuLt\n7c3Ro0e5dOkSCxYsoLS0tGMe+j9g5syZuLq6MmzYsPues2DBAgYNGoSfnx95eXltev/WBkJI0qMm\nC6bUaTk5OT10Uo4Qgm7duiGEYODAgWzevJmCggIOHTpEUFAQQgi2bdtGQEAA06dPZ9SoUWi1Wk6c\nOIG1tTUfffQRFy9e5OjRo+30VP89M2bMIC0t7b7HU1NTKSsro7S0lI0bN6rD3m2lNYEQktQe5Esb\n6T+taTjXwsJCjcqzsrKib9++QOO6x23btgFQUVGBs7Mzt27dYu7cueTn52Nra8uYMWN4/vnnO+wZ\nOrugoCDKy8vve3zv3r1Mnz4dgFGjRlFVVYXJZMLV1bVN7t+Z0pykx5ssmFKXcb/9N81mM1ZWVmqI\nQPfu3dUiajQacXJyUt+JSn9fSz3AioqKNiuYrQmEkKT2IIdkpS7NwsLinsk8Qgg1rECn08li2Qbu\nXp3Wlr3C5oEQTetxQ0ND2+z6ktRasocpPXZaKqLSP3d3D7CiooInn3yyza5vbW1NQkICkyZNUgMh\nnn766Ta7viS1liyYkiT9K6GhoSQkJBAREcHx48dxdHRss+HYJsHBwQQHB7fpNSXp75IFU5KkB4qM\njOTw4cNUVlbSv39/Vq5cqe6ROnv2bEJCQkhNTcXT0xM7Ozu2bNnSwS2WpEdDRuNJkiRJUivIST+S\nJEmS1AqyYEqSJElSK8iCKUmSJEmtIAumJEmSJLXC/wBa2JUOrTRVawAAAABJRU5ErkJggg==\n", "text": "" } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Monte Carlo simulations" }, { "cell_type": "code", "collapsed": false, "input": "from scipy import random\nfrom numpy import maximum, mean\n\ndef price_MC_LocalVol(s0, strike, T, gamma, sigma, rho, nbSimul, nbSteps):\n deltaT = T / (1.*nbSteps)\n SS = np.linspace(s0, s0, nbSimul)\n time = np.linspace(deltaT, T, nbSteps)\n\n for t in time:\n sig = np.sqrt(SSVI_LocalVarg(np.log(SS), gamma, sigma, rho, t))\n SS = SS*np.exp(-0.5*sig*sig*deltaT + np.sqrt(deltaT)*sig*random.normal(0., 1., nbSimul))\n price = mean(maximum(SS - strike, 0.))\n return price", "language": "python", "metadata": { "zanadu": { "is_hidden": false } }, "outputs": [], "prompt_number": 22 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Numerical example" }, { "cell_type": "code", "collapsed": false, "input": "from zanadu.Groups.ImperialCollege.Root.Tools.BlackScholes import BlackScholesCore\nfrom zanadu.Groups.ImperialCollege.Root.Tools.ImpliedVolLeeLi import impliedVolCore", "language": "python", "metadata": { "zanadu": { "is_hidden": false } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Invoking import hook for zanadu.groups.imperialcollege.root.tools.blackscholes...\nblackscholes imported." }, { "output_type": "stream", "stream": "stdout", "text": "\nInvoking import hook for zanadu.groups.imperialcollege.root.tools.impliedvolleeli..." }, { "output_type": "stream", "stream": "stdout", "text": "\nimpliedvolleeli imported." }, { "output_type": "stream", "stream": "stdout", "text": "\n" } ], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": "sigma, gamma, rho = 0.2, 0.8, -0.7\ns0, x, T = 1., 0., 1.\nnbSimul, nbSteps = 100000, 2000\nxx = np.linspace(-0.5, 0.5, 10)\n\nprint \"Consistency check for no-arbitrage: \", (gamma - 0.25*(1.+np.abs(rho))>0.)\n\nssvivol = sqrt(SSVI(x, gamma, sigma, rho, T)/T)\nBSPrice = BlackScholesCore(True,1.,s0,s0*np.exp(x),T,ssvivol)\nprint \"BS implied vol: \", impliedVolCore(True, 1., s0, s0*np.exp(x), T, BSPrice, tolerance=1e-6, itermax=100)\nprint \"SSVI implied vol: \", ssvivol\n\nprice = price_MC_LocalVol(s0, s0*np.exp(x), T, gamma, sigma, rho, nbSimul, nbSteps)\nprint \"Dupire implied vol: \", impliedVolCore(True, 1., s0, s0*np.exp(x), T, price, tolerance=1e-6, itermax=100)", "language": "python", "metadata": { "zanadu": { "is_hidden": false } }, "outputs": [], "prompt_number": "*" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "\\begin{bibliography}\n@article{Gatheral,\n author = {Jim Gatheral},\n title = {A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives},\n journal = {Global Derivatives, Madrid},\n year = {2004},\n link = {http://faculty.baruch.cuny.edu/jgatheral/madrid2004.pdf},\n}\n@article{GatheralJacquier,\n author = {Jim Gatheral and Antoine Jacquier},\n title = { Arbitrage-free SVI volatility surfaces},\n journal = {Quantitative Finance},\n year = {2014},\n volume = {14(1)},\n pages = {59-71}\n}\n\\end{bibliography}" } ], "metadata": {} } ] }