{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Part 1" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "using PyPlot\n", "\n", "srand(4242);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Objective function is\n", "$$f(x) = \\frac{1}{2} x^2$$\n", "so the gradient is\n", "$$f(x) = x$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "grad_f (generic function with 1 method)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function grad_f(x)\n", " return x\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose that our samples are of the form\n", "$$\\tilde f(x) = \\frac{1}{2} (x + z)^2$$\n", "where $z \\sim N(0,1)$ is a standard Gaussian random variable. Then\n", "$$\\nabla \\tilde f(x) = x + z$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sample_grad_f (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function sample_grad_f(x)\n", " return x + randn(length(x)) / sqrt(length(x))\n", "end" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "stochastic_gradient_descent_until (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function gradient_descent(x0, alpha, num_iters)\n", " dist_to_optimum = zeros(num_iters)\n", " x = x0\n", " for t = 1:num_iters\n", " dist_to_optimum[t] = norm(x)\n", " x = x - alpha * grad_f(x)\n", " end\n", " return dist_to_optimum\n", "end\n", "\n", "function stochastic_gradient_descent(x0, alpha, num_iters)\n", " dist_to_optimum = zeros(num_iters)\n", " x = x0\n", " for t = 1:num_iters\n", " dist_to_optimum[t] = norm(x)\n", " x = x - alpha * sample_grad_f(x)\n", " end\n", " return dist_to_optimum\n", "end\n", "\n", "function stochastic_gradient_descent_until(x0, alpha, accuracy, num_iters)\n", " x = x0\n", " for t = 1:num_iters\n", " x = x - alpha * sample_grad_f(x)\n", " if norm(x) <= accuracy\n", " return t\n", " end\n", " end\n", " return num_iters\n", "end" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x0 = 5 * randn(100);\n", "num_iters = 1000000;" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "noise_ball_size (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function noise_ball_size(dists)\n", " return sqrt(mean(dists[ceil(length(dists/2)):end].^2))\n", "end" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "alphas = [0.01, 0.02, 0.05, 0.1, 0.2, 0.5];\n", "ball_sizes = [noise_ball_size(stochastic_gradient_descent(x0, alpha, num_iters)) for alpha in alphas];" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(alphas, ball_sizes);\n", "xlabel(\"step size (alpha)\");\n", "ylabel(\"noise ball size\");" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "convergence_times = [mean([stochastic_gradient_descent_until(x0, alpha, 1.0, num_iters) for k=1:5]) for alpha in alphas];" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(alphas, convergence_times);\n", "xlabel(\"step size (alpha)\");\n", "ylabel(\"time to converge to distance of 1\");" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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rD89nZ2ffchgREZHK6nJOPuGfxrLrVBoAIzo0YuHIYFydNYKkqin135inp+cfVrVms1lVr4iIVEuRZ68wc3U0qdn51HK045nh7RjTxU+fe1VUqYsfNzc3/vWvf9G1a9ebnj99+jR///vfrRZMRETE1owmMyu+P83ybacxmaGltyuvje/EbT5uto4mt6DUxU+nTp0AuPPOO2963tPTE7PZbJ1UIiIiNpaSlcc/VscQee4KAPd18ePp4W2p46Rurqqu1H+D48aN49q1a7973tfXl3//+99WCSUiImJLu06lMWtNDFdyC6jjZM/Cke0Y2dHP1rHESgxmNdeQlZWFh4cHmZmZuLu72zqOiIjYSJHRxMtbTvH6jrMAtGnozspxHWnRwNXGyeRmyvr5rbY7ERERIDHjGjM+iebghZ8BmNCtKf8a0oZajvY2TibWpuJHRERqvK3HUpi9LpaMq4W4OTuweHQIQ0Ia2jqWlBMVPyIiUmMVFJl44ZsTvLvnPAAhfh6sfKATTerVsXEyKU8qfkREpEZKSL/KtIgoYi9mAvBwjwCeGNQaJwerbX4glVSp/obDw8PJzc0FYNeuXRQVFZVrKBERkfL0dVwSg5fvJvZiJh61HXl7YhfmDwtS4VNDlGq2l6OjIxcvXsTHxwd7e3uSkpLw9vauiHwVQrO9RERqhrxCIwu/Os5/910AoHPTuix/oCONPWvbOJmURbnO9mrWrBnLly+nf//+mM1mIiMjqVu37k2v7dWrV6lfXEREpKKcS8shLCKa40nX96qc2rsF4XffhqO9WntqmlK1/Hz++edMmTKF1NRUDAbD767kbDAYMBqNVg9Z3tTyIyJSvX0Rc4kn18eRW2CknosTL93Xnt6tqk8PRk1V1s9vixY5zMnJwd3dnZMnT/5ut5eHh0epX7yyUPEjIlI9XSsw8vSXR1lzMAGAbs29WDa2Iz7utWycTKyhQhY5dHV1Zfv27QQEBODgoIliIiJSeZ1KyWZaRBSnUnIwGGBGn5bM6NsSezvtxF7TWVzB3HnnnRiNRj777DOOHz8OQFBQECNGjMDeXqtgioiIbZnNZtYevMj8L4+QV2iigZszy+7vQPfA+raOJpWExaO8zpw5Q1BQEBMnTmT9+vWsX7+eCRMm0LZtW86ePWvRvd544w1CQkJwd3fH3d2d0NBQNm/eXHw+Ly+PsLAw6tWrh6urK6NHjyYlJaXEPeLj4xkyZAh16tTB29ubxx9/XFPxRURqqJz8ImatieGfnx0mr9BEz5b12TyzpwofKcHi4mfGjBk0b96chIQEoqKiiIqKIj4+noCAAGbMmGHRvfz8/Fi8eDGHDh3i4MGD9OnThxEjRnD06FEAZs2axcaNG1m7di07d+4kMTGRUaNGFT/faDQyZMgQCgoK2Lt3Lx988AHvv/8+8+fPt/RtiYhIFXc0MZPhK/bweUwi9nYG/jmwFR/89S/Ud3W2dTSpZCze1d3FxYV9+/YRHBxc4nhsbCw9evQgJyfnlgJ5eXnx4osvcu+999KgQQMiIiK49957AThx4gRt2rQhMjKSbt26sXnzZoYOHUpiYiI+Pj4ArFq1ijlz5pCWloaTk1OpXlMDnkVEqi6z2cxH++N5dtMxCopMNPSoxfIHOnJ7My9bR5NyVtbPb4tbfpydncnOzr7heE5OTqmLjZsxGo2sXr2a3NxcQkNDOXToEIWFhfTr16/4mtatW9OkSRMiIyMBiIyMJDg4uLjwARgwYABZWVnFrUc3k5+fT1ZWVomHiIhUPVl5hUyLiOapz49QUGSib2tvvp7RU4WP/CGLi5+hQ4fy6KOPsn//fsxmM2azmX379jFlyhSGDx9ucYC4uDhcXV1xdnZmypQpbNiwgaCgIJKTk3FycsLT07PE9T4+PiQnJwOQnJxcovD55fwv537PokWL8PDwKH74+/tbnFtERGwrNiGDIct381VcEo72BuYNacM7k7pQ16Xsv4hLzWBx8bN8+XJatGhBaGgotWrVolatWvTo0YPAwECWLVtmcYBWrVoRExPD/v37mTp1KpMmTeLYsWMW38cSc+fOJTMzs/iRkJBQrq8nIiLWYzabeXfPee5dtZeE9Gv41a3N2ind+VvP5hgMmsYuf87iqe6enp588cUXnDlzpniqe5s2bQgMDCxTACcnp+Lndu7cmQMHDrBs2TLuv/9+CgoKyMjIKNH6k5KSgq+vLwC+vr78+OOPJe73y2ywX665GWdnZ5ydNQBORKSqybhawOy1h9l6/PrP+kHtfFk8OgSP2o42TiZVSZlXKgwMDCxzwfNHTCYT+fn5dO7cGUdHR7Zt28bo0aMBOHnyJPHx8YSGhgIQGhrKwoULSU1NLV5xesuWLbi7uxMUFGT1bCIiYjuHLqQzPSKaxMw8nOzteGpoGx7s1lStPWIxmy7TPHfuXAYNGkSTJk3Izs4mIiKCHTt28O233+Lh4cHkyZMJDw/Hy8sLd3d3pk+fTmhoKN26dQOgf//+BAUFMWHCBJYsWUJycjLz5s0jLCxMLTsiItWEyWTmzV3nWPrdSYwmMwH1XVjxQEfaNa562ylJ5WDT4ic1NZWJEyeSlJSEh4cHISEhfPvtt9x9990AvPLKK9jZ2TF69Gjy8/MZMGAAr7/+evHz7e3t2bRpE1OnTiU0NBQXFxcmTZrEM888Y6u3JCIiVnQ5J5/wT2PZdSoNgBEdGrFwZDCuztpiScrO4nV+qiOt8yMiUvlEnr3CzNXRpGbnU8vRjgXD23JfF391c0mxCtnYVEREpLwZTWZWfH+a5dtOYzJDS29XVo7rRCtfN1tHk2rC4qnuALt37+bBBx8kNDSUS5cuAfDf//6XPXv2WDWciIjULKlZeTz4zn5e3Xq98BnT2Y8vpvVQ4SNWZXHx89lnnzFgwABq165NdHQ0+fn5AGRmZvL8889bPaCIiNQMu06lMWjZbiLPXaGOkz2v3N+eF8e0p46TOinEuiwufp577jlWrVrF22+/jaPj/9ZV6NGjB1FRUVYNJyIi1V+R0cSSb04w8T8/ciW3gDYN3dk4/Q5GdvSzdTSppiwup0+ePEmvXr1uOO7h4UFGRoZVQomISM2QmHGNGZ9Ec/DCzwA82K0J84YEUcvR3sbJpDqzuPjx9fXlzJkzNGvWrMTxPXv20Lx5c2vlEhGRam7rsRRmr4sl42ohbs4OLB4dwpCQhraOJTWAxcXPI488wsyZM/nPf/6DwWAgMTGRyMhIZs+ezVNPPVUeGUVEpBopKLrezfXOnvMAhPh5sPKBTjSpV8fGyaSmsLj4eeKJJzCZTPTt25erV6/Sq1cvnJ2dmT17NtOnTy+PjCIiUk0kpF9lWkQUsRczAXi4RwBPDGqNk0OZJh+LlEmZFzksKCjgzJkz5OTkEBQUhKurq7WzVRgtcigiUv6+jktizmeHyc4rwqO2I0vHtOfuIB9bx5IqrMIWOczMzMRoNOLl5VVi89D09HQcHBxUPIiISAl5hUYWfnWc/+67AECnJp6sGNeJxp61bZxMaiqL2xnHjh3L6tWrbzj+6aefMnbsWKuEEhGR6uFcWg6jXt9bXPhM7d2CNX8PVeEjNmVx8bN//37uuuuuG4737t2b/fv3WyWUiIhUfV/EXGLYij0cS8qinosT7//1duYMbI2jvcb3iG1Z3O2Vn59PUVHRDccLCwu5du2aVUKJiEjVda3AyNNfHmXNwQQAujX3YtnYjvi417JxMpHrLC6///KXv/DWW2/dcHzVqlV07tzZKqFERKRqOpWSzYjX9rDmYAIGA8zs25KP/9ZNhY9UKha3/Dz33HP069eP2NhY+vbtC8C2bds4cOAA3333ndUDiohI5Wc2m1l76CLzvzhCXqGJBm7OLLu/A90D69s6msgNLG756dGjB5GRkfj7+/Ppp5+yceNGAgMDOXz4MD179iyPjCIiUonl5BcR/mks/1x3mLxCEz1b1ufrGT1V+EilVeZ1fqoTrfMjIlI2RxMzmR4RzbnLudjbGXis/21M6dUCOzuDraNJDVBh6/wAmEwmzpw5Q2pqKiaTqcS5m216KiIi1YvZbOaj/fE8u+kYBUUmGnrUYvkDHbm9mZeto4n8KYuLn3379jFu3DguXLjAbxuNDAYDRqPRauFERKTyycorZO5ncXwVlwRA39beLB3TnrouTjZOJlI6Fhc/U6ZMoUuXLnz11Vc0bNgQg0FNmyIiNUVsQgbTPokiIf0aDnYGnhjUmsl3BOizQKoUi4uf06dPs27dOgIDA8sjj4iIVEJms5n//PATizcfp9Boxq9ubVaO60QHf09bRxOxmMXFT9euXTlz5oyKHxGRGiLjagGz1x5m6/EUAAa182Xx6BA8ajvaOJlI2Vhc/EyfPp3HHnuM5ORkgoODcXQs+Y8/JCTEauFERMS2Dl1IZ3pENImZeTjZ2/HU0DY82K2purmkSrN4qrud3Y1LAxkMBsxmc5Ud8Kyp7iIiJZlMZt7cdY6l353EaDITUN+FFQ90pF1jD1tHEylWYVPdz58/b+lTRESkCrmck0/4p7HsOpUGwIgOjVg4MhhX5zKtjiJS6Vj8L7lp06blkUNERCqByLNXmLk6mtTsfGo52rFgeFvu6+Kvbi6pVspcxh87doz4+HgKCgpKHB8+fPgthxIRkYplNJlZ8f1plm87jckMLb1dWTmuE6183WwdTcTqLC5+zp07x8iRI4mLiyse6wMU/1ZQFcf8iIjUZKlZecxcHUPkuSsAjOnsx4IRbanjpG4uqZ4s3th05syZBAQEkJqaSp06dTh69Ci7du2iS5cu7NixoxwiiohIedl1Ko1By3YTee4KdZzseeX+9rw4pr0KH6nWLP7XHRkZyffff0/9+vWxs7PDzs6OO+64g0WLFjFjxgyio6PLI6eIiFhRkdHEy1tO8fqOswC09nXjtfGdaNHA1cbJRMqfxcWP0WjEze16H3D9+vVJTEykVatWNG3alJMnT1o9oIiIWFdixjVmfBLNwQs/A/BgtybMGxJELUd7GycTqRgWFz/t2rUjNjaWgIAAunbtypIlS3BycuKtt96iefPm5ZFRRESsZOuxFGaviyXjaiFuzg4sHh3CkJCGto4lUqEsLn7mzZtHbm4uAM888wxDhw6lZ8+e1KtXj9WrV1s9oIiI3LqCIhNLvjnBO3uur9UW4ufBygc60aReHRsnE6l4Fg94HjBgAKNGjQIgMDCQEydOcPnyZVJTU+nbt69F91q0aBG33347bm5ueHt7c88999zQdda7d28MBkOJx5QpU0pcEx8fz5AhQ6hTpw7e3t48/vjjFBUVWfrWRESqpYT0q4xZtbe48Hm4RwBrp4Sq8JEay+Li5+GHHyY7O7vEMS8vL65evcrDDz9s0b127txJWFgY+/btY8uWLRQWFtK/f//ilqVfPPLIIyQlJRU/lixZUnzOaDQyZMgQCgoK2Lt3Lx988AHvv/8+8+fPt/StiYhUO5vjkhi8fDexFzPxqO3I2xO7MH9YEM4OGt8jNZfFe3vZ29uTlJSEt7d3ieOXL1/G19f3llpc0tLS8Pb2ZufOnfTq1Qu43vLToUMHXn311Zs+Z/PmzQwdOpTExER8fHwAWLVqFXPmzCEtLQ0nJ6c/fV3t7SUi1U1eoZHnvz7Oh5EXAOjUxJMV4zrR2LO2jZOJWE9ZP79L3fKTlZVFZmYmZrOZ7OxssrKyih8///wzX3/99Q0FkaUyMzOB6y1Jv/bxxx9Tv3592rVrx9y5c7l69WrxucjISIKDg4sLH7jeNZeVlcXRo0dv+jr5+fkl8mdlZd1SbhGRyuRcWg6jXt9bXPhM7d2CNX8PVeEj8v+VesCzp6dn8Zib22677YbzBoOBBQsWlDmIyWTiH//4Bz169KBdu3bFx8eNG0fTpk1p1KgRhw8fZs6cOZw8eZL169cDkJycXKLwAYq/T05OvulrLVq06JayiohUVl/EXOLJ9XHkFhjxcnHi5fva07vVrf1iKlLdlLr42b59O2azmT59+vDZZ5+VaJ1xcnIqLlDKKiwsjCNHjrBnz56jDJ6CAAAgAElEQVQSxx999NHir4ODg2nYsCF9+/bl7NmztGjRokyvNXfuXMLDw4u/z8rKwt/fv2zBRUQqgWsFRp7+8ihrDiYA0DXAi+UPdMTHvZaNk4lUPqUufu68804Azp8/T5MmTay6w++0adPYtGkTu3btws/P7w+v7dq1KwBnzpyhRYsW+Pr68uOPP5a4JiUlBQBfX9+b3sPZ2RlnZ2crJBcRsb3TKdmERURxKiUHgwFm9GnJjL4tsbfTTuwiN2PxbK/jx4/zww8/FH//2muv0aFDB8aNG8fPP/9s0b3MZjPTpk1jw4YNfP/99wQEBPzpc2JiYgBo2PD6olyhoaHExcWRmppafM2WLVtwd3cnKCjIojwiIlWJ2Wzm04MJDFu5h1MpOTRwc+bjyV2ZdfdtKnxE/oDFxc/jjz9ePEA4Li6O8PBwBg8ezPnz50t0JZVGWFgYH330EREREbi5uZGcnExycjLXrl0D4OzZszz77LMcOnSIn376iS+//JKJEyfSq1cvQkJCAOjfvz9BQUFMmDCB2NhYvv32W+bNm0dYWJhad0Sk2srJLyL801j+ue4weYUmerasz9czetI9sL6to4lUehZPdXd1deXIkSM0a9aMp59+miNHjrBu3TqioqIYPHjw7w4yvumL/07X2XvvvcdDDz1EQkICDz74IEeOHCE3Nxd/f39GjhzJvHnzSkxpu3DhAlOnTmXHjh24uLgwadIkFi9ejIND6Xr1NNVdRKqSY4lZTIuI4tzlXOztDITffRtT72yBnVp7pIYp6+e3xdtbODk5FU8137p1KxMnTgSuT0+3dMr4n9Vd/v7+7Ny580/v07RpU77++muLXltEpKoxm818vD+eZzYdo6DIREOPWix/oCO3N/P68yeLSDGLi5877riD8PBwevTowY8//siaNWsAOHXq1J8OVhYRkbLJyitk7mdxfBWXBEDf1t4sHdOeui5/vpCriJRk8ZiflStX4uDgwLp163jjjTdo3LgxcH2l5YEDB1o9oIhITRebkMHQ5Xv4Ki4JBzsD84a04Z1JXVT4iJSRxWN+qiON+RGRyshsNvOfH35i8ebjFBrN+NWtzcpxnejg72nraCKVQrmO+cnKyiq+6Z+N61HxICJy6zKuFjB77WG2Hr++btnAtr68cG8IHrUdbZxMpOorVfFTt27d4s1Mf9nm4rfMZjMGgwGj0Wj1kCIiNcmhC+lMj4gmMTMPJ3s7nhrahge7NbXq4rIiNVmpip/vv/++eDuL7du3l2sgEZGaymQy8+aucyz97iRGk5mA+i6seKAj7Rp72DqaSLWiMT9ozI+I2N7lnHzCP41l16k0AEZ0aMTCkcG4Ols8KVekxijXMT+HDx8u9Q1/WXlZRERKJ/LsFWaujiY1O59ajnYsGN6W+7r4q5tLpJyUqvjp0KEDBoOheFzPH9GYHxGR0jGazKz4/jTLt53GZIZAb1deG9eJVr5uto4mUq2Vqvg5f/588dfR0dHMnj2bxx9/nNDQUAAiIyN56aWXWLJkSfmkFBGpZlKz8pi5OobIc1cAGNPZjwUj2lLHSd1cIuWtVP/LmjZtWvz1mDFjWL58OYMHDy4+FhISgr+/P0899RT33HOP9VOKiFQju06lMWtNDFdyC6jjZM/Cke0Y2VEr5ItUFIt/xYiLiyMgIOCG4wEBARw7dswqoUREqqMio4lXtp7i9R1nMZuhta8br43vRIsGrraOJlKjWLy9RZs2bVi0aBEFBQXFxwoKCli0aBFt2rSxajgRkeoiMeMaY9/ax2vbrxc+D3ZrwudhPVT4iNiAxS0/q1atYtiwYfj5+RXP7Dp8+DAGg4GNGzdaPaCISFW37XgKj62NJeNqIW7ODiwaHczQkEa2jiVSY5VpnZ/c3Fw+/vhjTpw4AVxvDRo3bhwuLi5WD1gRtM6PiJSHgiITS745wTt7rk8aCW7swcpxHWlar2r+rBSpbMp1nZ/fcnFx4dFHHy3LU0VEaoSE9KtM+ySa2IQMAB7uEcCcQa1wdrC3cTIR0ZxKEREr2xyXxD8/O0x2XhEetR1ZOqY9dwf52DqWiPx/Kn5ERKwkr9DI818f58PICwB0auLJinGdaOxZ28bJROTXVPyIiFjB+cu5hH0cxbGkLACm3NmCx/rfhqO9xZNqRaScqfgREblFX8Rc4sn1ceQWGPFyceLl+9rTu5W3rWOJyO8oc/Fz6NAhjh8/DkBQUBCdOnWyWigRkargWoGRp788ypqDCQB0DfBi+QMd8XGvZeNkIvJHLC5+UlNTGTt2LDt27MDT0xOAjIwM7rrrLlavXk2DBg2sHlJEpLI5nZJNWEQUp1JyMBhgep+WzOzbEns77cQuUtlZ3Bk9ffp0srOzOXr0KOnp6aSnp3PkyBGysrKYMWNGeWQUEak0zGYznx5MYNjKPZxKyaGBmzMfT+5K+N23qfARqSIsXuTQw8ODrVu3cvvtt5c4/uOPP9K/f38yMjKsGrAiaJFDESmN3Pwi5n1+hA3RlwDo2bI+L9/XgQZuzjZOJlIzVdgihyaTCUdHxxuOOzo6YjKZLL2diEiVcCwxi2kRUZy7nIu9nYHwu29j6p0tsFNrj0iVY3G3V58+fZg5cyaJiYnFxy5dusSsWbPo27evVcOJiNia2Wzmo30XuOf1Hzh3OZeGHrVY/Wg3wu4KVOEjUkVZ3PKzcuVKhg8fTrNmzfD39wcgISGBdu3a8dFHH1k9oIiIrWTlFTL3szi+iksCoG9rb5aOaU9dFycbJxORW2Fx8ePv709UVBRbt24tsbFpv379rB5ORMRWYhMymP5JNPHpV3GwM/DEoNZMviMAg0GtPSJVncUDnj/88EPuv/9+nJ1LDvArKChg9erVTJw40aoBK4IGPIvIL8xmM//54ScWbz5OodGMX93arBzXiQ7+nraOJiK/UdbPb4uLH3t7e5KSkvD2Lrl66ZUrV/D29sZoNFpyu0pBxY+IAGRcLWD22sNsPZ4CwMC2vrxwbwgetW+c5CEitldhs73MZvNNm30vXryIh4eHpbcTEakUDl1IZ3pENImZeTjZ2/HU0DY82K2purlEqqFSFz8dO3bEYDBgMBjo27cvDg7/e6rRaOT8+fMMHDiwXEKKiJQXk8nMm7vOsfS7kxhNZprVq8PKcZ1o11i/zIlUV6Uufu655x4AYmJiGDBgAK6ursXnnJycaNasGaNHj7Z+QhGRcnI5J5/wT2PZdSoNgOHtG/H8qGBcnbXns0h1Vur/4f/+978BaNasGffffz+1at36xn2LFi1i/fr1nDhxgtq1a9O9e3deeOEFWrVqVXxNXl4ejz32GKtXryY/P58BAwbw+uuv4+PjU3xNfHw8U6dOZfv27bi6ujJp0iQWLVpUonVKROTX9p27woxPoknNzqeWox0Lhrflvi7+6uYSqQEsXuRw0qRJVil8AHbu3ElYWBj79u1jy5YtFBYW0r9/f3Jzc4uvmTVrFhs3bmTt2rXs3LmTxMRERo0aVXzeaDQyZMgQCgoK2Lt3Lx988AHvv/8+8+fPt0pGEalejCYzy7aeZtzb+0jNzifQ25Uvwu7g/tubqPARqSEsnu1VntLS0vD29mbnzp306tWLzMxMGjRoQEREBPfeey8AJ06coE2bNkRGRtKtWzc2b97M0KFDSUxMLG4NWrVqFXPmzCEtLQ0npz9fjEyzvURqhtSsPGaujiHy3BUAxnT2Y8GIttRxUiuxSFVU1s9vi1t+ylNmZiYAXl5eABw6dIjCwsISCyi2bt2aJk2aEBkZCUBkZCTBwcElusEGDBhAVlYWR48evenr5Ofnk5WVVeIhItXbrlNpDFq2m8hzV6jjZM/L97XnxTHtVfiI1ECV5n+9yWTiH//4Bz169KBdu3YAJCcn4+TkhKdnycXFfHx8SE5OLr7m14XPL+d/OXczixYtYsGCBdZ+CyJSCRUZTbyy9RSv7ziL2Qytfd14bXwnWjRw/fMni0i1VOaWn4KCAk6ePElRUZFVgoSFhXHkyBFWr15tlfv9kblz55KZmVn8SEhIKPfXFJGKl5hxjbFv7eO17dcLnwe7NeHzsB4qfERqOIuLn6tXrzJ58mTq1KlD27ZtiY+PB2D69OksXry4TCGmTZvGpk2b2L59O35+fsXHfX19KSgoICMjo8T1KSkp+Pr6Fl+TkpJyw/lfzt2Ms7Mz7u7uJR4iUr1sO57C4OW7OXjhZ9ycHVg5riPP3RNMLUd7W0cTERuzuPiZO3cusbGx7Nixo8Ssr379+rFmzRqL7mU2m5k2bRobNmzg+++/JyAgoMT5zp074+joyLZt24qPnTx5kvj4eEJDQwEIDQ0lLi6O1NTU4mu2bNmCu7s7QUFBlr49EaniCopMPLfpGJM/OEjG1UKCG3uwacYdDA1pZOtoIlJJWDzm5/PPP2fNmjV069atxLTQtm3bcvbsWYvuFRYWRkREBF988QVubm7FY3Q8PDyoXbs2Hh4eTJ48mfDwcLy8vHB3d2f69OmEhobSrVs3APr3709QUBATJkxgyZIlJCcnM2/ePMLCwm7YfFVEqreE9KtM+ySa2ITrrcUP9whgzqBWODuotUdE/sfi4ueX6ei/lZuba/EaGW+88QYAvXv3LnH8vffe46GHHgLglVdewc7OjtGjR5dY5PAX9vb2bNq0ialTpxIaGoqLiwuTJk3imWeeseyNiUiV9s2RJB5fd5jsvCI8ajvy4r0h9G97865vEanZLF7np1evXowZM4bp06fj5ubG4cOHCQgIYPr06Zw+fZpvvvmmvLKWG63zI1J15RcZWfT1Cd7f+xMAnZp4svyBjvjVrWPbYCJS7ipsV/fnn3+eQYMGcezYMYqKili2bBnHjh1j79697Ny509LbiYiU2YUruUyLiCbu0vU1wv5+Z3Nm92+Fo32lWsJMRCoZi39C3HHHHcTExFBUVERwcDDfffcd3t7eREZG0rlz5/LIKCJyg68OJzF0+R7iLmVSt44j7z10O3MHtVHhIyJ/qlJtb2Er6vYSqTryCo0s/Oo4/913AYAuTeuyYlxHGnrUtnEyEaloFdbt9XtbQRgMBpydnUu1l5aISFmcv5zLtIgojiZe/zn0f71bEH73bTiotUdELGBx8ePp6fmHs7r8/Px46KGH+Pe//42dnX4giYh1bIxNZO76OHLyi/ByceLl+9rTu9WNM09FRP6MxcXP+++/z7/+9S8eeugh/vKXvwDw448/8sEHHzBv3jzS0tJYunQpzs7OPPnkk1YPLCI1S16hkWc2HSNi//XV5P8S4MXysR3x9aj1J88UEbk5i4ufDz74gJdeeon77ruv+NiwYcMIDg7mzTffZNu2bTRp0oSFCxeq+BGRW3I2LYewj6M4kZyNwQDT7gpkZt+W6uYSkVticfGzd+9eVq1adcPxjh07EhkZCVyfEfbLnl8iImXxRcwlnlwfR26BkXouTrw6tgM9WzawdSwRqQYs/vXJ39+fd99994bj7777Lv7+/gBcuXKFunXr3no6Ealx8gqNPPHZYWaujiG3wEi35l58PbOnCh8RsRqLW36WLl3KmDFj2Lx5M7fffjsABw8e5MSJE6xbtw6AAwcOcP/991s3qYhUe2dSc5gW8b9urul9WjKzb0vs7SzbOkdE5I+UaZ2fn376iTfffJOTJ08C0KpVK/7+97/TrFkza+erEFrnR8T21kddZN7nR7haYKS+qzPLxnagR2B9W8cSkUqsQtb5KSoq4vnnn+fhhx9m0aJFFocUEfmtawVG5n9xhLWHLgLQvUU9Xh3bAW83zeYSkfJh0ZgfBwcHlixZQlFRUXnlEZEa5HRKNiNe28PaQxexM8Csfrfx38ldVfiISLmyeMxP37592blzZ5Xt4hKRymHtwQTmf3GUa4VGGrhd7+bq3kLdXCJS/iwufgYNGsQTTzxBXFwcnTt3xsXFpcT54cOHWy2ciFQ/VwuKmPf5EdZHXQKgZ8v6vHxfBxq4Ods4mYjUFBYPeP6jLSsMBgNGo/GWQ1U0DXgWqRgnk7MJi4jiTGoOdgYIv/s2/q93IHaazSUiZVBhG5uaTCZLnyIiNZzZbObTgwn8+8uj5BWa8HF3ZtnYjnRrXs/W0USkBrK4+Pm1vLw8atXSwEQR+X25+de7uTZEX+/m6nVbA165rz31XNXNJSK2YfEKz0ajkWeffZbGjRvj6urKuXPnAHjqqaduuvKziNRcx5OyGLZyDxuiL2FvZ+CfA1vx/kO3q/AREZuyuPhZuHAh77//PkuWLMHJyan4eLt27XjnnXesGk5Eqiaz2UzE/njuee0HzqXl4utei9WPdtP4HhGpFCwufj788EPeeustxo8fj729ffHx9u3bc+LECauGE5GqJye/iJmrY3hyQxz5RSbuatWAr2f25PZmXraOJiIClGHMz6VLlwgMDLzhuMlkorCw0CqhRKRqOpqYybSIaM5fzsXezsDjA1rxaM/mau0RkUrF4uInKCiI3bt307Rp0xLH161bR8eOHa0WTESqDrPZzMf743lm0zEKikw08qjFinEd6dxUrT0iUvlYXPzMnz+fSZMmcenSJUwmE+vXr+fkyZN8+OGHbNq0qTwyikgllp1XyBPr4/jqcBIAfVt7s3RMe+q6OP3JM0VEbMPiMT8jRoxg48aNbN26FRcXF+bPn8/x48fZuHEjd999d3lkFJFK6silTIau2MNXh5NwsDPwr8FteGdSFxU+IlKpWbzCc3WkFZ5FLGM2m/nvvgs8t+k4BUYTjT1rs2JcRzo1qWvraCJSg5T189vilp+//e1v7Nixw9KniUg1kZVXSFhEFPO/OEqB0US/Nj58NeMOFT4iUmVYPOYnLS2NgQMH0qBBA8aOHcv48ePp0KFDeWQTkUrm8MUMpkVEE59+FUd7A08MasPDPZphMGg2l4hUHRa3/HzxxRckJSXx1FNPceDAATp37kzbtm15/vnn+emnn8ohoojYmtls5r0fzjP6jb3Ep1/Fr25t1k3pzuQ7AlT4iEiVc8tjfi5evMgnn3zCf/7zH06fPk1RUZG1slUYjfkR+X2ZVwv552exfHs0BYABbX1Ycm97PGo72jiZiNR0Fbar+68VFhZy8OBB9u/fz08//YSPj8+t3E5EKpmYhAymRURx8edrONpfn801qbu6uUSkarO42wtg+/btPPLII/j4+PDQQw/h7u7Opk2buHjxorXziYgNmM1m3tl9jjGr9nLx52s08arDZ1O781APdXOJSNVncctP48aNSU9PZ+DAgbz11lsMGzYMZ2ft0CxSXWRcLWD22sNsPX69m2twsC+LR4fgXkvdXCJSPVjc8vP000+TlJTEhg0buPfee2+p8Nm1axfDhg2jUaNGGAwGPv/88xLnH3roIQwGQ4nHwIEDS1yTnp7O+PHjcXd3x9PTk8mTJ5OTk1PmTCI1WVT8zwxZvoetx1Nwsrfj2RFteW1cJxU+IlKtWNzy88gjj1jtxXNzc2nfvj0PP/wwo0aNuuk1AwcO5L333iv+/rfF1vjx40lKSmLLli0UFhby17/+lUcffZSIiAir5RSp7kwmM+/sOceSb05SZDLTtF4dXhvXiXaNPWwdTUTE6iwufnJzc1m8eDHbtm0jNTUVk8lU4vy5c+dKfa9BgwYxaNCgP7zG2dkZX1/fm547fvw433zzDQcOHKBLly4ArFixgsGDB7N06VIaNWpU6iwiNdXPuQXMXhvLthOpAAwNaciiUcG4qbVHRKopi4ufv/3tb+zcuZMJEybQsGHDch/8uGPHDry9valbty59+vThueeeo169egBERkbi6elZXPgA9OvXDzs7O/bv38/IkSNves/8/Hzy8/OLv8/KyirX9yBSWR26kM70iGgSM/NwcrBj/tAgxndtokHNIlKtWVz8bN68ma+++ooePXqUR54SBg4cyKhRowgICODs2bM8+eSTDBo0iMjISOzt7UlOTsbb27vEcxwcHPDy8iI5Ofl377to0SIWLFhQ3vFFKi2Tycybu86x9LuTGE1mAuq7sHJcR9o2UjeXiFR/Fhc/devWxcvLqzyy3GDs2LHFXwcHBxMSEkKLFi3YsWMHffv2LfN9586dS3h4ePH3WVlZ+Pv731JWkaoiPbeA8E9j2HEyDYDh7Rvx/KhgXJ1vadkvEZEqw+LZXs8++yzz58/n6tWr5ZHnDzVv3pz69etz5swZAHx9fUlNTS1xTVFREenp6b87TgiujyNyd3cv8RCpCX48n87gZbvZcTINZwc7Fo0KZtnYDip8RKRGsfgn3ksvvcTZs2fx8fGhWbNmODqWHBQZFRVltXC/dfHiRa5cuULDhg0BCA0NJSMjg0OHDtG5c2cAvv/+e0wmE127di23HCJVjclk5o2dZ3l5yymMJjPNG7jw2rhOtGmowl9Eah6Li5977rnHai+ek5NT3IoDcP78eWJiYvDy8sLLy4sFCxYwevRofH19OXv2LP/85z8JDAxkwIABALRp04aBAwfyyCOPsGrVKgoLC5k2bRpjx47VTC+R/+9yTj7hn8ay69T1bq6RHRvz3D3tcFFrj4jUULe8semt2LFjB3fdddcNxydNmsQbb7zBPffcQ3R0NBkZGTRq1Ij+/fvz7LPPlthDLD09nWnTprFx40bs7OwYPXo0y5cvx9XVtdQ5tLGpVFf7zl1hxifRpGbnU8vRjmeGt2NMFz/N5hKRaqGsn99lLn4OHTrE8ePHAWjbti0dO3Ysy20qBRU/Ut0YTWZe336GV7aewmSGQG9XXh/fidt83GwdTUTEaipsV/fU1FTGjh3Ljh078PT0BCAjI4O77rqL1atX06BBA0tvKSJWlJadz6w1Mew5cxmA0Z38ePaettRxUjeXiAiUYbbX9OnTyc7O5ujRo6Snp5Oens6RI0fIyspixowZ5ZFRREpp79nLDF6+mz1nLlPb0Z6lY9rz0n3tVfiIiPyKxd1eHh4ebN26ldtvv73E8R9//JH+/fuTkZFh1YAVQd1eUtUZTWZWfH+a5dtOYzLDbT6uvDauEy3VzSUi1ViFdXuZTKYbprcDODo63rDPl4iUv9TsPP6xOoa9Z68AcF8XPxYMb0dtJ3sbJxMRqZws7vbq06cPM2fOJDExsfjYpUuXmDVr1i2tuiwilttz+jKDl+1m79kr1HGy55X727Pk3vYqfERE/oDFLT8rV65k+PDhNGvWrHhLiISEBNq1a8dHH31k9YAiciOjycyyradYsf0MZjO09nVj5bhOBHqXfokHEZGayuLix9/fn6ioKLZu3cqJEyeA64sN9uvXz+rhRORGKVl5zPgkmv3n0wF44C/+/HtYW2o5qrVHRKQ0bLrIYWWhAc9SVew6lcasNTFcyS3Axcme50cFM6JDY1vHEhGxibJ+fls85mfGjBksX778huMrV67kH//4h6W3E5FSKDKaePHbE0x670eu5BbQpqE7G6ffocJHRKQMLC5+PvvsM3r06HHD8e7du7Nu3TqrhBKR/0nOzGPc2/t5bftZzGYY37UJG/6vO80baHyPiEhZWDzm58qVK3h4eNxw3N3dncuXL1sllIhct+NkKuGfxpKeW4CrswOLRgUzrL027RURuRUWt/wEBgbyzTff3HB88+bNNG/e3CqhRGq6QqOJxZtP8NB7B0jPLaBtI3c2Tb9DhY+IiBVY3PITHh7OtGnTSEtLo0+fPgBs27aNl156iVdffdXqAUVqmsSMa0z/JJpDF34GYGJoU54c3EazuURErMTi4ufhhx8mPz+fhQsX8uyzzwLQrFkz3njjDSZOnGj1gCI1yfcnUgj/NJaMq4W4OTvwwr0hDA5uaOtYIiLVyi1NdU9LS6N27dq4ulbtgZea6i62Vmg0sfTbk7y56xwAwY09WDmuI03rudg4mYhI5VVhe3v9WoMGDW7l6SICXMq4xvSIKKLir28K/FD3Zswd3BpnB3VziYiUh1sqfkTk1mw5lsLstbFkXivErZYDL94bwsB26uYSESlPKn5EbKCgyMSSb07wzp7zALT382DluE74e9WxcTIRkepPxY9IBUtIv8q0T6KJTbjezfVwjwCeGNQaJweLV54QEZEyUPEjUoG+PZrM42tjycorwr2WA0vHtKd/W19bxxIRqVHK9Kvmzp07GTZsGIGBgQQGBjJ8+HB2795t7Wwi1UZBkYkFG4/y9/8eIiuviA7+nnw9s6cKHxERG7C4+Pnoo4/o168fderUYcaMGcyYMYPatWvTt29fIiIiyiOjSJUWf+Uq967ay3s//ATAIz0D+PTvofjV1fgeERFbsHidnzZt2vDoo48ya9asEsdffvll3n77bY4fP27VgBVB6/xIedkcl8Q/1x0mO78IzzqOLL23Pf2CfGwdS0SkWijr57fFLT/nzp1j2LBhNxwfPnw458+ft/R2ItVSfpGRf39xhKkfR5GdX0TnpnX5akZPFT4iIpWAxQOe/f392bZtG4GBgSWOb926FX9/f6sFE6mqLlzJJSwiiiOXsgD4+53Nmd2/FY72ms0lIlIZWFz8PPbYY8yYMYOYmBi6d+8OwA8//MD777/PsmXLrB5QpCr56nAST3x2vZurbh1HXr6vA3e19rZ1LBER+RWLi5+pU6fi6+vLSy+9xKeffgpcHwe0Zs0aRowYYfWAIlVBXqGR5746xkf74gHo0rQuK8Z1pKFHbRsnExGR37qljU2rCw14lltx/nIuYR9HcSzpejfX//VuQfjdt+Ggbi4RkXJVYQOemzdvzpUrV244npGRQfPmzS29nUiV9mVsIkOX7+ZYUhZeLk588PBf+OfA1ip8/l97dx4XVb33AfwzAwyLwiDIqmwuhLggSiIuWYlii/suJprlTSE1MktzfUwtr1q55HJvV6srbuVu0lXcfZCUTQFFMxRUFhNhWGSb+T1/+Hhuk2hAwGH5vF+veb2Ys82Hr+Z8O7/fOYeIqA6r9LDXzZs3odVqn1heXFyMO3fuVEsool0cphoAACAASURBVLquqFSLxQeTsP3nR8Nc3dyssGaMN+zVJjInIyKiP1Ph5ufAgQPSzz/99BPUarX0XqvVIiIiAq6urtUajqguunEvH8HbYnA1Iw8KBRDyUhvM6NuWZ3uIiOqJCjc/Q4YMAQAoFAoEBQXprTMyMoKrqytWrVpVvemI6ph9sXcwd+9lFJZoYd1EhS/GdEbvtjZyxyIiokqocPOj0+kAAG5ubrhw4QKaN29eY6GI6pqHJVosOpCInRfTAADdWz0a5rK14DAXEVF9U+nz9CkpKdXW+Jw+fRoDBw6Eo6MjFAoF9u3bp7deCIEFCxbAwcEBpqam8Pf3x/Xr1/W2yc7ORmBgICwsLGBpaYnJkycjPz+/WvIRAcAvWXkYsv4cdl5Mg0IBzOjbFtve6s7Gh4ionpJ1kkJBQQG8vLywfv36ctevWLECa9aswcaNGxEVFYUmTZogICAARUVF0jaBgYFITEzE0aNHcejQIZw+fRpTpkyprV+BGrgfom9j4NpzSM7MQ/Omxvj3ZF+8188dBkqF3NGIiKiK6sx9fhQKBfbu3SvNLRJCwNHREe+//z5mzZoFAMjNzYWdnR22bt2KMWPG4MqVK/D09MSFCxfg4+MDAAgPD8err76K27dvw9HRsUKfzfv80B8VlpRhwf5EfB99GwDQs401Ph/dGbbmPNtDRFRX1Np9fmpLSkoKMjIy4O/vLy1Tq9Xw9fVFZGQkACAyMhKWlpZS4wMA/v7+UCqViIqKeuqxi4uLodFo9F5Ej13LzMPgdefwffRtKBVAaD93fPumLxsfIqIGotL3+aktGRkZAAA7O/2nYNvZ2UnrMjIyYGur/9wkQ0NDWFlZSduUZ/ny5Vi8eHE1J6aGYPfFNMzfn4CiUh1szI2xZow3/Fpbyx2LiIiqUZXO/Ny4cQPz5s3D2LFjkZWVBQA4cuQIEhMTqzVcTZkzZw5yc3OlV1pamtyRSGYFxWUI3RWHD76/hKJSHXq3bY4fp/dm40NE1ABVuvk5deoUOnbsiKioKOzZs0e6sio+Ph4LFy6stmD29vYAgMzMTL3lmZmZ0jp7e3up+XqsrKwM2dnZ0jblMTY2hoWFhd6LGq+rGRoMWncWe2LuQKkAZvV3xzeTusHG3FjuaEREVAMq3fx89NFH+OSTT3D06FGoVCpp+csvv4zz589XWzA3NzfY29sjIiJCWqbRaBAVFQU/Pz8AgJ+fH3JychAdHS1tc/z4ceh0Ovj6+lZbFmqYhBDYeSEVg9edw417BbCzMMb2t7sj5OW2UPJqLiKiBqvSc34uX76MsLCwJ5bb2trit99+q9Sx8vPz8csvv0jvU1JSEBcXBysrKzg7O2PmzJn45JNP0LZtW7i5uWH+/PlwdHSUrghr164dBgwYgLfffhsbN25EaWkpQkJCMGbMmApf6UWNU35xGebtvYx9cXcBAC+42+DzUV6wbsqzPUREDV2lmx9LS0ukp6fDzc1Nb3lsbCxatGhRqWNdvHgRL730kvQ+NDQUABAUFIStW7di9uzZKCgowJQpU5CTk4NevXohPDwcJib/vepm27ZtCAkJQd++faFUKjF8+HCsWbOmsr8WNSJX0jUI3haDX38rgIFSgff7u+OdF1rzbA8RUSNR6fv8zJo1C1FRUdi9ezfc3d0RExODzMxMTJgwARMmTKjWeT+1hff5aRyEENj+cxoWHUxESZkO9hYmWDvOG8+7WskdjYiIqqCq39+VPvOzbNkyBAcHw8nJCVqtFp6entBqtRg3bhzmzZtX2cMR1Yq8olLM3ZuAg/GPhrlees4Gq0Z1hlUT1Z/sSUREDU2V7/CcmpqKhIQE5Ofnw9vbG23btq3ubLWGZ34atoQ7uQgJi8HN+4UwUCowO+A5vN27FYe5iIjquVo78/OYs7MznJ2dq7o7UY0TQuDfUalYcigJJWU6OKofDXN1deEwFxFRY1bp5kcIge+//x4nTpxAVlYWdDqd3vo9e/ZUWziiqtIUlWLOD5dx+HI6AMC/nS3+PsILzTjMRUTU6FW6+Zk5cyY2bdqEl156CXZ2dlAoOHRAdcvl27kIDotBanYhDJUKfPSKByb3cuPfVSIiAlCF5ue7777Dnj178Oqrr9ZEHqIqE0Lg28hbWHr4Ckq0OrSwNMXacd7o4txM7mhERFSHVLr5UavVaNWqVU1kIaqy3Iel+PD7SwhPfPRA236edlg5wgtqMyOZkxERUV1T6cdbLFq0CIsXL8bDhw9rIg9RpcWn5eD1tWcQnpgBIwMFFrzuic1vdGXjQ0RE5ar0mZ9Ro0Zh+/btsLW1haurK4yM9L9gYmJiqi0c0bMIIbDl3E0sP3IFpVqBls1MsX5cF3g5WcodjYiI6rBKNz9BQUGIjo7G+PHjOeGZZJNbWIoPvo/Hf5IyAQAD2tvjsxGdoDbl2R4iInq2Sjc/hw8fxk8//YRevXrVRB6iPxWb+gAhYbG4k/MQKgMl5r7qgaAermzEiYioQird/Dg5OfEuyCQLIQS+PpuCT49cRZlOwNnKDOvHdUHHlmq5oxERUT1S6QnPq1atwuzZs3Hz5s0aiENUvpzCErz97UV8cvgKynQCr3V0wKHpvdj4EBFRpVX6zM/48eNRWFiI1q1bw8zM7IkJz9nZ2dUWjggAom9lY/r2OGmYa/7r7TC+uwuHuYiIqEoq3fx88cUXNZGD6Ak6ncCm079i5X+SodUJuFqbYd24LujQgmd7iIio6qp0tRdRTfstvxihu+Jx+to9AMBAL0csG9oB5ia8mouIiP6aCjU/Go1GmuSs0WieuS0nQ9NfFXnjPmbsiEVWXjGMDZVYPKg9Rj/vxGEuIiKqFhVqfpo1a4b09HTY2trC0tKy3C8hIQQUCgW0Wm21h6TGQasTWHv8OtZEXIdOAG1sm2L9uC54zt5c7mhERNSAVKj5OX78OKysrAAAJ06cqNFA1Dhlaoowc0ccIn+9DwAY2bUlFg9uDzNVpUdmiYiInqlC3yx9+vSRfnZzc4OT05NDEEIIpKWlVW86ahROXbuH0J1xuF9QAjOVAZYO7YCh3i3ljkVERA1Upf+32s3NTRoC+73s7Gy4ublx2IsqrFSrw+qj17Dh5A0AQDsHC6wb543WNk1lTkZERA1ZpZufx3N7/ig/Px8mJibVEooavjs5DzF9eyyibz0AALzR3QUfv9YOJkYGMicjIqKGrsLNT2hoKABAoVBg/vz5MDMzk9ZptVpERUWhc+fO1Z+QGpyjSZmYtTseuQ9LYW5siM9GdMKrHR3kjkVERI1EhZuf2NhYAI/O/Fy+fBkqlUpap1Kp4OXlhVmzZlV/QmowSsp0+PTIVfzrXAoAwKulGmvHdoGztdmf7ElERFR9Ktz8PL7Ka9KkSfjyyy95Px+qlFv3C/Du9lhcup0LAHirlxtmD/CAyrDSj5cjIiL6Syo952fLli01kYMasEOX7mLOD5eRV1wGSzMjrBzhBX9PO7ljERFRI8WbqFCNKSrVYsmhJGyLSgUA+Lg0w5qx3nC0NJU5GRERNWZsfqhG/JKVj5CwGFzNyINCAUx7sTXe83eHoQGHuYiISF5sfqja7Ym5jXn7ElBYokXzpiqsHtUZL7jbyB2LiIgIAJsfqkaFJWVYsD8R30ffBgD0aG2NL0Z3hq0F7/9ERER1B5sfqhZXMzQI3haDG/cKoFQAM/3dEfxSGxgo+SR2IiKqW9j80F8ihMCOC2lYdCARxWU62FkY48sx3ujeylruaEREROVi80NVlldUirl7E3Aw/i4A4MXnbLBqpBesmxrLnIyIiOjp6vSlN4sWLYJCodB7eXh4SOuLiooQHBwMa2trNG3aFMOHD0dmZqaMiRuPhDu5eH3tWRyMvwtDpQJzXvHAv4KeZ+NDRER1Xp0/89O+fXscO3ZMem9o+N/I7733Hg4fPozdu3dDrVYjJCQEw4YNw7lz5+SI2igIIfDN/97Esh+vokSrQwtLU6wZ642uLs3kjkZERFQhdb75MTQ0hL29/RPLc3Nz8fXXXyMsLAwvv/wygEd3n27Xrh3Onz+P7t2713bUBi+3sBQffB+P/yQ9OrvW39MOfx/hBbWZkczJiIiIKq5OD3sBwPXr1+Ho6IhWrVohMDAQqamP7hYcHR2N0tJS+Pv7S9t6eHjA2dkZkZGRzzxmcXExNBqN3oueLSb1AV5dcwb/ScqEykCJRQM9semNrmx8iIio3qnTzY+vry+2bt2K8PBwbNiwASkpKejduzfy8vKQkZEBlUoFS0tLvX3s7OyQkZHxzOMuX74carVaejk5OdXkr1Gv6XQCm07dwKiNkbiT8xAu1mb4YWoPTOzpBoWCl7ETEVH9U6eHvV555RXp506dOsHX1xcuLi7YtWsXTE2r/nyoOXPmIDQ0VHqv0WjYAJXjfn4x3t8dj5PJ9wAAA70csWxoB5ib8GwPERHVX3W6+fkjS0tLuLu745dffkG/fv1QUlKCnJwcvbM/mZmZ5c4R+j1jY2MYG/OqpGc5/+t9zNgRi0xNMYwNlVg8qD1GP+/Esz1ERFTv1elhrz/Kz8/HjRs34ODggK5du8LIyAgRERHS+uTkZKSmpsLPz0/GlPWbViewJuI6xv3jPDI1xWht0wT7Q3piTDdnNj5ERNQg1OkzP7NmzcLAgQPh4uKCu3fvYuHChTAwMMDYsWOhVqsxefJkhIaGwsrKChYWFnj33Xfh5+fHK72qKEtThJk74/C/N+4DAEZ0bYn/GdweZqo6/deEiIioUur0t9rt27cxduxY3L9/HzY2NujVqxfOnz8PG5tHTwj//PPPoVQqMXz4cBQXFyMgIABfffWVzKnrpzPX7+G9nXH4Lb8EZioDLBncAcO7tpQ7FhERUbVTCCGE3CHkptFooFarkZubCwsLC7nj1KoyrQ6fH7uGr07egBCAh7051o3rgja2TeWORkRE9ExV/f6u02d+qGbdzXmI6dtjcfHWAwBAoK8z5r/uCRMjA5mTERER1Rw2P43UsaRMzPo+HjmFpTA3NsTy4R3xeidHuWMRERHVODY/jUxJmQ4rwq/in2dTAAAdW6ixbpw3XKybyJyMiIiodrD5aUTSsgsRsj0W8Wk5AIA3e7rhw1eeg7Ehh7mIiKjxYPPTSBxLysT7u+OR+7AUalMjrBzphX6ednLHIiIiqnVsfhq4Uq0OK39KxqbTvwIAOjtZYt04b7RsZiZzMiIiInmw+WnA0nMf4t2w/17N9WZPN3z0igdUhvXqxt5ERETVis1PA3X62j3M3BmH7IISmBsb4u8jO2FABwe5YxEREcmOzU8Do9UJfHnsGtae+AVCAO0dLfBVYBdezUVERPT/2Pw0IFl5RZixPQ6Rvz56Ntf47s6Y9xpvWkhERPR7bH4aiMgb9zF9Ryzu5RXDTGWA5cM6YnDnFnLHIiIiqnPY/NRzOp3AhlM3sOo/ydAJ4Dk7c6wP5LO5iIiInobNTz2WXVCC93bG4dS1ewCAkV1b4n8Gd4CpisNcRERET8Pmp56KvpWNkLBYpOcWwcRIif8Z3AGjfJzkjkVERFTnsfmpZ4QQ+OeZFHwWfhVlOoFWNk3wVWAXeNhbyB2NiIioXmDzU4/kFpbi/d3xOHYlEwAwyMsRy4Z1RFNj/jESERFVFL8164n4tBwEh8Xg9oOHUBkosXCQJ8Z1c4ZCoZA7GhERUb3C5qeOE0Lg28hb+ORwEkq1As5WZvgqsAs6tFDLHY2IiKheYvNTh+UVleKjHy7j8OV0AMCA9vZYMbITLEyMZE5GRERUf7H5qaOS7mowbVs0bt4vhKFSgbmvtsOknq4c5iIiIvqL2PzUMUII7LyQhgUHElFSpkMLS1OsHeeNLs7N5I5GRETUILD5qUMKisswb18C9sbeAQC87GGLVSO90KyJSuZkREREDQebnzriaoYG07bF4Nd7BTBQKjCr/3P42wutoFRymIuIiKg6sfmRmRACuy/exoIDCSgq1cHewgRrx3njeVcruaMRERE1SGx+ZFRY8miYa0/Mo2GuPu42WD3KC9ZNjWVORkRE1HCx+ZHJtcw8TNsWg1+y8qFUAO/3fw5T+7TmMBcREVENY/Mjg90X0zB//6NhLltzY6wd6w3fVtZyxyIiImoU2PzUosKSMszfl4gfYm4DAHq3bY7PR3dGcw5zERER1Ro2P7Xk+v8Pc13//2Gu0H7umPZiGw5zERER1TI2P7Xgh+jbmLcvAQ9LtbAxN8aaMd7wa81hLiIiIjmw+alBD0u0WHggAbsuPhrm6tnGGl+M9oaNOYe5iIiI5MLmp4Y8KCjBmM3nkZyZB4UCmNnXHSEvt4EBh7mIiIhkxeanhliaGaGVTRPcLyjBmjGd0aNNc7kjEREREQCl3AGqy/r16+Hq6goTExP4+vri559/ljWPQqHAZyM64ccZvdj4EBER1SENovnZuXMnQkNDsXDhQsTExMDLywsBAQHIysqSNZeFiRFszU1kzUBERET6GkTzs3r1arz99tuYNGkSPD09sXHjRpiZmeFf//qX3NGIiIiojqn3zU9JSQmio6Ph7+8vLVMqlfD390dkZGS5+xQXF0Oj0ei9iIiIqHGo983Pb7/9Bq1WCzs7O73ldnZ2yMjIKHef5cuXQ61WSy8nJ6faiEpERER1QL1vfqpizpw5yM3NlV5paWlyRyIiIqJaUu8vdW/evDkMDAyQmZmptzwzMxP29vbl7mNsbAxjY95okIiIqDGq92d+VCoVunbtioiICGmZTqdDREQE/Pz8ZExGREREdVG9P/MDAKGhoQgKCoKPjw+6deuGL774AgUFBZg0aZLc0YiIiKiOaRDNz+jRo3Hv3j0sWLAAGRkZ6Ny5M8LDw5+YBE1ERESkEEIIuUPITaPRQK1WIzc3FxYWFnLHISIiogqo6vd3vZ/zQ0RERFQZbH6IiIioUWHzQ0RERI0Kmx8iIiJqVBrE1V5/1eM533zGFxERUf3x+Hu7stdusfkBkJeXBwB8xhcREVE9lJeXB7VaXeHteak7Ht0R+u7duzA3N4dCoajQPhqNBk5OTkhLS+Pl8bWA9a5drHftYr1rF+tdu2qy3kII5OXlwdHREUplxWfy8MwPAKVSiZYtW1ZpXwsLC/7HU4tY79rFetcu1rt2sd61q6bqXZkzPo9xwjMRERE1Kmx+iIiIqFExWLRo0SK5Q9RXBgYGePHFF2FoyNHD2sB61y7Wu3ax3rWL9a5dda3enPBMREREjQqHvYiIiKhRYfNDREREjQqbHyIiImpU2PwQERFRo8LmpwrWr18PV1dXmJiYwNfXFz///LPckRqE5cuX4/nnn4e5uTlsbW0xZMgQJCcn621TVFSE4OBgWFtbo2nTphg+fDgyMzNlStywfPrpp1AoFJg5c6a0jPWuXnfu3MH48eNhbW0NU1NTdOzYERcvXpTWCyGwYMECODg4wNTUFP7+/rh+/bqMiesvrVaL+fPnw83NDaampmjdujWWLFmi9wwo1rvqTp8+jYEDB8LR0REKhQL79u3TW1+R2mZnZyMwMBAWFhawtLTE5MmTkZ+fXyv52fxU0s6dOxEaGoqFCxciJiYGXl5eCAgIQFZWltzR6r1Tp04hODgY58+fx9GjR1FaWor+/fujoKBA2ua9997DwYMHsXv3bpw6dQp3797FsGHDZEzdMFy4cAGbNm1Cp06d9Jaz3tXnwYMH6NmzJ4yMjHDkyBEkJSVh1apVaNasmbTNihUrsGbNGmzcuBFRUVFo0qQJAgICUFRUJGPy+umzzz7Dhg0bsG7dOly5cgWfffYZVqxYgbVr10rbsN5VV1BQAC8vL6xfv77c9RWpbWBgIBITE3H06FEcOnQIp0+fxpQpU2rnFxBUKd26dRPBwcHSe61WKxwdHcXy5ctlTNUwZWVlCQDi1KlTQgghcnJyhJGRkdi9e7e0zZUrVwQAERkZKVfMei8vL0+0bdtWHD16VPTp00fMmDFDCMF6V7cPP/xQ9OrV66nrdTqdsLe3F3//+9+lZTk5OcLY2Fhs3769NiI2KK+99pp488039ZYNGzZMBAYGCiFY7+oEQOzdu1d6X5HaJiUlCQDiwoUL0jZHjhwRCoVC3Llzp8Yz88xPJZSUlCA6Ohr+/v7SMqVSCX9/f0RGRsqYrGHKzc0FAFhZWQEAoqOjUVpaqld/Dw8PODs7s/5/QXBwMF577TW9ugKsd3U7cOAAfHx8MHLkSNja2sLb2xv/+Mc/pPUpKSnIyMjQq7darYavry/rXQU9evRAREQErl27BgCIj4/H2bNn8corrwBgvWtSRWobGRkJS0tL+Pj4SNv4+/tDqVQiKiqqxjPWjVst1hO//fYbtFot7Ozs9Jbb2dnh6tWrMqVqmHQ6HWbOnImePXuiQ4cOAICMjAyoVCpYWlrqbWtnZ4eMjAw5YtZ7O3bsQExMDC5cuPDEOta7ev3666/YsGEDQkNDMXfuXFy4cAHTp0+HSqVCUFCQVNPy/n1hvSvvo48+gkajgYeHBwwMDKDVarF06VIEBgYCAOtdgypS24yMDNja2uqtNzQ0hJWVVa3Un80P1UnBwcFISEjA2bNn5Y7SYKWlpWHGjBk4evQoTExM5I7T4Ol0Ovj4+GDZsmUAAG9vbyQkJGDjxo0ICgqSOV3Ds2vXLmzbtg1hYWFo37494uLiMHPmTDg6OrLexAnPldG8eXMYGBg8cbVLZmYm7O3tZUrV8ISEhODQoUM4ceIEWrZsKS23t7dHSUkJcnJy9LZn/asmOjoaWVlZ6NKlCwwNDWFoaIhTp05hzZo1MDQ0hJ2dHetdjRwcHODp6am3rF27dkhNTQUAqab896V6fPDBB/joo48wZswYdOzYEW+88Qbee+89LF++HADrXZMqUlt7e/snLhQqKytDdnZ2rdSfzU8lqFQqdO3aFREREdIynU6HiIgI+Pn5yZisYRBCICQkBHv37sXx48fh5uamt75r164wMjLSq39ycjJSU1NZ/yro27cvLl++jLi4OOnl4+ODwMBA6WfWu/r07NnziVs3XLt2DS4uLgAANzc32Nvb69Vbo9EgKiqK9a6CwsJCKJX6X3EGBgbQ6XQAWO+aVJHa+vn5IScnB9HR0dI2x48fh06ng6+vb82HrPEp1Q3Mjh07hLGxsdi6datISkoSU6ZMEZaWliIjI0PuaPXe1KlThVqtFidPnhTp6enSq7CwUNrmnXfeEc7OzuL48ePi4sWLws/PT/j5+cmYumH5/dVeQrDe1ennn38WhoaGYunSpeL69eti27ZtwszMTPz73/+Wtvn000+FpaWl2L9/v7h06ZIYPHiwcHNzEw8fPpQxef0UFBQkWrRoIQ4dOiRSUlLEnj17RPPmzcXs2bOlbVjvqsvLyxOxsbEiNjZWABCrV68WsbGx4tatW0KIitV2wIABwtvbW0RFRYmzZ8+Ktm3birFjx9ZKfjY/VbB27Vrh7OwsVCqV6Natmzh//rzckRoEAOW+tmzZIm3z8OFDMW3aNNGsWTNhZmYmhg4dKtLT0+UL3cD8sflhvavXwYMHRYcOHYSxsbHw8PAQmzdv1luv0+nE/PnzhZ2dnTA2NhZ9+/YVycnJMqWt3zQajZgxY4ZwdnYWJiYmolWrVuLjjz8WxcXF0jasd9WdOHGi3H+vg4KChBAVq+39+/fF2LFjRdOmTYWFhYWYNGmSyMvLq5X8CiF+d7tLIiIiogaOc36IiIioUWHzQ0RERI0Kmx8iIiJqVNj8EBERUaPC5oeIiIgaFTY/RERE1Kiw+SEiIqJGhc0PkUxefPFFzJw5U+4YjdbNmzehUCgQFxdXo58TERGBdu3aQavV1ujnbN26FZaWlpXaZ+LEiRgyZMhf+tykpCS0bNkSBQUFf+k4RLWJzQ+RTPbs2YMlS5bIHaPWLVq0CJ07d5Y7BpycnJCeno4OHTrU6OfMnj0b8+bNg4GBAQAgPT0d48aNg7u7O5RK5TMb4MWLF2P8+PE1mu+v8vT0RPfu3bF69Wq5oxBVGJsfIplYWVnB3Nxc1gxarVZ60GNjY2BgAHt7exgaGtbYZ5w9exY3btzA8OHDpWXFxcWwsbHBvHnz4OXl9cz99+/fj0GDBtVYvuoyadIkbNiwAWVlZXJHIaoQNj9EMvnjsJerqyuWLVuGN998E+bm5nB2dsbmzZul9T169MCHH36od4x79+7ByMgIp0+fBvDoi3XWrFlo0aIFmjRpAl9fX5w8eVLa/vHQyIEDB+Dp6QljY2Okpqbi5MmT6NatG5o0aQJLS0v07NkTt27dkvbbv38/unTpAhMTE7Rq1QqLFy9+5hfd0463detWLF68GPHx8VAoFFAoFNi6dSsAICcnB2+99RZsbGxgYWGBl19+GfHx8dIxH58x2rRpE5ycnGBmZoZRo0YhNzf3qTkePHiAwMBA2NjYwNTUFG3btsWWLVsAPDnsNXHiRCnT71+P6/dntS3Pjh070K9fP5iYmEjLXF1d8eWXX2LChAlQq9VP3TctLQ2JiYkYMGAAAGD16tXo2LEjmjRpAicnJ0ybNg35+flP3b8y9Vq5ciUcHBxgbW2N4OBglJaWSuu+++47+Pj4wNzcHPb29hg3bhyysrL09u/Xrx+ys7Nx6tSpZ9aDqK5g80NUh6xatQo+Pj6IjY3FtGnTMHXqVCQnJwMAAgMDsWPHDvz+cXw7d+6Eo6MjevfuDQAICQlBZGQkduzYgUuXLmHkyJEYMGAArl+/Lu1TWFiIzz77DP/85z+RmJgIKysrDBkyBH369MGlS5cQGRmJKVOmQKFQAADOnDmDCRMmYMaMGUhKSsKmTZuwdetWLF26tNzfoays7KnHGz16NN5//320b98e6enpSE9Px+jRowEAI0eORFZWFo4cOYLo6Gh06dIFffv2RXZ2tnTsX375Bbt27cLBgwcRHh4u1elp5s+fj6SkJBw5cgRXrlzBhg0b0Lx583K3/fLLL6VM6enpmDFjBmxtbeHh4VHhIeSlOgAACG1JREFU2v7RmTNn4OPj89T1z3LgwAG8+OKLsLCwAAAolUqsWbMGiYmJ+Oabb3D8+HHMnj37mceoSL1OnDiBGzdu4MSJE/jmm2+wdetWqSEFgNLSUixZsgTx8fHYt28fbt68iYkTJ+odQ6VSoXPnzjhz5kyVfleiWlcrj08loif88QnqLi4uYvz48dJ7nU4nbG1txYYNG4QQQmRlZQlDQ0Nx+vRpaRs/Pz/x4YcfCiGEuHXrljAwMBB37tzR+5y+ffuKOXPmCCGE2LJliwAg4uLipPX3798XAMTJkyfLzdm3b1+xbNkyvWXfffedcHBwKHf7PzvewoULhZeXl96yM2fOCAsLC1FUVKS3vHXr1mLTpk3SfgYGBuL27dvS+iNHjgilUvnUJ80PHDhQTJo0qdx1KSkpAoCIjY19Yt0PP/wgTExMxNmzZ4UQFattedRqtfj222+fuv6Pfwd+r1+/fmLdunVP3Xf37t3C2tpaer9lyxahVqul9xWpV1BQkHBxcRFlZWXSNiNHjhSjR49+6udeuHBBAHji6dtDhw4VEydOfOp+RHVJzQ12E1GlderUSfpZoVDA3t5eGmKwsbFB//79sW3bNvTu3RspKSmIjIzEpk2bAACXL1+GVquFu7u73jGLi4thbW0tvVepVHqfY2VlhYkTJyIgIAD9+vWDv78/Ro0aBQcHBwBAfHw8zp07p3emR6vVoqioCIWFhTAzM9P7vD87Xnni4+ORn5+vlxMAHj58iBs3bkjvnZ2d0aJFC+m9n58fdDodkpOTYW9v/8Rxp06diuHDhyMmJgb9+/fHkCFD0KNHj6fmAIDY2Fi88cYbWLduHXr27Amg4rX9o4cPH+oNeVWURqPBqVOn8PXXX0vLjh07huXLl+Pq1avQaDQoKyt76p/BYxWpV/v27aXJ2ADg4OCAy5cvS++jo6OxaNEixMfH48GDB9IcsdTUVHh6ekrbmZqaorCwsNK/K5Ec2PwQ1SFGRkZ67xUKhd6E5MDAQEyfPh1r165FWFgYOnbsiI4dOwIA8vPzYWBggOjoaL0vMwBo2rSp9LOpqak0pPXYli1bMH36dISHh2Pnzp2YN28ejh49iu7duyM/Px+LFy/GsGHDnsj7tC/2Zx2vPPn5+XBwcCh3Dk1lL9/+vVdeeQW3bt3Cjz/+iKNHj6Jv374IDg7GypUry90+IyMDgwYNwltvvYXJkyfr5atIbf+oefPmePDgQaVzHzlyBJ6ennBycgLwaH7S66+/jqlTp2Lp0qWwsrLC2bNnMXnyZJSUlDy1+amIZ/2dKygoQEBAAAICArBt2zbY2NggNTUVAQEBKCkp0dsvOzsbrVu3rnIOotrE5oeoHhk8eDCmTJmC8PBwhIWFYcKECdI6b29vaLVaZGVlSXOAKsPb2xve3t6YM2cO/Pz8EBYWhu7du6NLly5ITk5GmzZtquV4KpXqiXvedOnSBRkZGTA0NISrq+tTj5mamoq7d+/C0dERAHD+/HkolUo899xzT93HxsYGQUFBCAoKQu/evfHBBx+U2/wUFRVh8ODB8PDweOKy7arW1tvbG0lJSRXe/rH9+/dj8ODB0vvo6GjodDqsWrUKSuWjqZq7du360+NUpV6/d/XqVdy/fx+ffvqp1IhdvHix3G0TEhIwYsSICh2XSG5sfojqkSZNmmDIkCGYP38+rly5grFjx0rr3N3dERgYiAkTJmDVqlXw9vbGvXv3EBERgU6dOuG1114r95gpKSnYvHkzBg0aBEdHRyQnJ+P69etSY7VgwQK8/vrrcHZ2xogRI6BUKhEfH4+EhAR88sknlT6eq6srUlJSEBcXh5YtW8Lc3Bz+/v7w8/PDkCFDsGLFCri7u+Pu3bs4fPgwhg4dKk0aNjExQVBQEFauXAmNRoPp06dj1KhR5Q55Pc7etWtXtG/fHsXFxTh06BDatWtX7rZ/+9vfkJaWhoiICNy7d09abmVlVeXaBgQE4Jtvvnli+eMrzPLz83Hv3j3ExcVBpVLB09MTZWVlOHLkCGbNmiVt36ZNG5SWlmLt2rUYOHAgzp07h40bN5b7mb9X2Xr9kbOzM1QqFdauXYt33nkHCQkJ5d6b6ubNm7hz5w78/f0rdFwi2ck96YiosSpvwvPnn3+ut42Xl5dYuHCh3rIff/xRABAvvPDCE8csKSkRCxYsEK6ursLIyEg4ODiIoUOHikuXLgkhnpwUK4QQGRkZYsiQIcLBwUGoVCrh4uIiFixYILRarbRNeHi46NGjhzA1NRUWFhaiW7duYvPmzeX+Xn92vKKiIjF8+HBhaWkpAIgtW7YIIYTQaDTi3XffFY6OjsLIyEg4OTmJwMBAkZqaKoT470Tpr776Sjg6OgoTExMxYsQIkZ2d/dQaL1myRLRr106YmpoKKysrMXjwYPHrr78KIZ6c8Ozi4iIAPPE6ceJEhWpbnvv37wsTExNx9epVveXlfY6Li4sQQohjx46Jli1bPnGs1atXCwcHB2FqaioCAgLEt99+KwCIBw8eCCHKn/D8Z/UKCgoSgwcP1vucGTNmiD59+kjvw8LChKurqzA2NhZ+fn7iwIEDT0wUX7ZsmQgICHhqHYjqGoUQv7tuloiojlq0aBH27dtX44+jqG4ffPABNBqNNDH9z0yfPh1lZWX46quv/tLn1la9SkpK0LZtW4SFhUkTxInqOt7nh4ioBn388cdwcXGp8J20O3TogKlTp9ZwquqTmpqKuXPnsvGheoVzfoiIapClpSXmzp1b4e2nTJlSg2mqX5s2bSo9GZ5Ibhz2IiIiokaFw15ERETUqLD5ISIiokaFzQ8RERE1Kmx+iIiIqFFh80NERESNCpsfIiIialTY/BAREVGjwuaHiIiIGhU2P0RERNSo/B/j+cX8ZBWxHAAAAABJRU5ErkJggg==", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(1 ./ alphas, convergence_times);\n", "xlabel(\"inverse step size (1/alpha)\");\n", "ylabel(\"time to converge to distance of 1\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "# Part 2" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "stochastic_gradient_descent_diminishing (generic function with 1 method)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function stochastic_gradient_descent_diminishing(x0, num_iters)\n", " dist_to_optimum = zeros(num_iters)\n", " alphas = zeros(num_iters)\n", " x = x0\n", " mu = 1.0\n", " M = 1.0\n", " rho0 = norm(x0)^2\n", " for t = 1:num_iters\n", " alpha = (2 * mu * rho0) / (4 * M + mu^2 * rho0 * (t-1))\n", " alphas[t] = alpha\n", " dist_to_optimum[t] = norm(x)\n", " x = x - alpha * sample_grad_f(x)\n", " end\n", " return (alphas, dist_to_optimum)\n", "end" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x0 = randn(100) / 10;\n", "(alphas, dto_diminishing) = stochastic_gradient_descent_diminishing(x0, 1000);\n", "\n", "alpha1 = 0.5 * norm(x0)^2; # same as first step\n", "alpha2 = 2 / (4 + norm(x0)^2 * 100); # intermediate\n", "alpha3 = 2 / (4 + norm(x0)^2 * 1000); # same as last step\n", "\n", "dto1 = stochastic_gradient_descent(x0, alpha1, 1000);\n", "dto2 = stochastic_gradient_descent(x0, alpha2, 1000);\n", "dto3 = stochastic_gradient_descent(x0, alpha3, 1000);" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(dto_diminishing, label=\"optimal\");\n", "plot(dto1; label = \"alpha = $(signif(alpha1, 2))\");\n", "plot(dto2; label = \"alpha =$(signif(alpha2, 2))\");\n", "plot(dto3; label = \"alpha = $(signif(alpha3, 2))\");\n", "xlabel(\"iteration\");\n", "ylabel(\"distance to optimum\");\n", "legend();" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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cyG233XbT47/55pu8/PLLPPTQQ7z++uu4urpiZmbGlClTiv08luQzfivV9Zm7ldatW7Nnzx4SEhKK/GIvVPg9FBQUVOnlKc/3zI2+5/R6fYWfS5SPBJl6YvDgwXzyySds2bKFbt26FVn/559/cuLECR577LEi6+Li4kx+CRw9ehSDwWDS6K+qxohJTU1lw4YNvPrqq7zyyismZaxoHTp0ALTqdrjxNRZ2V7e0tKRfv34lOnZcXJzxlg5otQbnzp0zdhEub1mLYzAYGDNmDGlpaaxfvx47OzuT9YUNtJ2cnEp8HdcbOnQojz32mPH2UmxsLM8//3yR7VxdXYmIiCAiIoJLly7Ro0cPZs6cWeFBJiEhgc2bN9OlS5db3vJo1qwZTz/9NE8//TRxcXGEhITw/vvv8/XXXwM3fv9XrlxJ7969+eyzz0yWp6WlmQS4kip8Hw4cOHDD96Esn7lr3ehaGjduDGhjwVzv8OHDuLu7Y29vf8PjDh48mKVLl/Lll1/y0ksvFVmfkZHBTz/9RKtWrYoErev/DyulOHr0qLER8s3KXRkKa8rS0tJMbvEV1lqJmkNuLdUT06dPx9bWlscee4yUlBSTdRcvXuTxxx/Hzs6O6dOnF9k3MjLS5PW8efMAGDhwoHGZvb09aWlplVByU4V/3Vz/10x5RvvcsGFDscsL780XVrMX/uK//jo9PT3p1asXH330UbFB4sKFC0WWffzxx+Tl5RlfL1y4kPz8fJOfaXnKWpxXX32VNWvWsHTp0mJrJ0JDQ2nWrBnvvfee8XbMra7jei4uLoSFhbFixQqWLVuGlZUVQ4cONdnm+s+fg4MDzZs3Jycnx7gsPT2dw4cPl/lWIWif69GjR6PX6409jYpz+fJlsrOzTZY1a9YMR0dHkzLd6DNubm5e5PP43XfflamNCsDtt99OkyZNmDNnTpHzFZ6nLJ+5a93os+zj40NISAhLliwxWXfgwAHWrl17y6A9YsQIgoKCePvtt/n7779N1hkMBp544glSU1OL9GwDrd3WtbelVq5cyblz54p8z5TnM1EahYEyOjrauCwrK4slS5ZUyflFyUmNTD0RGBjIkiVLGDNmDG3bti0ysm9ycjJLly4tttt0fHw8Q4YMYcCAAWzbto2vv/6aBx54gPbt2xu3CQ0NZf369cyePRtfX1+aNGliMhhWRXFycjK2YcjLy8PPz4+1a9cSHx9f5mPec889NGnShPDwcJo1a0ZWVhbr16/n559/pmPHjoSHhwNao9CgoCCWL19OixYtcHV1JTg4mODgYCIjI+nWrRtt27blkUceoWnTpiQmJrJt2zZOnz7N3r17Tc6Zm5tL3759jd0wFyxYQLdu3RgyZEiFlPV6+/fv5/XXX6dHjx4kJSUZaxkKjR07FjMzMz799FMGDhxImzZtiIiIwM/PjzNnzrBp0yacnJyM3Wtv5r777mPs2LEsWLCAsLCwIg1Wg4KC6NWrF6Ghobi6uvL333+zcuVKJk2aZNzmxx9/JCIigi+++IIJEybc8pyxsbF8/fXXKKXIyMgwjux76dIlZs+ezYABA266b+F7ERQUhIWFBT/++COJiYncf//9xu1CQ0NZuHAhb7zxBs2bN8fT05M+ffowePBgXnvtNSIiIrjzzjvZv38/33zzTZkHljQzM2PhwoWEh4cTEhJCREQEPj4+HD58mIMHD7JmzRqAUn/mrnWzz/KsWbMYOHAgXbp04eGHHzZ2v3Z2dr7lKMBWVlasXLmSvn370q1bN5ORfb/99lt2797N008/bfJzLeTq6mrcJzExkTlz5tC8eXMeeeQRk/dg+fLlTJs2jY4dO+Lg4HDDz3x53XXXXfj7+/Pwww8zffp0zM3N+fzzz/Hw8CAhIaFSzinKqJp6S4lqsm/fPjV69Gjl4+OjLC0tlbe3txo9enSRLrNKXe1+GBMTo0aMGKEcHR1VgwYN1KRJk0wGxFNK677Yo0cPZWtrW+IB8a5HMd1oC7tVXts19vTp02rYsGHKxcVFOTs7q5EjR6qzZ88W6T5Z0u7XS5cuVffff79q1qyZsrW1VTY2NiooKEi9+OKLJt1BlVLqr7/+UqGhocrKyqrI+Y4dO6bGjRunvL29laWlpfLz81ODBw9WK1euLFKmwgHxGjRooBwcHNSYMWNMurtWRFmvLV9hF9cbPa7177//quHDhys3NzdlbW2tGjdurEaNGqU2bNhwy/IppVRGRobxc/D1118XWf/GG2+oTp06KRcXF2Vra6tatWql/ve//5l0Ry/8OV3bnfZGrr0OMzMz5eLiom677TY1efJkdfDgwSLbX99VNzk5WU2cOFG1atVK2dvbK2dnZ9W5c2e1YsUKk/3Onz+v7r77buXo6GgyIF52drZ6+umnlY+Pj7K1tVVdu3ZV27ZtUz179jTprl34Hnz33Xc3LU+hLVu2qP79+ytHR0dlb2+v2rVrZxxUsFBJPnM3crPP8vr161XXrl2Vra2tcnJyUuHh4SUaEK9QUlKSmjZtmnHQQxcXF9WvXz9jl+trFf5cli5dqp5//nnl6empbG1t1d13323SbVkppS5duqQeeOAB5eLiUuIB8a7Xs2dP1aZNmyLLi/te+ueff1Tnzp2VlZWV8vf3V7Nnz66U7zRRPjLXkrihmTNn8uqrr3LhwoUy3esXRRXO/7Rr1y5juxYh6rOoqCh69+7Nd999x4gRI6q7OKIWkjYyQgghhKi1JMgIIYQQotaSICOEEEKIWkvayAghhBCi1pIaGSGEEELUWhJkhBBCCFFr1bkB8QwGA2fPnsXR0bFKh7MWQgghRNkppcjMzMTX19c4o3xJ1Lkgc/bs2SKzjQohhBCidjh16hQNGzYs8fZ1LsgUTgx36tSpW87iLIQQQoiaISMjg0aNGt1ygtfr1bkgU3g7ycnJSYKMEEIIUcuUtlmINPYVQgghRK0lQUYIIYQQtVadu7UkhBBCXE+v15OXl1fdxajXLC0tMTc3r/DjSpARQghRZymlOH/+PGlpadVdFAG4uLjg7e1docOjSJARQghRZxWGGE9PT+zs7GR8sWqilOLy5cskJSUB4OPjU2HHliAjhBCiTtLr9cYQ4+bmVt3FqfdsbW0BSEpKwtPTs8JuM0ljXyGEEHVSYZsYOzu7ai6JKFT4XlRke6UaGWR++eUXWrZsSWBgIJ9++ml1F0cIIUQtJreTao7KeC9q3K2l/Px8pk2bxqZNm3B2diY0NJRhw4ZJtaAQQgghiqhxNTI7d+6kTZs2+Pn54eDgwMCBA1m7dm11F0sIIYQQNVCFB5no6GjCw8Px9fVFp9OxatWqIttERkYSEBCAjY0NnTt3ZufOncZ1Z8+exc/Pz/jaz8+PM2fOVHQxhRBCiFrpxIkT6HQ69uzZU+J9Fi9ejIuLSyWWqvpUeJDJysqiffv2REZGFrt++fLlTJs2jRkzZrB7927at29PWFiYsUtWaeXk5JCRkWHyEEIIIUTVulHlRWWr8CAzcOBA3njjDYYNG1bs+tmzZ/PII48QERFBUFAQixYtws7Ojs8//xwAX19fkxqYM2fO4Ovre8PzvfXWWzg7OxsfjRo1qtgLEkIIIUSNVaVtZHJzc/nnn3/o16/f1QKYmdGvXz+2bdsGQKdOnThw4ABnzpzh0qVL/P7774SFhd3wmM8//zzp6enGx6lTpyr9OoQQQtQ+Siku5+ZXy0MpVaqy/vHHH3Tr1g0XFxfc3NwYPHgwx44dK3bbqKgodDodv/76K+3atcPGxoY77riDAwcOFNl2zZo1tG7dGgcHBwYMGMC5c+eM63bt2kX//v1xd3fH2dmZnj17snv37hKVNyAgAIBhw4ah0+mMr6tClfZaSk5ORq/X4+XlZbLcy8uLw4cPawWysOD999+nd+/eGAwGnn322Zv2WLK2tsba2rpSyy2EEKL2u5KnJ+iVNdVy7pjXwrCzKvmv3KysLKZNm0a7du24dOkSr7zyCsOGDbtpu5jp06czd+5cvL29eeGFFwgPDyc2NhZLS0sALl++zHvvvcdXX32FmZkZY8eO5ZlnnuGbb74BIDMzk/HjxzNv3jyUUrz//vsMGjSIuLg4HB0db1reXbt24enpyRdffMGAAQMqZU6lG6lx3a8BhgwZwpAhQ6q7GEIIIUS1uPfee01ef/7553h4eBATE4ODg0Ox+8yYMYP+/fsDsGTJEho2bMiPP/7IqFGjAG0QukWLFtGsWTMAJk2axGuvvWbcv0+fPibH+/jjj3FxcWHz5s0MHjz4puX18PAArs6lVJWqNMi4u7tjbm5OYmKiyfLExMQqv3AhhBD1i62lOTGv3bipQmWfuzTi4uJ45ZVX2LFjB8nJyRgMBgASEhIICgoqdp8uXboYn7u6utKyZUsOHTpkXGZnZ2cMMaDNd3RtR5vExEReeukloqKiSEpKQq/Xc/nyZRISEkpV9qpWpUHGysqK0NBQNmzYwNChQwEwGAxs2LCBSZMmlevYkZGRREZGotfrK6KoQggh6hidTleq2zvVKTw8nMaNG/PJJ5/g6+uLwWAgODiY3NzcMh+z8BZTIZ1OZ9J2Z/z48aSkpDB37lwaN26MtbU1Xbp0Kdc5q0KFv6OXLl3i6NGjxtfx8fHs2bMHV1dX/P39mTZtGuPHj6dDhw506tSJOXPmkJWVRURERLnOO3HiRCZOnEhGRgbOzs7lvQwhhBCiWqSkpHDkyBE++eQTunfvDsCWLVtuud/27dvx9/cHIDU1ldjYWFq3bl3i827dupUFCxYwaNAgAE6dOkVycnKJ97e0tKyWyoQKDzJ///03vXv3Nr6eNm0aoCW9xYsXc99993HhwgVeeeUVzp8/T0hICH/88UeRBsBCCCFEfdSgQQPc3Nz4+OOP8fHxISEhgeeee+6W+7322mu4ubnh5eXFiy++iLu7u/HuR0kEBgby1Vdf0aFDBzIyMpg+fbpxxuqSCAgIYMOGDXTt2hVra2saNGhQ4n3Lo8K7X/fq1QulVJHH4sWLjdtMmjSJkydPkpOTw44dO+jcuXNFF0MIIYSolczMzFi2bBn//PMPwcHBTJ06lVmzZt1yv7fffpvJkycTGhrK+fPn+fnnn7GysirxeT/77DNSU1O5/fbbefDBB/m///s/PD09S7z/+++/z7p162jUqBG33XZbifcrL50qbef2Gq7w1lJ6ejpOTk7VXRwhhBDVJDs7m/j4eJo0aYKNjU11F6fSREVF0bt3b1JTU2v8NAQ3e0/K+vu7xk0aKYQQQghRUnUmyERGRhIUFETHjh2ruyhCCCFEnfLNN9/g4OBQ7KNNmzbVWja5tSSEEKJOqi+3lqpCZmZmkTHgCllaWtK4ceMSHacybi3Vjg71QgghhKg2jo6Ot5ymoLrUmVtLQgghhKh/JMgIIYQQotaSICOEEEKIWkuCjBBCCCFqrToTZKT7tRBCCFH/1JkgM3HiRGJiYti1a1d1F0UIIYSocDqdjlWrVlV3MWqcOhNkhBBCCFF2vXr1YsqUKdVdjFKTICOEEELUcLm5udVdhBpLgowQQoj6QSnIzaqeRykH0e/VqxeTJk1iypQpuLu7ExYWBkBycjLDhg3Dzs6OwMBAVq9ebbLf5s2b6dSpE9bW1vj4+PDcc8+Rn59/y/NNmDCBzZs3M3fuXHQ6HTqdjhMnTpSqzNVFRvYVQghRP+Rdhjd9q+fcL5wFK/tS7bJkyRKeeOIJtm7dCkCrVq149dVXeffdd5k1axbz5s1jzJgxnDx5EldXV86cOcOgQYOYMGECX375JYcPH+aRRx7BxsaGmTNn3vRcc+fOJTY2luDgYF577TUAPDw8ynSpVU2CjBBCCFEDBQYG8u6775osmzBhAqNHjwbgzTff5MMPP2Tnzp0MGDCABQsW0KhRI+bPn49Op6NVq1acPXuW//73v7zyyiuYmd34JoyzszNWVlbY2dnh7e1dqddV0epMkImMjCQyMhK9Xl/dRRFCCFETWdppNSPVde5SCg0NLbKsXbt2xuf29vY4OTmRlJQEwKFDh+jSpQs6nc64TdeESvQ4AAAgAElEQVSuXbl06RKnT5/G39+/DAWv+epMkJk4cSITJ040zp4phBBCmNDpSn17pzrZ2xctq6WlpclrnU6HwWCoqiLVSNLYVwghhKgDWrduzbZt21DXNCzeunUrjo6ONGzY8Jb7W1lZ1cq7GhJkSurYJlgSDlHvwImtkJdd3SUSQgghjJ588klOnTrFU089xeHDh/npp5+YMWMG06ZNu2n7mEIBAQHs2LGDEydOkJycXGtqeurMraVKd3wTxEdrDwBza2jUCRp3hYBu0LAjWNpUbxmFEELUW35+fvz2229Mnz6d9u3b4+rqysMPP8xLL71Uov2feeYZxo8fT1BQEFeuXCE+Pp6AgIDKLXQF0ClVys7tNVxhG5n09HScnJwq7sAXj2u1Mie2wMmtcCnRdL25lRZmrg02VqVv3CWEEKJiZGdnEx8fT5MmTbCxkT80a4KbvSdl/f0tNTIl5dpUe3R8WBvYKOWoFmoKg03mOe3fk1sh+l0ws4SGHa4Gm0adalUjMyGEEKI2kCBTFjoduAdqjw4RWrC5ePxqsDmxBTLPQsI27fHne1qw8btdCzWNu0KjzmDtUN1XIoQQoh5ISEggKCjohutjYmJqbfdsCTIVQacDt2baI3S8FmxS47VGwYXBJuM0nNqhPf58H8wswPe2gmDTDfw7g7VjdV+JEEKIOsjX15c9e/bcdH1tJUGmMuh0V29F3f6gFmzSTpoGm/QEOL1Le2z5AHTm4BtyTbC5A2wqsI2PEEKIesvCwoLmzZtXdzEqRZ0JMjV6ZF+dDhoEaI/bxmjLUk9q7WlObIUTf2pB58w/2mPrXNCZgU9702Bj61KdVyGEELVSHevTUqtVxnshvZZqirRTBcGmoMYmNd50vc4MvNtCQHetjU3jLmDboHrKKoQQtYBeryc2NhZPT0/c3NyquzgCSElJISkpiRYtWmBubm6yrqy/vyXI1FTpZ0yDzcVj122gA+/ga4LNnWDnWi1FFUKImurcuXOkpaXh6emJnZ2dyTxEouoopbh8+TJJSUm4uLjg4+NTZBsJMgXqTJC5XsY502CTEnfdBjrwanO1V1TjrmAvf4EIIeo3pRTnz58nLS2tuosiABcXF7y9vYsNlBJkCtTZIHO9zEQ4ueVqA+LkI0W38QzSgk27+6Fh0VlUhRCivtDr9eTl5VV3Meo1S0vLIreTriVBpkC9CTLXu5R0TePhLXDh0NV1OjPo/jT0/C+YW974GEIIIUQ1kSBToN4GmetlJWvB5uCP2gPALxSGf6KNdyOEEELUIGX9/S2zX9dV9u4QdA+MXAwjvgAbZ61r96Lu8O/X2tg2QgghRC0nQaY+CB4OT/yljUeTlwU/TYTvxsPli9VdMiGEEKJcJMjUF84NYfxq6DdTmx4h5idY2BWOb67ukgkhhBBlJkGmhP45mcrM1QdZ+c9pDp/PIF9vqO4ilZ6ZOXSbCv9ZD27NtYktv7wH1r4M+bnVXTohhBCi1GSKghLaejSZxX+dML62tjCjtY8TwX5OBPs6E+znTAsvR6wsakE29L0NHouGNS/CP1/AXx/C8Si49zPwaFHdpRNCCCFKTHotldD24ymsi0lk/5l0Ys5mcCknv8g2luY6Wno7GoNNsJ8zrbwdsbG8cb/5anf4V/hpEly5CBa2EPY/6PCQNj+UEEIIUUWk+3WBquh+bTAoTl68zP4z6Rw8k86Bs+kcOJNB+pWigy2Zm+kI9HTQgo2vE8F+zrT2ccLeugZVhmWeh1VPwLGN2usWA+Ge+VrPJyGEEKIKSJApUF3jyCilOJ16hQPXBJsDZ9JJySra9kSng2YeDsZg08bXmTZ+TjjZVONgdQYD7FgE62eAPhfsPWHoQgjsV31lEkIIUW9IkClQkwbEU0pxPiPbGGoKQ05iRk6x2we42dHGz7ng1pTW9qaBvVXVFvr8Afj+P1dHBu78OPR7FSxtqrYcQggh6hUJMgVqUpC5kaTMbA6ezeDA6au1N2fSrhS7rZ+L7dUGxQ21kOPhaF25Bcy7AutnajU0oM3ZdO+n2qSUQgghRCWQIFOgNgSZ4lzMyuVg4S2ps1rtzcmUy8Vu6+VkbdKgONjPCW8nm4qfnj5uHax6ErKSwNwa+r8KnR4Ds1rQM0sIIUStIkGmQG0NMsVJv5JHzNkMDp5NZ3/BranjyVnFzi7gZm9lDDWFIadhA9vyh5tLF2D1JIj9Q3vdrC8MXQCO3uU7rhBCCHENCTIF6lKQKU5WTj4x5wrb3GghJy7pEnpD0bfR2daSYD8nOjR2pWdLD9o3dMHcrAzBRin4+zNt3Jn8bLBzgyHzodWgCrgiIYQQQoKMUV0PMsXJztNz6FwGB85mcPCMVnsTm5hJnt70rW1gZ0n3QA96tfSgRwsP3B1K2dbmwhH4/mE4v197HRqhjTtjZV9BVyKEEKK+kiBToD4GmeLk5OuJS7zE3tNpbIlLZktcMpnXDeLXrqEzPVtowSakUYOS1dbk58DGN7TRgAHcArWGwL4hlXAVQggh6gsJMgUkyBQvT2/g34Q0oo4kEXXkAjHnMkzWO9ta0j3QnV4tPenZwuPWPaOOR8GPT2jzNZlZQp+X4M6ntPmchBBCiFKSIFNAgkzJJGVkszn2AlGxF/gz9gIZ2aa1NcF+TvRq4UnPlh7c1sgFC/Nieipdvgg/T4ZDq7XX/nfC7eOgWR9w9KqCqxBCCFFXSJApIEGm9PL1BvacSiPqyAU2x15g/5l0k/VONhZ0D/SgZ0sPerXwwNPpmsHxlIJ/v4bf/wt5WVeXe7WF5n20Xk7+d4BFJY99I4QQolar90Hm2tmvY2NjJciUw4XMHKILa2viLpB22XQOqSAfJ3q19KBXS09u83fB0twMLsbDv1/B0Q1wbo/pAS3tIKCbFmqa9wW35jIppRBCCBP1PsgUkhqZiqU3KPacSmNz7AU2H0li35l0k3FsHG0s6Nbc3RhsvJxsICsZjm2CYxu0iSgvJZoe1Nn/am1N055g41y1FyWEEKLGkSBTQIJM5Uq5lEN03AWijlwgOvYCqdfV1nQMaMCQ9r4MauuDm4O1dusp8YBWU3NsIyRs0yalLKQzh4YdtZqaZn213k/SYFgIIeodCTIFJMhUHb1Bsf9MurEn1N7TacbaGnMzHV2buzOkvS9hbbxwLJzZOzcLTmzVamuOboCUONOD2jaApr2gzTBoPURuQQkhRD0hQaaABJnqcz49m1/2nWX13rPsO321wbCVhRl9W3kypL0vvVt5YmN5TY1LWkJBbc0GOB4NOdc0NG4/Gu6eDVZ2VXgVQgghqoMEmQISZGqG+OQsVu85y+q9Zzh24WpvJgdrC+5q48WQ9r50be6uNRQupM+HM3/DoZ9h+wJQBvAKhvu+Atem1XAVQgghqooEmQISZGoWpRQx5zJYvfcsv+w9x5m0K8Z1rvZWDGrrzZD2fnRo3ACza0cWjv8TVkZA1gWwdobhH0HLgdVwBUIIIaqCBJkCEmRqLoNBsTshldV7z/LrvnOkZF1t9OvrbMPg9r4Mae9LG18nbdbujLPw3QQ4tUPbqPsz0PsFaQwshBB1kASZAhJkaod8vYG/jqWweu9Z1hw4bzIPVFN3e+4J8WNkh4b4OpjDupdhx6KClb3h3s/A3q2aSi6EEKIySJApIEGm9snO0xN15AI/7z3L+kOJ5OQbADDTQa+Wnozu5E+fvM2Y/zIZ8i6DU0MY9SU0DK3mkgshhKgoEmQKSJCp3S7l5LP24HlW/H2K7ccvGpd7OVnzROtcxpx8Ccu0Y9pElQPfgQ4PSRdtIYSoAyTIFJAgU3ccv3CJ5btO8d0/p7lY0J7GUXeZz12+oOOVrdpG0kVbCCHqBAkyBSTI1D25+QbWxSSydGcCW44mA4pHzX/hv5bLMcdArlsQVmO+kS7aQghRi0mQKSBBpm47mZJlrKVpnrWbDy3n4aHLIEtnz4HOswjpdz/WFtKrSQghahsJMgUkyNQPeXoDGw4l8ce23Tx46hVCzbSpDj5hOBc7PcODdzbF18W2mksphBCipCTIFJAgU/+cTk7jwvfPctu55QD8oe/IFP3/0bdNQyK6BhDauIE2Lo0QQogaS4JMAQky9Zd+z3JYPQlzQy5/6DvyVN5T5GFBu4bORHQN4O62vlhZmN36QEIIIaqcBJkCEmTqubj1sOwB0OdwwKkH9118lKx8Lbx4OFoztnNjxtzhj7uDdTUXVAghxLUkyBSQICOuDTM5gYP4zOsVluw8Q2JGDgBW5maEt/clomsAwX7O1VxYIYQQIEHGSIKMAArCzGjQ50KrweQN/5zfYpL5YusJ9pxKM27WqYkrj3RvSt9WnqaTVgohhKhS9T7IREZGEhkZiV6vJzY2VoKMgLh1BTUzWphh5GIwt2R3QipfbD3B7/vPkW/QPv6Bng482qMp94T4STsaIYSoBvU+yBSSGhlh4gZhBuB8ejaL/zrBN9tPGiet9HG24eFuTbi/kz8O1hbVWHAhhKhfJMgUkCAjirg2zLQOhxFfGMMMQEZ2Ht/uSODzLfEkZWrtaJxtLRnXpTHj7wyQhsFCCFEFJMgUkCAjihW7FpaPuWGYAcjJ1/Pj7jN8HH2c48lZAFhbmDGqQyMe6d4UfzeZz0kIISqLBJkCEmTEDZUgzADoDYp1MedZuPk4ewsaBpvpYEh7Xyb1aU5zT8eqLrkQQtR5EmQKSJARN2USZobAiM+LDTMASim2HU9h0ebjRMdeAECng0FtfXiqT3NaecvnSwghKooEmQISZMQtxa6B5WNLFGYKHTiTzryNcaw5mGhcFtbGi6f6BMpYNEIIUQEkyBSQICNK5NowEzQU7v0MzG/dS+nQuQzmbzzKbwfOUfg/p19rT57qE0j7Ri6VXGghhKi7JMgUkCAjSix2DSwbA4Y8aHc/DF0IZiUbQyYuMZP5m47y896zFAxFQ88WHkzt34IQCTRCCFFqEmQKSJARpXLoZ1gxHpQeQifA4DlaQ5gSOn7hEpGbjrFqzxn0BYmmbytPpvZvIbechBCiFCTIFJAgI0pt/0r44RFQBuj8OAx4u1RhBuBkShbzNh7lh92njTU0A4O9mdq/BS28pJeTEELcigSZAhJkRJns+RZWPaE97zoF+s0sdZgBrYZm7oY4Vu89i1LaIcLb+TKlXyBNPRwqtMhCCFGXSJApIEFGlNmuz+DXadrzXs9Dr+fKfKjYxEw+WBfL7wfOA9o4NMNvb8jU/i3wc7GtiNIKIUSdIkGmgAQZUS7bFsCa57Xn/V6FblPKdbgDZ9KZsz6W9YeSALCyMGN8l8Y82as5DeytyltaIYSoMyTIFJAgI8ot+j3Y+Lr2fMA7cMfj5T7kvwmpvPPHYbYfvwiAo40Fj/dsxkNdm2BrZV7u4wshRG0nQaaABBlRITa+AdGztOeD50CHiHIfUinF5tgLvPPHEQ6dywDAy8maKf1aMDK0IRbmJev6LYQQdZEEmQISZESFUArWvgTb5gM6GLYI2t9fIYc2GBSr957lvbVHOJ16BYCmHvY8G9aSsDbe6MrQyFgIIWo7CTIFJMiICqMU/DYddn0COjNtksk2Qyvs8Dn5er7dkcC8jUe5mJULQEgjF54b2Io7mrpV2HmEEKI2kCBTQIKMqFAGA/z8f/DvV2BmCWO+g2a9K/QUmdl5fBJ9nE+3xHM5Vw9A75YePDugFa195DMshKgfJMgUkCAjKpxBDysjIOYnsHKA8T+D3+2lO0bGWcjNArfmNxyfJikzm3kbjrJ0ZwL5BoVOB8Nu82N6WEt8nKXLthCibpMgU0CCjKgU+TnwzQiIjwY7N3hoDbgHlmzfoxtg+YOQlwVugdA6HIKGgE9IsaEmPjmL99Ye4dd95wCwsTTj0R7NeLxnU+ysbj2xpRBC1EYSZApIkBGVJicTFg+Gc3vAuRE8vBacfG++z/6V8OPj2sSU13P210JN63Bo1AnMTLth7zudxhu/HGLnCa3LtqejNdPDWnLv7Q0xM5MGwUKIukWCTAEJMqJSZSXD52GQchQ8WkPEb2DnWvy2Oz6G358FFLQZDoPeg+Ob4NBqiFsHeZevbuvTHkYvKxKMlFL8ceA8b/5+iFMXtR5OwX5OvHx3EJ2lQbAQog6RIFNAgoyodKkntTCTeQ4adoJxP4GV3dX1SsGmNyH6Xe11p0e1gfXMrhknJvcyHNuohZrDv0FuJjj5aY2JvdoUOWVOvp7FW08wf+NRMnPyARjQxpvnB7WisZt9ZV6tEEJUCQkyBSTIiCqRGANfDIDsdAi8C+7/FswttYbBvz4N/3yhbdf7Regx/eYTUKae1NrfJMeCtRPc9xU07VXspimXcvhgfSzf7kjAoMDSXMeEOwOY1CcQZ1vLCr9MIYSoKhJkCkiQEVUmYTt8ORTyr0C7+yB8LvzwqFbLgg7ufh86PlyyY11JhWVj4ORWMLOAIfMhZPQNN49NzOSNXw8RHXsBAFd7K6b2b8EDnfwxl/YzQohaSIJMAQkyokrFroGlo0HpwdFHu91kbgXDPyn94Hn5ObDqCTjwvfa61wvQ89mb1uZEHUnijV8PcTTpEgCtfZx47Z42dAy4QbsdIYSooSTIFJAgI6rc3mXw42PacysH7TZT055lO5bBABteha1ztNeth0CLMK3djEcrsCw6nky+3sC3OxN4f20s6Ve03lFDQ3x5flBrvJxsylYOIYSoYhJkCkiQEdVi91dwYCX0mwm+t5X/eLs+1aZHUIary3Rm4NoUPIOgUWetbY57oLHG5mJWLu+tPcLSnQkoBfZW5jzVN5CHujbBykImpBRC1Gx1KsgMGzaMqKgo+vbty8qVK0u1rwQZUWec3AYxqyDxICTFwOWUotu4+GuBpnl/aNIDrOzYfzqdGasPsDshDYCm7vbMGNKGni08qvgChBCi5OpUkImKiiIzM5MlS5ZIkBECtC7dl5Ig6SCc3w/Ho+DEFtDnXt2mQRN4ZCPYuWIwKH789wxv/X6Y5Es5APQP8uKVwUE0crUr/hxCCFGNyvr7u0bWN/fq1QtHR8fqLoYQNYdOB45e0KwPdJ0MD/4I/z0Bo5dDh4e1aRNS42HDawCYmem4N7QhG5/pyX+6NcHCTMe6mET6zt7M7HWxXCmYnFIIIWq7UgeZ6OhowsPD8fX1RafTsWrVqiLbREZGEhAQgI2NDZ07d2bnzp0VUlghxDWs7KHlABg8G0Z9qS37ZzGc/tu4iZONJS8NDuL3yd3p2tyN3HwDH26Io9/szfxx4Bw1sEJWCCFKpdRBJisri/bt2xMZGVns+uXLlzNt2jRmzJjB7t27ad++PWFhYSQlJRm3CQkJITg4uMjj7Nmzpb6AnJwcMjIyTB5C1DsB3aD9aEDBL1NAn2+yOtDLka8f7szCMbfj52LLmbQrPP71bh78bKex67YQQtRG5Wojo9Pp+PHHHxk69Op4GZ07d6Zjx47Mnz8fAIPBQKNGjXjqqad47rnnSnzsqKgo5s+ff8s2MjNnzuTVV18tslzayIh659IFmN8BstNgwNtwxxPFbnYlV8/CqKMsij5Obr4BS3Mdj/VoxqQ+zbGxNC92HyGEqGw1oo1Mbm4u//zzD/369bt6AjMz+vXrx7Zt2yryVEbPP/886enpxsepU6cq5TxC1HgOHtBvhvZ84/8g41yxm9lamTPtrpasn9qTPq08ydMr5m86Sv8PNrPpcFKx+wghRE1VoUEmOTkZvV6Pl5eXyXIvLy/Onz9f4uP069ePkSNH8ttvv9GwYcObhiBra2ucnJxMHkLUW7dPAL8O2iSUa1646ab+bnZ8Nr4Di8aG4uNsw6mLV4hYvIsnvv6Hc+lXqqa8QghRThbVXYDirF+/vrqLIETtZGamNf79uBcc/EHr5eTWDPR52sPeHXxDjJvrdDoGBHvTPdCduRvi+GxLPL8fOE907AWm9m/BhDsDsDCvkZ0bhRACqOAg4+7ujrm5OYmJiSbLExMT8fb2rshTCSFuxKc9dHoUdiyC1ZOKru/5X+htWltjb23BC4NaM+w2P178cT+7E9J449dDfL/7DP8bFszt/g2qqPBCCFE6FfqnlpWVFaGhoWzYsMG4zGAwsGHDBrp06VKRpxJC3EzvF6FJT3BpDG7NwaM1eAVr6za/Awd/LHa31j5OrHz8Tt4e3hYXO0sOncvg3oV/8fwP+0m7nFvsPkIIUZ1KXSNz6dIljh49anwdHx/Pnj17cHV1xd/fn2nTpjF+/Hg6dOhAp06dmDNnDllZWURERFRowa8XGRlJZGQker0M9CUENk4wfnXR5WtehG3zYdWTWsDxbltkEzMzHfd38qd/kBdv/X6Ylf+cZunOBNYePM+Ld2u1NrqbzMgthBBVqdTdr6Oioujdu3eR5ePHj2fx4sUAzJ8/n1mzZnH+/HlCQkL48MMP6dy5c4UU+FZkigIhbkKfD9+MgOObwNkfHo0Ce7eb7rLjeAovrTpAXMF4M90D3fnf0Lb4u8lUB0KIilOn5loqDwkyQtzC5YvwSR9tSoOA7tp0B+aWN90lN9/AJ38e58MNceTkG7CxNGNKvxba9AfSGFgIUQFqxDgyQohawM4VRi8DKwc48SdsfOOWu1hZmDGxd3PWTOnBnc3cyM4z8Pbvhxkyfyv7TqdVQaGFEKJ4EmSEqI88W8HQhdrzbfPhQmyJdgtwt+eb/3Rm1oh2uNhZEnMug6GRW3n9lxiycvJvfQAhhKhgdSbIREZGEhQURMeOHau7KELUDkFDoMVAMOTD79OhhHeZdTodIzs0Yv20ngwN8cWg4LMt8dz1QTSbjsjIwEKIqiVtZISozy4eh8g7QJ8Do77Swk0pRR1J4qVVBzidqo0GHN7el1cGB+HhaF3RpRVC1GHSRkYIUXquTaHrZO35mhcg97L2/EoqrP4/+Lg3XIy/6SF6tfRk7dQePNK9CWY6+HnvWfrN3syKXaeoY38nCSFqIKmREaK+y70MkZ0g/RT0eBb8QuGXKZBZMOlk4F0w5rsSHWr/6XSe+2EfB89mANClqRtvDW9LgLt9ZZVeCFFHSPfrAhJkhCiDmNWw4kHQmYEyaMtcm0LaKTDkwejl0HJAiQ6Vrzfw+dZ4Zq+LJTtP66r9zF0tiejaBHMzGUhPCFE8ubUkhCi71uHQtLcWYnRmcOdT8MRf0OVJbf0fz0FedokOZWFuxqM9mrFuak+6Nte6ar/x6yFGLPqLuMTMSrwIIUR9JDUyQghNZiJsXwCtBkOjgt5/OZkwrwNcOg99X4HuT5fqkEoplu06xZu/HiIzJx8rczMm9wvk0R5NsZSB9IQQ16j3t5aunWspNjZWgowQFWXvcvjxUbC0g0l/g7NfqQ9xLv0KL/54gI2Hte7ZQT5OzBrZjja+zhVdWiFELVXvg0whqZERooIpBZ+Hwakd0HoIjPoSyjBppFKKn/acZebPB0m7nIeFmY4nejVjUp/mWFuYV0LBhRC1ibSREUJUDp0OBs0CnTkcWg07PirjYXQMvc2PdVN7MqitN/kGxbyNRxn84Rb+TUit4EILIeoLCTJCiFvzaQ93FczJtPZFOLmtzIfycLRmwZhQFo65HXcHK+KSLnHvwr/4368xXMnVV1CBhRD1hQQZIUTJ3PEEBN+rTWnw3XjIPF+uww1s68O6qT0ZfpsfBgWf/BnPwLnRbD+eUkEFFkLUB9JGRghRcjmX4NN+cOEQeLeDtiPBoxV4BYFzwzIfdtPhJF74cT/n0rUu3g/e0Zj/DmyFg7VFRZVcCFHDSWPfAhJkhKhkyUfhk96Qk2G63CdEq7Fp1lsbSC/xoDaYXoeHwNH7lofNyM7jrd8Os3RnAgB+Lra8c287ugW6V8ZVCCFqGAkyBSTICFEFLsTCge8h+QhcKHioG7RvsXaC3i9Cx/+A+a1rWLYeTea5H/Zx6qI2CeXYO/x5fmBr7KV2Rog6rd4HGRlHRohqlJUMMavgwA9wdo82vYFXECTHwdnd2ja+t8H9S8HJ55aHu5ybz9u/H+bLbScBaORqy6wR7bmjqVtlXoUQohrV+yBTSGpkhKhBDHrYvQTWvwrZaeDcCMZ+Dx4tS7T71qPJPLtyH2fStNqZiK4BPBvWClsrGXdGiLpGxpERQtQ8ZuZaG5nHNoNbc22G7c/ugoQdJdq9a3N3/pjSndGdGgHwxdYTDPrwT/45ebEySy2EqEUkyAghKl+DAHhoLfh10GpmvhwCh38t0a6ONpa8NbwdiyM64u1kQ3xyFiMXbeOt3w6RnSfjzghR30mQEUJUDXs3GL8aWgyA/GxYPhb+/rzEu/dq6cmaqT249/aGGBR8FH2cwfO2sPdUWiUWWghR00mQEUJUHSt7uO8buH0cKAP8MhVObC3x7s62lrw/qj2fjOuAu4M1R5MuMXzhX7y35gi5+YZKLLgQoqaSICOEqFrmFhD+IQSP0F7vX1HqQ/QP8mLd1B6Et/dFb1DM33SUIfO3cPBsegUXVghR00mQEUJUPZ0OQh7Qnh/+TevdVEoN7K2YN/o2Foy5HVd7Kw6fz+Se+Vv5cEMceXqpnRGivpAgI4SoHgHdwcYZspLg1M4yH2ZQWx/WTu3BgDbajNqz18UyfMFfxCZmVmBhhRA1VZ0JMpGRkQQFBdGxY8fqLooQoiQsrLSGvwCHfynXodwdrFk49nbm3h+Cs60l+8+kM/jDLXy0+Rh6Q50aKksIcR0ZEE8IUX0O/az1XnLxh8n7tFtO5ZSUkc3zP+xnw+EkADo1ceX9ke1p5GpX7mMLISqPDIgnhKh9mvUFC1tIS4Dz+yvkkJ5ONnw6vgNvD2+LvZU5O+MvMmBONCt2naKO/d0mhEBqZIQQ1W3ZGO3WkmcbMOTDpURQSms/c9fr0GZomQ+dkHKZp7/bw64TqYDW2+mt4W1xd7CuqNILISqI1MgIIWqnoHu0f5MOarNpZ6dBTjqkJ8B3E2DbgjIf2t/NjmWPduG5ga2wNNexLiaRsA+iWXvwfMWUXQhR7XxnrogAACAASURBVKRGRghRvQx62DZfe+4ZpE0saWYOOxbBrk+15QPegTseL9dpYs5mMG3FHg6f13ozjerQkJcHB+FoY1mu4wohKobMfl1AgowQdYRSEPU2bH4bHH1gygFtML1yyMnXM3ttLB//eRyloGEDW2aPCqFTE9cKKrQQoqzk1pIQom7R6aD702DnBpnn4Oi6ch/S2sKc5we1Ztkjd9CwgS2nU69w38faBJQ5+TIBpRC1kQQZIUTNZWEF7Udrz3d/WWGH7dzUjd8nd2dUh4aoggko75m/lUPnMirsHEKIqiFBRghRs90+Tvs3dg1knCu6Pv0MxEfDoV/g8sUSH9bRxpJ3R7Tn4wdDcSuY4mDI/C0sjJJB9ISoTSTICCFqNo+W0OgOUHrY+63pujP/wNz2sCQclo+BlRGlPvxdbbxZM7UH/YO8yNMr3vnjMPd/vI1TFy9X0AUIISpTnQkyMkWBEHVYYa3M1g8h9YT23GCA354FQ57WGFhnDsejtHBTSu4O1nz8YCjvjmiHvZU5u06kMmBONMt2JsggekLUcHUmyEycOJGYmBh27dpV3UURQlS0tiPBL1QbY2bFOMi7Avu/gzN/g5UDPBoF7UZp2279UFtfGHhKSKfTMapDI/6Y0oNOAa5k5ep57of9PPrVP1zMyq3oKxJCVBDpfi2EqB3STsHHPeFyCjg11EJN7iXoOwO6T4PEg7DwTtCZaT2dsi5Arxeg57OlnsNJb1B8+udx3lt7hDy9wsPRmvdGtqdnC49KujghhHS/FkLUbS6NYMTnYG4FGae1EOPaDO54Ulvv1Qaa9wdl0EIMQNSbsH6GNiZNKZib6XisZzNWTexKc08HLmTmMP7zncxcfZDsPOmmLURNIjUyQojaJeMcpBzV5mXybgf2blfXpRyDqLegaS+4kgprX9KWd3wEBr4LZqX/2y077//bu/Owqqr9j+Pvcw4zCoooKmIOOQ/giJrc1Cwt0yybLYduaWmi2fzrdtXq3m63uqVJk93CyrnSSvNmmaaiOaA454izYESioAJyzu+PrSABynDO4Zzj5/U8PHvttYf1pWc/8m2vtdfK49XvdjJ9zUEAmoZVYfK97WhRR/++iNiTZva9QImMiOTb8AksfAKwQbcxcNMr5b7Vsl0neHreFtIys/GxmHmmbzMeuq4hZnPZuq1EpHjqWhIR+bOOw2HghUUn135Ypnlm/qxns1r8b1wMvVvUIifPyiuLdvLgx2tJyThnp2BFpDyUyIiIZ4u8D2q3gbxs2DyrQrcKreLLtCEd+cftrfHzNpOw93f6vL2C77YWM1GfiDiFEhkR8WwmE3R8yChv+KTMA3+L3s7E4OhrWBQbQ5vwYDLO5jJqxkaemreZzOzzdghYRMpCiYyIeL42dxnzzfy+B5J/tsstG9eswpePdWNUj8aYTPBF4hFumbySxIN/2OX+IlI6SmRExPP5Vi1YfHLxc3DePhPc+XiZeaZvc2Y/0oXwav4cSj/D3R+s4a0fdnM+z2qXNkTk8pTIiMjVoef/QUAo/LYTVv3HrreOblSD78bGcFtUXfKsNiYv3cNdH6zh4O9Zdm1HRIpSIiMiV4eAELjl30Z55ZvGPDN2FOzvzeR72zH53iiq+nqx6dBJbpm8krkbDmu9JhEHUiIjIlePVndAzeaQlwN7lzqkiduiwlk8LiZ/vaZnvtjCqBkb+UPrNYk4hMckMlr9WkSuyGSCJjcZ5T1LHNZMveoBzBrRhaf7NMPLbGLxthT6Tl7B6r1pDmtT5GqlmX1F5OpyYBXE9zMWlnxqD5gtDm1uy5GTjJudxP60LEwmePT6xoy/sSneFo/5/0gRu9DMviIipRERDb7BxiraRzc6vLm29aqxMLY793aKwGaD95bv4873VnMgTQOBRexBiYyIXF0s3tC4p1FOeBvS9sD2BZC6vcKT5ZUkwMeLfw1qy7uD2xPk58XmIxn0m7KSLxOPaCCwSAWpa0lErj57f4TPBxWt9w4E3yrgEwhN+sDN/7J700dPnuWJ2UmsO2Cs+3RbVF1eHtiaID9vu7cl4k7UtSQiUlrX9oYh30C1awAT1GoFXv6QmwWZqZC+H9a+B/uX273p8Gr+zBrRhSdvbIrFbOLrpGOaEVikAvRGRkSuXjYb5J4FnwDIPQenjkJOFqx9H5JmQHhHePhH42snB0g8+AdjZ2/iyB9nsZhNjLuhCaN6XovF7Jj2RFyZ3siIiJSVyWQkMQDeflCjMdRpCzdMMN7QHN0A+5c5rPkO11Tnu7ExDIg0ZgR+84fd3DftF46dPOuwNkU8jRIZEZE/qxoG7QYb5a1fOLSpID9vJt8bxX/ujiTQx8K65HT6vr2CxVuPO7RdEU+hREZEpDit7jC2OxfabZHJkphMJu5oX4/vxsYQGVGNU+fO89iMjTz/1RbO5Jx3aNsi7k6JjIhIcep3gSq1ITvDod1Ll7qmRiBfPNqVUT0aYzLBrHWHufWdVWw7muGU9kXckRIZEZHimC3Q8jajvH2B05r1tph5pm9zZjwcTe0gP/b/lsUd767mo5X7sVo96tsMEbtQIiMiUpLm/Yztvp8cNlleSbo1DmXx2BhuahlGTp6VVxbtZFj8ek6cPufUOERcnRIZEZGSRESDlx9kpsBvu5zefPVAHz54sAP/uL01ft5mVuz+jVsmr2TZryecHouIq1IiIyJSEm8/qN/VKF+cHM9mM9ZoOpPulBBMJhODo6/h28e707x2VdIycxgev55J327nXG6eU2IQcWVKZERELqdRD2O7fzmcToHp/WFaT5g7xKlhNAmryoLR1zH8ugYAfJJwgIFxCexJPe3UOERcjRIZEZHLadTD2B5YCV+PNrYX93OdO17Fz9vChP6t+GRYJ2oE+vBrymn6T13F7HWHtPikXLWUyIiIXE7ttlCzBeRkGotNXiplS6WE1LN5LRaPiyGmSSjncq0899VWxszaxKlzuZUSj0hlUiIjInI5ZjPc8nrBfosB0PRmo7z/Z1j/X1j8HJw75dSwalX1Y/rwzjx3c3O8zCYWbjlOvykr2XRIi0/K1UWJjIjIlTSMgU6PQEAN6PkC1Otg1C97BRaNN1bK/uU9p4dlNpt49PrGzHu0KxEh/hxOP8td76/hveX7NOeMXDU8JpGJi4ujZcuWdOrUqbJDERFP1O8NeGY/1GoO9Yr5d2bvD3A0Ec6edHpo7epXZ1FsDLe2rcN5q43X/vcrQz9Zpzln5KpgsnnYCLHyLgMuIlJq507Bm80g9wwM+i98+deCYwE14PYPoMmNTg/LZrMxd8NhJnyznXO5VkKr+PCfu6P4S9OaTo9FpKzK+/dbiYyISHkcTQQbRjfTvxvDmbSCY/4hMH4HePtXSmh7T5zm8Zmb+DXF+DR75F8a8eRNzfDx8piX8OKByvv3W0+1iEh5hHcoGCvTcbixrdsegiPgbDpsnVdpoV1by5hzZkjXawD4YMV+7np/NYd+P1NpMYk4ihIZEZGK6j4eBr4HQ76GziOMurUfVmpIft4WXrqtNe8/0IFgf282H8nglikr+TrpaKXGJWJvSmRERCrKJwCi7ge/IGj3AJgskLoV0pMrOzL6tq7Nd2Nj6NSgOpnZ5xk7O4lnvtjMmZzzlR2aiF0okRERsaeAELimm1He/X3lxnJBeDV/Zj3ShdgbmmAywdwNR+j/zip2HHPu3DcijqBERkTE3pr2Mba7/1e5cVzCy2Jm/I1NmflwF8KCfNn3WxYD301g+uoDWt5A3JoSGRERe2va19geWAWZv1VuLH/StXENFo/9Czc0r0XOeSsTvtnOiM8SOXkmp7JDEykXJTIiIvYW2sT4qsmaC5s+u/y5p1Mh+5IVrHMc/2VRSKAPHw3tyIT+LfGxmPlhRyo3T17JuuR0h7ctYm9KZEREHKHjhUnyNnxSdJXssydh30/Gzzsd4PNBYLPB4mfh1XD4dZHDwzOZTAy/riFfjepGw9BAjmec494P1/D2j7vJ0/IG4kaUyIiIOELrOyCwFmQcgiUvFNRbrfBBDHx2u/GTcxoOrzXWalr7PtissHOh88IMD2bhmO4Mal8Pqw3e/nEP90/7heMZZ50Wg0hFKJEREXEEb39jbhmA9R/B4fVG+eRBOHmo6PnfP19Q/uPCZ9tHEuG1BvBhT0jd7rBQA329ePPuSN66J5JAHwtrk9O5efJKftiR6rA2RexFiYyIiKM06Q1Rg43yf3vD7MGw8k1j3zsAvAOLv+7ETqOr6Ye/w9k/4NhGmHmPwxekvL1dPRbGxtAmPJiTZ3J55NMNTPxmO+dy8xzarkhFKJEREXGkHs+Bxcco/7qwYPBvy9vg8fUFY2kAmt4MJjOcOwkf94GDq4x6szdkHDaud7CGoYF8+Vg3Hu7eEID41Qe4493V7P8t0+Fti5SHEhkREUeqVh/umwU3/N0oXxTWCoLDoXGvgrqb/2W8qQFj3AxA6zuh2+NG+dAvTgnZx8vM325tySfDOhES6MOO46fo/84qFmzS8gbiepTIiIg42rW9IeZJ6PtaQV2tFsa2aV+4bizcPxeqN4C2dxe+NvJeiIg2yheTGyfp2bwWi8fG0KVRCFk5eYybo+UNxPUokRERcZZre0NQOPgGGytlA1i84MaXCmYDvuVNeGI71OsE9TpDox7GFiBtN2z9wqkhhwX5MePhLozr3QTzheUNbpuawK6U01e+WMQJTDYPm5v61KlTBAcHk5GRQVBQUGWHIyJSWOZvkJdjdCuVxVcjYMscqBIGT+4Ck6n483LPwsd9IaAG3PUJ+AVXPOYL1uz7nbGzN3HidDa+XmYmDmjFvZ0iMJUUi0gZlPfvt97IiIg4U5WaZU9iAG59y9hmpsLGT8FawpdEh9fC8STYtxQWPVn42OY58EoYvN4EjiaWOYSujWvw3dgYrm9ak+zzVp7/aiuxs5M4fS63zPcSsRclMiIi7sAnEGo0McrfxsLSSQXHsk/Dxs+M7ZENBfVb58HUTsbMwTlZMH8EnD8HWSdg0VPlCiO0ii+fDOvEczc3x2I28e3mY9z6ziq2HsmowC8nUn5KZERE3EXV2gXlhMmQusMoL30JvnkcXq0HP71c+Jq03bD3R1j9TuH64iblKyWz2cSj1zdm7siuhFfz5+DvZ7jjvQQ+SUjWStridEpkRETcxcUvnS5a+pKxjtO6DwvXe/nBqD994bT81cL7Z9Jgw8cVCqfDNdX5LjaGPq3CyM2zMenbHYzUStriZBrsKyLiLs6kG7P9NvwLzH8UbH8aJxNUz5hoL+p+qN0alr4MK98ofM5Nr8DveyEx3viCqtXtUO0aiB5R7rBsNhufrjnIPxbtJCfPSng1f6bcF0WHa0LKfU+5+pT377cSGRERd7TijYJuJL9qMPBdaN6v8Dl552H/cljwKGT9BrVawaOrjHEyr18LuVkF50Z0gWELweJd7pC2Hc3g8ZkbOfD7GSxmE0/d1IyRf2mE2ayvmuTK9NWSiMjVJOZJ6PcfaDEA/vpD0SQGjDlqmvSG+2ZDm7vh/tlgNoNPADTuWfjcw78Yyyek7YFNnxurdJdR6/BgFsbGMCCyLnlWG6/971eGxa8nLTO7nL+kyJXpjYyIyNVo1/9g1j0lH7/lDej8SLlubbPZmLvhMBO+2c65XCs1q/oy+d4oujUOLWewcjVQ19IFSmRERErBZoOd3xjdTT6B8J/mhY9XuwbGbi554r1S2J16mtEzNrLnRCYmE4zp1YSxNzTBoq4mKYa6lkREpPRMJmNgcOi1EFQHOo8Es1fB8ZMH4ejGCjXRNKwq3zzenXs6RmCzwZSle7h/2i+kZJyrYPAiBVwukTl8+DA9evSgZcuWtG3blnnz5lV2SCIinu+Wf8Pff4fxO6H5rUbdzm8qfFt/Hwuv3dmWyfdGEehjYW1yOrdMWcmyX09U+N4i4IKJjJeXF2+//TY7duxgyZIljBs3jqysrCtfKCIiFRdU1/gkG2DPErvd9raocBbGxtCqbhDpWTkMj1/Pq9/tJDev7IOKRS7lcolMnTp1iIqKAqB27dqEhoaSnp5eyVGJiFxFGvcCkwVO7IA/Dtrttg1DA/lqVDeGdWsAwAcr9nPX+2s4nH7Gbm3I1afMicyKFSvo378/devWxWQysWDBgiLnxMXF0aBBA/z8/IiOjmbdunXlCi4xMZG8vDwiIiLKdb2IiJRDQAhERBtlO76VAfD1sjBxQCvef6ADQX5eJB0+Sb8pK/nftuN2bUeuHmVOZLKysoiMjCQuLq7Y43PmzGH8+PFMmDCBjRs3EhkZSZ8+fThxoqA/NCoqitatWxf5OXbsWP456enpDBkyhA8//LC4ZvJlZ2dz6tSpQj8iIlJBTW8ytrv/55Db921dm0WxMbSrX41T587z6Ocb+fvX2ziXW8Kq3iIlqNDn1yaTifnz5zNw4MD8uujoaDp16sTUqVMBsFqtREREMGbMGJ577rlS3Tc7O5sbb7yRRx55hAcffPCy506cOJFJkyYVqdfn1yIiFXDiV3g3Giw+8NQe8K/mkGZy86y8sWQXH/y8H4CWdYKYen87GtWs4pD2xHW5xOfXOTk5JCYm0rt374IGzGZ69+7NmjVrSnUPm83GsGHD6NWr1xWTGIDnn3+ejIyM/J/Dhw+XO34REbmgVnOo1RLycmD39w5rxtti5vmbW/DJ8E6EBPqw4/gp+r+zigWbjjqsTfEsdk1k0tLSyMvLIywsrFB9WFgYKSkppbpHQkICc+bMYcGCBURFRREVFcXWrVtLPN/X15egoKBCPyIiYgeNehjbY5sc3lTPZrVYPDaGLo1CyMrJY9ycJJ6et5kzOecd3ra4N68rn+Jc3bt3x1qONT5ERMTOarcxtkcTndJcWJAfMx7uwjs/7WHy0j3MSzxC0uGTvDu4PU3CqjolBnE/dn0jExoaisViITU1tVB9amoqtWvXtmdTIiLiaOEdjO2RdTDnAac0aTGbGNe7KTMf7kKtqr7sOZHJgKkJzNugYQNSPLsmMj4+PnTo0IGlS5fm11mtVpYuXUrXrl3t2ZSIiDhazWbQpI9R3vkt/PQK5DhnzpeujWvw3dgYYpqEcjY3j6e/2ML4uUnqapIiypzIZGZmkpSURFJSEgDJyckkJSVx6NAhAMaPH8+0adOYPn06O3fu5LHHHiMrK4vhw4fbN/I/iYuLo2XLlnTq1Mmh7YiIXFXunVFQXvE6/LMOnDzklKZDq/gyfXhnnu7TDLMJvtp4lAFTE9iVctop7Yt7KPPn18uXL6dnz55F6ocOHUp8fDwAU6dO5fXXXyclJYWoqCimTJlCdHS0XQK+Eq1+LSJiZxODi9Y9fxR8nfeJ9Nr9vxM7exOpp7Lx8zbz0oDW3NWxHqYKrM4trqW8f78rNI+MK1IiIyJiZzPvhd2LC9fd/amxerYT/Z6ZzRNzN7Ni928A3NEunJcHtibQ1+W+W5FycIl5ZERExAP1+Qfc/G946JL5ZDKcP89LjSq+xA/rVNDVtOkoA6au4tcUzeh+NVMiIyIil1ejMUSPhPpdoN2Fr5fS91fsntmZcOgXKGOngNlsYnTPa5k9oiu1g/zY91sWt01NYM76Q3hYB4OUksckMhrsKyLiBPW7GdvDa8t3/fqPjDE3r4bDx33gxwnluk3nhiEsiu3O9U1rkn3eyrNfbuWJOUlkZeurpquNxsiIiEjpnUmHN5qCNRdiN0FIo9Jf+9suiOtctP6ez6FBTLnWc7JabXywYj9vLNlFntVGo5qBxN3fnhZ19O+/u9EYGRERcbyAEAhpaJRPXpikLu88WEuxavXWecXXz3mg3BPumc0mHuvRmNkjulAn2I/9v2UxMC6BWevU1XS1UCIjIiJlU7WOsU2YbGxn3QNvNoNzGSVfc+JXYx6ai1oMKHz8wEr4+d/w/QuQl1vmkDo1CGFRbAw9mxldTc9/tZVxc5LIVFeTx9M3ayIiUjYWH2O7b2nhOWY+uB76/BP2LzNWzG52M1z/rPEW58j6gvOeOwR+wUZX04c9IPfCbMHL/mFsazSGjg+VOayQQB/+O7QT01bu59/f7+LrpGNsPZLB1Pvb07Kuupo8ld7IiIhI2ZT05uWPZJh9H6z7EE4ehLXvw9whxrF9F5au6fhXI4kBYwmEZ5Kh0Z8mWd33U7lDM5tNjLy+MXNHdqFusB/707IY+G4CM9YeVFeTh1IiIyIiZXPjS6U/98BKmNIOts839qs3KHzc2w9qXFu4bue3cLrw4sNl1eEao6upV/Na5Jy38sL8bYyZtYnT58rebSWuzWMSGX1+LSLiJNd0hYkZMOQbeOQniLjCEjSXzjlTu03R470nFq1b/HRFIgSgeqAPHw3pyP/d0hwvs4mFW47T/51VbDt6mbE84nb0+bWIiFRM6nZY9CT0eA6y0owBu9EjYemkoudeHB/zZ79+B6nbjOvXfWDUPbwU6nW0S4iJB/9gzMyNHMs4h4+XmRdvbckD0fW1VpML0VpLFyiRERFxERcHAldvCIE14aZXoP4V3t4s+RusfscoX/8s9Pw/u4Vz8kwOT83bzI87TwDQr20d/nVHG6r6edutDSk/zSMjIiKu5cEFEHk/jPwZHv7hykkMQO3IgnLKVruGUy3Ah2lDOvK3fi3wMptYtOU4t6qrye0pkREREcdo3BNuf6/4rqSStB4EzfoZ5WOb7B6SyWTi4ZhGzHu0K+HV/Dn4+xnueHc1n605oK+a3JQSGRERcR1mM9zxIWCC08cr/PVSSdrVr853sTHc2DKMnDwrL369ndEzN3JKXzW5HSUyIiLiWnyrGJPiAaTat3vpUsEB3nz4YAdevLUl3hYT321N4dYpq9h6RF1N7kSJjIiIuJ7wC18r7fzWoc2YTCb+2r0h8x7tRr3q/hxKP8Og91YzfbW6mtyFxyQymkdGRMSDNL/F2B7f4pTmoiKqsWhMDDdd6Gqa8M12Hvt8Ixln1dXk6vT5tYiIuJ6UbfD+dWD2hhdSwOKcpQFtNhvxqw/wz+92kptnIyLEn7j729O2XjWntH810+fXIiLiOUIagW8QWHNh8yynNWsymRh+XUO+eLQbESH+HE4/y6D3VvNJQrK6mlyUEhkREXE9PgHQLdYof/dUyQtVOkhkRDUWjomhb6va5ObZmPTtDh79PFFdTS5IiYyIiLimDsPAZIbz5xw+6Lc4wf7evPdAeyYNaIWPxcz321PpN2UlSYdPOj0WKZkSGRERcU1VakLnEUb56MaSz3Ngl4/JZGJotwZ8+Vg36ocEcOSPs9z1/mo+XqWuJlehREZERFxXrZbG9uShgrrEeFj2T5g+wFjP6aMbHJrMALSpF8zC2O7c0sboanpp4Q5GfpZIxhl1NVU2JTIiIuK6qtU3tnt/gB1fG18zfTsWfn4Nkn82jh1NhN/3OjyUID9v4u5vz0u3GV1NS3ak0u+dlWxWV1OlUiIjIiKuq25UQXnuEOOT7OLsW+aUcEwmE0O6Fu5quvP91cTrq6ZK4zGJjCbEExHxQP7Voe09Vz5vz/eOj+USF7uaLn7VNPHbHYyaobWaKoMmxBMREddms8H+5TDzbsjLMer+8gzUbAYmE3zxkFEXmwQhDZ0cWuEJ9OqHBPDu4Pa0Di/Dit8CaEI8ERHxVCYTNO4JEdEFddc/A23uhKZ9wT/EqDuaWAmhGRPoXbpW0x3vruazNVqryVmUyIiIiHsIb19QtngbW59AaPgXo3zmd+fHdMHFtZpuvLBW04tfb2fMrE2cVleTwymRERER93D9s9DuAbh3ZuH6gBrGNm2382O6RHCANx8+2IG/9WuBl9nEwi3HGTA1gR3HTlVqXJ5OiYyIiLgHn0C4LQ6a9ytcH1TH2K7/CLIznR/XJUwmEw/HNGLuo10Jr+ZPcloWA99NYObaQ+pqchAlMiIi4t6a3lxQTtlSeXFcon396iyK7c4NzWuRc97K/83fyrg5SWRln6/s0DyOEhkREXFvtVtDSGOjnBhfqaFcqlqAD9OGdOT5m5tjMZv4OukY/aeu4tcUdTXZkxIZERFxf42uN7Zb5sAXf4X0/RW/55l0OPtHwX7OGcgr2+Bds9nEyOsbM2dEF2oH+bH/tywGxiUwd8PhiscngBIZERHxBPW7FpS3fQHzH63Y/c6kw78bwmsNjKTowCr4Zx34uE+5btexQQiLYrtzfdOanMu18swXW3hy7mbO5KirqaKUyIiIiPtrcxcEhRfsH14L2acvv5jk+Wxjor0DCZCTVVCfMAUWjCrYn9IO4i8MMD6aCGfLt7ZSjSq+fDKsE0/3aYbZBF9uPMJtUxPYk3q6XPcTg8ckMlqiQETkKmYywd2fFa57tR6seKPka757Cj69DeJvgX/WhR3fQOoO+OFF2L245OuW/6vMXUwXmc0mRve8llmPdKFWVV/2nMhkwNQEvkw8Uq77iZYoEBERT7L+I1j0ZOG6iRlG4rHoSYjobMxFs+t/MKsUaziVpP1QuPUtMFvKfYu0zGyemJPEyj1pANzdsR6TBrTG36f893RnWqJARESk08PQ828F+2Yvo3tp7QewcTp8PdrY//Lh0t2vW2xBuWqdgvLG6bD6nQqFGlrFl/jhnRl/Y1PMJpi74QgD4xLYe6Jy58JxN0pkRETEs3QbA9eNNcrW87DtS1jyQsHxSdUg58K4lH7/Kfk+TfpA70nw3CG4YxqMXgvB9QuO/zjB2Oadh3MZ5QrVYjYRe0MTPn84mtAqvuxKPc2Aqav4Ouloue53NVLXkoiIeKa5Q2DH15c/54VUOLIO1v8XDiaAl7+xIGXzfhAQUvw1Ey+sbO3lD39LKdh/bDWEtSp3uCdOn2PsrCTW7DfWjLqvc30m9G+Jn/fV0dWkriUREZFL1e925XO8/YxFJ++eDuN3wtgkaP9gyUkMwBPbjW1eNhz6paD+vW6X/0rqCmpV9ePzh6OJvaEJJhPMWneI299dTXJa1pUvvoopkREREc907Q2F94cvhkH/6i8cbgAAFtRJREFUhfZDoFYreCa58HGLd+kG7wbXg9CmYLMWnVcmeUWFQraYTYy/sSmfPtSZGoE+7Dx+iv7vrGLhlmMVuq8nUyIjIiKeKbQJPPJTwX6dKGhzJwx4B0atvvxblyuJiC6+fsPH5b/nJWKa1OS7sTF0bhhCZvZ5Hp+5iRcXbONcbp5d7u9JlMiIiIjnCu9gJDMjV4BPgP3u22JA8fXp++zWRFiQHzMfjmZ0T2Mdqc9+Ocid76/m4O/qarqUEhkREfFs4R2gTqR979n0Jrh3llFudTv0e9MoewfatRkvi5mn+zQnfngnqgd4s+3oKW6dsorFW4/btR13pq+WREREKurYJviwB5jM8Pd0Y6ZhOzuecZYxMzex4aCxkOWwbg14/pbm+Hp5xldN+mpJRESksoQY3T/YrDCtl0OaqBPsz6wRXRh5fSMA4lcf4O7313A4/YxD2nMXSmREREQqyu+SNwjHNkLW7w5pxtti5vmbW/DfoR2pFuDN5iMZ9JuykiXbUxzSnjtQIiMiImIPl84SvHqKQ5u6oUUYi2JjaFe/GqfOnWfEZ4m8snAHuXlWh7brijwmkdHq1yIiUqk6/bWgnPA2/PJeuZcuKI3wav7MGdGVh7s3BOCjVcnc/cEajp4867A2XZEG+4qIiNjLpBCwXTLXS+Ne8OD8wudsmQvbF8CAKRAYapdml2xP4al5mzl17jzB/t785+5IbmgRZpd7O4sG+4qIiFS20esK7+/7CWYPBuuFLp+88/DVI7BrkbEit53c1Ko2i2JjiKwXTMbZXP46fQOvfrfzquhqUiIjIiJiL6HXwj0zCtf9uhD2LTXKycsL6lf8G9L3263piJAA5j3ajeHXNQDggxX7ue/DXzie4dldTUpkRERE7KnFrfDAV4XrZtwJBxLgWFLh+intjLc0duLjZWZC/1a8/0B7qvp5seHgH9wyeSXLd52wWxuuRmNkREREHGHfMvhsYOE6szdYcwvXRQ2Gge/avflDv59h1MxEth09BcDono15ondTvCyu+Q5DY2RERERcSaMe0OmRwnUXk5g7PiqoS5oBGUft+mYGoH6NAL58rBtDul4DQNyyfdz/0VpST52zazuVTYmMiIiII5hMEHlf8cea3Ah//bFg/62W8HINSN1u1xB8vSy8dFtrpt7fjiq+XqxLTueWyStZuec3u7ZTmZTIiIiIOEqdtsXX+1eDiGLmPdvwiUPCuLVtXb4d052WdYL4PSuHIR+v4z9LdpFndf/RJUpkREREHMXiDbGb4KEl0PEho+7SeWUGvFP4/PXTYI39x8sANAwN5KtR3bg/uj42G0z5aS8PfLSWE6fdu6tJg31FREQqS14uvFzMpHgPfQ/1uzis2a+TjvL8V1s5k5NHaBVfptwbRbdr7TM5X3lpsK+IiIi7sXhDbBI8sqxw/cd9HNrsbVHhfDumO81rVyUtM5sH/ruWyT/uccuuJiUyIiIilSmkIYS3h5ErC9fnOnYiu8Y1qzB/1HXc0zECqw3e+nE3Qz9eR1pmtkPbtTclMiIiIq6gTlvoFluwv+cHyMlyaJP+PhZeu7Mt/7k7En9vC6v2pnHL5JWs3f+7Q9u1JyUyIiIiruKmlwvKcx+EaTc4pdk72tfjm8evo0mtKpw4nc19034hbtlerG7Q1aRERkRExFX9thNyzjilqSZhVfn68eu4o304Vhu8/v0uHpq+nvSsHKe0X15KZERERFzJ8MWF908fB2sefDUSVk91aNMBPl68eVck/x7UFl8vM8t3/Ua/KStJPJju0HYrQp9fi4iIuBKbDSZVK/n4qLVQq7nDw9h5/BSjZ2xkf1oWXmYTz/ZtzsMxDTGZTA5pT59fi4iIeAKTCW59u+Tjcx90Shgt6gTxzZju9I+sy3mrjX98t5NHPk0k40zulS92IiUyIiIirqbjcGh1R/HH0nbDN7FwcI3Dw6ji68WUe6N4ZWBrfCxmftyZSr93VrL58EmHt11aHpPIxMXF0bJlSzp1KmbtChEREXfjE1jysY3T4ZO+sP6jks+xE5PJxANdruGrUd2oHxLAkT/O8uHK/Q5vt7Q0RkZERMQVvd8dUrYa5cj7YM8SOFPM/C5jN0P1Bk4J6dS5XN78fhfjb2pGsL+3fe+tMTIiIiIe5P65BeXb34en90HPvxU9b3KksWaTEwT5eTPpttZ2T2IqQm9kREREXJXNZgz+vdSBVfD9/8HxzYXrY5OM5Q7clN7IiIiIeJriPnVu0B1GrjASl0t9+bBzYnIxSmRERETcUUhDCO9YsH90Q+XFUomUyIiIiLir++cU3j/rOp9FO4sSGREREXcVGAqj1xfsL/tn5cVSSZTIiIiIuLMajQvK6z6ovDgqiRIZERERd2a2wOAvCvadtFq2q1AiIyIi4u6u7V1Qzvqt8uKoBEpkRERE3J3JBEH1jPKZtMqNxcmUyIiIiHiCvBxju//nyo3DyZTIiIiIeIKsE8Z26aTKjcPJlMiIiIh4glZ3VHYElUKJjIiIiCfo8lhB+cSvMDHY+Jn/mLFmk4dSIiMiIuIJajYvKL8bXVDePBMmVYPXr4Xs06W7V+5Zt0l+lMiIiIh4At+qlz+e9RvMf7Rofe5ZeLkWvNvV2N/2JfyjNnx0g/1jdACvyg5ARERE7KC4lbL/7NeFxdQtgrxsOLHD6Iq66Ggi7F0K17p2QqM3MiIiIp7i6f1XPufbcYX3c7JKPvdz1x9ArERGRETEUwTWgEH/Ldh/9kDRcxI/gZStkJ5sdCt9G3v5e1qtBeWsNPjjYOnH2jiBEhkRERFP0nIgtB4Et74F/tVhRDET5L3fHaZEwfyRV75ffL+CcsJkmNwWlv/LfvFWkBIZERERT2Lxgjs/ho4PGft1o2BiBtwWV/TcHV8XlKtdU1DuNqagfGg1HEk0ypmpxvZKA4udSIN9RURErgbtHoCkmXAwofjjf10CVcIKBg0fS4IDK41y6jYICIEtc4x9n0DHx1tKSmRERESuFnUii09kJmYUrbuYxACk7YZTxy45WIovpJxEXUsiIiJXixqNi9YFhBZ/7sD3CsprpsK+pQX7VWrZN64KUCIjIiJytWg/rGhdlbDiz426v/D+kfUFZRda10mJjIiIyNXC4mV0I03MgF4vgsUH+k8u+fxRvxSta3mbcR8X4TqRiIiIiPP85SnoFgtePiWfU6tF0brwDo6LqRxc7o3MyZMn6dixI1FRUbRu3Zpp06ZVdkgiIiKe6XJJzEV+lyxb4OUHXUY7Lp5yMNlsrrW8ZV5eHtnZ2QQEBJCVlUXr1q3ZsGEDNWrUKNX1p06dIjg4mIyMDIKCghwcrYiIiIfLSoP9y6HJTeDnuL+r5f377XJdSxaLhYCAAACys7Ox2Wy4WK4lIiJy9QgMhTZ3VnYUJSpz19KKFSvo378/devWxWQysWDBgiLnxMXF0aBBA/z8/IiOjmbdunVlauPkyZNERkZSr149nn76aUJDS/g0TERERK5qZU5ksrKyiIyMJC6umKmOgTlz5jB+/HgmTJjAxo0biYyMpE+fPpw4cSL/nIvjX/78c+yYMdlOtWrV2Lx5M8nJycycOZPU1NRy/noiIiLiySo0RsZkMjF//nwGDhyYXxcdHU2nTp2YOnUqAFarlYiICMaMGcNzzz1X5jZGjRpFr169uPPO4l9rZWdnk52dnb9/6tQpIiIiNEZGRETEjZR3jIxdv1rKyckhMTGR3r17FzRgNtO7d2/WrFlTqnukpqZy+rSxPHhGRgYrVqygWbNmJZ7/6quvEhwcnP8TERFRsV9CRERE3IZdE5m0tDTy8vIICys8S2BYWBgpKSmlusfBgweJiYkhMjKSmJgYxowZQ5s2bUo8//nnnycjIyP/5/DhwxX6HURERMR9uNxXS507dyYpKanU5/v6+uLr6+vAiERERMRV2fWNTGhoKBaLpcjg3NTUVGrXrm3PpkRERETsm8j4+PjQoUMHli4tWCHTarWydOlSunbtas+mRERERMretZSZmcnevXvz95OTk0lKSiIkJIT69eszfvx4hg4dSseOHencuTNvv/02WVlZDB8+3K6B/1lcXBxxcXHk5eU5tB0RERFxHWX+/Hr58uX07NmzSP3QoUOJj48HYOrUqbz++uukpKQQFRXFlClTiI6OtkvAV6IlCkRERNxPef9+u9xaSxWlREZERMT9uMQ8MiIiIiLOpERGRERE3JbLzSNTURd7yk6dOlXJkYiIiEhpXfy7XdYRLx6TyFz8aiknJwdASxWIiIi4odOnTxMcHFzq8z1usK/VauXYsWNUrVoVk8lU7DmdOnVi/fr1Jd6jpOMXF6Q8fPiwWw0kvtLv64rtVOReZb22tOeX97m50nE9V85ryx2fqyudo+fKNdoq771c9bm63HFHPVs2m43Tp09Tt25dzObSj3zxmDcyF5nNZurVq3fZcywWy2X/41/peFBQkFv9w3Cl38cV26nIvcp6bWnPr+hzo+eq8ttyx+fqSufouXKNtsp7L1d9rkpz3BHPVlnexFxkmThx4kS7RuEmOnfuXObj2dnZ/Otf/+L55593u/WdrvT7umI7FblXWa8t7fnleW6udFzPlXPbcsfn6krn6LlyjbbKey9Xfa5KOu5qz5bHdS05kuaoEUfQcyWOoOdKHMXVnq2r9o1MeVksFnr06IGXl8f1ykkl0nMljqDnShzFlZ4tvZERERERt6UJ8URERMRtKZERERERt6VERkRERNyWEhkRERFxW0pkRERExG0pkbGThQsX0qxZM5o0acJHH31U2eGIh7j99tupXr06d955Z2WHIh7k8OHD9OjRg5YtW9K2bVvmzZtX2SGJBzh58iQdO3YkKiqK1q1bM23aNKe0q8+v7eD8+fO0bNmSZcuWERwcTIcOHVi9ejU1atSo7NDEzS1fvpzTp08zffp0vvjii8oORzzE8ePHSU1NJSoqipSUFDp06MDu3bsJDAys7NDEjeXl5ZGdnU1AQABZWVm0bt2aDRs2OPxvod7I2MG6deto1aoV4eHhVKlShZtvvpklS5ZUdljiAXr06EHVqlUrOwzxMHXq1CEqKgqA2rVrExoaSnp6eiVHJe7OYrEQEBAAGMsY2Gw2nPGuRIkMsGLFCvr370/dunUxmUwsWLCgyDlxcXE0aNAAPz8/oqOjWbduXf6xY8eOER4enr8fHh7O0aNHnRK7uK6KPlciJbHns5WYmEheXh4RERGODltcnD2eq5MnTxIZGUm9evV4+umnCQ0NdXjcSmSArKwsIiMjiYuLK/b4nDlzGD9+PBMmTGDjxo1ERkbSp08fTpw44eRIxZ3ouRJHsdezlZ6ezpAhQ/jwww+dEba4OHs8V9WqVWPz5s0kJyczc+ZMUlNTHR+4TQoBbPPnzy9U17lzZ9vo0aPz9/Py8mx169a1vfrqqzabzWZLSEiwDRw4MP/42LFjbTNmzHBOwOIWyvNcXbRs2TLboEGDnBKnuJ/yPlvnzp2zxcTE2D799FOnxSruoyL/Zl302GOP2ebNm+fQOG02m01vZK4gJyeHxMREevfunV9nNpvp3bs3a9asAYxlzrdt28bRo0fJzMxk8eLF9OnTp7JCFjdQmudKpDxK82zZbDaGDRtGr169ePDBBysrVHEjpXmuUlNTOX36NAAZGRmsWLGCZs2aOTy2yl+20sWlpaWRl5dHWFhYofqwsDB+/fVXALy8vHjzzTfp2bMnVquVZ555Rl8syWWV5rkC6N27N5s3byYrK4t69eoxb948unbt6uxwxY2U5tlKSEhgzpw5tG3bNn8cxGeffUabNm2cHq+4h9I8VwcPHmTEiBH5g3zHjBnjlGdKiYydDBgwgAEDBlR2GOJhfvzxx8oOQTxQ9+7dsVqtlR2GeJjOnTuTlJTk9HbVtXQFoaGhWCyWIgOWUlNTqV27diVFJe5Oz5U4ip4tcQRXfq6UyFyBj48PHTp0YOnSpfl1VquVpUuX6hW/lJueK3EUPVviCK78XKlrCcjMzGTv3r35+8nJySQlJRESEkL9+vUZP348Q4cOpWPHjnTu3Jm3336brKwshg8fXolRi6vTcyWOomdLHMFtnyuHfxflBpYtW2YDivwMHTo0/5x33nnHVr9+fZuPj4+tc+fOtl9++aXyAha3oOdKHEXPljiCuz5XWmtJRERE3JbGyIiIiIjbUiIjIiIibkuJjIiIiLgtJTIiIiLitpTIiIiIiNtSIiMiIiJuS4mMiIiIuC0lMiIiIuK2lMiIiIiI21IiIyIV0qNHD8aNG1fZYRRiMplYsGBBZYchIk6gJQpEpELS09Px9vamatWqNGjQgHHjxjktsZk4cSILFiwgKSmpUH1KSgrVq1fH19fXKXGISOXR6tciUiEhISF2v2dOTg4+Pj7lvr527dp2jEZEXJm6lkSkQi52LfXo0YODBw/yxBNPYDKZMJlM+eesWrWKmJgY/P39iYiIIDY2lqysrPzjDRo04OWXX2bIkCEEBQUxYsQIAJ599lmaNm1KQEAAjRo14sUXXyQ3NxeA+Ph4Jk2axObNm/Pbi4+PB4p2LW3dupVevXrh7+9PjRo1GDFiBJmZmfnHhw0bxsCBA3njjTeoU6cONWrUYPTo0fltiYjrUiIjInbx1VdfUa9ePV566SWOHz/O8ePHAdi3bx99+/Zl0KBBbNmyhTlz5rBq1Soef/zxQte/8cYbREZGsmnTJl588UUAqlatSnx8PDt27GDy5MlMmzaNt956C4B77rmHJ598klatWuW3d8899xSJKysriz59+lC9enXWr1/PvHnz+PHHH4u0v2zZMvbt28eyZcuYPn068fHx+YmRiLgudS2JiF2EhIRgsVioWrVqoa6dV199lcGDB+ePm2nSpAlTpkzh+uuv57333sPPzw+AXr168eSTTxa659/+9rf8coMGDXjqqaeYPXs2zzzzDP7+/lSpUgUvL6/LdiXNnDmTc+fO8emnnxIYGAjA1KlT6d+/P6+99hphYWEAVK9enalTp2KxWGjevDn9+vVj6dKlPPLII/b5DyQiDqFERkQcavPmzWzZsoUZM2bk19lsNqxWK8nJybRo0QKAjh07Frl2zpw5TJkyhX379pGZmcn58+cJCgoqU/s7d+4kMjIyP4kBuO6667BarezatSs/kWnVqhUWiyX/nDp16rB169YytSUizqdERkQcKjMzk5EjRxIbG1vkWP369fPLlyYaAGvWrGHw4MFMmjSJPn36EBwczOzZs3nzzTcdEqe3t3ehfZPJhNVqdUhbImI/SmRExG58fHzIy8srVNe+fXt27NjBtddeW6Z7rV69mmuuuYYXXnghv+7gwYNXbO/PWrRoQXx8PFlZWfnJUkJCAmazmWbNmpUpJhFxPRrsKyJ206BBA1asWMHRo0dJS0sDjC+PVq9ezeOPP05SUhJ79uzh66+/LjLY9s+aNGnCoUOHmD17Nvv27WPKlCnMnz+/SHvJyckkJSWRlpZGdnZ2kfsMHjwYPz8/hg4dyrZt21i2bBljxozhwQcfzO9WEhH3pURGROzmpZde4sCBAzRu3JiaNWsC0LZtW37++Wd2795NTEwM7dq14+9//zt169a97L0GDBjAE088weOPP05UVBSrV6/O/5rpokGDBtG3b1969uxJzZo1mTVrVpH7BAQE8P3335Oenk6nTp248847ueGGG5g6dar9fnERqTSa2VdERETclt7IiIiIiNtSIiMiIiJuS4mMiIiIuC0lMiIiIuK2lMiIiIiI21IiIyIiIm5LiYyIiIi4LSUyIiIi4raUyIiIiIjbUiIjIiIibkuJjIiIiLit/weZXVUjanyDIwAAAABJRU5ErkJggg==", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "loglog(alphas; label = \"alpha_t\");\n", "loglog(dto_diminishing.^2; label = \"rho_t\");\n", "xlabel(\"iteration\");\n", "title(\"Optimal Step Size vs. Distance to Optimum\");\n", "legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "# Part 3" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = randn(10); y = sqrt(0.95) * x + sqrt(0.05) * randn(10);" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scatter(x, y)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "training error: 0.028\n" ] } ], "source": [ "# fit with linear regression\n", "\n", "f = [x ones(10)];\n", "w = y' / f';\n", "\n", "xplot = collect(-1.5:0.1:1.5);\n", "fplot = [xplot ones(length(xplot))]\n", "\n", "plot(xplot, fplot * w'; color=\"red\");\n", "scatter(x, y);\n", "\n", "xlim([-1.5, 1.5]);\n", "ylim([-1.5, 1.5]);\n", "\n", "training_error = round(mean((y - f * w').^2),3)\n", "println(\"training error:$(training_error)\")" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "training error: 0.0\n" ] } ], "source": [ "# fit with degree 10 polynomial\n", "\n", "f = hcat([x.^k for k = 0:10]...);\n", "w = y' / f';\n", "\n", "xplot = collect(-1.5:0.01:1.5);\n", "fplot = hcat([xplot.^k for k = 0:10]...)\n", "\n", "plot(xplot, fplot * w'; color=\"red\");\n", "scatter(x, y);\n", "\n", "xlim([-1.5, 1.5]);\n", "ylim([-1.5, 1.5]);\n", "\n", "training_error = round(mean((y - f * w').^2),3)\n", "println(\"training error: $(training_error)\")" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "test_x = randn(20); test_y = sqrt(0.9) * test_x + sqrt(0.1) * randn(20);" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "training error: 0.028\n", "test error: 0.094\n" ] } ], "source": [ "# fit with linear regression\n", "\n", "f = [x ones(10)];\n", "w = y' / f';\n", "\n", "xplot = collect(-1.5:0.1:1.5);\n", "fplot = [xplot ones(length(xplot))]\n", "\n", "plot(xplot, fplot * w'; color=\"red\");\n", "scatter(x, y);\n", "scatter(test_x, test_y; color=\"orange\");\n", "\n", "xlim([-1.5, 1.5]);\n", "ylim([-1.5, 1.5]);\n", "\n", "training_error = round(mean((y - f * w').^2),3)\n", "println(\"training error:$(training_error)\")\n", "\n", "test_f = [test_x ones(length(test_x))];\n", "\n", "test_error = round(mean((test_y - test_f * w').^2),3)\n", "println(\"test error: $(test_error)\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "training error: 0.0\n", "test error: 22058263.902000" ] } ], "source": [ "# fit with degree 10 polynomial\n", "\n", "f = hcat([x.^k / factorial(k) for k = 0:10]...);\n", "w = y' / f';\n", "\n", "xplot = collect(-1.5:0.01:1.5);\n", "fplot = hcat([xplot.^k / factorial(k) for k = 0:10]...)\n", "\n", "plot(xplot, fplot * w'; color=\"red\");\n", "scatter(x, y);\n", "scatter(test_x, test_y; color=\"orange\");\n", "\n", "xlim([-1.5, 1.5]);\n", "ylim([-1.5, 1.5]);\n", "\n", "training_error = round(mean((y - f * w').^2),3)\n", "println(\"training error:$(training_error)\")\n", "\n", "test_f = hcat([test_x.^k / factorial(k) for k = 0:10]...)\n", "\n", "test_error = round(mean((test_y - test_f * w').^2),3)\n", "@printf(\"test error: %f\", test_error)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "# Part 4\n", "\n", "Suppose that we use regularization such that for a polynomial of the form\n", "$$f_w(x) = \\sum_{k = 0}^{10} \\frac{w_k x^k}{k!}$$\n", "the loss function is\n", "$$h(w) = \\sum_{i=1}^N (f_w(x_i) - y_i)^2 + \\sigma^2 \\| w \\|^2.$$\n", "If $A$ is the matrix such that\n", "$$A_{i,j} = \\frac{x_i^j}{j!}$$\n", "then equivalently\n", "$$h(w) = \\left\\| \\left[\\begin{array}{c} A \\\\ \\sigma I \\end{array} \\right] w - \\left[\\begin{array}{c} y \\\\ 0 \\end{array} \\right] \\right\\|^2$$\n", "so we can still solve this easily with linear regression." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "training error: 0.021\n" ] }, { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "test error: 0.924000" ] } ], "source": [ "# fit with regularized degree 10 polynomial\n", "\n", "sigma = 0.01\n", "\n", "f = hcat([x.^k / factorial(k) for k = 0:10]...);\n", "f_reg = vcat(f, sigma * eye(11))\n", "y_reg = vcat(y, zeros(11))\n", "\n", "w = y_reg' / f_reg';\n", "\n", "xplot = collect(-1.5:0.01:1.5);\n", "fplot = hcat([xplot.^k / factorial(k) for k = 0:10]...)\n", "\n", "plot(xplot, fplot * w'; color=\"red\");\n", "scatter(x, y);\n", "scatter(test_x, test_y; color=\"orange\");\n", "\n", "xlim([-1.5, 1.5]);\n", "ylim([-1.5, 1.5]);\n", "\n", "training_error = round(mean((y - f * w').^2),3)\n", "println(\"training error: \$(training_error)\")\n", "\n", "test_f = hcat([test_x.^k / factorial(k) for k = 0:10]...)\n", "\n", "test_error = round(mean((test_y - test_f * w').^2),3)\n", "@printf(\"test error: %f\", test_error)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "regularized_fit_error (generic function with 1 method)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function regularized_fit_error(sigma) \n", " test_x = randn(10000); test_y = sqrt(0.9) * test_x + sqrt(0.1) * randn(10000);\n", " \n", " f = hcat([x.^k / factorial(k) for k = 0:10]...);\n", " f_reg = vcat(f, sigma * eye(11))\n", " y_reg = vcat(y, zeros(11))\n", "\n", " w = y_reg' / f_reg';\n", "\n", " test_f = hcat([test_x.^k / factorial(k) for k = 0:10]...)\n", " \n", " training_error = round(mean((y - f * w').^2),3)\n", " test_error = round(mean((test_y - test_f * w').^2),3)\n", " \n", " return (training_error, test_error)\n", "end" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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DJqKjo5k4cSL3338/LpeL/v37k5OTw8qVK4mJiWHs2LE1+jkiIyO58847efDBB0lISKBZs2Y888wzFBQUcMstt3jsz8sfKBT5g8gGkLVF0/JFRHzIxIkTGTt2LKmpqRw7doydO3fSokULVq5cycMPP8zQoUMpKiqiefPmDB8+HLvdTkxMDMuXL2fWrFnk5ubSvHlznn32WfcA59tuu41ly5bRo0cP8vLyWLp0KQMHDjzps6dOnUpSUhLTp09nx44dxMXF0a1bNx599NFa/SxPPfUULpeL66+/nqNHj9KjRw++/PLLgJxhVhWbYVRzUYZ6KDc3l9jYWHJycoiJibGukPnXweb/wsiZ0Os26+oQEfGCwsJCdu7cWWHdHJHqONXvTm2/vzWmyB9oU1gRERGvUyjyB1rVWkRExOsUivyBVrUWERHxOoUif1DWUqQp+SIiIl6jUOQP3N1naikSkcCleT9SU57+nVEo8gfqPhORAFa2Dk9BQYHFlYi/Kfud+eNaTrWldYr8gbv77BAYhrkEvohIgHA4HMTFxXHw4EEAIiIisOn/c1IFwzAoKCjg4MGDxMXF4XA4PHJdhaJKpKWlkZaWdtql1utMWShylUBRLoTFWluPiIiHle0KXxaMRKojLi7O/bvjCVq8sQo+s3gjwN8aQUk+3L0OEltbW4uIiJc4nU5KSkqsLkP8QHBw8ClbiGr7/a2WIn8RmQhH8s0uNIUiEQlQDofDY10hIjWlgdb+Qqtai4iIeJVCkb/QqtYiIiJepVDkLzQtX0RExKsUivyFVrUWERHxKoUif6FVrUVERLxKochfqPtMRETEqxSK/IW6z0RERLxKochfaEq+iIiIVykU+QuNKRIREfEqhSJ/EXk8FBUfhdIia2sREREJQApF/iI0FmzHl75XF5qIiIjHKRT5C7tdq1qLiIh4kUKRP9G0fBEREa9RKPIn7mn5CkUiIiKeplDkT9R9JiIi4jUKRf5ELUUiIiJeo1DkT9xjitRSJCIi4mkKRf5Eq1qLiIh4jUKRP4lIMO+1qrWIiIjHKRT5E03JFxER8RqFIn/iHmitMUUiIiKeplDkT9xjirLB5bK2FhERkQBTL0LR6NGjiY+P5/LLL7e6lDNT1lJkOKHwiLW1iIiIBJh6EYruvfde3nrrLavLOHNBIRAaYx5rXJGIiIhH1YtQNHDgQKKjo60uwzO0gKOIiIhX+HwoWr58OZdccgmNGjXCZrPxn//856TXpKWl0aJFC8LCwujduzc//PCDBZXWEW31ISIi4hU+H4ry8/Pp3LkzaWlplT4/f/58JkyYwF/+8hfWrVtH586dGTZsGAcPHqzxZxUVFZGbm1vh5nO0qrWIiIhX+HwoGjFiBNOmTWP06NGVPv/cc89x2223cdNNN5GamsqcOXOIiIhg7ty5Nf6s6dOnExsb6741bdr0TMv3PHWfiYiIeIXPh6KqFBcXs3btWoYMGeI+Z7fbGTJkCN9++22Nrzdp0iRycnLct71793qyXM9wd58pFImIiHhSkNUFnImsrCycTicpKSkVzqekpPDrr7+6Hw8ZMoQNGzaQn59PkyZN+Pe//02fPn1Oul5oaCihoaFer/uMaFVrERERr/DrUFRdixcvtroEz9Gq1iIiIl7h191nDRo0wOFwkJGRUeF8RkYGDRs2tKgqLytb1Vqzz0RERDzKr0NRSEgI3bt3Z8mSJe5zLpeLJUuWVNo9Vl1paWmkpqbSs2dPT5TpWe6Womxr6xAREQkwPt99lpeXx7Zt29yPd+7cyfr160lISKBZs2ZMmDCBsWPH0qNHD3r16sWsWbPIz8/npptuqvVnjhs3jnHjxpGbm0tsbKwnfgzPiVT3mYiIiDf4fChas2YNgwYNcj+eMGECAGPHjmXevHlcddVVZGZmMnnyZNLT0+nSpQtffPHFSYOvA0ZZ91lJARQXQEjE6d+TtQ1Kj0HDTt6tTURExI/ZDMMwrC7CV5W1FOXk5BATE2N1OSbDgKlJ4CqB+zZC3GnWUnKWwHPtoTgf7vu5fPaaiIhIgKrt97dfjymql2y2mq1qvf9HyM80W5Z+X+Pd2kRERPyYQlElfHqgNdRsVevdK8uP9//onXpEREQCgEJRJcaNG8emTZtYvXq11aVUriarWu86MRSt8049IiIiAUChyB9Vd1VrZyns+a788f4fzTFJIiIichKFIn9U3VWt03+C4qMQGgP2IHNsUe4+79cnIiLihxSK/FF1V7Xevcq8b94Xktubx/vUhSYiIlIZhSJ/FJFg3p+u+6xskHXzftCoq3mswdYiIiKVUiiqhM/PPqvOmCKXq7ylqIVCkYiIyOkoFFXCb2afVRWKDv4ChUcgJAoadoZG3czzGmwtIiJSKYUif1SdMUVlU/Gb9gZHECSngiPEDEqHd3q/RhERET+jUOSPyrrPjh0Gl7Py15SNJ2rRz7wPCoGUjuaxutBEREROolDkj8Ljjx8YZjD6I8M4YeZZ//LzjY93oWkGmoiIyEkUivyRIxjC4szjyrrQMreYaxgFhZcPsIYTBluv936NIiIifkahqBI+P/sMqh5svXuFed+0p9ltVqYsFB1Yb85OExERETeFokr4/OwzOGFafiUtRZV1nQE0OBuCI6A4Dw795t36RERE/IxCkb861Qw0wyifeVY2yLqMIwganmsea7C1iIhIBQpF/sq9qnV2xfPZOyAv3Zx+37jHye/TIo4iIiKVUijyV6fqPtt1fDxR4x4QHHby+zQDTUREpFIKRf7qVAOt/7g+0R+VtRSl/wTOUu/UJiIi4ocUivzVqcYUuQdZnyIUJbSG0BgoLYTMX71Xn4iIiJ9RKPJXlXWfHd4NOXvBHgRNe1X+PrsdzupsHu9XF5qIiEgZhaJK+Mc6RZUMtC7rOmvUFUIiT/1eDbYWERE5iUJRJfxinaITu8/Kdr0vm4p/qq6zMmWDrRWKRERE3BSK/FXZQGtnERTnm8fuQdb9K39PGfdg641QWuSd+kRERPyMQpG/ComEoONT7guyIHc/HN4JNjs07V31e+OaQ3gCuEog4xfv1yoiIuIHFIr8lc1W3lqUf6i86+yszhAWc/r3alyRiIhIBQpF/uzEtYrKNoE93XiiMu5QpBloIiIioFDk306cll/dQdZl3KFovefrEhER8UMKRf6srKXo4Obju97boHmf6r23bAbawc1QXOCV8kRERPyJQpE/K5uWv/m/5n1KRwiPr957o8+CqBQwnJD+s3fqExER8SMKRf6srKXo8E7zvnnf6r9Xg61FREQqUCiqhF+saA0QmVjx8ak2gT2VRlrEUUREpIxCUSX8YkVrKO8+K1PdQdZlNANNRETETaHIn0Wc0FKUdE75bLTqKgtFWb9BYa7n6hIREfFDCkX+7MQQVNNWIoCoJIhtChiQ/pPHyhIREfFHCkX+7MSWopoMsj5Roy7m/T51oYmISP2mUOTPwuMhJBrsQaffBPZUNANNREQEgCCrC5AzYHfAtf+G0kKIbli7a2gGmoiICKBQ5P+qu4L1qZR1nx3eCQXZEJFw5jWJiIj4IXWf1Xfh8RDf0jw+oH3QRESk/lIokvJ90NSFJiIi9ZhCkZQPttYMNBERqccUiuSEGWjqPhMRkfpLoagSfrP3maec1RmwQe7v8M7lsOc7qysSERGpczbDMAyri/BVubm5xMbGkpOTQ0xMjNXleNeyp+Hrp8BwmY+b94PzH4DWF4LNZm1tIiIiNVDb72+1FIlp4MMwfg10Gwv2YNi9Et4ZA68Ogs3/BZfL6gpFRES8SqFIyiW2hlEvwL0b4Ly7ICjcnJE2/zp4uQ9smA/O0rqp5esZMP96KC2um88TEZF6T6FIThbbGIZPh/s3wvkTITQWMn+FD2+Hl7rDT//2bsvR3tWwdBps/hj2rPLe54iIiJxAoUhOLbIBDH4c7v8ZBk+GiAZweBcsuBVeuQB+WwSeHpJmGLDw/5U/PvirZ68vIiJyCgpFcnphseag6/t+ggsfh9AYyPgZ3r0c5l0Me3/w3Gf9+gnsPWH2W+Zmz11bRESkCgpFUn0hkXDBRHPMUd+7wREKu1fA6xfB/11z5q06zhJY9BfzOKm9ea+WIhERqSMKRVJzEQkwdBrcsw66Xgc2O2z51ByM/Z+74Mje2l13zRuQvR0ik+CSWea5zM2e76ITERGphEKR1F5sE7g0De76Ds652FzjaP278Pfzar46dmGOuU4SwMBJ5irbNod5/mi652sXERH5A4UiOXNJZ8Of34Vbl0CjblCcB//3Z8jdX/1rrHgeCg5Bg3bmWklBoZDQynxO44pERKQOKBSJ5zTpATf8B5LOgaMH4J9XQVHe6d93ZC9897J5fNEUcASZx8nnmPcaVyQiInVAoUg8KywWrplvTt9P/wkW3AYuZ9Xv+WoalBZC8/7Qbnj5efdg603eq1dEROQ4hSLxvPgW8Od/mrPTtnwGiyaf+rX718NP883joVMr7rNW1lKUqZYiERHxPoUi8Y5mveGyv5vH375kziz7I8OARY8DBnS6Ahp3q/h8WUtR5hbNQBMREa9TKBLv6XQ5DHzUPP70Adi+tOLzvy2CncvBEWIuCvlHiW3AHgRFuZC7z/v1iohIvaZQJN414CHodCUYTvjXWLPVB8yNZRcdD0K9/xfim5/83qAQSGhtHmuwtYiIeJlCkXiXzQajXoSm50FRDrx7BeRnwfp3zLFC4fHmFiKn4h5XpGn5IiLiXQpFlUhLSyM1NZWePXtaXUpgCA4z1zGKbwFHdsN718DSJ83nLngIwuNO/V5t9yEiInVEoagS48aNY9OmTaxevdrqUgJHZAO45l8QGgt7v4e8DIhvCT1vrfp9aikSEZE6olAkdSfpbLjyTXP7DoAhfzHHDVX5Hs1AExGRuhFkdQFSz7QeBNe9Dzm/Q+plp399YmuwB5tbh+Tshbhm3q9RRETqJYUiqXutL6z+ax3B0KCtuar1wV8VikRExGvUfSa+L0njikRExPsUisT3JWsGmoiIeJ9Ckfg+tRSJiEgdUCgS35d8wgw0l8vaWkREJGApFInvi29p7o9WUmAu/igiIuIFCkXi+xxB0KCdeZypcUUiIuIdCkXiH8rGFR3UuCIREfEOhSLxD+7tPtRSJCIi3qFQJP7BvTGsWopERMQ7FIrEP5TNQMvaCi6ntbWIiEhAUigS/xDfAoLCoLQQDu+yuhoREQlANQ5FTqeT5cuXc+TIEW/UI1I5u0Mz0ERExKtqHIocDgdDhw7l8OHD3qhH5NSSNa5IRES8p1bdZx07dmTHjh2erkWkakmagSYiIt5Tq1A0bdo0Jk6cyCeffMKBAwfIzc2tcBPxCm0MKyIiXhRUmzeNHDkSgFGjRmGz2dznDcPAZrPhdGp2kHhBWUtR2Qw0u8PaekREJKDUKhQtXbrU03WInF5ccwiOMPdAy94JDdpYXZGIiASQWoWiAQMGeLoOkdOz280ZaAfWw8FNCkUiIuJRtQpFAEeOHOH1119n82ZzJlCHDh24+eabiY2N9VhxIidJbm+GosxfgVFWVyMiIgGkVgOt16xZQ+vWrXn++efJzs4mOzub5557jtatW7Nu3TpP1yhSThvDioiIl9QqFN1///2MGjWKXbt2sWDBAhYsWMDOnTu5+OKLue+++zxd4xn55JNPOPvss2nbti2vvfaa1eXImSqbgaZp+SIi4mE2wzCMmr4pPDycH3/8kXPOOafC+U2bNtGjRw8KCgo8VuCZKC0tJTU1laVLlxIbG0v37t1ZtWoViYmJ1Xp/bm4usbGx5OTkEBMT4+VqpVoO74bZ54I9GB47AI5gqysSEREfU9vv71q1FMXExLBnz56Tzu/du5fo6OjaXNIrfvjhBzp06EDjxo2JiopixIgRLFy40Oqy5EzENoXgSHCVQLYWEBUREc+p1UDrq666iltuuYWZM2fSt29fAFauXMmDDz7I1Vdf7bHili9fzowZM1i7di0HDhzgww8/5LLLLqvwmrS0NGbMmEF6ejqdO3fmxRdfpFevXgDs37+fxo0bu18EBe1rAAAgAElEQVTbuHFj9u3b57H6xAJ2OySdDfvXmeOKks62uiIREd9hGFCcB4U5p76VHANnMThL/nB/wrHhApsNsIHNfsLxCfcRiZDQEhJambf4lhAaVbM687PM+4advPiHUn21CkUzZ87EZrNxww03UFpaCkBwcDB33nknTz31lMeKy8/Pp3Pnztx8882MGTPmpOfnz5/PhAkTmDNnDr1792bWrFkMGzaMLVu2kJycXOPPKyoqoqioyP1Yq3P7qORUMxRpXJGI1FcF2eb/Aw9uLr/P2gr5mWagsUpUSnlASmhl/kM2/xAUZJkBKD8TCg6Zx87j37dhcfDIbutqPkGtQlFISAizZ89m+vTpbN++HYDWrVsTERHh0eJGjBjBiBEjTvn8c889x2233cZNN90EwJw5c/j000+ZO3cujzzyCI0aNarQMrRv3z53K1Jlpk+fzl//+lfP/QDiHcmagSYiAczlgsIj5SGi7HZoW3kIysuo+hr2YAiLreQWYw5BcASDIwSCQsuPHSHmsT3YbB3CMFt0MMyg5T42wHBCXiZG9g5zKEP2DmzHss268jJgz7fV+1GDwnEFRxHkI7sU1DgUlZSUEB4ezvr16+nYsSOdOlnT5FVcXMzatWuZNGmS+5zdbmfIkCF8+635l9GrVy82btzIvn37iI2N5fPPP+fxxx8/5TUnTZrEhAkT3I9zc3Np2rSp934IqZ0kzUATET9VnA9H9kLO75Cz9/jtd8g7eEJLSha4Sk97qZKoxhTEteVodBsOR7bkYFgrDjsakEsk+c5gCp0uCktcFJY4OVbipKjERWGBk2KnixKni1KnQYnLoLTs2OmixGUeO10GLqPsHlxlj40TH5+FyzjXXU8M+TSzZdDClkFzWwYtbOkAHCKGbCOabGI4ZJjHh44fHyOM8CIHm30gEEEtQlFwcDDNmjWzfH+zrKwsnE4nKSkpFc6npKTw66/ml2VQUBDPPvssgwYNwuVy8dBDD1U58yw0NJTQ0FCv1i0eUNZSdGgblBZDUIi19YiIlCkugCO74fCu8tuRveUB6Njhal+qwB7FEVss2cSS6Ypmp7MBm52N2epqwjajMfmF4ZB14jsMIPP4re7lEslGoxUbjVaVPm+zgQ2w2WzYbWDDRogNQoNrNefLK2rVffbYY4/x6KOP8vbbb5OQkODpmjxq1KhRjBqllY8DSkxjCI2BolzI3l6+dpGISF0pzIHfFpnjeE4MQKfr1gIK7JFkkMRuZwJ7nInsNxLJMOKPt57EkmXEcJhoijn1kiPBDhtxoUFEHb9FHr9FBDsIC7YTFuw44Xb8cZB5HxJkJ8hhJ9huI9hhJ8hx/N5uM887bDjsNuy28nu7jfJjuw2HzYbdjvkaW9n5E15z/D12m80MQydsHu/LahWKXnrpJbZt20ajRo1o3rw5kZGRFZ6vi1WtGzRogMPhICOj4i9gRkYGDRs2PKNrp6WlkZaWZnlrmJyCzWbOOvt9tdm/rlAkInWhpBB++xJ+fh+2flk+UPgPihxRpDvOYntpA7YWJ/K7kcQ+owH7jUT2Gw04SsXxtwmRISRHh5IQGUKLyBC6RYQQHxlCQkSweR8ZQnxECDFhwUSFBREZ6iA0yDe6mwJNrULRH6fFWyEkJITu3buzZMkSdz0ul4slS5Ywfvz4M7r2uHHjGDdunHvxJ/FBSeeYoUjjikTEm5ylsGu5GYQ2/9dsoT4uL7oVv4V3ZktRIuuOxrDpWAJ7jGRyqTgtPSUmlMZx4ZwdH8GF8eE0jgunSbx5axQXTkRIrbchFQ+r8d+E0+lk0KBBnHvuucTFxXmjJre8vDy2bdvmfrxz507Wr19PQkICzZo1Y8KECYwdO5YePXrQq1cvZs2aRX5+vns2mgSwstahg5usrUNEAo9hwL518PO/YOMCyD/ofiovtCFLgs7n1SPd2JjZDHOUjMlht9E2JYqLGsXSoVEMHRrFkNoohugwrbzvL2ocihwOB0OHDmXz5s1eD0Vr1qxh0KBB7sdlM8PGjh3LvHnzuOqqq8jMzGTy5Mmkp6fTpUsXvvjii5MGX0sAcm8Mq5YiEfGQkkL4ZQF8PwcObHCfLnDEstDWh3fze7GmsB3G8c0g2iRH0btlAh0axdKxcQztUqIJC1a3lj+rVZtdx44d2bFjBy1btvR0PRUMHDiQ023NNn78+DPuLhM/VNZSlL0DSovMtTZERGojdz+sfh3WvmEuLAgU20JY6OrJ+yV9WeHqRClBhDjs9G+VwOBzkrnwnBSaJXp2bT6xXq1C0bRp05g4cSJTp06le/fuJw201uap4nXRZ5kLkRXmmLM/fGSJeBHxE4YBe7+H71+BzR+71wU6aE9ibtFg3nMO4gjRJEWH8j9nJ3Nh+2T6t2lAZKjG/wSyWv3tjhw5EjCnu584zc4wDGw2m9/P2tLsMz9gs0FyB9izCjJ+USgSkepxucyxQt/9vUIX2TpbKv8oGsoiV3eCg4O5vGcTrujelE6NY7Hb/WM6uZy5WoWipUuXeroOn6LZZ36iYUczFKX/DJ3/bHU1IuLr8g7Cgtthh/kdVmIL4SNnP14vGcpmoznJ0aFM6NuCa3o1Iz5Si8LWR7UKRQMGDOCbb77hlVdeYfv27bz//vs0btyYt99+2+vjjETcylqHMjZaW4eI+L7tX8GCOyD/IEW2UF4ouZR3SwdzhGhSz4rhufNbcvG5jQgJ8p3VlaXu1epv/4MPPmDYsGGEh4fz448/uneWz8nJ4cknn/RogSKnlNLRvE//+fhGhSIif+AsgcVPYLw9BvIPstVoyp8Kp5JWehndz2nNP2/rzaf39GdMtyYKRFK7UDRt2jTmzJnDq6++SnBw+foL/fr1q5PVrEUAcwaazW7OFjmabnU1IuJrjuyBN0bCiuexYfBO6WAuKZpKcqvOLJ4wgNdv7Enf1g38ZgsK8b5adZ9t2bKFCy644KTzsbGxHDly5IyLspoGWvuJ4HBo0M5c1TpjI8ScZXVFIuIrNn2M8fF4bIU55BoRPFxyG8uD+jJ5dHuu6dVMQUgqVauWooYNG1ZYabrMihUraNWq8t1x/cm4cePYtGkTq1evtroUOR13F9pP1tYhIr6hpBA+fQD+dT22whzWudowsng6ea3/xMIJA7i2d3MFIjmlWrUU3Xbbbdx7773MnTsXm83G/v37+fbbb5k4cSKPP/64p2sUObWGHWHj+5CuwdYi9V7OPox3r8B28BcAXi69hH8EXc2kMedyRY8mCkNyWrUKRY888ggul4vBgwdTUFDABRdcQGhoKBMnTuTuu+/2dI0ip1Y2Ay39Z2vrEBFr5R2kZN4lBB/eTqYRw4SSuwhuN4TPR3eiYWyY1dWJn7AZp9tHowrFxcVs27aNvLw8UlNTiYqKOv2b/EjZOkU5OTlapdtXHc2AZ9uZA64n7YMQLbsvUu8UZFP0+khCD23md6MBt9imcMeoAYzu2litQ/VUbb+/z2i98pCQEFJTU8/kEiJnJjoFIpMgPxMOboYm3a2uSETqUmEuBW9cRsShzWQYcUyKmsYbt11Go7hwqysTP6RFGcT/ubvQNNhapF4pzufoG2OIyNxAthHFE3FPMuvOMQpEUmsKRZVIS0sjNTWVnj17Wl2KVEfZDDStbC1Sf5QWkT33CqIzVpNrRPB0g+k8feeVJEaFWl2Z+DGFokpoSr6fcbcUKRSJ1AvOEtJfv5qE9JXkG6G80PBJnrjjWmLCgk//XpEqnNGYIhGfcOIeaC4X2JX1RQKWy8me16+n2YElFBnBvN70SR66cay26BCP0G+R+L/EtuAIheI8OLLL6mpExFtcLra8ehPN9n9OseHg/1r+jXE336JAJB6j3yTxf44gSD7HPFYXmkhAMlwu1r36v5x94COcho1P2k5l7Njbcdg15V48R6FIAoMWcRQJaKvfeZxuB+YDsPScJxh97V1ag0g8TmOKJDCknDCuSEQCyq9L36XXjpcAWNX2IYZcfZ/FFUmgUkuRBAa1FIkEpMwt39HiazMEfZMwhj7XPGpxRRLIFIoqoXWK/FBKB/M+Zy8cO2xtLSLiEUXZe7HPv4YwilkT1I2ed8xRl5l4lUJRJbROkR8Kj4PYZuZxxi/W1iIiZ644n6xXx5DoOsR2mtDwlv8jLFQLM4p3KRRJ4FAXmkhgcLnYO/cGGh/byiEjmqxRb9PkrIZWVyX1gEKRBI6Gx7f70LR8Eb+W8dH/o2n6YoqMIJZ2eZ7e3bpZXZLUEwpFEjjce6CppUjEXx39/i1SNqQB8HbSRMZcernFFUl9olAkgaOs++zgZnCWWFuLiNRY6c6VhH9+PwDvBF/OlbdOxK7FGaUOKRRJ4IhrDiHR4CyGrN+srkZEaiJ7J8XvXkMQpXxp9KbXLc9pg1epcwpFEjjs9vKp+RpsLeI/CnM5+sblRJQe4SdXS5yXvky7hrFWVyX1kEKRBJayLjSNKxLxG0c/epDoo9s4YCSwtOtsRnZrbXVJUk8pFElg0Qw0Eb9i/LaY6M3v4TJsvNzgUcaNOt/qkqQeUyiqhFa09mMpJ6xVZBjW1iIiVSvM5diC8QC8Ywzj1muuJcihryWxjn77KqEVrf1Ycnuw2aEgC/IyrK5GRKpQ/OXjRBw7wG5XMnn9H6NZYoTVJUk9p1AkgSUkAhLbmMfqQhPxXTu+JuTHeQA8H3E3Nw/qYG09IigUSSAqW8Qx/Sdr6xCRyhXlUfzh8W6z0sGMHnM1YcEOi4sSUSiSQOSegaaWIhFfZCyZQsjRPfxuNGDt2fczoF2S1SWJAApFEojcG8MqFIn4nN3fwg//AOAJ43YeGtXD4oJEyikUSeAp6z479BuUHLO2FhEpV1yA8z93YcPgvdKB9Bx8OWfFhltdlYibQpEEnuiGENEADBcc3GR1NSJSZunfcBzeQboRz3vxt3Nz/5ZWVyRSgUKRBB6b7YRFHLWytYhP2Lsa47u/AzCp5FYeGX0ewVqTSHyMfiMlMKVoZWsRn1FSiPHROGyGiw+c/YnrfDHntUq0uiqRkygUSWBqeK55748z0LJ3wk//ApfL6kpEPOPrp7FlbSHTiOU5x81MGnmO1RWJVCrI6gJEvOLEPdBcLrD7Sf53lsA7/wPZ2yF3P/S/z+qKRM7MgQ0YK2djA/5fyc3cfnF3kqPDrK5KpFJ+8k1Rt7T3WQBo0A4cIVB8FI7strqa6lv3lhmIAL5+Go7ssbYekTO1+AlshpNPnL35veFgrjuvudUViZySQlEltPdZAHAEQ9LxJnp/6UIryoNlT5nHYbFQUgCfP2xtTSJnYuc3sP0rig0HT5dezbTLOuKw26yuSuSUFIokcLkXcfSTGWjf/R3yD0J8S7jxU7AHwZbP4NdPra5MpOYMA2PJFADec15In+7d6Nos3uKiRKqmUCSBy59Wts7PgpWzzePBj5u1973bfPz5w1Ccb11tIrWx9Utsv//AMSOEV4wx3DekndUViZyWQpEErhQ/Wqto+QwozoOzukDqaPPcBQ9BbDPI2WuOLxLxFy4XxldmK9GbzmEM6XUujeK0crX4PoUiCVxlM9By9sCxI9bWUpXsnbD6dfP4or+Wz5QLiYCRM8zjb9MgQ6tzi5/4ZQG2jF/INcKZyyjuGtTG6opEqkWhSAJXeDzENTOPv59jbS1VWfo3cJVA6wuh1cCKz509HM65GFyl8OkErV0kvs9ZgrH0bwC8WvonLu7dkZQYTcEX/6BQJIFt4CTzftlT8Nsia2upzIEN8PO/zeMhT1T+muFPQXAk7PkWNvyzrioTqZ31/8SWvYMsI4Z/2v/EnQNbW12RSLUpFElg63IN9LgZMOCDW8yuKl+y+AnzvtMVcFbnyl8T1xQGPmIeL3wcCrLrpDSRGispxDg+/u3vpZdyeZ/2JEWHWlyUSPUpFEngG/4UNO4BhTkw/3ooLrC6ItP2pbD9K7AHw6DHqn7teXdCcgc4lg2LJtdNfSI1teZ1bLn72G8ksMAxlNsvaGV1RSI1olAkgS8oFK58CyKTIONn+OR+MAxra3K5YPFfzOOet0BCy6pf7wiGi58zj398G/Z85936RGqq6CjGN88CMLv0f7i2XzsSo9RKJP5FoUjqh9jGcPkbYHPAT+/BD69aW88vC8zxRCHRcMGD1XtPs/Og6/Xm8Sf3m/ukifiK717GVnCIHa6GfBk0iNvOVyuR+B+FIqk/Wp4PF5lrp/DlpOq3tuxbB2+OgqeawevD4LOHYP0/zSnyztKa11FaDF9NNY/73QORDar/3oumQHgCHNxkroAt4gsKsjFWvQjA86WXc0P/tsRFhFhclEjNBVldgEid6jMO9q01W2r+NRbuWA7RKZW/9vAuWDIVNr5ffm7vd+atTFC4ufp0oy7mwotnnQuJbSG4iinIa+eZ145MhvPuqln9EQkwdCp8NM6cURccYQ7SDo+r2XVEPGnlLGxFuWxyNWd5SH+m9T9Nd7CIj7IZhtWDK3xXbm4usbGx5OTkEBMTY3U54ilFefDaEMjcDM36wNj/mmN2yhRkwzfPwg//AGcxYIPOf4Yet0D2DjiwHvavh/SfzFWo/8hmh7jm5oa0Se2gwdmQdDY0aAc2G8zuAgVZ8KdnoeetNa/f5YK3RsGub8zHQeHQ4TLoNtbsYrNpw02pQ7kHMF7ogq20kJuKH6Tb4Ku4e3Bbq6uSeq62398KRVVQKApgWdvg1UFQlAu9/xdGPA0lhbD6VXPLjcIc83WtBppdVpVNl3e54NC28pB0YD1kbCx/b2VCY6EoBxJaw7jvK4axmijOh3Vvw7o3za60Mg3aQbcboPPVNeuWE6mtTybAmtdZ42rHrY5pfPPwhUSH1fL3WsRDFIq8QKEowP36Kbx3jXl83l3w6ydwZI/5OLkDDJ0CrQfXrOXFMCDvIGRtgcwtkLW1/P7ogfLXXfk2pI4685/BMOD3NWY42rgASo5vHGsPhnP+ZM5sa3nBmX+OSGWyd2K81AObq5Srih5n4LDRWqxRfIJCkRcoFNUDS6bCNzPLH0c3ggsfM1ta7A7PflZhDmT9BoYLmvby7LUBCnNh4wdmQNr/Y/n54U+Z6xyJeNp718Kvn7Dc2Yn7Q/7C8ocGERmqoapivdp+f+u3txJpaWmkpaXhdDqtLkW8bdCjcOg32PE19L3bbDEKifDOZ4XFQpMe3rk2QFgM9LjJvB34Cb5/Bda/A18+ColtoO1F3vtsqX9+WwS/fkIpdqaVXsf/XtRagUj8nlqKqqCWonqi7D+BQBugbBjw8d3mYo+hMXDrYnPAt8iZKi2Cv58H2Tt4tXQk/wi/heUPDiI8xMOtqyK1VNvvb61TJGKzBV4gAvNn+tNz0LyfOaD8n1dq3zTxjFUvQPYODtnimV06hjsuaKVAJAFBoUgkkAWFmIO645qbayPNv95cPFKkto7sgeXmdh5/LboGe1gMf+7VzOKiRDxDoUgk0EUmwjXzzS1Fdq+AzyZav/eb+K8vJkHpMTYGd+JjV1+u79OcKI0lkgChUCRSHyS3h8vnmgtLrnsTvp9T/fc6S+DQ9qrXX5L6Ydti+PUTDJuDCXnXERLkYGzfFlZXJeIxivci9UW7oXDRVFj4WPVmpOXuh7VvmtuS5KWb50JjIKYxxDYxN9mNaVJ+nNDKPJbAVFpk7vsHLIq+jK3HmnJ1tyYkR1expY2In1EoEqlP+owztzf58R14/+aTZ6QZhrl9yOrXYPMnYBxflsIRYm55UpQLmbnmNSrTdihc8BA07en9n0Xq1qoXIXs7pRHJTDg4ApsNbjtfe5xJYFEoEqlPbDb40/OQvRN2rzRnpN221FyocsN8MwxlbSl/fbO+5qrY7UeZoSh3H+T8Xn6fsw9y9pqPs3fAbwvNW6tBMOAhaN7Xup9VPOfIXlhuLnI6P/528rIjGJ7akFZJURYXJuJZWqeoClqnSAJW/iFz77cju8192I6ml28REhwJna8yN6tN6VD9ax7aDiuegw3vgavUPNfifLjgQXOrkUBc9qC+mH89bP6Yosbn0XHXPZQ44cO7+tK1WbzVlYlUSusUiUj1nTgjLXu7GYganA0jZ8IDv8LFz9csEAEktoZL0+DuddD9JnP/tV3fwFujYO5wc5Cu/g3mf7Ytgc0fg83BW/HjKXFC75YJCkQSkNRSVAW1FEnA2/OduV9a+1HQor9nW3Ny9sHK2eZAbWeRea5xdxg8GVoN9NzniPeUFsHLfeHQNop63EH31YPJKyrljRt7MuicZKurEzkltRSJSM01Ow9GzoCW53u+eyu2MYx8Bu77CfqMh6Bw2LcW3roU3vkfSN/o2c8Tz/s2DQ5tg8hk3gm7hryiUs5OiWbg2UlWVybiFQpFIuJd0Q1h2N/gvp+h951mt9q2xTCnP3x4pzlgW3zP4V2wfAYAJUOmMOf7LABuv6AVNo0PkwClUCQidSMqCUY8BeN/gA5jAAM2/BNe6AaLJsOxI1ZXKGWyfoM3/gQlBdCsLwtK+pJ5tIizYsO4pHMjq6sT8RqFIhGpWwmt4Io34NavoHl/c7zRytnwQhezu6a0yOoK67f9682B8bm/Q2JbXKP/wSvf7ATglv4tCQnS14YELq1TJCLWaNIdbvwEtn4Ji/8Cmb+aK22veslcUDIiAcLjITzh5OPIJIhrpmn+nrZrJfzfn81FOs/qDNctYNGuUnZk5hMdFqSNXyXgKRSJiHVsNjh7OLQZYnalffU3OLrfvJ1OXDM4eyS0Gw7N+0FQiPfrDWRbv4R/3QClheaf59XvYYRGM+frVQBcf542fpXApyn5VdCUfJE6VlwAe1ZBfhYcOwwF2XAs+4Tjw+bjo+nmCttlQmOgzWAzJLUZYrYmSfX9/D58eIe56Ga74XDFPAgOZ/WubK6Y8y0hQXZWPDxI+5yJ36jt97div4j4jpAIM9ScTnE+7FgGWz4zWzjyM+GXD82bzQHN+pgtUG2HQoN26maryg+vwmcPAgace5W5AKcjGIBXvt4OwP9o41epJ9RSVAW1FIn4AZcL9q8zA9KWL+DgLxWfj21qtiK1GQItB0CY/lsGzNXFl8+EpdPMx71uh+FPg90cSP1bxlEuen45NhssmTBA+5yJX1FLkYjUT3Y7NOlh3gZPhsO7YesX5m3XSnPD2rXzzJs9CJr2NgNSmyHQsFP9bEUqLYIlU+Dbl8zHAx6GgZMq/FnM+XoHAENTUxSIpN5QS1EV1FIk4ueKC2D3SnOxyG2LzdWZTxSVYm5a2/ICc1Xv+JaBG5KOZsBvC82wuGMZFOeZ54dNhz53VXjp74cLGDhjGaUug4/G9aNz07i6r1fkDKilSETkj0IioO1F5g0ge+fxgLQEdi6HvAzY+L55A4hpUh6QWpwPcU2tq/1MGQYc2GCOudr6hdnFeKKoFBg6Dc698qS3vrp8B6Uug35tEhWIpF6pFy1Fo0ePZtmyZQwePJj333+/2u9TS5FIACstgr0/wK5vzID0+xpwlVR8TXwLc3p6ZAMIjjRDVkhk+XHw8cchkScf2x11+/MU5sLBzZCxEfb/aIa/owcqvqZRV3N2Wbth0LCze/zQibLyiuj31FcUlbr456296dumQR39ACKeo5aiKtx7773cfPPNvPnmm1aXIiK+IijUbBFqeT4MetSc0bbnu+Mh6RszWBzeZd5qdf2wkwOU7TSrQdts5gKVUUkQmQxRyeZClVHJ5Y9DoyF7hxl+MjZBxi/m4PIje06+XnAktB5khqC2Q8196E5j7oqdFJW66Nw0jj6tE2v3s4v4qXoRigYOHMiyZcusLkNEfFlI5PFZaoPNx4W5sOdb2LcOio5CSb45RqmkwByP4z7ON29lxxxvfC8tNG8cqrufIboRpKRCSgdzpl2L/mb4q6bcwhLe/nY3AHcNbK2NX6XesTwULV++nBkzZrB27VoOHDjAhx9+yGWXXVbhNWlpacyYMYP09HQ6d+7Miy++SK9evSyqWETqhbAYs4Wl3bDqv8cwzCBUISgdD1Elx3AHplNxOaHgEOQfhLxMc8xTfibkHTTPFeaYrwuOgOTU4wGooxmCklPPeNHKd77bzdGiUtomR3FR+5QzupaIP7I8FOXn59O5c2duvvlmxowZc9Lz8+fPZ8KECcyZM4fevXsza9Yshg0bxpYtW0hOTgagS5culJaWnvTehQsX0qiRdnQWkTpis0FwuHmL9MJYnNIiMxhFNKh0PNCZKCxxMneFufHrnQNbY7erlUjqH8tD0YgRIxgxYsQpn3/uuee47bbbuOmmmwCYM2cOn376KXPnzuWRRx4BYP369R6ppaioiKKi8h26c3NzPXJdERGPCAo1xxV5wb/W7CUrr5gm8eFc0ln/mJT6ybP/1PCw4uJi1q5dy5Ah5cv+2+12hgwZwrfffuvxz5s+fTqxsbHuW9OmfjwdV0SkmkqcLl45vljjHRe0Itjh018NIl7j07/5WVlZOJ1OUlIq9m2npKSQnp5e7esMGTKEK664gs8++4wmTZqcMlBNmjSJnJwc923v3r1nVL+IiD/4eP1+9h05RoOoEK7ooX8MSv1lefdZXVi8eHG1XhcaGkpoaPVnaoiI+DuXy+Dl4xu/3tK/FWHBdby+kogP8emWogYNGuBwOMjIyKhwPiMjg4YNT7/ehoiIVG3hpgy2HcwjOiyI685rZnU5Ipby6VAUEhJC9+7dWbJkifucy+ViyZIl9OnTx2ufm5aWRmpqKj179vTaZ4iIWM0wDF5eZu4HN7ZPC6LDgi2uSMRalnef5eXlsW1b+SaNO3fuZP369SQkJNCsWTMmTJjA2LFj6dGjB7169WLWrFnk5+e7Z6N5w7hx4xg3bpx7mXARkUC0avshNvyeQ1iwnZv6tbC6HBHLWR6K1qxZw6BBg9yPJ0yYAMDYsWOZN28eV111FZmZmUyePJn09HS6dOnCF198cdLgaxERqZm0peY/SP/csxmJURpPKVIvNoStLW0IKyKBav3eI1yWtpIgu42vHxHdBQwAABthSURBVBpE47hwq0sS8Zjafn/79JgiERHxjr8fbyW6rGtjBSKR4xSKKqGB1iISyLZmHGXhpgxsNvjfAa2tLkfEZygUVWLcuHFs2rSJ1atXW12KiIjHPfPFFgCGd2hIm+Qoi6sR8R0KRSIi9ciqbVks3pxBkN3GA0PPtrocEZ+iUCQiUk84XQZTPtkEwHXnNVcrkcgfKBSJiNQT/16zl1/TjxITFsS9g9taXY6Iz1EoEhGpB/KKSpm5cCsA9wxuS3xkiMUVifgehaJKaPaZiASal5dtIyuviJYNIrmhTwuryxHxSVq8sQpavFFEAsHvhwu48NmvKS518Y/ruzO0gzbUlsCmxRtFRKRST3+xheJSF31aJXJRqrZIEjkVhSIRkQC2dvdh/rthPzYb/L+L22Oz2awuScRnKRSJiAQol8tg6vEp+Fd2b0qHRrEWVyTi2xSKREQC1H9/2s/6vUeIDHHwwLB2Vpcj4vMUikREAtCxYidPf/4rAHcNakNydJjFFYn4PoWiSmhKvoj4u9e+2cH+nEIax4VzS/+WVpcj4hc0Jb8KmpIvIv7oYG4hA2cuo6DYyew/d+HSLo2tLkmkTmlKvoiIADBz4RYKip10bRbHqM6NrC5HxG8oFImIBJCN+3L499rfAXj84lRNwRepAYUiEZEAkVdUyj3/9yOGAaM6N6Jbs3irSxLxKwpFIiIBwDAMJi34mR1Z+ZwVG8YTozpYXZKI31EoEhEJAO9+v4f/bthPkN3GS9d0JSEyxOqSRPyOQpGIiJ/buC+HKf81V65+ePg5dG+eYHFFIv5JoagSWqdIRPxFbmEJd727jmKniyHtU7j1fK1JJFJbWqeoClqnSER8mWEY3PnOOr74JZ0m8eF8evf5xEYEW12WiOW0TpGISD0zb9UuvvglnWCHjbRruikQiZwhhSIRET+0fu8RnvxsMwCPjWxP56ZxFlck4v8UikRE/MyRgmLGvbuOEqfByE4NGdu3hdUliQQEhSIRET9iGAYT/397dxoVxZnuAfzfDbJDgyCyi3EhsggCYjSj4DaYGxONmtHEBYImuRq9McGY8SQucUMzR8clJEbNKHo0E5cTryfEmwhiTDAZAQHBuCK4sMYg+95d94NDjx0abJbu6m7/v3P4UG+9VfX002XVY9XbVUezUVhRj36OVtg0fSifWk3UQ1gUEREZkD0/3kLSlTKYmUoR/2ow7Cw4joiop7AoIiIyED/e+A2b/+8aAGD1C77wd5eJHBGRcWFRRERkAE5mFyFmfxrkCgFTgtzwapiX2CERGR0WRWrw4Y1EpE+++Ckf//NlJprlAp4f6oqPZ3AcEZE28OGNHeDDG4lITAqFgM3/dxWfn7sFAIge5Y1Vk30hlbIgIupIV8/fplqMiYiIuqhZrsDyY5fwdWYhAGD5JB8sDB/AK0REWsSiiIhIz9Q2tmDhoYs4d/03mEgl2DQtAC+HeoodFpHRY1FERKRH7tc0ImZ/Gi7dq4RlLxN8OicYY32cxQ6L6InAooiISE/c/r0W8/5xAbd/r0NvazP8I3o4gvj6DiKdYVFERKQHfrpxH0u/ysT9miZ4OFjiQEwYnupjI3ZYRE8UFkVERCIqrqzH+m+uIDGnGAAwxNUOCa8Nh7OdhciRET15WBQREYmgqUWBf6TmY0fyDdQ1ySGVAPNGeiP2z4Nhy1d3EImCRRERkY6l3ryPVf+bi7zfagEAof0csHaKP3zd+Dw0IjGxKCIi0pGSygasT/wV31x6eKvM0doMK/5rCKYNc+cDGYn0AIsiIiIta2pRYP/5fGxPuoHaf98qm/tMP7z7Zx/ILHmrjEhfsCgiItKSZrkCxzLu4ZMzN1FYUQ8ACPayx7qp/vBz4xvuifQNiyI14uPjER8fD7lcLnYoRGSAmuUKfH2xEDtTbuBu+cNiyNnWHMsifTAj2IO3yoj0FF8I2wG+EJaIOqNFrsCJrCLsPHMDt3+vAwA42ZhjYcQAzB7hBYteJiJHSPRk4AthiYhEIlcIOJldiB3JN5F//+EvyhytzfDf4QMw55l+sDRjMURkCFgUERF1UXltE05mFeLgL7eVP693sOqFN8MHYN7IfrAy4yGWyJDwXywRUSc0tShw5moZjl+8h5SrZWhRPByBILPshTfGPIWoUd6wMeehlcgQ8V8uEdFjCIKAS/cqcfziPZzMLkJFXbNyXoC7DNOC3TEjxINPoiYycCyKiIjUaGiW49fiKvyc9zu+zizEzbIa5TxnW3O8NMwd04I94ONiK2KURNSTWBQR0ROvprEFvxZVIbewErlFlbhcWIWbv9VArvjPj3PNTaWI9HPB9BAPPDvAEaYmUhEjJiJtYFFERE+UmsYWXC6sRE5hJS7de1gE5d+vhbqHkzjZmCHAXYZJ/i54LsAVdrw9RmTUWBQRkdFqvQV26W4FLhVWIudeJW7+VqO2AHKVWcDPTQZ/dzsEuMvg7y6Ds605JBI+aJHoScGiiIiMglwh4GZZDbLuPkDW3Qpk3a3E9dJqlVtgrVxlFhjqIVMWP/7uMjjZmIsQNRHpExZFRGSQSiob/l0AVSLr7gPk3KtEbVPbV/M42ZhhqIc9AtxlCPRsvQJkIULERKTvWBQRkagamuXILazExTsPcPF2BW6UVau9vfWomsYWlFU3tmm3NjNBgIcMQZ4OCPKUYaiHPVxlFrwFRkQaYVFERDpVXFmPi7crkHH7AS7eeYDLRZVolnf+FYxSCeDjYocgT3sEeT4shAY628CEL1sloi5iUUR6o6FZjuy7FUi//QBpBeUofFAvdkjUw6oamlFa1fYKj5ONGYZ5OSCknwP83WQw79Xxz917mUgxuK8NX6NBRD2KRxQSzYPaJqTffoD0gnKkFZQjp7BrVwzIsJhIJXjaxRbB/y6Cgr0c4Nnbkre4iEh0LIpE0Ngix+sHMsQOQ1RFFfUqTwhu5WxrjuHevRHq7YDBfW0h5YnSqJiZSvG0iy2s+W4wItJDPDKpER8fj/j4eMjlbX/J0hMEATh3/TetrNvQDHS2wXBvB4T2643h3r15xYCIiEQjEYTH/c7jyVVVVQWZTIbKykrY2dn12Hpb5AqczC7qsfUZIpllLwzzckBvazOxQyEiIiPT1fM3rxSJwNREimnBHmKHQURERI/gGw2JiIiIwKKIiIiICACLIiIiIiIALIqIiIiIALAoIiIiIgLAooiIiIgIAIsiIiIiIgAsioiIiIgAsCgiIiIiAsCiiIiIiAgAiyIiIiIiACyKiIiIiACwKCIiIiICAJiKHYA+EwQBAFBVVSVyJERERKSp1vN263lcUyyKOlBdXQ0A8PT0FDkSIiIi6qzq6mrIZDKN+0uEzpZRTxCFQoGioiLY2tpCIpFg+PDhSEtLa9NPXfvj2qqqquDp6Ym7d+/Czs5Oex+ig3i0tbwmfTvqwzzrX57VtYuZ547i1Mayj+vf1fma7NN/nOY+zWNHd5d/EvIsCAKqq6vh5uYGqVTzkUK8UtQBqVQKDw8P5bSJiYnaL01du6ZtdnZ2OvkH117s2lhek74d9WGe9S/P6trFzHN729fWso/r39X5muy/7S3LfVrzeTx2dL6vMeS5M1eIWpmsWbNmTY9GYeTCwsI0bu+orbGxEZs2bcKKFStgbm7es0G2o73YtbG8Jn076sM891zfnsqzunYx86wuHm0u+7j+XZ2vyT796DT3aR47emL5JznPHeHtM5FUVVVBJpOhsrJSZ/+zfhIxz7rBPOsOc60bzLNu6FueeaVIRCYmJoiIiICpKe9iahPzrBvMs+4w17rBPOuGPuWZV4qIiIiIwIc3EhEREQFgUUREREQEgEUREREREQAWRUREREQAWBQRERERAWBRpPcqKioQGhqKoKAg+Pv7Y8+ePWKHZLTu3r2LiIgI+Pr6YujQoTh69KjYIRmtl156CQ4ODpgxY4bYoRiVb775Bj4+Phg0aBD27t0rdjhGi/uv9ol1POZP8vWcXC5HY2MjrKysUFtbC39/f6Snp8PR0VHs0IxOcXExSktLERQUhJKSEoSEhOD69euwtrYWOzSjc/bsWVRXVyMhIQHHjh0TOxyj0NLSAl9fX6SkpEAmkyEkJATnz5/nsUILuP9qn1jHY14p0nMmJiawsrIC8PBx6IIggHWsdri6uiIoKAgA4OLiAicnJ5SXl4sclXGKiIiAra2t2GEYlQsXLsDPzw/u7u6wsbHBc889h++//17ssIwS91/tE+t4zKKom86dO4cXXngBbm5ukEgkOHHiRJs+8fHx8Pb2hoWFBUaMGIELFy50ahsVFRUIDAyEh4cH3nvvPTg5OfVU+AZFF7lulZGRAblcDk9Pz+6GbXB0mWf6j+7mvaioCO7u7sppd3d3FBYW6iR2Q8L9Wzd6Ms+6PB6zKOqm2tpaBAYGIj4+Xu38r776Cu+++y5Wr16NixcvIjAwEJGRkSgrK1P2aR0v9Me/oqIiAIC9vT2ys7ORn5+Pw4cPo7S0VCefTd/oItcAUF5ejnnz5mH37t1a/0z6SFd5JlU9kXd6POZZN3oqzzo/HgvUYwAIX3/9tUpbWFiY8NZbbymn5XK54ObmJsTFxXVpGwsXLhSOHj3arTiNgbZy3dDQIIwePVo4cOBAj8VqyLS5T6ekpAjTp0/vkTiNTVfynpqaKkydOlU5/+233xYOHTqkm4ANVHf2b+6/mutqnsU4HvNKkRY1NTUhIyMDEyZMULZJpVJMmDABP//8s0brKC0tRXV1NQCgsrIS586dg4+Pj1biNWQ9kWtBEBAdHY1x48Zh7ty52grVoPVEnqnzNMl7WFgYcnNzUVhYiJqaGpw6dQqRkZFihWyQuH/rhiZ5Fut4zKJIi+7fvw+5XI6+ffuqtPft2xclJSUareP27dsYPXo0AgMDMXr0aCxZsgQBAQHaCNeg9USuU1NT8dVXX+HEiRMICgpCUFAQcnJytBGuweqJPAPAhAkT8PLLL+Pbb7+Fh4cHTziPoUneTU1NsWXLFowdOxZBQUGIjY3lL886SdP9m/tv92iSZ7GOx6Za3wJ1S1hYGLKyssQO44nwpz/9CQqFQuwwnghJSUlih2CUXnzxRbz44otih2H0uP9qn1jHY14p0iInJyeYmJi0GRhdWloKFxcXkaIyTsy1bjDP4mDedYN51g19zjOLIi0yMzNDSEgIkpOTlW0KhQLJyckYOXKkiJEZH+ZaN5hncTDvusE864Y+55m3z7qppqYGN2/eVE7n5+cjKysLvXv3hpeXF959911ERUUhNDQUYWFh2LZtG2pra/Haa6+JGLVhYq51g3kWB/OuG8yzbhhsnnX2OzcjlZKSIgBo8xcVFaXss3PnTsHLy0swMzMTwsLChF9++UW8gA0Yc60bzLM4mHfdYJ51w1DzzHefEREREYFjioiIiIgAsCgiIiIiAsCiiIiIiAgAiyIiIiIiACyKiIiIiACwKCIiIiICwKKIiIiICACLIiIiIiIALIqIiIiIALAoIiINeXt7Y9u2bd1eT3R0NKZOndoDEbXv7NmzkEgkqKio0Op2dOHq1at45plnYGFhgaCgILVtBQUFkEgkyMrK0miduvgOiAwRXwhLRDq1fft29OTbhSIiIhAUFKRSsI0aNQrFxcWQyWQ9th2xrF69GtbW1rh27RpsbGzUttnb26O4uBhOTk4arbOnvwMAWLNmDU6cOKFxYUakj1gUERmopqYmmJmZiR2GxuRyOSQSiU4KFTMzM7i4uGh9O7qQl5eH559/Hv369euwrTOf1xiKRSJt4O0zIgMRERGBxYsXY+nSpXByckJkZCQAoKKiAgsWLECfPn1gZ2eHcePGITs7W2XZ9evXw9nZGba2tliwYAH++te/Km/FtK576dKlKstMnToV0dHR7cazdetWBAQEwNraGp6enli0aBFqamqU8/fv3w97e3ucPHkSvr6+MDc3x507d1Ru3bTe9vnjX0REBADg999/xyuvvAJ3d3dYWVkhICAAX375pXIb0dHR+OGHH7B9+3blsgUFBWpvnx0/fhx+fn4wNzeHt7c3tmzZovJ5vL29sXHjRsTExMDW1hZeXl7YvXt3h9+JQqHAxx9/jIEDB8Lc3BxeXl7YsGGDcn5OTg7GjRsHS0tLODo64o033lDJEQDs3bsXQ4YMgYWFBZ5++ml8+umnynkSiQQZGRlYu3YtJBIJ1qxZo7ZN3e2zy5cvY/LkybCzs4OtrS1Gjx6NvLw8Zd4evX2mUCgQFxeH/v37w9LSEoGBgTh27Jhyfms+k5OTERoaCisrK4waNQrXrl1TftcfffQRsrOzld/D/v37O8wdkT5iUURkQBISEmBmZobU1FTs2rULAPDyyy+jrKwMp06dQkZGBoKDgzF+/HiUl5cDAA4dOoQNGzZg8+bNyMjIgJeXFz777LNuxyKVSrFjxw5cvnwZCQkJOHPmDJYvX67Sp66uDps3b8bevXtx+fJlODs7q8z39PREcXGx8i8zMxOOjo4YM2YMAKChoQEhISFITExEbm4u3njjDcydOxcXLlwA8PA20MiRI/H6668r1+Hp6dkm1oyMDPzlL3/BrFmzkJOTgzVr1mDlypVtTtxbtmxBaGgoMjMzsWjRIixcuFB54ldnxYoV2LRpE1auXIlff/0Vhw8fRt++fQEAtbW1iIyMhIODA9LS0nD06FEkJSVh8eLFyuUPHTqEVatWYcOGDbhy5Qo2btyIlStXIiEhAQBQXFwMPz8/xMbGori4GMuWLVPb9keFhYUYM2YMzM3NcebMGWRkZCAmJgYtLS1qP0dcXBwOHDiAXbt24fLly3jnnXcwZ84c/PDDDyr9PvjgA2zZsgXp6ekwNTVFTEwMAGDmzJmIjY2Fn5+f8nuYOXNmu3kj0lsCERmE8PBwYdiwYSptP/74o2BnZyc0NDSotA8YMED4/PPPBUEQhBEjRghvvfWWyvxnn31WCAwMVFn322+/rdJnypQpQlRUlHK6X79+wt///vd24zt69Kjg6OionN63b58AQMjKylLpFxUVJUyZMqXN8vX19cKIESOEyZMnC3K5vN3tPP/880JsbGyHsaekpAgAhAcPHgiCIAivvvqqMHHiRJU+7733nuDr66vy+ebMmaOcVigUgrOzs/DZZ5+pjaOqqkowNzcX9uzZo3b+7t27BQcHB6GmpkbZlpiYKEilUqGkpEQQhIff0+HDh1WWW7dunTBy5EjldGBgoLB69WqVPn9sy8/PFwAImZmZgiAIwooVK4T+/fsLTU1NamN79DtoaGgQrKyshPPnz6v0mT9/vvDKK68IgvCffCYlJal8FgBCfX29IAiCsHr1apV9isgQcUwRkQEJCQlRmc7OzkZNTQ0cHR1V2uvr65W3Sq5du4ZFixapzA8LC8OZM2e6FUtSUhLi4uJw9epVVFVVoaWlBQ0NDairq4OVlRWAh2N7hg4dqtH6YmJiUF1djdOnT0MqfXgRWy6XY+PGjThy5AgKCwvR1NSExsZG5fo1deXKFUyZMkWl7dlnn8W2bdsgl8thYmICACqxSiQSuLi4oKysrN11NjY2Yvz48e3ODwwMhLW1tco2FQqFcoB0Xl4e5s+fj9dff13Zp6WlpdtjfrKysjB69Gj06tXrsX1v3ryJuro6TJw4UaW9qakJw4YNU2l7ND+urq4AgLKyMnh5eXUrXiJ9waKIyIA8eoIFgJqaGri6uuLs2bNt+trb22u8XqlU2ubXSM3Nze32LygowOTJk7Fw4UJs2LABvXv3xk8//YT58+ejqalJWbRYWlpCIpE8dvvr16/Hd999hwsXLsDW1lbZ/re//Q3bt2/Htm3blOOXli5diqamJo0/W2f8sYiQSCRQKBRq+1paWnZrW61ji/bs2YMRI0aozGst0rqqM7G1xpGYmAh3d3eVeebm5irTj+an9XttLz9EhohFEZEBCw4ORklJCUxNTeHt7a22j4+PD9LS0jBv3jxlW1pamkqfPn36oLi4WDktl8uRm5uLsWPHql1nRkYGFAoFtmzZoryqc+TIkS59huPHj2Pt2rU4deoUBgwYoDIvNTUVU6ZMwZw5cwA8PAFfv34dvr6+yj5mZmaQy+UdbmPIkCFITU1ts+7Bgwd3uQAZNGgQLC0tkZycjAULFqjd5v79+1FbW6ssZlNTUyGVSuHj44O+ffvCzc0Nt27dwuzZs7sUQ3uGDh2KhIQENDc3P/Zq0aOD4MPDw7u8TU2+ByJ9x4HWRAZswoQJGDlyJKZOnYrvv/8eBQUFOH/+PD744AOkp6cDAJYsWYIvvvgCCQkJuHHjBtavX49Lly6pXMEZN24cEhMTkZiYiKtXr2LhwoUdPvhw4MCBaG5uxs6dO3Hr1i0cPHhQOfC7M3JzczFv3jy8//778PPzQ0lJCUpKSpSDxAcNGoTTp0/j/PnzuHLlCt58802UlpaqrMPb2xv/+te/UFBQgPv376u9chEbG4vk5GSsW7cO169fR0JCAj755BO1g5Q1ZWFhgffffx/Lly/HgQMHkJeXh19++QVffPEFAGD27NmwsLBAVFQUcnNzkZKSgiVLlmDu3LnKwdgfffQR4uLisGPHDly/fh05OTnYt28ftm7d2uW4AGDx4sWoqqrCrFmzkJ6ejhs3buDgwYNqB43b2tpi2bJleOedd5CQkIC8vDxcvHgRO3fuVA741oS3tzfy8/ORlZWF+/fvo7GxsVufgUgMLIqIDJhEIsG3336LMWPG4LXXXsPgwYMxa9Ys3L59W3ninT17NlasWIFly5YhODgY+fn5iI6OhoWFhXI9MTExiIqKwrx58xAeHo6nnnqq3atEABAYGIitW7di8+bN8Pf3x6FDhxAXF9fp+NPT01FXV4f169fD1dVV+Tdt2jQAwIcffojg4GBERkYiIiICLi4ubZ7EvGzZMpiYmMDX1xd9+vTBnTt32mwnODgYR44cwT//+U/4+/tj1apVWLt2bYePHNDEypUrERsbi1WrVmHIkCGYOXOmcgySlZUVvvvuO5SXl2P48OGYMWMGxo8fj08++US5/IIFC7B3717s27cPAQEBCA8Px/79+9G/f/9uxeXo6IgzZ86gpqYG4eHhCAkJwZ49e9q9arRu3TqsXLkScXFxGDJkCCZNmoTExMROxTF9+nRMmjQJY8eORZ8+fVQenUBkKCTCHwcSEJHRmzhxIlxcXHDw4EGxQyEi0hscU0Rk5Orq6rBr1y5ERkbCxMQEX375JZKSknD69GmxQyMi0iu8UkRk5Orr6/HCCy8gMzMTDQ0N8PHxwYcffqi8RUVERA+xKCIiIiICB1oTERERAWBRRERERASARRERERERABZFRERERABYFBEREREBYFFEREREBIBFEREREREAFkVEREREAID/B1IcabSzFWscAAAAAElFTkSuQmCC", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigmas = 10.^(-3:0.1:2);\n", "training_errors = zeros(length(sigmas));\n", "test_errors = zeros(length(sigmas));\n", "\n", "for i = 1:length(sigmas)\n", " (training_errors[i], test_errors[i]) = regularized_fit_error(sigmas[i]);\n", "end\n", "\n", "loglog(sigmas, training_errors, label=\"training error\");\n", "loglog(sigmas, test_errors, label=\"test error\");\n", "xlabel(\"regularization coefficient\");\n", "ylabel(\"error\");\n", "legend();" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Julia 0.5.1", "language": "julia", "name": "julia-0.5" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.5.1" } }, "nbformat": 4, "nbformat_minor": 2 }