{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "using PyPlot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at using stochastic gradient descent with various methods to optimize logistic regression.\n", "First, we'll generate a training set at random from the generative model associated with logistic regression.\n", "This generative model is, for label $y \\in \\{-1,1\\}$, features $x \\in \\mathbb{R}^d$ and model $w \\in \\mathbb{R}^d$,\n", "\n", "$$\\mathbf{P}_w(y | x) = \\frac{1}{1 + \\exp(-y x^T w)}.$$\n", "\n", "This means that if we make a bunch of independent observations, the total probability is\n", "\n", "$$p(w) = \\prod_{i=1}^N \\frac{1}{1 + \\exp(-y_i x_i^T w)}$$\n", "\n", "and so maximizing this is equivalent to maximizing the log likelihood\n", "\n", "$$\\log p(w) = -\\sum_{i=1}^N \\log \\left( 1 + \\exp(-y_i x_i^T w) \\right).$$\n", "\n", "The gradient of this is\n", "\n", "$$\\nabla \\log p(w) = -\\sum_{i=1}^N \\frac{\\exp(-y_i x_i^T w) \\cdot (-y_i x_i)}{1 + \\exp(-y_i x_i^T w)}$$\n", "\n", "which reduces to\n", "\n", "$$\\nabla \\log p(w) = \\sum_{i=1}^N \\frac{y_i x_i}{1 + \\exp(y_i x_i^T w)}.$$\n", "\n", "Anyway, we can see that this corresponds to logistic regression." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# generate the data\n", "srand(424242)\n", "d = 20;\n", "N = 10000;\n", "wtrue = randn(d);\n", "wtrue = d^2 * wtrue / norm(wtrue);\n", "X = randn(N, d);\n", "X ./= sqrt(sum(X.^2, 2));\n", "Y = (1 ./ (1 + exp(-X * wtrue)) .>= rand(N)) * 2 - 1;\n", "sigma = 0.001;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's do logistic regression with regularization here. Our objective samples will be of the form\n", "\n", "$$f_i(w) = -\\log \\left( 1 + \\exp(-y_i x_i^T w) \\right) + \\frac{\\sigma}{2} \\| w \\|^2$$\n", "\n", "and the SGD updates will look like\n", "\n", "$$w_{t+1} = w_t + \\alpha_t \\left( \\frac{y_i x_i}{1 + \\exp(y_i x_i^T w_t)} - \\sigma w_t \\right)$$.\n", "\n", "Let's look at the constants of strong convexity and Lipschitz continuity for this problem, to get a handle on the theory/optimal parameters. If we differentiate the objective twice, we get\n", "\n", "$$\\nabla^2 f_i(w) = x_i x_i^T \\frac{1}{(1 + \\exp(y_i x_i^T w_t)) (1 + \\exp(-y_i x_i^T w_t))} + \\sigma I.$$\n", "\n", "It's pretty easy to see that\n", "\n", "$$0 < \\frac{1}{(1 + \\exp(u)) (1 + \\exp(-u))} \\le \\frac{1}{4},$$\n", "\n", "and so since we initialized such that $\\| x_i \\|^2 = 1$, from the way we generated the examples, we can approximate \n", "\n", "$$\\sigma I \\preceq \\nabla^2 f_i(w) \\preceq \\left(\\sigma + \\frac{1}{4} \\right) I.$$\n", "\n", "So we can set $\\mu = \\sigma$ and $L = \\sigma + \\frac{1}{4}$.\n", "What about bounding the variance of the gradient samples? (Again here I'm using the nonstandard definition of variance for vectors: $\\mathbf{Var}(X) = \\mathbf{E}[\\| X \\|^2] - \\| \\mathbf{E}[ X ] \\|^2$.)\n", "Well,\n", "\n", "\\begin{align*}\n", " \\mathbf{Var}(\\nabla f_i(w))\n", " &=\n", " \\mathbf{Var}\\left( \\frac{y_i x_i}{1 + \\exp(y_i x_i^T w)} - \\sigma w \\right) \\\\\n", " &=\n", " \\mathbf{Var}\\left( \\frac{y_i x_i}{1 + \\exp(y_i x_i^T w)} \\right) \\\\\n", " &\\le\n", " \\mathbf{E}\\left[ \\left\\| \\frac{y_i x_i}{1 + \\exp(y_i x_i^T w)} \\right\\|^2 \\right] \\\\\n", " &\\le\n", " \\mathbf{E}\\left[ \\left\\| x_i \\right\\|^2 \\right] \\\\\n", " &\\le\n", " 1\n", "\\end{align*}\n", "\n", "where this last line happens because we sampled $x_i$ uniformly from the unit ball. So we can set $M = 1$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mu = sigma;\n", "L = sigma + 0.25;\n", "M = 1;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is the optimal step size for SGD under these conditions?\n", "Well, from Lecture 2, we had\n", "$$\\alpha_t = \\frac{2 \\mu \\| w_0 - w^* \\|^2}{4 M + \\mu^2 \\| w_0 - w^* \\|^2 t}$$\n", "or\n", "$$\\alpha_t = \\frac{\\alpha_0}{1 + \\gamma t}$$\n", "where\n", "$$\\alpha_0 = \\frac{2 \\mu \\| w_0 - w^* \\|^2}{4 M}$$\n", "and\n", "$$\\gamma = \\frac{\\mu^2 \\| w_0 - w^* \\|^2}{4 M}.$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "w0 = randn(d);" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sgd_logreg (generic function with 1 method)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function sgd_logreg(w0, alpha0, gamma, X, Y, sigma, niters, wopt)\n", " w = w0\n", " (N, d) = size(X)\n", " dist_to_optimum = zeros(niters)\n", " for k = 1:niters\n", " alpha = alpha0 / (1 + gamma * (k-1));\n", " i = rand(1:N)\n", " xi = X[i,:];\n", " yi = Y[i];\n", " w = (1 - alpha * sigma) * w + alpha * xi * yi / (1 + exp(yi * dot(xi, w)));\n", " dist_to_optimum[k] = norm(w - wopt);\n", " end\n", " return (w, dist_to_optimum);\n", "end" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "newton_logreg (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# find the true minimum\n", "function newton_logreg(w0, X, Y, sigma, niters)\n", " N = size(X, 1);\n", " d = size(X, 2);\n", " w = w0;\n", " for k = 1:niters\n", " g = -X' * (Y ./ (1 + exp(Y .* (X * w)))) + N * sigma * w;\n", " H = X' * ((1 ./ ((1 + exp(Y .* (X * w))) .* (1 + exp(-Y .* (X * w))))) .* X) + N * sigma * eye(d);\n", " w = w - H \\ g;\n", " println(\"gradient norm: \$(norm(g))\")\n", " end\n", " return w\n", "end" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gradient norm: 3999.9774577369785\n", "gradient norm: 896.3972587628689\n", "gradient norm: 233.89715512117843\n", "gradient norm: 59.370770718984\n", "gradient norm: 5.959623034633453\n", "gradient norm: 0.06910877657919792\n", "gradient norm: 9.433183413409561e-6\n", "gradient norm: 2.777799306773163e-13\n", "gradient norm: 6.563211845551944e-14\n", "gradient norm: 4.618954771558417e-14\n" ] } ], "source": [ "wopt = newton_logreg(wtrue, X, Y, sigma, 10);" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha0 = 2 * mu * norm(w0 - wopt)^2 / (4 * M);\n", "gamma = mu^2 * norm(w0 - wopt)^2 / (4 * M);" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "srand(123456);\n", "(w, dto) = sgd_logreg(w0, alpha0, gamma, X, Y, sigma, 50000, wopt);" ] }, { "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(dto)\n", "xlabel(\"iteration\");\n", "ylabel(\"distance to optimum\");" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "srand(123456);\n", "(w2, dto2) = sgd_logreg(w0, 2*alpha0, 4*gamma, X, Y, sigma, 50000, wopt);\n", "srand(123456);\n", "(w2, dto3) = sgd_logreg(w0, 3*alpha0, 9*gamma, X, Y, sigma, 50000, wopt);" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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uU6ZMwc3NDW9vb1auXKnT/jvvvIO/vz92dnY0aNCAmTNnkpMja8Tpo0InPjdv3iQvLw8vLy+d615eXiQkJGjOe/bsybPPPsvff/+Nt7d3qUnRtGnTSE5O1nwuX75stPgLEp+bSiWO6dp2ZJyPEKLCUqkgO808n4f4ozA5WT2cwM1NvYxI165dmTBhAsOHDyc5OZkjR44wc+ZMvvnmmyK/UwpERkYyePBgnnvuOaKiopg9ezYzZ85k1apVOvU+/vhjgoKCOHLkCFOnTmX8+PFs27YNgIMHDwKwcuVKrl27pjkvzr///kt8fDy7d+9m8eLFzJo1iyeffBJXV1f279/P//73P8aMGcOVK1c09zg6OrJq1Sqio6NZsmQJK1as4JNPPin39606sjR3AIawffv2Mte1sbHBxsbGiNFoFYzxuau0IDslDityycGS/bG3aOHtbJIYhBBCLznp8GEd87Q9PR6s7fW+LT8/nwkTJhASEkLz5s011+fNm8e2bdt49dVXOXHiBCNHjqR///4lPmfx4sX06NGDmTNnAuDv7090dDQff/wxo0aN0tQLCQlh6tSpmjrh4eF88skn9OrVCw8PDwBcXFyoVatWqXG7ubnx2WefYWFhQZMmTViwYAHp6elMnz4dUP+hPn/+fPbs2cNzzz0HwIwZMzT3+/r6MnnyZNatW8fbb7+tx3eseqvQb3xq1qyJUqks8lry+vXrD/yBqgicrJ00x/FKC+Z1VZ+Hn7tprpCEEKLKGTt2LCdOnGDdunU6162trfnxxx/57bffyMzMfOCbkZiYGEJCQnSuhYSEcPbsWfLytEuRdOzYUadOx44diYmJ0TvuwMBALCy0v4a9vLxo0aKF5lypVOLu7q4zmWf9+vWEhIRQq1YtHBwcmDFjBnFxcXq3XZ1V6Dc+1tbWtGnThrCwMAYMGACoM/uwsDDGjRtn5ugeTKFQ4GbrRlJmEolKJY+4JANWHIhNIicvHytlhc47hRDVkZWd+s2LudrW07hx4/jrr7/YvXs33t7eRcojIiIASEpKIikpCXt7/d8oGYuVlZXOuUKhKPZafn4+AHv37mXo0KHMmTOH0NBQnJ2dWbduXZFxSKJ0Zk98UlNTOXfunOY8NjaWo0eP4ubmRr169Zg4cSIjR46kbdu2tG/fnk8//ZS0tDRGjx5txqjLrolrE/Ze20uCpSXtuY6bfQOS0rI5dvkObX3dzB2eEELoUijK1d1kaiqVijfeeIMNGzawc+dO/Pz8itQ5f/48b731FitWrGD9+vWMHDmS7du367xlKaxZs2aEh4frXAsPD8ff3x+lUqm5tm/fPp06+/bto1mzZppzKysrnTdEhhIREUH9+vV59913NdcuXZIdAfRl9lcOhw4dIjg4mODgYAAmTpxIcHAw7733HgBDhgxh4cKFvPfee7Rq1YqjR4+yZcuWEgenVTSedp6AeoCzxa0zdGygHvcTfu6WOcMSQohKbezYsfzwww+sXbsWR0dHEhISSEhIICMjA4C8vDyGDRtGaGgoo0ePZuXKlRw/frzUtyOTJk0iLCyMuXPncubMGVavXs3SpUuZPHmyTr3w8HAWLFjAmTNnWLZsGb/88gvjx4/XlPv6+hIWFkZCQgK3bxtuCZPGjRsTFxfHunXrOH/+PJ999hkbNmww2POrC7MnPl27dkWlUhX5FB5FP27cOC5dukRWVhb79++nQ4cO5gtYTwWJT6JSCUmxdGpUkPjIOB8hhCiv5cuXk5ycTNeuXaldu7bms379egA++OADLl26xFdffQVA7dq1+frrr5kxYwbHjh0r9pmtW7fm559/Zt26dTRv3pz33nuP999/X2dgM6gTpII/2ufNm8fixYsJDQ3VlC9atIht27bh4+Oj+aPeEPr3789bb73FuHHjaNWqFREREZqB2KLsFKpqvqhMSkoKzs7OJCcn4+Tk9OAb9PTTqZ/4cP+H9EhL59M8Fy69sJvHPt4JwMk5odjbmL23UQhRTWVmZhIbG4ufnx+2trbmDqdS8PX1ZcKECUyYMMHcoVQLpf2Mlvf3t9nf+JjLsmXLCAgIoF27dkZtx7OG+o3PDaUSbl+inou1pizivHR3CSGEEKZUbROfsWPHEh0dXeriUoZQ0+7eIoaWlpCfgyL5Mu3vDWr+7+wNo7YthBBCCF3VNvExFS879SDsRKWSHIBb5/lf1wYA/HPyOvn51bqnUQghKpWLFy9KN1clJ4mPkXnZeWFtYU2uAhItlXDzLJ0a1sTeWklCSibHryabO0QhhBCi2pDEx8gUCgW2luoBWfGWlnB0LbZWSro2UY/9+edkQmm3CyGEEMKAJPExgZRs9aakh2xtwKoGAL0D1V1gWyXxEUIIIUxGEh8TaOrWFIBUCwtIV8/k6tbUEyulgvM30jiXmGrO8IQQQohqQxIfE+hVvxcAKRYWcDsWcjJxsrWiU0P1jC956yOEEEKYhiQ+JlDbvjYA16xtQZUPt84C2u6uf6Kvl3ivEEIIIQyn2iY+plrAEKCWfS0AEqxt1BcSTwHQK8ALhQKOXb5DQnKm0eMQQghhHrNnz6ZVq1ZVpp3KrNomPqZawBAKvfFRqFAB3IgBwNPRltb1XAH4J1q6u4QQoqyWL19Oy5YtcXJywsnJiY4dO7J582ZzhwWoZ/Nu3LhR59rkyZMJCwszU0SisGqb+JiSl50XChRkk0+ShQUkxmjKQgu6u05Kd5cQQpSVt7c38+fPJzIykkOHDtG9e3eeeuopTp48ae7QiuXg4IC7u7u5wxBI4mMSVkorPGp4AHDN0lIn8ekdoO4G23fhFsnpOWaJTwghKpt+/frx+OOP07hxY/z9/fnggw9wcHBg3759AOzcuRNra2v+++8/zT0LFizA09OT69dL/kPzt99+IzAwEBsbG3x9fVm0aJFOua+vL3PnzuX555/H3t6eunXrsmzZMp1ygIEDB6JQKDTn93dBjRo1igEDBvDhhx/i5eWFi4sL77//Prm5uUyZMgU3Nze8vb1ZuXKlTvvvvPMO/v7+2NnZ0aBBA2bOnElOjvzu0IdsDW4i9ZzqkZiRyEUrS5rfvgjZ6WBth29Ne5p4OXL6+l3CTl3n6dbe5g5VCFGNqVQqMnIzzNJ2DcsaKBQKve/Ly8vjl19+IS0tjY4dOwLQtWtXJkyYwPDhwzl27BgXLlxg5syZ/PLLL3h5eRX7nMjISAYPHszs2bMZMmQIERERvP7667i7uzNq1ChNvY8//pjp06czZ84ctm7dyvjx4/H396dXr14cPHgQT09PVq5cSZ8+fVAqlSXG/e+//+Lt7c3u3bsJDw/npZdeIiIigi5durB//37Wr1/PmDFj6NWrF97e6t8Njo6OrFq1ijp16hAVFcUrr7yCo6Mjb7/9tt7ft+pKEh8TKRjnc72GE6Slw80zUEed/YcGenH6+l22nkyQxEcIYVYZuRl0WNvBLG3vf2E/dlZ2Za4fFRVFx44dyczMxMHBgQ0bNhAQEKApnzdvHtu2bePVV1/lxIkTjBw5kv79+5f4vMWLF9OjRw9mzpwJgL+/P9HR0Xz88cc6iU9ISAhTp07V1AkPD+eTTz6hV69eeHio3+67uLhQq1atUuN3c3Pjs88+w8LCgiZNmrBgwQLS09OZPn06ANOmTWP+/Pns2bOH5557DoAZM2Zo7vf19WXy5MmsW7dOEh89SFeXiXjZq//CuO6g3pmdG6c0Zb0D1f/j2HXmBhnZeSaPTQghKqMmTZpw9OhR9u/fz2uvvcbIkSOJjo7WlFtbW/Pjjz/y22+/kZmZySeffFLq82JiYggJCdG5FhISwtmzZ8nL0/5/c8FbpcLnMTEx6CswMBALC+2vYS8vL1q0aKE5VyqVuLu7k5iYqLm2fv16QkJCqFWrFg4ODsyYMYO4uDi9267O5I2PiRTs0n7d5t5fM4na/3EG1nGirksNrt7J4L+zNzSJkBBCmFoNyxrsf2G/2drWh7W1NY0aNQKgTZs2HDx4kCVLlvDVV19p6kRERACQlJREUlIS9vb2hgv4IVlZWemcKxSKYq/l5+cDsHfvXoYOHcqcOXMIDQ3F2dmZdevWFRmHJEoniY+JaBKfguQ+UfvGR6FQ0DvQi5XhF9l68rokPkIIs1EoFHp1N1Uk+fn5ZGVlac7Pnz/PW2+9xYoVK1i/fj0jR45k+/btOm9ZCmvWrBnh4eE618LDw/H399cZq1MwgLrwebNmzTTnVlZWOm+IDCUiIoL69evz7rvvaq5dunTJ4O1UddLVZSIedup+3xv52eoLN3Rfi4beS3bCTl0nNy/fpLEJIURlM23aNHbv3s3FixeJiopi2rRp7Ny5k6FDhwLqAc/Dhg0jNDSU0aNHs3LlSo4fP17q25FJkyYRFhbG3LlzOXPmDKtXr2bp0qVMnjxZp154eDgLFizgzJkzLFu2jF9++YXx48dryn19fQkLCyMhIYHbt28b7N/cuHFj4uLiWLduHefPn+ezzz5jw4YNBnt+dVFtEx9TrtwMaKaz38pJIQ/gThxkaTcnbVvfFVc7K+6k53DgYpJJYhJCiMoqMTGRESNG0KRJE3r06MHBgwfZunUrvXqp90b84IMPuHTpkqbbq3bt2nz99dfMmDGDY8eOFfvM1q1b8/PPP7Nu3TqaN2/Oe++9x/vvv68zsBnUCdKhQ4cIDg5m3rx5LF68mNDQUE35okWL2LZtGz4+PgQHBxvs39y/f3/eeustxo0bR6tWrYiIiNAMxBZlp1CpVCpzB2FOKSkpODs7k5ycjJOTk9HaycvPo9X36llcf9/KwiflOrz8L3i30dSZ8ssxfom8wqhOvszuH2i0WIQQAiAzM5PY2Fj8/PywtbU1dziVgq+vLxMmTGDChAnmDqVaKO1ntLy/v6vtGx9TU1po+4eP1qynPog/rFOnoLvrn5MJVPN8VAghhDAKSXxMyNtBvUZPpmt99YWruolP58Y1sbNWEp+cyYmrKaYOTwghhKjyJPExoc51OwMQb+ugvnDfGx9bKyWP+avHAm09KZuWCiFERXPx4kXp5qrkJPExoboOdQG4anGvG+vGaZ0BzqDt7vrzeLx0dwkhhBAGJomPCdV2UG9bEZ+VBE51ARUkHNep0zvQC3trJZdupRN5yXDTIIUQoiTyR5aoqIzxsymJjwl5O6rH+Fy+exnq3JviGH9Ep46dtSV9W6gTpN8OXzFpfEKI6qVgleD09HQzRyJE8Qp+Nu9f0fphyMrNJlTPUT2bKykzibT6odif+qtI4gPwdOu6/Bp5hb+OX2NWv0BsrUre3VcIIcpLqVTi4uKi2QvKzs6uXLujC2FoKpWK9PR0EhMTcXFxKXWXe31J4mNCjtaOuNm6kZSZxEWX2gRCkZldAI/4uWv27toWfZ1+QXVMHqsQonoo2EG88EaYQlQUZdnlXl+S+JiYr5OvOvGxqaFOfJLOQ2YK2GoXX7KwUDAwuC5Ld5zj98NXJPERQhiNQqGgdu3aeHp6kpOTY+5whNCwsrIy6JueApL4mJifsx+HEw9zIfMGOHlDyhWI2wf+vXXqDWytTnx2n71J4t1MPB1lVVUhhPEolUqj/JIRoqKptoObTb1XV4EGzg0AiE2OhYIdgk/9WaReQw8Hguu5kJev4o+j8aYMUQghhKiyqm3iM3bsWKKjozl48KBJ2/Vz9gPuJT4BT6kv3rlcbN2nW6tngf24P478fJluKoQQQjysapv4mEsDF/Ubn4spF8ltdi/xiT8M+flF6j4dXBcHG0tib6ax78ItU4YphBBCVEmS+JhYbXv1Gj25+blcqGEPlraQmQy3Y4vUtbexpH8r9cDmdQeLfyskhBBCiLKTxMfELBTab/mFu3FQ0199khhdbP1n26i7u7bHXOdupsy4EEIIIR6GJD5m8Jj3YwBcSL6gXcH5SvFjjVr5uNDQw5707Dx+jZSVnIUQQoiHIYmPGbSv1R6AM7fPgI/6mMvFJz4KhYJRIeoB0asjLsogZyGEEOIhSOJjBk3dmgIQcysGvO8lPvFHIK/4rqyng+viaGvJxVvp7DwcjYr4AAAgAElEQVQjq6sKIYQQ5SWJjxk0c28GQHxaPLft3dUXczNK7O6yt7HkuXY+AKwMv2iKEIUQQogqSRIfM3C0dtQcH0g8pC2IWFriPSM6+mKhgP/O3uTs9bvGDE8IIYSosiTxMRN/V/Vsrit3r0DL59QXT28qsb6Pmx09m3kBsCriorHDE0IIIaokSXzMpFf9XsC9FZw7vq4tyMst8Z5RIb4A/H74KsnpMrVdCCGE0JckPmZSz7EeAJfvXgavFtqCq4dKuAM6NnCnaS1HMnLyWH8oztghCiGEEFWOJD5mUsdBvSLz4cTD2s1KAS7sLPEehULBqE6+AKyOuESeTG0XQggh9CKJj5kU7NkFkJqdCv591Sc7Pyr1vgHBdXG1s+LqnQy2RV83ZohCCCFElVNtE59ly5YREBBAu3btzNK+k7WTZnbXheQLEDREW6gq+U2OrZWS59uru8lWRRTd30sIIYQQJau2ic/YsWOJjo7m4MHi184xhZY1WwL3FjL07wsWluqC5NI3JB32SH2UFgr2XUgi5lqKscMUQgghqoxqm/hUBIE1A4F743ysbMFLfc7Vw6XeV8elBn2a1wJglSxoKIQQQpSZJD5m1K6Wupst6maU+kKd1uqvVyMfeO/oe4Oc1x+6zLXkDGOEJ4QQQlQ5kviYUeFFDNNz0sH73nijuH0PvLdNfVfqutQA5K2PEEIIUVaS+JiRm60bACpUxCTFgG+IuiD+MGSnlXqvQqHg7T5NAPhq9wXOyDYWQgghxANJ4lNBhMWFgUt9cPKG/Fy4vP+B9/QPqkNII/Ump6+uKXnhQyGEEEKoSeJjZrZKWwC+j/4eFArw7awuuBj+wHsVCgVjuzZSV7+VTvwdGesjhBBClEYSHzPr7dtb90JBd9fx9WW6v1OjmprjD/+OMVRYQgghRJUkiY+ZvdP+Hc1xUmaS9o1P8mXILNsaPYueDQLgr+PXSMsqeZNTIYQQorqTxMfMnKyd8HH0AeDM7TPg6qctDP+0TM8YEFyX+u52AKw/WPrih0IIIUR1JolPBdDEVT0763TSafU4nwJlWM8HQGmh4JVH1Xt/fbsnlpy8fIPHKIQQQlQFkvhUAI1dGwPw+ZHP1ReevPemJ+VamZ/xTBtvajpYc/VOBn8djzd0iEIIIUSVIIlPBVDQ1ZWVl6W+0Ky/+uvN05Bxu0zPsLVSMjpE3U321a4LqErZ6FQIIYSoriTxqQC6+XTTHCekJYC9O1g7qC/E/Fnm5wzrUB97ayWnEu6y8/QNQ4cphBBCVHqS+FQADgVJDvd2agfthqVXyr57vLOdFc+3rwfA8l3nDRafEEIIUVVI4lNB9GvQD4CI+Aj1hc4T1V8PrwE9uq1eetQPK6WCA7FJ7DydaOgwhRBCiEqt2iY+y5YtIyAggHbt2pk7FACcbZwBWH/63sKFfo9qC5MulPk5tZ1r8HSwNwCjVh6UsT5CCCFEIdU28Rk7dizR0dEcPFj2riRj6lxXvXChinuJirU9uPqqjy/s0OtZU+5tXgoQcf6WIcITQgghqoRqm/hUNEEeQZrj5Kxk9UHg0+qvmybp9ayaDjYMf6Q+AOPXHTVIfEIIIURVIIlPBVF4gPOOy/fe8AQP01ZI1G8frpGdfAG4mZrF6YS7DxueEEIIUSVI4lOBtPZsDcC11HsLF7o31BbuXqjXsxp5OvB4i1oALN1xziDxCSGEEJWdJD4VyKPe6gHNa0+t1V7076v+emGn3s8b1029IvRfx+M5l5j6sOEJIYQQlZ7eic+tW7cYO3YsAQEB1KxZEzc3N52PKD9/V38A7mTd0c7G6jhW/dXSVu/nBdRxonOjmqhUMOLb/YYKUwghhKi0LPW9Yfjw4Zw7d46XXnoJLy8vFIU31RQPpV0t7dT6xPREvOy9oE4wKJSQcgVuXwLX+no9c1Jvf/acu0l8ciYHLybRzleSUyGEENWX3onPf//9x549ewgKCnpwZaGXGpY1aOTSiHN3znHy1kl14mPjAI611YnPry/CK2F6PTO4niuPNq7Jf2dv8v3eS5L4CCGEqNb07upq2rQpGRkZxohFAAHuAQBE34rWXvRpr/569RDk5+v9zFcebQDAH8fiibxUtk1PhRBCiKpI78Tniy++4N1332XXrl3cunWLlJQUnY94OIHu6j26Iq9Hai8+sUh7fPYfvZ/Zxd+DTg3dARi0PILMnLyHilEIIYSorPROfFxcXEhJSaF79+54enri6uqKq6srLi4uuLq6GiPGaqWLdxcADl0/RHpOuvqiXaHuqZ+GlOu5859uqTket/ZwueMTQgghKjO9x/gMHToUKysr1q5dK4ObjcDb0ZsaljXIyM1g15Vd9PW7N52963TY+aH6OD8fLPTLWeu52/FG90Z8/u85tsckculWGvXd7Q0cvRBCCFGxKVR67mJpZ2fHkSNHaNKkyYMrVwIpKSk4OzuTnJyMk5OTucMBYPCfg4lJiqG7T3eWdF+ivpibBfM81cfDfodGPfR+bn6+igbT/wagtrMte6fp/wwhhBCiIijv72+9u7ratm3L5cuX9b1N6KFgw9LopEIDnC1ttMcnfy/Xcy0sFPz4cgcAriVncuJqcrljFEIIISojvROfN954g/Hjx7Nq1SoiIyM5fvy4zkc8vFDfUAAS0hLIzc/VFgz6Vv319GbQ70WdRkijmoQ0Ug90/nr3hYeKUwghhKhs9O7qsihmbIlCoUClUqFQKMjLq1wzhipiV1dufi7B3wcDsLzncs0bILLuwkfe6uNnV0HgwHI9/8TVZJ78fA8AG8eG0MrH5WFDFkIIIUyqvL+/9R7cHBsbq+8tQk+WFtr/LBN2TODQsEPqExtHbaUD35Q78Wle1xkrpYKcPBUDloVzcf4TDxOuEEIIUWno3dVVv379Uj/CMPr49gEgKy9Lt+CZleqvyZfL3d0FsOS5YM1x1BUZ6yOEEKJ60PuNz5o1a0otHzFiRLmDEVovNn+RLRe3AJCZm4ltwSal/qGgtIE7l+DmGfAo3+y6x1vURqFQ5079lu7hwoePY2EhSxMIIYSo2vQe43P/IoU5OTmkp6djbW2NnZ0dSUlJBg3Q2CriGB8AlUpFyzXqRQc/7fopPeoXmnr+/dNwPgw6joPQD8rdxoUbqXRftAuARp4ObJ/42EPFLIQQQpiKyaaz3759W+eTmprK6dOn6dy5Mz/99JO+jxMlKLww5MqTK3UL/dWzvti3/KHaaODhQNC9gc3nElP5Yue5h3qeEEIIUdHpnfgUp3HjxsyfP5/x48cb4nHintGBowE4duMYmbmZ2oJGPdVfVXkQ8+dDtbHhtU6a4wVbTpOWlVtKbSGEEKJyM0jiA2BpaUl8fLyhHmd0y5YtIyAggHbt2pk7lBKNCRqjOf7q+FfaAveG2uP1wx6qDQsLBZve7Kw5X77z/EM9TwghhKjI9B7j88cff+icq1Qqrl27xtKlS/Hx8WHz5s0GDdDYKuoYnwItVrcAwNHakYjnI7QF64bCqb/Ux7MfflbWB5uiWfGfeqmCXVO6yj5eQgghKjSTreMzYMAAnXOFQoGHhwfdu3dn0aJF+j5OPMCIgBGsiV7D3ey7ugXd3tUmPjF/QbMnH6qdqX2baRKfV9Yc4p+3ZKCzEEKIqkfvrq78/HydT15eHgkJCaxdu5batWsbI8ZqrYt3F82xzss5rwDt8fqhD92O0kLB18PbAHDmeion42VtHyGEEFWPwcb4CONo6dFSc3wp5ZJuYb8l2uMdHz10W70Da+FiZwXAyO8OPPTzhBBCiIpG7zE+KpWKX3/9lR07dpCYmEh+fr5O+e+/l2/ncHOp6GN8QDvOByBqZJS2IDcb5nlozw0w1mfHqURGrzoIwC//60g7X7eHfqYQQghhaCZbx2fChAkMHz6c2NhYHBwccHZ21vkI49LZwsLSGrrP0J5npz3087s19eS5dj4APPvlXrJyK9ems0IIIURp9H7j4+bmxg8//MDjjz9urJhMqjK88bmRfoPuv3QHINA9kHVPrtMWqlQw597u6i/8Av69H7q9K7fT6fx/OwBoWsuRLRO6POAOIYQQwrRM9sbH2dmZBg0a6HubeAgedtrurJO3TuoWKhTQZpT6eP+XBmnP29WOQa29ATiVcJdt0dcN8lwhhBDC3PROfGbPns2cOXPIyMgwRjyiBPNC5mmOk7PuG8tTr6P66/kwyMsxSHsfDGyuOX5lzSEysqXLSwghROWnd+IzePBgbt++jaenJy1atKB169Y6H2Ec/Rv21xxvid2iW9ikr/b47DaDtGdrpeTAdO3GqM3e21JKbSGEEKJy0HsBw5EjRxIZGcmwYcPw8vLS2UxTGI9CoUCpUJKnyuPL418ypOkQbaFtoUHl6543yOwuAE8nW959vBkf/B0DwNu/HmPBM0EGebYQQghhDnonPps2bWLr1q107tz5wZWFQb3S8hW+PPYlNzNuolKpdJPOti/Coe/Uxynx4FTHMG12aaBJfH4+dIXXuzbCt6ZsZyGEEKJy0rury8fHp8LOfqrquvp01Ry//M/LuoU9Z2uPT/9t0HYPz+yljWHhToM+WwghhDAlvROfRYsW8fbbb3Px4kUjhCNKE+geqDk+kHDfysq2zhD4tPr42jGDtutmb03vAC/NeViMzPISQghROemd+AwbNowdO3bQsGFDHB0dcXNz0/kI43q91eslF/qHqr8eXmPwdr8e0VZz/NLqQ2Tn5pdSWwghhKiY9B7j8+mnnxojDlFG/Rv254ujXwBwJ/MOLrYu2sIGXbXHVw6Bd1sM6btRbXlx1SEA/Gds5vS8PthYKg3ahhBCCGFM5ZrVJcynrkNdzfFPp37itVavaQsda2mPv+lhsNldBbo39aJzo5rsOXcTgO/2XOS1rg0N2oYQQghhTGXq6kpJSdE5Lu0jTOeLY1+Qr7qvy6n1CO3xPsOs5FzYmhfba47/b8spgz9fCCGEMKYyJT6urq4kJiYC4OLigqura5FPwXVhfFPbT9Uc/3TqJ93C/p9rj7e8Y/C2LSwU/P56J835PycTDN6GEEIIYSxl2qR0165dhISEYGlpya5du0qt+9hjjxksOFOoDJuUFqfF6haa46iRUbqFEZ/DP/d2bX/zCLgZfm8136mbNMexHz0uC1kKIYQwqfL+/i7TGJ/CyYyfnx8+Pj5FftGpVCouX75c5oaFEXV6Q5v4RK6GXnMM3sSg1t78dvgKAPM3n2La480M3oYQQghhaHpPZ/fz8+PGjRtFriclJeHn52eQoMSDfd5d26W18dzGohXq3euOCjfOLLxFg7VbV3y1+wJleHEohBBCmJ3eiU+RrRLuSU1NxdbW1iBBiQcrvIrzzPCZZOVl6VboMkl7nHtfmYH8PKaj5thvmmFXixZCCCGMoczT2SdOnAioN8ucOXMmdnZ2mrK8vDz2799Pq1atDB+hKNGLzV/kuxPq/bna/tBWd6xPg27a47+nQP/PDN5+ez/dBSvPJabSyNPB4O0IIYQQhlLmNz5HjhzhyJEjqFQqoqKiNOdHjhzh1KlTBAUFsWrVKiOGKu73astXSy60UILi3uKCh1cbLYbYjx7XHPdcvIvk9ByjtSWEEEI8rDLN6ips9OjRLFmypFLNgCpNZZ3VVeBC8gWe2vgUAH8M+AM/50LjrC7shDXqMt6OBTvjbCnya+QVJv+i3R/s4vwnjNKOEEIIUaC8v7/1HuOzcuVKTQOXL1+WmVxm1sBZO1V9c+xm3UK/QksLLDDewPNn2njzSANtUrUyPNZobQkhhBAPQ+/EJzc3l5kzZ+Ls7Iyvry++vr44OzszY8YMcnKkm8McCt7yrIhaoVtw/yB0I868+m5UO83xnD+jibkmq3gLIYSoePROfN544w2+/vprFixYoBnjs2DBAr799lvefPNNY8QoHqBlzZYA5ObnkpaTplv4dqG3Lyc3GC0GO2tL5vQP1Jz3XfIf+fkyxV0IIUTFonfis3btWlatWsWYMWNo2bIlLVu2ZMyYMXz77besXbvWGDGKBxgRqN2fa+vFrbqFhcf1/DraqHGM7OSLp6ON5vzDv2OM2p4QQgihL70THxsbG3x9fYtc9/Pzw9ra2hAxCT35u/prjmdFzCpaofkz2uPTW4way4F3e/K/x9Q7tn+zJ1YWNhRCCFGh6J34jBs3jrlz55KVpV0ULysriw8++IBx48YZNDhjWrZsGQEBAbRr1+7BlSuBAPcAzfH30d/rFj79tfb4pyGQcduosbzeraG26eURRm1LCCGE0Ife09kHDhxIWFgYNjY2BAWpty04duwY2dnZ9OjRQ6fu77//brhIjaSyT2cvcD3tOj1/7QnAS81fYkKbCboVvnwUEo5rz2cnGzWewpuYnv2gL1ZKvXNsIYQQokQmm87u4uLCoEGDePLJJ/Hx8cHHx4cnn3ySp59+GmdnZ52PMB0vey/qOtQF4NsT3xat8Oou3fOYP40az8k5oZrjt389XkpNIYQQwnTKvGVFgZUrVxojDmEA/q7+XE29WnyhhQVMjYP59dTn64cZ9a2PvY32R2vDkau80KEe7XyNs4CiEEIIUVbl7n+4ceMGe/bsYc+ePcXu1i5M78XmL2qOc/KLWVPJ1hk8tWOBuLjHqPHsmtJVc/zsl3tlOwshhBBmp3fik5aWxosvvkjt2rXp0qULXbp0oU6dOrz00kukp6cbI0ZRRi1qttAct/6+dfGVXt+rPV5l3K0l6rvb66zoHPT+P2Tl5hm1TSGEEKI0eic+EydOZNeuXfz555/cuXOHO3fu8P/+3/9j165dTJo0yRgxijJSWih1zn+M+bH4is71TBDNvRhefkTnvMkM406nF0IIIUqj96yumjVr8uuvv9K1a1ed6zt27GDw4MGVrturqszqKrDpwiam/jdVc358xHEU929dcfc6LLq39k/bF+HJT4weV+FZXiAbmQohhHg4JpvVlZ6ejpeXV5Hrnp6e0tVVATzR4AkaOmvX0Tlx80TRSo6F/vsd+s4EUenO8gJIzco1SbtCCCFEYXonPh07dmTWrFlkZmZqrmVkZDBnzhw6duxo0OBE+WwcsFFzPG//vAffELnKeMHcY29jyYlCyc/MjcUkZEIIIYSR6Z34LFmyhPDwcLy9venRowc9evTAx8eHiIgIlixZYowYxUOIvhVdfEHhqex/jofkEqbBG5CDjSXW9xYy3HDkKskZMstLCCGEaemd+DRv3pyzZ8/y0Ucf0apVK1q1asX8+fM5e/YsgYGBD36AMIn2tdprjvNV+Q++4ZMA+H6gESNSO/xeL81x0Jx/jN6eEEIIUZjeg5urmqo2uLlASnYKIT+FADC1/VSGNhtatFJeLsx11732ws/gH1q0rgEVHuhcz82OHZO7orRQlHKHEEIIoctkg5tF5eBkrf0hmH9gfvGVlJYwPV732trBcPOsESODcx/01RzHJaXTcPrfRm1PCCGEKCCJTxUW6qt9c5ObX8IsKmt7mHVH99o3PYqvayCWSgu+GdFW55rv1E1k5sjihkIIIYxLEp8qbOYjMzXHwd8Hl1xRodBNfjKNu3M7QM8AL+q52elcazpzC7vOVK51oIQQQlQukvhUYc42zmWvrFBAq2Ha89l63FtOu9/uxp/jOutcG/ndAY5fuVPCHUIIIcTDKXfiExkZyQ8//MAPP/zA4cOHDRmTMKDCb31upD/gbUrf/9M9z802QkS6Wng7s3FsiM61/kvD+ffUdaO3LYQQovrRe1ZXYmIizz33HDt37sTFxQWAO3fu0K1bN9atW4eHh4dRAjWWqjqrq7AWq7Wbl0aNjCq98v1vet5Lgvv2ADOGnLx8Gr+7Wefa+Q8fl9leQgghimWyWV1vvPEGd+/e5eTJkyQlJZGUlMSJEydISUnhzTff1PdxwsRarG5Bqbnu7PvG97zvBpkpxg0KsFJa6KzsDNBw+t+lxyqEEELoSe/EZ8uWLXzxxRc0a9ZMcy0gIIBly5axefPmUu4U5hL2bJjO+Qf7Pyj9hg6v6Z7P9zFwRMVzsLEssqfXgC8i+PnQZZO0L4QQourTO/HJz8/HysqqyHUrKyvy88uwQrAwOU87T53z9afX89nhz0q+oe98qB2ke222M1w/aYTodNnbWPL7650058cu3+HtX48z9kcZRyaEEOLh6Z34dO/enfHjxxMfr1347urVq7z11lv06GHc9V9E+f3S7xed8xVRK0q/4aXtYGWve215JzBBctu6niufDNFNvDZFXTN6u0IIIao+vROfpUuXkpKSgq+vLw0bNqRhw4b4+fmRkpLC559/bowYhQE0dWtaZGDz9P+ml3yDpTW8G1/0+vuuBo6seAODvWlRV3eg9a3ULJO0LYQQouoq115dKpWK7du3c+rUKQCaNWtGz549DR6cKVSHWV2F5eTl0PqH1przB87yArgTB59qZ4Yx/jhY2oKjlxEi1HX8yh36Lw3XnF+c/4TR2xRCCFHxlff3t6W+Da1Zs4YhQ4bQq1cvevXS7rSdnZ3NunXrGDFihL6PFCZkpdSOz7p/7E+JXOrpni9pqf46NQ5sjbvQ4f1vfeJupVPP3a6E2kIIIUTp9O7qGj16NMnJRbc0uHv3LqNHjzZIUMK4tj+zHYDE9EQeW/9Y2W6aXswYm3/nGTCq4ikUuuv4dPl4B1tPJhi9XSGEEFWT3omPSqUq8ssI4MqVKzg7G3+bA/HwvOy1XVRJmUnkq8owYNnaTndLC4ADXxs4suLd37015vtIk7QrhBCi6ilzV1dwcDAKhQKFQkGPHj2wtNTempeXR2xsLH369DFKkMK4gtZoZ1AdH3G82MQWgAHL4OgPJopK119vdObJz/dozsNirtOjmfHHGAkhhKhayjy4ec6cOZqvkyZNwsHBQVNmbW2Nr68vgwYNwtra2jiRGkl1G9xcIDc/t8Qd2zcN3EQ9p3rFlqFSwfphcOov9fn9Kz0b0aVbaTz28U7NuQx0FkKI6svog5tnzZoFgK+vL0OGDMHW1lb/KEWFYWlhydONn+b3s78XKVt4aCGfdS9hgUOFAloN1SY+CVFQq0XxdQ2svrv9gysJIYQQpdB7jM/IkSMl6akiZneczTvt3ilyfcflHSw5vKTkGxtrZ/PxZWcjRFayb0a01RzLuj5CCCH0pXfiI6oOhULBsIBhRI2MKrKezzdR35S8Qajyvi1L9n1ppAiL6tFMOwV/15kbJmtXCCFE1SCJj9DY9sw2nfOWa1qy+uTq4is3LLQ9yZaib42MpfDA68S78sZHCCGEfiTxERpedkVnSS08tJBdl3dxPe26bsGw33TPUxONGJkuLycbAOZvPmWyNoUQQlQN5U58srOzOX36NLm5uYaMR5iRQqEodguLcf+Oo+evPRn85+DClaH3B9rzhY0hO80EUUJjT0fNse/UTTSZsdkk7QohhKj89E580tPTeemll7CzsyMwMJC4uDgA3njjDebPn2/wAIXp/fvsv8Vej0mK4c/zf2ov3IjRrfBhHbh51oiRqa1+sb3OeVZuPj0X7zJ6u0IIISo/vROfadOmcezYMXbu3Kkzu6tnz56sX7/eoMEJ8/Cw8yDi+Yhiy6bvmU6L1S1osboFqm4zi1ZY2la91o8RKS0U3L/G4rnEVMb+eNio7QohhKj89E58Nm7cyNKlS+ncubPOQNPAwEDOnz9v0OCE+ThaOxI1Morf+v/GkCZDiq2z4NRqmHa1aMEcF/j3g6LXDWhiT/8i1zZFFbOfmBBCCFGI3onPjRs38PQsuqt3WlpayVsdiErL39WfGY/MYFTgqOIr2DjAiD+KXt+9AG5fMlpc47o34vuX2hM1uzf13LS7te89f8tobQohhKj89E582rZty6ZNmzTnBcnON998Q8eOHQ0XmahQJrWdVOTaDzH39u1q8Bi8W8yO6UtaGi0ehULBo409cLS1Yvfb3TTXn1+xz2htCiGEqPzKvGVFgQ8//JC+ffsSHR1Nbm4uS5YsITo6moiICHbtkgGmVdnxEcdpuaaEZMaqBrx5FD5rZdqghBBCCD3o/canc+fOHD16lNzcXFq0aME///yDp6cne/fupU2bNsaIUVQQCoWC4yOO82bwm5prOfk52gpufjAjEZ76Qnvt2nGTxPb9S9qZXr5TN5VSUwghRHVWrnV8GjZsyIoVKzhw4ADR0dH88MMPtGhhmo0qhXkpFAqauDXRnG+OvW8NHUsbCBygPf/qUZPE1blRTZ1zSX6EEEIUR+/E5++//2br1q1Frm/dupXNm2Uhueqgc13txqTv7nmXy3cv61awvm8XdSNPbwd1QvZ0cN37mjV+u0IIISoXvROfqVOnkpeXV+S6SqVi6tSpBglKVGwWCt0fm8d/f7z0G+7EGTEarcVDWvHZ88Ga85dXHzJJu0IIISoPvROfs2fPEhAQUOR606ZNOXfunEGCEhXf6MDRpVeYnaw9NuLsrvv1D6qjOQ47Zbr9w4QQQlQOeic+zs7OXLhwocj1c+fOYW9vX8wdoiqa2HYiAe7aBPix9Y9xK6OUNXQW+sOt83Bpr9E3NH25s5/mODcv36htCSGEqFz0TnyeeuopJkyYoLNK87lz55g0aRL9+/c3aHCiYnvcT9vFlZSZRNefu3L+TqHVuy21W5qQeh0+bw0r+6g3NDWit/s01Rw3encz+fky1kcIIYSa3onPggULsLe3p2nTpvj5+eHn50ezZs1wd3dn4cKFxojxgf766y+aNGlC48aN+eabb8wSQ3V07MaxItcG/L8BtFjdgiWHl0DrkSXfnJdTctlDsrbU/bHeHnPdaG0JIYSoXBSqckx9UalUbNu2jWPHjlGjRg1atmxJly5djBHfA+Xm5hIQEMCOHTtwdnamTZs2RERE4O7uXqb7U1JScHZ2Jjk5GScnJyNHW7XczLhJt5+7lVi+4clfaPR5h+ILh/4KjXsZKTK4eDONrgt36lw7+0FfrJTlWsFBCCFEBVPe39/l+kMK7/kAACAASURBVC2gUCjo3bs3U6ZMYdy4cWZLegAOHDhAYGAgdevWxcHBgb59+/LPP/+YLZ7qpGaNmhweVvKO6AP/ehbeji2+8MdnjBSVmm9NewbeN739xVUHZYq7EEJUc+VKfMLCwpg+fTovv/wyL774os5HX7t376Zfv37UqVMHhULBxo0bi9RZtmwZvr6+2Nra0qFDBw4cOKApi4+Pp25d7S+4unXrcvVqMTuGC6OwUloRNTKKPwYUs1EpgJ2beobXrDsw7r7p5Rm3Ib/o0giG8mqXBjrn/529id+0v/GduonlO8+XcJcQQoiqTO/EZ86cOfTu3ZuwsDBu3rzJ7du3dT76SktLIygoiGXLlhVbvn79eiZOnMisWbM4fPgwQUFBhIaGkpgoU5UrEj9nPyKHRdKuVjud66tPrlYfKBRQszG8WGjxy//zhffdYHU/WNAQZjvDjo9g/9eQVMKbIj00q+3EL/8rfuPc/9tyioxsddJ15vpdfKduIuL8zYduUwghRMWm9xif2rVrs2DBAoYPH274YBQKNmzYwIAB2i0POnToQLt27Vi6dCkA+fn5+Pj48MYbbzB16lQiIiL4+OOP2bBhAwATJkygffv2vPDCC8W2kZWVRVZWluY8JSUFHx8fGeNjQOk56XRYqx3bEzUySluYmwXzPMv2oNnJ8FkwJF2AQd9Ci/J1j+Xlq2g4/e8y1b04/4lytSGEEMK0TDbGJzs7m06dOul7W7lkZ2cTGRlJz549NdcsLCzo2bMne/fuBaB9+/acOHGCq1evkpqayubNmwkNDS3xmR999BHOzs6aj4+Pj9H/HdWNnZWdznm+qtBaOpY2ZX9QToY66QH47aVyx6O0UHBx/hOcnteHWk62D77hnlXhsTSduVnzZkgIIUTlp3fi8/LLL7N27VpjxFLEzZs3ycvLw8vLS+e6l5cXCQkJAFhaWrJo0SK6detGq1atmDRpUqkzuqZNm0ZycrLmc/ny5RLrCsO4mnrfmKvJZVzhe8MYg8ZhY6lk3/QenJhTcmLsO3UTZ67fBWD2n9Fk5uTT7L0tBo1DCCGE+Vjqe0NmZiZff/0127dvp2XLllhZWemUL1682GDBlVX//v3LvHiijY0NNjZ6vHUQ5RI1MooWq1sA6r28tj2zDfca7iw/upxHaj9C+xe3wnclJyAARP8/o8TmYGPJ/KdbMPX3qGLLe3+ym9rOZX8zJIQQovLQO/E5fvw4rVq1AuDEiRM6ZQqFwjBR3VOzZk2USiXXr+suQHf9+nVq1apl0LaEcfX6Vbtmz4qoFUQNL7r44QNl3IEaLgaJ57n29chTqXh3g/pn+DF/D3aduaEpv5acqVM/NSsXBxv1/1xup2XjYmdl8J93IYQQxqd34rNjxw5jxFEsa2tr2rRpQ1hYmGbAc35+PmFhYYwbN85kcQjDu5mVRM2CjUyvHganOuB4L5md7Vz8Td/1gbH7DBbD0A71GdTam7x8FfY2lkz7/Tg/HSi+67P5LPVstNe6NtRMhZeB0EIIUfmYfRnb1NRUjh49ytGjRwGIjY3l6NGjxMXFATBx4kRWrFjB6tWriYmJ4bXXXiMtLY3Rox+wO7gwu1DfkruyXt32qvakbmtt0gMwYHnxN92IMVBkWrZWSuzvvcmZ+WTAA2qjs/7PlhMJBo9HCCGEcZVry4pDhw7x888/ExcXR3b2/2fvvMOaOr84/gkhEJZswYXgXrhx711H627d1da2apfWttRVrVatraP+RG3dq1Vbte699x4obsW9FRQRZOT3x4UkN7kJiQvU9/M8fbjvvC9UzeG853zPU9nY4sWL7dpry5Yt1K5tXvagS5cuzJw5E4AJEybw66+/cvPmTUqXLs348eOpWNFCKQQ7ESUrXh6mae2mHOt8jLtP7uLr4ktiSiKHbh2ipH9JYp88wDfmCi5xd+DkMp6cWIxL+h/Typ9Dze9Aa8Er9AJITE6h1aRdVM3vxx/bLlic90mNfPRrXPSlnUMgEAgElnnWz2+7DZ/58+fTuXNnGjZsyLp162jQoAFnzpzh1q1btGjRghkzZth9+MxEGD4vl9jEWKrNr0aVnFXI55mPuSfn6sfyeebjQuwFPJw8ePT0kdnayC6RtFvxAcfvnWDg3fu0fRRnGEy/JnvJBIevtDiWy8uFneF1Xsk5BAKBQCDnlen4DB8+nLFjx7J8+XKcnJz4/fffOXXqFG3btiUoKMje7TKNiIgIihUrRlhYWMaTBc+Mp7MnkV0i+aP+H3xf4Xv+bfavfuxCrORNUTJ6AJJSkzh+7wQAQ/18Xv5hFbg4ojEAxXOa/6W6FvOEIctPvOojCQQCgeA5sNvj4+bmxokTJwgODsbX15ctW7YQGhrKyZMnqVOnDjdu3HhZZ30pCI/Pq0Wn01Fydkmb5pYLKMfBWwf17ciLlw2D314AN8t6TS+DbjP3s+mUeamUWoX9mfFhmMjyEggEglfIK/P4eHt78+iR9Bt6rly59CntMTExxMfH27ud4C1DpVLRoWgHm+YaGz1m/JrP8thLYvqHYRwaWJ/IwQ1k/VtO36HvP8de+XkEAoFAYD92Gz41atRg/fr1ALRp04avvvqK7t27065dO+rWrfvCDyh48wivEM6AigPsXrfdJfNFBX3cnPDQapjQvoysf9Ghq1y69ziTTiUQCAQCW7H7quv+/fskJCSQM2dOUlNTGTVqFLt27aJgwYIMGDAAb2/vl3XWl4K46socklKSKDu3rKzvz/p/4qR24sM1H1pcJ7vuekUBzpZQCnwOf6cIn9XMnwmnEQgEgreLV5bV9aYhDJ/MI+5pHE+Sn+CmccNZ7YzaQQ3A5KOTiTgSobhme5FeeK3+XmpksuHTaNw2Tt00D8wWwoYCgUDw8nllho9arebGjRtkz55d1n/v3j2yZ89OSsrrVclaGD5Zj6TUJDZd3kSgWyAXYi4waNcg2Xitx/H87/Zd+DEGMjmgOCEphfZT9nDocoy+b0rn8tQvFmBllUAgEAiel1cW3GzJTkpMTMTJycne7QQCMzQOGhoGN6SUfyneK/Ce2fgWN1fp4c6pV3wyc7QaNf9+VoXCAR76vu6zD2TiiQQCgUBgDZtrdY0fPx6QsnKmTp2Ku7u7fiwlJYVt27ZRpEiRF39CwVuNg0rZNk8CNMmJr/YwFnBwULG2dw1ZzM+eC/eolO/VptsLBAKBIGNsNnzGjh0LSB6fyZMno1ar9WNOTk4EBwczefLkF3/Cl0RERAQRERGv3dXc20jN3DXZenWrrK97YHZmPr6bSSdSZt7HFekwdS8AH/y5hwrBPiz8rDKpqTp+XHaC0FyetA3Lk8mnFAgEgrcbu2N8ateuzeLFi1+77C1LiBif14OvN3/NxssbZX2RqnzQeWkmnUgZ00yv6JFN2Hz6Nl1n7Ne3BQKBQPD8vLIYn82bN8uMnpSUFI4cOcKDBw/s3UogsJmxtcaadwZVefUHyYBfWoXK2g8TkvRGT3pbIBAIBJmH3YbP119/zbRp0wDJ6KlRowZly5YlT548bNmy5UWfTyAApNiyyC6R9CjVw9CpzQYHZ8Lf7SGLqDK8HxZE9YJ++nbJwetk45fvCXVzgUAgyEzsNnz++ecfSpUqBcDy5cuJjo7m1KlT9O7dm/79+7/wAwoExhgHOyedXg3Lv4LTK2GIF5zbkIknMzC1S3mLY1cfCMNHIBAIMhO7DZ979+4RGBgIwKpVq2jTpg2FChWiW7duREZGvvADCgTGNApupH++cG2XfHBuq1d8GmWcHdUWx/7YdsHu/XQ6HQ8eP32eIwkEAoEgDbsNn4CAAKKiokhJSWHNmjXUr18fgPj4eFmml0DwMgj2DNY/PyXrVkOvEOKj2H/4cgzB4Su5GZtg814Nxm6jzND1LDp4laEroth1LmtlswkEAsHrhN2GT9euXWnbti0lSpRApVJRr149APbu3St0fASvlEsaBTWGm8df/UEUMC5i+m6pnGbjlUZsNOuzxNnbcQB8889Rpu24SPu0lHmBQCAQ2I/NOj7pDB48mBIlSnDlyhXatGmDs7MzIJWyCA8Pf+EHFAgsscdFS9PHJjEzk6tmeg0vgOweWo4OakDskySCfF2pXtCPb/89JpszdfsFGpUIJLe3ayadUiAQCN4+RJFSoePz2tHg3wbceHyD7+89oOPDR9BjF0xKS23XekL4ZesbZBJK1dwBzg9vjNpB+dpOp9MR8sMqs/7c3i7s+L7OCz2fQCAQvE486+e3TR6f8ePH88knn6DVavWlKyzx5Zdf2vxygeBZKBtQlpUXVpIC3FE7cCzxJnU886CKvQIJL9Dbs2sC7JkEXx4Gx+evQxc5uAE/Lj3B4sPXZP3/Hb6GgwP0XnCUmV3DqFXYUAB4+1nleJ6rD54893kEAoHgbcQmj09ISAgHDhzA19eXkJAQy5upVFy4YH/WSmZgXLLizJkzwuPzGjF412AWnV1E8cRETqRdtQKsvXKNnMkp0Pg3KPchqDXP+SJP6Wu+2tD5v+fbK41rMU+oOnKT1TmLelSmXF4pOHrvhXu8/+cexXlCBVogELzNPKvHR1x1iauu147QWaEWxyIvpl1zqZ1h4O3ne1G64QOGuKE7p+GPGlC0GbSa+kzbWrryMqZnrfx816gIy45e58u/DwOSobPtzB06T98HwOKeVSgb9GaUjhEIBAJ7eWUlKwSC14IUOyq3P4iWjJwJYYa+uDvKcyMqQHICRP7zUgUTJ245T+TVWL3Rk46xKvS8PVkzlkkgEAiyMjbF+PTp08fmDceMGfPMhxEIbGFcrXF8veVrxbG7Dg74paZKjcf3wM034w1/L5W2+Iyhb+c4+ZzjiyFfLXnf4XlQoJ5NZzbmg7A8zN9/JcN5zSbsMOtTqQxB0AWyu9v9boFAIHjbscnwOXxY/lvnoUOHSE5OpnDhwgCcOXMGtVpNuXLlXvwJBQIT6uata3Gsdt7chuuu06ugbKdne4mricH0b1fpq9YLEmKk59yWS1NYY2SrkrQpn5uAbFoG/neczacteJcsUL2gH9vP3uVunB1eLYFAIBAANho+mzdv1j+PGTMGDw8PZs2apa/S/uDBA7p27Ur16tVfzikFAisMrzacfjv6mQ8s+9x+w+eXYPj6OKSmKI+nGz0ATx/bt7cR6cHLM7pW0PfpdDr2XbyvGMz8a+uS+uf0TK9pOy4ysGmxZz6DQCAQvI3YHeMzevRoRowYoTd6ALy9vRk2bBijR49+oYcTCGyhWf5mVM1ZFYACXgWeb7MnD2BELtg8LOO5m3+Gkyue731GqFQqKuZTvpprUz7PC3uPQCAQvM3Ybfg8fPiQO3fMXfN37tzh0aNHL+RQAkFGuGvk8S1R96IAOBdzDpxfXHZehimPCzpIgdGWPETPgdpBxamhjbg4orGsv1tVy5ISAoFAILCO3YZPixYt6Nq1K4sXL+bq1atcvXqVRYsW8dFHH9GyZcuXcUaBwIy4pDhZ20drKAoamtOL9a4ulhffOArXj0gGywzLWjjDfL0pGRLEDVuK7854J+M5NrL7hzp8VjM/276rjVajlgU0AzQvY6j9lZSS+sLeKxAIBG8Dduv4xMfH07dvX6ZPn05SUhIAjo6OfPTRR/z666+4ubm9lIO+LISOz+tJ5J1I2q9qzweFP6B/pf76tmxOepDzhyvBwRGCKsGjWzC6kE3vCA0JMtsrBTiodaZY4lPcTf/q1P0RKnwCzi832yo1VUe+foYyFulChidvPMTJ0YH8/iLbSyAQvPm8cgHDx48fc/78eQDy58//2hk86QjD5/XlacpTnNRSKYmE5ATC5oXJxo9evCx3afY5CQdmwLZRGe6dBJRVMHy+8fdlnbv0Z3395WsEpphcceUoDZ9utft7sRdjEcTOlfMye/clfVsoOgsEgreBl1qrSwk3NzdKliyZ8USB4CWRbvQAaB21ZuOTvTzpGWNUu2tMUcV9UoF52TyoWqob+bb/DsCAnPJg4p4B/nzyzhTWbTXUolvi4UaPmIfyzW4csfO7eH6MjR6A83fiqDva3Pg69/M7OKqFZqlAIHi7eWv/FYyIiKBYsWKEhYVlPFnwWjLJ2zPjScAQPx9G+Xrz3tUloHGF0DakFpbH7Gx3daHTVnkBXo9UC87SxBcc5J/wEC5uh0c3pbikwZ7k8rIcw6Rk9ABM2X7xxZ5LIBAIXkPeWsOnV69eREVFsX///sw+iuAFcazzMSLqRti9brGHUUxM/xvQaioVclSwvCCNX3y9SVYaGJFb3tbpYOsoOJVxjS5F5reHWU1hdGF914ovqtm9zYnrkvfr9qMEvpp/mAPR9/n34FWWHb3+bOcSCASC15BnvuoSCLIaKpWKGrlr4K5xN8v6spUhu4dQO09tftr9k03zy6TFAZnFE+l0kJ6NdXGrpPkDhmKn9hC93azL281JYaJ10ktcfD3/CLvO32PpEYPBE77oGFE/NbL/bAKBQPCa8dZ6fARvLnMbz9U/d8gRoKzF4xWk1Mu/Z/6l18Zedr/zt8YmytFDvCD+vvRsqeDp8zClLot6VLFrybgNZwHYdf6e2Vj80xT2R99XXKfT6Vhy+CrRd82Vqmftiqb/kkhRPkMgELw2CI+P4I0jxNMg8HdM60yj3DkJSUpi8q070H4hO5/cIFuO0qyKXkvDvA1gTefnfueck3OZExLE3Os3KZX4VOocFSJ5eK7uM0x8fBfc/JQ3sYdrByiX16Ce/mWdAqBSMX7jWX2fk9qBpyY6P9aSOCM2n2NmV/MrvgOXHtB7wVFAyhhLzyjrVjWE6TuluKF5ey+z5uvqFAkUmZECgSBrIwwfwRuHg0ruyLyuceS6xpEz1XrhnqMEny3uC2nJV3NPzlXY4dnpmDPQoB+Uzr4/Dc+xV+wzfDJQmzgwoB47z92lUYlAnNQO7L1wj70XJc/NmZ/foe3k3ewz8uRcffDE4l7bzph7pnafv0e7KYbaYbcfJeif042edBqN286MD8OoXSS79e9JIBAIMhFx1SV4I2kc0tisr9W15Sw6t9iufQLdAvXPQ6oMAaBhcENaFWxlcc1DByOlZdNSFg52/q5xM9LyWPJT/Nydea90LpwdJYXnBZ9W5uigBpz9WcpKW/hZZaoXNBhan/992OJ2SklqxkYPQORV6zFKXWfuZ33ULX07JVXHd/8eZcnhq1bXCQQCwatCGD6CN5LwCuGK/X8e+1OxH6Bijor6Z09nT36u9jOrW66mY9GOzG86n5YFW3Ko4yF+q/kbg6sMxtXRVXGfqnmNNIBWfYsOGO/tyTpXF3gab9838vi24blMR1K+OGho75mouMTTVYPGSK+nVmGDB+bolRilJXqeJlsvgfHRrANWxwGWG2WJDV0RxcIDV/VXZQKBQJDZCMNH8EbirfXOeJIJY2qN0T/v+GAH7+Z/F0cHR76v8D3FfYsDoFFr9HPG1R5nca876YbHgWns1mqZ4uXJNwH+sOFHiFqa4RWWHkctN9VqFgXkZV+FLpRe0cJQSiNbTutr0+hWNdjq+OqvquufY58k6Z+fUdSdSvl8eZyYzNTtF5i5K1rf/+RpCidvPCQ4fCUHLykHUgsEAsHLRsT4CN5Ysrtm53b87YwnAgubLiSbUzYiu1i5WjKhcs7K7G2/F1eNK6fvn6b18tb6sTpBuZl+4xZhCYncdTQUOdVd3o3q8m5oPglKt1faVk7SE9rkCiRGrYN1H8nHUhVVhMwwLXKaTr2iAYxvVxpXJ8M/A2E/b9CXvIh/+mwV5/stiaTfEvOf41/7LjN0RRQArSbtFqU1BAJBpiA8PoI3lvIB5W2eaxzLYw+uGum6q7BPYba9v0021i1HAAD9/X31fdGaNCPjvx62veDGEWIUqsNP8/SAJw9sPmfxnPJsq4ohPkztUl5m9KRz5EoMKak6Fh+yHJfj5+6sf87j48JH1UIszk0n3egRCASCzEQYPoI3lso5K1scq5W7lj77q0PRDs90NWaKLXvEGWec/dMVrqbF7MTdhg2D4UG0fMGpVSgxzscbHtuuD2Sc+g7QqlxuCzOhecROBvx3nIFLT1ics7dfXf3zzdgEBjRRroMmEAgEWQ1x1SV4Y2kY3JBFZxZRJWcVwgLDuBZ3jQbBDThw8wAVc1SUFTl9Ubxf+H0WnF6gb0c6yd/xyMHI8DmxWPpv0AP4raDUt2OsXN35+iEIURZbZMdYqDfYpnOZ1vbKptVYmCnx9z55Sv7uH+qQw1O+R+96hRi74QzLPq+GSqViaa+qvBex06bz+D6D8rRAIBC8CITHR/DG4uLowpzGc+hRugflA8vzXoH3cHF0oXru6i/F6AHoX7G/rN0+l/wKbZmHG9/6+xJnHHdz/4J8k8GecPcsHJ7HbYVrrnRkafMZ0La8vNp8iJ+brP1Hp3IW13aoGGRm9AB8Va8g0SObUDSHdI2W/tUW8qeVz/h732WCw1ey/exLULcWCAQCBd5aw0dUZxe8DFQqFetbr7c4vtLdjTXubvQINBL5m6BgdEwoD0t7sstFq+/yc/FjXweDCvS8bB42n8u0tld+f7nh06BYgMW1xXPaVuXeydGBRT3MrxfnfVzRrO/+Y0nd+ofFUhB0p2n7zOYIBALBy+Ctverq1asXvXr14uHDh3h62vYPu0BgCwGulo2IdI5ondmrdSY08SmuVtLGcyUbMrc2tdkky9AKSkqWF0PNAHdnR+ISk9n6bS0c1fLfeSxlfgEE+yrrFSlRLq8PF0c05klSiixwOnJwA7QaNf8cuEq/JZGcux33zOnyAoFA8Dy8tYaPQPCysGZEGPNxWtZX5MXL6ICrjmpyJ6dgvPpJ2l7FvIvo922QowrrbuwiRu0gZXa5+kiT1/wAWi+o9b1hgyl14NpB6LGb40MaWj2Pg0pZvTku0UrafFICPH0MbobMNZVKZZYt5pEWU5TL23Bl9tncg7I5Kak61HZc3wkEAsGz8NZedQkEL5PPS38ua/tqfS3MhLtqB0qGBNE4Ty5KmgQyH3eW0sZVDoZYn2weknDhQa0WZqZp4WwYIik5bxkueYHOb5Ziha6lGReTKsOl3dJzaoo0nvBQmjPYExJiOT6kId2qmqel17FWe+vnAPg1Hyz5DFIy1hWqYVQ+Y+2JW7IxqwbWa8ble/EZqmALBILMQRg+AsFLIKe7XFV5VUvltHSACd5eFscmeUvXsCfuGVLL10avBWC9myvcjoI9k2CHQXWamEswp7n5ZjvGSl/3TJLGRxoFPI8MwtXJke8aFTZb5pgYA78Ew8ahUsfBmZKxdNXIY3P0b9j3h1R93grWvGG/bzhrcex14eLdxzT933Zq/LqZQgNWi+s8gSALIgwfgeAl0Ci4kf55RPURuGpc9UVOTVnk4S5rh4YEsU/rbChNYUIBrwLyjjUmdcl+L6V8KPc0z826/srjcXfQatR0qpSXxqGBrO9dg+3f1Yadv0tXatt/k+Yt/0r6OrWOfP3afvBrfrhz2tCXlCAZSQs6Kb/TiOk7L3LnUSLro26RqnTn9pJ4/ByepmNXY7h49zEACUkp1P5tC8evPdSPj1x96rnPJxAIXizC8BEIXgIatYZ/m/3LgqYLaJqvKQAtC7Zkc9vNNq3/KIflAOnWhVpbHLOKTwbqypt+AmBo8xJM7FCOggEe5HGKg51GNclu2FBsdEUfw/N/n0lfTy6TruAOzSZa255O6nWKS5tH7KT77AP8vf+y4ri9rDh2neDwlYxYdVJxvPHv2yn+41qCw1fata9Op+PK/XjenbCT2r9t4fbDBEatOW02b/tZ6x4wgUDw6hGGj0DwkijsU5hivsVkfX4ufhZmW2de43n654qBhvTwp/ZssvEn6+MJseZ90+rL27HXMn5PmQ5wcoXk6TmxxNAffw+WfQHAUM1MxaXXYp4AsPTIdbOx8EXHCA5fyYPHtn3XJ67H8vlfhwH4Y5tcKykhKYXg8JVE3XiotDRDqv2ymeqjDEZsheEbmb7zotm8qBsPxXWXQJDFEIaPQPAaEOoXqn/2d/XXP8/wMogGLnF3Y4OrXGjw8wB/GuXOib7m+tN4yy+JWmreZ1pCY367jA/7Xw9Y0MG8/9DsjNemse/ifVYeuyEzGubvvwJAmaGWdZIWHbzKjjQvS5PxOyzOa66gMG2rgZKaqtMbaLYQvsj2wrcCgeDlIwwfgSCLkNMtp1lf1xJd2dN+jywo2MGo3tcEby8OOzsR6eTEIH9fegf4owOSkGKFtrq6cE3jSNmQIO46OMCeiSQB611deODgQGhIEKEhQZzTWC9h8ULYqBzjVN+CeGKvvw4R8sMqUlJ1NsXhnL8Txzf/HKXjtL1W5+08d5dTNx+Z9W85Y109+tDlB9QZvYUjV2MyPIsxCw5csWu+QCB4uQjDRyDIAsxqNIuVLVfyW83fZP19yvXBTeNmYZVE55yBstIYt9RqyioERi/I5gGuvkzx8qRPgD818hoKlbbInUN6SE0xLLD1isbNH7IXy3ieETpX6covG48ZlWMzblj2oPRecIR90ff17UIB7orz7sUZrsDO3TY3bA5ekqrZd5iqbBh1nbFfsf96zBN0Oh0tJ+7iwp3HtJy4y+JZLZGU8makth+5EkNw+EpaT7L/ZyAQZBWE4SMQvGKOdT5Gj1I9GF97PHva72Fv+72UDSiLo4MjDYOtiwzawnfZlTWD9rhoYWUffYq8IklGV2FPpWylVGC5mysXNeZ6pzM8PQj3dCHh4w2gsv2fE5VvARb1qMIxbXe8dw7jhPYji3PXR92SGSU5vczrhgHEJeov9Kg3ZpvZeKtJu7gXl2hVJDHFJJts6ZFrVBm5iW8W2hDUncaBAfXMxCIL9l/NsBVRNu+RVUm/IjyQZkQKBK8jwvARCF4xKpWKnqV7UjuoNm4aN1w18pIQOz7YQXiFcLa/v93iHv4u/hbHDmu1iv1HtM7odJY9Dwe0zvIA55vHAMlg6pfdj3dzS1dxg/18CA0JGdwLyAAAIABJREFU4oqjI2N8vFnpDGF/V+LqJxst7m3GlT2Uy+tt09QnSSmydrCvsgdszPozGe5VbtgGmXFjWrV+6RF58HZ6fM7iwzYEdafh5+6Mu7OjWSWRqTvMg5+PXonh1M1nC7B+1bxJApOCtxth+AgEWQxPZ086FO2Al9aysOHCZgufae9bVqq9/8/bE2a/Z+jYNYHTGg2fGhVUfeDgoNcdapxHHpP0zrouNMydE7MLsr7npK9qZ8hZxtB/ftOzfAvM3BXN5lO3ZX1JKaky/Rxb+au7vIDqjdgE/XNySqqZ0WVKkUAPKoT46Nt+7oZisDu/r6O0RM/6qFu8F7GTRuO22xUsnVmU+HFtZh9BIHghCMNHIHgNeda0+LVulguOHtJq4d45KQ39+mE4vZLW6bE/adz6fLfV/a9rHPm+9qcw4A4MjiX1xwd02Po1k5qPhIG3OV5/AKEhQZxw0sCcFrK1znYk53edabj6mrr9AgX7r7Z5rTF5fd1Y3LOKvv3rWoMWT+Q1hfR+Iya0L8Oar2swu1sFfV9E+7L65xye5p63L/4+zJX78dQbs5Xusw/o+39cevyZzv+quHLfPBtw+1nrweACQVZFGD4CwWvKh8U/lLW1avMP2nfzvytrn3R2MpujyJ+1FLvbLG+T4dJAt0D+PreI0FmhlJpdimN3jzHx6ERSUlNot603AB/kymG27nMfgzHTroKyarUxOp2OUzcfMmylsjhhOsbGiBJlg+RXbsHhK/l5ZVSGxWZVaeVktRo10SObcH54YyrmS4uvir+P0urlR69TfdRmzt2Ok/UH+VgPYM9MEpNTaKUQzNxp2r5MOI1A8PwIw0cgeE3pXa63/tnb2Zud7eTaNJvbbmZApQHUyWO4clnpLv+AjagbQYCrIZ08yWjsWWX3ZpyYwfC9w836111SVmtO54v4CP5s4sX5FtcY8W4hZnQNszo/5IdVNBpnOQ4qnWI5syn2d66cV/9sGuszZftFs0DnjPZVO6jg7jmY1QxGhcAQL0JzKmegmRKaW/mMWYEm43dw+1FiZh9DIHhhCMNHIHhNcVA50KpgKwCmNpyKk9qJLW236Mf9XPxwcXRhbO2xiuuPdDpCjdw1GFl9pL7viVHG0+MMPB728t227zKc02BjY9Srv4U9k6hd2EpVeBuZ0rk8To7K/8wNebc43L8Igz35McQ840rJy5FO/WIBhPi5ScHgSWnxOY/vwoRycNGQUbY831KqFcj4WjIxKeumu5t6p4y5GycMIsHrx1tr+ERERFCsWDHCwqz/VikQZGUGVxlMZJdICnkXAsDXxZfILpFEdjGoBTsopJmX8yqM2kEKdC4XUE7fP9/DQ/8caeO1WD7PfDKvki3kSZJ8S0ecnagelIvLjiap8pf3AHBqqKHYayHVFfo6LrD5HdHD6lE/6gdyjQtksONMfX//xkVZ1qsKqqPzYXxpABqctFC41YQh7xbn6I8NmPJ+Edg5HkYGwc+BcOQvqUCrKQemMbedQr8JCRkEUWcWSmrWjUMNmlHGcUoCZTZE3WL8xrP6tk6n454wGDOVt9bw6dWrF1FRUezfryxaJhC8ybTKazAojGNZ/ufjRWhIEEednVjqYfmaplKOSvqYomq5qvFrzV9pkq+Jze+/kqYU3SlnIDFqNU1MMsRISYSEh2g1amoXllL31zl/z+eOS1niNMjq3iF+bqzvXQOGZYfjiwD40NFwzda9Rj5KJhw0FFC1gy5VgvF00cCIXLB+oGHgvx6WF03J2CjcH501dXESTDxR/35WmQ/CDPFXhy/bp2L9tpGSquPj2QcYs/4MH/y5m6SUVDpN20e5YRuoMcq2gsWCF89ba/gIBG8TDfM2kLWX3bBcxwqgY85AWTzQsc7HCK8Qrm//VvM3FjZbyDflvuGrsl/hpHZiRLURdp0pVEFdWs/5TTAyD+h0fNOgMP4YPmDLOJyzuGxL41g2t9VSMMDD4hxSkmFeK7PuAqqrVs87unUJKYYnJcnqPDNiLil2R49sQtEcUmxPNpdXUDLkGTDO3MqmdaR8sA85vZR1okC6+goOX0lw+Er+s0P76E3lupFMwZ4L9+kwdS87zkm15C4rZMo9DympOiZuOUfU9ddDFyozMZdiFQgEbxx7bsrLNHxZ/hu71qtUKjoU7UDbQm0B0Kg1eDp7EuIZIptztPNRzjw4QwGvAiSnJqNSqXBycGLR2UUU8SlCYe/ClJ2rnGWVoFKhNb1aGeJFicGxbO9ZDKZbP+PC1v4Er2gvNQabp6J/VDkX71fKD6uVY402OH9HcMJf8u+bVI519+d4Sh4qb3wfVjxbwdFobXuqJY7jqk4etxTk48LJG7HsPn/3mfZ92Xwy56D++fAgyXjO5SWXRDh6JYZSeSTNqTaTDXIHXy84QvMyuV7BKbMuKyNvyNr7Lt5XnHflfjyPEpItBuLbwu8bzzJ+41lGrTlN9Ejbva9vI8LjIxC8BaxquUrWNlWLtlYPrGx2g6GiUWvQqC17JxxUDhTxKYKjgyNaRy3OamdUKhWtC7WmhF8Jq2uneEr/6Jv5U7aOQruip6FdsIHpDL5vVIQKXkb1uf7raTZn4LkPKBTgAQemWTxDNuSBvF3Va/GY05DKx3+CWzYaPUGVobx5CY4dzl8bnr+vDfcv8sf5ukRrO3DzXta86jImvdSHi5OayR0NcWHvGVW6v3j3sWxNVvQ+TNxyTu+VCh38YkUZo64/5Le1p/Uq184WAuvTqTFqM8HhK6k+ajONx2/n1sMEq/Otccao8O7MnRcJDl/JoctZ/89VZiAMH4HgLSCbk/w3yaBs8mum3e0sCxN+FGq5jtaL5E9vTyZ6eVI1b25OOxkZSJt/httGWVfeIazrXYPqBf34pEY+ZnWrwCc18iFLwD8yz/wFj25I4oxW2Fjzgqw9SDNHejg23/ZvpNsaaDoGOi0xGxruOIXoH0qT29tVH1gNMFIz5bVQb04nv7/BUK6UT1KuTlVI/288PmO5gVfNqDUGkcpHCclmKuDPQ+Px25mw+Ry/GQlhWsP0uuvQc9RAK5DdEJM3eLn09+VZCuq+DQjDRyB4S+havCuOKkcOdzqMxkHueVGpVGaCiOnEJ73YWISxtZTT6wEmeXvyxMGBCC8jAyUg1GSWjkIBHsz5qCL9GhelZiF/yRsx1zxuJ0O+PAJ+hfRN/70j8SQONSm4YONv35V6KfeH1DTrau+4WSoLYmKAxeuc+feA9RijrIRGbfjoqFFICj4/fl1Z6VopMyyzOKFwRmMV8BfFzF3RAOw6f8+udT3mHaLLdPuFIWPjk5iwWTn2bdOpW3bv96YjDB+B4C2hT/k+HO58GEcH5dC+T0p+QuOQxmb9dYLsS1XPiHp562U4RxbrY3rFtO9PeBBtaD+Ihi0jeSZ8QqC7PLvmqPYTzms7Ud/feskKWs+QYokaDDX0tTeqoeZgoS7avbNmXXtTizJ2wxkOXlKOAckMjA2WJiXlStt5fAxXpekek5h45aDvar9kjeyl6zFPaDJeOajfVuPs8r14dhnFY526+ZB6Y7ayOvKG4h7roySjw9OO4PWtZ+5w5tYji+PJKan6q7qnyVLWXamfLIuDdpspJAdMEYaPQCAAwMPJQ5a5lY6pd+hF0KKAoU5Xm0LmZTBWu7sx0UvuFfkiux+hIUHcVqvh91Jw57TkOfm9FGyxklHWfLL1wzgrp+2P/6CU9XXpBqSDWjKABsdCoYbyOcVbmK9TQKuSjIZWk3bz4LHtNcteJDdin/Df4WtUGr6R4PCVhPxgiAsrlsPoqvTeedSpTykSKGXO7Y9+QOTVWDpb8FRklSu8qdsvWhw7cOmBTcZPjV83037KXo5ckbIMe807xLnbcfSYd4j4p5a1mBzs1AJtMHYbweErGbHavBzLL2tO6Z/7L4nUGz/WCA5fSfzTZPsO8QYjDB+BQKDHW+vNyOojGVdrHDMbzWRB0wUZ1qx6FloXaq1//qLMF4pzJnl7ciZN7ycF2JJWYLVuUFqmUEQFxXVm5K2s3N9lBTqdjo2XN/K0dj/z8Yz0d4KU901KSeK7bd+x4dIGaDMTmv2e4RFzqQxp49N3Wv6Afpk0GLONrxcc4aZCgG3HSmnlPaJ3wv/Kwl9tebe0QXtp9u7oV3PI58Daz7XN5N3U/m2LzXuNXX8GgPN3DMHcjxPlhsWjBIMHrGB2K/IKVvhj6wX+3ndZ1nfQKA5oyeFrFBpgW4HejlP3ZjzpLUEYPgKBQEaTfE2om7cu5QLKUcy32Et5R0n/kpT0L0m9oHp4a70tzmuVOwfJwGWN/cobayt0JDQkiNBlzTirMfFahdRgv4uWkrNL8vXmrykXPde+zdvNB3cptiU2MRadTkdSShKhs0IpO7csqy+upveW3tyOvw3lPsxwu1wqw/XJ/zZZ1il6GdyIfcKthwk8SrTsEXBSO4BOB3+9L3Vc2CIrs/HPQXl80tTO5WXtfD+sfHEHtkL802RiFa7cklLkXhFXJzVdqwbL+qLvWY9lM864CvFz019jpWP6MwgdbLh++qFxEVqVzW1418gmjGwpxa5VzufLj80s/z37YbHhqvdpciqHjEQjkzOoJ2fMocsxtJq0izI/reNfk7MmJqdkqVisl43Q8REIBJnCvMaGzKtt72+jxoIaivM+ypGdQ1qDaF61eMtXJylIv82pgL53DDWzWubOQeTFtN+c+11nx53D9Fjbzf5D944Cz1zEPY1j4ObebLi8AYBauWux5eoWs+l1/6nLpHqTqKa0V9+zMLs53D5BDYdn0wd6XhKSUqg8YlOG85wcHWBydXhqiD2xJMDn7+FM7SJyvaJUHfxv41l61i6gT4t/GVQZuYmY+CSOD2mIu7P08Xb21iOm74yWzYv6qREpqTpmmPT/ue08n9QwLzGi0+moOHyjvj1zV7Q+gDmdX61kcgVk05LLW14I94MKQbQpnwe1g4rHickMWW5eL86U502/T/cW9f3nKH3/OcrKL6vh7epElZGbaFIyBxHtlTW23jSEx0cgEGQ63lpvepYy194BZEYPQK5kZc9Eogqa5s5BrwB/Et+baPFd8SoVPTaYl5iYky2D64jcYeApXbNV/ruy3ugBFI2edJTeBYB7du5nL8xlR0f8VYZA6pZlX53o35RtFzKeRJqGj0mQ+Rc+yjE99YsFoHZQUSHER9Y/ev0Z/rTxfc9CSqpOH2B9+uZDFuy/zMpjN6g/dpvsusjfwxlA0QAbvuqUWR9A1I3n0yNydVLzRZ0CFMzuzpi2htix9DO4OVv3QaRfmyVmEM+z+qvq+uet39bK8FxNxu/QZ5GtPHYjg9lvDsLwEQgEWYIepXuwp/0evi3/ray/e4w8u2qBBQPloFbLVY2G7a4ulD9mnuU1K21dz43KBtYoX28emcQzXXZ0pHfJOhx3cuJInW+pu7Au4w6Os/l7Smestydx6XtX7wt9TnHl4RVqPj5Akzw5iXLSkB3pt/HFh64RHL6SeXsv0WveIZsKmNpzTaHT6QhfdIzg8JWMTotVsUTPWvm5OKIxXD9iNpZv57cKK6BX7QIALPzUPAbKODD3WbH0vT42Ct7dc+E+3y+KpNdfh8zmGRsHp4c1oo6Jd0oJS9lgtuLipEajdmB9n5q0NLryMubregUtrm8wdhsRFtLV0ykb5EXRHNk4NLA+O8PrkNfXjVNDG+GhtW5Unb0dZ3X8TUQYPgKBIMvgpnGjc/HORHaJpFou6YJoipe56GASEO3oSGhIEJ8H+HNGo2FEcHGre//m6834Zj9x8NZBi3N+yJOPOdk8uKWWUtF/CCnGhkfnaJcrkE7b+3L7yW2mHbes/GyJ6V6eVA7OwxfZ/bgc1gWy5aDxEoN0wG8+3mx3/hoVht/o+y85zsrIG1QesZGbsQmyD/y4xGS2nbnD0iPX+HPbeUJ+WEVwuPU4ml/XntJna83ff8Wmc3epEiwFt+9UDtCuUcA8PiuXl+FKp0vlvDa9x1bWR90i5IdVinXAHj4xxPZYu3byc3fWPzs7qpn+YdgLPaMSzo4WpA2M+LpeIU4Pa0SZIC+zsRuxCczZrVzzLZ15H1cCwMfNSf//QKtRM+ejijaf86flUW+F2rMwfAQCQZZkxzXLv2WXDQmiWVpF962uLrTKnYPohDsW56cz5fhUWdvfxV/W3qpOYpSvN/WCcvEUOJb87NXHlzdfbta3xc2V7uu6k5Iq9+I0fvwYZ1USF7UdUSMfexCfRKURG+k4zZCV033WATpP38dX84/IrmdMg1bTiY1PImLzebvO7+akJiCbFnZPhBOLFedMzLtV1s7jI49jCX+nqF3vtEZKqo7usyVNmq8XyD1Qu87dfS69oKZGOkVKHqV2FawU1DVhwSeVMp70WFnY0NlRzZKeVfmlVSgDmsh/dgUDDLILklK5geNDGuLipGxclc7jRZtyyl4mU6bvvEjLibu4+uDFipZmNYThIxAI3lo2td3EwY7KHqDTTk427TGw0kBZO7JLJJFdIsmbTdnbcf3xdUrPKS3rczD6rG2pVi7zsPOc9GHZf0kkuy8of3B+v+iYYr+x0WQrJ35qJD2s/UE+0Pg3/aP7TvmVYuuyeWDZF5K+0uG5uDipuTDcXBTzWVhg4qWaul2KF9p57i7tbUzV/rNTOcV+R6N4n7EbzAUmo01qkFmjYj5fBjU1ZGl1rx4in7CgE/yaD6a/Y3GP98OC+Lh6Pn7/wPDnZPtZQ+bf942K6J/fKRGoD+S2xLAWJWw9PpB1RCdfFsLwEQgEWZKt72/NeFIGjKg+gpmNZiqOuWuk36Cd1E58WvJTs/H2uQKt7j265mgiu0TSomALcrpJ3qcpDabox+3RPzrmbLh++VXzp8V5d+MSmbf3ssXxlFRD/E56bNCa4zeIvJaBCrUJBbMrizoCECLPvutd1xCbUvn6TDg0W2os7QUpyTg4qKhZSO5Zexb6LZEHVw9beZLHicl0sEOfpkFx5f+nnYyu5MZvNBg+qak65uyOtmhomrK3X10AulULIXpkE6JHNqF/waswuZpkDJ7fBCeXSZMvG9XRunYILpnX1VISRfRwdkTtoNJfZ41vVybDc9ly1WZKukjjm4gwfAQCQZbER+uT8SQrRHaJpGm+pmR3VQ5eXdfaoLOiddQqzrFG+vk0DhrWtl7LoY6HqJRDfs0x5505Nu21KJsVQ8OIA9EZx1+kx+8UGbiG/dH3+WyueYBvRvSolZbSnWQiHdD+H/CQGw9fqBbonytcmGBymHaAFCSdjlIx02cl5olymQwlmpXKaXEsxE/55//VgiMMXHrC5nf4uJl4CXU6+KsN3Ewz2uaYKHnfOQ3bx8CU2jDjHYiVxy41VDDU0vWWdobXIXpkE1ndNFvp17gIx4c0ZHLHcmzpW4tqBfzM5jSP2Gmmf/SmIAwfgUDwWqBV226clPY3XBEoGVBHOx/Fw8mQHbb5sv2u/XIB8msTjdq8tEfp7KU51ln5+skSc5It1zL7bK7lwGwl2kzebdf8HrXyM6BJUZqXTkupP20oW0GpdlCoAWg9ZWrUDjePcmF4Y84OrW++4VnJuDRO1/7jBaa0D1lmu1Ey9L204Pep9SXvi1G9t2xGmU/ppTgAlh+9LtsjIJuzrB09somsbWaEJGTgNYmoABuHGNpji8E9QyyWmSEFVMpn5RcCK9l9n9aU4oIGNCnKJzXy4+7sSKMSgQT7uVn0CBbsb5sq9OuGMHwEAkGWJbJLJIc7HWZE9REsb7Gcre9vJbxCOCGeUtyEp7Mn+TwNgZ7TG06nc7HOTKhr8Dy4adxkex7rfAwHlfyfvmq5FSUGzdjTfg9HOh0hskukzVdZlubtareL/hX769sJafM6OW4gWtuenur/iNa2x9XWKvE20ra85UDX3N4ufFw9Hw7pMS//Gok8tjCqeRZsSAnHOy8ODio0Nyx4ljYMQasxXLWkp7QnpaRSb8xWgsNXUmf0Fqsp+Za8RE9sSPVPx8vVCZ4+hqtp+kO/l4Jj/wDgaGSwWEv/rqrgGfmru5Q19a6SRyltf7v4n1xEMN1gSSc9e8uM2GvwW0H4rxecWikZd7cNge99GxRm2edV+ahaiPlSOzxnbwLC8BEIBFkaRwdHmuZrSqBbID5aHzoU7cCy5suI7BLJjg92sLT5Un1AcVhgGN+GfYunszwF/rNSn+mflQyRT0t+ipezF2Wym8dLtCrYCoAl7y7BTeOG2lLVdTtolq8ZHk4eHLptMBbCgvNwxNnwG/53GqnSe5S2G74o/0b+72eSVk56+QNbGNW6FEcHNWBSh7LUKxrAzK5h+hTqtuXz2LaJh1G19v1pmXL3LXhydowBDIaLa1r2UY+5UoFPgAt3HrPx5G2Lr7v9KFGx3zjg1xrZ00QLWdpLPrD4Y7gr6eOkBwjvt3Kd+GGVYL5Ki2lKz/Sqkt+P6JFNlGNtUpTPnSF3DPpKH1YJBsDXzYmDA+pZVr7eMxEe34Ejc2F+e6lvoiGVXaN2oGRuL7tr7xlXo39TeGtLVkRERBAREUFKiu2/MQgEgteTHqV6UNq/NKX8lSuuO6gc2P6BlE0VOstgRGxqswl/V38GVxn8XO/vWLQjc0/OJbtLdja2NZQ+qJOnDqsvGq4TOuUMZMnVGxRIkv8GflArqT8HJ/wl6y8f7KO/bglfbHvZC09XDe+E5uCdUMmAqVU4YxE/GU6u8vaDS/CfBYVqwCvFYEykl7PYcFJe6+rj2QeY93FF1p64Sb/GRWVeooFLj2d4pOEtQikU4E7rtOu9lmVy4aF1ZNbuSwx+tzhc2Q8nlpgvnFAOBscSZ6XIaDolc7gR6uNP8zK5CPZ1NRvnzmk4uRwq9ZR+RnetC0RaJCIM8lSCD/4ih6cvF0c0lhss6waCNhvUMBKRvGNBuyiiIvSyHgBetYCvPmvQlPZT9lKvaABTu5RXHH8deWs9Pr169SIqKor9+/dn9lEEAsFLxkHlQNVcVXF3yjiIeHrD6bg4ujCw0kD8XZ8/GwmgT7k+TKgzgaXNl8r6GwY3NJv7caBtRsiu8Ayqxyswuo2y4fdMvPOr4Xn5l/Kx/nKjxu+PUJo77EBNCiuP3bB4ddVh6l5m775E/yVyQ8e0IKgS7SsGUT5PNuoV9MTHzYlBzYox+N3iHBhQj8ahOWCa5dgpdozjw3KG2JnVkTc4dfOR+byhfqhGBRPieF8yRFJTIHqHdIUGUszOpqGwZYTUTs9wy1tVvo/aJHanjlwSAYAre6S092sH5UbPuQ2wazxsGgan0mKwzm2Ec+uVv7c7pyDOsjcNYEK7snxYJZgVX1Tj1NBGZnpMpkbq685ba/gIBAKBEmGBYezrsI+2hdu+sD01ag0189Q0M7yUrh3u2ZB63L16CDm95B9OrSyUQkgnemQTWtkoZAfIA2VDagLwOOkxjRY1koLB7xp5GC5ska/VaKFsZ1nXOKeJ9FBLqdzFflxj9jpjvZtFh65y9pZkeJy5pWCAWGJafabGdOdQeDW8XJ1QqVT4OaXA1QyCwjf8yOATjfTNHvMOWQ8MTw9I3jkOZjaBhfLvlV3j5e3bJ8HHKFZn4B34PO1MraZBJcveMqaYGLhzWxmel32e1tfS8nqQYn8sXUUC3loHBr9bnBK5PNFq1ITlfb6MSoBL9x7zzcKjPFFIyc9shOEjEAgEmYhpbbL6j62p5krGSL/G5orIeZWuXp6F5KcwvwMMMSqd0HQsAJX+qsS1uGt8uflLcy9GOvnTPqjf/Z/ZUF+NFOybkGSeJu3pIs+Kqz92G4nJKTQYu03f50E8HdXrlWOeEuPg+iF4dB1uR8GtE3D/IvzVFqaaGA/fnIFG5vXcvLBsZM3I9oeh4eINB2fCxp+k9rkN0s/NEoEloIg8Awy/AjA4FkJbg5ObtKcl4u9LX3ebFN+NvwcbBlteZ8z4MpAQC6u+k4KfZzaVAqIfXoehvvDPh/qpvyp4Bg/bWcqi5q9bWHToKkUHmRu5mY0wfAQCgSAT6Vy8s6x0xno3V0JDgojw8iQ0JIiHRsGsJVQXWVz2GKr9U+HMWiluBeDoAmqp5FlV7SoEMamDlCGklMljxr3zsG8KDPOHUyvkYx6BzDoxS97nY2HPhsMzfpcC12LMs9cKD5B/aEZqP2aYZoY+5imdMXVcYIRRVfsd42BSFRhfGqJNlLB98oFHAFT8DFOOaM2FLAG6FHhC7adGgpr7/oTlX8knJZoYTbObG57rDITa/cHJHRqOUHwHnx+AAhau48aXhtRUcxVtgB1jldcoMTII9v0hBT9Hb5fS58ekGdFG8U9KAdQtJu5i9Dp5HNG9uERWHLvOU5Oq8ddiTPSfshhvbXCzQCAQZBXWt15vVsZisreUmVY1bx72R19Bq9Php3pI2ahREGW+R0kgn+o3LuiktOoRaZleplozFjFJo5ahdua3A7/JupbEXaSF0tzsRt6o8Csw0rZMsb/3WVakBiihUr6qcSeelrvayzvT1ZGV6LlH+mpHdtOQqx9lPOm+SS20C0baUNlygcYF+pkXV9Xj5gct/oAJ5eGJiXclIRa2jbL5vHpKd5SyvGwlNQWsZC3+b9M5vmlQWN9uM3k3F+4+5su6BelTv5C+v+rITbJ1V+7Hk8fnBXkkXwDC4yMQCASZjNpBbVbzy5iw4DyEhgQx08n6h98MF+Uq6s9LbLJ5rapBu3+ELw/LOyt+hk6n4+6Tu5IujzYbDLoviR8+JyucB8ja3+a/TF5fV45rP7ZvI0cjEcJe+6FaH6vTnR1t/JicpiDgqN/Ew/KYMW5+8H009D0H3dbJx3ZNUFwi40Mjwck+p6B5hKJnyyITwiBGMkD/7q6sFzR/32VuxEoenQtpNczWHr9pddtbD1+sFtXzIgwfgUAgyAKE+tmuxWOJvKlX+LNjWY4NbmD7og1DYLOF6xeAmuH8vOdnxaHNcZfA0SjI2iMHn234jNoLazN492DJ+HFQQ4VP9FOKq6LTnnS7ZXv9AAAgAElEQVR0U6/md6+FdFXbrxDc61o4W3tXsW9RkzHytn8hqPcj5DKocJvG+ez4rjaU/MDu88lwMohonrh7grr/1GXZeYNX6u6Tu8Q9jTPMd/eHoIrwXoSh76nRufIoGCVu/hBcFb69AL1PQLY0raUa35rPtcT98zAuFDaPoHJ+Xwoo1GwLXxxJ5RGbFBZLJCuUuXhxRUpeDMLwEQgEgixAQe+CGU+ygQZnh5BtSWer5Qv0xN2WBAa3mgf6AtBzD0k1++LgoPxR8eXmL2XXNwt9srPrulRsc/HZxbRe3loaeGwQwVvp3A+A0ZpJDNLM4b2E//hRM4cyKvOq6Ok4kqw8kGBf8VXCLFxZ1fxe/2gc51NEdRn/MQFwbL597zHF6Prou23fcTv+Nv13SKrd66LXUXthbSr/XZmkFBPtIJ/8mFG+G7T8Q96XoxT0OSk9u/mCp1H2npsf1P/JvvNuHQmpKZQN8sp4LpCS9met0vCNFFAoc2EaA5TZCMNHIBAIsgCODhmHXF6zpcr20b+lGlt/1Mh47qmVlseq94XsRem/oz8rLxjmja45WjYtPiVRyk4aHMvQ/XLP0ZkHaQJ+OQxZQnE6qeZaK/UO2dwfNHJxRmMmacYpDyxRDkZWpIsUsD3p6CQ6r+4sL5GRvZjikjXO4bbvn07RZmZdF2IuEDorlJ3XdnL5kSGWadKRSXyz9Rt9u+zcslyINYplClLw7ByYDt7BoEmLmfkxBj7dBgq14vQUaarcP+i+9F8uBXHCP2uR19fNvF+B5JRUNp68xU0LV1ox8VmrJIYwfAQCgeA1Icaechk3bSiOuuJry2N1pZgjY2VpAG+tPO16+F4pi0t2VWPE2INjZUrP7qoEWSHQdBxJoabDUUZrJuFiUp+svtpCHbDzlq9czAipTqoulYlHJnL49mG6r+tuGMtmyAi7lGqnirUp78+Fftfh442QvRjD633Je0vfA+CzDfJ4m4lHJ5otf++/9wwNlUpeHsSY/jckg9OWIG1fBc9R+BXJE+WghmsKOkc3j9EteQG5TPSi0jEWoYy+F89Hsw5YfP2KY9ctjmUGwvARCASCLMKy5laykYBZnkYGQ56KaVcYKvh0u/ICS8J9sVclz8EzEBYYJvNOJeuka6jdN5QF/6Yfn24W3LvGfajZvJUplZjl9Aut1Ns5qe2mjwV612GnbQcbHAs/XDW0GwwzPKelic+JmqPv2ntzL1Mj0+qMGV3l5XVIVzlWuCpsO1veVsurtfN+WgaVkxvkLg89d/P3+f9sO78RVx8ZfR+m11QdFllcl+7FSkxJZP2l9SSlGnlaPNKKqPrkl35W2mzGKxX3c9k5ih0f5ebMsHfMxvL1W6WwQpnVGQQ/v2qE4SMQCARZhBDPEGrmrmlxfLW7G/Ed/+XpwDvw0Tqo+hUMjoEcJZUXTK0j6b+kc/+ipNUztjis6G35IGnByNfj5L+pH+ooeV7G1DQECcckxACw4dIGi9uFzgrlLw939CdJr5BuhL9KHq+z0rkfJVXnGe8UYTbXEnvvR7G562L44RpU+QK+OioZDq1ncObBGbOU/N8P/c7vh5Qy4XT4E2PeXfRdqJ2WXVbuQxhoUgoif11Z89FTO1SnjXhn8Tt8uj7tGq94S6iSVhKkaDMoqKz1czv+NiVnl+Sz9Z9Rfm55+mzpQ9k5RhIFn2yBZuMN6fzGBFr48wOoIsJwOjTtmb6PrIowfAQCgSAL8VNVw2/4q1qsontod9l4xZ19KDe3HAnJCfI4lQoW4l3mp6WS3z0nCeGt6mv55UXflRSZ6/4IQMNFhlpiC5suRJMWR1I9d3V9/87rO3mS/IRVFw0egGOdza/ZRvj5MCeb5bTuzxyXm/Utc5an+N9VOzDY14fLjvJ4qHiVivGHxvPxuo/5csvX3EpPv/cO5lbpD1h6dTOtlrVCiamRU/lq01fEFjAYLXtLLGVD/oVmc1PRkVD1Cxj0AJopGEwa+bWQceaWNf5u8rdZ367ruwidFUpMUhw0GCp5adI8Sj039OSrTXIBxZH7pAD1ndflHrIVF9LEKD0CoFwXcDSpEwbQbj4Ubgydl8ky8PRY+zPzGiIMH4FAIMhC+Gh9iOwSSWSXSPJky8OXZb+kqI95iYqweWGUnF2SyUcnU2FeBULvrEYxhPTMGlj6uVSFPCOqfwNdV4GzeRpzUV/DGRwdHHknxHD9Ue8fuRdCpVJxtPNRsz1+87VSliEDdEDtoNwsyuZOkzw59f33HRyoGJyHKZFT9H1rotcQOiuUuv/Upd3KdgzYOUBhRwObrmyiWoohqyzg3EI8r22VT8pRmip/VyFsXhh3EowqmafX3PItaBZvk5CsHOw7pMoQ/m32LwADKg6ghF8Ji2ervqA6yamGrLbu67qz/dp2Nl3ZxIJTCwBI1aWy/pJykdIftv/AyXsnLe6v0+lYcnsfZxv9BPlqQuNfJW+ZCXWL2B/7tLinQW7gkJ0lL14mwvARCASCLM7cxpbVdyOORPAkWRKUm5Cm9mzG4TnK/aZYywwyIbuL4YPw4dOHZuMOqhf78TLQT7lwZs285oVX06+0bsff5s6TO2bjMxrOUNyrv4V30OBnZlVsx+MkyZOUHtANoPNNi5n5QgruNTZSJh2dBEBwtmDZdi0LtqSwT2Eiu0TyfpH3AVjTag1ezsrp4+nfz5roNey5YbiqGrZXimNqtKiR4rp02q5oy+n7UrkJnU7HsD3DCJ0VSuisUMYdGsegXYNoucyo0Gnt/mZ7/NGpHMNbZKw11a9xEbpUzstf3StSNsibNuVy06xUTgoH2Cji+AoQho9AIBBkcZzUCtcTCkz3smD42Iq1QpkmlAtQ9iCtbbVW/7y3/V7cNebeI5A8OL+8E86JRkNtErhb6iHfZ0bTn+C7i7YeV8/+DvspH1he8TpumYfyWbcFleS3o4ZYo9insYTOCuXLTV9ScnZJlpyV6lxNODyBsLlhnI+RylckpiQCEP0wmmkNpDiZKjmVRRdzuefij/p/KI7NOzmPhOQEvt1qLkYYOiuUG49vWPp29bRe3po/jv5BydklWXB6gb5/+nFDkHuqLi0KS2OeyeWY/Jj2FYNkfeVUpxmnmYA/Bm/OJzXyM+S9ElTJ7wdIBU//164Mbs5Zp0KWMHwEAoHgNaBHqR4ZTwI2BNtwpWVKh3+h1TTIJl0hLTqziEE7B+mHWxU0j4/J7WHuaQHI6W64hnLVuLK7/W7+amzQ6JmZW6rp1CJXIHNP/cUHp6dQMiSIeCtp2UpjY05MJVZtR3p/GlpHSUdIZWutrvci6LWxl6xr/02pOOzmK1I9rkG7pJ/VH8f+IFmXTPOlzWXzPy35KRVyVGB+k/mMqWWiHm1EMd9irGqxiqFVzbPePlprQ72wDJhwxHrZi3GHxsnjxowZkRvOrGVM8fP4IgWiL3IeQnP1Ln7SzDSfH7UUBnvCo1vPd+iXgDB8BAKB4DWgZ+medCnWJcN5vVV3CA0J4vRnmzOcC0Dlz6FgfQiVVJZ3XtvJ4N2DWXLOUK37u7DvzJaZXt8AhFdQFvzL7mq4FhutSYBBDzjvJPdi/Wwl/qdisHKh095brGSmKbCulbz+1b/N/jX7mR5xNpwrFZiaet+mvU1Vl3/Z94v+uUJgBQCK+xXHTWNdFDBPtjw0L9CcyC6R1MpTS99/7K4NukxGuGnc2N9hv11rZhyfQcnZJaXrtMGxUG+IfMJfbWl5fiAHtXIjPL9aym5rEmqkObSws/R1dCGyGsLwEQgEgteEvmF99UHD+TzzWZ3beq0FI6nKl1C2CxRqJF0VNZTqcO2/uZ8vNn5hJrIH4GyqVwNo1BoOdjwou8pqWbCl2bz0ucbEJcebzTnt5ES8SsXptvLUaWvXYOmeF4BpDaZRI7dlterpDaeTw10uBljYpzB9w/rSsWhHfV+nnIH651F+fvx+fAq2EJckF3Cce9IQlxWULch0uk30KWdeQLWITxHFYHeA1S0NYpPb39+O1lHLqpa26+2k031dd8mQczT//65EiJ8rPzYrxu+hF2BiZdirfGWXVRCGj0AgELxGOKgciOwSydLmSxlXaxyl/UubeTKs0mAovDse2i8AV0Mwb7e13dhydYviErUFxWgntRO72+9mQ+sNHOx4EBdHZZVfH608aLjy35XN5tSPj6dzwRK03j+EnmUbscLNlSSgZIhtRkOFHBWYUGcCns6euDi6UDFHRf1Y1VxVCQsMs7i2Y7GOiv3zPFwV+00J9QulxgLLRlc2p2wWx6wR4hli1vc05SkRdc21jUbVGEVuj9wc63yMo52P6o3NPB55FD12gD570FfrazZWdm5Zy6UugJ2VDeKYGgcHuuZ7iOPij+B2FKxWfl9WIetEGwkEAoHALurmrUvdvJL+TJdiXZgVNUs2vs/FhQpPnrz0cwS4BTz3HjsL1eT0Hcmbtf1BFNuz+/GTWgspyinhSqhUKnZ8INUA0+l09N3al0dPHzG82nCr63K55zLrs6esZuTdSKvjlgxCW2heoDn/nTOoP19+dBl/V3/2tN+Dg8oBF0cXklKT0DhIho5KpUKFPH5JKRB9VI1R+ud7xun5RnTe3Z8+tfpQeot5XFKuw0Y1226fsF4bLvGRmXp3ZiI8PgKBQPAGUCZ7GbO+jwL9Ibg6NBkNPXZJBSlNOHDzgFk9LmN+qf6LxTF7WNNqjdXxw3fMdX+emBg985sqV0k3vuJJR6VSMbrWaP5s8KeZxykjNrm6cFFj7hdIN6rsxeZAagU+LP6hrD2iulQI1k3jpjeo0o0eSxTzlRdhXdNqjUyHKdAt0HQJAIdvH6bTpX+Z+o51HaQMuXPm+da/YIThIxAIBG8AxmrKxqyp9TmEfQwBxaWClEbEJ8XTdW1XvttmfjWxq90uDnc6TON8jV/I+XK556JSDnm1cVNV6owo7lvcrG9e43kWM8zsYWJdQ8HQrwL8aZ47p9kcT2dPm87cv6JBB6dTsU7Pda78XvmZ2Wimvt0wb0PLk60wqsYoXBxd+LvJ32YerpmNZlImexki6kaY/T8C+P3UbLO+1xmVzmLu2tvBw4cP8fT0JDY2lmzZnu0eViAQCLIK+2/up9vabrK+yC7KVzEHbx3kwzUfKo5ZWvM8nHtwjhbLWsjeEXknkvar2tu0PrJLJMfuHGPh6YUMqDRAn5r+Ioh7GqcYewRQ1Kco/Sr2o3T20rL+u0/uUnthbbMzvu4sO7+M/jvkIoaRFX8xlD8xQgdk6M/qvBTy1XpBpzPwrJ/fwuMjEAgEbxBls5fNeFIaloye54lJsUYB7wL62JKfqkg1yYr4FLFp7fSGktBeSf+SDKs27IUaPYDVNPOFzRaaGT0Afi5+svby5ub1xl5HmuVrJms7qBygSGMYdJ/rjmpS0voXubtRO08uopwsXLXlTgsoT4xTHs8khOEjEAgEbxBqBzULm8oLbKYrCNvK+tbKdZ9eBO+EvENkl0haFJQ8P6ap7kpMrjfZalbW/9u796ioyvUP4N9hYLgkAwjIRUFUFBUFRZTISBNOWB6tlp1YLn5ml5NakGJUdjOt1jpY2c1LnE6dmlq/ErOV1q/MIkQMvIZchUVGKGUCGXFVEZjn9wexY8S8DjM4+/tZa9aa2e8ze7/zDHvxrNnvu19z0Gg0GOfZe82s7jsuX4zBrr0HSV+Nzh6TZBQjxr83Hg9lpyA+YDCuGxYEAFjl7Ynf7LVY5dVjVtjKBmDOuq4xZT//cbuBn/dbpuMXiYUPEZGNGeM5BskTkpXXkf8biQ5jB9o629BypgW1rbXnXLgyPS4dJQtK4OZ4hUtfXKKsf2Rhks8k3DDkBuyetxsj3EaYtE8dPNUi/dj4996rpEf6Rp73PT3zfKFBxleT7Dt73wCz+3YHJ2HEyTv+LAjL/7jpY3XCe8ivOwiZOB+lWsGyQV5dC+fmnWMleyviGB+O8SEiGzX+vT8XlUyJSMFXR75Cef1fr9T935v+iyl+UyzRtfPKO5an3EjR0mNmeubs1emvIm5o3Hmiu6bN5/ycgzDvsEuePdbf5R7LxQPfXNxSKW/G/RuL/vjOVly7As/v7Vp2Y+rJU/h37a9dvwRdwey2c7nc/9+8jw8RkQq8dvC1C8Y0tDVYoCcXdp3/dUidlIpRHpZf7mDT3zch4fOuFdP/arX0njQajcnSErZkqv/F/9K2qMcdv7uLHgDIc/ljvJixE9D2j5Kjf/SCiIisboT7iAsHWYBGo8Hd4+62yrHHeo7F0oilaGxrvOBlLlun0WjwTvw7vWYJXpa2JpM7hVsTCx8iIpVbP2M9ms409ZvCx9r+Of6f1u5CvzHZdzIOzj+IlXkr8X8/Xt6stXbPYDi01Pabwke1g5s3bNiAsWPHYvLkvp0pQERkLT0H3p7PtIBpmD1i9oUDSZUc7Bzwr5h/KQvkXqofEz8EBp17YVVrUG3hk5SUhLKyMhw4cODCwUREV6F7x9+LJROXnDfmcpdhIPWx09gh/3/y8cEtH2D55OUAgB3/2KG0J4QkmNxlupugf82h4qwuzuoiIhvXc6ZSbGAssqqzAHQtY9BzzSaiy9HW2YaqxiqEeIRAo9Ggsa0RLvYuXSu8o+9mC3JWFxERndN//vYfLMxciGlDpuG1G1/DyfaTONp0FGM8+8/lB7p6OWodTe7A3X0fqIhBEThYd7DfzBbsxsKHiMjGRftHo+iuoq6lBwC4OLiw6KE+d7rzNACg5EQJbgq6ycq9+ZNqx/gQEalJd9FDZCllv5UBAAyHDNbtyFl4JhAREZFqsPAhIiIis+u5en1BXYEVe2KKhQ8RERGZ3dd3fK08D/UMtWJPTHFwMxEREZmdg52DxReZvRj8xYeIiIhUg4UPERERqQYLHyIiIlINFj5ERESkGix8iIiISDVY+BAREZFqsPAhIiIi1WDhQ0RERKrBwoeIiIhUg4UPERERqQYLHyIiIlINFj5ERESkGix8iIiISDVY+BAREZFq2Fu7A9YmIgCApqYmK/eEiIiILlb3/+3u/+MXS/WFT3NzMwAgICDAyj0hIiKiS9Xc3Aw3N7eLjtfIpZZKNsZoNOKXX36Bq6srNBqN2fbb1NSEgIAA/PTTT9Dr9WbbL5lini2DebYc5toymGfL6Ms8iwiam5vh7+8PO7uLH7mj+l987OzsMGTIkD7bv16v50llAcyzZTDPlsNcWwbzbBl9ledL+aWnGwc3ExERkWqw8CEiIiLV0K5atWqVtTthq7RaLaZPnw57e9VfUexTzLNlMM+Ww1xbBvNsGf0tz6of3ExERETqwUtdREREpBosfIiIiEg1WPgQERGRarDwISIiItVg4dNHNmzYgKCgIDg5OSEqKgr79++3dpf6jV27dmH27Nnw9/eHRqPB1q1bTdpFBM888wz8/Pzg7OyMuLg4HD582CSmvr4eiYmJ0Ov1cHd3x3333YeWlhaTmOLiYsTExMDJyQkBAQF48cUXe/Vl8+bNGD16NJycnDB+/Hhs27bN/B/YStLS0jB58mS4urpi0KBBuO2221BRUWESc/r0aSQlJcHT0xMDBgzA3LlzUVtbaxJTXV2NWbNmwcXFBYMGDcKjjz6Kjo4Ok5idO3ciIiICjo6OCA4OhsFg6NUfWz0n0tPTERYWptygLTo6Gl9++aXSzhz3jdWrV0Oj0SAlJUXZxlxfuVWrVkGj0Zg8Ro8erbTbRI6FzC4jI0N0Op288847cujQIbn//vvF3d1damtrrd21fmHbtm3y1FNPySeffCIAZMuWLSbtq1evFjc3N9m6dasUFRXJnDlzZNiwYXLq1CklZubMmRIeHi579+6Vb7/9VoKDg2XevHlKe2Njo/j4+EhiYqKUlpbKxo0bxdnZWd58800lJi8vT7Rarbz44otSVlYmTz/9tDg4OEhJSUnfJ8EC4uPj5d1335XS0lIpLCyUW265RQIDA6WlpUWJWbx4sQQEBEhWVpZ89913cu2118p1112ntHd0dMi4ceMkLi5OCgoKZNu2beLl5SVPPPGEEvPjjz+Ki4uLPPzww1JWVibr1q0TrVYr27dvV2Js+Zz47LPP5IsvvpDvv/9eKioq5MknnxQHBwcpLS0VEea4L+zfv1+CgoIkLCxMli5dqmxnrq/cypUrJTQ0VI4fP648fv31V6XdFnLMwqcPTJkyRZKSkpTXnZ2d4u/vL2lpaVbsVf90duFjNBrF19dXXnrpJWVbQ0ODODo6ysaNG0VEpKysTADIgQMHlJgvv/xSNBqNHDt2TERE3njjDfHw8JC2tjYlZvny5RISEqK8vvPOO2XWrFkm/YmKipJFixaZ90P2E3V1dQJAcnJyRKQrrw4ODrJ582Ylpry8XADInj17RKSrSLWzs5OamholJj09XfR6vZLbxx57TEJDQ02OlZCQIPHx8cprtZ0THh4e8vbbbzPHfaC5uVlGjhwpmZmZMm3aNKXwYa7NY+XKlRIeHn7ONlvJMS91mdmZM2eQn5+PuLg4ZZudnR3i4uKwZ88eK/bs6lBVVYWamhqT/Lm5uSEqKkrJ3549e+Du7o7IyEglJi4uDnZ2dti3b58Sc8MNN0Cn0ykx8fHxqKiowO+//67E9DxOd4ytfk+NjY0AgIEDBwIA8vPz0d7ebpKD0aNHIzAw0CTX48ePh4+PjxITHx+PpqYmHDp0SIk5Xx7VdE50dnYiIyMDra2tiI6OZo77QFJSEmbNmtUrH8y1+Rw+fBj+/v4YPnw4EhMTUV1dDcB2cszCx8xOnDiBzs5Oky8dAHx8fFBTU2OlXl09unN0vvzV1NRg0KBBJu329vYYOHCgScy59tHzGH8VY4vfk9FoREpKCqZOnYpx48YB6Pr8Op0O7u7uJrFn5/py89jU1IRTp06p4pwoKSnBgAED4OjoiMWLF2PLli0YO3Ysc2xmGRkZOHjwINLS0nq1MdfmERUVBYPBgO3btyM9PR1VVVWIiYlBc3OzzeS4f9w/moj6VFJSEkpLS5Gbm2vtrtikkJAQFBYWorGxER9//DEWLFiAnJwca3fLpvz0009YunQpMjMz4eTkZO3u2Kybb75ZeR4WFoaoqCgMHToUH330EZydna3YM/PhLz5m5uXlBa1W22uUe21tLXx9fa3Uq6tHd47Olz9fX1/U1dWZtHd0dKC+vt4k5lz76HmMv4qxte8pOTkZn3/+ObKzszFkyBBlu6+vL86cOYOGhgaT+LNzfbl51Ov1cHZ2VsU5odPpEBwcjEmTJiEtLQ3h4eF4/fXXmWMzys/PR11dHSIiImBvbw97e3vk5ORg7dq1sLe3h4+PD3PdB9zd3TFq1Cj88MMPNvP3zMLHzHQ6HSZNmoSsrCxlm9FoRFZWFqKjo63Ys6vDsGHD4Ovra5K/pqYm7Nu3T8lfdHQ0GhoakJ+fr8Ts2LEDRqMRUVFRSsyuXbvQ3t6uxGRmZiIkJAQeHh5KTM/jdMfYyvckIkhOTsaWLVuwY8cODBs2zKR90qRJcHBwMMlBRUUFqqurTXJdUlJiUmhmZmZCr9dj7NixSsz58qjGc8JoNKKtrY05NqPY2FiUlJSgsLBQeURGRiIxMVF5zlybX0tLCyorK+Hn52c7f89XPDyaesnIyBBHR0cxGAxSVlYmCxcuFHd3d5NR7mrW3NwsBQUFUlBQIADklVdekYKCAjl69KiIdE1nd3d3l08//VSKi4vl1ltvPed09okTJ8q+ffskNzdXRo4caTKdvaGhQXx8fGT+/PlSWloqGRkZ4uLi0ms6u729vaxZs0bKy8tl5cqVNjWd/YEHHhA3NzfZuXOnydTUkydPKjGLFy+WwMBA2bFjh3z33XcSHR0t0dHRSnv31NSbbrpJCgsLZfv27eLt7X3OqamPPvqolJeXy4YNG845NdVWz4nHH39ccnJypKqqSoqLi+Xxxx8XjUYjX3/9tYgwx32p56wuEebaHFJTU2Xnzp1SVVUleXl5EhcXJ15eXlJXVycitpFjFj59ZN26dRIYGCg6nU6mTJkie/futXaX+o3s7GwB0OuxYMECEema0r5ixQrx8fERR0dHiY2NlYqKCpN9/PbbbzJv3jwZMGCA6PV6ueeee6S5udkkpqioSK6//npxdHSUwYMHy+rVq3v15aOPPpJRo0aJTqeT0NBQ+eKLL/rsc1vauXIMQN59910l5tSpU/Lggw+Kh4eHuLi4yO233y7Hjx832c+RI0fk5ptvFmdnZ/Hy8pLU1FRpb283icnOzpYJEyaITqeT4cOHmxyjm62eE/fee68MHTpUdDqdeHt7S2xsrFL0iDDHfenswoe5vnIJCQni5+cnOp1OBg8eLAkJCfLDDz8o7baQY42IyJX/bkRERETU/3GMDxEREakGCx8iIiJSDRY+REREpBosfIiIiEg1WPgQERGRarDwISIiItVg4UNERESqwcKHiCxm+vTpSElJsXY3TGg0GmzdutXa3SAiC+ENDInIYurr6+Hg4ABXV1cEBQUhJSXFYoXQqlWrsHXrVhQWFppsr6mpgYeHBxwdHS3SDyKyLntrd4CI1GPgwIFm3+eZM2eg0+ku+/22uKI2Ef01XuoiIovpvtQ1ffp0HD16FMuWLYNGo4FGo1FicnNzERMTA2dnZwQEBGDJkiVobW1V2oOCgvD888/jrrvugl6vx8KFCwEAy5cvx6hRo+Di4oLhw4djxYoVaG9vBwAYDAY8++yzKCoqUo5nMBgA9L7UVVJSghkzZsDZ2Rmenp5YuHAhWlpalPa7774bt912G9asWQM/Pz94enoiKSlJORYR9W8sfIjI4j755BMMGTIEzz33HI4fP47jx48DACorKzFz5kzMnTsXxcXF2LRpE3Jzc5GcnGzy/jVr1iA8PBwFBQVYsWIFAMDV1RUGgwFlZWV4/fXX8dZbb+HVV18FACQkJCA1NRWhoaHK8RISEnr1q7W1FfHx8fDw8MCBAwewefNmfPPNN72On52djcrKSmRnZ1CuCewAAAL2SURBVOO9996DwWBQCiki6t94qYuILG7gwIHQarVwdXU1udSUlpaGxMREZdzPyJEjsXbtWkybNg3p6elwcnICAMyYMQOpqakm+3z66aeV50FBQXjkkUeQkZGBxx57DM7OzhgwYADs7e3Pe2nrww8/xOnTp/H+++/jmmuuAQCsX78es2fPxgsvvAAfHx8AgIeHB9avXw+tVovRo0dj1qxZyMrKwv3332+eBBFRn2HhQ0T9RlFREYqLi/HBBx8o20QERqMRVVVVGDNmDAAgMjKy13s3bdqEtWvXorKyEi0tLejo6IBer7+k45eXlyM8PFwpegBg6tSpMBqNqKioUAqf0NBQaLVaJcbPzw8lJSWXdCwisg4WPkTUb7S0tGDRokVYsmRJr7bAwEDlec/CBAD27NmDxMREPPvss4iPj4ebmxsyMjLw8ssv90k/HRwcTF5rNBoYjcY+ORYRmRcLHyKyCp1Oh87OTpNtERERKCsrQ3Bw8CXta/fu3Rg6dCieeuopZdvRo0cveLyzjRkzBgaDAa2trUpxlZeXBzs7O4SEhFxSn4iof+LgZiKyiqCgIOzatQvHjh3DiRMnAHTNzNq9ezeSk5NRWFiIw4cP49NPP+01uPhsI0eORHV1NTIyMlBZWYm1a9diy5YtvY5XVVWFwsJCnDhxAm1tbb32k5iYCCcnJyxYsAClpaXIzs7GQw89hPnz5yuXuYjo6sbCh4is4rnnnsORI0cwYsQIeHt7AwDCwsKQk5OD77//HjExMZg4cSKeeeYZ+Pv7n3dfc+bMwbJly5CcnIwJEyZg9+7dymyvbnPnzsXMmTNx4403wtvbGxs3buy1HxcXF3z11Veor6/H5MmTcccddyA2Nhbr16833wcnIqvinZuJiIhINfiLDxEREakGCx8iIiJSDRY+REREpBosfIiIiEg1WPgQERGRarDwISIiItVg4UNERESqwcKHiIiIVIOFDxEREakGCx8iIiJSDRY+REREpBosfIiIiEg1/h/zZ+42u5oICAAAAABJRU5ErkJggg==", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "semilogy(dto; label = \"optimal step size\")\n", "semilogy(dto2; label = \"2x optimal\")\n", "semilogy(dto3; label = \"3x optimal\")\n", "xlabel(\"iteration\");\n", "ylabel(\"distance to optimum\");\n", "legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is the best assignment of the step size after 20000 iterations?" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "etas = exp(collect(-1:0.05:3));\n", "dists = [ sgd_logreg(w0, eta*alpha0, eta^2*gamma, X, Y, sigma, 20000, wopt)[2][end] for eta in etas ];" ] }, { "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": [ "loglog(etas, dists);\n", "scatter(etas[21], dists[21]);\n", "imin = indmin(dists);\n", "scatter(etas[imin], dists[imin]; color=\"red\");\n", "xlabel(\"step size scaled by\");\n", "ylabel(\"distance to optimum after 20000 steps\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Takeaway: the theory gave us something good, but not the best.\n", "\n", "What about other algorithms? Maybe if we ran SVRG, the theoretically optimal parameters would be correct." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "svrg (generic function with 1 method)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function svrg(w0, alpha, X, Y, sigma, niters, nepochs, wopt)\n", " w = w0\n", " (N, d) = size(X)\n", " dist_to_optimum = zeros(niters * nepochs)\n", " for epi = 1:nepochs\n", " wtilde = w;\n", " gtilde = X' * (Y ./ (1 + exp(Y .* (X * wtilde)))) / N - sigma * wtilde;\n", " for k = 1:niters\n", " i = rand(1:N)\n", " xi = X[i,:];\n", " yi = Y[i];\n", " w = w + alpha * (xi * yi / (1 + exp(yi * dot(xi, w))) - sigma * w - xi * yi / (1 + exp(yi * dot(xi, wtilde))) + sigma * wtilde + gtilde);\n", " dist_to_optimum[k + (epi-1)*niters] = norm(w - wopt);\n", " end\n", " end\n", " return (w, dist_to_optimum);\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Optimal step size from our analysis was\n", "$$\\alpha = \\frac{\\mu}{5 L^2 e}$$\n", "and optimal epoch length was\n", "$$T = \\frac{5 L^2 e}{\\mu^2}$$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = mu / (5 * L^2 * e);\n", "T = Int64(ceil(5 * L^2 * e / (mu^2)));\n", "K = 10;" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "time1 = @timed (w, dto_svrg) = svrg(w0, alpha, X, Y, sigma, T, K, wopt);" ] }, { "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" } ], "source": [ "semilogy(dto_svrg);" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "time2 = @timed (w2, dto_svrg2) = svrg(w0, 3*alpha, X, Y, sigma, Int64(ceil(T)), K, wopt);" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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58mSGDRtW4PlJ//w5LVu2jOrVq+c6FngJczciIiLYtWsXK1as4JtvvuHhhx/mpZdeYs2aNQUO4aWnp9O7d29CQkKYPXt2vvjmzJlDdHR0rvf4+/sXOz5HKWHyNpUr597/8Udo08ahS9jtpqhlhQrZbZn1MR3Iv0REPJfNBoUkFZ4sIyOD1NTUrP29e/cyatQo5syZw8KFC+nXrx8rVqzAL++oQw4RERE89NBDPPTQQ4wdO5Y5c+YwbNgwAgICAJOcZGrYsCGBgYEcOHAg13ylgvz444/UrFkTgJMnT7J7924aNGhwwfNLly5NTEwMMTExPPLII1x99dVs376d5s2b5zt31KhRbN++nU2bNhEUFJTVHh4eTrVq1fjjjz+49957C43PlZQweaN9+6BOHbPdtm2xspywMFObKe+/twvVchIREecbO3YsPXr0oGbNmpw+fZr333+f1atXs3z5csAkNvfddx/du3enf//+3HDDDTRp0oTJkydnDVnlNXLkSHr06MFVV13FyZMnWbVqVVZSU6tWLWw2G//3f//HjTfeSOnSpSlXrhyPPfYYo0aNIiMjg/bt25OQkMD3339PSEhIrknVzzzzDJdffjnh4eE88cQTVKxYkV69ehUYx9y5c0lPTyc6Oprg4GAWLFhA6dKlqVXAA0vvvPMOs2bNYsmSJdhsNo4cOQKQNfw2YcIEhg8fTmhoKDfccAOpqals2rSJkydPEhsbe0l/B0Xm0IwnyWLJpO+cck4yXLnSaZfK+UpPd1KsIiIuVNgEX0/3wAMP2GvVqmUPCAiwV6pUyd61a1f7119/nXV8woQJ9qpVq9qPHz+e1fbJJ5/YAwIC7HFxcQVec+jQofZ69erZAwMD7ZUqVbL36dMn1/ufeeYZe5UqVew2m83er18/u91ut2dkZNinTp1qr1+/vr1UqVL2SpUq2bt3725fs2aN3W7PnvT9+eef2xs1amQPCAiwt27d2r5t27YLfm9LliyxR0dH20NCQuxlypSxt2nTxr5ixYqs4zknfffr188O5HuNGzcu6/z33nvPHhUVZQ8ICLCHhYXZO3ToYF+8eHGB93bFpG+b3a7+hOJITEwkNDSUhIQEQqyY/JOcDGXLZu9f4l9jQgKUL1/wMf2EiIgnO3v2LPv27aNOnTq5hnLEeVavXk3nzp05efIk5S/0YeFBCvuZKO7nt56S81Z5x+Y3bbqky4WGXjgxstnMKKCIiEhJpYTJm505k73dqpVTLpk5IJdX3bomcfrsM6fcRkRExKto0rc3c2HXs90OR49mVzDI1LNn9nERESkZOnXqREmfwaMeJl/i5CqUlSsXPkwnIiJSUihh8nZ5MxoX1AW40DCdzabESUQ8R0nvAZFsrvhZUMLkC+bPz71fSDGzS6HeJhHxRJlVo1OsWGxXPFLmz0JBFcWLS3OYfEGfPtC3r1tulZk0FbS8Smoq/FNEVkTEbfz9/SlfvjxHjx4FIDg4GJv+J1ci2e12UlJSOHr0KOXLl3fq0ilKmHxF3kXiXFyyu6A16QIDYft2aNzYZbcVESlQlSpVALKSJinZypcvn/Uz4SxKmHzJxIkwdqzbbldQb1OLFvDccxAbC25cE1FESjibzUbVqlWpXLky586dszocsVCpUqVcsiivKn0Xk+WVvi8kb7ePm/56Dx+GgQNh2TKz3749zJ0L9eq55fYiIiJFokrfYliU/1atCp9/Dm++aVZsWbcOmjaF115TzSYREfF+SpjEaWw2GDDAzGPq2BFSUuDhh+G662D/fqujExERKT4lTL4uI8Ptt6xdG779FqZMgdKlYeVKaNLE9DZZEI6IiMglU8Lk6/z9LRkT8/ODkSNh2zYznykpyfQ2de0Ke/e6PRwREZFLooTJF82dm3v/QoUsM0t1//lnwcfPnYOFC02BpcIU0m105ZWwZg1Mnw7BwbB6telteuUVSE8v/LIiIiKeQgmTL7r77vxtCxbAgQPZ+zmfpouIyN8Ldf68qUL5r3/lX+Q3M9E6exbKlTO9WIXUffLzg2HDzNymzp3hzBl49FFo1w5++aWY36OIiIgbKWHyRQWV2+7TB2rVgvj4gtcyyeyFykyGLlROftq07O3Spc1YW6b33y80rLp1zXym2bMhJAQ2boTmzWHCBEhLu8j3JCIiYiElTL7KboePPsrfXljl0/PnL3wsM5EaOfLC5+zZc9GwbDZTr2nHDoiJMaN+48ebgpcbN1707SIiIpZQ4cpi8tjClTllZLi/3LYDP06ZOd2wYXDsmOnkGjUKnnnGzHcSERFxNhWulPwuNNnbVR5+2KHTbTbo3dv0Nt17r8nvJk82k8JXrXJRjCIiIsWghKmk27rVedfavLlYb6tY0cxJ/7//gxo14I8/oEsXGDwYEhKcF56IiEhxleiE6dZbbyUsLIw77rjD6lBc55tvLnwsNRWioop33SlT8rdt3XrxEgSFuOkm+PVXeOghsz97NjRsaJZcERERsVKJTphGjBjB/PnzrQ7Dtbp1g6lTC54AXtDTdDn5+V04Wxk5EubNg169zFhapUrmUbdL7LEKCTEVwVevhiuugEOH4JZbTKWEY8cu6dIiIiLFVqITpk6dOlGuXDmrw3C9ESPgzjtzt50+feHzp083M7LT0+Hmm8123hdA376wZImZjNSmjWn78UenhNyxI/z8Mzz+uMnbPvwQGjQwQ3d6TEFERNzNYxOmtWvXEhMTQ7Vq1bDZbCxdujTfOTNnzqR27doEBQURHR3NRj2XXrjMsgF16kDZstntOXufEhPNY2uOykyY3nij+PHlUbo0/Pe/sGGDmQj+99+mnNSNN2oxXxERcS+PTZiSk5OJjIxk5syZBR5fuHAhsbGxjBs3ji1bthAZGUn37t05evRo1jlRUVE0btw43+vQoUPu+jY8S+a6cn/8kbv9zjvN8ihpaaZyd3E0aWK+/vbbpcVYgJYtYdMmeP55M4r41VfQuDG8+KKWVxEREffwijpMNpuNJUuW0KtXr6y26OhoWrVqxYwZMwDIyMggIiKCYcOGMWbMmCJfe/Xq1cyYMYNFixYVel5qaiqpOSY0JyYmEhER4dl1mNwpKSk72dq715T1doFdu0zhy+++M/uVKsGyZdCqlUtuJyIiPqZE1WFKS0tj8+bNdOvWLavNz8+Pbt26sX79epfcc+LEiYSGhma9IiIiXHIfr5VziM9J85gKUr++mRD+2mtm/9gxaN3aFLu8hAf0RERECuWVCdPx48dJT08nPDw8V3t4eDhHjhwp8nW6devGnXfeyRdffEGNGjUKTbbGjh1LQkJC1uvgwYPFjt9ndelivt57r0tv4+dnSg8cOADly5u2ceOgWTNYt86ltxYRkRLKKxMmZ1mxYgXHjh0jJSWFP//8k7Zt217w3MDAQEJCQnK9JI969dx6u4gIOHEC5s+H8HDYuROuvRZuuw1OnnRrKCIi4uO8MmGqWLEi/v7+xMfH52qPj4+nSmGLy4prTZqUvV1YwUwnstnMk3M7d8KDD5q2JUugQgVTOVxERMQZvDJhCggIoEWLFqxcuTKrLSMjg5UrVxbaSyQuljk+BvDUU269dVgYzJkD776b3RYTYxKqAwfcGoqIiPggj02YkpKSiIuLIy4uDoB9+/YRFxfHgX8+/WJjY5kzZw7z5s1j586dDBkyhOTkZPr3729l2BIaar5u2GDJ7e+7z9TkvP/+7LZataBTJ0vCERERH+GxCdOmTZto1qwZzZo1A0yC1KxZM55++mkAevfuzcsvv8zTTz9NVFQUcXFxfPXVV/kmgoubTZ6cvV1YNXEXKlsW3nkHXnopu23NGtPbtGWLJSGJiIiX84o6TJ6ouHUcfJ7dbh5jAxg8GF5/3dJwzp41FcPzSk/PDlNEREqOElWHSTyYzZa97cRlUoorKMjkcJkrt2Ty94f33rMmJhER8T5KmMT5pk/P3t6507o4cli/Hs6dy912333w5JOmF0pERKQwSpjE+YYOzd5u2NC6OPK47DLT2/T++9ltzz+vgpciInJxSpjE+XIOy4HJUjzI3XebkBYtgipVzHrB114LjzwCiYlWRyciIp5ICZO4Ro4aWbnqM3mQ22+HHTtgwACzP2uW6RD7/HNr4xIREc+jhElcI3NdOfDobpuwMHjzTZPf1a0Lf/0Ft9wC//oXHD1qdXQiIuIplDCJ6zRtmr19zz3WxVEEXbrA9u0werQpN7BwITRoAPPmedyIooiIWEB1mIpJdZiKKOd8Ji/5Udu82QzTbdtm9q+/3pSTqlPH2rhEROTSqQ6TeL5GjayOoEhatICffoKJEyEwEL7+Gho3hilTTMFLEREpeZQwiWtlZGRv79hhXRwOKlUKxoyBn3+Gjh0hJQViY6FdOzN0JyIiJYsSJnGtvCUG8u57uKuugm+/hdmzISQENm6E5s3hqacgNdXq6ERExF2UMInr5Z275GXjWn5+MHCgKVreqxecPw/PPQdRUfD991ZHJyIi7qCESdxj6dLs7csusy6OS1CtGixebApehoebgpft26vgpYhISaCESdyjZ8/c+7/9Zk0cl8hmMwUvd+6EBx4wbbNmmfnsy5ZZG5uIiLiOEiZxn5yLuDVoYF0cThAWBm+9BStWmIKXf/4JN99sll1RwUsREd+jhEnc5+67c+/fe681cThR167mqbnHHjNznT780OSC777rNWWnRESkCJQwiXslJGRv5+xx8mLBwfDSS+YJushIOHEC+vaFHj1g/36roxMREWdQwiTulbeqqpeVGShMZsHLF14wBS+XLzdzm6ZO9boHA0VEJA8lTOJ+PjxWVaoUjB1rCl526GAKXo4aBddco4KXIiLeTAmTWM+HepkyXXUVrFpl1qALCYENG0zByyeegDNnrI5OREQcpYRJrJG3l+nrr62Jw4X8/GDwYLMiTGbByxdeMIv4+uC3KyLi05QwiWfo3t3qCFymenVYssQUvaxWDeLjzbfbsSOcOmV1dCIiUhRKmMQ6eXuZfHBoLqdbbzW9Tb17m/21a01v05w51sYlIiIXp4RJPIvN5tOJU2ioqdWUOSR36hQMGgSdOsFff1kamoiIFEIJk1grI6Pg9ptvNl/PnbvwOV7suuvME3SPPmr216yBGjVg0iSf/HZFRLyezW734We8XSgxMZHQ0FASEhIIyVtbSBxXlF4lH/1R3bYNbrsN/vgju+2bb6BbN+tiEhHxVcX9/FYPk3gGV1Z2PHoUdu923fUvUWSkCa9Dh+y2666DqCjzZJ2IiFhPCZN4Bj8/04MUF3fhcxYuhOPHCz6WOffp77/N/qZN8MorZjs8HOrXN8efegoWLHBu7E7g72+G5fbsyW7btg3KlDFLroiIiLU0JFdMGpJzoYsNz6WmwuHD5vGy55/Pf9xuL/rE8ZMnoXx5x2N0Ibsd2reHH37I3X7mDAQFWROTiIiv0JCc+I6MjOxEaOfO/McDA6F27YKTJYDffy/6vcLCHA7P1Ww2+P5789Rc9erZ7aVLm042ERFxP/UwFZN6mNzI1WUGPPyfQNmykJycvT9qFDz7rBmuExERx6iHSaQ4una1OoKLSkqCffuy96dMgcaNYfly62ISESlplDBJyXChXqSDB90bRzHVrm2+hS++gJo1Yf9+uOEG6Ns3e567iIi4jhIm8XwTJlza+zOLYGZO7p42DZYtM9u7d0NCwqVd34169IBff4Xhw81I5bvvQoMG8P77Hj+yKCLi1Ryew/T333/z9NNPs2rVKo4ePUpGnrLEJ06ccGqAnkpzmNzs/Hl44AFYuRIOHcp/PD0dli6F22/Pf+xCP+J16piumm+/hc6dnRquO/z4Izz4oEmgAG68EV57zfRAiYhIwYr7+X2Zozfq06cPe/bsYcCAAYSHh2Pz4XW/xINcdhnMn2+Sn5EjYfr07GPJyaaOU0xM/vcV9v+Bli1NwrRpk1cmTG3awJYt8N//wnPPmeG6hg1h4kR4+GFT20lERJzD4R6mcuXKsW7dOiIjI10Vk1dQD5PF7HZTfuD8eVNmIFPOBL5lS/jppwtf47/x9uxCAAAgAElEQVT/hTFj4K67vP55/Z07YeBAU44ATDL15pvQqJG1cYmIeBq3PSV39dVXc+bMGUffJuJcNpvpQsmZLAFUqZK9vXhx4ddo2dJ83bTJubFZoEEDWLsWZs2CcuXMcF2zZjBunKnzKSIil8bhhGnWrFk88cQTrFmzhr///pvExMRcL29x6tQpWrZsSVRUFI0bN2bOnDlWhyTO8N132dsREYWf27y5+frHH+ADc+/8/GDIENixw4xOnjsHzzxjEqfMnicRESkehxOm8uXLk5iYSJcuXahcuTJhYWGEhYVRvnx5wjywavKFlCtXjrVr1xIXF8eGDRt44YUX+FvPZ3u/K66A9eth796LnxsWZp7Xh8KH7rxMjRrw6afw0UdQubIZrmvfHh55BLzo/zQiIh7F4TlMrVu35rLLLmPEiBEFTvru2LGjUwN0hxMnTtC8eXM2bdpExYoVi/QezWHyEZlltNu2zb94mw84cQJGj4a33zb71aubJ+kKmh8vIlISuG0O0y+//MI777xD79696dSpEx07dsz1cpa1a9cSExNDtWrVsNlsLF26NN85M2fOpHbt2gQFBREdHc1GB5d1P3XqFJGRkdSoUYPRo0cXOVkSH1Kpkvm6fr21cbhIhQrw1luwYgXUrWvWp7vlFujdG+LjrY5ORMR7OJwwtWzZkoNuqI6cnJxMZGQkM2fOLPD4woULiY2NZdy4cWzZsoXIyEi6d+/O0aNHs87JnJ+U93Xonzo+5cuXZ9u2bezbt4/333+feH2ClDz33Ze97cOVH7t2he3bTW+Tn58ZrmvQAN55x6e/bRERp3F4SO7jjz9m/PjxjB49miZNmlCqVKlcx5s2berUAAFsNhtLliyhV69eWW3R0dG0atWKGTNmAJCRkUFERATDhg1jzJgxDt/j4YcfpkuXLtxxxx0FHk9NTSU1x+NGiYmJREREaEjO2509C6VLm+0tW8wMaR+3ZYspeLl1q9nv2hXeeAPq1bM2LhERd3DbkFzv3r3ZuXMnDzzwAK1atSIqKopmzZplfXWHtLQ0Nm/eTLdu3bLa/Pz86NatG+uLOLQSHx/P6dOnAUhISGDt2rXUr1//gudPnDiR0NDQrFfExZ7AEu8QFJS9PXWqdXG4UfPmsHGjKUMVFGSKpzdpAi+/bMpaiYhIfg4nTPv27cv3+uOPP7K+usPx48dJT08nPDw8V3t4eDhHjhwp0jX+97//ce211xIZGcm1117LsGHDaNKkyQXPHzt2LAkJCVkvdwxLipvNn291BG5z2WXw+ONmmK5zZzhzxgzXRUdn9zyJiEg2h5dGqVWrlivicLvWrVsTFxdX5PMDAwMJzFskUXzDI4/ABebK+borrjA9TO+8A48+aobrWrWCxx4zRS8zRytFREo6hxOm+Rf5X3jfvn2LHUxRVaxYEX9//3yTtOPj46mSs9KzSFGMGpWdMO3bZxblLUFsNrOu8Y03wvDh8PHHZrjuk09g9myvXGZPRMTpHE6YRowYkWv/3LlzpKSkEBAQQHBwsFsSpoCAAFq0aMHKlSuzJoJnZGSwcuVKhg4d6vL7i4/JOdu5bt0S+9hYlSrm6blPPzWL9+7ZA126wIAB8NJLps6niEhJ5fAcppMnT+Z6JSUlsWvXLtq3b88HH3zgtMCSkpKIi4vLGjbbt28fcXFxHDhwAIDY2FjmzJnDvHnz2LlzJ0OGDCE5OZn+/fs7LQaRkqhnT7O8ypAhZv+tt0wJgkWLSmwuKSLieFmBC9m0aRP33Xcfv/32mzMux+rVq+lcwFhAv379mDt3LgAzZszgpZde4siRI0RFRTF9+nSio6Odcv+LUaVvH3P33fDhh2Y7I8OMUwnr1pkSBLt2mf2ePc3oZfXq1sYlIlJcxf38dlrCFBcXR4cOHbxqAd5LoYTJxyQmQmio2X7jDRg0yNp4PMjZs/DCCzBxoik7EBJi5jgNGmSKYIqIeBO3JUyfffZZrn273c7hw4eZMWMGERERfPnll45czmspYfJBOXuVNPaUz/btMHAgbNhg9q+9FubMgULKl4mIeBy3JUx+ef5LabPZqFSpEl26dGHy5MlUrVrVkct5LSVMPkgJ00Wlp5shuf/8x6xZHBAATz9tajgFBFgdnYjIxbmt0ndGRkauV3p6OkeOHOH9998vMcmS+KjbbsvefuEF6+LwYP7+pvTAr7/CDTdAWho8+SS0bOmz6xeLiABOnMNU0qiHyQfZ7bkn5eifRqHsdvjgAxgxAo4fN21XXAGbN5t5TiIinshtQ3J2u51FixaxatUqjh49SkZGRq7jixcvduRyXksJk4/KOSynp+WK5Phx6NYNtm3Lbrv/flM9XETE07htSG7kyJH06dOHffv2UbZs2VwL0oZmPmUk4q1eey17W4+AFUnFihAXZyaAZ5o71+SamT1PIiLezuEepgoVKrBgwQJuvPFGV8XkFdTD5MM0+bvYEhKgfPncbS1awKZN1sQjIpKX23qYQkNDqVu3rqNvE/FOWpvQIaGhJsd86KHsts2bzRIreZZ+FBHxKg4nTOPHj2fChAmcOXPGFfGIWO/cuextfcoXy2uvwenT2furVpnlVebOVaediHgnhxOmu+66i5MnT1K5cmWaNGlC8+bNc71EvN5ledakTkuzJg4vV7asSY62bIHmzeHkSejfH667DvbutTo6ERHHXHbxU3Lr168fmzdv5r777iM8PBybniISX/TZZ3DLLWY7MFDdIpegWTNTHXzqVFPkcuVKaNIEnnkGRo7Mn5+KiHgihyd9lylThuXLl9O+fXtXxeQVNOm7BMj5n4GkJChTxrpYfMTevWYNum+/NfvNm8Nbb0FUlLVxiUjJ4bZJ3xEREUoQpGQYMiR7u2xZ6+LwIfXqwYoV8Pbb5mm6LVtMlfCxY0HTIkXEkzmcME2ePJnHH3+c/fv3uyAcEQ8ya1bu/b/+siYOH2OzmblMO3fCXXeZ9elefBGaNoXVq62OTkSkYA4PyYWFhZGSksL58+cJDg6mVKlSuY6fOHHCqQF6Kg3JlRCDB8Ps2dn7KSlQurR18figzz6Dhx/OzkcffBAmTYKwMGvjEhHf5LalUebNm1fo8X79+jlyOa+lhKkEyftggyaAO11CghmWyyy0XqUKzJgBt99ubVwi4nvcljCJoYSpBMm7KG9mmzjdunWmh2nXLrN/660mcapWzdq4RMR3uHTSd2JiYq7twl4iPsdmg7yLSr//vjWx+Lj27c26dE8+acoNLFliCl7Onm3WQhYRsUqRepj8/f05fPgwlStXxs/Pr8DaS3a7HZvNRnp6uksC9TTqYSqBNDTnVtu3w8CBpoYTQIcOJnGqX9/auETEuxX387tIJeO+/fZbKlSoAMCqVauKF6GIt7PbcydNNhscOAAREa6/96FDMGECvPGG6+/lIZo0ge+/N0NyTzwBa9dCZKQpfjl6NOR53kRExKUcnsN04MABIiIi8vUy2e12Dh48SM2aNZ0aoKdSD1MJNXAgvPlm7jZX9TSlpcH118OaNe65nwfbv98s6Lt8udlv2tT8NbRqZWlYIuKF3Fa4sk6dOhw7dixf+4kTJ6hTp46jlxPxLnPm5G87etRMsPn999zrzp09C88/bz7piyMwMH+yVELVrg1ffgkLFsDll8PPP0ObNvDoo5CcbHV0IlISOJwwZc5VyispKYmgoCCnBCXi0fJW/Q4PB39/uOoqk+TYbNCnj6nX9OSTZhjNZoMBA+Dmm3O/9+xZx+9/8GDxY/diNhvce68peHnvvSZHfeUVaNwYvv7a6uhExNcVednL2NhYAGw2G0899RTBwcFZx9LT09mwYQNRWhBKSoLTp83XwhaeXrAgf9vbb1/4fXY77N5tJurcf3/B78+0fbt75k15qEqVzB/Pvfeazrv9+6F7d+jb1yRQl19udYQi4ouKnDBt3boVMD1M27dvJyAgIOtYQEAAkZGRPPbYY86PUKQkuOGG7Ak6a9YUnjDddFOJnMeUV48e8OuvphNv+nSYP98M202bBv/6V+H5rIiIoxye9N2/f3+mTZtW4ic6a9K3EBcHzZq5/j5PPWXGnDKfrwclTHls2GAKXv7yi9m/6SazFGAJeQZFRBxgSaXvg//MpYgogcMDSpgEcE83RuY/0Zz3UsKUT1oa/Pe/8NxzZrtsWZg4EYYMMVPMRETAjU/JnT9/nqeeeorQ0FBq165N7dq1CQ0N5cknn+TcuXOOXk7EuxWWuGzaZJ6cO3rUjB8Vx7XXZm9/9ZX5qsqNBQoIMJ1xcXFwzTWQlATDhpk/wh07rI5ORLydwwnTsGHDmD17NpMmTWLr1q1s3bqVSZMm8dZbbzF8+HBXxCjiHf74A86cMdthYdCiBVxxhZml/MUXsHp17vPvvvvi15w5M3s786GK3bv1LH0hGjQwc+dnzYJy5WD9emjUCAYPhvPnrY5ORLyVw0NyoaGhfPjhh/TI8z/mL774grvvvpuEhASnBuipNCQnxZJ3WO1iQ3p5/3lWrQpHjpgsoE0b58fnYw4eNENyy5aZ/TJlzHSwdu2sjUtErOO2IbnAwEBq166dr71OnTq5npwTkQKMGWO+zp5tvp46lfv40KGFvz+zlykuzrlx+aiICPj8c/PUHJiOuWuuMXnqyZPWxiYi3sXhhGno0KE8++yzpKamZrWlpqby/PPPM/Riv+xFSrqJE02v0cCBZj801OwPGwaPPAKvvpp97nff5X+/EiaH2WzwwQdw/HjunqUKFQqv3iAikpPDQ3K33norK1euJDAwkMjISAC2bdtGWloaXbt2zXXu4sWLnReph9GQnFhi4ULTXRIdDT/+aHU0Xmno0NxTwwD27TPLr4iI7yvu53eRC1dmKl++PLfffnuutpJYVkDEEpk9TD//DOnpel6+GGbMMOUHrr0W/qnHS506MGGCecpOBS9FpCCXVIepJFMPk1giPR1CQiAlxTwr36CB1RF5tU8/hV69crept0nEt7lt0nemY8eOsW7dOtatW8exY8eKexkRcYS/P2Su4/jFF9bG4gN69oQc0zEB09vUqBGorJyI5ORwwpScnMwDDzxA1apV6dChAx06dKBatWoMGDCAlJQUV8QoIjkdP26+au1GpwgIMPPulyzJbtuxAwIDzVp1IiJQjIQpNjaWNWvW8Pnnn3Pq1ClOnTrFp59+ypo1a3j00UddEaOI5HTbbVZH4JN69TIjnpUrm3273SwVOH58/l4oESl5HJ7DVLFiRRYtWkSnTp1yta9atYq77rqrxAzPaQ6TWOabb+D66812RoZmKbvAn3+aKg+ffWb2GzSAN99UwUsRX+C2OUwpKSmEh4fna69cubLXDcnVrl2bpk2bEhUVRefOna0OR6Rocq4v99tv1sXhw2rUgKVL4aOPTI/Tzp3Qvr0pl3X6tNXRiYgVHE6Y2rZty7hx4zh79mxW25kzZ5gwYQJt27Z1anDu8MMPPxAXF8eqVausDkWkaIKCsrfzFhQSp7HZ4M47TbL0wANmiG7GDDMhPHOpFREpORyuwzRt2jS6d+9OjRo1chWuDAoKYvny5U4PUEQKsXOn1RH4vAoV4K234J57YNAgs8byzTebtZOnTs2e8yQivs3hHqbGjRvz+++/M3HiRKKiooiKiuLFF1/k999/p1GjRk4LbO3atcTExFCtWjVsNhtLly7Nd87MmTOpXbs2QUFBREdHs3HjRofuYbPZ6NixI61ateK9995zVugirtezp/n67bfWxlGCdO0K27ebhxP9/MxyKw0awPz5+ddIFhHf43APE0BwcDADM9fCcpHk5GQiIyN54IEHuK2Ap4IWLlxIbGwsr7/+OtHR0UydOpXu3buza9cuKv/zX76oqCjOnz+f771ff/011apVY926dVSvXp3Dhw/TrVs3mjRpQtOmTV36fYk4RVSUqboobhUcDC+9ZFanGTAAtm2Dfv3gvffgjTdU8FLEl3lFpW+bzcaSJUvolaMkb3R0NK1atWLGjBkAZGRkEBERwbBhwxiTuSK8A0aPHk2jRo24//77Czyempqaa8HhxMREIiIi9JScWOPnn+GfIXHS0qBUKWvjKYHOnYPJk7PLDgQHw/PPm4nhWrFGxHO5vdK3ldLS0ti8eTPdunXLavPz86Nbt26sX7++SNdITk7m9D+PuyQlJfHtt98WOqQ4ceJEQkNDs15aP08slXNJlC+/tC6OEqxUKRgzxgzTdexoVqsZNQratjX5rIj4Fq9MmI4fP056enq+8gbh4eEcOXKkSNeIj4+nffv2REZG0qZNG/r27UurVq0ueP7YsWNJSEjIeh08ePCSvgeRS5KzRylzPpNY4sorzVSy2bMhNBR++glatIAnn4QcDxOLiJcr1hwmX1C3bl22bdtW5PMDAwMJDAx0YUQi4q38/GDgQLjpJhg61Cyz8vzzsGgRzJmTu3SWiHinYvcwbd68mQULFrBgwQK2bNnizJguqmLFivj7+xMfH5+rPT4+nipVqrg1FhHLqMK3x6lWDRYvhk8+gSpVYNcu6NABHn4YEhOtjk5ELoXDCdPRo0fp0qULrVq1Yvjw4QwfPpyWLVvStWtXty2LEhAQQIsWLVi5cmVWW0ZGBitXrvTK4pkixTJ1avZ2RoZ1cUg+t91mSmQ9+KDZf+01aNgwe6kVEfE+DidMw4YN4/Tp0/z666+cOHGCEydO8Msvv5CYmMjw4cOdFlhSUhJxcXHExcUBsG/fPuLi4jhw4ABgFgGeM2cO8+bNY+fOnQwZMoTk5GT69+/vtBhEPNpDD2Vvb99uXRxSoPLlzXDct9/CFVfAX3+Z6Wa9e0OeznER8QIOlxUIDQ1lxYoV+SZIb9y4keuvv55Tp045JbDVq1cXuL5bv379mDt3LgAzZszgpZde4siRI0RFRTF9+nSio6Odcv+L0eK74hFyDst5foWQEuvMGZgwAV5+GdLTISzMlCS4/36NrIq4W3E/vx1OmMqVK8d3331HVFRUrvatW7fSsWNHEkvIQL0SJvEISpi8ytatZpguc9pn167m6bq6da2NS6QkcVsdpi5dujBixAgOHTqU1fbXX38xatQounbt6ujlRERKjGbNYMMGmDTJrKG8ciU0bmx6mwpYlEBEPIjDCdOMGTNITEykdu3a1KtXj3r16lGnTh0SExN59dVXXRGjiBTFiRNWRyBFcNllMHq0mXbWpYsZrnvsMWjTBv6ZsikiHqhYS6PY7XZWrFjBb7/9BkCDBg1yVd0uCTQkJx7BbjdFgABmzIBHHrE2HnGI3Q7vvAOPPgqnTpklVUaPhqefhtKlrY5OxDe5bQ7T/Pnz6d27d74ijmlpaXz44Yf07dvXkct5LSVM4jE0j8nrHTli1qBbtMjsX3mlecKuY0dr4xLxRW5LmPz9/Tl8+DCVK1fO1f73339TuXJl0tPTHbmc11LCJB5DCZPPWLrUdBJmThEdNAj++19TokBEnMNtk77tdju2Ap6D/fPPPwkNDXX0ciLiTCpg6dV69YIdO2DwYLM/e7YpeLlkibVxiYgDCVOzZs1o3rw5NpuNrl270rx586xXZGQk1157bYmbxyTiEb75Jnt7wgTr4hCnCA2F11+HNWvgqqvg8GFTOfz22822iFijyENyE/75RTxhwgQeffRRypYtm3UsICCA2rVrc/vttxMQEOCaSD2MhuTEo2hYziedPQvPPmvKEJw/b4bmXn4ZHnhABS9Fisttc5jmzZtH7969CQoKcjhIX6KESTyKEiaftm2bKXi5aZPZ79zZDNddcYW1cYl4I7fNYerXr1+JT5ZEPNrRo1ZHIE4WGQnr15sCl6VLw6pV0KSJmRCugpci7uFwwiQiHuiNN7K3w8Oti0Nc5rLLIDYWfvkFrrvODNeNGQOtW2cvtSIirqOEScQXDBpkdQTiJnXrwvLlMHeuWcR361aTNP3735CSYnV0Ir5LCZOIiJex2aBfP9i5E3r3hvR0MzG8aVP49luroxPxTcVOmNLS0ti1axfnNYAu4nkcfYTqzBnXxCEuFR4OH34In30GNWrA3r3QtSsMGAAnT1odnYhvcThhSklJYcCAAQQHB9OoUSMOHDgAwLBhw3jxxRedHqCIFFFCwoWP2e0XHq+x2SA42DxydeAA9OgBf/zhmhjFJWJi4Ndf4eGHzf7bb0ODBmapFT00KeIcDidMY8eOZdu2baxevTrX03LdunVj4cKFTg1ORByQ9/HYnJ+Ufn5QpoxZpMxmgxdfhLQ0uOWW7HP27oVateCrr6BePbMa7MWcPGnKUv+zEHcuzZrB998X73sRh4WEwMyZ8N13cPXVEB8Pd95pil7+9ZfV0Yl4P4frMNWqVYuFCxfSpk0bypUrx7Zt26hbty579uyhefPmJCYmuipWj6I6TOKRChqKu+02WLy4eNe72K+HvPf78UeIjs7dfvgwVKlSvPtLsZw9Cy+8ABMnmrIDISFmjtPAgSZ3FinJ3FaH6dixY/kW3gVITk4ucI05EXGjc+fytxU3WQJITXVsfbo2bfK3jRhR/PtLsQQFwTPPmHID0dGQmAgPPWQKXu7aZXV0It7J4YSpZcuWLFu2LGs/M0l68803adu2rfMiExHHXXaZc68XFAT+/qbH6PRpM+aTlubYNT76CKZMcW5cUiRNmphR0alTzTS1tWtNEcwXXig4txaRC3N4SG7dunX06NGD++67j7lz5zJ48GB27NjBDz/8wJo1a2jRooWrYvUoGpITj+WOnt6EBLNKbEHs9oJj0OxjS+3fb3qZli83+02bwltvQcuWloYl4nZuG5Jr3749cXFxnD9/niZNmvD1119TuXJl1q9fX2KSJRGP9vbbjp2fnp57/9ixi7/nQskSaFVYD1W7Nnz5Jbz7Llx+Ofz8sxmue+wxSE62OjoRz+dwD5MY6mESr3Ch5OX8eThyBEqVgsqV4aab4IsvYMcO8zy6K5Ie/arxGMeOwciR8P77Zr9OHbO6znXXWRuXiDu4rYfpiy++YHlmn24Oy5cv58svv3T0ciLiLj/9BBs2mB4lf3+oXt0kSwDLlpmEpkED19zbZtO6HR6kUiV47z3z1x4RAfv2wfXXw/33w99/Wx2diGdyOGEaM2YM6Xm78AG73c6YMWOcEpSIOMn69ebrtGlmskrr1s5/rnzw4IufY7ebyoriUW680fy1DBtmctp586BhQ1i4UB2CInk5/Jvz999/p2HDhvnar776avbs2eOUoETESdq0MZ98w4c79r7U1Ozt7duzh+oKUq+eGeIrSKVK0K2b2f75Z8diELcoVw6mTzdP0zVsCEePwr/+BT17wp9/Wh2diOdwOGEKDQ3ljwKWTdizZw9lypRxSlAiYrGAADN0l5EBjRubZOlCSdfo0WaIryA//2wex8rcFo/Vtq2p2zR+vJna9vnnJoGaNcuxUlwivsrhhKlnz56MHDmSvXv3ZrXt2bOHRx99lFtyLrMgIt7Nzy/35O977in8/EqV8rdVqZKdMG3b5rzYxCUCA2HcOIiLMwnU6dPwyCPQoQPs3Gl1dCLWcjhhmjRpEmXKlOHqq6+mTp061KlThwYNGnD55Zfz8ssvuyJGEfEEISHw6acwf76ZPN61q1n2JFN8PHTvnr2f2aOUs4dJE2O8QsOGZk26V1+FsmXNcF1UFDz7rON1S0V8RbHKCtjtdr755hu2bdtG6dKladq0KR06dHBFfB5LZQVEiig11Sz8m54OBw9CjRpWRyQOOHAAhgwxVSfAjNC++aap4STijYr7+a06TMWkhEnEAY0bm8exli0zj2aJV7Hb4cMPzTS248fNSO3w4fDcc6YHSsSbFPfzu1gLT61cuZKVK1dy9OhRMvLMBnzb0SrDIuL7mjY1CdO2bUqYvJDNBnffbQpbxsaaauHTpsHSpfD663DDDVZHKOJ6Ds9hmjBhAtdffz0rV67k+PHjnDx5MtdLRCQfPSnnEypWNFPYvvoKatWC//0PevSAPn1Mz5OIL3N4SK5q1apMmjSJPn36uComr6AhOREHfPml6Vlq2FAFLH1EUhI89ZTpabLbTTI1bZrpidJyguLJ3LY0SlpaGu3atXP0bSJSkmX2MO3aBWfPWhuLOEXZsjBliikm37ix6WG69164+WYzUVzE1zicMD344IO8n7lio4hIUVSrBhUqmCflduywOhpxouho2LzZlBwICDBP0zVsaEoSFLCKlojXcnjS99mzZ5k9ezYrVqygadOmlCpVKtfxV155xWnBiYiPsNkgMhJWrTLzmJo3tzoicaKAAHjySbjjDhg4ENatM0/Rvf++KUHQqJHVEYpcOocTpp9//pmoqCgAfvnll1zHbBq4FpELado0O2ESn3T11bBmDbzxBvz73/Djj9CsGfznPzB2rKkkLuKtVIepmDTpW8RBb78NAwaYCuErVlgdjbjYn3/Cww+bNenADNO9+aZZckXESm6b9C0iUiw515TT/9N8Xo0aZiWdhQuhcmUzde2aa2DYMLNGnYi3KVYP06ZNm/joo484cOAAaXkWFlq8eLHTgnOlXbt20bt371z7H3zwAb169SrS+9XDJOKgM2fMo1UZGXDoEFStanVE4iYnTsCjj8LcuWY/IsIUvFQNU7GC23qYPvzwQ9q1a8fOnTtZsmQJ586d49dff+Xbb78lNDTU0ctZpn79+sTFxREXF8e6desoU6YM1113ndVhifiu0qXhqqvMtuYxlSgVKsA778A330CdOmZJwZtugnvugWPHrI5OpGgcTpheeOEFpkyZwueff05AQADTpk3jt99+46677qJmzZquiNHlPvvsM7p27UqZMmWsDkXEt6nid4nWrRts3256m/z84IMPoEEDs9SKRmnF0zmcMO3du5ebbroJgICAAJKTk7HZbIwaNYrZs2c7LbC1a9cSExNDtWrVsNlsLF26NN85M2fOpHbt2gQFBREdHc3GjRuLda+PPvoo1/CciLhIznlMUiKVKQMvvwwbNuFl9BUAACAASURBVJgfh7//hr59zXp0+/dbHZ3IhTmcMIWFhXH6nxl71atXzyotcOrUKVJSUpwWWHJyMpGRkcycObPA4wsXLiQ2NpZx48axZcsWIiMj6d69O0ePHs06JyoqisaNG+d7HTp0KOucxMREfvjhB27UYLqI60VGmq/qYSrxWraETZvghRdMuYGvvzb1mqZOVcFL8UwOT/q+5557aNmyJbGxsTz77LO8+uqr9OzZk2+++YbmzZu7ZNK3zWZjyZIluSZkR0dH06pVK2bMmAFARkYGERERDBs2jDFjxhT52u+++y7Lly9nwYIFhZ6XmppKampq1n5iYiIRERGa9C3iiAMHzKqtl10Gycmm4qGUeLt3m4KXa9ea/datTQmCJk2sjUt8k9smfc+YMYN//etfADzxxBPExsYSHx/P7bffzltvveXo5YolLS2NzZs3061bt6w2Pz8/unXrxvr16x26VlGH4yZOnEhoaGjWKyIiwuG4RUq8iAgIDYXz5+G336yORjzEVVeZmqZvvAEhIbBxoykG/9RTWnpQPIfDCVOFChWoVq2aebOfH2PGjOGzzz5j8uTJhIWFOT3Aghw/fpz09HTCw8NztYeHh3PkyJEiXychIYGNGzfSvXv3i547duxYEhISsl4HDx50OG6REs9m0zwmKZCfHwwaZOo19expcurnnjOVwtetszo6kWIkTP7+/rnmCWX6+++/8ff3d0pQ7hIaGkp8fDwBRRgWCAwMJCQkJNdLRIohcx7TDz9YG4d4pOrVYckSWLQIqlQxHZHXXmuqhicmWh2dlGQOJ0wXmvKUmppapMTDGSpWrIi/vz/x8fG52uPj46lSpYpbYhCRYsr81Hv9dWvjEI9ls8Htt5vepgEDTNtrr5nlVTKXWhFxtyIvvjt9+nTATMB+8803KVu2bNax9PR01q5dy9VXX+38CAsQEBBAixYtWLlyZdZE8IyMDFauXMnQoUPdEoOIFFOnTjB/vtlOTwcv65kW9wkLM5O/77nHDNft3Qu33AJ33QXTp0OeWRkiLlXkhGnKlCmA6WF6/fXXcw2/BQQEULt2bV534v8Yk5KS2LNnT9b+vn37iIuLo0KFCtSsWZPY2Fj69etHy5Ytad26NVOnTiU5OZn+/fs7LQYRcYG+feGBB8z2okWgGmhyEV26mEoUEybA5Mnw0Uemavgrr0C/fqZHSsTVHC4r0LlzZxYvXuzyCd6rV6+mc+fO+dr79evH3H8WJJoxYwYvvfQSR44cISoqiunTpxMdHe3SuDJpLTmRS5DzE04lnsUBW7bAgw/C1q1mv1s383Rd3brWxiXeo7if38VafDen9PR0tm/fTq1atdz2lJwnUMIkcgmUMMklOH/e9C6NG2fKDpQuDc8+CyNGmBJfIoVxWx2mkSNHZtVbSk9Pp0OHDjRv3pyIiAhWr17t6OVEREQcctll8PjjZpiuUyc4cwYeewzatlW1CnEdhxOmjz/+mMh/Hgv+/PPP2b9/P7/99hujRo3iiSeecHqAIuKDJk7M3tayRFJMV14J335rJoaHhpqlVlq0gP/8xyRRIs7k8JBcUFAQe/bsoUaNGgwaNIjg4GCmTp3Kvn37iIyMJLGEFMrQkJzIJcjIyP10nIbl5BIdPgzDhsEnn5j9K6+EOXOgY0dr4xLP47YhufDwcHbs2EF6ejpfffUV1113HQApKSleV7hSRCzil+dXj9a/kEtUtap56HLxYrP9++9muG7wYDh1yuroxBc4nDD179+fu+66i8aNG2Oz2bLWc9uwYYPb6jCJiI/58kurIxAfceutpuDloEFmf/ZsaNQIPv3U2rjE+xXrKblFixZx8OBB7rzzTmrUqAHAvHnzKF++PD179nR6kJ5IQ3Iil2jLFjPhJJOG5cTJ1qyBgQNNbxOo4KUYlpUVKKmUMIk4gcoLiIudOWMKXr78siksHxYGU6dCnz4qeFlSuTRhmj59OoMGDSIoKChriZQLGT58eJFv7s2UMIk4gRImcZO8BS+vv94sZ1injrVxifu5NGGqU6cOmzZt4vLLL6dOIT9dNpuNP/74o8g392ZKmEScwN0J019/wT/TCJSglTznzmUXvExNheBgU/By+HAVvCxJNCTnZkqYRJxg7Fh48UWznfdX0ZtvmgkoBw5ARMSl32v3bqhfP3dbRkb+pC2zdLT4rN27zaTwNWvMflQUzJplCl+K73NbWQEREafp1St/m90OBw+aZAmgZs2LX+fAARg/3kxSyclmM6/z5/MnS5C7vMHJk2Y/OBgGDCjytyDe56qrTMHLOXOgfHmIi4N27cxCvikpVkcnnqpIPUyxsbFFvuArr7xySQF5C/UwiTjB/ffDvHnZ+xkZ+Ws0AezZA0lJ0LSpmcUbHAzJySaxWbgw97mZvUY5h98Kk/krMO8M4CNH9DhVCXD4MNx5J3z/fXbbF19Ajx7WxSSuVdzP7yKN2m7NnCX3jy1btnD+/Hnq//M/tt27d+Pv70+LnI8Ii4hcTExM7oRp8eKCz7viitz7cXHmsae8yRKYhOvcuaIlS3DhxKpKFc1zKgGqVoV16+Cjj6B3b9N2443m9d57pgdKBIoxh+mVV15h9erVzJs3j7CwMABOnjxJ//79ufbaa3n00UddEqinUQ+TiBOkpkJQkNVRXJgSphLl1CmIjDQjvGCSqVmzCh45Fu/ltknf1atX5+uvv6ZRo0a52n/55Reuv/56Dh065MjlvJYSJhEncWcxnNdeg4ceKvo9lTCVSK+9Bg8/nL1/113w6qtQubJ1MYnzuG3Sd2JiIseOHcvXfuzYMU6fPu3o5URECuaKZKVdO/O1sEXCc/4C1Rp3JdKQIWaq3NixZo3ojz4y09meeEI5dEnmcMJ066230r9/fxYvXsyff/7Jn3/+ySeffMKAAQO47bbbXBGjiPiyCROcc53/b+/Ow5uq0j+Af5N0g9KWspVWShFkhy4W6FREts4UZNCKLDMgi4OirAo8j8CglGUEZKqiQxWBYXGjqD9ABhhcyialyjaBCrVSDItAixWhtIVuOb8/jk2abmnSNjfL9/M8ebj35OTeN5y0eXvuuecUFpqvExoq//Xxqb7OrVtAixZy+/vv6x4XOSQvL2D5cuDYMePY/+XL5RC5CsN6yUVYnDCtXbsWQ4cOxdixYxESEoKQkBCMHTsWQ4YMwTvvvNMQMRKRM1u0qO7HuHoV8PCoXP7bb8DNm0C3buYX+H34YTnoXKUCHnxQlp06VffYyKE9+CBw6ZJpWe/ewNKlQFGRMjGRMqyeuDI/Px8XLlwAAHTo0AHe3t71Gpi94xgmonp065Zc5Ks8IeSjqmkGKtYrU3FsUk2/3mqqWzah5nPPyfUziACkpRk7KQGge3c5lxMnvHQsNp+40tvbG6GhoQgNDXW5ZImI6lnFe7ermhtp40agX7+aj6PXG7evX6+5bvmJd8pPbQCwh4mq1LOn/Iht3Qq0bAmcPQv07SuXVuEQXufHpVGsxB4monp27ZrszXn55aovr5Ux14tUVCRn/K7N8iarV8s5nv78Z9PyzEygY0fA01N+E7q71+49kMv49Vdg7lxjrt22rfz4csJL+8e15GyMCRORQiy57GYtvV5eIszNBU6fNr0OQ1TOV1/JK7c6ndwfO1bm4S1bKhsXVY9ryRGR6/n224Y5rloNRETIbd4SRTX44x/l2Ka5c+XH5uOPga5dgQ8+4BQEzoYJExE5lhMnjNtRUQ13Ho5jolry9pYr9Xz3neyM/PVXYMIEYMgQ4OJFpaOj+sKEiYgcS2SknC6gpKRhz8OEiSzUq5fM55cvl8PfvvxS3km3erUcVkeOjQkTETmepk3lFMwNqfwlufJ33xHVwN1dzkpx5gzwyCNAQQEwe7aceuDMGaWjo7pgwkREVJXOneWddvn5wPnzSkdDDqZTJ+DAAeC99+RqO8ePy87Rl1/mijuOigkTEVFV3Nzk0vUAL8uRVdRqYMoUID0deOIJeRX51VeB8HDgm2+Ujo4sxYSJiKg6ZYv0jh2rbBzk0IKC5Ko7//d/QOvWQEaGvFw3dSpw+7bS0VFtMWEiIqrOuXNKR0BOZMQI2dv07LNyf+1auczh558rGxfVDhMmIqLqvPSScfvuXeXiIKfRtCmwbh2wf7+cZP7aNSAuDhg1CsjKUjo6qgkTJiKi6qxcadz+z3+Ui4OczsCB8q65+fPlDZ+ffSYnvNy4kRNe2ismTERE1Sm/DMuYMcrFQU6pUSNgxQo5d1NkJHDrFjB5MhATI5czJPvChImIiEhB4eFylZ+EBJlE7d8P9OwJrFrV8POzUu0xYSIiqsm8ecZtTmBJDcTNTa5H9/33sofp3j350evTh7Na2AsmTERENVmyxLjdpo1ycZBLaN9eLqmyaRPg7y8nmu/TRyZPBQVKR+famDAREdXE09O4ff26cnGQy1CpgEmT5BQEY8bIdehWrZIL++7fr3R0rosJExERkR0KCACSkuQ8TffdB1y4AAweDIwfD9y4oXR0rsdlE6aEhAR0794dPXr0wIcffqh0OERkz9LSjNu8fYls7LHH5Byq06bJ/Q8/lMnUjh3KxuVqXDJhSktLw8cff4yTJ0/i+PHjWLNmDW7duqV0WERkr7p3N2537KhcHOSyfH2BxETgyBFj2YgRQP/+wM8/KxeXK3HJhCk9PR3R0dHw8vJCo0aNEBYWhn379ikdFhHZq/LzMREpqG9fOen86NFy//BhIDgYWL2aE142NLtMmA4fPozhw4cjKCgIKpUKO3furFQnMTER7dq1g5eXF6KionDs2LFaH79Hjx44ePAgbt26hd9++w0HDx7E1atX6/MtEJGzeest4/a33yoXB7k8Ly9g2zbTS3KzZwOdOwMHDyoWltOzy4QpPz8fYWFhSExMrPL5bdu2Yc6cOYiPj8epU6cQFhaG2NhY3Cg3Ci48PBw9evSo9Lh27Rq6deuGWbNmYdCgQRgxYgT+8Ic/QKPR2OrtEZEjmjnTuB0drVwcRL+LiwOKi4FeveT++fNyyZWhQ+WddVS/VELYdyeeSqXCjh07EBcXZyiLiopC7969sWbNGgCAXq9HcHAwZs6cifnz51t8jmeeeQZPPPEEhg0bVm2dwsJCFBYWGvZzc3MRHByM27dvw9fX1+JzEpEDKn9pzr5/dZKLuXBBLuZb3ttvm+b5JOXm5sLPz8/i72+77GGqSVFREU6ePImYmBhDmVqtRkxMDFJTU2t9nLLeqIyMDBw7dgyxsbE11l+xYgX8/PwMj+DgYOveABE5ruHDjduck4nsSIcOciL6v/zFWDZrlszxc3OVi8uZOFzClJOTg9LSUgQEBJiUBwQEICsrq9bHefzxx9GtWzc89dRT2LRpE9zc3Gqsv2DBAty+fdvwuHLlilXxE5ED27XLuB0UpFwcRFVQqYCtW4FDh0zL/fw44WV9qDlLcGKW9EYBgKenJzzLz/hLRERkhx55RF4xnj8feO01WTZ4MPDMM3KBXz8/ZeNzVA7Xw9SiRQtoNBpkZ2eblGdnZ6N169YKRUVERGRfVq6UA8HLbNggpxTbu1e5mByZwyVMHh4eiIyMRHJysqFMr9cjOTkZ0bxzhYga2vvvG7dVKt6ORHbtgQdkb9PBg3Kc09WrwLBhwMSJwG+/KR2dY7HLhCkvLw9arRZarRYAoNPpoNVqcfnyZQDAnDlzsH79emzZsgXp6emYOnUq8vPz8fTTTysZNhG5gvHjTffNjH8ksgf9+wNnzsj5mlQqmfd36ybXqaPascuE6cSJE4iIiEBERAQAmSBFRERg0aJFAIAxY8YgISEBixYtQnh4OLRaLfbt21dpIDgRkU3Mnat0BERmNW4MvPEGkJICdOkCZGXJuZz++lcgJ0fp6Oyf3c/DZK+snceBiJyAEPK6xn//ayzT67mECjmMe/eAJUuAVavkR7dlS2DNGmDUKOf/GLvMPExERIpTqSqPnFWrnf+bhpyGlxewYgXw3XdAjx7AL78AY8bIBX05xVjVmDAREVnrhRcql3EQODmQXr2AkyeB+Hg5HG/nTjm2afNmTmZfERMmIiJrrV5duYyDwMnBeHgAixfLxCkyErh1C3j6abkm3e/3WhGYMBER1U1RUf0fc/58YMGC+j8uUQ1CQ4Fvv5XzN3l6Al98IedtWrtWjnNydRz0bSUO+iYiExXHLwlhLCsurn3P0+efy1uXAODKFaBNm/qLkaiWfvgBmDwZOHpU7vfvLye+rLjAryPioG8iIiVV/NuzfALl7g4cO1a7QSFlyRIALFsGZGZWXe/QIeDLLy2Pk6gWunQBDh8G3npLTkdw6JDsgXrjDdcdpseEiYjIFqKi5J10ej1QUgKcOiW/haZNk/tVWbcO6Nix8mW/GzeAAQOA2FiZmL31lkzKqhpTRWQljQaYNQtISwMGDgTu3pVTjj38MJCernR0tsdLclbiJTkiqqS01LpB325u8rLd2rXA1KlV13nggep7m8rjr3RqAELIS3Jz5wJ37siB4osWAS+9JHN1R2Lt9zcTJisxYSKiKik9F9OdO0CTJsrGQE7r55+B554zTkP24IPApk3ycp2j4BgmIiJ7oPTfoKdPK3t+cmpt2gC7d8u16Pz95ZXlyEg5j1ND3DBqT5gwERHVt337lDv3qVPKnZtcgkol16A+d07eo1BSAixdKnubvvtO6egaDhMmIqL6Fhsre5qEkIOzrXHvnvlvn7/+tXIZEyaykdatge3bgW3b5Fp0Z88C0dFynFNBgdLR1T8mTEREDenAAWDHDuCzzyx7nacn0KcPcOlS9XVefVUu/HX5spy/CWDCRDalUgGjR8u75p56Sv6N8MYbckzToUNKR1e/mDARETW0uDjgySeBwsLKM3hv2VK5/syZxu22bYGrV+W2v78cQHL2LHDiBHD//fLP/OBgeT0EkM/du9cw74OoGs2bAx98AOzZI8c5XbggO1enTgVyc5WOrn7wLjkr8S45IrLaL7/Ibxj173+zVryzbs8e4NFHLTumEEBAgDz2d9/J3ikiBdy+LacbWLfOWPbJJ8CoUcrFVB7vkiMichQtWxqTpYoefhj4058sP6ZKZexl4mU5UpCfH/Dee8D+/UD79rJs9Gj5+PVXZWOrCyZMRERKO3oUePxx4Px54JtvrJv8EmDCRHZl4EA5y8XIkXL/00+BFi2Av/9d2bisxYSJiEhp0dHAzp11X9mUCRPZmSZNZKK0bx/QqZMsW7ECaNcO0OkUDc1iTJiIiJxFWcKUlub8swiSQ4mNBc6ckQPCAXnzZ/v28p4HRxlJzYSJiMhZ3H+/HEBSVCRnFSSyI56ewJUrwNdfG8smTQJ8fYHjxxULq9aYMBEROQsO/CYHMHgwcPeuHOMEAHl58qZOlUquX22vmDARETkTJkzkALy85F10FT+mbm7yHgh7xISJiMiZMGEiBxIRUXm43SOPyLlbCwuViak6TJiIiJxJWcKk1dr39Q2i37m7y4HfZWtWl5YCa9bIXih7yvuZMBEROZOOHQFvbzlIJCND6WiIai02FtDrga1b5XxNLVvKyevtBRMmIiJnotEA4eFy257+PCeqBZUK+Mtf5PKJmZnAffcpHZEREyYiImcTGSn/ZcJEDsrDQ043YE+YMBERORsO/Caqd0yYiIicTVnCdOiQHBRCRHXGhImIyNl07Wrc3r9fuTiInAgTJiIiZ+PmZtz+4x+Vi4PIiTBhIiIiIjKDCRMRERGRGUyYiIic0YoVxu38fOXiIHISTJiIiJzRSy8Zt5s0US4OIifBhImIyBmp+eudqD7xJ4qIiIjIDCZMRERERGYwYSIicgU5OUpHQOTQXCJheuKJJ+Dv74+RI0da9BwRkUMrLTVuT56sXBxETsAlEqYXXngB77//vsXPERE5tPIDv3ftUi4OIifgEgnTgAED4OPjY/FzRERERIAdJEyHDx/G8OHDERQUBJVKhZ07d1aqk5iYiHbt2sHLywtRUVE4duyYApESERGRq1I8YcrPz0dYWBgSExOrfH7btm2YM2cO4uPjcerUKYSFhSE2NhY3btww1AkPD0ePHj0qPa5du2art0FEZJ9GjzZu6/XKxUHk4NzMV2lYQ4cOxdChQ6t9/o033sCzzz6Lp59+GgCwdu1a7NmzBxs3bsT8+fMBAFqttsHjLCwsRGFhoWE/Nze3wc9JRFRnH34IfPKJ3J44EfjgA2XjIXJQivcw1aSoqAgnT55ETEyMoUytViMmJgapqak2jWXFihXw8/MzPIKDg216fiIiq7i7G7dTUpSLg8jB2XXClJOTg9LSUgQEBJiUBwQEICsrq9bHiYmJwahRo7B37160adPGJNmq6bnyFixYgNu3bxseV65cse5NEREpRadTOgIih6X4JTlb+Prrr616rjxPT094enrWV0hERMq4eRNo1kzpKIgcjl33MLVo0QIajQbZ2dkm5dnZ2WjdurVCURERObDmzQEhlI6CyOHYdcLk4eGByMhIJCcnG8r0ej2Sk5MRHR2tYGRERA5k927TfbUaqOtdxEVFdUu8yt1EQ+QIFE+Y8vLyoNVqDXe66XQ6aLVaXL58GQAwZ84crF+/Hlu2bEF6ejqmTp2K/Px8w11zRERkxrBhlcvuu0/+W1AAqFTybrrayssDPD1NZxK3xIEDgJeXPO8TT1h3DCIbUzxhOnHiBCIiIhAREQFAJkgRERFYtGgRAGDMmDFISEjAokWLEB4eDq1Wi3379lUaCE5ERDV49tnKZRs2AN7ecnv8ePPHmD1bJjnlV0fIzQW++kr2OAHy3yNHgOLi6o8zaJBxu4rJionskUoIXsy2Rm5uLvz8/HD79m34+voqHQ4RkXnx8cDSpdU/r9fLhAiQl9tu3pRjnsr2a+pR6t8f2LQJaN/etOzgQeDll4EWLYCZM4GSEtm7VN7hw0BoKODnZ9XbIrKEtd/fTJisxISJiByOuaQHkElT587A+fNy//33Ze9T+eTJEr17A8eP165uQIA8d3CwvGTYsqU8Z9OmQKNGsjesbF6p5s2N2ypVzY/a1KlL/fKvIbvHhMnGmDARkcOy9Iv9u++AqKiGiQUA2rQBfv654Y5va/WdmLmy48eB+++v10Na+/3tEvMwERFRHTRUsnT2LNCtm9zOzQUyMoDMTODKFeD6deCXX2TP1u3bcnB6QQGQnw9cvQo0aSJ7w4So/gFU3rcFW5/PmdnR+odMmIiIyDK7dgEPPSTHJdVFWbIEAL6+8vJd7951O6Y5NSVYVSVZtXlY+hpL6rs6O1qGjAkTEZGrmTYNeOcd618/fLj8d+NG4G9/s+4YFSYkthle5iIrKT6tABER2diaNfJy2NdfAxoNEBZW+9d27GjcfvppeRfcP/9pLIuLM04xUF5oqOl+q1YWhUykNA76thIHfROR0ygtBdwqXHAIDpZjiSqq7isjIwNISQEmTpRJWPlenD17gNhYWV5YKO9us3bSS6I6svb7m59YIiJXp9EA//ufcX/6dECnM61TWlrzmJrOneXlOY1G7pfvUXr0UWN5XWYIJ1IQxzAREREQHl5zQmRpkpOaKieyLBvvROTgmOYTEVHVTpyQ/773nuWvbdxY9lS1bVu/MREphD1MRERUtchI3tpO9Dv2MBERERGZwYSJiIiIyAwmTERERERmMGEiIiIiMoMJExEREZEZTJiIiIiIzGDCRERERGQGEyYiIiIiM5gwEREREZnBhImIiIjIDCZMRERERGYwYSIiIiIygwkTERERkRlMmIiIiIjMcFM6AEclhAAA5ObmKhwJERER1VbZ93bZ93htMWGy0p07dwAAwcHBCkdCRERElrpz5w78/PxqXV8lLE2xCACg1+tx7do1+Pj4QKVS1dtxc3NzERwcjCtXrsDX17fejkv1i+1k/9hG9o9tZP+csY2EELhz5w6CgoKgVtd+ZBJ7mKykVqvRpk2bBju+r6+v03w4nRnbyf6xjewf28j+OVsbWdKzVIaDvomIiIjMYMJEREREZIZm8eLFi5UOgkxpNBoMGDAAbm68YmrP2E72j21k/9hG9o9tJHHQNxEREZEZvCRHREREZAYTJiIiIiIzmDARERERmcGEiYiIiMgMJkwKSExMRLt27eDl5YWoqCgcO3asxvqffvopunTpAi8vL/Ts2RN79+61UaSuy5I2Wr9+Pfr16wd/f3/4+/sjJibGbJtS/bD0Z6lMUlISVCoV4uLiGjhCsrSNbt26henTpyMwMBCenp7o1KkTf+c1MEvbaPXq1ejcuTMaNWqE4OBgzJ49G/fu3bNRtAoSZFNJSUnCw8NDbNy4UZw9e1Y8++yzomnTpiI7O7vK+ikpKUKj0YhVq1aJc+fOiZdfflm4u7uLtLQ0G0fuOixto7Fjx4rExETxv//9T6Snp4tJkyYJPz8/8fPPP9s4ctdiaTuV0el04r777hP9+vUTjz/+uI2idU2WtlFhYaHo1auXePTRR8WRI0eETqcTBw8eFFqt1saRuw5L2+ijjz4Snp6e4qOPPhI6nU588cUXIjAwUMyePdvGkdseEyYb69Onj5g+fbphv7S0VAQFBYkVK1ZUWX/06NFi2LBhJmVRUVHiueeea9A4XZmlbVRRSUmJ8PHxEVu2bGmoEElY104lJSXioYceEhs2bBATJ05kwtTALG2jd999V7Rv314UFRXZKkSXZ2kbTZ8+XQwaNMikbM6cOaJv374NGqc94CU5GyoqKsLJkycRExNjKFOr1YiJiUFqamqVr0lNTTWpDwCxsbHV1qe6saaNKiooKEBxcTGaNWvWUGG6PGvbaenSpWjVqhUmT55sizBdmjVttGvXLkRHR2P69OkICAhAjx49sHz5cpSWltoqbJdiTRs99NBDOHnypOGy3U8//YS9e/fi0UcftUnMSnLtaTttLCcnB6WlpQgICDApDwgIwA8//FDla7Kysqqsn5WV1WBxujJr2qiiefPmISgoqFKiS/XHFwE38AAACrNJREFUmnY6cuQI/v3vf0Or1doiRJdnTRv99NNP2L9/P8aNG4e9e/ciMzMT06ZNQ3FxMeLj420Rtkuxpo3Gjh2LnJwcPPzwwxBCoKSkBM8//zz+/ve/2yJkRbGHiagerVy5EklJSdixYwe8vLyUDod+d+fOHYwfPx7r169HixYtlA6HqqHX69GqVSusW7cOkZGRGDNmDBYuXIi1a9cqHRr97uDBg1i+fDneeecdnDp1Ctu3b8eePXuwbNkypUNrcOxhsqEWLVpAo9EgOzvbpDw7OxutW7eu8jWtW7e2qD7VjTVtVCYhIQErV67E119/jdDQ0IYM0+VZ2k4XLlzAxYsXMXz4cEOZXq8HALi5uSEjIwMdOnRo2KBdjDU/S4GBgXB3d4dGozGUde3aFVlZWSgqKoKHh0eDxuxqrGmjV155BePHj8czzzwDAOjZsyfy8/MxZcoULFy4EGq18/bDOO87s0MeHh6IjIxEcnKyoUyv1yM5ORnR0dFVviY6OtqkPgB89dVX1danurGmjQBg1apVWLZsGfbt24devXrZIlSXZmk7denSBWlpadBqtYbHY489hoEDB0Kr1SI4ONiW4bsEa36W+vbti8zMTEMyCwA//vgjAgMDmSw1AGvaqKCgoFJSVJbgCmdfmlbpUeeuJikpSXh6eorNmzeLc+fOiSlTpoimTZuKrKwsIYQQ48ePF/PnzzfUT0lJEW5ubiIhIUGkp6eL+Ph4TivQwCxto5UrVwoPDw/x2WefievXrxsed+7cUeotuARL26ki3iXX8Cxto8uXLwsfHx8xY8YMkZGRIXbv3i1atWol/vGPfyj1FpyepW0UHx8vfHx8xNatW8VPP/0kvvzyS9GhQwcxevRopd6CzTBhUsC//vUv0bZtW+Hh4SH69Okjvv32W8Nz/fv3FxMnTjSp/8knn4hOnToJDw8P0b17d7Fnzx4bR+x6LGmjkJAQAaDSIz4+3vaBuxhLf5bKY8JkG5a20dGjR0VUVJTw9PQU7du3F6+++qooKSmxcdSuxZI2Ki4uFosXLxYdOnQQXl5eIjg4WEybNk389ttvCkRuWyohnL0PjYiIiKhuOIaJiIiIyAwmTERERERmMGEiIiIiMoMJExEREZEZTJiIiIiIzGDCRERERGQGEyYiIiIiM5gwEVG9GzBgAF588UWlw6iWvcanUqmwc+dOpcMgUtThw4cxfPhwBAUFWfUzsXjxYqhUqkoPb2/vOsXFiSuJqN7dvHkT7u7u8PHxUTqUKlWMr127dnjxxRdtlkQtXrwYO3fuhFarNSnPysqCv78/PD09bRIHkT3673//i5SUFERGRmLEiBHYsWMH4uLiav36vLw85OXlmZQNHjwYvXv3xubNm62Oy83qVxIRVaNZs2ZKhwAA1a5w31DxVXe+2qpuhXgiVzJ06FAMHTq02ucLCwuxcOFCbN26Fbdu3UKPHj3w2muvYcCAAQCAJk2aoEmTJob6p0+fxrlz57B27do6xcVLckRU7ype8mrXrh2WL1+Ov/3tb/Dx8UHbtm2xbt06w/MXL16ESqXC9u3bMXDgQDRu3BhhYWFITU01Oe6RI0fQr18/NGrUCMHBwZg1axby8/NNzrNs2TJMmDABvr6+mDJlitn4BgwYgEuXLmH27NmGrvu6nm/evHno1KkTGjdujPbt2+OVV15BcXExAGDz5s1YsmQJTp8+bThf2V+9FS8/pKWlYdCgQWjUqBGaN2+OKVOmmPzlPGnSJMTFxSEhIQGBgYFo3rw5pk+fbjgXkTOaMWMGUlNTkZSUhDNnzmDUqFEYMmQIzp8/X2X9DRs2oFOnTujXr1/dTqzsUnZE5Iz69+8vXnjhBcN+SEiIaNasmUhMTBTnz58XK1asEGq1Wvzwww9CCCF0Op0AILp06SJ2794tMjIyxMiRI0VISIgoLi4WQgiRmZkpvL29xZtvvil+/PFHkZKSIiIiIsSkSZNMzuPr6ysSEhJEZmamyMzMNBvfr7/+Ktq0aSOWLl0qrl+/Lq5fv17n8y1btkykpKQInU4ndu3aJQICAsRrr70mhBCioKBAzJ07V3Tv3t1wvoKCAiGEEADEjh07hBBC5OXlicDAQDFixAiRlpYmkpOTxf3332+yEOrEiROFr6+veP7550V6err4z3/+Ixo3bizWrVtnfeMR2ZHyPxNCCHHp0iWh0WjE1atXTeoNHjxYLFiwoNLr7969K/z9/Q0/f3WKpc5HICKqoKqE6amnnjLs6/V60apVK/Huu+8KIYwJ04YNGwx1zp49KwCI9PR0IYQQkydPFlOmTDE5zzfffCPUarW4e/eu4TxxcXFWxffmm2+a1KnP8/3zn/8UkZGRhv34+HgRFhZWqV75L4d169YJf39/kZeXZ3h+z549Qq1Wi6ysLCGETJhCQkJESUmJoc6oUaPEmDFjzMZE5AgqJky7d+8WAIS3t7fJw83NTYwePbrS6z/++GPh5uZm+JmpC45hIiKbCA0NNWyrVCq0bt0aN27cqLZOYGAgAODGjRvo0qULTp8+jTNnzuCjjz4y1BFCQK/XQ6fToWvXrgCAXr161Uu8dTnftm3b8Pbbb+PChQvIy8tDSUkJfH19LTp/eno6wsLCTO7s6du3L/R6PTIyMhAQEAAA6N69OzQajaFOYGAg0tLSLDoXkaPIy8uDRqPByZMnTT73AEzGLZXZsGED/vznPxt+XuqCCRMR2YS7u7vJvkqlgl6vr7ZO2Viisjp5eXl47rnnMGvWrErHbtu2rWG7rrcOl7H2fKmpqRg3bhyWLFmC2NhY+Pn5ISkpCa+//nq9xFVRbf5fiZxFREQESktLcePGDbNjknQ6HQ4cOIBdu3bVy7mZMBGRQ3jwwQdx7tw5PPDAA/V+bA8PD5SWltbL+Y4ePYqQkBAsXLjQUHbp0iWz56uoa9eu2Lx5M/Lz8w1JWUpKCtRqNTp37mxRTESOJC8vD5mZmYZ9nU4HrVaLZs2aoVOnThg3bhwmTJiA119/HREREfjll1+QnJyM0NBQDBs2zPC6jRs3IjAwsMY77izBu+SIyCHMmzcPR48exYwZM6DVanH+/Hl8/vnnmDFjRp2P3a5dOxw+fBhXr15FTk5Onc7XsWNHXL58GUlJSbhw4QLefvtt7Nixo9L5yr4EcnJyUFhYWOk448aNg5eXFyZOnIjvv/8eBw4cwMyZMzF+/Ph6ubxAZK9OnDiBiIgIREREAADmzJmDiIgILFq0CACwadMmTJgwAXPnzkXnzp0RFxeH48ePm/T86vV6bN68GZMmTap06c5aTJiIyCGEhobi0KFD+PHHH9GvXz/DL9CgoKA6H3vp0qW4ePEiOnTogJYtW9bpfI899hhmz56NGTNmIDw8HEePHsUrr7xiUufJJ5/EkCFDMHDgQLRs2RJbt26tdJzGjRvjiy++wM2bN9G7d2+MHDkSgwcPxpo1a+r8fons2YABAyDkTWkmj7LpN9zd3bFkyRLodDoUFRXh2rVr2L59O3r27Gk4hlqtxpUrV/Dqq6/WW1yc6ZuIiIjIDPYwEREREZnBhImIiIjIDCZMRERERGYwYSIiIiIygwkTERERkRlMmIiIiIjMYMJEREREZAYTJiIiIiIzmDARERERmcGEiYiIiMgMJkxEREREZjBhIiIiIjLj/wEzwjRmRO118QAAAABJRU5ErkJggg==", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "semilogy(dto_svrg; label = \"optimal\", color = \"blue\");\n", "semilogy(dto_svrg2; label = \"3x step size\", color = \"red\");\n", "xlabel(\"inner iteration\")\n", "ylabel(\"distance to optimum\")\n", "legend();" ] }, { "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" } ], "source": [ "semilogy(collect(1:length(dto_svrg)) / length(dto_svrg) * time1[2], dto_svrg; label = \"optimal\", color = \"blue\");\n", "semilogy(collect(1:length(dto_svrg2)) / length(dto_svrg2) * time2[2], dto_svrg2; label = \"3x step size\", color = \"red\");\n", "xlabel(\"wall clock time (seconds)\")\n", "ylabel(\"distance to optimum\")\n", "legend();" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "srand(123456);\n", "time3 = @timed (w3, dto_svrg3) = svrg(w0, 3.0 * alpha, X, Y, sigma, Int64(ceil(T / 2)), K, wopt);" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "semilogy(dto_svrg2; label = \"3x step size\", color = \"red\");\n", "semilogy(dto_svrg3; label = \"50% epoch, 3x step size\", color = \"green\");\n", "xlabel(\"inner iteration\")\n", "ylabel(\"distance to optimum\")\n", "legend();" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "semilogy(collect(1:length(dto_svrg2)) / length(dto_svrg2) * time2[2], dto_svrg2; label = \"3x step size\", color = \"red\");\n", "semilogy(collect(1:length(dto_svrg3)) / length(dto_svrg3) * time3[2], dto_svrg3; label = \"50% epoch, 3x step size\", color = \"green\");\n", "xlabel(\"wall clock time (seconds)\")\n", "ylabel(\"distance to optimum\")\n", "legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Take-away: we can often do better than the simple theoretical recipe!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", ".\n", "\n", "# Can you do better?" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha_class = 5.0 * alpha;\n", "T_class = Int64(ceil(T / 3));\n", "K_class = Int64(ceil(2.0 * K));\n", "\n", "srand(123456);\n", "time_class = @timed (w_class, dto_svrg_class) = svrg(w0, alpha_class, X, Y, sigma, T_class, K_class, wopt);\n", "\n", "semilogy(collect(1:length(dto_svrg2)) / length(dto_svrg2) * time2[2], dto_svrg2; label = \"starting point\", color = \"green\");\n", "semilogy(collect(1:length(dto_svrg_class)) / length(dto_svrg_class) * time_class[2], dto_svrg_class; label = \"your suggestion\", color = \"purple\");\n", "xlabel(\"wall clock time (seconds)\")\n", "ylabel(\"distance to optimum\")\n", "legend();" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "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 }