{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Gradient descent\n", "===========================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n", "$\\newcommand{\\eqdef}{\\equiv}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This tour details Stochastic Gradient Descent, applied to the binary logistic classification problem." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We recommend that after doing this Numerical Tours, you apply it to your\n", "own data, for instance using a dataset from .\n", "\n", "\n", "_Disclaimer:_ these machine learning tours are intended to be\n", "overly-simplistic implementations and applications of baseline machine learning methods.\n", "For more advanced uses and implementations, we recommend\n", "to use a state-of-the-art library, the most well known being\n", "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "addpath('toolbox_general')\n", "addpath('solutions/ml_4_sgd')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Simple Example\n", "--------------\n", "We first illustrate the concept of stochastic gradient descent on a\n", "simple example\n", "$$ \\umin{x \\in \\RR} f(x) \\eqdef f_1(x) + f_2(x) $$\n", "where $f_1(x) \\eqdef (x-1)^2$ and\n", "$f_2(x) \\eqdef (x+1)^2$.\n", "\n", "\n", "Functions and their derivatives." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "f = {@(x)1/2*(x-1).^2, @(x)1/2*(x+1).^2};\n", "F = @(x)f{1}(x)+f{2}(x);\n", "df = {@(x)(x-1), @(x)(x+1)};" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Each iteration of SGD reads\n", "$$ x_{\\ell+1} = x_\\ell - \\tau_\\ell \\nabla f_{i(\\ell)}(x_\\ell) $$\n", "where $ i(\\ell) \\in \\{1,2\\} $ is drawn uniformly." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Implement the SGD, with a random initial condition $x_0$.\n", "Display several path (i.e. run several time the algorithm)\n", "to vizualize the evolution of the density of the random variable\n", "$x_\\ell$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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/bZ2YTxIJSWisyLNU09H1CghWG+GrURyj5gBZ5XHLn06GUQy0/npsxqox3xla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\nFAEFiRBCGgsFKQxx3zG0gRBCGggFiRBCSCaowxtjt2/fvnr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo1()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dataset Loading\n", "---------------\n", "We load a subset of the \n", "of $n=10000$ features in dimension $78$. The goal in this task is to learn a classification rule that differentiates between two types of particles generated in high energy collider experiments.\n", "\n", "\n", "First define a few helpers." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "SetAR = @(ar)set(gca, 'PlotBoxAspectRatio', [1 ar 1], 'FontSize', 20);\n", "Xm = @(X)X-repmat(mean(X,1), [size(X,1) 1]);\n", "Cov = @(X)Xm(X)'*Xm(X);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Load the dataset.\n", "Randomly permute it.\n", "Separate the features $X$ from the data $y$ to predict information." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "name = 'quantum';\n", "load(['ml-' name]);\n", "A = A(randperm(size(A,1)),:);\n", "X = A(:,1:end-1);\n", "y = A(:,end);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Set the classes indexes to be $\\{-1,+1\\}$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "y = rescale(y,-1,1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Remove empty features, normalize $X$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "I = find(mean(abs(X))>1e-1); X = X(:,I);\n", "X = X-repmat(mean(X),[size(X,1),1]);\n", "X = X ./ repmat( sqrt(sum(X.^2)/size(X,1)), [size(X,1),1] );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "$n$ is the number of samples, $p$ is the dimensionality of the features," ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "[n,p] = size(X);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Plot the classes." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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31KNO/co90q/tOGaLBULMvquplMpjbr3MmvpW4i6mb59uWPaakplHZ+LT++Tf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\nQmW7w4LycO7u9At8WvcyWIBO9R/kdDp/ceAXif+bCAQCsVhscHCw4qf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "I = randperm(n); I = I(1:500);\n", "options.disp_dim = 3;\n", "clf; plot_multiclasses(X(I,:),y(I),options);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Batch Gradient Descent (BGD)\n", "----------------------------\n", "We first test the usual (batch) gradient descent (BGD) on the problem of\n", "supervised logistic classification.\n", "\n", "\n", "We refer to the dedicated numerical tour on logistic classification for\n", "background and more details about the derivations of the energy and its\n", "gradient.\n", "\n", "\n", "Logistic classification aims at solving the following convex program\n", " $$ \\umin{w} E(w) \\eqdef \\frac{1}{n} \\sum_{i=1}^n L(\\dotp{x_i}{w},y_i) $$\n", "where the logistic loss reads\n", " $$ L( s,y ) \\eqdef \\log( 1+\\exp(-sy) ) $$\n", "\n", "\n", "Define energy $E$ and its gradient $\\nabla E$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "L = @(s,y)1/n * sum( log( 1 + exp(-s.*y) ) );\n", "E = @(w,X,y)L(X*w,y);\n", "theta = @(v)1 ./ (1+exp(-v));\n", "nablaL = @(s,r)- 1/n * y.* theta(-s.*y);\n", "nablaE = @(w,X,y)X'*nablaL(X*w,y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Implement a gradient descent\n", "$$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E(w_\\ell). $$\n", "Monitor the energy decay.\n", "Test different step size, and compare with the theory (in particular\n", "plot in log domain to illustrate the linear rate)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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xioqKDz/8MDY2ltW5ePFiREQEEeXk5LAZ4ampqQsXLrS3t58xY4afn19ZWdme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\nNxGpZtLcfTfVpoYDAJiW6plQyOEkoEA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo2()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Gradient Descent (SGD)\n", "---------------------------------\n", "As any empirical risk minimization procedure, the\n", "logistic classification minimization problem can be written as\n", "$$ \\umin{w} E(w) = \\frac{1}{n} \\sum_i E_i(w) \\qwhereq E_i(w) = L(\\dotp{x_i}{w},y_i). $$\n", "\n", "\n", "For very large $n$ (which could in theory even be infinite, in which case the sum needs to be replaced\n", "by an expectation or equivalenty an integral), computing $\\nabla E$ is prohebitive.\n", "It is possible instead to use a stochastic gradient descent (SGD) scheme\n", " $$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E_{i(\\ell)}(w_\\ell) $$\n", "where, for each iteration index $\\ell$, $i(\\ell)$\n", "is drawn uniformly at random in $ \\{1,\\ldots,n\\} $.\n", "\n", "\n", "Note that here\n", "$$ \\nabla E_{i}(w) = x_i \\nabla L( \\dotp{x_i}{w}, y_i )\n", " \\qwhereq \\nabla L(u,v) = v \\odot \\th(-u) $$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "nablaEi = @(w,i)-y(i) .* X(i,:)' * theta( -y(i) * (X(i,:)*w) );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Note that each step of a batch gradient descent has complexity $O(np)$,\n", "while a step of SGD only has complexity $O(p)$. SGD is thus\n", "advantageous when $n$ is very large, and one cannot afford to do\n", "several passes through the data. In some situation, SGD can provide\n", "accurate results even with $\\ell \\ll n$, exploiting redundancy between\n", "the samples.\n", "\n", "\n", "A crucial question is the choice of step size schedule $\\tau_\\ell$. It\n", "must tends to 0 in order to cancel the noise induced on the gradient by\n", "the stochastic sampling. But it should not go too fast to zero in order\n", "for the method to keep converging.\n", "\n", "\n", "A typical schedule that ensures both properties is to have asymptically $\\tau_\\ell \\sim \\ell^{-1}$ for\n", "$\\ell\\rightarrow +\\infty$. We thus propose to use\n", "$$ \\tau_\\ell \\eqdef \\frac{\\tau_0}{1 + \\ell/\\ell_0} $$\n", "where $\\ell_0$ indicates roughly the number of iterations serving as a\n", "\"warmup\" phase.\n", "\n", "\n", "One can prove the following convergence result\n", " $$ \\EE( E(w_\\ell) ) - E(w^\\star) = O\\pa{ \\frac{1}{\\sqrt{\\ell}} }, $$\n", "where $\\EE$ indicates an expectation with respect to the i.i.d.\n", "sampling performed at each iteration.\n", "\n", "\n", "Select default values for $ (\\ell_0,\\tau_0) $." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "l0 = 100;\n", "tau0 = .05;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "Perform the Stochastic gradient descent.\n", "Display the evolution of the energy $E(w_\\ell)$.\n", "One can overlay on top (black dashed curve) the convergence of the batch gradient descent, with a carefull scaling of the\n", "number of iteration to account for the fact that the complexity of a batch iteration is $n$ times larger.\n", "Perform several runs to illustrate the probabilistic nature of the method.\n", "Explore different values for $ (\\ell_0,\\tau_0) $." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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FCo2Ie/bsWasSmJp+++23nKPMfXx8vv7668mTJ+MF93bs2PH222/TB1MALaD3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\nGzZsyZIl9bpdEdItAelVh0sdvzEkTZhtRX3wGwOLOLqMyLU3A5zEMRv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo3()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Gradient Descent with Averaging (SGA)\n", "------------------------------------------------\n", "Stochastic gradient descent is slow because of the fast decay of\n", "$\\tau_\\ell$ toward zero.\n", "\n", "\n", "To improve somehow the convergence speed, it is possible to average the past\n", "iterate, i.e. run a \"classical\" SGD on auxiliary variables $ (\\tilde w_\\ell)_\\ell$\n", " $$ \\tilde w_{\\ell+1} = \\tilde w_\\ell - \\tau_\\ell \\nabla E_{i(\\ell)}(\\tilde w_\\ell) $$\n", "and output as estimated weight vector the average\n", "$$ w_\\ell \\eqdef \\frac{1}{\\ell} \\sum_{k=1}^\\ell \\tilde w_\\ell. $$\n", "This defines the Stochastic Gradient Descent with Averaging (SGA)\n", "algorithm.\n", "\n", "\n", "Note that it is possible to avoid explicitely storing all the iterates by simply\n", "updating a running average as follow\n", "$$ w_{\\ell+1} = \\frac{1}{\\ell} \\tilde w_\\ell + \\frac{\\ell-1}{\\ell} w_\\ell. $$\n", "\n", "\n", "In this case, a typical choice of decay is rather of the form\n", "$$ \\tau_\\ell \\eqdef \\frac{\\tau_0}{1 + \\sqrt{\\ell/\\ell_0}}. $$\n", "Notice that the step size now goes much slower to 0, at rate $\\ell^{-1/2}$.\n", "\n", "\n", "Typically, because the averaging stabilizes the iterates, the choice of\n", "$(\\ell_0,\\tau_0)$ is less important than for SGD.\n", "\n", "\n", " for logistic classification,\n", "it leads to a faster convergence (the constant involved are\n", "smaller) than SGD, since\n", "on contrast to SGD, SGA is adaptive to the local strong convexity of $E$." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 4__\n", "\n", "Implement the Stochastic gradient descent with averaging.\n", "Display the evolution of the energy $E(w_\\ell)$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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nT8ehpvj4+A8//PCKK64IpQwTJkyoW7cuHi9YsCDEkhtSu3bt1157jWLBly1b\ntm3btspkWNMxlyC9+OKLu3fv3r1795YtWyqfG64eZLfzAkIMEyPUqlULDwoKCspd0xkARo0a1a1b\nt27dugGAxr22b98+p9OJx0OHDu3QoUOIZUhMTKSQvIULF5a710Fw6tatO3nyZPrT5XJVJreajrkE\niWEYJgj9+vXDg6Kiovnz55eb/sEHH9yyZcuWLVs2btxIYobMnj27qKgIj8P1lb3++utr165du3bt\nsmXLwh1G0vPII4/QHN7vv/++krnVaGI27FuSol0ChmEizS233ELHTz311JkzZ5588snatWtXIKvV\nq1fjQZcuXcRsQ6Fly5YtW7aswE0NwUiH//73vwCwbdu2M2fOBJp4G/PEsoWkgMQrNTBMLNGtWzca\nFjp//vxzzz3XuXPnqVOnrl27NixL5cyZMzt27MDjLl26RL6gYdK6dWs8KC4uPnz4cHQLE0ViWZAY\nhokxatWqtXTpUtGg2bt378yZM/v169e0adNBgwbZbLbly5cXFhYGz2fv3r0kYJIJ3CkkSABw4sSJ\nKJYkusSsyw5hC4lhYoz69esvW7Zs1qxZc+bMEdvuU6dOrVy5cuXKlQBQt27d/v37p6enW63WRo0a\n6TMRLwwiSLm5uT///HPw8qSmprZr1y7cp9AgCtLJkycrmVvNJcYFCQAkUHJypGiXgmGigMMBdnu0\nC1Eh7Haw2QJ+2qBBgxkzZkydOjUrK2vJkiWrV6/WmETnzp1bsWLFihUr7Hb7Y489NmnSJHFZBCgr\nSElJSYFutGzZMponFIjp06c/++yzwdOUi7jIUMUWKY8N2GXHMDGLzQaqWiP/BVEjol69euPGjVu+\nfHl+fr7b7XY4HEOGDNG05vn5+TabrUePHkePHhXPixF3+fn5EXrfFefXX3+lYzO4EKNFLFtIOA9J\nAgVAim5JGIapOurUqSPLsizLAKCq6pYtWxYtWrRo0aJffvkFE+zfvz89Pd3tdlP02pVXXkmX79mz\nJ1DOrVq1SktLM/xo69atp06ditQj5OTk4EFCQkKLFi0ilW2NI5YFqV69jRDeYvAMw9Rs4uLiunfv\n3r179xkzZrz33nuPP/44Lni6adOmF154YebMmZhMDNoOIkjDhg0bNmyY4UcdO3asCkFKTk6OVJ41\nkZh12UmSaCExDHPJMXbs2PXr19P63GvWrKGP2rVrRwv27N69O9yci4uLaUnWiEBluJT9dRDDgkRI\nkBPtIjAMEwGmTZvWpEmTJk2atG/fPsRLrrvuOtquYvPmzRcvXqSPbr31VjzYsmXL1q1bwypJTk6O\nmFUlWbNmDa3zLe6FcQkS+4LEMExs0KhRo/z8/Pz8/P379wfxs2mgbfQKCwtF/JKaSwAAIABJREFU\nY2jMmDF4oKrqtGnTwirJ8uXLw0ofnNdee42Ohw4dGsGcaxyxLEjosksDT5TLwTBMJBDXPzVcvdsQ\nGp4BgCZNmtCxxWKhDZOWLl26cePGEDM8fvx45eO8ic2bN//nP//B46SkpMGDB0cq55pILAsSwmNI\nDBMbDBo0iMLkZs2aFWK4tse/2n/Dhg1p3Ah55ZVXaCOJ8ePHa0LDA/H0009HajGFnTt33n777SUl\nJfjnk08+GR8f+21yEGL54TmogWFiiYSEhEceeQSP//e//40cObLcgZzZs2eTc89qtWqae0mSpkyZ\ngsc//fTTTTfdFHwwqbCwcNKkSe+//34FH0BAVdVPP/104MCBv//+O54ZMGBAuZNwY55YFqRSeIc+\nhokJZs6cOWDAADx2u93du3f/6KOPaBcJkSNHjjzxxBOTJk3CP5OSkp544gl9sqeeeoqiHnJzc/v2\n7ZuVlWWoc+vWrevWrdvs2bNVVY2Li2vevHnwol68ePFsWQoKCvLy8tatW/fSSy9df/31o0eP/u23\n3zBxp06d5s2bRwGBlyxxqqpGuwxVxR31X1529kkAcMjuDKd8aYdTMrFMx44dKxC7XEM5ceJEz549\n9+/fT2dat2590003paSkJCcnFxYWHjlyZMeOHR6Ph5ZPbdOmTXZ2dqAAtqKioqlTp77yyivUGDZt\n2jQ9PV2SpGbNmu3fv3/btm3bt28nN11cXNy7776bl5dnt9uh7NJBhYWF9erVC/eJZFlevHhxiPvV\nQqW/blPXFjV2ubbeZyqACmAFp9sd7dIwTJWRmpoa7SJUK/v27RsxYkSI9kRqaur+/fvLzXPZsmXN\nmjUrN7cmTZpkZWWpqrphwwY8M336dMoEJ+GGTseOHT/99NOSkpKwHr+SX7eZa8sl4bLjqUgME0u0\na9du0aJFO3bsGD16tGYfWCI+Pv7OO+9ctmzZL7/80rZt23LzHDJkyNatW8eMGdO0aVPDBC1atJg8\nefK+ffseeughALjpppsCpQxE7dq1W7Ro0alTp9tuu+2FF17YsGHDrl27/vznP7Onjohll11i4uJT\np+8GABdYJbdTlqNdIIapGkzthKliTp06tX///gMHDni93tzc3CZNmiQlJSUlJXXu3LlVq1YVyLCo\nqGj16tW7d+/Oy8v7/fffGzdu3LJly549e954440mUY4YdtnF8lp24N80lgPtGCZWSUxMxMXrIpXh\nZZddZrFYaF9apjqJcZcdR34zDMPUFGJZkOrVK5167XBEsSAMwzBM+cSyINWufajUQlIU/3xthmEY\nxozEsiCVQVF4dizDMIyZiXFByvHvFcvDSAzDMCYnxgWJkCAnKyvahWAYhmECE+OCpIBvP+A08LDL\njmEYxszEvCBJeMAuO4ZhGJMTy4J02WWH6FgCRVF41W+GYRjzEsuCBIKFBABWcPFsJIZhGNMS44Ik\nkgEc1cAwDGNeYlyQRAsJvXYMwzCMOYlxQYKycQ0yeKJZFIZhGCYwl5AgAUAaZEevIAzDMEwwYlmQ\natc+BGUFiS0khmEY0xLj+yGBsHoQAHDcN8PEEiUlJatWrdq1axdu0HfhwgVJklJSUlJSUgYNGtS4\nceMK5On1epcsWXLgwAHcoK9FixaSJCUnJ7dr127AgAGXXVaRNvO3336j3c2bN2/eoEGDCmRyKRDj\ngmS3A9iFvxXFYfHY3HJ0SsMwTIQoLCzMysp69dVX9+3bZ5igYcOGEydOnDx5cpMmTULMc/HixS+9\n9NLGjRsDJWjTps3kyZPHjBkTlqIUFRV179798OHD+Oejjz761ltvhX75JUUsu+wQD6RFuwgMw0SS\nnJycjh07jhs3LpAaAcAff/zxwgsvSJK0fPnycjPMy8u766677r777iBqBAAHDx58/PHHk5KSPvvs\ns9BL+80335AaAcAnn3xy7ty50C+/pIi+hVRYWLh79+5ffvll165dBw8evPrqq9u2bdu2bduePXvW\nr1+/8vl7QPaATKNHyUq2osgAIEmVz5thmOrm+PHjgwcPPnjwIP7ZtGnT0aNHd+7cuVWrVufPn/d6\nvTt37vz888/Pnz8PAH/88cfo0aM3bdrUtm3bQBnm5uZaLJYDBw7QmR49egwbNiwpKenKK6/87bff\nFEXZvn370qVLi4uLASA/P/+BBx5o0KBBenp6KAX+4IMPxD/z8/MXLlx4//33V+DZYx81ehQXF//7\n3//u1KlTqhG9e/eeP39+UVFRhfNPTU11OlUA1QpOFQD/eSXZalWt1gg+B8NEmdTU1GgXoZooKSnp\n3bs3NV/PPPPMuXPn9MkOHz6cmZlJybp27VpQUGCY4W+//ZaSkkIpk5KSfvzxR8OUiqJMmjQpLi4O\nUyYkJKxevbrcAh8+fBiHneLj40eOHInXyrIc1lNrqOTXbebaEjVBOnLkyEMPPWQoRSK33357bm5u\nxW5BgiSBlwRJBZDBLUmq1xvR52GY6GHmJiayrFq1isRjwoQJQVKWlJSQAADAggULDJNNnDiR0nTp\n0uXXX38NXoC5c+eSJrVs2bLcHvPMmTMx8a233rpp0yY8jouL27t3b/ALgxDDghSdMaSTJ0/edddd\nGzZswD9r1arVtWvXhx9++Jlnnhk9enRqaiqlPHDgwGOPPXbx4sXK3E4ByQMy/WkDh6IA72jOMDWO\nL7/8ko7Hjh0bJGVcXNy8efMaNmyIf1JrI3Lw4MG5c+ficb9+/VavXn311VcHL8DYsWOff/55PM7L\ny3O73UESq6r64Ycf4vGDDz7Yo0ePa665Bs9r/HgMEh1Beuedd06cOIHHrVq1+vrrr7/44osnn3zy\noYcestvtX3755YsvvpiYmIgJdu7c+fLLL1fsRjRQlC0IEm5FkZNTsSwZhokaubm5eJCYmNi5c+fg\nievVq2exWPB4/fr1+gTTp0/Hoab4+PgPP/zwiiuuCKUMEyZMqFu3Lh4vWLAgSMrvv/9+7969AJCQ\nkIDmGg0dZWVlFRUVhXK7S4ooCNLBgwfnz5+Px61bt54/f77owwWAuLi4kSNHvvnmm/HxvuLNmzfv\n999/r8xNxVg7WkNIUcDlAocDXK7K5M0wTDVRq1YtPCgoKDh27Fi56UeNGtWtW7du3boBAIYkEPv2\n7XM6nXg8dOjQDh06hFiGxMTE4cOH4/HChQtR0gx5//338eCuu+5CW+2+++7DM3l5eV9//XWId7x0\niIIgzZkzh1xw48ePb9mypWGy3r17jx49mv78+eefK3xHWS6zXgMAyJDt8YDHAw4H2O1sLTFMzaBf\nv354UFRURP3aIDz44INbtmzZsmXLxo0bScyQ2bNnk43yj3/8I6xivP7662vXrl27du2yZcs0Okec\nPHly4cKFVAw8aNu2bZ8+ffCY5IohoiBIu3fvxoPGjRvfeeedQVL279+fjisjSJJUZhjJBdY08KAa\n8dINDFODuOWWW+j4qaeemjFjRoUHmFevXo0HXbp0EbMNhZYtW/bxU69ePcM08+fPLywsBIAWLVoM\nGjSIzj/wwAN4oJmfxEBUBOnIkSN40Ldv3zp16gRJ2aVLFzretWtXBe6FY0hpaQDCMJIMHhxGIjVi\nWWKYGkG3bt1oWOj8+fPPPfdc586dp06dunbt2kCWiiFnzpzZsWMHHovtTAShsIXRo0eLxtk999xT\nu3ZtACguLiafIYNUtyAVFRVROMOVV14ZPPHJkyfpmKJlwkWWfQeGw0i+jzzAMIz5qVWr1tKlS0WD\nZu/evTNnzuzXr1/Tpk0HDRpks9mWL1+OpkkQ9u7dSwImVcEk+Z9++umnn37CY/LXIc2aNRs8eDAe\nf/jhh6qqRvzuNZfqXqnh9OnTN9xwAx6XGySzZ88eOg59yFFEksDt9sUsiBsjAUAGZJETjy0khqkp\n1K9ff9myZbNmzZozZw71bgHg1KlTK1euXLlyJQDUrVu3f//+6enpVqu1UaNG+kzEC4MIUm5ubrmD\nBampqe3atdOcJPOoU6dO3bt313z6wAMPfPXVVwBw4MCB7777bsCAAcFvcQkR5XlQQbHb7TRDNpRJ\n0Rpo/pfTv1CDOD3WC5Lwl2q3R7r0DFNdBJzqaLeLdb4m/QvhB1lQUPDOO+8MGjQoISEhUPvWuHFj\nh8Nx8uRJzbWff/45pVm2bFmgW8yZM6fcJnT69Omaq86ePUsR5DNnztRne/bsWXL53HvvveU+qQae\nGBsFfv75Z1rBMDEx8frrr69wVrLsc9x5ys5GksFDfSP22jExiM0Gqloj/9ls5T5cvXr1xo0bt3z5\n8vz8fLfb7XA4hgwZotlyIj8/32az9ejR4+jRo+J5cVAnPz8/Uu8bWbhwIQ43xMXFGa5Zl5CQcPfd\nd+Px4sWLRXPtEif6i6sacvbs2aeffpqcvI8//niFx5AAQJJ80Q2a4G8bODIFr52i8IqrDFPzqFOn\njizLsiwDgKqqW7ZsWbRo0aJFi3755RdMsH///vT0dLfbTdtGiAPY4tCAhlatWqWlGW8XsHXr1lOn\nThl+RPHcnTt3PnLkCIVxiVAkxfnz5z/66KNJkyYFfcRLhmibaAYcOnRo6NCh5KwbMWJEcXFxBfIR\n18Rr1GgRgGqHMh4ML0jkzQNQ3e5IPwnDVAtmdsJEkblz54ox2U899RR9JO5bMXr06ApkTiucaVx2\ne/bsocXuQqRr167h3roCpRUJ9/Jqw3Quu02bNt1zzz00Vyk5Ofntt9+mJRvCZbefyZNHAIAipYGw\ntJ0EipTjiUixGYYxG2PHjl2/fj3Jw5o1a+ijdu3aXXXVVXhMrU3oFBcXe71ew48qEDi3Y8eO4Psw\nVZ7dAlV6o0oSAZfdihUrgiyegfTt27fcfRsLCwtfffXVTz75pKSkBM9cc801H3zwQbNmzSpfSMDp\nsZLsUWQZPKURd/ZMCdz4J8faMYyZmTZt2ttvvw0ATZo0CbI1n8h1113Xu3fvdevWAcDmzZsvXryI\nc4AA4NZbb8W1HrZs2bJ161ZcXihEcnJyDCfkFhUVZWVl4XGLFi3KbbsohO/999/v1atX6AWIVSIg\nSM8//3y5i0rNnz8/uCCtXbv2ueeeO3ToEJ0ZNmzYtGnTKjN0JJKWBsnJkJMD2Z7SzfoUkCRQ3GBJ\nAS8EXW41Lg7c7tIpTQzDVD+NGjXCAIT8/Pw9e/aI2wIEIT09HQUJ9wKlwZsxY8agIKmqOm3aNHEd\n8XIJtAvtsmXL8vLy8Pizzz4LNP5E3HzzzWgbffbZZ6+//npYO6PHJNF32Z05c+bZZ599+OGHSY0a\nN248e/bsf/7zn5FSIwCQZbBaISPDNz0WpyJlgRU1yQspEiiBAu3QcvL3exiGiQ7iZETD1bsNyRF6\nmmK32GKx0IZJS5cuDd1pdvz48WeffdbwIwpnkCRJXPksEDRn9o8//ghrW/RYJcqCtGbNmvT09P/3\n//4f/hkXF3fPPfd88803NJM54iiSjANI6KZzgA0AJFCckBnwEgWA48IZJtoMGjSIbIhZs2aFGK7t\n8f90GzZsSONGyCuvvEIbSYwfP14TGh6Ip59+2jBQ+/Dhw8uWLcPjhx56KJTQhj//+c/kQuS1VgGi\nGmW3aNGia6+9lgI/hg8fvm3btgjmbxhMIsulO5q7QZbA6wYZI+6sktvpNMjH7VYBVEmKYNEYJpKY\nOW4qsvzf//0ftV0Wi+XChQvB07/55puU3nCH2eeee44SJCUlbdmyJUhuZ8+enThxokZpKMruxRdf\npJP79+8P8YmGDRtGV+3cuTOUS2J4YmzUBOmTTz7p2LEjStG11177xhtvXLx4MbK3CCRIoggBlNEn\nw63uSxd6YBhTYuYmJrJcvHhRXGinS5cu8+bNM2w68vLypkyZIorNwYMH9ckKCgp69+5NyerVq+dy\nuQx1bu3atTRqFRcX17x5c1GQSkpK2rdvj2duueWW0J9IXDPiscceC+WSGBakODUaS/utWLFiwoQJ\neHzFFVfMnTs3rBCXEOnYsaM+xtFiAY8HrOBCH50F3ApIXvDtEOiS7DlWG00SdzggLQ2ys8FuB8Cl\nhxjGfBhW9VjlxIkTPXv23L9/P51p3br1TTfdlJKSkpycXFhYeOTIkR07dng8HppZ36ZNm+zsbM1G\noERRUdHUqVNfeeUVagybNm2anp4uSVKzZs3279+/bdu27du3k5suLi7u3XffzcvLs9vtADB9+vRn\nn33W4/HQMuTvv//+X/7ylxAf59y5c1dddRXOsW3WrNmhQ4cuv/zy4JdU8us2dW2pfg08d+6cxWJB\n2+imm27atWtXFd0okIWERhJaPXawA6hoMLlBRscdJQbwpUcLyeutopIyTKUwc5+3Kti3b9+IESNC\nnH+ampoaigNt2bJlocwwadKkSVZWlqqqGzZswDNoIdESQQkJCadOnQrrccaMGUP5f/rpp+Wmj2EL\nKQqC9M4779C40ebNm6vuRobv3Wr1CYzotZPB7QWJNMnr9qqCp47+GTr0GCbqmLmJqTp27typ2WpI\nJD4+/s4778QdXUPM8Ndffx0zZkzTpk0NM2zRosXkyZNPnDiBiYuLizHl9OnTT5w4QcER999/f7gP\nkp2dTXcZOHBgueljWJCq22VXUFDQt29f3K3kpptu+vjjj6vuXoaWaWambzcKOzhsYIeyXjsFJAUk\nWVJcNm9Ojs9TJ2K1Am+pxZgNUzthqphTp07t37//wIEDXq83Nze3SZMmSUlJSUlJnTt3btWqVQUy\nLCoqWr169e7du/Py8n7//ffGjRu3bNmyZ8+eN954Y7hrAlURMeyyq+7FVXfs2EF7Zw0YMEAJeXWE\nJk2aGO5rEi6ly3tDGg4VZUBWJjgzwemETJyfBIqSk+mwg8F6wx4Pr8HKMCYiMTGxe/fu+j2HKsxl\nl11msVhoQIipTqpbkLZv307Hs2bNmjVrVogXPvHEE6GPE5aLJIGiSACggGQFVw5IdrBlQJYMHgfY\nbODIABcAGGqSwwEAbCcxDMNEmOqeGEv72EcLWssDl1hFk8gGdjs4cJJsBmShE88GdjdYvJBiBwdd\nrig+I4lhGIaJLNUtSKKFFBVwDSGrFSTJt0wDkgEuGbI9IMvgsUKWBdwWcCtyhiLJNrB7IaV0BTwl\nKgVnGIaJcarbZSfGk0QL9LZlZIAlRUIFQmvJBnYPyApIGeDyQJoHZEUBACuAzQYON1gUkBxgc4GV\nNYlhGCbiRH9x1WghSeD2SrIzAwAkULLB58uTQKGl7XAbWdQhXPvOBg7Rg8cwDMNEiktXkAAj7vxb\nSmRAlgPs2SC7yi4Bjp8qIFnADQC4MKtbSQGHw+GAzIArsjIMwzDhcUkLEgCAJIHVCgAyeDLAlQGu\nbCkDABxgx62SwB8pTpqUDEomOD12T4Y9RXI5FI8CAB6Pb3oTwzAMUzEueUECgIwMACDDCH10CiQr\nkoy+O4yDAACQpGzZZgUXAGDUQzIoYLF4LI6sLMjM5C0qGIZhKg4Lks9rJ4GCtpETMrNBToNsi+JU\nQJLBk5Hm27vPagVJljLBaQMHAMhWySE5LeDO9oDNlYL+PTaVGIZhKgYLEgAAyLIESobbSlF2GHpn\nAbcECjgcFFaXlgY4e0kGD4U82MGWBVY3WByZSna2b+YscIA4wzBMOLAgAQCAzSaBIikeB9hwvhE6\n6xSQMsEpKy47OCQJ7HawWHxBd07IxNEjxA42B9icisXjUhTFZyRZLKXi5HKVHjMMwzB6qnsekknB\nuIWsLJBsHkXOggwnZMrgsYLLBVYAcEJmhuJKAS8md4FVghw3WOgMngQAp2JxgC0z05qTA6hMuLtS\nVhYoCtgMliJimAjQsWPHaBeBYSpLdDboqx7CW9TWYgFFcUhO8GQngwL+CUlZYHVBBq676gE5E5yS\n5PPF4VylTPCtaoeiJisuGziywGoHG6b0ekGSAPcG83r1N2YYhqk+zLzaN7vs/MgyKIpNybTJHlxi\nVQIlS3ZmgMsKWVmQAQBWWbFD6XgSpqF5sjik5AKrBdwZ4LKDAxcoovSYgGEYhjGEBckPrroqSQAg\ngWKVPFlgtUlZWVZ3BrjSpBxJAoeSkQEuDPsGABxhwggIMSeMhsgAF9gdigIOB1pfAABZWdX4RAzD\nMDUKHkPygx43SQKPB+x2mz0TAMAFaRJkgdUGLodiTYMs3DYpzSplumRZBo9HypJsNsWhSLJo/aAm\nOSHTDmD32Ch7lwsUBdLS/BObGIZhGD9sIfnBKDo8SE5WQHJJdvwrDTygKDawoyXkAJvsylS9SkYG\nyDK4FBkArIo2hE6SJYfkRN8dgG9bPwxzyMoClwtSUiAlBTIzgXcCYxiGAQCI8hbqVUnYW8d7vaok\nqU6nKsuq06lKkmq1ekGyg10CrwqgAnhBAlCdkl2VJNXt9npVAFUCrxckGdwAmEpVVdVuL/3IaXXL\nsup2q5KkAvj+F/85nVXw/AzDMDrCbhirEbaQBCTJv26dAjk5YLWCooDbDQBusGRKbpdkx/lJDrAp\nshUcDinL4XYqVruUBVbf8g0yAEBmpm/QCCctWT2ZbqfiX8dVG9ogyxDKphyK4gvVYxiGiUlYkMqS\nkQFZWeB2+0Z7ACArK81tywKrEzKtsgKyLINHBk+Ky5YJTo8HZIfFlqHYvBmyDBRx53KVLiDkAqtD\nsYLF4kop49aTZZ/84Ra05a4dzjvVMgwT27AglUWWfaM9bjd4PCBJksclZ2UmS+CxuQEAPB4JFJuS\nKYHi8khZkg2sVrBYXFkATmcGuEBR3G7fgBSZRHawWcAtKy63kiLLvvOKAk4n2O0USAEuF8TFQWZm\nGT3TwOu3MgwTs0TbZ1iFVNBVigNIqqp6vaoslw74yLIqy16n2wsSDSYBqF6v6pbtqiSpdrsqSU6w\nut2q260dJQJQ3U6vard7QbLKXln2ZYn3wRErzdiS1aqqqup2+5JhWSRJ9Xoj834YhrkE4TGkGoXN\n5lt1Du0kt9sXfYeWU2YmyDLY7biDnxVcSpYnS7KlKG68xAouyZIiWVLcYKEZS0imQ7J4bFlgdSoW\nyeNCY8zj8Q1diVNoEZfLF4OnKGCxgMfjs980k5l4n0CGYWKEaCtiFVLxjgAZSYQvnE5SrVYVQLXb\nfWcAyGBSZVm121VZVgHcIHtB8koyfuQEqxiDJ4NblSSv1Y5GktNpYE6hCSX+I/tJksqUVHOGYRgm\nCGwh1TTQSMKlfjIzweEASQKvF7xecDrBavVNJvLPbk0Bb6bkdkGGz8aRJFlSJFmSFA/gug/gcoPF\nCyk4k8kDcoriVlweL6RkKA7DEDv9WBFaaCCE27lc4PH4ggHJuuLYB4ZhaigsSEbgHrEWC6Sk+EQg\nJaW0mcclu+12X9QDKG6wSBLkyFZwOsHtVpxudMB57O4U8Fokbwp4aU90t5QpSwou5eAAm6y4JFdI\n+1JIEthspZqE4Q/gFyqHw6ehuHFtSkrA8Ad0AKak8EaCDMOYjGibaFVIZS1TMXgAow7c7tKPRA8a\nAIYq2O2+0263ivEL6HzzzYcFrx3svsTg9F0NXjvYNfNqA/3Tz6gNnthuL/Modnvp5FxfnIVbDULw\nTxmGqYmY2WXHghQyek3CxRj8/7wg4T8nWFWrFVd8cEtWTULUJBXACVYJvCgPqEl2sIeuNyEKldPp\nG/YSk3m9vuA9veRgaB8GGOJgGcMwsQQLUnSI/Hun6GwyniggwWpFpbGC0wpOO9gpokG1271ur9vt\nSytJvvWE8FMSITzpBhmDvHEBI4oFpxgHfbCDXpz0+iTLqtXqiy8Xy45WFNlPtLKRTyb90ez4j8B8\nDEE9U1XV7ebwdIYxIyxI0aFK3jvaO6Im+S0gr2x1S1YvSG7Zbrd6ZVl1SvZSlfB6yewg+XGC1QlW\nL0gSeEt9en5fm+heQytHkkrD6sQ/Q7GWUGbsdtXpVO121WotI3JkRYk5iFnh5SireIyhfbLsmyZl\ntfrS04EssyYxjOlgQYoOVfje7fYy7jtV9U2FxXZalr0gOSU7gODZkyTVbsexJ4wPJ03yWu1ekJx2\nr8+f5vYn8nrRqNKojigkpQon+SLIRR9dIK0ylBx/GVW32+dxDGSQoXkkXkt66Xb7HhdlCePkeSyK\nYcwDC1J0qNr3jpaCaAIIwoPHblkIKsBPhXEbu111O704IQmXD3c7vb7mm+wwv6eMFMLQdsFhIRFR\nKgxFBa0ilBCrVWsh4SVYUjSnMDEeiIWhzMlZJ+L1+i5kU4lhTAILUnSo8veOTbXmDPm2UIE0Yy/U\n3qMlovq0xwuSW7KqkuSU7KVZUnPudqtqmdgEcWwJPYGa+4iWk0a6NFtgiNniDTHkQQ8ZgXgJSZTX\nq5LlR3IsQuEgVSFLLHgMExYsSNGhyt87NsNi401SgG0khTFogiBQycT4CLtdlSSMdHBLVrvVWxo1\ngB/JVhxnEjUJrR9s6Mk5FjzqgdQw0CATiZyhJuGNqPiiE0/Mk2QJH86/qEWpUqNrsTIqgjYkGaXs\nFWSYEGFBig7V8d4x8ECjSdQ2U7MtzgkiX5zGL4cCJssqgM9gcrt9Dbfb65TsOC7ltHuxKaebYHCB\nocYE+kfxdfqrsMiiy46ggTOUNCyGOEaG6uhfPqk0xiGQ+JE6qmqo4oTvW3ypWACrtYzNqS88wzAI\nC1J0qKb3rtck1W9KkHtLE3tAc3zQukER0F/uVya75LTKXq2AqWWafgpGIK8a6ZamCKJUUCCfGPMt\njjNRpBwtT0730pRX82dpjLsUMIpPM2RFcYCqf41zCohA5cO7O52+1ybGOVLhRQ8kwzB6WJCiQ/W9\nd2x9NeNJYoC4xp+F/XlshulYtKJU1fgqsWF2u1VhXIdERW8ZkFOQdmbXa4OqlhEJvWxgbLcqDGyh\nw1AcOtKDRhg+Irr1SNg0xhlJKf2P6TUCqQpBFuD3hmKRNKWl//HWqGGV9BNWBaGXRx9GwzAVgAUp\nOlTreyf50Q8pkVBpgg0o8EFjvKDwiNli2y9aQ35Tyev2aiQEw76Dl1Qco78KAAAgAElEQVRsuzGn\nQPOZyJYytIFo6i45+tCCEaf00piTmDNaZppBL5I31BsagsKnF32JouqQYolDSjRCpzfFyGgTvwpU\nLM0DVoPTD/sTKJnBoYAY9OIyTIVhQYoOUXjv+k6sJgaOwg8wpcbKoBjtQBaH6JzyN9JivANZHkH6\n0RQRp5lppJFFcqCJDbc4ToPCQ0sN0b4cFKuhadPxjBgAT3dB+aEnE7VE40jElGKGJGB0UlRwekxN\nFIbexWdoHYrPgjlHykARv2oSVHoE7FXQ/o2oWyhF9GVVj2QysYeZBSlOVdXoru5adXTs2HH37t3V\nfVeHA1wu8HpLz+Dy2larb5lw+jMjA7KyfGtu4x4SuAcf+PeQkCTfnxkZpduh4w59uGcgJpAkxe7y\nSNZMxYY7+CkKuN2lVwQBM0tLg8xMUJTSUgRBs5Eg7rwunsQd3F0uLFrA+9JHuA8hrWIuSb5iYA74\nOPipzUY7foT0aB4P5OT4NomnnJOTIScHbDZwucDhAJsNcnJAUSAjA3AfEEyAd8fiaZ4d33paWhiF\nIXDfEty0HqsAgG+TRly7HZ8UK4Isg8vluyM9u8cD2dm+85geL8GD5OSKlIq5pIhOwxgaLEiRBtt4\nl8vXMNNJiwWcTl8jh7tEyDLYbKXpvd5SsUH18nggK8unD9gKYgOG7TQAeDy+zW1lGTweRQGUJbvd\n9zlKhdMJigI5OZCc7Lu/qBPUriEeD1gsAR9OlkvlCltAbDrxpNNZunctZkhPXO47A4CsLJ9GYwON\nUoQyiTcivcb0qCUAkJxcuuWu5na40y6Ar/XXfIqahKXNyCjVGzErUuisrFJ1pJeG34mox6giJDA2\nW2kfA3NAuUWN0YAbiIB/hxPUdSy8BuyxiIKN+wi7XGC1gtMZ8FVjlcGqh8+ekWHw3pgYxsyCxC67\nKsBwPEnjzUPHGY0GiHNsabIP/YlLyIlB5LReguhT8zsAvW6vuC4qedvIB4WuJxznF0PXMDO97w4d\nX74Vj4TpSvinKngiyflG4z14L7yRxpeJT2/oBMOT4ngJzV7CDGlJPc2kKIroI9ef2+0bqcI/KcBB\nFeYa09sV4/1oqImciuTYDLI4k+juE1+XZqCLvkYaHtNPKK4AONQUJHYD/EH/5DXVOAyZmMfMLjsW\npCpDVCBh9qt2UyWahqMZakJx0CNGRpAIiQP9FPSma5MozEwTYiC2UFgECo3DNLSGEI2piDFyOLBE\ng0AkVIZDMjhXSVyhldpxfSCDqpbqHIQQyY0qS/OFqbSERiEwQ/1aDxQWSCEY+I5RHcWJZHhHuimN\n/WjiKQylS1Q7isKgGlHh8SEaGqSqh6Wi9TVoMIw6BNSfEPtLpP30mBzgFxuYWZCi77I7fPjw//wU\nFBS0adOmTZs2bdu27d+/f61atSqTc/QtUxxPIv8OjmA4HKXjSR5PGc+OZqgJPThut0HO6EhCHxBm\nrh/5wTumpRm6Y9AXRKNUGscdgR48txuys31lRzcR+g41Yz/6rdMNTyLkiMNtcHGjW3Rn2WxgsZTx\nd4LgtkJ/lMMBycllzosFBr930WoFj6eM95SS6Ufl7Haw2SAz0+dzw8zR+Yp5kqstJ8fnQiTPG74K\n8Ub4KX4teC+Hw/dpoJEeh8M3OEiviL4mvSMR/GOLotcOD/CbAr//UIP4leFd0HPscPheizgoqPkG\nNc/I1ESi3zAGJpqCdPbs2ZkzZ37++eeGn7Zp02b8+PHDhw+vsCyZ4r3T7x6HkQyFh6SFWhccezEc\njtLnj/8QbD9w1JtAZdIMWYhXgaBIOvXCVpLuTyMiOA5Bw1hiNjiykp0NklQaU2AIjcnjeyIJoTEk\nzA1fG8o3jvfgGJyi+MJHUlLAZvPFC+CLFAUGINiwCpU8JaV0PIyCNWgITzxGOUlLKxNfgJcE7gOE\nBD51drYvrIMEDyUQiycO42nUwlCBsLT0XYiJsdjYOUhLKx2yxHcOAFlZZYYesd8AYQaY6MEXxUQF\nUzSMAYiaIG3dunXKlCm5ubnBk3Xr1u2jjz66/PLLK3AL0713Mb7OYvH96EVDgH7u2P5lZIDV6jOz\nQgwP0NxLlENNJAN1uSlIC/xREPgvaBgZZk8NImqA01k6tA5Q2kzT/yC0oXhDakCpxcd70kkqLIkT\nDvWjbgGA1+t7UDGsgLr5brevqKH06+kboFcimp2oDWgjivKGAYrUncB89B2AiIPhdhgTKBqLVAaM\nZMnIKBMrgYXE50LZE2P5AMokgLLfF1r4slwmOFQMBglSVDFuAjsWdrsvhgVtYkkCh0Or5VgMvJYM\naBRmttIqjOkaRoHoCFJ+fv6gQYNOnz6NfzZq1Kh79+7XXXddw4YNc3Jy1q1bd+DAAUp87733OsRO\neMiY8b1jm0fRY/gjE5supWxUNwbJiSZUWpqhHWN8LxQzffsqSaVZkZEC/sYMw6Up9BybHN0dsVlB\nEUpL83kiKY4ZWxzMkvQDG3Sn09dE4qOjBSbG7yEkwWiEBXH9oQ2JlhAlQ3sF7ae4OJAk3zG244GM\nGIzK83ohJaW0Cc7OLg3Vo8eRpFJjhVptNI8wapyejkyWShpPVYehw5YC9xWltEaQWht+HSRplBUZ\nkXQjUi+NbUefAvhqC91LLCGJk93uE2MEVcqcr9dsmLFh9BMdQbLb7QsWLMDjnj17vvnmm02aNKFP\ni4uLlyxZYrPZLl68iGdmz549ePDgcO9i3vdOvjgyBzQdeE1fndz8NAlFkkJ1muDMF8xKHN9A8MdN\neqNRO7qjOC8qgOUkTicCoY1Grxqdx8EYtDDE6VgkweC3RcSWhQbUAnmrNKCOZ2b6NABftr4lpZk9\ndC8KlMdug14mDe8FQi9e0+BSbD+O8bhcPkcidrGq2ooKC6yV2P0IlACrA/1Jw1eG3wV5oA0JdJXG\nGga/uSyOlpFfl747Ek4oq6/kC8A/09LK5BzoMenpNL01vfVWE/XPvA1jVARpz549d911V3FxMQD0\n6tXL6XQajhJ99NFHM2bMwOPhw4e//PLL4d7IzO8dwD8LBhtFmnsk/lBISwB8fiL6kdHQTSiuPEpP\nooJzTygmguaL0m9any0ZT6KtBmWCCjCJOOpApqCYBgfPUYpoIB3tJ8ybZhVjkemtoC2FjZHojBSh\nQAAkSE88iJ5B2UEjfT7iSY0TEq8Sb4Q9B9H0JZ2TZeOYleqEqhI17hUoEn2tgTSGTH2yejWfop2N\nb4ncyVRC8DtCSQVBmI8HUPqSRZ3Q3w69lKJfnMovPguZYvrzIHzFomKhkxsAcnJKZU+8igxNmnkN\nfmn0eHzxKdXjhzRzwxgFQXrjjTfmzJmDx59++ukNN9wQKOXNN9+cn58PAB06dPjqq6/CvZGZ37sP\nMpXEsRF99IHeZ0/nxbYZ3WtB9MnlKjWwRKsLGyS00pSyQRaYsyYsjLrKin/wJPh9dQ+NFiAZYxSA\nQO0a2iikCmhn4Lgb2pPUPInvgCSbwtX0Ph8UX4DSObwasCRiaXFgjBx0VDav1/fVkeFKvXh8IkIj\nkwCltjE1snhGnGaLhacwTHIbakBbumJRBhTciJ5JeskAPt8jvit8Lhrwy84OKUgEIJItLOkESRea\n7uIwJOmHvpdA1RkvITOI6lhGhs8BSCNbAL6XgwID4LMOydUt2lJkOIL/90FQYqzwWADstFHgJV4i\nCh5VVJpJre9aVQwzN4xREKRx48Z99913ANC5c+dFixYFSZmRkbFhwwYAqFWr1k8//VS3bt2wbmTm\n914GRfF5sqgm6tt3rPXkexJdZ9RppO4ftruBnC/UV8d8KJoKG1Ty2mEzj79Rxb+Sj74jp9HLkJ1Q\nilLqFqNHiYsrXe5B8o/6KP6xMNGewNKhGlEv2G73ndf007H1xMQ4lo4Z4jgTJcbodgjgScNRJbR4\nSI4p/J38dfhuAjn6xEhuvGNKSqnNJ0KOKX1gBd0Fv3NxGSk8EPsPVCNEm5VCFgEMvMUowKIlQf4r\nEdHdG3Xfo1hbEZRYelEkMOTBC2JJE1S1RGtY9AFqXg7ZSXQGVTNQX1FciYO+KbyW1hAxLCf9Cqm+\n0bdDfUjUXbG24IGZG8YoCNKtt9566NAhABg6dOgrr7wSJOUjjzzi9rdA33//fYsWLcK6kZnfuwHU\n+RSbEOqm0o9AKRv1ECiem6QLGzD9T0EMFZD9C+BQQ0sFoJ8RWUWoAJqfl2hXhSlLFAwo/rax4Rad\nXdjIYtABddglYQEetIrI0hKH2/AHn5zss2zwoXGJHTTISGfxT0OfVVwciL8VRYGUFN+XgOUR49kk\nqbRjS3PPAIyD4KmE4qQ1w/YxEOQDxJuCf8BD8cekUUsn3hQH6kLsa+O3QFMVQJhWhUGgmH92drBR\nKPNDNRDfG/3UIIQvhYyt4GnEe4nnyTAF8PktKQ32e8Q2AO+iEWAAnwZTH1U040jADh82b8NY3YJ0\n/vz5u+++u6SkBABGjx790EMPBUncp0+f48ePA0BCQsKWLVvi4uLCulcNEyQREhUQQrHJ9CHfFnW2\nDeO3RAkBKA1CIvMIofoL/p8FucDRptCIk2gS6f1EZO2F7EKiriuueUq/HE2UBBUWTShN1AM9rv6e\nFA2BWokFdzqNS6eUnY5M5hfGuOv9VGjkkYDRnC3UADpPbyUQ+JiakGsklMAKMR8sJBYMwGcRUvXR\ndJYjAs3/pgcnA5vOQMgx4obgs2C9E5eEjOBThOhjpN4aLcVLUFAiCCNz+M7pKwAotdvQhhNvqrHk\nAumfWEhRt/TdTvopAZR2y2bONG/DGP2VGgLh8Xj+9re/4XF6evprr70Wbg41WJAIav1RchTBcU7u\nbTwjOiMQMuY17Rk2WqLdQ6ETmmSa/jONw1IvjjQSf5f0G6KPxOBysVQhP73Y0wejEZQQoXE6mtYF\nAUKkFP8MZvD74hAaoApeYGyJ8NHFYSSEhAeEdcTFnrXoWNOgDwcAoTdCq7aL6SkTaiupvyyuRx9Z\nRNcT6RP45YRUBN8nDVkBaGflkR2mV2jsuGB/hcLrxQm8GA9Eln+QolKDjvauZgRRkxiM6i91HclZ\nR1KEJjgIcRn4WrAahzgOR24LsZ4Y1hAREn7RTkJSU83bMJpUkPbu3XvffffhRKW6det++eWXyWJX\nJDRiQZAQ0QUHYFwTNRUWoe4Zgs0DzUXUR79pRt5J4cS2k/4P1G8XZUzf4Reb5NDnVEUUelDyiQKU\nMc7IMUgNayCLKhDUFyY/IfiXJ8fcyP6j/Ok1YFvjcIDb7WtYxfhKcYEfhOSe7BKnszTihJpRwy4H\nvX6a00PpyU8MulZYEQLGxG9bnNkqtvXUIKJUUyC+vjzitGgC35s421p/YRBXp+yfsi0OrYlWHY7V\noXqhKawfFaNl4+kro6wogIX86PoYVZfLF32HLk3SGKhQTCNCfQvxJdDbxm+H5j7j94KfmrlhNJcg\nnThxQlGUxYsXL1y4EOPCW7Vq9fbbb3fu3LkCuZn5vVcEatw13V1EbM800kIfiaPbaHWRDwWzIv8e\nZSU66wIViUILqEXUDz5B2ZBbEWpN8UcTQS9MULCLDVCmybbbfYYo+mSwRFT8EIfGUGwInMIp+Yea\n0PyioCyaNUxRy/St4hlcrwOEkHsyFrGzofjnD6FWSVJpvCQ1T2IVoPUd6AxAmZtSGcTGjv7X1Dtq\noMXEctkF8RDDoSyaSowfiUss6nMA/3xnhCwwDbT9imZaLgiKhTUUW220b1AYyMalAlCx0aBBJRZf\nHa1/QeZIKJCo0w8RwnMfVBwzN4xmEaQ777xTURSaCYv06tXrzTffbNy4ccXyNPN7r3JEqdA430TH\nDTXG1BnW+wI0P3pMqZ9CiypIbSd1PsW+GUCZWxtKlBRgSKwqweJjBxmgVDzEBhSLr4lepOegEAyA\n0sgI0QtH4PQzxb+JosVSuu4fgE8OsTeN7iwazcJ5vuh7hLJCQp4rj7CdlaZ9FAUDnazBbT56fNI5\n8gGSrwnP4wg8lhyhOD0KsgC/1UXuO/L7kmMKBMEAv8GBdgxehV5Qw6lm+Cw4lQ0X/hDNSoBSmZEk\nn01DwdwazQa/S0KMlwvUH6u8hGBlEOdiBMmfCibWyXB/KGZuGM0iSOnp6UePHo2Lizt16pTmo759\n+/7rX/9KSEgIN08zv/fqhtw34o5/NMoJfmcKtjSYEr1LdDldJdr/1BjTR9ha45A6DVOQy1FsPoNI\njiIEySHBDbXqBd1oIBh1ULbDCxDGCA1KCL1XQ5FISSnjYaWZSTQeZrX6XrnoXsWvSAyl0zRwStmA\nTTpJHRgK3NJ8/9QhwSpAFju6xQgcxcELNV0acXKPZs0nMo/oWHScBvn+SbPFwEu6L1nv4G/BNU+B\nmwtrIFEXe2uk6DS0I64BidlqTFIMdaGXjNmKw76Uc7lBeuJr1xum5KCjm4rvFklJufXAge+C3SZ6\nRECQVqxYcf78+eBp+vbtKy4OFIQ//vjD6/V+8sknX375JQbjAUCPHj0+/PDDmJ2HVM2Q8URtCfoL\nKHoiyKiu4o+qoIovzoUSP8KfqX6kiiL3IDRl0ssegPbHDVAaVRFtxapYr1lcGAlNIswEh8RpUT5E\nNIOws08mKDVnmpYI3YYUBSBGu8XFAYBvlAWvCjTYTv0EEAJcQDCqyR6S/GHTIAwI4SwxqmviheCv\nC1h9sGA475iGXrD86BgWa6i4cLjij2YUt18Gvx8SdQ5dnehEJT8b1WLwq4Xo9hZFkSSWxJISoEpp\nIoTohYvPS1M5KBiS6jUI0Si0LiIIXyW+ATSqQJjOTlkRaEpSAbBUOTkwf755G8YICFK/fv2OHTsW\nPM38+fN79OgRVrY7d+7MyMg4c+YM/vnMM88EjxHXw4JUDho3Ng7rU4Bz8GYVPSCGuqKUXUZG74kA\nwY2ij8cLbjbRsqy0Tgt9Krp+oKx0BV253Dxg+0smC/WCAy3kRKqD7Tt+gdTfB8HfJTb94H8rel8p\npgkSaUZ3p1Zb8s8UxjzFiVyKsLo9FhXdlTTfmXYGEesafsn6sH4QFJFuJ9oZAGWekQqJLThtriG2\n7PRaqAKCvxOAOeBcaZR8cewV/M5VMg01IkS3EA1NKqS4aFagRYOwqLSeF3luRfUVp5ZTn83tLmMa\nSjoPrZkbRvMKEgAsW7bs8ccfx+NWrVqtWrUqrL2RzPzezQW51LBtKNdUEi8Ue5KiBog/fQjqc9Ob\nTUG8V4oQcGjYaIHQLFF7QyMV5cpetFH8s6lEyalMbrSliSFoOkj+WUogSB1+//jdkuBhI56SUqpe\nmqvoT4x4lnSTt7A8Tqev51Ox7f6oxuH+GqKuKP5VfGhLC1RlMhfQwEpJAVUtnZQdSJvpwBCq72Lr\nj09E0d7kYQOd6wyE75fsLU38pOIf3PL4twrDfMj1QD9BWv4cPXXYDyC3hfiAMR72XXWCBAAjR47c\nuXMnHn/99dft27cP/VoWpPDA7iv4V87BRjzEfYRIUcg9L/k99JiVON8dhK6jqA0aB125Gkbz/UKJ\ngNBnDsJgAnn8ELPKVcWgjjwIoxdoQonmheguM2yFNdpDftlAl0iSdp1cMmLp9WNAh2auWkSgmWdi\nnwSrtiTsNEjOPdxCRVFKDThUGgwtkeVS7x+mlPxTzVAJsA9BCwej6GqeSGPAiSYaRYFL/sWH9EEW\nHk9pZCBNdSILSbSc6KnxixYF22aDwYPN2zBWd1BDTk4OeuEuv/zyDh06lJte3Kji3XfftQSf714W\nFqSwIZ+IPpoglAaDLlfKxs7htdgDNOyuS7rBJPwNia4QQ3FSlNKmLsjyfYZFFRsDMLKrRNEyt10V\nKRSlVHXEdQKpdRNfjMYyEAPqxKUBsHEU+wAUgwllW09JmIcUKA5QtDY0X4jYS6H8MR/xm6TEqDSS\nVDqbiq4CwSeNQeSSP4wQ54eRMa//WWC/DsWG1jaJeMURTS5xf2HxU03fjwb/YjyoISyefPLJJUuW\nAED9+vU3b95c7mpA8+fPp935ZsyYcc8994R+LxakSqEIoXH0Yw0rIFvsEJLvP1DfW4yz1oRLiBoZ\nyKFHvdMg7r6woF+84g9PF91S1TtlyiSQaUWrBVJFoA477WArfmOieOBVYuuPjkF0c4m9As21tCYJ\nCF5hzAGHZBBafFbyr9cgGmRiIL5mzpMslybAa2nVJRGcIas3fchkJL+ZCLouyZdIG2dGcPMRUafJ\n/BIlio7N3DBWtyC99957r776Kh5/9913V199dfD0M2fOdPl76//6178GDhwY+r3M/N5rDIqwNDi1\nFkGcaaFkSLEMIqLbmz7VLGCgUTWxDSBJE9ffo5YsUh1UapLpFmQ/AVyCEhUKYlMYSmKSJU3XRfJH\n7qEcYiyOopTaYfoRT3E/LRQnFBj9mu6KPzCEBDXQlykaHwCldokk+byCoiOZ9lgxXJZCYyxCGAtA\nlhZGrIaKUsY7Dv7XIm6/lJEBf/ubeRvG6hakVatW/f3vf8fjl1566a677gqe/t57792yZQseL168\nuFOnTqHfiwUpYoi9L4BSkyVcm0mfrcZDCMLIeJAYB5Q0+pFJUpnCiG4XMm7CWYM8vPKTk55GYOgp\ndHsYMpVB46ClmUDkUUbFEoM3oeygV9XNZKMIUEUp3dZEnNuLyP4VIkTvtei0FC0bcVQJ01Bdk6RS\nMcOPyIVBA1okw3hT0ssYD2oIC6/Xe/vtt+Nxq1atvvnmmyCzi9asWfPXv/4VZyO1bNnS7XaHteA3\nC1LVopSNjkM0bmwQHO3lRnUrRiFB4o8VyoYwiG46CsTQmEc0UZO2xqjSNSA0A1H6zUQugYGo6kSU\nKMU/SQidb+KqWHhAtpe4nAj2Z8KKqqDqidUNl4fweIxdfCCMe2EyCnbA/2lSLSZDydEsVEg5iM8F\nUFqbNHZbcMzcMEZhpYa//e1vHv9X+sADD0ydOtUwmPvgwYOjRo06efIk/jllypQxY8aEdSMzv/eY\nggwdsmw8njIhBqIZQWohNgN6l7zHUxqrrR920nQgxXEGgNLfNHWb9ZdU5+pEeFPRXANBp8XNrpiK\nEqJjEDtR+CWQ+470jExZTTwFBVtTUDVCo5ySFFI8jSJMpQP/wJJhmA7dkYwtCveQhBnEECDWJzhm\nbhijIEhHjhxJT0+nGa833HDDiy++2LZtW0pw5syZDz74wOVynT17Fs/Isvzuu+9eQvsh1XTIeFKE\nACOUH83sRIQGnTENOvGoZ0tpAjnjqTUXP8WOKMVKaByDYp7VvCIRaZKilAb4iUIVqbgMJhwU/7YR\n1H+g/gxVT7RvKllZqIMk7tssSWWkDgDcbsjM9Pn3MOyQtk2hMTBFKY2PoIpMxiI9CPi7bTg8xvsh\nafn888+fe+458UxiYmKHDh0aNGhw4MCBX3/9lRYNAoDWrVsvXry4UaNG4d6FBSn6KP74b7KQyI7B\n5lj8CZIJhVAzgJC/iwRGTAz+35zogxetMdF600P+wOhudyp6duhdsTJFCdFRVqW3wEWb9KYyLhsv\n2mE0SEabKdMZzQ+CHAeiEx1TXn65eRvGqC2uumrVqhdffBH3Mg9EXFzc7bff/o9//KNNmzYVuAUL\nUg2GbAg8EAMHQLCl8NemH8oSoV+55vdKg0z61UPNENUt+i1DGYRjLgEoVB2X9cNodRobpU1sxcnf\nIIgTAHg8PA8pAOfOnfv3v//9/9u786iorjsO4L9h0xBBQVwyqIAp4FLpMVStSzQuNc2itRGlsTbE\nNYQENYQgkaaipSbYuqCJsWqo28FatZy45SQuDa64kmhEAReiBUkVHFAHWYbpH6/eXN6bGYZl3nvz\n+H5Ojucx82b4Mcb75S7vvu3bt0s3enB3dx86dOi8efN69+7d5PdHIGkQiyV+vYAob/gr4InLGL6f\nxL+czSexZeXSbOP/cbNsYF829kdgf9rzcvZzsekO5FOrJyyfY5s5CZvaiXacYmvzBGxBh5obRrXc\nfsIR1Py5Q4uxGFFC/4ZthsMTDRJaxA9zWMT+6YuST/T+UvyFnfz7s4zh38fiWxVK1ppj/R40hpob\nRgQSaA4b7BJdikL1By/YAes28Viq8VeR8M+yeWTRt7a4Apf/XtKn2HdnO5oR1RtCJOt7F4lm1FjZ\nbL07lvBBfWpuGBFIoF18MtHjplmIEH7eSGjBWSPOr1C3R6DDFpHz68WJ6kUOPd4egtXAv4rdIF20\n0IrPNqRUa6XmhhGBBK0A340QxrjYCll+1wnp2Be/RJvox83UyOZwHxt/a/GVESxg2P18+TKs9c9E\nccVvG0hUL94w7tcKqLlhRCBBK1PIbQrND+jxLTtrl/mVs9KbZVi7vInH55Ns/RKLKUVUb2SPYXud\n8hfgYF5Ku9TcMCKQoLUS9Sf4Jeb8CRbnlvjGmh9Yk15HZXH+ie1Xo1Rzb20lCL/fDr+vBL9MEQN9\nTk7NDSMCCaAh1jpD/DoFNkDHXz9kbViPfwfW1tPjDhn/J3t/h2IJxG/YGcjdt1AUXWTlFou2vwVx\n8SzNfrZCWTrqyC8+ZOxZ0wiWqLlhRCABNIZoVZuA3UiH6qcUa9Ol+0rYwLfvrI0ODGz0zQmaxmLn\nibipJlEP0uLEFb9unn9Weo4oUYSE44Ocv+MpXyQ74AdFCasKG6bmhhGBBNBUQrMo3WJcuKuTtE0P\nfLw3BL8kwdqVUqJY4hcKsjcROHp7Vj6iiOpVzqdvYf19CxlHD0uyD0e6MSBJLupivToZClMrNTeM\nCCSAlsCPevHrAthOZMJ/7Ooo/tZNrA8hnNPYdec8PpZEgWH/8Jr9+HCS3hdK1E0kJbov/MJ3vrMl\nKtKeS5K1Qs0NIwIJoKVJe06icCKysOu5qH1kI1fW5q5EN6nm233+ngpSookrckATzDf6oouirK1N\nF1XCz2A5brqI712JyiNJPmllZbyaG0YEEoAjidYLEFm9ipb9Li+9dxT/VjawpGHXP/GjbaL84+e9\npO/g6K6MtTkh4Vh0lZV0IirQ8Vv5iQqg+jEv+tWBnGkAUM0NI1P6YPkAABuNSURBVAIJQC6Fkutz\nG7y7hOhXeNuDePxyAH42SyDMObEWlu1SQY87ZzZuzMGvdLcdivxyA375g43zRcnHVvoRN9goGvkk\nK1vNyjPaxg8DilKK5MrLZlBzw4hAAlBCYf0N9+y/9ZGoUWYPEteTsC0wsF4Xir9GmD+w590szlfx\nT7Ev2XCiRSy6qP6CiELJlVLszdk+T0IwiO6MxSeTbNkgzUt+N3pWjLRCeam5YUQgASiK/brdhHCy\n8W4We1R8fjSftUkgqh9Loiiy1grbDgzRlBhLYulpomP+EX6dhRRfZ0sFmOgXBemqCousra2wMfdG\n3ALChqJOzQ0jAglANawt1Wty+8jPIYl+YWdjdIXc/a5trINgB2wrPNGZbI9a0XcX1UOWmlTpkJeA\nXfYkupOI6EyL7S97Q/Yh2DMDx4rkF+vLOSTIj3myGCMrXUzhnuRE9Wbd+CsE2HIM7n8hNTeMCCQA\nVbKRJc3ZttXGujL+/VlLR5a2P2cNvT2kJ0tTxMbdfqVdHCFp+JUFFt9fSlqwqBPJL09gWSh8I3YX\nEukSBuER/uOyk8WMsTbm2Sj836xojQxRqIeHahtGBBKAM5COxfH50SJDTKIIJBInENkdQiJ8I84y\nhr2V8LNYfGe+62btnVlPqMnblkvnfqTP2i8wsN5wq7RTaHuJB38g+kWBqFnXSz1+z9A33lBtw4hA\nAnBOfH6Ibp/RsiNLolaSLK1lIEloNbgVuigwpPMl/DgeO4d1jKQdOyLxAofA+ssCRd9CukUee3Pp\nyWQlLdhYGdUPNpLEBlus0ai/IGlfh7hPmP/wLc7bSftz6m4YEUgAmlAouXUscZ2Glpqlb05hVL9X\nxPANdyB3PSx7uRAqfA9G1O0Q9SdI0uiLJr3Yh2O7lyYdPRNCpcHxUv7vgqwMSPIdXOISpUmdnh8r\nFwUk/+zjd8aQnTIQSNB68f0nIqspJcMsvY0K+T+tXWjFD8rxvQ2h5RWtrZCmEf+sNB4aNRkmLYxs\n7nou+tbs74LvwLEf3+KgpcU+VtP+1riUwpCdMhBIAPVYTCmy8ls5/wu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo4()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Stochastic Averaged Gradient Descent (SAG)\n", "------------------------------------------\n", "For problem size $n$ where the dataset (of size $n \\times p$) can\n", "fully fit into memory, it is possible to further improve the SGA method\n", "by bookeeping the previous gradient. This gives rise to the\n", " algorithm.\n", "\n", "\n", "We stored all the previously computed gradient in $ (G^i)_{i=1}^n $,\n", "which necessitate $n \\times p$ memory.\n", "The iterates are defined by using a proxy $g$ for the batch gradient,\n", "which is progressively enhanced during the iterates.\n", "\n", "\n", "The algorithm reads\n", "$$ h \\leftarrow \\nabla E_{i(\\ell)}(\\tilde w_\\ell), $$\n", "$$ g \\leftarrow g - G^{i(\\ell)} + h, $$\n", "$$ G^{i(\\ell)} \\leftarrow h, $$\n", "$$ w_{\\ell+1} = w_\\ell - \\tau g. $$\n", "Note that in contrast to SGD and SGA, this method uses a fixed step\n", "size $\\tau$. Similarely to the BGD, in order to ensure convergence,\n", "the step size $\\tau$ should be of the order of $1/L$\n", "where $L$ is the Lipschitz constant of $E$.\n", "\n", "\n", "This algorithm improves over SGA and BGD\n", "since it has a convergence rate of $O(1/\\ell$.\n", "Furthermore, in the presence of strong convexity (for instance when $X$ is\n", "injective for logistic classification), it has a linear convergence rate,\n", "i.e.\n", " $$ \\EE( E(w_\\ell) ) - E(w^\\star) = O\\pa{ \\rho^\\ell }, $$\n", "for some $0 < \\rho < 1$.\n", "\n", "\n", "Note that this improvement over SGD and SGA is made possible only because\n", "SAG explictely use the fact that $n$ is finite (while SGD and SGA can\n", "be extended to infinite $n$ and more general minimization of\n", "expectations)." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 5__\n", "\n", "Implement SAG.\n", "Display the evolution of the energy $E(w_\\ell)$." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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BJQ/yaC0tQTQl//nPf/jr22+/PUbNtLS0l156iTvNVq5c6ayzffv2OXPm4Oth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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo5()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] } ], "metadata": { "kernelspec": { "display_name": "Matlab", "language": "matlab", "name": "matlab" }, "language_info": { "codemirror_mode": "octave", "file_extension": ".m", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "matlab", "version": "0.11.0" } }, "nbformat": 4, "nbformat_minor": 0 }