{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Forward-Backward Splitting\n", "===================================\n", "\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", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{\\arg\\min}\\;}$\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" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "library(pracma)\n", "# library(SynchWave)\n", "\n", "# Importing the libraries\n", "for (f in list.files(path=\"nt_toolbox/toolbox_general/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_general/\", f, sep=\"\"))\n", "}\n", "for (f in list.files(path=\"nt_toolbox/toolbox_signal/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_signal/\", f, sep=\"\"))\n", "}\n", "for (f in list.files(path=\"nt_toolbox/toolbox_graph/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_graph/\", f, sep=\"\"))\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This numerical tour presents the Forward-Backward (FB) algorithm to\n", "minimize the sum of a smooth and a simple function. It shows an\n", "application to sparse deconvolution." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Forward-Backward Algorithm\n", "--------------------------\n", "We consider the problem of minimizing the sum of two functions\n", "$$ E^\\star = \\umin{x \\in \\RR^N} E(x) = f(x) + g(x). $$\n", "\n", "So, we want to find a vector $x^{\\star}$ solution to the problem, i.e. a minimizer of $E=f+g$.\n", "\n", "\n", "We assume that $f$ is a $C^1$ function with $L$-Lipschitz gradient.\n", "\n", "\n", "\n", "We also assume that $g$ is \"simple\", in the sense that one can compute exactly and quickly its proximity operator, which is defined as\n", "$$ \\text{prox}_{\\ga g}(x) = \\uargmin{y \\in \\RR^N} \\frac{1}{2}\\norm{x-y}^2 + \\ga g(y). $$\n", "for any $\\ga > 0$.\n", "\n", "\n", "The forward-backward algorithm reads, after initializing $x^{(0)} \\in \\RR^N$,\n", "$$ x^{(k+1)} = \\text{prox}_{\\ga g}\\pa{ x^{(k)} - \\ga \\nabla f( x^{(k)} ) }. $$\n", "\n", "\n", "If $0 < \\ga < \\frac{2}{L}$, then this scheme converges to a minimizer of\n", "$f+g$.\n", "\n", "Sparse Regularization of Inverse Problems\n", "-----------------------------------------\n", "We consider a linear inverse problem\n", "$$ y = \\Phi x_{0} + w \\in \\RR^P$$\n", "where $x_{0} \\in \\RR^N$ is the (unknown) signal to recover, $w \\in\n", "\\RR^P$ is a noise vector, and $\\Phi \\in \\RR^{P \\times N}$ models the\n", "acquisition device.\n", "\n", "\n", "To recover an estimate of the signal $x_{0}$, we consider basis\n", "pursuit denoising, which makes use of the $\\ell^1$ norm as sparsity\n", "enforcing penalty:\n", "$$ \\umin{x \\in \\RR^N} \\frac{1}{2} \\norm{\\Phi x-y}^2 + \\la \\norm{x}_1, $$\n", "where the $\\ell^1$ norm is defined as\n", "$$ \\norm{x}_1 = \\sum_i \\abs{x_i}. $$\n", "\n", "\n", "The parameter $\\la$ should be set in accordance to the noise level\n", "$\\norm{w}$.\n", "\n", "\n", "This minimization problem can be cast in the form of minimizing $f+g$\n", "where\n", "$$ f(x) = \\frac{1}{2} \\norm{\\Phi x-y}^2\n", "\\qandq g(x) = \\la \\norm{x}_1. $$\n", "\n", "\n", "$f$ is smooth; we have\n", "$$ \\nabla f(x) = \\Phi^{*} (\\Phi x - y), $$\n", "which is $L$-Lipschitz continuous, with\n", "$$ L = \\norm{ \\Phi^* \\Phi }. $$\n", "\n", "\n", "The $\\ell^1$-norm is \"simple\", because its proximal operator is soft\n", "thresholding:\n", "$$ \\big(\\text{prox}_{\\ga g}(x)\\big)_n = \\max\\pa{ 0, 1 - \\frac{\\la \\ga}{\\abs{x_n}} } x_n. $$\n", "\n", "Signal Deconvolution on Synthetic Sparse Data\n", "-----------------------------------------------------\n", "A simple linearized model of seismic acquisition considers a linear filtering\n", "operator (convolution):\n", "$$ \\Phi x = \\phi \\ast x $$\n", "\n", "The filter $\\phi$ is called the impulse response, or the poind spread function, of the acquisition process $x\\mapsto \\Phi x$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "N = 1024" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the width of the filter." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "s = 5" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Second derivative of a\n", "Gaussian." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "t = c(-(N/2) : ((N/2) - 1))\n", "h = (1-t**2/s**2)*exp(-(t**2)/(2*s**2))\n", "h = h - mean(h)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "fftshift = SynchWave::fftshift\n", "h1 = fftshift(h) # Recenter the filter for fft use.\n", "Phi = function (u) {Re(ifft(fft(h1) * fft(c(u))))}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We display the filte and its spectrum (amplitude of its Fourier transform)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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kRzC/slgQCZzRITI1arJCZKTIwfK9rt0twsEREtNoiMlKYmsdslPNyPzVZVyblz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\nGBpBCAAwtP8HdC7PNFZq6LIAAAAASUVORK5CYII=", "text/plain": [ "Plot with title \"Filter, Spacial (zoom)\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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76IJ580q/306SgtRWKibauSlMRElJbC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\ntFp4e8PDA15e8PaGjw9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"text/plain": [ "Plot with title \"Filter, Fourrier (zoom)\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Fourier transform (normalized)\n", "hf = Re(pracma::fftshift(fft(h1))) / sqrt(N)\n", "\n", "options(repr.plot.width=5, repr.plot.height=3.5)\n", "\n", "q = 200\n", "\n", "plot(t, h, type=\"l\", main=\"Filter, Spacial (zoom)\", \n", " col=\"blue\", xlim=c(-200,200), ylab=\"\")\n", "\n", "plot(t, hf, type=\"l\", \n", " main=\"Filter, Fourrier (zoom)\", col=\"blue\", \n", " xlim=c(-200,200), ylab=\"\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We generate a synthetic sparse signal $x_{0}$, with only a small number of nonzero\n", "coefficients." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Number of Diracs of the signal." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "s = round(N * 0.03)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Set the seed-number (for reproductibility)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "set.seed(1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Location of the diracs." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "sel = sample(c(1 : N))\n", "sel = sel[0:s]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Signal $x_{0}$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "x0 = zeros(1, N)\n", "x0[sel] = 1.\n", "x0 = x0 * sign(randn(1, N)) * (1 - .3 * rand(1, N))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Noise level." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "sigma = 0.06" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the measurements $y= \\Phi x_{0} + w$ where $w$ is a realization\n", "of white Gaussian noise of variance $\\sigma^{2}$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "y = Phi(x0) + sigma * randn(1, N)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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XLkyJEjJvt4eHisWrUqODjYyrUREZFMySkIAYSGhgYHB2/fvj06Ovrs2bOpqakZ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\nAAAAAElFTkSuQmCC", "text/plain": [ "Plot with title \"Signal\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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SpzsT1Zpq3NOCfDMEwiyHYhdLlcp512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\nWzcja1Quaa2GRrE3hGg9tNK3L3r1w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"text/plain": [ "Plot with title \"Measurements y\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "stemplot(x0, col=\"blue\", ylab=\"\", xlab=\"\", main=\"Signal\")\n", "plot(c(1:N), y, xlab=\"\", ylab=\"\", col=\"blue\", main=\"Measurements y\", type=\"l\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Deconvolution\n", "---------------------------\n", "We now implement the foward-backward algorithm to recover an estimate of the sparse signal\n", "\n", "\n", "We define the regularization parameter $\\la$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Lambda = 1." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the proximity operator of $\\ga g$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "proxg = function(x, gamma, Lambda) {x * pmax(1 - ((Lambda * gamma) / abs(x)), 0)}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the gradient operator of $f$. Note that $\\Phi^*=\\Phi$ because the filter $\\phi$ is symmetric." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__ \n", "\n", "Write the code of the function grad_f." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "source(\"nt_solutions/optim_2_condat_fb/exo1.R\")" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the Lipschitz constant $\\beta$ of $\\nabla f$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "L = max(abs(fft(h)))**2" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define the stepsize $\\ga$, which must be smaller than $2/\\beta$." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "gamma = 1.95 / L" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We compute the solution of $\\ell_1$ deconvolution (basis pursuit denoising).\n", "We keep track of the energy $E_k=f(x^{(k)})+g(x^{(k)})$." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__ \n", "\n", "Write the code of the forward-backward iteration." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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SS89PT0119/vbS01GvFtQeRkfL3J9gB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\npV27tHy5P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58/n56enpiYOGzYMAASiUS1kkFaWpqQ\nqIWGhsbFxb18+TIlJSUuLk64Z9a8eXPteIQ1uIT7WF988YV2BSMjNPDyjWwhNTW1YsWKADp0\n6HDmzJmMjIwLFy60bt1adY/N8Dtvx9d2B8R3hPInMTFRWGhLJ39/f/H0oRqful9//VW8+qFg\n0qRJUJ8BzsgP/8WLF4sVK6bRWpEiRdatW9e4cWNx5Tw//CkpKcJFTTypvWogRbly5VR/SDIy\nMsLDw7VfeP/+/XVOg0JExsvzoyrMsiYsgSq4d++ezrXCJBLJ6NGjVdVOnTrl6+urXU2jV9yZ\nM2e0l8YCUL16dY3hrgLxg864uDidMRsZoYGXb2QLR48e1Xh2KZVKhTVbDb+rAru8tjsmviOU\nbxkZGStXruzYsWNAQICrq6uLi0u5cuU6der0888/awwo0/7UHTlypEOHDt7e3u7u7sHBwUuW\nLBEmCilWrJiBo/SVJyYmdu/e3dfX183NLSgoaNSoUcIsmrt37/bz8ytVqpThBlW++OILAE5O\nThpLN544cUK4Wom/i2dnZ8+bNy8kJMTT09PHx6dx48Zr167VfkpCRPmV50dV9fdeXPjq1asZ\nM2a88847Hh4enp6egYGB/fv3F68oKrhz587QoUPLli3r7Ozs5+fXqVOn/fv3a5/i0aNHo0eP\nDgwMdHV19fb2rlev3tSpU8XLOYhlZ2cXL14cgI+PT1ZWlr6wjYzQwMs3soXExMRu3bp5e3t7\neXk1a9ZMeHZsfPZjf9d2xyRRGjEnJFHhOXbsWGhoaEhIyPHjxy0dCxERmQav7ZbCUbFkJv7+\n/hKJ5MyZMxrlwjo8zZo1s0BMRET0ZnhttzZM7MhM2rdvD+CDDz7YtWvX06dP09PTz5079+mn\nn/78888eHh7CkCsiIrItvLZbGz6KJTO5d+9eWFjY9evXNcpdXV1XrlzZq1cvi0RFRERvgtd2\na8PEjswnJSVl6dKlv/3227Vr19LS0kqXLt2iRYsRI0bUrl3b0qEREVEB8dpuVZjYEREREdkJ\n9rEjIiIishNM7IiIiIjsBBM7IiIiIjvBxI6IiIjITjCxIyIiIrITTOyIiIiI7AQTOyIiIiI7\nwcSOiIiIyE4wsSMiIiKyE0zsiIiIiOwEEzsiIiIiO8HEjoiIiMhOMLEjIiIishNM7IiIiIjs\nBBM7IiIiIjvBxI6IiIjITjCxIyIiIrITTOyIiIiI7AQTOyIiIiI7wcSOiIiIyE4wsSMiIiKy\nE0zsiIiIiOwEEzsiIiIiO8HEjoiIiMhOMLEjIiIishNM7IiIiIjshJOlA8i3W7durVy58sCB\nA4mJiU+fPs3KyvLw8ChTpkxwcHC7du169OhRpEgRS8dIREREZAESpVJp6RjyYdGiRaNGjcrI\nyNBXISAgYOnSpe3atTNnVERERETWwJYSu9jY2I4dO0ql0h49enTq1Ck0NNTPz8/LyysjI+PB\ngwdnzpxZtWpVdHS0i4tLfHx8o0aNLB0vERERkVnZUmLXrFmzgwcPzp07d8SIEfrqjBs3Lioq\nqm3btjt37jRnbEREREQWZ0uJnbe394sXL5KTk4sWLaqvzuPHj0uUKOHr65uUlGTO2IiIiIgs\nzpYGT0ilUgCZmZkG6shkMgBZWVlmiomIqHBwoBgRFYAtTXcSEhICICoqykCdWbNmqWoSEdmo\nRYsWVa1addKkSfHx8ffu3UtPT5fL5SkpKQkJCRs3bhw4cGC1atXY4YSItNnSo9j4+PhWrVrJ\n5fJWrVoNGDCgXr16AQEB7u7uqampT548OXbs2Jo1a2JiYiQSya5du1q3bm2q8yYnJ//666+v\nXr0yVYNEdszd3b1fv37e3t6WDsSGWWqgGK91RMaz3mud0qZER0f7+/sbeDmenp5r1qwx7UkX\nLFhgtn8OIjuwYMEC034GHU3Tpk0BzJ0710CdsWPHAmjbtq0Jz8trHVG+WOe1zpb62AGIiIho\n3br1+vXr9+/ff/z48SdPniQnJ7u4uPj7+9esWTM8PLxfv37Fixc37UmFHnvLly+vU6eOaVsm\nsjOnT58eNGgQO7m+oZMnTwLo37+/gTpjxoyJioo6evSoCc/Lax2Rkaz5WmdjiR0ADw+PQYMG\nDRo0yMznrVatWt26dc18UmNkZ+PSJWRloUoV6B8uTGQO6enplg7BHlh2oJjVXutM4uZNPHmC\nEiVQrpylQyFbZs3XOlsaPEEaMjIwYQL8/FC7NkJCULw4undHYiK+/RY1a8LFBT4+6NgRBw9a\nOlB78eoVDh/GH3/g+HHI5ZaOhuwXB4oVhj/+QI0aqFgR9eqhfHkEB2PXLkvHRFQImNjZKoUC\nERGYOhXJyTkl2dnYtAlvvYVvvsHFi8jKwvPniI1F8+aYN8+isdo+hQJRUShdGmFh6NIF9eqh\nShVs3mzpsMhORUZGymSy6dOnh4eHr1u3LjExMTU1VaFQpKSkXL9+fcOGDZ07d54yZYpEIpkw\nYYKlg7UNy5ejSxdcupRbcvYs2rfHb79ZLiaiwmF7j2LzJJFIACiNG+0rl8t37Nhh+J6q0N/F\n2h6lr12r++umdphKJf77X7RsiVq1zBCXfRo7FjNnqpXcvInu3bFuHXr1slBMZL+aNWu2adOm\noUOH7tu3b9++fTrreHp6Ll682ITD/+1YUhJGjdJRrlTi00/RsSM8Pc0eE1GhscPELl8OHDjQ\nuXNnY2quW7euWbNmhRxOPvz+u3hLCWQBLvoqZ2fjl18wY0bhh2WPLl3C7Nk6ypVKjBiBLl3g\n6mr2mMjeWWSgmL3asQMpKeKCTNXV8ulT7NuHiAhLhEVUOOwwsTPyXp2gefPm27ZtM3zHbuHC\nhfHx8WXLln3j0Ezpxg3x1hfAHuCiqEQBvA/0BXoI2+fP620qOxs3b0IiQYUKkMkKIVYbt3Ur\nFApxwUOgpPDT48c4fBgtWlgiLLJ3lhooZn+uXxdv/Q8IBw4DOQNErl2zRExEhcYOE7t8kclk\nnTp1Mlxnx44deD1OzXq4u4u3bgA31PcnA9uBAFViJ5HoaOTlS0RG4pdfcjrq+fhg8GB88w08\nPAohYpt15454ay3wEXAeqC5s375tiZiIyGjqF7RbQAZwR5XY8XJHdsbREzvb1aAB/v03H/W1\nO9ilpqJ5c7VGnj3D9Ok4fBj798PNLY8G79/Hw4coVw52/zhIfRKZJ4ACSFJtW+Gs4ypKJf7+\nGydOQKFA7dp47z3ekSVH1KCBob0NG5orDkd15Qq2bsXNm/D1RdOmaNZM940GMhUmdrZq5Egs\nW4aMDKMqOzlhwADNwpkzdaeGf/2Fn37Cl1/qbW3TJnz9NS5eBACJBO++i+nTYbpljaxOkyZ6\nd8lkmi88NRXbtuHiRchkqFcPbdrAyUIfsosX0bs3Tp3KLalaFatXIzTUMvGQyTnIQLE3FxaG\nd9/FX3/p2BUejrffNntADkOpxPjxmDFDrTdLkybYuBElS1ouLHvHxM5WBQXht9/Qty9evswt\nlEjg749Hj9RqSqWYOxc1a2q2sG6d3sbXrdOb2M2bh5EjczeVShw+jKZNERuL8PD8vQRb0bo1\nGjbEkSM6dn38sdrlaft2DBiAJ09yS4KC8PvveOedQg9Sw4MHaN4cDx+qFSYmIjwcx46halVz\nx0MWZ7sDxd6cRIING9CuHc6eVSuvVw9r15qg/dRUZGTAx4c3ojRNnQrt2Rj/9z907oy//4aV\n9W+yH0zsbFhEBC5exLJlWLQIT57gk0/Qty+CgzF7NtaswcWLcHNDmzb48ks0bqx5rFKp0WU4\nAnADcuZ0unpV9xnv3MG4cTrKs7IweDCuXrXY3alCJZUiOhrvvw+N1Zt69cKsWbmb//yDbt2g\nsVjA5cto3RpnzqB0aXOEqhIVpZnVCV68wDffGMrpyYY4yEAxkwgIwLFjWLsWP/+Mo0cRFoah\nQ9GrF5yd36jZtWsxYwZOn4ZSieLF0bMnJk+2/94pRkpLw9SpuncdPYpt2zgYubDY499hR1K2\nLL75BidPYs8ezJ+fUzhhAj75BL6+6NcPixfrPlAigaureNK7S0Burzp9Heyio6Hv78KtW/jr\nL7z3XgFehA0oVQp//42YGMyahUOH8OGHGD4c776rVmfSJM2sTvDkCWbONPdcMzt3irfuAhlA\nZWGDs+07JtsdKGYqrq4YOBCurujTB2PG4P3337TBL79U+1wnJWHhQuzahT//NPcXOet09Kja\nAyVgI9ACyEl7DxxgYldYbOkDLMkPSwdrA+rV07tL30KR6rMG7AS8gNybe/Y9a4BUivffR9eu\nAPDJJ5pZnVyOAwfEBSeAK6oNPVPMFiL1x/F9gY6qjWfPdCegRGS8w4d1f1u7dg3//a/Zo7FK\nz5+LtxKAHsAS1fazZ2YPyGHYUmI3ePDgEiVKWDoK+zF6tN5dDx7oWMECmnOsXAVeAndV2448\na0BKika21Bn4TLWRlKR1QCFTfxiUBqSpNooWhYveqayJyCirVundtWWLxp0qB1WqlHgrS/R/\nALypWYhsKbFbunTp9evX33vvPQDKvFg6WBvQqZPemXVPncKiRTrK69c31KCBW4B2r2hRjaw3\nE8hN9NQvcOZgYCCLvY5xITKnhATx1gKgLpAz8jMjQ2MCeQdVr56h7C2vfgFUcLaU2AHw8PAY\nO3aspaOwH7du6d2lc7BYhw6oUUN3/a5dUbmyaaKyRVIp2rbVu7ddOzOGAgAYPx4+PjrK3d0x\naZK5gyGyP+qjLo4DJ4BXqm3eFAfg5ITZs3WPFO7VC2FhZg/IYdhYYgegIWeTNBG5XKPP3A0g\nd/GiK1c06wNwdkZ0NCpW1Cxv1AjLlpk6Pl0UCpw8iehoxMdb3cOO777TvZR4hQq6FyAvVOXK\nYc8eVKmiVlimDLZvR+3a5g6GyP4YmMPI21vHRdIx9eyJNWsg7kLl7IzPP8fKlRYLyRHYXmJX\nvHhxm37Sqr7qqCXJZBpfOl8BZ1Qb+gbGVquGs2cxdy7eegsAmjXD6tU4dEj3/SHT2rEDVasi\nJARdu6J5c5QqhchIZGcX+nmNVKsW9uzRnCKucWPExel+cy5dwsqVWLIE8fG6ezS+oXr1cOkS\ntm9H2bIoVgybN+PqVS5raxs4UMz6DR2q97bcsGG8Y5erd2/cvJnzzb9XL9y5g3nz4Opq6bDs\nmu0ldjbq0SN8/jnKlIFMhiJF0LEj/v47j0PkciQm4tw5pKXlUbPAQkL07jLQYc7TEyNGYNgw\nAPj2W/TpY47p62Jj0bmz2gR7qan4/vucMKxEo0a4eBHx8fD0RLVqOH4cf/6p4wn1w4c5D7UH\nDMCwYWjeHEFB2L/f9PE4OaFDBwQEwNkZP/+MSpVQpgzatcMff5j+XGRCHChm/QID8csvOhK4\ntm0xebIlArJibm45q7rVqAH+XpsBEztzuHYNISGYPx/37wNAWhpiY9Gkid5xVZmZmDQJJUqg\nWjXUrg0fH/TpgwcPTB/YF1/oLpdIMGLEG7WsUOCvv/Dzz1i+HMePv1FTQmuffQa5XMeuFSt0\nrwlhKVIpmjaFuzvKlNGdN6enIzwcO3aoFd68iQ4d8s71C0CpxPXrePwYe/bgwQPcv49du9Cl\nC4YPhy3f+LZzHCim7eFDTJuGbt3QsSPGjMHp05YOCOjdGydOYOhQFCsGAOHhWLkSsbG8HUUW\nxsTOHAYPxt27moVyOT7+GHfuaJYrFOjaFZMn4+nTnJLMTKxdi4YNTZ/bde+OCRM0O7dKpYiK\nQsuWBW/22DFUqoTGjfHxxxg8GPXqoVEjXL5c8AZPndIYZfYIyP17tnVrwVs2v+XLNdc1EmRk\noDDGBa1erbnEnGDRIqxfb/rTkalwoJjYjh2oVg1ffYUtWxAbi5kz8c47+PprS4cF1KqFn39G\nly4AEB2Nfv24TBZZHn8HC921axpT1+Z69UrHH9d16xAbq6PyzZuYMMHEsQGYMgWHDsHbGxIJ\nPDwwZAiOHsWYMQVvcO9eNGqkOd72yBE0b47HjwvYpnr6ew8IABaotm/fLmCzFqH+j5sM5M6a\n8NdfSE428en0LT1ieBdZAw4UE1y7hv/8R/OjoVTiu+8MTSZH5LCY2BW6ixfFWy+ABsBuPXsB\n4Lff9Da1aZPux5HahBuEp05hxYq8856wMJQqBWdn1KyJJUv0LjthjJQUdCEN8YIAACAASURB\nVOmiO8i7dzF9egGbLVpUvPUcyAaeqLa9vY1qRC7H7t2YNg1TpiAmxmKrL6gv4fpfILczo0Kh\ne4HXN3HmjHhrCjBNzy6yOrY+UMxU5s7Fq1e6d02bprucyJExsSt06nfmbwNHgdxOYTKZZn31\nhblGAXVUGykpuh+riWVnY9SonKH4//yDQYNQuTJGjTLT6NFly5CaKi64CeQ+P9boWGa8evU0\npv9V06RJ3i2cOIEaNdC2Lb76ChMnonNnBAbi4MECxvMmfH3FWy+Bl+LHyiZfPlx9FPZaYJ2e\nXURWSr3v6Z/ACtXGxYsa61YRERO7wvfWW7pnaFTt1aCewVwRLzkKoEiRPE733/9izhy1NC47\nG3PmmGn5QvWhnTeB94C+qu179wrYrKen3vjfegvduuVx+O3bCA/X7OR3+zbat8f58wUMqcAM\ndF6sU8f0iZ2+CaUN7yKyHurfFWcCn+vfS0RM7ApfuXLo0EH3Lm9vfPCBZmFoqN6mgoI0Hkpq\nunEDCxbo3rVggTlWuVHvBzMFuAW8UG0bDt6wb77B0KGahcHBiInRmI1Phx9/zB2JIpaWhm+/\nLXhIBfPJJyhXTveurKx8/JWKi0PPnqheHdWro3t37Nmju9rAgXpbMLCLyHpUqCDeUqhW7gLg\n7s7pM4g0MbEzhyVLUK2aZqGbG1av1nFVGjFC7+SWX36Zx4n27tXo33YXyNmWy7Fvn5HxFpz6\nyoCaT3+bNy94yzIZfv4Zx4/nTFwXGopNm3D8uFEzvKsnPVeA3Nt0e/cWPKSC8fbG1Km6d124\nYGyiOWECWrbEhg1ISEBCAjZtQps2um9qDhume3rkrl0xeLDRQRNZTvfuendFROT9vY4K4PJl\nLF6MH3/EqlWm7/hLhY2JnTmULo1jxzB5cs7Dr2LFMGAATpzQvQpyjRpYvVpHl7JRozBkSB4n\n0hp2uh3YqX+v6RmYqVgmwzffvGn7ISE5E+y1a4du3YydGPnJE/HWIOA/qo3nzwtl1QfDdu/W\nu2vFirzHx/zxh+7UcNYsHSNvnJwQFARf39yVxIKDsWABNm7U0b+TyAp99JHuFVNKleLgCdNL\nS0O/fqhWDZ98gvHj0a8fKlTA999z2ktbwsTOTLy8EBmJjRsB4IsvsGKFoR5OPXrg/HmMHw8/\nP0ilGDIE//sfZs3K+yz+/tplrwzuNaWsLEMpy4cfajxSMR/126LpQLpqw9fXAt/4tTr29VH9\nlJSU9/fj+fPzt0sigZcXzpxB9ep46y2cPo3hwznbFtkMmQzbt2P0aHh45JRIpTmL95QvX+hn\nP3ECP/6I8eMxb57ayjf26qOPsGqVWhqXkYHISERFWS4myide3a1UpUqYOhUNG8LNDUuWICzM\nqKNatdJ7G0Yme6M5h41x7pxGVza1YR8W/MLXtq3eXW3amDGO17QG02wwuFfTiRPirYXAHNXG\nyZN5nJcri5ItcnfHzJlISsJ778HFBQ8fIiYGFStizx4MHIimTdG+PaZMMfFDwxcv0KUL6tbF\n+PH48UeMHImqVTFqlD0PJz9yBJs36941eTJevNC9i6wNEzu7UqkShg/XvevTT1GpUuGeXX3k\nxAPgf+JtC85KMG6c7h7WRYua4OlwAdSqpXeXn1/encHVZ65ZAuRONCyX84kJ2S03NxQrBqkU\nfn7IzkafPmjTBr/8gkOHsHMnJk5EzZp6Z4MvgN69NVdVVigwZw4mTjTZKayN+iOXdCBOtZGW\nhj//NHtAVCBM7OzNrFkYOVKt85mTE0aOxMyZhX7qgADxlubIibJlCz0AfUqXxv79CA5WKwwM\nxO7dqFrVAvEMGaL3ztmgQXl3fdMeiKMSFMR7cuQQpkzB2rWahU+foksX09y3O3xY9wpAQM69\nQ7uk3h15FdASyH1AkOcsqmQlmNjZGycnzJmT+7Ru2DBcvYo5c4wdZ/AmgoJQs6beve+/X+gB\nGPDWWzh1CocOoXx5+Ppi715cugRLrdgUFqb7TuF77xm1/OVHH+nd1a9fgYMishlZWZg7V/eu\n5GQsXWqCU6hPyZkKbFFNJJ6Zabf3rvz8xFuvRP8HNDsrk/ViYmefVLfHWrY0R/9ilZ9+0j0W\noUsXy/RmE5NI0KQJSpVC0aKGOiOax9dfY9culCqVs/n225g1C/v25XYPN+Djj3W/mc2b5wwZ\nJrJviYl49kxcMBk4qto4elTrgPxT7y68DugG/KPattc7dgau0h4eOrp6K5V48MBu3w3bxcSO\nTKlFC8TGIjAwt0QqxciRWLdO/zGOqk0bNG0KAE5OOHkSo0YZOz7X2RkxMZg6NXeUcbly+O47\n7NqldwZEInuivnTsc2AS8IuevQVUsqR4KwMAkLu8tOormZ1p2FDvQj5ff602w/zLl/jyS5Qo\ngdKl4eeHSpUwc6axS5lTYWNiRyYWHo6EhNxlYd9+G3PmwM3NojHZHWdnjB+PGzfw1lsIDMSt\nW5g4kVkdOYqKFcXz9ShF/weAypVNcIr27fV2V/X0NGp9ahu1ahU++kjttbu64rvvMHZsbsmL\nF3jvPcyYkdsn78YNjBmD7t3teciwDWFiR6YnleZOh2uGvn2OTCbjPMPkcPz8DE3e1LOnCU5R\npw4GDNC9a8oUeHmZ4BTWycMDv/6KhIScBT8mTsTNm5g4US3VmzJF98xK0dE6RrSQ+dl2YpeZ\nmTllypTq1au7urr6+fl17Nhxt4EZcomIyC789BN8fXWUDxqke5mKAli0CCNHqnWQ8PLCnDlm\n6smano64OKxYgehoCyzqFRSExo0BoG1bjafSALBqld4DV68uxKjISLaU2EkkEonoW0NWVla7\ndu0mTpyYkJCQmZmZlJQUGxvbtm3bzz//3IJBEhFRvsjlSEjA2bNITTX2kGrV8M8/6Ngx9451\nqVKYORNLlpgsKhcXzJmDW7fQvz8AfP89bt/GyJEma9+A9etRsSJatsSgQejaFeXK4bPPkJ6e\n94FmkJKCBw/EBR2AMaqNxESzB0RabCmx0zB79uy4uLgiRYosXbr08ePH9+7dmz59upub2/z5\n89esWWPp6IiIHFdaGq5dy3t96sxMfP01/P1RvTqCg+Hriw8/1Mgb9AoMRExMzjJfvXrh7l2M\nHm36tfJKlULdugDQpAm8vU3cuE4bNuDDD9Xu0mVlYcECQ/McmZOLi0bvw2Piue5cXc0eEGmx\n4cRu5cqVAKZNmzZ48GA/P7/SpUuPGTPmxx9/BLBs2TILB0dE5JAuXULnzihWDFWqoEQJ1K6d\ns0a2NoUCXbrgu+9y5y7JzMS6dWjY0NjcDsgZquntbSfLH8vlGDVK9/oxGzfi4EGzB6TF1dXQ\nfKXvvGPGUEgPG/4oXL16FUB3oYfna926dQNw+vRpy8REROTATpxAaChiYpCVlVNy7hx69MC0\naToqr12bO3xe7OZNTJhQiEFas+PHce+euOAykKXa0LcYhpnp62UokYA9oayBDSd2xYoVA1BU\nPLUOULx4cQAZGRmWiYmIyIENGYKUFB3lkZE6el/99pvedjZtctBJ0dRvVd4GqgPzVdvqOZ/F\nDBmCYcM0C2UyzJ6dM+SCLMv2Erus198EhZtzR9VnGT9y5AiAKlWqmD8wIiJHduFC7mKGGrKz\n8fvvmoXXr4u3vgByl3NOSXHQlUmLFRNvpQAKIFm17eNj9oB0kUiweDF27ED37pDJUKQIBg7E\nP/+YaWQJ5cn2EjsPD4+goKAOHTpkZGRIJJIxY3LH41y6dGnkyJEAunbtarkAiYgckTCO4bUn\nQElgg569AODurnY0cFX/XkdRv76hSfKaNzdjKHlp1w4bNsDXF6GhWL48Z4gJWQNbSuxatWpV\nrlw5uVx+5cqVHTt2rFixQqlU/vvvv6oKNWrUOHPmTLly5UaNGmXBOImITMsm5uxUHxH5EHgE\nXFRtay8/Exqqt6mgII17V7pdvIivvwaA7dvx3//i/Hnjg7VS7u56+xfWr4/33zdvNNZBocD/\n/oeffsK8eYiP5+IWebOlZQH27t0L4NWrV5cvX04UUVXw8/Nr27btDz/8UMyYSwIRkVUSJuxU\nvh4bKczZGRcXJ2wKc3bGxsZ+9tlnP/30k8Wi1BISAicnZGfr3qt9R2fECKxYgcxMHZXFC1jp\ns3AhRo7MOd3du5g1C/PmYcYMm38gOG4cnj/H9OlqGUxYGDZudMRlZs6cwYcf4ty53JLq1bF2\nLUJCLBeT1bOlO3YCd3f34ODg//znPxMmTFi5cuVff/2l2vX48ePVq1eXK1fOguEREZmWrczZ\n6eeH3r117ypdWsdKXzVqYM0aeHholo8ejcGD8zhXfDw++0wziczOxqhR2LvX+JCtkUSCadOQ\nkIAvvwSA997Dvn04dAilSlk6MrO7fRstWqhldQAuXUKrVhodNEmN7SV2REQOxYbm7Jw/H02a\naBb6+WHLFqhPYJCje3ecP48JE+DnB6kUw4bh8GHMnJn3iWbM0D3Zm1KJGTPyH7f1CQzMWfGi\neXO0bKkxJ3AeLl/G+PFo2xbh4Rg9GmfPFk6Ihe+HH5CUpKP82TN8953Zo7EdtvQotjDI5fId\nO3akG1yr5caNGwAUfLBPRJagb87OkSNHWtucnV5eiIvDunVYuRIHDqBiRfTvj08+QYkSeg+p\nWBFTpuDMGcTFYfFiY0/0zz8aBVf073Isy5dj+PDcB9z79mHePEydmnP/z7bs2iXeugUogIq6\ndpEaO0zsNLqnGHbgwIHOnTsbU/M67/wSkSUUK1bs0aNHtjJnp5MTPvoIdevirbfQvz8mTSqU\ns7x6pVGQO89KWlqhnNEm/P03hg7VHF4gl2PsWNSogY4dLRRWQalPedMLSFf9Qz96BKUyfzcy\nHYcdJnb50rx5823bthm+Y7dw4cL4+PhKlSqZLSoioqysLGdnZwDdunVbtGjR0aNHmzZtqtrr\n4HN2VqyoMQY295u8I1+qZ87UO2h0+nTbS+z8/HDrlmorDcj9S128OLM6vewwsTPyXp1AJpN1\n6tTJcJ0dO3YAkNrHSoREZCM8PDwqVqxYtWrVUqVKCXN2Hjt2TNjFOTt79UJkpO5d2qM0HIf6\nY+hoIAX4SNg4etT2bnGFh2P5cr27SB87TOyIiGxaq1atEhIS7ty5c+XKlStXcnqPaczZCcCR\n5+wcPRrR0ToWuggONmqqFHul/oT6R+CRKrHLyIBcDieb+pv/f/+HTZuQnKxZ7umZM38h6WRT\n/8hERA6Ac3bmycMDBw7gq6+wYgWErjRubujXD9OmwdPT0sFZTsWK4mGkSvET6nLlbCyrA1Cp\nEnbvRu/euHYtt7BCBaxZg6pVLReW1bO1f2fg1q1bK1euPHDgQGJi4tOnT7Oysjw8PMqUKRMc\nHNyuXbsePXoUKVLE0jESEb0pYc7O4OBg7V2PHz82fzzWpmhRLFiAyEiULg0vLzx6pGNxC0fT\nqxeOH9e9y0afUDdogEuXsGcPBg9GdjZWrECbNnBxsXRY1s3G+o0tWrSoatWqkyZNio+Pv3fv\nXnp6ulwuT0lJSUhI2Lhx48CBA6tVq7Zz505Lh0lEROYgrGMmkzGrA4DPPkODBjrKa9TA//2f\n2aMxEWdndOiAkiVRvDg6dWJWlzdbSuxiY2OHDx+elZXVq1evtWvXXr58+dmzZ9nZ2ampqVev\nXo2Oju7Spcvdu3cjIiL+/vtvSwdLRERkVm5u2LcPn3+eu56HqysGDsSff8Lb26KRkRnZ0qPY\n6dOnA5g9e/aIESPE5R4eHpUrV65cuXJERMS4ceOioqImT57M+3ZEZN/yNWcnJ2N3EJ6emDcP\n06ejXj08fYrLl3Us2kb2zZYSu5MnTwLoLyyzoseYMWOioqKOHj1qppiIiGwBJ2N3KK6u8PDA\ny5fM6hyRLSV2wkxymaqlUnSRyWQAsrKyzBQTEZGF5GvOTk7GTuQgbCmxCwkJiYuLi4qKioqK\n0ldn1qxZQk0zxkVEZO04GTuRg7ClxC4yMvLgwYPTp08/efLkgAED6tWrFxAQ4O7unpqa+uTJ\nk2PHjq1ZsyYmJkYikUyYMMHSwRIREZE57NyJdetw5Qrc3dGoEYYNQ/nylo7JcmwpsWvWrNmm\nTZuGDh26b9++ffv26azj6em5ePHi1q1bmzk2IiLT4pydRHmSy9G/P9asyS05cADz5mH9ettb\nG9dUbCmxAxAREdG6dev169fv37//+PHjT548SU5OdnFx8ff3r1mzZnh4eL9+/YoXL27pMImI\n3siiRYtGjRqVkZEhLhTm7BSm7YyMjFy6dGm7du0sFSGRNZg2TS2rE7x8iZ49cfGig963s7HE\nDoCHh8egQYMGDRpk6UCIiAqFMGenVCrt1atXp06dQkND/fz8vLy8MjIyHjx4cObMmVWrVkVH\nR0dERMTHxzdq1MjS8RJZhlyOuXN170pLw+LF+OEH8wZkHdhJlojIuqjm7Fy/fn3v3r0DAwOL\nFSsmk8mEOTsjIiK2bNkyduzYzMzMyZMnWzpYIou5cQPqq+t9DxxUbRw7ZvaArAMTOyIi62Lk\nnJ0AOGcnOTL12XsygEjgF9X2q1dmD8g6MLEjIrIunLOTyBjly8PZWbWlFP0fAKpUMXtA1oGJ\nHRGRdRFm4jQwYSc4ZycR4OVlaOjrBx+YMRRrwsSOiMi6REZGymSy6dOnh4eHr1u3LjExMTU1\nVaFQpKSkXL9+fcOGDZ07d54yZQrn7CSaPRulS+so79cPbduaPRrrYHujYomI7Bvn7CQyUoUK\nOHoUY8YgOhpC54WAAIwZgxEjLB2Z5TCxIyKyOpyzk8hIZcvit9/w9CmKF0e3bti0ydIBWRoT\nOyIia8Q5O4mM5+EBAFyNBexjR0RERGQ3mNgRERER2Qk+iiUiIiJ7oFRi504cPoyXL1GlCrp1\nQ5kylo7J7JjYERGRQ0hPx9WrAJCUZOlQqHBs347Vq3M3x4zB1KkYPdpyAVkCH8USEZGdy8zE\nxInw98ekSQAwaBDCwnD6tKXDItMRFhB79kytMDMT//0vfv3VIhFZDBM7IiKyc717Y8oUvHyZ\nW3L4MJo0YW5nP8Q36jRERkKp1LvX/jCxIyIiexYbi82bdZSnpGDkSLNHQ4UjPl68dRfYrtq4\nfRtXrpg7HgtiYkdERPZMfcZatVs3hw7h0SPzRkOF4/lz8daPQCcgRbWt8YjWvjGxIyIie3br\nlngrGgCQJWwolbh92+wBUSEoVUq8lSX6PwDd68naKyZ2RERkzzw9xVvCjZ1MPXvJVrVrp3dX\ncDDKlTNjKJZme4ndrVu3Jk+e3Lx584CAAHd3dycnp6JFi1avXr1Hjx6//PJLamqqpQMkIiIr\n8u67enf5+yMw0IyhUKHp1k13uZMTZs82byiWZmOJ3aJFi6pWrTpp0qT4+Ph79+6lp6fL5fKU\nlJSEhISNGzcOHDiwWrVqO3futHSYRERkLYYMgb+/7l3jxkEmM280VDikUgCoXDnnB0H58ti2\nDS1aWCooy7ClxC42Nnb48OFZWVm9evVau3bt5cuXnz17lp2dnZqaevXq1ejo6C5duty9ezci\nIuLvv/+2dLBERGQVfH0RE6Ojl9Xnnzvc1LV2LywMN24gPBwAYmJw5YqhR7T2ypYSu+nTpwOY\nPXv2+vXre/fuHRgYWKxYMZlM5uHhUbly5YiIiC1btowdOzYzM3Py5MmWDpaIiKxFgwa4dAkL\nFqBkSQBo3x7HjmHePEgklo6MTK1cOVSpAgDvvgtnZ0tHYwm2lNidPHkSQP/+/Q3UGTNmDICj\nR4+aJyQiIrIJRYti+HDUqgUAH36IevUsHRBR4bClxE4qlQLIzMw0UEcmkwHIysoyUIeIiIjI\nLtlSYhcSEgIgKirKQJ1Zs2apahIREZGjyc62dAQWZUuJXWRkpEwmmz59enh4+Lp16xITE1NT\nUxUKRUpKyvXr1zds2NC5c+cpU6ZIJJIJEyZYOlgiIiIyq/PnERiIZcsAoH59zJzpiEmek6UD\nyIdmzZpt2rRp6NCh+/bt27dvn846np6eixcvbt26tdmi2rEDP/2ES5cAwMkJcjmys3PXG1b1\nzFUoAOSUz52L5ctzyjVqKpU5JRIJJBIkJeHVK1SokHO4doMApFIkJSEjAxUqqB0uGD0aY8eq\n/WarTqTalEjw4AGysnD2rNosjto1VaeWSJCeDgA9e+b0TtWuJhA+ZhkZuefS+VrER4nPK5HA\nxQVKJbKzoVDkvsB587BiRU4FfQ0qlbklqs3Hj5GdnfteabxdqlO7uEAmQ2YmJBJIpVAocv5Z\nhVfdvTucXn903NygUCArK7dBqRRPn+LIEZQvn1NH53soleasciOXo2JFtd8Q6Pp90PnmPHwI\npRLly+t4E1Q/CC+5YkXcvw+IpgNQ/aM4O8PJCZmZyM7W/AUT3ofs7NxdMhmqVcOIEWjfHkRE\nht2/j7lzsW0bACxbBhcXfPopvLxMfyKhB9bx47kl165hzBjExWHr1twrtiOwsdcaERHRunXr\n9evX79+///jx40+ePElOTnZxcfH3969Zs2Z4eHi/fv2KFy9unmDGjcP06bl/iY337Fn+1q1T\nXw8nf9Xu3MnHiTIy8lcfwIMHeVRITcXVq/lr0xj5fQ81GPmW6iNkSIa9emXsUkVKJW7efKN4\njDmR6hTXr7/RuQDcuIHduyGRYOxYTJv2pq0Rkb06dgzt2iEpKWfz9m189RVWrEBcHMqWNfG5\nfv5Zd/mOHVi8GJ99ZuLTWTMbS+wAeHh4DBo0aNCgQZYN45NPsHixZUMgsiSlEj/+iBcvsHCh\npUMhIuvz6hX+85/crE7l8mX06YP4eBOfbvVqvbt+/dWxEjtb6mNnPe7f1/vlgMihLFpk1P1L\nKgAun0g2LSZG77ORgwdx7pyJT5eYKN46JN4Q+ko5Dtu7Y2dacrl8x44d6ULPKT1u3LgBQKHq\nxAQsWyZ+ApsF3AReAdozXQolytc/K4ErAIDHwDlRofgHqB+SAiiBc68raDco/KxRTSgR3AHO\nAwpRPBAdrvpBmEQmAzgLAJBqBSaOUAIogHvC2wP46qr58HVloU1jGhR+0K4gMfgeil+R+M3R\n1+ArIEv9WKX6SzbcoJDFXAO8Df7zyYFUIyJMfr3LyN8HDRIgHcgU/dMrDb7kTEAOnNPVoOFf\nMI1/PjegApAz9eeyZYiM1AqN3syiRYtGjRqVIXSEfE1YPlFYQTEyMnLp0qXtHHBafbIRJ0+K\nt4QuIK9U26dO4a23THauu3ch+hON1xfqHI42TbEdJnYSiQSA0ri+bwcOHOjcubMxNa+Luiad\nOSPe8w5wPj8BAlgALMhP/dpvUC1fK+acBYLzUx9Av7wqnM5/m8ZYCLzJI0Aj31J9PjKizlGj\nz5L9xvEYc3htrR/eRC1V2qr+cSATEJZPlEqlvXr16tSpU2hoqJ+fn5eXV0ZGxoMHD86cObNq\n1aro6OiIiIj4+PhGjRpZOl4iHdSHowqrBqi+8MOEs83+/jsGDoSBKW7r1DHZuWyCHSZ2+dK8\nefNt27YZvmO3cOHC+Pj4SpUqqUq8vcX7hwATgAxACSgAqdadFaWuey1vwvgG9YVU4AaNpBTd\n4lIaEYBhQjtm7jYgvHUyI97D/IZnwd8HFbn6K1K9WO0Gdb58V2CIaqNYsQLETIaolk8cMWKE\nuFxYPlFYQXHcuHFRUVGTJ0/euXOnhcIkG3bjBk6cQHY2atXKWY3D5KpVE29p3mpR31twJ06g\nT5885jQZPtw057IVdpjYGXmvTiCTyTp16mS4zo4dO/B63QtB586585UAI4GRAIATQF1gCjA+\nP/EWqvVAb2AT0MUSZ68CeADngAnAd2/QTgjwEkjMu6IpjQd+BC4D/wAfABuBrnpqNgAevX7Q\nYBOuAEHAeGDK65JvgW+A04D2BX4h8CmwH2imr7n33y+UKB2ZkcsnRkVFcflEyq/79zFsGLZv\nz+1QFBqK5ctN+WBUEBGBMWOQnKxjV/XqaNjQNGeZMSOPrG70aHTvbppz2QoOniiIjh01btoR\nOShvb05oZ3pcPpEKycuXaNECMTFqE3UdPYqmTXHtmonP5eeHn3+GTKZZ7umJX3+F1ETZx19/\naRTkzh0lk2HHDsycaZoT2RAmdgUhleLECYfrj0mkwdkZJ0+a7AJNKlw+kQrJvHm6h4g+fYqJ\nE01/up49cegQwsNzrhJOTujeHcePIzTUZKd4+VKjIHeGYoUCrVqZ7EQ2xPYuyVYyBUDlykhJ\nQffuOr6OENk9mQzduyMlBaKup2QyXD6RCsnWreKtF+LRDBq38Uzl3XexZw/GjgWAPn2wYQOq\nVjVl+6oFfl7LfQ0lSzro/RcbS+wWLVpUtWrVSZMmxcfH37t3Lz09XS6XC1MAbNy4ceDAgdWq\nVTNbV2JXV2zYkLPSlFKZs5LJ1Km5S0tZ/L916wBgyxbLnL1y5ZxOGxMnvlE777yDoCBzBz9u\nHABcu4b16wFg82a9NUNDUbGiZd7hgv13+TIATJiQW/LNNwBw7pyOygsWAMCBA5rl2dnYsAGu\nrub5qDkcYflEf3//ffv2ffjhh9WqVfP09JTJZEWLFq1cuXLPnj1jYmI8PT1Xr15tzuUTyQ7c\nuyfe6g80UW28fIkXLwrrvMIdEIlph40BAP7zH727jJvxwg7Z0uAJTgFARA7CqpZPTEtDz57Y\nsUNjqrC8ffNNztcGIxn5h1+72vPn+UsaPvwQH36Yj/oAmjbNo4KnZ/4aNNK33+Lbbwt+uMG3\n5TnwXLytPcI9LCzvUxw4YOyb/8sv+OUXo2rqk69/5SVLsGTJG50OgFSK9u3x++/w8HjTpszG\nlhI7TgFARI7DSpZPvHwZNWvmMfCQyF4pFNi+Hd7euHABQUGWjsY4tvQo1sgpAABwCgAiojen\nUKBuXWZ15Oiys1G3br7vWFuKLSV2nAKAiMictm9HSkre1YjsXkoKtm+3dBDGsaVHsSEhIXFx\ncVFRUQZmAeAUAETkIPK1fGLB1sXetk28fw7wf0AG9NJYswTAZF2TTM8oOAAAIABJREFUk+tc\nK0UBKLX+JGnX1FkNwHPj/pyplj/um9fCgErRAsrCIc11hS2uYHh2U6X6isyGq6l+BvAd8H1e\nNXUS/h1lBlfNEb+ZGg0KZ38vr7WU5EC8njdf+7WsBFYZrGaA8HLy/FdOBWSvK/u/8apLrsAU\n4AthY9s22xiQYUuJXWRk5MGDB6dPn37y5MkBAwbUq1dPmPEkNTX1yZMnx44dW7NmTUxMDKcA\nICLSULB1sdWXDVgGpOXztPl9diV/g2pGHisowEO1PA/JVwAmPK9heeb9hsM25uxKo1+78TX1\nMeZwhdYPBZYGLFMldoU3ati0bCmxE6YAGDp06L59+/bt26ezjqen5+LFizkFABHZvXwtn1iw\ndbHr1MGmTaqtU8ANIB24CPQAvgAGC4G8vu0hxCN5fWNMIrqbJdG6f6M6RPm6U5C40JgGxTUf\nAi0BX+CgcQ0CUBhsUF+EGq9FfOyXwE7gzOtNw69Fu8F0oD5QFDhsdISGGzTwksXtNAceA3uA\nQ8D3QFNgvp4GPwSSgN2iY3U2KP7hOdAcGAR8+rrmSaAvMBboq+v3Ic8GxS9Z/OYEA62BmeoN\nLgXmAu2BqNeFi4CFQDQQpNXgeuAH4FcgRPSOuQIVX7eJOnVgE2wpsYOVTQFARGQrCrYu9uDB\n+PprvE4gnYBAAIDQ0bmkrsWFLcUHAOAEmHrF03wQHsXWeoPO6xUBmP0lCHP4BgJXAQCe+gNw\nA5zz/4+eAJQFXF5vCne9ShXCyyyqFVtJrfISAIAgXa8iAABQXl9gEgksPULdWDaW2MFqpgAg\nIrJ7pUrh888xb56l43AUPoDmClm2r7KlAzCNzz9HqVKWDsI4tjQqlojIcVjJ8olz5yIyslDW\nDCCyCRIJvv4ac+daOg6j2d4dOyIiu7do0aJRo0ZlZKgNQRWWTxRWUIyMjFy6dGm7du3MEMzk\nyZg8GX/+iblzceEC0tNx7RpKloS3NwBIJFAqc/8vkErh4gK5HBrzUwkVVDWFAbhSKVxdIZEg\nMxNyue4GFQrIZChSBDIZUlIgl+e0JpPBxwdyOY4cgbMzKleGQqGZhoobLFoUbm5ITobQ29BA\nTVWoLi6QyZCVpTmfn1ANgKsrZDLcvIlnz1C9utpsZzobFL8uAE+f4skTtZZdXFC6NDw8dLyH\nGg0KAWg0KFRzcwOAjIzcN0QITPhZeM+lUpw/j8xMBAUhNRX37sHbGyVLQqmEmxuk0px/EeGo\n27eRna35Dru6QqnMiVAIRogqLQ0PH8KYmcf8/ODrqyNC1asTNoUFDFUfCIUCDx7onYsnKAj+\n/rh5E3fvwscH/v455cnJePgQVapAJtP8BUtJwb17qFAhd6VEmQy1amHkSKOW37AqTOyIiKyL\ndS6fGBaW8xfuxAnUrYsvvsD48eY5c97u3UNAAHx8cOmSxWL44AP89hvOn4c0/0/Crl7Fxo2Y\nMQNyORYvRpcucHHJ+yiTCAjAvXvYvRu7d+OTTxAWpne2tgYN8OgRLl40tuXsbPzzD65dw4kT\nmDNHVSwT/R8AevbE/Pn5Djs9HT4+eve+/TY2bMDUqZgwAW3a5Cz5DeDbb/HNN9i6FbW0utgt\nXIhPP8XKlWjWLN/BWBs+iiUisi6q5RPXr1/fu3fvwMDAYsWKyWQyYfnEiIiILVu2jB07NjMz\nc/LkyZYOlkygShWMH4/y5eHvj549zZfVFSonJzRujL59NVKld4CfgJ6qbS+vgjR+7x7UR3hL\nRGNscfVqQdq0G0zsiIisC5dPJPMTnnIWxqpZjRpBlnuHzhn47PV4VQBo0qQgbQoPmkV+eD35\nDgB4eBSkTbvBxI6IyLpw+UQysw8+wOjRALBrF1q2xJEjpmy8RAl8/LHuXaGhaNu2IG2WLo1y\n5cQF44Bw1Ub9+gVp024wsSMisi7CoogG1k4El08kExEeaP7zT869OqUScXF47z3ExpryLLNm\noWdPzcJ69RAdXZAuiQAkkpxMVJubG4YPL0ibdoODJ4iIrAuXTyTzSEnB8+c6yrOyMGgQrl0z\n2TNNFxf89hs+/xxbt+LmTfj7o2VLdO4sfkSbbyNG4OJFLFmiVlikCFatQmDgG8Zr25jYERFZ\nFy6fSOaxa5feTnUPH2LfPhOved+4MRo3NllrUil+/hk9e2L1aiQkwM0NDRti2DBUqGCyU9go\nJnZERFaHyyeSGVy5It4SL3ELAJcvmzeaAmnRAi1aWDoIK8PEjojIGnH5RCNlZSEuDgDS0rBn\nD1q2fKMHfA7F2Vm8FQoAKK3aVk3VS7aFgyeIiMhWHT6MoCD07QsAL1+iTRvUqIHjxy0dlo2o\nW1e8JayE6qFnL9kMJnZERGSTLl1C27a4eVOt8PJlhIfj1i0LxWQ74uMxbZrevaGhaNDAjNGQ\n6TCxIyIim/Tdd3j5Ukf5s2eYOtXs0diUxYvRsiX27NG9t0oV/P57ASciIYvjvxsREdmk3bv1\n7tKXshCAq1cxcqTu8bBubpgxA6dOoWJFc0dlcsLs3YWxloaVY2JHRES2R6HA06caZbnDAR8/\nNm80NmXNGuhb1iQ9Hb17w9PTvAGZ2uHDaNUK334LAJs2oXNnnD1r6ZjMiIkdERHZHqkUWvO9\ntFH9VKKEeaOxKRcvGtqbkGCuOArHxo1o2hT79+fcq1MoEBODBg1w6JClIzMXJnZERGSTmjbV\nKPBW/dSmDUgf9c5z3oA7UEa1bdOTxTx7hqFDIZdrlr96hf79dZTbJSZ2RERkk1JT9e7SXpm0\nUD1+jPv3AeD8ebOet2Bq1xZveQP+QM6cdRIJatSwREwmEhOje5E0ANevO8pYaSZ2RERke5KS\nsHev3r0GxlWY1osXGDgQZcrg4EEACA5GSIi1T6T30UcoUkT3rqAg+PmZNxqTSkwUb2mupZGU\nZN5oLISJHRER2Z5Llww9WbtwwRwxZGejfXv88guys3MLT55Es2Y4c8YcARRMQAC+/hoSiY5d\nlSrh0SOzB2Q66mtp1AcAlFRt2/RTZuMxsSMiItuj/kfaH+gItNSzt7CsWYPDh3WUv3yJMWPM\nEUDB3LmDqCgolTp27d6NgAAMG2boMbc1e+cd8VYFAOK1NEqVMm80FsLEjoiIbE+1auLbM85A\nDNBRtV2rljli+OMPvbvi4pCSYo4YCiAqytBDyexsLFmC7t11Z35Wrm1bBAXp3hUWhtKlde+y\nM0zsiIjI9vj46B0h4eaG/v3NEcOdO+ItGSBT9eiSy3OGU1ghY2Zv3rkT27cXfiim5uKCzZt1\n3JkLDMS6dZYIyBKY2BERkU2aOxfBwZqFTk5YsgSVKpkjAG9v8dY4YJ24q776Xivy5Il4yx1w\n11ktJsYs0Zha7do4exaRkahTBwDKlcO0aThxAuXKWToyc2FiR0RENsnXF3//jSlTUKcOvLxQ\npgx69sSRI+jb10wBNGki3qoN9FBtVK2KkiW1DrAO/v7irRVANIDX63bkrt5x964ZYzIpPz9M\nnoxNmwCgb1+MGwcvL0vHZEZOeVchIiKySh4emDABEyZY5uyffooFCzRugOWYNMns0RitbVtc\nuqTaqvj6B39gLRCm2uHjY9aoyFR4x46IiKgg/P2xY4fmMz4nJ0RFoXdvC8VkhHHj9N1N7A2U\nV21oLexBtoF37IiIiAqofn0kJGDjRvz9N169QvXq6NnTTD38CqxUKezfjw8/xOnTeusEBZnv\niTaZFhM7IiJrl5mZOX369NWrV1+/ft3Ly6thw4aff/55G66Hah3c3fHRR/joI0vHkR+1auHk\nSRw+jOPHsXMn9u6FQpG7NzgYW7bAzc1y8dEbcPTETi6X79ixIz093UCdGzduAFCIf+uJiAqN\nRCIBoHw9jVhWVla7du3i4uKEzaSkpNjY2NjY2M8+++ynn36yWJRk4yQShIUhLAwjR+LaNWzZ\ngqtX4emJJk3QoYOjLNJglxw9sTtw4EDnzp2NqXn9+vXCDoaISNvs2bPj4uKKFCkyZ86ciIiI\nrKystWvXRkZGzp8/v0GDBn369LF0gGTzKle26qUy/r+9O4+Pqr73P/6eDAQyJqLsssgWkPKr\noViwVlEIJEDYbgIFEVtFg0pzr1AokcotcrG0UlLBq4/LfhWQ5ZZFEAmohAY0yiYXpGAdIGUp\nIA0JGCBhyfb7Y7iTSZiEIcx2zryeDx88+H7PSebjN5kv7znne87BbQn1YBcbG7thw4bqj9jN\nmTNn27ZtbYJ80QQAk1q8eLGkGTNmjB492tEzceLE8PDwcePGLVq0iGAHwFWoBzur1Tpo0KDq\n99m0aZOksDCuIAYQANnZ2ZKGDRvm2jl06NBx48Z9Xc3qdwAhibACAEHtnnvukXT33Xe7djZo\n0EDStWvXAlMTgGBFsAOAYFRUVOT4y9ChQyXt3r3bdevOnTsltWvXzv+FAQhmBDsACEY2m619\n+/YDBgy4du2axWKZ6LK4/dtvvx03bpykIUOGBK5AAMEo1NfYAUCwiYuLs9vtp06dOnr06NGj\nRx2dX331lXOHH/zgB5Jatmw5fvz4wJQIIFgR7AAguGzZskXSlStXjhw5ctiFc4eGDRv269fv\nD3/4g2P5HQA4EewAIBhFRETExMTExMTcvOncuXP+rweAIbDGDgAAwCQIdgAAACZBsAMAQ7JY\nLI6nygKAE8EOAADAJLh4AgAMqaysLNAlAAg6BDsAML+SkpJNmzZdvXq1mn2OHz8uqbS01E81\nAfABgh28r7hYf/mL8vN15YokcVgBCLjMzMzBgwd7suepU6d8XQzgZ3v2aMYMbd4sSf366ckn\n9eqratAg0GX5BsEOXrZjh37+c/397+U98+dr2DB17hy4mgADOnny5OLFizMzMw8fPnz+/Pmi\noiKbzdasWbOYmJiEhIThw4ffddddnn+32NjYDRs2VH/ELj09fcmSJSNHjrzj2oEgsnKlnnlG\nxcU3mqdO6c03tXq1PvtMrVoFtDLfINjBm+x29e2rS5cqdObm6uGHtWqV/uVfAlRWTeXkKCtL\nkj7/XI8+qqZNA12QHxUW6v33tWCBJE2frn/+Uz/7mazWQJcVMubOnTt+/Phr1665dl66dMlu\nt9vt9tWrV0+ZMmXhwoUJCQkefkOr1Tpo0KDq9zlz5sySJUtq165dw6KB4HP5sl54oTzVOZ08\nqRde0Kef3mjm5JT/aXRcFQtvmjatcqpzuH5dSUl67z2/F1RTjtPH3bvrv/5Lkt56S61aafJk\nhcjqo+xs/ehHGjNGX38tSVu3asQI9eyp/PxAVxYa0tPTU1JSioqKRowYsXz58iNHjly4cKG4\nuLigoCA7O3vdunVJSUmnT59OTEzcsWNHoIuFF+TkaPZsnTihs2eVlqbvvgt0QSZy6JAKCtxv\n2rJFx49r2TK1batp0yTpySfVpYv+8hd/Fuh9BDt40yefVLmprEwpKTpxwo/V3AHHG9v1Q971\n63rjDb36aqAq8p/iYiUl6ciRyv1ZWUpODkRBoSctLU3S7NmzV65cOXLkyOjo6Hvuucdqtdps\ntrZt2yYmJn7wwQevvPLK9evXX3/99UAXizu1dq3atdOECTp/Xpcu6ZVXFB2tZcsCXZbBXb6s\nLVskyeUZy25Mn65f/ELHjpX37N+vPn300Ue+Lc+nCHbwmpISnT/v2lFXquPavnpVK1bcxjcs\nLNTKlTp9Wrm5ev99Xb7slTJv7dgx7d3rftOsWTLTyvL8fM2erZUrJek3v9H69Sor08cf669/\ndb//2rUVVk/CR/bt2ydp1KhR1ewzceJESbt37/ZPSfCRffv01FOVJ7fCQo0apS++CFBNxvfe\ne2rZUikpkvSPf7hueUKKk8oX1i1d6ubLS0o0ZoyuX/dtkb5DsIPXWK26917XjlXSG5X2+eYb\nT7/btm1q104jRyonRxcu6Jln1KaNPv7YK5XewpYtVV7JW1ysjAx/1OALV64oLU0/+5kkzZ+v\noUP1wAOaMEF2uyRt3KikJA0YcIt/Tnbt8kepIS4sLEzS9Wr/YbFarZKKior8VBN8449/lNuf\nYUmJ3qg8fcIjK1YoOVnff+92Y6y0RYp0NCwW94Mv6cyZGwusjYhgB2/q29e19f+kx6R+Uk9n\nl4er7+12DRyos2crdObmKinpxqovn/rnP11bdVz+lAy7ujYvTz/9qV555cYA5uXpgw8q/Z9K\n0ubN2rTJteN+qY50n7NdWOjzUvHQQw9JmjlzZjX7zJo1y7knjOvzz6vcZNxgEUAlJUpN9fQe\nW61bu7bCXP6UVOH8rLEQ7Lzj0CG9+64kffyxPv00dO/cNnWqKt6BwSZtlno72z/8oUff5403\n3C93vXpVv/vdHVXoiYYNXVsDpY1S3yq2GkZKiqeZ+OBB19ZAKV96wNlu08a7dcGNKVOmWK3W\ntLS0+Pj4FStWHD58uKCgoLS09NKlS8eOHVu1atXgwYN///vfWyyWyZMnB7pY3JGKV5s1lBq6\nbgrZf0pq7OuvdeaMR3u2a6eKN3YcKE2Sfuxs387dhIILtzu5UyUlGjtWc+feeAdu367t2/Xo\no1q7NrTujuHQsaM+/lh9+7o/rhMZqaef9uj7VHNRUmZmDWvz3OOPu7ZqSwOcjbAw9erl8wK8\nLidHa9d6unNpqWrXdj1DUX60snlzde/u3dLgRs+ePdesWfPiiy9mZGRkVHHuPzIyct68eX36\n9PFzbfCuFi30t785W+ukMtdNFksgajIyd+dbwp3tunVlsahVKw0dqtRUZWXpP//TubGFNMP1\ni3/yE59W6kMcsbtTr72mOXMqf6768kslJobKrTEq6d5ddrtatKjcX6eOFi/Wffe5+5qbXLjg\n2oqSopyN77/34afY4mK9/roee6zKHVJSKh29N4aDB1VSUs32NlKk1MjZfuYZNzvVqqUFCxQe\n7mYTvC4xMfH48eOLFi166qmnOnToUL9+favVGhERcf/99/fr1+/NN988fvz40x5+TvKqzEyl\npUnSmjVatszAC8yDxJAhrq27nMu/JCUl+b0a46v4MImW0ifSWGd71CgVFupvf9P06apXT/36\nVXnn/OHDDXx2gmB3Ry5e1KxZ7jft2lVprVIIcXwGnTZNDz6oevXUooV+/nN99ZWGDvX0O1TM\nf2ukdGejSRMffop98UVNnaqLF91sCgtTSkqVP+4gV/EzRlPpx1JXl55npDypsbP9q19p5UpF\nR5fv0bWrtm5V//6+rhTlbDZbcnLyihUr7HZ7Xl5ecXFxYWHhiRMnNm/ePGHChAZ+fxzStWsa\nNky9eul//keS9u7VL36hLl0MvBQpGKSmqkMHN/2tW+vf/93v1Rhfly6VVsv0kcqv6YuLq7Cz\n1ap169SxY+Vv0qOHFi70VYV+wKnYO7Jzp6p5Qs/27Ro40I/VuLh4UfPmackSSZo6VX//u156\nSZGRt/oy74mM1Guv6bXXavjlAwdq9mxnq1GlTT6SlVXlLZSbNdPnn6ttW1+9tK898IAsFueR\nzkjpq5t2KT8Q98Mf3vhvxAgdO6bz59WsmaeHWmFiEydqzZrKnd98o0GDtG+feFxFzdSrp+3b\n9a//qvXrb3wAs1g0YIDmzFGjRrf6Ytykdm397nf65S/dbHrkETcHQdu00f/+r5Yv16ef6sIF\n3XefBg/WkCEKM/JRL4LdHal4QfXdkkW6x9mueD7Rf44eVXy8jh+/0fzrXzVxoubNU0aGYZ6L\n95vfaNUqnT5dub9x45qHxVuqZhXamTNunkhjIC1bKi7uxu06qxcRUeGjaps2Bj4fYT4Wi0VS\nWSBW1Oflad4895sOHdKHH964jQ5qoGlTrV2rs2e1f79KS9W5s5o3D3RNRjZmjC5d0pQpcn0g\nX3y8li93H9ciIjR6tEaP9luBPmfkUBoEmjVzbUVLh6UXnO2AvDlLSjRsWHmqczp6VE8+aZhr\nrBo31rZtlde6deumzEw3q/e8peJ9LB1vjfK7sxjlmRlVmT/fzS+kxaL69cv/3qOHvvhCjzzi\n59JgALt3V/fZ5ssv/ViKSTVtqn791L8/qc4LUlN1/LgWLtTkyfrjH7Vrlz79NISOgBrviN3J\nkycXL16cmZl5+PDh8+fPFxUV2Wy2Zs2axcTEJCQkDB8+/C4/XqP8k5+oSRPXy3CiXbcG5Dzs\n9u3av9/9pl27tHOnfvpT/xZUU9HRysrSgQPav19lZXrwQfn6jl0VT1U/JzWUWjrbUVE3fYGh\nOM44/Md/aM0anTun8HA9/rgmT1avXsrOVn6+WrWS31dtwTAq3pWjgVRLalLFViDwmjY11UG4\n22KwYDd37tzx48dfcz3AKl26dMlut9vt9tWrV0+ZMmXhwoUJCQn+qad2bc2eraefdnMk7Pnn\n1a2bf6qooKpnYTm3GiXYOcTEKCbGT6/12GM3ViVKktpLE5yNyMgqL54ykMaNNWeO5szR5cuy\n2crPSrRrF9CyYAT33+/aaiWdlRpUsRVAIBnpVGx6enpKSkpRUdGIESOWL19+5MiRCxcuFBcX\nFxQUZGdnr1u3Likp6fTp04mJiTt27PBbVU89pRUrKtyyrm5dTZpU5XoUX6t494FoqanUtoqt\nqODpp6u8lcmECYqI8GsxPhUZaeylwfC/bt0qpbfyVBcWxo05gCBipCN2aWlpkmbPnj127FjX\nfpvN1rZt27Zt2yYmJk6aNGnmzJmvv/765s2b/VbYiBEaMkQ7dujkSdWvr0cfrfTIVL9q3961\n1U36ruqtqMBmU3q6Bg2q/Jz75GQfXrEBeC4gl004WK2aO1eDB7u5IeL48Z4+UQaAHxgp2O3b\nt0/SqFGjqtln4sSJM2fO3L17t59q+j/h4erRw8+v6V5Cgho0UF6em01Nm6p3bzf9cOrUSQcP\nauVKbd+uS5fUurWGD+diAkCS+vfX5s361a/0zTc3eho00OTJGj8+oGUBqMhIwS4sLEzS9WrP\nJlqtVklFLo9DCjVRUVq4UMOGVf5gXbu2/vu/ZbMFqCzjiIjQ88/r+ecDXQcQfOLjdeiQ7Hb9\n4x+qV08/+hG3rwOCjpEW2jz00EOSZs6cWc0+s2bNcu4ZspKStG2bnnhCVqskWa3q1Uuff85j\nAwB4wQMPKC5O3bqR6oBgZKQjdlOmTNm+fXtaWtq+ffuee+65rl27Nm/ePCIioqCgIDc3d8+e\nPcuWLfvoo48sFsvkyZMDXWyAde+u7dt1+bJyctSkifx4BxgAABAwRgp2PXv2XLNmzYsvvpiR\nkZGRkeF2n8jIyHnz5vXp08fPtQWnyEi/PkYMAAAElpGCnaTExMQ+ffqsXLly69ate/fuzc3N\nzc/PDw8Pb9SoUadOneLj45999ln/PxsbAAAgGBgs2Emy2WzJycnJycmBLgQAACC4GOniCSCo\n2O1KTdW33+rsWY0bV+WT3ADA0JjrjIVgB9TEggV68EH96U+6eFFXr+rtt/XjH2vGjECXBQBe\nxVxnOCYMdhaLxWKxBLoKmNmXX+qXv1SluyWWlurVV7VhQ4BqAgBvY64zIhMGO8DX/vQnlZZW\nuQkAzIG5zohMGOzKysoC+ERFhII9e6rctHu3+O0DYA7MdUZkvKtivaukpGTTpk1Xr16tZp/j\nx49LKq3qYwtCz5Urrq3WUvmT2q5fV0mJaoX6GwuAGTDXGVGo/0wyMzMHDx7syZ6nTp3ydTEw\nijZtlJfnbK2UykP//fcz0wEwCeY6Iwr1H0tsbOyGDRuqP2KXnp6+ZMmSkSNH+q0qBLkRI/TV\nV85WmOuShiefDERBAOADzHVGFOrBzmq1Dho0qPp9zpw5s2TJkto87xr/59/+TWvWaOfOyv2d\nOinkH1MMwDyY64zIhBdPAL5Wp44yMjRuXPmjeOvW1ejRyspSvXoBrQwAvIe5zohC/YgdUDN3\n3aW33tLMmTp8WGVlio5WRESgawIAb2OuMxwjBbvbuu2w1+94Yrfb69ate3N/UVHR4sWLW7Vq\nFRYWLIc/S0tLjx49Gh0dTUnVoCRPlJaWnjhxYtSoUR4uRbDb7b4uCb7GXHcnKMkTwVmSaeY6\nIwW70aNHb9iwIScnx8+v6/gxJycn+/l1gSAxf/7829qfBakGxVyHEGeOuc5irHv5FhYWJiQk\nfPbZZ/4sOz8/f8mSJVcq3s/H6cCBAytWrOjevXurVq38VlL1Tpw4kZWVRUnVoyRPOEoaOXJk\nTEyMh18SERHx7LPP1mMBjgEx1905SvJE0JZkkrmuzGg2btwYVGWvWrVK0qpVqwJdSDlK8gQl\neSIIS0KgBOEvAyV5gpI8EYQl1ViwnN723COPPBLoEgAAAIKR8YJdgwYNygx1+hgAAMA/jBfs\nAAAA4BbBDgAAwCTMEOwsFstt3eIOAADAlMwQ7AAAACCCHQAAgGkQ7AAAAEyCYAcAAGASRnpW\nbFUCe1u7iIgI559BgpI8QUmeCMKSEChB+MtASZ6gJE8EYUk1ZrBnxQahkpKSrVu39u7d22q1\nBrqWGyjJE5TkiSAsCYEShL8MlOQJSvJEEJZUYwQ7AAAAk2CNHQAAgEkQ7AAAAEyCYAcAAGAS\nBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsA\nAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCXc1t27YtLi6ufv369957b2xsbHp6uu9e\n68qVK9OnT+/cufPdd98dERHRsWPH1NTUCxcu1KAkf5btf999993LL78cHR1dp06dxo0bJyUl\nff3115X2CdlReuGFFywWS1VbvTUsphy6EMdcF4SY66oR6nNdGWpk/fr1Vqu10mDOmTPHF69V\nUFDQtWvXm392HTt2vHDhwm2V5M+y/e/YsWMtWrSo9H8XFRWVnZ3t3CdkR6mgoKBx48ZVveW9\nNSymHLoQx1wXhJjrqsFcR7CrCefvTWpqak5OTn5+/ltvvRUWFlanTp0TJ054/eVmzJghqVGj\nRn/+85+///77/Pz8Dz/80PGuHjt2rOcl+bls/+vRo4ek7t2JaTJYAAAGbUlEQVS779+/v7Cw\ncNeuXZ07d5Y0cuRIxw6hOUp5eXmbNm2KjY11TD037+CtYTHf0IG5Ljgx17nFXOdAsKuJRYsW\nSYqLi3PtHDFihKRp06Z5/eW6dOkiafXq1a6dW7duldSsWTPPS/Jz2X6WlZUlqWXLlhcvXnR2\nHjp0SFKTJk0czdAcpUqfKW/ewVvDYr6hA3NdEGKuqwpznQNr7GrCMdE899xzrp2DBg2SlJmZ\n6fWXy87OlhQXF+fa2a1bN0l5eXmel+Tnsv1s48aNkl5++eWoqChnZ6dOncrKys6ePetohuYo\nOd/tVe3grWEx39CBuS4IMddVhbnuBv9nSRPo0KGDJLvd7tp55MgRuXys9LX169dL6ty5s+cl\nBUPZvvPYY49J2rt379tvv92hQ4fw8PDWrVunpqa6fqgN8VGq6i3vrWEx8dCFrGD4mTLXVcJc\nd0shPtcR7Gqifv36ki5fvuza6bhuq27dun4oIDMzs0GDBpKWLVvmeUkBL9unWrZsKemll16q\n9NGlU6dO58+fd+wT4qNU1WTnrWEx8dCFrID/TJnrbsZcd0shPtcR7GrCcS1MSUmJa2dxcbEk\nq9Xq05fOzc11XMhtsVimTp16WyUFsGw/iIyMlFSvXr0FCxacO3fu8uXLH374YcOGDSX9+te/\nduwT4qNU1WTnrWEx8dCFLOa6IMRcd0shPtcR7GoiIiJCkutx77KysoKCAklRUVE+etGSkpI5\nc+Y4Pii0b99+69att1tSQMr2m1q1aklaunSpa+d7770nKTo62tEM8VGqarLz1rCYeOhCFnNd\nEGKuu6UQn+u4eKImGjVqJCk3N9e107FqtVmzZr54xZycnNjY2JSUlLKysjfffPPgwYO9evW6\n3ZL8X7Y/OdYR9+/f37Vz8ODBkk6ePOloMkpueWtYQnDoTI+5Lggx19VYiMx1BLua6NSpk6Q9\ne/a4dh44cEBSTEyM11/u6tWr8fHxn3322YABA7799tsJEyaEh4fXoCQ/l+1nbdq0kVRUVOTa\n6WjabDZHk1Fyy1vDEoJDZ3rMdUGIua7GQmSuI9jVRHx8vKTly5e7di5dulRSv379vP5y7777\n7oEDB3r06LF+/XrHTRFrVpKfy/azxx9/XNKqVatcO9etWyfp4YcfdjQZJbe8NSwhOHSmx1w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"text/plain": [ "Plot with title \"Recovered Signal\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/optim_2_condat_fb/exo2.R\")" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We display the result." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We plot the relative error $(E_k-E^\\star)/(E_0-E^\\star)$ in log-scale with respect to $k$." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Over-relaxed Forward-Backward\n", "-----------------------------\n", "It is possible to introduce a relaxation parameter $\\rho$ with $0 < \\rho < 1$. The over-relaxed foward-backward algorithm initializes $x^{(0)} \\in \\RR^N$,\n", "and then iterates, for $k=1,2,\\ldots$\n", "$$ z^{(k)} = \\text{prox}_{\\ga g}\\pa{\n", " x^{(k-1)} - \\ga \\nabla f( x^{(k-1)} ) }.\n", "$$\n", "$$ x^{(k)} = z^{(k)} +\n", " \\rho \\pa{ z^{(k)} - x^{(k-1)} } $$\n", "\n", "\n", "Let us assume $\\gamma=1/\\beta$. Convergence of the iterates $x^{(k)}$ and $z^{(k)}$ to a solution is guaranteed\n", "for $ 0 < \\rho < 1/2 $. The weaker property of convergence of $ E(x^{(k)}) $\n", "to $E^\\star$ is proved, when $ 1/2\\leq \\rho <1 $." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "gamma = 1 / L" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__ \n", "\n", "Write the code of the over-relaxed forward-backward iteration." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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YkJDw8fPnz4kiVLamtr33333ebrfUvFAN2yPBn1pFlhniE91vP22l0r4sJq7a8/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\n3SpZq93VtZ5aURcuxs5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VBWsDK2MhosKS9ZXr58WfmyZbFl0cHy2PIV5StKykui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5LBDYyKhOQJ944okfffTRrFmz+vXrt/vu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\nPc2kHJwJn8JPRY18F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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/optim_2_condat_fb/exo3.R\")" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "As we see, in this example, over-relaxation does not bring any speedup, because $\\gamma$ is lower than without over-relaxation. There are other setting parameters or other problems, for which over-relaxation does bring a significant speedup. " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "FISTA-like Accelerated Forward-Backward Algorithm\n", "---------------------------\n", "We consider the FISTA algorithm introduced in:\n", "\n", "\n", "A. Beck and M. Teboulle,\n", "\"A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems\",\n", "_SIAM Journal on Imaging Sciences_, 2009.\n", "\n", "More precisely, we consider a slightly modified version of FISTA, whose convergence is proved, see\n", "A. Chambolle and C. Dossal, \"On the convergence of the iterates of \"FISTA\"\", preprint, 2015." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Given an initial estimate $x^{(0)}$ of the solution and a parameter $a>2$, the algorithm sets $\\gamma=1/\\beta$, sets $z^{(0)}=x^{(0)} \\in \\RR^N$,\n", "and iterates, for $k=1,2,\\ldots$\n", "$$ x^{(k)} = \\text{prox}_{\\ga g}\\pa{\n", " z^{(k-1)} - \\ga \\nabla f( z^{(k-1)} ) }.\n", "$$\n", "$$ \\alpha_k=(k-1)/(k+a) $$\n", "$$ z^{(k)} = x^{(k)} +\n", " \\alpha_k\n", " \\pa{ x^{(k)} - x^{(k-1)} } $$\n", "\n", "\n", "It is proved that the iterates $x^{(k)}$ converge to a solution $x^\\star$ of the problem. Moreover, \n", "the optimal convergence rate for this class of problems is reached,\n", "namely\n", "$$ E_k - E^\\star = O(1/k^2), $$\n", "whereas the convergence rate for the normal forward-backward is only\n", "$O(1/k)$.\n", "\n", "Note the difference between the over-relaxed forward-backward and the accelerated forward-backward: the later is based on an inertia mechanism, of different nature than over-relaxation." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 4__\n", "\n", "Write the code of the accelerated forward-backward iteration." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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nWJSHXhONsVAQAAgHVDsGONXC5Xq9UGg0HhE0BEqutn2a4IAAAArBuCHWuYzSfy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ze/z4cceOHZcVYfUuIaSyKrD0i4uLkySs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\nGb8Jn5WVZTp4//59ETFedYsnlJ+fv3jx4oYNG8bExNSvX3/Xrl1Tp04teNe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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/optim_2_condat_fb/exo4.R\")" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We can note that the accelerated forward-backward is not monotonic: the cost function E is not decreasing along with the iterations and some oscillations are present." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }