{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Performance of Sparse Recovery Using L1 Minimization\n", "====================================================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) 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", "$\\newcommand{\\Om}{\\Omega}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This tour explores theoritical garantees for the performance of recovery\n", "using $\\ell^1$ minimization." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: Method definition ndgrid(AbstractArray{T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:3 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:3.\n", "WARNING: Method definition ndgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:6 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:6.\n", "WARNING: Method definition ndgrid_fill(Any, Any, Any, Any) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:13 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:13.\n", "WARNING: Method definition ndgrid(AbstractArray{#T<:Any, 1}...) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:19 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:19.\n", "WARNING: Method definition meshgrid(AbstractArray{T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:33 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:33.\n", "WARNING: Method definition meshgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:36 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:36.\n", "WARNING: Method definition meshgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:44 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:44.\n" ] } ], "source": [ "using PyPlot\n", "using NtToolBox\n", "# using Autoreload\n", "# arequire(\"NtToolBox\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Sparse $\\ell^1$ Recovery\n", "--------------------------\n", "We consider the inverse problem of estimating an unknown signal $x_0 \\in\n", "\\RR^N$ from noisy measurements $y=\\Phi x_0 + w \\in \\RR^P$ where $\\Phi \\in \\RR^{P \\times N}$\n", "is a measurement matrix with $P \\leq N$, and $w$ is some noise.\n", "\n", "\n", "This tour is focused on recovery using $\\ell^1$ minimization\n", "$$ x^\\star \\in \\uargmin{x \\in \\RR^N} \\frac{1}{2}\\norm{y-\\Phi x}^2 + \\la \\normu{x}. $$\n", "\n", "\n", "Where there is no noise, we consider the problem $ \\Pp(y) $\n", "$$ x^\\star \\in \\uargmin{\\Phi x = y} \\normu{x}. $$\n", "\n", "\n", "We are not concerned here about the actual way to solve this convex\n", "problem (see the other numerical tours on sparse regularization) but\n", "rather on the theoritical analysis of wether $x^\\star$ is close to\n", "$x_0$.\n", "\n", "\n", "More precisely, we consider the following three key properties\n", "\n", "\n", "* *Noiseless identifiability*: $x_0$ is the unique solution of $\n", "\\Pp(y) $ for $y=\\Phi x_0$.\n", "* *Robustess to small noise*: one has $\\norm{x^\\star - x_0} =\n", "O(\\norm{w})$ for $y=\\Phi x_0+w$ if $\\norm{w}$ is smaller than\n", "an arbitrary small constant that depends on $x_0$ if $\\la$ is well chosen according to $\\norm{w}$.\n", "* *Robustess to bounded noise:* same as above, but $\\norm{w}$ can be\n", "arbitrary.\n", "\n", "\n", "\n", "\n", "Note that noise robustness implies identifiability, but the converse\n", "is not true in general.\n", "\n", "\n", "Coherence Criteria\n", "------------------\n", "The simplest criteria for identifiality are based on the coherence of the\n", "matrix $\\Phi$ and depends only on the sparsity $\\norm{x_0}_0$ of the\n", "original signal. This criteria is thus not very precise and gives very pessimistic\n", "bounds.\n", "\n", "\n", "The coherence of the matrix $\\Phi = ( \\phi_i )_{i=1}^N \\in \\RR^{P \\times\n", "N}$ with unit norm colum $\\norm{\\phi_i}=1$ is\n", "$$ \\mu(\\Phi) = \\umax{i \\neq j} \\abs{\\dotp{\\phi_i}{\\phi_j}}. $$\n", "\n", "\n", "\n", "Compute the correlation matrix (remove the diagonal of 1's)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#3) (generic function with 1 method)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "remove_diag = C -> C - diagm(diag(C))\n", "Correlation = Phi -> remove_diag(abs(Phi'*Phi))\n" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the coherence $\\mu(\\Phi)$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#5) (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mu = Phi -> maximum(Correlation(Phi))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The condition\n", "$$ \\normz{x_0} < \\frac{1}{2}\\pa{1 + \\frac{1}{\\mu(\\Phi)}} $$\n", "implies that $x_0$ is identifiable, and also implies to robustess to small and bounded noise.\n", "\n", "\n", "Equivalently, this condition can be written as $\\text{Coh}(\\normz{x_0})<1$\n", "where\n", "$$ \\text{Coh}(k) = \\frac{k \\mu(\\Phi)}{ 1 - (k-1)\\mu(\\Phi) } $$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#7) (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Coh = (Phi, k) -> (k*mu(Phi))/(1 - (k - 1)*mu(Phi))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Generate a matrix with random unit columns in $\\RR^P$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "250×1000 Array{Float64,2}:\n", " -0.00153558 -0.0873719 -0.0267141 … -0.00418114 0.0431689 \n", " 0.016081 0.0658395 0.0183717 -0.0977312 -0.173786 \n", " -0.0202818 0.10513 -0.0061723 0.0903024 0.0475056 \n", " 0.0174428 0.0767283 0.0283078 0.0351142 0.0178382 \n", " -0.0156658 -0.113847 0.0829878 -0.0569733 -0.082541 \n", " -0.159691 0.0178282 0.102784 … 0.0324298 0.0500197 \n", " 0.109889 -0.00281318 0.0497717 0.0133811 0.0990111 \n", " 0.158323 -0.00278128 0.0263971 -0.00234905 0.0866833 \n", " 0.000221441 0.00898388 0.0364112 -0.0818329 -0.0140391 \n", " -0.023077 -0.101275 -0.0164376 -0.0694768 0.056435 \n", " 0.0391143 0.0801067 -0.00795326 … 0.0105741 -0.0107431 \n", " 0.0457144 -0.00871715 -0.0343846 0.0428562 -0.0408472 \n", " 0.00232064 0.0631691 -0.0595921 -0.000329357 0.0098766 \n", " ⋮ ⋱ \n", " 0.0489705 -0.0196438 0.00785909 1.66286e-5 -0.0416976 \n", " 0.0460609 -0.0325308 -0.108784 -0.0299601 -0.0500156 \n", " 0.0730461 -0.0729764 -0.0382131 … 0.00106382 -0.0420094 \n", " 0.0996469 -0.0980691 -0.0351391 0.0462986 0.0486122 \n", " 0.0918515 0.106906 -0.0167351 -0.0218581 -0.101535 \n", " -0.0554057 0.00990167 0.0265645 -0.0473953 0.0306916 \n", " 0.0601045 -0.0544066 -0.0442649 -0.0428824 0.0270975 \n", " 0.0339008 0.0220354 0.0601455 … -0.0811251 -0.013028 \n", " 0.0160892 0.0403653 0.00898637 0.0820708 0.00224229\n", " -0.0368455 -0.040219 -0.0506181 0.0362769 -0.0364124 \n", " 0.0991768 0.0148596 0.067233 0.0141599 -0.0624272 \n", " 0.00481869 -0.0303919 -0.00353946 0.0225215 -0.056659 " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normalize = Phi -> Phi ./ repeat(sqrt(sum(Phi.^2, 1)), inner = [size(Phi)[1], 1]);\n", "\n", "\n", "PhiRand = (P, N) -> normalize(randn(P, N))\n", "Phi = PhiRand(250, 1000)\n", "# P = 250; N = 1000\n", "# Phi = randn(P, N)\n", "# repeat(sqrt(sum(Phi.^2, 1)), inner = [size(Phi)[1], 1])\n", "# sum(Phi.^2, 1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the coherence and the maximum possible sparsity to ensure\n", "recovery using the coherence bound." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coherence: 0.32\n", "Sparsity max: 2\n" ] } ], "source": [ "c = mu(Phi)\n", "println(@sprintf(\"Coherence: %.2f\", c))\n", "println(@sprintf(\"Sparsity max: %d\", floor(1/2*(1 + 1/c))))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Display how the average coherence of a random matrix\n", "decays with the redundancy $\\eta = P/N$ of\n", "the matrix $\\Phi$. Can you derive an empirical law between\n", "$P$ and the maximal sparsity?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA14AAAJhCAYAAABRg2E+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3Xl8VPW9//H3LMlMdpbsIeyLLJKwpmhd0CBWr63665XWtmKsdanaJba98Ostyu/2lttqFauot15FtO5VxNsq1cZdUQQSRPadkD2BZLLOJDPn90dgyBBCFpicTPJ6Ph7zSOd7zpl8oofIu5/z/X4thmEYAgAAAAAEjdXsAgAAAACgvyN4AQAAAECQEbwAAAAAIMgIXgAAAAAQZAQvAAAAAAgyghcAAAAABBnBCwAAAACCjOAFAAAAAEFG8AIAAACAICN4AQAAAECQEbwAAAAAIMjsZhcQCnw+n4qLixUTEyOLxWJ2OQAAAABMYhiGamtrlZqaKqu1630sglcXFBcXKz093ewyAAAAAPQRhYWFGjZsWJfPJ3h1QUxMjKTWf7ixsbEmVwMAAADALC6XS+np6f6M0FUEry44/nhhbGwswQsAAABAt6cgheTiGitWrNDIkSPldDqVlZWl9evXn/Z8t9utX//61xoxYoQcDodGjhypp556qpeqBQAAADDQhVzH66WXXlJubq4ef/xxZWVlafny5Zo/f7527typxMTEU15z3XXXqaysTE8++aTGjh2rkpIS+Xy+Xq4cAAAAwEBlMQzDMLuI7sjKytKsWbP0yCOPSGpdcTA9PV133XWXFi1a1O78tWvX6jvf+Y727dunIUOG9Oh7ulwuxcXFqaamhkcNAQAAgAGsp9kgpB419Hg82rhxo7Kzs/1jVqtV2dnZWrdu3SmveeONNzRz5kz94Q9/UFpamsaPH69f/OIXamxs7PD7uN1uuVyugBcAAAAA9FRIPWpYWVkpr9erpKSkgPGkpCTt2LHjlNfs27dPH3/8sZxOp1avXq3Kykr9+Mc/VlVVlVauXHnKa5YtW6alS5ee9foBAAAADEwh1fHqCZ/PJ4vFoueee06zZ8/WFVdcoQceeECrVq3qsOu1ePFi1dTU+F+FhYW9XPXpeX0h9XQoAAAAMOCFVPCKj4+XzWZTWVlZwHhZWZmSk5NPeU1KSorS0tIUFxfnH5s4caIMw9Dhw4dPeY3D4fAvHd/XlpDfWVqryx78QJsLq80uBQAAAEAXhVTwCg8P14wZM5SXl+cf8/l8ysvL05w5c055zfnnn6/i4mLV1dX5x3bt2iWr1dqtnab7gm3FLn37sU+1t6JeP1z1hQqPNJhdEgAAAIAuCKngJUm5ubl64okntGrVKm3fvl2333676uvrlZOTI6n1McEbbrjBf/7111+voUOHKicnR9u2bdOHH36oX/7yl7rpppsUERFh1o/RI2MSozQxtbX7Vlnn0cKV61Xd4DG5KgAAAACdCbngtWDBAt1///1asmSJMjMzVVBQoLVr1/oX3CgpKdGhQ4f850dHR+udd95RdXW1Zs6cqe9973u66qqr9Kc//cmsH6HHHHab/vyDGRqdECVJ2ldRr1ue3Sh3i9fkygAAAACcTsjt42WGvraPV+GRBl3z6CeqrGvtdn0zI1XLF2TKarWYXBkAAADQvw2IfbzQKn1IpJ5cOEvOsNZ/fW9sLtb9b+80uSoAAAAAHSF4haiM9EF6+LvTdbzJ9ej7e/X854dOfxEAAAAAUxC8Qti8SUm656rJ/ve/WfOV3ttZbmJFAAAAAE6F4BXiFp43Ujd/fZSk1o2V73huk74qqjG5KgAAAABtEbz6gf97xUR9Y0rrBtINHq9uevoLFVU3mlwVAAAAgOMIXv2A1WrRgwsyNX34IElSea1bOSvXq6ax2eTKAAAAAEgEr37DGWbT/yycpZFDIyVJu8rqdPtfNsrT4jO5MgAAAAAEr35kSFS4ns6ZrcGRYZKkT/dWadFrX4qt2gAAAABzEbz6mZHxUfqfhbPksLf+q31tU5GW/3O3yVUBAAAAAxvBqx+aMWKwli/IlOXYHl8P5e3WyxsKzS0KAAAAGMAIXv3UN85N0a+vmOh//39f26KPd1eaWBEAAAAwcBG8+rEffn2UFs4ZIUlq8Rm6/S8btaPUZXJVAAAAwMBD8OrHLBaLllw1WdkTkyRJte4W5az8QqU1TSZXBgAAAAwsBK9+zma16OHvTlPGsDhJUklNk3Ke/kK1TezxBQAAAPQWgtcAEBHeusdX+pAISdL2EpfueD5fzV72+AIAAAB6A8FrgEiIcWjljbMVF9G6x9eHuyr0m9e/Yo8vAAAAoBcQvAaQsYnR+vMPZijc1vqv/cUvCvXo+3tNrgoAAADo/wheA0zW6KG6/7oM//v7/rFTr+cXmVgRAAAA0P8RvAagb2ak6leXT/C//+VfN2vd3ioTKwIAAAD6N4LXAHX7RWP03dnDJUnNXkO3PrtBe8prTa4KAAAA6J8IXgOUxWLRf3xrsuZOSJAkuZpatPCpL1Reyx5fAAAAwNlG8BrA7DarHrl+uianxkqSiqob9cOnN6je3WJyZQAAAED/QvAa4KIcdj114yylxjklSVuKavSTF/LVwh5fAAAAwFlD8IKSYp1amTNbMQ67JClvR7mW/u829vgCAAAAzhKCFyRJE5Jj9N8/mKEwm0WS9OxnB/XER/tMrgoAAADoHwhe8DtvbLz+69qp/ve/e3OH/vZlsYkVAQAAAP0DwQsB/s+MYfp59nj/+9yXN2vDgSMmVgQAAACEPoIX2vnJpWP17RnDJEmeFp9ufmaD9lXUmVwVAAAAELoIXmjHYrFo2bXn6oJx8ZKk6oZm3bjyC1XWuU2uDAAAAAhNBC+cUpjNqke/N13nJMdIkg4dadDNqzao0eM1uTIAAAAg9BC80KEYZ5hW5sxSUqxDklRQWK2fvZQvr49l5gEAAIDuIHjhtFLiIvTUjbMUFW6TJP1ja5n+8+/bTa4KAAAACC0EL3RqcmqcHv3+DNmsrXt8PfXJfq38ZL/JVQEAAAChg+CFLrlofIJ+d80U//v/97dt+sfWUhMrAgAAAEIHwQtdtmDWcN05d6wkyTCkn7yQr/xDR02uCgAAAOj7CF7olrsvG6+rM1MlSe4Wn25etUEHq+pNrgoAAADo2whe6BaLxaLff3uqvjZ6iCSpqt6jnJVf6Gi9x+TKAAAAgL6L4IVuc9ht+u/vz9TYxGhJ0r7Ket3y7AY1NbPHFwAAAHAqBC/0SFxkmFbeOEvx0a17fH1x4KjufmWzfOzxBQAAALRD8EKPpQ+J1FM3zlREWOseX3//skS//8cOk6sCAAAA+h6CF87I1GGD9Mj103Rsiy/99wf79JfPDppbFAAAANDHELxwxi6dmKSl3zqxx9eSNV8pb3uZiRUBAAAAfQvBC2fFD742QrdeOFqS5DOkO5/P15bDNSZXBQAAAPQNBC+cNf92+Tm6cmqKJKmx2aubVn2hw0cbTK4KAAAAMB/BC2eN1WrRH/81QzNHDJYkVdS6lbPyC9U0NptcGQAAAGAughfOKmeYTU/cMFOj46MkSbvL63TrsxvkbmGPLwAAAAxcIRm8VqxYoZEjR8rpdCorK0vr16/v8Nz3339fFoul3au0tLQXKx5YBkeFa2XOLA2NCpckfbbviBa9ukWGwR5fAAAAGJhCLni99NJLys3N1T333KNNmzYpIyND8+fPV3l5+Wmv27lzp0pKSvyvxMTEXqp4YBoxNEpPLJwph731FludX6QH3tllclUAAACAOUIueD3wwAP60Y9+pJycHE2aNEmPP/64IiMj9dRTT532usTERCUnJ/tfVmvI/eghZ/rwwXroO9NkObbH18Pv7tHLXxSaWxQAAABggpBKHx6PRxs3blR2drZ/zGq1Kjs7W+vWrTvttZmZmUpJSdG8efP0ySefnPZct9stl8sV8ELPXD4lWb+5cpL//eLVW/TBrgoTKwIAAAB6X0gFr8rKSnm9XiUlJQWMJyUldThnKyUlRY8//rheffVVvfrqq0pPT9fFF1+sTZs2dfh9li1bpri4OP8rPT39rP4cA81NXx+lnPNHSpK8PkM//stGbSsmzAIAAGDgCKng1RMTJkzQrbfeqhkzZui8887TU089pfPOO08PPvhgh9csXrxYNTU1/ldhIY/Hnal/v3KS5k9uDcz1Hq9uevoLldQ0mlwVAAAA0DtCKnjFx8fLZrOprKwsYLysrEzJycld/pzZs2drz549HR53OByKjY0NeOHM2KwWLV8wTZnpgyRJpa4m5az8QrVN7PEFAACA/i+kgld4eLhmzJihvLw8/5jP51NeXp7mzJnT5c8pKChQSkpKMErEaUSE2/Q/C2dq+JBISdKO0lr9+LlNavb6TK4MAAAACK6QCl6SlJubqyeeeEKrVq3S9u3bdfvtt6u+vl45OTmSWh8TvOGGG/znL1++XGvWrNGePXv01Vdf6Wc/+5neffdd3XHHHWb9CANafLRDT+fM0qDIMEnSR7sr9X9fY48vAAAA9G92swvorgULFqiiokJLlixRaWmpMjMztXbtWv+CGyUlJTp06JD/fI/Ho7vvvltFRUWKjIzU1KlT9c9//lNz584160cY8EYnROuJG2bqe//zuTwtPr2y8bDSh0TqJ5eOM7s0AAAAICgsBq2GTrlcLsXFxammpob5XmfR374s1p3P5/vfP3Bdhq6dPszEigAAAIDT62k2CLlHDdF//MvUVC3+xjn+9//26pf6dE+liRUBAAAAwUHwgqluuXC0vv+14ZKkZq+hW/+yUbvKak2uCgAAADi7CF4wlcVi0b1XTdYl5yRKkmqbWpSz8guVu5pMrgwAAAA4ewheMJ3dZtXD352mc9PiJElF1Y26adUXqne3mFwZAAAAcHYQvNAnRDnsevLGmUobFCFJ+qrIpTuf36QW9vgCAABAP0DwQp+RGOPU0zmzFONs3eXgvZ0VWvLGVvb4AgAAQMgjeKFPGZcUo//+wQyF2SySpOc/P6THP9hnclUAAADAmSF4oc85b0y87vt2hv/979fu0Bubi02sCAAAADgzBC/0SVdPS9MvLhvvf/+Llzdr/f4jJlYEAAAA9BzBC33WHXPH6juz0iVJHq9PP3pmg/aU15lcFQAAANB9BC/0WRaLRf9x9RRdOD5BklTT2Kycp9erotZtcmUAAABA9xC80KeF2axacf00TUyJlSQVHmnUzc9sUKPHa3JlAAAAQNcRvNDnxTjDtPLGWUqJc0qSNhdW6ycv5svrY5l5AAAAhAaCF0JCcpxTT904S9GO1j2+3tlWpv/42zb2+AIAAEBIIHghZExMidVj358uu7V1j6+nPz2gJz/eb3JVAAAAQOcIXggpF4xL0O+uPdf//j/f3K63tpSYWBEAAADQOYIXQs51M9P1k0vHSZIMQ/rZSwXaePCoyVUBAAAAHSN4IST9PHucrp2eJklyt7Tu8XWgst7kqgAAAIBTI3ghJFksFv3XtVN13pihkqQj9R7duHK9jtR7TK4MAAAAaI/ghZAVbrfqse/P0PikaEnSgaoG/eiZDWpqZo8vAAAA9C0EL4S0uIgwrcyZrcQYhyRp48Gjyn25QD72+AIAAEAfQvBCyEsbFKGnbpylyHCbJOnNLaVa9tZ2k6sCAAAATiB4oV+YkhanFddPl+3YHl9PfLRfz6w7YGpNAAAAwHEEL/Qbc89J1H98a4r//b1vbNU/t5WZWBEAAADQiuCFfuX6rOG6/eIxkiSfId31Qr42F1abXBUAAAAGOoIX+p1fXjZBV2WkSpIam7364aovVHikweSqAAAAMJARvNDvWK0W3f+vUzV75BBJUmVd6x5fNQ3NJlcGAACAgYrghX7JYbfpzzfM0OiEKEnS3op63fLsBrlb2OMLAAAAvY/ghX5rUGS4VuXMVnx0uCTp8/1HdNfz+Sp3NZlcGQAAAAYaghf6tfQhkXpy4Sw5w1pv9be3lenC+97T797crqo6t8nVAQAAYKAgeKHfy0gfpEe/N92/wXJTs09//nCfLvzDe/rj2ztV08jcLwAAAASXxTAMw+wi+jqXy6W4uDjV1NQoNjbW7HLQQ5V1bj32/l49+9lBeVp8/vEYp123XDBaOV8fpWiH3cQKAQAA0Nf1NBsQvLqA4NW/lNY0acV7e/TiF4fU7D1x+w+ODNPtF4/RD742UhHHumMAAABAWwSvICJ49U+FRxr0yLt79NdNh+X1nfhjkBDj0B0Xj9F3s4bLYSeAAQAA4ASCVxARvPq3/ZX1euifu7Rmc7Ha/mlIjXPqrkvH6dszhinMxnRIAAAAELyCiuA1MOwqq9WD7+zSW1+VBowPHxKpn146TldPS5PNajGpOgAAAPQFBK8gIngNLF8V1ejBd3Ypb0d5wPiYhCj9LHu8rjw3RVYCGAAAwIBE8AoigtfAtOnQUT3w9i59vKcyYPyc5BjlzhuveZOSZLEQwAAAAAYSglcQEbwGts/2VemPb+/UFweOBoxPHRanuy+boAvHxRPAAAAABgiCVxARvGAYhj7aXak/vr1Tmw/XBBybOWKw7r5sguaMGWpSdQAAAOgtBK8gInjhOMMwlLe9XH98Z5e2l7gCjp0/dqhy503QjBGDTaoOAAAAwUbwCiKCF07m8xl666tSPfDOTu2tqA84NndCgu6+bIKmpMWZVB0AAACCheAVRAQvdMTrM7SmoEgP5e3WwaqGgGOXT07Wz+eN14TkGJOqAwAAwNlG8Aoighc60+z16dWNh/WnvN0qrmnyj1ss0jczUvXTS8dpdEK0iRUCAADgbCB4BRHBC13lbvHqxfWFeuS9PaqodfvHbVaLrp2Wpp9cOk7pQyJNrBAAAABnguAVRAQvdFejx6u/fHZQj32wV0fqPf7xMJtFC2al686545Qc5zSxQgAAAPRET7OBNYg1Bc2KFSs0cuRIOZ1OZWVlaf369V267pNPPpHdbldmZmaQK8RAFxFu048uHK0PfzVXv7hsvGKddklSs9fQXz47pAvve0//73+3BXTFAAAA0H+FXPB66aWXlJubq3vuuUebNm1SRkaG5s+fr/Ly8tNeV11drRtuuEGXXnppL1UKSNEOu+68ZJw++rdL9JNLxioq3CZJ8rT49NQn+3XhH97Tf721Q0fbdMUAAADQ/wT1UcPCwkKlp6ef1c/MysrSrFmz9Mgjj0iSfD6f0tPTddddd2nRokUdXved73xH48aNk81m0+uvv66CgoIuf08eNcTZcqTeo//+YK9WrTugpmaffzzaYdcPvz5KP7xglGKdYeYVCAAAgNPqk48ajhgxQvHx8br00kt1991369lnn9WWLVu0ceNGLVy4sNuf5/F4tHHjRmVnZ/vHrFarsrOztW7dug6vW7lypfbt26d77rmnS9/H7XbL5XIFvICzYUhUuBZfMVEf/mqubjxvpMJtrX8E69wteihvty74/Xt69P09qne3mFwpAAAAziZ7MD98//79ys/PV0FBgfLz8/Xyyy+ruLhYknrUOaqsrJTX61VSUlLAeFJSknbs2HHKa3bv3q1Fixbpo48+kt3etR932bJlWrp0abfrA7oqMcape785WbdcOFoPv7tHr2woVIvPUE1js/6wdqee/Gi/br94jL7/tRFyhtnMLhcAAABnKOgdr6uvvlr33nuv1qxZo8LCQn388ccaM2aMHnvssWB+a0mS1+vV9ddfr6VLl2r8+PFdvm7x4sWqqanxvwoLC4NYJQay1EERWnbtuXr37ov1f6YPk9XSOl5V79Fv/75dF933np5dd0CeFt9pPwcAAAB9mynLyb/11lv6zW9+ow0bNnTrOo/Ho8jISP31r3/V1Vdf7R9fuHChqqurtWbNmoDzq6urNXjwYNlsJzoGPp9PhmHIZrPp7bff1iWXXNLp92WOF3rLnvI6Lf/nLv3ty5KA8bRBEfrppeN07fQ02W0htyYOAABAv9En53h5PKdeqW3cuHHaunVrtz8vPDxcM2bMUF5enn/M5/MpLy9Pc+bMaXd+bGystmzZooKCAv/rtttu04QJE1RQUKCsrKxu1wAE09jEaD1y/XS99dMLNG/SiUdqi6ob9atXv9S8Bz/UmoIieX1svwcAABBKgjrHKzo6WpMmTdK0adOUmZmpadOmKTU1VQ8//HDAAhndkZubq4ULF2rmzJmaPXu2li9frvr6euXk5EhqfUywqKhIzzzzjKxWq6ZMmRJwfWJiopxOZ7txoC+ZmBKrJ26Yqc2F1XrgnV36YFeFJGl/Zb1++mKBHnl3j3Lnjdf8ycmyHn8+EQAAAH1WUIPXu+++q82bN2vz5s167rnntHjxYjU1NUmSLr/8ci1ZskTnnnuuzj33XJ1zzjld+swFCxaooqJCS5YsUWlpqTIzM7V27Vr/ghslJSU6dOhQ0H4moDdlpA/Sqptm64sDR3T/P3bq8/1HJEm7y+t0+3ObNDk1VndfNl5zJyTKYiGAAQAA9FW9OsfL5/Np586d/sf+joey8vJyeb3e3iqj25jjhb7AMAx9urdKf3x7pzYdqg44Nm34IN09b4LOHzuUAAYAABBEPc0GpiyucbKysrJ2S8T3JQQv9CWGYej9nRW6/+2d2locuMdc1qghuvuyCZo9aohJ1QEAAPRvIR28+jqCF/oiwzD0j61leuCdndpVVhdw7MLxCbp73nhlpA8yqToAAID+ieAVRAQv9GVen6G/fVms5f/crf2V9QHHsicmKXfeeE1K5b4FAAA4GwheQUTwQiho8fq0Or9ID+Xt1uGjjQHHrjw3RT+fN05jE2NMqg4AAKB/IHgFEcELocTT4tPLGwr1yLt7VOpq8o9bLdLVmWn6afY4jRgaZWKFAAAAoYvgFUQEL4Sipmavnv/8kB59f48q605sZm6zWnTdzGG685JxShsUYWKFAAAAoYfgFUQEL4SyBk+LVn16UI9/sFc1jc3+8XCbVd+dna475o5VYqzTxAoBAABCB8EriAhe6A9cTc166uP9evKj/ap1t/jHHXarFp43UrdeOFpDox0mVggAAND3EbyCiOCF/qS6waM/f7hPKz85oMbmExuXR4bbdNP5o/SjC0YrLjLMxAoBAAD6LoJXEBG80B9V1rn12Pt79exnB+Vp8fnHY5x23XLBaOV8fZSiHXYTKwQAAOh7CF5BRPBCf1Za06QV7+3Ri18cUrP3xK+DwZFhuu2iMbphzkhFhNtMrBAAAKDvIHgFEcELA0HhkQY9/O5uvbqpSF7fiV8L8dEO3X7xGF07LU2Do8JNrBAAAMB8BK8gInhhINlfWa+H/rlLazYXq+1vhzCbRXMnJOqaaWm6ZGKiHHa6YAAAYOAheAURwQsD0a6yWj34zi699VVpu2OxTruunJqqa6alaeaIwbJaLSZUCAAA0PsIXkFE8MJAtqPUpVc3HtaagmKV17rbHR82OEJXZ6bpmulpGpMQbUKFAAAAvYfgFUQEL0Dy+gx9sqdSr+cXae3WUjV4vO3OyRgWp6unpemqjFTFsycYAADohwheQUTwAgLVu1v09rZSrc4v1se7K+Q76beIzWrRReMTdPW0NF02KUnOMOaDAQCA/oHgFUQEL6Bj5a4mvbG5WKvzi7S12NXueLTDrm9MSdY109L0tdFDmQ8GAABCGsEriAheQNfsKqvV6vwirckvUnFNU7vjKXFOfTMzVddOG6YJyTEmVAgAAHBmCF5BRPACusfnM/TZ/iq9nl+kN7eUqs7d0u6cSSmxumZamr6VmarEWKcJVQIAAHQfwSuICF5AzzU1e/XOtjK9nl+kD3ZVqOWkCWFWi3T+2HhdMy1N8ycnK8phN6lSAACAzhG8gojgBZwdVXVu/e3LEr2WX6TNhdXtjkeE2XT5lGRdPS1N548ZKrvNakKVAAAAHSN4BRHBCzj79lbUaU1+kVYXFKnwSGO74wkxDn0zo3WT5smpsbJYWJQDAACYj+AVRAQvIHgMw9DGg0f1Wn6R/v5liWoam9udMz4pWldPS9PVmWlKHRRhQpUAAACtCF5BRPACeoe7xav3dlRodf5hvbujXM3ewF9PFouUNWqIrp02TN84N1kxzjCTKgUAAAMVwSuICF5A76tu8OjvW0q0elORNhw82u64w25V9qQkXTstTReOT1AY88EAAEAvIHgFEcELMNehqga9XlCk1flF2l9Z3+74kKhwXTU1RddMH6aMYXHMBwMAAEFD8AoighfQNxiGoc2Ha7R602H975clOlLvaXfO6PgoXT0tTddMS1P6kEgTqgQAAP0ZwSuICF5A39Ps9enDXRV6Lb9I72wrk6fF1+6cmSMG65rpafqXc1MVF8l8MAAAcOYIXkFE8AL6NldTs9ZuKdVr+Yf12b4j7Y6H26yae06Crpk2THPPSZDDbjOhSgAA0B8QvIKI4AWEjqLqRq0pKNLqTUXaXV7X7nhcRJiunJqia6elacaIwcwHAwAA3ULwCiKCFxB6DMPQ1mKXVucXaU1BsSrr3O3OSR8SoWsy03TN9GEaFR9lQpUAACDUELyCiOAFhLYWr0+f7K3S6k2H9Y+tZWps9rY7JzN9kK6ZlqZ/mZqiodEOE6oEAAChgOAVRAQvoP+od7foH1tLtTq/SJ/sqZTvpN+AdqtFF41P0DXT05Q9MUnOMOaDAQCAEwheQUTwAvqnMleT3igo1ur8Im0rcbU7HuOw6xvnJuuaacOUNWqIrFbmgwEAMNARvIKI4AX0fztLa/Va/mGtyS9Wqaup3fHUOKe+NS1N105L07ikGBMqBAAAfQHBK4gIXsDA4fUZ+nxflV7LL9Lar0pV525pd86UtFhdnZmmb2amKjHGaUKVAADALASvICJ4AQNTo8erd7aXafWmw/pwd6W8J00Is1qkr49L0LXT0nTZ5CRFhttNqhQAAPQWglcQEbwAVNa59b+bi/V6fpE2H65pdzwy3KbLJyfrmulpOm9MvGzMBwMAoF8ieAURwQtAW3vK6/R6fpFW5xepqLqx3fHEGIe+lZmqb2WmaVJKLItyAADQjxC8gojgBeBUfD5DGw4e1er8Iv39y2K5mtrPB4sKt2liSqwmp8ZqUmqsJqfGaVxStBx2lqkHACAUEbyCiOAFoDN/2oyOAAAgAElEQVRNzV69t6Ncq/OL9N7OcjV7O/7VardaNC4ppjWMtQllMc6wXqwYAAD0BMEriAheALrjaL1Hf9tSoo92VWhbiUuHj7Z/HPFURgyN9Aexyalxmpwaq8RYVk0EAKAvIXgFEcELwJmoaWjW1pIabSt2aWuxS9uKXdpTUddulcRTiY92HHtE8UQgGzEkknljAACYhOAVRAQvAGdbU7NXO0trtbXYpa3FNdpW4tL2Epeamn2dXtt23tjk1DhNSo1l3hgAAL2E4BVEBC8AvcHrM7S/ss7fFTseyo42NHd6bZjNorGJMf7O2KQU5o0BABAMAyp4rVixQvfdd59KS0uVkZGhhx9+WLNnzz7luR9//LH+7d/+TTt27FBDQ4NGjBihW2+9VT//+c+7/P0IXgDMYhiGSmqaAoLY1mLXKZexP5URQyPbLOLBvDEAAM5UT7OBPYg1BcVLL72k3NxcPf7448rKytLy5cs1f/587dy5U4mJie3Oj4qK0p133qmpU6cqKipKH3/8sW699VZFRUXplltuMeEnAICus1gsSh0UodRBEcqelOQfr27waFtJYGdsb0V9u3ljB6sadLCqQW9uKfWPxUc72ixvz7wxAAB6Q8h1vLKysjRr1iw98sgjkiSfz6f09HTdddddWrRoUZc+49prr1VUVJSeffbZUx53u91yu93+9y6XS+np6XS8APRpJ88b21rs0o7Sns8bG58Uo3C7tRcqBwAgdAyIjpfH49HGjRu1ePFi/5jValV2drbWrVvXpc/Iz8/Xp59+qt/+9rcdnrNs2TItXbr0jOsFgN7kDLMpI32QMtIH+cfazhs7MXes/byxeo9XGw4e1YaDR/1jJ88bm5wap4kpMcwbAwCgB0Kq41VcXKy0tDR9+umnmjNnjn/8V7/6lT744AN9/vnnHV47bNgwVVRUqKWlRffee69+85vfdHguHS8A/dnxeWNtg1hP5o0d74xNTmHeGABg4BgQHa8z8dFHH6murk6fffaZFi1apLFjx+q73/3uKc91OBxyOBy9XCEA9I6288bmnTxvrNilbSU9nzd2Yu4Y88YAAGgrpIJXfHy8bDabysrKAsbLysqUnJx82mtHjRolSTr33HNVVlame++9t8PgBQAD0aDIcJ03Nl7njY33j3V13lhlnVsf7KrQB7sq/GPRDrsmpsT4V1Rk3hgAYCALqeAVHh6uGTNmKC8vT1dffbWk1sU18vLydOedd3b5c3w+X8CjhACAU+vKvLHjgaz6pHljde4WfXHgqL44EDhvbFxiTMCKiswbAwAMBCEVvCQpNzdXCxcu1MyZMzV79mwtX75c9fX1ysnJkSQtXrxYRUVFeuaZZyS17vk1fPhwnXPOOZKkDz/8UPfff79+8pOfmPYzAEAos1lbF90Ymxijb2WmSQqcN3Y8iG07xbyxZq/Rugx+iUt/3XhivN28sdRYJcYwbwwA0H+EXPBasGCBKioqtGTJEpWWliozM1Nr165VUlLrPIWSkhIdOnTIf77P59PixYu1f/9+2e12jRkzRr///e916623mvUjAEC/09m8sa3+uWM12lNep5OmjZ1y3lhCjENTjoWxKWmtX4cNjpDFwrwxAEDoCalVDc3S05VLAADtNTV7taO0NmBFxa7uNxbrtGtyapwmp8ZqSlrr19EJ0bKxiAcAoJf0NBsQvLqA4AUAwdXi9Wl/ZX3AiopfFblU09jc6bXOMGvA5s9TUuM0PjlaDrutFyoHAAw0BK8gIngBQO8zDENF1Y36qsilbcc6Y18V16jM1fniSHarReOSTmz+PCUtThNTYhXtCLkn7AEAfQzBK4gIXgDQd1TUugMW8PiquEYHqxo6vc5ikUYNjfLvM3Z83tiQqPBeqBoA0F8QvIKI4AUAfZurqdm/iMfW4hptLXJpT0Vdu82fTyUlztlu3lhKnJNFPAAAp0TwCiKCFwCEnuObP391rDu2tahG20tr5WnpfBGPwZFhmpLWurT9lGOhbOTQKFlZxAMABjyCVxARvACgf2j2+rS3ok5bi1z+OWPbi12qdbd0em1UuM3/mOLxhTzGJUUrzGbthcoBAH0FwSuICF4A0H/5fIYKjzboq6JjqykWty7mUVnn6fTacJtVE5KPLeJx7DHFicmxighnRUUA6K8IXkFE8AKAgcUwDJXXuvVV0bHVFI99Lapu7PRaq0UakxDtnzM2KTVWk1PiFBcZ1guVAwCCjeAVRAQvAIAkVTd4AvYZ21pco32V9erKf0nTh0RockrgIh6Jsc7gFw0AOKsIXkFE8AIAdKTe3aIdpcdWVCxqnTe2q6xWzd7O//OaEOM4sddYapwmp8YpfUgEKyoCQB9G8AoighcAoDs8LT7tKqs9tsR967yx7SUuNXi8nV4b67S322tsdHyU7CziAQB9AsEriAheAIAz5fUZ2l9Zr63FNf6Nn7cWu1Td0Nzptc4wq85Jjg14THF8UoycYSziAQC9jeAVRAQvAEAwGIahourGY/PGWvca21rsUqmrqdNr7VaLxiZGB3TGJiTHKC6CRTwAIJgIXkFE8AIA9KbKOrd/EY+txxbxOFDV0KVr46PDNSo+6tgrWqPiozQ6IUrDh0TSIQOAs4DgFUQELwCA2VxNzdpefGLj523FLu0ur5PX17X/jFssUtqgiNYgFh+lkcfC2ej4aKUNjpDNyoIeANAVBK8gIngBAPqipmavdpbW+sPYvoo67a+sV5nL3a3PCbdZNXxopD+U+TtmCVFKiHawyiIAtNHTbGAPYk0AACCInGE2ZaQPUkb6oIDxOneLDlTWa3+b177Keu2rqFNtU0u7z/F4fdpTXqc95XXtjkU77G0eXWx9bHHUsY5ZrJP5ZADQVXS8uoCOFwCgPzAMQ0fqPf4gtr+yXvsrjn2tqpenxdetz4uPdpzokCVE+Ttmw4dGymFnPhmA/olHDYOI4AUA6O98PkPFNY0nOmQVJ7plh482qItTySRJVouUNjhCo+KjAx9djI9S6iDmkwEIbQSvICJ4AQAGMneLV4VHGgLC2PGOWUVtN+eT2a0aeWw+mT+YHeuWDY0KZz4ZgD6POV4AACAoHHabxibGaGxiTLtjtU3NOlDZoH2VdQFzyvZX1KvWfYr5ZC0+7Sqr066yOkllAcdinIHzyY6vujgyPlIxzCcDEOLoeHUBHS8AALrHMAxV1nmOBbG61g7ZsY7ZwaoGebzdm0+WEONot+ri6IQopQ9hPhmA3sWjhkFE8AIA4Ozx+gwVVzceC2N1AY8uFlU3qjt/M7FapGGDI9utujgqPkqpcRGyMp8MwFlG8AoighcAAL2jqdmrQwHzyU48wlhZ5+nWZznsVo0c2n7VxVHxURrCfDIAPcQcLwAAEPKcYTaNT4rR+KT288lcTc3+/ckCFvqoqFO9x9vufHeLTzvLarWzrLbdsVinXaMSWhf3SB8SqYQYh+KjwjU02qGh0eGKj3IoNsJOOANw1tDx6gI6XgAA9F2GYaiizn1iT7I2jy4erKpXs7dnf9WxWy0aGh2uoVHHwli0Q0PbhrOTjjnDmGsGDAR0vAAAwIBksViUGONUYoxTWaOHBhxr8fpUXN3UbtXFfRX1Kq45/XyyFp+hMpdbZa6uLZkf7bAfC2qt4axtMBsaHdhRGxwZzn5mwABD8AIAAP2W3WbV8KGRGj40UhdPCDzW1OzVwaoGHT7aoKp6j6rqPKqqc6uq3qPKOnfr+/rWry1d2EG6zt2iOneLDlY1dHquxSINiQxv11GLPxbSAsJbtENR4TYeewRCHMELAAAMSM4wmyYkx2hCcvv5ZG0ZhiFXY4sqj4Wwqjq3KuuPhbS6EyHt+PGaxuZOv7dhqDXs1Xsk1XV6vsNubX3UsU1H7fhctKFtwlpCjEODI8MVbrd29R8DgF5C8AIAADgNi8WiuMgwxUWGaUxC5+d7Wnw62tC+a1bZpqNWVedW5bHQ5m7pfE8zd4tPRdWNKqpu7FLNcRFhJwWz1s7aqTpqcRFhdNOAXkDwAgAAOIvC7VYlxTqVFOvs9FzDMNTg8fo7ZpW1gcGsqk1nrarerSP1HnXhqUfVNDarprFZ+yrqOz3XbrVoSJsgxiIiQHAQvAAAAExisVgU5bArymHX8KGRnZ7v9RmqbvAEzkPzz0sL7KhV1XlU627p9DNbfIbKa90qr+3aIiJR4TZ/KEuIdighxqHEGKcSYo7/79av8dEOHnkE2iB4AQAAhAib1XIs9DhOudfZyZqavQFBrPKkYFZ5UketK0vv13u8qj/SoENHOl9EZHBkWIfBLCHaocRYhxKineyZhgGB4AUAANBPOcNsShsUobRBEZ2eaxiGXE0t7eahBc5Tc/vDW3VD54uIHG1o1tGGZu0qO/0CIuF2q7971jacnRzY6KIhlBG8AAAA0LqISESY4iLCNLoLi4g0e32qqvOovLZJFcceVaw49jo+VlHnVrmr8wVEPN1YPGRQZNhJXTNnm+7ZicBGFw19DcELAAAA3RZmsyo5zqnkuNMvImIYhmrdLa2BzNUaxgLCWZtX6/L6p1fd0KzqrnTRbFZ/t+zUjzk6j81FC5fDzoIhCD6CFwAAAILGYrEo1hmmWGeYxiREn/bc4120k4OZv5tW1zrepS6at3tdtFN1zU4ObCy9jzNB8AIAAECfENhFi+vwPMMwVOduOenxxlN30o40eGR0smbI8S7a7vKuddHiAxYHOWleWqyTLhpOieAFAACAkGKxWBTjDFNMF7toR+o9xx5zbDrFI48nAltT89nrosVFtJmL1vYxxxiHkmKdSomLUHKsUxHhBLSBguAFAACAfivM1nZD6867aO0XCmnzmKOryb+qY2ddtOObWHfWRYuLCFPKsS5fSpxTybERAe+T4pyKcbBQSH9A8AIAAMCA17aLNrqTLlqL16eqek+7VRxPDmxd6aIdD2g7Sms7PCcq3HYsiEWcCGhxTiXHOv3jgyOZf9bXEbwAAACAbrAHdNE6ZhiG6j1elbsCl9cvczWppKZJpTVNKnE1qqzGLY+344BW7/Fqb0W99lbUd3hOuN16rGN2olOWEutUclxrBy0lzqmh0Q7ZrIQzsxC8AAAAgCCwWCyKdtgVnRB92i6aYRg6Uu9pE8aaVFrT6H9f6mpSSXWTGpu9HX6Gp8Wng1UNOljV0OE5dqtFSbEnd8vafo1QYoxDYTY2qQ4GghcAAABgIovFoqHRDg2NdmhK2qnnoRmGIVdTS2swq2k89vVEMDs+7mpq6fD7tPiMThcHsVik+GhHQPfseNesbWBzhrEoSHcRvAAAAIA+zmKxKC4iTHERYZqQHNPhefXuljZBrOnYY42BQe10G1Ubhvzz1L5UTYfnDY4MCwhkKcc7aW26Z9EOokZb/NMAAAAA+okoh11jEqJPu8x+U7NX5S53ayBrE9LaPuZYXus+7cqNRxuadbShWdtLXB2eE+OwtwtjJ7porV8H0qbUIRm8VqxYofvuu0+lpaXKyMjQww8/rNmzZ5/y3Ndee02PPfaYCgoK5Ha7NXnyZN17772aP39+L1cNAAAAmM8ZZtPwoZEaPjSyw3OavT5V1LpPCmYn5p0d76a1+DpOZ7XuFtWW1512SX1nmNW/p1lASIs9sYrj0KhwWfvBoiAhF7xeeukl5ebm6vHHH1dWVpaWL1+u+fPna+fOnUpMTGx3/ocffqh58+bpd7/7nQYNGqSVK1fqqquu0ueff65p06aZ8BMAAAAAfVuYzarUQRFKHRTR4Tk+n6Gqes+JeWdtV2usaVSZy63i6ka5WzpesbGp2af9lfXaX9nxio1hNosSY1oD2YJZ6frXmeln9LOZxWIYnW3/1rdkZWVp1qxZeuSRRyRJPp9P6enpuuuuu7Ro0aIufcbkyZO1YMECLVmy5JTH3W633G63/73L5VJ6erpqamoUGxt75j8EAAAAMAAYhqGaxuaATpm/c3asm1Za06Rad8eLgrS1+Bvn6NaLxgS56tNzuVyKi4vrdjYIqY6Xx+PRxo0btXjxYv+Y1WpVdna21q1b16XP8Pl8qq2t1ZAhQzo8Z9myZVq6dOkZ1wsAAAAMZBaLRYMiwzUoMlwTUzoOKbVNzf79zdqv1tga1o42NCs57vR7p/VlIRW8Kisr5fV6lZSUFDCelJSkHTt2dOkz7r//ftXV1em6667r8JzFixcrNzfX//54xwsAAADA2RfjDFOMM0xjEztesbHpNPuYhYKQCl5n6vnnn9fSpUu1Zs2aU84HO87hcMjhcPRiZQAAAABOJ9T3Dgup4BUfHy+bzaaysrKA8bKyMiUnJ5/22hdffFE333yzXnnlFWVnZwezTAAAAAAIYDW7gO4IDw/XjBkzlJeX5x/z+XzKy8vTnDlzOrzuhRdeUE5Ojl544QVdeeWVvVEqAAAAAPiFVMdLknJzc7Vw4ULNnDlTs2fP1vLly1VfX6+cnBxJrfOzioqK9Mwzz0hqfbxw4cKFeuihh5SVlaXS0lJJUkREhOLi4kz7OQAAAAAMHCEXvBYsWKCKigotWbJEpaWlyszM1Nq1a/0LbpSUlOjQoUP+8//85z+rpaVFd9xxh+644w7/+MKFC/X000/3dvkAAAAABqCQ28fLDD1dqx8AAABA/9LTbBBSc7wAAAAAIBQRvAAAAAAgyEJujpcZjj+N6XK5TK4EAAAAgJmOZ4LuztgieHVBbW2tJCk9Pd3kSgAAAAD0BbW1td1aJZ3FNbrA5/OpuLhYMTExslgsZpeDHnK5XEpPT1dhYSGLpCDouN/Q27jn0Ju439Db+tI9ZxiGamtrlZqaKqu16zO36Hh1gdVq1bBhw8wuA2dJbGys6X9gMXBwv6G3cc+hN3G/obf1lXuuJ/sBs7gGAAAAAAQZwQsAAAAAgsx277333mt2EUBvsdlsuvjii2W385Qtgo/7Db2New69ifsNvS3U7zkW1wAAAACAIONRQwAAAAAIMoIXAAAAAAQZwQsAAAAAgozgBQAAAABBRvBCv7JixQqNHDlSTqdTWVlZWr9+fYfnvvbaa5o3b54SEhIUGxurOXPm6B//+EcvVotQ1537ra1PPvlEdrtdmZmZQa4Q/U137zm3261f//rXGjFihBwOh0aOHKmnnnqql6pFqOvu/fbcc88pIyNDkZGRSklJ0U033aSqqqpeqhah7sMPP9RVV12l1NRUWSwWvf76651e8/7772v69OlyOBwaO3asnn766eAXegYIXug3XnrpJeXm5uqee+7Rpk2blJGRofnz56u8vPyU53/44YeaN2+e3nzzTW3cuFFz587VVVddpfz8/F6uHKGou/fbcdXV1brhhht06aWX9lKl6C96cs9dd911ysvL05NPPqmdO3fqhRde0IQJE3qxaoSq7t5vn3zyiW644Qb98Ic/1NatW/XKK69o/fr1+tGPftTLlSNU1dfXKyMjQytWrOjS+fv379eVV16puXPnqqCgQD/72c9088039+3/E90A+onZs2cbd9xxh/+91+s1UlNTjWXLlnX5MyZNmmQsXbo0GOWhn+np/bZgwQLj3//934177rnHyMjICHaZ6Ee6e8+99dZbRlxcnFFVVdVbJaIf6e79dt999xmjR48OGPvTn/5kpKWlBbVO9E+SjNWrV5/2nF/96lfG5MmTA8YWLFhgzJ8/P5ilnRE6XugXPB6PNm7cqOzsbP+Y1WpVdna21q1b16XP8Pl8qq2t1ZAhQ4JVJvqJnt5vK1eu1L59+3TPPff0RpnoR3pyz73xxhuaOXOm/vCHPygtLU3jx4/XL37xCzU2NvZW2QhRPbnf5syZo8LCQr355psyDENlZWV65ZVXdMUVV/RW2Rhg1q1bF3CPStL8+fO7/Pc+M4Tmts/ASSorK+X1epWUlBQwnpSUpB07dnTpM+6//37V1dXpuuuuC0aJ6Ed6cr/t3r1bixYt0kcffSS7nV+96J6e3HP79u3Txx9/LKfTqdWrV6uyslI//vGPVVVVpZUrV/ZG2QhRPbnfzj//fD333HNasGCBmpqa1NLSoquuuqrLj40B3VVaWnrKe9TlcqmxsVEREREmVdYxOl6ApOeff15Lly7Vyy+/rMTERLPLQT/j9Xp1/fXXa+nSpRo/frzZ5WCA8Pl8slgseu655zR79mxdccUVeuCBB7Rq1Sq6Xjjrtm3bpp/+9KdasmSJNm7cqLVr1+rAgQO67bbbzC4N6DP4v13RL8THx8tms6msrCxgvKysTMnJyae99sUXX9TNN9+sV155pV3LGjiV7t5vtbW12rBhg/Lz83XnnXdKav1LsWEYstvtevvtt3XJJZf0Su0ITT35HZeSkqK0tDTFxcX5xyZOnCjDMHT48GGNGzcuqDUjdPXkflu2bJnOO+88/fKXv5QkTZ06VVFRUbrgggv029/+VikpKUGvGwNLcnLyKe/R2NjYPtntkuh4oZ8IDw/XjBkzlJeX5x/z+XzKy8vTnDlzOrzuhRdeUE5Ojl544QVdeeWVvVEq+oHu3m+xsbHasmWLCgoK/K/bbrtNEyZMUEFBgbKysnqzfISgnvyOO//881VcXKy6ujr/2K5du2S1WjVs2LCg14zQ1ZP7raGhod1j1DabTZJkGEbwisWANWfOnIB7VJLeeeed0/69z3Tmru0BnD0vvvii4XA4jKefftrYtm2bccsttxiDBg0ySktLDcMwjEWLFhk/+MEP/Oc/99xzht1uN1asWGGUlJT4X9XV1Wb9CAgh3b3fTsaqhuiu7t5ztbW1xrBhw4xvf/vbxtatW40PPvjAGDdunHHzzTeb9SMghHT3flu5cqVht9uNRx991Ni7d6/x8ccfGzNnzjRmz55t1o+AEFNbW2vk5+cb+fn5hiTjgQceMPLz842DBw8ahtH+ntu3b58RGRlp/PKXvzS2b99urFixwrDZbMbatWvN+hE6RfBCv/Lwww8bw4cPN8LDw43Zs2cbn332mf/YwoULjYsuusj//qKLLjIktXstXLiw9wtHSOrO/XYyghd6orv33Pbt243s7GwjIiLCGDZsmJGbm2s0NDT0ctUIVd293/70pz8ZkyZNMiIiIoyUlBTje9/7nnH48OFerhqh6r333jvt38tOdc+99957RmZmphEeHm6MHj3aWLlyZa/X3R0Ww6D/CwAAAADBxBwvAAAAAAgyghcAAAAABBnBCwAAAACCjOAFAAAAAEFG8AIAAACAICN4AQAAAECQEbwAAAAAIMgIXgAAAAAQZAQvAAAAAAgyghcAAAAABBnBCwCALpgyZYp++9vf6rbbbtPgwYOVnJys5cuXm10WACBEWAzDMMwuAgCAvsztdis6OlqjRo3S0qVLNWvWLD322GN65JFHdOTIEUVFRZldIgCgjyN4AQDQiY0bN2rmzJl66623dPnll0uStmzZoqlTp6q8vFwJCQkmVwgA6Ot41BAAgE5s3rxZycnJmj9/vn+soqJC4eHhGjJkiImVAQBCBcELAIBOFBQUaObMmbJYLAFjU6ZMkc1mM7EyAECoIHgBANCJzZs3KzMzM2CsoKCg3RgAAB0heAEA0IlTBa/8/HyCFwCgywheAACcxoEDB1RTUxMQstxut3bs2KFp06aZWBkAIJTYzS4AAIC+bOTIkTp5AeCvvvpKXq9XGRkZJlUFAAg1dLwAAOim/Px8jR49WjExMWaXAgAIEQQvAAC6iYU1AADdxQbKAAAAABBkdLwAAAAAIMgIXgAAAAAQZAQvAAAAAAgyghcAAAAABBn7eHWBz+dTcXGxYmJiZLFYzC4HAAAAgEkMw1Btba1SU1NltXa9j0Xw6oLi4mKlp6ebXQYAAACAPqKwsFDDhg3r8vkEry44vkFmYWGhYmNjTa4GAAAAgFlcLpfS09P9GaGrCF5dcPzxwtjYWIIXAAAAgG5PQWJxDQAAAAAIMoIXAAAAAAQZwQsAAAAAgozgBQAAAABBRvACAAAAgCAjeAEAAADo8wzDMLuEM0LwAgAAANBnuVu8WvXpAV396KdqavaaXU6PsY8XAAAAgD6n2evTXzce1sN5u1Vc0yRJemH9IeWcP8rkynqG4AUAAACgz/D6DL2eX6SH8nbr0JGGgGN7K+pMqurMEbwAAAAAmM7nM/T3LSV68J+7tK+iPuDYpeck6ufzxmtKWpxJ1Z05ghcAAAAA0xiGobe3lenBd3ZpR2ltwLELxsXr5/PGa/rwwSZVd/YQvAAAAAD0OsMw9P6uCj34zi59ebgm4NjskUOUe9l4fW30UJOqO/sIXgAAAAB61ad7K/XHt3dp48GjAeMZ6YP0i8vG6+tj42WxWEyqLjgIXgAAAAB6xYYDR/THt3dp3b6qgPFJKbG6+7LxuuScxH4XuI4jeAEAAAAIqi8PV+uPb+/SB7sqAsbHJUYrd954zZ+cLKu1fwau4wheAAAAAIJie4lLD76zS29vKwsYHzk0Uj/LHq+rMlJl6+eB6ziCFwAAAICzak95nZb/c5f+9mVJwHjaoAj99NJxunZ6muw2q0nVmYPgBQAAAOCsOFhVr4fyduv1/CL5jBPjSbEO3XnJOC2Yma5w+8AKXMcRvAAAAACckaLqRj3y7m69suGwWtokrvjocN1+8Vh9L2u4nGE2Eys0H8ELAAAAQI+Uu5q04r09emF9oTxen398UGSYbr1wjBaeN0KR4UQOSepzfb4VK1Zo5MiRcjqdysrK0vr167t03SeffCK73a7MzMyA8aeffloWiyXg5XQ6g1E6AAAAMCBU1bn1n3/fpgv+8J5WrTvoD10xDrt+nj1eH/1qrm6/eAyhq40+9U/ipZdeUm5urh5//HFlZWVp+fLlmj9/vnbu3KnExMQOr6uurtYNN9ygSy+9VGVlZe2Ox8bGaufOnf73/XVvAAAAAOD/s3fvUU3faf7A30kg4X4N98QrCF6QS7iIitqpLVsvyLa1rp3zq8dW292t7XTYdkf66zjam9tqO3ZrHaf7G22dOY7WdlbtZT7qIRIAACAASURBVGw7jK0gVguKVVQEUYFAMOF+DZDk90cwU0qiBEIS4P06Z8+ZfL+ffHhyJuPy8Hy+zzOSmjt68H7eNew9eQMd3TrTdQ+xCGvnTcL69Cnw8xA7MELn5VSJ19tvv43169dj7dq1AIDdu3fj888/x549e7Bx40aL7/vXf/1XPProoxCJRDh8+PCA+wKBAKGhoSMWNxERERHRWNba1YM9+Tfw//Ir0NrVa7oucRHi/8yZiH9dNBVSL4kDI3R+TpN4dXd3o6ioCDk5OaZrQqEQixcvxqlTpyy+b+/evaioqMCf/vQnvPrqq2bXtLW1YeLEidDr9UhMTMTrr7+OmTNnWtxTq9VCq9WaXre0tAzhExERERERjV4GgwElNS34uKga/3tOiebOHtM9V5EAq1Mm4Ol7IhHiw8d4BsNpEi+NRgOdToeQkJB+10NCQnDlyhWz7ykrK8PGjRuRl5cHFxfzHyU6Ohp79uzB7Nmz0dzcjO3bt2Pu3LkoKSmBTCYz+56tW7diy5Ytw/tARERERESj0K2WLhwuVuKTIiVK61r73RMJBVipkGHDzyIh8/dwUISjk9MkXtbS6XR49NFHsWXLFkybNs3iurS0NKSlpZlez507F9OnT8fvf/97vPLKK2bfk5OTg+zsbNPrlpYWyOVy2wVPREREROREunp0+NvlOnxSVI1vr6r7zeACALGLEMtnh+OZn0ViktTTMUGOck6TeEmlUohEogHNMerq6sw+n9Xa2orCwkKcO3cOGzZsAADo9XoYDAa4uLjgq6++ws9+9rMB73N1dUVCQgLKy8stxiKRSCCR8IwqEREREY1dBoMB56qa8ElRNT49X4OWHz27dZtioj8eSpRh6eww+Lq7OiDKscNpEi+xWAyFQoHc3FxkZWUBMCZSubm5psTqx3x8fHDhwoV+13bt2oW///3v+PjjjzF58mSzP0en0+HChQtYsmSJ7T8EEREREZGTq23uxF/OKvHJ2WpUqNsH3A/3dcODiTI8mBiBKUFeDohwbHKaxAsAsrOzsWbNGiQlJSElJQU7duxAe3u7qcthTk4OlEol9u3bB6FQiFmzZvV7f3BwMNzc3Ppdf/nllzFnzhxERkaiqakJ27Ztw82bN7Fu3Tq7fjYiIiIiIkfp7NbhWEktPilS4uQ1DQw/OUro7irCA7NC8bBChjlTAiEUcvySrTlV4rVq1Sqo1Wps2rQJKpUK8fHxOHbsmKnhRm1tLSorK63as7GxEevXr4dKpYK/vz8UCgUKCgowY8aMkfgIREREREROwWAw4Mz1BnxythpfXFChTTvwKGHq5AA8rJDhgdgweEmcKjUYcwQGw0/zXfqplpYW+Pr6orm5GT4+Po4Oh4iIiIjIoqqGDnxythqfnK1GVUPngPsTAjzwUN9RQnkAOxNaa6i5AdNaIiIiIqJRrk3biy9+qMXHZ6tx5nrDgPteEhcsjQ3DQwoZkif5QyDgUUJ7Y+JFRERERDQK6fQGnLpWj0/OVuPYRRU6e3T97gsEwPxIKR5WyHD/jFC4i0UOipQAJl5ERERERKNKhboNn5ytxv+eVaKmuWvA/alBnnhIIcM/J0QgzNfdARGSOUy8iIiIiIicXHNnDz77oQafFFXjbGXTgPs+bi7IjA/HQ4kyxMv9eJTQCTHxIiIiIiJyQr06PfLKNfi4qBpfX6pDd6++332RUICF04LwUKIM904PhpsrjxI6MyZeREREREROortXj6Kbjfj7lTocLq6BulU7YE1MqDceVsiQGR+OYG83B0RJQ8HEi4iIiIjIgSrrO/Dt1Vv49qoGp65p0N6tG7AmwFOMFX1HCWeG+/Ao4SjExIuIiIiIyI7atb34rqIe315V48RVNW7Ud5hd5yoS4GcxwXgoUYZF0cEQuwjtHCnZEhMvIiIiIqIRZDAYcLm2FSfK1Pi2VI3Cmw3o0RnMrg30FGPBtCAsmCbFwmnBCPAU2zlaGilMvIiIiIiIbKyhvRt5ZWqcuKrBiTK12We1AMBFKEDiRH8snBaEhdOCMCPMB0IhjxGORUy8iIiIiIiGqVenx7mqJpzoOz74g7IZBvNFLcgD3LEgyphopU0NhLebq32DJYdg4kVERERENATKpk6cuGo8PnjymgatXb1m17m7ipA2NRALoqRYGB2MSYEebI4xDjHxIiIiIiIahK4eHb6rqMeJqxp8e/UWrqnbLa6NCfXGwmlBWDAtCEmT/CFx4Yyt8Y6JFxERERGRGQaDAWW32oxVratqnL7eMGCI8W1+Hq6YHyk1JVshPpyvRf0x8SIiIiIi6tPc0YP8co3xWa0yNWqbu8yuEwqAhAn+xme1ooMQG+ELEZti0B0w8SIiIiKicUunN+CH6ibTTK3iqiboLTTFCPN1M1W05k2VwteDTTFo8Jh4EREREdG4cqulC9/0JVr55Ro0dfSYXSdxESJlcoCp1XtksBebYtCQMfEiIiIiojFP26vD3y7dwsHCKuSVqS22eo8M9jIdH0ydHAA3VzbFINtg4kVEREREY9bl2hZ8VFiFw+eUaDRT2fJ2c8H8SCkW9B0hjPBzd0CUNB4w8SIiIiKiMaW5swdHz9fgo++rcEHZPOC+zN8dWfERWBQdhHi5H1xEQgdESeMNEy8iIiIiGvX0egO+q6jHwcIqHLuogvYnbd/FLkI8MCsUjyTJkTYlEEJ2ICQ7c7r0/r333sOkSZPg5uaG1NRUnDlzZlDvO3nyJFxcXBAfHz/g3qFDhxATEwM3NzfExsbiiy++sHXYREREROQAyqZOvPO3MizYdhyP/r/TOFJc0y/pio3wxSsrZuL7FxfjnX9JwLxIKZMucginqngdPHgQ2dnZ2L17N1JTU7Fjxw5kZGSgtLQUwcHBFt/X1NSExx57DPfeey/q6ur63SsoKMDq1auxdetWLFu2DPv370dWVhbOnj2LWbNmjfRHIiIiIiIb0/bq8FVJHT4qrEJ+uWZAoww/D1dkxUfgkSQ5ZoT7OCZIop8QGAyWerrYX2pqKpKTk7Fz504AgF6vh1wuxzPPPIONGzdafN+//Mu/ICoqCiKRCIcPH0ZxcbHp3qpVq9De3o7PPvvMdG3OnDmIj4/H7t27BxVXS0sLfH190dzcDB8f/o+XiIiIyBFKappxqLAah4uVA1rACwRAelQQViXJsXhGMCQu7EZII2OouYHTVLy6u7tRVFSEnJwc0zWhUIjFixfj1KlTFt+3d+9eVFRU4E9/+hNeffXVAfdPnTqF7OzsftcyMjJw+PBhi3tqtVpotVrT65aWFms+ChERERHZSHNHD46cV+KjwipcVA78nUwe4I5HFHI8pJAhnB0JyYk5TeKl0Wig0+kQEhLS73pISAiuXLli9j1lZWXYuHEj8vLy4OJi/qOoVCqze6pUKouxbN26FVu2bLHyExARERGRLej1BhRcq8dHhVU4VqJC908aZUhchFgSG4aVSTLMmcxGGTQ6OE3iZS2dTodHH30UW7ZswbRp02y6d05OTr8qWUtLC+RyuU1/BhERERH1V93YgY+LqnGosBrKps4B9+NkvliZJMfyuHD4urs6IEKioRtW4tXT0wOVSoWOjg4EBQUhICBgyHtJpVKIRKIBzTHq6uoQGho6YH1raysKCwtx7tw5bNiwAYDxmTCDwQAXFxd89dVX+NnPfobQ0NBB73mbRCKBRCIZ8mchIiIiosHp6tHhq0t1OGShUYa/hyv+OUGGR5JliAnls/Y0elmdeLW2tuJPf/oTDhw4gDNnzqC7uxsGgwECgQAymQz3338/nnzySSQnJ1u1r1gshkKhQG5uLrKysgAYE6nc3FxTYvVjPj4+uHDhQr9ru3btwt///nd8/PHHmDx5MgAgLS0Nubm5eO6550zrvv76a6SlpVn70YmIiIjIRi4qm3GosAqHi2vQ3Nm/UYZQACyYFoRHkuS4dzobZdDYYFXi9fbbb+O1117D1KlTsXz5crz44osIDw+Hu7s7GhoacPHiReTl5eH+++9Hamoq3n33XURFRQ16/+zsbKxZswZJSUlISUnBjh070N7ejrVr1wIwHgFUKpXYt28fhELhgHbwwcHBcHNz63f9F7/4BRYuXIi33noLS5cuxYEDB1BYWIj333/fmo9ORERERMPU1NGNI8U1+KiwCiU1AxtlTAjwwCNJMjykkCHMl40yaGyxKvH6/vvvceLECcycOdPs/ZSUFDz++OPYvXs39u7di7y8PKsSr1WrVkGtVmPTpk1QqVSIj4/HsWPHTM0xamtrUVlZaU3ImDt3Lvbv34+XXnoJL774IqKionD48GHO8CIiIiKyA73egJPXNDj4fRW+KqlDt65/oww3VyGWzArDyiQ5UicHsFEGjVlONcfLWXGOFxEREZF1qhqMjTI+LrLQKEPuh0eSZFgeFw4fNzbKoNHDIXO8bNlcg4iIiIhGt64eHb4sUeGjwiqcLK8fcD/AU4x/TojAI0lyRId6OyBCIsdxmuYaRERERDT6GAwGlNS04KPCKhw+p0RLV2+/+0IBsHBaEFYly/GzmBCIXYQOipTIsZyquQYRERERjQ6N7d04UqzEwcJqXK4d2ChjUqAHVibJ8VCiDKG+bg6IkMi5WPWM1+rVq/HSSy9ZbK5xm1arxd69eyEWi/H4448PO0hH4zNeRERERIBOb8CJMjU+LqzG15cGNspwdxVhSWwYHkmSIWVyAAQCNsqgsWeouQGbawwCEy8iIiIazyrUbfi4qBqfnK1GXYt2wP14uR9WJcuxbHYYvNkog8Y4uzfXqKqqglwuH+rbiYiIiMiJtWl78fkPNThUWI3Cm40D7ku9xMiKj8AjyXJMC2GjDKK7GXLiNXHiRAQEBCAuLg7x8fGm/+vu7sZ///d/48MPP7RlnEREREQ0wvR6A05fb8Choir89YIKnT26fvddhALcExOMlQoZ7okJhquIjTKIBmvIidf169dx7tw5FBcX49y5c/joo49QU1MDADyOR0RERDSKVDd24JMiJT4+W4WqhoEzt6JDvLEySYashAhIvSQOiJBo9BtWxWvixInIysoyXTt16hTWrFmDl19+2SbBEREREdHI+PHMrYJr9fjpU/8+bi5YER+BlUkyxEb4slEG0TDZvLnGX//6V/z6179GYWGhLbd1KDbXICIiorHAYDCguKoJh4qq8en5GrT+ZOaWQADMj5RiZZIc988IgZuryEGREjkvuzfX6O7uhlgsHnA9KioKJSUlQ92WiIiIiGzsVmsX/vesEoeKqlF+q23A/UmBHnhYIcODiTKE+7k7IEKisW/IiZeXlxdmzJiBhIQExMfHIyEhAeHh4Xj33XexePFiW8ZIRERERFbq7tXj71fqcKiwGt9cVUOn73/IyUMswtLYMKxMkiN5kj+PEhKNsCEfNczPz8f58+dx/vx5FBcX4+LFi+jq6gIA/NM//ROSkpIQGxuL2NhYxMTE2DRoe+NRQyIiIhotLtW04FBRFY4U16ChvXvA/ZRJAXg4SYalsWHwlAz5b/BE45bDByjr9XqUlpaiuLgYxcXFpqTs1q1b0Ol0d9/AiTHxIiIiImfW1NGNI8U1OFRUhYvKlgH3w3zd8FCiDA8rZJgk9XRAhERjh90Sr02bNmHFihVQKBSDWl9XV4eQkBBrfoTTYeJFREREzkanN+BEmRofF1bj60t16Nbp+90XuwiRMTMUKxUyzIuUQiTkUUIiW7Bbc43q6mo88MADEIvFWL58OTIzM3HvvfeabbQBYNQnXURERETOpELdho+LqvHJ2WrUtWgH3I+T+eLhJDkyZ4fD18PVARESkTlDOmqo1+tx8uRJfPrppzhy5Ahqa2tx3333YcWKFVi2bBkCAgJGIlaHYcWLiIiIHKlN24vPf6jBocJqFN5sHHBf6iVGVnwEVibJER3q7YAIicYPhz7jdfnyZVMSVlRUhJSUFGRmZmL16tWIiIgY7vYOx8SLiIiI7E2vN+D09QYcKqrCXy+o0NnT/5l5F6EA98QEY6VChntiguEqEjooUqLxxeHNNW5Tq9WmJCw9PR3PP/+8Lbd3CCZeREREZC/VjR34pEiJj89Woaqhc8D96BBvrEySISshAlIviQMiJBrf7D5A2ZKuri7k5+fjyJEjtt6aiIiIaEzq6tHhyxIVPiqsQsG1evz0z+I+bi5YER+BlUkyxEb4cuYW0Shk88SroaEBH374Ifbs2WPrrYmIiIjGDIPBgOKqJhwqqsan52vQ2tXb775AAMyPlGJlkhz3zwiBm6vIQZESkS1YnXgdPXr0jvcrKiqGHAwAvPfee9i2bRtUKhXi4uLw7rvvIiUlxeza/Px8/OpXv8KVK1fQ0dGBiRMn4qmnnsIvf/lL05oPPvgAa9eu7fc+iURiGvZMREREZE+3Wrvwv2eVOFRUjfJbbQPuTwr0wMMKGR5MlCHcz90BERLRSLA68crKyoJAIMCdHg0bavn74MGDyM7Oxu7du5GamoodO3YgIyMDpaWlCA4OHrDe09MTGzZswOzZs+Hp6Yn8/Hw89dRT8PT0xJNPPmla5+Pjg9LS0mHHR0RERDQU3b16/P3KLRwqrMI3V9XQ6fv/HuUhFmFpbBhWJsmRPMmfv6sQjUFWN9eIiIjArl27sGLFCrP3i4uLoVAooNPpzN6/k9TUVCQnJ2Pnzp0AjG3r5XI5nnnmGWzcuHFQezz44IPw9PTEH//4RwDGitdzzz2HpqYmq+O5jc01iIiIaCgu17bgUGE1Dhcr0dDePeB+yuQArFTIsCQ2DJ4Smz8BQkQjwG7NNRQKBYqKiiwmXnerhlnS3d2NoqIi5OTkmK4JhUIsXrwYp06dGtQe586dQ0FBAV599dV+19va2jBx4kTo9XokJibi9ddfx8yZMy3uo9VqodX+YyBhS0uLlZ+GiIiIxiNtrw5FNxuRV6bBN6VqXK4d+DtEmK8bHkqU4WGFDJOkng6IkogcwerE64UXXkB7e7vF+5GRkTh+/LjVgWg0Guh0OoSEhPS7HhISgitXrtzxvTKZDGq1Gr29vdi8eTPWrVtnuhcdHY09e/Zg9uzZaG5uxvbt2zF37lyUlJRAJpOZ3W/r1q3YsmWL1Z+BiIiIxheDwYBr6jacuKpBXpka31U0DJi3BQBiFyEyZoZipUKGeZFSiIQ8Skg03th8jtdQ1dTUICIiAgUFBUhLSzNd/8///E98++23OH36tMX3Xr9+HW1tbfjuu++wceNG7Ny5E6tXrza7tqenB9OnT8fq1avxyiuvmF1jruIll8t51JCIiIjQ0N6Nk+XGRCuvTIPaZssNu+LkfnhYIUPm7HD4erjaMUoiGilOM8drqKRSKUQiEerq6vpdr6urQ2ho6B3fO3nyZABAbGws6urqsHnzZouJl6urKxISElBeXm5xP4lEAomEAwmJiIjI2BjjbGWjKdG6oGweMGfrtmBvCdKjgrBgmhTzIqUccExEJk6TeInFYigUCuTm5iIrKwuAsblGbm4uNmzYMOh99Hp9v2rVT+l0Oly4cAFLliwZdsxEREQ09hgMBlRo2pF31ZhonaqoR0e3+aZhEhchUqcEYkGUFOlRQZgW4sWOhERkltMkXgCQnZ2NNWvWICkpCSkpKdixYwfa29tNc7hycnKgVCqxb98+AMaZXxMmTEBMTAwA4MSJE9i+fTueffZZ054vv/wy5syZg8jISDQ1NWHbtm24efNmv+fAiIiIaHxr6ujGyfJ6U1VL2dRpce30MB9TopU0yZ+DjYloUJwq8Vq1ahXUajU2bdoElUqF+Ph4HDt2zNRwo7a2FpWVlab1er0eOTk5uH79OlxcXDB16lS88cYbeOqpp0xrGhsbsX79eqhUKvj7+0OhUKCgoAAzZsyw++cjIiIi59Cj0+NcZRPyytQ4UabBD9VNFo8PSr0kxkSr7/hgsLebfYMlojHBJs01qqurER4eDqFQaIuYnA7neBEREY1uBoMBN+o7jInWVQ2+q6hHm7bX7FqxixCpkwOQ3lfVign15vFBIjJxaHONGTNmoLi4GFOmTLHFdkRERETD1tzRg4JrGpwoM3YgrG60fHwwJtTblGilTA7g8UEisjmbJF5O0pGeiIiIxrFenR7nq5vwbd9MrfNVTdBb+BUl0FNsSrTmR0kR4sPjg0Q0spzqGS8iIiIia1TWd+BEmRp5ZWoUlNej1dLxQZEQyZP9kR4VhPQoKaaH+kDIIcZEZEdDSrxudxW8rbe3F3/5y18QHBxsuvbYY48NLzIiIiKin2jp6sGpa//oPnizvsPi2mkhXqZEK3VyINzFPD5IRI4zpMRr7969/V739PTg448/hru7OwBAIBAw8SIiIqJh69Xp8YOyGXl9xwfPVTVBZ+H8YICnGPMjpaYjhKG+PD5IRM5jSInX8ePH+7329vbG/v372VyDiIiIhq2qoQN5fQ0xTpZr0NJl/vigq0iApIkBSJ8mxYKoIMwI4/FBInJefMaLiIiIHKq1qwffVTSYjg9e17RbXBsZ7IX0KGOilTI5AJ4S/ipDRKMD/7UiIiIiu9LpDbigbEbeVWOidbayEb0Wjg/6ebhiXqQUC6KkmB8VhAg/dztHS0RkGzZJvF588UUEBATYYisiIiIag5RNnaZEK79cg+bOHrPrXIQCJE70x4K+57RmRfhCxOODRDQGCAwcwnVXQ51OTURENF61a3vxXUU98so0OFGmRoXa8vHBKVJPU0OMOVMD4cXjg0TkxIaaG/BfNiIiIho2g8GAi8oWnChT48RVNc5WNqJHZ/5vuz5uLph/e3hxpBTyAA87R0tEZH9MvIiIiGjIrqhacLS4Bp/+UIOqhk6za0RCARIn+Jlmas2W+fH4IBGNO0y8iIiIyCqV9R349IcaHClW4mpdm9k1kwI9TInWnKmB8HFztXOURETOxeaJV1VVFX7zm99gz549tt6aiIiIHORWSxc++6EWR8/XoLiqacB9kVCAuVMDkTEzFAuigjAhkMcHiYh+zOaJV0NDAz788EMmXkRERKNcc0cP/nrRmGx9V1EPcx3fkyb6IzM+HEtiwyD1ktg/SCKiUcLqxOvo0aN3vF9RUTHkYIiIiMixOrp78bfLt3C0WIlvr6rNNsiYHuaDzLhwLI8Lg8yflS0iosGwOvHKysqCQCDAnbrQCwR8YJaIiGi06O7V48RVNY6er8HXl+rQ2aMbsGZSoAcy48KRGR+OyGBvB0RJRDS6WZ14hYWFYdeuXVixYoXZ+8XFxVAoFMMOjIiIiEaOTm/A6ev1OFpcg79eVJkdaBziI8Gy2eHIjAvHbJkv/7BKRDQMVideCoUCRUVFFhOvu1XDiIiIyDEMBgPOVzfjaHENPvuhBrdatQPW+Hm44oFZYciMC0fK5AC2fScishGrE68XXngB7e2Wp89HRkbi+PHjwwqKiIiIbKesrhVH+mZt3azvGHDfQyzCfTNCsCI+HPMjgyB2ETogSiKisU1gYHnqrlpaWuDr64vm5mb4+Pg4OhwiIqK7qmowzto6WlyDK6rWAffFIiEWRgchMy4c904PhoeYoz2JiAZjqLmB0/1J67333sOkSZPg5uaG1NRUnDlzxuLa/Px8zJs3D4GBgXB3d0dMTAx++9vfDlh36NAhxMTEwM3NDbGxsfjiiy9G8iMQERE5hLpViw9OXseDu04i/c3jePNYab+kSygA5kUG4s2HZuP7/7sY//NYEpbHhTPpIiKyA6v+pa2srMSECRMGvV6pVCIiImLQ6w8ePIjs7Gzs3r0bqamp2LFjBzIyMlBaWorg4OAB6z09PbFhwwbMnj0bnp6eyM/Px1NPPQVPT088+eSTAICCggKsXr0aW7duxbJly7B//35kZWXh7NmzmDVr1qBjIyIickbNnT34skSFo8U1KLimMTtrK2GCHzLjwrF0dhiCvd3sHyQREVl31DAkJARZWVlYt24dkpOTza5pbm7GRx99hHfeeQdPPvkknn322UEHk5qaiuTkZOzcuRMAoNfrIZfL8cwzz2Djxo2D2uPBBx+Ep6cn/vjHPwIAVq1ahfb2dnz22WemNXPmzEF8fDx27949qD151JCIiJxJZ7cOuVfqcLS4Bt+UqtGt0w9YExPqjeVxxo6E8gDO2iIispWh5gZWVbwuXbqE1157Dffddx/c3NygUCgQHh4ONzc3NDY24tKlSygpKUFiYiLefPNNLFmyZNB7d3d3o6ioCDk5OaZrQqEQixcvxqlTpwa1x7lz51BQUIBXX33VdO3UqVPIzs7uty4jIwOHDx+2uI9Wq4VW+49OTy0tLYP9GERERCOiR6dHfpkGR4qV+PpSHdq7B87akge4G2dtxUUgOpSztoiInIlViVdgYCDefvttvPbaa/j888+Rn5+PmzdvorOzE1KpFD//+c+RkZExpCN8Go0GOp0OISEh/a6HhITgypUrd3yvTCaDWq1Gb28vNm/ejHXr1pnuqVQqs3uqVCqL+23duhVbtmyx+jMQERHZkl5vwJkbDTh6vgZ/vVCLxo6Bs7aCvCVYNtvY/j1e7sdZW0RETmpIT9O6u7vj4YcfxsMPP2zreIYkLy8PbW1t+O6777Bx40ZERkZi9erVQ94vJyenX5WspaUFcrncFqESERHdkcFgwEVlC44UK/HZD7VQtXQNWOPj5oIHZoVhRXw4UqcEctYWEdEo4DRtjKRSKUQiEerq6vpdr6urQ2ho6B3fO3nyZABAbGws6urqsHnzZlPiFRoaavWeEokEEolkKB+DiIhoSMpvteHo+Rp8er4G1zUD52W6u4qweEYIMuPCsWCaFBIXkQOiJCKioRpS4tXZ2YmioiIEBARgxowZ/e51dXXho48+wmOPPWbVnmKxGAqFArm5ucjKygJgbK6Rm5uLDRs2DHofvV7f7/mstLQ05Obm4rnnnjNd+/rrr5GWlmZVfERERLambOrEp+eNs7Yu1Q58nthVJMCCqCBkxodj8fQQeEqc5u+lRERkJav/Ss88VwAAIABJREFUBb969Sruv/9+VFZWQiAQYP78+Thw4ADCwsIAGLsarl271urECwCys7OxZs0aJCUlISUlBTt27EB7ezvWrl0LwHgEUKlUYt++fQCMM78mTJiAmJgYAMCJEyewffv2fp0Uf/GLX2DhwoV46623sHTpUhw4cACFhYV4//33rY6PiIhouOrbtPjiQi2OFNeg8GbjgPsCATBnciAy48PxwKxQ+HmIHRAlERHZmtWJ169+9SvMmjULhYWFaGpqwnPPPYd58+bhm2++sWrGlzmrVq2CWq3Gpk2boFKpEB8fj2PHjpmaY9TW1qKystK0Xq/XIycnB9evX4eLiwumTp2KN954A0899ZRpzdy5c7F//3689NJLePHFFxEVFYXDhw9zhhcREdlNa1cPviypw9HzNThZroHOzLCtOLlx1tay2WEI8eGsLSKiscaqOV6AsSPg3/72N8TGxgIwPgT87//+7/jiiy9w/PhxeHp6Ijw8HDrdwDa3oxXneBERkbW6enQ4fuUWjhTX4O+lt9DdO3DWVlSwFzLjwrE8LhyTpJ4OiJKIiKxllzlegPH5LheXf7xNIBDgd7/7HTZs2ICFCxdi//791m5JREQ0JvTo9DhZrsHR8zX4qqQObdreAWsi/NyRGW8cbBwT6s3270RE44TViVdMTAy+//57TJ8+vd/1nTt3AgAyMzNtExkREdEooNcbUHizEUfPK/HFBRUa2rsHrJF6ibE0NgyZ8RFInMBZW0RE45HVideDDz6IAwcOmG2esXPnTuj1euzevdsmwRERETkjg8GAkpoWfNrX/r2meeCsLW83F/zTzFBkxocjbUogXERCB0RKRETOwurEq6OjAy+//LLF+7t27cKuXbuGFRQREZEzqlAbZ20dPV+DCvXAWVsSFyEWTw9BZnw4Fk4LgpsrZ20REZGR1YlXdXU1lixZArFYjOXLlyMzMxP33nsvxGK2uyUiorGntrlv1tb5GlxUDpy15SIUID1Kisz4cNw3IxRenLVFRERmWN3VEDC2cT958iQ+/fRTHDlyBLW1tbjvvvuwYsUKLFu2DAEBASMRq8OwqyER0fjS0N6NLy7U4uj5Gnx/owE//f+UAgGQPCkAK+LD8cCsMAR48o+PRETjxVBzgyElXj91+fJlUxJWVFSElJQUZGZmYvXq1YiIiBju9g7HxIuIaOxr0/biqxIVjp6vQX6ZBr1mZm3FRvgaZ23FhSHM190BURIRkaM5NPH6MbVajaNHj+Lo0aNIT0/H888/b8vtHYKJFxHR2NTVo8M3pWp8er4Gf7tcB62ZWVtTgzyRGReB5XFhmBLk5YAoiYjImThN4jUWMfEiIho7enV6FFyrx9HzNfjyogqtZmZthfu6YXnfrK0ZYT5s/05ERCZ2G6B8N1VVVfjNb36DPXv22HprIiKiIenq0eHM9Qb87XIdvrhQC03bwFlbgZ5iLIkNQ2Z8OBQT/CEUMtkiIiLbsXni1dDQgA8//JCJFxEROVRVQwe+Kb2F46VqnLpWj84e3YA1XhIXZPTN2po3lbO2iIho5FideB09evSO9ysqKoYcDBER0VDdrmp9U6rGN1dvmZ2zBQBiFyHujQlGZlw47okJ5qwtIiKyC6sTr6ysLAgEAtzp0TCehSciInu4XdX6plSNAgtVLQAI8pZg0bQgLIoOxoJpUni7udo5UiIiGu+sTrzCwsKwa9curFixwuz94uJiKBSKYQdGRET0U9ref1S1jpdarmqJhAIkTvDDouhgLJwWhBlhPnxmi4iIHMrqxEuhUKCoqMhi4nW3ahgREZE1rKlqLZwWhHuigzE/UgpfD1a1iIjIeVideL3wwgtobzf/F0YAiIyMxPHjx4cVFBERjV8/rmp9U3oL1yxUtYQCIHGCP+6JYVWLiIicH+d4DQLneBERjayqhg58c1WNb0tvoeBaPTq671zVWhQdhPTIIFa1iIjI7uwyx6uyshITJkwY9HqlUomIiAhrfgQREY0D2l4dvr/eiOOltwZV1VoUbWyMwaoWERGNVlYlXsnJycjKysK6deuQnJxsdk1zczM++ugjvPPOO3jyySfx7LPP2iRQIiIa3QZb1ZJ6SfoSLVa1iIho7LAq8bp06RJee+013HfffXBzc4NCoUB4eDjc3NzQ2NiIS5cuoaSkBImJiXjzzTexZMmSkYqbiIic3O2q1jelt/DNVTXKb7WZXceqFhERjQdDesars7MTn3/+OfLz83Hz5k10dnZCKpUiISEBGRkZmDVr1kjE6jB8xouIaHCqGztMTTHuVtUyPasVJYWfh9jOkRIREQ3NUHMDNtcYBCZeRETmWVPVSpjgj3tY1SIiolHOLs017OG9997Dtm3boFKpEBcXh3fffRcpKSlm1/7lL3/B7373OxQXF0Or1WLmzJnYvHkzMjIyTGs++OADrF27tt/7JBIJurq6RvRzEBGNVf+oaqlRcE3DqhYREdEg2CTxamxsxFdffQWlUgkACA8PR0ZGBvz9/a3a5+DBg8jOzsbu3buRmpqKHTt2ICMjA6WlpQgODh6w/sSJE7jvvvvw+uuvw8/PD3v37sXy5ctx+vRpJCQkmNb5+PigtLTU9Fog4F9ZiYgGS9urQ+GNRtMQ47K7VLUWTTNWtWaGs6pFRER027CPGv7hD3/AG2+8gaVLl5paxyuVShw7dgzPP/88nnjiiUHvlZqaiuTkZOzcuRMAoNfrIZfL8cwzz2Djxo2D2mPmzJlYtWoVNm3aBMBY8XruuefQ1NQ06Di0Wi20Wq3pdUtLC+RyOY8aEtG4MfiqlhgLpgXhnuhgVrWIiGhccNhRwzfffBNnz56Fl5dXv+uvvPIKEhMTB514dXd3o6ioCDk5OaZrQqEQixcvxqlTpwa1h16vR2trKwICAvpdb2trw8SJE6HX65GYmIjXX38dM2fOtLjP1q1bsWXLlkH9TCKisaC7V4/vbzQMqqoVL/fDPdHBrGoRERFZYdiJl0AgQFtb24DEq7W11aojfRqNBjqdDiEhIf2uh4SE4MqVK4PaY/v27Whra8MjjzxiuhYdHY09e/Zg9uzZaG5uxvbt2zF37lyUlJRAJpOZ3ScnJwfZ2dmm17crXkREY4myqdOUaBWUa9B+l6rWouhgLGBVi4iIaEiGnXht374dCxcuxKxZs0xHDaurq1FSUoK33npr2AEO1v79+7FlyxYcOXKk3/NgaWlpSEtLM72eO3cupk+fjt///vd45ZVXzO4lkUggkUhGPGYiInvq7tWj8EYDjg+yqrUoOhj3sKpFRERkE8NOvJYtW4YHHngAZ86cQU1NDQBjc42UlBSIRKJB7yOVSiESiVBXV9fvel1dHUJDQ+/43gMHDmDdunU4dOgQFi9efMe1rq6uSEhIQHl5+aBjIyIarQZb1Qr0FGNhX6v39Egp/D1Z1SIiIrIlm3Q1FIlE/apKt50+fRqpqamD2kMsFkOhUCA3NxdZWVkAjM9s5ebmYsOGDRbf9+c//xmPP/44Dhw4gKVLl9715+h0Oly4cAFLliwZVFxERKPJ7arWN1eNQ4yv1t29qrUoOgizwn1Z1SIiIhpBIzrHa+XKlaisrBz0+uzsbKxZswZJSUlISUnBjh070N7ebprDlZOTA6VSiX379gEwHi9cs2YN3nnnHaSmpkKlUgEA3N3d4evrCwB4+eWXMWfOHERGRqKpqQnbtm3DzZs3sW7dOht/WiIix6hp6sQ3pWocL71196rWtCAsjA7CgqggVrWIiIjsaNiJ148bWfyYwWBAQ0ODVXutWrUKarUamzZtgkqlQnx8PI4dO2ZquFFbW9svkXv//ffR29uLp59+Gk8//bTp+po1a/DBBx8AMM4YW79+PVQqFfz9/aFQKFBQUIAZM2ZY+UmJiJzDYKtagn4dCFnVIiIicqRhz/EKCAjAH//4xwFdDQ0GA1atWjXgma3RaKi9+omIbOV2Veub0ls4yaoWERGRwzhsjteiRYvg7e2NBQsWDLg3e/bs4W5PRDQudffqUXizAd/2DTEurWs1u+52VWvRNGNVKzaCVS0iIiJnNOyK13jAihcR2YM1VS3jXC1WtYiIiOzNYRUvIiIaGla1iIiIxo8hJ17Z2dlmrwsEAri5uSEyMhIrVqxAQEDAkIMjIhprapt/XNWqR5u21+y6gL5ntRZFByE9KggBrGoRERGNakM+anjPPffg3Llz6O3tRXR0NADg6tWrEIlEiImJQWlpKQQCAfLz80d9B0EeNSSioerR6VF4o9E0xPhOVa04mR8WRQfhnuhgVrWIiIiclN2PGj744IMICAjA3r17TT+wubkZ69atw/z587F+/Xo8+uij+OUvf4kvv/xyqD+GiGjUYVWLiIiIfmrIFS+5XI4vv/xyQDWrpKQE999/P5RKJc6ePYv7778fGo3GJsE6CiteRHQnpqrW1Vv4tlSNK6q7V7UW9VW1RKxqERERjSp2r3g1Njbi1q1bAxIvtVqNlpYWAICfnx+6u7uH+iOIiJxWbXMnvi1V4/ggqloLoqRYFB2MBdNY1SIiIhqvhpx4rVixAo8//jjeeustJCcnAwC+//57PP/888jKygIAnDlzBtOmTbNNpEREDmRNVWu2zA/3sKpFREREPzLko4ZtbW345S9/iX379qG31/iXXhcXF6xZswa//e1v4enpieLiYgBAfHy87SJ2AB41JBqfVM1dpqYYJ8s1aB1EVSs9SopAL4mdIyUiIiJ7GWpuMOwBym1tbaioqAAATJkyBV5eXsPZzikx8SIaH3p0ehTdbDQ1xrhbVWtRX2OM2TI/VrWIiIjGCYcNUPby8sLs2bOHuw0RkUOomrvw7dVbOH7lzlUtfw9XLJhmbPXOqhYRERFZa1iJV1NTE/7whz/g8uXLAIAZM2bgiSeegK+vr02CIyKytY7uXpyuaEBemQb55WpcrWszu45VLSIiIrKlIR81LCwsREZGBtzd3ZGSkgLA2Fyjs7MTX331FRITE20aqCPxqCHR6KXTG3BR2Yz8cg1OXFXjbGUjenTm/9m7XdVaFB2EBVFBrGoRERHRAHZ/xis9PR2RkZH4n//5H7i4GAtnvb29WLduHSoqKnDixImhbOuUmHgRjS5VDR2mitbJ8no0d/aYXSfsq2oZjxCyqkVERER3Z/fEy93dHefOnUNMTEy/65cuXUJSUhI6OjqGsq1TYuJF5NyaO3tw6pqmL9nS4Ga95X9/JgR4ID1KivQoKdKmSOHr4WrHSImIiGi0s3tzDR8fH1RWVg5IvKqqquDt7T3UbYmI7qpHp8e5yibkl6mRV67B+aom6C38CcnHzQXzIqWYHyVFemQQJgR62DdYIiIiIgwj8Vq1ahWeeOIJbN++HXPnzgUAnDx5Ei+88AJWr15tswCJiAwGA66p24wVrTINvquoR3u3zuxaV5EAiRP8kR4lxfyoIA4wJiIiIqcw5MRr+/btEAgEeOyxx9Db2wuDwQCxWIx/+7d/w3/913/ZMkYiGofq27TILzcmWvnlGtQ2d1lcGxXshflRUiyICkLK5AB4SoY9KYOIiIjIpoY9QLmjowPXrl0DAEydOhUeHmPvGA+f8SIaeV09Onx/owH5ZcZntS7VtlhcK/WSYH5kIOZHBWF+pBShvm52jJSIiIjGM7s845WdnT3otW+//bY1WxPROKPXG3BZ1WKqaJ253gBtr97sWomLECmTA/qaYgQhJtQbAgGPDxIREdHoYVXide7cuUGtG84vRO+99x62bdsGlUqFuLg4vPvuu6Y5YT/1l7/8Bb/73e9QXFwMrVaLmTNnYvPmzcjIyOi37tChQ/j1r3+NGzduICoqCm+88QaWLFky5BiJaGhqmztNz2mdLNegvr3b4tpZET6YHxmE9CgpFBP94eYqsmOkRERERLZlVeJ1/PjxkYoDAHDw4EFkZ2dj9+7dSE1NxY4dO5CRkYHS0lIEBwcPWH/ixAncd999eP311+Hn54e9e/di+fLlOH36NBISEgAABQUFWL16NbZu3Yply5Zh//79yMrKwtmzZzFr1qwR/TxE412bthenK+qRV6ZBXpka19TtFteG+7oZOw9GBWFepBQBnmI7RkpEREQ0sob9jJctpaamIjk5GTt37gQA6PV6yOVyPPPMM9i4ceOg9pg5cyZWrVqFTZs2ATB2X2xvb8dnn31mWjNnzhzEx8dj9+7dZvfQarXQarWm1y0tLZDL5XzGi+guenV6/KBsNh4fLNPgbGUjei30efeSuGDOlMC+7oNSTJF68vggEREROT27z/Gyte7ubhQVFSEnJ8d0TSgUYvHixTh16tSg9tDr9WhtbUVAQIDp2qlTpwY8m5aRkYHDhw9b3Gfr1q3YsmWLlZ+AaHy6Wd+OE2Ua5JepUXCtHq1dvWbXiYQCxMl8kR5lPD4YJ/eDq0ho52iJiIiIHMNpEi+NRgOdToeQkJB+10NCQnDlypVB7bF9+3a0tbXhkUceMV1TqVRm91SpVBb3ycnJ6Zes3a54ERHQ1NGNgmvG44P55WpUNXRaXDtZ6on5fcOL06YGwsfN1Y6REhERETkPp0m8hmv//v3YsmULjhw5YvZ5MGtIJBJIJBIbRUY0unX36lF0sxH55Wrkl2nwg7IZlg4o+3m4Yt5Uqen4oMx/7I2XICIiIhoKp0m8pFIpRCIR6urq+l2vq6tDaGjoHd974MABrFu3DocOHcLixYv73QsNDR3SnkTjlcFgQNmttr7ug2qcvt6Ajm6d2bVikRCKif59TTGkmBnuC5GQz2kRERER/ZTTJF5isRgKhQK5ubnIysoCYHxmKzc3Fxs2bLD4vj//+c94/PHHceDAASxdunTA/bS0NOTm5uK5554zXfv666+RlpZm+w9BNErdau3CyXLj4OKT5RrUtWgtro0O8TZVtFImB8BD7DT/jBARERE5Laf6jSk7Oxtr1qxBUlISUlJSsGPHDrS3t2Pt2rUAjM9eKZVK7Nu3D4DxeOGaNWvwzjvvIDU11fTclru7O3x9fQEAv/jFL7Bw4UK89dZbWLp0KQ4cOIDCwkK8//77jvmQRE6gs1uHMzcakF+mRl6ZBldUrRbXBnlLkN73nNb8SCmCfdzsGCkRERHR2OBUideqVaugVquxadMmqFQqxMfH49ixY6bmGLW1taisrDStf//999Hb24unn34aTz/9tOn6mjVr8MEHHwAA5s6di/379+Oll17Ciy++iKioKBw+fJgzvGhc0esNKKlpQV7fc1qFNxrRrdObXevuKkLqlADMjzTO1JoW4sU270RERETD5FRzvJzVUHv1EzmSsqnTVNE6Wa5BY0eP2XUCARAb4WtKtBIn+kHiIrJztERERESjw6if40VEw9Pa1YNT1+qRX24cXlyhabe4VubvbnxOKzIIc6cGwt9TbMdIiYiIiMYfJl5Eo1SvTo/z1U04cVWD/HINiquaoNObL2B7S1yQNjUQ6VHGqtbEQA8eHyQiIiKyIyZeRKOEwWDAdU078vu6D353rR6t2l6za12EAiRM8MP8yCDMj5IiTuYLF5HQzhETERER0W1MvIicWEN7N072HR3ML9dA2dRpce2UIE+k9z2nlTolAN5urnaMlIiIiIjuhIkXkRPR9upQdKMReX3J1sWaZlhqfxPgKca8SKmp1Xu4n7t9gyUiIiKiQWPiReRABoMBpXWtyLuqQV65Bmeu16Orx3ybd7GLEMmT/JEeFYT5kVLMCPOBUMjntIiIiIhGAyZeRHZW19JlOjqYX66BulVrce30MJ++7oNSpEwOgJsr27wTERERjUZMvIhGWEd3L05XNCCvTIP8cjWu1rVZXBviI8H8yCAsmCbF3KlSBHlL7BgpEREREY0UJl5ENqbTG3BR2Yz8cg1OXFXjbGUjenTmH9TyEIswZ0pg3/BiKSKDvdjmnYiIiGgMYuJFZANVDR2mitbJ8no0d/aYXScUALEyPyzoOz6YMMEfYhe2eSciIiIa65h4EQ1Bc2cPTl2rR16ZGvnlGtys77C4dkKAB+ZHGbsPzp0qha8H27wTERERjTdMvIgGoUenx7nKJuSXqZFXrsH5qiboLbR593Fzwby+Fu/pkUGYEOhh32CJiIiIyOkw8SIyw2Aw4Jq63ZholWnwXUU92rt1Zte6igRImOBvmqc1W+YHEdu8ExEREdGPMPEi6lPfpjW2eO9r9V7b3GVxbVSwl7GiFSVF6uRAeEr4PyUiIiIisoy/LdK41dWjw/c3GpBfpkFemQaXalssrpV6iY3HByOlSI8KQqivmx0jJSIiIqLRjokXjRt6vQGXVS2mitaZ6w3Q9urNrpW4CJEyOaBveHEQYkK9IeTxQSIiIiIaIiZeNKbVNnca27yXaXCyXIP69m6La2eG+2B+lBQLooKgmOgPN1eRHSMlIiIiorGMiReNKW3aXpyuqEdemQZ5ZWpcU7dbXBvu64b5UVLMjwrCvKmBCPSS2DFSIiIiIhpPmHjRqNar0+MHZbPx+GCZBmcrG9Froc+7p1iEtKmBSI8KwvwoKaZIPSEQ8PggEREREY08Jl406tysb//H8cFrGrR29ZpdJxIKECfzxfyoIKRHSREv94OrSGjnaImIiIiImHjRKNDU0Y2Ca8bjg/nlalQ1dFpcOynQo6/NexDSpgbCx83VjpESEREREZnndInXe++9h23btkGlUiEuLg7vvvsuUlJSzK6tra3Ff/zHf6CwsBDl5eV49tlnsWPHjn5rPvjgA6xdu7bfNYlEgq4uyzOayLG6e/U4W9nY1+ZdjQvKZlg4PQg/D1fMm2ocXDw/Ugp5gId9gyUiIiIiGgSnSrwOHjyI7Oxs7N69G6mpqdixYwcyMjJQWlqK4ODgAeu1Wi2CgoLw0ksv4be//a3FfX18fFBaWmp6zed6nIvBYEDZrba+44NqnL7egI5undm1riIBFBP9kd53fHBmuC9EbPNORERERE7OqRKvt99+G+vXrzdVqHbv3o3PP/8ce/bswcaNGwesnzRpEt555x0AwJ49eyzuKxAIEBoaOjJB05Dcau3CyXLj4OKT5RrUtWgtro0O8e7rPihF6uQAeIid6mtLRERERHRXTvMbbHd3N4qKipCTk2O6JhQKsXjxYpw6dWpYe7e1tWHixInQ6/VITEzE66+/jpkzZ1pcr9VqodX+IxFoaWkZ1s8noLNbhzM3GpBfpkZemQZXVK0W1wZ5SzA/Uto3vFiKYB83O0ZKRERERGR7TpN4aTQa6HQ6hISE9LseEhKCK1euDHnf6Oho7NmzB7Nnz0ZzczO2b9+OuXPnoqSkBDKZzOx7tm7dii1btgz5ZxKg1xtQUtOCvHI18ss0KLzRiG6d3uxaN1chUicHGhOtKCmiQ7x5HJSIiIiIxhSnSbxGSlpaGtLS0kyv586di+nTp+P3v/89XnnlFbPvycnJQXZ2tul1S0sL5HL5iMc62imbOk0VrYJr9Who7za7TiAAYiN8MT/SmGgpJvpD4iKyc7RERERERPbjNImXVCqFSCRCXV1dv+t1dXU2fT7L1dUVCQkJKC8vt7hGIpFAIpHY7GeOVa1dPTh1rR755caZWhWadotrI/zcTRWteVOl8PcU2zFSIiIiIiLHcprESywWQ6FQIDc3F1lZWQAAvV6P3NxcbNiwwWY/R6fT4cKFC1iyZInN9hwvenV6nK9uMg0vPlfVBJ2FPu/eEhekTb19fDAIkwI9eHyQiIiIiMYtp0m8ACA7Oxtr1qxBUlISUlJSsGPHDrS3t5u6HObk5ECpVGLfvn2m9xQXFwMwNtBQq9UoLi6GWCzGjBkzAAAvv/wy5syZg8jISDQ1NWHbtm24efMm1q1bZ/8POMoYDAZc17Qjv6/74HfX6tGq7TW7ViQUIEHuZxpeHCfzhYtIaOeIiYiIiIick1MlXqtWrYJarcamTZugUqkQHx+PY8eOmRpu1NbWorKyst97EhISTP+5qKgI+/fvx8SJE3Hjxg0AQGNjI9avXw+VSgV/f38oFAoUFBSYEjPqr6G9Gyf7jg7ml2ugbOq0uHZKkCfSI40VrTlTAuDt5mrHSImIiIiIRg+BwWAwf1aMTFpaWuDr64vm5mb4+Pg4Ohyb0vbqUHSjEXl9ydbFmmZY+kb4e7hi3u0271FBiPBzt2+wREREREQONtTcwKkqXjTyDAYDSutakXdVg7xyDc5cr0dXj/k272IXIZIn+WN+ZBDSo6SYEeYDoZDPaRERERERWYuJ1zhQ19JlOjqYX66BulVrcW1MqDfS+57TSp4UAHcx27wTEREREQ0XE68xqKO7F6crGozdB8vVuFrXZnFtiI/EVNGaFylFkDfb6BMRERER2RoTrzFApzfgorK5r/ugGkU3G9GjM/+glodYhNTJAUiPMiZbkcFebPNORERERDTCmHiNUlUNHaaKVsG1ejR19JhdJxQAsTK/vu6DUiRO8IfYhW3eiYiIiIjsiYnXKNLc0YNtX11BfpkGN+o7LK6TB7hjfmQQFkRJMXeqFL4ebPNORERERORITLxGEQ+JCIfP1aDtJ0OMfdxcMHeqtG94sRQTAz0dFCEREREREZnDxGsUcRUJMWdKIL4pvYXECf5987SkiI3whYuIxweJiIiIiJwVE69RZnPmDPh5xMNLwv/qiIiIiIhGC/72PsrI/D0cHQIREREREVmJ59OIiIiIiIhGGBMvIiIiIiKiEcbEi4iIiIiIaIQx8SIiIiIiIhphTLyIiIiIiIhGGBMvIiIiIiKiEcbEi4iIiIiIaIRxjtcgGAwGAEBLS4uDIyEiIiIiIke6nRPczhEGi4nXILS2tgIA5HK5gyMhIiIiIiJn0NraCl9f30GvFxisTdXGIb1ej5qaGnh7e0MgEDg6HLS0tEAul6Oqqgo+Pj6ODoecHL8vZC1+Z8ha/M6QtfidIWs503fGYDCgtbUV4eHhEAoH/+QWK16DIBQKIZPJHB3GAD4+Pg7/4tHowe8LWYvfGbLe+pA0AAAOi0lEQVQWvzNkLX5nyFrO8p2xptJ1G5trEBERERERjTAmXkRERERERCNMtHnz5s2ODoKsJxKJsGjRIri48LQo3R2/L2QtfmfIWvzOkLX4nSFrjfbvDJtrEBERERERjTAeNSQiIiIiIhphTLyIiIiIiIhGGBMvIiIiIiKiEcbEi4iIiIiIaIQx8RoFXnvtNcydOxceHh7w8/Mb1HsMBgM2bdqEsLAwuLu7Y/HixSgrKxvhSMlZNDQ04Oc//zl8fHzg5+eHJ554Am1tbXd8T1tbGzZs2ACZTAZ3d3fMmDEDu3fvtlPE5GhD+c4AwOXLl5GZmQlfX194enoiOTkZlZWVdoiYHG2o35nb/vX/t3fvQVGVbxzAv8tlWUMFlMu2kBfEiIvJRSHSSR0Z15IkuxljhI6X0dExxQGcymlyctIUI8lsKgZ0nMluaIyalxAKTYGBBQdQNLnMhC6WJhogLO77+6Pp/DpKpotnz4rfzwx/7LPvu/s9+szOeTzscfFiaDQaZGVlKZiSHMnd9ozFYkFGRgbGjBkDd3d3GAwGvPbaazh//rwdU5M9bd26FSNGjIBOp0NsbCzKyspuu764uBhRUVFwc3NDUFAQ8vLy7BPURhy87gPd3d146aWXsGTJkjve8/7772PLli345JNPUFpaCnd3dxiNRly/fl3BpOQo5syZg9raWhw+fBh79+7FTz/9hEWLFt12T2pqKg4cOICdO3fi1KlTWLlyJZYtW4aCggI7pSY12dIz586dw8SJE/HYY4+huLgYJ0+exJo1a6DT6eyUmtRkS8/8bffu3Thx4gQMBoPCKcmR3G3PdHR0oLKyEmvWrEFlZSXy8/NRX1+PmTNn2jE12cuXX36J1NRUvP3226isrMTYsWNhNBpx8eLFXtc3NjZixowZmDJlCqqqqrBixQosWLAABw8etHPyuyDovpGbmys8PDz+c53VahV6vV5s3LhRql25ckW4ubmJL774QsmI5ADq6uoEAFFeXi7Vvv/+e6HRaERLS8u/7gsLCxNr166V1aKiosSbb76pWFZyDLb2zOzZs8Wrr75qj4jkYGztGSGE+PXXX4W/v7+oqakRw4cPFx988IHScckB9KVn/qmsrEwAEM3NzUrEJBXFxMSIpUuXSo9v3LghDAaDeO+993pdn56eLsLCwmS12bNnC6PRqGjOvuAVr36osbERZrMZ8fHxUs3DwwOxsbE4fvy4isnIHo4fPw5PT0+MGzdOqsXHx8PJyQmlpaX/uu/JJ59EQUEBWlpaIIRAUVERzpw5g2nTptkjNqnIlp6xWq3Yt28fHn30URiNRvj6+iI2NhZ79uyxV2xSka2fM1arFcnJyUhLS0NYWJg9opKDsLVnbtbW1gaNRnPHX72g+0N3dzcqKipk565OTk6Ij4//13PX48ePy9YDgNFodOhzXQ5e/ZDZbAYA+Pn5yep+fn7Sc9R/mc1m+Pr6ymouLi4YMmTIbf/+s7OzERoaioCAAGi1WkyfPh1bt27FU089pXRkUpktPXPx4kX8+eefWL9+PaZPn45Dhw5h1qxZeP755/Hjjz/aIzapyNbPmQ0bNsDFxQXLly9XOiI5GFt75p+uX7+OjIwMJCUlYfDgwUrEJJX8/vvvuHHjxl2du5rN5l7XX716FZ2dnYpl7QsOXipZvXo1NBrNbX9Onz6tdkxyIEr3THZ2Nk6cOIGCggJUVFQgMzMTS5cuxQ8//HAPj4LsScmesVqtAIDExESsXLkSERERWL16NRISEnhTlvuYkj1TUVGBDz/8EHl5edBoNPc4OanFXuczFosFL7/8MoQQ2LZt2z1ITmR/LmoHeFCtWrUKc+fOve2awMBAm15br9cDAFpbW/Hwww9L9dbWVkRERNj0mqS+O+0ZvV5/yxdRe3p6cPnyZak3btbZ2Yk33ngD+fn5SEhIAAA8/vjjqKqqwqZNm265lE/3ByV7xtvbGy4uLggNDZXVQ0JCcPTo0T7lJvUo2TMlJSW4ePEihg0bJtVu3LiBVatWISsrC01NTX2NTypQsmf+9vfQ1dzcjCNHjvBqVz/k7e0NZ2dntLa2yuqtra3/2h96vb7X9YMHD8aAAQMUy9oXHLxU4uPjAx8fH0Vee+TIkdDr9SgsLJQGratXr6K0tPSu7oxIjuVOeyYuLg5XrlxBRUUFoqOjAQBHjhyB1WpFbGxsr3ssFgssFgtcXOQfCc7OztKVDbr/KNkzWq0W48ePR319vax+5swZDB8+vO/hSRVK9kxycnKv38dITk7GvHnz+h6eVKFkzwD/H7rOnj2LoqIiDB069J5lJ8eh1WoRHR2NwsJCPPfccwD++s2KwsJCLFu2rNc9cXFx2L9/v6x2+PBhxMXFKZ7XZmrf3YP+W3NzszCZTOKdd94RAwcOFCaTSZhMJnHt2jVpTXBwsMjPz5cer1+/Xnh6eorvvvtOnDx5UiQmJoqRI0eKzs5ONQ6B7Gz69OkiMjJSlJaWiqNHj4rRo0eLpKQk2Zqbe2bSpEkiLCxMFBUViYaGBpGbmyt0Op34+OOP7R2fVGBLz+Tn5wtXV1fx6aefirNnz4rs7Gzh7OwsSkpK7B2fVGBLz9yMdzV8sNxtz3R3d4uZM2eKgIAAUVVVJS5cuCD9dHV1qXEIpKBdu3YJNzc3kZeXJ+rq6sSiRYuEp6enMJvNQgghVq9eLZKTk6X1DQ0N4qGHHhJpaWni1KlTYuvWrcLZ2VkcOHBArUP4Txy87gMpKSkCwC0/RUVF0hoAIjc3V3pstVrFmjVrhJ+fn3BzcxNTp04V9fX19g9Pqrh06ZJISkoSAwcOFIMHDxbz5s2TDepC3NozFy5cEHPnzhUGg0HodDoRHBwsMjMzhdVqtXN6UoMtPSOEEDk5OSIoKEjodDoxduxYsWfPHjumJjXZ2jP/xMHrwXK3PdPY2Njr+c/N50DUf2RnZ4thw4YJrVYrYmJixIkTJ6TnUlJSxKRJk2Tri4qKREREhNBqtSIwMPC2nzeOQCOEEPa/zkZERERERPTg4F0NiYiIiIiIFMbBi4iIiIiISGEcvIiIiIiIiBTGwYuIiIiIiEhhHLyIiIiIiIgUxsGLiIiIiIhIYRy8iIiIiIiIFMbBi4iIiIiISGEcvIiIiIiIiBTGwYuIiIiIiEhhHLyIiKjfmDx5MlasWKF2DADApUuX4Ovri6ampjve88orryAzM1O5UEREpBoOXkRERApYt24dEhMTMWLEiDve89Zbb2HdunVoa2tTLhgREamCgxcREdE91tHRgZycHMyfP/+u9oWHh2PUqFHYuXOnQsmIiEgtHLyIiKhf6urqwvLly+Hr6wudToeJEyeivLxctubatWuYM2cO3N3d4e/vjy1bttyTX1fcv38/3Nzc8MQTT8jq4eHhePfdd7F48WJ4eXlBr9cjKytLtubZZ5/Frl27+vT+RETkeDh4ERFRv5Seno5vv/0W27dvR2VlJYKCgmA0GnH58mVpTWpqKo4dO4aCggIcPHgQxcXFMJlMfX7vkpISREdHy2pdXV2or6/Hjh07MGnSJJSXl2POnDnIyMhAe3u7tC4mJgZlZWXo6urqcw4iInIcHLyIiKjfaW9vx7Zt27Bx40Y8/fTTCA0NxWeffYYBAwYgJycHwF9Xu7Zv345NmzZh6tSpCA8PR25uLnp6emSvNWvWLHh5eeHFF1+U1ffu3Yvg4GCMHj0an3/+uey55uZmGAwGWa2mpgY9PT3YsmULkpKSEBQUhLlz56K7uxsdHR3SOoPBgO7ubpjN5nv5R0JERCrj4EVERP3OuXPnYLFYMGHCBKnm6uqKmJgYnDp1CgDQ0NAAi8WCmJgYaY2HhweCg4Nlr/X6669jx44dslpPTw9SU1Nx5MgRVFZWYsOGDbh06ZL0fGdnJ3Q6nWxPdXU19Ho9jEajVPvtt9+g1WoxZMgQqTZgwAAAkA1jRER0/+PgRUREdBuTJ0/GoEGDZLWysjKEhYXB398fgwYNwjPPPINDhw5Jz3t7e+OPP/6Q7amqqsK4ceOg0WhktfDwcDg7O0u1v38V0sfHR4nDISIilXDwIiKifmfUqFHQarU4duyYVLNYLCgvL0doaCgAIDAwEK6urrIbbrS1teHMmTP/+frnz5+Hv7+/9DggIAAtLS3S48jISNTV1cn2VFdXIyIiQlarqqq6pVZTU4OAgAB4e3vfwZESEdH9goMXERH1O+7u7liyZAnS0tJw4MAB1NXVYeHChejo6JBu8T5o0CCkpKQgLS0NRUVFqK2txfz58+Hk5CS7KmULo9GI2tpa2VWv3gYvk8l0S62kpATTpk3r0/sTEZHj4eBFRET90vr16/HCCy8gOTkZUVFR+OWXX3Dw4EF4eXlJazZv3oy4uDgkJCQgPj4eEyZMQEhIyC3fz7qZwWCQXeFqaWmR3UxjzJgxiIqKwldffQUAaGpqQltbm2zI6urqwunTpxEZGSnVrl+/jj179mDhwoV9Pn4iInIsGiGEUDsEERGRI2hvb4e/vz8yMzNl//lxcXExPvroI3zzzTcA/rq5RkhICIqLi+Hh4YHo6Gj8/PPPGDp0qLRn3759SEtLQ01NDZycbv13zoqKCowfPx5tbW3Sd8i2bduG3bt3y74vRkRE/YOL2gGIiIjUYjKZcPr0acTExKCtrQ1r164FACQmJkpr4uPjUV1djfb2dgQEBODrr79GXFwcMjMzMWXKFFitVqSnp8uGLgCYMWMGzp49i5aWFjzyyCO9vndgYKDsxh2urq7Izs5W6GiJiEhNvOJFREQPLJPJhAULFqC+vh5arRbR0dHYvHkzxowZo/h7L1u2DGazWbqKRkRE/RsHLyIiIiIiIoXx5hpEREREREQK4+BFRERERESkMA5eRERERERECuPgRUREREREpDAOXkRERERERArj4EVERERERKQwDl5EREREREQK4+BFRERERESkMA5eRERERERECuPgRUREREREpLD/AfBgZbNBkCPvAAAAAElFTkSuQmCC", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo1.jl\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Support and Sign-based Criteria\n", "-------------------------------\n", "In the following we will consider the support\n", "$$ \\text{supp}(x_0) = \\enscond{i}{x_0(i) \\neq 0} $$\n", "of the vector $x_0$. The co-support is its complementary $I^c$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "supp = s -> find(abs(s) .> 1e-5)\n", "cosupp = s -> find(abs(s) .< 1e-5);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Given some support $ I \\subset \\{0,\\ldots,N-1\\} $, we will denote as\n", "$ \\Phi = (\\phi_m)_{m \\in I} \\in \\RR^{N \\times \\abs{I}}$ the\n", "sub-matrix extracted from $\\Phi$ using the columns indexed by $I$.\n", "\n", "\n", "J.J. Fuchs introduces a criteria $F$ for identifiability that depends on the\n", "sign of $x_0$.\n", "\n", "\n", "J.J. Fuchs. _Recovery of exact sparse representations in the presence of\n", "bounded noise._ IEEE Trans. Inform. Theory, 51(10), p. 3601-3608, 2005\n", "\n", "\n", "Under the condition that $\\Phi_I$ has full rank, the $F$ measure\n", "of a sign vector $s \\in \\{+1,0,-1\\}^N$ with $\\text{supp}(s)=I$ reads\n", "$$ \\text{F}(s) = \\norm{ \\Psi_I s_I }_\\infty\n", " \\qwhereq \\Psi_I = \\Phi_{I^c}^* \\Phi_I^{+,*} $$\n", "where $ A^+ = (A^* A)^{-1} A^* $ is the pseudo inverse of a\n", "matrix $A$.\n", "\n", "\n", "The condition\n", "$$ \\text{F}(\\text{sign}(x_0))<1 $$\n", "implies that $x_0$ is identifiable, and also implies to robustess to\n", "small noise. It does not however imply robustess to a bounded noise.\n", "\n", "\n", "Compute $\\Psi_I$ matrix." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "PsiI = (Phi,I) -> Phi[:, setdiff(1:size(Phi)[2], I)]' * pinv(Phi[:,I])';" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute $\\text{F}(s)$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#19) (generic function with 1 method)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F = (Phi, s) -> norm(PsiI(Phi, supp(s))*s[supp(s)], Inf)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The Exact Recovery Criterion (ERC) of a support $I$,\n", "introduced by Tropp in\n", "\n", "\n", "J. A. Tropp. _Just relax: Convex programming methods for identifying\n", "sparse signals._ IEEE Trans. Inform. Theory, vol. 52, num. 3, pp. 1030-1051, Mar. 2006.\n", "\n", "\n", "Under the condition that $\\Phi_I$ has full rank, this condition reads\n", "$$ \\text{ERC}(I) = \\norm{\\Psi_{I}}_{\\infty,\\infty}\n", " = \\umax{j \\in I^c} \\norm{ \\Phi_I^+ \\phi_j }_1. $$\n", "where $\\norm{A}_{\\infty,\\infty}$ is the $\\ell^\\infty-\\ell^\\infty$\n", "operator norm of a matrix $A$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "erc =(Phi, I) -> norm(PsiI(Phi,I), Inf);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The condition\n", "$$ \\text{ERC}(\\text{supp}(x_0))<1 $$\n", "implies that $x_0$ is identifiable, and also implies to robustess to\n", "small and bounded noise.\n", "\n", "\n", "One can prove that the ERC is the maximum of the F criterion for all signs of the given\n", "support\n", "$$ \\text{ERC}(I) = \\umax{ s, \\text{supp}(s) \\subset I } \\text{F}(s). $$\n", "\n", "\n", "The weak-ERC is an approximation of the ERC using only the correlation\n", "matrix\n", "$$ \\text{w-ERC}(I) = \\frac{\n", " \\umax{j \\in I^c} \\sum_{i \\in I} \\abs{\\dotp{\\phi_i}{\\phi_j}}\n", " }{\n", " 1-\\umax{j \\in I} \\sum_{i \\neq j \\in I} \\abs{\\dotp{\\phi_i}{\\phi_j}}\n", " }$$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#27) (generic function with 1 method)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = (C, I) -> sum(C[:,I], 2)\n", "werc_g = (g, I, J) -> maximum(g[J]) / (1 - maximum(g[I]))\n", "werc = (Phi, I) -> werc_g(g(Correlation(Phi), I), I, setdiff(1:size(Phi)[2], I) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "One has, if $\\text{w-ERC}(I)>0$, for $ I = \\text{supp}(s) $,\n", "$$ \\text{F}(s) \\leq \\text{ERC}(I) \\leq \\text{w-ERC}(I) \\leq\n", " \\text{Coh}(\\abs{I}). $$\n", "\n", "\n", "This shows in particular that the condition\n", "$$ \\text{w-ERC}(\\text{supp}(x_0))<1 $$\n", "implies identifiability and robustess to small and bounded noise." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Show that this inequality holds on a given matrix.\n", "What can you conclude about the sharpness of these criteria ?" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 2000, P = 1990, |I| = 6\n", "F(s) = 0.19\n", "ERC(I) = 0.23\n", "w-ERC(s) = 0.28\n", "Coh(|s|) = 1.79\n" ] } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo2.jl\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 2000, P = 1990, |I| = 6\n", "F(s) = 0.20\n", "ERC(I) = 0.23\n", "w-ERC(s) = 0.26\n", "Coh(|s|) = 1.54\n" ] } ], "source": [ "## Insert your code here.\n", "\n", "N = 2000\n", "P = N - 10\n", "Phi = PhiRand(N, P)\n", "s = zeros(N)\n", "s[1:6] = 1\n", "I = supp(s)\n", "k = length(I)\n", "\n", "println(@sprintf(\"N = %d, P = %d, |I| = %d\", N, P, k))\n", "println(@sprintf(\"F(s) = %.2f\", F(Phi, s)))\n", "println(@sprintf(\"ERC(I) = %.2f\", erc(Phi, I)))\n", "println(@sprintf(\"w-ERC(s) = %.2f\", werc(Phi, I)))\n", "println(@sprintf(\"Coh(|s|) = %.2f\", Coh(Phi, k)))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "For a given matrix $\\Phi$ generated using PhiRand, draw as a function of the sparsity $k$\n", "the probability that a random sign vector $s$ of sparsity\n", "$\\norm{s}_0=k$ satisfies the conditions $\\text{F}(x_0)<1$,\n", "$\\text{ERC}(x_0)<1$ and $\\text{w-ERC}(x_0)<1$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo3.jl\")" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqMAAAHWCAYAAABDmICHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3Xd4VGX6//H3zKR3ICEJJJAgSpMSiixFyooUV8TVBSyAoLjWHyquva1ugbWAflcUVBBEbFhXVlnL0kWREhVBQQmQQBJCS68z8/tjyCSzhIRMJjmZzOd1XefizJlzztwZUu55yv2Y7Ha7HRERERERA5iNDkBEREREfJeSURERERExjJJRERERETGMklERERERMYySURERERExjJJRERERETGMklERERERMYySURERERExjJJRERERETGMklERERERMYySURFpNEuXLsVkMhEUFMShQ4dOe37EiBGcf/75BkQGX3zxBb/97W+JjIwkPDycfv368fbbb5923ldffcXQoUMJCQkhLi6OWbNmUVBQcNp5NpuNJ598kuTkZIKCgujVqxdvvvlmg2I0mUzOzWw2065dO0aPHs3atWsbdN/6Wr9+PZdddhmJiYkEBQURFxfH2LFj2bRpU43nG/meiYj3UTIqIo2utLSUuXPnGh2G06uvvsro0aPx9/fn73//O0899RTDhg0jPT3d5bzU1FQuuugiioqKmDdvHjNnzuSll15i4sSJp93zoYce4r777uPiiy/mn//8Jx06dOCaa67hrbfealCsF198McuXL2fZsmXcfPPNfP/99/z2t7/l008/bdB962PPnj2YzWZuvvlmFixYwJ/+9CeysrIYNmwYq1evdjm3ObxnIuJl7CIijeTVV1+1A/Y+ffrYAwMD7YcOHXJ5fvjw4fYePXo0aUxpaWn24OBg+6xZs+o8d9y4cfb4+Hh7bm6u89jLL79sB+z/+c9/nMcyMjLs/v7+9ttuu815zGaz2S+88EJ7QkKCvaKiwq1YAZd72u12+/fff28H7KNHj3brnp5SWFhoj42NtY8ZM8bluNHvmYh4H7WMikije/DBB7Farc2idXThwoVYrVaeeOIJAAoKCrDb7aedl5eXx+eff86UKVOIiIhwHp82bRphYWG88847zmMfffQR5eXl3Hrrrc5jJpOJW265hYyMDDZv3uyx+Hv27El0dDRpaWkeu6c7QkJCiImJ4eTJk85jzfU9E5HmTcmoiDS65ORkpk2bxssvv8zhw4frfX1RURFHjx6tcztx4kSd9/riiy/o2rUrn3zyCQkJCYSHh9OmTRseeeQRbDab87wffviBiooK+vfv73J9QEAAffr0YceOHc5jO3bsIDQ0lG7durmce8EFFzif95QTJ05w4sQJ2rRpU+t5nnzPKuXl5XH06FF++uknHnzwQXbu3MlFF13kfL65vmci0rwpGRWRJvHQQw9RUVHBP/7xj3pf++STTxITE1PnlpKSUue99u7dS3p6OjNmzOD666/n3XffZdy4cfz1r3/loYcecp6XmZkJQHx8/Gn3iI+Pd0mqMzMziY2NxWQynXYe4FYCXqmkpISjR4+Sk5PDli1bmDhxIlartcYxmNV58j2rNGnSJGJiYujWrRvPPPMMN910E4888ojz+ebynomId/EzOgAR8Q2dOnVi6tSpvPTSS9x///01JixnMm3aNIYOHVrnecHBwXWeU1BQgM1mY+7cudx3330AXHnllRw/fpznnnuOBx98kPDwcIqLiwEIDAw87R5BQUHO5wGKi4vPeF7l8+5avHgxixcvdrnn7NmzufPOO2u9zpPvWaW5c+dy9913k56ezrJlyygrK6OiosL5fHN5z0TEuygZFZEm8/DDD7N8+XLmzp3Lc889d9bXderUiU6dOnkkhuDgYAoLC7n66qtdjl999dWsXr2aHTt2MGzYMGeSVlpaeto9SkpKXJK44ODgM55X+by7JkyYwO23347JZCI8PJwePXoQGhpa53WefM8q9enTx7k/ZcoU+vbty/Tp03n33XcBms17JiLeRcmoiDSZTp06MWXKFGfr6NkqKCiosU7l/7JYLMTExNR6Trt27di7dy+xsbEux9u2bQvgHENZ2XJb2fVcXWZmJu3atXM+jo+PZ82aNdjtdpdu58prq59bXwkJCYwaNare13nyPatJQEAAl112GXPnzqW4uJjg4OBm856JiHfRmFERaVIPP/xwvceOPv3008THx9e5DRgwoM579evXD+C0IvyVYxQrE7Pzzz8fPz8/tm7d6nJeWVkZqampLq2Effr0oaioiN27d7uc+8033zifb2qefM/OpLi4GLvdTn5+PuD975mIGEMtoyLSpM455xymTJnCokWL6NixI35+df8a8uT4x8mTJ/PWW2+xePFi/va3vwGOlYBeffVVWrdu7UxWIyMjGTVqFK+//jqPPPII4eHhACxfvpyCggKXCUQTJkzgrrvu4oUXXuD5558HwG63s3DhQtq3b8/gwYPrjMvTPPmeHTlyxNlyXOnkyZO89957JCYmOp/z9vdMRIyhZFREmtxDDz3E8uXL+fnnn+nRo0ed53ty/OOECRO46KKLmDNnDkePHqV37958+OGHbNy4kUWLFrlMqvnb3/7G4MGDGT58OH/84x/JyMjgmWeeYfTo0YwdO9Z5XkJCAnfeeSdPPfUU5eXlDBgwgA8//JANGzawYsUKLBaL89y1a9cycuRIHnvsMf785z975GuqiSffs3HjxpGQkMDAgQNp27YtBw8e5NVXX+Xw4cOnLaHaGO+ZiLRwRlbcF5GWrXIFpm+//fa056677jo70OQrMNntdnt+fr79jjvusMfFxdkDAgLsPXv2tL/++us1nrthwwb74MGD7UFBQfaYmBj7bbfdZs/LyzvtPKvVav/73/9u79ixoz0gIMDeo0ePGu/58ccf2wH7woUL64yTGlZgMsLzzz9vHzp0qD06Otru5+dnj4mJsY8fP96+fv36Gs/39HsmIi2byW6vYekRERFpFPfeey9vvvkmv/zyS42ljUREfI0mMImINKE1a9bwyCOPKBEVETlFLaMiIiIiYhi1jIqIiIiIYZSMioiIiIhhlIyKiIiIiGGUjIqIiIiIYbyi6L3NZuPw4cOEh4e7rGEsIiIiIs2D/dTywO3atcNsPvv2Tq9IRg8fPkxiYqLRYYiIiIhIHdLT00lISDjr870iGa1c3zg9PZ2IiAiDoxERERGR/5WXl0diYqIzbztbXpGMVnbNR0REKBkVERERacbqO6RSE5hERERExDBKRkVERETEMEpGRURERMQwXjFmVERERLyP1WqlvLzc6DDEQywWC35+fh4vs6lkVERERDyuoKCAjIwM7Ha70aGIB4WEhBAfH09AQIDH7qlkVERERDzKarWSkZFBSEgIMTExWrCmBbDb7ZSVlZGTk0NaWhrnnntuvQrb10bJqIiIiHhUeXk5drudmJgYgoODjQ5HPCQ4OBh/f38OHDhAWVkZQUFBHrmvJjCJiIhIo1CLaMvjqdZQl3t6/I4iIiIiImdJyaiIiIiIGKbeyej69esZP3487dq1w2Qy8eGHH9Z5zdq1a+nbty+BgYF07tyZpUuXuhOriIiIiLQw9U5GCwsL6d27NwsWLDir89PS0vjd737HyJEjSU1N5c4772TmzJn85z//qXewIiIiIo1l+vTpmEym07ZffvnFI/d3p0HPF9R7Nv24ceMYN27cWZ+/cOFCkpOTeeaZZwDo1q0bGzduZP78+YwZM6a+L9/oMo7s59f074wOo1FYTGbaBcViNjXf0RnWoDZYQ6KNDsOjTEBCqxCCAyxGh+IxRWUVlFfYiQzxNzoUERGPGjt2LK+++qrLsZiYGLfuZbPZyMzMpH379kBVg97111/PFVdc0eBYW4pGL+20efNmRo0a5XJszJgx3HnnnWe8prS0lNLSUufjvLy8Rovvf72/7lleLvqyyV6vqfUtKWFp5hGa8/zGdFsMO+yd2WHrTKqtMz/akyjDu5Mei9lEt/hwUhJb0ScxipQOUSRHh3rFTFObzc6+o4Wkpp9kx8ET7Dh4kp+z87Ha7IzsEsPDl3bnnJgwo8MUEfGIwMBA4uLiGnSPn376iWXLlrF8+XImTpzI/Pnzgfo36PmKRk9Gs7KyiI2NdTkWGxtLXl4excXFNdYfmzNnDo8//nhjh+aTtgcFke7nR4eKCqNDOaNEcw6J5HCZZTMApXY/dtmTSLWdww7buWy3dybDHgPNOqV2ZbXZ2Xkoj52H8lj+9QEAokL86Z3gSExTOrSiT0JUs2hpPFFYRmrGSXYcPElq+klSD54gr6Tm75c1P+ewYe96ZgxJ4v9ddC4RQcbHLyLN0/h/biQnv7TuEz0sJjyQj//f0EZ/nRMnTvDWW2+xbNkytm7dykUXXcTcuXPVAnoWmmXR+wceeIDZs2c7H+fl5ZGYmNgkr92x7flc+PP2JnmtprTfUky6XwkAa1sNoWtF82vJMtmhTVkGCcU/EWCv+oUVaKogxfQLKeZfmIFjrHGBJYqDIT04GNydgyHdyQjuRqkl1KjQa1VmtbHrcB57juRTfVW8k0XlrNuTw7o9Oc5jnWJCHa2nHaJISYyia1w4fpbGG1ZRbrXxU2Y+O9JPkHrwJDvST5J2tLDWa0wmOK9tOCeLy8jOK6XCZuflDWl8sOMQ94zpwh/6JWIxe88HBRFpGjn5pWTllRgdRp1WrVpFWFjV38hx48axcuXKGs+12Wx8+umnLFu2jH/961+cd955TJ06lQ8++ID4+PimCtnrNXoyGhcXR3Z2tsux7OxsIiIizrgqQ2BgIIGBgY0dWo0mDJ/JhOEzDXntxvT6rtf5x7f/ACByzA1c0HmCwRHVwloOR3ZBxreQsc3x77G9LqeEWU/SPX8T3fM3nTpigrbdoH0/SBjg2GK6gLn5jNPMLynn+4xcdhw8carL+yTHCstcztmXU8i+nELe254BQJC/mV7tHa2nju79VsRFur/iRWZuMTsOVnW3/3Aol9IKW63XRIcF0CexlaMFNzGKngmRhAf5U1RWwcK1v7Jo/T5KK2wcLSjjvvd+YPnXB3hsfA8GJLV2O04RaXliwo35u17f1x05ciQvvvii83Fo6JkbOg4ePMill15Kq1atePPNN/n973/vdpy+rNGT0UGDBvHJJ5+4HPv8888ZNGhQY7+0VBMfWvUJLaswy8BIzoLFH+J7O7YBpz4YFJ+AQ9sgY+up7VsoOVntIrsjgT2yC3YsdxwKCIP2fR2Jafv+kNAfwto2+ZdTKTzInyGdoxnS2TFBy263k368mB3pJ5xd4j8ezqXcWtV8WlJuY8v+42zZf9x5LD4yyDnuNKVDK85vF1nj5Kiisgp+yMhlR/rJU62eJ8jOq72LLMBipkf7CGfim5IYRUKr4BrHtoYE+DF7dBcm9k9kzqe7+eQHx/fVzkN5TFy4mct6t+P+cV1pF6WlAEWEJukq94TQ0FA6d+58VucmJCTw5ptvsmzZMiZNmsSgQYOYOnUqEydOJCoqqpEjbTnqnYwWFBS4lDhIS0sjNTWV1q1b06FDBx544AEOHTrEa6+9BsDNN9/M888/z7333sv111/Pf//7X9555x3+/e9/e+6rkDrFhVYNxs4qaubJaE2CW0HnUY4NwG6HY7/CoVOJaca3kLUT7Naqa8oKIG29Y6sU1dGRlCYMgK6XQlTTDP+oiclkokObEDq0CWFCH8dMy5JyK7sy85xd5jsOniDjRLHLdZm5JWTmZvHpTsf/Y+XkqD6JUXSOCWPvkQKXSUa1SWwdTMqpVs8+iVF0bxdBoF/9WpMTW4fwwrX92PzrMR7/+Ed+ysoH4F/fHebzXdncMuIc/jisE0H+zaeVWkTEE/z8/Ljqqqu46qqryMzMZPny5Tz77LP8v//3/xg/fjxTp05l3Lhx+PtrPH1tTHa7vfa/Vv9j7dq1jBw58rTj1113HUuXLmX69Ons37+ftWvXulxz1113sWvXLhISEnjkkUeYPn36Wb9mXl4ekZGR5ObmEhERUZ9w5ZRjxccY8c4IAIa0H8LCUQuNDagxlBVB5neOxPTQqRbUvENnPj8wAmalQmibpovRDTn5pS4z2b/POElhmbXuC/9HWKAfvRMjnTP6+3SIIjrMs91mFVYbb32bzjOf/cyJonLn8fZRwTx4STcu6RnnFRUERKRhSkpKSEtLIzk5maAg94cWNbXp06dz8uTJBtf/3Lp1K0uXLuWtt97iuuuuc5a3rN6gl5KSwrx58xg5cqSzQc8b1PZ/626+Vu9k1AhKRhvObrfT//X+lNnK6BzVmQ8mfGB0SE0j73BVt37GVji8AyqqtTRe8Qr0mmhcfG6w2uzsPZLv6No/1f2+90iBy+Qokwm6xIa7dOefExPWZBOLcovKefbLPby2+YBL6+zA5NY8Nr4H3dvp51ikJfP1ZLRSWVkZGRkZdOrUCai7Qc8bKBlVMtogv3v/dxzMP0iofyhfX/O10eEYw1oOP34A79/oeJwyFSY8b2xMHlA5OSrtaCGdokPplRhFWKDxxTL2ZufzxKpdbNh71HnMbIKrL+jA3aO70Do0wMDoRKSxeGsyKnVrjGS0+S7FIx5XOW60sLyQ/LJ8g6MxiMUfuo0Hy6kkaP8GY+PxkMrJUVN+05HBnaObRSIKcG5sOK9dfwEvT+tPxzYhANjssOKbg4x4ag1LNqZRbq19Nr+IiLRsSkZ9SPVJTJmFmQZGYjD/YEgc6Ng/sR9OHjQ0nJbOZDJxcfdYPrtrGPeP60roqZn/eSUVPLFqF+Oe28D6arVWRUTEtygZ9SEuM+qbe3mnxpZ0YdV+WstoHW3uAv0s3Dz8HNb8aQR/6JfgPP7LkQKmLdnCzGVb2V9HwX0REWl5lIz6ECWj1SQPq9qvXvpJGl3biCCentibD28bQp/Eqjp8X+zO5uL565jz6W4KSpvvcrUiIuJZSkZ9iFcVvm9s7fuBv2MMI/s3QPOfx9fi9EmM4v1bBjN/cm9iIxwlpsqtdhat28fIp9eycms6tjrqpIqIiPdTMupD4kLUMurkF1A1bjTvEBzfZ2w8PspsNvH7lAT+e/cIbht5DgEWx6+knPxS7nn3e37/wia2HzxhcJQiItKYlIz6EE1g+h/qqm82QgP9uGdMV76YPZwxPWKdx7/LyOWKF77irrdTycotMTBCERFpLEpGfUhYQBjh/uGAWkYB12S0hZR48nYd2oSwaGp/VswcSJfYcOfxD3Yc4rfPrGXBml8oKa//6lMiItJ8KRn1MXFhjtbRrKIsbHYfr+8Y3wcCTiU8aRo32pwM6RzNv2cN5YkJPYgMdqzpXFRm5an//MzF89exemcWXrBeh4iInAUloz6mctxoha2C4yXHDY7GYBY/6DjYsV94BHJ+NjYeceFnMTNtUBJr/zSCaYM6UrmSafrxYm5+fRvXvvINP2XlGRukiIg0mJJRH1N9Rn1mgcaNatxo89cqNIAnJpzPJ3dcyOBz2jiPf/XrMS55bgOPfrSTE4VlBkYoIi3F9OnTMZlMp21jx451npOUlOQ8HhISQs+ePXnllVdOu5fdbuell15i4MCBhIWFERUVRf/+/Xn22WcpKirySLw//vgjV155pTOmZ5991iP3bWpKRn2MS63RIo0bJbla8fv9Skabs65xEayYOZCFU/qR2DoYcCwt+trmA4x8Zi2vbd5PhZYWFZEGGjt2LJmZmS7bm2++6XLOE088QWZmJjt37mTKlCnceOONfPrppy7nTJ06lTvvvJMJEyawZs0aUlNTeeSRR/joo4/47LPP3I4vPT3duV9UVESnTp2YO3cucXFxtVzVvDWPBaylybjMqFfLKMT2hKAoKDkJ+zeCzQZmfUZrrkwmE2PPj2NElxgWb0xjwZpfKCqzcrKonEc/+pHXvz7AY+N7MKRztNGhioiXCgwMrDOxCw8Pd55z33338dRTT/H5558zbtw4AN555x1WrFjBhx9+yIQJE5zXJSUlcdlll5GXV78hRgcPHmT58uUsW7aMHj168MEHHwAwYMAABgwYAMD9999fr3s2J0pGfYxaRv+H2QxJQ+GnVVB8ArJ3Qnwvo6OSOgT5W7htZGeu7JvAk6t/4v0dhwDYk13Ata98w5gesTx0SXc6tAkxOFIRcVo0HAqONP3rhrWFm9Y1yq1tNhsffPABx48fJyAgwHl8xYoVdOnSxSURrWQymYiMjKzz3oWFhbz//vssW7aMNWvW8Jvf/Ia7776bSZMmefRraA6UjPoYLQlag+RhjmQUHCWelIx6jbjIIOZN7sO1v+nIEx//yHcZuQD858ds1vyUw71juzDzwk4GRykigCMRzT9sdBR1WrVqFWFhYS7HHnzwQR588EHn4/vuu4+HH36Y0tJSKioqaN26NTNnznQ+v3fvXrp06eLW669bt45ly5axcuVK2rZty5QpU1i0aBHnnHOOe1+QF1Ay6mNiQ2IxYcKOXclopf+dxDToNuNiEbf069iKD24dwnvbM/jH6p85WlBKmdXGX/+9G4vZxIwhyUaHKCJhbb3idUeOHMmLL77ocqx169Yuj++55x6mT59OZmYm99xzD7feeiudO3d2Pt+Q0nMjRowgODiY+fPnc9NNN7l9H2+iZNTHBFgCaBPchqPFR5WMVorpCqExUJgDB74Ca4Wj7JN4FbPZxMT+iYw9P45nv9jL4o1pADz+8S5ahQRweUp7gyMU8XGN1FXuaaGhoS6JZU2io6Pp3LkznTt3ZuXKlfTs2ZP+/fvTvXt3AM477zx++uknt17/448/ZtmyZdxxxx0sWrSIqVOncvXVV3v1BKW6aKaGD6os73S0+Cjl1nKDo2kGTCZIOjWrvjQPMr8zNh5pkPAgfx65tDu3j6z6Y/Knld+x5mcDxqqJSIuXmJjI5MmTeeCBB5zHrrnmGvbs2cNHH3102vl2u53c3Nwz3u/SSy9l5cqVZGZmMnPmTN566y0SEhIYN24cb7zxhsfKQjUnSkZ9UOW4UTt2souyDY6mmVCJpxbn7tHncc3ADgBU2Ozc8vo2th3w8YUeRKROpaWlZGVluWxHjx6t9Zo77riDjz/+mK1btwIwadIkJk+ezNVXX83f//53tm7dyoEDB1i1ahWjRo1izZo1dcbRqlUrbr31Vr755ht27txJ7969uffee5k6darznLKyMlJTU0lNTaWsrIxDhw6RmprKL7/80rA3oYkpGfVBLuWdClXeCYAkFb9vaUwmE3+ZcD6X9HR8v5eU25jx6rdatUlEarV69Wri4+NdtqFDh9Z6Tffu3Rk9ejSPPvoo4Pj988YbbzBv3jw+/PBDhg8fTq9evfjzn//MRRddxOjRo+sVU9euXZk7dy4HDx5kzpw5zuOHDx8mJSWFlJQUMjMzefrpp0lJSXGZTOUNTHYvWOA5Ly+PyMhIcnNziYiIMDocr/faj6/x1NanAPj70L8z/pzxBkfUDNjtMK+7Y6anfwjcdwD8Auq+Tpq90gorNyzdysZfHC0bbcMDee+WwSS2VtknkcZSUlJCWloaycnJBAUFGR2OeFBt/7fu5mtqGfVB8WFVS4JqEtMpJlNVV315ERzebmw84jGBfhYWTe1H7wRHXb8j+aVMWfwNOfmlBkcmIiKgZNQnxYWo1miNtE59ixUa6MerMy7gnJhQAA4cK2Laki3klWgCn4iI0ZSM+iCtwnQGSdUmMSkZbXFahwaw/IaBtIt0dCvtzsxj5rKtlJRbDY5MRMS3KRn1QW2C2+BndtTR1ASmalp1hKiOjv30LVBeYmw84nHtooJ57YaBtArxB2BL2nFuf2MHFVabwZGJiPguJaM+yGwyExsSC6ib/jSV40atpZCxxdhYpFF0bhvG0hkXEBpgAeCL3dnc994P2GzNfi6niEiLpGTUR1UWvs8vy6ewvNDgaJqR5OFV++qqb7F6J0bx0rT+BFgcvwLf257B3z/Z3aAl/ERExD1KRn2Uy7hRtY5WcRk3usG4OKTRDekczXNX9cFscjx+ZWMaL6771digRER8kJJRH1XZMgoaN+oiIh7anFpG8tBWKC0wNh5pVON6xvO33/d0Pn5y9c+8ueWggRGJiPgeJaM+Si2jtags8WSrgPSvjY1FGt3VF3TgnjFdnI8f+uAHVu/UBzQRkaaiZNRHaUnQWqir3ufcOuIcZg5NBsBmh1lvpvLVL7WvRS0iIp6hZNRHqWW0Fqo36nNMJhMPXtKNK/q2B6DMauPG17byfcZJgyMTEW+ydOlSTCbTaVv1ZTOnT5/uPO7v709ycjL33nsvJSWnlxNcs2YNl1xyCW3atCEkJITu3btz9913c+jQIY/EW1JSwvTp0+nZsyd+fn5cfvnlHrlvfSkZ9VHVx4wqGf0fYTHQtrtjPzMVSnKNjUeahNls4h9X9mJUt7YAFJZZmf7qt/yao3HDInL2IiIiyMzMdNkOHDjgcs7YsWPJzMxk3759zJ8/n0WLFvHYY4+5nLNo0SJGjRpFXFwc7733Hrt27WLhwoXk5ubyzDPPuB3fwYNV4+KtVivBwcHMmjWLUaNGuX3PhlIy6qPCA8IJ9XcsjahktAaV40btNjjwlbGxSJPxt5h5/pq+XJDUGoDjhWVMfeUbDp8sNjgyEWlsq1atIioqCqvVsSpbamoqJpOJ+++/33nOzJkzmTJlSq33MZlMxMXFuWyxsbEu5wQGBhIXF0diYiKXX345F198MZ9//rnz+YyMDGbNmsWsWbNYsmQJI0aMICkpiWHDhvHKK6/w6KOP1utry8vLY/HixQwbNow+ffo4j4eGhvLiiy9y4403EhcXV8sdGpefYa8shosLiePX3F/JKszCbrdjMpmMDqn5SLoQvlno2E/bAF3GGRuPNJkgfwuvTO/P5EVfszszj8O5JUxbsoWVNw2iVWiA0eGJeK3JqyZztLjpx2JHB0fz9qVv13nehRdeSH5+Pjt27KB///6sW7eO6Oho1q5d6zxn3bp13HfffR6Nb+fOnWzatImOHTs6j61cuZKysjLuvffeGq+Jioqq8742m40vv/ySZcuW8f7779O+fXumTJnC0qVLPRW6xygZ9WFxYY5ktMxWxvGS47QJbmN0SM1H0hBwit3rAAAgAElEQVTABNg1btQHRQT5s+z6AUxcuJkDx4r45UgB05d+yxszBxIaqF+bIu44WnyUI0VHjA7jjCIjI+nTpw9r166lf//+rF27lrvuuovHH3+cgoICcnNz+eWXXxg+fHit98nNzSUsLMzl2IUXXsinn37qfLxq1SrCwsKoqKigtLQUs9nM888/73x+7969REREEB8fT33t2bOHpUuXsnz5cgoLC5k0aRJffPEFgwcPrve9mop+q/qwuJBqk5iKspSMVhfcCuJ7QeZ3kP0DFB2HkNZGRyVNqG14EMuvH8iVC78iJ7+U79JPcvPr23jluv4E+lmMDk/E60QHRzf71x0+fDhr167l7rvvZsOGDcyZM4d33nmHjRs3cvz4cdq1a8e5554L4JJwTpkyhYULHb1p4eHhbN++3eW+wcHBLo9HjhzJiy++SGFhIfPnz8fPz48rr7zS+XxDeiv/+Mc/sm7dOm6++WbmzZt32ms3R0pGfZjLJKaCLHq06WFgNM1Q0oWOZBRg/wboPsHYeKTJdWgTwmvXX8DkRZvJK6lgw96jzH7nO/7vqhQsZg1rEamPs+kqN9qIESNYsmQJ3333Hf7+/nTt2pURI0awdu1aTpw44dIqmpqa6tyPiIhw7pvNZjp37lzr64SGhjrPWbJkCb1792bx4sXccMMNAJx33nnk5uaSmZlZ79bRZ599lsWLF/Pmm2+yatUqrr32WqZOnUqPHs33b7wmMPkwl/JORZrEdBqXdepVb9RXdYuPYMn0AQT5O35d/vv7TB75aKfWsRdpgSrHjc6fP9+ZeFYmo2vXrmXEiBHOczt37uzc2rZt6/Zrms1mHnzwQR5++GGKix2TJf/whz8QEBDAk08+WeM1J0+euexcnz59+Oc//8nhw4d57rnn2L17NykpKfTt25f58+eTldX8/t4rGfVhLkuCFqjw/Wk6DgLTqe7Y/UpGfVn/pNa8eG0//E61hr7xzUHmfb7H4KhExNNatWpFr169WLFihTPxHDZsGNu3b2fPnj11jhcFRxd7VlbWaZvNZjvjNRMnTsRisbBgwQIAEhMTmT9/Ps899xw33HAD69at48CBA2zatImbbrqJv/zlL3XGERAQwBVXXMFHH33EoUOHmDZtGq+99tppLaS7du0iNTWV48ePk5ubS2pqqkurb1NQMurD1DJah8BwaN/XsZ/zE+RnGxuPGGpk17Y8PbG38/E///sLSzamGRiRiDSG4cOHY7Vanclo69at6d69O3FxcXTp0qX2i3GUUYqPjz9tO3LkzJO3/Pz8uP3223nyyScpLCwE4NZbb+Wzzz7j0KFD/P73v6dr167MnDkTi8XCnXfeWa+vKSYmhjvvvJMdO3awadMml+cuueQSUlJS+Pjjj1m7di0pKSmkpKTU6/4NZbJ7QV9TXl4ekZGR5ObmuozLkIYptZbS//X+APSK6cWKS1YYHFEz9MXjsHGeY//KxdDzD8bGI4Z7dVMaj3+8y/l4/uTe/D4lwcCIRJqfkpIS0tLSSE5Odll9SLxfbf+37uZrahn1YYGWQFoHOWaIq/D9GSRraVBxNWNIMrN+WzU54Z6V3/Pfn9RqLiLiLiWjPq6yq/5o8VHKbeUGR9MMJf4GzP6OfY0blVPuuvg8rh3YAYAKm51bXt/Ohr05BkclIuKdlIz6uMpJTDa7jZwi/TE9TUAIJAxw7B/fB7kZxsYjzYLJZOKJCefzu16On5/SChtTF2/hoQ9+IL9EH+pEROpDyaiPc5nEpK76mlWuUw8q8SROFrOJ+ZP6MLJLjPPYim8OMmb+etb83HxXmRERaW6UjPo4l/JOhSrvVKPq40bVVS/VBPiZeeW6ATw2vjvB/o4yYIdzS5jx6rfMfjuVE4VlBkcoYiwvmCMt9dQY/6dKRn1cbGisc18to2eQMAD8Ts0YTFsP+uUq1VjMJmYMSeazu4YxpHPVkrrv7zjExfPX8ckP+pAnvsdicXw4KyvTB7KWpqioCAB/f3+P3VPLgfo4tYyeBb9ASBwIaesgNx1O7IfWyUZHJc1MYusQXr9hIO9sTeev/95NfkkFRwvKuHXFdsb2iOOJy3vQNlwlbsQ3+Pn5ERISQk5ODv7+/pjNavvydna7naKiIo4cOUJUVJTzA4cnKBn1cXEhVWNGswtVnuaMki90JKPgaB1VMio1MJlMTB7QgRFd2vLQBzv5YrfjZ2r1j1ls3neMRy7tzpV922MyaV17adlMJhPx8fGkpaVx4MABo8MRD4qKiiIuLq7uE+tByaiPiw6Oxs/kR4W9Qi2jtUkeDvzVsb9/A/S7ztBwpHmLjQji5Wn9+Pj7TP78rx85XlhGbnE5f1r5Hf/67jBzruhJ+6hgo8MUaVQBAQGce+656qpvQfz9/T3aIlpJyaiPs5gttA1py+HCw1oStDbtUsA/FMoLq8aNqnVLamEymbisdzuGnNOGJ1bt4qPUwwCs35PD6HnruH9cV64d2BGzWd9H0nKZzWatwCR10iAOcZZ3yi3Npai8yOBomimLP3Qc7NgvyIaje42NR7xGm7BAnrsqhVem9Sc2IhCAwjIrj3z0I1e99DX7cgoMjlBExFhKRsW11qhaR8/MZWnQdcbFIV5pVPdYPrtrOFdfkOg8tmX/ccY9t4GF636lwmozMDoREeMoGRUVvj9b1Yvfq96ouCEy2J85V/TijZkDSWztGDNaWmFj7qc/ccWLX7E7M8/gCEVEmp6SUXEp76RktBZxvSAo0rG/fyPY1JIl7hncOZr/3DmM64ckO4cef5+Ry/h/bmTe53soq9D3loj4DiWjopbRs2W2QMchjv2iY3Bkl7HxiFcLCfDj0fHdeffmwXRuGwZAhc3O/325l0v/uYHU9JMGRygi0jSUjIoK39eHuurFw/p1bMW/Zw3l9pGdsZyaWb8nu4ArXtjE3/69i+Iyq8ERiog0LreS0QULFpCUlERQUBADBw5ky5YttZ6/YsUKevfuTUhICPHx8Vx//fUcO3bMrYDF89QyWg9J1ScxrTcuDmlRAv0s/GlMF/51+xB6tIsAwGaHlzekMfa59Xy9T78vRaTlqncy+vbbbzN79mwee+wxtm/fTu/evRkzZgxHjhyp8fxNmzYxbdo0brjhBn788UdWrlzJli1buPHGGxscvHhGREAEwX6OyRRKRuvQtjuEnFp/fP8msKnVSjynR7tIPrxtCPeO7UKAn+PX84FjRVz10tc89MEP5JeUGxyhiIjn1TsZnTdvHjfeeCMzZsyge/fuLFy4kJCQEJYsWVLj+Zs3byYpKYlZs2aRnJzM0KFDuemmm+psTZWmYzKZnK2jWYVZ2O12gyNqxsxmSBrq2C/NhczvjI1HWhx/i5lbR3Tmk1kX0q9jK+fxFd8cZPT89az5qeYP/iIi3qpeyWhZWRnbtm1j1KhRVTcwmxk1ahSbN2+u8ZpBgwaRnp7OJ598gt1uJzs7m5UrV3LJJZec8XVKS0vJy8tz2aRxVY4bLbGWkFuaa3A0zZzGjUoT6Nw2jHduGsSfx3cnJMCx/F5mbgkzln7LO9+mGxydiIjn1CsZPXr0KFarldjYWJfjsbGxZGXV3L07ZMgQVqxYweTJkwkICCAuLo6oqCgWLFhwxteZM2cOkZGRzi0xMfGM54pnVB83qklMdUiqloymKRmVxmMxm5g+JJn/3DmMoZ2jncef/uxnSis0REREWoZGn02/a9cu7rjjDh599FG2bdvG6tWr2b9/PzfffPMZr3nggQfIzc11bunpagVobHEhmsR01qLPhbBTH8gOfAVWjeOTxpXYOoTlN1zAqG6O77sj+aV8tOOwwVGJiHhGvZLR6OhoLBYL2dnZLsezs7OJi4ur8Zo5c+YwePBg7rnnHnr16sWYMWN44YUXWLJkCZmZNbfABQYGEhER4bJJ41LLaD2YTFVd9eWFcHiHsfGITzCZTNw68hzn45c27MNm0/huEfF+9UpGAwIC6NevH19++aXzmM1m48svv2TQoEE1XlNUVISfn5/LMYvFMf5JE2WaD61PX09JWqdeml7fDq24IKk1AL8cKeC/mswkIi1AvbvpZ8+ezcsvv8yyZcvYvXs3t9xyC4WFhcyYMQNwdLFPmzbNef748eN57733ePHFF9m3bx+bNm1i1qxZXHDBBbRr185zX4k0iMuSoAVKRuuUrHGjYoybhndy7i9a/6uBkYiIeIZf3ae4mjx5Mjk5OTz66KNkZWXRp08fVq9e7ZzUlJmZycGDB53nT58+nfz8fJ5//nnuvvtuoqKi+O1vf8s//vEPz30V0mCxoVWT0tQyehZaJUFkIuSmQ/o3UFEKfoFGRyU+YGSXtpzbNoy9Rwr4dv8Jth04Tr+OrY0OS0TEbSa7F/SV5+XlERkZSW5ursaPNqJhbw3jROkJ4kLj+PwPnxsdTvP34a2QusKxP/3fVfVHRRrZO1vTuffd7wEY3T2Wl6b1NzgiERH38zWtTS9OleNGc4pysGplobppaVAxyIQ+7YiNcLTEf747m19zCgyOSETEfUpGxakyGbXareQU5xgcjRdIrp6MatyoNJ1APwvXD0kGwG6HVzbsMzgiERH3KRkVJ5cZ9ao1WrfIBGh9ajJJxrdQVmRsPOJTrh7YgfBAx7D/97Yd4kh+icERiYi4R8moOCkZdUNlV72tHNK/NjYW8SkRQf5c85sOAJRZbSzdtN/YgERE3KRkVJyql3dS4fuzpBJPYqDrhyTjbzEBsPzrAxSUVhgckYhI/SkZFSe1jLpBk5jEQLERQVzepz0A+SUVvLXlYB1XiIg0P0pGxUkto24Ij4WYro79wzugJM/YeMTn/HFYVRH8xRvTKLfaDIxGRKT+lIyKU3RwNGaT41tCLaP1UNk6arfCwc3GxiI+59zYcEZ1awtAZm4JH3932OCIRETqR8moOPmZ/Wgb4vijpmS0HlzGjaqrXpreTcPPce4vWrcPL1jLRETEScmouIgLcYwbPVF6gpIKlYo5K0lDAcckEvZrEpM0vf4dW5HSIQqAn7PzWbtHdYJFxHsoGRUX1ceNZhdlGxiJFwlpDbHnO/Yzv4ei48bGIz7HZDJx07Cq1tGX1qkIvoh4DyWj4qL6jHpNYqoHZ1e9HQ58ZWgo4psu7h5Lp+hQADbvO8Z36ScNjkhE5OwoGRUXKu/kpmSVeBJjWcwmbqw2s/6l9WodFRHvoGRUXKhl1E0dB8OpSgQaNypG+X1Ke6LDAgH4dGcm+48WGhyRiEjdlIyKi+rJaHahxoyetaBIiO/j2D+yCwo0gUSaXpC/hRlDkgCw2eGVjWodFZHmT8mouFDh+waoXuJJraNikCkDOxISYAFg5dYMjhWUGhyRiEjtlIyKi6jAKAItjm4+jRmtJ40blWYgMsSfqy/oAEBphY1lmw8YHJGISO2UjIoLk8nkbB3NLMxU8ez6SPwNmP0c+2oZFQNdPzQZP7Oj9u1rm/dTVFZhbEAiIrVQMiqniQ2NBaC4opi8Mq21ftYCw6B9f8f+sV8gT8syijHaRwUzvnc7AE4WlfPOt+kGRyQicmZKRuU01ceNqqu+nly66tU6Ksb5Y7UyT69sTKPCajMwGhGRM1MyKqdRrdEGcJnEpHGjYpxu8REMPy8GgIwTxXyyUz/LItI8KRmV06hltAESLoBTE8A0iUmMdtPwqtbRRet+1RhwEWmWlIzKaeJCVPjebf5BkHiBY//kQTix39BwxLcN6tSGXgmRAPx4OI9NvxwzOCIRkdMpGZXTuHTTF6lltN6qd9Vr3KgYyGQyuYwdXbT+VwOjERGpmZJROY3LkqAFahmtt6Rqk5hU4kkMNrZHHB1ahwCwYe9Rdh7KNTgiERFXSkblNCH+IUQERACQXaQlQeutfT/wd/zxJ20DaJyeGMjPYubGC5Odj1/eoCVCRaR5UTIqNaqcxJRdmI3VZjU4Gi/jFwAdfuPYzz8Mx9Q1Ksb6Q79EWocGALDq+0zSjxcZHJGISBUlo1Kjyq76CnsFx0o06aHeVOJJmpHgAAvTBnUEwGqzs3hjmsERiYhUUTIqNXIZN6oZ9fWXVH0Sk5JRMd60QUkE+Tt+5b/9bTonCssMjkhExEHJqNRIhe8bKL43BDrG3WrcqDQHrUMDmNw/EYDicivLvz5gcEQiIg5KRqVGKnzfQBY/6DjYsV90FI7sNjYeEWDmhZ0wmxz7y77aT0m5xoOLiPGUjEqN1DLqASrxJM1MYusQfterHQDHCst4d1uGwRGJiCgZlTNQMuoByRo3Ks3PTdWK4L+8YR9Wm4aQiIixlIxKjdqGtMWEoz9PE5jcFHs+BLdy7O/fCDabsfGIAOe3j2RI5zYAHDhWxH9+1IdNETGWklGpkb/Zn5jgGEAto24zm6F9f8d+yUkozDE2HpFTbhp2jnN/0bpfsWuCnYgYSMmonFFcmKOr/ljJMcqsKgPjlqjEqv1cjc+T5uHCc6PpFu+o9vBdRi7fpB03OCIR8WVKRuWM4kKqxo1mF2pZULdEJlTt5ykZlebBZDJx8/CqsaOL1mmVMBExjpJROaPq5Z00btRNEdWSUbWMSjNySc942kcFA7Dm5xx+ysozOCIR8VVKRuWMXGbUF2ncqFuqt4zmHjIuDpH/4W8xc8PQZOfjl9bvMzAaEfFlSkbljFT43gMi21ft56YbF4dIDSYPSCQy2B+Af6Ue5vDJYoMjEhFfpGRUzkjr03tAeDs4VSKLPLWMSvMSGujHtEEdAaiw2Xl1U5rBEYmIL1IyKmekwvce4BcAYbGOfY0ZlWbousFJBPg5/hS88c1BcovLDY5IRHyNklE5o9ZBrQkwBwBKRhuksqu+IBsqSo2NReR/RIcF8od+jrHNhWVWVnxzwOCIRMTXKBmVMzKZTMSGOlr1lIw2gEt5p8PGxSFyBjde2AnTqdEkr27aT0m51diARMSnKBmVWlVOYiooLyC/LN/gaLxU9fJOGjcqzVBydChjeziG5eTkl/LhDn2fikjTUTIqtdK4UQ9QeSfxAn8cVlUE/6UN+7DZtESoiDQNJaNSK82o9wCVdxIvkNKhFRcktwZgX04hX+zWqmsi0jSUjEqt1DLqAZHqphfv4LJEqIrgi0gTUTIqtVLhew/QkqDiJUac15bzYsMA2HbgBFv3Hzc4IhHxBUpGpVZxIWoZbbDQGLA4SmRpzKg0Z2aziT8OO8f5eOE6tY6KSONTMiq10vr0HmA2Q0Q7x75aRqWZu6x3O+IiggD4Ync2e7NVRUNEGpeSUalVWEAY4f7hAGQWaAKT2yITHf+W5kJJnrGxiNQiwM/M9UOTnI/vXvkdpRWqOyoijUfJqNSpsvB9dlE2NrvN4Gi8VES1GfWaxCTN3LUDO9KhdQgA32fk8tdVuw2OSERaMiWjUqfKSUzltnKOl2hCg1tcyjspGZXmLTTQjxeu7etcs3751wf4KFXftyLSOJSMSp1U3skDXMo7adyoNH/nt4/kict6OB/f/94PGj8qIo1CyajUqXp5JxW+d5PKO4kXmjwgkSv7Or53i8ut3Pz6NgpLKwyOSkRaGiWjUie1jHqAlgQVL2Qymfjr5efTNc4xifHXnELuf/8H7HYtFSoinqNkVOqkZNQDtCSoeKngAAsvXNuXsEA/AD7+7jDLvz5gcFQi0pIoGZU6aX16DwiKhMAIx75m04uX6RQTxpN/6OV8/JdVu0hNP2lgRCLSkriVjC5YsICkpCSCgoIYOHAgW7ZsqfX80tJSHnroITp27EhgYCBJSUksWbLErYCl6cWGxGLCBEB2YbbB0XixyvJOuYdA3ZziZS7pGc8NQ5MBKLfauW3Fdk4UlhkclYi0BPVORt9++21mz57NY489xvbt2+nduzdjxozhyJEjZ7xm0qRJfPnllyxevJiff/6ZN998ky5dujQocGk6AZYA2gS3AdQy2iCV40atpVB41NhYRNxw/7iu9OvYCoBDJ4u5651UbDZ9sBKRhql3Mjpv3jxuvPFGZsyYQffu3Vm4cCEhISFnbOlcvXo169at45NPPmHUqFEkJSUxaNAghgwZ0uDgpelUzqg/WnyUcmu5wdF4KY0bFS/nbzHz/DUptA4NAGDtzzksWPOLwVGJiLerVzJaVlbGtm3bGDVqVNUNzGZGjRrF5s2ba7zmX//6F/379+fJJ5+kffv2nHfeefzpT3+iuLj4jK9TWlpKXl6eyybGqhw3asdOdpG66t1SvbyTxo2Kl4qPDOb/rkrB5Bi5w7wv9rBxr1r6RcR99UpGjx49itVqJTY21uV4bGwsWVk1z7Let28fGzduZOfOnXzwwQc8++yzvPvuu9x6661nfJ05c+YQGRnp3BITE+sTpjSC2JCq/3PNqHeTyjtJCzH03GjuGnUe4Bj+fMdbO8jKLTE4KhHxVo0+m95ms2EymVixYgUXXHABl1xyCfPmzWPZsmVnbB194IEHyM3NdW7p6erSNJoK33uAuumlBbl9ZGeGnxcDwLHCMm5/YzvlVpvBUYmIN6pXMhodHY3FYiE727WbNjs7m7i4uBqviY+Pp3379kRGRjqPdevWDbvdTkZGzSvRBAYGEhER4bKJsaqXd1I3vZsi1U0vLYfZbOLZyX1oFxkEwNYDJ/jHpz8ZHJWIeKN6JaMBAQH069ePL7/80nnMZrPx5ZdfMmjQoBqvGTJkCIcPH6agoMB5bM+ePZjNZhISEmq8Rpqf6i2j6qZ3U0T1llEtCSrer1VoAAuu7Yu/xTGA9JWNaazeqZ4TEamfenfTz549m5dffplly5axe/dubrnlFgoLC5kxYwbg6GKfNm2a8/xrrrmGNm3aMGPGDHbt2sX69eu55557uP766wkODvbcVyKNSoXvPcAvEELbOvY1ZlRaiJQOrXj4d92dj+9Z+T1pRwsNjEhEvE29k9HJkyfz9NNP8+ijj9KnTx9SU1NZvXq1c1JTZmYmBw8edJ4fFhbG559/zsmTJ+nfvz/XXnst48eP5//+7/8891VIo2sT3AY/s2M5QLWMNkDluNH8TFCJLGkhpg3qyPje7QDIL63glte3UVxmNTgqEfEWJru9+S8Fk5eXR2RkJLm5uRo/aqCx743lUMEhwgPC+erqr4wOxzu9PQV2f+zYv/MHiOpgbDwiHlJQWsGE5zfya46jVXRivwSemtjb4KhEpCm5m69pbXo5a5XjRvPL8iksVzecW6rXGtW4UWlBwgL9eHFKP4L9LQCs3JbB298erOMqERElo1IP1ceNqqveTao1Ki3YebHhzL2yp/PxIx/9yI+Hcw2MSES8gZJROWtKRj1AtUalhZvQpz1TfuMYflJWYePWFdvJLdb4aBE5MyWjctZU+N4DtCSo+IBHLu1OrwRHbekDx4q4Z+V3eMH0BBExiJJROWtqGfUAddOLDwj0s7Dgmr5EBvsD8NmubF7esM/gqESkuVIyKmdNtUY9IKwtnCqRpQlM0pIltg5h/uSq2fT/WP0zW9KOGxiRiDRXSkblrLksCVqoJUHdYrZAhKMeI3lKRqVl+23XWG4beQ4AVpud29/YTk5+qcFRiUhzo2RUzlq4fzih/qEAZBWpm95tleNGi09AmUpkScs2++IuDD6nDQBH8kuZ9eYOKqw2g6MSkeZEyaicNZPJRFyIo3U0qzBLExLcpXGj4kMsZhPPXZVC2/BAADbvO8b8L/YYHJWINCdKRqVe4sIcyWiptZQTpScMjsZLqbyT+JiY8ECev6YvFrMJgAVrfuW/P2moj4g4KBmVeqlsGQVNYnJbpMo7ie+5ILk194/t6nx819vfkX68yMCIRKS5UDIq9aLyTh6gJUHFR828MJnR3WMByC0u59YV2ymtsBoclYgYTcmo1Ev1wvdKRt3k0k2vllHxHSaTiacm9qZjmxAAfjiUy19W7TI4KhExmpJRqRe1jHqASze9WkbFt0QG+/PCtX0J9HP8+Xn964N8uEMfykR8mZJRqRctCeoBQVFwqkSWuunFF/VoF8lfJpzvfPzA+z+wJzvfwIhExEhKRqVeYkNjnftqGXWTyVTVOpp7CFQiS3zQpAGJTOzn+DkoLrdy8+vbKC7T+FERX6RkVOol0BJI66DWgJLRBqkcN1pRDEVaIlF8018uP5+uceEA7Msp5N1tKnUm4ouUjEq9VY4bzSnOocJWYXA0XkrjRkUI8rfw9MSq9etXbtPPgogvUjIq9VY5btRmt5FTlGNwNF5K5Z1EADi/fSQ920cC8H1GLrsz8wyOSESampJRqbfqM+o1iclNWhJUxGlS/6qfh5Vb9eFMxNcoGZV6U61RD9CSoCJOl/VuT8CpUk8f7MhQIXwRH6NkVOqt+ox6tYy6KTKxal9LgoqPiwzxZ2wPR4/LiaJyvtx9xOCIRKQpKRmVequ+Pr1aRt0U0a5qX930IkweUPUB7Z2t6i0Q8SVKRqXe1E3vAf7BENLGsa8JTCIM6tSG9lHBAKzfk0NmbrHBEYlIU1EyKvUWHRyNn8kPgKwiJaNuq5zElJ8JVpXIEt9mNpuYeGoik80O729Xj4GIr1AyKvVmMVtoG9IWUMtog1SWd7JboUDvo8gf+iVgMjn239majl2rk4n4BCWj4pbK8k4nS09SXKHuNLeovJOIi4RWIQw5JxqAA8eK2JKm1clEfIGSUXFL9Vqjah11k8o7iZxmYrWao29rIpOIT1AyKm5R4XsPcFkSVC2jIgBjesQREeQYk/7JD5nkl5QbHJGINDYlo+KW6jPqswuzDYzEi2lJUJHTBPlbuDzF0WtQUm5j1ff6sCvS0ikZFbeoZdQDNGZUpEaT+qvmqIgvUTIqbtGYUQ8IjwOTxbGfp5ZRkUo92kXQLT4CgB0HT7I3O9/giESkMSkZFbdU76ZXy6ibzJaqlZjUTS/iZDKZmFRtItPKbfr5EGnJlIyKWyICIgj2c6yWopbRBog4NaO+6BiUq0SWSKXL+7QnwOL4E/X+9gzKrTaDIxKRxqJkVNxiMpmcXfXZRdkqTu0ul/JOGhnsDV8AACAASURBVDcqUqlVaAAXd48F4GhBGf/96YjBEYlIY1EyKm6LC3Eko8UVxeSW5hocjZdyKe+krkiR6iYNqJrItFITmURaLCWj4rb4sKpxo1qj3k0q7yRyRkM7RxMfGQTAmp9zOJJXYnBEItIYlIyK2ypbRgEyCzSJyS0q7yRyRhaziT/0c/yMWG123t+hnxGRlkjJqLjNpbyTWkbdoyVBRWpVmYyCo+aoxqeLtDxKRsVtKnzvAZFVY+K0JKjI6Tq2CeU3nVoDsC+nkO0HTxgckYh4mpJRcVv1WqMq7+Sm4FZwqkSWxoyK1Kz6ikxvf6seBJGWRsmouC02NNa5r2TUTSZT1bjR3EOgLkiR04w7P57wQD8AVn2fSWFphcERiYgnKRkVtwX7BRMVGAUoGW2QynGj5YVQctLYWESaoeAAC+P7OFYrKyqz8u8fNCxIpCVRMioNUtlVf6ToCFab1eBovJTKO4nUqXpXvWqOirQsSkalQSq76q12KznFOQZH46VU3kmkTr0TIjkvNgyAb/efYF9OgcERiYinKBmVBtEkJg9QeSeROplMJtfW0W3qRRBpKZSMSoO41BpVMuoelyVB1TIqciaXp7THz2wC4L1tGVRYbQZHJCKeoGRUGkQtox6gMaMiZyU6LJCLurUF4Eh+Kev2aGiQSEugZFQaRIXvPcClm14toyK1mTygqqv+HU1kEmkRlIxKg6hl1AMCQh3F70EtoyJ1GHZuDG3DAwH4cvcRjhaUGhyRiDSUklFpkOjgaMwmx7eRWkYboHLcaP5hUIkskTPys5i58tR69RU2Ox/uUG+CiLdTMioN4mf2IyY4BoDsomyDo/FileNGbRVQcMTYWESauYn9qsZZv/1tOnatXCbi1ZSMSoNVdtUfLzlOSUWJwdF4qUhNYhI5W51iwhiQ5BjasvdIAanpWrlMxJspGZUGqz6JSa2jbqo+iSlPyahIXSb2rz6RST8zIt5Myag0mCYxeYDKO4nUy+96xhMaYAHg4+8OU1ymsdYi3krJqDRY5ZKgoElMbtOSoCL1Ehrox6W92gFQUFrBpzv1u0fEWykZlQZTy6gHaElQkXqbNKDqQ5xqjop4LyWj0mBaEtQDwuPhVIksLQkqcnb6dmhFp5hQAL7ed5wDxwoNjkhE3KFkVBpMLaMeYPGHsFNJvcaMipwVk8nEpGoTmd7dpp8dEW/kVjK6YMECkpKSCAoKYuDAgWzZsuWsrtu0aRN+fn706dPHnZeVZioqMIpAi2NFFI0ZbYDKcaOFOVChVWVEzsYVKe2xmE2AIxm12lRzVMTb1DsZffvtt5k9ezaPPfYY27dvp3fv3owZM4YjR2ov1H3y5EmmTZvGRRdd5Haw0jyZTCZnV31WYZYKULvLpbyTuupFzkbbiCBGdnEsvJGZW8KGvTkGRyQi9VXvZHTevHnceOONzJgxg+7du7Nw4UJCQkJYsmRJrdfdfPPNXHPNNQwaNMjtYKX5qkxGiyqKyCvLMzgaL6XC9yJuqd5Vv1I1R0W8Tr2S0bKyMrZt28aoUaOqbmA2M2rUKDZv3nzG61599VX27dvHY489dlavU1paSl5enssmzVtciCYxNViEyjuJuGNk17ZEhwUA8NmuLI4XlhkckYjUR72S0aNHj2K1WomNjXU5HhsbS1ZWzQnI3r17uf/++3n99dfx8/M7q9eZM2cOkZGRzi0xMbHui8RQ8WFVk5i0CpObXMo7qXVH5Gz5W8xc0dfxYa7cauejVH2YE/EmjTqb3mq1cs011/D4449z3nnnnfV1DzzwALm5uc4tPV3145q76i2jmQWaxOSW6t30WhJUpF4m9qv6+Xn723SNXRfxImfXVHlKdHQ0FouF7GzXlq/s7Gzi4uJOOz8/P5+tW7eyY8cObr/9dgBsNht2u53/396dx0dd3/sef8+SmexByE6CICKKSJAtRm1FQPG0WrV1qVqxeOw9IFqRe4+W20Lt6T3icbsoxbq33gqyqLgURTkBscoeiGURREVZsyFkX2d+948hQ1JDJZOZ+c4kr+fjkYeT30zgA/4S3vNdPl+n06n3339f48aN+9bXud1uud3uzpQGw9q1d6pjmj4gHAkKBGxQRpLO79dLW/cd066Sam0/WKXzclJMlwXgFHRqZNTlcmnkyJEqLCz0X/N6vSosLOxwY1JycrK2bdum4uJi/8eUKVM0ePBgFRcXKz8/v+t/AkSEto3vae8UoIRU6XiLLNaMAp3XdiMTJzIB0aPT0/QzZszQc889p5deekmffvqppk6dqtraWk2ePFmSb4p90qRJvl/cbtfQoUPbfaSnpys2NlZDhw5VQkJCcP80MIZTmILAZjuxbpSRUaDTrhyWpbgYhyTpzeKDamj2GK4IwKnodBi98cYb9eijj2r27NkaPny4iouLtWLFCv+mpsOHD2vfvn1BLxSRLT4mXsmuZEmE0S5pXTfaVC01VJqtBYgySbEx+sF5viVDVQ0tem8HP4uAaGCzomCVd1VVlVJSUlRZWank5GTT5eAkrnvrOu0+ultOu1Obb9ksh91huqTos2yq9MlC3+Opa6WMc83WA0SZDV8e0Y3PrpckXXxmql6+g+VgQLgEmtc4mx5B0zpV3+Jt0ZGGI4ariVIp9BoFumLMgN7q3ydekvTxFxXa/02d4YoAfBfCKIKGdaNB0O5IUNaNAp1ls9l0/fGNTJYlvbaF7yMg0hFGETSE0SDgSFCgy348oq/sNt/jpZsPyOuN+NVoQI9GGEXQ0N4pCDgSFOiyrJQ4ff+sNEnSwWP1WvsFy4aASEYYRdC0a3zPyGhgOBIUCIob6TkKRA3CKIKGafogcCdJscdPjWHNKBCw8edkqHeCS5K0YkeJKuuaDVcE4GQIowia9Ph02eRbqEUY7YLWqfrKg5LXa7YWIEq5nHZdM9w309DU4tVbn7DsBYhUhFEETYw9RmlxvnVarBntgtZNTN5mqbbcbC1AFLth9Ik12Es2M9MARCrCKIIqM9E3VX+k4YiaPE2Gq4lSrBsFguLszGQNy/Ete9l2sFI7D1UZrghARwijCKrM+BPrRktrSw1WEsXatndi3SjQJdezkQmIeIRRBFW7TUx1rBsNCO2dgKD5UV623E7fP3VvFB9UY4vHcEUA/hFhFEFFe6cgoPE9EDQpcTH6l6G+N8nH6pr13zvLDFcE4B8RRhFUNL4PAo4EBYLqBqbqgYhGGEVQMTIaBEnZ0vEWWYyMAl13wRl9lHNanCTpwz3lOnSs3nBFANoijCKoMhIy/I8ZGQ2Q0yUlHv97ZM0o0GV2u03Xj/SNjlqW9FoRb/KASEIYRVD1ju0tl9136gkjo13QOlVfUyq10CIL6KrrRuXIdnzCYWnRAXm9ltmCAPgRRhFUdpvdPzpKGO0C/yYmS6o+ZLQUoDvo2ytOF5+ZKkna902dNuz9xnBFAFoRRhF0retGa5prVN1UbbiaKJXMjnog2NpuZFrKRiYgYhBGEXTteo0yOhqYFHqNAsF22ZAMpcTFSJLe2X5YVQ3NhisCIBFGEQIZ8Sc2MRFGA0R7JyDoYmMcumZ4tiSpodmrv37CJksgEhBGEXRZiW3aO3EKU2BofA+EBMeDApGHMIqga3s+/eEaRh4CwpGgQEgM7ZuiIVnJkqTi/cf0WSnr2gHTCKMIuraN70vrSg1WEsUS0iSHr0UWI6NAcN0w6sSbvSWbGB0FTCOMIug4EjQI7HYp2be2jTWjQHBdc35fuRy+f/6WbT2ophav4YqAno0wiqBLdCUqKSZJEhuYuqR1qr6hUmpkKhEIll7xLl1+rm+j5ZHaJq3aVWa4IqBnI4wiJNo2vvdajDoEhPZOQMjQcxSIHIRRhETrutFmb7O+aeCkk4C0be/EulEgqC46M1XZKbGSpNW7y1Ra1WC4IqDnIowiJGh8HwRtR0ZZNwoElcNu03Ujfd9jXkt6bQvfY4AphFGERNsd9YTRANHeCQip60a2nao/IMuyDFYD9FyEUYQEI6NBQON7IKT69YnXhQP7SJL2VtRq89dHDVcE9EyEUYQE7Z2CgCNBgZBru5GJnqOAGYRRhAQjo0EQmyK5fSfFMDIKhMYVQzOVFOuUJC3fdlg1jS2GKwJ6HsIoQiIjPsP/mDDaBcnHR0crD0qsZwOCLjbGoR/l+Q6YqGvy6J2/M5MDhBthFCHhcriUGpcqiTDaJa1T9Z5GqbbCbC1AN9Vuqp6eo0DYEUYRMpnxvqn68vpyNXuaDVcTpWjvBITcsJwUDc7wnRq3+euj+rysxnBFQM9CGEXIZCX62jtZslRWz3F7AUlmRz0QajabTdePOvG9trSI0VEgnAijCJm260YP17AOKyAcCQqExbXn91WMwyZJeq3ooJo9HGMMhAthFCHTrvF9HetGA9LuSFBGa4BQ6ZPo1oRzfG+gK2oatWZ3ueGKgJ6DMIqQob1TELRbM8rIKBBKbGQCzCCMImQIo0GQ3HZklDAKhNL3BqUqI9ktSVq1q0zl1Y2GKwJ6BsIoQobz6YPA6ZYS0n2P2cAEhJTTYddPRvhmI1q8lpZt5XsOCAfCKEKmT1wfOe2+k004ErQLWteN1pRItMgCQur6dlP1B2Rx2AQQcoRRhIzdZvfvqGdktAta141aXqmaUA+E0oDUBI0Z0FuS9HlZjbbuP2a4IqD7I4wipFrXjVY1Vamuuc5wNVEqmfZOQDi13ci0lI1MQMgRRhFSrBsNgnbtnVjDBoTaD87LVILLIUl6+5PDqmtqMVwR0L0RRhFSbXfUs240QBwJCoRVvMupq/KyJUk1jS16dxtvpIFQIowipBgZDQKOBAXCru1GpsVM1QMhRRhFSDEyGgQcCQqE3Yh+vTQwLUGStHHvN9pbUWu4IqD7IowipGh8HwSJ6dLxFllM0wPhYbPZdOPoE6OjrxYxOgqECmEUIdUujHI+fWDsDinZt36NaXogfK49P0cOu02S9GrRAXm89BwFQoEwipBKiklSvDNeEiOjXdK6brT+qNTEdCEQDmlJbo0723cCWmlVo9Z8Vma4IqB7IowipGw2m38TU0ltCaeZBIp1o4ARbXuO/sfbO1XVwCloQLARRhFyrVP1jZ5GHW08ariaKNW21yjrRoGwuXRwmoblpEiSvjpSp/uW/p031UCQEUYRcmxiCoIU2jsBJjgdds2/eYRS4mIkSSt2lOiFj/YargroXgijCDnaOwUBR4ICxuT2jtfjN+T5P5/z7i5t+uobgxUB3QthFCFH4/sg4EhQwKjx52TozrEDJUker6W7Fm5RRU2j4aqA7oEwipBjmj4IOBIUMG7GZWep4Iw+kny76+9ZtJV2T0AQEEYRcoyMBkFsLynGdxoM0/SAGU6HXU/cNFzpSW5J0sefH9Hc//7McFVA9COMIuQyEjL8jwmjAbLZToyOVh6Q2M0LGJGeFKs/3DzC3wx/3qrPtXo3/UeBrggojM6fP1/9+/dXbGys8vPztXHjxpO+9vXXX9dll12mtLQ0JScnq6CgQO+9917ABSP6uB1u9Y7tLYkNTF3Sum60pd7X/B6AEWMG9Nb9Vwz2f37v4mIdOFpnsCIgunU6jC5evFgzZszQb3/7W23ZskV5eXmaOHGiyso6fmf44Ycf6rLLLtM777yjoqIiXXrppbrqqqu0devWLheP6NG6brS8vlwt3hbD1USpdu2dOCcbMOkX3ztDlw/xzfocq2vWtAVb1NjiMVwVEJ06HUYff/xx/eIXv9DkyZM1ZMgQPf3004qPj9eLL77Y4evnzp2r++67T6NHj9agQYP04IMPatCgQXr77be7XDyiR2a8L4x6La/K68oNVxOlaO8ERAybzaZHrs/T6X18xx1/cqBS/7n8U8NVAdGpU2G0qalJRUVFmjBhwolfwG7XhAkTtG7dulP6Nbxer6qrq9W7d++TvqaxsVFVVVXtPhDdshLbbGKqY91oQGh8D0SUlLgYPXXLCLmcvn9K/9+6r/VmMW8Ugc7qVBitqKiQx+NRRkZGu+sZGRkqKTm1gPHoo4+qpqZGN9xww0lfM2fOHKWkpPg/cnNzT/paRIfWkVFJOlzDutGAcCQoEHHOzU7R768+1//5zNe3aU9ptcGKgOgT1t30Cxcu1O9+9zstWbJE6enpJ33dzJkzVVlZ6f/Yv5/1cdEuM7FNr1FGRgOTzMgoEIluGJWr60b6vj/rmjyaumCLahtZGw+cqk6F0dTUVDkcDpWWlra7XlpaqszMzJN8lc+iRYt0xx13aMmSJe2m+TvidruVnJzc7gPRjZHRIGh3ChNTgUCksNls+v3VQ3V2ZpIk6fOyGs18fZssWrABp6RTYdTlcmnkyJEqLCz0X/N6vSosLFRBQcFJv+6VV17R5MmT9corr+iHP/xh4NUiarVrfM/IaGBi4qR43+kvjIwCkSXO5dAffzZSiW6nJOmtTw7p5fVfG64KiA6dnqafMWOGnnvuOb300kv69NNPNXXqVNXW1mry5MmSfFPskyZN8r9+4cKFmjRpkh577DHl5+erpKREJSUlqqysDN6fAhEvNS5VTpvvh3Rpbel3vBon1bqJqfqw5KWNDBBJBqQm6NHrh/k//4+/7lTx/mMGKwKiQ6fD6I033qhHH31Us2fP1vDhw1VcXKwVK1b4NzUdPnxY+/bt87/+2WefVUtLi6ZNm6asrCz/xz333BO8PwUinsPuUFp8miQa33dJ67pRyyNVM8IMRJorhmbpjosHSJKaPZamLdiio7VNhqsCIpvNioJFLVVVVUpJSVFlZSXrR6PYbe/epi1lWyRJG2/ZqDhnnOGKotA790kbn/E9vv19qV++2XoAfEuzx6ufPrteRV/7TkobOzhNL942WvbjR4gC3VWgeY2z6RE2nFEfBLR3AiJejMOu+TePUJ8ElyTpg93leuqDzw1XBUQuwijCpt0mJsJoYGh8D0SFzJRYPfHT82U7Phj6+MrP9PHnFWaLAiIUYRRh03o+vUQYDRhHggJR4+JBqZox4SxJkteSfvnKVpVUNhiuCog8hFGEDSOjQcDIKBBVpl16psYO9m3ePFLbpLsWblGzx2u4KiCyEEYRNm1HRtlRH6CkTMnm8D1mzSgQ8ex2m/7vDcPVt5dvw+bmr4/qv97dZbgqILIQRhE2jIwGgd0hJR3/e2RkFIgKpyW4NP+WEYpx+BaQPv/RXq3YzhtyoBVhFGGT7Er2t3PiFKYuaJ2qrzsiNdebrQXAKRme20uzrhzi//zfl/5deytqDVYERA7CKMLGZrP5p+pLaks4tzlQ7do7HTJXB4BOufWC03VVXrYkqbqxRVNfLlJ9EyepAYRRhFVmvC+M1rfUq6qpynA1UardJqb95uoA0Ck2m00P/fg8nZmeKEnaVVKt2W9uN1wVYB5hFGHFJqYgoL0TELUS3E798ZYRiovxbURcWnRASzbxphI9G2EUYcUmpiCgvRMQ1QZlJOmhn5zn/3zWm9u141ClwYoAswijCCtGRoOAI0GBqHf18L669YLTJUmNLV7duWCLKuubDVcFmEEYRVhxClMQpOSeeMzIKBC1fnPlORqWkyJJ+vpInf596Sds7ESPRBhFWDEyGgRxp0nHW2SxZhSIXm6nQ/NvHqGUuBhJ0vs7S/Xc3740XBUQfoRRhFXbMFpaW2qwkihms52Yqq88IDGSAkSt3N7xmnvjcP/n/7Vitzbu/cZgRUD4EUYRVnHOOPVy95LENH2XtG5iaq6VGo6ZrQVAl1x6drruuvRMSZLHa2nawi16Z9thtXCGPXoIwijCrnVHfWldqTxeGj4HhPZOQLdy72Vn6cKBfSRJ5dWNunPBFl3yyAd6es0XOlbXZLg6ILQIowi7jIQMSZLH8qiivsJwNVGK9k5At+Kw2/TkTecr7/iGJkk6eKxeD727SwVzVunXy7bp87JqgxUCoUMYRdi1nsIksYkpYLR3Arqd1ES33ph2kV7+13yNPzvdf72+2aMFG/ZpwuMf6tYXNmj17jJ5vawVR/fhNF0Aep6sxDaN7+tYNxoQRkaBbslms+niQam6eFCq9lbU6qW1X2np5v2qPX6G/d/2VOhveyp0RmqCfn5Rf/1kRI4S3PxTjujGyCjCru3IaEkNYTQgrBkFur0BqQl64Efnat3/Hq9ZVw5Rbu84/3NfVtRq9ps7dMGcQv3n8p3a/02dwUqBriGMIuwYGQ2CttP0jIwC3VpybIz+9eIB+uB/Xapnbx2pgjP6+J+rbmjRc3/bq0seWa1/+8tmrf/yCI3zEXUY20fYtVszWsOa0YC4EnzN7+uPsmYU6CEcdpsuPzdTl5+bqZ2HqvTntXv1RvEhNbV45bWk93aU6r0dpRqSlazJF/XXVXnZio1xmC4b+E6MjCLs0uLTZLf5bj1GRrugdd1o1SGJFllAjzIkO1kPX5endb8ap/952VlKT3L7n9t5uEr//urfddFDq/T4ys9UVt1gsFLguxFGEXZOu1NpcWmSaHzfJa3rRr0tUk2Z2VoAGNEn0a27xw/SR/eP0xM/Hd6uNdSR2iY9WbhHFz20SvcuLta2A5UGKwVOjml6GJGVkKXSulJ90/CNGj2Ncjvc3/1FaK9de6eDUnLWyV8LoFtzOe26enhf/SgvW1v2HdOfPt6rd7eXyOO11OyxtGzrQS3belCjTj9Nky8aoInnZsjpYDwKkYEwCiMyEzKlct/j0tpS9UvuZ7agaNSuvdN+KWeUuVoARASbzaaRp5+mkaefpkPH6vWX9V/rlY37dKyuWZK0+euj2vz1UWWnxOrWgv66aUyuesW7DFeNno63RTCi9UhQicb3AaO9E4B/IrtXnO6/4myt+9V4zfnxeTorI9H/3KHKBv3Xil0a++gH2vDlEYNVAoRRGNJ6JKjEutGA0fgewCmIczl005h+em/69/2nO9lsvueO1TXr1hc26s1i3tDCHKbpYURmAkeCdhlHggLohLanO31VUavZb+3Qh5+Vq8nj1T2LinXgaL3uHDtQttakCoQJI6Mwou00PSOjAUrKko63yGJkFEBn9E9N0Iu3jdJNY06s13/kvd2a+fo2NXu8BitDT0QYhRFtR0YJowFyxEiJx/8eWTMKoJOcDrsevHao7r/ibP+1RZv2619f2qzqhmaDlaGnIYzCiNPcp/nbORFGu6B13WhtmdTSaLYWAFHHZrNp6tiBmnfT+XIdb/X04Wfluv7pdTpcWW+4OvQUhFEYYbPZ/KOjh2sPc5ZyoP6x1ygABOCqvGwt+EW+esXHSJJ2lVTr2vlrtfNQleHK0BMQRmFMaxita6lTdXO14WqiVHKbMMq6UQBdMLp/b7029UL16x0vSSqpatD1T6/Vms/KDVeG7o4wCmMy41k32mUpuSces24UQBcNTEvU63deqOG5vSRJtU0e3f7nTVq0cZ/hytCdEUZhTFYiO+q7jPZOAIIsNdGtRf/jAl1xrm/AwOO19KvXt+mR93bJ62VJFYKPMApjGBkNAhrfAwiB2BiH5t8yQndcPMB/bf7qLzR9cbEaWzwGK0N3RBiFMTS+DwKOBAUQIg67Tb+5coh+96NzZT/eB/+tTw7p1uc36lhdk9ni0K0QRmEMje+DICFVOt4ii5FRAKFw24X99cytoxQX45AkbfzqG/34j2u170id4crQXRBGYQwjo0Fgs51YN0prJwAhctmQDC3+twuUmuh78/tlea2ufepjbd131HBl6A4IozAmPiZeya5kSYyMdknrutHGKqmh0mwtALqtYTm9tOzOC3VmeqIk6Uhtk256br1WbOfnN7qGMAqjWkdHS+tK5bU4DzkgrBsFECa5veP12pQLdcEZvSVJDc1eTV1QpBc+2mu4MkQzwiiMal032uJt0ZH6I4ariVLsqAcQRinxMXrp9jG69nzfEiHLkn7/15164K0d8tD6CQEgjMKotutGmaoPEL1GAYSZ2+nQ4zfk6ZfjzvRf+/ParzTl5SLVNbUYrAzRiDAKo9jEFARM0wMwwGazacblg/XwT4bJebz308qdpbrp2fUqr240XB2iCWEURjEyGgRM0wMw6IbRufrT5NFKcjslSZ8cqNS1T32sz8uqDVeGaEEYhVFtT2FiZDRA7abpGRkFEH7fG5SmpVMLlJUSK0k6cLReP35qrdZ/yV4AfDfCKIxqez59aV2pwUqimDtJik3xPa7cb7YWAD3W2ZnJemPaRRqS5WvZV9XQoltf2KA3tvImGf8cYRRGpcenyybfWqPDNYyMBqx13WjVIclLiywAZmQkx2rJlAKNHZwmSWr2WJq+uFjzCvfIsthpj44RRmFUjD1GaXG+H1oldawZDVjrulFPk1RbbrYWAD1aotup5yeN0s35/fzXHlv5me5csEXbD3IwB76NMArjWjcxVdRXqMnTZLiaKEV7JwARxOmw6z+vGapf/cvZ/mvvbi/RlfM+0g3PrNOK7YfpSQo/wiiMa7ujnnWjAWJHPYAIY7PZNOWSgfrDzecrJS7Gf33j3m805eUt+v7Dq/Xsh1+osr7ZYJWIBIRRGEd7pyCg1yiACHXlsGytmzlO/+eaof5z7SXp4LF6PfjOLhXMKdSsN7bri/Iag1XCJKfpAoDWI0ElwmjAaO8EIILFu5z62QWn65b8fvrbngq9+PFefbDbt769rsmjv6z/Wn9Z/7UuOStNt188QN8flCqbzWa4aoQLYRTGMTIaBO2m6WnvBCAy2Ww2ff+sNH3/rDR9UV6jP3/8lV7bckB1TR5J0prPyrXms3INTEvQzy8aoJ+M6Kt4F1Glu2OaHsa1HRml8X2AkrKl4y2y9OUH0tv3SFtflsp20eoJQEQamJao318zVOtmjtevf3CO+vaK8z/3RXmtZr2xXRc8WKg573yqA0frDFaKULNZUdD4q6qqSikpKaqsrFRycrLpchBkFfUVunTJpZKk7/X9np6a8JThiqLUE3nS0a++fd2dLPUdKeWMknJGS31HSQl9wl4eAPwzLR6v/vvTUr348VfaYNC6cwAAC8lJREFUuPebds/ZbdLEczN1+8UDNOr005jCj1CB5jXCKIzzWl6NenmUmr3NOrPXmVp29TLTJUWnPSulwt9JpTsk6ztGQ08b4AumOaN8HxnnSU5XeOoEgO+w/WCl/rz2K71VfEhNnvY/z4b2TdbkCwfoyrwsuZ0OQxWiI2ENo/Pnz9cjjzyikpIS5eXlad68eRozZsxJX//BBx9oxowZ2rFjh3Jzc/Wb3/xGP//5z0/59yOMdn8/eP0H2l+9X0kxSVp781rT5US3xhrpcLF0YJN0YLPvvzXf0TLL4Zay8o4H1JG+/6bkSow+ADCovLpRCzfs08sbvlZ5dWO751IT3frZBf10S/7pSktyG6oQbYUtjC5evFiTJk3S008/rfz8fM2dO1dLly7V7t27lZ6e/q3X7927V0OHDtWUKVN0xx13qLCwUNOnT9fy5cs1ceLEU/o9CaPd3+3v3a5NJZskSetuWqdEV+J3fAVOmWX5eo8e3HwinB7+RGpp+Odfl5jhm9Jvnd7PPl9y8/8FQPg1tXi1fNshvfjRV9r2D6c4uRx2XZmXpdsvGqChfVMMVQgpjGE0Pz9fo0eP1h/+8AdJktfrVW5uru6++2796le/+tbr77//fi1fvlzbt2/3X/vpT3+qY8eOacWKFaf0exJGu79ff/RrvfXFW5KkeePmKScx5zu+Al3iaZaO7JHKdkol26XS7d/dLN9mk3oPlDLOlTKGSqmDJAdT+wDCx7IsfV5eo1WflmnL/qP6hxl8DUpP1Phz0pWVEtfxL9BDFZx3hVyu0I8eB5rXOtUvoampSUVFRZo5c6b/mt1u14QJE7Ru3boOv2bdunWaMGFCu2sTJ07U9OnTT/r7NDY2qrHxxHB8VVVVZ8pEFMqIz/A/vnvV3QYr6aGSJCVlfefLpFqpaqPvY0+oiwKAk3BI6v/ty0ckrd8viQ537aw8fYQyU3NNl3FSnWrtVFFRIY/Ho4yMjHbXMzIyVFLScX/IkpKSDl9fVVWl+vr6Dr9mzpw5SklJ8X/k5kbuXyCC45w+55guAQAAGBCRnWRnzpypGTNm+D+vqqoikHZz43LH6f7R92vPMYbbIpqnWao7ItVWSI3MWACIHJak+iaP6ppaFPl9gsIr1h3ZyxY6FUZTU1PlcDhUWtp+Z25paakyMzM7/JrMzMwOX5+cnKy4uI7/ctxut9xudsb1JA67Qz8b8jPTZQAAgDDr1DS9y+XSyJEjVVhY6L/m9XpVWFiogoKCDr+moKCg3eslaeXKlSd9PQAAAHqOTh8HOmPGDD333HN66aWX9Omnn2rq1Kmqra3V5MmTJfmm2CdNmuR//ZQpU/Tll1/qvvvu065du/TUU09pyZIluvfee4P3pwAAAEBU6vSa0RtvvFHl5eWaPXu2SkpKNHz4cK1YscK/Senw4cPat2+f//UDBgzQ8uXLde+99+qJJ55QTk6Onn/++VPuMQoAAIDui+NAAQAA0GWB5rVOT9MDAAAAwUIYBQAAgDGEUQAAABhDGAUAAIAxhFEAAAAYQxgFAACAMYRRAAAAGEMYBQAAgDGEUQAAABhDGAUAAIAxnT6b3oTWE0urqqoMVwIAAICOtOa0zp40HxVhtLq6WpKUm5truBIAAAD8M9XV1UpJSTnl19uszsZXA7xerw4dOqSkpCTZbLZOfW1VVZVyc3O1f/9+JScnh6hCRBvuC3SE+wId4b5AR7gvvs2yLFVXVys7O1t2+6mvBI2KkVG73a6cnJwu/RrJycncLPgW7gt0hPsCHeG+QEe4L9rrzIhoKzYwAQAAwBjCKAAAAIxxPPDAAw+YLiLUHA6Hxo4dK6czKlYlIEy4L9AR7gt0hPsCHeG+CI6o2MAEAACA7olpegAAABhDGAUAAIAxhFEAAAAYQxgFAACAMd06jM6fP1/9+/dXbGys8vPztXHjRtMlIYw+/PBDXXXVVcrOzpbNZtMbb7zR7nnLsjR79mxlZWUpLi5OEyZM0J49ewxVi3CZM2eORo8eraSkJKWnp+uaa67R7t27272Ge6Pn+eMf/6hhw4b5G5gXFBTo3Xff9T/PPQFJeuihh2Sz2TR9+nT/Ne6Nruu2YXTx4sWaMWOGfvvb32rLli3Ky8vTxIkTVVZWZro0hEltba3y8vI0f/78Dp9/+OGH9eSTT+rpp5/Whg0blJCQoIkTJ6qhoSHMlSKc1qxZo2nTpmn9+vVauXKlmpubdfnll6u2ttb/Gu6NnicnJ0cPPfSQioqKtHnzZo0bN05XX321duzYIYl7AtKmTZv0zDPPaNiwYe2uc28EgdVNjRkzxpo2bZr/c4/HY2VnZ1tz5swxWBVMkWQtW7bM/7nX67UyMzOtRx55xH/t2LFjltvttl555RUTJcKQsrIyS5K1Zs0ay7K4N3DCaaedZj3//PPcE7Cqq6utQYMGWStXrrQuueQS65577rEsi58XwdItR0abmppUVFSkCRMm+K/Z7XZNmDBB69atM1gZIsXevXtVUlLS7h5JSUlRfn4+90gPU1lZKUnq3bu3JO4NSB6PR4sWLVJtba0KCgq4J6Bp06bphz/8Ybt7QOLnRbB0yyMDKioq5PF4lJGR0e56RkaGdu3aZagqRJKSkhJJ6vAeaX0O3Z/X69X06dN10UUXaejQoZK4N3qybdu2qaCgQA0NDUpMTNSyZcs0ZMgQrV27VhL3RE+1aNEibdmyRZs2bfrWc/y8CI5uGUYB4FRMmzZN27dv10cffWS6FESAwYMHq7i4WJWVlXr11Vd12223ac2aNabLgkH79+/XPffco5UrVyo2NtZ0Od1Wt5ymT01NlcPhUGlpabvrpaWlyszMNFQVIknrfcA90nPddddd+utf/6rVq1crJyfHf517o+dyuVw688wzNXLkSM2ZM0d5eXl64oknuCd6sKKiIpWVlWnEiBFyOp1yOp1as2aNnnzySTmdTv+IKPdG13TLMOpyuTRy5EgVFhb6r3m9XhUWFqqgoMBgZYgUAwYMUGZmZrt7pKqqShs2bOAe6eYsy9Jdd92lZcuWadWqVRowYEC757k30Mrr9aqxsZF7ogcbP368tm3bpuLiYv/HqFGjdMstt6i4uFhnnHEG90YQOB544IEHTBcRCsnJyZo1a5Zyc3Pldrs1a9YsFRcX64UXXlBiYqLp8hAGNTU12rlzp0pKSvTMM88oPz9fcXFxampqUq9eveTxePTggw9qyJAhampq0i9/+UvV1dVp3rx5cjpZwdJdTZs2TQsWLNCrr76q7Oxs1dTUqKamRg6HQzExMbLZbNwbPdDMmTPlcrlkWZb279+vuXPnasGCBXr44Yc1cOBA7okeyu12Kz09vd3HwoULdcYZZ2jSpEn8vAgW09v5Q2nevHlWv379LJfLZY0ZM8Zav3696ZIQRqtXr7YkfevjtttusyzL15Jj1qxZVkZGhuV2u63x48dbu3fvNls0Qq6je0KS9ac//cn/Gu6Nnuf222+3Tj/9dMvlcllpaWnW+PHjrffff9//PPcEWrVt7WRZ3BvBYLMsyzKUgwEAANDDdcs1owAAAIgOhFEAAAAYQxgFAACAMYRRAAAAGEMYBQAAgDGEUQAAABhDGAUAAIAxhFEAAAAYQxgFgDAaO3aspk+fbroMAIgYhFEAAAAYQxgFAACAMYRRADBo+fLlSklJ0YIFC0yXAgBGOE0XAAA91cKFCzVlyhQtXLhQV155pelyAMAIRkYBwID58+frzjvv1Ntvv00QBdCjMTIKAGH26quvqqysTB9//LFGjx5tuhwAMIqRUQAIs/PPP19paWl68cUXZVmW6XIAwCjCKACE2cCBA7V69Wq9+eabuvvuu02XAwBGMU0PAAacddZZWr16tcaOHSun06m5c+eaLgkAjCCMAoAhgwcP1qpVqzR27Fg5HA499thjpksCgLCzWSxYAgAAgCGsGQUAAIAxhFEAAAAYQxgFAACAMYRRAAAAGEMYBQAAgDGEUQAAABhDGAUAAIAxhFEAAAAYQxgFAACAMYRRAAAAGEMYBQAAgDH/H/orLa4FaWgWAAAAAElFTkSuQmCC", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Insert your code here.\n", "\n", "N = 600\n", "P = Int(N/2)\n", "Phi = PhiRand(P, N)\n", "klist = Array{Int64,1}(round(linspace(1, P/7., 20)))\n", "ntrials = 60\n", "proba = zeros(length(klist), 3)\n", "\n", "for i in 1:length(klist)\n", " proba[i, 1:3] = 0\n", " k = Int(klist[i])\n", " for j in 1:ntrials\n", " s = zeros(N)\n", " I = randperm(N)\n", " I = I[1:k]\n", " l = randn(k, 1)\n", " s[I] = l./abs(l)\n", " proba[i, 1] = proba[i, 1] + (F(Phi, s) .< 1)\n", " proba[i, 2] = proba[i, 2] + (erc(Phi, I) .< 1)\n", " proba[i, 3] = proba[i, 3] + (werc(Phi, I) .> 0).*(werc(Phi, I) .< 1)\n", " end\n", "end\n", " \n", "figure(figsize = (8, 5))\n", "plot(klist, proba/ntrials, linewidth = 2)\n", "xlabel(\"k\")\n", "legend([\"F <1\", \"ERC <1\", \"w-ERC <1\"])\n", "title(@sprintf(\"N = %d, P = %d\", N, P))\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Restricted Isometry Criteria\n", "----------------------------\n", "The restricted isometry constants $\\de_k^1,\\de_k^2$ of a matrix $\\Phi$ are the\n", "smallest $\\de^1,\\de^2$ that satisfy\n", "$$ \\forall x \\in \\RR^N, \\quad \\norm{x}_0 \\leq k \\qarrq\n", " (1-\\de^1)\\norm{x}^2 \\leq \\norm{\\Phi x}^2 \\leq (1+\\de^2)\\norm{x}^2. $$\n", "\n", "\n", "E. Candes shows in\n", "\n", "\n", "E. J. Cand s. _The restricted isometry property and its implications for\n", "compressed sensing_. Compte Rendus de l'Academie des Sciences, Paris, Serie I, 346 589-592\n", "\n", "\n", "that if\n", "$$ \\de_{2k} \\leq \\sqrt{2}-1 ,$$\n", "then $\\norm{x_0} \\leq k$ implies identifiability as well as robustness to small and bounded noise.\n", "\n", "\n", "The stability constant $\\la^1(A), \\la^2(A)$ of a matrix\n", "$A = \\Phi_I$ extracted from $\\Phi$ is the smallest $\\tilde \\la_1,\\tilde \\la_2$ such that\n", "$$ \\forall \\al \\in \\RR^{\\abs{I}}, \\quad\n", " (1-\\tilde\\la_1)\\norm{\\al}^2 \\leq \\norm{A \\al}^2 \\leq (1+\\tilde \\la_2)\\norm{\\al}^2. $$\n", "\n", "\n", "These constants $\\la^1(A), \\la^2(A)$ are easily computed from the\n", "largest and smallest eigenvalues of $A^* A \\in \\RR^{\\abs{I} \\times \\abs{I}}$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#31) (generic function with 1 method)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "minmax = v -> (1 - minimum(v), maximum(v) - 1)\n", "ric = A -> minmax(eig(A'*A)[1])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The restricted isometry constant of $\\Phi$ are computed as the largest\n", "stability constants of extracted matrices\n", "$$ \\de^\\ell_k = \\umax{ \\abs{I}=k } \\la^\\ell( \\Phi_I ). $$\n", "\n", "\n", "The eigenvalues of $\\Phi$ are essentially contained in the\n", "interval $ [a,b] $ where $a=(1-\\sqrt{\\be})^2$ and $b=(1+\\sqrt{\\be})^2$\n", "with $\\beta = k/P$\n", "More precisely, as $k=\\be P$ tends to infinity, the distribution of the\n", "eigenvalues tends to the Marcenko-Pastur law\n", "$ f_\\be(\\la) = \\frac{1}{2\\pi \\be \\la}\\sqrt{ (\\la-b)^+ (a-\\la)^+ }. $" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 4__\n", "\n", "Display, for an increasing value of $k$ the histogram of repartition\n", "of the eigenvalues $A^* A$ where $A$ is a Gaussian matrix of size $(P,k)$ and\n", "variance $1/P$. For this, accumulate the eigenvalues for many\n", "realizations of $A$." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[1m\u001b[31mWARNING: hist(...) and hist!(...) are deprecated. Use fit(Histogram,...) in StatsBase.jl instead.\u001b[0m\n", " in depwarn(::String, ::Symbol) at ./deprecated.jl:64\n", " in #hist!#994(::Bool, ::Function, ::Array{Int64,1}, ::Array{Any,1}, ::LinSpace{Float64}) at ./deprecated.jl:629\n", " in hist(::Array{Any,1}, ::LinSpace{Float64}) at ./deprecated.jl:644\n", " in macro expansion; at /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/sparsity_6_l1_recovery/exo4.jl:22 [inlined]\n", " in anonymous at ./:?\n", " in include_from_node1(::String) at ./loading.jl:488\n", " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?\n", " in include_string(::String, ::String) at ./loading.jl:441\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at /Users/gpeyre/.julia/v0.5/IJulia/src/execute_request.jl:160\n", " in invokelatest(::Function, ::ZMQ.Socket, ::Vararg{Any,N}) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:1502\n", " in eventloop(::ZMQ.Socket) at /Users/gpeyre/.julia/v0.5/IJulia/src/eventloop.jl:8\n", " in (::IJulia.##15#21)() at ./task.jl:360\n", "while loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/sparsity_6_l1_recovery/exo4.jl, in expression starting on line 11\n", "\u001b[1m\u001b[31mWARNING: hist(...) and hist!(...) are deprecated. Use fit(Histogram,...) in StatsBase.jl instead.\u001b[0m\n", " in depwarn(::String, ::Symbol) at ./deprecated.jl:64\n", " in #hist!#994(::Bool, ::Function, ::Array{Int64,1}, ::Array{Any,1}, ::LinSpace{Float64}) at ./deprecated.jl:629\n", " in hist(::Array{Any,1}, ::LinSpace{Float64}) at ./deprecated.jl:644\n", " in macro expansion; at /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/sparsity_6_l1_recovery/exo4.jl:22 [inlined]\n", " in anonymous at ./:?\n", " in include_from_node1(::String) at ./loading.jl:488\n", " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?\n", " in include_string(::String, ::String) at ./loading.jl:441\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at /Users/gpeyre/.julia/v0.5/IJulia/src/execute_request.jl:160\n", " in invokelatest(::Function, ::ZMQ.Socket, ::Vararg{Any,N}) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:1502\n", " in eventloop(::ZMQ.Socket) at /Users/gpeyre/.julia/v0.5/IJulia/src/eventloop.jl:8\n", " in (::IJulia.##15#21)() at ./task.jl:360\n", "while loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/sparsity_6_l1_recovery/exo4.jl, in expression starting on line 11\n" ] }, { "data": { "image/png": "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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo4.jl\")\n", "\n", "# klist = [10, 30, 50]\n", "# P = 200\n", "# ntrials = 200\n", "# tmin = 0\n", "# tmax = 2.5\n", "# q = 50\n", "# t = linspace(tmin, tmax, q)\n", "# t1 = linspace(tmin, tmax, 1000)\n", "# dt = (tmax - tmin)/q\n", "\n", "# for j in 1 : length(klist)\n", "# k = klist[j]\n", " \n", "# # simulation \n", "# v = []\n", "# for i in 1 : ntrials\n", "# v = [v; svd(randn(P, k)./sqrt(P))[2].^2]\n", "# end\n", " \n", "# figure(figsize = (10, 10))\n", "# subplot(length(klist), 1, j)\n", "# h = hist(v, t)[2]\n", "# h = h/sum(h)/dt\n", "# h = [h; 0]\n", "# bar(t[1 : end], h, width = 1/20, color = \"darkblue\", edgecolor = \"black\")\n", " \n", "# # theoritical law\n", "# beta = k/P\n", "# a = (1 - sqrt(beta))^2\n", "# b = (1 + sqrt(beta))^2\n", "# z = sqrt(max(t1 - a, zeros(length(t1))).*max(b - t1, zeros(length(t1))))./(2*pi.*beta.*t1)\n", " \n", "# plot(t1, z, \"r\", linewidth = 3)\n", "# xlim(tmin, tmax)\n", "# ylim(0, maximum(h)*1.05)\n", "# title(@sprintf(\"P = %d, k = %d\", P, k))\n", " \n", "# show()\n", "# end" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 5__\n", "\n", "Estimate numerically lower bound on $\\de_k^1,\\de_k^2$ by Monte-Carlo\n", "sampling of sub-matrices." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo5.jl\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Sparse Spikes Deconvolution\n", "---------------------------\n", "We now consider a convolution dictionary $ \\Phi $.\n", "Such a dictionary is used with sparse regulariz\n", "\n", "\n", "Second derivative of Gaussian kernel $g$ with a given variance $\\si^2$." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#33) (generic function with 1 method)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sigma = 6\n", "g = x -> (1 - x.^2./sigma^2).*exp(-x.^2./(2*sigma^2))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Create a matrix $\\Phi$ so that $\\Phi x = g \\star x$ with periodic\n", "boundary conditions." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "ename": "LoadError", "evalue": "could not open file /Users/gpeyre/Dropbox/github/numerical-tours/julia/ndgrid.jl", "output_type": "error", "traceback": [ "could not open file /Users/gpeyre/Dropbox/github/numerical-tours/julia/ndgrid.jl", "", " in include_from_node1(::String) at ./loading.jl:488", " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?" ] } ], "source": [ "include(\"ndgrid.jl\")\n", "P = 1024\n", "(Y, X) = meshgrid(0:P-1, 0:P-1)\n", "Phi = normalize(g((X - Y + P/2.)%P-P/2.))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "To improve the conditionning of the dictionary, we sub-sample its atoms,\n", "so that $ P = \\eta N > N $." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "300×300 Array{Float64,2}:\n", " -0.053469 0.0881115 0.0868037 … -0.00996989 -0.0585636 \n", " 0.0164402 0.0796902 0.0188055 0.025722 -0.0623569 \n", " -0.00646314 -0.00191052 -0.0352827 -0.0794237 -0.0370294 \n", " -0.017269 0.0359245 0.0216832 -0.0292265 -0.0679947 \n", " -0.123559 -0.0629753 0.103768 0.120796 0.0438559 \n", " 0.0111852 0.0228867 -0.0079232 … 0.0242139 0.0488305 \n", " -0.0345084 0.00608496 -0.0685556 -0.0298552 -0.0461946 \n", " 0.00276266 -0.00457426 0.0113843 0.0393407 0.0983607 \n", " -0.0249077 0.0357367 -0.135996 -0.0339714 0.0289777 \n", " -0.0181583 -0.0337565 -0.0658213 0.0393399 -0.000954676\n", " -0.0437137 -0.0231178 0.00312412 … 0.0214733 -0.00883125 \n", " -0.0419627 -0.0250297 0.0321096 -0.071469 -0.0248835 \n", " -0.0845728 -0.037455 -0.0904906 0.0099785 -0.0838841 \n", " ⋮ ⋱ \n", " 0.143837 -0.0761286 0.0498835 -0.04545 0.0629725 \n", " 0.0923194 -0.0468798 0.0501927 0.0728482 0.0707002 \n", " -0.022314 -0.0734589 0.0360122 … -0.13949 -0.00776711 \n", " 0.0291248 0.00661235 0.0134569 -0.024864 -0.0150424 \n", " -0.0189033 0.0970626 0.0418395 -0.0294127 0.116598 \n", " -0.00428868 0.118131 -0.0264479 -0.0932343 -0.154828 \n", " 0.0778051 0.0158298 0.00234603 0.103604 -0.0754831 \n", " -0.101757 0.0495662 -0.021641 … 0.00244892 -0.0197873 \n", " -0.0217769 -0.0662395 0.0509761 -0.0209067 0.0325256 \n", " -0.0235321 -0.0225997 -0.0209772 -0.0167986 0.0485945 \n", " 0.0234176 -0.0300984 0.0518727 0.0182376 0.00600304 \n", " 0.0165291 -0.00807928 -0.0190766 -0.106576 -0.00476109 " ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eta = 2\n", "N = P/eta\n", "Phi = Phi[:, 1:eta:end]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Plot the correlation function associated to the filter.\n", "Can you determine the value of the coherence $\\mu(\\Phi)$?" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c = Phi'*Phi\n", "c = abs(c[:, Int(size(c)[2]/2)])\n", "\n", "\n", "figure(figsize = (8, 5))\n", "plot(c[Base.div(length(c), 2) - 50 : Base.div(length(c), 2) + 50], \".-\")\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Create a data a sparse $x_0$ with two diracs of opposite signes with spacing $d$." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(::#35) (generic function with 1 method)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "twosparse = d -> circshift([1; zeros(d, 1); -1; zeros(Int(N) - d - 2, 1)], round(N/2 - d/2))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display $x_0$ and $\\Phi x_0$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "ename": "LoadError", "evalue": "DimensionMismatch(\"A has dimensions (300,300) but B has dimensions (150,1)\")", "output_type": "error", "traceback": [ "DimensionMismatch(\"A has dimensions (300,300) but B has dimensions (150,1)\")", "", " in gemm_wrapper!(::Array{Float64,2}, ::Char, ::Char, ::Array{Float64,2}, ::Array{Float64,2}) at ./linalg/matmul.jl:309", " in *(::Array{Float64,2}, ::Array{Float64,2}) at ./linalg/matmul.jl:129" ] } ], "source": [ "x0 = twosparse(50)\n", "\n", "\n", "figure(figsize = (10, 7))\n", "subplot(2, 1, 1)\n", "plot(x0[:], \"r\", linewidth = 2)\n", "subplot(2, 1, 2)\n", "plot((Phi*x0)[:], \"b\", linewidth = 2)\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 6__\n", "\n", "Plot the evolution of the criteria F, ERC and Coh as a function of $d$.\n", "Do the same plot for other signs patterns for $x_0$.\n", "Do the same plot for a Dirac comb with a varying spacing $d$." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo6.jl\")\n", "\n", "# g = (C, I) -> sum(C[:, I], 2)\n", "\n", "# figure(figsize = (8, 5))\n", "# dlist = Array{Int64,1}(1 : N/20 - 1)\n", "# criter = zeros(length(dlist), 3)\n", "\n", "# for i in 1 : length(dlist)\n", "# s = twosparse(dlist[i])\n", "# I = (supp(s))\n", "# criter[i, :] = [F(Phi, s), erc(Phi,I), werc(Phi,I)]\n", "# end\n", " \n", "# criter[criter .< 0] = float(\"inf\")\n", "\n", "# plot(dlist, criter, linewidth = 2)\n", "# plot(dlist, dlist.*0 + 1, \"k--\", linewidth = 2)\n", "# xlim(1, maximum(dlist))\n", "# ylim(minimum(criter), maximum(criter))\n", "# xlabel(\"d\")\n", "# legend([\"F\", \"ERC\", \"w-ERC\"])\n", " \n", "# show()\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Julia 0.5.0", "language": "julia", "name": "julia-0.5" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.5.0" } }, "nbformat": 4, "nbformat_minor": 0 }