{ "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": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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", "$$ x^\\star \\in \\uargmin{x \\in \\RR^N} \\frac{1}{2}\\norm{y-\\Phi x}^2 + \\la \\norm{x}_1. $$\n", "\n", "\n", "Where there is no noise, we consider the problem $ \\Pp(y) $\n", "$$ x^\\star \\in \\uargmin{\\Phi x = y} \\norm{x}_1. $$\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": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "remove_diag = C -> C - diagm(diag(C))\n", "Correlation = Phi -> remove_diag(abs(Phi'*Phi));" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the coherence $\\mu(\\Phi)$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "mu = Phi -> maximum(Correlation(Phi));" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The condition\n", "$$ \\norm{x_0}_0 < \\frac{1}{2}\\pa{1 + \\frac{1}{\\mu(\\Phi)}} $$\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 $\\text{Coh}(\\norm{x_0}_0)<1$\n", "where\n", "$$ \\text{Coh}(k) = \\frac{k \\mu(\\Phi)}{ 1 - (k-1)\\mu(\\Phi) } $$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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);" ] }, { "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": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coherence: 0.31\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": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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05Il/6JOKBpMrAwAAAAaG4IUhyW6z6hdfnanPjY+TJNU1t+umx7apuLbZ5MoAAACA/iN4Ychyhtj0m0WzNT09RpJU4XJr0ePbVd3oNrkyAAAAoH8IXhjSopwhemLJHI1PiJAkHalu0uLHt8vV2m5yZQAAAEDfEbww5MVHOvT0rXlKjXFKknaXunTrkx+otd1jcmUAAABA3xC8EBTSR4Xp6VtyFRseIknafqRWdz1boA6P1+TKAAAAgM9G8ELQmJgUpSeW5Co81CZJ+tveCn3vD7vk9RomVwYAAACcGcELQSU7c5R+s2i2Qm2+S/cPHx7Tj17bK8MgfAEAAGDoIngh6Fw0MUG/+GqOrBbf88c2H9Ev3z5kblEAAADAGRC8EJSunpaqH//zdP/zB9/Yr2e2fWpiRQAAAEDvCF4IWjfkjtb3rj7P//yHf/pYf/6o1MSKAAAAgJ4RvBDUvnHZBN3++fGSJMOQ/v2FQm36pMrkqgAAAICuCF4Iesv+6TxdPztDktTuMXT70zv0YdFxk6sCAAAATiJ4IehZLBb9+J+na975yZKklnaPlqz7hz6paDC5MgAAAMCH4IVhwW6z6n9vmKm54+MlSfUt7brpsW0qrm02uTIAAACA4IVhxBli068XzdL09BhJUoXLrZse26aqBrfJlQEAAGCkI3hhWIlyhuiJJXM0PjFCknS0plmLH98uV2u7yZUBAABgJCN4YdiJj3To6VvylBrjlCTtKXPp1ic+UGu7x+TKAAAAMFIRvDAspY8K09O35Ck2PESStP1ore569kO1e7wmVwYAAICRiOCFYWtiUqSeWJKriFCbJOlveyt1zwuFqm9m2SEAAAAGF8ELw1p25ij9etFshdp8l/pfPirT5f/ztp7Z9qk8XsPk6gAAADBSELww7F00MUEP3zhTzhDf5V7b1KYfvPyxvvjwZm07XGNydQAAABgJCF4YEeadn6K37r1MC7LT/GN7y1xa+Ov3deezH+rYcfb7AgAAQOBYDMNgvdVncLlciomJUX19vaKjo80uB2dp+5FarXp1t3aXuvxjDrtVd1w6QXdcOkFhnfeEAQAAAKcbaDYgePUBwWv48XgNvfhBsR58Y79qm9r842kxTi2/Zoq+OCNVFovFxAoBAAAwFBG8AojgNXzVt7TrFxsP6Mn3jqrjlGYbuWPjtGLBVE1LjzGxOgAAAAw1BK8AIngNfwcrG3T/n/dq0ydV/jGLRbphzmh95wuTFB/pMLE6AAAADBUErwAieI0MhmHorX2V+q8/79HRmpPNNqKddt2TP0k3zR2jEBv9aAAAAEYyglcAEbxGFneHR09sOaqH3zqoRneHf3xiUqRWfHGqPj8p0cTqAAAAYCaCVwARvEamyoZWPbhhv17acazLeP6UZP1w/hSNTYgwqTIAAACYheAVQASvkW1ncZ3ue3W3Corq/GOhNqtuvnic7rpioiIddhOrAwAAwGAieAUQwQter6E/FZbov1/fp8oGt388Mcqh7119nr48M11WK+3nAQAAhjuCVwARvHBCk7tDa/9+UL9994jaPF7/eHbmKN23YKpmjo41sToAAAAEGsErgAheON2nNU360V/26q97KrqMf+WCDH3v6slKinaaVBkAAAACieAVQAQv9GbzgWqtenW3DlQ2+sciQm2664os3XzxWDnsNhOrAwAAwLlG8AogghfOpMPj1e/e/1QPvfmJXK0n28+PiQ/XD+dPVf6UJFks3P8FAAAwHBC8Aojghb6obWrTQ2/u17PbiuQ95U/VJVkJWvHFqcpKjjKvOAAAAJwTBK8AInihP/aUurTq1d3adqTWP2azWrRo7hjdc+UkxYSHmFgdAAAAzgbBK4AIXugvwzD0+sfl+tFf9qqkrsU/HhcRqnu/MEk3zBktG+3nAQAAgg7BK4AIXhio1naP/u+dw/rVOwfV2n6y/fzU1GitXDBVeePjTawOAAAA/UXwCiCCF85WaV2LVr++T6/uLO0yPn9Gqr5/zRSljwozqTIAAAD0B8ErgAheOFe2H6nVqld3a3epyz/mDLHqjksn6PbPT1BYKO3nAQAAhrKBZgNrAGsKmLVr12rs2LFyOp3Ky8vT9u3b+/S6LVu2yG63KycnJ8AVAj3LHRen9XddrNVfnq64iFBJUmu7V2v+dkD5D72jP39UKv4tBAAAYPgJuuD1wgsvaOnSpVq5cqU+/PBDZWdna968eaqsrDzj6+rq6rRo0SJdeeWVg1Qp0DOb1aKv5o7W379zmW65eJzsnU02SupadNezBVr46/e1u7Te5CoBAABwLgV0qWFxcbEyMzPP6Xvm5eVpzpw5euSRRyRJXq9XmZmZuvvuu7Vs2bJeX3fDDTcoKytLNptNf/rTn1RYWNjruW63W2632//c5XIpMzOTpYYIiIOVDbr/z3u16ZMq/5jVIt2QO1r3XjVJ8ZEOE6sDAADAqYbkUsMxY8YoISFBV155pe699149/fTT2rVrl3bs2KHFixf3+/3a2tq0Y8cO5efn+8esVqvy8/O1devWXl+3bt06HT58WCtXruzT11m9erViYmL8j3MdHoFTTUyK0pNL5uixxbM1Nj5ckuQ1pGe3Fenyn72txzcfUbvH+xnvAgAAgKHMHsg3P3LkiAoKClRYWKiCggK9+OKLKi31dXUbyMxRdXW1PB6PkpOTu4wnJydr3759Pb7mwIEDWrZsmd59913Z7X37uMuXL9fSpUv9z0/MeAGBYrFYdOWUZF2claAnthzVw28dVKO7Q67WDt3/5z16dnuRVnxxqj4/KdHsUgEAADAAAQ1eY8aM0ZgxY/SlL33JP7Z161YtXrxY999/fyC/tCTJ4/Hoxhtv1KpVqzRp0qQ+v87hcMjhYHkXBp/DbtPtl07QP1+Qrp9u2K/f7zgmSTpY2ahFj29X/pRk/ecXp2hMfITJlQIAAKA/TGkn//rrr+s///M/9cEHH/TrdW1tbQoPD9fvf//7LmFu8eLFqqur0yuvvNLl/Lq6OsXGxspmO9mi2+v1yjAM2Ww2/fWvf9UVV1zxmV+XdvIwy87iOt336m4VFNX5x0JtVt1yyTjdeflERToC+m8nAAAAOM2QvMerra2tx/GsrCzt3r273+8XGhqqWbNmaePGjf4xr9erjRs3au7cud3Oj46O1q5du1RYWOh/3HHHHZo8ebIKCwuVl5fX7xqAwZSdOUp/uONCPXR9tpKifLOwbR6vfvX2IV3xs7f1hx3H5PXSfh4AAGCoC+g/l0dGRmrq1KmaOXOmcnJyNHPmTKWlpenhhx/u0iCjP5YuXarFixdr9uzZys3N1Zo1a9TU1KQlS5ZI8t2fVVJSoqeeekpWq1XTpk3r8vqkpCQ5nc5u48BQZbVa9OULMjTv/BSt/ftB/fbdI2rzeFXZ4Na9L+3U0+9/qpULpmrm6FizSwUAAEAvAhq83nrrLe3cuVM7d+7UM888o+XLl6u1tVWSdPXVV2vFihWaPn26pk+frvPOO69P77lw4UJVVVVpxYoVKi8vV05OjjZs2OBvuFFWVqaioqKAfSbALBEOu/7j6vO0cE6mfvSXvfrrngpJUmFxnf75l+/pKxdk6HtXT1ZStNPkSgEAAHC6Qb3Hy+v1av/+/f5lfydCWWVlpTwez2CV0W/c44WhaPOBaq16dbcOVDb6xyJCbbrriizdfPFYOey2M7waAAAAAzHQbGBKc43TVVRUdGsRP5QQvDBUdXi8+t37n+qhNz+Rq7XDPz4mPlw/nD9V+VOSZLFYTKwQAABgeAnq4DXUEbww1NU2temhN/fr2W1FOrXXxiVZCVq5YKomJkWZVxwAAMAwQvAKIIIXgsWeUpdWvbpb247U+sdsVosWzR2je/InKSYsxMTqAAAAgh/BK4AIXggmhmHotV3l+vFre1VS1+Ifj4sI1Xe+MFkL52TKZmX5IQAAwEAQvAKI4IVg1Nru0f+9c1i/euegWtu9/vGpqdFauWCq8sbHm1gdAABAcCJ4BRDBC8GstK5Fq1/fp1d3lnYZnz8jVd+/ZorSR4WZVBkAAEDwIXgFEMELw8H2I7Va9epu7S51+cecIVbdcekE3f75CQoLpf08AADAZyF4BRDBC8OFx2voxQ+K9eAb+1Xb1OYfTx8VpuXXnKf501NpPw8AAHAGBK8AInhhuKlvadcvNh7Qk+8dVccp/efzxsVp5YLzNTWN6xwAAKAnBK8AInhhuDpY2aD7/7xXmz6p8o9ZLdINuaP1nS9MVlxEqInVAQAADD0ErwAieGE4MwxDb+2r1H/9eY+O1jT7x6Oddt2TP0k3zR2jEJvVxAoBAACGDoJXABG8MBK4Ozxat+WoHt54QE1tHv94VlKkvj9/ii7NSpSV/b8AAMAIR/AKIIIXRpLKhlb9dMN+/X7HsS7jaTFOLchJ03XZ6ZqSGkUTDgAAMCIRvAKI4IWRaGdxne57dbcKiuq6HctKitS12Wm6NidNY+IjTKgOAADAHASvACJ4YaTyeg29/nG5fr+jWJsOVMvj7f7XRU7mKF2bnaYvZqcqKcppQpUAAACDh+AVQAQvQKppdOu1j8v1amGpth+t7XbcapEunJCga7PTNG9aimLCQkyoEgAAILAIXgFE8AK6Kqlr0as7S7W+sFR7ylzdjofarLr8vERdm52uK6ckyRliM6FKAACAc4/gFUAEL6B3ByoatH5nqdbvLNWnp7SjPyHSYdcXzk/Wtdlpunhiguy0pgcAAEGM4BVABC/gsxmGoZ3H6vVKYYle3Vmm6kZ3t3PiI0I1f0aqrstJ0wWjY+mMCAAAgg7BK4AIXkD/eLyG3j9co1cKS/T6x+VqaO3odk76qDBdm5Om63LSdF4Kf64AAEBwIHgFEMELGDh3h0dv76/S+sJS/W1vhdwd3m7nTEqO1HU56bo2O02ZceEmVAkAANA3BK8AIngB50ZDa7ve3FOhVwpLtflgz+3pZ44epeuy0zR/RpoSoxwmVAkAANA7glcAEbyAc6+m0a3XdpXplcJSffDp8W7HrRbpookn29NHO2lPDwAAzEfwCiCCFxBYx44369WdZXqlsET7yhu6HQ+1W3XF5CRdl5Omy8+jPT0AADAPwSuACF7A4PmkokHrC0v1ys4SFde2dDse5bDrC+en6LqcNF04IZ729AAAYFARvAKI4AUMPsMwVFBcp/WFpfrzRz23p0+IDNX86am6NiddF4weRXt6AAAQcASvACJ4Aebq8Hi19XCN1heWasPH5Wpwd29PnxEbpmuz03RdTromp0SZUCUAABgJCF4BRPACho7Wdo/e3l+p9TtL9be9lWrroT39eSlRWpCdRnt6AABwzhG8AojgBQxNDa3temN3hdbvLNWWXtrTzxoTq2uz0zR/RqoSImlPDwAAzg7BK4AIXsDQV9Xga0+/fmepdvTQnt5mtZxsT39+sqJoTw8AAAaA4BVABC8guBTXNmv9zlK9urO0x/b0DrtVV05J0rXZabpsMu3pAQBA3xG8AojgBQSvfeUurS8s1fqdpTp2vOf29FdPS9G1OWmaO5729AAA4MwIXgFE8AKCn2EY+rCoTusLS/SXXWWqbmzrdk5CpENfnJGqa3PSNDOT9vQAAKA7glcAEbyA4aXD49V7h2r0SmGp3thdrsYe2tOPjgvvbE+fpqxk2tMDAAAfglcAEbyA4au13aO/76vUK4Wlemt/7+3pr8tJ14LsVGXE0p4eAICRjOAVQAQvYGRwtbbrjY/L/e3pe+hOr9ljYnVdTpqumZ6qeNrTAwAw4hC8AojgBYw8lQ2teu2jMr2ys1QFRXXdjtusFl08MUHX5aTpC+enKNJhN6FKAAAw2AheAUTwAka2oppmvfpRqf5UUKIDlY3djjvsVuVPSda1OWm6bHKiHHba0wMAMFwRvAKI4AVA8nVG3FfeoPU7S7W+sFQldT20p3fa9U/TUnRdTro+Nz5eNiudEQEAGE4IXgFE8AJwOq/X0IdFx7V+Z6n+8lGZapq6t6dPjHLo0kmJuiQrQRdPTOCeMAAAhgGCVwARvACcSYfHqy2HavSa+P5hAAAgAElEQVRKYYne+LhcTW2eHs87Py1al2Ql6vNZCZo1NpYliQAABCGCVwARvAD0VWu7R2/tq9SfCkq06UCVWtu7t6eXJGeIVXnj4nVJVoIuyUrUpORINmwGACAIELwCiOAFYCBa2z368NPj2nSgWpsPVunjElev5yZFOXRxVoI+n5WoiyYmKDGKZYkAAAxFBK8AIngBOBdqGt3afLBamw9U690D1Sp3tfZ67pTU6M7ZsATNGRsnZwjLEgEAGAoIXgFE8AJwrhmGoYOVjXr3QLXePVCl9w/XqqW953vDHHarcsfFdTbpSNSU1CiWJQIAYBKCVwARvAAEmrvDow8/rdO7B6q0+WC1dpXUq7e/nRMiHf5OiZdkJSgp2jm4xQIAMIKNqOC1du1aPfjggyovL1d2drYefvhh5ebm9nju5s2b9b3vfU/79u1Tc3OzxowZo9tvv13//u//3uevR/ACMNhqm9r03qFqvfuJb0astL73ZYmTk6N8yxInJSp3bJzCQlmWCABAoIyY4PXCCy9o0aJFevTRR5WXl6c1a9bopZde0v79+5WUlNTt/IKCAu3bt08zZsxQRESENm/erNtvv10///nPddttt/XpaxK8AJjJMAwdrm7Su5/4ZsO2HqrptWV9qM2qOeNidfFE3/5hU1OjZWUTZwAAzpkRE7zy8vI0Z84cPfLII5Ikr9erzMxM3X333Vq2bFmf3uPLX/6yIiIi9PTTT/fpfIIXgKGkrcOrwmLfssRNB6q161idvL38TR4fEaqLOpckXpKVqJQYliUCAHA2BpoN7AGs6Zxra2vTjh07tHz5cv+Y1WpVfn6+tm7d2qf3KCgo0HvvvacHHnig13Pcbrfcbrf/ucvVewtoABhsoZ3NNnLHxeneL0xWXXOb3jtU4wtin1SrpK7Ff25NU5vW7yzV+p2lkqSspEh/2/q88XEKDw2qbwMAAAStoPqOW11dLY/Ho+Tk5C7jycnJ2rdv3xlfm5GRoaqqKnV0dOi+++7Trbfe2uu5q1ev1qpVq85JzQAQaKPCQ3XN9FRdMz1VhmHoaE2zNnfOhm09VKNGd4f/3AOVjTpQ2ah1W44qxGbRrDGxuiTLtyxxWloMyxIBAAiQoApeZ+Pdd99VY2Oj3n//fS1btkwTJ07UV7/61R7PXb58uZYuXep/7nK5lJmZOVilAsCAWSwWjUuI0LiECN00d6zaPV7tLK7zbeJ8oEqFxSeXJbZ7DL1/uFbvH67Vg2/sV2x4iH9Z4sVZiUofFWbuhwEAYBgJquCVkJAgm82mioqKLuMVFRVKSUk542vHjRsnSZo+fboqKip033339Rq8HA6HHA7HuSkaAEwUYrNq9tg4zR4bp6VXTVJ9S7u2Hqru3D+sWkW1zf5zjze3688flenPH5VJksYnRujzWYm6eGKCPjchXpGOoPqWAQDAkBJU30VDQ0M1a9Ysbdy4UV/60pck+ZprbNy4UXfddVef38fr9Xa5hwsARoqYsBBdPS1VV09LlSR9WtPk38T5vUM1amg9uSzxcFWTDlc16Yn3jsputeiCMbG6ZKKvbf309BjZWJYIAECfBVXwkqSlS5dq8eLFmj17tnJzc7VmzRo1NTVpyZIlknzLBEtKSvTUU09J8u35NXr0aJ133nmSpE2bNulnP/uZvvWtb5n2GQBgqBgTH6Ex8RH6t8+NUYfHq53H6rW5M4gVFNfJ07kuscNraPuRWm0/Uqv/efMTxYSF6KKJ8bqkc0YsMy7c5E8CAMDQFnTBa+HChaqqqtKKFStUXl6unJwcbdiwwd9wo6ysTEVFRf7zvV6vli9friNHjshut2vChAn6yU9+ottvv92sjwAAQ5LdZtWsMbGaNSZW387Pkqu1Xe8fqtG7B6q1+WC1jlQ3+c+tb2nXa7vK9dqucknSuIQIXdx5f9jcCfGKcoaY9TEAABiSgm4fLzOwjxcASMW1zZ0hrEqbD1TLdcqyxFPZrBbNzBzlmw3LSlB2RozsNusgVwsAQGCMmA2UzUDwAoCuPF5Du0rq9e4nVXr3QLU+LDqujl52cY5y2nXRhAT//mGj41mWCAAIXgSvACJ4AcCZNbo79P6hGm0+WK1NB6p0uKqp13NHx4XrkqwEXZKVqLkT4hUTxrJEAEDwIHgFEMELAPqnpK7Fv4nzloPVqmtu7/E8q0XKyRyli7MS9fmsBGVnjlIIyxIBAEMYwSuACF4AMHAer6HdpfX+tvU7Pj2udk/P33oiHXbNnRCv6ekxGpsQofEJERqbEMEeYgCAIYPgFUAELwA4d5rcHdp+pFabDvjuDztY2fiZr0mMcmhcfITGJoRrXEKkxnX+OiY+XM4Q2yBUDQCAD8ErgAheABA4ZfUtvm6JnW3ra5va+vxai0VKjXZqXGKExsZHaFzCyUdmXDjLFgEA5xzBK4AIXgAwOLxeQwerGnW4qlFHqpt1pLpRR6ubdaSmSVUN7n69l81qUUZsmMYl+ELZ+FPCWdqoMNmslgB9CgDAcDbQbMCieQDAkGG1WjQpOUqTkqO6HWtobdenNc06XN2ko9VNOnLKo76le/MOj9fQpzXN+rSmWVJVl2OhNqtGx4f7Z8dOnS1LjnbIYiGUAQDOLYIXACAoRDlDNC09RtPSY7odO97UpiM1TTpS1aSjNU3+cHa0uklNbZ5u57d5vDpY2djj/WXhoTaNiY/ovI+s62xZXEQooQwAMCAELwBA0IuNCFVsRKguGB3bZdwwDFU1uE/OjtWcnC07WtOstg5vt/dqbvNob5lLe8tc3Y5FOe3+TounzpaNTYhgPzIAwBlxj1cfcI8XAAw/Xq+h0voW3z1k1b57yo7W+EJZcW2zOrz9+/YYHxHqC2LdQlm4wkP5d04AGC5orhFABC8AGFnaPV4dO97S5V6yozVNOlzVpNL6FvX3O2dKtNMfyk7OmIUrMy5cDjvt8AEgmBC8AojgBQA4obXdo6LaZl8YO63JR2U/Oy9aLVJ6bJhvb7L48C6zZemjwmSnHT4ADDl0NQQAYBA4Q2y9dl5sdHf4mnp03kt2agfG483dOy96Dam4tkXFtS3adNqxEJtFmXHhGtfZcfHU2bKUaKestMMHgKBC8AIA4ByJdNh77bxY19zmX7Lo26PsZChrdHd0O7/dY+hwlW954+mcIVbf/WPxERqXGKFxnQ0+xsaHKzGKdvgAMBSx1LAPWGoIAAgUwzBU3djmC2RVTV3a4h+pbpK7h86LZ+KwW5URG6bRcb57yDJjw5UZF6aMWN9zui8CwNlhqSEAAEHIYrEoMcqhxCiH5oyN63LM6zVU7mrttmzxSE2Timp67rzo7vDqUFWTDvUwUyZJMWEhyowL6wxk4cqMDVNGXLhGx4UrfVSYnCE0+wCAQGDGqw+Y8QIADDUdHq9K6lpOdl2sblJRbbOKapt17HhLv2fKTkiOdnQJZZknZs7iwpUS7ZSNe8sAjHB0NQwgghcAIJh4vYaqG90qPt7c2bzDF8hOPC+rb1E/tymT5Gv4kTYqzL988eRSRl9Ii4sI5f4yAMMeSw0BAIAkyWq1KCnaqaRop2aN6X683eNVWV2rio93BrLaZhUf9wW0Y8ebVd3Y1uP7tnsMfVrTrE9rmns8HhFq899L1mU5Y+fvIxz82AFg5GLGqw+Y8QIAjCRN7g4d6wxi/lmz450BrbZZTW2eAb1vfESoMk5dwtg5czY6Llxpo8IUwr5lAIIAM14AAOCciHDYNTklSpNTuu9VZhiGjje39xrKSupa1O7p+d90a5raVNPUpp3Fdd2OWS1SakyYMk4JZaPjT86aJUY62LsMQFBjxqsPmPECAKBvPF5DFa5W//LFotpmHTslpFU0tGogP3mEdrbJz4wN72yVf2pnxnDFhNMmH8DgYMYLAACYzmb1NeBIGxWmvB6Ouzs8Kjne0mMoKz7erLrm9h7ft63D2+uG0pIU5bR3DWWn7WFGm3wAZiN4AQCAQeOw2zQ+MVLjEyN7PO5q7VzGWNuiY8e7Nv4oPt6s1vae2+Q3tHZoT5lLe8pcPR5PinJ0bZEfG66MzvvLUmPCaJMPIOBYatgHLDUEAMB8hmGoqtHdNZTVtvhb5ZfVt8ozgD75VouUEOlQUrRDyVFOJUU7lBjlVFKUQ8nRvl+Toh1KiHTQAAQASw0BAMDwZrFYlBTlVFKUU7PGxHY73uHxqqy+1T87VlR7avOPFlU3unt8X68hVTa4Vdng1sfqecbM9/V9nRlPhjKHr55oR2c4840nRjnksLO0EUBXBC8AADAs2G3Wzn3Dwns83tLm8c2UHW9WUc3JJYyl9S2qdLlV3eg+48bShiFVN7apurFNe8vOXMuo8JBTZs98Aa1bUItyKiyUgAaMFAQvAAAwIoSF2pSVHKWs5O5t8iVfR8aaJrcqXW5VNrR2/upWhavVPyNW1fn7js9Y0ljX3K665nbtr2g443lRTvtpSxpP+7Xz95FsPg0EPf4UAwAAyNeR8cRSRimm1/O8XkPHm9v8YazC1aqqBrcqO0PZqUGtraPnZiAnNLR2qKG1Q4d66dZ4QkSoTUnRTiWeGtKiut+XFu20y2KhUQgwFBG8AAAA+sFqtSg+0qH4SIempPZ+nmEYcrV0qMI/e9Y1mFV1jlW43Gpp95zxaza1eXSkuklHqs8c0Bx2a5eGICeXNnZtFjIqPISABgwyghcAAEAAWCwWxYSHKCY8RJN6Wd4o+QJao7vDN0vWZZlj96DW4O4449d0d3hVVOtrLHImoTar796zU+43OxHMEjvHkqOdigsPlZVW+8A5QfACAAAwkcViUZQzRFHOEE3oZX+zE5rbOvz3np0IaBUNrZ2zZydn0Opbet6I+oQ2j1cldS0qqWs543l2q8Xfav/0xiDJ0Q5ldG5SHR7Kj5TAZ+FPCQAAQJAID7VrbIJdYxMiznhea7vHd9/ZKfeenQxqvrGqBrdqmtrO+D4dXkPlrlaVu1ol1fd6XnxEqDLiwjX6tE2qR8eFK3WUk/3PABG8AAAAhh1niO2MrfVPaOvwqrrxtIB2SnOQEzNoNZ/Rar+mqU01TW3aWVzX7ZjVIqXGhCkzLswfxny1+Z4nRjm43wwjAsELAABghAq1W5U2Kkxpo8LOeF6Hx6vaprYu95yV17eq+HizjnVuUl3uapXRQzjzGvIva3xftd2OO0OsviWLp8yU+YNZXLiinSHn6uMCpiJ4AQAA4IzsNqtvb7Fop6al99xq393hUcnxFv/G1MW1vs2qizuDWV1zz/edtbZ7dbCyUQcrG3s8HhMW0jlL5pshy+hczjg6LlzpsWFy2NmEGsGB4AUAAICz5rDbND4xUuN7aRDiam3vDGQtOnbcF8yKapv9Qc3dy55n9S3t2lVSr10l3e8xs1ik5Cinf3bMP1vWOXuWEu2kKyOGDIth9DQpjFO5XC7FxMSovr5e0dHRZpcDAAAwrBiGoapGtz+YnZgtK+p8XlbfcsZ7zHoTarMqPTZMGZ1BbLQ/nPlmz9jPDAMx0GzAjBcAAABMZbFYOvcSc2rWmO7H2z1eldW1ds6QnVjG2KKi2mYdq23utTtjm8d7xo2noxx2/9LFEzNlo+N94SwjNlxhoSxjxLlD8AIAAMCQFmKzanR8uEbH99ylscndoWOdQezUe8uOdc6aNbd5enxdg7tDe8tc2lvm6vF4QqRDo7ssYwzzL2dMjXHKTpt89APBCwAAAEEtwmHX5JQoTU6J6nbMMAzVNrX57yUrqm3uvMfM1/Sj5HiLOnpZx1jd6FZ1o1sfFnVvk2+zWpQ2ytmlRX7GKZ0ZEyJDWcaILrjHqw+4xwsAAGB46vB4Ve5q9Qexkx0ZfUGtssE9oPcNC7F1mSE7telHfGSoohwhcoZYCWdBaKDZgODVBwQvAACAkam13dNlhszfjbHzeUNrx4Df22a1KNJhV5TT3uXXSGeIIh12Rfufn3o8xPer066ozmNhITYC3CCiuQYAAABwjjlDbJqYFKWJSd2XMUpSfXP7aU0/mlVU26Jjtc06drxFbZ6e2+RLksdrqL6lXfUtPe9x1ldWizqDWcgp4c1+WqgL8Y9HnXb8xLHwUAJcIBG8AAAAgAGKCQ/R9PAYTc/ovrG012uossHdpenHseMtqmtuV6O7XY3uDjW2dqjR3SFXa4faetnL7LN4DcnV6nuPs2G1+O6XOxHMuoW1UwJbtDPE//tTw1yUM0ThITb2T+sBwQsAAAAIAKvVopQYp1JinModF/eZ57s7PGpye9TY2qEGd7s/lDW0dqjBH9LaO4/7njd0nnPivEZ3u1rbBx7gGjrfU933q+4zi0WKDLV3CWb+sNbbbFy35ZZ2RYbah1WAC8rgtXbtWj344IMqLy9Xdna2Hn74YeXm5vZ47h//+Ef96le/UmFhodxut84//3zdd999mjdv3iBXDQAAAPTOYbfJYbcpLiL0rN6n3ePtEtp8wazd//uG1o7Tjp+cfTs15LW099yG/7MYhq9Vf4P77GbgJN8SylPD2k2fG6OvzMo46/c1Q9AFrxdeeEFLly7Vo48+qry8PK1Zs0bz5s3T/v37lZSU1O38TZs26aqrrtKPf/xjjRo1SuvWrdOCBQu0bds2zZw504RPAAAAAAROiM2q2IhQxZ5lgOvweNXk9qjhlNDW2MPsm+uUY43uE8fb/cGut33U+uLEbJ46t1r74ozUs/pMZgq6roZ5eXmaM2eOHnnkEUmS1+tVZmam7r77bi1btqxP73H++edr4cKFWrFiRZ/Op6shAAAAMDAer+EPUCcCW8OpyyRPC3MNp8/WnbKc8r+/PF035I429fOMiK6GbW1t2rFjh5YvX+4fs1qtys/P19atW/v0Hl6vVw0NDYqL632drdvtltt9cs8Gl6vn3cwBAAAAnJnNalFMWIhiwkLO6n28XkPe4Joz6sJqdgH9UV1dLY/Ho+Tk5C7jycnJKi8v79N7/OxnP1NjY6Ouv/76Xs9ZvXq1YmJi/I/MzMyzqhsAAADA2bFaLbLbgiq+dBG8lQ/As88+q1WrVunFF1/s8X6wE5YvX676+nr/o7i4eBCrBAAAADDcBNVSw4SEBNlsNlVUVHQZr6ioUEpKyhlf+/zzz+vWW2/VSy+9pPz8/DOe63A45HA4zrpeAAAAAJCCbMYrNDRUs2bN0saNG/1jXq9XGzdu1Ny5c3t93XPPPaclS5boueee0/z58wejVAAAAADwC6oZL0launSpFi9erNmzZys3N1dr1qxRU1OTlixZIsm3TLCkpERPPfWUJN/ywsWLF+t///d/lZeX578XLCwsTDEx3XcYBwAAAIBzLeiC18KFC1VVVaUVK1aovLxcOTk52rBhg7/hRllZmYqKivzn//rXv1ZHR4fuvPNO3Xnnnf7xxYsX64knnhjs8gEAAACMQEG3j5cZ2McLAAAAgDTwbBBU93gBAAAAQDAKuqWGZjgxKchGygAAAMDIdiIT9HfhIMGrDxoaGiSJjZQBAAAASPJlhP406+Merz7wer0qLS1VVFSULBaL2eVggFwulzIzM1VcXMy9egg4rjcMNq45DCauNwy2oXTNGYahhoYGpaWlyWrt+51bzHj1gdVqVUZGhtll4ByJjo42/Q8sRg6uNww2rjkMJq43DLahcs0NZFsqmmsAAAAAQIARvAAAAAAgwGz33XfffWYXAQwWm82myy67THY7q2wReFxvGGxccxhMXG8YbMF+zdFcAwAAAAACjKWGAAAAABBgBC8AAAAACDCCFwAAAAAEGMELAAAAAAKM4IVhZe3atRo7dqycTqfy8vK0ffv2Xs/94x//qKuuukqJiYmKjo7W3Llz9cYbbwxitQh2/bneTrVlyxbZ7Xbl5OQEuEIMN/295txut37wgx9ozJgxcjgcGjt2rB5//PFBqhbBrr/X2zPPPKPs7GyFh4crNTVVN998s2pqagapWgS7TZs2acGCBUpLS5PFYtGf/vSnz3zN22+/rQsuuEAOh0MTJ07UE088EfhCzwLBC8PGCy+8oKVLl2rlypX68MMPlZ2drXnz5qmysrLH8zdt2qSrrrpKr732mnbs2KHLL79cCxYsUEFBwSBXjmDU3+vthLq6Oi1atEhXXnnlIFWK4WIg19z111+vjRs36rHHHtP+/fv13HPPafLkyYNYNYJVf6+3LVu2aNGiRbrlllu0e/duvfTSS9q+fbu+/vWvD3LlCFZNTU3Kzs7W2rVr+3T+kSNHNH/+fF1++eUqLCzUPffco1tvvXVo/yO6AQwTubm5xp133ul/7vF4jLS0NGP16tV9fo+pU6caq1atCkR5GGYGer0tXLjQ+OEPf2isXLnSyM7ODnSZGEb6e829/vrrRkxMjFFTUzNYJWIY6e/19uCDDxrjx4/vMvaLX/zCSE9PD2idGJ4kGS+//PIZz/mP//gP4/zzz+8ytnDhQmPevHmBLO2sMOOFYaGtrU07duxQfn6+f8xqtSo/P19bt27t03t4vV41NDQoLi4uUGVimBjo9bZu3TodPnxYK1euHIwyMYwM5Jpbv369Zs+erZ/+9KdKT0/XpEmT9J3vfEctLS2DVTaC1ECut7lz56q4uFivvfaaDMNQRUWFXnrpJV1zzTWDVTZGmK1bt3a5RiVp3rx5ff65zwzBue0zcJrq6mp5PB4lJyd3GU9OTta+ffv69B4/+9nP1NjYqOuvvz4QJWIYGcj1duDAAS1btkzvvvuu7Hb+6kX/DOSaO3z4sDZv3iyn06mXX35Z1dXV+uY3v6mamhqtW7duMMpGkBrI9XbRRRfpmWee0cKFC9Xa2qqOjg4tWLCgz8vGgP4qLy/v8Rp1uVxqaWlRWFiYSZX1jhkvQNKzzz6rVatW6cUXX1RSUpLZ5WCY8Xg8uvHGG7Vq1SpNmjTJ7HIwQni9XlksFj3zzDPKzc3VNddco4ceekhPPvkks1445/bs2aNvf/vbWrFihXbs2KENGzbo6NGjuuOOO8wuDRgy+GdXDAsJCQmy2WyqqKjoMl5RUaGUlJQzvvb555/XrbfeqpdeeqnblDXQk/5ebw0NDfrggw9UUFCgu+66S5Lvh2LDMGS32/XXv/5VV1xxxaDUjuA0kL/jUlNTlZ6erpiYGP/YlClTZBiGjh07pqysrIDWjOA1kOtt9erVuvDCC/Xd735XkjRjxgxFRETokksu0QMPPKDU1NSA142RJSUlpcdrNDo6ekjOdknMeGGYCA0N1axZs7Rx40b/mNfr1caNGzV37txeX/fcc89pyZIleu655zR//vzBKBXDQH+vt+joaO3atUuFhYX+xx133KHJkyersLBQeXl5g1k+gtBA/o676KKLVFpaqsbGRv/YJ598IqvVqoyMjIDXjOA1kOutubm52zJqm80mSTIMI3DFYsSaO3dul2tUkt58880z/txnOnN7ewDnzvPPP284HA7jiSeeMPbs2WPcdtttxqhRo4zy8nLDMAxj2bJlxk033eQ//5lnnjHsdruxdu1ao6yszP+oq6sz6yMgiPT3ejsdXQ3RX/295hoaGoyMjAzjX/7lX4zdu3cb77zzjpGVlWXceuutZn0EBJH+Xm/r1q0z7Ha78ctf/tI4dOiQsXnzZmP27NlGbm6uWR8BQaahocEoKCgwCgoKDEnGQw89ZBQUFBiffvqpYRjdr7nDhw8b4eHhxne/+11j7969xtq1aw2bzWZs2LDBrI/wmQheGFYefvhhY/To0UZoaKiRm5trvP/++/5jixcvNi699FL/80svvdSQ1O2xePHiwS8cQak/19vpCF4YiP5ec3v37jXy8/ONsLAwIyMjw1i6dKnR3Nw8yFUjWPX3evvFL35hTJ061QgLCzNSU1ONf/3XfzWOHTs2yFUjWP39738/489lPV1zf//7342cnBwjNDTUGD9+vLFu3bpBr7s/LIbB/C8AAAAABBL3eAEAAABAgBG8AAAAACDACF4AAAAAEGAELwAAAAAIMIIXAAAAAAQYwQsAAAAAAozgBQAAAAABRvACAAAAgAAjeAEAAABAgBG8AAAAACDACF4AAPTBtGnT9MADD+iOO+5QbGysUlJStGbNGrPLAgAECYthGIbZRQAAMJS53W5FRkZq3LhxWrVqlebMmaNf/epXeuSRR1RbW6uIiAizSwQADHEELwAAPsOOHTs0e/Zsvf7667r66qslSbt27dKMGTNUWVmpxMREkysEAAx1LDUEAOAz7Ny5UykpKZo3b55/rKqqSqGhoYqLizOxMgBAsCB4AQDwGQoLCzV79mxZLJYuY9OmTZPNZjOxMgBAsCB4AQDwGXbu3KmcnJwuY4WFhd3GAADoDcELAIDP0FPwKigoIHgBAPqM4AUAwBkcPXpU9fX1XUKW2+3Wvn37NHPmTBMrAwAEE7vZBQAAMJSNHTtWpzcA/vjjj+XxeJSdnW1SVQCAYMOMFwAA/VRQUKDx48crKirK7FIAAEGC4AUAQD/RWAMA0F9soAwAAAAAAcaMFwAAAAAEGMELAAAAAAKM4AUAAAAAAUbwAgAAAIAAYx+vPvB6vSotLVVUVJQsFovZ5QAAAAAwiWEYamhoUFpamqzWvs9jEbz6oLS0VJmZmWaXAQAAAGCIKC4uVkZGRp/PJ3j1wYkNMouLixUdHW1yNQAAAADM4nK5lJmZ6c8IfUXw6oMTywujo6MJXgAAAAD6fQsSzTUAAAAAIMAIXgAAAAAQYAQvAAAAAAgwghcAAAAABBjBCwAAAAACjOAFAAAAAAFG8AIAAAAwJBmGof3lDXps8xHd8sQ/VFzbbHZJA8Y+XgAAAACGjJK6Fm05UK0th6r/P3v3HhZlve+N/z0zMDOcz8yAgMpBERBBznRwpSimluyetTLbz5M/W1Z77+ywWHVt6Wq5spO7pRXttKz9W1qudZlWTz9raQsttDyhKEoCCoqoIDDDmWE4zDCH3x9jU8SMcZwZ8P26rv7gvj/z5TPXXrt8+73vzxfHq1vRotaY7y2MkX7LcckAACAASURBVOGh1DA7djdyDF5ERERERGQ3HT1aFF1pxbHqFpy40oqrLd1Wa8/VdjB4ERERERER/Zq+fj1OX2szBa3qVpQ3dMJotFzrJhYhLdwPd0T6445IP8yUedi22THE4EVERERERONGpzegrL4TJ6604tjlFpRcb4dWb7BY6yQUYG6YDzIj/XBnpD/mhHrDWTQ5xlIweBERERER0ZgxGo240qzG8WrT44Mna1rR1aezWj8ryBN3RPjhjih/pE7zhZtkckaUyfmtiIiIiIjIZhSdfThe/eNAjBYoVRqrtSE+Lrgz0h+Zkf7IjPCDv7vEhp3aD4MXERERERENS2dvP07WtOJEdQuOVbfgSrP1gRg+rs7IjPDHHZH+uDPSH2F+rjbs1HEweBERERER0S319etxtrYdx6tbcKy6FWU3OmCwMhBD6ixE6nQ/3Bnph8wIf8QEeUIoFNi2YQfE4EVERERERBZ19vTjw6NX8NHxa+jW6i3WiIQCzAnxujl50B+JYd6QOIls3KnjY/AiIiIiIqIB1Boddhy7ig+P1lgcjDFD5o7MCNOjg2nhvvCQOtuhy4mFwYuIiIiIiACYHincWXQN7393Be09/ebrziIBlsUH4+4Z/rgjwh+BnlL7NTlBOdxQ/K1bt2LatGmQSqVIS0tDcXHxkD53/PhxODk5ISEhYcD1jz76CAKBYMA/Uin/h0JERERE9CONzhS47v7LYbz+daU5dImEAqxIDsXh536Dt1ck4F8SQxi6Rsihdrz27NmD3NxcbNu2DWlpacjPz0d2djaqqqoQGBho9XMdHR145JFHsGDBAiiVykH3PT09UVVVZf5ZIODLfUREREREOr0BX5ytxzuFl1Hf0Wu+LhAA988JxjMLohAe4G7HDicPhwpeb731Fh577DGsXr0aALBt2zbs378f27dvx7p166x+7t/+7d/w8MMPQyQSYe/evYPuCwQCyOXyceubiIiIiGgiMRiM+Mf5BuR/exlXWwaOgs+OleEPC2cgWu5pp+4mJ4cJXlqtFiUlJcjLyzNfEwqFyMrKQlFRkdXP7dixAzU1Nfj73/+OV1991WKNWq3G1KlTYTAYMHfuXLz++uuIjY21uqZGo4FG89OhbyqVagTfiIiIiIjIsRiNRhy8oMRbBy+hStk14N68GQH446IZiA/xtlN3k5vDBK+Wlhbo9XrIZLIB12UyGSorKy1+5vLly1i3bh2OHj0KJyfLX2XmzJnYvn074uPj0dnZic2bNyMzMxMVFRUICQmx+JmNGzdiw4YNo/tCREREREQOwmg04sjlFrx5sArnb3QOuJc63RfPLZqJ1Om+duru9uAwwWu49Ho9Hn74YWzYsAEzZsywWpeRkYGMjAzzz5mZmZg1axY++OADvPLKKxY/k5eXh9zcXPPPKpUKoaGhY9c8EREREZGNnKppxZsHL6H4WtuA63NCvfH8opm4I9KPMxBswGGCl7+/P0Qi0aDhGEql0uL7WV1dXThz5gzOnTuHtWvXAgAMBgOMRiOcnJxw8OBBzJ8/f9DnnJ2dkZiYiOrqaqu9SCQSSCSSUX4jIiIiIiL7Ka3rwJsHq3D0csuA69FyDzy3aCYWzApk4LIhhwleYrEYSUlJKCwsRE5ODgBTkCosLDQHq5/z9PREWVnZgGvvvfceDh06hM8//xzTp0+3+Hv0ej3KysqwZMmSsf8SRERERER2drFRhTcPXsK3FwduaIQHuCF34QwsiQuCUMjAZWsOE7wAIDc3F6tWrUJycjJSU1ORn5+P7u5u85TDvLw81NfXY+fOnRAKhYiLixvw+cDAQEil0gHXX375ZaSnpyMyMhIdHR3YtGkTrl+/jjVr1tj0uxERERERjacrzWrkf3sZ+843wGj86XqIjwuezZqBnIRgOIkc7hjf24ZDBa8VK1agubkZ69evh0KhQEJCAgoKCswDNxobG1FbWzusNdvb2/HYY49BoVDAx8cHSUlJOHHiBGJiYsbjKxARERER2VRdWw/+u/Ay/u/ZGzD8LHDJPCV4an4UHkwOhdiJgcveBEbjz/MwWaJSqeDl5YXOzk54evI8AyIiIiKyP6WqD+8euow9p+vQr//pj/R+bmL8+28i8L/Tp0LqLLJjh5PTSLOBQ+14ERERERHRrbWqNdj2/RXsLLoOjc5gvu4pdcIT8yLw/2ROg5uEf8x3NPy/CBERERHRBNDZ24//OVKD7cevokerN193E4vw6J3TseaucHi5ONuxQ7oVBi8iIiIiIgfWrdFhx/Gr+PBIDVR9OvN1iZMQj2RMxb/Ni4CfO49CcnQMXkREREREDqivX4+/n7yO97+7gtZurfm6s0iAh1LC8OQ9kZB7Se3YIQ0HgxcRERERkQPp7O3HV6X12HK4GkqVxnxdKAD+19wQPL0gCqG+rnbskEaCwYuIiIiIyM5a1Bp8c0GJgnIFTlxpGTClEADumxOMZ7OiEBHgbqcOabQYvIiIiIiI7OBGew8OVChxoFyB09fbYOmQp4UxMuQunIFZQTzSaKJj8CIiIiIispHqJjUOVChQUK5AWX2nxZop3i7IjpXjXxKnYHaIl407pPHC4EVERERENE6MRiMqGlQoKFegoEKB6ia1xbrwADfcGyfH4tggxE3xhEAgsHGnNN4YvIiIiIiIxpDeYETJ9XYUlCtwoEKB+o5ei3VxUzyxOFaOxXFyRAZ62LhLsjUGLyIiIiKiUdLqDCiqaUVBuQLfXFCgRa0dVCMQAClTfbEoVobsWDknE95mGLyIiIiIiEagV6vH95eacaBCgW8vKtH1s8ONf+QkFCAz0h+LY+VYGCNDgAcPOr5dMXgREREREQ1RZ28/DlWaxr5/f6kZff2GQTVSZyHmzQjA4jg55s+UwcvV2Q6dkqNh8CIiIiIiuoXmrptnbFUocKK6BTrD4LnvHhInLJgViMVxctw9IwCuYv4xmwbi/yKIiIiIiH5hKGds+buLsTBGjuxYGTIj/CF2Etq+UZowGLyIiIiIiABUN3XdnESo/NUzthbHyZE01QciIce+09AweBERERHRbcloNKK8XoWCikYUlCtwpbnbYh3P2KKxwOBFRERERLcNg8GIMzxji+yAwYuIiIiIJjWDwYizte3Yd74R/yxvhFKlGVTDM7ZovDF4EREREdGkYzQaca6uA/vPN+LrskY0dvYNquEZW2RLDF5ERERENCkYjUacv9GJ/WWN2H++0eJjhGKREHfP8MeS2UFYEM0ztsh2HG7m5datWzFt2jRIpVKkpaWhuLh4SJ87fvw4nJyckJCQMOjeZ599hujoaEilUsyePRtff/31WLdNRERERHZgGpDRif/6ZyXu3nQYy7cex4dHagaELiehAPfMDMCbv5uD0y9m4f9dlYIH5oYwdJFNOdSO1549e5Cbm4tt27YhLS0N+fn5yM7ORlVVFQIDA61+rqOjA4888ggWLFgApVI54N6JEyewcuVKbNy4EcuWLcOuXbuQk5ODs2fPIi4ubry/EhERERGNMaPRiIuNXdhf1oD95xtxrbVnUI1IKMAdkf5YFh+ERTEyeLuK7dAp0U8ERqOl4+DsIy0tDSkpKdiyZQsAwGAwIDQ0FE899RTWrVtn9XMPPfQQoqKiIBKJsHfvXpSWlprvrVixAt3d3di3b5/5Wnp6OhISErBt27Yh9aVSqeDl5YXOzk54enqO8NsRERER0WhUKbqw/3wD9pU1osbC6HehAMiMMIWt7Fg5fNwYtmjsjTQbOMyOl1arRUlJCfLy8szXhEIhsrKyUFRUZPVzO3bsQE1NDf7+97/j1VdfHXS/qKgIubm5A65lZ2dj7969VtfUaDTQaH6adqNSqYbzVYiIiIhojFQ3qbHvvGln63KTetB9oQBIm+6HZXOCsDhWDj93Dsggx+QwwaulpQV6vR4ymWzAdZlMhsrKSoufuXz5MtatW4ejR4/CycnyV1EoFBbXVCgUVnvZuHEjNmzYMMxvQERERERjoaZZjf3nG7G/rBGViq5B9wUCIGWaL+6LD0J2nByBHlI7dEk0PA4TvIZLr9fj4YcfxoYNGzBjxowxXTsvL2/ALplKpUJoaOiY/g4iIiIi+sn11m7sO2+aRnih0fLTRslTfbAsPgj3zg6CzJNhiyYWhwle/v7+EIlEg4ZjKJVKyOXyQfVdXV04c+YMzp07h7Vr1wIwvRNmNBrh5OSEgwcPYv78+ZDL5UNe80cSiQQSCbepiYiIiMZTXVuPefR7WX2nxZrEMG8siw/GktlyBHm52LhDorHjMMFLLBYjKSkJhYWFyMnJAWAKUoWFheZg9XOenp4oKysbcO29997DoUOH8Pnnn2P69OkAgIyMDBQWFuLZZ581133zzTfIyMgYx29DRERERJbUd/Ti6/ON2FfWiB/qOizWzAnxwrL4YNw7W44QH1cbd0g0PkYVvPr7+6FQKNDT04OAgAD4+vqOqpnc3FysWrUKycnJSE1NRX5+Prq7u7F69WoApkcA6+vrsXPnTgiFwkHj4AMDAyGVSgdcf+aZZzBv3jy8+eabWLp0KXbv3o0zZ87gww8/HFWvRERERDQ0is6+mztbDThbazlszZ7ihaXxQVg6OwihvgxbNPkMO3h1dXXh73//O3bv3o3i4mJotVoYjUYIBAKEhIRg0aJFePzxx5GSkjLsZlasWIHm5masX78eCoUCCQkJKCgoMA/HaGxsRG1t7bDWzMzMxK5du/Diiy/ihRdeQFRUFPbu3cszvIiIiIjGUZOqD1+XmQZknL7WbrEmJsjTHLam+bvZuEMi2xrWOV5vvfUWXnvtNUREROC+++5DamoqgoOD4eLigra2NpSXl+Po0aPYu3cv0tLS8O677yIqKmo8+7cJnuNFRERE9OuauzQoKG/EvvONKL7WBkt/yoyWe2Dp7CAsiQ9CRIC77ZskGqWRZoNhBa+VK1fixRdfRGxs7C3rNBoNduzYAbFYjEcffXTIzTgqBi8iIiIiy1rVGhRUKLD/fCNO1rTCYOFPlpGB7lh2c2crSuZh+yaJxpBNgtftisGLiIiI6CdNXX04dLEJ+8saceJKK/QW0la4v5spbMUHY4bMHQKBwA6dEo29kWYDhxquQURERESOx2AworyhE4cqm3Cosgnnb1ge/T7Vz/XmzlYwZgV5MGwR/YxDDdcgIiIiIseg1uhw7HIzDlU24XBVM5q7NBbrQnxcsCw+GMvigxAb7MmwRWTFsILXL4drvPDCCxaHayxatGhSDdcgIiIiuh1ca+k272qdutqKfr3lN1JmBXliQXQgsmJkmBPixbBFNAQcrjEEfMeLiIiIJqN+vQGnr7Xh0MUmHKpqQk1zt8U6qbMQd0b6Y360DPdEByDIy8XGnRI5Dg7XGEcMXkRERDRZtKg1+K6qGYcrm3DkUjO6NDqLdVO8XbBgViDuiQ5ERrgfpM4iG3dK5JhsPlyjrq4OoaGhI/04EREREdmA0WhERYMKhyubUFjZhB9udFg8X0soAJKn+uKe6EAsmBWIqEBOIiQaSyMOXlOnToWvry/mzJmDhIQE8z9arRb//d//jY8//ngs+yQiIiKiIerR6nC8uhWHKpU4XNkMharPYp23qzPmzQjA/OhAzJsRAG9XsY07Jbp9jDh4Xb16FefOnUNpaSnOnTuHTz/9FA0NDQDAx/GIiIiIbKyurcc8GKOophVancFi3UyZB+bPCsT86EAkhnrDSSS0cadEt6dR7XhNnToVOTk55mtFRUVYtWoVXn755TFpjoiIiIgs0+kNKLnejkNVTTh0sQmXm9QW6yROQmRG+GF+tOl9rRAfVxt3SkTAOAzX+Oc//4k//elPOHPmzFgua1ccrkFERESOoL1bi+8vNaOwsgnfVzVB1Wd5MEaQlxTzo027WpkR/nARczAG0Vix+XANrVYLsXjwc8BRUVGoqKgY6bJEREREdJPRaESVsguFF5twuLIJZ2vbYbDwV+YCATA3zMcctqLlHhyMQeRgRhy83N3dERMTg8TERCQkJCAxMRHBwcF49913kZWVNZY9EhEREd02+vr1OHGlxfS+1sUmNHRaHozhKXXC3TMCsGBWIObNCISvGwdjEDmyET9qeOzYMfzwww/44YcfUFpaivLycvT1mf7FsHjxYiQnJ2P27NmYPXs2oqOjx7RpW+OjhkRERDSeGjp6zYMxTlxpQV+/5cEYkYHuWHDzXa2kqT5w5mAMIpuz+wHKBoMBVVVVKC0tRWlpqTmUNTU1Qa/Xj8WvsBsGLyIiIhpLeoMR52rbzWGrUtFlsU4sEiI9wg/zZwZgfrQMYX4cjEFkbzYLXuvXr8fy5cuRlJQ0pHqlUgmZTDacX+FwGLyIiIhotDp7+vH95WYcuqjE95ea0d7Tb7FO5ikxTSCcGYg7Iv3hJhnxmyFENA5sNlzjxo0buPfeeyEWi3Hffffh/vvvx4IFCywO2gAw4UMXERER0UgYjUZUN6lReHNXq+R6O/QWJmMIBMCcEG/zYIzYYE8OxiCahEb0qKHBYMDx48fxj3/8A19++SUaGxuxcOFCLF++HMuWLYOvr+949Go33PEiIiKioWpS9eGzkhv47EwdrrX2WKzxkDjhrhn+mB8tw29mBsDfXWLjLolopOz6jtfFixfNIaykpASpqam4//77sXLlSkyZMmW0y9sdgxcRERHdit5gxJHLzdhdXItvLzZZ3NkK93cz72olT/OF2ImDMYgmIrsP1/hRc3OzOYTdddddeO6558Zyebtg8CIiIiJLFJ19+PRMHfacrkN9R++AewIBkD7dD1kxMsyPDsR0fzc7dUlEY8nmByhb09fXh2PHjuHLL78c66WJiIiI7E6nN+D7S834pLgWhyqbBh1oHOghwYPJoViREopQX04hJCKTMd/jbmtrw8cffzziz2/duhXTpk2DVCpFWloaiouLrdYeO3YMd9xxB/z8/ODi4oLo6Gi8/fbbA2o++ugjCASCAf9IpdIR90dERES3p/qOXrz1zSXc+cZh/P7jM/j24k+hSyAA7pkZgA//TxJOrJuP57JnMnQR0QDD3vH66quvbnm/pqZmxM3s2bMHubm52LZtG9LS0pCfn4/s7GxUVVUhMDBwUL2bmxvWrl2L+Ph4uLm54dixY3jiiSfg5uaGxx9/3Fzn6emJqqoq88+cFERERERD0a834FBlEz4prsX3l5rxyxc0grykeDA5FA+mhGKKt4t9miSiCWHY73gJhUIIBALc6mMCgWBEhyanpaUhJSUFW7ZsAWCanhgaGoqnnnoK69atG9IaDzzwANzc3PC3v/0NgGnH69lnn0VHR8ew+/kR3/EiIiK6vdS19WD36Vp8duYGmro0A+4JBcD8aBlWpoZi3owAOIk4JIPodmKzd7yCgoLw3nvvYfny5Rbvl5aWDvlw5Z/TarUoKSlBXl6e+ZpQKERWVhaKioqGtMa5c+dw4sQJvPrqqwOuq9VqTJ06FQaDAXPnzsXrr7+O2NhYq+toNBpoND/9S1alUg3z2xAREdFEo9UZ8O1FJT4prsXRyy2D7k/xdsFDKaH4XXIo5F58bYGIhmfYwSspKQklJSVWg9ev7YZZ09LSAr1eP+jAZZlMhsrKylt+NiQkBM3NzdDpdHjppZewZs0a872ZM2di+/btiI+PR2dnJzZv3ozMzExUVFQgJCTE4nobN27Ehg0bhv0diIiIaOK51tKNT07X4v+W3ECLWjvgnpNQgKxZMjyUGoq7ogIgEvJ1BSIamWEHr+effx7d3d1W70dGRuLw4cOjamq4jh49CrVajZMnT2LdunWIjIzEypUrAQAZGRnIyMgw12ZmZmLWrFn44IMP8Morr1hcLy8vD7m5ueafVSoVQkNDx/dLEBERkc1odHocqFBid3EtTlxpHXQ/zNcVD6WG4rdJIQj04O4WEY3esIPXXXfddcv7bm5umDdv3rAb8ff3h0gkglKpHHBdqVRCLpff8rPTp08HAMyePRtKpRIvvfSSOXj9krOzMxITE1FdXW11PYlEAomEJ8gTERFNNlea1dhdXIvPS26gvad/wD1nkQCLYuRYmRqGzAg/CLm7RURjaMzP8RopsViMpKQkFBYWIicnB4BpuEZhYSHWrl075HUMBsOA97N+Sa/Xo6ysDEuWLBl1z0REROT4+vr1+Gd5Iz4prkPx1bZB96f7u+GhlFD8r6QQ+LvzL16JaHw4TPACgNzcXKxatQrJyclITU1Ffn4+uru7sXr1agCmRwDr6+uxc+dOAKYzv8LCwhAdHQ0AOHLkCDZv3oynn37avObLL7+M9PR0REZGoqOjA5s2bcL169cHvAdGREREk88lZRc+Ka7FF2fr0dk7cHdLLBJicZxpdys93JdHzRDRuHOo4LVixQo0Nzdj/fr1UCgUSEhIQEFBgXngRmNjI2pra831BoMBeXl5uHr1KpycnBAREYE33ngDTzzxhLmmvb0djz32GBQKBXx8fJCUlIQTJ04gJibG5t+PiIiIxlevVo/9ZY34pLgWJdfbB92PDHTHQymheGBuCHzdxHbokIhuV8M+x+t2xHO8iIiIHNuFBhV2n67F/3euHl19ugH3JE5CLJ0dhJVpYUie6sPdLSIaFZud42XJjRs3EBwcDKGQBwgSERGRbXRrdNh3vgG7iuvwQ13HoPszZR5YmRqKf0kMgZersx06JCL6yZgEr5iYGJSWliI8PHwsliMiIiKyqry+E7uKa/FVaQPUmoG7W1JnIe6LD8bKtDAkhnpzd4uIHMaYBC8+rUhERETjqauvH1/90IBPimtRXq8adD8myBMr08KwPCEYnlLubhGR43Go4RpEREREPzIajfjhRic+OVWLf5xvQI9WP+C+q1iE5QnBWJkahtlTvLi7RUQObUTB68dx7j/S6XT44osvEBgYaL72yCOPjK4zIiIiui119vbjy9J6fFJch4uNg3e34kO8sDI1DPfNCYa7hH+HTEQTw4j+bbVjx44BP/f39+Pzzz+Hi4sLAEAgEDB4ERER0ZAZjUacrW3HJ8V12He+AX39hgH33SVOyEkMxkMpYYib4mWnLomIRm5Ewevw4cMDfvbw8MCuXbs4XIOIiIiGpaNHiy/O1mP36VpcUqoH3U8M88bKlDAsmxMEVzF3t4ho4uK/wYiIiMimjEYjiq+2YffpOuwva4RWN3B3y0PqhAcSp+Ch1DDMCuL5mUQ0OTB4ERERkU20dWvxxdkb2FVci5rm7kH3U6b54KGUMCyZHQQXscgOHRIRjZ8xCV4vvPACfH19x2IpIiIimkSMRiOKalrxSXEdDpQroNUP3N3ydnXGA4khWJkaiiiZh526JCIafwIjD+H6VSqVCl5eXujs7ISnJx95ICIi+jUtag0+L7mB3cW1uNbaM+h+2nRfPJwWhuxYOaTO3N0iooljpNmAjxoSERHRmDAYjDh+pQWfFNfiYIUSOsPAv9v1dRPjt0khWJESiogAdzt1SURkHwxeRERENGJGoxEXG7uwv6wBX/3QgLq23kE1d0T6YWVqGBbGyCBx4u4WEd2eGLyIiIhoWIxGIy4p1dh/vgH7yhotDsrwd5fgd8kheCglFFP93OzQJRGRYxnz4FVXV4c///nP2L59+1gvTURERHZU3dSFf/zQiP1ljahuGnzmllAA3BkVgIdTQ7FglgzOIqEduiQickxjHrza2trw8ccfM3gRERFNAlea1dh/vhH7zzeiStk16L5AAKRO88Wy+CAsjgtCgIfEDl0SETm+YQevr7766pb3a2pqRtwMERER2d/Vlm7TY4TnG1GpsBy2Uqb6Yml8EO6NkyPQU2qHLomIJpZhB6+cnBwIBALcagq9QCAYVVNERERkW9dbu7G/zLSzVdGgsliTNNUHS2cHYcnsIMi9GLaIiIZj2MErKCgI7733HpYvX27xfmlpKZKSkkbdGBEREY2vurYefF3WiH3nG1FW32mxJjHM2xy2gr1dbNwhEdHkMezglZSUhJKSEqvB69d2w4iIiMh+6jt68fX5Ruwra8QPdR0Wa+aEeGFpvClshfi42rhDIqLJadjB6/nnn0d39+CxsT+KjIzE4cOHR9UUERERjZ3Gzl58XabA/vMNOFtrOWzFTfHE0tnBWBYfhFBfhi0iorEmMHJ76lepVCp4eXmhs7MTnp6e9m6HiIjoVylVffj65jtbZ663W6yJCfLE0vggLJ0dhGn+PGuLiGgoRpoNHO6Aja1bt2LatGmQSqVIS0tDcXGx1dpjx47hjjvugJ+fH1xcXBAdHY233357UN1nn32G6OhoSKVSzJ49G19//fV4fgUiIiK7aOrqw86ia3jwgyKkbyzEhn9cGBS6ouUe+OPCGTj0x3n4+pm78OQ9kQxdREQ2MKxHDWtraxEWFjbk+vr6ekyZMmXI9Xv27EFubi62bduGtLQ05OfnIzs7G1VVVQgMDBxU7+bmhrVr1yI+Ph5ubm44duwYnnjiCbi5ueHxxx8HAJw4cQIrV67Exo0bsWzZMuzatQs5OTk4e/Ys4uLihtwbERGRI2pRa/DPctNjhKeutsHScyxRge5YFh+MpfFyRAZ62L5JIiIa3qOGMpkMOTk5WLNmDVJSUizWdHZ24tNPP8U777yDxx9/HE8//fSQm0lLS0NKSgq2bNkCADAYDAgNDcVTTz2FdevWDWmNBx54AG5ubvjb3/4GAFixYgW6u7uxb98+c016ejoSEhKwbds2i2toNBpoNBrzzyqVCqGhoXzUkIiIHEJbtxYF5QrsL2tA0ZVWGCz8lzw8wA3L4k3vbM2QMWwREY2VkT5qOKwdrwsXLuC1117DwoULIZVKkZSUhODgYEilUrS3t+PChQuoqKjA3Llz8Ze//AVLliwZ8tparRYlJSXIy8szXxMKhcjKykJRUdGQ1jh37hxOnDiBV1991XytqKgIubm5A+qys7Oxd+9eq+ts3LgRGzZsGHLvRERE4629W4uDFxTYd74RJ660Qm8hsOFDrQAAIABJREFUbU33d8Oy+CAsjQ/CTJkHz9UkInIgwwpefn5+eOutt/Daa69h//79OHbsGK5fv47e3l74+/vjX//1X5GdnT2iR/haWlqg1+shk8kGXJfJZKisrLzlZ0NCQtDc3AydToeXXnoJa9asMd9TKBQW11QoFFbXy8vLGxDWftzxIiIisqXOnn4cuKDA/vONOF7dAp2FsDXVzxVLZ5vCVkyQJ8MWEZGDGvY4eQBwcXHBb3/7W/z2t78d635G5OjRo1Cr1Th58iTWrVuHyMhIrFy5csTrSSQSSCSSMeyQiIhoaFR9/fimQon9ZY04erkZ/frBYSvEx8X8GGFsMMMWEdFEMKLgNR78/f0hEomgVCoHXFcqlZDL5bf87PTp0wEAs2fPhlKpxEsvvWQOXnK5fERrEhER2UpXXz++vajE/vONOHKpBVq9YVDNFG8X8+j3+BAvhi0ioglmRMGrt7cXJSUl8PX1RUxMzIB7fX19+PTTT/HII48Ma02xWIykpCQUFhYiJycHgGm4RmFhIdauXTvkdQwGw4DBGBkZGSgsLMSzzz5rvvbNN98gIyNjWP0RERGNJbVGh8KbYeu7S83Q6gaHrSAvKZbMDsKy+CAkhHozbBERTWDDDl6XLl3CokWLUFtbC4FAgDvvvBO7d+9GUFAQANNUw9WrVw87eAFAbm4uVq1aheTkZKSmpiI/Px/d3d1YvXo1ANO7V/X19di5cycA05lfYWFhiI6OBgAcOXIEmzdvHjBJ8ZlnnsG8efPw5ptvYunSpdi9ezfOnDmDDz/8cNj9ERERjUaPVofCi03Yf74Rh6uaoLEQtmSeEnPYSgz1gVDIsEVENBkMO3j953/+J+Li4nDmzBl0dHTg2WefxR133IHvvvtuWGd8WbJixQo0Nzdj/fr1UCgUSEhIQEFBgXk4RmNjI2pra831BoMBeXl5uHr1KpycnBAREYE33ngDTzzxhLkmMzMTu3btwosvvogXXngBUVFR2Lt3L8/wIiIim+jV6nG4yhS2CiuV6OsfHLYCPCRYEifH0vhgJE9l2CIimoyGdY4XYJoI+O2332L27NkAAKPRiP/4j//A119/jcOHD8PNzQ3BwcHQ6/Xj0rA9jHRWPxER3Z76+vX4rqoZ+843oPBiE3r7B/830d9djHvjTNMIU6b5QsSwRUQ0IdjkHC/A9H6Xk9NPHxMIBHj//fexdu1azJs3D7t27RrukkRERBNeX78eRy41Y39ZI769oES3dnDY8nUTY3GcHMtmByEt3I9hi4joNjLs4BUdHY3Tp09j1qxZA65v2bIFAHD//fePTWdEREQOTqPT49jlFuw734hvLiih1ugG1Xi7OmNxrBzL4oORHu4LJ5HQDp0SEZG9DTt4PfDAA9i9e7fF4RlbtmyBwWDAtm3bxqQ5IiIiR6PVGXC82hS2Dl5QoKtvcNjycnFGdqwMS+ODkRnhB2eGLSKi296wg1dPTw9efvllq/ffe+89vPfee6NqioiIyJH06w04caUV+8834ECFEp29/YNqPKROWBQjx7I5Qbgjwh9iJ4YtIiL6ybCD140bN7BkyRKIxWLcd999uP/++7FgwQKIxeLx6I+IiMgudHoDimpasf98IwoqFOjoGRy23CVOWBQjw9L4INwZ5Q+Jk8gOnRIR0UQw7KmGgGmM+/Hjx/GPf/wDX375JRobG7Fw4UIsX74cy5Ytg6+v73j0ajecakhEdHvQG4w4VdOKfWWNKChXoK1bO6jGTSxCVowMS2cH4e4ZAZA6M2wREd1ORpoNRhS8funixYvmEFZSUoLU1FTcf//9WLlyJaZMmTLa5e2OwYuIaPLSG4w4fa0N+843oKBcgRb14LDlKhZhwSxT2PrNTIYtIqLbmV2D1881Nzfjq6++wldffYW77roLzz333FgubxcMXkREk4vBYMSZ6+3Yf74BX5cr0NylGVQjdRZiQbTpMcJ7ZgbCRcywRUREDhS8JiMGLyKiic9gMOJcXTv2nW/E12WNUKoGhy2JkxDzowOxND4I86MD4Soe9qvQREQ0ydnsAOVfU1dXhz//+c/Yvn37WC9NREQ0LP16A07VtKGgohEHK5RosrCzJXYS4jczArA0PggLZsngLmHYIiKisTfm/3Vpa2vDxx9/zOBFRER20devx9HLLSgoV+Dbi5ZHv4tFQtw9wx9L44OQNUsGD6mzHTolIqLbybCD11dffXXL+zU1NSNuhoiIaCS6+vpxqLIJByoU+K6qGT1a/aAasZMQd0f5Y3FcEBbGyODlwrBFRES2M+zglZOTA4FAgFu9GiYQCEbVFBER0a9pVWvw7UUlCsoVOF7dCq3eMKjGTSzC/FkyLI6VY97MAD5GSEREdjPs/wIFBQXhvffew/Llyy3eLy0tRVJS0qgbIyIi+qWGjl4cqFCgoFyB09faYLDwd4A+rs5YGCPD4jg5MiP8OfqdiIgcwrCDV1JSEkpKSqwGr1/bDSMiIhqOK81qHKhQ4EC5Aj/c6LRYI/eUYnGcHNmxcqRM84GTSGjjLomIiG5t2MHr+eefR3d3t9X7kZGROHz48KiaIiKi25fRaERFg8q8s3W5SW2xbrq/mzlsxU/xglDIx9yJiMhx8RyvIeA5XkRE40tvMOJsbTsKyhU4UKHAjfZei3UxQZ5YHCfH4jg5ogLd+U4xERHZnE3O8aqtrUVYWNiQ6+vr6zFlypTh/AoiIrpNaHUGnKxpRUGFAgcrlGhRDz5jSyAAksJ8zDtbob6uduiUiIho9IYVvFJSUpCTk4M1a9YgJSXFYk1nZyc+/fRTvPPOO3j88cfx9NNPj0mjREQ08fVq9fj+UjMOVChQeFEJVZ9uUI2TUICMCD9kx8qxKEaGQE+pHTolIiIaW8MKXhcuXMBrr72GhQsXQiqVIikpCcHBwZBKpWhvb8eFCxdQUVGBuXPn4i9/+QuWLFkyXn0TEdEE0dnbj8OVTSgoV+C7S03o6x889l3iJMS8GQFYHCfHgmgZvFx5xhYREU0uI3rHq7e3F/v378exY8dw/fp19Pb2wt/fH4mJicjOzkZcXNx49Go3fMeLiGh4mrs0+OaCEgUVChRdaUG/fvB/ajwkTpg/K9B8xparmGdsERGR4xtpNnC44Rpbt27Fpk2boFAoMGfOHLz77rtITU21WPvFF1/g/fffR2lpKTQaDWJjY/HSSy8hOzvbXPPRRx9h9erVAz4nkUjQ19c35J4YvIiIfl1dW49p7HuFAmeut8PSf1383MRYFCtDdqzpjC2xE8e+ExHRxGKT4Rrjbc+ePcjNzcW2bduQlpaG/Px8ZGdno6qqCoGBgYPqjxw5goULF+L111+Ht7c3duzYgfvuuw+nTp1CYmKiuc7T0xNVVVXmnzkFi4hobFQ3daGgXIGCCgXK61UWa6Z4uyA7Vo7sWBmSp/lCxLHvRER0GxqTHa/29nYcPHgQ9fX1AIDg4GBkZ2fDx8dnWOukpaUhJSUFW7ZsAQAYDAaEhobiqaeewrp164a0RmxsLFasWIH169cDMO14Pfvss+jo6BhWLz/HHS8iIhOj0Yiy+k5z2KpptnyuY0SA6YytxbFBiJviyb/wIiKiScNuO15//etf8cYbb2Dp0qXm0fGnTp3Chg0b8Nxzz+H3v//9kNbRarUoKSlBXl6e+ZpQKERWVhaKioqGtIbBYEBXVxd8fX0HXFer1Zg6dSoMBgPmzp2L119/HbGxsVbX0Wg00Gh+GmusUln+W1wiotuB3mDE6WttpscIyxVo6LT8qPbsKV43x77LEBnoYeMuiYiIHNuog9df/vIXnD17Fu7u7gOuv/LKK5g7d+6Qg1dLSwv0ej1kMtmA6zKZDJWVlUNaY/PmzVCr1XjwwQfN12bOnInt27cjPj4enZ2d2Lx5MzIzM1FRUYGQkBCL62zcuBEbNmwY0u8kIpqMNDo9TlxpxYFyBb65oERrt3ZQjUAApEzzNT9GGOLDM7aIiIisGXXwEggEUKvVg4JXV1eXTR8t2bVrFzZs2IAvv/xywPtgGRkZyMjIMP+cmZmJWbNm4YMPPsArr7xica28vDzk5uaaf1apVAgNDR2/5omIHEC3RofvLzWjoFyBw5VN6NIMPmPLWSRAZoQ/FsfJkTVLhgAPiR06JSIimnhGHbw2b96MefPmIS4uzvyo4Y0bN1BRUYE333xzyOv4+/tDJBJBqVQOuK5UKiGXy2/52d27d2PNmjX47LPPkJWVdctaZ2dnJCYmorq62mqNRCKBRMI/TBDR5NfRo0XhxSYUVChw5FIzNLrBZ2y5OIvwm5mmM7buiQ6Ep5RnbBEREQ3XqIPXsmXLcO+996K4uBgNDQ0ATMM1UlNTIRKJhryOWCxGUlISCgsLkZOTA8D0zlZhYSHWrl1r9XOffPIJHn30UezevRtLly791d+j1+tRVlbGw52J6LbVpOrDgQtKHChX4GRNK3SGwTOWPKVOyJolQ3acHHdHBcBFPPR/nxMREdFgYzJOXiQSDXic70enTp1CWlrakNfJzc3FqlWrkJycjNTUVOTn56O7u9t8DldeXh7q6+uxc+dOAKbHC1etWoV33nkHaWlpUCgUAAAXFxd4eXkBAF5++WWkp6cjMjISHR0d2LRpE65fv441a9aM9msTEU0Yta2mM7YKKhQ4W2v5jC1/dwmyY2VYHCdHergfnEU8Y4uIiGisjOs5Xr/73e9QW1s75PoVK1agubkZ69evh0KhQEJCAgoKCswDNxobGwes9+GHH0Kn0+HJJ5/Ek08+ab6+atUqfPTRRwBMo+4fe+wxKBQK+Pj4ICkpCSdOnEBMTMzYfEkiIgdkNBpxSak2j32/2Gh5OmuIjwsWx8qxOE6OxDAfnrFFREQ0TkZ9jtfPJwj+nNFoxD//+U+o1erRLO8QeI4XEU0EBoMRP9zowIEKJQ5UKHC1xfIZWzNk7lgcK0d2nBwxQTxji4iIaDjsdo7Xt99+i7/97W+DphoajUYcOXJktMsTEdEt6PQGFF9rw4FyBQ5UKKFQWT5ja06otylsxcoQHuBusYaIiIjGz6iD129+8xt4eHjg7rvvHnQvPj5+tMsTEdEv9PXrcby6BQXlCnx7UYn2nv5BNUIBkDrdF4tj5VgUK0ewt4sdOiUiIqIfjfpRw9sBHzUkIntTa3T4rqrJfMZWt1Y/qEYsEuLOKH8sjpVjwaxA+LnzWAwiIqKxZrdHDYmIaHy0d2vxzUXT2Pej1S3QWjhjy1Uswj0zA5EdJ8c9MwPgwTO2iIiIHNKIg1dubq7F6wKBAFKpFJGRkVi+fDl8fX1H3BwR0e1G0dmHgxcUKChX4NTVNugtnLHl7eqMrFkyLI6V484of0idecYWERGRoxvxo4b33HMPzp07B51Oh5kzZwIALl26BJFIhOjoaFRVVUEgEODYsWMTfnQ7HzUkovF0raUbBRWmsFVa12GxRuYpwaIY09j31Om+PGOLiIjITmz+qOEDDzwAX19f7Nixw/wLOzs7sWbNGtx555147LHH8PDDD+MPf/gDDhw4MNJfQ0Q06RiNRlxs7MKBCgUOVChQqeiyWDfVz9U89j0hxBtCnrFFREQ0YY14xys0NBQHDhwYtJtVUVGBRYsWob6+HmfPnsWiRYvQ0tIyJs3aC3e8iGi0DAYjztV14MDNna3ath6LddFyDyyOkyM7Vo5ouQfP2CIiInIwNt/xam9vR1NT06Dg1dzcDJVKBQDw9vaGVqsd6a8gIprQ+vUGnKppQ0FFIw5WKNHUpbFYlxj24xlbckzzd7Nxl0RERGQLIw5ey5cvx6OPPoo333wTKSkpAIDTp0/jueeeQ05ODgCguLgYM2bMGJtOiYgmgL5+PY5casaBCiW+vahEZ+/gM7ZEQgHSw01nbC2MkUPuJbVDp0RERGRLI37UUK1W4w9/+AN27twJnU4HAHBycsKqVavw9ttvw83NDaWlpQCAhISEsevYDvioIRHdSldfPw5VNuFAhQLfVTWjx9IZW05C3B3lj+xYObJmyeDjJrZDp0RERDRaI80Goz5AWa1Wo6amBgAQHh4Od3f30SznkBi8iOiXWtUafHNBiQMVChyvboVWP/iMLTexCPNvjn2fNzMA7hIenUhERDTR2e0AZXd3d8THx492GSIih9fQ0WsejnH6WhssHLEFXzcxFs6SITtOhswInrFFREREJqMKXh0dHfjrX/+KixcvAgBiYmLw+9//Hl5eXmPSHBGRvV1pVqOg3DT2/fyNTos1QV5SZN8cjpEyzQdOPGOLiIiIfmHEjxqeOXMG2dnZcHFxQWpqKgDTcI3e3l4cPHgQc+fOHdNG7YmPGhLdPoxGIyoaVOadrctNaot10/3dsDhOjsWxcsSHeHHsOxER0W3C5u943XXXXYiMjMT//M//wMnJtHGm0+mwZs0a1NTU4MiRIyNZ1iExeBFNbnqDEWdr21FQbgpb9R29Futigz2RHSvH4jg5ogLdGbaIiIhuQzYPXi4uLjh37hyio6MHXL9w4QKSk5PR02P5cNCJiMGLaPJp69biVE0rjlxuwTcXlGhRDz5jSyAAksJ8zAcah/q62qFTIiIiciQ2H67h6emJ2traQcGrrq4OHh4eI12WiGhcdPb04+TVVpysaUXRlVZUKros1jkJBciI8MPiODkWxsgQ6MEztoiIiGj0Rhy8VqxYgd///vfYvHkzMjMzAQDHjx/H888/j5UrV45Zg0REI6Hq68fpq20outKKoppWXGhUwdr+vsRJiHkzArA4To4F0TJ4uTrbtlkiIiKa9EYcvDZv3gyBQIBHHnkEOp0ORqMRYrEY//7v/47/+q//GsseiYh+lVqjw5lrbSiqacXJK60oq++0OO4dMD1CGBvsiYxwP2RE+CE93A+uYp6xRURERONn1Aco9/T04MqVKwCAiIgIuLpOvncg+I4XkePp1epx5vpPO1rnb3RCby1pAZgV9FPQSp3uCy8X7moRERHR8NnkHa/c3Nwh17711lvDWZqI6Jb6+vU4W9uOkzeDVmldB/r11oPWDJm7OWilTfeDj5vYht0SERERDTSs4HXu3Lkh1Y1mxPLWrVuxadMmKBQKzJkzB++++675nLBf+uKLL/D++++jtLQUGo0GsbGxeOmll5CdnT2g7rPPPsOf/vQnXLt2DVFRUXjjjTewZMmSEfdIRONPo9OjtLYDRTeHYZyr64BWZ7BaHxHghowIP2SE+yMt3Bf+7hIbdktERER0a8MKXocPHx6vPgAAe/bsQW5uLrZt24a0tDTk5+cjOzsbVVVVCAwMHFR/5MgRLFy4EK+//jq8vb2xY8cO3HfffTh16hQSExMBACdOnMDKlSuxceNGLFu2DLt27UJOTg7Onj2LuLi4cf0+RDR0/XoDzt/oMD86WHK9HX391oPWdH83pIf7Ij3cDxnhfgj05PRBIiIiclyjfsdrLKWlpSElJQVbtmwBABgMBoSGhuKpp57CunXrhrRGbGwsVqxYgfXr1wMwTV/s7u7Gvn37zDXp6elISEjAtm3bhrQm3/EiGns6vQFl9Z2mYRg1bThzrQ09Wr3V+lBflwHDMIK8XGzYLREREZGJzc/xGmtarRYlJSXIy8szXxMKhcjKykJRUdGQ1jAYDOjq6oKvr6/5WlFR0aB307Kzs7F3716r62g0Gmg0Px2mqlKphvo1iMgKvcGICw0qFNW0oOhKK05fa4dao7NaH+wlRXqEnzlshfhMvsE9REREdPtwmODV0tICvV4PmUw24LpMJkNlZeWQ1ti8eTPUajUefPBB8zWFQmFxTYVCYXWdjRs3YsOGDcPonoh+yWAw4qJChaIrpkOLT11tQ1ef9aAl85SYQ1ZGuD9CfV1G9b4oERERkSNxmOA1Wrt27cKGDRvw5ZdfWnwfbDjy8vIG7JKpVCqEhoaOtkWiSc1oNOKSUo2iKy0ouhm0Onr6rdb7u0uQHu57M2j5Ybq/G4MWERERTVoOE7z8/f0hEomgVCoHXFcqlZDL5bf87O7du7FmzRp89tlnyMrKGnBPLpcPe02JRAKJhBPRiG7FaDTiSrPaPAzjVE0bWru1Vut93cSmoBVuekcrMtCdQYuIiIhuGw4TvMRiMZKSklBYWIicnBwApne2CgsLsXbtWquf++STT/Doo49i9+7dWLp06aD7GRkZKCwsxLPPPmu+9s033yAjI2PsvwTRJGY0GnGttccctE7WtKK5S2O13svFGWnTb+5oRfhhRqAHhEIGLSIiIro9OUzwAkwHNK9atQrJyclITU1Ffn4+uru7sXr1agCmRwDr6+uxc+dOAKbHC1etWoV33nkHaWlp5ve2XFxc4OXlBQB45plnMG/ePLz55ptYunQpdu/ejTNnzuDDDz+0z5ckmiCMRiPq2npRVNOCkzVtKLrSCoWqz2q9h9QJadNN493Tw/0QE+TJoEVERER0k0MFrxUrVqC5uRnr16+HQqFAQkICCgoKzMMxGhsbUVtba67/8MMPodPp8OSTT+LJJ580X1+1ahU++ugjAEBmZiZ27dqFF198ES+88AKioqKwd+9enuFFZEF9R69pR+vmQIz6jl6rtW5iEVKm+5oHYsQGe0HEoEVERERkkUOd4+WoeI4XTVaKzj6crGk1Pz5Y29ZjtdbFWYTkaT7mYRhxU7zgLBLasFsiIiIi+5vw53gR0fhr6uozPzZ4sqYVV1u6rdZKnIRImupj3tGKD/GG2IlBi4iIiGgkGLyIJrFWtQanrraZd7Sqm9RWa8UiIRLDvJERYXpHKzHMGxInkQ27JSIiIpq8GLyIJpGOHi1O1rSZHx+sUnZZrXUSCpAQ6m1+dHDuVB9InRm0iIiIiMYDgxfRBNbZ24/TV9tQdDNoXVSoYO2tTZFQgPgQL6SHm4JW8jQfuIr5rwAiIiIiW+CfuogmELVGNyBoVTR0wmAlaAkFQNwUL9OBxRF+SJnmC3cJ/1+eiIiIyB74pzAiB9aj1eHMtXZz0Cqr74TeStISCICYIE9T0Ar3Q8p0X3i5ONu4YyIiIiKyhMGLyIH09etRcr3dPAzjh7oO6KxtaQGIlnuYHh2M8EPadF94u4pt2C0RERERDRWDF5EdaXR6nKvtMAet0toOaPUGq/VRge7mqYNp033h5y6xYbdERERENFIMXkQ2pNUZ8MONm0HrSivO1rZDo7MetML93ZB+c+pgergfAjwYtIiIiIgmIgYvonHUrzegrL7TfGDxmWvt6O3XW62f6ueK9Ol+5l0tuZfUht0SERER0Xhh8CIaQzq9ARUNKvMwjDPX2tCttR60pni7mM/RSo/wwxRvFxt2S0RERES2wuBFNAoGgxEXGlXmA4uLr7ahS6OzWi/3lJqDVkaEH0J9XW3YLRERERHZC4MX0TAYDEZUKbvMwzCKr7ahs7ffan2Ah8QcsjLC/TDVzxUCgcCGHRMRERGRI2DwIroFo9GI6ia1+dHBU1fb0NattVrv5yZG+s3HBjPC/RAR4MagRUREREQMXkQ/ZzQaUdPSbR6GcbKmDS1qjdV6b1dn8zCMjAg/RAW6M2gRERER0SAMXnRbMxqNqG3rMT86eLKmFUqV9aDlIXVC2vSfHh2MlntAKGTQIiIiIqJbY/Ci205dW49pGEZNK05eaUVDZ5/VWneJE1Kn+5rf05oV5AkRgxYRERERDRODF016jZ295gOLi2pacaO912qtq1iE5Gk/Ba24YE84iYQ27JaIiIiIJiMGL5p0mlR95scGi6604lprj9VaqbMQyVN9zQcWx4d4wZlBi4iIiIjGGIMXTXgtao05ZBXVtKKmudtqrdhJiLlh3sgI90dGhB/mhHpB4iSyYbdEREREdDti8KIJp71be3PioCloXVKqrdY6iwRIDPUxj3dPDPOG1JlBi4iIiIhsy+GC19atW7Fp0yYoFArMmTMH7777LlJTUy3WNjY24o9//CPOnDmD6upqPP3008jPzx9Q89FHH2H16tUDrkkkEvT1WR+oQI6ls6cfp662ms/SqlR0Wa11EgoQH+J1c+qgP5Km+sBFzKBFRERERPblUMFrz549yM3NxbZt25CWlob8/HxkZ2ejqqoKgYGBg+o1Gg0CAgLw4osv4u2337a6rqenJ6qqqsw/85wlx9bV14/T19rMjw5WNKhgNFquFQqA2SHe5mEYyVN94CZxqP9ZExERERE5VvB666238Nhjj5l3qLZt24b9+/dj+/btWLdu3aD6adOm4Z133gEAbN++3eq6AoEAcrl8fJqmUevW6ExB6+Z497L6ThisBC2BAIgN9jQHrZRpvvCQOtu2YSIiIiKiYXKY4KXValFSUoK8vDzzNaFQiKysLBQVFY1qbbVajalTp8JgMGDu3Ll4/fXXERsba7Veo9FAo/npEF2VSjWq308D9Wr1KLnejqKaFhRdacX5G53QWUtaAGYFmYJWergv0qb7wcuVQYuIiIiIJhaHCV4tLS3Q6/WQyWQDrstkMlRWVo543ZkzZ2L79u2Ij49HZ2cnNm/ejMzMTFRUVCAkJMTiZzZu3IgNGzaM+HfSQH39epytbcfJm48OltZ1oF9vPWjNkLmbd7TSpvvBx01sw26JiIiIiMaewwSv8ZKRkYGMjAzzz5mZmZg1axY++OADvPLKKxY/k5eXh9zcXPPPKpUKoaGh497rZKHR6fFDXefNd7RacLa2A1qdwWp9RICbeRhGWrgv/N0lNuyWiIiIiGj8OUzw8vf3h0gkglKpHHBdqVSO6ftZzs7OSExMRHV1tdUaiUQCiYR/+B+qfr0B5290mIdhlFxvR1+/9aA1zc/VfGBxRrgfAj2lNuyWiIiIiMj2HCZ4icViJCUlobCwEDk5OQAAg8GAwsJCrF27dsx+j16vR1lZGZYsWTJma95udHoDyhtU5qB15loberR6q/Whvi7mRwfTw/0Q5OViw26JiIiIiOzPYYIXAOTm5mLVqlVITk5Gamoq8vPz0d3dbZ5ymJeXh/r6euy7wAWcAAAR/klEQVTcudP8mdLSUgCmARrNzc0oLS2FWCxGTEwMAODll19Geno6IiMj0dHRgU2bNuH69etYs2aN7b/gBKU3GHGhQWUehnH6WjvUGp3V+mAvqfnA4owIP4T4uNqwWyIiIiIix+NQwWvFihVobm7G+vXr///27j0oqvP+4/gHFhYQuSkiAt6QxAqYICiEJFPNhAm2sZr0ljqWasaYSSZOmphBnba2qVOn2oTESq2Zto4mk2nTm7E2STGpQmoSBIeLGW9oxUuKLiYYAQEB3ef3R+L+siqGi2cP4Ps1w4z77HN2v0e/w5yPz55n5XK5lJaWpqKiIs+GG6dPn9bJkye9jpkyZYrnzxUVFfrjH/+osWPH6vjx45KkTz/9VIsWLZLL5VJUVJQyMjL0wQcfeIIZruZ2Gx1yNXu+sLj8WIOaLnQdtEaGB32+6+BnQWvMsCF8VxoAAADwBX7GdPXVtLisqalJERERamxsVHh4uN3l3HDGGB2uP6/So5+otLZBZcfO6lxrZ5fzo4c6PSErO3G4xkeHErQAAABwU+htNuhXK17wDWOMjn7c4vnC4t21DWpo6ehyftSQQK+glRQzlKAFAAAA9ADB6yZgjNHxhlaVfh6ySmsb9HFze5fzI0IClTV+2GdBa8Jw3RoTJn9/ghYAAADQWwSvQeqjs62eXQdLjzbI1XShy7lhQQHKShymOz6/T2vSqHA5CFoAAADADUPwGiTqzrVp9xeCVt25ti7nhjodmjZ+mGfXwZS4CIIWAAAAYCGC1wBV33ThsxWtz8PWybOtXc4NCXRo6rgoz31ak+MjFOjw92G1AAAAwM2N4DWANLZ1ak3RIe0+2qDaT1q6nBcU4K+MsVGeFa3bEiLlDCBoAQAAAHYheA0goU6H/ll9Ss1XfHmx0+GvtDGRnqCVNjpSwYEOm6oEAAAAcCWC1wAS4PBX5vhhevfwx0obHenZ3j19bBRBCwAAAOjHCF4DzMoHUhU1JFBDnPzTAQAAAAMFV+8DTHxkiN0lAAAAAOghdlwAAAAAAIsRvAAAAADAYgQvAAAAALAYwQsAAAAALEbwAgAAAACLEbwAAAAAwGIELwAAAACwGN/j1Q3GGElSU1OTzZUAAAAAsNPlTHA5I3QXwasbmpubJUmjR4+2uRIAAAAA/UFzc7MiIiK6Pd/P9DSq3YTcbrdOnTqlsLAw+fn52V2OmpqaNHr0aH300UcKDw+3uxz0c/QLeoqeQU/RM+gpegY91Z96xhij5uZmxcXFyd+/+3duseLVDf7+/kpISLC7jKuEh4fb3ngYOOgX9BQ9g56iZ9BT9Ax6qr/0TE9Wui5jcw0AAAAAsBjBCwAAAAAs5nj22WeftbsI9JzD4dCMGTMUEMCnRfHl6Bf0FD2DnqJn0FP0DHpqoPcMm2sAAAAAgMX4qCEAAAAAWIzgBQAAAAAWI3gBAAAAgMUIXgAAAABgMYLXALBq1SrdeeedGjJkiCIjI7t1jDFGP/3pTzVq1CiFhIQoJydHR44csbhS9Bdnz57VvHnzFB4ersjISC1cuFDnz5+/7jHnz5/X4sWLlZCQoJCQECUnJ+ull17yUcWwW296RpIOHjyo2bNnKyIiQqGhoZo2bZpOnjzpg4pht972zGWPPfaY/Pz8tHbtWgurRH/S057p7OzUsmXLNHnyZIWGhiouLk4/+MEPdOrUKR9WDV9av369xo0bp+DgYGVlZam8vPy680tKSpSenq6goCAlJSVp8+bNvim0lwheA0BHR4e+853v6PHHH+/2Mb/61a+0bt06vfTSSyorK1NoaKhyc3N14cIFCytFfzFv3jzt379f77zzjt544w395z//0aOPPnrdY5YsWaKioiK9+uqrOnjwoJ5++mktXrxY27Zt81HVsFNveubo0aO6++679ZWvfEUlJSX68MMPtWLFCgUHB/uoatipNz1z2euvv67du3crLi7O4irRn/S0Z1pbW1VZWakVK1aosrJSW7ZsUU1NjWbPnu3DquErf/7zn7VkyRL97Gc/U2VlpW6//Xbl5ubqzJkz15x/7Ngx3X///brnnntUXV2tp556So888oi2b9/u48p7wGDA2LRpk4mIiPjSeW6328TGxprnnnvOM3bu3DkTFBRk/vSnP1lZIvqBAwcOGElmz549nrF//etfxs/Pz9TV1XV5XEpKilm5cqXXWHp6uvnxj39sWa3oH3rbMw899JD5/ve/74sS0c/0tmeMMeZ///ufiY+PN/v27TNjx441L774otXloh/oS898UXl5uZFkTpw4YUWZsFFmZqZ54oknPI8vXbpk4uLizC9/+ctrzl+6dKlJSUnxGnvooYdMbm6upXX2BSteg9CxY8fkcrmUk5PjGYuIiFBWVpZKS0ttrAy+UFpaqsjISE2dOtUzlpOTI39/f5WVlXV53J133qlt27aprq5OxhgVFxfr8OHDuu+++3xRNmzUm55xu9168803deuttyo3N1cxMTHKysrS1q1bfVU2bNTb3zNut1t5eXnKz89XSkqKL0pFP9HbnrlSY2Oj/Pz8un3rBQaGjo4OVVRUeF27+vv7Kycnp8tr19LSUq/5kpSbm9uvr3UJXoOQy+WSJI0cOdJrfOTIkZ7nMHi5XC7FxMR4jQUEBGjYsGHX/fcvLCxUcnKyEhIS5HQ6NXPmTK1fv15f/epXrS4ZNutNz5w5c0bnz5/X6tWrNXPmTL399tt68MEH9c1vflPvvvuuL8qGjXr7e2bNmjUKCAjQk08+aXWJ6Gd62zNfdOHCBS1btkxz585VeHi4FWXCJp988okuXbrUo2tXl8t1zflNTU1qa2uzrNa+IHjZZPny5fLz87vuz6FDh+wuE/2I1T1TWFio3bt3a9u2baqoqFBBQYGeeOIJ/fvf/76BZwFfsrJn3G63JGnOnDl6+umnlZaWpuXLl2vWrFlsyjKAWdkzFRUV+vWvf63NmzfLz8/vBlcOu/jqeqazs1Pf/e53ZYzRhg0bbkDlgO8F2F3AzeqZZ57RggULrjsnMTGxV68dGxsrSaqvr9eoUaM84/X19UpLS+vVa8J+3e2Z2NjYq25EvXjxos6ePevpjSu1tbXpRz/6kbZs2aJZs2ZJkm677TZVV1fr+eefv2opHwODlT0THR2tgIAAJScne41PmjRJ7733Xp/qhn2s7Jldu3bpzJkzGjNmjGfs0qVLeuaZZ7R27VodP368r+XDBlb2zGWXQ9eJEye0c+dOVrsGoejoaDkcDtXX13uN19fXd9kfsbGx15wfHh6ukJAQy2rtC4KXTUaMGKERI0ZY8trjx49XbGysduzY4QlaTU1NKisr69HOiOhfutsz2dnZOnfunCoqKpSRkSFJ2rlzp9xut7Kysq55TGdnpzo7OxUQ4P0rweFweFY2MPBY2TNOp1PTpk1TTU2N1/jhw4c1duzYvhcPW1jZM3l5ede8HyMvL08PP/xw34uHLazsGen/Q9eRI0dUXFys4cOH37Da0X84nU5lZGRox44deuCBByR99smKHTt2aPHixdc8Jjs7W2+99ZbX2DvvvKPs7GzL6+01u3f3wJc7ceKEqaqqMj//+c/N0KFDTVVVlamqqjLNzc2eORMnTjRbtmzxPF69erWJjIw0//jHP8yHH35o5syZY8aPH2/a2trsOAX42MyZM82UKVNMWVmZee+998wtt9xi5s6d6zXnyp6ZPn26SUlJMcXFxaa2ttZs2rTJBAcHm9/+9re+Lh826E3PbNmyxQQGBprf/e535siRI6awsNA4HA6za9cuX5cPG/SmZ67EroY3l572TEdHh5k9e7ZJSEgw1dXV5vTp056f9vZ2O04BFnrttddMUFCQ2bx5szlw4IB59NFHTWRkpHG5XMYYY5YvX27y8vI882tra82QIUNMfn6+OXjwoFm/fr1xOBymqKjIrlP4UgSvAWD+/PlG0lU/xcXFnjmSzKZNmzyP3W63WbFihRk5cqQJCgoy9957r6mpqfF98bBFQ0ODmTt3rhk6dKgJDw83Dz/8sFdQN+bqnjl9+rRZsGCBiYuLM8HBwWbixImmoKDAuN1uH1cPO/SmZ4wxZuPGjSYpKckEBweb22+/3WzdutWHVcNOve2ZLyJ43Vx62jPHjh275vXPlddAGDwKCwvNmDFjjNPpNJmZmWb37t2e5+bPn2+mT5/uNb+4uNikpaUZp9NpEhMTr/v7pj/wM8YY36+zAQAAAMDNg10NAQAAAMBiBC8AAAAAsBjBCwAAAAAsRvACAAAAAIsRvAAAAADAYgQvAAAAALAYwQsAAAAALEbwAgAAAACLEbwAAAAAwGIELwAAAACwGMELADBozJgxQ0899ZTdZUiSGhoaFBMTo+PHj3f7mO9973sqKCiwrigAgG0IXgAAWGDVqlWaM2eOxo0b1+1jfvKTn2jVqlVqbGy0rjAAgC0IXgAA3GCtra3auHGjFi5c2KPjUlNTNWHCBL366qsWVQYAsAvBCwAwKLW3t+vJJ59UTEyMgoODdffdd2vPnj1ec5qbmzVv3jyFhoYqPj5e69atuyEfV3zrrbcUFBSkO+64w2s8NTVVv/jFL/TYY48pKipKsbGxWrt2rdecb3zjG3rttdf69P4AgP6H4AUAGJSWLl2qv//973r55ZdVWVmppKQk5ebm6uzZs545S5Ys0fvvv69t27Zp+/btKikpUVVVVZ/fe9euXcrIyPAaa29vV01NjV555RVNnz5de/bs0bx587Rs2TK1tLR45mVmZqq8vFzt7e19rgMA0H8QvAAAg05LS4s2bNig5557Tl/72teUnJys3//+9woJCdHGjRslfbba9fLLL+v555/Xvffeq9TUVG3atEkXL170eq0HH3xQUVFR+va3v+01/sYbb2jixIm65ZZb9Ic//MHruRMnTiguLs5rbN++fbp48aLWrVunuXPnKikpSQsWLFBHR4daW1s98+Li4tTR0SGXy3Uj/0oAADYjeAEABp2jR4+qs7NTd911l2csMDBQmZmZOnjwoCSptrZWnZ2dyszM9MyJiIjQxIkTvV7rhz/8oV555RWvsYsXL2rJkiXauXOnKisrtWbNGjU0NHieb2trU3BwsNcxe/fuVWxsrHJzcz1jH3/8sZxOp4YNG+YZCwkJkSSvMAYAGPgIXgAAXMeMGTMUFhbmNVZeXq6UlBTFx8crLCxMX//61/X22297no+Ojtann37qdUx1dbWmTp0qPz8/r7HU1FQ5HA7P2OWPQo4YMcKK0wEA2ITgBQAYdCZMmCCn06n333/fM9bZ2ak9e/YoOTlZkpSYmKjAwECvDTcaGxt1+PDhL339U6dOKT4+3vM4ISFBdXV1nsdTpkzRgQMHvI7Zu3ev0tLSvMaqq6uvGtu3b58SEhIUHR3djTMFAAwUBC8AwKATGhqqxx9/XPn5+SoqKtKBAwe0aNEitba2erZ4DwsL0/z585Wfn6/i4mLt379fCxculL+/v9eqVG/k5uZq//79Xqte1wpeVVVVV43t2rVL9913X5/eHwDQ/xC8AACD0urVq/Wtb31LeXl5Sk9P13//+19t375dUVFRnjkvvPCCsrOzNWvWLOXk5Oiuu+7SpEmTrro/60pxcXFeK1x1dXVem2lMnjxZ6enp+stf/iJJOn78uBobG71CVnt7uw4dOqQpU6Z4xi5cuKCtW7dq0aJFfT5/AED/4meMMXYXAQBAf9DS0qL4+HgVFBR4fflxSUmJfvOb3+hvf/ubpM8215g0aZJKSkoUERGhjIwMffDBBxo+fLjnmDfffFP5+fnat2+f/P2v/n/OiooKTZs2TY2NjZ57yDZs2KDXX3/d634xAMDgEGB3AQAA2KWqqkqHDh1SZmamGhsbtXLlSknSnDlzPHNycnK0d+9etbS0KCEhQX/961+VnZ2tgoIC3XPPPXK73Vq6dKlX6JKk+++/X0eOHFFdXZ1Gjx59zfdOTEz02rgjMDBQhYWFFp0tAMBOrHgBAG5aVVVVeuSRR1RTUyOn06mMjAy98MILmjx5suXvvXjxYrlcLs8qGgBgcCN4AQAAAIDF2FwDAAAAACxG8AIAAAAAixG8AAAAAMBiBC8AAAAAsBjBCwAAAAAsRvACAAAAAIsRvAAAAADAYgQvAAAAALAYwQsAAAAALEbwAgAAAACL/R8RZIg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"text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo1.jl\")" ] }, { "cell_type": "code", "execution_count": 11, "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": 12, "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": 13, "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": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 15, "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": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 2000, P = 1990, |I| = 6\n", "F(s) = 0.18\n", "ERC(I) = 0.25\n", "w-ERC(s) = 0.29\n", "Coh(|s|) = 2.16\n" ] } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo2.jl\")" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 2000, P = 1990, |I| = 6\n", "F(s) = 0.18\n", "ERC(I) = 0.23\n", "w-ERC(s) = 0.25\n", "Coh(|s|) = 1.65\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": 19, "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": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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QQ9ixY4e5SvrOO+9ArVZj9OjR+Pbbb1FRUSF2mA7P6mT08OHDiIuLQ1ycaZhz9uzZiIuLw0svvQQAyMzMNCemANC2bVt8//332LVrF2JiYrBkyRL897//dci2Ti1ZzWQ0U5cpYiQOIrxX9XH6EfHiaGG83OWYGB+Fn2YPwtpJfXBbhyDzfTq9Aet+u4Lbl+zFY+v+wP4LeRAEQcRoiYjsJzQ0FHPmzMGpU6ewf/9+qFQqTJkyBc8//7z5nPoKeq7K6mH6wYMH3/QDpLbdlQYPHoxjx45Z+1JkRwEeAVBIFdAb9cjWZdf/gJYuvGf1cfpRoBvn+diTVCrBkM4hGNI5BBeyi7D2tyv46mgayiqMEARg99kc7D6bg44qb0y+tS3ujQ2Hp0ImdthERHbRu3dv9O7dG0uXLkVaWpr59sOHD2PIkCHm61WLtR999FGX3p1SIjhBaUKr1cLPzw8ajQa+vlyha6s7v7oTKUUp8HLzwv/G/U/scMRVlA0s6Wg6bjMAmPy9uPG4gMISPTb9kYpPfruCDI3lilp/pRse7tsaE+PbINSv9oWNROQ8ysrKcPnyZbRt2xYeHh5ih0N2dLP/t7bma+xS7UKqhup1FToU6YtEjkZkPirAN8J0nJkMGA3ixuMC/JUKTB90C36ZMwTLx/VE7zatzPcVllRgxd6/MOCNPXjqs6M4crWAQ/hERC7CIfuMUtP4+7xRH4WPiNE4gPCegDYN0BcDeeeBkC5iR+QS5DIp7uwRijt7hOJEmgZrD1zGd8czUGEQYDAK2HY8E9uOZ3J3JyIiF8G/8C7EYkW9q7d3Am6cN0rNLjrCD0vHxuLA3Nsxc2gHBHlXb81atbvTgDd+xgc/X8C14ubfuYWIiJoek1EXwmT0b7ii3mGE+Hpg9h0dsX/u7Xh7dAy6hlbPNcopMu3uFL/4Z8z54k/zrk9ERNQycJjehbDx/d+ExgKQABBMze9JdB5uMjzYKwIP9AzHocv5WHvgCn48nWXe3enzw2n4/HAad3ciImpBmIy6ELWSlVELHr5AUEcg7xyQdRKoLAfk4mxXR5b+vrvTJwevYNMfte/uNDG+Dcb0iYQvd3ciInJKHKZ3IWx8X4uqeaPGClNCSg4nMkCJBXfWvbvTf74/g3ju7kRE5LSYjLoQb4U3fNxMK+hZGb2O80adhsXuTpPr3t1pCnd3IiJyKhymdzFqbzWKCoqQVZIFo2CEVOLi30dqrqjnvFGnIJVKMKRTCIZ0CsHFnCKsPXAFXx1NR2mFAYIA/Hw2Bz9f391p3sguGNIpROyQiYjoJlw8E3E9VfNGK42VyC/LFzkaB6DqDkivzzVkZdTptA/xwWv3RePgvNvxfGJnhPlV7wZyPrsY05IO4+ez3P6WiMiRMRl1MTVX1GcWc94o5O6AOtp0nHceKNOIGw/ZpObuTh8+0hM9W/sDACqNAmZsOIrDV/jFi4jqN2nSJEgkkhsuI0aMMJ8TFRVlvl2pVCI6Ohr//e9/b3guQRDw0UcfoV+/fvD29oa/vz969+6Nd955ByUlJXaJ99SpU3jggQfMMb3zzjt2ed7mxmTUxVj0Gi3hvFEAfxuqTxYvDmo0uUyKkdGh2DK9P+7qYfriVVZhxJR1f7A/KRE1yIgRI5CZmWlx2bhxo8U5r776KjIzM3Hy5EmMHz8e06ZNw44dOyzOmTBhAmbNmoVRo0Zhz549SE5OxosvvohvvvkGP/74o83xpaammo9LSkrQrl07LF68GGq1+iaPcmxMRl2MxYp6VkZNuIipxZFJJVg6Jta8yElbVomJaw4h5Zp9qhFE1HK5u7tDrVZbXFq1amVxjo+PD9RqNdq1a4e5c+ciMDAQu3btMt//+eefY8OGDdi4cSPmz5+PPn36ICoqCqNGjcLPP/+MIUOGWBVTSkoKXnvtNXTs2BEzZ840396nTx+89dZbeOihh+Du7rytCbmAycWwMlqLMC5iaokUcilWju+FR/77O5JTC5FbVI4Ja37HlunxCPHxqP8JiMi+Vg0CinOa/3W9Q4An9jXJUxuNRmzduhX5+flQKKq3M96wYQM6deqEUaNG3fAYiUQCPz+/ep9bp9Phq6++QlJSEvbs2YN//OMfePbZZzFmzBi7/gyOgMmoi+GWoLUI6gAofAB9Efeob2G83OVYO6kPRq86iIs5xbh6rQSPrvkDmx7/B/w82SSfqFkV5wBFGWJHUa9t27bB29vb4rb58+dj/vz55utz587FCy+8gPLyclRWViIgIABTp04133/hwgV06tTJptfft28fkpKSsGXLFoSEhGD8+PFYtWoVbrnlFtt+ICfAZNTFqJQqSCCBAIHJaBWpDAiLBa78CmjTgaIswMd5596QpVZeCqx/rC8eXHEQ6YWlOJOpxbSkw/jksb7wcJOJHR6R6/AWqc2ala87ZMgQrFixwuK2gIAAi+vPPfccJk2ahMzMTDz33HOYMWMG2rdvb76/MX2OBw8eDE9PTyxbtgxPPPGEzc/jTJiMuhiFTIFAz0DkleYxGa0pvKcpGQVM1dHOI8WNh+wq1M8T6x/ri9ErD+KaTo9DV/Lx1GdHsWJ8L7jJOHWeqFk00VC5vXl5eVkklrUJCgpC+/bt0b59e2zZsgXR0dHo3bs3unbtCgDo2LEjzp49a9Prf/fdd0hKSsLTTz+NVatWYcKECXj44YedeoFSffhX2AVVtXfKK81DhaFC5GgcBOeNtnjtgr2xbnJfeLubvoP/dCYHc788DqOROzURke0iIyMxduxYzJs3z3zbuHHjcP78eXzzzTc3nC8IAjSautsI3nXXXdiyZQsyMzMxdepUbNq0CREREUhMTMRnn31mt7ZQjoTJqAuqmjcqQEB2CRuCA+CKehcRHeGHjyb2guJ6NfSro+l4bfsZbh1KRGbl5eXIysqyuOTl5d30MU8//TS+++47HD58GAAwZswYjB07Fg8//DBef/11HD58GFevXsW2bduQkJCAPXv21BtHq1atMGPGDPz+++84efIkYmJiMGfOHEyYMMF8jl6vR3JyMpKTk6HX65Geno7k5GRcvHixcW9CM2My6oIs2jvp2N4JAOAXAXgFm47TjwJMTlqs/rcE4b2H4yCVmK6v3n8ZH+79S9ygiMhh7Ny5E6GhoRaXAQMG3PQxXbt2xbBhw/DSSy8BMK2Y/+yzz7B06VJ8/fXXGDRoEHr06IGXX34ZQ4cOxbBhw6yKqXPnzli8eDFSUlKwaNEi8+0ZGRmIi4tDXFwcMjMz8fbbbyMuLs5iMZUzkAhOUBLQarXw8/ODRqOBr6+v2OE4vU9OfYK3Dr8FAHh9wOu4+5a7RY7IQXw2Fji/03T8r6NAYMtduUjA5j9SMPfLE+brr98XjXH9WosYEVHLUVZWhsuXL6Nt27bw8GArtZbkZv9vbc3XWBl1QaHe1VuCchFTDTWH6jOOiRcHNYuxfVpj7ojO5usvfH0C209wpICIqLkxGXVBaiV7jdaq5iImzht1CdMHtcPjA9sBAIwCMGtTMg5cvPncMCIisi8moy6IuzDVIZzJqKuRSCSYl9gZo3tFAAD0BiMe/+Qw/kwtFDkyIiLXwWTUBQV6BkIuNbW34QKmGpQBQKso03HmcYBtr1yCRCLBovujcUdXFQBApzdg0tpDuJhTLHJkRESugcmoC5JKpFApTR+8HKb/m6p5o5WlQM4ZcWOhZiOXSfH+w3Ho19a0y0pBSQUmrP4dGYWlIkdGRNTyMRl1UVWN74v0RdBV6ESOxoGw+b3L8nCT4eNHe6NrqGkFaKamDBNW/458nV7kyIiIWjYmoy7KYt4oq6PV2Pzepfl6uCFpSl9EBSoBAH/l6jB57SEUl1eKHBkRUcvFZNRFVVVGAc4btRDaA5Bc/7VIZ3snVxTs4471j/WDytcdAPBnmgbT1x9BeaVB5MiIiFomJqMuipXROii8gJCupuOc04C+5e0BTPWLDFDikyn94OfpBgDYfzEPz2xOhoH72BMR2R2TURfFLUFvIizO9F/BAGQdFzcWEk0ntQ/WTOoDTzcZAGD7iSy88PVJ7mNPRGRnTEZdFCujN8F5o3RdrzatsGJ8T8ivb2S/8VAKlvx4XuSoiMhRrVu3DhKJ5IZLzW0zJ02aZL7dzc0Nbdu2xZw5c1BWVnbD8+3ZswcjR45EYGAglEolunbtimeffRbp6el2ibesrAyTJk1CdHQ05HI57r33Xrs8r7WYjLqomnNGmYz+jUUyyhX1rm5wpxAsGRMDiSkfxQd7LmL1/sviBkVEDsvX1xeZmZkWl6tXr1qcM2LECGRmZuLSpUtYtmwZVq1ahYULF1qcs2rVKiQkJECtVuPLL7/E6dOnsXLlSmg0GixZssTm+FJSUszHBoMBnp6emDlzJhISEmx+zsaSi/bKJCofhQ+83Lygq9AxGf27kC6A3AOoLGNllAAAo2LDUVhSgYXfngIA/N+202ildMP9PSNEjoyI7GXbtm0YP348rl27BplMhuTkZMTFxWHu3LlYvHgxAGDq1KkoKyvDp59+WufzSCQSqNXqOu8HAHd3d/M5kZGRuOOOO7Br1y688cYbAIC0tDTMnDkTM2fOxLJly8yPi4qKwsCBA1FYaN0ucVqtFlu2bEFSUhJOnjyJ/Px8AICXlxdWrFgBADhw4IDVz2svTEZdmFqpxl+av5Cly4IgCJBUlX5cncwNCI0BUn8HCi4DJfmm3ZnIpT3aPwr5Oj3e3X0BAPDcF8fh5+mGoV1UIkdG5BzGbhuLvNK8Zn/dIM8gbL5rc73n3XbbbSgqKsKxY8fQu3dv7Nu3D0FBQdi7d6/5nH379mHu3Ll2je/kyZM4cOAA2rRpY75ty5Yt0Ov1mDNnTq2P8ff3r/d5jUYjdu/ejaSkJHz11VcIDw/H+PHjsW7dOnuFbjdMRl2Y2tuUjOqNeuSX5SPQM1DskBxHWE9TMgqYmt+3F2/4ghzHrIQOKCjR45ODV2EwCpix4SjWP9YPfdvyywpRffJK85BTkiN2GHXy8/NDbGws9u7di969e2Pv3r145pln8Morr6C4uBgajQYXL17EoEGDbvo8Go0G3t7eFrfddttt2LFjh/n6tm3b4O3tjcrKSpSXl0MqleKDDz4w33/hwgX4+voiNDQU1jp//jzWrVuH9evXQ6fTYcyYMfjpp5/Qv39/q5+ruTAZdWFqZY1FTCVZTEZr+vu8USajBNPw28t3d0NBSQW++zMD5ZVGPJb0BzY/Ho+uYb5ih0fk0II8gxz+dQcNGoS9e/fi2Wefxa+//opFixbh888/x/79+5Gfn4+wsDB06NABACwSzvHjx2PlypUAAB8fHxw9arnewNPT0+L6kCFDsGLFCuh0OixbtgxyuRwPPPCA+f7GjFY+/vjj2LdvH6ZPn46lS5fe8NqOiMmoC7NYxFSchW6B3USMxsGE19gWlIuYqAapVIIlo2OgKa3AL+dzUVRWiYlrDuGL6fGICvISOzwih9WQoXKxDR48GGvWrMGff/4JNzc3dO7cGYMHD8bevXtRUFBgURVNTk42H/v6Vn8ZlUqlaN++/U1fx8vLy3zOmjVrEBMTg9WrV+Oxxx4DAHTs2BEajQaZmZlWV0ffeecdrF69Ghs3bsS2bdvwyCOPYMKECejWzXE/47ma3oVZtHcq4SImCwHtAA8/03H6EYC9JakGhVyKleN7Iq61ad5WXnE5Rq86iBNpGpEjI6LGqJo3umzZMnPiWZWM7t27F4MHDzaf2759e/MlJCTE5teUSqWYP38+XnjhBZSWlgIAHnzwQSgUCrz55pu1PuZmC41iY2Px/vvvIyMjA++++y7OnDmDuLg49OzZE8uWLUNWluN93jMZdWEWW4IWs/G9BYnENG8UAHQ5gNY+Pd2o5VAq5Fg7qQ86qkxDdblF5Riz6iB2n8kWOTIislWrVq3Qo0cPbNiwwZx4Dhw4EEePHsX58+frnS8KmIbYs7KybrgYjcY6HzN69GjIZDIsX74cgGmF/bJly/Duu+/isccew759+3D16lUcOHAATzzxBP7v//6v3jgUCgWZ1z8wAAAgAElEQVTuv/9+fPPNN0hPT8fEiRPxySef3FAhPX36NJKTk5Gfnw+NRoPk5GSLqm9zYDLqwlgZrQeb31M9/JUKbHo8Hr3btAIAlFYYMO2Tw1h/8IqocRGR7QYNGgSDwWBORgMCAtC1a1eo1Wp06tSp3sdrtVqEhobecMnJqXvxllwux1NPPYU333wTOp0OADBjxgz8+OOPSE9Px3333YfOnTtj6tSpkMlkmDVrllU/U3BwMGbNmoVjx47hwIEDFveNHDkScXFx+O6777B3717ExcUhLi7OqudvLIngBHvbabVa+Pn5QaPRWMzLoMYpN5Sj96e9AQA9gntgw8gNIkfkYM5+D2waZzq+dRZwxyvixkMOq6zCgGe3/Invj1ePMDw+sB2eH9EZUilbppHrKSsrw+XLl9G2bVuL3YfI+d3s/62t+Roroy7MXeaOAA9TSxo2vq8FK6PUQB5uMrz/UByeGNTOfNtHv1zCUxuPoqzCIGJkRESOj8moi6saqs8rzUOFsULkaByMjxrwDTcdZyQDN5nvQySVSjAvsQv+c293VBVDt5/IwriP/4drxeXiBkdE5MCYjLq4qkVMRsGI3JJckaNxQGHX583oi4BrF8SNhZzC+H+0wepH+0CpkAEAjqYU4oEVv+Fynk7kyIiIHBOTURdnsYiJQ/U3+nvze6IGGNI5BJ8/EY8QH3cAwJVrJbj/wwM4fCVf5MiIiBwPk1EXZ9HeScf2TjewaH7PeaPUcN3D/bD1n7eik8oHAFBQUoFx//0d245niBwZUfNxgjXSZKWm+H/KZNTFqbxU5mNWRmsRVqO9BZNRslK4vye2PBmPAe1N2xHqK4146rNjWLnvL35IU4smk5mmqej1epEjIXsrKSkBALi5udntObkdqItjZbQeHn5AYAfTfNHsk0BlOSB3FzsqciK+Hm5YO7kP5n11Al8cSQMALN5xFqn5JXjlnm6Qy1gToJZHLpdDqVQiNzcXbm5ukEr579zZCYKAkpIS5OTkwN/f3/yFwx6YjLo4tbJ6zmi2jjvH1Cq8lykZNehNCWnNeaREDeAmk+KtB3ugdYASS3edBwBs+D0FGYWl+GBcT3i5808xtSwSiQShoaG4fPkyrl69KnY4ZEf+/v5Qq9X1n2gF/gV0cUGeQZBL5KgUKlkZrUt4T+D4JtNx+lEmo2QTiUSCmUM7IDLAE3O+OI4Kg4A953IxZtVBrJnUBypfNganlkWhUKBDhw4cqm9B3Nzc7FoRrcJk1MXJpDKEKEOQocvglqB14Yp6sqP74iKg8vXAE+uPoKisEqcytLhv+QGsndwXndQ+YodHZFdSqZQ7MFG9OImDzO2dNOUalFSUiByNA1J1B6TXv7dlMBmlxut/SxC+erI/wv09AQAZmjI8uOI3HLiYJ3JkRETNj8koWfYaZXX0Rm4epoQUAHLPAeVF4sZDLUIHlQ+2/rM/ekT4AQCKyivx6JpD2HI4VeTIiIiaF5NRYuP7hjD3GxVMW4MS2UGIjwc2Pf4PJHQJAQBUGgU898VxLN11nq2fiMhlMBkli/ZOTEbrYDFvlP1GyX6UCjlWTeiNR+PbmG97b/cFPPv5n9BXGkWMjIioeTAZJVZGG6JmMsp5o2RnMqkEL9/TDS/c2QUSiem2r46l49E1h6AprRA3OCKiJsZklNj4viGCOgJuXqZjrqinJiCRSDD1tnb4cFxPuMtNf5oPXrqGB1f8hrQCLiwkopbLpmR0+fLliIqKgoeHB/r164dDhw7d9PwNGzYgJiYGSqUSoaGhmDJlCq5du2ZTwGR/rIw2gFRWvTWoJhUozhE3HmqxEqNDsfHxfyDASwEAuJBTjPs+/A3H0wpFjoyIqGlYnYxu3rwZs2fPxsKFC3H06FHExMRg+PDhyMmp/cP5wIEDmDhxIh577DGcOnUKW7ZswaFDhzBt2rRGB0/24avwhafc1GKGyehNhNfcp57VUWo6PVu3wtYZ/dE2yFSNzy0qx9hV/8PuM9wljYhaHquT0aVLl2LatGmYPHkyunbtipUrV0KpVGLNmjW1nn/w4EFERUVh5syZaNu2LQYMGIAnnnii3moqNR+JRGKujmbpsriKty5cxETNqE2gF756sj/6RLUCAJRWGDDtk8NYf/CKqHEREdmbVcmoXq/HkSNHkJCQUP0EUikSEhJw8ODBWh8THx+P1NRUbN++HYIgIDs7G1u2bMHIkSPrfJ3y8nJotVqLCzWtqnmjZYYyaMo1IkfjoMJ6Vh9zERM1g1ZeCqx/rB/u6mH6/TQKwIvfnMLnf7AXKRG1HFYlo3l5eTAYDFCpVBa3q1QqZGXVPrx76623YsOGDRg7diwUCgXUajX8/f2xfPnyOl9n0aJF8PPzM18iIyOtCZNsUHPeKBcx1cG/NaAMMh2nHwFYQaZm4OEmw3sPxeHJwbeYb1tz4LKIERER2VeTr6Y/ffo0nn76abz00ks4cuQIdu7ciStXrmD69Ol1PmbevHnQaDTmS2oqqwBNTa3kIqZ6SSTVze9LC4CCK6KGQ65DKpVg7ojOiGvtDwA4m1WES7nFIkdFRGQfViWjQUFBkMlkyM62nESfnZ0NtVpd62MWLVqE/v3747nnnkOPHj0wfPhwfPjhh1izZg0yM2uvwLm7u8PX19fiQk2LldEG4rxREtHI7tVt2Hac5JdGImoZrEpGFQoFevXqhd27d5tvMxqN2L17N+Lj42t9TElJCeRyucVtMpkMALhQxoFwf/oGspg3eky8OMgljehe/Xu6/QS/NBJRy2D1MP3s2bPx8ccfIykpCWfOnMGTTz4JnU6HyZMnAzANsU+cONF8/t13340vv/wSK1aswKVLl3DgwAHMnDkTffv2RVhYmP1+EmoUiy1Bi5mM1im8RjLKyig1s8gAJXpE+AEATmVocfWaTuSIiIgaT17/KZbGjh2L3NxcvPTSS8jKykJsbCx27txpXtSUmZmJlJQU8/mTJk1CUVERPvjgAzz77LPw9/fH7bffjjfeeMN+PwU1msqrelEaK6M34RUE+LcBCq8CmX8ChkpAZvWvEZHNEruH4niaqePFjpNZmD7olnoeQUTk2CSCE4yVa7Va+Pn5QaPRcP5oExq4aSAKygug9lJj14O7xA7HcW2ZBJzaajqefgBQdxc1HHItV6/pMOitvQCAmAg/fPPUAHEDIiK6ztZ8jXvTk1nVvNHcklwYjAaRo3FgNRcxsd8oNbM2gV7oFmb6I/9nmob71hOR02MySmZVyahBMCC3NFfkaBxYGOeNkrhGRlfP8d7JVfVE5OSYjJKZxYp69hqtW2gMILn+q8M96kkEiTVW1X/PVfVE5OSYjJIZk9EGcvcGgjubjrNPARWl4sZDLqddsDc6q30AAMdSCpFRyH+DROS8mIySWc32Tmx8X4+qFk+CAcg8Lm4s5JISu3OonohaBiajZMbKqBUsmt9zqJ6a38jo6t/XHSf55ZGInBeTUTJjZdQK3BaURNZB5YMOId4AgMNXC5CtLRM5IiIi2zAZJbMgzyBIry/MYWW0HqpugMzddMxFTCSSxOur6gUB+OEUf2eJyDkxGSUzuVSOEGUIACaj9ZK5AaE9TMf5fwGlBeLGQy6p5lA996onImfFZJQsqJWmD7eC8gKUVXLY76Ys5o0eEy8OclmdVD5oF+QFADh0OR+5ReUiR0REZD0mo2Sh5rzR7JJsESNxApw3SiKTSCRIvF4dNXKonoicFJNRslBzRT0XMdXDIhllZZTEUbPFE1fVE5EzYjJKFtjeyQoB7QB3P9MxK6Mkkm5hvmgdoAQA/O9SPq4Vc6ieiJwLk1GywMqoFaRSIDzOdFycBWgzxI2HXJJEIjHvVW8wCth1mtNriMi5MBklCzWT0WwdP9TqVXMRE6ujJBKLVfXcjYmInAyTUbLAxvdW4iImcgDR4X4I9/cEAPx2MQ+FJXqRIyIiajgmo2TB390f7tebuXPOaAOE16yMsvk9icM0VG+qjlZyqJ6InAyTUbIgkUjM1dFMXSYEQRA5IgfnGwb4XK8mZxwDjEZx4yGXVbUbE8AG+ETkXJiM0g1UXioAQGllKbR6rcjROIGqeaPlWtNuTEQiiI3wR6ifBwBg/8U8aEorRI6IiKhhmIzSDWrOG+VQfQOEcxETiU8qlWBEd9NQfYVBwO4zHKonIufAZJRuwF6jVuK8UXIQd1oM1fN3l4icA5NRugEro1YKi6s+ZmWURNSzdSuE+JgWIP5yIRdFZRyqJyLHx2SUbqBWsvG9VTxbAYHtTcdZJ4BKttUhcUilEiReH6rXVxrx89kckSMiIqofk1G6gcUwfQkrow1StYjJUA7knBI3FnJpNVfV7+BQPRE5ASajdAOLLUGLWRltEIvm95w3SuLpExWAIG8FAGDPuRzoyitFjoiI6OaYjNINlG5K+Cp8AQDZJVyR2yBcxEQOQiaVYHg30xfK8koj9pzjUD0ROTYmo1SrqkVM2bpsGIwGkaNxAupoQCo3HWcwGSVxjeRQPRE5ESajVKuqofpKoRLXyq6JHI0TcPMEQrqajnPOAOVF4sZDLq1f2wAEeJmG6n8+m4NSPb9QEpHjYjJKtbKYN8oV9Q1jnjcqAJl/ihoKuTa5TIrh3a7vpFZhwL7zHKonIsfFZJRqxcb3NuC8UXIgid3ZAJ+InAOTUaoVG9/bwGJFPZvfk7jibwmEn6cbAGD3mWyUVXConogcE5NRqhUrozYI6gS4KU3HXMREInOTSTGsq2moXqc34NcLeSJHRERUOyajVCsmozaQyYHQWNNxYQqg44c/iWukxV71nPtNRI6JySjVKkQZAgkkALiAySqcN0oOpH/7QPh4mFqO/XQ6G+WVHKonIsfDZJRq5SZ1Q7BnMABWRq1ikYxy3iiJy10uwx1dTEP1ReWVOHCR1XoicjxMRqlOam/TUP21smvQG/QiR+Mkai5i4rxRcgCWQ/X8YklEjofJKNVJrayeN5qt47agDeLfBvAMMB2nHwEEQdx4yOUN6BAEb3fTUP2Pp7KgrzSKHBERkSUmo1Snmu2dOG+0gSSS6upoyTXTQiYiEXm4yTC0SwgAQFtWiYOXuKMaETkWJqNUJ4sV9SUc3mswzhslB1OzAf4OrqonIgfDZJTqxMb3NuK8UXIwgzsFQ6mQAQB+OJWFCgOH6onIcTAZpTpxf3obhbG9EzkWDzcZhnQ2DdUXlFTg90v5IkdERFSNySjViY3vbeQdDPi1Nh1nJANG9nYk8Y2suVf9SX65JCLHwWSU6hTgEQCFVAGAyajVwuNM/63QAbnnxI2FCMCQzsHwcDP9yf/hZBYMRnZ6ICLHwGSU6iSRSKDyMjXMZjJqpZrzRrmIiRyAUiHHkE6mofprOj0OXeZQPRE5BiajdFNVi5iKK4pRpC8SORonUnPeKBcxkYNIrNEAfweH6onIQTAZpZvivFEbhcUCkJiOWRklB3F75xAo5KY/+ztOZsHIoXoicgBMRummuKLeRu4+QHBn03H2KaCiTNx4iAB4u8sxqGMwACC3qBxHUgpEjoiIiMko1YOV0Uaoan5vrASyTogbC9F1I6Orf6e/P84vmEQkPiajdFNsfN8I4Zw3So5naBcVFDLTn/6dHKonIgfAZJRuSq1kZdRmYdwWlByPr4cbbusQBADI0pbhWGqhyBERkatjMko3xf3pG0HVHZCZ+rRyJyZyJBar6rlXPRGJjMko3ZS3whs+bj4AgMxifmhZRa4A1NGm42sXAL1O3HiIrrujiwpyqanbw46TWRAEDtUTkXiYjFK9qhrfZ5dkwygYRY7GyQTcUn2sSRMvDqIa/JRuuLW9aag+vbAUx9M0IkdERK6MySjVq2oRU4WxAvll3LXFKv6R1ceFqeLFQfQ3NVfVc696IhITk1GqF9s7NYJfjWRUkyJeHER/c0dXNWTXh+q3n8jkUD0RiYbJKNWrZnsnNr63Eiuj5KACvBSIbxcIAEjNL8WpDK3IERGRq2IySvViZbQR/FpXH2uYjJJjGVljVf12rqonIpEwGaV6MRltBL+I6mNWRsnBDOumwvWReg7VE5FomIxSvbg/fSMolIDStGqZlVFyNEHe7ujX1jRUf+VaCc5mFYkcERG5IpuS0eXLlyMqKgoeHh7o168fDh06dNPzy8vLsWDBArRp0wbu7u6IiorCmjVrbAqYmp9KqYIEpvJJti5b5GicUNW80aJMwFAhbixEf1NzVT0b4BORGKxORjdv3ozZs2dj4cKFOHr0KGJiYjB8+HDk5OTU+ZgxY8Zg9+7dWL16Nc6dO4eNGzeiU6dOjQqcmo9CpkCgp6l6wsqoDapW1AtGQJsubixEfzO8mxqSqqH6k5yGQ0TNz+pkdOnSpZg2bRomT56Mrl27YuXKlVAqlXVWOnfu3Il9+/Zh+/btSEhIQFRUFOLj43Hrrbc2OnhqPlUr6vNK81DB6p51/GssYuK8UXIwIb4e6NMmAABwMacY57M5VE9EzcuqZFSv1+PIkSNISEiofgKpFAkJCTh48GCtj/n222/Ru3dvvPnmmwgPD0fHjh3x73//G6WlpXW+Tnl5ObRarcWFxFU1b1SAgOwSDtVbxaLXKJNRcjyJNRvgc6ieiJqZVcloXl4eDAYDVCqVxe0qlQpZWbUP71y6dAn79+/HyZMnsXXrVrzzzjv44osvMGPGjDpfZ9GiRfDz8zNfIiMj6zyXmodKWf3/nCvqrcReo+TgErtXt3jacYK/30TUvJp8Nb3RaIREIsGGDRvQt29fjBw5EkuXLkVSUlKd1dF58+ZBo9GYL6mp/AAXGxvfNwJ3YSIHp/bzQK82rQAA57KLcDGnWOSIiMiVWJWMBgUFQSaTITvbcpg2OzsbarW61seEhoYiPDwcfn5+5tu6dOkCQRCQlpZW62Pc3d3h6+trcSFx1WzvxGF6K7EySk4gsXv17/hO7lVPRM3IqmRUoVCgV69e2L17t/k2o9GI3bt3Iz4+vtbH3HrrrcjIyEBxcfU37fPnz0MqlSIiIqLWx5DjqVkZ5TC9lTz8AYWP6ZhzRslBJVrsxsTfcSJqPlYP08+ePRsff/wxkpKScObMGTz55JPQ6XSYPHkyANMQ+8SJE83njxs3DoGBgZg8eTJOnz6NX375Bc899xymTJkCT09P+/0k1KTY+L4RJJLq6qgmDTAaxY2HqBbh/p6IifQHAJzO1OJKnk7kiIjIVVidjI4dOxZvv/02XnrpJcTGxiI5ORk7d+40L2rKzMxESkr1vDhvb2/s2rULhYWF6N27Nx555BHcfffdeO+99+z3U1CTC/QMhFwqB8DKqE2q5o0a9ICu7p68RGIaWWOofgd7jhJRM5EITrAZsVarhZ+fHzQaDeePimjElyOQXpwOH4UPfnv4N7HDcS7fPwv88V/T8WM/AZF9xI2HqBap+SW47c09AIDocD98968BIkdERM7E1nyNe9NTg1XNGy3SF0FXwSE8q3BFPTmByAAlosNNi01PpGuQml8ickRE5AqYjFKD1Zw3yqF6K3FFPTmJmg3wd3BVPRE1Ayaj1GBMRhvBr8aWoFxRTw6sZgN8rqonoubAZJQajI3vG4GVUXISbYO80CXUNNcrObUQ6YV1b91MRGQPTEapwVgZbQSvEECmMB2zMkoOruaq+o9/uSRiJETkCpiMUoOx12gjSKWA3/VNHgpTAcdvYkEu7N64cChkpo+Hdb9dwfYT/H0noqbDZJQazGJLUB23BLVa1Yp6fRFQVihuLEQ3ERmgxIt3dzVfn/PFcVzK5X71RNQ0mIxSg/m4+cDLzQsAkFXCYXqrcd4oOZHx/VpjVGwYAKC4vBIzNhxFqd4gclRE1BIxGaUGk0gkUCtN1dEsXRacYL8Ex8IV9eREJBIJXr8vGu1DvAEAZ7OKsODrE/y9JyK7YzJKVlF7m5LRckM5CsoLRI7GybAySk7Gy12OleN7QqmQAQC+OpqOzX/w3y4R2ReTUbJKVWUU4CImq1nswsQPdHIO7UN8sPiBHubrL317CifTNSJGREQtDZNRsgrbOzWCRWWUW4KS87gnJgwT49sAAPSVRjy54Qg0JRUiR0VELQWTUbJKzcb3TEat5BsOSK7/yrEySk5mwZ1dEBPpDwBIzS/Fs1v+5PxRIrILJqNkFVZGG0HmBvhcT+Y5Z5ScjLtchuXj4uCvdAMA/HQmG6vYEJ+I7IDJKFmFW4I2UtW80ZI8QF8ibixEVopopcSysbHm62/9cA7/u3RNxIiIqCVgMkpWUXmpzMesjNqg5rxRTZp4cRDZaEinEPzr9vYAAINRwL82HkNOUZnIURGRM2MySlZxl7kjwCMAAJNRm1isqOciJnJOsxI64tb2gQCA3KJy/OuzY6g0GEWOioicFZNRslrVvNHc0lxUGitFjsbJsNcotQAyqQTvPhQHla87AOD3y/lYsuu8yFERkbNiMkpWq5o3ahSMyC3JFTkaJ8NdmKiFCPJ2x/JxPSGXSgAAK/b+hZ9OZ4scFRE5IyajZLWaK+q5iMlKrIxSC9I7KgDPJ3Y2X5/9eTJSrnFhHhFZh8koWY29RhvBL6L6mJVRagEeG9AWI7qZvqBqyyox47MjKKswiBwVETkTJqNktZor6lkZtZLCC1CaFn6wMkotgUQiwZujeyAqUAkAOJmuxavbToscFRE5EyajZLWa+9OzMmqDqhX1RRmAgVsqkvPz9XDDivG94C43faR89nsKvjrK1mVE1DBMRslqHKZvpKp5o4IR0GaIGwuRnXQJ9cV/7u1uvj5/6wmczdKKGBEROQsmo2S1IM8gyCVyAEBWCZNRq3FFPbVQo3tHYmxv05etsgojZnx6FMXlbP9GRDfHZJSsJpPKEKIMAcDKqE24op5asFdGdUPXUF8AwKU8HeZ+cRyCIIgcFRE5MiajZJOq9k6F5YUorSwVORonY7ELE5NRalk83GRYMb4nfDxMoyffn8jEut+uiBsUETk0JqNkk5q9RlkdtZJFZZRbglLL0ybQC2+PjjFff+37MzhytUDEiIjIkTEZJZuw8X0jsDJKLmB4NzWeGNgOAFBpFPDUZ0dxrbhc5KiIyBExGSWb1FxRn63jFoBW8WwFKLxNx5wzSi3Yv4d3Qt+oAABApqYMszYnw2Dk/FEissRklGzCymgjSCTV1VFNGmA0ihsPURNxk0nx/rg4BHkrAAC/XsjD+z9fEDkqInI0TEbJJpwz2khV80YN5YAuV9xYiJqQytcD7z0cB6nEdP3d3Rew7zz/zRNRNSajZJOaw/SsjNqA80bJhfS/JQjPDusEABAEYNamY8goZBcOIjJhMko28VX4wlPuCYCVUZtwRT25mCcH3YLbO5v6ExeUVOCfnx2FvpJTVIiIySjZSCKRmIfqs0uy2dTaWqyMkouRSiVYOiYGEa1MX2KPpRTi9e1nRI6KiBwBk1GymVppSkZLK0uhKdeIHI2T8a+xJShX1JOL8Fcq8OEjPaGQmT561v12BduOZ4gcFRGJjcko2SzUu3reKPeotxIro+SiekT446W7u5qvz/3iOP7KLRYxIiISG5NRsllVZRQAMou5iMkq3ipAZmp3w8oouZpH+rXGvbFhAACd3oAnPz2CEn2lyFERkViYjJLNLNo7sTJqHakU8A03HbMySi5GIpHg9fuj0VFl2vzhfHYxFmw9ybnnRC6KySjZjI3vG6lqRX25FigtFDcWomamVMjx4SO9oFTIAABbj6Xju+P8O0LkipiMks1q9hpleycb+NVYxMTqKLmg9iHeWHR/tPn6q9+dhqakQsSIiEgMTEbJZiovlfmYyagNLHqNMhkl1zQqNhx3dDX9LckrLsfinWdFjoiImhuTUbKZp9wT/u7+AJiM2oQr6okAAK/c0w1e14frNx5KwR9X8kWOiIiaE5NRapSqofqckhwYjAaRo3Ey3IWJCAAQ5u+Jfw/vZL4+/6sT3J2JyIUwGaVGqRqqNwgG5JbmihyNk2FllMhsYnwUekT4AQAu5BTjo1/+EjkiImouTEapUbiIqRF8wwFITMecM0ouTiaV4PX7oiGTmn4n3vv5Iq7k6USOioiaA5NRahSLXqNMRq0jVwA+15N5VkaJ0D3cD1NujQIA6CuNWPD1CfYeJXIBTEapUVgZbaSqeaO6XKCiVNxYiBzArISOCPf3BAAcuHgNW4+lixwRETU1JqPUKGx830gW80bTxIuDyEF4ucvx6qhu5uv/+f4MCnR6ESMioqbGZJQahZXRRuKKeqIbDO2iwsho0xfdfJ0er28/I3JERNSUmIxSowR5BkEqMf0zYmXUBlxRT1SrhXd3g4+7HACw5UgaDv51TeSIiKipMBmlRpFL5Qj2DAYAZJdkixyNE/KvsSUoV9QTmal8PTAnsbP5+oKvT6C8kr2MiVoiJqPUaFVD9fll+SirLBM5GifDyihRnR7p2xpxrU27vF3K1eHDPew9StQSMRmlRqu5iInVUStxf3qiOkmlEiy6Pxry671HV+z9CxdzikWOiojsjckoNRoXMTWCwgvwDDAdszJKdIPOal9MG9gOAKA3GLFgK3uPErU0TEap0aq2BAW4iMkmVdVRbQZgqBQ3FiIHNPP2DogMMPUe/f1yPrYcZhs0opaEySg1GiujjVQ1b1QwAEUZ4sZC5IA8FTL8595o8/XXtp9BXnG5iBERkT0xGaVG45agjcQV9UT1GtQxGPfEhAEANKUVeO179h4laimYjFKjsTLaSFxRT9QgL97VFb4ept6jW4+lY/+FPJEjIiJ7sCkZXb58OaKiouDh4YF+/frh0KFDDXrcgQMHIJfLERsba8vLkoPyd/eHu8wdAOeM2oQr6okaJNjHHfNHdjFfX/D1CZRVsPcokbOzOhndvHkzZs+ejYULF+Lo0aOIiYnB8OHDkZOTc9PHFRYWYuLEiRg6dKjNwZJjkkgk5qH6LF0WV7pay6Iyyi1BiW5mTO9I9IlqBQC4eq0E7/98QeSIiKixrE5Gly5diknXX1MAACAASURBVGnTpmHy5Mno2rUrVq5cCaVSiTVr1tz0cdOnT8e4ceMQHx9vc7DkuKqS0ZLKEmj1WpGjcTKcM0rUYFW9R91kpt6jq/ZdwvnsIpGjIqLGsCoZ1ev1OHLkCBISEqqfQCpFQkICDh48WOfj1q5di0uXLmHhwoUNep3y8nJotVqLCzk2tZKLmGzm2Qpw8zIdc84oUb3ah/jgyUG3AAAqjQLmfXUCRiNHZIiclVXJaF5eHgwGA1QqlcXtKpUKWVm1JyAXLlzA888/j08//RRyubxBr7No0SL4+fmZL5GRkfU/iEQV6l29iIm7MFlJIqmeN6pJAzjNgaheM4a0R9sg05e4I1cLsPEPTnEhclZNupreYDBg3LhxeOWVV9CxY8cGP27evHnQaDTmS2oqq0WOrmZlNLOYi5isVjVvtLIM0OWKGwuRE/Bwk+G1e7ubry/ecRY5RWUiRkREtrIqGQ0KCoJMJkN2tmXlKzs7G2q1+obzi4qKcPjwYTz11FOQy+WQy+V49dVX8eeff0Iul+Pnn3+u9XXc3d3h6+trcSHHZtHeqYTD9Fbjinoiq/VvH4QHekYAAIrKKvHqd6dFjoiIbGFVMqpQKNCrVy/s3r3bfJvRaMTu3btrXZjk6+uLEydOIDk52XyZPn06OnXqhOTkZPTr16/xPwE5hJqN79neyQZcUU9kkwV3dkErpRsAYNvxTOw5d/POLkTkeKwepp89ezY+/vhjJCUl4cyZM3jyySeh0+kwefJkAKYh9okTJ5qeXCpF9+7dLS4hISHw8PBA9+7d4eXlZd+fhkTDXZgaiSvqiWwS4KXAgju7mq+/+PVJlOgrRYyIiKxldTI6duxYvP3223jppZcQGxuL5ORk7Ny507yoKTMzEykprOy4GqWbEr4K03QKJqM24C5MRDZ7oGc44tsFAgDSCkrx7k/sPUrkTCSCE3Qo12q18PPzg0aj4fxRB/bgtw/iXME5yKVyHH7kMGRSmdghOQ9tBrD0+s4yHROBcZvEjYfIyVzKLcaId3+FvtIImVSC754agK5h/Lwgak625mvcm57spmqovtJYiWtl10SOxsl4qwGpad4bK6NE1msX7I2nhrQHABiMAuZtPQEDe48SOQUmo2Q3nDfaCFIp4BduOuacUSKbPDGoHW4JNq1F+DO1EBt+vypyRETUEExGyW6YjDZS1bzRcg1QphE3FiIn5C6XYdH9PczX39x5Dlka9h4lcnRMRslu2N6pkbiinqjR+rYNwEN9TF/sissr8fK3p0SOiIjqw2SU7Mai8T0ro9bjinoiu3g+sTOCvBUAgJ2nsrDrNLcoJnJkTEbJbjhM30jchYnILvyVCrx4V3Xv0YXfnISunL1HiRwVk1GymxBlCCSQAGAyahPuwkRkN/fEhOG2DkEAgAxNGZb8eF7kiIioLkxGyW7cpG4I9gwGwDmjNmFllMhuJBIJ/nNvd7jLTR9z6367jBNpXBhI5IiYjJJdqb1NQ/XXyq5Bb9CLHI2T8Y0ArleWOWeUqPHaBHrh6YQOAACjAMzbehyVBqPIURHR3zEZJbtSK6vnjWbruGjAKnIF4HP9/WNllMgupt3WDp1UPgCAk+laJB1k71EiR8NklOzKYhFTCeeNWq1q3qguB6hgf0SixnKTSfH6/dGQXB90WPLjOaQXloobFBFZYDJKdsX2To1Uc96oJk28OIhakF5tWuGRfqY+viV6AxZ+cxKCwK1CiRwFk1GyKza+bySuqCdqEs8N74xgH3cAwE9ncvDDKX5ZJnIUTEbJrlgZbSSuqCdqEn6ebnj57m7m6wu/PQVtWYWIERFRFSajZFcqL5X5mJVRG/jV2BKUK+qJ7GpktBq3dw4BAGRry/H2D+dEjoiIACajZGcBHgFQSE3b8LEyagNWRomajEQiwSv3dIOnmwwAsP5/V3EspUDkqIiIySjZlVQiNVdHmYzagPvTEzWpyAAlZt/REQAgCMC8r06ggr1HiUTFZJTsrmreaHFFMYr0RSJH42TcvQHPVqZjVkaJmsTkW6PQNdQXAHA2qwhr9l8WOSIi18ZklOzOotcoq6PWq6qOatMBQ6W4sRC1QHKZFIvuj4b0eu/RZT+dR2p+ibhB0f+3d+/hUVf3vsc/M5Nkck8IuRETbooooqgIMaUqSjACtdrds6s9bXHTY/fBgorZp1q66+3p2eKul6KUVqv1sltQrBWtVVGMCIqACuIGBEQBCUJuQG6T+8xv/zHJJClBmZnMrJnk/XqePE5+85vkG57l5JvvWt+1MIiRjKLf5SR2NzGRjAYgvbOJyXJLDTSBAaEwoSBds4tGSpJa2j365YvsPQqYQjKKfjcsucf2TpzC5D/WjQJh8W+Xn67c1HhJ0tpPq/X3/+aPP8AEklH0u57n0x9u5M3db3TUA2GREh+ru6/q3nv07pc/UV0Te48C4UYyin7Xc+P7yqZKg5FEKU5hAsKm5KxcXT7Ou7SoprFV//n6LsMRAYMPySj6HUeCBonKKBBWd337LCXFefceXb7pgD7cf9RwRMDgQjKKfpccl6yU2BRJNDAFhFOYgLDKS0/Q/ysZ6/t84Qvb1NbB3qNAuJCMIiR6bnzvsXhT90tihhSb6H1MZRQIi9lFI3VOfpokaU9Vox57Z6/hiIDBg2QUIdG1brTd066jLUx5+cVm6143WnfQe0wMgJBy2G265ztny9G5+ehDZXu0v8ZlOCpgcCAZRUiw8X2QutaNdjRLrhqzsQCDxPhT0vTjKSMlSW0dHv37i9vYexQIA5JRhETPjnqS0QDQUQ8Yccv003VKeoIkaf1nR/Ti1i8NRwQMfCSjCAkqo0Giox4wIjEuRr+6unvv0V/9faeOudoMRgQMfCSjCAm2dwoSHfWAMZedkaNZZ3tnd4662rTotZ2GIwIGNpJRhASV0SBRGQWMuuPKcUpxxkiSnvvwoDbuPWI4ImDgIhlFSOQk5vgek4wGgPPpAaNyUuN164wzfJ//YuU2tXa4DUYEDFwkowiJOEecMhMyJZGMBiQlV7J7qzJURgEzfjB5uM4bni5J2lvt0tPv7TcbEDBAkYwiZHITvVP11c3Vane3G44mytgdUuop3sd00wNG2Dv3Hu3ywhY664FQIBlFyAxL9jYAWLJU1VxlOJoolN7ZxNRSJ7XUm40FGKTOHJaqcwu81dFdFQ3aW91oOCJg4CEZRcj0XDd6uJGOer+xbhSICDPP7m7IfG07y46A/kYyipDptfF9E2/gfqOjHogIM8Z3v5e9tp0/rIH+RjKKkGF7pyBRGQUiQkFGos4+JU2StP3Leh040mQ4ImBgIRlFyJCMBqlXZZQmJsCkmWdTHQVChWQUIcP59EGiMgpEjBnju/+4fpV1o0C/IhlFyAxNGKqYzr0yORI0AGn53Y9ZMwoYNTIzSeOGpUqSPi6v1cFjTNUD/YVkFCFjt9l9HfVURgMQ45SSO6sxVEYB43p21a+iOgr0G5JRhFTXutH6tno1tVNJ8FvXutHGSqm9xWwswCA3o8e60Ve3MdsD9BeSUYQU60aD1HPdaD2nvwAmnZqVrLE5KZKkLQdqdbiu2XBEwMBAMoqQ6tlRz7rRANBRD0SUGUzVA/2OZBQhRWU0SHTUAxGl1xZP23hPA/oDyShCispokLrOp5foqAciwOk5KTotO1mS9MEXR1VVz1puIFgkowgpNr4PEpVRIOLM7Nxz1LKk13fwvgYEi2QUIdUrGeV8ev9xPj0QcXp31fO+BgSLZBQhlRKbosSYRElURgPiTJHi072P62hgAiLBGbkpGpWZJEnatO+IahpbDUcERDeSUYSUzWbzNTFVuCpkWZbhiKJQV3W0/pDkcZuNBYBsNpvveFAPU/VA0EhGEXJdU/Wt7lYdaz1mOJoolNbZxOTpkBpoAgMiAV31QP8hGUXI0cQUJNaNAhHnrLxUFWQkSJI27D2io642wxEB0YtkFCHH9k5BoqMeiDg2m00zx3uro26PpdWf8Ic2ECiSUYQcG98HiVOYgIg0k656oF+QjCLkmKYPEpVRICKdk5+mU9K9U/XrP6tRXVO74YiA6EQyipCjMhokTmECIlLPrvoOj6XVOysNRwREJ5JRhFxOUo7vMcloABKHSjHe6guVUSCy9N4AnzXxQCACSkaXLl2qkSNHKj4+XoWFhXr//fdPeO8LL7yg6dOnKysrS6mpqSoqKtLrr78ecMCIPk6HUxnxGZJoYAqIzda9brS23HsGIYCIcF5BunJT4yVJ7+ypVn0LU/WAv/xORlesWKHS0lLdeeed2rJliyZMmKCSkhJVVVX1ef+6des0ffp0vfrqq9q8ebMuvfRSXXnllfroo4+CDh7Ro2vdaHVztTo8HYajiUJd60Y7mqWmI2ZjAeBjt9t0RedUfbvbUhlT9YDf/E5GH3zwQf3kJz/RnDlzNG7cOD3yyCNKTEzUE0880ef9ixcv1q233qpJkyZpzJgxuueeezRmzBi9/PLLQQeP6JGb2HVaiUfVTdWGo4lCdNQDEYuueiA4fiWjbW1t2rx5s4qLi7u/gN2u4uJibdiw4aS+hsfjUUNDgzIyMk54T2trq+rr63t9ILoNS+7RxNTEm7Xf6KgHItYFI4YoO8UpSVr7abUaW5n9AfzhVzJaU1Mjt9utnJycXtdzcnJUUXFyCcb999+vxsZGfe973zvhPYsWLVJaWprvo6Cg4IT3Ijp0VUYl6XAj60b9Rkc9ELF6TtW3dXj01q6+l60B6FtYu+mXL1+uu+++W88995yys7NPeN/ChQtVV1fn+ygv55dvtMtN7rHXKJVR/1EZBSLajPE9z6rnD27AHzH+3JyZmSmHw6HKyt4LtCsrK5Wbm3uCV3k9++yzuv766/WXv/yl1zR/X5xOp5xOpz+hIcJRGQ0S59MDEW3yqAwNTYrTEVeb1uyuUlNbhxLj/PoVCwxaflVG4+LiNHHiRJWVlfmueTwelZWVqaio6ISve+aZZzRnzhw988wzmjVrVuDRImr12vieyqj/UoZJ9s5fbHU0MAGRxmG3qaRzqr6l3aM1u2jUBE6W39P0paWleuyxx/T0009r586duuGGG+RyuTRnzhxJ3in22bNn++5fvny5Zs+erQceeECFhYWqqKhQRUWF6urq+u+nQMTLTMhUjM2bTFW62PrEb3aHlJrnfUxlFIhIM3tM1b+6nRkg4GT5nYxec801uv/++3XHHXfo3HPP1datW7Vq1SpfU9Phw4d14EB35eYPf/iDOjo6NG/ePA0bNsz3cfPNN/ffT4GI57A7lJWYJYmN7wOW1tnE1FIrtTaYjQXAcQpHZ2hIYqwkac2uKjW3uQ1HBESHgBa0zJ8/X/Pnz+/zuaeeeqrX52+//XYg3wID0LCkYTrsOqza1lo1dzQroeuIS5yc9ALpi87HteVSzjij4QDoLdZh1+XjcrXiw3I1tbm19tNqX5c9gBPjbHqEDWfUB4mOeiDizTynR1c9U/XASSEZRdj0amIiGfUfpzABEe8bpw5VWoJ3qr5sZ5Va2pmqB74OySjCput8eolkNCBURoGIF+uwa/o47yxQY2uH3t1TYzgiIPKRjCJsqIwGiVOYgKgw8+zuP7xfZQN84GuRjCJselZG6agPQOop3Y+pjAIRa8ppmUpxevuDV++sVGsHU/XAVyEZRdhQGQ1SbLyU3NkERmUUiFjOGIeKO6fqG1o69N5nRwxHBEQ2klGETWpcqm87J05hClDXutHGCqmj1WwsAE5oxnim6oGTRTKKsLHZbL6p+gpXhSzLMhxRFOrZUV930FwcAL7SxadnKSnOIUl645NKtbs9hiMCIhfJKMIqN9GbjDZ3NKu+rd5wNFGIjnogKsTHOjTtTO9UfV1zuzZ8zlQ9cCIkowgrmpiCREc9EDV6dtWzAT5wYiSjCCuamIJEZRSIGpecnq2EWO9U/es7KtXBVD3QJ5JRhBWV0SD1OoWJZBSIZAlxDl12RrYk6airTZv2HTUcERCZSEYRVpzCFCQqo0BUmcEG+MDXIhlFWFEZDVJ8qhSf5n3M+fRAxLt0bLacMd5fta/vqJDbwy4iwD8iGUVY9UxGK12VBiOJYmmdTUz1X0oeTnYBIlmSM0ZTx2ZJkmoa2/TBfqbqgX9EMoqwSohJULozXRLT9AHrWjfq6ZAa+DcEIt3Ms7sbN19jqh44Dskowq6ro76yqVJuKnv+Y90oEFUuOyNbcZ1T9a9tr5CHqXqgF5JRhF1OkncjaLflVk1zjeFoohAd9UBUSYmP1cVjvFP1VQ2t2nLgmOGIgMhCMoqw6zqFSaKJKSC9KqM0MQHRYGavrnqW1wA9kYwi7IYl99j4vok3Zb9RGQWizrQzcxTrsEnynsbEVD3QjWQUYdezMlrRSDLqt7QeR4KyZhSICmkJsfrmaZmSpMN1Ldp6sNZwREDkIBlF2FEZDVJSphST4H1MZRSIGjPoqgf6RDKKsOu1ZrSRN2S/2WxSWr73cV25ZDHdB0SDy8flKMbunap/dVuFLP7fBSSRjMKArMQs2W3eoUdlNEBd60bbm6QmNtEGokF6YpyKTh0qSfqytlnbvqwzHBEQGUhGEXYx9hhlJXi3OWHj+wDRUQ9EpVk9purpqge8SEZhRNfG90dbjqrV3Wo4mihERz0QlS4/K1cOe3dXPVP1AMkoDOGM+iDRUQ9EpYykOF04OkOS9MWRJn1yuN5YLHVN7Wpp5xQ8mEcyCiO6KqMSG98HhMooELVmjO85VR/+97+WdrcWvbZT5///1Zr8H29qxQcHqNDCKJJRGNF1JKjEutGAcD49ELVKzsqVzTtTH/au+vf3HdWMh97Ro2v3yu2xVN/Sodv+uk0/+uP7Kj/aFLY4gJ5IRmFEz2l6KqMBSBkm2Rzex7U0MAHRJCvFqckjvVP1+2pc2l3ZEPLv2djaodtf3K7vPbpB+2pckuTbZkqS3v2sRpf/Zp2eXL+P06EQdiSjMKLnND2V0QA4YqTUU7yPqYwCUWdmGLvq135arZLfrNOfNn7hu3b+8HStWnCRnpwzSXlp8ZKk5na37n75E/3zoxv0WVVjSGMCeiIZhRE9K6MkowHqWjfafExq5RcHEE2uGN89VR+q05hqm9r0b899rOueeF9f1jZLkhJiHbrjW+P0l7nf0GnZKbp0bLbeKL1EP7pwhO91m784ppkPv6Olaz5Tu9sTktiAnkhGYcQQ5xA5HU5JJKMBY90oELVyUuN1wYghkqQ9VY3a089T9au2H1bxg+v01y0HfdemnDZUry+4WD/+5ijf9lKSlOyM0a+uHq8V/3qhRg5NlCS1dXh03+u7dfXS9dpxiM35EVokozDCZrP5qqOHXey1FxA66oGo1rOr/rXt/fNHeXVDq366bLPm/nmLahq9ezinOGN07z+drT//n0IN70w2+1I4eqhWLbhY//fi0erKVXccqtdVv12v+1/fzTZQCBmSURjTlYw2dTSpoT30C/gHHE5hAqLaFeO7lysFu8WTZVl6YctBTf/N2l5rUIvPzNbq0kt07eThstlsX/EVvOJjHVo480yt/OkUjc1JkSR1eCz9ds1nmvXwO9r8xbGg4gT6QjIKY3ITWTcaFCqjQFTLS0/QecPTJUm7Khq0tzqwtd9f1jZrzlMfqPS5j1Xb1C7Ju7n+w98/T4/NvkC5nQ1K/phQkK6Xb/ymFhSPUazDm8R+Xu3S/3rkPd398g41tXUEFCvQF5JRGDMsmY76oHAKExD1ZgYxVe/xWPrTxi90+YNr9fbuat/1b0/I0+pbLta3J+SdVDX0ROJi7FpQfLr+fuNFmpCfJkmyLOnJ9ftVsnid1n9WE/DXBnoiGYUxVEaDlHZK92Mqo0BUCnSqfl+NS99/bKNuf3G7XG3etZw5qU49NvsCPfz98zQ02dlvMY7NTdFfb/iGfjHzDDljvGlD+dFm/eDxTfr5X/9b9S3t/fa9MDiRjMIYNr4PUmyClJTlfUxlFIhKBRmJOqez6rjjUL2+OOL6yvs73B79Yd3numLxOm3ad9R3/dpJBXrjlks0fVzOV7w6cDEOu/714lO1asHFmjwqw3f92Q/KNf3BtXrzk8qQfF8MDiSjMIaN7/tBVxNTQ4XU0WY2FgABOdmu+t0VDfru79/TPa/uUmuHd//PgowELbu+UPd+9xylJcSGPNZRmUl69icX6ldXj1dSnPcUuMr6Vl3/Xx/qpmc+0pHODn7AHySjMIbKaD/wNTFZUv3Br7wVQGSaeXb3e2FfG+C3dXi0+M1P9a0l7+jjg949P202ac6UkXp9wcWaclpm2GKVJLvdph9dOEJvlF6iS07P8l3/28eHNP036/S3jw+xXR/8QjIKYxJjE5UalyqJymjA0uioB6LdiKFJOivP+1748cE6HTzW5Hvu4/JaXbnkXS1+c4/a3d4E79SsJD0/t0h3XnmWEuNijMQsSaekJ+ipOZP0wD9P8FVlj7radNMzH+kn/7VZFXUtxmJDdCEZhVFd1dHKpkp5LI6d81s6HfXAQNDzrPrXtlWouc2te17dqe/8br12d57O5LDbNO/SU/XKTRdp4oiME32psLLZbPruxHy9WXpJrwrvmzsrNf03a/Xs+weokuJrkYzCqK51ox2eDh1pPmI4mihEZRQYEGb06Kp/5v0DmvHQOv1h3V55OvO4ccNS9dK8KfpZyRmKj3UYivLEslKc+t0PJuqRH56vzM5O/oaWDv38hW364R83qfxo09d8BQxmJKMwque6UabqA5DO+fTAQDA6K1ln5HpPPNpb49L+I97kLc5h189Kxuql+VM0/pQ0kyGelCvGD9ObpRfru+fn+66t/+yILv/NOi1d85nqmtgGCscjGYVRNDEFqVdllCNBgWjWs6teks4fnq5Xb/6m5l16mmId0fPrOj0xTg98b4KemjNJeZ2nPzW3u3Xf67t14aIy/fLFbfqsKrDTpjAwRc/oxoBEZTRICemS09v4QGUUiG7XTi5QTqpTyc4Y3fGtcfrL3G/otOwU02EFbOrYbL1Reol+dOEIdR0E1dzu1p83HlDxg2s1+4n3tWZ3lTwe1pQOduba8AD1PoWJymiA0gqkqh1S3ZeSxyPZ+RsTiEY5qfF697bLZFneozgHgmRnjH519XjNmTJST7+3X3/ZfFBNnSdGrfu0Wus+rdborCTN+cZI/dP5+UpykpYMRgNjtCNq9TyfvrKJEzwC0rVu1NMuNVJdBqJZrMM+YBLRnkZnJevuq8Zr4y+m6ZezzlT+kATfc3urXbr9pR26cFGZ/uOVT2h2GoQG3ohHVMlOzJZN3vmbw41URgNCRz2AKJEaH6vrLxqttT+7VI/+aKIuHN29RVVDS4cee2efLrlvjeb+abM27T3CtlCDBPVwGBVrj1VWQpaqmqtU0URVLyDHddQXGgsFAE6Gw25TyVm5KjkrVzsO1emp9fv10seH1NbhkceSVu2o0KodFRo3LFVzpozUlRPyInJLK/QPKqMwrquJqaa5Rm1uzlf3Gx31AKLYWXlpuu+fJ+i9n1+m0umnKyvF6Xvuk8P1+tnz/61v/udbenD1p6pq4FSngYhkFMb17Khn3WgAOIUJwACQmezUTdPGaP1tl2nxNefqnPzufVVrGtv0cNkeTbn3Ld2yYqu2HawzGCn6G9P0MO4ft3cqSCn4irtxHNaMAhhA4mLsuvq8U3TVuXnacuCYnli/X6u2V8jtsdTutrTyoy+18qMvdcGIIZozZZRKzspRTBTtw4rjkYzCuK4jQSX2Gg1IUpbkcEruViqjAAYMm82miSMyNHFEhg7VNutPG7/Q8k0HVNfsPcXpwy+O6cMvjikvLV6zvzFS104qUHpinOGoEQj+lIBxbHwfJLtdSus8eq+2XKL7FMAAk5eeoNuuOEMbF07TPd85W2Oyk33PHapr0b2v7dKFi8r0i5XbtKeywWCkCASVURjXszLKxvcBSi+Qjn4utbuk5mNSYsbXvwYAokxCnEP/u3C4vj+5QO9+VqMn1+/XW7uqJEkt7R4t33RAyzcd0LC0eI3KTNLIzCSNGtr538xEFWQkyhlDV36kIRmFcTlJOb7HVEYD9I8d9SSjAAYwm82mi8Zk6aIxWdpX49LT7+3Xcx+W+053OlzXosN1LXrv8yO9Xme3eausozKTNHJokkZlJvmS1vwhCYpl7akRJKMwLiM+Q7H2WLV72qmMBuofO+rzzjUXCwCE0ajMJN317bNUevnpeu6Dcr267bD21rhU29R+3L0eSzp4rFkHjzXrnT01vZ5z2G0qGJKgkT0S1a7K6ilDEuSw28L1Iw06ASWjS5cu1X333aeKigpNmDBBS5Ys0eTJk094/9tvv63S0lLt2LFDBQUF+uUvf6l/+Zd/CTRmDDB2m125SbkqbyhXpYutnQJCRz2AQa7rdKfrLxotSaptatO+Gpf2H3FpX7VL+440aX+NS/trXGpo7Tju9W6Ppf1HmrT/SJOk6l7PxTnsKsjorqiO7FFRHZYaLzuJalD8TkZXrFih0tJSPfLIIyosLNTixYtVUlKi3bt3Kzs7+7j79+3bp1mzZmnu3LlatmyZysrKdP3112vYsGEqKSnplx8C0a8rGW1ob1BjW6OS45K//kXodtwpTAAwuKUnxum84XE6b/iQXtcty9IRV5v217h8yer+mibtrXHpiyMu31R/T21ujz6vdunzatdxzzlj7BoxNPG4af9RmUnKTnHKZiNR/To2y8+DXwsLCzVp0iT99re/lSR5PB4VFBToxhtv1M9//vPj7r/tttv0yiuvaPv27b5r1157rWpra7Vq1aqT+p719fVKS0tTXV2dUlNT/QkXUeLf3/13/e3zv0mSlly2RPnJ+YYjijL1h6Q//5P3cf5k6ZsLzMYDAFHIsizVNrerqqFVlfUtqqpvVVWD97+VDS1qd/u3W0l8jF1ZqU7lpDiVnRKv7NR45aQ6lRgX3lWSRWdfobg459ffGKRA8zW//jXa2tq0Hr7kmQAACXVJREFUefNmLVy40HfNbreruLhYGzZs6PM1GzZsUHFxca9rJSUlWrDgxL8sW1tb1dra6vu8vr7enzARhXISu5uYbnzrRoORRLH8rl0JyqV3/81oKAAwYMRIyuj8CMCXXQ+aOj8M9OmuHnG+cjMj90AZv9rGampq5Ha7lZOT0+t6Tk6OKir6/tetqKjo8/76+no1Nzf3+ZpFixYpLS3N91FQELn/gOgfZw4903QIAADAgIjspl+4cKFKS0t9n9fX15OQDnCXFVym2ybdpj21e0yHEr2aa6WaTyXP8QvzAQBmWJbU4fGo3W2p3e1Ru9sT9rNJ4p0J4f2GfvIrGc3MzJTD4VBlZe+O58rKSuXm5vb5mtzc3D7vT01NVUJC3/84TqdTTmfo1zYgcjjsDv1w3A9NhwEAAMLMr2n6uLg4TZw4UWVlZb5rHo9HZWVlKioq6vM1RUVFve6XpNWrV5/wfgAAAAwefh81UFpaqscee0xPP/20du7cqRtuuEEul0tz5syR5J1inz17tu/+uXPnau/evbr11lu1a9cu/e53v9Nzzz2nW265pf9+CgAAAEQlv9eMXnPNNaqurtYdd9yhiooKnXvuuVq1apWvSenw4cM6cOCA7/5Ro0bplVde0S233KKHHnpI+fn5evzxx9ljFAAAAP7vM2oC+4wCAABEtkDzNb+n6QEAAID+QjIKAAAAY0hGAQAAYAzJKAAAAIwhGQUAAIAxJKMAAAAwhmQUAAAAxpCMAgAAwBiSUQAAABhDMgoAAABj/D6b3oSuE0vr6+sNRwIAAIC+dOVp/p40HxXJaENDgySpoKDAcCQAAAD4Kg0NDUpLSzvp+22Wv+mrAR6PR4cOHVJKSopsNptfr62vr1dBQYHKy8uVmpoaoggRbRgX6AvjAn1hXKAvjIvjWZalhoYG5eXlyW4/+ZWgUVEZtdvtys/PD+prpKamMlhwHMYF+sK4QF8YF+gL46I3fyqiXWhgAgAAgDEkowAAADDGcdddd91lOohQczgcmjp1qmJiomJVAsKEcYG+MC7QF8YF+sK46B9R0cAEAACAgYlpegAAABhDMgoAAABjSEYBAABgDMkoAAAAjBnQyejSpUs1cuRIxcfHq7CwUO+//77pkBBG69at05VXXqm8vDzZbDa9+OKLvZ63LEt33HGHhg0bpoSEBBUXF2vPnj2GokW4LFq0SJMmTVJKSoqys7N19dVXa/fu3b3uYWwMPr///e91zjnn+DYwLyoq0muvveZ7njEBSbr33ntls9m0YMEC3zXGRvAGbDK6YsUKlZaW6s4779SWLVs0YcIElZSUqKqqynRoCBOXy6UJEyZo6dKlfT7/61//Wg8//LAeeeQRbdq0SUlJSSopKVFLS0uYI0U4rV27VvPmzdPGjRu1evVqtbe36/LLL5fL5fLdw9gYfPLz83Xvvfdq8+bN+vDDD3XZZZfpqquu0o4dOyQxJiB98MEHevTRR3XOOef0us7Y6AfWADV58mRr3rx5vs/dbreVl5dnLVq0yGBUMEWStXLlSt/nHo/Hys3Nte677z7ftdraWsvpdFrPPPOMiRBhSFVVlSXJWrt2rWVZjA10GzJkiPX4448zJmA1NDRYY8aMsVavXm1dcskl1s0332xZFu8X/WVAVkbb2tq0efNmFRcX+67Z7XYVFxdrw4YNBiNDpNi3b58qKip6jZG0tDQVFhYyRgaZuro6SVJGRoYkxgYkt9utZ599Vi6XS0VFRYwJaN68eZo1a1avMSDxftFfBuSRATU1NXK73crJyel1PScnR7t27TIUFSJJRUWFJPU5Rrqew8Dn8Xi0YMECTZkyRePHj5fE2BjMtm3bpqKiIrW0tCg5OVkrV67UuHHj9N5770liTAxWzz77rLZs2aIPPvjguOd4v+gfAzIZBYCTMW/ePG3fvl3vvvuu6VAQAcaOHautW7eqrq5Ozz//vK677jqtXbvWdFgwqLy8XDfffLNWr16t+Ph40+EMWANymj4zM1MOh0OVlZW9rldWVio3N9dQVIgkXeOAMTJ4zZ8/X3//+9+1Zs0a5efn+64zNgavuLg4nXbaaZo4caIWLVqkCRMm6KGHHmJMDGKbN29WVVWVzj//fMXExCgmJkZr167Vww8/rJiYGF9FlLERnAGZjMbFxWnixIkqKyvzXfN4PCorK1NRUZHByBApRo0apdzc3F5jpL6+Xps2bWKMDHCWZWn+/PlauXKl3nrrLY0aNarX84wNdPF4PGptbWVMDGLTpk3Ttm3btHXrVt/HBRdcoB/84AfaunWrRo8ezdjoB4677rrrLtNBhEJqaqpuv/12FRQUyOl06vbbb9fWrVv1xz/+UcnJyabDQxg0Njbqk08+UUVFhR599FEVFhYqISFBbW1tSk9Pl9vt1j333KNx48apra1NN910k5qamrRkyRLFxLCCZaCaN2+eli1bpueff155eXlqbGxUY2OjHA6HYmNjZbPZGBuD0MKFCxUXFyfLslReXq7Fixdr2bJl+vWvf61TTz2VMTFIOZ1OZWdn9/pYvny5Ro8erdmzZ/N+0V9Mt/OH0pIlS6zhw4dbcXFx1uTJk62NGzeaDglhtGbNGkvScR/XXXedZVneLTluv/12Kycnx3I6nda0adOs3bt3mw0aIdfXmJBkPfnkk757GBuDz49//GNrxIgRVlxcnJWVlWVNmzbNeuONN3zPMybQpefWTpbF2OgPNsuyLEN5MAAAAAa5AblmFAAAANGBZBQAAADGkIwCAADAGJJRAAAAGEMyCgAAAGNIRgEAAGAMySgAAACMIRkFAACAMSSjABBGU6dO1YIFC0yHAQARg2QUAAAAxpCMAgAAwBiSUQAw6JVXXlFaWpqWLVtmOhQAMCLGdAAAMFgtX75cc+fO1fLly/Wtb33LdDgAYASVUQAwYOnSpfrpT3+ql19+mUQUwKBGZRQAwuz5559XVVWV1q9fr0mTJpkOBwCMojIKAGF23nnnKSsrS0888YQsyzIdDgAYRTIKAGF26qmnas2aNXrppZd04403mg4HAIximh4ADDj99NO1Zs0aTZ06VTExMVq8eLHpkADACJJRADBk7NixeuuttzR16lQ5HA498MADpkMCgLCzWSxYAgAAgCGsGQUAAIAxJKMAAAAwhmQUAAAAxpCMAgAAwBiSUQAAABhDMgoAAABjSEYBAABgDMkoAAAAjCEZBQAAgDEkowAAADCGZBQAAADG/A/ifDKya/ruRQAAAABJRU5ErkJggg==", "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": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 35, "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 include_string(::String, ::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?\n", " in include_string(::Module, ::String, ::String) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:577\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at /Users/gpeyre/.julia/v0.5/IJulia/src/execute_request.jl:154\n", " in invokelatest(::Function, ::ZMQ.Socket, ::Vararg{Any,N}) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:587\n", " in eventloop(::ZMQ.Socket) at /Users/gpeyre/.julia/v0.5/IJulia/src/eventloop.jl:8\n", " in (::IJulia.##18#24)() 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 include_string(::String, ::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?\n", " in include_string(::Module, ::String, ::String) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:577\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at /Users/gpeyre/.julia/v0.5/IJulia/src/execute_request.jl:154\n", " in invokelatest(::Function, ::ZMQ.Socket, ::Vararg{Any,N}) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:587\n", " in eventloop(::ZMQ.Socket) at /Users/gpeyre/.julia/v0.5/IJulia/src/eventloop.jl:8\n", " in (::IJulia.##18#24)() 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" }, { "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 include_string(::String, ::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?\n", " in include_string(::Module, ::String, ::String) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:577\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at /Users/gpeyre/.julia/v0.5/IJulia/src/execute_request.jl:154\n", " in invokelatest(::Function, ::ZMQ.Socket, ::Vararg{Any,N}) at /Users/gpeyre/.julia/v0.5/Compat/src/Compat.jl:587\n", " in eventloop(::ZMQ.Socket) at /Users/gpeyre/.julia/v0.5/IJulia/src/eventloop.jl:8\n", " in (::IJulia.##18#24)() 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" ] } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo4.jl\")" ] }, { "cell_type": "code", "execution_count": 23, "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": 24, "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": 25, "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": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "include(\"NtToolBox/src/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": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 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": [ "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": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "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": 32, "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\")" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "raw", "metadata": {}, "source": [ "" ] } ], "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 }