{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Active Contours using Level Sets\n", "================================\n", "\n*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n"], "metadata": {}, "cell_type": "markdown"}, {"source": ["This tour explores image segementation using level set methods."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 2, "cell_type": "code", "language": "python", "metadata": {}, "input": ["addpath('toolbox_signal')\n", "addpath('toolbox_general')\n", "addpath('toolbox_graph')\n", "addpath('solutions/segmentation_3_snakes_levelset')"]}, {"source": ["Managing level set functions\n", "----------------------------\n", "In the level set formalism, the evolution of some curve $ (\\ga(t))_{t=0}^1 $\n", "is computed by evolving the\n", "zero level of a function $\\phi : \\RR^2 \\rightarrow \\RR $\n", "$$ \\enscond{\\ga(s)}{ s \\in [0,1] } = \\enscond{x \\in \\RR^2}{\\phi(x)=0}. $$\n", "This corresponds to replacing the parameteric representation $\\ga$ of\n", "the curve by an implicit representation. This requires an additional\n", "dimension (and hence more storage) but ease the handling of topological\n", "change of the curve during the evolution.\n", "\n", "\n", "Discretazion size $n \\times n$ of the domain $[0,1]^2$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 200; \n", "[Y,X] = meshgrid(1:n,1:n);"]}, {"source": ["One can create a circular shape by using the signed distance function to\n", "a circle\n", "$$ \\phi_1(x) = \\sqrt{ (x_1-c_1)^2 + (x_2-c_2)^2 } - r $$\n", "where $r>0$ is the radius and $c \\in \\RR^2$ the center.\n", "\n", "\n", "Radius $r$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["r = n/3;"]}, {"source": ["Center $c$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["c = [r r] + 10;"]}, {"source": ["Distance function $\\phi_1$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi1 = sqrt( (X-c(1)).^2 + (Y-c(2)).^2 ) - r;"]}, {"source": ["__Exercise 1__\n", "\n", "Load a square shape $\\phi_2$ at a different position for the center.\n", "adius\n", "enter\n", "hape"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display the curves associated to $\\phi_1$ and $\\phi_2$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": 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F1Wy7q12RKD0nSc9eW6XlxnZJTRx2K3AYvA/HF5j0HNb6w67dsNWSwyNL5UjqMJVur2il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\nD2c7jgFrYSfiAAAAAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(1,2,1);\n", "plot_levelset(phi1);\n", "subplot(1,2,2);\n", "plot_levelset(phi2);"]}, {"source": ["__Exercise 2__\n", "\n", "Compute the intersection and the union of the two shapes.\n", "Store the union in $\\phi_0$ (variable |phi0|),\n", "that we will use in the remaining part of the tour."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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VlmmZ+uE7rIicC2xKqq80CEwSdUlJYLFMS+AlpefNS9KcdFAVTyO9GTa5xip+THSOQ8DH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\nTEqz5798/rwrh8V6DHBVQgj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"output_type": "display_data"}], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Mean Curvature Motion.\n", "----------------------\n", "The mean curvature motion corresponds to the minimizing flow of the\n", "length of the curve\n", "$$ \\int_0^1 \\norm{\\ga'(s)} d s. $$\n", "\n", "\n", "\n", "It is implemeted in a level set formalism by a familly $\\phi_t$ of\n", "level set function parameterized by an artificial time $t \\geq 0$, that\n", "satisfies the following PDE\n", "$$ \\pd{\\phi_t}{t} = -G(\\phi_t)\n", " \\qwhereq G(\\phi) = -\\norm{\\nabla \\phi} \\text{div}$\n", " \\pa{ \\frac{\\nabla \\phi}{\\norm{\\nabla \\phi}} } $$\n", "and where $\\nabla \\phi_t(x) \\in \\RR^2$ is the spacial gradient.\n", "\n", "\n", "This flow is computed using a gradient descent\n", "$\\phi^{(0)} = \\phi_0$ and\n", "This is implemented using a gradient descent scheme.\n", "$$ \\phi^{(\\ell+1)} = \\phi^{(\\ell)} - \\tau G(\\phi^{(\\ell)}), $$\n", "where $\\tau>0$ is small enough time step.\n", "\n", "\n", "Maximum time of the evolution $0 \\leq t \\leq t_{\\max}$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Tmax = 200;"]}, {"source": ["Time step $\\tau>0$ (should be small)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["tau = .5;"]}, {"source": ["Number of iterations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["niter = round(Tmax/tau);"]}, {"source": ["We use centered differences for the discretization of the gradient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.order = 2;"]}, {"source": ["Initial shape $\\phi^{(0)}$ at $t=0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = phi0;"]}, {"source": ["We now compute the right hand side of the evolution equation.\n", "\n", "\n", "Compute the gradient $\\nabla \\phi$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["g0 = grad(phi,options);"]}, {"source": ["Norm $\\norm{\\nabla \\phi}$ of the gradient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["d = max(eps, sqrt(sum(g0.^2,3)) );"]}, {"source": ["Normalized gradient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["g = g0 ./ repmat( d, [1 1 2] );"]}, {"source": ["The curvature term."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["K = -d .* div( g,options );"]}, {"source": ["Perform one step of the gradient descent."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = phi - tau*K;"]}, {"source": ["__Exercise 3__\n", "\n", "Implement the mean curvature motion."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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mujq6gCdWz14NbY8NEjYsj1qFNYKKSHhk45iNS8Sl4/ZIRWwc2BcsQ3sSqcDe\nKsGeI72JunX7jS4+zpAqaTucjWLYYWoIoihUzRc4ie26Df7yWUap/3y4vym06wo3YGeAaDmYVBMT\nXlLMeqPmdrjaUZzHx8eLi4sxxoODg5WVFQA4PDxcXl7GZMvCwkJoDyPWNw5zL6QB3ox+6/aUUXCK\nt77yBiy0Z4qq2ds8c6XSq4MMRUFZL7GKKYQM8zkb0Serqurw8HA0GmHINR6P19fXX7x4AQA3b958\n8eJFCGF9ff3Vq1e9Xm9tbS2EMBwOFxcXgQ15j2w8fUz4lGDZYE57/ra+kMwUBozsJdlasa7oz6Pt\nbXyTJH855gGeQpwMgjFiDH2qmV6aaaxtjBZYVVWj0ejk5ATTKfQwAJ8BHB4eHh0d9fv94XCIQRgk\n7hqdAEvnKeQTI7WVPBQ1fDuZznD8f1/6UudlcpwemVMaLbsl1jILUYlCX3Fo3vEaDodHR0fLy8to\nvdbW1tB6ra+vY+HGjRs3btx4+fLl2tra6urqwcEBPi0bDodig2J3UEDymqUTNckL+a8RrURLCfAo\n7j94oCvnCh6BTYCYVWNJM1ACTv0FpSVQMhOi4mILzTiOuq57vV5sizMTvuhNpTKHgb0omkqMIDKB\nFyiflMdYtHFKFfJQT5/A1EE5TomYNk6ZRfpvShGpayeoqE0FrVu3X+rXEIuAiQjYm/vExnH7tWUi\nJykoJl5bhobD0BWB6XWjlTDnKUquR/N0ZaR9LeEG7Iwx3f1UC16vzrc8Go36/X6v18PMYYxxf39/\ndXU1hLC/v7+2tobJlpWVlar5UDJntrk7sVMuVNElUahZ3iO2p/ygraVsWFBTxtXWHPPUvdBO/uRP\no+P88Gh7G5rgPoWSy2HyXFxfHKC0uLi4sLCwv78/Go1u3Ljx4sWLGCOlELFQVdXNmzdfvnzZ6/Vu\n3LhRVdXx8fHy8jJ3s/TeM9YOWPIwNq4heYfcneJ2qGZz1mgDxpVC4LNSiZ3y/tCBbA0GOBewPl1z\nBTdgF4qS226Gi0Tl8u1nzFLKTHLUbIomaI8HCdlHzVAceAHTuXBFxZTbsf0YbM6lO3PQDpBuoLma\nadC5hXxLzijOdrCeUZFwODm5ywVN4EXrgjJgKbaHdjJD6AjYQCpgU+DrszqHWnADdvkQN3p939ft\n+/3+ycnJaDTCccN1Xa+tre3v7wPA2trawcFBVVWrq6s4T8HCwkLJroWvZ7qiwoLyBEhkicTMsQjz\nRuuSG8tdUW1uQ8KVdlwDmGzBB6ULCws4LH5tba2u65cvX83n+QEAACAASURBVN68ebOua3wGBgCv\nXr26efMmAOCiqqoODg76/f7KygqOZspMFZhnO/eZqD20yU+WDNqGKuXhEfiWxcAQaKsgttMPdK7u\n3b//ZG+PH8tcqcMN2HnBpFGKW4U2LDS5tdFotLCw0O/3MU8YY8TMIQAcHBysrq5S8qRqfyJLSE7v\ngguAGw9o0hpchJ3DDjN/haqpxpQu9afTx5xDJ/RS8HBjY5D+PCMif+lTbXRcgiM4KIVIgw9jjDj4\nEJpRiJhCfPXqVVVV6+vrIYSTk5OlpaXMPZ2TXDBQZw65lyYe1pqGCiy7FZuZryNLnnNxQZv/oHxK\n8yjy1+K6wg3YBNAKNAuZpamWqb8p0Fsp4kkvMGmJdJ/YvkBsQ2QOoa1GEi1/JJA6XnOR6Bi0R22I\nzGHNRi13KtlxfsArsruzg9Oii0upW+q/KUVkmGkSD1h8I2aIJ4HwLZsSiCqLqIMqbmOoP7H5Xivf\nZkmBekWb1f5fxT5cCY2co4Xi63ad4QbsVHi4sdH5bUa9NFWG9j09VRlCwNeWx+Px8vLy0dERphAP\nDg4AYG1t7ejoqKqqpaUleqPZVHLqxmEGXnz8FfmPFIGJY9GbFYt0Z3iYxR1e7heLzbqGLwycKvxj\nwWbLzF9oM0EIwQRygHLmq6urdV3v7++vr6/HGDFhSIUQwqtXr3D4Br5JsrS0hIOYRBKCeqLZjs2o\nULffzaIanX7oLEDbeom9iCEbgWXOS7y3+ZSDG7DJYN7xM3dwIdFUWdsSbWP43xgjzb29tLQEAIeH\nh6urqwBwfHyMbzRjmlFEM3pHHGQwYjuPB+x7fZD4zrI+OeZf3hMKtqB94+A3FGCJFLPDqWNxnAcy\n/Bc00H87RWFuGU0FPgbr9/tHR0f4JOzVq1d1Xa+vr798+RIAMHMYQrhx48bBwUGv18NBuUIF3KhE\nlTMEy4AJHgYW8/FtRpZdNAuBBW20KTp801bReeCenOgVzLcK/EXmidFpw1L0hbZZKgfO0kuFqqpw\nVgIAwEIIod/v46J+v48tsSaEgG1oI3w7FZucifSTeR9Tz7qdwaRzzOuZ4mICF3OhHSb2dnexIIgN\naaOV5z9PmmnOawlgRgEdOPxLDOc1YiNiL/yIiPYpquv55seJTy6YNanZ5fleamumRK5HzX/xnbD5\nhEdg0yBYLiQXRqpSrJiqyYNvv9/vI++XlpaGwyEALC4u4hymOOzKvDvoXecDICzQG1rkgYrOgGXd\nqY1wURFiL1yloZ1C5DBt2J27d3/vrbd0veOsoC8Erw/KVtFSsQjSWuDE4H8xCBuPx0tLS3VdHx0d\nra2txRgPDg5u3LgBAAcHBzgc8ejoCGMvnPm33++L7eMedUCTj8CI8JFlzvUh84I4hFA8UxStOxH/\n5xNuwCaDqeFUZVD2DE5ht/iKoXneG5tcIuZYAKCuaxo3n7FeumOmYvlf0i1lDrkZS52NoO5ukWUO\nxRhlYcbME5vCk709zyecH0LbLPFK/Vc3DpbpKuc88ryqqpOTk/F4vLKygo9+V1dXDw8PAWBtbe3w\n8LCqKhw3X1XV4uIikc1UUN42CL8tqLmquRsXspZMvCJi7oUXtA+nEw/5v/MDN2ATA0n5ZG8Pv2lZ\nqMBKva6fGtoe2DBCbMC9v6Amc4K2OynkSllE/EupFT6yg+9FO4mx/agA2vcgKHsuyLtEHabTQsfL\nH4+bOJMr6JgO/AoCwMbm5sbDh+W0F2VzGDrVg5UVqOsaM+QhhH6/j94PxlhVVeHU1ZQ8NzOQwTLD\nCP6KiO4YP3Ys1OqTC6IBQYzCDwUzRfEBHYROCcyhQNyATQbOV1HPG2hOg6K12KYpElFZsRkxeLAC\nSpPiqTUpJLQfBugDKQy8xLp6UyFtwEI6cyj64Lg6EBeUyvz65gug/BiwRKFJG9lHTzAOG41G+BGG\n4XC4vLwMADSaCVMRfFP8+Rm0MwfRSiQK11AbWmAuI+82r+ftTZNszhRlBl7Cbrk6ODzpUoTM/Rq/\nawCJtD4vmw06IayO6VpqiEUh+xAboTXDHybzZ8upwR26XqxIm6VKrk/+2wmX8cXDpA1Ytk0wHwoM\nVbkKYowYftV1vbi4SM/GkIH9fp/skxALgodB+ohM/mvqdsIkvKa9yX+T2054Ex6BlUKrjhYJi6Kd\nL9MdSxXwE3xYCCHUzXTyofHsIsuo6Ft/aDuGqRSili7fTlBjLiBrxXUlXyWwKXr51mLz/mldnDl0\nGV8KQntIAr3LzJ/u6AK0YyDalKip2Hv3GJdoktRqLgxKQtATXwy8OO0rNQTRPDpuyaJKbPDOCFbr\nv7R3ftL4E4HQfnJMh1yr5KHmf1R5i1Nf2JmHR2BTQt/NBdG5YMIpkIqoQjr8ygRkIW29ENoDTTme\nZsiVd0VNr1OUU706qwvnOA2EGdgcDMz7+xRa0MZGqyDFZ73I3DJ3/kRBH6kWgmZ16m+qge2dKUNl\ndkYUHAiPwCYD18NbT558/s4daOaFI7VAe5ACrlhSwPAoWmFKYEn5qLLk0B5hwX+1K1pymFpOGZvH\nl4aETxpZVCfa1ImZolyrVwrCJIj6Sg20CyrwqtpDkzTtoR3qQYL2PEbRneRdLWQ7tLMXot4UguY5\nWDEW7zO14bqgUzepSXMg3IAVwRQYp7uoCZOjYpm0mn1qiFdWiae+uNPYTk1A+66hxdkJrp9OLaWE\njRBWNpY5wi7gKwVNe2C3b365oVgCmu2iRjtqlI426aE7GazhFakCMLFnQLzle6SO8Z1Snytrpiho\n20htt1wCeXgKsRRamfmlE0GnTTpTJRPB7LMJklA+fzhp5jCfRTyfK+Y4exDJaT4OyiJyjhVyvmo/\nPBaL8inBQraHbOZQF4KyXoKxIkOoNWLyPAMos1suExMegRUhWGNnq6qit8E2Nje3BgPUD65SJRIm\nuiBGbYCVOUT3bTweI9Gr9thiTe6g4qFOmNKCdthk7oXKQRn4yFKpdETU+arrqbXjSiG0k2C8vkqk\nCqt2njC0BwHyRcAoFFlIVFXVeDwm/gNA3R67BIqZgUU/E0FYFGAhlHkqQsJa82MUiqZTVLMp8CsV\naOo+OEy4AZsAQSUNxNJJgfIWSUKeReHMzhA9ZaIKTRc0WQ5o3x3ytwmxC23AuGjF7SCyFIpjVhC6\n8uen4T/VCKpr2nNqkR6xJ7Gd2YO2LcwUaHWhrxIDVqkRmMAcNd5Jzvxwusy5awfhKcQiiLszrxdt\nJlIvFXiqRGRIdI2ZQjF3UXh03EbqAVTlCcPaev3FvClwA+y4stAs4iqgDwFvNCOYTsN/TmNNe96S\npu6lNmb3IP2oVRRwXU3alBb4ItGMUz1Pfm01z/1yXkd4BFaE0M4D8DQgH4v4aHu7JIWIAuN+GUku\nND4dxkOxnULh0oLmEycxESfFrAtJSNkb2rjesnlmQL3+Etp+biphoiXtuFII7fiG58kJqQy5+KvZ\nzvlDBglJwjOHnP+UJOAFsCwB33gGwlyJjQv+09ao82RE9aFx0AEKCfDTm9LaRNKYKx15BFaEoPxQ\nQU2z3kQq8NKVqWArA73Zqv1MW4AbD+1I1tYz6k5X1DRLonzOl8txNkgxh+p3d3awhoZymMkAnSdI\nBVuiMsP/FNWrdkxGiO3nUqE9CNAkvGC+uShmYy9TEWKn3G6Bq2NCuAErRcYmvfXkCbb5YnZuU6Fh\nrdWUqlPgH/rS2jbvJuahaTmZAs7AtHYZGwZtf5P35NwuoGN6cP6kGCV4LghpqsA0P6aVKkHIumtB\nJRWxPkV4k9Lab0s5bXXiWbJJe3DmTwtPIRahYp/8AOutTNES2imU0Mz8BGw4FjSv8fKZoiorhaId\nurqdM9FWgQp1e2gGtFMiQrpCmcAGd0QreBL3tTjJTFF0Q3HpXlkI2hM4//d2d+/euwcAm4MBDsTl\n61bZUYiRDXkARhXNf6RlYOP6YjriF4syBxiVKSLmawsE7TCuUknRqJ4FcIFUp54pypWi4RFYEbTv\nKf7SA+2HGxspfzMkkiRVOx8ykdcpPFBzF6LbAlHlNGorWyKkrst5QFZ+rsyrDM6c1N2Zt9T8L5GA\n1kK+Rm+8UvkGzfnQNoEZwlMBx+7jlMG80Ml5QX7n/3nADVgpTG2YOtlg00oJJQvpmqrWotW3g5Sw\ntcjzXRWmJVpebcpWmVaNt4FE/oQL23GVwQkjCpyQ9FIzH46Yoq4grWhcyO3Mpsy90xFFNQWGyczI\nshchBPzEeVVVWMAafClT0960XrR35//ZwlOIRajYF304HStrOCIAYFawZlNrR/UuCKhhV6GZjaZu\nXgWL7YlzuPEAa/CVzvuJTEjKnGgdcvuk1w3ME4+JwVfAcqdV804Mh2v4ioPTHhhhqia1WKkU+tb2\nNs4Liqt0Zg6J9qBSiCJzqDlJhaBGxnPaUxnaIyqjirSoBhuMRqNerwcAo9EIV0QDBgA4k/XCwgKu\nrv3FKjHBPD9XusYxKTwCK4J2RU1QIpFGc5g+ZlBBWKWCs3I/VDQWG9QWBdrzAgjLBOw+JdIpZBcB\ngOYESQHaJtMxi0hxXtdQEEaLRAykGa7VITivyZ+RXgrQToGCNZhCMBYAxuMxWq+Tk5Ojo6OFhYWj\noyMqHB8f9/v9fr8/HA7JAKckAIlQT5xql8l0cANWBNNCcPQa0CqbgwGOEuwl0O/3eaGvoCt5Dd+C\nhql8KmAPteT0wy0E+psxxuFwiC1HoxE2w1wK/6AlN34Z8+a4+jA9JA2kHHlvyPwM58Uvp7FWQX5p\nnv/CjvJDS3Ge4jAscGJjQddEy9VLSYB3QBTAMmMuljzcgBUh7+Vx35BkDCxDIlpWXWHZ1Oj0RkE5\npIiowi+uw6qqRqPRyclJv98/Pj5GD/Tk5IQyKlHlJMG1N/vI0ymoMItW5I+BtQkMBTmGUBaHTUp+\nAc7V2AyaxdgLg63FxcWlpaXDw0MqLC0tLS0tUUB2cnKCcRgaPLDiLbFHs+yYDm7AipARrVaUGJGo\npZsRZ7mwTelmxAwJ00UQhod0WFXVcDhESR8fHy8sLGAB/d/hcDgej0OTRQGVJPGQa3aRNwka9EIk\nAAy2tioV+gt+akrnBSI2oqVn9gqsAZOColTgmcPFxcWjoyM0WlQ4PDzkZmxxcbHf7wtPTmxWwOVw\nhnADVgRUC89OUHqQL6JKWnFzMMAakQkRBZFXSeVSRCIxkznkWRQhZgEdNokaeqwt8ooUn4nMiZux\nawPBJZ2artoZ8op5bwBg5g85vUWhp/KKZgpRaE2rUli4SsWIMZFvEFSPajAUbyn+6q2ZNY6zhRuw\nIuQdz0oFZL/31lu0rjm22HQwy6FdUdNclbiiHNrejMfj4XBIz64XFxcxhUiFhYWFXq+HQRiw6O28\nr4jjApCnk1YBMpAGdDzc2BBWRBN4Ii0IuZmVGebzQzMdrKqqMDe+tLS0vLx8dHS0vLyMURcv4CIK\nyFAFw+Gwbr/yn1FBTOcVHRPBDVgR8rrV5artim5sbqZ0y8XZbbi6zBVVgmWrQvrRl1mDksaE4dLS\nEhqtxcVFUcAEI38GcObn33EpSBFemCVtVPjnLk0L1Ml8vU2zENKmiw5B/GbA3bWjoyPKHC4vLx8e\nHqI9oxQit3D4eLhqfz9Fw6Vx5nADVoRM8kSUec6EPxLAoVmphIlOm+QHWZnotHCFBxutZwNCmSVZ\nEU+bzDoEq6t2jk4TnoPbMJ0DTKUQecteOlWuO6P/agmYx5g3Npr2+lerw3FhcANWhJCItFLuIf0V\ncVjKhxUbMf+aMH1PkuukposjNl9ywYzKyckJxmGYOcQaXLSwsGA+xJ56144rAsF2zbcqHYeF9qBE\nzfk8201BZXYd2iEXsKgrFIxgApZvEClEHmkdHx8vLy+vrKxgRp3ksLi4iG+YOOEvGG7AipAyPEJO\nQlf4m88lZixTid3KmzHR/4nUFZqJhhcXF09OTnAYMWobdYs1mELs9/t1M+/OGZ52x+XCJJXpPJlW\n58ne3s7jx7gpzCVqVqeUpQWVkl6G/EGZLq0Cvqiu6+FwiIlxNFqYSySLRU+/0LBhzfLy8snJycLC\nQmVNN+M4V7gBK4KZnShJ62ECJJVLzIy5KkwkmmYvb8n4cWl7Y6rdvIvpm0Uoe9LgmBXkKVfC/157\nRG5nClH/8v3yQqVGAqdMoCkEhKB6hvDCIma2YzYwmzlODzdgRQhW3kOLJOVCVu1c4sONDQzFgnJd\nO/1T035kYB5L6hiFnquqwukGMENCuUQsUA3OCFc1X5fI7MIxWzAZlXGYTCY/2dvj4xJDIroylWX+\nZuwTcTio2Assh4zqoUkh9vv90WiEKcTj4+OVlRVKIWIchjWYUV9ZWTk+Psb8BA1iMnfdeZ7P6pLN\nG9yAFYFLV8g1Lzxe4DYM2AAtvQXTqokOpAQ83aEFFXUhSNKUQqScCeYS8UVmdLQz9w5wlc4gtLUQ\nrCs3PDyXiO84pzif2UiK8JlFiIw0OPNjjOPxGMfEU8IQC/isCwukAqxZXFwcjUb9fp/3R+x3Om06\nOuEGrAg8eaJzGiZ4MpAKv/fWW9yMUVLFHItlvrNZpUdb5W0bPxxTS+LGxLfca+YUNwtYLrnROGYL\nnSQXS/MjbPmEv4OtLZPnnTvSzNf87wRkg0ssEKtT++Jyy3QACvL2jqnhBqwIgqn0V7BWO5KC7pUa\n1vHFhw8zz7dTW8jLMnUI+aODdAjV7/dxugFMlWBSEWcyxddfzM7kd+q4+jAZGNqukqhM/WJB2LDp\neN7J/9AOgDQJBT/5Rnq9Hn4nBdPmKysrmCekzCHVYByGk1mjQMAKuVJ9A1fHWcANWBE6PcSeCp7M\nCIzq+VQdALCxudnph5rOYKfO+V6EeEzli43jrlHYmCTBQ+AFbXRD1w3oYq6a45TojIc65aBHJ3Eb\nlpm3Xu8uxfwpTB1fUfiOvKbH0gymLqhjIWHpU5znNUH5jqLl+V7jGYcbsCKkRGK6jZXyT4U8EG89\neSJCMdMSZABnkWQXW0hB69PspPh7mo45Lh3mZdVWxOR5Sg5VOw6j0UyiZYZUKfKHgsCLrwIJzldV\nhfmGhYUF/DDY8vLycDgcDocYhA2HQxy7hLFXr9eD9C3C3BHv0rlewWsPN2BFMHWo9Rksk6Yb80ox\nOlGIVtw48jJO9Vz8DUrzKeHpXedNcqqHuhuZSsfVgXmVTVoKu5Xhv7ZhYjSTSbw8QGUUODQVMzW0\n316vhxlyHKOBg5hwgCKNOaTMoegnTDiFlWNquAErQkmiQyRPeurpdGrKHP6W2MONDZ08mSJ/wjtv\nShoS8yzgxgsPkPdTdy9v2FzVVx95DqSS5Bme8EXahvXSb3eZ1OL2xiSYaZl4WYNTmp7vUgHfVsZF\nWJniP+9qp05dC1PDDVgROOO1HrSuzJt45s4ubFinDmHCwCvfoETzKYmaNxRai+/oNL11XArEXVhf\naLNs3r75ilQpxnRoymX4D9n5ZVKNYZLcA3Wg17wlQgVxLOYJ4XuBtGDNSkch3IAVQcgvZY1SN/dg\nKVnUvPXkye7ODu7OtGFwilesUlvrFHDJ0aXOTAq6b2d1mRxnC7qs/EKn+C/aBMtu6QbchoWs0dKk\n5Z3McEw0Tq0iYB61rtcnpLz/uquik2a9g8MNWBHyKbXONIuZPOSomlwE7RG/pdSzxjjlhUFbyMgj\npc/MgfTaoyjFNFdUyFu7lKp5387tGjomhiBAJ9vzDSr1DiX+kt/GE4maOSaLOm0Gb2mip97v7Dw0\n8xmBuU1t9lK050K+hCs9s3ADVgQtoSrriJktg+XHCR3yXGKwXDbRqymOAtouXkbwKdmnDFVI3GVC\nO3DUB+K4mtBXVvNW81nfrIUidEvaI//6K6Rf9jDlICBWhDThza6axNY8ryz5612kVNB5FI483IAV\ngfPSJLFooFsGZa5SShATx3GKZ/RA0H/1RkT9pALONCgUc0nPHZeO1G1acN78NTlgyoFzHrJGK9NV\nk2P5rZm0N/tZIgqT5+auIe3DhbZIHZ3oX3YHZgO9JrmHH68LIVChqir6lDjSDgshBKxPNQAAbENf\nw+v1evQXgeumxEkIXZaACxUn3hXfU8elsQ1QH/QzEZSTWzUT+5o3vozIHVcKnPbAPt7I+Y9laLOa\nN+N3bfxAD8mBGgPA7s7Ovfv3AWBzMNgaDKBhkcl/DT4RhmA7lfkh8P7Tl4C4Qquuzyvz49L75bSv\nEq6q1kLqQrg6UvAIrAiCatpfMz2yfMFkPDKVXg774sOHJr813VN/ecugLI0pPO1spnKGKYeUH6mW\nqO6SgMv1isC81eYvuvmreZ7iBodu0AmxbuFGxNGFguFLmcM3t1yiBdFz8IG7BXADVoSgdEu81IwP\n7dt3isSa0zDh8yFNffE3KDOW6YC47xTCfF6dOi16p/qQXZlXBybDUxSq0tbL/KvBR3NMRwPNq1SN\naWymRko45mHy/ohuT3fU8wxPIRaBXrnHzEPVpODwhfyqqsbjcWB5DP5lIMpLYDYD2plDbIxpvarJ\n7wHAk729O3fvQtco4U7GC4lOlDmEruSh3hf/5b2t0nY9dWglR+c4V/TYsFjOECRqJoVIqcJerxfa\nmUMqVE1Or2KpQtodUoXKwOhaApISJcyhIbOQHvUf67nM6cDNkxOUd1i1M+fQHgUT0vY+Bb4j14IJ\nj8CKEKxgwmSkWTD/arJy1hK++PBhZ994ObXZDE7je2qEtqEKbec0c+xnfM0cp4a+pvoSa1F0Uj2D\nTGfKVw8W7bkqM0c0KXgGIigXrfM8QEL1/KjP9JJeN7gBK4LWpylgsxCyeoZ03oP2btYU9rxT1VXb\n0mT0Wa5k88zkz4Dum0v30mFePnGPFnQKBZ6cvvoEGo4oxtMXwtymiTzty9muVw8J05U5CakjnejY\n5xOeQiwC5lIosWBmGwLLHFKCBX/14CtewOQJkp6PudLdCAkbJhpzzXSOOQwsBQRlww47EdqupXn7\nSN3dMht0XDDEKESefAtshCGnvUgV4sWlxDgwalGNGGdIe++83WtS0Y4wLR9Y2tykPX8cMJ0KQtsD\nM7stqJ5x7FJaCG031EFwA1YEZHlojx4m20BS4WN2aWwupJ9j8b+ntxliU4ENCw5ti0JHJKQb2TDi\n0/SEF/iuO11y0UmxQccFo2qeHvG/sXl7hD8P47QXWgArr2BefX3pRWOzk5z2gZlVsTtdCM3j59Do\nGpTpygshQ/XAHv1y5OOw1Jkx95s6IXMFN2BF4BEYeW3ILXr4TEoI7YfYIvBKxVsZ1qbKJkgnPPbS\nHqi2XpCQa6ExMzsW2jap6no/zJS3uRdX7wWAaA/tQRyhufWDor0IucgEVu0RGRnm7zx+fP/BA0hk\nzk16EJd4V3EV/p6lGXhV7SEephDE3zwnRa84iN695lOZIuXI+S+uhVnpcANWBGIkkp6GUXEPtGID\nnzIyQ5RYBXq1E9LmIbQ9ytCOurhPqrcTlOMJp04eiu6Jfpo3IL5Ur2tu0HExEERC2lM9uXHA3rjX\n/I9dowfNnYqalI749qkx3yP1h29KBF5TxF5mhzmNzSPtfAwGabFkzs88wwdxFMF8KlvOyxQpU80Q\nKaaKer6WuaMq8bxa/D1bXPz7YfjWgeMMwa+XedUKyZ/fS6ql+TaYoITJGQHBTN7tcgJP0Sxk8wqZ\nzoMifyGmWGXW4RFYEUQKMbRjl8wYDTGTTSpzwveVYmGGnVqxPIuiU0DlgddEAVm+5/oWA9ZcDym1\nd+7oyd6eu2NnC3PsEi4K7PUpsIhUNSlE/pcXMjdx3geTDBoVmymKb4oPp4rsES+XwOmTEEF5WhOx\n3TR7KS3oPeq/8wM3YEWo2oM4gA1zggnjKhOiTWF7zWn6G9q3A/o1H1nDmWYOzd7yHor+V82DMfOk\nza0yrwLoEojnRppy4pKVqEBXmm3MXul9idWppmqGWWE9CZk/uit57tV5lkTZ7J5J9Ux8Zp6T1GmZ\nT7gBKwLSiLufkLgdC1mmqGny8ky6F9qPwQJ7XBHZ8BMt2nOyYVre/PA71Qvt8wyu3guEuHbcDNAg\nW40MkUzy67+pVXhLzopgPQnjm6rao5liM/3H1HkIk4Ri71TQdqsz3yD6b54BB7gBK0Sv19MJB2SS\nHmTIkyf5ueQz0s0rhK/OVSEyh6RtkTkEJd2LQVAGSSOjbfMMXGT/5w2pjzBAY89SmUNQKUTzUnL+\n8zINX9JiIW50zhTFOyz435mBmEgXmoRB2dHQtmQVm2sKl+K4xEo9XMxYuI3NzVQH5gduwIqAjOEq\nnc4D5Vvjf81yZl2t/MDu73qpzhyG5mHABGfhdNCq5p0nSZunFNRJg/nW7cVAMFOMQkzdWAU/aZUS\nzutrKmRFZcGNig2DJJ5TWfNfm64z1IKmeuqMdY7v0Keuc6dzBTdgRSAmcbsFyniU6/msesWFTb86\nT3jxmUPdVVEuPGm8sWh/Ad2ec/A8G6Qf8KSuhW4gyrylWCu1NZ4qFPTgK/JHX1RJQVhgXubZasE8\nKN3hvLvWKQcHwQ1YESiFCG2XreStZNpIoZg1UttBcDeTu5867QOXlDkUSAlbHFQql1i4ccfpoR8U\niVycSJjzVcQl02VQEtDXd2Nzc2swCGqODx1vxXbCPKS/TnkBPlxQZiwoQ6sJH9SgRE3+lBDmlvZu\nwIoQ2pZGKDAvgJLbbmEfaHf67gDtiX/0U2usP4+EyaTQJxPU44HMYHpTwI7zAJ1wHuVTTYb84hpN\ndLHExeV7CdYAJVCM4kujGjycksBZKcI0LcEyYHC6uaZw+3u7u9Uca8ENWBFIRaFttzJUM3msy9N1\nRpSphkdj0OQ8g5UwuRQDltd2J0Aduz7PjjNEisP6ZppifsjamMy+xCKTCfQoulJTj0I78KI3XkT4\ndd4qEAfLT5o4rpJXnvm6qd3NmxzcgBWhYrPmUI4ilTaktVJihgI985qHGxvbW1tavVEBGk1yDcNl\n260UQsENUcwaxwuZDTrOBBWbQl6kECH7Vr55zzUL/u+S6QAAIABJREFUuh6xt7t79949XllZn1YI\n7LE0VygWaIRwpebC10I4pwgMsmaMjj31CjNPKvK/m4MBbZNvZ97gBqwImoIhnTkUZEqVp+tGaAeC\nYrOd73tdHQOmTwspGQreD9OinU8BnyvEKRVn27w00Ob/6S/Kw40NfAwmaM9v/aAeblXNPKWQSBte\nmBBSPOedT1Fdn1hwnrfhBqwI/PHSeUwhzyG2wysR5vOtTDQGV8lumdA3Jo3UmA7zi9Uu8jMBD98D\ni2nM3AOkAy/9lxDaZi8lJW6KKAUCyjgF5rEJFUyqhXLJFJItWHaIjlT4bWYExitxU7s7O73ESZsT\nuAErRWi/iZIiTZjWbund6S3rmwLfUbikmaJOCXHGxK2w8/2w/AYdp4HJQF42r525YvnuaMv0XZWN\nzU1KofOtiTG3wBxN/uhXaAFxkYowz0ZoGzBumQTJdTbi4cYG39o8E94NWBFCdtjVdHItAX8SQOaT\n3M+KfSpiVjKHAkHZe1PYKdOlb6DzLOZzAhEMGP34U6gzPOfCQIpFnPZgWTKCfgEAEio4V2noMyOo\nmyK5nqqDQBNwQPZ0zQncgBWBTFdQYzd4g/PYKZa/+PDhlx490tl8fkPRS6+s3TKhT6ZpungihVzR\nvd3d3qV1/NrCTCHq/CGoSwbtGzShZFFg4zVoTqmNzc1H29vQ5DA17UXOMG+6Ll4X5sFC+6ihYK4p\nvp293d2g4rMLO6IrAjdgRQjpCMwkzdRMynCRs5wnM6M1Uw6tPkM2TKsarI84p07R3Gr4/GCSkLNL\nNMuYq/I9hvYLKrQIx+KaLzuKr1OGqTIQZ6WUkuNNGTDNcEF7Cr92Hj/utdeaqAPXBv4FpVJMxMuz\n2mMIYW93F//+v1/8Iqe1nquimmWkPgwY2BhiARq+sbuzM7cCvgDw2yuoe25qlc6a/O4IxH8A2Njc\nNMlfwq7OD1T2zgin70mK8zp5SIv4CeSZmGsPj8CKEJjHxCGWnn4vUb0cXVU/djIebmxgIhGsMVcw\nCw+9SiDONlieKX+OXaksituwM0FQEVWwIgZQRu40uwtqZl5KJEKTS6RICy5jpqgzQWi7XEE5BynT\nBc3sG8LgzSfnPQIrwgXfFgV9uRP6xYcPg3qxMcx4+MUh/NPA4ks6Um69nuztacFfzGW69tAnNliR\n7ulPeEg4iITdnR1q/HBjY2Nzk9Mjz6LOiOeCIYKwTPfw6LT1IiGI6zKHEuj+9ocDAMbjMQDEGMfj\ncV3Xo9Goruu6rofDYb7Q2YAXaLP4TaPRaIQe5Xg8jjHicEQC+qGQnt5tRq+svkVycXLTBQC7Ozsk\ndbwRhOZxNzb4nd/5nQvs+3XDaDQC9k4VkTPF//F4PBqNUCOa/7xetESS406R/FwIvPDgC18Qndwa\nDFJjl/ISuBiB5G2JcAI41YXdAoCdx4+53UKe0+AOsaPf/d3fPcvDuKpwA1YE+koeF+F5GDBUKf6i\n3SIDFmO8c/eu2b0vPXqEhWt2NVGT5qvKAPBkbw8ASMC8QG3cgJ0G5LeZBkybK26f8gZM1BDtcb/a\nblEHYoyUTkyBfDvCldKFadK0uRLAwAsAeHDG3TWx2TlhvhuwItTNpGoXZsC43aICQoRicwgctVG1\nU4t81kRqOScyPidQVEQ8LDdguGg6A8bNlVlA4GvO1xuYO+W5wUoN3TJzhnPCfB/EUYRQ8J3ls90d\nMJeqas8x/2RvD/92uqLXDCRmc55EmOPXOc8Jgb3CTDWprNeZ7zeoZ2xV85lK1CPy4VpaMswWQvvl\nmaAedDnh3YCVIqhnM+e9o6o98XZU87+99eQJLTq//lw66IT0rZFaJGxMrVxiP68ruCE5DdMmUg1F\n0lG9sFyxMYf4+9aTJ3HGn/6K20u/7BUxOOd70dWHG7AiXHAERjuFthdcJWaKgtkUbQm035DXs17L\nMTU49y7+lHLDGRIv7EN2yMbVF4U+q6kAV4di5urzBjdgpTBt2PkRSNA3NlOU4lJtwOYBWts6i+KS\nPkME9ZEtTssL60Ov1yMHDrreepxdUZg0FnGYXjTncAM2AS6LMeSBVu3v8s2uVqdAJhS7tD7NAUpy\nDxdwCcQueGgIWSFcZY1kzlveXF1KQuhqwg3YzIC8sNiejG4eqJzJtHRWOk6J05zVs70iIiFxjVXg\nTC6EG7DZg+mNOhwXg3NNmxfaoUKHpgQzZPk88NLwUVsOh8PhmEm4SXc4HA7HTMIjMIfD4XDMJNyA\nORwOh2Mm4QbM4XA4HDMJN2AOh8PhmEm4AXM4HA7HTMINmMPhcDhmEm7AHA6HwzGTcAPmcDgcjpmE\nGzCHw+FwzCTcgDkcDodjJuEGzOFwOBwzCTdgDofD4ZhJuAFzOBwOx0zCDZjD4XA4ZhJuwBwOh8Mx\nk3AD5nA4HI6ZhBswh8PhcMwk3IA5HA6HYybhBszhcDgcMwk3YA6Hw+GYSbgBczgcDsdMwg2Yw+Fw\nOGYSbsAcDofDMZNwA+ZwOByOmYQbMIfD4XDMJNyAORwOh2Mm4QbM4XA4HDMJN2AOh8PhmEm4AXM4\nHA7HTMINmMPhcDhmEm7AHA6HwzGTcAPmcDgcjpmEGzCHw+FwzCTcgDkcDodjJuEGzOFwOBwzCTdg\nDofD4ZhJuAFzOBwOx0zCDZjD4XA4ZhJuwBwOh8Mxk3AD5nA4HI6ZhBswh8PhcMwk3IA5HA6HYybh\nBszhcDgcMwk3YA6Hw+GYSbgBczgcDsdMwg2Yw+FwOGYSbsAcDofDMZNwA+ZwOByOmYQbMIfD4XDM\nJNyAORwOh2Mm4QbM4XA4HDMJN2AOh8PhmEm4AXM4HA7HTMINmMPhcDhmEm7AHA6HwzGTcAPmcDgc\njplE/7I7MBv4x3/8xxgjAMQ26rrG3/F4jDVYoBr6iy2phtYFgLquacuXe5ghBPzlqKqKClimQq/X\nw1/6i4uwHgtUQ796FV6oGui9hzSo23QUjtPj3XffBQDNfCIzEZvzn9cIXWja0/YvHZw8mnic/Kek\nPW8ppMT3YvIfAHgB2rSfQ+Z7BHZaXBH5ORznAaf31YFfCw03YEUQ1KG/JqUyPNOLyL09bRfPAvnj\nytTn2/BjLDk55W3ENq/UybwGmJQP1/jM80MzT0v+FImWZmXJdlKr59e9xvAUYil4IoUXxCJxYzXb\nn22X8jhNVsHUiThA3L4o0K+uwV99WvhfWheUsGmR2Is4ZKqcw6TKmUOQmUM0SP3O0K2WMznVABhR\n+VqC9pzMQg58FWGZdCUWOPP56rxvc8h8N2BF0DdxIWPewLzvm+uevhuTbqGE1lx1up4XQKnOlDTv\nrd6sPiKxKb4I2ioVNWLRnGj4/GCaKLNNiv/naqj0xs/jipu050vztNeb4pLRq6ROsmggVsn08HrD\nDVgRhKGKWeQb6M2mpK5vH/rWkLlBEJXNx7y6QPvSPmOmS7xj+oj0aaH6uq6rqqIC/gIAr+fdxqVc\nvdgsP4ij33eGTw99Wcv5D1mxTNoHk/PmdgSxBSXyzpO2EPo8QJb2PMHAQayOCS1zwgMAljmxqSUJ\nITBQ52kLvV6v/CTPLlzeRTAJl1E1rSXWTSlZSNHcl9kNsQooieqbe2gPYSK58k2lIjBe0D4g72Qq\nlyIapI5RnxmxVgiBBB/Vrcc8FY5JoZkMXX5JiqKZy5rZNf7SMF29WUgwX1ivQjMWVSylu2rSntst\nkZwQvOXnSpw687RkhNB5CPMAN2BFSPGMlppKhjT/xF9za3x4ff7WoDuc8kOpEBMenHnU9DdvrkS9\n1rapZB3qifODBTJX3FHlXeWHJk6CYzpk2GtyUqwoVCM2pdfiuwDFfyhjPlixV2iDyJ858IyFAEV7\nLg1dA0o7YAkkE/OJPZq9jcrizgPcgBVBvKpFf/kLMbygf3lBiB9BNWYzLpv7Dx5M2v+dx4+ByRhY\nBGa+X2XeZWKT5cDoh/J+MZEPJEsjUoK4CJRrTC+48FsMFfhbL/xA+C8oo7W0tDTpuXIQxKtaJi05\nXTPkFzQGZcnyAKY+/CUVPP7yl2k7D77wBWBsh4QBg4ZsopIjKhNCWW7dH6I35QmJ4VwI/C/fIzc8\nnNj8EKJKM4iepyRwvWHYc4fGd7/7XS4ebcD0C5v4Rie96Um/XNJgSZcbPGpw7/79Mzyc3Z0dYr+w\nZNyKCKlTQbyGyd/fDOxFzhBCv98P6Xc/g/X+pvkiJ2Tf38SDMgV88+bNMzxv84a3334bC3mucpLz\ngq4n2oOKLYSfBwBUOD3/kfDQ5bdpRmnah8T7+4LtfJEpEC0lzX+wDC3vp2nAEDdu3DjNGZsVeARW\nBO2KQrHbyFuCciR5ezJ+iDt373Z2bHtrC9rOLDRU3tjcTK1Ft4O93d3YHgcBTBjRSmuEdsZPHFdQ\nGULdRp8EnR7kS7EzInOYMWCOs4K49Hme6za83twyb6wTFXfv3TurA+H2b293N7QjeyqAesSlTwKw\nlJ2uAUvsor1YEdq0F2OXaBU+ZKnEgM0JPAIrwtOnT7GQ0rAZgUVrKildELPs1HWdShIONjdB3f0z\nCO1YarC1lWq5u7OjQx/h/WXm1DEdz6DmzukMvEI7EOS3Fe1+Qtp60d+f+qmf6rq2jiT+5m/+BrIP\nwPIZCM1tYFZBB23YMh9sDTY3o7IoHJwSGcJDE5aliEdM0w0yiQdTCPnAi+9XZztM5osCWNbrJ37i\nJ7LX9prADVgRUMmgPMeUNarb0HJNGTBTvdxuibsA7xWHYLYgfQhhczDQO9rb3dUG7DQpxJSSaeMk\naa1kaFI90DZg0LZeGQ0DwPvf//7ii+yQ+Ou//msqc+4VptCjSipwaL/NJP/WYMB3Hady3TKcp3Q6\nkTNlQiYyYFwI3G4J2nP+5/cujgW6+D8nrpsbsCJ85zvfwULsGsSRMWDC0xRS1wkTki7pts6OJxbg\nzA4q54AKMSX9ZG9PWBShLiHISV3RUByBQXtkR17A+sAB4AMf+EDRBXZY+Pa3v40FYT/EY6qMARNP\nv0z+13Wtyb+9tVVnR+FCNgITv4L2OruOGQjOQ+IqwTRgwZqiVxTMxIMpLtNqikMQ/AclAfz7Mz/z\nM1Nd8xmDG7AifOtb38JCbEdgXJbCUOkUIq/ni7TjubmxITYOKgIrkTEkXFEtS51soWhMR0tan6a5\n0oWUARPl0DZgoASsD1CXER/60IcmuMyONr7xjW9QWXBPWKOUJeMNTP53kl/TPsN8TXuwOI8E05zf\nefw4T1G+qOTTCqkITDuF+q/uOTAhQ5cD98EPfnCKKz5zcANWhG9+85tYEHLKC1jbLVEjHE8MuTLD\nsUQE1nntQpf1EpoRAZlwS81UfnkuJSQ8UH2bgLJvRuiCxkc+8pGS6+sw8fWvfx0LUWXwTAOWyjfw\nvyQQPUYJn2+Z/AeVP8yQPyTCr9B2jFK0x1EeKa5yA1ZOe9MFFNsUvRKdxxpoa0EcMsecuG5uwIrw\njW98Q4gntlMoOoUoIjD9wSQh4K3BQOQYRe5F3D4gm0vRbhoHWIPjSaUiwfLWkyfcXGnpTueKppTc\nacD00eky4Rd/8Rcnv9qO/8HXvvY1UIM4wEohpiyW+Z08wfztra1oDfcQ/IcC5pu0B8t1E7TX0RjS\nXjtwVKnjKvHSCK2bieo0/7kKuGBLJMBrPvzhD0951WcKbsCK8Fd/9VdaxqaxEZEW/75fKvAabG6a\n4ieQpLWeaSO8XC5joWSS1tb2Nu8hPujOmKVCA8adWTOFEpQBSwkYlHS1kgHgV37lVya+2I4Gf/mX\nf4kFbT8E7VMpROHA6cddg81NnWzUlgxU8oO2UML8qv36FzAHjpuQctqHgghM0z7vt5nyFAcCxQbs\nl37pl6a86jMFN2BFMJWsbYzOGY5GIxKwDrzwSbXwXlOuKEySSzGVzCWRisC4xkRq5cneHvcodQSm\nPVAzhZgXMBkwUB4oKPVCwm7Rol/7tV+b7Eo7GL761a9SmZOt7hrExA0YeXKxPVIJE4bRelomCtpw\n8i4JmGzREH4b579J+2AZsIy7lqd9oQGDYgdOq2BOXLfewBqH5hD4r//6LywIOWWUXCsI60VPvMST\nA7Gpwr8akBhtb8qewOXxzuuvv/7OO7ToU0+ffv9znxNthMDyqjO1p2F2G1QEoC+HxpyMxTon/OAH\nP8CCoJMJTkXB57qu79y9++nmZUpgCXOzsU5CUIPU7nTHeM91mSO2Y7g87TMMF7rQq9DSwvNvKreQ\n+T/90z9duJeZhkdgRfjzP/9zLKQYoy0Qxl48AuMDrnjmRARthbkUyBokoRbTA4UmqSI8UO4kohfJ\nfdLdnR0RcnUOI67aMB3PEg9UH5cuC/zmb/7mpNfaQfjKV75CZU62kgiM+F+rtOHmxkbdfiocVeIh\nWhFYrV4jMWGaFk17Tv6gEoNVe5jizuPHJfOiFUZghZlzOgRQBlIcrMbHP/7xwqs803ADVoQ/+7M/\nA+tJACnKfFhNv0LD+NBrUgPGlSxsWAraDGg7IZSsH01jDRczjrAnfaamgMsoeWoDZhb0UVP5E5/4\nxISX2vFj/Omf/ikWYsL3TxkwYv5oNOLM3xoMzGFNJQZMkx8U/0OX3yZoH5R1ES6XGNyB6cT84FvN\n//LMoZk5L+S/+DsnrpsbsCL8yZ/8CRaEhDJpEBJw3Z4aauPhQx6ixfb4DrEpLWChZCiIwIQYUhLS\nYhPWaPvRI9r+zuPHXMn5Z2B64zwUA+YRc4DldYYC35PXf+pTn5rwUjt+jD/6oz+ickxHYNAIgbtl\nOvbCF7x4TkJIRtBebBzSERiWBTcKaS9cN50z4LQHloHodNdE1iEUGDDqM+kCFPN1gR81lT/5yU9O\nfsFnD27AivDHf/zHWBBOKIELmOyTyBxi3t8clygMGG2NNg7tgE/YMOqbvr9rDack1GnA+v2+mVSZ\nKIWolQxqeBi0Hc+UgM2/Ar/1W781xeV2IP7wD/8QC1FFYNBOIRJRKeUgYi9MG05hwEy/LeW6BeXu\naNoDAKci96UyHNYZiJIUIqe92CkvQDs1Aor2piUThyzw6U9/eqprPmPwQRxF+M///E9IDyYWNozr\nkzSM1svUqrBYpgEzw7KM1CHtqKaQEglX1Pdef/2N5vn2/3777e+/+SYkXrE0xSa2qXsl+qwPRN/I\nUjc4xC/8wi9kDtmRx3/8x39goeQScG+srmsxXik/xZqoydBbSCDFAVAsMgv6r/aTsPDOG2/QyI5P\nP336/Tff1MZSb6QEJttFYQoJ+IvMjh/jD/7gD7AgmKQ1hoEXeqB81AZmDrmLql+RyURgKZrG9t3f\nNDyQfg9GR0X5t1soFKNhHTj7TiqFKPIzeqfCNeY10GVTNXT9m2++OfnVdvwPfv/3f5//1cTjuQGi\nvbBeNGSD8z+qDETKjYP2G82gbugCgjOaZrwgwqM87Xu9Hn9RDCfsyOQbMrQ3M4eC+Sb5y83kb//2\nb09wpWcW1WV3YDag7YdpVHglt16o4bzvWQIu9fF4zG8KNGaEl/WKfC3RJgPeWyxvNQbs/oMH4qaT\nWjFVk+kJPxDzeHV7gcuhy3WBZngKtRpnhKDMYRfFkmQQFzp16fNEOpPGMcbNjQ06tLv37vFFoqVe\nt3DvwtILLes7QOoQLoMvlwBPIRbh3/7t37CgfUDhJCKfPn/nDq2LL2yaD7oEv7WdEHcHWtQJaKca\nMtCZENMHhHaqEAD+4Y03Xv/e9wDg00+fvvvmm5l1Tf8xA34I5tnuPGTCRz/60ZI9Okz867/+K/+r\nLwSV+V1VpM1j+9mwHnwrhFA4HFFoJEP7vAQEJzVXReEdlkX/9Ntvv9vOJZYTXvew81cfoCkExJxM\nouZfZC5C3fVFZuFA0YqbGxt1wocqyaWYKhX05R1DaOOhnxVTITafeY3Nd2NxERbQaNV1TU+/add1\nXW8NBphLvHf//s7jx7wlFnAjWK7YJ2VTKRRojx8DZQIhfVMotI6OcghHPnVX5azmAzfG4zFmFGN7\nSg4qiHXLDRjvj4bmEkEPI0JOYgIQd4SMpQK0+V/X9ebGBuUSMdFCX3km7YiNUxZR90f0k/cfulxA\n57xHYEUgVzRjwKjAhx0KcUbrjbGUK5o3YHybpsKFzjNqpwLXgx6aISIwrKc47H+//fannj79v2qq\njvKTHNM+qT7hkHU/CXMyoc454V/+5V/4X9NycAaKR1+RxUklY24F20siMLEUuthO0BQ1TYVpS0II\n3/vMZ/7hs59F5gMO6/jc5zJel3kazX7qo9CEhwLyf+xjH8ufgesBfwZWhBR1dAPugQq9mVrNVBYi\nk8c3n4flEdlNJ1Uvlm6zEcZ37t7l7cXqqZ7r5xy1lf03HwDkH4pcJEmuMQT5eaUpBzHmtrbG005B\ndc2Q/GMk828hTHnymhjjFvP++SOxDPLPejXzTf478wmeQixCtKKZyJ5+EZNoFUwepjKHdV3reX6x\nJuWZkuxBzSkFbVeOO4CpFIpIIVLeL7ZTKHSktcql8JMw2NykF2Xu3ru3t7tbNylE3DgV+N4hPeu8\nGcOlXFpPpJwTUvdBIhu/z5LrNtjcrNv3Yl2IzXhd0s5YzdDBJQBtEopuCIicQYb2nP+xGcRbtxOG\nkeXSSYOUHufpxDt37+IL/pFlzkMImJzkCUPOf2iLlA4BrEjOpPo8898jsCJwH9P8FeEXfuLIBLlI\npluX8qfyyEQwU8MMoVK+c4xxwL4ilhmgpaH7ObYMf531uFO4BK5cd6QiMN4gT3vtn3Ui4whmwpFC\nCeT706lTzvz7Dx4UhmIa+hB0oGke6Twz3w1YKbQNo8q6kSU1ztCUS5oX8iLJ07pTGJnOiH1pQ5Wy\nZKLzMUaeS7x3/35J3/LdNo9UCDW/kQsmybWHMFTEBHruSx9JMe1W3oHL16dIkmHOdEjJQSzlhz/Y\n3CxMJ4qjSxndlJ3mzUxQgwsmxmXBU4hFiFamDrlLpGmlUNLgjIzW823+l3YhbJ5pTTkoq1CxWa5F\nLgWzHJTfiDHyzAkkEoaxnVSkTEjdxGGUS8SbGn4VUIzCMlMooqCPxTxAx/nBpBYt4vdirNze2hoP\nh+atOR9CaRWYdqKc+ZNmzkUKXScMdQ0w2uOmaFAuAODdAMkf2eBbaKc0TdpPlD8vWXqN4RFYEbhs\nzHpt2ITCOcRS3XIiJ5TuAiLVYN5HUjC9Y37v0L3SS7GwubExXShmHrWuzJxYjQvix5xB2BJy3bSZ\nSV3o/LXWhXKcJvYy96hpn2nD04kAcO/+fR6NmX0T9wGhplSv9CoCl8GLS4BHYFNC3NYphUKTbnQK\n6fxcUeHNmR6oCLxq5lfyzWLjunkcje15G1qRCrhfHorhZPw7jx/jHoP1+ot2nPWxiAN0XBbEHZPq\nRY5rIv5r2usMhEl7Tn4R0JiJh9AM2RDve8WCDETN3m6EduhGkdbGw4dV+zss+HYBRmNmKAbWZL78\niGI6FJ5zLbgBmx5CTrqyENw+ibJZ6DRgkEjKaSOBaiRZYqFWuUGxlLfRW6CNb25s9Hq9jcYnJTPG\nxWkaML6IHxE/yeJgz+J6OkrB6dd6+pXIdZsGjC9NEd7cmqB9TBswSPAff4mr0DAZa4DRXrOdavgq\nYnUA2NzYCO057HlGnfeWF8iMQTGrtfbnCm7ApoHQEp87JzZf+TKtVKeMRWOx6KwMmNChWa9Nml4a\nG4tlKhnBHwxAY8ag7ZBC+mGYiNXAEvaca/jiIeinKwWT84oQDM+4a7wGWBqAUGLABFdj2zOL1sNd\n/ZvytLi1Q/KHEDZYXpFm7gDLgNFf8ZBYt3Eg3IBNCa43XmlaqXw6xcyl1GyUh6nzQgOmB3HwsRtk\nHmLbpcXGVAjt92boSKHRFd8UbpyvpZMq0CgZAHAOqsCg+x8SOPvr6ugCZ77OnOehH9PG9tilWg1i\nIvKnDFhokmzaaJVnzmv2hpkmeW29GQZqvjT+vhdZxxDCYHMzhLDZHqaIhd2dHWgsFnWY97xuZ93B\nLVkbbsCmgXAMsXJrMIgJZ7MQtfI9ud3KK1n0UN/f6aZfs/AIVPIkMMcTsinETNRlmqLNjQ0U4WZ7\n9jL+uWp8D1T3n98OSMngYr4MaOZDWea8ttTBnbNOtlMBmoevIQR856mqqvF4HFgWIagkISGVOS/8\njSrxIMgP7VAMf5H/gvzoAaAPhxBmWEsptr+aNOdwAzY9UEjkhJZoWEtXqLrO5lKmM2AkMJG7F0l/\n0Y0SkQeVhBHGjPeE+oMOaWinVhA6wUj+MjDXmG5D4DbsYhGth0/bW1txOIwsKjLZntcCL6QIXzdT\ncozHYzRRo9Go1+sBgCgQJ7WjlsqcawfOJDxfBdK5AbFBQf6UD4eTAgcr8KKz7TaMww3YxNCKonpT\neNwOETLjtXQKJZVLqdmEUuiBAgDPY8RmWCA5pJjcw0Jk6RdxY8Kt8QIpM7I0I60iNo6JSq406gYw\nzeODbgAQ2UVoJxiFpGM7w4k7Pedr7vgxiHuUB9MM14TvRCq1iAVohjgiq4fD4eLiIhaw5uTkZHl5\nGQCGwyHSAy0ZUo7TvlaZc6qJ7UdrNcscCheKbyq2J6GnVEFguUSughDCxsOHWBDMx1PK8xAi+c+3\nhphz8rsBmwZRxT2Dzc3Ynp8w42+mYJqo1F/cL7miw+Gw3+8DABZIwNSf0I7AIouuYjvA4n8hPXaj\nag87FFnEmnmg/C9YuRG0ZP9TtpxTkjQ/7fwuM+cyvjCIWzyvn47tnPOmFugXGXJyclLX9eLi4uHh\nYYxxeXn54OAAALAQQlheXj46OqqqanFxMYQwHo+5S1dbqQIdaQHLWpPcNMlFChHUIA5ojyupVZod\n3xsL7ZgMOY+Pxzjb+V5oy6Tuc73uVxZuwKYBCZh/djkvV9Ggs31GydBkUeq67vf7w+EQJX18fAwA\ni4uLJycnIYSFhYXRaFRVFZoxaJ5RZ3SbefTF+5MSPzTSqlUKkf6CZcB4GafkqarqIfv6LUlat6fz\nObcavjBEy3rRo1/RQPAcsoTnNkyXkU7D4XACY5O6AAAgAElEQVQ8Hi8sLMQYDw8Pl5aWAGB/f391\ndRULa2trAHBwcLCyshJCOD4+7vV6/X6fQjFubMgSxLb3lrJkwiGr1Esj3ERBwoBxyxeb5EQIIcaY\nGa/IewuNJRNOW5zXpKIbsMkgpEj1wovUf+t2UjGD/BuddfNMCCfzrqpqOBzGGNGSAQAW0G6hAdMC\noFs/ZghJTrE9pgt3SgWxbmjGH/JcClk1EqrQLXS9v0x3Gf204N79+4+//OXIhnIEZhQ9DrsAcGJj\njTY2WgjcCeukPTWmzDlaoNFoNB6P+/1+Xdc8hYhmBuVAhRACftuh1+vhdvr9fmQPUKHt+sS2ASY2\nZmgf2wlDnTkM7RSiKYSqPdrQHK+IWXQSI+8wHQuwWG2u4AZsYsSCLEr+r6l/gbqdPCRhh8YVXVxc\nrOv68PBweXk5xshd0dXV1RACLqqq6uTkpNfrLSws1CyPR9sk25aPwOpEjlG7q0F5oNxWQZcBExCe\n6YMvfAEAdnd2qOfUmfO85g6AduZcj10CKwIT/NftM/yHJpTv9XrHx8dI+P39/fF4vLa29uLFixjj\n+vr68+fPAeDmzZvPnz8PIayvr7969aqqKgzIjo+PMVZDK0hU4fw3E+kT0T7Pf7A4by7Cv4PNzaqq\n+AwAO48fi73T2Q7z7bS57KdBbJsu/HiKbmBKFwpsm6nnGCNaL7RGh4eHmEjZ399/9erVysrKq1ev\nsLC/v7+/v7+0tHR4eHh0dNTv93u9HsZnepvle9fetKjUG+T1Ge9bQ7TfGgweNV9dAoB79++nunru\n136+ERmxzUrzN3+xUktxWPxwOETrdXh4uL+/v7Kygtbrxo0bN27cePbs2fr6+vr6OhZu3Ljx4sWL\n1dVVVMHR0dHCwsLx8TGmImicCGe1ZumktJ+U2+Zaoid1+zux9x880F1ywoMbsClQrkCOvGzMGpPx\nlE4cjUaYJBkOh5g2oRoqjMdj/tlMvk3z7VH9l948FTUpjNrQNRrYhlrygsBWO52o7wUu6XNFtHIP\necLXaSdJ819zvmbvPiMlsBIJrwnJeY4sqq23p821CuktfjnDJ5WD2YCvO9jc3Gbfdhi3hyvzE3g5\nhLgCcAM2PWgYMSFmXdFUgcC3IwAAo9Ho5ORkYWHh6OgIXdHV1dXnz5/fuHEDEynkk2Lh5cuXKysr\nKysrBwcHx8fHCwsL9MCA32L0vSZ166kt5/QMEdt2iNcTuA3TPZxnJV8MxBnGr3+BCrbMtfSV0peP\nL8XnuwsLCzjCcHV1dW1t7fnz58+ePbt58+azZ8+o8N5771ENRmMvXrxYW1tD8i8tLdFQjhDCWE0N\nrAnPCSmomKo35aArRY3YY63MeWSf2XvwhS+Ibjjn3YBNDM2bTk2m6jVS5IbmI5kxRnTQeHvTNeOx\nF3cwxe7G1lto/O90yHudKVdUuLpjFQjWLLVy/8EDU/aXQYq5QFQRWLTsVjnVC9vULPGgVTBm0RXV\njNmQkPF4DEw+mti1FYGZlZycnLGdCQYdZqVir5EVyQ3YM2AhczpLl0CIKwA3YJMhT5TUDTQqLxXU\njUCvS5Whec0LnwTQY4Dnz59j7GUW8LH2y5cv19bW8OWYxcXFfr8/bj43PsUtplbuZ7QcT7M+1dJc\nyvdYMw83NuYcQc8GOE51gR1Z6NMblScnFvHfzFriCo7H45OTk8XFRcw3IOEx5Lp169Z77713+/Zt\nLNy6devWrVvPnj3Dwo9+9KNbt24R+VdWVuhJ8KgZuEvmTbNaVwoGisYZSpvrpirFrmslPe636dM1\nt7R3A3ZmyEs3w7C8mGOM4/G43++fnJwcHR0tLy+/evXqxYsX+OwaDRUWqEYsevny5cHBAdowHGFf\nsxd3TJhiFsLuFHDsMnKZe4TQsOjPVvtlZ5KxPp+O8wCfvpKgaQwJuxXbfpveVF3X+Cby0dHR0tLS\n2tray5cv19fXb9269fz5c7Re7733HhotTCFi4dmzZ7To5s2ba2trmGzHlyPxBf+6PRAxQ/5aOVKd\nZC6kuslwvR3RBzo/NIgJEg7x/MAN2JQgruAQRH0DNX+jZTZ4DW3BbFyzJ1iism7iEq4Hswzt24oW\nlc6f1OlEiolMRmWkHoCLVWiPtUoe1izDucW+3S7uAud2zecanJC8ErocCE11sUq0AGm9RJUJEPV8\nXaKElk8+T5jhdor/IhmohZBvTFTnBc55/rnnqLxDcTLPnABXE27AJoYgx0abVZOuDuqOIP7iezCY\nTsGx8jdu3MAMCQZbmFohD5SSJ7zN2toaBmGLi4sYhIkO5KHvFFR/VkhtWfSBQ/e/7AI6zgtRma58\nA3MV5PxoNDo+PsbhGxh+0fCN27dvI+Ex2Lp9+zYVXnvtNYzGbt++jeTHIOzw8BAnpqmb1+Sp0Ml8\nbid4ZQn/M21MBYmN6/6Q38YTiWd8FWcK/iLzNOCk2RoM4Iy8fpOLMcbRaITplOFwiOmU0Wh08+bN\nuq4xTxhjxOQJADx//hwLL168uHXrVlVVL1686Pf76+vrh4eH/X5/eXl5PB6LqQWFYSB10TSmJHg+\nHRyweU7xF+vN6QlMiFcyxTZ196gyxri9tUXeg+7/nL/geU7A0/v4y1/GN8pTDUo2AgnXLTQTGFZV\nhYMPkee3bt0aj8fPnj0bj8fortV1jcYMANCGAcD73ve+Z8+ehRBee+01AHj16tX6+noI4eTkZGlp\nKbDJoInexJlaTZNGnazVNFS1mi8tVcBdZBpwlVXtaYVr6+VlcdLm2Yx5BHZBuDCGZdjMLY0opPxE\nkdmoVbLFHEY1ag/TSqUNzURKnc0cCqcY+4+PBFKH6bh4mCZq6o1MveXQTLkEVm6DvLSxNRBXJ/c6\ns3+mLkoap8gvOoag0Rw6RJv6VM8uPAK7IEwdEIQQ+v0+zoizsLCAKUT0Seu6vnnz5osXL4Qr+vz5\n86qqbt269eLFCyxUVbW/v3/jxo2qqkaj0cLCgt6RiGCE06c9ULEosIlzUgVqSQU9xzzfmugGgZam\n+i+26bhgnCb8jTEiS/ELKfv7+5hvwNjr9u3bdV0/e/bstddeizFi5hAAMAMRQnjvvfdee+21EMKz\nZ896vd6tW7f29/f7/f7KyspoNOr3+5X6Ngowpgm28+inZlP3QkEERm1SDcSmwBrewgvQNsP3HzzA\nGevnGR6BTQOuT/H5j7PaLCE2KcTj4+ODg4O1tTUchXjz5k20XjiwGDOHaL1u375Ni7Dw6tWrtbW1\nw8NDfBW6bn86HayBIVGhTifuo3paYBZ0G3NTZjd0J6GZut5xYZjUMk1hyULz4S4cN7u2toYPenGU\nPD4Joye+r732Gg0+1DU4BBdfI0Hmh/b35HCPGeYLGpv8z0CLSDO8Zk+86q6HvlQg8KVzCI/AJkZG\nkyIKMeszMQpkp7UNiVneoe3NiV8e6FAbE7F5BkCIKnEf2aT1VKC1YuPYmrPOBzZhPPWfNgXsaUHV\nfEWQL6rZvMOkcB7AcWQO0zEd+CnVD8AET0RlqhlvrzmsC4JO/ELrTUX2nUle0AYAmkG8ZCRS/eT7\nFSoI7adrnPBatjgniOgS/QrmA5ssGBtvDQboNzvt3YBNCcEVTR2tXl1pyk9vB18CwxQiZgJjjJhC\nRJ8UADBhiIWXL19SoaqqmzdvVlV1dHS0srKCb3Hipy9F97iKzEKdyJnojxvRxsVoDmC3AHPj/MNj\n3OXkdw3T5bz/4MFbT56YJ9BxVpiI5J3rZhZhCnE4HOIoxNFohEHYeDy+detWjPFHP/rR7du3Y4zv\nvffe+973PgDAzCE0g5hCCM+fP6exSwsLC0tLS+PxOKhMHTDPSS8CNrCiVqnylIXTI6T0NontdXvC\ne8i+PyDI77R3A3YG0DJO1ei/oo1GjHE8Hi8sLJycnAyHw9XVVfyiBA4+xNFZMUbMsQAAZg5DCC9f\nvsSnX69ever3+2tra/guJ35IiSuZ+sC1oQWc0iG0P1BEx8LvDtB+BgZK84E9DKibb55Bwsc0zZgw\naY5zQghh5/Fj/S5zxozlb/qgmI8pxBACel11XeNgwhgjPgnD4fIAgAlDKoQQMJeIj34BALPuAIDT\nKppHRL4RKHPFv3IH7RGDnY5d5qg526kQ2XM4TX7qqqZ9bLt65ZfyGsAN2GTg/BP1YqlZMx0oEYFj\ni/ELy+S1IeOxAABYwPZY6PV6vV6PFoG613AINVbsG5ixnSqBJstXq6EZ/39717bdNo5sC6Bs2U5P\nfnPmB073zMNEcuYhtz4f22sSXySLPA+1WGezqgBCsuVYUe0HLQgESZDcm3UBSNoCa8xmDocxYYJL\nVQcweTJMB9sV1J0l8OJwme8ynMqErywSwg9j4I4SGMaEm7QR8qjVUQvDMMhHyUtA5gzTdMJgEual\nxOBQSCraepqaNDk66YwsFQuqVOD2/AwRBuxApHJ0RcblxDZuQfiqNiIK4bxf13Xskw7D8P37d86o\n/PXXX8MwYApRJh9+//6967p3797lnDkJaWWvdqrCrN58VR3lh15qvUDT7CIWrNdJbZlD9TdwbKg7\nL5VVgDyZ3YIlP1NL5i49PT3x88j4+COnEP/66y/OHMq8RM5JENHd3R1PPuQv4bEPVwHGYWTmHJKR\nxgERWGVTtoC0tzpdr1brcT79OduwmIW4N4SI375+VZV1WJdNgiT8K8DGHHthYbFY8LvduMCRGS9l\nU8eLZLiYCzQGOpUDHLx5VvbhGPd1UKVC5cGX3rwypzfTFAcP3Fv87h+dt5hfAYo569tbvDW3qMDK\nwZI/jfmGBPkDLvAiZj5mFCTHwOO7ogJeMbd9sFtCfMX8F3nGyyX/bvruKEV+V4mK/8rte7lLfRqI\nCOxAJON7pkJMQ+WoC8slyFpMdH4t6W634zjs7u6Oxwa+f//+/v17glcP8FsMOPbijzgP4wS/wYxO\nWS+v5GBiTT+dtejepDACwwOXkYY8ffVASZCzEdgZqveVkUz8RIbSri4qxK6TZzcmHvi1Un3f393d\n9X3/22+//fjxo+/79+/ff//+nTMQ//3vf1NKf/vb3+7u7nLO19fXRMRbSFWPDSGhTyWuUoy1DdwC\nGbZXxnot27GHWP/7H3+c8zyOiMAOQZraqg+rlb1Hz6K9pcjm4uKCbRg/1/L4+MhPd93f37Nu2Z7x\n9yN41oZMXxTx2A6QZ3fFGxUtlTxE6zCqxi56eIDMitaqWnXs6Nc44MG1BMgo8lhN5Tt7XSBd13Eu\ncblcbrfbzWbz7t27m5ubh4cH/morE/79+/c/fvzgd37e39/zg1/8+dbFYrEvW0qMVSpw6e0SHlv2\n5nkvF5VuSCexwwdcyl8DEYHtB6U9rG+3Q8M4PsTrqoL85YRJ3/csY+a9fBJisViwByfGiSdZcYH3\nxanFNE22tB/sMB0GE6gIzAZkPczdwMIwHcQeYOIi1stvns6qV/IudThwJCAHvn758vsff5BhvtBb\nVdpCifbIfyY/X1YZxOq6jlXAeQWmiiQVWQWSURRe7Qu0Ii6rkdsEczF6mOUhLYXJGSYxqhkoBM97\n9TAw7Bo229vzJH8YsANhVZHa0N7SXTGPX/Pi2fDb7Xa5XBLR4+Mj50z4BTxExGPgCcalaTpS7Rbs\nkSphDDATrASVOUxTm0TVzKFyM1UNdqliyQLHAxJS/X0OvStc4m9RsjfGb5RfLpebzWYYBk5FDMNw\nfX292WxSShyrDcMwO2tjFsjDBB5n770gSrWn0fPL8LCXcr9ctqfplCVFfrWLQKQQD4Gw9svnz1Lj\nclrVHybgNB3xzuNM+r7vOan49PR0dXXFQ8rL5ZJFfnl5yaaunjlUhRJYSL157Y3NjRycOSyZMeyA\nEnDI+JWBLGLwKyEUaVWNbbAX7dkaMa8uLi6Y88vl8vLykgvMeU6V73a7i4uL51svBZfbfRUu4WeT\nhy6lLfMDjIjA9oYITGwDEa1vb1cfPqhUCedJBnhIi7xUiSrIvEEa5xOzuUqjl8dIo0vIszNSSpw8\n4QJvgWdk1S1TO9BmJJjNMZs5TDBJJJUzh9ZXdYUdAv5ZwEuG8/owY4aEH2DS0CztS5lzYRp2A+cc\nItVnZ9gegMEEQEP5oUYpCIeR3rJUjhdlLvwnyNsj+bFQ6uG5ISKwQ5AgxsLK50PNLU4w1R4nGZO5\n9auW2MYVQKlAXprCKkR05bqcs95oBbjxEOobhBBPHiNxmUwmvt+L/yrxwNyWxIPc64XemJE+EmTj\nLXx28xCHZR3U3uWvfZP1GQokDNiBEMnJFw1c0dKh6rUCtqpWG3e7UemSWyAwzKpg5WEVW5JoZA5/\nDVhS0dwsXOuTlchfsl5YyU+D9fAOGl46wPyg4wF5qHLm1l1T5G/x3qwoqPpsSSBSiIcgmRQiEa3W\n6/VqpXIm7twqJbnBTNVD11KMR855t9vl8Y0Yw3S8lzzD8xygTgbwPdV5wN/SEaH9s4bz4MxhKPmn\nIE0fhGLI5Do3MYhKKfEf/w5mBpC6iWNn0nSa0rFhdaEOBIecyTP5afqCtH76jiikvSpTcN4gIrDD\nYT2+gnPZCjcTiJlDaaZqkmexXA9utkBGouhpDtNIy3UtK65oBQRyxc5QiPaNAVkn6Qd8JUeJ2C3k\nV40zwDYepkNNijYvi7p2ZvPkFS3g9hXtS4dj689WI2HADoSYjZSSDAas1usDpJum+RMrXWXJVKYR\nV1Q9tF2dLTCU6pQNk0pr1awxqwuYPOliH6RMnvMb+ClAorqVlvkVIbjJQ0V7q4ics31FdXrRFCLS\nmGt2ux0XmM9UMGPPGestaYGC8x4ihXgI0jRdgHBTiKmaXhsgZ5imzzMmmLPUj1P+htHf3O12THfx\nQ0U5hx0X6kok2o/f+pP94nlQJlAdGo0JFmxPkTk8caDhkSea8ziHltvk8YE//OvyH+vl6mM9FpTZ\nEPnwXl6EG2iQmJz8FBoRSWG326WU5LsQyHBZXbSMh0nVtGEJzz+oXxURgR0I5UWqXEpj4IU3gmQc\nz9JvJQITuH0WMVQKNsxCuygmE0Org8eoB+OHDnMxVoj5LcAlm6QfsskBzjJfqUD9VipxC9K35xwa\nmxZ+tjKlxO+v6rqO39zGb2XkmpwztxlGC6pUc5gcGJbngxGs2+DcEAasCSVVuDajJFdXvRWJ2kRK\nO9wOSz/dAhUmx7Ma+YXZRKQKhykW96U6iZUlrQZ+LhST7UiYMloVllozVlKBrXSlRM+wYcMwpJQk\nutput/y2qsfHx8VicXFx8fDwwE9SixnbbrfcXrTQbqhKNVLGjrm9PewwfyWEAWuFtVVKXTIStr69\nzePHTSrANvzKbSxLDX8tRa1ra0q7aDw6a7RYkOyKDsPAr/kYhmG73fKreqTQ9z2/+6P0tQg7QtYy\npm17+BKXMbAHlKFSi5j2imYiByQhokJXxXzLc9vA3YvtbQskkcA87/ueXwcs9FYFLktBfRLF0r43\n48cl/rv2LOAiDFgTXA1TWeGpCuuBugX0Oq3rahVbgj0clIoty+gXZ0hyzpvNhu2oeKDoim632zy+\npK7sdDoqtXaLwtl8wygxPOcs71S7/fixxHbLVauCXMg9lBpkL4xL+8dhTLDdbrfdbheLxePj4/39\n/XK5vL+/v7u7Wy6X/KmHq6uru7u7Hz9+8Pur7u/vLy8vF4sFR2MpJZVLLHG+1AGqZh1CBRZhwJqA\nkkvTDAlq6c9v37j9ar2uB0bWxxTv0has79kSgWHH7OGomt6bTChZEXE8d9NPUFoPlNcqOZ7KRpa0\nbX9b8D+///6MKxxwYH0gZSGEYB28e3CWmZbDs+VGwiPzS96bhVgdzDeobIQtSMglnMeC4n8l5FIS\nIMP8sFsVhAFrgvXsEiQS3XDHfTKm5Foqu6j8Sut7upuquLdWyWk69EUw+ZAKrigX2BVF55S/+y4v\nC0/e67StXBHPkWjI+xVgKZRgDJVReZikJAFXBXWZWKq7qpEOW+YrDOO4FxOeGX51dcWFy8tLpjqH\nXEx4JQeOw2RUTFIRVMhwuFrYi8bBeUEYsCZYHdJ0BoToSga0pYFVnSpbcZZWqSxyjZbts0D5egIW\nc86ZE4YsYNStq2QWMA96s4DJUyzu3dbY0z4rVGwgN9DAS6HOosoiHgaukDYVHDi3bP/axi2cL4Fn\nYbC7JnlCTCFK5pALVg42l+iGVi5KgVegBWHAmtAiRUbXdTibo5smDN0sisqZuLnEyvC1TZ50ZuS8\nomcJvGyuw45FY3pQDVmrQexhbqQa924FXJfxYdYusC+sFZFfbsB/hYf4bXtURIn5pRpXEZV11V5Q\nArNmbIBJ8JwDV6k/YTUqQgSCPCfvPb/1zGGJycryBbdLCAPWhJJ/J/LAvxnGnG4/fpz1Ol1/094y\nckOsNuuT4hFxQZmT3W7Xdd1ms1GZQyk8PDxI4eHhYblcXl1d3d/fX11dXV5e8nSPnLO8swB3Mave\nEOqbQp3ntkGaTqlXzpMrActey/mSItQG63APkA1M13Xb7fbh4eHq6orJzKz+8ePH9fX1zc0NF66v\nr+/u7rjw48cPruRYTYI2lgAm0mVHFR+OIvw6FGHAmjArDyU/mc1Bow1zbUzJMlX+lmQ8+1fJuBQG\nsZgvLi5EyWyrsCCLLi8v2Z5xDaccWcAZ3jJAc1kUhVLLkPcro8UqWPLL6m4iMU1NjkvpigTUUpft\nlvmVY8w58/s1lLt2d3fHposNFRbQjF1fX4sDd3V1xRLouq6Hl4PUwyxqI3aQ30UYsCZYHWYvU5ch\nlYFDMm4WBfMhlSSJSqFUpmNJl9yOiarVoak0xWBeK4CwswdthsRNntgNunsPvCkoqru8Ugas6zr0\n3j7+5z8u4VW5MuHWbVkiP/YQyxVLJoSnKRtbZs+WQFOn0G3g9uTFr+AvjzBgTZh1RV2IDfuwWllf\n0vUoZ28Qrq9acjyVE6rKg8lj8FwsjKskT8jOqQxis9cp87Uk68KNF4sFzwRR20eEXN8+kD91dikC\now2zBE7TcKrEatug0oc8jeRc/lsMw/D09MSPMzK9mcw2c3hzc4MpRFYBB2GiFCnwk5EVhg/7xF6B\nCsKANcHKw9WJMkUppc+fPvEW5B2JFaNVErZSfjJ2q92MJW8YjDEMQ86ZxYzWiDOHkiphAbNWucCD\nB0rA3TSL8pyTHyL/WajbjDrk0WZOJFq6Woa70nBZPWuu6sxnDMOQUlosFuy0SRpcvLSbmxtbYL9N\nGTZx4FgCFxcXPLOR9mdv2La9EAasCRkSFJipUEmMbOZc8burGbcfP9qEiVvTnjDpyjMP3fuCFXOj\nn1jPe7iqm80NhkTfOJDSinIqX2fJj8zn6bjuS9GsXiq0rwih1CXLf3uYs+kBN+ldQQuxg/wvgjBg\nTXAdOtcrRN+QyzgYtlqvS26m65bWC2pHqh5tVd0VlWPs+36z2chUQ0khso/J4Zcq3NzcLJdLFbRd\nXFw8PT118HaGwCmixHaXZsjG7E1lUg1KNsZy2xXIbE9c0PQVBH3fPz098VOMzGqOoiRhiAWOw6SA\nkVkpAxFW6tgIA9YE68e5yrFLeUW0YTKx3v0t7aW05QOkK38VOIXIYub0IE4sllSJpBAli8LtHx8f\nuT0/0czDYNTwKoTAmwXaD5f2toGqx+f6kfmKz66VsvttN6KW+Uj7NCb3cs789PFyuZR8ODpnPDle\nModYg/aMmS+S4RRins7JDBwDYcCawHIqJfFKlZgJUTZs9j2Hs1kU6VLJpbVAbUtnUNXJuKj2LuAu\nwq2523HPaqO84y7ws2BZbVWA0rCFEvOtQOqcz9OZkKVfl/CqbA/TZXJpUcUoWuZTgb2l3VGDagKI\nMGBNKLmEqeBOJuNL5mkcZnOJyYRZ2XNObQdKoOkLD0vCY3BN3/fb7Xa5XG42G5mawQEWZ0jYx1RJ\nxevr68fHRy5IClF5oO7u3EWBtwPLNFVWurAEtsznXGJJNbNaaGF+iyhonIi72+344cWHhwdOMzw+\nPt7c3Lx7904iLS5IjQ3RmPmcQpQMhOQPKwwP8j8TYcCa4LqfJbe0AjUqMPsBpMpe2j1QezuoII+f\nfreua9d1aWpQ7dbEaKlFVP74pyoE3g7qZG6nfVd+LLJlmpLL9lnyV6A4SVNyzoI3QiPJXbNNJiaz\n/FeFkMABCAPWBEtQW1NyFdUdvxSHVbaA+6qDClIko1V1dFzIOS8Wi6enJ5mRIQEWD4ZhQRZxmWO1\n5XLJnwHMY66mtFMqK3bf+sCRoKiryiVyWvJzWcbD+HX1aoOlgt3mXoqwKqCp5ei6joMwmbIk+QYO\nuWQMTNX89ttvMsuDJcC64Lf68gBbRXHJc90qDA/yuwgD1gRXUVY/FQuEf3Fku5JLrNuzFq26hXrj\nvu8vLi622+1ms8GEoRiqzWbDi6SGm93c3FxdXfFrqLquU/vlg7X7VQiVvilYqlsT4jLcdb8yzOmQ\nT67YLVcK7t86yLAO7QoRDcPAThuz+ubmhlnNRuvdu3dstGyBrRf7bSyBzWbDErAOnOoGnmFVoFDB\nPggD1oRKuqPlmRU7TUPlEivrZpMhcSvxbuLeVlyDau8UXOZdcyFXIZ3hLfBfu6PZmw6ZEbvK5XCX\nhuxfHHWqtz+thZCNl2ify89c1qmotCB8rjRLY86cawiS50haV2vIfFnEJy03W1w+FZa6ybier3LB\nTw9hwJqg6Jg9g1FRjntDxzhMretyvSIDJHryvM7SIppKhffCPik/y8XTi8UnxcyhxF6cV9xut7vd\nbrFY8As4Kh0oneHGSntduBxfZH5x1ImNnLEEdqWRpyl0+eir2lpjZTvISz8Q8GexWFxeXkocxtkF\nJjwXOBWBBdQFZykuLy9ZAmqPVCY/1qdmW9XS5kwQBqwJdYNkjZP6awtpasM+rFZKXfVtzorTFU9L\n+zTasL7vWdLb7ZYzhyhpFDlbL0n9SzRmd0ee+ZTyMxEftHxxVFy0ZIxZ6TdNNZKmj/ZXmiE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"output_type": "display_data"}], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "prompt_number": 23, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Levelset Re-distancing\n", "----------------------\n", "During PDE resolution, a level set function $\\phi$ might become\n", "ill-conditionned, so that the zero crossing is not sharp enough.\n", "The quality of the level set function is restored by computing the\n", "signed distance function to the zero level set.\n", "\n", "\n", "\n", "This corresponds to first extracting the zero level set\n", "$$ \\Cc = \\enscond{x \\in \\RR^2 }{\\phi(x)=0}, $$\n", "and then solving the following eikonal equation PDE on $\\tilde \\phi$\n", "(in viscosity sense)\n", "$$ \\norm{\\nabla \\tilde \\phi(x)} = 1\n", " \\qandq \\forall y \\in \\Cc, \\tilde\\phi(y)=0. $$\n", "The one can replace $\\phi$ by $\\text{sign}(\\phi(x))\\tilde \\phi(x)$\n", "which is the signed distance function to $\\Cc$.\n", "\n", "\n", "We set $\\phi=\\phi_0^3$ so that they are both valid level set function\n", "of the same curve, but $\\phi$ is not the signed distance function.."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = phi0.^3;"]}, {"source": ["Solve the eikonal PDE using the Fast Marching algorithm."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 25, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi1 = perform_redistancing(phi0);"]}, {"source": ["Display the level sets."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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CIxrTnkbHZHlax9sg2luCx8dHHdgc0XnYDfVodyyEtMmo/8QN8yQUkjCwf559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\nzFvIBxjrxh+GCoHpJUElENi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"output_type": "display_data"}], "prompt_number": 26, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(1,2,1);\n", "plot_levelset(phi);\n", "title('Before redistancing');\n", "subplot(1,2,2);\n", "plot_levelset(phi1);\n", "title('After redistancing');"]}, {"source": ["Edge-based Segmentation with Geodesic Active Contour\n", "----------------------------------------------------\n", "Geodesic active contours compute loval minimum of a weighted geodesic\n", "distance that attract the curve toward the features of the background\n", "image.\n", "\n", "\n", "_Note:_ these active contours should not be confounded with the geodesic shortest paths,\n", "that are globally minimizing geodesics between two points.\n", "Here the active contour is a close curve progressively decreasing a\n", "weighted geodesic length that is only a local minimum\n", "(the global minimum would be a single point).\n", "\n", "\n", "Size of the image."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 27, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 200;"]}, {"source": ["First we load an image $f_0 \\in \\RR^{n \\times n}$ to segment."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 28, "cell_type": "code", "language": "python", "metadata": {}, "input": ["name = 'cortex';\n", "f0 = rescale( sum( load_image(name, n), 3) );"]}, {"source": ["Given a background image $f_0$ to segment, one needs to compute\n", "an edge-stopping function $W$.\n", "It should be small in area of high gradient, and high in area of large gradient.\n", "\n", "\n", "We use here\n", "$$ W(x) = \\al + \\frac{\\be}{\\epsilon + d(x) }$\n", " \\qwhereq d = \\norm{\\nabla f_0} \\star h_a, $$\n", "and where $h_a$ is a blurring kernel of size $a>0$.\n", "\n", "\n", "Compute the magnitude of the gradient $d_0(x) = \\norm{\\nabla f_0(x)}$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 29, "cell_type": "code", "language": "python", "metadata": {}, "input": ["g = grad(f0,options);\n", "d0 = sqrt(sum(g.^2,3));"]}, {"source": ["Blur size $a$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 30, "cell_type": "code", "language": "python", "metadata": {}, "input": ["a = 5;"]}, {"source": ["Compute the blurring $d = d_0 \\star h_a$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 31, "cell_type": "code", "language": "python", "metadata": {}, "input": ["d = perform_blurring( d0,a );"]}, {"source": ["Parameter $\\epsilon>0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 32, "cell_type": "code", "language": "python", "metadata": {}, "input": ["epsilon = 1e-1;"]}, {"source": ["We set the $\\al$ and $\\be$ parameters to adjust the overall values of $W$\n", "(equivalently we use the function |rescale|)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 33, "cell_type": "code", "language": "python", "metadata": {}, "input": ["W = 1./(epsilon+d);\n", "W = rescale(-d,.1,1);"]}, {"source": ["Display it."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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CcH19PZVKsZnJAg2Hw1AodObMmfl8fnx8PJ1O4/E42sVbt25dunQplUrd65ig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\njbNnz25ubt68ebPdbovbIX34OFmgsOj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zsrJC8ZnkISZSvV6v3W6XSqV2u02MNR6Pv/Sl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nLStu1MJvP2228PBoNisShKmXa7/fTpU+J3PgLjp/EBQUX5Kp+Jc7AsbVfhM0ZtKc3jZbNZmtnZ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\n19fpn2udq+rr63FPEAx3zu3s7CwvL1tJP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OIz7Gr9jaAg5BvlztcYEXd3d5eWlgKnXsqB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\n", "output_type": "display_data"}], "prompt_number": 34, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(f0,'Image to segment',1,2,1);\n", "imageplot(W,'Weight',1,2,2);"]}, {"source": ["__Exercise 4__\n", "\n", "Compute an initial shape $\\phi_0$ at time $t=0$,\n", "for instance a centered square."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 35, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "prompt_number": 36, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display it."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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HE4Y+nmJjY2NaPsqtSWo74qnX6XSwMmGM+su//EszK5VKpIHAHsUjG7vWwPPa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IAJgiAIqYQGMEEQBCGV0AAmCIIgpBIawARBEIRUQgOYIAiCkEpoABMEQRBSCQ1ggiAI\nQirx/wDlX3hyqTYSEgAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 37, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "plot_levelset(phi0,0,f0);"]}, {"source": ["The geodesic active contour minimizes a weighted length of curve\n", "$$ \\umin{\\ga} \\int_0^1 \\norm{\\ga'(s)} W(\\ga(s)) d s $$\n", "\n", "\n", "The level set implementation of the gradient descent of this energy reads\n", "$$ \\pd{\\phi_t}{t} = G(\\phi_t)\n", " \\qwhereq G(\\phi) = -\\norm{\\nabla \\phi} \\text{div}\\pa{\n", " W \\frac{\\nabla \\phi}{\\norm{\\nabla \\phi}}$\n", " } $$\n", "\n", "\n", "This is implemented using a gradient descent scheme.\n", "$$ \\phi^{(\\ell+1)} = \\phi^{(\\ell)} - \\tau G(\\phi^{(\\ell)}), $$\n", "where $\\tau>0$ is small enough.\n", "\n", "\n", "Gradient step size $\\tau>0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 38, "cell_type": "code", "language": "python", "metadata": {}, "input": ["tau = .4;"]}, {"source": ["Final time and number of iteration of the algorithm."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 39, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Tmax = 1500;\n", "niter = round(Tmax/tau);"]}, {"source": ["Initial distance function $\\phi^{(0)}=\\phi_0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 40, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = phi0;"]}, {"source": ["Note that we can re-write the gradient of the energy as\n", "$$ G(\\phi) = -W \\norm{\\nabla \\phi} \\text{div} \\pa{ \\frac{\\nabla \\phi}{\\norm{\\nabla \\phi}} } - \\dotp{\\nabla W}{\\nabla \\phi} $$\n", "\n", "\n", "Pre-compute once for all $\\nabla W$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 41, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gW = grad(W,options);"]}, {"source": ["__Exercise 5__\n", "\n", "Compute and store in |G| the gradient $G(\\phi)$ (right hand side of the PDE)\n", "using the current value of the distance function $\\phi$.\n", "ormalized gradient\n", "radient"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 42, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo5()"]}, {"collapsed": false, "outputs": [], "prompt_number": 43, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Do the descent step."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 44, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = phi - tau*G;"]}, {"source": ["Once in a while (e.g. every 30 iterations), perform re-distancing of $\\phi$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 45, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = perform_redistancing(phi);"]}, {"source": ["__Exercise 6__\n", "\n", "Implement the geodesic active contours gradient descent.\n", "Do not forget to do the re-distancing."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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o67j+MC6h0WgUt04kQIVCAQX0f/u3fzt16tRzzz2HJMbhcBhxCxOU2Wy22WxW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1ovrDparRY6KOwzSqUScYV56mJz8Dljatl1CiGYPQFQPMu/azAYnE4nzWcej6dWq124cKHZbCIX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"output_type": "display_data"}], "prompt_number": 46, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo6()"]}, {"collapsed": false, "outputs": [], "prompt_number": 47, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Region-based Segmentation with Chan-Vese \n", "-----------------------------------------\n", "Chan-Vese active contours corresponds to a region-based energy\n", "that looks for a piecewise constant approximation of the image.\n", "\n", "\n", "The energy to be minimized is\n", "$$ \\umin{\\phi}$\n", " L(\\phi) +\n", " \\la \\int_{\\phi(x)>0} \\abs{f_0(x)-c_1}^2 d x +\n", " \\la \\int_{\\phi(x)<0} \\abs{f_0(x)-c_2}^2 d x\n", "$$\n", "where $L$ is the length of the zero level set of $\\phi$.\n", "Note that here $(c_1,c_2) \\in \\RR^2$ are assumed to be known."], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 7__\n", "\n", "Compute an initial level set function $\\phi_0$, stored in |phi0|,\n", "for instance many small circles."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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0vGXjRqzHSCpLBvt8PpvNtnbt2nA4XCqVXnrppZFKT2Pjpz0P18tYR3NxsvgN\n7LnnnqNB0BQN8WeD5WGMAZEQcsf27aphc3q9sr0vV1nxwRiaCSG7d+1CKLTZbG632xoQrYZRSw/+\nfeDBB+elRxAEY2Jh1GO1jaoGNi89O3fsoIaBwq36eggh+z7/+Vp6rE2UyWTq6zFdMpMeaxPZ7fam\n9Wzbtq3Zu+9C0oiBkfmHNtPj/7yKzjdt2rR+/frJycnXX389lUphU65CoYCCPYxIZQ2F8lVPjkrC\ncrmM2GXS4/N6jdUfPT09g4ODiqKkUqmJiYlEImE9oaZpoVDI9CuO47BG1OtvvDHf72uUdO3b347R\nO3jq7Owsyj1KpVI2mx0cHOzr68vn8y+88EKDy3M00f7N2x4zsAvOr3/96/rRGYt1yrL8yKOPmo7d\nceedxhVgEQ3p7GDKnt27bQawLV6tgDinW1CMeU8reqwxGgY2Xz3WJrpr507jAr5N67E2UTabbUJP\n402E3KtBPVdccQVpQxo0MFKtS6pqmGvwbVVB3fyWLVsEQXj11VcnJibcbrfT6SyVSpIk2e32eDwO\nA+M4rv4HYQa03+9/05K1dIXDmHTl8/k+/OEPL1u2bPXq1TabbXZ2Np/Pz8zMHD58OBqNYpvm5cuX\nv/vd7966dWtHR8fs7OxLL7308ssvDw0NuVyuUqkUi8XwWRzHYViuifZZv25dIBDAU3IwGOzo6Bgd\nHR0eHhZFEVud+f3+K6+8MhAIHDp06OTJkw32V5+H6/V/zsAM7ILz4osvVg2FNBrCwOhuUnTNvUZA\njZ+pQs/lciH2VY2JtazCGp2h56GHH57X971v716THuNAEV6gk/Pi0WNtImRgF4mezZs3z+sjLhIa\nNzAy/2GV+YZCVVU3b968evXqU6dOHT58WJbl/v7+XC6Hvb58Pt/s7KyqqjzPJxIJJCLzkrRxwwas\npVsqlW688cabbrqpr69vYmLi1VdfjUajxWKxt7cXm4r19vY++eST8Xj8S1/60sqVK+Eop0+fpg92\nK1as8Hq9r7/++k9/+tPnnnsum83CV8rzWQFk29atwWAwnU6juDGXy0mSdMkll2iadvz48ZmZGXRR\niqLY39+/YcOGqamp3/zmN8Yh5zk515eMMAO7GDh06FDVUEgDYqFQoNEQszRUVZ3TxlAub6wvQO85\nNbCqMdGY8dTSAzFGSaVSqRU91iSDdnI2p0dRlIcfeWTOlt+7Z0+DeqxNlM1mLx49GzdunPPkFyFW\nAzOteFuVOcNiE3FQ13We59/5zneWSqVXXnkF0RwbVJLKNuLKeLgAACAASURBVCWZTAbZfLFYNIqc\nU8+lg4PFYnFmZkbTNFEUP/rRj/7xH/+xz+f7yU9+giwqEAgIghAIBJLJpCzL119//UsvvdTd3f3J\nT37yhz/84Y9//OPu7m4U0/M8XyqVbDabx+PxeDzhcFgUxfHx8d/+9rfPPvssVgHOzrUUCHbm7Ovr\n27BhQzKZHBsbwx2lqmooFEIdx9TUVD6f5zgunU7b7farrrpq2bJlP/3pT7HC/bzathEba7pkgxnY\nhefVV1+t+iBvNDCafln3tqdDvlxldVdrqbcxCUPngL1S8GYNiLUSC/rCGJ0hqVwut6LHGKDxwjhK\n14QeaxO1qMfaRNlsthU91iYyVhjOV8+6desu4A3cNCYDQzvUX0XpHCHL8pYtW9atW/faa68dPnxY\nEIS+vj5ZlnO5nNfrLZVKiUSis7MzGo3OKQ+ToLPZLHZ9I4YN4a666qobb7wRiRf6DOlR+Xze7/ej\ns2HTpk2ZTGbt2rXd3d1f//rXZ2Zm8JNyuSxJEm4kPNVhq+VIJBIOh2Ox2H333Tc7O+t0Oj0eDwTQ\nnnMMa2E3MkiSJKmnp0dVVVmWMXVaURRJkkql0uTkZD6f13U9k8lgvseqVavWrVt3/PjxF154wTbP\nisTGsVa+zMnFb2CLfzsVURT1s6G/wgAJOi4QcGtFQ+MhVecqGWMiDYWAhki8oc4Wi9bFACEJC9I0\nracWTeup00TN6bE2kc1mWxA9pJqBzVdPy/fgRYGu6xfEvXRd7+rqGhwczOVy0WiUEIKOWY/Hg4Cu\naZrf7x8YGEin03NGTI7jUM536aWXXnbZZRzHYXdmbGiiqurhw4exTaWu63gA0jQNZR12u13X9Xg8\n7vf7s9nsK6+8Ui6XsQlZKpUSRdFut9NdeDRNS6VS2OUrFAp1d3c/9thjv/3tb3/xi19ge2VMLLPb\n7ViesVwu40Cv1+tyubLZ7MjICF3XY3p62uVydXZ2EkLcbrfD4dA0TZZliBwdHQ0EAl1dXZFIZHZ2\ntpFSjuYuxLk47YVlkfxx1gGh0Bimjb+lBiYIgqkU23qIKXoa68WNHVPWUGj8FU5YR48xOkMSNbDm\n9JhUmWJ3E3pqNVHTeqxNZHzsaFqPUZIoik3rWdD7ccnBcdzAwEAmkzly5Eg8Hg8EAj6fTxRFXJRQ\nKLR8+fJsNvvGG2/MGbgFQcCMrk2bNr373e+ORCJYtz4ej6dSqdHR0UKhAAfCPcDzvM1mQye8LMu4\noOgeTKfT8Xic53mO4/L5PNaVh6OgI5FWtMqyPD4+PjU1FYlErrnmmksuueTf//3fUTl56tQp5G0c\nx6G3WatsvyIIgqZps7OziUQCT7Q8z8diMY7jJEkSBKFUKhWLRfQi6LqeTqc7OzsvueQSvOf8XJpF\nwOI3MBoKieUZxJiBYau65gyswaTHlPHU0kPPTyXxPN+inqqqmtYzXwNrUI/t7AysdT2khoHNV8+C\n3YtLD6Rf3d3dr7766tTUVH9/PyGE53l0qcmy7PV616xZMzIyMjY2Zg3cnKHXy+l0rl+/fuXKlV6v\n1+/3T01NnT59WlEUnudhThzHoVQ9nU5jvApZDmwJM5pxttHRUbfbHQ6Hz5w5o2kaxqWwE4qu63AX\neBJsBgImJiY0TeM4rqenB6dCKom8KhQKYYeUycnJZ599dnp62m6349GzVCrplWWIXS4XzA93V7lc\nxg02Ozvb2dkZiUQCgUAqlWIe1iCL/4/TZuiMMsU1PH9pmlb1Wb4Rw6j6UG+vrH1ueqLHv/rZWPVY\n04vGDax+kmEM063oqdVETeuxNhG9aq3oIRYDa07PeblPFy09PT0oYXe73X19fTMzMxhAIoTYbLaZ\nmZmf/OQnIyMjerUOLvrDYDD43ve+d/Xq1TMzM/CDbDabzWbhIqVSqVAoYAEndJNyHJfNZvP5fLlc\nRh8jakZUVXW5XKdPn04kEldeeaXP5xsdHZUkyeFwFIvFbDYrCAIdGIZLCYIAL7Tb7dFoVNd1n88X\nDAZ9Pt/AwAB+i8/C4VdccUVvb+/3v//9sbEx3Mwo+oXmZDJpt9sFQcjlcoFAAJNQRVGcmJgQRXHT\npk0bN248dOhQyVK4z6jK4v/jxD1E/8tZ0CubtNaKhsaz1QrQxphot9uNoZAOieGHpnNa9dDoTCWh\nO6JpPVWjcyt66jRRc3qsTWSrdNy1qIeewWRg89KzELdhW8LNf9jfhN/vlyRpfHwcg16oX5ArO345\nnU5FUUZHR+mkK7vd/va3vz0cDh8+fHh4eFgQBJfLNTg4eNNNN3V2dr744oupVArLQeFSQh5uA0wE\nxgMHFhiET2DMib5N1/VkMonC+ve9732//OUvZVm22WzJZDKfz+dyOdweWDVR0zSHw5HP5zOZTDgc\nJoTY7Xan04nczuv12my2QqGQz+cTiQTSwZMnT65fv/4zn/nM008//dJLLxUKBY/Hg1qVeDyeTCYj\nkcjAwADaBHPOkJ8NDw93d3eHQqGenp7h4eHWL99SYPEbmCkAcWdvXc/zPB6yFEXRNK05A+MrNQL4\n1+QTJqwnNOmh0ZlKmq+BmfTU7yhrQs98DWxeeqwG1ooeUs3A5qunyTuv/WnRvQghXq8X01SWLVuG\nHjnkIjabDbF7amoqGo3yPB8Khfr6+vx+/86dO9/3vve9/PLLL7/8crFYjMVimzZtuv7663/605+e\nPHmyq6uL47hCoYDeyKGhodnZWZvN1tnZqWkaeucEQfB6vRCPpapUVaXTufL5fLFYHBwcvOqqqzRN\nQw3F2NgYugpxa+EmRH0yUjGfzwdjwwhWLpfL5/NYOzGdTudyOZvNRotmk8nkO9/5zo0bNz799NP/\n+Z//iYlfPM8risJx3MTEhNfr5ThOUZRgMIjSx6NHj5ZKpeHhYUmSwuHw0NAQx3oRG2ApGhh3dmeU\nrut0NMUUCrXKgtb0WEIIb9mzyvRQb+xCNMVEUzpYVY9pTA49nK3oqd+R2ISeWk3Uuh6boQuxdT1G\nSYJhdfn56lnAu3FJwXGc1+vF9iV+v5/neRQ4cByHwopkMjkzMyMIAiHkgx/84O23357L5XRd/6//\n+i+seOtyuZCaHDp0qFgsdnV1IdzLsowFQgkh2A0ZnyiKIm4JJENY2gOvacaWz+cLhUJHR4emab/4\nxS+effZZp9OJHki73Z7P57EiYjqdxoMObjxCSDQa9fv9mqbxPF8ul5E2EULwmuM4m82maRqKRIrF\nYmdn5x133LFly5annnrqV7/6Fc/zWISe47hEIgEBiqIkEglRFH0+3/T09MzMzKpVq3p7e5cvX97g\n6ohLnMU/D8w4eYjOH8ILVVUVRUHFEQ2F6GSwjqYAYyrAcRwNi8aA6HA4aCi0dtzNqYf+SyUh1Wha\nD/2XSsLffNN66jRRc3qsTYTH9tb1UEmCIDSt55zen+eOea3EseDouv7Wt7518+bNx44dO3LkCJIY\nXdeLxaKmaV6vN5fLxWIxm82GbbSefvrpH/zgBydOnKDrnOGiY+OuQCAQDofj8Xg0GuU4DjYTCoU4\njpuenk6lUoFAADmQrutut1vX9enpaezIpes6z/MoWdR1PRwOnzp1as2aNcFg8Nlnn5UkCcXrkJFO\np9FxKsuy0+nErSJJUrFYTCQS2NxAq0zVKBaL6GksFArpdFrTNEmSvF7v8uXLvV5vMplMJpMul2vL\nli1ut/vxxx9//vnnw+Ewx3GpVMrtdnu9XroTZkdHx8TExNjYWCQSeetb31oul5999lmtsjf0hYLN\nA7vwyAZoKDSu41Aul9UK1s4oY0DkDFTNMFRVxSMbzQasJ5lTj3FyLn2cbEUP/jVKKlcWQm1OT60m\nalqPtYnQFdOiHqOkqhlYg3ra18MuIB0dHegKwxQo9CKgLxcDVPF4XNM0PD52dnb+7ne/Gx8fD4fD\nNptNUZRsNoucBsNd6N/r6OhAyoKnlnK5bLPZkMCVSiVMKXM4HLIsY44wcjU8Es3OzpbLZeRYeIAr\nFApI3RRFwcAnajFIZXEQTdP8fr/D4SiXy/TNeH8mk4GxKYoSi8WKxaLdbvf7/ThPJpOJRqOZTMZu\nt8/Ozo6Pj1977bU33HBDIpE4fvw4Vt9HhlcqlVwuV7FYHB8f1zTN7XbHYrEzZ8709/d3d3dPTExc\nsOvXJiwtA6saE2kGtiBdiKqq4gnOGgcb1GOK0UYDa06PaJmtbOwWa0JPK12IVfXUaaJW9JAGuhAb\n0cMMrAm6urqKxeKJEyfS6bTH47HZbLRPj+f5TCaDC6rreiAQ+LM/+7MTJ050dHSUy+VkMknvTxiV\nLMvo93M4HLiOKKPIZDKwRo7jULaHsStMiO7o6HC73TBLLJCBnkBZlnEePLlKkqRpGjJ+9BnyPA8j\ntFWmkOJwOCWqPOCysizj/TabjeM4nIEQkkgkUH9fLpc9Hk8sFjty5MjNN9/s8/kee+yxsbExVK8Y\nh2bRLLghR0ZGwuFwb2/vzMyMYlhZn2FlyRmYKSxikBYxUWu5iEPTNPzX+CxvOnxOPcaOMkjCi6b1\nGIM7ziBXliVtTk+dJmpOz5xN1LQeUreIo0E9Ldx9SxRJkjo6OtLpdDabdblcTqcTvYKY4VssFpEt\n6boeDoc/97nPXXbZZSdPnkQOpCiK3W4nhGA9JzpwhXEj/FeWZfTx4k5Af6OmaTzPK4qCpA0pICoJ\nUWSBfsJVq1apqorKwFOnTqVSKafTiZRLURSYVrlchsHouo4ZyggUHMdhqUaYFgwYE5mxPojb7Ub6\nSIWpqipUxsWvuuqqT33qU//xH//x3//936qq4iTofkQpP6aO5fN5JGEul8u4NzTDytIyMNyXppiI\nH9bpkjKerVb/mLEzCn9jeo2pwXPqsSYZ8zWwqp1jRknGEokm9MzXwObUU6uJWtdDJamGBcPmq6fJ\nO28J4/V6NU07depUsVjs6elBTMfYMCFEVdV8Po+Hj49//OPXXXfd7373O+Qufr+fEMLzPEakOI7D\nhUbSJoqiLMtYfYPjOMwC1jRNlmWe5+EB2J/F5XJ1dHTQPXHgdtiaub+//8iRI4FAYOvWrZlM5rXX\nXsMVpwU7sixjrUJN0ziOQ8oliiJdL5QaEs/zsiyXSiVFUXiehwGn02lRFFGgCEP1er0rV67EjXfj\njTdGIpFkMvnyyy8rioI8D/kfvqbb7c7lclNTU11dXYFAIJPJmG5IhpHFb2A0AlZdzhz3n2qpCzBG\nQ90yoGIN0MZoSA2sanCfU481RpsMbL56dAuyLLeip1YTNa2nahO1rscoyWRg89Jzju/QxQbP806n\nc3p6OpfL+Xw+p9OJvQUIIQjxTqcTu3bdfPPN73//+4eGhkZGRjB7EtkS0mWU3cuyjD8obJVCe9tw\n9TFIls/nA4GAKIrFYrFYLNpsNhRTOJ3OYrGYy+Uw+kUq88PK5XKxWBwbG1MU5ZJLLuF5fnx8HNO5\nkBoiDdJ1PRwOBwIBWZaxkr2qqvT2QBmkJEmEEI7jPB4PdT54m81m8/v9gUAgEol0d3dj+rbP59u4\nceOtt95aKBROnTrl9XpRoI+xN0y4npmZSafTqE4UBIH1ItZh8RuYKfwZoYFSqVEXMKdhmMoBcJQx\nAzMeBebUo1SgemRZbkWPbukck2W5FT21mqhpPdYmWhA9xGJgzek5L/fp4sHpdAYCgVOnThFCvF4v\nuugJIaqqohQCTbpmzZo77rgjFov96Ec/cjgcmBqFt9EdVehoE5ItXdfL5TJSIqfTqeu6qqqoiSCE\nYN1e3Hh2uz0YDHIcB3vD3aJpGlbHWLZs2dTU1MmTJ6PR6LJly7CKLkbUCCGyLOu6DhN1Op1YZj6T\nyaTTaaR0GAzDjWT8dpjl5nK5OI4TBGHZsmW9vb2aphWLxeHh4Ww2e9lll2FFqyuvvPL5558/efKk\nw+HA+o34OtioEwkrpjyjm/SCXcuLnsVvYNY4aIqJ1MCsT/QNGgYdUMEhpplDnGEqLp4c6+uxJhnz\nNTCTHlNWQQwG1pye+RrYnHoab6J56SE1DGy+ehbuZlwSBINBPBxgKSaEeKRNhBCn04ly9oGBgXw+\n//vf/z6dTvf29iK7IoR4PJ5cLoe0CX1xpHLHol4Dn4KnEFR2uFwu9OaVy2Vsd4IJW5lMBl4I8xME\nIZvNnjlzBnOo8atkMokJyKqqCoKAXShlWcYdgp3G0P2I5TxwF3EcZ7fbeZ5HfyZcp1gs4m/f6XT2\n9/cvX75cUZSJiQksMaVpGnKyTCaDnkxS2SIAJ8/lchzHFQoFFAnb7fauri5sVH2hLuXFz+I3MBrv\nqj7Uy5UMrM4TvfFsjaQXRgMzxnRjxlNHj2xJMqz7gc1Lj/UQdNk3radOEzWnp2oTLYgeKgnhqTk9\nzd56S5RQKDQ9Pa2qajAYhG14vV5YSC6X43mebpo1PDycyWRCoZCu64VCwe1246FEEARURuDmR06D\nxAslFThtIBBAbkQIcTqdKHZHYb0kSZhnhvRaVVX4HyEEd4LD4Uin0/jLwtnwIpfLxeNxubLRCbUl\nfAv0PXIc53a7MfQgyzJ6C0VRxCIgfr9/1apVgUAgnU5Ho9FoNIrxPJ7nE4mEx+NBf+batWtVVcVP\ndF33+/0cx6HMBDMNMDzm9XqxBw2jKovfwGgQNEVD406J1oBIo+Gjjz1mPNvuXbusAdoUDasamDW9\nqKXH2lFmNLAm9JhiNByiFT3GJrJuhbx3z5756qnaRAulB01kNLD56mn21mtvTFv9NrKrLwKxLMux\nWAx/Vii7yGQyiqL4fL7u7u5AIIAZYNjvMZ/PC4KgKEoul0skEshs4DRYAgqDQ06n8z9+8hPjZ916\nyy26rmPZeHqzOZ1Ot9sNI0ylUoQQFF+gf48QEggEdF232Ww+nw8zseAicDiO43Rdh6Ngi0s8xMiy\nTCoeiaoQXdf/v//9v416PvQnfwLj6evrCwaD8Xh8fHwc+7Jih/G+vj5VVWG3fr//7W9/+8qVK8fH\nxyVJggV2dHTE43FVVWHeuL27urqGh4dNz1iNXK8GL1m7syQMzJhh1H+oV+fan97oH3SLelM0hD2Q\nyrO/sVcNf6tz6jF1lN3/wAOt6MFvjZIUw+I6Teip30T0V43rqdpEC6WHNlHTemqdefFRZ396+qs6\nYVHX9d7eXpRCYH4VavZoXQYhBMZwySWXXHHFFXKl9I4QEggEJiYm0N2Xy+U0TRNF0WRaRv71u9+l\nr2+/7TaO41Bbi6c9pGKEEBTuu1wuTG3GrKy+vr5ly5ZNTEwMDAwQQrCUcDwej8fjoihiAQ4MgBFC\nqHtpmvajH/+4lp4f/q//RV9/8QtfyGQymUwG/irLsiRJg4OD6D/Ed4xEIjfffPNTTz0FQy0Wix0d\nHT09PSg7FAQBe2n29/eHQiGsP1L/utT51SJ2ssVvYAhwxlBY9dEeb3jo4YcbPzOC5n1795o6o2RD\niYQ1NM+px+SpjUuqpQcY9cDALh49tZroItHT4PnbmjpxsOo7rTFR07Te3t7+/v433niDEGKz2WBj\nXGUZFPTplcvlUqm0devWcDiMd2JfZkEQwuEwzMzhcBj9aU6+9e1vE0JuveUWZG+apgmCgLQPm0Yi\nywmHw5qmzc7O6rr+y1/+8le/+tVHPvKRUCg0Njbm8Xh6e3t9Pp8sy8ViMZ1O67qOlAsdnkZ/mpO/\n+fKXCSE33nADlq4PBAK9vb3d3d0jIyOTk5McxzmdzhUrVgwODobD4WQyiXFBsbIVg6IoHo+nUCiM\njY2Fw+GBgYGqvYitX7JFwOI3MNrLNGeYfuTRR40H3rVzpynM0dD21IED9G0PPfzwnt27jaFQURRr\nHKSd+43rsSZeO+68swk95OzojG6TBdFjaqJaeggh+/ftq6OnahO1rod+0MGvf70VPWSx02BvofFt\nppio67rL5dq2bZsoivl8nqvUOGBkSJZlQogsyzabLZ/PB4PByy+/vFgsTk1NkcootSiKwWBQUZR0\nOm1yrxs+8AEU4ymKgkoKjEt1dHTAusC/fve7d2zfjkUxsGowcincOT6fT5KkWCyGAsXu7u5Nmzat\nWrWKrqkoSRJWU8RFR78iqki++2//ZmqKD3/oQ2plnSpJkux2O9K+7//gB/Q9P/rxjz92662YneZ0\nOk+dOoWiEk3TcrnciRMnLr30Uixt5fF4BEFIJpNI+9B1iaHEiYmJ/v5+v9+P31a9Xs1dssXB4l/M\n97nnnsOUfjz6lQ3IsoyqXFmWjX1xO3fsoMMqtKPJGODQ4X7g4EF6yO5du2w2G6Y3ut1uuwE6mxIv\njDKq6sG/Dzz4YCt6CCH7Pv956KH/UrBeatN6rJI0TWtFj7WJ0NHUtB5rE9nt9qb1bNu2rYUb8ILR\nyGK+TQx0mY7CIaqqbt68ee3atceOHTt8+LDP51uzZk2xWIxGo7IsYwgKI0/j4+Nbt2797Gc/e/Lk\nyVdeeQWhn+d5LLyrKMqDDz1ET/4nN90kV3rw1MqWKLBGDHchX/nmt75FD/nwhz4UCoUkScLoWiaT\nQe7l8XicTmcsFotEItdff30sFjt8+DBWyiiVSn6/H0vrJhIJTB2LRqO42YweeesttxSLRaGy30ou\nlyOE9PT0hMPhfD4fi8VUVdV1/V/+9V/pIXv37CGEaJpGKvuTYcKZoijXXnvtwYMHT58+jT1iMFMb\nlfdYGnhyclIQhGuuuSYajb788ssYXG/ikjV3lUk7LOa7+Aeo6SC/6bne+ERvdK87tm8vGcDUSOML\nyh3bt9OjHn3sMVPXlnGERq1GHT3G6HzXzp2N67lr50564AMPPlhLUot6rE3Uop6qqlrRU1VS03oW\n7ma8uDD5UONxzfjOfKGg63p3d/fy5cvffPPNI0eO6LqOJ6R4PJ5Op7GUFHImBMTrrrtu7dq1qCr0\n+/14gPD5fDabzehet992m8/nw/ww7PqIDSQVRXG5XKhcxxCX8bL+4Ic/zGaz2F4ZVYiRSMTlcuE6\n+ny+vr6+XC537NixWCyGKsF0Oj0xMTEyMpLL5bq7u/v7+91uN2YoG92L9n/AhxRFkSQJq2QJlcV/\ny+VyMpl8zx/+4Yc/9CEc9fAjj4TDYZzQ6/XKsow6DlVVOY7z+Xx4gflqkiR1dnb6fD58NXzxqamp\n7u7unp4eTdOau2Smdzbe93jxs1QMzBSYjAGLutfOHTtuv+02movUB2+7/bbb6AfBw0w+UStA19Fj\n7BnbuWPHvPSUy+WdO3bQw6taV1Ubm6+eOSVV1XP/Aw9U1WNtojp65MpCjudNz4LejxcjTXQrGQ8p\nFIuDg4M+n290dFRVVUEQ0un00aNHY7GY0+nEMBj2UonFYnS1wFWrVvX393u93s7OzlAoFA6Hv/DF\nL+KE/+Nzn7tr5040Ps/zPp+P47hyuYw1opDfcxynVkoHi8XiRz/yEarnO//yL7Is+/1+v98PQ0Ih\nvsvl6u/v7+npicfjo6Oj6EufmpoqFAo8z8fj8TfffHNkZCQajQqC4PP5jCk7bhtVVfFUBGF+vx/e\nPD4+jlwTw2+SJLnd7s/+xV/g2L+8914sFJJKpbC2oSRJHo+H5/nBwUGXy4VNwgghmNBNJ5yhDmVo\naEgQhJUrVxZLpUYuGVej3GORdR6CpWJgmAtifbT/8v3303fiYdzYZ1U/FKKHwehhjzz6aNWnePrp\n1hd19OzcscMkqRE9sizTGE31mCQ1rkcxlDBY9VSVVEcPMRSF1m+iOnroUGWDeoySmtOz0LfkRUHr\nJWrGA3/+i1+MjY2NjY0RQtCzp2laKBTq6enRdb1QKGAlJ0JIOp3+3ve+98wzz6xevXpgYEBVVVTf\nffozn8Ebdu/axVVmL8iyjDXdkffgGrndbsziQm8e9kbhed54WZ86cCASifT09GBVxkAg4PF44vH4\nypUrt27d6na7NU3DeowooJidncXrUqmE6o+//pu/oWf7+Mc+hrnVQmUFEJfLhZMgrYzFYslkMp/P\ny7Lscrl8Pp+maaVS6S/+/M9xhs9+7nPxeDwWi8myjDWuCCHYvrKrqyuZTMIy8/k8VkAuFovIwDiO\nKxQK0WjU6/VWbXkrdUaF6IGLJglb/AaGkjO1BvRtt992W51QaOocq+Nh1uSGxkEjc+q5a+fOOu5V\nX48xR3no4Ydb0UNr/Kx6jJLm1EM7eWrpMUlqUU8dSU3oOTc35oVkoQqsjYdHo1G4Dqb6wm+SyWQi\nkSiXy7SMvqur67rrruvt7S0UCoQQm82GzU3oeegej1iDg1SmHqPCQlVVFE2USiWcQdd1VVUxHHXP\n3XfT83Ac19fXt2XLlvXr1w8ODk5MTBw4cOD06dOyLHs8nve///0bNmzgeb6vrw9bZU5NTRWLRezO\nNT09Tc9zy803Y4GocrnMcVxHRweWbUS1CD66XC5LkoSZAxh1gy/OzMzQ8/zPv/s7eBJtomg02tnZ\n2dfXh7ZCMpdMJkulEu5S7KfKcdzhw4dpBf9CXbLF4WFLxcCqRkbaOXbH9u2KYYilzhO9NTSjm46O\nhz32+OP1faIRPffcfTftLmtRD7F4auN6aPpl0lNHUi09xkyujh6rpKp6SCVzmtclM+mhwe7+Bx6o\nr+ec3ZuLARoQD/3+94jO2J1EqOyepVX2Kfb5fISQDRs23HnnnV6v94UXXohGo8Fg0OVy/emnPoWT\nfGH/fvQ6oreQEKJpGs/zKORDOT4hBKsreb1eQRCwzoWu66h+vPuuu3Cqv/rSl/x+v81mQ0WiJEnL\nli1TVfXpp5/+0Y9+5PF4UDqB4TRseplKpaampqanp//u7/8eJ7nhAx/ADaBpGnr26DYuKMeAucJu\n6RwyuBEmtL3nD/+QtlUikSgUClixHlUbmUxm1apV2NOZEKKqaiKRQGpI1w3RNC2eSOAMktN5Tq9m\n27HkDMwYFul7TEMsNCCWqmGMhsYD6dmqxkGArpU59aiWUZ8m9NAelVqheU49dHawVU8dSXPqefiR\nR+bbRCY9O3fsmO8ls+oxNXgdPefmxrxgnNP5rajbZ2O06gAAIABJREFUxGpPqqpyhlUl0+m02+1e\ns2bNxMTEb3/728nJSexrHAqF6OEY8bLZbKlUKpFI0EtGHRG1Ffl8XhRFVOVpmuZ0OiORCFb1LRgS\ni3g8/vrrrx87dmxycnJwcPAjH/mIz+ebnp4Oh8PT09NHjhzBXZFMJmGZyWRyaGgIO3sBr9cbCARK\npVI0GsXyTrIs67rO8zzt6sDiVTBRp9Pp9XpVVY1Go7lczuVyeTyemz74QZxN0zRCCD4xGo3quj47\nO9vd3e3xeNBv6fF4VFWluSnuyXA4TPU4F8LAFlMStkQNTNM0Y/pVP0DTkrY60VlVVZr03P/AA7U+\ntD44/J6776YJRyt6aIB+7PHHW9FDDIUwdTyjcT11LspC6anaRE3rOTc35iLB7Xa/653vxGuv14vI\njsJC5DfIvXRdj0ajkiSJonjo0KHJyUm6GO4Hb7oJh3/lH/4BvXD5fB7jSRhzwuK8WEVFkiSMe6Eu\ngxBCl9nN5/PY6Pnmj34UJ/zUpz+Nkr9isZhKpbAaYalU8ng86XQaZ0ulUpqmYUALNY3BYBCH33Lz\nzRzHKYpCCKGpVblcRtkhuknxLcrlsqIoqEjkOE4zJO7wNrz+z5/9DGtr4bsUCoVEItHV1bV161ZR\nFNPptKqq+NbICDFnwPgIhSWAGZTFb2B4MpozGlo9w9glZQyFpmhoPJye0/px+tlY30ALiDVLv9kF\n0UObiNaD1WmiBvXQkaeqH7eAeqxNVF/Pgw89VEfPObs3FwO9vb1KpfthemZGEARU3OEnmqbhtzCS\n7u5uu92eTqftdjvW4cXPQSKRSCQS6XQaY0XIimw2m6ZpxWIRvoiJyaVSSdM0zOJSVdXpdKKPkeM4\nWZaNf90zMzMzMzNYAiOdTufzeYfDkUwmX3/9dU3TsPoGNlzGvDGn0/nVf/xHHIstpLFCIzaDFkUR\ni2vQ/FLTNCSdmqbJsqxWtrR1OBwov7Tb7aYUyu12B4NBeLnT6QyHw+9617uwYRgGwFRV9Xg8brcb\nMxDGxsdx7OVvfWskEqFDg62waCoSF/9KHLphtydjfKRvoAHLGhNp4MOsWCwCSwgxLtagVhvtr/qJ\nVV/X0UMlNa1nx513YhGKqg5RXw/tr7PqsUqSZbkRPfRrWvVUlWHys8b1WJtIUZQ6eupfsnNxW15w\nFiSEiaIYCoVmZ2fpTzwejyRJuB8cDgdCPBbd4Hl+zZo1dCIXHi9o8/6Pz31OnpnB4BaOgo1h61G9\nskskKvIVRcHQl6IoqDW32+0oDBkZGSmXy1RPMpmEJJ/PFwgEUKfu9/tjsdjRo0e7uro0TcOOKqqq\nypVJWiCfzzudTpfLFQ6HdV2XZbmzszOVSmUyGVVVbTYbFkjErGRMbabL0uMOdDgcwWAwEon841e/\n+qlPf5oQsn79ekJIqVRKp9ODg4P4gps2bdq2bdvw8HCxWEQ+hwJ9rTLwBkZHR3t6elasWHH48OHW\nr93iYEkYGKnkYUbw209+4hN6Oj2nZ2iaxvO8NTobD9R1/c477vj6N75R6+OqvjbpIdVSxqb10NMu\nuB6TpHK5PC89jz722P59++pIskKn6zWix9pEVuuq+jWr6lnwe3LRgCL1kZER+hPkKLSFkYJks1lF\nUdxu98qVK7EOBeogbDYbHbKanZ01rsarqipddEPTNEVRENBLpZLdbsd68/l83mazhcNhLIYLN8pk\nMslk8uaPfvTfvvc9nC2VSuXz+UKhkMvlnE4nOidzuRzq/lHyTgiBWuO3czgcy5cvj0QiWIQ3nU77\n/f5CoYAkD16F10jCSqUSFjaEh0mStHr16mAwiBwR5/yDP/iDcDicTqfHx8c5jovFYjabraur60Mf\n+tBrr7129OhRNE65XA4Ggzgt1ZNKpVKpVCQSGRoaKizQ8FW+UGjrbGypdCEaX9cPWzQ+0phYrqxp\nRPugrE/rdc5sklFfzyfuuecc6SHVHGtOPQ02Uet6TJKsb9h1772tXLJaR33innvm1MOoBWrKja2E\nq+B2u/1+v6qq6XQ6mUxOT09rmrZq1apQKITIjk1PiGGxImRjKDXUdR3vQdbl8/nsdjsqJlRVzWQy\nmLaFYTaO49xud29vb29v7+Dg4MaNG8PhMO3VVFU1m81OT08PDw8fPXr0yJEjU1NTqPSjhRh42ML5\n6Xe59ZZbent7V61a1dPTs2zZssHBwUgkgi+I0S9ULZZKpUAggE5C3HipVAqJlM/n6+zs7O3t7ezs\n/L/LGObzsVgMPaXHjx/Hfivlcvnaa6+9/fbb4abwP8yMhqkTQiJdXTzPnzp1iuM4Y9lLi7S1e5Gl\nkIHNiV7DdYxhsVQqORwO42O7NSIvYLCzSmpRT4va5myi89A+db5aI010Tq/XksXlck1NTRlXzLPb\n7ZiShcZHEQSGpjZt2kQqU6BwCAaNcKCu68io3G63z+dDzWGpVJJlGTkNDpEkCdcRk7GQamN3kmAw\niKWnNE3DZmCEEIiB1QmCgMEzjKuhepD2QpdKJYx14UBBEK644oq3vvWtqP6fnp622+1Hjx5F6TwS\nRFEUXS5XR0cHvFDTNMzl0jQN1SgTExOEkK6uLpyEEHL48OFkMklnaqOuJB6PT05OJpPJ9evXj42N\nYbEPRVGi0eiKFStwIBbzTaVShUIhGAyOjo7WWnFjScEM7KyVV+jyr8SwtjqGZDEHxfRb07Gti/na\nE0/csX27VVKLelrUNmcTnYf2efxv/7ZxPdYmqqXna0880YqqpQzGlmKxmLFVvV7v7OwsliJMp9Mo\nENc0bf369StWrIhGo9gtjC6JS8s9UL9nt9sxhIafEEJKpRLyLRgD7A3mEQwG0adHKiOjNptt3bp1\nvb29TqeTfPe7pNIxCK8qFAroLcS/qAHBp6Oq0OVy0Yzn29/5zsiDD2K3aKSGkUjkxIkTyO3QQW23\n2z0eDyY1Y1QPORNKQlRVxYwCyKZfMxAIQO3U1BQqEsfGxkZHR0dGRuDTqVQKm8KUy2WpkiGVymWn\nwyFJUjabReGlcaivadq9C3HxG5gxhPEV6J/c15544mO33ioYwKAx/ngwxIpOErzGf/H0h3IjCs/z\n3/jmN3Fa02fRT+cM+yVW1UMMY0hGSc3poR0X1o9rUY+pifCE27ie3bt2ORpoIuMbdu/ahWGwRvRY\nm6i+nvqX7Fzdmu0Mx3HhcDiXy6E6g/5cVdVAIJDJZLCbSTab1TTt9ttvv+eee1566aVDhw5hnV+3\n200HSnGgz+cTRTEQCIRCIQR9jGZxHIciw2QyiclSsViM5/murq7ly5f39fWdPn0ao1MDAwNdXV3Y\nAOUzf/ZnOC0mKWMEC1XvmMgFvySEKIoiiiLWppqYmLjsssvod7HZbOl0GiUn4XB4ZGQEtft4YsNq\nUtSQ4vE42kFVVb/fLwhCuVzO5/Ozs7OYVIBzhkKh0dHRUqmE7A1zsb1e7zXXXHPFFVc4nc7Dhw9/\n5zvfefHFF9HIr732GtWDDHJsbOySSy4JBoPYjKZF2tq9yFIwMFOMpoGJvoGGLWNAxCMSfotOeY7j\n8CuKKRSazmn9xKqv6+ihkprWQ/fBMsXlRvTs3bMHhYhWPVZJOMOceujXtOqpKsP4K9OxTVyyOnrq\nX7JzcVtecFp89Mb68Zjz6/F4SKWmIJvNojgeo49ut3vr1q133nnn6tWrjx07hrnGXGVtX0VROjs7\nceD/+9Wv/vQnP8HE4Uwmc+TIEaz4jkuJjju3210oFOAoTqdzdnYWDhoIBLq6ukKhEGxDlmVfRafb\n7Y7H41gvkY6iIXdxuVy0EF9V1TVr1qxbt+4973kP+drXcGyhUPB4POiFhnlgRURRFL1eL7qg8WyE\n5A9pJZaoJ4RgzV/Uzd9dGWodHx+PRCI8z4+NjaGY3uPxuFyufD5fLBZ9Pt/69es/8IEPKIry2muv\nKWdvphoKhTDRDbWUMzMz2pKfpLgkDIwzPFxbI5fpWZ4WUJFKrKR3Cc/zCIXo+rA+1NNzWj+uakQ2\n8vn77sNUMN6SXoiieP710CZ66sCBO7Zvr99E6AiaUw/d6LLqxy2gHmsT1dfz+fvuc9TWs4B346KB\n53lVVZPJJDH06Pb29OSmpmjXVjAYfN/73nfjjTdGIpFisfiWt7wFrqOqam9vbyAQwCJP9JybN2/G\n0oiTk5OlUsnv91922WWjo6OnT59GVQguNJYG9nq9mDdWLpdRrw/bKJVKxtHNP/3TP33++edff/31\nXC6HvyyqVtM0GJ7X67366qu3bt3a09Njs9kmxsd7envxvej8EFVVsfGKqqpYGSubzaqq6nA4sAgv\nUjqHw4E3a5qGbTM7Oztp+kUI8Xq9SCJ1Xe/r68tmsxzHJZNJn88XCoXQM7lt2zafz/dP//RPx48f\n53ne7XLl8nlCyMjoqOR0yrLscrmWLVs2MjJSMqxPPy8WwRocYPEbWNVQyPP8/n37sBjHN775zY9/\n7GM0DtJQyFVGU9AJjlhGHcUYoxEWaf/h/n37rNGwEXD4E08+uXPHDmNoxh/AfPVQA9t1772t6CEV\nj6/TRFplQ8tG9NS5KAulx9pEreg5J/dlm8PzPMalCCHTlSVrk8kkNY+Ojo7rr7/+gx/84OrVq7PZ\nLJa17e/vX7NmDXaPxAynoaGhgwcO7Ni5kxCyrKfn6JEjmqa99NJLp06d2rp163XXXTcxMZHL5fr6\n+hwOx5EjR5CUYIwNO37Z7XZFUTBChqvfvWzZ/9GTSGwUhIGBgWuuuebnP//57373u0Kh4HK5UOkD\n71y/fv173/veNWvWOJ1OlBHKlbWwV65aNTE+juWpeJ4/ceLE+Pg4z/OyLGPWM8/zoihiIcR0Oo1V\nfXVdD4VCK1eu7Onp4Xk+Go2OV2Yif/ITn3AfOYJp/oFAAGtZISPUdd3j8aDisbe39+qrrz516tTo\n6Oj/Wci/UiaD9fJHRkbQIE0b2KJhiRqYKX7VCYW0AptGw1oxmp7N2k9FqZVbmPSYojNGmOarh+5m\nRBOO+eqhvYj13QLPm43r2btnj2OeTWTSc+DgwTu2b5/XJcPC3iYPa/CSnbN788LgkiQ8gLfSi4gR\nR1MfF8dx/f390Wi0WCy+/e1vv/XWW7u7uzOZjK7rnZ2dgUCA53m9Mt0qn8+fOnXqV7/61cjICN0H\n5fvf/344HPb7/bfccsull14qCMKyZcuuvfZadN/hGmFLMMwnw8SJTCYzMTHR09PT3d1t3Iea53kM\nxW3YsOGSSy7p7u5+/vnn+/r6gsHgq6++msvl3vGOd9xwww0dHR2lUikej4uiaJp6hbwKVSfJZDIW\ni+FWn5ycJIQEAoFEIqFp2vLlyzE5GtoIIfjiv/71r998803ak08IQUkLz/Ozs7OYNKZpGt0n7JVX\nXunq6tqyZcs73/nOj370o4cOHfrNb35jbOFQKDQxMXHmzBlUu+Co+XJOF8M8zyw5AzP2IBmTsNtv\nu42WWdMYapzSRLu2BMOwCg2LNP3ade+9XsNHWD+9ET1PPPnkXTt30o/GdM7m9BBCxGrFC43ooa5s\n0mNtImpgtfQYDb6OHqukqnpI5Zmj8UtGt8Cgep548kmcav++ffa6es7l7dmuIPJqhj2Cr9y2bc/7\n3x8MBr/yla9omvZHf/RHq1evxmr0oiiWSqUzZ85gwYtcLsdxXCKRwO6RkiTRR5Mv/tVf/cWf/7nH\n48GgV39/v67rs7Ozr7/+uqIoPM9LkoRiv3Q6XS6XuUpx/JtvvunxeGw22/JK3Xk6lSKESJKkqioS\nr4997GOY7Lxu3TqHw+F2u2+99VaUWqC4n3Z+jo+N9fb1EUI6w+GpyUmMtMEs0RWJHkvs0TU2NsZx\nXDgc3rRpE9Yq/Od//ufvfe97kUikVCoZ3YvOOUNehVnVyWRSURSsFIyFr44ePbp8+fINGzZcfvnl\nr7zyiiAIktNZKBYJIadOn+4IBGCBHR0dMzMzS3w2yFIxMKEG9G3f+va3sa0XDYVCJbegtwiNhoIh\nybDZbMZ9x03RuU5YrK/nqQMHjMvJz0uPsc/9vr177dU+qEE99+3diy24jHpqNVEdPXS0qZYeobZv\nNa3HKMloYPPV0/pNeFHB83zrSRiMIWXIANatW9fV1UUq2woPDAwUCoXJycmJiYmxsbFUKpXNZkVR\nRMWEIAiKojgcDtQ+GDMJnudTqdShQ4ei0ehb3vKWbDb7xhtvJBIJr9eL9QMVRaGLBZdKpUKhEAgE\nisViLBaj7kUqW0xg4V1ZlsfGxvr6+rZt23bmzJl8Pt/d3X3ZZZehezAej4dCIVgmz/MmS+hetuyl\nH/8Y059xP2A9XywrrGna5OTk8PCw0+ns7u5ev379pZde6vP5sCOlcSGoj3/sY6KqchyHWxSTvbAW\nCYpECCEoyhdFMZlMZrPZZcuWuVyueDweDAZDxeJsPE4ISSSTXo8HJ+c4br4GtpjSL7IUVuKgwYgG\nJngMbpQv7N9P34nQZjfgqIbxDSb32rN7N+2eEs8ue6v1oo6eAwcPmiQ1osdms9HOOqrHJKlxPcak\nx6qnqqQ6egghVfVYldTRs2f37nnpMUpqTs9C35IXGFS4tLinRldX16uGCu//573vxaTmo0ePqqq6\ndu3a5cuXy7J8/Pjx3//+98ePH0e/Iqo2yuUyyhRpCZ8sy5+ubAn2d3//96hoIITMzMwUCgWv1+vx\neGRZxpzfUqmE+c504zGe5xVFudOwI3MmnSaEwL10Xe/o6LDZbNPT06qqer3eWCwWDoe7urqQ3mHz\nF0EQsCIw1iE8MzxMz/aBG24YHh5GpQY6CWVZnpqaOnPmDMpYHA5HPp8fHx8/efJkPB6//PLLr732\nWqfT+Q9f+QrOgF3K7JWl6/GMlU6nS6USJgmoqoqsLhAIDAwMwAK7u7sxo+Dyyy//7Gc/+3+/XTaL\nYbMl7l5k6RiYKUIZx0J279qFdx44ePBb3/52nThojYlG99q9a5e1+s4aGefUs3/fPnrOAwcPzkuP\n3W43RueqlQvG103rmVNSVT379+2rqsfaRHX0GPPL86NnQe/Hi5H5epiu67985hn63/Xr1uVyOV3X\n3W43euH6+vokSXrzzTePHTuWTqfFyoAozWg5jtM0DVXpWPRLFEW6F+VDDz/85fvvR4EDTAi5ER3y\nxM4pqVRK13VJkhwOx5fvv5/qeeaXv0S2h1Wa8FnBYFDTNKwCPDY25vf7OY7D4vQoX+R5HitXkco2\nkseOHqXnfODBB0mldAXD0h6Px16pHyGV/VZsNtvExMSJEydkWf77f/gHHLt71y5d19H/CTHo+US3\nIalMiy4UCjabrbOzs7+/3+PxoA4TA4cDAwPr168/8NRTVM/hI0cc/z97bx4e11nfi79nnX0fSaPR\nYslrvcROyOJQtnJ/hS4PT2mhAbKQxE4ClISuSezEJtwLSYCE9gJtbxMCCaEFEgotKS0tt6QNGBzw\nk8T7Lkuy1pFm3+fsvz8+97zP0WwazTjYlvL9Q48szznzmfe88/28391mQ0LK6/SULwtZsgV62cm+\nffvoWA2pZmSwLMvFYlFRFNorlhCyc8cO2vuVtiCyZnhDr1lVIdgLZ3yUN1oVq/UXK4y6ePATX5i2\n8RBC9jz4IPDQn1RQTNo2nlpINAbWHp7aJcrn853gqV2iKupaEp7t27d3sAEvmljTGRpJlVJr5WBe\ndckVW7aAZjweT39//9zcXCqVuvvuu3/3d3/3pZde+vnPf85xnCiKGGVCCIFtUSqVUJvFMAyKhaPR\naKVS4XmeTjMhhPzrD36gadrk5OTMzAzP8+iWi1xBZLfLsmy3279q0ex79+zZsGHDFVdcsXr1anSF\nx6NE7M3j8UxOTr700kvXXXfdxo0bM5mMoigul4vjOJrri+0nimK5XD506ND7//AP6c3vufvudDqN\nijRN00BdTqczGAyiAUdPT08oFNphjukhhHz20UcxIAadOVEcViqVcrlcX18frE+Xy4XU/KGhoWAw\nGA6HMRqmUqk8+eSTBw4cuOaaa4aGhiKRSCwWs2oqQojDbl80z6iNp/z/LrQ0Cbs0ZfkT2P79+5tr\nZ3SnVhTl8489Zr2wKm2BWErKaAQFsuv++wWLoAlpI4W4KFtQoSM3qey4/fY28NTqaBBY53hqMzvq\n4iGE7N2zpwme2iUqFAqd46GQrIH0NvBcffXVdbfWJS6tEBikRQVXe4Tv7+tjGAZGDMuyNpstkUj0\n9PTcc88973jHOw4dOvTiiy9ioIksywh0+Xw+wzAwtQS7BcYu+Ay57I9/4QvWd3nyiSemp6fRHjCf\nzxcKBVmWBUFwOp1Vh5J7/+IvBEGIRCKbN2++7rrrCCFowOF2uwkhGBE5NTX14x//eOvWrddee20i\nkVBV1ePxwH0H8wi56YVC4fz58ydOnBgbG/vLv/qrqg9+0403GoaBemr4MG02W6lU+uu/+Rvry/7h\n7/8+kUhMTk5i5Ar6ktjtdlmWC4VCOBxGPn04HA4EAtSkEwQBboNwOPzSSy9997vf7erq2rhxo8fj\nicfj+/fvtzpvl/rIluQ8fIPALr4cOHCgriqk2hAEhpAvEgSWJA/s3k1dWxBU+DfSiY2ooko7tw2p\nFo81UIRf8FW5dPDULhEssEsEz5VXXrmkt7hEpHUCI0v3L60eHo7H48FgEHof+fSglre97W033XTT\n5s2bFUXZt2/fsWPHQFQgBqfTCechzGWe5wOBgMfjQXTK4XCwLFupVHbt3r0kPISQT9xzDywtURTX\nrl37vve9D1aULMvUYcgwTCwWe/HFF9etW/fmN7+5VCoZhiEIAswgQRB0s1ni9PT0kSNHJiYm5ubm\nCoWC1chrUR584AGwey6Xm5ubg3MSvk3wtMvlWr9+/apVq86cOROLxXw+H+aEeTye3t5ej8ezZcsW\nSZI+9alPnTlzZtWqVW63e25uDt+OcrmcMRsWtyhtxL0ufQJb/lmI3MJmDVbBC0RRpGlse/fsUVWV\nznJsLrt37eJ5XlxY9kQVIr8waZtGVjRNa46HLOweQnPrO8RTC6ltPC0u0VLx1EK6RPC0sviXu0C7\ntUJjNlEcGhoq53IMw6AXLSEEdgO60Pb19a1fv14URZ7n161bh3wH1GNJkoQSYASB7Ha7KIqGYSiK\nEggEkFjh8XgkSXr6a1/TNO2uj3ykFfB3f/zjiE7BtSjL8tTUVDKZ7O3tdTgcOOgI5uwV5BlSGw5t\nCemtcB8UfhUKhVQqhQbwt9x8s6Zp337uuVbw/PEnPmEYBlMoEELy+TymyQwODqK7I7o+chz3a7/2\na2vWrLHZbCgyQw8ReBodDgcSEa+66qqNGze+/PLLmUxmeHg4m83i6GYYxm//1m/5fD6MPWsuyyZl\no1aW/5ezSjvTHGuqEDHuAdoQCb579+yhRbJVHuf777uPZlfbLBkHjTiM/tGqEJvjsUZuAOlC4REW\n5nS0jce6RLXMsXvXrqXiqV0inucvFB4sEc/zbePpdAtePmLVdA39iprmdrvRuxYsBR8G8hEYhunv\n7+/r68tkMrquo2XUyMjI6dOn0UUQoSP8DtMHRk8gEECjJlmWV61atX37doZh/ikUMgwjGo0ePHjw\n43ffbcVz8003ORwO0JLA8xzHwZtCCLHb7cViMZPJRCIRhmE8Hg+6FKLFhizLhmFgiB1Ku+C9pBsM\n/JrP51OpFMaGCYKAP950441IFySEPPf881Y8jz/22Lvf/e5kMvniiy86NU1V1XQ6jQtBSLA7WZYt\nlUput3v79u2iKB48eLBcLs/MzHAch2XxeDyhUAihwfPnzzMMs3r1ap/Ph84jyPVwu92FQuHo0aMb\nN268ctu2kydPchzXobfwMpUVQWDND/JIcKJVRDQXAGLNwSOEWHuoV2XNUd0nmunadc/1ixoWVu0M\nSHDNt42nkbSNx7pEn9y7t+oS29Lx1C6RIAgXBA9dIr4my7F1PB3vwctSGqk/hmEymQzHcaABQRDw\nDRLMJIi+vr5yuTw6OqrruiiKPT0927ZtczqdExMTiUQCVcx4cJg1KooiIYRl2UKhcO7cOZANrJPR\n0VGO4zZv3rxp06bPPvoomrsjG96uaSAh9AbEvBK4fGmuIADjiMOyrNfrlWUZE7w8Hg/P87QVE15P\nn7VhGJlMJpVKybLMsiwsRbQCgfVjs9k++IEPpFKpQCAQjUbtdvu2/n5BEGBsgb2Q7o9+vgzD4LO7\nXK7+/v5rr732+uuvf+GFFzKZjCzLYC9CCGdWH6I3h6ZpiURi9erV69ate/XVV+fn54eGhlBzDYek\nKIpgX13XVwJd1cry/3JCFVrVtPV/KYFha1axV9UlVdqTtRTtchbHVK0qtP6X1bCoi8eqnQGJElh7\neOoaGZ3gabREbeOpXSLrsaNtPFZIPM+3jeeC7sfLXvB0kLYHc4oWJhNCUJ518ODBAwcOIMxz/fXX\nb9iwYe3atS6XK5lMJhKJqakpQgjP83BCplIpjIvs6uoKBoNoVHHo0KHjx4+73e5t27axLIsBzeVy\nGe+L5ygIgt1uz+Vyuq4zZkmvLMtIhYjH45lMxufzybJMCBFFEWxHCEHWiSiKyNSH11HTNHTKQDv5\nYrGYy+UYhkHOBQTsqKqqoiiU/PDW4+PjNptNEIRgMDg3N+fxeAKBgCzLpVIJES8MX/Z4POvWrYtE\nIkePHkW2PfKVJElyu930HJDL5eLxuN1uT6VS/f396PPr8/m8Xm82m4XJC5sylUqhZ//F2g8XV5Y/\ngVFVSGqG8FotMHwJ2yOwFo2eKounEZ4q51hVBUx7eOqiahvPUgmsRTzCQgusczykAYEtFc8F24vL\nQgzD8Hq9s7OzNpsNPXkRRoJNZrPZZFlGI1qGYQghgiCoqrp161ZBEM6dO9ff379169azZ8+iuTvL\nsm63m2GY6enpUqnk9/sFQfD7/T09PWi2m8vlDh48mMvlkPKOEczU+BZFEeaLw+FAekg+n8ff8dAJ\nIfBtAhshxOl0IqUef0QzjkqlAhtOkiTMkMTnV3+TAAAgAElEQVQGMwyjXC4j84K3tAMFZwSDQZZl\nc7mcw+EQRbFUKnk8HqfT6XA4kIUkCEIoFAIlA7amaWNjYyMjIyhiwzvCocqyrNPpRGYjboIlTaVS\niqIwDIP6ARi+eHdAumhb4RKQ5f/lFCzOqCq9xrIsjJu6Z/lWCKPuoR4uRKsbyvrTWCi1eGrNi9YJ\nrLmRYVXTneBptERt46ldIvrUOsFDagisPTy/kn16eQgeDfpIwXGXz+djsVg0GvV6vYQQQRDK5TLq\nqGC7zMzMyLI8PDwciURgtWzbtm316tXxePzo0aOHDh2Cmw4KWpIkzFLxer0+n8/lchWLxZmZGTRe\nYhjG7XZj3jHHcV6v12azaZoWj8fT6TTHcS6XC/zEsqxhGMhx18yZmYZhsGZzS5hlsLQEQQARMgxD\n7Sr8UZZlXdfhmSwWi8CAmgEQZzablWUZdmepVOJ5PhKJ2O326elpRVHAx2hzhfEraG2MjYcbIm4H\n56HD4TAMIxaLSZIkiiIlS4B3OBzlchl2IcMwHMfB5rsYG+FSkeX/5eQt4VmyMI4CoSeaRtrQerdG\nCtqqE8WFfWNpSAx/rLpnLR6qnSkkjuM6wVNXO3eCp8kStYendono17JDPPQOVQS2JDwXYhsuE2EY\nBlUNPM+jQy6dwgXjwOl04heGYcANgiDMzMwcOHDgt37rt971rnexLJvP56emps6fPz81NYWIF6Y+\nQlP7fD6YRyAklmURH0KhFS2iAH8gCBcMBovFYjqdxtwTQggIDD9plhYxZ4BhhiRg8zwPYqhUKqw5\n2Y6YY/modw4BMCQQama9fKFQMAwjGo2GQiHEvZBOGY1GBwYG0OMRhmalUrHZbPA9UockFg2sjBWA\nPYe/syxrs9nw8WG9ORwOGJqVSgWmIcuydru9asOvKFn+BFalgBiGIQttBcMwsFN1XW+PwFgzR4A3\nYwNNvFK1N6zCQ782FNJSCawKT3NHWRt4lkpgS8JTS2Cd4CH1CGypeNrcectUGIZBM3UYFqgRxigs\nYib98jyPiFe5XHa5XDzPT01NTU5OhsPhQqEwNzeXSCSom9Hr9XZ3d6dSqfn5eUoYuq7DoEFlmCRJ\n6XQaxge+EYQQZDDicYOEQFroFwUvIjGbyTGmC443K88Mw0DwCfVhOHfSz+j3+x0OB/ofYsw0mlGV\nSiVBEBAD03Xd6/XCUAMYOPQGBgYGBwfHx8fPnDmTTCZpARxyNb1eL1LkBUFAAgvP83a7nef5bDab\nyWTwGWVZhocWvbJ0XS8UCihow6G8WCyCw9hl166zdVmJBMYsdEYZhkGjKVWqENvR6o8i5uz5JkaG\n1YVYpROrzMG6eKpicjgzdoKnuSOxDTyNlqhzPILFhdg5HiskztJdfql4LuBuvNzFMAxRFL1e7+jo\nKMMwiP3gLzzPo00GnhRsCwR4GIaZnZ09e/Ys7Dae52lbCoxaHhgYkCQJVxlmhwtd12F88DxPq6Pw\nGs3MZcdzx+kEmt3r9WqahrsBM/0FvjtN0xC9g4+R53nYRrquw7DD64PBoM/ni8fjSP2gt9V1HbtC\nlmU0M8SQMFhCSBLJ5XJTU1OnT5/G+Gm6S4E5n8/D8svlcuhniB1YLpeTySTMVsBWFCWbzYbDYVqi\nYLfbBbPaGjxNPxSz7AbXtSLL/8tpJbC6zihCSFUqtvUsXzeg0khBV7kQ6ypEK7a6eKzOsSoCaw9P\ncyOjDTyNlqhtPLVLJJg52Z3gsd6hLoG1jucNoQJfH7Q8Dn/Q6azZpRe9QOGRUxQln8+jEuvs2bM+\nn6+3t5dhGNpFkGEYqGA0ZQeFCJamuihDRrgI9IAHh8MKXoasB/TdgFGI9obEbL0P5Q6Wwn6AFw56\nH0Y/rCjDMBBYQj3W6OiooiiCIDidToSvODOoRrkTRxzDnPLM8zxso9nZWThIYTyBtARBQL0X6s+c\nTif6uqEHB1I6YUeClqhKwf3D4XA+n8dgaHwXkN9xkfbCxZeVQmBVetCqDbGPqSrEBtKbppXTm1C1\nWGWBUT1ojaxYtWETPFxNekIVgS0VD/1JIVmjdG3gabJE7eGpXSL4fzrHQyFxZveH9vC8IVRgG8F8\nQSRGVVWe58EuhmHk83lEjOx2eyAQQE6H2+3OZrNHjhxxOBxr1qzx+Xwcx9lsNoZhUqnUqVOnUDiF\nvA+kv8NdpmkarDrqEoQw5mAtjuMqlQroAZEtlmUrlUo0GmVZtlgsut1uwzAYhikUCqBJUBQ2BhgO\nhCoIAhIdBUFwu93BYJDjOHSZgvvR7Xbrug4zkRBitRThVIQ9h2oBhMRQLg3/Kpr5sixrs9lA87ib\nJEnoDgUSBUhKwKI5IVoURZSvGYZBqUvXdQT5ftX74NKQ5U9gVd3zrD+hB+GRuCAWmKZpPM9jV1Wp\nVHqTRfFQ7Uwh4eTYNh7N0pkJP+k3sD08bVtgjfDULhG+yR3iIYtZYC3ieYPDqBiG4ff7u7u7jx49\nCt8g7A9d18ETTqeTThmGww1dJFKpFDbef//3f8fjcXSNGh8fR9EV1D3uBncZjDCaiYdkfZgyMPhE\nUXS5XPiugeTgyaQ+Rr/fTwihNIA0Crj+MCKSMfvZo+QLjIJthhZZoVDI4XCgbSNMIliKLMuixlnX\ndTS8p8csfMZEIhGPx/FifNdgjGLHIqzFcVy5XEYdGExA/C/P80BOzAozp9Pp9XoNwxAEAc2o8CBQ\nWIZRZyvWDltZBFZXJ+KIVFcb6kuPOcEpYSyUJeGp0tFWAmsPD1/TbsMa12kDT6MlahtPkyXqBA9p\nIQbWCp43CMwqhmFgcDA2EiK+hmHQ0Y6EELT1Q2td1FfF4/H5+fnu7u50Or1///5Vq1axLIuEOoZh\nEOvCs0BQzTAMJHHgcbMsi3RHmESwpyuVCtpY2Gw2mHSapuHrDAMa5oumaalUCk0rYLHBjiEmvQE2\nDHFsKoK51U6n2+1GBw2WZQcGBgqFAkwxVVWBh56BUGSNJH4kGeq6Tsu5MFHF6/WuXbvW6XSOj4+j\n7s1ms6EMDt5LQoggCBzHIVUEkAKBALVuXS5XNBpVVTWbzTIMg2RFzuyStQJlxRFYlVrEdsSXRO84\nCxFfD5ZlrWf5qssXxUMVNIWEX9rGY1XuuAPd7u3habJE7eFZdInaxkMh8fWyEFvE08HuW24COwAr\nScwvl81m8/v98/PzMBegTykfoOM72veh95Ldbp+dnXW73YIgwKvGMAyeJuq9aAOnfD7PMAy4AedC\n6g0mhMBEg/8Qrnv8LyJYNLMDIMFqAO/z+axGD7GceDRNg63mcDi6u7sjkQgaFdpstmw2m0wmOTPy\nhEvgjURXRhTGaZqmKEowGDQMA9n5ME+RYNLX1+d2u2dnZ+GQRJMOWuaMzckwDLoMp9PpzZs3r1u3\nbv/+/YQQ2vMXn4LneSTRIK520fbERZWVRWA4OlXpRPyxiUvKerdG/jGrM4rjOHphc+1cF0+tkbFU\nAqvrHLNCsoa+2sCzVAJbFE+jJeocD4WkWTpeLhVPmztvOQpWEuqSYRhU72KKChbKbrdrZgMLpDDA\n1kECYalUymaz+Xzebrcjwx5PDS/QTH8+IYQ3MxXRvQlRW1rOjD+yZg0MHqUgCDBWEomE3TLmEanw\ngUCAM5PvkSuBz0II8Xg82BL4FJQyA4FAJBLBlnO5XPF4XNd1h8Ph9XqxZ7AUtB4LFIt/dnd3ox8H\n+scj9AWfZDKZRDQuEAgguQNGJ5I40FBKlmX8vn79eqwMISSbzY6PjyP1H29kGIbX6wXTX5wNcbFl\n+RMYHM1yvYmI0Ikoh9QsUqUNjZqASq0zirO0JqJnPYiqqnDZ05BbczyqKRSPYpaYtIenNq0OKqBt\nPI2WqG08tUuEktUO8Vgh8UtpJVWF56Ls20tTENdJJpPQ9cjls9lshmEgJFYqlVavXs0wzIkTJ9A5\n1+125/N5sIjX64XaLZfLyLBnzaa0qNCiBpxiOgnK5TJjdp1AxRjDMChbRmaEYRgOhwMZH9gYHo/n\nuuuuA12BXBG4wq7Ao6fF0fl8HgXC6EHl9/tLpRK6WPE8f+WVV87Ozh4+fFhRFPBTJpOheWFOpxMp\nITzPo34LvT/cbjfSOubn5+FZxcrA3ITOwcAUjuNA+ZqmoT2j3W4fHBxcu3YtZq1JkpRKpd75znce\nPnz42LFjmN08MTEBAk6n0z6fD/07VuZJa/kTGD3C1xWrBUZ14lIJjPqjcAm/sHKIsZTismYn0CZ4\nau2MpRJYFZ5aowTfxrbxLJXAFsXT+hItCY8Vkma2bG4Dz4XbjJe9sCyL3Hc8X94sWy6Xy8Vi0TCM\ncDi8fv36gYGB4eHhVCoVj8fz+TziOoQQ6GvDMBRLBh1u4nQ6VVWVJMm6hRgzRwONdAkhtJ+vy+Uy\nDINlWfoCjCzRNC0QCPT39xPTmEauIN3zxExTLBaLoB9KbDCqcNZRFKVcLofD4U2bNo2OjiKVA+/I\nMAw4A7SBv+AtQJaKoiSTSV3XsSa6riuK4vf7V69ezfP8mTNnyuUyfJg0wZLneYxd3rZtWygUymQy\nhw8fHhkZwaDL9evXb9q0aWxsLJVK+Xw+uieRMrYyqQuy/AmM6juq/qoEBNbkRG+9W13zQls4E9JK\nYFadjl8WxaPUGBkICLeNp/YSVVU7wdNkidrDU3eJLggeCknTtLbxtLv1lpvA2ILGx9LBhAoEAjSn\nIxKJvPzyy/Pz88gzRNeJdDqNEl1cqKoqOADPmhAC84sQgpwLvBEeEGvJ7sOxA7/AVoYzjVIOnmxP\nT09XVxd2CO6JmxBC8BpZlnO5XDKZRDdeKqo5KgUmGirYotFoV1cXbWyvmmlfuC1NwmTN7oiGWVKG\nf4J6I5FIX19fIBCIxWLoSswwDP4Ltv7Q0NCWLVuQoPHzn//81KlTc3NzcA5VKpVwOIxx1cViER0g\nEVpTLdG4lSnLn8DUhUEUK29VEZhaL6ximHEReiqvVdBV2rAugdWaF43w1DrKaglsSXiqdDS0Rid4\n6ho9neCpu0Sd4KldIiuBLRXP67xDLyfRNA3zGInZyh1+v3g8bhjGwMCAIAgnTpwoFoulUqlYLPp8\nvp6eng0bNhSLxfHx8dOnT5dKJYS+KAvizqVSSdd15AoahsGZ8Sr01IADUFEU0Ab8urB1kKwomLNd\ngsFgf38/OoOATmClUfzohwvm48yUK7TbqDrZgCFCodCmTZtmZ2dVc4pKqVSqVCroNQy6RYtCzJzU\nzcwgwEPOhaIoMEZR7oZDJJI4eJ4fGBi45pprRFF85ZVXzpw5g9YeKCEAPPhdYTVWKhVYbDQFcSV7\nuVcEgVktjOaHeuqVevwLX2h+2/vuvbeRM0oxazKsp3iq01vBoy50lEmStCgeQsjuXbuaOMeskGCB\ntY1HVdXawced4Km7RJcOnkXvvGykdqpvtVQqm+bnsWhYH4/HQwjJZDKapm3cuNHj8UxNTWmalkwm\nKRvZ7fbu7u7+/v7e3t7XXnstkUgwDAM7hud5MAfS+XBMoT5DjuO++a1vNUd044c+hAeKsuienp7h\n4WF0igK3IR9EkiS8AMl7eKzwWyIDAv5DVVURx8JfSqWSz+dbt27duXPnEAn7p3/+5+Z4PnzLLSAe\nbKR8Po/cE2Lal4o5vZrneY/H09vb29/fPzk5efjw4VgsxvM8asvA1hzHybLs9Xp7e3sjkcjZs2dR\nEgfSEgThP370o0Uf6zKedbn8CUwzu9E0NzXoa1qhCkIIXnbfvffWOqMU076xnuKpal4UTxWnfvZz\nn2vxk0KJP7B7d13nmBUPCOzSwdNoiS4RPC3e/7KWxanLlBMnT5KTJ90uF1IMisUi8tcNw1izZo3f\n75+dnUUeBMdx5XIZ8yrdbndPT09/f7/dbn/11Vfn5uYwKgWJGLo5YYsGojRN+/t/+IdW8Hz7uecI\nIXfecYckSU6nc3h4OBqN6rrOmM07YGmh4SHlyEqlMjs7yzCMx+Ox2+2IaSmKIkkSpn9RDyfcm36/\nv0U8eNnNN90EKyoQCBAzO181B1ijAoyY9Wejo6NjY2OgfMaczInmWFgN5BnRUS/YmflCgRw+3Aok\nPNxlSWPLn8Col2lRNf35xx6runbH7bdXHdIZhnnm61+nLwCN7br/fqsqVFW1Vg8CAGdpg7Qonocf\neWSpeAghn/3c56rwkIXaGR6YNvDULtEdO3damaBtPHWXqA08rSwRCG/vnj2t4yHLXWrZq66ys76s\nUCySYtHv87lcLkVRCCGIhCFBEYnduVwOHjZFURKJRDabRRFYMBiEF47juGKxCJ8b4lhwBX/r29+u\neutPPfRQPp8Hw+lm86cv//Vf0xd89WtfI4R8cu/e3t5euNfADdQDrKoqOAxt7wFAUZRIJOJ2uzVN\nQ10aISSVSqHHLi7kef7XNm78tYV4PvTBD6JAGwE5p9MpCMKXvvxl+gIYjh+44QZCCM3+oO5u2h1K\nkqTp6elkMolPxzBMuVwulUpOp5NlWXAnOE/TNNasvRsbH69aH4elbKDRYy2Vy8uPwxhjuQcA9+3b\nh/k6dAAPFRyvisWioiiPPf649arbbr1VM6f+0BgPVXAcxz37jW9YX3//ffchGIv8KNEimIZHf7HC\nqIsHPx959NEl4eE47ulnnqmLh/6kgv6hneDZuWMHjTwhWtAcDyFkz4MPNsJTu0QYaNsET9Ujq8JT\nu0SiKLaNZ/v27e3uvospVAU3F6uaW1TBGYZRXlgz2xeN5nI5WZbXrVu3c+fOeDw+NTUlCEIul1NV\nVRRFv9+PZrW02he9fWdnZzFPi/bVRRrh89/5Dr35n/3pn2azWVyomVNU0DAXrnXDML7+7LNWPCeO\nH+/p6SGEIIeCEAKXoGo2bDxy5MjExASqa7xebzgc9vl8TqczFAr5fD6e59HUyuPxyLI8Pz+/afNm\n6/1v/NCHiDnWWdM07C6v18swDDIVdV23KocPffCDMCupBYatpSiKYRiYsQLSQn4KLDC3240YGGhy\neHg4GAz+0z/90y9/+cuKaYdB/r//8T/GxsZmZmaaBGuX9IgXXFgqtf7iiyLLn8Beeukl6EHrT6sU\ni0WrKrzt1lvVhcnZ1uO8NT2B53nrTr3/vvugCrH5rBrQ+rMKSS2eKtvrjp07UXfZNh5xoWCWRCd4\naPCpClLbeGqXCCMnGuGRZXmpjwxxb57nv/b00/TCvXv2tILn13/91zvaghdJWiGwpbKX2+3evHmz\nKIr/9z//k/7d43ZLkvSWt7zlPe95z9zcHIYjw7QiZo0XzA5sAMzQSqfT2WwWzxctcVmWfe755+lt\n79i5E7ExURRZloV5ROezEEJUczRzOBz+m7/9W3rh/NwcnjVqftGughBSLpcnJiaOHDmSTCZVVUWx\nV1dXVzQa9Xg8fr/f7/e7XC4k/cMe8pltCQkhn3rooZmZGRCnKIqGYciyjM2GhoSFQgFkXBW6u/22\n23Rdx7cYHMwwDGq0kdLJmLPK8NHw7ugtifTO7u7uUCj04x//eN/PfkZv63a5vF7vpk2bZmZmRkdH\nm2cbtcdhlz6BLf8MK+of0yxlQ6pFrKrww7fcQm2R5oKXffiWW+i1jz3+uFKTHVf1vlSa4LGyxc4d\nO5aKZ+eOHXXxVL1Xh3gWhbQkPLVL1ASP1fbauWNHi4+MwqZ4CCEPP/JIK3heh115SQhVak6HoxWl\nxjBMPp+HceyysGO+UBAEAUXBiqIg4AQnmCRJ6XS6VCppmoZu64ZhJBIJxMlEUWQYhroQrex12623\n0tOMZiYHgs9CoRCGFzMMg7buHo/nE/fcQ6/t7umBHYOOUAhlzc7OHj169LXXXpuYmEBCIOZvjY2N\nHT9+/NSpU+Pj4xMTEwAGB7KVvebn5tasWdPb24v8fkIIGjDCekPOPcMw+NSapn3ghhvgPySEfP3Z\nZ0FdDodDVVUYarRNIiEEiZGapiEpEVfRSQhgRI7jrOwV8Pt1XUcldStGiPURtx7vvPRlpRAYdn+V\nhlJV9TMPP0xf+eFbblEsA78b6cQqa8DKYZ9/7DGqCq0akL577S9VeFRLysDOHTsQ6VkSHkVRqI6m\neKogXSg8dSG1gacWSRM8NO7VIh4rpCo8xJKk2gTP67ArL75Y2av1q0AqhBCGYXq6u+nf4eJjWdZm\ns2maRodVQr3CAkb3WwxbwUNBAjoMLGvc6xP33NPd3e3xeDDsUZZlVVVpfodhto/Ci1VVDYfDv/mb\nv/mDf/kXeodAMCjLMn4vFArT09Pnzp07cuTI8ePHZ2ZmstlsNptFk458Ph+LxcbHx8+fPz8+Pn7u\n3Llz587Nzs6GwmF6t/GxMZ7nV61aFYlEvF4v8j4AAwjhQseeQUdEGFL0Dt/81rdkWUbYz+VyYWXw\nuQghDocDlEw/FxIgZbPijRBSLBbp3dasXs2a89g8Hg/cjK3I8uOw5U9g8ClpDYS+rDl7oWFoKxxW\na9xQPWiVRnhoTt0dO3c2Ya/meBRLa+rPfu5zrxMeK6RF8dyxc2dzPFWQFsVDzC6XS31kbeB5fTbm\nxZT29Jdhlmd5PB74ZkPBIP4rk80aZvt5WZZ5ngdjBQKBaDQaCASg3ymTUYsKjXet73LXnXc6HA50\nv3U6neFwmOM4tBZTzcJkePkEQdDN5oRoVzE/N0fvo+u6JEnFYnF6evrIkSMnTpyYmZlBvyhN01iW\nBZEYhlEsFuPx+Ojo6OnTp0+dOnXy5MmzZ8/S+8xMT7MsqyjKunXrNmzYgEbAujmFjlYUIMxGcTIM\no2najttvp/ehrnXV9F6iqRshRFVVwzAkSUK7KSCk+1bTNI7j6M5fv24daxZQa5qmKIrWlpNgeXDY\nSiGwupqROscQRKG5bU1O9LWqGfv1tltvxa0e/8IXmvNEK3juuvNO6i7rEA+p4dTW8VjNLyueJpAa\n4am6VetL1AhPG4+sbTyvw668VGRJ5heUMsMwaC+LNhO9kQj+98cvvohu6729vYFAAEFHj8fj9Xq9\nXi9sDpgagjlwGe0wKpUKzVC/8UMfKhQKs7OzcPTlcrlCoQCeo1k5MFPsdjv658JQ03U9GAw6nc6p\nyUncqicSKZfLIyMjr7322smTJycnJ+fn5yVJstlswWCwp6enr68PXQcHBgbQpHFubm5ycvLcuXO/\n99734iaZdBrUK8uyx+Pp6enx+/2apmUyGXAVwzButxudgnmehzGEfA388sEPfAC3+sfvfpeYKcqI\ny+q6jt2omZM5UbasmYOY0aSRNwd1QnBQQBa+KIqFQiGXy71OT/zSlxVHYFa1SF9TFWKhClGqJ1Zt\naL2Q3q2uHoQgYW9RPFpN1KcNPNRR1kg1L4qHVgfv3LGj9SVaFM/nPv/5pS5RJ3gAqRM8r9vevMiy\nVF2GkuR0Oj0/P49/QtvSF/T09Lz5zW8eGhqiCRGimS+OamKWZbu6utCJw+l0+v1+m81WtpgCLMsW\nCgW0T+zq6hJFEX3cWXPAt67rcP3R20qSpChKJBJB0bRusZhjsRj8gclkMp1Ou93ujRs3rlu37oor\nrrjiiit6e3u7u7sDgYDX641Go5s3b966dWtXV5e1s3sul6P5Gpqm9fT0DA4OIvJEg3yqObqTM2e+\n8DyP4BxS4endJLPxFSFElmVQI8MwGMji9XoDgYDT6YQT0mazoWe/x+P59Gc+gzusWb0aCS/4mHSw\nGV3nVmQ5ORJXKIHpum41v2oJw6oQ4YzCz0baWdM0avQ8/Mgjjd60ueDyu+68kxocneChmuXxL3yh\nEzzEkgjThDNax9PkoVwoPHWXqG08r8/GvGjSidpSVRVql5gZni6Xa4uZaE4b/MPkQv66pmmKomDq\nMfLmYT0YhgHF/f0XXsDlN914IyEEiht3EM1pmbBpkB+hmB5yECohBL1xCSGlUslut+dNi+S67dvH\nx8dnZmbm5+d1XV+9evWqVaucTqfP50PxMhp24M7gJGvp+re/9a1cLlcqlcCdoCLQlSiKLpcrEAj4\nfD4KCcmEWBZZlpGpr6rqH77//bjh9194AQPACoUCsVhjoihyHKcoimEYLpfL7XbTrHqXy/XBD36w\n9inQbYlmKCjEbvuxXr6y/AuZcU5cVBvWcoZsafJrmJP06LVVFa+LKkRjodS+4NHPfpZeWwvpV4+H\nLtEdO3dqlqHVdZcIX8VF8dyxcyey2Ou+XYt42ntkojlBqg08r9vevMwEyd8DAwP4JxI0DMOAQUYI\nee/v//7//dGPJHPAlSRJuVxO13WMZ3Q4HIqizM3NiaLo9XoNwygUClXmF0iC47hUKgUC0MyeSYh7\n4QXQ+OVyWVVVh8OB+mjD7LhhfWSxWAzDtwYHB4PBIIae2Gy2iYkJm80WjUYRfBJFMZVKqaqaSqVo\nYdnc3Fw4HK5UKoiW5fN5BJ9AQmAyQgjy4zEVBROWNU1DP0N4AoWFE71Zlg0EAt3d3UePHkUVR29v\nL6aroMRN13WWZf1+P75W9OOEQ6GwIKDkGW5YNKnSFnrXV5SsCAKrq6/pC6jCqtWJVCFCG2JvEbML\nHFWFtRq27jvW/b0JHgqpbTw7br8dTSjqMkRzPNRfV4unFhKCAYvioR+zFk9dGNb/otfuuP12XZKW\n+shUVW2C53Of//wn9+5thOd12pkXV9qLhbAsOzk5uX37dsMwUKukaZo1BnP48GE0jiKEVCqVZDKJ\njhjoGiUIQqlUymQyUPTgIXqt1+vFlC/wRLlc1jQNQSb0UgIfqOZ8V+h3/J0QollmVFLBvJJwOBwK\nhTRNK5fLPp+vUqmMjY0h0yQWi01NTXV1dcEBaO3EPTExoev6wMDAqlWr8KaiKLrdbtQ40zwUmj1I\nGR3+RkmSUHBdKpVuufnmf/jmN7GAbrcbgUBN0+Aw5DjObrdv3LiRZdl8Po+ejUgvFAThN975TuAx\nDMPlcmUyGetH1jQNPobaThzNn/4y8B+SFUJgxLTDrIL//ehHPmLkcotyBs5Etdq56sB++2234fhW\n9+3q/l6Fh9QzGdvGQ297wfFUQYLSaa3G3eYAACAASURBVB3PY48/vnfPniaQaoXWfrWCp3aJaqmr\n7sesi+eC78nLWgzD8Hq9brcbJq9mtjiCjI2NwWFLVx6DPzRNc7lcXV1dPM/H43FJktLpNFyIuPCB\n3bv5YpEQgp0DryBIBQaHYk5SJqbRo+s6DJFyuYy5lIZhwJv36iuvXH3NNYQQlF4hbzCXy6FNPjHL\nq6empvL5vKqqGDtJ+1RBstksLBtd1zE3khBSKBSQ0A/bETafLMtob4jJlnhfgFEUxZr0j2ZR2KUo\nf1ZVNZFIZDIZOAzT6bSu63CZdnd3r1q1iuJBEZ6u62gpout6MBj0eDwwVZsXMjeSy72/1IogsFo9\nXvW/tWKlDdnMZCVmLmwTW6H2zlUwmuNpBKlzPKQeY7WNpwqSJEkd4qmCVPuC++69F50nW8FTu0Sd\n4HlDrKLr+vz8PGxcRLys/ytJkqZpiHVBWWtmfy+UiOEX2mqyYjamgjeMM7vuYuVhpmCQGGO25YU3\nmBDicrno487lcoZhaJpWqVQymcy5c+euJoQQAu8lfIOaOezb4XD09vZOT09PTk5qmuZwOJBRifmQ\n1k9aKpXOnz+fy+VCoVA4HM7lcmAR0CryRxClkyQJBybDMOjIZphWvDkAmpjdTFA9VqlUkGMJQpqe\nnsY9dTMXN5fLjYyM3GbiQVDQ6/WiJTFWGyG0tp/mZc1eZCUQ2KJiNGAdq1pE9q312F6rAS+IsvvI\nXXcRSaqF1CGeDrEtukS/gvVp8tFaWaJGeD5y111feeqpToCtNNF1PZvNwhKCV826qjgrqOYcu3K5\njOAQTBlZlq0PwuVyhUIhXJjJZAyz5BnZEHBNg9IQdsKbUn81a46ETiaTo6OjaKVYKBRisdicWRCG\nq0qlUqlUMgwDNy8WiyhNy+VycBhQ5JLZafCPPvYxVpYJIalUKpPJzM3NoZV+Npstl8swg3Rdl81i\nZNHsHI+iMerEhvOTcozL5YLPkKa/q2ZvDni5YUGC47ECuHBo1SolkYCjklqiyNhcycesNwiMWM9c\ntP0r/R3nd+wn1jKi1/rK2vu0LV956qnbbr21FlKHeDrEtugS/QrW5wt/+Zet46ldokZ43mCvpQq6\n82FtYX5Z41gejyeVSqGiGU+BtXRhJ2Z2D6JiMGXobTXLPEnN7OBOXb6EEDgV0ebD6XQiyxGEqqoq\nSC6Xy6XTaaT54e3gPwS7IIMDBpmu6+A8AINRSPH83RNP3HXnnfgdWZTxeBymEuJwaHtICKFpJrqu\nq6qKWi6wESxIkDFuRT+1bg5xhgceTm/EDuEPBJVSPOPnz4uCAK8p8hUZhgmFQkjvbPvLdbm7EJd/\nGr1VbdVqsa889RRTT2hgFqcndNDBP+uqRYi1d23Ve1Up2UZ4rH/sHE+jO3eOpwrSUvHcd++9zZeo\nFg8uaRFP7RI1x9P8kb0hVpFlWTezOg3DoK11IW9+85tR6ov193g8MEGQpO50OuFAQ68NUA4uRHYf\n+nTQxsogSMkcl4yQEt6OeufwTxDM/Px8JpNRFOUbf//3uC3YxTCrgwEGdIj0RQTJQEuiKFpLhsvl\nMnzjAKMoClyjhpl1BXuLDm3By1iz7zDeGjYfTS1xOp0Mw6jmoFoYWODjUCgEsne73aFQKBqNDg8P\nV01CgGsRTRRxCdfZyLrLmr3ISrDAGIuarqu5GDPhm2YfcJap84QQfFEZhuEtgpdZL2TqmQXWt6v7\ne108tZDaw0MTgtvAc/999yFvoi6eKkh4zaJ4mBpmagSp0QtaxFO7RM3xNF+iC7shLxHp5OhtGIbL\n5cpmszQWRUyL59prr/X7/f/2b/9GCIFV1N3dDZdXpVLBJfC8KYqCWjFc+HdPPIGWbOAAXdeh3Gnb\nDphfdrtdlmUkhiD9Hbl/iHoaZod4ChUMBBtRlmXsgWAwGAwGMcSEWlGw/6wp74hvwRENkqCFYthd\nCES5XC7OHN0imnNSPB4PckbAx5RQQZYwLtFoGAQJ5BzH9fb2rl+/PhKJlMtlVF4Tc3adz+fDp8AK\nUPoXBKGycMbNypEVQWC1BgFrydip0oO1qhDOccbsYVOlE61q0XrP2nes+zv9y+5du5C5vqhqbg9P\n1ZsuiodeXounFhJrNkpojocOlqzFUxdGXTzPfP3rt9x8cxuPrBYPvefuXbtsjfG8TjvzchSGYRRF\ngc9KlmUodGpevOmqq/583763ve1tb3rTm/L5PByJSFsvlUrxeBy/wIyAIrYSBs/zeGput1uWZfQt\nRLMJZOsh75EzEz3y+bzb7cb9aQ49jQ9B8MQdDgfy+B0OB1pJeTye+fn5VColm52CYZ+Jovinf/In\nX/zSlwghPp8PdWy4odfrxRBq7C5d1+12O8wyh8MBZsUcanw6wzBwQ6uFlMvlUOyFYm3DTJtkWTYc\nDq9fv97j8RSLxampqfn5eXzMfV/84p/86Z/iNWjpi9YBgiBIkoQsyqU+x+WRQ09WCIExCw/skAcf\neAC1w5xFqB40zB6drJmKjX9CFcIRUaUWOTMS8OADD9hq3q6uRq4SXP61p5++7dZbrZDwxW4bD1lI\nQp3jqV0iuHo6wcPW8GsjPO09srp46Gyw5ngu4G5cBgIOow1tOY6LmRkT119/PVpXXHHFFYZhOByO\ncrnMMEwmk4nFYpIkdXV1ZbNZsALLssVisVgsvvf3fu+Ff/kXQojX61VVFb2dMCQTwSeWZb1eL4gT\nbIQgHDrZy7KM1yChHEVUwPPxP/ojo1gk5kxksJ3L5UKbDzokEzsTzRXRngOXf+Wpp265+WZipjv6\n/f7u7u5UKhWPx+FIxIV0Y9PsFYZhRFFE2r2+sJ0mbbqhqioy8kVRRJlaJBLheR4TXlAHzbJsuVyO\nRqO4dm5+fqC/n+d5fEY4J8GIK3aXLn8Cq6ubrArx2W984+abbqJ6kKpCxgyrYLNCl1FGsepoqEUa\nAGvyjs2FYq5SzTQrtz089917by2hdoKndol0cyLz64qHZtK38chq8SxKqLXrsDyEFrG27UXkeZ5m\nuofDYTI1hb+Pjo4ODw9zHNfd3Q0yKJfLxWIRaYQcxyGFged5LCzyEehp40tf/jLyJpD4AOchrA3o\na57nkVXPsix4CPckhHAcVyqV4HaD/UQsDTvQvSIQCASDQXQpVBSlVCohIoV3BOC+vr6I2Z6YEOLx\neFiWhXWFomywEc6UiP/RiBfK2jizexYcjzzPU//hjttvF81Ph3ForJkEr2na9PR0LpfLZrOlUone\nmWXZtWvXUjywMrHh0fsR1dxLenztTdK5NGW5fTlrpa5KqtJf3/zWt6hqQ9MaOpy3VuhgWatOpANY\n//zP/gw3r/u+jWwLXLJ71y7c5OlnnrFq2zbw8JbqHGpwXEA8TSB1gqcRpFobrnU8gFSL5+lnnsGt\ndu/a1RzP67MxL2ORZRmd4BVFOXjoEP745uuvR6eomZmZEydO/PSnP/2v//qvn/3sZyMjI7qu+/3+\nvr6+DRs2bNy4cXBwEJ2f8Misj/Wpr341nU7H43FVVT0ej8fj8fl8brcbWX/YCYQQlmVRCwXjA7ZU\npVJhGIay10fuuguFZTDUeJ5Hh1yI0+mkFpjL5YK1hJvncrlHzUapf/fEE7izKIrZbHZkZCQWi8Hp\nZ7fb0a4XrwSpwBuJyoF8Pl/lz1QUpVwuo0UnPUUZhpFKpcbHx6emphKJRDabpZRss9m6urpWr179\nwve/jztMTE7KspzNZrEImUwGRXKv37O+xGX5W2A4tVmP6rRm6FMPPfS/Pv1pvAxjC3AkRNor7d1A\n9wc94FvtDDo4FUI1uFWPU9VJHS918VhhP/uNb+zcsQOXsCy7VDxUOz+we/cCQAtVeXt4Gi1RJ3iq\nIOFnLZ4Hdu/GYKRW8FghoUtCLZ5WHlnHe/CSk06MMPjiotFoLBaLJxL07319fR/5yEfm5+eff/55\nzuzLjqRBl8vl9/sxzhiv9Pl8tAuGoig7d+ygTyQQCKDpBnq3g4GQSYFcQWLO+sLrkdCB04aVLZDc\nUSwW8QKHw4GqYcMwEonE0NDQVVddhUGXDMP4/f5gMOh2u1mWjcfj1umRTzz55O233YZyK5/PhzQN\nFO8bhgFvnmYOPkWreGTYI/pF474333STrmkMw/A8D9tRFEUEsTRztBjE6/WCYru7u51O5+zs7Ozs\nLMUTm5tzOhx2u93n88E25RYWADSX5WR+kZVggdHDNT3F82ZTNZ7nP7l3L1729DPPWA/yi1o8VmVH\nv3u77r+feqj4hVkDjX5phIeYDUytkNrGUwWpPTwtLlETPMRiOTVfokZ4rJZcG4+sFs8n9+5dFM/r\nsCsvIVlqPJ9l2VQqxbJs3sw8JIT09/UVi8XZ2dl0Ol2pVGBqgFfARrFYbHR0FBeWy2XkuxcKBZvN\nhjHHH/voR3Grhx95BI2UEEULh8Pw+zFmXijOFqzZ9gIGliiKhmH83RNP4Cb/63/+z0AggFQLTNVi\nGAZphygcjsfjXq93w4YN/f393d3d/f396HCBt3C73Q998pPWjwxbXDdnLnu9XuARzZxJpGxwHCdJ\nUqFQwCJ8+7nncIcb/vAPcajied7hcAiCgBgYWmkIgmC32zGrZXBwsK+vLxQKob1vKpVKp9NTU1Ob\nN22yPjIwJSKL8Ja/Hs/60pdl/uUklviNVUNZXUn333cfXvn0M88014N1dSLVhvffd59Qk7xQqxkX\nxbPXzJp98itfoZDawEMIEeoFfqy/LwnPkpaoLp69e/bUxVO7RJcUntdhV158sR7Al6rXOI77r//+\nb/rPLZs3+3w+WZbT6TRMXmSKcxY7LJvNTk1NjYyMvPrqq4cOHZqdnUUSPLQ5+hNS+dKXv0yzDRmG\nwWQcQoggCJjFBTLgzBwKnucVRfnb//N/cPlnPv1p5Gvg/jazpJ3jOCQHsiwL4oxGoz6fz+fzeb1e\nURRRHI2xnENDQ4+Z/ayffuaZrz/7LI4yLMt2dXX19fUhIzGfzxeLRUEQaP9ioFUU5bnnn6efCCYX\nnJw0NAsCs9vtoVAIk8n8fj8mUOfz+Ww2G4/HS6VSLpc7d+5cPp9fNThIbzgzO4uAotXf0FysT3l5\nmF9k5RBY7UGer+cA/NrTTz/7jW9YFR9yk6y/UHn2G9+gaWzEYjBV6cRatlgUz54HH7RCag/Pngcf\nbASpQzxVbNEIjyiKLeKpi6oTPHUhtY3nwm3GS0uqOKxFGmMYZs6cn0IICfj9oIdEIjE9PW232wVB\nQIluqVTCSsLnhj6ECDuxLGsYBs/zSMeXZblQKNC5WYSQp7761S99+cvxePz8+fMYxSIIAvz8aLdR\nqVSQMSFJ0l/97/9N2euRhx+G37JcLsNsgmOZMwuf4ZoGbfA8T8zwgc1mQza81+v1+/1o0vHHn/gE\nhfT1Z5/VzdEwIGCYQYqi4GxULBYTiYSqqt/93ve++73v0Qv/6GMfW7t2bX9/P4y/XC4Xi8VkWe7t\n7WUYBuZmsVicmZkZHR09f/78+fPnMbqFECKKYjKZHBkZQbPHQXOWDSHkxMmTxCx5XPSpLUv2IoQw\nLbL35Sv79++ncw5li6CmBF8zVPh//rHHrBfesXOnvrBnOc3wtupBQsiu++8XLIIM3Sq/Fv2FwmiE\nhwodublUPISQvXv2WCHBe0bxeDyezvHcdeedVWEqawb8U1/9aut4apcIh9Ml4VnSEi0Jz9VXX73I\nJrskxdpUoonU8lYTBVf1YofdTggZGBjw+/2GYWzZsuUd73jH6Ojo1NQUy7KSJHm9XqTkYTE5jisW\ni+jwi2CP1+uVJAn96W02G3bUd/7xH63v8sjDD2Myi2DGg4vFos/nCwaDn3zoIesrP7l3b6VSCQaD\nvb29o6OjaCsM9xrLsqj8FUUxm81GIpE777zTMIz//M//pOMleZ6XJAlhM4SmEFut2sx/8ed/Ho/H\nRVH0er3QHmC1fD5PfYZUPnLXXZIkbdu2bc2aNS+++OL4+LjX602lUvl8fs2aNZguLYoiIrhYJRSW\noXJg69atsVjsO9/5TqVSsZlt73OWmdF4Co1ciEt6uHUuX2gZX4Ky/AnswIEDdVUh1YbYgtipSBCo\nlSYtXx/YvbvKPnA6ndiIdXViI6qo0s6A9JmHH+4cD9XRFBJGMV06eGqXKJ/Pt4KnvUeGuFfreK68\n8sq697nEpUUCgzQyv5oMjgqHQsj2DgaD3d3dkiRFo9H3v//9qqoeP34cHjOYOMViked5pL/DION5\nHpORBUGYmJgolUo9PT1Q0MgLr+IMKnsefPCRRx+t+1+fffRRQkihUOjt7e3v7z9y5AhcecSck2Kz\n2UASILkbb7xR1/V//dd/TSaTDMMUi0WUncHtKcsy0ixZlpVl+Vvf/nbdN/3YRz/6xJNP1v2vD9xw\nA8MwXq83k8n09PTcfvvtU1NT3/ve99CACk1JVFVFDA/fQaQ1lkollMQ5nc7t27f/7Gc/+4//+A88\nzUqlksvleJ7PWmawtfi82jC83iCwiy+vvvpqXVVIFSKd/I1DkKqqdJZjc9m9a5fVzQVPFCWwujrR\navE0wgMwVki1psaS8NQaGZjL8HrjIYTs3bOnFTy1S4ST6SWCZ8uWLS3e/5KSJREYpEUvotvluuaa\na+Lx+OTkJLIt+vr6VFWNRqM333yzz+d77bXXGIZBtrcgCMViUZKkbDYriiJyKwghSF7P5/OZTIbj\nuCuvvNLlcp0/fz6VSqFnUjKZpBVUzWXnjh0Oh2NwcBCeRuzwbDY7OTkJzxvLsoFAIBQKoT9Id3d3\nIpG46qqrPB7PL37xi3Q6LUlSJpPRLcPEs9msoii6rrvdbiRo6LreiFar5P3ve5/dbkf24+DgIAqW\nP/zhD/f39//whz88cuRIqVTiOE7TtHQ6LYoiWvInEgkEyex2ezAYTCaTa9euHRgY+Pa3vz02NhYO\nhzELtFKp+P3+1atXz8/Pnzl7thU8pF234aVPYCsijd7q6aIxT8rcOPHRNFyO4/bu2YNL6jLZ7l27\n8GKbJVpTVyda/2iNrzTHU9WNQtO05ngIIQ8+8EAreISFwZ628XzqoYeQN4xWJo3wcBwntoandol4\nnr+AeCi1t4enpX22LARqbtEjvK6qhJDBwUFVVScnJwkhbrebYZhYLHb48OHrrrsOpIXuTcjvYBgm\nEokwZhe3SqVSLpfxfJH+t2rVKp/Ph5x7NPwNhUIP7N6t63oul6PphVZ58IEHVFXNZrPFTIbjOFVV\ne3p6Nm3axPN8KpUaGhrq7e1NJBL5fB6KGK2E16xZ43A4/vmf/zmZTK5fv35oaMgwDNQOAw/6ffA8\nj1QLlmWRCTI3N3fzTTfZbDav10urzarkAzfcwHGck+cJIdg8OHhFIhFY829961tDodDRo0fRDp9h\nGKRpBAKBcDgM76XD4cjlcna7fWhoaHx8fGJiwu/32+32dDqNujcUTRNCXE4nvhcX0Oq6vGRFEJix\nUOh/QQ/ComfNIcK0lkjXdYyZt96NYRjaRaIq44DqPtFSS2RVkXgBpYpGeKzamTMrPJrgYVnW1hRP\nI2kbD12iTz30UFUSVHt4apdIEIQLgoc+Mr4my7F1PB3vwctMFtV6sK7C4XA0Gp2amgIBCIKQzWZP\nnDixfv16QkixWLR6xmArK4qCzBosrCzLtIVuJBLhOG5oaCgSiaDGC0OfWZbN5XKfuOeeRCLh9/ud\nTicyEp1Op2hmQAiCgG+xz+dDmqIoiul0esOGDVu2bEHi/sTEBLL2h4eHUafl9XqDwSDP80g7xJ1R\nYsya3YRRcIbcE/N7z1YqlTt27gTPwdmIm2ia5jCMcDgsCAJsKfgk3W73tm3b+vv7U6lUoVAYGhqy\n2WxjY2PxeBzZKLC9wuEwLEjDMDRN27Jli8fjOXnyJDwB8XhcMWeD9fT0gF9p6duyJ6pGsvy/nNgQ\nVjVt/V9KYDjBWdmr9pIq7clainatjqlaVWj9L6thURePVTvT1mqd4KlrZHSCp9EStY2ndomsx462\n8VghQSu1h+eC7sdlIlC7WB9Jkqanp/v7+/1+P0qs3G438ugYhkEsR7F0MrTZbIQQjM7C41ZVNRKJ\noG4M475gisG9HwgEhoeHdV1PJpOFQiEYDIqiiB2i6zp+QWagKIqpVArZiel0Gne22Wx+v9/tdg8P\nDyPHvVwu+/1+Qkg6nVYUJRgM+v1+QRAYS3Z7MpmEa7FQKGQyGYBnGAYTkzmOwyUI7DEMg74bSL4Y\nHBxEbCKTyQSDwY0bN1511VWFQuHYsWOJRAIp9aFQCJ8Ub4FcfJ/PZ7PZwuHw8PCw0+k8ePBgLBbz\neDzoBgLm5jhucHAQ6fs8z7fRSmo5yfInMKoKSU13CasFBudhewTWotFTZfE0wsMs9GcCXod46qJq\nG89SCaxFPMJCC6xzPKQBgS0VzwXbi8tFGIYpFouZTCYUCgWDwZmZGTwCu90+Pz9/9uzZd77znel0\nOpFI2Gw2WCF2u93pdMJuAD/Br8hxXKVSwX3S6TQeYigUCoVCsiwfPXp0amqKEALDiOd5GEmCOdQR\njxIvyOfzExMTSFZEvgbyMmw2G9pQrV69GgmTs7Oz5XKZEBKLxZLJJILWPM+HQiHa2x6WzalTp15+\n+WW8Ke1zWC6Xu7q6tmzZIknS+Pi42+3mOI7WFOfz+bVr1/r9/v379+dyue7u7kgkwrLs4cOHf/nL\nXxJC0CzYZrOBzCKRCBohIs9QkqTe3t63vvWt586dO336tCRJYHHD7FuPpI9yuYxkzou4DS4FWf5f\nTsHijKrSa6xZXV/3LN8KYdQ91MOFaHVDWX8aC6UWT6150TqBNTcyrGq6EzyNlqhtPLVLRJ9aJ3hI\nDYG1h+dXsk8vM6EZGb29vTMzMwzDJJNJv9+vKMrx48ff/va3b9iwIZVKEXNcFiaP4AGhbjeXy83P\nz0uSNDAw8La3vS2RSCQSCYwjiUajCBSNjo4mEgm4IlmWxa3ATLiz0+nELGObzYZ0YjATKrTwxOGH\nVFV1bGzs7NmzPM8j2U+W5ZmZmZMnTwaDwZ6eHl3Xy+VyMpksl8sej6enp6erq2t6eprO3CKE0B5R\nq1atete73iVJ0ksvvTQ3N8eyLChQFMX5+flEIjE4ONjT05PP5wcHB71e79zc3MTEBCCB6gCpVCo5\nHA6n0wlIuq7D7DMMY3Z2NpVKCYJQKBTQQZEQout6b29voVDIZrM8z6/kPvSQ5f/l5M1ZJBCmRgyz\nBWcjbWi9WyMFbdWJ2MpUFYqW9oNVerkuHqqdKSSO4zrBU1c7d4KnyRK1h6d2iQTTcdchHnqHKgJb\nEp4LsQ2Xm+i6ns/n0+l0T09PIBBIp9MIg3m93mQyeerUqfvuu2/t2rUHDhyQZdnr9aIVoSAIdrsd\nSXQulwtZCQMDA9FodN++fXh2Xq83EAjkcrljx47Nzc0xDGMtf0ZASDZnWsLSYlnW7XZXKhVkErpc\nLqh7w+wGgsGVPT096XR6ZGRkeHjY5XLBWpqbm8N+o7yoqirmuUxPT586dQodgcETqBVDIQpmsqxd\nuxa1WShoA3GePn16/fr1vb29p0+fPnXqVDwel2X57NmzmUzG4/GgVADGE1I8OI5TFAUTmX0+HyKL\nP//5zzOZjGj2qocR1tPTg/zDTCbzhvlFVgKBVSkgZuHkX5ZlsctxjmuPwFgzRwA/q3iiSmpvWIWH\namcKaakEVoWnuaOsDTxLJbAl4aklsE7wkHoEtlQ8be68ZS049qXTab/fHwgE0ORQ13WPxyNJ0unT\np9Pp9ODgICwGu92OXIZQKGQYxuTkZDqd9nq9V155JcdxsiyPjY1hSKbH40Gd7yuvvHLy5EkQhqZp\noiiixTsGjsAsxvwUtFzhed7r9WI/0OAQVLzNZoPvUZZlXdcFQUDHDUVRMplMqVRCbj3oECnvmUxm\nZmbG4XAgzqeZEzgZhkGGCD6R3W7v7e0tl8szMzOohpZlmWXZZDKJ7IxYLJZIJGZmZkBsQFUul7F1\n0RGf53mn06lpmmEY6XR6YGBgw4YN4+Pjx44dg83KmSNDYbzabDYMXWOXe5fOVmQlEhiz0BllGAaN\nplSpQl3XycIEbmJOW25iZFhdiFU6scocrIunKiaHHdwJnuaOxDbwNFqizvEIFhdi53iskDjLtJSl\n4rmAu3HZiGb2X9d1vbu7e3x83DAMlNlyHJfNZl955ZWrr746HA739fVJkqSqaldXF4iEmBMA8vl8\nPp8/efLk8ePHMYUrEon4/f6DBw8eOHAA/jHKLpioks1mbTab2+3WNA0+Q8PsostxHFoaImSlmcMq\ndV1nGMbhcIAOo9GoqqqxWCwQCKCdIC0lRiU16BBvSggRBAHRJlhLQO7z+ViWBSsHg8FsNut2uzFp\nE6XQGCqNq2RZhlrAcqGKkRCC/ElCCMuyDodjZGTE4XBcc801Ho/nlVdemZubQ2sSZHCAroLBYCqV\nSiQS7MLW+ytWlv+X00pgdZ1RhBBrKnbVWb5uQKWRgq5yIdZViFZsizrHqgisPTzNjYw28DRaorbx\n1C6RYPYF7wSP9Q51Cax1PG9IleBkoOt6uVxGPnoymUSHdbvdHovFRkZG3vOe96TT6R/96EdY/3Pn\nzvl8PqjyoaEhVVUPHjx4/PjxWCxWKpXQnHDVqlVwwcViMbAUmj+B9hiGgfsOGwBDvNBlkWEY8Bbq\no1EcjewMmo5vs9lcLtfg4CB647pcLnwWGEYwnjSzayLLsrihYo7cdJgCAOiIoSgKwzBdXV2yLCcS\niWKxiKzL7u5uFJ8xDINPgXdBwRkhxO12l8tlp9Op63o6nQ4Gg7/xG79x/fXXr1mz5jvf+c6+ffuw\nV5GcwjCMYRh+v19VVQQO7Xb7pV9l/CuQlUJgVXrQqg1hgVFVCFteb5pWTm9C1WKVBUb1YG3kqeo+\ntXi4mvSEKgJbKh76k0KyRunawNNkidrDU7tEoiheEDwUEsdxneB5Q2rFMAyoV5fL5XK5EokEWMTr\n9ebz+UOHDiWTSY7jzpw5k8vl61zrPAAAIABJREFU4PgyDMPhcHR1deH1SJEQBAHJiv39/T6f78c/\n/vHRo0c5s8c8LA/4CXVdB6uhgUVPT4+mafl8nhAC96CiKKlUKhQKeTweTIJ2u92RSAQDyeB/Gxwc\nHBkZqVQqIBKwIOrJ6PZAwiTmONNDpKZp2Co+nw/dRGFxGoYRDAYNw5iamorH44FAYNu2bV6vl3qt\nUQ9QLpdhk3Ech48simKxWNQ0bXh4+E1vetPmzZsHBwf37dv37//+7xgtjUtQUoZdDZuVM2MKF/X5\nXxKy/AmsqntebSMi7KoLYoFhizMMQ91ZtTdZFA/VzhQSPOZt48FPKyRZljvB07YF1ghP7RLBXdMh\nHrKYBdYinjc4rK5gJRH76e/vh2WAjSQIwunTp3/yk5+8+93vDofDExMT0LmlUml+fn56ehq2BWsm\nFqqqGgqFVq9efebMmZ/85CeVSgXTGlHF5XA4MGoEeYPIMyyVSj6fr7+//9ixY+Pj4/D04qmhhprn\nebRMA0cODQ2tXr0aeymXy2UyGVSqCYLAmtnIPM+jPSMq1bDBOLNbDTE7AqNcmm4qbFev17tp0yYY\nkdu2bctkMmNjYzDIYDjimAXjqaury+/34wP29vaiZvnEiRPPP//8L37xi9nZ2UAggAtlWcZqY4Z1\nKpWCC936FV7JsrIIrK5OhLu8rjZsFFBppKChDXFcqtWDLeKp0tFWAmsPD1/TbsMa12kDT6MlahtP\nkyXqBA9pIQbWCp43CKyuILTjcrlkWe7u7t6wYcPx48c1Tcvlch6PJ5/Pv/DCC2vXrr3++utzudzI\nyAgsD0StYH8o5pgVh8OxZcsWQRBee+21WCyGUl80ZUeOe09Pj9PpjMfj6HPv8XjS6XQgELjmmmuS\nyeT58+cZhoGzEbEupPbBy1culwGpv78fRKIoCvISPR4Pvq02mw2E4Xa7XS4XHHR0v+ESnHg8Hs+a\nNWv8fj/SSdAIyjCMoaGh66+/Hj5GpFCeOnUKVEoBuN1uVVXtdnt3d3dfX5+iKD09PYqi7N+/X9M0\nSZJeffVVlGOD3RVFQVMSh8NxxRVXYEKYYRhwS17s539JyIojsCq1iO8PdKLecRYiXA0sy1rP8lWX\nL4qHKmgKCb+0jceq3HEHxexJ0x6eJkvUHp5Fl6htPBQSXy8LsUU8Hey+5SxYfFmWk8kkz/PoSY9B\nWbB+Tp48+YMf/OCP//iP/+AP/uCFF144fvy4YRgOhwNhqnQ6TQjBc1m1ahXqeb1eLxLiYQahe2F3\nd/fw8DAhJJPJ4FEistXb28txHP6IvzscDmwYePLhJGRZlhBy7Ngxt9u9ceNGukV1XUd+v6IogiCg\nSYeqqhgkRp1++LAgHk3TQqHQwMCAzWZLpVKyLGez2bm5OUIINmQgEMjn82jAqCiK1R8jmJ0+OI5D\n1YHL5WIYxufzbdy48ciRIz/96U+npqY8Hg/P8/CIolUHISQQCHR1dXV1dUmSlEql3iAwKiuLwFCB\nUaUTaVlGI5eU9W6N/GNWZxTHcfTC5tq5Lp5aI2OpBFbXOWaFZA19tYFnqQS2KJ5GS9Q5HgpJs3S8\nXCqeNnfeChDdTFuPx+NoPgs+KxaLHo+H47iXXnopHA7ffffdO3fu/OY3v3ngwAGHwwG7hzWzwOnQ\nZI/Hs3Xr1qmpKSTQO53OYDAYjUa7uroCgQCiaH19fel0Op/Pw+ZLp9N4axAhz/NITdR1HUxQKpUQ\nQ8pms4cOHSoWi319fW632+PxGIaBEcylUgk0Aw+nw+Eol8upVCqbzdIZyvheo01UMBhEIxK8AGSp\nKEo6nUbq/Pz8PBpQEUIMczKLbgZrYaQKgjAzM8Oy7FVXXZXJZKampkqlktvtZlkWhcxo7MswDGJ4\n0Wj06quv5nn+hz/8oaqqxhv+Q0LISiAwqgHrzuNQFAUuRHVhXoBVGxo1AZVaBW3VhpTA6ir3RfHU\n6ugqAlsqHqNGFEXpBE+jJWobT90l6hyPFVIVgS0Jz+u8Qy9jAQfk83n0pF+9enV/fz9qbFOpVDAY\n1DTt+9//vs/n++hHP3r77bfLsnzkyBGke+DxcRxXqVROnjwZiUTe8pa3DA0N/f7v/35fX9/IyIii\nKIODgxs3bgyFQg6HA5XLLpdLURRMGY1Go6dOnULjdnzvnE5nqVRCSTVaIOq6jtZQ2PaTk5N2ux2z\nxyqVSldXVzAYzOfzuJwQgixBsBqtPCOE8DwfDof7+/u7uroUs8lvOp0uFouIS6HRFMuyiURiamoq\nl8tJkoSNB4MSxhxSImVZRhTN5XKdO3fuueee279/f3d3N7hTUZRKpQJa9fv9Q0NDiUTi8OHDqNRm\nWxvBvEJk+RNYlfqzClWUaoO8gEUJoyodAFdZLTCyMLUB5kVzPKopFA++MG3jMWqcY4qidIKn0RK1\njad2iS4IHlJDYO3h+ZXs08tS4OlyOBypVAo9kFDXjPbqyWRyYGBAkqQnn3zSMIyPf/zjN9xwgyAI\nx44dYxjG5/PB/4ET5NGjR30+3/bt2/v6+rxe79atW2kHRUKIqqrINoQp5vP5rrnmGlVVkWqo63qx\nWIRHLhAI4OiDcZqhUEjTtEKhkEql4JP0+/1IX5yamlJVFbyFVvSyLAtmyyhd1wkhcOIFAgFRFLu6\nuqLRaDAYBEcSQvL5PEqYqWnldrtnZmaQ+M5xHGO2fOR5XpIkSZKQ3wjXosfj6erqOnPmzNjYGMdx\n5XLZ4XD4fD5d13EHQkgkEsEnOnr06L59+2BWXsQnfqnJ8l+LWj1YpRMpgdWe6FskDBpQwSVVO4yx\n9JJgWXZRPLVGxlIJrApPlVVBLATWHp6lEtiieFpfoiXhIQ0IbKl4LtxmXG7CMEwmkwmHw36/X9M0\nOMEwg1hVVfRZ9/v9586d++IXvygIws6dO9/73vcWi8WDBw/yPO92u3Uz0pPNZkdHR4eHhyORiNvt\nRiSsUCjAJYjmAIFAAG2iAoEAuinCmMOTRc0DTJxYLKbreiaT4Xm+p6enu7s7HA6DzBRFcblccCFy\nZoGKw+FgGAbt5LED4crTNI0QoiiKz+dbtWqVIAiGYWBLoGM9DDWGYcrlciwWw+tR+4xfQI0cx9ls\nNpZlYYe5XC5JkrZu3SpJ0ssvv5zNZp1OpyzL5XIZ42bAiMFg0OfzIejV1dVFCOE4TjED2G8IWQkE\nRvVd3UO9YlpgTU701ru1Yl5YCcyq060WTxM8So2RgXNu23hqL8H3s208TZaoPTx1l+iC4KGQNLMv\nQxt42t16K0Iw5gNJ3sjm6O3tzefz8XgcKeyFQiESiVQqleeffz4YDL73ve/9nd/5nUqlMjIyMjs7\niyJoGFizs7PxeLyvr0/TNNpXF2aN2+1GrRjHcX19fX19fbquVyqVdDqNB4SHiNljaFeBSBIyAFF9\n7PP5CoWCYUY6WZb1er3RaHRmZgZchY4eMMUcDodu5vgEAoG3vvWtb3/72/P5PLrdI59CVVV4L+H3\no7+jWRQ4FcM5VVXFzXVdR95muVz2+Xw//elPR0ZGDMNA/mQ+nwfrg1yDwaAkSXNzcyiCttvtNpsN\nyS9vCGT5ExhVglXakIZYKIFZFeKiU+oxnJ6e6K3asC6B1ZoXjfDUOspAYI3GDS+Kp0pHgyE6wdPK\nEi0JT90lunTwNLnt8pNGs30htYMTDcOoVCowKTKZjCAIkUgkFAph1FY6neZ5Hhl0s7OzzzzzTDQa\n3b59+/ve976RkRHYGdlsdmxsLBaLzc3NnThxor+/3+VyTU1NSZLEcdx127fT91qz8K29hHyGkDvv\nuINhGHR+yuVyLMt2dXUNDAyAGDD32ePxwKxBfXoqlSqXy7quMwwTCoXQgAr94A3DwGguYqoOm822\nbdu2a6+9NpvN6rp+7XXX4d3/qMES/c5v/7bNZgsGg4VCoVKpRKPR4eFhVVWTySSalSABZGho6Nix\nYz/72c/gYyyVSnQUJ8xKh8MBqJioiSEyaEzV4SNbTrIiCMxqYTQ/1LdCXRC8DGqxShuCHoh59rd6\n1f7/9s40uI3rTNenGztIAATBRQslcxG12PJSUimOXJYT2+OkPKncqXFmKk6kaPMkUzOZ3LllW4tj\n59Ykk8WWnMyPJM5NYluLLU+s8pYaLyk7jrexYmuJrM2OpJAitdHcBGJHo9Ho++O7OPeoGwBBgLTY\n0Pv8UFFkd+Pl6eb39jnnO9+x2Wzl6BF/+t3vfa9KPXSAKIl6YJXpKbOJJqSnYBNNHz3ltH8NUDoO\nGo4RwyKlUVAmoaIo0WiUtrk6d+4cNTXtvdLQ0HDq1Kndu3f39PT09PR85jOfueWWW5LJ5K5du1Kp\nFL1VjIyMHDt2rL6+PhwO/4+/+ZtyZD/62GOMsb//u7+jYUZKhafSGJFIhKI/Y4yG4AKBAC1VZoxR\nv8fv93NjUFVV13UqOkz24/F42tvbr776almW53V3l6Pnld/9jjH2pTvusNlsV111VXt7O21TOWfO\nHFrHls1mb7rpppaWls2bN8disfr6+gsXLtDzbLPZqJQiY6yuro5crb29/fTp07TWTRXGD8u5X/yw\nWrUxSa/1hJY9e/bQ00m7m3P4Sz0Nsquq+tCWLebT165ZI8a47Tt2mI/ZtHGjWDqvrq7O4XA4BejF\nir7gMorpETFLqkAPiRElUSGcSdGzbu1acQ6sMj3mJqJdcSvQU04TTVTP0qVLzZ8y/aH0h3IoGAoN\nIc98jOEAMgZN08gS6uvrGWOnTp0Kh8PUi6VCiIqihEKhL33pS3fddVcoFHrttdfefvttmjGSZdnr\n9cqy/OOf/MSsZ+D8eU3T0un0yZMnjx49umHjRvMx//xP/5TL5TRNo2Lzo6OjNClFRe7b29u7urq6\nurrmzJmzZcuWoaGhjRs3Hj9+/KmnnqKahHa7vbu7OxwODw0NkZjFixcvXLhQVdVbbr3V8Fnvv/fe\nyZMn+/r6KGn+8W3bzHoe+fnPh4aGaJNlWuPc2toaCoUOHDjw6KOPfvjhh9QvpE2i6RRd1x0Ox/z5\n85ctW+b1evv6+j766KPh4WHyNi2//Gvc21HOPR2X6V9usfYN7J133ikdo2nb1i1bt4pnrVm9mqZV\n+Hu6OKZks9l27NwpHr9xwwYeB6mATcFQSFsZjesZmUzmBz/84WTpMUdnMrAJ6TE00fp16/jMk67r\nNBpTsR5zE8VisQnpGbeJnE6nGGImpOd6YRTLQpRpYIZIN26MK3E8lcelFWDU59A07dSpU2fOnKF+\nrdfrpSqFTqdz5cqVa9ascTqdb7zxxtGjR6nn5HK5fv7II+L1n3/uuQULFjQ1NcViMbvdHo/H33vv\nvQ8++CAejzudTpvN9sgvfiEev27tWlu+OjPlxCuKQguWZ86cecUVV8ycOXPJkiWPPvroRx99dO+9\n9/b29u7atSsQCFDpy1Ao1NfXl06n29raOjo6urq6bv/rvzZc/9prr12yZAkZtsfjoV0xP/744/7+\n/oGBgRdfekk8ftXKlfQszZgxY+HChR0dHUePHt25c+fx48dpQotcnwYGaWbuyiuv/MIXvhAIBF59\n9dUDBw7ouu5yuegvgjpn4i2o5n6Ny/Q3sNofQuRzJNl83po4aEaIoXDN6tXZbFZTFJ4XIL7O82Gl\nlV/9qt1u52F6y9atGzdskPK73omJDNmLq6eXo0d0r7vWr0+n09XoEQfE6GCzmPL1/L8mytffEiVV\nrKdgE5XQU8Et03V9zerVoh7G2AP331+OnqqfwenLhEKheBg/MZlK8ROpugQl5lFancfjmTt3biwW\ni0QidIAkSU1NTZlM5umnn45EIt/85jdvv/12u93+zjvvZLNZGg8ktm7ZwhjrliTKLE+lUg0NDQ6H\nIx6Ph8NhSuqLx+N3fvnLDofjiSefpLO2bd/+9X/4h2w2m8vlaIcwVVWdTqemaZSUGI1GaVgvl8uN\njo5SnXtZlt1ut6IotJ+yzWbz+XwLFy78q9tu43r+57e+lUgklFRqcHDQ6XQODw+/995711133ZIl\nS4LB4IkTJ8bGxsLh8B1/+7eKorz08st01pO7dq1ds4Y+tL6+/u2333766ad7e3tnzpxJk3ySUFZD\nkqQrrriiubl5cHBw3759Bw4coOUB2WyWiktV4EYl7lcNUPsT1IZoyP/LEUPh11at4n2R0tBhX1u1\nip+7ZetW1ZRcYPhcc3Q26xFndNavWzdZegyfVb4ecdh9/bp1ZTbRhPSYm6i0ngpuGdezft06fm6Z\neibvYZxeVOBeBY/n16GOuD2/jfWZM2c+/vjj5ubmT3/609Qd1HWdKi1RAv0rr7yyc+fOZDJ50003\nBQIBsdf+ve9+d2RkhDHW3t5Oqe2tra0NDQ2pVIo2OKZhSf6mctf69fzcXz/6KKVF0IpmquFE+0cn\nk8l4PJ7JZFwuVyqVoi2hM5kMz2mMRCJ+vz8UCjU3N4vu9d1/+7dwOEzriM+fP3/o0CHaSGxkZOTI\nkSPRaHTWrFm0PlpV1VwuJz5m23fsaGtrW7Ro0fHjx3fs2HHy5Mnm5maPx5NMJmkHsmw2S79Le3v7\nrFmzMpnMsWPHTp48yRjzeDw0SiRdnA3r9XgmdMsK3q8a4HIxMBoZN7/a//v3v8+P/NqqVTQ8xSkR\nCvmglhijH9qyhYdCMQLyTzd/oZm6Gvxq69eto95G9XoMkiakh88zmfUUlGTWw/+Yi+kxKylHTwW3\njPRPVM8UPJWXnmrcq9hZkiRFo1FqatqvJBwOx+PxYDDY3d2dyxd0z2az1IVKp9PPPffcI488Eo/H\nf/If/8Gv87+/8x3ymKuvvrqzs7O/v7+np8fpdOq6TsulvV4vzQkpimK326nD97/+9V/5FbLZrK7r\niqI48/uBpdNpVVU1TaPUfLvd7vV6qdai2+2moviU7EezUHy3MMbYLx55JJvNyrJMT0U8Hv/jH/9o\nt9vvvvvuO++8MxQKud1up9Npt9tpAxcaRL3n7rv5FbZs3drf37979+6hoaHZs2dLkkQr1Sj/XpKk\nXC43Z86cjo6OYDDIGKNMespFJLOXJKlgBk1l96tmPKz2DYzGlLQi8MNKh0La2q4czzB3bngcFCmm\n50cPPkjXuWv9+hLuNR30iJJK6xH7cD968MFinzUhPRXfMtLDX9jL0TMFT+U0opoBpf8/eJgPiNT1\nSaVSVM02Ho+fO3duZGSkubm5q6uLRncVRaEXtWAwmE6nn3322Yceeohf84c/+IHX6509e/b111+/\ndOnSZDJ55MiRgYEBmh8i+5Hzm5jkcjlFUahqlMfj+ZdvfpMusm37dr5c3e1219fX0zSnoii0xTNN\npzHGaG2yoig0UUpDx7Isr82/5fz2hReo9xONRjVNU1WVOk8vvPDCE0880dvb29LS0tLSEgwG/X4/\n7SLd2NhIi7q+cued/PeieS/aioVm6bL5rTh1XZ87d25XV5fNZhsZGTl9+nRvb++5c+fobYAexSrd\ny3xubXjY5WJgBSMjH6yjSRQ+v1Lijd4cmmkYas3q1XSprQ8/XNonSugRu198uKx6PQYPq15PCUnj\n6mEmTy3dRMX0VHDLRD2GX620nil4Ki8xkxINi0Gmouu62+0OBoMOhyMSiVAV3ba2NsqvofE9VVV9\nPp+qqrueeorOPXrkyMKFCxcsWHD11VcvWbLE5XKdPXs2FArNmzcvk8mcPn36448/pn6JpmmKoqiq\nSisv6+rqQqHQjBkzNm7YQJfasXPn4OAgrXR2OBx+v5+qeIRCISo6RWkRHo+HfMvj8Xi9Xkoh/j+/\n/CX/deLxOG0jSV5CygOBgKqqe/bsOXz4sKIoVExk9uzZVHSKeod+v//zn//8K/nJsP0HDrS0tGSz\n2ZGRkVwu53K5aEaQMWaz2VpbW8m9BgYGIpFIJpOh7+eEslKTQi1NgLHL0MDEsMiPMUyx8ICoFEKM\nhuKJ/GoF4yBBCXvF9DyYfw9dv26dQVL1egpKqlhPCUnF9PCBuwcfemiiTVSNHpJUjZ4pezZrAXMn\njDFGg3VUOenChQvnz58fHBxMp9MzZsxobGxkjCmKEg6Ho9FoKpWi3SOJGTNm3HbbbcuXL583b15d\nXR31jdra2kKh0MmTJ999990TJ05QocJMJpPNZp1OJyVf0KZcc+bMWbBgAb8a9bQURaH5KkVRksnk\n/Pnz3W73sWPHwuGwpmlUuonusi2/bTe/wov/9V/hcJiMkLZxoRJT4XCYrGjv3r0nT57UNE3X9Y6O\njuXLl3u9XlVV582b99nPfra5ufnFF1/kV6MGUVU1lUpRrXr65qxZs6g8B9XOpz9em83mdDppwfXk\nvnDUkofVfhZiwahE0AFrVq/WFMUcEHm840fKsszrlzNT2SSe5FbiE0vDNfMOx6To2frww9++775J\n1FNMUmk94hvD5LZPOU1E5VMr0zNpz+L0YEq7X5xEIkGNn81m+XaRjY2Nc+bMkSSJKtYrisIYGxoe\nplNuveWWv3/mmZtvvnnWrFmMsUgkEo/HZ86cabfbx8bG+vv7+/v7k8kkbSNJvS7yJ6rEIcsybTb2\ns5/+9F++9S3GGLmRqqr0ACSTyVmzZuVyuaeeeur9999XFGV0dPSaa67p6ur66KOPKCskHo+LlXRG\nR0fPnj07PDysKApViqIOFu2cIknSiRMnZsyY0dbWpmma1+tdsWJFQ0NDLBZLp9Ovv/764cOHz549\n2z1v3sm//IUx9ufjx5ubmhhjvNi81+udM2dOKBRKJBLRaDQajdIKSCqiqCjKlD5+NZCRWPs9MBqy\nMEclXpnJMEhl6PTQSz1NqIiDUfxI8XS64A9/9CPzx+kXU0LPXevXmyVVo4cVCtDj6uF/OQX1GCRV\nr8cgqbSRVHDLCurhM2Gl9UzZs1kjFAyCuq4nEgnqTGSz2XQ6PTQ0dP78eUmSOjo6yJboTvFT+vr6\nfvaznz344IPvvvvuX/7yl2eeeeY3v/mNzWajXVFisVg8HpckiXpsTqfT4/EwxjRNS6fTkUgkEomM\njY0lk8kZM2bQBZ97/nkyTtqvMpfL+f3+48ePv/zyyzSouH///kQisWLFCtokxefzuVyup/7zP+n0\nF55//syZM+FwWBfK/nZ2di5YsICKyvv9fl3XM5mM0+k8evToY489dubMGZ/Pd/jw4SeeeGL37t29\nvb20xTP/HROJRCKRoGXLTU1NtJOnrutnzpzp7+8fGRmh7TTJd9WL6/Za3WymgtrvgenCZhlifOQH\n8IBljok88FFGEL3LM8YMC6rMEbbgJxb8uoQeLqliPevWrt22fTu/5oT08PE6sx6zJFVVq9RTUIbB\nz0jPurVrc4oy0VuWFZZ2mU3xwYce+s4DDxTTM2XP5qVkKqKh4Y1e07RUKtXU1KRpGr3lqKrqdDpn\nzpzZ1dUVDAYHBwcpV57I5XLJZPK11147cOBAc3OzLMuLFy8eGhoKBAItLS2dnZ2apkUiEb6wT1GU\nbDZLG3FpmibLss/no5QK8ZqyLIdCoWQymc1mqT5ILpdLp9OBQODEiROvvvrql7/85S9+8Ysvvvji\n6OioeLspFYU+grR5vd4FCxZ4PJ6hoSFa9EZZjoFAYO7cuc8+++xbb72VSqUGBwcdDkcgEHA6neRY\n/JqUSMIYc7lcixYtyuVytH3z2NgYfZ+XLabtY9jUZFt4PZ7aSOK4LAyM5fthIvTTf/zGN/RodFzP\noD8Dc3Q2vLCvXbOGChcV/LiCXxv0sEJdxor18MtOuh6DpEwmMyE9W7ZufeD++0tIMsPXfpWjx9xE\nZusq+GsW1DPpz+Tlg6qqw8PDXq+XOk+aplGV3q6urs7Ozvr6+mQyyZJJxlhjMFivaQ6HQ5blU6dO\nnT17tqGhIRwO9/X13XrrrbfffvuyZcu6urp6enoikUhdXd3g4ODevXsHBwep6gdjzO12z5w5c9Gi\nReRSRENDAy15zuVyfr9//vz5qqq6XK7h4eFAIBCLxZ577rnOzs7Pfe5zLS0tBw8edDqdbNcuOlfX\ndRqZlCQpnU7Pnj37uuuuW7ZsmaIoVHrYbrcvWbLkmmuuOX369P79+1VVHRwczGazwWBQVVXKMaFZ\nQG4YmUyGBjzb29uz2Ww4HD5z5kwymaQPokk4xhhlSIJxuSwMzBzHDT81I9oGZR/R1C49ZCX6CuYr\nG2SU1lNMUvV6WCHHqliPQZKiKFXqMUiqUo+5iarRczlDSd7VXEFV1XA43NLSwoeXBwcH3W63LMs0\nA8RGRugwPv9Em4ppmnbu3LmBgYGjR4/+/ve/v/nmmz/1qU/NnDlz3rx5tDb5xhtvpEq46XRaluXm\n5uYrr7yyqakpnU4f+uCDa6+7jjFGWzmfOXOmvr7+9ttvv+qqq7Zv3/7hhx/quq5pWjKZHBwc3L17\ndyAQcLvdCxYsuPbaa7nyjo6OgYGB3t5eRVE8Hs+qVas6OztpZTEt5KI0kAMHDvzhD3946623ZFmu\nr6+nzb6p9ylJUiKR0HWdpxHquh4Khdra2nw+H20oQz/KZDJer1fXdVVVqaZ+NW1ePlafBqt9AxsX\nvYjriGFRURTa+NXwU8O51Yv5xte/zhTFLKlKPVVqG7eJPoH2ufeeex7+8Y/L1GNuomJ6vvH1r//q\n17+uRlhtU/1TTbkzY2NjNDhGvZmzZ89SRjslJbJ8JjBjjGyAkvF8Pl9TU1M0Gt27d29PT8/BgweX\nLVvW3d1Ni5pvvPFGmkBijNFwIq1CExMxOjo6jh8/3tnZuXTp0ltuueWDDz747W9/S0N8mqZRFv6f\n/vSne+65hxIgFy5c6GSMMdZ36tSVweCVV165f//+SCTS0tKydOlSVVX7+/uj0Wh/f39fX9+f//zn\nY8eOUUKK3+/nm1KSHpp1oxwT3oxz585ta2vLZDJ9fX0DAwM0Fmqz2WiejNY1F3SvKbIZS7sXg4Gx\n/D4a/GuCCSXyaIzCZrPJwg6H4pHm61TMr3796zWrV5slVamnSm3jNtEn0D7cvcrRY26iYnrgXp8A\nNHgYiUQCgQD1UeLx+PkgT24VAAATU0lEQVTz52lbLPEwxlgul6NEc1VVx8bG4vF4S0tLe3t7LBZ7\n+eWX33jjjXnz5s2fP3/x4sW5XG54eLi5uTkYDNLgm67rTqezubmZalkxxpYvX37bbbe1t7fLsvzm\nm28+//zzw8PDvBoIvdOMjY0FAoFQKKSq6qFDh25kjDHW3tHx9G9+c8MNN9x6661jY2O9vb07duxw\nu93nzp07ceLEhx9+SAuNc7kcVeLIZrO00lmW5Wg0GolE+DPJhPeA2bNnJ5PJ/v7+CxcukHu53e5A\nIEDto+Z3YjIzRV0l9MCmO2LYKhjFCkJBkKcA0IQKlbguGBZLXNkgo7SeYpKq18MKxfqK9Rgk0TRD\nNXoMkqrUY26iavSAySKRSDQ2NtIaXhrBGxgYoB95vV7KLJckKZ1OU7+E3EXTtNbW1rq6utbW1pGR\nkYMHDx49evSNN96g7InGxkafz3fFFVd0dnbSOmK/3//p5cvpsgcPHrzjjjsYY9u2bXvppZc0TaNR\nR+rn0eoxstWenp4jR4688sorb+fV7ty586c//WkgEEilUrTUzG63Dw8P0w7UmUyGek6pVCqRSNDG\nKORhjDFDL4qvLUulUr29vZSKQr8j/eI06fXJP2+Wdi92mRgYKxT16Ke//NWvvvqVr8gChk17GWP0\nqEmSZBegw8QTJWHrqYIfV/BrcyTl4ViUVJkeyeQEk6XHIImOKV/Pxg0bXCUlmdm4YQPlcZSjx9xE\npfWUbqJJfyYvW7LZ7NDQkMfjoS4LTY/Rj0YvXGhuaqJ1u4wxSZL4rVRVdWBgwOPxNDY2zp49mxL2\nEonEyMgIzTaRG/l8vvr6+qamJq/X+2z+E2Ox2DPPPLNv375jx4653e7W1laq9c4zj0KhEGOsp6eH\nFhGLQ6Z79uzhyz/sdnsgEKD8IJfL5XK56HPJt8jhckXWbNlstlg+KeP8+fPkXowxWlJGiY5T0tyX\nAZeFgZk7BOL7kSEOmkMhvQlKksT3GRJjohgWxWuaP7Hg1yX0FAvN5euhnHV+zQnp2bxpE2XSm/WY\nJdEVqtFTUIb4I95E27ZvX7VyZQW3zKyHX3Pzpk2u4nqm5sG8xEzF2FGZF0ylUm63m1Z3RSIRlk7T\n9xcuXDgyMjI6OqqqKi0TZozlcjnq66iqyrP1dF2ndX6UxU4LpUdGRoaGhihfg3/W7373u1Qq1dPT\nQ09Ff38/FZ0aGxtTVdXj8VAnT9d1GnWkGk6Erus+n0/XdRJAWYWyLGezWVqtRevPGGOKomimkmM0\nPNjQ0BAMBtnBg/RNGsCUZZk0ZzKZYrYntuqkp7zXRg49u0wMTLr4hZ349n330dphmwCPg/QiRkfy\nJ0zOD0k5HA5zWOSjBN++7z6X6eMKRuSCeh57/PE1q1eLkux2ezV62MUmVKYeHtzNesxNZLfbq9Qj\nm/y1mJ7KbllBPY89/ng5eib3gaw9KoiGVA6KSq23uFxUjCOTyQSDwZaWFspTj8VilBBB99dms1Gx\nJSoQlclkKGEnm83K+SK/lNyRzjtiQyAg7dsnyzKtAqR1wel0mu4+ZVhQiQ1ZlpPJJL30BPz+SDTK\nGBuLRHyaRg8eCWZCT12W5Ux+h0kRm81GFe5tNlswGAwEAlwPY4z+NGiZh2GdcjntbPURv0mn9g2s\nYGwSA+KOnTtp90VxhRDLd91s+Qxsemq5o4gxmsIi382oxCeWhms2hGZ6N6xYz4Z77zUbajV6zE2U\ny+/IXEIPN7CK9Wy4996tDz9cjh5zE5XQM+4tm6pH8xLB3+gvbUCklHpJknihivf37p3T1tbW1tbU\n1NTQ0BCPx6PRaDgcDofDOaGqMo3+McYkSaIxPfqO3W6nXMREfh9hur4kSeRzNOckyzJVcuKjhdwm\nzSL5ECKH57JqmiYJQ/SU2e92uylzsr6+nuqMRKPRvfv20WGhxkaPw5FIJMzdtUtCDdhhrf1xmikY\nkgzxSwxttAMe31HeDP2IDhNP5Fczj1NxivUt6JTNmzbRFR7fts0gqXo9BSVVrKeEpGJ6Ht+2bVw9\nxSQZ+nAT0kOSSujZvGlTaT1T9mzWAtVUVqQuVDQa5d8ZGRnp7e09ffo0Va8IhUIdHR3t7e0tLS28\n5K54OsuPMTLGaFKNuxe/vqZpouvQVlvipfjgM6dghWJWKMlC1/X6+vpZs2a1t7d3d3d3d3fPnTvX\nZrMNDw+Pjo6Ojo729vbyg4PBIF8tMCGK6amMmhk/ZJdhD0wcQXrg/vtpR5UdO3d+bdUq/ljzGEq1\nG8TXeTmfUiGGTrvdLnZ3fMJHmD+9hB7Rdez5qrh6vhxAxXpcF4+bVaandBPxHliVesySDHp4J2yi\nt4zGncx6qKlL65nKx/PSME06YYQkSR63O5VOM8ZS6bRXklRVjUQiPp+vrq5OlmW/39/Y2Ej1LcPh\n8NDQkHRx9g13I/H74u8l2pWS342s4BI3upp4HfPaQXpPcrvdjY2NtGRN0zS73Z7JZBKJhN1up92f\n6U9gZHSUzr168eLY0JB5b+WJUuUt+2RKOX9iXC4GZivCfZs30x6JTzz5JO0DyUOhLV8MSfzzkIXE\nCh4Qn3jySTrgnrvvdl4cDUuExdJ6Hnv8cb7fB+U7VaCHmaJzxXoYY3xtTbEmqkaPrbhviYieOqFb\nJhoY/0UYY/dt3uwcT8+kPIfTlmoC4mRFQ0mSQo2Noxcu0DXduVwikYjFYqFQiF443G63w+Fobm72\n+/206osxRuXbKd3D5XIpihLJd+a8Hk8ul7Pb7WQt9ApI953ecuLxOH/Zymaz9FhmMplYLOb1ejVN\nc7tcaUVhjKXS6VBjo9frbW1tpQXygUCgrq6OhgGTyeTY2FgqldJ1nXY4kySJllTTufx3HBgYqMa9\nJiWVo5b6XkS1dWKmP6+//jrfFIqXJxfrlP/797/PD/7aqlW8pB7vWxiioaGTIUbnTRs3UloUvaPx\nQS0+tOV0OjP5PauK6clkMg9t2UIXXL9uHWVkVaOHwyVR1e0K9JRuoor1mJuI9qKtUo8oyeVyVaxn\nxYoV1T6FlwKv11v6ADGcVeBAk/sur+u6GO7dLhdjzGazBYNBn89nE/rBtHLL7Xan02naTzmRSDgc\njvfef58fM7+72+122+12Xdepzpnb7aaR5FwuR5Ne9JoiSRJV0aWKvTRBRaXIvF7vocOH6YKfuekm\nXddlWdZ1nSqWDQ4ODg8Pc68iqANHj19aKLTfNnv26Oho9cPR1dyyCs5NCuOx05PaN7A333xTjM6G\nUEi9fl4oluW3+hVrvxY0DIrR4kjUxg0b6C+EDMwQCvm/BiVmPaqq8q2iiZVf/Wo1epwX43K5fD7f\nhPRkMplymqhiPeYmisVi1esRJVEPrDI9N9xwQ+XP36VjXANjlQbEKp2vzCu3trSkUilad2Wz2ei+\ny7Ls8XgcDofNZqNVX5IkvfPf/y1e5KYVK+iOZ7PZRCJBJfBpCk3XdUr6oP1QaKswOot6VJIkJRKJ\nXC7ndrslSdq3f7945aVLlkiSRPtbmpM++FPX2Nh47vx5/v06r3cSw+wnectgYJeed955p9iLPP1J\n0CMuBkRGu1wKsyl8QoUPSYmhkDG2ccMGCoUOh4M2WSj2Xl+iY0F6+L8GSatWrqxMjzlMFzSwieoR\nm4jPgVWmx9xEtIN7xXrMTfRkvsR4BXquv/76iT93l55yDIyZhpVKR7cJHVwZho8I+P3kOgUPdrlc\n4fzWxkRnR4fT6aQCGYwx6oFJkkR+pmlaXV2dz+fLZrPpdJoq7Xo8HipbZbfbvV5vOBymivXpdNpu\ntxuuzxjz1deLaYTUr6LH3uFwDAsbxDDG/D7fpK9T/sRuGQzs0rNnz57S0ZlGrmkPxh//5CfmK6xZ\nvZq+MARl4p677xYnV8jASgTEcd1CRBwrK1MPY2zTxo2OizHEaDKwydKzds0a3gPjtUgmpMfcRLQv\nbZV6ijXRRPUsXbq0YDtPc8o0MFZ8aqR08tuUZgEU/ERffT1jTNO0gj8N+P08n5CeIho65u9YlElP\ni8+ocAY99rIs2+12SoXnA4zl6PH7fDTSYDAtjsftnqIs1nHvyKTcMhjYpefAgQOGIGiIhlQ2lE+i\nGIbvSvPA/ffbLl755HA4vF6vGBDFyCgaRjE9JKYySQX1mGM07yNOEz3mJorH49NHz+LFi8u8/rSi\nfAMjyp/h/2QS2CaUcdDa0kL5GjTYqCiKI79k2O12M8aSyaTNZqN+Fd+pQNM0l8tFE2msULYUJYDQ\nKub6+vreU6fK1DPdmqgyPTCwS8+hQ4fM0dlgYGIWAJ9KoboYBfn2ffeJmXJi1jiNQjjzC4/MAbGg\nW4h6xOhMkjKZTDV6xABNX4iDnBXoIUrYxkT1mJsoHo9PVE/pJiLrqkzPokWLyn/epg8TNTBOibB4\nSXKvS+txOBx8U2b6IhqNZrNZp9NJCRdkQplMhjFG38xkMjRsGI1GPR5PXV1dJpOJxWJUy4MvXqaF\nz5Ik0fe9Xq8sy+l0ulh/i03L9qnqyjCwS86xY8eKvcgbDEwTMJR44IjLbA3p3Twmer3eEu/1JToW\nYg9DlEQGVrEe83AZGVjFeko0UWV6zE2USCQmRQ+XZEjfn5Ce7u7uKX1Ep4iKDcxa6Pmt4PiCsILL\njXkeo5xfLMiP5GeZr8D/K644LPgRNcn0N7DaXwdG4wPi3L74U3q9omhryGQznyImBRjS7WwXr3zi\n8Nd8/iO6YAk9Yi4fSaJaOBXrMagyxO4K9BRroor1mJvIbrdXr0eUZLfbK9Yzqc8jmGRERynmK9yZ\neMKRuLzPkAdvvjjDvgTTldo3MB4KmWntPT2UZGCaptEoRAUGNu5Lvegc/LLF9PDrc0myLFepp6Cq\nivVM1MDK1CNKItuoUg8rYmAT1TNpzyK41MCEaoza/+PknQxzXJNlmTo3Bd/lyzGMgi/1NPTEY6IY\nIsWORTE95u5F+QZWupMhhulq9BRroor1mJuI37Vq9DCTgVWm5xN5TgEAE6b2/zjt+b1ICMmEruvZ\nbNb8Li92TQynmwO0GBOdF5fd49kB9E3DNc16eHTmkmw2WzV6CkbnavSUaKLK9JibyCGUrapGD7+C\nwcAmpGcyHkMAwORT+wZmCEDSxTv/yvmNvbPZbC6Xq8zA5HyOAP1r8AkD5gsa9PDozCVN1MAMekoP\nlFWgZ6IGNiE9ZgOrRg8rZGAT1VPhkwcAmGIuRwOTLh6M0nWdz6YYQmEul2PCTIyUX3JfupMhDiEa\nYqKhO1hQj2FOjkY4q9FTeiCxAj3Fmqh6PQ5hCLF6PaIkm1Ccd6J6JvFpBABMIrX/xykaWMHBKJbf\ntq7YbIp5QqVYgDYMIRYMiKK2cQfHDAZWmZ7SnYwK9BRroor1mJvIkd/Dsxo94hUKGlj5egAA05DL\nxcAMcVCMhtQD46FQ0zR9vLRyfhEeFg09MB4HzTNPhuuY9dhM6QkGA5uoHv4vlyTO0lWgp0QTVabH\n3EROp3NS9HBJNputGj0AgGlI7S9kBgAAUJPU+GZ9AAAAahUYGAAAAEsCAwMAAGBJYGAAAAAsCQwM\nAACAJYGBAQAAsCQwMAAAAJYEBgYAAMCSwMAAAABYEhgYAAAASwIDAwAAYElgYAAAACwJDAwAAIAl\ngYEBAACwJDAwAAAAlgQGBgAAwJLAwAAAAFgSGBgAAABLAgMDAABgSWBgAAAALAkMDAAAgCWBgQEA\nALAkMDAAAACWBAYGAADAksDAAAAAWBIYGAAAAEsCAwMAAGBJYGAAAAAsCQwMAACAJYGBAQAAsCQw\nMAAAAJYEBgYAAMCSwMAAAABYEhgYAAAASwIDAwAAYElgYAAAACwJDAwAAIAlgYEBAACwJDAwAAAA\nlgQGBgAAwJLAwAAAAFgSGBgAAABLAgMDAABgSWBgAAAALAkMDAAAgCWBgQEAALAkMDAAAACWBAYG\nAADAksDAAAAAWBIYGAAAAEsCAwMAAGBJYGAAAAAsCQwMAACAJYGBAQAAsCQwMAAAAJYEBgYAAMCS\nwMAAAABYEhgYAAAASwIDAwAAYElgYAAAACwJDAwAAIAlgYEBAACwJDAwAAAAlgQGBgAAwJLAwAAA\nAFgSGBgAAABLAgMDAABgSWBgAAAALAkMDAAAgCWBgQEAALAkMDAAAACWBAYGAADAksDAAAAAWBIY\nGAAAAEsCAwMAAGBJYGAAAAAsCQwMAACAJYGBAQAAsCQwMAAAAJYEBgYAAMCSwMAAAABYEhgYAAAA\nSwIDAwAAYElgYAAAACwJDAwAAIAlgYEBAACwJDAwAAAAlgQGBgAAwJLAwAAAAFgSGBgAAABLAgMD\nAABgSWBgAAAALAkMDAAAgCWBgQEAALAkMDAAAACWBAYGAADAksDAAAAAWBIYGAAAAEsCAwMAAGBJ\nYGAAAAAsCQwMAACAJYGBAQAAsCQwMAAAAJYEBgYAAMCSwMAAAABYEhgYAAAASwIDAwAAYElgYAAA\nACwJDAwAAIAlgYEBAACwJDAwAAAAlgQGBgAAwJLAwAAAAFgSGBgAAABLAgMDAABgSWBgAAAALAkM\nDAAAgCWBgQEAALAkMDAAAACWBAYGAADAksDAAAAAWBIYGAAAAEsCAwMAAGBJYGAAAAAsCQwMAACA\nJYGBAQAAsCT/F0DJnIsK9j+7AAAAAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 48, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo7()"]}, {"collapsed": false, "outputs": [], "prompt_number": 49, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Parameter $\\la$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 50, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lambda = 0.8;"]}, {"source": ["Values for $c_1,c_2$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 51, "cell_type": "code", "language": "python", "metadata": {}, "input": ["c1 = 0.7; \n", "c2 = 0;"]}, {"source": ["Step size."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 52, "cell_type": "code", "language": "python", "metadata": {}, "input": ["tau = .4;"]}, {"source": ["Number of iterations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 53, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Tmax = 100;\n", "niter = round(Tmax/tau);"]}, {"source": ["Initial distance function $\\phi_0$ at time $t=0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 54, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = phi0;"]}, {"source": ["The minimizing flow for the CV energy reads\n", "$$ \\pd{\\phi_t}{t} = - G(\\phi_t) $$\n", "where\n", "$$ G(\\phi) =\n", "- W \\norm{\\nabla \\phi} \\text{div}\\pa{\n", "\t\\frac{\\nabla \\phi}{\\norm{\\nabla \\phi}}$\n", "} + \\la (f_0-c_1)^2 - \\la (f_0-c_2)^2. $$"], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 8__\n", "\n", "Compute this gradient $G(\\phi)$ using the current value of the distance function\n", "(phi$.\n", "radient"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 55, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo8()"]}, {"collapsed": false, "outputs": [], "prompt_number": 56, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Do a descent step."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 57, "cell_type": "code", "language": "python", "metadata": {}, "input": ["phi = phi + tau*G;"]}, {"source": ["__Exercise 9__\n", "\n", "Implement the full gradient descent."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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NxkwmU6/XITxKCDGbzfl8XqfTtbS0HDhwYNu2balUymAwwO2D32Y0GlHZATuH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\nXQkVwBQUFBQUdiVUAFNQUFBQ2JX4/wFa/BF5fgjGNwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 58, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo9()"]}, {"collapsed": false, "outputs": [], "prompt_number": 59, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["__Exercise 10__\n", "\n", "In the case that one does not know precisely the constants $c_1$ and $c_2$,\n", "how to update them automatically during the evolution ? Implement this method."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 60, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo10()"]}, {"collapsed": false, "outputs": [], "prompt_number": 61, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}], "metadata": {}}], "nbformat": 3, "metadata": {"kernelspec": {"name": "matlab_kernel", "language": "matlab", "display_name": "Matlab"}, "language_info": {"mimetype": "text/x-matlab", "name": "matlab", "file_extension": ".m", "help_links": [{"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md", "text": "MetaKernel Magics"}]}}}