{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Geodesic Farthest Point Sampling\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 the use geodesic computation to perform image\n", "sampling."], "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/fastmarching_5_sampling_2d')"]}, {"source": ["Voronoi Segmentation\n", "--------------------\n", "A geodesic Voronoi segementation is obtained by computing a geodesic distance from\n", "multiple starting points.\n", "\n", "\n", "Compute an image with bumps."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 256; % size of the image\n", "sigma = n/8; % width of the bumps\n", "[Y,X] = meshgrid(1:n,1:n);\n", "x = n/4; y = n/4;\n", "M = exp( -( (X-x).^2 + (Y-y).^2 )/(2*sigma^2) );\n", "x = 3*n/4; y = 3*n/4;\n", "M = M + exp( -( (X-x).^2 + (Y-y).^2 )/(2*sigma^2) );"]}, {"source": ["Compute a metric by rescaling |M|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["W = rescale(M,1e-2,1);"]}, {"source": ["Create random starting points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["m = 20; \n", "pstart = floor( rand(2,m)*(n-1) ) +1;"]}, {"source": ["Perform the propagation using the Fast Marching."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["[D,Z,Q] = perform_fast_marching(1./W, pstart);"]}, {"source": ["Display the distance map."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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rELBetvey8Sy6LmW/7N/kfZr6suKzydengoe+LmAwauhHX5W9qgz5m8ZcjKFF\nO+LbgvF6dnVm+PHfYsDQziv/yp2w5aJdsw6sQ3y5ZeoD6+JoJq1YWJ6CDm17CKkct7gLw210aNKQ\nHKEgn2gmLwLVa1q9Ei9uxS4s+TCxAgHTD3glThKw9HRXSviTn5LxKtqvtL7ieBUBX9k1L4a72ucR\nxWbwFsOch+gGQ09YmxmvuBGn/paxpslIk6/Ma49M4uqF4le5TrXyDmiTuh8wWiaZvxPUvR1mS1p1\ng3spYGEwfjUuYmlHLoRzSOhYEfPUK8Bw4hzWIGD7SQFL2tOKSKCLgpDu+NV9v1WvJl9DAzS4LkUW\nfS6pdqSKRFqxj3u0jxr2Rvb2eDw2+HQLv8UB2AHbeHyHODpio3vCYNTLw7mhh/AYYm+9+UUVzBLD\nkaUTUFOyomimlSRVGZ5T79EmUW+ECUujI4aajL1dbfum2XbygbCQqJneLyMLs+pksbyzWOLa7dcp\n6hV4qXDipdovrEPAOmFVVPKDE51eTsiPzP9LXyHmRx5CbIyY5fYLoqB0SxYgmuq0lI+r7JJ6Qbx9\n6zD6woftOGee0u6beYMivv5/B6VSrjQlfS2qo3VgPuXTJwMa2IuhnE2monP9tt2HJPvwQksAcizE\nNJjvy9bAOqF6PRtasQnWIGBSHKyAydxzKV3FFyp7Mb91YE32dVNK37DSJb/2aYeBR5dJV9r9NxCD\nwB9imKwBPPod9lu02QhP8jmzWiAxw73ifwobmXWliXL+Yteay6VrmNLDBelKAiaHjgzIMKODQ79r\nHxp0B7RJwFL+YRAwZiG+X77xRXzpD9/3TiyZC7ZfWIeAqRCi6tNvcrlyIo0PURs6MYO0SMp+pRBi\ni2sTlQyNaXpDSyp0KUlSJvsDAB5bPDq8aZJC4Y2PYcT7WHiIu7cFGry5xd0OH4q8xA7oEJ5qwrB2\n3Q029bTTs/6D1Jp8a0eLHjVts9jjBfEUs5zZAU2P9tNowtp49hpgB3igFb1isddwu/t0237q3aaL\ntybje5l9P2z7Mt6nMsmrBhJpv96S58USL1u6AmsQsGJHk4zoQTSJSa6UA+vEfT/yNZjg4aYQTRxW\n783fXk2yEutxaONGC088PeGfArjCvxycxZudjq8NnVXVHPoXx0b/bH3JOwg7EfFuQtV4ctBK2Dqh\nZ41yYIhzpADwIXdpHq7p2+bNuK8qWLkCAQu8Rk7Ha6nXFwEAazJnJ8US16BeWIeAdXlDh9g22hZV\n2iyXey+IFhViKeQdYA3gys+DqR6bMWaYMuIPcStpE7Ht7JghHUkAACAASURBVBscHBqYFrsL6hUP\nMxmuRut1hbeSsdMXVdVd+4jd0x91huQhjrcbaWiVThRS/DbdTARS31hjto0jtUfeP19cl4atRJbm\nsxIBkw8AIxewpFVONIyBbe7DUHFgUaw2TRYwlCHEtI6UB/8GokOmiwKmNEcs37d404rY5pBoeIX/\nXYQQd8AOHzRos1zIsJvynSmpX+dIB48zBXXos/8DWZVq6oXkwGTfX1eakk5hI6oPQPsI5+MpQKlX\nLN2feOGV80Mb8GPu4hp4wVji60YOl6Jbbx0/lPx2949/uVn2o8cvy0oETBof1WTL23cICVF3/Mhn\nQ6FNrqQiavs1NMMqEujz/YRQR4x+YdOib+KOtfGnlCq+BbaZesUdULqlyqcx+V9mWvKKMqZyYKTi\nO1P76a8TMyCv2qF7qzd1nkKIEA5MrkhGMNdwZdR5/qD1/2IUrW+80M4wj0NCDZOs4TJV6uXzn1J7\nJlMNxWfj0CsVggmGARuxYtlrBtMBN6zD5zvWVQQs6SgAB9eiD7q1zb1KFLAP3JCD0hhHE3lx6bJa\n5c0UGzw0gddhr5Vl7USNh3qxtePE/FnXpVyLy2tXRhdTBSOvrjVcHG+B1KrXZqka9qL2K0ENS6zh\nGlUWB3kIsRPhpKYgNb3DBwAcvBsWRei7kjEtoAf6Bo9uEIhuFJ1MGce0Q/VuYy8y5GT/jGzePR5b\nXDdwLd7cisWjgP3tLXbAzRBKHJSsBRrI0WlTvZwWP3Rm4uDt5Ddtj5DPLq1pEtltOsi/OR5xSDhp\nQgLp45Bq2YlBslwu+PL8jdWXSgexH+nx9JSpYx2zPd71UTRh71K0FEvVsNeBGhZYyQUqI4QoFaxF\nEl7Ni1H1HiGEKC2Yt+tdMzZ/jdlCX9ycyk1Ma0t+IQrEI9AA1w0eU+sLoMF1o0RLmjDVAXZcxqb/\nX2hLVyhb9VIalj5hZ/EBsIvf2zzod8D202GkQ2mzkr9VgcSRx9w5y9qVdSz/Sim2XnJlJA17nm59\n6TfxjV976X1aEK9jv4hkDQKWCVL9lcq1ZcU6hr4rK2DImsDeDe9naeJcjVxZTSxVqNGZkFic4h22\nYZqD3w7rb8desIKGCfUCgJpuxd90ecKEbYD+SLPvSp9RwzZx53dxz6WA7QEH16F91HreGPVypk6d\nz+tP1bc9NGXCLun6+D0AwM+fttB7tFwWmjAJTRgu6wJ9DWL9HNIDW/IJZOnqZBDKAw0eU+573srq\nRlQFEjshYGnmtJaQJd/iJqYohtUGAQsTdzqEeO2yt1tJB1aQsaKfQqmJT1HEvjBZLq0VK0YO26Be\nH0bd/VAoWaiSu/i4dgO3R7uHfxytWNr15KakhoV6dI+xfhALXlSaj8u7mBPjRskfl1ot5+chqGES\natgaBEzeSNtXKqsCCr9mcT+b0+jNTXtcsIsPILdqzT7/mwUZ06NdV/hNOX389HFTstumja2/sV9W\nt+LhzXBjyOvP1A0qP5q4KmASNxqI3d5G0Q3deF0cQSUdnQc8msdRfbq80mXlSiVzysEiLu/F+uXq\npKMuHt5COdF7vQgnRRG/BGBG7iI17JX4kzO8YTnGxVydEzjTGiXJmf4gCoYTVskbq2Tb6mZUGi8U\nKkNqmP2aJrryKlIjuxXbtOrVYOP8TO/l4aJhEVWlTFgx4PaoK87ny6lFx8euPsjV6yb+/QjYAw/x\nFV/AEDL1aH6Y3TIUbxwKgluM0crONJ+vRa19fVz93g8APH3+R9/3jpAjLFF1XpAfed878G5QLdsc\n9XKxkTvkLZ/sAyt+fFa2GqcbW7WHQ//cFb5SdnVqdtn1ZTvAov3KF50xQG1RvexPYb82x+u3MHEj\nUjbCUdwAt8BHePjwb+Fj4KMoaVthLq/1AwJHT+pYsosVfzJP0a2Kq9/7QVCvd8/858a+8cVX3A2y\nINZwdabODWl3VHOl2i0/JA9kH9VZJYXNidXKrPkGfYvOoROi8iZtKwXDEAthDd0VvprvUpvp0nW+\n+1sTP4xKtml8SKCXafSnqZdt6L3Y/XjE7s0YhEuZK1LynDke7b1ugY+Bj/FN/IOfufpjAN98+gc/\nc/jjoavvIVbqFm6P5nGsrLSbNj7ZbPJMx0bb02GKywtyRWu4PiJWt65+7QdPv/m2JuykKOKpGnZR\nscTPAAD++oQlPtv82evsymJYwwXq8rZUkgJ3cnpXiig1woR5YbZkR0r9STKI5vYaw+NioxoEVMtf\ntAwN0FSdhGmdlWjJ+KGcfmQoeqkSamL6bHQqh6rrwgmwsrbFHf5OUC8Af4rP/czuj/FQeC47RDqL\n3kvOOGWqivaryb9ekP361//mf56e4Rev/vm72ZOX5Zyt2JdOkaKRz5ymYSvnUi7Q40hRSVOS6ljt\ngWnnlHTZrHeXp3mLVan1eSdGhJKFNKvPG1TZqWUaWeRtsfAZ6e1WEKJ1pJ6U+FgbVdQNk4uYFj22\nPVGvB9zg/o+e/rsvXP37//XpN7+Eb4xvoPaiYvI1hq0o0RlqU+mWihPWdE9OlDWwNI6KFnlVvvGZ\nEzXsr6leJ7PYq/MEbP5FQjbP6bmuVGjylqzY9SXVDnFOmdCW94BtY2LCp63YaCM2mnZSSld8xPe6\nKacaqlhj1LCgXip+WJSx+LKVjUMpKV4G7EZ9yAxkGgNe3hF04tjihuLfFJE9xHjtd+AO/Rdu//13\nn37iN/C/NQ+P+A5wH7M5DuN4vVLL0knKYoGbsRKOhxCbXMPaCxGwF+FFoohkLowfnsgakjjs3bss\nIJ/oK0LVVeb0kxMhCgBEQ7kx1iprXJMKtVl5OhQmjRGwOfrIV5GiwUJlc3JnNtWdUhLg0z9dLmMP\nwD3wCT7af6/57iO+CzwAe4w+LCh7n9Wv2h2X1Kv2mXZgdvq6BexF+NJvvu89eE984zOvtWaqV2Al\nV2emKGIwDpdrGGJrmqak5rcRqxoL4pmtrxrpQkG9Un23QOfwmLyMix7H5zO5TNush6hrmOrxmlFH\nzsO58JSZDAJO6FL+CVHEJn9CC+J4shuHVFuHeJQP8Qwg2jKrXp2uYpdLzxA5rKms1aqiql1iNxiA\nf3T1OwD+9dNLhBZTXsZaxWkOn3vfO3DxXNDVOYXTWlJGtpSIAbAkKo1d4ApfFa+ULG53EJPhsxUB\nwg7oHPa7OMaH6oQTFm3TDtIlB1tqc4dmG99hD6oHnt7RLD9wMcMvte9ehBBN5HAstIBD08H34ybU\naCXJ3gLoejR7AMCDmBpSNu7iebgX5iwo2eMYC0Z+6IXIYRonuBUz2UK6SRBVfpECVmM6g2Mqikj1\nqhPU6/4zuHnpbi3ar8QKrk5tA1wcjEP5CxsDlJ04qsNlbNiik5ONX/7ZmJBUl/uuzsG36F3ewmNs\nU2VAcdp+iWOdNl4p83CUrqEcu8FsDRU/ja6Y5MNSDab6jVuMLqoXjhdx6A3ZX7kXvV8d0I2/FPzV\nROTQGixlwor26+Lih0Xv9cz8wxOla+0D+74cVC/JZV2gZVK7bmN0siX2ouGUDkx6I+TWozMrKUWg\nrN5AjGSYmvlDEwesEn7nWtgF+fdYFHEz6TileqVC0jCXEgpl5blSWR00AD9kc6QoYvJsENYyCXUj\nBayJVZFuGPaih+yQxQ/VLYODqRb5myocVa+VOTDy4sjg4QuaMKqXYg1XZ2j1pROwbaCLr+PqEEcj\nvMJXRTucMuO3IqdD+YEUsYppgpvt+GRxslBOiJQUx6HVjsZJNqPb+FVtoaZq+fiHNR8mXJeJIqaK\nSVWYClbHEW1lXG/j4fpQzBTLi4MeMgp7tA/iAfFGbLcTMd2HIXh4iCscUwU3saJkLanCRDqi6mcU\nq/ZuE+onHevloezXE34UwBVe5YnmlVDs97r/DIC3lTGql2UNApaESuUWQAiYyiQEgCf80zgiBuKv\nEC130iIVzRKRvpoVkE+LOdErpnyKy5vUmv2ysS8Xjq2gW8p7mfhhELDT7ZcTFdMAHRzQ9PrBbPV8\n3PAMQQ93EDUgRT0N/f843jVkB70xI2jYsGHNijkzTz49VcgFCxhZClSvImsQMGl2IPQBosWCbIyv\n8JUnfDmql2znZAsHI2AyZ6AFGp1kIVMO1NJetNpe7LjLBazWHOct72Ze2qEkadg46ahiKd1SUzq4\nXt8aNLkhQzoxPZy0V+mZhShgqWtMHu4QX20mK2c6TmjVzgENPDYerkNTHaPkQrnCD4IJK/xEE/bW\nPNuHUb1qrOH6DGMhJhlLLbtstNL9fagQf4WvirZNJvxto4dSYyE6MVZhOxR3GAtNDGqFVcZncsd1\nyEeZEXcZQsDcjOBYCzRQ8cNaOLGYhejhvNu4ph/DmGlPVPJhkt5UzVLzGrjD8CqTJj655XPpSkff\nAK5H+yncpxhyXjwAeLFgukHARpyZiRigmtLkU4oV6ACHAz4I6tWhCbW0e4n/hWdIMX3Dxg/JTGYm\nzc+XMerWUdYgYNbayD6wVsyGvJm1N/OqFSwJ2MaNHVRbs1ArNEB1EDV56+6EHsixIZSlKIW/5nSA\nSaT9Gj2Hy/dBTWnyXECXH1f62wEeroPLNQx5QcZ2XZ/1n8keL2zGYyzXia2cCStmHJh3o/HKOgUJ\nOcapj3zdx2eca0pG9ZrDGi7OGNLKOppg2l2lSb4SuWvxAQCHN9u8QW5wHRMOZcqGVC8VsCpmOMDs\noIx92WeV7GqFgMXVnKxhWSKi3JPap8ljtOmvqG/n4R7LAgYxJdWNPD1uk1dF0YHV1H1C+MWUpF5J\nwFLhaO0R8mysklG65rOGi3MnAnbe6EMb44cuFtpRk8bW7mZQpL8d1agDvBvUIfkkJVcyaVCG/pRo\nTQtY2pFi+7sVE9vh9ZV25MPpXMTQRndoHHxstb1Lz3MhV/m42EAba67N9UdmwwsPHEwNEEOmfbay\n4b/jRhy+VUpVA604k6nQTBak7LVAA4/NAW1QrwPasJsHtFD9guuG3WA1XmTEjaBkP/tE9TqBNVyc\nNjYYUM0eYpOWhpJSYcN2eINwGxtrtbLprhfV7B5Vr7RaGAFTVkwUiuolVla1YsqBZSZszqeJopUq\n2wlDG7eRjczhxrL+XyiVG/mBF0OINW2rFfKvHa6T91IOrLh3hEj+4U88/dX3rt73XqyUFVyc1w6P\nrRGKqFibBr1sLzvRsorWbtOOORytaKaRR7uUgCV7ZLXNSpccLjgx3Y7nbfF1yXgBqNmvYnys3F4f\nFbC0eyo+6PIwqTNHreKN8qiLMtmY8oQnm1YyV1Yv9oGR+fzDn3h637uwalZwce6CNphmPN3Idw5d\ni67FI6JNCDTYxG6t+D6TsRBqzotVSXMwEcJKDb3SrVqDrhSiYkSuxWuXayHEYt9YNRcR3jVxWMNO\ntP7I9zD3UlnAsMvlqijYaVWSOQ7MWjFrc+04h6LgsQkBw6BYe2yDkqUQIvvACDlzVnBxSrGp5Uc0\nYiCMLuYlSu2ReRlt3pSnFdrbfNVuSiVD3tyj3qArATPbSq9Nme76OprKYUdHHEemd0KrlPFqxAPG\nSbdcrsSdKfjKSVGHLI8X4nw5U9WyMJ20OWm8bBLHdKWRNUP79d5ZwfXZmPYUJiql7IJcsBECppQM\noiGuta01JUOuW16EJZVNlH+V7rpy2NDGD1Us8WhCRygPY0pZ3ZIClgyl2nlV4XKDauajxwtTt6pg\nI4eq/nMl824j5cpqGAWMHIXqdQ6s4PrcmWZUto9JNmwXlLx5TwKWHklu88o7ag4awA1Zgil2F/4O\nY7/bEGJac/53U5Gr5MBsQcmYWHe1b8yFHUz2NBVSjbk8/ikdWKpSGya1h3mSgKXPhFwV0xEd0IwP\nKYc4oQwhygKTOMg0VK8zYQUXZ2sayqKANfk8MFGpJi9s85AXjgjYphTWyxyPi+MQIr3OZCANLW99\nVdFsTRsyuZ4iWfKCdGA+rzrkrlFFDt24umG6Va/aLrh8QyXrWe0Dc/lZi/UvH1KWlksqWTpwmcdR\nqyWyWqhe58MKrs/GNJQq/BWwsTvZVtrx4Nt6O5u3pJt6arscSFf9VSjz9AzpKq5EbsI22frdYFLG\npHjXdEtW7Bz7hZIDk+cCpcjhhAOLUzp3XTNetcghQ4iEnD8ruD5lCDEdbkoKSCNJ1fxZKNRe1aHC\nXABK/VKNyIOsOjCjXrJs4362W2tOULGofLbOxjyOMKxTiiI60+PV5AUcixxOqJeqf3maikkc0wLW\njH1dE6mGtsA0elKD3uvcWMHF2YiyFDAZQoSZx8apiiHEqF61fqmJOF5gpgPLd9AX/1qZnHBjEwwd\nYEN5o3MRUy3JwKD8JCVTM+BZDuzUEGJUsjS4hhQwm2044cCoXoScOSu4PltRti1jI6areWTigBWw\nNhMtzNCP9GsoKLkqfrUoK2aDinZP1OK10KIi2wEbOZSB2aKSofIVRrqsP3bmTFkHZnPl4xTfaONV\nHCaqZrxS5JBJHERC+3WGrODilC/DMOG+Qd6st1A3+/HuftMMEbn01HAtlIeSkLy9gCmKbkzugCzM\nUVZJ2IchipjqzapRUbTsPDAaJgswp0CdC0waLwffbFRHlwoYTuTKFyOHdGAkQOk6W1ZwfUqPVXRg\nTf2nXMA28C0OScBs/1Yq2H4pNU/aO5XHUSxMoFyU3W5xyrT3go0iujgkR5IWmXPoThcw1B2YPREo\nRQ7zJM8QMJQJGipFvhg2nNAte14IIefGCi7ORhxlsU+lEQ1lUcAcrt0gV1bApuWq6M9wzIHVUjmK\nWA2ridZ871Xb0ujAZAI9hG5ZMVMF9dduApVzAXFSxFmzxuuogM00XnRgBLRf580Krs8QQlSRw2JX\nCsYWU+W+p3IQMJcn+GG28VIOrChaz1MyKWOpPDOtwzozuUUHnz0kp/5KI3VUt+TqlYxNxA9dwYHJ\nDMOaboUQYrHHK31SRxfVi1ioXmfOCi7RZrJBzAVsIwSpKGBptNw5IcTiTxj2perAJmKJ8zWsuEtH\nFUuuJDFu1GF4LCw5LZfrkIvlOcZr2oHVbjjCc124TsHAYop8LWVjItVQKhnE6ZiocHLZUL3OnxVc\nn3YUIiNgSrdSoSZgxUItcqiMVzGEOP23WCjy9uFEtZ7yFqeVzBnFUqJVCyEq9SqdrzAI7xzjdVTA\ncMx4UcMIOXNWcHHuyt1aEEkZrj6Ue02u1IKo5xzOcWCq3ZyvZ0WeLWNqcRtG0/M4OPjhL+DU+5Vn\n2i+fxw+h7zbCe0+S8Ew8mzxfwJTxstV+tJLJBUPvtRRWcIm2ukGEGCxjYqyKOQ4sxRJRErBaCDH8\nnSNgtkmd37wWbd9MK1bbhI/Zial7LEwZe8sA56LIOaFn1nXNcGDBbwGwCYTFTA2bsmHH561ZrlPN\nLrlUqF4LYgWXqHBdGze040VHpX4qipl1bGEKKhkTyCVNReqO6taEyMG0sF7kvgekYappWK3aas23\n1CqlXvIn5HqWiVlckSZKl8dGBfeUFNlBeIvDGxYHmLcCVqxPqtc6oXoti8u/Sjfbse2e05VVFDCl\nWzKJI/1UczNWwCQTonWSpKHU5motKe1ScaDhOYNQyGOxZbXpoeDEFLNudeA+77KquSv7tLIdgMM+\nv1x4hc0EdrwxcnFQupbI5QtYCvGdKmA2hFjULaltaSsodYbh7QTMzmPLxRqw5q+oqWmKjarJsrSP\nahOqbOWzOL/cRAoY2sihjQpav+Un8xI9XB8O0c+TrnR8FDBCzhIK2JHsjNqvxSE5it4LdQErRrFq\nSnbUkOGYhqEuYOnr0dWqTSTNq22rWChWRc2ByQeQbUeXUrKiA3uDdhgj/xDVqyZdNp2ErADar4Vy\n+ReoDPHJhItkqoq6pcbaKOpWmKESQoxdPrXsOx9S+EIo6xHIkhc8NsgdCUTLjsmHlqZtk/VbaZ8n\nBBJ1abTUVEoplvyqNlcbL8PmZSi/JQsdmk+xxQHogAegix+lXlKxVBZJegrtZuahk+VB6Vo0ly9g\nE0kZRf8klaxovJRuySQOhz4TLVXArNS7JGzO9cCjx8bF/IikW05k4U+4MRupq4UTkatIbZ0KOz3t\nmNqiLRfXpj61PrBa5DAVDmgf0eABWsAO4iy4/K8shI8X0wkh58flX51yzPjpATXkFDXe/ITxivP0\n5Rc5om7CMNmGYhQz11SVTJok+UgT6qpjw4kw6jUhYNNWrChpE/ugdtj2gakQohyAQ3oy+dlj23uH\nA6YEbEK31PAf5HKh/Vo6l3+B2hCi9VtKmaREFSfG6X0WlVIfTIYQE5PqJWNZzvXO9XCPcGjdGxlm\nLOrNTBmzdmd6hYnpr6hI1wTTDsyGEFXAcI/tAW3vHe6BA3CALiQBQy5XLh/TWb3r+fIvkTVC6boM\nLv/qnPk8cpIrW5ACFnWuH3VLFTDbgak0gYk+GC8a3PhTCjP6SjjRxaeM42YLeRZWM+x6YATsqHRN\nT6/NbF3ghIBZ43VA23cOB2CP4e+DELAulhHrNlRm/h7nYZetRSOEnB+Xf3XKEGJRyWQ2hw0Smh6v\nN4MyHUoChkkHVjQkEw6spFvjInHmwZkBRSVLf60fKgqMFRJMCtj86OI0Vr1mClhKNRzVax817MEo\n2T7WW5IrH7+2QrcaU/PkUqD3uiQu/+oshhBtUsYW+zBDKuSu63GQqCRXEwI2x4FJEcJkCHHmB3BN\nP6Q1ukcAYTyLuE1dkC8WUQ/5Tniy4qomytNYJzctYL40BOIDdo9oBpsVdOsuFr4bC59EVXs8DHr1\nN6OG7aJ6beOULhY8u8EuDarXhXH5V+dECFHGCe1HOLB+lKuibqnCfAfm8r9F6YJoRlWh6BLiFIfe\nuT50lSmm9aYoYMhlDCUlmxlarO1PWn9K4piwYsmEDeqVIofShO2j/boD3vj43QEOn+7waYMPYhTR\nRzfmRWXKs0OWD9Xr8rj8q3PiQWYZP5RdX9p4JXE66sCe3Qc27cBUPrdcsDE/+UzVwhNpMcY45H2k\nyikG7oq6VZOro4ZseqL8daIPrChdIX44phdKGUvSFf6+kZNS6LDFmxb7JhTH4Ta6WEhujCwfqtdF\ncvkCpkKIqn8ryFWIHOaxxMdBotQIDketGEoCdmoO/VHjZd/06IDOeDIVY3S9d5kyoaJezwgkHjVk\nxSlyevqbHhKYGAsxJB/23g0qJXu87qJUfQLch7Dhd+LPDzE+eABaoMUPb7FvsY0nrs2tGNVr+VC6\nLpjLF7CJIQ1rIcQsP179tVasFkK0ujUzhGiTD1GaDSWVKsYVS305RU06KmDqry28jSE72gem7Ffv\n3eC90igbB5EuH8TssRNJHfv4c5MZrt7h0Izy34n696WzRpYD1euyWa+AqfI40fdluVJWTClczYHV\n4oeoOzBvdMjnMxSnyE9jVqIyRwxH3RhyiZoWsAn1mhCz6X1QDzX3cIUTlGRsfGz5ID9P+DUAV/gt\n4BCr5gA4PDaDrtlbEArYYqF6Bb519dOh8NmnP3u/e/LiXL6ApT4tlbuRIoci+bAfmz8vCp2JHBY7\nw9LnLQWsKEi1yGFTmq0r/WpOdc3uqClpTlnApHTN8WHFr+HvxFiIKYSoO70OJSvWq1MltpadIQ94\nBD/nxEmkgC0ZqtcauHwBU498WeM1CJvvtdnqjM2yv06EECGUDKIdVGZoWrrkrygZL5jZnAiPqW35\n8glXMlPs+nqGgNXUa6JvbMICSjEbgocTY6BkletSXvwVviqEvcnrrlAvFLAlQulSXJ7xSqxUwGSq\nYfirI1HSbMm/M/PpYRzYtIBJBbI2a0K3UBIwu1qDlZ8JxZoTRZzpwya+Hg1jhk8Pl5ldW8+phjdA\nn8bYSA92hWpttYZNVhch5Ay5/Os1BAmV6xLPL386KpPsQfFiis8n1kKI0w+Epb8Jl/+VbgGVOKEt\ntHlHlxJCZU3ysz3hcopfUbdWypnVBGxORLG4A+mx60ff6PPVGRmTNfkmPOS1jZWVvNc2fm2BBtdH\n9J4sAnqvtXH51+v0oPIF42XzAmzAsJiOqJQMJp8eoqAcGCrJhxOFJm7CmYk+rmceNctVDCeirkMn\nWbGJ8tQ+1GKGKtaXBKxz6INKycqNuhU+G5c9TkclWyZUrxVy+ZepFDCTRv+oE9hOEjD1k83msCYM\nsWxlKemWLaBUQMm9yVQ6l+9ATlGcJjRMzoCKu3qegNX83JSAqbSMmrUNCvVGCliqr2aUsVqqy+Vf\nHJcD1WudXP41WhewvqxbNfWqyZUNKtoQYnw/80h6FfPG6JB1AxAPckmtki112oDatEHqkJyIaeWo\nCJhcVs7zsgIWJoY6m3WYsjIHE4a8BqMDuxZy5oySXf71cQlQvVbL5V+gaYgN6b1c1486ZB8eUp1h\nxdz6iV6xR926TkUQe7geQHjPFxww9sfYN1SlHi8v2uH0FVHJZjzPJPuZ5Meb5PWjAiZXqArFv2oN\n02Yu7eH44Jft9Eo1m6or/LSNUx52IqUeY8VdizF8m4qMXf4lsmAoXSvn8q9O5cDGceWV0zoaLSw6\nsC7v+sqla5aA2UDgI1xwZj5/Q1USp8xemCH7Jrq+Shqmvh41YWlms+7jAnZSQW43yzy0riupl/zb\nCDFrgc7hsR1/Dv1eE7qlVkjOD6oXufyrMxewinr5U9SruKCHFwP/4hQBQ+mm3/VwnbBWLl9YNrJd\nbrncsfCaEZuZHxwTMLtm9VNxDUcFzKvIYapKe4CqNuX4vGFK1wwzJHlrRJkhxOVwqer1B1c//bOX\n+9jWi3P5F2hMoxfPKSv/VIsN7k0IsRMT96PryoVM5x7WdUTf6KtP08P1cI9wKWDohato4npVM23d\nXy6bSh6KIUQZSwTQxW3UBCy8/bnmwN5GybxKPixWqMtFK1VIK2RMnhs5v30js9S2iw4h/qunfzLx\n6y9e/fN3ticncanSRZ7B5V6dEQc/jLLhc89UCxsWCzXj9Vh4DOxo/DDu2OiXUpjQGgAHNFLDlDNo\n8vVOGi8xV9V+JfWab79q6vVSAjbEDzHr0MZaS9IlMXL97QAAHmNJREFUHSrympXGq+bALv8SKfOv\nnv7JGWrYGtSLJmw+l391juqlNEw6ppPUK/3UZ1rWxRYyFayGSVJzmjTMCWel2s/gxoZ2VrXIQHaA\ncu1mw7VEiZqSyRnUGobqhZ9yTvl2TxWwQn2VDirtirZiXW6/bLVaGSt+1sq5adga1IucxAquTvl4\nlsx9n5mFKCOHIoR46PUqlQPDMQFDKYSYZlaqFqKD7Ru4Lra2SS0Tcj9Q3bZVqTBI7gFtKqsQolKj\n/BB8Kii7VosoFv8WC2Pe/LQDsyFEB3TiVcuupGGoODBbWDEhzPjeZWxt0vUHVz8NgD7sKCu4Om1o\nLzXxKtAkW6sJ+2Xe0mwjh0U7JAtJq5xoVH1seJ3Zo3GEjX7GZlS5xITrkj1hac60VNz/qQ0UlaxW\nrupWOoqJuwBlYIt3BMqEqRnmfC6Ff/Th7zxzwR//nau//MHL7sx81qZeZD4XdHXWsBE9Zzr2GykR\npuXyWr1MBmImizaJA3mhiM9Phs8T42XU0ClH4s3G6gawFjD0pXeXWAE7Si3eOCFmVd0qFookP5oU\nS2VmIi+7fGZcvoA9W7oSTz/+o+9Rw9YJO8OOchFX5zTWbCEPKCU5SsYH8avsjwLgRyGzo9IX1WSi\nBXZ5weUF6SuQG7UmZNhLm1ZTMrW9ISBXjh+mKOIeW/VEs1iHl4XwcAJi/FBFEZX+FWOJenANWVlH\n9d8GA8O5s+OSOLO2dEx26GRnVG2ZvL1oKZ5+/EfxNQDAr7zsisssyHj92E88/dX3rl5jzYwlTrPY\nq3M+KrKUkPfjLmpYI0RL6YlZdDp+KLeA4yG9KeRKMhNWdFp+amMTiRvSeMlYolw8yZVdc8rmqPVv\nKQErSNeEbh2tvmLwUN4jOLGS2sxWvUiRr70jDSOBd2zF/vxffHYo/S/vbJvPZAXXaGOaqoDP23o5\nBu688JEKTdWeX357DUs6m+3ysWhhrelXAmNFS2ZzyAWl3wofD9dkaSTjJpTxUrHELDP+6N/SUQzr\n87lKpUIj+hIhbkqshin1Up6X1HhlK7Yg+/VueDcaNkrXQliBgLWjhnW4hrAFDTrX9GNAMFmxgAwO\n5nrmcuEoWjFUml8v2l65qpoTQOzQyZLnH4VrlFFEmG3nWMUKchXih3tsD2jvcNt3bqiWdMAOvXOP\nMc52HQc3CZHD9EmbKMYSC6Px1gqy4ibcmLzJkCHEdMpqp0SZM3kddGYeUuMVZIzSVSOEE/GiEcXF\nKZZiBddoA+82Kk8h/tJt270Lg+nWHFiuKsX6UmJ2NH5YtBPelK3sVR2Y3ZXilnQgNAseJiXrDw57\n4BAFLPUPpRFAHB6bxsfhJeO6s24wGKtXcF01u1pT4qLptAfoxVlDVHqX2zX5q9qHNI/6Smq8w44x\nghfqGFu6dAUu/+r0bqN6d1ILG8ZIbJuDQz88M+RF9MnGpqY3lBdOioEV/0qLZj1fORdxgsH8THV9\nBR+GB2CPQcNCPaTxltpRw3qne7nsQ81pK1mG4fMEzH6tWTFbKIYQQzn5LXuqXP6VTPMSHWO0X/N5\nnoxdhm4lLl/AQmQsNNAP2KWW2sO1OHyIT3Z42DUP292nQ2UkJUueI+mZqK2aT5rjwNLEooapxrbY\nyHuUHghDZfOAkI/CEIhBtx6w+yF2uAe+DTwAD8AhZrXsonrtRJ5Lg75xnWuCCbP5GlnksLifE/VV\n0/9U6OpLmaPWFQrzuDfMsmnxy79EXo63sGKUrufx51f3c2f9rZ99zR15P1z+1Sm7eUIfT8gUDwkI\nofF18Nvm06nXauTSZfH1rxN38DUNc/k8MD959bMqHzMNyh4lJcMBeADugTvgHjgAbXybcfJeUm86\n9G0WMLTjcZTfhDItveqvLUwIdm0TRduHvJwqOq8schqnWzGqF3keqxAwaTJSoUPT4hDHqve3zZ1r\nei1g0PGoU+vr6P29j2XbcsqVOLMGH6KIp2OzEIOGvUGLPfAA3AGfAHfAAdjGVz6GbaVeMfHElUy1\nVwmH1bGgZnpHJWOozzxHwOxPMNtKBScK5FRO0TCqF3k2l3917rF9wG6P7R7bT/DhA3YP2H0bHz9g\nd4s7D3eLuwPaW9zdbL8PH15+ePztUDZepbAtpJ0Bca01iZJlZ9rhKRkob3ETC4Xho3APfAJ8AnwT\n+Bbww0+ADvgQf6eBB25i/DCsX6RI9o3uDBv7vdQeqkcN5ghY8RZgjm5BbG5ilJTaLQbjh2/JvHAi\n1Yu8DT/yvnfg1ZFtdBCze9x87+GjT//d9i+6j+9xE7TtgLbDtRatY63YSRbIhq/kSiZWVbQKXv5c\nXEVpjcotIepNh2bIm98Dd8AP75/wXz7h7wHfxf/rx5wONYKW2JC31XTUDE1/pkeZLM5ZG/dSlosz\n24nqFQPkeXxt6sfzVK+n7109vc6wGuTFufw7TJliF7TqDrdPPzr8B/3803/cYr/DQ5inaR5Vj9e8\nTYyFWnNXFBeVZCALdp60/syrHTUoxc2Pk8Xq0xhZ9wDu4tQ7YIvD7Tjglt2Qy9ZWTjucFjNUCqgf\niPVbp+qlXMSuueaLl85fAgB+/B1usRJOPFv1et+7QE7g8gUskZ60VROz70UJEk3bHInyZuLEIvYE\npJllJ5md0wPozT7b/RONtUMvHzoOT3GlAnbADbAHPg9863NX3/9/YgjR4Ra4AW5iTofNdok1mQUP\nJ4yRVJGJIUxq6qLmKQokKiFEu1G5WsnptzKkTK5h5yldgatn7dsrDYRIjnL5F2honcOnxSGYrav/\n7wnfAn4GP49/s8PDFvsWhwbdrFv1V7spL+qZ2qhWqKJ0qZ0XCzvnrYYN2ZghX2MHfBja91scgBvg\nFtgBWyFd+RuzNqU7A70ndseKclU0YTBfYWYualhtyvS2AtYRXwbv0ntJYizxnNWLLI4LuzoLBN0K\nzmCHhzBxv/3Owxd2t7i7xd0oYP6x8JYUlNs42/w+jzktpDfNac2WFXYl31E1mKGUsY3z/dYNAuaB\nRmQh3sSC1LBm0n4ppT2qHNM/wawt/S0mhtgpPp5Z5IWigMms0Mu/RN4RX/pxXLkLVC/ar/fI5V+d\nW+zDI18tDg7+Bvch5zA8yPyT+M4t7m5wv/M/HEagkC9iTp+oaqX0hYJ6vYhFCyupOQGf/plvODq4\nNvOj4VmC0Hd1i7v7m5vHtsEB+DB/kDlJV3qQOY4wKQdFHHLopVoUC8jLRS2p3TrYqreHb8ODcgdq\nW1c1jsLT64QoqF7vl8u/OpN0pdHTQ7QwCFhwYDs8DLp1yEWr1D5OiNaL6FZam35mWfyk5in/rCZG\nB1aMH4bPFvuHdtffukGl0hAkba5b0X5tREAyG2Z+QkpRKk9PhKl0WTjqwIq7MaGaqU7V2+AIIWfG\n5V+dVsCS7WhxuMF9CCEOY9dOqBcAr5tTK1qyaX1BPZPr15lxqhW208WvNniYlCwFWn94sxv6t9JY\niClgmIb2b4auLzUIvd56cQ+PClgxw6J441BbaqZu2Z2BuSYu/xIhZKlc/tXZ+jeN60LzGsKJcjDf\nG9y7rh+GUEpPO6WPCSR600GGV9MqRVkpfWmOeguegodJrrbYA3DwOzwM6YhbHLbto2/U61QArVsq\neHg8+bB4Z/CMp5vlIdc+xV8PYqPqp16sdjMc7HDshBgYPDwHVnB1dnCud66He1RvDW7QuUM/IVe6\npevLBgBm4rNJBqt4YmrTCztk98yHw+5V/DAUOjRB2AAEw3pwbbdtAPRwm7guJV1i3eKpL7sb05/p\n2dSxFAtKCK0VU3LV6dOq66t3ANA9a/QwQsi7YgVXpxhLvnGPwOPYueRzv3Uw0pU3fKqxfQ1OSnyT\nAjLXo0QRCqIVCmlc42CkUsQ1vGkl3z2f1hCmpHnKr/sq7kNNtI6mCMq/iQkDZ39S9yU9SrsV/Wbf\nAFHMyFtz/5fAT7zvnXghaL/OhBVcnHs9IC8gGqt9FKqHmMShEhGTsD3qwSiKMnEqL3ACilutSUWH\nphkSWJJchSWCCQueTL47DdJg5aQXpmTJh0kepseCqmUGTjiwooCpFcKsR85ziHP2dj/S3OkuIsUQ\ntyedEGK5/0sgtvs/tvBHwahe58MKBKyrD3fRGa2SSfO5A1P6NNGiFqecytwTM73tkg2yUcSgQOm1\nXukVM+rdKPlGxtd9pb9lzzTnMz0nzGoRnVJxwVqCfma8aj11yG3wCi6Qd85ffe9quRpG9TorVnB9\nWgGTraGUrknroJpZ1P3As5k+GSc8knRM1cJ4HCmKmJQMUcCCCQtf1RtSQqGsXihVEAqVeeRTjCWi\ntFr5t5gzYrfeK92yT60rAVvBNfLKBPt1AVC9zo0VXJwHUU5tn+ro6mIsUXaGibLvs6YOpi09FWfK\nsr0slu2Che/WfqkGvQMcnPPpSbjwRrQD2i32B7Sp9yuFEKWGhSlpOqLC6fzD2q2AnaEmJdM+DOao\nfSnDUArYkGSYbHUKJhYFLOZcDuXboyeUnMTiYomUrvNkBQImWz3lElQ7VjdhquV8G5ulsEqWyi7X\nMDvb1MmzuyuOPUQRpQMbh/SNnWFxUac0rPz6Sm/qFqXalrt0qgOb1rCaNEIlGcoAsZwbYmOp1jvR\nE0aeyYT9Wkoskep1tqxAwLpYsI2szxu0uoZZM4BnyVituouuy87gzPxTK5V4/VWO6psSEcOP4Wua\nMVkus8phSvbmlFSwqnN04vQHeUEevtKtVO6tqE5EiuV/FCekqwN5LksPHlK6zpwVCFgIIaoWMLVd\nyYGlDA47plRXbUiRT69RFCRZUOqlvjaVsisuo7A72oUnCjoA4YlmDFXSyMSNkBSvesKKH60Cc8KG\nyidZU4SSxNjbB5lWmkKIbyDWiHyNqSLs2zmtA/OiZsnJzFEvKgR5Gy7/jcyFJvKY39LtZq/VS677\nGUyoF46Jmf5pItSIvMXOC/KJrvRWMPmEcnrSS7kxVehlCNGK5UyzVcy/6Mwpsz915sSFIOjxue0M\nxYkpwEjIwvnVP3jfe/DyrODucqIZtRpWUrUXbMCmczdQkqiibg0TN6Wp1pCpk+zDtPKgiGKuar+X\nKmTC7utfZ4rZhMIhj/PJA0zz9L6iUnKZYt6IcmAwmyQnsPTgIVkEKxCw1EYhb6+UgMlsDvlAWK8X\nQsmKFZmIHMJITGo1m3yKG4fPzQub0tu5igUbeXSQMUCVbXgkYIhs2Vm+ykYLrdtRtxHhJ5lYCFFQ\n4xaGintMsx7M8t6crs7MnOaRqtis4hp5UShd5J2xgosztX3FtrUWTIof5R8wT72cmcFKF4y7gtGz\nKX9lNKkwpRp5RE2TVBnRaRWMVyhbv6Wk3v6kvtpzUbzPQDJYefX3Lo72VNTGooC5uupK7BRCyBmx\nAgErtq0zP33Whp3UnhVr1pV+VXo2S72ujTurKVZlvVKWbOdWPN7sIGoKV2j/rarB1K2dUuwJC4XH\ntF55P6IOb0K9VFdWTcDSTrt8IpkL7Rd5l6xAwKYdmAxSmZ7+2s35dKtWq1OlXhMhRGWoZFAwfLLX\nS6pAYu0j1ujdJkQO5QPLJwUSg3plr6+c/kyEE20sUaaGDk9xqcXSSZCy7M3ydil5BrRgPuHLAK7w\nFXGeKWAnQPV69/wVfu7H8Ptz5/7VP8Bv/ayd/PSrVwCufmsBz+Qp1pGFeOoHBfs1E6teNVOEvPWd\njgJKAcKmoEmTfk0Xpru1JsKJELZsfIQ51TPyClSuZr4VS4ozDFpY+/jCTUc5LUep5VRu4RO+bI6K\nHIfqRd49axIwlBpKOzFO8fkKMNmYTcgSKuWZH61Qm7o1m7/SkmKVaq4cTswG4ChWkLKrMxXLqkxB\nh6b1bL4HrHKFrxi3TMilcFnJ9Cu4PmW7acOJqoWUDd28EJKLq3Txr/rJfnWiXMs5lIU2la9N8LAY\nP5wMKna4lsFDGUIsDoFY+5wQP5yWEitDh+S9DmJSWiadGXVL0JTOZZcvpc6YPBW4wlfFdNgZSA3a\nr/fIaVFEFAKJSwweBlZwcRYDWUVPkP/1ZjUWl08v1qaVtEpgr+rAktEqdGud+PHYWNdlHZh6AqyY\n4lG2X9Zj2ZmPylsWObSKlz5hZxqhOhPrVecwiZnLJxbPCZmC6kXeF+sIIeJYs1Zp3+zkgGrYjoXr\nZolLMSteujFc59+n8zWqAnba817qbyqMA3CoSkZesNVb07nspBQz64tmuZipMa1eap45J4eQy+JS\nAokruDin28qamAmc+Fuc7s2vta9zjJeMHA5TruMPKTYoC9N6locTbfAwBQxPfZz5+N2A8lVFs2W1\n6RFCmYohROXApP1yYttHkwzDnI2IPcq1yVNBqtB+nQPTUcQn/ByAKzVDJSNxWazDgdl2Vv5qy9Zz\nRext+Uk2SzaKTWW6/Jolzdds1oTxqg/AYeUKQM1+iRqKE2tma6ImZ1qx6v3FRMKhSuI4ekbt9Akn\nTAEjCyaoV5nl+7AVXJwqgISSmFUUy01pWXb/X/tVltXfUDiSxLExatbkX9WSk7HE1AE2bbZglKws\naXMECRVNqalXj/z0SOmy0120UIEuPWhgTqA6kzVL7MVXOrDj0H6dP1f4/SkNWzgruDhtizlhCwxS\ndVTBi+bN1qNtI2HaSycETHVvOQAfxFIKA27rscRj4UTvNge0xRDi/MzDzIHZKq05sJqnUs4qCx5O\nPPUlN6bOA3L5ye4urvBVM4+8O1DKRwE7AtVrKejg4QWxjouz2NTacGJi2nnld+yn2i9ZeL7xqvmw\nejix1tclKqnwWNhEYaxYW8mqUKQ8fVrrimqploVQI3WikuYVz4CcU50ZQs6dk5PpL4IVCFgxhFic\nJ0eqmLJTPp9YXFYWlDtAbryQN5bjo8pWsRrzk3JtVsmG3I3ruakZY5UUQohjCqL1WNPYYCOs2tU0\nqahePj9FcnXqPgH5uZopYKADI+TMWcHFOd3pYiOKAZdSxYdvtQJMJRZnVg1qMXI4jhGVIodOxAld\nKflQhRArscQUJwxRxGIsMZmzWn5HrKF4WEcjh7byYRbJyifYryd8Oc8nVDvU5CKnpE473pQuI86b\no4BNwPjh++IGuK/89BwTtvBcxBVkIWJ2UAtzG6viHX7t05hy0Vnh2kxqKmNqWI9V3FL8qnI3it1d\niMo0nXyYJdCrGp5pxeQidvHse+3mYkiID39LK5U+bP6n2HmYTDIh758b8bfIX11uvkaRFQhY0SXM\naGdlXMlOmSNdVrGK6uU2FfWqdXcVY4mVLjHvNtPuSunWdBr9VMWq6XPqV9VsoaaLRtcZ76XmqWlS\nbeLRnwg5I2oO7JksOZl+HRdnTcPmNbWpHZXxRV+PIrrS31CwXV+o9Xi5kkpN/C0W4oNfE0mGELql\n4oRFJeuzYz0dd4pLGysvVfmwvNAwpXZp95r8jDnhzORSqq7lDE2+QjLA+OH74oWla/ms4OL0uXQV\n8whU/0j8yfV6mmxK1XRZsOqVBGyYuKm0ny7v8XKi0FQKxYhkAzQ44IOgXtMJ9HMeC4MMIaJuvxSp\nsmqCn6mPM58G6Ew5rdcuoiS9jWe3MefYiXmk/RKna+OyXSWEnBkruDpr6nWaDxhQt/FyuvqLuvGC\nfSVK0YEd9Vs2qJjLoY9jzM8Xp2I6Yvqrq3S6jmo/aTclf574yBqdXkROL3anTcheAzhs8tNGBLRf\n5HxYzdVZbFJna1iqJl+psprxgmpZlfGqCZgq2L9W5Jz+alPnJzrArErN7QmbX4PF2pZ7vgH6CSmS\nlVpcvvg5KmDGAl+XtkzIQljVA2EruDqLruuoh4h/UxRR/mK/ulI56+iqiY0Md6mJqSBjiU2lIMKJ\nvhkSN1LkUBakLTs6mC+Eeo0piBN1mKrOOq1pVQqH0Dn0TXKqQCvChp1YV9q8rE0bcm3inPZ9YCma\nG5faNFmdq50khJwf67g6bc73BMYryAkuN2Gu9DcrpGCUMgYT/ulo/PCYS0uCVBSnUEYpdwPGcqnC\nCRkcUslsQRokJWbahKUfGiFdVopszaZF0j6rpZAtIqsd+cZJhPFDclas4AKtqdecnrBQPf1YTItK\n0YLVLWW8pnWrlkxofyrOZjRMyZVKoEeeLg+jZDX1OoIR/sIMSbFqT2qFys00rImj9HaiymursJWC\nym4ln9Vg48ryRwEjy2Q9UcR1XKC1qNf0E81uVCoVSEyzQLRyY3NndWtCftrST3NCiC4LG4ayx0bm\nFk6MuDHxWFgxpR5zZMzqkxf14kuVleQJMV4I4E1bWizNmvq00ipgqklWH8p9YMoc2xNBASPkvFnB\nBVp80nY6Tc58tZPtXwfo7LXifb01VWrOorVSP5XWENTraOZhLQsx1s34X8JmJFar1FW+Sr+kylKe\nVHUN2RxN7L5KwcMm9oT5ypK5/gdrBcA79GIXN2IHJqK78gQTQs6PNV2d87PnrZPIO3+8ad8G9VKT\nppVsot0sqlepiZazqe6u+S/9KibQF5PpZ1XdxPQJJZNH1wFw6CG+N/l9R1HAjLynU1BLQkS9M1LO\nQwg5S9ZxgRZDiLW4ohNTkkvY6LF9M91CqU1EyTDVerBkoa0UmqlMxQ7XIWBokw+LCR3Tb2Q+Qb2k\nzKtH5IoF2Zklw4GIktTF5487h8et6ADz0ZDVshBFDW5ivTVxx6yA1ZZWp48Qcq6s4AIthhCPomQs\napiaZSw50yyi1Dge/UznaFTWlobrPWq8VNhQ5XGUKq8SRZRVZKXLzoA8sV7OnL5Kr5UKfYofdmJF\nMAKGsXY2pUo7KmATH0LIWbKmq3P2Y8sDLm9zcx82VNwmbw1xeuP4vE8WOdzMf59yMUfDSlTRhx2p\nK1VvxenprzcFpUTSnA09WM24d+UlHeCwcVrgbSqiXQ7Cb6kF13SJELIs1nF12shh7SHc2kNLcdmx\nvjbl9rMgM67uwIopG8VCU54nDDYv44RHX/Q1R+2O1KczhWI5TUlhQ+muIArK7CKPK3qga4avfVGO\nXJb52ZQcWPEQlIAh1y2GEAk5b1ZwgRb7vYpfjxJqqxdl5RtgJto1ODODM+s5Ko1xnmL3Va1nC3m2\n4Wkea7pOrL8pzuaMcUo/NWIlKooo7zk6B6CcUjh93wBxUyJ3UiXaoFzPhJAzhFdnhdTkWVuGmLhh\n51ft3VEFqsmYlTSU55+TZ4jhUMrZhjDiN7d+ZooWTJ2osp1NWiIlYDBlW2PFzHhv1j//doEQcpas\n4+o8yXi5YzMk9Xq2c3r2J1+5zN04mliIkp69VQdY2p85yYeB5Kisu5IFZwqNKKCSkWGTP2shRFf6\nK9eDuDjMsoSQs+Hq6enpfe8DIYQQcjI/8r53gBBCCHkOFDBCCCGLhAJGCCFkkVDACCGELBIKGCGE\nkEVCASOEELJIKGCEEEIWCQWMEELIIqGAEUIIWSQUMEIIIYuEAkYIIWSRUMAIIYQsEgoYIYSQRUIB\nI4QQskgoYIQQQhYJBYwQQsgioYARQghZJBQwQgghi4QCRgghZJFQwAghhCwSChghhJBFQgEjhBCy\nSChghBBCFgkFjBBCyCKhgBFCCFkkFDBCCCGLhAJGCCFkkVDACCGELBIKGCGEkEVCASOEELJIKGCE\nEEIWCQWMEELIIqGAEUIIWSQUMEIIIYuEAkYIIWSRUMAIIYQsEgoYIYSQRUIBI4QQskgoYIQQQhYJ\nBYwQQsgioYARQghZJBQwQgghi4QCRgghZJFQwAghhCwSChghhJBFQgEjhBCySChghBBCFgkFjBBC\nyCKhgBFCCFkkFDBCCCGLhAJGCCFkkVDACCGELBIKGCGEkEVCASOEELJIKGCEEEIWCQWMEELIIqGA\nEUIIWSQUMEIIIYuEAkYIIWSRUMAIIYQsEgoYIYSQRUIBI4QQskgoYIQQQhYJBYwQQsgioYARQghZ\nJBQwQgghi4QCRgghZJFQwAghhCwSChghhJBFQgEjhBCySChghBBCFgkFjBBCyCKhgBFCCFkkFDBC\nCCGLhAJGCCFkkVDACCGELBIKGCGEkEVCASOEELJIKGCEEEIWCQWMEELIIqGAEUIIWSQUMEIIIYuE\nAkYIIWSRUMAIIYQsEgoYIYSQRUIBI4QQskgoYIQQQhYJBYwQQsgioYARQghZJBQwQgghi4QCRggh\nZJFQwAghhCwSChghhJBFQgEjhBCySChghBBCFgkFjBBCyCKhgBFCCFkkFDBCCCGLhAJGCCFkkVDA\nCCGELBIKGCGEkEVCASOEELJIKGCEEEIWCQWMEELIIqGAEUIIWSQUMEIIIYuEAkYIIWSRUMAIIYQs\nEgoYIYSQRUIBI4QQskgoYIQQQhYJBYwQQsgioYARQghZJBQwQgghi4QCRgghZJFQwAghhCwSChgh\nhJBFQgEjhBCySChghBBCFgkFjBBCyCKhgBFCCFkkFDBCCCGLhAJGCCFkkVDACCGELBIKGCGEkEVC\nASOEELJI/n9z+iEiedjiWwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(1,2,1);\n", "hold on;\n", "imageplot(perform_hist_eq(D,'linear')); title('Geodesic distance'); \n", "plot(pstart(2,:), pstart(1,:), 'r.');\n", "subplot(1,2,2);\n", "hold on;\n", "imageplot(Q); title('Voronoi'); \n", "plot(pstart(2,:), pstart(1,:), 'r.');\n", "colormap jet(256);"]}, {"source": ["Geodesic Delaunay Triangulation\n", "-------------------------------\n", "A geodesic Delaunay triangulation is obtained by linking starting points\n", "whose Voronoi cells touch. This is the dual of the original Voronoi segmentation."], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 1__\n", "\n", "Using |Q|, compute the faces |faces| of the Delaunay triangulation.\n", "To that end,\n", "extract each quad of values |Q(i,j),Q(i+1,j),Q(i+1,j+1),Q(i,j+1)|,\n", "and add a new face when three of these four values are different (this\n", "corresponds to a Voronoi point).\n", "Display the obtained triangulation.\n", "ompute quad of values"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display the obtained triangulation."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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ff5IsPkOWVhBGgRHisC32EkQjsDAUU0AOeyVyWMEhQ7E+5LKPIxFYOAcmBQY3GrPxE1AW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\nTjbfcz+8/6fCUeHGa/a/iM0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JVmap/OGUwAu014kRc+FvncE4TokV1LXesCl+tKCOI1qF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\nAAAAAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(1,2,1);\n", "hold on;\n", "imageplot(Q, 'Voronoi'); axis ij;\n", "plot(pstart(2,:), pstart(1,:), 'r.');\n", "subplot(1,2,2);\n", "plot_triangulation(pstart,faces, M);\n", "colormap jet(256);"]}, {"source": ["Compare this Geodesic Delaunay triangulation with the Euclidean\n", "triangulation."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["faces_euc = compute_delaunay(pstart);"]}, {"source": ["Display."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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DNpqx+1q+GMMFzOH+ufIOvwNsgPf5GeoaX84GsDBtTwOLeV8Flfk4vK5dxAz5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qhAZG\nCCGkSmhghBBCqoQGRgghpEpoYIQQQl3wXdkAAALZSURBVKqEBkYIIaRKaGCEEEKqhAZGCCGkSmhg\nhBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqE\nBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGk\nSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQ\nQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZG\nCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpo\nYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKq\nhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRggh\npEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCE\nEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQG\nRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRK\naGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBC\nqoQGRgghpEpoYIQQQqqEBkYIIaRKaGCEEEKqhAZGCCGkSmhghBBCqoQGRgghpEpoYIQQQqqEBkYI\nIaRKaGCEEEKqhAZGCCGkSv4ff/nwTvF+jf0AAAAASUVORK5CYII=\n", "output_type": "display_data"}], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(1,2,1);\n", "plot_triangulation(pstart,faces, M); title('Geodesic');\n", "subplot(1,2,2);\n", "plot_triangulation(pstart,faces_euc, M); title('Euclidean');\n", "colormap jet(256);"]}, {"source": ["Farthest Point Sampling\n", "-----------------------\n", "To sample point uniformly according to the geodesic distance, one can use\n", "an iterative farthest point sampling scheme.\n", "\n", "\n", "Construct a metric that is large in area where we want to sample more\n", "points. The front should move slowly in high density sampling region."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["W = rescale(M,3*1e-1,1);"]}, {"source": ["Choose the initial point."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["vertex = [1;1];"]}, {"source": ["Compute the geodesic distance."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["[D,Z,Q] = perform_fast_marching(1./W, vertex);"]}, {"source": ["Choose the second point as the farthest point."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["[tmp,i] = max(D(:));\n", "[x,y] = ind2sub([n n],i); \n", "vertex(:,end+1) = [x;y];"]}, {"source": ["Display distance and points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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UOqTLZ/0OLDqNZQ9tHnWRuOk1MweRR12L7XFkKvlPIlooJ7q02tIwo4gscughxEdSWy/o\nXD94uHAjO17Z36rcogCrPln1wA5DiNXxYiFE+kgshxNXvF7isg/uyFr2zQFtCDGVw0nkSFc6KDGU\nNVlz7+AqtLTzoRyT6uP0srZpOSB/gGTd8Rqd0nXyj2Rm50MFJNtCEGtZIjnpTbB8GKb+3pQTcA/s\nQdXeCNF/8SUGdjSL2AOwZR9qmCfKLQYw6YHV0Ry1TDR4SEch5oAhBVgGW34Ydg0nLuXCXciB1sEZ\ngbwNRofjh/q1X3Zz2HeqKNjkUjXF9ZhS2/tHOoERblk52W+HNock0+hF9yy33SmaZYyUzjIktEI7\nyZRA8zZjMWji+DOwfv4mLjOPngFg5A0vGjxk/laNHJ7bsOECLPh23r2u7/h7KSFEakSsOahIAUY9\nsOYlwYCEE0oIMbOqRg5fcc6OVw4hXrBktmWGXbBcsPx9/v6+xJ1eF+FspRJmrI/KriPs6yemEvl/\nYpFkhfE9DufWjOo3cNV9YLZl3Mqb+xapv8U4NXPHJZL7VPffNySWRlY/QhS320mNE/ajiLfmAVqG\neQjxwbRXhOtkjT/Upup4MQ9MPgOjRsT79QNRbW0IYUNAwBaX94RLHbtRPTAWUbxgAbAUh2vBJYWw\nxXD1uhLxwOqDrYoneuAbbYKpOT883ULUIcycbY+gTuuWi26iF8s5SC9oiSNriaUMXeoGOts+XNqn\ntoUfFYoykUoiTZxg+l+Y1UEZddZayhbJR/L7GHrondUj6xkA1tzJXOnFbBY/pJHDmOhzrwwtFWDV\nCGnb3aBUXB3Z4edpRQhbiNtL/CEBViOHuc5dyqj5XJ5rLFEFWI0l1pRQyLJVq7aYTp11Gn0xDdLr\ncAt3MKFPrz7SiqFGC+8jWb8UnXKBLLKW0mxylf5pbvMw6khHiiWSzfQWcZKxVj5Do38SgMV8J6PE\nD9kwjRxLPF+Nf5XIYebTv/GfmVvVoEHFkDaswA/yf5OZB1Ydm1rdyxcUw7It8W1Z3s7Law4nLrjk\ngGFG1yvOAF5xzq8855T/evl+xXD9Zm8dzSGN+mbYVq1QFlBvDKW4of3FsKfl2Hs0jXSu0lYhwGZv\nglM/3dhCZ3ihNdspo9z/SNGCZsstqJO6Sid/mQ7HH3YWjU9NBzWVE/YkAAMg3C/mhGnDEb+1jheL\nH9LfBZdw2fbB66/k6xjMA0ui7tYPz5dHUQHbefm5YpWOVzVyLDEhvGJ9X+KxBxbEIW+0EP6U62vr\nEF1s1kIByzDCB9goYIaa/xZ/azAby2PtvL8FeT4GgSdXsYB3zdj4Xmq0UCZaYze0oRzbbrkH9pDa\n72T0imINoy+fN4yCYYxb2QjrhtficlGA1beyIFyXPNX/xgIy3CQhxvdzfM31LI8KAeHWgkv+3R+G\nLQEJWIxYonrg76HFKTRDdbacarOo07pH6GWtNUiAPgqkIVakD7r69VQWaoRwN/FX3XIQZZPZpK1R\nimvvtBR0gUDovhAiWx0QISL3wB5JoTf4kE0kfviCH5VV2T7jNccSz3jNIcQzXpfLGy7ABfi7EOvH\nXQCrb1Jf9sKcv/88Lz8zvV5xztCqgxIj1jxeMSC9xvP7S/ncRyBj6+uHpuRXptaALZL/0QICLYqo\nWkMOnTMH2+NLtvdOR0uNEQLcatjckvscBNiIYR2QujvLiGRWpV0w8kjsyalESj4SFbT+LYaYyCcQ\n2cOOGVrzcwCMmtbUvhZ2Ckl+KUpzxd52xytHDjsemHwGFkqfH4gHVvGR9sRlecvogvDAyljHNWJN\nIWwhgCKpc7D85KjEYukYSHc9rNSWPkgvlm79HhpHJDuJheP7GSlFh2Tqb8forKIeKLOh5Vea55Vh\ndDYb/Wwdgw/fqFuSxsPrGQB2cJtD3xOrE2WDSq8FlwVvDbpewZ+BvbbPwGi1qHtfy04hAFb8p2Uh\no+dr5LC8/rwDDOEtLjv2Qjd4WE/IFsj+Kk5BaoX0sdTEeer7M+oQXdaiTn+vpveNTuYAtI7XbwLY\nyDbVvTPDKmF/Fba6hiuaQcYPZSSQo0gsVfOj8GwfvoG2d5qqNT8DwMqne62B8tTOIw/DPlC+Bg9l\nCPF8+bmz6j8LtP4urtiPMYChLUx9k3othcEeUTz/++eyXGjkMA9NzKFFlKr5di7EewXQILD5kn2N\nbCT6hV+GLnL29m1JUDm6Hlwj6LqJAP1uW8VVNmQ0raSctCzqrqzZO47jI0emHqJ60FYeNkVhFHqp\ngUFm0NmjaKE9/tCaHl5PA7Bi6lWKxA9z8DAg0Q/MS29sd7aoB8YmGUKUHlhmFR2IuJAnWJdS1BUh\nbEu85G9zsPLU951PIW0xXEOIURymPAMbOx0MY7ciiuV3wj2UrLsTZlvZDsEil0octSlsaBU0w9rn\niN1JVMs+eIgWyfqbpfkH+l05RkMdxEFn6Voyp5ofaNvobO31CQBmjT9U74Ai2B0NQ9f1ExuSWPRh\n2EoehqnPwOozqkTCfQuZBQHYBQiI8b0SixaMPrDdH4OFgcdgde8bxYyFnJE8roeV2syt7p8lWtyw\ngNP5JZ236ngNbqlf9nGqqds8PLjD/HJiB4hu5jZ4CIEuhh+LWyq0WE7zAxzugT2QVGKJQfM1nFg/\ntFGHINIQ4gt+LOltDxi+4mpc2hBiHc2xXf/DCSq/NoT3UpbXUoC1FAPFLQvAmQzKSHh5+ZFr3gt+\nYM+4j+/Y7Ri2FK4glAPr5dnY6Ax7GDZyctXoousRdMgtOtuBw3jXrkKJd8+jHf2t6OocnGX3GdY5\n4hsPunekYpIBQyt+KCOHnSgi+wdPEe88Wijth9cTACyrX5+IE0Yrh/TDItZrbLAONVSnFet2EEEM\nADbEt57jhXDdUXxZWWHYN+8j1re48IOympB+mlJrWImuGdXp4K3MIzCxCDdAL7XfBzHkbq2C93nW\nAdjhsVqlUiEnM8tGZzfMU+s5AQitI9WPH9L8fecMEMQCromT6DkAJiufTG9vfxi6rjxL25VeF3Cb\nTDWjCrBEipOA+I5wIQAL5ClauMIypC0GjlV2b9XrCOQhX1ND4RNroJipOrtM9dHV79FlitpJA2bl\nE/SKIotMCaIUfUQdLuowTP5aB0ePEu3sYeYgMusFVwKAFsMkyeRSlWTKo6+p0JX1BABjlYbGD9ls\nvH47Sn69N//uYcNX4IcwXvdYYvrJ3wfrvAZ2Ljt/+YlwIf/hZC0BQKDEC4FXLOe3FMIZr3kYfR7W\nkcdxlP/gvL7HuG+kbkoNIeai7J/kqCfLqsIVbxVyh0/L+ht0/W6prXsQXSBVhP52uufqTFEjAMCp\nfMiNPm9Gm9JhX+doOun3HXfnoGEUUoWTOqnuJhk+ZoX+OlFENZbYMXY7kfeX6fda2fTweg6AQTtQ\nrS72w817/DARLq1tLHEF1qvvdDgIMZDPJUZg2RBWETlkU0IMypBZWoPf5c2gPCEgx85vCJ06X1Uf\npNdIHtmdH/XpFX+Mg53S3Sq1+XcM2XBUmEEcLmzD4hwvlxjpThKrzXJas2r+fU9y4AbTDH3AEwCM\nqnOX1wLMuvFpcKQC5l0SZ3+qlVrnhTZelEEby3tZLbSbIDsN0XxsC4BHEY8aDMFVh1uHSHPmPbgs\ndFFbBUWHTyxdm9hDL+2dJ4VkdA9WYaVkBexkvpXdFq7Y0bMV0c3ZJjZ02ZccM6yTTWa4rkUjQnIQ\nxyTuF54FYP0OvbSlb+3Xw+gA+v3fK6+bOWQjT2/NK2GvAmC0RGVo4TWEmavNmb4Hlkt4KStcgIiw\nbjFeCybHcfy0+ohjmEG0P9e8Ui+iRQPZ79LfvmG2KIVbUaTcBLCOBvtcC+WqMXIaZLEl0uyThLgP\n3OiEBw9jg2oI0V5kxA8xH8OeoJ+yDlHeBO2m7pXvty3dicYXrRqSVV/TiiRbyHmO9oKk3FI1d17j\njT8oluvr6iZ6SRsimz2pAw4tbsn7LVkoS/QBrrVo8GhU4xDfLOcg5YN5aJ8YQlRXVPqjeYjF9Bzd\nlmwJWsUaCSgrOKm8eleWWDc01a7fgb/meSeDL1SAiUrMDLOZ0cOvKSf6LnPQarGa6JpId3TbEPVG\n7aplfo1eUbMtV0zdtqUk8rBAh5VN5jkEmLUUWpnV1ifRpX01iuzq/hCimiEgKS8vqySbhGfPAbCq\nbtsIoibxC8+efqXm0VQCf/olHTK1LIE89sqsCGxluq88nn7pFbU5um7jGThfmKMiuxR1uMVmJYrk\nr1WThFvBIod00O9SFi3tUgkwtk+mNGCos53z0QGYPA3SGHmRmeaJO736IwbHQ4jyubi2ong1dTZi\nMT0NwMbvv5Qs5MJKN6pcezonFpoemMyz3yyydRJfjd6sBVb1bkAUW+13VOHftFnXrVJ7a5CeWM6q\nvXXH9Sg27bKtX4Y0+TCMlsjCUm0XQRj0aNQK2Ke5dSbUg5aL1KnNwN5Z7tyPHt1bH0cas6H0TdA6\noHl49jQA60jc6FHv+5qisqS9xjZuTOl5JN94kdOB3bl7dT2dOlVBXdR3TNB2xiC29rYyI5nqeLHH\nY7ArMGtarDH2MdbXrQAjB80X2dBi9CI7bxr5IaVYns4qTTb1/npmeSfncn1VydbdJ9O4x0Gn64u4\n1wQGpxowPLcpkfxHcssDoyii3JL3kcnAm7T7p0o9MR2AybOClsTirW3qew2+fUxDglGMl+7HEgMb\nfNiPIroHNpnEpcqjIBI5OQmBV2v62y6hCw/rgH4BWHMSmXjZpD1J/XP9Qd1KL3Ut1ftoEyTdpLNF\nuaXGEqG1DTX2paZD+GHMJ7NOjHVuBgE2kOd0V1Sw436NhRy3BkvsVmBOeuGJAGZdD3ohjZNBCaE0\n7VIvZXVFW7HRrtq5p1XWFE06f0pKKSE7qBs0SZ113ayRHhqiktmssqhGCSQZJqdAnDP5MEyqdqxr\nO6uCLRB0fSSWqP6OAEym30KvccLRDVob52dphFIz9AdPA7As9R7kujB0p1OI27WNiUHAoYx+j2Xb\nsUUJ3aEcS0wbNX9UIG5g+0Xlh8yO/U68uaaTeuPUNwb76VodAZTgoXy4tbSUiuTTn9KgPhndJ0TP\nixZgh1RDW9U71V4F/a0As4cjfsOKApiRyOG4oUYRr7/p9uDhJE7YcwDMqsTt1UrhCgDGg2wEbEq9\njOW15G/X//JVl6xtS6xia9O1lO8XsIm4X6rBq6CsizRl65+4SSqyqye1Y5Yp8pcZbS28JmrLWRWX\n09J9GEb3LFtrsLta1Q8LZDvUHjlJtwJMsj4AZNTGLXG/D3lm3P2SfcK03Kp6AoAdBg/RXDbJrWsK\nA5SY4rvy5ffYxjOyJJ6ugZPuLvKk8jUb7HDGqqPtlrqmV4deQcswshHQjnmkxnKYLQbPyEfZ655S\nCPl3qzdn9f87qP+piEGutj3aCPsHbZ2kEYBBOfARepVVP4FY7SSefh228nlI9gQAw9HtRmHOO2L9\n1yT5N08XLPk3xjUs5U3ABVcjFQM4vzVe19re/6W2wkfxH6EXAAtwJvNsikjxRAu2kmLnqWnknZus\ngzo6Q/119SS7YTkrfSmrq4bSMaP9Pynq4EPqbJU6vNfwCLzseb5F/g9aAxK7j1wRUwgphDXGK8xo\nQ0ZryHo+cmPXQfygBybQJSf5r5Nv+GcoInioRw7rv12mX2BIrT3z/1LBswCsyurBS2KNIlaMMTuE\nrXl+xaYEJMT3fZOxbBuiSljbwDfjWTdZwSqbHkK06qVSQZP4ZYtck2qcXjS9gzThfokliu+lNpkI\nLDiFVL9MveDCPLBr60NqjBDeQ+Qtuh4Hc8XQ2jTbHedpDGAWvX7TBOGHHfcDVTJ9hkb/BABTO2To\nMKsAq22GGitijO+ddpg3srxf9xDI7SBI26lT8wjgZERXWphRN5FhLP82ByWPnTIsQavOM9Rc17Fk\n6+44F+OriOXB6NlVeoW2ySz4FtaI9YzX7DSc8Uqjagq3EALSXtWBFMIWAq/qlVWUYfWX5ux0gdLx\nkr82wP4wvTSvjgQPk2j4Fs/mcb/wLABjcYZAPgXffrvwPcYLllwVLliqM/6Kc64T5/PP/eq+lO2/\nlCpbthmA8wVp29OSFqivDlWlVfiP0qTPJcDyUmZfSuIZl/CvV5xfcb5goVONKL4jWl9Q5OEC0DJZ\nnGcZ7lOYqU18Qd3kgXUCZIb71XGwlva3TiVI/h/hNf/T8yBggmkAACAASURBVBf8yB5YBlgoIUR6\nr3bBQkPlzf1liOuSRwkb9VwSjhn9syVhZhinoHhCA7AZHXOoDjWUKTH/Z8LUxg9vGn84Q5N9AoBB\nVGI1vUzZCWNPlaqdwml/DFZdLvoIK2sFgLBieW/u/DoAw7e2kUcxG4GIFE7yide1bDmKeHh7BZbe\n8desKnxH1XaG/VMaoRddeth/t/SC0ZWrkwidy/+6l41wrZ3X6o3ikAEI7ROy6q4BeI9Rqf+0KXZO\nj3Xy1NOgGWoorzJGLmKJEmz3Tfnc6V2f6mOpXtrD6zkAhqPbDXKTsi5NzJCiIk9LfGuifEu50i3A\nEBAT4kb+0RdpStcWfTIedC+cXljASkIZVst5wx0WP0HyfKnprlnUiQda9GK2Cqg21yC9tKe+3wqx\nKrcWXGosMe8hO14R64oIYEWsrGJRdPIkeN3jirXtJUKvsG/3+nt4/lSMiQMf+TivlX4ruo4yi+Ch\nbPv9e9xJ9AQA6182Oux9vQ6R6EwxrCFuzeBDCbBQ/g1zbmRlWEfVXu2/kddfVIC1Y7fYyEOJsQ3h\nIGIA8runqA4aRKI8rbfKnbB/UGpLV0OIMPppmjPQjruHLis94hSu//S8OmEMYHRoEnO8KsmusQdi\n52l3xUJb+Vk7hFYr+15rEOcDzUvKuWCqv9Vn2Ie5NUCvDrdmc7/wFADb2g49tP99awUuhDcBl/OS\nK1l+GJbtH3jJTeKM14RwXl7j9/fryMNYVr8AlzK7lt+EsO5t8SoaQwxkPPECfC/E+l6eFnwHFqzx\n2w+8/MDLK875tz4Jq8ZegEvZtTrR6rvB4Juqj1dqq8Nw/Q7d54F1fsuk/rdl1euyhjtFVMfrjNf8\nDKwa2RtDcbPqTVs1skOWGabGS3JixLoPy8rvkEGr5h9wwtjbXdVguKokq/jJiYxJI//rq59nB786\naN6a2DdNmP3wegKAISGFavKLRNkWgYQthTXEPIgj1wzq5VSqxfi++17V8WIeWK4Zsa1JVbH8tiOy\nrChiiqc6WEP1vVbELRX3q/Pf6vT7L9ma5e3ZuA49LcfYP6JOYx/xwLTVDfescb/YNkITbWP9L3sM\nlis2BCGyQ0Y9sLz/zDYU140SLk9bCKiBxNQWvu+HtUdK0VVLpTJMFv43uFw0p/bact/96tgPr2cA\nGICxK1p8lHXhxKrcqsZ5ed3rCuNWIJsC2fIhwOqrnfQt5jOwIC0nNuZQDkFc831e3Zc14gisJGrq\nn6nCnZ7D9bmSPTG1WYqa2C5VESUZZ9ALWldeSVY9s4BUgZRbYgYVBVvzARogr4ICsGzkREoy5I/C\nsfuoPt8B4PopXvr7cUoN0ssauFgjrkPj5qlmRlfWMwAsYS2HWYZX7AZK6I8aCzaE1+W8lKSEsOBS\ngxI1dnFeXpflbV+3xiHX8pEOEkK8fvmm3vTVqYYQz8X9eiEhxDOw4G98z0HCv/E9BwxrCLFOFyx4\nBS7Yf9kkQ4irjB/26/hNtfvQCWOZxzVP2/rnZT3JobbqYEkoEfvUJtw1sV6YPQOrvzRgWIdy5NZH\nQ4jZCct3cjkPG38fsbKX/Svz8neqdpuchNDWtDo7SC9oz8BoSmcYfX2Vuz96nhvpvbkXT3Ykpn9f\nK1v8A+s5AEbNjvsVrhG/LYY19DywS/G8lvPb3ixr5LA6QHS2LUgPYOfG/brgXx2vq05bbjXjFfd6\nOiCqqkqyBxGtsY9ZwgeURbJbPTA0o+etXVkhRLE9Col2GCEA5EBihlDOWRfFcgeaIVdXr3kYq5gH\nFsgQ/Gqz8rTlTdLokIwtYiSjdtAeax26YuqiUVCV0627XLM5Yc8BsM2+onQ0RyTguWA9X+nFSIZM\nFgBAXNb9K/UqwOgNETQPrH6eQIQQa+QwO1j05eVcnmq/I5qjNqwDb9wvkN/Pqrk3OWF376Jqkgb3\np9VHF8vQccuMjqJDKWspyabChg7EiOk9hD0qCKA+D6OxxLopCrCas/6yWGIpS5J0bI9A8cMGnbC+\nf2YBqU8vm3Zt8BAGuqwUy3h4PQfAsOI9AiSEWAOGsRiXkreMqv+5nNewj4/IHwjItf+C5YxXABcs\nObS4LJdlucT8LfoLcCYhRAkwFpKhAItlOOKCFd9ywPCC5T/x72zUECKNJb6neA0evorIoTUo8eAO\nrZ46dtt2k8Jda90nVpNnaHy/XRZ+VA+MQctYxIKBMGzVS6vVIeW/oTYueoP4inPOHrEu4VLHJeaY\nx/64F6BvhlUfq8YSc8ywhhArolgsEYRbKsBKwRUPDLeHECWWYA9HlIMPjfjhe9PJpO5tq2zuFrc+\n8Vb2d+pJAAYg7fUqESeJekjUFStO2Ps55mZTHa9r5BAXtE3iZfkR4rYTcS0sXEV1QdvgxXtg2fFa\nEdn3olQ/rPG95LOujhPGb8OgZmoz4K5K/Scxxnb65/f7aPqgB4YWTWJjRqDxILHFBnW82FOu3H0v\n61uM+1COvFYNIdYxh/RXfdwlR3PUxOrP0YKB4IrNWn6YhBnaECIZbaGQrObsPB6TnBtlFWvi5ezr\nxjyN5hkAht3xsQKJNfRXAXa5Gm9LEzmsAHvFmT0fDkgxrHtEUYYQ0VYLwwNL4ZQRRQEmv3xYJz1y\neHgjtpdGotU6ex/XeE373Nbzj+DzQWTRS83ZXwoA/PUvutCKIlIlNqd8RKM+0w24Rg5jXMO6xbjS\nR1/7IqyBjDyUm63ZaGsN7deBKbqCVlVookovEG5ZT7zURItSwyHEsXeW6/lX/S1poF3xgfUMAFvL\nYcbrcEQaQkzFQHGb0o68zIOfyznEtCLmZpPHSuWhifkZcn7a/Ipzdu3Py2tc1t27X0U1yqpdwIKE\nU0J4xTk33WxcsPzASzZqLLEaeRTitgb8IEHC19ZY2+DhheBtG79hG9dnoeJ3oO6ZHTLLS5LMkVFE\nYp+0DVvbkHbrAbwX7yrXcAA1cli/2BuQ6hiNJV4i1hf8yOFBkBBixV4NIVKDDkdE8eGYi1YK2Kt4\nt0YR0b6/zAwVV+qYQzuE2EYO+3euKz//eltnAJtBzwCwrASQKGL1iujA+lBSAkkJQMAl7o6X9MBy\nI6E1DKWyLriESJ6yolSLgIQTSNurg4ApwKRBp/21ZWvq1Gl99Lx6xkAWDdbo8Afrvuwgx1eZpIF+\nSANO1XV2IDNDG9uS3EDSZkt1U92v6k5RD6xS54yflV55UcZYfVeMzqojRKoHtpJvKubfSiZGMul+\nVeNTPDDrGVjfCVP4JJuyhSgIQ52doYk8A8DIBexEERnAQLw04H2JOVGNHDKA1dkaxK/tLYSmzdR7\nw/qZnOyK1RAi41ZNeU/RfNkr2RhL9ISwqtqH2U36Bx963eSTzdBAP0f9J2HMaTqKCR4+61IdLzab\ncsfP6UUBVm8Wa/NZs+dhPAPLTS/PVruO+KB7yRnqinl31NaOcIhe/SAhY9JhHgkzJXI4+M7MoaHe\nbTy8ngFga3nWtAJhH45YxwfG1liAV2AtYytq8A14X+J7jCmG7FrVyGEei0hDiPVDOPWFRFrXs+qN\nIfXAcgOrscQaQqTGBUsTOfxB6CUjh/IJ2ZZauKn3b/JGriOLBL+7ao3s9LDkI9nmlbwElt+kjscg\ni+TrX2180dwhjHukFe/LPoYw56pMesU5h+jprWH2q/JsHRJM/z0YdcJCebs59/ip+0Yz++2ezVGA\nVWNk6nhg1SCvNpPIodp8rRS0Rp9zn3If+0f0DAADvz4ykAhthP1CNlAG2f+M54QLyj1drlj1hq42\nnlA+okhralugvc3UpiW/WFpJRt/92tbAR8lbIcSkpRzcd6G9W04iUdU/4s2M4GfQLXuGgR6qi3S7\nBxY0kh2K1alUG6I+iCM3lmpUV6zSLr/HUtsdCrpQbg3ZLE0P4o3msDcM82EYbbzsZpTdntLGLn0s\n+QwMXdTJWCKn14jXZflbdZZepvFG/xh6BoCl9jdhC8r1lg/DSAiRDvF4W5Zc6fN9IoDsjdXbQxpR\nvAlg1QNjrliNHG6XcHWw2OgM9WUvdozKt+chZu/TrQy7qeId4rOf7Rn41NGtgzigMOzj/URSG2Lz\n/tZKPg0FgivVCOSRc9kDf+hVV8kNkD7uYmADiSIGo6qoGGMkkx4Yyn0tSxzxwFqYvUP1ru6gF+xf\nCPux9SQAo1FEAAnrsl/LAG6ghBCzEUu8cbn+85T3GP/Py7+/Yc0jo3KFq//HqIYQaUWEHUJkAKOu\nWLZ/4rwjqgYJf4CnrCX4uQq2XYOH7Oat3xrq2RvU76tL/S3XEvbjh4Oc62SYTlZozwaV6oHJjx+i\nteUeqtSaVWNfwBqvblblRw0h1nvEWL4pRe8RayxRvt1c4x/ReKNZjSJSQzubxwCDNoijAqx2CNSm\nRk5XSJa25tQxAwOtWeJNXh1oeR5bTwIwCqgE5N48XC8/NKN6XVC+04GA9yWmEGg0gIUQZVUmZbre\n/akAS2RgfUOmi42oTixR+XCUrJ43Vdj7woYfrG/qHi3wWI7XoUP2j0REf5MsdKEFFVsqFnU2o24p\nK2k3FW0FpIMPqStWF6HritHv3tYhiBVOaB2yjgemul+JDE0sB5qkMR5CtMKJR9PRy14w7A632CrQ\nls6gJwEY2osGIGELu4OVSl+fJQ0QmIXyL5gDkLDF8LqcK6sowKQHhlLLWYiDRv/rw7AMsH2svPSx\nJLqs+GE2hu7KoFXnjkZI8LmiGxwkUwdjhyWfpBGbOqQXnTUu1olkuWOfqki9Yw/AgjGMnoYWQQBW\nSWA9A6tby/np6MRgfIPDGo7IWrHkljRUDwwtt7ovhInPRI0DjBkQOWmjt3I+vJ4EYCsJeVQ7YYu4\nhJ1GoWRE+TpGNeq/XY4lqBjLf16O2JbwFpe3uPz38nLSXkIcARhKCCUhvGHZ66vkVseodl0xleDn\nVq1OU4Co9RirwiNV6M9UsyT2VcuvemkjQcUZGnFP/eAhyyCiiCeeoEQOD69tp+ct//YBZBRiaL/V\nm8hwRBQ+oYTaUNCVh3UchhCrb0fH3MtRiCyQqJJsEGCSZJ0QIjE2wAgY2ifz4GxD5IHIwDqDh9eT\nAEz2yOUqpeKHVXSpHljt/9kzszYAvYXwFpc1RFoj0cbKy+55CHFF3HJzuJQNyjjhSMCQGqnzT7/k\nbZg8P1KDfXqnXn1WFFHix0qR0GKH0PG3pm4g/cAfW2Qs7TxHG3S26tk1pk2MRawBibwNaUTyJV/q\nXdUQInXI6mBgGkLse2DBqOTjThidrdFCOQrxIGY4/lhL0oilW7/d3vHxNXX7vEPsEq3YAtAyrJ6S\nC7nAMjEUbwzlY4Zp38gWwxbCe0AmGY4AtnOrVlYKMEkyK4Vx60ov1gjQ1lncXk87DOivcusidHc0\nzi0VYzO0zk9T50GXXGo/ABvsLZI4wam9SmJKgQ9wVydKMgqqbNSx9cy1ki87p/ajiCjQ6o9CLOcg\n0TydyKHNJytgaH/ecO0iapBbajq9KBB5Hl7PALBEwoZo4yABCNgCtoDXcGXY2oYNQ2mB+Z91BRJC\nDGV0YijvPocyG7DFkP9z+TvrAihGWR2lBOqTjBqptbOxQYscUgNGzR2pvGrN+WDi4Y6SSB9sZ6wH\nhZhVU2aXyi1qW6HAALT/u5JllMhTryclmbyDIlMeTw8CEtVAwVIgj8QqxjIGlvKaJiXi2v6P5rod\nNtyDGdoJ5dyiv8w4HMTBYon7UEPIB9gDrhjazBCL1EuAbjcwg54EYDSKUROzihtFY4m00SaCK5QP\n1ad2wxV4gRgoJIPoMVSA1enSGhJgyXC8qDEUOZS11aq2fZdF1qKRFCtRFaOOTFERReHEQKUuslKm\nlhVIFJ7WPlvohYGMN/lkzGBTaKCiOl70i1Bon3hVjK3tFxHpII4aKmTP2EDAWbNZGvHAqjHsgbVe\n1+/zt9R2L1v/PAx7EoDRzk5etBWI+8D6tUCIYSyQzUSyjbp0JV+fKh4Y3wgrAtp6Jj2wjitmcStv\ngUcOZRQRt1dPFRVWHnVWTbESqyS6WBnkxZWdJcSp7yCNLZ1XnfOvXqmSyMZudLZ3uEMq1nuiqZX5\njZR+CJGii8UPQZ6B1XfF5GAN+ikpFkKsv6VoV5shTXW/QKDF7P57YPyJV3ta7gFYJwXCkEibh154\nMoDRjowFFROAPZZYMZZaFEXCpEg2ICKHV8crkh3KHpiWjk6UZAxOjGSJ+GR1KY8cqtEHkF/Zr/Rl\nBaY6izqrdBKhwZLxTFJq8CjYinJdSbUZdXiBhEN2EsnU2eo4XmoiPc2B/NJ6twLAe2ycKgDy7eM6\nDiIP2Y1Yq1GXJvIWZieEWMOPLHLYiR9COF5oXa46OxJCVJ51tSPC8imgp0hvxzcFDNU81KhXDW3K\no+oZAAatd5NGQdN72NFVx3QEwbNEFoEksqXSA5PlYndJDGASY6uRJwHvbENpgF7sJAyqf2cub/Pv\n88wOxXrHjiEPkF4nyjAIjM3QjnUN3l6AV1Naqwc3MC7KsNBcKPlpRBTGUFsdwaEaFYcyhCi/lBjI\ndxE7sh6D3TKIgwyRh9FGO3eb/UVoE9HmlHmoAbHZh9czAEztwqzLuAJhf8e5EojddQbiWqkAW9tV\nRjwwaBWauVbpcEyGxS0c2WrJcO1amlmIDMxWuTXot31EHYzJDGgZBnEePr14/6D6F4L8nkzHTN+q\nbB1qZgatmtjWRzmeHgJabIQhNSTGaiyx5vx9IcTDZ2AA9heTySGXltsaHYzJRBh56iK0iywDxlqP\nrS/QOA8l+2iIECIIf7Az7Gfc23MkC2XA8CJSGNhgnGbrBkqFEzXWNuXqeHWGGqqNQ5ZG1ch9uNXh\njVOtr6TZ9dwFO53xWD1MhrHQps+rYZcLQR+1EcSsxNWh5FVK5OLUAVAJIE6Y+ln6+jlEaUD4RtmI\nWCPe2egPycj6Sw2p8VGI7ayIFuIIVyqxYM9ai8YNiMQZ9AwAg9aX0UVsKWHbFvcEtO1ZemB1JyrA\noJ3pQ4DVSX0qllOUsKFa69k+1EIcahxdhzzDjXWPXiDrUmbVq1l/rUVo89CUryTr/kO7t5K3XNYd\n2Md7DnmrQJywGtCjsx33qzMByFE7+iyNDrKv6XWpVeT+MzBm5P+9OQotuVRNOQQYPZ83GZ2NPLCe\nAWC046uzob1ulrGWkR1t267UC5oxAjBZe6rBnuV2DH20IUgKtfs1t68OukZI9hE/rMMtRqPOFoLx\nq26WbX9ejbjOAMAHbrBc6pXEgCuWtGpPm09qE8uvjPKxJ1U3ASwgISFgQ2heZGZbGHkGNgywbT+u\nTkO0YiKdFGubah7LUNNBlkr7gfUMAMtiF2TVujCbSO/5dipc3TMWMGQTiAHjNFsMk2E/GRHcGLTq\nmkmbYBiqrCrR5xY7Wqvn64BQVdJmWfmtNloTJedCu7pVgM6iKdTxm4pBv9XbueVgvxJjrPKr+6e4\nQntNSFVdQ6RPqtjbXSDD5WmYEQZdsrGEtxy9CGELYQPeEZBwQsuwtrDXWUo1I4q4KdVQoqW2X9zr\nXY00awmnQ5Kpi2bQ1O1zUJJSVkeWf2NJ0QZj5DGKtD3LQfOsL4B9mq0ul/IILZj2N5QPhy51mgLE\nUR/q0LvqA6wPP7mXWrAgZmn/xwovQUWVtK2xpZO02nukgUXSiy7v3IdAXLr7lNoTXy6RNc5Culaq\nT6ZNpxC2vd2U48o+WcCWkNASi7lixiCO4mbJ30Egsfzq0PY+lgYNi15qHrro4fUMAMuiHV81qiTJ\nmIjnteEaVKxr1w1bd7LMVquarPd00j+u0Q+ry1qv7rujDntUSt1EMmmriezapTZPEul9SZKhhZ96\nrzOjOh6YETYMWgqz5eW9Q0msW078RuAxgjHJsJqNGntp17adJmSGAQhhKzs9yUDijqtaVGpYjOkg\nqiZamce32TfobKfMchHaRY+qZwCYvA6pbXyMPFlBuFS1BQQg4L184nANTS6M3bEeVqkrtDA20hbG\nLNp6Olg9Zbn7uAp2Im48NVSd0wRxdId3sCqW2L1LZRiIMbXaQ5D/38u607KuLV3ElqJNtFSvSWhn\ni1HHIoIQCy2ckhg3f/haWAjb3oLXXn1sWKWWXBqshQ0y5rMoZTGpv6ifmRoPrC/QPkeU2n6Kths1\nc9ZKckZiUOCV2r6J0OJI/wy7Am006XB8Uh9g6s466tBrBGDqW3LMQHNe6Bhuqo3dZKA9tHpNQ3tp\n1u7RMbHt1MQvIFHzLHpRu1N7+xU7tLVgUMZNgnS8aMCQpkj/zDJ2gOWrXR+Cy4svy6M2I9ndq7Q4\nJI00av2txk3ckiW0FtFEq6t4bD0DwBKpqjUFovuDsNlGaufIusvSJup4RQbKcYBtNEliCV2Soa2G\nI4YqlV63costFfftJ20/qvYjK5m2ijF2ctRLQ4fqqJsOwqhlSt11pxK7P5C3JWivgnW1rS3cLdlp\nBgDXKKJ80KWSjI0hZGyrKU35V3KF6cXv1xdmq78q0j5oyO3387CSsEVWipX4wHoGgOGoM2Idmeya\naTUPor6LbmArdgbSO7rnmXHlppu0keqsGqrG0aXOWhP5xxyyx5T9ZlXvxNRBy3lAJgi36BREiqQd\nunctMzcQ6W+x2Q7JrEX9exhVh6eQgqRcH/Zwq46woI++8ixLrGHDmk6+4pF2JwylCtRXPPulVXt5\nqDWz/R1E0U1wOtzpHb9W4sNr5vZ5m2grkSmsI1N7NNadre0GQ7s62j6gUyNUzIzX9Juq503q06sm\nRtM4BWUlaPf1VjWUrYsaO8rrTUO9ItRA6auowXZp1Qrcdd4eRvKsyp66z7DDWw2WGMRlva+DKadf\nOlVWUFEO6JBOWELIIw+bq1or0sgFt+4JO6SBqLcjS9XZTiKMDfYLCTuDzPOQegaA0c4odH/v2yBL\ntKDY2RqzR6ptpx3grppo9TrqHXh/igBwIjFFK7go98zOhDyaRCZ2iO+xvTQgPlkg10XurOZn9QQ3\nVowHVhiYVXElEQU7g5pzRMPn2CIZzcCMJg+9nkFrNGqx1e4eombWxPHGOkgpuceRFLVsI4vkIT+q\nngFg0BhmZUCbrXMvGoy2Lu9X5Szbdd+wKj4+qQ7K8quGRqndKCknkUVdlW2blYLKavDqtGKPK74v\nJXd9W07tq3K6dM6+iuR9iJy10NWpC9bSw77kMANphZvtTt3qgbVRx/draWmvcNhW5B0V2gZntdoO\nivrQstY63G9/UT+PTH9sPQnAQO6vqMHuytlFo3msbbItoF3F2rJVPGnIWnZTZZTbR/eiqzfY/alg\n6sQTeh8rQWuo5erQC9pb3k3O8vU7vukoLg27s6Gz1JhQsuAq0uQdVz+lc9U6GBs/i9opl27WuAdG\nXTGzNVNIsNYsc1LjkB8WtDok629B/R0pz2Bmajy8pm2cN6jTB0k+HUJrZEfUwNFJTpp9682VauCW\no1DBouJKW3TSuNUhGdsPWkMeEANYvUScW63xHkUSewYm6wa70fkqCsasRaYOsWSK3Lh6y3K7+OhB\ng2QolJLDDmn+K8lq+Sm06Jh1u0C6Mfh7U7bDnP3E+zKrxgPrGQAGjSjs4nQ6rNpZMrZZd7DqXe5I\nCaU9WCWt1Q+l9ky0y2HjMjQo/atNiAMkQ7sTWQp2KCrAOl86bv4fdf62asVdaD95jHb90EJucnVq\noqyt7K4C7QVSr1oQK46w6naeUX+LJbIMnWH0/DFY/Q1tM5Ktx2pbgzeZydj+Ic/GF308vW88sJ4E\nYCAMYzZLSW2Nxu034/0dqfmtlFtr2UdqnIoU2XXVKfKYYSRGTpf/O80CmHWSOgALwmAZ8pR9sLV+\nXSGQKGJqLxDr0tj9yoSSZ1VFmnob08/WwZ66X2vRZ5Msz8q1iH3qfWijZOJGZ1GfMX1EfRxgh0X6\nuPHYeh6AwUBLvlDBMGQ602EHV1fvZ1Bnx3HVaWrWrvs9lkUv8sRLcqtjSICx73XIksrbWBVgIEbn\n37Sj+mFsZ8yQtzJfoo1Y5JDpQdjyxkauyFLkDU/nNkXdWlcqyWQGaty0dX2Nfnd/SJ10e34rw58x\nZtCXaJwHYtzKomQCsZmRjH6tGire+o2bla2fOEisTqVjBLVYBW1gYcUO8apOrXe1lIULyRtFnqBt\nmPVrHYB1/kfahRgrSakRwXyh8qK3ReMeM77KuMSOV2Th+xBgEmbWrc5h2awy3CU5NLHOsjwj21IA\nw2zLOOTW4W8/cdC4tdidxMfWMwAM3fvoPsbURMuANntYsMPE+7h1q2QHBoU5J5Jm+VuLDbCF7CGK\nfdI9szZcR2NEAScQntVzXz9jKcco7gMUo/gMAzPoncqcOnSSqGHRTs0mf6HVHfUeRWY7LLatcQfr\nTlcMRvs7ZBLaisdSDle0ElVjsJAjOa3ER9WTAAyCYZ1Z1nOp3ZlFKTW9j7RbGdZZC11UsyKpN9Xy\nRppOsQkGSm7lWWnI8R1Be7sZAhkNeAioInG80F4c9l+ppbECyOHESEAHceMCMTutgj07AqRgZIDI\nIPdFc/ZPpL30ZvB8llLbzqR9E5lG8CZnZbqa5zDxI5kfWPM3zhukdk8QvWYwbLYpCTy5TZY4WMK7\nE+Ui9frKm2rGLTkMY9kfelE45VznknJuF3VIxnbSB1j1qCjAEokTUiMvfW0dsgwp+uG7BFwiNsq9\nVMCY2qH2/ZuPx5YFFZne9646dzvjE4y1jCKdkNCii3z+kh7K6NUZzcnqnoUZadzNqkGAoa2JaqKV\np5PNATabpI/CUiSQgrBBrjDr41gffHchBxNvknXvjYPuh73mFYVfRaelNYIWVFQBJqHfAVhmUixG\n3cJa9pIN+rF+utndD8NRLHGSdqzK4haMY4V2IVQKqleNVSVZGOtuSs1sI6eS7FbP7H5PTjpYIHVJ\nzo7/Hm5QNTp2f/ZWpD28nhBgGGMYuhiTS2UGiJyd8tyxSC4duZrWDXaHZJGzaoRbHVeMAOxEPizP\n/uFFQkghAEgIWwwNwDJxKHrYmMbQ0ocZa103xxI7oBt9tAAAIABJREFUPfHkMtjAbbVSoD2ZINcO\n2opol1rEgpGhm/+QPcxXG1yrIRO6bs0IdSyk/QHHy8p2ODu+6CE1fxM9lsQVBjiE9gJ+5Gb8IxXh\npnXlIVBZ3ZX0iYhxClfPKbYBwzhsFA/sFFPcXy1OCy4AAlLcSXJlmPK/M0JYQ0wI6xJXxA1hDxjW\nyGFl0lpCiDRyGNoQYqVdAn5WJw7tkA/rNM6jKFIO6QVRO2AAjN3kDGZjq8CYbSHUh9P4UgDXl8BG\nOu6kTTLP4C8GtqAaVuLhgdy3ygzcqpq8iX6CVG8MA4lWCrTVbyrPp8u6D+/0LmWqOLN8L9XfWjjt\nTmGHVgZYxFpJZkWE6L99WhGzfcGS7cuybDE0rlgqpaYGSgZqrMT4BryH8vTLcsUmV7Bn1UUSSOoi\nmU7XYtlkkeSiMnvqwqmv4+dkVoc+svmbHK/xbH2jY1vFfhqMfZUmeiDVCaNL8TGMoZv+KepscPwi\nst7FylDcr29X82pIdLHZM0/5V9i5dcZrxhUF2IgHVgGW3/JZEQPSGuK6xA2h+QjUhQBMvtBVSbaW\nw8nk22SXPL+s+5YRQ86qFUcFHrPrrHS/umUbGbLReRjWg1+HWBY/UrvWCJk6SLNmOwVQC9lJGU+c\nE11ZX6WtHksFkszA8qh8YlfYSv9jUkvOJLsTtD2KGO1+Cj04vbTGoqR8i2sG1Qt+ZFBlgGV0Lbgw\ngMl3ThnAVsQLlmy84pyNH8vLusT3/KCOxhIvAEjkUE2pftuav/wL0letxS2bqkFTHXpa0rDcKWnQ\nh46fO5HKwHx0moKWXqorfziI0cRSEhno7CDMPgiwjm2l9NOtReNbfjw9D8CyDjEG212z1rWcsAdR\n59aa3RK3KdTxYpijYFs0Y8EppDNeM8CykT0wGkK0oojVA1sR82zmVkKIWFfE7IFdsFSHbEX8eT7j\nUmgU9vWb3hZkUKI8rnd6HmqOeZqyVMcDQ1sRqKH+SoP9Woblb7FSkTxq/PBwlqVbj9A4e6hGXJO7\nAWaB6oOOl5V4uPQO+D2kHrDD/QOyEEUzoIuxw6VVN53h8epz34Vj/RDIbDvR4KE1sadf9feMb1gX\nXBjAItb8DEx6YP1nYJlb18hhAVi2AWTPbA3x/Rz3MR0VYGiN6mXJp2InYItlZdkZT6sRjEmXC1o1\noemHhDuqYgreyCzzoqSzxQy6CtsCzbnLggeVdLzk0ls9MAmnmwBmFfVw0R3rTkKy+dvnnTpkGI7c\ntT7JZLbP1Ygr2RfrP0iPchJdTN/xagH2L1wyqJZiUJJV9+smgGVosWdgEesFC4Dqil2wvC2LArBY\nThgFmPTD8LUehgV7tuM2qbZKJnbqPuiBEXSpfKpLxdoK4dTMQ8NApH/WcVZu9cBGAGYl9gvziXkm\nQVfW5E30Q7qDQINeVz//J6qPYdbrMJvSqSVVx8c6E2Mpj76y8R2nkBZcvuPvzK3v+DuD6gU/mCsm\nAaY+A6tjNyrAXnHOdjYuWH7gJRuZZxcsf79831LYn3jFAq1YxnfkMGM+c3TERyr/P2yjQxVn/p6v\n5UZ2SNb5ZQZ7Bqbm6TteVq0UDJNxZjXy3PHSrrUrHU0wwDO4Vt8DsxKpwWw5O7ioLwfYF9K4NzPI\nPJn/U/TxiyW3IPoP1f2iv6o3tuBb2F0uOVVuZZJlaNEh9Z1nYHX0PAsh5qXV8arhRABnvF7C8r5E\nLOUoL+VSVCMWP0z2p1/GCbvPA7O4BXKK1JxyO+MkKzq14zXa4uveVd8D63tvijrej5X/IwDrG7JU\nI+W5T1Nxq2rm9vnJ6nszMjP++NlTd3pTsWHc/aJJaf2xhluBc6tOFFfSiO1TseqB1UdiAAI2eogJ\nJ/oMrIYQqzdWAZYHdNQx+jvJAt6X8qSrkiySs1gZltpT8t6ejUlbNuzbFWaPOGEdA+3Zk1gSlNKL\nSvL0n3KNxBhDC8JrBsmbQ7ow38hyv1S/jW7tzwBsRCNbO/qvnw8iBxgVvbA3OWRMv/WsDrJTdkus\nF9GcrG9lTgYPlzZyeC6/LzjFa+QwGxldnVhixBrW7fpdqCR6CiCELcQN4R0B5+UnAlI41cjhgks1\ncuQwYn3FuT4Ve8X57/P3LQbQkRnZuABnEktEWZS15u9LQXwjcTapuGKzd3tg1bhpPL2aufjBJxEw\ntCYQaI3nv94h9QGjGqJ+mhlUpFk7VQ11lukQMKd7V5xK0zbO366P+Fj9qvfnz7nKLWGfSlpsexZr\nCOICxJ1eLGCoplzH06dt/+BTIi9jsQ6ido4VPBEhbufldUXMr46xyGH9NlVmWEJYcPkZz0jFA6v+\nFjVUV2xDe5bm1Kd7YDJFemBstn/j1C5ij0IPg4Smm0U22CxlvIFGHWhLqyTMVG/s8LdvVH0ENveu\ne+td/D+rxy/hP6uPYKy/zRF9fL+dLWh9T+fGuRrtVEcbSmixWGLEuqS369cL2T9QBukCWNEqWiIC\ntiW+xbDmyGEGWDYuJVCYSVYG31/elmXfwtJyix4Xm1JlWJq4jagF7zCsQ7LOUhVmMGx7oq9/WUMw\nDh908SEbAopN41M9JFWqBybzgGQbcfVkkVrqjPcUT6tpG+cfFatIf+yk1f3KPXY6Vtmj4Kj/iEDQ\n3Sz2uKtGDs/AGaeYXvCDBgzPeP03/jMbNeU7/t4Dhn8Xl2sl/7XronUQ1AOjIc1XICIs2/eX/0rx\nR3bCcggRJXKYh3XkV8decY5Y//vlZT/QSzniGkusj8fYu2Ir/aeXc6rjgUmM9f2wvqF6YOpSe5Jx\nP/aeu1wk34W3Vgewxw/VCVowUHXCrC0ksQVoW2DGwIeF+4n1Ev0mPT4eHr+ED6gOV37fHj+yL6sn\na7sx1euKIpFMC3nlS7pi1QMLl213uep34i9GCJF5YG0I8TogPgERIW3LcsljN0AcrwWX/JuLlCqb\nk/DAgpZSp+3LeWCq+4W2Okj/qU84ywOTSGOcI3s/aZ4TNVTXSs0gF+0G4wpVPx1jHhhENe64YgJd\nqmc4ok7maSvuDXqGY/x9ki7Db93Xp+xC7W+00fMGtKpz9o2MJ7TQdcbrgjdcsE+vJHh4kweW2mGQ\naS9DwHZeXvMa9NFXHrtYSfYN6/sSrwBbu9yq0/5xqWkDOVZ9GXS/WAozQE7UeDaIxFAT9Pe9QDhE\ns8kM6uOxkr8lhuVgyQzQMljuV2cLrctFc7EUucNbVc/0yHbCZ+zxH5QD7LM0Xls+sovxLai309b9\ncHG/1BCiFkX8V9j5lEOIOU5YY4k55d/4Pzu0/rMA7Ecx6H/tov9tGW15qwdWPyJ8KaVa98Is/35b\nlrdX/Ed+6JUjh9moj8fym2Fv52V/uxm4GnVg/YWc4/1UqV3vPJLMkLZl9LHUd61ia7CboWoACPv/\n2elE/+h/LeiMM+wvPQj9jQQDD52wzurbngCygY4BO4VJrZrJXjSiuWA2beOcUmrd+NxLILd22I0R\n9wuG+yXwRj9sSCfqh+30uqDxwC7g4UT6eXhaNNrfgZQkAQsh0AIAy3KpjpdaqoSwhriFdlR96Lpi\nJ5D/1zyh+nWhjy5o3hVND5qtrs6yQcuwJyjjL5hBs3WGbChLZQhRdZsgDJbt0ANDm7jxrR6WQkrG\nJqz8lvtlVeK5cCU1beP8OqpV6PddC7WvYvfS3dtqGr4LO8Cs8YcNwCq0Xj8VYKncwmMflxGwLUsT\nOaxGHnafp7e47OsyjKkTP2mzSS14h2GSQPRX1BflXMkT2JkN+cL1xg2KSKD5oMtapNNLzkJDikRX\nRyrJtBfPDvfTl5UhiKUd1E1bp7m+zIF8AX06yVhfZfRAJ/GVjdbZklFE+tWoHC2kscQX/DjjJ16B\nv4FXEkLMKRJg9BkYDX8QXuJCqLOUoYOX8k+fV+CMl+W/QxlPn7utM/bHY3loYkJ4W5b9TC9lX+zN\nsDrcI+93DRO/+CnvWzqL+gxTDZVJGAsh7lXvGgBkMUD2L09ZqJCNQlQzkNXf90vMhgvdNGWNeGA1\nZWsWss1YBrM7Ylc1iUSZ8vX0tY9uUqUPX5fD1bWYjuV+sd6nuF/WdPW9OhMbxPHedgIbAoB3hFRc\nLhTkUMcrl7aOjL8gO2HyX7fUsh07XoPnbwoFe9YCGEg1QFslOoZMhDif4gzLkYfQ3C/L9+p7YMzQ\n+cAcImizNfF2D0zdzyDDrIJkSWdLJtYzrd4XqxufsdbPWOZn0B0MU/OrfVjbkwWj66HcIo/BTuQG\nWaXX/qENyioVYJfdA1vb93NoKeI74jv5L5RLF2ArQtxi6MH1hLQ/BuswjJ2Ebdo2IgveYVgfYCyD\nBTC06RBntaRYX41CF0V9tql5gNYDkt4Q0OSByGCRxEIaSU8avQ5JJsuVJZmkJkq8WSmdfc2iaRvn\n19fdDJPQ6jOKgCq0QR5tAL310Y064UeJHDLjUkKIF2BF+skjiNYjsLjh/N8Ip+KE5RBiAM4k9Afg\nB5CwvLydwyuAhHDGK3sYtuDycznvay1kdeaWxbtO/6MpaokjfthNTlgks4dT3Oklw4OHIUT19ziE\nmLb9+o5HCy3gyTzqoqyNrw1Swy2GMZtphFv4EjV3XM9zpF9V1hUcvrKyR7PdkZPodFiMLmJthmas\nxNm6NCkX8QhMAiwRlCwbwqWgK5Q1Q7uLFVgRl7XTte1O2IgHhlKISTVSNTrogn3b01mk+mdkov8w\npS2U6YqpwcOxEKLAiMUe2O7XoWckF4n3vWBA61aGZQUNZsmw6QY7KZNq9vK77pDmqKmdDnjvw+6R\nFSPHDzsMuwAX0FydMRypMCyzbWdYXkbp1U5x4bfn7O6eA0w96i8j9VhGfC8YlEJ7rqCdPSO//ODh\nTYHBW0OIii8lZ2siM6Dl6bhlxvbktuVvf7dUQWSgMOvYdMu0Rsh9zVX35yqt6yYFMat1SJ1b5nbo\nPB2+Qb8dRcfTN698sSknlu9y/GjRRruFWpyl7DkBC7AC338SrGW9lpJf9tzLyyX/w7BcsDyMvhoR\n63uMzWgOObIDYnZG0RCirAt9o8MtaQSyu2AY7XOvTghRxhI7gcR+dHH36604oQokaImWH0ZVs208\nQW6bGWgNtlWVN0HLYNkjks7ZFJq3dbo+T6xXshZpX1xtO44SsaG9Rv3WRh6yoXtNugdWS7QSI67k\nwdWq7CVgk/FDOvEoItoDnxpaVBa0qP2JAOvmOQ37WIPZBlbcGlYkGxqSKsymKR0EGqvKTbKCHDKM\nSfW0qHNWbeaxyTzqXiaq/hMV1fUR2Rfa8tNkT0Q6CGi9zBVUSaAp2xvDWTNLm3FoXbHqIK1A3Mpq\nKsYyw+JB75YH6is9L+3HZ28cIwBDexIgzgnEaYGoG0fMG6eXvFg3rcg2AmjcOvSALHT1pWFMXaiW\nRa5iyaJXJ5F5VyrVrJI/uGZvo19bt4YBpFivXBNRu5Ymo7pqniIQr12JDOxcIzbWA7C1GbhBfyt9\nIIpTXy/Oyt+QWt7EII6Wh/IBGPPG3oOIHMozpJ6WiSRHIY44Yeqxy7sZNvgQosKU6dbI4aHBLigb\nRhRqMEB690nMdnwp1bvqOl45Q8eLUz0wxjBoW6XXx/KxButpaLcf7N1NoXlbp+s3SN5xK1lSNegN\nMiDaZeIpnU5jJRlpm6yOFpuC1dEUg96G83JCO0DZoc+uzjFCO96bAFbtYXoNBP0+a9K+gaEiQvV9\nLA9M7emNRZ3tqa6YVZaqQx9rxEBro93mjJq02K5PlRVcErOSBMQQLySDY8fgmt6SQ2GYftfb3VD9\nABTtKFlKc4AquWdvHIMAgzgJNbEDMAoqNjtAr7LV64X4RIABwsGBUWHUPBCrjEjklBCUdhK/6ro3\n0ctyziTGQK7wpCSbq7Suz9It173tqkwPTDZKMWlpCvVAtmRtLKgrU4aFIw+sHx78Ai2jH0KksxbA\n6O8tALPQJYfVDA5HlGFDGSKuBo8cykBip/6p1XG8ym7KeuqstXOauZ7+Q3qFdkWr8jIQsj3KlMfX\nF2imT6VO5XwkjTWCzi3n8DY+ssJXV98DwwDA7vLA+mHD3z9pgw+hGbDxQlP69UrLI7kFe7az/07m\nLBqlkEhTUQfNIWP7mqGL2TVRUV3zaKxasSBWspd+4k6fSIMAUzGGOwH25+mFNvx44NowD0jaVsqh\nuvk7DGNl7GxGRRRrOGwRDAN2LPHoUB5L3ugfXL/J5bqlitK+ICCV8uTPDF4N2Q+KKWxqcrMezLXb\nVdStEKMWL5eQFrg5qM84Qw+qwVGIIGcP7fXoACzy9BF00RgggMEQohxKKl9hjliv/zYliRCiTFT9\nM1Yr1MydmnMUP0R3qSSZdb+RxO+tothjJMNdG/ynNFFRXb9Nw81OkoAYp0ABlcUA9m4Sh90nsh5V\nAZ7hAWQ7lfcDKGVZSnOAMrgkjn0+ycatAkxyqxoSbNq1ufU1rw7YPrK0R5qOv2W5X4dXf8xL61co\nNeXQFaNiKOr4ZOg6Ye6BuR5TNzpb1kqp/jU8MGg4aVNMd4p88JBtwPrPJzojSRmOPbDxY59UHYBZ\n7hebtQAmHC8A1an6RHTdtArQRZflXcFOGZFY5eOOPS0vvSwMTh0vitGo5qQG2u2r6z6+5iqt61ap\nAYZapRO2oDsfIO25TivSEvL/JckfG8x2TVnCm/ofWOo/Lll+XvdTv8qLfdtKp1q/hVj/I3Q28K82\niU0BtYTUyAXeMZZEQIkdOz0Jk6qGEEdI1geYMJjXhS7AMnJynpGAIQ0SWotEtvYrL8kwOlPVeE66\nip1gVS62NzlLYSN/kwaqjiTGZAZZvAeXA2x2HdbbgWyd1oumeTG3hk3y47/0P2EiAifE8rZYJDuk\nbyuDtFK5pQjgpG05NCsoZWsL3Bx45w59aqn+lrXoFoBVr4sCTJLsPp/srmnj9VarvddZeWX7fJKZ\npTYt8RbJkqp7szhUXTQY6XQpdbyYEzYXEuYqresjYtVYLLQaNlkqwUCdsITL/hhM/lfMtXzP/k0B\nGMjOUxtXpADLk4muK71OqtdVpy17YPJeF21RZpcFMOnqMkPatuMl43gW2z4YJJSvhSn0Qvd2pH+j\ndpN+QyVRQyV1UWdvKtIYopKWjdJu0ljiFIV0qTr0vWQG2aBTfXzAkq+eUfMt+ZinC5aI9YKFGefl\n5x4wTMC5bDYbYf964XJB3IDygmkQPQn1wPJ0rsHD/wAW4Cym5Trlwlyw5HLWAtfCKy+6WnfuU8Ns\n0RI79LKdMOZyUeMmN2sklrjgUlM6byuX2fdewHDw/eXBSSp15kYXoQUJNJYw8qohxL5UekmMqXt/\nZDnAvozkjZR1cbVFVsfdtmHpeHEjXELczMdgpUsNhWHAlXfyY740crgA4dQ+ClOft0XIp1/KA7A+\nrqZou4fqRA4hcAUFY+z/T0rjIz6WXOtwQIfMMIqcERodSl3RZtjvqESp628lgR85K/mn5pxFDrDH\nF+PN4Y3XTXdmCSnQuf3XmDZBLAqJfShHFEM5Kr3Ik67l5zVAlUSh20dahF5sswuxCcDUsRvZ5vFD\nq+Orvx9+tvGP6QMAq6FCEGhRmxFIphziyvLARhYpwcPujVdPtyLtiGG3qhMeVBelNgNNYU4VCPDU\nHqQDvFk0XYFdI0qibrObttpqw3Uuh/NYbC0DpP7jkgsuyxKQLlhyJ5INAK84AwhIy8vbvvOXsnoO\nRb4Cqfy/5hUhYFmxrFjER4BZCBEnEkN8Kdz6XmKJLyWK+AKccQn/esX5FecLFvpbI4r8f7qoH8qj\n/yJ6Xt0yCpERqyxUHmuh5RZ3idpBHCxg2IFT/7VlauwZ0rZfKRkNvilyWDWSp+Y8TBHnW2JG2sxI\nbQa5w6S9rX6fWH8xixxgX0Bp+DomMZuaVqrevbbdwUZ8LzldsKRwCnHbMZOK7wVioOAwABHxgvoJ\nBZDlAMI34oItV+Ov/+8XgF//6y/66AsRKZysguVpd78OOzh6Em44vQ+mYBScJNIgYf/XMizvSk0c\neWDGaKf+M7Ce74Vb6NUHFdoNspQP63Bohszw/+AXgP8bf4HgzYolWr+qEll9Ik1XYBfVHX1rrcli\nXZVekmQr1tiDxAXLOb/wZQEslP9iuZYHX3EP8zXNiMYQz23YMGvhU/W06KgNitshdIEYU0vcnJ/a\nA6OeFvuFETlU4YQjJg2SbDyKaN5t9Dl0qP5GPoNhKrTUYRR0NtuZXmoRrGddqV3EgGeFHCfSXKV1\nZfVvpGRtZC2ybfRbwloCiSuuRnWSQgkhYn/9+D3ES2gihwB+4CU/alpwSQjn82v4XkZzAHgtryXX\nf8O8tP9GGcYojmxUgL0AC379r7/wvQw+LMYP/F85ePgDL9mos3Vc4h7ApFP7r5ybkNQKbBrpJ9E3\nckJD220ydElj0P1SHS/5Htgd/0WFvshcxyUuuOy+F/033km7cNLAmOddZSV2ZlupnJBY6lCEYSk7\nXlKdUsg9DpZqFk3ZMl0DovTqjAFJjanez9YuIF7Bti5xRQziYRg1dj8M5KsblIu4C2B1xHw7dD4t\np0opNlHvkONqqDubq0VfRV0oli7tvhPGcEUX/dkQohE5rAfUuVZq3ZZ51MTO7F0aZxta6kglsW5N\npEulT6Z2ENPdrM1VWpclq+Kp6aJ65w9KqdCqkfh6kxt3gGVQyfhhA7CsGvQ7t/7cKm6cq/oAiwRj\n5+bdL0YsGk7ccr+6imO0YLbB6NLmUGxO6K6b6EV/O74Xmx2ZJMn6Ly/v40FG7jmGbkqKBhN/cxVQ\niSWNPsOqzTbIuNXZPt3CLHKAfSUl0RZqehJ52uaeCsOqP8RCiFnFeDsvKQSQyGHEuiKe8ZqNCxYA\n5+V1Wd72LVyKD5cDd6+FHJdrKa7Kxafj6GsIMZJRiAsuy7/yOMO/8T3HDKuRY4l5IOJ7ingFXoFL\n+aUhRHVEotntzaEKMOmHMUpJQ+KKzVroQhlzKI0OmUJ3FOI1cth/VZndCR3SzmIeSCLIrGoPS0IF\nosUmcscYSBuOpKSqWNOh22d77xSJps+iiYr6zEp3XSl571XT6dIE2E5YRVpoY4AXvJ+v/k1oQ4h5\nN9lICOf6zlf14S6lCPQziIm0J7Qe2EI8sFh8r4i0nCqi6nB59hmOC5Z3RI6okUDizPTC7R5YNdTf\nT/HARl5V1j4ZtfEKaaGoylpkpVj6MLeYLEfKCvGpbbiDMfmgSy5i+TG8/QeUA+zLSIVcv2a2d5vV\nCZPcoonh2vtf4lLpRUkGICC94pw/m7ss5RuJK2FYuMsDO1/jhyme6GteFr34oy/55pDZIfbveh9d\nHceL2uP0QvvEqxrVzaIpklt0accDk3lG6dVB2iG3BhfdLkaUzlLpBkmGJbKoI5VMKhGpgQl5MF2B\nXVmdmye16sqaX43iBK0l/4UsyXot24iNsS3hx/mlRg4XXDK9spFHJL7ivCIu8RLjel5+XuN1lxZg\nrJgo7KwAC9cQYgqnOrbwb3zPxn/i3zQlxxIvWN6w4EcJGL62xqr9rnT84TovwJbrhbzq0Tywo/+i\n0kYO2eBDtLiSif1YImwbxmUfrguHIbu6PcvNgtY7x3azzJaEo8XoszCIDU4hB9gsktX7jhUlycI1\nfbObeu0OWCwx4K14XSxyCCBirY/H8m8IKS5riNu+ehIhxCrqgZEQYlr2V5Wr46V6YNUPe+t/eqM3\nfAOkY5tSN3lgfYYdYgzG6Plq3OGBXSOH8jJl9ZnE7oogZsdxJZeOVYqOa9XPplLNYhItlPSr3ANz\nPbgY22g9l5W/ztaaTLppyir6xEtwi46Mv8QFhFv1zbD6DCwP68hv80SsMaxxWUPYro+jJMBQXK4K\nsIAUTtmfu2D5gZc66LFOEmZXdLFXviTGeDFkfzmZpIPVWSS5hRZUbNaKHKrZKLfUdC3nu3l7YU0w\nCKemQ9h9sH1SLRiBGd2b5bRRWx6N5WCxtSS6psPYREV1SVCFbgZodVVt3Ni78C1gDdfIYV2pOkkV\neSRlW8LP5RxCWnDJYasLlgWXDK1s5ADjK86x/DvdJV5CvIaMAOx33GW/Caf6Hd7sTiWEDLAVsQKs\nxhJlUHF7DWbk8JWAjbGtCR5ODDAaQmQMswBWjcH4IbVVV6ym9COHrVE+LGaNOYThOrOAIbQ8Heyh\nvdqWwapDO9txjxghkvilm+z0y9YDMIYx1cGiW7CCh4cP2B5KDrCvoQ7MZF2ledC23cADiZYrJgbW\nX85XfytTJyBVIzthKH1ZnmWjpQGEkPJG8jbrt+TzEzX6gajqimWviwYV8/Se4vFHN5LWFV7PxsT0\ngjEKEbfTC12GWc6W4VcdjEIMGPgPKSMokvYdRl92NitIKFPUJ1JWiE81ZH5auls9MLr9KTRRUV2f\nIrWGV8cqAVCGI6Zye2vFEoH3JaYQ6jgORrLsaQGoHlhOZ50aKWUAAVj9qmH1wCjAWCzxFectBQVd\nFsN4P2j1iJOpEzmk9t30qoZ0vKQx5oGRIRsYoBfsRfICqgYMQ509TB/TYRQRLXg6Ri2ORCBdRPOM\nuHoT1XgH2NSSdbV/Vwdi5F/qYYU9w7rsjbxyLZQv88YWZtW4AMAWw8/lnGJYcKnPvSLW/M+aI9Yz\nXivM6D/epd0lObbmn2dWgOVZ6YHlEOI+5jAXqQ4+/GFHDineUo4fSr5NKTkKcRxgaClFf1XHC9ow\n+k4skRoArmFDetb7AcNEqqK11JrQGvUXR0tvVydA13m+JY071OkFBov9+JqlnK5xqbdZnRZBa3gC\nyhg8taeoQam1bCaWzGU0/FvcB9DXwYcA6GzuvPKnFMcBxkKIdZwhJdn+wvJFUEqdZL+2ycOeGGAS\nUZ1FklXQGDbCrU5cUQ5HDHW0oeV4yZTBpWgNKokrmQdang+IoQsaUTr+Fs0goYg2RYr1AlYGOjuF\nHGBzafyGTM1Jm0wSibW5r9jiFVoYMy7XNpfDiTRyWB+JyWdgrMvLmcu2Y57Nz8DqaA4JsBVxf+i1\ntgDrDEFkMNsgsIapASafgakeGIbphRY8GCP/uuovAAALPklEQVSZyi0+cuc+RMlsIIZFqQ7SDlk1\nUBf64zjkBu574gWNW5JAbK3OMzaIzU6huUrrkurfVEFrUMTZ2rPJR1vAe0AIe0YaS6z/IWUpHf5S\n6BWv/395i+G/Xr6fQsohxNxn1RBiIP8jg3WUpPS7+wWghhDraA4aS9yfeL0WGtUQIh1zSEOIMnK4\nQoscPkUIsdp/AGDNUEO05ziRs04XwTDQZpYk60BOZpCLIK78J1WEwedb1LAeXHUaf83QYRjdEYRj\nN4UcYNOpT6zD+pxF66qsyaVNr6F56AXbSPwjHbksWwxvcUFAHYVYezQaQkTbS1YPjIUQ1eGI2yU0\nTFJHbVgeWO0xzeDhxAD7TSFEFk7shBDVsRv71uQ5ZihCa/RnPwtOqZsCI8+ArJBgJ3PH8eozCSIb\ntE25B+Z6EEluqXdpnTs5kLbePgxLu0e1GxJgdRv1Mz+BfPxpBSLezssaIgshWvFDUqDGA2MvhF2w\nbCnsTlUyvKsRdKWv9uirajCE2GEYY5VlMJIdfYlDfJkXNrc6xLIQNcKtDskGU47UB9VhnNDaTp9e\n6sMwy4djQB15kPaAcoDNKEms/iK1iqoPw8A7gPcAlF4mdj0wGmasGyjfbtti2EJIMdD/kYG2m6u/\n0gOj4zhWxA2h52aNOF7VeAdBmTVNKcsD62Cs44FZxvjHNRp63cctiMvyQW5Jhlkpt2vE2RpZV3XF\n+h6YiqubBnHMohnL7JJit1/92zL5DIwaNCYIIOI97H1abduVZ6FkjMUoXtf+P1Ni8ynebQlvYUEA\nAv47viDgdOSBZWOrr6ZV/FyIkROlB6Y+8Vrbta4oo1/F/woAO+NVTbeefrHZESdMne1x63CC9qBL\nzYM2pUM12BmszNBmYc/a6vhYnSdest12mrcKp8NeQJZzxoruAPsykrdQ1l0XS7dIRtp0Kt+XCuV3\nbY26yUhAAIKcWIxQpggEbCFsIbwHsnFZBGjjKujH7AcdL+aBpfrVqJFudT6NO17SGKQXtdmjL1yd\ns81E0eEpZykj+DmEk5WZLu3rN9QIK4RYl6bWvukZGA22uAfmmlHyzk/e/6kAW4GILQEBa6kvsQWY\nyq0KnkgMAbB9QvvL+hoYAEuGK8b+UYv1AEz55uEXQVdW/xkYne3HD6ltRQ5liuJ4YcC7YlXoEGkw\nlmIATuzyqld7JM8HxOo7TVeJNZIy/tis7lras2iu0rqq+jdMtH6qlZZW8lW0o7VlVAKALWArscQK\nrUCMGjlcC5/qP/GKrVEBhpZhMHxC2mcxgI2TjBkbexTWgdmsuulLHHd4YNUQANO4BePUymDgSIqk\nHcum5oc2y/iHNptcV2qgjsibR7reSAgRRyn3xRKtkswiB9i8kgxLokrLVdC2F7pIVmOGNOyxROo2\nMUPuYSUjEheSP2obYSWVvVUFjeWK0aWqkTq+F9r90aLMJ/VjvjeN4KC/HQ+sGld0YRhXKmzQvSbq\n9WEVtk8vtAbbTh9XLH9Xd/DgMISoptwRS0TbTNGmz6KJiuq6T+q9l3ozJ1s2NUoscQsAcc+oE5au\nIz+uTSG0OavLtRK7FoEVvP7Wjs+KJVJKdZC2jzlU6SW7W9pNzif5fKuz6DByyGZ1dKGLK4ttEDaM\nRTKnSil6uJ+Oq8+rESwGiHaW2XcHDNVF9VBCa9T0WeQAm1pJ6/UlqFK3YsttwnCy0r76e9xdsfpY\nq3yAAzRUeCmzl7IZ6nXFdvPoAkzypQMwOa5w/1AvxD+lVw3Zv04pdRTip0YRN+AIRXcvsvL0M49n\nw43GLeo3MJUrqs2K0AkY3kqyup1+OR9fUxTSdZMk1dgieeNlNSjLWLFFoB2amBfWb/sK6jV7rh4Y\nWobJ8sLo0TqumIRUumnAITXYyZlJv9MD25RT9fvg1N8Ibsn2EePDOowE3pRNZriVZFSy15ii3jvA\nZlcHV3SpWj87MXDWMdAHX4VRG/Zwohjwwf03FWA0D4yDuAlgqiulDJenT8PYRtnO6BmYT5/4JQ7y\na6AL3RN5a2ZrLdhGGsv2EUle3qKO49XJ1kn5CK7ULbO+YArNVVqXKgtOzE5a9aasimWV6hzR51RB\n207Ae8R7wImMMKwrRWEwsDF0WXeAaq83QjLliddhwFDtQadUHYU4/kKYiCWSIGHWIXLuNtQxhOPG\nrelWThgGE1tdW9hRhzrjKSzxcNG4KzaRHGBfVTcxDO3S/maz2sGIW8AaOJ+qUWCnMAx3AQztG0Uq\nmzZ1WQdUrJ+eXswDG36RuUALxiWAOHkyzx0GPmbcwSR2kbtMeoQa8bmO1xdwvzBhgV2q0o2XktFL\nNawVU/Gq0OTMEcXaDiicLA8MNr3abZu4oRN3vNTc1itF0GZZFziZbnmReduT1E7fohSMs/VZSLvj\nEsmSW2WjshLV669m3rTEopFo4U1xwpvU305NCeSIJ6LCREV19SUZRlMsVo20i0SGGyYCH7QU3L8N\nhbcAlKAiCOxUgMFgmLw5lEhCi6Qrt6S/xYbh42iINzOm1IK360y/Fx7EAMS5gThPd5BsMMNNS62S\nHGZmZ0CeByPPYC3pIATDuPpcV0xqohrvAPvaGmQYuw+DqNuySsvnZKlsKgJpDyqC7IF5XfJXLT41\nWJdESbShpVQ1RjpOqzNWD3weKe8x273wTfSyfkcgNw6kwy33dyGPV17eTh65SM7+Ef0OV0ymTyoH\n2FdSOrqgfYZB1PCbWs3K+bdFoMQVLYCpRi0sNSzubCxpZGIbQnfRtOpQWO2j+0YfLTLPyCKVW4e0\n6xxdB1ed6mStPrjoU3UTTu5mm5p5RpI5wL6YJMMqUVgGC1pUK2kd2WBf5IUWH6x7LF7aFrFh/7cs\nWSdSqEPmgpRuq6kSPIcf0bNw1e9Np1X9FKJ6EDcxrH8zYf1+kG2dRLn6rXs53IW6HTXDxhd+XL/P\n3/pi+uvXr1//dBlcLpfL5bpZ/+OfLoDL5XK5XPfIAeZyuVyuKeUAc7lcLteUcoC5XC6Xa0o5wFwu\nl8s1pRxgLpfL5ZpSDjCXy+VyTSkHmMvlcrmmlAPM5XK5XFPKAeZyuVyuKeUAc7lcLteUcoC5XC6X\na0o5wFwul8s1pRxgLpfL5ZpSDjCXy+VyTSkHmMvlcrmmlAPM5XK5XFPKAeZyuVyuKeUAc7lcLteU\ncoC5XC6Xa0o5wFwul8s1pRxgLpfL5ZpSDjCXy+VyTSkHmMvlcrmmlAPM5XK5XFPKAeZyuVyuKeUA\nc7lcLteUcoC5XC6Xa0o5wFwul8s1pRxgLpfL5ZpSDjCXy+VyTSkHmMvlcrmmlAPM5XK5XFPKAeZy\nuVyuKeUAc7lcLteUcoC5XC6Xa0o5wFwul8s1pRxgLpfL5ZpSDjCXy+VyTSkHmMvlcrmmlAPM5XK5\nXFPKAeZyuVyuKeUAc7lcLteUcoC5XC6Xa0o5wFwul8s1pRxgLtf/314dkAAAAAAI+v+6HYGeEFgS\nGABLAgNgSWAALAkMgCWBAbAkMACWBAbAksAAWBIYAEsCA2BJYAAsCQyAJYEBsCQwAJYEBsCSwABY\nEhgASwIDYElgACwJDIAlgQGwJDAAlgQGwJLAAFgSGABLAgNgSWAALAkMgCWBAbAkMACWBAbAksAA\nWBIYAEsCA2BJYAAsCQyAJYEBsCQwAJYEBsCSwABYEhgASwIDYElgACwJDIAlgQGwJDAAlgQGwJLA\nAFgSGABLAgNgSWAALAkMgCWBAbAkMACWBAbAksAAWBIYAEsCA2BJYAAsCQyAJYEBsCQwAJYEBsCS\nwABYEhgASwIDYElgACwJDIAlgQGwJDAAlgQGwJLAAFgSGABLAgNgSWAALAkMgCWBAbAkMACWBAbA\nksAAWAoHxUpipdrzmAAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(1,2,1);\n", "hold on;\n", "imageplot(W, 'Metric'); axis ij;\n", "plot(vertex(2,1), vertex(1,1), 'r.');\n", "plot(vertex(2,2), vertex(1,2), 'b.');\n", "subplot(1,2,2);\n", "hold on;\n", "imageplot( perform_hist_eq(D, 'linear'), 'Distance'); axis ij;\n", "plot(vertex(2,1), vertex(1,1), 'r.');\n", "plot(vertex(2,2), vertex(1,2), 'b.');\n", "colormap jet(256);"]}, {"source": ["Update the value of the distance map with a partial propagation from the last added point."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.constraint_map = D;\n", "[D1,Z,Q] = perform_fast_marching(1./W, vertex(:,end), options);"]}, {"source": ["display old/new"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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/5IqJcFj5p1bMIv6dsGlYr9XgFUY89GoIV9PlV++q38PzNKYFtmQAzKuPHe2Uq8qN/waY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\n", "output_type": "display_data"}], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot( convert_distance_color(D,M,1), 'Update distance', 1,3,1 );\n", "imageplot( convert_distance_color(D1,M,1), 'Update distance', 1,3,2 );\n", "imageplot( convert_distance_color(min(D,D1),M,1), 'New distance', 1,3,3 );"]}, {"source": ["update"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["D = min(D,D1);"]}, {"source": ["__Exercise 2__\n", "\n", "Iterate the sampling process to add more and more points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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p4xDgBtYLfcLMjpdLhb0qork8s89HVClDBhKQduylgvu5VXDnDtGwdGGxgLH/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OMqqgsVAZm/cYZjAC5xG0INrBZIpfzhZeumkLfWxnGMz1SitvmkA9ZVDvGDGH7iYcfGxqgngLsX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\nMIVCoVAMJNTAFAqFQjGQ+G9oUXyzKCWTqwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["__Exercise 3__\n", "\n", "Display the geodesic Delaunay triangulation corresponding to the\n", "sampling"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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kzYuoBNYRCyTKZg7cPIrFEdVrOSFdhvB8V8cK0vAlDEuP0ZOG/2l5DTmwVocc+4EvJsVs\nImelLCXKk/SI0bD3xPY3aVeOVBlXCTmRlMOUVXIv1eNJYKcrldBrYKrPJ4BCd4YpbAUOhJi/3duz\nnIi0DyMKWEckrhkHPTDVH6AXtP1KPPxPdEClThlvrPLAyiuW0f7N7mySoMMQmwFArAWdRppdS9Nr\nWVpJYI70BfEH8+3n6NA0ZkrIPEmv3XdHtfcQYQuLohQswr+acE0dugf4WrdOnWyOIG7sgLA5mXG0\n84VDhpnv0D7VncGteEp8Zsp02ppSERuAQ9UNa+bfrpnfu5bK/Dz94C5xQZ3+G/HWm7RL16goIS/c\nqbu1jhBm7Beb8cCUJ3lNMsKrNt0xoGCrTLwAQM+OCI/eu+zfZxmcsKhejYgC1hESExKZ9l34LBvO\neK8M66ADIsAfxAt76VUjYKogB0PMQGgDpgPAGS9bgv/PnK162mRvONm7cNftF3jNdtLbSr1KyC+F\nXiH3a8I0O0kN/1QGrCp/zRx7EDjN2tqlXTAIzrWznOhoxrEDbBGRjGA+2yay0p8CozGzaIO3Zwuw\n23shnQUyYIBs8gqSK5dpzVpxRR35jXgLwC/owP8Um6wb9ewByr+kivmpacBJDGWo0XZYd4YpvBx6\nlt0Alpf5Ub3aEMeBdURSt+BgN0JtD2xVUvTQf4aOmG++Jt5X0rUeZ7P8ipwZ4izY6C/gTHijN6rj\nYjNwBupb4vb6e8fp8Y/oZ8qxUx0M9bHM6wZwZvpZzc0zOPbFb9zcqObOjmjGNwiyXqBVoZn5arAX\nVyxVPkd3X6XVdBX09ai7tTIf08jyK1dp9Wn6oTpKwL+JF0yZAFyn2il0Kszj/IFxkAqHgI+aard4\nKX3dx4RF2o9A9MDmAvNr/VngpXo9ZWMIE7I0s0O9SnvfF6+p058Qn5+ju1Ncq9J5BzD9X/S2ngKq\nZOm7rO+8MpsX3LpcpdVndR+A6gxQ01ABmKDrw5y9dPbqoIq0DXaCMFQvGeWEweu1dh4+pl2NG6Tz\nb4D5ivy31cr1f9Le9Tg7hWmIPwK4R3xHVHGePtHJ7q8FbiZ+VxXoJaYWivlHgRJIkKbXUuSn6KGH\nxVf+FSZkOZSS5524tK9feM6rj7feDgIl+Sa3mBgZSIwpG50QBawbJvRy6QahdqgZ4KX8IT4YcxIz\nmAamoYatCGMdZ/U8pIUdQkyApLHRR6eB/NpUOq2GOauBYuZohsEgzepubVPJvHoL1BZ+zcxHvEHP\nEefED2/sFIjzVq9o8IsCWUuUQdAJ0/gl7Vfp8pOYqfcq5s8AM1rAWiE+9Jj/NHAIolqG7zvgu6Bp\nZBhUQ/t5baHj54nmf6HyHx1Na2m9GTipHLvCZy0UsdHWFVHAusFOJwbs5KsUSDGRlsoTMhnDGQbH\n6EnVd32bGNIJYAYYgJs2zrIlKAtXwHwQgEPANCCRTV2ZTGYSFDlSMyD6GTpyBjmAS/foGQd4/KRk\nrWYJmwCPAsfZ0440Zml32S26qkUzvuGQo5mfAXdU7tdLtC/T5J/EjEm7EPeADmkNUw04PyK3DgSI\nS0DTQpdbQnttpMirphu3o5IR3hSG3CkrbTErAxGPMJwpfefaxgo6YZH2c0AUsG4w9H6S8JnXm50C\nKYKJ8j30r9PEbWIIQGwEfQAMYNIr6DHtk+XArOWAqa6usAc2U2tSb6ovUW4QfzcH1d0BmEQSK/rP\nTVUCE8DwKnBH4C7Ww2PZBzLPz4xjBseiYoJR5RnCpyHma/V6jg5lOGPCD4r/dA7iHgAQW0BvV2xX\n02sIgNZVigXg+0sAcL1z1YJrpmQYDJBdSbOAgDn8Lx0NM3i25frA7tZ8ep9+CxnsFdVrNKKAdYPP\ncy+2LlF3gJktRS7Lehpu8QrobYj39ee86hIrhihHyUiF1/X02zmQQ5bDRNbDx96mnWf0ra2qJoEK\ns6aoWWP3Ce2EmW/ekJ6waMY3B4K9R5xObHlVn/yyHFrRvLxWrwoDt6iuGkzIp9eBKWAKWA9kwAP1\nYny8DhKlVTGn/i7z+aM+7VxNYD/hRV0GsAcoQ4mILUurtEvaTqqdMHMX/7SIRkQB6wbea62wQ+AD\n4uEUFT90/LAMA/RBx6GWPSIA77KW3QzKK74ZtmJGJwCruXz6uOOuKiN+H73U13UoeNAnbdaw+vEM\nngCO2lHE5UTsu77J4LNFTVedAE/U79tn6EiKs3zMflpeQx8YgA5AvAAC8FugXhkZV4H+sJ4h+y7g\npL7PAFjv12RG21oGAGaCe2VN6prPIE+RX0rZpCDc6+Jl9/E22jdT83GUAvuAl0f9RsF5OJtQH/U9\nPP3jRNp3RRSwzvCdMBaaW4VCzW3IZSxFnpbXqvyrA4G4uh7T4uKINre/AQk35oeAvp7bbWBlMwJQ\numWqUe09rcfBSBZO4W+lWfVI570ZTs1jm84wLPHM9IvleEX7XyRwnvjdYBoP0akEZ50GXM3Pgfum\nVjmJfbYUpYJJlX1an6ZQ6eQfQS8BqZsD8u/02Bk8oDIePxWbHqJTq1DM8qqaUcyOK1Yx/z67doe9\nWdc+AF4Z+VMxLHByzsjeOSAKWDf46mXvV9OyqQiG2RIU9cTuoWmiiAUNjrAcDpMDr3I7zDlk5o7X\nmxkNfZIeOaMrYC1UwSMnTrXN0Up7vtbTmz6t15hYTsSw4c2HIHnUHj3n5730jcSAE69iftHG/AyY\n9g6qccVmck8BnLdnWBQfgt4GimqqDgDn6O6+PQW2qsAs+1Zj5N+NfRyz06h8bNPxw7kizje9VIgC\nNhco3r9E+FD3Zsuqced3famt6uVSWwgn9DCwvjcMLNX+Ug3dZ1aXNUzkUHlgfxU6oJ80Bw9r9TI4\nCai5PDbruX2WB4uiXvGlsARgGlY7UluqFSMn6LrEWcP5BMXzVh8X0Dz+d6CX8zGxib7NRWUaEqAJ\nCNOP/G51TaWfhvNmyMqX4tF1dLGeZ4ZPuGGYf8GfIeSkLaZN4YTFiqsrkkfGLhRRwLrB6QTmO5kH\n5udxVDaah9uhYJLkZ9GrcumfXVSmbwaT0VVMm55zZ00WX7q4ekl+Emw+bAEOLcs89NH3ulnBSEF/\nDC2VIm77B/AP4PPmawTT+cy19jPL+Be2/xAbtZgOQet4Wm11d5xDwW2trnUz/z/1petco5+4tMzf\n0TDzVrWU3ZLd95ZCnEpqLnDk/nnhCxhXMomyPZAigKeBLW5csF5o0vHcylkWPHyv2knHgRI8ejNC\nwGD/nXAe78RCfqG5I6rXzQ2/YdMZdBi0B/Rq2zkvAq+YiaBYwQmWh/XlHvC45W49A1W9BvQJqiqv\n6v+xrV4TBFxFdQZQn+o/7d72J507/LRDZ97I6Jx1QhSwbnAYHjheGtfH6IfEsB7bVULYHP0PVn6F\nzeXLvlEVjrAz3Tl/zU5dDV6BNXS57VkacUwXOowdnT+WaIbDqII3BrvpjU/op8foyYu0ji5W7SoA\n4n13St//sCkdTMZ7AdgMPA1sANYC4pp3EgBlYlWhwVVSbN8h8DtWi3sJ6+Y3teG2eX3LgUV79VrQ\nyYdNI5ojwogC1hnB977XYjMSIlFaQqTty/C1ZEIBYBvwlidjjlqV+mriL9UeOlQd9uWzqYZtjxPA\n1o7nzRGOdC1cdaK1LxlGUeUZOvIr+sBiPgK0x7qa+SVwENi34KoJgTvFpafEZy+K30uUv6IPSLtx\nBNBGgS0CLzLp+gnhMUe6Ft6N0v0KvNHWRPuoYXNAFLDlBt1fFVSyhJMp8WssAn4n5pT1G8SR0acA\n8zX+GDZceRC/dF0WIwufik1NlBN62gp6LHzZPd3uThOBnY5jt0381q+GVemfLd6E8vNhfnfaOxoW\nZawRUcA6gzs2O6neaQf0Skj1t4TkeR/iN/oMy12DBPbbIfZfA78O9VtVX5UQX1QfaU99uLqjroBV\nbT/kiNAeF5/owuJOyx3Va6XBeFGv1gIgThAuWnqwTfz2WfHniod3Ak8BW3TP1s8tHj8a4raD/cAn\nwBHgFHARgAwsLUanQbYkNQrUTsKrzGaDjzcCC+wGmyvtYzixE6KAdQOP4oUIr+zWkZASEwEb9QRM\nbY59bA+lBt4GiAv2efYZjnq5YuY8y2gY/3DkZAQdsdTqFRVxyaBi1zup6rDZKACspquP0El+1lPi\ns56w8gUJwUg7zG5fmQTwoiNystovALwD7AEOq3D5xEVad4ye3EcvdXoEpzAftMyF2IRFWVQhalgA\nUcDmAt8ANgpl2EbAzFYgKVEtwiJ01y89Yw3sMtOiqsJeO6LyCvCCPuqD3rCW5VO3U/dl9ZXh/jT+\nd+hfGyGhXriGRd9rBcIZzFFahxTlnqRjv6T9al/YB0rcyTvMbMBqn8lv+u9Mzzaz75kkDnqJDW1M\nUEKqPrCXxYdtT7FD4H3h1r8r8xeIBdI+algbooB1g5MaWLqHuG7xrbJUA7XK173VJ76gkik7Pdub\n9dym/NVAv7CXmk1h7mi8rvvp67CA+RoWPgbd194dTQGhpV5SORr20sChisd801ArId+hdw7QL8LX\n0Sw1MIR/Ue/ZB/wrkAIH2Pee8Btw+lJiE8Q9uF1Yc274zpyFjwU+FR7zEWJ+EB077DgWhfaxS6wR\ncSDzXODnBaIaqFKklm7lSHOkCYosvaKm8YVafPksACAHvgWATF9J6tFi6uMhIAH0dDn4ERslA2Wl\nXPFSFFil7shXtiwhh6W0lsps0qkR2K/fM6/MqycgOl4rGY562cwflrKU0nC+CAcLdBttALoXgjH/\nYX3chKpVwPCoNx1iVfgF9AKxLnbRm330zmL9P+GB/0+oBCmIo1Stt/cak7avBACsMddu8C7dPfPA\nIjLfmbmjaR3nsUP0wLrBt949Vh4HDxtyb8xqISRuLGUtc6L4pvaodU2Co2TqUyWQWPHD93TiV4HE\ndRydx4FJzHcetQWhpeDbENVrJSNIHpv5invm7/9NP/cvI96F+IPlhDmBCd8ETgejkX9wd3xN95+g\nxw7Szw3/vxSPViNVTlNd/zcJThblFXXW2o6/hI2R3WDLMMYx+mFA9MDmAKNhhT3pUwEUmNUtUOUJ\n5UgHyCTKetGHw8AZoAdIa1qBnu7GKu2rKjO+2FSZzNoGyAbI1H3NKQWSeiYDp+ZugzrYwDaHgE6L\nSvhYZvWKArnYKG3aywDzi8RifoLCmSHJ+D7iU9CTVZnrxmlmEFKbA5c3H3QcWI98cvUZpIb5rgvI\nya8KzxBy4HMn0Khmo1/gBDR80qklpf1O2w9bilusJEQPrBu4GZuCwqNCTfrEpUsZ1YCvzJcBvXoz\nYy0l0JvAJKztUWADcB9wZ1N9JoFedc1crja34wKWI3Xnp3IewVIv/2kdfKAL7ZMRmCZR9L1uCfjB\nZ5v5hvaG/DBJGdeB0yC2sIH4jI0y1jsngSlN+4dHMZ8Ogo5XzOeG5jbgzlMj8+8lrCGschy8jcBT\nHTI4WrrBqjk/2J4lov2clh+7xREFrBucrqNQRM7P4DDtQTpndVnh9/bFh7gduAO4E7irYVUuFzqL\nq5QTwTsCGEJazc9gH1gdQgxmcDgwHWAjJ9RZTvUaawNeWvjq5XeDeblL6shFWlfKCcVS0kMK/YXB\nAKzVzO+EtGa+crn49rnpcG7v960+XgXO21ffDDzbresrGEVcNtrHUWIVooB1gxM/dCbnzSsPjDcJ\n++htNjM+9WwPy0PTAEx6BPCmMBDQ1+mhj57Z1N3VOevoYr2MS4sfNkTIvvljN6GpG+Ct6HvdOhh6\nvlcz89XfHeJddURx0jCf5rI4D90PeiSUUniokflO/LyN/C7zTwOn7Ns8D2yd+/j9t1h5eWgfNSz2\ngXUE7wYwlvw24V0BVKYyzGWephJlH71qMTCNQbImTXJZDFGOiO7XM+7wHu1/AnrAb5hJTwGTGCRr\nZjCpxNJYcnVHZNZSZP5097X75buWLYGUvV4eB4/+cxveZf98ESsRZTW1YcH6wApgF+EtzfwBhpB5\nmiram2/OYLJAkiRFNnlF9fEGW2lmZa+K+aYTLAG+1IdMR9oW0DmUvYkc6QwmDecd8lcVy5vbbRbz\n1aZWs9xk104l336A0bhRzB/3LrEoYN0wLKtVSvh6JwZqRa8UgzQrIVPkffR+L6ohLofpJ9OYzjCY\nmvquOrkB9HNNeN6XLXWyxn5QD+JZABAbcJVWT2PKEbA/i+Fv/vUAACAASURBVGo922Euq4UygzJm\nHqRNtJoCpnt0CHG7vUBtkw2jA80WbufjZbfLhRJFNVNZLWB8jR9dHqRZitxIyG56YwbTBRKJUqZl\nml4DgBPARu8OL4EKRjHNfDMumfYCPTan9BQU5x0B4+EHHKcRzLcCD5zen+gz+BzWan5FEz/frcMP\npul2MzC/kjHirpgQ7lxbtxyigM0FTZ0BWwSOEUoMS1lIty9KBTckyhyr0+yauKdxfT/xR9Cv9C5f\nwFLwJiZPvhqRgtXWjeH0eLW7Xy5IBxLtaM+uwKkjwHk4J5Me08jJcqGs/w3yR3EsqZhv1gFnnK/S\nOpqYj8zObFRESOwTMtBJqMFdQuA0pT7zCyTfivvq2o5gfrC5xvccAEo2zBo68LAHdcB/OxaZ+QvB\nTmBH4Oe91TUsClhHFCjSKvqvGqHOkM1BNZhlNkv6Se/vYoPa/SbtmsG0suQS8uE7voK/Ru2BOt4u\nfgcAtDskYAnQA30PcTsA3CO+O0T/7LRGrfoMvEaoE1QZNspaQ5eYwR6y8zjqIM98bNiBw8kYfryB\nKKvYgwkhKuYbD+xZgaMEAAn6kzX9ZjApUSoPDMAAWZD5AqAHAgJWT712WJN/smb+BvH3Q/TcDCYV\n7U0Eor7uSOY3CrJjBfuAUntgCtv8PJQFM3+X9uEWyPydY9ieiwLWEdqSoW24sI8PdOC+xKWp2pam\nMaUKKfJN4tP6/OtAvw7I0BEIFn5XY5HpiBYwPdlUmU700QMumItPY0r1Byhjrr5/mioBU1vhBVIC\nURT/49xAgMDuJdCbeTtnEQuHcq9QaRg083kYfACUQIJhUv1PPUYnTKMNQAn5vPhTff51oA+zZjIe\nsEknoaPgAID1OmNerimQOMznIfRLhvxHCDM6qh/sAB6i2UEz4B9V8LBlCP9u/ZXFRWT+aEQB64gC\nSCoB431gvyT8XgBMwArgnqpN9hCdmsGMKv9G1IHyk/TINPrZ5CBBIYuhsjH6BiigPTcAEJtAFysB\ny+XqAolqaR6i/22L+BjAa+L9X9AB06E9YxIc+7YBB3sCAh3cLU1RBy1p9PNjVEf7NBd3zo8dYEuE\nsmZ+U/hBCxg2VLRX7hcAldPxmnjfnHuafjiNPJscAHp23h/ZHhgDfQ/IaphjH70cqcN81W5T/Eef\n1cdptPG/FfPLBua3NOD2AiWFmE/YLrB7WZjfcvLY+V4KUcC6o6yziq08CABMC9gvamL0XL0+op8N\n0AdQQiYosmSQJLOVHBagiwAg9DBOVbhMawbICiSqp5pnW/GegGGh7x1MOOQ1L9Hc3mwykoUvktmC\nuTY2ZWfLj1gING+GHn9+TvijAFhyh4aZlQN2u+0T+ukAfTXp1GWSa8UVAOIe0OX6P9MwnwgFVnHO\nOzMDuMy/U5jbt/G/RDPbmxhV+15u8L+Gk9DUHXN6AwdlbEylSyEKWEcUVa/UrO4PyHXDU2G7wF6y\nLPk6zaAoIevBlcA79M5Z5ANkPfRT5AkKlXCfpIXK11JN14sk72SLKq0VV47QP5eQJtz/Ju1Sr4aP\nxZYf0uk+epfKHm7XNqyCk343mHHChuZtFLBvZiFzGAozYiLwOaCjmEk7+ytiKWB4wsIPuZ76TEF5\nYC/o//9zdKkEJL4SZqpevEp7e+ifRV/NNZUizzAAqoVZ+9k6qLW9AOCK2nkG96tuYyVdffRUBOJV\n2vu+eA3Ax2LLvfTNDCZny6R2v9DAeeN+1f2+QeYbvIjO0E+uEprmJ2MK3ZmvTnClS2AnOTtv6QwO\nRAHrDEN6iSJBrn0AJ5Yiga2azzOYTZPv1t5jjv+UPjmLvrLeAbIMA4myEjAUAGQ16AYAjtGPSsin\nxV/VR9V/tpPeVhpWIHmGjnwqNgH4u9iA7ylgw04fmGmQzqJhaIxRr+dbf4q9QCmAUDhl+7yWnDDw\njba7SUeHbCmg220oMJsCqJjPBewtUS9QDqiQ+aV76qmgnqEjZ1GYiaYSFBkGKfJDNKXigX/DjxTt\nnxCfq68cpR+fQaIEzMwPYELo5srTmBoOJHLoOD3wAaHP+B/IWnIS6jnzt4z6NRTztwVnetQwA/wX\nYggYxXy/6VYl0+v67CT6rwurwMpAFLCOKOrlYWeT2tPivdl9+xsz1aq1CnfTuWndAu1pGVMClqBI\nUHD1AqBm195D/1RCbhfvqZ1qmoMf01EVWrHuxe/ueGAFa41avV+8+fl06+N/UFWqggQg6gFhyla3\nsb97zGmtcCzTP78MHQ1q1chOgoh5gLXbOPNz+5d2uMdov44uTqOfaAFTbFcCluhgxVPis/30yxdF\nPcHa3/Ajs7idmeZDCdgA2d107jtxD4ChuA2nCTm7Yx+1gDkeWN1uc5jvDF528IH9qNtQidYe1hPM\n+W+d2bz8UAuH/aN8vy9du8aZ9lHAusO01AqU2vp4LmLBGkBgRnWZJrIyR670KanSeKXqAyuQpMiV\nehkNU4tSmkVSXqc9vxW1efxVPP1DOj1ANkHXh2q6+/t0NjOAPVQJGO+oMzY7yx/kwdbn3W8/tQ9p\nF/gkHdu6rRw2Mm846Fo5O3c1H4pYIJzsBs18JwX3t5rqBwibmQlcpgFKqa1FolScV3Mn8mk7uF+1\nm97oa+lSf5WGqXCiM2O1Naoann/FmW85WyxXKoD9dizdkIonIkqvbAjPT3vNPhT8uo9ga8yfvM0w\nX51vtG2McpqigHWE6apWTVEJKVECEniE8KVORPRxjDCDYSGvJFmeVetNqPih0i3VFOXqpcDXFcuR\nPkNHCiSfiafU0Wqc2Xk3dAPACqE4HtgsRvVVfVTdPKxbjjz4icVcw17rNgcP9B3RoGfBWEoLb6Mr\ntojQHWAO8/OGH/gFxq6TFfMv9CYnZDWiOcNA9YGpv7+gA/8mXgAA8d5/AQTwK/rgb97i5o6ADQcS\n5wl3CQDYKHCQWUHT0JFZALehDR+F+oCbsFf/VWx/jUmU1LTnSU/qNN8cWjwt/tGP1S98tOUtgihg\nHVHqZqc25mspVukuAYU/etqwjzCjTSjBMJeXsh4SrJKF6fri8cMmASt0f8AaupwjHZpFxu5id9zK\noigDL4R4oV23Drd2aMtRysF3fsBM9xVgX+t9W1CGIip8z3a2s6PrFjFXlIz5OoR+La2O3E/4RwOv\nDhCmta0UGEp5KesN0kwtkmfI/+/CmlqKgP8dD3DaGw9M8b+eII27gCaA+SvdAWYE7Nt22h/1usEc\nSKYlhtXBZpnvkCnm81X0zBWajMK0vczV/DaikyRSd0XqwnhFFKOAdYSxYWbMs8qkw8v34W2mXoWe\nViMHEsymyWySXEp7Eyg7CtisWl5ZNSpPkxlzo2BlGv1OiJ8QCuCv7dZ7gvVjF9U96wrMyQYcFvHV\nL1/Wocg5wVGvFiXjH0f2qEXMFVy6WDdwkagfewTzzahnCeQYpvJKmkHiUtpbhWJWzath43+KTQL4\nAZ03Ajargu4mkGAE7ACRcvhe03dWzB/4S1Y6OBFKQezufhlIRnUnnG6gyO/kNL6sDznNLMnY7o9a\n4VkhjiGML/PH6FEXA3Z/ABKUki65WiIAvER1loe0iaoyuFKgxFDKa0layKRFwKplvZTFmX7pY4QB\n8KxAcGDKX5oM+Lyuee5pVbvd+nbS7ortZ0b7InCg4bJB1woh9eL7W/rkxqjtubzg7/cCQwm0Ml9R\n7OVGIZltvdkF0WF1sA9CCeJtzOd9Ygpd2KIoZxpkTc5TsKFmaGz4z8elvAjXeF9GOMRv4pPcXnjl\nufs1XogC1hEmZiHZ35KGgVYkAHw4h2FRQ2A4yqTnBOJmMEEYgrVgudcVjBm2WHUTW4LNTzbDI14A\nDrZ+sckyfZT2XfbM8esRc0JpD86Xhv80vCP8jbkwfyGgV0bdaIIw5E2/YPZ8F/K/7O1pb721vFSV\nFWxtPsHBPltuuzfmxgVRwDqCc72wZeymxN16RYmhMdq8VbpaugHgyQbHAXYa7PJHbEjZVsBf0zAY\nCWkRIT/AIqNhLyUKPdSxZCHE+WIfVXN7qknXJPC0K0LiBFV3M5vSnee76eK9xEbr8yFgZkM33Qpm\ntO/3jgI4qAXJ/3GafiuVKtUy2vKAV6XSs0TDdpPisURTMt7UuIlfwTcdSvsNu1xE+YRqxXEGZiqJ\n+n3Itisbhv0y4IEgXhgZVPF5Emxv+jsPsfGhW4BP2MmOKPoa6RhtOUqcnGST8bLkJYPhifnxm8n/\nCFV9vSmbh9oUzOQ1RaVh4hOiZ2v2iqNUpfI6hC2AvVQ3w3LgtyI8q9O3AmuoA/OD+4Mw7pdSryDb\nFbYCH7VaioNDFBo6rcMnTczneSVNLc4xYn4UsI5wfC8FKfAN4T733Lu1GRsDNmsr8xZoUneKh5u2\nyrim7UkznKBI7n1LGcAlAVz3zjZX8d9BI0nfZLqOM+oXDgObdflZ4EjDHZ1QSemZYtAy/c6z0jsU\nMW+YH9Nkc1QIM3+gsz0KbSs5MwTDefP3FVHJ134CgLPstr4TZgSsPUp5RR29akcdzIUQIr+Bw7EX\n7UNo5Tm0t9ruh9UNNYHDVJsG9E4zlMWpVbDBZ9IU94xn6y0aeUcUbNooqz/MsWQB4DuBdVS/gQum\nWGYmHl+9mgQMzPQKz5gLiMcIXwjVGhVrSBswgNt033Vp/w02SB10j/JL27aD5xwDntLlTcAx9oTw\nytxWTTlokPsamqgYHwNeYjj/QdZb1V/cC99q5hsBS5iScdonNkGmvduau3Hm2sEG8QjhS8381YQS\nmDUn3AF809Bo8wscQeYftI86VDdNtGeBo6MuZZ6wCUlDG26kLPmB9Fsf4/KcCwYnfcIapCVQBhqE\nlwRKPbev43hxA3bUy2+rBQXM98bU62MVIQdwnY3ZvAs4HZKuFgP24WiSU9cktN+XMb6e/FPACfs5\neYFXj7c9Ha1C6PcaGWCJmBP4b1ho96qGZv55QOcNKuYb3UqZkslmAZuBhaCA/dm2sx9WEwhUzL+m\nvnYVMNklqll5wtaw4KMFYVKQPtIFh+EtThg8cgZRvToqDa6vwA0hGI1QMOHNvfp8jBvzo4B1B+eH\n9F67ChcBPY3pFYHVrIXKX8WmjdUiYKX9l9ug+au27zTzq2miCqsa2ACctK/ieF0tdA8GTFT5WW9P\ni2GrwikAgJqkXInZSfbTOPcNGq3a+XzDmc63xsuSlwZBB8Vv95Qu89U7mXvFpU37EviT5u0vyIqE\n+82Yjz3pKu3geTXPoSL/OaBEHRTZCBzz/HtuXUEEw4C+Ffh2K72PPsx9qyadwHEAwBOhrwRjDMGa\njyPzo4B1hEMIk5HlrM2cA+cAPQP9NYGC3NB/k/uFEHXR0BqFnVdV393o2zfMhh/VNhwUMA6fDy3e\nlUJi23O7HwavYl+zh3SeGd7rxqk2b6v6LloZ6b1I8P0wsN/2lCYe88OuCBQ0Iupg4MyCDfs//DNb\nve6lagEXl/lOaOIk8Kg+qsLXh+fCfJPpfogddXjOy+Z2G4HTzSbNH8/MRHqK7QTwtI6x++QHEyfT\nP7fPtgKMFfPH5TkXjKYWjZPWoayKvaOHBa5JFLJRuppe9U3vc6dPesgrk9uemmPDh73LtTwX7Jr5\ndmuQeodankqBO4gP6uHVQZezXcBa2NvSUI3ojhbab2Zl895krbdZgdnrKGQVVGtJWZrxaK8KX9nS\n9QNCCfQ1C2rmX2azS/Emnmq0mWUWNgOHOvhesMdpNRE7WFbI2HebwCuQhvY0kd+vOb9L9MAiwijt\nsrQDIgZmobCvdQvrduAyhhJDiVlZrQqYeC9537dxYh6wOVxnCZuG6DkmYGbj2RObdXNypA37ogVm\nqE0eWFCTg04bvI66qw3PGdwUPmFlyb7ru2IR80bpfZT2InjQAlZqi/ia+Ra3YXgV1xIAdRvOYdDd\nhH6I+d/Z6rVaO15DaM6bOQScVENjFKrMk2BV2npwTD1CbDms9ztV96MOkjXLUna1Jg/MVP4yq6qR\n/0d117XzLOanNgH8g577hbFi/rg85+KB++kKQdkpmCWvBS5XFq6ajcqYEfJV/LvBfre7A1zWsjsG\nX/dH2IpHW0KjiR0Ehaep8YwGY/YebMK7z5BPGHIH8H1DA7O9ngq+9Y5LC3TpwQnvMB/AEZvzvobd\nAVwFJIbAUNbXMOmCViQQgBoBwrCKqtMCjTZziXaX/RP2xgewtVnDwHpYg+rVshncAVxvZT4/2YwT\nd8gv2QnBV42DMeV8FLCOaCFHYZcNoflX1gLn6qPKIQMwy97yAaI7dw/aJ7914Z3mG/CWDi3QJkHy\nzfV84NBEyHkLouRJ/7frWa/4S8oJmJYsKGp+ZP8VGLFY4K0BTmnzli/s/31z/imdrQPgjponhvkG\nl2zmD52U3uuYbfHCTR2KkI3wSIMz+YUKEgaT48F2+ltTPNT2SlfLmvw+jEKr1H9Vx6Gq8PfaOXtQ\nZ6MU3lObmMoh76cwGBcxiwLWHV044djzcZ1ZBOAe4GtPGFD/HQYux27q2Cc8S869/fxkZ1YnX8Mc\nx4tXL/Fs1dAm1aIlgdbBbT7RVL0yqte8GAqsIZQShcQwqXzW2oCdNoF6ZZhWf/B/Z1zMeCnR/hvy\n+JWz8S7Yu4BvQi2ay0Cume9Mrqhia3mI87xKJ9g58E52/h60+7eUIfAqmakxjrbqVlLvnOChUarE\nqdfK/Eu6kLHamSXZ6/dAymhfsvihQcKed0ypHgWsIwyTfFfdcYOclzfvhXpQZxy1vN1NmV/WMUVf\nwI55jVD/W9x6HQ3zPSa/gWkKrLE5kQINA1SDw8M4TL16hC+0hl0RuNtMnWWUrNC/PHe2EnahwBCl\niMVAqf/ngu/HA4zwQQ3jDbj7WHqeCTCaXPh72GXP6UO89eZw20hj0whl56+BM53uVgQWhTnqiZaX\nRjxhp2WZI0qcvhV4jMLMN0mVj5HrLlaPYsISa4Hv9W9rGG7Wkj6qH3+sEQVsrvA1THonOOAaxm3S\nENyEaPyv+x4Y/7uRHW2xXnORoIY59fdfQ76MSevc9gHaIwWsBB6neg2n7wTupVqOC9Vn4HzfdHHz\n39DX/kjvhaO0f8bSm53dsNenrqNhG3QDzqBgYqbwjUdav/XmtO185jvf9VEbgjOhIgHCJW7imoBS\nr8QjP/+d0hDzzWovz4TUy/wkV8wXJOsDcxKe+dWD5B8LRAvvDm6oTd5YwQ5xb+aoTud9FNWgRcf9\navqP8E2x9Cwc9iwDQQM2Bb7KiaNhvlzBUye16QTCzLbhoJIFH9F51RTAT6g2729FNVi1GusmUQKz\nKYsypbAkLvFeA85TR8wP7c210rYF/jINkh9ATngClaNz0lYvpW3GJ2tvuhkUo05wOGDqfxCQFJ4S\n3h+2qfcY6XI4b879KVUzhvxV4Bfk3tOgZ6uXoboqJCaufpvuGFZXN37qKX12wvg/jogC1hGlbZ9B\nuuy33QLfthWe0O6/o2Htd+eFoBn7p6Ghno6GmaGaQWfLM9bVwDX97V5IwPxwou9BwW46K2P8OeGP\nWsP+LvA4mfkeK8OuW6Z86Izkph+DKouNJuZ/EGKXw3nz3cPAZgKMN0YA8ChL2Dgempe6ic/m4ycN\nzB/5Nm9vNarByB6nV7N9aYjzdnwdk/ZNfqMf942Q+8UFrAC+1d9S/WR5EspdBMt1kuPJ/Chg3eGE\nSoIxE152fDW+sMjTwGHvxw/+XwTbks59P2qIujhlfn0eS1SrnDjqxVVIG+uErIpGwJQHxqfbbwon\nOvd3AkLGdF8lFHq6cRVUfJyq3pA8KGDSfoWZLplxNOYlAyf8Nnunc5rDeZi/oeWTFY40/H+1MN+k\n1BYNJzjVngc2sDJhNTMFQ/jUtY+K/O8Qfi0AYLJBKCd17ZzJQ/j2Y8JfBQBcEribIIFLZtzk5VBC\nRznfJ13ZGMdnXhicBql/VCHopXEN26wHmvhX9q/mfFSFLc2Hmr7epGHPakF1BMdWocRrY3J7lg1L\nZoBd0qmO2RI7+PoS1UtmfC7q7m6F1Wrm1oTJFa+wHFtjvkHwdaslSuHgcMNp7cwPntZe9pVEAlvC\ni4q5EFWLLSPXA0savDGF7QL7dCrHi5rP+8mlfelR2KmpnaKvA4YO553vjEtEMdp5R/B3Itcw5xxo\n0y09Pqn9H9ljaDjaXbqmPQi1Q7tA2pXZDBxjgmO3MFcxW01ZfKOndctZ8ykJCRj//eCFUEo2lWMO\nvE74rbb5LwSeISTAPwBo76tI7OQO550VPbBFAX/7N5Ez6Ao0BR4dFOz6wYv7e0zhYGhnFyjaVO2/\nwKIwOA8kbIoADTPe4zlyOZ/aRmMw5bXepjzal2xtv1KvO1MCP6NqvuMe6hSn1Wa5Tng/Oxjtx+XF\nPi7PuRgovdelY9hNbUnHkk0X1BY7h6LFCFuEbX+r1wV2ff+jtMc4PwWc9MIiKVbbi3Nm7Eo9pmrm\nBD+W6LQRuYCZGH7OZExtOwk7KrulT9m6vSpumQOFxCxPpgf7tWNn2CLC92j3sP2dxKPB1ynZ36aj\nTXu6JOwE329O4sYxAclSJQHcBVzHhF6W9oK3XBKfHX8PEzNjNycIGwUArAck8KA+/2uqamrUy8QM\nc1bIdX+u+tG0egkAmToh0UP++bMbSyvG58U+Ls+5SHCi6k1RRNlcUF83GrbVbkiOvPX8TvDryZuF\nfK6pR/VgHb1NsFCiEyF5lQLLxnNj9jOMgwJWMrvjL6Wy6k5wE53/LsT9pHOvJPPD+J2c/6mIBUL9\nJ223P8KmVtDrkixjyIKozuxya44XWo+OxFb741HbFgxuQ0LVkR9S1debeWuSAdim9xwmK4SusIGd\nf5kFD6HZLlksPLfblsEUf3PyMBhClOPG/HF5zkWF74rx8sg2qSMnW4H9rf8Rwau9GDrKy13+Zw37\nncE656vG5ATzupQBZzqCB2BStzczFkjxnLAJlFJvrKJSbUO1mzdCc7sRuovwlvvWoH9oDYNpjfJU\njvlFliLa0RIwh1c2qAeNCezzxpBtBQ50vmPL0S7Ml7Z6HbZbWAqX68hhqjmv+K/o/SpVhN/hKdlm\nvecqQbraI4A12QAO8wsv6qD4PwAK0CuBhXLriYIHEqVksUSH8+MSfogCNj+0NHPa7dmAG/OLwL6F\n1aRpv19D2bA5E/9cr/q9UqZPmd4UetqwM1ZIlfCVKfIERYJCokyqkVxQf0tI9bdAUkpZyKRIkhzp\nUJ01qG0YW133q0bKfMErptFrrDfYrI6YK4Ixhl32CfBi4Ib5r7Ezedq9Yrvi/wvzIn8wiT9YJanv\nwsFTlrjHlNTrJFwQeIgq/vs8P0hV+WlPZu4ICA8B/4wzSrq+Eg/7J3SFsT6lWVcSW7F4LHEsMC7P\nuWA0RQsR8saa7NnBB8Aruvwy8MHca7U3dOWWFqjz0dn4UpO3IaXaqTJ222MmNMnapxmQYCItMwyM\ndKlCu4AVSErIHGmBZJBkJeQgzYbCZAw39Z0AmT2GtZ4+sdTKFt2vRYFh/lv2Toxi/jZ2vkNU579m\nHuTv2OOl9rzI9hzy+mYlawrdjlWEWf3JcLvHBMzZeZGQYbXMExSXRLXKXZCxX4iNod1zhCNgJXAt\nZbuMCYzLi31cnnMx0ESLYFez9E7w9wDYa7dSu9ShyzlNvXQyVOAbW2ryksC9xIOBldNjgic8tJJh\nQpYZBkbAzF/ZGkJUGpag+FSYfrjRED8nDACw/oMEuOb3B0QsClqYL0N7ttk79zZ8kTfgutQBo4wl\nyHxHvZyuI+lSRQIZVYkbnws8Rxb/00BYYrXMMwwSFFN0MkWeIofYjDnibjo3QFYgGQ4kBsB9Itx0\n4/aomD9h5lobR/KPy3MuEoJxubfY0WDfmPT28IsYDXslZOpBjNS8liaYbLBhk/bOlpr8VmCKrMhJ\nj11psmqETmRlD/0ERYZBD30jXWpT0pWggO2BKd/r1+LXTc8wQdeVK+YmOr9N1SL0fKbyAihVUqLZ\nFRMRFxGGvbsa9hu+cfXaY5/DD6md8yB/Ozjznf62j1qZr6FUakpPMP2xwBtUyVVPe129apuQZQ99\nRXvF+QyD34sX0YDd9IZpuqmoQxV7QDbAdIq8QDLIsitrq344l/lvUDVdifGy1K94JWF7of2wsUAU\nsHmgYweYvxMNCrdH2/Zr2ubnVBP/4uigYUH1SjAhkbJluj4T+IVtwAaTmOiVCYoe+kq3lCWr1igX\nsKReKwIAnhV/bnmk5+jQAFkfva/sQGKNdwXepPpxuTGXiV5XiccSIxaOHbrQHofgYcbdzbkVCyT/\nnlbmK3Df7kBru80WMONgGah2m+F/CvQw0asabYr8qvyhqCSzKe69Xbx3iJ5TTTelXgNkJeQAmeL8\nXzzXzWL+e5r5FudV621MmR8FbN5okTE0KBkaWkb8nG1zMeORVQoaLdrUK9Et0K+07fxB4B3dm80E\nbKJXTmImRd5DfxIzxpiVgKlYohGwBMUG8femJ/mIfqZsuEDSx9k+en8VTzedDOi5UKWxXmbM1xK9\nN3pgS4Qm5jvqFfxW+xXayb+t+ZAjq93Vy+kDY5m0ZjqYHQIfUSVgk0CKiaycxIzi/CRmeuj/Trix\nUK5hXIS2iI8BHKfHjYBpDyz7g6gzTX5Ip2cweUWsBYDTVKfj9xjnnQiExfzogUV0wkiitOucOWc3\nG2SzLWT/Bnwszsgrj4Rt2Ny6nyGY4cO/FtirOwM0jETxghNO2Si+aLn313R/jrSEHGCg/LMCyQ7x\nrjnhMToxg8nvxD3uN01NAsOlzRMh0nspwTXjLfvQruYGnHMFhd0eq0feuunKTnR9Pys75zuSxnYn\n7j48L3CUjLYZwqvNUa9j9GSCYqP4guvWZVoDYK2oZvN8Qnx+kh75z+Kv6uO/0kvbxXvm5B/T0Rx5\npV5gA1fgTXPjMl+OG/PH5TlvNEZGPGCb8fZWDfOv3PL/ONIh0wYxoWc7NI1QPj38awJHyHhg6+ii\naoSmyE3BhFOeEJ831YYusirgHwVWmRZohsHT2qQBLIDiAAAAIABJREFU/Io+mMG0RPmd+vw9YQa4\nTwA6BZFvkjlds1I3QqMHtrjYaX9U3NvB9jg9ZAgJUpDYhvzzZn5pu2j7Qi/0UNRBBR7MOsgpyzNk\nc8FUnV5ZmWGgCD+JGe4zAThOj2cYZDiTaOLRVYg7ACDrXwFAF6ETFfFP4kvzxX8RH/6LdtTeoN0z\nmM6R1k2/HvANVcx/TWC3HhDNF2qAYr7TGXbrIwrYIqJLq9M508EurzHb/dYjbxpUL2bSkqUamoSr\ntwnvahveJHCeCBCAChtOYdoI2Mviw5Z703H90H/TFUmABEk6mySzWXYll/07hJnlHnvo9RzTEuXH\nopqzbk0yuNLTXRMvCOwj5EzJpC4oE55N2IeIBWJHt0M7G8+yMJL87RrmHDLM5+rlJOW3Ml8t8eUI\nmMmwPUjYKgDgYUHAFJ1ThHeSZk/QYynyHs5kGMh8KMy6dWeqf8WdoGOABJ2A2Ng4g/BB+rlqtOXa\n7bqbzuVgzAfjPHRBnZuYplucSipiQWjqu+4CbsZ+e5af1h1OHwAC6gU22XxiK9l+UnNpE4C7dEFs\n+D/owCRmfiMaFZeOsxnezni/Cr9Lhjs21Op1nB6fxnRuhU7QQ79IEzNEp5ocpNBrW0JfTZVrS45Y\nOvjq1b0N1w6f/C0NO6dv7IPQ3Ue12wyxeARCZ3MYvZkW98BJrABO0UOTOJsiT/JZ9FEN8FA445UT\n0CF7JQl2nRxnVbrTa+J9tXMSMwNkLvMdAePlMWN+FLClxjwGFRoNe6vVjP3RZh1vJFlBS9pEQNFq\nMTtK5M048G/ihdBcN6BzeioNtfFYB7+/elOUQALBZlK9TGumkWcY8HboT+mTaeQp8tqME51s5Q9L\nlWpwDCK9FxXcwdrRfEjBj2x3CS10iUA4PN/OysFE/CYOaOY73V0O85OAt0Raww7Rc5OYyTCdYSCL\nYc15ddo+oA/aA6EUts+MK4QMA/WXN91MQu/s94TbBQA8L7CPKv77zC/Hi/nj8pw3FH7MpPvP7muY\nc+UW+2zZ40VRgr6X2rYGdcrCObo7wyDNr2EGOAvkqJqiIwUshWCvIPoayK/ItJQoB8hUyhaU+4Wk\nQCLp/AVxF6ATnU0lYYcQE5WUNS7t0KWEHz/sHjacR09MS+vNuawjdcH0RSejIRQ/tFOTgh6Yj330\n0nqcTTEzhekpfIcZIAdmgD6E8a7O2P2wZ0YI2BS+y3Q2k8LrtGdaeWBI8iStW2+G86lefgUss2mc\nmB8F7IagxbDV/whvirZr2EgEO7HtzdjVV6O1KogpfIccmAamgRmgAGa0gBV2oAPMjBOIP9QXoUPA\nWaBEOnVtMp1J2Rrzk5hRaccALqhdTwkcI+RabksmwJWsy0jvJcA8Or0cjBxJYuAzfxc7xNGiXqYc\nMgFDxcf0yGXeessaBUz1+2YYTOG7ivZawGqctQRM/A70E017f6DYcWAaaXZtMp0xA04U7VUoIsPg\ngjk5Zf1eSsPAkyfHiPn/6UZX4JbB/IzZhxnZwS/opyl3QTuPNwD3AXcCt2NW4IrAP+apXgCEgLgD\nYgPEJh0/5FHEhs1Sr916Qu4BMEA1JQ8AYA+9rkaSqc19PhPw8aOIY2PGSw/FxoWrVxPKVuY7/HcG\nnAUzPqRXgK1hqAXMOT2x/4bwrPhzRdEcfBO6P45+BieiCAADoA/xR0AFIV8F3oEABCCeqMjP222c\n9inyCbpubm+F+seY+ePynCsTO+0ZEILJYF26vsILMo2AWqlvCpgC1kOmZcmmxgAggNP0Q394Mh8V\nQ4+xEKKSnksAgLshvmOn/RyYBsp6tQiZDNfeWQ2a6aGvGqE5UonyXvrmW3EfYC/dUtrDUlVhGOm9\nQOzwCgrzVq+OX3SYb+AoWceEewlXqZgHlsCKIjojSVL06GLfJL8D0B1g94lv6XtgBpYHZnC2XmGc\n1mnaf14ngNCTwLQd6psGMsikSog8Rk+eRV9xXg15zjC4ZE5OQ1EHOXbMH5fnXLHYCewggL9BWh2l\nltkKmrGOTbSRApPApGvGKfJ/opNfikeJVaCH/nWakNNDnAUGEM+6FzbjmK87VPuu7gmnh7R6lTq3\n0G75KgEbIEuRl5AZBt+qAw8LHKPGEKIcn8EwSwCh003Vp/rA4jpeLRjJ/C5xCBn6aDrA7Je+QuJq\n2CVxZ0VU4L/Tqz3jQwHidtAxYAZVH9g0u9V0JWDlrFUJMg8y7a3gOgMUMHPW99BXugVATQswQFYL\nWMJab5z/ivyz4/JiH5fnvJVAeEvMf8TYMXucV4pViRWIc1I5EiDFaj3pAOyXyJ3iEl0F+lXKBr1T\ntUbFX9y73haaHe57IFllt0PN1PIshd5kZ6kCj7EEDNiJKEbMA8JbQbT6f1829apu2lCNFulyAoKw\nRcsuOCFoBds4ViM3wzv+G73zAM5kGPDAg3gKtKcSMPF7Xc81wIUqgYnPHmrwPYCZqtFGT0J8BgDi\nBRCbOaSHvvK6wGa9uZvOVRPTPCtwiCz+8/DD2FB/XJ5z5aJhzGMX9eKTETiBEgNp/rgFq6u7nlHe\nBV9GWRfokapDOx/ijuanSIByFlJpj/m6+QsAuEqrz+hFxczqYlb1nRZ0sO8jYhGwEPVqGQo9V4x0\nvPz/+CZ+e5FFuMy/psckv0T7EpwxDKTrMAF11e9F3LvSXWNNApYDchYydy3STGRP55GzDjBDfp6j\n6DbR/GcZA4zTs97KUJ0BThsTbCfsPdK1YUfpbNUz63uZS5ygx9Q8h+Iu0GHdWd1n2fN9DIYYAKeB\nAfC/gP/s1eNvarqDIbK+vl2hc+v1rNxpeS2VeQmpWqBq8bCH6FS1rK3R5cJL5Qg+esSKR1NSbotu\nOTulVfQbQKH2npn5sIoEDEDHgUFFVN4+I0AMrY8+qi61KyAABehxiM/tgO0Aae9aKnMVNjd3L/lD\n8XhJaT/IROiutyKiia9QcBse+Z/YomfSNWNHxrSAKQ0zX7PieE56YR/IkQ+ronHPfPR13oYcIh3o\nfmkncStHmuUlpKmDJaUbBI5SHTnxt4hbECr8MNexJZ5M+WFF2My/vQql/oo+SNHnE/iajFnaGXAv\neT9x45Li6ugV4ErVJcy/rq6fZnWjzWxr6HI1z+8mgQPksn3MmB/T6G92NKRsdOwA8+TKLzu8d2RM\nYhWLYJgvJyjoe13DrVYmMXLgmitqz4cqx0/ANZ18z+SOjgIF+BLPgUBKk3SNjQ0vPsh95aplRZa3\nEjt85tt73gK22zNxcPiRQbjl4BufMd/ADeUVQ4vtzTgI7PN2/g9vT0DhNgaYPyKEPpbMjwJ2k2MH\nPA3TH+eXxIG5hdiqKGNp/urdpbvAE9vMHNlmrSJVbQH8X7og+Gp86hz9dfE767JKsYxuuQLW8hzj\nZMmLDKZhjH47FiZjHXvR6rtw5gvsBHaGHK/twLYOy5QrdGb+HdXNn6NDnHgV8w1XfxP+9mHgoOY2\n5/y/AiVwCDgKnGqvgM18bgLW0zQFSscDUcBuZvAE4p1mYyd017AGpk/og/yvvfnGo1Y8Qgk6rqv3\nXj3dRjlbz7yhWqhmifVdQMEG72xxpukovMTiEijA13Q2hbvpXP1kzvONjfUuLYhELSEtEyEuLpyx\n0orzfgL9rpCSvWYvZakwivnO8ZeFs4cTrxpKXwIFxPPwlrGssTmQkATYCU8FcK7xAhD34HYx+6j4\nMqBh13Xz4nlRPYV51jFDFLAFYnniKjubP87bD7PhN0zrQIvr91QFZ9WhUguY7X6ZQdTvhBSK+2rm\nCgq023hgQ14Btym6UbjxHzS+tSIWgGXQsLnO9BGchuNl4MU5D953mP9gpZiP0El4JiDWWtNPN4U6\nX7aX61LgYYkC8JZqDeAp8dnL4sPfiLf+JJ6v6iCrpEcCaJug34ixZX4UsJsWxpiDlsybn03dAAuG\nNgY3cMH20KFqjx7cCWhdK4GtDRc2j7SFnaxK1hrO+pirnRE3BvPTsI5nznueqt3AntBU9FvDy5bM\nBbzZBOBB8Y87xSV+Av0K9AxwfxUhPAP8v+zotobB9CWwBXhKfwz0cx8CnQ588VOx6VtxH3kD9cYW\nUcBuTrSrl8KyaNgCsJmVnXDPorQR19DlxbhMRAt8+jkatiiu2I5u6jXyXnuBD7y0ic3AJiYWHaBX\nDuIE2yZ++6z4Mz+L9oMaprI6zMqq0sQGir0CvGyfTxN1JxneBPRwZrqOr+n+4/T4yCrT+2MqaVHA\nbkJ0eSmoht3iaZjfUCzrIGFpK04JWWrXDBKkpwIXX9TJyfwLe0N5UqbBvNmcz75Gb1vxQHPHMqh9\nWzzrjX7aEmLnooYT3U6vhV1NYT9wwNu5UU9gPQco4r0rrGeki7r310v8M58+MicD/41997/Y1/8G\nuIhQ6N5m/n765Zu062f00TN0ZGSNxwpRwG42zDWQwjWsfSLEUdRmisV3KhOqRcsIWOJaLwDoFW4f\n1jsOenNUme2gPudhNWY0gbhQX8ckNJeY4HXw6xN+hDGz5CWGr1KLomFLN709gIPAIeATb/+dgDUt\ndYD2AK5TCfmlePRPoh4DcooeOk8/sKart3PuEzaQ7EAohx7aDzsCnDSjpfWIafqlNRDNYf6fxPOf\nik2Nj1t6hTFAFLCbCvOz5xYNC5KaveOHYdHimzIetZ6kPi4Lo1QJkIDerL4qvgVWV9NHKbCJ5erN\nfOSnWdPqMKFTt1Y3NTVxBSz4DhonS74RmFM40efzkqoXb8UcBo4BJ6zjQ4FLAn8XhiQ8ygcAtwkz\njxSAnfT2Qfp5ZQXSa4tpKiceyYP4hM02mqrhzOb7Iea/LD58T7SFWMSvqH5cjBHzo4DdPFiIPfNg\nfMuAmLKhzOzd2XjAsD6XeWBs0p3K/q/VL4JjtklK1mZVm3mpCNgCJuvvBL2uqnyOTJ1c92tsbPiG\nwiFq93yNRVev9v9vdfQ08LV75HOBTwX9oY5Ckzey+FXaazHQmWvtj8Dn1bcyvXsT8HxzEhOf7sOa\n9sn26krIjeKLTeJT5+vOuALxOo0t86OA3YSYnz1zDXPGpzTrlkmIR0i9SqDAsHQ9MLU0V4FV3Kvy\nZxM4r5e0Veu0qL9my/wFb/UHetvy19TtcqRqUWZVkwLJsJR1hvIrwtWwiMXBSDbOtUtsKTq9OkIx\n4zzwPXDd7G2Z6ule+ubHdJQTz2e+g/XAhtZKCGATsFFNBLrKtgF9TfEExJ1YW7tmAPBjOvoInVxN\nV811KiX7rXCZPzYmME5DBm5qdEk7HIk9LIT4io7Al97/suthNUmX2fI0TVDk2liVnAyQTWYXUDau\nvD4J3AV8o+faNVpjmphqDbLrZrGVL/WrxIhbijKZMALmaFhg1HPIg4xYFvA5AXcwGjt6Nj/HKzTh\nYBjqv1zqsvQOGWZIrKaqVfVlYwrft+K+b4G/Nt+vRfwAnAL+HfjnhqNrAZoFZvVF3gYyiJcDZ75N\nO8/ggbNICiR1YPMwYbOu+bjSPgrYzYBFUS8FrmEv1wm5jShRSvVvy6Y8sL/oKeJrhyyxQohBtGR9\nXVQz+U6AhvaB7cBhqxvAdHqZbrChGpnT0LUX8ziWADtG8dPRMLQGGOdNdS5LfuOsfb99TrlUbz+a\nqCazVvUw8ngKSIBzevyyK37vBgaEfUQ/GyA74/VDAw2BFVVwDOrWRRSwG45Fn9RgL+sGe1HnE/sh\nBvYx6H4xJ0yta25uMECmPLBc9tPeNQzCqx6NHJmiFpVw1UtBRx4HyMztVEFt9Ww8H1E1oQ6v+Zi1\nQ28aWK4SWXOhLWnKRgvK0F+tcCVQtE0YP0HXH8CZ9TibYaAKPfTX4+wDOJP2r6HfEC6cRDpAes2N\nEZh1zmnCWnLFoF6m/Dqm5d1n8MAZZIb5KvxQnXqYkAN7CNs0+QtG/rFB7ANbFMzbIBfXqo198lkJ\n/Dl1bBlrihzmdWFYyJwF+wfI+uhVf+UaTAKTgdrQ46Afgu4FrQOtBq2ay6NMApMYyDX1jWwZs2qo\n8L6w1GvMLPmmQdWt5UgC2UcXG00ed9BDR838CwJ/DzS0zK6huG2gJURthpDoAZPAyUBtxHcQ14Af\nIFmHbHW9v7cK6RrgB8AU6JHwk9A3IKqZ7zTgLolqKTF3WrY/OX3A40L9KGA3EAtUr2AEwYBr2FZ9\njhNlK4ESw9LytxwN09tsWccujCWrrcwmMOlmRuFXwJTe1gPrgSnQ/aD7QT8EPQR6DPQk6KcND9dD\nmU2YW/B3R450tkzC61k4TzEcFzO++RDgc3t3UTd0D1f40uUzvyaseJLEc1SnRRyoK3tB3GX0w2b+\nOsV8HGe3ep2tBHZBMx8AQPdXVoD1EN9CfNlQ8R76WOczvwo8GOSheYJNGzQKWMQyYokiKh+wMl+Q\nK6R8TR1ghdfWA3hWRWVX2rKEuu1ulojRuok/hyON4o7AXUx/mFWrEnibJdODvawiFgdz5ictfmB8\nHvDdMl5eWxfv12noLzEiHak17Cvx8OfiCZ+QivniCS17HwAZ6NX6wuIL4Cudl68I/xXE5401Fq3M\nr9M3jpAlyvz5Sv9Jb2VEAbtRWMTEDQ6HuPtYHseWcDsUZbvvZRafNTDNwxlMzmByGlPGsuiE53g9\n4BX0ZuaWCy54tlZcmcGkuRePqFSLYPpO2KfCdr/GxYxvNogQq5dxtr4yVODMv6s+dx3VzDdEelEg\nB44QTtcy9rHY4jM/T1mIUHOe9NNbTucXnnTZUyma3+c+8a3P/D7vZ+bM/7m+iTHecWJ+TOK4IVgi\n9WrCfr0m17PAYS+iUmCY1DYsbWP21AtAHz21SqxEWSCRKIGvqmPrgQTIgQzos24q3r0sId61LkiH\ngQyYBFKUvbqDe7P4y056ewaTOVJlyTnS4UC64uoEUqzVWZrzIyPmjJGJiMtwBdQpGG45uEdzri7z\nvAuy2m2cSAP99xzhnkpc/iBeAPAG7Vaz1GcYSJTA36uvrNcDuQrQB4G1yeocjT3VIBIjWnQVl9M1\nZuDXZvEXAC/RPqNeV4R2GY8Qpu1VxRT+LrCGNPOjgEUsFZZBvZQNGxKridlUNsdm4IjXIC0wm9QC\nlrPMeKVeiWURffTMwpI50hfF79X+b+jeAjNJMosC6AOZJ2AAAPFifSk6CiT1IOcCq2YweZwmn9CN\n1R3i3efokOl4mC0TDIB+gwcGfa9ZjJUZ34RwUvvsZZ2XKI9DMvXiugXWaOPT0l8EChQJEBIwRSqV\nNXiRkAG3VQ/xntj+Ju1S5AegBOx7WoV8thrbWNicZKCDerqN1Bo92U/XzWDyOP1oGlPPiz+pnR+K\nlx+jE677NWhtvVXM53tvZUQBW2YsXd+A3xR1cFBnc2wCjjGD10qmVj5yEvmMYbNrW30ADANkCYpe\n2pfJsH6BlEBeX1CwFZrouBoIVnUPDLCmQKKChPvpl0YXPxZbHqMTOdJZJJYi8sjnTwl/Zsn04S6C\niGXDDlSiFZykY3E1rIX5XNU224e+rujhsN0QiUcjCiDHarpqeqF+I96CVmj1dwZZL+1LDIUe+RhO\nWsnY9Inaei7Tmj4bJbKT3t6hYxT/Ljbyb4sjhBkv34o/7pjRPvaBLSeWZ/63lr5rs8jDU8BGO2+p\ntFTB6f0auH1gpg9AWTKAffTSWaw/gwfO4IFpeXc+uRoPoNp+VBUs9ToHc0I+uXpa3q2+fhbrpzE1\njak3qZ6k+AuxsY9e5Xj1WZVMI9Q0eC8JnYVVjJUlLzEWha4LmcDeqUAL8xEiP1/Z8jhwqmb+0B43\nYoi0XVQc61eUu1akfIUwR58mxYXbxFDcgRH4UW0O5fpqGsSzWK82xfwZTP6CDvi3AECbhOWBqZrf\nr08cIiRrtzKiB7ZsuFEDORWMQ3SIGfNG25IlCgkAuZ7rqdSFgfVOGA5kP+s5iyOfxXrjliUoMgxS\nmadZnqBIUNwuZvnJ12migDTzQvEBXqaTvEDyDB0x60cMxW04TZagFraM1fXjjmTE8qMlSD5yto6F\nw3fI+Jy6ofi5Yn6hQwUGJn6ubeHKZLaKvp/EzLfGz2rAefpBjjwV16y9hBITajaZHOk94ju1+yzW\nmy5elb6RI32ITkE8HLi0n8FUq9XYDWaOArb8WP5pCKT9kWvYw8DpenpCJWCmQVpq9eIdaicIM5hF\nMp1NGTP+GX10FoWZI7ESMOQpconyCZZ99TXdX0KeAUxOPBewAonJvFJitoYu193XGwQOU+2BFQ09\nAbX7NS7t0GXEyOjfyC7enfZpS9clpsB6XPEJCzkkOkqome/7LQO2gII+NJsm09lUy5i2T+inEuUZ\nleVEpeotflD8AwAETtGPzHRoQCVgZ/CAGezFlSx8A0fArGrfDpwfKwGLIcSFoHsYZHnSDsuGjz6h\n+aLnG+oG6ZBFIJw+MGMkWjaGRd36cWYr4EM+uXodp8eDY5ODWzVbFVJcZq+LzcLtADCFdeY03r6O\nuDmxiGs6o/k/ms+M+5F9qLQ2zvzHvcR0Hqm2me9gL73K544xyUfH6XF1wsPiK7PffCvI//+fvfcP\nlaPa80U/X3aFtKRDOmQHI0aSoOIJXskRRxxxxCtO8AaviEjwiS94gyNO8AZvcIIj3o1H9kjuISOZ\nQ0ZyJSN5kpHMIU/yJO+Qd8iIRzKSKxnJEa/kiJEkJCFbskM6pIMdUs33/bFqrfquH1Vd3bv3Nju9\nPjR7V1etWlXd/fnWZ63v+q7vyttt/mdNPRMIlBgKxB7YDGBa1csPGk68neaQ3D4ImNVdVwAnsqbm\n1VrW3mzpauwWKCb04LOubxGfP4PJmu6BqQj7BppmeExhF7/wp/zyiVya0miV6oEp826jdkGNe00C\nRxj360C2DYRXOdAIzduh84ETcQzs50BPVC9KYN/1EqpkEckN/2UYu8kIioALEQAStGpZfcYd/QHh\nZbb4nwJ1IAVdZp4fmNi2kd4DMM5vKs+5itTVzvasJfcn/EL3wADgZd5xEnVFe8X/s6SS/QaSNBJE\nD0zqa46wpt2oiAI23ZiBlAQlluxvyOBDR8NOZ4fa9WwYTAqYmU81qbVNK8qF9mirVq+hPYrJJhoN\nNGtom9T1Cq/zluPaqNSilI6AKQ1T7sRJjF5CI4vFNxHzuxjr9SPjN4Sn2HUhWv6f4RoJmBFUX9Ok\nvzoH60uUy7qadYWgN4yAmVjDBJ0ErcQ1JhO7ZPivQ2qL5wlAxRC+ytukgL3J4+/QGICN9N4rvP09\nyu7wJJab0d82ak7Hi/YyryXrEh8SHmHZI0QnBS4jWwh9uJgfBWxa8fMGbkDIFWz1Mjs/Ax7VhW8D\nzgNAJ4VZK7Jofoxs9DVxdbSWJkmCVInT13SvOfg8706QTubtUHVbieyEmWEwtdFC3R3iUuY6zhjT\nD4pPCI+wFUzfSYGLIkXQEJnx9YH+PA2D0jCjPJvEzh2htcGcHpjYNjNJ7uIsya/kf0tHc9SABwlK\nUa7xvKTVQHMZ0gaakvm/oU0AXuSdicfDppgCZhzmP9ItVqFDrGIgaYce931Xk/9zwl0s+lqS6iuB\nI8PD/Chg04efcf2Ikp81FX/VxiExu3MxcA5IcKXu1iR7YG1gg7YlPTGlkyQXGqPNekMGaN3HR47r\nRmiRgJkeWAv1FEmnleQekkk74HASeJnxvjDj23VT9CpspV0JHB4eM55ZDDzsou/QRN9/Lr3W2+0g\nJseFDuFC1H6GToIrSX4G7B5YqjeeE92tM7hSr19p1EeStInGrXxaBS59qwMIP9ArVD7GB01Urcro\noXAcd7RQv0o3WZ9MmZUhvzKEpxif6Et/R1jEaJuYW2c62LAwPwrYNGGG1avreIAhtGPMiv1Sw24B\nzgMJ2jXLCoyANW1jmdBdpQS4zVrkaC7/dFwMA5QImDVDuSVc/E074FBtPM74vTbjHwhzGVdlwInB\nEI0EXAeY4kDvQEITpXpts53nDtQew5aatd2u5Q6GzwmPcFYEuvtlsJ9xBqgDLXSS5FK9caneGEnS\nBOkCvlhDW3aqzIQQaN+j6sBdIHss7SCjiVy91AwWs/0A40td/gIB17SDQn7GIWJ+FLDpxs/oOQy+\nTb2SCPXDzqMDdBIgyU41Bj4JfKxNaJxzAZPN0mOMGq5O4Gqtlo+iObfgB1MpMzSzp1OtZI6AtYSH\nB8BVAi6HfJ1D1A79uTGosbE+3ImG21K9toYKmLewG3CpoE2SRSS2hEw18yNoAx9q4m1nTAAtoK6n\ni9WBGjq1pJMkV2u1SwnwEyPJc1ApsNyYY8vXPp3n0BDeN4RbGWfNSXOAc9qKjgL36g81LBNIYhj9\ndGCGc/WWIChX/h5lxnJdo8V6VMALa3I6OS1PvZTv3n9NhnbKV8vedgbAnLSKi+QI+nwxnnGk+MNG\nTDemTviS8PqSyn318pmferol99uvToq5XjC9PxgcTFjjv86zmQoSSK6h/u1n7OFKzG8jvzf3Iyis\nxtAg9sAGjp9LvUp6XbDjOBy0hX/kMPCg3j8/64e1dLZThd9prXqWMQHUgLeFeu1knNFRizW43S/p\n0ZF25zwjjFNE9sbsuThoASMs1iS8BThmK+0aYF8P319EdwQDEQdO+F77YVK9ttiHpBfd7DFoi6Et\nEY6ocFV3wr4j3MVZNYb8L2ry17OOV5afV9JeVWCYf5SR5rG7FnYzzoTI37QNwfD/airCDm8DvvHc\nhsPSeosCNlhcD+v4OXCsNzgqYGy4ZmuY9iVeqgWWc5oEfmvvfFNbtS9gKHDkOLGOqd3kbHl/zUY2\n7nUe0IusZ4Ebbe8yEbMOFcM6HHNT6iVJ7o8BKyQ2BRMxDBZ6JKqUHN8Ktk/q8+paxgzn/Xbb2pBo\nSazTBV5ll+otT9iuGiM5DagZY/cMLfOjgA0Q10nQvP/Wt2Q/lCMVyXU8DfPt4S7Gp8Isn2EkyNRL\ntkC7CpgzEiYFLBXSldo7O6ne2wa+B+7U9T5oJxkZFjOecYx5YRcDJ3zXsA7H3Mojb/05kbA35DCY\nh6Ydu3Ef5wLWyoI4rEbb290Uqwi/ESc+wLmfhpw2AAAgAElEQVR6ZR0vCEtwulyK+fuBJ+3PdYMj\nCtjU4Vgaftahr7TabyplDJ7CqZEks47DYuCiW8F3wtLUfCzzZEi1aKVCuoIxksZv7wiY/5JDcVau\n3tQevgawRphxxGyH1RXTIz9j5JZx4CsWBL0VHCVLBB0Nr85lazenwCV9zWWcxyjKuj/qJlrjDJVc\nw759eoXRBj7wTv9S7JmnVqp0aO8z3/jMh0XAiLkkL2VEBqK/C+02zo3rRL0UkoK3if1Xbvgv1ZjM\n1yIyLHHt7HbOxwDkX7PhXFlBPihgC5jUqpYtYPlkL1/WUnutQn3bkd5TQIj2sss1Y8O9YwgmVXIv\nPUXmO8RVf+90mb+A8wW9vu0mWi+ze1/+ALDjgfiivM5zNv/VaY/65YaE+bEHNlj87OqFXhyJRaeb\n8YDMlyhNgaWGLeAstNcRMIinASoImNOncuSprRY6atuG7v894C1aGDFwGN2ayeHecfYuxwAFFgmr\n7kL3TaDtUJbzzo254jVcIlwqvdnHONfECVOZuCl4Aib5v4xzUl/xxUxm6zisjWJ4XQ6xB1YJflNU\nWlSoMfizI9gaLWmTOqNV+fgVh3o2hMtZmRHdW0NIwPwrG6T233bImHPpSr1Wpwn/SO3ttap6i9aR\n5H0h6HjwmD912nfXwuDv1+9AU1X0cNFlerKzP+hbwvwiDctc5bAbbbcV3+m+MPOHgPaxB9YPnPZg\nqDE4fbhOAh310rMd4ApwpbRsRdzKriV3Uk/c5Av2hsIe4DnXcImGwZhnACHmF+E6Ier0gbPWW6Jb\nUKndbnOaixAkLXEkpiZYQzbUUuCY3mn1CwHI9aYtlg8B7WMPrBJkU9T3ZmD6G4M/I36Wxu9UECZ0\n5HnvcHpgM878vFFYcOmiVmNSsL25p8sXMP9EwNUwEvJi+AIGz/EgPRAdFAhaGvI0qJflORxC5sce\n2HBim96oMr4ddK8f84rJ15xp/wQRsxX9+CrIGwar7PMwg14AtoZ86Q7nUcJ8yqcMJ9bc504NHeBq\nkokZvOv4d6T+dsyuVHS2fKHyC6jz9+pD6zCUiD2w3kGBRmeVdugs/qqdj3x9fBAK/RAYynboDKGY\n+bOY2+W4LplfiKBFXOf3PDVEAesLPlHi13hdIf5A04T4xV7PGD4Bi8l8+4LDiRuaIrMS8QeaJsQv\n9nqG/3Pc6D9Q7IFFRERERMxKxB5YRERERMSsRBSwiIiIiIhZiShgERERERGzElHAIiIiIiJmJaKA\nRURERETMSkQBi4iIiIiYlYgCFhERERExKxEFLCIiIiJiViIKWERERETErEQUsIiIiIiIWYkoYBER\nERERsxJRwCIiIiIiZiWigEVEREREzEpEAYuIiIiImJWIAhYRERERMSsRBSwiIiIiYlYiClhERERE\nxKxEFLCIiIiIiFmJKGAREREREbMSUcAiIiIiImYlooBFRERERMxKRAGLiIiIiJiViAIWERERETEr\nEQUsIiIiImJWIgpYRERERMSsRBSwiIiIiIhZiShgERERERGzElHAIiIiIiJmJaKARURERETMSkQB\ni4iIiIiYlYgCFhERERExKxEFLCIiIiJiViIKWERERETErEQUsIiIiIiIWYkoYBERERERsxJRwCIi\nIiIiZiWigEVEREREzEpEAYuIiIiImJWIAhYRERERMSsRBSwiIiIiYlYiClhERERExKxEFLCIiIiI\niFmJKGAREREREbMSUcAiIiIiImYlooBFRERERMxKRAGLiIiIiJiViAIWERERETErEQUsIiIiImJW\nIgpYRERERMSsRBSwiIiIiIhZieTnvoHrHkT5NvNMnz5jdQ68/um+yYjphvkF+/v5+iBA1ytWuaWp\nEO/6Z340KxvE8VsogaSLQk9f1xRPn7E6B17/dN9kxHRj5pnf9ZQqdU7ltq9/5kez8hBdiMXw6fKz\n1zkdtxQR4WDmWdr1lCp1TuW2B2JZ0TxnHNGF2BuoF44GW0dEKUaS7ItPkG8Ekeq/aUmFE0AbSIE2\nAL1d/oK9kf1lbApeoCe7DLcJiQjjvVQzGDD/95m/6A2J6iwoYGnZ6V1PqVJnH9ftdu7/0NZRCQWV\n/F31GkorHwvWXmRWQ8L8KGAzjnkJarZ0FWmYoy8p8GOwxjqQAKn4K5WsLfbA3oZ9VkpF8tMLiitR\nFvgzyFhERL9IetKwEAZDe8K4r2GxxxfHwErhNd8Ie7Tm+K8aUAOgNxLGYu90jWWcnwehXmbDUa/v\nslP9X0vXeV6rXNveKOmWwd7eWFD/FvueuqOCpc2QjA1JO3TwCDAfwN4Q5+VG9raQ+beydTbyv/yV\nd8W7WbKVz/q39JPDdsadXpkD3ZwQG1XJAsvaoktWwVixeRr0x/wxlNl+oM4hYX4UsG4QlhxSr6AB\nKwGbD5tzLpUfsDUMXidMWc2n7nnFdV7Wlty2BcwRNt+GXyqufwssVLFk19gIAMYR8IFMu4wNiRkP\nHraAiTf7Q7Q3nFdve2R+AgD8e++KjwgB+4qc5xTNY7SBjiKk4fwt9nUPFXvU0Y35Bluq096rJEh7\n9Mj8vIbib9WtcEiYHwWsO4Qbfa9nt45ome2bwnU9wPjSJt4z7FhyBmUyH9mFH2OkwOd65+2MNuC2\nTC8L6WqHBMwx6fX26dv1tdV42FbbenuwZG1URW8lpkvJhsSMpwkFA0if2Z4Gh/9zAmesYnwdoj0E\n8z8kAHiBkQraP8MZW428mapu5ZzdV6G35tsXPix47tB+nV1yu+mKAVsBAJvF0XINk5SWJB8vLoZQ\ngT4qd+rMKxwS5scoxO4QGu/YXNGrQL0AfEl43G4xfEyoI/D6iCz1epbxLKOuHx0AHtBvlzlNkPnF\nN+bc9jpbvXYA27073my/7Tpo6siVj/HQobECYesfjDHGGIhibNggsE9sPwo8GCbYiKDHMsbtmpl1\n4DG2mP8x4beC+R9SXrIuLqXeGvV6jPOjZykXzbnQOqpwQm88aDMfgvkSO0IfeavYfqOY+b7AFMFn\n/lg35net3KlTOT8084cAsQdWCboput92mPgbdgv0dsYPHo2e56zge4VBVu45r3M+ktXW1v4Eo6Wb\nlWrjlHPeRdud6PTGnhQld4WCEk1EYvVOWJG9FalauDfmDKH1Eb4YCNmKPO8doge2XzedVovjJyz+\nz01wVZe/i7PQIuNveJbzsiXMH2cASIG3PZ+hqqQNfCJ6Yy3B/yum2vPIB+GO2n71NXatkvkb9M5t\nguSyARdseAWPdg3c6M78Yg9hWffOZfmNTvsYhdgTngQOhjwnCbLekGDdKra+3ec561Et0SdtZWwm\nhMZm2VS0gwFbd0wI4ShQ04dqQAtIHL1cCFwE4MnPg/bV9ogCJiixBFXisipKjikmvfxT7YpNvYYI\njb3AWgCim3UEuF8fXQFczIJg5wn9WMVZz0kNbgEAaImwlWLmYykAIC0wiiVAS5jS14T7OA+8vWLK\nyk5cTdD1YbtKh/kK2+wyagz4DQBycNcb3Oq1jdWd+ZwPHlesMBBCAqIbW8NiD6wSRFP0kCdgdSDB\nSA0dIR4P6Bao8X68yviN3t6ujyZADfx0oLNPBzlvGhrdagEbdOHXGS3kLdCWboe2IGWsbCwd+4Uw\nIhTcYYbB4ImWr2HlzsOurkUUhVqF7rwMYUJHnvcOov8HeFq/OyxabHmwX4Bgj2UCxh+5vxvtYNnw\n4ydDzPeqzQ9t0Zw3pvQ45/z/lgBAB3ew8IWUMl8x2fjStwsTgNh4w7+r4iDAXkPni4IMezOlcNPt\nhmZ+HAPrFQUDYFK97uNc4xReZ6tR2ADqQEO/gjBH6/aGgRk/qHkvPSrmMNd+e7Ag/LGoU17eWR9I\npyc4PBZxXUER/px6EyDYIx75ZYENhPWEdYS1hJB6dYHh/Ov6yuZa31K+JwHbsSQe852PUwVbgp3C\nATF2PCgy0ZfQFdGFWBEHtPfcCTisY6SGRMVBAdB9LyU25ttdAiTALsZ6AoB1hMOiKRrE/YRznDcT\n5ZwuU2cLaAIp0NS3k5qOHaPlBygqv8RR0aer2ZVCtzclMTbbA9rQBYKOxJLYDWWNY33ZfA+nULT8\ngaFmbxvy14GfOBis9HnvsuTgPCMFbgnVs5GwS497KXxCeMH21atG3lX3VAYIR7QVJdrtCG0zCiaa\nQ/rSq/jMp4ix4PT/Hr/KYeR8FLCKqIkN8RqpoQ5c0kxTzU/TZzInLdFWb7A8fyD43M2qUzbMIly4\nJQopAVMCVAOawiTVxndF/De3ZYwZYk+iN3wUWXIV92D/GEA01Q3tRZlOSG7YwUojCTr91npR99K8\nSLkGX5yHVhp6LmVF1xP2sdXoGhW3+QijCfYjpzLcDxzV24bqCeM57wTTGAwlVxskuqpOxQbfGIJJ\ncG505scxsEog+jcxAnwaZpB6ga1eSrSM9+8NfegzzvbXgduynQv4YoL0AmXhUuZn8I3vZj7XRi1F\ncgX1zOZPMJrIXm3k27+ukB0OAL6xoxOd8YC2GAZQk2NMD8wPR+xJvSoWHgt9G72q4xisKRARPYPo\nD0BNR/2c0MFKdcxNUANfCuhEHnzUAHu6QMwjSOto1dD+kW5RO+VvvYqPAkiRfEv3oMQoPmM0AX/w\n+ClGE/jcjWAMV4IDbAclEnYCqQhHtFBcZ39jYIFpYcVRiAjFfQQiQczOIZkHFntgFeGMEiVAgrlC\nvWD3zZzpLA3kPbN8X/MUrTBv/yN/liD9lFYDeIwPpkg+p0fVIWXqt/LpFmXzNMlUrpqJfguyALrc\nPbopmoRcJX4nLNj3SnR01uAhhseNcfbkexxGd8o0QA4RrQDOZXsSIClIejnOWUOtHipA1ODzdbQc\n5huqj2JSMv8/8Dct1E/RClfJHi0g/CeFhuAfYDekHoyXig1pCwFsE14X7sMrHp6A7EWFyGJFV5lK\nMOSsRxSwinB8KTUrbhjA42yFWozaARdLgBpGGmkDzRqfPkO3AQCtgKbsC7wrwfEE6acAgE9p9Yu8\ncznv+pDyicbZWQAAXkx0jbGi2NxeYDRBn1hNUcI1MU3tXgA6tMyJ5kjttwA26ckxvQ59+cWqj4SN\n26dEzDySMPPrwI8Ez2dF0MwfBUb1HmCEr3VoDqvC2uUgmf8L3vE+bQCgGnAGy3Hy/yU5YVHMMNFv\nrauLbY/5JmZ3BapChdTnc8L0JbZ47ocgn4t2SnSd++xeRWh5T1XdmIgCVhE14HsdPVzD3MRSr8e0\neqm5WaO5ASuMLEnraDXQbKD5R7pX1svAr/gtpV4JUhjDo5cALOe3UiTvUGCGB8/xBhD2MtrAJDCZ\nz3cmAPcxskypc7wnwIPAIaFbiRgbQLexa9ManW7LmWIASETfcKKMasp5qNRLwSXhBsJnjFHgnuzI\nzXyuhjMNPooC5tfQRmgY+DXemuK4f0+GwX4MZHbJZxktkHKqq+jEuQmu1rSr/HvtOb8fAZipzU4w\nfRCOhwA9Tl6uMq/fuor0MXKgxzZ0iAJWEcKSR2p5xgEAT7A17lUHRoElloAtxZk6WqOYbKDpV/0r\nepuAffxUgpRDh7qAOROtSR3l4cQrSmfmXOCqao0u1LvU2N5Bmwx+LKKBErm+nYdd1agoWWIfGja8\nhj0gqMCN08BtADBSQw24oCn5BKMh8hbuZqwjAHiUcD4nsiL/H7RXUOJtensvP2OabhIMEG0G8A8F\nd1Y4tvk6ZwFNEOpzlTDC6MhciEXhvz6K/Odq53gFR9/U01iPIxRby33lqbmREAWsIhKG9uB1dM8G\nwCNshRbXsw1+2NKdX6JZQ/tzerQkouBp+qTXeINVfHQCS9poXqo3sinMAFpAXXg7nrJDtmrAVTOV\npy3cKcp1Y1LeGfvcIca0g5ZcMVf3ABH7YTMJm/mXPOYb1ACjK4uzUr/kow1MOo5BibX0MUrUqFfs\n4Mz9kHq9xwToyEmcgdXvCADWAzt1MUlsk1PKWZ8BjqPPlpmx4liMiAEgTmSuCFfpGXrKlx6yzr2I\no+7Jf6R7v6QHURAR3neY+FKcWYozSzCxqDaJJbrbNyqydbymR9QfExM/88ynyi8q8XTB7GbY8cSm\n++UbcxUEx6irn9X1xDhmNijU2BsxYuhcG840/NGADv2R7i1Rr3JwgbD9H7znCd7/Z3wkcGwDuXP/\nDWoQ0zcT4B4ApK2PsF+Y4UvFVlAC1UkKfApRoIp6RYXrAbEHVgm+GQNwF0bJC/dYOevO0/zA0Ws8\n0kL9JBrL6ZTcTwDoyad4Xwv1BCkSXBgdtRK/AWjoiV5mZ810wmr62Df2eIBKHbTHHgyT2BzaOXAU\n5d7uLygxoj8UPB/qgahav90mEQxZzJifCn92BSzFmXepmIQbCVv11Mk28BhnK+opvmfMl0ZyiDKf\n+z6RN+slYIewHHM5mdjad0gMZPWvIsRmWQCxBzbT+He+T77N3JHzgfnhrlhystOYvLQ8PUW6wfgH\nfsSU/ISeVp2wUUwuqDXl4Dn22B1EhVMkOmEypYjTnn3OWycsux2x3V/3S6G/Thh66YdFTB0FA0XG\n5SC7OAUCtpNf3MPPfiZIC9P1Ucxf2JsT4u9ps86oayF/u5kCzLcWXrlF7z1qd7b2ivrCs8GKMcUl\ngbo7FfxvacgHwBAFbKp4hfEWYytjN+Mg4xjjdJcO2P30lZEip1kaziVjAjQAAOf45gaah/ghU+ZD\nWl9HS00OtVIbSH+JP40t25Ibh+w0cdAaJldLMo5EqV4D7MdXeQT0muo+YtD4iAKJ0ArETgXfqvCl\nTLfOAR7ze3WkM/A87/5LPpiZEjMuiio3Ed7RN6lwijTzZZpEOSqmsEcc3SDKBDEmXiWYYktLzm4e\n1y/1jQ17Gy4KWCUQLocPvEd5/KGeATPK5/2CB/kxf2dY67YCW4Ft2jt/P3ASOmsBlrR/XI6Ty3Hy\nMD9gzviEnv53un/CFALwPec35g8G1ICRRD+BEvt1ANgvSr8EbOBsQGKTvuGtgxCtvjthUzw3ojpq\nhGvOrkxp3iO8TbyBNDfACwNLKBKwlj7+T/T7X9LXWbFjwMnysaKqUL4HVe0iTI40Upyzq3mPXObL\n2S9ZbhH/tdvcEmMjY6MejVP5aNT8/TeCgbh+l0hMdu4PQz1PuSuigFVEjebltkGywbiJZATH3Fp7\nFJN/yQedwktx5jLP48vgc+CjKMNx/ZJ7DM6g0bq0FGeX4ozSMDnWnW1fE7OqzesFL4F3QMOg/+a+\nlNKU9tcDxkrfRkwFCUYSy/X3BBsidU3X9H/zM4FiK0HOgnT94n/QG/9M2drKk7Q4pTkYBU4wDolr\n6rWeGU4f8XKBgwJKw0ISuxnZy8e4idGQGkY9e7xLZoY5h2IbDogC1hNoGefS9aJg+HOZd2IkSWto\nqxfZOreSvqvjiklayHvA2wuu8j7ofdB74Be1IG2EaedmNbTQQLOO1gF+3K+B55A1vJUACfhD3Vj+\nljjPUu94EeXbPZh2uSoywl6DtYbahqcTiZk0QquYHuKMTm8WrLkGPMH7Fe3/hZ+tozXDzZ2RJM3u\n8GB+ZdPC4x9MYpprIdGCELN1Fa62BdgSjC3Utm9SyRgUORv9nWOx71UFMQqxGkaSTAxWMb4mAKgD\nbzLe0UrwIAFo8Hnl7h81Y1bAUV51L30NtTjqYaAFTAATwCTwCvBe4TXpg9CoWJ494ArwLfBt+Bkx\n33bneIsZ8ZWAw6cynEboVKI5poIYlDjdEM8HmefznULuGOYvwURw2v60okNznD1BXyXBLdYLtvY+\n8bHKZGfYBeS5XasdXvJHAasG6WxTUMa8k7EUWJPZ8wVavJSPjmLSmPEhfmiJ9ABOAE0tYBOg3wam\nUpYPaPcx3A2A35iCWnWHPxjQU7IMY4R9oEjDhtSeBwYiyGTwdzNqyOLRS+EIWDh6fmB3OfMww2Al\nwfRBBLIaFpSMHa8eEAWsGhKhYQq/JmzVa1d+wyZ4/Wu695e8q4GmUholZnwaWf7ep8FbgDPABOhj\nwGR1m5stwZf5OpAf6gO/9PLOVcZhscZKG0gJKQfcKSqxb8mEsH5y5/SnzUbDWFx3WuV6CMHfVuqv\nEzAumL+YLkz7nQ0Mh+11Y1PCc6E8HcHFXasjnDtRM3+8d/Ua12sPGeYPl+bF9cAqgWSu3i+0LW9j\nLAWWAg1gae61c7/Qa8Bx0Mp8B78A+lC8HUG7EwhCDrZe8aq44nLgDtAct9if8+EmGsdxR2ciwUmg\nCV4TeP7QzYwmcLWtVxVriXUzzZLNa51PRFaKbtn27Ck7omVmTpK3PozQTxOnKhmSVZEGjJBaWbt2\nMerAWmetg4J1WWewy/XnfPg47rjQGkUrWw82HGmygNE2zDdsbwkBW+vcufeNSLe53wOrmti36Bur\n3vcacubHHlg1+D0wuAuALeMTcuGiHHOAw+ADoDWarx/mfaxrwGQHLWC5d17Y9n4Dfl2vwtzI5ocp\n3u/kF1+iDwCAHlzFR+toXao11L3RbuZ1ng0mciuxIzgS6RshwE6KGESVHKaBQyEX01iphlVyNnar\nJKJ3PMtYAiwFEmBtFtyxgC820LwDx9lLGaU6FrwbaOqFUash3HTz0OJ5x3GHGmB+nbdMYlRNiLxQ\nHzWtybCshplvNtaKwjuBl/S7bWIe5BtTnsgfWmKiS+stkMx3yBEFrDIM1V/gLDZXCNhctOtoPcH7\nYS9fpKDihgv4mm/7+BNQ09qW688kkGbhiGbq1xG+73iWkAoA1LzmSzWdN6dmrUBBD+mcp4lKrgNf\ntAAIS94pdm7S6yQ5CGbWcVB9oCsGFl5neIbzuFbRjKuhnU2iLwCt6/k5exj4E7DSGMWtwNlAsfl0\n5XtuIUtd/8arvK2GtlwqM7sBAI5b/gJhHmvmIxRJr7DLo/RW4Tkv0rCK1C3KOxWZ3wOigFWDM9NR\n7qwBNajQ+d+F1Ktv+Hk6sqnNH4BfBJogvaLsNR45jlYN7V38wnr6EMAX9PAyPpE9cdpZexnGgL8g\n3M3ZR3B1a1opMRVJi5gpMAe8iB8TXtQZ6DWdwFzDyYEz/0Enk+/Zwj7ZHfRDPmxMm9yb/ozN2s30\nImMC+J0ukjPfaXiZZZp3F6yi4mgY+g21iMwfAKKA9YIEAPgDbQPrCACdZiykS8BX/dZ6EKLrJFDW\nY/vAepugkyCtoS3XVUqQjiDtJEnhj9zlxzeJTf126ABRsuByT8+F8EhARJ8QGpY7CT6wBIIAEJ0C\nTpXX1MfFQ3scDSuKb1S3OMLXOmcSnNQH3mRMABC5fS/5FSR6USEAe1Hcp7Q1DL1HsZdLVw9VUWgM\nbKgQJzJXg5OnQoBv86zawUHwDnCxw3w10AT+CfhHcfr/LL4Xp1vGR4EWzATqcX5THfqB7lRZ6vP0\nvm+JU62P43y84BxP2EkRBwV/waR+su84chXVawBgpkVMtzNWMSpEwxf+jq/1cM1/LGZ+xYwwD/Gh\nm/lcxvyHRX8r4CYk253iJwhRR4O032L7Dyty1ZqeHPrGeuWtaz7DxvwoYL0gAX9SGE78CH/2Iu98\nnbf8E7/4bzrZLkHEpXswda0HXgL+qzDLvy64SsBu7wVSqO6X6oeJ+00tow0K00jwsHGkyNymBptC\nO/tAHvVuvores+/kJ4okpxEDgiLF42X9KHY8fgAuil/h3R6u9l+LmV8RygoKma9yEfgn4R7xdr9X\noAjVNczPwTEOjAva98HbPHSe+qxh1iMKWDUUjfJqLOMTxnLUK+dTCqSgt12GEXBIvJ1KQBEtVPeY\nLc3+Mmdtxis036yNi132Fco+zsN6Y19JoSnDnfIivp+pp4kaar/KgNHHOEMKPgRUyJc4cOQC5jBf\nehmWmXSO8xm3MWTwsLMgQ1dYGsYY8+Q8LF36kEw6hSlEOQ1Xx8sgjoENBqdoxSngDs69DRd5wUK6\nBHjjR7cDJ0GdfM7yPxWMgfloF65ZgcV0AbgAYBvfAV2zRGbNrzN+fT001PwJm/4szsCUz4jrDWGJ\nWlx4qGT/1EGAE81fyPVFzBesgwwQPisd7i2Kv92iojk8J6fvHh8Uh2O2jgyxB9Yb6Jky63ufNrxD\ngTaUWT82W8yyY3H9r4pdcv8E/IuqoXK7dRP95n3aMIVnhEm2GHSkOBmI+2gAyQZp+SLr44PoikUM\nBvSCyym6OH1KVAnSb0bAP/CrfplCEb3QQzOO85exVIf5YSZztwL6ENBPJwwxrDf2wCpDt8xk9FJm\nBNcYc3J7UIHs53lRVuxpET1Y4IosMjNVnMRb3Az8aBc6DL4Dk6OLyjP38HqicXGdqcYV9pdTp4+W\nY68Ze0vCGiP6QhHzF9ICvpj5r23MpLKd50VEFwCkSMLXXV9dqx719uxke/4+YzO5UYjlqJLzsCfI\n9t+wI/bAqsE87j/OEhDQLpZmcSuffoQ/k2eM2nLCAD8P+hL0XfgKwSCu9f7OH/OGJ0ldBA7xQ/v4\nqa3cS9SXCzOU3etIQBX07feosiBFxDTjwwDzUyS/7LK63TRiBmSS8zQcEtXVqydU6YRF9bIQBawX\npPb2Xm1BcyhFkiJ5gXe9xoX9EvqorG6T64KAfxB6thY4rLeTudkGP4Ncp2pAgjZq6h7aqL3AuwJX\n38kqnCTD15Rtd0wRmcIgLe6jBYcBumKKXvuShf6qXDGiX/g5L1PgQMb8KzQ/RdKDM64beq2KgVG6\noPx7f0MF8Y47GW8xXmY8xXiMSy/0WXh3d4Q9hMVB7f3p0MAmkN0wiAJWDep5bpaTeJOdJ7wSD6Uf\n2/jVYNuwvMH4V6LYfzOrmgPQ81MYWcZ6QC/LBACge4E62qipV4rkQ/J7bvojpN7O/JjBZ87hyijy\nSA9kzDkOic04jHoVM7+NGrQz4J/5+SlecFo6Val4iRVhvBlUaimGA8A+YC+wG9hdoHNbga16Klg+\nIcyrEL2ztKQTVt2Ihsg0ooD1hVTP7vosm+M5SYv/Fz34z7Sujdom+k2Q9wTw8+AngFXdrzA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jAHUss8w2jpr3ZjnwPYTTSUenWQWMNs33A220wZ6g5GyGMDAHdzFhWZAh3YrU6H8U+KQewg1IeR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\nA/NHswvWRgJwxF0bqWYSZTRxE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"output_type": "display_data"}], "prompt_number": 23, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Lloyd Relaxation\n", "----------------\n", "The farthest point sampling strategy is greedy and does not move the\n", "positions of the points once they are seeded.\n", "\n", "\n", "To enhance the sampling, it is possible to relocate iteratively the\n", "points at the center of the Voronoi cells. This corresponds to the Lloyd\n", "algorithm, first developped for vector quantization.\n", "\n", "\n", "First with a constant metric."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 25, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 512;\n", "W = ones(n);"]}, {"source": ["Seed random points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 26, "cell_type": "code", "language": "python", "metadata": {}, "input": ["p = 40;\n", "vertex = floor(rand(2,p)*n-1)+1;"]}, {"source": ["Compute Voronoi partition."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 27, "cell_type": "code", "language": "python", "metadata": {}, "input": ["[D,Z,Q] = perform_fast_marching(1./W, vertex);"]}, {"source": ["Display Vornoi cells."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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G6Fogx91gwqvziTOM3Eoka4aRXpmwhajDZXqVOD/0euMXuZWBkR1FzEcDU+Ay\nvZDOqhLGtDCz5FWM+pUPASaN9ALqQXplxRq9rBMuH+h3iZkRYqplevX5YcRivdvWZX+TfsLKcWJs\nerFGH4sGhkqtT69Hmq890nwtycXs4Ta9akb3EkCAYR4z9SuJJOk1erHkMqYPw9iP17Z4w570kkGA\nAWulzzByy5LYGCO9xLBGj+qoH31tR2LZNnPJnvSSRIBhhrLmh8nd335n1V9PdAGLEGCoS6r6dX/7\nnW5yuDa94Eo/S9ysYnQveQQYsBDRVbPHwjme2aGOAAOAJfo2dj7cp3sl1SLAUBGD6xuPNP+kfQmV\n+lTzy/718+0nFa8Ei7FGD6B2wzCDIzQw7FPKCqLB+gUtphLr35t7L70I9/Jsvyg0MEBNivnhVSFc\ntf5KamNnZtinFxYgwFCFQuvXVRsvzPlU84z2JexnJ88QhREiJpUyP6zAVSG8oX0NnhBaBaCBoXyF\n1i+U4B/bJ7QvwTEaGCDtkb/vPwYs4UOkqF9e9RnG54HFIsCA7AaJldYbh6dfpBdqRIChcLrzwz3R\ndfeV4ccrSxjRhXoRYCiZSnrF9a0EGQZNB+Fk9xjfg3BS+1qqQ4AByWQbFcKoYWgRY/IIMOzGDv1s\nq6KLElaQk+GADBNDgKFYueeHKfsWGebNREoNPxiMMMuKAAOiMSrETBSyrAgwlClt/ZJILEqYH1GZ\n1Bcykiw5AgzYSbppkWEeLM4h2lhyBBgKtKB+MRXEHCsTiE3FtAgwFMhxGlHCDEsVPMRYKjzMF8X5\nk/YFrHT3ldpXgC2S583JcDDcV8QCBBgAqCHG1iDAUBbv9atDCTMm97iPDFuGAANMIsPMkDmsIsMW\nIMBQkDLqV48MM4BVC8sIMJSisPSCAaSXcQQYimAwvX7chB83a9+EEgbsRoDBP5vpNXqxGBmm4SCc\npH7ZR4ABqa0PLagiurzgSRxwzmD9So7HcwhKm17/3Dzavfi39isJ3xYdGhg8s5led7cZ3pNBooRM\n6TV6jVQIMCCDPsNyhBk8ILEEEGBwy2b96t3dkl6+pK1fzAwFNG3LP2MAkF7THK3z8Js2BwIMAOAS\nI0QAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYA\ncIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFg\nAACXCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwJQRN2UAAABNSURBVAAALhFgAACXCDAA\ngEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYAcIkA\nAwC49P8Bwvbft3yl3gAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 28, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf; hold on;\n", "imageplot(Q');\n", "h = plot(vertex(1,:), vertex(2,:), 'k.');\n", "set(h, 'MarkerSize', 15);\n", "colormap(jet(256));"]}, {"source": ["Re-center each point at the barycenter of its cell."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 29, "cell_type": "code", "language": "python", "metadata": {}, "input": ["for i=1:p\n", " [x,y] = ind2sub(size(W), find(Q==i));\n", " vertex(:,i) = [mean(x);mean(y)];\n", "end"]}, {"source": ["Display updated partitions."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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EVp8sBzqMb3f5kjqNyakXMAMBE+9LZRkgXYvJO6korV48WQq+CJhgXzY79epfxCLpVH1d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\n", "output_type": "display_data"}], "prompt_number": 30, "cell_type": "code", "language": "python", "metadata": {}, "input": ["[D,Z,Q] = perform_fast_marching(1./W, vertex);\n", "clf; hold on;\n", "imageplot(Q');\n", "h = plot(vertex(1,:), vertex(2,:), 'k.');\n", "set(h, 'MarkerSize', 15);\n", "colormap(jet(256));"]}, {"source": ["__Exercise 4__\n", "\n", "Perform the Lloyd iterative algorithm.\n", "etric\n", "eed random points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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qaJJDuYiFFVhu8dZezcJj1om86hnbWLMBSIcAyydl2/D+RBl2tHH9eIoXQIma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\ngE/iSGHLf0+7l1PdishuOd/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"output_type": "display_data"}], "prompt_number": 31, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "prompt_number": 32, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Now we define a non-constent metric."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 33, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 256;\n", "x = linspace(-1,1,n);\n", "[Y,X] = meshgrid(x,x);\n", "sigma = .3;\n", "W = exp( -(X.^2+Y.^2)/(2*sigma^2) );\n", "W = rescale(W,.02,1);"]}, {"source": ["Display."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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TJQOsMo10AqocmDU4qeYJqiZMzRCmSgfGUojbOW14/JoMtyfdWPqzXNJ1VVkxabloveq9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\n", "output_type": "display_data"}], "prompt_number": 34, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(W);"]}, {"source": ["__Exercise 5__\n", "\n", "Perform the Lloyd iterative algorithm.\n", "eed random points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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1aduTndgapmLSzI1JKKo8WftwRgfZ50xD9tkmc7GaRIz9O43/s3QwKK7kkKhX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"output_type": "display_data"}], "prompt_number": 35, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo5()"]}, {"collapsed": false, "outputs": [], "prompt_number": 36, "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"}]}}}