{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Logistic Classification\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", "$\\newcommand{\\eqdef}{\\equiv}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This tour details the logistic classification method (for 2 classes and\n", "multi-classes).\n", "\n", "\n", "_Warning:_ Logisitic classification is actually called [\"logistic\n", "regression\"](https://en.wikipedia.org/wiki/Logistic_regression) in the literature, but it is in fact a classification method.\n", "\n", "\n", "We recommend that after doing this Numerical Tours, you apply it to your\n", "own data, for instance using a dataset from [LibSVM](https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/).\n", "\n", "_Disclaimer:_ these machine learning tours are intended to be\n", "overly-simplistic implementations and applications of baseline machine learning methods.\n", "For more advanced uses and implementations, we recommend\n", "to use a state-of-the-art library, the most well known being\n", "[Scikit-Learn](http://scikit-learn.org/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "addpath('toolbox_general')\n", "addpath('solutions/ml_3_classification')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We define a few helpers." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "SetAR = @(ar)set(gca, 'PlotBoxAspectRatio', [1 ar 1], 'FontSize', 10);\n", "Xm = @(X)X-repmat(mean(X,1), [size(X,1) 1]);\n", "Cov = @(X)Xm(X)'*Xm(X);\n", "dotp = @(u,v)sum(u(:).*v(:));" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Two Classes Logistic Classification\n", "-----------------------------------\n", "Logistic classification is, with [support vector machine (SVM)](https://en.wikipedia.org/wiki/Support_vector_machine), the baseline\n", "method to perform classification. Its main advantage over SVM is that is\n", "is a smooth minimization problem, and that it also output class\n", "probabity, offering a probabilistic interpretation of the classification.\n", "\n", "\n", "To understand the behavior of the method, we generate synthetic data\n", "distributed according to a mixture of Gaussian with an overlap governed by an offset $\\omega$.\n", " Here classes indexes are set to $y_i \\in\n", "\\{-1,1\\}$ to simplify the equations." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n = 1000; % number of sample\n", "p = 2; % dimensionality\n", "omega = [1 .5]*5; % offset \n", "X = [randn(n/2,2); randn(n/2,2)+ones(n/2,1)*omega];\n", "y = [ones(n/2,1);-ones(n/2,1)];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Plot the classes." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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jQ0+k/tjdLHF4pGim2WKjiIf11GwU2AOTTqF1gxiqPxcpd1t7uOr94PogY8fi\n6Ce/aZBBWhMqjUrUiYzRmUKyCCUsh639lq2hZYVVKgKAfV7qFAwLXEx2QtIoA1peA2kBAvM2WCCL\nGQ8sTmPju8jKqlqyPWuwC9AOGQFGdLh24ZFKE/l8Yos4hVoCA9B3RF1Ri48SmA5Xb+/k0E9+06CQ\n3ZrQ6/cArFWsA7TbqsFSBLHXDT40e+mAm5C36SUJ6aqmLMMNe91E6e8ClMJOKO6Ax98YklxNMgAN\n5HPYw3qQGWBEWzyD6ZJo8IkrEVrEp9BG8HCQcEeZvoqULcbKs5Scm5gYMkjrQNSJBvEgY8oiBigk\nFZjcW65H9fxOPupEU+vrWLC8NVg8DWiShlkRNueBHSPLBIYYPQvcJSojWZq4Z6X0dIuYqmmkW8MC\nNmn4NunNLJNhYqOUWQevNNJSQP5KyL0r0Vq2CpF7kzivaxvtAA4iRkPXCMIJMkgalmQUdqd92AbI\n1OcmL+ptJ3WDpI9YlCxCJOs05SHFKUTxw75FT9xBRbgzs6ZiK4g9IYZF1d0E6JoV5E30segV0kqX\ncN48LWxaq8yNSid9isxltoAsU1uROYDD4VQwgpgQMkgplmQUHpVqUAVwCAAxs7XllNW/1q4BDMfj\nQTxItswXS6YA0LkXw9id75uWtuAMN/Z7tm8wNgJL+AvbFe1y2tCsoGMSc+yHaX0pdfVSjGK0bd7z\nPpq1sl9vgK60k75Al9vFFsYSxNiQQUqxJKPwqPieD5AVAPKSF5lrkiqNSq6U0z7850q5SqMy1b7b\nyM4UoLvizKd1lqzBZdkptkAd3fIgU8dEI2rehBDtLGaJJIslmVucB8jjp9Z6ZkJuznYuofKA0qVZ\nrleSnuMX9sMpZEdMCBmkhOUZhcfA9/xaUAMwB4AgeeGyQtauj5inLEJN1okxPbPjJUda2IO8GLgd\ng2Y43wF2GkwdY4ec5G2yqJekGhB+iVTESJjbRrqYngid2T0zqWPdtJ7b5XqxWZVOYfmK0TQSMSGU\nXDXBNgp3VkCcVg2rQRjkS3lNBlBGH3zP96/x7e1k6iMG/UGv3ysWitPsvQE1WSdGmwh1+LBvLqjD\n5paYUKJpyJpqV0sXAPayiiTtI8VdHxWeaAC0AbZQum7WUVXC0E+XSPcchAl9VAhceJBYt+3xW2Ra\ndyV1QMqUGpqzibPAYLtep3TdxNiQhwTgMgqPKE5bCD74taDme748/z5KBNJFH+Eoi5gcbbJOBo5E\nCrQ50xhStdNzvZ4QiONjxT3TqqU73MURCQ4sHYuRLwW8q1gfgeV2KrgDBW60XIQJbWQF2RZsjbb4\nGfH1ahvU2nswz4plOqYEkQktjAUAKO2Vev2efZlisVDsNtXnyKWD2c4kxljQ2OJgPwAAIABJREFU\nL2K0LI/t9XulvZJ9SWdrvzW35HisVmnBnJcBsnKm4WqnAEnpucLNN7OFTV7ajcQEAKEiLpDI7Bhw\nn8aSsA5/7yKAw7SX00c79B3S6GHE1bl3ANCJMi8w4Jayr82FMTG0MHbToJAdAEA1qPb6PXsIxlGc\ntnB8zz8fn0/+GD0CmdJHqKOUmyxiioTVahgE2to5DFx5jxkbqQWxhilJdTMYtGu1Mi9AJxkkD2XE\naaNSquq7wK2F2rFCOoEQWKuVA7c9fXm+b9iC+GJiIYbhwwFAAbSROoCtjuiAKb4nnLyLvIAhUN1x\nYmLIIAEs3yg8NvWongrK7QFspXVdWfNATB9Ra9dMo9QC7oPvF4rFfq+HB8otgHK68p6aM81S7XSH\nZ7ETgzjeLUJhN+BnbKYb2eFfllhRwbFjD7h3ZZ/yaaY9G2zzxNn7Sv6eBvpgI155T7QASsTPpQOS\n1SmjhBTSnQdk0oT4kGrrEZNDBglgOUfhsRjK1vFzfpjeKQDoQ71dNwkTLPqIRaVnZetYAx7OCvl2\n8ZgvSm5j7NVOGcKi4N3w4CtsA26kg9wXMYOyxRelAp9ocSn5KiyHParWUbrUTjuL+MVO2u3L7ECg\nKzQu1iE1+F3SPdtA3+CYEsQYkEFKWMJReCRsyVVL6ZqdDhFIpo+IDqNBPGD7+54fboWz6r0VsRop\nVGxrMiYOBv1eTxJ3Za5hYk7JSe7osN0s6UfZXbxG0Tvg7wt7S8w0Bjx0tm/OvCB8o0zDaalppMvt\nngQzIUsNyOxoAaWLVfcJDC0E3CBRbT1iKpDKboiqUhuu71l6MpKrimFPiUCa8iRVw2q32W3tt9hN\nODo4qoaLGXScViMpy2DtR7G4UwHgHGoEkKBOuoviXbwaSXKkheQs4pkXhIRPShAHikLPYjjB0CWR\n7EdaHtvnCYREeiTpXNJG5lHt8cVSwnCK1VqQmQOElHXElCCDlGJ5RuGRcEqu2pcjkJl5knzPD8vh\nwm8CS6ww6pjoclSAAm5gWOUToRSrsTV5ncfVce10+AtLvYG3I3Us03DaP1ixReQNkhq0L5gWpnRo\n53y/2e2KVEB2k0ZaBmJakOx7HXCRrQtEBFJbzW8J45PxYMA0CK6V95yPYnEwUfC7ndZYM9iCVjFj\nZCpJjpFiaF2+WzstTCjwpUJts5KbzQa5l00CVNwvuZxWq1GpxKhjWA24xWe/QqUFiYJzlakpQj/5\nTWNTPKSVS+A9Ek7JVVGGodXKkyTqRxhz3uie0DOPAu40CifpJH/BwOmu2T6ZgTWt/1QCaKSz+wBA\nmf9pT6nnFDFLbxSXk7xot7dqNRF/w4t/g3TRDakFQJFJsYhYLqNeq/V7PWnRMUGMzfp7SJISmk3O\nr0Qgzp1BPMjv5AFs7kAtqImrzu/kB/HA9LTve/7RgUa0tmB4xXH7MljHo5gmu40e/EvoIHYXd/i0\niqfUFJcQLpfJf/J4GjpcTFY4ZwU+8WNZgmrzDtPbRc31Q/ai1SqHYTwYtOv1ThSJZA2ZC2yxEEN1\n77Qwud0UBQ4TekjXXXfdtHqyaSzKMV1/g7QqgakJSeyuYVTDqRmiTlRpVOyjUbfZnU+2upGI6vVD\nVMrIcfiTjoL0QCwicoBchwLAyXQkTRscE+xxi2J5t8kNj4ieNrlKgn1oe7wn6uJfsETMkHwSUPue\nYrD3SqV+r9fkM08iUOlo58Qh7Lankl9IIcrpDSmTGySK+I3BAu/bOofs5h+YmkVg0NImfqsaVo+6\nR9rAynH3GCcKWqpsdSMRVqvNbtdSec9+lNiCLz3gYzdeAyvUdDh4BVlz+5kp5sT/Yu1qAWVVYEhR\nNeBhQG3ErJCO1+Hlq6KFUi7XqFQgrfLwUK/0UVDlKnBkUlgjfYgylyvlchTBI8ZgYQbpU5/61N7e\n3itf+cqdnZ13vvOdFy9enPopZlpGQbITs6jsZ2lT+5aLbL0e1QfxACBjXmJJ8iSpkxOe75fD0NEU\nCTrtNhuUGQ2kwA4BmunvSICSooqblDmCg8NMjzBdW+nSfFKUT/pTVKbwFHOltVJdbiSEUWELhHGm\nWpZxvGxogZ00UoplJBI+5GtaqmA0KpWdfD5S5PgEYWEBIbvHH3/8tttuu/vuu6+88srrr78+juPz\n589fccUVH/zgB2+44QbLgSM5krMLTGknpTQpEiYODFqCjZa3WHLVersuTZXJWYUApcYU8Gf1hYc0\ntRlRx56cKOVyYBC/CXCwK+BzSGAW3WkDa5YI2EF6TghQfgTgbQLAFoCH0rni72/MXTftqUWvQrS/\nkP81u91CsSgy1cZcwq46fFrYN0VS39lDlIJJIngUslsIC7xvCzBId911V71ev+mmm9773vdeccUV\nAPCJT3zibW972zXXXHP33XdfdtllpgNHuk2zS+CtNQZj5NW2YEu70BnzdPpuNzMmnFTqUT06jKpB\ndabplPQmZPTvqiWdXQdNwMSKtRCzStLkjZRTjvXwIvpYLMIE4GlJRdrTAB0rPgo8oJu+v9gumkws\nbqpQLDa7XYChykOYpSbvp9pggF57DtaXgSOQZXafx5WGk0FaCJs1hxRF0aWXXnrHHXcwawQAt956\n60033XTx4sX7779/WmdxUUKPGpiyTEqlspLBpIHBVLAx4qETHBAxxyHVCSdbt7MmnDCzCEuqNCqV\nUi5nmpzAkTc7LNxnSWcHAH0lVCXco5gvF5WCWiLDm4cKvIqkCaYImDhvlE401+ZLkQAdiMd99fuL\nxehafTlmmIFCFHL1fZZjyePm9pBnq1MbbHN9YNmcVUgFbz8pnZ0grMzbIB0fH3/zm9+87rrrnvGM\nZ+Dt+XweAL7+9a9P60SpBN4SfOOoz/iu6XnE9rEq+w3TLnQASnzSgCWfYeNNwbgcZhAPVGuR0W3n\nPEnDsGSQnCuz3N8YZJgQh6EtqtdLuVy7VosHA3s6Ozwlox2RccZSnNFAWr4jWisoMz04yVCc1hTg\njdopItB9f8Ucj8t3UEgzyoq6ocPfymxQWkGF37JIPFhrh+zOUGlzwo15G6THH3+8Xq+/+c1vlrY/\n8MADAODzVCWTMxxeDdPQo1oj1/Q8mLEUa0MVnDR6xSiSokU8qCNrkd1tfq8sKYLmplfMzIjqMrSJ\nAkisEfvdEliSxUm7hektUVqYIKZVpLtV1m0U0oM26rB8Oehr1dElNxIdlr6DwjaEaXPOsvwx9twa\nFBK7/bRTaJF4xOh/0CUbJObMmTNnPvKRjyy6FxnM2yBdeumlr3rVq2688Ua88fOf//wXvvCFa6+9\n9tprr53iudyV0C64qKXlKMbogcGhCm7POnrpu8h7oloLa7d9z7evFJ6pXhEzXh5VgRTuY/NDLpEl\n+4hcKBZFVjd8VIQ82A4/RNgV6W7ZHRFAeRmw/ySFAZmH7PIdlATc2JyrgmyXBtlrUbEwRIJ1NUSp\nPkRtSALWpU1a8dhjj/3BH/zB+9///kV3JIPFr0P6zGc+88Y3vvHyyy9/xzvecckll9h3vo7j2PgU\nE3g7pefBq0JGDAziGZpkkyWMYomVlNM74+4Zum03mZk+1iAemCaTRl2YNV4eVYEU7mP/2+9Wcl5T\nf/gLsZIJH6jG3zoGJybTs2GoTyBYH+GoL4e0BFwsm01mqkoldpau7kBtg1vKa0EZ9c0S+QSAc/fe\naziJhlF/5ssADhQvleT9Rz/60X333feKV7xiijP0M+R4cXz3u9/9kz/5kxMnTrzsZS/70pe+lLn/\niRMnxjvR0YWj1umWv+3XWrXxWmCNQBGgCHAW4Dj97ywkb4ktLYBtgCKEp0K1qVqr5m/7rdMtvDFp\nYRtgF6AIsKuchf0T7+JuXODbT+l2zuq2vW/F3aL+8HQj0u2ttWrDUyvvmrhwdJR9jw2cbrXU29ay\n3q1dgFMON/t0K7kbrVqN7SwOv5Bu9pThZu8aLkq6tAvKWxdg+L0oos/Tcn/E/i3Dd0GchX9Js7/U\n6hfcdF7TJWz7fuanrzL2T34qh48Evu3iVs/t7CY+/vGP53I5MdrfeOONLkfN875JLOyW3X333S9/\n+ctPnDixt7f37W9/2+WQBd4mRjLImoY38X00D8TaYTo8FaaGN8fRS5xu2220MHRbmEyTCeme7WaP\n2bwP4kpTPdyV37UgBn29wQ01Bp6xWyyyE55W+mi5W2LEdzGBrVpt2/czB1/1bp11MHvbuieK4/RD\nxYUsE1s0NHLW0LFttN30hKN+wU3ds1/g2W53xB/cahikU2FoeTqxfGPnwPnz5+/ieJ63/AZpMbns\nWq3WqVOnnvWsZ91xxx0veclLHI9ahlUFAxjkS3kAeW3ksL4qw9OvkNUuBvI9P5XqtJ+dN61YKDJB\n3XB7oMy28519zy9uFaN2pHZbdGy4bFbpuUvm1mR9TTu7xKnTwqzR86jKC2nTS0S1i4fEuyITXWAu\nryC1D1wPrSKW/khLvDJzxx2k07CqO+BvhH19rulapA50uOC7aWgwSL9WFzwN+1YsikR5Ksk3WqyF\ncmYl1iHt5PPxYGDMq+v7B0dHs+6DC0zb/NnPftZlz0WNtAsoYX7PPfecOnXqhhtueP/733/llVfO\nvwOTYKrtXQ2rg4sD02rWxA6BfpgedNIzNHjqQx29+gAA3WZXZGRIzJI6EvCdB/EgakemkuSaDA7A\nV0u2IVfKheWwFtRq7VoyjaBOa+BZKzHwGypyOykgfD+o1VhG1GSexve3rFXghLJOGNN2OmcB8NVi\nW4rhDvjce99sAtX21XU5ojU2auO75XHVpOUWejx1gvSxiwmeIH2Ww/TEksAzXItoTTR+iJrVNigm\nycRNYzuUePmMpPNhuBUE/V6vbTBImZN/q0umLrQ/GPR7Pbb2i8hmzh7Zj370o1/+5V9+0Yte9NBD\nD4167MJDdgLtpJS/7WfEcbTvagN01riMNC+VEUg8NQwfFHeLare1sTXcc3/bPz4+Pjo+Su1pihM6\nTIB1z3ZdbvKFo6PTrda277dqtsmnjIBJesbIElBS/7HzskigpX3TDVDv1rZuI76FamRPirlKX6vT\nuE0US5T+baf/ZF+TU0qzosEWwAVzCPFCujXxYeHGj3WX4PrrQix/yI59Pezx9d1icdbdOD4+/u80\njz32mLTDiRMnlj9kN28P6YEHHjh//vxznvOcZlMTkKpUKs9+9rPn3KUxYLW9sXwue7lP36CyCvjz\nPH62DAFCgJLmQVfNMlcNq0EY5Et53RM+OksHBvEAd9uWoKjE8+oUYNAf9Pq9YqEo+VjJubSYHoUD\ngD7U23WXFIIsj2pmeWzLQtoO/5fsyT+ECOCQLxflbqQmsdthFGW2Lx0iWhPbY5Dv1qFuI0NSsuHd\nYsV58rhfxYJmw6oc6fQ/wMN3Ip7aTvewj76bZe7uChcQ17YQ7bN7hd1Wln+9XasZXUD0ObKCIEG1\nuga1z4NqdRlcw4cffvjJT34y3tJsNnd3d2d93qkzb4P05S9/GQC+9rWvaZdo3XLLLSthkFSyVyn1\nDW9ZAnRlrhdOB9lU1ECiPNR5KdPCttlWF4mxFpmQalgNykG70661a8YpFIb1BzrFVOLZARM0brLh\nUqRZa6DwFDO+YhaMrSXqDwYsUmdvX3xuON5VUEochehcwjbgWyiMGZNQSw8VUTriF3GbeohaMEzb\nJfVqRfAQ2+CTWYFELQG/sSLdLZtjM0ULuzzyiafiGpVKu16fbkG/+YNzqBvi6/qKxtPlSU960jvf\n+U685eUvf/msTzoTFuWajcHyhOxUbFK0FhLt2mNGp9ORkd0kzuaomU702aoQCoUPirtJ9KB1uuWg\ni0peYBW4k/zd+u4Ub/toARMeVtKGJ3E8ajsd9bS3L8Xfiig027IK2HZ1G/E/9ZMsWv/Zo8VF5RRn\n082qF2L/dgg1/DESPZ9KtyBFXPX338zyh+yOJ9CFzhkK2W0QqdR54kkpSs8R9wEiXeYZ4Tw1uG/R\nNwboLFSDaq/fA08ntwPZO3Fy6RpJN3Bwkq0stmkc0OnUd6ebI9w9YGJJ+y3Ck6D4Pdp4qtS+qiwQ\nHlVojLwCAPQBdpQIq3BoVPEFoLiiGpezu3H7AOeUGuTiugKDRMLlwV+9sTH/7gBAoVhkDpDt/udy\nY6cDXwbCajUMglI+b3ENCUd+bNEdWBP0qfPUpfxtlJA5AtjRJazrjJlRYqR8sk6JJxRrlBxrzcl0\n3D2eYsYmOzhgIiGNm5lpvwVsi/hYMtsXsywFNL5jAj4JhNMZMKScrQ3+7VAz5gGXbhcMqRBUa4Qv\n51CpfosvIURVCkXfgloNzNnqRBhKvbEeTz4r3tXuBvj+r3rqVd8PajXP94cfqO8H6XUChBOLcs3G\nYJlDdoywFcohEq02azt7H8cUD9IWu+IOt+kYebNcLDu12FNdAmx5d4q4BEy0SRzU8OQxilmJ6KmI\ntloyY2zziJlpASwTsBVRyzitw6n0uUxdFWfRxuW27eG19JVeQCkq9OFEFudMBzmHskCO043tdh13\nUz/clQjZCRx1oYtiJUJ2ZJAmQrIHyRAsfriZQX3zPkxsjU+Ej/K3/SS/gzLim/TZaueHg59uTHIx\nIfacTFPJ2ORE1rjpMtUkTQKxpk6n39LKtU8jE+KU90H5Luym28EttHjuCXwWu021nPSsrqvqdRXR\n/JCkJpdGW8c5vLG10atlkNaGjcvUMB7LkKlBoBYy9z2/1+9BAWALrYBXEYkB+hn74Arr+nqvyhY2\n58SKuoo8DmLprmg+JfjeQe2gxBP2/N/LBlMSD6XP6ZLn/V6PJRW1fCDJgUodYDFnA8pi2ADNFogk\nBRGfmwm0eR/SQmqc1oEFx5po1kqNE9pTIXiJUN940j0+n1RWLlyie3ysSU6hJB1wubH7rZbn+y67\nqWq0lcjUsH5sVgnzsVmqr5fRQuChxTJ4iJ3N+7AK60PjwUS1AZ+e1k4Q89w8Io+DZIoY+Z38MFlR\npEk+M5KYYklgtRWEkhgvdokHg518HqyZewy3M6HJb39adDJEGm21mXi6Sp/x2U/yxptKC9hAOtpU\n9aR9lOYJbxG21uPXWA7Da3y/rZsC6aaHC5cb2z0+dtxNPR0ZpIWwWSXMVx1bRXAAaBtqIwnwEg/r\nPkwRl6wW6vM1SSIv20n9BDHbny3d1dbcS9bwgm5Gmz/VT7HE0dxgC2nZI7xUCGCvVGK5W0xT9GCt\nVAS8gF6Zl1lqKvtLwodAETLg1nCzgEwdcOldSSdeUM8inTpAFyWdVLu0SChXYv6iL7QMPFUS9vPK\nShV5MXVv1z447kYQ5CGNTMq9wIgMmvtcLJWZStO6z3H3OOpEw3qsnvJYjtXBEV8kGadifRJy5jpV\nX4ycM20Ly08plwPD3Yr5C0mB7eJ5WD5MlqRACtP1h7L5jMO1SN8v8RxiCgYyH0vydS0uGj67VkRu\n8hc12UIdk+GOnjOXPKSFQB7SyuBSERwOkQNkeiDvZ1SBZmLrZLWQeFoWJwq4RrydLlwaA1iLpg9T\neuMWMEoyBXuRvVFL8M0UqWIsA18rAEjaXCYc17ovoDhJpqf7sFrtHh3100J3UR3c/l0o66Tb6veL\nHXvADYlapLWPHCPpLJLWHNIfu+SHsfNa/EVNFXlH0TNpo4ksyEMajdJeqdfv2eZ+Gug53PRADmh7\nW7OP0CYk9uOAP6DaJzoQ6iSQLXNdh098I+cMdMINPCNlf3chiEIA9rvFjBCbanKclofz5xso4bf2\n6V4VVuD8ctrvQpnf+4DXnvB0848dpJKJ0l8lrLZQHR2pJ9LZD9IfvnQi090AQyEJaQ5P18AIuzHI\nQ1oIJGpwYp63iQnVqkFVWhba6/dKeyWnEI8JadgIUgOMSFgnB9bEEKKN4+iQKg9lRBo9gOawbE5r\nvxWWQ61ww17baYFqiE4UNSoV9snsAMTK3QJxrSjo5DLfzmphiP3FDmrwShptmYEc7p82JFsAZVQD\naY+7zW0UfwsAyvwt0cOY+0Ms2oqVEU2+g3hQCWo1bU/YsXG6CNOezhyqN0SriJsFZJAWAhkkJ+Zz\nm+wP/k7V6sD8SHxg8298zz86OAKThE+1gjvKCIcej0VrAJDMRY1qRz0uL4sADgG2AC5OqQTfDNgr\nlViNuNjhMb/Z7YoSNUzfbJqbsSPpyzHMQIo/C9wFbaen7YQNAMOUknCbMj+9faRZwKZXmOot5eyQ\nNkL97NqQAHPMiEMGaSHQHNISIc2yDOKBZJ80KYIgNfcTlsNk9kCE5w/4RMEOSh3kyXMX1aCql/Cx\nYVKa6OigyQGd3o8pvwGgHtUTZYTLVAlWVrE8RmKCSgoPGuYZFqXQC6pVAGin685pdgMAgHZ9OM2m\nnQHaQR+vJDbDW2KeEVzlsN3G3QiQTi9U+6PM5eGpLzFLZJHYQVpB5/Hu9Xs90RP17LgD4JYqSfhG\nUb2+k893uO9IEFNgEatxx2TW64eT3Ae72bl87NkQMir1besW2fPD9cdqM9KIA835IHDynuyF/oYL\nH17mrmtTjiX4pouoEddyuFacqZrRqtXUGnemW3JK3aIkdT7b7RazsgGJ/pxyOGnRnOkHf0ryt6ZY\nZD3JuCH8z5b1ROwyWbqm4XlnliyHMjUshAXet831kFR5mK0+EHrwr0f1fCmfvMsFQ8Jzypbhxenn\nT/QkX2lU9MdqH1y3AMCa5BkgWW8kXDH7o69JWeXpllupRHw6wirzmx1CssU8JMfHfEFYrTa7XZZW\ngInBwCEZq9iiOgqshdjN7cB6F8vnYHLjhC+l5lvfCgKnFLS8G+fMJwpqNZaTW1qlZHETN40lEZ2e\nOXNGW3BuBViUJRyDadltNS9crVVzqQ/EHvy1ToPcckbeLr2HZDtWfXDddTjRNnrYtj/62p+fpUOK\naT+vJV+CNjPsnOB+Er7WFs8Ihx/zGcwxkhwm92Ss0me4Wyyy1iQfomi990Xuo2SeVP2HvSLswEmF\nw+0paLeVHICSvyh8oIyC8dOu/bNCHpJ2VJnb2TGPPvqoex5VLZTLzolpTbVpJQPFQtGo546UVZSZ\n2mv7vLCYfZZ0EPbJa6Gpw0IJxxMJtDltIEtZJZ1FEmPpstwsUG7H5NcwGMS6d5nqDNLVSyEtTxD6\nCMdb0jfrEbCw374KgJGpcAuQGxQoE0JxWj6eqjNkWJeakqejm6DVZwthfaZ8cSqskKhhGUSnP/rR\nj/7+7//+9ttvP3PmzI033vjZz352vHZI1DB9tL6zJetPEpGTZpYjNKUvsCwadAyOifgIPl3m5HUH\n7Sm65HIiTMCHRh5pTLZnFkaK0o0AQANgz5Dlpgy5Um6YY2IuiE+cBd+CVouFqiCtSmjXamw23hJ3\nEvoILUkoTNkinQjSCoKY24nhslC+v6drSnvSAkDI2y/oaibhqHD3+DhV9c6wLrXZ7bIbxcyJsD0i\nFZPYklkwXrNmdgOwjCrz/BV84hOfeNKTnvTSl770zJkz8znjLFhDg1SP6rlSrtauDeJBpVHJ7+Tr\nUTKlkVgdQxY4AGV8b6MdCmh/CT5nkxRWC/ixuKkYtRbhwDzfAT8YW5b14/3tJxLWiJ2O2bMwlW5a\nZATPnuJQZyeEBXWQ2800tq5+4u/vtc/dey8bPVUFIktzp32L5Wpzn3QBa928ErfX4tuBswYecP8p\n1rWvPWkfiTQDZTe83fN9VQUnzZMxb0YsUWJLsiKkP5SQdIPa8+6VSpumu3Oce541L37xiz/60Y/e\nddddd911l+epg9RqsIYhO63vnFTdFniG5RjAB/pD61r/cmpYB9DFcUzBMS3sQCn6Jx3b5dul2J0u\n10PS5sm0IVHWKsl9wHY3RtULAnThW0nwKCyHSeoHawWNe/v3zjqhg/YT3x74luASZC2bZVE70y0B\n/hWIeYog+4liw/qeEnrNPI+O+XOQsAdrMZbFUiLvH/5edA1jgiWrRSR90cxndITFXb/6gx+cvXBh\n7EbmEHpyWeFnyS05I6677rpnPOMZqxiyWyuDlJEdB9RfHjq4D7AHfsEf9AfDjZa8Bgfp7eqczU7a\nCHmKTdJ2Rgxj6p4hACg/feA9xCtkvfSYZLJDBTSmFvi7JiuYnp0Y1n/KqqCRPCHOJrZu/8QLMZz9\nquYoSz4C7RJh6ZYcDOWEw5VgtkW4AJ6SSreBHngkk2Z6klE/2MzF2RYz06hUOlFkfOLCk0/iXXNW\nC9004pjrZy1ze6Myh4E1O5fYIlIVr65BWquQnd131siXSygC0gYAqG5Va0EtmVmxBcvTAwMObe3w\nmSfJGuFIhym+00DRP0CTDHguQjvJUEhHgjy0XbdmNmGfnwLQ5eApDtzn9IUP4kHxZNHYH749qVg4\ns9i6/RP/zlX6o0Sk0/SWaIN9FHE6sNbhdyJWjjKdyFPCqyLY2efaFA8d5aVPWuZnPJm6PmOw1hKN\nFDuzyR6jrl03FaStItEwTiPKZ3RktTTl1aAK4FRHhnBhfQzSaAuAsPoAhhYlLIfVsJoYpMxhhoHn\nV9roT2lIa6AW7MtbxHljPinFED99iRhlbWDNiqCfdKJOWg24BxClTSDukmlNPyc6jJI+WyY9WB86\naBJrerH1zE98cAX0dDZJVSUwGtxX1BpxcZ/a6E6UUYP2E4UAXe7BlJARUvNKhGiqSchf8JcuSLem\nLkvKNDNjyxPUrBYdtzO6ICVrDye2bXMgGSusvwIpHyZhYX0MUlKpwdGKALJSnVTFB3B76kmEZ1KS\nGYbdL8k0mZJ8QDSOH621vYq50TKdSLKUwnb209vBMOPFdt5PrmgoiDA9qDN2UN92hiZQZDYaG5dP\nvO7Lm/voctW3wCqiFB+mCIt10m1mnghr6nDH1ShsmU8+AZooZBymW5McOBcz4yJPwNmVUqTVeo5n\ndGEMp23huOQSW0C3Vpb1MUhOVkR6Khby5T4cd4/9a3ymBHN56tEMAyJWZi8+ah8G+Pz1cfe41WwN\nn4EbipHA9kP9UzqRLbDC/SFLPBNfeDl9RQf6B/XULK5qApm1mCyhg8s7sLr+AAAgAElEQVQn7sVG\nWykNIB0ldIa7L54W8KUzuVpmLVr8Voi+HehOZJs0bYQ4RL6U+ORdzIyTrj0wBpqEWs/9jJmsrqa8\nGlaPukfaX8Fx93ghiYZXl0sX3YGpkbIi6lSvGEyBL3QNkkdN3/MH8SBRagFUGhU2Yz+IB8MnQAYf\nZoqFYrAV1Nv1cCuMDqNBPNDPBgg8pBpoG+Y/heMF4Ht+klNcnBeH2gqGmeiLaakePpHl4V9E0tTt\n0sQSIFdPXFGMKmigES7xfrRd5T7chLF1l088jmHPINQocQOD37KMrX1+R8WlD9eBDgalfF5tzXIi\n0UdxbwzfNSig+9o9PmZz/tg1YTNMeDLU8v1iZgbr2o2/FWuBCbZKyfP9vVLJ5YyZZDptfYB2vS5y\ntC8VPvi1oJYMBW0AVEeGGIn18ZAyfWcopxe6cl9E1GgQD/KDeDCIB5annm6zG5bDoTUyzQZgTEud\ndBtZB4YxMUgbDPsUlKc8dasP/xGf1NFqNABtb6CwZDctdk8WngB46fU1eHCyOosTRjNcoiXSUlBI\nexI43sXGaEcHW372V9ecKnm+8YmCWk2oA2K+g+67lmxPPljfB2tucib8tH+/mJnRyhMA/1bcyh05\nLdhya2pCp23hVMNqt9lt7bfY1/Lo4GixxSpXlLWSfQPAAAZJ5lPpibQAEPDYv6fIoNUH+b2hsyIM\ng1hDI9VMShosuBWTEZ3BD8P22jvMlggnyeO1BNT2hfx0jz/9BnzUYW9FykSax/eUut1XFMSh+Yrw\nDuJA662YVtkk0yculOU4BU5bV/WVCYvLQZBZqU9Id0UlWTzaxoNBo1Lp93plZZWamByMAZVbTefy\nMY3F4iMCJKSWq9Py2x9xD0n7/ZLF3IZkQiPJte3VpLTycS0ulRJH1ZFvbD2k1ZV9r0/IjmHynWvt\nWjLs6otap70HNDYM4gELDeHlnMOaScKwtVF6OkscBHi4Rw3iiJieai8DZBuA/9zbaSOBg0rszzh9\n3jaK/uBTiHlzCTxA7puvKEB3IEwfaI2/pPy/CciMlrDgkrAcbBxv87fwGpegVsPRMIYarTQ9+3fa\nbTbJoSpCWGCNfdTDx3zfZ7VoRX8wzEEVn3AS7Mzl2BAfVquFm2/eK5UAZbSLAA4B9rkxyDYzSgfY\nDVH6YiOsVsMg0EcsR7EfzGmz3f+51KhdD1bYDC8io+uYuOegPbpw1Drdwgl3R6hRVDQm8z7OqpmU\nndV525y02d4sPhB1zFjWZpc3KJ3RdIpTumThRf7uLsqYja/olNLObvpcx+ls26hvrdOtKX431E/c\nxIWjo9OtlrGED08Wvi0lwFY+TDWzNb7NahJ2Kf22tj/sNdvN+FX1fXGgOFfL8LUqpnN1j3ND3DBl\nBx8Z0/0fC6qHNB6U7duJsR1JpwLezYx0QSzElN/JD+JBRgYHNmmvzmJr8dAOUrORIY7DWi5r0vkk\nQSUR4wiUDrjknohRgramuRvd9J+xLsdEOS3HYFNTHYCFpgO3I0XDGPZnf5z1oDNS0ExBlBt3qb8u\nwmUm1xpgmN181mizg4+BHI1c7kwNawmlDnJi7Nvkkt5juPjeMGT7ns9KjGcYNmkIhrTJEa/LAH0e\nkWEGTG22lD5EGm+6yJZ4/NT71hkpe89VC4onN6Szq/MkuB1VoZ4eKac1gTQj8NgKPMrH3tKOj2pR\nBu0zSff4mI22QbVqCkA5Vb4Qs1BZGYBg3Pw9i0Xc/3996KG/f/DBsdshgzQeZJCcGPs29fq90l4p\nYzguGOb28T6MzJI1AFDgQzkzOTHyZq5Bj9CHBqmCyHQGvFemHK9x+vH4EFkvMTUlZhVceg6K/bCc\nXZthFuC4e2zPMrfkBknC/uwv+TQRWrg6tOyo5pDYorYmnAP71xCLKewFihjuyoJlY4XqIa0TlMtu\ntrgudAUH0TZkSVMZ+3ypfQgAaSl2iLK+YF8qRrkM+ryRmL8w6bwDdDheqItfdKzp2/B2D6XOEytk\n+4owT5zd0E5+J78kOfmngloZCCMW0ERoTUHMxd8eb0E6SkrRFtXrpVyO1cUAgD6vPxWhpEuqmCJz\nMSljFutJ1doWBDE5m2KQMpYoAR/BXYyN3bCBW1ZWT3k3QLkMYrTs1N5aQ3lL26Dn1vNmWtttsj3i\n7DvIpkbD3ZJFVOaeT543aHkQC2hEaFPMHsXixhtMgkjRJmUUBb6AuI0eVNhHjWN9LhmAYNo5DrDt\nbFQq9hJKBDESG2GQwJreA5ooxVjmkM2wGDZwy6cnPJiCOZeny0pbPFvjmRsU4Rt7z/fSlWHBvHJW\nnJ0NliWdLbf2fMK8QcuDWByqvfGqKQ/ScdNOFJkyijLEc0UMENRq/V5P+CUui0lZO475e1xYrWzc\nxGqxYnNIv/W/fys6jKpBdbxF/vWonixYAQCx6LWQzrhjFEihRaZYZaCdtnFZG2vVUIDHS+W4tAZ8\n8LM0CEhwofZ8y1AmCpDoA3dD1S+oGi9rz1v7rdXKO2nRI7hM5Fh0B+AgfpT2d1/MW9Ct4R2PMUoo\nTcjkc0hT7MxGQaKGDKTkCGMXHmXBIpaGLigHSco4/IPWC6T4u1pxs4q9dBpw25Yxec3DNJmtdQE6\nAA2lwQjgECnlmgB9nY4uRFenChbU2oPi7GVrXV1rz5dW9q1iLxnnItQG63OC/dgmCgCK/ZMnB57a\nzvQQJZiK1s5ud4eZ/aYHqRI2jZUJ2Q2TIwTJJEQqeY8zvueH5ZBlmtLPLQX8wV/NSgZosthD+6tp\n3OyRsQLAOX6sFhHcKzu0xnaW4nsRmoIQOwvzJoxN5qTRcCZdd3ZmdSwJ68xZ5sCBelRn+ddddp4d\n9iCVfSKHZcCw6w5cQrzS/qJK0MXBwJTabngi3598mmd1s3ETK8QKGKRKo5Ir5bQR+skLj6bmlkrc\npRCBrAAp5QQBf/eAr0495FuAv9COEF30JOwie4t5WiNta0Im3gZoKA2qM+yQFjiAg/gC2x71WspZ\njYC+5y45+etRPVfK1dq1QTyoNCr5nXw9WsCck0vJOJeJHEeToz0WJ3US+w+fHHo9NbUrY7rTPBOV\nUCIIN1bAIE1RQKx94m5HaECQftChrhUxToj+9NNREjylJLlZ+HEXsjQUHmoNlNbYACkcGtHgjrn0\nEaPEXSX76LLHbY/kMkLai3IRyvNjhy5pFtNyiCfEpWScPeO1i3jT/i0oK/tv8W4Iv4QVKAq41bFb\n0PFY9WzcxEqw7AYpu0y1m4DY8sQtjX1DXMYJoREIlMkSHMpjY4M4ts/13OCgRBe/8YLOaRMOTZzW\n3dmLBAI/tRZ1u3Rph8Ns6E4aLwAAcMzJP1OHeCQcg1SZpRzAQbxpOras2x8L8ID7JZ7vX+Rrb2dR\ndHWKlSYIwsSyGySnMtUOAmLtE7dl7OOnN4wTnoMjcsjDemH6WMYeMk6W8H8BIExPHYT6m5Ak297n\nR9mXSgI/tWV0wStiJLuLVeD2Rrh7F5ZdFSh2hzjqRHObUnIPUllqFHWPjzMqD6F10up6hH3d/gLJ\nL2H2ZkbTPNMqoUQQFpZdZeeS9ccuILbnsAEAOADo8BqyZf7uDtI0e+Y0qRa5rkka7qGInJoLU8Jz\nrrQk/CRwThEEVo37Pt+i6u4kDbKpkTQusjqnNLgTaCxHot/r7ZVK9r5gObUtK6ih8pBoPDJ8v0xi\nT0AfJlPQMbEfZH34OA/eOEyjhJI7pLLbNJbdQ3LJ+mOXbBmfuE/y1zvpBfHRMA5WLBR9z09N3mDs\nogCGNNEcm5dQSo2Mmmehj87iEosr86VLWvGFsD2q7g5vBC4ltzh5AFBwDbi5OMQAc5pSGjVIxSZy\n9lst5kykUg2pJWXTjYeo6K4wJ6Zat6DzS5g/B7Oe5tFdSEALY4kpsTCDdObMmd3d3VtuuWV7e/vt\nb3/7+fPntbu5lKm2nMU2BXWIXksGAIZjHytLPDwpsyWF1D4yQoanWkGGZYJHa6sc8ywIMqcsWB/2\nszTuontSmA7QwNnmhlkyvXjPk64KlGpQTdrU0uY9n8uU0hhBKkvWO9VcSY17AGXkjZXDEO8PXLAS\npeOBYi1qwM8462kem90liMlYTMjune9854c//OHLL7/8BS94wfe+971///d/v/zyy++8884bb7xR\nu39mmWoTtsITjaxFnTAMBg6X5R4gHXZmDO2kQSDgsgxSgJfsl0C9CdDVbbeH0aT4mzB4mRU6mumN\njbQoEb+WopHd5AK7zW6xUNSdAwBgEA80S5VxH4DHreKkJsjRwZQXYyp9mmWQyrnxzCpBogQ4WAKx\nq5b2m0J2m8Yltbm721/84hdrtdpznvOcv/iLv3jd6173mte85vnPf/6nP/3p++67b2dn59JLNVXV\nr4KrcpD723/42yceeQLOATwMvufvvmrXMrQxfM9vH7bhohITA4A7AR4GaKadlSsBrgX4v8lfn/o/\nn2IvSnslAIACwKv5nv+Xj/uS79VHPtadAADgAbwKIGfQvwk8gEPQdPVKgHMADwAcAjwMAAAPA7sJ\nyVF3clMRAhQA/g3gYb4/O6SR9l26ADcq7bN3tTcKuOEJAK5Nb3wA2EfwnYe/k/QH94RFBf8b4AF+\nTx6G8xfPW5zaq668Kge53rkeXOTzbYwY4E6AGKDMO38lwDn4zgPfScKqs+OqqyCXuzgYxN/5Drvr\nnu+/aneXlcibW+OFYvHGX//1awuFfzt37lW7u//n//0/aZ8rr7oKcrlzvV4BoK/78FfOGgHAe9/7\n3ttuu23RvSDmyLxL1B4fv+Utbzlx4kSn08Eb9/b2Tpw4cebMGcuB+Z/LO5apFhxdONLXlD6drrEt\n/dsFKEJ4KjwWNcvVRlpZ1cqLSr3ws9knHdb5PlYOFP+2lcLk+Czb5lrp2wCtrPZtxbc1G495+XBN\nT8Q9QX1wqVx+dHyU6vC2rgO8D8XdouOXYRKmUud7Ho3zEuDSv1l0ew5QDfJNYwFzSF/84hcvueSS\nm2++GW/8pV/6JQC47777LAde9vhlIuuP47mMU1AOibRZDtahJgLS8bfQLNcVaOeQMmL8uv5Igt84\nvXwfUJbuDlrhBCiLuehAaG5fvNZOmOim1JmvM3RQLCoPjkvSIB/8WlCT5STqh8UEEFuTzdK7YS+J\ntESNc9EBbnxuVcwJYkI08bGZ8thjj/3nf/7ns5/97CuuuAJvf97zngcAX//616d+xmpYDcIgX8on\n6QxwqL5tmDLhI91QE8F26/PJIUHAWxPrk0RkTB2dPZ5TVRrisTZhJ53tFJCt6qCN4nRiqoatQxJJ\njPp8DRPWRKj9x+0HABcBOqC5UcCn1A0TeNnquD4AQGaIVVANq0E56PV7iWxh39jt1UoZPgfCarUc\nBJYStwSxtMzbQ/re9773xBNP/NRP/ZS0nW357ne/O4uTqk/cKTV5lC40x0e68/H5ZDQM0rl/sANR\n5lZHSvMDhtE5BDgw+FWSzA94g/hPKSWEnByGd6CDOiD5Fpb1maFBdydOjXR00rSNkzpuRG+GpcGd\nRGO5sczUnyOI2TFvlV0cxzfffPMLX/jCj33sY3j7t771rRtvvPEXf/EXP/GJT6hHsTpGP/jqD57y\nyFPYljG0N7jwRDWsSvUsAFIOR1gOhxkBsLpM6NmS6wEArvsSbxW4fs+ljpE4b8gbbPPD47S/pa9C\ng1awSnUxpA6UzMt1u+kDRVMBQMg7XE67aOnVqU7quHFLToytsSRWFFzHiFR2G8W8PaRLLrkEAB57\n7DFpO9vC3sXgHHTxVfGj/9+jv/W/f2u87yguPAEAw4koaRGSsEZiQMezPsITitHg3kinEQqUowRi\no0jxECi56cTh2N8yLWnCHWOWoIDewh3AzonLwiPRFNuhg94N5ISnLkXix/ZmtA6uY5JWYhX5F86i\nO0LMm3l7SA8//PCLXvSi5z3veZ/+9Kfx9n/7t397xSte8bKXvayVVqbmSjkAeV3L5I/G2fmEAKUU\nwst68Iofsc6GeR44jVDEJ6j060EATurq6QkkL0raLVLieFs8eese6g8oHZBWDoHbwiPRGcPtCssh\nWztscmVgGh+Z5OBO2BqxEtA6pE1j3qKGK6+88slPfvJ//Md/PP7449gfGgwGAPDMZz5TbLHYjFwp\nJwbB8bBl8BQGCUfA+hmDcmrRDACEACFASScQKPDa5JCtAkhMi7SbVtFwqNNQ9A0KBdyUWdYBW2k3\ny3C7RP4F5sokReK5yWSRPcN1jgBzcGnSiCDWmAXIvn/u537u0Ucf/cd//Ee88R/+4R8A4AUveIHY\nMsUySBKZJS3k0+EtLmUdBJJAgNHnEgbIUgEUFLl5Q0kxLjLyxciGBXyLCDBqc/EB13SoG4X1Fac2\n3y5cAaQaVlmyJd/zWWBtJJk+QRCbzLw9JAD40Ic+9Ou//uu33nrr9ddf/8pXvvLixYt/9Vd/9eCD\nD/7u7/7ua1/7WrZPaa80iAdyGgWGB9CEwd6gtFfqNrvK29lkLOxnlsOUxnsP4EDTH9gD2FPib2JA\n30d5xDso5TaLjGnDeqIFphTfAziZ1kqI1EcHisfWACgDXANwiE5tSZVUUryoAy7/0/pPCmzNFoNc\nGYIgxmMBHtJll13Wbre3tra++tWv/tmf/Vm73f7+97//h3/4h3t7w9IILjLikTTEuFasLYO4WFhq\ncp5i3VGin4b5/FQe8XNoHywB31GW1rIehnwFbjrra7KbyWPrKCnM7ftLXtReWnMBhtvFN9bb9XpU\n1xbkJQiCcGRJ6yG5yIgd58klebeY0qi1axrRASuEap/qFyN1OdWfBE8pgITlD120P/N1dnRTO1Jr\nISqYw47qOGgiPCXDqbsSXcAOiawaDU++BJd6RUzKXw2q5EsRJkjUsGksqUECYUgMg6C7qMGk07NI\nwlwHbnXEB+XdEPVcLDBi+zfNsj3QJc8WPWxydbVjcm510ZJ2f9N1sbBoA9WNVdcw6a7C9MSgfUSg\neSZChQzSprG8BgkmXhFp13aH5dC/xk8kYQDAR8ZkrLQs8LTbIYGlmKyX9los0nMtBV7Ywm4499Pp\n70QNC9P+ls6UAbaUarPsPly0VfHQPjfMSMpPrB9kkDaNpa4YO+GKyEydHpaECT1YxgLPsrXSq8B9\nFsoi25M0fh7vgJhPss7rpPpmmQDLFHYDOiO+wAO++Ml8oCSGrDQquVJOW4Rw1tX2Vo6oXt/J5ztR\ntOiOEMT8WGoPiSFWRD70rw89+PcPOh4VdaJKo2L3IUzF4ozRPJPTo2IPpgnsLo5oBLtNeLkuWNfe\nStE5MQG2r9s/szPaq3OYysI3Ob+TH8QD022cR7W9VSCq19uoSplai29zIA9p01hqD4khUv487aGn\nuR+VnX8aoN6u68+olj8Ap9oKALpCFalu8X0Kw26YujdsxEuL60KAJndKhEgvwqWtdXNFrLXYLOo7\nqRyCO6M2BeYqHhGPEKKbnLn8C69n2mSYNRLucTwYtOdeRZMgFsIKGKTxcBGO9/o9k0ZZWuAJkGU8\nGAWu6s4MprksjMVFj4Tla/Dc5GxeR1r6Kk5kOrXYH+fiK/CTaueupGpMuDX1KiKAEu9MBwCt+prk\nEWFDaFQqpVxOF9GEUi7XqFBIk1hz1tYg2RYbRcONlUYlv5OvR5pxUHhmybR8Vm0FAJTyB6yzUAL3\nSSBAQ7loKuQGxuNP1NoaGfjUwggFKB4odhaLltTOcGuXmmOLlasQaY14+1EnYuuTkk9kemvL1o9+\nrweWibxebwF9Iog5sgJzSIJRA8pG4bhu1sei8nJZFNVtdkt7pWQjm1PBSmisKS+nM3m7TwKJMhCB\nIn7Dq4U8ZHXwqcs2ORwAQKBIvaW0EZCo5oZzbIICvxtS+w2d1zXx2rK1pBNFjUolY1ax2y0Ui3Pu\n2AKhOaRNY209JACohtWj7pFmlkWHReXlUlvh3v69w+0B/x8nsvO4x9NJLzDSTgI1FWsU8VN30uI3\n4C+wEK6s5NArZ2Vq8JRafyW5Ivtx95g5i2yObfhGATlJUvti6RI2ulRtT8dhuw2Zs4r1jQ5pEmvP\nOntIDJYRACdbS1CWE9lVXraFtBJ4RSqzE1uo0h07vMyzQphaECN4pAtzlXUabuydsHcb6GLjLB0d\nFvUpZhvfHE1tQ+nCwZo6T7fAdpN9I0a/19srlewf0X6rVQ7DOXdsgZCHtGmss4fEEPKE4SbtrDFk\nqLz00jvQZQTHCoIyWq/DNh7wuR88ncMIALoovdAOskbSWfroqDIf8fHQL04N6Fzuoj5xonLyGlv0\nxBqpF47btztkMHTgqNoew/N9yJxV3CRrRGwg62+QgMsThkuOzKOkXeUl2zaDYQPIUjRIVSQ83lrI\n9y+jo7RnidMpwzMTwopeaVFFfcJs7AM0k/7kSjn2z3jhov1OVpcAwnJI9Skwnu8HtRpYvjtkjYh1\nZwHlJxZFsBX0+j3bKNnPVnkx21Zv1wfxwFjfz+PPtDhUBVwpAIr3oK7mwaE8exXBpnOtP+C9UgUF\nqqhPuGWRzoyZuiTaN61PQl0axANaBisRVqthEJTyeRHZHaYMXJ3QOkGMzUZ4SAyXdTDJPlay6/sJ\nc4KX+wBfP6R6D+pqHtFJq5ORHOVY68/jf7qL0WNDwNDSpTYKJ5LCewx8P6jVPN8fqmG450QQa88G\neUjVoNrr9+xFu11GyWzDJkZ8STcRI5UBPpyN79h98XS7ac/S56E2u/fD7GKZ+zGekj4c686FEWLi\nwGba1WsDlHSq9IArKdwcsg3X1FkIq9VyEPR7vXa9vrFJg4jNZG09JLVYnG2p7CijpEsOCNv0EqOB\n1p96yKUQagjcmuksIuJn934ArWAFRYwOhuRD7K3AnG5V7VIMxUIxVZCXFN5j4fl+OQwPjo7IGhEb\nxRoapHpUz5VytXZtEA9wIobM5US+52tTNki4GLbULEsEsAdwDf8z4GE9bGxCJK4rcclD5lmafL4q\nNi9pApwWjR+1zzce6CrGBuZsEWBIHM737za7wwTq+zVtl8R6JoIgCMwarkOyl9sxLicqyHtasBcP\nHC7HiXQuThMZpA6KfcXplUkHvAy56Swe2tmENuDWSQfc+uk6T6E1WwQ+pICWWxmqJkqLwKgWHzES\ntA5p01grg5RZkY8Nl/JSWTwQt41l5SRs62TFlAzOHiRmkvA4vmNYZltAyyO1KYi6aDtOFKTaP3F1\n4m7gSn04OZDak4J1labbylZRPWSepojqo68HZJA2jbUySO7ldpI9pcFat6dAHePUx/9ioZhYRM+a\np0B4HmqpIQZWGUSGrBAipofPwtPpyVawiw4UOfH6aMEstmTYtlkq53KWyu+h+ujrBBmkTWN95pDc\ny+0M9zxIWyNlT+DiCO2kFFsny6aUmA1L9A59vk7IUoCVYRLRSdNLTaUp4JNG4iwNbo20eoqSIvDr\noBkjyeQEAGFG4vBioShV2jVcybyRskgM4oE+y1EaVQJDEMT8WR8PqbRX6vV79lKtxUKRpeV22bN4\nsiiPZd7QDBx3j7UP4yDGRHu8K0DZ7bRYXBNp9shzK2srwnR7KEZ3oEnpPWwz1AcMVQ9yGUJkjgFb\nCfKolhnykDaN9fGQXNTYbJmR456ajG3x0OdgPhPegT2MP9d7bpKjKDNxXB8ZBuymjFrTCOfWsyyk\nFYuE8DIpqWisp4gA1ZzlnuxBat3H+ZN0yeCVmrIUjudREQQxC9bHQ3KpWsQm3pNHaeueANYZoADl\nw95XNNzicIuHZD+FJFWQpIDqUcLFsbp9w2knFcvFxkjCEKZ8TcjSNDoyuYMVdaJKo2K/591md5jP\ncFyPipgn5CFtGuvjIWUuMwrLIXucH04VNNLVUSW7YpkBwsl7GuaE3JYlRJ71FMIaScuDYutRkLWQ\ntq9LnWC/2A5fJyvm2/iarUqjYkq0qi0upZ2nmZaDNUZ99PE8KoIgZsf6GCSwVOTjizHlKBwb7tN7\nJs/FmbEvPPZpdQSQlTrBcgrgDhZewepZj2LYrSD/M5VMwX6xgNbGRgClpKmoEyWmxWFAt1gdx4hZ\npujAPWCbXIqzBIYgiLmxVgYJdFWLmOdkeZyX9nR51oa2gy9lSp3Q5QO9/RSsnTJyTSwptCUnyWQF\nAQAgLIeJVF302d4TqXqFuDqwWTI8oGutjqOD5ehCjZoXagyPiiCImXO8Opw4ccJxz6MLR63TLX/b\nr7VqbIu/7UMR4ALAcfrfBYAiQBHEnt2zXSgC7Cp7sn+7AEWAU8lR2Xvif9sALYBjgLMOB+J3WwDb\n/KSWo7YBttPnEn9K/dnlt8KlJ9uoSxfSb501HHgWoAjF3WJ4KpQPZPdc3EDDJ+Jv++zjSF0OvwTt\nh15r1ZJznU23tgtQhPBUiHd2+ZRbp1tjfEuJKeL+kyfWg/XM9s2qFokn4uyCEX24uXCzOBbAIXm2\nwPKUjdVreAWuh1oznUIo4nDVu8yjBDhp95bSH+HSufQk1s1dBbxv2hkpHiJLnAxLSSeTg9UfJIuX\ndaKDXCmnig6qYTUIg3wp75JFwuVTpiwPBDFn1i1kp2Wk+EymOAKAZzpIWjedNWkNIC2CYBT4Ppbw\nWtsglzAdJWzMPl8yFchihOTUYnz3UBDSGuiTzTm2ZBJoY8ZzABgkfwE/FkYTHZgCtpo9HSQwup4R\nBDFD1kf2baHX75X2SnZNcGu/hccgW6o6tqWMlN9WoXm9U681apqmuoY8dRjVP+ikXR981AHvEutP\nBHAIEPAsQULOHiBfrcG13R1zm0xTrl5jZMv9ymaqMhcg6z8Uaemuik7GLXDPnmf6lEeVrRMzgmTf\nm8ZGGCT3JUoYTQ5WSEfexLhpHpRZWCmJPmHYUBvp7FAZVSg3pV2QmtoCuIiOKqSf+j1+oHRICLDD\nlXuSp4LbFOo+rTk32FS2SinzOQD2lQoX2HaaDFI/tRZqEigf+TJDBmnTWM85JAkWn6m1a8PqeQxr\nfKYaVnvnevocrIyAz0D0M7Jfp1RtHspqGnL3pQ2wBVDgFSjsCoLBzlsAABPjSURBVO8Cyo4qOhZz\n4wHp7N3nkLHBW9roLKwzTX5DpDZj3qZ2uiV9J5PudaDeridzPPYJqsN0PFNKSKE9FqZZBL0aVoNy\nMP985ARBqGyEQYIRZ7yHR7Gq557OGgFabcqIh/NGLKkdiAx7upn5YSHwMvcS9tAOkCWXiNPeQwcd\nCGkZhUi7UEhvafA92aDPxn3srwjjV0DyCtV4FHh28C2eoA8g2AoynwOSUyufSJKbXGg6Ziw6kCQw\nBEEsik0xSMBnvJP4jGI59Ie4KO54O8/1nqs+ZdvSAXTk9apy3MyqYUu0c9JGyQcKdaeLAA7R4cyS\n2Y1fP8t4ALdkaWthfw5I5vZApwkEpKrouzq1BEGsNBtkkGD0+EzmM7405YBHyWHGPHvkrZ9OZloG\n2Eorv02GULgyDXPtJeGEidOJgkmSiM5u/AAgBsmcD/uj3BasNbA8BwwTRkjhR3yZWeFQgiDWho0Q\nNUzIeFqsoZDBLjPDioMufy1kCwa5RKq4+A4P32nlD0IX0EfVK6S5JYY11SwTaGABW+L6KLeFIZlq\nk/Itoxi8Jys+SHSwUZCoYdPYLA9pPMaI9SVLcT3uNFicDzHgin08XsLVFCUDPuFf4KIDFyeMnQ6r\n2sTcEu6POtODTK803aLxmbi1G/QHtXZNWA7f88/H5wHgud5zcR8tMb2heeadrAU1MkUEscaQh2QD\nl0VwX90CQsuwz4UDDoXAAXSGp4wkeWIHPPoDr9JkccKY/8FOJ8mkuTfmF/xBf6D2IdMjYSnmjMKN\nDoTl0L/GtxfB0yjscfguNtaVJ9Yb8pA2DTJIeiYsJDpcinvStno0mTHaS04hr1UqcCm20IWHAKCr\nM1vIqk57jvtJhlWorf3W+fj8eJecBCcNMcPhdaVDhVLAMyloZFLYW1fCEusKGaSNY6GZ9EZjnpkW\n3XN6ajm6cJS0wBJ9Fg0JT1EeT5wQtrhbzExdCtsAp1Fr6s5nleyuRZTgVUmEeqxLSptJ63TLKVGs\nLrkqTnjqcsmsk8TmQMlVNw0ySDL2BNVS0mgLqeTT2A4VUYLts3pT55R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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options.disp_dim = 2;\n", "options.ms = 5;\n", "clf; plot_multiclasses(X,y,options);\n", "SetAR(1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Logistic classification minimize a logistic loss in place of the usual\n", "$\\ell^2$ loss for regression\n", " $$ \\umin{w} E(w) \\eqdef \\frac{1}{n} \\sum_{i=1}^n L(\\dotp{x_i}{w},y_i) $$\n", "where the logistic loss reads\n", " $$ L( s,y ) \\eqdef \\log( 1+\\exp(-sy) ) $$\n", "This corresponds to a smooth convex minimization. If $X$ is injective,\n", "this is also strictly convex, hence it has a single global minimum.\n", "\n", "\n", "Compare the binary (ideal) 0-1 loss, the logistic loss and the\n", "\n", "(the one used for SVM)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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ATavsQSNBjVwLQSqTtB9mBlxSZQ8aCWrkcggSAPVZX9NI2D1oJKiRKyJIAFRm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\nWFiojMTHx7dp0yYqKqq4uFj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = linspace(-3,3,255)';\n", "clf;\n", "plot(t, [t>0, log(1+exp(t)), max(t,0)], 'LineWidth', 2 );\n", "axis tight;\n", "legend('Binary', 'Logistic', 'Hinge', 'Location', 'NorthWest');\n", "SetAR(1/2);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This can be interpreted as a when one\n", "models the probability of belonging to the two classes for sample $x_i$ as\n", " $$ h(x_i) \\eqdef (\\th(x_i),1-\\th(x_i)) \\qwhereq\n", " \\th(s) \\eqdef \\frac{e^{s}}{1+e^s} = (1+e^{-s})^{-1} $$\n", "\n", "\n", "Re-writting the energy to minimize\n", " $$ E(w) = \\Ll(X w,y) \\qwhereq \\Ll(s,y)= \\frac{1}{n} \\sum_i L(s_i,y_i), $$\n", "its gradient reads\n", " $$ \\nabla E(w) = X^\\top \\nabla \\Ll(X w,y)\n", " \\qwhereq\n", " \\nabla \\Ll(s,y) = \\frac{y}{n} \\odot \\th(-y \\odot s), $$\n", "where $\\odot$ is the pointwise multiplication operator, i.e. |.*| in\n", "Matlab.\n", "\n", "\n", "Define the energies." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "L = @(s,y)1/n * sum( log( 1 + exp(-s.*y) ) );\n", "E = @(w,X,y)L(X*w,y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Define their gradients." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "theta = @(v)1 ./ (1+exp(-v));\n", "nablaL = @(s,r)- 1/n * y.* theta(-s.*y);\n", "nablaE = @(w,X,y)X'*nablaL(X*w,y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "_Important:_ in order to improve performance, it is important (especially\n", "in low dimension $p$) to add a constant bias term $w_{p+1} \\in \\RR$, and replace $\\dotp{x_i}{w}$\n", "by $ \\dotp{x_i}{w} + w_{p+1} $. This is equivalently achieved by\n", "adding an extra $(p+1)^{\\text{th}}$ dimension equal to 1 to each\n", "$x_i$, which we do using a convenient macro." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "AddBias = @(X)[X ones(size(X,1),1)];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "With this added bias term, once $w_{\\ell=0} \\in \\RR^{p+1}$ initialized\n", "(for instance at $0_{p+1}$)," ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "w = zeros(p+1,1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "one step of gradient descent reads\n", " $$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E(w_\\ell). $$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "tau = .8; % here we are using a fixed tau\n", "w = w - tau * nablaE(w,AddBias(X),y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Implement a gradient descent\n", "$$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E(w_\\ell). $$\n", "Monitor the energy decay.\n", "Test different step size, and compare with the theory (in particular\n", "plot in log domain to illustrate the linear rate).\n", "etAR(1);\n", "etAR(1);" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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77z0iOnXqVFJSUnBw8OjRo1Uq1S9/+cvGxsaeu69du5aV/Od//icr+eSTTw4c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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo1()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Generate a 2D grid of points." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "q = 201; tx = linspace(min(X(:,1)),max(X(:,1)),q); ty = linspace(min(X(:,2)),max(X(:,2)),q);\n", "[B,A] = meshgrid( ty,tx );\n", "G = [A(:), B(:)];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Evaluate class probability associated to weight vectors on this grid." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Theta = theta(AddBias(G)*w);\n", "Theta = reshape(Theta, [q q]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the data overlaid on top of the\n", "classification probability, this highlight the\n", "separating hyperplane $ \\enscond{x}{\\dotp{w}{x}=0} $." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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MHJtWLhhTW5uugXpN5YjocCEIZaED0qWXXnrLLbf4Nn7ve99ramq69tprV69e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\nEs8Cj+gnL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dW2NNfSXFdzXc2VVEfl/gMwlVOmcsrZQvFsoTidbzdy7QaXG7l6O2HcRUNv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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf; hold on;\n", "imagesc(tx,ty, Theta');\n", "options.disp_legend = 1;\n", "plot_multiclasses(X,y,options);\n", "SetAR(1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Test the influence of the separation offset $\\omega$ on the result." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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CINlicEUkeUwpKQLcylTBxG9urKKDJY0TWCbAWs5jiNOrpW8W02lJBKEEEhFd\n0WXblSha/0mdk8bObiqIfNe0lMNCZ0HhQIdIgeKhXYNA1p9eevk4AFicB+nKHGUS8PRZT3O6oVOs\nnTioihM2DpWH+NlAYyUcZWE4oj1HJbBYpgnjjgLMAFZilRQQEiceuUIIpEEin0MoppQU3sWUJCtt\nY2JJMWDitzxYJQc7GpdtCnHzPXkwTqunCha/VGa5qNF4ryVC+XMdHWizklACs1oQ6Ny5/5XKfmW9\nzVMdLrpDLnWAxCEUA4WzkmSo2lA2jjN+OpOubNo8Efqv5zT7Ot0GCHCrl8DygMwJQeBuAW6bJXMD\nzaBVIZjIa5TdH03nTOVQFLtDSu53ENNS6oC3d5vN1CMLQiDlhUEfQrF49pmv/qjKTtvY1UUPi+P5\nrZK2WMIQpGRH4woXBMGfGAPK+QaDPjvAooEbxW9ja/TaDxNCMXfTBznGIpvY2d221LLEap5Fg/Ks\n+c0OoUiL0yjsMchKQhx4mXSyLC29fKz2wZl0mbSQ9UY5A+Fxadea+8fMQRsoBTJSZ9qPnfRi9bcI\n/TvqXm0JbdY6IBR3f7TVdM1m7oE48Sg/CIF0BEEOoZjSR/UkK21DA89vdbTF2dAHNxpnzGMQUYzz\neTTo11Zp2sY2cOXseCGUpz5Hnzeb2NEbf8imt8DwwoA8ScsuH9d2bwTQU2k9NcHxFjYGFodtIHWe\n8KqA1VaFHNkREoye62h/B+lVa6JVe19pczniEU14hRJ0nfZc2aA4WdCdxfTIOfHIGSM0ymgI4Rz5\nDT43FjTIxy4AyTIJI6rvCX0HwzaMH8gbLphPCNwCSKCdrJdDhrJ1fMisQtt5IWQo42W5Ej67XQEa\nsL/xzGDpVUWnrRKR38cQQ1hJCEDWny4b51/4ldFrXjuoveUZuTJzcZVpCjvaY4RHBECtvl4CQTUX\nR0q6kdDsUvtqPwqlXtD7xmwydoFECPEIlsfRAIQSiMQRj9hypawAjgHnhhA/cI0YYWdMOGBECyQD\nOx2hQyhyubFEHuSZJBG1YZUot0dzpnGe+XlJtoSLzYW9jJxLa6fI+pvO5eaMcjvcPFdCnzf/Eqtm\nDGXkt8BAEUyvWte79uWeu68eveDCIsOXv6opXXrT2PIb4zkzGp9Ft4Tr6pDbwGgvypGWTMNkmvSK\nEZ9dYNhjMTTRvwoAyAo9LUk2JeQaFgwsqoCsoLwNkThWA1fBgisrmoE8ypvY7TCFNGIYkSY7t6Mw\nD3d67gSKXG6sm68ld81cPlGTmQImi4Gzsxd0COsT5Uzt7NwKu8gINoq5o3mRw+RlnmX69c+bTewI\nbn7A9J04hOKoYqAnya76Y3fxdcqqJw927Mvc8qsDZ921696/fG4Ycu+v9wM2VEzLWwAAIABJREFU\nUZcsuKbeMYkV+gwkfjtVq++5jrY0mioJ8dBHZCvsjjV0eUv0EzKCrwK4Mscb47gyjkgiNyHRnNhk\nliDtEwJjLU2JPWet6p90rc3QEYcRrSG5Ik+1yQG53FiWM2GJGiqBVtMWvn8DTbMwwM7gsNre0Edy\n4xXkJSPZ5pQtpkpvYyTttfZl+mG1bPq8fR0PnvXy+v1fvFqZfYfN7wK4HUIxiJrfUqBYTXa79xsZ\nGJDhbtUfuoGcGtERy6x68uDSy8aRbwm/vPxxH+BY9J0p2a60ZzY+s6SI1fpRNvoNgEgCCitjD9Mo\npnuZLQrEy9uohXSXdyIGIA5ZQSSMlghkRZNGNdQJ62C3/ky+VEp+7t//upLcT1rUwNhUyZesRoxc\njEgNaYhgjvw2I5cb65AhARPj1QIbqMW8QR+YBO7aYOhgWpRl/hCLc2V7z3ziERpMljc+spzf8plX\nwtzONs8bVRDo3CG/8gubFQgcM9y7ru/Mmw6sfbGftdz8YFfxddZe+6IbP735f/eSbmteO9j+ecol\n/pPBmfbq9IRXz0WB8gPr9GndtcZwgnjIJI2Yru8YpICqXE8S0k0GhRKAglktiMS1lqY8JkuPvSAl\nX9p36p39UxeogbFJ+ZLes1aKMg0GCIE0lDCnInW39wJUF0EeDMCDjyyKmpiZ6ExVlPOZwcEQj0Sw\nge4o2UrylJEzrSxv7M3CGxUNK19HjwdUTI9Mn3eDor03oj89/ZSmf7dcxdQ37j/3sdnyR+6p7CIV\nadDgDXf3rusrvOLze9f1tu/Jfufn3WfedOAnTx4EsOmDJGDSe2jQwaaPEvc+feCsJZ9pFjzXVCTy\nInemPeY0redSlBTTQGZ/tlqYNRjvVAGL9YESjJiZssM9iyFwTgZWAxs4PrOzW7MaQmpgbHrsBb1n\nrUzJlwKAPU36975YuPU+X+c79o9xAkKY7I4s3n66PXIQ8QjQRPLr7D2bZl9LLRCloRAz9dFBbGwj\nnW01N6qKM3cQXqmnlnHGyTGqeDnHI7ANaa2+Qw3tQ+RfAyd7qvSnm8X0tgz6vLXEvUwNOcUdrxse\nLvLW6iktPyfXZ2z4t7K3VitnXNsx4y7Tr2ABdiqSOIRioLh3XS+Qs321x7L3rus9eay/Y29Gp/fU\n66RC+770qqc6c5+drVeKfn9mR3uGj7w5jg1s5DZGVgszgp+kEVhHnU8xk6mZmSVoEJ1C78mHnbIW\nXkky2K17oo42ANM5Sf69LwZoWtJIq8EqBNKRxXULz9jyvX1RYD35bOf1ieoDkAjqOdZy4DGYNqTM\nJh6j8qwBaAIqgdXcURSuMhKcAlSrvwW/MPIuaKT9S03dYvqz/IBvNeOb3B2iQKxrx6jPXj90cq4Y\nJZFGuRfIoe2Rt+7PUyAJDBSeUPKmuuTaF/stw95uebAL0JOZpc+mxiQweDDRso5zQy62yAowzmy1\nJCzO1aZyXxhsJqnWf+RRpVsziepmLqcot2GLAu0RtMiIxLX1sMnU4Enpk2YP1GdJpFHuCUZSDdaR\nLpCGJPLbIRVpfGkBgM44rgRiMuK8q99gdqi3eenLXE0UcC08szlvSKvoXq6B43wmmRxTMbTh4CJx\nwb1ZavTnYih66UW7hRJI0OcNJbTNJl8QnOhRk/723x9987cAvvD898ZvecLyBYL/jew+7dqP5vxM\nRH4POTa9lwIc0xIImTmEazfQaggNjpYAg3upjs4c4wRMLQAqMBwPL85rYY16n6vhuUC/4rV8bs0y\n5QimNbEqsi0RSBGtMU6PR2Jxd30z70M+oEpScOfjvs53rJ9gy93p8DknfDzeSPUhOUZ+ZwOHGxe+\n+pUt5z7019+/99n40sIrF54JIBLH6hh+04ZIAivitJ+sL4HKBIzBT7vb8h6mamAG1HPmddaZbQnZ\nZs8gIxX9wohVkI/E5d8stVwlIV6MzaVvGUBWEI2hvE0LkJ3VgllxXUFw0L/7vngNGT16++uwjwcu\n2dVi9XMIHBbWPJ9q35N1SUuIcZTmEK7dYAp4MZRLAKdP82TGaK+W9nGOAmXIc2EOkzAtP0a1fLrm\nbzWjvE3rpdC6E2x/2BLRPQjJpWXwHmrDQECqrI7kGqwjXUMacvz0la0/3fQJuf6XZ969b9NH18wo\n++1jVdff0BhLQFZQHsaKiL0VgqgpvIm6yuqkvgZ9Njv0G9J6vUZVzWkijZQP+b0hL0scLBsKlxu/\ngRsim5QqaPOThMF4BIqMSByyktOy2NwsBnjS3/6bXAQPbnd4C8W6t5fsaumaOMv0vcDgseaFFOCW\nlgAuZ8D2v4d+rKIaD6/ow02PAeeZcY0C5WVMPgszWxHZJPxUJm2eoYHeCkBbORTZ+kGaoeXSBrY9\nmj5pdmryfJtn4BAY5duzUUodcHqC1AFv77ZM4Snusx23GKkaUt4Y6CEUmjSiO6bPunrv3/RhurTw\n8oVnjystUuxOVWk06R/k2iGklWgh/O6VbUjZK8CgicjcbpRZMNi2FFYLk/VvBMXUwlbI96cfW2Zp\nlVUTIbSVo2UWHonoRCE/U7Br+7Tn/n3ac/8Otyitsnfvt/k+X4hDKAxYtjAIuIS9LV1caOGz4UHa\nCbku4bYefAarsx7DbhfjEhXsl5Qbns/CDFPVc/F1eiFg1ub5ZZKPnZaMTB+kM4woIPXv8+9Yj/zo\nzdf1tusTnPA1WIVAGjL88zNbQqtetBQeZT95siXc/a8/u2jaDZFEyBQUNJezlTHwLJpPNjuBQm1x\ndgKMn3M198qI0r+u5pElel8X22Ba3VTL/9AbNOq4zCV2N70gc3kL7T7N2pLuGvktYIeyUglwSUtY\nOrfg7n8qBvJOp2P/u+z/NR8r3Gq6u2rU3d1ySRqU/KQXW1i9nulMKn4ihHDI+niv3SSgNQojI+sf\nJBHC/LA2qvCNRYFtj9qsLIfUxH90fYITvgarEEj5wvUEipfbDwC2wqOlY++40qIPpB7AJiiIfx/X\ncEc8OHAvC1UwwNm+z+7byO0QCfPPtHk284LZKMbJhps2UMuMia2bK9Bcrlko7dS/mOn8JnBvITuB\nZAn+EAqRimSHslLPsoUBwDaVZsG8IICFF/uB/IQEOBnD5swzF9sAu+weAkJALM3OYWGMPtlwZkLg\nPwJA7rhY9ihkdesjkCqoncPxQVZGOPfPoTZXJSkbGOf6BCd81TshkIYGazbvau9KOAiP7V29b3Ts\nvX3O2QBnirZ7HxO3DXklDyibHTYCjLfOE8SsZGE+5hGeY1hqlPmmjpYZwu2uTmjLt9CApJFA/li2\nMPjRC0WWwQi9T4/71Z3FYFlKMAmJei6doI5S71xOgc77WLyctk0QtYmPYFhC7c/ONRVBd0BzuW+b\n6FiysN05HoyHsKgcAFZGMG0W6mVNvGpRDPyCbR6khmbaEdudq0wi5RscnuCEl0YQQQ1DhbXv7wBc\nHLAPbPrgJ5efB+QRFMRrHs4h3aRbFRfdYFhDvYltmIHC0rHMh3cTsKWuo9ENLICC+YQNN3WzzCRi\naAsj3OnihGZBHiwWfeMt7VJStfo5BIYAZapn2cLAmqZ0u5Il/8tlEzwL5oVYBy00fB2VCob/Hlmf\ndmpoUfI7iYGgmqPPeqvjJJoojTUCTUANsJtG95kXZoBMUykULroHNJR8icZNzWFIFdo3i8o1+WSx\nZpsHqaW3Jlzi3/FUptw8hQ4p+dKTRn0xtvU+8xP0nLXKeeyJgRGsIdHIb/7gSxbC4Bz5rZrMd8sv\nKgNcdkxXTY9MLinSlCTXoCDQr1zNIzIwU28eMd1apwYxg3s+AbKG9JGoPqKXaUiGmxosM/U0Wha5\ndhId66z+sfsrQGLUlPi5d/F9DgXFQUpDj2ULg42rSn51Z3HZBM/S6sIPfz1maXUB+Wrti/250HBD\nhSpe0WemZruz6uCoxzAbGqPPWq4gNwCZu0uMLqCOboOq9AszhEvwqwKdrUYvVOo0bS/OPKAOsHkQ\nWcnZnMmTZQMnIY/ohl1FU5Pj56n+MewJVP+Y5MjIioXQkIYKZSVBwGXHdNWMCIDb55z15J74zo9M\nziQehpBWuxxD9rGOq5jA1jCgPEECpptUm3a+M+nCFnNTMRljeHBWMYj3WrFU2FYAutR3M8ig7bPu\n7C0+eeob9+8pv/bTcxZbdRQYekybmi6bECROIx5rSK1VQrS1el8fT2POqj+4IGxLPUamtGQYXkVL\nz5GxjEf4SaL0UJUYl3cN/YFMcn6h5+A6zOVuxCekr6brMT1IeRtievOEb98r3kNt6ZNmu0qX1Ph5\n6fA53p5PR1TRIIKRJZAkz2CsPflUcIiEQ8vmTLtn06d2wuPa6WWk4U+b4zs/6slt4hzex8QuEXPj\nXt4kwg93fS9YokafPsKeok7fItOE/Eq9OcVSt5P1GVSkTcl1sTPejN7+evzKxXvKrwXghe0hFIM4\ngQIi8nvgWFpdULU0lSNaRle88GDWWmZJY4qRzIkiAsVEVIqN5Zmhhiro0EuUVkDhirdW6RWyGspB\njDJhzxoyXRt/lKWl6Gqg+pz+QWoVhPVeWo38+/f5d6xPTZ5PKgn5lWf9+19Pypey0qsMqn9MOjxm\nJDiNDBhZAmnIIfmTakorGrRszikLL550xg9eNQuP9v+4GgDUTJ/k/dN7cQCoofEIDu/jKrpbBGeF\nYHBQfdgMzi4a863B8ZDC9TedMaMZQ9ZxdpJGvdR0XGRFZ66eGRNk9fQNxkbvPesa0/pc0B0aVZwQ\n1VQPF5aHJJWVegE95Zij5gwnMdTpNRVe9TdssEgUg6GSiBk8C/CkJecxiqzTzcGp4x1n0cU/C+UX\ntRng9pCrzeT/xqJM8Wne7q2kMdixNqA8mxp7gVb/e2RjBPuQBg7XyO+yvtCyOdOmlhQwE/bJJYXf\nm3MG30fzITW5BQVV0W/B5QzxBnE7D5DC7Q0HGl/L3iOsdrirG4C8gCpNTgXHRcZDOo/VYi4tpI77\nPQYhkASOHIhXCeCI1kxIvIQw5GWD230wulrHFbVq4Cg2pucLcyOTKPXAXC5cgj+dyzCqifvr6r2s\nyUN0MVCCZ1XBmAS05FEijdgvJCX3B5Tncv1GcHKC0JCGGMvmnPJP08te6dj/001bvzlj6v+ZTaRR\nOkF/6sklhQA1gtfaHLRKCvPwqhL528qxtMP+bqa+GqYZ7AXBK0mGAFnWaHjFNFLdaC73dmgAVnPH\nXli6AbhFxmNoDqOiU1drxqCJEWnk82XTad22SQ1I+QTasRMoIA6hGBQslaSl1QULrg+eefkBowUs\nxpmoLNXiuZzyQexytbQDr3Cso0wBN9cpkxxGuxjQANRaady888mVNfiIPkswM2CN5kj7TZsWWWdg\nXB6MR80lzhtjd6THXtA/dYHN/UYEhEAaMrCa31NLCr49ffK3p0/uh9/cbXJJ0eSSoh1dPTpHkaLn\nK5hUJQL28nZmkibOKOdgErR0TdWY6ojHOGcA46d6buXgbsQ8z26LXBlBRSzH1BaWjS1PAPj7xfnV\nSxY4ArA23GU9S6sL176YaFeyOrcloxlnAxdTo2v1faI0RMIQKWOgT6K7LwYagCYbB89iLtmIT+Zr\noPZDuLEG8hZdnBJEpJEl4/JgPMo718gvxOx45kOSRgiEyQ6wifx2GeJmvrND3do3d3T15A4rarIi\ndz77j9U7qRtIiRR+/2hpEjS0sADZWlMdcWZKq6ZyCFQNMlRwqNZ7pB0XWaPkuthZNkjZb4HhhqXV\nBY2rSnRheGZLGg9m4FrN2ejm6qtxMAcP9KTF0yeAxXS7E6OdzfJP4SYh922gx13GoAvHtrOWk7vn\nczJ5VBsVVYxpu4ppELstOLZmqya2u5xMGpEQGpItsoG0J3lYv08QKbOS9PLuvQBQCZTSfR9jQugF\nBh/IwMwdeUZDOJ91xB/TBzptLfeR7dlgMoa00kbG2FXc/pcPxnNcZK2Sh2Xj4PbR21/fL3/F9L0G\ncSrSkYalkgSgbIKnfXcWoMGWoOTqrLs3UIllCAqA3tzXaNrNECtxvSnK1CD/HOK5Weg2qHizZI0q\nYAlQD5012cF4WA0A32q2YFxXHrX8hfzKc5lTTwNGqJI04jQkT3Awms1Aa37b4bXn46Ne7wHolo0P\nVVjH2a0IFTO2ISYIwjD5REPETJs0fptZZbKPR01nA9bRVHnLMnPgoh5gdbaNpSWHW2StkpdlA/Tc\nWAKvz9Z11FlQaPeVAySvhU1VIE9oCbO8IIGLWqyruxrlalkxiiXswCQcn80NoNakDxnkHz8JgyEU\niNUUrrIKwymlATYxbnjMtnYRqQvOS50N3M2dI5YMIF/pQsADowD4975YuPU+X+c7VoNONAgN6XDB\nR3674rUX4qEEAJPThYC9ymNciwExt2gIRW8JkU2TMBt9FVV3zLtaB8ZupN5stoW03JA22m5Cf9OM\nJv3h0ZYg/CkC7YYtOvZkcx9q9AaufPQCpjPJnFRzyPuZCwvwDh7XoLgYF31TRWeO6QWSOUTCsKtj\n5yTJucNheVMCedZ4BJChxBFTjDwKk72O/4V4geRXnmXRd8Gdj4+EPNkRpyEdJlwjvwGEpKTdVxMm\nFJItFWC/fZJNHGXgsQa9xOLZiW3fojaeWNYzSmt2wbSrdWVshZMncAxA5+2Q9NYrI7rYPWcT/eBS\nkRy+FQW/hwpa4Qbm1OQNXPnoBaQxxikcNdxOqJFzScr2lkCeevKJ5zZQm2yq3GhpFQBCCYQSiCRw\nZVyTRsvjuCWuzcFsHFXAyoh2BlicngHWEsmRvxo8yeEXMmTIEmnEFEUpdSBwop+HJDSko4TVr3z4\n+Ob2yB74gEgcMtACRxWHVxxkjn5ZtZIoUENpuZIa4vgIJQI7BYTltMO0q83npE6mzEUdc/KXcN4s\nuuWMR7A8rmXWJ8OTA5077Ez0dtJIRH4fTdi5kTr2ZAD6X8x05dU2ujv0eoHlNoT5Ndl2h7kkayhF\nRekdFeq8ZNQzoHhuS4cQnCqbrGjBIxGsj2jf/Ec5QhHIChDXRpDjlJsjdGAl0IpEDPEI3YMCfTPv\nm9i/L9b6PfMv1BP9BbttsGOtb//r1qaHLXenw+f0Tzoxa94LgTT0uGfTtsc2K9+fc9q3p08G8LNX\nPrpv00fkq+1jEJoFWcGVcSiAIiNh4Ad2RjjTLaCvANZArXCMVJkYMNQEIvS+26ZQEO9ebuC4lCWm\nuka77qZ+adLfMid/sbX5ZRG0M54BBGdeFWv9k5k/W+7aRkaYU5EEjjlyhVajXFxDDf1ryGSI0sO3\nCHmYQz3NYKZm8pe3QseoBk8OpWXyL0q/dbAZRjkzMrj5Qb+1sQokYmguR1ymLXphQx7I9VDzU/fP\nBbAreJJ/8pW+fa8o/fvIz6AGxqb0uhGJtbMTjt6eT91+vuMVQiBpUIMpqX9gLm7Vn3rsl3uantt7\nQ01ZZWUpgJ+8unXlxg7y7W3PbCa5sZo00hPxemg26FBCq3utHa7KG6zN2EAt6c6GcsYS9RzvKVw3\nPgaoVu+RYnBm7Fp9fKAhJxHcG8eGq8iRSErnjv7OP+2+8LtjNq9XqKrUXzLl87Ovtnp+gWMDs5Jk\nLLQapblBUa7uKtugENVHoclDbMvFlGxeW2LUy+Li+HzpSpMGX6OPVoWjDlRJlXtL/nK0CjQ6Cpvy\nNsdDzRtxoHRC/0nfBSAlD6Umz0+f9FXvoTb/jqfM5VZ9+1+XkvudWDx1wNu7LVN4is1yj2N4V6xY\ncazXcPSgZt/PpJ9VM/TYAl8WmdzWW6LtUlZrVL1ZiXZgjVLWC+CxX+/619u2tsYOdndnXn318+eb\n9vR0pxe3dgCADFwDSOhqT/+t43PNjlHLhTD0oHMf0j50htFdDFnB7E+QSFOC5mbQsQ3ZFe7Wq0cG\nyPTMsW5gMdAKdNN/MlAMXAPcAwBopefHsHnIzN1AlL4CDB0U4EFqKpkNFNOKlj+mz1UF9AA/4F4f\nUcBsWigGWpHeh1904pYEegCl/c2+0jOV2XcU7Plw73m1n8x/5NDJF2SzEhvBrlV6IdFg76TPE8yo\nAELpnHsvkNbceN5Mzp/nodcSvbjooqmnnz7W6nc8jqGq72XVvwz9tGndYR9lEzxrX+rHbk5Bf4Jz\nPRYDpwLXcjUKGbpNFwq19b0KdAOrgQbgB7BkHE20dCN36ygwGzgV+DtwDTAReAVoApqAbqq4Mz7q\nAT4BYGKxdUAP8CCwG5htenhmQq/Uf0se8wmkffClqXpkQ/CZ3T1jlb3+ovM18vMVZgunpuWLs6PL\nkdF5nQM7nvQk9zuzuJQ6kA7ndZz5RfNOP728NJ+ewwEj0RIyuMhvAxp+vQucv7E5nFjU3mH0iBKC\ncghCjSIRQjyC5QmqIRlmYGHZ2l3pMRCuwbWWgbPsGJhaYIM+mJW39ddYdWDhEhs4J7AhJkLmXMd8\nBzNqAP0Zz4GuHfunX73l1g3K7DtIF58vazNY4BjAE9K9NHWFVsH91zuE6tToFW6eEZZwhjjmMXUI\nluFvDRqbsI7aBvlbGzShmE3YQjU3LUxDWKOZ72SNi9vKAbgQ/GdjPoBVWI2h8HyKnhtrCS38oSQv\naXTcYSQKpMPEf/64fd6sdwxUHTJr666xasiF5nypAoql9KqlggGUUVlskgPn1Nlw3VxTbrys51sW\nMWXZwRzsZEguMTwaXLiKP+M50LmjuOMNm955YXCpSAL5g5dJFoVWa202MZakSMBsazJniMuHcaJ0\nuKXwc4aDnIvqTX/8nFU2TARTvRJLNADAxPY9hW/e5u/4g/l7XiZlA+PgxuIn6skUQiANGK3vHIKe\nqutlxEMmFsonCLXBqDBZa+lMxeHhzI35nAZbqw94BdeHvWJYAmyV/pxNvpshnDfvsiu1im6E/Mov\nTF0HCefIb4EhwdLqgg+fGWOUQAT8LsdZ0YE+4LMh72rcDhq8uRQVI1EHOadQ80OdjVXAkomg8Z0W\nR+dI8LICqX9PoOMPzrkHamBskipJlix+okojCIE0UDz/5wPKrqSBqhvIBwML5aEiaLqFQasww9wu\n23AjgTPX8TRuWJ65DAT/+rBkDoM0YnPWuNhwIgmsjOhG7J9+FfmYj7FODUiufQAkgznOT9NrkYo0\naBgNd1nP0urCsgkea/sY3BQdAvLfT/SSWH5GaYU7Y8Ks4teaaqAYhJ8ZBm61swqYmYgKm0icnj1h\nQ/DkREqSHFH0yrWBbY8alsArSSn50tFnrbRk8Z6zVp2oMd8QAmmgeP7PB2Ci6uVxACYWIrzhrHgr\nNPsvH+nFM7ZCww14bqzJT7Cxu5jXRizsZveSnfyTTToWrzZF7QdGEQ9hRUQ3Yv9028g64U8atiCF\nVn91Z3HZBM+cL/oBvbBxJkXGI3Np5ALyK2lqts6xUFK2kWI6vbMTyK6dCbNaq5UzuUiFTRXQTBKS\nrAj+3WYtyaGWTuA99LHNUjTsCoxNypeogbGMxVX/GNfjz493CIE0MCy8uRQm6o0kAJhYyNXNC0po\ndVwBYwcmNJyPZw5dbTI5gQzg1TJexTFsV2OcVtSgvxG/c5QdDe60J0lxN245qS9BqsAl5QBwYOZV\nHp8ok3ocwKAkASib4FkwL/jhr8don2s4OeRMinxPklS0gSM2B8bhKRZW50aaR5EhzizGzyabRBG/\ncuSETUUz7mpDPILmCo4jKcFHErglrrMmEC1L6t/jPdRmmNsU3XBp36l39k9dQIx4vWf/6MSuGwSR\nh4RgGv3aj8BSkbL+tCelNRpqfssT/TCl6EQSWBHHiogpAaKKyx7lg6dz05lOB7dLoSC0zPJ+LLMo\nFM7uETMxrUEtIzNsoLlKbD0x/WrNK+QXr3D5sCxOLwrEtJXcEkdbHC2zuKlqueE0IWnzsg+tnkfg\nOMPS6oKqpSk00Hpx1W6k2ES3R7xlz1AWTzZVfICeGjcAjbQCnkOdiBpgpj4HnMCsbNVwGd92K48B\ntKjdBgCAFAFg5JdIHLPiaKPL5O8QA3w7n8mcUW7+GXmogbHpsRfkSgqd6CXAR7xAGiBKJwVuuHnC\nY7/cY6Dqm+NQgEdgwQxTSwo6uvqMIiRqU5DUkgk3AHXUrOGQM1iVX24gMwAqpoKVCveV3QplKrcM\nahNDLDfJIxGUk4j2qL5AOGifKBIx+Lve8Jecb/pa1GgYprA9k4KPBY+aSvsQ8NTC3u+8Za+Wy6uF\nibrMO6SYPg7Crk5EA81qspNYbP5GU/kS08qJKJoVRyWwqBz1sjW/xBuRCKGizVhNVYtNmGBgPwCQ\nAsVqstvcPkIgqap7TbATBpnU75KJ28l1ltVl6M9JZVasgWlIAJiGxBo9Heq8q96HiaovWj61oXVP\nvJOY8DC1pODbMyb/dNMngImR1pmcvYoWpCSHi5VOSpFMq6imiUQN9uWQiTQy6FIGriOsXskdFG1e\nm0zvZblCmXqJ2UoquUBYMoSvEENWstqmEFEMWAxfyfmjpzcAyNLsSyaHzBeZtBbOwMrZ8Ucihft6\nyUVxQttIBrgSdqycnZQ8BOCHP5x92WWnWi3rOEYm+9t05tYjfRdLgQTg3nV9967r1eoJkf9xfvPE\nl2mQqWBQbPYr4KrkwZ7myb0Wc5MoVJ6xOhGMsO2KaRlYYIP9ygEAFc1ath6AabMQD9nySyiBvhZd\nc4xa6HtmPy5ZqTvuAmkgStIP77388iun59//2EJoSIPCxEDNTROb/vK5siup7cPkYGVl6Q0Xld0w\ns/SlbT33bNq2cMbEbZ3Jn276RMdIjXTzaBd6FEMi3o0wbVlHRyl55Aw20igDajHT7ROZWrMEaOJK\nEDmoQTYr1B6BpYzwG1hDiVVWXq/BqTJesPRKmx9a4DjD0uqCdk9m7W/7NWFjZxlTqEORvOV5+1g9\njfaU9TskO5pXOBNfNaXAKu7IYzJJlNO6eFiywFwnmx4JYagli7VM+WArjCIRw+/C+FancTKiHqmB\nUZYyacRCCKTBIOtP3XDTxIsvG7f5zd6G/91Recn4mv9vMjkVKRIOLZxWf+EWAAAgAElEQVQxeuGM\niQBOf/BvgJ7c8yiknSsgpFAuzT9n0OAB4vUhgrl6+7t9bWOHFWrShd2RR5X+I78qe4t8cMJVhvsc\naWOdeBEMLe5d17f2xcTS6sIF84KbXkgB+pgXdnYfU4/MjskGvcDgk09dab6R68kX+eVdsEsAhZYJ\n52FmAQKz0xQAUNGs3YeQ88oIABeOvjWCp2L6wt6zH7cZkB9OXE+SEEiDhzwxMPGSospLxlt+u2bz\nro6uPiMj8S90Mxg3kiGMnWr0vOpI/ZqtvIby/xL9Xo8PiHAVbOZF8nF67I7MTG/5UDWUt20s8kE5\nL/XILKLEIRTHEMyNpNnoAADf+Xn3d37eDVC1g+XJNrk5JqOcKmMprpxpHqaBDVankluqR2YW4M3d\n3DKI3wh0sesjWllkwIWjZe585GyoNDnxYr6LeW80kt1IQiAdKax5bxdgYiRC/Y7qAgAonBWbd97m\nI8+ItKjlwpzM5nty4SrY7FbI1CAmL6NUe7NZ1awEWmIWi5nZeeX2invVoTkgXuAYQJNGhte3QosG\n1ej9QHYaObOq2XlGnWneYSD0+yHDOg0sUOfkoA13IhLH2PDkWOcOgEojmapL9hwtKzg0Y1nh1kdT\n8tf7T1lAvhQbI0uIECYdVFp3NevP6x2p2h8gu2zONMAqfc85OalKXzLLwDD55AxWmb6iKREAZTbQ\nNViCD4KyXKH5jrJVGQiuT6gFkbguISmUQOEpt26/8l6+u0hFOo5w8wMHC6/43FiqjoUVgGrnzpWx\neD+TQxliZ5q3G8jIcq5NSb3FppOW7GcjtvSNdz3/VuX5zRXchI4cXaWgChi1+Z7UuC8xaWSAa7lV\nC5yg1UaEhqRLRbKEIRUpT5SVFABWW6daIEq3jbIpvJuAbRvX0d1clOZYEDiE0s7lTmXmfTxkK8eX\n+XJW1KwUmtwKzfLJrFfRPrUKyoHGOGQFnWHEIxibmBQeO3/PKbcR3UjyZVUbj1E+zqRDQS8faCdw\ndPByKz0x1tIHw8RPLaVhO4280j3SB7CneeeBlW5xQIxB3By0iRg+nTsfQK+0QzdhrW00udqsrbQR\n8H/+7qGBWI/dDXcnoidp5AokTzCVHeCJfANCWUno+3NO/emmT5yEh6K3JDDwjhwCPscC9tJCoWY6\nPvV1Lr0X9B4mOObhlurzOQiqbeQTmypm7PObZvwygt/NQiSO9IU/nvDCw55R8/dcftue/H5GM7w+\nlUV+CxwrrHk+1b47a/H6ZqTLi598TM3OBuSoDc27DsxHaDUCVfYBR/VAk7byneGdQWV9NrHDYkJ9\n/lMkkasdrN2nb5f/83dQfJrlYkWUDYEw2Q0AznY8yW8sqfL92adt/lGFlnegr23Vdvd155eNB+hO\nzblkFruo1Sf0MFuc2UbB2JU5lgkIV9cCG2hYrVWhOS1IabWpVJ35jvy0MBrlACyqQEtEOzBm26GH\nY9fO3/31XJaMNNRF6sQhFEcHa0gonaUwIG/qBlOLndlNMfXnwTyjhnJWMtXOXS3Pdutk7XU0wc4w\nqh6YS2/XCACe0KT+3eutJ6zNHWAWSeDTFlrikrtP0dZHLav92sHdcHfCYYQJJO+QGXay9t4jhpCU\nnNpX8P05p04tKWCMNKWk8K45ZxaomdvnnA0AsmPJLJaKwZiZhSQs4eoZkz0j8eIaWMUcaMCM3ZX6\ncD7Wk0mpRo4/N9AD0EDvzpZNd4WygqoYftOGSAKROGaxfEBZC3zI9u3s3fqw0082dHA9gULU/D4c\nLFsYBGyEAaFDXvy4uk5hL66Yn7KVa6/hnDfOA0HvawneVmFeNuNBmuTbv+upsze8aTuhrC2SF0X8\nTIkpl9msAxAECWAkm+yOGr4/+7RvT5/S3NF136aPrplRtnj2maR9ckkh4ObI4cUJMz4QW0QTsFrP\n0nV6Pqnitp/MniDrTR8OMJsTZS7KdrHReHJXM2LAzUCVgloFl5SjscI6YOnz52YEJ88fdeY9hhv2\ndTzQv2d9aPIdgfG2Zb8NGETkt8CQoKxUAkzUy6LUZFPRoFr7sE8GBwOyQcCQPrJ7jR8NzlwGzbsZ\nSaAtTCeMWVNvLI8JaxXLZiSmXIoBUqOLJ+mEcyMJgXQ0MLWk4JvTR39z+skAErRxcknR7XPOfmDT\nB07sFKO1Ixs4QRKlX8X0MsOQurGEm43fCZrvYh7OWL1Sr8A1AEBFJ+IhxDlzeVTRhr4ewa0ylsfR\nFqZrsPIkp/a/yf8+ffEHe+MPkevev38/sf0XgfFX++Q7DT+jKG03fFBW6lm2MHDPmqSOevnwgSX2\nVeMUK7pdbR/po9BYOFlv34s6BRQY4Si0Ktq0QeEImGLvkjZuMyHhBfN9usvmmxdlCG0QniQhkIYe\nfl8ylbau9GXA7XPOuvTiL1z6g6et2YmpJk00/kfhbAug9bvsMg3ZJBwXhRKIKlBkKKA1Ty2HE11q\nnX65dKcXjeHOEDrDWBlBrYKb46ijeYLNAIBF5QCcPMnZ2M7UgTf9Y84jbZo0oq+nbGxHYvsvik0C\nSWBYYdnC4MIb/Gd8oye3TzJEqZnrnFZyhVPZXodtrWps4mh4SRalKbc8y7Bv7UxzBsOAvjJ9VOEy\n9OKQQ1BklziI33RikdWEV74zpfPgdpP5AJ9e/R64+opCSbKD2G8CAIK5aIUhTEXKB5P6im6Z88VJ\nJUVGRw6LdOC3e/w5mIRbXM+Hhj7VA1CACNsEOmR+2Jj7KzoRA36eQJOC5S1oi2svh1yeIFuboye5\nd9vDAA59sOzz5rMtc0S63zo1EV9iM4URh4LePHsKDCHKVM+yhYGyUk9un2So272aozHiLpW5o/MI\nWNgC6W8QA4YIGp7+DSxjlh/8JFF6YXCXAhVt2sJlIB6Bkgf1NgAr4ojoQ3gicbw9686O8+9KjJrC\n7pMsmrJrura1svRrGkIbRrgnSWhIeWFwqUj5IIT0LXOmXzHjlLfa9zy86f3LZp7y65c3A3Tf16Rn\nHoVWjXTLmTDauKnvJxFCPIJEiKpHzsOt9LaWEOQIIvHcfrStnO4o2asnCix2CfMNTpwPIHXgTcDW\nNpI59DqsLHUi8nv4YNnC4MKL/S+3Zu5Zk2zfnTX+p8v0BEjXs5GqrKr7yFRQEWnHKLaW07SilDUs\nLXXgkhyiFt2YtXklXwoILtRbo6BWQY2C5jBWRhBV0BkHgJYrr0mnPbtOuy68s6XsrdW7T722/Ut3\nkSQ5Uoe+OzSK6ElCSbKE0JAGhjzVpoFiUknRFTOm/en2K2+aM+OmC2fI4WK28yoNF19yxhkzEqMA\nTmtxLdIKPW+T6yWa8pHPHhDQb0JprBERaQT94yd2XHNjp9ld5BzmGwOA0KT5iZ1PZRM7HeSi2r+d\nyKQBQUR+H2WUlXoWXux//mdcJrgBTAbYRdnxAdy8PrSaKlJmgmea1hIuOYHJP4YqKsZiVG5xxLar\nWVOPAL00snsQZrVWAJps9FoLInEA2PfFa0iv1JjJyhnXvn79q+1fuss0hQVc479HDoSGNJSQ/ElS\n85shJCUTqrU/qUDN9EkWhqab5syYN/P0WLtS/3Ls6zNOW3DhOX2S7+CFhz48qNT9/iVdXINzpiEL\nouM3ocj3SAit7ksD7cz8SQrQgGZgTGbimAmXqh8/mxhnUrbcwp+Ck+cD6N/1lLYeS9QAMSR3/nfB\nGb+16SEwjFBW6llaXXjvul67//Q5X/dv+mvK2l3aqC8iZ9CHkF9qbVTvYQUXEMHkENWQSKVUkqSX\nU/Fn0ls4ni0rK+YgU8S+/3E67fFBp82TKFBSSaSzoDBPJWkwoQ0nipI04gSS3WGXg0DWn/Kkjkit\nB7mkuGrGqRUzziAfC9Q05FEXyKOuvujQpta2vcqhvI4qJ+LHsAmFySjnMJzZN6q4DtSe1pfaNfOJ\nR2NkuGWeYK11+NO4SzYDUKEWnnJr19tvOr9lfCddY/87AY6R34zzwTE/H9ekeo5gqY4RiKXVBQuu\nD555+QHzf3rv0+MA3Du+b81f+zuUTE59r+HOimRKtqU+BDeKNSs0LCBiHVX3iVSTkYghEQKAwMwv\ndBb8Xbt7Hb1v1JZ6KzpR02aMvdh94XfZPYmFeaBWZVFJiECY7IYvQjCm8V5z0XlLb7jy5vlfyzU5\nZBrWccUXNuhrLrhFLkC2HwtNpCVCCIVxS5zOYwm2LW0AFHgKJxWelivT4AlNBlxsI/5x+eYkCRxz\neELJsqxnaXVh2QQP+08vm+BZWl0IembSgrkFj3y3ZOp4ahtoomLAoA/BVOvBNbXWDJaEx6IqmJUP\n6AxjdOU5isz5Uw33tQqdqFH4mgwAcCB65e4Lbwfgsyo7ogZyYokZk0XWth1GnIZ0dOAQ+R1COnEY\nP/v48Kjx4fLm1o8/im+3Td0g7USLkq0SYJlRrs4+U4SgyjSWoAaIIRHBzW34Key3rgoABM/9cXLL\nw/6yKwpPuw0AaFiit2BS4Sm39m572M424qoeCQxDLK0uWDAvuOm91L3rehfMCwFY+2KCnZm06g/d\nU8d7F8wtALB2Q1+HkrEIz7PUh2rzTjniEbWqhCJrxVID35qxd+NGxLnKW/x9a7nQCVkThE0KwN35\n/XveU9MepOHxZbJpTcqalSS7+r9DfFjX8a8kCYHkhKw/7Um5/0SqPyUdGdudGW83vLm1qe3si6Z8\nBKvUDcKo/J5xib2Jo4mLO+KGhDtpGB7sGb4BgBZitCKOFRFbg7uv7Ap/2RX+siuAnChiKDzltuCM\nqw6sv9j8lgnP+likwR53ICbxsgmesnnB9j1ZJoeAXJ5ZRyyz6g/d3X+Ur68o2PRBctUfujv2ZnSW\nWwcfpKynWGJ/buSGGCjW0UPZsrH5nIu+/pf4r7W7m+/LoiTqAOiO2kuOndT5ZS3XlZWrJ0qSw0mS\nZk+SHUbmwX1CIFG4HUJxuNMj1Q8XoRVSMwmrMAeC1x97+/WGt8h14qkPMQuIATWmTMMYLaAQRzxi\nKycqQmhmpg85x8bfatYu4yQK1tlqDzSH8WkLaoBpsNi6hr7VCljIIR6ezsmFkdsSylNZZQdZmyc0\nOXCSzlInDqE4HpGTRlGL/Ovi65TrKwp++d2SOWcHzr5t7wD0oXX0JHKZXpNbVHH1sfijY+09lOfM\nnH5SSTGg14ps7uu/8fWe3Xs+2fLOyU/98vPzr9h56a3BXklK5aSRUJIOH94VK1Yc6zUcPajqe1n1\nLyolGsmXVTOcAMhorzyJa5SyrFG7UL3ZXGPWa7gAvcjSizS0iwxYizY8LXkA+JA1tJC/hp5P/uuf\n2aqmpHEq0BYGdgOnArOBa6m68yCgQFZw6ieoAt5KAE1AE9BNi90pUJtR+wkkIB5Cpw/oBoBQAudu\nR6JTu0W4E1XAW+QWsv5t8iDNiCpG5z5UdCKq0NkSQCvQDal4ku/06z0TzgPgoaZ1T1biP0pZCQCy\nkj98fvCkr/mKy9PdH4Um3TDqzAe8xbMAZLM5+zu5Zi0eD1R6LVE2D2a0fWjC7w+lUwAC6VwJdm9G\nu/bQi4vmTDr9tDBOLBAiP4YLkHyZf/6/fd9cdUiTBN2mdNdi4FTgCXT1qN+9rChc5IGETR8kLSjt\nVaAb6NaICjLQDTyhUSy6gSbgEwDAJzQoFMCfgSgQBZ6wSdejm7brvnWdFCoCsL09brz7bkChxDxK\n9kz/pkf+cqZgdM/kM3d94/qDp5/vyUKCJBEyzkqSR0VWUrOebFbyeFTuL9SsREiU0CcjzqQvSOiT\nUSaArC/I6BPeoJTRnSEgeQPIGE8VMELf4aJ5p59eXuoyZNhAaEhDDHPk9+Hj2ftefq9pK7nO7TXj\niNvoJRXN2sBQHFcCMTlXd45Eu5K94PI4ahT8LoyVEcgKbomjkm43yY06Q/Y1V8hJSDEghpURVMSw\nPA5FQXMYH507yXPKFd4ZN3vyM7iRDaYnNDkoGxUjgeMUm95LAcBMqnbY5Jl1xDKbPkjOOTtw93XF\n13+r4Oyr95opbUvdya9sSX6nYbc2SqHD+eqL5BaEdvloUsfcg/Nnnl2EFCTMuqgiUnnu7+7+mfnu\n3tETfGde7Dl3UTpVgAxUb0YCkDaaMXglCfZkn4+SNAQ4npUkIZCOOAaRimRAR+suds1bPiJxrADq\nTfImJJeEK790VmX0pW/fjzhkBZEwWiKQFcyKQ+FLdSegKJilaPJlMXfTGuCqsH1BTAKatQ4gBrQl\nICvYdu3TZo4dHA6/mqqrpV5gyLHm+VT7niyi9MAIRy/Oqj92P3f2WABlGe/dV49e+3IPCwovO8l3\n/VeLy07yTftKqP3z1NrXDrXHUi7FG2V9RGitrf3ttz+8bR9CzMElJ4rPuehrH7W+26McIHf3jx5f\ncPbXghcsBJDMpjJZnwqA2k6yvmwaHl8KGT+8UKWUBCqWCNHyf70+NQNdcgLzJLlipHmSRqLT2BNy\n03mHDULIvPf81i5Foz/zXnN5HBti+FYbQgl8tfyLc+MlF1bMOXfd7XJNxX45LNdU+OUx5NC8WS34\nQmLMgRu0DaShAgM4x9BqAEC1jHiI21dW0a7r9DUxgVrO07tn9j/m/3Sq3/3kCAMsI2vzBDsbTSTG\nH1Hkzu4zR2/zaACA6ysKWMPd1YXPLR3/yHfGTD3Je/fVo7fUnbz0ijEAsv70ssvHaZ3sqi/GqMna\nnEKgP9mPFJ3b1bqjEOlCNV2EVLGUAnDORfO+tvDW6BXXh0rGTZk9v/zW/yr96tVBT+5dIXlT8GZU\nbwY+TctJUwJW/So5apL8daBSVnSRhICz+O/kQGjyBD64T2hIxwADivx+nxrrYLPXjCSwRIGiYGzi\n4Hnrbu7hQifkmopQ5bl9rZ/ub3gpWHle8Q3f6FEDAPofa2QT1gLQp89quUOsvNBMKruWWNg9okou\n+/Bv9W/l80QZP7yHVZBWYFhj2cLgxa29aKDKimNczAJOIAEoG+8rG+9bcGERABUpqV8j5jWvHWz/\nPOVefRFWUQytAFCroDmMWgXz41gMPPb7l3ZslFTgaxfNLo9+CUAxUhhTVBSOjvni7N5soJfbLAU8\n6aQnncnqeDbryyLlgT0980oS8j67y4wRdSaFEEgWUIM5Thh05Hf+h1CYUaCm+yTtpl+94Usd/6aZ\n7Jwrp0yq/KL5K588ZpQ8ZlTlOd3UbBi44ZIplRf8/fqVMFVw3UBH1QCdccSIl3i1rd2jvA1hBQrQ\nf9LE3XMuH9zDWoIPWBI4vpA7u09x8eJcr5dGDljT0gW4WP80GLLuqKD6Da1Zd1UEzREAh9AJAI8/\n9eyYja9Oj84458J5pEMx0YqyoEFI6M9qvCN5UyqgAsSTlPYDUH0pCURJQlZNewjpOlibXT1J+cTa\nnajlVkeiyc4WwSNSOHVACKlGSi2Rc7q8Y00DTK6yEEiW2FM6Fgsvg5XhjqAVCCX0s1tlrR+6cln/\n+IkdV/3zW6vXf3b1TXa3Sx+tAj3iEIrhAHJ2H0A3UBuAGLAYqAbqcxVAep8e98vvljhPxc6CWTp/\njDahJezaqeSrpRQbA9ZHAOSKBQM40Nn1cvMmAMVIFUvW9vyAN+X12L4fMjYU7qMWPK9Phb5qA0xW\nOweMnMINQkPKF4d/AoVDKpKDEa+ktPirN3zp1cfeJR9t9poDkEYE0sVfUdf8BVyBfwYig0IJjP3C\n3P1/36DdoJYmPNVp3TxnVO2d+409F14KgBQ5Ur0ZLWLel0Ham/Vl8wy0y62KRiuZIQ6hOI5gPLtP\nn81aNsFDKjh4gqlsv54jbNIBp47zAW5ZcaRASR3NyaN6vNqsdVxUjnrZ9lDK+3+04qyZ0X+Yfx2s\nlKQktdfplSSPUJKGFiNdIFmwRB7I0443VJh9wznfqDx9xfW/t4vBvuqlf+2VBrie0nFYeBnW/EXW\nMziTcAfnzS2cfwdCC/avulF3SwBA4NaNh/9cDA5ySOA4BTm7b83z6XZF8/CXTfAAWDAvtLTa0VKn\nl0nEfl52ku/u+eFVT3Xa7siqOD1JH3RaTSl3PUk5sz+YfGf7p8VIdUvJHn1YbIEn1e9JA0gCzJOk\nejNZn5dtuZgnSUtjoDZnJpbI/snSk+RaBXiQOA5l0kgXSEcHDpHfeaKvtPiCmnM/bPoIyiFwbFgk\njz658mwAhWqayKQipHrcSkIQSAsvly/+SmzhMrOE++TpJ0kfb29p0axvJ7b8NaPsIbeURsneM83V\n8QQEjMid3fdY0k4O5b8jXHrFmAVXjzqr5jPrrLiYlrXw9385b2N718rmjoUzJk6Je1/6dIeCvgZA\nV0TVABoW0dnZtb097pt6NvRKUiKjY16iJLEQcIOSBM6wNwglaYRjhAqkoTqE4sidQGHGBTd8+cyL\nT9/RurPlsbdPqyzf2tQ2rfKs6TUX9Fr9JxZLqW7VD6AYqW74ARRLyW41UKTf/Sml49IL5ntfeFXZ\nvY9IuMyE8T1fr+CnKpz17eBZ8/o+29L/+lpPeZX/vBsAZAYffa2D6tdyOOyQTyqSc/zSkdp+CuSB\nslLPwos9119YNLBhNoa7srRv4VdGr3ntoDErjn6s+fK4aeM9kXBpzczSVDqAOfjaN6bENnf9Yc1H\n22cC/b2uYRFvbtzwjRtOA2BQklj8N68kwZfJAgYliUR+G5QkAKySUP6l7XRHpQwu1u54cz6NUIF0\nzPH/2Hv7MDmu8k70111V3T09PaMZfXjKskAtI7AwwWrEcvGCMVYUSwOXBRMIWW2iTDvBWXJvsok2\n+GqvY5BFZJ47sTdadi9L7oUs3VdwlU0MMdlkmTGrSDEYTBJMjwEj4g+1ZFmuseyZkWamp7uqumr/\nOH1Ov/XZLVmSe6Tze/To6amuOnWq+rzn/Ti/9z3dM78zaNZ5JHtQHxjUb8iP3gjg7WPvCFVFXSKX\nNBecFADrVz9o3/4ue+rZ7Fe/Xv+F98zu/JcA4NU3yuBI6s3Xpd58uxm1enueeDXM71efLSvRU+jo\nJFHW6598fNUffGDlpj+otr5jflIZAJr/1xbAXzjxmpG+7bf3vff21x09OfvLX/12B6IqsHnzTQBa\n1AY2yhxAwZLT6kBKsUygCQgniSXJCieJgZZbtckHqpOiNu6LfA9XQZKsFOxLCE298AzcPvfyUf7c\nkdXK9nfOlg4s/eovZpRlkzUscSUjmvK6fpX2Bx9YuX6VBvAtl1amPr3jGnFCQjPBpS/DWXPrVvQD\nnYiqwD8vvDkXVgy4L2mlk2YqSLRTPWE3ZrAleGJsUr2QoBxNkr3akrilQvKCi4HgmwJwtK50g6td\nnGzPIPP78qMv2XoWmqn+asCY3/b5l2Y4X0jmdw+iY22UZLqD7Pjk8d4PrJr8t9d96VfWrl+pfep9\nq5/5gxs+tX3EiRXAjStSv/eeNwNxW/z9L5vfIg7nEmZ/wswlzWzSzHq54IwCnlAsV2mJqqM6ttYa\n3qL+iFBLquqopIJDkAL+ajbu61y1IbmcwmDLqa+vOS4p87vHkUrapqOmFItF7ZRA4nooLoD5LSHR\nQuyOMOtXaevfo+165woADtqsV5aizmocs+T0TMJsuBqA3be8+ZduX//uT0+EbvH3xU//mxrUGpBL\nWHCxEJBTYaWZvpGvNuPLrV5AivdF3pNi+UBOFp2ts1B06TZ1jwxe+7TcC0CCrQVxU1HYjBfeYHQd\nsGCJMGZshkJYnRK9gIvuJIWeE+UkpWEByMBet5T97fe85boV/TTF+5qhgV987zuysFl1O3EVdZJ8\noexWniwrbcduHeskgSTJgjhJvtJ2uERO0vKB9JAuPs5rB4ouC37HIAubsRsugPndO5CpSBLd58kK\niKAFTQ0MOkkgwYm7b7nhwzetf+zEzBe+/WM3gdGbNv7yrW9fSqhLvE22J4XPScomTBAxbTtJSlNU\nEmIHfAlJAJJqUw1sIytwUTbuu2LYDVIhLT8IHSZUUSiCzO9lCrkJxZWBV59rcQFFJn1g7NbrVvR/\n7Kb+7Zs3AlhKqHX+bRY2ACpTgm5Xc0J6nlAsl/BOxZ4UIPkM1NLy70nhrTPyavakuGJw9dqkF2sT\nivil1IuCDJq4eLy7fr5Cm7tIhIXLj2DszlclrBtcbfyl5YpOFSadVOsEFsdj8sgYRoJux7h2aU6f\n63Ob8LKH+ly7j/8p9qSgdDtGbcgopqDbpUTiQmBPCqGkgiG7UEQxca7CPSmuXoV0eRDD/O64aHR5\nmN9ZrpYElejyML87ZjRdGGVWopfx6q1AN2ypyaeTWmcSnQTC/2ZyJ9RPn2szg48dzIKuIVms3Gp/\noOIq00mMa9c+qjYdrnWaWmslKaE6CdURg9m3ktR9uVWf/XSllluVCikSryHzuxcgOEUXF5eB+S2x\nfHFhDCMfYoIWaW+Okc9JEp+ZkxS8XDhJ/i8IuwHRg1w6SR2RcF05QUhISEhIvPaQHpKEhISERE9A\nKiQJCQkJiZ6AVEgSEhISEj0BqZAkJCQkJHoCUiFJSEhISPQEpEKSkJCQkOgJSIUkISEhIdETkApJ\nQkJCQqInIBWShISEhERPQCokCQkJCYmegFRIEhISEhI9AamQJCQkJCR6AlIhSUhISEj0BKRCkpCQ\nkJDoCUiFJCEhISHRE5AKSUJCQkKiJyAVkoSEhIRET0AqJAkJCQmJnoBUSBISEhISPQGpkCQkJCQk\negJSIUlISEhI9ASkQpKQkJCQ6AlIhSQhISEh0ROQCklCQkJCoicgFZKEhISERE9AKiQJCQkJiZ6A\nVEgSEhISEj0BqZAkJCQkJHoCUiFJSEhISPQEpEKSkJCQkOgJSIUkISEhIdETkApJQkJCQqInIBWS\nhISEhERPQCokCQkJCYmegFRIEhISEhI9AamQJCQkJCR6AlIhSUhISEj0BKRCkpCQkJDoCUiFJCEh\nISHRE5AKSUJCQkKiJyAVkoSEhIRET0AqJAkJCQmJnoBUSBISEhISPQGpkCQkJCQkegJSIUlISEhI\n9ASkQpKQkJCQ6AlIhSQhISEh0ROQCklCQkJCoicgFZKEhISERMfyEIEAACAASURBVE9AKiQJCQkJ\niZ6AVEgSEhISEj0BqZAkJCQkJHoCUiFJSEhISPQEpEKSkJCQkOgJSIUkISEhIdETkApJQkJCQqIn\nIBWShISEhERPQCokCQkJCYmegFRIEhISEhI9AamQJCQkJCR6AlIhSUhISEj0BKRCkpCQkJDoCUiF\nJCEhISHRE5AKSUJCQkKiJyAVkoSEhIRET0AqJAkJCQmJnoBUSBISEhISPQGpkCQkJCQkegJSIUlI\nSEhI9ASkQpKQkJCQ6AlIhSQhISHRKyjt27dzw4adGzZMlEqvdV9eAyRc132t+yAhISHxGqO0b99k\nqQRgbO/e0WLxNelA+b776BE9n99RLBb37r38nXmtIBWSxMUHk+3XSrAlJM4Ll18ThArI1kSidXdg\nBzAFVAAAR66mKVoqJImLCZ9sX4UmnsSyA9MEPjWAS6MJQgVkulplAboCsAfQ+bcGUAYmgNFicc+X\nv3zRO9ODkApJ4mIiVLavKhNPYhlh/M47J0qlKDUAogminP7zDQYIN2iMCIiezxvVKoBDpBuiMzsB\nPZ8/dPz4BT3iMsPVpZCazlft5m9dosadeqr1oaG1DjVUAImGlrTUpKkmLTVpaaj1W3bqrNtfhzqb\nSD+nDD6f6D+T6DPc7LP2ypebOaMxPDe/JtFIpZaS6VoCS0qzrtXraqOuJEz3dXPzAHL1+VRjXm3M\nJ8x5divXXPD0hh+/bEiffkideyJKtu2hLY21H73MXeqIT9//gQ/c8dbXuhcXGRc2yNnobQ3dhsoG\nrbqYUWrZ52vXvZjMPqsM/jQxPNW85lhdP7W0Ov38GuWc0lhI1+uqU8Pr5uZz9fnsudMJc749FC/7\nIDxfZJ9+IGHNRqkBAK42bA1tSZ05LL5iR6w127Qzh0OPR90rc+KLymJbqTCjbZQovwJwIOzC3UAF\nqOc/3sxefwHPuLwGuWTZXXwk05bviKPZ4nNCMwGkYQHIwAaQhd0PKwcrlzSzCTOdNKE0oTZtDU0N\nCdVJqk1Vddjlc31Z0ZSdHnBTA5f6cboEE7Y9XtnWgTHyrUTPIpkxERi6jma7mrUCS0NuY61TW+/O\nvyE5uy41k9OWaoNN9DVTGUtVHTeVoMMykcq1PvXM4AyFOvdEwpotBLQRAB0oAAAS1izTOmwkF8iR\nqONRYCIgzme2mhAQkA8+sONabONXDNTXugNXDpIZUzhJLaRtNFQ3bSUampNq6aQkkMIClnJwAbdv\n2G20Tk5gIalBRc1NvaIt2YBjK7aWVDQkbEdVHUV1m0jMQwGyAHJAqjEPwE0NJMz5RCrnd5IuIzrK\ndsWaVWrPXZiJJ3F5wAZwMm05gJu2mw2VOUyD1gxq6Gs2AWSTdk6zcjlzsjEwj8Gshn7VURfS56Cd\nwsj1jXkV8IzG1EDP+knq2R8gVg2weFq40//UPTpwIOx4MBgQEzzYCowyAQHKQAEoAZPAGDDKzywD\nAOwVb78Iz9zzkB7SxQQzM0EtzbQNwE1bAJyU7Wi2o1muZmmqmUmYGdjDTmPYbaxyG1nX1hO1keTC\namUhpy2p2pKbNs0+p5F10ddUMlYmYyuq66YS82llri+7kBkw0x4LtG2Z4nIbp0K2S8BOHoIQuKpM\nvGUNj5+Utt20ZffXm9naYHZmJHH2+ua5NzTPbXFefpfywg2DJ5UVM7WVZmOVnc41+nPW4rAys2Jt\nbXCtNbDWTQ30vp/EwmvliG/F8SinH8BuMtRjggHxwYMK+bAVKAMGMA7sBEpAhetFNzV0Xk+3TCEV\n0qVCMPpB/0xopqaaaVgZ2H2u3efaNHCXTpopxfIF7gCIwJ2AnR4A8JoH7phs7w6IE8NVZeJdGRCj\n101bjmY3szVNNVnsbthtrHbrq5WFVemz6Fs0+xwRu2N2kmjEYyH1ErQzh7NPP5BcPA4y41NUiHsU\n5fQbgaGu89idUntOnNwxeMAaoQdpTE/oxaA9x55CnXui+wfvfciQ3UXA/oONg4/Y9+5K7dquRQXu\n4NVJSSABZGyzz23W0cwkmqtY7C6BhaQ2rC0CMDWNBu6YNrLVJA3crWzM2+kBtTEfEri7jNESRxtm\nHyi/rgwUiWzbQ1suT2ckXg3EAGaxOwB2fz1pqSrmBmtmZsnsazb7XPvd2qlc0jyWtE4l7Xl1BYvd\nnbX759MDwFpGcACQYHSbngncUSaC+MAm/QI/xyBqID6gpwM6GeriuHbmcHP99fQurJ1SIBzHzjd4\nB6LIfgBcLmK+p0iffih15nA8n2IZQSqkV4X9Bxv7D7bCdHc9WN9/0Ny1Xb3nl1oKKZm2WrSltO0C\niYYGgC4maZaZsexhF3BazmoNqp6orVYWADSc1AJgpxUTKSCZXrJQ1zIZu15XhU7K1QfYSpLARdRJ\n2pnD2twT5pptUbqEneCkhpTF41EhcgapjZYRWOCutZ7U0Ny05QB2fx2Aplkj55Bx7C3Oy/2K1d9n\nZhTzpGItKsNpLZOrmwtIPY+B180BWJtiS0q9pJMEE0GYTTq3mdjBSa4eGMpcUZW8uoRpLAM4BBjA\nbr4axK5VFo8zx0iojXHS7DhQBnYARW/AMDSmJxQSjQT6n8KaTZ05LBWSBFraiA+NExVn/0Hznl9q\nn9DWSQAAR7OTVvudJzQzbVl1qBnYfa5Sh5JN2P2wckmz5pjppGkqqt0K3CUzqpNUm7CTquo0bYV2\ngzpJF+W5Oppg9ATFmkWsOC3e+NmL0iuJy48WxwFwuIuf6ltI11LDbuP17sJiUlvUUrNW/1Kqz+xL\npTNWxk4u2hoj3a30mkqvrU6KT0uA1zESbO8KME60wjhXUczpHyUmF7xLp+nTD9G7M23kix8USLQw\njhAEgEcC1bknRIxOaMcYPsWyg1xDukDc9WA9s30eBeAQt6x2AIeAUWQ/+Mpvfi6E8NaiNmg2ZTdk\nEuYKLPW5zYzbzKC5ym2sdusjyYVr1IVhbXFAranakpsynYzlam5CdViwXrAbBLWBLia9enZDR0qr\nOIHZj/HcWRpSl1guSGZMQdIRBAfBcaAEh1v6n2UcB0pweH5oQHAceoHgEM8sANBY+1FXG3a1YXPN\nttob77bWbDPXbANXM3Rpp5UzS67VA59FAJCBzROHgCJwoDVPYDc5IZ7zzaCdOUz9JLF8dSUlV0gP\n6QLx6FQTAHSeQQdgvD0Hf/tHbUZDy0kiFHDajqaadSuVgZ2Bwp0kJQdrIWFmE2Y9mUopVtNRgVRT\ng2o5rp1UVUdVHSDp8OnCTA8M/PQL6dOT5us/1hx+VdyBOEPyqXtY5I3aaJP8QyhESD2ZPR4f/ZPo\nWQgvn8XuHM1OatYKLC25ypKrrnbremJxWlmYTZ99qW9luq+Zsi3bTjZSCvWTXlsieOe0BMBNDdXe\neLc4LmIAUU4V+8e+LXOPJ8r9ioof6MAezgaqBFaYSly+BBLWLMJWaq+Y5AqpkC4EBx+xTkw7KBDz\nSQyQCaCAExXn0R9Zt761pXuCgTvxWdHMASzAyvW5KtAAAAcjSg3AopoCsORoAGpNrZ7VMoAKG3Wo\nahIAk/nhn/7noZ9+gbWWfvr/dtPX2KvfZV33odCVpI7LQjGG5ETABBPsoHLAJBTHWZvswitsAfZq\nAE1OAuACNuCk7EFLEwSHrGLnNCuXNP/HihWC4KAupBdVlXEcrmE6SdQTuew6qZuUI8pEAKE8xC/t\n7OGrUPFnxihCFs0T3B8RFZwIXBKzUjsa8RTLDlIhXQgOfssCgEqcUfTZP1+89a3e1AGaJ8t1UlKz\nGN2O5ckyxt1qt07zZAGYmtbMpGxLY3myqYyFumaryfm0wrRRWyc2XtJeeNi67kOeW6cGtBce7sjM\n6Sa/VfxJq9VV+MugoITaK3IB9ipBWyc1NEbPcYBmtiYIDhm32ac0+xWrmlspCA4Z1VEX0ozjkKt7\nCQ643DrJWrNNWfxSvNkk0hJYkIB9jneq2LeMsBB/ZlA6wFXIJDmZmrUISBnIZFPi7hTTeUKxLffk\nCqmQLgT37kpvn6oBcUbRrtu1kCu7C9xlYWdd2xe4qylNW9NUEri74W9/f81TXwvXiX9/p736lsa6\nXxa36IaZ040hGZ6g7uXOloBJfk6Bm5A6ULyyFmCvNnh0kpfgwDgOeW1GEBxUK6HYLY7DQmZAEBxe\nk5IiLC0h3mwSMQMaBoiXhQqwk2uC+DNDdWGZdyDKrC3wP8eAaS5lI4R8Mc6vMng30qcfUmrPLV/J\nkgrpQnDCcIAORtF6PUlzknxRO3CRdiyL5SSxwN2wCwArnQaSqCVUkMBdTRl0MlYd7cDd4AvfR0x4\nbf4YE/70ya+oM9+PWRYSw7cbQ3Is7HYVwp0V9FYRi2AQbNfQ6J9EL8NHBEfaZslJAAaBzFIOTfS5\n9rvUF/r7zR8krVNJu6auSGlaGgDwvNlKTmpVBL68RHAWpm72b1AWj0elHAltlD79UIKHAdApFg0y\n2uPP3MH/LHHPRg/zexiECE94GwHxhILOE7g3tqwlSyqkC0ErZBdrFO0/2HjkgWyITvIG7phaEnmy\ncNHnqhk0+9zmatRDCtwBLHC38h+/nj57Kk4nNl5W5o/Z6XXKwtPoblmoG0NyFH7oRA9FSYsvhbD7\nBdiOi14Slw00dieSkxzN1jRrXc3MWMOzzXQ2aeey5vcV86Ri1ZRhIJNRnXp9gCUnMbLdZUtO8iUn\nRKUcibQEUZCbnVDuJAt0nMefOemlldPSDPGxPp8oGbHUCfY4ieVMbZC07wvBvbvSQIcyWOEhOwZS\n4I5CFLgTxYRY4K4/YWYTZkqxEorlKq1iQsNTD6NjheAXvqGdqyTMmZhBTyudMM4ruCgKCFkKaiN6\nO0TQW1kL4s+tXHLiq9tpZw73P3VP6szhhDWbPv1Q9ukHZDW8HkEybTEiOM9hsBKauSKxOOw2VqOu\nJ2p5beaa1Fk1s2AOWHbWzWTsZBbPDw2IwkLtYleXkgjuy15go87Vhg1e40oMeDbYfL4FG9UxsiDG\necczK/xzkBQeL8J6QJQQzVwX7trylRTpIV0I1o8kgA5G0a7tnGIXH7gjhRsSgAakrdSQ26Lb0cDd\nC2oNwBLgNJU6tBff/4mNn/+HDuu0q9+tvvwYzodfZK3ZtnpoS+XpByr8hMlAFC7qdoglGgku0ASZ\nGmIcoCs4HX35QsTuAAiCAyvikAI21M4JggMt4rCilhAEBxG708TOSZfAT4rLXrBmXW2YxeXYwBOO\nlI9OfQQoAlvDnCrfFkrF6DNF8CDKs+ky1qd7ZYeCulPgivb831lPQCqkC8H6keS9u1L7D5pRZbCE\nNmKI2ZkClkp1EqxUJtEucNfnNrOwcwmrP2H2Ja1G0jaTtq00HVWpXbMWHddpV9+SPPezZKdB72Pm\nvDz3RMp7gq/lCkmYKJFz4oMP7PIR8qfgMvlYfx1zoZbvmu0VAx/pztFsZGvpmpWBHSziYGf7kvVm\nJmP7ijhcuuSk+OwFsUqUPv0QK6kQOtiECeULuIWOcxAaN5UaQTeI6kz3EfIozl6JBPTo4y9HSIV0\ngbh3V3rXr2k33L4YNIrqj8RFIWiBOzRUUUzI0eykpSU0UwMyVjtPdnWiDhcLCW2lugDAdNRmqu4C\ntZG1xo7f0ie/EFMa0k0NqC9/BxGDvkT4RcxToZtj6hH+kEgvH+dxD4GOW8uwvh3oRAfvmAulSVfp\nNUWQCG4DSUsdrM2I5KS+ZLNfsRjH4cTK/pTmpl9xAIjkpJVAm+CAi6mTukmDFatEDDHa4hBQ6Lqq\ngo/XI5ZO4zsTJcLBCHkoZ08EA4V7t3yXkaRCunCsd5P37kodfMQ+YThsUKwfSe7a3vmVhubJJk3V\n0VqMu7RlMbod0A7cbdBm2IGXeOCu+uFP9P3cHZV/vyM0pFAGJr7T9iR2A2O8JnHJa8T1P3UP+0AL\nAoXoDO+RSbLEuptLUYwfNspjd0y2oxwgFk6JE2AZu+sBhCYnWSvOCYJDxm0CyCbsXNb8i8EVguBA\nkpMGwAkOuKgch26yFzp6PEIKxgM5quXYnfR8Abrd/KYxnQmlWhwJO98Xxxsn1SL8olT90nKMJUhS\nw6vCvbvSjzzY98VPZlgQ72cH+1t8hwDaZcEo0ragNvgK3AEQBe763GbWtXMJM5s0M4qZStpK0naV\npqM6J6+51hy6DnwUGty408NkoAzs5J4NAuur4rPBQ9VRDIUCV2zgdVN82eYUFW88YYxcGLo2K4qj\nBDf6o5f3P3WPr36lxGsCupsfAEpwWOssMo4DJTiwrSaTWYQQHC4Sutx5T8Age3dRsMHGBiEVqErs\nTnoMYngLvkNMZwrcr6IhhxhR0r3nRInScgzcJVzX7XzWlYKm81W7+VuvYQd8K0ktP6mhsjzZpKUm\nTTVpqUot61qpeSvXgDabSM8l0rOJdEVZNe1mDbf/uLVyxs69ZK5Ysvp+7lO/P/hP/3ggwjWpALuB\nAnCAH9nJa+brAT8JgA4cAiaAce9VFDsjQnns/K28HZ+7Nu4VsPgOI+CWHfF+ewTYDVSAev7jryYu\n8en7P/CBO956wZf3Ji7/IBej2jnXl2hobBirtT7U+l+2hl9M9P+deu2PsOpHpv5cfWSutlI51597\nObnwcr95LjnQaK6bnW7lJwmaw6vzkwR7u+A1uQw+DqP4BaPAHn5QDDbKXxAeiR5mLYHrFd/wLnGn\nKrQzIOdXvLFB0Sai+UQdRen3//LJZTTIpYd0WRHuJxEKOPOTXM0C4POTsq6dS1g+P+nYO9Y+fjPG\nQ9dYAw6+8Ht08q3u9Y0qneqlGoGrGJj5NhZm6+30hvvQhfW6x+uWbSWOHXuQFq992dJbr0xEcMFf\n5y6+IXF2gzYzpC6q2pKTseorHFV1klmIivV2euBiccGZh1TgkzLzYHaScRizmziD4fVdStxfF5dT\nt6lA2mH6rEwuAVAEjkR05gA/H94oIm3ciNBGo+TaIIR0//sP3zR+550RZ/Uc5BrS5UZMqqwDcIKD\npWimBqywAbefERxWow4XSGBBSQF44e//aum7fwEAGfzZJjyeR9HA3mr7RkGijtA0MaFnYaAFA+Vx\nAWt+yRhfKwqVE51XjYxnFom7g8wC1CAVeYXLvXLXlYEoLjjLmR05h+ubafD1JJEzu+JsUqwniZxZ\nzZzHq15PEvndYjano7HjilHFy0rYyj+LUbczWgqY+IiRHKyU6uuM+EwDDzEiRjFB7iVEqcR3whG+\n106gcvRo4OoehfSQzg/7DzZu2LV48BF/TuvFArMuAbialdBMAGlYzEliFPB+WLmEmUuaM0wbcTuq\nmsF9+XY7oUQdX/pezN4wCAuUT8RepXMbUMTcfOcU+OpUfBYhww6gRDoQbIpBlm/oKdD1pFZlLM1K\n9S3Q9SSRM0vXk+b6smxJybOedKF+kkh3BTDGR6wYNvGJqL5En9C4HAJSMOEdzAiMeQSG7iGeMAuu\nAkWD8YIZDE4wUSoReaHuXQEwqtXlopOkh9QtQncrj6IwxCMmLam1zTmvJ6RZJmw0XG3YxbDbAFCD\n+g9/9V+nKk+G2FG7kbgNowaGjnmoPgLs3Ar/ymcn7sujpCNfBYw2ddW3lhNvXYpgN+UvBW29Mvei\ngsyiA1yfjXqXo3w1uw7ItKTeQxQXHMDI0tmMYwNoccH7zIxiHluTo0XBW1zws6cvSlFwmt/tG2Px\nXFAGsaITCioFpbCF2NDqw4IKZHB6UcF71Rhfu40RsT3ExDRIcSMaEqfVjCCY4vv2FW67LeKBeghS\nIXWL0N3KL0whgegkX1qSyzeeYaCBu2GnUU8qqxP156tVwDvTl9piMaEjMwTdQL7qcedLvAK3j+0G\nYF++7V1VNyGTh27gjqrnDrv5ElEoxkigQyc2Zkx6hy/fkImckO2tsZntRW9aUkSnJC43hE4CIDY+\nt/vrKWt2dc2EhYzb7HPtbNLOpU1jYHhOWWlr/Tk0ckBdVS8uF/xFbVhbs02be8KwZtm4YhkFHcPF\nCKzZ+KwiKgXBHCAjesz7jhgkv2KMFC8OxRhf36UFhMaIDxcqLyLeuGMsquHeggzZdYZnt3IvCTqz\nff6uB+uX7tY0cAcgg+bjladm5s757SgvP6GeQTXf/qZEfHnDewVDSxt5L/fpkm7Yqww0FB5l6xmc\nlReMe4hq4jGBi61ke15ai0+ityA4DoTgwOrdvSFxVhAcWOyOcRxCCA6vAtaabUv5jwsHWsTx4sPF\nIJJChX6zl5Izzs2mYGrEVm/5VDHmK4Ejm/mRceLAhcJHUKLtMMQH+kaLxYiGewvSQ+qM1m7lEdZ+\n69vzR4yT5KsnxAJ3w24DDr49dQwgYy2aaXAUKBioHGvnLgS31PvcJpT08MuvBYoGvnys/bjiqijr\n8hBfFmaIt/UYA0JoL5+m1L0vu8S5FQXSf9HUct8l80pCcKMKlxe7823o997sM9/nxe5E7O75IX9R\ncAAuLpwIrs49QfelLAA7OHPBF8obI2PP5+KXvHqiQqqcxMQAKIIVFsQReq3RScSCtRt2dFEJYrlo\nI0gPqSPau5VH/OAnpp1Hn7xwndT6ICp/p9lSsA2SKpvQTE01M7AzsH/7PW8ByECO5SccGwKi81vL\nwNGhuMtb33qOxZU01snJ6GTrbQ5UTKGrtWJGKHm5FeLWBpFnybXrNbCBnUxbrC64o9l2f93OLmmD\ns6u12bw7d2Nz5p2Y3pZ+dlP2haGBM41ViwurHWW4nhp0Tl4zeGp45GIRwUXxEYY9ZIdWX3IC0xaF\ngItfCkuQKHszKCiC/hDC/BvfkhWT0KCIlYCdXjJeyXu7joE+AAYL8i8HSA+pA7rf+uhV3ihYT4gt\nCIMF7oC0ZfW56toV/QA3mYwOYlGvYG4IxhwqgdBzBZjQUc3EXV6t4OgQbptrHSvybSuD1qUoc0KZ\n5fG2HlWpUeHvUcJQou7dKM/eZXeXXLuewv6DjYOP2Pfusn7l1n52RKyMOpalaGbGNvvc5iq3MZKs\nbdBmam7KdNRaU2lYmUzGtu0kS04SfhIuiOBAS/RWCF9gLOC+CNCQmkE431HLmUG5YfD5Q0H/xrdk\nJRovequGB+MHBl9DFe10w9RYRgpJekgd8Gq3ProARNcTWoGltwyqn3jPz7Vu3YV1VM17CpwwsICY\noXe+fF++faBC1EMw9XWCxDEmu+N2C0SFvyci3LsJ3hqkNuol7D/YyGyf33/QPDHt3PVg/c13zd5/\naIlunmT31/d+99lNX/j24ad+fH3zXKH5yj9PvPjO9EnhJ6m5Ri5npgad54cGhJ+USOUSqRxwfn4S\nLdFLc71DrS9KpC5wbqrgC3RMpPWB+kMlHsT2seMEqEFYIjSE0Ax0ukZleK26YGfEQaNaLe3bF9HZ\n3oJUSB3g2frIB37Qt9nEBSPp3bKPBe4ENNUEkIH9e+9581/u/7DHOoI3NRzt4wWjnQ9BxWAMyFfJ\n5UGUAWCM6xwamgvaYoa3kgJzeqKy033QI+aIjtQGAIs3flZyvi8nRB5eaEJem4k61opm33+o1vou\nbd//N6/0feLpP/zmy9VZ89e/8U8f+Pw3vvboPzCCwzXqwpC6uP7h/+dNf7xj9bG/8BVxuIDkJF/B\nb0rJCY2VFUkNnjES1sP5xOUYaAyAJtJVuF3ok4IgZy+0b0wVifzZCd7OkU7GXyt+ft99gZ72IpT7\nlklHLwpc90eO+zfndclQLgHg0SebmPbOnQbwecDAru3aB9/VOfK5/2DjrgcbQ7nE5jco9HhCbbq2\nQv503KaCZhKqk2gqruK0FnaBpJNM2AqQaELJ2Jl6Qj19dnGxbraG3hSwADwGTAILAFrj8fiPUQBG\ngVFgEfgUMA3cwi2sU+sign58fabvx1jw7jSxwMe9DnwESBA+klgcnkL7bU0DBu+dAL12gYQgBCaA\nSaAABLVNDpgCDMAe2tIcuLHjm4/Be7e96U2bRl5NCz2ICxjk3WD/wcb2u5cefbJ5dtH9b9+1xYeD\nj9hnF92D37I/dt9SizpZBB1z9//h0skZ6wP/rO99n3kFaP/2505YT5yY/vS7NyoJnDl42NxzYPAn\nU8rS/OCxv1391EN9ztzs6951Vkn32UjbJquCj6YJAEq69SEaqem/Tlpz1Jr5Gh/pXyND8UDA3JkE\npoFngAVABxYCJpHv5ClgY8isAPC7iKH+DG/Wh2leBuVTnHr6GLAQ6FsO2Ah8DQCwkUcUP8LXvYrA\nODDJpV8I7BHgMX7y5/ftmz5x4pY77oh/da8tZHHVrnAi4dxw+yLgXzyJ3/qIgWbUgm9R4Utgcuqp\n+w8tfeVw/Q92Zv/VLTkAaKgAaNFVtdaXsDRzKVd3U2fRN5tI/3Te+k+P/uS7Uz9td4ymsFY8NDkA\nBrAT0PmGEQCqeVTzkXUfdQObCMuONn/IK4Qi9U/nsXURcCh43baocPyoN4eXpT3FF45s9m+or78r\n5s13hCyu2j0y2+cB709LBsT6keSJace/kSr4mGOI+O0/fFN+9j9WA03iyXt/WltIN+rKjSdfENVX\nIXJmY9eTlNpzmeqXCqRAcAkoexdmCoHywb7OjgVqE1PsDqSj0r2Vox+3fb540gPcQBQ81fibjvFF\nowOk8d1hJe8KRGB3Ano+f+h4T+ftSVJDV7jgrY/QRUbt/oON/Qdb0vWbn1u4/1DtV27L3vPBNsVt\n/1+/8pXvzu/dtrZ4k66pZt1KZWBnoHzl73743SefjRr4Pm0EQgMVzOzvVVEHNiCEqPB7Rz188aK3\n+Z1EhQiqq4hg0DVYuuyErmmyOwI0WQpJrrucuOvB+sFHrPYCfdh4OzHhRMZexaQY8dt/8++rnwgb\nwtj/5pm3/uJT7/1jSnBICD0Uy3EQ5ewErabI+QICwcVT3ZugqvMnjuHmeDoMgBTQ8z1uOTJBo71D\nmN6ptDEli1eAnQFFyFreweN7gkzR+h2q1crRo71cskGuIXWL7rc+EuiYUSsWgQESeX/J+eyfLzD+\n9/1/80r/bxy//69nTsxYv/4XJ67/4x9+5tvHMwmTFbj7zQ085gAAIABJREFU4QkD6Iq0LdCigQLg\nApCv4r4q8vU2USFTR77aTtk74A2pha7oipA6IuIb9I4+BMPxBhfL+KVaSWe4PGhl2hmxNkUMBJcg\n4revZ/ChofAmc88/nsuZlODgpgjHIRqinJ1vZYXm8YQunhYJsVvvtDwzSpIoBDZHR8ER+/LGyP/d\nZKBTbpFoc4zPNDp/kAPccGy13NvsBqmQzgPrR5K7tmvdqCKGuIxa4NGpZksVhWms3C8Z//pLr3z2\n6+falxRQnTX3HTmV6lt48DvH3vOfv3n67GIcaTsTopN8vAaGvVUcqeDLx5Cv474qvvc48lVPfcaw\n5v0rumP8/EPeMxE4Jwh2fNzLfYifC6Q2ujy468H6iWkH6JxjEL7Ej664oHduwoabUSItsyZTc6cH\nZ7+dGnTODai+5KREKofUQAzHwVqzbfCNd/toNTR6HG/usA/FaG7OGD+HPlkBmAp73IlOLw9eDkJ8\n3xgoDU+Eu6l29Om2Fvevt2sISYV0qdBNRm3rzwiN9dWjSyG6SkfyU9/f/+3jJ88uATxrPIgAaRtk\nQNNdWBjKOvblsbeKvdVwpRXWvLcFfgsaFfEFtePtPmrujcXOBZJcd9nQ4tEJ/6b7AcEgxtxk4Cu0\nL6lmUM201NK+vKfJNX/7hUzGVlQ3fOekWLyoDZtrtrnasC9Lgd48KvJGvx0LS3UQydp0S72xiDfR\nMRAH/qo6umUCOveHRslXW0lAnrLPxe/Q41UbpEK6VOicUcsQbzWNBXRVMD2hHJnAvYOIII0zCB5q\nBdiXR+I23JdvzwgP59tX7Y6owO/LPA8adDr5IHrajd0nYg7iTzoX0J0FJC4p/AFnsfdcKIRNUSIH\nu8+UETEAsotKq8lto8pwfXBoKVjEoZvkJFHOztWG2ZECz+PWo9MSDvF02t2c5kDFDp4ue/RcOcLF\n6TIQV+7klgXjozsJ//sQvzXtgEFlv7e1ESSp4dLh3l3p7VO1Duvy6GL5kl1e4muXoauiE4EE7goA\nTBqYIsue1TwMHWNVTHIZKgP/IQ+gzbmoVoA8T1ECwCmkO0Kab8UHWBdY4/kqRo3WOVHrt5RQ57P7\ndO96VYmTv5lSNNdss6Q2ulzwB5y7WeJnP+ekn4m6/e7ao1PNdhSYIboMYwIYNVA/BgAL229pvuCm\nlxxVdWzVU8RB647g4GrDCeuJhDXL/hRLNb4aQgLMRBwlZlDZe2aUCLI3YXBmBH3cbl6eTpwkYer5\n+rYjSP0g5wsGyQR5OtGTI8uBUC0V0qVCO6N2nEeaRXyXmk/xGmtHoLJjFE0NvNgO5wkVjLZv0aJ3\nAwDu5BtM1DM4qkcWZtUN3HasTU4V+o6KATMeHyeNH9uEeh4wkK9G9pRx6ig7qEAmNCax9KHZw9lD\nW6Q2umwICTjrgYm2xGtysMlPjL0JCCbqiWmnxReHd7oVv33EKDk6hJuBwR1bNmVfeGJo2NYyuZcd\ndSHNdqkYaGTXzUJtDCQAdLFLhahoJzRKke+PVw4Q1YSJWAQQIHNHd7mFMg84b/U+rvgW3gwLIU0G\n+eCz0qgYFngfELAUS7wRFrU7QpSlns9HvZyeglRIlwrrR5K3blYenWq2hqpwNEa9YzDeahr1rsnE\nxPfY+RMtyXCPArz5MnA0z8/cAUyhXkE1j0wdQKR4ZYba9ASDp51TCCmtehtnPtYd1bie+oy7QkBB\nlz1NogKoc0/IdaPLhvCAc5FMtAJs8hvj8yKZm2/drBx8hG7vBSAw3e722mrg1LsKMr+78V986Jaf\n4PkXVgxPK/o5tW/gFTc7rwHpc3X1FEaub8wzIngilWvpJPjzk2hFO/DoVoW4QezOBbIURE3EItFb\nHZmiFa+Xo3vDZQj4QLTQeNHraYHfK8oVmwQOkNdWClthQkBZ9j5kpYaLDFaR4eyie9eDjSefdQBA\nJ7naUzxlHMACj0BH1IAASP7bs2GpDQJ62wbL1LHuFG6bgw7kgPs34Ss/xxspelLo7WpcLYS5l3Hb\nHPL11gGRJa6TFPRTm/B4ROOP2ziRwR0vh/eU9e0jwH6gQMqkgtiwgSZx8sxhpfZc6szfukqfk7lW\nO3M4c/pr7PP5/UgcslJDFNbryYOPWK0qAkEwJplO6m1McYUkCmkA/vHPfuNR4BnSFC0vIvSADkyi\nVm989J1vqSeVZ9zhGlTLSaGpak036SRtW2m4yZV1MwEkgUTTbNdu8BZxSBt/k3DqB/iQg7eMCIMQ\nuEIYl5AN/o1cwkJFsMS/FYUYFoiY5Phn+u0ULwbxEfLmhJQxxBRr8HVyN79XsAAK+0GemZsr3HZb\n7/tJ0kPqCryAccpXto4epxUZ2qlFobsZUxzg6dd6WLY3uASwRuLje6PABOoZZOrYzdv7syHSiIBO\nbLNQjAEV7Mvjtkr7CuHcCMNtQ1TjPOoS1dOo+KXvoQNNtipmpk8/lD79EPsqffqh1JnDlgzoXVR4\nSjjSIRe98NOKGO8h9bRjLHwGXzSqyI+XAeD02cWZ488U8vln0yezCfO5pM12mO3X6oNqs6amTzVG\n1s0Cvh1mCXwV7cA9np1hAseYDrt5XxAWWEOECIayFXQeTxM1FHSvcI95V0zhDXZ0jIawm052/YMs\ni13MpULqAKpm7nqwvv+gyQr/BI+3aNxUxozYYDO8k3GQ1wm+oE+pSju9YWPaCG/52CZU89ANVOqo\nZyKGto804UMZIJVV6RUQu5ad5+4VtKdCG0U9dIwojpKMF6apK9Zs6sxhqZAuIlj29/6Dpn9upiNA\nQAxsOlPGnCa+ZeOgxOdpNoPuaAtF6dEffun1K9+ZnM6lrGzSfDppvqSsmlcHB4AsMFvPnsLI0NLA\nyrOn27E7dqU5D750tBnhCJICRDwtNLB2yBvxYxiPDoix2EeovcUwST4IE01IWdBWLHntVdpyNz9I\nj2cgMciQXQdsv3sJaDvDZ591H32yee+udPv4AgCcXXTDw0yiminDQzzc0SX28Bi9L+5X5CfQ+B45\nzX4Zc0OwVdQz0YG+rwU8fwZuIj78Y8/hcX46C/Lt3ohqTOM6MIkTGRR532hPfSUgGZiQdyxnmePR\n80Uub7cAG4GTZw4nrdnzKrcqQ3ZRYK7/7/xv2qNfb3pqdtIRQNEKDAHgE23MaewnXwQMYDePXomo\n1rPtMXHy7NI3nqy69cWfy6+1koklqGedPstJ2Uk1bbqOqS41FTeh9luWL3anGd/sO/GlhFMHMAVM\nAs8CnwdyfJgJKRzjcWMxPqMCa7fwC2nE7/PkfF9sMvA0IeVWpwJVkYXKmfYuEYn3FESXP8j+hx8O\nu7q3ID2kSLRLeAWc4cz2+ZbFTq2jbsq0BRfr2YVBrs8ennQX5Y2LgDfFHi5wBlDG3AS/adANEh5H\ndHhiw80oGthbBYg5Rus7HC108LEMw19uK7jSK+DjNUQ02Wa4igJ6E8AhEtCTeDXwRJ4f4Osx9Afr\nps5ax9PA9xJHIKjgHdLPn6199dEffvzWzdmk3fKT1BrjOOTqDUFwoLE711wQtLod3OhhoiCoRQf4\nussk/98nSTSqXeQHi176XIEwHUJjkwZngcenbOjcLaNCQV2x0GmDYZRvVklrE9M33Qrn93wGEoNM\njI1EfOEfIECIiQozGZz8vTW8ShDGAT3gLIgpeXNEB0RIkC47lwOnITYnUY9IwPNmKfpi6AyM7xDX\nOFAw2skcDEZgmVwYm+JDbJOerW8L/AMjoCesWaX2XOBSifOAr7JiC1QKQhdMgsc7njYeJg4MvruP\nYuv+0v//jcmRRG1EWRjWFrOZc27aTGbsYBGH1HN/2l/5Hdqwr0mDcNcBz/ikaehifg/aRqP8Qhp9\njJokdNKHmNMOkLJ44o5lYHf0tMHA+hAaFRTPeMR193z5y2Gn9BykQgpHx8I/LYPnECmpEApfGZAu\n954UUyy71leIQczEo8Ahr2m3I+w0BCouCA1jcCqdkEud24R84Cduw9s2oULywFlnWeE7z9N5Gy8a\nrcKOvlcoOqLzugyiarhARJN+ZRZ869qZw4FjEl0hphZwS3kwxNsLXZ7GQAcH270u9O4TAPCz6inf\nDrMLqx1luM52mBVFHJT5fxINxxiBYg2SKqEiKclYiC7hI7wi8A9RkwSIH9/RZKWTQYFvRRE/bdBe\n+V52iR/ZftfvBW7bu5Ahu3B0KPzDhuQePjQqncJM6DQkK14KzgT/KpSDBH5TIyDhQe9DYJx3suLR\nYQZwoILdBVQzAd4Pj4vNDXnkVgT59lYxFrF7BUuEAl9N2835CJt5LyaAah77dKCKKbLOVAAOBJIK\nKQ+KQnD2JvlrkHtSXDBaIQHdmxskYqMTfABPxKZ30tE4HrZziYAQhxJZ34/mQZw+u3im+uxN+byI\n3T02PDCvDg6g3kpOglp77juJxkui4ZjZnAXKmI1VDGTajfHjxdihKHYnCsUYj4zQNqNOK/P3UeBt\n6lwXx08bAmIGKnlf85Pferi0b6i4d2/E/XsL0kMKR6ued2jYwWfwdBNmEhGBUIyRcxh8Rh2bGrYG\n6iZu9vbQp41AFJuIVkz4g+XHhrCzwPlyxUALOlBAPYP/OoStXIZpkO//rCJfRYb4WG3PKfCIEzyC\n/3geR2/D47yA3p/cjGres0blK2EX+nA0iCdebbAKuHbmcPbpB9S5JwINSLTRCgmAj5Bx4peLWOoe\nYE/s1vRinZBGx6J2sGdhgK38N2bXUj9enMY13588+uNhp7HOWdyAc29QZ/q0JTdtLq5wRexuxfGv\ngwy2bvwScYRKJ5Wq4FAEf6BK4GSK8wphitAGrXrXzbQhUOFvWtgGrR+hWl0u+5dDKqQoePIwfPBV\n7tXJIAoNM4GPrC5HLohRVwK2EimtcFdciIK44wHvsmZMtIJ2uwAA9Yz3iXwYA4DH863nECl4QkTz\nVRQq2HQMmTpuruL44y0eRPARxVWt+q28D/UMqvnWE7Mzi2iH+9h0ZES83VFylU8baWcO9z91T+rM\n4YQ1mz79UPbpB2RALwrtTY196gSEXCem9tBJGhHjLXga+80mAgoMETLCR+bH37Yy785tcM69yTn7\nTkxvyR0fGjjTHFxksbvBoaXTt/yuaKObAtv0bjp5Pir3xYBswftAHWOThS5OE3JJ9VOwk74+UIgf\nJPRH2JpIjN95Z0RLPQQZsgtHZB6GGIY0RleM9u31wMj1RfaC45RKfpBeU44gjjPlJDIaQqMV5egk\nuokOUceCgTHvpssV7u5MAZU6dAO60XqgqEc8BNy5CSU9vA9/BugGcKzVgk4qu1QisoePeNv31Rai\nVKspyHSlSLQ2PQodGL4wFkORVNQpRC/uTwQ8HnaVOBh1x1GvBuBTb7U+N5idQQ19zWYGzXdrp3I5\n84c8OSmrQVm3Cnw8dBNKF35JKcKhYdfqfFWpEgiUBU+G1xaFlz4aetooOZOdPE563s20wYIELAM3\nku179Gig4z0HqZAice+u9K5f0264fTFkIkTYMBHsTjoYhVrSCQczOCTF0AOX/JiU+GBYA96xPM7b\n1APnIIK2N9Fh4B8hyzxlvoW5j+bAELO+ALGPbYTQzA3FteBrbYf3CHWPaAUz/8t76h57aIssiyfQ\nSm9AF0VDC95vxfIgQ3C8Bc2pCX6mET93koNkeH1m8qW9W9cNaAsNSxt2GmuSSyPJhetSsw0nNdfU\n6na/cq1+6ubfXff458reXNeo2ZxpglKgp2JxNmbpiI6uUFu0QGLq7MnGw04T+cHBmYO+e0QrPKa+\nO4Yoe3//ckiFFI/1bvLeXamDj9gnDMfDqA7VLqMk6U/ANynGL9YzR6BMRDd+joBX2gGPF0NN2pKX\nuD3pXW0WK6QRm0MUyUMFJw0ajhvlXwWFswLs7lTcoV7B3iHsmwt/SQZ/6+z1TwE7+beLN36WNsYS\nkuLrD11ViKp9BcFliJvJAHRhqNPxFm9OsUvi71jxhg1HW6XElX/3xNjbV/2X//XGtGXNOul2chL3\nk9xf+IRy40fwX27t0i+J72nQAIKX0iQePWiLVgJ6ywg7rUyO09cgxFqP0I4CLLW7Y4iygmVQPUgq\npDhZBfOTtmt3PVh/dKrZlXYZ5Qye4LBFYOTqXqI2G1OV7iQ2VIbKwCjP+qMmbWjor+jtGLspmy/C\n+HLBLoiZCvyJdwAjYY/Izi/p/F6hGAMq+HAeo5X2AwmwJx7lqxJiSdnVhhPWbPbpB8w125iTFKxg\n5u+5NavUnmtmr4/oxxWFmNpXBx+xb92stLgMPvNFxH7HiMqJN9R3E2ufXRIfwTO4y7DDWzyHXTLO\nzwGx2MaACRw9fg7ZxYEahu2hdVisJdUFVaulUvN2tpbO1E//v0+/8FeNN63TTyOzcCpqNi/wxNwu\nDT+RcR7qiBR5MHIcftCWQ0/zvcWYmIjvTIEyL1iMjiHKnq8elHCXw65NFwtN56t287fEn1RWAawf\nSTJZDV54w67FE9MO20G8jVLAXBnjtRsZCny38BIROSGH4luExbABHIgYXBVeweGA9zibp3XgAO/D\ngdjiixPEH9odEhrP1FE08IVqXBfY51FgB+mUcGWEG8aanxtCpRDWc7RP2nSstRbFOsuUWfBxw/oL\nVxu2hrYoteeUxePxL6/Zv6G+/q5P3/+BD9zx1rCzljF8g7y1HZHPkw6Cvd9SYKEfPLY2yteTQi0w\neolOhneJjHx6eWhP9IDxj0Aqwm6ggm/9zvqfv27V/NkRI5E7nhw8lez/CVY+fOQfqt9u10zK1DG0\nuO765+AM35Q+84+JxkvsuJtaaa14W4rQW2LHY7umg87rPqCTaHbfsgi16GSd1WdIGVyaRUUXGqwJ\nvstg30Sven+PvquaZedLSj8x7VD9JBCZJFsM/PJi9mcY4zS5MqHSToS5CHSZBd1tF70jcFznUQ66\ntUuorap7E3Ir3hGt8wBaBtVMXBfYdUdI88IaHSV58qL5boo76EabVsdaCH1c+gr5D4gEoS3Ev7yr\nIV0pJNE1qs4o+PunKx4FwsZmvovITygHtBG9RLjMdORvBfRozqe4ljbFUPT2cwwAPvPItJ1dGszO\n6O7Cjc3Zjc65d+Clljbil9czMFad+t4Hd//0vf9p4Z892Hjjb7vp1dZ1d9Ru3Gddd4epv09sah7P\nxBPeDHVQumS+deT46TyiwRDj1oNrI5GyFfUuy17xaocol0P1oKs0ZBdfp27Xdu2Ln2zPxHFJskIa\naShMoByYeQ1Ck6sAE8AU8WAqPCVeuB6VTguyPoiEWfDqxOgU+psI2/GTfd6Jo0NxXaARR51fHROy\n31PHviruy0eeNGrgNpIMuJUsYfgeVzQQ4vhVv9Tx5QXTla48hNS+olHU4JwaVThxgtdKKwas8Rjn\nOygaRkRcTOdlsUOb8pHuygDw7Z/Vyz+Y+Y039zGCw4G/+ru/evJ4+/JSu5Pui79/VjvwfHbHda//\nmD1yW8KcTwCuuWDp71fmjynWLDqFuYTPNkbeWejoGicPYQSi5qEtlyI2q/VBiHWZHIl6l6Ehyt73\njRiuUg8pvk5d61uO8CRZX6IPIqx+2nIhcNwXwxbrkjoxokKtndBhTjtZIJaV4Q2qCAgLkLo5wnPi\nTtLnhsK7wB6rSL4qRidNivpAe6s4Xg0/yT2Kbx5rW+HUhfNpo4r31YJ89qU3hvb8atBGfreeDtdQ\nbcTQsbRVcMoMXsJQCE2H8a6fCJ8+ZiWH3p388L9Znr7+j370me8+s1qbrZwwPJf7/Dzr1EvWn7JK\nd25qAEAilQNgXfsvAq22UQmIb7HT6KLBCD3QSLBl4Wrq3nS6ICgLA0AhMoUdBtDs3+Bqw+3G8/mx\n5ZMYezV6SB3r1J2oOI8+2bz1JoUdC9+szBcKC7IGGKLsR3gZcTo/UuFmVTE6tynYGXoQvKkSGfii\nynGRnC/6rBM7VHhOlVZ/Hs6jWvF3QSfUWF8vRr30JAQ8tHwV97HtlPhJ+XqbyCfub3gzPybC2LFR\nYcsKMLz2o5XTDwVfno+Pd6XC79bT4RozVmM8afZLUGMkuLgfvBdtJ0jpBiFNdLy77nUQpnCiYu37\nHy++frVy8uxS6/JoztxPJt6VS39ofXpP9txpAAnASa0S94mnazDsJPIXta2meIiOAQNw/bGD1y6a\n6CTWe7jQxTtSAJbyH1cWj7ONK3/lwIFltFB6VSqk+Dp1Y0AF2z9Z++InM4x3F5IkS3PXQ2VggluC\nMfSdgreK1iixB8WoDPJJhecUNdJ1/lmoulBmnRjmh7ysNRC9CAAYNfzN7wBGuWL19UK8DGGFG2Fv\nem8VYwb+bAj78igY+F41+AugzD9UeMu+EApiw5Yvn/1Bc802be4Jw5plFzLKQ9gVVyDu3ZXePlVr\nGTcTfLiWI+br8S7mObFsKK4CjzoVyckT0YrKp9sYfAM76u6UKiAccwPYjd/4s1Pty2N1Yc3+ARTY\n6QG1MQ/ATa009feljG9SlRfkVete+Wv2b1AWj5eJ2URVly97uBhtUsIbNOlGgVW8JmsQYn3U1Ybt\noeHlGAm4GkN2cXXqyPG7HqzfsGtx/8EGu+Rn3+pvB5rYuI+RAbFHWZRYglfg9kXJhL/Fmi0CB8gw\nF55TVGiMWsSF6JgJXdgRXRJBB6F5KgBwyGg/XIG3p0dUNROhF2EwRr3pfB3TBm6OrjNEA0uj3iV2\n8TJCIcTSWrNtKf/xxtqPutqwuWZb7Y13Xz1lGjxuvQgFx8zX6CQRtHCiiIYFXYnzqthDffqOPAF6\n0xI/YpDTOulCp3mqmq3OrFjLYneJVM7S339NaiVVsoKuMda+zoOkOXeNNkw7DsKmCz7EGFFpQihC\n33cxWqxF48Iq8PmZ9OBy1EMCV6NCiqtTVyHKxsu7Y0my60eS7XkxXgbQSSxBeHcFbqgaPFVBjMrd\nXgEWQ5WBjnR4P0fNOxN8mB8ha8V0yarCWwZ0Azt5SZIDAQ5rqCQD2Mn/nOCnxbzpqPUh3du+j0rE\nzixFN8vE0tWG7aEtV5UqYmBuPQCUOblud+x8jU6/U9lr5YA7v76VoW50m6/GRqGLu49xU0i0L1bF\nDvAzx0kHghgDgNrSf3x+aGBmxdra4Fo3NaCdq7xkzugBQQHP7DEIOUMwOV+yZk0+nMSb2x3xEMVA\nj0TCVegT07i0QTwneCXiSl0fvToVEpHV0F911ONVZLbP3/VgHcC9u9KPPNh36+bW2lKcDHQjlqPE\nxhSqAsCOMLPK10kjYLwVyAoQOjlneqDPQSu4gtuOYtMxj7ILfVuhEAIcf60ecbzgbXxHdK/pXlFX\njFheFLTd+qigEkOJ5JR1/I1ZjZqtfBCWidFBQefaEre6qK1Djf8DXnso9O5lLmti3AhnvEDcGXQQ\nOnXVR9xUYq4vy46pLz/G2qAbd4lgpFguDQYaRBqTHiC8BR9CELVFB/XoJ/bFAA4Roin7qtm/YfCN\nd4c6Uos3fna518S6GteQEF+n7gg5j0efBe9u/Uhy/UgSaLZPMMJiutTk9H0lxJJ5J+xyGiIv8y0n\nJqKlSydWKi2pOMqbio/I6964P7WCOe6rYo5Iix4bZ6coRNA4gteO8UfXA4wJ4SSxI8Ix0skHH9P+\naqMtdIN27StWjgHEhBr1psEaXfzGhQAngl4+zhdVGMqelUgPuY6OavHzFyLuPtrKQGh9y0aGSP1m\nA6LIl2vQQegGr39/Y8FaVNWfptdubsyb63dmfrRXCNwoqSUrYESvAoNbXWJJNeYVjvGkeXZCsdMK\nk85zzGl8BICyePxFbVi7QtdHlfuWDyPw1cN1f+S4rVzuISQAnJh2z067mAIWAB34CPd7csBGAMBD\nwBTOLrq3blbXjyQBfOy+pVZzB4CvAQiLhOQAAFPANFkZYmd+nsflbuFnbuTtgLS2kY/0jcCzwEbv\naF0AJoEF/gHAY7wpHZgEpiNW/Mc5s0dIrOgSAL19oyOVloguAs8AC+TOU+RP8NeW4G0cCLwJ8Xy+\na6f45Yb3uO+DDixwKsmneJCmyF8P6+HXgAUmlqve7fR3WxPovdve9KZNI12evFxABzmAWzer/+17\n9olpnobCxsxjwCTwmPfKmN9Y4PPRCyZ0lOjAM+QHpuNjT9h9p/jEnwsbDUVgije4wM2pqTC5mwYW\nIoVO2fDBzLVbFQdNW7Hd5MrFRhJu+vm/NLhH/qmwJ2YPOs3lFUCOFK2c5s3vAPYDn494hYw1TmcF\ng1ihvpPFa5gkIRL2Fv8dsAicPHPYTQ03rvuok1mr1F+0Vr278bpfjRr2y2uQX9WlgwCcmHYenWqy\niFxIERSiA5g2OjHttAJfEyTLx+BxAzrLj3vd/ignjEFwSOm6p6+1CmlqKuBEiD4X+FPElBAJdkkn\npHDu1BQNfPlYK77C7LUyCakbXmdogif1xtRKCYXvrdNHoQ96hPNuY2qrnK9vdDWUDgLw6JPN7Z+s\ntf7QA2xv8Ok7+AuFnsx+gK2xrYlh3GWtevA52yCBgVFOtGFDajdvkx7xDTiDzPTeEb7u3379paVV\nmB/MnlOSM5pZ15QXE0NLtWt/+EeZ4wcL3nBZ8LFESIKh4g1q0OfWve0EJwCfyIa+hgp5CAT23d0J\nuNpw7Y13RzfTxvIa5FdpyE5g/Uhy1/bkej25/ZO1kNxy8WcZ7aCHwflswkKMijYc4nUQDG+gIwha\nYSGqtW7E2yClXWMIpME/C97i32PABI4OYcPN2FtFwWj1TmSDM9DudFNsGF6NyUCjH+KtHwo86Fbe\nTZ82Em1WgKunZOp5obW7hG/8jJNXTwOj7GDUYNOjuePiuJjFY3IexgJqbJL/T422ijfuNwrs8B7x\nSROd7PkIv3ZF7sa3bV7T/+wPktappF1TV6Q0N/2Kc3a4fz49gLf9H2+zXqmc+u+IfW7DGwikouOb\nMPZwWxReCabRTZD35Lt8mrQfat61RnugQLB25rA294QoMbxMcbUrJIZwiRWDcZof8S1ciCShivcS\nhjEeWxjl5xuBxRuGEineM+F1fejAj69ITPtmRO9W3+ilAAAgAElEQVQDAa/QCvis4wkArUJ2d25C\nJg/dQLnacrrYuYVAd9ApQ2KPdxr0iWIRAH/onaRejG8eCwVTeNqZw831UiEB3hr24XVJgubXBDeh\ngifT36ASe4IYSPG2Q4Ek4bFmQ422IIVBOCbsRpO8TXgauXVjtvi2NZ/51vS/fOu64nve9m312p9g\ncV1qZsnRXnJU0x5M9zVV1WmklLm+7BzXRvHPLcZ2hYhAcMKgjtwOHlWeII9i8EbilR+6Hu3amcOC\nZJE+/RDLh12mtFKpkID4SkIT0fZgmcfWytzsp8GKorfUcYEsaAr5KXlVjpiqC6S0nTgSI957yIqR\nz3PyaTXwTFifdxVqAfLHYVuM76i2jjH4pEVMVr7nm+RGLbxPE1O0LJjRLx40XuFdDSVTO+IP/7/D\n+8rz7PNdD9Zb4Wg6fkJTucd5PgA6DbZuTkAXabaFCKOqyP8UE79w4MSRCgCs35w8UXGCVtfCV9Yl\nGpq6mNl18xuVWtZcmplrprOKndOsXNI8lrROJe15dcXA0tLGhz69+sdfK3B6afxj+cjq6EJrl/lS\nkBEm0x11epej/UraGflqpH370KGSEDsYldNj8LrWTGbEwo8eXeS77B1xojU69Jh3NUoOxqc0TZIj\nOjk5uN6CiIrjo8BuvtvsVk4Y8DpS77sN125qzx6UPyWuEM9X8nKD4e1IfNEy3ZunSx+04j0I78Fl\nHay4WNhX/nLr01jE+PG5OCVgq9c6iSoKPhb4EHUCuktFgte/GfMulVB6mU6C5IXWJSemnHZqYBkw\nsP6a5D0fyyFtu2nL7q/b/fVmtpbqW9jgnHtD89wW5+V3KS+8ve/kxtzpvsGXG6vswVPfY29iqovH\nKhOCNTolVtCHEGQOnUhqN5eLgV0iWed0tKdPP9T/1D2FMGJ6/1P3pE8/FPFAvQupkDoV8w4yeRjo\nrFkhFpHOLwTRNGxgFknS61ZvbdaiN/OTxv3gPeKDEO8SGbNiXFe8kTraGXHOHsIrqJDZyvcIAIC5\nIY/yINYq9nhrNwRVrdFFipQvWEEfmmakUJ0kJi6pjbbu3prYmmj/PQlsDjDigkM6+FPFD7ZuTkAn\n22GUHPTliY97J36de+oim/tAW1j2HzTX64kvfjLDkgt/+qXhe381DYDpJEezHc1uZmtpWENuY9ht\nvN5d2JicW60sDKi1oR8+nJo7XSD2UPxjGTzornt77YM4vofknRcCV3Wj08EjB9SyZQ4WG+0xOyNj\nee6MLEN23qpfFCU+EjsGHwSM2DXhYI5DjNPOIl/CoPLFwuhBkCiAKKI6RqIDUZ1hRyaJ+hHaa2f4\nVfUJZDaheAzgMctKYH4rxMbHY0BjOT4zWjzo4Bvvrjz9QCBII3OPAOBo5SgQWOlkU79vRLEhHbN9\n91ayiAfSArytIeIEhihazWjYaYJTJywh8Ahexcs5A/88BkzghOHu2q7x7Z5Np55Kpi2noSFtu4AN\nJC11sDaTWTL7ms0+14aCfs0aURb+6ftfF29C7+KxdG934uNpACb5BpkVMoVQMyD+cgBr+jdUFo/D\n+5OCj/Yud0YOu0nvQnpI0ZWEurQHK0AF9UcGGC+8hSijhSLeaS8T4QQ5IuBbHPI5QB3ZEOBz+Y4I\nRRFx1dEhgNTdCqpsI+7qOAgl5DOj6YPOnDlsrtlGq+uzOnWd2r7Ccef4nYmtiXCHW1SZKpOpUQxd\ndLHpA8JWIqNGo2hKBAN85QSOROg5IyCAYj2JEtRoZQ4dKODEtPPok03vlUimLfbBTVsAXM3SVHMF\nlobcxlqnttqt64nF+X/1UZBexxeLGCUbTlLt5UNQa/t8r2CAIepye2jLmcXjMeE49ewP0MnT0sjG\nuMsCUiGFVRIKlsmKHTv37kq1FqIY4jUNuvP5KzzN4hBwBNAjxBsRcT/R4Y6dGY1Yyoq4qppp6SSQ\noikxAaHgPeNfZ4F0hz6oiEJczSVTo9DyjaJUiw4c4uNH1Fwb7/RTGWGDDWTn7VBlI1qLqoAVpeeE\nG0LtKpCRMRa4hB9kFZAZkplW8clk2kLaRtpu5pbs7JKzYm4wO5PHzPXNc29tzrwDL70pb9Pmi9G1\nTRFI9ovXXvbQFpNvWyw4deLMYqfL2cDuGI5jw353hD25TGk+MmQHBCsJMYgN64TDEQw+FAAd/o3P\n40N8OmevduO0i/Eo4lPUFI1xRsQg7ZgZtLXroA2/al8et1UAXi5hd0RAKOaeUa8TpCKMb+ZhnxM8\n/WKZVte/FChNlKpGtQNFLJjGyUZI/E8VdIzgbcrH1abzbpkX5KnwMHIR2BpWKoohahCKB6E9EYOz\nDAC7btdoB5lOorE7u7+etFQAKWBkCXAA4Ja1ucfGti+UH6GjccybNuSmr7FXv0t74WFfNK8YXfhH\nRI9XD21h4WXxPsRdivxI8HJzzTZrzbZuwnGZ6pfYkeBmZ+J3WHYyIhVSC+2qX4YDEMuxGD30WO6e\nETBR4jWNcCt8YxyBDY3peCx685nAK4nFT0MdO8PQ5V5q/Koxw3fA83CVTvfU+aOHzkvg1csqfAnM\nF0CXyUY+lCfZrxLxtVAtwPqRZMuPF9ZM/E81SsZ2ITAexDATe8zRgnVieI+SRaNR7+6NOimIF2NX\nHfFqJp1Hs0daXeILSCFgOslNWw7gaDaytRSwopZacpXXuwuLxXc8+wu3VnbdGxyNdnatPbKted2H\nEuY8AO2Fh4NWlO41EQG42rC4Nas4xzjZhegxTx0jkT/UMRwn/Em6XFj0NrjstBGu5lp2Qdy6Wf3g\nu9Unn3NOTLt+8QCvPyVqTonoFq1sxRAaCanwYbIIsIK8tNJdCdgdKCDm60MO+A7wLK/sxvoT7CeD\nzr2V+M4AKPD+UOR49TB6Lb/q4R/7m9GBZ4DJ7u4ZLJmm84MsVJMDnuVTZbBs3XPWXNKabQ7cGPbY\n54flVeYrCnk9X54sd6heCOzarn3x7kxreIvfIP6n+iIwSgo2glOuF4D/HZgEnuHFCse9cTmGYE05\nX7XR/YABPBY7CH1eGuv5Ri6MAICDj9is2iS9OqE2XVsBkFAdFwkAbtJ1FScBtw/2gN003ZSScDMr\n3FPugPni2dpijY3Gxop1pzf/+o9+/ovJ4XcklLRmm83hm1bn3nLizNFJXkKSPe4CYA9tSdZfbN/U\nqWtzT8CpO/3Xp08/pM18l43hj/L3YQSknMFcs43Wo3NTw+rcE6E/6TgpKFj0isangDLwNcAAFm/8\nLJOR5TXIpYfkwfqR5K7btUenmn7LscgdFLEPrI+3KoxHGmwKjUkxS6nodbwMfi31BWgfSgE6nx44\nh4KG9WI6g+4SGMlVRT6hiGauyYwY9Wnf1VH3pM9KzeuSN+DOEGU0L0c+66VDXs8DHShi60eSX/xk\nBsAJw/VfH8+F072+kfgwHjjfhyingB0XEtRlkBde6fBqPrZvWWvjTQIRuwPASHcOYPfXAWiateFs\nf8Zt9inNbPHG7+zYcvwHL6e+8g3j3R889/Z/Yy+kkwt4HgOvmwOwNtWYN3KvV/X3aTPfN8wZ6tD4\nk1KBBM9LDV0EKnCnSoA6RgKONozonzTYLPUnl3Xlb6mQ/GilJQXHArX1QnmrDEZ0TOoIn3fFFDDm\nTeP2BdAngHG+ikNDHFQmY6ehVj3I0HijiMbEqzTDE0i87SjqgcjiS/VpEE2D2BfA9spYuWabcebw\nBH/inSQAIhAfQJdl6wTyej6v56tGNcbyYFS0E4bTpt7o/I1H/VQCVCsgYDbpfvXQblbMvmL06vwq\nIUHdBHmjpMPbYGb7/K7tGtO7PlAieCt2B6xILNZdda2zuKQoN6ztq4+85djPb3txaXX6eVexrYyd\nXLQ1tnPSysa8mxqwX/8xe+XNysLTKeO/WyvelrRmU2cOR3Wt/6l7wMdwycsTFCeHqiLxlblmW+rM\nYd9POtGJiVIBGtd9ZPmKhlRIfrTSktB1FkWFSKavRLAvVg6+7k+ngHhiQoVzBqIGfjf99C3U+h4h\nXqWRqzL1kGca5R0xgGoeho58tT1DRa15P79mmwb4NnQ5ObQFgDb3RMKahSxb1zVapIZOS3Ptgt8M\nwl9B2LoOBY3uRg1Cn6kktNQY93x14AD3q+jwi1pPBRkuMe7AAU83xL5lFMlMeHJSurYgCA59yWa/\nYvX3mRnFPLYml9YyaUBVnQU1NZ8eANauPHtaBRK519uplfbKdwLI/uTT8V2Dl/MdnB6c1FAMQdRa\ns03QInw/6RUsGlIh+dFKS4oS74JXXGNSC+moLJLjwkaiwbQYgydKY4kPHS3cIq8MJGaoPd4s3RgO\n4Q7O4OGz0hgvT1ckz/cneVTzrT+PbUI1D93AzdXwNW+21mqt2WYPbVEWj/tqQdpDW9S5J5htGGM0\nLzs+66VDi9QgIqG+GFpwIqRHJkhBVYTxKivkwqjZVyd7M1D3peI1znaSz75GyrGDMEY6KjzSMAFw\nR/DWm5TABUDAT2oSgsOSq6526xuTc9NKLpGqm30pdbCZtJOZjM38pJVnW40kUjnXXFBnvt+BBQeA\nFFoNnR4oAyIUoRvxJazZK1g0pELyg6UltZncPvEWMjZGZv9QQRW6JKqu/nh3Bg8iZJJOIpVoB0g8\nBZ0FtnqlJIZDKFqbQr2C/BCKc/565Tq4NuIzXb2Cah75anuvip0BUiwAVxsOsrddbdge2pI6czje\naF6ODKJLhL1je1t5SCAlGBA9ERYCldVBzqmEaQWGSmBo+RQDiJaiAVyfRvT9tMXYzVO7WeMkSmD/\nwcYjD2R95zInCV6dxBaTBgFRxCGr2P2adap/JdulIgukzzkAFlV1Zmltrj6fPXcaQAJQZ77fsWsC\nr2Yp1Ge32UNbsk8/cAWLhlRIIWinJcWAxjFCzSQRtfBJdSkQTunIzPYN/KBbZhDCBWKnlSNcOVAp\n8cX0gkGbUqvD1byf+3vnJpT08LnvKKAbwDEPqzXsOf2ICqCLDi5rkbvoaJEaGCZJOmpHNr8vwNQp\n6BeS8IKwRSChHs4rzqx7F5wE4qVDDFSuBHw5SQLB5CSnYQuCw8g5ZBybcRze3ncyo5gnFWtRGU5r\nmYzqqAvp5PE/Hf7Zny9t/HVnzXtUwH7dLyo/He8ouLgYS6E+u+3KFg2pkMLRTkvii8CeHA5q8XVM\ng9X5B0Qs8MYbPAjIZDCwrpMdLqKmFZ1XCQquihYDHEJxu5JHvKoZ7Mtjb7V9pFW1IWLumxtqHTD1\n91n6+2HOR7wsP2IC6LJsnQ95PX/f2H33le9rOyvoLtIF7xCii0BBTmQw4YXBpxgY4ldGY+LhXnMH\n6CQdwmPjozQmJ0nAn5wEpPoW0rXUsNsYdhsblblFLVVvpk41NXNAWffXf6pPfoFdOPDkficzYl/z\nXvuarR27xnDR13uubNGQCikS9+5Ks83NWPiutUUFlbFKFwUXRKxMVCEqk0WVnd6TQwPoFe/AD9Uo\nDLpXpH3GJlMzLKodlBKm0vTAE3kXZKsV3EcUUklHNRPXmXoFc0MYmoOlv1980+XWlqEB9OXLZ72k\n2FvcO1Yc27B1Q/tQN5GujiugRsS3W/lqU1AxoLshWggQ8HaQnTDFyfDKArxHxE15NzpqI4+fBAiC\nA1qxuxyamE2kBcHhpGIxbdTWyPXp1Mk/X3rjb5iv/1jq5J9HExsv4XrPFSwaUiHFgW1wvmu7dsOu\nRSBg8bHFoW7MJCGco1yKSmTkxoRKxvjeYWLgd5+3Ad5gkZRsYf3sGGuoAJORs1UCKBr48jGU9c6d\nqecxWsFE5Xfsle90lNx5bW0ZRXyQCCKP/H1j95UmS1WjCnQX6Qq62gjE8WLifqG80xI/2HGIHvDa\nZ+BEG18E4kinNU7ejSjOdxBt3h0gkpMczdY0a13NnLXTfa6dTdq1/3Bo1eQT4fr68A7z2ttXbH6g\nMnV3qOAu3vjZhDV76dZ7rlTRkAqpMyJ38KMhNURYcGw5RwhniUf5fVTQ0NUm1vKYd8m3G40ySrZ8\nZqeJVaIJ3vMYKaHaNGI+OjqEEpCpAoUOndljtLqjLDytmjP0obvZ2jKU+CARir3FvWOjY0d+uP/X\n/+hPO0e6YvyYjuujzMsR28vSeF2ZfIjXiDqxz+I3wkAYe3CnRwncuysVTIztCpx0B8CxLEUzh61G\n3VVWo25OPYsYSsLcj0+/4V+nrrtDPfOoyJYFcVYu9VLoFSkaUiF1RvgOfoJHFOPf7OAKqcz/ZxDZ\nGIJiS+MkY9w8PMCTkARFokuNIjoQVcgSkUpUN3BzHZVOsbhqBZ8bamUmxXemaLTuUzFnwo3Np+6x\nh7Y01gZLx0icN/J6/td2bH3uxYP7D5odIl0xrrYwRzp6OWN8bNM1UdFIzBCdJNaVuGPMmpNwp8Qw\n5o+zfiS5a7t6vtoomJwkijiMLJ3NOPaTk8/UjbNxGnnpRdSOmxt+1V797uTs1P9s71yD47iuO/+/\n/ZhuDAYvEiJGJC2AIRVZToqYvCwppmnSsimm1pFkS5VEiSCMtlbr2LHXUpVVdK1piywjrmKZVfSH\npOxdlSMiSEq76/Vqd7MVg9RmpWjLGyfZSoHcVGJH4grQYzWQKIIABoPp93643T23px8zFEGyKZ7f\nB9Zwpqd7MHNvn3vO/Z9zCrU/B2AN/IK4wHp/7/dcCcggdSa5gx+fz5Wgu92pFP+GE85DMRwxKxgk\nce5Vg+Ono+LySpAPVBbMW/x203ZfiG9QIzUM8qWdm8+8+O4YcHEQ83qH+9H8GCpzGJvH/Fjqh6nW\nWk+ASgFdLQ5PaChj6ltm8jppriWbTPBjZgXNW7aXc0joXVIT1me1wIXKHqJtny3bG6sBByN/xd5x\neaHmvQdT1Ea8iAMXOPzd6VfQySJrr84YP/d1Txt2ync3Nt3hvxZV7ryP93uuBNQPqTPJHfzEW2wV\nOCG0qwi5R/hvJalr0X5Bq10OdnrngpnJF5gngv8eCtqEnUjv3PKssFn1bLRYw4ng1hAG8SDk6gIA\nnrx/mF/2vnkAMfsaMg0A9U8d+X+/9rtbl7feOZ/8YbwX8cxPgC42udl12Noy50zsDrb3w5841K2I\nP3rbqIbQpDjxVfFJsW0YH2kVYY2VNkQR83L4fzPu/Qj8sDDemFKU4ZKQdJNrHPxufprtaZbd23SK\njf7ihX/+yC3oMAOw9DO/0ejfavVt9Qp9rFBKuxB18OoeMkidSejgF7/FloWmkuGS8KBwQDd9OcO5\nVxYep93OJ2M3F0SbcoYnKQOnhJe43q/avviduKv/plHpkc9uAfCXYiyujeBJ58y/OXcrfvL4985X\nfn/r0jambQ8/zFgTR+Zb7+iow8B12Noy57QGbQhfM4Urp/DXnxZ+5ZMxmzEdW4e13aQPBQspxFqr\nJA5RzgvAs9GqENn3/nEh3hiMJF5TNeVt3ZJok6yBlW07TXSyyP84/vAbQyOm1mdrfdwmsUIJhb74\nVXi6N5mijpBB6orDE9pPn+9trfg66ogQTPi54HGad1CLiSP4FnFViJsnXosf0PZ8m4sWXqIWeyl6\nzrXv7fi3kyMAJv7lyF889/MXmxibDz5SSgDQW33LOfvdxsjWi798b/PX/3vPbX+6WXpAb2JsHs/9\nuCUNF+9siVyO/pXIwB+0nHAElqN+djnqx4QhtcngLWleTttpE9dSFcH+HYxmzvIDjgXHoNO9fzq6\n0uKnOuTXVH3sePPyv67QJrmq7RbsLbewyUe3I30GLFXul4pY1eS63mdqfQC80BQl2SSiG2gPqVva\nO/ihO2VtNyrtaSHfCEH0o20pmnitctASJpTVPRs7JszPjb80DQC3DMsP7+1FkCEIALcok49un/3z\n8+X55o+RrritAdNo/rtxb9t9pVu/qfdvMX7x2OiFL938472JWgq+c1GNfoTwj36fiYVywqgn7R2X\nXzrjpI7AsEphuGMUuvLHhOixuP0jblJylc3BqGNUjZUCQrSJZU3IwOumLzOE83Amg8yEQ8Ds5Ybv\n2oo48IRZu7f58BeGHrl38O5P/318Bvxo5q+1i3rpTbOOgtilQgFg1gGg0Nd9GjgRQh7SJXB4Qjt9\nvGd0JPjSOq7pnhAeJxKaLnHCnxSWoi8EhiT7WoeiDln8EvH7UfDe1847C+/YnmYB4GtDV7Uf+eyW\nE3/wwa8++KEPr/dsHyhG9iHCUwWPzaW/RY/DFFdR3Dc3bX3tw483+7Ynxmmmg6U2Z6P0r0QG/p5/\n2gg8E/1vW943gBPR/dG2OFsNOAY8BMxGN3uQGa9D4LWHDlY1fc8pvG5VePt08AnLQMWvqdrd95FK\nK3an2Z5muapt9zbtnc7kv7i5XNbDv0MtD9kP3zfY946xeU0eapZKZqHffW1Lfxi78wN3ID/pvUAd\nYy+NwRJ78rtG6//xnph/GEy/enTzNh61C8Nx54RJK3ZRfQCoAHyv9Ez6tQ4Ce4KNorYek+El1lLe\nWwFqWG64yw3vd7/37kBRHt+mM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo2()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "Test logistic classification on a real life dataset. You can look at the Numerical Tour on stochastic gradient descent\n", "for an example. Split the data in training and testing to evaluate the\n", "classification performance, and check the impact of regularization." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "exo3()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Kernelized Logistic Classification\n", "----------------------------------\n", "Logistic classification tries to separate the classes using\n", "a linear separating hyperplane $ \\enscond{x}{\\dotp{w}{x}=0}. $\n", "\n", "\n", "In order to generate a non-linear descision boundary, one can replace the\n", "parametric linear model by a non-linear [non-parametric](https://en.wikipedia.org/wiki/Nonparametric_statistics) model, thanks to\n", "kernelization. It is non-parametric in the sense that the number of\n", "parameter grows with the number $n$ of sample (while for the basic\n", "method, the number of parameter is $p$. This allows in particular to\n", "generate decision boundary of arbitrary complexity.\n", "\n", "\n", "The downside is that the numerical complexity of the method grows\n", "(at least) quadratically with $n$.\n", "\n", "\n", "The good news however is that thanks to the theory of\n", " [reproducing kernel Hilbert spaces](https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space)\n", "(RKHS), one can still compute this non-linear decision\n", "function using (almost) the same numerical algorithm.\n", "\n", "\n", "Given a kernel $ \\kappa(x,z) \\in \\RR $ defined for $(x,z) \\in \\RR^p$,\n", "the kernelized method replace the linear decision functional $f(x) =\n", "\\dotp{x}{w}$ by a sum of kernel centered on the samples\n", "$$ f_h(x) = \\sum_{i=1}^p h_i k(x_i,x) $$\n", "where $h \\in \\RR^n$ is the unknown vector of weight to find.\n", "\n", "\n", "When using the linear kernel $\\kappa(x,y)=\\dotp{x}{y}$, one retrieves\n", "the previously studied linear method.\n", "\n", "\n", "Macro to compute pairwise squared Euclidean distance matrix." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "distmat = @(X,Z)bsxfun(@plus,dot(X',X',1)',dot(Z',Z',1))-2*(X*Z');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The gaussian kernel is the most well known and used kernel\n", "$$ \\kappa(x,y) \\eqdef e^{-\\frac{\\norm{x-y}^2}{2\\sigma^2}} . $$\n", "The bandwidth parameter $\\si>0$ is crucial and controls the locality of\n", "the model. It is typically tuned through cross validation." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "kappa = @(X,Z,sigma)exp( -distmat(X,Z)/(2*sigma^2) );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We generate synthetic data in 2-D which are not separable by an\n", "hyperplane." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n = 1000; p = 2;\n", "t = 2*pi*rand(n/2,1);\n", "R = 2.5; \n", "r = R*(1 + .2*rand(n/2,1)); % radius\n", "X1 = [cos(t).*r, sin(t).*r];\n", "X = [randn(n/2,2); X1];\n", "y = [ones(n/2,1);-ones(n/2,1)];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the classes." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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VaUWe6zuA37eJpnxo075jKGX0kriI4CPAERCwcQSDVI9ht6tH2FjNvL4WMNSW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options.disp_dim = 2;\n", "options.disp_legend = 1;\n", "clf; plot_multiclasses(X,y,options);\n", "axis off;\n", "SetAR(1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Once avaluated on grid points, the kernel define a matrix\n", "$$ K = (\\kappa(x_i,x_j))_{i,j=1}^n \\in \\RR^{n \\times n}. $$" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "sigma = 1;\n", "K = kappa(X,X,sigma);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Valid kernels are those that gives rise to positive symmetric matrices\n", "$K$. The linear and Gaussian kernel are valid kernel functions. Other\n", "popular kernels include the polynomial kernel $ \\dotp{x}{y}^a $ for $a\n", "\\geq 1$ and the Laplacian kernel $ \\exp( -\\norm{x-y}^2/\\si ) $.\n", "\n", "\n", "The kernelized Logistic minimization reads\n", " $$ \\umin{h} F(h) \\eqdef \\Ll(K h,y). $$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "F = @(h,K,y)L(K*h,y);\n", "nablaF = @(h,K,y)K'*nablaL(K*h,y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This minimization can be related to an infinite dimensional optimization\n", "problem where one minimizes directly over the function $f$. This\n", "is shown to be equivalent to the above finite-dimenisonal optimization problem\n", "thanks to the theory of RKHS." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 4__\n", "\n", "Implement a gradient descent to minimize $F(h)$.\n", "Monitor the energy decay.\n", "Test different step size, and compare with the theory." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo4()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Once this optimal $h$ has been found, class probability at a point\n", "$x$ are obtained as\n", " $$ (\\th(f_h(x)), 1-\\th(f_h(x)) $$\n", "where $f_h$ has been defined above.\n", "\n", "\n", "We evaluate this classification probability on a grid." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "q = 201;\n", "tmax = 3.5;\n", "t = linspace(-tmax,tmax,q);\n", "[B,A] = meshgrid( t,t );\n", "G = [A(:), B(:)];\n", "Theta = reshape( theta(kappa(G,X,sigma)*h) , [q,q]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the classification probability." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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mMSEzx4/2Ds0Ear8QMnz/3yd5xciSX+3sY74TQXljzbe5FiAeEtGVrejKlow5\nxc8V0fNa0fNanFBsaiDkhfDrAbdGfEtHjKIaa+NS0rp7lalaxDr3W6ov5eMODiYcIa0t7AJucuX5\na+3bZdeuFuwKOkk5zZzbB0PRECjqkiP30fRpmqVkbgI9wA8eFV0/tHer17yhcYX3yc0ckRaStpO8\n408BHCeJs8i/J7JKawol+oslbZ8XGJvunUFlKg0qU2kIYHDoyU3BMWBTcGzqy5yI7I0Vvtj/L4PN\nrUfZ9GQ0CHAUQkD9PW5oIoATg5wYBMJTH4v4JZ97G/xKpmHLFHoSUlY3lv5Q5AmWEUb5Z/2Ez9Eu\nm3LHlwb7RNqM9kHDPn9Wix1M1YPhoi1cpcJhGXBNubbIR4Mo56fFFSKbVaEoramz8w31FhDS1GXG\nvk1ltt6OzxfRS1vhy8eIrrB3q384+hX4ymaO+NEpYPLjTHUYfzmtAXXHpONWfzUVAU/WSsBuonDC\nS8bpwwVqS3vwFD9Nn1SNUogx6OBN/7sPNF87T2M+aADzQWN+WwN48ngJPx1P3jQ+8YqIV0Qn/ndx\nJuR7ifDdklhIl6DSakgn6kx6xYpJwZSa/pXRTBZVH8EdnVJCqtM1LeZOqxTdZdR3dZAR3XnZsKGj\npZXDs9a6Ag7nCLTC29KFSpTNTjVzoAERr5MBjF0wBbtgF3Sgzcm5Zz88P3BzPCDCF03MbX04fMU4\n5wmumEjuYo7qVbf6ytGGLpu8lQ27mGgTdrnp81xxH5OP9P/Cq4zxC4CKxhrZefkynxJuECG/HfPC\nQIWLMq0d83x9cqA+Hc1VOkPEpGDDCBOC0OOmBlcMMymST7zwDZQi/JWCA8N8SOYicnBwooa1xIYN\n80BaxUC5qMFiOZHeKNytLO8Pesarz8MybrSzhl5LIh9C18Hzg2q7y5YuWwM+4/EP8pyYy6Pzbwq9\ncSmTQ5AMrzerv1eGXHcF5NLcSZnEEQDm2fCfSc4xlGFn/i4xieKnwHDR5YWPhXPByiykzHbGgVfm\nyfPOJzyfK66qaKwzMt93g6MDLwaOsPkIm+WG/DtPAzh9dEC+eM9gkhvKoed9O/QX2+K7k4CXHCPm\nspjLfO6nSoTShI+OAFlVw/vaKc1krvopxFwc8crMPNzasCd0yGdzKNM4FBq0FtFdWrhy3gBw5mzP\n9zun4AhpLWEQUiYuUdb72TvDSkJaMSrS9pCGlB5I1ZSFb8ZU/LwwV42cIqPyzXwg4uc9HvX5O8Ef\nRhta4Y8qKtI8JG+xFeDF/tFh5v7X1Ke+deCux6N/Sqr6fFqbGZdd6Tw3hUw9rnxMGREF3Bjx4fls\nem27wJGSXY1KPbJFXzwl+M+itLFa53GzbAehGqSRcPMRXg4cYXOHJiD/HmHzJDX9EAAAIABJREFU\no92Nsh0SPYH8G/Zced73Qz9qi3+cjDa0wjO/0eSnfT5HqZYeYL5BFNimf719vjQvUR5ttaZGn6hU\nh+c38oWVhJQR43mF6rszZ5zvbulwbefQNyQb5SdjUpUvoAktlUutkzVjErW3DqQ3+LDPg/P8bsSW\n6LxfrVm3V7Te8rbR5/x951t3TX/h31z/vfFfgEPKNoK25Kk9qjdNv8MX/SU0xiriV0PeCa+iKLX5\n+avyxPiHRPScVvRkC+D0QsTP+3zOHhTsykYrUTV4fnFeotFc3kKJEX4t4pXzvHNVXs9h3cNZSGuJ\nDRtkT5m3kOwuO4p2sTqQ7OV1Yc+LOqpSAOjpQXm+mcplS9NntozhczMJYLxojge5YDBJ9rMJZCRI\nGUYXNrrANu6Vf9XG5wEOwSEAjiSmwNRj3KQpp+QdXhfxy/NQ1PSUbCwBFs9R3mD6hODugChRQXBZ\nzM9H/E4IMHAhABtJ2kcYphKwmQVxAcpCOsRWbTBJn97peeXKk4Z6CKS0D82TO/zvtS1TlHYFzFdN\n/2p1iLu9TzxQi1zIv/tzDsCYi+eYLGu6KhSOsCtddnq7joVU5nDVFpKHw1LhRA0OfcCi6sYY6srd\nSImz5QlTsMNYSi4PHUg/qJx+Ht+QLqMVwfRzjZ2Sdziyzowk4J0h/6nD+DwviPn1kPYcvxmepUeH\nF4xj1VVEldO/ZOZ1A1H67y6YSd/A4wmfry2xxg5PcziX3dqipulTeJW9ZOUR8IDHSbsDRxo3o+k0\nnS0gbTZl8nJG6fMlEmXwD/1+p/GGZODfTMJFDANsGeyM0Ab0X//IKVCGUUd56o4mQ/73/TDtprpP\nyTt8u8MXfF7aLZ1ftFINXRlbkkiG4jGbI/4owoN5Y90D/1Tyd+hBgIFLDFMJ2MRg40lg2+bPy7/z\ngy8DDrH1EFuBTqMJHGpsfTIcBKO5VGwp/q7gHpuWXoR0mhWzaoOoYAhifg3yhNfgE0sVOBTORqqU\nfferBS/RfydwFtLS4QhpbWEPjVtmuSz/WX0j4EtUzSKaVr29DCZJorIsTD5jnGzmB0Irg8UYW1V/\nN8wFzQXgOu6Sf+VGI3oI4F6DiujNwolOJzOLvqt7D+s7/KXgPZ1Vn11smZ9p7sZqt84sW/9xhh4H\nGJIrbVxGSgPSoLH5IaDRfOi6jXcBcwwj+UlsBeTfx48PaTlijAj/aUJ8caIsKDgc06FiVu1olMSQ\nInWT/NdAc5LKw/uE4LNLVdxRY34SNXbNaws5Rs9PMiWyDsuCc9k51EXItVTNIorULJZpFa/ercID\nZY4+HUtoGUe1tCF6nlm8LAQxrdCoa8k7bC1zKT4jEV4zHr7u4cIpSsB4zEQIlE7/akW9T1kiML4S\nGF8DiQOwBfbDKIzwaw0+sUrv5bA+4Syk9YCaLruaEobVct/FXERVjpmM8+2xeumCygbg0ctbDMNW\n2Abwso3z0iQaZQa4jru8e58CuFdVQjudIHoqm3IhhqsipkTFO2yOise6mWadFXQCtocFiwQuH/pZ\nlcF3Usk+e7lbgaFHGXoUYPAIwOS/YOpOxp9LawtB8zHgzc3bgG2b7pWmUmIwbdw6t3EYONXwAY4Q\nbhRsmAjum4oWQpPK5Wc6HrKzTArYhtyUI/l9MNM96K9BoD76Vi/f3ZKDSXbfXWbX/pMZyC2YlHmK\n3YPn0AecheRQFzEXaSNJ0s+UCkprRtmjxrz7VbciYU/fUDgAn9988/zozUuu7R8Idg5zW5oGL415\ncwiUjuivrsEus4LJEdqCrsdtDT42zKxYcjXPBiYDNlzJhEf4A25a4IpDTH6xvzuE14133nhwviHm\nhiFIqFx/piJEhHhxT8cilOXUSTczReke9K0CZRvtUL5fJ3B4psHJvtcSGzbMAblMDWboyC77zmwU\n7laW9wfBScHv58uDXFpuYMrgKkv6hmbRTMn2+BkpXmCE7V4bGGXmBm4HNkcPAtwFsv3kxUfongL4\ngJxPqjAU8+qInwl7jfsdwe8KVWljRP+hdnKCHZMjxrVKnjHerrpsSaijYjbF4nJDJ26VG68ZAbIV\nPnOBynChpCInNl0C3Ms202CaY/ipIx6fmeSzE7oCXkwQ8eaw95lOwcc9uj6h4LfUmvGZObCW2QKR\nsQ5WpBZY2pMk7HhJh1/vs9ksbWbfLcvgkCnUsu+Cac1nzmxadm2fuXCEtJYwCMlMC5DP1EDJbmaj\ncLeyvF8MCO4U3EHRikcaU7lIjT1dkOyS9qpD0Rtb8x+4+YLhBQweuoHbhw49DtAGYC558OIxMHJb\nv2oEcpXb106x+j2CLwd0lQ/Gj+l6+HGFC+62Bp3yrATNiBvnS69dQeR700yXqT14Uw1myyvcepKb\nn+jld9AKxuMbLwPuZZv8ey/bDu+4ErJNOtLOfqaF88/G1DehcnG//DpYEczzzohX9t1GxcjzuyVx\nAznG14UZQkqNB86c2bxCtX0mwsWQHAqg89R5nAz4UsRVcjfi6ga3BBwq7OJ2GHNjzUjStFGSDxQB\nu1QXJtH+j2dk0KhffLjBX5f0v7tha8TbFGG8LuSqiId97hF0vYSZpAtuVtCM2B4W3D+0ZiUI198c\npq9aK9yuke7h7r2fmJ/5tcImbcP7Iz4y3/tMR1X+b/3JNo3P3RJEJJ3vTio21VyllWIjh6cBnIW0\nltiwQYbja7rsyO1SY7eyPIXCPHUaMRd5nMQ62m0aIu+ZnJ2UGT6H508E35/yfhAm979ERMOt8PfG\nL9t8HJCG0Zv59OjiAYAZwzYCjnDiFBgLGL1jmO94pZXzY35jrqA5arrgOgG3VWUlGOsgukVHVxNl\nA/svBeyvqvBfdHjLd5U6PO3Bk2OCy9717G9F37MsDD88l/1M9xRNf7avSJupo5mHd3UyCdV02ent\nQt+dly7XLrvCF3WoBWchrRMszZ+28vo6nadOdigZp5xkI/to1xR55/XVevgc86Louf9b+BPj0VNj\nvt8WRyajba1w3zjwMjH/Zj4NyL/D0X3JTdtqptGDAEfTCxh9NuA7nq1y3Q73CF4b9ootLrhJei64\nWUFHH7XOYZoVCNWVzlplePajfaFsmvR9gapYIcagw4cEL+0QPAQwJIk97KVenXqEb0XfszRp3KHr\nQzdlEI9Ck97i5HuUpq587mxq1Sutg9gPu6qFdpUCOctVA7ndvibMxjnd3dmYn35uwxGSQwKdpw7b\notRQY4W9Zi6jc4bYkiR1zxlErrD3slY01lpm/T9Xo/89mCakShfcx4Z7caYE1p5V3nBW0BZJcd4H\naD+6grg25OvNigrvtNLhtFwmytqk81eJxjeF/7W29tZiTHZuqofbZwtof12UdvE1k4Vlv9blJbaK\nOpwrcIS0tugrEcPqjr90njopNLAsSm0f7QJjRQveAPt6xPaNxvm/Nt+4Wadg4DqAq4NDwFu5VdpG\njfmHAG5XM40OsfAoGKv5SNtILhjx+pC/q+p/CZgcSUyfjhQ1FA7/ZwCDikw6repZe2lB1VXdDm3R\no5yEjUqOLgeZ78ePxEbdyiddhWqeVvAkwMYH8KSpdJzxM7SpaNL4nePheaI51s5Qm0wWMWaQU50g\nYkbdoBaWnenwEkDwmYD7Qn66dmApP6HLctTctfzWzKOZ+UluHtJy4QjJAYw8dZ30otTpc3oJ6yx9\nMgYbBemUZS2D2Pzvt1f2FS6p0f+yD3Ylpk+CwuG/GZTP24m7DfEGRs86aruqR1RVHsKVgh+zI+Sg\nKKWC11R5C8UGoKpJX9WKHw3zZ5mppFrQgh1F61CMqYBTPpkhvfQfw4LPCD4rCxt8QvCZZazm57B+\n4QhpXaFMy7Dq0HnqpPC60ilXNtqNGfI4QUlPrmV4Tej8IPSDdndkBOA6tvtt4K3cKv8Gc48BvdBR\nByA6ldhG0jDqphd1fW7MtSF3i/LKjeZMH3LDf513L4Ko3E6cgU7RqF5GTizWZfnRFRfpLcJrQ14B\nH6OACva1GYAuxKoZ5d8uBI8BbDyBgImrmXhuaZO+ZPTVP2gcpUH4GxPiD1Mp7+Qrmiw1ph5uWtKj\nRXl4JaZ66T9eNcIvkxrfyGR31/fTGBIWU8kMKQ2ky8tSD57t3+k5D6eyW0ts2HAXkJ54RJHKDuNo\n4Ubhbh6lJ/h8vcmf6l2rMisreTDXN4q51OM7WGV4+5W2qvvykc7cQeDawbvezidRhOTfdSrpvpWn\nLjwNxkyjBbhN8DcBrw/ZGqV6ha7gD0VR5SRhFKYcNxVguyAyAiCVi7FjdKUzNZZwtx5tRoT+yqcj\nmhXKPwmAH3N1xHVhcapWX2Uekh/fRjixlSsGVZHRpHcevBa4i+uAO8JXvOyKNxZ+K5rGgreRIbyU\nQ5OOsqfN06aKxJn7iiKaEdfM9/QT/cI+LYkaoruMyk7OQ7puqfVxcBaSA6Dy1KHIxu6kiWBUOfcy\n840kG1V6/BJXzEiZJWbDnwv+P5Fs39LgDsFVEdeFSYkfMiLjNJnKWVKOaxfcjPJX6gBIIcYULZMe\n1R+ocVUZAiDR8q240mF7yJaI0GdWcGXE68L+fvbim0xcytSlhKpJxYW0bkyd8wPxo3O/NSF+b4Ki\nb0XeUyeHBxnbtWNcQnrYEJXYnF1xlOBDhDuJrum3WRzWIZyFtJZQFlKctv0tFtLSZiBVnJBZB3ZK\nmQdjaSeNFs41lTyhk142YneRyWFCDoe1gdX+7pmd3gzwdj4pLSTv9qcAZhLbaPEw9NYz4gQswLtG\ngKyVY2b96XoqRGS6gaTpU2a4ocojZcHkZ8dolL1np8ZVZUeLTLdVSkdEyYBf20mpDK1qiaX4YtoN\nJn+I1vMYfx5sS3Qoh4auBmYYnWH0BWF04op/pe+sP+j42cL7XmhWYMwgp/3qW2caVfYliYFJwYQw\n7hhfTHQNoRmBqo9lZnDIWEjmHF+H/uCSqzpk14FtwcGShKcSOhXmaHrZCG0bVC5RAUSva5WcVYo/\nbvCuEWjCfvXgfUk+zg+O8KmGep2YkVBVURKGNn3KDDdU0Ai1cgZFmUEzhZkMrQfSJ0yp1LNmYf6e\ne2FH8UtNjnBbg3UC8RSt0zwcM/680nP+QQThb0/EzxdyN4L4AhH+6ETnZQfnB2+OnyUifjHmhRgz\nZ5vGt0475SqXJAbFRoEaN3lPIGZweJrDuezWFmdZ8F3wcQccKlwHNh+C1qiUfVfK8NrfPQO80btd\nGkZv55MDnz4NcDsA9xI/BGqC5nGlS07WFy8RBTysRAGzgk5AEzodw7dGhTPNj0HqHTpGGKkkmN+M\n2B4bYgF9VDeEFhruzbVg5p4d20tllA6zKzSd1gziZyTM2gyP1d9k40nEfYAhgVgA2HrdA4An4gEW\ngZkPj95305g/2xb/bjLa2QpfMi7XBIme1YpoEeKdesjnbwT/AX7g8S3zM+nUU3h+rMFUUGJGsZvo\nGub7jSrl16rItJBd4+CwYnCEtK5Q6Kmzn7xcBBxCRZtNX0MLRmF3SrBwcYf3DjNu55uQXxL8WakM\n73IRvbP1Ru924O188p38d4BbDUEdLBzrURFKTfe3AY9XJWJIMi+o+vSeLWElUtnLz8pZq9MwVipV\n1p40XyoFTG6QHrlC6QSMdfD9Is2b9aVCH9Fdlem0hQ7fgXL3sWQm8SCAFxuUBZtHHxzYtAgMsMiL\nb+DFYvYdDwO0s7eLF18W8bLoyV0+tzfZZX4mdWJw09C2jkvwjxa9nIalx8sr8TJNUshPDisJ57J7\nRkNwp88xVIhIOugkplTYRcPjiSYfk9sZZ1XUc8e9MeRfh7QLPX7hz03MzT8cfmB8CVWdk72PdWGl\nTr6HysR4yl1ws4JZwfaQ94aGv1IHlozsbLMi2Uh0a4Ga/ynPLPG/yQv9kJEQP07f0/pS8nG96bRj\n0KTr9fjpaYqYjaQ/E9kMdn/vTEBoHZfgPaE4yeHpB2chrQfUNIlWHvlVJKZVTCivdAI8npAXdgos\nB9r8rYyFhwScPxF8fyr6QbLGaHypiF7bCj8+LlUMUt79dj7JrUAvF0P3GOSS1C1ADK8L+ftmDXch\n1qxHZYZbQDdKMiZInV4noGuysdEQbUHXyyXBaxrmZMngXRKYqXkTXTpBdTqiyZHVnU5r9+Dpc8wS\ncYzB9BmN0YcANrHIABB7HnDf8LBpSPU8gOFgfLoR8n8Kft/MFUSlv7dyXNIBMUPnPdZ3xXjjwnMG\ninbzBpMzklYYjpDWM1bx697kj32OFXbdO5ITeqI7PYYN0jaTMR82iPhZ8GEI4AI/bIxH3xvzL2qL\nr05G21rhn44D2/12j4pg4NOn9XwjTUXkcgJJDeIXa3VXQLkzJyghUq1B3t1LLLQl4rYGoV/MBJ2Z\n3IP0Rg3/mx/TjGhGitisLyXXajoL02nLvm0L6mhG8SkeBfDnUic3bnhoVMwAMR4Q+97hrc3eXRaM\nD/VRP+R34F/Cq/RnEqTT2UmYgUwvhMpxSbS11guXTnclzdGUu+yc726F4QjpGQe9vB7pXm5SMBXw\n7jDppvUhcwBbJmOKeEPIr2YK42eL6CWt6KbWMit8p+AOYezvTc/+iXLmUYYPpuBA0tWJLl2Pbj5T\nzVTvJp2A0E/YAqxpFzLlMuxeOx04ShCYRK0o7oNLE+6lSe5pipCNsDvglohvyTf2eX6Hx/LDhjl+\nr8F/9eK/h8qJcjUJyWHdwRHS2mINxlaajXQvN2lM6Xh/A08QRERhz9EF7DGm66RD9fKeN4dyXfPz\nh+Q+Uq88nMxWeeXQHPBWbpUWUjLf6PasikF76sycQAkbZRyLB3JZIiRMPpgqiEhsD7mtkctUk3ZQ\nyoSnqTYyoblnl8p+ox/dqRi8b8mp47aHbCnJ7jPeZrpJ6PdHcstHxhKy9xE9O0nNZmrecBhYCAaB\nLn53ow880hRgpHtagIUBgFN+yH+IuNHnoOBPInaGjAn+JOCuiO/ofFQRrw74gs/fEyNCQlFO4Utn\no/y7FmZfzbvsBnLnOywRjpCeQdCLvZIeyvemdOyEw8QdQsF0mOrqd5WHZlSnfWnE2+fZv4IVvqXB\noTKB70zSAfmxisRImHyQi4P1HFx71GllGRz2Vps7yWl6bnANp+JtDR7x8eOUejsVtVIvJQ9tDwmr\nPFR5kltZ3CX4UsBoyGtX7UExl0XcEHGD5KuQd0S8psm4x3dihub4j7A4wrvkySKkBRMUUPhImzZv\nW61aOqw+HCE9gyAFdXuMJAuWKR0fhSCiYQTMy3xXkUq74zOHAGBzb9XRl288glpq763c6t91CtCh\no4VyFQNwzC7whZGQ7aGKxEjIrv9AaaKgUKsbNDOXPaLK3GHUaMqWuqp89pJ0G+qqmuptU+lg6rnl\n7Cg7ya1s4juNxfTSTfsbHBBcE3FjWHDypkcZlGsneknKh21v/TzQ9fwTDAEnNg8BT3YHkzllXTW5\nbGEQ4PSgqSIXfFLI+QDgcWKEmzKPa4cIiAJi1bZeTBD1MmAt46UlCk2lyhiS606XC9eC6wQrkjbY\nFmLNT4DtwJy1x+/6SQdLle8qSjZC/6J295IRmskC2Jc3Qk1FQDD3mJk1NX6oN98or2J4IOCkXeDb\n4fIumJEYCS2ntoR/OqrelmlAVDBBksdGS0FGVc61QukExkbaNyjpRysdTFQGmVaJjSR6WvOdcJgn\nOswIdoYFZw7ApmMAXjr10MgN7YgAkH/vbl7XG3ronO3A474mJMGfajbKQ5u7hAQRns+cIIgQofxG\nnPQ51uXFgjsDvhhyfcTSPHj5qbJUueycv24F4AjpmQI5AVZn/RmDvQGxtcePO9ziJ11G5XTFRHD7\ntcnOJSPLr+2tDR6oIfCdVeGT7SFdQQfFB1RRKFXTgCrNndH0mTMJ1YmucgxmpBOjRRnZaqi37UGm\nVYJlcffdcE3ETSW1XSYaTAbcTlGosqAuMTMRwxEYNm2DWzxOqrvdIrgj4idDXr8q1XVYaThCWg+w\n5Egt2+4bIa9vcky7oFowHTBPRY8/J2h1qn1XOkNz9OoxXgHDXLi1C9zA7dJC2jR/DHpZU1FZUyUj\ndNMqhkXtrKOP8Ekvrh+o3D/l7+X7dPUFZY84XKUUN5/YhE7aXhlTyouWUTKTVoMoMrOrty1BphXH\nrDD8nyUm5tf83tqomTyjjQdTFtJg8OTI1jZwnI3A8cGND21ugJE5MHHceTzlNXhfwO154tmt3MJl\n5i4G+0s2MvjspOCOpRJSmZ3kUgqtFhwhPVMQczFpF9R4SLsqYB5ESb9h911psyR6RWv5VX1ALy7e\nqRU+yQ7nO7C7KlHQHKc8tUqQ/d0k8krxDMagQ9dT1NJU66SaCIyXaqYKK9XbZUGmFcSsyGV/mCl+\nhZMdjvpsLq/t0uDzBXLE07F6VWVz7oHDipyKjDrgNyO2zju9w7qHI6S1xWoMqYpHajEXhVwvuEO7\noESNgPn+qJcmtMx31dTm0Y+3Eo/9CKPMADdw+9boAeipGORt59UdTsCnBH8TcJ2x1F7PWbelIsOp\nRJiJhNUI/8hrt0TKILBMxWzCmJHpJ8j10Ubr9AydShdnM1s4W6XezgSZZM21VG/5yESMUnk7TIxB\nh88KNnVAmbYYa1iII7K6AAyxaeMxYFtwLxAiwoYAngq9JFOhCikFj/2VxzfzxFMzwZ1GaYo7ji0p\nwR3957hzWDpcC56TKEx8Ajwr5YKKGQ6ZE6XdcStKRqaWUL22jdo3n4FEy3Atd93A7cDo4gEzayqH\nCJ9KngD8seAvRPJMudReM+J1Ia8NeViy3L7SDKc3zicdcSfITR2tCv/oHtyPuXE+nbfbeEQ2RUJT\npeSrNKeo4eLMFdZXb8+udKJVS8Sot+x8urZNNXrQhCQ1Ch4MPgkwJGkpSNZT2vbWe4GjbDrKJuDz\nm7cly9Grpa6Cb/8PzhQQTx21o245qyF10ufrXX6s6DY1ZXL5WUfOZbfCcMlVn0EQzEhqCVRv44U0\nw4sTH1c6E+qZNjfPJw4TFCcFhqmAKo+fLcLmxBLqk7BRkCQMPelxUEBG64xKXZp+sCaVw4Xah1bp\nmk7j7ax8IJ/wVM5tKuY5yjPL6tMooiizMCpYKqm+odMzZVYo0WrWxMS4P+kXUbW9R3Ao3/cvpw4b\nxinKrGouMjVlNJtRl+SbSUWWWgR3r1x9HVYFzkJan1jBodYA0GB/wP16BKwnzwTQCZ8QEAYXEz0h\n+wMR04og7ZQruBCA8F9MhD8+zjAMA7x86Agwyox02THTs42A6FQyIJ5s0C4Zkn8QmlFa69xSS6bv\nTU40++7tlqmjY4rDqoQA+QjNdFPdwUSr1GJLNdOUVZ6H2jCWSqqZ+8diytilehYUmJgamaCX8Qpd\nLzFqfzLi9SGxMpVOqJVnBx8F8DrJbb1NTwHDzbl5GsCRjZtPbfIBbSfFFwpOpuzPqTQ/ZVaY2qkW\nmpf2W424IRFXVTVGHVNpsch3h3PZrQhcCz590YeLwOco6SDLqJo2swuC8OIw+j/wj3ni5iBiOOTy\n9NoTZRfGngjfMg6wlUsaJ4DruAsYZWbo0OMA7YSKFh4FY77RVyxD8hlCn/fOFWmdgZzW2TZ1tJmi\nIrtTKxOh6YvnslnvWuW8tV+JvwOD1Wv762ymzFITrRabmBpjxlAgN4/qZIc7BDtCYtWVdBUhyZHH\npqPIBfrk16DZOLzVOwR0aM42RkDl0w2Jj4tww4R4YiITmAwMDWcmvIWxJH2NuCERV9dulUJ9Xc2j\nDkuHc9md+wi43+MJywjY4wk/fpzo1cHcm4JwKOOUs10Yh/4j7X7rc0/lUnseoV/sSUvWJjfQKyzx\npDUj3jtXK8QyK/jYcCJ6zroNTagOTz46uXP+dQKjGpGijcDo+o2lkh6pwSWVpkxP49cPkvrnnWUY\n5Vql3SxY6un9I9zS6Pu5eYQXjYc8LG2dHaowUKOCohWmerWu9Kf2w0YOawZH8uc+Ar5I5QoyfKbD\nj4f8TMQOn4cEf+HxHX2C7cIvT3ZuHGGYEdooC2lz9GDPUzcPyjETQRfurDEknxWITl2t8/ZlTx2d\nLZIJVKZIkP6xYufejFIr7zSS3Ulk/GA1jJtZc27QyiValbdt1tD1F1iB+l3GYIZjambSgJpZJE3h\noSfx59WtgAZbtx0CDrG1s7EJnBJ+cp8hgDASfG9CfH/CrAKwpUQ7Z75rq9wubfORuo2SQr9iBydq\nWC6chXTuI2QnRSPgKdjVGz++WhbGDEVsn+OP9GkVQ+eRsg6yFDeG1ffVLizpSXvvHNAzX2YNUyY5\nrZ45VYZCmcD2zOqxU8XKiGILQ6uVR9XA3oS5NqrVuJkVTI4kSwImlFCv3ewwb9sTRJSbmKVWoKr/\nSY+jS3IY5uGdCfWN9ZK/+ZcOVFQrw79jRt11YwjuWpnKOawynIW0ttAp7FZxbJWfEjtl/MLlj9bj\ncT3pvsHHA9py7L670i//vhZwtXfItJBowxwARwhP957ShRh+2BL1KZKczabNl9save1Zw3KqaU5l\nUCkTGAkrUiQUB7HqqJV3pk6eLTJuCuYG1W43Cwpuq29SZGIWW4EaY9BhRvCeTkrdABwHPwTU1LMO\njeZDwNbBQ4fYCnx+0zaAjYmF1DhzU7A4VfRppPTnU3DA4CqzMTLBp8OJA+DuUK6DskTYUzYU7jos\nBa4Fz33EXBwyKpgpDBerX+xfhvwrAAZ8vorqEezp3KLR1iWbTgAjtCUVeXNPAcwloezu46kEMTHE\ncEHMtSF3i+p5QhKp3jNddTM5KSX5Se2olAm8d66C54rzn9YJso+qkiLjxjY3aHdBQjygGVXPlrXd\ndiZ1N5N6E9K18uuVUbLMuexTNC1FpwECKV44oohzW2czR4C5TcPAaTEgK+N/v0355NZOeiw1o45q\n6G9mUfO8P+Lqed5a3C61kKcltx7SCsMR0jMCITvhVTAue8LC7gh+AYgY8fi29s20yv3y83tujkZb\nlyRD4f5wXcjV8PtURH2S5ekC2KeIsdyUWQ3Fc7fDrEj6dwvPFQexknc4tCWeAAAgAElEQVQAishc\ns1GJcWNnyqR7NpcCCmvNlq24bRqdgAtjmpG6ysqvV/czDihE8LUp7/uhRUTTKRpL5VqCUfUqe9Iv\n5/P15VbRYZXhCGldYZVGWANAyMXwBsFnyXVHM0ZfFNAGthhHp9RGZgJo9IEWMMwcsI17GyceAuWp\n68BDkFtXYsFIn/rD1oShs2ZetUjl18xXPehDFJC3G+oontuCtjDUdGV3zr1OUre9RWSuc7OWGIWl\nTDmVdrYa7ZbxwmVsR4nbGjWmHAVJJWXIyvSRgs2o1d9d+RHrT1x+AYJHAFAq8M3bHpQWUoN54EGx\nmYDgrmmqRDRycJI37UyiGi3KYdvEnqyhPsoWlnV96QrANeIzBYLPBNxHUXdUOMmjVbwCeILoNa3l\nV8kS9SkOclhNmcLkpLPWLDvba6zHqusjNRSa1QrvnKjRVJ8OKud3hsx3VUgBS5ky/1GB6NIWFbaj\nWdvqLj8qeAr7oFk6KTgRXCwP4WvGm4+07Z/GWLlpN2ZoR5olQT3B3Z3lEpLDKsIR0tMadVYGGxB8\nRhpGEhFMqZ9u2frd0+mJILpfCgVRQLz1Zn6p9bLBeWAb9yZ/5boSctnQeZ2irBc9KqxoPupTHOSQ\n4or+Fc92u6HOeqzmtRjcU3jnsQ5h08i2tNewPEwbqFwiIVHAlOUfVUf7p8ptx15toyoC7lgDVxl+\nVeylA2Ban6PtpBPqHkAQ9tQNm5tZCyl+tqDq0xglC93A5iV5TYlSk1Yma6gDZxKtFlybngPIT4BI\nfaySjfIGEOpHnu/KJMx+adIcYh+5ib2Tz9nZ3NK6URLS0Pzjyb2OAMSPpWR1GIRUuTJucZCjhmit\nvihA2w2l67FaiHpGSaUzR/fCjFKjkYty5AtJuQFn007FAqYs+6jGioL7+miTbofJEVVb6uWHtYgK\n9qs0TtOwE5pJSh/tshtIf8QLadFdcFylZphPEdKFQ91TG/14owivnBBfnsh8Gvm4WwZl9KNljPrl\nVnN6rFPZrQBcC57LaPCJgPvKDKBAzd3Md2X53m9CAGaXGnamwy2tG1e2wqWxk0BVq7wn7UsU0Ano\nBAkllE2qtfX+oypwsafIs2lqvMq5rT1D18OPi52KKaaMyj8qbSDkWwbVVZvvYtdNUvWUGZU8alSZ\ngLW15nUQXjXOS8e45YoivyBlzymnH3Ypow6XrOHpAEdI5waKP0efr1Her8qfd94NNqN6v48LpgJE\nTNsv7lKnd9x0ZnTDn+15FodUHxBCWstgOusq51uVxk6CuitKSNRKGKoiQ02zw6vZL28x4uaFwi9N\nSFbLJvRV9CXnVEwxJSXNosvLzEfdXPrprXLdZLPaL9rLbFoeADMtpFhZSNJz232qNy1pKHocaATz\nwCaOPrBxK8AQ4ZBg44Q4PpHzC9by5pmfodyQefhCrs1NRcp/GfvqD8vUDQ5LhyOkcxYB99lT2Onu\nNPMLPwCh4aALZY9Z0qXOds6sSG1nBZ1AqRIK+9YWPKZoIFiqKABVLm8SJASQpPDpGJ2Z/doDqgV3\nFFH1bjWNc0uFZdMtCdhop+KIJteyZiFnIGjorrpwlaG81GJLtV9U15DVXEY9fvblGF9R8yFlpl2g\nZsuaJ5uDhGXPjXU4G3CEtLYoHFItWo/WhdTU2ftVikadY/BRkdyCQB0u6VIf6XDvradHjiSxge4p\ngBNFOu8yzBrk17G75nQwZgmiABNasDWqsprvUS9rjq7tvX9gqB52q7tNpedtzqgHFaKGkH27EiLe\n1qgyEA6ogYa+ueVdWjCqxPR62o659FDJU947V5ELI7No3aL6AsiRxgnwpdwlTNQNPQtJbE1eH4Ju\nov8eM1adkMS9q8i0C3LcGhSpw425sWXfx5rJ6zLnu150xeBy2a0HrIqlH/IGKjKf9ba1W+imBleO\nQFNlV5awLnw2+Sk4AiGESbCjq6LZi7l/efQEYGNGP2jWiV6PIrq8d66nRyhL423L1W26eGYMC2YK\ndhWdVnatSTwymrLLGK5n3iWPmSrjSWW3k6Rrz2ieCA1yOffeq6eF5d8lMhixmZaqlzxF6tprZk/X\nn3hs/DsB8SniUxDCUThKg/kG85s4esHQwgVDC3JYEG4ZB3bDbqOFdOoQTT+6vvvSS9qizNQpo0Xl\nV9i6kHm++g5nG47bz1lIC8k+qkYN9PWo85M+kI6BV7lxxl4CDyylhhVpbMpdc5X5gUrlcxnBlk6B\nisElO9PurEL3UKYFzfk6+9PvUqZqMx+dR07IbhNfyGm2z1edtMF/Xa9eO5iWSOYLsdKTjeogvkDo\n7S1pE72VVvkdVop6/XUIitSk9NzUXcE9Ia87S2/i0CccIZ2zkIoGqhRVe2BGdTt7A+KMFqCGvK31\nFIR0nwTlmVlIq73LUJ3GJt29zuZSD1hQ3YOj6Fb2xSYvtgBr5H9v7hJd212Gys6ixZDoR8juh4xI\ng9JsFskoUzk7rJlQ2linRjvoa3WFSRNwerKRHZlVVLX+G2Na0sbjif5lMHoS2BQcFYTAg8FmIL5c\nhEMT4sREUy0LaxJ3oFR+qO/gbuOorOM+Q02qPw01N/ZgbUKq6ZFzjrsVg2vEdYIV9g9oRcO+8hW3\nUd1pS406d+W1AFXyttb5cBTCpKPRhJSR1eVfr6YQzhzxtvshJMAP8eVTzB4883Yae3I1Sa8Mm9Sk\nqcbk+Us0lZr+rlapFgOqheyzojc/adacCqYxA1uKlH4dUBRS0A5BkUoaiCCA/RAZZkizN9loCZCD\nEmlcLahvyMZIrZF1FExC2rgZYAj/e23UZ1VlohcUHoCduU9Dv/oIH4y4cp631HsDN8Ho7ME19DkI\nOf0I9XvOT67PKxXkqPN/huxo5n79rVKh8Jl3w61LrGQtIZxkVIm0/ExiVpQmt54t7L5Jv5qm20Je\nbKnOPTBW2DOD7BYq3WVcsjNn8Gk+KGd6P2ZyJClLJZTLeAhR5tqoEUhRbs9HfE55uXYIjOhgOj6U\ncu6NrtZkozoILxtv/mN7Wr1Tpec5A9Phqk+Tf/fBLvB5eFXq7bA8OEI6B2E665o5t3tLBe/zXCBM\nLUDm168lAFJcMERrEOaTce7Ck6kkqnGVs46aQjhTypyWn83mUslRkmiu+M76oXmXkAktEG8B6S7Q\nfklkRDBMD2mUXj22Vcz0423FRoGx6EZZsE1ixiAko60y85ySuuWS6c0KOgEjMe2iAFLNhXdNZPRq\n2oWbfEOexNNyO9i0LbGQ2AjAEPHFAlXZyrm8FFvUTKvWMh2cOpjk83CXK/p5m8p1Y113uly4FjzX\noJ11HYNZMm53OdjNc4GImQiZEEW//gjg0ubLnxUd27nzBdMjD/c0TEtCrTxyo9l3Q+VR7Wnzconm\noKgXxsgCnfee1eHFTEylUlP+mJqlZHJY/pK0ASubpZfsZ6/Rm5Z5CAO1PMeOdPiqfJ6Tzo8ts8Fq\nU6xN+rTVnGxkR+yJ8IoJ8fDEtMqaWhbRi5R/0cLX8hPIhA4FBzt1CcnhLMER0rkG7azbYowrO3BA\n9Ye6fyvkghtDZuQiErlf/0ibnzr49vfwx/A9ZlQM4DgYE48ky5gTqcqCY3WFcBmMQYfpZrr7mep1\n+j0qKlylgHSJ6pEreDFS05VIT4exXNKCKBdPKuSwFhxWwRudL1y+gilDt3sIo6LwlT3QpZLppUwx\nRd4yQXj9hXctKEvcEMjqhQBB/JjwQuBCrwucGvLxCa8a55/GOJGkEQoU95iG0Rbjje15/kxjW4k2\nrlzSq7g+cxXhGvdcQ8gbmnxtGvYZ40qJvWpjVP1QC7nACxFAQKh+/V5MEEFrtMH8xoVHIREyADwG\nauIRuSSqdtiEcDLMNWPQ0pSa+ylhdj/5kH5U3jmRhKBmVYc7K6y8SLoLlJRj9yKNqoc20wyR4bAp\nFXzXzqYIUFoP3ZWi+KYQWpe/z1AAdpTtYKWxTlC6bsVt9MFGs+WRPA1NSz1C0oucAyGiEQIbOY4i\nJCA+09aV0nXHCIIeVuV2vt5jtLoxzOiXkCrhpi4tF46QzjXEXEKu68v4rvTQuXD1OECExBHCZ04Q\nRIiQMzfvOdMahf+ysrX18+vaYVRxr7IqZtLluvuxr58xmg6rKHo4HDDW6fWeNl7cb8QiTGLXaoj8\nJdoxhJEPA/V0bbFm2C7IUZd+qQ7srudUlC0wY/y10lhiii1pzUOJWetyU5WYfD5TX2f8kl5MLYPg\nyWnUZzidU5ZoDR41+Fo2XrR088jhbMBlalhbZGyJFZgfHnNxyBtRCdWaKuVCC/YZqwegVrfBmPce\nqHwtAXgxRAzPIUIA0WoIwk0clRPsCRMHygnlr5NChsq8DHlsDwsW1gPlYYwMW0Gvzqa7H/kmhV0q\n6S7euCo/n8bXo3vdFqjHjRpKv8Co1XQubUCQ6xdNg6mTZhfzbhRNPt1jmAOUSMoywTazoZpGBfIw\ny2dyR4NUqggLepG8seSSjJYk802I1b99gg0/wcTzCL/PTRFX/BYzU/dt5Lj8RwA++ITBOHAARtV3\nWEJPZc4YyWUvGqXyV9DmQ7U133k4M2gV4QjpHETIDSEflttlfbUslB6PiDfqo01FXWYulu7IyKpW\nuKN7XjPs31K1NElVj5apzr6TBLs1VKf1SFE/e+O8SrSjcSDdjeWJfdowKjNdJukQlMT+ojfSdwM0\nIZkvFRgdcCZEpAlvb270YcqlM9CFFtIaAxKFSCFuayjlRe5FJkfSq54X4U+E8WpNwlP82fTx/Gnm\nkn0mNEdHxtjD8qLmMCPsrT3psO7gXHbrE8sZhQ0AMX9PlWN9Sv1c5/mwz2HB8U7aBaUxGCaqXEHY\n0zLIgAeQS81QmR12VkUdHvHLswfpfmNPundG9TQ1su/0nDVGj1U28Jc6i152bdOLOFZE7BmVhOkk\njXK+OC0HJzdMmMn1ppmXapXrzKSHcFfuttqpaAl07Slxb1KcKsKEPctGvoV1DOn/afC5kk/8VTvu\ne8noh16756bEQoL4IhEyIZjIvASGB1STddmLNo2pwxFXurxB6xmOkNYDKumnb34KmKNGXw1E3Bjw\n1x7HzY4uqxIIj3vtuWAkCOLHJu9g6hHGn6R1CgwtQ80qzqajDgksAqlm0SHZ/dRZLiGj2B6FKBGO\nF/oJt4dc3lULvyqVQWI2ZmBqFoISNfl+2GvINHQHqd9oqjzZQP6lMpkj9B0OlFiKrXIaw6hVXp6n\nyPuURyEqs2xYWvirVib7TuerGzl+3tDi6aEBgEHC88c5M8b3Cpfse3WHL3SMjyJ/zqgxFAnZEfDl\ngC8vO4Dk5HarBeeyOzchw0iVEYQ2n5vnwwG3oWZ77DPSKktPjGS1w5OHb5s6vOENTPwd4T9z0wau\nGGZS9F2xVNRB+6/K7DiKSLUFB9MCAbuzRvvcDsKeAmfUrOBjw4nbcFYYy5Drvtua7LxXVdK+IdRz\nJfYWxd/zwaRM/U3oE8zmMiNelkqagS4JrYPOuDcNwssEhDSqs2yUuPvuD3jczmRRN+yEmSPhBhHy\nvpiNmdaFL6CqrFsr86IzplSHgx7dBp8a5g8F95TU3mEt4Qjp3ISptcvAGDD+EgzAQMivYvSNmWiI\nLP/JsYs/Pd1JzpB+f48JkSwzUUfOUBB1qNGv9chzCnYZXrJMp1wYXKFIbmA4o2YFkyO0BV2P2xp8\nbLh8LYxCTKt66psXvkvh3fJRn3QwyfZShZ60skrKOOGoqob2y40a54ypKpnkXR4QSnR01mbR7r5F\nuFuwd5gvBtxf4xOfm75jiBNS1MAgeOAR8hsd/nyeD8Q8LzTmZ+WpPDCGU+Y5Jjy6goOOk9YhnNV5\nbiLmkpA3Cf6yzLEecX3IvwZgIOZyrBM95xu0p79a6Pd/DVwf8Qvz2SSqeU4qiDpkwjwZaANor8FD\nWgiuPU6UOGtQ/hozVY9iY6mpy1gAXc/w/ug725sG1bM31Tmjqs4URUr0jNpOrjUwHGhlPsCDKrQW\npIX8lZXcoyqgE9+Z0Fo0fWejMvmAUJ0sG/kcTp/SxGb9xN+w83kHiR4bCkBxEnDKi9kUcaPP3wr2\nU56XIYKDBt3rc7JeaGUwLUNu57DycIR0ziLkZ+DV8Fv5bi1kV8A9AX8t9XUxl4W8X/CRMvbqWv3+\nh31+oaoyxVEHk07KelLSs+1lX6JLIkApEVR1/Rg/JvQhSk+JNIyM6abRzwbpGbXy5noWcXJBSdPo\nnl13e2aGiMIWm1aBJYuvsmNkxTENkR3lPbGlkkFufW8zb4Fu6iBN3qoy+YBQZZYNPcerZ3Ga9Gn9\nxK8d3XiQUvh8RW5Ywo4ZNYxlrtoMXwYcJ60fOEJaJ1gs2V4WQi6BNwn+MtOtyTFmgw8L/izibSHv\nDfn3BP+GqCB0PPTZn473fsbSez7W4bDPZd3cUQPFUYdKJRiqvGwwrBIKyHW+Z0UikNsScWO3ZK6r\nbBlfVcDkD218oAhDP7dQGiCVaVNGbTtGvp/CFmup1SjyraGh9XiFrrl8T4yqzEy5fkEzU1Mlsmum\nD2VUdunKzBpLBUpsL59NLDOxVqy+WPKJv2n04o0cD4gOyw9oUC1cwQAQcLvHt6mictS9TSu3jMCW\nkfbbZVNdebgY0rkMwV8J/jJfrj3vHv8g+KgsDM8T4Y9MxM8ROiwcv0D848Svf+nAEajw+/+VqKhJ\nadShpRQKueW3eyibSwXj7SQPkB9zykvYSAaEpoOkPCs0MMMOOva91xhX6zfNeBeD3K06RTI5TSRl\nLaatE3toylTBaRT2xB31uPxEXfNFxtRCR+RmilJCfqoyhfpvP2QkTLWwtJwkbLrwoPgTP/NeJve8\nsKQe8urbUe9aiLHc9kyVLerRHeGDLp60TuAYfm2x8oJvQHB7wJyMIZEevxYOWOGKiF+cH5gOLxqP\nXjrmX9wWd0xG72iFvzp+dePQWzpH/6DzDbvf/5VRRUUrog7p2iQ1zoukNdRg2HQlZbxDMv/3WIfQ\nV2H5wpffYeSukNir7mM+t5UODhVWOJNWvLDFptLmlMVX2VSr+Zq8le+JzR5XV3JaOd9252aWafrJ\n0GGNgFAepm1qJg2q0IUHBi9OA4gf0PoJiAiIgICIIcC0kDwg5D1N3kVV2FE2/27YU2+uGiA4KOXg\nbpbS2sIR0jkFwWcEn5XbDW7G8MTIX2a54+Jv5C8/vlhEI61opMWbAYY48ZLg+1DRYb0qSiYkla0P\nW53b24QM/Mj+PdOXTKm85YYryeId+ljmtoUvP2OUmMGkDAKlVTNXzLZEdApbTBNYYCjXC1tD3rbM\n1aaR6XEDY6ERVI+rK6xibNvDhEIujJkVKuRWFRAqhFyfInNOndUXnxfzjpA/F/xsxMfOwOvhBAGP\nAUOcSAjJV6KGZLr3i+SOncr156kHD3YCG0vcqN1+Vjd3WBU4QjqnoNlIQ4cVqoLoof/P7e5zR/L3\nfF7w3LePNT45PV/WYW23dlgaF8ZW8dhuw0zR/UTH6EumjM5a9TTSlWTPGpCgUkFQmZ7VrBuqTe0P\nNVusMLZeGJqS2J02aSNjMSezc62jVCTFtV0vRSFyoytsASGJWVGd1Vtie43VF98Rcm3Er8hbXV5x\nQ4mYHw35RcF/o2pgE/ShougtFULfq5s7rDAcIa1n9OGv08uWa+SH+3bHhTg52bl4BE+NSX35p+vT\nfXfr+R951fwV7ynosP7fNqgEQnYc1qwY5ZxdGN6TfWly0n1JkXOsGf3/7L1/mBxHde/9Ed7gDuzF\nLXttGtDFbRAwSXSvx1jGa5CzK2zQEozNzxBdQmZ0E3LDzX1j9ORJFN6Eu7vXSZzNL8WX1y8kN4ln\nCYmAl1/i5wpsPJsYkImBVhCwDjZugRxaeG2NE5m08Rq/f1RXTXV3VXWvJFuy3N9Hz2qmp7q7qqan\nTp1zvuccu3VICQBMmpaCmBqbXInyjSPtSCVNjrz0XTDdqFPKjaEzEZArZddOANE7Vjg4Z5W1s+Qq\nwWNKu66X5ltcZVbvoYV2Tk6+UtrkHL4k0SoLHyErObwMEIwlp42uAA+PjmQmu9NGAB72YrbBK8bZ\natzYsGoWhaFUSFPd/ASiEUinCFTZcpy/Scc2OllrW7MBwoeYeQW9m4ZFkoKUqXq6kUC2awZ25v0c\neifQwozUxbdbRzWrrl7uu1hddsg4fuPgK13e+kKfaKua6F6la0LranZi4UZdmRpV3GWnKcxoXs5S\n15kKqLziqhkwydpydJHNIYTJP9cPcw0W88qTnxIOiH2NQy++7qmsn5es5skpICaAnw242eOessXX\nONzIrpkrqC/NW1118wbHE41AOhlQmYy0AqJsuXrr2O47DBfBYD45pysC44HTvBVglCO+0H8GTL+Y\nzu30b2H2bF59N1tikD/sOsUmhrvmJO/n0Dpxdax5fQJJFXMrMQIFeVOWNMbB13F5z5WWft206DaU\nwdV7NVaFI4+D6J4tzEg3HuaVKrH0R23LimuXtYOI68aLgqfsEHL454Sa5adm5WlIrNcl6zzAtX1G\ntRqyAEeklr0MMDa2PMYycMgPMn1d6EkPZOtVzBsSJn2+HPJRj3tVb23DLbEohpo5pdKPNNXNTxwa\n2vepgJBPqdeO7T7ufDRndxjJMrXg4ZF6pMJk5zMQOYLCB+ke4q79/Gq86tpNQ06wpRPtRGMSoy0h\nlaMib0wjL2kCe/kG5HEjFP1ap3rrFyzctNSTcJDx0WvdSMDGcV+Q0rebNRDzefVeJuJSyJF66+RH\nl8sXleHyz0HsG7Jd9ENrZQpgbQpaiilhtVt5EAYwQNTXGmNZ/MOXD+SI2DyPqH8pz0iY3Mvv7uV3\nl/j5GsMdYkr2qweb5YSJL824wWjwmKHRkE4F6OqRe7tvs7wDydndR7OPUCOakpLhKPaJ/XrGMd1m\nVXD1d53GLrfmuAPmJR0DmYNW3dHpW499rhvXau65b0SV8XAO5oYkdVW9achgVC23QLtGndkOHDL4\nk4Zdq5HVe/i2kMrIrdEeP6SclXBxyhltrq+hsoIUP22TXzLKGjT1ZE8MGoF0cqKu7iG4DG3pK6lc\nggTKlvfkyd3sWRjJzCMeqfgrXmS0bln4KLUzvN1wO8+zNprh6Fy/mq8VDhh4DArClpIAKBm7hhnt\nHC7vKWhruem6ss2UzLlQFnId6SxZ0KSR1mErOayO3F3IhqxjKOkXpBiYM80A2kGG9DJbgagK9rZS\nXnXZswBzLhl2OOLbPj85yD0/R8AXD9gAYIzlzFA8Ss5kd/9IackSb1dSzqwcblt+S/oRo7fV5656\nMqmpQ3Gc0UzlicWxeo8El0H/UVXuwsvoc5j/INck+ZNXAmlUyKJUdnPF0N1V9d7hPC+jTh7P3Hpa\nWOJ1AdCVoiUhHNCRM2JT2gjg6bA1r0ttzbXJVJOCa6ILaArBlCYnlNRUvUVjvbt3Ezvkrt6Y8LQk\n6Q0zQF7WMlR0jOWLssl38EEoaUI13HI3hjw/yvmQUnI+pMxKDJnJDj2BkNo35ZBy5oD1Pnc4JP4O\nGaY1Z+E8Ki2uNtGuWT+PM5oJfRxDcBnUZjSoygyX8NKUc0LeV7hOyFzMtY9NnwWM0ZS2ltURtYGW\n2UFH22yjrGQ8F26hdKlym2HF8cScmZQIzs+X5aHkkSJvUbXtJqZkywWA2cniQHRJn/XNMgO5+CpT\ntrpFjeft4oOUNaEacVEXHAPFzggVDx7YjdJ6T8+XEQF2+2hDtDsxaATSSQiHvpH7SAQe6ZvRrt1X\n0meX2GcKgaTbzUP+IOba4dZzRPy/AnikI7pOlMLD2bvKehPHCxMxg5DIuNLoNhejQ6AQ6ANAFBAF\nTMZD5WwiZuBlNfqKF9G8NWK51+sDRUqcGNdfsTrv0YJcytdPtM5TpdCQC5kxFoYQkj72mZ/SbqrP\nQCcvOKXQ1THkeevd03uljJMF6IqgRbLqAmmoJymbMBmpAUomu+F6ldOTlDTSJ3U+u/JawOOw3tM6\n5MqGaHdC0AikxzFiXtHmW+XNaGERThlLuBRo8c6Azxnt5ty7Jrm9u/SCGx7D7q8Cw8W8oMRUFhiY\nN22DAeiHRIGpMJJudtP4zVctZct9JpACbfvtNrVt0TgRxk5u1m5tlLuFegzSpTTwrJXCs5ynBQQl\nNU4KiSgg9mknUjAL9WHB2SvjwKv09OOrHrX5Y5/bg3zSduUKSlm7l9/0+Xab/6P3tE52i4bXcELQ\nCKTHEYpKSMoZmDajXblKAzFXxrxGHPfZT8luviCXSn/Qzw5pGtIIK5mGJH1Ibk3ouOtJuTgY5EKy\nRRIK5mGHRoczOgR0XWqr/EgL8By2L8eiyotEAecOOOCXFmtkrwrfQS9vH1PZ5NzcM+W7MsbLKCid\naSGTjhOxgRiSmTp1BPlOJjmxIWYjU5VKc6XrHUIw90OLJtTWmAN5GTbdH644K4W/4r6Z50jzIeU0\nJE/Tit4b8rdqHNs1UVuYVKEkqZ72LJQXtIM0AukEoRFIJwOOMud3ypkxUyEL5c3onuzFJTGvEgcD\nFj2+r9vNe3llw0vj8MBsvGlavB2RNx0RRjrZkaMj1x01inEwU9J4lUhZulAviw+wVYqlBZmhdYfc\nS+s+FaW1TMn7tiHSLHWFxXpPfmXv5ac1kIkYqNdJtILi5AsMCmhLJtKJpUekLoZZ0oQJQb0LtRBj\nt/qVwDyDhfxclfQOPx3aMK2+vST/FshbBQsm34LJbuTIw/7oALRs3yVSg5BGxl2ENqmHfb494Dkx\nl4XcNJ/Pi4vL29pIoxODRiA9vhGzBS6Ca0xOo3fpLQP+Hs1u3jP5XMJ4Jmb6set9FSrjYLLoHKoc\nAoGmfKgCenOaxlBw8BQS2RVSAZUXa10hUDcq1Let7KSCSmfuIKgoG2Be21MqkRJRkzFRysAzCYmC\n+qUbIalQ5hZDooDJlL5FE5qdlGfJ3hYZ8EeLFr8TsNtm+1RbC+kKuiniOTGXhwwivoz2zSQWAd3n\nmuPT0QarRyOQTiqUFY9qVSTmTHhFwK0J90mn0VkJ46Vmr2vzjelEdsAAACAASURBVHnJfLb5XPi9\nNUnUXfqdG1YKz0apI4+BklSnikEGt0MgkNYZ5RTRpUW7ZL4J8gdLrGsCCCzV+SyKRXUngV0QaKSU\njswuUVgyd8ki6GXFbkHOjBRR030DFwPIUufZptS+CRhEUthAXx+4Ro7IMjWYsg1dkPDapeEliyY7\nqSeNjh4BTvNWHh7NLMhk/4343IZ27Z4mwRfyTwSQ8MKQG0Nuwv7NaN5Wv9GNTiwagXQqIOZnEsZ9\nvhXyqYSLY64st0k5GxlIYwwgUTtg/yv9x6LTNTBRo4rBsHS3wyGg/taXFsrxjbbIFZSnso6JU7Fw\nd1K8njIxAwtUDqHk7bLcKDAzMoZcDPGRLbGeGr4RSmLlR33V0tBmeN24ax7u8i1XroeAj3jc3S7t\nB+a0kenfecKFk7xdtDnf/s0IUdQUQzrhaATSyYz6SshKytMSLk642NYiZW3Mz4Z8QPn4rWaw78X+\nP/YZX5f77EQ8KXWiYs3FhzClo8ApLQrcAXWucjuolNVCedpsEW9bS1WUdC+Ru5PqFnpC9HbJ9UGV\nGTOSDSQjI5cgNbKn9FBXMH5q16x3k0mjOtmG7vJ53iD3yQpazgbgCILU4DO4d3QMpA/pdIIHd6Pl\nJqS0HyA/o0oaieN78jRDNdwlXttEHZ0MaJKrnlisNkPp0V825MMhH1BvhTNlgSLETz3869kVRuS/\n01Y4Lfv4URBLiyHXjWsxQBK7W3KvjbRcKZSFjVpnt0IPtsJWzfqEfGFbxMl/VFCtAhlpJO6rtAdb\nIlS9qwId2QFbJwu3CLQMoPOg8c4zIe1OI6omJ9CGH8B2Seggr5kZB2781D5qQT+ptrLCzSFo+VWz\nh/VBeFAmWz3CKEfEP5XtVzDsYt4GbJf7AVP61qzvu0p3bpsenOyBLzLr66DZzR9/NHP6REHIR9D8\n1kIUqR15VzbLLO9bOqc/+l1adJZ9y/h1BbdKISpW2YtkAR49RV5WmRs5bLcZSukE+qJl1IFUfaZK\nHUVBBSSdXzLHGW+hvPPRcIwgI14rzZi6tqeMbOorV5jLf/eF1bqgzC1UsBlF/qE6VtZjCUVKGSru\nDnW3kx8oUjfaUeI+NLS6kwqNhnSSoKDTHJ3mZD6rxV9Nsk1tJwUC055RbYuTy7spnvgn9CQtg0Pu\n37Egk0ayK3o1hKLlp6NF56jlrJOJq90twgFXLdGJMjVC1GXoRFwdywAaTBY8tONJSWvBrgNRW0dB\nm9YpuZnXz3WoWclQPVLIFWMtKLn6jQqjQ/vKFZSNsTccuCj/MZmWlLlKNiMshnkrawHyYFkgDfWk\nvIbkkRY0JJ9/FKe41V1lIi1rnroSO3zgG4F0cqDRkE55rPh8Ey3kxrEjFwtFclmXVKwECJkEeN6D\nAN7xeWIqy75lFGG1/HVl2QXdrTI3FE4q0cBEPkR0mKfOq/JF6WToQHPDFOD2slDSUdRllZAIYJ98\n7b7FViCTtcMRVRVjzUkjexXzXDSuJj7FnqBP8VNfcMedoz4/qc49WJBGimUnBNmo+O8IIqXvKEdy\ngbEewf0fFCe61d3tzue8LfmVMlyvkUYnCxoN6RRHwBc97m1rgSuOCnARJC/oLr3tUU8gVFn2LTPc\nzec/zbtVhhE/JQVLx0RMJ5JSyuaL0tllu7TXRqg9dlkJ6GnkhZ6mb92s0Rz0EysryrUNjO2hHVLf\n/Isb7cwTwd1feTB0vAyjVvOKlNI4O27fUgRSk5uIpWJa8pZN93Oc76NAzK+LF251F6fmqSKPI+hz\nzRKvPaY+NTh+aDSkkxDHi+awAgTsRcuh496RJ353adMNsuJRTkPCux9gBMFvGHm4dJXaqEPEyjQk\nt05jV7AK5eb8lKuWmEgtZSZuhkRyqcW96iQ7I68E9PJrZMFLZDxO1S1E5NPWYRJVh2aZaTzbTZ42\n11eePRzZN2Knz0GF6mNWTDUFSzQwVhAa2prT7K+ofpKRGpAa0gip5MJVPhqOQSv3UopfalUHzbL5\naKHRkE5xxLwSSXilakfuPRQ/Bl2qQ8TaF1TUO4cKulcZw/royhel6wrK9xPJyzq1gSKvz7ZjRxrf\neibun/sWU5mYEUlUqdIsM5Q9bQK9vM9JjTeQV6uaT7fqU9gECMVUd+kpusqxIOU/RuFL9o6TBK5H\nw/2cq7nxGIzzJyGfOw49a3A80Ij6kwHHl/m9on+tKWchzRSVm/7kqZ3MqwwPrnjAkZHRzIrvHYJh\ncsuRh4/+0alDxDo/oZ3YS+dRTfcy5sCeiDk/kWzyQrRQV7qm9EXOFjYUlFKOti0JScsniiGcD+fD\nvPMWm4cd2d2SXhz35h/pLVQTNS+/eAHlcxJ+rC116XNiPusU/FWoX/UK9RuQue1UfUilGwGcPcvz\nZsQXu9QiDvlownhcfDSoodySpbMgYhBycxMSe5KgEUiPI9jklutLTDkr5sqQj9XJcOz98IDgOEH2\n94gvBZLyLXsAIw8W7613wi1g64S7ilXMWjqPCqf2YsiBQZZj1JoGO8l3oHyLXVKhCUqZe3S71nZ5\n3J6QdAhdTgT25EDkVZx9mhmzModCYW3WVTo9EanAlGSxV81nKIXrxGoK/tpgLaMlSQ5FgST++jP6\nQNKIOCSMs9GknOVxr7iM+zlHEh4Zfu3vSLignjOpWTMfRTSTe+oj5lXwYvgt8da2IwfCwfFMrroY\nVomEGt6IwvI3pC0498CxnxmaVHgTDDszEVt1r+k+UcDulpbpYE/JGKRrEpFUL0SfHaEx0v5WFAzl\nWxQUrK42OQs1Nv+6+NnjTK8nrrOlWnc+v/QN1ld9jg++u437esaB9CFI8JZemXJWi/e0qzRP8uWl\n1FdUu2x5g0cRjUA6qWBTLSqLEJWdxGgHV2LOgCsDvhCyHNn9+vPAh9YkB7pLb7xBaEgD3x8Ix69w\nJMhyACP35245ku/iojPiFSpEQgGF5a8Wh5vhsq4XPdI7M2kxPeVcXF1JNxd+8Ha+uh3SNRfUoImf\nLxPNKRZfoi2cyOs7gmRVGj018J5MLBpoA9cvIrrnqBSVaIkbenJ0pcs+GrLHHHZnM9kd6TsGkvhj\ncMU4v4NkCHYtsdSYVEH5FVWWLa9cLZvl9FjRkBqeKIh5VcRv9/llkWXV4df37+wf470cEa8KKhRH\ndUVoTm5M1OFwt2GXXIe2aCllglxnbF73THDq+sqUxr4rQFHmjZ/qbfZIRUoXmYVT3LmIAtkNwSnf\nLL/CuXyyO3WRKudQxi1U/RHc8dJlH1NNyIgv9Phh7BqIt9z23yrsdQVVtsDw2FHaUajGQIsPNwSH\nE4tGpJ9YHGVpPksz47eZ6U8hHw/4QsxVMa9r8W6xHBXqWWdbxcOxv78/GEwCg3VSQxI+JKkhSXJD\n8ZYfbvHVoIKQvRga5NNknEmCRYuhT6GCwy2GYSx6BOwsdqZsejK7uGycEH2JdBvTVCFzvZlORnAr\nWKIzHfm67BaidJFKYmVJmzRetkCfe3RR9iGNwBfnsw4b0YGIOGQqysR9JJWkKTnfSoGcl1bSqfw1\nxFfkWQkOzTr5GKHRkE59hHxikreGfMxjucVftXg3MgC0W2qc5Zr83CxH4AgD/GXGlhljDMZkSelR\nawKhrLiAk0Bc0J8EJmIWQ2Yn6YcMvCyz6mJoHZSBw62gSARKD1iQu+WoBjtcKWrz+SUbE0tb13LK\nn+oHp/JJHHqShL2qXER6bJPKBFVQE3uAVqbWHUEamBKUJnBo+HZ2slRLafVYtKTQNWOFEVbEPzx4\nw3TlQHYm7MpT95HKrV71KZG631Y5T5S+t0ne0eLD2oGa0qgRWscBzSSeUgjZE/ClmC0JL5JHPhXy\naUqb4Ar+90/ZVkcXvlwj4tVRum3YUvP9OEhcEzEDT65xZV0Bufyo18hhy85cN25WxcwuLuQVyPvK\n92lkbpsnfUpb9hKNz61nAK1UsPSFU01gmYY+D12tZR1nG9pr5anS3tqEdx0smhyKl8WrucTZ4bDP\nloF0E4Cu03uEaZ70r0jZUxuCw4lCI5BOEhhNc6uITwr5bMhnxOsWu0L2DFgf8KVCM2myYgHm8nE4\n6GvmuV0GAJl6BCv+acCI/7AigXvaieIx+opOByhD2YjK+pOA09BXRkXagiC/FKkRMkzwI1SxRRN9\n2Y/xA1n5W7EeMFfsHg7E+Kng1y3I12URovrmkBxtTXoJmeqo+7tZNqsknCkj1x5pySoYCaXwtoV2\nVWKoEGv7jLJAKjzrI6xkf0fgGSHnzXDXjG0g3fwXXeYt4pwnJO9OTbbHwOc7A56z6tE2ODY0AukU\ngZBG4lc/Dx73FaRRIreE+iY4Mi1TyXO6HIFl0ASS+BuMHRIeJY9cwKIw3L085t3tqp2+UX+yCSr7\n9jyTRvazDNJIYLPW0qKKLZa8XH7K1XuJAhDGqyQvV4JcptdiGOyCdiEhKXdaYpUckkNlNoryTAd3\nDYa2XWUQHqntpgqEBYdZKRSpJhw7hnfAxoQ3avuMbCXKy6VMIAHPn+aiDh84rzyQr/aLj1tX7gF0\ngeSeJwGlKi1AyE1RXYHUrKLHDY0P6XGPFu+f5Dfami9AIO+jybwDmzU3f2KqFdd/7iNLlxxlctUz\ndTpAAepgWX9aqMoU4BlkUnbEflbubackI9VkibrWQc5TUvZyDTwWw5IrJZBeHF132SUXv06pSJxA\nQUQpL5RQsIzl+1Qz5SSpmrSsmYCRcLYlzyTU87Tqvi55nfNtAt4Od6KjO31+f5wv1PQqAfeH/GiG\nNBwOJA1UVGwBgU7jrJon8Vc3qQIJL6zdswbHDY1sPzmxCmOdz53IX73DirNV++Gh2c/ULjzl2Qn/\nhSMIY534+/BgJPEDICFA05BGTkfWoxhibcrmmJtD506/rD/VIIMt5rfnWShS1VkuXSQpbaHJ8mrb\nNvV9caJuaitfpCM96VMwJ8uaRqUT5+GQZjCVVrJwwMDT0lIEGnm9K3uCU7rrw1cqcNdEOFMvdlmm\naCp3r9WSv10pdBcADnsAN7T4WMhUQjsGhgtSzmSnjq+Z5hsdntZn3TtIXu/FLwl5Q6WlM6qaJzEr\nasrl7+LC1Q24wfFAI5BOPoR7CG4lfjnJxsq2Abd5HFa/ercVR279sh8hELM15dkh8wmvifn9Y+/7\nS2NeCH+CwUZ09V6uGzd5Smpk2Stsz/cF2qcO82DHMhFodipNTgwpEmoGe7BHrlJGOV+oS6r3J5J/\njScuyBvpkwCdSKs3saMUiqscPErjcQwfbWcQyGgqFeGr7FP6FC1o4orcTmJ3a3X8b1cK3bwX7d6I\nvw3547jedR8MuafLwUkg5eCA/+TzNQeVpEYaCiJpEN0lLa+NNDpRaATSyYRwD6G05rTeT/gZkouI\nX+Y4I+A2tOhMtxVH6RjK3xHzszCacDmMZWpZKnPZCT1pGV1DYmxflrLBz7Kt6j4k8WIsZjN8tZQE\nwZoxSMC50S1szydEetaqs4rBJoWJsMmJAIJ8Am9x9/Pt4m2XpFmr/uhOLNsGQTdsSrmrEkbsblnW\nUSWN6gx/weQ9CvIzINDLq3oJbJXtd+VKYNTEhDGFrl2Ffwa8MeF95QuNlP4CjIT8aSgZ3ZFplDfL\na1M1TwpCLKWsXeL19UbZrJ/HGY0P6WSANNAJaaQM+t5hws+4z4x5GXIlqVNgQkAtlQE3avWjU0hF\n+FFmuBtAQkKg/rFOrte+iEdSpaVzeKk9CcLVcclTopSV+fwKIeVZ2Vg0rCZnP8sgjQoT4S7ioPtX\nlEuml7+U+ijJe8YjjSbu2CAolnFe7i4qZ1VhyVQ2wJ2a8mcbPtJWVfYeqRfl8er+tkS+tXvyHDDX\nMneo8PAF7forjKzoj9VIce8jpFGhv/oolYW1EJyE1rgA8Wh7HPb5do0hlqXRSCOijhHN9J0caO0i\n+JJ5z85vkGxk6Y3G81LORP7q6xSY6OR/hy2uD/lgwuUxbzu6jv9NyJ6AK2I25MWGLf+mrX5B/dR2\n6OlZ25btMXaWnYPsp/SnzdpBRd2m5PtBm/Qd8gqFJbi2+0LNVY7gJ6yCHekEQj4hXRk4s92iHWyX\nSsGhbG0WEmKgO/3mYItsYNMXDw17u7gaop1BIa5S4b8b0X+IySr/aevBbQE9hx1UDW5eet+6Fqbh\nzZoFe4sM39q+Oopdg+OJRiCdHPDvALttx7/Tdl7K2piXh3xmXrKialonNNfJoZC/jfkfWR2kh1c4\nMgKayY4AOMg6YGXstJGxhwF8/nfItWF2tb9qcWbIxQk/HVePdcJSv2DSJKhcFxEyTKC843VPREFO\n9GQgji2hzgLs0sKJlExShLSgJO1VgxruCyF3h1x2vcPAnOb7UQ0CeVM96CaQz0FHLq4SQ1EU5OkV\nBbeZaqPbFecBYp/rxldRcmKiEF+M7JgRHYiYfQqTP7AvSyMwgv/vfUd/y+Pral9p4THpScmu1Oks\n8qGCYmfsX7OWHgc0k3gSIPgS3n3OPfth/DsZPNd4dszLYCP8vvrVVXLcDGoYlyS8dqnoo3chk0by\n139fxKfDWgIJi/5kE1TWiyhlS9/1t7UEDXXIfj3toM7eNvIUBSLthe6s6sqtuI6qDYIudw02MX1x\nxbSad7Wgm0Ajms/nr6CmwuE2K99a6Iu9oc+pMn1GATmFWHXMLqE7D1VcMPhhz/tRXP6tVEYJD69Q\nElcK6mtpSA0nCo1AOgkQ/CNU2XbCzxKZBRIQsxZeHvCPHoeV0ahsxBKwqmHslW6kUcgCY1nm3nQM\nOOitAw6yLlx3YNtn6f24+df/dthoSaxQB6sttKPLMD+VC7rKrm2cCFV2L9LIZkF+mhzbbzHSnpZz\noeCs6pQm3SEXNRgkq94Noe4YV/NABt2Us+q1NUZz5bjKUHZFZAmMBLYzO5mxVNxpcAX076iybkj3\nkUwNEg6kldICFTw0j+m34nBOqfHZxJUamVSP3NKoWTMfRTSTexIg3kL7jgrbjoECniuDFPOyhI0+\nd6Z8ZsBzA24zrntO18m/+OwdMJYJJGmyE2trHIZATBiuO9D/HmD99d/pa4WY3AM/HtBl2CDMO6Lk\ndjdnzlK2NWHOUquU2ki73UsC83kOnr7CHpKekkRL4lCWi3KjrnSOfYWbGhMsufWtqfx4yUe/usdV\nvix5NWtHTptUpkVb7iUd6jtaDF2FGd+UwNMBPf6oiPj06fZKv/BbqXJOVYirSGMU9rnWOgyXJbHB\n8UEzlScB0jOhaq2pEZOUsjZhY8JGIOVMkUxIWbCCPBesgEwN488jrnDfpXcb8WHXr/9wxLd9nj2o\n7O+qsRhWVaYwljxXsqErj3Q129oOabYSMx/Vrteg3OJGd3lhK15283S1T+eZLVAHy9Or9vk2fSuQ\nnrDC5Bg5deVxlfdDupoVaapSwYq4GjveRMyFljC1f+sDUiDZkT4ppPRbqVNnw22VJPv5NNkZTjAa\ngXQSID2TeIpwwbrWFKXRSulF8XsUjqVQOpbaMm+ZWw3zuDtkLj6yE2Q00jIcBDgYrgNiwvmvLULF\nr/+mkHMHfLWGPacmFqtK0CroBiKEJ7+cNwi5vre1oJwdGuPKMUcCu0oOisSpizgmQW7Uc/a6BBby\nxkD1bNgMskaNeA7asEVW29thYsPrNPHyszcldc3tdhdUGwJXGtxFbSfhx2yGKOCwvMXZKVcm8gkW\n/8lKsStZxoYh0ieH8VNmwh/M6L+VmvxSI9Q2w+Owh20bVVM3apbTY0UzgycH4i1wEVxjWGv6f6S1\nc9c4L3ybt6lXnXomH4/vhfxZ/PC1IFlZ0mQnWHYx4dvf8mP97Q+5f/3f9vm2D/XsOXWQSaOSmcsI\nZSCKfebbpoWqp61SZXOPe47Q6s/q6Tn1vN2Fxa+sWMxb8i8oJBptuUDL7plyWZehq8aKrKFToQvj\nMso5EVyqqHqOFCA7hmlwFzXxs1jaSVyQ8NKYSxK+4/OpkM0Jr49Zr3JQedlfYbJL8cqPfPqkc8uO\nUrTvraflLlfj22OJTNPDIUrhR+7lsZFGxx/NJJ40iM+EKYIvkdyX/UrStSQXHfX1VP5vsXbtlL86\nt4s9gEl+POHNS7zHeNlzgzVQj13eqVXWyA1HcjnHllzAXPuVPNdOdRXNveSYo5u16yhB0tZK6yxo\nsbGB/NThTFcd0O2BZVp2ANuhk09Mp9SjgjxDs7YtmK7ZLY2rMNIgH0ZAlYsmyWx3s5PZJ0L8ZGqf\ntpO4OeSlMWtTnpFwccJY6ZJuhP8+G/5gxqYWzpdylyu4H9huNjeHfb7dVJ04gWgE0smEeAvJRfj/\nXCdpkAmZntTi/QG3teVypzhlXWf5sikt343P4tBklwDcP/CB2A8fCp731s4975r/vsuZIa7SHR6v\nFB42uDJGVxWOM8RmKnZwR4aOFsw97jkq233003UveSTHjj3nkC5C3LRs5F9dxZmSQwAi+f0V4BCH\neWQTpQbV1Rrbxl6YASVTNfEDhuStovbELy6BnhLodGCoIR1hFF1DUslMfjBDXrzq/d2cu/+wO4Hm\nAouk/tTO0ySlG/VzEc+3DFWh0Y0eLTRTeZIhPZNkYx0KgwN6/m9Km/6OxeSjr2Ye3wkfmI2fOm28\n/n/vnv2b533/vBm7kaegBNQQHka4MkYH2ZbcXThuwhibqcpDzJfMPQLGaNNDMF/K1CAaqEoNgfbC\nZqBDUywi7QUmuZs4L9jRluQpkzJkvGYhgnQK5ukvEHrEQqfcI/8WyOsOF01kF35bNV1Q3v3O1T8M\nrV3bgi+ZEzTMVwn0tsY+EVBWTKXxZu5ajumn1+AY0eSyexyhmkQdcuM4v6/n/0YmdI5kAjkHAo0B\nEB6ZUensSOAgHOQO1seEMWH4dGYCwidrGcQCbROtXqs96uqToeHOGC2PL4YVF/FjJmP8VA5ETU1X\npo4RmNeWq662sAWycpI+IuRr8VbssVWuOVVsaWe+DlWp89nUqdW0IHfn5Cpvu6A4cQcckvVFyi23\nlm4dyO94h1axEQYDbaLmIcFPNe5fwR5bOBjIC5aFX2HSAmhz2MvCA9S/LCui+DdKiif+qVSL/rf6\njjuwmvuXaS6aTlspkByb+CaX3bGimb5TBCE3htyk3uq/0kALR9EVo8JOulwWhwfXJF/vLm24ATKu\nXbwhvIP1AOuZvpBzD7JtX4nHrK6uKwGrT4aGLWO0wjzUKxw3EXN+wu4WsV8Sb528klQ20yWwVQ5Q\nH1GSt/hQpZEUBq4UC7VHWG20Z6Tl2ZuvallAwVAp1c1zB8VkGWIbkSV7dbjWKuOACgpoxMdDXhAp\nVp001o1mf4cmuxQguLXnHTYkaEBa5Crvv9npy0uyI25pZMym6vi0warRTOIpAiGNAunGLqzh3XxS\nm9qWFfwH+o6bzh8EZNmeMvRVr7bw0GFlJTDc09aklQ83++WpERwBoUbYJPa8VJL0lmhE6oXVLMq6\ntmH7zupcEFkJcFXygJKlkeGOoRPlkmUoymIx6FiP8E3kFQrowR55X3108wAvXs3DEHxl3naHmk4u\n7PJa2C/7/JHh5AaPLRqT3eMeLT44yduVtUbZKOZga94zpLbytS0reA/F/jf7WTTSQe5eWbdEa4lW\nPHIuIdOXAnb+sVr1Vik8FAQrIbuU3jkpNlZ1wcxgWDY9BaWl3GYl2y7vru47J+to1Cn+MS8rbijX\nVCf/nekdq3NBsbOIarQsE84wxDk5dgw5y+d8ToMcSnqFHmyWzZS/Kn/3n04Y0ax0ylgn/h1h9Aij\nmYaUEk9OY3rQ5rVrux9Dh7ymQjcasdjiRvINaEx2x45GID3uIYIndJeH+I0tyGgWsWCqVdTxy0xK\ntG0g/Oas7dbh04Aq70LbJTwWQ64bL6W41jBhLKG0FSKm+6ug7eUyxVnE2xBuT4V+sJ1foAvX6clN\ngTLQzWuzHEg7Z6CJDdWxsiDRoYT9guXW5ZYCZUsjdXcME3GuzJV60YlyFxneVHfXLOTu/qJVbk3S\ntWHhDrrDbmfp/qWRVchrj8Or61CDRweNPH98I+DLBQoDRfJttgzWp+/mLSskZ3YU+ZuYO9avB+5g\nfbj+QAgzn2Jm2eld0Mor6FisnXzBVkKpEovhMEIz40fshLad1Y0chdtKZrR4igVXGcd62gzYUqhH\nsv4BFrq5fsHCiaInZb3H0TLJZzZSAmk16mYh+616MaTXz9vpdtJkfG2f0XwNWA/pPfKzvwN84Aij\nwoeUjobx5EzYn1EPWsEKVxk/5iYJWjSkygQNjQ/pOKOZxMc3Ar6CJmMcSfiV7c79y1Q7abWUJSPd\nskBaonV56yZg+mI6Z3De31mXeD/lAtNKl0mjYBiz0tfiZxfDXNq6iVVWplgsSbucA6nM6tZ7eNS+\nCOQt0K68JZ/EgdJOQeeRT0mNR5c0bioBtVvqg1XxTM5CiPUxUShPZZ+il8c5E9iQyiBFkfgrSA1K\nIJESXzw93p/R1SB959C1x491pJR0yOuE8RqjtIUfGeVTg6NBM4OPb8Rc1ubbSsbUWTDdv0yxb06G\nO8duZR/C+5lJ+Wv4jjxtLOWihFsDLkgyJ5DOWHcnXwgHQ3a4rjmtqjJFWdpl9joxzq6W7GALtDPn\nUCeypBoScPgi1OQG2vwaNwVTmvhRB6PcCnrVUjbqM1J2T1rofzdrUbGFWxda7pSuLyUIE+3utdXN\nSvgxbU9+s3YV8zmDo7l461Pbgq/1Ct00himXY+z2SClsk9cJLzqaPjV4FNAIpMc3UtYiF6KkHi0L\n+y8zyCeM7vNNWJclnBSHDnJgJQSWRlqxdy4Qrj8ATJ9Fp0//DH772VyZcFnMMlwZcyQrQ5s9Z0Is\n1Uq+YNGcKuGQdpnYUIOfkoTfOSAr8ANVEtuoP+n6UH0GtjqoraBC6AoJMd+W32hiSurTyV9NYxkM\nW0oHXiYIo6EQmoiPT5pBHZnUd6qYnw15bpTRGVB/T8tpSIORM5YZAwb4ImOIf6Bfvl5559CV+SvU\nZASaBDfqT/3MA+VGpW5Ew2g4Lmhm8PGNlLUxl4XcNK8ZGi49OwAAIABJREFUKIzQE7sYd9JoS1nK\n0xNeAykcYaDV6zsIMcDS+tYSLaRAYj1hRBcm9wIsyVzhaV4UgTP5ghIVq09bJ7AYSn6ETR5YBq8M\nVsVUQ4V5QSaUU8k7C0bSBXmiY1OgS7vCToHcGCdEGBawU9Pnupbp2lyyPSL7o6fPkFdeVSHEmpio\nETf2oiRbuYfGOvGfEEhjAMuM6T6k4Kae968xJQuoceegUyALaUPIq0opZ9bTjRpL3WOHZiof94i5\nHC6EPxRv3QanwCR+5HVek3J2yEcTpmLezKrzXtaCK/lC2eDYgz2ZQuDO8rCoOY1A1kqIpNhguPSH\nAwaelR8xETMIiWwSW0DM2pxGrlN9rlOZp/ANaYpOQUIMNbZE6nMKUWm6VISvgrparziK4y6Kih22\nq5ir5de1/mxbcJM5Y9CCU9fX0zmp3chOqT8lvGipIm9JgxOARiCdCohZC5cFfMXjcJXzFqy+9n9I\n2LSX62EUVlDe5AcAqSElQw1pPxuAqQ17ANbDOoCxuwF8WW92pKQhWTfRC3mDYy9PkIKBx6Lddldw\nGhGZspHKpb8TufgRwzkp08ELEydmU9eHjCJHocAb0Q+aaAWG5LCFjum37mqOMfJCND+KR0kaAX4q\nXYCWDm+UdY+KGpIv9z8BwDJjwmT3wMqo/099nBbQ8s6hY08bsiDbLPFmZy4u48Lo1o0ak91xQDOD\npwhiLk+4cJw/xGlwcvhWPJZDPhrzpke1n9ZNdEG3MLHUjM6kaqeReN0dxn7a+BG5S5Ff3B3Xj2BO\nS3FhHB3apsCk6EyWxiUwUUgO684+HkhFKtLKMORxjGy6SsS+1S56TV8WPaqN4D097x5rxqC2tjFQ\nT/hUSRoJdHLf58Wr7EiDxwiNQDpF0OKDAV8Wy+ZW0/IljHVuAh4wyRsSLlvibZCGzAd8NuYdCW/K\nPElSQ7o7XbfktYAlXgC01t9OCDC6H8B/INv5HimVDrTu+rfIBWOPi7o+O1l0JrkpEpmZRguCcegH\nxUtNyeSkjusLRPnjjogYXUpp66hwrcW+ocauuS67gFMVy4yTUggcLzadDTlxvlCku61Ni4FHOQ1p\nTGpIYwAJgdCQgr+eo4ZbVCBhMqBvG6KauT7vlC/rr37GeKPCi0ZDOg5oZvAUgZ6vwUh+rUnAA3y+\nFvK3Ie8Tb1v8SsjvJd//xfjJ0yRZllXuYP+GDYAw3L3/n2/vDZh+Nl1huLs9k4KeiWXn2vWrftgF\ngO5MqqxPkTlg5LmOFdl8KWVIXNCIDOWJS7R42D2wQybqLus0kUzVmt8pDLyMjmGMEZ6IOT9hvp0v\nc06FKtaJMiFXvmAZiyFRQDvJhX8VPi0f15ET5908sV4+iHr4UZZG9TQAxuS0rwNNIMW/PN3+fN9t\nAVXwWKZiSoh5hXUABtSkMzQC6bihmcFTAYV8Dd38aqDXMTOisNP0+L6QRprB7LvhQzPxkw3lkf6/\n3jc+MP9N8Xrbt5g9h+6/86tVHXbt+qkQMGKRFTWQqutTiFnYmZ3ryNVmvpSeLoFSCXB94uY0qaNS\nM5Sd7OWdQke2D1xMdz8tVl/Nbm1RxYTkqBO8tajxQcQLXSgu1kuoYRDngUbE2MfhiG/7/OTA1ZMy\n0meFWGRML//QAh7fj3ldyIfs8UYXx/zM6nrQ4LFFI5BOBozUqXXkQCFfA/nVINLWLsdOc0qauALZ\nfpdskP2kH1iTfL271LoBIGZpQwu4VUgjuUrGETOjTEsS70BqSAXD3Uo++cJwqUUqNEZIAbAoy1jU\n4RnrUTuL9voX5kvpZPlyfbyCBkpRWly1JAs3qIToaqcQaELOZJ+claFRUYCfEvt2P1ZJFVuVoyjH\nTiwJxQJbxBYWVmdn8LmQ/xwNw4+GxjrxN9ONno6mIaVPDQfhpB/3dRnTK+1hxPGI7w/4yZgJ+LWy\ndtrnXUC9H1rNMhONSnT80UzoqYBCvoYC1K/Xbc1QDKUpLXRjSjMDLuSrUfz73K/+cOHvjKvkGrgy\nYXYJN/yUA77cWe+Qa/T2KgGjJaWuFcqaDM91ZbMuX8qRiGlzydBpara70PO23Cm08wnuhMVPNwZ2\nYGGYczYT2A4/loXF7kbm9bH3fxbphDMJS0PIlPOL23hUHqx4Ynoq7uskiTLfJZKRWiEfingHvCbg\nHxKWZbzRWfUyAzU48WgE0kkIm8JkVaT0fA22ZbmtsYzK1gy1X5+SbwuJBTKD2UOx//X+4KxJYn74\n5S+AdZX8is8YLGsRskYUeQR1WGqaK6iaGI1cJSOAfYF1vTZcKsr3LT/AosHI0sxP6SR2mpzqbcEY\nqBu+AjkbVQ7AyXh1aRdyoV3uSuel44WwsDo7g42y3gRaIGymIa3LNKSYEDjIukTcdUD65FDNViK/\nzPIOQRYG+Wkg5rUJL/ZZCvlowktiXqX9cAor3orpYAFu1xGND+k4oik/cSpA5GsA5ou8o+GyvAVu\nlhpIvozDsFasTkgOZM4adcGsGsU3ZlmGr/a4J3askgc9bvfxJZ9qxPTP7HgoF2LIj6QgUSbs9Sm4\nWZYykhxod4XA3KU2V/FAdNibDTxDaXDDFdQYRf+FBrZLM5u6yyfIbED1kavH4RhmUhK9cly6TBpW\nOrd8cS/KVz8aBf80/NOkxF2X/TvIOvHvwYH34MBjmfRJYbxxBtkQZ20Qn8ydmTKWsGkvfxDzKsAu\nLdzHjYWOyrFHI6X2DY4SzfSdIlD5Gmwb8bl8sgbdCi+IzTeXrqk4AZHMUAkkYx0gM4c4fQbXhPyx\nxWEjYHY8dO15my3ekVithmUSgb7Th/s9rht3scWGbAvP1Lf8AFFcA2ezxVA2E+u7UoOUE0hgSss9\nID5d0OJ5q8yYOtejDvbpi/qqUktQdMjlCN+mmINrVx+BpCO+cJqVDtF5VCmKPt84hvs0OPFoNKRT\nBzFrYy5LWas24gKBVkmOkrlIwJEyNJJXE8LFGxxgGQTjrkyQ087s/oAx8BnqSYVVKdvRGy/SkX2V\nIxlWjy1huLa25Wh3aeGRmjrSDxl47G5x3TiLoflqEzGdyFQFtTTAq5akH8XZLPa1DHuFjql5n9Ls\nY3rdP/JmzALUwZ2AdUSLpiqIOXXK2f9iagl5XKmbObtrR9vyyAYF3Siz141JLsM6CFn2z1r2z4oJ\nY8KDrMty0g1gQPj52eDrm9MfC6mus3dPXiYdncriYHvrCpPtX4OjRzN9JxYqPqeQYafwttzeDJGv\nwefbLT6InZaVsjbirT53taRJqLz51hdA3YEc3jcTr5nmcDhsZPEZdNeSypRDYuOe5h+4MYfjoT30\n0kNFGM2ESkLasagRJbKcO4n4kGPtHGA7qdUsW6Dde3sHe2KqKth2ykrZWLSTtodGtsr+T5mPCy2z\naHftGmIOYp/2ADRy3RiZ0yj7G2beI+VDEs9N+KHZsD+j37ySuRPyoYi36x+FfDzg8zFXJrxYHiv8\ngmzLoDtFkP4CLR1Sg6NHI5BONaSsTbgw5CaPww5HdchnAm5TH83lE0kn2upXXiS5d03yje7S1Ax3\nzdhWye7D1V2tpCTUyfBNwYEhLtLLx7GK65fKpJbZYugGqMCVv1MF+gxvbWqWcRZrcNld7IlddjOm\ncgyawn4dpO3h5Lv7H+RlVX74GO2uQTHmYE9I22m8tUFIoyBPqHOITiDl7OHp7A75qHjd4oaQj0mO\nw/FA+H6CzxH/F5KyCtngKNEIpFMQxrrm8iOxIz8spFGQj67ZU3I+2RZJ/94+T76LF3f4wnnlVfKR\nHfBeAO8Oxu4FTUNakS8+G/KlIOMRGElo9YNphmtrJLnaAnM5il2Rs6GxxRbDYSaCnAFqh1kMiL5V\n+k4yv1xUwwnk1p/EGjyVL54k7lWSEALuKogqwmkype9JqVPqf/bVbHd9NRM1CN/jyZBcJ1h13hlS\nN1qf/b2D9ZD9vf+I33rHtqDfK3S/51QUg4wvsujz9ZjXJlwqpJH2kN8b8rGYV9Wm1RXeSk0o/BDh\n+7JjrT8j3EWyhXhbs5weO5oZPAVRjpPV0ZErTym8JOdTx71I/jD2/6U/YJJLZvh6jyQWZ64LRl6/\nZVQKIDM+FfLpMHu9u5UpGX5qLQlRB2LX3w81T0wh7fdU6RzBFouYnRx2Jotj1UdeSsSk+lb0newp\nSQt1I6r29pW0gkgTtMhO7sluVxbe7hR/yp+UnVcgVsuvoJxQo/zV1CF8X7zKbxPwv94vd7/rVBQZ\nPsbLLf6ixV8YH3J4S8KLl9i26j4pCGk0fMYOEb6H+Bgu2ECiEUiPR1R6kqrjZDt2a17MlT63+9zu\nXiTDL85GL5lkwzR+h//Y9z72W8/YsuVPu/cDJLszc+ASwb2geZI8pDTS7EhUlYQoYzEsZlfL3Dk2\nv5ljJOQFGHnx0NWcIm1YyG5k9p2IFHZTWp1y5OQ69vZU6U+RqZ8LYBHetVL8FYYMwGScZbRTX8GE\nllDD+NVU2l1fnAxdR76qsrUOQiDTkGLvXFHvUfiQgndak3wju28T/XrO20R+G4VPfW43XZhq3ah1\nPUHfYsjeTHIFS4b0Wg3qoxFIJwNG8gF6K6Xj7rOKqBMna1EYiGDA8wc8v83txkWyJxO8JU/ryOTf\nIS/qnrFr6gdwG38JjAd7g/YhgCW8GMgMd7/d4jMWO9J10E64eq99uBKLFkd9Rdpvow+j7FuKTKki\nlFNkO0jugNl30pGLZQFdF5c9u6/bN2IRtOHgKBP5EEC3mBKuII0EKhPiTdiz5b6znwXAKoE0+lQA\nQhDKaAtgPxuEsU4IpJ94/1tt3Z8rcW26+QbqMVbt5/MBx22IuNfn9gEvkK1scki9lQLJ/wY4DNlf\naVbUY0RD+z4FURknW5ZGAlnoKx9PGaPENO7BZo3NG949G949u6qO7XPIjKqasApDR30ni9DshzV0\ngqQkk4zCOch/ZGovluZs1S4Qpt2nC+Qp0ZlzCGdUM6uYtMVQHqxD5lZahjaZq8JiyHXjxGkx+Hdt\nysvj1V1KIX7zNJbuK0UR2GEvfaRetE3JbIGQj6+6W8Hn8L7vesa8f8G/zXBig9po5PmpCXecrG2z\nO599enHKGTGvDvmobobRLST7IHowDg/OxAenAe7gUDsAIr8N3MbGK9qfBNgPdwCsu5f3BBxyyoxB\nVBHa6XDUZ1nj6gd4JiUTk4Ay9zjJddh8J1XWuXDA+UkWMJTLUGdhT2TpWVczaUOJ4ta69lTkda3k\nNy7mVVVRLvY5A24OeWHCFTGQM9aJLg8tdS2AZOzpwBItYbJ78KAHrInm946TxHSSXPcXJH++UyPl\nodJ7E40/v2P4kG+qSqJKntUNwc1Q9YyFfwG/ZGnRoBqNQDplIeqah9xUsLbPV61UPt9KuCTmqpDl\niFvcRiPevyY5r7t0+Q2V/XlPDTvSoj0bN5W1+KjhidlaEs7GguJtM+tM5w5YfSdTcKgiCbcoO1SU\nNCb2RB3j26IxY8JCVeiSmDHLZNbRVsuc8ijgdUtctHoKwxAfnuUjMyngsdTiNSHdhOk4+1BVFa5D\nEym7jiLt04RNq+5b/Eba+yueseSqVV+2gYY1jzzyyInuwxMXa9b8JaC5gsovjG/LcDUIORzyh2jL\nI/Z8DftM1iagnWUDKGK7+JFvuXnw85MArwa4avSjv8RfAlcknxT8bz5BDOetAWR1Ih1R5p65pm8d\nzHyb2Dedm79Ctn/Wl2BFNFB6knApiFPEwHp5s46YKcVlSPBTs38rlzBboQPd4a2N2kbsM9+umNar\nljigsjzYJ03IuaGE0y/YM+VyVXBOZjigY9kcXDfOwNNyICoksJUzU2b3DgNgQ0A6jEbOh8sBeDUH\nNz0LeB8/J/5+eeZ6Fns2V1mQ0Foi5VkedyPl6VSeU6kz7hLYCoGWC1A9IH3Kmydb+lT1WhG+30v4\nt9ZnLHk9S3/0yCOhedYa1EDjQzr1UU4plJSMTMoo15EHd+Uv4k7ZEu6rdiaFMHNA3sbkLLnAubM2\n+2wU5gEmU7nwlLOs7pDchF2lakZR0ZWSdUm1L+USVcikRZBfobraQUplXoGCxa940ezgYqjd1DJp\nrgBV0ZOdecqfDudk2hLRVrrr7vP4Vj13YA7f6IPVVTbwifnNvfRjfoUSa1I92IH2ABf8hpql7hgQ\n/zzxe83PWP+bLP3RMV28QWOyOzlQZtnVzCREvgGWZiMxUwkX+9zZ4v3iUGQxwck0/myVDZIa9vr0\ntFD4itgPEI23b2MjsCHYH248AJknafogr4k5H4M569p+xQjrxLtM7IXQVIjWYdmJ7HOh3A4mc6LD\noVXwVxhX9jqFM4ZE9p1Whp66+IQtQDWQfHRKVG/nZNpodXWsiHtCLo1AK00+8iwAWvJ2GxFPSET7\nX2c/fN/C6/C+4xByaUTsb2SQxnTa7B7wPTSjI3kqndaRYWC0GPESv6g1cZO80XxImjMpfhZsI/g0\nSSKf/meRvLpJZHdc0GhITxQILjja+uNI4x9oDWzEsZ5cJIHg7t74deeFi9V60rNjfivmGRod66yU\nqbi6/8Pkqk5dYSKmE3HVUta+8pRMztnmIpKnl+SKy6FFzl9hW9knHIUz0Ka+I/8GeV1gCrSEqlaV\nay5fzKILO2VVDufM2FBHVX1xPTfSrbO3373mzf8285HD6XeyMRqRqeE7gYBPDviePuV78npvviN6\nLotjVo8U4v9K9E6Wfof0mcS/wt4bif/H8bnyEx6NSD+xqFR9Co2PrgBzBpUuiKqgyURrYCOOFUl3\ngzjsz8R3TAMHNoS3jW4ENiA1JOFEOYi/zLWHeWXCXp8/DtmU8PqYgazjp2Ac54Q93qVAN9DjZhyn\nRIGWts42Fz2DXKkVeTpXPEthMZRRvaVUCKBpXZGmnHbzSUu7uaAobCpXr4K8UMndKKOOqvryJKPV\njcHY6YBMEdSGjQD7vZ+6jY17Z3aLvoQxkVG9E8jkyathJeCTYjTKzursCPNSOZSuI1v1I+MRe6mk\ndB1JSPJGrZnXJFc9djQC6SSBLplGSi+MzVaNmJe1uVMsUJWpPgvJCrqa0SiwW7l485rkgu7S+hui\n8Tawl/HW6BKwYePXRQ/Ekjf+ZcYTphJiIJ/jTkd5nHWS2dQ/pVYAqUljqHViYljZF01RvSpLRbFU\neYFMFhSTlhY6VhTY6iO34CRnJ6ysqFRpbHxZgi9vGCJF0Yas8ZHWU4Gd23747d471CN0SQ0h54U7\nUn4QJ7/Q5qvzsFM+kzgzYIg5iHlNvbXOKIfKWb2VBDIeb3D0aGbwCYSUM9Vr92bU2EDRksWP3Bqu\nflf/+HXZgImqZDb1T7H6XQTkXJRLg9c50Sgmy1TpfjhMgFQkgtuUU7thLSd9FSp3HxJKgi6GxcxM\nOhyq6t/0ZXIgJw71vwfskPQ0LyWMiUOXbEk9aM2mIXECcSa5OloW8IJ/TXHwUsZiXlujUw1OPBqB\ndGKh5t+m9BhVoqPUk1LWxrw85DNUGTqMDboQSAOIa889iP2P9+9ePwncNraxxRLQ2rgEjMQPi9Vi\nZBkgOJBZ6lbyg0ktmZQUKpPZLJbWU+MpdaxPYKicVOdEa1ULSyCquUZt15pzyGZYG3jSnFiTkaIN\najHMlTYvlFDSMRZzGXwl4LCUGWMpm5JhPm+Ry3vkXKkbbQRgE7ew6Wu9ux+I97elqo2QvDG3wrsx\nczeUCE8j4pAwzvrelfWO0YRXIEn7QiB5LPt8c8BPmKZgxPnaVveoqYf0aOG0mZmZE92HJy5mZ/8J\ngB/BkyTB5Ena2x/JhoW3yLNWjQHPhYt8/gE4pDnOgQSul/5yISf0Bj2Yg0MW9QjZZh8cAe+7B5Kf\n7rLM4Nn+mdz3LzzzTO47yLpnP+273AcBDGCMpyzDgzwNfgA/Ak/yC1fkFPxIm5GaWAyziKV0hNvH\n2Bfw4IjVDOWtsEbQE2xzMQXXwAMsrnC/R2t5eOL9Hsmo9cRwUBR+e9aTjuSzTwOjsB4+RDrCljvY\nF8AhS2YnMbP74Ah+yvhB66CKN/pQ3iWoEGnr9+tgH+lINm8ZAlhPukzs52r1jsgntTVgwzLrjvAv\no7zsIP/3fv7zgHNgHYzCOWfgCbm4CZ4JL4dnEwXnLzD15e1fejAeANdLCmEX2nDFgDUQewxSOV7y\nLYTF8gHiFWKPLy8zD0dkk/VwJ7wOfhfaMAr75OPqsZxwaWmqdDbdk7QX6rg4+GTtuPglPln+9aQc\nEn+fDE+amWmYYkePRkN6wiFmLbx8nM8YDR03w3ZINHOK7oxQLwp77l5+t+0N4vCvZ+P/egIyH9ts\nYjZMxAxCIttcCJiSF8S+3OGbdvSF2KNKEsQgchafrY3ijaqMfsPE5EWOCiSwqyKZ0NqUsxNelGRh\nsDXxH6c339+/y7izmY7pJLzCJw5JPVMLaRoeaF9HJ+9f049LH1lZGjU4GdEIpBMLo8nOQWqoPLcW\nEjYmfEa+zq1FylI1BYm2xgbOCBYD4+6GmfjF0/eH/t5144gS1RCui9eN353dFRiw7laAI3IM+l8k\nx0EPy1q0+zYqbWK25GxDN0phLhSkzFBZ47J1X5dD+SnQGy8qIoPTl5OVYsIuPGpIWQPboltVRGiu\nRgH1BWI/t1goh36hrsQ6WCdodcpStwkgWf904BY27WX8R/P/gBxiWUCHKVMJC7DUconwNMLzSQfZ\nhLlNkiWBVMm1s7EbcJrsmuX0WNHM4BMRujOpALVvRhrojCvVgmy5x76a8ZY1yRu6fODq49Lnz4Xc\nHGavjb4Nd6Y7Y56FYrVyB/KxscN1v11iY5OJ68WQA4N88uyqhdNP6SQmskBtKWtlWzjqBwqB7OCF\n78jk8V0+51Vx8Orgkf4+1SkjOtArS9ZCi4g0ZFeUBW45nICNevQ4QmPuPKlQ3mSN5C3dtrNWjZiX\niRdBPl1OJPPs4FypAhkks2BvA/h/399Hex/tvYzvZfwWNjEO47ARNsIGeAG8gFA6YnxRMkfGdHja\nTjyTRrK7hUIJ1TYxU+6foQxbMM2FjnxsbCYI1eI+lY/MlI2H9kM9WrYAdbDNwGMwKNZxcMxveUTW\n8NiutrhPycRQW2HO4mFCclQSiLJzxVcwIv+Nav98oRsJnvcG2CC/4k2k46en46ffyOU3cnmfyUPb\nesSHtHkyYB7CuKoFdJLh1FoCfEm4dIlftlyF0i9u5Jj+nQ6n22/VoAYaDenEojD/K/mDhiRAqzxu\nRov3B9xmU33m5BLtWKl0x5KLcXco9m/oDy6avG3DRiAkXsdBYNOmzwMsZ7XOvSOsuxs0G52OXS2+\nVGWLW1VWbIEhnWyr02C1wxD0U4dll3G49cu6fTlbIGK+zVVLWWSSoZ66QsmKqDpmDRLao73eLF8v\nyPkxQovEAi5Mhkwyj2H6VLQCsPyUJNRNAnA5N3I50GfyvtmPH555g04Kd8yfV2OGuwlA15pdnZjX\nlAjfRlqdexmsx7I7baRZTY8djYb0RITPnVSly1Gp/o3QjycWc1eW8OVds8fSVeAOhy1Oagk5laWM\nvH4jsBhqbxxzYQr6qcxjZLhsF26WemU59+vTZRpB2N1ivs39npQ0zu8gNwrAmZFoui8/QlMHqZg3\nxc6+0M6zr4PDMx8r3BZNyRZQ8ycik7I+mGa4q3VmS/7DJIs9KkujBic7Gpl+YmGc/3IJ85HScex6\nkvGjIQJu8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BVwM7xSzk64NGFzyD3wa2Wr0g4IUsaTYbXpjubZ1o1tIpYmjIls/LTKguoR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\nGnDrnmxHy65uc6cAr5W03JMEwVJTYdoMx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf; hold on;\n", "imagesc(t,t, Theta');\n", "options.disp_legend = 0;\n", "plot_multiclasses(X,y,options);\n", "colormap jet(256); caxis([0 1]);\n", "axis off;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 5__\n", "\n", "Display evolution of the classification probability with $\\sigma$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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D4/39zATSXCCM+S6t31SlPciJJDEJSFKCAkFKIukHjl/qhPR6o8QL32zZ+1cz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\nZOVqd8NS66kbG0dRrQvDeqP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gHu9o//6mkqdurBxXpXN6gFwafdGrVXurzwqP81VGVs1C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\nA+3+e026h2ayQ2evs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo5()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 6__\n", "\n", "Separate the dataset into a training set and a testing set. Evaluate the classification performance\n", "for varying $\\si$. Try to introduce regularization and minmize\n", "$$ \\umin{h} F(h) \\eqdef \\Ll(K h,y) + \\la R(h) $$\n", "where for instance $R=\\norm{\\cdot}_2^2$ or $R=\\norm{\\cdot}_1$." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "exo6()" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Multi-Classes Logistic Classification\n", "-------------------------------------\n", "The logistic classification method is extended to an arbitrary number\n", "$k$ of classes by considering a familly of weight vectors $ w_\\ell\n", "$_{\\ell=1}^k, which are conveniently stored as columns of matrix $W \\in \\RR^{p \\times k}$.\n", "\n", "\n", "This allows to model probabilitically the belonging of a point $x \\in \\RR^p $ to a\n", "the classes using an exponential model\n", " $$ h(x) = \\pa{ \\frac{ e^{-\\dotp{x}{w_\\ell}} }{ \\sum_m e^{-\\dotp{x}{w_m}} } }_\\ell $$\n", "This vector $h(x) \\in [0,1]^k $ describes the probability of $x$\n", "belonging to the different classes, and $ \\sum_\\ell h(x)_\\ell = 1 $.\n", "\n", "\n", "The computation of $w$ is obtained by solving a maximum likelihood\n", "estimator\n", " $$ \\umax{w \\in \\RR^k} \\frac{1}{n} \\sum_{i=1}^n \\log( h(x_i)_{y_i} ) $$\n", "where we recall that $y_i \\in \\{1,\\ldots,k\\}$ is the class index of\n", "point $x_i$.\n", "\n", "\n", "This is conveniently rewritten as\n", " $$ \\umin{w} \\sum_i \\text{LSE}( XW )_i - \\dotp{XW}{D} $$\n", "where $D \\in \\{0,1\\}^{n \\times k}$ is the binary class index matrices\n", " $$ D_{i,\\ell} = \\choice{\n", " 1 \\qifq y_i=\\ell, \\\\\n", " 0 \\quad \\text{otherwise}.\n", " }\n", " $$\n", "and LSE is the log-sum-exp operator\n", " $$ \\text{LSE}(S) = \\log\\pa{ \\sum_\\ell \\exp(S_{i,\\ell}) } \\in \\RR^n. $$" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "LSE = @(S)log( sum(exp(S), 2) );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The computation of LSE is\n", "unstable for large value of $S_{i,\\ell}$ (numerical overflow, producing NaN), but this can be\n", "fixed by substracting the largest element in each row,\n", "since $ \\text{LSE}(S+a)=\\text{LSE}(S)+a $ if $a$ is constant along rows. This is\n", "the [celebrated LSE trick](https://en.wikipedia.org/wiki/LogSumExp)." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "max2 = @(S)repmat(max(S,[],2), [1 size(S,2)]);\n", "LSE = @(S)LSE( S-max2(S) ) + max(S,[],2);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The gradient of the LSE operator is the\n", "\n", "$$ \\nabla \\text{LSE}(S) = \\text{SM}(S) \\eqdef\n", " \\pa{\n", " \\frac{\n", " e^{S_{i,\\ell}}\n", " }{\n", " \\sum_m e^{S_{i,m}}\n", " } } $$" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "SM = @(S)exp(S) ./ repmat( sum(exp(S),2), [1 size(S,2)]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Similarely to the LSE, it needs to be stabilized." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "SM = @(S)SM(S-max2(S));" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We load a dataset of $n$ images of size $p = 8 \\times 8$, representing digits from 0\n", "to 9 (so there are $k=10$ classes).\n", "\n", "\n", "Load the dataset and randomly permute it.\n", "Separate the features $X$ from the data $y$ to predict information." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "name = 'digits';\n", "load(['ml-' name]);\n", "A = A(randperm(size(A,1)),:);\n", "X = A(:,1:end-1); y = A(:,end);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "$n$ is the number of samples, $p$ is the dimensionality of the features, $k$\n", "the number of classes." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "[n,p] = size(X);\n", "CL = unique(y); % list of classes.\n", "k = length(CL);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display a few samples digits" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q = 5;\n", "clf;\n", "for i=1:k\n", " I = find(y==CL(i));\n", " for j=1:q\n", " f = reshape(X(I(j),:), sqrt(p)*[1 1])';\n", " subplot(q,k, (j-1)*k+i );\n", " imagesc(-f); axis image; axis off;\n", " end\n", "end\n", "colormap gray(256);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display in 2D." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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JCGl0dPRDH/rQ6aefbprmZz/72Ze//OX83WQyedZZZ/3yl788duwYf91xHADn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\ngpeUYwXEDMwSnY/8zFZGcCGtyueLYBtsADt3VvfsMbdsyT7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hVPN5k5o6+ce07oGr+Irp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options.disp_dim = 2;\n", "options.ms = 5;\n", "options.disp_legend = 1;\n", "clf; plot_multiclasses(X,y,options); SetAR(1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display in 3D." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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r2pDGkDHQ00CYogIbbVs2taswOFXveFe3Q0OhT8OHQVFku1Vgm9Aev5LNeYqu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BAMhO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\nlbdgaGji0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options.disp_dim = 3;\n", "clf; plot_multiclasses(X,y,options); SetAR(1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the $D$ matrix." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "D = double( repmat(CL(:)', [n,1]) == repmat(y, [1,k]) );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Define the energy $E(W)$." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "E = @(W)1/n*( sum(LSE(X*W)) - dotp(X*W,D) );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Define its gradients\n", " $$ \\nabla E(W) = \\frac{1}{n} X^\\top ( \\text{SM}(X W) - D ). $$" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "nablaE = @(W)1/n * X'* ( SM(X*W) - D );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 7__\n", "\n", "Implement a gradient descent\n", "$$ W_{\\ell+1} = W_\\ell - \\tau_\\ell \\nabla E(W_\\ell). $$\n", "Monitor the energy decay." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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BLzxIygKT4PF41q5dW11drZSy2WwZGRnLly+fOnWqfh+jTAJBMiefz+f1epOT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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo7()" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Generate a 2D grid of points over PCA space and map it to feature space." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "[U,D,V] = svd(Xm(X),'econ');\n", "Z = Xm(X) * V;\n", "M = max(abs(Z(:)));\n", "q = 201;\n", "t = linspace(-M,M,q);\n", "[B,A] = meshgrid(t,t);\n", "G = zeros(q*q,p);\n", "G(:,1:2) = [A(:), B(:)];\n", "G = G*V' + repmat( mean(X,1), [q*q 1] );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Evaluate class probability associated to weight vectors on this grid." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Theta = SM(G*W);\n", "Theta = reshape(Theta, [q q k]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display each probablity map." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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qbMNSRJMwZKtFRXdDdjDzMBL6lmrILmBOqUFSBiNiXBKkEVJv0Ij51UgHNHS6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\ndk52iIAAaxbWLOzuXKhGrcOgepnq0CbbMYouKlXsSTupFl+bjAoqxUI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf;\n", "for i=1:k\n", " subplot(3,4,i);\n", " imagesc(Theta(:,:,i)');\n", " title(['Class ' num2str(i)]);\n", " axis image; axis off;\n", " colormap jet(256); SetAR(1);\n", "end" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Build a single color image of this map." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "col = [ [1 0 0]; [0 1 0]; [0 0 1]; [0 0 0]; [0 1 1]; [1 0 1]; [1 1 0]; ...\n", " [1 .5 .5]; [.5 1 .5]; [.5 .5 1] ]';\n", "R = zeros(q,q,3);\n", "for i=1:k\n", " for a=1:3\n", " R(:,:,a) = R(:,:,a) + Theta(:,:,i) .* col(a,i);\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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kUfE6LQ/JKOwtq9W9ZYbEhuufvxMOpygcQ3I4cbR006ZOi6eOoaqQzCkUuS0A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rFE6CorNhusbhhIF9oAkUWJgxUSFznsl9d/sMlVfrJVCbrpmWG//H2aAEgUx4brWv91J5+MufO1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\n7DtIrpqu2pdvXdKuad109GK1Ir/l3EQQV6RmfaFgRLEhYLqHfIw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options.disp_dim = 2;\n", "options.ms = 3;\n", "options.disp_legend = 1;\n", "clf; hold on;\n", "imagesc(t, t, permute(R, [2 1 3])); \n", "plot_multiclasses(X,y,options);\n", "axis off; SetAR(1);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 8__\n", "\n", "Separate the dataset into a training set and a testing set. Evaluate the classification performance\n", "and display the confusion matrix. You can try the impact of kernlization and regularization." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "exo8()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] }, { "cell_type": "raw", "metadata": { "deletable": true, "editable": true }, "source": [ "" ] } ], "metadata": { "kernelspec": { "display_name": "Matlab", "language": "matlab", "name": "matlab" }, "language_info": { "codemirror_mode": "octave", "file_extension": ".m", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "matlab", "version": "0.11.0" } }, "nbformat": 4, "nbformat_minor": 0 }