{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Neural Networks\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 fully connected multi-layers neural netorks." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We recommend that after doing this Numerical Tours, you apply it to your\n", "own data, for instance using a dataset from .\n", "\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", "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "addpath('toolbox_general')\n", "addpath('solutions/ml_5_nn')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Some useful helpers." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "dotp = @(x,y)sum(x(:).*y(:));\n", "max2 = @(S)repmat(max(S,[],2), [1 size(S,2)]);\n", "SM = @(S)exp(S) ./ repmat( sum(exp(S),2), [1 size(S,2)]);\n", "SM = @(S)SM(S-max2(S));" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dataset Generation\n", "------------------\n", "Build a synthetic data set for classification\n", "\n", "\n", "Generate Data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n0 = 100; % number of points per class\n", "p = 2; % dimensionality\n", "k = 3; % number of classes\n", "n = n0*k; % Total number of points\n", "x = zeros(p,n);\n", "y = zeros(1,n);\n", "for j=1:k\n", " I = n0*(j-1)+1:n0*j;\n", " r = linspace(0.0,1,n0); % radius\n", " t = linspace(j*4,(j+1)*4,n0) + randn(1,n0)*0.2; % angle\n", " x(:,I) = [r.*sin(t); r.*cos(t)];\n", " y(1,I) = j;\n", "end" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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d0472rrFBRVtaKB7QRwHjHIwMPHmyyvGQZHNTsRQfi8lH3jUaivfK7tP5pPP3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\nfbz/j/CP7PhhwKihNl/UlIZxccQ76Dg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "col = {'r' 'g' 'b'};\n", "clf; hold on;\n", "for j=1:k\n", " I = find(y==j);\n", " plot(x(1,I), x(2,I), '.', 'color', col{j}, 'MarkerSize', 20);\n", "end\n", "axis equal; axis off;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Class probability matrix." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Y = double( repmat((1:k)', [1,n]) == repmat(y, [k,1]) );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Building the Network\n", "--------------------\n", "We setup the network. It is parameterized by the dimensions of the layers.\n", "\n", "\n", "The network is composed of $R$ layers, and operate by initialyzing $x_0=x$ and then iterating\n", "$$ \\forall r=0,\\ldots,R, \\quad x_{r+1} \\eqdef \\rho(A_r x_r + b_r). $$\n", "Here $\\rho : \\RR \\mapsto \\RR$ is a non-linear activation function which\n", "operate coordinate by coordinate. The intermediate variables are $x_r \\in \\RR^{d_r}$\n", "with $(d_0,d_{L+1})=(p,k)$. The matrices have size $A_r \\in \\RR^{d_{r+1} \\times d_r}$\n", "while the biases have size $b_r \\in \\RR^{d_{r+1}}$.\n", "\n", "\n", "The final value is obtained by comparing the predicted value $x_{R+1}$\n", "to the data $y$ using some loss function\n", "$$ \\ell \\eqdef \\Ll(x_{R+1},y). $$\n", "\n", "\n", "Load the loss and its gradient.\n", "Here we use a multi-class logistic loss\n", "$$ \\Ll(z,y) \\eqdef \\log \\sum_{i=1}^k e^{z_i} - \\dotp{z}{y}. $$\n", "\n", "\n", "Note that in practice the computation is done in parallel over an array\n", "$x$ of size $(p,n)$ of $n$ points in $\\RR^p$, where the class\n", "probability to predict is an array $y$ of size $k,n$ where $k$ is\n", "the number of classes." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "dotp = @(x,y)sum(x(:).*y(:));\n", "max2 = @(S)repmat(max(S,[],2), [1 size(S,2)]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "stabilized log-sum-exp" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "LSE = @(S)log( sum(exp(S), 2) );\n", "LSE = @(S)LSE( S-max2(S) ) + max(S,[],2);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "stabilized soft-max" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "SM = @(S)exp(S) ./ repmat( sum(exp(S),2), [1 size(S,2)]);\n", "SM = @(S)SM(S-max2(S));" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "energy, y being a target probability distribution" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "loss.F = @(z,y)sum(LSE(z')) - dotp(z,y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "gradient" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "loss.G = @(z,y)SM(z')' - y;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Load the activation function. Here we use an atan sigmoid function." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "rho.F = @(u)atan(u);\n", "rho.G = @(u)1./(1+u.^2);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the activation." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = linspace(-5,5,201);\n", "clf;\n", "plot(t, rho.F(t), 'LineWidth', 2);\n", "axis tight;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dimensions $d_r$ of the layers." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "D = [p 15 k]; % here a single hidden layer" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Initialize the layers randomly." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "R = length(D)-1; \n", "A = {}; b = {}; \n", "for r=1:R\n", " A{r} = randn(D(r+1),D(r));\n", " b{r} = randn(D(r+1),1);\n", "end" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Evaluate the network.\n", "Bookkeep the intermediate results: this is crucial for the computation of\n", "the gradient." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "X = {};\n", "X{1} = x;\n", "for r=1:R\n", " X{r+1} = rho.F( A{r}*X{r}+repmat(b{r},[1 n]) );\n", "end\n", "L = loss.F(X{R+1},Y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Network Optimization\n", "--------------------\n", "The network parameters are optimized by minimizing the non-convex\n", "empirical loss minimization through gradient descent.\n", "\n", "\n", "Initialize the gradient as\n", "$$ \\nabla_{x_{R+1}} \\ell = \\nabla \\Ll(x_{R+1},y) $$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "gx = loss.G(X{R+1},Y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The successive gradient with respect to the intermediate variables $x_r$\n", "are solutions of a backward recursion, which\n", "corresponds to the celebrated backpropagation algorithm.\n", "$$ \\forall r=R,\\ldots,1, \\quad\n", " \\nabla_{x_{r}} \\ell = A_r^\\top M_r $$\n", "where we denoted\n", "$$ M_r \\eqdef \\rho'(A_r x_r + b_r ) \\odot \\nabla_{x_{r+1}} \\ell, $$\n", "where $\\odot$ is entry-wise multiplications.\n", "\n", "\n", "From these gradients with respect to the intermediate layers variables, the\n", "gradient with respect to the network paramters are retrieved as\n", "$$ \\nabla_{A_r} \\ell = M_r x_r^\\top, \\qandq\n", " \\nabla_{b_r} \\ell = M_r 1_n. $$\n", "\n", "\n", "Perform the back-propagation." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "gA = {}; gb = {};\n", "for r=R:-1:1\n", " M = rho.G(A{r}*X{r}+repmat(b{r},[1 n])) .* gx;\n", " % nabla_X{r} \n", " gx = A{r}' * M;\n", " % nabla_A{r}\n", " gA{r} = M * X{r}';\n", " % nabla_b{r}\n", " gb{r} = sum(M,2);\n", "end" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Implement the gradient descent." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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JamhNAcedJACwMQgkq4GFwAHAtiGQrIl4agPhbUkAYFsQSNYEF0kAYMMQSFYG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\nvn379rm4uOjubWxsPHv2LBG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo1()" ] }, { "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": [ "Grid for evaluation." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "q = 100;\n", "t = linspace(-1,1,q);\n", "[Yg,Xg] = meshgrid(t,t);\n", "Z = [Xg(:)';Yg(:)'];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Classification maps" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "V = EvalNN(Z,[], A,b,loss,rho); \n", "U = reshape(SM(V{end}'), [q q k]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Turn it into color." ] }, { "cell_type": "code", "execution_count": 22, "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) + U(:,:,i) .* col(a,i);\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Final display of points and class probability." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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JvX1n6Wvx9Z227F7a5y6ASeeyc9M3kHFdPr/HDgDgLMtuVitrk5IoirucofZO\nWs8foWw2OVvmi0aex3iQpueV6SMWpWn9b187wu7vqp9oGl+abzWNhTmzW4Vp7Z92zmM/0vUF2bQL\nX0N/8j+Ez5vGBbROubfwzm592zn0Ljt1uLvnGfR+vDNo3YCzXj7e3+gIWjNsHXrgqMbpmnx86Mfb\n4NAj406X8S/JgAkYDzo7tKcvbjsGwBgzr1bNotqA8Vk0Yb558x3SLmy4LnTZ3QI0SC8ILTQwoC+7\n3Bkh5HwyEVLmVSWVkkoJKYPNxbkZ42fTCwBQgJHzU+CqXFjFuVDyY3HzOjnflOUdeWLQIL0IqkVd\nL1p1GQtZchm/5BJ8SuubVTsbEFJey+U0SePNjjvkKFBGV1IQQmIWbDIwlRJSjzLqyipFN+xhgAbp\n9JGltNYIAFStio9l+vohq5reBsd10ydoaDuZ47KzCRqssg4AJsu2zaWTVmDktNxubFflMCnnosij\nIOyP6312ToG+bqty/mpW0K7E/Np8Yjvf61ZTtzKzplGZ/m5L064Jc112Xk2XvT9uptS8+8Q5tG7A\n9/DGbv0SPjaNTxw/npXhnTsuu5lppXcz0rrsZtBr+axDb9ptBYC0E+lFTp4Fq81jvUPPTeHapQhZ\nqw3oce7tEumN9ltnWee2UsYc4DKZOYmF+lMOwocNlaq3GqRt+SkwU8PD8qK9Ny+EajFceaNq5c1Z\n8EIYpElt8GZLQ46CWkm3JCAAfCzmyzofJ83jvuS5IcVl44cCzpBOH6N8L3EK30bW8CrCkSejFJUy\nmlMW81v7TgsxnPICQC6qXFSzKIt5L8ePWMgIdQ0VIUQZdVXOASALkhDz4T4raJBOHxYyWQ5r/3hr\n971kMKz9XBhjPuTXNiNGTtlFMrvV16E3K9nm1SpioXu2y+TsuloIJQGAUaaNLrs0RddqMTBgyBOD\nBun0ic5CVSu3LOy9a8LaWItv49ZOvyO+e2Glqt8eF2377LrvTAq7p3O4NzP1PXDOR5zO1oQL6F+i\nV2baNK71Zd9J2s4K2siElXqDk6DBOFNUM0pa4Y7D3Sa7XgHtOUvoA1RL0qYSv4J+PG/gfdOwonBw\ncjrMTBslmkBf33YCbVr1qemzj8/IUCnu7hmT9ru5jVJcA8C8vHHzM0mt5lU+jSdk7bq3KcUTHjUG\nxovUKnDWMBFCLuI2tndTLqt1jcO8WiXDKRrGkJ4OfE0+fSij6ZuExxwAaECTyzh6GUXKNxH5BHW1\n3FZLAnk8xvmZKrmtZtWYmEe3LbLefpDypHAdyPCQpwRnSC8CymhyicLWliQIq1GK1aKqwttHL5AD\n4TI5K2W1EsVYnBJsTvEwiCc1YNbwZwQNEvJo7HLojevyMel451Zt+/yq74y6Yb03rgAAIABJREFU\nV2fqFhgdf5DZ0AYwxiyKHHyYkW7c9aRp0r6Du/43K/u2amxwPHVWIO4qvHXnljBOgT4zVpxvwG5W\nnZvLlaFbd2JF+kCIHeQ1nNvOT2CYm/XckX2vTOuIW8DUdt50+SYmZGk7rfvONibQe/kSaP14Ienf\nANi6UpwSps3apCTkkQa6nvFha9pcMAAQ8Sji0aJalc4E6zI5G+8J3W3MwmRerdzNnDJGwPsDuo3L\nzvOJyD6gQUJeFsvS8xINGwTBh4BUilF6wpqLNDlfFR9tGIkQkkXT7YdsYRplSRBXsqaEJDzaft8S\nHkrdS8Y5ZZfxZMv+yGODBgl5WYyddQBACEmj51opvJFVmZdVVySC82k6OUmzxGgwTd/UIpeqDnkU\n7bIiO+GU8TDZ8xTTMJ0EidSaEAhedlatQwANEnJq1FVdVzUAMMbSOCZ7CJ0uJ2eEkIPyrZRVZa0R\nAAgpF/lylt196nDIEEKTMAPIoJPePe2nk6CdHx/UT+AlggYJ2ZNbv7SStbZX1tyluO7q8rk5vKeL\ntnPmyL6DuktFsyEWtVrldg4kpJRSnk/WHuIB50KuSYQppUrrebFssldEQZQm7SGu7Ft1sZ8a+hhS\nadrisDZuBACSDJMD6TWFdxdD2ir7LurhYk8hpTHUFy/r++wHaScVrOwCS6UTWFqSNrB0o1sNtK34\nBwCXpBWFT52kR1Zfnps+YLbsgkzzLsLkZhua9oGlPuxkUxCF0M9WeScWZ90igPUURF3BQPCwqyCe\nV4R96849/gD23xPxg1NU5HTQWg88clKpolrTEM/SzPUIEUImcXq9mttcSpWoFqsbeG68uZ00KpIf\nGqnVsi5LX2lg5OnBGRJyOgymPg21FEnUzwwIIZfTWVmLWtQBD5IwWhSrwSFSCa0VvdPSloeCcy5H\nl/O8Qzo9rspl3ayoFUAIeZ1MGGq+nxU0SMiIx3CkjxTebpt2k4Gg6ucuZ1fto2Haq4iBdXn53FJ+\n1h/oLfUkpPy4mE/iJAxazxUhJAmjJIwAwABx0wRYtAZCiXa8L9b/5rrsamhNnau9ViNPnVfh7brp\nxtm+0zibL9cmalky8SYFX699Z0fr8eMprx+Pto64pekFZsvOfWezPADAmWkv1i3lV3V3oOyclnnn\nxgSAFbTnnDpa8GmfSrz34yXWj2e6OinQ22M7broWYfK4yLa72hyVtlnWZe3kdzDGfCxWb9Ohys7r\n0PNtRR4AfB1AToeAc69AS2s9z1elT18HAMT3Uvzs9aIY47PJeRCETXuSzkKs2fOgrOQoC77R2vd2\ngjwZOENCTorZdDJfLL2TnlVZeKvwZXFaL9eeTZwFh+Aca+wQAIq/HgXvjwTA7Dnt0casRG0AAkpT\njjnCHwY0SMhJwRi7OD9TUt0sFoNNGx5AQCk9y84WxcKq7JJk9ugDRZ6bhIfF+iSJErJn3iCh9Tsn\n9LgU9es4xQom9wcN0nHydK/MZO1/m3byj2dbBmv3KNYl+Y7L/pCLD207KfpjmBoeOzhnA2eMEE9w\nqKzFeJIkleSMX0zObTDGhilcZbYNwAgnhiS61N2auFGiYehoPWt4F0Majnq45840Qp7D+wThrmC9\n7V0LiY0CSzXpX/NzaONAS+hjKp/CV03jwlzZzml3N0RXCdfNhl6Tdmtlel1J2YWdbAQOAGakvZNW\nIB5BL3y3sR93tZgbEIKeYTlaryicAMyiuFLC9dFdxInPpni+qA/lWvYpofVNXV3E8ZZDkH1Ag3Sy\naKGL61ILDQA85vF59OxxkaeEMzYW3Q201KsyL+pWFB6HcRpngLwYKCFv0mkh61KKgLIsCPl+mRqk\n9oSays31L5D9QYN0mhht8g+FrYEkS7n8ShJCeMyi2YuwTGEQjA2SK8PLq9JaIwAo6xIADtYmNSuQ\nDiGydUpQQrIgyoLbZXlHJdjjgQbpNKlXwq3IBwBgwBgjcilLlb1N72WTtjskvH6UDteVZBM00C7J\nd7Lq/9gvP7adUdWfyArE/aN3PjoKwrwsXa8dpTQOwmYfA5BXxeDosi6TeAJrXjXX8dUaA2l6l1Sf\nEMHVcJttTjlnT6/se3hlSsllV1CVEJKlF4zxpp9SNlAVbsiJ7el23JLWUen4JzsHWgVu1vDWj/cZ\n9MLuN6bVhVufm61A6LbtCQFA+pKg22HQTtHvyr45sSuC+6XBXqec7z56vXyeQ7b/su1ujNJx3Yos\nCNBTd3/QIJ0mqtq4pN9oIwoZZieuCyKEXExni3zVzJMCzmfJ8SVy1lotVn3Axhizyq+CIK7rrjwr\nj9L0bMPRyGPxKkneF7l13AWUzsIIDdL9QYN0mrCIqXqjTZIvwCABACFkljmVsNcfF5TSQUjpAHNp\n12KY0c4YY60RAAhZLZbv7YWk8b7LlYpqVYrCGEMpzaLMW5ywEOJGSk7IWUD5Mbt5hVaVFACQ8oA9\nRErvgNJP0qyUUhodUhZzfJA+DHgfT5MwC8TYa9fBgu1/kw//6CE+P57NtsBF+4mTeT8wW5fPzbhq\n6/KtZXzwNjvKuq5lTQiJeBT0Dw4yibN5viYNz0Y5Vde8WJ1/STp/NbrT0W3IFb7REbcJs/WfXlyz\nmpdzIBQAlBJBEDPq/wMvq1VZ5/bwRbGYJDPXJhmg16sbqVun2VyoWZwK/qb5Z0H6jKs2L8MnptPg\nwbXdav2c2s1V0Rl+14HGOwedrelnc7ACgIFqfMgGV9vwp3ZT5kVXn35ZV+dRkgTBrnysPZu+OUpI\n2rvpcG70MGB87jQhlKSvErrB8AST058eNdws58tiVQtR1fU8X1SiX3cS8GCWTjkLAIAxPk1nweGV\nML+DiiEvrvPiuqpXy9WHVX7l3aesh+n78vXCqXmVW2vUMC/9ZXYPnFpJa40arit/hUbkEMAZ0slC\nA5q9SaHRf38stDIAQCiJzyPKXsSLSFlVUq35LZfFKuSBdc0FPJitTQsOjjCI67pQd5UUS1XnxU1j\n1cIg2eKtGuQRF75PrJUKD7Wu7iZKX77dXIpZGI37kWcHDdLpQwOafZJprUED5S/CFDXUo2RlAKCU\n5vyYnqqT7KIsV7UoGqEd56H0XdcmhGyjUFW92hJhQkE5cgigQToR6kUtc6GVCVLuXWlEKd3hoH2w\nCcK2BA1uqIXaunx12zi/6oc4XbS7cucdl/piUQ818rHa25V96z4c4j67u3CIcWMbwwE1/5ZKLVYr\nrTUhJA7jaG3NUxe10toY3em5206paqtfl7KmlFFCpRKMcUKYlGsFn7aQl3PO/QYpiSZuwCwMYrFe\nIogQYnjWfJKbNdzmPl915fu+AV/arbIThau1TBYt1NFwx11ehrpL9GDWYoN7JWUY7xlzlo9KHaV8\nKNGWWiutGaV7ro09yOn0KYAG6RQoP5aybB/bD7PS6CSIgmiwNpYQ8lzTI6n69HrGmKIqNEDi2CRj\nzCq/kV3AIwwjKaW3Ip/WKkqyLLhs/llVeVUvjTGMcm3UppR93TAqMVLuEUICvubCagyS1fgRQmbH\nKS4PGU944IaRJmHEKHUtyvsirzvXbkDpqwSz0j0baJCOHi21tUYNL2Sl0U6iMBRK2BqyhJBZOt1+\nyONRlEMzUFVFHKU2oOVaIwCo623znrouwqCdkQQ84jyUsjLGaKOFGC74dVFKidGMyhijtR5Uk8ri\naRwmUlSU0pBHhBCAo9QCnMdJqoJKKQCIOQ/WnZM3VVU7gUah9ceyeJ2kAKCNQcv0xKBBOkqMNlpq\nAGAh866BvdNKo4f52+uVzmvK7M61pftPsS67sKvLZxOqAkCat8fbonzuOQdjNcbUdW20YYzZQnwA\nMEmyNErKumaUhjz0rTTyLPN3auj1z2jr0dK+G8Wch3V/4c6OtfAUydZaNWkXhBRS3qKKtlIiL+Zx\nPM3zjwPJAyGE80hrTQm1ASRLVS/BC6Hj6n+UBlEUAIDp/mswTnrZZeeLszlVXVF4YVoP4Wem9+PZ\nE3EnF0PVndP6A9cccd0SgTV36N61i0LGQ+Z/1q3EMCBXK3VTVbY/C8KzKAKsxfckoEE6Pup5XS+6\nt35KwplHrEz5C/rzUUrN53P7T8bY+aSvH0EpTZs0zLdPnv2ABJz7cusxAFiubm5ljRqEKJQSWg/P\naYxRSkyy1wAAJXEnTIRQYzyzHEb9hQ1fLK6VatqNTUIeGzRIR4aqlLVGAGC0qec1oWSwBjacHtyS\nmsdjsV76SCmVl2UaH1Z91SSOxXJtdhIEISGkrss7WKOGsTXq+lX3obMwTKUoASAIkuXq/XhnSlmW\nXt5tACdAyFitNuY0aViJen+DVEp5XVXKmIDSsyiKjk0o/7y8IBHwaSCWw4eX0SY8DwnrfGKUxJfx\nC1lpBABKesL44jbC6CdAKUWApEliJyJhGGXpDABqsZdG7s4zGEZ5FE2iaLJJ2D3NXr/k6dFFFD9g\noCgX4kNZKmMAQGj9viiqXdYOccEZ0lFhwJsNiNLHX2m0qdzzLTvXZN9dku84b8d88b4ffFR1WZ8d\nJ1NzuFZKSkMIMMZ26299O3ir5I2zEXkL63mjCdSNIa0H/z8uy1p2Ii7OJ9nZ5nG1MBYkyaSuirqd\n3MRBEOf5tbuPtwJhOxjKvIMMw7Su80GPNxf4OJ4EbuHBtT2HJQqlIwqvugJ9NpgEALJLAU5NP8Ob\nkNbparxBSC/b7ch+ASZG6ds0W9S10IoTOg3D90UxyOS9v8W6qYdvQldl+Wl2oDVNDhA0SEeGN2tq\nY4R2rzQ6CYrruRLtg4xzns2m40ezNwmQ0VoZzQglD5Fec09u8spaIwAQUq7yRRwllDIgpBnq2GU3\nmZwDQJLMmmLqzbUlyawo2qc2ISRNL7UWtsdCCEmTC+9g4mgGANYmhWHa9LxwKCGuR+4sij6Wa0rF\n/dM6jAv3qb2VFwigQTo6wmkoS9nUgW0IsuDlLDkqFytrjQBASlmsVpPJxA0jMcYGASRjzCJf2nQ4\nURBlT1WKoqiHYZ5a1LWoASCKkiTOoiipReUq5RKb49WYslxIJQihYZg08yQpJQBw3qbgI4RWVQ6g\nAShjAaMsCBLYTBzNonCijaKEEfIC3l9uT8z5qySdV6XQmhF6FkX3SeaNwvFbgQbp+EheJWIlGrV3\nMAl4fJ8v8YH+WrwCNtcFZl12juybdS67dNE6ec6v+62haI+hznnqchhxqas6S7Kz2VlV18QApTQK\nB9MjssgXbnK2SlSUsiQaP7it2ttegddl10O7i+RO0gG633qdqioIkDhOp5PzWtSNTQrDuAn2GGMW\nyw/dzE8VhZCyTpJZY4osnEec+97fN7+XE0KZL2+C+2Ow6uoNhf56dO/HsyfsRzgnrXEVToG+oiv6\n5+j5YQLtVK/u9nTl9eNygrD2NXmwhsDdSnyHuFeVCzGvq2aik/Lg3HmzWT+EAIDSutaKAkSdxZoE\nwXJd358FL3054K1Ag3R8EErCaQjPtsTzEKGUJnG8KegwThVa1oXPID08jBK1oQgIAFR1EccpAARB\nFARrdqWuy4EfUogyijK6oaIEcn8qpa6rfuVWLoUuzWXs/53cVNWyU4dTQl4nSSOrAwBrk6ZhOBu+\nHiHbwB83ckwQSs167QB6p4DQ9vw6D8h5Fn9YbEydsGUY3gx1WsvnMkjGmLy4lqqGJkwVzwLvzOyY\nmVfDdcSllN58DZVSS2etkjbmfVF8lmUAcBZFZ1GkjGHorLs96ERGjolkNpwYZtPd0aCxrLkpg/QE\nBIwm4UYTwpz0AcaYslzl+byqCthgq/TmydZjY60RNGn3ihv7z7tRafrb1Wf/V/ETvy9ePcQAHwDh\nq5PkVSUsR/kdtDHueia0RncDZ0jI3dn+N0fc7V2QiTh/8rZQ7PSmfTGaOitcbZJv9xDGWXZxXueF\nUYoyGicJpZTsCtlMkmyRry1KzeJ0fBH+IrQj3Ow1NlzEnCw4No1Qc5axrsGSdtoKpeRy2RbTE6Kq\nqpV32ZAxyhnm1ttPfFGSvc3Z4DO01mPzU9UFS8K1wFOzs/OaayXgBemDMV+T17kw71YKYAYAX8jz\n3xSf/6VZO4/8DL7fND5xEhTFnVKcrQmybbZvPerrcb8vG+ska7GodoeY83H9pMA3BR+r6ZAHAQ0S\ncmRQRuNpxm4zVwh5OEunZV1poxllSaO6fjSEJtIQTgwwWJb+aUQQhEmc2WHk+Zp62xjjtR7PtYLV\n+GQa3ixEe/IhX1u6UCj2m+WP/Kn4e3c+4X0opZxXlTKajmSHWeCPACWcj/M77F26AtkIGiTkFKiF\nWOWrroQdn6WTwbM74MFAn/ZI/J/Fv/Jd2U6/Ql5K5XlqU0on2dQ40sRxmQnlW+EfhE8hxBjjLVl7\nZ9V4rTzLu3+3evssBqkQ4rpbdaSNBgBKSBM3yoJgOlqBpLRWxkSMB1S4Lr6zKEKF9/1Bg/QyubUP\n5xb4SqlZBxJ1ZN9B3T7RZlftRCHN+79wpobHrp+8P49ScrnqPXJSykW+nGXjJZ/exN77Yj0/rqqb\ndWpvbhQA/P3qJ78rX9ut7pJYlyROAQzsen4lybQoeidmmp2vW1krYd75HNyQI30PmiNrsRpvErK6\nWXzNWZClZ4Q435Lrqe3+4RboA8oBhndGU/bPg58AgIx+bHpm+oPdGnQOQ+LYgNCaNceBZpfkUd9X\nO5az34yEDATIZ5OJ3c29Z9dlmXermBmh0zCqlKSEZEEYMeb4OdGhd0fQICFHT1EOZWxCSqUUe/K8\nlr8lPt+5DyEkHEmBKaV6PaIehnEQxjyIlBIA9Gmmd5vwzpAapBI3izZnK2dBls6s0ZRSGK0CzgdK\nSE5pMwtxOy+ioWF4GsbiEbXBFbmoq9zJqaGMLqV4k2JaoIcEDRJy9HgjzM2DRiq1yBfNs56zYJpO\nnz2R6HTiydaTTc6Wi2v7cGSMJ8nUtMWNwmevxcMY32KTLFKJxerqbHqhlFys5vZyojCcpWu5My6n\n4cdFbb+4OIBvZhsKNT05mzxvuRjeAaH1uLAhch/QIB0Dmx0AWuh6URttCCfhNHzwJN/+P02vd2bc\nteaya7upcnIxFO1oz67aRuwUG7SyhfVCfx4YpeOHZTPnuFne2B6pxNXiqnl8UELDIOQsqKVgjG1a\nUuMV1Lll5Ti0r8ycCACY0WKuPWEeSgmjLOAsCkPo9RTOySmbnb2q61JrzRgPgnDdXeRWpRvdg51J\nSL23zWfEx0dIWQtR7vQuWrTWtSiLsnBnHlVdFwGLw3aSpwlhnL0+j4WolIY4JAEnV+S82fpb7E80\nDRb2E1/T5cr6UfED2zmD1pEYOgPn/fymbaz9SfTOy7aVhmG+nhE1DUIgxLoB7bm9MyftWzpj1qSH\n6L67BWiQjhhZyvJj5+ioQZUqeZM0NkkrXV5VTRpWFrLkMj7hfHdJnFTrz5QojCily2Ic+TCNfECD\nkqp3vxBCJuk5YfddVP9vxr/9N/OfG/drbS5mrW9nizQtDA+rhpOoy3Hy1p1IKfVoQU9Z1tYgNRBC\n0vj55xazKAYAa5MmYTTdUPrIKwpHZd3DgnfziKmu1xbzG22qq6pp5O8KmxRc1Wr1de45/lQYV2Jt\nlhmNpWubMMYs14s73I3flW+371ALUZaFGC2rPEC0VnewRrAhd8YhL9yZRfGn09mn09ln09kmawQA\n56PKSefRYb1AnAA4QzpixuLZxgjJQg42GW1ELoL0NPM8rvLhTGhV5pMkY8xTNXwTxhit1X3WJwnD\n/nH9be8mSqkx5nqxtFMHSul0ev7sAa0t6D2CRmMIIXGcjGUmAT/6wqmUkLdpNq8qabRV1j33oE4N\nNEgnReOX8xbx08rcXfa7a+t6FKNLyrCu/21wY0hRF0OazttG6MwcaOf12e6F9wbbpZIGIImSqq5u\nkbau39OmAOiPtaGjkPSjDE3bDqG+NhtrC03SeJnnriNLa71azSfT25cj6hNW7/9t+hXQ+37QBrLJ\nGefcGJ2vlk1JJ855NpkCMVmWrVb9WwIhJMtiO17dmWHllPIrTRt7e6c/aRq/Tn+23xq13tQ/R/9f\n2/kTdZvT4Vz14vhYd1G97vtyF/Bav/WGwKQTHR29KxhjCCFncQy3+UPyJolHNoEG6Yhh4bBYX5AF\n0JmlAfWiVpVKLpMTCyZ5l2c2tpAQcjY5W+ZLud/LPmX3+nOYgN8R92oSkIDPl0Ovqdx79vYsMF+R\nw7UdGINmkW9rVntzHoYhY6wsS611GPI4jjC2j+wDxpCOmPgypkH/DfKYh9MQNpfsU7XK351aMIlS\nOg5aSCWvF9dFWQgpAh5kSTYZ5W4YkCb3reeR0vItvRn3s+N8AyCEJOnGe5Jsvp/GmKqq8jxnjE6n\naRyfWlJw5PHAGdIRQyhJ36RaaqMNYcTVfGdv0+JjOS52rpVWlWLRY/q+vZkaugQNVPaDjFftMOwS\nFC4dn4nvPN73bM54rUfZl7Uuqj6SQQhJojQvV/af0/RMKlGLmlIWRymlzkr77rPdpAzcdAVnoV/C\nmZDWwMekBIDP+buv67PBSN7N61eXUcCZWE/cwDn3XaSjGO62Pv3kopnQhAkP4vO6qo3RYRSJWsi6\nppSGUcgDT7YFANBaL24W7SIwKcuyms1Sxpl7EdaLpR2XnTDthMyo1gp+bfqtVSemv2GXtvNfD/+f\npvEnxO/YzjeyzVGb6FbyE7h5b007Zub67PxO3WGna4C9fuCjfO84MHCGdPRQTlnIBiuQCCXp64SF\nHsMjNyefPlL0Hlk+jTHWGjX/nK+uwyCeZOdpMn2oXKvMm4QUoKzEZBK7TzRCSDo5gkX+hJAojpqs\n6lEcZbNpMsl4sPFFNl/m7sPaGDOf509WfQo5dtAgnTIs8Hy/QXxqWrtwQ0rmndwsP9biITPW/BT/\nQ2+/1ppRenmeZWnEOU/T5Px8dpIr/OUonYEx5vpqKeXdU4MjLwd02Z0y4TQU6xJwGlDqs1JHTRzF\nVV1502NvxxiTFwulpNZayIpSFkVZGNw9o/aP8ncclITxfKsVWSRxGMXt1pczazDGLBbFxcURzAiR\n5wUN0inTBJnKqzaYxGMenz/IUr69vOVrytru/ZjJ/thk2T6ak7zt5I5NsYfv82Fn07OiLIQQewrq\nXKq6qz6gVVHMtZJh3KqxqRMmaZIDAUACfWhqAq3geEIWAPC/FD/vs0YQhUBJeyo7U1gTBdj062sZ\nyTv1uXMrjc1iTUaNQduDp2qfExjx6Z+d7Ow2/9P6nt15DABAEHFReb4CrXV/UNfSpn83MiboNtLu\nkP5OSt0qIwrZFwj+yNplyD9kv2E7/6xp25/DD5vGVPdZ8qIu1ZMxTmDJ3mdXID6+Bq8o3A1F9asF\nkDtyai/LCAAYY6zXnjIaTsJGdCdLufp6pcVpOk+SOJlNZmeTM6/6ixCyZ/Lvqs73T/Hg8kP16tfq\nP+rdlJd3OeExkk1jxvGpgtwRnCGdFFro4mNhlAEAykhymQAlxUcnSaU2+Yc8e5ud2GokC2PsYnbR\nzJM442VVNusZoyAihJZ1WVS7Y+yr5bsse0XZ7YJt/1T8yKZNVSVNFhxyXoaHghAyu8gW17kUazaY\nUiqlptSfWAhBGtAgHSq3jzAYbYoPhY0YaWXy9wUdva4abWQpg+RBpQ3Gdez4OjvPDxMe2XfUabap\nM3m7Qx4CewjvlrjGUezeyTiMKaXLvF/Yv4nV6sMku6SsX0PDQRijjZIxldClYT2DVmT8in79in3c\ncsKiqiYTBo6UXDvfjOFtJwn6lK8mrrtG6XR27biVNRvnkN7pSX3zYNf/JttbZET7SyCls2CojMed\npmqvmgjnxyO7eaf1sGkyOY/nH3Ot+luvtZ5frwCAcTabpY1tXsuK3Rfba++LcZyf2rSjldALWCrV\nVua9Ia9s5x+S9rXg5+j/1zT+GDii8K7oX+r4XQNja+65rsjuG9n+p+gWJux+8MZ17m07GBmCbyun\ngyeFnTFK+BaL7Cd5kqVcvlvNv1wsvlpWy2r3AcdAyMMsmezeD6Ao11KLivK6Wvygzr82y++bxR/A\nSGv+58Lf3nK2qn45IgYghJy9yrJZlGRhGK299SqpFotTW52NPBRokE4Hbwo7L/sov1WtiqtCKw3N\n2vtlfTg2yWitlLzz6pYoiJIo3bmbmyVPiELVTgU5Lc3y+yBWUfnDQLRpwlNS/keTv7npbO504YUQ\nxkGcRmPBtxQKVyYhXtAgnQ6E7eUeYCHbR/ldzocLdKrl8xdNMMasbm4W19eL+fzm+qrI7/iuvY/A\nwQ35iHpUWklLk38ZVz9M89+bLL/DjACAPx38zl+/+K++Hb/zne5uIz16mneaAerlmWdkHzCGdDoE\naVgvhPH9/TcQSgglPNnrS/eK8YwyZFOFZ+dz2v85zxzaude58GT75t1nUbOmoh2TLxbueqOqKhln\nUbBntrT+jCEPCSHb39OjMGWd7NvobWpypoo/tvrVD2d/vPnn2+ir75ZvBvsoBWFyDQCmi2+ZtDfw\n5FU7zVJvPvTDPZt3ezqyFBtw492QmE8s7xpAGzpSvRk2XQwJbGSo6BdgkWW3Zui6z4RErtqirmbe\nJyknRRttMjaS5aT8IYZ4heBCiDxXRpswDOJkbSmC/U6M87qsu3Nq55GliA0s9T+AnLT+2HfwWdP4\nHvSu1D9J2va34Q9s5wW0Nz92kkLZhEM25uf+OIlX4d3Lx71lk5Hd4AzppEjfpHxz0SOjjZa6uqlW\nX692+ve81dCfV5tnjFGjDNllMSy9syeztM+VQAiZpNPAyW8dhUnsuPU21Ti3hKIPOH0z8s2QAD68\nf4lpRtMsGsgLGaNFXkkhlVJFUc5vdmtMkBcCzpBOCkJJfB7DeSxLWX7c+KTWSlfzavsi2WgWFVdr\nZwjT+1b4vifGl4thXC17Txjj55OLZslRk8uusTpKybHgO46nQu5bWumb8deMaGWGFn215K9eH0oc\n7smgjM4u0mIllFKEkCgKVsu135VSqq7qKBr+uqRSVSWMMWHIo83Z85Byy+9IAAAgAElEQVRTAr/m\nE8Aza+ExTz/JxFJooVjE6sUw/CN9y+lbDAAAj3h8Flfz9ikcpmE8HRmw7VmSfdm+Xdl3WLVt1rkZ\nt+cZoNzzcw12JbLr387XFYjtOdtJkoHuPnLGDNFC1Hm50lpTSpN4EgThdPqqKBZC+C2K5tGsk31/\na/LPf/H13/s77/7CeLcf/g+/dP6r/y5bzvj1K/Wtq/7wy26WkDjnt3puJ4MFcQoXtlfiXpfVkivn\nXlmVtnDuVeepswpv47jsTOeyI47inHTDoI5i3XRuQGI/cS3hAwEAwlg6acdQFp7kgXUtwjBe76ls\nib+qruswzNIM1v14ViDu+vEkaT+ogi5BOJzbrT8032waf9z8M9v5U50u/Fvwhe2ckfYbiUz7jXDS\nfwu001hSXzrdtb9IlG/cBjRIJwtlNDqLCIDWemyQ9lmkGSRBaJcr3aI+6SOSZFmxXoo0SXfr5W6L\nELVdq6S1XuXzOE4Zi9J0dnPjFSzQ6uxTt+PnX/1Dr0ESf/vfeveX/6emHbz/1tn//e897MgPmbqq\ni1XhnWWy9QLnWmu34CwAVHXNeRCFzzxHdylFVdalMjriwTRKmj+oWsm8ro0xSRAkd835+5JBg3T6\nUEopowOx057ShkMjiCJKaVkURmvOg6YswgMGjrXWlaiKaijeK8scIAeAIIgGkyQaZTydrbogE1Hi\nZ//gHyxXG8zkX/tl+Mu/0jTF6y/e/9J/BwDB+28l/+IXiGyfX/L8i/LzX9PRitZZ9IM/xW+++WCX\n93yIWuSjmrmWMFyLrgnh0XMKUR+OQcqrIu9SIJairqR4nc2WdZnX7W+jVnJV16+zvVa8IZajfCoh\ntyW5TPIPuRUysJBF02MNsLMgyIKA3s8IGWOUVoxQcDLZVKJaFcstRwGAEFWUzupyZbSijLPJJXEC\nTqxaxdd/mAJcwIcpLBYwqri68NRgFa+/0Mn/Mfn1XwIAef5F/kf+XtOvw1Xx7X8Qf/9f4/PP73SV\nB4TXU9cQRkPVw4HnWDLGWGtke+ZlXknhdkqtvlzcEEKyIJyEx/rn9sSgQTow9n3Oev5ijTKbliLR\ngE4+nYhcaKWDOBjnE7od40H6h+2mDupGovpOKocC8Q1Xv+aS3zaw7SfqTrMq87LqAgOMzbJZIwHf\naY3acxs5Obto2qWq5eIaAOLgWsdJcP3e7vafwn/7V+GvDg+e+hVlKvuo/vzf4SYu6O8ONlWf/1pI\nrp1P7y6jC+SQNTF3Zx0rTx4gkzsFIFbZsME9mhHjxqLseRb9iz/pDjf+AGA7WiU3ppetq6ququn0\njHWCeM4jgOHCryhMjKFuVh6beWhdIN4Flogn21AO7Wg/wGvb+aX5RtP4I/AvbeePw+81jc+6rOET\naH8eWq8ZnoaBNeoHacyyrjCOtCco+z4Fyuty+YPF6qvl8geLerFRxxWkQTSNBqtijTanmv/bS1XX\n1hoBgFRqkS8A4A7llKoyF/NrLWotapavgo/v3a3/Nvytn/nJ/3l4zC//tU1nU1AAgBkFycc9x0gQ\n7kgOslz2unlCSJquObvCMOL8YApL3n4Ct6pfnLrybuAM6egpr0uZ929n9aImjAabVyNZjDbFVdGU\nSgKAaBaF2aH46B+Psh76joSU5jba8ebJaIypix15Iv767/zX//mf+f6v/s4vm+UUpgv45b9mA0hj\nBKwiuCBAj90CaWWUUIQQHvVTtyiJRe2fQzQYY6SUvBNShmEUBGFdV8boIAg5PaAnFaWcMa5uX3kL\n2ckBfc3IOvu+hbnWqKFe1PsYJNcaAUA1ryijPL7VT2JU5A16d9maC8eWcVsr+DbYCMZ59+w7PR84\nKDU38tRtdvJJ30xIGc18C4HHBEHIQw5gzGiJrpf/5td/BeBXAGAB8Fd+Mfre5j0lKa7Jvxj3R1EG\nsZPmdVwlzxFh2xzersLbdMkU1lKJWy+qPVw6vxkrCg8dfUHYVbcLnGvvonnNaMorVXWSTkJIdp41\nCjrG+eRsVqxWSipCCCFkvIDMAFnL/w0kCpNuk9PtHtFcAbib28sRvSi8vz+ye+JV0KvM59Amnnhv\nej/eV9DKJr8N320aP9o1AOBtGkH+BSic9zww6LI7brwi2i3Zgyxaa9caNbjpU402ohD1qvbmIjte\nwsBjqjljhJBJsrvGdpp18rlb+m3efRaIT199Bt+I+C1KpBNCwj3ywB4IstTVov9RGWNW130oiHGW\nzaZhFBpjvMuZuW+d2YFCKGQ/ApMfS7I32ewbhO5IjZiGt/jSXzJokI4brx5pn9yp4IuY2GCSKMTy\n62V5U5aLavluJYptzpbjIovTwU3L4vaJH4XhxfRsSwU5SikhFACUEOVt8rr+9s+G/+V/39bsmYSz\ns/gVJXv96RljVsttZZYOinoxmvQYI52p5Gq+qCt/it4kPUKFNOVNUo84uXS7CSGTKGt+ZoSQNEyy\naFtWFMRyPK8kx83Wt+n7SXDCaThY9xqf734d8xqtxl9ntClv1gItxU1JKOXhA/xa3PW1krdX3td4\no5493UO8nZ6Eol6HHgAAUEbOp9O8LGshOGNxFIVB0CduYORiNsurUgjZvMjbOSghJJ1ODDVFsRL5\nXr6a3/9J/p/8ygUAFBMN0Bp1zQ0FmITT+fxmn5NoreY3X4VxHGXZ2qX198K5azaPg1Ogz2YCNY4e\nj9StDM/Ytw3qTG6sI865e06nMz7nKxmViGougIAhYIio67HWjnHOeRiGEbVRou1KybXsu96CeGTQ\nWNPggfXj9bdCdDK8nPRT5GvTCik/mvZN4mv4xG793LTO1x8h3wMAoEAmP3JR/57RNWFxFoYAMAln\nABCAAP/rH+IBDdLRE04jGrDqpjJK04DG58leMySAcBLW6xUlolkEAN75kKzkgxikQ4BSOtma3yGJ\n2wzUhoAUUkjJKOVxBABaa481ChmM/J8A8Df+s41v/bet5F2XJQC0NulQ4QmV1dAo2SwMXh0j52Ec\nH41PcguGMBpddP+6Y8Jf5EQeMS8cHvNbihEAAKJpRDmtF7VWmsc8mkVNhm9/XOqlpuTiAecBhy5y\nLoVPy0DpF3/mPPtQRXORXlUAcPWa/e3/4Oyf/OzG0EJ9ex1wXZZRlomqUlIQQoIwpuyw/n6jKRMr\npUT/U4nS2DpIve7lA18Dizwxh/WDRp6YIAmCZBjkD5KgHtXi45huGQA2zWwoqSe8nrS36G/8FWuH\nNsbehNew7SKfz5Voz1mXZZxNgvCwghOTT8PqGmQlCSFhGnLWi/3CKKqKtVx2hJDwwMaPPC/4lHk+\nnmTKsTmYshHKaJAEruOOR3xstzZ+incHWyKO9/tWSduu4naz5P3RNp7khkj66m1rKaWHrbXIx5Zx\nrw/XhiJ6QbWT+UJwAwAmoOBosBu++qnwH/1CP+P5wY93yuO00yU7V92UmuMhEyNrlc4yHgXGmHJZ\niKoeDJ0QotaPKVdLFgZ+5597g2wKBu7KtYcONAOeYJ1x7n4v2VfOR2o22DNMQqspM31iDgKEpLNZ\nsVg0EjtKaZKdAekCU24YyP3f+tYN2SDcgnjDiOLu5A5dWzrPw5K0ltKKwq+M9cjBlWlVDO9MH1j6\nFvmia/Ty/gs4Gk3KIYAGCfEQn8VBEtSrGgCCOAiSACtfNhBKzOdT8v0+A9D886i8uPXfURiHZV66\n0wXGGY8CaFKYT9MgDPL5WvocQum4IpSWkga7y7EfCIzxyfmFUQCtsw79dcgaaJAQPyxkSZgQfGSM\niZj58TPIJWjzh3+Uq+guaycIIdNXs/xm1QSlKGdGm/m7ax4FcZZQRnkUpOeTalUqISln8SSti1Lf\nPr/RAYJxI2QTaJCehBc1vfDKtVl7C0TUP1KXF60H6eas3bVwAgqiaDsD5yFsk3wT557aauzESrT9\nI/Os93cH2TmfwKY7KOL+kKvLtv3F502DAsB3f0w3cocvfrQ/UZl1nrruhMYnZwcC6UUGAOWyrDvl\nnqzEqpbp5YQyykKehr1OL4RIVkM3H4v4Wgk466t006GTYU0/8CVpBUcU3rfXOtv7YkTvvyVjzf5a\n6SzfjfZ3DlmX0RCtVVkulKoZDaIo4069ebPbZ2x3bbdqNydId4he8+O111WT9oNW0Escbzo/3rU5\ns53Wp/e1eWs7v9n58f7VbcNCWtAgIchzYoyp13XkxphqUWqttVQAEMRhPEsBgIU8iENR9nqTeJoR\nQl7C647Warlsc9dKVcu8TpJZGGD6g1MDDRKCPCfezEzSyUMqylpJlV1OASCepWESi0oQSoJ4WEbo\nhCnLYdmOopijQTo9MHUQgjwnhO42KlqqJnpU51W5zJUQTX7Sxx/doSClZ9mW1qcQUUNccIaE3BpP\nTm3fs9Gt2KZZOw+ok/4hcvW29T798Fvt7/Dzd/3hk+4RtKYh62YOei2wNAwduW4sX1JsUF1Mq3bq\n2OWdSvvmom18fOXGkLrGRd/5/lV79sXMGWPYxZDsJ/oCKE2DMsI421K/rh1wrcqyUN3qJSWkKKv0\nfAqwnsnHjYyMe91b0OX27mv6SedpYOvyuZ11G00htVOmxO7gjSGZ9av1tEedPg8kpcxjfnrJuOeX\nuN2RuRZ3635iZu32DZOFe0XhC+i/+HkXT5pDH1i61m1g6S9tHQ/SgDMkBHlm0st0dw1fY9T6Wlol\npLrT6tpjJAyH6YUYC1/UHPGFgAYJQZ4ZQsjk1Y5c1+XSkx5N1i/IILk2ibEwTc+fcTzII4EuuxeE\nt3zdXQ4ZH+/mYPYlodZW9u247G7etC673/vptnNWO+v1w9bL9+ZD35kVbTuQfad12XnzQdRR2y6c\nEHjeKbNXk37PIh3uWTqHWEn6yklwas9TJE6Oie5irTNtq7wZAEDWkjC6TyErH8bTdD7SWGeaI9e2\n/re+4RboE9xzSNX5N6tenm865x7Z7rJbq9ZoW958G15IHM+iaKK1IoS1CZx8h4zvBfH7Mb01HF3Z\nt80g4RGFq+7JaUXhALDqkoXfGMePB9ON14SMwBkSgjwzspL5Ve5aIxrQZI8aIkF8+iXnXQihjAW3\nTZSOHBE4Q0KQZ6a4Gbnj9G71XTzN6H5l148OrVVVrbRWlLIoyuiueqzIyYAGCUGemXFpD6005Z6n\ncJCEzayIBXy3H/A4UUquVh+6NghRZNkrxrbl9kVOBjRIyH54Xe59emxPAVc3hmRVxCLqHVOrs3bP\nH367Dc5T57GzeNPu+cnX/SHTVXtIKHwxpE4GvJ7vpqtL61U1M+Pp3KZ5dgMoUHZ5yl0htD+HjmUP\nO0IIIZSEaeQmcSCEhFnkmy54RfeuwrtL+VP1IndTdpfRDX0tIZBtuxdmw2iV06mG2b7///bOpMmR\nLcvr504+aYiIjMx8r6vppqsnwFizwIwlCz5AmxXLXsCez8AaduyaDwBmbWypBZ+AFZs26Kouuqiq\n9/K9nCJCks93YCH361fuV1OMrtD5bdLjyt3lUkp+dM/53//xuwTtl323T5LfDkem03ftyXcc2sMa\ne3uf2GMBvqmatyWofjEJfKJwcHThOek+IkusIR3D65zyI8gJ4WlJNQkAIJxFwaTpmshDkVxPX2uO\nzmW43ggXwJ4POENCkBcmnsdaadU2QQ+SIJw2U5lwGoXT5ue2MSa7SVUlAYAyGs+n3rQegpwuGJDO\nCSvBNb0B/27urm6+olsMT+yIkxehNlXiZkXaZJpznqrdXLYb3zse1bJt33f3thucL5v0XVR0T2gl\n4My6Wpuh+nd/Zsv2n+v8r92UXTuNcfNVNqHlqqMdd4K+/nsbyZuJ0cYoTRjdJmfIvqa6NXTQSqc3\ni+nby765avt6jJu1tHYUubO8tJW0G/uo8xpM3ZoyFF2Wj2Tt4ZUnZecovPfJvrtHwRhTFsv1HCgM\np4wHQsR1vaHyECIeVNk2uMcyBq/NyBbX8F2fZ+2cx6bvlHNfrYjjBYLs4/VnAJBjUZUql6UszmXR\n5UgglFDBtkUjVUs9sBeqUs9q2RPCGJOuPtV1rlSlVJVlX+s6j+IL5jQ+ZywIIyzDnAs4Q0I6jDbZ\n10zXzUSDMppcJ4QSLTUY2PHjHXk4ulbFslgn7njIo4vYtcaxCT2XvQ54I6cslj2FYZHfCREnkzda\nK6M1IYQyDnBmHcXOGAxIZ8kWB8pyUdpoBABa6fw2N8rYFgnBNAinYZeAag/flJPZHnHdkB5msQBk\nO1i2GwvnEOucqUR3iLVOmGTdYNQq0XgrveOu9WqXx3NO3r/WjVF7tW7eyya0aidfVfpSdnoz72CM\nyRaFVppQEsYBCz1fuvVPAXt3lqXMvmaTzk+IsMBzFOMcDNlrymDaVJtxTCaGKjs3EWftU4nrb2G3\nva/W76MKnsH2TVe6328QALSqKROUMiDM2XlnK789z7fnoIPzeF6hoOMg3A7Wzp4Ks1DHgAEJ6ajz\n/g2i98O8WlWMMxHhopBDMcbc3KQ20tSljOdxMJDVVVnVmytoqWRZs4CXy6LOKwAghLj7EEKC5LQb\nAhHvzRotU88YDEjIcVRZhQHpcNK07EWafJHbgKSVXv8IGPYmBwBVq3JZ2OmpMYZQYrQBAMpZPJ2e\nut21CGKVV+4IpYxSvCmdL/h/j3SwgHlrFci9qXyG3Eoqxlmd1/lipyrBmF4/WaNNfDHloQBw06Cn\nihCxVnVVZes/KWXJ5LqqUlmX60dF2xO2KG7X0jtCaBRdcB5tOydy0mBAOmvc2g8xEF1G2eds/Rt8\nG5TRbhG7V0jtPazddeP+2h5ed/Lo7sHFYDcA0G1Rxy3kJM0NDcK2mCScKMDaCMuc5yY7bbWtFlw5\nKaXOu0A4yvWQ9B6FzXeVMSLl4C2hRBuzOxpRzlTtEzLUigfrJ/O23Wu/0YVzy161tajMMSq3hhNd\nccxn7J05SnFbQ3IdLIY1JH+DPpduMIzmQTjVSq31C2n6Wau2CaGqlKqi6DLLvijVTKSM0Xl+kyTX\nrhLPy77C0p5w7sxryfAAM9hwdyCEOXue/O+G5wQLbkgHZXTybhJMAxawYBJMv5kG042vPaEknOO6\niiOIBobclFFKqV8g19671hIGb0ByzRrKLE+/3qzuPhXZYmiIdyoQQhkXlPG6zm00WlPXuVLSRiNL\nWS6f8QKR5wNnSMgGhJJw1oWccBYywaq0MsYwzsJ5SCjZq8EtV2WV1cYYymg8i3hwvoYCYSik1EXR\n3FIpo5PrybadmWDJ1RQAqqwsl8VwB0JIk68DyBdLWTWnratC1uX04t3wkBNC1p6XXFXpcHAYopDX\nAQYkpMGxXXBHgUecR5ufk8Hqe1dRXSzLKmvuF1rp9DabXE+4bdHtasEHgc39eWxTShs/hm3qz01T\ntQapCW8eDZ1Gf7w9KdunBbd0jf58sm/HoRQK29zOeYd67gTJJAxnoZKKUMIYW5d+uPB89Wx/I1l6\nKk+EkORqSggFAK2UjUbNcxlTFYWQzRpSs+oWk5pl0y/OuE4NQ7W310d15Wb52lfuvi/eTN2Qvd7k\nhqxfWg/GhBy8GfeuIR3j+NC/YOP7IbbZ/W9gheLYsCKHgG8W8sjYaGQpV6V3z/OBEMIFZ2xjpphc\nJu6fIhbWZdVrohrNE2te51XleWcYJ4QQiW8wCoL+nDIM93R8R04UnCEhj4mqPWoB7+99hId89n5W\n57XRhkfcBhst1fAdc5N1AOC1VSWUnbSjAWNBFF0WRdN+ghCaJG8IoWE4ByB1nRmjKWVxfEUpLjx4\nnWBAQh4TyjyZGcZxIr5BuSrXK2Epo9E84gF340j2Ne0pFNbJOneEB6K3ThYAgnAGpz1HAiFizsO1\n16rblC8MZ2GIjnavHwxICACA0Ubmtcwl4TSYBV3KyFtY6g5r/7UPM8Ij3jNmDefR7gqC9i7Ybzfc\nmg0ZPiOAbqOg7cVXF46wuK0ncZ8W3NV/D13MpWuZHTSjrqC6bBv0Se7UEna+2HJZlE6NLbvJkqvE\nOgPVed+yAQBEHFHGm3e7XX4UT9/k6a3RCgAIoaG4pioyaRO3zN1ldz3t4MalD43K3Te6VXsTx22I\nWMNz9z9sWEPyN+iDfYPtY4Syo9s+7S5fbf1j146eU3uexfj/OrQbIdIDAxICRpvsY9osP6qUzOro\nTdwXMhxMchXnt8XagIAQEs3Dc1bZDSmHNbZlmVw373ZvJWw76Ml5UsYn87faaCgYpXsW5SDISYAB\nCYFyUfYWw5a3Bf/2/nXj+DKKL6OTrmc8Ed7lR+6giESV9jUgTGwtmVBCAaMR8lrAgPRKOTRPYABA\nZn3JltFGS0Wd2o93Rbq/5d2hTek8Acttl6e8+9mck3N23SbyZJu7qx2DcJu+C5xXyawW3E3ZtQd5\n3b6tsXcedU9t29e5yT2Pe3Q71BParaGU2j0pZ5Qzt/URZTSInOhu02VWae6aKdw2mTqzuOgGu8Z6\nXVKua8Fnc3duLz6r9nbdvm2/Qm/KbvBpqKtca80Yd1XaUhZlmWpVMxZE0fxgecLBia89P4OOTqBt\nUXvvOvmWPB6yHwxICBBGjBra27zEpZwBPOBy0+BOa22MIYTUeSVLyQSjnKpSAgAPRTiLwYBWui5L\nAGBUcDF2swytZJZ+tcUwyvhk8hYA6jov8rv1oFJVmn4+xAQIOR8wICEgElEtNwobhBFKaZ3WqlZM\nMB5zbM33eHh+MmupikXhToxcJ29ZVfli1f6VU8Yn86unvcaHkWe3rjRDK1mWqzCclsWit2dR3E4m\n75/36pDxggEJgWAeqEqpsrkbEkriN3H6QyNzkCCrZRVfxwBQLStZSCpoOAvurXpAhsiy36F8fUOv\ni0rVsqd00EpWZS7GWjrSWq912y51lYbhdCggHO6JnDN4TzkF7jM5OS5zHb/daPW2+m7l/mm0yT5l\n9k9d6/xrAQCzn/iEDx7/FI+iGgBkIYtlqZUhhETTIEyEe9FddwWn7GLH3PU21rLFeoG7Rj5Wq+z6\nCYm2nuT6CQ015cpZVmVrSGniDLZu35tmOrv+wyaXk3yRV0VX0YrnsfT5qK7x6u5kWQnSFGbMXTdb\nMjdvmq1V91/jaQ4LzvvibQ5rD3e04KZ9kcTr520bBVM2XCPFeGSAcBHLesPjPAimg0+qx117D09b\nptmt9ja79tsxjPjAgITcH6PNvVN5spDZbRNWjDH5sjTaxJOR/up/XOJ5HCRBXUpCiYgDQghhss63\nG4YS0nNh4yKCEdtfJJM36eqL/ZNSFkZzAIjiy8IYKZv/dxFMAlzuijhgQHoO9iy4e/oJ0LHwhMts\n84ZHfM/JmkmF16LUfV2d9K4dKRZ9cXORVpHb7cL+8vZK73x0AjRnZlO1866w6ga9MyQ6mIp4F8a6\nEwlnqejhrXYAABhnlLffPgNMiCAJq8xv+hcnF3l62x1LI2He2KWv5su1fciK68zGVbazHLfjke0o\nZedPzqSqWw/rHtK+v8a/9LWbKhEqkuk7WedaScYD4ZjRRcmV0doYRakAIFpLAOPV2u3/iPv2ePb5\niGuu6n0YVXZHgAEJ8RBehLrWujWmI5QE06DcDCEPrCHpoa7vNaK1LosaGAkisbvjeDiNRRzKUhpj\n6rw0WgMAISSezRgNpxfv6yo3xjA1ZfQE+qVSyoJw6g0QhFBCqNZ1nn01Zv0yaZxco0MdggEJ8UAo\nSd4nspC60oQTkQgA0FrXq2ZmwUIWXT/otkgZefUxKUsL2wkpXxXJLA6iXfdcymgQhwAQJpHWBhTQ\n9bolBYSQIEwAwOQnEI32YozO0s+bf36aTL/1dqBAzgcMSM+Lm8U64rD+vs+Tl+ARB+fuF16E65kT\nYaRXOuq1QvfQqRqaf6N5mN1sWIH2RA3DrkuwRekwvAx34aYVJrgVfdvjnDmJSTq48o0W5u13xebu\n3EE9+J+tpbTRaE22zEUo/P6AXU/sdoUsIUD4uuW7KbtL75Jynxq1tLl1RA12DWzp/M853dftGOkW\n+jbJPbJ0JCo27LlqDfsize7PsXe99MYO3k4ZdZXuLynt+9oc+LV6tswetjA/Cvw9ghwHFfRR1iTx\niMeXoT1VmIjodTVHryqP6qAqsNUpAMA6U4cgPXCGhDwTspRaGh4w243CtqTzT6rGR04UALDDvjXa\n1520Lut1Um6IMSa/S1UtAYAJHs9nJ/fT2hhdlSstJWVCBBNKt5rqUuZJXZLt+yNnAgYk5Mkx2qQf\ns/Uy2xKABWxyHe89ajdlJZXSQcD50a0K7sNXVv+Wt5oODe9JNCd7KvCUei5Mya0zg/TLwq7dUbVM\nv95OL9/d83JfAq1Vvvq8fglKVXWVJpO33sADAJxHlAqtu8VYlApvx1jkrMCA9Czs+a179ARhd8ed\nI57Zf/bjdtdKlzfl2uiBJzy+7Ffds0+Z6yauKlUsq3AWDOpKfj/WjSw8BSX14jZb3/jSvBKCXU6T\n3nk2uiV1ZqSO42qr9qau7HuwxnFdNKlB/9ZsKAw/moILzgm1FZYNu1EAAAgClg8KJcYYrXUTq5yr\nrPO6t5LUGFNndXOPXs678Y/fNBvtGtiu3RE4pSNXrt21PnLKaO2KV5K2YcCRfXeHqL0+qs12md31\nXkKe3zi2QP3/2mTyriqXtcwAQPBkT/XoiM/kQR/5vedDufaLgDUk5EEYbfKPubUdkpnMPue9HYZq\nurr1Fzfa6O2TBi/LRe7e+OpaZbl/+c5jsTB9N3QASJVn0IUz/6+9XqePNVr72iCZU7LVUapfHjP7\nbIGCcDaZfDOZfIPLY5E1OENCHkS1rHp3WFUpLbVtXeG9/xptjDbZTaGqdcNTEs2DdT1pN1rroZVO\nVtbJlsLMkyKN/loUhZKUkDgIJlH/Grjgsu5LG7ySEO8SJUqwpoKcFxiQnpmD8wCPVNHeZ6Gw7+F9\n12sXz7qoqgtIlFNCSS8siZhnX3N7rDEmvysJo8LpLevVy/qEAmCM6TVB30jZWWM6JxLY8jn19UPq\ntaIWmkPd//lPOf2hStfKBW1MWpbKmFm8URtLkmhxt+EKyAWnhLti6r4AAB3TSURBVLXn764nCOMq\n25j5EUJ5+X6dKdRtmg4AzJe3zcaynVV4G5O7Ive6b1sH4BhO2POkTgnHugG6PhmdEt8j+x761DEW\nPOhz7F0E8Cz8ZfUf/qL+q6lZ/Jz/7D+F/35F5r0djm/1hRwEpuyQB0GY57vJgo3PVXS5MXUglIhE\nDCNZle5JggEAZdQ7mVitPOtaHouIsmhTABYwVirZ09EVVaW0Lus6zwupFAAwzmbziVU3BGEwvdja\nh3dyecV4EzkYCyaTU1I0AEAUX7oSBspElPh7ZNR1lqY/rpbfZ+knV9cwEv5z9i//svqPU7MAgH8l\n/+t/yf7ZS1/RGYEzJORBBPOg53pHBXVbzQIAj/jkm6RaVloaHnIAMzSyg7bhgotWWtWaUsJFFw+m\nF/HyNuvtWZY1o2SYNHssvhHJUstUVQAQiyDh4mO+Gu52u1o1UaooOWOzyykX/OJqttv/ew0hJJnP\nXd3Byf3MTiZvtZJKlZQGTXAdvIaqXFbVcr2tdZ2ln5LJu/GYBv2p/ps/1X/jjkzN4i/qv/pr8W9f\n6pLOCpwhIcchC5l+SFffrdIPab2qKaPJ+8TOk1jIEp+kmzIaXUbRVVilVbmsvIk+s1kcKpbl8nOa\n3eWrm+zu08oKprlgs0vPU1SDas3jMmHifTB5H0wSLm7LXPplCN0NWCqVrvLhPq8byrgIJnaqN8RG\nI0uWfiryryNpjPQv5H/3Df78+a/kPMEZ0vMwMLt+UTZLJDvZlGbXWV3eNJMbo015VwKAmIrJtxP3\noG0W4MVN6dU4rNHK1JXiAQOAOq/LrCvbGGNWN9nF+7Z3jm+Jj9ad9tq70tZbWNo4U7vHUI/ubksw\nmTwo0VSV1WQyXFvjtTFvv4mOS3en8P7k9FS1EvCi3dNpWdRNsKRr7N1sk8LZs/XzJoumhkTc81g9\nu7f1kffl7NkNAEBr/48GKQulqmTynhB6xJqGJ+AH8gfDwf/F/nlvZPfklYzke36C4AwJOYLqrl/b\n7/U+381aU7eDOm9u9FXev3MZY2wXO8Y9lSRCoCiqYd7v0SnViDsRjRtKt/4CNkYPJ0/Pz8/Fz4YS\nhp/zn73IxZwhGJCQIxjOb3bMeO7B7gYNm3v2R5TSaVp+/brymsg9nLSuvhTpTZFt82EbXrwI/Jkr\nrbSSo8hQPT+cb3Ur1/uWdj0P/y7+b3aetCLzf5P8jx+oZ9qEPAWYsnsWXssMfijgPtxode/0CAB4\n1Jhh84AN97daCaW03h4Il8tcvJna8ODN49mkindCNcz4fU5T2RY5ii0zpFCIourmi4SQSTLpJaCU\nUulypW2vo3jGRQjQpd3Ml05cZz5+22y1Dt/gdt4rvW33rCe5z6nByQeSTu29qxefP2V3YO7ORxS/\nKfKvtmnsxvGEv2y+bs3f0X/6ryf/MzZZbFZf6fv9Bww4OTXKeMAZEnIEwazfYlxMHk0fFUwEb9ch\nhdOQbUr14nmklVlLG/aaO8hHnX/kdS0PKLkzyq5m8zgMBeeTOL6az4dzptViaU0ZjDFZthhJMf85\nieI309lPhum7IOjnyl6QnCT3i0bIQ8AZEnIEYiqMNrZuFMyCYN4PUdvwrlgKpgGhBLQRCaeMur8t\np28nZVrJUhJCeMiLZbmuDxFCkvmzNqnLB6tihxBCoiAghEyiuJtIbO5TlZ4SV1XlUbR1cdIrJk7e\nFvmNUiUAEEKj6M0Od3DkTMCAhBxHMD8iCLlQRoOJcFe/UkHDWQDbcz3hJAgngdFm8bFb9GOMSe9y\nLpjVOAzh/Ohbm1RqVZZSa07pJAgCx4lub2WLEHIxme7dzWtYp85VIkEIjZO33d+Y50IwICHPSXgR\n8ohXaW204TEPEpvu23Urr3JPrVuEnAm2loYTslEKmkwjIJsFo8GTmM3CklTqJk3XI0rrUsqLJAnb\nxTRxGJZyV9ighGxYqQ5cw9elEcGDAvorkwRNoA7g9nL9p/7wk+407aDJHe34sHRUexTeG4PWW2jV\nqfPJ3cB5yG0Ou6dc5OMehtwYhJBNMCAhzwoLWRzaNS4HHeK3ZzUmnobxNAQAYqAq6qqSlFLGaFFU\n6apgnCZJJMRBU6VF2o8Tizx/N2vu6QHjSRBm1VZPceWb+gxhjHMupLOGiRIW8HPM1yGIFxQ1IGOH\n+YIK20zKBZGYzmPOaLYq1sIHJfVykdXb03ouw4jSK/ZMo+h6OptGD61dTafzMJxQygghgieTCMvm\nCNKBM6Szxr3pvrzedhN7bSLkjFO31yrjVIR8uGeW9icx6aoQV9P+fhtsfd2GbCSsKGVl7bcCSoJ4\nM7XVOj74El8xm8dsDgA6nUM7WdIffr/Z8ct1dwFWkF25XgyDpJz0Kbwd2wWSNRk/snBkbG07PmIF\n4trXi2+vU8OhOT2PQfiaus6q6m69uovzJIr8lqzIOYAzJOQEmF5PwknAA8YDFk6C6fXEu5vHnvWw\nZFoycGWNAo9wo/YJECilSfisqr/XhFJlWd7YtcZSZkXxBQC0ltsWICOvGJwhIadBNL2Pk/eB1g9J\nFCltynZZq+C819nInm0Y866SOQAorQ1ovt0aB/FSlne9ESmL1eq79TZjYRS9IQR/N58L+P0ZG48l\nPHq5DNw91FYPpTlPGAdlvrFmKIr93RxsoLKD00k8jSOlNaWEAjPD6zMkEVFabWTtBONKm7v8zgaq\naTgNrTuOFfNpp+JVNqHO/PitHeu2V04zb6t/c5NydtuaMtSelB1xTBlg0Wbn7pyU3VBcZ3wpOz+H\n/8c1e9ZVplQOQINg7q432t0PSakyzz8nCVbazgUMSMjrIZlGxpiqaO5xYRxESXhEk15COGMAW2Nq\nEkbKqKJdJ8spm0ezr9mtO21alSvBBHYfBwCtVVUtjVZa125SLgyvhGjKWpxHXhsh5yS11pr6/N2R\n1wcGJORVMZnFk1msasWOXxt7CLNokgSJMZoQwiir6nqYxMuqbBrOvIefD+vme96HyvKG82idiAuC\n+e6ABAAACqvdZwL+NyOvkCeKRs3JKeWMM8oAQBqPrFxjNR6gyG93PGobI1EqyL7Z5N4dkFcDzpCe\nmbNfm/5Ids7GKWMM++mRjT3tIPENes5JBiOwRcMdkiCFfj/1gEREcgCndFR3igz9pfHLMb9zmhq0\npgzgmjLY4pByvqeS9zfcxnp5WxlauqYMrVl46qgT64Ha+3Bj7z2fYgL7ikMbJ/MFdYsQ0/uKGl5w\nIcPZf83vC86QEOT+MMojviH/Y4TFzK9KR9YQQhnbb4dICAvDizC82Lsn8mrAGRKCPIhZMOOUF7I0\nxggqpmKGv48BgItE1v2545o4fuv+KcS0rlfuCC6PPVswID0PJ3uLGt2FH+8L4MXbImI4qH1ZLMfR\ngCgKAAlME9oqqmWXTDN1Mw9Qi+72an7902bjx2+6way1k3A13FaQ7abs7KB1WCi7ZbnE+i/cdROL\nzqChcPYcqr03Oy+ChyO04FF0lWu17i4BAJRyxiJKhZUzWMLwQuva7slY6ItGYzMS2c1pXe2IwICE\nIMiTECdvtZLGaELosB3fxp7xW62VMWrvnsjrBv/vEQR5Kg6PLpQyAFTTnTsoakAQBEFGAc6QngVv\nSnl05ZknZWdW3ftWGPuvq73e+SRtmWeLi/k+s+quStTqv50aEmlLR+u6UYNsftST2vkqtaUavWjF\n3L/9afckv2u3V52RD2kNgcyGf0+7vfGMbenIugRlnVK8Mwe6dcRpWWsjJJ2LHKq9N96K7pS+QZfB\nu/rQDzYWYM4XnCEhCIIgowADEoIgCDIKMGX3crymPN6Rve8O42hL6Y7dYm7w56nIIFPnZueILztH\nyyaBRlLHYeGmUS2b3/xxs/HrP+/Oc/emPbnjRG5zkdRJltlLc1vnWV14mxi0Um+ALlO3MWi79ilH\nNaCH78AD3nCHYz7Cj5+dG12+70S/0S8EzpAQBEGQUYABCUEQBBkFmLJDEOQ4qnJRVcv1tgimrt2c\nUpUxcIhVHYIMwYD0mnik/PlTyHYPPefBx/o1yvYsvkf3ulnrvsya1F3RhVbNl4VlnZsqtc1YP3X+\nbOr//llz7l/9k2boS9cc1naMdWpEQETreC1ktydr2lgYt9Bla0hWzL1yjL1t6ci1ALdqb68TUvf+\ngEMroB+8t1W5rNtoBAB1tQIgQTiXVVaWN+0ro1H8llLRP3jz5E/BQz68R1wWVoaeBkzZIQhyBLJO\neyN1tTRa2WgEAMboPPtosC8UciQYkBAEORRjtDfM1IMoBQBS+t2+EWQbmLJ7Bdw/AfLCGtmhHcDe\nTMju/n67TQe8Cm/Vt+4GANoKu2nRJZ1Y2sis+U3Xnpx+1+Ti9N/9Izuo2kyd/vyTZijrDiGqVYq7\nbz9v7/Juyo4725Y2/0ZsUs7x8O4ydX5Thu7FOv4XR6i98/SjZ3RLA73N0DU6PfYQ/6dv52fyBF7V\nSYEBCUGQg5B15p0eBVt66DEWescRZBuYskMQ5CC09szYOI+5SLhIehIGxkIMSMix4AwJeQBeC07P\no9s4yHGV7DdFHQx6TRlcvwPVpuyko6NrNXW0aFTLfBnbR/nnximV/eb37aD+ZZOpk3//j7tzf/69\n5tG8ydSZ2rk16zbn5r4Ea9DAnCkIbbfdN8C+CpuUk772fXtMGbzv1R5zVW9qjrFovXOcvK/rlZIF\nADAeCTEdXPpYeYBkDtV2jwsGJARBDoKLpK6WbtaOEMpF55kkxLSNQwhyHzBlhyDIQRBCo+Qtoa2n\nH2Vx8v5lLwl5ZeAMCUGQQ6FUJJNvN4YwaYU8HhiQTpQnSM3f585y/GV4ddu7zcLvYd2tD1V4b1h3\n503piC2aNBT/+MY+yv7+D5tz/6JTeFe/aUwZ6q/f2EGdDUpH2in4d6UsX37CbUHYFpbct6yTa9vz\nuLWxbnB3uWjjKb2jD+CV142QpwNTdgiCIMgowICEIAiCjAJM2Y2AI7IH40iG7F67/pBkiN+IwTO4\naZ/aJuV8KTubxSLK45Rq03QAwO4al1LxoXFKZb/6o+40v2iE3dXv/tgOytt36w2Vd+oy3WbqTGvK\nYHT31I5T6r6fg743gww2jT875xv0C7u9Iztb8GktZWaMFnxiNQ5j+XAOwezc6YABCUGQI1CyKPIv\n6+26WnKehNHVy14S8mrAlB2CIIdijLbRaI2U2XoxLII8HAxICIIcilb1cLCWHqtvBLkHmLI7CZ4s\nO3/P9Pqjq713mgP5fYB8NRKr8HaU0NYciFTdp520TfbYXVf74d83yzzpL5sqkXIU3vV3f7TekHfX\ndlAVzeG67mpRtnQEtnTk2GzbqzUbr3pPvcjHoHK20U/Pd/KDq0RetK7L4sbzwLCL3xgY5UUhu8GA\nhCDIfrSuvb0nAIDzxDuOIMeCKTsEQfZT5r65EQClwrWzQ5CHgDOkl2NPSmFkIto9nfG8o3tMGcgw\nleT20PMNemXNQy8G18ObVE0CjWad5Ta7bcwU2HedwwL5xZ+sN2Sr8Jbf/6F9VC4a1wZddPdfLa3C\nu/sqWZG3MZ7OeH4RdsdOZbafPS7dB5uy7/ov1tpTPRJiHoTzA67wGcFM3SmDAQlBzpeqXNblEgAI\nZWF4yXi0bU9CmdGqNxiEM+/OCHI/MGWHIGdKVdytoxEAGK2K/ItS5badw/CyN7IjeiHI/cCAhCBn\nSl315dpVcbdtZ8ajMOwWwHKeRNH1tp0R5H5gym5sPEfp6EHuPgecvvl3b2HpwE6vvnLRZvtX20TV\no/CmWfNDnt52+SX2u6aHAvnbP+tOY0tHH/5BM7LobsG6bLrHaqf9q2nbv4J2O7Ta0pFP4b2nhuRy\njw/D7je/w7uiyFsosqxblR9/SU8P1o1eCzhDQpBzhFJx4CCCPBsYkBDkTBHBpDcSRBcvciUIsgZT\nds/LM3VIezwOU3uTvWLlQ228d/kvALjW3V4vhuYHPsm6eju9bXTJ9He/153nfze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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf; hold on;\n", "imagesc(t,t,permute(R, [2 1 3]));\n", "for j=1:k\n", " I = find(y==j);\n", " plot(x(1,I), x(2,I), '.', 'color', col(:,j)*.8, 'MarkerSize', 20);\n", "end\n", "axis equal; axis off;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Check the influence of the number of layers" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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WP3naevXCzjW8tHQN5m5YoXzBV2Gem5nr96xy4BXc3ICbj9RFae2FDfPkXKfg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\nkk5xKSSx2sl1iukaxl+nC37zgaAGzuJcxz7EK+JUCUD05aequ84ecZ7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YtgVWkCwWi8Wy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\nFmMwXzdQyDDI8GXA7fQyb6/mf/y9dGEDA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exo2()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%% Insert your code here." ] } ], "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 }