{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "An introduction to the General Linear Model, t and F tests" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "This notebook comprises two sections. The first section is an introduction to linear regression by Ariel, the second takes an example from fmri data and explain t and F statistics.\n", "\n", "It builds upon the following chapter : http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/pdfs/Ch8.pdf in the book Human Brain Function (2nd edition) and upon the review in Neuroimage (Poline and Brett, 2012).\n", "\n", "In this notebook, in a first part we will explain the General Linear Model in a simple case, assuming first that we are analyzing only one region of interest or one voxel.\n", "\n", "In a second part, we will take an example (cf the \"principle of stat\" notebook) and run an analysis at each and every voxel." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Regression - introduction (by Ariel Rokem)\n", "\n", "This section is based in part on chapter 3 of \"The elements of statistical learning\" by Hastie, Tibshirani and Friedman (get full pdf [here](http://www-stat.stanford.edu/~tibs/ElemStatLearn/)). \n", "\n", "## Why model? \n", "\n", "Models are mathematical constructs used to explain measured data. In cognitive neuroscience, models are usually used to quantitatively describe specific parts of the nervous system (e.g. neurons, voxels, etc.). Typically, we seek to understand changes in the level of a signal measured from the unit (e.g. spike rate, or BOLD response), as a function of the inputs into the system (e.g. stimulus presented, cognitive state of the participant, etc.). Accurate and precise mathematical models derived from the data are useful in the following ways: \n", "\n", "- **They allow you to explain the data you have**: summary statistics of the data, such as the mean of the responses of a voxel, or the variance of this variable, are often not that informative (especially if normalized...). A model can give you a good explanation of the data you have observed, in terms of background knowledge, or theory.\n", "\n", "- **They allow you to predict data you haven't collected**: In many cases, assuming that the parameters don't change with changes in the independent variables, models allow us to interpolate and predict what the dependent variables would have been like in other values of the independent variables. Even extrapolate to conditions that have not measured. For example, because measuring in these conditions is difficult for practical reasons. \n", "\n", "- **They allow you to specify your confidence in a specific theory**: By performing some form of statistical testing, you can specify your confidence level in the veracity of statements about responses to a particular condition, or differential responses in different conditions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Definition of a linear model:\n", "\n", "Assume that we make a measurement $\\bf{y}$. Here *bold-face* indicates that we are talking about a measurment *vector*. Say, of length $N$. This measurement is a response in our unit-of-interest to some inputs: $(\\bf{x}_1, \\bf{x}_2, ... \\bf{x}_p)$. Each one of the $\\bf{x}_i$ vectors also has $N$ elements. We will make this more concrete later on, but for now, you can think of the $\\bf{X}$ as representing different input streams. For example, different locations on the screen.\n", "\n", "A linear model assumes that the expected value of $\\bf{y}$ given a specific input $\\bf{X}$ can be expressed as a linear sum of the $\\bf{x}_i$. That is: $E(\\bf{Y}|\\bf{X})$ is linear in the inputs. \n", "\n", "Let's break that down a bit. All this means is that in the noise-less case $\\bf{y}$ is a function of the inputs, $f(x)$, such that there exist $\\beta_i$ which satisfy: \n", "\n", "$f(x) = \\beta_0 + \\beta_1 \\bf{x}_1 + \\beta_2 x_2 + ... + \\beta_p x_p$ \n", "\n", "You will notice that bivariate linear regression, which you are probably familiar with is simply a subset of this, with N=1" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def linear_function(x,a,b):\n", " \"\"\" \n", " A linear function\n", " \n", " Parameters\n", " ----------\n", " x : ndarray\n", " Input variable\n", " \n", " a : float\n", " offset parameter\n", " \n", " b : float \n", " slope parameter\n", " \"\"\"\n", " return a + b * x \n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "N = 100\n", "x = np.linspace(-pi, pi, N)\n", "\n", "a = np.random.randn() * 10\n", "b = np.random.randn() * 10\n", "y = linear_function(x, a, b)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x, y, '.')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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p7Oxs1dfXmxkWEHdoOiMcUxPCsmXL9I9//EMffPCBsrKyVFVVJUkKBALas2ePAoGA6urq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\n", "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "t = np.linspace(-pi, pi, N)\n", "x = np.sin(t)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x)\n", "\n", "y = linear_function(x, a, b)\n", "fig, ax = plt.subplots(1)\n", "ax.plot(y, '.')\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x, y, '.')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi-linear regression: \n", "\n", "Now, let's generalize this to $p$ inputs, where we choose $p=10$\n", "\n", "For example, let's consider an output which is a linear combination of $p$ sine waves. \n", "\n", "To account for $\\beta_0$, we make sure that the first column is all 1's:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "p = 10 # Number of inputs\n", "\n", "# Preallocate a matrix (make it a matrix of ones to account for beta_0):\n", "X = np.ones((N, p)) \n", "for ii in range(1, p):\n", " X[:, ii] = np.sin((ii+1)*t)\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1) \n", "ax.plot(t,X)\n", "ax.set_ylim([-1.1, 1.1])\n", "ax.set_xlim([-pi, pi])\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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8+yw8OzLC1UVFGI1LcLuPIpLeFeP0O5kKunEouTS5XAy5h9jUsYnKvEq8Xi82\nm42ampqke6xWK0aDAenvjxMBgMXCVPMAYX8Y/Xw9AIODkJOj/hRF4ReX/YJHHb+kVPHSsmdmNm8b\njWslTucuFpdeQL+zP+W6vIkqPIUeGBtT3UL33AOPPw4iKW6hKNauXUtTU1PSlgfdpWuZ2/EqBOJ1\nWrVKVar7fH72Tk6S4etPCkrqM/WU5pQyODkYIwKAuo0bMe/ciXP7KFklWeiqdTO2M6DrQBmpwtea\n+n46OzuprZ2XZNEdPAirV2tpbGzE4/GoAbSCesrKwLGzFebPp9Zcy4BrEFau/Ke4h8IHD9CWX017\n+ybmXHoWhu4wJZ1zMMwbobVdoae4mPDgIBmaLPLy1jM29gY89hgFF+XjPDhFwBF/B5kaDReZzbwc\nsQq+9PqXuGbRNaytSIgXZWerMaHf/z5+LGoNRBCsmYPV5qLUFHe/1eTX0jcxwCWXqP9vqN7AhuoN\n+CpejRFBYnwgitra2hgRuN3HMJmWpe2HjLY+MnwavAsjmnpk5p7cO0nOqhwgWc4Bas219Dv7Y3EC\niZjN6SyCqio15PAXh4NLCgpSnh+zCGw2iIyDWr0em9lM18GDaesMyRbB5OQuis3r4nKeADVO8AYS\nDsL999N72SeTrAFQObi6GmyHh5KJwGoFux3n9glyNxShdHWqGmMEU1NTtLa2smjRIvLW59Ha00p9\nQT25ubkUFRWpY8Nc+zfFCd47RGC3Y8eKXg9lZWEm9X1oRtQ9dFasgOYW4e3xcS4tLCQz04xWm4/P\n15W2qHZHO3XmOq60WHh9bIxvbfkWV86/EqffSUtLC/X19WgT1eQIzmpoICSizvBRWCz4dveSf248\nPtDeHvPUAFBkKOLuC+4mxzTMsTfT79MTDAfpmeihxlyDSJjJyT2UFZ5NSEK4p9xJ1xocObjMo4R+\n8whcdplqEUxOgss1IxEYjUYWLFjAvoRJst+ZS3kZsGlT7FhJibp9x8/2jvBBi4XOsRMp2SlWoxW7\ny5ZEBBfPn8+JkhIcv3xrRrdQFB5PC1lTdbgOpAZEOzo6mDt3ZRIRNDXBqlWZrFy5ks2bN9PmaGNu\nwVwqKsC9vwXmzaPEVKJmfiX6tt4thELoWzo4pl3CyMheijYUYuxSMLWb0FY6aG2F7VNTGHNysNvt\nqlbpeB3uv5+Mz30S8/lmRl9IdgVF3UNvdb7Fayde47vnfTf1uddfD088EQvSTyeC8YpC1voKk5Ie\nfCMlBLPXUcrsAAAgAElEQVTtLFoUL+b7F3yfPZk/4C+bfOzbt4+zzjor5VHJrqEWDIb56fvi+edx\nnVeJyx1xw0SCxZP7VCJIlPMocrNzCUmIcHUYJUPBc9yDyMksAuE1h4OLpxHB5OQkHR0dLJ03T7UM\nE8bpVHk5jra29HWGmHIBqkWQm7tGlXN38qaY2dnlZGVZcW39FQQC9FpPSyECUN1Dw0eH1DheFDod\nGI243uoh78x8NS70xBOx083NzdTU1KDX6zEuMdKd2U2NVu2nxYsXc/To0bic/5V47xCBzcbh4RLO\nOAP8/j7EkodiV7Ngysqgu184My+PvMgEbjQunTFOEA0MnZWXxytDfTx19Cn+6+z/wu6yp3ULRXFW\nbS3jBkPyQYuFqaMDKfGB+mmZfTc13ERGYQ87t6Z/id3j3ZSYStBpdXi9bWi1ZrKzrWmFMaN/CCqq\nmHjzPvjUp9SDhYUwMkJbWxv10x8ewZlnnsm2bdti/w8MQPmVq5KEEdS59NlGPx+2WGgbbUsy4wFK\nTCU4BiK5sJHdZnO0WrrXrSP46qZ3RAQG/by0RNDZ2cmiRRuSgv0HD6pZr+eccw7bt2+PDdqKCggd\nb4V58+L99M/IHOroYDI3G7t9EaWlPiZNbWgCUHA0TKBglLY2Ydu4k7o5c+jq6lK1ysEXkaxMWL+e\nwssLk1wiABsLC3ljbIzPvf4l7rv4PnKzUwOLLF2qxguiSQDTiGCgWM9SlzHplq4jVjS5dhK4gfLc\ncr7ywcvoH/CzYMF5mEymlEdFiUBE8Hha0OtnIILGRoIbVsXHntkMoRCe3YOYVpmS5DwKRVGwGq0M\neYZiVsHAgDpvTlf6q6uhuTOMOTOTal2y1blv3z6WLVtG5sQEFBWR2Mi8+fPR9qda10AsO2duwVxE\nQkxO7iUnZ/WMk67ZfCGOHT+DT32Knl6FqqrUMpcsAeeJaa4hgNJSfNs7yT0jF264QbXoIhbQoUOH\naGhQk1QUjYKt2kZpX2mkvCUcOXIk7XzwTvDeIQK7nV1dVtatUyeS7KIF6q6MbjcWC7gnFC7Piaey\nnYwIoqbp+rw8tk2M8+V1X6GuoA7XlIvDzYdnJIKVpaVMN8qkqIhwly0WH4D0RJChyeC0NWaONwcI\np3FZTddIojnMVpM1VRh7e8k2VDG2IgxrI+6CoiIYHaW9vT2tRQCpAeP+fii/6Tx48UU14BzB8lVh\nOg9mMi8zgKIoFOiTR6PVZMXXdkzNCkkYbAWrz8fs2Js2GyIRXm8LOdZFKUQQCoXo6elh7ty1iEwx\nNaUGjJuaYNkyqKmpoaenR7UIClWLIKtTdQ1ZTVZsLts/hwgOHaKt3IB/sJ7aWj2Trj2E5tZS2evC\noQxhzBOsEznU19TQ1dWFwbCIsHsC3+c/DIqCabkJ95Fkq68oM5MyjR+3vp4PLPxA+ucqSnwyGR9X\nnecN8Wy3tnyhPplfGLeZCWpc+IPJu7p+Yd3nUHK3kWk+P+2jCgoKyMjIYHCwjXDYT1ZWSfo6jYyQ\nVZEw9hQFqaomfLwT0zJTkpwnIirn0fUE6dxCEHcNzeQWWrt2LYyMqOMhAQtWrqRgbIxgmmyNUe9o\nTM49nhaysorJzCyMy9T0vmAVY4bjcPPN9PaS1iJYvBimeodSiECKSwi29pJzWo7q4/Z6Y9lf0UBx\nFH15fRQ1qe1YsmQJR48enbFOp8J7hwhsNt48VhLpu1YMxgVqJw8NESCMFEyxNhh/+SbT0hlTSNvH\n1MBQ68B2wgEXFy69FY2iwWK00NTeNCMRLMjNpc3tTtpBdSqYhzY8jq4urp20t6uB4um47N8W4nIW\n88zRZ1LORSc3UH2U0fUDVmOaF9/bS1afF/fKgvhEnGARnIwItm/fjogwNaWGGIoXW2DNGjXvOwLT\nIi/69jz6xzuYWzCX6TvEWo1WwgluoSjmaOahzbAROoXUeTyt5M9rwHXQldSXAwMDFBYWqqZxhMjH\nx9W1hHV1UFlZSXd/N3aXnaq8KiorIdfWkmwRzJmjugUGB2euwN8bhw6xrzBEbrCc6uoKXK6DhEsb\nqDa6sbvt5NVMsdBRyJyIRaB4POQ0B3Cfpy4mMiw04G31Eg7EFQQRYWLgVRbM//eU/k/C9dfD00/D\ntm2wejWJkf9DuW7K7MkpkHabhhyNhSH3UNLxrIwsLMZRWsdDM26HXFdXR3Pz2xgM82eu0+go2WXJ\nrr1Qfhk5JWNkGDKS5DwRUTnPPy+fia0THDscTksExcXgcyucnZW6RiUWH0hDBPNOP51yv5+dDkfK\nfVFrQFEUnM5d5OTEx1467du0uR/3XC3k5MxIBEuWgDIyzTUEBLKKMJW4yTBmRLZhvT4W54kGigF8\nQR8jmhEMb6seiMWLF89aBAQCyPg4u04UsXw5cdPUaoWhIbZOTGAsDhIYiafgncoiqDPX8dU3vsoZ\nuSZ2uVS/vdVo5Xjv8RmJwOz1Ys/IoD/BxHR26tCbJpMGRjqLAGDeqizsipGfPv3TlG8ZRFcQQtxH\nCRFNafqL7+0la2cLvsJ4zjVFRUzZbAwODqakjkZRXl6OwWCgo6ODwUG1+zIyiGuV0TbVjuE/bqRt\ndAbtzWgls6c3hQjCg3qyxckRtzvlnihEwni97eSVLybDlIGvKx687uzsjAXpo++vqUlVcjMyoKqq\nio6xDqrzq9FqtFRZvOS4bTBnTtxyUpR33SqQQ4fYZp4gL5hLaame7OxqfNnzKNGNMeYbY6p8gmJ7\nXowIeP11dFKKV6O+1wxDBtmV2Xjb4vGjF1peINd1jGPhvJPvU19TowZFn3pKJYIE7MgaIq9/NGkh\n1eAgmLPSTyaZ4RGmAmY2d21O+6i6ujqOH987c3wAYHQUfcVK/P4BQiHV4vNrS8gtUdPlEuU8EVE5\nzyzIxDDfwKG3A2mJYDIURIp9VDvzU86djAiya2upVBSeOZw6JyRaKZOTCWNvhkk3609bCOlChEIu\nenpI6xqqrweTZxhfbrJF4PObyS1LsIRvuCEW52lqaoq5hqJyHmgJEHQGWbhwIa2trRTpi97HMYLh\nYcLmQgosGWRlRXzMhvmqemC3s8vppKRUGEjw2xgMC/D5OgmHUz9s0u5oZ8w7hsPr4MaqBrZOTABQ\nbCymb7yPefPmpa2GMjiItqoqaWHNxFEtmcpE7H+RmYmguhpGJJuGwZU81vRY0rmophQO+3G7j2Ay\nqSmFamA24cVPTEAwiE6K8YX745lRhYU4WlupqqpKG+iOIupe6e9XM18BuPpqeOstormtTdpx8gpg\nV/sM2pvJiqFvKIUIXB1asoNedp0kR9bv7yEzs4CMDBOm5aYk91BHR0eMCKIWXdQtBOqHjGxTtthE\nUscJ+rNqQKtNHrTvMhGEDh6gpSSHLMawWHzk5q5h0lOBMdSDWWdmqKQLpdcQJ4IXX0RfvhqfL54x\nYlxixH1YJVAR4VtbvsU9p3+ckAjNHs8MT47g+uth9241PTEBh7xdauQ/IZ12cDCNTEUwOdlGTc46\n7t52d9rH1NXV0d5+bOb4QDgM4+MohcUYDPNxu48C4PFaMJrUYPjJLIJonYwNRpqPqWmY0/Hm+Djm\n8hDD/cmLFQcHB/F4PNTW1qYlAoqKMIqwLU0iQWKdTumWdblQGrej09fi9XbMaBFkZkJZ5hDtzmQi\ncDty0OfF5wuWLIG8PGwvvEAwGKQ8MijbHe3UF9ZjWmXCucOJwWCgoqICz7DnfWwR2Gz48kuwWtV/\n1ayFeTGLYM/kJHUVmiQi0Giy0elq8Xiak4qa9E8yOTXJr5t+zRfO+AJnm81sixCBIWwgrywPvV6f\nvh4DA+QtWJBEBGOHtWR44ubm8LAqBOm+2JmVBcW5YdaP38DdW+9O+oJUVCtxuQ5iMMwjI0MN8qVo\nJX19YDCQcenVaLVmpqYijS4qYqKjY0a3UBTl5eX09fUlE0FuLlx4IfzpT4gI2ycmaFgCh/tn0N6M\nVvIHx1KIwH3My5QxhyMn2dclMdBoWmHCdTBOBGrqqOouiVoE0UAxgF6vJ7s0m3K9WvFydwutopJ2\nsbGYYfewGn9ZvFhNOXk3MDmJYrcznDOfYLCdgoIhcnLWMG4vI2u0nVyDBXOVnd72jDgR/PnP6JZt\nxOuNbz5lXBonghdbX0QQ/m3BVVxUUMAbJ1t8AnDttep+DAlB3qica+rnJqUoDg5CWV6qphsMBpmY\naCEnXE/LSAt7+vekPKauro6Ojm517KXDxIRKPJmZSRb55HAB2ahkNGOMIEHOjYuMtPVlpLUI/uJw\nUD9Hia0ujuLIkSMsW7ZMtcxHRlJcMigKzpwc3AcP4pn2xbeolRIKefF4mjGZlqfUKYbXXoO1a9Eb\n5zIx0YXDoWbapYNFhjhsi9dDRJjsNZKdOe193nADh375SxoaGuKZh5F1DfnrVVcZqO4hW7stLud/\nBd4bRGC34zZZKSmBUMjL1JQNnW5OzCLY7XSypDozxS2cLk7Q7minIreCXf27uHnZzczT6/GEQvT6\nfOCCwuqTZLwMDFCyalUsBTPkCeG1Z8GUDyKfVJzJGoiiZo4wfrQAs97My20vA2rqaPd4N7Xm2ohG\nEs8XT3EN9faqz7riCvT6WrzeyCAvLMTb03NKIqioqKC/vz+ZCCDmHjrh85Gt0VBTlkGPa2aLwDrk\nTiICCQmeFg8UFdA2Q3YGJFhzRIhgBovAaFyCx3OMgwclRgQA+go9eSF11at5qJXDgfkEAuriKGOW\nkTHvmBovOdXk+ffCkSM4akrIcM/D5TpKbm4HOaY1jLXmoHgmyAnmsqh6gtZWqK6upruzEykqQl+z\nLv7uANNSNWActQa+cfY31D2rcnLYl2bfoSRYrZCXpy4oiyCaIq3U1cWIQEQlguqiVE3XZrNRUDCF\n3Z7BF9d9kXu23ZPymLq6Orq7R2Z2DY2Oqn2PSuQu12HC/jDOgXwynQNJcp7ShAQ5D1QacfsVpu0e\nAahEsLo+K4UI+vv7qYjeMDycahEAUxYLC3p6YopfFFGLwOU6gNG4iIwMfbxO0y2CF1+EK65Ap6ul\ns3OIsrKIe3U6/H6yw172d8RdWP4eP1NKIRnO5PgM111H01tvsWzp0qQ61RfUk3dWHuNb1dXWS5Ys\nobW5NS7nfwXeG0RgszGuUy0Cr7cNna4WRdGC1YprYICgCAsrtEkWAYDR2JASJ2h3tDMVmuL2027H\nkKluEHdWXh5bJybwO/wYi5PT7ZIwMED5aaepu5AC3jYv+noDSlGRqoVwaiKYuzSDE+3CZ1d+lp/s\n+gkAPRM9WE1WdFodHs8xTKa4QKSksB08qG7LuHYtOl1dXKssKiI4NPSOiCDFIgB187rdu9lus7Eu\nN5diq2APtqXX3gzFlDuCSHV17Jiv00dWcRbZxRamRkYYC6RfOHcyIki0CLTaPDIzi+jsDJPYJKVQ\nQedWA/Oa9lbsefNiCkCJqUSdTAoKIE1Q8B+Cri4GLDqC9jrGxg6Qm9tFxlAdmUXZKAsWUDGkYYHV\nSX8/aLVGcrRa7Oedh05Xg9/fjYiqnRqXGHEddrGlewvegJer5qtbNJyWk8Ped/LN6dxcVTYiiGne\n9fWqUKJuw6LVQpW5JEXT7e3tpbJSi80GH1v5MRp7Gzk2fCzpmtraOfT2etDrZ5CxBCIwmdSx5z7i\nhtpqlN7uJDmfjkQ578kwUqXxMj0ePej34wyFOK0uMy0RRN0qaV1DgKayksqBgSQLK5o6Wl9Qj8dz\nDKMxPvaiFkEsRhMKqVsYXHEFen0dnZ2utG4hAIaHmcqzcORovBHOHU6yV1ajTNdYa2po0ulYlpCa\nHrUIclbnxJIqoimkMTn/K/DeIAK7nZEM1SJInEiwWhkfGGB1Tg7l5UoaIkgNGB+wHWBwcpA7Vt8R\nO7Y+QgTOASfa/Bn86yIwMICloYHByIv0HPeoq4ktFlUL4dREUDdfw3CuiUvDl3Js+BhHho4krbT0\n+brJzo5PsCnm6ebNqvM0IwO9vjbuZy4sRONwzLiGIIry8vL0FoFeD2ecwfbWVtbl5WGyjBIOQ6E+\n1UIyOiZxZcNkVjwI6T7qVndeLShgTSDAnhkmL6+3Bb1edS3o5ugIuUKxjcYSLQKAzMwVuN1KkpvN\nZ/ARHo2YxS0tuErnEfVExfzMZvO7ZxGMjWHL9DPRWUdu7ggmUxGeQwGMDUbCixZROhjAonFRVaUq\n5nNE6GpoICPDgFZbgN+vCq2+Xs/U4BQPbX2IO1cn7BxrNNLh9eI+1QfsRdS4SGTSiq2UTbAIBgfV\nMEK6BITe3l6qqwsRgbDfwGfWfIbvNX4v6ZrCwiAul4Jvpm/VT7MI3O7DOPc60a2pAYeDEwNH02+d\nTbKcnxjPoirsJjiZnFCx3+VipcnEnDlK0g65oBJBWXTF/wxEYJg3D7PdzqYE2Rj1qrGLQn0hPl83\nOl187BmzjGQoGUxORWR51y7V+qqpQa+vpbc3MDMRDA2hsVpIjE1P7JhAt74m7RYohzIyaIgokxBP\ncc8szESTqSFgDyRnDv2VAeP3BhHYbAxK1CJojRNBcTF+m401ubmUlZFCBCZTKhG80v4Ka8vXUmyM\nB3HW5+ezdWKCoY4hgtkzbBU9NgZ6PXmlpQQCAVwuF54WD4YFhr+KCGprYSjHhG+fj0+e9kl+uuun\nSfuc+HxdqtsrghTz9PDh2KIhvT7ZIsh2uf52iwDgggto9PlYl5tLOL8doy81dRSAzk76i7KT0lrd\nR90YFxmhoIAVU1PsdDpT70NNHY2+PyWSQ+866MLr9eJwOOKDGfD51lJQ4Ipphv6gH2+GF3d/JCup\ntZVA7fw4EURzrM3md88iGBujV+PC2z+XqipBp5uDq8mFaZkJu9VKrVuDyzvMvHnQum2IOeEwXUbV\n6tTr62JErmgVMudmcmLXCW5adlOs+CyNhsVGI02ncg+5XKp/PrKxWkymEiyCGBGkSUnu6+ujqqqS\nkhJ1nrpj9R08f/x5Rjzxycnvb6e8XE/HTB/WSCCCrKxSRMJMHO0kZ3U+lJdjP74vZXFiFIlyfvy4\nwtziAJ7jyUHy/ZOTrMzJSdqBNIp3YhGY5s/H6vNxbHgYX2Q1dnRxqaIoESKYk1KvWF9F3EIAOl0d\nvb2atBlDAAwPk1VejM2mGvAA7sNujKeXwdRU0rodgI7JSeZG9o3yB/3YXDaq81VS0s/X42n1MH/+\nfLq6urDoLX/1WoL3DBH0BUpiFkEsa8FqJWNoiNU5OWmJIDu7mmDQSSCgagDegJejQ0e5bcVtSdct\nN5no9nrpPd6LW5kh9TGy2ZyiKJSVlalZCsf/NiIYCOtw7nLyiVWf4OljT3N46DD1BfWISIpWkped\nx1RoCm/Aq9r2djvR7UJ1uniMwGcykRcIUJ3grkmHkxHB+AUX0JmdzXKTCY+uDa1zhoZ0djJSbEoi\nKPdRN8bFRigsZKHPx640RBAKuQkEhpPaF3UPdXd3U1VVRUaCw9XjWY7ZHN96oWOsA0uWhb6ePnWi\nDwTIqStOtgjcEYtgYiK+9cI/EDI2RifjFCollJcb0emqcR9yY2ww0pqdTV0wC7vbzvz50PpSG3Pm\nzqUros6q7y8+qXaXdPOhjA+lrCJedSr3kIiqqFx0EUR2gD2lReBKtQgqKiooKYmkmOrNXLXgKn5z\n8DexazyeFqqrLbGtJlKQQASKomAyLcU53IRplQmqq5loOzSjRZAo583NML9e8DRPI4KIRVBertYx\nmKCzDQwMnNo1VFHBXKORiqGhWIpzsjXelWSNwzTX7Isvqt9YAHS6OQwM5FBRMYOMDQ2hWIspKIh/\nP8Hb5sUw30iskyOYnJxENBpympthfJyOsQ6q8qrQalTvhGGeAU+Lh6ysLGpqasicynz/uoY6PVas\n1mTXUNhiIWd0lNU5ORQWgtutLtSLQlGUyAZ0qlXwx2N/RKNoOK82eXdFraKwwuslS4wMe4fT1yFh\n19GysjIGBgb+ZiLoGdPiPubGarJy1fyr2NK1hbkFcwkGR9FostBq4xOBoigUG4vVF/+Xv6ibjUXS\nW1XXkDqRdExMUKQoaNNGruKwWq2MjIzS3y9Je+cB7KqqYtWJE2T29zOuaSc0PIN10dnJRFlhkjB6\njnowLDZAQQE1Hg87nc6U/Hevtw29vg5FidcxmkI63S0E4HYvIC8vHnhud7RTk1tDb2+vOpDKy6mo\nVFKJQKtVv2byTnzr/4/wDPXj0uvIzQ5QUpKFTlcdswiOZ2VRHczA7rKrFsHeCeaccYaaOUTUolMn\n1UAowJtZb7LBtyHlGafl5LDvZG2ZnFT3Y7jkkti+UbH99S0WoqsHEy2C6RNJX18flZVxiwDgE6s+\nwcP7H469R4+nhdraOScngoQVvwbdEvyaZkzLTFBVRaDjxIwWQaKc9/ZC3ZKMFCI44HKxwmRSs++K\nkxW/mEUgMiMRUFFBtVZLid3OwYiFFV1cCqQoYZDQVx0d6hhfo6aWZmToGR6upaRkhLQYUheTRda8\nEvKECIwEyK7Mju1CGsXAwAClpaUoZ54JmzcnfRsBwDBfXXAIasBe49W8T4nAZqPVWYLVKvHUUaDN\nYCDX5cKi0aAoKf0LRH2V6hLuh/c9jCCU5ZRNfwI1Q0PkltXh9DvT7/cd/SANKhH09/errqH5cSJw\nONR4UjoZjKKoCAIhhaEW1S/+2bWfpX2snTn5c9IKIiSYpy+8oO4UGnFMZmZaCYU8BINO2vr7VTfO\nKXLOtVotFss8MjOF6VvKbJ+c5Ey/HzZtYijYjrd/ZovAVxnXlCQkeFo9GBeqFkHOxASmjAzavckb\n7KXboyaaQpq4mCyKiYkK8vK6CYXUctod7SywLqCnp0fVgM1mKipIcg3FtLd3yT3kHeonqC8lM7Mf\nq1XIDFcSGA6gr9NzNCuLMl8Yu9vOvHI3LfZ85lx8cQIRxIn8uePPEZ4bRnciNZC6ymQ6uUXgcKgT\n8LnnwrZtuCZHmfBNqHKuKLGvlUWJoNBQmCLnUYsgumU+wBkVZ5CpyYwtMPN4Wpg7d+HMROBwxCwC\nAO3YPDIautQPFFVXo+3tn9EigLicDw9D+fJs3Mfi1vloIIAjEKAuktqd6B4KBoOMjIxgtVpVbVCr\nVWNe01FeTvHUFPqBgTgRRILqIkGmpgbJzk5OVYrJ1Isvqhs8Jmx7PTJSg8UyzUcVxbC6z1BUR/S2\ne9HV6lAyFJI6GXUNRFlZmfqpwNdfT0mx1c/Tqxl5oBKGW3mfxgjsdo6NWikoGAYyYp/H2+Px4M7P\nj2nj6dxDBsN8vN522kbbODZyjMrcSjRKarcUjI4SLCmlyFCUsvweSLEIeo/1os3Tos3VqrP78HDM\nGjjZjgCKArV1MBDMJuAIsKJ0BWEJc3zkeEqgOIrYbp+vv64KeGQGVxQlNpm0tbXhMRjiduhJUFjY\nQGFhasRvu9PJupISeP11hv39TI1URLNik9HVRbiqKqaVeDu8ZFmzyDBlxDJ21ubmsmva5JUU6I/A\nsNCAr9vHiZYTsYyhKIaHtVgsfnw+9YtQ/ZP9zCuZx+joKIHhYcjPTyaCRE23oOBdCRiHHKO4M0oJ\nh09QVORBBooxLDbgI0yrTkehJ4DdZafatovezFrmLFwYIwI160udVH++5+dcctklKXsOASw2Guny\n+XDNFDCOEkFBASxYwMDWlynLKYvLecSXEiUCjaJJkfN0FoGiKHxi1Sd4aN9DgBronz9/9TtyDQHQ\nU4lSHRmQ1dXkDU1QkZsmJzQCNXZhZ2QEKtfokiyCqDUQ/TZx5DMHgJr6WlRUpC6knCF1FIDSUkwe\nD+Hu7hgR9Dv7qcitwO/vJyurGI0m+YuAMZnatInY3t0R2O0lFBXNsF5lSN1nKGoReNu8GOZGsoKm\nuYYGBwcpLS1V1/Js2kT/ZD8VOfF+SrQISkpKCDlD70OLwO9HXC7sgQIyM48nTSR7nE4CFovqNyc9\nEWRnV+D39/Grg7/i4rqLKTSkXyegdTgYz82deS+PaUTQc7xHdQtBzCI4lVsoitpahVFrHt52L1Oh\nKRQUnjr61EktAnvnEdXsnRadigaM29raCOblxdJYT4bc3IXk5CRP0iERdjmdnH766fDGGzi8Dgr1\nhQyl4UQ6O8morY/1k+eoR40PAFGn6Om5uSkB43REoMnUYFhooO1QW4pFYLeDxRLE71dneofXgcVo\noaysjLHOzhgR9PYm9NO7bBFoxidwhCy43UcpLBwn2FqIaZmJox4PeYWF6FweRr2jmA+/wUi4QF1L\n0N2NiMRI/OjQUVpHW7ny7CsJ+8JJn2uEeMD44EwB4ygRAFxwAY4dbybLeX4+jI/HiACSSTMYDDI0\nNERpaWkSEQDctOwmXm1/FZuzi0DAwYIFp79jIgh2mAnnqQIUqCyjYiyUfhfVCKwmK13DdvR6yF+k\nx9/rJ+xXffAHJidZkbCtdMKnkN9RfACArCzC+flIayuHXC7CIjE5P6kSNmlT93JK+Hzn5CRMTWWh\n0zWn3APEXEMWi/qnp9WDfm7ESpnmuogRQUMDjI3hGOlNen/6Oj2+Lh/hQJjS0lJ8I773oUUwNESo\nwEJxiSZlH/Tdk5NoI6uLYSYiqMTr6+E3B3/DhuoNKTtpRuEeGUEpLMQ8U2rWNCLo6+xLJoKREXp6\nVAE9FaKZQ952L2PeMcx6M290vsG463hK1gJEAlbH96lpo9Py1aIB4/b2djQWyzuyCPT6enS6ZMJo\n9XgozsqiqLYWcnNxOO0U5xREOTalLwy182L95D7qxrAo0heFheBwpCWCmfaxNy010dnRmWIRqEqV\nBr9fnekdXgcF+gKqqqqY6O6G/HxKS1XCCAZJzq9+lyyCTKcLu9fK6Og+zGYb/gP5mBpMHHK5KC8p\nQRkbJ1+Xz9T+VwmIFo3GSE5ODjabjczMYsJhH7858AtuXXErWdosdYVxGqtg1cniBA5HfCn7hRfi\nOLA9Wc4jRJDg3UwKgg4ODmKxWMjMzJyurJKvy+fqhVfzzKH70Ovrqa2to7e3l2AwTXbddCJoNhPS\nDdxIj18AACAASURBVCESYsKSR82EctIN9EpMJXSN2LFYQJOlQTdHF9t/KRoojiLRNfROMoaiUCoq\nkO5uzFotHT5fTKbSZQxBRLmwtatBiYQlxL29UF7uxe+fIYMq4hoqLo64htq86OclEEEC2w4MDKiu\nIY0Gzj8fR19b0vvT6DRklWXh6/JRUlKCy+Z6H1oECdtLJKaOBsJhDrlcmMrKTmoR6HSVON0nqM6v\nxpRlmpEIbDYbNWVlaLPM6Tt5cDCJCAZtgykWwfBw6sr2dKitBVuGHm+bN6aRXDbvMjpHdqS3CIxW\n7H3HVRN/GhEkuoayy8vfkUWg0VSi0SQHU4643SyNpDVy4YU4fGOU5KchAp8PRLAUxl1DsYwhiLmG\nVphMNLvdeCPuDHUf+9a0+9Rk12bTPdSdYhEMDYHVmp1CBJWVlbj7+sBsJitLnXvsdnWbiSH3kBrc\nfJfWEugmvfSOlQCd5Ocb8O4D4zI13bO2pATGx7HqLQz1NmOxKAwPE9+FVFHI1tXy9ok/cPOym4Hk\nrSYScdKFZWNjcYtg3TocQ90UZCQEgNJZBAlrCaLxAUiZowD4+MqP09jxJHr9fLKzs7FarWrAfjqm\nEYGvLYRWyWdqys5IkYEyp5w0k8tqtNI3Zo+NIcNCQyxOsH9ykhUJRJDoGnonawiiyKiqotDvZ2lm\nJgddrphM+f0zWONGK/bhziRrAIjsMRT+/8l7k2BJ7vu+85O15FJr1vaq3t4rgMbeAEWBQ4k0ZckQ\nKQUlK8YkJ+yY8cQcdJAc4ZibHY4QD56Db3PwYXSbCMWYlEOWRcsEQUoWZdoBSQBJdGPpRne/Rm9v\nq32vyqyqrJxDLpVZmfXea0qABeoXwQMfquvly/zn7/v7fn+brzvcZz+JNAQWo2vuB/xU4okE41tj\n1tfXae+3F+f8jPZTAQSDVLB09N3hkPOKQrxSOZERiGIF02jzf7z4v7kPPfzXHHNla4tZPBdeo7vE\nCI7bx1aiGFwgOOUMunbuHBxOJcZ7Y/ea/ukL/5T+cG/1YWw9tHIDAUZwkV7vDsfHxyS2t8/ECAyj\nzHTqT3K9NxzyrA0E41/4eYz5jI1SIggEnQ6oqq++OgAEzSZKNMpTiQTX7TK9yeSYSEQmHg8OYdLL\nOswhtzSgqVaD9fWkTxpyGIFWrVoODtw8gRyTUWIKba398UhDsxlxbUpjuM72tlVSOHx/SPLZJO8M\nhzy5vg6DAesTkeMXLlAsCTQaCyAA6BspnsnleKJgFUB4h8957VRG4ACBJNF6+jz5huc7VJVpo8Nk\n4t4yXy+Bkx8AAtIQwCtbr7CpmDSmVkTr3VbmsyUgGO+NXWm2aQ4ZKFHCtcbFNR31/EAwujmiP5ux\nr+tcSS66/v86jOCpVIqLmsZbnQaGaZCIJ+z+nRWFGqNaAAgs9i/5yn995pGG6vUzSkNgBWHjFnnJ\nP13V6SVYX1+nelBdnPMz2icfCKpVOlKwdPStfp9Pp9PuvCGw/PRy1VB12KA9gV+//POnAsHV3V0G\nkUyQEczn1tthP6z19XXqWt3dUUw+D90urbpxJiAolaAzjfqA4BfO/wLZmMaHvaATKI8EqnG7CSWE\nERwd7VEoFCxp6AyMQNPyjEb+tX1eIGj/7AvkR1ApGsH3ttu1gMCW0ObTOePbYxJXbFDMZq3mptmM\nZ5NJ3reBwFvttWxVscpmbDMgG9RqsLmZQ9OCjGDWaASAADx5go9DGup0GMoxMlKKrS0VUdhGEAVi\naozrgwEvZDKQTnPuWKP6/EXXKXiB4P12m1/aecb9ylXS0DOJBA80jX6YJOMFAqD1xDb5B54yaFVl\nfNShUlkUMnhzBF5G4EgZ3ry0IAj87No6f1G1noN3f7Frum6Vqdo6/qw3Yz6eI6d20PVHtMYtRinJ\nCiRWWDlVpj5eAEHySpLRzRHX7bMZ85wPZ0GN1fB/xhwBwOYmF2WZzeGQH7UPySt5TzNZCBAk1qgK\nI8yf/3nfzx89gt1dGdPUmc2W/qbh0PIZqZTlno5M5sM54oadiA6pGnKBYGeHlgL5+34flHjCShiX\ny2Wq1Wr4HKQT7JMPBMfH1KMVKpU5uv4ARbE2vrzV7/Mz6bS7EBrCGcHvXf895tEicdMaO52Xg0Bg\nmibHx8d8ZneXhpAK3uBm0zrgkgSAgkLEjKBn7ZKaaNSKuo6bZ5KGikXojPxAYM5HKNEYv/f+fwp8\nvnzjAdWCbHm7ACM4x9HRgVU6Z28pO806nRTdrn+OjBcIWtKcvClTHt0PZwTZLCkxhSAI1G/VEddF\na9EGWDqnLUU84wGCVbIQwKFxSHlW9v3MNB0gWEPXH2Haib2cnGNnZ8dlJkB45dDHwQjabTpKhFQ0\nyvq6TGy0iXJeYV/XESMR1kQRVJWd+x2qF8pOKskFgr7e5y+O73NFXUR/yWeT7vA5r8UjEZ5dlTBe\nBoLtIvkP7i/+u6oyqXV9U6q9jsSaM+SUJFu3dTme2JDnfOvuj5kYk3BG4PQQ2M56fNcql5TlbRcI\n9KRsBRIrrJws0554GMHTCYY3h5Ys5N0TjjVaSRStX+uThk6qGgLY3GQnGiXf7/Nu58gNDFcli1P3\nDxEQGKz7i0wePYKdHcE/78sxOz+AIFhAcGiiXFIWgc7amnXhNqi7OQIsX9RSIPff/WPUE09aTWWy\nLJNMJilIhcfKE3zygaBa5XheplDoEovliUQsZ/z+cMjzqZS7pQzCgeAb732DUuZpdH1/JSPo9/tE\no1F+plzm0ExwvAwEHlkIYHxrTEkqcXTsoR92uHcWRlAsQqMNc21Oo91wNUpJ3ub/e/ffBZbWlP/q\nfaqKEajTBmvcdr+vUipl3C1lp1mjIdJoXGdu67Vjw+ChrnPZrr127tNa/f2V0pCzZ/bBew+s0RJe\ns+UhLxDo+iNkObwf/0HjAeusM+ss/u5u1+qRymY30fV9xrMxESGCElfY3t4mPhi4CdL/YYyg3aYt\nCcSmc+u9b68jX5B5ZzjkBUfGUFW27jWpriWcKmMXCP7w5h9Syr4As0XTXDwXRxAFpvVgL8unVk0i\nXQaChGBJQw6dU1WMVscPBB5G4JWGIFweMmdV8ukrvL73uiWNLn9g6WxqdzWUS4orDbXGLWbpxMlA\nkCrTNz1AYJdNvt3t+xLFjjnyUEAaOika29pifT5n3mox1DukpRymOV95PoX/9t8okwyZzWTFZL4J\nwI7VFisqSyVoNFnIQmAFjoUC1GqMRiMmkwmqHQyMZ2MikSjKG2/6vlJ5wpKGwFIk0kL67x4jeDip\nkM83kCTrYZumyY3hkCuJhI8RZLNWv5Xzrtxq3OJocMRW7iU07dFKIDg+PqZSqZCKRiklyzxazhEs\nAcHogxHlbJlDL+oUi0RbZwOCdBo0TSB6IUHtsGZXLdwnk7zMhdwFXt973ff53H/9K0ZMMbtWNL5s\ng0GBQkE6EyOwmkwF0ukxDRs0PhiNuKQoiHazTGvcIp/boPzwrSAQ2NIQWC/uozuPrI5ir9mVQ88k\nk7xvN7jp+oH7/Jbt/v377JR2GH+4aEBz3qVoNAuY1Pr33We3s7ODNB6fzgg+BiBoygbmSGdtTcM8\nXEM+L3N9MLCCFIBIhHWpQHXaDkhDv/fO7/H3Lv4vgYhSOa+g3Qv2eawcNbEMBFqb/M5T8Jd/af3A\nZmgnMYItz8zn5YTxfD5hNmvz5Sv/K//u3X/nyhM+C8kPKBcVJGnbeve0FkYmfaI0lJNzTBmRtXtc\noskoYlnkwa0eLy0xAliUkD5OjoDNTUq6TrVa5VxsSiSeYTqtEY2m3B0gPvvBDyx5aMnpPnzoAMFF\ntynQNU/ViKrCcCwQvbjU4Gbf5KOjIyqVissWXB/1F3/h2ywnbUnMOjNm/RmVSgXZkP/uMYJ7ozK5\n3KHrSA4nE5RolHw87mMEguDPE/z++7/PP3r6H6EoC53yJCAAeD63HUTaECDYKG/4gMAolEhr9TA/\nHTBBsN4ZfSdFvVH3la/9k+f+Cd947xuLD9dqCIdHlNMVzE43FAh6vTS5nHAmRuCsqNze3mDf9p5e\nWQjsw7h+nvKtH1CtLlUmdBZgVE6WOTg8WCTNHbMZwY4k0Z3N6MxmdsNOOBDs7++ztb2F9uHC+TlA\nIAgCkrRNtfeB++xUVSVrmvTtcRpeIHBLSD8GachstWjKM/ROm0Khx/zDEsoFxWIEDhDoOmuFXaqD\nqisNOb0EPzr4Eb985X9H1/cxzQUbks/LoUDwYsoqSw2Yt3wU+/lduWo5EwBVJdb3A4G31PY0RjCZ\nHCGKZf7nZ77Cd/a+Q1JNhgOBB4zGdxdA4Lx7ZjZ7IiMQBIH4pExMXXy3dEVhfkvznU/HNjbgww81\nDMMg67wXpwHB2hqp8Zhqtcp6RGcaS60sHQUsIFg773O6prlQaZfnRQE+RhCJgCrO0MpLjMZOGHtl\nIbCfXapkOQnPZD0hIqBcsioN19fXieuPN2/okw8Ex8fc6lZQ1QeuI7kxHPK0M7vbAQIbPR15yDRN\nvvneN/nas1+z6enZgOCl3CZDveuXZ0KAYHN30wcEWrrEuWT9xK5irxWLMC4naXQbLhBI0i6/ceU3\n+Pbtb1tD5sBqZPnsZ6koawiDgSWOLlmnI6Kq0zMxAmfYnDN8DlYAQWGLcmpI7Wipm9WjzZdTZY67\nx8jnl8Yi2CWkEUHgSiLBjeGQyWQ1I6jVamxc2GB8188InI10krRFtbfnPjtBEMgJAvu2Uwwwgo9J\nGtIbx3TkKP3OPvl8jcn7eZcRuNJQp0NhbZfqsOpKQ8lkkpgS40sbXyIhZhDFCpq2mKssn5d9u5wd\nezKR4M54jLFcNugtH8V+fi9+xgcE4tgPBAWlQEfrMNbH1Ov1RbKSIBA4bK6YKPLzOz/P2/23qS1X\nESwzgrtj5IuyTxqKOMMAT7DIqIyQ8gwzvBTn6mEMORJ0ZYUCPHgwYMMeBgmcDgSZDJKmcXx0RJ4x\nAyG5MlHMgwegaZTLF33BYbNpyZapFP5R8I55gAAgJ0wZ5JYYgV1C6ksU42EEn/E8P9ucPMH6+jrm\nwPy7Jw3daFXIZO4iSZYzvjEa8bTzosmyNXbBppzr65bffq/2HsPpkFe2XrGjktU5Ai8QvJDOEBez\n1IeeqoujI18zyejWiO2ntn1AMFBKbCmn6/OOFYswyiu0ht6Gll3KqTIvrb/Ed+9+1/rgD34An/sc\nu7EChiyFrkNqtyGTGZ6JEThA4OwlgBVAIOcp/k9P0O5GfFMefdJQskxtVEM+twQEtjQEuHkCy5kE\nZzyBDQRPbYRKQ2A1Bdb69xbPbj4nbZrctx395qb1zOdzT338x8AIxo1jupLCaPSAfH6OfkNE2BV5\noGk8mUhYycB6HbW07TICexoK8+ycn8v8HBCUF+RzMuN748DvS0ajlEWRe8sLAZaloXGL/Kf/nrWf\nYDaDbJbEpMN6ZQEg0UiUglLg/Xvvs7a25ttzvdxUZrE569n94+f+Ma8dvUa9XndzTEC4NHRJQZI2\nmUyOaY2axHKFE6UhALNfZiYvHNzBjsCVg/BBioUC7O+PF7LQfB64FwGLx5lLEr3DQ1LzIS3klYli\n591b3t+wv4+7PW1lstiTp8hOdbqJpXfEIw2tBII33vD9E6dyqFKpMOvM/g4xgtEIczKhZWSJx++5\nEaWPEUBo5dA33/8mX3nmK0SEiNtd3NE65JRgHbsXCJ5LpTDFpV4Cj/MzDZPx3pjd53d9QNCNl9iI\nr5hcGmLFIgySMu1pO9DQ8pVnvsK/f//fWx+0D+M5VPSUFPpdrdaEdLplhSjTqX8E65KdmREoeaKf\nfYVcfODHFo80tKasUTfrSFtL1+WZvftMMskHgybz+ZhYLDjewzRNarUa289v+6ShanUBBLK8TWPo\nabLp95nEYjywgcxKKlvvn1sfn8lY5bZh5ZZ/QzZpHNOJJikUDBKJc0wOJ+wVDZ5IJKx8y7VroKqk\nzDj1UZ18YU6jAbebt5kn5qxHLAewnHBcJQ0BPJVIcHPoKS8dj61aT/t9mJtz65xXzlk1lu+8A/E4\nOhKbqr8stZwq8+69d335AQjmCCaThSz75Se/zF8d/RXJVJK2l3F5gGCuz5nWpsjbMpGISDxeoDmq\nIuZLJzIC04RJu4weWzi4u2sGlRX+zmoknC6AoNOxEnDx+MrfAWBmMoyOj4nO+rRRGIzvhTOCH/wA\nPv/5wP4GL+mQ5V10/YD53JPc90Qx0+YUVZjSniwtvLKlocdhBMqTissIxvXxY+0k+GQDQbXKrFCm\nsi4wmSw0Zh8jgBAgsGWhZ74GgCiW6WotkmLSnfHtNS8QXFIUZjGV+31PSNRdaPPafY34Wpyt81s+\nIGhGS5SFxwOCviTSoeNjBAC/ceU3eO3Oa4wbx9Ye2pdfZstMM0yKod9Vrw9IJo8tXfEUeWiZEfRm\nMxrTKeflRcTiPYxls+pPGHukofw4TyffIRJfOmaeVZFPJxI8GtxHFDdCxwsMh0MEQaDwTCEgDS0Y\nwRaN4fECCDodJomEr7vVmTnkJkEjEeuZnRKB/nVs1mzQEtKsrxuI823Eisg7kxHPO2fzBz+Ap54i\n2u2RkTJE003qdfgPN/4D57fO06hbCOsdPgerk8UAVxIJbnonzDqykH1ve3pvcc49zqQrqKwr/ntR\nTpa5fXjblx+A1dIQWFu7fuWJX0HKSv48gQcItHsa0raEELOuSZK2aI6byIXKic9jMIDo2Cohdez9\n/JTUYXg3skOAXSA4rXTUNkFVmdRqdLQ2G8kSzeGHq4EghBF4yU8kIiJJ6+i6p0HTc3hHt0eUcib1\n+tLZt2lXaI5AycPLL8PNm75pwl5G0Dvq/R2ShqpVtKzVTOZozL6KIceWSkjfu9siIkR4af0lAAQh\nypg1cnL4wCsvEMQEgWyixNstzy48DxCM71qU19lJ4FhtXqJgnh0ICgVoT2L0pB6pich02kIUrchg\nLbnGyxsv86Nv/T9w9SqIIhvzJAM5nCLXag1Udc5s1re++AxA4DCC94dDnk4m3amO4DmML75IefqI\n6j1PJOlhR2pHpZMLebGXpKHG6OGJ+YG1tTXkXRn9QGc+nds/90tDrXHdBwRGOm2No7bNGTlVTpb9\nYyY+QnnIbDVpmSrl8ojoaAPlvMI7g8EiUfwXfwHPPAPtNuVkmUm8SqcDf/D+f+TFiy9St3UiWd5x\nu6cBpF0J7aGGaQRHCASAIEwWcu6TDQSTCbTnKoXoEhCkytyr3QswgjAg8Cb6v/rMV9El3Z8n8HhH\nJ1Hs/j3SNu1xh0Rp/URGUKtBOuJ3um9lNSKH09B7UShApxP1j5c4QyNPJJcjMZvRGDa4mF5jHDZe\notm09LFnngmshlyu4pYk//PzSkPjO2NKFSHYmGkHbCsZgSzDs8/CD3/o/jenhLRSqdB61HqsMROf\nbCA4PmaQtMZLOFFJ3V6Kvualf0uM4MaHHb727Nd8EageKaFKS9Ut7q9ZAAHARqrCjbbnwXoZwQMN\neVdmfX2do6Mj90EczUqo08djBPXmnLE4hoc1JGnLt7DlK09/hf0/+4/uIozyTKYrBx/6bDaj0+lQ\nLq8zmRzaTQqr8wTLQLAsC4HnMIoi5fyM2l/eW/xHjzSUqWVoJ0ISsh5paEeSUIwqxCvBzwHVapW1\ntTUiYgSxIqI/tJr0loGgrXUWDq7dRsjnfYzA+ZVKXEGMinT17kefMO50aMyKrK11EFpWD8F1b8XQ\nm2/CSy9ZQJAq09SqpDMGD476vHzpZdeRiqL97GyLKlHi+Tj6YXAG+GMDwRtvUK3CMK4S6QUZwX5n\nP5QReHMEVhC2iFp/6cIvMRSH3Hno6U73eEcnP+BYLL7JYDomUdg4EQjqdVDjCyAYGwYPmRIvxJkc\nTQKft5ZRSWcvHbVNyGbZVVVq/RpPpEtEJvvBqqEf/tCKyqPRExkBWM/P2T0N+A7v+M6Y9Z2Imxty\nLZuFXm81EEBAHorn4kTkCIVIgep+dXHOz2CfbCCo1WiLa5RKE8AkGs24spBPZvAwgvV1k+OjCF99\n5qu+rxqZKlkxXFpZBoLzmXXu9jwPttdzq3X0BzryroyiKCQSCVp2xPlIt8pHz2rFIhy3OyTnSUYH\nQY3yH175h6Sv3WDy8ovW56dxWmJwHn29Xiefz6Mom0wmR6cyAqcAanNzk/39fd4dDFYDAVA+J1O9\n5vEKHmkoc5ChGQv5XR5pSBAEnhZ79IW14OdYMAKwxu06CWN/1dA2bW1ATs651xAvlXxA4CEhC3no\nI2YEkXafLgVyuSHmgdVD8O5gYA3vq9Wsc3PlijV4zu5viKe7/L21f0R5rewDAl33z0ZZVTl0JZnk\n5tDTeRxWOuo4kqeesjaTvd9EV9SALONc0zIQqKo1McLBG10/9DE6Ja6wu7nLn737Z4t/tMQI5IsL\nqXESKZKKx4nm8ydKQ/U6FOVF9H1nPOaCLKOcC78XhQJoWvKxgYBslu1MhuaoybPpFAYQi/ln+/Dm\nm24Q5ltXSRAIJGnDevdg0RJvM4LR7RHrl2NBRpDJQLf7WEAAljwkHotMJhPWQvobVtknGwg6Hdpm\njlKp52rMgUQx+BhBLXINo7fG08VnfB8ZmWkyseDtMAyDer3uOiOAK+oWR94bvMQIpB0rOeqVhx4O\nCijDhq8J5CQrFuG410KNqIyaQY1yLbnGzx5G+bOi1UCUn0apx4PdptVqlXK5vHAmpzCCZtP6SCaT\nQRAErlerJwLB2lN5qrc9UYdHGordjzGPzBlOlmbjeL0ycD7apmqGv6A+ILiguAljLyOIxdL0ZyyA\nvNNBXFvzSRNe/HNr5D9iRiB2B/SFHOn0kPndEtOdOCY2W33rLfjUp2wNsO06E016yCu5X2XNc/0+\nR2LbqoRxMR5HjEQ4ntgRcljpqONIIhF45RWO/usdZukgEFRSFdqTdkAaEgSLFVSrVjI/rAfk6qWr\nvHXnrcUPTpCGRmaGTDxmvUOnMIL19KK/4YPRiKcSCeRdGe1B8F6oKhiGwtra2SaPupbNspFI0J10\neTYxo0EIW33rLfiZnwEgLaYxTMM950stEzajs59fv2/NvrC79Md3xmw8HQ9lBGa3S7/fp+BBlVAg\n8PgU+ZyM/lCnUqmQWzUpOcQ+2UDQ69GcZnxdxYFEMfgGz/3JwR8Si0YZDPzJmeFcJh0LRtTNZhNV\nVYl7pKaX8ju0Rrb+ZprWw7UZgSMNgR8IjtsShpQ4c3KyWITGoEVeyjMehkw+PDggacb4fzt/DkBG\ng2o0WA3kAIEk2fLCCYzAMKwgVVWtSH1ra4v3HjzwAcHUmDKajtwFIuWXt6keTBfjgz3SkH5fpySW\ngofRu7EbqAhN7hnBai2wgKBsh/7yBZnx3THTqXWd3mGk/VmcVFR3ryFeKjGZTNDsUkoPCVlouh9x\nd7E80OjNMySTbSY38hxvCDyRSFhs9c03LUdiX0M5WWavtYcmHrAdv+oDgmg0g2nOMIxFs9iZE8Yn\nSUMAn/kMRz8+xMyGMIJUmb7ZDzACWOQJDKOLIESJxfydvT935ed4ePCQnt6z3hHPdWh3NR8QDOdJ\nMnHcDudVVq/DlrpgBC4QrGAEMAfayPJjAkEmw5osoc91LokDHplrzLwBnGkunh+441Scc36iNOSJ\nYEzTZHxnzNZVMZwR9HpUymUinh4J3/Pb3rbWbt5bSLPSroT+UGd9fZ0UIXPRVtgnGwi6XWpahnz+\neHXpKPii4D/64I9YWzMDs1L6szjJaFBnXJaFAJ7KbjKftKk58ypk2XoggP5QDwWCeh2M/Nmmf4Id\nNI9bFFIFJvNHwTrmt94i8rOv8J27r6PPdBJDnUZ8ij7z68YLRmBHlScwgm7XOn9OK0JpYwO9VmPD\nI5m1NWtRjiO9lZ/IUo1uwK1bVinmaOSuytTua1TSleBhzGatz9n5HNWsc3Ma3nK9LA1pH2pu8Ye3\nh6g/g2TEdn7tNkIuR7FYdBOuXvz7WHoJDANZn9KbKmSzI/R3Eny4ZvCksyv3rbcsacF2fuXkGj88\n+iHnNpK0m3HW1tbca7e6pzd88tBJJaSPDQQfdInmg064qBSZxCeB8w8LIFg1GmRnY4fcPMdrd16z\nUFuWQRQxDRPtvoZ8YSENDeYSqejMOnz9/sqdBPU6bBVzDCYD9Jl+KiOo1WpEox16PXHxBWdkBKoo\nICNjTvcZRNe57+3N2N8PbAP0juQ4URpyBs4B08YUIS6wcSkeBAJRZB6JcK7sH7boe36CEOgnkHdk\ntIfWghppKv3dYQRH4yzZ7MPVpaNgOZ5+n73WHvVhnc2yHAgELUcSHO8bBgSVdAVh0uLOeOzLD5gz\nE/1QR9oOSkONBghrno6hU6xYhO6kRTFXZCbvBxnBW28hvfJZnlt7ju/f/z5Ct4eRSQf2KfuloZMZ\nwTKlTZTLbPR6vnzLsiMpl6Em71gUtdez7nUkwnwyZ1KdUMlVgvXMguCL/kTjmB/rwaFh4AcC+YLM\n+MPxcmMmAL3pjIRgywp2nsIbVS8zguPB8UcrDXW7DKUoxsigVFxnPjS5mZrwRCLhjyglCWIxNiIq\nd5p3ePHCpl3cUvI1ZS0njFc1lYGdJzgJCLwTdn/2Zzk6NIkXMwEgkKYSQlrwNZM55iSMvc1kXiuX\ny6QmKf7w5h/6PKO+rxMvxokqi8KH/lQgFZ1gRkyr32HFys16HcprEUrJErVh7VRGcHBwgCwPF8f9\nMaShlGASn8XRtPtExB1ueRPwjizkeS+8vQTLVUMBRmDnB5ygMZOxZnwtt/dMFYWLS1VOYUDuzRNI\nOxLaA4319XWiWvTMvQSfeCA46GVQVauZrDmdMjYMXwQLuDTrWx98iy8/+WXyeSEQCPamBgkhOLAr\nDAiKiSLGtM/NQc+XH9APdeKlOBHRuq0OEJimdQajlbMDQSoFs3gLNVvEzFeJG0tLve3D+OUnv8y3\nbn0Lul2ErBqIAPzS0MmMYLnp0iwWyS45yjAgqM5L1mH0ykL7OtK6RDm9YsezLQ+ZpokxOebAp+GV\nNwAAIABJREFUyNGahuc4vDmC8d0x1arpAwJ9pjOdm0QNGwRtIHCcKSwxgo9jFHW7TUcWmPU1Sukd\n5HMyt8Zjq6P4/n1LJ3aSmKqKPNDo6l0+dfkc9TqIokgymaTjgKVXZ2Z1shhsRuA0lZ3GCDIZjpQL\nKLFZAAiMvoEpm4Fpt7BoKvM2k3ltbW0NY2Dw3bvfRaserkwUA7S1LqqkWM7yBHnIqbosJ8scDY65\nZQOBtCuFMoKDgwOSSc0PBGeZA5/NkpxPiepRdP0hKXk3HAg85q0cCpOG3GfnAQLtoZVPFITFngev\njUWRXY/+qc90JsaEZNwT6C4Bgbwru9LQvD//28kIXn/9dZ566ikuX77Mv/k3/ybw3//8z/+cbDbL\n1atXuXr1Kv/6X//rE7/P7HZ51M2QTt9Ckja4ORpxZbliCNwM/B/d+iN+/alfX5aoAejoY5KRMfO5\n/0CFAUEsEkOOJ3mvVw8tHXXMAYLh0JJbYo8BBIIAiUIL2cxDoYF57DlZpukexl978tf4T7f+E2a3\ni6CqtMd+xx2Qhk5gBMtAMFZV5KXk3bIjKZWgPkwwf+tHvkSxdl9DPidTUAqBawLchPF02iAaTXEp\nlXdHUnvNywhi+RiCIHB8z8DLmNtaG1VKMpnY45pDgMDLCAoJ+5o+SkbQbtOSwRiMyUY2US4o3BqN\nLGnIkYUcy+XY+/At5JjMRjnu4vRywtgrDUnbEpPjidtX4bWANLSqasi2hryNoncCidpOq0PMiFk6\n/5KdJg2Vy2XqtTpXK1e59v6frkwUO9eUk3NWrf0JCWMHCAqJAnd6NdRYjEws5jo/c+4vxDg8PERV\njZ+IEcjTCfPRHF0/oJQ8xwdeIPBUDDnmnHPD8L0GgFVxZJpTK8fT6bgvmf5QR96x/EUpxDUMo1G2\nPLPD2lrbXZTj2tWr8MEH1opYrHOhPdQol8vobT383Quxjw0IDMPgt3/7t3n99de5ceMG3/jGN7h5\n82bgc5///Od5++23efvtt/lX/+pfnfid83aPnpAlGr2LKG6G5wcAMhnMXo93j9/hF87/gs8pONYa\ntygkiv7GD8KBACAtZfmgW13IISxKRx1zgMA9f2FP+wQT1RbRiYIwVZjuex7+3p4FbuUyTxafJCWm\nGNYPEFSVjuaPpgLS0AmMYDmS6SQSCKcAgSRBMiXQvlWzC71tILhnAYEqq3T0kAjPfghOI+AziYQ7\nktprXiAQBAH5gsz+zZmPEViORHU3ldG2VlGuYgSqbN+njzJZ3G7Tkg2SkRlCJ490XuaepnFJUXyJ\nRgByOW7dsUZCe4+IFwiWpaFIPIK0Lrl9FV7bkiR6hkF3NjudEQAtIY/SPQpE4vV6HXEuBs4UnA4E\nqVQK0zT5ld1f4drN76/sIQBoaS0KiYK1e1pVVwKBE0yrssrNXo2n7Hc9mogSTUeZ1vyM8uDggGJR\n+ImAQNI0Zr0Zk8kxuymPNDSfWzOalhiBc86dKRZeNU0QhEXVnkdKdhgB+CrcXesJAhsefxY6C01R\n4NIleO89AGLpGBEpwlpqjUFjEPrswuxjA4I333yTS5cuce7cOeLxOF/72tf41re+Ffjc4yxcNtpd\npFLGdSY3w/IDAKKIEYvwq9t/HzkmrwSCYmIjAATOPPBlyys59gaNRYaV1YzAzVE54yXPaLF0C3Mk\nEZmU0B56mMoSNf3yk19m2DgkmiusBAI3KlHlMzOCWjLJbMk5hB3Gclmguv0puH7dN2rDBYKww2jT\nMseRPJNMcmOJERiGQavVouh5eZWLCsf3jAAQWCBuA0EII8hkrA2B0+kSEHxE0tCkUaUlQyYxwjzO\nMdq2BsIp0Wjg+RnZDA/uX0ef6eQLcx8QONe/LA2BlScISxhHBIEnFcViBSeVjzo/m6RIHdwOBQJF\nUFYCwSJHEAQCQRBYW1vjM/nPcH/vh8zzFivRPtRQLgQZQSFRsZ7fCWM/nDyrKqvs9esuEIAliSxL\nZYeHh5TLMeu4T6fWATjLHPhsFmmkobU1dP2Iy5lz3HIE/Dt3rHOzBCjOmVoOphxzE8benqMlRrAM\nBG3DoHwaEIDV2PajxcYyeVcmN8/RrXb/9gHBwcGBrwxta2vLnW7pmCAIvPHGG7zwwgt86Utf4saN\nG8tf47deD7mcYTKpIYrrqxkBMJAEfmPzFwFWAkEptbuIKm1bxQhKisqjYZO5RxfXHmhIu4sBa5VK\nhWq1Sq02t86NqloH4YwmJFoYA5H4vIz+yBP5LVHTX3vy15h3OsTU1UDgRCUTZWRlpSbBCikvEOjz\nOa1Egv4SaISt8yyXoXbxFXj//YA0lJWy4YfRloacZOMT9ghlrzWbTXK5nC9ZKV+QOT4wQ4CgYs/t\nN0OBIBJZEAD3mj5CaWhYO6AjSqjZLsZDleq6wBOKYtXo/vjHVg+BbcdxjeelbRLxBIradwlbqVRa\nKQ2BlSc4MWE8HJ7KCEwT2v0Y6Uc3AveiXq+TjCVDn5/TCrLcVey1crlMdBTl3DzDfty6Tu2h/x1x\nrqmY3D5RGhoOrWtNJq3n93DY8APBuWDlUL1ep1IRLSBwKiFCxlUHLJslPhwhaAKaJrKlqAwNg85s\nFioLweJMhSwJBDxA7pWSlxjBcozYmE4pes7+iUDw4x+7/1fakchpOZqHzb99QBA2UGzZXnrpJR49\nesT169f5Z//sn/Hrv/7rKz/79a9/nf+r1+Je7//m3XdTRCLx8IohYDAZ0IxP+cWCFYUtA4Gz77aU\nPr+IKm1bBQQFJUfGHNNptfw5gp0FIxBFEVVVuXevbwGBnbQ+q5lSi0lXJh4vn8gIPrP1GVKjGeNk\n3CfDGIZBs9mkZCenRHEdfXIUqON3zBvNfDges7W2RmPpdIYzAqhWXoTbt/1AcP4URtBqucnGy4oS\nAAKvLOSYckEJVA1ZQFAiEpGYzVq+qqG65/odeejjYAR6/YhOTCGfbzDdS3OvMrcSxTdvWuG0xznf\nntd5JXUFVVaJJTvU65bTO0kagtMTxrd6PasCxz6fzjn3Pr9+HxIJgfiF7cCZqNfrZMVwIHcwdLmr\n2GvO9b8Q2+La1Hqv9Ec68rY/Wdwat1hL20HYimSxkx8QBOv5HQ5bpzKCer3O5qZs/VlnLR0FixEM\nxqTjSfr9AoJggfit0Sg0UQynMwJXml3BCMKkoaqmkfOMlV8JBC+9FGAE6W6aznGH+vt1vv71r7v/\nW2UfGxBsbm76Wv6X198BpNNpEvbD/eIXv8h0OnVHNCzb1//lv+R3TJNXfu7/5JVXztOfzWhOp+xI\nwVHMf3L3TzDSKTJ2UL0MBMPpEDEqkk2eD80ReFu8HVNllVJkQqfZXJkjAIsV3L8/sAoFHhMIZvEW\nWjuBlFhfMILp1JJgXn7Z/VzUhOQU9iZVutoimmo2m2SzWbcZzqWnK/IE3uDx9njME+vrNO3KHvcz\nIYdxbQ2q6hPWoo4Qach7Ta4tSUPnZZlHmsbUU0PurRhyTL4g0+hGfMli55okaRt9eM/qUUinfRG1\n8ytbLcjKWbp6F9OJ0Jfn9/8N2KRRoy2kyefrTG6kuFGYWoxgyZGYpsl17QEviNuossok0iUatfx3\nEAjO1l0MFhA8rFbdcl5YnHMptnhH3Gf+8ssWKniedb1eJ6fkQp+fNQrHRNNaiGL4nChnZeVlM8cb\no1vMJ3OmjSniur+qzwKCywtpKIQReEf4q7JKXeucyggajQa7u8kFIwjz0GGWzSIPJ6higl7POs9P\nJRKnAkFX6wZKsB1blobm+pxpa4pYse7FcvpwOp1S13VSxqLJdSUQvPAC3Ljhsnx5R2Z2MCOfyDPa\nHPE7v/M7f3uA4FOf+hR37tzh/v37TCYTfv/3f58vf/nLvs9Uq1XX6bz55puYpkl+1RKJXg9NypLO\ndJGkDe5qGhcVxTcl07HX9l5DKVRcJ7wMBD5H4mEEmqYxGo3IeVtYbVNllRw6/VbLSkabZijtLZVK\nHB5OfiJGoEVaDBsplOzWIin4/vtWI4t3E1m/j5FQeK910xe9ObKQY64zWVE55AWCO+MxV1QVWZbp\nel7MlYwgvmV1b6fTVg9BbYK0Ka1mBB5pSJI2ESMRNiXJt1QljBHI2zKtcTTACJznN6nftu5NJOKT\nhpxf2WyCGBURoyKj2fgjk4eMVoMmKsXCPtFJifcFexnNkrRw7fgaw6RIcRJz75WzstLLaGKxHPO5\nhmEsEuqndRfXqtXT8wPOM//0p61w25Owr9frFFJBuRGsKrh02mQyuYAgBPsMwAKCWq1GYQz3on3u\n3ryLWBERov53tDVuUck+ZQVhK5LFXiAQ42n0SY9NT9An7UoBRtBoNDh/PmPFPJ6ijlNNFJlFBTZE\nhV7PUhieTCS41e9b+xs8QZhjZ2EEXiBwyqude7HMCI6PjzFSKSKeHdQrgSCZhPPnLd+AJQ3pD3Q2\nyhvEIjFG02ARxrJ9bEAQi8X4t//23/Lqq6/y9NNP89WvfpUrV67wu7/7u/zu7/4uAH/wB3/Ac889\nx4svvsg//+f/nG9+85urv7DbZRzPkE5b4yXujEZcVpTAx0zT5LU7r5Fb23Wd8NKoG48j2fIBgVdf\nXzZVUkmZY7R2G7JZpo0pETlCLO1/KYrFIrWa8dhAMDfnjM02/XoWpbSJvm+Xx4VFJN0u0Vyee+17\n1EcLxxcGBCdVDnmjGed+lkold4m99155rVyGaku0mh8GA/RHOtKGNW/+LMlipyFpWR4KAwJxU6I1\ni1MsBlmKJG0xqe258tQyEHgDADdP8BHJQ0ajRUdQKRTGyJUCt50egqXn98e3/5gLF15C6HTIytY1\nOTUFXkbg5ni8vQQrksVg7c2YNBrMTykddYHgpZcsIPDIMo1Gg7X0WnjVF6CqE3T98sp7sLa2RrVa\nRWi2uPLkZ/nvf/nf3WZLx+bmnPa4TTnzJNNpg3kmeaI0BDAQFJLm2Bf0LTOC6XTKYDDg3Lm0FfN4\nJJmz2ECJsBON0+lYEfuTiQS3qlXL4aaCzY+PKw3pj3Q3P2DdKz8QHB0dEV3KKa4EAvDlCeRdq7t4\nfX2dRCRxpjzBx9pH8MUvfpFbt26xt7fHv/gX/wKA3/zN3+Q3f/M3Afit3/ot3nvvPa5du8Ybb7zB\nK6+8svrLej2GsSzJ5DGiuMneeGyV5i3ZteNrJONJUsXFrPPVjGALXV8ksFflB8CSF+T5CMNO/oTJ\nQuA4I+GxgaCv95GjCTrNJHJqg2gqyrQ+tbRAT6IRgG6XSFblhcoLPOgsFmAsA4FLT8Oy5fg7Im+P\nx1xWFN+YBlgtDdXr9t9Xr7uykHOfTs4RLMoPLycS7J0CBCMzSpQ54njR5OR9fkbzwWIfgqoyGo3Q\ndYtNhZaQflQJ41aXDhkKmSzirkxzOmVbECwKf/Wq+7E/vv3HPPPEz0G7HWAEy9LWMhCIGyKzzgxj\nFJyRFY9EeErTGHqi4FVAkMsBL75ojQjxgH69XqeSq6x0JNnsmNHo0spb4EhDNJt8+rlf5r3r7wXy\nA329TyKeQIwpiOIas6R5KiNomiKS4a8wc3IEjqLQbDbJ5/OUShFaLTC7jwcEXVlgWxRoty0X+WQi\nwQfDYfDdc+6Ffc7PWjWkPfTnE5eloWq1ak1jPYWNu+bJEzjdxZVKBcmU/vYBwd+o9Xr0yZBMWo5k\nFRC8duc1vnT5S+58b1jkoxw52rnB8XiR2azjrpU7CQhUWSVqDBYPdql01LFisUinE31sIGiNW2TF\nPJ2OgiStW3TvkQ5vv+1zJIBbifCFc1/wdRKuZATOTJfl37kkDT2RSASi6rDD6JbjSxLs7/uAQIkp\nzM052mwpci0UMFtNZrMe8bj1hp+FEdRqkBdnaI8W3+dckyiWmTeP3AYqQRAoFosuo/Hi30edMI51\n+3TmKXJynkElyiVFIXLzJpw7566NPOwfstfa4+nLn4VOxwcEy4wAnMqhRcJYiAjWS78iYXxZ1+l6\nnN+JjCCVsuYBXbsGWEy60WiwWdg8AQj6jEbnVt4D9/pbLT774q/R+rBFZMPvcrzXFI+XmSbnpzKC\n47mEsAQEsYxVPz9rzuzP1ykWi4ii9Wdpjb5V4H9Ga4tztuJzWi0LZJ9QFO5GoxjL755tzjmvt7UT\npCEPI3h4MiNoNBrEC4WfiBGIZRGja1ApVYjNYj/lQNDt0iVDInHfkobsCHbZvn3n2/zK5V/xOeFY\nzDr3zj12brAgRInHC0ztBTKnAcF8NkTq95mk04HSUceKxSL9vmQd4nQ6kJBbZc41tdsZRLFidQze\nG1qNI88/H7gXZLN86fKX6Ok95qaFcCsZQQggeSePDg3DimAlyScNGXODnt5Dlf2z2V0gEAT48EMf\nEAiCEJ4wtqUhUVxHEKxjeElRuOPRqL2TRxc/g0LC8JXTLoCgwrxd87V1ntRU1tW7H1lTmdQf0TEU\n8tE1GmtYM4auXbMib9u+ffvbvHrxVWKFossIulrXlYYKhQKdToeZvVd5ZcJ4BRBcGI2oe5zfiUAA\n1r14+20Aer0eoihSSpfCk/1AOt1mNNoK/W9gMYLm8TGMRmTL2zw9fZr7ifv+3++5JlGsMFX0UEbg\nmczAvhHHmAXnEXkrhxqNhlstVyiAVjs7IzDmBm3RYD06odm0zlkiGmWt3+fBCy+E/hvnnFe73dBk\ncSyWZz4ZY2oaJJMBRuAUOzqtNI1GA7FUOjsjePFFePddmM2sAGFLoiAVEHThTMtpPrlA0OvRMrLI\n8oeI4kYoI2iMGrxXe4/P7X4u4Py80eFyVDKxd6KeBgRdrUNhOOSRJJ3ICEajhMUIolGrEzBklMKy\nWX0NKt1unlgsj7wjo799YG2NWT7Qdi/DC+UXME2Tt4+sl3llsjgECDqdxeTRPXvhR8SOqB1H2tW7\npKU00Yh/JaZ7L6dT2NtDuzdygcC5V4GoJJOB8RgpsqjIWmYEYVVDjQYUMuYKIChjtps+IPAmXL1V\nsx+1NJQcaTQ1kdy0zH5hbo2WuHbNx+Ze23uNX33iV10wUiWrO9WRhqLRKPl8nqZ90aFAsGLyJsDW\ncMihp5z6VCAol92EY71ep1Qqrc7xAKlUg+Ew/P2wvq6M7lQuCQKXJ5d5y3zL9xk/EJSZJrVTpaEH\nsyjjkLEX3jxBo9FwGxELBZg0zg4EXb3LKBEnFxlSr9uAYxg8ef8+H1y4sPLfqbJKY9AJZQSCIKDM\n1iCdBEEIMALws4JGo4FSLp+dEaTT1lhqe1qDtCNRoIA5Nn/KGUGvR2uaQVFuYcQqtGczXxUBwHf3\nvssXzn/BKpez5w055nUKy1HJZGJN7DsNCDpah+xoxB1RXJkjyOeLTCapxct2RnnIuqYE83mU8Thi\nMYLrR76I0jWbEaREK4n1n2//ZyAIBLFYHsMYMU9KAWkoTBYCf0S96iC6QXWvB5ubaDfayOdPAQJB\nwFSTJPRFbfd5WeZA15nMnb3EQWnIuU59P5wR0GkHGIEjr3iLBNzcxUchDc3nJLUpHT2K3CpyJ29Y\n9/Ptt93nNzEmfP/e93n14quuVulck1cvDjaV+XsJpC3Jdy+8Vh4MePA4QLCzA3fvAmcFgmP6/dW1\n+fl8Hvp9TNsBF7tFvjf63spyZFGsoMuDE6WhuWnyYBpBn40Dw/C8jMC5frCe+6x5diBojVvoSZmM\nOaBet33G3h5PNZvcOqEfSpVVWqNwIABQpiXMtBWsLjMCCAJBcmPj7IwAfHkCeUcmOU5ijIyfciDo\ndqnpWZLJGvenshvBes2VhcCXI4DVjEAUy0ynpzMCp+okNRhwMxbzbSbzmiRVEIQh7l6bxwCCrCii\nqlZtsrwjo9/tnwgEgiCQElN8+863gSAQWHPt15kljMA1+IDAU4Hl1dhXHcREAoyZidntwqc+5ZOG\nYHXC2MjKyKNFVUs8EmFblt0S0jAgaLchvya4jGA2nzGYDMhIGUSxjNDpY3oSpKfOG/ooGEG3y1CM\nIAowf6TyTla3GMH16+7ze+PRGzxReIJSsmRFc+MxuWjKrRoKGzwXxghOAoJ8v8+evHgOYc/PN4Hi\n4kVr1v5s5mrsKzvDgWRyn14vfKEQQCQSYUdVmdlnSTgUGJaGXDu+FnpNolhGk7orGcHaGhxOJqjx\nOBkpE5CsTmIE887jAcE0pZCaaxwf2wuorl3jyWh0MWoixLJy1lIJVgCBpOeZJ0Vrq1sII/COmWg0\nGqS3ttz31HvOV5onTyDtSqQHaaa96U83EExbPbqkyWZV9jSNy0ujJYy5NQL3i5e+aP3gjNKQlxHU\najU3qlg2VVYZDztETJMb8/lKaUgQSgiCp1TzMYAgE4+Qy1nz1KVtCf14HkwUg2/cYSFR4Eb9Bq1x\nKwAE1t+3zlSZBq7BWzp625NvOQsjEATYUgeYksz8pZ9h0o0gbSwOuavHL5mRjiKP/Qf7ki0PDYdD\nZrMZ6aUEX7sN+fWImyzuaFaSNSJEiERk4sMY86y3GiN8AqkqeXIEf9OMoN2mLQskmGA8UvmxPOaJ\net1KTNnn6fW91/nlS79sfd7ez1Ccxulq3VMGzy0BwfZqIEh1u9xTFHSbYZ1JGkom4YMPfIxglcas\nKA/o909OwG5ns+iShDEyMAYGn7v6Ob6z953F719mBLGm1Ri1NJLcYQR3x2MuKkrodXl7CRwgA7uK\n5zHKR1vjFrO0QnKaQBRFer0eXLvG5WLRl8NatkxcZRbrhlWXAiBPshipGLP2DCEmEMssl5ovApVG\no0Fue9uSkQ3Dd85XmmfmkLwjk2gl0DraT3eOYFLrMlOSKyuG/nL/L9nKbLGdtecbnRkIFjkCb8Jp\n2TJShki3j5HJcL8xYq7NiZfigc8Zhsp8XlvQ4bMCgdYiE4d8XqPRAGlLROvLJzICgJyc46X1l3j9\nzuuBXcvW37fBRB6FMgInklmWhk5jBAA72S5GWmWy+xJirI8QW7CzVfLCLGEiTfyO5LKdMHaufbmH\no9WC0k7UZQTL1ySOJGaeF/F/yATSdpuWbJKNj4lG1ojFo+Tfecf37L6z951FkAKgquQ1wddHAGGj\nqM8uDUXabWKFgrtd61QgUFXr//z4x+7Zz0gZ+nrfLUBwbDbrk043abeXdn8s2VYmwygetxqotiRe\nvfQq37373cXv15bevWktIONqmoUNmQzuux52prz5Eu+7WyxCZPB4QDBPy4iaQrlc5vj4GN5+m4vn\nz3P3hC50GZVEvsMq9UjU0xhJa7TEcj8F+I9io9GguLZmBQ/9/umyEFhB4vXr1na8XRm5JjNsDemM\nf5oZQbPHLKWsBILX9uyyUcdCcgSnMYJms+lbHO21aCRK2UxAJk3n/gh5Rw5tPOv1JCKRJn1Hk38M\nRpCKzsjnDQsIaDKdZ5kXy8EPe4BAlVWuVq7yrWvfIplMIi3lTSRpHV0ePpY0dBojANhMdZgoWfTc\nE0izI6sMybZVQDBVZoia/7k5CeOwiiGwXpTSbgz9wGqwW76m+DDONLX43V4gSCatQFPTPHLVRyAN\nTZs12oqJmmxjSGtWI5knUXzYP2S/t8+nN/07CbJ2Ys9JFi9ffyxWwDCGvp0ZDhCETu1ttciWSm5v\nxpmAIJWCH/3IZQTRSJSkmKSv+3NKk8kBhUKUVuvkGWLrySRDJzm6LfH5c5/nx0c/dncchL57S2Mm\nnDFBgmAzAjl8hpV3U9myNBQbPx4QmGmJ+EikUqlYQHDtGrvPP8/xZOIyrGWLz1WU3GqnK44VZsrc\nN2zOawEgKBZdf3EmIMhmrY1Bt25Z378PcSNOfXD6xONPLBAYnR7zZAxRrISWjn7nzlLE9Rg5gsmk\nimEYdDqd0PESjm3OU5jpJIlDg9hOeGTUaICiDBfduY8FBGNXLxbeu44ojZgcBrd4LQPBU8Wn+NN3\n/zTUkYriOhOpt1Ia6s5mDOdz1kVnBsrp0hDAutJFV1T0bhxJHlg7E2xTpVVAoBMb++nxZUVhzwaC\nZTYD1otSqFgd3NP6NAgEA4FpYjFZ1b/7d5Ew/ij7CIa1A9pinHz+mEGyaAUpntLR1/de55cu/JK/\n+iqXIzOeWxKAas0amk7DuosXgQpY8+eFmMCsE9wiRqfDWrHI3VOAwD3i2axVW33tmi/ZGuZ0df2I\nQiF+6q0rKQpdQHukIW1LJOIJPrP1Gf7s3p8Frsmt2FsaPOdt0jqJEcRyMTBg1psFksWi9nhAQDpG\nfBS1GPHeHsxmxLa32ZIk//5i7++fqkjZE4BAE5kmZtbgvZ2gjOwAwWw2o9froaqqC4pnAgKwzti1\na65kqMoqjf7pe9I/sUBgdrqYmSiiWA4wgtqwxt32XT6z9ZnFP1hywN4KkrCopN1uk81mQ/e1OrZu\nKExTCs+2RMab4Z+zpGHtJwKChDCkVLLnqb/9NlLR8DVSueYZhZ2Vs0gxieQkSSIXHMktihuM462V\n0pADqg67yWQy6LqOpmmhI6gdq8gdRnHVnqEStSiqbauSxVNZIzb0R5ROjiCsdNS5znze1sYf6YEX\nJNqfoycWCb1VYyY+ymTxuHZIJyZTyvdpFONclGVfxZAvP+CYqpIaTujqXQTBJJ9fzBvyN5Wtn10e\n6vVYX1tbyQjGY6ulxX11VNX6wfXrPkcaljCeTqsUCsHd38tWFEU687k1UsGWQ3750i/z+t7rgWuK\nxVTmcw0zk/YxAnvPELDIEYSdKUEQEDdF9H09wAjkyeMBgZCOEhvYDYkOiAsCF2XZBdaA6VliqdVA\nEBvGmCjaiYyg1YJ2u42qqkSj0cdjBGANoLt+nagSJZqNosZVWqPTA51PLBAI/R5kDMxYicZ0ypZH\nAvmTu3/CF859gXjUo9k7Dtim0I5DGE/HzM05Ssx6G5yoxHuQVlnZkNFSMhcbEVqVcIrcaEA2O104\no8cCgh6lkmTJBNeuWZVDIRuplhlBV+vyXOI5Jkpw54AkraPFG4HGNsfBLs9s8nbnnnQYS/EOg1gW\nfV9HPJ/xAUFYYs8wxswUg8jQH8mek2UOdZ3DFUDgOAVpW0J7pIUAwQxdWfRpLI9p8I5GgEC7AAAg\nAElEQVSi7mqehrLHWIh0mumNY1rRFOvqlP3CnIuzmfXMz59nNp/xpx/+qVU26rVcjlhvYA3Dm45W\ndhevrBx6tHQuZjPQdc7l8+yNx4FzDotn7iqaDhVRFOoHBz5GsPz8JpMqpVLCGt9wwq3LR6M0JxPf\n+OlXL77K63uvB8ZiW4ynbCX7Q4DANE3u2lveVk21lbasc+EDguwMca4turZOsda4RSQN0eHcOvu3\nbrkgflFRVgKBOVaJKKsTs7GRwEQe+cZP++6VHZP4fM/jMgIbCMBKGOeiuZ/uZHF00EXI6jRMlfOy\nTNSjz3/37neDL1o8bi0Mt7P+DhAs7wGNxwsYRo96/XhlfsCx0kxinIizXhc4KoW/DY0G5PPmT8QI\nFFqUyykXCKSni8EXHvxAYDclnRPP0RSCE0ZFcZ3J/NgaB+GpgHCcwm1Potj9O+2E8UmHsRDv0hNs\nRvBc2ZrSaFsYjZ9Oq5BJIyz1M8QjEXZkmb3Dw5OBwI6CA0DQ09Hkxe/K5XIMBgOmdhVKgBGIonU2\nTqgGeVzTanXakRRrisjdvMHFBw+sFzQS4a/2/4pddZf19NJoc1X1zRtyGOvyTgVRDCaM5W05yAj6\n1kiFS/b8prB9t8sb6VxJ5oUXqB8fu84o7PlNJlXS6TyCYDGLVZYVBGq67mMET5eexjANbjdvB5P9\nYgUjFfNJQ4581ZzNEIB8PO6e82WTtiRad1vEYjEUp/JN7jMQ0qzM4i6ZBQQzIv0JhUKB5oMHbn7n\noqKsTBjPBiqmtJoRRIZTporO+LB7Yo7ABwQ/CSOw3z2nqaw/DY6TCVzb6d/8t9Pi4x6C2ufAyPoi\n2Lk553t3v8erl14N/iOPE3YcwvINFoQI8XiJavXuqYygMI0zkKOoNZN7+eDgL3DoPY8FBE6kJJt1\nyuUMjeMpHB8jPVfxL6hxzFM+6ry06lylJbQCL7DlSILdxU6OICzf4iSMTzqMOTq0sYHg0xcCjCDM\nkZDJht6Ly4rC/ePjABCYpp8RBKQhXYeZgR5dAGAkEiGfz7v332EEPrkjnX6s8eCn2aTWpCOkyM0L\n3FCnXHz3XdeRBKqFHLO9gHNdjlNYZjSSdMZeArtc8ryi8EDTqI2aJ/cQwGJN5PPPU2+3T8wRTCZV\nRLF8atFVyjSpDodujgCsyP/Vi6/ynTvfsfdNL/JwoljGSEYCjCCft2QhRwJeVYAgbUkc7x373t18\nrEePsw+ca41bRFJjIn3NYgRHR2diBJOeihFfDQRCrw+ZLHrv6MQcwV+LEWxvW8hcryPvyhRmBYbG\n6ZMMPrFAIOk9hGyLD2dpX37g3eq7pKU0F3IhreBnAAKwopJq9f6pQJCbROjLEeSqwQfZkCQuFhBU\nKvHHAoLRdERUiCLHZNbWZBoHOjz7LPI5JcgIDMOKZu3iZUc77ba7XNi4wPfvfd/3cYvx9C0d1tu+\n7uQIQsZ5Ozr7SYcxa3ZoG5Y0JP3MOcuh2EmYMI15MqkiZHIrgeA4RBoaDCwiI4p2FLwMBJ0Oppph\nMq36/l1YCakckzExrWF4K4bw/aQ2b7Zpm0nSgyLVkknhhz88OT8AlhfwDJ5znIKqqozHYzQ7Cj1z\nU1mvB+k0ciRCRRT5oHt8csUQWNPZolFG588zMwy3hyNMj59OLSBYMcjWtYRhcNDv+xgBWHmC1/Ze\nIypEUeKL8yaKFWYp08cIHPDfs/MDq64JQNqUOL7nB4LUvEfPzJx5/1Br3CKW7CP0RhQTCRrDITz5\nJMCJOYJxJ8s0ekKpZq+HkCkwmR8jbgSLS/5GGIEgWLPIrl+3pCE9Z+1KWR76uGSfWCCYE0HKHPHB\nJOEDgu/e/S7/4OI/CP9HHifsJGaaozAgKFOvH5wqDam6QFcyiRxNeScT1OPBcjqbm8pjAYEVJWWQ\npHWryaRhwtWrli6+zAjsF97ZQuU4kkajwcsXX+Z7H37P93FBiCCKFavVfQkI8nlCS3HPkiNIzbvU\np1kmRxOkLRmee86lqKsiSkEthTrgS4pCs14PVD15k4ahjMBeUTk9AQgcx+UMCetoncdeGHSaCb0e\n3bmM2i2T31AQ7GRjfVhnr7XnL2JwbEkacpyCIAi+6w+ThkKBoN93k6OXFOVsQGBfRzuXoxSJuDLS\nSYzgNCCQdZ2Dfh/TMImpi4KKX7zwi7zx6I3Qd2+amIXmCJzS0VXX5NyL+kHd1/8jDPqM4pmwXUyh\n1hq3EMUWCALFapWmoljVVMAFReGepjEPSYyMmioaJwMBiSKxCx0i8aDrdXxSvf7XYATg5gmkbYnM\nOIM4F1cODnTsEwsEo1iGbFbntjbzRbCh+QHHPPXJznjao044I6jXD09lBBnNpBWZE5EiHMRnjI2g\nPNRuw/Z28rGSxa1xC1VKIIoVq3y0J8KLL1rJ4mVG4KkYAu/KvCafu/I5vnf3eyybKK4zT4rudTiT\nR0nNmJgmpbi/Ma5UKlGr12hrbXJKeDltctLheKQSy1njgL1Jq7DE3nRaI6quhTOCRIJ+oxE+XsJ+\nVKE5gk4HIVdgMqlhehqgvDp7YAKp1v0bl4Zi/SHdmYgoVLigSPDhh/DMM/yXe/+Fz5/7vL+IwTEP\nI+jqXZ/k4m8qezxpCGw5o187MxB0gJJhuMMR3S5sj00mNeLx06WhyGCAFhMxNg1ffkKVVS7lLyFG\n/ZGxKFaYJPRQINhbkoZWJYvrx3X/u9vroYvpMwGBaZq0tTaZuICQzbJ2/z4Nz8L7ZDSKGotxOAkG\nfv26ytg8weH2epixIrHz4Z9x2O7RUc/PCH5SINiSSA1SRKfRU8dMfGKBoC+kKRQE3+EYToa8efAm\nXzj3hfB/FNJdvN9cxQjqpwJBajynMZ8gb8nshtQXmzbD3d3NPjYjUCUZUayQSIA5Nxk99RKxQoy5\nNscYeADHkyiGICMYT8fcbd31fb8krVs6rB2NO5NHH06sqaPLjXGlUonDxiFyTA68uI7JeoejQQZp\ny6b/zz/vMoKUmEKbaUyNhXw2mVSJ5jZC78VFSWLS6QTuv7fmXfr/uXuTIEnS8zzzcfdw99j3rMyq\nrOqqyupqdAOd1dwAEAQ5ArqrAUFm4kmUdJKONJlJmquOMNOJd5rMKJPNQQfJNDdixjhUd9WwJRAA\nwQFIogu9d2VtWUtmxuYeiy/hyxw8PMLXyKWLY1P4zGjGzopIeP7+///7ve+3XVSxniSAYDhEaLaQ\npCqOs7qd8tpMLCWr5ywNKYbBDAVTOse18RheeQUUhXfuvsN3dnLY6oIRhJJH9IKNM4LTA8HLpRIP\nJ0cnBoLxkydsVKtBy3PS3rfv+yeWhtB1hEoDYzMtp/z61q8z9+KSqixvYpeMTGnobkQaymUE2ypH\n/TgjQNeZl07GCMb2mKKkUilegEaD9uef03fimW3XFrUuSRsdVbG9+D6Pma7ju+cQL+Zfyq0WPH1q\nxhnBaaQhWJ49dVulNCwh2MKvLhCM/DrNdoHD+ZxLC7r43v33+M3zv0lNzel/kgEEB9ow1V9fUbbo\n94fHAkF5NucIC2VbYScjm2A8DljH1lbnVEAwNIdUCxKKch7mczp+n/7WV4KmcYu0yaXlAEG/36fb\n7fKda9+JlfQHf9953DLL5wgvhHDuc9K63S5PR09T6xT7nYbGk1lzBQQRRiAIwnJgfGi2fYDU3M68\ngOuGAaUSfqKGIyoNiapIoVVgOIu8v1FQIBYUBa6Kro5tM/GcpaGSaWGLIiO5y7XHj+GNoD34u3vv\n8va1t7O/tMjYiUpD4QUbZQSyvBEbngQgNSTwgkKqpY1Xg1heLpV4Ouun3l+smCzyHNMnT4KLNMLo\noheJ6+oIgowklY8HgvEYqdRk2koHLL/U/VLKqw86kI5PxAiyLjd5Q2ZoDuk0I7KuruNWTgYEQ2NI\nY8HGqdepffopU9teZp1Bfpxg0BeoK438dE1NwzW3EDbyF6zVgoMDOyUNDc30PZVrr78On36K0oaq\nXsWbeb/CQODVKTYVLqsqhYUH+87eO/myEGQCQW+ipRZYljcZDPRjYwRFw+YZBupFlWulEnuJzRFu\n4GgHz5NcOpqpUS34wWb89FNayoShFaR0Fi8lagkSQBB6uWHA6TvXvpOSh2T5HE7ZXz5HmDG0Zxjs\nZADBxsYGh9rh2o0oT0bsz1oo2wsg2N0NxjIuvKlkwHg+P6DQfilzLbTBgEKjwYMEsEaBAII4gWZp\nNNTF37+IEQRFgas4QTTzJnNK2XMGgqrl4BQ89ostrn3yCdy4wce9j5EEievtnBm/C1YSVmHnSUNB\nVttqeFLwMyHdfC7BCHrGKBMIshiB9ewZ3e3tJRAkA7NhfABOUJit60hyi1kjnZ67Ud7Aci2ejiPj\nN5VNrJKWAgKl5jB23WXFe15XVEEUGJfHNKTIoHpdx6+dDAg0S6OmFJdAIO7txWZCQLCeSSDw/UVa\ncim/Wyu6jjPewK/na2mtFvR6bkwa8nUdzYzs8+OsVILLlxE+/4ROp4MzcX51gWDgtKChxLqO/vfP\n/3t22mhoiR4m7TYMZ+kFVpQthsPZsYxAnZgciibqRZWdDC8h9Lja7Taj0QjXdVd69JoqHM3SKEtO\nsBnff59W3V1eCmGQdPXhOBDU1ToTe4LruZTLZW7u3OS9++/F6KqibOKUnRQj2DNNdorptLZut0t/\n2l+7EQVtxEyq42wsvl+twvY2fPopkNZ0bfsAuXM18wLu9XqU2232EkCQurgugYQUzJuACBCcnBFo\nlraaHPc8zPep2i5CyeKzaolrP/853LixZANZ/aiAJRgdFyOA+PCk0FJFZYkYgWbpqRbGeUBgHx2x\n8fLLuTEe2z5AlgMgWFuY7XkwmaDQZlxMr+/YHnOpfolbe7eWP1OULQxlkJKGtErAVpcV74t9nmyG\nBzBWxjT9COjpOkLjhEBgatTkoHUNhQLU63S63RgQZKWQ6nrA/vNiF2F23/ygi1fOf5BwPaOMwB+N\nkMTIPj+JLRj5uYvnsHX7VxcIpoUKQ6mxzCJ4qD1kYAz4ta2M7pyhZTCCkRkMBIlaAATWsUAgj6c8\nKUxRt9XMQpPQg5UkiWazyWAwCCJCohjkvOfYyBxRFu1gM965Q6sjxYAgJQ1FBrFIokS5UKZzvoMg\nCJyrnGOntcNPH/808vdtBlXHESDodAINNo8RDI1hap1ipmn4cg2jGQGSSJwgSeVt+wCltugMm1iL\nfr9Ps93OZVihWZcsakRkwEXgPIsRJGMEvh/xdJ8nIzAMbAkaqsf9tsfFH/0IbtxYHx+AwIuzbZqF\n6toYAcRnZoSWihNEpKGKJCG7UxwxXiiYBwTeYMDG668How99P/XuwvgAsF4amk6hXKY8rzGW00Aw\nMkd8qfMl3t17d/kzSarhVH18Lfjf8xYjjA8VIyZb5jXDA9BEjVq0q62uI7VOBgQjc0SlIAayrOPA\n9nac0ZNdVBb2Q8od5DOZQLWKc7+BK+f3/mm1QNOkGCPwtNHJ2UBoi7NXvVSlMC/wbPRs7cdfWCCw\nlBJPvcZyc9zau8VbO2+t79ed0W9oPE8zAknqMp16axvOAYjjCU/U6ZIRrLu4Ypsp0QAvaZqlURKM\nYDO+/z6tC6UVEGyr2I8jGQsJRgBQKVRobq3AISkPyfI57KKRZgSR9LyodTodxvaYupJTlGOa4Hko\nQoFZJfL9ROZQeEA8z8Z1xxQK7UxvPJS1kl5XCgguWFSjPacXXnDgMWczglIpwOHZLNIM73kCga6j\nq7Ahe4hbEgVBwO62+OHDH/Lm1TfzvycIUKvRcZUUEHQ6nZhHqijnsO3D2NdTQJDov696M3Ti7zZV\nUAbLWMXGlSvBu7l/PxvETwIEi2eoGTW0jGwazdJ4Y+sNbu3dWnZPFQQBsbUJIw18n/E4eGf3nXRa\nc96lO3JH1GZxIJA7J5eGKpIXOGGzGWxsBIz4GEYQnqFcIFishf1JBUc4yu4WC9TrLrZdoR6+u0YD\ndG29E5Zlkcyhilf5FQaCksIDp7b0YN/de5ebV2+u/1IGI5g66UUej4O2JIKQE/0HcF2EmcHT0hjl\ngpKZX5wLBMdcPJqpURTGK2noSj0GBNbjyIFPpI8ClIUy1Y3VBfnda9+NAYGibGJHWlH3+9Bs++xb\nFpczgECWZYqNIkUh/W/BAwdgVPUcpsVIVlEOEMznh8jyRjC0PmMt+v0+FzY2jpWGrHMWFTvSP2aR\nO68oWzGPOdmmIdWB9DlKQ/Nhn7EKmxLUGzbcuMFPHv2EVzqv0CmvjzlRr9OeF5ZAMBoFzCXpkeZK\nQ2uAQHJnDIhLC5mMoNFAHI+DYPHi/TXUIAAaXl7JGEGuNDQe49dqVPQKmpsBBKbGTmuHYqHIB0cf\nrP6+ynkoiGAYmTUEoeVdukNrSEWP7AtdR904uTS0lGUX+7rT6cTWv1Mo4Pk+g0gA+VhGoOv49TrO\nvoQoyLhu9vlX1Rml0oWVhFivI44np2cEIRBsq5SdMof64dqPv7BAMC+JfDqvsVMs4vket/du52dk\nhJYRIzD8NCPo9/s0m4XUYYvZeIxQrVLwFJxNh4ok0SgUeBrJLz47EAwpCQbyRILhkNblCBBcTABB\nBiNQfIVKZ3UQfufS7yynlsECCBR9efkNBiDW52wpCoqYvSXK7TIFJ6cTq6bhN5tUbJtJNEc+AgTR\ngGP0IskDgpc2No6Vhoy2QWUaP/ABEMQZQbvdRtO0IEbDal7130eweDp4hi5LbAoim15vGR/ILXKM\nWq1GcwEEihKoiJNJFiPYZD4/ASOITHfz3SkH3urdzOeBw5tqyNlsokynARAsKlRlSUaRFKbzIPMn\nGSNYxwj8co2m0qQ/St/CYaD/7Wtv8+7dlTykKJt49XKQLZORMRRaVsDYcRzG5phiLwIauk558+SM\noCxaARAcHUG5nAJiQRBSKaQhEORVPKPr+MUackdGUTdTjC60QkFHVSPjcYtF8Dy60vpJcCnb3gbH\nQaka1OY1+tP1f/wLCwRO2edDu8KVYpH3D96nWWzyUuOl9V/KYAQWaUbQ6/VotdT1QKBp+PUGVbPK\ntBwckGRa2VmBYGj0aBSbCB98CK+/TqstLoFA2VaOBQLZlSk1V4dGLah886Vv8t799wCQpDrzsrvU\nYQcDsKrzzNTR5e+oq4jznO0yGuFXG9QLDpoR6bF/+XJwk/V6saKk44Cg1+vx8vnz7JlmjEKngKBp\nUBpHnnkJBPEYQRijCS/TWAdSS3u+QNB7hi7LdEoq1x7cg91d3rn7Dm/vHOOkANTrNCyWwcbQ286W\nhhKMIJk1FKksBpjbYw68FVtbxNXTfdjqdWRzkceeUxR44hiBruPJVbrn4tJKaJoZnL23d96OxQkU\nZQuvpsJolFlDEFpWV9TBYECz3sR5HEml1XVKW/V85hJ9JkujKMxQ5vVg74piav0hLQ8tGUFG8V3w\nizU8uYJ6UUWWz6ViPKGJ4ohCIVIDIQjMKyW23PyzmWmLVhPq7AF1o87QWP/Hv7hAULERC13KksS7\nd9fkZ0ctceCbLY+5lM6m6Pf7tFrVmFeZMk3DL9epubXli98plWJyRlSDjY58PJ4RDGiVNoJA640b\nMfotd2XciYtruMvnSAKBaIso9Xjh182rN5fZGYIgINTb+Ppg8ffCtGxmBopDk2sy5LUr0TQ8tUar\n7scPW9j35P33Y5Q56lFmyTL9fp9LGxvIgkAvQr+TUsasMqMyquA7C7BYBEiTjACyU0iX3ttzrCzW\nnx0ylhSKapdrd+6gvXKZj3sfZ7eVSFq9TtVc5XyH7z2WdcbppSHP9zDmYx45K5DOlIUAp1ym7Di0\n2+1YJ8vk+wuBoNEIlj2jqD7I35cqdM/HPerQNCtI3X7z6pv85cO/xHKs5d/n1gpLRtBo+TyzbV46\ngTQUxpdicTRdp3r+hEBgjigLM5RPnsFieHySEUA6YHwSaciRqijbSmwcbtI8b4AgxF+MVS2y6aVn\nixxrb7yB2vuYxqSxnAiXZy8sEFD3uVQOAqK37t06Pj4AqQu4WJ8gOmUKYlzy6PV6tNv19YxA1/GU\nKnXqyxef9BKSjOCkbSaCVg7ngkO4uxsDAkEQUC9EAsYZQOAbPlJFiv3s5s7NWJqe2OziL2SywQBG\nJSMzdTQ0qSzhTrM7rDIa4UpVWlne4cKrjMcIjpeGut1uJrBGGYE216iJNexni7VYBovPMZ/38P3s\nkZVRRvC8K4u1Z0fokoJT2mLnb/6G26Wn/N7l3ztZ6l+thjKzls3wwvdeKBSo1WqMFimVWdJQoVXA\nsyJV5xEgmNgTSnKZ+1YcVLNyIYaOQ1OSEEURrl+Hp0+D+oYcIBDFVdPSlOk6rl/i3KVzmYxgZAbZ\nMO1Sm1e7r/KT/Z8s/r4t3KqwBIJCzeVSsbisFwot69I9Ojri3NY57EN75SDoOvWL9RONnRjODqir\nFYQ7H8K1a6Bp2UCQYP8nCRa7fhl1W10AQbY05DiH+NHUV8AoyZxz1s+GzrQ33kB9+Dc0Rg0mzmTt\nR19YIPCaMjvFIqZj8uNHP+bbV3PaSkQtESMoVDSw0kGYXq9Hp9M5lhG4YoVGYaUJXktkDq2VhrQM\n+rgw3ZrQKl8I0vcSjAASAeNE+iiAO3URSvFDs7u5y8gc8WD0AACxuRUM92HR6Kqcpt5R84s+83F+\n6bzjV2h3hbTXtbsLd+7kXiR50lCn04mtp+cFH4v+qZoVSAvLtVhcfqIoUyg0mM9Xl0808yM1k+A5\nSkOTgyN0UaFf3mJHlnnnyQ9PJgsB1OsIkUs3mTkU7p8saUgQhHj8KJI+qpkaTbWB7fuMFgV+eYyg\nN5/TDONEhQK8+ip88EE+o2ONPDQeM3fLbO5s0u/3U5kyoTQEBHGChTwU1Ll4S2mI2jwzmy2XEWx0\nkbtyzEEonqsfOzsBQlm2HZy9L38ZNO1E0lAIrOuAYD4PgGCdNGRZBzhOPB4wK8u05xn9qY6z3V2k\nj/6WDXeDmbd+3sYLCwROW2KnVOLHj37MVza+crLy62QxV1HDNxopL6HX67Gxkf+yANA0HCqx4FCy\nzcRZYwRje0YnBIIEI4BEnCCDEcwnczwlXmgjCiJv7bzF7Xu3AZBaFxDGwebo9+GpMlnLCDzZwxjl\nnCJdx3FKdC+I6QthAQSnDRZ3Op3Yeup6UKMmRYiOZmo0K83Myy8ZJ4ge5hQjeI7S0OzwiLGoMCo1\nqbz6apDWfPWtk305UlSWBIIokAUXyVGssR5Eisp8P8YIQsDcKRa5F46tzAGCI9OkFj0Q4ftbBGZd\ndwL4SNIqKy23uljXcewSzStNBEFglhj+E60Kf3tnFTBWlC3mFWfJCOyqnSlbZgWLQ2loCYq+H2j9\ntdqxDfIARuaAVqkbsPE33shlBMnq4vCsrwsWz+0S6kV1rTQ0ne5jWfFJauOSSNuSMj+/1r78Zfj0\nU86Xt7CE/LoleIGBwOgEuftr+7ckTZZjk7ksNAS7kRpOFUgT59czAl1n7lZoVlbBoeOkoZMAgemY\n+PhUZ6Xgy63WekaQkT5qjkxcOS3j3Lx6c+l1yfXzMHdxzTm67nNfnq6NEcylObNhjlcxHjO3inQv\nSemD9vrr8OGHNOVaLFicFyPwfX8FBBFGkCVlaJZGs74AAscJ6hkW4wiTtQTR9Q+zhipyBcuxmJfU\nwFXMFLpPZ/ZgwERQcESVwfVLjO0xr597/WRfXgBSQ22gmVqKEYRAIIpKUHjlxBd7GSewrCA+sxjf\nGrYniEpteUBwMJtRdt2VsxRhdJqlLUE8WiGdW12s69hGEXVbTXnVphMkAhQLgfPxjYvf4OPex4sW\n0JvYJRNGIwYDmJWtTCclK1gczlpWtxdrMZsFLT0LhRMBgWbpNEuLCXtf/WouI9hWVfqOw2yxZ8Kz\nnvVMy7WYqsdKQ5PJIwxDjTmnY1WgaZ9sulrMymW4dIkLlTau4OY3w+MFBgK9LbNTKnFr74TxgdAi\nl7BmacheI+XN9Ho9NjdfOjZraG6VadfaSw9gU5aZuS76gn5HgeCkweKgz5CM+mQWHELSY3XVi4sY\nwXweXH7Vaux3zAazTA/g5s5Nbu/dxvM9ZGULryKj7Y+pNwDRp13ISQ8FLCzGRzk6uq5jz4psXC2k\nPcN6HTY2aB7qJ4oR6LpOsVhEVdXYxZWMD4Rr1W61g7UI2cDigkrWEkQPc3hxLZvhzReFI5P1OuqJ\nTB8xERXKc52fdS1u7tzMbyuRtLDfUA4jiHqlazOHEqmjISO4GgHWzGIy4HA0whdFllNcEtJejM0t\nLFca0nWsSRFlW0k9fygLhWujFlR+96Xf5b377y3qXGb44zHDIegli6sZTsq6YPESFCPM6CRAoFsT\n2l4tANGdnYChNZuMx+NY4zlJEGIdh8P1XCcNWWMVZVtZKw0NBgeoqhcLWY1Un7p5xpnau7tslguI\ntrh2dvELCwSHbZWWb/BJ7xO+cekEGRmhReIEmqlRJA8Irh4bI7ANNcjoWLx4QRCWl1fYgvq0wWLN\n0qjKIsreMMi4IdiThcJqrO6SEYSbPHHRTI4mmH46xedy8zLNYpM7B3cWIwEltEc61ZYf6+OSZYZn\noB3kbKTFJj93Xc4+aDdu0Px8/0TSUBgoBmKMIBMILI12tx2sRSJdMpk5FAWC6IXwvOWhwmyMIRbY\n6H/M/6HcP5OTktWBNOmVrs0cSqzFaRhBv9/HUtXVWoRAsJBhkvEBWCMNjcdYmpzJCGLNAhf21tW3\nuLV3C0mq4lZE/FGP4RD6xVkuI8gKFm9sbKykoVMCwdie0dak4OyVSuA4iIssqkHij8xyVPKAwNd1\nzFGUEWQDQa/Xo173Ys85VFyq1hmB4MYNtjDAYG2/oRcWCIZNhQ8e/yW/+9Lv5vbIz7QEIyhL2UCw\ntXX9WEZg6UU6G53YAoeXV9iCOpzxUqvVsCwrGDl4LCPwkT94vAQCiG/iJRBkxAdM02Q+mTN2sr33\nMHtIUc7hVgTGj3WUurtWFnI9F9Mz6T/NLkrxdR1zqLL1mpJ90HZ3qX3wGRN7ggIVTSAAACAASURB\nVONaOM4IWe6GCxNbizBQDHCpWOTAtrE8L/Pi0kyN7lZ3deAjXnAyRhD1SDOB4DllDqmmgSUpXOh9\nyv8++Slv7ZwwPgDLtcgLFp+kqMx8ZKaqimMxghMAgVOKTK/bCoqbGlbQ0z7G5haWxwj8ocbcKiF3\n5UxGkIzrxTLbGg280SHDoc8zNbsHVpYev2QE26dnBK7nYrgOrSdmcPYEYZnYkSUPhTGX6CztmlJb\nNn2MrUU/yKwr1AtrpaEgYzH+nH3ZoWI4mZ8/1nZ3OWcc4hkeg1l+m9gXFgiq7Qr/971b3Nw5hccF\nsUt4ZI6oFtJA0O/3OXfuMr5v47rZurg/0rBmJTrn4kAQxgmSHqwgCKuA3xogCBrOuSg/21tKQxDf\nxMtgsa6ngKDf79Mut3PR/+bOTW7du4UsB5kZ06c6UsNZGyjWLZ2aUmPQz95I/kDDFcq0L0rZOeW7\nu0h3PqCqVOlN9igU2gjCIviVuIDD+ABAQRC4qKo8MM1MRjAyR3S2OynPD07OCGLDaZ4DIyhZFrYo\ns10SaFbaxxc5Rm2xFlnDaU4kDYV9qBJrEaZp7kRapedmDfV6eNXq6p0IAuzu0jzQ1kpDWRes19cQ\nO00EUUhdpFnNHsPMtofaQ4R6G0/r0R+CXHdoZsiWz1sa0i2dSkGi+FlvdfYWCkJWwPjqghEYRrBM\npVLQDK+qVFN5+35fQzoXAJ8kNfA8E89Ls/bg+aXYndSTLEqzNe1u1tnuLtWDD5Esicf9x7kfe2GB\noNXucvve7ZNnZIQWSd0M6GkztuiO46BpGu12O+VVRs07HEGjTqvcimlvIV3MuriWm2ktEAwoSw7y\nR4+XA7MhwQguqNhPbfyRluoR0O/36VQ6uTNKv33l2/zo4Y/wxQZOycE81HGPqSoOPcr5fI6RkX/n\n93XEc00kSaBWy8iMjejM/cm9+EWSWIvY4G4CYM1bT83S2HhpA/uxHdRExIAgnTWUxwg08/lVF1fn\nNl5BwVenZ9ubur6sTl3HCDKloZApRrKnYFW4daVY5KFl4fr+WkbgJ2Wy3V2aj45iweKo5TKCgYaw\nGVz2KUaQIQ2JgsibV9/k9t5thGYX9BH9gc+VjezYVVbL5y8iDWmWFnQevRNh4xEgyGIEexlOX1bA\n2B9qiFvBhwRByATy2WyG7/t0u2LsOQ8KJsXp+uHzubazgzreQ7Fk9nv7uR97YYGgVKijmRq7m7vH\nfzhqkc6fmqnRLMUZwXA4pNlsIklSKvMkan5vhHiulfJKwkKTrItrGTBec+kMZo+pFWSE66+udCXi\nm1hURQqNAs6jYQoIer0e5xrnYk3CotYqtXi1+yo/P/iMednBOhphlu21jCD0KLMOAwSbXFp0O828\nFF55BR49oqnU6U3urwWCKCOARUquYaQuLt/30S2dTrcDAniHWkIaSmcNhc9eqQRxdtt+/o3nqnMH\nVy7yofLk9Gx1jTSUXPssaUjekHF0B6+vZcYIiqJIV5Z5bFm5BWW9Xg+x2Yzvzxs3aO49Pn2MQNcp\nbAcvLRUjMLM7at7cucnte7eRmpv4msZEF3h5IzuHPtkML3z+breLsq2kHITjgGBkjqhIHvIv9+G1\n1xb/I42lNJRkBHlOXxZTEcZjpIsrKSxLHgqfvdVa1eP4vs+BZCCPjymAyDNJQvlSF9VUeTp4mvux\nFxYIRjOdN6++ub7tdJYlYgTtchwIosHKrL7vofnDEdL5NBAcxwiOjo7WA8H0CXXkmCwE6U2sbqs4\nD/uZjGCjvYEqqcsmYUl7a+ctbt9/D6+qYvf7TMrW2hhBeGizdFIAxjrSdivzOYEA0F55haYr058+\nigNBwvuMrj/ke12z+QxZlJElebEWg9haJD3mMPPDcRwEYTki+LkXldXmLmKxzP+p3MufnZ1na7KG\nkhdRZlGZKKBsKTiPBpkxAlisp2muZQSFdjvNCD66vzZGkHXBCtMJhUutzOfPYgSwChiLzS18bYpc\n8nm5mu2kyJIc2+ehR12pVJBKEmJFxH06PDkQGKOg82jzShDgg/XS0CLmMhj4xwPBbEzhpZWDk5U5\ntAKC1XPO5jOmpQLiF3BS5F/foWSUfjWB4GHvg9N7XBAHAlOjW23ENkc0WLkuqCOMx0iXOqmA1eVi\nkUemST+xOeBk0tDQOKDuSMcDwUUV93E2I+h2u/mFLUT6DlUrzAcDpmWTl9T8Fgjhoc06DADCdEzh\ncnCr5OaU7+7SMHz60ydxjzIRI4iuP+QDa/RyU7YVnMRaKMoGjjNYtpkQRZFWq7XM/AjXs1lsMrKe\nHxDUbY+iXMR57VVapQyXe+2X01lDYSvqk0hDEDgI7pNRXBqKjDm8Wizy+dSIZbRFrd/vo3Q6cXb0\nla/Q+Gjv1OmjgjFGvhq8yySjib6/qF1tXaWiVOjJMowt5GMSGaL7PCkrBmdkdGIgGMyeUJVExNfe\nWP1wsT+znKBGoYAqCDzoObG1TBW6eR6CPUXZWX0oK3MoCwg0S8OvZ+mtJzfhxi5Vu8zhUX4r6hcW\nCD548O7pNVhIxQjONeKMILqZZDntdYUmzHTky+2UTlkURc4pCvcTmwMiQFAsBgVQkZbVoY2MI5oz\n71ggULYV3GejXCDIHZlH0Jb6zsEdvHqNuTak1QI5p/00rDI8MhmB7yNaU+Sr7eVzZsoEu7s0NYuR\ncZhmBOPxskhiHSOIerDRrBN1W8U7iEtDglCgUGjG2kxkBYzD4q3nIg15HmXHp66qfH33H57++2FB\nWTGQPBQlqIWKtqIOZZAsaQjCtRjmM4JSiU96FpVKkJIcNdu2MQwDpduNg2K1SrO5hWZkA0HmO7dt\nBM9FuRw8R4oRmBpNNbsbwFtX3+KXdh9pakF1fSJDdJ8nZUX1oor37OSMYDDbp04hfvYW4JznBO2U\nSnx26KQYQezsTad4YhH10qpx3DppKAqsmqlBo/nFnJTdXRqWQl/Pb0X9wgJBzZ9ytXX19F9MxAi2\nWmlGcKw05PuI1gT5WmdZGWk6q2DO1WKRB0fZQHB0dLRKS8u4eEbmgNbQPpE05B3lBIs7nfzCFqAk\nl/j6xa8zVkWEsc5We/02CC+SzMNgWfgIqJeDSziXEdy4QbM3YWj04heJJAXpFtOA3ucxgiT9jkoL\nwVqkQTEJ5FkB4+cpDVmjAVMZ6qp9NidFVUEQaAnlVAdSVVUpFovoi2cMpaFkHChrLaKMYKdY5NOD\neS4baLfbCBlrUfzKG+D7mI6FJMU9+WTBIwDjMa5UQbkYMM2TMgII4gR/ObqLZM5xK2ZmMVlo0X2e\nYgTbapDUcUIgGM6e0HCE0wFBscj9ozQQxM6eruOKFdTtFes+qTSkWRpSo/mFGAG7u3RmEiPjV7CO\n4O0rv3e2LybSRy+040CQjBFkSkOmiS9Iy8svK07wuO9lAsHyMORcPKNpn6buB4MlIpYFBH4/DQRR\nRrCugOTm1ZscSnMK0ymXN9b3MQkvkkxGkNjkaxnBkwFDc5DyKKPeeNKraxYKKIJAPyENRdMP1W0V\nf5BeiySQR9f/7wMIDh48YqyI2HKfb770zbP9knqd1lxKAQHEGU3Q60dY9P5ZmbKtBGsRYUfRtdop\nldg7cnJTR7vdbraTsrtL05exhG6q8LBUCvA81qpF13EW3TaTz758ppypW29efZP3Ht9hrhSQi8O1\nsmV0n6cYwbaKPzx5sHg4O6A+czOBIC8+drVUYr/vrgcCTcPxKijbq3qnk0pDI3OE1GzFWPOpbXOT\nDbvAeP4rWFl8pvgApILFlzaauTGCXGlI03CEYMgEZABBschhPx0jiG2mnItHn45oFc+lqoWzgAAt\nfuDhZIwAgoDxnqehmlOunVvf2XBtjEDXcbzycpPnHrbtbZpTF202QpbPxf8tshZJaQiCy2uQIQ2F\nF4myrYA+zgCC+GzfLGnoeWYN7X34Cbos4m2wZIqntlptWbwVfU7IriVIFZVtq6CNU9JQKKPtFIvs\nH7m5jKDT6WRXWe/uUnd8LCE77pF0AHxNx3FLqBeCM1KtVpnP50FBJflZQwDdcpdm9SqGrLBZ1nOn\n5sHxjMDXTp4+Oho/C2TZK1dWPzwBIzhIOH3LuNPCvN4oOCPnVkAQ3C15WUMRRmBq1MqtAG2/QAuU\nrWKdmZ+dPAL/HwPBn//5n/Pqq69y/fp1/uiP/ijzM//23/5brl+/zhtvvMHf/u3f5v6uU2dkhLaI\nEXi+x8SecHGjdmppyNe04MVeCF5sMjC7UyqtryMInyMLCOwZnXq6CCkrRpBsJRB9/qzOjFH7zfO/\nyUPBpGTPeOUkQJCTNRRs8tJyk+f2nREEGhuX0KxJmhEs1sL3/ZQ0BHClUMSYxjEvKi2o22rQUjsB\nismAarK6ODac5jkwggcffoguF9h545Wz/5J6nbLpBs3w3HlMasuqLs6qJWCy2hfhPq8pwdpsKQoz\nTaTeSnuXSyDIWovdXWq2g+HXU9+D9Ht3Hg7wChXEYnDFCEK8qCwvayi037vyHWaFIi9V1veEiO7z\nJCNQthWEyWS5FqVS4FTntaIejZ7QFOvBkIXQIkCQxQh2SqUUW02evfn9Pp5SRZBWzl3W3RLu/aQ0\n1Cg2jm1df5xd7GxhFtIxydBygeDDDz9M/ey9994784O4rsu//tf/mj//8z/nww8/5L/+1//KRx99\nFPvMn/3Zn/H555/z2Wef8R//43/kX/2rf5X7+zYqG7n/ttYWMYKxNaYiV2i3JCaTVTVsEgiypCHn\n4QBXrCCVA0klGRy6Wiyia8KZgGDs2rS3vpL6eRYjEIw0EEQZwbomU5IoUT93nbIz4yub61t0rKsj\nmD8Yxjb5Oq+rsX2VsWPnMoLZbIYoipTL8WlMF+YV1JoXO59RRpC3FsmAah4jeF7jKp99fo+xJPPV\nb/2Ts/+SxUyCMGC8rpYgr6gsuhbhPpfEYK8KgkDHLCHV0i0LYtJQci2uX6fmOJhO9qSs5Huf3x/g\nleLAHN3/6xgBwFtXbzIRK1xV18/aje7zLEYQXQtBWL8/R7MBzVLiXgkzuZpNdF3HceLrtlMsoo+E\nFCOI3gfOwyF+Jb4WedLQxsZGKljcUBux2OZZ7PK1HeZKfpuKXCD4p//0n/JHf/RH+L7PbDbj3/yb\nf8O/+3f/7swP8td//de8/PLLXLlyBVmW+ef//J/zp3/6p7HP/OAHP+Bf/st/CcDXv/51RqMRBwdr\n+v2cxRYvNkRaUQx+FE5YirU4KLRw3TGeF0dS594Av7h6sVnSkKmJZ5KGJq5H59rXUz9PbuBCq4Dk\nTnEL8d7lJ40RAJw//3Vq/pjXN9bPQ43WESTpsfOgj19erUVusBio7lxmOhcQxQQDWcgySY8utA2z\nRKEe71sR9SiVTQVxPsMrx7uwJnPtj5WGviAQjJ8+Zlwo8BtXTtEEMWnH9Bs6ThpSthVEe4q/6Eib\nFZRtGCX8WrplQYwRJGWyQoFaSWWmZbc6SDGCRwOoxi+/UzGCl34PTaxxUc1PeYRjYgQXVUR7EmOK\n64BAt6e0W5fjP1yc02T6cWiXVBVTE6k2VrMhkmfP3R9ALZnI0MFxhvj+6nJeOnGLJCHPi6zTF3RU\nXv76b+EW89us5wLBT3/6Ux49esQ3vvENvva1r3H+/Hl+/OMfn/lBHj9+zKVLl5b/ffHiRR4/fnzs\nZ/b388uiz2QhEEQ8yujmiHoVgiAiyxupwzZ/OIghfLPYZGiudteWouDqEkri8iqXy0tgzXqxnuMw\n8aC7m844SWZmCIKAXDCwjZUWHab/1ev11DNlWXfjuzQEjXbhmGDxQmPOYgTOo2Fsk+cGi4HqzkUm\nWfMxFmuRJQtBcHGRuLiiurdQEChIM+ZmXJc/ThoaDqGu1oMmYdXKF44RuBOdiaQsve8zWaSobGgM\n13YgzfIqpZJEgRmOG3ju0X0eWnmmYFXSF/py7+eAYqWmMu1n68zJC9Z7kq5xCdff9/1jGUFFqaDR\npOnu5X4G4mcvyQgKrQKSF3eW1gKBZ9E5n2DjkXOaJY3KokhhImNWVs5i8uy5z0YIrfhaBOnNbebz\nFbCHzy9JQfW7rkf2+RcEgktvf5Of/uf8f89tQF8oFCiVShiGgWma7OzsBHNMz2gn7cmeTIfL+973\nv//95f//rW99i29961sne5DFgo6M4XIj5gEBrAKOqnpx+TP38QAxssnTOfsCTAqMijNg5aVGddJy\nxoudfPb/IAKVc+m02GIxkC4NI5g3ASAJU2YTldCfDz0KQRDW1hGEpqu/SR2du8O7XO9cz/3cMmuo\nlmYE7tMhYuNkHlf5yibTn/uBq5Ohw2YFigGqM5V5JS7sJpuWFYQpxrhINL/kJNKQKIjUlFow/OML\nMoKCbTKTzjBSMGqhFFFa9RsKVdput8sHH3yw/Kgsb2IYn6R+hSRMMScqMtnN3ZSJwuylKRD/eb/f\nZ3d3N/fSqVQVZr1ssEwyQfdQo9CO//5w/Q3HQBTEYwPqI79N2f5s7WfW1REIgkBBmGGOVUJBK3d/\n+j5j36N97Wvxn0ckmdyCyonMqDQBiqlngqAvWaGTBr1QelaUrVR8LHzO5fs7IxC89957vPfee3z8\n5DNefiIB2awg92b/2te+RrFY5Gc/+xk//OEP+S//5b/wB3/wB6d+kNC2t7d59OjR8r8fPXrExYsX\n135mf3+f7UQaZWjf//73l/93YhCAoIqmWGQyPEgxAsdxGI/HNCODcbN02CTCN9RGLEtgMgFJgUcZ\n3QXXVRf3PnyPyhpnMrmJJW+Kpa2uvuhBOC5YDPChUaPqT/mLu3+69nOhvNBoNDAMAztSCOcfjhAj\nBz43WAwUyzD2gL2El3cMI5CnMnbVxvZW9Dvp6YruFFOLxzqypKGsxnONYoOR7H4hj8v3fUqujXGS\nIfXrLDKl7CxtJvB9JM/AGgaAlNncbSKjldJ7cwnEOZdOuSIy6WXvqVTWUG+E0I3/74Z7/zg2ENrA\nbaNad9d+JrrPk04cloWAh9VbOZO5QLC/z8SH7vavxX8eWYu8gLGrS/SLq/VMJo/4fQ1xM51tFc1K\nnE6nS+cbVucoFiM4Q7D4W9/6Ft///vfZ/uoO/6uQP843Fwj+03/6T/z7f//vkWWZ8+fP84Mf/IB/\n/I//8akfJLTf+q3f4rPPPuP+/fvYts1/+2//jd///d+Pfeb3f//3+c//OeAvf/VXf0Wz2WRzczPr\n130xq9cxes+WmzFc9OFwSKPRQIoMxs2q4PSPRgjd1aImPYDhEIp1NzbIPrR1QNB/8HNqYv6UsNgm\ndl1E18TqrTzQ6EE4LlgM8FkfbFHh/c/+r7WfCzejIAi02+3YYfAWnUdDCxu6WRkSUFEYMwX899+P\n/0MkRpDFCLShSKXp8TDyS2Pa92I0o5WQk2U5eHchy0wOsI92IB2JVm6190ns7vAuJXeOra6Ptxxr\nkTYTyXGVWY3nUkAwneIXVKxngeeXdem6eoEjNb03l0BcrQZFAV58JnKp6DEdZO+p5AXrD1aNCEML\nGcFx8QGAkeMwdDrUnAN6s7QXHtq6YDHjMa5cwX6yksHygMC98zOmLrTLcec0KQ0lGUFwxAUe+asi\niobaQLf0lbqhaUgX0kAQzRxKPnv4nLGsoS/gqBzc22cqVXL/PRcIvvrVr6Z+9i/+xb8484MUCgX+\n+I//mO9+97t8+ctf5p/9s3/Ga6+9xp/8yZ/wJ3/yJwD8o3/0j9jZ2eHll1/mD//wD/kP/+E/nPl/\nb63V65jDo6XGHC56aiOR7XX5Aw1xMw4EUQ9gOIR6k+UQkKgt5YksIOh9Sk3Oz+CJbeLJBF8pYz1d\nbfIoIzhJsPjBkcusUOLxw7/GSwxCD83xHEzHpKpU48+/MH+kIUYO/NrMDLeHKohM7vw8/vOINJTF\nCIZD6LSEGLDGGIGu4xerqznOC5OkEoKg4LrBOrfbbYbDIZ7npYfThJlDZ4wT/PDvfkDFtaGanV55\nYjum8VwyayjVZkLX8YrVYC4B8VhKaIYmclCc4SVk2OX6i2KgPyby1kuFGbrnQUYCR4oJ6mOkC/Gq\ntfAiPQkjuGcYjOZttgs+f3HvL3I/F66TYRg4jkOlErnsdB2/WIvti7y9aXzyV9ge1NR4gBtVDQDR\nsjKloeEQqg2Pe9bqrMuSTLFQZGIv1m+sU7iUruCLZiXmAoH5xYPFxtyAvs1UzgeCfPfz78G+973v\n8b3vfS/2sz/8wz+M/fcf//Efn+yX5bVPPIk1GtjDHo12XBrKAoLMVtSahnThxvI/s4Cg1WI5xi5q\ny810/nzqxQ4m+9TPV1PfCS22icdj/Ep8kycZwXFA8KTvYSolrkkyf/fs7/iN87+R+oxmatTU2jJW\nkzwMgq4jXYy/h9DbXgy3WpptH9AolBjd+Ttixy2UhkSRl19+OfUMwyFsdoTYesYYga7jV2rLyy9q\nIZAXCg0KhQK1Wo3RaESr1c5uRa3rkAFGx9lnP/ozXndtZs3sgqsT2zJr6Aoja0Tr/CmlIV2HyL7I\nChZrQ4F60+eZbXNBjUuLy/0fXjxhPYJnUxYN9GYD7tyBzXS/odgFOx0vO4+GFjKakzCCz2cmI7vN\nBnP+t3u3+YOvZMvS4bsLnz0WU9R1/GoaCO7fT/+e3qOfUW6L6ZhkpB1Mt9vl8DAOvMuznmD/4XNV\n5SqiMUZ6KX1XRaWhEzGCp/ndQ9fZjx79iO6sjKlWIKeG4oWtLObOnbN/t17HHfZTMYJsRpDhdY3H\nMYRP6vHDIZxrC6eThiyLoa9Rr+RfJLHDtjik0U0eixEUj48RHA587GKZ3yhdWI0ITFjy0Ea9Ut/3\ng/a6iQOflzlk2wfU1RqjvUSNyjHB4uEQLnalfEawKKxLMgJIx3jC54+2oo5NKTsDI/B8j4PPH1N1\nHarbF079/Zgt1iIrRhBepKHkEKQ3T/G8yN+9GEqzBIKMS3c4hKsbhRiwOo6DvsiXXz5HZC3m80Ma\nxRajupp59qJSmztzkZwp0oUcaegEjODjI4uZUqViubl7E1b7PJNNZpyRPEbQG3xCTc4J9EfaTGQx\ngo22kGL/4XPNe3MKkoG0kdbno9JQ8vlTjOCMMQKAW3u3aI5F7NIZpKH/39sXAYJGA1dLZw2dRBpy\nZy6SG9/kST1+OITtrsg900xlQeVKQx99xKhbpFXKZzlJIBBajWAc38Kiz18sFBEQYs3woub4PtoQ\nvEqFl6UGt+/dzvxccrZsVKd2Bg4FcZba5HkBY9s+oFnbQBs8iZd3LmIEecHiwQCubEjLiyscShNl\nBEIzGwiyMoeyGs99kSllv3j2C7bN69TdOd2Xrpz6+zGLSENhjCBsRR0W2s0WTX1W6c1Hq+/rOrQa\ncSCIXLqOE/T3u95VYsAaHcgEpFJIbfuAVqmLVhIgGeMhDv7WYwtZMRASY1SXweIMuSppnxza2NUa\nhYmNbuk8GD3I/Fy4z58cPkk7EbqO0I6fkUwgmM8ZmM+oq9nFctHq4qOjo9g/hUAw932G85VMG94J\n1r5FQZqmUmlhvTTUbkN/ENnnX0Aaun3vNqWxg1vJVxteWCBwfv7R8R/Ks0YDX1s1vQovrnxpaAUE\nwSafxTZ5ljS00RapSxLPEsHHXEZw5w7DhkyjeAog6DSYH83xnVUL51jDtjXy0L5lUZwp+NUqm47I\njx/9GMtJX6TJiyR6kVqPLQqymdrkeUVl83lwmYyunl/lRMKxjGAwgOvn5OXFNbEnFAtFCmFgfbEW\n1mMrBbxJIP/7aDx3a+8WLXGbujNn+9q1U38/ZomCsmgrasiqJUjIQ7qO2GksZbJkc7fRKHAur5WL\nMUaQAuHEWtj2Ae3yFiNpfiwjCC6/WWpfhM++ruFcaHcPHfx6HXE65+bVb+U6KhC8v0dHjzIZgdht\nxCTDTCD47DOGF8rU1ZyLck2biUAaEoJB9pH1DN+f9diiIMxSs8XheGnocBTZ52fcmwNjwMeDexR1\nG6mRH796YYHA/rtHx38oz+p1BH18QkYQ9yjtxzYFyYht8rwYQTjcOmq5jODOHbSiT6uUaL8QsRQQ\nNOrIXRn7WbDRk8+/Dgj2DIPSVIFGDWk84ssbX+Yn+z9JfS6pMUcPg/XYoiCmD3yWNOT7PrZ9SKt8\njtHOhfhlcoJg8ZfPK8uDlqqWHY8R2w0EScDV4nnSedJQ+JxLILDO3nju1t672L5Abe5y/tql47+w\nzhLDaaLPCSfIHBqPEToN3ImLZ3opGSbcm9cig+wh7URkA8EFRu4MPvpo1ZNlYc1Fp2TPW5wR0l5w\no9FgNpsxmA2OBYKHPRe53UCeFXj7ylfXykPNYpP93n4mIxDPNbEPbXw3cBAygeDOHYZbFepqzkW5\npvFcuJ47pVI2EOxbSO4kEwiSWUNJaehIj7y7s9YR3H+PX7vyD6lObIRmPgt7YYHA/Hhw9rasjQbS\neHqiGEFAvXv4i6yaJcJHNnlZLmO7NrYbXMjLzbEYqhK1GCOIan537qCJLq1yfrpsKkZQq62GdJPe\nTOuA4J5pUpgqFFpNfG24HBGYtHWMwH5sI/nTVLO3LGnIcYZIUplWqcPo0kYcCBZecNb6Q/C7rm4U\n8Bb0OxUADddiW03JQ0kgz2o890UYgeVYPPjljxgKIvW5S+f8+VN9P2WJrKHwOfMCxqk6l4WDoJxX\nsJ5YqRhBdG/eTQBBbO1TMYIDGqVtbM/G3tqAu/H8fkkKsk41LTgjojtL7Ysw/fhQO1wbI3B9n8OB\nR6XToDAT+Z0Lr3H73u3MGdwQvL9no2eZjEBoNpDbMvaBnVrLpd25w7Ap5ctVi32xnDkesbz1DN+f\nvW8iOrNgcRIWFqv6vp9a/3YbepPIuztjjOD2vdu8sv0PKE7nyJ18teGFBYK+ugkPsnXDY61epzCZ\nnYgRiKKMJNVxnOBms/YtJGcSAwJBEFaTrmA5GDzpJUDkIqpWwTQD0Rbgzh10z6Jdzi6giz4nsAyE\nqRfVpQYaNq0KbV3AeM8w8PUCcreDr2vLoeFJO44RSE7a88sCgnDoeUNt4qeIywAAIABJREFUoG02\nUozAH4+xbZtqxoEZDKDTEZZDalKMIFyLTCA4vt/Q8t2dAQh+sv8TvmdepGf71C0otvMZ3YksMqXs\npIwg1sUysRZJRhAm2+0k2GpKGsqIEajqVrBWb3xprTxk7ZuI87SDED7/kX60lhE8siyqsyLFbgNp\n5rNRLFBVqvzy8JeZn28UGxzqh2knYpFEoGwry32RBwSjokezlJMtFgbwGw0mkwnzSCwgygii6xnu\nqfm9Ab5aDpAyYaJYRJLKOM4wM0YwnH1xRnBr7xbd9g2Kho26kb83X1ggOGheOnvAuNFAnRhLD2Bd\njADil0mwySepyy8aMF5KQ8VivjQkCKvD1u/jmTpT16VVzvcoM4FgOw4ESWkor83Enmky1yXK5zZg\nPOYbF7/BLw9/mfr82hjBvoEwN1LeTlaMIBx63iw2GbVK8XdXLoNlca7dTqXvhU5WqbRiWClGkHHg\nQzuxNHTGmQS39m7x3dkFdGOC7IJQzgk4ntQWz9BUG8v9tK6WQFG2UoyAWg1lW8F+bKcCs+HePK8o\njByH2ULiyWQECSAI35/22k7m2QsZlv1gBLKanoW5eP7BbLCWEewZBi2jSGmzjjh1se0D3t55O1ce\nahab9Cf5WUPqtrqME5TLgaoVO5bvv48u2DTzZNlI47lkQeVaRmCNcB4N8NfUloTvLwsIYvv8DEDw\nSHvEwBjgSCqqNae4mZ8W/cICwZNi7exAUK9TnNrLRa7Vggvn6GiUAwSry8R+NA4KbhJTk6JUfp00\nVKlUcF0XwzBWdO/OHeyvf4mZK6/NpshlBI8tLMvCMAwaa4LYUdszDGaaSHmrS2EKsuDw2xd/m//x\n4H/EPpcM7EUvovmDIX6xHO8bRHaMIHqRjGQvWPCQZgsCbrnM5Yy6kGi5yLGMIMKOQjtOGvqiweJb\ne7d4Sa/gzsaMFSE1UOjUtmiBUncLQTM8zz2mzUSizmUBijFGkCENiYLAlUiAMzNYHAHFkNE1i01G\n17OdsNABcB4O8atpNgDB+g+N4VpGsGeaVGdF6hsqgiBgj59wc+cmt+7lA8FgNkif3cXgpqh8mip4\n1HU4OmLkzGjnOWGJNhPR9c+LuYR7yn08QFgTpA3rlJIxmnYbdDuyz2u1IGPAyy78zLLb927z7Svf\n5sh4QtGeU9nKX/MXFggeie6ZgcCt1SibzrKKMMwpPzqaZwJBtILTfZTuLQ45QJARLI4N6AgbWr3/\nPvM3XmLqrtEpWS8NRRvOZT1T0vZ0C3cOSreObBaZzw+4efVmyutKepRRacLdH6ZaDUO+NLQEAmsU\njAOMvD+nVOJiRopdKLNBnBHE1ikSL0kWlZ2qFfUpgWBkjvjg6AO0iY9nmejyF+g6GrVaDXEcDJPR\nLf0YaSiDESyAYPZ4xnQ+jVXLxoA14qgcFyyOMbrLm2sZgftkADmXX7fbRbf0tft8zzBQpwrtNnjV\nIu7wEd++8m1++OCHyzhc1JrFJpqtpRmBpgXsPyEZxs7RL3+J//prjOfmFwKCK8Ui+5bFfHFRh3vK\nOxgidPL/1uD9PUsBca0GtqBRVxbflaTMau91dmvvFm/vvM3IfErFMahc+BUEgn1PPzMQTEsSbVtC\nFFZ/frPpYxjFmEcdWvQycZ8MMzd5EgjabbioqvTmc8wEii83U5QRvLbFxGEtZV4nDR0dHcXiAwBN\nNT4yL7Sx4zBZDNMQGnVkQ8a2n/HWzlupOEHSo4wO6HCfDhGa6bXIkoZiHqWZBgJLVbmQoSlHL66r\ni5hLKv0w9IIzGIEkNfB9G9cNLry1A+xPKQ29d/89/pfNr3PfcfEdm7HynAr1E5lDx7eijjCCyL7o\nP+1TVaqxfR5eXBB3VFLSUEaMYAkEnQrs7yeGFC8cgJ6HPxhn7guAjY0NJs5k7T6/axiIY5lOB/xa\nGXf4hE65wyudV/jp/k9Tn2+qTSbzSTYjCIEgr5bg/feZ/9Z1Zq5CMy91OwIEyYBxuJ6KKLKlKDxa\n9MNqFpsMJ0NEdwLtdUCwyXD4AFmWlw3nIHBOS60Rqh9Zp1M4Kr7vc2vvFm9dfYvp7BkVd0rl/K9g\n+uiB3Q8yF7K6mx1j46JAw4pT+FptTqNxObPtdSgN+a6P1xshtNKbOAzu+X6Qq91qgSQIXFRV7ucF\njEMgeP997CsNJo63ljKH+8QwSDGCrPhGXrD4nmmybVdotYLyeXkqYtsH/PrWr/Ns8own4yfLzyZl\nGEmSaDab9J/1g5GIGWuRJQ3N54coyuYqMLu7GytMMmSZrQx9PeXBhtJQMmsoBwgEQUCWVwNcsuoI\n6mo9aBJ2yuE0t/Zu8U+k17l//Q1Ed85M+YItqENbyDLh+0uOq4xLQ1up9NEwRjA4TKdpxoAgwgjW\n1RH4voPjjJDlbvBMzgReeQUiLbEh+L29hy7FlpUrh3S7XQzPOFYacvVC8N5rNdxR8PflyUONYoOZ\nN8tlBMnYURII7BuXMDw5H5xOwAggkIfCOEFDbTCajCi27FRhXdQUZYuDgweZadNqQ6PgnA0Ifnn4\nS6pKlUr1Io2ZRUPQkFq/gkDQo4935WX4+ONTf1dTfBoJ/KhULKrVy5mfD6Uh+8BGrWVv8jAwO5mw\nLAICuJYRJ4jVEgyH8MEH2OdkJnP72NL75SaOBEjtJzZHR0cpIMgLFu+ZJpt2JdjAjQbSDGz7GZIo\n8e0r347JQ1m9ajqdDk8+ehJs8gw5J6yGjRKhmEeZwQgmoshmxCMKLQoEl4tFHpkmw2SLgog0ZD5K\nV1JHGV249r7vL9cybBJmlORTA8G39Q4H7S8he3NmyhkH1ictUlSmWVpMaktKQ4VCG9fVV20mIoxg\nOBim9lMy5nI3jxFEYgS2fUSh0EYQpNWeSrw/WOS+73sUW3ZmJW34/JZgHRssNoZi8Jz1Br4WVPPe\n3ElLlwDVQhWn4FBP/m9qGjSbsWBx+JwxIHhlg6kr5oNTAgii1cV5DKtZbDKajSjW0wWXUVOUTY6O\nMmogALmmIc7PBgTv7r3L29feZs8wODfzaKJl1jKE9sICgV7Xsa997Uzy0FD1qJpxuUZVZ1QqFzM/\nH14k1mMLNWeThzJMdGNA3EsILcYI7t6FbhfNH1AQJRRp/fzg5SZeHHipJCFVJZ7df5aWhnJiBHuG\nQccoroBg4i3lhbd33ubdvXeXn80addjtdjn47CD3wBcKqwlLoaWA4PXXA49ygRZjYKOYvkhDmQ1A\nFUU2FYVnyYKkxVrIXRlv6uHO8ovKVFVFVVXG43GqA6mu+Cc+aPv6Pr1Zj8sPNXRhE9V1sDKA7EyW\nkIaiQJBkBEGbiXOr2dohEFxQGY7TQdmzMIIwPgARuTEDCNptGDzzUBv5QFBr1xA8IXefjxwH2/fR\nhwLtNgiNNv4oAL5vXvomv3j2i5RzI9oick1Os/k1MYLRiKAO6c4d5pdqTNfJsjmMwDSDDKSQyF6L\nZA41i01G9gilaq69gBVli6OjZ5lAIJU1MCPfPUUtwa29W9y8epM906Q28aj4k8x03tBeXCCo6lgX\nbpwJCAaSjWp7qxx+oFAYo6pbmZ8Pe4LYj22KjWyEDw9tFhB8vg4IPv8cbtxgMN2nruQ3hQotCQQQ\nzKk9vJ/Oo84DgnumSd0oBRdso4E0tpYX5dvXgjS9sHgnjxEc7B2g1q3czZXM157PF3UEoYTWaAQ3\nx717AIw8j05G069kk9mdUolnxjBVWUy9jiAIsQyR0PImlaVaUaveiWMEt/du8+2r30a480tcE8qe\ng1POaVFwWksUlXU6EJKArDYHsVqChTQkFkXMpkldjO/VpAd7zzRxXJfRaEQ7utARmSwEcSCX0UHw\ne/tHfnD55eyLYrOIOM+/dvYMg2ulEoOBQKcDYqMLYx3f9yjJpczMNt/wkZITnUKNttFAqkvgg6M7\ny+ccDoGHD6FaxVamTBz3xIwgBIJwLUP82YlKQ8UGuqejqNntJUJTlE16vaNMaUgoaXjG6RmB5Vj8\n5cO/5M2rb7JnGFR6c+aiAnlN9XiBgWBSnGC1rmc2wDrONFvHLMmxQy+KGrKcnUccaMwHWPsWSsXK\nBILwgkteXNci9Du0WNbQgwdw4wZD4xnNYj6FDC0LCNSLKof7aSDIm1J21zAoz5QlIxDGJrYVtLjd\nae1QlsvL4p2ROUpleHS7XQ4fHeauBcQzh4L2EsFlUiwUEQUxaIZ348by/Q0ch2ZG0U0KCIpF+sYo\nnTUUWYt0Cml25lC1GrShtu3F+1O8EzOCd/be4ebVmxgffURrNqLi2VBfL+ud2BJTyqJrWavVsG0b\nM7KnwswTILYW1nmLmhO/kKPrWZEkGoUCnx4dUalUkKMXReTSiQLBMu4UvrtItW8Yy1h3+ck1GbL7\nIAKBbHlZKOE4gactNJrIRnFZ0JlVT+BMHIRSgg0YRpBpowYpqJlFZe+/DzduYNsH6LZ9bGUxZANB\naNci0lCxUETwBQQ5u71EaIqyRa83zGQEvqLhTCLPdEIg+Mn+T3i1+yqtUos900TuWZhyPhuAFxgI\npvIUS70Iv/jFqb87MkeYFTVGs3x/gChmF1yEwWLzsYlSWs8I+v14O/triUITSDCCx49hd5fB9BkN\ndX1HRlhs4oG/1MVhAQTPDk8sDX1uGCiTBRDIMqgKzmjV6zyUh+bunLk3pyzHg7idToejJ0coReNE\nQOC6YwShgCSV48/1xhvL93dkWWQdl2j6KAReVyxryPcDQF8UtWUBQd4Q+2gr6maxSV+yg3U9pnWJ\n53vc2rvFP2z8JvdqNXbmI2q+jRx90C9iCWkoyggEQUjp1Ms6F8cJ9IrFcBZjw6BixVlm8vLaKRb5\nxZMnaY80FiMI2BxE3t2FC4Gs92yVsdRqwWgiIMuzYGEzTCyJuDM3t13EXcPgvFUJZCEheA7Fqizf\nX1acwB7beEoiv16La+LR1OIlENy5A7u7TM3HOL6X2uextcjIGorKlrAqKgv/tgCER2tjBLJ8juFw\nnMkIXHmErZ+eEdzau8Xb194GAoYl9BysY5zMFxYIjIKBPSsHKWyJ1rDHmWZqzKul2KI6zhG+n715\nJamCIEiYB0NkxchE+DCIliVl3DfN2DSoGCPo9eDGDUZmj+aaFtShtVqgH5qBEL+ISKvbambnzqxx\nlY7v89CyECby6kJoNPCGaSDQLI26Wk9pr91ul95Rj4KcDwRR2SXqUYbPlQSCQ8OgmnE5ZDGCqR1p\nQT2bQbG4rGLNYwTHDbFvFpsMvWnwezIGCkXtzsEd6mqdy4907v72b9O0DqhhUeyefqBNpkWAQLM0\nGo3gzww7G2xsbCSAYMEIQkBcvC+jbVCeri432w5+R3SI106pxEdPn6Y90mJxObozFiMIg8WCEHt/\nEKylNpMoCNNcILAEC8ESmE6nmf++ZxhsGKWVM1WroRilZQzk17Z+jYPpAY/1x8vvmCMTR3LivygJ\nBJEU0iQjGEz3qSnlzIxBIFgwwwDXjYFwElTbsowkCPQXknPVrOI7xwRpRQVdV2i30/ElW9QwRqeP\nEby79y43r94EAobl913m5fVO5gsLBGbBxNy3YvLCSU2zNObVcmxRbfsA112P3Kb+JLPbJuQzgook\n0SoUeBxJc10yAkWB2Qzv2kvotkGzuJH6vUlrt2H2TI89g3pRpa+lgSDZDA/gkWlyTpbRF3UEwcO3\n8EdHS0/mzatv8qOHP+Jomt0TptPpMBgOKIhGrhYcZQRhfCC5VuG7832fp9MppYx5wVnAatnj2JjK\n5FpkVRcfN8T+NEVl79x9h7d33oY7d7j7+uv45mPqnkVp4zkBQdhmYvFMYTVsuJ5pIFj8fYtYSWhG\nw6Csr4BgOAzu5+h9t1Ms8vnBQdojDVugjMfZMQII3l8ECNpt0OcSkpcvh2imhoqa6usf2p5pUp+V\nVu+8Xkc2lWUMRBKlVIPEcX+MJ3jxYrMsIMiRhoazpzTyOo8m1mKdNATx5JDKtIJg62uBAGA8Vmg0\n0lexhcZscDpGMDSGfHj0Ib9z6XcwPY+RNcYfibiV9c/wwgKBVJboP+invJKTmGZpeLVqbFEN4wm2\nnR+sVZRNbOMgs70u5AMBpOMEy800GECphO31sagdmzoKwe82DvTYBaxeVBlMBylpSBCEVArpXdPk\nWqkU28RCo4k8lXHdRW+bUovXNl7jfz74n5nP1O12GeiD3LWAOBBkMQLN0uD6dXj2DH1/n4ksU8io\nmkwzAhXXma1aBuvptbAepaWhZJuJ6BD7sAOpZmqpQqose3fvXb5z7Tvw/vvcvXyZmf2MumtR20rr\nvGeyjFbUnc46IFgwggQoTitTioNVJlbWdNedUon7BweZGnUoD+UCwRtvxJywatnH8kVEc5zLCDRL\noyyWU108Q9szDCpTNQ4Es8IqKwr4zrXv8M7eO8v/7vf7lMRSPJtokToaWgoIBl4ws/LVVxkawfS1\ntbZ4J+VyGd/3mc1mmUAQZmJ5lkd1WkWYjY8FAl2XqNfjbNjzPUxvzLgXOV8nAIK/uP8XfPPSN1EL\nKg9Mky+rM6RJ6dj41QsLBIVqgcP9w7MBganhN+oxRjCZPMIw8vPAZXmTuXXI/0vemz1Jbp1n3j8k\nMhPIHbnXXr2xu0VSJJta+FFjWfZYpCRbluXxeOw7R8wf8F175opzMRH+H+bKnyO8jhd5JI9EyRrb\nsrVREpt7b9Vb7ZX7CiA3fBcHyAQSyKwqipow5TeCF8zOQqGAc87zPs+7hcbBh58T2FsIBK44wVSa\n2N+HiKjq1a3EmYHArHg3fHQtSmMQHHCaDxjfs7MyPItY01DMjMdrfunSSwIIAhhBTsvRNJuEAjqP\nOub2YMVBMgvETwOOsgxPPUXlu98Vm7bpj2fMH17KxABZoTW2NeE5L/g8wWLnPp0OpE3z9HGV+lDn\ne3vf45cv/DK8+Sa7SpYqLVLjAani6YzuTOZ0u3S9u1xuFicolUoeIJjGQOaAoK/2UauzNb3o4Dqs\nBGetOPchYgTi/XnW09zeG1YGpKQR40ZzKSNIRVKBjGA4mbBnmsjdyGwPpdPIfcm3Nr+5800mdmv4\nWq1GQk5442FzjMAXLK6M4PJlJmHJbnlxCpuzn4UTo6lWq4sZgWEwOByQklKE2p2lMQKAdtsinR56\nPusOuqhynEbdlUBxBiBw2kqAANWPRLuEuuGl/Y7gQwwEoXiI6nEVa46ensVaZgsp7dXb2u1H9HqL\nc/jDFLGyDUK9duCLTSkpesMe1drYDwRzAeNkMslwOMTY2QHLEkAwiZ06rAMEEAyq3nsw0yZRoihz\njfDAHzDe0XWuxGLeIGwmg2qkPa0KXrr0Ej/Y/0EgOKUnaVqhFlIn+FmAt82EO9jou6dnn6Xy2mvI\nuZwPCIZDoY27f0XbbBOJpGYpufPS0GZQsLjAaNTEsoR26/aozysN/fPjf+aZ8jNkIkl4912ajQjH\nFqRHA2L5xbMkzmVz0hCcgxG42FE33EU5nK2JQCCIxagsGBHqPAt3jMBZ5+PJGJ58UtTB2Gx3sD8g\nHR0zabSWMoK0kg5kBLumyaqi0KqHPIxA7uNptb2tbZOL5bh5dBMQNRDpaHopELgdhGwWGk0JnnmG\n4fAEg8zpTlhAwHgRsO7oOuaeSSaSIdzpncoIms0RyaQ3LtUyWqSVjLdC/wwxgld3XuWzl0R8YMcw\nuBTpIPcl5NzPKRBYqkVbaTMsX4Pbt2eRtDNYy2ghaznPhm80dmi1FjcNC+l5wpsd38Ez/XcpRFpJ\nU2m3ffR7nhE4XkXNvu/B4Ij+JHrqHFcQB8K44b2HxqBBRspM86TdNh8wvqfrXFZVb8ZDJmMH5Gab\n7cXNF9lv7xML+4NYST1JW2r7vHG3zccIAoPFIIDg7beJlko+IHBadbg17ZbZIhZNe4HAdfhFihFG\nrRETV8GgJMmEwzmGQ3H4/DRA8Op9Oz6ws8N4ZYXh4YgTQyY9HJPI/5RDaRxzB4ttucPNCIrFIicn\nM6lkWkcwdzJ1pA7KgYI1EbJDkDS0Fo2iN5ukAzq/kkphtZoMh7UpI3DWedtsiw68V65Mx46aeyaZ\n+ASp1VwKBLl4LpAR3DcMLqmq9z7TaeTeyCMNgS0P7Qh5qFar+RMjml5Wom6pU8kwkYDhSGLw5HMM\nBkcYpE7fewHVxYsYwX1dx9w30ZQM0d7yymLLsmg0DBIJLwt1mj16gOCUtblT36E37PFM+RlA7PVt\nuU20PyKS/zmVhsaRMX2tz6Ahw/b2uVpNNI0mkVx+iq79fp/JpMNwKDIrgkzqZJFWmwuBAMRhUuk2\nT40RgB2wvHULDIOBvk9vLJ+JERQKMJmjm7VajayS9XnCzj0FMYJ5aSjaVz2MICpHuZi9KDb8nMXb\ncTrjDtbcIey2pTECxRtwrN69i7qy4gOC+dRREO8urWRmQDAHRlJIQllTMA8Wy0OlUml6kJ638dw3\nd2bxgf0XX+RCLcRJXyU1sFCyP9sYgRsI3AdpOJxlPNaZNCqeB9YcNMlEMgxPhJMUdHCFJIl4t8so\n6D2m04ybB8hymlBoVmOwKGBs7ploKQu5s1gaahpN8sl8IBDsTIvJXECQShHqDrz9lPACQbVaJZ/I\nL2UEkWKEcXvMWB+LtGG5S+PCDQaDQ/RJ4vS9F1BLsIhh7RgG5p5JUU0xkfC1rHdbt9slEgkTCtU9\nnzeNJrl4hk7HVfd6mpOy8yovX355mv10T9cpSy0iholS+jllBMPQkE6iI3S/c8YJWmaLqFaYPtRa\nrUaxWEDTpMCh6wBUs0jFxqlAUO8HA8E9V34xQCGVohoOQzLJqLm7vMTdZfk8hOYkmUqlQi6ROxUI\nLMtiR9dZl2Ke0ngyGSK9sG+zXdAucNg9ZN7GB2MS0QRWq/W+00en3tszz1DZ2yOxuiqAwPWMgjzY\nltEiq2ZmDCvgfQTHCWZFV4uAoGW0ltLv4+4xD5sP+eT6J+GNN9h5/nkuNyWqukLakE7Vgs9sNhhl\nVDGcZmJNPMA6DwSSJBGNlhjX9j2euOhTNFsXQQcXQLTTob8ICBoHnncHiwPG5p5JKW2IdxjQLgTE\n+yulS4HS0H1dnzICd4wg1DG8HVaBX7rwS/xw/4f0Bj2xf1PFpUAgheyisj0TLIvcpEJ97Wk7Pqee\nSxpaBgSbdsfh3p7BqhJHTyxvGSNae2R8f58zWS6TcflH6fRSaegbO9/gc5c/N/3/u/0+GnUUUydW\n/jllBBEpQj1ZFy/2nEBQ1+vEi2vTh+p07gwcY2fb5CALWm0pEGSUDO1B03d45cNhLMui7mppkZck\natvbkMkwru/TGgzJLxqV57JkEuKjNqPE7B6q1Sp5Le9rrQDeDqRHgwEJWWbcCXslF00j3JN9i7EY\nL/Kw8dBX/GPummST2aXPYp4RuGMEnq6omkZFVclFItN0WseCgKCu11lNFBbGCCA4cygaXWUwEKCW\nz+dpNpuMx2NvsNhoLgxag91k7uIvEw6F4eZNdq5dY7vboWnESQ+spb1czmX2oRMOhYmFY3QH3aWM\nQPx9K0zqBx4gqOt1iqXitBFf0PMEoNGgtZARHPmAYFHA2Nwz2dDamDFt4YCeul5nI7exWBqKxajV\nvNIQnR6DwZFnHSajST6+9nH+/t7f0+v1KKaXAwHY8tBjE46OKEg1amHRwrszCp++984IBLIksaUo\nNB71KakKvdjy1uQCCHLecaP2c8rH897ZHs78kgAbjof8w8N/mAaKR5bFI9NE1tukrTbRws8pI4iH\n4tSV+owRnLGWQB8Kzzyq5acP1Q0E8+2THRs9zDCJnIhqygXeTkLWiKZa086jjkmSxJW5OEFhMKBa\nKonNVj+kNTDInaGgTJKgFGvTl71AUCgUghmBMvO+g1JHAdGPpWf5FqOFhRySea/6nudzY9dgRcsK\nz28B7T1zjACopNMUul3fIbwICDaTxYUxAljECFYx7TYa01barn5D03ta4g1M4wMggGB1laJRYzSO\nMpGkpRLAucxVwOQwlWWMQPx9ZazayRQInHWubWhTUFzECIxajZOAWdGkUkyaJ4GMYMroHCCwLMw9\nk7VsGz262Pus63U2C5uBjCBQGkomkfp9ZGLTNhOOfe7y5/jqG18lm82SVbPeGMFc+ijYiQS7Jty8\nSSE7plqTMM1DOiNO33tnDBaDkIf6+yYFVaGjLp9YJ/Zu2eeE1fU6uVjOCwTJJPR6gVPKvrf3PS7n\nLlNMiMw1p16oUdPJhVs/v1lDqUiKethmBOfIHHIesKRpPkYQNFDFsdHdNAxPsNLphd6OikayEOxN\nzgeMC+021UwGMhms5glNs3smIAAoKm06rmZilUqF0krpVGnoXlB8AOzGc6PAxfjxtY/zjXvf8Hxu\nPjbZymcZxWILn0U8LrTNXq+HZY2R5dlh7QMCRaFYq4mN66K+gUBg1NlIFOhNJrRHo8CAdRAQKMoa\ng8FszoIjD00ZgbsZXsAisCxrFh+oVqHdZicaJT6qEJ1M6Ckf0FAaEKM/EwnodgPbTGiaRq/XY+AK\naEWjK1iN2vTFOutc3VSXAsFwOMTsdtkNakiWTmO16h42B3Pvr1wWacD7+5h7Jiu5Lt3w4sBrXa9z\nYeWCD8gc2dInDdnPIjZewTQPPD/z8uWX+dY736JQKPjbqSxgBMZjA15/nXw5QrUq2q+3h+NzAcGy\nYDGILMHx/oBiLELrFN9AyNKrDIc1LGvWNbdu1Mmpc0CwZErZvCx0b5odOCIXWl7dDB9iINBUjUao\nIajexoaI8h4fn/pzzgZxv9izSEOD+yGiugLpxR0moxMNVVsCBK6Acb5SoRaLYWUyTBo16nqLbOxs\nvWry4TZty8sISpsl35hG8G7anaAaAgBN83Qgdayu1/nM9mf4+s7XPZ+buyZbRQ1znvq4TJLEIX58\nXCMaLftGaLqLfypA8eAAryC6mBHkY/lZSm6QNBSQQuqWhsAPBGpYRQ7JDNLJQGnozeM3iUfiXMld\ngZs34bnnuG+ahK0KCQZ04x/QLALHAvoNOQdCKBTyDUiJRMrivm18c4lsAAAgAElEQVQv2FnnblAM\nep7VapVsPs9O0ICndBqr3VgeI7BbTVg33xAxgkyHdigYCCzLoq7XubR6yQcEleGQsCSRi0S80pB9\nH7FRwfP+AG6s3qBeq5PUkmcCAg8juJCcAkFrMDg3EBwfi4SCREAN6iVFJXwyIqfKNJXlfavE2VMk\nHNamWW0we3/u9z69j4A4was7r3rjA7rOEzYQpKXTaxk+tECQjWVpTpoYj4zAvieLbAoErqDgaUBg\nWRbGYwN1kGeSXLzhQ8MM0fQZGEGzSaHXozoaYaXjTLrh6XCUs5gmt2mMvYygfLEcyAjcevy9oBoC\nsDuQ6mIKmztYq9f57KXP8t3d76IPxb1PzAnD+pCtokZ/SVtbEJu5Umn4PMr5IreKYVDc2TmzNJSL\n5bjitPd+H9IQ+IHAua9uPBy4CP73vf/NF574gvgfGwgOqn3MxDHZsIGRPL2F+LnMKSpzTSlzd5/2\np5CuQKvjB4JNZSkjODk5YbVU4jhgpKpTZe2LEcxPvnv2WUbff5dQPERBadMKbB8IvWGPiBxhtbhK\np9Nh6Er5vqvrXI3HHUUMz7C6VArFzPqAICSFeDr5NCNl5L+nufRRAGVLmTKCwrX8FAiaZv99AMGE\noGJsgCvdCEZKIjWYUIv6U7rd5pw9821QAqUhCIwTVPtV7tTu8OLmi9PP7uk6T6gyzaZKyjq9uvlD\nCwSFZIH2uI25a4o86TPGCd4PIxjVRoRiIdRRlklyiRdsaoSTC4DAXVT2xhvkL16kWqsxTsrQS5xZ\nFgLI0KY29DKC1aurp0pDO0E1BACahtRsIctxRqPZA6jrdba1bW6s3Jj2gDf3TZQ1hZVEnG5o+fLJ\nZqFS8R8k895btdmk2GoJ9+q8QPBTSEOVSoVkUpSgGIY9nCYeCmQEX7/3dT5/+fPif15/nfrzz5M9\nsWjnKuRkg+ESpvi+zPb8ghgBBPcbCrV6gUDgBIsXAUGpVGJbUXxdckWgtut/f4rmAwLzRw9RNhQy\ntKhPghmBc0+hUIhcLueZq3Cn3+cJm63m83OKYzqNYmo+aQjginKFZqh5NmloU8V8pMPBAYXrBapV\ni8HgkIbRPjcQ1GrSQiDYqoWoFSBujKmGF+Sj2zYDgpWzAUFACuk3d77JL134Jc+wn3u6zpVIj35/\nm+R4cXafYx9aICilS/TGPaSkxLAyfP+MwLI8MYKgYLHx2EDdUlHNNOPE4kdm9TVC8eD0Lg8juHmT\nwlNPUavVxPV6yrmAIGm1qZheIFi5vMK4O/YUUoFXhlkWI6DV8qRYWpZFw2iQVbN87vLn+Po9IQ+Z\nuybKpkIpFqN9SrvmXA6q1b7vIIlH4gwnQ8yRia7rjEYjkk8/LYIKc0Awf3A57++ymxHMLfJoOcqw\nNmQymD0LIQ3NMk8cj1qSZjn6mqrRiOHzBtpmmx8f/phfuvBL4oObN9l56ik+2ozSilXQpD4T7fTU\n33OZPUbLCcwmEjPAcu5/vro41DZ9MQJlXWFwOGAysgKB4Pj4mFKpxBPxOHcDgCDU0QNjBJ7A7LPP\nYr5zgrKhkBo3qY6WA4Fz/25py5EyfLKQfR+KmfAxAoASJQ6sA5LR5ExutKxgaWhLwXxsYD31NIWy\nTLU6AiQaRpPsGXsNgZN1FqZQCF7/pWPYLVmEO32a0QnmaPFc9VqtRj6ft9uEzGJ05wGCb+x8g5cv\nvez57K6ucyHcQe+toYx60zbti+xDCwS5RI5oOspoYyTkoTMGjKeLUVFEIMowTmUE5mNx+EWNBOMl\nCsCop2EpwYxgXVGoj0bo47EAguefp1qtMkxMkHrhcwFBfNTm2JgLFpdLRNeivhRSx1OqD4eMLItC\nJOI/EJJJ6PeJSLOiq86gQywcIyJH+PyVz/ONHREwdoAgH4nQGHtHQs6bAALDBwTTZnhmi0qlQrFY\nRHr2WZE66gICH3NhgTQ0BwSSLBFdEbOcHZPlOJIUZTQS13fXEhSLopO5pmrUoxPfIvj7+3/Pixsv\nkoja2TwPHrCztsYTzTAtqUaWLuHC2d/fmcxOYXN3IF3aZiJSQu6Mpoff1PuOhojkIrQeDZAkmJ+m\neXJyQrlc5olYjLuu1F1ATH3rmqcyOq5fxzwao6zKJEZNTsxgUJwHAvf9O9JQYIprOk3UiAUCQb/Z\np1AscL9+f3ZP/b6YszEXwwqnw2CNGT35CfJ5qFRGjOSV6Tpfaq4DOBqNoijrvv5Ajk12B3RWZTr1\nOoNU3NcK3m1uRuDO2lsKBJ45KpaID1yZxQfGlsUDw6AkNRk1cwyjCRFoXmIfWiDQFA0lo9Av9UXA\n+KmnxNjHoKCXy+rGbDE6L/c0IHAYQcSIMYwtPvwGbY1xJBgIZEliW1XFBKPXX6fwqU9RqVQYxUdI\n3TOkr7lMHbQ56gpdfDgc0ul00DQtMH/e2bRORbEkSX5POxQSAblhbuqVuDftjdUb1Po1HjUfYewa\nKJsKuXCY2iltPbJZqNVGPo/Sua+WIYCgUCjAc8+Jh38OaWjHMBbWMpwmD7mBoFAQiUCaqglNt932\npOh9fefrfOGKHR946y24do2d4ZCtaogTvYs26RAtf0AtqB2zU9jcMsx8mwkPEIzSWGGmKazuda5s\nKhy/OwjMcHGkoScCRqpayQRyb+RpGAgBQBCNYuauoYSbxMwWR4YWONvHvabmh+s40tAiIIjoSqA0\ndHx8zCeufoLv7X1vdk8BqaOOqbE25sbH7HduoZM7296b88Tj8S0SieCZCsYjg9BWlE6jwSgZ981Y\ndps3RnAGRjAXI3jr5C1ikZhIYrBtzzQpRCJIoxMmjTjDM0w+/PACgaoRTUfp5/qCEaiqaGt8ygxj\n92J0JJEzMYIthageZRRbfPjpjQzDUDAQAMKL7XTg9m2Sn/wklmXRCfUIdSfnAoKo0Wa/I15uvV4n\nlxO6q7qtimfhsmQ0SW/Y406/y2XbHaxUhBfssUwGxchMvRL3cwpJIV6+/DLf2PkG5q6JuqmSkSRO\nThngIhbxGEVZ9/2bEzB2GAHPPy+mXS0Bgok1oWUI3XxDUagNBlhB+hGnZw4FMYKMmqEx6ohYhb3Z\nLMvif9/1B4pv9/uUKxJHjTDZSYdo4QNqOOeYzQjcQVA3I5jvQCp3JoySMB6Lw8n9/pRNhZO7w6VA\ncCUW80lDw9gQuS8RCnmTGHyBWcBMX0bpPybcbdKSNOZVpvl7cktDE8sSwU1bGvL1v0unCevhQEZw\nfHzMrzwt5hP0hj1Gk1GgLOSYMj7C1K5SKECtFqZvZd4XECjKBooS3IrEfGwS31YxGg0mqWTglEDH\nnIFS7hiBe53PJwnM38fX7nyNX3vi1zzXdCTgweCASUthnPg5BoKMmkFOyHSTXZEJAOIw+clPlv6c\nBwjSaSwbCPL5/KmMINyXGcQDVrhtvZqGweKXfllV2Xn4EC5dQorHKZfLVIdN5O4Z8pgdG42QxwMO\nmiKtYnqQQiAQOE3C3mlXuHIqEKQCGQHA5698nq/f+/pUGoqPx1RMk9FocVaEcGqlQCBwvMrp/T/z\njAAC+6SbTGZN5xxrGS1SSgo5JBOSJJ4ELFkOLPBbxAiczCH3QeqWhqZFZTYgvVd9j5AU4lr+mriI\nDQR3dJ10vc9JRSM37qMWVhY+h/dl9mJ0e9/LGIHUbDJOR6aHiQ8I7o8Cq4rdjGAeCMxoi3Df8o3u\nDBqBasorKNX3oNlkkswE7qNFjOBgMCAdDpMKh4MZQSpFuC8xGBz6qtyPj4/5zNOfYbe9SyqaEr2x\nFgHBcIjae4Ahr6Fp0O2G6YzSZ9t7Tg8q+/eHw2VkOXivG48MCpcSjOzMpUVAYNnxyXw+72EE7nV+\nWozg7+79Hb/6xK96ruvEW0xzn1BbYnKGWdofWiDQVA0pJtFROkIaAvjYx+DHP176c/OMoH94SDQa\nRVVVP/ra5jACuQ+mEkwHAToVDd1aTAOvxGLcOzmBGzcAWFlZ4cRsEukOyalnBIJOh0kiRa0u0ioc\nNgOgXlAxHvq9dE3VuNOuLGcEmoaixwMPEhDFO99+8G30XR1lUyHU7TKOLx4wAs5ZFjkbEMRisL4O\ne3uAWOuJxHQCZeA9PTMcYi6QABalkDrSkDv9cioNKf7qYocNTOsgXn8dy2YE0d4JjcYq2sgkXvL/\njT+VOdKQKzA7HyNwp4/SbDJJK8FAsKFQ3R0vZQRbqkplOKTvivsMrBOsSEhUs7psvg4EwNRTKI9+\nBK0Wk7S2GAhUPyO4a8tCsKANRjpNqGt4YjyOHR8fs766zsuXXyYSioj7WgQEt26hZIeYJxahEGQy\nfU46qbMBgSyLNWo/C0kqIkkBhwUCCDavpJBaLSQteG44QLvdnp49bkbgfnfLYgR1vc4bR2/wme3P\neK7rMALT3MdqjU+tKoYPORBMohPa4fbMC34fjKBzcDA9SItFAQTz+qbDCOTumIHSXjh4u3WSpjdq\nTwdmzNvVeJzbhiH0cKBcLnPYbxLtnqGgxTFbE3fOXzcQKNuKjxGAeFb3u4IRWJYAglJp7kuZDBFd\nWcgISokS1wrX6D3soWwqYkhHOs3xkiK+bHZMqxVfHCNwBYsB0d/evt6y+IBjTxoG3UUSwEIgEIxA\n0zT6/T6maXoYQctszSbaI+ID07TR8RjeeovqU08BMDKPaLTzZM0RsdLawufwvmwuWAzLGYEAgnjg\n+1M3VWqHk0AgcLKGZEniohPDss009xlnVB9NdtpQO+vcsiyME1AffA8aDeRcJjD7blGw2PFgAW9V\n8fQXCi9YUbxFgYZh0O/3yWazfOHKFxhOhuJZBdQQAPD66yhXUlMFQdPaVLrq2feeyxufTHKMx0e+\nrziZe09spgh3OshafmGw+OjoiNVV0brczQjcz8kptp+GrFwxgld3XuUzFz5DLOLNAHADgdQ1CWV/\nzhnBKDyiZbVmjODZZ+Gddxb3kiaAEbiAIBoVhSzuNPKJOWFYHRJdjRLq9Bkn5OlIR9+1q2HikTjd\ngb8EHOB6PM5tRZkCwcrKCge9Nkr/fEAQ0tK0WuJc8khDSxjBo26Vy6pKrydytH0VkZpGpCcvZAQA\nv77x60z0CZFCRDRFy+W8XumcpVI1ut2ip4Wx+56aRpNqtToDguefnx46y1JHHXvCMGgsyI9WNmb5\n89PPXNKQJEnTw2iRNNQddPn+3vf59xf/vbjAvXtQKnE7EuGZSQzSdVpmkpwuE8r9jILFZ2xFLQ6/\nVGCMR9lUqJ1YPmC1LGvKCABf5pBp7jPJpnw51eGQd50Pj4fIqTDy5XWoVgnlljCCAGnojq7zhF1B\ntih9VBS2rXmAwMl4kiSJz1/5vBgM1a8uZgQ3b6I+szJNqMhk6lS60vsCAtPMeOpSHDMeCafxYixG\nvNtF1nILGcHR0RErK0JSFMOTGljWyPOc7AbFs0Qh1z187e7X+NUrv+q7rhNvGQz2CXd7RPI/x4wg\no2QwJZNat8a4P2bcG4vT7eLF6aCMIJtnBPrJiWfEY6kE7rPNKaCSZEl4wZmCp0LVseFQsMagQJpj\nm5EIDUWh89GP2r+ryEFXJ9YfnQsIpHSaVErsfY80tKli7plYYy9jSUTTdM0W64oSLAuB3Yo6tJAR\nAHwu8TmqmaqQSVotooXCUkaQTB7S6QRX3fiCxQAvvDCl3mdhBNv9PscL8qPVTXXmINjmloZgFidw\npKHpu7MZwbcffJtPrH2ClGJXLr/+Oty4wZ1+n2dbUeRLLbrjKFmD4KYzP405wWIlOFicy+Vot9uz\n6lw7Jzjo/SmbSuDz7Ha7yLJMwvYK5gPGg8EB5DKBeql7nRsPDdQLqgDyVotoSTsTI3BLQ1dPkYYE\nEKx6MoeOj48plwXbLCfLJCIJfrD3g6VAoHzqynRdZDIn1PrniM+5ZBnDSKDru76vGI8MlC2FsCSh\n9Xp009kzAYEkhQmHcwwGFd8698hD9rMYT8Z8/d7XffGBid2z6aISxjTrhPsdlFM6j8KHGQjUDIZl\ncHh0KKonnYDxkjjBYDzAGBmkovbGzmQYOOmLtvmAwI4PAMIbzxYDPQHHgw0KpDkWevSIKycn3LG9\nn2IxxlE/RswYkTutoMUxWxpyvMOK6/5DaohIPsLg0MuIpHCSkjQgJElLgSDUGTMcVrCsSSAQXNYv\nU82IcnZqNaKrq0uBIB7fp90O1vDdMYLp8//Up0RR2WBwJiBY73bZD2r2AkRXo4waI8b6TPOe7zfk\n6OyLGMH/uvO/+PWrvz67qCtj6FozjLzZQkcma1g/GyBoNGbN8CzLIw35qnObTcjmGQyOfes8uhql\n1g1RnCuAcrMBwBcwNs19yBUCqyzd63wKBM89B6ZJvJQ8FyN4v9KQGwhAjLD87t53g9NHLUsAwS9/\nFPNQOEup1AENQz83I5hMoNdT6HYf+b5iPDJQt1UYDlGGQ1qxxY6hGwhgNmnuVCBotXjt4DXKiTLb\n2rbnmvumSTYcJjKuMBxeIhfp/HxLQ2pYRZZkDk4OZn3GQXglC4CgoYtK2WngL5NhVK97gMA5FBwz\ndgXVA6DdRtbWAtPYnLS3oEDa1G7e5Jquc9um3/l8hForihmWyI/P2MLYBgKR/oZXWiE4c2goJyiE\nBDgsBAJNI9TuIstphsNaIBCYeybqlsrX7nwNajViGxtLpSFVfUi3mwjqmhscI8jlhG71k58sLSZz\nLN/pcBCPYwb8AkmWRArpoxkrcPoNOTEeJ4W0WJzVEbSMFmSzWI06X73zVX79WgAQ6DpbNRlDqxBW\nQRl9gLMIHLOlIVVWCIfC6CPd12bCk0LabBLKCp15fp2HIiFaikI27E199gFBPO6pJTDNfUKFlYVA\n4KzzKRBcuwahENl86FRG4DTNG00m3Lfbo8MCacjO2JmXhuaB4Hr+uphjHMQIHj8GVSW0tUokF8E8\n7JNK7dM0O+cGglYLYrEJ9brfCTIfmQIIOh3MZJJOaHFBmR8IRGW/b52737sdI/ja3a/xa1d/jXlz\ny0KGcZ2ycnp7CfgQAwEIeeGgfuA9/D72sYUBY9/hlk4zaTQ8B+lpjEDOrgdKQ24gWJg3/OMfc11R\npkAgnD6JlmKRGyyv/JvaHCNwS0MQHCfQQ3EyiM+WMQJaLdvrOggGgl2T9avrfPXuV6FWI7m9vZQR\njMd7JJODwKFKvqyh6R+gwve+t7AFtTu7Sm42sXI5f48c51IXVfQHs38Lh1NIUojxWGisDhA4Gy0d\n1abS0MneHTRVmxXqWJZYV88/z51+n+KxRSN0REEd0YtFF7bjft/mlADr+vRZLW0812wSyq9hmsHv\nrhVW0MZepngWRhAqrAdKQ4GMYGsLJhPy2jgw+84TwFZVFEXhnZMTSpEIcbvyNVAasqW6ZdIQwPXC\ndVpmi271wA8EP/6xcBIRUllvd59s1qA9bJwdCOxDuFqFXG4SOFxnyghaLcapFHVLOQcjEH/f/DoP\nkob+7u7fBcYH7roCxYZxiVykfWrDOfi/BAT1ep2XXnqJq1ev8vLLL9NcMAHqwoULPPPMM9y4cYNP\nfvKTp143F8/R0BuEN8IzRvDcc6KoLCC/3bdBMhmsVmsauYcARvBYVNIC0G4TyW8vlIbyeX9nTY+9\n9hrXVla4ZQOBpg2pNoe0VIj1lzenmlqANHQaI2haCvGJ+J0nJ4sZAc0mirKBae4tBIJrH73GzUc/\nwBoMyG1vL2UEprlPJjMM9A4zaoaG3qDb7ZJ1yyrpNLz22pmkIep1YoUC7823RnCexUU/KAYVlUUi\nIiA30TNTaeho75ZXFnr0CMJhRmtr3DcMErtjGuMq2YhJP/EBt6B2zGYFzppa2niu0SBcuLDw3TWs\nCNpc1b2TMeTYpqJQs1NIx2Od8bhLqLgRyAjc63wKBKMRRKOUBnu+jvD6UGdsjYlHZm1Fi8UiP9nb\nm8pCgZ1HYRolP00a0lSN7cw2Jwd3/Yffa6/BJz4BiLkE3cPH5PNjehP/s1po9iEssu6kwNRp45GB\nsq1Aq4WUyXBsRc8MBIv23jwQTNot7jfu86nNT/mu6c4Y6vcvkJP/FTGCP/iDP+Cll17izp07/Mqv\n/Ap/8Ad/EPg9SZL4h3/4B15//XV++MMfnnrdjJohXUrT1bqzwy+Vgs1NeO893/eDGEGo0/EAQRAj\nULeE5sdgQCSzvVAayuWWMALLgh/9iGvXr3Pb9royGZ1a36AXjyAtGUrtsVMYgbKt+A6/mqUQtoHg\ndEawiWnuBh4mxq5B+mKaz2kfx0wnKJXLSxnBYLBPLmcFAoGmatS6tWlV9NTyeXjrrTMDQaZUWgwE\nF1SMB0GZQ7M2E+6isn5TNMMbphJ0jh55gcA+SB4ZBuVIhNFDk2qvhhbqYaY/4BbUjs2lkDqMwMle\n9gBBs0mkeJHhsEK1f+J7d/VBhFTHy5ycrBvHQnYK6T1dZzA4RFFWkXwN8YUFMgI7bbNce4d5/6Bh\nCM/bPZeiWCzy9uHhNGPIcaZ85CqVgsGA6CTvccKCgKCcLNM93l0KBMqmgl7bp1AAnfMDQbUKKyth\nXytt8DKCSDbL/ih8ZiBQ1eC9FzSl7OULnw3sj3TPzsAaDA7o9zfISO1/PUDwt3/7t/ze7/0eAL/3\ne7/H3/zN3yz87qIc/SDTVA1tRaMRa8yCxbAwThDECCL9PmtrsxzweSAwHossAOcAjrpSEN3miREE\naYL37kEqxbWNDe72+0wsi3C4TigRQo9Hlw6l9lijAZkM+bzolRIoDbkYwdiyOLGiMBKpfmcBAsMQ\ni3G+I6PTXuKL+U9Ri1uUTwEC09wnlwsFBg41VaNheGU5ANbW4O5d6jV/3nsQEBTKZd6bK3hyLHYx\n5gMCNyPwF5WJZngPaBLt6p7+7vzwh/DJT4pAcTxO/0GPerNFmjYT7fSN9r7MVV3cMlrEYqKuycG9\neSCQsnmi0RKVzgPPc+r3YWRJhI/8QFCaKyhx5CHT3CcaXcenR9nmrHNrYnkOP4pFyo9/5GMEQY5F\noVDgzsHB8owhwOm4F+1EPTGeICBIRpPQbtNRXVLrZAI/+tEMCLYUjM4BhUKYgexf5wvNBQSFguRL\n4Z0MRKq5sibOi6imocsJGvpZGcHm6YxAljEUmS+v/0rgNW/bxXmmuU+7vUaaf0XSkCfNa8nhIUkS\nn/3sZ/n4xz/O//gf/2PpNV955RX2/naP/mGf7+x8x5squCBOEMQI1MFgoTRkWdaMEdhAMN/X3rFT\nYwS2R5IKh9HCYXZNk8HgkMxKCj12DiCoVqFYJJ+Ho6MRoVCIuItLq9teOeShYZBTs3RscFoWLHak\noWbvISEp5ClUsSxr2l7il1MfZTcsuj6enJwsBG/TPCCfjy5kBJ1Bxw8EhQJks9T39TMxgjWX1DZv\n6kU/I3AHHBd1IP1m48esj+JiSL1j9vu7o+tcD8UYDes0WyoZmkj5xaMZfyoLqCVYWFRmTydTlA0q\n3Yee51SpQEGbYDw4AxDYAePBYF9UhJ/CCAbHA+S0jJyQxT2sr1O++89nAoJiscij4+PlVcWOFQqE\nW6Yd4xE9foKAoDvoUhop/GPz5uxn794VoOrU22yqDIxDMgUZrJCvIGuheYAA1tbWODiYnQXmromy\nqiCFRXq1lE5zJVmgGeAYjsdjMVnQ9fyFNBTMCJx33h/2aUTGfKH873zXHNqB92vxOKa5T6NR4k3j\nkFf+6I945ZVXeOWVVxb+aR/YoNWXXnqJoyN/pd1//+//3fP/kiR56KHb/uVf/oXV1VUqlQovvfQS\n169f59Of/nTgd1955RWOvnrEG6++werlVcwDkRImyZJgBH/1V76f8XQeBUxVJTkek3flq7kZwag5\nghCEM2F4aDMC26O0LMvzd9RqooRBVjVuVW/5b9hFTa/F49zu9ykMjkiXk+hV8/xAEIHDw4Hn3kEA\ngfnYnN7frX6fS6kCzT1xkJyFEVS6D3ybdtQcgSSexepQ4d2Uypu1N4nFYjSbTa/OD4zHXSxrKDKj\nAgKHyWgSY2yQL87lCmoarK9TPxqeCQi219a4fXDAxLIIza2roBiBoqx6pKGgDqTfqH2f/2y4rjUe\nC8fi4x/ndrXKjWqY6JNdqtU1ylKDUO5iwAP9AMyRhoqar5Zga8sfIyCbRTE2qfT2yKWem17m5ARK\nZTB2vM9iESP4YbuNKe2jKGsBPQ6EafY6n8pCIIDg0iXS/98fMRhb6Lo0jXkvYgT7JyeeYjJf6qhj\nggITTYhkhnA4HQgETaOJZkr8r5N/4ov8v+IfXHsPhDQ0vHVMNLMK+hllIZimbi4Cgml8AKaZS9dT\ned4Z9hlNRh7HolqtomkaEdeUvxkbVxcygld3XuW5ZAxt4Pfh7+k6m4qCGgphmvtUq1k+K434jf/6\nXwXTBv7bf/tvgX/aB8YIvvnNb/LWW2/5/vvSl75EuVyegsTh4aFv8TnmeObFYpHf/M3fPDVOkFEz\nKBmFo8qRN3/+xg0xm2CuX/78YjzWdTKS5NGo3YxgygZgyghkOYVlWVOvZHrt04LFtrQAMyAYDI6I\n51PoyjkZQaFAPg8nJyMPmwGQEzJyUmZ4IrTLW/0+11LF6T0FtpeA6bxgVd2k2tv3xwceGKgX7WdR\nq5FZu8jf3PobyuVyYMDYNIVHWSpJBCRXEJJCKJJCujgnq2galErUG5IHCJx5t565zvU66WKRjCyz\nG9B+PFKMMNbHjDqzxIH5YPF847lkNMk/d95B7boOzVu3xJD2XI47/T4XT0JEr3Wp1UrkaRPOLxhV\n9dOaEyx2FW+5vcPp/U8mLsa6Sa137Hl/JyewshHCeGiIaX62zQeLQVS/v9fvnyoNOevcAwStFpRK\nSGurlLIjDysIAoJcoUCrVuOS3TTwNEZArTZNAXbar+dcP5BRMzT1BkrP5K/3/57h2NbvXXsPhDQ0\nkiuEEjJWP8cp3dRdNyxOZMeZ8jGCx3bqqPMsMhmuJZJEIwnRDM9l87IQQDicZTIZ+ta5Gwi+cvsr\nqNli4Hnxbr/Pk4kElmUxGOxTrSZRzH9FMYIvfelL/OEf/snWdo4AACAASURBVCEAf/iHf8iXv/xl\n33f6/T6djjhce70er776Kh+1K3AXmaZohJNhjo6OULdc2rimwcoK3L7t+f78Ytxvt0lYlqf3fMGu\nnxmPXfEBmG40SZJsecgbJ1gaLB6NBDB97GOA2Gy3ej0GgyNiuaSY/fs+gKBatVhf9zc7c6eQ3ur3\neTpT9gBBICOwN6NiFaj2jnybVt/RiV2OTf/YjYvP8lfv/RWlUilQ6nOAYGVFNBUNMmWikCzMVQZr\nGlY6TV2PeQ6F7qCLGlZn4/iccV2pFB9JJAIDxpIk+QLGbmnIqajt9XrTWgJzZLJeuoxkWUx7Kbs8\nytu6TvkA5Itt6vU82Un3g29B7ZjDCBSNpumvLp7GODqdaYc+Rdmgple9Ds8xlFclwrmwZ1hPECN4\nKpHg3X4f0zwQ0pBzCi3oQOpjBJkMPP885VjLE2sLAgI0jVinQ9R2xJYCgc0InL13YncEcDtxmqox\nbDeRFIULxSf4zuPviH+YYwTRchQrWaU7iBIZ5QIZa6DZ3sIyRjDvOF6NxZDDKd+ZEAQEkiQxiWyg\nylHP2EnnFYwmI75656tkytu+KWUA7/Z6fCQenzqp1SOQh0ZAPxm//V8Bgt///d/nm9/8JlevXuXb\n3/42v//7vw/AwcEBv/Zroiji6OiIT3/60zz33HO88MILfPGLX+Tll19edlk0VQNVsAxlW/EGjD/2\nMREgctn8Yjw8OWEQDkN31hsoHBZruV6fYwStWRrWfIUqeGMEDWMuOvrOOyKTyf75a/E4D/sVJEkm\nnIrSkUJnAwKnY1yhQKEArVY4GAhcKaS3+n2e01bomB26vTHD4YLaJ0mCTAa5O6Y7DpNVvQe0fs8L\nBOWtJzFGBjEttpARRKMCCA79sXUAwqMwanYu9VLTGIVjhKwxseiM0fkOEmfMmiTxkXj8zAFjtzQE\ns8O0UBCPtqbXeLL4lKcVNa+9Bp/8JN3xmNpwSGxvRGi9TrOZITPUUYsfcMM5x1zB4oYu1lRgvyE7\nPiD+vk0aRtPHCEoliF2Koe8IcBuNRjQaDZ+0WIhEUCSJjrEngEBVxaaYA1pnnfuAQNPgYx+jbB35\nGcFch109lUJ1HWiBVcXTG5sxgsHgwCcLgWApoXYHK5PhS9e+xFduf0U4DG++Oa0hAJBCElK5TqMy\nQbVyBGSBLr6HU4BgXhq6Go8zCSen78+xICAAMKQi2tzec4DgXx7/C1uZLWK5UjAQ9Ps8accHotF1\nuoddJonUmWpc/q8AQS6X41vf+hZ37tzh1VdfRbMX7draGl/72tcAuHTpEjdv3uTmzZu8/fbb/Jf/\n8l9OvW4pUcIMmxweHnqri0H0rfn+9z3f9wHB4SGGovgOYUcm8DAClys9X9gCMyAoJUqc9OYOxjlq\nei0Wo9F/gKJsIcUl2hZnA4J+X7zUeJx8HrpdhbW15YzgvX6fp5Ip0Yp6r0axuGRd2AFjnSzpiDc1\nzdgxiF2ZAYFUKPCbH/lNWnIrkBEMBsKjXF1dzAhkQ0ZOzRXSaRpGo89KpAZvvz39OCg+4LiPH7Hl\njCCbDxjPg7i7uvjkZMJua5etzJanFTU//CF84hPc7fdFjvZ9AwrHtNopNHNA/GcFBLY05F5TbplA\nzM5tMq5Wpy0uVHWTptENBAL1kop+XwBBrSZSd8Nhf5jwqUQC3dybtQ8PkIece/JJQ5oGL7xAuXv/\nVGmoqWmEXNcNrCp2zIkR2NJQEBDIIZnNSYpxOslvXPsN/vb232K9+aYI3rm8H8uaYOUqNI7GJELn\nAAKHEVSsxYxgThp6IhZjEE5z3PPukUVAoJNHi3q7DDhL8a9v/Q1fvvblwLnFIBjBk4kEg4EAAuOk\ndaYW1PAhrywuJ8t06XJ0dCRSwtyFVJ/6FHzve57vzy/Gg4MDRvG476E6AWMPI3B2E/ikIcuaAUE5\nWeakN5dJM0dNt1SV6GiPiLLFODqmMZicDQgcVwSn8HRCobDl+5rTjrpqzykuRyKUk2XuHhwHy0KO\n2QHj3iRJOuJdGvPSEPk8/+H6f2B3srtEGlpbKg3Rg0l8rj2EpjGqNFnVdM/7+6mAwBUwluU0ljVh\nNBL02dHZi0V4cNClmChijI1ZK2rTFE0Mb9zgtq5zLR7HeGAwSu7THUbI6TLyzypGYEtD5WR5epC4\nGYEsy2iaRvvxYxcj2KA5MIMZweUYxn3D/swvCzn2VDyONTwiGrUBLiBzyFnn+kPdLw194hOUmnc4\n3p+J70FAcJBOo7sWx1liBM7eCwICgAuhLIOEytOlp8Xv+PZXPHsPYDA4IjRKUTlukgqfQxqKxSAS\nwah2g7OGHrliBG2RtpmLRAhHc9xteR1Hdwtqt/WtDOmIF5yjUVBVi79+41t8+fqXfXOLQaSJ39V1\nrtuMYDS6RDbUJqSdnjoKH3YgSJRpDptCGtpSvIzgxg24c8cj+wQxgkkqtZgRPHAhvCvKOs8I+v3Z\n3Ao1rKKGVa8maHuUjsmSxNORGn15nYE8oNofnB0IXCd5ONwikdj2fc1hBLf6fa7H40iSRDlRZuf4\nrECgkgp7A+36jo56eRYsJp/nF7Z+gW64y87uju9SDj0tlwUQBGWYDhtDBtG5impNY9Josrohnx0I\nFsQInGfhbjMhYjz+6uJCAQ6Ph/y7zX/Hcfd4Jg298YYYgRqPc6ff56oqvOrW4BFSPEbelD/4hnOO\n2YygnCiLe8KfxFMsFuns7k6BIBpdpT0coykzecHDCGxpaBkQfDQ2ZIiCLMdn9zF3WjrrvHZcm+0R\nRxqKxymvSBy/PcsSCAKCe4qC0e1i2DMQzhIjWCYNAWxaafREFEmS+PL1L3P8f77qAwLDeEhkvEG1\nVkVTzsEIAKtYJNatoGleILAmFuaeqx2NS0rOJ8q809jzXGcRI+hN4qTC/s2Szg6wukUBcAGjFB8Y\nBuVolIQsY5oHtFrX2M6eLVAMH3IgWEmucNI/IRKJYOZMLyNQFDGf4LXXABhPxnTMDhllhpCHh4dI\nmraQEfTv9ok9YXvBrt4M8/LCfNpbOTHz4Oj3BSA9+6znd1yWa9SkFfpWn8NmP5Dq+czFCAAsq4aq\n+mUJdVvFfGROgcB5Vo/rpwCBLQ11xxESoRmoTowJg+MB6qYXCOSQzAvXX+DN+2/6LuXkocfjQmae\n7ypiWRbdoy6DiB8IQq0mq9czpwOBfQCXIxHGlkUlYA5FcC2BHwhy+THdZowvPvFF8e4cRuAOFPf7\nfMRUQYaT6i6RdOpn04LaMXvDryRXAhkBCCDoHxxMgWBigT6GmDSLmZyciKSn2KUZIwjKGHLserhJ\nQ3ItlAUppCWlRKvcQo7b8p6r62f5yTwnd136/9z7G1kWdwyD1dXV6WG6NH10Lmvo6OgoEAjWJ0m6\nceFR//aTv03ijXc9siyAYTxCiW5T69TIx88HBEOtyOV0hVBIPPtms8lgMGBwNEDOyMgx17OwC7m2\n06vcbfsZQSAQjKMkw/72OHLmmBe1/yBS1uerXrFlIXuvDwb7tFoX2cqcrb0EfMiBIBlNYlkWpY0S\njWgD45HhlWRefHF6mDSNJmkljRyaadKHh4dEcjmfN14qwdGjMdbQIlKytfIl0tC8tllOzjw4bt4U\nk7fm5uquScfsWiU6ow671TbWOaUhy7IYjY6QZf9mcIrKbvV6UyAoJ8sctM7GCNpDSIRmB4n+QEfd\nVkWhzNwf/LlnPsejA387XidrCGB11R8wbrVahPQQzbnRg2ga4V6T1Sez4pnbuzQwWGzfg+QEjANY\ngRMsdq8Ld+aQEyx+vfbPSIS4nr3hZQR2oBhExtClYwn1ySHNpoWcjKDpY3/L4w/KbGnIWefdQdfn\nnJdKJfTDwykYNY0miXCYoacVw0waOgsj2JLrHExys2e2oKisGCrSveQawuSaDFb++CbH+7MDbf79\n3dN11hWFzY0N9uzxpEHDiKY2lzW0iBGUxyotRazT/yf7UTarA95d8UotpvmIeOYidaNOKXU+IDBT\nRS4mBdMJhULT1HhPfAA8QHA1s85ux7sBFgFBZyyTDPmbKLajt3lSsauJy2XmK/be7ff5iJ0dZJr7\nNJsbrCX/jTACSZIoJ8vktnJUehWksMSw6koKfvFF+O53gQUa5cEBSrkcKA0d7oyJX43PisaWSEPz\nnozbg5uXhRzLTg65My6IzAsUrAWN+DxmZwyBfZCGGuj6fIcuUfQlRSQeHrqAIFHmpHcGIGg2aQ2G\nxKXZMzF2jFl8wLI86R1fePYL9Bo9jrozrdeyxgwGx0SjQgMNihPs7e1RjBdngOm6B8VosboWEgew\nDeQ1vebNOpnTEa7H44EVxmEtjBSWGNVnh1JQUdlf3fpLUtoAWbfZnEO/7fc3tize6/VYP5SIfrRB\nr1ckpEyIDSdn3mznNhuMJMuaOhfzZ/La2hrm0dEUjOp6nUxUxTTF0JTJZOY/RMoRxr0xo/ZoKRAo\n42NaoRJ7Tm3GglqCwqhAZ8Oup7GsqS4OUP7Faxw3olNNcH7/vdPr8XQiwfr6Ovv7+0wmM+YSaDYj\nEDGeEUdHB4FAUBxFaShC1gy9fpPKhRJ/fs/b0sYwHpEoXaZpNVlJZ88FBL14ka3YTPJy5CFPfAA8\nz+KZ7AaVuQSSRUDQGoyJSx2P43Kndodh/CGp4TXxwSmMQFQVl9lQFuWK++1DDQQgDrj0apqjoyPi\nV+Pot11o+uKLInPILkZyL8ThcEij0UAt+VOxSiU42p3MZCHwSENBjGBeGpoejC6P0m3R0T4/0VP0\nh33i+VWkTidYSHebixEcHByQSJgLA13qBZXG/b4HCGrm0enSUKtFc2AQY3baeALF7bYIhkRFnvPm\n+iahXoiv3PrK9PvDYYVwWCMUEt8JAoLd3V02tA0PgIgbV7GQWM8bHka3LEYA580cWvMVlf3le3/J\n+kqUYTtLb9BjmE4Kr+vxY3jqKXZ0nVI0SujxEPlKlW43QyrUEe1BQj+jbRSJiGfd6UzlxvkzeWtr\ni8HJiQcIsmoS0xRedqMhEmaiUeE4xS4JhjTfcM5tprlPOLLKO87zXCANZftZ2iV77/R64pfY2Wal\nG+scTwrw6BHD8ZD+sE9amQHm2zYQbNiM4OREnJvKorEcmQz0+0jDIYqyxvFxMBDkTJlKxHYGX3uN\n6Iu/wF+8+xee7xjGI2LJC3RSHUqkzh4sBlrRImtRPxB4GIFlidoOO1Pphfw2Hb3CxN7f7lnL89Y0\ne6Qi0rRVOsCfvf1nPPdEiaNDe50tYARPuhhBtZpjRTpegqxe+/ADQbKMWlA5Ojoidi1G/47rMFhf\nFz1t7971VxUfH1MsFgkFBF6KRTg5ZgYEpimKi+zNJssZLGvMaCRe1nz+sydG8IMf+IBgPNaRxm1+\n0hmRjWUprKwycXcTW2QuINjf3yebHS1cxJFtBWt3wGVbkiony7TGZ5OGmmYX1ZplPun3/IFix9Lp\nNIzhT1//0+lnblkIFjOCC4ULvrQ6gHZIYz3RPB8QnCNgLDqQioOyVCrxYP8BWTXL5qpKtSpRSpRo\nx0OwsyPamkcivNHt8mwyiX5fR9o4odWKk5YaGKkz9ql5v+YEjJPCucjnxXJ1iuY3NzeZNBpzQKBN\nGYFL0RTP4rIIGC9jBKZ5QFLd4F2nNmNRv6GmRjNrM1lXLQNAviDRJs3wO9+nYTTIxrKelizzQLC/\nL7brQpOkKSBFo2scHwcDWcaUOJFt0P/BDyj/8q/TNtu8c/LO9DuG8QhV3aYT77Bixs/FCOpykRV5\nBgROjMOTRtvtzuovgCuZdaRBgwfGLD7jzFr2XV+vk48Vp+/Psiz+5O0/4VeeeZJpglKp5AGCiWVx\nq9/nI/E4liWmDFarKYqTI7H5zmAffiBIlIloEQ4PD4lfjdO/PXcY2IdJUOro6upq4ClVKkGtKRG/\nassuTg2B/eIkSSIWu4hhPAACGIETI9jfF7v2Ix/xXN80H6OqG+Qkk6SSZWVlhUEsdnrm0BwQFArS\nQiDQ18N8pBYmYnur5USZnnQc3F7CMTtYXNcbaEqS4VAseH1H99QQuP9YSZJYWVnhJzs/4dDWQc8C\nBLu7u1xZv0LTaDKaeINjzUmGFbUpakF+9CMYjc7GCBYUlc0zAlW9NH13xWKRw6NDfuvJ35oWlZWT\nZRqKBQ8fgt3r6o1ej2cSCRFvKBxxdCSRtOqMMsEzkz8wsx0VJ3MoEsFuLyL+eWtri1CrNRXX63qd\nfLywEAicgPEyIBgM9ikmtnnHeZ6L2kycZKjHbYCYGw8ZCkEhaVD5P28HyrJvz0lDBwenAAFM4wSR\nyAVara6n665jKX3ModwXXvk//ROhX/xFfvvJ3+bP3/1zwG6eaAogaEfblFqxcwFBhQIFy88I+rf7\nxK7FZs/C1fGzEC9gjbrc7Ij9vUgWAvv9JVYwDPH+3j55m96wx6efvjwDglQKe14mALumiRYOkwmH\nGQyOiURynJyE0Iyjf1uMgKQI/MavxdHvzAVa7HqCoNTRtbU1giqeSiWo9eTAjCHHVPUSun4fCAgW\nO4zgO98RB8mcdGAYD1GUbS5HRkSiacrlMnr0DP2GXOmj+/v7lMvBDd0Aqitw5WQWGC8ny5jh0xnB\nuNlgOB6ixTemXnNQDYHbyqUyv5D/Bf78HbHZpn1qbAsKFu/t7bG1sUUuJuI7jg0GUJ9o5EL27ODN\nTTGf4BQguKCqVIZDunP9pcBfXRyLXULXRcproVCg2+zyW9d/a9pmopwoU1FGYl384i8C8KaLEYyT\n++zthSmEKz+7FtSOBdQSbGyAHV9lc3OTaK/nYQT5+Mr03c3r7rHLMfT7+tKsIdPcZzt18VRpKLWf\nohZxzUyea3dcLsPxDx743p0xmfDQMLgai52dEcA0TtDvl8lkVGTZP9Uv3h+yK3VE2/dwGC5c4Lef\n/G3+4p2/sBMsakhSmBEKo9CI/Cwf4Ux2NCqSHQYAwa0+8eu249j2BmnlkExMyfCD6mNAnD3LgKCY\nmO29P33nT/mdp36HjfXQDAgkySMPzccHotF1jo4g2Tv+t8UIhspQSENXY2dmBIeHhzNGMHdKZbMW\n3XGIyEUXEMxtmljsMoaxY19LHHbTe3IYwT/90/QgcZugphfYCJmMwylWVlboyfK5GMHBwQEbG4u9\nmZ3VCZv7s/8vJUqMlQr5QsAAYccyGUaNGrlYDlXdwjR3scaWCIRdDJaGQLQWfyHzAn/89h8Ds9RR\nxxYxgs3NTa+MhvheX9EItW3JYcH7m08xkSWJJ2Kx6RhQt80XlUUiZcbjPqNRmx+d/Ag5JlOiNK0f\nKSfLHIXslN5PiSlQb3S7fFSJY+6ZDOU99vZk8nId62eVOuqYu5YgAAhWV1dJDIcMnOEuep1icmPq\nUToZQ9Nnceks0tA+19KXeLfXE/JggDRkTSySD5NUJ/YCnJOGAMoXYhzvdKk3Dz3v7na/zyVVJRoK\nTRnBmYDAZgSdTpZ8PrhxstIzeCy1mfzjP4i9J0m8sPEC3UGXdyrvTPdeQ2+QDWcJP+5jGEL9PYvt\nD4qkBrNNt7a2xv7jfUatEcq6HeAIOC/y8RKvN8Q7OY0RlFIXxd6zLP7s7T/jd5/+XdbW4MCdgeoK\nGL9ry0Iw23vHx6A2/w1JQyvJFQzZ4PDwkNgTgvZaY1fQ9bnnYGeHevsoGAgC3NVxdUhaGtGa2Kmj\nAS073Yzg8WPhuDo23bRLgWCbomSghxKUy2VaknRuaejChcWBrh+sDsjen3nH1igKZpqJEjAcwDFN\nY9IQB64zqczcNYkUIrP86AVAUJbKPGo+4m7trt2wbFbfsDBYvLEhMqxcmUOHhzCIa7PCgxdfxPre\nd5emjzq2KE4w33hOSHuXMIz7/NGbf8TqxiqPHj2atqJeSa5wUHkwbTzVHI2oj0Zs1EJES1EM8yEH\nBxPyUotQblHi+wdkNiNwPyc3EMiyTE6WOXKKsow6hcQmo1GDycQMlIYa9xpMJhOSSb+sNZmYjEZN\nivE1kk5X1wBpaHA4oCgXOdbtdzcnDQGUVmSO125Qf+8nnnfnyEIggOz4+Ji9vcmZGUGrFUfTghMr\nQq0241SC+r98a7r3QlKI//jkf+Qv3v0LUUOgbE/Xk7GjL1K+Au1hr0i852UE+4/2iV+LI4Vszf/g\nYNr22bGN1Cq3msIzWwQETofdUvoJTHOXHx/+GEmSuLFyg3RaxIU6TtPjeUbgChRHo2ucHE2Qa35A\nWmQfeiAoJ8p0Jh0ODw+RYzKRcsRbWBaNwnPPUd+754sRrK2tiQdVrXpaVvfv9Mmr41mGVoA0FItd\nnsoLu7uiP/z0nmxGYD1+JIBozhyNMmP1aRJnZWWFupOWucgmE88hvL+/z9WrWd9IQMf+Md0nXB0z\n7om/q1oF2RAppAstk0FqtW0gEPTUEx+AQCAolUrUKjX+01P/iT95+0980tA8EFiWxd7enmAESS8j\nODyEScoLBPoPvysOb2eAyGQS6IE+FY/zdkCcwJna5m7BrKqXaHdv8T/f/Z88e/1ZHj58OGMEiTK7\n1Vm19JvdLk8nEpgPDZRrFo1GF1leQRt3iOTPlp73vu0URgCQBR7bJ4QTIxAB8X1/sPiCysHuASsr\nK4HBysHgiGi0jCTJPJVIiDhBQAdSfUdntbQq1rllLZaG1m5Qv/fWQiCIRqPk83kePBicmRE0mzKa\nZgR/p9Uimi1yfPOfPU7Y7zz1O/zxW3+MYTxEVQUQ5NN5jAcGhYJ1ZiC43ymitL1AcHh8OJOFIBAI\nLqZXOe4do4/Hi/sMjXQkSUJLXMI09/jTt/+U3336d+0ZLuKSU591jhHMpKEDTPMS5WgDKZlckobl\ntQ8/ECTL1Mwa3W4X0zSJXwsOGNcrj4MZQSQivC5X03z9rk4+PZl9FCgNCY9yNBLA7H7v8UiciCXR\n+vQnp5kDbnMYwWTUgXCKcC73/5P33nGOneXZ/1dl1KWRpmlmp/fZ3dlevLuui7ENxibGdrDBFBMS\nwNhJcOIQ4JNgUqgJJRQ7GGzABhuHFvd1w2WLt/fd2em9aIpGvUvP+8fRkXQkzezyvuDf72Pff+1K\nR0dnju7zXM913Y2xZDKP++WZ1yu1k02n501OTrJuXTnT01KX61ybjkYJqwSmdiOhc9mh9YaEszBd\nM9fsdtQ+X4YRRCLjytYSsCQjcLlc3LbmNh499WhBsLiiQlon5L7vHo8HjUaDzWZTptqSdnRHDhCs\nXIk7OE+ZPmfR9/mk2a1593aj1cqRzJYpaxqzBo1NQ2wmW3lsNLZyfOI51jrXsqp9FSMjI9lgsdnJ\niG9UurHJJCflQPFQBN3qRRYXnZSVtVEaD6KvvDDq/X9tcrA4p0hRAQSJBIZUiuG0s8o7XXnaVb7r\nqg1q5krnaKwpbE0CykD/arNZihPo9dKGKgdkQ2dDlHeVU6IpkUazFpOGnDBr78Q93qeoAckFAoDa\n2lrGxy+cEczPh3E4UiQSRRi014vR6mCGAHR1ZV7eWrsVjUrD8PyBDBCUmcsoKS+hzCouOE4w6rai\nTsSkFuhIjf9CkRDq1pyldGpKqRUDNZZqylI+ekKhJYEg+9tJz97jZx7n1tW3Zt5XyENpRiCEUDAC\nqaq4lVVlFx4ohrcCEKR3SnKFn6mjSMB4+3bc/tniQAAF8lC4P6ys2SgqDTURiYwxOZmgsjKzPmes\nOm7AtWNt0WvOpad1lgrmrFaGIhHlNi/fcmShRCLB3NwcDQ3VUvFbXiD2WCDARqsV80ozoZ7s0Hoz\nzqLpmhmz2dAGw5QZHJlB2or201C0RaR877fWbiWeihOKjCmAQKORCJWc8TYxMUFdXZ30WXMhI9CW\n5wCBWo17SzdlyWx/9qWa0mxKA0Gx0ZnG5mx7BZCAfGD2dT689sM0NTVlGMH8PDhNlcyE56XsDK83\nkzoaGY6gaZvH7XZgsTZji4YxVPyJOo/KJgeLl2IEXi8RvZ7xSUl2yF1MZCDIXw/mHHPU2+spZrls\nbpXJtGTmUPBMEPNqc1ayKiINOZ3g0tWlN2HZWEo+ENTV1eFyaS+YEUjdYisy0mzGUinw+7EkNLg2\ndira7KpUKm5ffzujuUBgLMPYZsRRkrhgIJhfUCEqstOrVCoVFfoK/FU5G5AijMBpdmIXfk4FgxcE\nBOHIKKV6G6urVmfeVwBBOoV0MhZDr1ZTnl6ApKriejpKLzxQDG8BILDpbcSTcapqq6Q4QWeRgPHl\nl+OO+yjTZlvRZtJHoQAIQn0hqlaolIwgTxpSqw3odFUMDc0p4gOyOT1xXGtbC15PpeLEYjPo9XW4\nw27arE5GDQZ6g0HE+YAgfQ0ul4uKigpKSkpoaIDRvA4PxwIBNlgsmFaZCPZID/LcHJRqnYWVvLmm\n1ZLQaanBmhmkrcgYgqKMoLGxkdHRUVQqFR9dcwPxZAytVrlQ58pDcqAY8tpxIP0Meqdd0ZzIvaWb\nspwpY0sBQbVOh0mjyeRr55ppZfZeAMRVlSRjE9y86mYaGxuV0tDEIq5STUaWOREIsDadMUSti7k5\nIxrDCsoiakoq3hxpSPbzUDxEXZ0kRwLg8RA3mxkbkzJSlEAwURAsBnAZXNTqi6+64XA/RqPkt6vN\n5iVrCWQgyADUUtJQwILbrKZsQXom/YkErliMFmPWp6qqmojF1Es3nJMtzQhcLhfV1SuIRPKAwOWC\n8nIq54K4Ogr/vg+v/TDx2ARC48wCQbuRUuIXBAShdFaqqqpSoSCUi3I81pzOANPThUBgcWJMeDkZ\nCCzZeVS+Jq3WSiyV4i/Wvl/xfgEjmJ3liN/PxpwW2+FwPx5PA83GtxkjkNtMOOocSzOC8nLJGc9K\nuePy4OhMQUqeiB3uD1PdrFHGCIoEXQyGFoaGFhTxAQB8PpwLEVwNhZ4djU6g01WjVpfgDrtZVVrN\n6Xgct8lEIv0wF7W8QLE8kKaxsRAIjvr9bLRYMK00ETqbZQTl+vMwAiBs1lOTNKLX1xKNThIeCimB\noMj0kNbWVgYHJU39z1o2MhpKkRLK7KTcW3w+RmBaXZZ+PAAAIABJREFUkQcEa9spc+VUfy/TpnKT\nxVJUHjKvMRM8lQWCl8d7aLEasOltGUbgcEgb2/JDfbgsKrDbSS4uciYYZE26hoCKGWZn1UTVZiqi\n2j9dwznZ0oxA9nNXwEVtrVSikkoBi4sIu53xNDLkSkORSKE0BDAjZqhOFt8thkK9mExSKwN5WllK\niIIU0gwQyEBeRBqS657cKxyUnZGePTnDRZOzW7dauzCbveefn5JmBC6Xi5qaxkJGMD4O9fU4B2dw\n1RX2f6q11VJjVPH78TOZ+eXGNiOWWOyCgEDu8KKSNURAJARl0TIWNDlBhiUYAfHFDBAUK4aTfztf\n1Md0OMFNHcpEk2LS0CG/n61pIEgmw8RiM7jdldTp3maMAKSbbKm2ZGoJ8hlBSqRY1CVxvHYAkBpu\nlZWVZQdH5zACkRKEB8PUdmnPCwRGYysjI8FCRrBvn7TARQuDv3KgGKQffoOjhuOBAPHKSkRmm1fE\nlgGCfPw4uoQ0lL/oFjNvqZ6aoBq12oBWW0p4fuqCYgThcBifz0eVLoo3aeP5wecVx/whjMBanwcE\n1aWUeeNZPWSZ7mSbrVYOFwOCbiUQ/PT0LmyaCEIkMoxGrRbSaV/pw69OkLLbmZqZoUqnw6bREOoJ\nkbROMT0dJ5BUUR5V/emBIM0IINu6xGiUVKv5ecDjQVNeztjYmOTn4UUcBgd6fT0+3wzhcMFGnYnQ\nBJXB4kwmHM4CgV2rpbykhP5wWCENxefjpCIpdLW6rE8tJQ25wG3XU3ZIGjKULwsB6PUtlJQUGWyd\nb2lGMDY2RlPTqkz6dsbGx6GqCqcriMtUKA8mEn70ag0/OfVbpTQUCjM5WXB4gWUewZzB5pGRCFXm\nKmYW0s4tRNEYgdPiJBJZ4KTLhV6vx2Qq7BEmX9Pjpx9HaCqxaJTrWIE0NDvLQZ+PLWkgCIf7MRha\ncLk01HDhqaPwVgGCdJuJ6elp9PV64vPxTLYMgD/qx6Q1UvLSK0BefAAUQBCbiqG1aXHWa7Lsb4mJ\n70ZjC2NjyUIgeP11nDVtRRddOVAMaSCwr2AsEkHU1qKdn1fMT1ZYTsO5TMYTFEhDi/E48/E47Uaj\nlE47EiEVkwLftfbzSEPATLmeGrcUVNVp6lDVzFPiyAmAFAEClUpFS0sLg4ODhEK9NFVeygNHHlAc\nk1u3dz5GYG/KA4KohzJnI7z0UvqPLEwdlW2T1cqRnBkUssmMQAjBgHuAXvcQen0Nkcg4FosFs9mc\n1p4FC/sGqTRVELEZmZiZYZ3FQnQsitqkJibGmZrysRiJ/mlbUMuW0wKlaFGZx4O+qoqxsTHJz0tM\nlGhKMBjqcblCVFUVTqQbWxijcqEQCIQQhEK9GI2dmde22Wwc8PkU0lDwTBDzKnNmzsVS0lBlpeQu\nbl2Ksv0nIBYrCgRQC1zASlxejpifZ2RkhK6urcUZAeBsWo0rVGx86igmYxOHp44w6ZvMAEGVN8DQ\nUMHhBZZRZ3OAIHQuxIqanAE1Pp8UFMubB+s0O3GHZgnNz1O5hGQjA8GDxx6k1rE+U1QmW02NkhEI\nl4vDfj9b0sVrMptzuaAi+TaThkDK+9bYNMzMzKDSqDC2GQn3Z+UhKUOgAk6dAq9XGR8AxSoV6pNm\nEGSCxcGgtDgXGQBtMLQyMaEtlIZefx1n+4aii64cKJavy2muYKXJRElNDVGDQaE9KuwCpaFj6cCm\nWqVCrVejb9ATHggzNweN5dXnZQQTdjWV89JORButoWR1jvYZi1F0iwkZIAiH+9jSeBOvj77OpC/7\ncOfW7eUygkpzJe6wm2QqSTIp/fllLXZFTYU77KaseVUWCJaThpYIGOuqdQghiLviPHTsIT645oOY\n0plfQEYeqjCFmDfWU21bQchUgmtujnVmM4ETASzrLESjo4yNxcG4iC2UeNOkIaB4LYHHQ0lVFclk\nktHZ0UxChF5fx8xMrGD/4vP5iMQjGAYNinRagHh8HlBRUpJt3bDNZmO/z6eQhoJnJVkIchjd7Kxi\nVgZICRSlpbAQ9VBW2wb792f8U/m9VcRiI+e/F3Y7+P2sqKrCbu/KpG9nbHwcfD6qu7ctuQkzGaVK\n4565HgkIWo2Uu7wMDZ2n4SPSIux0QiarAAkIaptqs0BQRBaCrJ83BQOYlyjvd4fdxJNxxn3jtFZu\ny7QJkU3BCMrKwOfDLgTV6QaQMpubmQF79G0qDQmzYDq90hg7lM3n3GE3ZaZyqUr11Vez7SVky1ml\nwv1hTB2mLOjLslARAdNobGFqyqpkBOEwHD+Os/uiZRlBMpXEF/VhN9hZb7FQ0tDAosm0dObQBUpD\nRwMBNuY8aOZVZkJnQ8zNQUvV+RnBiC2FPa3Hq3xOtG058pYsyRS5F3KcIBTqpcy2jlu7b+XBYw9m\n3l8qRqBVa3EYHMyH5pmbk05fUpnHCMJuylZvloBArrdYAgicOh0WjUbKwsoxlUqFZY2FxROLPHjs\nQe7YfAcGQ7YWJJM5lHQx13kJTosTn0nD4twcay0WgieDmNaV4Pe78PkqqKxdwBhNFgXFP6qVlkqb\nkUSieObQ4iIqh4OGhgZ6RnsyQFBSUsXCgpmqKmXLjeHhYZqbmylxlCiyqCC7kOTWF1xktWaBIC0N\nhc6EMK3OdrWd801LQYuCHRFUVSfxx3zYr7iG+EsvccTv56K8tt3BoJ1gsLdotpfCNBriZjMbGhsx\nGJqIRicQIieJYHwcJiZwbrty2U3Y7etvZ9w3jsPgQGPRUOtIMD5emIadb4OD0NZGASNo6Go4LxDI\nfu7wu1AvMX3HHXZzavYUt6+/HaOhMVMdLpssXAgh3YuIw8GVORctszmXCyz+tyEjcJqdxHVSmwmg\nIE4wG5ylwlQBV10FL764rDQU7g8rGcESshBIMYKZmQolEOzdC2vW4CxvLJqzL8cIFsILlBpK0ag1\nrLdYCNfWMqVSsaRYuQQQyNKQ/Awd8/vZkAMEcrbM3By0r5AGjucHcnPtnDmMdTod+JpxoqrP+RuW\nGSElAcEAkcgQRmMbn9z0SX589MckU9JCJAOBEELBCIBMZ81Mqw5ZDkkX+c0GZ6mo75JqB06fPs9M\nQylOsFTA+I2X3mCtcy2dFZ2ZWhDIAkG1v4/p2k04zU4WDYLgwgLrLBYCJwLoN/hZXKyivHwTKxzj\nRE36P10LatnUaqlvjcdTHAjSQdr6+nr6JvokPwdUKjWBwErKy5X3QQYCywYL/mPK96SFpEPx2gar\nld5QiGgOM5EDxSD9dqmJcWlxLFK85FixgElTiuaqazhx9izNBgOlefUfs7Ml6HTzuJcrqExb0Ghk\nzYoVqNU6dLpq5WI5PAxzc1RddGVRP5c3YRfVXkRSJBnySL+9vd1AZalYNnsbpPZFxYCgcUPjeYEA\npHul805K97KIzQRmODR5iL9Y/xcYDI2ZxoiyWa2S6iR3zXeXl7MjnFU+QqG+DCPQe96OjMDiJKgK\nZhhBfubQgHuA1rJWeOc74aWXCoFAZgRCZKQhu11KF4tPFqaOyhaPlxMM2nA4ctpYP/UUXHedYs5s\nrkmVjU3SNTmkNL31FguuqiqGotHlgSCn4ZzMaEpLpboquZO2HCiWzbTSRKhHYgS11XrMOjOL4cWC\n0wOE42FOG/0YpyXamzhWT6omRzw9DxD0959Bp6tGozGyrnodNdYadg3sArLqm8fjQavVYs25RnmB\nywCBXi+BXvpeKH6/F188LxBsWiZgPPDGAHduuROQq8NzgGBwkLbJ1+g3rpUmupXEMXi9tBgMBE4G\n0HbMs7BQjtXajd14jvifuvOobDmtqItJQ9jtNDQ0cGb6jHSf0hYIrMJuV/rg0NAQzc3NWDdYCRxX\nxlJyM4ZkM6jVdJvNDBiNGUagAAKzE+P4DDQ3F710Y+0AlZpW2LGDvTodO/Im9YH0MzudicyksuVs\nUa2mK70hyu33BUhb9ksvRW+yFvVz+dmLJCQm9MvTUut0Y5uRenv8vHGCokDQG6Jle8uFAYHZSXh2\niLkiqaMAx2eO01nRSWtZK2ZzN8Hg6QKWlCsPTZaWsjHdUkUIQTjci8HQybwriXpx/oKH0sBbBQjM\nTnxJH3Nzc8RisYJagoHFAdrL2qW5wQsLTA0OKoFArlL1+TLSkEolrUWBoaX7dUxOqqiqmiUWS3uQ\nEPDkk/De92YCe7k/pBApotEJ9PoGBtwDtJe3A7DWYmGwvJwev5/UUplDeQ3nanOqb+Q4QSCZZDQS\nyZSbgwQE7tNhgkFpo71c5tDQ4hCioQHV6ChCCCK/ryFmOJc94LyMYFARaPzkpk/ywyM/BLKMYGxM\nyQYgqzMrmve1tcHAACmRYmhxiLayNonRvfTS/zUjmKyZxDHm4LqO6wC5X1SONHTsGJ2NUfrGTTjN\nTgbUYRrDYUQoRXQ8iqicYWHBTElJB3oGUTnOl/j+R7LcVtT5jGBuDsrLqa+vZ8gzJPl52vz+Vmy2\nEcWphoeHaWlpwbLeQuDY+YEA4CKbjRM6HbjdxOZiiJhAt0LSpZ0WJ7apBcQSQKCuGMCeageDgX2X\nXMKOIinSk5NQV6di8gJSd2aTSVrScpzURTb97CUSEijefLN0XUX8XGbjQ4tDNNubeX30dUY8I5g6\nTKzQRZcFAiEKgSA+H0fEBRXtFSQSCfx+/3kZwezcCNG6OqbzutylRIpJ/ySf2vQpAHS6KlSqEmIx\nZbcBGQjiqRRDNhsdaT+Px2cBDYFAOQ2meWkWe36V6zL21gACi5PZ0CxNTU309/dnGIG8CPcv9EsL\niVoNV17J9MCAMkYAUFODmJgiMhzJpEtWVUFobGlpaHwcamq82aDVmTOSx3R3Y9FZ0Kg0+GPZBSkW\nm0GjKUWjMdLvTl8TUKrVUlNaisdiIdTXV/yPTGcNBQIB4vE49pxUPVkeOhkIsMpszswgADB1mejr\ng9ZWgUZTmK6Za/3ufsobOiEcJtq7AIuVCFWUWCwdwC5SVSxbY2MjLtcCWm1b5rVbVt/CnrE9TPgm\nsFik0EJ//0whEOQzAoDWVhgcZNI3SamhFIvOAjt3wp495xlum64lCAQKdlMPBR+iab4JDVIDvQJp\naHCQjus66OuTrqmXAA2RCMHTQUxdJmKJMWZntSST9agjo+gqLqyh1/+z5baizmcE6dWpoaGBychk\nxqcAvN46LJZzilPlSkP5QJCbOppr22w2DqaBIHQ2hGlVdoSrRWeh2aMi1lB88Yvb+jGGpWva19rK\njtdeU7yfSkkbhNZW4wUxgolIhLo0q8gFcobTMsp73wsU93NZGup399NR3sHt62/nB4d+gHWzFWdg\n+cyhhYXsbBwZCEK9UutptVot9Ryanj4vI5jwTLB9zRp25zWYfGHwBQA+vO7DmdcsljUEg6cUx8lA\ncCYUIlJRgVGO2+RkDK0s+8NkIXirAEF6IVm9ejVnzpyhpLxEml88KzW3GXAPZHdKV13F+PS0YkcN\nQE0N0SMj6Kp1mU6b1dUQHVtaGhobg9raaLbC8amn4PrrM8HUfGfMTR1VXBNSn5xAXR2RYt4Yj0tt\nB+32THwgN6AnB4zzA8UAWquWCYuVjoaU4l4VswH3AO0VHdDQQPiFc9g22TCbc5xxGUZQUlJCVZUJ\ntzubOWLWmblt7W3cf/h+QLqfZ8+6M4Fi2ZYEgoEB5X0qK5P6x7hcyzKCynTe/2BOwHgxvMgvx36J\nvkKf6USq1ZYjRIp43E1jQwOjHg+Nt13M1BQ4dE56NX6qPR4CJwNY1lqIREaZmUngjxmwhCPoKv7E\nfYZkW6rx3LhA9PVBezv19fUsqhYVPrW4WIHZfFxxKlka0jfoSUVTmf5LqVScSGQEo7GNfNtms/Ga\nWg0LCwpZSLYuv57F6uLAHNQPoPG0Mx6JEDUYaP1f5fxgeURlY2P1eYEgkUgwGgxSqZGBvDX77D39\ntJTZl9605ft5KhUhHnej09Vk2PhdW+7iJ8d+gnqtmooZH0ODSwerZTagUiEBs89H6LQ3M4xGnkuw\nHBCYhAks8M7m5gIg+OYb36SxtBGdJttKxWxeQyBQHAgO+XwYa2oyfVtkIJiZgXbrHxYohrcIENgN\ndiKJCJ3dnZw+LRWuyJlDiVSCMe8YzQ6Jus5t2EA4GqUu/8eqriayfwTrRVntetUqCI8tLQ2Nj0Nj\noypLT9OykGz5zphbTDbgHlDs3nba7Uw3NKAu1nhOlkLUakV8QDZZGjqaV24u27TdRqtdoqLLMYIB\n9wBtjjZobCS6rw/rZusFAwFAba2WmRllwPDubXfzw8M/xBf1UV0NAwOBC5eGBgcL7hNXXilJAOdJ\n28wvLPvp8Z9ybfu12NbYMoVlue2oLcPDmFUq3DWVNDWBf66CY9YAtsFBgsf9mNeZiURGmZwM4sZF\nu6oC1Z86dVS2NCOQ/TwcD2OxQJNuCmEyg93OiroVRPSRjJ8DLCyYsVh6SSalv1cIwcjICM3NzVIW\n1QZLJk4QiYyg061ArS7U8JsNBlwWC8LtJng6UAAELR4Vs1WF6dUAi6oB4q429vl8XFxWhsrjUeQ7\ny3MI5LkEy9no6Chxq5WSdEZZbit4du2CpqbMsYWbsHH0+lpUKk3Gz5sdzVzWeBmPjj5KozPFwNml\nkygyshBIykJZGdETU5muoxcCBPHFOLYaG5fa7QogGPeOs298HzvqdyiOVzx7aZOB4KDfT0VtbQYI\nZDbnckGz6W3KCOTCltqOWs6ckWaTmldJBUSjnlGqLdUYtJKDn1xcZK3BgOrIEeVJamqIHR+jdHs2\nHbC7G5Izy0tDDQ1GiZ66XNDTA5dfnnk/3xlDoT6MxlaEEPQv9Ct2b1c6HJxqbMRYLHNimfgAZKWh\n/T4fm4sAwZjaTKNKiplUm5euJeh390txi8ZGEqeGsW6yKulpkfYSuVZTE2ViQpmu2OJo4V1t7+L+\nQ/dTUwNjY9ECRlBtqV5SGup3K+8TO3dKekJOr5pitiknThBPxvnuwe9y15a7sKyxEDiVlUQy7cSf\neoqmigpGRkfp6IBjQ3aCWh+q0lKihwaxrLMQDvcxPi5QlQ/RlbRdcK/3/2dLMwJFARewrayPUL0k\n5aSsKYRfoFNLO0ohYHxcRV2dmWBQeiZmZmYwm82ZQL1lfTZzaClZCKTna1N5OQm9nsjJ+UzqqGx1\nC3EmigyKEUIwE+snPNHOPq+XHaWlcPXV8MwzmWNkIJAnlS1nAwMDaGtqMkFrOVgsUik4eBA2bswc\nm+/n4XBfpodSxs+Bv73ob/nuwe/SvlXD0MjSPS4UQABQWUnsbBYIGhoaGB4aKpxSlWNBV5ASRwkb\nLRYGw2E86dTP7x78LqsqV7G6crXi+OWA4JDfT11DQ6Yzppw6OjMDddq3KSMAadEtbyjPMALbxTa8\ne7wFO8oTJ06wbs0aeOwx5QlqakgNTGDbns1x7u6GksWlpaHxcWhutkv09JlnJCfXZaldPiPw+w9h\ntW5hIbyASqVSdEPtMBoJtbVJTi3nh8mWlzGUDwSNjTAwmmI2Hlekjso2HDJQG/Rn7tNy0lBbWRui\noQGGR7Busirp6TKMIJHwUV0dZ2yssLH75y75HN858B0qqhJMT4viMYJ8RiBLQwv9SkbQme4qefZs\n0euQLZcRPHziYVodrWyv3y61mjidbTWR2VU++SRNXV2MjIzQ2QmHeiyk4gFSK1eiOnMW3UofsViI\nmRkzpc0DrJxJwpo1y17DH83yq4vTm4sNpl4WK6R0z4nQBCX+EmbTC4NcvNfQUJNZTORAsWzWDdZM\nnKBY6miuXWSzESgtJXZ2WskIIhFs/hij5sIk/IXwAmq1ivmJMvb6fBIQ3HKL4tmTZxXX1taeFwj6\n+/uxNDRkgECrlRhZ4sQeaXOwbl3m2Hw/l589ULLxyxovQ6/RE1k5RiRS+OjJVgwIEgMzGSBYv349\nAwcPShuUJTYp8yPzCJNAp1azxWrlDa8Xb8TLQ8ceosJYofRzwGxeTSjUq6iVWLECJqYEfaEQzY2N\nBdKQywXVqj+svQS8lYDA7ERfrmd0dJRIJIL9Ujve3V76Fvoy6A9pILj+enj8ccUwmqS9EpV7FsuG\n7EK6ahXYIrMky4vv/MbGoKWlgmh0itQzT0jxgdxrsmR77Qsh8PkOYrVuzbCBXJ1fpVJx2dq1UqF9\nPkXOYQR9fX2KhxkkIBgaEVzlcCiaeYH0Jw7Paame8WbuU7H6hkgigivgoqG0gbhlBfrUDLpaHWZz\nN6HQGYRILQsE4XAfzc0rGBwsjHF0V3WzZcUWJlOHmZsrKYwR5NcRgFRFqtezMHZO+YB4vdIOOR/I\n82xrmhH4YhG+vPvL3Hv5vUBh8zmjsZWI+zT09tK0aRMjIyN0dMDZcypKjeX4quswa0cJlxwnGl2L\n1boGXfUgDaMeWFu8zfgf3WprYWQEUG4uOtV9TFmkxbvf3U9psjTThfT4cWkmUi6jkwPFsuUGjJfK\nGJJtm83GgtGKJu5FV5PTEnx0FF9VKdPhwpYO/Qv9dJS3szAPZ91hNlmtcM01EnNOX2cuIzifNNTf\n34+9rS1T1atSqaSiwNcelTZKOQVt+X7u8x3EZtuq8HP5HPfsuIeHxIOs0EYyMed8yweClL0C1fxc\npiHjxo0bmTl2bElZCGCyb5KwRkprv6S0lN1eLz8++mPe1fYuJvwTBUCg0ZjQ62sJhbIJJCtWwOiE\nYLXZjK66GmZnSaViRKNjGI2tUgPWhOvtzQgWIgu0tbVx7tw5DK0GRFzQN9on6d5pO3nyJGuvvlq6\nozkZDCFPKUaLB7Uue0ssZkGFmGM4sDQjaGoqQa9bQfT07+Haa5XXlPPQRqNjqFRq9Pq6Qt07be9d\nuZLxVIrwYF7pfA4QHDx4kK1btyq/xwlBn4p3GAsDqMPDkoIh+qQsmqViBEOLQzTaG9GqtYSClZhM\n86hUKrTaUrTacon1LAMEoVAvbW2dmS6k+faFS7/A3sXf4vOZCoCg0lTJQngBgymp2EyJ1lbUg0PK\ne+V2Sw/8Y48pJmblm6OkhPUWC/ce/x0tjhYubbwUkLKoIsMRUlFJDzYYWghPH4VrrqGptZWRkRGa\n2lLMDmmps1YzY3Bgs07g8x3E623GZluDzngOy5wX2tuX/P4/qm3aBGkpM/f3a4r1MaiVFu8B9wDV\nJdWZLqQnTkgbZItlbYbRyYFi2UydJqJTURL+xHmBYIvVyqLGgrkhppxsNjxMqLaqKMuUgrJt1Hcm\naZmqwKBWS4z5ppvgl1IOvwwEDoeDWCwmpWAuYf39/ThXrVLMRTAaW4iceUmqtMorUpTvkxACv1/a\nhOX6uWwf6P4APRU9OGNBBs4qpc3M35IHBNGYDWtTNLNetLe3o5+fJ76MXDh4chB/wk8yleTS0lJe\n9yzyXwf+i7u33c2ge7DompAvD9XUwJxLxRaLVXqw5+aIhAbQ6+tQq/VSe4nw25wRuIIuuru7OX36\nNCqVitJLS+kZ6ckwgng8zrlz5+ju7oYPfAAefTTzef+4BYM2T5/3+Uhq9ZwaKKR6Xq+0DpWWgjFk\nJ3xxU2FXzpyiMp/vADbbRahUKoVGmWtXVVQwaTbjOnZM+UY6ddTv9zM0NMSaPEkipRJQGWVlsBAI\nenpg5WoVJRUlBE8Hl8wa6s+RYHwzDvTJ7DEWS1oeOg8QtLevZ3h4mFSRxnnb6rbhLEshcCqKyQBK\nNCVYtKVUNSplpXDjClb7DFj1OcefPi1pwWo1HDpU9Fpke7fDzoNjZzNsAECtV2NoNmQmtxmNLUTi\no3D99ZnqYl+NH/WEiRqLkyFhxCTG8PsPsLhYSUlJJ3WLfSS7OopOn/uTWFubJA0tLCh+P6e3jzPx\nLCNosjUVMILchSRfGlJpVZhXmwmeCC4bIwApxVmNDVGZNwp0eJhEY13RzYXs5/bVYaqGcvwm59mT\ngUClUtHd3c3x48cLziPbwMAAtevWkdsz2pCsIiwmpQSCXCDIuU+RyBBqtRG9foXCz2XTqDV86eov\nYTHP0bOncIr94qI03D53jQ+7zVhqs0WrGo2GrXV1zOdIw7nm9XrxLnopNZSyEF5ge2kph3weVjs3\nUG2pxqa3Kf08bflAYDQC+iRbKZMKL00mwlNHMRo7EQJOngRb5G0aLIbCFFKA0ktLGfRlkba3t5eG\nhgapBewtt8Bvfyv9wsDiOT3aaF5T8tlZwpZK0mEHhckD61UqMA5ECF1ROIQmV6eUdySQk52TZyv0\nembLyhg9cUL5RpoRHDlyhHXr1qHLc7aDPh+mmjjh6UIn7OmBlSvBcbWDxRek6tTZ4GxBjn1umqan\nz4QmtJCZLWk2ryEYOLlssDgU6qWqai1WqzVT4Z1vf9a+GaGqI5aMFbxXqnHiqFcuJrPVNjaG8/rK\n79sHF18MH/ygAsiLWWp+LzH7Ji5puETxeq48pI/ZiRnCJK+5LAMEJ/WLqOMaHCVOzsVU6DwD+H2H\nmJ3VkdSW0eUKULJ+07Lf/Uc1tRo2bIAjR7ILXCyGxT3GcZ+0sA+4B+iq6sowAhkIdLoahEgSi7kK\npCGQ5CHPiUmSyYBiznQxMyTL8ZvymiKOjKBqbl2SEbQ52gi3eRG9OYvcpZdKPn32bAYIAC6++GL2\n7t1b9LsTiQRjY2M0rl8vLfppWdd02kN4vVNarXPkkFw/lyVZ+ZoUyQdpu6HrBkqc47yxr/DvkHsM\n5RIh/4QRo11Zh7G2ooIxeR5rnp07d47Ozs4MU4nFvKSCw9y2418VxaX5ltmEpW0xHidVHmVVOJ2x\n5nQSHT+OydTJ+Lh0W0oW3ubBYlcgywgAzBebmVJP0eKQHpYTJ06wTg4o1dVJ3Pm55xBCsHhUjSoa\nzAADAHNzpCqqigJBZmD94iKlz4zhWV24uCkZgaRRAksyAoBkfT3egQHli2kgKCYLATzvdtNUZC4B\nZIGg7Ooy3C+4MWgNGLQGPBGP4ji5wE0Igf9YGJzVmQZ4ZvMawrPHJFq/xDDscFjqc5I7pCbfyhIz\nIOr5+os/KnjPJJxYq5UP4Ui5mi5P3q573z4AjAQrAAAgAElEQVTYsUPaVebFeXItnozz4L57KTPY\nCwba5waM1Q8/inWhEo/6TGYuwaueRRrbUmgjTob8XtBrMHpKmZiYx68NsMNtRfVmxQdk27xZAgJZ\n8hgeJlFdx/CUnkQqwahnlHUN6xgbGyMYlPxTiqurMnGCoaGhgviSdYMV38gZjMaOosPsZRNCwMJK\n4ot5LGx4GH1b15KMoLWsjdGGOaZP5WxSNBq49VZ47LELBoKRkRFqamrQm82Z3ksIQemDhwg5/IgV\nK6Tzpi3Xz/1+5bNXTIJRqVRsv8zJ4JAgnlQu5vmyUHwhTmjBhE6lfIZazWZ6log29/T0sHLlygyQ\n//vr/84qXZJxlb0oS5EtnxE843ZTXp1i0ZX+W6uqSEz1YDJ1sG8fXHJRXErRzesEez57ywCBnIK4\nevXqDBC4G904gg40HummKYAApMXksccI94XR2nSonE7FpDJmZ9HVLQ0E9fXAT36Cw3ktnvAbyk6I\nOdckRIJA4BhW6+ZM6uhSP3zZypXo8nfU5wGCXW43G9tKCiaVQRYI7Dvt+Pb5SIaTmevKNXmnFJ2I\nolKroDk76MBsXoM4cXRJTVyIVDo1tmNZINi9+/d0di3wH4/tZ9qv/BuFvxpHnfKazpbGaJjPeSgn\nJyEQkK6js1OK87z6atHv+vb+b9NR1s7NzlqeyUvJtW2z4XnVI2WafP/7lNX+GYuLL2bmEhweG2N9\nl5qk28lsYpZ4l5OK2RZGR8fwamfYMK968wLFsm3aBIcPZ3+7vj7UXR1MTMCYdwynxcmGNRs4evQo\nJ08KVq7Mdhgwm9fgdh9jZqawqtuy3kLAc25ZWQggeDJI2LaFzrNHGM8F1uFhbF3rCvxJ9vPFEie1\nnQnGR9QoxkR84AOEfv5bIhGRqQ28+OKL2bdvX1Fpsb+/nzZ5NS4vl2TK11/HOKVG79GQqi1c+OR7\ndSGMAODdN3biD1bysxM/U7yeDwSe1zzo19SiWlAqCCuAo0uwYRkIqi3VnHSd5OETD3P3yivZ7fVm\nW+AUMaOxjVhshkRCip38dm6OjnqtYi5Bckpq7fLGG7BzjdRyJBcUL8TeMkAg775bW1txuVwEAgEG\nvYM0pZrw7pEyZk6ePMna3Af4pptg1y68v3dJaaO5TfMBZmexNFUyNKQkCpAGgroU/OAH6P7yHgyG\nRnw+5W7JorMghMC1eAi9vg6t1o47LI0dLDcWl1i6t26l0uslkvswpNNHiwHBQjzOuVCISzr0BUAg\nRBYItKVazGvNePd4izbEkwPYgSMBLJssqHIGHZhMnVhfmSJ1vTIYLls0OolWa0OrtS0JBIlEgt27\nd3PTDeV0Bj7BP770j4r3Z4ed1HUpr+mIyUPFVM6u6403JDYg71yXkIcG3YN8Y+83uO8993FdeTlP\nLyhjD/bL7YT6QkR/+TIYDDjWf5zFxRcBKK+vp9njYVWnGt9AOf4aP+EmDbYJB72986jLB2iZ8P9/\nAwSyNBRwQW8v2lUdki48IS0kq1atIhaL8eKLrtxMSszmNQwMHKCmpiY7lU9+b62ZqHoAg275wPfC\nMwuU3tBFpLKS13LbRAwPY+pYhRCCQCy70st+/r+eGB+pd9LdLclVGdu4kUlqWVEezfycNTU1lJaW\ncu6csi0GSPGBdnkj4nRK9Pf730d111/jCKwkWiRG6zQ7mfZPEggcx2rdLJ1niUQNgK4rDMwlzfzn\nk99WMOZM++m0eV7xYLy4oWB2iM3v59TCQtGAd4YRWJz87PjP+Lvtf8d7qhrY5/PRt7D0NalUGkym\nlYRCZwglk7y8uMhFrbpsdpPTiZiZxGSSgGB78x8eKIa3EhBYnEwHplGr1XR1dXH27Flp5+1ow7Nb\n+lELGEF5OVx+Ob7HT0tAkDtGC2BuDk1NFc3NkN8CaGwM6j2npVTGrVtxOK7KLCayyXNmB1wvZ3Yk\nMjVdioZ37thBbSzGvpx+/MzOMptKEQwGaW1VxiJeWlzkMrudlkZ1gTQ0PS2pOTJLLLu6LBMnmA5k\nAS+SiDATmKHR3oj/sB/rJqti0IFaVULlXg3hd64qes25gcalgODYsWPU1tbynvdYiQ3u4PfDv2fv\nmCQDjI9DZN6J1q7cTR1KjFESTWSTu2VZSLZbboHf/U6aAZE2IQR3PHMHn734s7Q4WrjcbudUIMB8\njnar1qkpv66c+a/thrvuwmrbQjQ6STQ6jbq6mlavl85OmD9ZhrfOi6/OT/ykn0CgkvbyU2Aw/EGd\nHf8olg4YV0e0TAemEX19qDo7qauDw0NZn3r3u9/NCy/Msn599qNm8xoGB08WyEIAGpMGTcckmoXG\nZb9+4ekFyq8rJ3HFFbifT48h9fshHEbldEo+lcPy+t39tDja+M38PB9yOtm8GQ4fzjmhSsXkFR+k\nVihrBy655JKi8lB/f38WCK6/Hn7yE3j5ZfjIR7D5VhB0eAs+47Q4GZk/iNHYjFZrVfh5MTOZVdj1\nSd7j/Svufv7uzOsFjOAVD5arm8kfdKyansbW1cWJ/BgfWSAIx8MMe4b5zLbPUKnTcZHVypHZniUZ\nAWQzv15YXGSz1cr1V2t4+mnpvWS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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "def linear_model(X, beta):\n", " \"\"\" \n", " The linear model\n", "\n", " Parameters\n", " ----------\n", " X : 2d array\n", " The design matrix : a matrix of regressors\n", " \n", " beta : 1d array \n", " Model coefficients\n", " \"\"\" \n", " return np.dot(X, beta)\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where `np.dot` is a matrix multiplication:\n", "\n", "$\\bf{X}\\beta = \\beta_0 + \\beta_1 \\bf{x}_1 + \\beta_2 \\bf{x}_2 + ... + \\beta_p \\bf{x}_p $\n", "\n", "## Aside on matrix multiplication : \n", "\n", "The multiplication of two matrices $\\bf{A}$ and $\\bf{B}$ is denoted $\\bf{AB}$. This is only defined if the *inner* dimension of the multiplication matches. That is, if $\\bf{A}$ is $m$ by $n$ and $\\bf{B}$ is $n$ by $k$. In that case, element $i,j$ of the multiplication is defined as following: \n", "\n", "$\\bf{AB}_{ij} = \\sum_l\\sum_k{A_{ik} B_{lj}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Back to our regression problem\n", "\n", "We choose a set of random $\\beta$ coefficients and generate $f(x)$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta = np.random.randn(p)\n", "f = linear_model(X, beta)\n", "fig, ax = plt.subplots(1)\n", "ax.plot(t, f)\n", "ax.set_xlim([-pi, pi])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "(-3.141592653589793, 3.141592653589793)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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NtsPUqcazN6uVKm0RPXNWtGh37UplhCLqoa9doy9GEYt5API87ZgT7YceeghT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\n/wND4vAciJ69IAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, $\\bf{y}$ is not going to be linear in any particular $\\bf{x}_i$, only in a combination of them:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "ax.plot(X[:, 1], y, '.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Noise\n", "\n", "Unfortunately, the noise-less case is not a very realistic one. Let's assume that the output is additionaly corrupted by noise, $\\epsilon$: \n", "\n", "$\\bf{y} = f(\\bf{x}) + \\epsilon$\n", "\n", "which is distributed according to a Gaussian/normal distribution with zero mean:\n", "\n", "$\\epsilon \\sim \\mathcal{N}(0, \\sigma)$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y = f + 3*np.random.randn(*f.shape)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(f, label='f')\n", "ax.plot(y, label='y')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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xIcROURS8YS9MWpNkJ3hqgEooeMrMYwfSEztFkR4PN9+MxLACel5idbkBWmMA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\nZIOJCJzSOOccorytN5Fc9lTbxRlwcvrvP/MM6bt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ZNvOOYrh97MPGYUSqIq1OaoB7x65S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\nYtHS3+JR7ze70QbbXsz9vLGOnW+7oy9XiHZRjIAZe2gKe5Bm7Kyws73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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the linear model\n", "\n", "Solving the linear model, means finding an estimate of the $\\bf{\\beta}$ coefficients that generated the data we observe\n", "\n", "In other words, we are looking for procedure to estimate the coefficients (we call the estimated coefficients $\\bf{\\hat{\\beta}}$)\n", "\n", "\n", "### Criterion for a solution\n", "\n", "A 'good' estimate of these coefficients would produce an estimate of the output, $\\bf{\\hat{y}}$, which would be close to the measured data points.\n", "\n", "Where: \n", "\n", "$\\bf{\\hat{y}} = \\bf{ X\\hat{\\beta}}$\n", "\n", "One way to define this is by saying that we want the residual sum of squares to be small, where the residuals are: \n", "\n", "$\\bf{y}-\\bf{\\hat{y}}$ \n", "\n", "and the residual sum of squares (or RSS) is: \n", "\n", "$RSS = \\sum_{i=1}^{N}(y_i - \\hat{y_i})^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding $\\beta$ - a first solution\n", "\n", "\n", "Another way of deriving the result is to minimize the sum of square of our residuals:\n", "$\\sum_i \\hat\\epsilon_i^2 = \\sum_i{(Y_i - \\widehat{Y}_i)^2} $ :\n", "\n", "\n", "Since $\\bf{\\hat{y}}$ is a function of $\\bf{\\beta}$, we can think of $RSS$ as a function of $\\beta$ and we want to optimize it with respect to a choice of the elements of $\\beta$. That is, we want to find a minimum of $RSS$ with respect to $\\beta$. \n", "\n", "Mathematically speaking, we want to find a value of $\\bf{\\hat{\\beta}}$ for which the first derivative of $RSS$ with respect to $\\beta$ is 0 \n", "\n", "To find the derivative, we re-write $RSS$ in the following way: \n", "\n", "$RSS(\\beta) = (\\bf{y} - X\\beta)^T (\\bf{y} - X\\beta) $\n", "The derivative of this function is (we leave it as an exercise to the reader to prove this:)\n", "\n", "$\\frac{\\partial RSS}{\\partial\\beta} = -2 \\bf{X}^T (\\bf{y} - \\bf{X}\\beta)$\n", "\n", "Setting the first derivative to 0 and dividing both sides by 2, we obtain\n", "\n", "$\\bf{X}^T (y-\\bf{X}\\beta) = 0$\n", "\n", "$\\bf{X}^T y - \\bf{X}^T \\bf{X} \\beta = 0$\n", "\n", "$\\Rightarrow \\bf{X}^T y = \\bf{X}^T \\bf{X} \\beta$ \n", "\n", "If $\\bf{X}$ is 'full rank', then $\\bf{X}^T\\bf{X}$ is [positive definite](http://en.wikipedia.org/wiki/Positive-definite_matrix) and it can be inverted. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.linalg as lin\n", "\n", "def ols(X):\n", " \"\"\"\n", " The matrix which solves the OLS regression problem for full-rank X\n", " \"\"\"\n", " return np.dot(lin.pinv(np.dot(X.T, X)), X.T)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "beta_hat = np.dot(ols(X), y)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(beta, beta_hat, 'o')\n", "plt.xlabel('Real parameter value')\n", "plt.ylabel('Estimate parameter value')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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KqBWvNIiIdNfmc0+pVCosXrwY69evb3U4Q2LRICLSXZt3T1lbW+O3335TT4dOZAqpqZlI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\n8cUXX3zp8dKVwbq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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using $\\bf{\\hat{\\beta}}$, we can calculate back $\\bf{\\hat{y}}$, the estimate of the output and compare it to the actual output: \n", "\n", "$\\bf{\\hat{y}} = \\bf{X} \\bf{\\hat{\\beta}}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_hat = np.dot(X, beta_hat)\n", "fig, ax = plt.subplots(1)\n", "ax.plot(y, label='$y$')\n", "ax.plot(y_hat, label='$\\hat{y}$')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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mdqMROHYMTtO4sRV7oK0YoxEIDTPDknAUsUPOJVldEXuuKhey+HocOyZOu9jp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\n", "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The so called \"hat matrix\", or $ H $ is the matrix which defines the transformation from $\\bf{X}$ to the estimate $\\hat{y}$, so it's the matrix that \"puts the hat\" on $y$: \n", "\n", "$H = \\bf{X}(\\bf{X^T}\\bf{X})^{-1} \\bf{X^T}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "H = np.dot(X, ols(X))\n", "H.shape\n", "y_hat = np.dot(H.T, y)\n", "\n", "plot(y, y_hat, 'o')\n", "plt.xlabel('The original output') \n", "plt.ylabel('Linear estimate of the output')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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333zTpZ3269cPffv2dWkbRDpKHzEk5pdT8/12DYY0GI0rsW/fEZe3SYgScNb8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\neHp64u2334bRaERDQwOSk5M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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "GLM, t and F-tests" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Grasping some data" ] }, { "cell_type": "raw", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "First, finding some nifti or img on the disk. Let's assume we have some data in our current directory:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import nibabel as nib\n", "import os\n", "from os.path import join as pjoin\n", "\n", "this_course = 'pna'\n", "\n", "def load_images(course):\n", " if course == 'pna':\n", " PNA_DATA_PATH = pjoin(os.path.expanduser('~'), 'data', 'qcpna', 'bolddata')\n", " img_fname = pjoin(PNA_DATA_PATH, 'smallbold.nii.gz')\n", " if os.path.isfile(img_fname):\n", " img = nib.load(img_fname)\n", " print img.shape\n", " return img\n", " else:\n", " print \"where is this image: \" + fname + \"\\n\"\n", " return None\n", " \n", " else:\n", " files_1 = [pjoin('ds107','sub' + \"%03d\" %i, 'BOLD','task001_run001','meanabold.nii') for i in range(1,15)]\n", " print [(f,os.path.isfile(f)) for f in files_1]\n", " #files = [os.path.join(scans_dir, 'snn03055dy%i.img' % i) for i in range(1,13)]\n", " files = [f for f in files_1 if os.path.isfile(f)]\n", " return [nib.load(f) for f in files]\n", " \n", "img = load_images('pna')" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(64, 64, 35, 42)\n" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Once we have these images, we want in a first step to extract one voxel value. To do so, we know that images spatially normalized have an affine transform that allows us to compute the the position of a (i,j,k) index of the image in the template space. If we have the (x,y,z) position in the template space, we need to inverse this transform to get the index of the (closest voxel). " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Now we load the affine transformation from the first image (it's the same for all), pick a voxel in the MNI space, and compute the conversion parameters from MNI space (in mm) to voxels space (indices of the 3D array)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# transformation from voxel no to mm\n", "\n", "try:\n", " M = img.get_affine()\n", "except: \n", " M = img[0].get_affine()\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": true, "input": [ "# mm to voxel no\n", "iM = np.linalg.inv(M)\n", "# coordinates of voxel of interest in mm (MNI space)\n", "posmm = [-20.0, -42, 34]\n", "(x, y, z) = tuple(posmm)\n", "# coordinates in voxel space (in homogenous coordinates)\n", "posvox = np.dot(iM, posmm + [1])\n", "# We grab the spatial part of the output. Since we want to use it as an \n", "# index, we need to make it a tuple\n", "i,j,k = tuple(np.round(posvox[:3]).astype(int))\n", "\n", "print i,j,k\n", "vdata = img.get_data()[i,j,k+2, :]" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "24 20 26\n" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Let's display the values of this voxel - and display a slice of the 4D volume." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.pyplot as plt\n", "\n", "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(14,4))\n", "ax1.plot(vdata); ax1.set_title('the time series')\n", "ax2.set_title('the slice at z = %d' %z)\n", "# time t = 0\n", "t = 0\n", "imshow(img.get_data()[:,:,z,t], interpolation='nearest')" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 20, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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j8uTJhhxTYU96Y8bZDDhGpDcAEBYm0maWlzveB8MwDMMwDMNUN8qgfuzYscjI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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The GLM machinery: any difference with linear regression?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We will model the data using the GLM, then ask questions on the parameters of this model, a concise and fairly general framework for asking question to our data. \n", "\n", "$$\n", "Y = X \\beta + \\epsilon\n", "$$ \n", "\n", "In a first example, we take X to contain two columns. Let's assume for a moment that our data come from an experiment with 12 subjects in which odd scans are from condition 1 (or group one if each scan is from a different subject) and even scans are from group 2. The first column of X will model this with, with $x_{i1} = 1$ when i is odd, and $x_{i1} = -1$ if $i$ even. The second column will be a column of ones, modelling a constant offset. We note $\\epsilon_i$ the noise at each measurement $y_i$ under this model.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "$$ Y = \\left[ \n", " \\begin{array}{c} \n", " y_1 \\\\\\\\ y_2 \\\\\\\\ y_3 \\\\\\\\ \n", " y_4 \\\\\\\\ y_5 \\\\\\\\ y_6 \\\\\\\\ \n", " y_7 \\\\\\\\ y_8 \\\\\\\\ y_9 \\\\\\\\ \n", " y_{10} \\\\\\\\ y_{11} \\\\\\\\ y_{12} \\\\\\\\ \n", " \\end{array} \n", "\\right] \n", "= \\beta_0 \n", "\\left[ \\begin{array}{c} \n", " x_1 \\\\\\\\ x_2 \\\\\\\\ x_3 \\\\\\\\ \n", " x_4 \\\\\\\\ x_5 \\\\\\\\ x_6 \\\\\\\\ \n", " x_7 \\\\\\\\ x_8 \\\\\\\\ x_9 \\\\\\\\ \n", " x_{10} \\\\\\\\ x_{11} \\\\\\\\ x_{12} \\\\\\\\ \n", "\\end{array} \\right] \n", "+\n", "\\beta_1 \n", "\\left[ \\begin{array}{c} \n", "% \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \n", "% \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \n", "% \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \\small{\\textrm{1}} \\\\\\\\ \n", " 1 \\\\\\\\ 1 \\\\\\\\ 1 \\\\\\\\ 1 \\\\\\\\ \n", " 1 \\\\\\\\ 1 \\\\\\\\ 1 \\\\\\\\ 1 \\\\\\\\ \n", " 1 \\\\\\\\ 1 \\\\\\\\ 1 \\\\\\\\ 1 \\\\\\\\ \n", "\\end{array} \\right] \n", "+ \n", "\\left[ \\begin{array}{c}\n", "\t\\epsilon_1 \\\\\\\\ \\epsilon_2 \\\\\\\\ \\epsilon_3 \\\\\\\\ \\epsilon_4 \\\\\\\\ \\epsilon_5 \\\\\\\\ \\epsilon_6 \\\\\\\\\n", "\t \\epsilon_7 \\\\\\\\ \\epsilon_8 \\\\\\\\ \\epsilon_9 \\\\\\\\ \\epsilon_{10} \\\\\\\\ \\epsilon_{11} \\\\\\\\ \\epsilon_{12} \\\\\\\\ \\end{array} \\right]\n", "= \\left[ \n", "\\begin{array}{rc} \n", " 1 & 1 \\\\\\\\ -1 & 1 \\\\\\\\ 1 & 1 \\\\\\\\ -1 & 1 \\\\\\\\ \n", " 1 & 1 \\\\\\\\ -1 & 1 \\\\\\\\ 1 & 1 \\\\\\\\ -1 & 1 \\\\\\\\ \n", " 1 & 1 \\\\\\\\ -1 & 1 \\\\\\\\ 1 & 1 \\\\\\\\ -1 & 1 \\\\\\\\ \n", "\\end{array} \\right] \n", "\\left[ \\begin{array}{c}\n", "\\beta_0 \\\\\\\\ \\beta_1 \\\\\\\\\n", "\\end{array} \\right] +\n", "\\left[ \\begin{array}{c}\n", "\t\\epsilon_1 \\\\\\\\ \\epsilon_2 \\\\\\\\ \\epsilon_3 \\\\\\\\ \\epsilon_4 \\\\\\\\ \\epsilon_5 \\\\\\\\ \\epsilon_6 \\\\\\\\\n", "\t \\epsilon_7 \\\\\\\\ \\epsilon_8 \\\\\\\\ \\epsilon_9 \\\\\\\\ \\epsilon_{10} \\\\\\\\ \\epsilon_{11} \\\\\\\\ \\epsilon_{12} \\\\\\\\ \\end{array} \\right]\n", "= X \\bf \\beta + \\bf \\epsilon\n", "$$" ] }, { "cell_type": "heading", "level": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Finding $\\beta$ - a second solution\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In the equation above, we know the model $X$ (or at least we assume this model), and we need to estimate the $\\beta$ and the $\\epsilon$. To **estimate** these, the simplest is to first multiply the left and right hand side of the equation by $X^T$, the transpose of $X$, to get: " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "$$ X^T Y = X^T X \\beta + X^T \\epsilon $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In the above equation, we search for an estimate of the noise ($\\hat\\epsilon$) that is **uncorrelated** with our explanatory variables (the constant vector or ones, and the $x_{i1}$). In other words, in matrix terms, such that $X^T \\hat\\epsilon = 0$. In terms of the *estimates* $\\hat\\beta$ and $\\hat\\epsilon$, we therefore have:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "$$ X^T Y = X^T X \\hat\\beta + X^T \\hat\\epsilon = X^T X \\hat\\beta $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "This equation is called the \"normal\" equation. Now, if $X^T X$ is invertible, we have " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "$$\\hat\\beta = (X^T X )^{-1} X^T Y $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "If $X^TX$ is not invertible, (which will happen if some of the explanatory variable can be computed as linear combinaison of the others), we can always take a pseudo inverse of $X^TX$, denoted for instance by $(X^TX)^+$, and compute the $\\hat\\beta$ with $\\hat\\beta = (X^T X )^{+} X^T Y $. \n", "\n", "A full description of the pseudo inverse (here, we assume the *Moore-Penrose* pseudo-inverse) is out of the scope here, but we can think of it as acting as the inverse of a matrix, such that :\n", "\n", "$X X^+ X = X$, and $X^+ X X^+ = X^+$, and both $X X^+$ and $X^+ X$ are symmetric.\n", "\n", "If $X^+$ is a the pseudo inverse of $X$, we have $\\hat{\\beta} = X^+ Y$ (and $(X^TX)^+X$ is also a pseudo inverse of X).\n", "\n", "In any case, we can compute our best estimates for $Y$ given the model $X$ with : $\\widehat{Y} = X \\hat\\beta$, and our estimated noise or residuals by $\\hat\\epsilon = Y - \\widehat{Y} = Y - X\\hat\\beta $. \n" ] }, { "cell_type": "heading", "level": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Applying to our voxel data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x0 = np.asarray([1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1])\n", "x1 = np.ones(12)\n", "X = np.vstack((x0,x1)).T\n", "print X\n", "X_firstmodel = copy(X)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]]\n" ] } ], "prompt_number": 58 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy import linalg as lin\n", "\n", "# take only the first 12 values of the data - for \n", "# scale voxel data for better visual display; make its mean == 3.0\n", "Y = vdata[:12] \n", "Y = (Y - Y.mean())/np.std(Y) + 3.0\n", "vdata = Y\n", "\n", "pinvX = lin.pinv(X)\n", "betah = pinvX.dot(Y)\n", "Yfitted = X.dot(betah)\n", "resid = Y - Yfitted\n", "print \"Y:\\n\", Y, \"\\nresid:\\n\", resid, \"\\nbetah:\\n\", betah\n", "print \"mean of Y: \", np.mean(Y), \"\\t mean of resid: \", np.mean(resid)\n", "\n", "# make this a little function as we will be reusing it :\n", "def glm(X,Y):\n", " \"\"\" a simple GLM function returning the estimated parameters and residuals \"\"\"\n", " betah = lin.pinv(X).dot(Y)\n", " Yfitted = X.dot(betah)\n", " resid = Y - Yfitted\n", " return betah, Yfitted, resid\n" ], "language": "python", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Y:\n", "[ 3.71749728 2.35802875 3.80812852 3.2643411 5.07696582 3.80812852\n", " 2.35802875 2.26739751 2.17676628 3.62686605 2.17676628 1.36108516] \n", "resid:\n", "[ 0.4984718 -0.42294577 0.58910303 0.48336659 1.85794033 1.027154\n", " -0.86099674 -0.513577 -1.04225921 0.84589153 -1.04225921 -1.41988936] \n", "betah:\n", "[ 0.21902549 3. ]\n", "mean of Y: 3.0 \t mean of resid: 1.62832710278e-15\n" ] } ], "prompt_number": 59 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot the results\n", "x = range(12)\n", "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,4))\n", "ax1.plot(x, Y, 'r-', x, Yfitted, 'b-.')\n", "ax2.plot(x, resid, 'g--')\n", "\n", "# Again, we will want to reuse this code, let's make a tiny function:\n", "def plot_glm(Y, Yf, r):\n", " x = range(Y.shape[0])\n", " f, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,4))\n", " ax1.plot(x, Y, 'r-', x, Yf, 'b-.')\n", " ax1.set_title('Y (red) Y fitted (blue)')\n", " ax2.plot(x, r, 'g--')\n", " ax2.set_title('residuals')\n", "\n" ], "language": "python", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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evRgyZAiuX79eabtO4zqhfwv5TdVSJauQlJWEqcFTjXaMZnWb4frr13Hw5kEc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\nRrQZwTsUo6DWzYQQebh2DfjHP9jUiecW5ZoiS7x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"text": [ "" ] } ], "prompt_number": 60 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Anoter way to compute the residuals is to compute the so called residual forming matrix $R$ :\n", "\n", "$$ \n", "\\hat\\epsilon = Y - \\widehat{Y} = Y - X \\hat\\beta = Y - X (X^T X)^+ X^T Y = (I_n - X (X^T X)^+ X^T)Y = R Y\n", "$$\n", "\n", "where $I_n$ is the n by n identity matrix." ] }, { "cell_type": "heading", "level": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Interpreting our estimates of $\\beta$, changing the data and the model." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "At the look of our results, it seems that there's not much in the first regressor. We have $Y = 0.219 x_1 + 3.0$\n", "We can check that 1) the residuals have mean zero (they are \"uncorrelated with the constant x_1\") the mean of the Ys is equal to \\beta_1, which is the case because $x_0$ has mean zero. We could also check that the residuals are uncorrelated with $\\bf x_0$.\n", "\n", "While the first coefficient is small, especially with respect to the residuals, we still have to see whether this coefficient is \"significantly\" different from zero. This is the topic of our next section." ] }, { "cell_type": "heading", "level": 4, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Making a slightly more general example" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "But before going into testing, let's make our example a little more general. Let's assume that our scans are divided in another 2 groups split, where the first 6 scans are of one condition (or group) and the last six ones of another. \n", "We can model this with a vector $\\bf x = [\\textrm{1 1 1 1 1 1 -1 -1 -1 -1 -1 -1}]^T$, which will model the difference between the first and the last 6 scans.\n", "Another solution is to include two regressors, one for the mean of the six first scans and one for the mean of the last six scans. Let's adopt this parametrisation of the model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "vdata = vdata[:12]\n", "Y = vdata * 1.\n", "print mean(Y)\n", "x0 = np.asarray([1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1])\n", "x1 = np.hstack((np.ones(6),np.zeros(6)))\n", "x2 = np.hstack((np.zeros(6),np.ones(6)))\n", "x3 = np.ones(12)\n", "X = np.vstack((x0,x1,x2,x3)).T\n", "print X\n", "\n", "second_X = X" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "3.0\n", "[[ 1. 1. 0. 1.]\n", " [-1. 1. 0. 1.]\n", " [ 1. 1. 0. 1.]\n", " [-1. 1. 0. 1.]\n", " [ 1. 1. 0. 1.]\n", " [-1. 1. 0. 1.]\n", " [ 1. 0. 1. 1.]\n", " [-1. 0. 1. 1.]\n", " [ 1. 0. 1. 1.]\n", " [-1. 0. 1. 1.]\n", " [ 1. 0. 1. 1.]\n", " [-1. 0. 1. 1.]]\n" ] } ], "prompt_number": 61 }, { "cell_type": "heading", "level": 4, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Let's add signal (== something that is in the model) in the data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Add some signal to our voxel, for the sake of the example:\n", "\n", "Y += 0.5*mean(Y)*x1 - 0.5*mean(Y)*x2\n", "\n", "print Y, mean(Y)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 5.21749728 3.85802875 5.30812852 4.7643411 6.57696582 5.30812852\n", " 0.85802875 0.76739751 0.67676628 2.12686605 0.67676628 -0.13891484] 3.0\n" ] } ], "prompt_number": 62 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's fit our model for the new model and data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta, Yfitted, resid = glm(X,Y)\n", "print beta, mean(Y)\n", "# (beta[1]/2 + beta[2]/2 + beta[3])" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 0.21902549 3.17218166 -1.17218166 2. ] 3.0\n" ] } ], "prompt_number": 63 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot the results\n", "plot_glm(Y, Yfitted, resid)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+wNUVypXJyrdvsDVp0+b/WyvLCnNCCKG3jKwMNp/ZzJO1/utAVM21GidHnqS4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\niBSJgzARERERKdL/Af5P3kGTM5XrAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 64 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conclusion : we see that the fitted data (blue) are fairly close to the actual data - residuals are small compare to the size of the signal." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "What if there is signal not in the model ? " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Let's see what results we would have had with the first model (that doesnt have the regressor modelling the \"on off\" shape, but the new data that have this signal:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print X_firstmodel\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]\n", " [ 1. 1.]\n", " [-1. 1.]]\n" ] } ], "prompt_number": 65 }, { "cell_type": "code", "collapsed": false, "input": [ "glm_result = glm(X_firstmodel, Y)\n", "plot_glm(Y, glm_result[1], glm_result[2])\n", "print glm_result[0] # the betas" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 0.21902549 3. ]\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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0bCkXgca0bJm8TOODD4zbbn5atxadwDAaNwYOHBCdgoheEhUVhbNnz8LX1zfH\n45OnTkYJ6xIAAD8/P/j5+QlIp73IxEiM3D0Swf2CX1kEA0CZEmVQz7kekM+5SeVty2NWu1m48fAG\nbj6+ib039uLmo5soXbw0QgeEGiC9abBSWWFis4l4lvUMZcFCmEyfrvu/i50Rfm78eODuXWDdOkNG\nySk2FvD2Bo4eBerUMV67SnTxIvDee8C//4pOQqQVc58dfZXk5GT4+fnhyy+/RPcX3pFTqVTo+GtH\n7Oq7q8Bi0pQ8SX+CJj82wWfNP8MQnyGi4xCRIEbfR1gvZs6UdxbYutV4bX78sbxTBItgw3N3l3/w\nSEoSnYSIAGRmZqJnz57o379/jiL4OZVKhcA9gWbzQ4AkSRi8fTBau7ZmEUxEWjGNQvj5EonRo+Wb\n5wxt2zbg8mWgsLtckG6KFZNn3yMiRCchUjxJkjB06FB4eHhgXD7r9jf22oiTsScx//h8I6crmmsP\nr+Fp+lMs6aSMHTCISH9MY2nEcxMmyMccr19vuEBPnwKensAvvwBmsu7NIowbB7i4ABMnik5CVGiW\nuDTi6NGjaNWqFerVqwfV/+9OM3v2bHTq1AnAf32OfRKLN396E9v7bEeDSg1ERi4USZKy+0NEymVe\nu0a87NkzeeZw1iygZ0/DBBo3DnjyRN7HmIznt9/kA1Q2bhSdhKjQLLEQLsiLfb6Xcg9Otk4sMInI\nbJjnGuHnXntNXiIRGAgkJur/+n//DWzYIG/XRsbFE+aIzE6FUhVYBCvUmrNrcPPRzYKfSGTmTKsQ\nBoBmzYB+/eRiWJ+ysoARI+Qi2NjbtBFQqxbw4IH8i4iITNreG3txPOa46BhEBmd6hTAAfP01cP48\nsHmz/q65ZAng4AD076+/a1LhWVkBDRoAZ86ITkJEZu6niJ+w/qIB7yUhuDu686hlUgTTLIRfew1Y\nu1be4uzePd2vFx0trzv+4QfLOrrY3DRqBJw+LToFERVR1OMofL7/c6HrpsPjwjH5wGSzuIHPnHk4\neeBy4mXRMYgMzjQLYUA++njAAHlLNV1IkrzMYtw4+e15EofrhInMWoVSFXAo6hCCDgcJaT8xJRHv\nbXoPq7qtQm3H2kIyKAULYVIK0y2EAWDGDOCff3TbaeDPP4EbN4DPPtNfLiqaRo1YCBOZMVsbW+zo\nswO/nP8FP5/72ahtZ2my0GdLH/Tz6ofudXIfAkL6Vat8LUQ/jkZ6VrroKEQGZdqFcMmS8hKJMWOK\ntkQiKQkPULBvAAAgAElEQVQYOxZYtQooXlzv8UhLNWoAqalAQoLoJERURM6lnbG7725MDJ2IQ7cO\nGa3dGYdnwFplja/bfG20NpWsuHVxLO2yFFmaLNFRiAzKtPYRzs+kSfKs7qZN2q3xDQwEMjLkQphM\nQ8eO8trvrl1FJyEqkNL3EX6Vg7cOImBLAP4Z9Q+cSjkZPNeNhzdQtmRZONo6GrwtIjJf5n2gRn7S\n0uQdB6ZNA3r3LtxrTp4E3n0XuHQJsLfXrX3SnylTABsbIChIdBKiArEQfrXrD6+jpkNNAyciIio8\n8z5QIz8vLpG4e7fg52dmAh9+CCxYwCLY1HCdMJHFYBFMRObOPAphAGjSBBgyBBg1St4J4lUWLgQq\nVgT69DFONiq851uoKWyWjYiIiEyPXgphtVoNHx8fdOvWTR+Xy19QEHDlinxMcn5u3QK+/ZZ7Bpuq\nKlXkv5fYWNFJiMiEnY47rbhlKURkfHophBcvXgwPDw/Dn0lfooS8RGLcuLx3HpAk4KOPgE8/BV5/\n3bBZqGhUKi6PILJQF+5e0Mu2avtv7sc7G97B/dT7ekhFupgYOhG3Ht0SHYPIYHQuhGNjY7Fnzx4M\nGzbMOD+9N24MDB0KjByZ++31jRvlmcYJEwyfg4qOJ8wRWaRSNqXw+YHPsefaniJfI/pxNPr/2R/r\neq4zym4U9GqRiZE4f/e86BhEBlNM1wuMHz8e8+bNw5MnT/J9TtALOwT4+fnBz89Pt0anTQMaNgTW\nrQP69ZMfe/QIGD8e2LJF3pWATFfjxsDixaJTEOUSFhaGsLAw0THMlpuDG7a8vwXvbHgHoQNC4V3R\nW6vXp2WloefGnpjYbCL8XP0ME5K08vyEOR5iQpZKp+3Tdu3aheDgYCxbtgxhYWFYsGABdu7cmbMB\nQ20/dOYM0KULcO4cUKmSPEOsUslrg8m0JSQAHh7Agwdcx00mjdunFc2mS5vwyb5PcGLoCVSxq1Ko\n10iShGE7hyE5Ixkbem4w/FI7KpS159biwK0D+LXHr6KjEBWKUbdPO378OHbs2IEaNWogICAABw8e\nxMCBA3W5ZOE1bAgMHy4XwMeOATt3ArNnG6dt0k3FikCpUsDNm6KTEJEBvOf5HgIbB6Lb+m6FPpks\nOSMZaVlp+Ontn1gEmxB3R3dcTrwsOgaRwejtQI3Dhw9j/vz5xpsRBoD0dHm9aXy8PBP8/vuGaYf0\nr0cPeXu7wh6QQiQAZ4SLTpIknI4/jSYuTfSQikR5kv4ElRdUxpPJT2ClMp8dV0m5hB6oYfSf4kuU\nAH79FRg8GHjvPeO2Tbpp3Jg7RxBZMJVKxSLYAtiVsMP2PtsV9wMhKYd5HLFMlmffPnkpy6FDopMQ\n5UuJ45cS+0xElkPbMYyFMInx4IG81/OjR4AV324j06TE8cuYfZYkieuBiUivhC6NICq08uUBR0fg\n6lXRSYjISI7HHMep2FMA5J0lxoaMFZyIiJSOhTCJwxPmiBTl4bOH6PFHD+y+uhsf7fkIH3h/IDoS\nESkcC2EShyfMERndkCFD4OzsDC8vL6O33fWNrpjScgq6ru+Kef7z0KBSA6NnICJ6EQthEoczwkRG\nN3jwYISEhAhrf3ST0bgw8gJng81Mh187IP5pvOgYRHrHQpjEadgQOH8eyCrchvtEpLuWLVvC3t5e\naAYvZ+PPRpNuMtQZPFiDLFIx0QFIwezsgCpVgMhIQMDbtESUt6CgoOw/+/n5wc/PT1gWMg3uTu6I\nTIxE+9fbi45ClENYWBjCwsKK/HoWwiTW83XCLISJTMaLhTARAHg4euDyfc4Ik+l5+Yf16dOna/V6\nLo0gsXjCHBGRyfNw8uDSCLJILIRJLN4wR0Rk8jycPBCZGCk6BpHesRAmsby9gUuXgIwM0UmIFCEg\nIADNmjXD1atXUbVqVaxZs0Z0JDIDFUtXxJkRZxR30iJZPh6xTOLVqwesWSPvIkFkQpQ4fimxz0Rk\nOXjEMpkfLo8gIiIiAVgIk3g8YY6IiIgEYCFM4nFGmIiIiARgIVxIe/cC9+6JTqG7xERg2zYgPV10\nkhfUrw9cvQo8e6bVy86fB/76CzD35Ywajfz9dfWq6CS6S04GtmwBHj8WnYSIDEEjaURHINIroxTC\n3boBp04ZoyXDuXQJqFMHGDvWvP+Tf/wYmDsXcHMDNm4Uneb/lSgBuLvLla0W5s4FRowA3nwTSE01\nUDYj+PNPYNIkoHlzYO1a0WmKTqORJ/cXLpT/TjT8/5LIokiShIrzK+JJ+hPRUYj0xiiFcOfOgA6n\n3xldXjOMn3wiF8N2dnLdZq5q1QJOnAC2bweqVhWd5gVFWCe8bh1w+TIwbx5ga2ugXEbw7rvA2bPA\nzZvA22+LTlN0VlbyD7xHjwJnzsgfE5HlUKlUqFa2GvcTJotilP+qPvpInvEyBwkJck2W12xWpUrA\n118Dr72W83FTfWv+q6/kt9zz0rChPGv3Mi1XJ+jPK06Yu3EDyO/EVysroGXL3I8nJACZmfqLpy+r\nVgF37+Z8zMoKUKmAMmUAB4ecn9NogOPHTe977M4deVnKy8qWlX/P6weTffuAmBjD5iIiw3J3cucJ\nc2RRdCqE09LS4OvrC29vb3h4eGDy5MmFfq1aDbz3HvDokS4J9K9iRWDnTu1msxYsAL7/3nCZiqp3\n77yL3fwkJclb+go52+IVN8xVrAh4eWl3uaVLgd9/10MuPbO21m4ZR0yMaX5vxccDx45p95p//jHv\nZUVEBHg4euDyfRbCZDl0PlAjNTUVtra2yMrKQosWLTB//ny0aNHivwby2dhYkoDDh4HWreXZMBGi\nooCsLKBmTd2uk5Ii/6pQQS+xiuTWLaBGDd2vk5IClCql+3W0lpkJlCuHzJgEaEqV0cvyE0kS971l\nCu2T7pR4uIQS+0yFt+3fbfhfxP+wq+8u0VGI8mT0AzVs//890IyMDKjVaji8/N5uPlQqwM8vd6GQ\nmGj4HQ2io4HBg+XlAfq4ia9UqdxFsCQZ/i1tSZLfbm7dGujaVS7qdZVXEXz4sOF3NEhT22BFha/w\nhqcNtmzRzzVf/t56+BCYNcvws5IJCcBnn8l/L4b6+w8Kkme89fF3/ipnz8rv3Jw4YZjr//UX8NZb\nhrs+EemXh5MHbifdFh2DSG90LoQ1Gg28vb3h7OyMNm3awMPDI9dzgoKCsn+FFXDX3OrV8gzt4sWG\n2wkgORl4/XXg+nWgXz/DtJGYCAwdCjRtCuzZY5g2AOC33+SdE86fB4oVM0wbly/LOxoEBMhrQw1h\n/Xpgp/QWfn9vK/r2NUwb6elyQe/mBixfbpg2MjLkv/Nnz+S/G0PNCDdvDqxcKe9k8vChYdr47jv5\nB6xmzeQlM4bQpIm8q0zfvsD8+YZpQxthYWE5xisiyqmWQy2cH6ndDj9EpkznpRHPJSUloWPHjpgz\nZw78/Pz+a6AIb7OdOSPP3E2eLC8dNVdqNbB1q7wE49NPRafRzdOnwI8/ykV36dL6v74kAapffgZC\nQuSq2IBu3ZL3hPb1Ncz109KAkiUNc+2XnT0L+PgY5tr378t/18boS2amvCynXDnDt6UNJS4TUGKf\nichyaDuG6a0QBoCvv/4ar732Gj59oeoTPaiOGAH07w+0aiUsgl6cPw9s2gR8843oJDlpNNpvkzVz\nJjBqVO4dEnDpEtC9O3Dtmt7yaePxY+0KsevX5WU27doZLlNRxMXJO1DY2RXu+ZIkL1Fo1cq01jRL\nEhAcDHTqJG4rNtHjlwhK7DMRWQ6jrhG+f/8+Hv//gstnz54hNDQUPoaangIQHi7vGauNiRPlt6pN\niSTJbznHxRX+Na6ugL+/wSIV2apV8jZt2qhaNZ+tzerUkRfYCthKJC1Nfps+Obnwr3nwQJ7tNzWb\nNwO//lr450sSsGyZ3B9T8uCB/MOfKRXnRERkWXSaEb548SIGDRoEjUYDjUaDAQMGYOLEiTkb0OPs\nQlycvKdsXrO7Go08oajtNluiRETIb2nn9Z/806eAjY3x3l7XRVYW8ORJHrO7L3xeq7XLrVoB06YJ\nmWbNzJS/7kTPKXF2VIl9JiLLIXRpRJ4NGGFQ3bxZnpV0dgYOHjTfGaT4ePkGqOXL5Rm9Tp1EJyq6\nrVvl0+vi4oDQUC1e+Mkn8hYcn39usGzaOHhQ3st3zRpg0SLA21t0oqJ5+hSYPl3eYu/JE3n9vbma\nOlX+wSsw0PA/uCixKFRin0k7GkmDmKQYVC9XXXQUolyMvn2aaGq1XHAtXmzeRTAgF4yxsfIRteZc\nBD99Ku/+4eYGbNyo5YtfcbCGCA8eyEc5DxsG1K0rOk3RqdXyv42DB+Vt3cxZjx7yD1iG2iWFiF4t\nU52J2ktrIz3LwHudEhmBRcwIkwW5dk1eDG2Ki29JcZQ4fimxz6S9OkvrYPP7m1G3ghnPEJBFUtyM\nMFkYNzd5+4bERNFJiIgoH+5O7ohMjBQdg0hnLITJtFhZyUf+mdDyCCIiysnDyQOXEy+LjkGkMxbC\nZHoaN2YhTERkwjwcPXD5PgthMn8shMn0mNgNc0RElJOXsxeKWxcXHYNIZ7xZjkxPVBTQrJm8nxyR\nQEocv5TYZyKyHLxZjsxf9ery6RYshIn0LiQkBHXq1EGtWrUwd+5c0XGIiIRiIUymR6Xi8ggiA1Cr\n1QgMDERISAguX76M9evXIzKSd/4TkXKxECbT1KgRcPq06BREFiU8PBw1a9aEq6srbGxs0KdPH2zf\nvl10LCIiYXg2E5mmRo2AFStEpyCyKHFxcahatWr2x1WqVMGpU6dyPS8oKCj7z35+fvDz8zNCOiIi\n7YWFhSEsLKzIr2chTKapcWP5XGNJMu9zs4lMiKqQ/5ZeLISJ8pOWlYaTsSfh5+onOgop2Ms/rE+f\nPl2r13NpBJmmypUBGxsgOlp0EiKL4eLigpiYmOyPY2JiUKVKFYGJyJylZ6Wj67qu0Ega0VGIioyF\nMJku3jBHpFeNGjXCtWvXEBUVhYyMDPzxxx94++23RcciM1W2ZFmUK1kOMUkxBT+ZyESxECbTxRPm\niPSqWLFiWLp0KTp27AgPDw/07t0b7u7uomORGXN3cudRy2TWuEaYTFejRsCCBaJTEFmUzp07o3Pn\nzqJjkIXwcPJA5P1IdK7F7ykyT5wRJtPVsKE8I6zh+jMiIlPk7sgZYTJvLITJdFWoAJQtC9y4IToJ\nERHlwdfFFzUdaoqOQVRkLITJtHGdsP6sWwe8/768JR0RkR74VPLB5y0+Fx2DqMh0KoRjYmLQpk0b\neHp6om7duliyZIm+chHJeMKcfiQmAuPHAxERwPr1otMQERGZBJUkFX16KCEhAQkJCfD29kZycjIa\nNmyIbdu25bgLWaVSQYcmSOn27wdmzAD++kt0EvM2cKC81OT994F33gEuXQIcHESnMnlKHL+U2Gci\nshzajmE6zQhXrFgR3t7eAIDSpUvD3d0d8fHxulySKKeGDYGzZwG1WnQS83XggPyDRFAQ0KQJ0KsX\nMGmS6FRERETC6W37tKioKJw9exa+vr65Psdz66nI7O2BihWBK1cADw/RaczPs2fAyJHA0qVA6dLy\nYzNnAp6ewJEjQMuWYvOZGF3PrCciIvOi09KI55KTk+Hn54cvv/wS3bt3z9kA32YjXQUEAJ06AYMG\niU5ifqZOBf79F9i0Kefjf/4JTJkCnDsHlCghJpsZUOL4pcQ+k24SUxKx98Ze9K/XX3QUIuMujQCA\nzMxM9OzZE/37989VBBPpBY9aLprLl4EVK4DFi3N/rkcP4I03gG+/NX4uIrIomZpMfLL3E9ExiIpE\np0JYkiQMHToUHh4eGDdunL4yEeXELdS0p9EAH34ITJ8OVK6c+/MqFfD993KRfPWq8fMRkcWoVLoS\nMtQZuJ96X3QUIq3pVAgfO3YMv/32Gw4dOgQfHx/4+PggJCREX9mIZD4+wIULQGam6CTm46ef5K/X\nyJH5P6daNeDLL+Xn8K1wIioilUoFdyd3RCZGio5CpDW9rBF+ZQNcb0b64OEhHwjx/7uU0CvcvQt4\neclbz9Wr9+rnZmUBvr7A2LHyFmuUgxLHLyX2mXQ3dMdQ+Lr4YkTDEaKjkMIZfY0wkVFweUThjR8P\nDBlScBEMAMWKAatWAZ99Btzn25pEVDQejh64nHhZdAwirbEQJvPAE+YKZ+9e4ORJ4KuvCv+ahg3l\nnTkmTjRcLiKyaP5u/mhVvZXoGERa49IIMg8nTgCBgcCZM6KTmK7UVHlJxLJl8nZz2khOlpef/Pwz\n0KaNYfKZISWOX0rsM5Ep0kgaqKCCSqUSHcWscGkEWSZvbyAyEkhLE53EdH39tXxynLZFMCAftrF0\nqXzjHL/GRETCbby0ESN2cc21obEQJvPw2mvyvrcXL4pOYpouXpR3ili4sOjXePttoG5dYPZs/eUi\nIqIiWRq+FJ1rdhYdw+KxECbzwXXCedNogBEjgG++kY+j1sWSJcDy5fJpdEREJMTZO2cRnRSNt2u/\nLTqKxWMhTOaDJ8zlbeVKwNoaGDZM92u5uADTpsmHcWg0ul+PiIi0tuz0MoxqNArFrIqJjmLxWAiT\n+eAWarnduSPvELFyJWClp3/Oo0bJ64TXrNHP9YhIEa4+uIr5x+eLjmH2Hj57iC2RWzCsgR4mN6hA\nLITJfNStC1y/DqSkiE5iOsaOlWdvPT31d01ra7mwnjwZuHdPf9clIosmSRJ++PsH0THMXvTjaIxu\nPBoVSlXIfmzl3ysRFhUmLpQFYyFM5qNECbngO3dOdBLTsHs3cPYsMGWK/q/t7Q0MGgR88on+r01E\nFsnNwQ3xT+ORmpkqOopZ86nkg2/afpPjMSuVFb478Z2gRJaNhTCZFy6PkKWkAKNHAz/8IO+oYQhB\nQcCxY0BoqGGuT0QWpZhVMdR0qIkr96+IjmJx+nr1xfGY44h6HCU6isVhIUzmhTtHyIKCgJYtgfbt\nDddGqVLy4RyjRgHPnhmuHTKKTZs2wdPTE9bW1oiIiBAdhyyUh5MHIu9Hio5hcUoVL4VB3oO49MQA\nWAiTeeHOEfLSkF9+ARYsMHxbXboADRrIW7ORWfPy8sLWrVvRqhWPwSXDcXd0x+XEy6JjWKRRjUZh\n9dnVeJbJiQl94r4cZF48PIDYWODJE8DOTnQa41Or5T2DZ88GKlQo+Pn6sHgxUK8eEBAg37BIZqlO\nnTqiI5AC9PXqi5QM3tBcFJIkvfI45ZoONeHr4otDUYfQpVYXIyazbCyEybwUKwbUrw9ERAB+fqLT\nGN/y5fKa4MGDjddmpUrAjBny7hRHjuhvmzYyWUFBQdl/9vPzg58S/61RkbxR/g3REcxSSkYKmq9u\njuNDj8PWxjbf5/3Z+08Uty5uxGSmLywsDGFhYUV+vUqSJEl/cfJoQKWCgZsgpRk7FqhSBZg4UXQS\n44qNlXdzOHoUMPbsnkYDNG8OfPCBXBArhLmNX/7+/khISMj1+KxZs9CtWzcAQJs2bbBgwQI0aNAg\nz2uYW5+JLMGqM6uw59oebOuzTXQUs6ftGMYZYTI/jRoBu3aJTmF8Y8bIO0WIeIvbygpYtQpo2xZ4\n5x3dj3ImgwjlDh9EZkeSJCwNX4rvOnJ7NBH4HieZHyVuobZ9O3DpknzIhSheXvIxzuPGictAesEZ\nXyLTceT2EWSoM9CuRjvRURSJhTCZnzfeABITgQcPRCcxjqdPgY8/BlasAEqWFJtl6lR5+7rgYLE5\nSGtbt25F1apVcfLkSbz11lvo3Lmz6EhEBGBp+FIENgl85Y1yZDg6F8JDhgyBs7MzvLy89JGHqGBW\nVvKWXmfOiE5iHF99BbRrB7RpIzoJYGsr37D30Uc86trM9OjRAzExMXj27BkSEhIQzB9myECO3j6K\nLw58ITqGWVBr1EjJTMHA+gO1el2mOhMT9k1AlibLQMmUQ+dCePDgwQgJCdFHFqLCU8p+wmfOAOvX\nA/PmiU7yn44dgTfflHeSICJ6ia2NLXZf2y06hlmwtrLG7r67YVdCu+1AbaxtEB4Xju3/bjdQMuXQ\nuRBu2bIl7O3t9ZGFqPCUsE44K0veM/jbbwFHR9Fpclq4EFizBjh/XnQSIjIxdRzr4NqDa1Br1KKj\nWLTAxoFYenqp6Bhmzyi7RnBPStK7Ro2ATz8VncKwvv8eKFcOGDBAdJLcnJ2BmTPlrdSOHQOsrUUn\n0gtd96MkInlG2Lm0M249voWaDjVFx7FYPdx7YPze8fjn3j+oW4GHHRWVXvYRjoqKQrdu3XDx4sXc\nDXBPSjIESQLKlwcuX7bMrbxu35bXQR8/Lt8caIo0GqB1a6BPH3lbNwukxPFLiX0m/Xtr3Vv4sOGH\neLv226KjWLTpYdORkJKAH976QXQUk6HtGMZdI8g8qVTyrLAl3jAnSUBgoHxwiKkWwYB80+LKlUBQ\nEBAfLzoNEZkQDycPXE68LDqGxRvRcAT+jPwTaVlpoqOYLR6oQearUSNg6VL5xLVKlYDKleXfnZ3l\no5jN1datwPXrwKZNopMUzMMDGDlSPuxj82bRaYjIRIxvOh42VjaiY5isT/Z+gk41O6GDWwedrlOp\nTCVc//g6ShYTvLWmGdN5aURAQAAOHz6MBw8eoEKFCpgxYwYGDx78XwN8m40MJT5enpG8c0f+8/Pf\n79+Xl008L4xf/P3FP5tiwZyUBHh6yjtFtGwpOk3hPHsG1KsHfPcd8P/H+FoKJY5fSuwzkTE9fPYQ\nbkvccDXwKpxKOYmOY3G0HcP0skb4lQ1wUCVjy8oC7t3LWRzn9Xtiolwwv1wsv/y7szNgY6SZjY8/\nBtLSgB9/NE57+nLgADBkiHz6XenSotPojRLHLyX2mciY5h+fjwt3L+CXHr+IjmKRWAgTFVZWllwM\nx8e/umhOTAQcHAoumCtW1K1gPnUK6N5dLiYdHPTXT2MZOBBwcgIWLBCdRG+UOH4psc9ExqLWqFHr\n+1rY0GsDmrg0ER3HIrEQJtI3tVqeYX7V7HJ8vPwce/vCFczFi+dsIzNTXvM8aRLQt6+YfuoqMRGo\nW1c+frlBA9Fp9EKJ45cS+0xkLLuu7sKMwzMQPjxcdBSLxUKYSBS1Wi4GXy6QXy6a796V9wd+sUB+\n+lT+FRIi74hhrtasAZYtA44cAV57TXQanSlx/FJin4mMZeZfM1G9XHX0r9df79f+9/6/CI8L1/q4\nZkvDQpjI1KnV8g19Ly+/GDgQcHERnU43kiQfABIVBezYYZ5LPF6gxPFLiX0mw/jjnz9w5PYRLO3C\n08+M4cbDG2j6U1NEj4uGrY2t6DjCaDuGmdgt80QKYG0t34Dn7Az4+IhOo18qFfDLL8DEifKuFyEh\nQNWqolMRkQAVS1fE2YSzomMohpuDG5q4NMGGfzZgiM8Q0XHMBg/UICL9srKSb5gbMgRo3ly++Y+I\nFOf5oRp8h8F4AhsHYmn4Un7NtcBCmIgMY8IEYPZsoG1bec0wESmKUyknFLMqhoTkBNFRFKNjzY54\nkv4EJ2NPio5iNlgIE5Hh9OsH/PYb0LMn8OefotMQkZHxqGXjslJZYXTj0fgxwsz2oheIhTARGZa/\nv7xW+OOPgR9+EJ2GiIzI3dEdVx5cER1DqCPRRzD5wGSjtTei4Qgs6bzEaO2ZO+4aQUTGcfMm0LEj\n0Ls38PXXZrFNnBLHLyX2mQwnLSsNJaxLQGUG/94N5b1N78Gvuh9GNxktOooicPs0IjJd9+4BXbsC\nXl7AypVAMdPeuEaJ45cS+0xkKLFPYlHvh3qIHheNMiXKiI6jCNqOYVwaQUTGU6ECcPCgvH9y9+5A\nSoroREREBrPyzEr09erLItiEsRAmIuMqXRrYvh1wdATatZMPFyEisjDpWen48cyPGN2YSyJMGQth\nIjI+Gxv5OOa2beW9hqOiRCciItKr83fPw7eKL9yd3IVl2HFlB/69/6+w9s0B1wgTkVhLl8r7De/e\nDXh7i06TgxLHLyX2mQwrS5OFZ5nPFLk8QJIkoTcKzjg8A3FP47Cy60phGYyNa4SJyLwEBgKLFwMd\nOsjrh8lgJk6cCHd3d9SvXx/vvvsukpKSREciBVh0chG+CvtKdAwhRO+WMaLhCGy8tBGP0x4LzWHK\nWAgTkXi9egEbNwIBAcCGDaLTWKwOHTrg0qVLOH/+PN544w3Mnj1bdCRSAB6qIU7F0hXRuWZnrD23\nVnQUk8VCmIhMg58fsH8/MHEisGiR6DQWyd/fH1ZW8rDv6+uL2NhYwYlICdwd3VkICxTYJBDLTi+D\nRtKIjmKSdN7EMyQkBOPGjYNarcawYcMwadIkfeQiIiXy8gKOHZMP3oiPB+bMAaz487ohrF69GgEB\nAXl+LigoKPvPfn5+8PPzM04oskjVy1XHw2cP8ST9CexK2BmkDUmS8Ff0X1h0ahF6uvdE/3r9DdKO\nOXqzypsoU7wM9t/cjw5uHUTH0buwsDCEhYUV+fU63SynVqtRu3Zt7N+/Hy4uLmjcuDHWr18Pd/f/\n7pDkjRdEpLUHD4Bu3QA3N+Cnn4DixYXEMMfxy9/fHwkJCbkenzVrFrp16wYAmDlzJiIiIrBly5Zc\nzzPHPpPpa7CyAVZ0XYEmLk30et20rDRs+GcDFp1chLSsNIxrOg4D6g1AqeKl9NpOYak1agzcNhAr\n3lphUjcH3k66jcplKqOYlWkfYqQP2o5hOn1FwsPDUbNmTbi6ugIA+vTpg+3bt+cohImItFa+vLxM\nIiBALog3bwbKmM5/KqYsNDT0lZ9fu3Yt9uzZgwMHDhgpERHQtEpT3Eu5p9drXntwDS3XtIR3RW/M\naT8HHdw6wEol9h2kPdf24PrD6yZVBANAtbLVREcwWToVwnFxcahatWr2x1WqVMGpU6d0DkVEBFtb\nYMsWYPRoef3wnj2As7PoVGYtJCQE8+bNw+HDh1GyZEnRcUhBlr+1XO/XfN3+dYR9EIY6jnUKfO64\nkHGoW6EuhvoMNehODktPL0Vg40CDXZ/0T6dCuLDfTFxvRkRFUqwYsGIFMGOGfPBGSAhQs6bBmtN1\nrZo/cRwAAAupSURBVJmp+/jjj5GRkQF/f38AwJtvvonly/VfoBDpk1qjRqYmEyWL5fzhzdrKulBF\nMAAM9RmKD7Z/gE2XN+HHbj8aZIb0yv0rOJdwDtv7bNf7tclwdFojfPLkSQQFBSEkJAQAMHv2bFhZ\nWeW4YY7rzYhIL1atAoKCgB07gEaNjNKkEscvJfaZTFNSWhJWn12NJeFLMK31NHzg/YFO18tUZ2Le\n8XlYeHIhZrWdhWENhul1dnhsyFiULl4aM9vO1Ns1SXtGPVCjUaNGuHbtGqKiopCRkYE//vgDb7/9\nti6XJCLK24gR8uxw587yzDARWaTrD69jbMhY1FhcA6fjT2NDzw06F8EAYGNtgy9afoFDgw5hVcQq\nfB/+ve5h/59G0iD0RihGNhypt2saQoY6Az+f+5k/7L5A5yOWg4ODs7dPGzp0KCZPnpyzAc4uEJE+\nHT8O9Ogh7ybRtatBm1Li+KXEPpPpuPrgKlqsboFhDYbho8YfoYpdFYO0k6XJQqY6E6/ZvKa3a6o1\nalhbWevteoagkTSovbQ2fu7+M5pVbSY6jkFoO4bpXAgX2AAHVSLSt3//BRwd5V8GpMTxS4l9JuOI\nfSIf4FJQcZuWlZZrPTDpz6KTixAeF451PdeJjmIQRl0aQUQkRJ06Bi+CiUi//hfxP6z4ewUAIP5p\nfL7bqYksghOSEyz+BLYPvD9A8PVg3Hl6R3QUk8BCmIiIiAzO3dEdB28dRP8/+8NzuSeO3j4qOlIu\nE0Mnwv9Xf9x6dEt0FIMpV7Icenv2xo8RP4qOYhJYCBMREZHBNXZpjKcZT+Fd0Rs3x9zEu+7vio6U\ny5p31qCTWyc0+V8TLD+93GJnh0c3Ho2VZ1YiU50pOopwXCNMRJQPJY5fSuwz0csiEyMxePtg2NrY\n4qe3f0IN+xp5Pm/l3yvhWcETLaq1MHJC3Z1LOIf6zvUNesCICLxZjohIT5Q4fimxz0R5UWvUWHhy\nIaqXrY73PN/L9fn0rHRUX1S90KfbkXFoO4bpdLIcERERkSWytrLGp80+zffzmy9vRj3neiyCzRzX\nCBMRERFpaenppQhsEig6BumIhTARERGRFtacXYM7T+/grVpviY6iF0peDsVCmIiIiEgLGeoMfOv/\nrcmfJFdYb294G5/v/xwJyQmioxgdb5YjIsqHEscvJfaZSOmiH0dj/on5+P3C7wjwCsDEZhPhWs5V\ndKwi4clyRERERFRo1ctVx/edv0fk6EjYlbBDw1UNMTF0ouhYRsEZYSKifChx/FJin4kop8dpj3Hl\n/hX4VvEVHUVr3EeYiEhPlDh+KbHPRGQ5uDSCiIiIiPROrVGj9+be2PbvNos5fpqFMBEREREVSKVS\nobdnb3zz1zfw+sELv134DVmaLNGxdMKlEURE+VDi+KXEPhORdiRJQujNUMw+OhtRj6Mwz38eenn0\nEh0LANcIExHpjRLHLyX2mYiK7kTMCaRlpaFNjTaiowBgIUxEpDdKHL+U2Gcishy8WY6IiIiIhErN\nTMXn+z9HTFKM6CivVORCeNOmTfD09IS1tTUiIiL0mclkhYWFiY6gF5bSD4B9MVWW1BdLMXXqVNSv\nXx/e3t5o164dYmJM+z8nfbCk70NL6Yul9ANgXwqSoc5AliYL9VfUx5DtQ0z2+OYiF8JeXl7YunUr\nWrVqpc88Js1SvuktpR8A+2KqLKkvluKzzz7D+fPnce7cOXTv3h3Tp08XHcngLOn70FL6Yin9ANiX\ngpQrWQ7zO8zHtY+vwbWcK4pbF9d7G/pQrKgvrFOnjj5zEBGRAZUpUyb7z8nJyXB0dBSYhoiUorxt\neXzV+ivRMfJV5EKYiIjMy5QpU/Drr7/C1tYWJ0+eFB2HiEi4V+4a4e/vj4SE3Gs6Zs2ahW7dugEA\n2rRpgwULFqBBgwZ5N6BS6SkqEZHxmdMOCoUZswFgzpw5uHLlCtasWZPruRyzicjcaTNuv3JGODQ0\n1KhhiIio6Ao7Zvft2xddunTJ83Mcs4lISfSyfRoHTiIi03bt2rXsP2/fvh0+Pj4C0xARmYYiH6ix\ndetWjBkzBvfv30fZsmXh4+OD4OBgfecjIiI96NWrF65cuQJra2u4ubnhhx9+QIUKFUTHIiISqsgz\nwj169EBMTAyePXuGhISEXEVwSEgI6tSpg1q1amHu3Lk6BxUlJiYGbdq0gaenJ+rWrYslS5aIjqQz\ntVoNHx+fHGsGzdHjx4/Rq1cvuLu7w8PDw2xv/pk9ezY8PT3h5eWFvn37Ij09XXSkQhsyZAicnZ3h\n5eWV/djDhw/h7++PN954Ax06dMDjx48FJiy8vPoyceJEuLu7o379+nj33XeRlJQkMKFuNm/ejIsX\nL+LcuXPYsmVLnkUwx23TxDHb9JjruM0xOzeDnCy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"text": [ "" ] } ], "prompt_number": 66 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* First, clearly the fitted data (blue) are far from our actual data. Noise is large, and ressemble the data (accounting for the shift in the mean)\n", "\n", "* You may notice: the beta estimated with these new data (we have added the \"step\" function) are exactly the same than the ones estimated on the original data. Why ? Because we added in the Y something that is completely uncorrelated to the model X_firstmodel. No regressor in this first model can pick it up, therefore the betas are unchanged. \n", "\n" ] }, { "cell_type": "heading", "level": 4, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Changing the model $X$ by adding a regressor that is not in the model" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "Using the previous model, let's add a regressor $x_2$ to the model that is uncorrelated to each and every column of $X$, (ie adding $\\bf{x_2}$ with $\\bf{x_0}^t\\bf{x_2} = 0$, and $\\bf{x_1}^t\\bf{x_2} = 0)$, $\\bf{x_2}$ is in the third position, the $\\hat\\beta_0$ and $\\hat\\beta_1$ would be unchanged. But the Let's check:\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = X_firstmodel\n", "x2 = np.hstack((np.ones(6),-np.ones(6)))\n", "X_ = np.vstack((X.T, x2)).T\n", "print X_.T.dot(X_)\n", "glm_result = glm(X_, Y) # original data\n", "plot_glm(Y, glm_result[1], glm_result[2])\n", "print glm_result[0] # the betas" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 12. 0. 0.]\n", " [ 0. 12. 0.]\n", " [ 0. 0. 12.]]\n", "[ 0.21902549 3. 2.17218166]" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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+wNUVypXJyrdvsDVp0+b/WyvLCnNCCKG3jKwMNp/ZzJO1/utAVM21GidHnqS4\nk4HtlIRVk6WWjcugQvjSpUu0bt0af39/mjZtytNPP02nTp0KfuPHH6vtBtauNeTwxpOSonZ6mD0b\nSpY07bGqVoWVK9V5EG++qU4ROXv2v9dXrVKLZisdDb5vwAC1WYisMCeEEPrbF7sPX1dfqpTJOdJT\npngZjRIJU9l1cReD1gwq9PZ1y9flUsolrt0xzjfr9s6gQrh69eocOXKEI0eO8PfffzN+/PjCvbFU\nKaNPkTDI5Mnw+OPQvr35jtmpk9qmrWVLdf7spEnqXX82MBqcQ4MG6iocqalaJxHCpg0ePBhPT89H\nfis3evRoateuTePGjTl8+LAZ0wl9hZ8Op0vtgm+wFtZvb8xeyhYvW+jtHR0c2fHSDko5F2WBAvEw\n86wsl5fHH4fnn1dvItPS4cPwww/w2WfmP3bx4urCHYcPqwtxVKumjkgXoruE1ShWTC2GjxzROokQ\nNm3QoEFs2rQp39fDw8P5999/OX36NHPnzmXEiBFmTCf0tS92nxTCdqIoK8oFVA6QKTJGol0hDOqS\nxPv3q+sEayEzU+0ZPG0aVKigTQYAHx/1br9ff1VHym1lNPg+mScshMm1bt0aNze3fF9fu3YtAwcO\nBKBp06YkJydz6dIlc8UTeto6YCvNvJtpHUOYQWRcpCykoSEnTY/u4qIuu9yrF7RurfacNadvv1Wn\nabz0knmPm582bbROYFTp6bBnD7QJDoZt27SOI4Rdi4uLw8fHJ/uxt7c3sbGxeOaxcNDkyZOz/xwa\nGkpoaKgZEooHOegePU6VmpbKyPCRzO82HycHbf8pF0V3KeUSt+7dopZ7La2jWK2H+7/rS/u/Pa1a\nQe/e6hJw5lxDODYWpkyBXbtsbwTWQiiKujhIy6lBOE2frnUcIezew701dflc+x4shIVlKlWsFOeT\nz/PT3z/Rv1F/reOIIjqUcIhgr+B8/y6Kgj38YT0sLEyv92s7NeK+Dz9UOwv89pv5jvnaa2qniLp1\nzXdMO1OsGGzYAE4N66kfPG7c0DqSEHbLy8uLmJiY7MexsbF4eXlpmEgY6t3W7/Lxro/JUrK0jiKK\nqHOtzqx8fmWR3y+L3xjOMgrh+1MkRo6EK1dMf7zVq+H4cXUZN2F6Tk7qaidRUVonEcJudevWjSVL\nlgCwb98+XF1d85wWIaxHxxodcXF2Yc3JNVpHEUWk0+mK3BLvuwPfMX6b1DGGsoxCGNQ2Yn37qiO1\npnTrltrf0vUKAAAgAElEQVSpYs4ctWuDMA9ZYU4Ik+rbty8tWrTgn3/+wcfHhwULFjBnzhzmzJkD\nQJcuXahRowa1atVi+PDhzJo1S+PEIi+7L+4mKTWpUNvqdDrebfUuH+78UEYG7VAt91rsi92ndQyr\np1NM/LdHrzWf79xRRw4/+gh69jRNoLFj4eZNtTuDMJ+lS9UFVH75ReskQhSavmvW2wJ7PGdLUu/b\nevzQ4weCqgQVavssJYvQRaEs7r6Y6m7VTZxOWJLrd65T9cuqJL+TjKODo9ZxLIa+1zDLGREGtYfu\nwoXq3N2kwn0i1svBg/DTTzBjhvH3LfIVHg5nPFvIiLAQQjzC2etnuXbnGk0qNyn0exx0Dux4aYcU\nwXbIraQbVcpU4cSVE1pHsWqWVQgDtGgB/fqpxbAxZWSoPYNnzDB/mzY7t2EDrDnqC1evqr+EEELk\nsvH0RjrX6lxg67SHSccB63Qp5RKZWZkG7SPEK4TIuEgjJbJPllcIA3zwAfz1F6ws+p2UucycCe7u\n0F/azJhby5awe48DNGkChw5pHUcIISxS+L+yrLI96fFzD/688KdB+wipEsLJKyeNlMg+WdYc4Qft\n2wc9eqgFccWKhoW4cAECA2HvXqhd27B9Cb3Fx6uL5r12cRy4usKECVpHEqJQ7HG+rD2esyW4k36H\nip9W5OLYi7iVzH+FQGEb0jPTcZ3uSuKbiUXuGgHqHHF9v0GwddY9R/hBzZrBiy+qLdUMoSjqNIux\nY6UI1kiVKv/fDCQ4WOYJCyFEHu5k3OHj9h9LEWwnoi9HU921ukFFMBS8AqEomGX/BKdMgb//NqzT\nwKpVcOYMvP228XKJopEWakIIkSf3ku6MCjH83pgnlz4pX5VbgQNxBwjxCtE6hsDSC+ESJWDRIrXv\n7+XL+r//xg0YMwbmzlWXORPaql4dbt+GxEStkwghhE1q6dOSabumaR1DFCAyPlIKYQth2YUwQNOm\nMHAgvPqqOs1BHxMmQJcu0KqVabIJ/eh0MioshBAmNCpkFOtOreN88nmto4gCNPdurnUEgTUUwgBh\nYeqSyPpMkdi3T50WMX266XIJvbz+Olzxe1wKYSGEMBG3km4MCxzGjD3SL9+Sfd/texpXamyUfWUp\nWURfijbKvuyRdRTCD06RuHSp4O3T02H4cPjsM3CTGw8sRdu24BTYWAphIYQwobFNx7I8ejkJtxK0\njiLMQFEUWi1sxbU717SOYpWsoxAGCAmBwYNhxIiCp0h88QVUqgR9+pgnmyiUbt3AtU1jOHBA/2ku\nQghhg27du0XoolCylCyj7dOztCfjWozjXPI5o+1TWC5HB0eaVG7CgbgDWkexSkYphDMzMwkICKBr\n167G2F3+Jk+Gf/5Rl0nOz7lz8Mkn8N136pxUYVm8vdX/LrGxWicRQgjNbTu3DWdHZ6O3wRrfejwt\nfFoYdZ/CcskKc0VnlL95X331FX5+fqZf5rF4cXWKxNixeXceUBT1prq33oIaNUybRRSN3DAnhBDZ\nwk+H06WWrCYnDBNSJYTIeCmEi8LgQjg2Npbw8HBefvll86xGFBwMQ4bAK6/k/nr9l1/UkcY33zR9\nDlF0QUHq9AghhLBjiqKohbAsq2w3rt+5zvpT642+3/sjwrIqpP6cDN3B66+/zowZM7h582a+20ye\nPDn7z6GhoYSGhhp20EmT1CWTly2Dfv3U565fV9sS/PorODsbtn9hMt9/D2lJPRlxWj6sCMsTERFB\nRESE1jGEnYi+HE1xp+I85vGY1lGEmey6uItvDnzD0489bdT9epf1pk21NqSkpRi8Wp29MagQXr9+\nPRUrViQgIOCR/3g8WAgbRfHisHix2iO4XTuoXBnGj4dnnoHm0pfPkpUrB4tP12bEwYPqiL7M4xYW\n5OEP6mFhYdqFETZv+7ntdKndxeTTCtMz01FQKOYoC0tpzVQLaeh0On553oBVeO2YTjFgHP3dd9/l\nhx9+wMnJibt373Lz5k169uzJkiVL/juATme6ofqJEyE6Wl0+uVcvOHYMXF1NcyxhFAkJUL8+XHGp\nisOO7VCzptaRhMiXSa9fFsoez1kriqJwN+MuJZ1LmvQ4Q9YOIbByIK8Gv2rS44iCPbH0CUYFj6Jr\nHRM3F7Bj+l7DDCqEH7Rjxw4+/fRT1q1bZ1Agvdy7p843jY9Xu0T06mWa4wij+ucfeOydHuj69oHe\nvbWOI0S+7LEotMdztnX7YvfRZ2UfTr92GmdHmTqoFUVR8PjEg+Mjj1OpdCWt49gsfa9hRu3XYvKu\nEQ8rXhx++AEGDYLnnzfvsUWR1akDupBg6RwhhBBm0My7GTXcarAsepnWUezav9f+pUzxMlIEWxij\njQjnewAZXRB52bwZPv4Ytm/XOokQ+bLH65c9nrM92HZ2GyPDR3Ls1WM4OjhqHccunbl2hq1ntzI8\naLjWUWyaZlMj8j2AXFRFXq5eVXs9X78ODtazwKGwL/Z4/bLHc7YHiqLQ7PtmjGsxjuf8ntM6jjCR\nPTF7cNA50My7mdZRNKPp1AghCivLzYMMD084dUrrKEIIYVZxN+M4ddW81z6dTscnHT7BvaS7WY8r\nzOtg/EEWHVmkdQyrIoWw0ETfvrDJa4jMExZC2J35UfOZe2iu2Y/bxrcN7aq3M/txhfnIUsv6k0JY\naGLJEni6m4OsMCeEEW3atIm6detSu3Ztpk+fnuv1iIgIypUrR0BAAAEBAUydOlWDlCL8X1lNTpiG\nfyV/Tl45yZ30O1pHsRoGrywnRFEUL47a+m71aq2jCGETMjMzGTVqFFu3bsXLy4vg4GC6detGvXr1\ncmzXpk0b1q5dq1FKcTn1MievnKRV1VZaRxE2qIRTCfwq+HE48TAtfFpoHccqyIiw0E5gIPz1F2Rk\naJ1ECKsXGRlJrVq18PX1xdnZmT59+rBmzZpc28mNcNr6/d/faV+9vazyZme+3v81UQlRZjmWTI/Q\nj4wIC+2ULQve3nDiBDRsqHUaIaxaXFwcPj4+2Y+9vb3Zv39/jm10Oh179uyhcePGeHl58emnn+Ln\n55drX5MnT87+88PLTgvDWMq0iJv3bnLz3k28y3prHcUuzDk0h5ZVW5rlWAMbDyQ9K90sx7IEERER\nREREFPn9UggLzdy5A0n1nqDqgQNSCAthoMIsaNSkSRNiYmJwcXFh48aNdO/enVN5dG55sBAWxhVc\nJdgiCuHFRxaz/fx2VvVepXUUm3fr3i3OJZ+jYUXz/DvX1LupWY5jKR7+sB4WFqbX+2VqhNDM1q0w\n5Pib0jlCCCPw8vIiJiYm+3FMTAze3jlH+8qUKYOLiwsAnTt3Jj09nWvXrpk1p717o/kbVClTResY\nDGkyhN0xuzmedFzrKDbvUMIhGns2luWtLZQUwkIzLVrA/tgqZBw4rHUUIaxeUFAQp0+f5vz586Sl\npfHzzz/TrVu3HNtcunQpe45wZGQkiqLg7i59Ze2Ri7MLY5qO4eNdH2sdxeZFxkUS4hWidQyRD5ka\nITTj4QGhoZDwx1V80tKgmNw8IkRROTk58c033/DEE0+QmZnJkCFDqFevHnPmzAFg+PDhrFy5ku++\n+w4nJydcXFz46aefNE4ttDQyeCQ1Z9bk7PWz1HCroXUcmxUZF8mz9Z7VOobIhyyxLLTXqBEsXKh2\nkRDCgtjj9csez9meTfxjIlduX2H207O1jmKzDsUfwtfVFw8XD62j2AVZYllYn6AgmScshBAaGNts\nLC82elHrGDYtsEqg2Yvg1LRUnl/xvHyoLQQphIX2goJkhTkhhE17c/ObHIo/pHWMXMq7lDdbWy9h\nPi7OLuy+uJuLNy5qHcXiSSEstCcjwkIIG5aWmcb8qPn4lPMpeGMhjECn08nCGoUkhbDQ3F86f46e\nLKY2FhZCCBuz6+Iu6pavS8VSFbWOIuxIiFcIkfFSCBdECmGhuVPni3HGq7W63LIQQtiY8NPhdKml\n/SIawr7IiHDhSCEsNPf889CjQ4rMExZC2KTw05axrHJBFEVhzKYxxNyIKXhjUaDTV0/TbnE7zY4f\nVCWIqIQoMrIyNMtgDaQQFpYhOFjmCQshbE7MjRiu3rlKYBXLbw+p0+moVKoS/Vb1k+LJCCLjIjVt\nmeZawpU9g/fgoJNS71EM+uncvXuXpk2b4u/vj5+fH+PHjzdWLmFv5IY5IYQN8innw4mRJ6ymGHmn\n1TsUcyzG1D+nah3F6kXGRxJSRdsV5Rp6NrSa//e0YtBPp0SJEmzfvp0jR45w9OhRtm/fzq5du4yV\nTdiT+vXh/Hm4dUvrJEIIYVTuJa1nGWsHnQM/9PiBOYfmsOP8Dq3jWDVZWtk6GPwxwcXFBYC0tDQy\nMzNl3XpRJJevO/NVhQ/g8GGtowghhF2rXKYyC7otoP9v/bl6+6rWcaxSWmYaRy8dtYopMfbOydAd\nZGVl0aRJE86cOcOIESPw8/PLtc3kyZOz/xwaGkpoaKihhxU2pkQJmBA/khH7vqPY449rHUfYqYiI\nCCIiIrSOIYTmOtfuzOedPqeEUwmto1ilk1dOUsOtBqWLldY6iiiATjHS+ns3btzgiSeeYNq0aTkK\nXVm3XhRWQLWrfPfYlzTb8oHWUYQA7PP6ZY/nLIQp3M24azEfJLKULLuZK6zvNcxoP5Vy5crx1FNP\ncVBueBJF9ME7KVQ8vVvrGEIIYTBFUYhKiJIPFXbMUorgd7e9y8z9M7WOYbEMKoSvXLlCcnIyAHfu\n3GHLli0EBAQYJZiwP08P96bG1QNw/brWUYQQwiCnrp6i2/JuWscQgjoedWRhjUcwqBBOSEigXbt2\n+Pv707RpU7p27Ur79u2NlU3YG0dHCAiAqCitkwghhEHuL6Kh0+m0jmI09zLuaR1BFIGsMPdoBhXC\nDRs2JCoqKrt92rhx44yVS9iroCBZYU4IYfXC/7WO1eT00WtlL5ZHL9c6xiMpisKKYyu4ee+m1lEs\nRp3ydUi6nSQdQPJhHzOnhfWQhTWEEFYuJS2FfbH7aF/dtr4hDQsNY8ymMZy5dkbrKHlKz0xn2Pph\nDFk7hCFrh2g2PzsxJZE76Xc0OXZeHHQOBFYO5EC8DDLlRQphYVH+pDVTtrbQOoYQQhTZtrPbaOrV\nlDLFy2gdxaj8K/kz8fGJ9Pm1D2mZaVrHyeXanWtkKVmcHXOWf6/9y6wDszTJMSp8FKtPrtbk2Plp\n5t2M01dPax3DIhmtfVq+B5BWPEIPlxKyuPRYaxqdXQ0VKmgdR9g5e7x+2eM5G9vv//7OrbRbPOf3\nnNZRjE5RFJ756RnqlK/DjI4ztI6Tr3+v/Uvz75uz/+X91HCrYdZjV/2iKtsHbqeme02zHvdRFEWx\nqfnqj6LvNUwKYWF52reHt96Czp21TiLsnD1ev+zxnIV+rty+QsCcADa8sIFGno20jpOvc9fP4evq\na9YCMOFWAg2+a8CVcVfspvC0NJr1ERbCaIKDZZ6wEEJYqPIu5Tk07JBFF8EA1d2qm70YPRB/gBCv\nECmCrYgUwsLyyA1zQghh0SqWqqjp8Zf8tYQpO6ZomiEvkXGRhHiFaB1D6EEKYWF5pIWaEEKIPCiK\nwpQdU5gUMcki52A76Bx4vOrjWscQepBCWFicDK9q1Ln8J3fOxGsdRQirsmnTJurWrUvt2rWZPn16\nntuMHj2a2rVr07hxYw4fPmzmhEIUXXpmOkPWDmHtP2vZO2QvfhX89Hr/iaQTJN9NNlE61ZS2U2hf\nwzLb5qVlpnE4Qf7OP0wKYWFxnJx1uJbO4MAvZ7WOIoTVyMzMZNSoUWzatInjx4+zfPlyTpw4kWOb\n8PBw/v33X06fPs3cuXMZMWKERmlt06Z/NzH74GytY2ji78t/m7TIvHnvJk8te4qk20lEvBRBpdKV\n9N7H94e/Z/CawXZ7M+jt9Nu0XtiajKwMraNYFCmEhUVqWfcqe7bc1jqGEFYjMjKSWrVq4evri7Oz\nM3369GHNmjU5tlm7di0DBw4EoGnTpiQnJ3Pp0iUt4tqkn/7+icysTK1jaGJ+1HyGrRtmsiIzLTON\nlj4t+a33b5QuVrpI+/iw3YfE3Izhq/1fGTmddXAt4Yp3WW+OJx3XOopFcdI6gBB5mTwmGZdFs4BO\nWkcRwirExcXh4+OT/djb25v9+/cXuE1sbCyenp45tps8eXL2n0NDQwkNDTVJZluSpWSx8d+NvN/m\nfa2jaGJah2k0nd+UeVHzGBY4zOj7L+9SnkmhkwzaR3Gn4vzy3C80nd+UFj4t7PKmthCvECLjIi2+\n44c+IiIiiIiIKPL7pRAWFqlsmwAYHQmKAtKGRogCFbZd08Mjdnm978FCWBROVEIU7iXdzb54g6Uo\n4VSCn3r+ROuFrWnp05L6FetrHSlP1d2qM+fpOfRe2ZtDww7hXtJd60hmdb8QfrnJy1pHMZqHP6yH\nhYXp9X6ZGiEsU5Uq4OwMFy5onUQIq+Dl5UVMTEz245iYGLy9vR+5TWxsLF5eXmbLaMvCT4fTpXYX\nrWNoql6FenzS8RN6r+zNnfQ7Bu3LlPN4e9TrQZ8GfTgYb7w2nWmZaSz5a4nR9mcqIV4hHIiXrkwP\nkkJYWC7pJyxEoQUFBXH69GnOnz9PWloaP//8M926dcuxTbdu3ViyRP3Het++fbi6uuaaFiGKJvx0\nOF1q2XchDDDIfxDNfZpzOLFo3QkURWFyxGTejzDtFJOP239Mp5rGm3oXfSmaGXssd8np+xp7NqZu\n+bp2e8NgXmRqhLBYSlAwV/48QQXLaxUphMVxcnLim2++4YknniAzM5MhQ4ZQr1495syZA8Dw4cPp\n0qUL4eHh1KpVi1KlSrFw4UKNU5tOZlYmDjoHs63wtbrParv7mj0vOp2OeV3nFem9aZlpDFs3jONJ\nx1nXd52Rk5mWtSykUdypOMt7Ltc6hkXRKSb+WCDr1oui+mfenwwe587u5AZaRxF2yh6vX7Zyzs/+\n/Cx7YvbQvkZ7OlTvQIcaHfAp51PwG4Umbty9wbO/PEvpYqVZ9uwyShUrpXUkvQxaM4hmXs0YHjRc\n6yh2T99rmEyNEBbrsW512U0ryMrSOooQwopkZGWQqWSybcA22vq25fczv9NkbhOWHl2qdTSRh7ib\ncbRa2Aq/Cn6s6rXK6opgsJ4RYZGbjAgLy1atGmzdCrVra51E2CF7vH7Z6jlnKVlkZGVQzLFYrteO\nJx2npltNijsV1yCZuHH3BqtOrOIl/5fMNpXlYRtObeDM9TOMbjpa7/feuneLSp9VIvmdZJwdnU2Q\nTuhDRoSFbQkOlhvmjGXZMujVS21JJ4SdcdA55FkEA7y95W0qzKjAk0uf5NM9n3Ik8QhZinwTZSzL\nopex/dz2fF8vV6IcgwIGaVYEAzSo2IAPd37Inpg9er/3XuY9prWfJkWwlTKoEI6JiaFt27bUr1+f\nBg0aMHPmTGPlEkIVFAQHpNWLwZKS4PXXISoKlsuNEkI8aP0L67kw9gLDA4dzLvkcvVf2puoXVUnP\nTC/wvReSLxRqO3tW3qU8L/72IkmpSVpHyVc112rM7zqfPiv7cPX2Vb3eW96lPK81fc1EyUxj/an1\n/JX4l9YxLIJBUyMSExNJTEzE39+flJQUAgMDWb16NfXq1fvvADb6NZswk61bOTjuZ/x2z8PFResw\nVmzAAKhYUR0RfuYZOHYM3OUO94LY4/XLHs85L5dTL1OxVMVcz9/NuEtqWioeLh4ANJnThK+e/IrW\n1VqbO6JV+d/W//H35b9Z23ctmVmZFjt6Om7LOE4knWBt37U46Gz3S/Px28ZTwrGEwav1WSKzTo2o\nVKkS/v7+AJQuXZp69eoRHx9vyC6FyCkwkNePDmL3zkytk1ivbdvgzz9h8mQICYHnnoN33tE6lbBg\nUgiTZxEMcDjhMNW/qk7Q3CDe+P0Nziefp7lPczOnsz4ftP2AK7ev0GROEz7a+ZHWcfL1UbuPuH73\nOp/t+UzrKCYVUiWEyPhIrWNYBKPdLHf+/HnatGnDsWPHKF269H8H0OmYNOm/Txyybr3Q13j32RTr\n05OwWRW0jmJ97tyBRo3giy/g6afV527ehPr11TnDrWUU60EPr1kfFhZmd0WhTqdj54WdtKraSuso\nept9cDYlnErwkv9LJj1OWmYa+2L3sfXsVjxKejCm2RiTHs9WnLt+jlkHZxEWGoaLs+V+xRdzI4bk\nu8k09GyodRSTibsZh/8cfy6/dVnTudmmoO+IsFEK4ZSUFEJDQ5k4cSLdu3c3KJAQD4toP4X9Hk/x\nzi+BWkexPu+9BydPwooVOZ9ftQomTIAjR6C43CmfH3u8ful0Op775TlWPL+i4I0tiKIo+M3yY17X\neVZZxAthbl6fe7F78G58XX21jmJUZu8akZ6eTs+ePenfv3+uIlgIYwjtUop3PBdpHcP6HD8Os2fD\nV1/lfq1HD3jsMfjkE/PnEhbvj3N/cPHGRa1j6GV3zG4AWvq01DiJsCcLDi9g85nNWscokhCvECLj\nZHqEQYWwoigMGTIEPz8/xo4da6xMQuQkLdT0l5UFw4dDWBhUqZL7dZ0Ovv5aLZJPnTJ/PmHRBjQe\nwKwDs7SOoZd5UfN4OeBlm/uaV1i2n/7+yWq7hoxtOha/Cn5ax9CcQYXw7t27Wbp0Kdu3bycgIICA\ngAA2bdpkrGxCqAIC4OhRSLfOi40mvv9e/Xm98kr+21StChMnqtvY2df/4tFGBY/iXPI5rWMUWvLd\nZNacXMOAxgO0jiJs1OXUy7mey1KyOBB/gGCvYA0SGa6NbxsaVGygdQzNycpywjr4+ak3d/1/lxLx\nCJcuQcOG6op8jRo9etuMDGjaFMaMUVusiRzs8fpljee88fRGfoz+kaXPyhLKwviiL0XT+cfORA2P\nytFN5NTVUzyx9AnOjbGeD432QFaWEzYpPbAZX067IwOXhfH66zB4cMFFMICTE8ydC2+/DVeumD6b\nECbQuXZnfujxg9YxhI1q6NmQAY0H8OJvL+ZYcTAyLpIQrxANkwljkEJYWAWn4ACSTl3n3j2tk1i4\n33+Hffvg/fcL/57AQOjbF8aNM10uIUxM5gYLU5rSdgp30u/w8c6Ps5+LjIskuIp1TosQ/5GpEcI6\n7N0Lo0bBoUNaJ7Fct2+rUyK+/RaefFK/96akqNNPFi+Gtm1Nk88K2eP1yx7PWYjCiLsZR9C8IJb3\nXE6obyinr56mdLHSVC5TWeto4gEyNULYJn9/OHEC7t7VOonl+uADdeU4fYtggNKl4Ztv1Bvn5Gcs\nhBC5eJX1YnH3xXy480MAanvUtvoiOOZGDANXD9Q6hqZkRFhYD39/mDdPbacmcoqOhvbt1e4alSoV\nfT89e0KDBmrbNWGX16+Hz3nViVVEJUQxtd1UDVMJYTkysjJwcnDSOoZR3Mu4h9t0N5LGJVGqWCmt\n4xiFjAgL2xUUBAcOaJ3C8mRlwbBhMHWqYUUwwMyZMGuWuhqdEEBg5UC+O/gdKWkpWkfJZcIfE0hK\nTdI6hrAztlIEAxR3Kk5Dz4as/Wet1lE0I4WwsB5BQcxfVpI9e7QOYmHmzAFHR3j5ZcP35eUFkyap\ni3FkZRW8vbB51VyrEeobypK/lmgdJYdjl4+x8PBC3Eq6aR1FCKv21ZNfMfb3sfx6/Feto2hCCmFh\nPYKDiT19l3XrtA5iQRIS1A4Rc+aAg5H+Oo8Yoc4TXrjQOPsTVm90yGhm7p+Zo3WU1uYfns+ggEE2\nNTonhBaaeTfj9/6/M2rjKFadWKV1HLOTQlhYjwYNaJm8gd07M7VOYjnGjFFHb+vXN94+HR3Vwnr8\neLicezUlYX8er/Y4JZxKsOXMFq2jAOq8xqVHlzLYf7DWUYSwCf6V/Nk+cDvNvJtpHcXspBAW1qN4\ncZrXv8k7z/yjdRLLsGEDHD4MEyYYf9/+/jBwILzxhvH3LayOTqfjjeZvEH05WusoAKw+uZrGno2p\n6V5T6yhC2Iy65etSpUwVrWOYnXynJKxK6WYNeKrYFsBP6yjaSk2FkSNh/nwoWdI0x5g8We0gsWUL\ndOxommMIqzGgseUswb00eilDmwzVOoYQwgZI+zRhXRYsgD/+gKVLtU6irXHjIDERfjDxsrLh4TB6\ntNqezVQFtwWzluvXtWvX6N27NxcuXMDX15dffvkFV1fXXNv5+vpStmxZHB0dcXZ2JjIyMtc21nDO\nKWkpFHMsRjHHYlpHEcKm3b8vwEFnPRMIpH2asG1BQXDwoNYptHXkCCxZAp99ZvpjdekCTZqordmE\nxZo2bRodO3bk1KlTtG/fnmnTpuW5nU6nIyIigsOHD+dZBFuL0sVKSxEshBl8vf9rhq0bRmaW7d6b\nIyPCwrpkZICrK8THQ9myWqcxv8xMaN5cXQFusJluFEpIgEaNYPt2daqEHbGW61fdunXZsWMHnp6e\nJCYmEhoaysk8ekFXr16dgwcP4uHhke++rOWchRCml5KWwjM/PUMFlwr80OMHnB2dtY5UIH2vYVII\nC+vTsiU9HVfz0bwK1KmjdRgz+/prWLkSIiJApzPfcb/7Tp2OsnOn8dq0WQFruX65ublx/fp1ABRF\nwd3dPfvxg2rUqEG5cuVwdHRk+PDhDB2ae56tTqdj0qRJ2Y9DQ0MJDQ01WXYhhGW7m3GX51c8jw4d\nvzz/CyWcSmgdKYeIiAgiIiKyH4eFhUkhLGzcmDGcKt6Qah+8TPHiWocxo9hYtZvDrl1Qt655j52V\nBS1bwksvqe3a7IQlXb86duxIYmJiruc//PBDBg4cmKPwdXd359q1a7m2TUhIoHLlyiQlJdGxY0e+\n/vprWrdunWObwpzzhD8m0MK7BU899lQRz0YIYU3SM9Pp/1t/rt6+yuo+qyldrLTWkfIlc4SF7QsK\n4rELW+yrCAb1prWRI81fBIM6Cjx3LkycqN6kJ8xuy5YtREdH5/rVrVu37CkRoBa7FStWzHMflStX\nBqBChQr06NGjyPOE65Wvx5f7vyzaiRRR/K14u2z2L4QlcHZ0Ztmzy2hVtRV3M+5qHceopBAW1ic4\n2AKJFQ8AABS5SURBVP5umFuzBo4dUxe50ErDhuoyzmPHapdB5Klbt24sXrwYgMWLF9O9e/dc29y+\nfZtbt24BkJqayubNm2nYsGGRjterfi/+vvw3xy4fK3poPS04vIAtZy1jQQ8h7JGjgyOTQydT3qW8\n1lGMSqZGCOuTlaXeMHfuHDziph+bceuWunLc4sXQtq22WW7fVgvib76Bzp21zWIG1nL9unbtGr16\n9eLixYs52qfFx8czdOhQNmzYwNmzZ3n22WcByMjIoF+/fozP44NVYc85LCKMhJQEZj892+jn87As\nJYuaM2vya69faVK5icmPJ4SwXma/WW7w4MFs2LCBihUrEh2de9Uha/mHRFiZ0FB4910y2nXCydaX\nhXn9dUhOhoULtU6i+v13tWvF339DqVJapzEpe7x+FfacL6Vcou63dTkz+gzuJd1Nmmnzmc38b+v/\niBoeZdLjCCGsn9nnCA8aNIhNmzYZuhsh9BMUxKxvsmjbVm2ra80SE6FnT3jnHbh06aEXDx2C5cth\nxgxNsuXpiSfUFm5TpuR6acUK9eU5c+DePQ2yCbPxLO1J/0b9OZJo+r+A86Pmy0pyQliod7e9y8kr\nuds1WguDC+HWrVvj5uZmjCxCFF5wMIN0i+jeXV3zwZqnDHt4qLMMUlLg3XcfeCEjA4YNg08+gfIW\nNifriy/UEeq//srx9J078MILsHGjOogtbNvXnb+mXfV2Jj1GUmoSm89s5oWGL5j0OEKIoqnjUYe2\ni9ua5UOxKRhljvD58+fp2rVrvlMjpCelMLozZ9TpETEx3L0LxYubt61uUWVlQVoalMinDaOiPHAe\nX3wB69fD1q0WeXLK3HnoFnwPu3eDo6PWcYzC0H6UtsDSpoOkZ6Zz9NJRAqsEah1FCJGPlcdXMjJ8\nJKt7r6a5T3NNs2iyoEZBhbAlXVSFjVAUdSj1+HGoVCnXy2fOqPfSdeigQbZHmDJFXRCvwMYLFy+q\nSxvv2cPUXx7j1VfB3bTTMPVy5Qp07qywr3gojn17qW3dCrBihTpiPGCAGQIaiT1ev+zxnIUQhgs/\nHc7A1QP5+bmfTf5N0aPoew2z9duMhK3S6SAoSJ1D+1Tupv5JSXDhgga5CvDWW1CyZAEbKQqMGgVj\nxpBZ8zHKlrW81aTLl4cVK3Q43v4O2rSBHj2gSpVHvicwEFJTzRRQCCGEWXWp3YUVz69g2q5ptPVt\ni84Cv8nMi4wIC+v17rtw+DB07w6VK6uFWOXK4OmJ1q0k7t5VR0D79SvCisSrVqkLVxw+TH6rhmRk\nmO8UExLUrmk1a+azwXvvwYkT6tLPRXD1quV2wbPH65c9nrMQwngURdG0CDZ714i+ffvSokULTp06\nhY+PDwstpcWTsH2jRkFIiDoqPHeuuvRvUJA65Fqpkjq14KmnYOhQeP990r6ZS+v6V5n77nnunY1T\nq0kTmDULatRQC+EbN/R8840b6gpyc+bkWwQDTJ+uTpHeskUdQDaF+Hh1xkP9+vDAtNnc3n1XvWlu\n3Tq9j3H9urpQ3uDBcOpUkaMKjSmKwlPLniIpNUnrKEIIjVnLSPB9sqCGsD0ZGXD5slrJJSTk+H33\nMVc+/LsbV+6UYn9WCLryHjlHk/P63dMTnJ0Lffhly8DPD/z9i5D9tdfU4eR58wo8xeXL4eOP4auv\noGPHIhyrAMePww8/qG2M81mx9z/btqnV7LFjUFq/NeivX4evv4azZ2HRoiLHNQl7vH4V9ZxfXvsy\n1V2rM+HxCUbJEX0pGp9yPriWcDXK/oQQ9kGTm+UeeQA7/IdEWL5r18C9bIY6mTg+Ps+iOfv3pCT1\nTrU8CuVMzyo4ev//40qV9CqYc9m/X53mcexYoe+My8pSf9d7+oUpDBgAFSrAZ59pncRo7PH6VdRz\n/ivxL7os68L5MedxdjTg7wHqCHPAnAA+7fQpHWpY2B2vQgi9ZGZlsu7UOrrXzb30uynIzXJCFIJa\nZzqpRW3lyhAYSEQENHoujxo0M1MdYX6oQL6wO5bnwzuwv2Y/dAnx6jZubgWPMFeqBMWK5TxGerra\nM/izz/RqD5FXAXzhAuzZA337Fv7n8frr0LUrtDPkRt/PPoMGDdSJ0U2Mswzue+/BiBEF3ocnLEDj\nSo2p7V6bX0/8Sp8GfQza16GEQ9y8d1PTO8+FEMaRfDeZCX9MwKOkB62rtdY6Ti5SCAvx/zZuVGvU\nXHWoo+N/BfMDBV41YEMS6CocUJ/IzFRHjx8eUY6Ohs2b/3vu0iVwdc1ZIN+6pR5cn+o1H6mp6uwK\nfQwfDtWqGXjgChVg2jS1oN+5sxDtMR5NUeCxxyxvLRGRvzFNxzBjzwyDC+F5UfMYEjAEB50lfNUh\nhDCEh4sHB4cepKSzYf8mmIpMjRCiEE6cUGc91KplhJ1lZqqNeB+efjFgAHh5GeEAebv/1/DUKahT\nx4QHefFFOH8e1q41SfPju3fVAXVzTAexx+uXIeecmZVJ6OJQVvVaRYVSFYq0j5S0FHy+8OHvEX/j\nVdZ0fx+EELZJ5ggLYURbt8LkyXD6NMyerbbLtUZZWdCixX9F5L59Jiwks7Jg3DjYtEn95eNj1N1/\n+y3Mnw+RkYZNyS4Me7x+aX3OCw4vYPXJ1aztu1azDEII6yWFsBBGdP06/PEHPPkklCqldRrDnDyp\nzh/u2NFMN9d99pna0mLjRrUHm5Eoino/YYMGRttlvuzx+qX1OUclRJGlZBFUJUizDEII6yWFsBDC\ncvz4I7zxhrrYRmvLu0miIPZ4/bLHcxZC2A6zL6ghhBD56tcPli6Fnj3VFfOEEEIICyJdI4QQptWx\nozpXuGtXtWPGiBFaJxJCCCEAGREWQphDkyZqS7XPP4eJE023LrSwGBdvXKT3yt4yzUIIYdGkEBZC\nmEeNGrB7t9pT+eWX1XWihc3yLutNVEIUe2P3Fmr7pNQkEycSQojcpBAWQphPxYpqG46EBHU56dRU\nrRMJE3HQOfBayGt8tf+rArc9c+0MjWY3IiNLPhwJIcxLCmEhhHmVLg1r1qhLxv1fe/cfE3X9xwH8\neQrWyiwzROBgaID3w1NwIJuJXxQPC4TC7g9gJSnwR42K1lqzrY3a4sdcP+zXWkxTWwOzRrCEW1Dd\nZvG9qB30Q+mrX8dtBwesX/jVcCK3z/ePWyyFs/v1uffdfZ6Pzc077nw/3xOfvPx8PndXUOD+cBGK\nSo9kPoLe870Y/d/oDR93aPAQKg2ViFnEl60QUWhxECai0IuNBd57D9i+HbjnHvcn0VHUWXbTMjy8\n4WG8/e3bHh9z1XUVR4aOoCarJoTJiIjcOAgTkRgqFdDYCDz+uHsYHhoSnYhkUJdTh2+d33r8eve5\nbqxZvgbaOG0IUxERuXEQJiKx6urcn0BXWOi+fph8duLECej1eixevBg2m83j48xmMzQaDdLT09HS\n0hKSbOkr0tH7cK/Hr7faWlG7sTYkWYiIrsdBmIjEM5mADz8EKiqA9nbRaSKOwWBAR0cHtm7d6vEx\nLpcLdXV1MJvNOHPmDNra2jA8PBzClPNJkgT9Sj1MOpPQHESkXHxlAhGFh/x8oK8PKCoCJiaA+nrR\niSKGRqP5x8cMDAwgLS0NqampAIDy8nJ0dnZCqxV3SYJKpULLjtAcmSYiWkjAg7DZbEZ9fT1cLhdq\namrw7LPPBiMXESmRweB+r+GdOwGnE2huBhbxxFUwjI2NITk5ee62Wq3GN998s+BjGxoa5n6fn5+P\n/Px8mdMREfnHYrHAYrH4/fyABuG/TrX19fUhKSkJOTk5KC0tFXqEgYgiXEoK8NVX7o9krqoCDh0C\nliwRnUo4o9GIiYmJefc3NjaipKTkH5+vUqm8XuvvgzARUTi7/j/rL7zwgk/PD2gQDsdTbUQUBVas\ncF8mUVHhHog/+gi47TbRqYTq7fX8gjNvJCUlweFwzN12OBxQq9WBxvKJ+b9m2MZteC7vuZCuS0Tk\nSUDnHBc61TY2NhZwKCIi3HIL8PHHQGqq+/rhyUnRiSKCJEkL3p+dnY1z587BbrdjZmYGx48fR2lp\naUizrV2xFq/8+xVcvHIxpOsSEXkS0BFhb0+18XozIvJLTAzwzjvAiy+632vYbAbS0mRbLtBrzUTp\n6OjAE088gV9//RXFxcXIyspCT08PnE4namtrcfLkScTExODNN9/Ezp074XK5UF1dHfKzd6uXr8aW\nlC3Y8t4WmLQmPP+v50O6PhHR9VSSp8MHXrBarWhoaIDZbAYANDU1YdGiRde8YE6lUnk8QkFE5LV3\n3wUaGoCuLiA7OyRLKrG/5N7zlyNfYvux7fh639fYnLxZtnWISJl87bCABuHZ2VmsXbsWn3/+ORIT\nE7Fp0ya0tbVdc5RBiT9IiEgmXV1AdTXw/vvAvffKvpwS+0vuPUuShM7/dOL+tff79AI+IiJvhHQQ\nBoCenp65t0+rrq7G/v37AwpERHRD/f1AWZn73SR27ZJ1KSX2lxL3TETRI+SD8D8uwFIlomD7+Wfg\nrrvcv2SkxP5S4p6JKHpwECYiChIl9pcS90xE0cPXDuNHNhERERGRInEQJiIiIiJF4iBMRERERIrE\nQZiIiIiIFImDMBEREREpEgdhIiIiIlIkDsJEREREpEgchImIiIhIkTgIExEREZEicRAmIiIiIkXi\nIExEREREisRBmIiIiIgUiYMwERERESkSB2EiIiIiUiQOwkRERESkSByEiYiIiEiROAgTERERkSJx\nECYiIiIiRfJ7ED5x4gT0ej0WL14Mm80WzExhy2KxiI4QFNGyD4B7CVfRtJdI4G0fp6amYv369cjK\nysKmTZtCmFCMaPo+jJa9RMs+AO4lWvg9CBsMBnR0dGDr1q3BzBPWouUbJVr2AXAv4Sqa9hIJvO1j\nlUoFi8WCwcFBDAwMhCidONH0fRgte4mWfQDcS7SI8feJGo0mmDmIiMhPvvSxJEkyJiEiiiy8RpiI\nSCFUKhV27NiB7OxstLa2io5DRCScSrrB4QGj0YiJiYl59zc2NqKkpAQAsG3bNrz88svYuHHjwguo\nVEGKSkQUeuFyBDUYfTw+Po6EhAT88ssvMBqNeOONN5CXl3fNY9jZRBTpfOntG14a0dvbG9IwRES0\nsGD0cUJCAgAgLi4OZWVlGBgYmDcIs7OJSEmCcmkEi5OIKDx46uPp6WlcvHgRAPDnn3/is88+g8Fg\nCGU0IqKw4/cg3NHRgeTkZFitVhQXF+O+++4LZi4iIvKSpz52Op0oLi4GAExMTCAvLw+ZmZnIzc3F\nrl27UFhYKDI2EZFwfg/CZWVlcDgcuHz5MiYmJtDT03PN181mMzQaDdLT09HS0hJwUFEcDge2bdsG\nvV6PdevW4fXXXxcdKWAulwtZWVlz1xVGqqmpKZhMJmi1Wuh0OlitVtGR/NLU1AS9Xg+DwYDKykpc\nuXJFdCSv7du3D/Hx8dccWfz9999hNBqRkZGBwsJCTE1NCUzovYX28swzz0Cr1WLDhg3YvXs3Lly4\nIDChZ576ODExESdPngQArFmzBkNDQxgaGsJPP/2E/fv3z/tz2NvhiZ0dfiK1t9nZ88nyrhEulwt1\ndXUwm804c+YM2traMDw8LMdSsouNjcWrr76K06dPw2q14q233orYvfzl4MGD0Ol0Ef+imCeffBJF\nRUUYHh7GDz/8AK1WKzqSz+x2O1pbW2Gz2fDjjz/C5XKhvb1ddCyv7d27F2az+Zr7mpubYTQacfbs\nWRQUFKC5uVlQOt8stJfCwkKcPn0a33//PTIyMtDU1CQonfzY2+GLnR1eIrm32dnzyTIIDwwMIC0t\nDampqYiNjUV5eTk6OzvlWEp2q1atQmZmJgBg6dKl0Gq1cDqdglP5b3R0FN3d3aipqYnoa7svXLiA\nU6dOYd++fQCAmJgY3H777YJT+W7ZsmWIjY3F9PQ0ZmdnMT09jaSkJNGxvJaXl4fly5dfc19XVxeq\nqqoAAFVVVfjkk09ERPPZQnsxGo1YtMhdk7m5uRgdHRURLSTY2+GJnR1+Irm32dnzyTIIj42NITk5\nee62Wq3G2NiYHEuFlN1ux+DgIHJzc0VH8dtTTz2FAwcOzH2jRKqRkRHExcVh79692LhxI2prazE9\nPS06ls/uvPNOPP3000hJSUFiYiLuuOMO7NixQ3SsgExOTiI+Ph4AEB8fj8nJScGJguPw4cMoKioS\nHUM27O3wxM4OP9HW20rvbFn+ZUX66ZuFXLp0CSaTCQcPHsTSpUtFx/HLp59+ipUrVyIrKyuijywA\nwOzsLGw2Gx577DHYbDbceuutEXM65+/Onz+P1157DXa7HU6nE5cuXcIHH3wgOlbQqFSqqOiDl156\nCUuWLEFlZaXoKLKJhr+n60V6b7Ozw1M097YSO1uWQTgpKQkOh2PutsPhgFqtlmOpkLh69SoefPBB\nPPTQQ3jggQdEx/Fbf38/urq6sHr1alRUVOCLL77Anj17RMfyi1qthlqtRk5ODgDAZDLBZrMJTuW7\n7777Dps3b8aKFSsQExOD3bt3o7+/X3SsgMTHx8998MP4+DhWrlwpOFFgjhw5gu7u7qj5QecJezv8\nsLPDU7T1ttI7W5ZBODs7G+fOnYPdbsfMzAyOHz+O0tJSOZaSnSRJqK6uhk6nQ319veg4AWlsbITD\n4cDIyAja29uxfft2HDt2THQsv6xatQrJyck4e/YsAKCvrw96vV5wKt9pNBpYrVZcvnwZkiShr68P\nOp1OdKyAlJaW4ujRowCAo0ePRuwQArjfReHAgQPo7OzEzTffLDqOrNjb4YedHZ6irbcV39mSTLq7\nu6WMjAzp7rvvlhobG+VaRnanTp2SVCqVtGHDBikzM1PKzMyUenp6RMcKmMVikUpKSkTHCMjQ0JCU\nnZ0trV+/XiorK5OmpqZER/JLS0uLpNPppHXr1kl79uyRZmZmREfyWnl5uZSQkCDFxsZKarVaOnz4\nsPTbb79JBQUFUnp6umQ0GqU//vhDdEyvXL+XQ4cOSWlpaVJKSsrcv/1HH31UdExZsbfDFzs7vERq\nb7Oz51NJUoRfeERERERE5IfIfhkqEREREZGfOAgTERERkSJxECYiIiIiReIgTERERESKxEGYiIiI\niBSJgzARERERKdL/Af5P3kGTM5XrAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 67 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "If there's some correlation between the regressors already in the model and the added regressor ? then the parameters $\\beta$ will change. But the critical piece of information is what is or is not in the model, it is its \"flexibility\". \n", "\n", "What happens if we have too many things in the model ? \n", "\n", "Two cases \n", "\n", " * Those things can capture some of the noise (the residual variance decrease)\n", " * Those things cannot capture some of the noise (the residual variance doesn't decrease)\n", " \n", "In the first case, we will be **overfitting**. In the second case, we simply loose some degrees of freedom.\n", "\n", "Let's now see how we **test** the parameters that we have just estimated. " ] }, { "cell_type": "heading", "level": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Testing the $\\hat\\beta$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's go back to our second model. The model and the data can be displayed as little images: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = second_X\n", "f, (a1, a2, a3) = subplots(1, 3, figsize=(10,3))\n", "a1.imshow(Y[:,np.newaxis], interpolation='nearest', cmap='gray')\n", "a2.imshow(X, interpolation='nearest',cmap='gray')\n", "a3.imshow(resid[:,np.newaxis], interpolation='nearest',cmap='gray')\n", "titles = ['Y','X','e']\n", "for ix,a in enumerate([a1, a2, a3]):\n", " a.set_xticklabels([])\n", " a.set_title(titles[ix])\n", " #a.set_yticklabels([])" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 68 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "There are two main statistics to understand with the GLM: the t- and the F- tests. First, we have to assume that our data $Y$, or equivalently the residuals $\\epsilon$, are normally distributed. We write $Y \\sim N(X\\beta, \\sigma^2)$, or, $\\epsilon \\sim N(0, \\sigma^2)$." ] }, { "cell_type": "heading", "level": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "GLM and T-tests " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Most often the t-test is used to answer the question of whether a linear combinaison of the estimated parameters is zero. For instance, let's take $\\beta_1 - \\beta_2$ in the model above. This can be written with $c^T \\beta$ where $c^T = [0, 1, -1, 0]$. To see if this quantity is too high (or too small) to be expected if we only had noise in the data (and therefore that we can reject the hypothesis that it is zero), we compute the t statistics:\n", "\n", "$$\n", "t = \\frac{c^T \\hat\\beta}{\\sqrt{\\mathrm{var}(c^T \\hat\\beta)}}\n", "$$\n", "\n", "and it can be shown that t follows a student-distribution with degrees of freedom $df$ that we will compute below. \n", "\n", "Let's first compute $ \\mathrm{var}(c^T \\hat\\beta) $. We have\n", "\n", "$ \\mathrm{var}(c^T \\hat\\beta) = \\mathrm{var}(c^T X^+ Y) = c^T X^+ \\mathrm{var}(Y) X^{+T} c = \\sigma^2 c^T X^+ X^{+T} c = \\sigma^2 c^T (X^T X)^- c $. \n", "\n", "To compute the t-value, we need an estimate of $\\sigma^2$. We dont have access to the true $\\epsilon$, but we can get an estimate using the residuals $\\hat\\epsilon$. We therefore compute the **Residual Sum of Square** (RSS) with\n", "\n", "$$ \\textrm{RSS} = \\sum_{i=1}^{12} (Y_i - \\widehat{Y_i})^2 = \\sum_{i=1}^{12} (Y_i - X_i \\hat\\beta)^2 = (Y - X\\hat\\beta)^T(Y - X\\hat\\beta) = (Y - X X^+ Y)^T(Y - X X^+Y) = (Y^T R^T) R Y = Y^T R Y $$ \n", "\n", "where $X_i$ is the $i$th row of the matrix $X$. To obtain the estimate of $\\sigma$, we compute the *expectation* of RSS. Here, a couple of mathematical tricks are useful, involving the trace of a matrix (which is the sum of its diagonal elements). In short, playing with the trace and the expectation, we get : \n", "\n", "$$ E(\\textrm{RSS}) = E(Y^T R Y) = E(tr(Y^T R Y)) = E(tr(R Y Y^T)) = tr(R E(YY^T)) = tr(\\sigma^2 R) = \\sigma^2 (n - \\textrm{rank}(X)) $$ \n", "\n", "It is not necessary to understand all the steps of this derivation, but it is interesting to understand the essence of what is shown above. In words, what this says is that if we were to compute the average value of the residuals sum of square, over many experiments, this sum of square is less that the sum of square of the true noise $\\epsilon$, and it depends on the rank of $X$. The rank of a $X$ is the minimal number of independant columns needed to construct $X$. Here, while we have 4 columns in $X$ but $\\textrm{rank}(X) = 3$ because we need only column 1, 2, and 3 (or 1, 2, 4) to reconstruct fully $X$. The more independant parameters we are estimating, the less degrees of freedom remains to estimate the variance of $\\epsilon$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Following the equation above, and letting $p = \\textrm{rank}(X)$ we can estimate $\\sigma$ with $\\hat\\sigma$ where:\n", "\n", "$$\\hat\\sigma^2 = \\textrm{RSS} / (n - p)$$\n", "\n", "This estimation is also called the **Mean Residual Sum of Square** (MRSS), and $\\hat\\sigma = \\textrm{MRSS} = \\textrm{RSS} / \\it{df} $ where $\\it{df}$ is the degrees of freedom $(n-p) = 12 - 3$, the number of observations (here, 12) minus the rank of the design matrix (here 3). In other word, this is the estimation of our noise.\n", "\n", "Coming back to our t-statistics, we can now calculate the **Standard Error** (SE) of $c^T \\hat\\beta$ with $\\textrm{SE} = \\sqrt{\\hat{\\sigma}^2 c^T (X^t X)^+ c} $\n", "\n", "The t test is then : $t = {c^T \\hat\\beta}/{\\textrm{SE}} $\n", "\n", "Clearly, for t to be big, we need the SE to be small, and / or $c^T \\hat\\beta$ to be large. Notice that the **SE** is composed of two elements: $\\hat{\\sigma}^2$ on the one hand, and $c^T (X^t X)^+ c$ on the other hand. If the noise variance is high, then we have less chance to detect an effect. The second factor introduce how much the effect we are testing is correlated with other elements in the design matrix. If for instance, we are testing for $\\beta_0$ but we have a column in $X$ which is highly correlated with $\\bf{x_0}$, $c^T (X^t X)^+ c$ will be large and we also have less chance to detect the effect. This led to some work for optimizing the design, once the questions of interest are formulated as contrast of the estimated parameters. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Let's compute this statistics in our example." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 69, "text": [ "array([[ 1., 1., 0., 1.],\n", " [-1., 1., 0., 1.],\n", " [ 1., 1., 0., 1.],\n", " [-1., 1., 0., 1.],\n", " [ 1., 1., 0., 1.],\n", " [-1., 1., 0., 1.],\n", " [ 1., 0., 1., 1.],\n", " [-1., 0., 1., 1.],\n", " [ 1., 0., 1., 1.],\n", " [-1., 0., 1., 1.],\n", " [ 1., 0., 1., 1.],\n", " [-1., 0., 1., 1.]])" ] } ], "prompt_number": 69 }, { "cell_type": "code", "collapsed": false, "input": [ "betah, Yfitted, resid = glm(X,Y) # fit the model\n", "RSS = sum((Y - Yfitted)**2)\n", "MRSS = RSS/(len(Y) - linalg.matrix_rank(X))\n", "\n", "print \"RSS :\", RSS #, \"\\nRSS metho 2:\", sum(resid**2), \n", "print \"MRSS :\", MRSS #, \"\\nMRSS method 2:\", RSS/9 #checking\n", "print betah\n", "\n", "cT = np.asarray([0, 1, -1, 0])\n", "c = cT[:,newaxis]\n", "pXTX = np.linalg.pinv(X.T.dot(X))\n", "\n", "t_num = cT.dot(betah)\n", "SE = np.sqrt(MRSS* cT.dot(pXTX).dot(c))\n", "t = t_num / SE\n", "\n", "print t" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "RSS : 6.00239575609\n", "MRSS : 0.666932861788\n", "[ 0.21902549 3.17218166 -1.17218166 2. ]\n", "[ 9.21394696]\n" ] } ], "prompt_number": 70 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "To see if this is significant, we have to see what is the probability of observing this t-value or larger under the null hypothesis. We first import some utilities stat functions form scipy." ] }, { "cell_type": "code", "collapsed": true, "input": [ "from scipy.stats import t as tdist, norm as ndist" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "prompt_number": 71 }, { "cell_type": "code", "collapsed": false, "input": [ "pvalue = 1.0 - tdist.cdf(t,10)\n", "print \"t-value = \", t, \"p-value = \", pvalue\n", "\n", "# if t was 1.8 ?\n", "\n", "t = 1.8\n", "pvalue = 1.0 - tdist.cdf(t,10)\n", "print \"t-value = \", t, \"p-value = \", pvalue\n" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "t-value = [ 9.21394696] p-value = [ 1.67422278e-06]\n", "t-value = 1.8 p-value = 0.0510261215673\n" ] } ], "prompt_number": 72 }, { "cell_type": "heading", "level": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "GLM and F-tests " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The simplest and generally most useful way of thinking of F test is to think as the test between two models: one which contains the regressor or factor that we want to test for (refered as the full model with design matrix $X$), and one which doesnt (the reduced model $X_0$). To test whether the model containing more columns is better, we compute the difference between the estimation of the noise variance between the models (variance estimated with $X$ versus variance estimated with $X_0$), normalized by the estimation of the noise variance under the full model. This is : \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "$$\n", "\\begin{eqnarray} \n", "F_{\\nu_1, \\nu_2} & = & \\frac{(\\hat\\epsilon_0^t \\hat\\epsilon_0 - \\hat\\epsilon^T\\hat\\epsilon)/ \\nu_{1} }{\\hat\\epsilon^T\\hat\\epsilon/\\nu_{2}} \\\\ \n", " & = & \\frac{(Y^TR_{X_0}Y - Y^TR_{X}Y)/ \\nu_{1} }{Y^TR_{X}Y/\\nu_{2}} \\\\ \n", " & = & \\frac{(Y^T(I-P_{X_0})Y - Y^T(I-P_{X})Y)/ \\nu_{1} }{Y^T(I- P_{X})Y/\\nu_{2}} \\\\ \n", "& = & \\frac{(\\textrm{SSR}(X_0) - \\textrm{SSR}(X))/\\nu_1}{\\textrm{SSR}(X)/\\nu_2}\n", "\\end{eqnarray}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "with $\\textrm{SSR}(X)$, $\\textrm{SSR}(X_0)$, the sum of squares for error of models $X, X_0$\n", "respectively, and:\n", "\n", "$$\n", "\\begin{eqnarray} \n", "\\nu_{1} & = & \\textrm{tr}(P_X - P_{X_0}) = \\textrm{tr}(R_0 - R_X) \\\\ \n", " \\nu_{2} & = & \\textrm{tr}(I - P_X) = \\textrm{tr}(R_X) \n", "\\end{eqnarray}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that $\\hat\\epsilon^T \\hat\\epsilon$ = $Y^t R^T R Y $, but R is symetric ($R^T = R $) and is idempotent ($R R = R $). Geometrically, it is a projector." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "It can be shown that under the hypothesis that our true model is $X_0$, this follows an $F$ distribution with $\\nu_1,nu_2$ degrees of freedom. This is the case because $P_X - P_{X_0}$ is orthogonal to $R_X$ (since $P_{X_0}$ is in $P_X$) - it can be shown that in this case these two sum of squares are independant. \n", "\n", "Let's take an example with the previous model and implement this with code. Say for instance that we are interested to know wheter there is an effect of the step function in the model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "print X\n", "X0 = X[:,[0,3]]\n", "betah, Yfitted, resid = glm(X,Y)\n", "betah0, Yfitted0, resid0 = glm(X0,Y)\n", "PX = X.dot(lin.pinv(X))\n", "RX = np.eye(X.shape[0]) - PX\n", "PX0 = X0.dot(lin.pinv(X0))\n", "\n", "F_num = (sum(resid0**2) - sum(resid**2))\n", "nu1 = np.trace(PX - PX0)\n", "F_den = sum(resid**2)\n", "nu2 = np.trace(RX)\n", "F = (F_num/nu1)/(F_den/nu2)\n", "print F, nu1, nu2, F_num, F_den" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 1. 1. 0. 1.]\n", " [-1. 1. 0. 1.]\n", " [ 1. 1. 0. 1.]\n", " [-1. 1. 0. 1.]\n", " [ 1. 1. 0. 1.]\n", " [-1. 1. 0. 1.]\n", " [ 1. 0. 1. 1.]\n", " [-1. 0. 1. 1.]\n", " [ 1. 0. 1. 1.]\n", " [-1. 0. 1. 1.]\n", " [ 1. 0. 1. 1.]\n", " [-1. 0. 1. 1.]]\n", "84.8968186247 1.0 9.0 56.620478202 6.00239575609\n" ] } ], "prompt_number": 73 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import f as Fdist\n", "Fdist.sf(F,nu1,nu2)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 74, "text": [ "7.0423196532412472e-06" ] } ], "prompt_number": 74 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "The relation between the significance of t and F test " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this, let's imaging that we have two regressors that we are interested in. For the sake of simplicity, let's assume that these are not correlated. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Regression versus correlation : how can things so similar be so different?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's make a little function for testing the beta_hat (we assume they are estimable) " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def t_test(betah, resid, X):\n", " \"\"\" \n", " test the parameters betah one by one - this assumes they are estimable (X full rank)\n", " \n", " betah : (p, 1) estimated parameters\n", " resid : (n, 1) estimated residuals\n", " X : design matrix\n", " \"\"\"\n", "\n", " RSS = sum((resid)**2)\n", " n = resid.shape[0]\n", " q = np.linalg.matrix_rank(X)\n", " df = n-q\n", " MRSS = RSS/df\n", " \n", " XTX = np.linalg.pinv(X.T.dot(X))\n", "\n", " tval = np.zeros(betah.shape)\n", " pval = np.zeros(betah.shape)\n", "\n", "\n", " for (idx, beta) in enumerate(betah):\n", " c = zeros(betah.shape)\n", " c[idx] = 1\n", " t_num = c.T.dot(betah)\n", " SE = np.sqrt(MRSS* c.T.dot(XTX).dot(c))\n", " tval[idx] = t_num / SE\n", " \n", " pval[idx] = 1.0 - tdist.cdf(tval[idx], df)\n", " \n", " return tval, pval\n", "\n", "#print t_test(betah, Yfitted, resid)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 75 }, { "cell_type": "code", "collapsed": false, "input": [ "n = 20\n", "x = np.random.randn(n,1)\n", "X = np.hstack((x, np.ones(x.shape)))\n", "print X.shape\n", "m_y = 0 \n", "m_y = 3.14156\n", "\n", "e = np.random.randn(n,1)\n", "y = 1.4 * x + m_y + e\n", "plt.plot(x,y,'o')\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(20, 2)\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 76, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 76 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is the estimated beta ?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "betah, Yfitted, resid = glm(X,y)\n", "#print Yfitted.shape\n", "t, p = t_test(betah, resid, X)\n", "print \" betah = \\n\", betah\n", "print \" t = \\n\", t\n", "print \" p = \\n\", p" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " betah = \n", "[[ 1.49135871]\n", " [ 3.2565731 ]]\n", " t = \n", "[[ 5.22092063]\n", " [ 10.44492969]]\n", " p = \n", "[[ 2.88492490e-05]\n", " [ 2.27580943e-09]]\n" ] } ], "prompt_number": 77 }, { "cell_type": "code", "collapsed": false, "input": [ "# do this the other way : let's have y be the explanatory variable:\n", "\n", "X2 = np.hstack((y - m_y, np.ones(x.shape)))\n", "y2 = x\n", "betah2, Yfitted2, resid2 = glm(X2, y2)\n", "print \"compare the slopes : \\t\\t\", 1./betah2[0,0], betah[0,0]\n", "print \"compare the residual variance:\\t\", resid.T.dot(resid)[0,0], resid2.T.dot(resid2)[0,0]\n", "t2, p2 = t_test(betah2, resid2, X2)\n", "\n", "print \"betah2 : \\t\\t\\t\", betah2[:,0]\n", "print \"compare t values : \\n\", np.hstack((t, t2))\n", "print \"compare p values : \\n\", np.hstack((p, p2))\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "compare the slopes : \t\t2.47618681684 1.49135870604\n", "compare the residual variance:\t33.4062605805 9.04611997931\n", "betah2 : \t\t\t[ 0.40384675 -0.13895912]\n", "compare t values : \n", "[[ 5.22092063 5.22092063]\n", " [ 10.44492969 -0.87105303]]\n", "compare p values : \n", "[[ 2.88492490e-05 2.88492490e-05]\n", " [ 2.27580943e-09 8.02402760e-01]]\n" ] } ], "prompt_number": 78 }, { "cell_type": "markdown", "metadata": {}, "source": [ "##But why is that ?##\n", "\n", "$y = x\\beta_0 + \\mu + \\epsilon$\n", "\n", "compared to \n", "\n", "$x = y/\\beta_0 - \\mu/\\beta_0 - \\epsilon/\\beta_0$\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Fisher z transform of correlation coefficient:\n", "\n", "def fisher_transf(rho):\n", " \"\"\" take a coefficient of correlation and z transform it \n", " see en.wikipedia.org/wiki/Fisher_transformation\n", " \"\"\"\n", " return (0.5 * np.log((1. + rho) / (1. - rho)))\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 79 }, { "cell_type": "code", "collapsed": false, "input": [ "corr = np.corrcoef(x[:,0],y[:,0])\n", "z = fisher_transf(corr[0,1])\n", "\n", "p_fisher = 1. - ndist.cdf(z, 0, 1./np.sqrt(n-3))\n", "print p_fisher\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "9.81377091236e-06\n" ] } ], "prompt_number": 80 }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "GLM over the brain volume : see \"simplest_glm\" notebook" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# An example of a t-test with 20 \"voxels\"\n", "# from nipy.modalities.fmri.glm import FMRILinearModel\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 81 }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "t-test and F-test significance" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython import display as d" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 82 }, { "cell_type": "code", "collapsed": false, "input": [ "def F_test_reducedX(X, X0, Y):\n", " betah, Yfitted, resid = glm(X,Y)\n", " betah0, Yfitted0, resid0 = glm(X0,Y)\n", " PX = X.dot(lin.pinv(X))\n", " RX = np.eye(X.shape[0]) - PX\n", " PX0 = X0.dot(lin.pinv(X0))\n", " \n", " F_num = (sum(resid0**2) - sum(resid**2))\n", " nu1 = np.trace(PX - PX0)\n", " F_den = sum(resid**2)\n", " nu2 = np.trace(RX)\n", " F = (F_num/nu1)/(F_den/nu2)\n", " return F, Fdist.sf(F,nu1,nu2), nu1, nu2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 83 }, { "cell_type": "code", "collapsed": false, "input": [ "# Set up a model with two regressors - first uncorrelated\n", "\n", "n = 20\n", "age = np.random.randn(n,1)\n", "likes_pies = np.random.randn(n,1)\n", "\n", "x0 = age\n", "# assumes likes_pies has no correlation with age : remove the correlation\n", "x1 = likes_pies - (likes_pies.T.dot(age)/(age.T.dot(age))) * age\n", "# check with print x0.T.dot(x1)\n", "x2 = np.ones((n,1))\n", "\n", "# \n", "X = np.hstack((x0,x1,x2))\n", "\n", "print X.shape\n", "m_y = pi\n", "\n", "sig_e = 1.5\n", "e = sig_e * np.random.normal(size=(n,1))\n", "y = X.dot(np.array([1.0, 1.0, m_y])[:,newaxis]) + e\n", "\n", "betah, yfitted, resid = glm(X,y)\n", "plot_glm(y, yfitted, resid)\n", "t, p = t_test(betah, resid, X)\n", "\n", "F, pF, nu1, nu2 = F_test_reducedX(X, X[:,[2]], y)\n", "print betah, \"\\n\", t, \"\\n\", p, \"\\n\", F, nu1, nu2, pF\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(20, 3)\n", "[[ 1.39775805]\n", " [ 1.00581096]\n", " [ 2.52847904]]" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " \n", "[[ 3.46320756]\n", " [ 3.82996098]\n", " [ 8.39050781]] \n", "[[ 1.48591762e-03]\n", " [ 6.70372529e-04]\n", " [ 9.48074406e-08]] \n", "13.0946461759 2.0 17.0 0.000361508973007\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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FsDDNVsPF5u5dlgy3aVP3OX9/1jlCw8RUb7/+ygZ5aHi92knfokWLDBSY8YWH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\nrQI+/X2EDkNUHO0cOW2qUdVUBQcbB6Nqu61ObECsxmff3zz9Jo7dPsZ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"text": [ "" ] } ], "prompt_number": 86 }, { "cell_type": "code", "collapsed": false, "input": [ "# Set up a model with two regressors - correlated\n", "\n", "n = 20\n", "age = np.random.randn(n,1)\n", "likes_pies = np.random.randn(n,1)\n", "\n", "x0 = age + .1*likes_pies\n", "x1 = age - .1*likes_pies\n", "# can you tell what is the expected correlation ?\n", "print corrcoef(x0.T, x1.T)[0,1]\n", "x2 = np.ones((n,1))\n", "\n", "# \n", "X = np.hstack((x0,x1,x2))\n", "m_y = pi\n", "\n", "sig_e = 1.5\n", "e = sig_e * np.random.normal(size=(n,1))\n", "y = X.dot(np.array([1.0, 1.0, m_y])[:,newaxis]) + e\n", "\n", "betah, yfitted, resid = glm(X,y)\n", "plot_glm(y, yfitted, resid)\n", "t, p = t_test(betah, resid, X)\n", "\n", "F, pF, nu1, nu2 = F_test_reducedX(X, x2, y)\n", "print betah, \"\\n\", t, \"\\n\", p, \"\\n\", F, nu1, nu2, pF\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.991989590541\n", "[[-0.10010842]\n", " [ 2.6387875 ]\n", " [ 2.89779484]]" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " \n", "[[-0.04694278]\n", " [ 1.24034419]\n", " [ 7.0355948 ]] \n", "[[ 5.18447054e-01]\n", " [ 1.15847549e-01]\n", " [ 1.00163387e-06]] \n", "44.6566022043 2.0 17.0 1.70932466497e-07\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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29oaPjw82bNggdEhEjcoryvHFmS9gZND4JFXVrDAh+oQSYT5cvMgKPf/8k+0D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\njWG29vsSkXUxdQxzkDEWIpLYt98CV68yESYiIpICl0YQWRAPD6C4WO0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"text": [ "" ] } ], "prompt_number": 88 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's an illustration of how the various situations one can encounter from J. Mumford: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "HOME = os.path.expanduser('~')\n", "d.Image(filename=pjoin(HOME, 'code', 'pna-notebooks', 't_F_test.jpg'))\n" ], "language": "python", "metadata": {}, "outputs": [ { "jpeg": 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FKTmIkYRW9pO0V8xkxH+jvM5omEaIxH3uMuqPkMn5njItaTz6tWM83uLGET+D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\nBcOOfRne1qkrFED1SuF5KPj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"metadata": {}, "output_type": "pyout", "prompt_number": 145, "text": [ "" ] } ], "prompt_number": 145 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }