{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Demo of bayes_logistic" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The package bayeslogistic implements Bayesian logistic regression using a Laplace (Gaussian) approximation for the posterior distribution of the fitted parameters. As such, it is much faster than using MCMC. It requires numpy and scipy to work.\n", "\n", "Briefly, Bayesian logistic regression works by defining a Gaussian prior on the parameter vector $w$ such that $p(w) = \\mathcal{N}(w_0, \\Sigma_0)$. Crucially, $w_0 \\ne 0$ necessarily (non-zero mean) and $\\Sigma_0$ is an arbitrary covariance matrix. Note that if $w_0 =0$ and $\\Sigma_0$ was diagonal with identical values, then the problem would reduce to L2 regularized logistic regression. \n", "\n", "Inclusion of this prior imposes a penalization upon the log likelihood of any data $\\mathcal{D}$ we observe. One then has to minimize the negative log posterior which is equal to the following objective up to a constant.\n", "\n", "$ f(w|\\mathcal{D}) = - \\sum_{i=1}^N \\{ y_i \\log(p_i) + (1-y_i)\\log(1-p_i) \\} + \\frac{1}{2}(w - w_0)^T \\Sigma_0^{-1} (w -w_0)$\n", "\n", "where $p_i = e^{X w} /(1 + e^{Xw})$ is the standard logistic probability. This can be minimized by any gradient (Hessian) based solver. Here we use scipy.optimize.minimize\n", "\n", "Under the Laplace approximation, the posterior to the parameter vector $w$ is given by a normal distribution $\\mathcal{N}(w, H^{-1})$ where $H = \\nabla_w^2 f(w|\\mathcal{D}) |_{\\hat w}$ is the Hessian of the negative penalized log likelihood (log posterior). \n", "\n", "$H$ is the same Hessian function that would be used for a Hessian based optimization (such as Newton-CG) of $f(w|\\mathcal{D})$. Even if we use a gradent based optimization (such as BFGS) we still need to compute the Hessian to evaluate the posterior distribution. Of course one can use a diagonal approximation to the Hessian (and we allow for this) if there are a large number of parameters.\n", "\n", "Using the full (Laplace) posterior of $w$, one can calculate the full posterior predictive e.g. the the probability $p(y|x,\\mathcal{D})$ which is a moderated (relaxed towards 0.5) version of $p_i$ (the standard logistic probability). This takes into account the uncertainty in our estimate of $w$. \n", "\n", "\n", "###This tutorial will demonstrate several features of the bayeslogistic module.\n", "\n", "1) How to run the code for a single iteration. Specifying a prior.\n", "\n", "2) Calculating the moderated (Bayesian) probability of an event\n", "\n", "3) Different optimizers, the choice of prior Hessian, and setting bounds\n", "\n", "4) Online updating of a logistic regression model\n", "\n", "5) Weighting data points\n", "\n", "6) Variable selection and sparse models." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Import the bayes_logistic module and any other modules needed for this demo notebook" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# import bayes_logistic\n", "import bayes_logistic as bl\n", "\n", "#-------------------------------------------------------------------------------------\n", "# These are imported for use within the notebook. \n", "# bayeslogistic imports numpy and scipy.optimize automatically\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import copy as copy\n", "from sklearn import linear_model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Make some fake data involving sine waves" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Set the number of data points and variables\n", "N1 = 10100\n", "p = 11\n", "\n", "# make a 'time' vector for the sine waves\n", "t = np.linspace(0,100,N1)\n", "\n", "#------------------------------------------------------------------------------\n", "# Make a Correlated Feature matrix from sine waves of different frequencies\n", "X1 = np.zeros([N1,p])\n", "for _ in np.arange(10):\n", " X1[:,_] = np.sin(2*np.pi*0.5*_*t)\n", "X1[:,0] = np.ones([N1,]) # bias term\n", "for _ in np.arange(5):\n", " X1[:,_+6] = (X1[:,_+1] * X1[:,_+6]) # this is where impose the correlation\n", "\n", "#------------------------------------------------------------------------------ \n", "# make a parameter vector\n", "w_true = np.random.uniform(-0.5,0.5,p)\n", "w_true[0] = -1 # bias parameter\n", "\n", "#------------------------------------------------------------------------------\n", "# make some binary responses\n", "mu = bl.logistic_prob(X1,w_true)\n", "y1 = np.empty([N1])\n", "for _ in np.arange(N1):\n", " y1[_] = np.random.binomial(1,mu[_])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1) Simple Bayesian Fitting\n", "\n", "One always needs to pose a prior parameter vector and prior Hessian matrix. This can be whatever makes sense given prior knowledge. \n", "\n", "Since this is a simulation, we're going to \"cheat\" and make a prior parameter vector and Hessian matrix using a small sampling of the data. \n", "\n", "We'll also demonstrate how to perform a Bayesian fit for the first time! " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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E+9EC2qKOIaDs2IYBfLaHapuNBOxahw5bJ2lBacdQfJoMMRCpvW8RS2h6f00f\na7JlkXwSlKYQmtxU13RLI0DasoA2wNkKPBp5XjK8PWlfG0Lrbndxc/vxdPF3l6fCCsBoBtA11ggU\nqcKPfwy33ca2ooA//dMwFLzPFNOIrJUe+ciwlOdTnhL8Qs87b2P1b5zGrcne6wWQbs+Vupo6/vgA\n8HNzMDu7NtfMytpD1S8WnxHEiKcqoLKKKzyu8PjCoUWFln20sFBYKAxSGEwBplBMqdjCY0tPWVaU\nZZ+y6NMrF7DGBcgsA2RW5QKVKyiLPv2ipCj6FEVFUbkBeNbWzzoK3mi0hGozHB/8IjXAZW1RbK0H\nr+lk9A2E+gRAY+q7cOwIxaTlNoF0abH9MBiOb+UjVlIGMNlYTHW0a13dHenT+M0BVKY7U5hs+x3U\n5RRGfauuPpdp5R1AKq06GQem44ByBbbH5ZPgcxKMLkMZQNda46DogQ8Mw8BluQ6dmkL3vjdcfnmA\nqEc8IviFrrVbwFKlY/6lHHXU2gcEHXBAWJHq8svhuOPW9tpZWXuapviSVGgi07VeicjZAJBVQWVL\nqqrfrGxk+z0KWzWR6taEaPcUVArr2DG/ibmFTcz1Z5jvz7BQ9VioegFIfYFTi8fgRVADWBCrmEKx\nhcP2KgqtKHWBCotYi/b7ARxNhdoKjANxaB2shKJ1P+L9oAa8QY0N8Co6MGqOAOi4fCn7LKgFTLh2\ntALjJWG3CJZ1xL5ImM8dEjgtqKEaR5JkuNzMhCQD697IPJcpgaZmvjT5MfmkfWkOA3hN8/T5tIft\n2z6oi8B8e9fObC9m9F0HZQDdKDrooI0Ln7VmZ8McoW95S7CKXnBB8G3caLruuhBAdOWV3fvXy4Vg\n61b4+MczgGZlrbam+lINcFTDZxokNADRksqW9PsVhXEsmGqwwpFxwY80uZg1jvmFWebmZ1hYmGUh\nAmjlSipf4rTARwDVMM9SMHxZRQqPKT1WHVYrCu1TSoGYCJ7GoSbAp0oVAFQ8Gtd41zgpfdiM92YM\nYgwqFhVtXAGHCWVaE9lieXTc1AhfNYA2rKcxmMjH4XSJEBoPd6mVNNKlAyoZhs4GPtO8htD6erFf\nTbCUJH8T08Bnmi/Wpk4pfKbPpgs+29bVxSzJE7QUGB3372KdIHQPnuRxnfT97693D5YnkWAFff/7\n4TnPCcFS4yyNa6kf/hDe9KYw1+Yxx4Rf2L/0S+vdq2GdeGIA0I3wvLKysoYsoOoMfgg+C6qqoF+V\n9Ps9FvpRUeOcAAAgAElEQVQlC/1eSAszzM/PMjc/y9zCLHPzm9gxt4kd85vYMT/L/MIs8/0Z5qP1\ns+/KYP30FqcmAqigRsBosIBajykctqwo4uT2vZkFerMLlDP9kHphX1E6bOkoSkdR+rCWfaHBTcCG\nJNZgjCBiELEIlmBzKmMqknxcskvI69SygDYcp0mKrgJDc5X2Q6r6UC0MklsY7HMV+H6cyzSdWL+i\nWYJU/SBNnl+qldrQ2ZXchNxNOK7rerTK0/7RTrlv0qnHWT8Xs5Ku8FdXtoCulaoKXvpS+Na31rsn\nK6PHPjZE5z/lKcGX8u1v3/mVmHZWCwshsvzd74bPfCYA3l//dZiyqihgy5a17c9iOvzw8OL9+tfD\nhP9ZWVmro2m/KHXYAupctIBWBZUp6NsCa8qhSeIl9VmkBliDqmCsY6Eeek+G3/uupO8KKi1wxCF4\nJFimLIj3mCJYPwtxOOnjxOCNINZE66cPFk8TLJ9eHEqwgKrqgLsKwXtBXbCABsOkRKNkOnUQY8o7\nW1eDZ5q6rKC+ZeyrrYa1hdANzuWiddO1U7KvsYAmeVcaicYZZ+WcZjstw7AtL7WItmWS/W3TZLsu\n2TXOONo+RVc5PT0d+ToqA+ha6Pbb4RnPCMs2PuxhYf323UH3vS987nMhUv5Rjwp+oasd1KMK//Zv\nATrf976wzOVznhOmidp//+G2m5M12Vv16yKRwTB8BtCsrNXTlF+ubR9Q76P101msK7BVSWUc/WaF\nIke6tjv18TEZ6+hH6Gzgs7GAlrjEB7S2gEo9BK8BS61UFGLwxqJWMNbgJcKneLwoqh6vPuaK+pDq\nOCSsoFbwNYBGBhMM2kDQYiA6TTmpq4fe0wsOGRjj8LrUAFpv1zCXHK8C1gxgs4FQk0CnacGnSSA0\ngd8REJxkAR0Hn5Pq2+fsAk9h/HWXMPw+LXBOOqZrf1e+BsoAutr66lfhyU+Gpz8dzjwTnvtctnX5\neq4XFC1XmzYFf8s3vCEE97znPfC4x638dW6+GS68MFxrbg6e/exggT300LGHjKzJvhG0dSu85jVh\nGdWsrKzV0TIsoGEYvsBVLsJnGS2ftQW0tqVpNOqF+T1VBWMcfVdbPMswfB/LlS+ovO3wAY1D8Hgs\nDi+GwlR4Y1ALxhg8HhUNOYrXUPKqGO/xXvFeEQfeAmZg/fQxslrEoOIjhKZqk8s0ANq1L6bU4pgO\nwQsRQhlUSLozAVebQKVL8gZGzQBAtc41Xs/Ecu2Tmgb9wHjobAcfTZMmjXOn0OnH1O/EEPxiqoGz\nPm16ubQNTL70GoBoBtDV1HveAy98Ibz5zfDbvw1sUCharkTgT/4kRHmffHKY4uj005cf7LN9O3z4\nwwE66+VBzz03WFt3kblIR7RlS/gx8qMfwc/93Hr3Jitrz1VqvewYhq9MganiCkVx6N3Uw+91Foff\nvTeoNxjrqFxB35cx6r0c2naa+IASfUA1wKygGHFYY/BWKK0gXnHW4EVDQhvw9KoD8PQE+KyDdWzg\nMzEGMYrGidwDfKZkMQkql7odYXPI+hktkqLDEIok7/AaVt3gWOKxNWg2lk8zDJ/eJEmH4bOBrrpf\naeT5NFbQaRPJeSc8m87rpccugfiWYgntGo7vOt+kay2l/RKUAXQ1VFXBwvXRj8KnP73xgmFWS7/5\nm/ClLwWL79VXh5WUNm1a2jm8D8P6558fVik66ig49dQwvL/Uc21EbdoUIPTii+GZz1zv3mRl7Z6a\n5gtSgBgx7r3BuzDs7UxBVflBtLsMg0IYtg8WT+cHKxs5bzHW4XzRBBxVGnNf4DRYQNNpmBofUNFw\nLe+xtgIfR6rVhyF4NEEexSkRQsNUnxKtn+IUqQgWxGgJDe6UMQJeuh5M14/5cT/wp2jbWNdkmOtq\nCB1q1Gpb79LYd29a0DlmW+uyHcBnc67U7zK9wM6AZ1egUcf9jDyXFLZrEl+iBXSxkfouEJ0En11W\n0DUcfocMoCuv224L/p5lGax2e5qV6373gy98AZ77XDj66ACRBx+8+HHXXx+mdTr//DDJ/XOeA//x\nH7vn2ulbt8JFF2UAzcpaLU37nZ74b3pvGqA0tQU0Dr3TTLcUhnnDsPuw36hzFmN9tHLasOxmLDd1\npEPwtQU0TDZvTAhCGnBJ8Au1VoZjrhXES7PwkcRgcCmAijgdp8RheAYL64y4bU6imZ3dR3xGDN3H\nYBS6w/LXblvHIxkSyLQta6dtlXVwHU3KaZ81Ja42dC4Go13gWdct9pzGQWcbitN8Sk1j8azrFgPN\ndQDRDKArqauvDlHhJ58corGtXe8erY/23jssc/m617HtAQ+ABz4Q7na34TabN7Pt7LPhn/85BBR9\n4xvhuX3oQ/Arv7LrDrFPoxNPDG4KVRWi9bOyslZW036BarCA1sPo3lmccRixYaUkikHUuxIGyqPP\np2+gNQQtOV9gjIsR7nWke1z/vS4n+xSTjEQrgsfESwkDn1BXCUYFrxIXQxLEg/eCeMFVgJMAoIVA\nIWi0gmoDoRKvVftqTtJS372J2W0EAjVaN2PZtyEwKXcBZAOYbgCdGoEzhc8mJzlPnYTgByqta4+D\nzvZ2Gz5dq9z1LKSj3JiCO65Pki+ipUDntFbQ9nHjrrvCWva3n4gcD5xNMPi/XVVf29q/Bfgo8M1Y\n9UFV/evlXnfD6cIL4UUvCpO0P+1p692b9ZdIcEO48EK2XXvtyO5t110XhtWPOQb+1/8KS1Vu9In4\nV0r3vneYLeBLX4LHPGa9e5OVtftpiRZQnwzDO1NED83RdqqJr6g3OFdQVWGJzarqY6wPlk0ELyYp\nCypmUK5XQooXqYfgpS4T2nsRbCU4DcmowahgvOCcIE6QShBncJWgcTEitXWEvUGMhJQGCi0ZMqd6\nmsNJfWSu5MMwNYSmbSJwpsuLeo1t4w3VEKqWZt17byPU1v6fdsB4KXwOAWBHP5cUfNSe/9Mn503V\nBaBpP9oUOOYPtgssJ+1rQ+e08LmG0JlqWQAqIhZ4E3AMcDPwryLyL6r69VbTy1X1icu51oZVVcGf\n/Rl87GPw2c+GuR6zBhrngrD//iGKfU9zUahVT0qfATQra33UMFC0gDqDE4s4j2AZLA1ZWz7bAGpx\nrgpru7uCypUYG5aXDMHYEmNq4pKbcchdoWmDSIiClwCewVczHmfieaxQeYPxAT7FG6QySB0VXhmo\nPFoYbBF8P9UIag1qAgiHyeiFsA75Kq0/oz5CpKeJPNcIaA2I6iDyXX2AzLq9tMreD+CzySN81tZU\nrSGV0ZH0NBK/ibKvP3jfkY+rGwef6RB8GzK7gHNcWu5zZzJ01m2WCp9roOVaQI8ArlfVGwFE5H3A\nSUAbQHfP8dTbbgvR7bOzwd/z7ndf7x5N1EUXXcE551zK/HzBzEzF6acfy4knHr0+nbn3vfdc+ITg\nB/p7vwevfe3ibbOyspamnbCAGomBSGKJ8dgNvDTR7hp9Pn2BcxWVrShchbWOoqowNkJVzXlxYSCp\nfRshWSZ80E7iMSGP5XisrwJ0Gm8CfDqDVDbCJ9AHCoMW2lg/TbSA+rgUp4gFMUjTsS5CWe5Drn0d\n4y7xCQRGqGuW4oxRVnW0lfqwvn0NmCbW+2IApTV4pvDZlEnYUZIUA5C0PdTdlZYShJTmXZoEpO3J\n6KeA0UlwudRjJsHnGoPpcgH03sB3k+2bgCNbbRR4pIhcS7CSvkRVr1vmdddftb/nM58Jr3rVhvf3\nvOiiK3jhCy/hhhvObOpuuOEMgPWD0D1Zv/7rYYGCb30rBG5lZWWtnKb48lSRwDZSD3criEWcNucY\ntno6rDc4a7HWUdkCaxy2cljrsDYAqFgdpDiULIUiGgKZ6vXjJU7CLkaHj4mJmGslGG+o1CLeIt5A\npeBiX/tAJWgftAjJxInoxRiMsXixiNRUaxkekt6ZB9i13xOmUqpPn5BP7fpYWz/reaM05uIieLoI\nnjFXF26oAVFlaNhetdvyqbETWkNwvcpSCn/jrJ+LBSG1l9+slUKmZ+egc9pfTgzD5TT5JCvoYpde\nJRhdLoBO062rgYNVdbuIPAH4CPCArobbtm1rylu2bGHLRltKsdYFF8Cf/in8/d/DU5+63r2ZSuec\nc+kQfALccMOZvPGNL88Auh4yBk44IUTDn3baevcma4m67LLLuOyyy9a7G1njNO0XZmIBFQmQ4LAB\nPG0I/PEx6Mh5g/UW4yJwGoexvpU7TKFI4QOMFh5ThIAiKTzG+BBshIaJ7aPFU6xiCo/YsCSnFINt\nLQRxFvE+uAe4IkJnSFoatK9oofhC41rwwfppjAlD8MYQopRSAF3sYXXVT2qbnFNb202baLGUBELT\npNWgjI9EHS2gWtBYM5Ukr1Nt9XQMAo9q6GzDZxtCu8pdENqGzxpAJZa7ANQk2+2+JM9lLbUYfK5R\nd5YLoDcD6Rw7BxOsoI1U9Y6k/EkReYuI/Jyq/qh9shRAN6T6/eDvedFFcNll8JCHrHePptaOHd0f\n9dzcKltuN2+w5TA3kk48Ed7+9gygu6DaP5Bf+cpXrl9nsnZO9cisjxZQn+xqltY0qDq8D5ZE5wJY\nGhfWhrcmQKWJEFrvs95jCodRj6lXfzcuzPOpAWIMYYJ4Y4lWT48t43Ext6VHHYgrgrWz0gCdDYAK\nWgT/Ty00uksK3oJpgpAsInWqIbRrHHepVNLedslDrQErglfNo81SnPXwuwNJoFMiVTdAWkOoDs6d\nJkjAMynXPqZN6gK+NmwudRi+TvW9S0dew+gkC2jar53QtFbQtH37+KVsr6CWC6BfAe4vIpuBW4Cn\nAyenDUTkQOAHqqoicgQgXfC54fWDHwR/z732gquu2vD+nqm++1249tqqc19ZjvNhWRntlis/rZSO\nPTZMsn/nnWHu06ysrIkSkYOB84F7Eb4a/0FVzxlpuBMW0HoC82Z9eDVhyUtjQoS6CXN1GucRE6yX\nxsQlOutt67Clw2pMVFhx+LjCkbVV0zcRP/ABjRbQAJ0O23PYssKWLoxqVxE+XQ2gAn1BS48vfcgL\nG62fAT6NFUziAxrgs0CkYBDjP4k2ljJeW8OgxmH2OgApgc/64dYQSmL5pErgsy7XVlA/DKAkls/4\nGQ7KcQ146s8zgcvGD3RcaoPmJCBtW0Bh1PqZWl8nWWK7nucEjQPLSW26huC7LjtNN1YQSJcFoKpa\nichpwCWEn1XvUNWvi8gfxP3nAk8F/khEKmA78Ixl9nnt9ZWvhGUgn/UseOUrN7y/Z6rPfAZ+53fg\nKU85ls997oyhYfh9930ZN9xwPDfdBPe5zzp2ck/VfvvBkUeG1bJOOmm9e5OVtSuoD7xIVb8qIvsA\n/yYinxqZeWXKL8l6GU4IPqCKIDV8+uifGeEzTBYft6PvphFFTLJtPYWvKLSP1YoCSyFVWNvdShOL\nE3xADUZcHIKPQ/Slw/YqiphsL66K5DQmYuBRBNC+oKVtht99AT4GIUkDn3UQko3D8AXDQ8DtB7aT\nZYUmkr1ruqcaANPgI9wweNIf5FQ08DYEoLS4rRXpXvt8qot5e3h9EnymZTdlin1ojklB1LfK4yyh\nqcaQ5VKAc5rjpoHPVbR+wgrMA6qqnwQ+2ao7Nym/GXjzcq+zbjr/fHjxi8Ma5E95ynr3Zmqpwute\nB69/PfzjP8Jv/MbRXHQRvPGNL2duzjI76zjttOO57rqjOeqosGrowx623r3eA7V1a5iOKQNoVtai\nUtVbgVtj+U4R+Trw87RnXpnaAgpKgFCRGCgkEuGTsMRlHSwkhDaiceqkQR2x3lhPoX3KCJ5e+nhj\nwryctdujegwGI9IslRksoIotfbSAVhQzfcqZfuComsf6hGCjnkEXDFoafOkjfCquoPEBrS2gJppF\nhQKhAErotIB2WeOm3Z+CXFwaM4XQthW0Hn6vIa6G0PpGpR/LCXTCcLkBz+Ra2iyhlFg/x8Fn1/52\n28WG4lMAbYPnUqFzzB/tNODZVTcJPHfG8rkKysuwjFO/H8Dz4ot3OX/Pn/0sjOzedFPwFqhXwjzx\nxKNHAo62boX73z/MA7+LMfbuoa1b4ayzYgToKs3Pt5tr2ymnwI03ju7YvDm7gOzGiq5fvwp8eWfP\noV4G7CIyWPVIAB8As/4SD6AZtofayaCdsZ6SBZxYetKP83FK+KZ1IKoYLB4fwFcIa8HbAK/1EHzR\nqygjgOIJ1s4qWjz7Bi0d2jP4BYstPL4MAGptCBh3VhIf0HoIPlpBRyygi4HlEtpoDWYGJFmTfWgI\nPIGzFEIbyl6I5QigI3TUfGAMg58ZTYsOu08Lm11W0bYPqJnyHJNgdFrTPdNZOlMYHce44y65BlCa\nAbRLP/hBWM1on30CwbWXkdzAuu46ePKT4XGPg/e8B2ZmFj/myU+G+943GOG+8Y2wgNHuvBLmhtIv\n/ALsuy9cc002Qe+sbryRbZdfPlK9be17krVGisPvHwBeqKp3jjT4r22D8j22wAFbxp5LawsdoCpx\nGBkCadYXHJfr0HZYCcmDCX6imCKUrQ0R8pXBVQZTCNaZMAm+CxbYwVSVyZRNEXBE4kKeccUkE4f/\njVGsVZxRjB0ka8NwvI2WUVsovlSKAnypyfKiwxZFbbYjtcSlmgYcKcmWoEmbgSUy5vUzHHpgg6c+\nZA2dyucyhUs7oe2kJBOuN8kyuliaJsiovnUlXeRgBBy7LJiL1dHa364buv74rg3t79JUUHpZTIsr\nA2hbtb/nc54D27btUlap978fnv/8YFA79dSlHfuwh8GVV8Jv/Rb893+HGaZ6vdXpZ1ZL9TB8BtCs\nrEUlIiXwQeBCVf1IZ6MHb1vCGZNvVemAhbRdatGDwbByU+2h71DrUONRibnxeNEGpWxcWrMiTDBf\neRPn+CzCVEt1wFE0AlbbS6odBW7O4hYsfsHgKwNOEsuqhoAnY/BFhRaC9gQqRSrFOG2i8rUKeNsZ\n29OuS1h1UCdDj0E1fQ5dFss677JWWoYBM4VLm9Slx7T8S0c0zqrZHiJfBBZH1La6pvcTrbKS1Dfb\nyanb3g+SPNh0ezGQ3BlNw9RD9zpu3yRtianWK8e2zACa6l3vCua/c88NZsFdRFUVllP/8Ifhkkvg\n135t585zn/vA5z4XgpaOOw4++ME9e7GiNdPWreEDfMUr1rsnWVkbWiIiwDuA61T17LENp7UbaBua\nWrnq5HZD9UpY6acC61DThs8AoF6I67qHtd0H8Bnn+ayKMBLtgEoQhf5dBdWOgmquwM9bfN+E4fgY\npxMspj5ODeVQa6AU6IG4CJ9esbjgm1qZOKe7DOcaJ+dv8q66wTHNk2gso8MW1W747ALRGkLbls16\n3tIu+JTWNZoPtZXS88HoNErjYLStcf0nKXfBZ0e5sa5ry6o5DuJXQGOhU8bUpz+4VmdIdI8E0BGf\nMe/hhhvgjjvYduWV8Iu/uF5dW7K+/314+tNh06ZgvF0uMO6zD3zoQ4GHjjoqTHl6//uvTF/XQxtq\n+dFxevSjg+/DrbfCQQetd2+ysjayHgX8LvA1Ebkm1v2Fql481Gra78sUAtqmwKFhYoatVG3zYF02\nHrUV2q+C9VM8XlLrp2IRnCcCaFzbPa5qJE4jeDKIdlfF7Shwc9ECOh8soFpJsID6gQXUiMdahxYC\npSK9sBqTURfmIzUFhS3wleBdvcRomIYq5BFGk7q0fqgOidwmi+DSJF/NNoR2BfC0ATRdSnQcfNbl\n9jA+HdcYB55tmG7fT+pH23I/6ARRWrCZnG6orKH9pP2d9cl528P06aPR9v2Ms1jT0WZlQXSPBNCx\nPmOPetQuBZ9f/GKAz9/7Pfjf/3vlZoeyFv7mb+ABDwhs9E//BBt1UapJ2mWWHy1LePzj4ROfCB9m\n1sroppsGL/Os3UKq+nmmsW8uxXMqhc+h4VCtTYDDwNk1KXrcVokWUHFonP9T8eE/VbyGkXXxgvEJ\nfNbzfFYaJpnvEQKPFgyCDsBzfjAEr30zagEVF3itAFMOht09hkIczvbxhcVXBu/iEqMugKWPvqje\ntevitgv99U7QaM3zagYuoCPw11YXiNbQ2eXfqQwCplJLaAqt6Xnb8JjCpUva1zDqO9pNawGt4bM+\nZ4z8FxkuqyQAKKNgOAKWO2MBbVlRJzRrLJ71MZ2WUB2tGzrJyr1P90wAHadi13gcqvCWt8Bf/RW8\n4x1hBHc19LznwaGHhvn3X/vapfuVrrd2qeVHt26Fj3wkA+jOaPNmtn31q8GH5IADQt2OHXD99SGy\n7p3vHNRn7Rmaegi+/l9q0YxQ0l51p2sd8nad+DD0LtECGuPdFe0AUBMBVMEZqGwICu8To94NulAF\nr8UFE1I/RL5rYgEVr4iCQWPwE4hVfOExPY8l+oWaCm8NvrT4SnCVGcCmC2XnJMLpoN65JJq+CrDo\nMYgG9wBRIUS8j4OnCT6TnRbQFArbFtAuK2P7A01T6vtZW0DbQ/CLwWeX9TMdfh93j20rKAwNvzd1\n6TOrfwQlp10Ki3Y1TmFXZfA5jQPPEeuodD+WFdCuQVxZjbZvhz/4A/ja14IF9LDDVvd6xxwDl18e\n+Oi//xvOPHPXicv64Q+7/7zvumsDLiTwhCfAC14A8/PTTV2Q1Wjbm98MH/gAfOlLYUaBWgsLcMYZ\n8Ku/ChdcsGua8bN2TkvxAfXNRkjqh8s1ZPoWbPqOclzfXOsUPT99DaBe8T40d04QFwG0smF6zgq0\nF6da6hu0FyygGn0+fWWaqZh8P0TQhxUwawsoYY7SIlg+FY8XQW2Yi9SX8dgYje9dyF0V69xw2VcG\nqQxOwoT2AXOjtVdNmEu+c0qnWu2h8nFD8TV8prmycj6gwuCDnhQl33UP7X53XTuB43rIfShPnwHD\nUNjkNQDGyjacLhdG23w9DjxVW5bPxOqpre1lahdBiSwIBp1HPCKUv/Sl1YfPWg9+MHz5y/D5zwdr\n6Pbta3PdndXnPx+WWf/3f+9efvTKKx2///sh4EqX9A96FXXPe4a5Zq+4Yr17suvpiivCDAIpfEKY\nxuF1r4O3vQ2e+czgp1J1/01k7WbqmBKyMzUGtWh5SqGlnshcXQRMB96Bc+CqQar64e+q6of5o/sV\n9Ct0waELDj/vY1LcPLg5cDuEaodQ7TBU2w3Vdku1vaC6q6B/Z0H/zpL+nT0W7ujRv3OG/l0l1fYy\n+ILOD4bgSYbggw+oo7COoqgoyj5lb4He7AIzs3PM7DXH7N5zbNp3B5v23c7sPjuY2XsHM3uHfb29\n5ultmqc3u0A5u0A5s0DR64dUVtiiwhYOax3GurCUaJhZH5loImvD57gPI414r1PB4hCaKgXh1AJa\nD7t3BSB1WT/HWUK7LLkT/D/T42rIa7P60OpOmkBhndLudVnlO5Jvnae93U4wfL3mB1jSr1VQBtBd\nRB//ODzykcH6ef75YUn6tdQBB8D//b8h2Omxj4XvfW9tr7+YVOGTn4Sjjw4zaD3xifC+9x3LYYed\nMdTusMNextve9njuf3/4wz8MEP+KVwS4X3fV0zFlLU2XXgrHHjt+//HHw9VXh19tj3scfPe7a9e3\nrPXRtAA6Ap+t+SC1ThFCvU8gtA2iIWlVoX0X0oJHFwJ8+nnFz4GfE1ydGgi1VNst/e0F1faC/l1l\nA6H9O8uhaZh8EoSkSRBSHQVvjKOwFWVZUfb69GYW6G1aYGbTPLN7zzG7946YzzG71zwze80xs6kN\nn33KFD7LAJ+mhk8TrtWsDDVxCBvGWw+7IDSFz8V+PXSp/Vm2gTOF0PZnPqn/7Xtp+6N2uBc001Wl\nEEpSX2+noFnDXwqILRhtjlksjWuX1KfXrzs1ZP1sPZIVZNE9cwh+82Ze/M0b0e99n2/ufSAiyn3u\nc3fusXnzevdsRM6F5efPOy8sl1lbQNdDMzMBfs88Myxh/rGPwS//8vr1B8Lz+eAH4TWvCeW/+Iuw\nhkBw5z2aXm94+dEXvOD4xv/zz/4szP9+/vnwqEeFOeGf/exg5b373dfhZk48MUz/dfbZ5MCZJejS\nS8MUapN00EFhjrLXvQ4e/vAw1dqTnrQm3ctaBy3FB1QYQKi0wTNJvp0cuFZdhBlFUVW8eozGsg9R\n7s4TotcrQSoTIt1LH/w+SxPXdQ+rG9kirj+v2vh6omO2IcCgjWvYe0K5aT9o6ytDtVBQ9S12wVIV\nFrNgcbbAGEtl6pWTBvdDvA/1FhMDlMSMs0TWmhY8a/hsQ2A7AGmpQ/Dp8Lt07OsqLwbRdb/q4Kl6\nXzv4qNW/+m8t9f1Mh9Wb+T91AKjoFEPv0xBhApJpEBLRJ3QoMKkuS+vUdYdXTjJY+WB9JSK6Vn25\n6KIruPPkF/LFO07hHF4IwGGHncEb3nDchgpO+dGPwpycO3aESPQDD1zvHg1UT3r/zneGyevXWvPz\nwa3vrLOCdfZlLwv8trPc1u8HPjn//JAfe2yA0eOPD0HqayLVsCTVpZcGv4esxXXTTfArvxLmI5t2\nGogrrwxD8k94QpjuYdOmZXdDRFDVlX07Z+2UREQ5ZcrvEhctm64FlCPb49ql9R5Rj40rD5m4EtEg\nxe0yrlZUgC3DqkVN+2TblgwAFI9hci4oZsrcV4b+fEG1YKkWCvoLSTmprxZs3BfLY46pFiyqnmQC\n01a5nU/brh2ENE15sX2ToLMrLdYOwhKnMXWVp61ryvFV0rxRWn/PI28a7WbDTjZPrbKtfMRC23Yd\n6HAlWFTj34175BD8OW+4hKPu+BGXMhi2C9HRn1rHXg3r6quDW9vhh4eh740EnxCshB//eHAJeP3r\nB5b81dadd4brHXZYiDt529vgC18Io9fLMRqWZTjH+98fpog95hj4P/8nBFb/yZ+Ez2PV71EkdOKi\ni1b5QruRLr00fFhLmYPsqKPCB3r77cGU//Wvr17/stZHS/L/hMGSmsmQbeoDqhE86+F3Xw+/uzD0\n3viC9psheJJheL+g0QdUcekw/A4ThuB3hCH46q6CfjIEv1APwd9VUm2Pc4HGIXgf14fHBUNlWKoz\nTEV506kAACAASURBVERvox9oWcYh+NkwBD+z13wcgg9pZq+5wRD8bJ3CEHxR+4A2/p/1MLwPKQ7B\nD1aPaufSkY8bvh7nAzrO93OSH2jdhxQg236gjslQmaZxVtykLzrJOlsPxbeH3dvldKi9VdYxbbr2\nj/iCpuWONumQfGMZTfKRTqf58rRHAug9f/IzLI7/5EFD9ddea3n72+Hf/z28V9ZL73pXsLy97nUh\nbdTZoY48MkTiv/Od8Ed/FKyIq6Uf/ShMO3XooeGaH/0oXHxx8Edd6dHqu989gPUXvhDS/vuH1Vkf\n+tBgcb355pW93pCyH+jStJj/5zjd7W7wvvfB6acHx+G3v33tfkVlrb6WEoQ0NPzesnqlPqBtCE19\nQKsk9Yd9QP2CR+c1Qij4ORof0GpHhNDtdhhC7yoHEHpXj366FOe86ZyIXtAGQGv4LHp9ypkFerPz\nzGyaY3avOWb3iWnvOWb3DlDa2zRPb9Mg+KicWYg+oBW2rCHUYWwVfUBDEJKIR0YshF1ayjB8VwDS\nuGH4trqsl9OkDqvmVPfRhk6TwGbiA1p3LQ1IGoHP1uXHBguN2TfR57Oj3RBspvDJ9PkytUcOwb/p\nwcez13/+PM/lnUP1D3rQy3n4w1/FVVfBLbeEJS2PPBKOOCLk97nP6rrmzc/DC18Il10WltXcVUZh\nf/azMCG+c8GCeLe7rdy5b7kF/u7vAuQ+6UlhhaYHPnDlzj+tvA8wev75wef04Q8PQ/RPfjLsvfcK\nXmj79uCv+O1vr5Mj6i4k58LQwDXXwMEH7/x5rrsOnvGMsAjFueeGXxxLVB6C3zgSEeV5U3yXKAOQ\nrFr5YnUjZQ+uCtHoBoyVVmrVjbQZv99apSgqrK0oChfzCmuHy8N52rbVzla4yrAwV9KfK+nPFyzs\nKFmYD9t1/cJcQX++ZGFHGfK5YrC/qS+a9mEI3i0xxTD+oW2X1LWtpeMsqF31446tP/yVyoXB0HmE\naGn5rkoK0K39nW3TV0m8VufbJfk7lzH19b4agNsgvFjdxPbTKA/BD+mp+9/JVfv9aKjusMNext/8\nzeO54AL4r/8K3/9nnBFmdnn3u8Nw+M//fICgV78aPv1p+OlPV65P3/1uMMTcfjtcddWuA58A++0X\nApIe+MAQqf/Nby7/nDfcEKyQhx8ejArXXhsgdD3gE8AYeMxjwpD/zTfDc58L730v3PvecMop8JnP\nxBiEqIsuuoLjjvtLtmzZxnHH/SUXXXTFdBfaa6/wh3DJJatyH7uVrrkG7nWv5cEnBPD88pfhHvcI\nc4Z++ctTH1p/zlkbTEuNgK+tn2kQ0kgUvGtZQFPrZ5yKqd8Py3D2XWsaJsXPheR20ETAu3QaprvS\naZh6Id3RC8Pwd5VUO0qqHfVSnBbtj1pArXHRAuooyj69mT69mfk4/B4j4PfdEaZi2mdHmIpprzlm\n9ppPIuHnm0j4ehqm2gpq6kh4EyLhu6Pgx2kaK2iX5bPLjzOFyi5NsoBOOxVTu+/pPSwCwNqyjGoL\n2ob8LetUWzi7rJpd9ZMsnq16P25fx3VJ6oYe6cobCPc8C2i/D/e8J4858N3cuddX2H//Ojr68RMD\nkFQDlF51Vfh+uuqqgeEltZI+9KFh+sGl6NOfht/9XfjTP4WXvGR1rayrrTe9KUTJf+ADIbJ8qfra\n10JE+6c+FYb1Tz89TJG5UXXrrQFEzz8ffvjD8DkefPAV/O3fDi8BuqQgt7e+NUxmeuGFq9jz3UCv\nfjXcdltwCl4pffjD4ZfPi18cpkmYsOrC8FKv2QK6USQiyh9PYwHVYMWsoh/nSLmVOxfm+EzLrtXO\nK8YIpl45yJimbExYUcjYtF6S/d3tbOEpe33KMkyNlKaiDEPsY/f1Fkbqy7KPqwzzO3rB8rmjN1ze\n3mNhLpQXdpTN9vyOHgvbY91cj4Xt5dBxqingpVbMdj6u3FW3mP8lU7Rpt130D2OKNqkSEJUOYG7X\nSQrTdV3bB7YxWU62bKb1i1lIU/hNn4dOUR5nCZ1K49+Nex6Afv7z7Pj907n/HVdz443L86/s9+E/\n/mMYSr/5zTA10RFHDKD00EOHofKii67gnHMuZW6u4Hvfq7jttmP54AeP5jd+Y9l3tyH0yU+G4emz\nzw5R/NPoC18I4Hn11fCiFwUG2G+/1e3nSutrXwuR+eec85csLPz1yP7jjns5F1/8qsVP9N3vBkvc\nUiK790Q99rHw0peGaPaV1He+E/5wN20KvywOOqiz2XHH/SWXXlp/zhlAN4pERHn+NN8lEUD7KWhW\n0G9BZX9Muaut8xhjB0tXik3g0iKSwKYk7YzFyKAsMjjGFj4EBvUW6M0Ey2Qv+mn2Zhaacl0/vD1P\nb6bftK1zVxnmt88EuNxRDpXnts9EEA1gObd9poHN+e0BQutyOCZsq1dGgXIchE67rws0mVA3bdvO\nv5xF/l7G7a8BtB5O77DYdkHnSH26T5LLdf0td9TJYu3aADoJSCeA6AoC6AYNb1lFfepTXDHzeJ53\n8vKDe8oyzADzK78S1k0HuOMO+Ld/CzD6wQ8Gn8UdOwZAClfw7ndfwo03DqxjhxxyBjt2AGycKaCW\noyc8AT772cHyndu2dVt1VcNI82teE5jrz/88WE5nZ9e8yyuiX/qlEDR21VVF54JGc3NTwuTBBweH\n4yuv3Dkz8p6g+h/a0avwb+a+9w1/wK96VXAEP+88OO64kWZ33bXnvT53GU3rXNaMmibD8GkUfOcQ\nfNUdhNQPFlAVD6aI5wzX8Eaa4WoxoCKICNQgWsNoU7ZN2ZYecWEOUaMeg8eLQY2gVqAkrgXfFQHf\nbyLb63xmdh7nTBhCNyGgaHDfYanQQbyVUPQNrhRs32CtHR6CN57h4K1xD7k97E5sb1rt2u3T+mnK\ntU+mtspLOXZSm3F1ydC7dETDp9CXnmLkkdV/h+19U0CoMgWEtjfj8xkCyuR5aXPi5Pj2c9p57XFv\n0OqTl/KW6/+at/7+6px/331hyxaGlp2+5ZYApFddBW9966X8+MdnDh3z7W+fyRvf+PINNQfpcnX4\n4cEqfNJJcNllV9DrXUq/XzAzU/H85x/L/PzRvOY1wYr80peGIKaNGu2/VM3Odi/32OstYWqFE08M\n0fAZQLt12WVheGFFI8ASFUVYAeJxj4NnPSsEKZ15ZuNfc9NNcO21eVnPDatpAdS0fEDbEdTpJPRp\nFLxvrYBU596DFPG724Zf3iKomAigQIRPEYG4xrqIASka6GzK2DAhvfcY9VgcXiq8NWhhxkbBWxt8\nQEMUfD+AZ/TznNk0j6sMEOYPBW2WuG+mNnWCrwRXCcWCwZUmTFYffUDFxgh4GZxjcT/QcSA6qd0k\njduvY8rt89flLqCaBJ/tvOWbWsNmeyL6xbo0sr/dcEpL6MQ66fDlTMBzxLLZhs+OUy9Du8lX/pT6\nyU/wX/t/7Lv1UfyP/7F2l62Dl570JPjiFwsuv3y0zdTWsV1IBx4If/7nV/DsZ1/CXXcNoPuznz2D\nQw+Fs846mq1bJ7rZ7ZI6/fRjueGGM4Z8QPfa62V861vH861vwf3uN8VJtm4NZvXXvGb1Orora2en\nX1qqtmwJzt6nngqPfjS8971c/dPDOOkkeNrTjuWKK4Y/56wNomneKfV3q8BIMFLb+tlYQH1i/XQd\nEOqTUUsBcSiCiEcxAwNYDaBECI1R1EIRAXZQLsoAngZHIRXOWHxh0ELQHg2A1vOAmnot+KF5QAN4\nzu41x8zecw2AgobYk3SWqcrgK4OrDEVlKHo2rJhUWKwtmjlAwzygqQW0S23onASfXe3aH1jXh7jU\nNuMsre392mrbdcy4+2tbPce1i9epp0EaAfiduedFjklXWRpSFwVLq9nKWT9hBQBURI4HziY4L7xd\nVV/b0eYc4AnAduAUVb1mudfdGelnPsuXi0fx+y9YvzHemZluq8ns7DpOPLqKOvfcS4fgE6DfP5PN\nm1/OE5+4+1h8U9WW7HQJ0NNOO57rrz+aI48MkfQnnbTISY44IkQ4ffvbcMghq9/pXU2XXhqWB1sL\nHXAA/Mu/wBvfyPyvHcW5eg5veNfJPOUpR3PRReFzzpMWbDBNC6CGaAVlAFJSW/SSoXjvB5bPJhK+\nNQdovw/OJ9/XksBnF1wMgk9kaO7LCKGUQIHvBQC1UlGZgtJafGnwPYE4ET01gBpHYVqT0M8sNPA5\nu09YB34AoOH+1OvAAloJzgXrp+sLVWkoSostLaaoMEXRrAdfW0EH9zUNiBqGl7Gs9/tW27qPTMjp\n2F7smAnQONLncffQBdTtiPg2jC5FkyB0AmAuyXo6DkTTfe1zrBx8wjIBVEQs8CbgGOBm4F9F5F9U\n9etJmxOAX1DV+4vIkcDfA0ct57o7q1vedSlX7vN4XrKO3NNlHTvssJfxghccv36dWkXNz3f/ie2O\nFt9UJ554dKdLxVFHhdHcK64IKy2NXebTWjjhhLAq0h//8ep2dlfTjTfCT34SnG7XSiK8UU7nY73H\n8NG9nsGmj38Kjj2n+ZxFRoPOstZR6Zxo49QQV5374bxd9hpTq25oiH7gS9lYGMPFWhcftqzpWJix\neAHfNyFVBhfzkMKa7FoJ3hnUmTB87sK2d4KP67Z7X6fEuKtpz2ofVQ1gaRSxdfKYwmNLjy0ctnTY\nXkz9imLGhpmrNK4bTzx5PcSvyTNpyh5NLX8pQy1rqDcdVm/n9f4pUqfVcgxgjkwP1QGj2j4m7e9S\nwK6+n5XQtFC58vAJy7eA/v/svXu4LUdZ5/99q3rtfU4SrkMMhEQOIDEZFQlXuR+5Bk4QmRHlKiiP\njwjE/MCfoFzk4MA8OAoCAWKGW7gahBEvBCb7JHDkFmKCjKCADGEiBOQy8PAzJJy9V1e9vz/eql5v\n16ru1Wvf1t771Jen6Orq6u7qXjtnfdb7Vr3vvQF8hZmvAwAiugTAYwHo3Ha/AODtAMDMVxHRLYno\nFGb+9gbvPbfsR47gx8//rYWGOcpZx84775w9Nf9T63iz+M5SzAL5tKfJ+pn3vlfWvGR16JCkxSoA\n2tbKCvDwh2/b3A3nJETa5ZcDl159Nvbf5jPAeefh8O1vD9zlLsBJJ23LOIrm0NqQf19YVrHHUvsQ\nUD5saxY4dazgkzOhI8MXCmvQ6bKmDf2yb9cZADOBvRSZo2ngags3tqjHMVe7ha0qmGoEYx1stRSy\nFsnCoQiG3lGzgn3t2BLGayOMxxXquoKrLbw3cj+IkZYsw1QMM/KwSw5V7TCqazhvJRs9GXgHsaaG\neJLMCjLjPgcYTfcx2Yfe73gf00ohM33vnLQNhMxO13lynHMAqupMmKyQz1lI9bjScXe4xte1n6rL\n+pvrt/naKIDeHsDX1f71AO4zoM9pALYVQL995VdBN/0Qj3r+z2znbbPqso7tRR1vFt8huvWtJZXo\nn/wJcK97SYD9Q4cyHR/xCIl4f+ONW7fYZjdqZQX4hV/Yllv98IfAk54kCao++cmY5eskWRn/6U/j\n8Gc+AwB42baMpmiwxgMAlAOA1g4YexUHNEBoUxIInQoQDrRD1UDVN/LFrUyCjaE1WjZljqarjQDo\nmsV4VMGuVrABPqXUk7SZZjIVQAB0Gas/WmqyIdVrFdzYwjkD7w18s5hG2MlYHwDUwzqHytdYghHr\nLUXLqoBj3CLZl624/JG0x31q4LMLNvsgNK3nACw+VwKDOdjsbUtBVcFmbyamTLD6BmT1vTR8zgOa\nKWynUw+6tP0QulEAHWoHTke+Wfbjwfr7VxzBKXd5OO59iwWaP49DHW8W36EyRsJO3e9+wBOfKGEn\nX/7yJBLALW8phHrFFdsGXDtedS1ppy64YMtv9c1vylqws8+W3ABT0yVOOQX40pe2fBxF69DagAgF\njACfygI69m1LaCyNO15bQRWEAmhbr3IwtB4raEBGDhbQsEI9wmc9DguExhZ2tcI4wCeZEciEcEkK\n6CaL+kmsnzH95uoI47UKdW3hXLSAGjBRCFfJoIrFBb/sUHEdLJ/heCXTYtkzvA9g6cP9XNrGoV8A\nVsdgCm1hjKAA+VOaF5I6PgcNlilkNjA5pJ+CygielOynIJrtl7N+9llB+0B0lvWzz+q50R9N82mj\nAPoNADoP3ukQC2dfn9NC25QOHz7c1A8ePIiDOpbRBjQeA+aKFZz6B7+4Kdcrmk/Hk8V3Xj3gAeKS\nf+pTJeLPJZdIes9G554r80ALgIquuUbipG5xGIvPfQ54zGOAZz5TwoSl03aOHj2Ko9ddh8NbOoqi\ndWuoBTQCqLZ+6hKtn44T93sCny1W6oPPzsFkLqQglGliAY1WUAWhdq2CsTXsqIKxI1mhHmJ1CsT6\nAKKTqarjYyNxva/Kth5XqMcVfABQOWMCoI0L3jtUbMCo5T+MsHbK1wFAnYJOB3jHSbtsKdZJINQT\nQAiWUNLP3+c+Xk+9w5pJaVtHPXdO42KnBDy7rKDK2klpXY91PbA5jxt+yLsd0r4+bRRArwFwFyI6\nAOCbAH4FwBOTPn8D4DkALiGinwPwg675nxpAN1N//ZcOj6g/ips//fVbcv2ioo3o5JOBD31IIi7d\n857A29+uIgydey7wqlfJF95uztG6Wbrssi0Pv/Q//6dk8rrgAolPm9PBgwdx8MABHP7XfwVQXPA7\nTkPngEbwbOaAahc8q0VImXmgjWkSyFs95/3vVUOoqkcXPKv5n47gnLjf3TjE6LQVxpVr5nyCliRM\nEk8W+3gWSyUAAc+xuN7HawKfrhYXvAtzQOOjSJhSiUfq2YPJifXTAqgYZsSTAAE1T8KlugChTRuD\nasAbCchPNQemD8uwWN6tYFRuAZF+v+l82yHbjCUzB5dT24y7PIVTNu26BksdI5TinNAOCG1KCphD\nQXQWlObe5TxwunnaEIAyc01EzwFwGeRP8S3M/EUi+s1w/CJm/hARPZqIvgLgRgC/tuFRz6mP/Ldr\n8LBTT9tyq0lR0XplDPCiF0nc+Sc/Gfj1X5cMUvaMM4ATTgD+1/8SX/DxrpUVeTFbpAsvBP7wD4G/\n+iuZHlG0SzXEBQ+0c8C7BEJTC6i2gqZzQKG2vW7g9UkslxFA42p4C1cZ1OMqZCcK4ZFIr5Lywe0e\nLKghuDwYqOsK9djC1WERU23hxlXbBa8toByC4ZObZJ4cM8wSw459E5u/gdAaTXG1AlQjIOpqKPbh\nZp4rG4RoAkAexrqgVPfX9dx+CpKJBXQmkKrzUosmm+l7ZRcfJYHrs+MH5gfMLkCd9QNp+yF0w3FA\nmfnDAD6ctF2U7D9no/dZr77wBeDAl1dws2c8fFFDKCoarIMHxSX/pCfJQu/3vAe47bnnSlak4x1A\nf/AD8Y0/4AGbfmnvZU7uBz8IfOITwJ3vPOCkAwcmLvhcdomixWmoC95F+ExXwKeLkJQVlJM5oEDi\nNo31IV/6vQNsSlz3FF3wzhlYpyDUhPSdpkoAdOJ2ZxYrpHMyBudssHgGq2esh1XwnkmsnATAMgw4\npPskSWFeA2bEcLWHdRauJvixgKUfBxitATeGWD3HYZ/kXP2YzCx5ALyU/veYvuu0X66kfZI5nl3Q\nmQPO3PGWRTO1fiYltY5Ser5+tj74XC+gznqP26c9nwnpwguB37n1EdhzXrjooRQVDdIpp4ihL6Yi\nv/R55+Ls970QeMlLFj20xeqjHxWz5P79m3rZm24CnvIU4PvfBz71KYlSMESHL764qb+sTI/YWRrq\ngnfK+umUFdT5NpSmLvicBRRAN2QO/fuYviiH/4sWUI4u+NrAWJkDSqYCGcmERLKUR1zYHBcCqSDz\ntQGI4b2V1fQ+rHoPJa6Cb1zw0h0EhiUPsoDzsijJew/rDZx38GOCG6MpJm4tSd1IaQyQ6gHjHFcy\niuua99aXsrOrPVc6wiuldVJwmsJmDj4biNQueJquszonrWd/rMwDnEOtobn3ttH99WtPA+gNNwB/\n/a4b8NrxZyXoYlHRLpG14mm+//2Bxz71gfjy//cvGH3z27CnnrLooS1OKyvAIx+5qZf81rdkfddZ\nZ8kCsJDqvWi3azxwFbxPrJ+58EudC5F0iQCRuo67gHSI4uRPJBbQSRgmYy3M2IaMRFWTdYmBZqyy\naEmtnh8bWXzNJFZODtbOaPXkyVYyOUFc8MYDDMk7zyxzQdmE6xgBzzVI9qQ1wKwBpiI4G8DS0ITZ\nwjtprLM+rPAnaPpEd9ak+H5SsOqBztQN3gJIg2kQ7QBQbQnNWUCzq9pngOeUxTSeNwQs57WM6jGl\n77Rrf2u0pwH03e8GfuusozD77y3z6IqKdpke/nDg0/+whE//7MNw9SM+jKd95On4sR9b9KgWIGZZ\ngPTsZ2/aJf/pn2SN16//uhiXixFzD2mQBRTK8uknMJqGXsqGX+IEPqOGAOc6/tBac0CD9dMYOGMg\nCQkjFVchrmZMXR/Sao4JdW0wGhvUSwZkGBJxM6x0B8AU6xQebeKCpwA8Fh5MBDNZNhSuIeDp1gJ8\nVgRXQfZtgE8DUHTpx3v6yep+iv2mIDTWI4T2WfVy8JkGhs+AZg48KYHMFEJTAE1d7q0V7QmENgCM\ndlvn389mWEPTd9b1DnPamn8c9yyAMgNvfCNw6Z1WgPtu7arZoqKt1KmnAqe88lzc5o8/iHvc4+l4\nz3uABz5w0aPaZl17LXDsGPBTP7UplztyRBZ7vfrV4n4v2mMaOge0ie+ZQKiO+5lmQopzQHUey845\noHofPfvpaiZuHWtZQJULXuZ9xomTYc5nE+tTud1Hwfq5ZmCXrFgzDfUbCk0YZ8NiDBBn+kqfeg1w\nI4KpCMYCtSWQnYAnBWCLMU0RrJ7sCMYSfLCSIvZtZDD9fnJAlEKchs8OAE0toENLek78IdIquTGp\ntuziI73PyTZ99i7g7Duu74Wkva++NdqzAPqJTwBra8BpXzoC/MF7Fj2coqINyZ77KPz07/w/eNM7\n1vD4xy/huc8Ffvd3ty0b5eK1siLhlzbBTPnmNwMvfjHw/veXmTl7Vo0FVINcBvoaSnMd+d9zEBou\nq93wIHWrLhDts2511YMLHioNZ3TBGwOqDUBWWWS5gc/KqZSdYyn1yMCuWZiQ4x2Gg+VRtnpfjHQh\nXJJhWfWuj1tu0nSSAewaoV6VOZ8CnqEkYY/YU7Oq3zhVWv2Bifs9vrvoik/fUYRK/Y5z1k/bGsfU\nnNDe0gOo2c8495kPONb6ITMUPocCKdZR31rtWQB94xuB5z/ha6A3fA+4290WPZyioo3plFOAM8/E\nOSd+HFdf/VA84QnAxz4GvOMdwH/4D4se3DZoZQX45V/e0CW8l1BX73+/vLszztiksRXtPA0Nw+RT\n2Gx8120zYi4WaGsOKDAbNNcnDv8XDbbkCN4YgSIIfDIzfIBP5wg2LDayY4O6MrCVgR0Z2KqCrWqY\nysNUspDIWAbpfQ77RkCGiJtMSKbiJig9VT6cK/t2FbCVgakEQI0RyyYZBXkKpNkb+Jpg6gCsVuAz\nWkHlyS0mtG+St9IFVxnAhEUbRrsg0kwfyxWjoDSCI6utp44xIWP5VMcpHo/PuB747ALS9D2l9Zy2\nFkb3JIB+61sSTPot9zsCPOxhx5GZqGhPK4RjOv1PH4qjR4EXvlBWyV9yCXDf+y56cFuo8Rg4ehR4\n05vWfYkf/Qh42tMkveaVVwK3uc3mDa9oB2qICx4RJhPYZAWcnLreu+Azp42AaPviOg4oO4KjCFMM\nsIWNq909wagFR7YigUJrYSsLUznYqpLtyMOMJLuR8R7WS5xPhocxALEP623E+mls6FuFnPD6/JGH\nGdHE+klGgSQBLMHXmzimnsDOw1UEUxmYcbSYCtRRA4PaAjrrhVOmmEyJ4+qxgGYh1ATwzBSffN5G\nt6ktB8hswWhybs5SP9jV3tWvzxLa1zbP8fm1JwH0zW8GHv944IRPHtnyrClFRdumQ4fkD/vVr8Zo\nRPjjPxYX8i/+IvCCFwDPfS725kKaq66SwJwnn7yu07/zHeCxjwXueEfg8suBffs2eXxFO09DwzCx\nAlBd94zJZEoFn43rnZM5oClApF/283zhTwNWcztP8EQhmKaRDEfMYLYwYbW7sQE+rYGzRoLUWwdT\nWdhYHzlUSx5mycE6j8o7+BBk3hoSdzsDBCcsZqKl08MuedglB7sctqOwraIbPbqrJ27waPFsADRM\nDbBjgrcsoZqMLI6ixrKo31NK/F1WvYw1swWfNrF4JhZQDZsphJqOOsI+o235bPi5Bz4bhlTnNQyZ\nA0cAg0CzC1ZzELoeGN0c7TkArWvgoouAv/1rDzzicuCP/3jRQyoq2hzd7W5iyvvyl4Gf/EkAkq/8\nqqskZeTHPga87W3Apz71MbzudStYXa2wvFzjt3/7ETh0aBdPdtxA+s0vflEMx09+MvCyl+1RQC+a\n1tAwTBE80633mvpUPcIoOlioz8qU++PLzPlMjwfXrvfacset4Ymr2wWQcxIf1IQwTcbBWB+Oexjj\nYJccqmUHWztUzsFzjQoxvWYN8uKKn2RCwgQ+l+Xcal8t1wj7dkQgGy2fRkCyAVATYn2akMkpzE2t\nDEzl5TzLYQ4oBwDU7y2W9H2l77fPAhrd8Cl8Dljt3gCnsoK2LLwQ+IxTVCOIauBswSfQWiXfgk79\nfH1WzvUcS++BpG17YXTPAegHPwj8+I8Dd+PPisXk9NMXPaSios0RUeOGjwAKAAcOAB//uGTyOfPM\nj2Fp6TJcf/0rmuPXXvsiANi9ELqyArzylXOf9tGPAk94AvBHfwQ8/embP6yixYkk9tA1AK5n5sdM\ndRgahknDJVLQTCA0WkwZaqtK1gK63i/vNoyGVO5iQQSBYWA8wJ7hDWCcuLCN8SBjQGEr+xInVOqy\ntUs1Rq5G5Wt4GLAJQGUB4xjey5xSS+KGb+aABmtnteww2lej2udQ7a8x2lfL3E8TwVMKMwEs0Clz\nPg1smJvqx2JRNdbIXNLG+qnfWpf1c6gbPueCz2RB6nK5d4Go3oLCFFVSMwbCE2graIsJSbGhHeFg\n0gAAIABJREFUAtQpCG1OyGz7js2ygK4XRjdXe25y5BvfCDzrWZismi0q2ks691zg0kunmpeWgNe8\nBrjd7VZa8AkA1177ClxwwZHtGuHm6vvfFzPmnInZ3/52gc8///MCn3tU5wP4ArpIZOwGlHpSrx0w\nVmk4mzzwXeGYMA2eU/DQBaRDLKGTOkdrZ0jDKe5rmqTPHFvUY4t6rcJ4NZRjFcY/WsLaj5awdtMS\nVm9awrGblnDsxmX86IfLOHbjMo7dtIy1Y0sYHxvJOWshH3yTCz5E/wyr4E0A0GrJo1quUe13GJ0w\nxtIJYyydtIblE8dYOlH2RyeMMdo/DpBaY7Rco1qqUS3XsKMadqmGGdWwlYOpwrQA40DGgcgB5DCJ\nbToV9T/z/tL3miw4mrKCmvhgydZKH2qi508XE03CsV+sx2PRSqrP01DbAcDZqRtd21lAmbtO7p11\nnbM92lMW0C9/GfjHfwR+6ZcAPOoI8LznLXpIRUWbq4c8RBLF/+AHwC1vOXX4lrfM/yd9zTUWz32u\nOAR0ue1tJevSjtUVV8hE1+Xl3m6XXirTDo4dq3D99TV++MNH4OjRB+Gss7ZpnEXbJiI6DcCjAbwC\nQP4f+aGr4CPQcIAa5qRtVr0ZlR4hNudLnac3XgK/ExnAc+AaASwiyWVJISYoheTqRBz2PUCyreoK\nHmsSfJ7E8kkVYMYM5yS9Zgw0D4qcxZP5nvvEAjraXzfQaWwALDZgb8Ocz2D5HFtxudcGdkksoHZk\nm1X1Uias1n6P0Yyo44FqCM29+z4LqIa+ZCFSlws+XYCUWkDjcOIwPSYPkjNQNnVqH5v6/FMLZtex\nIZbQ3PtarPYUgF54IfCMZwDL9Y3A1VcDBw8uekhFRZurE0+UKPQdYYmWl/NfvKed5nDaacDXvgZ8\n8pPA178u5fvfB253u2kwPf10mcpy+ukS5mnI3MkIgZs693SAJ+PSSz+G88+/DNdeO7H8HjjwInz1\nq8BZZ+3SaQdFffpTAL8L4OadPYa64Fswk8JNxzFOz9fq+6If8sXPmS0FV3Y0shpQM54IGRwsa21L\nYdOP2u3VuEaT6cgQqAJoxDBLHra28N7Bh1ScCLE+m9XvYc5nhM/lE9ewdNIaTGVAjevdSppOb8HO\nwNU+pA+1cGsGbs0Gi6qFjaGgDASWGwiNpJbCZ9+774PPYN3sAs6mnrjes4uPApCa8Jn6eEtSddWu\nf49MQWjmUTr/NoZCZ9fFh1pOh1hWN649A6A33gi8853AZz4DWY1x97sDJ5206GEVFW2+4jzQDID+\n9m8/Atde+6IWjN35zi/EK15xDg4dmr7U6irwjW9MgPTrXwe+8AUJYxb3jx0DTjutDaVp+fjHpyFw\n1txT72VN1U03dWxvZDz0A5fhsjv+Dr71xkl72ndlZQXf+U572sF1170CF1zwkt0777UoKyI6F8B3\nmPmzRHSwsyO/Q530swB1xYJWANeqI9mqOiXthOQaFuBcIPTkss05kVKcbFnDM2PK8sfimJ8aF6fj\n5YRrJmPwTlJ0SrimEIe/pqa4muDHkGPjkGYzljWCWwLqMWDXgHqJYNdI+tWAryWUKjs0EQSIQ9JP\nkhBP1gK2AqoKcCNGNWL4JcAvM7hmoDaAC+MPEQZYrRTnJuqAB3MAVFbPrK3G+vyhweZT1/hUPfNe\n+0ByMGTOow7YpI72Lphc17j6QPRoKLO1ZwD0z/8cuP/9gTvcAcBrj0gS7aKivahDh4CXvlS+NRL/\neQSuCy54CY4ds9i3z+G8887pBLHlZeBOd5LSpR/+ELj+eoHRr31Ntp/+NPC+903aVldX4Nz03NOn\nPvUluMtdHpSFzPEY2L9fygknTG/v4v4F9/sR8Df/8pM44cRJ35NOkvWFse8//EOF73xnetzHju3k\nuQVF69T9APwCET0awD4ANyeidzDzr7Z6Vc8YeLkOi2cKmU09bDuPR+i0AKtV1zpMU+PC95lj8d4h\nBFQDpz1jWc82hm/yIX6oA7xjAc4AnQKYhHqNYFchKTZHk1BLxkwsnmCDepUwvslg/COD+lgA1bEA\nKYf5s8QyNcAYhrUetgJGIwDLHObcGhg2MDCw5CWvPfNkERYHuy4bgAU+pYTn4Thnlif9QyEOue5z\nsTzDVINeg1+OuTTXpSDXZ6zt6tcrCn8bQ0hXbUkPkqIZXZ0yw8o5N6AeDCXqZZ099wSAMgNveINa\nKLuyArz1rQsdU1HRlukOdxC/+d//fTYC/aFDD9pUy99JJwFnniklJ2bgAQ+o8KlPTR87/XSL170u\nD5nLyxljgtbrVoA7PwIXv7nf7fPud9f4whem2/ftG+qGLdotYuYXAnghABDRgwH8v1PwCciikOFX\nRduSGbYtyOxrU9cABeunmWxh0Kx0bk5TREU+muomhU1oD1bR1lg3oz4BN/YM71gslzWLJTPkda+r\nmNtdp9acLK5hmMbV7taA8Y8MxsdIAHQV8GsUABQCoHIGDHlUFuCKgREDywTyDPIeFgbWECprVHQs\nCqFYYyrPEFOUjTyHl+fxPkCoRwOu3gvks09c7rmSuuZT6+dU6XnFqYb2mxKpv7vMsZbVs+8YtYG5\n6aO2nDnW9ee3CdoTAHrVVcANNwSj5ze/KeUe91j0sIqKtk6HDokbfgekQCICTjopP/f0drdzuM99\n1nnhlRVJXzRDXdMOzjvvnHXeuGgXKf+VOC+Aavhs5kt2HYv7GWiVmwtAsoLPaOVsQLQPPgM0cMZ9\nP5MAhh7XFlAGuzyE1hVgRgjxRQkmxPkkCiAKC7ADs4FfA+pVsX7Wq2IB9WOAI4AyggXUwxiCNYCv\nCDxiwBOM9yAWy6cAKKkEVdREAZCtkZX63sF7C89eQNpzyCXATWIrQ+H8+P5z4ZSmSnhNfb99GZNf\n0EOYf73KjiEHpTkLqYJQPV59YX0ZfZyTfupym6U9AaBveAPwW78VMm4eOQI89KE7fGlvUdEGde65\nEm/sFa+Y3XcbtOkQuLo6SXY/Q/NOOyjaG2LmvwPwd9mDZuhXWw98UrLtg1Hdzho6Vb1hzNBfxxed\nRDCfnNO487X6vQHdap+nrZ8NrDlxl7uxzM90Y4JZI7iKUJuJBbQJWaSsn+z9xHK6SnCr4rp3Y4If\nk8znDI9qAFgDsPWoKgItAYYJjgkGHpUhOEuoRyHklFfbJpWnabbO+QCeDHIM8gwfozg5iQkvTDlr\nHqh6TdoiGt3zOXW54DcLSKfumwHPlvUzZxHVbeo6rM9P2vQzb7LVU2vXA+h3vyuGoNe+NjQcKfM/\ni44D/dzPyeqhr31NVgYtWJsOgZ/6FHDWWcCtbz34/gU4ixoNtYBGcMyBZR+A9p3XAKcGzxRCIfDZ\ntLOCzrgYqUVE6aA79vuO6f1gAWWxfLJjsXzWgB0DdUWgNWFNCa8khYjUHEwFgs6AA7z6McGvCcD6\nNSgXPMJCJMAYRmVl9b1hwIBgCbCW4CvAj4IF1ctU92bBlBMAdc7AOwvnPIzz8M4LiDqGcxLUfrKm\nK+SWZwDeBK7PwafaT61+SNq01gue6wG71kedQCZ1AWfqd++xgsZnTUGUVd9NtILuegB961uBxz0u\nfE95L8me/8t/WfSwioq2VtYCj3oU8KEPAc985qJHA2CTIbAkkijaiNYLoA3vzYDRPhBtgDNsfdrG\nk4w5UOdlLVBJ24a3cYxhoY6fzAFlhwZCzRhwFjCGUNsJfFKY9xnB2XsDdgbsbIBYcbn7GvBjWVnP\neg4oAya8LwoA6gFYEjb0FuAqnL8kwOmc5LaXwPsGzjkJ5+QcTG1hnIerPcgxXM1CtAQwcRu9ItCn\nsBn3tbVT92mJpnmu+cyTj7NLQ2G087dEAptd9ebvMn7u6oLp9IF0KkFq/dxE6NTa1QDqnMT+fP/7\nQ8PnPw/c7GbAHe+40HEVFW2LDh0C3vWuHQOgm6qVFeXWKCqaU0Nd8NRl1Zz3GCZf/jpxj+fJl3cr\nexJPjkc1jMDJl70GyM2q60VIaFbB+3rihidLKnEPIc5HZRZa5Jhi00mKTTA3sMkBaHWRkExyKXHB\nh3zzBJm1EOCzObcGXE2oHcGNDeoGQh3qWiC0rj1M7SWQfe0FPmsGiBve9wCIw/QBTgFU1xX0z7Iq\nD4XMDUGboj5t7ew1ZvYBaRwTTXZ7QTRj/dxk7WoA/fCHgVNOAe55z9BQ3O9Fx5Me+UjgN35DYhqd\ncMKiR7N5+u53gWuvxfpXLxUd9xpsAe2BylY9Y/nMHQcEggJsgRRoEiZpPE2EzGgNVfduztP0QknJ\ntQ05FokiuOCbOaAyb9K7AJ9NBkmxfAp0yVbmfQb3e23gaws3lgz1EjmKZeKlSlvKET6DCx5Gno3B\ngA3vwAe3eYBiOKCuDeoAn9XYoK4t6trBjAVCaexC3nsvbvfwGTJCHPhgEPWexO3ewFcOQHN1TOp9\nGgKcm+GGz1lBp+A0hVB9oxkg2mfx3AIr6LoBlIhuDeC9AO4A4DoAv8zMP8j0uw7Av0P+tMbMfO/1\n3jNVk/c9amUlaSgq2sO61a0k2sNHPiKLkvaKLr9cspiNRoseSdFu1TyLUCNA9oGoBtBsX9WnoR6e\ngCT5ibWTeAJnlPSFPkdDaAqRJtM2q0zOaYVgivBZixvcqfTl+t7MobgYsF4A1I0lsxGRxPmcBJ6P\nj8Ph1UwC0oNC+k2Dpn9zvLkGMB4T6jGhHhuMxxZ2XMOODUxlYcYexnqQ9aCxWD+ZfHC9c8P9ngnk\nEaA4A5roaGu9d8wPoX1QOg/INUPpAc0m7WcGPFvPk14UbfhsgFRZP7cAPKM2YgH9PQBHmPm/EdEL\nwv7vZfoxgIPM/P0N3GtK114r2Tb/x/8IDceOAVdeKdGxi4qOF8WsSHsJQC+7rMz/LNqY5nHBA22w\nzMFnCpydUBrh0oc2HyycNOnrNZkkfSOsEmOyQr65CabBc559fR1u5oHqMEzOMagWCG1dJ8bfDHM+\n48IjX0tedzc2MMQgeFnfE+9MAqKxTSygIRg9Qkim2IZJXZKAMqqxwXjNYLxmYccW47GFWXMg62Cs\nA1kPmMn7i+gpvwFYDnmAHKnUmYmFc+a+/nvR7xHDwWyIhXSoWkPQEDpjH8iDpYZP1jeIbRl43SQo\n3QiA/gKAB4f62yG5l3IACkx/jBvWn/0Z8Gu/JgGtAQCf+ARw17sCt7jFZt+qqGjn6txzZdpJjB24\n28UsnowXv3jRIynazVqXC17tTwFp37G07gO8eNWX8/DJkZBUaTIg6UmjOrVn39YnbfpcTNo1fIZF\nSOQg8BnhS4+UVQxOR7C1QVUb+LGBXbOwSwxjBD6NkbolltihxBJXP1h7DWLfuPVyDnnYVjujWjOw\nIwM7qjBeq2HWLIy1YvVs4DMWhkcoLBAaD8ECVEcLp7JoautiCp9Q+zmEaVkMZ2w3qtQKOhNCMenX\n+b2Qa++A0RRaN0kbAdBTmPnbof5tAKd09GMAlxORA3ARM79pA/cEIKn8Lr5Y0gE2Wlkp8z+Ljj/9\n5E8CS0vA5z4H/OzPLno0G9c//7P8qvyJn1j0SIp2s+ZZBT8Fnpl9zDjesoCG2EHNHMIIhTEzl3Kx\nmwiaLsCoU9QUg1lGiMzllzeZfU0KGkLjAwMx1SezWD/ZyAr41sJvRrB6itudQygkOzbwI4YbBzis\nGGZkJL+7haTYNAS2BGtZ4M8wYIOl03gBVOOlbyyGYa2DtZKm0xiPajUA7uoYdmRhKgdTiQWUjBSQ\nF9c7fABPgU/nAeMmWZymLKBABkbTrX5nHSDXBZubYu3MEV8PhE61AS0L6ORgtxUUmbZFuOCJ6AiA\n22YOvUjvMDMTdeaKuj8z/xsRnQzgCBF9iZk/nut4+PDhpn7w4EEcPHgwe8G/+AvgXvcC7nxn1Xjk\niESkLyo6nkQ0ccPvBQDdJeGXjh49iqNHjy56GEVdmncV/FAQ7esT5jOCAmi2vvwTDwUzmnzvjQXP\nhXNDoRyA5sBTl3Ddpq7hMw5KxjOxgAI+LABqFkEzgtt9so2WT195uDHBjgxcZWAqhq0sbAVUFcAV\ngIqBikCVzL80I7k1RQsoMaxlVJVHVXnYyqOqXKtuLQt0rtYwtoKpapCtQNZNQN14yP8EPC0zLAPO\nM4xjmNjVUjv2Z/MqEgtnCp8aUKfeIYbN75xlHR0KdylcphCq54HmQFSPJ4XrFDT1giTddcodvzER\n8/rQloi+BJnb+S0iuh2AjzJzR7bo5pyXAvghM78qc4yHjuXe9wZe+lKJQgMA+Pa3xRL0f/+v/BdQ\nVHQ86cgR4A/+QOZA73adcw7wm78pwX13kYgIzJv8r3PRukREjDt8d2BnBEtkrKu2PvA0Hf3AgKvD\ncvKYWiipe9fuk+sf+zgXQKALOGcVm20n4xtrorEOtnIwtm61TbZ1pi3WJ8eqkcNo5GW7JDA5GjlU\nIy/7sT5yk/ZRrl32q5HH2rF9WF1dxtqx/Vhd3Ye1Y8tYW92H1WNSYj1ti+etHtuPtdVl2T+2D+Px\nEtAFm111DZ9d9fg7Id3m2ob0jUCYWt+B5O9N/Q0ibQfarnl17ehq57QdaCVM6DoGTANqp7r/bdwI\nrf0NgKcB+KOw/aup2xKdAMAy8w1EdCKARwB42Qbuiauvligt5+gMf1dcIatmC3wWHY960IOAL3xB\n/sM4+eRFj2b9OnYM+OQngUsuWfRIina7hrjgpwATHTA665hqj7DgYt1iQhaKAmRiZWPFAyvrJ9UA\ndAG6gTK3z+gmCEzaYiB6kjmgTU9Gk4PdWHFjUy2ubGMJZI3M2awYZKz0sYBfAngZ4KWQEnOZYUAS\n/Si64pnDnE8PG6F1aVKWlvW+FwvoyMLYGmRrkKkA48A0KZ49PHs49nCeG+undWIIp5qUBdS0rYGp\ndTDd77J8Jq+ytR16bKjS1e9TQ+qwfLasoplxaSiN92nq6TFsuvUT2BiAvhLAXxDRMxDCMAEAEZ0K\n4E3MfAjivv9LiSOGCsC7mXllIwO+8EKJu92KsrFL3HZFRVui5WXgoQ+VwLi/+quLHs369fGPy0LC\nW95y0SMp2u0a4oLvtGqqY72LzDPHWyYsDZ6KHBrKC6TH2gWvwXMctowJaEb3ut63aMNn3OYeOGri\ngo+LdxAeqRmSI3gzmUMZwZOsLC5qtRkGL8t8UjgPwyQjIkiQ+QohE5KsbhcXvLjfo4V0adlheV+N\npX0BRJcdjK0CeNZALOTQLDdiD+89HAt41jXDOimmRgPHwucBQqdeSQpWKZR2tHVB5RAg7TsvJ0qI\nMIXQFogiD6OcnMeU/klMg2c8X8MnoX+sc2jdABrCKj0s0/5NAIdC/asA7rbu0SX63veAD3wA+PKX\nWzcUF+SLXtR5XlHRnlecB7qbAXRlRYLrFxVtVPNaQE0PiJo5+sFPLKENLMbUlUArHWc0M+r5nxFC\naRxKPZkv2gJQDZ4aOuNz9wEoNfeP6TgBwDM3AejZo4kF6iNs6kIGZGJ/2bJjwHsYb2DhYYngDEl6\nzZiKM8CniQuQgpt+aclhaZ/D8n6HpX01lvfXWFr2IDsG2Sq8Exfg08HDydxP9qi9x8hLLvjKMeoI\nnxWDbHiOuBCJaPp1TO9Mt+eAVGte6FwPwDWQmVhDp6yeaFs+U6tpOo4UQtP7bRJs5rSrfNYXXww8\n5jGJl/GLX5RVwGXVbNHxrEc/Gnje84C1NfnvYTdqZQW46KJFj6JoL2hoIPoUJnOwaTL9us5pLKAO\nrUVDTG341EHoGxDNud/HmMCmVfVoYdWLjfQzp9SgSSTYOxV8MocV8F6supIBCQBROyMSEciYcCyu\nmg8B5Z2B8QYGsgq+sgKffhQBVO5JCCvgDcvCo5FYO5eWayztr7Fvf43lE2os73Oy6MjUYNQA1eJ2\nh4PnULxH7TycF/i0NcPWgB0zTBVc8CGlaNYCOvWOhmgAfG4ViGq41BfIgSZl2lPgTMegLam5P6H1\njLlHuwZAvRf3+7velRyI4Zf2QgzEoqL16ra3Bc44Q+LhPuQhix7N/Pq3fwO+/nWVV7eoaAMaFIaJ\n0HKjz9oO6QMVeDKGV4oWUEBxY5yDGcDThAVIAbRAYwBrEACNFtBcSed85mBUPW8sIfMQQ9zmRDIX\nFFBfpRFCEcATBFCAT7Cqh5Och2EDA4PKEGpLGFmARwCcPK/MAWWYEHKpqoL7fclheZ/Dvv019p1Y\nY98JY+w7QQAUpgLTCDA1mARGXQBQ58UCWntG5RhVHSB0BJix/BmQRXsV/BA1kDWj/yyoXC90zhqm\ntnSmfVPwDD8WWmDZZxHtut8WWEJ3DYCurAA3v3kmPfSRIxKRvqjoeNe55wKXXro7AfTyy2XcZSFh\n0WZoaBimofCZ2+baIhhyWFDEAT5tsIBGXowhm4y2fioXfGP9XMMEKCu04TOFzlQphej5qGL1nIBo\nhyhLM/FhWxxj2MKSF/isCK4C3Ijg67YLXtzwPswBlZXzo2VxvUf3+74Ta+w/sZb4TQE6teWz9j7A\np0NdM+rao6497BrDjmSBlKkAqgRAYVQsUHS8Lt3e5ZbO9eWknjtv3S73Ofr2lg6r7dD7bZEbftf8\na//GNwLPfnbyHldXZeHCO9+5sHEVFe0YHToEPOlJwKumopztfJX0m0WbKT/HNyYN2DbQSG2vNyVb\nIITxJCmeJMF6sw2F49a2C+K2CheK1k+bKWl4pan5AMhTRd+ExYRceAKbuX6sgLSVWz5wtXfURJqK\nOd3rkN9dUmwa2FUbAtpb2JGFrWqYyoJsjWPHliUM09oy1sZLWKuXMK6XMHYj1H6EmkeoYVGThSML\nb42UkQGPCLxEQE3BGB0svblX0NpSHh77trHkfhfk1qXN6hNfceYjWXd7HGvu/ulYurTJILorAPS6\n6zqis1x5JXDmmcCtb72IYRUV7SydfTZwww2ySu+MMxY9muHyXjwZL3/5okdStFfk+75FlfQ0SkN5\nqIwWJIa4MmNbsx6ItFFwAp+OJKl63Hoz2Xo7KVzJPFBlkWy2rUFq8ExBtAtKgTaF9BFE64HV+ekk\nQd0vLojiZGE/BfgkuJpQ1wZ1bTEeG1QhfaepatiRgKYJcz3jgiOmETw7HDu2D8d+tA8/OrYfx1b3\nYXVtGavjZazVS1jzSxj7EcYYocYItalQGwtXWfjKwC8ZyeDk1WNULN7o1uulZJ+b/QZWm6IsqBsp\nsyAwvur04+sCzSH94n0Npseg60jaodqG/BnNoV0BoBddJIt7TzghOVDCLxUVTWSMWEEvvXR3Aejn\nPiehlw4cWPRIivaKhgKoXi3MHOYJog2mRGHOZuxHba+2YekTb9kkM1JW0AiiLStosHZ6D/gIoWE7\nRSRp3M+urbaG5kxgQLflUxNG3OqV99qNrwk9hVBS1k+Cqw1cbYL102C8Fi2dFnZVQNTYGrABQMNc\nTw+H1WP7BDxXxRK6uhbg04kVdBytoMEC6qxtLKA+pA8VAJX3SBU3YMWtiATpK5djGla51Ze6oW29\nBUldfwy57RDLfWrF18HvKanHY1Dt8aPV19Uf/Qa14wF0dRV461vF0z6lI0eAP/mTbR9TUdGO1bnn\nAq97HfDc5y56JMNVfkgWbbaGuuCjRbMBzwCTGj611ZNIrm3iMbQhFGjDZ2P91PAZodMHC6hX8MlJ\nAdohl9Kg811u+NQV36Uc7QBt8sjNOdAEEyBUw6cHvDcNhNa1pPHUEGqqUIL1E6YGGdcsNPJwWA3w\nKdbPfVgbL2NtvNy44cc8Qo1KClVwxsJVBt4FF7yX52ICiBiwE9ikxAIY04/G1foTYKOmP6v+U1bC\nPqBcT1sKlEPbuo5poKSkrrdxPFDt8RqbZPmM2vEA+v73S4rrKYPO974nrsb73nch4yoq2pF66EOB\npzwF+Pd/l1V7u0ErK8D55y96FEV7SfNYQFPrZ84TrWE0WjsjdOovcCBYPJGB0KRwtIIm7vcpM5iK\nJ9pbCMhaP1MXvKae1stI9jV4poWm2sRASFI8wXkjFlAnFlA3dhiPbXC/Oxhrm0DzCBmOxPrpICvd\nPdbGYvVslWABbVzwLADqTLSABhc8GxmL+hwnFlCSIPwRID2JtTO0sVcWTs8NiDYQ6lk+5xyAbka9\n62NJP6J5jsW1ayl8amt+VCZ/Qmt/k0B0xwPoG94APP/5mQNXXAE88IG7N+ZhUdFW6KSTgPvfX6Du\nl35p0aOZrRtvBK66Cjh4cNEjKdpLcgO+IQkToNTWT93WwKhu5/CFnfTVc+scqa1yw+esoFNWz3Ts\nwcLYAsyu5fhdi5FmvYh4H70f633mOrWv4NN7gndiiXS1Q11bmNrBrDmMKwuyDmQqkA0hqGJqTdQh\nvqeEWFodL2GtDvM+x0tiAa2XJm54DlZQSiygbOBB8CCwpRBEgIGaGxCjJqBAgFG1Tyz7DYh6NNBJ\nwWA9FYwAA7dD+6YfT07zHEsjeKWA2Sf9A2sTtaMB9LOfBa6/XryKUzpypLjtiooSHX7604FrrwWe\n8xzg9a+fHDhwAIcvvnhRw+rWxz4G3OMewM1utuiRFO0lDbGARpd6Cpxp4bSto29w97bAM877TOGT\nlfvdR/DEBD5bEBIHkFo3zYB6jjC64DxnQtPWTszYEsAGzCa4383E+lkbuLFFXTmYcQDQUGImKEbI\n7Q4Xcru7CWzWy2L1rCdl7MMc0OiCDxZQxxaODRgGbKgJLoAKIBdA07UhkkKgfAFObj5D8hz6Bat2\ntHyGVfWNFVS/0hxI9rV1Hd9safh0mP7TyAEmJ/2GAutA7WgAvfBC4Dd/MxMakFksPM973kLGVVS0\nY3XddTj8la9I/dvfbpoPL2Y0s1XmfxZthQa54FOrZheEZqyfU23RiooJoDQAShP41KvgYyaidPX7\nFIxMEfA6y4x30dynrz1nnQ01ppCbnQRAvYF3Fs451LWDqT1o7EDWg4wDGR/mfDoweQFP8iHWp8T5\nXPMjjN1k0dGaG2HsJ/tNKCaq4IIF1FsDDwNvZBESLIEb+OTwmXCATgopRNEAJ+LCpQBlTJReAAAg\nAElEQVSY5CB9bIRQAVY2mETK6n4tm7Ofaj3HU/B0M87XVv0hsLoO7VgA/cEPgPe9D/jSlzIH//f/\nBpyTEExFRUW7VysrwNvfvuhRFO01DVqElIPPUAe6YRQaQjHNeKnrvVVssKIl8Km92gy0Ji4mAeSn\nbzhrP3nmTuUIIwelXTJgdmA2YO+DBdTD1Bb12MPYCJ1eAvA34Ck53RvwdJJec1T7MMdz1Fg7p/Y5\nhmGqZCW8DfFAjQAwV6QsnSyAGS2gIVoBhfm6HOHUcYBOaoCVVH84lvnCMdtq12+dgX+Cg491WU+H\n9tULjSJ85kA0nSYwz++YObVjAfTtbwce9SjglFMyB6PVpKTfLCravbr+erHSnn32okdStNc01yKk\nAJLgaahErCvrJ3SfBFiB1lxCWVWt3e+czAONMAoFDenN06XIeptr6+s784XMuT/RZAESw3sH7w2c\nYxjnYWqPeizwSTYCqAeTB8OL5ZQ9XLB8upDjvWZZZNSsdm/thwVIzSKkStzvZOCNASOMRwEVeVbg\nKbDJDpIB1QVraABSciwQ6niyX1N73VfMcb9Rpa91Xpf+kP7xz6jP8hn7xrIeY/oc2pEAyiyZj97y\nlo4OR44AT3jCto6pqKhok7WyAjzsYYAdkre7qGgODQ7DBDR5snVe7U4IBSYWUCTW0nBPbfFkbf00\nwe0eXfDotn5OWUCB/Df/eto407aRetz3kg2JfYBPD+MYrvYw1oMsC3gaDyYW8ES0gDJchFDHqJ1H\nVbMsLkJSkrYxxbZg/YSFJ1mE1GRqip8bB9d7TA/qAKoDeNbBtV4r6KwDhNaYQGesU/PY/a++r73v\n2JBpt3E7pM8sl3tX2QzA7tCOBNCPfARYXpbFvFMaj4G/+zvgzW/e9nEVFRVtolZWgEc+ctGjKNqL\nGmoB7QLP3nquv7KExtiRGkDZTKydbNHEmmxAFBPw5EA6TRrM3CTDLg3tF/umDzl0m2lr4JPhvWyd\nY5DzoDrAJ7FYPsHwLBDqmOG8R+UZtWNUtcCnHTMcWdSmki1Vzb4EnpeFRzXUcRMsoMEK6oma10pG\n8tBzjQCekHqtIVRDp8z7pBpgq44ZOUbh2lMrxGdx+pB6CpddsNlXT/eHrE1LwVP/CaYzQTZBOxJA\n3/AG4FnP6vCwX3UVcKc7ASefvO3jKira8TpwoL3g6KabJJzELW6xoAF1yDng8stLIomirdG8ueCz\nrEXKxc7ttqnz1JeV/gKP4BnnerbqVvUjtCyfLQtozsTVVZ/neJeltNcM3LnPYMgq+JAT3gUArRlk\neGL5JLF9VmAwGNYLgLrQv3YMW0txxjbxPZt62K+NhUPSbsL8T0uyAj6UJmY/MShAJwfwRM2hHtsD\naMbwTQE+m7ivBu1Xt9EZEl1tXSC53nY971PfI26t6htDz2oLaB9Yr1M7DkCvvx44ehR4xzs6OpTw\nS0VFncqGWnrb24BXvUpgdCqf7YL02c/KBO/TTlv0SIr2oua1gLa2pjk0AU7lxk3nfKZbbf3UJbrg\ntdu9gU/X4X5Pg8Fjjjoy9Z730DnZr+tYWgQomQEfFvyQYzjDAnkUepBYP2OxnmE92vA5ChZQK3E9\nY4B5Zw18JWGWnLXwMAKeMPAkx13sZw04rICHZcAGEB6jAU4eI1hAAR4r4LQEMgAbBgyB9McyTl5b\nGtJooMF45rE+t/h6CiXX1veI8GnUNo0VusnWT2AHAuh//+/Ak58s8bSzWlkBXv7ybR1TUdGu1tOf\nLj/cnvc84M/+bNGjEZXwS0VbqaFhmNIqARJnx0x1mbaO5i817VInsYQyhy2Soq2f2u+pl1n3mbu6\nTGCk6kiukQ46fS9dpSvTUrB8tuATwWoIgBSAgsNsBNkax7AOMHW0fAJmzLAjSFD5KuR2D3XHIdB8\ncLM7DmGXotvdxr4EHkEoJxbDwAigMYFrBlVi8cQYIBssoWMSl7sByJLMiCCeZMrSP0LS19W3P0/f\nWR+vH9An7ZfCJ5K+MburTry1xRC6owB0bQ1405skyVFWP/gB8E//1DE5tKioKCsiAc+zz5bctjsh\nQ9LKCvCCFyx6FEV7VUMyITUgEcAqhVDd1rRH66eCuKzlKgOfSOEzHg8mNCZIWk4TtjYc66OOtC3X\nJ/PcDeXMsnLmMit11TGZXeARYmpOHs004AkYz3AhCZKpBD5NBdgxYCqpmxHgRwQeSU55PzLwniTQ\nPZHApiEwkv3KwI+kPy+R5IQfARgxyGJiAV0DeATQGGIlrQg0ZrANEGog1lCCwGd04ce5n1HaJd/1\nGuc9huSjXM9Hn+6n4NgFrdoaOk9CrXVoRwHoBz4AnHUW8B//Y0eHj3xE4HPfvm0dV1HRrtfNbw5c\ncglw6BBwz3sCBw4sbiw33AB85jPAgx+8uDEU7VoR0S0BvBnAT0G+Kn+dmT/d6jQ4DJOJJ2AaODW8\nKeuXDCK0szoWm8I3dmtOp5k2Yuo+MVglp3ke9US83JaSfaj9cI+mLd3mqKILPgekAg3wGR/BufBo\ncUQsBkgBUIB8ANCwIMhUgLGypbDlJYJflvSe7CWskic1v9MSPMtqdyaSuZ+WJP7niOCXCLwEYAmg\nZQYswOMAnVYBp0XImBRA03DYkrxhAggM1u9Mg14XXK635CAyVx/alv4OycFsCpy53xh72QL6xjcC\n553X0+HIEeDhD9+28RQV7Snd617A858PPOlJEkliNFrMOI4eBe5zn50zH7Vot+m1AD7EzL9ERBWA\nE6d6DF6EpNztUxCqrqEtnvFYF4SmgBkBFGm7b8MqjALRSAWaKnL72pLp1QCQOT4PfGr6SGHTZNsZ\nAELcTe/D63E0YTQGDEsudbKAcQSyAT4tQDbs27BfkUyNDekuBTIxSa/pKVhc5R4crJRx3iePAnwu\nE7AMYB+AigU+1wJ0VgSqFIQaGTebMAeUwsAJyC40mwWgXTMWZh2PH1/fb495t+m49fhT13sXjOo/\nlU0Qccw9O++JRI+HZPg7E8C9mPkfOvqdA+A1kEd8MzP/UUc/PvVUxnXX9Xwv/sRPiJn0Z35mXWMu\nKjru5T3w6EdL/vVXvGIxYzjvPOD00wWG94iICMy8Sf8sF3WJiG4B4LPMfKeePozqXwdeUUEUpVSQ\nbKnvmPq2ZvXNz9xTD/1adWWy4hx8zipuYD9gsjR8cwoZAUiELbW21MyppGSb648ApNgHYB/A+zGp\n7wPQ7HP7WEe/pj4CeI2ANZpsx3o/HB9Tq1+7T9hfJVnE5CgPk10zFYb0TQFyM+o1ZAFV3A6pzzo+\nSN3/Nm7EAvp5AI8DcFHnbYksgNcDeBiAbwC4moj+hpm/mOu/f/+LsbLyCBw69KDpg1/9KnDjjcBP\n//QGhlxUdJzLGEkzdve7Aw99KPCQh2z/GFZWgPe+d/vvW7QXdEcA3yWitwH4WQCfAXA+M9/U6jV4\nEVI0+8QtMOWublk/ecY27RcvkwmnxNrXmlBHA6uaIlxSz/lDOal39dH3zr2XLkuoLm2A5WjJDVEA\nYhB4YgBMApY+AKcL2+DmljoldXlU4miBDG5xyzKf00Es3RyeiSCucwtQxcAIwBIDyyxQul/axPKJ\nxu0eLZ9oxoKpuY8E+Uio+WhYnkW/4r7psn1tuWPA9G+GPkP4kLbcn1Taf5YFNPfntAGtG0CZ+UuA\n/PLv0b0BfIWZrwt9LwHwWABZAL322pfj/PNfBADTEHrkiGRNKek3i4o2plNOAS6+GHjqUyUc0o/9\n2Pbd+7rrZDHhXe+6ffcs2kuqANwdwHOY+Woieg2A3wPwB61e/k/Vzs+FkiqCXwqhCYBOua67XNha\nfcczMDoFommJwBnhs+sesX9KC6SOd41zXvC0SZvM0dTwKXNfJ+ApcTRzW9PAZ5Me1RJI/PaSRcly\nAEsJ70QhpioFWCcKYZZ0vxGa+Z+0D8CScreH27IycDNN/6yYYvoA1LKiiqZfVR9kDt0CwwzZQw3k\n+vdGeqxrZsW6ofNoKLO11XNAbw/g62r/egD36Tvh2mtfgQsueMk0gK6sAL/4i5s+wKKi41IPfzjw\nq78qIZo++EGxjG6HYvil7bpf0V7T9QCuZ+arw/77IQCa6DnJft1xufiNq+FT44dRWyR1YPLNHK+h\nv+k3q/S513PmLaitVpc5K5AP9R1PTHTU0ZbCZdONpou+Thfg9LwKdpDUmWGLmkIYJUwWGsXtGsQi\nypi418fBlV6TzFV1AZ5DDFdmNcZQJKh9KBVN/myGvDpKngto//ZJf9vMawFN39XCdDCUqJd19uwF\nUCI6AuC2mUMvZOa/HTCSOV/DYQDAl770cRw9ehQHDx6U5roGPvpR4PWvn+9yRUVF3frDPwQe9CDg\nNa+RGKHboZUV4LGP3Z57baGOHj2Ko0ePLnoYx52Y+VtE9HUiOoOZvwyZ3vXP0z37El+3rohp+Ewt\nkTngjIr0ALQhNQeGXXA5FEC7QDR3jtYMK2cOPFvzXWf0TSCtVaZANBlG7pVGpQbiBrqo/Sqa3O7c\npNcU+KT2gqMRxIU+DvBZU4BWAVC5boTPZAjawhkNvhYTCM292rSt6xl95hxg+BzPWX9KO1i9AMrM\nG11y/g0Ap6v90yG/YDt0GABw5pkvmcAnAFxzjWRMud3tNjicoqKiRqMR8J73yIr0Bz9YFiZtpepa\nQqldcMHW3mcbdPDgwda/US97Wfev/KJN13kA3k1ESwCuBfBr0126LJ5ahDx85sAz1xbVdX4faHbR\nQle/IX5WfW7uWQfAZ9/+kL7ahd5l8Zy6Zo9ar4fAHiDPsk2toNEC2kAoiwW0gqx2X4OAZU1tCI3W\nz3AdeY0EtCygYcgRPj2EnuJHE1+x3na1xefK7et+KWTO2nYZwfuM4gvWZrngu/6KrgFwFyI6AOCb\nAH4FwBP7LnTnO78Q5513TruxhF8qKtoa3fGO4ll4whMkNufNb75197rmGln9Xn5IFm1AzPyPAO7V\n32uoBXQIPHaBZ07RjzrLPDXvsXn9rgNAtAsup+oZt7te9Z/CZSeITg+h1ZChCAaahT+UMwgHcBQr\nKMvvjpDZiKtgCY1zPqtwrWj5HFPjtkcM9xRijYKTtxdzwGsLqB5Pl/r4ehYYdv2JDLV+5q6d/oks\nWOueiEVEjyOir0Nmd19KRB8O7acS0aUAwMw1ZDLOZQC+AOC9XSvgAeCRj3wJXvvac/ILkEravqKi\nrdEv/zLw8z8PPOtZwDrDsg1SSb9ZtG2qBxQ3sMxjeRxirXRqm9brjvqsMc3yu+b8wj1g2WXFTOd5\nGqPqqqTgSchYP9EuOV+19oEn4NlYLQN0TsASQLRw6pBKq+3QSg18Kjd8kwOgSRAAFao1PFt0v1vI\nvNI03ac+PgXbybNlobrj404/+vR3SZf7PffbZOr9dhzfYq07Duhmi4g4O5YbbgBOPRX49rdL4Oqi\noq3STTdNAtU/7Wlbc4/73x942cskmsUeU4kDunNERAxcNbD3dDih7viYQ/pFC2ifn3Re3+osU9h6\n6oQQtDNAp022Rh3v66f7d1g9e/d7+hgC9oXV6/sZtI+BfQzsA2g/t4+FfexH0y8ek7ocwxKrRUeY\ngGwdYNa1j6HW7vm4H441C5fUa8U667m2IdOD09J3jo7j2VVqAGsD+y44Duj26OhR4N73LvBZVLSV\nOuEESdX5kIcA970vcMYZm3v9H/wA+NzngAc8YHOvW1SU1TyLkBhtnyqSepcoqcf+Q4ByPceGEsfQ\n8Sbu89YcTZM5lmvL1Fsu91mgmY5L7WcflyDhj6TOXuKBck2gGkDNUh8DbFnyu6t4n2CIqz1CZVr3\nwQoaLKDcvCqaGI31eGnGx5P7WNL6ZpddpJ0PoMVtV1S0PfqZn5GV8U94AnDllcDy8uZd+6MfFQvo\nvn2bd82iok4NWYQETMATmG2iAqYhLm7jRMA4p3TI8uV56l2kMZRGcpCXlK7FQlP16KbXQGowDZ1Q\nx5GAqRpT069D4VWwJ4n56QF2BHIc3NIEuAl4wnLI8w7J/R6Mt9x8NAE0HSbAmYPPhj4RVsHr8WLy\nsQ+ZnxmfQz9Trt+sj3KjbbM0T99N0M4PxlcWIBUVbZ+e+UxZmPSCF2zudcsPyaJt1dD5nXWyzU28\n09vc3MtZ9a45oF3zQNczH7XPDJaxfHaB50yrJk3c47qe7mvgNKreACom9ew4g3IG31YYpgCSNUko\npjAPFCEME8J80Dj3c5JaE+0QTG4CpPBI4HMy3iZjkqXJnM84B9QmJQ0unz7e1HPN+Mhz0beG/EYB\nth0sh2pnW0C/9jXge98D7na3RY+kqOj4EBHw5jcDZ58tqTof85jNue7KCvDsZ2/OtYqKZmpoGKb0\nmzn3DU3JNtZ9ckxfo4sU1tOeM2MN3eaeNwFOvRgpB6KzgDR1syPZaitoqw2TtvT1cmbfI4RhQmIF\nJYkB6khc8GNqpqxynL4a4ZGBZnFRTKUZrZ2xPWZuYj22ANIqVVITGzR+XDpZlVb8M4klC9WY7yPf\nyJ/BUG0DrO5sAI3pN0vWlKKi7dOtbgW8+93Af/7PEprp9rff2PW+8hXg2DHgp35qc8ZXVDRTQwE0\nuuBtaBvyravNWdoX2+eXnbcwhGi0DzcqHWPO1JUbs6a6FEI1iOoFRSa/bUGn6g+sY9sx5AYKub2N\nKTAdC4TWDFgCWwZZklzxlsAm7BMmIT09IDnr5dqMcA8k+wE+NYO24BGY+I/jRxY/eofpZ+r6iHIW\n0C4AxYy2Ice7+vRpC0F05wPoIx+56FEUFR1/uv/9gec8B3jyk4ErrgCsnX1Ol6L7vW+eV1HRpmrI\nIqRIFLP+tlPLpy4aPFMT1XrAM+eqn5cA+iA0eY6+cEvzltTKqa2HzW7XMU157bGmMUBjEPoWhDoW\nl3qAzzhNVfK8MyhYZ1mDZfI+mrZWn8mYuRl7Ig2g+s9O/zno3yz6eO7PxKENoOn11rufO7Zgl/zO\nNS16D1x+eZn/WVS0KP3+78sXw3/9rxu7Tpn/WbTtmmf+Z9+ku6FzL+e1eg6dozpPPNIctWil8Dyj\nzAuguTzw6XxQDaFT8IluSGNM5n7GmKANhCLM5USY/ynxPTnUY853XkOY/xnb0cwDjeGX4MQFP4kI\nGS2o8XnQjgUa54Cm8z/1HNC0pM+l/2S6Yn/2hX7tmgc6j7r6bzGg7lwL6Gc/C5x8sqTgLCoq2n5Z\nK674u98dOHgQeOAD57/GeCyh1N70ps0eXVFRj4a64If0GVq6aKDLsjm0LZ0QmY5bU01Xv4z1cxZs\nzgLRXLaj9F6U3JfQ7pMe71LyOtkTyPPUKniZ+8kN+DIxQDS5Mss9uXk8AlS9cbkrq21j+VT9J+dj\nAml6+NGwrv8Eup4p/bijBXSztSDI7NPOBdBiNSkqWrxOPRV4y1uApzxFfhTe+tbznX/VVcCd7yw/\nJouKtk3zxgEdolkAGh2K87jfu5Y5pylv9P2RbFPwRLKfO0ct0U7ngnbO/9TgqY5FEM1CZTKWTuCk\n6UcAmo+HGWHxkcAmPJoA8dH9LtZJBgf41ENqPmGPiVW2cdPrfZp8jCl8pqva43ldczA59NWzNNJ+\n8eNNDeNDZlH0tXW1D3HLz3tsA9q5LvgSfqmoaGfo0CHgP/0n4BnPwNypOldWyjzuogVos1JxzrJS\nppbOdJsjjJzJa1YoprRf1xi6Vp9o+ExgU4No32r31Oqpwy91puGMAJdaSElVU/hMqDEuCmpeLbVe\nCTehmNC44GNKTm7c79SEYUJww/M4pu9EE4opvlJxwyfgHOCUYxKs6IJPSy6Jln7t+uNJf6vMO/Oi\ny+gOTP85DNU2WkR3JoDeeCNw9dXi9isqKlq8XvlK4F//FbjwwvnOu+yy4skoWoDmnQOaAmkfdOa+\n/XPw2WcJdZltDjhr5ElkHhCN6rHepi73WXNAU/DsAs5sm7r1rGkQ6nG4BWzUzNmMbnh2YT5nk0Yy\nAKfKC9/EAA2QinpyHfYkpVkFH1/bxEI6gU/qjwPaB56ZZ+uE0FmG8dzHngPR9L47RDvTBf+xj8m8\ns5NOWvRIioqKAMmK9N73Ave7n6TTvOtdZ5/z/e8DX/yipPYsKtpWbXQOKGXqBDQxdght32r0tcbt\nvPCZs4TqCYFdK1q6bEh9ftkMaM4CTiIJh5jdEmTZecf9p4Bn4DHdJwaID2k4Kb4aEyyYBIC4gdqp\ny4ZXTx4SG9QGa2cahQuYAKe6COvXrRch6ehdOZicZf3Mud+1Cz5jNM5u43jTP1vG1LO07p9qm+F0\nZwLokSPFalJUtNN0l7sAr3418Cu/AlxzDXDiif39r7gCeNCDNjelZ1HRIA2ZA5rCjgbMHGh2bfvg\nc9Z80D43vAbQSBLxfvq+KYh20UhKLJnSpNkcCqVqG8X6nh1KAYs7+qbu5AiijuWRHZqg8y1X/hTs\nyfvgCJtVuFYKYvFVcvIYhGDtRdv9rgE0/VhnueD1c6Ugmk77zX10+iPmpA8n9RyE7gDtTBf8ykqZ\n/1lUtBP11KcC97oXcP75s/uWhYRFC9O8LvhZcy/73N6pH3QIfKZ+1ZwrflZ60NwYkNlG9YFnUk8X\nHvW53lMXvA7DpHk5N8e0uWcy1NxcxtYrpTBnU7ZcJ2WMdlnTLvg4/xNSXCjRBd+44dN3gglQds3/\nHOqG73O/d83MGDr/c545oF3H521fp3YegH7zm1LucY9Fj6SoqCinN7xBpsm8973dfZjLAqSiBWro\nAqOuOZ593+6zSlTX/jxlI3Qxy+KZrIDPrYYfUs+Fb8qFchqqvlfWx/EtYAuAWqsS43/qNqfKkKm0\nmVfYAs2umRLp4+eAO/fMuXcz9HhO2wSWQ7XzXPBHjkgO6o1kXikqKto63exmwCWXAOecI9bQO91p\nus+//Itszzhje8dWVASg1/3b6tNHDOpYCmed1BGTg+s60E0zuu5UPb2evtdUPCDZctexnjZu/Neh\nHu6rLYBNHWiCwOsc6OmjxMftq886rvdnQVWqvo9zljtcg2xfPw3EQAhqj3aAhRRo49i0FTVaUruM\n19Sz7TuW9unT0Pe6BZC6MwG0uN+Lina27n534IUvBJ74ROATnwBGo/bxkn6zaKEaCqAzrIIzCSbC\naQp6fe7wlC50PYJovH4kmFZuSUxDL01AUo+DM6Cam5wY4TMFT1AAKFUH2iAat12PuZH6vIbf9JVm\nfkv0AmWEyvjq3YxzYt8xJhCausz1eNM/JR2sXvfp+62ynv107DtEO8sFX9JvFhXtHp1/vgSYf/GL\np4+V+Z9FC1UXRM4olNKKmT7eKunxNHi7SYpVJd2v1FYVPcmw1S/Us3kgwyTEeJ8sdEZINWqfMvuk\ngIsm8NnMEKDumQupFXAj9RREcx+5/uhjPWcMTqEy5+ZPo2HFMk7KGtoW0D7rpy76o9IhnZZUGWES\n5qlrrqmeb9r1jDlwn3d/C7SzLKCf/7y49+54x0WPpKioaJaIgLe9DTj7bJk2E4FzdRX4+MeBd7xj\nseMrOo411LYyy+qZgczG4thlXtNu8777xm1qbov0Euqk+2nLZmZ83DEmSs7JWkBN2xKqr+dpstI9\ngklsi0PVmuVWH9IvtnUZk4dAaF9J5TN94qyIrnmocaagXjOWWkFzLvho+ayS9ngsuvaHTl/oayP0\nfwYL1M4C0BJ+qahod+nkk4F3vhN48pMlVecppwBXXgmcddb8aTuLijZNfT7ItF8HRBJNH29Bp25L\nTU9d8JmOKyWe1O/r2/0iEOqxsbovJf2yz6bG25oDSm34TK+Tg9E0CtR6wLPvWGr97AInSuodj9t6\nFV33SIGa0XaVp1ZSqHq6xi035nh/m2mL7WlQg756up8C5yzIX6B2FoCurADPetaiR1FUVDSPfv7n\ncfg2twHOPFMC1P+f/yNfZAcPAgcO4PDFFy96hEXHneYF0KR0rghPYS+3v4H7tsAzFnSAZw90piDZ\n1abBs/eaaMNLCp5eHZvHtTukbx90aenHSvfTArXV19XzP9NjVvUxmMT61L8bcqvzcxbQrnmhNnPe\neooee5+63vc2aWcB6JVXAu9736JHUVRUNK9udSsc/vznJTxT1Ne+hsMLG1DR8a05ADSFy779TujM\ngWrXuLpMdB0xQxkZ8FRtXdBIyANnziyYWlE1eMZxN5ZP1a7d1lobnW+oLXldlsQ+9T1u13g1hKZt\nGjxz1tRcSNa+RUg2M67c+byBun629Fnn0RYC6boBlIgeD+AwgDMB3IuZ/6Gj33UA/h3ym2DMzPfu\nvOhd7wrc4hbrHVJRUdGiVFa7F+0ozQGgMy2fKYjm2jWVANMmwnivxKXeFEabSBSAkuqvYVSDaMv6\niTaUcno/YJqg1PP0QWsDnOHa6WVTzQueui2Fqllu+PQx+7hbj1fDrr6nSdrix6KvoacezLJIUrKN\n10jvlbr5++oa0vU7I7W/EW2xNXQjFtDPA3gcgItm9GMAB5n5+zOvWFa/FxUVFRVtWOsE0FnwOWUN\n7QDX3kmREURT4NR1bRILpNGCz556FjzTemZpeCtkU66k1+hQH1TO0ye25WAuB6KU1PXr1Y+bg+Z4\nLf2xcLLNLVLSfTFgC/RH6Urhe1bRv2nS8ev30Afu2+x211o3gDLzlwCAhlk+hv1rUBYgFRUVFRVt\nWOsAUG3JzFk7s8Cp2lvudx2tPd7HJ9uUcFL4VGYxDtZGDZw52CRMLKPxHbRgVD+zXhmfiQSQBdhE\ncVy51z0PZObaNDil8Jmem+Pj3G+CoWPVBukUPNNr5zSrPYXl3HhyWZ7S/b5xuEybvv6CoFNrO+aA\nMoDLicgBuIiZ39TV8fDv/778R3CgLFwoKioqKlqvhgBohzmr0/IZ4TQ9ZpJjOTNdakZTls3GB5tA\nZ7SAMqOZ4hKBrwHSpE0/+ywYbTIfKfMgJ8+enq8BWINPn3VtaHsOArvgc6NueKA99vQjQdJnVr0L\nTIccy/XVABq3Ru1H+HRoj0U/T+7zGQqd2wSnvQBKREcA3DZz6IXM/LcD73F/ZuuQWjAAACAASURB\nVP43IjoZwBEi+hIzfzzbMyxgOHrddTh69CgOHjw48BZFRUUL1YED+QVHBw5s7zi2SUePHsXRo0cX\nPYyiTg0E0N74nzTdJ4XOXB8AbZAEMAWcerJe3DeqXe2TdsFDAWd8hnjppE/rUUlBRQBLDZ+tOaPJ\n87ZCMWECw3pMs0C079isc7rc8KlycBnb0im6fWNYD3ylEbgos4+O9tx+BFAHWbBUY7LyPvbRFs70\nzywF6SFagEWUmDd2VyL6KIDf6VqElPR9KYAfMvOrMseakRx+8INxuPzjXlRUtEtERGBOv/WLFiEi\nYuBdQ3oCFNLQxIxD6Ra2+1iz1dfIrSbZaEEbMIA2YLaO0Yx91U4aoJN6hM+ueoTv1vSEROuBUX2M\nMJ0ZKM0SNO8xbXLLQWcXiPbVNeCmsJtbNT/kmAbQNLh9bn9Iv5jFKc3mVG+gPkjd/zZulgs+e3Ei\nOgGAZeYbiOhEAI8A8LJNumdRUVFRUVFGAy2gvYtutKUz45KfsoZqesj5jmdA5lzmPnXK4OfNPHsa\nA5RUW7oavrGyUtvi2VhjZ41xzuNDXlnuseI2LenHo43PuY8AA4/Fa1u11ePT70ePw/ZsGe3MSumf\nqn5WPRZtRE+N8jnIXo820VK6kTBMjwPwOgC3AXApEX2WmR9FRKcCeBMzH4K47/8yLFSqALybmVc2\nYdxFRUVFRUUdGgqgXf7QBDZTt/vUsWQ7mGwG7GtYym2h23i6z8xnJ7RScE7FAU1JRt+T5geSefqv\ng8n7fk9MQVvuXvMGgQcmAeR1ik39p5COTUNomhM+XsNgAp99z8DJOV2xWXegNrIK/gMAPpBp/yaA\nQ6H+VQB3W/foioqKioqK5ta8AJoBz04YTSyeLatouvK9z5SGOdpiUwdgpvCZPubUVDsNnwo6NXy2\nFiEl5zV9VXOqjYKp5vg+pWDWZfmM9a486xo++4LBp1tS9dyYTNKu4bPKbCt13S74zIFwLsRU138G\n6bPPU99E7ahMSIcf/GCpHDiw0HEUFRUVFe1MEdHvA3gK5Gv/8wB+jZlXk15DroSW9ZMUpWRd7R1t\nqZt+Cjzn2WbaSFlBpyyiPOmqQbMZQg9FTLnfc/CZWkrjONTlctCb03qAdIj1UYuSetfiID3uHGDq\nMquNMIFG/U4ouYduTyE0lpG6Vjo/tMt6G8eSm1OaaoGwmdPOAtCy8KioqKioqENEdADAbwA4i5lX\niei9AJ4A4O1JzyFXyxSDLLl0wmem3lw7R2sbqLeAU1s7Y13DZ67OCVykcBnG2gWfGkLj6elQN0P6\n+qk7fIh6hj4VnCC9by7Yexp/M23XAN53L/2nod3vGj5jSS2gubFq8LSqnrOY7lDtKAAtKioqKirq\n0b9D1t+eEGJLnwDgG9Pd5gDQroxGlINQPQ9UrxDX5wBt+IRqS5W2ZfpE2GysnwpCAQWWKYiqdqRb\nDZPJc8c2/U5y4NoAa+axZjzSYA21fKphtcaUWhw1GHbdJwXMWdvcGCza1lINodpKGSE0gmdcwa8B\nNPdOckDcZTHdwRBaALSoqKioaFeImb9PRK8C8DUAPwJwGTNf/v+3d+5BVlR3Hv/+7oy8JIGxMPJm\nEEICMWtiUlHcMhCDQBZQUrUJgi/clSqf4KZMBTDRMWL5SKIrpszD1ZiwYdzETcVBDAxqBqwE4lKJ\ns1mRMhBHCCghCT7JjPP47R/39uX0ueecPn1f3Xfm96nq6tPnnO7+dQ90f+/3PLqwZrEOqEGE6l89\nCk1Ur46QV6cjKqcqU4WnJjbBFsFpEp16nkN0BuXWb8njRJ1KNdmaRKdtrYXkvZjOo4tQfdHzddcz\nmK+zDuHYodWzOaCDUPj7xRSfHqdtQgd1f/2eVbG53YQIUEEQBKEmIKIpAG4E0AjgTQA/JaJLmPnH\n4Zo/VdJn5BYTlkkZSbOSQk3stm3A326KYUuZhGZIiKqOaE65kFI/OEaB2NBtMtLKgn1csZqc3jKh\niid1HQeb6WxbfL6/rgtSgr2ZXndBo7oSmP4kyu+dgsVn7tFA7PZayqIEOhxpI225JRoRoIIgCEKt\n8EkAv2bmvwIAEf0MwLkANAF6aW6t2086wWTz6lw4ugjVhGlIeAbJQJBWAFefy7ywVMUmxxBrqoAs\nNW2DPESLeTdnU7LN5FUdQl1YusRn1D0zCUMfN9XUrB982UgXguqI+WDS92AxCVo1Nl2IBv+cTS6y\nTWzbhKrNADcyO7cE3GatKQJUEARBqBX2AvgaEQ0F0AlgDoDnC6vVeRyKEJoDh9SZwHNpUha9mV5d\n1ENGEdfJs2k8k9A0OZ2heraTFys+dXVsiNvVadN1v0zmrK2+SYSaxKjLmdT3d8WkxuWKSRefqsAL\nJpnXR+oHBAJUb/7X49bvkzooKVB4cVzfYN8oV7QMiAAVBEEQagJmbieiHwHYjexr8rcAvl9Y0+fV\nFghQTYSS4oLqjmgw+Ehvcje9oH1EjIuo/Z3i06VyVfGoruGRVgWnzQF1CMtQvnIsU31XM7B6CJsT\nGjWNkskpNR3PFZdJGLvEXSAk1Unm9UFDwXkD59PUB9U276jqWpr+C5hiqzfE6HI/yyhERYAKQoqg\nSjXjCWWDCyb1FqoJM98D4B53Ld9XmzoLuOp8BmJUfwvrTmiQNIioUt1QXZBQbsO0DwGFk827TqSK\nR1OeTXxGCVUg3ydVDc4mMEOxafXiOG9xHD5X30yTmDXh636aYlAHDGVg/6a6+i33YK2LT12Eqr+b\n9HJXTK4+orGb4P0RASoIKUMETnqRHwi1QpwmeNOi9/tUHVDTAj+RZAohqp7N8QQQmog+ssxUyVeI\nltIUH+GOhoSoUl4u8WlzRF0uaME1aDG50npMJmcxqN+j3wMF0wj8Xkuc6r3Sp5kK8vV4gt9eQdok\nQivcDC8CVBAEQehn+DbBq30+LQI0ztvYpOVsZXq5zzH08oL9TU6nbdtXaMZoineJzcDBdYpQJW0S\neMWIUZfzWUw/UFNsegzB2tQEH+UoBrezV9vPdA16PKr41O+d7X6Y/umrbmqF3E9ABKggCILQ74jT\nBG8YfBSkQ86nyQVF2AHV3coo0RklNlVcTmioXpTzqbueLhe0GJGqxVEgRB1N7mDkB3XZBJ7NabS5\nn8U0wZsw/S1t4iyqCT5qP1hitQ2eUmPRRWMfTghTPQ7Tb65gW+2jmtHOoYraEhABKgiCIPQzfF9t\nplHvivC0zpWTewPrIjTAJTx9XVK9vvVlz5719H18RKerTM9TThyaGcAgOE1uqH7/opp9TbraJUJt\nAs616HiY4E73tddzH4I9/ijxGRxPzTOJcXVSff33l8v4LyMiQAVBEIR+hm8f0KCfpzrgSBv9nq8T\nuKCK8FTfyqb+wVHi0iff15UL1XM1vev5uoh0CUyfMqW8wPn0FKEmweMSP6ylTc3surDzcUF9hKgp\nNpMIVSetN8VvEqBxRHIQgypCM7DH4up5YnJSbddaAiJABUHodyxfvhwTJkzA7bffnnQoQiLE6QPq\nWELzgJrmAoX95WwzEk314MgveOGzIelje5pEqa/j6SM+bZatKjAdglNf+4gfVYRFOaAmZ1FPq8e1\noV6ySSCb4gnOrYtPk1NaZziWfly9LIjFVkc9jz6oqR4n5iOtg/n3V4Uc0Ex0FUEQBKCxsRHPPvts\n0mF4QUQyYn1AU++xB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# to get going, set a prior parameter of zeros, and a diagonal hessian \n", "# corresponding to very low regularization\n", "w_prior = np.zeros(p)\n", "H_prior = np.diag(np.ones(p))*0.001\n", "\n", "#----------------------------------------------------------------------------------------\n", "# randomly permute the data\n", "r = np.random.permutation(N1)\n", "X1 = X1[r,:]\n", "y1 = y1[r]\n", "idx = np.arange(100)\n", "\n", "#----------------------------------------------------------------------------------------\n", "# Do a bayesian fit with this random sample\n", "# The default uses a full Hessian matrix and a Newton's conjugate gradient solver\n", "w_posterior, H_posterior = bl.fit_bayes_logistic(y1[idx], X1[idx,:], w_prior, H_prior)\n", "\n", "#----------------------------------------------------------------------------------------\n", "# Now make this posterior our new prior\n", "w_prior = copy.copy(w_posterior)\n", "H_prior = copy.copy(H_posterior)\n", "\n", "#----------------------------------------------------------------------------------------\n", "# and remove the data points we've used already so that we don't refit our prior later on\n", "X = copy.copy(X1[100:,:])\n", "y = copy.copy(y1[100:])\n", "N = 10000\n", "t = np.linspace(0,100,N)\n", "\n", "#----------------------------------------------------------------------------------------\n", "# plot the prior means and Hessian (inverse covariance)\n", "\n", "plt.figure(figsize = (12,9))\n", "plt.subplot(221)\n", "plt.plot(w_true,'bo-',label = 'true value')\n", "plt.plot(w_prior,'rs-', label = 'prior')\n", "plt.ylim([-2.5,1.25])\n", "plt.legend(loc = 'lower right')\n", "plt.title('Prior Parameters')\n", "plt.subplot(222)\n", "plt.imshow(H_prior)\n", "plt.title('Prior Hessian')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default solver is a Newton-CG solver (from scipy.optimize). This utilizes information from the Hessian to achieve rapid convergence. One can either use the full Hessian, or a diagonal approximation.\n", "\n", "In general the full Hessian will be more accurate ... at the cost of added computational time, which may be an issue for larger problems." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Shape of full Hessian (11L, 11L)\n", "Shape of diagonal Hessian (11L,)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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zZuvloOAprmdW23ZczCIpjhg3DIkgMQbMJhOzNCdBKcxrokziZWlgXM73Nwum\nk0qCWdq2mjbRNn790bjjEBiBZXIs0TFB4vjkWNsDzUlwhnTrdyVgToKyQ6mlvDPgOFlGIp+mcvU9\nF7gtLHex0gBu5cqVLF++nJUrV3L22Wfz8ssvs+WWW3bPAFM0btw4HnvssaIf89VXX71BLLyxZMmS\n1HjHruuyxRZbcM899/DFL36xS8YyduxYLrjgAvL5fLt9n62srKpTntZRapISAjyBgoDvBPgSEDgB\ngVNA3QLquuC54DmIJ0hoMHZyilsT4Nb6uLUFcrV5k+qacb28cbHIK4WChmCsFGoVL694NeDmYskT\nXA+zJLYnxQVMHEdiq/6lAGarZaZb8posjwC5BKrTQDirnER5pKRPcGx8mVBcTT5elkxZv/g5iXZB\nRnm5vquF46SFmUS/Ub4aV4w0UE66kJQbV/LloVxd2riqgd94m0ouNxuvLCx3sbIAbsiQIfz73/+m\nb9/qVp7qau20004888wznHrqqRx88MHceeed6xXQp0kzlmTdd999ueaaa7p0LFtuuSU77LADjz/+\neOZqilZWVp2loHITFFVFgyiB7yt+AfyC4OeFQrOQbzLLV7s5Fy/n4LouEoaGE/EQPEzojAKuB02r\nczSu8Whe69Hc6JJvdik0uxQKZpU+VUExlmNxjCHazSlujeLVBnh+QC4I8DUgwMfNh6CrLc80jS0K\nYrg53Bb30+ooZeaoAGgNQXEQjq+qRyyf5kOc7De5Teaj/pKK+nYoBcksq3Yly2px+cKU8o7uQ2vr\ndby+XF382DTXkUrXlZWy7gmJfJrK1fdMUIbs1zSrLtbgwYPXW1CO1K9fP+655x4OPfRQ9tprL559\n9tnuHlKq3nvvPX7zm9/w3HPPpda7rtvFIzIaN24cDzzwQLec28qqZ6lKa6EaYA4CCHwIfCHwBT+P\ngeUQmAvNDvkmh+ZGt5ia1ng0rXFpXOPRuNqjcZVH46oQlNeEoNwUwnLBwS84BIEQqInDgVAMv+zk\nFDcX4NUqubqAXH1ATS+f2j4+tb19aqLUKyBX75OrD8jVBQauawMz8bAmMNCdUxwvCMPYmQgb4mgY\nYSMLdrKsqVFKK4snP6M8Dd4iVfLpzXILSTs+eR3xfLnxV7rOtoBzVllb6yq1y7rHldqVa18tkPdc\nWVjuYi1fvry7h9AhOY7D5MmTmTJlCmPHji27MmBXau3atdx+++2MHTuWoUOH8q9//atb/b3TFPkt\nW1lZrWscRV45AAAgAElEQVSVg4UWaFBarMtBoAQ+RctyIYLlvEM+hOUiMK81qWmNR9PqCJZzNK7K\n0bTao2mtR3OjR74ptCrnXXzfwQ8cNAghMLQsO+HkPrdGwzjOIRD3MoBc26dggLlXlAxMe/W+icxR\nGxhQrjGg7HpBCMwtETYcB1LDxwFVv1iUTUlYrha0ygFylkU5y72hHOhVgsdyQFktZHYmHLcFbiv/\nnbe9T6ukrBtGF0lVufzyy3n11Ve75fyTvj2JJZ8saVXe0L+BGVfNaHN/EyZMYMcdd+Soo45i4cKF\nXHHFFV3ui6uqPPnkk/zpT3/izjvvZI899mDixInccccd9O7dm1GjRnXpeCpp+PDhrFixgjfeeGO9\nA3krq41L1blhoEEIy5FlmYQbhkMh8iV2nND1wmmJo6yemcinPqo+rifkm9yiVbm5yTOW5XxoWfad\n0LIsaDh/r2hZDhQvUJTATO5zfBwPCgUH9SEIKNlGYy63VR+CkC2LwTE0dv0tNYmyxH1KhdVyAFtp\nv1xZvDwtpFq1wAytXUiiuvYAblY9sbo0l4ty7hbJfNSu0jjbYx1Ou09xlfOxrqZ+45aF5S7QqlWr\nOP3001myZAl77LEHTz/9dJePYcknS3jkc619pfl3+/vcZZddePbZZ/nKV77C4Ycfzl/+8pcuiSO8\nZMkSZs6cycyZM8nlckycOJEXX3yRz372syXtGhoaUo/PKl/XchyHcePGMWvWLL797W93yxisrHqG\nqrCOhS4YhFblFmAW/AIUCoIbAnMpLJtUXJ0PPwwP5+F6kG9u8VOO8n7exS84+L4UYRkRcEPLcqC4\nqngaoCLgCLiC5MDNaxHk1Y+7i8T3TZKCoL7pOvBbUCxQEA0BHdAiACfvV9J3Od4uDs2UyZMoT6oc\nSCePq9aqnFTa5x/E6jrLQpyE8/gxaf7HWaCcbNeecbbFWlztfcz6G+l5srC8jrV48WImTJjAXnvt\nxaOPPso555yTuiLeuga4N199BT7XunxJBy3d/fv35/777+dnP/sZe+21F3ffffc6iTCxYsUK7rzz\nTmbOnMlLL73EiSeeyK233sqee+6ZuUjL+uIiEte4ceOYOnWqhWUrq3WqKi3LaItlOUixLIdRKsR1\nEMfFcYxVGcKkLhq4aGBiKbuecdso5N3SbcHB9x2CID7BL2ZZ9sBRxUVRJ4g4HCen+AUz6TDwISgI\nQWo+hHxHCQoY2JboTgiiIIEiIikYGUFwmvUxCcrxsixojpcloTytLHlc/Phy0Bw/RzklLePVQnBb\nILRa8M3Kp1mY1wUsxz/P+H6aJKNd2ue38cvC8jrUgw8+yMSJE7nooov4+te/joh0KcCpKs+88wzT\nF07n7doP0hs1Nnb4PK7rcskllzBs2DBGjx7NVVddxcknn9zhfn3f529/+xszZ87kgQceYNSoUZx/\n/vmMHTt2g12C+9BDD+XUU09lxYoV9OvXr7uHY2W1kaoKy3IEypHPsq8xV4wYLDebUG4iJpQb4qKE\nVmUNV+YLAgI/wPHEWJBDOPYLTnFyX+kEv5jPsgsOiisKIShH65qY6BxKkDcQHwGynw+30b4rSN7A\nsB8arc0lCqoargoo4KdZlCsBZ7JNGthG2yzYjSvNkpw8phI0l1Mly/i6sthWsh63JR/vrzPHmQbN\nWZ+RZuR7piwsrwOpKr/61a+YMmUKd911F/vvv3+Xnv+9Ve9x0z9uYvoL08kHeU4bdhqDVvblHVa2\navtJXSOFoIDndPxP4fjjj2ennXbi6KOPZuHChfzqV7/C89re78svv8zMmTO5+eab2XLLLZk4cSJX\nXnnlRrFUdJ8+ffjSl77EX//6V4499tjuHo6V1Uaqan2W48DcAspOHgqOsSgba7KZbCYStya7xeWr\nTTI+y74vBOFkvsAXgiC0KvtSnOCnQDSHTbwIlBVxAxPL2QfXV/xAw7jNYYSOghDkW6J1OGFeXCFw\nwI8WM4kgyFwiGoSW7FRjbBoUxeuS5dXCbjw5ZINWuePKgXlS5cYeP66zITQOntVYkquB5vhxUV1n\nQX2WdT+tLKttz5ONhtHJWrVqFSeccAL33nsvCxYs6DJQbvabufuVu/nyrV9m6DVDeXXZq1z/5et5\n/fQXuPDtz+GtWJN6XKNXYNSMUbz1yVudMo7ddtuNZ599lhdffJExY8bw0UcfVXXcsmXLmDp1Knvt\ntReHHXYYqsrcuXN57rnn+Na3vrVRgHKk8ePH2xByVlbrVNVEwwhQgjASRsz3N3LDKAh+cxgRIx4J\nozGKiOGF4eM8E1t5VY61qzya1uTCaBgu+fgEv9ANI4hWwJPQBSMWOs4tho7zyfUOTBSMPlHoOBNO\nLh46Llfnt46GkQujYRTDxhGGjtME82RZRpOpXOSISiHjKoFbpDS4TlsKOg2gk9eUdi1ZUS/aG16t\n3L2qlK/muPaMp9rrytomob6abc+RtSx3ohYtWsSECRMYMWIEjz76aJe4CvzjvX8w/YXp3PLPWxi6\n+VBOG3Yat064mT5PPAs/mwb33QcjRtA/35uG6StaHf8xfThqp6PY6497MXXsVE74/AkdHtOmm27K\n7Nmz+dGPfsS2227LzjvvTJ8+pcvPNjQ0cP311zN79mz+9Kc/8fDDDzNu3Dh+8YtfcOihh3ZbLOSu\n0Lhx47j44osJggDHse+rVladr2q+zBU0JXRcOFHOuF6Icb3AQUOAU42syi6+H7Mu540bhhJLIRgr\nFH2Vo4SIsfQ64Khp5RAUjzOB7Uzc50KTAXc/LyY6R5Ng5hhG7hxmrNFS1MaaDE4A6hp/Zsk07qbd\nqyxrYrn7mrQgR/vx48q5ZSSt0FnPxqxxJf1xs8qz4L0S3JerT7MIR/m2WpJJ7FeC62rbQanfdjXW\n4njbao/ZOCVZq5xV3YHIEcBVmBkP01T1skT9KOA+4M2w6C5V/UVKP9rRsXSn5syZw6RJk/j5z3/O\n2WefnTnprDO0fO1ybvnnLUx/YTofrv6QibtPZNKwSWz39mq46Sa45RbYcks45RQ46STYcksmjxrF\n5JSVAyfX1TH5xBN57sJJnDT3LA7c9kCuPuJqetf07pSxDh06NDVc3qBBg2hubmaXXXZh4sSJHHfc\ncT3Kh/fzn/88N954I/vss093D8WqEyQiqCEjq26WiChU/kVLRPFyedyaZnI1edxcM15NHq+mGS/K\n55rNfk0eLxfW1TSn5M2+4xWMr4MQ25q8+euQkAGltLzVMS3lgQ+FJsdYuZvCRVLCrd8UL3OKUF3S\nrqTMtNFML5X2fAdHxyStwZ2RXxeqFoSrLSdl/JWur1JZ/BztCWeXVl+NH3hb66rRARvFs7FDlmUx\n04KnAocC7wDPisj/quoriaaPqOqRHTnX+ipV5Ze//CXXXHMNd999N1/60pfWyXn8wGfe4nlMf2E6\n8xbPY+wOY/nVIb/i4JqdcG+7Hb5zDHz8sQHkv/4VdtmltIOGBiandbz11lBfz56HTeT5P17Dt9bc\nyR7X78Gtx97K8K2Gd3jcW2yxRSos53I5HnvsMYYMGdLhc6xvqiamdeSKYWHZympdqDrLsqKgEASK\nE7liFMCX0FKLA6G/sgYOqg5B4BL4gbEsFzz8nFLIK16zsSyLg1mZr+XQkq2EwCxi2hnDdYu7RGl7\nIQjA9TSM92ySOE6LNTmCLA2MRVoFJ3BwAnAK4IT+zIZtktbBLKtye8riVtZI8QgRkshHSvNtTlqW\nsz7P9oy1EvhWA82k5MtZiqupT5aVg+CsukrgHLeyx8E3TdHnBa3/ZjZ49m2zOuqGsTewSFWXAIjI\nbcBRQBKWN8o7u3LlSiZNmsTSpUtZsGABW2+9daef4/WPXmf6wunMfHEmW/fdmtOGncZ1o65gwOyH\n4ZzL4e9/h2OOgd/9Dg44IHzyttbkGTOYNetRfve7eTQ1edTWFjjvvMMZN26kaTBnDn1PP4sZxx3H\nLaf+kMNvPpwL97+Q80ecjyOd7yrQ0NCwUYIyVBfTevz48Zx//vlcfPHFXTcwK6seo7YuSmL8lsWH\nwCGMKtECbRqEYd8iUC4E+AUPN68UcorrKV5OwzBzxg9ZXBBPW/KuWanPGI/N8tNR6Dhxw3Ze67wG\nYlbi8wRxzaRDHDXRORBQBzCgHARmARP1TQg5xzUAHkXDkBI+SgJkWr7adklITqran/Hj1tU4WMbB\nLW2MWWPLKqsGlKvdL9d3GiCnuWJUEzqurYCc5ouctA7H7005F5n4NW6UOFdRHYXlrYH/xvbfBpKm\nMgX2E5F/YKzP/6OqL3fwvN2uN954gwkTJrDffvtxyy23dKp/8sqmlfzlpb8w/YXpLFq+iFN2O4V5\nJ83m8y8shStvgtk/gpEj4Wtfg/Hjob6+Yp+zZj3K+efPZfHiS4plixf/GMAA85gx8OKLcO65fOWU\nyxjxhz/ylZd+xbw35zHjqBls0WeLTru+jV3NfnPFNvvuuy9vvfUW77zzzjp5ybKy6tmqDMsKRVA2\nkTAMwPphLGJF0MCkwA9X3/Mc3IKL4wW4+QA3XFLa9cD1wPEEJ2cswU7OwLET5QEVxXHCvIPJe1pc\n8trJxY4Ll6w2sBzgeE5oWQ5BWRTEQUNQ1cBBgwD1HQI/wPUcgqi9I2F7wXhDp0FQJcCstE0CbNyS\nnIS2eJuslIxbHB9T0pe2LeOrlG9rHVT2Rc6C4qx28f1qAblSWfyepaVK6pmQHKmjsJz2epfU88Bg\nVV0jImOAe4Ed0xpOnjy5mB81atR6t1xxpNmzZzNp0iR+8Ytf8LWvfa1Nx2b9RL/tJtty2ndOY/oL\n07nv1fsY1TCK7+/3Pcas3JLcn2+Fr46GhgY49VS4+mpoY3SI3/1uXgkoAyxefAlTpvy0xbq86abG\n3/n22xlywtk8ds5ZTN6/wPDrhjP9qOmM3n50m865MUtV+e+K//Lyhy/zyoev8MqyMH34Cp+88wls\nX/54z/MYPXo0s2bNavPfkFX3a/78+cyfP7+7h2GVqWq+mgxEqJrJfRK6YRgJaAjL6uAEISz7Ln4h\nwHFdXDeE3NAS7HrG+uvm1ESm8A34umpCw7kSGNeKooFOjbuGiwHs8DinJmjpo8aAvDhOGNki6iC0\n5CpFSDbRPByCgrEqB14YDSOyLkcTClPvUxYgtqUuvG/FbUBrYM76bNJAWWgNw8lxZ11LWwC4o3ky\n6tNguFy7ZPsk/FYDyOXaVAvFcfVsQI6ro7D8DjA4tj8YY10uSlVXxvJzROT3IrKpqi5PdhaH5fVR\nqsqll17Ktddey7333st+++3X5j6yfqKvfayW5+c8z2nDTuPXO5/HZ+6eCz//ITQ3Gz/kxx6DHXZo\n99gbG9M/6sbGlKgTJ54IBxxA7swzueSB9zn0N5fw1fvP5IRdTuDSQy6l1qveir6+LTndVhWCAouX\nL+aVZa8YMA6B+NVlr9Kvth9DNx/K0IFDGbblME7a9SSGbj6UE186kUd5tGLf48eP57bbbrOwvAEq\n+TL/85//vPsGY5WiKtwwlJYYyxoH5bA6MG4NQWAiYziuWVjEcV1jEXbDFC0s4oLjOXi1Aa6veH6A\nGyhKYADXAfEVCYJwjp+Gi5IY6HZrFLc2wIu2tYpXG6AauVKY8G8SucUpZtyBGatGK/kVMOPMR+OT\nog905o0objvDygotYJYFzMm28WPik93SgLScz3USFNPKKsF/pbJkXiocW8kVI619ctyVoLgaaI4D\ncyWXmUhpn2vPVEdh+TlgBxFpAJYCJwInxRuIyBbAB6qqIrI3IGmg3JWqZgJWUpF/8rvvvsuCBQsY\nNGhQ1efL+3k+afyEjxs/5rXXX0xddnrAqnpedL+F/PDP8NKlcPzxcMMNsO++pJgD2qSPPoKXXiqk\n1tXU+KnlDBoEs2bBtGkcdPz3eeGH53HG8ufY94Z9ufXYW9lp4E5Vnbs7l5xuy+e8Nr+W1z56rWgl\njsB48fLFbN1va4YONFB8UMNBfGPPbzB086H0r+ufet5qI6EcccQRnHPOOaxdu5b6KlxprKx6ukRk\nMDAT+Azmm/x6Vf1d65ZpUJbSJh46LjxGQ4ty4IITumA4TrTctYFW49pgQFkcilvXE7yCkgsCgiDA\nI0BFTAy3yIdZCQFaDAAX3S8CEzO5VvHqAnL1QRGWzXrVYaxkjLVZA4qQr6FF2S2YFf/cvOJ78VjL\nEWhHwFQOMpP71ZYXP6VEyrLCUuaYuM9y8sWn0mebNsZyY24PPCfrov1KEFyNe0ayv86C5vj3UvQS\nkwbN5QA52U/PUYdgWVULInIuMBcTOu4GVX1FRM4O668DjgO+LiIFYA3wfzo45g5r/tMP8taY91uV\nL5nTOmoDwOuvv85RE45izxF7cu3V17LEX8LC1xfycePHfLz24yIIR/vJ8rX5tfSv68+A+gF85H6a\neo7a9z9B5s6F73wHxo6FmppOudbnn4djj4WRIw/nxRd/XOKK0avXhSxdegQffQSbbZZysAicdRYc\ncgibTZzIPa7DH354DPtP35/LDr2M04adtk5D5HVUWVb8T1/5lBsX3lgCxktXLmW7Tbdjl813YejA\noRw79FiGbj6UnTbbifpc20C2oX9DyWS+lU0r+ecH/2TQLqUvWJtuuinDhg1j/vz5jBkzpj2XaGXV\n05QHvqOqL4hIH+DvIvLX1hGYqpngF0JrCMqRd4MEoI4gvhA4YeQJcULgNNBcnJwXLVkdxjp2PJec\n7+NrQE4DAnxUwol5nuD4fmy5a4y1OVze2q1RvFo1C47U++R6GWBGScCugeTIKm5g2UCznwc3JwaU\noxRBfatf4dsCxNUCaDX+x+XAOs2PthpornQNHVl4o5pjkmVZEFxtHYkxl4PgauuSn0d0jiQwJz+f\n+Gcb1a+/3/vrSh1elERV5wBzEmXXxfLXANd09DydqsbG1OKP5GNOvedUA7kh9L7793f5+PaPcQ9x\nWb7Lcp6991kG1A9gQN0A+tf0Y4DXhwFuH7aWenZ1hzCgVy3962oY0MdjQMFjQLNL30ZF1q6F1Wtp\n+PAi3iJlAli/vnDXXZ16mdOnw/e/D9deC8cdN5JZs2DKlJ/S2OhSV+fzjW8cwWOPjWTECGNE3jHV\nkxwYMgTmz0euvJKvn3oZB1z8LU56+krmLp7LdeOvy7Swdrf+/eorqVb8l5b+i4eXPMwuA3fhzC+e\nydCBQxkyYAg5N9cp5037deL0+05ns/rWbyRRCDkLy1ZWlaWq7wHvhflVIvIKMIhWEZgqWR/DNhqG\njwsNbb4aqJQAY/mNQsiFE+pE3OIPfWbfHBe1czzfRKTAR/FNH56PkwenRnECB0/NlDwkjJzhaYuP\ncm1QtCrX9PKp6RWEqNMCbNGCI1EKChK6XoBbI2biYU5wkj7LcTfgcvckE8LKpQhkywFyEpTjSrMq\nJyE5zcKZ7C8NmJMr1dHJWyXbmhxt2wLPSTeM9oBxWj5+f5NQHuWTcBwH454JyZHsCn4x5ZoKHPrw\nWwxYC5ushjsWruSuf6/ib0O256A3POQfa2Htx7DmHVizBlzXRKLo1av6bdYfWyeGZ2tqgvPOg0ce\ngUcfhaFDTfm4cSNbJvOFOvJI2GknE3Xu9tshc06l68L//A8ccQS7nnoqCwYP5ntf7c3w64Zz89E3\n86Vt1k186bbqnRXvMGfRHGa/MZv/1n6Q2mbQit7cdPRN62wMkydNgiVLSso2rWnmmhHPc9YeZ7Hj\nZi1vJePGjWPs2LFMnTp1vbbSr8+aNGkSSxL3G4xffHe6AVmtW4Xuf8OBZ1rXVmlZVrOenqqiodVW\nDP0SgYUUTc6mrckXx1BshzgmAgU+6gg4grg+kjOg7BbMpL8gaLEsS9GyrEXLcgssB9T09s351I3Y\n3kByIRYTOi/4efDyQiEX4HqC4wVh5IwWUBbRMqhTyRJbCdQikPJpDWTVgHK0TUJzHCDj0JZ1Dclr\niYNyNbBcrq7SMeWAOLmt1Cberj1gnJZPu6fxyBvxbRyU0yC554GzheWY+q2tYeLuE1kBTPzjH/nA\n6cvzt17NVttskw6/XttvX/97Z9AwvbULyCd1dZ1wBfCf/8Bxx8E228CCBVDNonhnngmf+5yZ1/fL\nX8Lpp5dpvOuu8Mwz1F98MVPP/SOH/3ISx/7lWL6x1zf48QE/xnW6dpnqvJ/nqbefYvYbs5mzaA5v\nr3ibw7c7nKN3PppnP5nH26xufdDatfCzn0HfvtCnT+k2Ld/Wz3nJktTVEl/cYgjfmfsdZn1lVrFs\nl112wXEc/vWvf/GFL3yhrZdvBSxZsoRHUu631car0AXjTuB8VV3VusVVsfwIkBEpvWjs/xAusWf2\nw2Wji9vUUGZJAFR8L/RLjkLA1Shus+LnHfyC4vsaLmgiBpqDcGnqkmvT4oQ+xzXnKE4mjJIX28aS\nWww5Z6JrRFZrJzYmN6fhy0BI3/HrCfdb7kkCdGP7mW1a5ZPbJOymgWJafVY+7dyVUrlzV1tWSUnY\nTNtWguVy468mn9ZnpTFVsy2nhWHauGRhOa7aWl7bf38mTJjAqFGjuP3qq6npJN/hSBO23JnJj7SG\n5ckH7tzhvv/2NxM447vfNUbgthgqDznEWKLHj4fXXjPQnLG+ifGnvvhiGDeOI7/6VfbY70ucOuAh\nHnrzIW4+5ma22WSbDl9LOS1duZQHFz3InEVzeOjNhxgyYAhjtx/Ltfv/ir1fWYH30Hz44f/lp4UU\nUAZwxFjK338fFi+GlStNWrWqdX7VKnO9aTCdBdjvvZd62n3e3pq/LF/E7DdmM3aHsYCxTI0fP55Z\ns2ZZWLayqkIikgPuAm5W1XtTG7nfqaYnil/+JVAcS8Vfpcs8TDUBIyGraBiKLkp+AYJ8aAkOl6rO\n5wQn58RC0AWhj7TGLNrQvMYhv9ah0OiYZaybHfyCGOj2zap90TDFoRi32Q0t2l5BCXxjQQczCRDC\n/TBFlxFnX1UpXpLZd4rtIYDI/1qVUveJpN9xmmUynuLWzsg67dPahSLNUpzcVgLkNHXU/SDN1zrr\n2tMUh9F4WaVzpo0v7soR7Udt4i9+adssv/G2XMvwMEWaXsUx6796JCz3b6zDu+tTVtXAzstayt8q\nCAcccACXXnopZ5555ro5eUPGstMNDe3uUhUuu8yEX77lFjjooPb1s/PO8PTTZkHA446Dm26C3r3L\nHDBiBLzwAlv/4Af89efP8Oufj2avP+7F78f+nmN3ObZ9g0hRISjw9NtPM+eNOcxeNJu3PnmLw7Y7\njHHbHsaUXsex5aPPw/Vz4PWrYf/94dBD4Zxz6H/C4TRMb+2K8Uldf7jooupOrmos0UmAToPqTz+F\nt982y46nyFWHK0dfyXfmfodDhxxKjWtexMaPH8/FF1/MD3/4w3bfIyurniAxfg83AC+r6lWZDTPf\n9OMKAU+VltjFkUWZlrxIa26J7wulFlcljLARA+aCEBQkdJkwsFzICU6TGLcJxyRxneIpo2GIKM2r\nXZrXOuQbHfJNTrGfoBBZp8MDnJhrR05xa8D1wfNNLGklQAXcQsS7LdFAWiKDxFg4zsUqaMijpsws\niCJICOFx4EoD5vjNS0tBrH0UpSnNrSANjrOAmcS2HIAmgTk6pq2gnPWSkNZPtVBeadxJxX8Fift8\nl/uMssZf7bVs3OqRsEyhD2+v+IB+qxyWOH1QVT5tamJ1YSWPPf44I0ak/WTXOZrcyT6UK1bApEmw\ndCk8+yx89rMd62/gQPjrX83igAceCP/7vyaKXKZ69YIpU3CPPJIfnnEGBx8zkpPmfY+5i+dy1RFX\n0SvXq13jeH/V+zy46EFmL5rNXxf/lW37b8uYIaOZsu05jFj2Ad7vH4YF34Vhw4xZ/MorYZ99SqKI\nTNhqKJMfaQ3LbbLii5hr7NULtqhyFcOXXoIP0v2lx+4wlqkLpjLlmSlcsN8FABx44IEcf/zxLFu2\njIEDB1Y/NiurnqcvAacAL4pI9Fvvj1T1wZJWTjVf5pErQgwQonwaIEcqMo2WslWR0SJQ1mKUCuNb\nbKzKhWYxK/1FyXVa4ig7Go6kaNoFgXwEyo0OhaYWy7Lvi4mzHBtHFF3DyYURNiIgRsFRcM2iJeqH\nYB+0rGJYHHdsAqFZxZCSRBBecBBZpBUTECvLspx1IwPSIS3ZJgnFaftZluW2KGndjY8nCbNxC3S1\nwJnsM9lv0rKcdg1tBdVyluX2jrnnqUfCcu+ttqDp8cV8iA+0hHLbd9991ykod7ZeeslYgQ85BG69\nFTprxe3aWpgxw7hijBgB990Hw4dXOOiww+DFF9n7vPNYOE/45rf/w57X78mtx97K7lvuXvGcfuCz\n4J0FRd/jRcsXceiQQxnbZzhX1u/GoAefg/nXmbeBQw+FCy4wS3737ZvZ53/dOsbUDWZt45BiWX3d\nmwxyO8c/vM0Kv9GuHH0l+0/fn1N2O4Ut+mxBXV0dBx98MA8++CCnnHJK94xtI9T777d2d7LasKWq\nj1N+RQWjqi3LMUDWuEk3AuYESBTbRIdHZtaYZRmKE/GCoMUFwy2YiXh+s+B7QsF1ivGaRcKV+URD\nRm4JCyeOhpAcpmYD3H7eMRbrIHLDCFfocynGbnZ9JYhAWQITGcMjhGUDxoEfA/sgLC/mJayTsJ0p\nC6J4zaqRqzelbhgRjEFr8CpnVU77jMq5V7QlYke1qmQBTmtbCZgrKWnRLje2tGvJOi7+Fpc2tkrW\n5TRo7png3CNhedmn76aWd7Z/8rrU7bfDuefCFVfAxImd378IXHihWTTw8MPN+ihHHlnhoP79YeZM\n+t11Fzd985vcdNbe7H3y3gzeZDBb9926JNpDQ/8GLr/kcuYumsucRXOYu3guW/fdmrFbjeQ3jGa/\nV4aSm/owOAsMiB9/vImBt+WWVV/D296ezGssNTjRCKNzP23DnWiHGhKuNkEA//iHcdMAdhq4ExN3\nn8iFf7uQG466AWgJIWdhue1qaGjgxRdfZKuttmLzcBn4lStX8sYbb3D66aczZcoUepf1J7La6FQ1\nLK5AF38AACAASURBVMf9DBLW5XJgEFp8S7lFi3URKBfB0xf8Ajhh5IpCs4m97LhS9FGOwtO1wHJo\nxRWMJblZKOQFv9kxqWAWTGlxw8BE4IhWFPTAqQEvsig7mFByuSB0C2mxfJttCM5hpA2n6G8taMi/\nWoi8i4UgHKdExnlNsypn3cMk8FJFu7am2GfSKh8pCfFZqgZi06CyrfBcabxZY8qyeichvFpATp6n\n50JyJFGt9IF0jUREu2osmzX0Yvlba1uVH3jggcyfP79LxtBe5fPwgx8Ya+9ddxkvhHWtZ56Bo482\nxtzvfpfqJg6+/z6cdRZbvz6LpSe1DuOU+5tH/dheHPLZkYxp3oYx/1jDZ//6jDnuoIOM9fiQQ2D7\n7as8YWuNGDGZZ56Z3Kp85MjJPPJI6/J1qnffhT33hGnTYMwYPm38lJ2v2Zn7T7qfPQftydKlS9l1\n1115//33yeU6J95zT1FjYyObb745//nPfxgwYECxfNWqVZx77rk8/fTT3HbbbQxbh/9YRARV7dnf\nJuuJRETpmz7JtrUiE6ufyIfUiJ9Rn9JWfRzXx6sLqKn3iyHgcnXhIiPRfpQPy72oTdQucYw4YTSN\nvBjXi7xjoDkv+AUD0VF50Se61X4sn3eKy2JHLiJRii+Znawz+2qAOVnvE4PlSsmtsl25OM3VgnJH\nXDKqVZYLQ1sTtIbS5LV0pKy94+qo1fyAjeLZ2OMsy6ubV/OJtgblDUHvvQcnnGA8D557DmJcsE61\nzz7w1FPw5S/D66/D1KlQkee22ALuu4/c53sBrReBGfAJ/Pe+naj513yzpPehh8JN5xr6dzsWfu6V\nV8yEx7//PX2J72ee8bnwQvjqV82kxi7RVluZnwOOPRaefppNPvc5Ljn4Es6bcx5PnP4EgwYNYsiQ\nITz55JMceOCBXTSojUNPPPEEu+66awkoA/Tp04cZM2bw5z//mcMOO4yLLrqIb37zmzaedU+QW6Vl\nuRjdIYzGoKGFWaHFDSOSlBxqiiLLtCnU0FJdjIcc91kugNNMaE0W039kAVdjnlV1woVGWiYGiqPG\nihz5KPtCUGiJhlFiWRaMz3I0SMGsHlhQ48NcAN8PTP/52IIm+Rj45o0VXAqYyYLh6n9RTOkg9BaR\nILRjFP89RVbLLAtz/OYlrcppdZUAuC37yQ8u8XmmqprnRBrktteanGyXZh2vZoyRVTlt216wt+q8\nlTA2ED341Ez6NXX3KNquJ54whslDDoH77+86UI607bbw+OMm2MOYMfDJJ1UcJAI16Y7U9U0ONZde\nBh9+CPPmmaUG99ijQ6D83HOGRUeNMgbpm28+nO22+3FJm+22u5ArrjiMfB4OPhj23tvA/7Jl6X12\nqvbf3/i2HHssrF3LpGGTaPabueWftwBmgZIHHnigCwaycWnevHkcfvjhmfUnn3wyTz31FDNmzODo\no4/mo48+6sLRWXWLwkVByiendF9iqbhPyxbKMESLW4ZCSySMZDSMQuhvHKZCo5BvEjN5b61JzWvC\ntNqhaZVD0yrX7Eeh40K/5WLouBgsF+HWjSb4gVurePUm5XoH1PQOqOmt5HoruV4BXi8lV6949eDV\ngVuneLXg1YTH5wQnF01GjLmOOOZkImm+yhLLR8oC5gia48lPpCC2TaZ4H1mgXK1lOQsQ0wCyLe4M\nWdCZHFM5N5J4X8k+s/5A46HhkuMt5zZT7vp7pnocLN/z+DR2GjCQbbZpwPNq2WSTbenffxt23XV3\nGhoaunt4raQKU6aYiXzXX28inlXljrcO1K+fcf/4/OeNMXjx4g50Vl9v3C06uBiLKjz8sHFrPuYY\nE8HjzTfhJz+BE08cydVXj2b06J9y4IGTGT36p1x99RGce+5Ifv1rs4DLxRcbq/l228GECXD33WYF\nxHWm884zSyZ+4xs4CL8b8zt+8NAPWNW8qui3bNU2zZ07l9GjR5dts/322/Pkk0+y/fbbM3z4cB59\n9NEuGp1Vt8hxqkgpwFwCzqQDc1EhyEgIyjEf6GIItqI/cEs0jCgiRqEpTI1CodHAcD4OyqsNKDet\ndmhe4xYjYhTC0HFBGDouioZhVgWUlmgYHmZRlFrFq1Pj3tFLqemj1PSJAXO9GmCuU7w68GrBrQ1B\nuUZwcoSwDI5nwttJHJhT3SvKgVdHQDkLmKsJHVdJlQCxWits2jFZ54grzX2imrFWAvn4Z5IFzeXG\n3nMBOa4e5bPc7Dez5UW9mZn7Pif/9kFWrDgJ+B8Attvux1x99ehWy0F3p1avhrPPhn/9y0DckCGV\nj+kq/f738H//L9x5pzGYZqlhWH/eOvrTVuXb3rMJS16oxjydriAwFvZf/tJYuX/wAzj55JLIcW3S\nihXmWmbONPf7hBOMm8Y++9Bel+lsrV5twox861vwta9xyt2nsO0m23LxQRczaNAgnnjiCbbbbrtO\nPunGqffee4+dd96ZZcuW4VW50uKcOXM4/fTTOfvss/nJT35S9XHlZH2W1x+JiPKZ9FjnpdKir7HZ\nhimIlyXqWpWV1ov4eDWKWxPg1QQmdFtNgFsbxMpb6r3alLZRm1pTLm40WinZppVlbZNlQUHwmyha\nuE0y+4Wm0v2SlHGM3xyL9dxpKfFZdUo+riyIbW++ksW3rW3jqsRGbX0hyAL6rPGUq68k67O8wemR\nv9/NjsuUaxcHrFixAjisWLd48SVMmfLT9QaWFy0yltLhw+HJJ02Y3/VJ3/iGscYecwz89rdm5cA0\n9W+so2F6a1hu7/LehQLcdhv86lcmxN2PfmQmH3bQzZl+/cwy36efDkuWwM03G1gGsz3lFDqybkyp\nevc2szP33x+GDeOyQy9j9z/szhlfPINx48Yxa9YszjvvvE462cathx56iIMPPrhNwDtmzBief/55\nTj31VA4++GD+/Oc/M3jw4HU4SqsuV1Vxlgl9loMwbnCYHAn9liXhVpuAOC3+r7TLcP3qYvg4H6Qg\n+I4iIvhR2LUIXgNBfSdcBtvBLZiJdG4e/BoxS15H1u3QCFj0FS4xEEqxzkTXEGP1LjkGECUoCAVP\nihZocUHCSBol/WPuQzHWcugzLa6Uuq60ySqZBNlyx6ZBYJrrQqU28bJyfxvlIDitrJq6SnCZ5l/c\nVlXz994eYG8PHG+c6lFuGPc8/HuOzu3GshVrgJVA6fLCL7/sct99masVd5nuvx/22w++/nUT73h9\nA+VIo0cbF4if/tSkoHXQCyaMOIJRDQe2ShNGHNGmc61da6zZO+xgAkr89rfGR/m44zoOykk1NBg3\njtdeM5bmpUuNv/ioUTB9urFCd1g77gh//CMcfzxbN9Xw3X2/ywXzLrB+y21UJX/lLG211VbMmzeP\nMWPGsOeee3Lfffetg9FZdZuqcsNwWoAv0wUjnmjNRgKt3AoSoByEMYqDYjQKKVpwi/7KjWLcLNaY\n1LTaoXm1a3yWV7ut3DBKlruO+ywLxmc5irNco3ihG4ZXr+luGEWf5bBd6IYR+Sw7OXBzLS4YZhEV\n46vc2l85K85ypLSJeOVcMbLcMtJ8liulLFULvuVSOVeGrL7jaovLSKWxRONJ+zyytuVS1nX0LPUY\nN4xAAz7743oe3u23HHPxLF5+eVPg5pI22233U7bf/mIWLIA+fcxP8HvvbdIee5iydSnfh8mTDSDf\ncYf5pX5D0AcfwFFHwTbbmLHX13de3ytWmPDKV11lgPVHPzIvEl2tpiaYNcvA8/z5MG6csTgfcgh0\n6Ff8Cy+EBQtofOBedrluN6466CpO/tLJLF26lL5lFlyxMha8rbbaiieffJIhHfBReuqpp/jKV/4/\ne2ceJ0Vx9/93dc/sLpcQgWg8AaPxvsF4gAciKnibmIgxSqLm55lEo8boE5NHjXc0xiuPt4kSFW9U\ndvFRQKPiQaIx+iSieIt4c+zuTHfV74+q7qnp6Z7p2V3YZbc/r1dZ1dXV3TXT4/LpT3/q+z2cSZMm\ncemll9LUgbcemQ2j50AIoVhnSYqRijBWmipaFgyrrrMt8HHyEjenNFnNKZycwo3tUzg5aWpl7Zfh\nuGCsMOqvE9ZKq8Flfeg4yjlwgsQkphauKo1z0QsNjVfabxcUWwV+u2P6dL/XZjzVrU6Ztzqu329z\nSkFBKghV3P8WHRlTL2opyGmU4LRqcTUyXG27nrFx2x0Zk+bhoJ6+WugdNow+oyzP++dMhiz1+NYB\nU/na15YzeHC5PLjBBmdx5ZUTeOwx+PRTePxxveDr3Xe1H3aNNWDLLeGYY7Qg+PLL2hLQVfj0U9h3\nXx1x4sUXVx2iDPD1r8P//q8WanbfXYdK7iwWL9bq7qhR+rtubi4p7t2BxkZtObn/fm2R2XFHraav\ntx784hfwyisdPPF//zcIQdNvzueyvS7jrKfO4tvf/jYtLS1dOv/eiFdeeYVBgwZ1iiiDztw5f/58\nPv74Y3bYYQdee+211MfOmDGHiRPP7tT1M6wA1KMsBwv9hOmzleaKyBjE8IXqyrIy0TB8zyjKhZKy\n7LVbUTCCBX7LXApLXdqXurSZUlhWGhemuy46lrJsNEljpRBBuutGrSznA1V5gKJhkKRxkAwV5nx/\nvS9nRcTINQWL/ERMRAwHx7HV5WBhX1DHKZNRpFGWTZzrmspyV2bxSyLK1dTk6GeOHhN3fvt7iG6n\n8VvXM8e4xX1xUUuqKctxc+9b6DPK8pmX7YP71kJ+e+U/GT58OGutdQOOM5/VV3dpavI56aQJVf3K\nhYJOwjZvnk7SMW8evP++9hQHCvQOO8C661L3grAXX9R2gu98By64oJNKZTdCKa2M33qrJrZbbFHz\nkAq88w5cdhncfrteZPeLX2hvdE/Fa6/pud5+OwwbptXm738fXnxxDn/4QzPt7TkaGz1OPnmv5N/X\n4sWw/fao3/+eCUuvYcjfhzD4y8HceOONK/fDrGK45JJLWLhwIVdffXWXnE8pxQ033MBZZ53FRRdd\nxNFHH101JvOMGXM45ZSZLFhwPpApyz0FQgjFiOXpBisTcDjMtGFU5jKF2d6OtMvU6CICP1R+Hbey\niJzS2fWCPjNO2ONylB+XV8YOoUyECqWjXDSgVelGXbumL9hnj9fHmHZek/diq7Z+eAEJby1ZQby2\nyu1iq8Bbbsa2mX7rHKrCw12N9HVmMV50uyPtOKKZdl/cuCTU+ych6XN2RNmuNqbW9eodUw29Q1nu\nE2RZKcXGvxzIXzb+FXLTPTniiKl8+eU/eecdrRh2FJ9/rn2zAYF+7jlNlG37xujROgu0jRkzSkTq\nk0883n13L266aRyHHNK5z9lT8Je/wE9/qi0L++yT7pjXX9eJRB54AH70I/jZz2CttVbsPLsSUmp7\nxm23wd13zwFmsnz5+eH+mtFW5s2DyZN5dcbNjJt+JO7NLh99+BFOd8UJXAUwYcIETjzxRA444IAu\nPe+//vUvDjvsMDbffHOuu+46Bg8eHDtu4sSzaW4+z2xlZLmnQAih2KAyEVIFlLJIcjGmHUeSi5Wk\n2m7j4zgBAQbHCYgwCMcixg4hQdbpqZW1v/w4J6e9xK4JA+c2oqNomJIzfaV25Ri9j7AtPaHJriG/\ngVc6bLcG+wTF5S7F5dp2UYg5JiDbSkKl9zYuhFvafWV3tc661pg0BDntmBWFuNcYScQ97T4Strti\nXxJ6B1leRTXM+vDam8+x3Gtlu4NP5IKrrmLgwL049NDOEWXQiUEmTNAF9N/ed97RvGfePP2G/aWX\nYJ11SgS6UJjDH/84kzffLBGpddf9lQk33DMicXQWU6bAiBFaLT/rLB0hLQkvvqjDv82Zo8e98Qas\nvvpKm2qXwXF0kpM99oD33mvm8cfPL9tfM9rKmDFw3nlsdvQZTLngu9z+l2m8+OKLjB49eiXMftXD\n8uXLefbZZ5k+fXqXn3vTTTdl3rx5/PznP2fbbbflzjvvZMyYMRXjWlv7xJ/PVRNpHjJN1ryQXEhh\nomiYdmDBkFCKsyxKXCQMrhB4IErkTxlngQyGKhCOjnwhfJBB8hBHZ+hzTK0LYe04Wln2fUXOV+SU\nyRJo3p4LF2QenEBoChKSBP7nYHFfpEhfhNfGKbcqBAlVVLA4sQgyr+M6O66j4yw7TllikpKjMziP\n/QVBJfmNs0fE2SaSiF9Sn6Kc0Nl90X1xSLIf1CLQaYS+esaISDs6x2g7rSKeBqs8r10h6BN/7e+b\ncRkHto5ArLYajz7azH/+cyb33df11xFCZ7pbf31tqQDta3711RKBnjatmaVLy4nUu+/2rLB1XYGd\nd9ZZBydPhpkz51AoNFMoaEvCSSftxcCB47jgAm1jOPVUbd0YMKC7Z9018Lz4/61aW2uE7TjmGHj2\nWX4zbRE3blDghmk3ZGQ5AXPnzmWbbbZhtdVWWyHn79evH9deey3Tp09n8uTJnHbaaZx22mmh0v/p\np/DKK124aCFD1yJt6DgZ8XAGJFlQSZSFKOcvgghRxviVlQk3F/iXBUIqhCNQQoePC0O0GYu0roUO\n+Rb2Kc3X8wopTaITJAhlFvIpHF9qYhtMIzgumsGvqeRLzvdT+B5YVB4lleWzVuG6R+npOMqhX9nO\n4idsouxS2x+c1lcceJhtslyLFEaJtY20RDnuuKQStz/pM9vni/bFjQu2RZXtamS+Wl8ceoa7oKej\nb5Dl91u4eMufsGTJEl544SX22GMc66+/cq6dy8FWW+lyzDHwn//kmD27clxbWxfHP+sBGDUKfv3r\nORx99ExaW0sPCLNn/4rVV4fzzhvHEUd0PJFIT0VjYzyJevVVn48/1gsiYyEEXH01X9t5Z44dM5ob\npt/BdZdeV9U321fR0ZBx9eKQQw5h++23Z8qUKTz++OPcdtttLFmyBvvuC+PH78Xf//4r41nO0KOQ\nyr4UEJCEBU42cU7Di+wFfmjCrETAp0UY+zgISxzWRq2u3K8VZDdv1GSjKAtHIXJSL+JrELiGLIMm\n12UZ/PImdXUYOk6SH6BwveCD6EkqH02YfRWS5Jynvc1ug848GBBlO3tf+QK/KNm1vxciX1wcMY62\nK55MIiW6rxqS9lcjxGlLEmyCW42Qxinw0eOSHgLqIfNJSPxBV5ln30OnDZFCiL2FEK8LIf4jhDgj\nYcwfzP5/CCG26ew168G7H7zOQvEV4w49lSefnE0+P5pTTuk+CTOJSDU1+St5JisHN93UXEaUAdrb\nz2eLLVqYOrX3EWWAk0/eiw02+FVZ36hRZ7H77hPYdlttOUlEv34wfTq/u+9VWj9ezp+e/NOKnewq\nipkzZ64Usgyw/vrr8+STTzJmzBg222wbRo9u5rTT4J57SunUM/QwxKWwrijRiBiiPNGGIKaOK0qX\nwMagtEorAyuDZ9Jde9FU1zoMm46xLCgYT3D7MofCUpPqeomOilFYpqNlFFodinacZU9HxFCBrBzY\nO4I4y4Ff2RDlhoGKxoGSxoFSR8KwYy33j4uGoSNhlEXDyFlWjFBddimPhhEXISKATZjtNNXRGMtJ\n0TCqRcWoJzpGR1CNoNqfmZg2Me04olzvHJPmUqskzT3pvqV5KOm96JSyLPQj5R+BPYH3geeFEA8q\npV6zxuwLfFMptaEQYgfgWmClBUa7/8GLmLzkG+SGDufPf26hoWGv0GPcHTj55L1YsKBcjdpgg7M4\n6aT6knSsKmhvj/+Jtbf3PiU9QGCnueqqc2hrC6Kt7M2kSeN49FEd5eOUU3RIwlgBbORImm69nXGH\nH8BZ157JD3b5Af3zPTQzTTfg/fff58MPP2S77bZbadfM5XJsuul/43l7kM//gDfeOJxC4TwmTRrH\npEnjEOK82ifJsBKRgmgoFSmmr+rCsyRECEboylBl25UzTCIf1gECk8xEK8KyGKi/AukpnfDEE0hf\nmQQoAuUrlC90MZn3wix8UreRQkvf1oVKlhDMwkNK0TtMOLogRnQQZcMt6oWFylhFwvlb32UpUkbJ\ntlJyrwTfkSp98pqL/etRftMk3ujM+LTKbIBAcbbrlY2+rRJ3BJ21YYwB3lBKLQQQQkwDDgDsQKX7\nA7cCKKWeE0IMEUKsoZTqgmi8tXHfm49w8rd0mInHHmtm6tQ/p3tDt4JQjUj1RvQ1JT1AQKKi2Gcf\neP55+N73YO5cHXJu6NCYE+y9N1P32I8znn+IS+ZeyK/3+O2Kn/QqgpaWFsaPH4/b1akbE6AUnH++\nzhz51FO7s8Ya8zn66KPp378fTgM4af2xGVYeZIq/L0pp6Vd7EKw6MAEHtUWkKwRKUSoVylucTzaN\nXzXaZynWUiGDzIBh8A5NpP2CwG/HpLF2EK5E5JzQ+ywcQWC7kL4II1l4bQ5+wUEWhSHgmlQHUwg9\n0Ca5Sq5BoDxZGocm18pXKPOdKfP9KUOay/sNeQ7rgCALlFIIJVA4+vuvSVyr7a+H9HaEIEeV486Q\n4Oix9aAjxDetLaQrrtU70FmyvDbwrrX9HrBDijHrACucLH/62Xu8mPuYvQ49g3/84z2WLFnMr361\nUl0gsUgiUr0RfU1JT4N119Vh5s46S8fpnjYtPtnK3tdcw/9b+36ufPxijt7ux6w3eL2VPteeiObm\nZiZOnLhSrlUowLHHwj//Cc88A9/4BsBwHnroIfKNLsXWvvuPR49GPWQ5ZJ+yvCQpzxW3vNqr6/Bi\n1ti4V+/RtrUdkExJ6CsO7B3a2qFwCgI/D147ODmB52JSUyuEI41MrFDm+sqQ5WKrg2+y+PkFHfEi\neGYIVF8hdFQO11XIvEI2yNIYFAKFEEEUDRmSelRJbdbbsmw7iBiilLC2S8q8SmUV6ExfVxX7fqUl\nzNXIcdCXljSn9Rt3VMXO/sZB58lyPaaajhzXKTz8wCWM/2oY/ddan/NOuZkRI/Zk2LAsbu3KRF9T\n0tMin4dLLoFx4+Cgg+D00+HnP6csoc2wr3+drbbbnvWf/CenDz2MaT9/pvsm3EMgpaSlpYULL7xw\nhV/r88/hkENgtdVg9uzyaC1SSZwGTVQy9ED4aSKVKCvFnlUCdTmWNJcOrVSUA1IWR3ptohJHWuLs\nHoEtIVBjVSiEl1Rls/iuGBBl8FzHCkNnrm2YqZKGqMogXbUmy167o8myp1VnbdEgjMqhbRgSNw+q\nsTRNIZQOb5cziwNlQJpVqfiltrT7rRB1SmiVWmJIePgV1SLM9WwnZRfsCrJs3+M09zt676PjiWlH\nj4mOSXpDEcwz+1vVGXSWLL8PrGttr4tWjquNWcf0VeDcc88N27vtthu77bZbpyZ332v3csjIffB9\nePTRZn72s240K/dh9CUlvV7st59OZnPYYXrh3y236PjdASYfeCBvz1+XR96/lzlP3MK43Y/qrqn2\nCMyfP59hw4ax3norVmV/802YNEmnoL/4YvAp8Ld3X2DOwtnMefkh5sx7nmJR1j5Rhu5BGmW5jCwH\nzE1a7aiybHkGKjhtElG2ByURlihRLmPkuqUihDNCmGUBfBe8vEC4EKy7E6E2ZAhTqPIKvDaBXyhX\nlW1lOaRuQYKUYNGgDHYqhNDqtZtT2j8t0aTZN2TYaktf4fiqtPAxINHC3C4BAk3StZU6DemtRobr\nSencEfJsj7V/FPUQ5QC2whwdn6Q829v1XCsN0qrafQedJcsvABsKIUYAHwCHAd+PjHkQOBGYJoT4\nNvBFkl/ZJsudxbKln/O/ufe46cDTmTFD0t4+i2OOuajLzp8hQ1dhxAjtXz79dNh2W7jrLp35EWDS\npEnsf/31XDTuOE6+/zhe3Hp/3K+tgllbuggrI2TcM8/AQd9dzmGnPsugrecw4c9zmPfes2xUHMy4\n15bz408HcsvYn7Fe7jLaCxlh7pFIS5ZVRFEOiLKMepZVeEg5p00iUvagOPUxZi6xFyjZPzRhLhFN\n6RuiXAQ/J0oh48wCPS0L24q4pU4Dfrv2KfsFU4qO9iH7Jc+ytlgIHEehcuBKiVAOQkjd7yrcnMDP\nyzDqh/RU+Rx9UMFCRF8hPFAm6Yr0tJrsABKhpys1adZLAGsR447ur0WM69mH1ZdEmuNQjfSmQT3k\nPM7uEUXcXJL29z10iiwrpTwhxInATHTcmBuVUq8JIY4z+69XSj0ihNhXCPEGsAw4utOzToGZD17O\nmKWDWX2DzbnoyJcYNmzoClejMmToKBoa4IorYOxYrWiefbbOaLj55psjpWTzXY9n8AcPcMNpe3Dc\n/7yUMo5s70NzczOnnXZal5/3y7Yvefrdp/nTzDnM+Occ3GP/wfONmzDub6tx2py32en/BjPkkClw\nxuHaaC4EXHJ5l88jQxdBpkwYI70SYVYJhFlG/cpBLazaJmRJNgwi++LGxZBlAj+vRZYDC0YOnKLQ\nSUocodNqh6qsvm6wKFBJTWSlp3dJT5QW9RWFDkVXNNE0Igv8HCvniBDSRMoQuEWBbAiOp4wwh8p3\nWAxhdvQY4amQbwZEOUzeIoPPUIv4ptkX7bPPXYsgp+mz75VNmOMU4mq/DbuPmP5q46udu5rNo9rc\n6plX74cohXrpXgghVFfO5Qenb8i3v7YFe3/3Xrbc8iJ++MP3ueaaP3TZ+TNkWFFYsECHlxs5Em68\nEc466wTWW289Jh6+BxOv3ZnXB/2Sr/3yN909zZWOpUuX8o1vfIOPPvqIAZ1M97h42WLmvjOXOW/P\nYc7bc/j3p/9mDX8MS54fzZVbexzw1Dz6/+NfcPDBcPjh2lweib6x+tBBLG9vBaB9mY9Sqm/+K9LD\nIIRQrPNBipGWDaOMMHsJ/X6JXFf0m+NCltmZQtm2k1Nh7ONcY6ntBtv9MIlHgqIqtt1GyPfTsZNz\nTZruBCHnlC/M9O1ahOmu9ddhxnmE40MV2uyXHvhFyuqydlFbye06aWxQJ5PiWnWtffUQ4XrIcu37\nmW6sDVFnnXZfR7eT+pIwtlf8beyVGfyK7a3McBdw4f63ccV1MGxYM/vs89PunlaGDKmwwQY6Vfip\np8J228Epp0zm7rt/xxlnnMFBWx3Gb+66lCtmjYU99+zuqa5UzJ49m9GjR1cQ5aN+ehQLv1hYqroh\n/QAAIABJREFUMX7EkBHccsUtALz31XshMZ7z9hw+WPIBO6+3M2PXG8sV4y7llRM/ZLMX7mKcug6n\naSKcfKqO89fYmDifzz5dErazLIs9DHXZMCJh46RlvajwLFMpGlbYMVJct+b+oMjSVIPpGW7ueCBd\noUmnA35gv7BUQh3BTYQuk5whpULo/tLHFpQW3Nk2DMABR+ksgkIIlKtwJKicdYwUZrFhadGhb7Yd\n12wbD7UvACFKNFNhUoJTSgMefo4k0ttREh2nLFfbTjM2iqi6XI8IWEvdjY5NUoRrvd2oNfe47b79\nN65XkuXZM65mw9Z+rD5qR26+eTltbfM6vVgwQ4aViaYmuPpq+Otf4YQTdmPZssP49NPP+O/Jl7Pp\ngoc49qTvsenMl6APWYuSsvYt/GIhs0fOruj/8OUPOer+o5jz9hyWFJYwbv1xjFtvHMdtdxxbDt0U\n93+foPDHO2iffhEDh4xh00um4Hzvdh3+IsOqjbQ2jLLFfXac5STibB8LJfsFJC/wS0NmwhNaxTBW\n+/IhYdZKrnANOTXTKD20ifKP4RMqw27RkFJzGWVdzs7JYqfQxg2OUZVjTPGLAr9gonMUwCkInBz4\nrjCROURIlEtk3ibpev4lohx8p2kIcj2Eul5SXKsdd+86i2qENon4dqVLIA2x7lvolWT5vnm3cuDQ\nXbjrLhg5ci79+m3DoEGDuntaGTLUjcMOg2226cf22+/G5MmP0dx8OGfv8Rt+6l/NzEMPQcx9qqr6\n2ZvQ3NzMHXfckXr8522fs+M6O3LGzmew8bCN9Z/8Z5+FC26Cu+6ifa2RXPbRFJYeeQm/vX4Ncr3y\nr2EfRao4y1gEuQOJSWJJll6qVn6RWmSm+ut6HTpOmDjLRg32FNIRJaXWmks4baMQ64WAJaLsNujj\nRGQ+QpS2w31G5Q229aWstpmzAJPKG71YMCfwcoYwuwLhGMIcpA0PrmKp2jIYFxJq+ztNIsH1EGab\nLFNHO83+mLcBqZD0m4gS1Oh20u8q+iBWjVjHXSOqVkf7+i5x7nWrhKTvcb/8Fwft/VOuvhrWWaeZ\nCd2Z3zpDhk5io43gggsms3jxw2y/PezSdDzvD83z4GZ5OPnk7p7eSsHbb7/NZ599xtZbb12xb+Hr\nr8ce0/9Th+O2P45NPpaIs8+GUaNg6lRYYw1evu5vjPr4WQb+8iQuuDEjyr0OdtzkxGL5j2sSZZsw\n28UmdTa5i/ZBPNGo8HNELwCYKBZBBj9r+n6YmMSQ1HYdEs5rd3Td6ujkI8sdisscCktdCktdiksd\nistdimEGv2hSEhHOWIggzrLCyUvcBkWuUZJrkuT7+zQM8GkYaOoBPg39ffL9ffL9JPl+elyuSZJr\nVLiNJlV23kTuyGmbhnCFjuLhAEIYhTwNOU4qbo120v60JTqHOHJfK1wdVfrTIE7JrvztaPIurXbc\nmLhCTE3Cdu9HryPLL8y8mdX8HEvYh8WLYcGClhUeaipDhhWNgw6axOefz+Ssszz2npBnb67g51t9\nSNtTT8JNN3X39FY4WlpamDBhAk5MFBCvfXn8QV98AVtvDRMn6lR8994L//oX9212NuOP3YBrr+0z\nzxp9DzajDEst8mwnIolJRlLGSyxSk0iakxTKOCQT5cDrUJbsw/54AVEuCLx2QsJcbNMZ+oqGMBeW\nuRSXuRSWmrZJd+23a5ItY0LHQZDcBNycJrq5BkmuUZLv55PvZ5HlgT4NAyT5/qbEEeUGXZy8PlcZ\nYXYCZTmOcFYjqdVIspvQTkOi05LmNMQ5DVHG6icyphbSEuB6iHEcIe57JDlAr9NT7pv7Pxw0aAzX\nXguHH/4h1177Httvv313TytDhk5h7bXXZv3112fUqGeYPXss3/nOBIqTtuLi/xrFf514hiaF227b\n3dNcYWhubmbSpEkV/VJJPhmQQJalhCuv1PH4HAel4PLL4fe/h8ce04snM/RSpMrghybFWOZeFGVm\nXyKkOTQQU0mQlW3DiBKi6OvtsklYdZwqWLq8lAJhwq8R2C+U0N5fJXCNTcPxBI4JBefktC3Czeva\nyQlDUqVWi01SEZXT5BWla+UEyjJhBr9gvJPTxziu6csp/HaBk3P0+V2BcBxEUCONtcIp2UkkuMGC\nQ6MuCyHAEQk2jCRVOW1fnA2jK+rg3gX2CyeyHR0bt13LIhEd2xGktVHUsmP0TfQusqwU97XN5+pd\nbuXQK+G882axxx574EZCPmXIsCpi0qRJPPzww1x00VjmzYMfnHIZv/3HDuxz5vmMPuQQeOEFGDq0\nu6fZ5fB9n1mzZnHFFVdU7Lvk6UtwpWDcLSAi/4Z80bQ67LorAJ6nVeSnnoK//a1PrYvsm0gVDQNK\nRNmQm8B+YZNk7JoY54RN6qS1rax2lCjHeUujKp+1HUzPeJCxo68EUzMk1PFN8QJiLBCuwA+IbE5o\nspsXuHmJm1coKXHDCBgC5QBKhemuhWtIdV7h5qRRhqWxVOhtPy/MOIEQDjiECw6Vckqxon1hshAK\nZE7p+RS1jxonyYIRR5zTWjKiY+x70JnabgepVaKkOa4dPUccUU4ixNWIcq19tch4NXLct4ky9DIb\nxmtP3sPSBnjpX4ex337w7LOZXzlD78HkyZN5+OGHARgwAO69YQMmDj+GsS88zaubHAJTpoCfliSs\nOnjhhRdYe+21WWuttcr6570/j8ufvZxjxbeYvRCefLu8HLjmxgB89ZVOK/7mm5osZ0S5DyCtZzm0\nX1h1UgY/BZXh4wJFuZoFw0bHXqmXPMuU0khbMYv9IBOfZcPw2kRowSgud40VQ/uWi8aGEXqWTTa/\n4CsJra0o7Vl2AjW55FnO99Oe5Xx/SeOAkme5zIbRT5Jv0raNnGXDcPPgBDYMVyvLTmjDcCzCnIYM\np/Evp7VkVLNhiEgd1x9tV7PlJLWTfidJbyWSHrLstxNx7YQHs/gnwhrz6P3oVcryfY//kQMatuT6\n611uv11x8MGz+M1vftPd08qQoUswevRoPvnkE9566y1GjhwJwLTjz+KbhY2Z/MBfeeytFxh1zm9p\n3nk8f/hDM+3tORobPU4+eS8mTRrXzbPvOOJSXH/V/hXfn/59rtnwp7wy778Sj333XZg8GXbcEa66\nCvL5FT3bDD0CqUPHWSSiQkWO2xccB5VKHJT0p6iqnGTHSOEnVQqUowVvocyMRJjJ2pECZTy/0nU0\n6XQdTTxjtx1DeEF5gC9BCQTCpLDWWf+0yozJ1qdtF+HivkZJrskvtRslTt4xmQQ1wdbRNfT3oaSA\ncIGiMhn+hM5AaBFmEVgwREdIsUCT3VoE275fdjuuL+1++36WEniXK8rVzmP/LuJ+J1FUI7DV2tXs\nH/acom9Bqo3vG+g9ZFkp7v/yOY4YcTnPrAYDBvyTAQMGMGrUqO6eWYYMXQLHcdh3332ZMWMGJ554\nIgCDGgdx6d4XcsXgn/P75gdY7XcjeSd3De3eZgC0A3+ccxv37rQpNz7+WDfOvuNobm7mnHPOKes7\n4ZET2HPAFhxyzO95Zdw4zo1R1D8dNIKddoJTTtEJXrK8Ib0HQggXeAF4Tym1X8WAtDYMFUNMY9v2\nMXY7ST2upTBHT2T32SqgNAKv0teSShNl0Ek8JNpb7Afh2TAh5YxXOKiFU7btNqgw+AdobqrTWpfS\nXSvDi4QwNoycsV40yFI0jCZJrp9Pvkl7lwOiXP71CpQvtXDvCVxPIYtKJywxRNmxwsaVq8pJJWlx\nXdoFefa9IqEvbjtJ+Y0jyNE6emwaglyNMEP8DzOpr5b1Itofd52++0e015Dl9+bNYsHAIs2zf8wJ\nJ0BLS2bByND7MGnSJG644YaQLANM2XIK17xwDTucM5NHHxnCXe2LgNmlg9rg4Pmr5h+5r776ir//\n/e+MHTs27Lv9H7fz4oKneOHypXDrbZy7zz4Vxz30EPzoR3DddTpjdYZeh1OAfwHxAfTTZvADixSb\nPmUTjJht69CQPJTxjXpsGfZckoqZo1QoREnsdkDI0qK4kGga369uG6IsnLK22xg8AJR8yY7jIHOq\nFDou2O9gbBjGq9wgcQMbRj8/tGM4riJYOFCeREUgPWHUZIVbVPgN4BYVbg78XKAql5TlyogYHfEq\n16ssx22n2Rco6NWIsaixL0qYg/PGIUqKqxHmuDFR1LqePabvoteQ5fsf/T0T/G/R8nQDd02Dgw9u\n4bjjjuvuaWXI0KXYa6+9OProo1m6dCkDBw4EwBEOV+59JQdOO5BtVmuAxZXHLV0quOACWHfdUlln\nnZ6fz+SJJ55gxx13pF+/fgC88dkb/HzGycy6XdD/pjtg770BmDFjTmg9WbTIY9GivXjssXGMGdOd\ns8+wIiCEWAfYFzgf+HnsoLQ2DIiQ4Zg6cX/QtEmPvcCvXi9qgjXDkFaFJsygUMKoyuYSAox9wSyu\nwxBkUwSmNqw050kEgV0CHFfqiBlFK3Rc8AmEvcBP6tBxTT75Jk2UtU85IMtmymHEC4GU0vihNWEO\niLIfxFp2RURdTlKSO+pXjiPLAaqR4bTbcdYLSCbPcSQ5TlmupSrbqPYbTnuOjBBXQ68hy/ctnsOG\n/lkceSQ4ThtPP/0006ZN6+5pZcjQpVhttdXYYYcdmDVrFgceeGDYP2btMUz85kSe2mE6PFx5XC6n\n+OorHTLt3Xd1+eADGDJEL3izSXRQ1lsPvvENSBtMxiasXeWVtlNcF/wC379lP/7rcY+trrhHx082\n1z3llJksWHB+eNz66/+KxYsBVl2vdoZE/B74BZCclzy1DSP8T7SzynaA6Ot0IIyIENT2uA4QZVOU\nEiFp184PFTmjIAzNFkcyRfkiNlnURwaqsptz8PMKv0Ev8ivFWQ7sGYENQ2lV2SjLYSKSgR5uzjUH\nuWa+Isz1Ij0H6St8T5ErKPwCuDlwDGEWFlHW6nJnlOSkRXqBnznJjtDZvig5tttJZDmJMEN10hxH\nhmu14x5A0iIj0r2CLH/2yjyeH7Kcf958MnOfhKeffprNN9+cIUOGdPfUMmTocgRRMWyyDPC78b9j\n5HO38+9nYKNPy4/ZYIOvceGF5X1SwqJF8M47JQL97rvw3HOlvk8+gTXXLCfQUVI9fDg88kglYV2w\n4FcANQmzUtDWBsuXQ2tref3AA82ceea93H033PXyUQx/ewHf2PAhzn9hIq1z9Zi7727mvffOLzvn\n22+fz1VXnbNKL2zMUAkhxGTgY6XUfCHEbokD1W3WxlZAZeZH66xUf+WdhrxUO3e0jhIWFVPb14My\n0qhKbWX7d8v809VsHzoLoPKDxXYx+Vs88ItBreM1y6LOFCgLAr9BlCJwNAj8gqPHeTqxiTSJEZFm\nXqHlQ5WT75zEzQtyeYFsEPiNhqx7gK/19NLXIaxnG4GK+MtLY4Nt+zgRHld5b5LuWVehGilOItJd\ndd24B7a468Sp+Ulja2G+Kb0LvYIsP/zAJeywZARi84FstBHceGPl6vkMGXoLJk+ezMUXX4yUsiyj\n3ZoD12TIzH7suMFSthhYfswXXyzQrNRa5eY4Wjn+xjdghx3ir1UoaAU6INLvvAOvvw4tLaW+ZctA\niGZaW8sJ64IF5/OjH53D9tuPiyXCra26tLVpO0i/ftC/f6kWYgGffLKMRx/dgtUbL+Nvo/7KT778\nK08PnUi/ZXrM174GTU3xf8ba2rL46r0QOwH7CyH2BZqA1YQQtymljiwfNrWOU1Z7hZ2k6iX1xxHd\nakS51thAIU+zaK0WuQnmp1fvBemzwwgVAXH2MMRY4BUEbkHgtZv4zHkHxwmy+tmeavDaRRiOzm9z\n8ArCEOiAOINQlELRuRI3p2M95xpFmHlcKBXaP5RyzVxLtTJh/HQ4PTQZDmsZqvBBuL3AQF35EsF+\nEIr2R+9H3L64/noeomzCDPH3Ls6WEdRJbRL67Gt0JTmOYhtTAtzcyfP1DPQKsnzfe7NQ7x7LCcfr\n7ZaWFv7whz9076QyZFhB+OY3v8mgQYOYP38+20XS0DXk+/PRPkvt5X0ArH97K/zwh3D99ZqNpkRD\nA4wYoUsSli+H3XbL8fzzlftWX93lJz+pJML9+pXaTU2auEdx3XUtPPPMXlxyxANs03w6t337QsZf\ndmjFuOZmjzfeqDy+qan3xZzu61BKnQWcBSCE2BU4rZIoQ7p/2up5fZ2GQEePt1Hr9XeUpESJS5wV\nQRBPmKPzskhyeK4IYQ6VZWUUY22R8HMCzyQ10dE0TLQL61LK2C38gonr3OaGsZv9gjAptI21gxIR\ndl2FzElyeaAR7ceWCoEm5K7r6LkpU0vXzNcthcC2M5NLk8lQStMupQgPvorKOxNVXpP2xyH6xiGp\ntserhDrYH1g37PHVjk1DkquR5bi+Wv19E6s8WV7+xms8vvqXDJl1KpMnw+LFi3nzzTfZIUkqy5Ch\nFyCwYkTJ8siNN+EdPq4YP2LHHXUau7Fj4d57uzQzh1Z44xdUrbeez+TJHTtvc3MzB2+8MUffcRhH\njj2M8Yf8InbcySfvxYIFvyqzgGywwVmcdNLeHbtwhlUJCWwmzVuFKMGIFqhOjKP7apHkJGU57piA\nNNnEKeiPq6MkJ5iPTaqCPm1IVkoaEgrStwmztmA4BR0H2ctrsqzjNWvSjCAMERe4IfyCwGvXSU68\ndm3RCBb2KV+E0wiVZUfi5kDlg4+qEErhCIVryLLO9OciwwzkSreD3DFBtA1fWAsKRUkxN59bSeJv\nZdV7Z9+PasfE/W6SzpdElKOkOQ1RjiPMcSS51luO6HYtpbtvYpUnyzOnX8yGn6/JwUd/nVwOZs2a\nxa677ko+yz6QoRdj8uTJnH766fz6179Od4Drwm1/gcsv156LadPCVNBdga4mrMVikf9tbmbbxTP5\n5KBR/PaHtyaODXzJV111Dm1tLk1NPiedtHfmV+7lUErNhoqXKAZpyXKaUu34NH0BokTZXggW3Z/0\nij7JduEQT26i89LXDO0JMmLFCIhyDpwieAVjv3AcPEeZmM2lc5aFhzMeZq/dwW+3fMzFErkNvBDa\nt4z2LTdoaVgoB4EyqrLEzTuGxFs2EelqUu+XCHLQ1sVBBJ8FhaN0LWwPc92odWT0d1JrfJQoE2lH\nF4dWI8pJ5LiWgt3RdnSufQerPFm+940ZyNcP5UeGM7S0tGR+5Qy9HrvssgtvvPEGH330EWuuuWa6\ng4TQ2Tm23BK++1045xw44QS6IltHVxPWeddcw5peG1fuM5Bnj3qYvFv94XfSpHEZOc5gIa1fPZr+\nN7pt2xcCxCnN1VTFKPGIhhgLiIwdOUFZY+POUaskzbXUH3h6NRG1FvcVtf3CKWg12XMFYVY9c+pS\nHGWtGktfoDwRLgb0A7+ysWGEKbQxoeochXIhl5MIkz3QETopip+TyLwgVxDlXmorS7nvC2thYoko\n+55E+mauBETZTL/Kt5H0HdU3ttbDlY3oPYr7G5yWKKcl0NE3D3FvI9Ls65tYpcly8b23eWToJ4xb\n91TWXBOUUjQ3N3PmmWd299QyZFihyOfzTJgwgUceeYSpU2svZir4hdLGhAnwzDNw4IHw0ktwzTXa\nONxJdBlhnTWLh8/+JYt3HMAfJl/NBqtv0PlzZuhjSEuWA2IRkGRhtaNpiqGSjBDZV+31u11Ho15E\nCbOyxiSpzNHzVlP/IqTJSMKBqmxHxvA9rSr7Jv20MGRZmDjO4JSyf0tKZDkgrkEplrbD2M3KzFTo\niBjk9LwdoTMPuq5A5gwRbhD4nraI+EVNjH1D6B1zXt8TSFfiewLhSXQs6WByWvkWjjJfa71vCbpi\nbBpUI6H1EGR7bmnJcnQO9dZ9B6s0WZ5992Ws/uXXOPV4/Y/p66+/juu6bLjhht08swwZVjwmT57M\n/fffX0aWRwwZAW+VxiilePvLt3ml9RXe/PxNRn1tlN4xapQmzEcfre0Y06frLCXdjeZmOOIIbvx6\nI9vtPpopW07p7hllWCVRD1mWVm3bFaJZ2YLxaQhzLdIcwCbEUR9q9DxJZLgWgYmfpypb4Bd4lktW\nDO1PVqX4x4HKHSycU4Giq/A9ofmpFTZOBQQ6DCOHFQ0DnbVPKRwhUA5IF1ROhMcGxF0Wwfd02Drf\nhLJzihLf9bUS7UiEEPgi8Hg7KKVTHCqpdKbDRKKcxmKRZn8tG0+95NL+fdVDkGvts89frV3P76tv\nYJUmy9P+fi/DP9uHnXfW283NOmSc6ILXyhky9HTss88+nHTSSbS3t9NoUvHdcsUtsWOvef4axt48\nlkcOf4St1txKdw4YAH/9K1x0kfYx//WvsMsuK2n2MZg5E37wA2669Ed8cuxF3PHTO7pvLhlWcaT1\nLAeKrLT6AkSTTNjjk6wYUVR7vR5HqpL6ks5V61pRwqX7VKC8ShkumgttDkXwHUOUhUmjjQ7PpgwR\nVdIQUU8gPRkmOSFciFdqh31KXzvInRJq4a4qHeOHojf44BU1cS8VoSN0uAKnqIkyQhqLiPVGQDko\npRB+KUth5ddTL4Gu1l+PBSNA0v2s9kAWR4bTEOSk31C1txHV9vU9dJgsCyFWB/4KrA8sBL6rlPoi\nZtxC4Ct0wMiiUqpLEtCqjz/m0WEfcNzWp4aWy5aWFo48MiaKUIYMvRDDhw9ns802Y/bs2TV9+seP\nPp5h/Ycx4fYJ3PPdexi3vrFLCAFnnglbbQUHHwy//S385CcrYfYRPPYYHHkkC++8lp/dMpUdd96R\nYasNW/nzyNBLUI9nWVgl6k+O7q9FXNPYMOIJbPyr8yT1Ogm1CF2wGRNn2VP4QbI/hzLRSZNkE0HD\nd4wCbTLyFQV+wRBSEwO59BG0ZxhDlEs2DFlKtKdK/frY0jm8gibJXoEwbrNXEDiuJsylzH8mpbeS\nYag5Ryqko/TnEWnoXtrvOu5BKeF7jkU1AhslyEnkOK6d1Jd0rbg51eqr1t+70Rll+UygRSl1sRDi\nDLMdZxZWwG5Kqc86ca0KPH7TlYjCQH5+jA5+XSgUmDt3LrfeemtXXiZDhh6NyZMnM2PGjFSLWr+7\n2XcZ2m8oh951KH/a708cuLGVAXCffeDpp0s+5quu0plCVgYeeQSOOgrvvulM+b8z2fjLjfnOft9Z\nOdfO0EtRjw2j1j/+tqJsk+Yky0QtNTCuL+7YuHatvvTHBhExSp5lEGYBnXCCdCh6fioQbKUT+ptD\n20ZR4RaNgguhZ1i3zRmCfWZ/YIvQxxiiTel4k6sPt6CJspPTUTl8s+iw6Ji4z0IiKMnXOimJ/jyO\nryNuSM+KDR37/XR2u9a9s5HmgStuXNq2fc5a86mH9PZNgmyjnuTgUewPBMz0VuDAKmO7/Ju+54Vp\nbNm+OwNNprJnnnmGjTbaiKFDh3b1pTJk6LGYNGkSDz30kEn9WhvjR43n0SmPcvyM47nhpRvKd264\nITz7rM5xvfvuOnXfisaMGXDUUfDgg/y20EL/XH8WvbyIiRMnrvhrZ+jFcFOWIKmH3Y4m+qiW9COK\nqCpot6PFvpZr1UHJ1ZhzNNYyMXWcvaPkiwjiLGtvccmvHFoeCjp+st8uKLYJim06Q19xuUthuUNh\nmUNhqUv7UpfCMreUwc8kJIlm8NOEOAgdJ026a0muwSffKGno59HQz6dxgE/TQI/GAR6N/X0a+/s0\n9PPJ9/PI9/PJN0lyjT65RonboM/hNkicnMLJmdotZRqs7sysRymOs8xEv+ckVPMBJ/0+or+VNO1a\n+6plfkwqGTqjLK+hlFpk2ouANRLGKWCWEMIHrldK/U8nrglA4eMveGLNhfz2gNKpspBxGfoittxy\nS4rFIq+//jqbbLJJqmO2W2s7Zh81m4l/nsjHyz7ml7v8svTKddAguOceuOACGDNGt7/97RUz+Yce\ngh//GB5+mNlfb+V/pv8Pd+9+N9/3v8/GG2+8Yq6ZoY+gnlTncWRAUR7aLRr7NumYqGpYz+vtaogq\n2HGKdnR8tWMJ00VLHx0xwqPk70UYMi1M0hJwzWI+WRT4eXCLCjevYzK7eU1OdZEmVrJu4+oMncpV\nYQQ6nZTEGu+W4iuH53H0+b28oGiU5SDmsxCO8VMb4mdUZekbD7ZXOoewnyVSfc9p2/Xst1HN3mC/\nsbDHxm1XU5GT9sUhndCSflzvRFWyLIRoAeKCuP7K3lBKKZG83HRnpdSHQojhQIsQ4nWl1Ny4geee\ne27Y3m233dhtt91iT3jvedfzWb8GvrNnaX9zczMXX3xx8ofJkKEXQggRZvNLS5YBNhy6IU9NfYq9\n/7w3i5Yu4vd7/x5HGHLgOHD22bD11rD//po4//jHXTvxBx+EY46Bhx/ms8034AfXbc2N+9/I32f+\nfZVYpPvkk0/y5JNPdvc0MiSiK8hyUKdR2uIUyOi4WttJY+LIblI86DiVtLLoBX6U0kVLtL3CXF6H\nhhPhwjzHqM+OJ5AmYYnMg5/DqLng5pRWik1b5SRuTugoGHlVEjhRYeg4PV7iGkU4aLs5Q5pz2oKh\nU22X/MmhOqokUsrSQkVPW0ScnER4migHto94itJZ20uato1a1om4cVCdNEe3o+er9bnjPM71juv9\nEGlf31YcKMTraC/yR0KIbwBPKKWqykFCiF8DS5VSl8XsU2nnctzETfl0m7W458JZAHz22WeMGDGC\nxYsXh1EBMmToK5gxYwYXX3wxs2fPrvvYL9q+YP8792ed1dbhlgNvocFtKB/wf/8HBxwAe+wBV1wB\nDQ3xJ6oHDzwAxx4LM2agttuOQ+46hPUHr8/v9/49++23H0cccQSHHXZY56+zEiGEQCnVsxl+H4EW\nbj5MOdqPFBnTV60/ui9YEAjlpCXJJpFmLJTHfo6S46Q6eZ9wTJa+HCaTnlVX9AlEinFuXpLLB7YK\nTXzLtu39qWpFoTVPsS2v60i70Naga9MftlvzFNrM2OUNel9bnsLyPF4hR/2kuB7CHLfdk/pqWU46\nsq8WxvaKv42d8Sw/CPzQtH8I3B8dIIToL4QYZNoDgL2AVzpxTV59bikvrvd//Pi7J4SovwV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inb19LSwj333NNNM8uQoWdi4cKFvPnmmwB89NFHK+w6jnC4dK9LWeNva7DzTTsz89KZfGvYt8L9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\nE3379qV79+7JZbqj9Ftbdu/ezfjx4+nVq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ZuY0MMtdIFpK/O2nlCOaeU2e7Bs/cqCbLTZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Take a subset of the data just for illustrative purposes\n", "XX = copy.copy(X[0:500,:])\n", "yy = copy.copy(y[0:500])\n", "\n", "#----------------------------------------------------------------------------------------\n", "# Fitting using the full prior Hessian. Note that the full posterior Hessian is returned\n", "w_posterior, H_posterior = bl.fit_bayes_logistic(yy, XX, w_prior, H_prior)\n", "\n", "print 'Shape of full Hessian', np.shape(H_posterior)\n", "\n", "#----------------------------------------------------------------------------------------\n", "# Fitting using a diagonal approximation. Note here we store the diagonal as a vector and do not\n", "# need to supply a full matrix. Note that only the diagonal of the posterior Hessian is returned.\n", "\n", "H_prior_diag = np.diag(H_prior)\n", "w_posterior_diag, H_posterior_diag = bl.fit_bayes_logistic(yy, XX, w_prior, H_prior_diag)\n", "\n", "print 'Shape of diagonal Hessian', np.shape(H_posterior_diag)\n", "\n", "#----------------------------------------------------------------------------------------\n", "# plot various results\n", "\n", "# plot the posterior parameters and compare to the true parameters\n", "plt.figure(figsize = (12,9))\n", "plt.subplot(221)\n", "plt.plot(w_true,'bo-',label = 'true value')\n", "plt.plot(w_posterior,'rs-', label = 'posterior using full Hessian')\n", "plt.plot(w_posterior_diag,'gs-', label = 'posterior using diagonal Hessian')\n", "plt.plot(w_prior,'ks-', label = 'prior')\n", "plt.ylim([-2.5,1.25])\n", "plt.legend(loc = 'lower right')\n", "plt.title('Posterior Parameters')\n", "\n", "# plot the posterior Hessian\n", "plt.subplot(222)\n", "plt.imshow(H_posterior)\n", "plt.title('Posterior full Hessian')\n", "\n", "# compare the diagonal elements of the full posterior Hessian with the diagonal posterior Hessian\n", "# any differences in fit come from the full Hessian's off diagonal elements\n", "plt.subplot(426)\n", "plt.plot(np.diag(H_posterior),'ro-', label = 'Full')\n", "plt.plot(H_posterior_diag,'go-',label = 'Diag. Approx')\n", "plt.title('Diagonal Elements of Hessian')\n", "plt.legend(loc = 'upper right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2) Moderated Probability\n", "\n", "For a given set of fitted parameters, the MAP estimate of the logistic regression probability can be obtained using the function bl.logistic_prob. However, this only takes into account the MAP estimate of the parameters. We also have information about the uncertainty in the parameters (that is the full distribution, not just the mode) which can give a more accurate estimate of the probability. The full Bayesian estimate is given with bl.bayes_logistic_prob and requires the Hessian as input." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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q7lU+AYqIiEhSaYCkSDlZtCgYFPnZZ9C2hGmvt2zdwo2Tb+SJGU8w4uQR9Nmn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\nNKvdLCNOYY8YAd9/D2PGRB2JiBSyoPI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Do a one dimensional example (a single feature) to demonstrate how the logistic probability\n", "# is moderated when uncertainty (the full distribution / the Hessian) is taken into account\n", "\n", "# create the inputs\n", "# note, the inputs need to have dimension !!!\n", "Xlin = np.atleast_2d(np.linspace(-5,5)).T # X needs to be 2 dimensional\n", "wlin = np.atleast_1d(1.) # the prior parameter needs to be one dimensional\n", "Hlin = np.atleast_1d(1.) # the prior Hessian needs to be at least one dimensional\n", "\n", "#-------------------------------------------------------------------------------------------\n", "# get the logistic and moderated logistic probabilities\n", "prob_lin = bl.logistic_prob(Xlin,wlin)\n", "bayes_prob_lin = bl.bayes_logistic_prob(Xlin,wlin,Hlin)\n", "\n", "#-------------------------------------------------------------------------------------------\n", "# plot this example\n", "plt.figure(figsize=(12,9))\n", "\n", "plt.subplot(221)\n", "plt.plot(Xlin,prob_lin,label = 'MAP Prob')\n", "plt.plot(Xlin,bayes_prob_lin,label = 'Moderated Prob')\n", "plt.xlabel('X')\n", "plt.ylabel('Probability')\n", "plt.title('1D Example of Moderated Probability')\n", "plt.legend(loc = 'lower right')\n", "\n", "#-------------------------------------------------------------------------------------------\n", "# Now calculate the moderated probability from our above sine-wave example using the full Hessian\n", "logistic_prob = bl.logistic_prob(X,w_posterior)\n", "bayes_logistic_prob = bl.bayes_logistic_prob(X,w_posterior,H_posterior)\n", "\n", "#-------------------------------------------------------------------------------------------\n", "# plot a histogram, across the whole data set, showing the absolute value of the difference\n", "# between moderated and regular logistic probabilities\n", "plt.subplot(222)\n", "plt.hist(np.abs(bayes_logistic_prob-0.5)- np.abs(logistic_prob-0.5) ,25);\n", "plt.xlabel('Moderation')\n", "plt.ylabel('Counts')\n", "plt.title('Moderation Histogram')\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###3) Using different optimizers\n", "\n", "There are two other options for optimizers. BFGS and L-BFGS-B (which allows the imposition of bounds on the parameters)\n", "\n", "Neither of these solvers utilize Hessian information for the OPTIMIZATION. However, the prior Hessian is still part of the OBJECTIVE FUNCTION so it still needs to be supplied. You can use either the full prior Hessian or a diagonal approx. However, if using BFGS or L-BFGS-B it probably makes more sense to use a diagonal approximation.\n", "\n", "Of note, to keep BFGS and L-BFGS-B solvers stable, the gradient vector is (by default) normalized to length 1 before being supplied to scipy.optimize. (This is not done for the Newton-CG solver.)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IanXYXawjB8y1hjIOZStLlLcWfk7s3Wv4vl9+2eicTUta8d29e7dUrVxZwj08\nSmdPYxlk1iyj8/eXXzKn5VV4CzpluAVwUkQiROQOsBLolSFPT2CxSVl/AVyVUhabALtm2zb69uvH\nwQsHuXItnvH92xTrxKDu3TvwySdd6NJlCv7+wXTpMoVPPulapvy7abGzM+8Hs7fPvH5DeaBVK2P6\n8V9/QYcOkHZfzB71ezC/h+HzreBXgTeCg3ksKYnYN98sPoM1JCUZq3d+8YUxU7NFCyO+chVn7J1s\nsHfKR+dEXlQ6YwD6AfPSfB4KzM6Q53ugTZrP24FmZsoqtCdTCjEnT4ozSNSFCzJy1Rix7xqsGw8W\npry18HNLUpIx8qVqVZGNG9OnpbR8fzn7iwzu00eG29lJcnFN2SvnxMSI9Ogh0qlT5lmZdo7W+V6d\nrKD9yLldNiRjG9MiS6L98N57tKlWDUePyqz4fQV96/4PFxdL1KxJIaUlP3v2FOLjrbG3T+LFF8tu\nCz+3WFkZ63G0aQODBhnrP7zzjjGyI2W0Q4+VPVj13ipe2LuXuf368ezRo8Vtdrni/Hlj4aSmTY3W\nbrp1SGJikGTzi23lhoIKbyTgneazN3Auhzw1TXGZCA4OTj0OCAggIO2YrHyw5vvv6dujBxtPbCHx\n3/q8Nrp2gcrT5I/u3TuUe6HNinbtDNfDsGHw4IOwcqWxAE+K+D6+/nHmfD2L5x4eQtOZM2n50kvF\nbXK54LffjMWfnn3WGO6ooq7C7t3c/ukntm7axDtn/+G2mQX+c01emscZA4Zwh2N0rlUg5861Vlio\ncy32wgWpBHIpPFxaftRX7hr4ZaGWr9EUJklJIu+8Y0y33rr1v/gUt8MHE54UbxsbuXj2bPEZWU7Y\nvFnk7srn5ecxK0Wef16S7r5bwhwcZFTNmuJa0V7c61QSpz5OYuWY/4XQC9TiFZFEpdRoYCvGCIev\nROQPpdQoU/pcEflBKdVNKXUSuAXksFdt4bDtgw9oWrky1tVd2R+1nfk9v7JEtRpNvrCygsmToW1b\nw+3w5JMQHPxfy/ep75+ie11PBgYEsO3ECWzKymyTkoCIsQjzzp38MXcn9fbt5KDDFf44ch8TlWLF\nlSs41PLGoakDVj6xjO82gRceeAGPKm4kkL9O4jK7A8VwPz9atGnD5UEdmPFtKNe/WkmFCoVWvEZT\nZFy8CIMHG3rw9ddQrRp8/+f3jFwTSO13b+AfOIr3Pv20uM0svYjAiROwc2dqkMREjrh0YPHVRth2\nu8KmAzvJuQfTAAAgAElEQVS4desWnXt35qzvWQ4kHuDl1i/zwgMv4GznDBijGmIT4gBIuJWE5GEH\nijIpvLdv3KCaqytHDx6k+ernCbB6gxVvdSuUsjUaS5CUBG+/DV9+CcuWQceOhvg+OX8AtnNh9sKl\n9O3bt7jNLBEEBwYaLdaM+PkRvGiRcTN/++0/od21C5ycjPF8HTpwulYjeo77lYiIFVSocJL+/R+n\n9SOt2Ri/kR2ndmQSXHPkdeufAvl4CzNQiD7ezVOnSmtnZzl4+i9REzzl1OkCLkOm0RQT27YZft+3\n3hJJTBTZcHCFuA1T4lrJWf7444/iNq9EEOTvL2Jmlk5QrVr/LZrcsKGxy8Dy5SJnzsiNGzdkyZIl\n8uCDXcXaupLUqjVE1q//QQ5HHpaBqweKxwwPmb5rutyIv5ErG7DwBIoSyZrly+kbEMDkb5dQJ3Yw\nfj7aH6YpnTz8MBw4YOy798gj0NJrIItbvEBSm1i69XyEmzdvFreJJZfbt2HkSGO2yvHj3J41iw1O\nTgycMAFvb28WLFjF0aNP8NprkXz/v0msuLOEh5c/zH2e9xE+JpzX2r2WbSu3IJQ5V0NiQgI1HBzY\nExJCo80jmN12HaN6NSkECzWa4iMxEd5809j/7etlyVybUY/+F8/QroY/29ZvQ5XjfdqaVKuG68WL\nmeKveXpy8Px5du3axfLly1mzZg2NGzdm8ODBuLv347nnqjD+/45zuNLbhPwTkiuXQlaU+12Gd33x\nBd729myOsULdceHpHvcVt0kaTYGxsYF33zV8vo8PsOK67xKW2jgRejCUl6e+XNzmFSvXbt0iDDKF\nf6Kj8fX1ZezYsdStW5dDhw4RFhaGtfUoRr1xkXumDuLDqwEWaeFmpMy1eEc3aUKNKlWYf68f91Zv\nxLpXxxeCdRpNyeHsWRg4EN6JGMofPaJ5cfkW5iyaw6i+o4rbNMtz5w5+9vacNjOLzKVCBfYcPMjd\nd98NQHIyjHrjOCsvvE2F+iFMaJf/Fm5GynXnWlJiotSwtpYd81eKes1V/jh3vsBlajQlkdu3Rd4a\ndU6uWlWRUS+PFSsXK9m0f1Nxm2V5Xn9dfG1t001kSAm+np6p2Q6cOSbeLw0U20ke8saW3Hea5RbK\nc+fa/5Ytw83Kis8jk/CiFQ28qhe3SRpNkWBrC1O+8OLS4Jfo8dkZmrQaRO++vdlzak9xm2Y5duyA\nxYupVLeu2WS/Bg04fvk4fZYPouXnAVS+fR+Rr4bzdhfLuRSyoky5Gsa3bo2jwIzGlQjq/QSvPzqo\nkKzTaEoo8fHcqdeIsQ5zWXFrMjHqIL731Cbq3wQkWaGshJpebjSr04RFHy8qMjMCxwUScS0iU7yf\nq1/R1HvlCjRpwrYXXqDr5MmY0w67KnY4vuICe1/mqfte4P+mOhfZkrB5dTWUGeEVEWrZ2TFu1Axe\nqTSVG0GRVLStWIgWajQllLVrSX5jCqPbhfL5PA+oDDilz1Ip0Y1r56KKzISAwADCaoVlivc/5U/o\notDCrUwEevViq50dw8LCSLRNJNo2OlM2+zuOOKkLvP+OM4GBhWtCRvIqvGVmgOuB9eupkJzMnBsJ\ntKv1mBZdTfmhd2+sPvuMOfes5As7W+TqHbiaPst152v0X9W/yEw4dukY1DIfX+j1njzJv4l/sy/s\nDm0mtOHonqPG3jYZSFzenG++cKZjx8KtvlDIi0O4KANmnOOABAUFmXVmBwUFmc2vWnjItr9Cc50/\nr+Xr/Dp/Sc6vbKzMxmOjzMb3fbaffPP7N5lCv+f6mc3f7znz+d0bupvN797QvVDKzy5/w34NhWDS\nB//C0ZO85Jc86F2ZcDWICPUrVqR9h9Gsab2aqKBwrFSZ6jfUaHLmxRdxnD+H2PjMQ6usKlZgxlsJ\nnD1LuhAVBdWrg7d35uDjY/ytUoUcfaMWcTXExrKpfn1GXL/Ohm3baNWqFQD39GjC782PZMreeP99\nHP3+cOHUnQPl0tXwe1gYtxMSWGmfwFNNhmnR1ZRPpk7FZr75Vcvs7W0Zb2ZIe0ICREamF+Pjx2HL\nlv8+x8dDzZrpxThjuHr1mllXw9Wr17I0NzkZ4uIgNjZ3fxM/eYzgC5fpMSSUlStbsXChkXbiz2ho\nnrn8yMjMft+SQplo8Qb36MHpX/9kxVM3OPrSLu6qclchW6fRlA6cHGy5FZ95g1EbW2vi4xKwtrbO\nc5k3b8K5c4YInzlDplbzmTMQW+FeqFQ507m2sVE0rfWbWTG9cwccHIxQsWL2fx2PvMa3R97nscHb\n8W30YLq0MW824Tqumer2tL/Gvyd0i7fIWBMainutHtR2i9CiqynX1HWpjGv8pXRxt4HfsKJnz54s\nX74cV9fMIpUdTk7QoIERzCEC7do9xp49wZnSGt4bzKxZ5sXUzi5nFwbA+vnzeWbJDDYvWEDzwAcz\npS9f/ijbtr2TKb5Jlyk5F15MlPp38r8OHuTqrVscbBrH6A7Di9scjaZY6d2wIaGQLuwBXmrVirp1\n69KiRQuOHz9eqHUqBU5OmVvZANWrJ9GyJdx7L9Sta+wn5+YG9va5E921q1fzzPPP88MLL9A8izFh\nY8Z0pk6dyeni6tSZxIsvPpzXS7EYpb7Fu+b992np5MWW2jsY2Fhv76PRmMPayopPPvmEpk2b4u/v\nz7x58+jdu3ehlT9mTGfCwycTHj4tNc4Qv675LvO7777j+cBANjdpwv2ffJJlvtK4k3WpF97VW7Yi\nNZvxcJ1KVHbI7GPSaDT/ERgYyN13303fvn05dOgQQUFBWFkV/MW3sMVv9erVjB41is12djRdt87Y\nlC6H+kuy0GakVAtvxJ9/cubaNWyfusHUB8YUtzkaTcklLi718IEHHuDXX3+lX79+HDp0iGXLluHi\n4lLgKgpL/FatWsWLo0ezpUIFmsybBzVqFLjMkkapFt7VMz7gPvvKHKx8iq518/9Ko9GUGfz8CM4Y\nFxkJR48a+47dey8Anp6ehISE8NJLL9GyZUvWrVtH/fr1LW1tJr799lvGjh3L1nvu4b5GjeDRR4vb\npKIhL7MtijIYpuSNZq6ecn/LpjLmhzF5PlejKVesXCni4SGyc2empHnz5omHh4ds2LChGAz7jxUr\nVki1atXkyJtvitx7r0hcXLHakxfI48y1gghlZeBH4C9gG+CaRb4I4DfgELAvm/LydKGRZ86IK0o8\nptSU/ZH7836nNJryxrZthviuX58pae/eveLl5SVvvfWWJCUlWdy05cuXS/Xq1eXo+vUiVaqIHD9u\ncRsKgiWFdwbwqul4IvB/WeQ7BVTORXl5utB3RrwkbRydpOHsRpKcnJzH26TRlFN+/dXYtvirrzIl\nnT9/Xlq3bi19+vSRGzcKd6Hw7Fi2bJkhuvv3Gy3dL7+0WN2FRV6FtyDdmT2BxabjxUB2Y1MKfRXM\nNatXE9+qKk80GV6uN/rTaPJE8+YQFgZvvw3/93/G7AcT1atX56effsLd3Z1WrVrx999/F7k5y5Yt\nY8KECfz44480XrIE7roLnnqqyOstdvKi0pK+hRqd5lil/Zwh3z8Ybob9wNPZlJfrp8vpiIvihBKX\nN53l3PVz+XlAaTTlm8hIkcaNRcaNEzHjWvjiiy/Ew8NDfvjhhyIzYfHixVKjRg05duyYyPffi/j4\niERFFVl9RQl5bPFmO6pBKfUjUM1MUrppIiIiSqmsFlpoKyIXlFIewI9KqRMisstcxuDg4NTjgIAA\nAgICzBY4Y+wc6rtWoHLdVni5eGV3CRqNxhw1asDOndCzJwwfDgsWQIUKqcmjRo2icePG9O/fnxdf\nfJGJEycW6pvl4sWLmTRpEiEhITRwcTFauatXG9PaSgGhoaGEhobmv4C8qLSkb6GeAKqZjqsDJ3Jx\nThAwPou0XD9d7rarK426ecjSI0vz+FzSaDTpiI0V6dFDpEsXkZs3MyWfO3dOWrRoIY8//rjExMQU\nSpULFiwQLy8vOXHihNHa7tRJJIt1b0sLWNDHuwF4wnT8BLAuYwalVEWllLPp2BHoDBwtQJ3s2HGN\nUwn/ENkslj4N+hSkKI1G4+AA331ntIA7dYKr6beu8PLyIiwsDCcnJ9q0acM///xToOoWLFjAlClT\nCAkJMcYNv/++sTblG28UqNxSR15UWtK3UCsD28kwnAyoAWwyHdcGDpvC78Dr2ZSXqydLtwc+lIZV\nrOWJ74YX6Aml0WjSkJwsMnGiSMOGImfOmElOlk8//VSqVq0q27Zty1cV8+bNk5o1a8qff/5pRPzy\nizG87fTpglheIsBSw8kKO+RGeK9cEbnLqrF4d3eUkH9C8nWDNBpNNnz4oYi3t8ixY2aTQ0NDpVq1\navL+++/naRjn3LlzxdvbW/766y8j4vp1kdq1RVatKgyri50yLbzTpsWIg5WVeE2pIknJlh/krdGU\nC5YsEfH0FNmzx2zy6dOnpVmzZjJo0CC5detWjsV98cUX4uPjI3///fd/kUOHijz9dGFZXOzkVXhL\nzXq8ycmwYOYKqlYRnmg3Um/vo9EUFcOGwcKFxoiHzZszJfv4+LBr1y5sbGxo27YtERERWRb1+eef\n8+6777Jjxw7q1q1rRC5dCgcOwMcfF9EFlALyotJFGcihxbt5s0ijis2kUjcb+ePyH/l+Mmk0mlyy\nZ4/R8l1qfvRQcnKyfPzxx+Lp6SkhIZldf5999pn4+vpKeHj4f5F//y3i7i5y+HBRWV0sUJjjeEsS\ns2fHEXH7MPXv96aBexZ7kGg0msKjdWvYsQO6doVLl+Dll9MlK6UYO3Ys99xzD927d8fLywsvLy+U\nUkRGRnL27Fm6d+9O7dq1jRNu34ZBg+DNN+G++4rhgkoOpUJ4IyJgX9h6nConM/LhF4rbHI2m/NCo\nEfz8M3TubIjv9OmZ9uzp2LEj9913H7/88gvh4eHp0q6mHZ42ZQpUqwajR1vC8hJNqXCUzp0LtV1n\nceN+xYDmgcVtjkZTvvD2ht27ITTUmGGWmHl/NXt7++zL+PFHWL7cmCGn11Yp+cKbkABffXWb3y/v\nw79pA9wruhe3SRpN+aNKFQgJMRZV79s33Y4WOXLpEgQGwuLF4OFRZCaWJkq88K5eDb41tmDjmsSo\nHuOL2xyNpvzi6AgbNhj7vXfuDNHROZ8jAiNGGOtBdOpU9DaWEkq88H72GVRSH5J0jxXdWwwtbnM0\nmvJNhQrGcLDmzaFDBzh/Pvv8kZFw5Qq89ZZl7CsllOjOtUOH4OzZRKKu7qHv802oYF0h55M0Gk3R\nYmUFH30E770HbdvC1q34+fllzhcTg9/vv8PWrWBra3EzSzIlWng//xwe7vQTX29OZHS/ScVtjkaj\nSUEpeO01w2fr78+i7783WsEp3LoFzZoZnWl16hSfnSUUZYz9LX6UUpLWlmvXoFYtaPdAAP+L282l\nnXf0ThMaTUlk/XqCBwyA+vX/W0/3zz+N6aaPPELwokXFap4lUEohIrkWqBLb4l28GLp2TWbDxp8Z\n9URzLboaTUmlVy9o0IDgI0cyJQVnM524PFMiO9dEYM4caN02lASHRMYNerO4TdJoNNnh6lrcFpQq\nSqTw7tgBdnawLWQq3j7W+LR5pLhN0mg0mkKjRArvZ5/Bc88JO37aw8h7HtAzXTQaTZmixAnvuXPG\nzMQadbaTYJ3ImCFTitskjUajKVRKXOfal1/CkCHw6fypNPS0xuXBLsVtkkajyQk/P4KziNdkpkQN\nJ0tIEHx9Yft2oZl/BT58sDkvrNpb3KZpNBpNtuR1OFmJcjWsXQsNG8Jfl9eRmJjIqKGvFrdJGo1G\nU+iUqBZvhw7Ciy/Cx2takvDLfn49fgtyWm5Oo9FoihmLtXiVUo8rpY4ppZKUUvdnk6+rUuqEUupv\npdTE7Mo8eRIe7ZHELzv2M6ZuMy26Go2mTFKQzrWjQB9gblYZlFLWwKfAQ0Ak8KtSaoOI/GEuv4PD\nG7z+WRLqljBk+JgCmKbRaDQll3wLr4icAHKaytsCOCkiEaa8K4FegFnhDQ9/hy+WetLCRWH16KP5\nNU2j0WhKNEXdueYFnE3z+ZwpzjwVYkj49wo977jrKYgajabMkm2LVyn1I1DNTNIkEfk+F+XnrefO\npS9cTuZHFxdahIYSEBCQp9M1Go3GEoSGhhIaGprv87MVXhF5ON8lG0QC3mk+e2O0es3j9w/tE63x\nuK+7Fl2NRlNiCQgISKdRU6dOzdP5hTVzLStH737gLqWUH3AeGAAMyrKQC6foHedKvVceKySzNBqN\npuRRkOFkfZRSZ4FWwCal1GZTfA2l1CYAEUkERgNbgePAN1mNaACwuSx07P8Y3bt3yK9ZGo1GU+Ip\nURMo3Cop7u3cHL8ajVj08aLiNkmj0WhyRanegSL6ESGswa9wqmJxm6LRaDRFRolq8eIDKPC08eTf\nk/8Wt0nFit7qSKMpmZjTzFLd4uWM8SfeM7547SghlJSHokajMSisBlGJWp0shfjY2OI2QaPRaIqM\nEim8JCcXtwUajUZTZJRI4bVJLpFmaTQaTaFQIhXOvYIe1aDRaMouJUp4/U3BVa/DqylEAgMDmTJF\nb5qqKTmUKOENNYXeDRoUryGaHPHz82PHjh3FbUauUErp4XmaEkWJGk4W7O9vHOidSbNl06adzJq1\njYQEG+zsEhkzpnOep1kXtAzTuMUs0xMTE7GxKTn/XnponqZEISIlIhimaFLI6n5s3BgmdepMEpDU\nUKfOJNm4MSzXZRe0jKFDh4qVlZU4ODiIk5OTvP/++3Lq1ClRSslXX30lPj4+4u/vL6GhoVKzZs10\n5/r6+sr27dtFRCQ5OVmmT58uderUkSpVqkj//v0lKirKbJ0NGjSQjRs3pn6+c+eOuLu7y6FDh0RE\npF+/flKtWjWpVKmSdOjQQY4dO5aaNzAwUKZMmSIiIgsXLpR27dqlK1spJeHh4SIiEh8fL+PHjxcf\nHx/x9PSUZ599VuLi4nJ1XzRln6x+l6b4XOtdiXI1aHJm1qxthIdPSxcXHj6N2bN/tFgZS5cuxcfH\nh40bNxITE8Mrr7ySmrZz505OnDjBli1bspzhk/LaP2vWLDZs2MDOnTu5cOECbm5uvPDCC2brHDx4\nMCtWrEj9vHXrVqpWrUqTJk0A6N69OydPnuTy5cvcf//9DBkyJFfXkpHXXnuNkydPcuTIEU6ePElk\nZCRvvfVWvsrSaLJCC28pIyHB/Ov71q3WKEWuwrZt5suIj7cusH3BwcE4ODhgn4sO0rlz5/LOO+9Q\no0YNbG1tCQoKYvXq1SSbGcc9ePBgNmzYQHy8Mavx66+/ZtCg/1YYDQwMxNHRMbWcI0eOEBMTkyfb\nRYR58+bx0Ucf4erqipOTE6+//jorV67MUzkaTU5o4S1l2Nklmo3v0iUpjeMg+9C5s/ky7O2TCmyf\nt7d3zplMRERE0KdPH9zc3HBzc6NRo0bY2Nhw8eLFTHnr1KlDw4YN2bBhA7GxsXz//fcMHjwYgKSk\nJF577TXq1q1LpUqVqFWrFgBXrlzJk+2XL18mNjaWZs2apdr0yCOP5LkcjSYntPCWMsaM6UydOpPT\nxdWpM4kXX8z9ZiGFUUZWowTSxjs6OhKbZvp3UlISly9fTv3s4+PDli1biI6OTg2xsbFUr17dbNmD\nBg1ixYoVrF+/nkaNGlG7dm3AaP1u2LCBkJAQrl+/zqlTpwDzHWoZbfr33/8WY3J3d8fBwYHjx4+n\n2nPt2jVu3LiRm1ui0eSaktPtrMkVKSMPZs+eQny8Nfb2Sbz4Ytc8jUgojDI8PT0JDw+nY8eOWeap\nV68e8fHx/PDDDzz88MO8++67JCQkpKY/++yzTJo0icWLF+Pj48Ply5fZu3cvPXv2NFvewIEDmTRp\nElFRUel8uDdv3sTOzo7KlStz69YtJk2alO68lA4NgPvuu49jx45x5MgR6tevT3BwcGo+Kysrnn76\nacaNG8enn36Kh4cHkZGRHDt2jM6dO+f63mg0OZKXnriiDOhRDeko6fdj/fr14uPjI66urvLhhx/K\nqVOnxMrKSpKSktLlW7RokVSvXl2qVq0qH3zwgdSqVUtCQkJExBjV8NFHH0n9+vXF2dlZ6tSpI5Mn\nT8623k6dOomtra1cvHgxNe7mzZvSq1cvcXZ2Fj8/P1myZIlYWVmljlRIO6pBRGTatGni7u4uPj4+\nsmzZsnR54+PjZdKkSVK7dm1xcXGRhg0byuzZswvlnmlKP1n9LsnjqIYStR5vSbGlJJDTOFmNRmN5\nsvpd5nU9Xu3j1Wg0GgujhVej0WgsjBZejUajsTBaeDUajcbC5Ft4lVKPK6WOKaWSlFL3Z5MvQin1\nm1LqkFJqX37r02g0mrJCQcbxHgX6AHNzyCdAgIhEFaAujUajKTPkW3hF5ATketdNvRiqRqPRmLCE\nj1eA7Uqp/Uqppy1Qn0aj0ZRosm3xKqV+BKqZSZokIt/nso62InJBKeUB/KiUOiEiu8xlTDt9MyAg\ngICAgFxWodFoNJYjNDSU0NDQ/BeQl2l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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Fit via BFGS. \n", "w_posterior_BFGS, H_posterior_BFGS = bl.fit_bayes_logistic(yy, XX, w_prior, H_prior_diag,\n", " solver = 'BFGS')\n", "\n", "#----------------------------------------------------------------------------------------\n", "# fit via L-BFGS-B so we can impose bounds\n", "\n", "# first make a list of tuples with the bounds for each parameter in it \n", "# (see the scipy.optimize.minimize docs)\n", "\n", "bnd = (-0.25,0.25)\n", "bnd_list = [(None,None)]\n", "for _ in np.arange(p-1):\n", " bnd_list.append(bnd)\n", "\n", "# Now do the fitting\n", "w_posterior_LBFGSB, H_posterior_LBFGSB = bl.fit_bayes_logistic(yy, XX, w_prior, H_prior_diag,\n", " solver = 'L-BFGS-B', bounds = bnd_list)\n", "\n", "#----------------------------------------------------------------------------------------\n", "# plot the true parameters and the results from various fits. \n", "plt.figure(figsize = (12,9))\n", "plt.subplot(221)\n", "plt.plot(w_true,'bo-',label = 'true value')\n", "plt.plot(w_posterior_BFGS,'rs-', label = 'BFGS')\n", "plt.plot(w_posterior_LBFGSB,'gs-', label = 'L-BFGS-B with imposed bounds')\n", "plt.plot(w_posterior,'ks-', label = 'Newton-CG')\n", "plt.plot((0, 10), (0.25, 0.25), 'k--')\n", "plt.plot((0, 10), (-0.25, -0.25), 'k--')\n", "plt.ylim([-2.5,1.25])\n", "plt.legend(loc = 'lower right')\n", "plt.title('Posterior Parameters')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4) Online Updating" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bayesian Logistic Regression can be used to update a model in real time, as data points come in. While it is generally more stable to do the updating in small batches, we can do the updating a single data point at a time, as we demonstrate here.\n", "\n", "To show the reduction in error as we continue to update we will plot the root mean squared error between the fitted and true parameters. We will compare these results with those of batch learning (using sklearn)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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u7IN4p05QWWkQlyRJUnkxiEuSJElFsNUE8VWrDOOSJEkqH1tFEO/cOfN65cri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\nuIiISBXKyoJly0j5fjEr/5NI0pREOuQspgMrcRiR5JBG3T1/GYG6EBd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Update model one data point at a time\n", "\n", "rmserror_1 = np.zeros(N,)\n", "t_1 = np.linspace(1,N,N)\n", "\n", "w_bayes = copy.copy(w_prior)\n", "H_bayes = copy.copy(H_prior)\n", "\n", "for _ in np.arange(N):\n", " \n", " # update based upon a single point\n", " w_bayes, H_bayes = bl.fit_bayes_logistic(y[_:_+1], X[_:_+1,:], w_bayes, H_bayes)\n", " \n", " # store the average root mean squared error of the fitted parameter\n", " rmserror_1[_] = np.sqrt( np.dot(w_bayes - w_true,w_bayes-w_true))/p\n", "\n", "#--------------------------------------------------------------------------------------\n", "# Update model 100 data points at a time \n", "\n", "w_bayes = copy.copy(w_prior)\n", "H_bayes = copy.copy(H_prior) \n", "\n", "nstep = 100\n", "niter=N/nstep\n", "\n", "rmserror_100 = np.zeros(niter)\n", "t_100 = np.linspace(nstep,N,niter)\n", "\n", "\n", "for _ in np.arange(niter):\n", " \n", " idx = range(_*nstep, (_+1)*nstep, 1)\n", " # update based upon 100 points\n", " w_bayes, H_bayes = bl.fit_bayes_logistic(y[idx], X[idx,:], w_bayes, H_bayes)\n", " \n", " # store average the root mean squared error of the fitted parameter\n", " rmserror_100[_] = np.sqrt( np.dot(w_bayes - w_true,w_bayes-w_true))/p\n", " \n", "#--------------------------------------------------------------------------------------\n", "# do batch fitting using sklearn for comparison\n", "\n", "clf_reg = linear_model.LogisticRegression(penalty='l2', dual=False, tol=0.0001, C= 100,\n", " fit_intercept=False, intercept_scaling=1, \n", " class_weight=None, random_state=None)\n", " \n", "clf_reg.fit(X,y)\n", "\n", "error_batch = np.sqrt(np.dot(np.ravel(clf_reg.coef_) - w_true,np.ravel(clf_reg.coef_) - w_true ) )/p\n", "\n", "#--------------------------------------------------------------------------------------\n", "# plot the error as a function of the number of data points used for fitting\n", "\n", "plt.figure(figsize=(12,9))\n", "plt.plot(t_1[0:N],rmserror_1, 'b', label = 'single point updating')\n", "plt.plot(t_100[0:N],rmserror_100, 'r', label ='100 point updating')\n", "plt.plot((0, N), (error_batch, error_batch), 'k--',label = 'sklearn batch')\n", "plt.legend(loc = 'upper right')\n", "plt.xlabel('Number of points used for fitting')\n", "plt.ylabel('Average root mean squared error in fitted parameters')\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 5) Weighting data points\n", "\n", "The code has the capability to individual weight data points (NOT classes as in sklearn) differently. Instead of using resampling of points, we weight the points directly in the log likelihood. The log likelihood now has the following form.\n", "\n", "$\\log \\mathcal{L} (w | y, \\eta) = \\sum_{i=1}^N \\eta_i \\{ y_i \\log p_i + (1-y_i)\\log(1 - y_i) \\}$\n", "\n", "where $\\eta_i$ is the weight of data point $i$. \n", "\n", "The weights are specified as an optional 1D weight vector, the same length as the data points." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4000L, 11L) (4000L,)\n", "(4000L,)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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mmFiOZsQDeKz/5ReOTLt7t/Xy/fvz4ndqKnjgjIvjFXqtnVGTyIMG8cK3k1IP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\nexhu8TFjjDGt49cYxlbgOiBWxSwFilX1YMKvsG0bnHYaRBT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#---------------------------------------------------------------------------------------------\n", "# Make a data set using two different parameter vectors to show the effect of weighting\n", "# half the data will use one parameter vector, half will use another\n", "\n", "# Number of data points and variables\n", "M = 2000\n", "p = 11\n", "\n", "# make random feature matricies\n", "C1 = np.random.random([M,p])\n", "C2 = np.random.random([M,p])\n", "\n", "# make two parameter vectors\n", "w_true_1 = np.random.uniform(-0.5,0.5,p)\n", "w_true_1[0] = -1 # bias parameter\n", "w_true_2 = np.random.uniform(-0.5,0.5,p)\n", "w_true_2[0] = -2 # bias parameter\n", "\n", "# use a zero mean prior for illustration\n", "w_prior_weights = np.zeros(p,)\n", "H_prior_weights = 0.1*np.diag(np.ones(p,))\n", "\n", "# make some data\n", "mu_1 = bl.logistic_prob(C1,w_true_1)\n", "y1 = np.empty([M])\n", "for _ in np.arange(M):\n", " y1[_] = np.random.binomial(1,mu_1[_])\n", " \n", "mu_2 = bl.logistic_prob(C2,w_true_2)\n", "y2 = np.empty([M])\n", "for _ in np.arange(M):\n", " y2[_] = np.random.binomial(1,mu_2[_])\n", " \n", "X_weights = copy.copy(np.vstack((C1,C2)))\n", "y_weights = copy.copy(np.hstack((y1,y2)))\n", "\n", "print X_weights.shape, y_weights.shape\n", "\n", "#---------------------------------------------------------------------------------------------\n", "# make two different weight vectors to see that even if you fit the same data you can get \n", "# different answers by weighting the data points differently\n", "# (this is a somewhat contrived example to be sure ...)\n", "\n", "weights_1 = np.hstack((np.ones(M,),np.zeros(M,)))\n", "weights_2 = np.hstack((np.zeros(M,),np.ones(M,)))\n", "print weights_1.shape\n", "\n", "#---------------------------------------------------------------------------------------------\n", "# Now fit the same data using two different weighting vectors\n", "\n", "w_posterior_1, H_posterior_1 = bl.fit_bayes_logistic(y_weights, X_weights, \n", " w_prior_weights, H_prior_weights, weights = weights_1)\n", "\n", "w_posterior_2, H_posterior_2 = bl.fit_bayes_logistic(y_weights, X_weights, \n", " w_prior_weights, H_prior_weights, weights = weights_2)\n", "\n", "#----------------------------------------------------------------------------------------------\n", "# And plot\n", "\n", "plt.plot(w_posterior_1,'bo-', label = 'w_posterior_1')\n", "plt.plot(w_posterior_2, 'ro-', label = 'w_posterior_2')\n", "\n", "plt.plot(w_true_1,'bs--', label = 'w_true_1')\n", "plt.plot(w_true_2, 'rs--', label = 'w_true_2')\n", "plt.legend(loc = 'lower right')\n", "\n", "plt.title('Using Different Weighting Vectors')\n", "plt.xlabel('parameter number')\n", "plt.ylabel('parameter value')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6) Variable selection (sparse models) using p-values\n", "\n", "We can calculate p-values on all the fitted parameters using the function get_pvalues. These can be used for variable selection, similar to what we would do for L1 regularization." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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C7S8U+k6pPvjsf3+WVCbFwkkL+e55361Y36j9fOdX36Fb6+ag0Qex9LylFdt/pRX1XeEZ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a4mYZMLvTgPaIx3YzTjHTfi9GX7SJmpUOCtjp0nvEorwgX4ytO7Id5Q4imuhxEzvDyJSr8HwajE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fBY4GXgE8BXx5iXlX5P4SkRDwI2CbMSbm/mwFnWPL5Xs0Gu2za2QF/aZqQfvtEjSq325n4f0k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\nwa/UMTLJu40q4a04lBh6FIXsBymMYrKnsWX3/u8MF8mx9cjFpGQvvuVM0yB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# make a data set with very many parameters, most of which are irrelevant, so its prone to overfitting.\n", "\n", "N = 2000\n", "p = 200\n", "\n", "# random feature matrix\n", "X_sparse = np.random.random([N,p])\n", "\n", "# make sparse parameter vector\n", "w_true_sparse = np.random.uniform(-1.,1,p)\n", "w_true_sparse[np.abs(w_true_sparse)<0.9] = 0\n", "\n", "# make some binary responses from this data\n", "mu_sparse = bl.logistic_prob(X_sparse,w_true_sparse)\n", "y_sparse = np.empty([N])\n", "for _ in np.arange(N):\n", " y_sparse[_] = np.random.binomial(1,mu_sparse[_])\n", " \n", "# make a zero mean prior (since we are looking for sparsity) \n", "w_prior_sparse = np.zeros(p,)\n", "# and a diagonal only Hessian because we have many parameters\n", "H_prior_sparse = np.ones(p,)\n", "\n", "#------------------------------------------------------------------------------------------------------\n", "# fit\n", "w, H = bl.fit_bayes_logistic(y_sparse, X_sparse, w_prior_sparse, H_prior_sparse)\n", "\n", "# plot the fit withouth the variable selection\n", "plt.figure(figsize=(12,9))\n", "plt.subplot(221)\n", "plt.plot(w,'bo-',label = 'fit')\n", "plt.plot(w_true_sparse,'ro-', label = 'true')\n", "plt.xlabel('parameter number')\n", "plt.ylabel('parameter value')\n", "plt.title('Fit Without Variable Selection')\n", "plt.legend(loc = 'lower right')\n", "\n", "#------------------------------------------------------------------------------------------------------\n", "# calculate the p-values to do variable selection with\n", "pvals = bl.get_pvalues(w,H)\n", "\n", "# plot the p-values\n", "plt.subplot(222)\n", "plt.plot(pvals,'go-')\n", "plt.plot((0, 200),(0.05, 0.05),'k--')\n", "plt.xlabel('parameter number')\n", "plt.ylabel('parameter pvalue')\n", "plt.title('Pvalues')\n", "\n", "#------------------------------------------------------------------------------------------------------\n", "# Do variable selection\n", "\n", "# get indices of the p-values < some cutoff. Here we use p<0.05\n", "# in general one would want to get this cutoff via cross validation\n", "idx = [i for i in range(len(pvals)) if pvals[i] <=0.05]\n", "\n", "# now refit using only those parameters with p-values less than the cutoff\n", "w_short, H_short = bl.fit_bayes_logistic(y_sparse, X_sparse[:,idx], w_prior_sparse[idx], H_prior_sparse[idx])\n", "\n", "# fill out the full parameter vector using only those that were selected\n", "w_sparse = np.zeros(p,)\n", "w_sparse[idx] = w_short\n", "\n", "# plot the true and fitted (after variable selection) parameters \n", "plt.subplot(212)\n", "plt.plot(w_true_sparse,'ro-',label = 'true')\n", "plt.plot(w_sparse,'bo-', label = 'fit')\n", "plt.xlabel('parameter number')\n", "plt.ylabel('parameter value')\n", "plt.title('Fit With Variable Selection')\n", "plt.legend(loc = 'lower right')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }