{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Mean Field Demo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this interactive demo we introduce the Mean field method to solve the foreground/background segmentation problem. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we review the dynamical system models of neurons in the chapter. A neuron is described by two variables: a continuous valued variable $ u_i \\in \\{-\\infty, \\infty\\} $, and a continuous variable $ q_i \\in \\{0, 1\\} $. Roughly speaking, $ u_i $ represents the input to the cell body and $ q_i $ describes the probability that the cell will fire an action potential. These variables are related by the quations $ u_i = \\log(\\frac{q_i}{1 - q_i}) $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dynamics of the neuron is given by:\n", "\n", "$$ \\frac{d u_i}{d t} = - u_i + \\sum_j W_{ij} I_{j} + \\sum_k \\theta_{ik} q_k $$\n", "\n", "$ \\sum_j w_{ij}I_j + \\sum_k \\theta_{ik}q_k $ represent the direct input and the input from the other neurons.\n", "\n", "The definition of free energy is\n", "\n", "$$ F(q) = - \\sum_{ij} W_{ij} I_{j} q_{i} - \\frac{1}{2} \\sum_{ij} \\theta_{ij} q_i q_j + \\sum_i { q_i \\log q_i + (1 - q_i) log (1 - q_i)} $$\n", "\n", "The update rule of $ u_i $ can continually decreases the mean field free energy $ F(q) $, see the chapter for more detail." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the image segmentation problem, we use $ q_i $ to represent the belief for foreground/background. Mean field algorithm is used to solve $ q_i $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initialization\n", "At the beginning, we need to initialize this demo by loading a few python libraries" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Initiialization code\n", "%matplotlib inline\n", "import numpy as np\n", "import numpy.random\n", "import matplotlib.pyplot as plt\n", "import skimage.color, skimage.transform" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load data\n", "Then we load the image from a file, normalize it to be in range (-1, 1)" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "original range: 0.00561378787879 0.770716255013\n", "remaped range: -1.0 1.0\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAREAAAD7CAYAAABNPKDeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDFHph3QLAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# im = plt.imread('../data/gibbs/gibbs_demo.jpg')\n", "im = plt.imread('../data/gibbs/moon.jpg'); im = skimage.transform.rescale(im, 0.1)\n", "\n", "plt.imshow(im)\n", "grayim = skimage.color.rgb2gray(im)\n", "\n", "# Linear map the data to -1, 1\n", "scale = grayim.max() - grayim.min()\n", "I = 2 * (grayim -grayim.min()) / scale - 1 \n", "# I = (grayim - grayim.min()) / scale\n", "\n", "print 'original range:', grayim.min(), grayim.max()\n", "print 'remaped range:', I.min(), I.max()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run MFT algorithm" ] }, { "cell_type": "code", "execution_count": 122, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define a function to compute mean field free energy\n", "def F(Q, I, W, Theta):\n", " E = 0\n", " E += - np.sum(W * I * Q)\n", " E += - 1/2 * Theta * (np.sum(np.roll(Q, 1, axis=0) * Q + np.roll(Q, -1, axis=0) * Q +\n", " np.roll(Q, 1, axis=1) * Q + np.roll(Q, -1, axis=1) * Q))\n", " E += np.sum(Q * np.log(Q) + (1-Q) * np.log(1-Q))\n", " return E\n", "\n", "# Define logistic function\n", "def logit(x):\n", " y = 1 / (1 + np.exp(-x))\n", " return y" ] }, { "cell_type": "code", "execution_count": 129, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAR0AAAEKCAYAAAAvuYFYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY8AAAEPCAYAAAC6Kkg/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIqK2JI+IiKgtySMiImr7/0xC4z6zKqImAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U = numpy.random.random(I.shape) # Initialize the state of neurons\n", "Q = logit(U)\n", "\n", "Theta = 1 # smoothness\n", "W = 5 # data term\n", "\n", "# plt.figure(); plt.imshow(Q); plt.xlabel('Initial state of Q')\n", "energy = [F(Q,I,W,Theta)]\n", "for i in np.arange(20):\n", " neighbor = np.roll(Q, 1, axis=0) + np.roll(Q, -1, axis=0)\n", " np.roll(Q, 1, axis=1) + np.roll(Q, -1, axis=1)\n", " dU = - U + neighbor * Theta + I * W\n", " U = dU + U # Update U\n", " Q = logit(U)\n", "\n", " # plt.imshow(Q)\n", " energy.append(F(Q, I, W, Theta))\n", " \n", "plt.figure(); plt.imshow(Q); plt.xlabel('Final state of Q, Belief for foreground and background')\n", "plt.figure(); plt.plot(energy); plt.ylabel('Mean field free energy'); plt.xlabel('Iteration')" ] }, { "cell_type": "code", "execution_count": 127, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAREAAAEKCAYAAAA1hWHWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvU+MZdt33/Vda+9z7r3V/fq9389OHCuyYgYMkZyJJxk4\nAwtFQgpiEhQJKUIZMAEhRjET/sziSKAIBgiIEyUIhURCscwEMINIZoIABYhEQEKKJSeyf0bY7/e6\nq+qec/Zei8Fa+8+5Vf36/V5VV9ert7+t0/ucc+vee251n89d//bapKoYGhoa+rbiT30BQ0ND320N\niAwNDT1IAyJDQ0MP0oDI0NDQgzQgMjQ09CANiAwNDT1I8ds+kYj+DIC/CiAA+Guq+qsXj4/c8dDQ\nC5Kq0n3n6dvUiRBRAPB/A/hlAP8UwP8M4M+r6j/qfmZAZGjoBel9EPm27swvAvh/VPW3VXUD8F8B\n+Be/7cUNDQ19d/VtIfLHAfxOd/xP/NzQ0ND3TN8WIsNVGRoaAvDtIfJPAfxcd/xzMGtkaGjoe6Zv\nC5H/BcA/S0Q/T0QzgH8ZwG883mUNDQ19V/StUryqmojoXwfw38FSvL/WZ2aGhoa+P/pWKd5v9MIj\nxTs09KL02CneoaGhIQADIkNDQw/UgMjQ0NCDNCAyNDT0IA2IDA0NPUjfehbv0HdDRABA8AHUPXDn\nXNUDEmt6764d3/Oyeu9ztB6MFN/z14DICxYTgZkQAiGw7zNfHNtod6yCoGi3rtaNLm5nvbOzlyig\nSlAt++j26eKcQlX9XBvrvuiAyTPWgMgLFhEQA2GKAVNk2yYfu3OBCQSBEUEcGLLfVwVBoBd2y966\noGo9iACihCy2byMhazkmHxUiitxtolrPQxSZ7rzR0DPSgMgLFhEhBMY8MQ5z8C3iWPcDjnPAFBhA\ndpCIjZrbPgSEDIOEQaR3QypYuuOcgZQNFikDKRtQUvbH6r4iiSBlRcptJBJkuGWC4dY8Zw2IvGCZ\nJcKYpoDjIeJ0iLg62nY6Trjy43lih0QGqY++lXMWQTGQaOftFIDYuWaJpEzYErD5aMeELQNbMrDY\nsWBLvmXClgRMAGUAKshCAI3gyHPWgMgLFpPFQ+aJcZwDXp0mvD5NeH3l22nCq6sZx5kMGppASDCI\nJD/mEpb1e7mBAkrVIrk8vyZgTQaOdWvH/f62EZYkWDfBGjJ4yyBqlk4WBTMZUIaerQZEXrCKJTJH\ns0ReHSM+ezXhzesDPn81483rGW9ezTgdA0g3AweS7wcDiCaQY6RApFgd6nHXBpD22LICy0Z3t4vz\n0yZYQkbYCEwEogx4ADZnRSLxDNPQc9WAyAsWESFWSyTi6jTh9dWMz1/P+MFnR3zx5oAffHbAq2MA\nYQNhdYCwA8TwwQCoEsNAUcFRrZH9+fNKOK+EWx/v225XQgxigd0SVlELqCYRpEDgRLAk9PBnnqsG\nRF6wWmA14HQIuDpGfHY14fPXB/zgzQE/9fkRP/XFEa9P0QESwNUCYXNkFCBYZoZUUCZylvStKlW3\npj93uxJul7bdlP2VcLswpmiAC5w7gMABotgyI7CYO/PpfoVD30ADIi9YzGiWyCHi1WnCZ6/cEnlz\nxE99ccIf+cEJb145PNQsEC4WiNeNsEqDCC7goXt4lMdvzoybhXB9JtycCaeFcX0mHM5UARKZwcQo\nGdyS6k1ZsCXGymQxkkGRZ60Bke+A6M7ONxMTWUxkCjgegsVEriZ88dkBP3xzwE9/ccQf/eEJX7yO\nboUUC8TiHwwFqYIhYM0gBAdGD4/796/PhOtbxrsD4XomvDszDhNhjoQpMqIXvhERFKU2RCpAllCK\n5OxzXH704dw8Hw2IPCOVClPykS/Gct6iBOol66WiFDaSj1C8vgr46TeMH75mfHFF+OwEvDooTpPg\nEDMmTgjYABWQboBugCao14iICljtBlcA5KAAmtVRrJG+hoT8DzMQGIgBmIJijsBhAnIW5ExelSpQ\nVZTIBxMhkAFmCgETC+agWDbyytZSyGbVrKLqx6iPDz2tBkSekaxEnRF92+1z2ydS29CNkDvnXp0i\nfupNwA9fE754BXx2UodIxhwSIm/mxkisAKkQ0Qw4QEgBKIG03OruzjR0OUDIQ6DkMACiQ2SOasVn\nk0HAOuoRoFZKxqRgOHSYMQXGHBhziDhGYNkESdSK0US9SA31OGUFhJAHRZ5cAyLPSNX9iAHTFHbj\nPAVMPjIBTBanYLLqTnaI2Gjnrw4BX7wJ+MFnjC9eEd6cgNdHwWnOOMaMiRIYmxWT6QbIBtUE0gwV\nAdxKgKCCpPlUVGb3lQQwymw+Avk1EiKbFZIjIYvaPBj1Z/jnYBIEUoNOIEyBcAiMQww4TsBpMois\nSbAmxZYVayqbgBI8LTwA8ik0IPKMREytwnSOOPh2nCMOU6znAqvffLnehIx859zpwHjzivH5a8Kb\nK+BNtUQEc0yY2HIxpAGQDRC3RMQsES1+gtq3PDzgWghQ9x0oNXLhMYzg7swUgBwUEt3wcPeLCRZv\nIXULBJgCYS4QmbRC5LwSlo1x3gTnTbFsgsACIoZCIAJQHhD5FBoQeUbikpKNNsfldJhwOky4Otp4\n8jEGRaAMpvy143FmvL4KeH1ivL4ivD4Brw+C05RxCBmRk6VxJUPdlYFkg4jYzDkVLXPxzIIgq+kg\nIqjvF4AolaK0YokoIgPZ3ZlSamLuGDxoKgisiKyYGJgDcIiEYyQcp4DTRDhPhPMquFkFNythWgSB\nzZJRFYgQUlCzSIaeXAMiz0jcWSKHySDy6jTX7bWPU1AESr5lBPaxnrOZufNEuDoyro6EqyNwOgJX\nB8VpFhxiwsRAgIKUKzwMIBmaDSAFIiqAileVMhwmZG2tyC0RBqpVQorAhBAUUw14eryGYeAIBo/I\naoHXAMyRHCKM06xmgcyM20UwL4IpZMSS+gV8Up+9F9MoSvsUGhB5RupjIsfZJsm9Os347OqAz14d\nbLw6YI6CQAmRUzduiOQBWEoGkQifqcs4HgiHWXGcBYcp4xCAiSyNCyW3PMwCMYA0kEhWqBAgBGUr\nQDOYWDUrfN8SRp5FQrNElAEErzkhRaAGjokVk1sqhwAcIrBOjGVSrBuwzoplU9xMjClmxGqBWAxk\nS4o1EsLWql6HnlYDIs9IJTszuTtz5ZbIZ68O+PzVEW9eH/H56yMOURB5QyTLsNg+IzL72AKa1kOE\nMEVgnoApKuZJMEUgsoKRLeui7rpkgYpAs0IqRDxZI55iNkKAS6sittQvKaprQwQEUgeIuTAW+1AE\nFkyeUTELxIC3RuC4EdYN2CabqLdtwLoBp0kRQgcQt0CWSXHepMJl6Ok1IPKM1BeHlZhIsUTevD7i\nB5+d8IM3J4fIiok3TBwsJVrhQZgY1U0oXcxCMNciBLGYCot1OQOBBO62uPuSFeqbezeQTObSBAKX\nupCal/FMTZfBYSiUCRHFAgEyK4KIZWtEICJIEdiizejdIiFN3iJg8xYCPhP4OAm8BMYAIpadud0E\nU+nUNiDySTQg8oxUszOdO/PaLZEvXh/xgzcn/NTnVzhOgokjJl4xccDE7Bv5BkysCJxrypVKRrbU\nmBBsxixgbojCK7ZK/KPAw0CSk1kiqmQLp3pBmfie1vJ0qi5NgMU/mABhRSyFa2qFbKpiDYoSI00G\njJQIKZOdS4ScCCkzjlEAmAtjAAk4r4rDUrqzSY2TDD2tBkSekUolKhfTn8Q3y7ZEyubCkPi+be3n\nynPtxiWY7V9XNO0bImt9QysqK+C4s7WKUJXynBbAVC8vU/8E6kFURemRqvt+qZc9V0vhmfq1+qzh\nQB5LYXurKVrJ/HEinCbG1UFw3ghLYmyZkTJDJCAydr1axefklPftHxt6HA2IPCuV6fbWntCKwBJY\nE1g3sK5gDTYxTr2uA7YpMlRz/ZbPqlDSvoyjlsnX/e6LuwCjB0kJXvbHZnoYgbRcsZpxogpwsIl7\nd2ABXECl3OBAzntomcWjng72TA+VACzhOANXG2E9MFJWiDCgVoR3mMgn8bWKVjs2F8iqWz2wMvQo\nGhB5VrIJb4Qya9a7jVWIxAYR2UCcHCReHMYGkHLjW+pEO1emh0lzb4CamGmWR2+J6IUlImgAQQMF\nM8A+7i2Qe6DiXdDq+/j7a2eZ9POB2IvR5ggcJ8LVTG59aAVIDMBpIqtk7apat3oMIPls4Sf9d33Z\nGhB5RmozURwg3t+UvdOYAYRBomBOIEmwCqsEpQzRDGafEUvaJrbtAHIPVPQSHvfvq8KXbzCXQy+g\nwL6Vmbm9C/Ned0abG9XcGzRLpLo3ZokcooEiH9jK3JUNIAzMgXCapFa1lsrW86bgrcRUzDoZejwN\niDwnFX9BO0sEyabp62bT9IXdEkkgyt5OMAOcoWSWCJHNoymuR4FGDw7qrBTgHnj0s2TrDa8goXqp\nzB1ABBC2c5aGvWf9mB4q6GAi5eday8USvymzlblO5LO4iAgBsLYFdt4slNNMuF0ZN4tXuAarVwEA\nUesmX9fZGXoUDYg8M3lbn2qJsBpESBms1jCIBQ0gJAB5PIQcJJ6B0QIQhsOjA4qiWSLQu+5LBcr+\nsZLJLfUaxPZaQnYpe4i8b1GqNm2/hCZKRSv6Yy1JZHQxEThACEyMQK3K9TQzrmbBu0Uwe+MjA0aG\nqGV91kAVKkOPowGRZyWt1ohZIqnBQ8gAUtyGsjYMCbTbhHyVlmp92FT+u9aIevm6vfNdaOgeKg4B\ngnPL5uNZDKfM5u3eQy/A8T5XpugyOduOPdvkMZFDJJ+8x4gsmCPjuCmuZouF3B4Yh9vstSN2LaIW\nWF2TIo7K1kfXgMizUrFCSnaGuwxNA4jdxN4/RH2ePgkUAiWF+Nz9anlUq6NZJuV8Sf/eBYg2t6Z7\nrMIJd4O05ea8dGe+Li4C7J9fskn2Oi2mE8hmAwPwGAhhjmzr10yWjdkyrHo1wOfR2OcqrQPOG+0e\nG3ocDYg8I/l/+5ad8fVfysovLL6xuz3V5ler1CC1hS79+F5LhIv1gHsskQsrRPWOJQLtYOEHNY1c\nPgf12RlcuDVdMNVfizsLhjvYoRTJwWb8Ag0gEnwpTi1LcdpkvGVjh0RyC8QyM+dNMUdBHJWtj64B\nkWclv0u1pHfJN4BVfROwknss5au8X/Bazc3APv5R3RfF3hKxGnYrcb8Eh6+L2wday2Xae7e7sb8v\nK0Tkbnr30jop4GAPyoIs8GlxF62vR7AaFGXq4ihUwyh2jrBsJYjaXJjzprieujjJgMijakDkCWTf\nrnTxbevpy+5b+PWR8erAuDoQjjPhEK2/RmQrtjLzXlB6mZYoZLkZDUFaV51sLoLuXBAG4BNgaiCz\nBj3FLQjZHxfrpMyT0daCqL5MvaouK3P/hhb+gT9R20XbdWr9nZXfUX+9AL1n3wKtcyRMAb4sBVrD\nZ8KeeEMP1oDIRxbBZ+eymeEhwCbEsfnnoXvsB68DvngV8OYq4PWRcXVkHGfz/es3aH/z3dF9D7SM\nR61+13YONStim3ajqtZ6j3KTq0dUyfNI5HelNwWw9yF4IbzFeNTHclwosodbAUaxoKgWmRGX+76h\nSlVbAKXsl8/S54h3v5ORlfkYGhD52PJv0inYeitTtB6i8z37n18FfHEV8OaK8frEuDowjrMttdD7\n8uVW2t0SenkC8HUf9mnTav/7PdgZJMYJhwZ6oEh3nuuEO5ubU+5wn4pnBSgVGj1A6j51EME+q3Ov\nxVYsEbXPpNpZQdq7ctSB5L5x6GNoQOQJZFYH4TARDpNB4Xi5PzPeHBmfnQI+8/HqwDhN7L48aqyg\nMy4AFKDoDgjktgAr7P5m//b2HyguT1+oUSyU5nbIxVgsixLqJU/zlrucYYFhrsHebobNbr8c74Oq\nHUCKBVJiJe2Dlr/s0qs1gt1r36laGyD5aBoQ+cgydwbV4jjOhKuZcTowTjMZKGaLg7w6MF4dgo+2\nmTuzDwjubv5e2naqtVLm0JRYBBwg/q3eXBx0IDFwXI4GKvIUrqV3qBAKAJHvk3TB17sWSQ+R3vK4\nk4K+sFD6j1w/nzZgtnfa/TK+Zn/oMTQg8rFFvpZKtNiGTWNnC6L6VvavZgPKaSIfzZ1pEPFv/+7L\ndefWXN4r7m1APdhaLZLuHFCpUuC0c2N21kgPjEK0ktttbkyLXwDauS64DyK4cF14H2zex0T6qAgc\nTJc8LSjxfR0A+dh6EESI6LcBfAUgA9hU9Rcf46JekgilY5lNUz/OZOA4MT47Md5cBXx2Ynx2FXCM\nhENkHLyMu+zPkwdW3ayvMUV0cY467H2d6qIUI8HdlWKNlFhDb4mU+MddmAhAJUDrV0DmwpjcCqES\niCmWzgVA+pjInVhIC6zyhUUCd80KPOpH3R30Nkn9LQADIB9ND7VEFMCfVtU/eIyLeZminTtTXJfX\nJ8bnr4IFU18FfP7KVn2bgncn68dQAqstN9lbI+3k5TlLyzKKRdJBpcRFtL3gHhwKhewAomotCrXE\nIerfBRpGqjtWR43g7uMVXCACqvCocRHuUrwt8VNTTC0eorvPe7npgMdH12O4MyPr/gH1gdWjx0E+\nO1oq9wev2xbZ16H1mymw7ds5M/Pvtc77sYMCPNap9b7VHTxsv31r76yRPhZS+iWq1Jev3T6o/w/Q\nAYR6aLSLo/48iuXRp3UNHrVylbvaDtESu+3y1bgARYPU5a9p6OPoMSyR/4GsWed/qqr/+SNc04tS\n8fdbYJWrO/P5FeOLVwE//Czgpz+LXkXaFqUELo9pf0+WsQfHPWApxV97eKAVfhVX4aIupMRDAIF1\nTdNyFVDiVvNxEfcgD6zeZ4mUDE85ZwV3BRxufRQrxPuzlpiItF+KWUNq+2WuTv+x97+cu2AZejw9\nFCJ/SlV/l4j+CIDfJKL/S1V/6zEu7CWpzkINrS7EUruMU8nKHLkFCev/e7IYwH1f6v3Yq95c5bD7\nRnbLY2eZ+Le6dJWqLcjanl9AdrmYOFNbT4ZIwQUAsFYEtXqVmhtVrB7VVu5eYUFlPaxSE9tTrn1o\nA1mDptfA1ewO14I+8mUzFPMEHCbgOAOnQ7sGA2fbx8X5oa/XgyCiqr/r4/9LRH8PwC8CGBD5BqLL\n0e+TdrvQ/ZCoz6sRzuZOVNeiu/FLUJLUX9JuEhG3TNyKEJUGEi0/bpWo7G4RQcDMHvRkEHFbxKqv\nMO3iFgVGCu+b6tmlCilfza5kYbg3wwrwpLlbKvubvX5QbaliW7sHmGfgeCBcbYLXibFkwaYBCTaT\nUUR98p6N/b6NQB4U+aC+NUSI6ApAUNW3RPQKwD8P4N9/tCt7oeoDSG02bBvr967i7vfwhUVen8e4\nCyXATH0f6xM7l4U6N6POupV2c5qrYQQhgq05Q9RBhDqIdFZAyf7W6y6VHD5qbx+V9X2pxj+oe34F\nHjrL4T7PxAFaFwCbPBt2IFwlxiKKVQUZigwBBUVK4i0EBCkJtqxI3b4tFD5Csx/SQyyRnwHw97xe\nIAL4L1X1v3+Uq3rhonv2L0Gy0+6mKbNWUG8ces9YnqzdC2gXH5ByN5asTDHfFfbNDgWIrJM7Wwam\ngaNYJLSDSYkB9Z+hc0DKld+BSP0d9G5YuTxqLlAFkHavSx1wGQgBiDFgnhXHxDhlxaaKDIulKCtC\nVKwpY93EtpSxbILVmxYZQOg9/yBDvb41RFT1HwP4hUe8lhetr0th3QGIdtGAzmqvd5P/cAHGbo5J\ndw64jEEoLEi6n2C3yxf35jtZNzXzbfyWrfUbdAGRLqbB9993Svvfgl4itLdQiuHUxSjuPFfbs7W4\nUwqEYMuGHibgdFBsaoVM4gChAMQJOK+52xjMGUwJgLkzabSE/0YaFatPrc6FuRvLaI/dtUb2P1FK\nxsus10t3oroE0iyOvgbE4h/iHdMvYihowGh1HPZ6DRYFHCUW0pWv8wXpus99ub+zMLSHnS+EBT/2\n5Tlrm7bd77QknMktkbL2MOGotjKPesSWIhAiYZqBm3PC7ZL2y3CqxUK2rGASDH1YAyJPqPusEcL7\nAdKskGaZ1CBJ77p4WrRkgfoCLSEAYt2/QH1PjxJYtEhlgUUJbDJRfX1G19djB5BmATXrBN5Jfn+d\nuwhyB5YSLC3dzlTaQldAF0hVB2OxjIBWeu+vSzDLKAbCNBEOCmQQxC+eIiFM/tgKzNGW4CzWFKB1\n4at1K02ehz/zIQ2IPLEuodGfBy4SDrg42ZnvDSCoy2bWdCmX5RxKlqSbu1IBIshZIWLuDZdiNi7I\ncliAPAVb4h691aN3rJ/acpHa6C/WzlUCGhzEm9YLYO0dc++CAeLrxGj3fHJvpgWn7UEiW7x8UsYM\ngpB1JOJIiBtjngmHjXHcCFNcEUOzsmo7xSSIK1eQDoR8vQZEPpH2wc/u/GXgscRHtB03k94nsF3A\nIwSAudQ4qK8X0xoEae2nKshZLIXqFCKQlchXN4Zq9SzvsjClLF07iOj9EKFSddpGuAVlC20Btra4\nZ25KVknVl+HRBgxCDfhQ/UX66zFAatmZCMbBfzEcA0JmTBNjzoxjZpySfSZbaAseA1Gsm2COeTdX\naejrNSDyiUXdBty1PvYWCdXHLi2R4lIYQGysBV1Sqj29dN23HiKlZJ2Ly+A4Y5T1XdhvOu0gUsrS\nvdisPq7mPuxgQr7+jbsOZPEUyRbfSbUmpFgXJaCqFSIFIFTKbKn9jmqglwgBjImCWSASECVgEsYm\nAUcJ2CRgzQUgHkRNgjUJzmvAtDBi8IbPwxT5oAZEnlq9a6LwIqwuXbn7D3sRLXEjpPjv5eZpq9x1\nN3m5wQjo60RqBlebRaKqYCkVpt23fGeJmBXCDR7VddHq5vTnCzz6/R1YujiEVa6SxUPKMhHlamtd\nCzzuoRfWGFrsxT84k01YhDCIGawBQQOiBswakDRgy4xtEyxrxnkVHJaMOWZM0QFSr2/oQxoQeRL1\nmQdbwU2EbMmDDEgm5FTcFuru9JbypOKfdx2/2jc2VTCI2PsR2poxKgRborK3e7ilY0XtZmM2UBDX\nb/ayVVekfaT22S6/qt1SqvNbuvNVYp9Fa1n/RYaoXFsAgmduiNuEvPo76N2q3RyezsLTttXfhY/w\nqQX9zwzL4yfTgMgTyEIT9p+2Lp3gS1Nmh0nOXZqyPqmZEzUeqVQDmru7xF/bWnuUgKq5C1JuHBBK\nk2UDRbEQtFagFgthDxC09++snJ2tr929d8c3c4m2ApZyvLtpu/4ibDUfqg4btPO9G4UKkFIc5+vs\ndNdVx7LEhFDbdL9dBrGHPqwBkadQuVfUb2zptmwAybmryfCnlX0qrkx5/OJmtvtQ6/tIlxbNnSVi\npkHpQCYo5euWnSkmfDPliVsA9G4UuAGkzygBXRD4PvkqemVFrX5yYfvcXvXq1gg8vrN3k/YAKS6d\ngahvhtRev/z+C9AbSLofrRbb0DfVgMgTqboz0qyQsmpbgUhdnwZdMBKorsQOIEBnibQbt6wqZ66R\nGqh8bDdHs0S4NFS+KGPfWSL1espWYhKoZStlH0Bb96Y7997fi+yhc+nOoOSBfXcfrFUHXWeZoa0M\n2KPAZkQTWmuUYn2gQaW7jmGIfHMNiDyBuikqkOrWGDjMEjGQaLfAkn3pejf1AhFqKVYAFzeJ/dXV\nYrnVUwCC7kbxruwlUFrqRHqAcHvPfUykQ0N3AYoGj52JhHtgUghDQF0Dp/xsAUgL3TgQGzjqtRSQ\n9HDTHVsv5x5eWCEwsOxggp3rM/RhDYg8kewep108RLp4SMoWQAS3oi/tb1xCnS27uytrLEKbzw8Y\nUAq0avCy9UMtAGGvZH0/QDorxC/l0rXprQ5CmfKPO/QoMKiZlc7NAwqEGhTYe8JK/wL+gzUuU8wu\nsjiIdJ3TqLxwH1jtYyIVKOgAQoMdP6EGRD62dr52Md9LTMQyMyUuQsXdYPLOY8XkKGXnBAoAKUG9\ne1gBRg2s1irVfUaopZF5n8VgbzBUism6yXXFpWqB1c7MwYUro/a8sjJds0ra7+CCNu2H2sU1Pnnb\nVjc87gRtW3B3H0yxxco7V2YHEuosjz4e0kb7Wer/6YY+oAGRJ1DvzhhAeksEXXam3LAtBgKUY6od\nuwo07Eu9W9FF1W8Obe+H8t5tCn2RTdm3u7otHNXFZkr8Zfdt7+o8lnKVdWnLDhZfGxfp3Yzysp2r\nViC0C9T2nhJdfCC3RuxSLwIc3e/fa+7sd3gBkgru+ubvu/ihogGRJ1L5whV3Z7SzRHKtE2kWRzOt\nyw3cIFK/NcVcnjLztQBEhFqV527x733dSblDrK2hz8TlPThaILOlme/7bPWh4qlc3nwlqFHH9/+u\nKkguYi7799y9a3XpCH2dSLNCSvp2587c49JU4Lz/8oYuNCDyBKpVqd233T7Na9YIF7AQeU+OZqe3\nGbL+H11qW2QADhBViAdT6zcs7KbdWxDkzyT0SzP0NRo7kOyee98HNP+l3njFNbkPJuXxiyn9Oxek\n26EL96nslX4iDR7lE9Xf+IUFom2WcLfVbM2F69cHe4e+XgMiT6ASi9ylaUvsganGI1r2wznhVksm\nBbJbEv6/XH0CXS1dF/UbpN0s9TbVZpD09271OhRtKYby81ysG3suK2xdKg9UkPsqtTaj3HU1fnLP\nL6FXf3FwS6E0Z65zY1oZfnkXdJjYn/d9tQmHW7ZuZeeNsCTgvAHLBpyT4rwJzivjxzcLvrpZ8PZ2\nw/U54XZNWLaMNQlS7cMy9CENiDyV+rjCrg4DDSLdDFgzu7UtkwCgZFzsMe9QVqCx20dNnWq5yf3b\nf+/UdJ1P1Rki3fv7KGST+Mw66deJ8VLz5nHtAFI58T4L5vKrvlgWxdW6U/TVFbTTHh7l1RRoPUGS\nYNkyblfgZgNuV8HtmnG7ZtwsjLe3C766WfHuvOJm2SpEtpyRswyIfEMNiDyhSoC0Fo9xD5BW+9CC\npPC5MACg1RS3fbdICjzcdKlNh/znumzqRSalvS5gr8vkLQRJa8VoXS/KrQ7eTcBTb07U2f50cWvv\nDtR/C91F7X6mwKOdVPQX21khNdyxD6CUKt2UBWsinDfgZlXcLIrrJeN6CbheEq4XxrvbDe/OK65v\nN9wsG84eG2eWAAAgAElEQVRrwrIlbMUSGU2av5EGRJ5CuwBlizfUBsfU3Jk+qyAVDG6VMKyuQ0tD\n5dbysJ3rfHrs71ODR4kiXH6P24S9cn0KVFgImhXCUhbZVl+es50rFomiuTndmff/frTfLeZMu/Jm\nEHRuSx917X5G/XNsIlgTsGyK21VwvQje3TLenjPengnvzoSbc8LNsvnm7kzK2JIMS+Qn0IDIE8pM\n+4uirktLBADQFk0Sd0MEpbGQPd4igNhFA++rADXPQO/czgUk6hZLKwMp7RL3Ac+axVGA1b6lGVpr\nOso5+hpeNN0Fyz4wuy/6ahxpvpL2x93PZW+yvCbBeVPcrsD1mfD2TPjqlvDVjY3n1cDRj8WdSVJW\n/xsg+ZAGRJ5AVP6mNi+mt0b6xZ9qoBFmfdSAJfb78Jsd2nUBK9IaOUBbX6a3C+5aIfCfLc+rt3AP\nEWhrduRBVPjnKU2V9+90nz5gldTLbwHmer5QsE8ZXYROzJ0pMRELpt4uwM1CeHcLfHUDfHlt47Jl\n38wCKcdrKq0jv/Yyh1wDIh9b3Y22gwe3oGrd/I4wPhgopIOFuSxykZ8oN343+v2tvXtRAqvauSvY\nWyPw9+3zHgVWNUKh1jUN3c+U+E69ml0wuN/Zw4PKu2v7sct1aWr84zJcsjOpGlQUClFUiJglorg+\nA+/O6hBR/PjaAq9bNvdl8/01CbZkloh0lbRD79eAyJOou3lqEVcpMy+b5VjrWriVG936uJ2JTWjf\n1S3xo91blGUy0cb+kkp1KRwgFVZfP1YDv8R4fH4LuTtz56Yrb76TE+DODdqCo7070wdSK0zu+mYo\nWaUsis2zM+e1xEQUb28FX90ovnyn+MNri3sk0bujCJLHRAZDPqwBkadQDaq20vLLVK9VolJb+Bqo\n2ZlaC+Ld2atLhBYIbedaHIMqQNoylFTTvBduTQ2ruDvVTbjZQaZPhhBAUjrLowGmvGD9YbTnf40r\n0wdQ7cf7grrudeqHufuSCls/17IzluK9WQTXZ3GICH58nfGH78SXqbB6EGuXUJYTRT0e+rAGRJ5I\nLThJe5emlpsTIOQJ0DLb1/9jZ998H9Ddqnfe/3h/jlBdl929h8vbeA+NWmMi3X7J/NQ4icGDfP6P\naOtCVh4vLlR9PwJ2X+uXbk6d9FasjgaQXZOg+qJ08aHK5/DO7WJuyXmzupDrJePdbcZXNxlfOkQu\nLqTuDnT8ZBoQ+djyb7UkVkV53gS3q+BmyXh7a6uvxTINv6vBVunqsX3fpsnrDhx7ePjkue4xoIzq\n8Uijy2X/U7NC7KTFUxxnPjenVJ8z313jZh/vKZDyQLF2JffopxS2M33oFvUK/HgXNd07csDFDa9m\nhWRfrCsXC0PFYWfAkwLHoUfRgMhHlsIYYIE+xdmrJefItraJ3+miQCAF23cvGAqG2EjlWOtNXG7W\nfsZt3xmN9/faxRVhF0PYRTYBVAAUIFS4EEJoy1LYollaF8/qinLLq9QIb7NGWre2fRS2BGh6gPRX\nXeIl1F037eIjCqouiWhAWelPlaGtL+M3/acb+oYaEHkClYWRls0skZvFF0cq943a8o2RgciKSDZO\n3X5kv2FLlSiRWyNdr5EKlr7mZB+n6IuyLnjSWRBa9mx0C4YICMFAFvoFsy7cKurKZOkCEv3f33js\nXR23jHZzdZX8Rwi5LsylEGWIsoPkYqr/0KNpQOQjqwT6WrZAEEP2dV7R0pFZcQjA7Nshat3XYLdT\n3FkAuAONS7DUa9CyMDbVmg47364RQLM8+noWYGf1BKYKkrq8JvcxGr0Ljmp1oFogxUrp+77uxnvP\nt671NV5SY0g2NjdGIMLQChK+4zYNPY4GRD62tLgzZS5HthJxbRaKVVYKThNwnAinCGwT4TQBOtkt\nGZlq9/NwBxp9PKSV0wPqdSZUg4/NDTAXRur3uamBo/Vz5e71Q1ADCWuzRqhzbdDNjXH3pb5wTe58\n2AJpQVXsIFE2AV1AhCGgLssivnF7bgegocfTgMhHl3YLRSuYLCsgghpsXTabXfpqJlzNhHSw3qtl\njZjIhKz2TWzp4O7mxv5G30GkWhrky9FYeZedQ00jQ20t3ubOdOCoi3mX5TkNIFbbchGjKZZIH+/o\nQVIgcd+5D47tsxgMuMHEAaJgt0TMChENkBITqevuPOgfc+geDYh8ZCn2U9MBy9bkrNgyY9kYcxTM\nkbEcCduRvTs7g0GIzJgjQdRKQksf1F1GBt18HLRJfYUUImYdmDFCte6jm3JjYxd3rMVwZO8ZuIwK\nriDx6yjxmuIGQe8PnO7cFzvXWybV3dD7xt6SMCgI3FWB/X7EISIi1RKxn/M0cQXJcGceUwMiTyBR\nszqwCUQUOTO2pIibIAbCFCxTkzJDhAFlENgBojhmtiwvMZgVIbSYxWVKtwKlWAGinq6lBhBXDxG0\noSuCK+AghEAeUG0WyKU701aiK3LXoQPKpTuj3c+aA/YeC6Rza4r1oWjxjgKUmtLV3AVWS85rwONj\naEDkI6sUP20oRVCELWv3De8r2TMgEgBlMIIDJOA4AVuGuzMloKlucfSZk2KRNOukxBUY1i6x9DKp\n38glW1Nh0kyRkvFhJnCw0UCi+8xMXysCdLcqecn9Hgp3IdHd2HdcnItznUUibomoMrLDQhDMnZGM\nLAEqubkydRwxkcfWgMgTqNQuZKBmPnzXRj9QFQeIVoCsM5DE1o8ByNO8tCs2I+BOUJVKUJKoFo7V\n9wI6d6ZUpHb2Q7FEurk9IXAHj5KRKdvdrJF2GRiUFKy2ArRyvI+PdFeod0FS4yHF+qguTYA4TLLA\nj5sl0gdXR2bm8TUg8gTa1XO9t1JSLXuTCOeVcLsSblbCcSUcF8IhEuZImCLhEGExCWIEZgQSBGaw\njwSxZTHRuTllfssuCEpgYu9ktm+SdHdDG4s9Ue9HasVru49ItQisfv3XWcp7WJghtA/IFqvBOqwR\nsnrXMtFuEyQ/l9V6h7y9zbg+25yZ29UC12sSpGz1OKNY9XE1IPKMJApkrxk5b4qbVXA4E6ZSmObf\n8IdJMQXCFBRTUMTAvs+YALMgAJ9ha9aClgBo+TYvlW7+7VwDtnwBEv+z/wankjH2a9K6dMW++LVB\noRW3tdfp6z3619UCEGppXnGArB6gXjNq7c2aGWsmbIlwswFfvlvx5fWGr0oD5iXjXEAyGjA/ugZE\nnpEsZgIrj98EtwthCmIxB8CnuQOnSXGIhMOkVpQWFYeJ68TW4NFWsyzELQ2tIQ/d1cQzFK1wbGd1\n2ItUhBCA1lsAKNWj1IGkrny3i2vYcb1173FfLleLKVaJkh0LCEkVa4Z1b08Zy0Y4b1Z7s2xmxd0u\nih/fbPjqNuHtbcK7c8bNmrFs1jMk5WGJPLYGRJ6RWjMdxbIpboIg7ABila9XB8ZpYpxmxWlWHKVN\n7w8MTGrVbERq68r4d73XuMGSxS24CnSxjhJQrSAB9kHQmsOBdU2jNitfe2ODepOkvYZeHMMtkc76\nqC0AqJW0Cyw2tGXFOZnbcrsCN4uP9Vjx9pzw7ta2ZomUjmWjd+pja0DkGUk9Fbwlc2cCK4jEa02A\nlIHFH3t1sG9lCySaNRBYMYlXqXaxDzM8zBLhEijh8q7mI4XqzuD+Bb37m17L/JoOJGgGyuXM26a7\nQU3tLJEy1lX9PMNTYiNmiSiWBOtWtijenRXXC3B9VtsWxfWScLOUuEgyS2QVbEm9i/sj/GMNVQ2I\nPCNZZSthzQreHCBq6/VuSbEkxe1GWDazVpJ3PANZ2nUKwCGWTM4eAiW4Wq0JaSBRbRZIq1YtLsze\nFqnPL25NAUlxR3pjpXvGvWe6ilqguDCttqS2TiSCwKb4b1J+D4rrRfD2bB3L3t4q3t4qrs9W/Xte\nM25X8bGLiWQdbQAeWR+ECBH9dQD/AoDfV9V/zs/9EMDfAfAnAPw2gD+nql9+xOv8XqiUwq8JsNuG\nkIWtND4RDpviZiGsm32jKsrMXgfI1KeDu1RtCaoK9j0CtN3MlzNyL2GyV6l6benqanxo/1N3Tt3R\n3hLpLY/OpYGV7ZeYiPVNzQaR0q3sRvDja8G7c8vGWOPlsm9jLpba0KPpm1gifwPAfwzgb3XnfgXA\nb6rqXyGiv+THv/IRru97JcvOAKsXgWUBUhIsEZg28oyMWSplLZjINrv3MAGnRA0iBBAxyOtKIOTr\n1qC5M2K1IKpdnUcpYUerY2k00O643PxdbrfTziChu4/1qgAp+7TvamaBVSCpxUSWJLjZxLqVnQU/\nvsn4w3fWseztbWm6bC0St2Tzk1Ju44iJPK4+CBFV/S0i+vmL038WwC/5/t8E8PcxIPJgWQe0ls7c\nsscqVp+C72XnW/YZJBQwBWCOwGkG1mRxk2aJmDUCFEvEQQKgTO4T5WqJELVeJW2pzK4upFow/U3Y\nB0gvdGGK7OOtJax7AZDLfeogIp7+Tlb/8W7J+Oo248c3CX94nfEHXyV8dSu1p0j2re57cHpYIo+r\nbxsT+RlV/ZHv/wjAzzzS9XyvJQpotpt3y90NXOITflNmCWBWxAAcZwPIqw1YMyF5G0A4CJh9iUwQ\n1K0P5RJ7YJtPo1YJaynhi+bPNe9zFxyX9yLVVK7eeYplbC3ySn6i1p/hLkC0A4i6c5cVHlgtHdyt\nxeSPbxK+fJfw/71L+Oom7/qlWIBWW+ZIi/U09Fh6cGBVVZVKK6yhB6n/j/51kQRbmJpw62vM3hwE\n1wvharFWAqcFOJ2tcK3NGTELxdq2+vR5FahY4jfs3Jlu5i5Z1sbiL6i9VneRjC4bBHRZGrQgZomh\n2FiWntBaA1Km9QvQ7bcakevF4h3XZVusIvXG+9XeeDD1vObH/UcZ+qC+LUR+RER/TFV/j4h+FsDv\nP+ZFDX29+noSa7dIeDcJDpEQfTIc1Cpba4/R2iKwm4imDPWVuiMTYigbdseB/VwNktjrUxejLWM5\nJ774k0gLZvbnavMge6kOJA0i/fmbVfAHbxO+vDZr492t4GaRmrodbsqn07eFyG8A+AsAftXHX3+0\nKxr6oPoS8PNmtRFzVMQg1RoQtRaLBgvtwCF7iKhlcObIPjfHmkhPkTCHdtzliNEXhbyvt1DKgiQZ\nOdt+zrY+bl0kKnvhF1CB0UOkB4jC6kK+vE748tqWfXh3zrhdxFO3ipwxUrefSN8kxfu3YUHUnyai\n3wHw7wD4ywD+LhH9RXiK92Ne5NBe2nVKO6+KmyjWf7UDyJaBOTZwoE6Dpw4iFhthZhymgMPEOExW\nTn+cgDQRDmAoBZvQp9ziGCUpU2s9tM8YY0sZW4Jvii37mOym33y5SltlrodGg0h/ftkslfvVjUHk\nuloi2orIBkM+ib5JdubPv+ehX37kaxn6hrImR2WOjSIure1irmlQm6SHDhi1eKvr8KVKCGwl9Mc5\n4nQgnDIjCZCVocQgZoQQwRr85gbQBSv3m8FkzYRlgxXGbYJls+N1ta73y5axbslm1dL98Oj316R4\ndyt4dzaAvPNZuudNsGb1+M/T/1sMjYrV76RaTIRwWytbGVksPrBsjNtFEQPVPiF7cABAeyww49UB\nuDoS1szYPB2q7sJwCIgSETXW9WlL2nUfIG0wOSfgdlOcV8F5YascXYDzqjgvpZLUIIJ74IELkGxZ\nbWr/IrvxvAq2bczO/ZQaEPkOqhSiWeNnWBW7CFImLA6W68kCon3/jntHWB/Xc2KswkgiyJ7WJSZw\nYMQUME8Rk0bL8sC6xIs2mIhbJuLHt0lxswluFsbtQrg5AzdnzyadBbdLxs05myWCPTiAPu1r+ykD\n580qT89uzdioXUzkKX77Q5caEPkOqlgifQwkZcWSCLNXts4RdXU9szpsBHCxb8FTAwgja2y9RyIh\nRsY8BWwSkXWyLIsDRGBr6hRw9I/dJsHNFnC9Zrw7E65vCddn4N2t4vpWfMtIPhvuPojYaNeZRT2W\nYtu6i6/4NIABkU+iAZHvoFStVyuSuR0pKxYmRF8TJpaGyrtq9HZQbthyMMWAJAFZBUoCYgUHIEbC\nPDEO2SCSNFpmqINFhnevv4DKOQlutox3K+PtQnh7Bt7eKN7dKN7eCN7eZLy9ThUidin7gvieCQWU\nWaz+xbI8VuGbc0nxDop8Cg2IfAclCqioLQWRS6m6dpPm2pKal7oECADMk0IQK0BCUMQIzDPhkBin\nXCAzWel4gYYC2StJ8wVIblPG9cZ4tzDengk/viV8dQN8dS348TvBV9cZX11npJz31/QeWbGctirU\n/hhtf+jpNSDyHVS9id5b1fqT3U1zAqaYMcWMeRLMk2KeFYdFcZgVxxU4bcC0mhWSgR04ytZD5XqF\n9flYFO8Wxbuz4O25TNkXfHVrE+dSHs09vusaEBkCUJb0FCwp47wl3Cwb5hgQAyMQg8mLxlCAoRUo\n0lsm3tX+7c2CdzcLrs8rbs8bzmvCumVsyeIgMoo6XowGRIagUG+9KFi3jPOacBMDYljB3uVMYU2R\nayBV8TX7wPXtine3C97drrhZDCLLahApLQoHRl6GBkSGanzBFh23fqTTsiGwN2tWg8yy5ZqVkQ4a\n9bjbvzlvvq24OW84LwnrlrxZslsigyIvQgMiQwDKesEGkWVNCN4Vra7glxXnNe/rQ/SiPsRHVcXt\nmnC7GDxulw3ndcPi7kzJpAxb5GVoQGQI6jNrizsTmGvz5R4ut1Nos27VXJwClAKScm7ZDEbLmrBs\nyWMiCVuZeDdiIi9GAyJDBos6qU9AlKCqyCJIOdc4yRRDLXHfzZvpAFLOrylj2zLWZM8vx1uyjIzo\ncGdeigZEhrxs3iyOEkQtgdZly5hjxhQZMfAOHkDXOQwNKAC8n6kgOTS2LEjJoJQ9OzMY8jI0IDJU\n3RZrQmgASSxYE3sFLCMEm+1r824aAC6BUs5ZX1PxPqcCyftj1f6ZQ99lDYgMAWoLOm0qyAIQSbcG\nTVt2gru+qPWp971ccWu0jaL9uVZ5OvTd14DIkLshdlePDqVDP6n4wz8yNDQ09H4NiAwNDT1IAyJD\nQ0MP0oDI0NDQgzQgMjQ09CANiAwNDT1IAyJDQ0MP0oDI0NDQgzQgMjQ09CANiAwNDT1IAyJDQ0MP\n0oDI0NDQgzQgMjQ09CANiAwNDT1IAyJDQ0MP0oDI0NDQgzQgMjQ09CANiAwNDT1IAyJDQ0MP0oDI\n0NDQgzQgMjQ09CANiAwNDT1IAyJDQ0MP0oDI0NDQgzQgMjQ09CB9ECJE9NeJ6EdE9A+7c/8eEf0T\nIvoHvv2Zj3uZQ0NDz1XfxBL5GwAuIaEA/kNV/ZO+/bePf2lDQ0PfBX0QIqr6WwD+8J6H6PEvZ2ho\n6Lumh8RE/g0i+t+J6NeI6ItHu6KhoaHvlL4tRP4TAP8MgF8A8LsA/oNHu6KhoaHvlOK3eZKq/n7Z\nJ6K/BuC/ebQrGvokIiLzT4lAIBCV/fIY7RzYD/mytP/rnvdr+9o/oPecA6BQqAJQvXdf7a87zxv6\n+PpWECGin1XV3/XDfwnAP/y6nx963iIiEBGYGMxtpDvHDpr+7/eAhfzB/md6EFH9Ib/xtYFDUfYb\nFFQVIgKRMgpEu30/b3QZekp9ECJE9LcB/BKAnyai3wHw7wL400T0C7B/638M4F/7qFc59NHFRAiB\nEZgROIC7fTsfwMwVFNTDAOismAaXAo3dY/7EYukABogCDtscIdqORRQ5Z2QRG3NGym0fyFAls0iG\nnlT0sX7pRDT+Nb8jIiLEEBFjQAzB9kPwY9ufYkTgsIMHUQ8RuvuYWzjlPeo5O+GPKQQOC4eJHWuF\niMCsjG1LSCkjpYQtXe7bsQFl6GNIVe/1Tb+VOzP0skQgMBMCcwVG3aYJs+/HGKulQW5pdAZFFz/Z\nQ2QHkIt9wCCh6rCAuy5wgDhYUs5Ytw3blrBtG3hjMG0AtLo6RAMgn0IDIkPmctAeIvM01e0wTZin\nGdMUDThugexgQnvrhAswuMRbOqAw6rlqaejFCANIsUq2lDGtK5Z1NbeqAMgBwpkxSpc+jQZEhupN\nz8wIIVaIHOYZh3nG0cfDNN8FxXuO2QFS4FECs9xDhR0iCmToDiJZe5AYRM4h7ACiqhCPizClen7o\naTUgMgTAMjGBPSZSIDLNOM4HnA4HHA8HHOe5szKsyIiIfHR4uFXCBRjcZ3382M8ZRBT5AhxZ1aCi\nigwDyZo2Awh3ABFBShkhJYfLp/sNfp81IDIEULNEqjsTzRI5HmacDgdcHU84HuZqbTBht19gUvcd\nIswOkB4m3fkeGm2EA6WdW9YNRFYbWQCSU8a2BYQLC2XoaTUgMmQuiAdWQwiYggVUD/NklsjxiKvT\nEafDscKjWB/cwYPJ4iUM2sMi9DBhhPdAJKnugJLcEsmqiNMKYG+BbCkhrhtC8DqWERP5JBoQeeHa\npVhr3UY/EqYQME+zby2gOsfZgqrRt2lyYDgsdhChHUjuxEGYLlycVrxGAEhbbGW3D21Zn5oe3gd0\n/ZM+9a92yDUg8oJVqlCJubor7bhVo8YYcXUwi+M4H3CYD5jjhClYbUggNstDtbtVL0pVtS8Ws6Iv\nUbUbPnc/XkcrI7rjztR4CHYuzrJuuLm9xe35jPN5xbJsWLfNa0OsanUUvX8aDYi8YFn9B4PZ4gbh\nPeMUIo4Hy8KcDpaFmeNstSEcPPZBlkbxArHyDpaAJSgB5LVIFSZ+Y4uqF5KJ1314bYdKzcjkGlj1\nmEgNrNrj67bh9nzG7e2CZVmwriu2bcOWEnLOBpFRrfpJNCDykkWwrIuDIsbolamTj3Y8xQnHOeLg\nNSEHd2diZ4kQUOeltNiD4tIiKWdsLosiq5eqi42ibT9rthRuycp8TYp3TQnLecV5WXA+L1jWFeu6\nIRWIqIxpM59IAyIvWK0S1dK2U5y9AtXGKU6YphlzjG2bgu87eKolYu7M5Tv0GFF/TwVBRJGyIElG\nyhkpJ2w+JklIOWPLqULi/cVmVs265WzgWKzgbFnMEklbcndGx+S7T6QBkResEhMJPh9mmiYcpgPm\nefbxYK7LNFlqN7Bvbd8gYjGRdpPeDWIWmDRLBMgi2FLGmsztsHHD2u3nDhR3y947yySLl71vWFcr\nf1+3hM3ny4yYyKfTgMhLFsFTqgExmgUyzzOO8xHHwxEHH+dpQiRCZEJgG8t+YEIgsjioqrsydy0S\nYA8SUbNEtpSxbgnLtmLZNh/blkUcHD7pDqggqTN4AUiWOtFu84l3ZWsxkaf6xQ71GhB5wSqB1VKF\nWiyR4+GE0/GEk4/zNCF4BWoggEl9BAIp6qwUrX+ht0aUepfGErM2dd8hsiac1w2364LzurRxWZBV\n7m8FoPvj0gog+dT/nPuWABkiOgKrn0gDIi9YvTszhYh5mnGYDzgejjgdTrg6XeHqeOVzYhQMAUFA\nWvZ9VK3n/ZVR7Q6CdxSj+giAGhPZUsayOUSWFTfLGTfns43LGVlytSD2TYl0d07EszmXjYm64wGR\nT6MBkRcu6tyZKU6Y5wOO8xGn4wlXxyu8unptENEMSAY0Ayqgum/niztjKgBRM0M6lfyNCJolsiUs\n64rbZcHN7YJ351tc397i3fkWWXJ7nl6+Tjuq/UZ2bRFba0QDyIDIp9CAyAtWm8PCPs0/1pL2apXM\nBxymA6AJKgmQ7CNBLUUCQKEigHY9RIAOIMWfqY9AVZGLS5Mz1i1jWRPO6+oWyYLr83k0EXoBGhB5\nyeq+pW0T2yRDc4bkDMkJGoJbIeJbqTsFQAywghBq3Ulr5sxefMY1FgKQtSn0VK8qAUqdqzLK01+a\nBkRetEqwwSEi4luGuMWhDhKoxUP2ADEoGCzMdSFqsCgwAbj+rKqdF+1hAgDUORsDJC9JAyIvWBZn\n8MRpb4V0IBFJUAlmgViZWH1+a2FIIA1daRl1FgVdnCuWRwNID5LdtQ29CA2IfB904dKYFZKrFSLZ\nAUHNCmmzaM0SKZiof2uDhsVb/bjsa7/hzngZkB367mpA5IWrZDHsDpbq0lQrxEHCzUPpZtq2LmWl\ncxk6GAA2WsKXvLbDH99ZIZdTeOvFDb0ADYi8dHmMQwtAVKDaWSLuzqi3KFNc9CAhttgqEZgBUSpr\nOlRroqRnGzhwTzykPTZiIi9LAyIvWheB1c4SqTERd2fAhGB18pbKLSveXbQzhBg7xEGiXqfeQNL3\nFOncmXpNNAyQF6YBkZesUphV1qmtIMl34iIEhhL73W6F7q1rO4MDg5kBsupRhrcXcahAAaVS/AWv\nd20btHdrhl6SBkReuGqGpmZnui2nzp1RKAHKNcJhQVVujY04cO1fKABItEvOtOrVMiu3L2fvLZWh\nl6UBkWeufhHsn/i5XSFp7QdSCsokdynfBHC0d1MCwZZfsFgI+3o0DA4BbXVUK0VnBwZRye4Usb1A\nV1PSitR8v1sFr0rHhP7vmgZEnpFqT9Tdwk/crSBn6670t10X2rzDmrn0Tj0ccXU44upw8G3G1WHC\n6RBxdYg4zLbebvC1eEM0aMQYfLTjEBhZFBJKvxCFZB/F3JwsHi9B9G0GkECUQJRBJCAWECmIgZRT\nTT+XSXT1eJeaHmh5rhoQeUZqq9B5X1TuR27rq4CqRVAg0pKo7fxUIDIfcCrrx3gf1avDjNMccToE\nHGfvuepbLPsFJqFYIgQRcmCUJSzh4HCQaIFIADABNAGYAUoAZQuisKAUum4p+Uxcb58oYmO2Nooi\ngjwA8qw1IPKMRNV1MMsghli7klk/1IAQYl0LtxWG7SFSHptjwGk+2AJU89xgMk+2HSac5ojDtIdI\nsTps0l6zQpi5QkK0AEP353xslsgEIFeAEKlvAAVg25K1TMwZObVWipkykH2+8LBEnrUGRJ6R9otq\new9UbyZU9+PkLk2tF7WNcHEOmCJbB/d5xnGe7hmjN2juO8Bzgwk3mPQQUe0h0u37phUiU7M+KJsb\nw2rhkkCgwFi3FduWsKWELSRw2kDJYieqMEvkU/6jDH1QAyLPSEQEdmujLKo9z3O3sJQtrF0sEbNA\ntNMm/k8AABTySURBVM2hJd2BZIqM4zThOPvm+6fZV7ebIo5zwCEGe1/vPRL6/QoSc7V2AEEPFGr7\nAIAIUDR3hsRjIfCNwMHWv1nWiDXaGjJhW9vyFL6kRBbGWNnueWtA5Bmpt0RiNIAcfDGp43zA4WAj\nMzk4FEwNGryDikHkMEUcp1ihcZjM+jhOU92fY6w9Ryo4OHTn2OMyVGtAxNO14tP8xUvhC1gIBhAi\nsVYCxQJhqzshh0iMEXFdEUJZS9cW+RYV5CxgSqPA9ZlrQOQZab+odmscdDoccTzaWrinwxGBGUQG\nC4Ze7Evdj4FxmAIOBR5lfy7nbJyjdXSvsKDQ7fNu3wpU27yYCpOLc+AI9O5Lb4EEBoUADhEhRv88\nZTKfL9adBSkkA86gyLPWgMgzklki7s5M1hO1LKh9Ol7h6nTC1fGEyAwm63/aWx9cYWLnYyAcYsA8\nBQNG5LY/BczRxinsgcHEtnQmM4IDhalBRIk6cOyn+wt8NTwWEEUQWyq3LPDdA4TDBA4GMJC7MJ6h\nSTkhbKFO/ht6vhoQeUaiO5bIZC7M4Yir4wmvTld4dXqFGKhCIzgw7LhZIUyKKQBzZNsmxhwD5sg4\nTP05W18mUANFA0h3TLaery2ZSR1M7jn2FHQfA6E7AIngOLmlYaVrIoIkgpQSYoit1H5YIs9aAyLP\nSCXFW5a27LuzX51OeHV6hdevXmEKXKER3PIInWVSjiMDcyRMkTFHcnD0x3bOoLSHRQUI2jkm3oHD\npsR0ICkbqFogFR5sAKEQwSGZFRKTdU1DtyREStimCXFbETh4Veun/pcZ+joNiDwrlYly3bR9nyhn\ns203SNogajceSLpmQrIbCV5ZSgxlhQpBRSGZoQw/Zm+baJPnRGVXJ69QSIUTgyGQe6wPAXUwMdfm\nvGUsqzVo3pIgZytGUynVLQyi4PGXiBAmxDBjmhKmKWOeBYekSFmRhcBhqxMI993e+4rWUU/yKTQg\n8szUborWSFlSQk6bbdsKEkYgWzZSSRGgUD8O5DcYCUgJGYxM7GNAIIWwOlz8piY2gIChEAg8+0Nc\nnBNfh4YqRFozxX18RCpEBOeUsWyCbRNsSZCS1hJ5aJlHE8AUrcAuTojxgHkSpKxIGchCEASEuNZ4\niUru1qDJ3q3NtjHF7+k1IPKMVKfs15sl7SyQvK3IUwQJdfBQh0eDCvtjJITg8MhgCCmEAoQVyl4o\n5q9lPT8MFARCBlWAlEUiqKR30UZL63bnvDnRkgVLEixJsSaHSFbk0lReizXCYI4IPCGGjCkK5lmR\nBMjCEGUoAkKYkcWXzMwJWTJyThBh5Jx8EuBYSvNTaEDkWemi54cv65BzsURWpC2CmDp4NJDwhVVC\nwkhufWQKyAyzQjhCmCBMUDaXpa6z268l460P7Zy1PyygyD7a0jRlvzwGbFmxZsWabX/L5ppIdnAB\nIFg6mTkghgkhCqZJkYRwEIIoQxAAighxtbV3s1lkKScwMVLe3AtUiIzgyafQgMhzkmK3NkztPJY2\nSIrIKSBvwWf4NkvE9nEHJqSEQBGZBEKCTIrMwQASLC4ivkiVrQ+jtc0hSh/V2hzN9rNXp2avTi0w\nqccOlE2AJOoj6ph9rk0BE1EwSyQopqDIsVkgBpAJxBNCXLFtG1JasYUVvK3YqPR5VbDku20Fhp5E\nXwsRIvo5AH8LwB+F/Xf6z1T1PyKiHwL4OwD+BIDfBvDnVPXLj3ytL16KS3emBFQTct6Qt4AcQrNE\nKkjQ4FFjIgpSdnAoMgHCgCQYRDJBgkCF62LY3bpVXXf2/ZbLJg0edtyBRAjJgVJHsTF3r01askIR\ngRUhKqISZndhQBHECRRmcFgRwoJtC7UATQGo2GxfqgVrQ0+tD1kiG4B/S1X/NyJ6DeB/JaLfBPCv\nAvhNVf0rRPSXAPyKb0MP0WULw+L/582skMBIm5WNK/XxkGaFKFnrwkAKVjaAOETMnfHp/JkhWaBB\n3CJxl8D7FpWJdOpT/su5AossMEDI/lwdYe5I9uBr1jKyz63pLRFFCEAUgmiAIkApATyBQgKH7BAJ\nrW6kW/4iSEJOo57kU+lrIaKqvwfg93z/HRH9IwB/HMCfBfBL/mN/E8Dfx4DIo0hx2Uw5QVKAhA0S\nCDl4wyKgi4egFpw1oACkjEiKzEBmsgZC2QEScrVC2tZ6hLQp/n2fEGs6lBwcbbw4ryh1s1DyGlry\nulrSmhK2DmrWRT6wNT9SZJ+4l0FBDCAxg+NkvVSoWEjeeyQnJHbrZDDkk+gbx0SI6OcB/EkA/xOA\nn1HVH/lDPwLwM49+Zd9DtYbKvSvDkByQEyMzIXv1p7obExwYtUcqFOznGQGJgRgsiJpDsUB8q7Ci\nCo7sQMn3HGfxrEk2cCQHR8rtsZTtHIihHLxkNQBsfVxRl6aw/otMasVtQRARAEidc8MiCFERRBDC\nWmf3qqg3MUpIKSJwtI5wwxL5JPpGEHFX5r8G8G+q6tve91RVpdZ4c+hBamvmlhoIc2k2SCK3KOy+\nLDFPC6yis0JQAUMqiAzk4JZIIEgwgKgESJZmhWQDRt0ujlMuowMkY7e/CWptRxKAKABBQRxq2TsC\nGVNQlqQw6yGwugvjk/VEwQFgVURRRAFCWOw3VCboibl5W1yt9yuX9YCHnlofhAgRTTCA/Beq+ut+\n+kdE9MdU9feI6GcB/P7HvMjvi0oTY5uCX9oClNYAwXuMBOvtASBQcWN8dJiwn59iwBS9Q1oMNaZg\nbgFX96B2cu4KtbT8qUtOlP6nJciqu4Ar5OIY2jqSqQDKIFEoxCfbkb8mLlyqC3i5u5TSZundnFq9\niHSVvaNA5JPpQ9kZAvBrAP5PVf2r3UO/AeAvAPhVH3/9nqcP/YQqDZkDM0IsM3mtr8jRe6SejrPN\n4u1g8V6IBMY8TzhMEw5zxDRPmKbJpt97IyJin9eiYtaBenMjotbGEG2094C/R7cxWZq5dGv3Bu/F\nw7BytFJvQlZ2j2TB2ixIvm0iXldi+ykLtixYtxXn5Qbn5Qbresa2Ldi2FSlvkJwHSD6hPmSJ/CkA\n/wqA/4OI/oGf+7cB/GUAf5eI/iI8xfvRrvB7JCLURs02k9daIx7mCYfDjOPxgNPxgMlbAVCFxl2A\nWD+RgHmKmCcD0jRFxMn6tdamz+wd5JVAytaBrAAEdaWH2m5A6jnqAAKw2n7gMqcGzowyt6fkjgVe\nYQ8UyyNn5CTYcsaWMtacDRwpY8sZaxas64plvcWy3FaIpLQip1QbOo+S90+jD2Vn/kfYP/d9+uXH\nv5zvuciXrPSO6zEaAMwSOeB4PODqdOz6iRg0qNvvoRKYMU0OoxgMIjEgTs0SKa4NlR4g6kDp4GGW\niFYLpbyPkDdScpAEWKFaGUvxq/YA8Y+qAoC8f4g3ak5bMoik5FvG4uO6rVjXM9Z1wbp1EBmWyCfX\nqFh9Rirrzli6M7j10FkiB2tQFGsrgNYe8T6ohMCYQkCMfVwlIMRoACldxohBqhUecEvj/2/vXGPl\nqqo4/vvP7X214IOHQki1iIBARJvyEqmiJA0vtaIJ4iOihhoFbERNIKjUT5gYQRCDgmj5IFhJACFG\noGKBikSglLagUtAWRJGKAmJzZ+bMneWHvc7M6XTuben03plp1y+ZnH3OnLP3PufcWXfttddeqyFI\nCsKkRHJ1z4WHuTYy4GEB8q0VjLzKfVjcQyQ5xvqR8fGkTdQyarUa1SyjmtWoZBmVmm+zmgd0rpLV\n0jAmyypk7v6eayIhRLpDCJEeomFUHUgR15vBmgdT1PaRYUZHRxjMwyM2BEdTkGyhlZTkhtmSp57Y\ncpuCJQ944yUfeqggQPJtIYq8ax91n5o1WYq9WtBA8m09n0FqCJCSayOWvFZl1H2WpVZLbu1ZlpFV\nq1SzjEo1o5xllKtVqrUsGVdrVd9mrol4KlCrd+u17faEEOkh8ty3A6WkNcxw4+rw0FDBJjLC4IA8\n4ntTkKhFKxHmEdq1ReqHUks5eYDS1ETqrRpIIbK8/DxwAQJWSrmo8jy+A34n+U/adY8UvcyaxlVD\nyWGs4ZGbUatVkgCpVqn4p1ytMlatpHUz47U0O1P81LLmTE1oIl0hhEgPkRtWSwXD6tBQ0kRSmMRh\nZo4OMzhQ2kJYFDWQLba5jcU1nMa+R24vKbnQA6heb6TvTIJEjTYaLvWYD1VyBzfXPESuZGC5Ixm4\nndOoWzNPTtJCXFMxkkeuayI1H6ZUqxWqlQrlaoVypcJYJQmR5GDmCxPdhybft8bCn2C6CSHSQ0w0\nxTucT/GODDM6MsrgjNJWAqOdMFGjznxookJe3+YxzNIsTS5I/Pvc5tHQRGjW6SMfStAIbjSQX+Cx\nR4BkT5U1BEpzgV/6NDURt3NkZarVMpVKmXKlzFi5zFilTJbVqFvTJ6Te8A+p+wLCOpEKvDuEEOkh\nmjaR5uzMoPuJ5MOZmaPDDM4YaMyY5Gkiinln8uOpTq/bHcpUaKuBWRIgDUHSMpxpCCQfyhiN8Ijg\ndg/PSeNWV3ffB6sbubd7I9SAf5dc7XObSD6cqSQh4tO55fIYY+UyWS1rOLGlqtzastWxYLoJIdJj\nFLWFhj0jT2jVyMlbatE4WvdzwdKm/jbHknNYQ9q48FDLBY047i6M8iBGBbtJ3v+87NpKEiJF1cQ1\nk0I82brlw5TcI7WWZm3Ga25Mre2U5xvsfCbyAQl2I1at39jtLgR9TAiRgFXrn+52F4I+JoRIEAQd\nEUIkCIKO0FRZtCPGSBDsWphZO7v81AmRIAh2D2I4EwRBR4QQCYKgI6ZNiEg6WdKfJT3paSb6Fkkb\nJa2VtFrSg93uz6tB0k8kPS9pXeHYXpKWS1ov6S5Jr+tmH7eHCe5jiaRn/b2slnRyN/u4vUiaLWmF\npMclPSbpS368L97LtAgRSQPAVcDJwOHAWZIOm462pwgDTjSzuWZ2TLc78yr5Kek9FLmQlEfoEOBu\n+iP9R7v7MOAyfy9zzeyOLvRrR8jzOx0BHAec67+Pvngv06WJHAM8ZWYbzSwDfg58aJraniraWqp7\nHTNbCbzYcviDpPxB+HbhtHZqB5jgPqAP34uZ/dPMHvXy/4Bifqeefy/TJUQOAP5W2H/Wj/UrBvxG\n0sOSzul2Z3YCu1IeofMlrZF0Xa+q/5PRj/mdpkuI7GrzyO82s7nAKSTVc363O7SzsHx5bH9yNXAg\n8E7gOeC73e3Oq6M1v1Pxu15+L9MlRP4OzC7szyZpI32JmT3n238Bt5CGa/3M85L2A+jnPEJmtskc\n4Mf00XuZLL+Tf9+z72W6hMjDwMGS5kgaAs4k5a7pOyTNlLSnl2cBC4B1k1/V8+R5hKCP8wj5Dy3n\nw/TJe9mO/E7Qw+9l2jxWJZ0CfI+UWeA6M7t0WhreyUg6kKR9QIrH8rN+uhdJN5KSse9DGmd/E/gl\n8AvgTXgeITN7qVt93B7a3MclwImkoYwBG4DPF2wKPYukE4D7gLU0hywXAQ/SB+8l3N6DIOiI8FgN\ngqAjQogEQdARIUSCIOiIECJBEHRECJEgCDoihEgQBB0RQmSKkXSxL+9e48vTe8qLUtKbJZ21A9ct\nlfSRNsffJulRSaskvWXn9LJ7eHiBr3S7H71MCJEpRNK7gNOAuWb2DuAktlyI2AscCHx8B66baC3H\nQuAmM5tnZn/dViVydqD9Yh0DnVy/DcKRahuEEJla9gNe8PAHmNl/8nU3kuZJusdXAt9RWCNxdCHg\n0XfyoDuSzpZ0qwen2SDpPElflfSIpAckvd7PO0jSr73e+yQd6seXSrpC0v2S/lLQIr4NzPf2Fksq\nebsPuva0yK+XpKs8sNRy4A20LLuXdCqwGPiCpLv92AWS1vlnsR+bI+kJSdeTXNNnS/paoc0lhTq/\n4W2ulHRDrhX4s7tc0kPAYkkn+bNY6yt4h/y8jZL28vJRklZ4eYlSYKMV/jzOL7R5sfdvJXBo538G\nuzgpL2p8puIDzAJWA08APwDe48cHgd8De/v+maSlAACPAcd6+VJgrZfPBp70OvcBXgYW+XeXkVZ+\nQgpe81YvHwvc7eWlwDIvHwY86eX3ArcX+rwIuNjLw8BDwBzgDOAukuDYnxTL44w293wJcIGX55Fc\nuUe934+R3NLnAOPAMX7eAuBHXi4BtwPzgaP9+Q0BewDrC3WvAK7y8gjwTOG+ry88jw3AXl4+Cljh\n5SXA7/xd7A28QFqSkfd5BNjTn/kF3f5b6uVP5OKdQsxss6R5pB/E+4Blki4EVgFHkGKSQPrj/Yek\n1wJ7mNkfvIobgNMLVa4ws83AZkkvkX5skP6bH+kLAo8HbiqMEIby7uALuMzsT5Ly2BStQ4kFwNsl\nfdT3XwMc7Pdwg6Vf4HOSfjvJred1ngDcbGZjAJJu9npuA542szy05AJggaTVvj/L29wTuNXMqkBV\nUn6/Oct8eyiwwcye8v3rgXOBKybpowG/sqQl/lvSJpLmON/7XAbKkm5j62cUFAghMsWYWR24F7jX\nhyafJgmRx83s+OK52jqITusfb6VQrhf266R3WQJetBTrpB3VSeoucp6ZLW/p26nbuKYd1nKNaNoY\nNrece6mZXdPS5uI21xdpraNdOzWaw/aRlvOKz2Oc9Azb9TmYhLCJTCGSDpF0cOHQXNJqzCeAfSUd\n5+cNSjrc0grNVwozOB/b3qYALAWy2ZBrEW7HOHIb175C+o+fcyfwRUkzCvcwk7TK9Ey3mexP0qy2\nxUpgoaRR15IW+rHWH+adwGf9HCQdIGlf4H7gA5KGlQL2nNbuvknPc46kg3z/UyTBDel5H+Xl4mxS\nO+Fgfp8LJY0ohXw4nTCuTkpoIlPLHsD3XcOokcbXi8ws8x/6lT6EmQFcDvwR+BxwraRcg3nZ62qd\nDWkt5/ufAK6W9HXSeP9G0hi/3TUAa4BxSY+Sgh9fSbJZPKI0JtoELDSzWyS93/v4DMmmMxEGYGar\nJS0lLWkHuNbM1iiFAGz0xcyWKwUmfsCHYa8AnzSzh304sZa03H9d4XkU2ylL+gxpGDfD2/uhn/Mt\n4DpJ/wXuKbTbdnbJ+7zMn8umQt+DCYhQAD2GpFlu98DtJ280sy93uVtdI38erg3dC5xjHtQ46A1C\nE+k9TpN0EendbCTNyuzOXCPpcJI9Y2kIkN4jNJEgCDoiDKtBEHRECJEgCDoihEgQBB0RQiQIgo4I\nIRIEQUeEEAmCoCP+Dytky5b8X0IvAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mask = Q>0.5\n", "fg = im.copy()\n", "for i in np.arange(3):\n", " fg[:,:,i] = fg[:,:,i] * (Q>0.5)\n", "plt.imshow(fg); plt.xlabel('Segmented foreground')" ] } ], "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": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }