{ "cells": [ { "cell_type": "code", "execution_count": 1540, "id": "513df8ba", "metadata": { "collapsed": true }, "outputs": [], "source": [ "from pylab import *\n", "def ls(A): \n", " \"Normalize a matrix to be a stochastic matrix.\"\n", " return A*1.0/maximum(1e-6,sum(A,0)[newaxis,:])\n", "def vs(v): \n", " \"Normalize a vector to sum to 1.\"\n", " return v*1.0/maximum(1e-6,sum(v))\n", "def unary(i,n):\n", " \"Generate a unary vector.\"\n", " assert i" ] }, "execution_count": 1625, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fSx0rQfmpPxlz9pcpFLYhdX8KioyABsv2XV/bbjyXBIIqckt7mTtBe79Alnn7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Ga8CcB8jQZt1H0k2Pu5PGhXnZjOiLgCWgZ5pnd4eFgHDhzQ+Pi4hoaGOoI68868oCxXV1e1srKi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\nLmnLOuUqN0oDpYwJQARoA1UaEfuY+qP8+SqDbIPyJGhmMHBd3d2d+wd4b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JBz+rYbt5VA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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "letter = 1-mean(imread(\"../scans/chars/letter.png\"),2)\n", "gray()\n", "imshow(letter[:300,:300])" ] }, { "cell_type": "code", "execution_count": 1626, "id": "32112033", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1626, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "h,w = letter.shape\n", "ch,cw = h//30,w//26\n", "lines = [letter[i*ch:(i+1)*ch,:] for i in range(30)]\n", "chars = [[l[:,j*cw:(j+1)*cw] for j in range(26)] for l in lines]\n", "chars = array(chars)\n", "chars = array(chars>0.5*amax(chars),'B')\n", "Es = chars[:,4,:,:]\n", "gray()\n", "imshow(Es[5])" ] }, { "cell_type": "markdown", "id": "113623e0", "metadata": {}, "source": [ "The individual letters aren't centered, so let's do that next." ] }, { "cell_type": "code", "execution_count": 1542, "id": "edb064ea", "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.ndimage import measurements,interpolation\n", "\n", "def centered(image,size=None):\n", " center = array(measurements.center_of_mass(image))\n", " tcenter = array(image.shape)/2\n", " delta = tcenter-center\n", " shifted = interpolation.shift(image,delta)\n", " if size is None: return shifted\n", " h,w = shifted.shape\n", " th,tw = size\n", " ch,cw = h//2-th//2,w//2-tw//2\n", " return shifted[ch:ch+th,cw:cw+tw]" ] }, { "cell_type": "markdown", "id": "3dc2f12f", "metadata": {}, "source": [ "We now have a stack of letters \"E\" in sequence. We put them together into a long row of letters." ] }, { "cell_type": "code", "execution_count": 1637, "id": "8c4c1811", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1637, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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V8WUxDEagl5eXU1RUFC1dupT69etH6enp5Obmxm91effuXZ2lp2o6glABGVpC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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Es = [centered(E,size=(35,30)) for E in Es]\n", "signal = hstack(Es).T\n", "figsize(12,8)\n", "imshow(signal.T)" ] }, { "cell_type": "markdown", "id": "359eecdc", "metadata": {}, "source": [ "Next, we are going to transform vertical slices through this input into tokens, namely by clustering." ] }, { "cell_type": "code", "execution_count": 1638, "id": "68a7d378", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1638, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn import cluster\n", "km = cluster.KMeans(k=5)\n", "km.fit(signal)\n", "centers = km.cluster_centers_\n", "figsize(4,4)\n", "imshow(centers.T,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "5e138924", "metadata": {}, "source": [ "We can now represent the signal as a sequences of numbers, each indicating\n", "which cluster center represents that particular slice best." ] }, { "cell_type": "code", "execution_count": 1639, "id": "623f759e", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 1 1 1 1 1 0 0 2 2 2 3 3 3 3 3 3 3 3 0 0 0 0 4 4 4 1 1 1 1 1 1 1 1 1]" ] } ], "source": [ "outputs = km.predict(signal)\n", "print outputs[:35]" ] }, { "cell_type": "markdown", "id": "079089fa", "metadata": {}, "source": [ "We have a fairly reasonable number of examples for each slice type." ] }, { "cell_type": "code", "execution_count": 1640, "id": "56757967", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Counter({1: 278, 3: 230, 0: 194, 4: 102, 2: 96})" ] }, "execution_count": 1640, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from collections import Counter\n", "Counter(outputs)" ] }, { "cell_type": "markdown", "id": "73f2d440", "metadata": {}, "source": [ "We can also reconstruct the original signal in terms of these slices." ] }, { "cell_type": "code", "execution_count": 1642, "id": "6814ee2a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1642, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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jP06kuC0Rz7yTCAaLRDBYJILBIhEMFolgsEjE/wAgT9uihfAkcgAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(centers[array([1,1,1,0,2,2,2,3,3,3,3,3,0,0,4,4,1,1,1])].T,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "584ebc12", "metadata": {}, "source": [ "Manual Construction of a Model\n", "================================" ] }, { "cell_type": "markdown", "id": "6f2ea80b", "metadata": {}, "source": [ "We'd like some kind of model that represents characters fairly well. How can we construct it?\n", "\n", "Let's start by constructing the \"average character\" and look at the sequence of slice codes it corresponds to." ] }, { "cell_type": "code", "execution_count": 1643, "id": "9b165822", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 1643, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AV155BTMzM9i8eTMef/xxnD17FufPn4emadiyZQuefvrpRve1IeCf/DTI6yEM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\nbIkFajxJeMlDEqYW+4C+dzg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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "unaryEm = mean(array(Es),0)\n", "figsize(4,4); imshow(Em)\n", "s = km.predict(Em.T)\n", "s\n", "xlim(0,len(s)+1)\n", "plot(2*s,color='r',linewidth=3)" ] }, { "cell_type": "markdown", "id": "7873ad7f", "metadata": {}, "source": [ "Now we don't know how many of these slices we actually need.\n", "\n", "Well, we do approximately, but for the sake of argument, let's construct a generic model\n", "that just represents the sequences of slices." ] }, { "cell_type": "code", "execution_count": 1648, "id": "79efecff", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 0 2 3 0 4]" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 1648, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "s0 = s[s!=roll(s,-1)]\n", "print s0\n", "figsize(4,4)\n", "subplot(121); imshow(tile(centers[s0],(10,1)).T,interpolation='nearest')\n", "from itertools import chain\n", "sr = array(list(chain(*[[x]*4 for x in s0])),'i')\n", "subplot(122); imshow(tile(centers[sr],(5,1)).T,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "c5689a1e", "metadata": {}, "source": [ "Durational Models\n", "==================" ] }, { "cell_type": "markdown", "id": "389d252e", "metadata": {}, "source": [ "In the figure above, for the first case, we have 1 state per output. This yields a very\n", "compressed image. We need a _durational model_ (thinking of the $x$ axis as time).\n", "\n", "The second case uses exactly three states for each output, giving rise to perfectly uniformly\n", "spaced outputs.\n", "\n", "For our first attempt, we are going to use self transitions; these allow variable durations\n", "in each state. However, the probability distribution for how long we stay in a state \n", "has an exponential distribution." ] }, { "cell_type": "code", "execution_count": 1657, "id": "1be5aa41", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1657, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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cLoe/vz+0Wi0uXbqE3NxcREdH49q1a0hLS0NMTAyys7PF82jkyJGYOHEi2rVr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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(18,8)\n", "subplot(221); xticks([]); yticks([]); imshow(imread(\"Figures/states-1.png\")); xlabel(\"1 state per output\")\n", "subplot(222); xticks([]); yticks([]); imshow(imread(\"Figures/states-2.png\")); xlabel(\"self-transitions\")\n", "subplot(223); xticks([]); yticks([]); imshow(imread(\"Figures/states-3.png\")); xlabel(\"3 states per output\")\n", "subplot(224); xticks([]); yticks([]); imshow(imread(\"Figures/states-4.png\")); xlabel(\"durational model\")" ] }, { "cell_type": "markdown", "id": "26e4b342", "metadata": {}, "source": [ "However, by using combinations of states that output the same symbol,\n", "we can approximate arbitrary distributions.\n", "\n", "Particularly simple to approximate is a normal distribution for a durational\n", "model, because of the central limit theorem about sums of random variables.\n", "\n", "The duration in the individual state is exponentially distributed." ] }, { "cell_type": "code", "execution_count": 1668, "id": "ada3877c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 1668, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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OHpU6O62uBAAiX0wEv8Nhtvo5wQsAA4uJ4Jfo7gGAwSL4AcBmYib48/OlN980p2gGAJxf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\n4VicMtzsHHB0ttf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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(6,6)\n", "p0 = 0.9\n", "decay = vs(array([p0**n for n in range(100)]))\n", "plot(decay)" ] }, { "cell_type": "markdown", "id": "b19a0da7", "metadata": {}, "source": [ "But if we add up the durations of multiple states, we get a peaked distribution\n", "that approximates a normal distribution." ] }, { "cell_type": "code", "execution_count": 1667, "id": "aadc1004", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 1667, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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SGAqSaL2lALALiSgWMRQk0XpLAWAoEMUihoIkbCkQkRYxFCQQQh+hwAVsRLGHoSDBqVPA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\niIj8GApEROTHUCAiIj+GAhER+f1/fGb8W3sMdEUAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(6,6)\n", "result = vs(decay)\n", "for i in range(10):\n", " result = vs(convolve(result,decay))\n", "plot(result[:400])" ] }, { "cell_type": "markdown", "id": "d485e72f", "metadata": {}, "source": [ "Transition Matrix for Manual Model\n", "==================================" ] }, { "cell_type": "markdown", "id": "a05f7b35", "metadata": {}, "source": [ "So for now, let's just build a model similar to the model below." ] }, { "cell_type": "code", "execution_count": 1679, "id": "81cc5de0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1679, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YqVMnfvDBB/J4c2pqKgHUOUwyffp0enh4MD093dKS60StVnPTpk0MDg4mAGZmZrJTp04E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\nYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(6,6)\n", "xticks([]); yticks([]); imshow(imread(\"Figures/states-2.png\")); xlabel(\"self-transitions\")" ] }, { "cell_type": "markdown", "id": "9ef39ccf", "metadata": {}, "source": [ "This is not going to match the \"durations\" of our character models very well,\n", "but we can still have the learning algorithms optimize it." ] }, { "cell_type": "code", "execution_count": 1672, "id": "df340823", "metadata": { "collapsed": true }, "outputs": [], "source": [ "ns = len(s0) # number of states\n", "no = len(centers) # number of centers" ] }, { "cell_type": "markdown", "id": "5f245c20", "metadata": {}, "source": [ "Here, we implement the state transition matrix.\n", "Note that we set a \"probability floor\", since we are going to use\n", "the matrix for estimation later, and zeros (=something that never happens)\n", "don't work so well.\n", "\n", "This transition matrix can be thought of as a linear function that\n", "maps old states into new states.\n", "\n", "Note that a lot of literature on Markov models uses the opposite\n", "convention for subscripts. Our transition matrices are multiplied\n", "from the left with a column vector of old states and yield a new state." ] }, { "cell_type": "code", "execution_count": 1699, "id": "e8b323a3", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1699, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = zeros((ns,ns))\n", "for i in range(ns):\n", " A[i,i] = 0.6\n", " A[(i+1)%ns,i] = 0.4\n", "A = ls(maximum(1e-2,A))\n", "figsize(4,4)\n", "imshow(A,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "0aab1a93", "metadata": {}, "source": [ "We still need to write down how the individual states correspond to output symbols.\n", "In fact, in our case, that's quite simple, since each state corresponds to a single output\n", "symbol (but not the other way around).\n", "\n", "The `B` matrix is what makes Hidden Markov Models different from Markov chains.\n", "In Markov chains, we can observe what state the chain is in.\n", "In a Hidden Markov Model, we have imperfect information about the state of\n", "the system.\n", "`B` is a kind of \"confusion matrix\" or \"error matrix\" for observing the state of the system.\n", "It's really the simplest such system; there may be much more general kinds of observations\n", "and errors we can make.\n", "\n", "In HMMs for speech recognition, the \"observations\" are actually usually the \"slices\"\n", "(short time spectrum) at a given time, and instead of approximating that as an output\n", "symbol via clustering (see above), the relationship between the observation vector $b$\n", "and the state is modeled directly." ] }, { "cell_type": "code", "execution_count": 1700, "id": "c055413f", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 0 2 3 0 4]" ] }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "B = zeros((no,ns))\n", "for i in range(ns): B[s0[i],i] += 1.0\n", "B = ls(maximum(1e-2,B))\n", "figsize(4,4)\n", "imshow(B,interpolation='nearest')\n", "print s0" ] }, { "cell_type": "markdown", "id": "7263f66d", "metadata": {}, "source": [ "Sampling from the Distribution\n", "==============================" ] }, { "cell_type": "markdown", "id": "c9dc76de", "metadata": {}, "source": [ "First, let's define a simple function to sample from discrete distributions in general." ] }, { "cell_type": "code", "execution_count": 1688, "id": "0ddec4be", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def rsample(dist):\n", " v = add.accumulate(dist)\n", " assert abs(v[-1]-1)<1e-3\n", " val = rand()\n", " return searchsorted(v,val)" ] }, { "cell_type": "markdown", "id": "17504043", "metadata": {}, "source": [ "Sampling from Hidden Markov Models happens in two stages.\n", "\n", "First, we sample the state sequence.\n", "\n", "Then, given the state sequence, we sample the observations." ] }, { "cell_type": "code", "execution_count": 1689, "id": "56851a8d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 1689, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ZfPHvAcSDj8oHVAo+2bDRvydG1X374t8DiLSW2lr6n2VF99qgthYYPVqs53Xg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\n+GVBVqxDHOuzCj4+tDcKPpX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jCyEkLX19fVi+fDlmzpyJlStXnvhc5tqlLk/B6urqcN99\n9+HKK69ET08Pli9fjrPPPjvPVxFCAqejowNLliwBABw/fhzXXXcdrrjiCsybNw/XXHMN/uVf/gVN\nTU147LHHDJeUEGI7y5YtQ0tLCw4cOICpU6fia1/7Gv7xH/8xcSyZOXMmrrnmGsycORN1dXV44IEH\nmHZBCElk6NiyevVqRFGErVu3oqamBmeccQa++93vAuDYQghJz8aNG/HII4/gnHPOwdy5cwGI167L\nXLvU9CXZyxNCCCGEEEIIIYQQZ8mV0kUIIYQQQgghhBBC7IWCDyGEEEIIIYQQQohnUPAhhBBCCCGE\nEEII8QwKPoQQQgghhBBCCCGeQcGHEEIIIYQQQgghxDMo+BBCCCGEEEIIIYR4BgUfQgghhBBCCCGE\nEM/4/5u6OFLeviRlAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def chain_sample(A,n,state=0):\n", " states = zeros(n,'i')\n", " for i in range(n):\n", " p = A[:,state]\n", " state = rsample(A[:,state])\n", " states[i] = state\n", " return states\n", "figsize(20,2)\n", "plot(chain_sample(A,200))" ] }, { "cell_type": "markdown", "id": "f62f0a0e", "metadata": {}, "source": [ "Here is code for sampling both the state sequence and the sequence of observations." ] }, { "cell_type": "code", "execution_count": 1690, "id": "62d31df6", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hmm_sample2(A,B,n,state=0):\n", " states = chain_sample(A,n,state=state)\n", " outputs = array([rsample(B[:,s]) for s in states])\n", " return array(outputs,'i'),states\n", "def hmm_sample(A,B,n,state=0):\n", " return hmm_sample2(A,B,n,state=state)[0]" ] }, { "cell_type": "code", "execution_count": 1691, "id": "ef1b1f9c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([0, 2, 2, 2, 2, 2, 2, 3, 3, 3, 0, 0, 2, 2, 3, 3, 3, 3, 0, 4], dtype=int32)" ] }, "execution_count": 1691, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hmm_sample(A,B,20,state=s[0])" ] }, { "cell_type": "markdown", "id": "86b8c154", "metadata": {}, "source": [ "We can now generate new, random images from this." ] }, { "cell_type": "code", "execution_count": 1692, "id": "ed66e52d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1692, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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FxjfIbA9NkfX7fUSjUbRaLTSbTfR6PaFHN2tprUBXBlrd52xKNtT+vV4PiURC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\noG5CWVkZKioq1KyGnmx6cQ0Il4mTbKnNJlfPUP350p4OyVWf9TRtYzG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ewZ49e/Dll18C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\nRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(centers[hmm_sample(A,B,200,state=s[0])].T)" ] }, { "cell_type": "markdown", "id": "b3274f98", "metadata": {}, "source": [ "It's a little hard to tell whether this sometimes looks wrong because of the observations\n", "or because of the state sequence, so here is another sampling function that outputs the\n", "\"best\" observation for each state." ] }, { "cell_type": "code", "execution_count": 1695, "id": "3a842918", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def best_sample(A,B,n,state=0):\n", " states = chain_sample(A,n,state=state)\n", " outputs = array([argmax(B[:,s]) for s in states])\n", " return array(outputs,'i')" ] }, { "cell_type": "code", "execution_count": 1694, "id": "58aa951a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1694, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Kqn7eR072/7wTDCo6ZRDNbhh7sMkX1ZrORqg6xk4ZSal1hcrO8avg14HK9bkJ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\nnL9P9a+vr2N6elr5zpUrV0SwSzayWq1iYWFB0MsDrFQqJYJ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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(centers[best_sample(A,B,200,state=s[0])].T)" ] }, { "cell_type": "markdown", "id": "0b935db7", "metadata": {}, "source": [ "Since that looks kind of noisy, you might be wondering whether the model is doing anything at all.\n", "Here is the output from a completely random HMM, but using the same output symbols." ] }, { "cell_type": "code", "execution_count": 1697, "id": "7b92f613", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1697, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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NUGRQYgo2dKC2bcsMqk7BhL8MtijYVJeDeAXJCxlg3ARWdUokC+SUaBe5GuDI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cHMzAzm5uYwNjamdIH3h5cPhUJYW1tTDjibzWJychIjIyN46623EIvFEAgEkEqlkM/nUSwWMTo6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\nbJycoNyF2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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(centers[hmm_sample(ls(rand(5,5)),ls(rand(no,5)),200,state=s[0])].T)" ] }, { "cell_type": "markdown", "id": "819c8c33", "metadata": {}, "source": [ "Forward Algorithm\n", "========================" ] }, { "cell_type": "markdown", "id": "ca8bbfd3", "metadata": {}, "source": [ "To get started, let's compute what's known as the _forward algorithm_.\n", "\n", "This algorithm computes $P(s_t | o_t ... o_1)$, that is, it updates our current\n", "estimate of what state the system is in based on the current and all previous observations.\n", "\n", "To do this, it starts of with an initial state distribution (e.g., uniform), and\n", "then computes the posterior of the distribution given the observation:\n", "\n", "$$P(s_1|o_1) = \\frac{P(o_1|s_1) P(s_1)}{P(o_1)}$$\n", "\n", "Here:\n", "\n", "- $P(s_1)$ is our prior\n", "- $P(o_1)$ is the first observation\n", "- $P(o_1|s_1)$ is given by the observation matrix $B$\n", "\n", "As usual, we don't bother computing $P(o_1)$ explicitly and\n", "instead just normalize.\n", "\n", "Now, to do the same thing for $P(s_2|o_1,o_2)$, we reduce this to the above\n", "problem, by observing that all the information about $o_1$ is already contained\n", "in $P(s_1|o_1)$. \n", "\n", "However, $P(s_1|o_1)$ is the state distribution prior\n", "to the state transition, so in order to get a \"$P(s_2)$ prior\", we\n", "need to multiply $P(s_2|s_1)P(s_1|o_1)$.\n", "\n", "This then gives us the complete forward algorithm:\n", "\n", "- obtain a new prior by computing $P(s_t|s_{t-1})P(s_{t-1}|o_{t-1})$ using the $A$ matrix\n", "- update the new state using Bayes rule and the observation $o_t$\n", "- repeat" ] }, { "cell_type": "code", "execution_count": 1701, "id": "9ba8ff2e", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hmm_forward(A,B,observations,p=None):\n", " if p is None: p = dot(A,ones(len(A))/len(A))\n", " fps = []\n", " for i,o in enumerate(observations):\n", " # update P(state|ovservation) using Bayes formula\n", " p = B[o,:]*p\n", " p /= sum(p)\n", " fps.append(p)\n", " # now compute the probabilities in the next state\n", " p = dot(A,p)\n", " return array(fps)" ] }, { "cell_type": "code", "execution_count": 1703, "id": "71d55f6a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1703, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(6,6)\n", "fps = hmm_forward(A,B,outputs)\n", "figsize(5,5)\n", "imshow(r_[signal[:30].T,fps[:30].T/amax(fps)],interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "e6a6166a", "metadata": {}, "source": [ "Note that there are several things that this is _not_:\n", "\n", "- the sequence of most probable states at time $t$ does _not_ necessarily belong to any sequence of states that can acctually even occur (\"path\")\n", "- the most probable state at time $t$ is _not_ necessarily the \"best\" state given the observations\n", "\n", "C.f.\n", "\n", "- \"The old man the boat.\"\n", "- \"The horse raced past the barn fell.\"\n", "\n", "**Homework** Construct examples for these two casees." ] }, { "cell_type": "markdown", "id": "165d7b3e", "metadata": {}, "source": [ "Viterbi Decoding\n", "===================" ] }, { "cell_type": "markdown", "id": "7f5bc3d2", "metadata": {}, "source": [ "Let's now look at the problem of actually finding the best path.\n", "\n", "The algorithm for this is quite similar to what we have already seen for string edit distance and dynamic time warping." ] }, { "cell_type": "code", "execution_count": 1564, "id": "eb77a341", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6 5\n", "900 5" ] } ], "source": [ "print ns,no\n", "print len(outputs),amax(outputs)+1" ] }, { "cell_type": "markdown", "id": "6cb7393d", "metadata": {}, "source": [ "What we want to find is the sequence of states $s$ such that the likelihood of that\n", "state sequence given the observation is maximized:\n", "\n", "$$\\hat{s} = \\arg\\max_s \\prod_t P(o_t|s_t) P(s_t|s_{t-1})$$\n", "\n", "The key insight is that once we know the best path to each of the states at time $t-1$,\n", "the subsequent search doesn't depend on it.\n", "\n", "So, we maintain the accumulated probabilities in an array $p_t(s)$ (called `probs` in the code).\n", "\n", "In addition, we maintain information about which state at times $t-1$ actually\n", "gave rise to the best way of coming to each of the states at time $t$ (called `pred` in the code).\n", "By tracing backwards, we can reconstruct the entire best path." ] }, { "cell_type": "code", "execution_count": 1565, "id": "c38a91dd", "metadata": { "collapsed": true }, "outputs": [], "source": [ "probs = zeros((len(outputs),ns))\n", "pred = zeros((len(outputs),ns))" ] }, { "cell_type": "code", "execution_count": 1566, "id": "bcbd5531", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.1646382 , 0.00163059, 0.0013433 , 0.00129166, 0.00028223,\n", " 0.00154323])" ] }, "execution_count": 1566, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs[0] = vs(ones(ns))*B[outputs[0]]\n", "probs[0]" ] }, { "cell_type": "code", "execution_count": 1567, "id": "5a5012cf", "metadata": { "collapsed": true }, "outputs": [], "source": [ "for t in range(1,len(outputs)):\n", " for j in range(ns):\n", " for k in range(ns):\n", " c = probs[t-1,k]*A[j,k]*B[outputs[t],j]\n", " if c>probs[t,k]:\n", " probs[t,k] = c\n", " pred[t,k] = j" ] }, { "cell_type": "markdown", "id": "1a9f7a5b", "metadata": {}, "source": [ "Let's look at the probabilities." ] }, { "cell_type": "code", "execution_count": 1706, "id": "0d88276f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1706, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "xlim([0,60]); figsize(12,12)\n", "imshow(probs[:60].T,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "09c03797", "metadata": {}, "source": [ "That's not very good; the probabilities become very small quickly\n", "because we are multiplying together.\n", "At the end, there is no information left." ] }, { "cell_type": "code", "execution_count": 1707, "id": "bae367ca", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0., 0., 0., 0., 0., 0.])" ] }, "execution_count": 1707, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs[-1]" ] }, { "cell_type": "markdown", "id": "07c7ac55", "metadata": {}, "source": [ "We need to rewrite the algorithm to use logarithms. With that, we obtain:" ] }, { "cell_type": "code", "execution_count": 1570, "id": "bddf0f13", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.80400496 6.41881359 6.61262349 6.65182564 8.1727776 6.47388061]" ] } ], "source": [ "costs = 999999*ones((len(outputs),ns))\n", "pred = zeros((len(outputs),ns))\n", "costs[0] = -log(vs(ones(ns))*B[outputs[0]])\n", "print costs[0]" ] }, { "cell_type": "code", "execution_count": 1571, "id": "f6a4e520", "metadata": { "collapsed": true }, "outputs": [], "source": [ "for t in range(1,len(costs)):\n", " for j in range(ns):\n", " for k in range(ns):\n", " c = costs[t-1,j]-log(A[k,j]*B[outputs[t],j])\n", " if c" ] }, "execution_count": 1572, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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oQGJiIrKzszFv3jycOHECRUVFmDJlCnJycmBk9N+WIwY+UddSXbyK9O9+RqlnCvo4nIUk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\nAn86MwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(211); plot(costs)\n", "subplot(212); imshow(costs[:60].T,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "99477e8c", "metadata": {}, "source": [ "We can also trace the predecessors back." ] }, { "cell_type": "code", "execution_count": 1573, "id": "5b7f95bb", "metadata": { "collapsed": true }, "outputs": [], "source": [ "t = len(costs)-1\n", "state = argmin(costs[t])\n", "states = []\n", "while t>0:\n", " state = pred[t,state]\n", " states.append(state)\n", " t -= 1\n", "states.append(0)\n", "states = array(states)[::-1]" ] }, { "cell_type": "code", "execution_count": 1711, "id": "37e78d0d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 1711, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ERCRE1qoXjz32GL7++msMGTIEJ0+eVKomUpjeasVIsxlVrggM1TSjJCgINh8XBdJbrUho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\nbJky8VIAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(18,8)\n", "xlim(0,60)\n", "imshow(costs[:60].T,interpolation='nearest')\n", "plot(states[:60],'ro')\n", "plot(argmin(costs[:60],1),'b*')" ] }, { "cell_type": "markdown", "id": "dabe722b", "metadata": {}, "source": [ "Note that the state estimates above almost agree, but not quite: the minimum cost state is not always on the best path." ] }, { "cell_type": "markdown", "id": "0c4684a0", "metadata": {}, "source": [ "Plotting the state transitions and preferred output labels on top of the data is also useful." ] }, { "cell_type": "code", "execution_count": 1729, "id": "31374fee", "metadata": { "collapsed": false }, "outputs": [], "source": [ "bout = argmax(B[:,states[:60]],0)" ] }, { "cell_type": "code", "execution_count": 1735, "id": "aca10c60", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 1735, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ywe333HOPVq5cOeEDAQAAiJJRb+edOHFi8Fbdl19+qV27dqm4uFjHjx8f7PPS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\nNcAAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,8); xlim((0,60)); ylim((35,-1))\n", "imshow(signal[:60].T,interpolation='nearest')\n", "plot(2*states[:60],'ro')\n", "plot(bout+0.5,'yo')" ] }, { "cell_type": "markdown", "id": "752e58fa", "metadata": {}, "source": [ "Here is everything wrapped up into a single function." ] }, { "cell_type": "code", "execution_count": 1576, "id": "017d8214", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hmm_viterbi(A,B,outputs):\n", " ns,ns1 = A.shape\n", " no,ns2 = B.shape\n", " assert ns==ns1\n", " assert ns==ns2\n", " costs = 999999*ones((len(outputs),ns))\n", " pred = zeros((len(outputs),ns))\n", " costs[0] = -log(vs(ones(ns))*B[outputs[0]])\n", " # propagate the costs forward with dynamic programming\n", " for t in range(1,len(costs)):\n", " for j in range(ns):\n", " ck = costs[t-1,j]-log(A[:,j]*B[outputs[t],:])\n", " pred[t] = where(ck0:\n", " state = pred[t,state]\n", " states.append(state)\n", " t -= 1\n", " states = array(states,'i')[::-1]\n", " return states" ] }, { "cell_type": "markdown", "id": "6e6f23f1", "metadata": {}, "source": [ "Let's make sure it still works." ] }, { "cell_type": "code", "execution_count": 1736, "id": "a749c6b6", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 1736, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YRwo5JdVcL37P1eL1XDSAV1KNHfZtZCvOSAEAAFgiSAEAAFgiSAEAAFgiSAEAAFgiSAEA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\nAQAAWCJIAQAAWPp/3jCm2r5D53gAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(signal[:60].T,interpolation='nearest')\n", "states = hmm_viterbi(A,B,outputs)\n", "figsize(6,6)\n", "plot(2*states[:60],'ro')" ] }, { "cell_type": "markdown", "id": "79788784", "metadata": {}, "source": [ "Viterbi Training\n", "================" ] }, { "cell_type": "markdown", "id": "576ee919", "metadata": {}, "source": [ "The Viterbi algorithm gives us a simple way of \"learning\" the matrices `A` and `B`.\n", "This is called _Viterbi training_. While commonly used in some applications, it \n", "differs from the Baum-Welch procedure originally used for training Hidden Markov Models.\n", "\n", "(You can think of Viterbi training as being analogous to $k$-means and Baum Welch \n", "being analogous to Gaussian mixture model; the latter uses \"soft assignment\".)" ] }, { "cell_type": "markdown", "id": "13ba0e4c", "metadata": {}, "source": [ "The idea behind Viterbi training is that, once we have aligned our observations with the data, we have an estimate\n", "of the hidden, unobservable variable, namely the sequence of states.\n", "Once we have that, we can directly update the `A` and `B` matrices simply by counting." ] }, { "cell_type": "code", "execution_count": 1738, "id": "d7457dc3", "metadata": { "collapsed": true }, "outputs": [], "source": [ "states = hmm_viterbi(A,B,outputs)\n", "A1 = zeros(A.shape)\n", "for t in range(1,len(states)):\n", " A1[states[t],states[t-1]] += 1\n", "A1 = ls(A1)\n", "B1 = zeros(B.shape)\n", "for t in range(0,len(states)):\n", " B1[outputs[t],states[t]] += 1\n", "B1 = ls(B1)" ] }, { "cell_type": "code", "execution_count": 1739, "id": "d6d8851e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 0.61538462, 0.38461538, 0. , 0. , 0. ])" ] }, "execution_count": 1739, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A1[:,1]" ] }, { "cell_type": "markdown", "id": "dd880cf4", "metadata": {}, "source": [ "Here is a comparison of the transition matrix before and after.\n", "The structure hasn't changed much, but the probabilities have been adjusted." ] }, { "cell_type": "code", "execution_count": 1741, "id": "9fd5d9b3", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1741, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,8)\n", "subplot(121); imshow(A,interpolation='nearest')\n", "subplot(122); imshow(A1,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "95611cec", "metadata": {}, "source": [ "As a consequence, the durational model has improved." ] }, { "cell_type": "code", "execution_count": 1743, "id": "fb104288", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1743, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Jq0ploHGUDRsNArjn/Ml/d2o/fUfHi263C9VqFY6OjmA2m0G9Xjde\n74ltwvJkGqiyrSKrbuVdHhBwypNlv9frQa1Wg+PjY9uNQPP5HE5PT6HT6bhyIFSmh8MhNJtNKJfL\nkE6ntVNnw+EQqtWqmE5CXuM1uI1GA4rFotb4AwA0Gg04OztT9iNtr1NfUZ6hoxqPx9o+GY1G0Gq1\noFKpQDqdhlKpJHQ/FApBvV6Hk5MTo3Op1+s2GaRypvtO5fBM8oPv9/t9ofuycyiXy9But432Q1U+\np17LsmwzO7o+cSqP1kn7p9PpQLVahTt37kCr1dJ+R1GtVqFerytviaJyzHWiNNhyQ7uTbKn05/T0\nVEu7U/06oN0GAJuO4NWqxWIRWq0WnJ2dQb/fdyyLyrEc8FI6dctXKJ9Ueob+x2Sb/YauHSogTTLt\nlUpF6Dv1n4vFQryXyWS011TPZjOoVCqubTMF14+68UVUp/3oh06nA6enp5DNZiGdTmvfK5fL0Ol0\nHOMeCiozTjAGu88//7zy7z/84Q9ZRCA460u8AhvqdWTc7XahXC7DYrGARqNhe1ar1aBSqUC32zVm\nQKlxVK1bpODwAo2D0xqWTqcjaK/X69wm23B6egq1Wm3pykRTNoSbSaXZH/m36TvZcKLxlnmBd7Gj\nIyuVSo7rdmi7ZJmhAxWvI1pKO1fenaabTOVhH7RaLSgWi8KAIubzuRi0uTUiyG+8Az4cDovrd1WY\nTCZQKpVs99ojfd1uV9DVbre19fZ6PSgWi7YyaFuQJpqZ0vGMZnedbMRisRBtxMAcdd+yLCiXywAA\nxgCs2+1CqVSCbrfLnnHCJRKqIFHV3zh4oLp/dnZme6dcLsPZ2Zkxi6LTQad68d+LxULIAdKuSghg\neU52Avun0WjA8fExTCYTSKVS2m8o2u02lMtlpe5TOXYj/9gGJx3myla1WlXqDwbBqqCTyrCboIP6\nRDoLh4PRSCQC8Xhc6JmTrcPyaB/L8kNlV7ZVVAeHw6HNljSbTahWq+JKaZ1t9hs0G+jki020Y7BK\n/ed0OoWzszOIRCIwHo8hGo0qy6a22Uuw6+RHkX6dTpvK9WMJA9Zfr9chGo3CeDzWBv4AryXezs7O\nXCUuqX47YW03qMnBrtOUt9c66MjdC1DZu93uUoa03+9Dt9uFbrcrNhbopvvRYXGdsIkXXEdpop2L\nXq+3pKwIXcDt1EYK+bkc+OpAeaTjRbPZhOl0Cq1WCxaLBXQ6HcdgF8tTjVp1htwtOFNM8vtOwa5K\nZqjst1otmM1m0G63IR6P297pdDqeRsw08K9WqyLo1Tne+XwO3W7X1gfYd91uFwBekzcMHFXA7B6+\nr6OJsymRDpacbMRsNoNarQbD4VBkvHq9nq0tvV4PSqWSI+34DWfAGg6HlwbSOvmh7Wi32zCfz6HT\n6UAymbS91+12odPpaINdnQ6a6lVlO/F2JHlWC/WHyq2uj2Qb3mg0YDKZQLPZ1AYJMkajkVb3UX7d\nLGOQ26gD1/9Q2ZL1x0Q70uFmKaBME23HaDSC09NT6Pf7EAqFhF1wKo/y0CkhoJIhKj+z2QzOzs5g\nNBqJrCj1PzrbvA5w+5jSTm3EcDi0xQeIUChka6Mu0PRqm+UynOB2Wd6qMZWMer0O4/EYGo2GcVYP\neeEl2F3Lml23CIVCEI1GIZFILBnlVUHXeHntGJopkTsC195wRu4odCZDEAqFxKjaxAt5WtBE+3Q6\nhW636zlrTtsoQzdqcrOmzQtQZuLxOMTjcZsjpej1ejAej0WmEN9zoklHl9cF8jraufKeSCQgGo0q\nDZJOf3CAhXzp9/uCF1QW8D23O10pn+bzObTbbbHkh+OI4vG4LQgaDodCVk0GD2VaJ49cPcM+SCQS\nRhlH4EAB20jXxQKAJ9o5WQd5UGGyEdQmUH7Kus9pryrQjUQiEIvFluqlaxABACKRiPihdVH9wWwS\n7pTm8Gw6nUKv1xPTxW5OT9D5AC8DV+yDSCRiDLi5/keWLao/spxRhMNhQQfXvlNeTKdTiEajogwA\nEAM4k56pyqT06nyhTn5oG9HX4uwJfbZqksENwuGwjb86cGmXZzO63a7I/urs5Sq2mQPUaTe+SPYr\nfvQH5YVJp1f1U05YW7CLHRyLxSCTycDm5ibs7Oz4WsdsNhPKu8ooBEdvchl+TGlTRKNRFi9GoxH0\nej3o9/uOHc/ZAGPCqpsjnNa0qdYFOn0Xi8Ugm83C9vY2tFotkWWT13HKwcSqyimvM/OCeDwuaFdl\ny1XY3NyETCYDsVhsqV6d/iwWCyEjvV7PloGQeeDHRgPObINlWZBIJMTPcDi0OVbObAXNJHEh8ywS\niUA6nYaNjQ3Y3t622Qin6XTdFDCH9lU2daCuRKNRSKfTShtBs81004xcn5PdUk2Nh8NhSKVSsLGx\nsVQv9iPKWSqVEj/4dzlziuUVCgXY3d3V0oI2vN/vi/6RN0M5wa/NNIhQKATJZBLS6bRxKYUb/6PT\nHxPtKAvpdJqd5cYBA/ZJPB4X7ZjP5zAcDmE4HK7k21Q2PBQKQSKRgFwuBzs7OzZbjXsKkE+UD372\nmxugjUilUsbB2Hg8FnqHPKO06/bwcNd9e2k/109RO8iNvdCvUH1fFVydXjXecsLaM7vorLe2tpRT\nk6tgMplAKBQSCu4FdO2O3BF+BroAr/ECHZnuyDYAEG1x2o1sop0LbOMqRs/pue63Dhgwbm1tiZHx\neDxWblqi7fZrndcqU2iUdu50zNbWlgh2ZVD9oVOOi8Vr67Tn8zn0+32b4VXJ8Sq8oXJmkhPM5GWz\nWSgUCmLt6mg0EoEMZ523G71T9RUNGLe3t8W6WNNmHLmNlAY6Newn7XIbMNjFwY1sI5rNpghYqOPw\nw25FIhFbcEqBy6VGoxHM53NIJpNQKBQgn89DJBKB2Wxm003M6uJ7pmB3MpmI/kHnSjdVceCV7zpQ\n2guFgvY9rv8x6Y+JdjrQNQVkFKPRCEKhkNgUivq4sbEB4/EYWq2WTR9XkVUKDHbz+Tzs7OzYNtwN\nh0OwLEvQZNK18wLK+8bGBmSzWe17uEEV/Y/sc3U8pO+ZsIptdtIPtIMbGxvGeEOmJxwOi9lCP0D7\n2CnwX+da7XPJ7KLzd9op7xbD4VCMGr3CSdn8NAgmR0bRbDZhPB47Dg78MhR+ttHt9ypQmWk0Glpe\nIN00KPELXttFs9JcxeVmdqnxwZEyGmPTEgw/+MNZG4XBWjabhZ2dHYhEIjAcDqHdbgtZ5Ww+cRvo\nqvSMBrvcwbDcRnkph5+062ByUIvFAgaDgVij7sVuUZ5RvpmC3UgkItaWTqdTEQju7OzAfD4XNFFg\nwJjP543BLgZe9AQPL/bIT93HzC7SrgPS3u/3xdpwE306/dF9R/1FJpNh0d7v92EymYiNlfF4XGRb\n+/0+jEYjsCzLlylqObOLPNvZ2bHNauGaVrThJj07L2DWc3NzEzY2NrTv4dp3TDRwaefYS3yP/uaC\n439pQM8NdnFtMvoVr6dEUCAvOD51nbKw9g1qdA0ad3ctF5ZlQSwWE2c6rgITg50MGbdMXEOTSCSM\nvBgOhxCJRFydy7tOmGjwWrfpO7pOla5nNa198kLPOtpFb3Thyjtto1wv5QUtbzabQSwWg0gk4rjB\nbVVQPjmVj9ndZDIJ/X5/qe+49Llph07PcK2aWxtBy3PTdhM9OqiW+ehsRDweX7ILXoNC2alQnsn1\n9no9Ua+8Jp3KoIxwOOy4XhD1BctYZWDm9A23/7k+i/ofbvmmwYmKDpXuO5VPacJ1tIlEAmazGUSj\nUc98ltsnyw/VfbrGGNcOyzro5HPXCW4fTyYTpf3Q2QgZ6/LNnP4z6bQOcnv97IfzHtDIeENvUFss\nFjYlWicznZwLZ6TF3bwUj8e1G5bWAbdGx23QoPutA5UZ5AVng8YqU99eylEBNz242RRg6m+dzGCw\nyw3ivLTJi6Gjm5JocOYGHHl00jPsg0QioQym1gU3ga7qW8yOq+THFFg60cGBTm6pfMob6FAG5d33\npg1vMqgcr2Pw7FaOUeecaPfL/+i+C4fDrn2nHFjSMqbTqU0f/Qp0Kb2qYBeP3zKdSqCrZ13g+uLR\naMT2P16xDpkHMG861QHf59oZv7GKn3L6du2ZXWq8ueuOuJjP56JjsC4v0AVh1LF6yaCYMk4mXtAA\njztqXGdGb5WRq/ycE/DKu+l1vFh1el6VVdPRzYWcleYgkUhogzGa6aPl0cyu6qgoP+EmE0QdHga7\nmCFYx3ITVXmynnGzb5Q+WfZXyYS5yezKgTqFbvDg1TbpMnOmeqkDpQMaVRaIyoIpo0n7x2ubOOD6\nB66dRv/DGXB6kR/ZDnIgZ+Zon04mE0+DPt3SF7kMGlhTGR0OhxCLxWxHAaq+V9W5LnB5Swd6Mu0m\n/V6XrZPL5GZ2ufKDuu1nZnedvHADY7D7yU9+En7wgx/A7u4u/OxnPwMAgKeeegr+7u/+Tuzu++pX\nvwq/93u/py0jGo2KtWB+nduGwA1f3J2qKpg6AgXar07CNTT5fN64fnk8Hi+Njk24W0LkNtDlfkdl\nJp/PQyqVMh4Pc5GAay4LhQLbUGAbVXKMvMjn87YNb3hweTwe9yVI9wM4rYvrDIfDoZDj8wp0AV4/\nCSCXy8HGxgbUajWxHtrNUgT5/fPICuNa11wuB1tbW7bnjUZjKZDwi6ZwOCx208v19vt90Y/z+dz2\nnkoGAV4LJuhmTR2dePOfar363YJMuw7xeFzQvg5QO2iigyISiUCtVhO2BH3kxsYGWJblyq+oYJrZ\nxP0Km5ubS5tzq9XqSn7ab5jknWKxWGhppzbiosguhcmW6DAej6FWqyl1+o0OYwTxiU98Av7iL/4C\nPvaxj4m/WZYFTz75JDz55JOsClABdnZ2fBf2VCoFp6en4hD9uz1yQOjowEBge3vbKEiTyQTK5TJE\no9G72iZTsL9OunBTxe7urrimVscLr2v7VO3yo03xeFxsbOGukyoUCpDL5bSnMeAGE6o/k8kEqtUq\nJJPJta7XpeVyps1w89L+/j4Mh0NIpVJrmwLU0YMbe7a3t6HdbgsboZpt4ZbplT6nAFt+hhv8tre3\nl96t1+uQSqXWsrwpHA7bBikU/X5fXPM8m83Eppf9/X0hg/J683A4LIKs/f19bb14lWgikVh7Bohb\nLg6WNjc34dKlS9r3Wq3WWmWL6v7e3h77m0qlInxiIpGAQqEAe3t7EIlEoFQqufbDHDm2LEsE5vv7\n+7bEVigUgnK5DLFYzLGP/U4w6UBthKmPAWDJ/3D90N2OR3ATHm7S5WA0GkG1WoVEIuFrP6yTF9zB\nhjHYffzxx+HWrVvKwrmgCuv3ml0MirjGxgvcZIKc3qeOzJQN6Pf7kMlk7nqwC3B3lJgGjPV6HbLZ\nrM1Q+oF1tYEG6qYjbSgymYxooww6WKT6Mx6P4fj4WAS7d1P2EbgjG51ru92GdDoNkUjEd6PppGfo\nyLrdLuTzeU8DYj9o5gRA1HZR2uWgpFgsKgNLP4COUZWFbTabkMlkxCUSNBA8Pj5WBuA0YDQdwYc7\n+NeZsPAixxjQmwKhRCIBR0dHYorYb9qp7jsFZIhwOGwbOKMt3dvbA8uyhF9xC3mGQ24r6j4ecUZ3\n8c/nc8hms2x/dh4+LxKJiCMdTbydTqdG/3O3/bMJaEu2trbYWdrhcLh2v7IOcOj0NDf8rW99C77z\nne/AY489Bl//+teVZxE+/fTTAPCaU/61X/s1uH79OqTTaS/VaYGKTa9HvchA4cPje3RoNBoiSPi/\nCDTys9kMtre3haF8IwCDXbw6moNkMukY7M5mM5v+jMdjyOfzS9PadxM02N3d3YVarQbpdHqtmztU\noEeP9Xq9N6yNkNfZFQqFtWXK6aUScvnlclnUS9/b3d0VMqhaxoCyYEI0Gr1w/UMvxDBlVNftf+gx\nhtzMLgaWNNjFZNN0Ol3Zr2BQoepvPGd3sbCfMTsajbT27W6BHj1m4i1NPL3RQC+V4NI/GAy0Ov1G\nh2up/8xnPgNf+tKXAADgi1/8Inzuc5+DZ599dum9p556CgDst/74ndmdTCaQTqfF4nevoxDO9Cy+\nZ1qzpPqhiEQikEwmYT6fGw1kLpcTazidApl1Zp90C/BNbVS9p/tWB1yrtlgsIJfLQTKZ1PLCy5pK\np3apnnFBaedeKoGbeFQ7YKnM0OBnNBpBJpOBeDwudsN7XSOtg9sNmrhuDw1sLpcTm+/c6Cdn44pJ\nBnGt2nw+h0KhAOl0GuLxuCMNqmdul4jQ97gnR+DmF9xQgrTLwUE2m4VEIuHY3070qviGaxiz2exS\nsEt1cDKZiPc2NjYgk8kImmi5eOxYJpMxtn8+ny/1j9elSU7t5YLywnQGKwaP6H+80qd7hrKAa885\n6Pf7NprwBrVCoSB8sNtNalSO6bF3lKeWZdn6mwa7zWbT5s9My8dWtb9cIG+d+hiXDpliDNMGNSd4\nkXWZ7zrQdcncYBflBfXRj0TKumfTuDbadbBLDyf+9Kc/De973/uM76PzxykwPzEej4Vi+7lrEKFT\nPNV7+EMdl4xoNCo2CJh4QZ0Lt12rBL0mw6dqi6mN8req/zt9h1NGkUjEtnnL9J3btV5eA3EnUHnn\nHsiNO2BNG9Rk/cFgFzO7pk1qXtb0yrxA3prKQOeayWSgUChANpsV8u5mE52uH7l6ho4sHA5Dr9ez\nOX+nSzGwjVzdd6KdOyCUg13MjFLQYNeJn26nINExYh/K9WKQhCeDYJCQzWbFgIu2FTN9eI6uDjhj\noeoft/LqJDNccINdmmzh9LNOf3S00w3N3GC31+vZgjMcfBYKBWi326IfTfXq6DcNMKncyMsVaMCI\n31JeuNUZP4C+2GkgIfsfjo3Av3EGbl5ss/ytDqirqIscoP2mOr0qaP96tf2m9/HHyd+6DnZLpZJY\n4/KP//iP8NBDD2mJAHhNqJDpfmM0GrGzNjq4zQismtlFQ2oCVTDTyGrdawp1bTG1UVcO528IPGoM\njZGOF1SBuEoiB0wUNIDyquR4HJjbWQxd8KbTn+FwqDRKqsX6qw6E3PCWZnYxOFMdP2aCU39y9Swe\nj4tMFydT4YfDpbRz9ETud0q7DBzcOJ2B6SYzjkC7hPsfKHDwTe1XJpNZyuzStmDwg/KgAwaM2D8m\nOTbBbSbbBNQ33LCnAyZbkHav9Ome0YDMRAdFp9NRZnbz+byYaaHnAnN0UjXAVPkEHLDL5dVqNW1m\nV6VzKtvsN2jW3MRb2f/ostBebe6qPtwk0+hD6eZPJ+Am+nVkdp10elU/5QRjsPvRj34UXnzxRajV\nanDlyhV4+umn4Uc/+hH89Kc/Bcuy4Nq1a/Dtb3+bRcQ6hFd2FKuMQjgOgmsUdHRweeE26FpXVpe+\no0TzRPIAACAASURBVAp21wk0LKhwTrfJ6bIEOqyzDV4GXjp6dDIjT3/Tb/3aVOCWP9RRyf3mdsTu\nRBNXz2gQRp/JcFrKY3qHQ7MTL+V+1F0wIr/nd1+r+knuR13/csujUPXPKnx2M0NlKoe2Uweu/1nV\nPrsJOmRbid8jn53sqIkO/G3SOyf5UX2jmyldJ9z0sYln67S/JnD4I/tsDkx+xQsuCi8AHILd559/\nfulvn/zkJ71RtCb4YSTd1neROnDdOA/D41T/eZV5UXjuBuflFABWX/vrF7wE4U7f6dq4qr476Y/b\nIOxuQhfYrZpskL/3O5D3CjcBhVOgDXC+7fErCeQlYOLQxBlcrhtu+5fbj+cd+K4Dfvn98+IFh9Y3\nxXb/VTuGu5RBZ9DoKMhPZeWUd17K5KfR81q3ql6/s213O6DwAl1GZR31rBrw+pmJdNNXTvqpmhnw\nM/jya4BF23G3HKlJb1YJeNc1sHVrm89Dts4DfgYsfvs3p8HBeQziV/mW9qmK3jdqkCvDj364KLxY\ne7A7n8/Fj9+Nnk6nMJvNRNnrYCp3XRPW77Q2az6fw2w2M74nt2udOK+1RW6AfJrP54IXKt7StUDc\nBfCq7/0Epd3N5g86LUyh05/zkH0ZHB3APlPJMHe9rtt3dXRQ+eHySV5P6CbQNdFuolVHu7yZbjqd\nrs0mmOqV+3E2m2n7mFOe3CZVGV702MRjt+Wh7JhOVFlFtkx/c0uHiSb0N5PJxGZL3YD6Ng69Klul\n61+uXvgNN31skk1TfHC3gzyuDlJQ+cEy3iw4l2B3MpnAZDJh707nYjAYwHg8hul0upLDd1JkJ2Wn\nAm+igRod02kMw+EQJpOJo2PjGqFVoCqbqzheMZ/PRb9iH6uMtNd2m/pxVT5iH2P/cYB3yqs24en0\nZzQawWg0ssm+k4x6gTygcJLH6XQK4/EY+v3+khz7JatOZVCe9fv9JT45latzyl5od1snpV22EaPR\nSPBT5qmqXLd0ouOXnT/242w2E4HuaDSy8VYO+EzlUaj6x82Ah9MutxlV7ANsow6DwWAl2eLQMR6P\nYTgcGumQaaL2EvtqMBgo/QonQOcM+OT+pu8Oh0MbTU6DwvMIsPAcdE4fO9Fu0j9OW9bVXpMt0YHK\ntF8Dazc67ac/l3Fuwe5wOPT96DHsGF3mjwOOw+A6eqd3qRE1OQDZOHihnQun8lWOYt0BNgaMw+HQ\nyItVAqh1B7vD4dDV0WMAoLwsQKc/GOyqgkkZqwa63DIWiwXMZjPhXJE+qp+rGjsaFDrp2XA4dDUg\nlttLB7BeaOcEWrIjoLTLNoLLTy/9TeuVL0PBv2GQje9hoCrLINKAgdZoNNLWq+oft3rotwNFHUY5\n1sGrbHFpo7bERAcF9hUGKzj4VOmjG8j+TfUc6xoOh7Z3dH1My1XVtU5weUv5qaN9Pp8rlzHczUAX\nAET/j0Yj9gVHqgHsqvDL9q/67dqDXXR+vV6PzXAuer2eUOBVgl3VvwHcr9Vz6lQcqWPWS4d+v29T\nMC+0+4W7MfpGBe31ekuZHxUdfjlGP9pE5Z079RiPx8GyLOU5u1ge8gGBTkUXaPgBWb44Dh0dSLfb\nFXK8yhS1iS5dOZi1wQttcKDgZqbEr6lJtwae0i7biMFgoJzx8aO/MYgdDAZLmS7sR8zsYvDU7XaN\nNKEs9Ho9LY2q/lmHfXFTHtrpwWAAnU5H+x6lnaMbbttFbYmJDhNN0+lU9AHtRzdQyZrKFuNMXK/X\ns81q6bL3qjLOC1TPnPpYTqhRG4Hwwzf5DRpvcAdLqhm5VbFOXrgpc+3B7nA4hGazCdVqFXq9nq9l\n1+t1qNfrMBgM1jYq4DoVWfhVGI1G0Gq1oFqtGhWsXC5Ds9lkDQ7OQ5k4bfMTw+EQGo0GVKtVKJVK\n0Gw2jdmhi4TBYAD1eh1qtRrbwKTTadjZ2VGez6vTn8lkIv5GndfdNCjz+Rx6vR7UajU4OjqC09NT\naLfbKw1GVbQ4ZUsnkwm0Wi2o1WpwcnICZ2dnjtPATpm3Ve0Ld6PpeDyGZrMJtVoN2u227Z3T01Po\ndDoiw+9nX0+nU+h0OlCtVqFer9ueVSoVaLfbYgDe6XTg9PQUjo6OoFarQbfbXQqgZrMZdLtdqNVq\nUKvVtLQ2m01W/6wCt/ZrOp1Ct9uF09NTuHPnjva9RqMB9Xod+v3+WgbRo9EIms0mlEol9hXRlUoF\nGo2GyK72+304OzuDk5MTKJfL0Gq12INwN0DdPzs7g2q1apOHYrEIjUbjQtnw8XgMrVYLKpWKsY/R\n/+iSU9i3F3Fj82QygXa7DdVqFZrNJuub4XAItVptacDyZsDag93RaASNRkMIDYXXHYz4HRpKDCru\n5iiKAzRe5XIZzs7OxN/lESIapdFodNfbxAku/MZwOIR6vQ7FYtFmbO5mtocLDNRPTk6g2+2yjl4p\nFAoQjUYhm80uPaMOj+rPdDpdq1FyylyoQB3e8fExVCoV6HQ6a3GuJozHY2i321Aul+Hk5MQ2IHY7\nC7CqE3PSH5kmdMLlchlqtZqt/mq1qgws/cB0OoV2uw2np6dQKpVsNGGwi2v/MCi+c+eOoEm1ma7b\n7UK1WoWjoyNbebRN7XabFTD6AW75cht1aLVaQracyvfSNhzolkolwV8nnTw7O7PJOwa7x8fHUKvV\noNVqeZ5hNWXo5IEuXSpRqVRc2/B1ywIOiMvlMqRSKe17pVJJBOrrnhX0GxjsVioVqFQq4u8mGRqN\nRnB2dib8ykVsl1ecW2a3VCpBtVq1PVs12O10OsJQrop1Z24A7I6sVCqJv+uCXa5RejMJJMDrASMN\nds8jK+BH9hEzu8ViEZrNJitgHAwGkM1mYWdnZ+kZ8kLWn9lsps2q3S3oMrt+rdX3omfHx8cic+h2\nScHdAKW9WCwuBbs0swvgH82TyURkbO/cubMU7KI9opndVColBlzyOlDM7GLAqAt2u92urX8uQh/I\ntOsg0+43MFFULBaF/XOyJ61WS2R2AV6blq7X63BycgLNZlNk6N3CSfeo7h8fH9s2qdXrdRtNF6GP\ncUBcqVTEngkVarWaLbN7UYJ1DmiwS+XYJEOTycT3JMpF4AWAQ7B7dHQEH/vYx+D09BQsy4I/+7M/\ng7/8y7+Eer0OH/nIR+D27dtw9epV+N73vgeFQkFZxmw2E2v45Gm5VSGvT/ICOg3hNJUp/1v1nmn0\ni+unnHjR7XZZG5w4tPsBVZZvnY6J8snEi1XabzLeq7SL28cUyWRS20ad/sxmM7FekvaF37LgNhOK\n6/Y6nc7Sejc/aTLJoLzWEdegecnM+Ln0ggNKuyw/uO+BZlzc9rfu3fl8LupttVraeuk6wHa7bVuX\njeUvFoul93T14hpB2Yb7Jcc0s87tA8oLkw7raFfR4AXUlqjW86uA9hLlXaWP65oJov1NA2qkSR70\nmtbFr3tZgEnPKCjtJhthOkd7HX6SUya3jRR4go2TvfSCdcYpnHKNwW40GoVvfOMb8I53vAO63S48\n+uij8MQTT8Df//3fwxNPPAF/9Vd/BV/72tfgmWeegWeeeUZZubyz3k9wTy3gwm8Fk2mipzGYeIGL\n+d20ax2XalAl9hIM4DPVb9N3ssxwdhC7PQ/VdMoEtxwd7bh5jCvvpl3SdGc4LQ838amMsF+Xb6iM\nuJOc0Q1MdFevmzJM9KpoctIzuimHwwcTfW5o5+oP/dH1NwBoN6166W9ZB+nObble+cgz+p5ppzo9\n9koHWoYMtzbNr8w9PcXApMN+ypbqW1OfcGjCPsB2UHvh1V7qBpoou6j7dOmSacOTbId1ttlvuPHF\nqmMk3cxKc9fru4WTH+W2kWIymfhynKsO6+AFd3BkDHb39/dhf38fAAAymQzcuHEDTk5O4Pvf/z68\n+OKLAADw8Y9/HN773veygl3uhh0uaCBE63QDyiSTAHMNqSnrhMbLiRfycT5eaOfCybjoRt7c7K4q\noNSVi6ABoykQXEeAj89WCXa9HBfkFOzK5SGPOMHkKg6EZhBVZcug9HLpU9XnRJNJBk1H13H0yel2\nJze0ewk6dfLDHTxwdFoX7GKwQkH7UQ5iVTQtFgtjeRSmhAVXv/0KchE0yPTr6DGd/nCCFS+2BPuK\n6oJOfjhwkm05sKaZXdm+yXqmCnjXDW4fO9Guo5lrL73YZi6vuG2kwGB3leNcZayTF/RbJ7DX7N66\ndQt+8pOfwLvf/W6oVCqwt7cHAAB7e3u2xc+Ip59+GgBeW2eWy+VcpdK5oJm/VTolFApBOBxe6gy3\nt48gdE6YHgNj4gWd/vVKOxe0jW4VzkkZnJytDnT6DpeqqHhBbx6T2+IFboJ4Du1cec/lctqpMp3M\nzOdz2zIGyguTHHsdEOpueKOIRqOwWCxgNBpBp9MRRw5hf3DKwECJ24+6YBePa5OndbltlGlYB+2q\ndpimHjG4wrLD4fBK/S0Hu6blE2iPaPau0+ksLaXBH7qModPpaOnArBPNOOrk2NSOVXVfLg+PYTPp\nMPofpzXpJv0x0U51n8sLurQCy8C+wr+HQiGIRqOeeKazkfTouk6nY9tjQZcbAoBWz84jyEVQPYvH\n49r3ZF9sshEUlmUJ/TRhnf6X2kGuL0J58XMZA8q/04ki65YFVrDb7XbhQx/6EHzzm99c2jFuWep7\nrL/4xS8CAMB//dd/wX/8x3/Af/7nfy5tUFsV4/EYOp3OSuf3hsNhiMVi4kcuH29Z4W4CkjO8cnnd\nblccq6UDBnlOu9iR9ng8zl7TJcPvNlKozn9F4276bjgcis2H9Xpdy4twOAzxeFz0G7ZjFYe3arCL\ntOMRPBykUinodrswHo+1MlOv123lzedzaLfbMBwOYT6f22SBbrhYLBaCL6ryOcAzgJHXOseLAcpg\nMIBarSaCodlsBqFQSHwv6xkFGmiUSx1MA5PxeAy9Xg8ajQacnZ2xbAS2EXmI03/4nZ+069qCASLS\nLstPq9VS9res+7S/ZZ2mwRXlG67Vw2PuKHBtLmYFB4OBOBmEyiBty3Q6hX6/L45a1MkdbozD4CgS\niYh2cY/bwoyiX+tRcT18q9UyBivU/zgNpHT6Y6J9MplAr9eznfjghNFoZLMlOPCMRqNisJJIJISs\nublwAEBvwynParWabdocz96dTCZgWRZEIhHBC2y/binLuoDy2Ww2jX4PB8xIO9oISrvsO+X+1snQ\nKraZ46dQfpziDYrZbCZ02q+Ak/LMpNPUdq5j07VjsDuZTOBDH/oQ/Mmf/Al84AMfAIDXsrnlchn2\n9/ehVCrB7u7u0neouKh8srP2A3i8zSrBLjrhVCq1dMYpGhi3Vx1Tg0CBjsyJF3g7kZPyI+3pdBoS\niQSbPgpsI64R5kLXRtU7br9DA312dgaNRkMb7EYiEUgkEuLomH6/L6btvIDS5tVpUtq58p7NZqHb\n7Sodnk5/FouF+GaxWNh4QTMVi8VC7Bb3yhfLsiAWi0EymYR0Ou24phWvJsXDzDHYjcVikE6nl/SM\nYjKZiKyJk17rZIkGCWdnZ4JPTm2MRqOQSqUglUoJZz2dTkX7ObRbluXJUNNgVzcg7vV6gp840FPp\nPva3Sqd1Mo48UwW7eNHEbDYTwW4oFBLfYLBLy8YMEZanc5x48gENdpPJJKRSKfYAHjPIq+g+Bbax\n1WoZbfB0OhWZPxNQtlT6gz5BRftkMoFutwsAYBxkyd/QC5zQHi0WCwiFQrBYLMRAAnfcu/WfKr3D\nYBfPdaXBLso0DRiRF8i78wx0sb5+vw+WZRnXs2L/jMdjI+2ynuF7qVRKG+AtFgtx4YpbueX4KS/B\nLp6q4edGRqrTppMv8FStdR1VaQx2F4sFfOpTn4KbN2/CZz/7WfH397///fDcc8/B5z//eXjuuedE\nEEyBjNJlpvwATp2smtmNx+OQyWQgk8nYnoVCITGV5KYDdILIzeziHeNOBoA6PJl2Lmgb3YATtJoy\nu9xgt16vi/u9ZWCAh7MNOBW7CjjtMgFpdyPvhUJBDNp0MqMKdpEvmOlDOabnRiLvcYrRSyBGA8Fc\nLqfNVMznc+j3++JnPB6LgSJmOtLptPI8YQQaWU4/mgaVqGe1Wk3wySn7FovFIJVKQT6fh3A4LAI2\ny7J8p13VDsz06BwU2rr5fG7jp6z7lmUpdZrqoayDNNMl14sZLFxqMBgMxPvYx7KOczO7aMOxDKrT\npullCgy2/TqeEAO32WxmPNaS0m4ClS1Zf7AeFe3o18bjMTvLjcEr8hOzz8PhUAQcyWQSLMvyFOgC\nqOVHzuzK+wuon6a8wKSO35vXnYDySQcUKiDtNFB3op0GxblcThvgoU4gLVzIeqyDabbGVDb2lV+Z\nXQx2c7mc4wAW/dQ6YAx2X3rpJfjud78LDz/8MDzyyCMAAPDVr34VvvCFL8CHP/xhePbZZ8XRYzKo\nQuNI3+/R23w+X/kkhng8DltbW3B4eLh0zmmlUoHj42ORqeJCXkuqotnEC8ygOLUrkUjA9vY2HB4e\nwvb2Nps+itPTU89txHbqgNPadIG6iTcUuH7RdCpFKpWCvb09ODw8BAAQ5ztyr9b02i4nuJV3umlE\nJzNyecgf/C6VSsHu7i4cHh7ajgFcLBZwcnIClmW5usKYIhKJQKFQgIODAzg8PNTyZjqdQrlchkql\nIs7/RTmOxWKwubkJh4eHYr2/Cr1eD46Pj8V0mgm6vsJNDlR+nAYv4XAY8vk8HB4ewsHBAVSrVaEX\nlmUJG6GaxUJ0u104Pj4WZ9Fyge3AH538UD1IJBKws7MDBwcHS7pfKpXg5ORk6YppqoeyDso8o5Cv\nWkYbhjTRZ7QdWJ5J5rAs7J9MJgP7+/tweHgI6XSaxb92uw0nJycr6z4F0m6axZBp1yEcDmv1p9Vq\nCdrloIvSwPVx8hIVpBEDsK2tLdjb24NYLCb0TD5qzgkm+VHJLi6fwOxyLpeDg4MDODg4EBfwrOO0\nJhOQVqfBv0x7Pp8X/Yg308m+U26jLiu/WCzg+PgYLMuCbrfL9heyHju10yneUL3v53rdbDYLly5d\ngoODA+PMWLFYhOPjYzGI9hvGYPc3f/M3tYr8wx/+0Fgw7QSO0fMCPzomHo/D9vY2XL16Fa5evWp7\nlkgkYDAYuM5IOzlhzNzqwF2kTWm/9957XdGIwClbv9qoesfLd2g0TYF/Op2G/f19uP/++wHgtVFh\no9Fw1Q4dbX4Eu1x5pw7TNECSy5OD3b29PbjvvvvECSr4bSgUgl6vp9xIygE66ytXrsCNGze0Wabh\ncAihUEgEunKwu7W1Bffeey/cd9992roajQZMp1PW9ZYmWaJGnqNLoVAICoUCHB4ewvXr1yGdTgvd\nD4VCsLW1BVevXoVr165pyzg7O2PTrmoLDg519pLyEwe6165dg3vuucf2XiwWg8FgAKenp8p6nIJd\nuV6axaNBgjzgomXLwY+O//L6z0wmA5cuXYIHHngANjY2WLyrVqswnU5X0n0VTZzzczmyhYPFK1eu\nwPXr122ZvtPTU5hOp0tXNNPyOQE1/Yb6RNoW1MG3vOUtkEqlYD6fQ6vVcr0DXqV3+G/UOSpDlE84\nqDw4OIDr169DqVTy5H/8AAa6TkvxZNrRRmCQrrosK5fLweXLl+H69evaAA8HIb1eD8rlsivaOX4K\n/ajb2MuNvHGQzWbh8uXL8Na3vtU4MxaJRKDf7yvtlh9Y2w1qNMhZV2Z31SlngNcDxmvXrsGNGzds\nz2azGVSrVfZ6KQD7qEuVFeCMtLhGFLM7165dg+vXr7NplOuqVqvsKUMA5zYiTJldp93FNANuCnb3\n9vZEsNtoNODo6IjdDhVoZsorONl7CupUdTKjyuzSn2QyCbu7u/CWt7zFNmjDNVjlctm4XsoE6qxv\n3LihLQc3cxSLxaVgAR3t1atX4ebNm9q68GrR4+NjI01yNlR+RvuAYyOoI7tx4wZYlgWnp6diUwWH\n9nK5DM1m07UMysGDzkZQPUDdf8tb3gIPPvig7b3xeCxoV9WlOu1ADk4pZHuE/8a11XSpktwntA9U\nkG04DXZNWXSKk5MTaDQaxtvO3EJulwpc/0MHizdv3rTpTzabhUajAbdv31aWj3S4OZmC0kR/R6NR\n4evy+Ty0Wi1HPZOhs+FUfuQleNRO0ezo9evXIR6PQ61Wc+V//ICKR7r3ZNox2I1Go0rfKbdRN0Mx\nm81EEoK7TAXB8VOm2RodZL/iBzCz++CDDxoHsMPhECqViufN9k44l2DXj6BUh1U7JBKJQDqdhs3N\nTVtGDOC1aXGnRdUqmASRwwtum0y0c1EsFiGdTq9F2Zy+N0G1LkxGLBaDbDYrpnEzmYyrgYmJtlWC\nXQ7t8vtOwa5KZuh30WgUMpkMbG1t2WRhOp1CoVCAZDLpOVttWRYkk0nI5/Owt7enNUadTgfy+TzE\n4/EloxmJRCCVSsHGxoZRVufzuav1mqa+cmO0Q6EQJJNJKBQKsLu7C5VKRWwuCYfDkE6nHWmfTqeQ\ny+VWlkGn/kZ+6nR/Y2PDuDEGoeKbSm4pDykvdQEhXcbAGbjTZ1SnuTZtOBxCNpv1Rfdlepx0mCtb\niUQC8vk87O7u2ugcDAZGu6XiuxPkd/H/KDNbW1tQKBQgl8utFGS6tVX4DeVFq9Xy5GP9ANLJ8UUA\ny/1Yr9eVvhPX+OfzedjZ2YFcLqcsdxXb7Mb/uo29/Ax0kRe5XA52dnaMyy0LhQKkUqmVZlVNOH8J\nu2DAI3xwhyVFMpk0Hh1yt4HnJapo5yKZTEI0Gr2wbTQBN2Xhhiw3xxW92YBynEqlbLKARw1Fo9GV\nBia4ySCdTmuD3fl8Lo4+k+vC0xicZBVPkzjvfsQ2JhIJyGQyNr3g6lkqlXI8XscvmPi5an/fTeCx\nVOl0mm3TzpPvXoDrZZPJJGQyGZv+3E2Zudt6hqebXGQfK0NnI1TvOcnxdDqFRCKhtJdvJtD+Nun0\numOR//PBLnVk8q7mi+40qPHyehrDGz3YxQAPIAh2kRdUFvwKdqPRqDDypmBXZ7zlMnS4CMEuOmEa\n7HL0DAOI88hSmWh6o+s0DmC5Nu1uyQwXsmzRLG4ymYR4PH4ufSUPiM9LVilMenbRgTYMg1hdoC63\nUSfHGOxe5BjDD3B1et28WLukX/RORMGMx+NLC8nRGFxURQyFQlraucBD6S9aGzlygwMVPGfUj3b4\nIa9+Lu3gloW8kGVhNpuJzNEqdNEZEF2wO5lMIBqNKoMOrqyiwbsbgQteaIBODIN2k42gOE9dMvGT\n0n7ekNdxukU4HBY6zbVpKDMXzYZRUP2hwe55yju1EavyTDWY5YL2MerMRY8TAOx2EGnX6Rntb50c\n46ZBt7b5jcArCq5OrzveOpc1uxe9c+gGKs57OqjWrrn53iv8WjurW4PF/V5Hl+7HD6h4zF3HZCrr\nvGXWJINuDaGOJ174rlpL7NTnHBpNz5xoXbeeyXW7abtMO3ftm9f+cdPfJh3k2kAnWvyCX7xA+LUG\n0StM8qTr+3X6C7luJ1D+6WRlFTvlRWfuJpxswio2wysdbp6dN9y20aufMuH//DIGE3QM5wSFbr5d\nBX5lIlWCiLuAdYLEGRx4CXS9ODm5PhNWbReHlrsBndH1alCdBgS6Z34Z4LuhZyYn5VbeneSMQ4OX\n97jB7rpAyz8PfXBq10UKntzqxjoDXi/20o9AV0fDKjpznnAj224CXTd6z33/IgW8TvDTT6lgzBcf\nHR3Bb/3Wb8Hb3vY2ePvb3w5/8zd/AwAATz31FBweHsIjjzwCjzzyCLzwwgtGwt8I0AmeSqmdOkUV\nfK2TF6agctUfU51OdZt44KVOHQ1eeLAunqpoc9OeVWXGRM+q7XDqO6d2c/reDU1+6hm377j0uaFD\nbodbut3oF+dbv+C1PK/yse72rIqLQD9HRrh0ONkLEw2qMi5in8ng2DnVu2719M0k/+tsKy3XCcbM\nbjQahW984xvwjne8A7rdLjz66KPwxBNPgGVZ8OSTT8KTTz6p/VZ3HI2f8GP05+QM3JQj02XKHDqV\nva5skI4Wt99z2qh6bvpOxX/LMo/y16XUThlETv9w6ZJlR/Wd3E4nnui+40LXf07Oz+k9J3pM8ijT\npJIlJ3kxweS0OXripyzqyuLqjalcVVmqaWpd3W7baXqXK8erQCfLnO+80s6hh9bh1FYuL9zYhVXB\nrUsns3c7GOPw3kQ7t9849tIP6Hytm7rWlVH3g1+699lHtZoe7u/vi7MOM5kM3LhxA05OTgCAz5R1\nTkes4th05en+7yTgJkEz/W0V+D2K4wZTnHfks/o49K3qPLwaL847bmjz2heq4I2z1AIDZFX7VaNg\nN7SoyjEZ71UDQpNDdtt3tC4va2dNAbfpW7eg/c5ZIy8HnabA3ClwVZXvVL/q3yqZdTMgVLWJy0u3\ntplbJucdv+SKW6cXmmT9V9HClRNd37q19To63ijg2jmuvfTCA+55uG6DRyzbb6xi+3VwQyd7ze6t\nW7fgJz/5CfzGb/wGvPTSS/Ctb30LvvOd78Bjjz0GX//616FQKNjef+qppwAA4M6dO+J++XWMZPwK\neL04NyeskrVwG1x5pdOp3U50eOG9k5LKwZupHtmIrwJOkMktw62zdqpXVR4nY+Il0DXR6dZ4cza2\nOLXBBD8PQDfVzQ3k5TJWSQro+lsVvJi+09XjJrOro8+pPCeerTL75eVdbnmqf8vg+h9VoEmfuQkC\nnGCiyRTomvrBzeyciWYqEzI9dwvc+nWD6FVsmde2c/yF6RsTaB+tI5HIGSBwsVi8flkGh1ZWsNvt\nduEP/uAP4Jvf/CZkMhn4zGc+A1/60pcAAOCLX/wifO5zn4Nnn33W9s2Xv/xlAAD493//d/jnf/5n\n+PnPf76WIyU4V/6ZYFmvX58p0ydfd+sHaH06YMc5tclEOxdObVxHsM9xDrRtultu6Htcw8lxKqso\nuUw7B07XJ5vKQ97oZMEPGaa8NbWL1k/fU9GoA+cqaS7NoVAIwuEwy0ZQOaLX6XLbjrSrrlF17kn/\ntAAAIABJREFUohNBHY2qLsuyxA1nJt03BexYj07GVeXJ9khuJ+1fuR1Ip0mnaP94sWlcGXcTPKv6\n0ol2pzJV/Wqqw2swSGlS6aQs305QybMqAKY6R9uIQYlKl9zYbj/B7WOZdh0PVQMYJzlexTZzBvm0\nT9zEB9TGrAoVz3Rwyw8sG8Ae+OrgGOxOJhP40Ic+BH/8x38MH/jABwAAbHeWf/rTn4b3ve99S9/J\nhjsSifh+5/Fi8dq9z7Q+t8AOwGtBKfBvtJNMTkQ2+CqaOLyYz+eiXaYONNHOBSfQMv2No3Bepjgp\nn2azmfiR3wmHw+JgdDeB0qrt4tLOQSQSEWctqqYgsY1yeZQnTnLsdjBEZZqWi7Tq2oF0RqNRiEQi\nNvqwDJOs4jmLTnpG3zHpGaXBKRNF5UnWfQ7t+L7bYFduh05+aDs4/e3kxGV+YHlyvdQe0ffC4bBN\nBmX9QdmNRqPGga/cLg6vue2lMuMmC8axq1z/Y9IfJ9rxW65dM/ETdRJpWMVequSH9jeVIaRpNpst\nya2KhvMIemUadKC0y3KhawPXZiwWC9f9gN/hb07iSKXTJlCdXjW7S4Ndk+8A8JboQL3mfGcMdheL\nBXzqU5+Cmzdvwmc/+1nx91KpBJcuXQIAgH/8x3+Ehx56SPktQmdEVwVt5CrBLjVEFNTZcbMGJifM\nDfy5goaCrKKdC66joMD3OcsRdIEuJ/BAw6z7RnZIXGXRtYuT+eKUrQtOdaAGVxe4qfSH0muSY68Z\nBCrTpvIR2F/Ydtp3tAyTrGIdpmyX3HYnnnFshMpByRkJDu1UBnVyJter0i+V/NB2mHRfxz9Z/7jB\nLrVH6KCxn2WaaD20PFOwK8uxrPtOcAoYOP0gv0/bqAPX/5j0x8n+4vvcwSqd1pX7iuqlmyBLTuao\n2kxlUpZdSpMq+HGrM35AHtjqQGmntoDSLmcs5YGzToawTK+ZXfpbBS+JRicb4RZc3wHgLSkDwJcV\nozV56aWX4Lvf/S48/PDD8MgjjwAAwF//9V/D888/Dz/96U/Bsiy4du0afPvb3176FpkkX1HoJ+bz\nOUwmE5hOpzCZTDyVEY/HxY1DstBHo1GIxWIQj8chHo/DbDYTKX4KKvBYVij0/9l70xjJrvL+/3tr\nX7uq15qe7unpGY/HnsEYOzHmDQ5IYBwSxcFCMlgILGySiCiJIlCANwnLG48jRVEEiYQSFPmnSA5+\nQ7CEMBYSthKkxCKxwWEc8DLj6X2vrn2//xf+P9fnnrrLubdudVW3n4/UGru76tznnvM8z3nOc7b+\nqTv6u9V99iLdbhftdhvtdrsvmylCt+C4GawTTgpmF+yLN524BbtWv3MzolAoZFwvmEqljDbudDqm\nz9HtO5FIRNlxiI5Ifm+ntlPFj76nUinjJh35uXbl6bpu6H273bbVY78OlTouaotYLOaqa+LtQul0\n2qTHYhkqo3sreUU7E28rs7IzugI8nU4bMjj5iEQiYXpH0fbpZjWvmQmVwTIFg+KAjW4bkvWH3kG8\nZtRKJtUBurwOUbziVIT0rNPpQNd1U+ZerFvRfuTynIJdsQzSk6Ayu2Jnq2oD1AYqM3CiDdrhZD9O\nspM9ebnWl/pEai9qq2g0alyrTPrmxV9SHVLbAP3+nW70S6fTJt8qykR9KckgtouTbw4aOdNtR7fb\nNdpYvPGNvk/tQ7d4Auj7nJ0e0zITv4G9StLIzpc4lSnGVEEEuyp9B33Wa1JG7Kfk+EDG0YLe//73\nW06jf/SjH3UVgpQ1m81iYWEBly5dQjabdf2eF3RdR6vVcnU2Tpw7dw7z8/PIZDJ9lZzJZHD69Gnc\neuutCIfDKBaLKBaLKJVKps+l02nk83lMTk7i/PnzWFxcxMTERJ/BptNpzM/P45ZbbjFdGSlDQUKr\n1XIMds+fP4/5+Xmk0+mBR8JW2aVcLofJyUnk83mTQygUCrbvKJchKi/9tzwSlsnlclhcXMTly5eR\nz+dNzlvkwoULmJ2dRTweR6PRUHrPWCxmvFMulzP97eabb0ahUEAqlfLtbHO5HM6cOYN3vetdmJ2d\nVfrO4uIiFhYWkM1m+55L9nPrrbf23StOOtJut3HhwgXMzc0hmUz2TaP7yeqmUink83nk83ksLCxg\naWkJ+Xze0TlHIhFMTU1heXkZt99+OyqViiHj6dOncfr0aUs7E3GSl2SanJzE2bNnsbi4iFwu11dn\nqVQKp06dwi233AJN00z1ZEc2mzW9o+i3wuEwTp8+jWw2qyy7k/2IhEIhnDt3DtPT04jFYiYfIX9H\nDArJb1nZvkqGk2QkEokECoUCbr75ZtTrddP3xIBODHaj0aipbkX7icfjmJmZwfnz53FwcOAa7FIZ\n58+fx8zMDOLxeCDZvUwmY+ix6vXDFOzK0/FWsqv0P7lcztZ+nN4xk8lgbm4Os7OzysGKGFjS9d0U\nbFy8eBGnTp1CKpVS9guRSMSoP+rfZmZmkEgkTPoTjUZNtt9sNk0yUT1Fo1GcPXsWU1NThn6THPF4\n3HiW7JuDRlxu4RTsirLH43EsLS1hcnIS4XDYFB+kUinjO/F4HGfPnsXk5KTjtd1iG3gN8FT6UfKD\nFy9edIwjZESdDmIZA/k3t2uh/dh7IpEwdPMXv/iF42eHfl0wdRrValW581eFFNGtI3Nifn7eNtgV\nA41wOIwbN26g0+mgXC6bPkdKv7S0hAsXLmBhYQETExOOwbN8eoVIp9Mx3slptHL69Glb2VWRg1Ei\nFAohn8/jzJkzOHv2LOLxuPG3yclJI9BQ6fzFslWMe2JiAouLi6jVaigUCkYby3Vx0003YW5uDolE\nAs1mU2kKjDrhpaUlLC4umv529uxZU2fgBwrUa7UaFhYWlL4zMzNjG0xls1mcPn0aly5dMtmP2NG2\nWi0sLy8bgYZVsCv/txvJZBKFQgFLS0s4f/48zpw5YwSWKsFuq9VCrVYz2m56etoI6L3qDEHO++zZ\ns7jpppsMmeTPUcB48eJFpFIpUz3ZkUqljIAkHA6bbD8UCnkK1AGz/SwtLZkyP/J3zp07h5mZGUSj\nUVOwOzExYfqs6OvoWEi7ga5dHYodpfi3ZDKJubk5XLhwoS/7Qh1fq9WCrutG8CQGu61WC0tLS4b9\nxGIxzM7O4qabbnLsaMVgotVq+Qp2nXSG6pOCFBXEbJRTUkKW3Y50Ou1oP3Y+kWz/woULmJ6eVpJd\nTJRQtp3e48yZM0b7iEksp3qORCKYnp7G0tISlpaWcNNNNxkJBvF70WgU09PTOHfuXF/w3+12DR0J\nhUKmgFF871gsZuubg4ay1DQbYYcoeyQSMYJYMdi95ZZbTLoVjUaxvLxsBPRuwa74/6qo9KPkw2++\n+WZb/yND/QrpT5DBbiwWU5pJ8NJPJRIJzM3NYWlpaXTBrpzZDYfDfUHioIjBrpOzcWJychKnT5+2\n7DTI2XQ6HYTDYXQ6Hezv7/eVIXZQFy9eNIJdedRFxqFpmnF+sRUU7FoFeCJTU1MDZ3btOgnqrJeW\nlvCud73LlFnIZDJKmV1ZceXMlx0TExM4c+YMotEoSqUSWq0Wms1mX13Mz89jdnYWiUTCyLa71QM5\n1PPnz+PSpUumv83Ozg6c2RVlr9VqSt/JZrM4deqUY2bXyn6azaahJyS7VWZX/FcVMfi5dOmSEQg6\nOSIKds+dO4dkMol6vW7Il06nlbOjdvKm02kjU3HLLbfYZnbJHoG3BhIqPiIej+PMmTOYnJw0Mrun\nT582NqaoBrv0L2V2l5aWcNttt9lm5jRNw9LSkimzSz6iUCiYPiu+Rz6fd83sOgVVVpndubk59Hq9\nvqyaGNBSsEs/ZJutVgszMzNGMBWPxzE7O4tOp2PKesnIPnxxcREzMzNKHaPb+wJv+SryzaQTblCw\nSz+qsttBGUG7zK7de2YyGSwsLODy5cvKsvd6PaM9KNiln+npaaN9qtWqUlAhZmxvu+02nD171gh2\nRf2hoPjcuXNIJBKmAY4YMOq6bgS7YiBImV0aIN16661K7+sX1SUiouwATLKL8YHYPuFwGEtLS0rB\nrvivKqr9aCqVQqFQgK7ryoMlMdil9hoU8m8qmV2vdUF+68KFC66fHVqwS8TjceRyOei63pepGBR5\nvZcfaJrLauSTSCQwNTWFbreLWq2G9fV1y0AomUxiamoKp0+fxsLCAqanpy2nzGKxGCYmJtDr9fqm\npEVU1+xmMhlMTk6asq5+sDIcGrnSSFuUN5lM2r6jVbliJklFoWlqgnTGbhnD5OQkJiYmjKlGFQcQ\njUaRy+VQKBRw9uxZ099yuRzy+bxjB+cGyQ7ANJXnRDKZRC6Xs2xHJ/sRdT+XyyGXy1nKLtaLahAf\nj8cxOTmJ+fl5nDlzBtPT066DqlAohFQqZQSMzWbTkI9sSSXDYNeOiUTCGJwuLi7a6mA0GkU2m0W3\n20UymVTyEdFoFDMzM4Z9k7x0BM/k5KRn2cl+zpw5Y7uES9M0zM7OIpPJGB0wyW63drbdbhtLp6x0\nxq4zdLI/6rw7nU6fDon+yGnN7sTEhKGD4XAY6XQaMzMzxpp6K2QfPj09jYmJCU8bbp06f/LNCwsL\nOHPmjFJ54jIGtw1qXnTLbWBipe/5fB6FQkF5lkjexyIux8hkMshms5b+0q59SC/m5uZw9uxZFAoF\nZLNZy02wqVQKU1NTCIVCpn5LXFqh67qxLIPel+Rw8s1BIy5jcNugJrYvya5pmuGPut2uaaY2HA5j\nZmYGmUzG1d/68c2q/ajoB1Uzu4C5XwkiszszM4NsNuu6Bt9PXcRiMeRyOcfkITH0YJeMLBQK+c6+\n2iEeC+JlTYpIPB5HNpu1DBIo0AiFQiiVSkZQbOWUyEgpQ2fVCdE0paZprtkOeieno8cSiQQymcxA\nwa6dgoXDYcN5zc/PmwItMiLVzl/cWKQycovFYiadoU0Ccl2k02lkMhlj9KxiKBRMzM7O9nUgyWTS\n1Bn4gWQPh8PKAzDagGb1XCf7EXU/mUwadSHjN9idmJjA3NycodOJRMJ1ZJ5IJIwBSKfTMeSjTtNN\nV50CF7JHWSaZSCRiBIrJZNIkhx00uKPMOD2LplpV7EyUW7YfuzWImqYhm80inU4bnYGdjxDbOx6P\nI5PJ2A7MRJsTf2fXfuFwGMlkErqu972n6I/EHf4U1NAPtX0sFjMGDKQLTp2m2D6ZTAbpdNrz6TJ2\n+u0nYNS0t0+6cOqgVfsfWhZjZz92slMbT01NKS8BlGUSd8HTpl95raxbsJvJZDA9PY3Tp08jn8+b\ndJUQ2zsSiZh8tSiTruvIZrPGoFKUgXznzMyMclv5hWzUbTOclezJZNKQl3yEmNigga7KDKEf36za\nj5IPAuAp2BX1J4jMLrW3yoZTlYSVCCUQVezjSILddDqNeDweSMWJ0G7EXq830O55ux2Z8XjcUBjV\nYLdQKNhubKBOOB6POwax4js5vZfXI67sUAl2xZGrmPlQKVvO7LohdpZ0+oVVXYhH6sjPsoOCRyuH\nKp4R6xfKalHgoAI5XisdJPuhuiDEUy16vZ5pd7EVgziR+fl5o2y3YJemBdPptKndKHOjEsQ4BS5i\nsGvXVjRdFovFDIft5iNk+cj2KWj2IjsFS6L9OK0XpfcgG7HzEWJ9hkL2RwrZdaDigFNuR9JZGgza\nPVcsX9M0kw6K9hMKhZBMJg17s0P24VSG19NlnGYDyDd7CXZV7EW1/xF1yy7YtRvcZbNZTE1Nmc62\nd0KWSfS9cgAv6ohKsLuwsGC0qWwLou3LgzS5jqiN5aw2JVGsEhFBI/dLdjjJLsYH8hpo+pyKvx1W\nsEttEYvFlC/dkvuVIFA9McpvZndsgl0yrkGn2u0I4jw4+q7VkWK0rieTySCRSFh2eOFw2Miy0ro+\nK2WkunCbJpfPuvMjuypO9UfHN2Wz2b4pdNXA1U+7iDrjVhfi+6s8i9o0lUpZvpP4rx8o+A5K352y\nS3LbWemCyqDJ7rl0jBAFPyoOUMz6ybKp6Ko4uLGTyc3OxDWX4rNV6kAMJsn26fcqsovPcbIfEXla\n0s5HqLS3lRxyGeK/BL2vFVZlycEuBVaiDakOHFXfyw4n2yffnE6nPS2jU50q9qpbdm1lJzut43Ya\nMDjJZDcwcbIzEWrHVCplzIDaBex27W3lA0QZZZuz8s1BI+qpW7BrJ7vsI6y+66Qbop168c9ekihu\n687tyh80pvJTpp+kJb2jymklQwt2rZzjMJ5BRut3GQOVY1fJZAziWZPy2lH6Hf3dagpRLtNNHtEh\n+ZVdBdoEJ7+X+E7ymjR5aYKbbLQMgZZlqMpMDtqpLqgs8bgUp0194rvKywxU3kkVr/qu0unIn5c7\nLat6pc2OVm3shKjP4totNznFszNJRsquqrS7k6x+7MyLj5DfUewIVWUn2cTzOd3OARfP4xVlt5JP\ntiErmcT1/mIdyueEO/k8+bmintFMBACTDtplZVQyZ2L7ePVpoo+y0xkvZ7GLS1G8yu70WfFfWXYr\nfRfbWhXZ5kQbIf0R12DTc+2eIeuxio+0qjNR98S6kO3da1v5RXVpnd3gwMpHyN8T/7VCbgNV3+yn\nH1XF62DIS7luZTnZgh2ifrox9MwuEeQoQSyTDvb2G+zKo0sRcVTspJRiUEgnN6iMFlXey225w6Cj\nMDsFIyWyemeaEgPgGuyS0dC7eDEgMRNhVRf0N13XlQ1FDphExA5u0MFZ0PpuVZ68ttsqcyTqphz8\nOCEPdlT0jIJL0g+Sj9pOpQwxYHQKXMjOAHsdlPXHyUfItiRn9lRkt+q87HRNfrasd6rtbSWT0wBW\nHHg4ySP/v7iGj6bj6RIU8TpVK/txe5bYPqJNq+KmMyqDYBG793CT3elzTm3lFOx69e9ie9CaXWov\nklU82pKebVe+rMfiEgi7urHSH9EXiO9kZTNe2sovoq/3qp9WPkLWd1V/Qe3gxTd7HQR57YvEtgoC\n1cDcT+Dv5fOOwW6j0cAHPvAB4yiT3//938djjz2G/f19fOITn8Cbb76J5eVlPPXUU33nxorGP4ys\nLtB/i5Rf7AIFGvXR5iAxayMiGmmr1XKculOpCxp5uzWiaFB+lzHQjnn5vcR6peOFCFpf5fY+Yucs\n/qhkQqhccjRWDlB8d9JRt45HbCv5tARx17jfG+lE2b2immkjRD2xCxTo6Bw73bVDbn+xbDs5KXtE\nNiOOup0CchHxjEcrOxOPwRLXasuIQaOoPyodm9iRUSCtIrt45JPsE+xO5qD1fVYBtoxcn3aBoXhs\noXwElPxjVWdOzxXbX57xEtd+qt5YJrePWM+qnbSdDwPMeqx6Ogr5N5VgV7X/sbMf8cQSWXbRX3pZ\n0iH6BdFGqB2bzWafv3QKdkU/IPp+q+SQnUyyDVJdiG3np638Qnsc3HTUSXandd0q/pIGHfTuqr7Z\nyYZl/PRF8ukrg6JSF4CzHdsh+lg3HIPdRCKBn/zkJ0ilUuh0Onj/+9+P//iP/8DTTz+Ne++9F1/6\n0pfw+OOP48qVK7hy5Yrpu88++yyAt6eEgsiWyZCzGeQ0BtXM7vr6Ot544w0Ui8W+MkqlEt544w38\n7Gc/w/b2tu1Uj2pdiCPJYWd2r169itXV1b5bk3q9HnZ3d/GrX/0K2Wy2b9OKynTW3t4erl69iu3t\nbQDAzs4Orl69amwQs0OsJ8pU2GV26Wd9fR3Xrl2zbB+RZrOJtbU1vPzyy30BrTgN61dX/ei7GLRb\n6aBdeaQjcrZEDnZfeeUVbG1teToNpVqtYmVlBS+++CKq1apyZle8gtNPZnd7exuvv/46Dg4O+v5W\nLpdx/fp1/M///A8ODg4c7UzshMRlNHYEkdnd2toyfESv18POzo6t/YiIg2rxv+X2tlsOJMv0v//7\nv9jY2Oi7VbDT6WBjYwO/+MUvEI/HTce2iXVm9Vw5s0vLVWT/a/UOKrvdrTJnqj5tbW0N165dw+Hh\nYd/fDg8Pce3aNfzsZz/D1taWUnmU2XXbVCPL7vQ5u3daXV3FtWvX+m7lBIBisYjXXnsN//mf/4nV\n1VUl2eU+UXyPXu/tY8l2dnbw2muvWZ4bL9Jut7G1tYVf/vKXxuY0Ox9p196iH5Db+JVXXsHq6ipq\ntRra7TbW19fx8ssvB7KUzAlxU7DTs5xkHzSzS755c3PTU7KuXC7j9ddfx3/9139Z+knCyaadEPuV\nIFCtj1/+8pfY2NjwNNCp1WpYWVnBz3/+c9fPui5joJ2VdATU5OQknn76aTz//PMAgIcffhgf/OAH\n+4LdH/3oRwDeXsMX1FpIEQoQvIx87cpxyqppmoaDgwO88cYbjg5V0zRcv37dtmFVjzvxsmZmkEAX\neKujWFtb67sAQeys2+1239ElKspbrVZx7do17OzsQNd17Ozs4JVXXkG9XnfccCHvGrZrY3q2rus4\nODiw7fBEGo2G4VDlDkYsz2+dirKrOhhx3Z/caTrZD33Hai2Z+Jlr165hc3PTU7BbqVRw48YNhMNh\nbG1t2ZYvI8or2qdqAFMqlWwHLaVSCW+++SbC4TBWVlaU7Iymb1XXv4v/el2zS36gWCxC13VjsGhl\nP/JzxWfa+QiVNdoAcOPGDayvr/cFu+12GxsbG/j5z3+OUqlkmoGiOhPX41o9lz5LP6LuyvWnenyX\n05pIFZxsn9oEgPGvG172JPjVLWJ/fx/Xr1+3lP3g4ACvvfYagLcuEFJBlslqzW6v1zPsbH9/37Gu\n2+02Njc3cfXqVTQaDdO0v/g9WW/l4M+ujdfW1oxgt9vtYm1tDbFYzNWPD4rfNnbyEfL3xH+tIN+8\ntbXlKdil5Jqu6446rRpvyHidTXBD1aavX7/uK9hdXV1V2oSn6S4S9Ho9/MZv/AZef/11fP7zn8df\n//VfY3Jy0hhR6LqOqakp0whD0zQjc6dpGiYmJoyD5oMkiOBElUajgcPDQxweHlpeF0wXEsTjcdts\ns3jMmVsH4Mfp+6FcLhvvJXaOoVDIuKiArlAV5VPJaHQ6HVQqFeOHdtHbnQdLiEeK2TlXGaf2EaHz\nU3O5XN+OX9WMuhOi7Kr6Lq6P9qIzKgGkrutGvRweHio71VQqZdSTyk5XQsx0eM3QAW9l3klWeTCS\nTqcNfaRbmtzqjNrgKHwEyV4sFlGtVo36y+Vyrrc00XuEQqGB2ht4qzOkOrQ6/5N+RP0UnyvLKvsj\nuzaW16/alSeXLT/DK26+OZ/PI5fLeTpr1G1JSVCy1+t1Q/ZKpWL6WzabRT6fRz6fd73Ax04mu6xj\nq9Uy+QU7IpGIUX+5XK5v7S1By3FEv20nk4jY/+i6buubg4bkU2njYfXFom8uFovKmVTx5CcnnSab\n9nqUnx+/HQSiPqomZiKRCBKJBOLxOPb29hxlds3shkIhvPTSSzg8PMR9992Hn/zkJ6a/2ykLOdlw\nOIxisYhKpTK0qYmjaBRxrZNMq9VCqVRCs9m0nNojxAO+VeriKN7L7ipeXddRr9fR6/VQq9VM8uq6\n2vIR+hyV3Wg00Ol0UC6XHd9fnHoTgxUnut0uGo2G66iQAnCSQySIYNdKdjfE53rVGRUdaTabaDQa\nnpb6tNttlMtltFot16UhMrI/8KLH3W7X1c5arRbC4bBtsEtOXswqHoUtibI72Y/V9+g9xKDBb3u3\nWi3D1uTv0hXOpVLJ1E7itK7TUXeEVTAjb+ShslTOJx6kfdx8Mw3k/VxUoUIQslt17jR48iO7XVvR\n33q9npK/7PV6qFar6Ha7xr92wa6oP07ZThGx/9F13dY3DwMvU/vD8h/km730N2S/tVrNMYi18oOq\nHHWgC8CwYa9LUlUDc2ULyuVy+N3f/V3893//NwqFAjY3N3Hq1ClsbGxYHnhNGSTKVnQ6naFuVBs2\ntN7JSinpbwAcp02pLtrttmsgdFTKRsGo1XvRQnXKEIiyqUzfiZ8D3p52l8uzei7VlTiN7IRT+8gy\nUVAiGxXJ67Rhww0r2d0QpxftdMbOflTkFDc0qSLqtNe1W1aBkJfn2s0Y0N8ajYZpCt1qYynVm+pg\nKQhIPprutLMfq+/RD20ksvMRKu9ht+mI9NsKClZoo5nbc+0yd+LmU2oDlY52kPZR9c1eNzEfRbCr\nIruu6wMFK3Zt5dVfinoqL7ETN8DZ+T6repL3Y9j55mFxFG3shB/fDJh9jR3UJn6WkI4i2KVYxGs/\npRpbOi5j2N3dNaYx6vU67rvvPnz1q1/Fj370I0xPT+PLX/4yrly5gmKxaFqzS46T/ltlSsgvR9Uo\n5MitOgx5Q4bdNIBqXRylookBqfxcpzVNqlMd4udU9UCuJ5X6cGofuWynTWiDTuH40XfxmV50RlVG\neZ2n6nsMsllPtd2ssAtiZZlU6+wofYRoTyprAul74r+DtreTTduV7UfPrOpWbA9VOxi0fbz4Zq+M\nWnY/Nmglk1VbqSQsxE1O8pIgOdh1WhpgV09yQmTQDcJ+GHYbO+HXN/vpR1UZRaBLz7XzW3aIuul2\neoRjsPvyyy/j4YcfNgT49Kc/jb/4i7/A/v4+HnzwQdy4cQPLFkePHaWiMgzDMAzDMO9sfAe7fuFg\nl2EYhmEYhjkqnMLZ4R5mxzAMwzAMwzAjhINdhmEYhmEY5sTCwS7DMAzDMAxzYuFgl2EYhmEYhjmx\ncLDLMAzDMAzDnFg42GUYhmEYhmFOLBzsMgzDMAzDMCcWDnYZhmEYhmGYEwsHuwzDMAzDMMyJhYNd\nhmEYhmEY5sQSGUahQ7iBmGEYhmEYhmE8w5ldhmEYhmEY5sTCwS7DMAzDMAxzYuFgl2EYhmEYhjmx\nDC3YfeaZZ3Drrbfi5ptvxuOPPz6sxzCMEsvLy7j99ttx55134u677wYA7O/v495778XFixfxkY98\nBMViccRSMu8UHnnkERQKBbz73e82fuekj4899hhuvvlm3HrrrXj22WdHITLzDsFKN7/2ta9hcXER\nd955J+6880788Ic/NP7GuskcB4YS7Ha7XfzJn/wJnnnmGVy9ehVPPvkkXnnllWE8imGwT1DhAAAg\nAElEQVSU0DQNzz33HF588UW88MILAIArV67g3nvvxa9//Wt86EMfwpUrV0YsJfNO4bOf/SyeeeYZ\n0+/s9PHq1av47ne/i6tXr+KZZ57BH//xH6PX641CbOYdgJVuapqGL3zhC3jxxRfx4osv4qMf/SgA\n1k3m+DCUYPeFF17AhQsXsLy8jGg0ik9+8pP4/ve/P4xHMYwy8ikhTz/9NB5++GEAwMMPP4x/+7d/\nG4VYzDuQe+65B5OTk6bf2enj97//fTz00EOIRqNYXl7GhQsXjAEbwwSNlW4C1qcssW4yx4WhBLtr\na2s4c+aM8f+Li4tYW1sbxqMYRglN0/DhD38Yd911F/7xH/8RALC1tYVCoQAAKBQK2NraGqWIzDsc\nO31cX1/H4uKi8Tn2p8wo+OY3v4n3vOc9ePTRR40lNqybzHFhKMGupmnDKJZhfPPTn/4UL774In74\nwx/i7//+7/Hv//7vpr9rmsZ6y4wNbvrIusocJZ///Odx7do1vPTSS5ifn8cXv/hF28+ybjLjyFCC\n3YWFBaysrBj/v7KyYhr9McxRMz8/DwCYnZ3FAw88gBdeeAGFQgGbm5sAgI2NDczNzY1SROYdjp0+\nyv50dXUVCwsLI5GReWcyNzdnDMA+97nPGUsVWDeZ48JQgt277roLr776Kq5fv45Wq4Xvfve7uP/+\n+4fxKIZxpVaroVwuAwCq1SqeffZZvPvd78b999+PJ554AgDwxBNP4GMf+9goxWTe4djp4/33349/\n/dd/RavVwrVr1/Dqq68aJ4owzFGwsbFh/Pf3vvc946QG1k3muDCU64IjkQi+9a1v4b777kO328Wj\njz6KS5cuDeNRDOPK1tYWHnjgAQBAp9PBpz71KXzkIx/BXXfdhQcffBDf+c53sLy8jKeeemrEkjLv\nFB566CE8//zz2N3dxZkzZ/CNb3wDX/nKVyz18fLly3jwwQdx+fJlRCIR/MM//ANPFTNDQ9bNr3/9\n63juuefw0ksvQdM0nDt3Dt/+9rcBsG4yxwdNt9piyTAMwzAMwzAnAL5BjWEYhmEYhjmxcLDLMAzD\nMAzDnFg42GUYhmEYhmFOLBzsMgzDMAzDMCcWDnYZhmEYhmGYEwsHuwzDMAzDMMyJhYNdhmEYhmEY\n5sTCwS7DMAzDMAxzYuFgl2EYhmEYhjmxcLDLMAzDMAzDnFg42GUYhmEYhmFOLBzsMgzDMAzDMCcW\nDnYZhmEYhmGYEwsHuwzDMAzDMMyJhYNdhmEYhmEY5sTCwS7DMAzDMAxzYuFgl2EYhmEYhjmxcLDL\nMAzDMAzDnFg42GUYhmEYhmFOLBzsMgzDMAzDMCcWDnYZhmEYhmGYEwsHuwzDMAzDMMyJhYNdhmEY\nhmEY5sTCwS7DMAzDMAxzYuFgl2EYhmEYhjmxcLDLMAzDMAzDnFg42GUYhmEYhmFOLBzsMgzDMAzD\nMCcWDnYZhmEYhmGYEwsHuwzDMAzDMMyJhYNdhmEYhmEY5sTCwS7DMAzDMAxzYuFgl2EYhmEYhjmx\ncLDLMAzDMAzDnFg42GUYhmEYhmFOLBzsMgzDMAzDMCcWDnYZhmEYhmGYEwsHuwzDMAzDMMyJhYNd\nhmEYhmEY5sTCwS7DMAzDMAxzYuFgl2EYhmEYhjmxcLDLMAzDMAzDnFg42GUYhmEYhmFOLBzsMgzD\nMAzDMCcWDnYZhmEYhmGYEwsHuwzDMAzDMMyJhYNdhmEYhmEY5sTCwS7DMAzDMAxzYuFgl2EYhmEY\nhjmxcLDLMAzDMAzDnFh8B7vPPPMMbr31Vtx88814/PHHg5SJYRiGYRiGYQJB03Vd9/qlbreLW265\nBT/+8Y+xsLCA9773vXjyySdx6dKlYcjIMAzDMAzDML6I+PnSCy+8gAsXLmB5eRkA8MlPfhLf//73\njWBX07TABGQYhmEYhmEYJ5xyt76WMaytreHMmTPG/y8uLmJtbc1PUQzDMAzDMAwzNHwFu5y5ZRiG\nYRiGYY4DvoLdhYUFrKysGP+/srKCxcXFwIRiGIZhGIZhmCDwFezeddddePXVV3H9+nW0Wi1897vf\nxf333x+0bAzDMAzDMAwzEL42qEUiEXzrW9/Cfffdh263i0cffZRPYmAYhmEYhmHGDl9Hj7kWymt6\nGYZhGIZhmCMi8NMYGIZhGIZhGOY4wMEuwzAMwzAMc2LhYJdhGIZhGIY5sXCwyzAMwzAMw5xYONhl\nGIZhGIZhTiy+jh5TYWJiou93mqYZP4Su65Y76OTPidB3hnCQhDKdTgfdbhfdbtdRDjtZQ6EQIpGI\n8TNqVE7QcGqT44Rdm/R6PXS7XXQ6HfR6vYHLU4V0IRqNIhwO99mJVflu7eDHfkifu91u3/uL3xH1\nNhQyj5ftZJfLDofDiEQixvvayS4+V24flXrXNM2oW9HORqHvXvVErjc/fsYJp3YkVPRM5XNOjIM/\nd4Lqv9Pp9MkYtO0TYr2Os8/140v8lPdOgHwi+cVBGER/7NpA13VT3DNsVHRBtJ9qtepY3tCirNnZ\n2b7faZqGUCiEcDiMUCiEXq9ndGBWn6MfEfE7ozKIXq+HZrOJRqOBRqNhK4fYQVPnTIRCISQSCaRS\nKaTT6aMS3RY3gxDbY5ydrxsUQJAeibRaLaNNO52O5/L8OoBIJIJUKoVUKoVkMmnYSDgcttQflQDE\nj/3QuzcaDVPdyO8YjUaRTqeRSqUQjUZNZZBty7K3222j7Ha7jUQiYfyIMsqyi88V26fdbisFgWRn\nJK9qcBa0vvvxW91u13jfZrNp+zm/OhiNRg29i8Vilp8Zdj3JPnLc0HXdqH83u/CDbPuEbAfj6HPF\nwZis02L/qFo349C3j5JIJGL4qXg8PlBZFOTa9QNO2Ol0p9MxbMHJHwWBXdwkI9rPyILdmZmZvt+J\n2cxwOGyMlmXlFjt7OetJ36HvjYJer4dKpWIK2K2gkRA5dJFQKIRkMolcLod8Pn8UYlui2vmL7eHF\ncMaNXq9n6I8c0NbrdVQqFQBQNmZq10GcczgcNnQhl8uZMm6ivvd6PaWRul/7qVQqqFQqht7avWMs\nFkM6ncbk5KTJKVMW1Ur2RqOBSqViyJ5KpZDNZjExMWHSJ1H2cDhsaqtarWa0D8liZVtyXSQSCUxM\nTCCfzxvPUtF38lNB6Hu320W73fY0a9DpdFAulw0/Y4dfHaRBy+TkJBKJhOlvKnqmaZpJz/wEZE72\nOA7oum7YhRwABGn7+Xwe2WzWVO/j7nOdfEm1WjVstdVqKZVHuuBm0ycVGnzm83nfCTCxP6d4i/RI\nBfL99CPqdqvVMtnCMCF9crMt0X7W19cdP+s72F1eXsbExATC4TCi0SheeOEF09/Pnj3b951QKIRo\nNGpM2YjGIge71EhWnXW73TYyO6Og1+vh4OAABwcHiEajtk6asgL1er3PUUYiEWSzWczNzWF+fv6o\nRO/DammJFeIUyzg6XlUoy9jpdNBut01/q1QqODg4QCwWcx0lEpR9q9frvjMS0WgUuVwOp06dwtzc\nnDHlHo1G+4IklcEJBYxWS2Sc7Id0OhKJmDqoXq+Her1uZGmSySSmpqZw+vRpk1PWNM1W9mq1ioOD\nA8TjcVQqFUxOTmJqagpTU1MmGWUHTe3U6XRQKpWM9imVSoZMTkFSOBxGNpvF7OwsTp8+bWTJjlrf\nyc958Vvtdhv7+/s4ODhw7Kzk9lHVwUQigampKczPzyObzZr+puoXxMHNIMEu6eQ4ItqFKGPQtj8z\nM2Oq93H3uaJ9yzZ4eHho9I+NRkOpPBoU1+v1sRz4DJtYLIZ8Po/5+XlMTk76KkPUHzm5qIKu66b+\nUdTpZrOJg4MD7O/vD33pZbvdNvk0O8h+CoUCrl696limb4k1TcNzzz2Hqakpy7+/733vs/yO2JGJ\n6XI52BWXO4iQcxzltFen08H29jZ2dnawvb1t66R7vR729vawu7vbF9DH43EUCgXccsstI71q2cu0\nLrXbOE6pqeK07qhYLGJ7exvb29solUpK5bVaLezu7mJvbw+tVstXh5dKpTA/P4/Lly/j/PnzJhsh\n+yB9V83s+rEfevft7W1TB9Vut413bDabyOfzWF5exuXLl032L2f6xHV75XLZKLtYLKJQKBg/crAr\nyi621cHBgVHGzs6OSSY7YrEYZmdncfHiRVy+fNlw+irBLskR1DIGr36r2Wxia2vL8DN2uiW3j6oO\n5nI5LC0t4fLly33LzlQzu2Jb+V3GIM7wjRu6rpvsQtQ10fabzaav90+lUjh9+jQuX76Mc+fO9WV2\ng9TBoHHa47C3t2fUmWrioF6vG/2lajb4JJHNZrG4uIjLly9jYWHBVxlyZteuH7DDaZ9ArVYz2nR3\nd9eXfKpUKhVDF5wGwWQ/ly5dwk9+8hPHMgcKz52cqlWwC5jXeNF0hVU5dhkY+o7bWo5h0m63sba2\nhvX1daytrdkaZrfbRTweR7vdxuHhoWm0mkgkjGDXrq6OCpWAVxwxjqPjVcVJf3Z3d7G2toa1tTUc\nHBwolVev141M6P7+vi+ZRIO94447LG2E5PUyOPFqP/Tua2trqNVqxu8bjYbpHXO5HJaXl3HHHXf0\nzUqIstMzut0uSqWSUfbe3h4WFxexsLCAxcXFvvWiouwka6/XM7VPNptFOBxGs9l0rPdYLIa5uTlc\nvHgR733ve40MpOoGv6Ayan78Vr1ex+rqKtbX15HP522/J7bPwcGBctCYy+Vw9uxZ3H777VhaWur7\nu5eAdxCfILbxuNHr9Qw/v7q6ahoE1mo1RCIRQwf9DnQp2L399tsB9PvacczqAs46vbm5adhquVxW\nKq9UKiEcDqNer6NYLA5D5LEmk8ngzJkzuO2223Dx4kXf5cj647XPtrPHcrmM9fV1rK6uYnNz07d8\nKuzv70PTNNRqNUf9Ee3HjYEyux/+8IcRDofxR3/0R/iDP/gD099/9KMfGf/9W7/1W/jABz5gfG/Q\nYElcrzcK2u02rl+/jsnJSWQyGdvMEk3vHB4eYn193fTeYmb37rvvPirR+whiN/Vxw05/tra2MD09\njYmJCeWRa6VSMTo7t7WVdiSTSSOze/fdd/fZiLgjdZj28+abb2JqagrZbNZYbwe8tf6OprBCoRDy\n+TzOnj2L97znPVheXjaVYSd7sVjEzMwM8vk8tra2sLy8jOXlZZw7d851MwaVIbZPLBYz6t2pPsRg\n9+677zY21I1C3736rVqthpmZGUxOTiKdTtt+T24fVR2cmJgw2vHmm282/e0o/cKo/bkTuq6bfL04\nCCyVSko66ATN6ly6dMmwfeD4+GO7tltbWzN8yeHhoVJZ+/v7aDQa2N3dPTbvHySU2b3ttttwxx13\n+CojKP2xOgWhVCrh+vXryOVylqdtBcnGxgaq1Sp2dnZs30XXdZTLZbzxxhtKyzR8B7s//elPMT8/\nj52dHdx777249dZbcc899xh//9rXvtb3nSAbQvz3qNF1HfF4HKlUCplMxnYnc6fTQTKZtF3PJk4D\njorj5lyDwE5/otGosXNfdYMa6cIga5jkKSe5TWQ5h2U/sVgMyWQSmUym7xmJRMKUFRWXtVjJJstO\ndUs2k0wmjXpz0n9RVrF90uk04vG4ku1YyXscgt1IJIJ4PG60iR2aphnt4wW5LeW/if8Ok1H7cyd0\nXTfZhVhPvV7PV72LyLp53Pyxky+lOvOybGdQX3qccfKrXsoQ//WDXZuSP6LNxcPk8PDQ1b9rmoZC\noYB77rkHv/M7v4MnnnjCsUzfWkXTl7Ozs3jggQfwwgsvmILdozDWUTkEWntMDS8fv0R0Oh3E43FE\no1HXJQLM0SPXezgcNjo21d2w1MZ+N+jYyTQK+6H3T6VSpt/3ej3bTshuECdDm1MpWFUNEjRNM5Zv\niO1Dx/OoljFOy29U5dA0zaizTCZjGww6tY/qc8ahbsZBBitEXy8uKWi328oDLhWOW6Ar4uRLVZfV\nVKtVxGKxkSZ/xoVR6oDoc0VkHz5M6DjEIJfw+PKOtVoN3W4X2WwW1WoVzz77LL761a8GJtRxgBxg\nOp22XUBN54k6BULH0bEdd8iYZUQHrboznILdk+CgxU5d1Etaey4feu9Fd8lR0kDCzwBBDnb9dozH\nxebEYNdpGQMFu342Mo3DINzOHscF0S5EfWu1Wu/oTKQT4XDYqDPVtqUB7EnwpaNkWHYr+/Bhkkwm\nAx/4+LLSra0tPPDAAwDe6uw/9alP4SMf+YjpM3YLzMW1ILFYzPgRG6jX66HVaqHValkGHaMeAXe7\nXeM4MaesLWWAaXQiGj29Y6VSGelifDomSr7BR6bT6RhtMo67pr1gpz+VSgXtdhuhUMh2aYoMHbVF\nm8n8dNrdbhfNZtPQBbkckpOO+aMfO/zaDw1iKai0ekfgrUFcrVZDqVTq010r2TVNQ6PRMDZyiuXJ\nMtBxRqLsVIbYPlSGW6BEF8BUq1UUi0Ukk0mj/pyyBiRDq9UKbOOUV7/VbreN5TSxWMz2Pf3qYKfT\nQb1e72tHCrLpx0leqiO/J5GIzxzHQYiu64ZdRCIR0ztSZ2y33EgFOr6sUqng8PDQVO+izx3HzXuA\nsy/pdDp9vsQJ8QbJcR78DAuyx3K57DsmEPVH13VDf7we5WZlj81m0/Dhqm3qF/LPbrog2o8bvoLd\nc+fO4aWXXnL8zMrKSt/vxNtyACCfzxs/4uiYTi8oFot9i9ut1jYeNbqumxrertMUO3O5E6ID43d3\ndy3r6qjIZDLG4f5OwW6j0UCxWESxWDRt0jhu0HS41a0yFFx0u13l6RPxc36D3VarhVKphO3tbays\nrJhueBPlTSQSRls5Bbt+7afVahlHV8kXPRC9Xg+NRgMHBwfY2NiwDFbJxuXbEslmnG6Fog2dJLt4\n/BIFoHL7uDnDSqWC3d1drK6uIp/PY2JiAtls1tFh047wYrGofE6oE378FtUZHWtl9z2/OkjtuLm5\nadokGAqFjDpy8gu6rhuDiGKx6OucXHGd4rieOkBtINuF2CaD2D4dy7e2tmaqd/K5BwcHgehg0Ign\nr8htR76k1+v59qXvNJrNJg4PD7G1teU7JiDdyWaz6Ha7hm2qnogBmI+8E6GkTLPZHLqtkm252ZVo\nP24Mbf5ldXW173fiAeIAcPr0aUQikb6dfXSA/MbGRt8RF0HeHz0IooP2E+y2221UKhXs7OxY1tVR\nQeek0oYhOxqNBvb397G2tqa8u3YcoayV1YULToGwU3mDdnjtdhulUgk7OztYWVkxXUBA+h6NRpHJ\nZNDtdhGLxRw3LJH9bG5uYmNjw/Q3J/ux67xkPaZAcGNjo+/6VDvZxXqlbKFTsEu2T7LSSF8sRyWj\nRhdaULDb6XQQCoX61iXL1Ot17O7uYn19XSlr4IYfvyVuXHTSRyc/4wQFUxsbGyaZaGARDof7NmWJ\nULC7vb2N9fV1X1eI0uwXtfE4YndeqTwIHHSgu7a2hna7bVw4ROfOejm+6yihSwusZgWdAmE7VAOc\nk4oY7Dr5dyfoYpJUKoVWq4VisYi1tTVP5+KK/aPoo1X9URCoDnyo7xxpsHvjxo2+39H99pQRpduN\nCoWC6XNih/f666+bBY5EjKUPo1orFQqFkE6nkclkkE6nbTsDWSGsMrs7OzuWdXVUdDod4yYlJxqN\nBvb29rCysqKkWOMKTavFYrG+zpU2AmUyGeW7ycWplkEzu1tbW8hms6apYVHfp6amEI1GXY99EY+7\n82I/ok6LdSMH9PV6Hfv7+30BjjhtJstO67yobu2ylJSVXl9fx7Vr10xtRSc50GkRKsEuXWhBA4lQ\nKGTcAOdErVbD7u4ubty44fv8ZJFoNGq8i2qwG4lEjPZwO43BT7Bbr9eNDL04aKElEel02nH6XNd1\nY8B+/fp15csDRGjJEP2MG5qmmexCtJkgB7pbW1tYXV01Bhh0Kx7p4N7eXmDvFBROvoRsNZ1OK7er\n6gD2pELB7ubmpu+Bn67rSKVSmJ6eNo4jXFtbU84Ua5pmu7yUEi50Gs4w8ZLZHXmwK3eywNvrK6iD\nTKVSmJ2d7buBhQ6vX1lZwa9+9StTGdFoFPF43DjlYBSEw2HMzc1B13Ukk0nbUY5bxomy18lkclii\nuqLrOiYmJowpJztqtRp2dnZw7dq1kWaiB4U2TiQSiT4nnM/njet6VR10EFmIdrttjMA1TTOmihqN\nhknfC4WCYTNObUWXC6yurnqyn7m5OczOztpuuqH3pE74zTffNK0t03XdsO9ms2k8K5FIYGJiAnNz\ncwiFQsbJAuKh9AQ5aJKdZI3H45iamjLah57nVvc0qNzc3DQ2teVyOZw+fdqxDilj+cYbb2Bra8vx\nGSrQRjMvG5ri8Tjm5uYwNzen1Ll41UPKHN64ccOUvSZZJycn0el0bP1sr9dDuVzGxsYGXnvtNeVb\nB0VCoZDRvolEwvP3h42maSa7sBqoDGL/YvYtmUwaiYdut2vo4LVr1/pmaMYB2riXSCT6dGR6ehpz\nc3OWSQU73qkZXYJmT1dWVnzfIBcOh5HL5TA/P49ms4m9vT28+eabePXVV5W+r2ma0aZyUiKVShk+\n3G1mbFBUdUHsO9040mBXvPsaeKtzPXfuXN9Vuk6ddSwWQyKRMDaajAJa/J1MJjE9Pe3aeVk1nJi9\nHqWBx+NxnDp1yvWaUQp2r1+/btm2x4VIJIJEImH8iBQKBeOu7WGfIyhCHR5lSulO8Hq9btL3ZrOJ\n2dlZVKtV19Gum/1YBft06sLk5KSpbmT9pawnZVsJWs9rJfvMzExfoGuVDZcHuiRrMpk0bqzK5XLK\nNkO3t9FyKOoI3DZUVatVbG1t4Y033ghkcEfZbavAwI50Om1kFq2OAiL8Bgk0WxONRk03BtLAYmFh\noc83i/R6PWPA/tprrynfOihCmXZq43FD0zTDLqanp01/CyI4I1tdX19HOBzG1NQUFhcXTcHuG2+8\nMdLZPztoUEQ750WazSZisRjy+fzQA6OTAl1QEovFfC+dymQyhn8j+75x40ZfP2CHpmmGPSYSCVMi\nb2JiApqmIZPJ9NnCqCD7Gbtgt91uo16vGxuczp07h2Kx6CmzS+eAUpZmFNBB79PT0333R4s4OUPK\n7ALwNf0XFLlcDufPn1fK7FKWQdVwxpFIJIJUKoVkMtnXuXY6HeRyOZw6dUq5EwtioELBbq/Xw8HB\ngWEjtVrN0LVUKoVer4elpSXUajXXzK4f+6FA1ynAAd7O7LZaLVMZvV4PtVrNkF+UvVarIZPJYG5u\nDsDbtiFndsl5rays4P/+7/8MWZPJJHq9nhGsqi4zoWUMmqahWq2iUCjgpptuQrvddqzDSqViBLvX\nrl1TepYTdAyTVWBgx8TEBNLpNGZnZx3bw68Oiu0o1mcikcDCwgJKpZKx4dAKObPrZV0gEQ6HDR1J\nJpNjdyIDbQydmppytQs/UGaK9rMsLi6iXC73ZXZfe+21QJ8bBDTYpSPDROimxXa7faS+9DhDwW6n\n0/G9bGVubs7YLEq30b355puegl3R54rB7vT0NDKZDAqFwtDbSrV8se90Y2jBrtXuUcrs0jIGscMR\nnRx1gtRgIrQj1u/VrEGg6zra7bblEVyqzlrXdWMN8yh32opHiTnJTjvsRy3voIhHXlkdrWI3eJE/\nS58JonOmjV2tVss4povsRNT3ZrNpDAydnuvXfkgX3BxNt9tFp9PpGyDR6QFOssv1JrcD2QWdjCFu\nRpPLUEG2M7Jbp0wpfY/aJAh9p7rQNE3Zb8Xj8T4fqaKbqlCAZTWrI/o3p/JFXfBTT+KGw3E8jSEU\nCinbhR9kvyq2d9A6GDR00gIdeSeiWmfjNrgZJWSP1A/4Qax30Zeq6o9oi7QhjRD7HxVkv+7lO37i\nKDeGFuxaVYh8pJKIvOuPkCvJLiN0lMjPdjpnV/yRGfV7kAwqgZsfxR1HxDqX6121LlT+Pqhc4hS/\n/Hu35/u1H/qbrK9Wz7KqQ6+yW9mGLLtYht9pY7t3VmnDoNYROumdHeI7e+0EVGWyqhf5ZAE3/yaW\n50cGen632x274Ef2CW524QdRL6jurexg3HDyJaq+SmTc2n4UDBoTWNW5F/0Juk2JYbatan0NLdi1\nynradVhOwaD8WdEpjOpyA7kT8tuQ4uhrVHhV4HF1vKqIxizXu18HPagh2wWGfoNduVwRJ/txCgTt\nglCxDCv5rd6HynMKdlXeX7XureRw++6gu+ytZLDTOzv8Bp1eZLLSBat6tnsulRP0QGRckC/qsLKL\nQezfyk7EssXPjBtOvkRFbxkzfnyEjF0f4SXYtfK3VLbVTPww8OLbSWY3HIPdRx55BD/4wQ8wNzeH\nl19+GQCwv7+PT3ziE3jzzTexvLyMp556Cvl83lIIq9+JFSh+xioDZYX4cqNyAPI7+JVjkE4iKMTn\nu8kxalmDQKxzu6wn/beX8oKSTQ4MZX0ftK2c7Metbuw+a/d9K/ndniW/o9WP3fPd6sJLHQat61bP\nd0NV3kFllb/v5blW/+3n2VQ/4xYYWdmk/Pcg9GRQHR8FTr7Eqc4YewatMyu79VKWbI9WF9YcRZt6\nfYbKZx0XSX32s5/FM888Y/rdlStXcO+99+LXv/41PvShD+HKlSvKAomCiRVq9WPX8au+2LBxkt3q\nXVQ6jFHg1g522cbj/jNoXai2r5d2kOWw6/wGaSv5WbIMTuU5ySz/zs7pyvatYvtynQxS56p1OCyd\n8yqzW105tY9qffitJzsfHaRNjhor3Q2i3u2eJdf7qP3kIPqsqrtB+9LjziDvL/tIPzpkJ4Oq7wzq\nJ2g9cMzs3nPPPbh+/brpd08//TSef/55AMDDDz+MD37wg5YBr1Nlif8tNoj4OTvFlz83CqyckhWq\nxjtq41bpcJza5Lhh976yIaswDKN0k3GQtpLtz6ps+f2d2t3KHu2cp5WjlMu1+55VGV500aoMlY46\nKH1XDRCsvkPva5f1DMIunXTBrly7gYnX546DT7eDNgVa+YWg/KGdH7Kyo3HCjwmCtjYAACAASURB\nVC9xYli+9DgyqC1bDZb8PNupjxwmXuRWfTfPa3a3traMG88KhYLtgeviYfPymaa6rptux6AKJJwa\naVyMX2x0u/U1tCHPLUgYJapOKejOf1S4BYlUF17WVQblpJ2CRPnHb1s5tZ+dTst6rFKHVvKLZdOO\nYasAQg4i7MrwWu9WAa/KewSp717LEvXRKdgNMrurqmuDdKh2zxu3ZQyAvV8Ypu1b/YwbfnyJE8PK\n6B0Xhq1Hfsqw2quh68PfZ6SqB91u1zhFyY2BNqg5LSKWD+WnDk5+CTreQryZRjz6QkZ0OqPa2EXH\n7bTbbeNaVCva7bZxVIdVw3l1BsOAOjK5DWTs2uO44aQ/dEwL/ahARzQNMtKVO1M5gBB/D7xlM25t\n5cd+Op2Oodfi+1u9o1UAJndWsvxi2RTsynpHR1FZZdTEMsLhsNLRRnZ16KbvQWw8lOXwau9ie7Ra\nLdujufzqoNPghurVqZ56vd7AfkFun3HzMbqum/RWtAs65mnQLJfYDmK9D+MEjiBx0mnS3Var5dmX\nvlODXQC2vtnL9wHnPsAN0R7FtiD/66VN/aLq0+i68UQi4Xpfgedgt1AoYHNzE6dOncLGxoZxSLyM\nVWOJHTl1JlZnLDrdke0n+xY0csdtd8abGOxaMer3IBmAtwcddohn0x53Z2RX76KDVr2usdVqeTp7\n0A6r6X2SVe4MVduKvi/iZD8U7MvvL+uxXSdnlekTg1QxcBODXTvbF58lDzDD4bByvVs5b5U6FL8/\nKKIMqufJyn7GruPyq4NilkYetIhBl5288nnVg2R2j0Owa2cXg+iHbEuifTvZ8bhA+mPlS936R5kg\nEgfHmSBiG9luveqPmGSQg10/beoXLwMf1WUVnoPd+++/H0888QS+/OUv44knnsDHPvYxy8/ZHT1m\nl9kVHWo4HHbMrIw6I2rV8VpBztBKTrGjGZfMrmoAdZxxykbI7aqC24DGi1wUCKlkdp3ayq/92Dkz\nOZiyc8hWgbr4LDE7Rt+1C3blY5fITkjGSCSi3DHKAwmr58oEre9+MruyPtrJM4gOOmV2rXyzSBAX\nQciDuXHDLdgNMrMrZ9TH3eeq+FIviYOgfOlxZtDYRu4jvM5QWSVXCD/9o1+8BLskrxuOwe5DDz2E\n559/Hru7uzhz5gy+8Y1v4Ctf+QoefPBBfOc73zGOHrMTVkbO7IqNYXd+od2B9sO4utELh4eH2Nra\nQiaTsb26tNPpYHt7G5VKxTb4pyBgVIjLLNyMwsvZpuMMdWDye1QqFezu7mJ1dVXZmOk7tVpt4MxW\np9MBYA42gLf1XexcB2krO/splUrY2dnBjRs3cHBwYPy+Wq2a3pGCT/nKXfo9yU7vRdeEHxwcYH19\nHclkEtFoFLlczvJdRNnFZ1UqFezt7WF1dRXxeBy7u7uo1+vKdatpWt+gwW8d+sGr32o0Gjg4OMDm\n5iZSqZStHHL7eJHHqh0jkYgp6HA733eQetI0zZBjkJujhoWmaSiVStje3kY2m0U6nTb+Vi6XjXr3\ni6if9CMng8bZ55IvlSmXy9jZ2cHKygoqlYpSWfv7+9jf3x/L2+KOAtEe/fYl8uDLq/7IPlf8Hvnw\njY0N5SvP/bK5uamkC3Lf6YRjsPvkk09a/v7HP/6xa8F0JbCVYED/VKtV49qtTaQOVOUFh0G328Xe\n3h4ikQiazSai0ajt59bX13FwcNAnq7jIe5QjWXEE5WZgVuurjyNkHHK9l0olrK+vo9vtYnt7W6ms\nRqOB9fV1lEqlgYJdURdo8EFZM2oftzXgMl7t5+DgACsrK2i1Wkgmk8bvm80m1tfXcXh42JfVlcuw\nk71SqRibWZvNJuLxOGZmZmxH72L2mj4jtk80GsX6+jrK5bJrPYhBpjhgOGp99+q3NE3Dzs4OQqEQ\narWabYclto8XXyLqnSgTLRFx8wvykhC/9UQB0zhm9DRNw/7+PqLRKNrttimxUa/XDdv3i9gGNIMi\nJkbG2efSQMVq9rJYLGJtbQ2dTsc0QHCiUqlgY2NDOTg+aYi64DezK2dEKdD1oj9i0kKkWq1ie3sb\nmqYp+d1BKBaL2N7eVkpmqNbV0G5Qs8uMkcO2Wpsn/re4pldkHNa5djod7O3todlsYm9vz1aRdF1H\nuVxGuVzuk5few0tjDQMvAZRdmxwnxMykHHSUSiX0ej2USiXT6SFOdDodo40HkUnM2Io2Iuq7uJzA\nqa382s/BwQHa7TYODg5MAzjxHeXlFTJ2slMHVq1WcXh4iJmZGZw7d64vkyXLLrZVqVRCt9tFqVRC\nOBxWqnfZzlQHd2JGJAh99+O3er0ednZ2UK/Xsbu7a/s5uX28lG+1ZlfM7HoZBPupJyd7HAco2G21\nWjg4ODBtRvZb7yKi7VvZ9zj7XCedLhaL6HQ6KBaLylnAVquFcrn8jg92VWbu7LBaWuPVNu3skXSy\nWq3ansIVFI1GA+Vy2XXWRKwzN4YW7Fo5rlAohEgkgmg0imQyiVgsZnmSgaZpiEQiiMfjpgwT8PYm\nGru1sEcBjWworW+nmJSxsJN1HDIZqopCbWfVJscJMbsm62itVkOr1TKCKdXyrKYfvSAGFKT7ZCfi\nOikvGclwOOzZfiqVChqNBorFYt8GLXkzjlWwS7JHo1FjTS3J3mg00Ol0UKlUUKvVsLu7i2q1altG\nPB5HIpEwTe9S+5TLZWiaZtmGVojP8KLv0WgUiUQiEH0X38PLmt1ut4tarYb9/X3bz1m1jwp2gSzJ\nqKJr4XDY2A3tp57kKfxxxM4uRNn9IraBXO/hcDhQHQwa2TeJiL5UNdAKoj6PMyoDSzfkZVpe+2xx\njbqc3aWBTbVatT2BKijETc1u8qrW2XAllgiHw0ilUkin05icnMTExAQSiYSxoUb8XDKZRD6fx+zs\nrKmMZrOJarWKarU6smBXHtE6jcJUp5xHCcnv9B6xWAyZTAbT09N9bXKc6HQ6hv5YjVytdqE6IWYO\ng0DTNCQSCaTTaaRSKbRaLUNe+XN2kJ3lcjlP9iO+v7wWVzXIJtnT6TQajYYR0FLGipyYuE5cziqS\n7c/NzZlkFeWjKVQ/9a6q79lsFtPT04FkmqguarWaJ7+lMvMTtA4Sbuv9NE1DPB7HxMQEZmZmfGWj\nqPOs1Woj34dhx6B24RWq82g0avjcw8PDQJ8RBKJvsvIl4iZUFYZVn+80yA4jkYgRa6n22bquG21a\nrVb7Zt2OalbdaoPcoIwk2KUgNpfLIZFI9BlDJBIxPicfbUYdT7PZtFwXfFTYTePKDKPRgkSl4wdg\nON6pqSnb4+aOA81mE5qmod1u902RiG2qmnUXp/WDgALGiYkJTE5OGg5HXKjv1lYq9tNqtfrsR+xs\n5CVGKu8YCoUM2aemplCpVKDrOprNphHIULbSbkAh+wjKENfr9b51nX7qXVXfxcGd27oxFWi5hVW9\nO0Hv67ZsJUgdFHGqJ9LVbDaLmZkZX+tK6cxkGoSOI4PahV9IB8mWxg1aR95qtfo2Evn1pePcVx4H\nRP8WjUaNYFe1z+71esYZ5lZLCOzW8wbNMHRhZMHu3Nwccrkckslk3/pdMbMrN1IsFjOmMkeJ6lqR\n42S4Th2bGOyOuu4HoVarod1uW3asfg0syDYWs2Wzs7OIxWJoNpvGJhiVYM2v/Vit3xT/piJ7IpEw\nMsqRSASNRsPYvEdr0azWJRJyoN7r9VCv102b48SlFIOgmtkN4pidaDRqakcV6P1G4WfEulHN7Npt\n1HWCBkLjGugCg9uFF0T7FnVwHE8oKJfLaLValoG434HAceovxx3ypV6CXUpE1Ot1hEIhUxZX9OFH\nsQQz6IHk0IJdK8cgrvtMJBKIxWJGNkB+qUgkglgshlQqZfp9vV5HJBIZmzMIg2iMcXgPwPldqO0S\niURfmxwner0eotFo39IZET9tGmRml3Q/mUyi0WgY+u7leWRnVvYTjUYd7ceubPn38vdl2Wu1Wt+z\nrDpBuVxaByqu6xen052+64Qsr5u+03rJIPSd6sJJ75xQec9BdNBJJid9ENvKzxGKdAMStfE4o2oX\nQTHuPrfVaiEWi/nyJU5wwBtMTCCu2VXVn3a7bcRldkuYjmv7HGlmV97kJAa7IrTBhpyoSDweNzrQ\n44KTcoyLg1eZoo5Go8d+g1qn07HVu1EiZnTETT+ivns5K9HNfgZ9fytZrGS3CtQJq5G7vEFNdLxW\n3/cr71Hr+7j6Lbt2JFTrKZFI+D4vXGzj49qRDoLVbI2u62PvcxuNRiC+ROSd2P4iQcUDtORGTD6o\nQJ8fh8Gnqi5YJUGsGFlmlw6Wt8rsio0kHwGVSCQ8d/7DIIipVNX1g8NEtWOTg5DjSrvdts2w+c0Y\nBonsoMjxyKcjuLWVGHSKJBIJ25kRrzrtltmlYJcyBGL58o+IGKiLZVjJ6kVOr5ldyqoFoe9i4O/F\n3oNasuGG07IFt8zuIMGuruumweeoO1grRtEGYrAblA4GjdNA/Kjq7KTi1w5kO/baZ5P/tsvsHud2\ndQx2H3nkEfzgBz/A3NwcXn75ZQDA1772NfzTP/2Tsbvvsccew2//9m8rPSwUCiGZTBobWLLZLGKx\nWF+FhkIhYy3Y9PS06W/NZhPJZHLoR18wZmj9Ty6XG+nGwEEJh8NIp9OO6wtHaci0Vi+TyWByctLQ\ndy/ZE9ooRuv9RPyUZ4e8YUeUfWpqCo1Gw3iWqpMMh8OG7FNTU9jb20M8Hu8L9ocNbe7I5/OBrE+r\n1+ue631UHYvqoE88MWByctLXrUp0+xv1A8exEw0Kq6V85HPH8TiuXq+H7e1t7ovHCFGHaO+GVRxl\nR6vVwu7uLuLx+IkKdAGXYPezn/0s/vRP/xSf+cxnjN9pmoYvfOEL+MIXvuBYsNNO66mpKZw6dQr5\nfB6pVKpvao8CkqmpKczPz5v+1mq1sLGxgUgkMvJKH/T5FCyM8j1Un02bJWZnZ8duCYAXYrEYtra2\nEIvFRq4/IqQLmqYZm8tOnTqFdruNjY0NI2BUkVm0Mzv7iUajlmUNsqFElr3RaCCVSnnSF9n2d3d3\nkUwmB8r4+bGzWCxmbBK0uw7cC41GY2z8lhV+dYE2JBYKBV+nVpTLZWxvbyORSAS+ISVIhimXPGik\nZ8XjcWSzWczNzQ39elY/6LpuXB0bhC9h3iaIuqOjx2ZmZpQHS81mEzs7O0gkEiOPTVSR7ccOx2D3\nnnvuwfXr1y0LVxFARuzITp06hcnJSeM0BrvPyY1UrVaRyWRsO+vjxnF5BzHYDaLzHxWhUAgTExNj\nF+wCb+tCIpFAPp9HoVBArVZDOp32lD1xs59sNjtw0GX1XQp2JycnUSgUUCqVDNlVnyUG6s1mE6ur\nq8aAOAh5VXeJ08zS3Nyc8nWnTvipi6PALkhRkVE8faNQKPia8Ukmk8jlcoZPGae6OUqs9FIccI3j\nmt12u41sNnti+uJxIIh6JD0Sz2lWTRY0Gg2srq4aCYbj0q4qcvqaf/jmN7+J//f//h/uuusu/M3f\n/A3y+bzS96gjo6Mw6JxduSHEo5Pkv+3v73vu/JnBIcNpt9tj6XhV6Xa7yGazYxuwiwHE3NwcisWi\nr+yom/34OSbKDVo+QbLv7u4inU57lp18RLfbtT2Le1BUztnNZrPodDrIZDIDP29nZ+dE+i1qb13X\nfa3ZjUajmJiYGFt7HCW0JKjT6QQy4AoaMfHEjAcU9NF6XTpnV7WN6vW6bVx23PHseT//+c/jr/7q\nrwAAf/mXf4kvfvGL+M53vtP3OavOiTZ8ZLNZ5PN5ZDIZYz2eWLHimkO5nImJCWNz2yh3NquOeFRO\nYhj1BjUVOehmq16vN5abJVSpVqtIpVK2+jOqo3Ko7uma30wmg3w+j2w2a6xRp7ayOxKG8Gs/Tu9h\ndWqC3Vp7+YZE2pglOmK7dxHX7Ha7XWQyGSPYlbO7XjfSaZpm8jVOdRiNRpFKpYzrpQdFbEev99QH\n+TkZu3ZU1bVYLIZ0Og1dd7/pzYper4d0Om30A+OYSfJiF36g+pXrnQZ+uq6PZYJhYmJiLH3pcWbQ\nmED0b+RLJyYmlINd8t9kj16PvAySkZ/GIB5O/LnPfQ6/93u/5yiA6WH/f8CUzWaNDQ3y5hPg7Q6f\nNryIkIGN+mgMSvG7VbBbQ7h1JsNGpUMD3ur8aYPNOG6WUKVSqSCVSllujBTxutt/0FM5xA7PLmAU\n1/U6QU7Ozn7E4NnuPayCW6tgVX6uVaDudLasXRlUPmXh5TK8rsN1CrCtEPU9iOsxxUGGF3v34me8\n6qBdXYiDAidZSb90XUckEvG1ka/b7SKdThvntR7FYfVeUbULv2WLP2K904ArKB0MmlwuZwS74+JL\njzOqvkm1DEouUvJDBfLfVj5X5CjaSEUXxPd1sxHPwe7Gxoax6eV73/se3v3ud1t+zmqkJ2ZtJicn\nTQYuf5fO6ZRf9qRkdmUHNypUA4BIJGK033GG1k5S5yoidmheHE5QGw1pJG2X2e10OkojfyrDal2y\nUzbG6f3ld7TSGVH2yclJZLNZI1Cnz4oBu9W7iLZP07iJRMLkeEVZvDhELxlLOp4uqIyaOMgYVmY3\nqIBXDnTdMrt0aoAf2u22YyZpHPBiF36x0stoNGoELOOIyizRqHzpcWaQgFeeGUgmk8bmTxXI51rZ\n41G3jddBkhuOwe5DDz2E559/Hru7uzhz5gy+/vWv47nnnsNLL70ETdNw7tw5fPvb31Z+OHU49OOW\n7bGqWLnDGgVBNvY4ZHa9fG4cOyMviLoXVDYiCESdF21ElldFX/zaj59lAWIZYlBpJbvqpif61+rd\nvcrqJrMTQU6r+/FbR6WDg/qgQeopHA4rLy0ZBUeVwRL/lX8/rj5XpS8HeGmCFwa1A7tBqhefF0Qf\ncZSovptjsPvkk0/2/e6RRx7xJxGCc2SjdohihimIcpijZxzr3ip4tPrvIJ7j9Psg1386Pc9LuUF8\nd9Rt7vX5w86iOOnBUQ7CxzXQBdQv3QniOaNOfHjlOMl6nBiHerXSxXHOuA+c2R3Ww4NozHHI7AY5\nfTUqRv38UWL13uNqzEDwAa/dqF1Fr712zkEF0n6+7yUrPmy8ZnaPIuB1kukoA95xaB8rRjXLcxyw\nG6iMsx89DgyS2R2WHMd9icnQgl278xt7vR46nQ7a7XbfFJb8OfoR6XQ66Ha7ymdBDpOgnn8c3kNs\nj1HLOwhO+jMu79Xr9dDtdtFut9Htdo0697J+cxD78VIP8mdJdnqOqC8q5Yqyy2X4bR/6rt86DEIv\nOp3OwO8xLAY5bWDQegqqjU8i4+5zh+VLxvFdj5pBfJ3433b9gB2iPVrJMY7rdVU50mCXjvFpNBqo\n1+uIRqPGjzyCoIBYPvan0WgYQcAojcJrB273+1Ebturzqe2o7o8r9XodrVYLnU7H0pC9BkXidweB\nnklBXrPZRL1eN/TdS4fn137E97YbrIqfswp0SfZardYnu0r9irLXajU0m82+QNFNTrk8Mas8Kn1v\nNptotVqe/ZYXffSjs3btrPpMGpRRO3tFbONx8IdWqNrFoOXL9T7uPpd8qR9fwtgTVH2J+qN6glK9\nXu/zubJs42anqvKMJNiljpw6IvkYJOrwms1m36084xTsDhrojsOUgOp7iAOV43z0WKPRUAp2VQmy\n/cRgt9VqmQJGMYOiEuA52Y9bB6UymncLdslpWsnulkkUA2Yqwy7YVUXOeLjR7XbRarXQaDQCCTT8\n+q1hBLlu3/Xi28R68hPsyoPPUftDK7zYRZDPoIHEuPpcP77EiXFs+6MmqIETYPbHrVZL6ftWCYag\nZVRhGMmmIw12yTHW63VUKhXouo5wOGzZabbbbdTrdVSrVdPfqDHGJdgNuqM5alRloLaj+j+uVKtV\nUyZJZFTZCDkQE3VfzJ6oDo7c7CeoYN/ObhuNBiqVivEsL05TlL1SqaBer/cFu16xCnTdyul2u0bA\nrdpROEHlDDOzOwh+6gh4a9qz0WigWq36Csiq1aoRzI3rdP0w28Cp3kkHq9VqIDoYNEH6EuZtgogp\nKHFCfXa9Xlf6vtWMnF3544AXOY707spOp4NyuYytrS2srKxgdnYWmqYZh7cT3W4X5XIZu7u72N3d\nNZWxubmJw8PDsTT+k0yz2USxWMTu7i7K5fKoxfHN1tYWDg4O0Gg0Ri2KJb1eD9VqFXt7e1hZWcHW\n1hZKpRLa7XbfBRF2HJX90OyELPvu7i5WV1exvb1tyK7a8ZGP2NnZwdbWFnZ3d1GpVI78soFGo4GD\ngwPs7u6iVqsNXN7W1hYODw893cZ2lBkUvxuMarUa9vf3sbOz40unisUi9vb2Aqnj445sI+Rzd3Z2\n+gat48DGxgaKxeKxTn6MG7JPHYR2u41SqYSdnR0Ui0Wl7zQaDezu7qJarfb53HEJcP1ypJldqvzt\n7W2srKwYge7U1JTpc9ThbW9vY3V11fQ36jSazeaxr3ziOLxHq9VCsVjExsYG9vf3XT/v58ieo/jO\n3t4e9vf30Wg0bD8/yvbo9Xqo1WqWAaNqsNvpdFCpVLCzs4OVlRXT38h+Wq3WwBkEOdNsFaiXy2VP\nAZ4Y7K6srGBnZweVSsW0lMCv3F6yTY1GA8ViEevr6yiVSn1/96p3m5ubKJVKnuv9qHTR6zIP+lyt\nVsPe3h7W1taUs0di3ZVKJezv76NWq3EmUIIGXOvr6zg8PAQwXn5VDHa53YJlUB8HvB1vbW1tYWtr\ny/iMU9s2m03s7e0Zwe4wl+4cNY7B7srKCj7zmc9ge3sbmqbhD//wD/Fnf/Zn2N/fxyc+8Qm8+eab\nWF5exlNPPYV8Pu/6MDGIXVlZQSqVwtTUlOWOceqsb9y4YfrbuGR2g2r0IEdyfp+v0sk0m00cHh5i\nY2PDZDh2jJNTFikWizg4OFDumI8aMWBcXV01ZXZVEe3Mi/0MqtNiZndlZcUI1L1Mb8s+grIMg66b\n9WpnFGhsbGxgb2+v7+9e9U4cZJwUdF1HvV7H/v4+1tbWUKlUlL4n1l2lUjEyu+PakY5KLsrsbmxs\nGDM04+RXKWPImd1gCDoWEINdsR9watt2u22b2T3uOAa70WgUf/u3f4s77rgDlUoFv/mbv4l7770X\n//zP/4x7770XX/rSl/D444/jypUruHLliuvDaN1ntVpFqVQy1vxYrf0TPydSqVSMNbvjwDhsMjsK\naG1epVKxzHQdFyqViu2GD3FKdxRtSoMOOomgVCoZa4y9bFAT12r5sR+39xezuvIyBnpuuVzuk10F\nWXbRRxxl+5C+l8vlQPRdrAtVjmKdrlU7enkura8ul8u+ljfRGkGrdZ/jxjD1zsq2x93njrMvPc4E\nFfSKa75V9Yf6Hlp6Jss1rqjI5hjsnjp1CqdOnQIAZDIZXLp0CWtra3j66afx/PPPAwAefvhhfPCD\nH+wLdp02n9DuXdqwIafLdV03dqTLayvl3dnjgJtiOk2Xj9oZiE7WSQ7xJI1xXe+qgtMOYhGvzmbQ\nNhR1QdR9cWes6vOoDKu2kk9IsEP1wg3ZbsVNqHayy4GVle3TiQ60AcauDJV6F+vWi763Wq3A9N1t\nh7MbKvo46LIU+f/d6klubz/1JJ6OYiXHuDGMi2isBhtUt7Thcxx9rmpffNS+9DgzaEwg2qyfPpvi\nM7fTUY5qNtqLf3dDec3u9evX8eKLL+J973sftra2UCgUAACFQsFyWtuuY7TqyORKlY8oExm00wgK\n1Ssu3ZR3nAzbSRZyvFZtcpxwOgLKz9WyQWYwxE5ODBi9Hr0lHl9mZT92HZTd+1u9o5N9i4NZq0DV\n6nt2studnOEVt0BdRgw0gtB3v4N0FT8ziA7a1YuoYyrBrt96kgef4+QPCbdbwoK0fbEOnPrBcWBY\nvvSdTlD1IB8FqQIFu1b26KdN/RKEH5NRCnYrlQo+/vGP4+/+7u+QzWZNf/NyxaN4fFW5XO47Vohw\nmob1Mx04DDRNM26Ac2Lcb8FRDaBoSmRcp9RUEadNZTRNQygUsrzVzwmr2Qm/6LrueHyXl6ykV/tx\nen+6Gc0toyxOa9MxdRTsUtmxWMw4W1t+F/HIL9FH0KCRyiCZvNwORDKq1GHQU8h0fJQXWcX3VfEz\nwziO0S2zK+qqn3qirNM4L2OgdhBPDCKCtH0RGjiO8zIGv77EDspGerVp5m1E3yb6UlX96XQ6Jp8r\no+qPBmUYuuAa7LbbbXz84x/Hpz/9aXzsYx8D8FY2d3NzE6dOncLGxgbm5uaUHtbtdlGv11EsFhGP\nx3F4eIh6vd7npDudDmq1Gg4PD7Gzs2MqgwKAUR6yrWkaotEo4vE4YrGYbcPrum5MhQ66+32YkGI5\nyUeB7sHBQV+bHCeo87DaKBQOhxGLxRCLxRCNRpXK6/V6RvsGsVFD13U0Gg2USiVEIhFD3+XTCNwC\ntVqtZhxbJOJkP5FIxNBpsWMX39FJj3VdR7PZRKlUQjQaNYLVbreLUChklJ3NZpFIJBCJRPreRZR9\nd3cXpVLJuLBAbJ9QKGSyLS/1q6rv5XLZOFZrUCj49+K3NE0z3jcWi9kGDart4wWVeur1eoau7u3t\n4eDgwPNz2u02yuXyWG9yikajRhvIR2RSnQclv9jJB62DQVOr1VCtVi03z0YiEaPOIhG1CWQKzqhO\nGe+IdtvtdlGtVj312d1u1/C5st1TooL8+DARL8M4kmBX13U8+uijuHz5Mv78z//c+P3999+PJ554\nAl/+8pfxxBNPGEGwG91uF7VazRgZlEolozMUX4gWSVt11oMcYB4UFOwmk0mk02nHYLdarRoZkHFE\nXuNjR6vVQqVSGVvHq0q73UalUrFsj3A4jHg8jnQ6jXg8rlQeBXKUTQ1iOpMCRgom6vW6aU2jW1uR\n/VgNFp3sJxKJIJFIIJ1OmzooekcavNlB8pbLZZPs9P1YLIZ0Oo2JiQkkk0kj2BXfRQ7U6dKBXq9n\nDDDT6TTC4bBxSoPXjlGlDmlwF5S+1+t1X8FuNBpFKpVCKpWyDXZV28craTIJBgAAIABJREFUbpkV\nMdjd3d1VOpJQptvtGpsmx5VIJIJkMolUKmWyC9JVCkyDQNTNoHUwaGjzk50vJV+imjhot9vQNM3w\npYw/SIfa7bbnYJdO1BFn5Ajy4eSPhkmz2YSmacZysiBwDHZ/+tOf4l/+5V9w++2348477wQAPPbY\nY/jKV76CBx98EN/5zneMo8dU6PV6Rsfd7XZNmV2nDk+k0+l4uut5WFCwm81mbUeulBUhIx5XxGyC\nHScl2CVH6uSgM5mMsjHTMpygnDNldv+/9s4sRo6jjOP/ue9rd2dnZ3f2sL121padYLAQD0YggWMi\nhEkEMkQcFjhCMkIIOeJ4AQIPxEFCCAWQIshDEFJIXkL8EhMhJSH4xQLZBDAoxsfi9bHIxx62d3d2\nDh6ir1NT00d1T/dOz+73k6zxzvT0VFd931f/+qq6moQEiTnK7Kq0lVP/EW1aHLmrXqNYdvJzWtMn\nClUSu9QJGg10b9y4obUVZXapfcLhsKN6F8WEldhdXFzEzZs3XbF3J3FL7FxyuZxhDKF10W4KBJVB\nsDi4uXnzZtsDTFSgdalG06bdRkxsZLPZFuFGZXbT9+mV2tPPMZdik1Fml3w1Ho8rnY8EFgvdziD7\nMUsamn2X1u3qZXbFGO4lNJvp5o2ZpmJ37969hoHuj3/8o+0fE9Pr4k1mtL6HoKBOC6xFvFojZYdg\nMIhcLoeRkRFUKhXDkWuj0cDMzAwCgUDXs9FmyGshjaB1QH69DhXM1k8nEgkMDg5iZGQEhUJB6XzL\ny8uYmZlBo9HQNn7vFKpnGtmK5VVpK1oLa9d/0uk0yuUyRkZGWsT+ysoKZmZm0Gw2sbCwYLluV6/s\n0WgUfX19qFQqGBsbw+joKPL5PMLhsKHvk1CmGJRIJFAsFlGpVBCLxXDlyhVt0KwK3WNgZx2sG/Ze\nr9dtr6kNh8MoFApanDFCbJ/FxUVX7megepJjs3yMaGdO6onq2M9rNDOZDMrlMiqVSotwW1pawpUr\nVzTf77RPEm+EE9elO61brzGLJalUCkNDQxgZGWm7z8eIO3fuYGZmBrVazZdrlHsF0X7s9tl0vF6b\nRiIRLYbTLl1eMTc3h5mZGS077QZr+rhgWexSUJY7Hgqieilsr27EsEMwGEQ2m8XIyAjuu+8+JBIJ\n3eNqtZomdK9fv77GpVRDpVOj46ju/bokQwWyK73OlcTuli1bUC6Xlc5Hj7JdWFhw7a5sqmegXZyr\nthUAQ/8x6qCoU9+2bRtyuZz2Pi3FWVxctJyhMCp7NBpFf38/xsfHMTU1hUqlgkKhoCt2xQAti11q\nn2Qy6XiAoVKHwLs3Cblh705utCCxOzY2hqmpKcO6F9vn6tWrHZeVsLoZRRZkTupJZf10NwkEAshk\nMhgeHsa2bdtahNvi4qI2AHTz9/TEih9jrlnbpVIplEolTE5OYmBgQOl8t27dQq1WU360LaOP2Kc7\n6bON+kdKWIyPj2NyctLNIrdx/fp1VKtVR0ujjFhTsQu0Tu2LmV15WwujEYkfgiNldiuVCqamppBK\npXSPq9VqmtBVXaTfDSi4qmyj5tcsgypmd+JT5nDz5s3YtGmT0vnm5uYwPz+PK1euuLZURRTkemW1\n2gHFqf9QZnfr1q0tHdTCwgIWFhZw9epVyy2wjMpOYndiYgLbt2/H4OAg8vk8IpGIqe+L5yGxu3nz\nZmSzWczPz7c9TtwKUUxY1aGbWTUncYvE7ujoKHbs2GFYXnrwhVX72EGlnkiQUVs5qSeV9dPdhgaB\n9913X8uTQm/fvq35vlvo7Tji15hrJXaHhoawdetW5cTB7Owsbt++bdunmXeR/dZJZteojxTF7o4d\nO7wovkYymcTNmzcxPT3t2jnXPLMr/l/8W28PN70gaCRU1pJAIIB4PI5sNovBwUHDaZpqtYpcLodE\nIuHrNbuEitj1e8ekgpH9RCIRpNNp9Pf3K0/TRCIRZLNZ5XVpdssnBh5xxG4l1Oi7dvwnFoshk8mg\nWCxq+2jT+7lcDrFYTMlG9MoeDoeRTCZRKBQwODio+YUspuSyi+UV2yefzyObzSrfSKjHWtq7k7gV\nCoWQSCSQz+dRKpUMM6zxeFxrHy9QiV2dbBHU7XhuRSwWQzabRbFYRH9/v/Z+OBzWbNCNWR0ZcWs+\nP8Zcs+ulXVcGBgaUY2m9Xkc2m/X8Tv+Nhl37MYpVoVAIyWQS+Xze82UMi4uLSKfTrtqCf9ONPiYQ\nCLTcuW6U2Y1Go9pd570gdjc6tBtDMpk0bFOZ5eVlxGIx3T04ew2j669Wq4jFYh3NTtDNVrSDCW09\nZrd84t3A66XejRBvjkqn04YxZHV1VWsfjjPuQ7Fe9oulpSVHdrwRcBJLk8lk2/ZujH+Qd6HyErIF\nN/fzZS91gCx20+m07nHVahXxeLxtqpbxJ6IgM2pTmeXlZa3D6/U2pn12ZZt2Q+xSoCSfceIXsmDu\ntEx+R44zRoFfFLuMu9DDg/T84t69e+t+wOUUcWCqGks3wgC2lwkGgy2Dby/xwhZ8ER17USSEQiGt\n4Y1uUCOHD4VCvr9Gv5dvLQgGg5rgM2pTGRJt6yFAk5iMx+Mt1x+Pxzu2Y7lunZxPPAeVyenIvxfs\nncQuCXyja11aWuqZONOLUKzX84v14vtuQ8Joo8bSbuNFHJDjkZfQ4H1dZXbF7VaMPvMrZmWXjzNa\nZ+mH9Woq1+H3tnALlTWxRsfb+Z4edmxB5Xc6KYu8jlb+14ndivVkVGdGZde7mVXlOvXuD1DxWz9g\nZVvy53bLbdSWKr+r9//1iF5deOX7nbSln+g0lm5U3NzCzgvWon3s2oJKnXVd7ALtjdILhq4qEM0a\njW466qbgteMYvdAu3cCNIO2m0HVaBru24MRurQSSFx2j6Ge9JnQJu/Wightxx2/1tJa4JXbNBhsb\njY0udt0Wum7X41q1i934roKp2L18+TK++MUv4n//+x8CgQC+8pWv4Otf/zqeeOIJ/PrXv0axWATw\nzlPVPvaxjylexruYdXy9YOxWBqUSDP2Q2SWshPtGwW42wsn3REQRZmUPXos1vfPr2XEnQtfKL1Su\nzY2Rfy/YtEr2tBPRZSW0zM7XC/XnJlZ10anv03nE115FxX6MviP/f6Mg7qXu54HoWg5GrH7LTt9p\nKnYjkQh++tOf4j3veQ/u3LmD973vfdi3bx8CgQCOHj2Ko0ePulp4Ox2SX0TiehqFqmQYev16zezG\niWBwIxNhFtzk89JxenvvqnxfPo/Rd8zErip6x8rnsJvRdtP+xM7FqDxu27vTQYKK0PKibuT/G/2+\n+Or0d/yKUf164ftGfaBfY65qPFXBbRvuNVRFmypGW7uqfscMr9tI1Q7sDAxMxe7Q0JC2n1o6ncb2\n7du1DbTdnML0w965TrDbCTnt5L3ESDzJx/ilvJ2i6hx2A7Td74mYdXB6n6m857S9jDp1+Riz3zAr\nux1hpCJCVUb+en/bEXPdxolosItRHVjFhU5+U/ye39uAMBv4u13vvVInVjiJpRtR8LrR3nrxzUmC\nwuk6frdQtQVbD+lRPfDSpUs4ffo0PvCBD+DkyZN4+umn8Zvf/AZ79uzBT37yk5YnyzhBbzN6o0r1\nQxAQG8JK7PYKfhnVeYnKOmknwsLNtpY7UFXBK39m13/MrsXOSFt8tboxTE+Mir7vVOSKx6sIXhmr\nOnSCG0s/jI7xItaIDwUx+lyvrHZ/oxcwGwSaDe6cINe5n/sRtzO74ivjjE6WbJktpfCirzNCVejS\nwzJcu0Htzp07+PSnP42f/exnSKfTOHLkCL73ve8BAL773e/i8ccfx7PPPqtbWPk9ehRiKBRqeaSd\n3rF0vHyBALr6RBmxbFbPjjcyDL84NNW/araT2q2XIduRbUilTWXo2E7bU+5E6bxO7d2J/xhdv3h9\nVpkso7LLPmNWX3LZxe/L57CbIbaTSbRrC2Y4aUe7caYTOslQdhoXjPzRD8j1L/uFm3Wvdx43bdBt\nrGKJWHcquFWf6wGndSDGN0oa2LUfehqiXsKD2sdrexR/y+oYQO0pcZZid3V1FZ/61Kfw+c9/Hg8/\n/DAAYHBwUPv8sccewyc+8QndgsiQyKV9C8V9IeXOh/bUjEQiLe83Gg3U63Xt/91AFOz0T49wONwi\n6vXotmOLgsFKANA1y23SSzSbTc1+9GzOqk1lrNpXBRpwUFuIZRDtXQ5kZhi1lZn/yHZNiHYslkPv\nOozKLp6X9k80GuiKvl+v13XPYbfe5eOs6pACqV4McoKTuCW2h9lDS1TijB6iyDLKJFpldqnNndaT\nmT/6AVEsUD0TXvi+WO9u26DbkE0HAgGtDQnRbtcylvYyRv7oBDFDa7fPFmOuHBf0+gcvUN0zXPQf\nK0zFbrPZxOHDh7Fjxw584xvf0N6/du0ayuUyAOCll17Crl272r6rp/zlDo8uSA6oYhCVG8kPgVFs\n9HA4bPjkonq9riR0u+ncqgLK74FXFXHaQ0/siu2qglsBWvy+WAaxvKoDEzpWr63M/Ef2T0LvGvWy\nqrJfiGWXhbT4Xb3pMvJ98Xrlc6jWuzz9plKHbtu7k7glDx6Msimd2KBRxt6O2O2knsSOyo9iV7Y5\nK79wgmyfwLt14eeYS9m/Wq1mmjiwG0s3Mp1qAtGGnPimuMRL9n0n/aNTnMR3K0xLfPLkSfz2t7/F\n/fffj927dwMAfvSjH+H555/HmTNnEAgEsGnTJjzzzDNt343H423v0VNVIpFIy+M+9TIL4mMyRer1\nOlZXV7G6uto2mlwr4vG4VnazUY5Zg4nCoJsOLmbYzToberrWWjwX20sajYZmP7VareWzWCyGaDS6\n5tkIcRqYRJ6Y2aTyik+VsRJq4qN/Rcz8JxaLab9tlsESg54skszKHo1G256QpCd0xccK0/fFc9jJ\nZIqZOfGJhnq/LeK2vddqNdRqNVtxi54SR3Xmttg1akf5SVZm9USP0k0mk47qqdlstrSx3yCbUfEL\nJ4i+T/VO7Uy/7deYS/5Nti1iFEvMsLM0aT1itFzGDmJ8k2OpCuSPFKtE3zeK4V5gJ77TsbINypiK\n3b179+pOuT300EOWhX3ggQfa3qMOhMTuxMQE+vr62h4LF4vFMDg4iC1btmB+fr7lHPV6HdVqtati\nN5FIYHx8XCu7WeZWziYRkUgEhUIB+Xy+45v7OmFychKDg4OmjyMF3tmNY3h4GFNTU54/KtBLRLEr\nd65bt25FqVRCMpm0NT3eaXCOx+OaHeRyOW1AKAvGoaEhjIyMIJPJmLZVLBZDsVi07T+bNm3CwMAA\notGoaRY3k8kgn8+jUCggFou1HEfljkajWsCsVqsYHh7G8PAw0ul027mNyr6wsKB9f3V1ta19VOo+\nHA5rZc3n89i8eTMGBgYQi8VM6zCbzaJSqWDHjh0oFAqmv6EC1YWduNXX14dKpYJsNms5Q+TEBtPp\ntGZ3ok/HYjEtvoniSyYYDKJQKGB8fBw7d+5sszUVqHOlNvYbwWAQmzZtQn9/f8tMA+Cu7xcKBQwN\nDWFsbAyFQgHhcBiZTAYjIyPYvn07stlsp5fiOmJskoXGli1bUCwWEYvFbMfSjSp2k8mk5o9OBzeb\nN29GsVhEPB5HMBjE0NAQtm3bZksrkS/KYrdcLmv9j9dtpHp+0X/eeust02M9y0WbiV0arRoFkXg8\nrnV4clahVquhWq2iWq12TexGo1GMj49rQUm1ExL/H41G0d/fj7GxMYyNjXleZiMmJydRKpUQj8dN\nDUwUu319fWtYQnehAK3XuY6Pj6NUKiGRSNgK0PTqNFDH43EMDg5ibGwMw8PDmlgkwUhlLRQKGBkZ\nQTabNf0dOp9d/zETu+IrdcLj4+PIZDItx+mVvVqtor+/vy1Q6l2DXHZqq2q1irGxMd32MauLSCTS\n4mfUGVh1wiR27927p22/2AlO4lY2m8Xo6ChyuZypbcn1qWqD5NNjY2MtA+5IJNKSiDA6XygUQj6f\nx9jYGJaXl3H37l2l3xVpNBqafVerVdvf9xqavTQSu/Taqe+Pj49jYmJC61dCoZDmZ3fu3Gm5T8Yv\niINZI7Fr1a+IyFPwG41kMqkNeAYGBhydY8uWLdpgPhQKoVQqYevWrboz7Xo0m00tTsliVy+Ge4mK\nX4l9p+/ELqXC4/E4yuWyFkTkzG6xWES9Xkc6nW45h9hpWKWtvSIcDmNsbEwpsyu+ipDY3bRpE3bu\n3Olpec0ol8u2MruBQADDw8NrWEJ3aTQaWFlZ0RW7xWKxa5ldGtxt27ZNE4uyYEylUprYVcns1mo1\nW/4zOjqqK3bpOumVOuGpqamWoBwIBEzLPjw83CZ2jTK79XodmUwG1WpVa6+BgQEMDQ0hmUxieXlZ\nObPb19eHiYkJ7Ny5E+Pj45rYNavDTCaDSqWCcDiMO3fumP6GCrVaTbsOVbGbSCRQqVQsxS7gbK2f\nOIAtlUra+2J8M8vsAkChUMDY2Bii0ShWVlaUf5sgsUv//EYgEMDo6KinmV0a3G3fvr1lxpD8LBQK\nYXFxsdNLcZ16va7ZtBxLqF+xm9kVXzcaJHa3bduG0dFRR+eoVCpafItGoyiVSmg2m+jv71f6vih2\nq9Vqi9ilmGiVbHEDVd8i/5mcnLQ81jOxOz4+3vaeuGY3Go2iUCggmUy2BdNQKIR0Oo2BgYG2hdB+\nWLMbCoVQLBaRSqUs19ZQo8nrcCKRCLLZLEqlkm5drRWFQkGbOjcjFoshm82i0Wi0ZPN6DbM1u7lc\nDvl8HtFo1NY5qX3p1S7RaBT5fB5DQ0MYHx/XfCQcDresi4vFYujr67McpYdCIaRSKdv+MzAwgEwm\n0/YdeTlOMplEf38/KpVKi0gSlzFEIpGWqft4PN5SdqNAFg6HW3xfXHKSzWaRy+UQjUZbxK5ZnUci\nEWQyGc3PSqWS7jXKxONx5HI5NJtN5HI502NVcBK3YrEYBgYGkEwmTY+T20fVBpPJJPr6+jAyMoKR\nkRHtfdX4FggEkEgkUCgUEAgEHC1D8Pua3UAgYOgX9HknayxjsRhyuRzK5bKW0aN6p8+azaYvlzGY\nxdK+vj5ks1nbN9bZteH1RDweR6FQQLlcdqwJBgYGkM1mNVvNZDKo1+vKmV0ALf4oit1EIqHU/7iB\najyLRqPI5XJKs2+eiV0xeBKBQEBbsB4Oh5FMJrW1JSKhUAiJRALNZtNw66R6vd7VrcfS6bRSBtBM\n7GYyGQwMDOjW1VqRSqWQTqctO/9wOIxUKoVAIODLmyVUoa2OxO1ViEQigUwm4zhAh0IhR3eUR6NR\nZDIZFItFLZMjb99Vr9e1bI+4TlYPp/6TTqeRSqUMbz4gG04kEpo4F7P8VAdull1sq3g8jnQ6rV2T\nSjAk8UxTcLlcDqlUytLeI5EI0uk0gsGgKyLMSdyiO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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12,6)\n", "subplot(211); imshow(centers[hmm_sample(A,B,200,state=s[0])].T)\n", "subplot(212); imshow(centers[hmm_sample(A1,B1,200,state=s[0])].T)" ] }, { "cell_type": "markdown", "id": "d39e6e97", "metadata": {}, "source": [ "Let's wrap this up as well." ] }, { "cell_type": "code", "execution_count": 1582, "id": "89976bff", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hmm_viterbi_training(A,B,outputs):\n", " states = hmm_viterbi(A,B,outputs)\n", " A1 = ones(A.shape)\n", " for t in range(1,len(states)):\n", " A1[states[t],states[t-1]] += 1\n", " A1 = ls(A1)\n", " B1 = ones(B.shape)\n", " for t in range(0,len(states)):\n", " B1[outputs[t],states[t]] += 1\n", " B1 = ls(B1)\n", " return A1,B1" ] }, { "cell_type": "markdown", "id": "9bc28e0c", "metadata": {}, "source": [ "Forward-Backward Algorithm\n", "=============================" ] }, { "cell_type": "markdown", "id": "5d56415b", "metadata": {}, "source": [ "Above, we already saw how we can compute the _forward probabilities_\n", "\n", "$$P(s_t|o_{t-1}...o_1)$$\n", "\n", "What we might want to ask instead, however, is the probability that\n", "the system is in state $s_t$ given all observations:\n", "\n", "$$P(s_t|o_N...o_1)$$\n", "\n", "This is what the _forward backward algorithm_ does for us.\n", "\n", "We observe that\n", "\n", "$$P(s_t=s) = \\frac{P(o_N...o_t|s_t) P(s_t|o_{t-1}...o_1)}{P(o_N...o_1)} = \\frac{P(o_N...o_t|s_t) P(s_t|o_{t-1}...o_1)}{P(o_N...o_1)}$$\n", "\n", "The second factor is the forward probabilities that we have already computed.\n", "\n", "The first factor is an accumulated likelihood over a path. It is similar to the forward computation\n", "in the Viterbi algorithm, but instead of finding the best path, we add up the contributions from all paths\n", "that arrive in a particular state (we couldn't do that in the Viterbi algorithm because then we wouldn't\n", "have had a way of tracing back the best path). To propagate the probabilites backwards, we use the\n", "transpose of the state matrix.\n", "\n", "In the algorithm below, we renormalize the first factor after each step to avoid underflow." ] }, { "cell_type": "code", "execution_count": 1744, "id": "c4688c76", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hmm_forward_backward(A,B,observations):\n", " p = dot(A,ones(len(A))/len(A))\n", " fps = []\n", " bps = []\n", " # the forward step\n", " for i,o in enumerate(observations):\n", " # update P(state|ovservation) using Bayes formula\n", " p = B[o,:]*p\n", " p /= sum(p)\n", " fps.append(p)\n", " # now compute the probabilities in the next state\n", " p = dot(A,p)\n", " fps = array(fps)\n", " # the backward step\n", " p = ones(len(A))\n", " bps = []\n", " for i,o in enumerate(observations[::-1]):\n", " # update P(state|ovservation) using Bayes formula\n", " p = B[o,:]*p\n", " p /= sum(p)\n", " bps.append(p)\n", " # now compute the probabilities in the previous\n", " p = dot(A.T,p)\n", " bps = array(bps)[::-1]\n", " smoothed = array(fps)*array(bps)\n", " smoothed /= sum(smoothed,1)[:,newaxis]\n", " return smoothed,fps,bps" ] }, { "cell_type": "markdown", "id": "96ccfb0c", "metadata": {}, "source": [ "Given our nice state sequence above, this would look completely boring, so let's run this with some noisy transition matrix." ] }, { "cell_type": "code", "execution_count": 1748, "id": "50d8436e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1748, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(6,6)\n", "A2,B2 = ls(A1+0.5*rand(*A1.shape)),ls(B1+0.5*rand(*B1.shape))\n", "smoothed,fps,bps = hmm_forward_backward(A2,B2,outputs)\n", "imshow(r_[signal[:30].T,smoothed[:30].T/amax(smoothed)],interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "c90aafa8", "metadata": {}, "source": [ "Here you can see the contributions of the forward and backward directions." ] }, { "cell_type": "code", "execution_count": 1749, "id": "bb156765", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1749, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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449K1f/nLX6Rro0nlJavyxmJyclK69sqVK9K1AHDu3Dnp2sOHDyttOxpU35Cp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\nMhgGMxGRwTCYiYgMhsFMRGQw/w9g6b4rdiTMtQAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(311); imshow(smoothed[:30].T,interpolation='nearest')\n", "subplot(312); imshow(fps[:30].T,interpolation='nearest')\n", "subplot(313); imshow(bps[:30].T,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "53eb2cda", "metadata": {}, "source": [ "Compared to the _forward algorithm_, this algorithm does take advantage of all the information in the label sequence.\n", "\n", "However, it is still not guaranteed that the states that maximize the posterior probability at each time $t$ actually\n", "are all on the best path." ] }, { "cell_type": "markdown", "id": "caff83f2", "metadata": {}, "source": [ "Baum-Welch Reestimation\n", "=======================" ] }, { "cell_type": "markdown", "id": "56f27e26", "metadata": {}, "source": [ "The _forward backward algorithm_ now gives us everything we need for the second HMM training\n", "algorithm, _Baum Welch reestimation_.\n", "\n", "The idea here is similar to Viterbi training, but with two important differences:\n", "\n", "- instead of the sequence of states on the best path, we use the most probable states at each time $t$\n", "- instead of \"hard updates\" (0/1 indicator whether we are in a state), we update using the state probabilities computed by the forward backward algorithm." ] }, { "cell_type": "code", "execution_count": 1750, "id": "79180064", "metadata": { "collapsed": true }, "outputs": [], "source": [ "ns = 5\n", "A0 = A.copy()\n", "B0 = B.copy()" ] }, { "cell_type": "code", "execution_count": 1751, "id": "d27c5eae", "metadata": { "collapsed": true }, "outputs": [], "source": [ "_,fps,bps = hmm_forward_backward(A0,B0,outputs)" ] }, { "cell_type": "markdown", "id": "18f8e757", "metadata": {}, "source": [ "The re-estimate of the matrix $B$ is quite simple: we compute the probability of being in state $s$ at times $t$\n", "and then update the \"soft counts\" in the new `B` matrix." ] }, { "cell_type": "code", "execution_count": 1588, "id": "91b6c127", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def re_B(A,B,outputs,fps,bps):\n", " B1 = zeros(B.shape,'f')\n", " for t in range(1,len(outputs)):\n", " state = vs(fps[t]*bps[t])\n", " B1[outputs[t]] += state\n", " return ls(maximum(1e-3,B1))" ] }, { "cell_type": "code", "execution_count": 1589, "id": "c8c8af8b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1589, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "B1 = re_B(A0,B0,outputs,fps,bps)\n", "subplot(121); imshow(B0,interpolation='nearest')\n", "subplot(122); imshow(B1,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "7545ba12", "metadata": {}, "source": [ "The re-estimation for the matrix $A$ is slightly trickier, since we are updating counts\n", "for a transition.\n", "\n", "To do this, the correct procedure can be described as follows (I will not prove that here):\n", "\n", "- we compute the forward probabilities to get into states at time $t-1$\n", "- we compute the backwards probabilities to get into states at time $t$ and combine that with the observation at time $o_t$\n", "\n", "We might now just want to update by taking the outer product of the state vector at times $t-1$ and $t$ and add\n", "that as soft counts to our new transition matrix. If all the values were 0/1 (as in Viterbi training), that would be correct. \n", "However, for soft updates, we also need to take into account the existing weight assigned to the transition by the existing\n", "transition matrix $A$ (we counted that in neither the forward nor the backward computations).\n", "\n", "Therefore, the full reestimation for the matrix $A$ looks like this:" ] }, { "cell_type": "code", "execution_count": 1590, "id": "b6701122", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def re_A(A,B,outputs,fps,bps):\n", " A1 = zeros(A.shape)\n", " for t in range(1,len(outputs)):\n", " state0 = vs(fps[t-1])\n", " state1 = vs(bps[t]*B[outputs[t],:])\n", " A1 += vs(outer(state1,state0)*A)\n", " return ls(maximum(1e-3,A1))" ] }, { "cell_type": "markdown", "id": "172bd27f", "metadata": {}, "source": [ "Running one reestimation step has an effect similar to what the Viterbi update had: some of the weights get updated,\n", "but the overall structure of the transition matrix isn't changing much." ] }, { "cell_type": "code", "execution_count": 1591, "id": "a5031db1", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1591, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "A1 = re_A(A0,B0,outputs,fps,bps)\n", "subplot(121); imshow(A0,interpolation='nearest')\n", "subplot(122); imshow(A1,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "dab2953e", "metadata": {}, "source": [ "Let's do some more updates and see what we get." ] }, { "cell_type": "code", "execution_count": 1592, "id": "db3ae569", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def reestimate(A,B,outputs):\n", " smoothed,fps,bps = hmm_forward_backward(A,B,outputs)\n", " return re_A(A,B,outputs,fps,bps),re_B(A,B,outputs,fps,bps)" ] }, { "cell_type": "code", "execution_count": 1593, "id": "f737e189", "metadata": { "collapsed": true }, "outputs": [], "source": [ "for i in range(50):\n", " A1,B1 = reestimate(A1,B1,outputs)" ] }, { "cell_type": "code", "execution_count": 1594, "id": "c0668a19", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1594, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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tJco6/3ojjrnVahkV3ERxEMoI7pBzsp1Unuj4VDrpNhegNp6O0608UYj4hr4h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OXrp0CRMTE6ccFH9tKpXC3Nycrg00Klu73Uar1RJ+v7CwgLGxMUQikaEIhEOhENNlGaMyc3Nz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\nKdtJfnVQv8o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bb75Z8HPLsliOGC1u8sGys7155plncO3aNUxOTqK7uxs/+MEPtL/LsrI9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\nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(20,6)\n", "subplot(211); imshow(centers[hmm_sample(A0,B0,400)].T)\n", "subplot(212); imshow(centers[hmm_sample(A1,B1,400)].T)" ] }, { "cell_type": "markdown", "id": "0051c2a5", "metadata": {}, "source": [ "As before, the reestimated model gives much nicer outputs than the model we started with.\n", "\n", "The odd variation in character size is a consequence of the fact that the width of each part of the letter varies randomly with an exponential distribution.\n", "Given the small number of states our model has, this is pretty close to what can be achieved." ] }, { "cell_type": "markdown", "id": "f08215d6", "metadata": {}, "source": [ "Constrained Models and Parameter Tying\n", "================" ] }, { "cell_type": "markdown", "id": "a911753d", "metadata": {}, "source": [ "A simple way of dealing with this would seem to be to adopt a more complicated model with more states and transitions,\n", "as suggested above in the section on durational models.\n", "\n", "The problem with that is that we have limited training data, and increasing, say, to 100 states requires then that we estimate\n", "10000 transition probabilities; we don't have enough training data to do that.\n", "\n", "The way out of this dilemma is to constrain the structure of the transition matrices (i.e., force some of their elements\n", "to be small or zero) and/or to \"tie\" parameters together.\n", "\n", "Here, I will illustrate a simple constraint on the state transition matrix, a restricted for of Bakis model.\n", "\n", "To do this, we generate a mask of those values in the final transition matrix that are allowed to be non-zero.\n", "This matrix allows self loops and circular progression throuh a sequence of staes." ] }, { "cell_type": "code", "execution_count": 1754, "id": "f2210608", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1754, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "ns = 15\n", "from scipy import linalg\n", "v = zeros(ns)\n", "v[:2] = 1.0\n", "bakis = linalg.circulant(v)\n", "imshow(bakis,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "eb946071", "metadata": {}, "source": [ "Now we start with a completely random set of weights, albeit constrained by the form of the parameters above." ] }, { "cell_type": "code", "execution_count": 1755, "id": "726f6217", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1755, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "A0 = ls((1.0+rand(ns,ns))*bakis)\n", "B0 = ls(1.0+rand(no,ns))\n", "subplot(121); imshow(A0,interpolation='nearest')\n", "subplot(122); imshow(B0,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "3b774f36", "metadata": {}, "source": [ "To estimate the parameters of this constrained model, we estimate the parameters of a general\n", "model and then gradually restrict the model into its desire form.\n", "That's not the best way of doing this computation (for that, you should modify the\n", "forward backward and reestimation procedures), but it will do here." ] }, { "cell_type": "code", "execution_count": 1756, "id": "dddf2b4a", "metadata": { "collapsed": false }, "outputs": [], "source": [ "A1,B1 = A0,B0\n", "for i in range(2,200):\n", " A1,B1 = reestimate(A1,B1,outputs)\n", " A1 = ls(A1*maximum(1.0/i,bakis))" ] }, { "cell_type": "markdown", "id": "44255839", "metadata": {}, "source": [ "These are the final transition matrices." ] }, { "cell_type": "code", "execution_count": 1759, "id": "5781f5a5", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1759, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "subplot(121); imshow(A1,interpolation='nearest')\n", "subplot(122); imshow(B1,interpolation='nearest')" ] }, { "cell_type": "markdown", "id": "5de1bdda", "metadata": {}, "source": [ "And here are randomly generated samples from the final output." ] }, { "cell_type": "code", "execution_count": 1760, "id": "216db7bb", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1760, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ADQ0Nipx79uzBgQMH2Et4leJDDv58cL/frzpCkmPnzp3o6Ohguom4eA66TvjU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\nHTp06NABAPg/u36O3QYcmUsAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(6,6)\n", "imshow(centers[hmm_sample(A1,B1,400)].T)" ] }, { "cell_type": "markdown", "id": "53adba3c", "metadata": {}, "source": [ "This looks a lot nicer than the other models, and spacing and size are much more controlled.\n", "Keep in mind that we started with random weights!\n", "\n", "However, this model still cannot represent relationships between different parts of a character:\n", "if the first half of a character is \"wide\", then the second half should be as well, but that\n", "relationship is not represented here.\n", "To represent that, we would need more complex models (e.g., with multiple parallel paths)." ] }, { "cell_type": "code", "execution_count": null, "id": "cabf6ed2", "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }