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@tillahoffmann
Last active February 11, 2017 18:33
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Different approximations for regression without known covariates.
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"import util # https://github.com/tillahoffmann/util\n",
"from tqdm import tqdm_notebook\n",
"from scipy.misc import logsumexp\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simulation of regression with Gaussian mixtures"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"num_groups = 10\n",
"num_points = 5000\n",
"num_dims = 5\n",
"\n",
"groups = np.random.choice(num_groups, num_points)\n",
"\n",
"intra_scale = 1\n",
"inter_scale = .5\n",
"\n",
"means = np.random.normal(0, inter_scale, (num_groups, num_dims))\n",
"x = np.random.normal(0, 1, (num_points, num_dims)) + means[groups]\n",
"coefficients = np.random.normal(0, 1, num_dims)\n",
"y = np.random.normal(0, 1, num_points) + np.dot(x, coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x115c7f198>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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05+g55BluzX+AOyrLMYSk4N0AqcU6Svxt91SYFL3WwIy/LCK7wE/E0piz7zQ0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WvfnTj88rFDEF9YQUGDQ7ndSziQwp2dpS6aiztI9GT7NGTawSo0afn8FKzSgLfoZRwe3GTz4k8n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EUChYfOgTN3Hdjx/hqef2cs/9W/jgNTfx0GMeLUUIwWeuOZ/yjEpZv4tv2CGSgPqUzifedyaK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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115bfdc18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(x[:, 0], y, c=groups)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def posterior(coefficients):\n",
" \"\"\"\n",
" (Unnormalised) posterior obtained by assuming conditional independence and analytically \n",
" integrating out the latent covariates.\n",
" \"\"\"\n",
" predictor = np.dot(means[groups], coefficients)\n",
" residual = y - predictor\n",
" var = 1 + np.sum(coefficients ** 2) * intra_scale * intra_scale\n",
" ll = -0.5 * residual * residual / var - 0.5 * np.log(var)\n",
" return np.sum(ll)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.28483378, -1.24525869, -0.52493599, -1.75355872, 0.19723687])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Run a sampler starting with the \"true\" values\n",
"sampler = util.AdaptiveMetropolisSampler(posterior)\n",
"sampler.sample(coefficients, 5000, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x115c945f8>,\n",
" array([[<matplotlib.axes._subplots.AxesSubplot object at 0x115d542b0>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x115e8f588>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x115ed44e0>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x115f2a2e8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x115a60748>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x115fa9e10>]], dtype=object))"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Fihg4ocsTgiG7Yx8jscn0pFtnOOz21atpXz3FDoxz50DJStj/v6qNn2aK2JE+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\nc6n0PyFyAnQTobJwAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115c945f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(values=coefficients, burn_in=1000)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x116097358>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x115d7ff98>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x116137e80>))"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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EEwAUb6nwuA4mxHKJcRUIzMY4DUX01Fp1tA6fP7UaRX+pf1pzjJfvV+WNJwji+upmfP2v\nArfP1FjLCZSje9xdafcUnMBnTzgWfMsP1eDgds59mcihcFlEiS31yq0YaIhoDLh7pD9jrA+AN/hd\ndwEAY6wfuAe+GUQkvrcnM8YG8P+ExYY7AJxijHUD8BaA1/wxZtdv2vWaKK9pRouEtvSDjHeYFrzx\npHNNawS4BxLbGMNxPn+eL5eSMDypXH5K1Lf4ZgFxdTy02hgOVXnvLehrrJUSwRRQmQCOiN6X8ttc\nuY6IthHR90TUSWI/AICI7iaiQiIqrKio0GWADTUis56N2ddOLPwF4vpbvHffH3bTGgB88exafPnc\nWqc2O1aVouF0C5bN4hRFITPCkV2n8MWza/HRP1bC0mJF/elmp7tb6odf8uF2zHl6DRpqWvD9a4X2\n1ExiSOJpybWvI7tOYt6/N2DjEofqLwjWku3q7PQAp5mcPF7veGpSL6EAALvWHsep4/XYsfIoKkvr\nsGb+fllhInyGFV/vQaPod/ru1UInBwypo+0TQ6ivcLtzH4BpjLFmABAJm94AfhdtqwanTSkxHsDn\n/OvvAYwjP9Q9EX/Ft81a75Q9GwAu/++fksfVynj2acGbFEKnZPLRNbY4ZvX9IicBny6hIF1+8S6J\nB+asLbGXPPEGpZzPZ7IGJTV015/sJwA5jLH+AJbBcUO5H8jYTMZYPmMsv127droMUOwB5zRP8t+6\nk4YFAAzY/Kt8cNqNN96IyfeNx6FjxXj2y79hze7FiIl3mPUEAfPTO1sx+8nVTqezKaznLHx7C8oO\n1mDTL4fQ6lLWOTKGuxgba51vPMYYDmwuB7MxNNVzT43VHta1PPHNiwX45l8Fdk1UtXxi3HisvJZj\ntdrw17y92PzrYdSfdoz7dEWjmyeekrVCbr4VhN6ZJ5/QHcBIIiogopVENITfvhXAeCIKI6Iu4Mx2\n4oe5Wfwa7nMiIWR/QGSMWQCcBpCq94DF2sHyPe4PjlLak154MzdK5eWbtmQX3lrmCGEQl6vXqv2I\nsTlUqIDiKrj/9ZP6MiVS1PBxUf6o6xZML75SON9EWQCc7EmMMfHj+8fwkxlCjgbR5MgYQw0vkGqr\nOO0iNilS8jg5vvnmG7x37x9O21pb3G/QY1LrRgq2BGFNZdvyUpSV1GDik+4Pz80NjidSZmPYvfY4\n/pizG6MmdUeEYAYUX2DMfRMAtDZbER5phrXVBnO4yUnLFF6XH+bs83vWnUB2nxRYmm3oOaKj7JqP\nzcbw8SOr0NrETQ5blx1BTCLnXeeq5RzdU23/DCeKT0tqiAL1p5ux7DP3m+/QjirJvkMBIloGoIPE\nrmfA3a/JAM4FMATAPCLKBfAZgF4ACgEcArAG3BoVwJn3jhJRPIAfANwMbu1JzQOiMKa7AdwNANnZ\n2Zo+TzC/Ym80qB1H3dd3KuucH+7EbvG+fL6Xfi7Cm38boJhlQgoi384r9rLTgxs+Wiu7Ty5TvFqC\nKaA2AMjjn/iOApgE4CZxAyLqyBgT7DVXA/BblKVN4knOItKgEtOiUfQnJz8PbOKeBE2iTMveTnax\niRFODgay41MQUOKJv+yg9AKqeHyMOYRJ3almpERxecLEqxZST4ZlJTX4fpojQHLs/+uFP0QBt6Yw\ngs3CnO6e3z7lBMT6n4ox6flhiIp1dgQB4GSiEw0AADDnaemgwMUfeI5Sl/suXM8RSjDGLpTbR0T3\nAZjPuB9zPRHZAKQxxioAPCJqtwbAPr6/o/zfWiL6Gtza7xw4HhBLiSgMQCIAySAjxthMADMBID8/\nX9O3tnq/e/bygOEnH5gtRxwPkL5kjJi/+Sj+eXUfvKuxgq6vQl/Ks88XxJV39b6lgmbi480Kfwfw\nCzjBM48xtpOIXiQioRb6g0S0k4i2AngQwK16jqG5oRW/frIDTfWtsFrcv1qnlCYSDhHiGBqrQnVJ\nq8WG5V/s4taVXFDyJBNfiI118sXEzOHyPyNjQOnuk6gud1yUa+bvt6vjzMYU6+KI1fbTFc4upH+4\nZIMQ3MulbqD60y3Y/NthHNvvrh1KjltVK99Y++MB1FTqe7P6mf8BGAsARNQdQASASiKKIaJYfvtF\nACyMsSLe5JfGbw8HcCWAHXxfCwHcwr+eCOAP5geVUk1GBX/hLx/N30Rplnz1tznnX7/6OBp5hDpb\nQcXHHyGogbqMscUAFrtse170+ikAT/nj3NuWH8Gfc7kF232F5Uhq7x642trkMIut/8k9piI6Lhxr\n5u9Hn5EZiIxx1wwEDm6tRNHq45JxN0pTwqalJQB4M5tCu4S0aFSXyUfFL/iPcxXSsoM16DownT8/\nc2hn4otJKg2MB5OJ2UywQN4cWVPZiB/f2KTYh+P8gZnY9hWWYfClOQE5lw58BuAzItoBoAXALYwx\nRkTpAH7hNaqj4Mx4ABDJbw8HYAa3jvsxv+9TAF8Q0X5wmtMk/ww5eAIqEGEEG0v0y2yhN4EOovA0\nT3nDWZlJorK0zi6cBKQmeMGUJ0d1eQNKd5/CoR1VGP+we3S2gDCvKzk6SCF40LU0KbuVeqMFnCh2\nODIIAqV4cwV+KN+Ia/5voF0+lOxwmGg8CSjB5CknW5S0TFeaG3334lKD3kHL/oQPx5gisb0EgFvK\nDsZYPTiHCam+mgBcr/MQ3QimR38gJuhjOpdr15NAV2HwR+mNszIX39yX1+vST+luLi7H0mpTdGLY\nU+BbxgK5nHYCStqTHMVbOOHLbMw+9tZmLuuCsNYGADYLQ/HmCs4s6OFqMfMFHuXGoyX+yNfFVbVs\n+sUo9eFP9Mrq7Q3eOEm0JQJ1DwmUS2SN8HUEZ6UGpRYykapJtaaiEXvWO4SQ1WqDReTufXCr/EJx\nsD3Jti0vRViEs+RZ9e1enDexm/39ko84h4RL71HOwl53SjmtiUxlAkmMxK5nNvvL61BcURdUL76z\nXD61ic/fJgVUdVkDfpyxCaMn90Byh1hs/vUw9hWWoeKwdFlkObQ88a+df8D++vMnV7s9OpyqK8ec\n5dNQ03AKRITzel2BMf2uQ0rHWHvckD84ddxzbJNFwtV99ffunkW+lqooO+i/z+kLp07UY8VXXFqc\na/9vEABg+Ze7gzmkM54L31wJAPjvJO9TgfmKP+Jy/Enn1BgcqtJuDZEjGJ/edcb09TdokwJKCrXC\nqX1OPMpKtAkyV6Q87kxkxoRz70Wndt3R1NKA1+bfi55ZgzEwWltcSTBxDQLWSgiGHRn4mciw4K0i\nuNaSOtsIhoCuc8kAUlV3hiaL9SdJ7WPsT8IAMPDibHTITcB83oNsdc58VMYclTw2KjYMTTHaF+jT\nGjJxXskE2f2JsalIjOUC9aMiYtAhqTOq6yvPqkk7LStOMgg52CR3iHW6XgBgzJSeDl84A6/xY6KI\nNofe4iQUFEhfE9OeNU4SHbslYdLzQz22U8pMoBdVtSdQWrUfOem9ztjEpd4gtd424KLgapB5Q9oH\n9fxtnQe+VhlWYIAeHeJ17S8UBNTQLik+Hd8mNSg5UjPiMPJveRhc84hTYlQxefnp2FekXF3SF5pb\nG/HJry/guuH3Izoi1i9OEsf2uWf9DgXcchcCSO6gX+FEb1AKcjYwCCQEwh//dwHGzlipW3/BJszk\n2/111t2d/cd0wrnju8ruF7Ih+AOr1YKPf30B+XnjMCB3JAD/rMv8OGOz/p3qQKREmqNgP+WxIGY6\nMNCHzKToYA9BFxgYUmL1q/AcCuXOzuRs5kEl/4ocye1k9s+vyhjDVyvfQIekbIzrL4qPPANNfMPG\n53p1nHSgrn7fd1qnOM3H6Flu3CA46J1bLlgwpm/2i1AoyOnrCM5aATXsqlzJirT++kmLT+zA+n2/\nYe+xzXj1+7vx6vd3Y+fhgjNRPnm9buZNQLEWUjrGaj7mbFoDNAhtGPQNLk6LDX4uPsPNXGf85STR\ntWM/vHvP727bd66S9iYMZZLS9Vs30tPEJ9S10oJFQ/olAwN/whhg1vGGSI3Tz1zoLb5Op2etBiXg\n6sUVHmFWdVxYpLp2bY2o2HBd1cwGqVIbXlJxpM5zIxdKtgWxHISBgRMMPvoUOPcWAsaBxGj5JNpq\nOOsF1OjJPRCToP1Jw+Jj0OqZjJ6eh0ppoLRiDgu+zd3AwFsYa3v5A3018Z31AioiKgzDJ4i8+trW\n9aE7TfWtuqbUN+nolJKaod1JIjVT+7qVgYE/YNDXxOdLOfpQ4awXUADQbVC65mMiY87e5Ts9TQd6\nrvkltlPvbnzb9PPRuW+qpgS2Bgb+hDEGk4mwZqq789bZiiGg4CgToYXuwzr4YSTBQ8vkrqeJzxeb\n+znjOuHuty9wbNAg62ISIhAeaQ4NQ72BARyGiQyd4rrawqVtCCg4P8UrFdW77J5+jmPamCnwdAUX\nS5KX71mbzOqRrNt5yQcJldEtycmpRau9m8iIgzIIHdqCQNEbQ0C5kJju/PSS3tmRHyst27HGoXUy\nbLW04PX59+PV7+7Cy/Nux6INsxXbS5WgDwTR8Z4dRuKSo3DFA/11OZ8vGlTuwHbOGwi4+mH15R26\nDkpH/zFZ3g/AwEBH/j62m+dGGmgL8s4QUC70GZWJvhdk2t+fM64Thl7VBZndk5CQ6hBeWjWoMHM4\nHrxqBp66/mM8dd1MFJVuwMGyItn2o29yq+Bt57onBqNdtrrEkqMmddc0TiJCaqZnZ4OcfmmIS/E9\nEFDPNSgiQqee6pNTcgKqk27nNzDwhSE5viVWbYuclSv9J/79bzTvci5IN+J4PSKiwnDsjtnIARC+\nlysLEflOEtIBpAM4dDMwcG81wiJMiCwOw8DTjhieurgs7MubKHtOIkJkOCfgrDYLrDaLUzLHnH6p\naG602IsXJioEw3bITcQNTw/Be/f+4fGzemM2uPC23ti4pAT7NyonzY2MDkcdfKv34m06lkBmATEw\nOBNpCyZDQ4PiSekYi7hkzxpBek482mXHo6HWPcA0s3uS4rE2mxWvfn83ps65Dj0zByOnfS/7vh7n\ndsSExwbbtZLoeN8C3BxovEqJq9t0yV3S5d2jJBK++oInDUoYhxpNiySu5vTO8egzKtN9h4GBgV+5\ndUSOz32clRpUh6ef9thm1bNrUFPZhBEST+oAsFhCexk1KB1H98oX5DOZzHhq4kw0NNfh41+fx7GT\nB5GR0gWAwzPu2kcH4fiB05KehRl5Seg2WJtLPFPpRj1sfC4KFhQ7qSHhkWa3Krq3vX6+442PKsuA\ni7JRX62sgQmCWlXOPAm76/VPDQFwZqaUMjDwjeCqUHoEHRsalAzXPzUENz4/THX7Tr2S3RftAVz3\n5GB0OSfNaVtMZBzyOg5A0ZENbu0T0qLRQ8aF/ZpHBqLfaPWL+uffkKe6reAM0qFLon2b1PXla4bk\ni+/oY3993nWORWG5sUqZKUZPll6fa2uelWcq64qrgj0EgxBAj/vREFAyRMWGIyVDfZaB4RO6Obk8\nR/Ppk4R1ptrGajQ0c7niWizN2HN0I9onORbo1XgFqjFznTfRMeln9Ui2a2amMMKw8bm46QVpoZvd\nOxW3v3G+k4bW+/wMpzaZOriXZ7iYQXucywnjnH6pGHNzT3R1FfIuEiqzRxL6jJQ22fmaVsVAH2au\nKg72EAwQ/DWoZovv6eDOShOfPzCZCBHRjq/TLKTw4f/UNFThi+XTAROD1WLFoK4XoF/n4fb2nubW\nmER39++Lbu+NhpoWrP5+v31bp14OTyDxePpdkIX8y3IUzxHtkv14xIRuGHBhNsoP1WDxB9vd2gtj\nPv/6PPz13T6nfROn5oMxhh9e2+i03TUZb+c+qXaHh8R2Meg1oiPev2+5fb/rPaYohFx23Tb9fOl2\nBn7FFuyZ0SAk+HLdYbx8TT/PDRUwBJROuE6cUXHhqDvVbJ/EM1O7YurEj5A7sB069UrB2h8PoKXR\nYm+f42IGdEPinu8+lNM+xAJKPI74lCgkpHGeg1Kl1S++sw9+/WSn/GcyEWKTIhF2Qjpze1g4tz0j\nz905pH1OguQxnkqsu36PmXlJ6DMqE+md47H8i90yR0kf65rnLzYp0uOal4FBW6EtPCYYJj4vcY0v\ncvUg6zsqE5ExYYhLjrJv6z8mC+Nu6YW+ozJx11uj7NtH/i0PZolS87e+dp7mcbmOI3dAO0x4fLCb\nuQ4A8vLZe+xwAAAgAElEQVTbu21TxvmSHzGhKzJ7JGsKKhZkiJRQExCbVk1mE0bf1MPuYamkQHXs\nlii775pHB+L6p/LxwIdjJV3UDfSjrWXkDgY/3Dfcc6MQJ8rDw6gaDAHlJa7BrMLT+2X39sNl9/RD\nn5GZuGPGSKdSHhndkxAR5a60yrlBxyY63N6VnobE60pSJrCOXRP9sj7TsVsSrnlkIJfTTsT1T+XL\nHkMmwv3vj8E1jw6UbXPt/w1y3yh8ARKfY8iVXRAVG+4WpCvOGZjZPdnp+zxTIaJ/ENEeItpJRNP5\nbRFENIuIthPRViIaLWq/gm+/hf+Xzm9/lIiKiGgbEf1ORJ11G6NeHRn4hJ45M73h0Yu0JQmQwjDx\neYvLXSg4MOQOcCzyC0LBLhxkrhcp7ckNhYstuYND44iK0zdOyRnPU09S+xikd5Y27wH8d+HFDGaX\nTxL7hl7ZBUOv7OK23aTmez2DIKIxAMYD6M8YaxaEDYC7AIAx1o/ftoSIhjBmDzKYzBgrdOluM4B8\nxlgDEd0HYDqAv+kzTj16OdsJzS+xfUIkymrUmcmTYnyv6BvUO5iILuWf7vYT0VSJ/ZFENJffX0BE\nOYEfpQwu8kIqSFTA07qLnugdSKsWYVIaM0U+RZNqJGSxYDZS811OeHwwRk/ugcjoNvf8dR+AaYyx\nZgBgjAmpPnoD+F20rRqAvBrLtVvOGGvg364DoGNSwuBOrhEK1Qk6p0qbo3PTtNUFu3agf4O/9RDy\n/tCfKMC/bdAEFBGZAbwH4DJwN9iNRNTbpdkdAE4xxroBeAvAa4EdpXoiY+QFw+DLOiOzRzKyejmb\noG55dQRufvnMtzUDwKgbe8AcbkLHrsrZNNQglWE8q2cy8i/PwZgpPT0e37Froqwr+hlOdwAj+Ye1\nlUQ0hN++FcB4Igojoi4ABgMQJxmcxZv3niNpW+8dAJbInZSI7iaiQiIqrKio8DhIbyZXPbWuObcP\nld332MUyD1Aaz+9v85k3X0e3dO0FO7Ui/p0eu9iDCU+HryiYj5hDAexnjBUDABF9C858Ic6gOh7A\nC/zr7wG8S0TEgm1chXOW84lP5is+radmxOGaR9zXXMQOFJ7Q8xNffEcfNNa5p2qSQ6hUq5T5u++o\nTPSVWEvLvzwH5YdqcXin+uBNm9U9/QWZCMOuzlXdx5kKES0DIBWp/Qy4+zUZwLkAhgCYR0S5AD4D\n0AtAIYBDANYAEFxEJzPGjhJRPIAfANwMYI7ofFPAaVuiwlrOMMZmApgJAPn5+R6vRG8mV4J+T/zn\n5qbK7pNzgW8Ljh3Dc1Oxv7zO/t7fs2RkmLR3r/38OvyiwRRQmQCOiN6XAnCNIrW3YYxZiOg0gFQA\nla6dEdHdAO4GgOzsbH+M14kwUTxP+y7yay6uWK1W5OfnIzMzEz///LPq48RrW5644oH+KC+pkd2f\nN8ThvTdxar5n1+soE/4aFINLM7UXUhOEiprEtvbT8WbKCxQyurdVGGMXyu3j14rm8w9o64nIBiCN\nMVYB4BFRuzUA9vH9HeX/1hLR1+AeDOfw7S4EJ/guEMyGwYKIAhJZKncKreLJ3yMN1aBzsSD3NERP\nAkzV+XzuwXukPp5bXKaKNtxGxmYyxvIZY/nt2qmfzAPNf//7X/Tq1ctzQ56rHx6Acbf2wqgb1XvE\n5PRLw9Cr1Gkb7XMSPAq/P/dVYm1xFaYtUY5D0ouwCDMe+HCspEZ2lvM/AGMBgIi6A4gAUElEMUQU\ny2+/CICFMVbEm/zS+O3hAK4EsIN/PxDARwCuFq1l6cKvRWWajwnUdCynQWmVB/6WpXLDGdxZfTaX\nYJuZLu6jNYzFnWBqUKVwtpNnATgm06aUiMIAJAI46euJ/5y3F5VH6jw3VMmPMzYhrVMcRt6gLERK\nS0uxaNEiPPPMM3jzzTfxzwU7UN3Yiv9Okne51lLfyF8IN0vwDatnPZ8B+IyIdgBoAXALY4zxnnu/\n8BrVUXBmPACI5LeHAzADWAbgY37f6wDiAHzHP60fZoxd7e3AmlqteGTuFjx2iXdab6AUBrlrWKuJ\nz5dbYUhOMjaUnFJsIzecl6/pi8v++6cPZ/cN8bg8aXkxEb6Ll2AKqA0A8vhF3aMAJgG4yaXNQgC3\nAFgLYCKAP0Jh/cmVPSdqkdbJ8wLlww8/jOnTp6O2thYA8PnaQwCgKKC0kJAZC8aY7uYBR38h99Wf\nVTDGWgBMkdheAsBNMjDG6sE5TEj1JWtK9IbNh6uxZMcJVNWrX9sUQ7quQskjp0F1TIzCwOwkfLP+\niOR+PfnyzmHo8exSr46NDldvNvPHVOkkoHTv3R2PAoqIugIo5eMuRgPoD2AOY0y+roQK+DWlvwP4\nBdzT3WeMsZ1E9CKAQsbYQgCfAviCiPaD05wm+XJOAU+ajlqEdZUPzXWY6qHPn3/+Genp6Rg8eDBW\nrFihy/nF5P29N+7+YiNiNx/FhEH6ljEXLkQ1FS/kMJkJNqsh4NoqwoK4t5NWwDQo2fMT/j42zy6g\nspKjUXqqUb4fHyZ/NWszcu7cwV6aOlXfan8diLGo0aB+AJBPRN3AefIsAPA1gMt9PTljbDGAxS7b\nnhe9bgJwva/nCQVWr16NhQsXYvHixWhqakJNTQ1MB+uRdtVjuvR/oLIeIGBPWa3bvsNVDUiJi0Bc\npHcKsz3O2Ieb8uaXh6MuiHnwjp9uRLu4SIS1seDdkIG/NAoOnkRCVBhqmizK7V0InIlPZg0KQKzI\n8SkxOlxRQPkbvb6PMBPBYmPI75yMwkPKZkU11DU7ftdA/GRq7lYbY8wC4FoA7zDGHgfQ0b/Danu8\n+uqrKC0tRUlJCb799luMHTtWN+EEKLt0jnp9OSZ/vM7rvgX7vOsZKuua8dPWY6oE1+bKWswoLAlK\n+pXqhhYMf/UPvPhzkefGBl4h1q5H5oWuk5LZJD3lETlnPvB0mWq9ikumXaHxCN9parXCYmOYMDAT\ncRIp1nwlEJ6GagRUKxHdCG4tSPCLDk66ghBGKrg0FDhazT0Fbi097dXx+8pq7U9Nrh/xhYU78Y9v\nNqt60vz34t34bmMpqupbcLCyHtsVxrOuuArLvPAEk6OGzxq/fI+uzmoGIsRrO4u2H9d8fKAyFIwf\nkIF7L+gqOQIxwb6b9Qh2FhwxvPGqVENtU6vnRj6iRkDdBmA4gFcYYwd5p4Yv/Tus0Ees6gKARYOA\nGj16tFMMVM7URboU9wKA+mYLXli4E40tXH/Hqr03UzRbrLjorVX4xzebAQCr9jpnEdjGC5kWicBa\nV/aXc6ZHm41hzBsrcNW7f8m2nTRzHe6c45o6Tp7GFiteXbILTa3S36HDRKm6S58holgiLgEWEXUn\noqt5b7o2yTfrDwd7CKoIN5sw9TL3bCRaBULfDPnM+f7Em+fghhaLrPi/+Vz1OYKvc1nbnr3mkPbB\naMSjgGKMFQF4EsAm/v1Bxtg0fw8s1Hll0S4AwGniJmerjxpUcUU9AM5G7ktfX647jNlrSnD52767\norZ6cGoQnpptNoZj1Y1YsOWobFtBgOshI6rqmrFCpA19+lcxPlpZjE//Oqh4XICti6sARBFRJoBf\nwbl+zw7oCALIkh0ngj0En1BRrNqJcDPhv5MG+GcwkNcovSkGSUSS5rh/XtUbCRryVZpNQIxonS4Q\n64YeBRQRXQVgC4Cl/PsBRLTQ3wMLNowxLN1xQlZY1Da14qP4JsxO4Bb+LTbPWoQSwoU39Yft6Pr0\nYg+tPXOwkhN4nkyPvxWVobhCOibM080g7LYyhhs+WouHvt2CVhltSmir5QYT+jpW3ej0OW6ZtR63\nztpg15gEQdpikT73qYYWp/4CBPHJWCcAeJ8xdj24nJMGIYirQAh2NIvc5J/iZYbw8tomH0bDcfO5\nOQFPCaXGxPcCuPQo1QDAGNsCwL22QRtjwZZjuPfLjZi1WvqpnDGgxszQwv9eR6sbsdEHLxnGOPPc\n3ELv4jCmL90jud3q4Ua7a04hxs5YKT0mlfO51cZQzqfgFwTQyfoWnJSIiREPZ7GHtYrP15SguKIO\nI6b9gQ9WHrBvF7RNQSuzO3HwnTPGnATayz9z2m55bUC9CImIhgOYDGARv63NpVfXi2C7Twf7/K5I\njWfJQyORHKtdQBGAHUfdU59p/chR4SanY0LFi8/CGHNd0Q72GqLfOVHDPXGU1Ug/ebhqApf+509c\n98Ea+/tWq03TutLaA1Xo889f3LZP/mSdU79aUTIXenpK9KxBcfvf+m2f/WoVDhn00m8Y9NJv7seI\nXr/9+z776+KKOlQ3OAu06oZWu5PH2gOOZLOCQLLaBZQwXu7vqNeXI1ekhbb6qN16ycMAngLwIx/f\nlwtgeTAGEgikHQ/OHFwFgtylf0W/jnx70sVk/NWdrulH5Qn3ECKhdTwmkV3z/tGefz8iOEmlkDDx\nAdhBRDcBMBNRHhG9Ay5bcptGyDsn50opN3lbbQzv/L4P+S8v0xQtvqHEOYNTi8WG5bvLsXp/laJm\n1myxKprx5ATU9tLTOFTVILlPwKOA4v8u21VmFxIe3XNFDcTmgrEzVmLAi5xAG9CJK9lRcLBKsj/h\nXMJna+BNfX/s5taljpzkhJrNRcMKJIyxlXzqoHf598WMsQcDPpAAEW4OMRVEI24mvgA9g5/XLU1y\nu9QalKfLWG6/mstf7S3irEGFhpv5PwD0AdAM4BsANeCeDs9q5BwIft52DDN+24vTjdpcMF17+27j\nEdw2e4Nbu4YWC6Yt2Y1mixWtVht6PLvUSVtwRU5AXfXuXxj9xgrJfXXNFryyqAhNMms69jGLuhYu\n1voWCx7/bquqY8pqmjB3g7z3lzhfGREwb8MRfLP+sP3Jb8gry3D9h2vwwQrO/Fd03NmMIZg3zaIn\nRcYYFm49ppvXpBxENJyIigDs4t+fQ0Tv+/WkQaShxbfvUzzVRSoUHPQbGudaX6fmczop103z9pnq\nrpHuqy9KgkS4H9UKG/EDe0hkkuAXep/h/511uP4Gaw9UoXNqjP1p3ZUdR72LN3I1t7ku+LdabQg3\nm9D7ec4M+OW6Qyh4epzHfqXc3ys8rMV8sGI/Pv7zID7+04NXHMTaEPd3yicF2H3CPZuFwJ/7HJVS\nqupb8OQP23FhL+esx1F81dyhXRyJchkDnvhhGwAghbfDW21MMemm1cYQbuai6QU+X1OCF34qwq0j\ncvDC1X0UP5+P/AfAJeDySYIxtpWIRvnzhMHEkwelFgZmJ2Fdsc85oTXhep/LWQLE17wvWtb8+0Yo\nmtil5n418sBbs6M6YUMBX6tT48W3nIj+cP0XiMGFBC4/yI0fr8OIafIf33VSn7fhCL7fWOpUSEyK\n1fudC/q5ypUHvtqEnKmL7O/rmi3YK5HWSMzGQ6dwzxcb3bYPeWWZ4nEn6+W1P0FbAYCyGoegE8xo\nSsIJAJ7+cbvbtsEvO49H+OydU6TLc6s12X2x9hDKa5rsZpRzshLxwk9cNonZa0pU9eELjDFXjxf/\nqm1tlO0vXOz3c7ia8oV8lmK3auf2vpmOzSbSnHZLTeYGb0Wm2k8SaEOumm/oMQCP8/+eA+dyrj6K\n8gxHrPp+XaA9GPGJH7bhse+24sI3V+KJ77ciZ+oit4BXAGh0CTJ1XVeSiga/9n3lpcD3l+9XPc7a\nplaU1TTBYrUpBl2+tlS6JpSuT1bM6Y9b/y0qzXOvLN6F0W+sQDyf5qV7+3gPR+jKESIaAYARUQQR\nPQbe3NcWueqcDL/1HR/l//hm18v33gtysffly5AULX/uC3u1xxX9O3o013k1Hi/uJ5Oc44ZMX1q1\nLSJ3ITkwW//PLkZNoO5G0b/VjLFHAYz266hCCHH8gNTTvxbmFZYCAH7YVOqxrSf3cDX8LjJDekrT\nf8fsQgz79++Y/ou0u7on9MrLtedELdbzDiM2Jm1E0VJnpqHF4UQS4DioewE8AK4qdCmAAfz7NonV\nR09J8fUTjBAk18uXiBChsBZGAGIjw/DeTYPw7o0D7Y49Oo5IxRZnzCZCjUT6IdfjLugukSvR5QtI\ni4v0OCoCkJmkvcq2FtSY+FJE/9KI6BJwhQPPCrzNAK7EAZnAWDG+ZqaQ41BVveR2QSh4yoHXJS1W\ncrvWSHw5LvnPKscb5nDzF5tI5cwucgjf5P+2uNbD9B+MsUrG2GTGWHvGWDpjbApjrMrzkWcmSllH\nxvZM19RXMGJY5Mx1rmOREp6dUmIw546hHs8xJCcZF/dWV2VWajiengHDTGRfv1Wic6rDdC58HNf7\nNy9dur6deAxd0+O8ymyhBTWz70Zwn4MAWAAcBHCHPwfV1pEKmnOlWSavnLc0tlpx86cFTk4KUhRX\nSgswAeGCFMclAcCpBul1q/dX7Me5uakaRup8rgjeTt8schoxKUhDKcEejDy+RDQLEnMtY+z2wI/G\n/yg9UL0/eRDWFlfhtlnuXqkC3j7fzLtnOG74aK2XR3t/fm8sBt/dO0LzMVowy9wXckMVO2m4evFJ\nCkjR/wDwj7F5+OTPYvv7PhkJ2HnM89ymBTUmvi6MsVz+bx5j7GLGmHymzzbGxkOnkDN1ETYecvYq\nunVEjk/9etKQOvpBdfYknNQgjPtGleU7pi/dgwke1srkYHB4Sok98ZS0tTs/d58Eg5S25mdwGSQW\nAfgdQAIAz6rzGYqcVysARIWbkeXpehb9plf1V1/NR+zp6Q12l3YfLQB6Ow9Ie/Epn6VvprRhy034\neDi30v0lFlxhZnLOYv/gSLw/eZCH3rUhq0ER0QSlAxlj83UdSRBparVi5qpi3HtBVze7s/BEcN0H\nzk9phYd8c4P1lG/vqfm+rXf5i0AWcbMxh0lFnKZIyXtq+R53BxQ5+fTa0t3YV1aLT24Z4tM4pWCM\n/SB+T0TfADhrHuy0khQTjtomC+bcPhQj89Lw3IKdku0GZifh3NxUJ29SMd/fO9yr8weq3IdapDQ0\nJaVt2aMXoFt6HNYcUP8QKueExCWXlRmXy2t/LUUIKJn4rlLYxwC0GQH18apivPnbXsRFhuH287tg\nsESKHlfUmOnU0KN9vGQV3FAmUBrJT1uPIUGi0JonV3ZX5OzkH6w4IGsW8QN5ALQtxrQhXL1UXRF+\nopzUWEXz2fz7ODOZnIDKz9GmUQmnkjeDKR/nL7R2301mzcib84lf35CfZXfuAtwF2bNX9sbyPSsl\nj9UDWQHFGLtN53OFLIJ311vL9uL287ugSiLJqYEDPYMyPfGVF679oFYABDDu8laq1eWvJ0AiqoVj\n7ZYBOAGubM1ZidwapVa4HHj6/WaCNq52YpUXWPpOzXp2p9SXPZOEqI34I151ToazgBJ9UwSgazvf\nBKMnVLmoEdEV4NIdRQnbGGMv+mtQwaK2yeJzZdyorDlglng0n7gWAEBhNTDHFMNSI1075kzTngDg\n5UWhHc4T3/M52CxxqN/3LICAu5cDABhjAQ26CnXCPGiqWiZkV2GQFheByjrvHirNgoCS06BkfAqD\nYRD0Vmi5HiZ8f06pymQ6FwskpmIMemuWatzMPwTwN3A5+QjA9QA66zuM4CK+BLXFH1nh6qgVHl+E\niOQC+/vIDv9DdOa3ILOyd1ywie32KqKzPwnAmWwwx+6Fv52JTWEOfwSpwGh/QUSDlP4FbCABRA+N\nxpcuCp+9SHH/05e7V9AVEMy/3go4fyGdLDbwYtEptRNzFnZKcWJ6oUaDGsEY609E2xhj/yKiGQCW\n+HtgwUKtyYfMtYjr/gqaToxH6yn5hVlzNG+iotDOcmMKPw1TuHd5BLUQnrwGUR1+RmPpZFhq+0k3\nohaYIk7C1txBl3NuOlytSz8qmaGwjwEYG6iBBAo1t0ww6/+NzGsHQDoDijCswZ2TtXXqZ2Ghr4nP\nubP8nGTMXlOC3hkJKOedipzWliDvNCL0dfeoXPTsIGUk0Pd7USOgBLetBiLKAFAFQL0f6BnGsWp1\nXmoUzk16UR0WwBRehebySyH9dQo/WFBqEslCERVgljjA5u7+a4o8hrC4vWipGq37eU0RXPwUhUk4\nmZjrYTLXIyJ1BcKTNqFu7zNgVt8sZaaIcjBbFJglwXkHtQLMDHXZvtTDGBuja4dnAP725PIVpcl+\ndI92WLz9hOq8eoEqwyGFXslir+yfgaE5KUhPiMIKCa9X+f4cb24+t3NANDo1AupnIkoC8DqATeBG\n+bFfRxVE5KrLusJs9uU4RKT+BWtTBiw1EhYcJrgJSQsoc+xuxGTPRt3eZ8Gsei84WkDhp8FanQNl\nTVFHENvlPdia01Bf/JjbUVGZ38IcWY6WU0MBm3TCVu8RLnL3izu2y9swhZ+GzcJlqyBzg88CKrbr\nmwCA2l3TnLbH93wOlroeaDziP18gIuoLrsy7eO12jt9OGCTUZBMQT+wTBmVi/qajku1c57whORo1\nG6k+Qfj3tf3QtZ17FpR2fEofzV58Po9KO3qtQQFAegJ3SUoJ3LioMNlzmfjnuUB5N6oJ1H2JMVbN\nx3V0BtCTMfa8vsMILu/8oT6pqh3m8ku4CKDPbs13eh+d9TkovApCQuvwlJUwxxxARMpqAIApSvqG\nBYDI9MUwRR/SPMTI9F8R1+11gJzt67Fd3uPOGSkdM2GO5IIuiRjik4oRnrRe87ll4b+28MTN/AYG\nU+QJbjyCiZH3vjPH7nM52Kb4PQEAhauPTwuL8y7voBqI6J8A3uH/jQEwHcDVOvT7DyLaQ0Q7iWg6\nvy2CiGYR0XYi2kpEo0XtV/Dtt/D/0l36m0hEjIjy4SXNrZ6tA/ZKy9lJeH3iOd6eyiuIgJuGZWOY\nREYTuVQ/AuUeStPY+9HZhqnrRK/QV22TBQBQXtOMH+8fgUcu7G535ZfuinewCJAmqcZJYisRPU1E\nXRljzRLl389KyE0jcr4KUmIjnbabo8oQ1+11RHb4CYAVUe2XILrTbNFxzP6XzM4JByJSVyE25wPJ\ncZgij4HM9aCICpiiD4HMdTBFlNmP4xrJu/hSmHw9JYABHWciqqN8yBuFV/Ju3Z6ZNKQThM9pjuYq\nUYSn/IXY3P/AHF3i+Ey8oIrq8LPT8RFpyxDb5R2Y44pkz2GK8D1bhk5MBDAOwAk+ZOMc+JjDkojG\nABgPoD9jrA+AN/hddwEAY6wfgIsAzCAi8b09mTE2gP9XLuovHsCDAArgA6s1BIfGRoZpij2L1pAY\nWIw4h6bS2QTtT2ugrt/joKQCdf2gt/3E56ecvaYEA7OT8dCFecgVuY4zwK55Mub43IHSLNUY4K8G\nl4NvHhFtIKLHiChb53GcUbxx/Tnw5IVmIuDqczLg+pOFxewHzFwCVDK1Ovbzf8wxxYjr/jLCEoSq\ntMrnic19GzFd3kFc1xmIzfkAsV3fQGzXt5zakEIfcXmvyXcuY5Z0YEVctzcQlfk1YK5HePJahfFa\ncdUA9/LW5ijuBqEIuTyqDOEpq0BhpxEWx2lUMZ0UrGRM4ZKmVsT3moqIFIcZt128dNZmHWhkjNkA\nWIgoAUA5gE4+9nkfgGmMsWYAEAmb3uDSKQnbqgGo0YheAqfZNXlqqIQaN35vn7efuKSHV8ctfXik\n/bWeJc8D5ewhmepIBxPfFS5ppFLjuOKfsQoJmJ2q6PJ/A7USp8bEd4gxNp0xNhjATQD6g0sYe9bS\nNzMBFObsNs4s8RDXozMR4fJ+Hd1+SVNkJeK7vyTRq6BZHHL6q8a5whTu8FIjs8RcQxb+b6uq/lzH\nJOafV/UW9cv1FRa7D5HtfuUcRqKkS4kkdpmNe/+6xL1PJmiY0seFJW5EVPvFiM760q51KQ9Z/omb\nzJwDTHjqn/ZtL43v67lP7yjk124/BpdweRMAX7OadgcwkogKiGglEQk5mrYCGE9EYUTUBcBgOAvD\nWbx57zniZxsiGgigE2PMWU2VgIjuJqJCIiqsqHBfVG+2+O4A9NL4vshOiUH7hCin7XL55TyRlRxj\nTzQspY388vAozL5tiChQ1fPsPzLP8YAVjNRIeghH11EP4r0Xn76il8w5xRWExTFUMvFhOquWqlyY\niCiHiJ4A8C2AngCe0HUUQWTFHpkkl6YGUJi7e/KzV/RCj/bxiOk802l7ZNoyp/URExHv3eThB2PO\nzyR2AcMIMbkzEJv7lvRxGojt8jbC4nYivudziGwvNR85Jhhuncw+OLeWU86VCoFjMPPrSCS405PF\nIRgB2KL22ds6w33+iBTpuTs643vuhUndQz6T0aDC4rciPImzZJG5wb59Q4l/Soszxu7n124/BGd2\nu0VNdhYiWkZEOyT+jQfn1JQM4FxwBUTn8QLnM3A1pwrBlZpfA87qAXDmvX4ARvL/bubNf28B+D+V\nn2UmYyyfMZbfrp17LaGcVOkSLC59KO4f0zMdq54Y45fYGqk7sEeHeIzukS7pspMtUcn59vO6YM7t\nnktq6IXUPC+37vPkpfJxXlxf8nOQ8LO41ouT0poAIJ8XaP4oQySFx7MQUQGAcADzAFzPGCv2cMgZ\nxa0yJQDi8qaBTC2o3TUNYYkbEZ3xHWr3PI+U2AjJH9wccxgx2Z/a35tMgm3e02MP15cprBYRnT+E\nrZmrF8Ns0TBH6hNgSmENiO70BQBIOjxEpC63v+bWxTjC4t0zRji743KCjUxWe5wXY9yFHpf3IkA2\n1O152flcyc7fN1PQeLxDfKM5BG901jf21+L1w1N+SmtFRAsAzAWwgDFWovY4xtiFCn3eB2A+42b7\n9cR9kDTGWAWAR0Tt1gDYx/d3lP9bS0RfAxgKYAGAvgBW8NdyBwALiehqxpjmatmCmUgNgQw2FSZ0\nNRO00GTV42OQGONeRddELpO233PxuZ9ATsZf2tf7eEFhDU6tm/3L1/bF7ed3sXsBuhKMNahbGGOD\nGGPT2ppwWn10NeJ7TYUpUlzIjsEcsx9kckxc0RnfAQAi0/5Q7I/MDo+fDWUrUd1cDluLcn5QwVMt\nIu0PhMWUOASIq5cgAJgaAFLnVSTvuODeb2S6IzmuWChGdVhgf71m6li8feNApwXusIRtom45AUVk\nQQpIeJoAACAASURBVETaMpC5BWSyICL1d8TmKWTFsqmf3MTcdF40/j6mG+cJ2W6p3THELNJiozK/\n8thPtMbihxp4E8D5AIqI6DveW076rlbP/8AH+hJRdwARACqJKIaIYvntFwGwMMaKeJNfGr89HMCV\nAHYwxk4zxtIYYzmMsRwA6wB4JZwALh/bZ7fmK1ZXDWaklPKkyZzaZKfGIFGhzLvc51D6fJ/eot1B\nUlqDkmkren3PqK5uAbRKssfGlNuIz8kYEBlmRq+OCdKN/YCaNSjpEGwf4Kvz/kZE+/i/ksEORGQV\nuccu1HscC/ZzE3BEu2X2bWHxOxHTWTrlj7UpC0dVlpuYvuVprG1+FmFxexXbkYmzxAiea0TCFeN+\nOcb3eBGx3RScGkREZXwrcz7vknZmJEXzTh98P+Y6RGc4KkqYo44DAGJyPkKk6PuMTP8NpjCHSc0V\nZlPnpODq6PHTyYfw8EVdEZ39GSLTVtgdQ8Qeh+EJ0iUbxMRJZEvXA8bYSsbY/QByAcwEcAM4Rwlf\n+AxALhHtAGduv4XXptIBbCKiXeAS0t7Mt48E8AsRbQOwBcBR+CmGcWzP9lj26AXyDYTL2sv+HxjT\nFf2z5Nej8hUyQahJlqpUBFOyTw1tk2O9ewiT447zuzi9F2s/2akxWPrwKNV92b0YXb4k8TtteRLV\nt1VDYAyJ7kwF8DtjbBoRTeXfS2V6bmSMSWdZ9ZEmSxOWlHAZm8Lji9AcfhKsNUVy3cmBDV0kgv3k\nsPhQn048yYvhJnsrt45ikjdPqZmctdBsbUakmRcmpmY+n57vMLUalITzh8Vmcax5eUmsl27MaiCi\naHBla/4GYBCAz33pjzHWAmCKxPYSAG7uboyxenAOE576He3LuASUyo07zG3e9f34JT3x+CXy+7+7\nd7ibCcxuvlMQJ0yl4PRl4vXmUKljhHW8Z6/ohd93laGkqkHV2MS73Us8c3/UyOdgZNFQ1KCIyERE\n/qhTPB6Om/VzANf44RyKDPnKuUhdtKw5iInazMPbe2/136BUYo49gOjsTxDbVSntm778UvILviz6\nEhabBVEdv0N05jx9OlapQYmTvwpYbBaJlqEBEc0FsAucSe49AF0ZY/8I7qj8i9Jaj/Ag0D7eVyun\n/LnltCBVwkWjBNLSXO36jhipWDGxx2G42TF1+yI81cSB2YNzVcingGpQjDEbEb0HYKC+p0V7xthx\n/hzHXaPbRUQRUSE4j6RpjLH/yXVIRHcDuBsAsrOlw7QYYyAiNFvd13HM0fzahYtp7cIRW1AgimU9\nXn9cbgii85gkAnn1I6rjfCfX8kDwz9X/hIVZ8NqG1xCuowlacKrwBisL6QS8swDcxFhoDzJQDO2S\nghnXn4PL+umTAFgNSnXABAStwJMG4WlyjosIw8i8NFzcu71bNWBvJu3UOOUHN+dquMonkPPIA8RO\nEkrHK3bvV9TYN34nouvg8B5SBREtA+cd5MozavsAkM0YO0ZEuQD+IKLtjDHJUpqMsZngbP1I657G\nblt6G54f/jy6JHbB7B2z8eG2D1HfqlzyIjr7I9hanNOhFJya69bu2b+eVezHn8IJQMCFEwBYmP7a\nSnT2Rz4d76pBUYR2r8cF5U/iqtMz8OJazpFj1qWzAAAvrHnBp7Exxpb61EEbg4hw3eAs1e1/e2QU\nth/VJ2mNkpehGjMg4D5Ju7Y3mQhf3DEMJZXuc4w3GpQWfCkK7TEOTKNVLy9d3zJoagTUPQAeBWAl\nokZwQpgxxhSfoz24y5YRUUdee+oImcVjxtgx/m8xEa0Ap8lJ13r2QBjpt9aw4MACz40MVOK9XdtV\nQMV5YfIsb9kXsBL2BurJax+PvPb6THauMT5i7HFQntZxJIr8SbfTMDCNyKcX8iBcFfbJefF5+zm0\npLFSgxovvnjGmIkxFs4YS+Df+2rkWQjgFv71LeDiMpwgomQiiuRfpwE4D4B8EjYROQk5mHXpLHRJ\n5Lxdbu17K/668S+sn6yc9JSrTxREffYso/HwnTDHHPLcUIYJCyfoMo7cpFzMunSWXXsCgBdGvKBL\n3wbBR00clOZ5Vaa9lLDQS4NyLh7oeK1l7O4yTjkOyrVgoSf01hbVBOoSgMkAujDGXiKiTgA6MsZ8\nSXE9DVwU/B0ADoOr0gs+o/K9jLE7AfQC8BEfjGgCtwalSkDJER0WjZUTC3DB98Mk90d10N2T3UAB\nc+w+h1u9F9S0SNSUCiGIKBNcBQD7fcYYWxW8EYUOEWEmtPiYIsnV3dobrDY+2NwHLcSpnahhamwE\nqupbdNOq4qNk4rM8an+iNy63m01GQEt6EcpYO2bdOgRNrVbJfnxFjd3rfXAh+WPBJZesA+eVNETp\nICUYY1XgMj27bi8EcCf/eg0AmZKr2tl46CSu+4BLpxPPp51qLJ0MS11PxPd8Tq/TGGhAKfN4QkRC\nyAsgJYjoNXDu5UVwJGlkAAwBBWDJQyMxTmXtNSlKpl2hyzj+x2fzrmnSFh+oZh5OjeMElB5axZ9P\njEGKTDyV5/7l96vJJOHJCWNMT4ePm9Z4Mk+oEVDDGGODiGgzADDGThGRvpFnOlNcUY+/fbQW/57Q\nD13bxWHmqgNONZ9qd78IgADGPZGcEzsJW+ulA1sN/IdrOQ0x6THpARNQByrq8PT87QCAufcMBwA8\nNX+b0iFquAZADyHzuIEz6f7LIu8VNU1qnYDUa/yesjQIrH96HMLMyqstnSTyAwpoieFy1YI8ZpJg\n0q/l0NvEpybVUSsRmcH/MkTUDqFWv1wFTmlYWIRdOAFAva1M8Vg9HSwM1BETrncl34BTDC6H5VnF\n+AEZnhudibg5EXiOuWIqXLgBrrqtnHakamgahIJ7MLNMJgkvBY3eJj41AuptAD8CSCeiVwD8BeBV\nfYehL7ntYjH3nuHoyhfeuntUVyx9eBTiI8PQMdE9ULDWekKxP19drJdNlM4KcSbz9pi3/dp/IB8K\nuraLw9x7htu1JwB4dUJ/X7ttALCFiD4ioreFf752GurMuD6w1XJ1w4N64E15DUeX+jteiUO8PAkF\npd2eMmlodXDV28SnxovvK3DlNV4FcBzANYwxndIIBJbt/7oEa59yW/oCqas64jXtY9sjMy7Tr+cI\nNKM7jfZr/3ERcZ4bqeSjCz+Cifz7G0uwENya7Rpw9aCEf20aT6YqgSgF1+9AcnFvrnqA1ZOAUuFE\nwLVz7PFUTt4XbKLx+lKbSi4FFcm89kTATXxE9AVjbDdj7D3G2LuMsV1E9IWuowgSQk2TeLNydPut\nfW712Fd8uHLMxtLrnOM2/zPmP7ir310e+w1V/F02oeR0iW59tY9tH/ACc4yxzwF8A4dg+prfdlaR\nkyptqg03m7Dn5UsDPBp3BmQnAVCXdQJQEQfl1NZzuQ9vsYrGq+XZS2u+Qq5Iofr+g2Hi6yN+w69H\neUxAGcrccX4XJEaH4+5RuQCAoQm3Kba3Mc9Lbpd20XazjcsehwcHPaiq7e19b9fUd1tAzXeuhtzE\nXHRN6hpwAUVEo8HVZHoPnCfsXiJSn2a6DRBhNuHnB0fK7o8MCw0tCuAcq7QgN2k7OyTw27wbkp07\nJdzpnQSUh+OJIFsKxbUelhIh5SRBRE8RUS2A/kRUQ0S1/PtySATWnkk8d2VvbHn+IvTJ4OKNB2S1\nx/Zbtsu2b7Q0on+a8prEbX2UhZwvZMWrTxHjDUM7qK8U+sYFb+ChQQ8BgF81wDCT92tQqVGOdFV3\n9rsTgPxT7IQ8fYJ9JZgB4GLG2AWMsVEALgFXxfasoV18ZMAqr3rLxEHcvXXf6K6K7bxJNvL+5EG4\nZkCGogeeGp69srfbNptToK6nGC7Cs3xJd28ykgvdqzk2YAKKMfYqYywewOuiDBLxjLFUxthTuo4i\nCBARxvVqj1WPj5GtSHlBFlff5ufin/HVFV8pTmYJkeqTa0wdOlXTWM3kvyfNx/Ifwztj38GXl3+J\nx/Mfl2wzsftE++tLci6xT/oPDnoQ3ZO7+2VcWtaMRmQ4J9wf1H6Q/bVwU4WbnB3qsuO5hMLRYfJF\n9nwknDG2xz4OxvbiLPTqC3XSE6JQMu0KDMqWrycFuE/OshqUSJ/pk5GI/0waqHv6HwCwajQw2IWM\nF4L23RsHYfKwbPTJkK/HJRAME98zRDSFiJ4DACLqRETqH7lDnGyRjXxctrMDxfXdrwcApESlAAA2\nlW2S7KNzQmdNQqRjbEdNY/RFm5BjWMdheHHEi5jcazJiwmNwTrtzYDZJfwZhDS4tOs1t37SR01Sd\n746+d2gSZlImOTkz3bPDnJP3in+LpEhujcHVnCo8bOhlSpSgkIg+JaLR/L+PcRY4SYh5YEy3oJ7/\np7+fj1eu7atLX8LE7ml+D1Tmb5sGScONic8l6LLP7iQheQxHTlosXrm2nypBG4w4qPcADAdwE/9e\nyCTR5miyckXxbux5Iz648AOkx3AR0sJTtqtgESbsJ4Y8gXCz4+H4lt634L1x8l+Rp+SkuYnc2tj5\nmefjwws/REasI7bkqaHKyuuUXm717NA1kTNfPDPMkUh+eMfhuDbvWifhJ0zmYv4z5j+IDeeKNEoJ\nyrzkPMXxCGTEZeDF8xRKv7uQGp3qtk1O23E1gXaM436ntOg0nJdxHgBO8xMTYebiTvwooO4DsBPA\ngwAeApdR4l5/nSwUuWmYdNmbQNEvKxGTh3XWpa+YCOeHt0CvabritAblg5u5p0ZaEykLY3EtO+8t\nagTUMMbYAwCaAC6TBICQziThLVlx3ETXOaEzzs88383MFBXmHEM1ImMEtt+yHaOyRjk9tT825DEk\nRsqrw+I6RutuWue2v0NsB/t4zss8z2kcUkJEYOl1S/HkUPfCxP+75n9Y9bdVmNRzkn1bg8W9DPtF\nnS/Ck0Mcxw9uPxjDOw5HalQq7up3F2ZeNFP23FKINS4TmdA7xd2WLuAqeIU1o96pjmMaLY2Sx4rX\nlwpuKkBeEic0p/SaYtcKBYGUHJmMKb2mICOOE/rCX71hjDUzxt5kjE1gjF3LGHvLyCpx5qJWIAVK\nbNlEAsqXZPzyx3r3SYgI654ah3n3DvfcWAVqbEdtIpOEGvq364+5e+aifQwXGyGUc2iyNDm9v6jz\nRfjt0G8uGYWdhZlJQfZXNzvqOQnaidOxfF+CaVE8AYsnbNdjlGKtkqOcbexWm3sdvQhzBKb0noLe\nqb2RnZDtJGA8eRz2SO6BPaf2OG17a/RbuHnJzQA4sxsR4ZfrfkFVYxVuWnyTvV2kORI39boJN/S4\nARMXTsSB0wdwe5/bUXC8AB9d+BFGzuU8wZQWaReMX4BGSyNiwmNwSc4lON18GtfmXWvfnxCRgFmX\nzEJech4SIxPBGMN7496za1h6QUTzGGM3ENF2SFXYZsznCGCDwKO6HEUQTHyxKhxRPK1B6akRdpBI\nhuAtagSUayaJiQCUK/adoVyVexVyE3PRJ5XzrBcKHAqaU6uNSygpCA7hL+AuoKS8xl6/4HU8vvJx\ne/9yPDnkSWwq24Qrc68EAJTVO1IxdU5wN1lM6TUFd/e/W/nDuTC4vXykgNjJQA1zr5yLzLhM3Ljo\nRhypPWLf3jfNYf8/WHMQAKextFhbnI4XvALDTGH44eofYIMN4aZwSc/K+8+5Hz/u/9GtsnFuUq79\ntSBoXcnvkG9/TUQYleUXr++H+L9X+qNzg9AmUKY/T4HFYojI7rF87UBtCQOCXSnNo4BijH1FRBvB\nZR8ncJkkdvl9ZEGAiJwmVcEUJ7gtCxrUxZ0vRu/U3rgiVz6jcl5yHi7MvhB39r/Tvu3SnEsxLnuc\nm0eZKzmJOSiYXGB/X9da5zTGC7IuwMpSRyZoKbOeHKM7jcaKIyswMks+PkUrglbXMbYjjtQewYsj\nXkTv1N5Oa1bF1cX2166FBsXtzCYzzJB21kiPScd9A+7DfQPuQ7/PdUt0ryuMMUFy3s8Yc/ph+Azn\n6n8sg5AjVIpbWlUGFgtkJcdIZoCX6yWYZd7FqPXlLQPwJ7i0LdFEpO0R+wzlnHbnoH9afzw25DEA\njok1zBSGCXkTEGmWz8gcaY7EW2PectOWpITTo4MfxScXf6J6XO+Oexejs0YDAJ4e9rTq4wDO627x\nhMWajlGLYILLiMtAj5Qe+P/tnXecFEX2wL9vI7sL7JIFyRnEgAQjiiIIGFBRzKLeKeYc7s5wqIfx\nvFMv/E5UUDwVMStiBEVPRQlKUEAyLEFyWpZddvf9/uiemZ6ZnrC7szOzs/X9fPrT3VXV1a92tvt1\nVb16D+CWI28BrDZ6CJxLGtFpRFT1R1LsScZgl7RhcZciyfnPJX2YcfuJiRYjZsTrxX7P8B6xqagS\n3swTQTQBCx8CLscKte4RV7HiQ6U0uZm5vHLaK97zMYeP4cbpN4a1XOtcUHnT2it6hV/ke2anM5lZ\nONPPgOGJE59gytIpjOo6Kuy1zmFIsOa83Oa9YolzmON3h/6OK3td6Tfk6TQSuaDbBVF7Lk+05VQ0\niMi1wHVAJxFxxuxogPWBZ3AQag1ishF1wMIalcLH5cd1YOwH0cVvjUZpBpmZV16kGiGaOahRQCdV\nLY1YMsU5/uDj+fGyH0Pme+ZiYk1Wehb/OPkffmn1Mupx2SGXuZZ/+PiHeW/Fe3y/8XsObRq/obCh\n7Ycye9Ns2jb0Ny8OnI/zmJD3aNzDO/8UDYH15Gbk8uLQF6smbM3xKvARlnNl54rsPaq6PTEixZc7\nT+3GcZ2D18ylEjXtizJeVMWzRDyJRkEtAgqwXBzVPX79BFr3g9zGEYuGsrCLlpFdRga93KvCGZ3O\n4IxOZ/D+ivcr5caoupzX9TzO7ny235owN9o0aMPUs6fSun7rkIuD3XCa8s+6aBaZaZle8/FkQVV3\nAbtE5Glgu6ruARCRBiJylKp+H76G2k+iF+jWJJEX6iaH4kqT6AMmWmVCBtyImUxVIRoF9Qjwo4gs\nArzrOFT1zBqTKlnYuwVeHQW9RsK5E2r8dmOPHRvT+s7sFN+fSEQiKicPbtaIkfjnoH96j2t6mDIG\n/B/gnKstckkz1FISbGUekZO6NWf6kqr3KZJEz0aloF4CHgMWkqLrn0Jir39iTYpMHVRUwJ4NkF+z\nzmdjzVtnvsXCLQurpNQSiKjD5EtVK0RMaObaSrQv7GR5sTsJN3cbyQiiksaCMScaK759qvqMqn6h\nqjM9W41LlhQk9/hspfn6Sfj7IbB9ZeSy8WDnWti8JGKxro26MrLryDgIFFNWishNIpJpbzdjhYGv\nFiJyo4gsFZGfReRxOy1LRCaKyEIRmW+H+vCU/9Iu/5O9NXfkjRKRX+y6Xq2ubHWJZFREVcEbEiSg\nPXcM6cYRbQoY0CWxc4nRfNF9LSKPYEUIdQ7xuXtOrc0UbYUJQ+GEO+DwC6Dm/LQlhpVfWPtd66Fx\nx/Bl48FTtgHH2F2JlaNmuAZrkfu9WO+B6UDlVlMHICInASOAw1S1xKFsrgJQ1UPttI9EpJ+q9x/4\nYlWdE1BXF+CPwHGqusOpuAzBeOZoIgcsTD7NVRUrvi4tGvDu9bH1slIVolFQve390Y601DQz/+Zp\n2LYM3hkD3Yb7FFSiFwOEoqIcykogK9p4M55/wwS3Z8UMePe6xMpQw6jqZuCCiAUrx7XAox6ffvY9\nAHpiKUBUdbOI7AT6Aj+Eqesq4F+2b01nXYYoCKmIkkQ/OZVSOJGuObETV02aQ5fmsXHuGmui8SRx\nUjwESQpKHVE137wChj2eOFmi4d3rYMHk6HsgyTIu8en9sGdj5HK1GNtn5VVAexzPmapWJzxyV2CA\n7XJsP3CHqs4G5gMjRGQy0AYr4nUbfApqooiUA28Bf7Hnxrracn4DpANjVfXjEG25Grv317ZtYj2U\nG2LL4J4tXD1MJAtReZIQkdNE5C4Rud+z1bRgCeG3n33HG+dXv+c0fzIsert6dYRjwWRrX1k5D+yH\nKaNhy9LIZavCthUwNh9+ftc9f3+AQi2zR453rIHXLoSibf75W5Za9W1dHntZa473gHzgc+BDxxYW\nEflcRBa5bCOwFF0jrNGMO4EpYo09TQAKgTnAU1gLgj3+pC5W1UOBAfZ2qZ2eAXQBBgIXAs+LiKur\nfFUdr6p9VbVvs2bNKvt3SEmiCfmeLCSL6XtViKigROQ/wPnAjVi9xfOAWmVOFTXrHKEvyg8Ez0E9\n2MR6UUarEN4ZY/XEKmp4LsvFMzmqsDdg1Gb3Bmu/Yjr88q5lNFETbJxv7X9+xz1/11r/89kvWPvv\nn4Wl02D2c/75C14PXx9Yhh+lwSFEEkiuqt6tqlNU9S3PFukiVT1FVXu5bO9hKaG31eIHLKvapqpa\npqq3quoRqjoCa93iMru+9fZ+D9YiYs/CuELgPVU9oKqrgKVYCssQhojroOIiRd0hmh7Usap6GbBD\nVR/ACl5YM3G+k4mKMoeCUl8aVL7nMf2BmInliu1l3cuCKfBgY/hrF5ji8DaxfYW1n/uSfb6qZuTx\n+vavsBRlJIW+yfYItHu9tf/ykcAK7X1APZsXw+Kp1vEzveG1WE/5VIupIjI8xnW+iz33KyJdseKy\nbRWRXBHJs9MHA2Wq+ouIZIhIUzs9E8vD+iJHXSfZeU2xnukkMe9MfkKug0qS3srRHX0BP5NDoqoR\njYKyFwOxT0RaAQeAysUsrw0EvqzLDxDye6my1n2eHkAkln4MT/aA3ZWcnykPUFBvX+WT8Zf3gsu3\ntsNOtO7nn168A/5yEKz+X+XuH4g39IjCAwXwXIRpTI+syz4LUZ/9iBXv9E//99Hw+sU+BbgqqVY/\n3IylpIpFZLeI7BGR3dWscwLQ0V40PxkYbc8nNQfmichiLG/pnmG8bOAT2yfgT8B6wNM9/QTYJiK/\nAF8Ad6pqwNiq4dqBnRItQpW45OjUGOSKRkF9YI9NPwHMA1ZjDRWkGAHKqLw0tCIq3QsThsVuPdGq\nry3T71n/shbSbrV7aCV7YeJwmDfJGlr8398DLrRf3AHhK/zId5nULpxtXx7wbbV+HpQVw1d/rVIz\nguTyKI4Nof0XAr4hygMOI5XCufD8KdZ82a710V0PsGmRNaT6/o1WexKEqjZQ1TRVzVHVhvZ5w2rW\nWaqql9hDfkeq6gw7fbWqdlPVHvYQ4Ro7vUhV+6jqYap6iKrerGp56rWHCW9T1Z6qeqiqTq5+q1OP\nkAH+ktuIz5+kFCo6wiooEUkDpqvqTnv8vB3QXVVTx0hi90Y4UGy9CP3Q0GbmS6fB2m/hy0ejvEmE\n/5CXToc3Rvvus32VNUy3fi6s+cZ62QJ8PtaaR5oyGh5ohFepThwGn/3Zve40l5/Y4yEjcPjN0/Op\nzvovVd/TW+YS4XylSy9n0ZvBadNutxTpbz/DfPt7SARWf2Mp6z2bfGWdCvrV8y0LwXmTYNodVW9H\nNRGRE9y2hAlkqBa+iLThh6uTZIQvaeSoLmEVlL3Q71+O8xLbGWa1EJHz7NXrFSLSN0y5ofYq+OUi\n8odQ5arF37rDuIPgx5eD8yIaQ1Tzv8BZf+Fs3/nUW6xhOreeR2mRZeDgVCJblsA3T4UQMYwz1tnP\nW0NwHmMK59xRaZHVkyp36Z1VVLinz3vZqs+jPJYHDNltXQ6TovUP6DLvpAo/PGsdr/3Oke7oQe0u\nhAO2sUTxDv8qXzwdnhsU5f2rzZ2O7T7gA2BsvG5uqGlSRAMkOdEM8U0XkZES29m/RcA5wFehCohI\nOpZyHIa1EPFCEameu/BAnENHs/4dnB9oJBEsZOi6nRZnnnLrfoBFtiHXJ/fAPwPmgAoD1lUucjH6\nkmhjTNpsXwHTH3TPK7d7ODvX+tetaimnGQ/Bt88EX/fcQHjINwlL8U5rHswz17Zthfv9Ao05/PIC\nem2ev9mHt/vS1n3v/tEQaMW4z55Kycjxl3H117B+jmX+P2lEjS7AVtUzHNtgoBewI9J1htpNPD1J\nvPL7o7j/dPdXYjJ6tKgK0XiSGAPcBpSJyH6sTwetzni6J2R8BJ3XH1iuqivtspOx3LxEF6UrGv4e\nQd/t3+meXujxGiNWTyItPVhZbV4cfN0LdpDVXiPhO9szt3NNUHkUIbe++2fkMoF8/SQce1OYAh4j\nBPv9qRU+WaY/AANu8y/uMSP38Fg7OOTsyHJkhfFA/mCjAJFsZbnxJ1/a+jnQ8Azr2Dn/tyPAwMU7\nNGvvK8qtXqmHd8ZY+00LoMWh7sOgsacQiFEYVEOiicc6qMdGHsq67cUh84/r3DTl425F40kiUT4w\nDgbWOc4LgaPiKsEkOxS5Kux3GGCt/tral+61ehLtB8DlU60J+pxGkH9w9PM4b48JnbdzTXDanDBh\nP7avguwQ3w0vDAkjhFqK0rOOKCMbMnOCi5Xsga+ecK8i3BolgBl/gcMvDF/Gya5C9/R1di9zp+Nf\n49mAqZ2F9pxWjr3u9L3r3eV79gQY+QIcem70ckWJiPwDX9c7DTgCy8jIUItIZEC/8/tV3WtHqsxB\nReX+X0QaYS3iq+dJU9WQw3P2NZ8DbvGc77EXHUa8rUtayP+WiO5YVK1hteNuggYHhQ6h0Wuk+9Ba\nsUsw1MXvW3uPwvqP7Vzx2u8CXuQBTXEOSS371F0OCPa4EIkPbws2xfawNczarefteZnmdo9y5Rfu\nFnDLPrP8FTpxW4Ts9nR89QR85zKM6kaXU2GLSw8UYO9v1n7uxNDXz3nBd7yrEOa/Frrs+rk1oqCw\nvDp4KANeU9VvauJGhponcMgsRd7/SU9EBSUiv8da09Eaay3F0cB3RHAWq6qnVFO2Qix/Yh5aAxvC\n3G88MB6gb/t8ZeJpcMZT0LQLfPOMNZdStMUy5T7iYvjpFfeKQi1e3RdhichMh0L6v2P884o2w9KP\nfOcPO8LCdxxoeXaIBStmVO/6zY7R0xKHcpx4GjTpBO2P9y//22Ko7+IEe+Eb7vU7zcjDUVZS+bk2\nN9Z+Z4UXCYekwdZl8IE9BHiF7Y3o/XBDomGqE2mrqmtV9aUqVWBILirZgUqWnkuSiFFtonkLavyK\nRwAAIABJREFU3Az0A9bYjmN7AyE+02PKbKCLiHQQkSwsz9DvV7m20r2+41DKCaCJS7jqfVvhg5vD\n1//FX6KXpazYGgoEaHlY9NclmkCjgtI9lnl8IEVbqnmjWh3mxOuAUEQiujYy1E5CzZ+ninFCshCV\nJwlV3Q8gItmqugToVp2bisjZIlKI5TbpQxH5xE5vJSLTAFS1DLgBa8X7YmCKqv4cqk4/mnaxvoSb\n2q7FjrsJ7orSrU/PEe7pmxYGp2W4zNO4UVEO+W380yo7fJdIrvgQznSx5lsxwze8GUtWhR09ji0i\nvv+XKxy+XN3aG2WNjuMkCLpliCdJ04NKFkGqSTQKqtD2JPEu8JmIvAe4zN5Hj6q+o6qtVTVbVVuo\n6ql2+gZVHe4oN01Vu6pqJ1UdV517kpkDf1gbnH7ei/7nPU6Pvk51cdIaqtx/AoJ/OS3MagsHApyx\nBvnMiyGh5tJiTswfZA1xbKjFBL7vI/3XJFo/+N2+Fv8XRmPF57EfHisiX2CFEHCNG5P01Mu3YidN\nHG55aMhvCz0cC0cvCDOZ7kY0ZuGRqA1Re3/9xDImmPlY/O4ZysQ/1sRirsufw22fewLkOPzvVXt5\nhiH+BL7bI0fU9d8bqkdIBSUi9bDCVncGFgIvqGpSeeOsMldM8z/vfjosmVqJyLQxpDYoqFdHJVqC\nmiPGn7qqGsZ1hyFVCPVvo978xKqoRPfgYkW4HtRLWJ7Lv8bnzSGCpUAt5YynoXkPaJ8AV2kHQi/E\nM8SDFHmSDUlBRprQMr8etw1O/YhE8SCcguppR+JERF7AFz469chrCiff6zu/axU83iE+914yNT73\nMbhTUt0IGIa6QOBnTGhPEsJ3f4ybv8eQJLoHFyvCDcB7HafZFnV1h9zG0ZVrEIOwWJHWVxlqltnP\nJ1oCQxIT6L08kZ4l6iLhelCHB0zw5jgmf81kL0BGvchlIlEb5qAMhjpOsBVfavRQkp2QPShVTbcD\nrXmCrWXEKvBayhCtmXmqcWgMjSYG3B65jMGQJMxfZ61f3L0/jGd+Q8yIixvnlOGO5f7nO13WVQXS\n9tiakSWRjHwucpnDzo+ursYJDqmdmQDLTUOtZW+JNdsxd03tiZyycVdgMNbag1FQlaF+s8pfExia\nIpac8XTkMvGgkYtBydnPRnetM2xGdclvCzdW0mF4iwi++gx1mlDrnmowlFjMKa+oRcIGYBRUKLLq\nx6aeshr4ehkyDk59GI64JHZ1Ruu2yY30zOC0aKyI0jKs8OxV5ZSx/ufXz7Kc2kYiO993XFG37H8M\nVcPMOSUGo6BCEYsXV3pWzRhBtDkKjrke0qOKlhIdZdVYj7X116pdd8FrwcqtMoYnh5wNrXo7ro1S\nyTp/k9rkaspgqALltam7F4BRUKEIVFCN2le+jmGPEVNHWCfcae3b9AtfLhxjYuSIVWLgMKHrEEgL\nUFCVkS89C67+0nceKjJu9wD/iqV7fMdGQRnCUGYPj9Vm8/IKo6BSkIJ2vuObfoKrI3h56n+1/8uy\n82DofWlsZTr5XsuXYCTuXu1/3qCV77jl4bGR5b6tsaknsAeVnlWJa6Mse9wt/uf5joCWZojPEIYX\nv10NwLSFm/zSa9M62PevPz5yoSTFKKhQOIeOGnfwhQ8/6lr38v2u8ldql7wZ/PId9nhoq76mtmuU\nYysZKG/0B/7nf97pizXloeeZ/ufNelTuHm6kpUH9FtWvx+mstd9VlZv7S4tyiDPQuEXENxxYV5cK\nGCrFzn0xcAydIA5tnR+5UJJiFFRIQnSLT304uIcCkJYerBgCadjKX/E5OeNpuOZ/0OoI9/yhITyJ\nB/YA3D7tBtzhfz76fRg9Fa74KLhsZYhWQYSSPZDT/lo57+LR3j+wp5WWDrcvsf4uxorPEAVptanL\nlEIYBRWKUOO2aWnuiigt3VION8yFWxzBDZ1KQCtg8APwu8+Dr6+XDwcdCk26uN/36Gvc06OZQwl8\nuOo3hw4DoJ3dm+vtsAYMpUC9dTn+ZdKinIcKJTsEG5GEmkdycvhF1j4jO7r7ByoySbN6xIPug1GT\noqvDUKdJSzMKKhEYBRWSSk4seowGmnaGAsccRzvHkJ5WWMN+bfrBvSHCorc8DM55Hg49z5d22Xuh\n79u6X/ihtoYHQ3YD6HAC5Lms4xq7C0b8y9kQ3+ENc/3LdhoEf1zvOw/Vg/G89MfuCp4z63aatR/4\nR2vvUbCdB9u3j+Jf8sx/WL1YN/P2QK7/Idigo3Sfe9lagIjcKCJLReRnEXncTssSkYkislBE5ovI\nQEf5L+3yP9lbczu9rYh8ISI/isgCERke4pYGjM/7RGEUVCj6XB592WNusBRBJJy9hYws6HOFI9Px\nCBx2Hox0ODFt3jN0nTkFcMev0PIIf5k9PaFbf7Z6GqM/gDuXu1YBWEYgN8yBs/7tS8tr6l8mM8c/\nZpabMsltAj1HhL5Pt6HWvudZ1t7zN+kyJHSdgaRnRB5O9dCsW3CvbM+G6K5NMkTkJGAEcJiqHgL8\n1c66CsCOPjAYeFLE7w95saoeYW+b7bR7gSmq2hu4AHD88IZAzBBfYjAKKhQdB4bPdw6LnTou/NCU\nx3KuRS//9KGPOk7C9diieDh+Px1Of8p3fsFrlsl2tA9WqyOgaRcrLtbN8+Gc5yzl53QF1P9q/2sC\nreMA+l4Z/j69L4U/rIXm3a1zj4LyyBkL8/VAAuuMtXVl/LgWeFRVSwAcyqYnMN2RthPoG6EuBTw+\nNfOB2qm144TRT4khhis96xgn3wc//je6smO+grKS4DmTzHqW9d7WX8P3HKIZygpctNuwpbVVhUbt\nfeu+blkEpXuhUbvgckdeCu/f4J828E/udeY2sUKLiFjzbR48VnSe9jvfBEdcDBsXwIh/Qn5reCKE\nl4iRL4TvUTnnyu7fEd08V3LSFRggIuOA/cAdqjobmA+MEJHJQBugj733xHCbKCLlwFvAX9SKITEW\n+FREbgTygFNC3VRErgauBmjbtm2oYilNvUwTKDkRGAUVjuNugTb93fMqs14HQk/oX/ouzH8VmnV3\nuf/NMOv//F/o8SavibVFS6iX/9VfwnoXP3kezxHeNtoKKq+5/3AjWPNUh18QXMeh54aXydmDSnLl\nJCKfAwe5ZN2D9bw2Ao4G+gFTRKQjMAHoAcwB1gDfAh7zzotVdb2INMBSUJcCk4ALgRdV9UkROQZ4\nWUR6qQa7PlHV8cB4gL59+9beVZ9V4LqBnfj3lyvo1z7KIWVDTDEKKhyDHwidF02vJhryD/Z5iAi6\n/4PWVhu4+K3wVnUFbf2NRzycfK9l5HHI2dZ5Zj1rvVhnlw/6S96smmye38oz75XEqGq4nsy1wNt2\nD+gHEakAmqrqFuBWR7lvgWV2fevt/R4ReRXoj6WgfgcMtfO+E5F6QFNgMwYvBbnW/04tdsZQqzEK\nqqpUtgeV6nQJ+V4NT3YDGHCbf9pRY6ovj5O0dLhtMeQ2jVw2uXkXOBn4UkS6AlnAVhHJBURVi0Rk\nMFCmqr+ISAZQoKpbRSQTOB3wrHFYCwwCXhSRHkA9IIRpqcGQGIyCqiqBPuTqKmO+jt6iLt6cO8F3\n3LBV6HK1hwnABBFZBJQCo1VVbdPxT+we1XqsYTyAbDs9E0jHUk6eYF63A8+JyK1YBhOXa2B8c4Mh\nwRgFVVWSfC4jbrQ8LNEShKbXyERLEFNUtRQIirGiqquBbi7pRVgGE251/QIcF2MRUw5PmA2juROD\nUVCG1OOuVZVzmWQwhCCUeflhrQviK0gdxSio6jB6auyMJQyxI7dxoiUwpCj5OZnsKj7AKT2aJ1qU\nOoFRUNWhw4BES2AwGOKAZ3bOM01nIuzGBzMOYjAYDBHwBCz0zkUZ/RQXjIIyGAyGaLE1lHF9FB+M\ngjIYDIZKYvRTfEiIghKR8+xwARUiEtKppYistkMI/CQic+Ipo8FgMIjdVfLOQSVQlrpIoowkFgHn\nAM9GUfYkVd1aw/IYDAZDEIE9Ja+RhBnjiwsJUVCquhjMj2wwGGoXnh6UeXPFh2Sfg1KskABzbZf/\nIRGRq0VkjojM2bLFuBQzGAw1h/m2jg811oMKFzZAVcPEMPfjOFXdYPsa+0xElqjqV24F63JIAIPB\nUDN4FJFnaM94K4wvNaagwoUNqEQdG+z9ZhF5BytUgKuCMhgMhlgTNAeFWagbT5J2iE9E8uwga4hI\nHjAEy7jCYDAYEooZ4osPiTIzP1tECoFjgA9F5BM7vZWITLOLtQD+JyLzsUJXf6iqHydCXoPBULfx\njOyZIb74kigrvneAd1zSNwDD7eOVwOFxFs1gMBi8mHVQiSVph/gMBoMh0QQN5RlXR3HFKCiDwWAI\nwYAuzQA4q7cVkblhjjXoZIwk4oMJt2EwGAwh6NA0j9WPnuY9f+OaY5m5dDNZGebbPh4YBVUNtLQU\nLS8nLScn0aIknJJVq0gvKCCjUaNEi2Iw1BgdmubRoWmHRItRZzCfAdVg1ajzWdr7yBqrv3zXLopm\nfV9j9ceSlcOGs3LY8EpdU1FczN6ZM2tIovAUL1hA+d6ihNzbYDBEh1FQYSjfvZsdk1/3riIPpGTJ\nkhq9/69HHc3ayy+noqQkqvJlW7dSsX9/jcoUjvKdOytVftODD7FuzDXs//XXsOVWDB3GsoEnVUc0\nPypKSlg96nwKb7whZnUaDIbYYxRUGH7tfxSbxo5l/4IFQXmlhYXe47Ioff9VFBWx+cknqSgtrZwg\nFRVRFVt2/ADWXvm7ytWdQPZMnw5A2ebwf7/S1asp27SJiqIidrzxRsgPBg9aUYGWlbnmVRQVgZ23\n77tZVZDaYDDEizqpoLZPmsTi7j0o2xpdFA8tLw9KW3HKYO9xRVF0Q0Vbxz/HtueeZ+frU7xp+5cu\npfDmW8K+dLXcX0EVL1hARXGxa9niefOikiWQipISvzoPbNjAnhlfeM/Ltm4NqVjL9+6t2j137wZA\nMjNd80vXrGHPFz4ZCm+8kU333U/RV8HerkrXraNolqVwlp84kCW9DvXmFS9cxOLuPdh4330s7dOX\nbS++6M2LpOwMBkPiqJMK6reHHwFg1/sfBOV5XsLOl65khLclCfW1HkS5Va5i3z5v0qoRZ7Hnk0/Y\n9fbbqCqrzj2PXR8EyKWWgirbupVdUz9k9ajz2fzk31BVtjzzjF9vzsOuDz6gZOWq6OQClg86haW9\nj+TAb5vZ9uKLrDpvFIXXXWeJvWcPy44fQOH17kNiv/btF/V9ALa9MIFNDz/sPV87ejTltrJysvqC\nCym89jrvedG331n7H35A7V5lybJl7P/lF1YMG87ay68Agnu0q887D4Cdb7wJwO4Pp3nzyrdtq5Ts\nBoMhftQZK76yLVvY/emnZLZo4U3b/PjjNLnyCvbOnEnJylU0OGUQKwYPoeW4cZSu9r3cd771Nplt\n2oS0UAvXgyrftYttL0xg2/jx5I8YAYDac0r75v3oLVc063u2TZxI6fIVbLjzLvbNdgQQLi9Hy8pY\ndvwAb9Lujz5i/8KFFM+fz57Pp5NzuM/pxr45c9hw510AtH/rTTJbtSK9QQMkI4OK/fspnjePvGOP\n9ZfT7k0W3nQj++f7hjTLd+/m1/5HWTJ+/XXIdnrQigpKV65k5zvvkJaXR3aXLmQ0acJv4x6m3X9f\nJi0nh81PPBF03b65c2lw0kkU//QT5bt3kzdgAOU7drjeY/sLE6goKqLF3Xez8owzg+7vYXH3HtQ/\n+eSg6yXd911WtnUrGU2bRmyXwWCIPympoEpXrWLNpZdx0AMPkN2xA9temOD6UgRriGfdmGsA2Pn2\n2wD89thj3uEngJ2vv07J0qVIZiYVJSXkHtXfr47V519Au1f+y4Z77yMjPx+tqKD1P56h+McfWX/L\nrd5yuz/6CIAdkydTtmUL6Y0b+/ICek07p/iGAUtWr2bjn+7xyy/fto1i++u/oqiInW+84Wv/mrU+\n2UaeC0B6fj7555zDjsmT0eJiWv/rn2waN856OTte6iVLl/rdJ1ABFC9YwG+PPoaWlrJ/0SJy+vTx\ny1/S8xDSCgqocDGYWNqnLy3H/SUo3Wr/VDbed79XUUZi5+TX2Tn59aD0PZ986ne+d8aMoDIly5Z7\nj1eddTYdp01j05//DEC7lycBsPG++6OSw2Aw1BwpqaDcSG/a1PXlt6RHT++xx+9WhctwU/FPP5HT\nty/7FyxwNZpYc/El1rWNGlG+YwfLTxwYVEY9w4fbt7NvzhxIj26Edc0FF5LWoEHI/APr1/udb7zn\nnqAy5bt2sX3iRO/59kkvU7ZhI7p/P+XbfT0V3e9vMVj2229+56tHnQ8ZGWDPyxXPnRt0LzflZGVU\nsPGPf3LN2j1tmmt6Zakojc7isbYiIjcCNwBlWA6U7xKRLOBZoC9QAdysql/a5bOAfwID7bx7VPUt\nEckGJgF9gG3A+aq6Or6tMRjCk5IKKqtDB++XMECT311Jg1OH+Bk2uFESwdy5eM6csPlAyGGpQEpX\nRT8/BFCxZ0+lykdi3/fW+iqncoqaaOfcEkBOr16Vvia7o///C0DLhx6EvzwUK7FigoicBIwADlPV\nEjuQJ8BVAKp6qJ32kYj0U9UK4B5gs6p2FZE0wNNt/x2wQ1U7i8gFwGPA+XFtkMEQgTpjJJHVunWi\nRTDEge2TXk60CDXJtcCjqloCViBPO70nMN2RthOrNwVwJfCInVehqp5hhBHAS/bxm8AgEeMC1ZBc\n1BkFBdD87rvJ7tI5ZvVld+8es7oMsWHn68HzUilEV2CAiHwvIjNFxGM+OR8YISIZItIBa9iujYgU\n2PkPicg8EXlDRDxWQgcD6wBUtQzYBTSJX1MMhsjUKQXV5IrL6fjBB0h2dkzqa3777TGppy6Q0bJl\nokVwRerVS7QIfojI5yKyyGUbgTUk3wg4GrgTmGL3eiYAhcAc4CngW6w5qgygNfCNqh4JfAf81XMr\nl9u7LgoTkatFZI6IzNkS5aJ0gyEW1CkF5aHbvOCJ/aoQaM1XVTJaJf7lndGiBQWjRtVY/Q2HhJ//\nc9Lg1FND5jW67NJYiEO6vWQgw2FJmQyo6imq2stlew9LCb2tFj9gGT00VdUyVb1VVY9Q1RFAAbAM\ny/hhH77goG8AHueRhUAbABHJAPKB7SFkGq+qfVW1b7NmzWqo5QZDMHVSQUl6Omn5+dEVTgv9Jwrl\nAaGydJkxg/xzzomqbMtHHqHBkCExua+T+icMoOWDD5B/7siY1w3Q9IZK+L2L0rtDpJ5ww+HBzmtb\n2guEvcYsYX7fJORd4GQAEekKZAFbRSRXRPLs9MFAmar+opabjA+wLPgABgG/2MfvA6Pt43OBGWrc\nahiSjFr1dMaS/DPOiKpcTu/eIfNiOaeceXCriGWa33UXBWefRetnnib3mKPDls3qEDokgNu1aXn1\nAWjxhz+EvX/LceMAyGjenB5LFkeU2UN6GDN5gO6//Bw2v9FFFwKQ27s3WR06kNOnj3fBs3v5izj4\nb0/6pdXr2ZN6vQ6xBUq30nrUqnnECUBHEVkETAZG20qlOTBPRBYDdwPObubdwFgRWWCne8alXwCa\niMhy4DYg9A9vMCSIOqugWtx9V8QyPZYsJr2gIGI5Dy0ffSRkXqBxRlp9SyF4FuuK/SWfd9xx3jLt\n35jid42z59R2/PiwQ5UHjR0bJJtnUW3TMWNo98p/SW/m86CQ3sSSI71+fTp/NZMu333rL3/XrjS5\n8goKRp5D98W/0PmL4AWwVgXpIWU6+JmnXdNz+vZB0tJ8Rif2h7zTC0Tu0UfTeeZMGg4bRsepH9Du\nxYluVXnJPzP4A6T9W2+S1aYNAHlH9afdy5No9eijYetJJlS1VFUvsYf8jlTVGXb6alXtpqo97CHC\nNY5r1qjqCap6mKoOUtW1dvp+VT1PVTuran9VXZmodhkMoaizCira4bmWDz1I0xtuoPvC4MW5gdQ/\n/viQee1ffx3JzfWeN7/D+pBtMMh+CYv1U9Q75BBvmezOAUotxzehL5mZpOXm0tWxNqv9W2/Scdo0\nGgwZQk7vI+jw3nvevIKzzvIqQSSN3D59oMI3ouPsDWY2b+7n1qnD22/R7tVX/MqKrYg6fzWTJldd\nReevZtJx2od0+uSTkL2hhkOG0GDY0KB0SbeW4+UdbfXs9nz2GZ0++ZhWjz9Gy3HjyO7ZgwaDBpHZ\norldPj3s79djyWJyjjjC/95nnIGIkJaTQ7tXX+Hgv/+d3H79SMvLC1mPwWBILCm5UDda0m2vD/VP\nGcTez6f75bWf/BpgTaI3u+F6v7yOH00j3e4BAaQXFNB1luXItNntt7Hlyb9583L69iHr4Nak5ebS\nfd5cimZ9T0aTxpCeTlpeHg1POx2AzIMPtvatWpLdpQsly5Z5lYAHyQ62OEvL8ym9et26IRkZtLZ7\nKvW6daXRRRex68MPAcjt3599s2d7X/Tp+fk+Z6kS/K3Sctw40nLqUa9nz6A8D5nNm9P89tusk+bN\nvekdP5zK3q+/ZvOjj/mVb/33v7P4o48BaPP886z7/e+97fT04gCy2rUDoGDkORSMjG5+DqDTxx/5\nnXeeMZ20hvmk1/cpotwjay7IpMFgiB11WkEd/PRTbHvueVo//TRLDvH3QBD4Be4k2zG/0/71yYgj\n5HuTK68ku2NH8o491vrSz8ryuzbv6KO8x11n/+Dt1TQ8/TTSC/LJO+44Gg4dSum6dZZLIQfOHpQH\nv3kwl+G1FvfdS3N7OLPpddeSf9YI7zBXywcfYM0l1nRFpstC5soohkCyO3Uiq2PHIAUF0Pallziw\nYQPpDa15qaxOnQBofNllfso9Wg568AE23f9nmt18E1nt2/vlZbaKPLdnMBiSkzqtoPL69yevv2Uq\n3vmLGay/7XaKf/wxZPkm14zx6zkBfl7EwRp+ajBoUFT3F4cFmYhQf4DlrTy9oIAce+6r0UUX0XD4\nMHIOOyyoRxVUn4vRhoh4rd0kPd2rnABy+/al+8+L2Dd7TsxM5iPJA9b8j4c2z40n9yhLaadlZ5Pe\npAlNx4yJqn6P4USjUaNoMHhwSG/zBoOhdlKnFZSTzJYtaTtxAgc2bHDtTQA0v+WWOEsFB91/X43W\nL+npfr26WJNz+OEUnHduyHyPUvbQ9Zv/RV33Qff7PI4b5WQwpB5GQTlIq1eP7I4dEy1GStH+9cmJ\nFsFgMNRSjIJKAfJOPKFqXskNBkPKUpCbyYjDa/ccrFFQKUDbZ59NtAgGgyHJ+On+2HuciTd1dh2U\nwWAwGJIbo6AMBoPBkJQYBWUwGAyGpCQhCkpEnhCRJSKyQETecQRWCyw3VESWishyETHOLA0Gg6EO\nkage1GdAL1U9DPgV+GNgARFJB/4FDMMKaX2hiIT2uWMwGAyGlCIhCkpVP7XDTAPMwor6GUh/YLmq\nrlTVUqzwAiPiJaPBYDAYEksyzEFdCXzkkn4wsM5xXminuWLCUhsMBkNqUWProETkc+Agl6x77PDV\niMg9QBnwiks5N0duISN+qup4YDxA3759TWRQg8FgqOXUmIJS1VPC5YvIaOB0YFCIUNOFQBvHeWtg\nQ+wkNBgMBkMyI+66oYZvKjIU+Btwoqq6jseJSAaWAcUgYD0wG7hIVcPHBreu3QKscclqCmytqtxJ\nSiq2CZKjXe1UtVmCZUgqwjxbkBy/WawxbaoZonq2EqWglgPZgB0tj1mqeo2ItAKeV9XhdrnhwFNA\nOjBBVcdV875zVLVvdepINlKxTZC67UplUvE3M21KLAnxxaeqnUOkbwCGO86nAdPiJZfBYDAYkodk\nsOIzGAwGgyGIuqagxidagBogFdsEqduuVCYVfzPTpgSSkDkog8FgMBgiUdd6UAaDwWCoJRgFZTAY\nDIakpM4oqNrkGV1E2ojIFyKyWER+FpGb7fTGIvKZiCyz943sdBGRZ+y2LRCRIx11jbbLL7MXRycM\nEUkXkR9FZKp93kFEvrdle11Esuz0bPt8uZ3f3lHHH+30pSJyamJaYnBinq3EP1u2PKn3fKlqym9Y\n66hWAB2BLGA+0DPRcoWRtyVwpH3cAGvBck/gceAPdvofgMfs4+FY/gwFOBr43k5vDKy0943s40YJ\nbNdtwKvAVPt8CnCBffwf4Fr7+DrgP/bxBcDr9nFP+7fLBjrYv2l6on+vuryZZys5ni1bppR7vupK\nD6pWeUZX1Y2qOs8+3gMsxnKUOwJ4yS72EnCWfTwCmKQWs4ACEWkJnAp8pqrbVXUHVpiToXFsihcR\naQ2cBjxvnwtwMvCmXSSwPZ52vgkMssuPACaraomqrgKWY/22hsRhnq0EP1uQus9XXVFQlfKMnkzY\n3e/ewPdAC1XdCNaDBjS3i4VqXzK1+yngLqDCPm8C7FRf2BWnbF657fxddvlkao/Botb+Jin0bEGK\nPl91RUFVyjN6siAi9YG3gFtUdXe4oi5pGiY9rojI6cBmVZ3rTHYpqhHykqI9Bj9q5W+SKs8WpPbz\nVVcUVK3zjC4imVgP0Cuq+rad/Js9vIC932ynh2pfsrT7OOBMEVmNNQR0MtYXX4HtFDhQNq/cdn4+\nsJ3kaY/BR637TVLs2YJUfr4SOQEWrw3L5+BKrIk/z0TuIYmWK4y8AkwCngpIfwL/idzH7ePT8J/I\n/cFObwyswprEbWQfN05w2wbim8R9A/9J3Ovs4+vxn8SdYh8fgv8k7kqMkUSi/1fNs5Ukz5YtV0o9\nXwn/h4njDzccy2JnBVbQxITLFEbW47G61guAn+xtONY48XRgmb1vbJcX4F922xYCfR11XYk12bkc\nuCIJ2uZ8gDoCP9iyvQFk2+n17PPldn5Hx/X32O1cCgxLdHvMZp6tZHm2bJlS6vkyro4MBoPBkJTU\nlTkog8FgMNQyjIIyGAwGQ1JiFJTBYDAYkhKjoAwGg8GQlBgFZTAYDIakxCioJEZE9tr79iJyUYzr\n/lPA+bexrN9gSGbMs1U7MAqqdtAeqNRDJCLpEYr4PUSqemwlZTIYUoH2mGcraTEKqnaKmDVEAAAC\nNUlEQVTwKDBARH4SkVvtuC9PiMhsO0bNGAARGSgiX4vI+1hemhGRd0Vkrh375mo77VEgx67vFTvN\n80Updt2LRGShiJzvqPtLEXlTRJaIyCu2B2RE5FER+cWW5a9x/+sYDFXHPFvJTKJXCpst9AbstfcD\nsVeH2+dXA/fax9nAHCzXJAOBIqCDo6xnRXwOsAho4qzb5V4jsUIHpAMtgLVYMXQGYnk9bo31YfMd\n1qr8xlirzj2LvgsS/Xczm9kibebZqh2b6UHVToYAl4nIT1ihApoAXey8H9SK5eLhJhGZD8zCcgTZ\nhfAcD7ymquWq+hswE+jnqLtQVSuwXMS0B3YD+4HnReQcYF+1W2cwJA7zbCURRkHVTgS4UVWPsLcO\nqvqpnVfkLSQyEDgFOEZVDwd+xPLDFanuUJQ4jsuBDLXiyfTH8g59OvBxpVpiMCQX5tlKIoyCqh3s\nwQpP7eET4Fo7bAAi0lVE8lyuywd2qOo+EemO5Y3ZwwHP9QF8BZxvj8U3A07Acijpih1XJ19VpwG3\nAodXpmEGQ4Ixz1YSkxG5iCEJWACU2cMJLwJPYw0BzLMnU7fgC+fs5GPgGhFZjDWWPcuRNx5YICLz\nVPViR/o7wDFYbvcVuEtVN9kPoRsNgPdEpB7WF+JtVWuiwZAQzLOVxBhv5gaDwWBISswQn8FgMBiS\nEqOgDAaDwZCUGAVlMBgMhqTEKCiDwWAwJCVGQRkMBoMhKTEKymAwGAxJiVFQBoPBYEhK/h98taI2\nWZ66ZAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116097358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=coefficients)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Approximations"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class Posterior:\n",
" def __init__(self, num_samples=100, method='independent'):\n",
" self.num_samples = num_samples\n",
" self._x = None\n",
" self.method = method\n",
" self.sample()\n",
" \n",
" def sample(self, *args):\n",
" self._x = np.random.normal(0, 1, (self.num_samples, num_points, num_dims)) + means[groups]\n",
" \n",
" def __call__(self, coefficients, method=None):\n",
" self.predictor = np.dot(self._x, coefficients)\n",
" residuals = y - self.predictor\n",
" \n",
" method = method or self.method\n",
" \n",
" # Method 1\n",
" if method == 'independent':\n",
" ll = - len(y) * np.log(self.num_samples) + np.sum(logsumexp(-0.5 * residuals ** 2, axis=0))\n",
" # Method 2\n",
" elif method == 'joint':\n",
" ll = - np.log(self.num_samples) + logsumexp(np.sum(-0.5 * residuals ** 2, axis=1))\n",
" else:\n",
" raise KeyError(method)\n",
" return ll"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"rng = [10, 50, 100, 200, 500, 750]\n",
"independent = []\n",
"joint = []\n",
"\n",
"for num_samples in tqdm_notebook(rng):\n",
" sampled_posterior = Posterior(num_samples)\n",
" row_i = []\n",
" row_j = []\n",
" \n",
" for _ in range(10):\n",
" sampled_posterior.sample()\n",
" row_i.append(sampled_posterior(coefficients, 'independent'))\n",
" row_j.append(sampled_posterior(coefficients, 'joint'))\n",
" \n",
" independent.append(row_i)\n",
" joint.append(row_j)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x115c9fda0>"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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rr6qlf67Ppt4wnZYxQSJSkrAgYTLVQb/X9XVAX5t6w3RexgSJpkCkTcKqm0xm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\nCxLGGGNisiBhjDEmJgsSxhhjYvr/AV9nY0/AhvtQAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cd48b70>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1, ax2) = plt.subplots(1, 2, True)\n",
"ax1.errorbar(rng, np.mean(independent, axis=1), np.std(independent, axis=1), marker='.')\n",
"ax2.errorbar(rng, np.mean(joint, axis=1), np.std(joint, axis=1), marker='.')\n",
"# Analytic integration\n",
"ax1.axhline(posterior(coefficients), color='C1', ls=':')\n",
"ax1.set_title('independent')\n",
"ax2.set_title('joint')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Method 1"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sampled_posterior = Posterior(20, 'independent')\n",
"sampler = util.AdaptiveMetropolisSampler(sampled_posterior, mode='reevaluate')"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.19121192, -1.20503956, -0.56903666, -1.81105778, 0.2585696 ])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler.sample(coefficients, 2000, callback=sampled_posterior.sample, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:root:function values may not be interpretable in the 'reevaluate' mode\n"
]
},
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x10cd4eda0>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x115ce5518>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x116287390>))"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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hr9GyUnTX7quK4WjC55gx9+X2yEDnPHmC/8v/bNAsPG29W6zEEpZ/5rA2g7Sb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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cd4eda0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x1162305c0>,\n",
" array([[<matplotlib.axes._subplots.AxesSubplot object at 0x116560d68>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x1165839e8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x11658f8d0>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x119c63c18>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x119ca8d30>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x119cfdb00>]], dtype=object))"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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zkPAGTanFxtp92etmizIugbkG1WhLS5A6FU4ccPq2A2vW+EigCzSmXWVk3O1s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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1162305c0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(values=coefficients, burn_in=500)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Method 2"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"sampled_posterior = Posterior(20, 'joint')\n",
"sampler = util.AdaptiveMetropolisSampler(sampled_posterior, mode='reevaluate')"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.02048826, -0.41009819, -0.01136451, -0.51676237, 0.16462366])"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler.sample(coefficients, 2000, callback=sampled_posterior.sample, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:root:function values may not be interpretable in the 'reevaluate' mode\n"
]
},
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x11a1aa4a8>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x11a1a5160>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x11a1ea2e8>))"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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R9lqwLzd/ySvLX2FN0ZqwPueKkgWoOpn1x4kkhQgkmPAPJ93KupC/vZjLTx3G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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11a1aa4a8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x1187c9b38>,\n",
" array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11a426c18>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x11a46e240>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x11a479748>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x11a50a4a8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x11a550828>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x11a5a55f8>]], dtype=object))"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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35+R+vqQUdScVx3Y6Y+VyxKL3w0AnUzqeIFgzyU58uTV/36l3TXzLl3tWdU7Z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\nTkYOLJAArwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1187c9b38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(values=coefficients, burn_in=500)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.3"
},
"widgets": {
"state": {
"03813d69385342829891b7070f0527a1": {
"views": [
{
"cell_index": 13
}
]
},
"21c037fe6780430f8752be30be0495f8": {
"views": [
{
"cell_index": 10
}
]
},
"5ac09dd80b74495ba608cccb91e8e6a2": {
"views": [
{
"cell_index": 5
}
]
},
"d5cf412945c14f13b19f583b020b694d": {
"views": [
{
"cell_index": 19
}
]
}
},
"version": "1.2.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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