{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Poisson Regression\n", "\n", "Gaussian process models can be incredibly flexbile for modelling non-Gaussian data. One such example is in the case of count data $\\mathbf{y}$, which can be modelled with a __Poisson model__ with a latent Gaussian process.\n", "$$\n", "\\mathbf{y} \\ | \\ \\mathbf{f} \\sim \\prod_{i=1}^{n} \\frac{\\lambda_i^{y_i}\\exp\\{-\\lambda_i\\}}{y_i!},\n", "$$\n", "where $\\lambda_i=\\exp(f_i)$ and $f_i$ is the latent Gaussian process.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Load the package\n", "using GaussianProcesses, Random, Distributions\n", "\n", "#Simulate the data\n", "Random.seed!(203617)\n", "n = 20\n", "X = collect(range(-3,stop=3,length=n));\n", "f = 2*cos.(2*X);\n", "Y = [rand(Poisson(exp.(f[i]))) for i in 1:n];\n", "\n", "#Plot the data using the Plots.jl package with the GR backend\n", "using Plots\n", "gr()\n", "scatter(X,Y,leg=false, fmt=:png)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "GP Approximate object:\n", " Dim = 1\n", " Number of observations = 20\n", " Mean function:\n", " Type: MeanZero, Params: Float64[]\n", " Kernel:\n", " Type: Mat32Iso{Float64}, Params: [0.0, 0.0]\n", " Likelihood:\n", " Type: PoisLik, Params: Any[]\n", " Input observations = \n", "[-3.0 -2.68421 … 2.68421 3.0]\n", " Output observations = [3, 3, 1, 0, 0, 0, 0, 0, 3, 4, 7, 3, 1, 0, 0, 1, 0, 3, 4, 4]\n", " Log-posterior = -65.397" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#GP set-up\n", "k = Matern(3/2,0.0,0.0) # Matern 3/2 kernel\n", "l = PoisLik() # Poisson likelihood\n", "gpmc = GP(X, vec(Y), MeanZero(), k, l)\n", "gpvi = GP(X, vec(Y), MeanZero(), k, l)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of iterations = 10000, Thinning = 1, Burn-in = 1 \n", "Step size = 0.100000, Average number of leapfrog steps = 10.029000 \n", "Number of function calls: 100291\n", "Acceptance rate: 0.801400 \n", " 4.052686 seconds (24.20 M allocations: 2.026 GiB, 8.23% gc time)\n" ] } ], "source": [ "set_priors!(gpmc.kernel,[Normal(-2.0,4.0),Normal(-2.0,4.0)])\n", "@time samples = mcmc(gpmc; nIter=10000);" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Sample predicted values\n", "xtest = range(minimum(gpmc.x),stop=maximum(gpmc.x),length=50);\n", "ymean = [];\n", "fsamples = Array{Float64}(undef,size(samples,2), length(xtest));\n", "for i in 1:size(samples,2)\n", " set_params!(gpmc,samples[:,i])\n", " update_target!(gpmc)\n", " push!(ymean, predict_y(gpmc,xtest)[1])\n", " fsamples[i,:] = rand(gpmc, xtest)\n", "end\n", "\n", "#Predictive plots\n", "\n", "q10 = [quantile(fsamples[:,i], 0.1) for i in 1:length(xtest)]\n", "q50 = [quantile(fsamples[:,i], 0.5) for i in 1:length(xtest)]\n", "q90 = [quantile(fsamples[:,i], 0.9) for i in 1:length(xtest)]\n", "plot(xtest,exp.(q50),ribbon=(exp.(q10), exp.(q90)),leg=true, fmt=:png, label=\"quantiles\")\n", "plot!(xtest,mean(ymean), label=\"posterior mean\")\n", "xx = range(-3,stop=3,length=1000);\n", "f_xx = 2*cos.(2*xx);\n", "plot!(xx, exp.(f_xx), label=\"truth\")\n", "scatter!(X,Y, label=\"data\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Alternatives to MCMC\n", "\n", "As an alternative to MCMC, the practioner is also able to compute the approximate posterior using variational inference. This is done through the approach described in [Khan et. al.](http://papers.nips.cc/paper/4535-fast-bayesian-inference-for-non-conjugate-gaussian-process-regression). An approximate density $$q(\\mathbf{x})=(2 \\pi)^{-N / 2}|\\mathbf{\\Sigma}|^{-\\frac{1}{2}} e^{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol{\\mu})^{\\top} \\boldsymbol{\\Sigma}^{-1}(\\mathbf{x}-\\boldsymbol{\\mu})}$$ is used to replace the true posterior.\n", "\n", "Syntactically, this can be found in a similar vein to mcmc by simply using the following statements." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of iterations = 1, Thinning = 1, Burn-in = 1 \n", "Step size = 0.100000, Average number of leapfrog steps = 7.000000 \n", "Number of function calls: 8\n", "Acceptance rate: 0.000000 \n", " 1.517399 seconds (1.09 M allocations: 471.231 MiB, 6.14% gc time)\n" ] } ], "source": [ "@time Q = vi(gpvi);" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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iTU1vQ1kqs/WiCKEijdZoa/UGuNs3D4To8ccfZzuExMLBRFgMd7UgztT01JelMJ4IJUJJbnIO9JeJA3PmzGE7hMTCwURYVAeJEMSXOlNDWWpRDA5UlloE95EAhItziTAjKR0h1O3sYTsQAOiBCW40NxenFMbgWGWpxXW9uhgcCIB4wrlEiBAqSSmqNcHFDOKE3mpMT0pjbgWZ/kpTimtN8EQIQHi4mAhLU4rgrhbEjXqTriQmj4MIoZKUAr3FGCC8GcgMosfrJQY5gpOJMLWoHp4IQbyo69WVpsSigRAhJBPJMpPS9RZYj4n3QllcMJR9QCg4mQhTiuogEYJ4UWfSlcakp0xQaUoh3EfGgVAWFwxlHxAKbk26HZSTPNbisdq9Duam6gcgZupNjSWaGFWNIoRKUovqTI1XFEL/+6j4Ar4NtVticyyJUHxj2TX9tzz11FMIoXvvvVen0/VfRzD41+C8M337IIQ2bdr09ddfd3d333bbbbfcEqPVo+IJFxOhgKKKNNoGc9O0zElsxwJAVDqd3WKBKDWGS2yWaArXVm2M2eHiFUGk29Ubm2NJhZIBW5599tng4oLl5eX91xEcbh+3271y5cq6uroHH3wQEmEEuJgIEULFmsJ6kw4SIeC7epMuNgMn+pSmFkPLQvQkQsnvZ/yW7SgQGmqNwMF+/etfI4RKS0uDiwWCcHGxjRAhVJJSWG9qZDsKAKLVYGqKZb0oQihFphYJRF3O7lgeFDBnQBZ0Op2D9+HFmn9cxt1ECDNFgThQb2qM2diJPiWawnpTU4wPCmjXt8g7QkgsFp84cYIQsnnz5uH2ARELOxEGAoH//Oc/CxYsePDBB7u7mbrrLNJoYTgUiAMN5qYYV40ihIpTChqgQoXngosL9v161113PfPMM8uWLUtJSRluHxCxsNsI169f73A4PvroozVr1qxevfrhhx9mIiyZSJYuTzVaW7XqPCbKByAG3H5Pl7M7TzU2xsctTik4YDwc44MCej3//PP9f124cOHChQuDP19xxRVD7oMQglUMIxP2E+GuXbsWLlwok8nuuOOO6667jomYgopTCuqhdhTwmc6sz1flCilhjI9bpCmAlgUAQhf2E2FnZ+fu3bsfeeSR7Ozsv/zlL0Pu4/V6FyxYMHj72LFjn3322QEbfT6f1WoVCgd+WYyVjqlsr56hmhxuhDw13HlINPF0Hs60VuQpckwmUwSvjeY8qLCyzdbe0dMpEYgjeDmn+P1+s9ksEjHbv93j8TBaPqCF3+83mUzhfh5UKtWo11HYHy+Hw0EIeffdd7/88stXXnnltddeG7yPUCi8/vrrhwxILpcPjEAk8vl8g7eXpZd807Rr8PZ4Ndx5SDTxdB6MrvaS1MLI3kuU5yE3eWyXryfGHVaZ4Pf7PR4P058HphMtoIVAIJDL5eF+HiiKGnWfsP/5NRrNTTfdlJaWdv3112/YsGHIfYRCYehNuEKh0OPxyGSyAdvHZ5a+fWrV4O3xarjzkGji6TzorYZLtb+K7L1EeR5KUgsNztbJWRMiezl3+P1+qVTK9OeBxhqIr7/+eu3atXV1dQKBYPLkyYsXL77ooovoKjzBCQQCmUzGxOch7DbCWbNmbd++3ev1btmypaysjN5o+stWjrF7HXavg7lDAMAonUVfpClg5dBFmgKdWc/KoROW2Wy+6qqrHl/2VF7HuN8WPfg/2t8n12fedePdS5YsgapXjgs7Ed59993Hjx9fuHDh8ePH//znPzMRUxCFqAJ1fqMFLmbAS93OHiElTJGpWTl6kUarg/4yMeTz+X79618XOSa+vnDVVZOunzBm8sSsqTdMu/XdRZ/aTniXLFkSTeGw0BLTwk6Eqampy5cv37Rp0yuvvJKTk8NETH0KNflwVwt4SmfWF2m0bB29GJ4IY+vdd9+Vd6tvmzUw4QkFwgfnPFbxXc22bduYOC6sxEQLjs4sE1Sk0cLFDHiqwdxUzFK9KEIoPSnNj/0mt4WtABLNe++9d+uMoTtGUIi6Zfrt7733HhPHhZWYaMHpvlJFmoI9zQfYjgKASDRZmqdlsjn4p1Cd32jWp2RNZTGGBBEIBE6dPFVy8bjhdhg/ZvIHu98IvUCr1frGG28cPnxYqVTeeOONwY0HDhxYvXp1R0eHRCK5+eabFy5cGFyJqby8vKioqP/2KN9OAuL+E2ETQYTtQAAIG7tVowihQo0Wmthjw+fzUUggoIb9OhULxS6XK/QC33zzTYTQhx9+uGLFirq6uuDGVatWzZ07d/369S+88MIHH3yAEAoOyy4sLBywHYSL04lQLVVJhJJuZw/bgQAQHkxws7WlgNUJAqFlIWZkMlnGmPQue8dwOxjNhpKSktAL/PHHH++9916FQiGXy5cuXRrc+Pbbb0+ZMmXHjh3r16/vP9f2cNtB6DidCBFczICfWmxtqTKNTMTmaMgijbbR3MxiAAllwYIF26uGXdF+Z/WWISfbGk7/MeB9P//973/fuHGjWq2+++67++883HYQOs4nQrW20QIXM+AZ1utFEULB0UfQshAbjz322Ff1n9d31Qz+02H9wUrXicFLzI/gvPPOW7FihdPpdLlcfb1sjh07tmjRogsuuODIkSMIoUDg7OI8P/7445DbQei4nggLNPlNcFcL+KaRvaH0fZIlyiRxUqeji90wEkR2dvYn6z5+YvtD647/1+GxBzeanL3vH3zz9WP/+OLLL8KaFez+++8nhNxxxx3Lli2bOvVsd6ff/va3Dz/88D333GO1WmfNmrV8+XKE0Hnnnef1egdvB2HhdK9RhFChWvtF7Va2owAgPI3m5kvyf8V2FKhIrdWZm8coMtkOJCHMnj37+x/3P/3007f+90o5UmCCscR/+x23H3riUHp6elhFqVSqxx9/vO/X4LpL119/fd8czn1dQwev1hTVe0hUnE+Emny91YgJEYQwcSoAHNFoab5L/Ru2o0CFmvwmS/OFObPYDiRRaLXaVatW+d7xtbS0iESi7Ozs+FhHJe5xvWpULpJppKp2x7DdsQDgGh/2dzg6c1XMzrsUikJ1PjSxx55YLC4oKMjNzYUsyBdcT4QIOo4CvjFYW7IUmWIB+9UthRptI1w7AIyGB4mwQA39ZQCfNFqaC9T5bEeBEEIF6rxmqxETzHYgAHAaDxJhoQaqdwCfNJmbCzWcSIQykUwjVbc7OtkOBABO40EiLFDnN0EiBPzBnSdCBC0LAISAB4lQq84z2loDBEaJAn5osjQXciYRatV5TRYD21EAwGk8SIRSoSRVltJqa2c7EABG5w14u5zduaqxbAdyViE0sQMwGvY7toUiOBwqjwP90QEYWbO1JVuZJaS40m++QJP/WfWXbEfBAwaD4fDhw2xHAYZVX1/PXOE8SYTq/EZL88V5F7IdCACj4FS9KEJIq8oz2lowwSMsEgQWL1587733fvfdd2wHMixCCMY47gcmtjs60+WpomGGHl122WUMHZcfiVCrzjvUeoztKAAYHad6yiCEZCJpikzTZu/ISc5mOxbumjFjBscfB/1+v8lkysjIYDsQBnkD3us+v/3rhWtHqFBhaJ0pftwkQsdRwBd6i4HdZQgHK1RDx1HAA3qrMUeZzUqzAj8SYb4q12hrhXHBgPuauJcIC9R5eug4CjivydLM1rXDj0QoE0lTZSmtdug4CjjNF/B1OrpykrnSZTRIq87TWyERAq5rshi0LDUr8CMRouAqo9ALHHBbs61lrDJLJOBWj4YCGEoI+IDFZgUeJUKo3gFc12QxaDlWL4rOzjjaggksVQ84jcVmBd4kQqjeAdyn51iX0SCZSKaGtcwAt7HbrMCbRAjVO4D7ONhTJgguH8Bx7DYr8CYRaqF6B3AelxMhtCwALtOz2qzAm0Qoh+odwG1+HGi3d+RyrMtokBYSIeC2JouBxWYF3iRChJBWnau3GNmOAoChGW2tYxSZYqGY7UCGAFWjgOP0FoNWncvW0fmUCGF+GcBl7NbtjKxAna+3GgiClgXAUVA1GiqtKldvhSdCwFEszosxKoU4KUmc1OnoZjsQAIYQIIFWe3see80KfEqEBep8PTwRAq5it25nVFpVLgxAAtxktLZmKjIkQglbAfApEQbbCKF6B3CT3mrUqjj6RIjOtixAIgRcpLcatSo2byL5lAiTJUqZSNrt7GE7EAAGwgQbba35rF7MI4MRFICzWF+zhU+JEJ3tBQ7NhIBz2uwdKTKNTCRlO5Bh5UOna8BVrM9NyLNECL3AATdxdih9nwKYpBBwFes9rnmXCPPhYgYc1MztBkKEkEaqphBlcpvZDgSAX8CEGNhuVuBZIsxX5UI7B+AgLo+d6APzywAO6nB0qqUquUjGYgw8S4QF0EYIOElvMXJ2NH0faFkAHKS3sj/uiGeJMEWmwQSbPRa2AwHgZwSRZquRy11Gg7QqaCYEnKO3GAvYblbgWSJECOWrc5rhoRBwSbezRy6SKSUKtgMZBczWCzioydIMT4RhK1Dnw0RrgFN4US+KYCgh4CS9xahlezlr/iVCrSoXpt4GnKK3GrhfL4oQSk9Kc/ndDp+T7UAA+JneamB3WhnEy0QI/WUAx+gtRu53GUUIUYiCfteAU3pcJrFArJImsxsGTxMhXMmAQ5oszbyoGkXB+WWgZQFwButD6YP4lwjHKDJsXrvT52I7EADOamZ7yuDQQTMh4BQu1IsiPibCYPVOM9zVAm6weKx+HEiVp7AdSEi0KkiEgEM40tGMf4kQwfwygEs4vgzhAPmqHBhTD7iDI1MyidgOIBJaaOcAseXDZG0D6fUQAUVJhUiAkESARAIkFqDqLgMlyP3GiFOl1Ix0SkixHeuIcpKze90mT8ArZW8RVAD6sL4SYRAvE2GBOm+bbhfbUYBEgQnZ0EgarMEVoQeuC13fY5SKcw92EITID53U/FyqTM3dZCigBGOVWQarsSSliO1YQKKzex0evyctKZXtQPhbNQpPhCAmCCGbm0mVeWD+6+PwGpKkZ29pe9zk43q8phZ3uobdn3X5qly9tYXtKAA4O8sohdi/ceRlIsxJHtvp6PIFfGwHAuLf9hZ0vHukrOb0GhWSX9Tt6GxkRRXZasDuABfTIQxAAhzRZDFwZPEyXiZCkUCYpRxjtLWyHQiIc7tb8cEOPMIOGLu9AZtUlDlge4CQQ53kP2fID50YE26lQxhBATiimRtdRhFPEyFCSAu1o4BhP3bivW2j5DCHtyVJnE1RQ9ftOP1km4G8W0Oa7RzKhVp1Hlw7gAuaONPjmreJEO5qAZNO9pCtISQLp9egkI5yS9vqIB/Uko1N2OGnJ7Yo5SWPbbW1BUiA7UBAotNboWo0OlC9A5hTYyZf6DEJoUrT4TEmSXNG3Y0QcrKHrKjCRgf7j4YSoSQ9Ka3V1s52ICCheQJek9ucrRzDdiAI8TcRQvUOYEiTjaxrxDi0hOX0GhWSUG9prV6yqpYcG7HrTWxoVXD5AJYZrMaxyiwBxYkcxIkgIpCXnGO0tWIyUkcGAMLV7iRrG7A/5I+VwzOwy+jI/Jh8qceb9Zjd/qRaNczNBFimtxgL2F6GsA9fE6FMJNVI1e2OTrYDAfGjx03+W0/cIbedERLw+LtlkuxwD3S0m6yuxTYfa8kQ+poB1gUHEbIdxVl8TYQIoQJ1PsyaCOhi85E1ddgeTnJyelulogwBFcn0TM128k41YavJUKvOh9WtAbv0FiN3lrPmcSLMV8MaFIA2O1qIxRveS/rPKROBYJPh0S4WcqFWnWuwtpBB08UBEDNNlmaoGqWBFtagADQxOsjp3rBf5fQYFVEkQoSQH5PNzSw0GSrESUkieZezJ6ZHBeAnARJos3fkJofdrMAQPidCdR5UjYLoEUK2G0kogyUGcHpbksQ01O0c7SararAttjMGatV5UDsK2NJia89ISpdwZgkUHifC4FBCqN4BUTpjQpHN/OLwGKJ8IuxjcJCVVQFzmHWz0dCq85otMPU2YIeeG8sQ9uFxIkyWKCVCSY/LxHYggPWAqZIAACAASURBVMd8mHzbGkkWJIQ4fW0Kyeij6UNk86G1DdgXqwFBBeo8vRUqVAA7OLIwfR8eJ0IE88uAqB3oQGZPJInQ7e+QCFUCgYzGYNqdZHNzjDKhVpULLQuALXqrgTtdRhH/EyGMoACRs3rJ9x0RVq07PMakcIbSh+hUD/mxMxa5UKvOh5tIwBa9xcidQYSI74kwHzqOgih820q8kfbXdHpGn247Mt8Ykd7GeMt3ikxNEDF7LEwfCIABCCIGWws8EdIGqkZBxNqc5FRP5PnG4Wuhq6fMAAFC1jViq5fxXKhVQb9rwIJOR5dSrFCIk9gO5Gf8ToRaaPAHkdpmjGrBXKfHkBTydNvhsvvQej3F9OBCuI8ErGiyGDjVUwbxPRGmyVP8OGD12NgOBPDMmV4SZfWjw2OkscvoYEYH2tMpZq58dHZRT5ibCcRak8XAqbETiO+JEAWbCeGhEITDj9HOlqg6pHh9PUKBVCRU0hXSkI72Co4zuWaTVp0LY+pB7OnhiZB2BTC/DAjTgQ4c5dB15hoIB9hiwK2MTcxdAB1HARv0VngipJsW2jlAOOy+yIdM9HG4m0Nfjzcafow+ayROPyOFZySlufxuh8/JSOkADENvMWpVkAhpBU+EICzfthJPyCsODsfhZWQQ4ZDMHvK5DuOoevYMjUJUnioH7iNBLHW7ekUCkUqazHYgvwCJECSQdic6QUerm8PL1CDCIelsZE8bIxWkcPmAGONgAyGKg0SYqchw+BxQvQNCsc2IacknTo+RubETQ9rXjipN9OdCaFkAMcbBLqMoDhLhT9U70AscjKLSRJromLHF67cQRCQidfRFhY4Q8oWedLtpzoUw9TaIMb3FwLUGQhQHiRCd7fwGvcDBSPwY7YhuyEQfp8+oiFUDYX+eAFnfiP20TkRaoM5vNMO1A2JHD0+EDIF2DjCq7zuwyUNPUczNMjqqNif6xkjnQ2GWYozZY3X73TSWCcAIoGqUKVoVVO+AkVi85PsO2kpzeAyxGTsxpMNd+GQUU6QOIKCo3OSxeiu0LIBYsHisARJIlaewHchA8ZAICzWwGBMYyTfGyFeZGMzhNbL1RBi0pRl3uWh7O4Xq/CaoHQUx0WhpLlDnsx3FEOIhEWYpMk1uC1TvgCHprITe/pYOjyHiNkKP3dKlq/R7XNEE4MVoXSNta9lDywJgiNPprKiosFqtfVuibyA0mUw1NTUeD03tHD+JMBE2NjZee+219IYSMQElgOodMKQAIVtpbVTzB+wB7BGLU8N9obm16ZM/Xf/afO3W+296eU7m5ufvc1tNEYfR6UJf07SWvVYNs/UCmvX09CxZsiQjJeO6S28Ym5Fz4403GgwGhFBTFE+E1dXVc+fOLc4vWXzDklRN2kMPPeRwOOgKOJJEaLfbly9fTntOjgZU74Ah/dBBaKxFRD8NpacQFdarfC7H6vvKf+XL23zvd2sWb9x0z66M6o5P/3oLiWK+mOM95AQdjYVaNbQsADoRQq6//vquw5aN9+xas3jj5vv2KlvS5s6d63a7I+4p09PTc9lll030z/zqvn1rFm/8bMm2Y1+dXrx4MV0xh50IMcbLly9ftGgRXRHQAqp3wGB2H9rXTnOZkfWUqdixrlScdfeFvxcLxQghhUT5aPkznrq61orD0QTzVTNuj3omidzk7B5XrycQ3TTkAPxk3759zZXGv8x7OkmiQAiJhZJ7Zz+U5FRt2LAh4kS4atWqyZrpt85cLKAECCG1TPPUVf/4duvu2tpaWmIWhfuCTz75JDc39+KLLx5hH4/HU15ePnh7bm7uyy+/PGCjz+ezWq0CQVStlWnClBNtZ3p7e6MphF20nIc4QON52NwiMtlpPp8WR6NUnOVyhdfI11p76pycWf23iIXiydnTWqpPpBZPGfIlGGOPx0NRozx6rq5Aiwu8UmFY4QyUJc88bagoUmmjKoUZfr/fbDYLhdG9Q/7j0Xn48ccfp4ydLhT8ItTpubMO/njQfaFb4KZ63WF/UR87dmzAFSQTy8ePmXTo0KH09PSRX6tWq0c9b+ElwmPHjh0/fvyll14aeTexWPyHP/xh8Pbk5GSFQjFgo8/nCwQCg7eHpSyjeHXNp1EWwi5azkMcoOs8NDtQvYuSSGgJ6mfuQEu6apYkzHJlimSLe2DVvcVlzlWqhisqEAhgjEc9kJ2gvSbxjdGlsEJNfqeve4piYlSlMMPv9/t8Prgu+HIeXH4kV6Va3ZYB281uc5Iso0CdF9lbUKvV5ibzgI0WlyktLW3UAkO5qw47EZ48efLKK68M/lpeXv7qq69Onjx58IGvv/76EMsUCAQSiUQqlYYVyQCFEq3JYyZCJBNFVQ6LaDkPcYCW84AJ+VZHhEL6J+d0eVtUcm24N+Zls6/+8tMbF5+/TC3TBLc09TRUdFVcct6c4YqiKMrv94dyoGobOm2lZmVE/uxblFrQ4mjj5mdPKBTCdYE4fB48AdThIq1O0uZErQ7S7aGsefOOt/3ZYNLnpZy9QTM5e/fVf/vwuU8LU1Bkb+Haa6+9b+3vbp1xp1ycFNxS2X6q09t2ySWX0HJOwkuES5cuXbp0afDn8vLyHTt2RB8BLYIdR5utxrLUYrZjAew73EXanfRnQX/A7sduiSgt3BfmTjm/6Lrf3L/2jkWzfpujyavrrPro6KrL/vi8InUMLYFtM5IcBclOCq8LT58Cdf43ul20RALinstP2pzobOZzkkETNpHkzJyL73/6jyvvXjTzrpKMcUaT/qMj749fsOS0XKywZ71eEbgwUzAjY7RK/1+6+uqr51x36X1r77ht5l2ZyWMq28+sO/nh6yteVyqVtLypsNsIOatAnd9kaYZECBx+tLuVkUWLIusyGnTlw6/oZl+97euPLI270/LLblm5LatsGl2B+TFapyPLJiCZMJLYCtT5jTBbL/ilAEFWLzJ5icmDbD5k8xKTB5m8xOylRu3tfP5tf8w/Z/b+DSu/1K3WjC2Y++L7hefOOWF4KkN5brcbbW7GR7rR1XmCPGUYH9fVq1d/8cUXn3322XeGbVOmTvn+nf3jx4+P7i3+LPJEyJ3HwSDoOAqCdhqxO+qld4cU5eRqRefPKzp/Ho3x9NfrIZv16JaiSBJhX8dRqZDuNlXAKw4/2tOKO1zI5CF2/3AJL6S7zOwJM677f2//onDPz7PVtznR+zV4RgY1d6wgKeQsdP31119zzTUmkykjIyPU14Qmfvoowjz6ACHU6qRndN2QHB6DQsa5+YL7VJgifO8CSpCjzG6GKSkSW4WJvFmJD3eRZjux+VA0g1wH8wdsmHgl4p+bFQhCR7vIaxX4h06MaT1WBOInERZq8pugeiexEYS2NDN4STm8zQoJF2dK7PN1M+6JaM3CAg3cRyYum498qsPrdNjhY+rqsQ9Tm+Lyk20G8k41MTjYzIXxkwjHKrN63WaYcTSRHesmLUxeTg6PQSFlYSXC0Hkx2tBEAuHfDBSq4T4yERFCTvaQNytxFa3z8Q7m8DYnDT9VfZuTvF9DNjZhO2OZeGTxkwgFlCAveSwsVZ+wXH70LU1L7w7Jh20B7Imgy2iMtThIBPPpQMtCAur1kDV1ZGMTdvkZP5bDY1BKR6pNCabk1yvwD510rhUTovhJhAihQg10fktcu1qJk8nr2eE2KKX5kXUZjbHv2nC4FU3QspBQMCEHO/BblbjRFqOU4/CE1KzgDqBtBvzqGbyzBVtjOOtfnCVCbaNZz3YUgAWtTnK0m9lL2ultVox4S8sdmKANjcQTTtdZaFlIHL0etLqWfGMkdK3kFQqHxxD6Kp4uP9rfTv7vDP64HhvssUjVcZUIYThUYsKEfNVMmO54Zvc0s7seb1hMHvK1IYzvOQElyFflwACk+IYJ2deO36zE+phklz5ev4UgLBGFtzA9JqTWQt6rwe/X4EoTsxd4/AyoR9Dgn6gOd6FW5rucOdzNGcoLmT4KjU72kBIVmZIaal1ugTq/0awfn1bKaFSALWYP2aQnTbGqC+3P4dEro+hu3WwnzXaSIqVmppNpGkbij6snwixlps1rd/iiXpkG8IfNh3a1xqKKx+E1KDk8iHBIW5qxJeSGliKNVgf3kXHqZA95qwqzkgVRcNyRLNpmBZOH7Gwh/6lERhf9aSuuEiGFKK0qDzq/JZRvjDisxrDIeP0mhCixUMP4kWjlDqANTaGOVi7UwOrWccgdIBsa8camWFwmwxm1y2joPAFk89HfYS2uEiE623EU+sskigYrOdMbi5vc4CyjMTgQ7fQ28n1HaIlQna+Daye+NNrIm5X4VEyukRE4PHqOz0QRf4lQq4OOo4nBj8lWQ6w6f7ub6bqljb3drcQYQhtqpiLD5XPZvPYYhASYFiBkTxtZUxvTQQhDIojYPYYkbjcrxFsiLFLDCIpEsa+ddEc0nVgEHPwZOzEYJmhDI/aMNkiZQlSwv0xMggIM6nKjd6vJnlbM8pMgQgghj69bJJCJBclsBzKSeEuE8ESYIHrcodb40cLublJIC2J2ONr1etB24+inC6ak4DtCyNFusrIq0MbAepyRcXibFVIt21GMIt4SYZo8BSFkcpvZDgQwa4uB+GM1HJgg4vAalfxsI+xztJuMOp9kEdxH8lmAoA1NZLMex3Kk/KgcHh7UpsRbIkTwUJgATvUQnTV2N7xuX4dYqBQKkmJ2RIZ8ocfmEVuMCqFlgbc8AfJJAz7Ndr+YwezuZmUUq3jGRhwmwiJNPiTCOOYJoB1MTq49GC9uaUPhDqDPdXiEtSmKUwrg2uEjmw99UIvrLZzLggghh7dJIStgO4pRxGUiLIC72ji2swXbfDE9osOjV0i43sgRIqOD7G0b9utSLVWJheIuZ3csQwJR6nSRd6sD7ZycR4SggMvbliTh9OJlKC4TYaEaqkbjVquTHI35t7TDHSdPhEH72ohu+BlGoJmQXwwOsqqWhD5/UIw5Pa1SUbpQIGU7kFHEYSIs0mibLM1MT8EMYg8Tslkf6jwpNLJ59cmywhgflDkEoQ2NxD7MU3WRBmpHeaPKTFbXYqefu991dq9eyfkuoyguE2GSWK6Wqtrs4S9OCrjtxy7SFvP6H4J9Hl+nXDI21gdmkt1HNjVhMtQtBTwR8sUPnfizBhyzvtORcboNSXyoTYnDRIjO3tU2sR0FoJPdh/a0snBch88oE48RUHG1TgtCqN5KDnYOlwibYh4OCAMhZIcRbzPwoNbL7mmCJ0LWFKcUNMDFHF+2GrB7tLlRmGB3Nyn5PJR+BN+2kJZBU68VqvMN1hYf9rMSEhiVH6PPG2M6m0Q0IBGyqUijbTA1sR0FoE2NmVSMNhicIXEzdmKwAEHrBy1kLxFKxigyjTY2nr7BaNwB8mEdZutaCFcAu3wBq0ycxXYgo4vPRFgMDf5xxBMgX8dqcu3B7J64fSJECPV6yJf6ga1MRRqtDu4juccZoFbXkhgvLh8Nu6dZIcmjKPpXTaJdfCbCPFVOt6vX5XezHQigwbctxOJlMRHqlTIe1O1ErMJEjnX/4vRCywIHWbzoE72EOzOIhsLhaeT+UPqg+EyEAkqgVeXCCr1xoMVBjrA3vNsXsGDik4rSWYsgJrYacFe/m8ZiTSG0LHCKyYPW1JNeLw8erfqzufV8WbwsPhMhQqgopUBnbmQ7ChAVTNDmZhYGDvaxu/XKeJlTZgQ+jNbpsO+nRXuKUwrq4drhjE4Xer8mYPKwHUf4HPxpVojbRFisgeod3tvfjtmdOMruaVTG0VD6EXS6yHbj2Z/HKDI8fo/FY2U1IoAQQi0O8kFtIMZzCtKCIOLwNEMiZFmxpqAeqnf4rMeNvmtnuUXE7tHHa5fRwQ534aPdBCFEIQqWcOGCeitZVYtd/BzJ4vZ1CAVJIqGS7UBCEreJsCSlUGduIohPbcugDyFki4H9WTPs7qZ4mlxtVF/pz3bNL9YU1JugdpRN1WaytoFwamXBsDjcTck86SmD4jgRqqTJcpG8w9HFdiAgEsd7UCxXHBwSIQGXrzVxngjR2WlIcb2FlKQUNEAiZM/JHvKZDvsxj+/jbR69UlrEdhShittEiBAqSYG7Wl5y+NGOFva/Ahxeo1ScKaAkbAcSUwGCPtVhpQya2FlzqJNs0hM+J0GEggNw+TPuKJ4TYXFKYb1Jx3YUIGy7OsUuDkyob3fr+NLUTy8fRj/0aPVWox8HRt8b0CdAyI4WstUw9Hzo/GJ3N/Lo8onnRFiiKYT+MrxTb0VVFk58LO0ePY8aOejl9oslosyKbgPbgSSQdid6r4Z8387bVsF+/NjpC1hk4my2AwkVJ75xGFKSUgjtHPziDZCtxtF3iw27p1EpSaCeMgMkibX/rdU5+NllkV98mOxsISurceugOdB5yuFuUkjzeTG5WhD7ibClpaWiosLppG28WCAQqK+vr6yszJRlmD0Wu9dBV8mAad+2EjNn1to2m+oczTZHbwfbgcQaDvh79DX+bkmrueHjeuyNh0cU7mqykberyP52NieOQAj5Pa6OutOWdnpm47J5dDzqKYMQYnOVtSNHjtx33336GoNGntJub1l2/7LnnntOLpdHU+b69ev/9NCfsB2JBGIHZZ1w67SGy5qmZU6iK2bAnBYHOcyNTr5um3nbqw/WbdvSqj7VZe9QT5hy7d/eSC+cwHZcsXByy4ff/udvGiylENVFehwPCiWL7rq9hBIJeHN3zxcuP9nZQo71IHZbBAM+754Vzxz59M0cRbbVbRFkZ17ztzfzpl4YTZk2T5NaVkZXhDHAWiLU6/Xz5s574FePXnHJtRSizC7TCxv/333d961evTriMrdt23bP4mXPX/d/U8ZORwjpexv/39oHX0t77d1n36YvcMAITNBXzYTdm+I+n//ttmKz5KV7diokSkzw58c/+uC+8t+vOy1TpbAdGrPObP/04L8e/79f/6cscwJCqK6z6vFXHxKKJbLbFt1SiAT8qenivgoT+boZc6HmedvLf8aHjq+984s0RQZCaHft9n88cO1vPzyYlh95JnO4G3PU8+mLkXGsVY2uWLFibuHV8ydcRyEKIaSRpzx11Uuff7q+vb094jJffvnl+2f/OZgFEULa1MLHyp9dv/IzeiIGTNrZgjkys35H3WnLmZOPlj+jkCgRQgJKsHDGnTNTp5z8+r9sh8a4A2v+9dCcvwWzIEKoNHPCn+Y8fmDNv6pMZCt7K2HFGbOHfFSP1+k4kQXdNvOpL1c/c80/g1kQITSn7IobJiw4/NlbEZeJid/pbeHXAFzWEmFlZeXUnOn9tyilyYWpxdXV1RGXWVVVNTVnRv8tE7KmOLodDgc0E3La4S5ygDMrbnc1Vk4YM1kikvbfOHXs9C5dFVshxUxXY/W0nJn9t0zLmdnVVI0QOtxFdrdCa2FUCEKHOsmblbjOwpVPe6+hPleVq5H/oqpjas70rsbIP+1Or0EmyhQKpKPvyhmsJUKVSmV2mQZsNDl7k5OTIy4zOTl5QJl2r82P/EKxMOIyAdPqLGSrgUPfsNKkgZ8ihJDZZZIqIv9k8oVUMfC9m1w90qSzb3xvG9msx3wf6M2WHjdZXYu3GrjV+UiSpDQ7ewdsNDl7o/m029yNShmfesogFhPh1Vdfvfn0eq//58VFDjbuEyjRtGnToilzw4mP+2/ZeGJt7sz8ZntL5IECJrU6yDodt75b86fP1tmaqtpP922xe2w7qreUzr6axahio/Siq9b/8gracGJt6UVX9f16tJt8XI89AS79g3FegJD97fitKtJk49x5S9OOQ2kpe+q2923xY/+Xpz/v/48eLptbx7sZelnrLLNw4cINGzbct/aOW6bfoUlKPd167OuajR99+pFIFHlITzzxxOW7Ln/0iz/Mn3CdWCje37D7jPXYwlfurDPpylKLaQwe0MLsRR83cOsGGSEkVagu/tNfH3n5dwun3TFuzKQOa9vao6vzrryhYOalbIfGuLm/f+6DZZebtjxyedl8hNDuuu0/WA7e+8Lp/vvUW8kHtWhRMaVKrLnnImSwk83NpNPFuRQYRFHUr59856VHbqlsOz0971yr27L++MeBMu20axdHXKbd05ihPJ/GIGOAor3nrtlsLigoMJvNoey8YcOGTZs2tbW1zZgx44EHHsjNzY3y6D6f75133tm7d6/P5zv33HMfeOCBrcZdLba2h869N8qSmebz+SwWS3p6nC+G3scdIO/X4E7XwO0YY7fbnZSUxEZQZxl6v+hsOtO1u6dHX6vKzJlUfkvR+fNiHANb58HvdR/5/O3mEwcQQnnTLvSe8+Ovxq8QC1UDdlNJqEXFVFYS4/1I/X6/yWTKyMhg+kC082G0t40c6KCnLzSjnwd7d9uhT9/oqDslV6WWzb56YvktEY+FJ4Tsr7vjgpK3xQJGmhIwxvNSbZcUp9JbLMuJEDGfAE50nll5fM2b85czVD5dEioRBgj6qB4Pub4EFxJhZeurqYpzstRzWIyBC+cBIXS8+Ult2oJUxTmD/yQVUrcUUSUqZnMhTxNhnYVsMRCzh7ZvV458Hkbl9LacMjx3QXHknU5HxlAiZH9mGaaVphTpzE2YcKwCLoERQr7UD50FOcLmaVRKedbIwZBkWbHdM/TM9Z4A+bj+7Fq+oI/LTzbr8Uf1mMYsyCM2T6OShzP0xn8iVIiT0uSpeitnprBMeN+2kpM93P2OCGC3x9epkOaxHQgnJMsKbe5hl3AJToOwp43EwWoJ0cMEHesmr1Uk9M2B3dWQLOVfh4z4T4QIoXGpxbU99WxHARBC6Fg32d/O6a8Ju1unkOZTFAy5QQihZGmR1dUwwg6EkD2t+PNG4k/sOhedjayowl/qsZMDw+RZZHXXJ8shEXJSWVpJTe9IFzOIjToL+aqZ69+XNrdOycNbWobIJbn+gNUfGGVKigoTWVOXoDlAZyMrq/CaWtzB1a6hMUMQsXua+DXddlBCJMJxqSW1vfBEyDIODhkcks1Tr5KXsB0FV1AUpZQVjFA72qfZTt6pDpzqSaBK0hYHWVOH19TiVm7MDsg6t7ddJJBLRGq2AwlbQiTC0pSielMj9JdhkdmLPmkgXBsyOCSbS5fMt3kxGJUsLbG5Q7qPNHnQhib8ViWuMsd5q2GXi3zagN+tIVzu8xV7Njdfrx02l2GKGaVEkSZPbba2FKihBwQLnH703zps8/HgKwNjt9vfpZBwaL5gYcCnsrVqrEaVtaUle3p3WmmMA0iWF3Xbj4S+f6eLfNpAxsipS7LRRA3i0eqsobB60d42fLyHcL9uI/Zs7oZkGS+bFRIiESKExqWV1PTUQSKMPU+A/LeOdLv58bVhc+sUUi2LPWUUzh611ai2tqgsRpVZn2rvUDg6BD9VZsw6saZRO/vIOYutyWNjFlKyrETXtTbcV3W4yDodyVNQl+egwuR4yIWtTnK4k5w2JXq3oBFY3XXatAVsRxGJREmE41NLanob5hddznYgiSVA0LpGwqMWFJtbx8otrdjnvPy7l7K6KsS+gXPtYEpoSc4xq3O90uRC/b6ipn0FzQdrSucfm3qbSxaL9RHl4rG+gNWHbRHMFWJwkNW1JF9JXT6WKuBnOvRjUmNBhzpJs503H2NWEETsnkYVPBFy2bi00j3NB9iOIrEQhDY04nrOrDgTCqu7bshZVBgl9rnmf/t0VlclQsglU1tVOWZVrjk5p0uW4c4stiqzsODsdXrknMUzTn5U2rBzQs2WEt2uMxNuPD3pJq9Izmh4FEUly4rsLl2KIsIJ8ZvtZFUtKVNTl2RTuQrepMNuNznSRU70EHeA7VD4wOVtFQuSRUJeLtKSMIkwtVhnbvLjgEgA48Ni5BsDqTDxKQsihKzuem3azbE8osjvuWL3/2Z1VdqUmVvnPd9X5znklFqOpLR9F/7x9MQbZp1YU9B8cPqpj8fXbjkx5TdVZVf3JUsmqOSlVlddxIkwqNZCai0kQ05NS0Uz0gVJXP3uwYTUWdChTtJoR/Hd5YdeVld9Mm+7W3P1w0g3mUiWpRzTZNGXpPCyUxPv7G0jP3TyrC3FH3D4/GaFNCdmRxQGfHP3vpDdccaRlL513gvW5OxQXmVW5++89ImMntrzjr6f3XH6wsMrplRuPDF5YW3pfEwx0g88WVrcYdtPS1FdLrKzBe1pC0zQUDPSqQIlV3rTeDFqc5IGKznejXjRsYtr7J6GZB6OIAxKlESIEBqfVlrVUweJMAaOdOHdrfz7KrG565WyopiNKRIGfPP2PJfXesQpT/36ilCzYJ+utLItV/xDazw069iqFEvz7EOvj6/bunf2IyY1/V1eVfLSuq4PaCzQj9HpXnK6l6gkaGqqYFY60khjnQ4xId1u1OZErU7S5kQtDgLLLEbD6qotyryT7SgilECJcEJaaXVP3XUl89kOJM5VmsjXBraDiIjVXa+SxahuR4D9c797Ma/1iEum+br8eUtyhI+h+tzzDTnnljR8O+PkR+m9DVdvf2zrvBd6UwpoDRbJxJkE+z3+XqmI5ln/rV60vx0f6KBK1WRGOlWUTIkZuw8hhJi9VIuTtDhIiwO1OYmPZ3UW3EVQwO7RwxMhD4xPLf2ybhvbUcS5RhvZ0ETPAmyxZ3PXjVFdEoMDCUhgzr7l+cZDbqlqa/kL5uie4TAlqC0p1xVeOnfv83ktR67e8bet5c/30F3zoZKVWF11GcmMLLiKCakxoxozQQgJKSQTUTIhkgqQTIjEFPG7RGM8RCZEUiFJElEqMVKKqWQxkQhHeogkhJi9qMuNutyoy0U6Xajbg7wBSH2McHiaZeJMoYDZflvMSaBEWJxS2GJrc/ndcpGM7VjiU5sTrW3A/B1lZXXVlWb+lumjCAi+9PtXCpu/90qU2+Y+26vR0lKsXyjZcdmTc7/7h9Zw8Jrtf9s677kuWofeq+QlNjdTibC/AEEOH3H4zv6KMXK7RQ0/P7v9fI8lFVLJYqIUUyoJUoiQSowUYsrmDJFO8QAAIABJREFU65/2eHlDxkcWV41KVsZ2FJFLiCnWgkQCYaFGWwuzbzOj10M+qg94eNvR3OPvxgRLxZmMHoUi5OIDrxY37vGJk7bO+zu908RggejbSx5ryr9Q4rVftfOJzO4aGgtXycZZ3XU0Fhg9T4B0u1GTjZzqIQc7yDdGsqER7zDiEz2k1UkgC8aSzcXvGXoTKBEihCaml1XS+u0Agrrd5MM6YveNvidnWVy1ajnDs5cR8qtDb5TqdvlEsm/mPN2VRv8dNBaIdl3yeEPBpRKv/cqdT2Z20fZpT04qsbnqEeLt8z5gktVdq5KNYzuKyCVYIkwbV9VTy3YU8abBSt6rISaer8dtc9erGE2EhFx0+K0JdVv9Iun2y/+3fcxkho6DKcHe2Y/UF86R+BxXfvvkmK5qWooVC5LFIo3D20JLaSCe+LHT7etWyHg8gWWCJcL0cRU0fS+AoKPd5ON64vLzOwuis40cDN7Snnt89YSaLX6hZPucp9vGTGHuQAghTAm+u+hPuoJLJD7H/J1PBOesiZ5KVmZ1QYUKGMjmrk+WFlGIx3OVJFYizFaOCRDc5exmO5B4gAn6uhlv1uMAP/uI9kdIwO7WMTcvRqpZP6VyPRaIdl72ZGtWVPOzhAhTwj2z/1JfOEfid83/9qmszoroy1TLSy0uqFABA1ldNaokHveUQRxJhBuN4n+fCXxcj3e2kKPdRGcjJg9i6Mt1YnpZBTQTRs3lRx/W4R+7eJ8Cg+yeJpk4UyRIGn3XiJx39F0BwZXjrjWOncHQIQbDlOC7i/5cVzxP7HNd+e2TOW0noyxQJR8HT4RgMKurltddRhFHhk/4MTJ5kMlDavtN0CwRUqlSlCpFKRI0PoXKo2mu3onp4yu6ay7Lv4iW0hJTlxt9Uo97ed4o2J/FVaOWj2eo8LHtJ3Nbj3klyhNTbmXoEMPBlGDvhQ/5hdIJtVvK9zyzY85TLVmRTymulBW4fV0B7BQydscAeIcgYnHVlmXdz3YgUeHEE+GQvAHS7iSVJvJ9B3mvGq+pxW1OGoqdnD6ushuaCSNXbyHvVcdVFkTBW1o5I7e0AoIvOLISIXR88kK3VMXEIUZBUQfOu7+mZL7I7ynf9Uw07YUUEibLCq0ubg2iAOxyeVsFAhntUw7FGHcT4QA6G1lZjdfpcJRLvI5PK603NXkDXroCSyhHu8nHDdgddyO0LK5qtZyRnjKlDTtTTU02ZVbl+F8zUX4oCEXtu+CB6tIrRQHvvN1/V9laIy5KLZ9gccF9JPiZxVWjYaw2JWZ4kwgRQoSQChN5owKv02GTJ8JCZCKZVpVb26ujNbT4FyDoCz3erMc43pIg8vpNgYBTLqF/0QmxzzXzxIcIocPT/ycgFNNefhgo6sD5v9fnXSDzWK/89im52xJZMSr5OAs0E4J+rK4ahmpTYolPiTCIIFRhIm9U4q0GbI9otZRJGePPdFfRHlgcM3vIqhp8vDvuciBCKDhwIqmMQvSvfjClamOSq7crrUynvZj2wsOFKcHu2X/tSitT2drm7X1OGFGliFpeZnXXwip9oI/FVc1c+3rM8C8RBvkxOdRJ/n0G72wJexDb5IwJZ7ogEYaq0kRWVBODI26/+yyuarWM/is5ydkzpWI9QuiHWfcgbiy55xdJd8x50q7IHNNZeemBV1D4+UwsVEuEGqeXn8uLALr5Aw63r0spK2A7kGjxNREG+TDa347/fQZvNeAOV6hX9ZSMCWe6qghTAzTihydANjbhz3Q4DsbLj8DiqlIrJtBe7MyT/xX73Y35szsyJ9JeeMSc8tRv5j7jlSiLmvbNOvHfCEpQJY03u+gZoQ/4zuquUclLeD2UPojfiTDIHUCHOslblXhlNf6hc/Rv7cykdIlQ0mJri014PNXiICuq8MmeeE6BCCFMvHZPc7KU5qH0qaam0oadWCA6Mn0xvSVHz6TO33Xxo5gSnnNm7YTar8N9uUY+3gr9ZQBCCCGzq0otn8R2FDSIh0TYp9VBthnIy6fxOh3W2cgILRmTMyac7oS72qERhH7oxO/XkN5IeyTxiNVdp5TmCwVSeos9/9h7wRH0FhX9fXCiZxw74/sL/oAQuvDwipy242G9Vi2fYHZCywJACCGLo4qh7tYxFleJMMiPUYWJrKnFb1Ti/e3YMVSHmqkZE0/RNAFjnLF4yaoavM1A4mDitFCYnRUaOc1Vl7ktR3NYGkEfupqSK05OukWA/fP2vpBqagr9hXLJWEw8Hj/MU5joMPHbPDpIhFzX7UY7W8irZ8j6Rtzu/MXX+tTMSafgiXCQChN5qxLr7QmRAoMsrmp1Ep0NhAKCzzv2HkLo+JRb2RlBH7LD0/+nvnCO2Oecv+spRcgT8FKIUsknWOChMOHZ3A1Jkmz+rkrfXzwnwiA/Jqd7ydtVeE0tbvmp62OhJt/qtfW4TOzGxh2eANmsx+t02M3blXUjgq2uWo2czkRYVr891ay3KbMqx11HY7GMoKh9F/6xPWOiwtlTvvtZsd8d4us0SRPMLkiEic7iqtDImVpNLMbiPxH20dnIO9X4/RrcaCMUoqZkTDgNtaM/jct8qxIfjdNhgiOwuRulojSRMJmuAsU+14yTHyGEDk+/i+UR9KEJCCU75zxpSc5J722Y890/BCSkdXc18klmJw3LWQBeMzsr6a1NYVECJcKgZjtZXYvfr8Fjkyed7DzDdjgs09nI25WBdTpsTsgp58yuCk0Snbe0wRH0nenjdNrZNBbLKLdUtX3u026pKr/l8PlH3gnlJcmyQo+/xxewMh0b4DBscVVrIBHyWrOdNDon7W6uqDEn3GNQkMFBPqjFa2pxh4vtUNhjdtDZU6ZvBP2Ps5ZyZAR9iCzJOTsveyIgFE+q/nJqxfoQXiFQy8ZbnFChkrhs7iapMFUsVLMdCD3CToT79u1bunTpDTfc8Kc//cloNDIRU2wo5QVWT+eHtZZ3q/GpHtLmRAnSPNbuJB/V4/eqsd6WoDcBQYQQs6tKk0RbIvxpBP1F7RkcGkEfovbMSXt/9TChqHOPf1Cq2zXq/hrFJJMLakcTl9l1RqOIkwZCFO56hG1tbf/85z+XL19eWFj4xRdf/POf//z3v//NUGRMo5BQI59gdlYYhRcYf+pEIxdRKVKUIkEpUipFilKkKEVCqSVEwKsb/OFYvOi7Nny8B+HEGBoxModHLxGqJaIUWkrrG0F/eMZdtBQYe7qCi+Vu04WHV1x88N8uqdqYM3OEnTXyyTUdb8YsNsA1ZseZMapLY3zQ9N6GkvodoouuRIjmVZ/CToSXX375+PHjEUJXXHHF2rVr6Y0mxjSKSSZnRXryBX1bXH7i8qNWB0L9JmATCahkMVaIqCQRkotQkggliSjF2R+QXIiSREgipMQcrmY2e8jBTnSkC8fdAkqRMzlPp9DRQBjAyOQlFx1ZIyD41LjrrMljoy+TLRXjfy13mc4589ncfS9+Xf5iV1rpcHsmy4tc3k5/wEZjVyPAH9jirB6f/bvYHEzuMhU37Smr35Fq1iOEetMUaGoxvYcILxHOmDFjxowZCKFAILB69erLLrtsyN08Hs8FF1wweLtWq33rrbcGbPT5fA5HwEWxMFudXFDaZl/pUo3eSmYLuUwhhYIZUYCIRIgQQgIKSQRIISQaCdJIsEaMNBKiERPRLxOnz+ezWq0CAW3pFBPS6hI02AUNNqrLw+Es/UsYY4/HQzH/CN5jP5GeNNvlCqON1O6nLD7K7EMWn8DspSxeZPYJnAE0M9D0aMePbqH0HuHNGY2+qepAtjzaO46YnYcB9o+7RWrvmtC0+4pvn/p8zvNmZfZweyZLyzrNx1OSzmU0Hoyx2+2O/XngGk6dB7tXJxaq/V6pHzHYxUCIfYVtR8Y37dG2nxCQAELIJVVV582Wp5f19vaGXo5arRYKR8kv4SXCoCNHjrz77ruzZs1asmTJkDuIxeIXX3xx8Ha5XK5QKAZs9Pl8UqlHgiQRRBKlVMm46k4TErolQjoHPuOf/u8P/k4QCqDeADL8smdmshilSJFGTFKkSCNBIuL3UkQmVEoERCogclGEn3iXHzXYUJ0V6WyU66dWTwkLZzdCgUAAYyxhPGJsc9eOy/qDRDj6gTBBR3qofR1IQBGNhEqRII2UFKhQioTSiIlKjOYdWEcRUlsyf+FEzUkz2tImFAvQOWloiobIIr3Bi9V5GML+Cx+UBVyFhh9u2P/cpvLlTvnQtccpiil2X9UYyUWMBoMxZus8cAqnzoPTUadJmsxcMOm99WWNu0r0+4ILZ2JKYMyaVl1yZWPu+X4kuFxjGZxHRhDK00V4iZAQ8s4771RVVT3xxBO5ubkjHHjOnDkhlikQCESigJCwMn+5UJM0weauzFQxezEPyYmR04VafrqjwljgdiuSLD+fB6kQyYSUVIikAiQTIZmw/3+UTITkop9+FiKbj9RZUK2FGB0/NwGOdhvERRRF+f3+Ue/gomR166TiVLlk9AZCnQ1tM+JkMfqfUsGYoebQUNnaipr3Y4GoYvICtUxwSRa6JAu1OdHRHvJ6DSpSUjPTqcLksFc7jM15GIZw7+y/Knb+LbOr5uo9z3w1/yWfOGnwTmnKaVVt/2Y6QoqihEIhS+eBQzh1Hsyu02M15UwEk99y+Nyj76dYmoO/dqcW1xXPayi8LDhJE4WQEGOxWCyV0jw5cHiJ8NSpUwcPHnzttdeEQmGwTkku5/f8OilJU03OU6wkwlF5AsgzbJsetPVFxew8nZI0deR9Wp1oewt2B9CVuYKi4RvCplZ8LiC4pnieIym9b2N2Ero2iZo7ljrVQ74x4gChpqejc1IoBQ8G2SOEkF8k3T7nf6/95q9pJl35nue+ufyZwfMDKKVFHr/Z6zf9f/bOO7yt6vzj77m6utpbsob3XrEdO4kzScheEDZ005YWSksHo4W2UAotbfmxWkYLLZ2MFiirEEISQiB7OfGK7XhvSZa1t+44vz8UQghxYsuyLdv6PHnyyFf3nvv6+Nz7PeM97xsvh6Mk0wKMWXewpST1R/EtVhj2LDr257zO3QAQFKnas1e25q5xKjPje5eRGJsQ1tXV9ff3X3XVVWeO7Ny5M94mTSoqSXmfc+tUW5FksnH46tLVl430rYfGuwahywuXGlGl5kLLMpKAPb9zF4eI+tJrP/+tiAcLU9DCFNTvh+N2/EwzV6RAi/QoRRiP32GCCQnk21c9ePn2u0yWuhUHHtu97G782ZpACKnEpc5A/eR7DyaZQjzBU2KBkU/E00kqu3ffksPPikJOhhQcm/u1pqLLucn1GhmbEH7ta1/72tcSLr/aeBAL0jkcDtFWIV8/1bYkmSQ4HPGE2pTi8+RRozk4YsMHbXiuGn2vBAkutrgwp+lNHkt3Zi2/cLqlNAmkSdD6VFRrxy+1YwWFl+lRviIxPB9GxitN2bbm15dt/3FO994wJd+/8FwvQbWkwulPCuHswhFoUIkq4lWaKORccvjZ7N59AGBNKdmz5Edu2RRkLovFWWYmgQCpxOVOf51RuW6qbUkySbiDLVJBBo/4zLoXxlDvxLsGIV0C3y5ACuriIiUMe4ra38cI1ZdeN5r7CniwMAXN18EpN+yx4O2DUK2BeVpEJrBLr1ORsXPFfRt33VfcutUv0dbOuf7sb5Xisi77f6fKtiRTgtN/Ilv3pbgUldOzb8nhZ4RhD80X11R85WTRFjxFncPZLoQAoJZUDPuOJYVw9uDw1akklWcfsQTh7R5OyIMv5RKGUa96z2l+m08He9Oqh9U5o787D0GJEpUoUZcXDg5x+6x4vg4t0CJxoj6LFv2cj5bdtXLP7+bV/isgVLXmrT3zlZhKJYAXCPeJBelTaGGSSYPhAv5wn0JUNM5ypAHb0oNPpw8eA4C+1Pn7F93mE+viYWCMJOrDN4moJXPbhv4OwM3ayKuzDYf/RIHhluhnFsNeCz5mx2tNqEI9ht4onw4Ut74LAHVzYsy+my2DbBkxHMIHbfBUM1eqREtSQC1IxOnSroylwurvLD38x2WHnmT4orNDiqslcx3+uqQQzhJcgUa5qJBA49g4gXFx27bq43/n04EwJTu04Oa2nFXxMzBGkkIIFKkSkmpPsEMuGjGORpIZQ4RxhxibXJQHAJYgvNXDKSh0SyGS8cemQCWtWwVhn1lfZtWNq3esFaLL02G1ER214b+24hIlrDAgaeI5lzYXbBaGPPPqXrx03yMMj+pNq44eV0sqza4P0kb2PEoyk7D7TqglsS8Qqp3di48+a7Q2AEBXxtIDC28NChPC5Tg5BgIAUEurHP7jU21FksnA4a9Vicsw5u234hc7uAVa9MWcMasgyUbmNL0NALVlMQ4Hz0FMwgojuq2EEPDgj83cB4M4AUPAnyj/Yl3pdQTHrN7z21RLbfSgSlzmDjZzeFbm8Zp9OP21amlVDBeKgs5LDj555dbvG60NQaFq14qf7VrxswRRQUgKYRS1eK7df2KqrUgyGTj8J/jU3OdbuR4fvrkQzdPGMhVZ0L5DFHLaNPkDxsqLnz1qRDxYY0LfKUYhFv7YAoftJDOqRLmTx9GqrzcVXs5jI2t2/8pgawIAkieRCDLcgWTC+plPIDLAYUZCjW0anGQjcxv/c/3b3y5s3w6IaCy+8r9bnu3KSKyt28mpUQAApajYH+5LRhCe8bAcHvLW1tNfXmqIUQIBgOCY8qY3IH7DwXOQ89Fl6VCtwR8OEk814eUGqNIm0EaLAwtuITBT1Lpt/a7731v7G5smXyOtsvuOq8YxY5ZkWuDwnVBLx9Lzwzind3/18b9JfVYAGDDMPVR9i1ORMVH2jYOkEAIAIIKvEs+x+0/o5cun2pYkE4U1CO/3tJqQ4hsFWtkodkeMRF7nbqnP6lRk9KadJ7J8vNAKYYsp4sTiDwa5QzZYaYRiZWLIIUL7q7/HjwRyuz/e+MG97639rVcyr2nwiTw4f+ThJDMGu/+4adTe9SnDpxYe+4ve1gwAw+rcw/NvNusTN39hUghPo5FWOfzHk0I4I8EY9lrxkWG8THFcJ5g/HhVEGJc3vwEAdXOun4Q9T6kSuDGfaPPArkHu0BDekEaYzhP1c7LBCH287C6E2Zyefet33ffuut/Uc/4QbRHyDVNtWpKJguNCnuCp0tS7Lnqm1D80r/aFvK7dCGO/WHOi7Iut+es5lNDLcEkhPI1GuqDD9lJyE8XMw8/AG90ch+E7hUTLwDGt9KbxlJbVt1/p6vVKDZ3Zk9dnypdDnoyoc+B/d3LFSrTKiGJOahEvOER8vPQuAR1IHTy+8YP7j1fPGfYdS1MlfUdnLHZ/nUyYRxIX6ojJfJY5zW8Xt75HcAxNCutLr20ouZoh4xwgeyJICuFpBKRayNe4g20KUeFU25IkbvT44PUeXK5Cq00owjhCEZtcPI6/L8YVDa8CQH3pNZMcCxEhmKtBRUr0kRk/1cStMqIpXzhkefydK+7dsOs+w9DJja31b+S6kkI4g7H7azTS+SN9qx9qmtP8VmbfQQJzGKHW3HXHKr8aEMU5j/zEkRTCT9FKq+2+o0khnBlggANWfGgIX5lJ5MoBAIZ9R9TSKgSxC1ja4HGtoyMgUrfmromboWNByIMNaWiuBm3t4+qdeHM6MbXxuxlSsH3VLzft/Hm1te2fRh8/YKHFydnRGQgG7PDVZGZcec5xgmOye/aVNb+ltbcBAMvjt2Wtqi+5etKyRsSLpBB+ila6oNn8ZI7uK1NtSJLxcmY69JYi4szmdIevZpzhoec2vgIADcVXsqNI5ztxGETwzXyixo7/1c5VqNGlBsSfuul8mi9+f82Dm3fcU+jtTz3yc/PiP4QF0imzJsnE4At18HgSEWU6c0QQ8Ra1bis5tVUSGAaAoFDRmLf5QPYmM6GKcBhcI+aJQwBaIdIKIDFcv06TFMJPkQpzGdYfjAye/fdOMu3o9sEbPbhKjVYYP33WOC7kCjQVm26PuVjD0EnD0MkwJWsp2BQXO8cDQjBfi4oVaOcgfqYZr0+FYuWUvVfClGzbmodKDv+wjT987a77tq39dYQ/hgTiSRKfYe9RrbQ6xECQwxLXYNWptyr7PhSwIQDoEme+kHLFv6UraIKSm5Gczwl4F2qKHIAtiH00NoghVYJSxWASgXKqIwsmhfBTECCttNrmO5KhPncGIMm0AGPYY8U1w3BVJsr+7I5Qu79WLiq88FL/hYkOB08WXU7zEyUZtYQPV2aiHh+818cdt+NNaUg1RS+UoFAZqfrFid4f39zVtn7XL7av+XWETJRaSjJKfAx0e3G/H0IshDkIszjEQphDYQYXk4faIrem9A7ebf7nWud+AjBGqF47f0/uFWZDpYyC7/MRdXrNYVQtMMSiwQAM+HGDA94PAoc5kwhSxcgkQSYxSCZdl6aBEBIcAwhNjm+CVlbdPfxqUginI34GXu/mAODmIkL6uXY97Dukk1XHXLjW0ZE6eDxCik4WbxmPkRNBphRuKSIO2fDzrXiZHhbp0JRMOrGyXEqUfSLFNt/asm7X/dtXP0iT0yEB8ezGT0OPH3f7oMsLfhpnSlGGFIwkCAigeISIBwICc9jS2u99KXhwzqm3eSzN8KhTOatPFm9xKTKEANkx3VfIgxwZ5MhOt1QvDYMBGPDDoSHOHAAGg5JCCgrLKaTgg4ICBYXkfKzgT1TTTgghzDq1Pd9ppiJ+kgnzmLCA9vGYCMmGKDrAjwQJzEZIkdlQPmicO2CsdCkmMM69Slx+MvJEmHEIyGnj75QEANo88E4frtKgFYbzPCoYs8O+4zm62HNKV9W9hDBuKdwUphIx9hCBYEkKKlHC2z24xY2vyEBTksVCrVz6ZklvkbfWMHRy7e4Hdqx6gJnSxdQk5yXIQrcXd/ug24s9NGRIUbYMqjRILzxPF4rA2N/6zyXDvorO/2KE2nJWH6u80S/WxNckGR8VKqBQAdEBZYQDdwRcEeShsTsMnR5w05wngjw0JyJBUkwuz43v/RNDCPX9x1MGakf6lkM8iglm9h/O7D8MAD6xbtA0d8BYOWiYGxQq4msJQjyttGrYezhVtTG+JSeZIEIsbB/A3V64OhNljeCl4fTXS6jUmDs3Wnt7+sARmhQ2lFwdu6ETj5JCX8s/ncVihQEW6CZ7ZKiTLjrueHfr2ocu3/lTk6V+7e4Hd6z8xdQ6FiU5gyuMG13Q5MKOMGRIIEuGrsgkjOILTWWmDh5fVPP8E6bB64dZS0rpofnfHtZMRooeigCdEHRCOGuiFQEABuQNc+XK+AekTwgh7C5Y15q2jKbEDE/A8IVhvoThCRhSQPMlNF/IEaQkYE81nzCZa1PNtdKAraB9Z0H7ToyQXZU9aKwaMFVadKUsLz6pa7TSxQOurUkhnBa0eeDdXlyohFuLzixRnIch7wGdfHHMd6mqfwlh3Fy4OShUxlzI5IAAqnUoTw5v9eBmF74iEynHEUZnrIgoE0Uq+kn3e2t/s3nHPanmE2s+fuiDFffG69lMEgNeGjc5odGFHWEoUaL1qUS6BIiLNQqlu3dhzV/TB44NU8gqFJgr7ziUMfVRtxCAlA8S3oguqTGTEEJoTZ9nxRdyufaLNa25a1pz1wDGGme3yXw8zVKrtzZqHZ1aR2f5yf96ZMY9S263pJSO3xiNtLLF8nSEcVNknIebSeJImIWdg7jDA1d+zi/mHDCww76j2boYA2Tr7G0Z/Udovqih5JrYSph81AL0jQJ0fBj/5RRekgJLUiZv1TBFtmTIe1Chv2nrmt9s3vnT9IFjq/f89oMVP+OIhHjVzB5CDJzy4CYX7vNBvhxdokd5cnRR/QMAYdhTVfdyUet7BGYjfMl/y8sVSmWPcepVcEKZbq0TIbs6267Obii9hsdGDEPNJvOJrN4DCu/A5h13nyy64ljljeNcliAQpZFU2XwHU5Ub4mV1kvjS6oZ3+3GxHL5bfPEtdE5/g4gyCEhtbPeqqnsRAJoKLov7PPyEggDmaVGmFN7uxZ1evCUDKSZlaKiTLTnRd39eyjddyoxtax7atPOnGf2HV+79v93L757kWDyzkzALLW7c6MR9fsiXoyoNuj4L8Ua9zTS366MlR/8kCPs4xGsu2HS84it11t/kyC+fSJMTgukmhGfB8qgBY8WAsaJm7leq6v9d3vjanOa30vuP7ll6u1VXPJ6SU+TL+uxvJ4UwAQkx8P4A7vXBNZkoc3T7toc8+1JkMSY/Sxk+lT5wLEKKGkoTenVwJLRC9M0CdMCK/9KKVxuhUjPhWiimUilC7g42K8UlDlXW+2se2vjBT7N79+N9j3607McJHnl5+sJhaPdAvRN3eHCWFM1Vo+uzxxZmgcDsgpq/lzW/CQD9pqrD87/tVGSE6KEQbVVKEjdrRLyYxkJ4Bo4gj839amfmJcsPPKZ1dF62/cen8jccnvetmL23NeK5zeanIrSd4sfZOSrJeGh143f7oVgBt45iIBgFc/Sw90iO9oux3fH0cLB4S0ggj62EKQcBLNWjAgV6q4erd+AFOlSoQBfc8Txe9IplQ569SnEJAAyrc7at+e3GD36a070HAH+07CdJLYwvgwGod+BGJ9YIoVyNLksjhGN/qQvDnpV7Hk611HIEeaTqm43FV0SPWz17tdLF44lKOF2YOY3Socp6Z8PjtXOux0AUtW7b8t7tKcOnYisKEXyddKHVuy++FiaJGQ+N3+zB7w/ANZloY9oYurp2f41EmBlbh0Zva0kbPE7zxQ0lV8VweUKhE8JNBUSVBh214ScauR0DeDgUf4+DKHrZsiHvQYxPu/YNq3N2rHwgQopyuvcuO/QkwhN131mFO4L3WvEzzfj1Hiwi4aZC9I18Yp4GxaCCWnvblVt/mGqpDYg1W9c9fEYFAWDIs9cgvySedicqM2FEeAaWxz9WeWNPxuLl+59QuXsve/+uhtJrj5d/KQanNb18eYftH+nqKy5+apKJxEfDXitucOB5WnRr0Zh8mA+1AAAgAElEQVSDalo8e2LOMRkdDp4s2pKYewfHCoGgTI3K1MgRxifs8K92UFJclQaVquIcqlTATxFTJof/uEa6IHrEqivavvrBDbvuK2jfiTh275IfJdcLYyPMQZMT1zmwLQSlKnRFBkobXzC7/I4Plh1+hsdGLLqSD1f89Ox8Ef5wL80F5eJxLTNNF2aUEEaxaQre2vyHeXUvzml6s6Lx1Yy+Qx8vvWOs21+U4jkRxuMP90kEE7h/P8kF8NOwfwjX2vFcDfpeMSEZuwc+w/qdgfoiw/diuLt+qCnVfCLClzQUT/vh4DmoBWi1CVYaoc0DJ+ywY4ArUaIqLYpjyl+DYoXF8/EZIQQAa0rJjlUPrP3wl/mdH/KZ0IeX3J30Ix0TgwE4MsRv83PZUrQ4BeXJxzu/TXDMomN/KTn1LgA0F24+OP/mc/4iFs9HBsVyNLqQadOdmTM1ejYsjzpS9c2t6x9xydNU7t4t2+4sP/n6mEpACBkUKyzu3RNkYZILEOTQrkH8TDPHYvhuMbEuFcWgggAw5N2vEleQvFj6zFX1LwLAyeIrZmouBQJBoQJ9IQfdWoyUAni9Gz/bwh0ewgEmDoWnyJY6/LUM6z/7oFk/5/21D4UF0qzeA+s+epBkwnG400wnzMGxYfxcC/dGL6j4+LZi4vrsOKzyioLOzTt/WnLqXZZHfbzk9v3V3/1cv4SzePYYZDN818QZZqYQRrHqit667KmG4qsQcNXH/3bJwScJbgxPuUG+wuLdA8BNnIVJziHEwkcW+GsHFWLhO8VoYxqSjmMrttn9oVGxKoYLDdbGVHNdhJI2FM/8uXEZHy3To9tK0IY0YjAATzVxr3TiU27MjWMtj+RJVeKKIe/+c44PaQvfW/O7oFCVNlCz4cNf8OnAuEyf0QwG4H+9+PcnuS4vrE0lbiuChRomLtGo9baWq977oX6oySfWvbP+/9rOl1zT4a8T8tTiWTMfNsNnJxgedXj+t6wpJZfuf7SwfbvMZ9m1/Gej7OOLBelCUu3w16olVRNtZ5IIC0eH8X4rzpbCl7MiqYrx5i4IRPpD9JBaOjeGa6vqXwKAhuIrItTMHA5+HgSQJYUsKWI41OrBR2z47R5cokLlKpQRUx0Ylau6h18xKdedc9yuzt66/ncbdt5rsDZu2vmz7asfnL4euRNBhIMGB66xYz+NytRwaxGS8xEAcHHqkBe3bVt85FmCYwYN5bsvuWek3bFm9y6DYmV8bjkdmMkjwjN0ZyzZuu7hgEhtstRdvv0uudc8yguNitVm164JtS1JiIGPLfgPTdxQEL5ViK7JAhU/Do6FZteHBvnKGDy/jdYGk6U+LJCenAXDwc9DElCiRF/NI75diKQkvNGDn2vhDo19ylQjqQzTTn+47/NfueRp765/2CMz6extm3fcIwo642P6tCXIQpsHdpvxC+3cE41cpxfWmIgflaI1ptMqGBcIzC458qelh54mOKah+Kr31/x6JBVkWK/DX6ufHf6iUWaFEAKATZP/v02PO1RZSnfflm13GGxNo7kqRX6JI1AfYdwTbd7sxE/DB4P4ySbOHYab8tFVWXHLmYAxa/F8ZFTGMi86r+5FAGgovmqWZ5dVCdClRvTDErQ+jbAE4akm7j+duNU9+t0PhFGxyuz64Lzf+aT6d9c/7FRkqFw9l+24W+Ybipvd0wEMMBSEmmH8di9+phn/oZE7OMQBwKIU4oclxHXZKEcW5wTufDqwbvcD0UXBj5bddXj+ty7guGtxf6yVzid5s2U6BGaPEAKAT6x7Z/2jPWkLhWHPxp0/y+/88KKXkIRYJ11o8Vz8zCRjwkPj9/vxM80czcItRWhLJlIL4/nc23yHxVSqmEod64Wp5jqDtTEkkJ8sSri8g1MCQpAlhSsz0e1ziCIF7LXi3zfijyzYQ19cEI3KVRbPxxyOnPfbgEj97vpHhrSFCs/A5h13K7wD8bY9sYhw0PHJsO/hOu7VLtznhzQJXJuF7q4gvpZHrDSifDnEsBHwokgC9s077k4bqAkJ5NtW/6o9+yJznoOuHUbFuXPaM5sZvkZ4DjRftOvSe+ed+FfFydeWH3hc6eo9WnnjhbteJuX6k4OPp6uunJpspzMOZxjvs0KzC1dq0XdLzpNBNy4MOrebVOtjuLCy4WUAaCy5iubHbzPBjIAiYK4GzdWgoSAcs+Nnm3G6FM/TEPmKEf3rhXy9TJQz5DloUKw47wlhgXTbmofWfvQrk6Xusvfvfn/1r+zq2PK8Jih+Bnp9uMcPvT5sD4NRBBkStCiFSJOAaLI2Uursret2PygKOt3y1B2r7nfLLtI7dAeaMALF7Ng+eIbZJYQAwCHiaNXXvVL9kiN/qjj5msxn3rP0zgvE6ZaL8klC5AzUqiWVk2nnzMMWgn0W3ObBVVr0/VJi4l4EgciAP9Knky4a64Wp5hPR4WBT0cyPMhwzKSLYlIbWpaJWNz5s497tQ+VqmK8B5fmmtVOVG3vtr48khABA80U7Vt6/5uNfpw0e37zznu2rHrDqiibS/AnHS+M+P/T6oNePHSFIlUC6FK0xERlSICe9L53du3/F/sdIJjxgmLtrxU9H4/zV73o/VblulmwfPMOsE8IoLQUb/VLdyo9/l9OzTxxw7Lr03gvkFkhTbxpwvpcUwpgZDMBeC+7340V6tDmDoCZ4Pn7A9b5RuZpAY27bVXUvAUBDyVURcrw+qzMeEkGJEpUokTUINXb851M4XQrzNJAl/UxiSK10Xqv1eV+4SyoYcajHkIKdl/5i1d6HM/sObth17/7q77XnTBt/RYzBEcGWAJiDYAliSxAIhDIlkCGBKg2hE8Z5qW9MzG18dV7tvxDGLQUbDyz4zmgiGEQYp9NXW2T4ziSYl1DMUiEEgD7T/Hc3PLpu9wMGW9OWbXd+tOzOkXJW6OXLO4ZeDNEWId8wyUZOd7p9sNfC2cNoSQpck0WQE78kzXJBq+vjBTmPj/XCtMHjeltzUKhoKkwOB8eAXgSb0tBaEzrpxAeG8Os9WEVBqgSlSSBNjLQCIk21vs+5tdhw2wUKYXn8XSt+uuzQUwXtOy/d/6jJUntwwXdofiJ2RxgOhkJgDmBLECxBPBQCCQ8ZxGAQQbWWMIhxHP08Y4bgmEsOPZXf8QFG6PC8mxpKRps7ZdC1PUW+lEfMunWB2SuEAOBQZb298fF1ux/Q2dsu2/7jtpy1R+Z94/O7mghE6fhLaw88nWW8TpddzOOPK9/hbAADtLlhr5ULMmiZHpWrR5URNC6Y3btU0ooYsg9GQ8k0lFyTmO/fBIf/yQoih8EShAE/7vbAfgv20ThNsjqV/X440iW2DSoVCm1WIUGeJ0oCh3h7Fv/InDJnyZE/FXR8kGJr2b38brsqZ/J/FwBgOfDS2MsgTwR7aXBHwMeAh8beCPIyWCsAgxgZRDBHRRhEIPjMJP+5DZ1jaFtXSyTg1WUXC+WqSTBeEPGu+egho7WBJoUfLburJ33xKC/EHD3g2lGZ/sCEmpeYzGohBICgSLV1/f9VNL5afvK/BR07MvoPHau88VTeevzJjAbm2N3PPnDiP89kKbI6mbes4F13x6Ola6+bWrMTFgxw0on3WTECWKZHJcpJ9jHi+hxbS023j/Wygo4PUmyngkJlc+HmiTBr9kAgMInBJEYLdAAAQRb1uoT7njQ7P5yXq87zhTx9BJ1/61P5SzemiJBWANRnl4rbctfYtIUr9z2scXRt2Xbn4XnfPJm3Ke5G0hwEGOyjkZ+BAIP9DPgZ8NMQYLGXBh8NIRakfCTnc3IKyfggpyBVAnI+IeNjBUWMvld3as872x7+oYYVSChpl6ur/JqbVn/v1+ftB8QLhWdg3YcPKLwDAbFmx8r7h9W5o7/W6tkjFWbNnmgyZzPbhRAAGB5VU/GV9pyVSw7/KdV8Ytmhpwo6duxfeFu0N7r72Qec27a+8OU3tNIUAGiy1P/kV98VK7XZC6bNMsbkwGKod+B9QyDh4dUmIk8+BavtQ95DAlIhFxWM6SppwLbo6J8B4Mi8b8acwzLJeRHxoP0vdxobQ8/e+K5CpAKA431H7nnkK7R055HUyuEQSEikE+IUIdKJQCdEKgFw8vT/bXh8Yc1fS069u+TIs6nmE9vnfgfEY56s8zHgjYCHxu4IeGjw0OCOYC+NfDTGGMQkkvI5CQliEklIkPFBLwIxScj4IOXDJ87Mn2/CY2jU/fWH3v3Z13+35cmK1CoAcAYc92+9ayd7z/o7Hhvr7zJKcnr2LT38lCDss6tydqy63y8ew7wIBtzreDtf/60Jsi3BQTje6cFcLldWVpbL5Rrl+TRNP98QsOKE2LyZ071nUc3z4oCdQ0Rz4WVHyr74m405f7/2xTRl5plz3qp75V22/guPvRHfW3McFwqFxGN/4KccVxjXO6FmGHQifImeGGXi+JEYTz0c6/5xlvY6rbR6DNdgvHHXfanmEz3pi3Zeel8MN50gpm97OJtIwPvoWtPrX39fJf40v8+/Dv/5qNZ7xS+exxhcETwUAtvpf9gVhjAHCAGFYLP30AO9T8oZ7xClfbj4Jx2qEgHxqe9JiP3sjVhgMQCAj8HeCPIwWEiAnAI5Hyn4IKNAzgcFhWQklvIRNSlbF96496uXBExfnPf1M0dsvqEvvLDlx7sspGDM0+8Xbg98OrDkyLP5nbsAoCd98UdL7xzrDP+w71j38H/mZz06VsMmGY7j1qi9y3PVFz91LCTEiLDDx+ulMQBQxOnFJIqAaHh1PoF5BIh5SDApbbcza3lfWnVZ0xtzG14pbfmfpHHHYzScrYIAUGqq+Of+seWymJGEWGhy4jonHg7BHCX6Yi4yiKbSTcDpr+dwWCNZcPFTz6KkdWuq+URIIN+36ELeHEliwzXYoxelnK2CADDHVPF+298AACFQCZBKAIWnXbZPtx8GQ4SFMLf470X5Vx5+JNN+8pH6e7blfeHN7C+wn8QAUX12pZ7inX5jSEhCzsdyPsE7v2fW5DVRe2/rnLKNZx/RSVNUfLnb2qfJGNukxYVJsZ26dP+jcu8gw6OOVX69sWhLDL6qvfbXM9QzLePY6EkIIWzzEe0BAIAwx0UHqGEOosHvIyziMPhZTkIiowiMYjCKkEEEseXlGQ00KTxe/qWetMVLjjyjHWjwR7whJiQ8a8Zs2DcklI2412LGw2Fo8+B6B3R6cY4MLU1BefLJ84W5AN321zLU14xpTVLuHVxw/O8AsH/RbUHhZDgyzDaEMoXdb+MwR6BPdcnmGxLKlBe4ikRAkiAGBBrdzvUPVRx/Yf6pNza3vVzpbfx46Z2jmPFLgOYIIJQqh322s4+wHOsKOoTSC/3uY4LgmKr6l8sbXyMwZ9Pkf7zsLpc8LYZyXIFGmvWmyEfrVjPzSAgh3GCgrVgAACO3YOSlsTkAg0E4Msz1+0+vyeuESCcEkxhphXFu+3Z19jvrHyns2Fn9XuNrx1/8avXpqXMOc68ef2Hlwqzc7o+9EoNXlvL5FyifCfEjfor2U5EgFfFRtJ+K+ANitVuR5pXop28+UlsI6hy41oHlfKhQoc3phDhhfhVX8GSYsesVy0Z/CYG55fuf4DOh9uyVXRlLJ8622Yxcn67MLXyn4fUryk/7lzEc83rtv4tuGm22ZA7xDpZ+wZY+79J9j5os9Te8eVNP2qJTeesGTFU4sYM9FV665bUX/7E8bzWPOD2d9Wbdf3QllRJ1SlzKV3r6L933qNbexiGids4Xjld8MeZ3S9fwK5maa2ZVxM1zmK5rhK4INgfAHABzEFsCwAGYxGAUIZMYTBKI41YeX/uJF29dX65ftCjrkhAT2tr4pl1j3rOyUvxJZkyGFHglepakBGE/n/ZTET+B2ZFK4wjSK9G7FWkuRZpbnuqWp7nladG9/Im5JsRh6PVDmwe3uIEAKFNBuer8MUTidseY6uFEz71G5eoxJY4pP/nf6uN/94s1b1z2xwTMvpuY7SEGrK31L31/83LDonkZi3xhz9v1r1Hlc6797csEb1Rv7TP1IAq5Fh/5U1bvAQJzAOCTpLTmrW3LWeOVxkdX4g7H0K/+5HqupX1L2bUSSnq058CB4ZovP/2eLqckltLObg8YF7dtW1jzPMmEvVLDx8vutOhiKTOK09/Qan1uYc6T00IIJ2iNcLoK4Tl4I3gwCOYADAawOQAYgVEEJjEyisEkHq8u0qHA8TeftzTXiHm4vKTMW9ZbElEvcwnlPqvUZxWGPeecz5CCCF8SoSQRvpimJGG+OEJJpQGbwj0g9VvR5yo8LJC65OktuWsbjIuF0oTIzeanod2LW93Q6cNqCvIVqFCOjJPyTo5BAJz+ulbrX8b0JKtcPVe+90OCY7avfKA/dV5Mlk4sM0YIASDs99S88RdLax0h5IgC+2XXvjP6uD/n1IM4YC/o+KCgY2c0mRpGaMBY2Zq3vjt9UWLOtZz6+H/tB3dEAl5D4dx5V32LEstiK+esDoHzkoNPZvQfAYDW3DUHF9wyzri4NT33pKk26eXTIxl9UgjHgCc6jxoAcwAPBgAQGEVgFCOjCAxiUFHj0kVvsKN+8LeLsp/hEQIA4NMBudeKMBuhxDRfEqYkF3ggeSyt8A4qPH0K94DCM6B09ym8g1TEd9psSUp92Q2tuWum5JHGAOYAtLlxmwfbw5AjQ/lyyFeguCTFHj1jFQAMuKb7xxmaq1NkS0Z5CcExW7bdoXV0NOdv3J+oPjIzSQjPpqH/IZVkbppqtPs1z18PGJus9YXtO7J6D/DYCACEBPK2nNWt+eucioy425wIcBwXDgZLbccWH/2zKOQKU7J9i2/ryhjDWsB5GfYd7bK9ND/riemSVCAphLET1cVoPEBzACIcNorBIEJGMRhFoBGMuQ2cHHxMSmVmaq+Ni3mikCvVfGJuwytKdx8AeKUp9aXXncpbN9FyyGJwhLE9BPYwDAWhw4tFJCqQQ74CZUhgqvxfxioAQ569fY53qrIeHn2Y4Hl1L1XWv+yVGt+47KmEjSMzU4XQH+6t7fvlopynRxnH68L1IAj78ro+LOjYoXF0RY8EhQqv1OCVGrxSo0eu90qNXqneL9Yl+ILihSE4Jqdzd3nja2rvAAAMGObuWXqHX6wZZ7EY2KNdt+elfF0tqYqHmZNBUgjjRoA5vbhoDoA5CH4G64QgIZGYBBEPJCSISRCTIOIhMYnFJBLxzvVGDtKWmu67q7N/T5FxczXELJvesXvhqTdUrh4A8Il1dXOua81bx/Li4yDro2E4DPYwtodgOITtYeSJYAWFNELQCkArhGwZKMc3Vo4LYxIADkcOd36/2PhDpXi0ayQ6e9vl2+5EwG1d+zuLfs44LJ1YZqoQAkCL+Rk+T5ab8rXRnDzKetDa2wrbtud276Fo/3kKIUivRO+VG7xSg0+i84l1PklKQKz1i9WJOaF6BpKNFLa9X9b0ptQ/BABeqaFuznUteevjEsx7wLnN5js0d1rFVEsK4UQRYsEWggCDAywEGAjQEGAhyECAwQEGBVkcYEBKgoICBYWUFCgoUFIQ9r9AIE+pMW4Ta9EHXiISZfUdqKx/We3sBgC/WFtfek1L/gZ25ERRUTAGPwt+Gjw0+GnsZcBHg48GH4N9NPLSmE+AVggaAdIKQCMErRBUVEJseziHMQlAt/1Vf6inNPXHoyycx0au3PpDlbu3sfiqQ/MTOojGDBbCCOM80vWj+VkPjyaK/VjrQRywy3xWuc8s81llXrPMa5H7LOKg47wnY4SCIrVXovNLdAGR1ifReWQGuzpv/IOt8UPR/pJTW0ub3xaFXADgVGQcLbiyv3DNBTLLjwmG9R3u+sHc9F9KBNNpMnkmb6ifWoQ8SJfAyOGUEMbgZ8AVAXcEu2gYDkOHF7vDV+fAD3bbT5FkvpJCn/iQQojFn3yA6KcwhzAHgEDIwwDAJ4BEgAAEPARnbQTGGFiWT/AgzC5BJYuXOA59qfffef7OxUefy6977QXjta+lbGQQ+WmBAAAQ5E7fLsKCmAcSPsj5IOEjGR/UAsiUgpQkpHws4xP8aeARNjZCtK3fsXV+1iOjv2TBiX+p3L0uZcbRylENR5JMBBSpylBf2Wp9vjzt3rgXHhBrAmKNNeUzMwQkG5H5LHKvWeqzSgPDEr9N4rdJ/TZR0CEO2MUBO9hazj7fL9YMawps2gKbptCmzYvwJXG38wKIQq7Slv+VtLwbHd3aNAW1Zdd3m6qD4bA4TioIAJ3D/9bJFk0vFZw4kkJ4cRACKR+kfEiTnBFLBCC1uG9UOv6cYXjEHYFP5A+EnwS0EPJOC6mAwIgAwBBiCQCgOWAwYIAwi+Gs0FAYA01zQkE0mD1yqRf/OW9Rme3o6paXTa7223v+/DX71p0V324zLDhdIAAAiIjTnwTkBZbIEm/cFw/ahv6Wptos5I/We95gbSxteYtDvI+W3HHREXaSCSVNfbm5e/ew78jY4uHFCsOjnIqMz/vREJgVBx1Sv03it0n8w5LAsNLdoxtulwTsksDBzL6DAIARcsvTbJoCmzbfpi10KLPjtVrxOWM4jaMjr/PDwvbtJBMGgEFDRd2cGwaMFQCAOe5iBYwBb6jD5j1YnfOHOJY5rUkKYezoFcstng/p4NZC9YUz2I0YJeDsHzgOh0KsWHz2QRRWLnwvrzpj4Gj1ib9rXL1f2P/L/tR5h+Z926WYjRHiz2bYdyQQ7ptjvGOU5/Pp4IoDv0cY15bfMKzJn1DbklwUApGFhluaB/+gEpfxiCnzV+IQzyfW+cQ60J11FGOld0A33Kq1t+mGT2mcnUp3n9LdF43kyRGkXZU9rCmwafJt2gK3Ip1D45hswVjl7jVZ6kyWOqO1MepAjhHqSV9UN+f6IW3hOH/BEeBOWf6Uq/sqn4hxL8fMIymEsYMAFeq/U9Nzj05WLeTrJ+w2qDetuj91XvGprVX1L6UN1FxtrjtZePmJ8i9EqITbBj45MKy/1fKXEtPtiBhd3xzjJUeflfnMw+rcE2U3TLB1SUaFUlSqEld02F4o0N881bZ8FoRc8jSXPK0tZxUAEByjcXZph1t19tYUe6vC3aezt+nsbdEs3jRfZFfnDqvzh7T5w5oCj8w4mjvIvYMmS73JUme0NIhCzjPHPTLTgLGyqXCz87PxjeNLr+NtkifVKy6duFtMO5LOMuOlz/H2sO/Y3PQHx7kRZzROAcKwZ17ti4Vt2wjMBYWKmrlfOzt14sxgNPXQYn6KIASjfIHy6eCl+x/L7DvI8vhvbfrDhL5i4sgMdpY5A8P6j3T9qNj4A5WkbKRzEq0eKCaosbdrh1t1jjbdcJvMZzn72zAl80s0UU9UhhSyiAQAlhQwPD4AsDwKYWwYOhl1AY3iF2sGDRWDhgqzodwnGXGeP171EAj3He+9d37WI6NfU0goks4yCUqaaovNd6Tf+b909RUTfa+QQL5/4XebCzYtOvacyVK/7NBTRa1bDy34jiWldKJvnTjYvIddwebqrMdHc7LMZ1m7+0G1qydMyT5ccc/EqSBJAA9BeMTgeknOA8mTFBm+22x5emH2E6PcVjjlREiRWV9m1p9WbmHYo7O3aodbo8NEUdApiHgvWkhIIDfryweN5WZDRWxhsmMDY7bJ/Icc3ZenqQpOHEkhHC8IoRLjD2p67lZJyqWC7Em4o0OV9d7a32b37l9Y81eto3Pzjru7Mi85UvWNC3QnZwwR2t5qfa4s9W6CuHgGXaO1cfXHDwnDHqciY+fK+zwy03huzSeQgsISEskpkJAgp04ndJXyQcZHIhIwwKAfd3igzY0HAsDFe65lRqKWVur880+Z/1SSeudU2xILIYG8zzS/zzQ/+qM46BCGvQRLAwDJhHiYAQAeEyY/OYIwN6zJcyizp2Qip9P2MkWqjcq1k3/rBCcphHFAyNfn6b91cuCx+VmPTNrKf1fG0t7UBWVNb1Q0vpbTvSer90BH9qX1JVdPl6m/GMDAnhx8Ik25SS66uBNBcet7i48+R3BMb+qC3Zf8JOZ4jAggW4YqNKhYCdQIOe7OnJkqQakSWG5EEQ66PLjVjds82BOJ7c6zhdyUG2u6f2J27TAq1021LeMlIFIHRHGetYsXDt8Jq2fPguzHRh+DafaQFML4oJctc/kbW8xPl6TeNWntjOVRtWVfaMtdO//EP3K7Psrv+CCvc1e/aV596bVnpm5mEp1DLxE8KkNzzYVPIzhm8dE/F7duBYC60uuOVd4YW+9bJ0IVaihXI/nYA+5QBBQqUaESYYytQdTuwe0e3OvDXHKU+DkIRJWm/vhE78+lwjyZMGeqzZmZhOmhZstTc0x38XkJEdY/0Ug6y8QNzNHH+36ulS7MvNib+ryMczFc6rOWNb9V0L6Dz4QAYFidc7L4yo7sS+MVh2LSGKkehjz7OmwvLsh6hORdyOdbGPas2vM7k6WO5fH3L7ytNXfNWA0Q8qBUhSo0KF0C8Y1EHGRwpxda3fiU69PACyORaE4iE43Ne7B96B/zMv+PIj+T9Xq21cNIjKceWC58ovdnesWKdNWWuBs2ySRDrE0DIrT9WM89BYabtdIFY702Lg88RfsL2j8ob3pdHLADgFdqOFm0pSV/A0MKxlPsZHLeevCG2uv7f12R/oBUcKGJX7WrZ+3uB2U+S0Cs+WDFz8e0DYtAkCdHFRpUqABygkPPMRzu9kGLC065OC99/nNmoQB0Df/H6a+rTH/w7F0xs7AezkvM9YAxbhp8lCAExcYfTIRhk0xSCKcH3lBHff+vylJ/LheNbdd2HB94ko3kd+wsa3pL7h0EgJBA3lR0eUv+hoRdvTibz9dDkLac6Pl5oeE7mgt2LzL7Dq3Y9yjFBG2agp2X3hsYXbhIIQ/y5KhQifLkSDTpCwUY48EAtLjglBsPBT/zJM5CAcCAmwYfB4AS4x1nxuKzsB7OS8z10DH0T3eotTLtl6PddBsn+ASQBEIAgjOhJU//CPYQuCMx6tHa3ikAABvvSURBVE5SCKcNdl9Ni+WZyvQHxIIxxH+J+wOPMM7q21928o2U4VMAgBGyaot70hf1ZCwZ5bbfKeGceogwzuO992aoLzcpN5z3fIoJpg7WZPYeyu3+CGHcnrNy76IfXDSCmkaIChRQoECZ0kSJPO4IgyuCSQQkAgDgYdrr8aZoNXwCA4CAhxACRwhbgmAJgCWILQE80mhy+oI5urb/QakgI1//7eiRpBBGia0eeh1vWdwfVmY+NKFBZGR8ZBCDUYwMIjCKkWoU009+Bgb9eDCAB/1gDoJn1LqIOW6t2rMsN85R0ZNCOCFY3B932l6szHhQRI1WcibugTdYG+e0vJU2UEOyp/0XHcrMnowlPelLhtUJ55twdj3QrOdE7316+bJMzXXnnCYJDGf0H87sP2y01PNYGgA4RByr/Hp96YgLtASCDCkqUKACBWiFiaF+I0PTtNvt1mq1FzjHz4AlEJVGbAmCPTQT9mywXOBE7y9U4orclK9CUgg/IYZ6GHS932t/uyrj1xT/XNkQkyDhIzEJYh5I+ac/S0iQkEAREObAR4OfwQEGeSM4wIKfBh+N/QzQHACASgBGMTqjfNJxDzW9n6RSH/TjoSCmeEhCgowCCYmkJJbykYQPMj6SkCBAjMvp1Ol0Fy90LCSFcKIYdO3ssb9WkX6/mEodzfkT/cDzmVDaYE1m78GMgaPRkIYA4JPqu9MX96QvtqaUjCtkYvw4Uw8Rxl3Xd79GWp2j+9KZb7WOzoy+gxn9hzXOToQxAHCIGNIW9aYv7MlY7JadW9UEAqMYZUhRhgSyZFMw+RkzoxHCc4iwuN8PvX7o9eF+P0Qu5o+TsDCs90Tv/WpJZW7KV5NCGGWs9TDoer/X8eaGggdTZQY5dTqLnIwPCgokZOyzIBEW408y50wJDMM4k0I4vTC7P+yyvVSefu9oNtpP2gNPcIzR2pDVezCz/1DUpwYAQgK5TVvgUGY7VZlORZZTmT5VCUuj9UDw/fW9v8wQVswll0iCdlHQqfAMpA8cOxObiiaFA6bKnrRF/akLgsLP+BkKeChNAhlSlCGFVDFQU/fQjocYhPBsOAzmAO714V4/9Hqxn4mvdRMOw3pr+x+QCwtytTeFw+GkEF74/aCgkE4IehGkiJBaCDs6Xv+ga8cTa35tmHFBNpJCOC2xeQ+1Wp8tMd6uklRc+Mwp6PlinDLcmtl3MKv3gMI78BljCNItT3UqMx2qbKcy06HM9EovnkP1whAcw6dDFB3gsWGSCVO0n2QjJBOmIj4eG+HTQVHIJQo5xQH7MGd7Ns1zuZlebz039UxArOlJre5NXzRoKD+zEMgnQC1AWmFU/JBehInpH391nEJ4DsMh3OcHcwBYDtMYWA5oDhgOWACaA5bDEQ4wIB+NmXhm+xkXDBdoHPgdSUiylLdIJcqpNmeKOfv9IOSBXvyJ8gmRXoyEn2yS4jD3VM1f6qwnH1n1gEakmkqLJ4akEE5X3MHmxoFHMjXXpqk2XeC0qZ0CkvnMWkenytmtcvWqnV0yn5nAn3kjMqSA5fEZnoAjKA4RNCUCgAhfggFFvwIAkqV5TJjADJ8JIY6j6CACjk/7AUAQ9o3SkmMq9Lcs8uvdbJWXHxCpgyJVQKgOiNUBsXrQMDekz1cJkUoAKgpUAqQWgoqKwxJFAhJfIRw9Xhq7wuCKgDOMXZHTHzwRxE7F6iOHmRbz075Q39z0n31+oWs2wCeQSoDVAqQgWTLsyTWqNQJQjBDhwRfxP7j/UQ5zD1xytyTWUEoJTlIIpzEh2trQ/1uJILvIcMtIQTITai2EZCNKV6/K1a1xdqtc3WpXtyjovPhlF4RDBE2JaZ6I5VE0JaJJEcMT0HwhR4l5lIAnFLFi2U6ipTbSdpX+KwXZSwRiMZ9AFA8EPKAIoAhQCYCfIC6eE89UCeF54TB4aHCGcb8fOjy43w/MZMXI4Ti2c+i/Q74dJabbleI5k3PTSYYiQESCiERCHkhIUAlALUBqAagFSMbH0Z0kFxWAdmfnL/Y+vCR1wa1V3+BNtzAaoycphNMblgu3Wf/sDrWVmm4/75JhQgnh56GYIGJZPhtEHMPjWJIOAYAg4geESSYc9dtkCZLhCznEo0kRJogIXwSAInwpADACiVJIyPkgp0BJITkFcv7pBXwBDwDA7LM+dOBxEV9094LvQwgniABMIQklhOcQYXGPDzq9uNODh0Lxf4ecTfS5COP2JsuTRvmqbO0NaLq95RFCCgo0AtAIkVqAxTwkIkFEgpAXFT/MG8VM/gUEAAN+49S7LzS++oP5N6/KvGQCfoMEYoKEcPp40U1zeISgyPj9Ic/eur4HUpUbMzTXEGg6VX6EFAEJYRhtf0XGRzoh6ERgEiOdEFJEiBzBKRUD/l/b+3+re/nLc669rmgLQzPukDtudieZACgeyldAvgIBgJ/G3T7U6cHtHuyesPDiKkn5gszHTlmerun5SZHh+1Jh1kTdadyIyE+n7nVC0AlBK0LUp43/85o3rkkOs8/6yOGnQ0z4j+sfMY17IX/WMp3exTOAFPklSlFJi/W5Y113FBhvUYpmSB5BIQ9MEpQiRCki0ItA95kn/0J0uLqfOPInDPjJtb/JVIwh/kCSBEHCR6UqKFUhALCHIMziEAuAIMwCh4HmgMVAc5jhgMUoxIIrgh0hcISBHuPkKkUqytJ+bnZ/WNf/S4NiVZbmet4oUnHFkegATkSCmAQRD0Q8EPORiIfFJBLxQMwHMYlEPDxpWwtojnmt5e3/NL35pdJrri+6gkiM7U/TlMQSQoRQdFNnNOWbjA9SPpLxgU9AhAOGAwZDhMUshjALGFCIBQ7jMAteGhxh8NHTYOMUxdeUp/1s2HuoafBJhTAvR/dlETWuPHlTAg8hvRhSxZAmQakSpBHgscantged/2j4996+QzdVfHlz7roZ4OeZRCOEEcY36POfPRHsCIMjDM4wOMKnP4cvtvfRqFilkczrtP3rUNdt2ZobTMrVAJ8RAAIhIQ9H19ui/6LTj598AAAIMaetYLhP9TjEoqhxQhKExOmpyzOXi8iR2ie64I8TAga8p/fgc7X/zFKkP7fhMaNUPwk3ndkkhBAu0zFqNSHjg4QPo5guH7HlhVlwhMEewtHnyh4GRxj8CamOWtkitbSqz/FOTc9PtdLqTO01Al6i7/hRUJAmQWkSlCoBo/gcv5UxPP/OkOs/TW++1/nBppw1L1z+Rxk1w5eHk5wXOYXkFGSdjvx1uv2E2HMXHBmGc7lCWu3ZjUQF8MM2R/tf6//ZPvD2F0uvvzRjeXQ8RKCR9npfoH2OpukmSi8NAz44cOwfDf/GGN9Z/d15hotsykoyShLCWWZCnQJCLDjC2BECVwScEewMgTMyZe7gn4dhfX3Odwac76vEZTrx+hTV1OcRRAjJ+KASgJI6vdShEoBGiCTj7jX1uPv+e+qdj3r2r8le8eWSa7Tni4udyE4ik0myHqJc2DmixlL3r4ZXhgLD1xZdviFn9UzdMwAAgXDg3ebt7w/sRoi4seyGS9IXzc78ujPZa3TyH3gOgzuCXRFwhsEZBh+No31JAmEhD3gIKB6iCCAQiEggADCAIwTOCDjCODqTE2bjaQ/LBQecO/udWylSZlSu0csuEfElIjK66gASPgh4EGKAwUCzEOaA4XCEgwgbXXe50F/wzJQOAZjiAYmAz0N8BDwEQhIQgJAHBAIhD8n4WCVAKgFSUji+eYjCbGRP34F323f2efq35G+4smCTUqAY6eSkAERJ1kOU0bz4moZPvdrydo25bkXGkk25a0u0BZNm3iTQ5e7d1vHBjq7dWdKML5dfO984d3ZKYJSkECYWfho7I6eXN5zh07Foo/AJOHt65pzpGgRYwDvPtyRm6IDHjrv39O6qtZ6o0pdfmrlskWneaDq5UWcEgKiWj/t3ixMRNnLUXPtR7/6DA0dLtUUbc1cvS1tEEhfxfZ+m7SHuJOshyuhffPagc1vnru2duzDAqsxly9MX56kSLqb86On3Du7pO/hh91532LM+Z9X6rJXCCBV3AZh2JIVwhnN2PfjpwJ6+g3t6D9QNnSzWFlQbq+YZKnKUWdPCo6TPM1BjqTtiPl5rbSxQ5y5PX7Iyc6lKONoQWcn2ECVZD1FiePG12Nt29+zb03eQxdwi07wFxspKfZmUkkyckfEixITqh5qOWmoPDRwLMMFlaQtXZi4r15USCE2QAEw7kkI4wzlvPYSY0DFL3ZHB4yes9a6wZ462uFRXVKzJL1DnJo6PSZAJtTs7m+1tJ20tjbZmHsGr0pcvMFUtMM6VU2POgpZsD1GS9RBlPC++bnff4cGaY+bak8MtRqm+TFdSoi0oVOely1MTZLMBBmz2WU/Z25vsrY22pi5Xb6E6b56xYqFpXoE69+wp0KQQRkkK4QznovVgDzobbE0nh0+dsre1OTvllCxHmZmpSE+Xp6bJTKlSg1qknoQhoyPoNPutA15zj6e/zzPQ4eweDjpylBlFmvxiTWGZrnicztzJ9hAlWQ9R4vLiYzi21dHeONzSMtza4mi3B53ZioxsZUaGPC1NZkqVGU1SvZCc8F2JETZi8Q8NeC193oE+z0CXq6fT1SOlJAXqvGJN/hxdcbEmnxohp3RSCKMkhXCGM6Z6iHYkO109Pe6+Xk9/v3fQ7LN6wj6dWKMVa7QitVKoUAoUCoFMJpDJ+BIxXywgKQlfjACNNEcUoIMsZgN0IMxGAnTQF/F7Il5P2OsKu90hry1odwQdFr9NTIpMMr1JasyQp2Yq0rMVGWlyUxxjGybbQ5RkPUSZiBefnw50u3u7XD29noE+z+Cgz2z2WYWkUCfW6sRqpVCpESrlArlcIJPyJWK+SEpJhDwBn8eP/n8eIzk2yASj/wfoYIAOeiM+b8TnCXsdIacj6LKHHLaA3Rv2GaQpRok+TW7KUqRnKtJzlJmjnDVJCmGUZIi1JJ+CAJmkBpPUsCxt4ZmDETYyHHQMB+y2oMMZdLnDnk5Xjzfi80X8fjoQYSN+OsBhzk8HzlumiBSSBCnmiygeJeaLpHyJjJIqhHK9JKVIk68VaTQilV6SIhihx5okyXRBwheXaotKtUVnH3SG3MNBuy1gd4XcjqBzOGDvdHX7Iv4AE/RHAiE2TLN0kAkx3HlSO5IET0SKeARPTIpEfJGYFMkEUhklkVPyYk2+SqjSiFQ6sVYtUs5mh89EJimEMweKR0XVcaoNSZJk+qESKlRCRf50djRNEjNJIZwyenp6Wlpa9Hp9WVkZjxeHqUWO41paWnp6evLy8vLz88dfIACEw+HGxkaHw1FSUpKamhqXMj0eT319PcMwc+fOVSrjk3DVarU2NDTI5fKysjKRSBSXMpMkOB0dHW1tbWlpaSUlJQQRB+cXlmWbmpoGBgYKCgpychJXEV0uV11dHY/HKy8vl8vlU23OjACPEY/H8/Of//zKK6+89957PR7P509wOp0KhWL0BUYiEZvNNlYzpjU2m+3aa69VizXVmUuyNLnFxcX79u0bZz00NjZWV1enKtMXZi1LkRlWr17d1dU1Tjvfe++9zMzMfF3R/IxFSrHqm9/8ptfrHWeZTz75pEalmWOaW5E6TyVX/epXv+I47uwTxloP4XD4Bz/4gUKsnJexsEhfajKaXnnllXEamQjMwufivNA0PTQ0dM7B/v7+jRs36qQp1ZlL05SZlZWVx48fH+eNjhw5Ul5enqHKqs5copHoLr/88sHBwXGWGUei9cBx3EMPPaSUqypS55WZKjUqze9///upNm1SOW97GD9jHhG+8sorer3+F7/4xXPPPffqq6/edNNNEyHPM5sbbrhBYlO/dtN2ihQAwEdtOzZt3FRXXyeVxrgjwuv1rlu37vrCG6/+xhcRIJZj/3HoT5s3b66treXzY0zfXl9ff8O1N/x60xNV6QsBIBDx/2b7vTfffPPLL78cW4EA8MILL/zuvv976qp/pqsyAcDqNd/9h9skEsntt98ec5l33XXXgbePvHTjOwqhEgCaLQ03f+MWg8GwfPnymMtMkshwHLdly5YCVPbqTdtJggSAdxvfWL9ufcupFrVaHVuZQ0NDGzdsvLX6zvWrLwcAmqX/uPexq6+++sCBA2ONJj+hPPnkk399/O/PX/+KXmYEgH5Xz12/vFWpVN54441Tbdr0ZszzCfv27bviiisoirriiiv27t07ETbNbE6ePFl3uOH2lT+LqiAAXJq/bnnm2n/84x8xl/n666+n8bOvmful6FI8j+B9c8n3aBu3a9eumMt87rnnri77UlQFAUBMSX66/ldvvv6WzWaLucynn376+yt+ElVBANDLjHetvu/pp5+OucBgMPjX5/967/rfKD7ZsF9sKLux+pY//vGPMZeZJMHZv3//cJfj1kvuiKogAFw25+oSZcW///3vmMt88cUXK3UL1xdfHv2Rz+PftvzHPc19R48ejYPF8ePpp5++c/V9URUEgDRl5g9W3D2eJyhJlDGPCO12u16vBwC9Xu9wOM57TjgcLikp+fzx7Ozsf/7zn+ccpGna6/WO1YzpS01NTb6u8Bwn7BLDnKamppHq86LU1dWVGOacfQQBKjLMqa2tnT9/fmxlNjc3rzdcffYRCSVNV2bV1NTEXGZra2vJ3M9EFS/Ul/Z091gsFpI83RTH1B66urqkpFwr/UzijmJD2UdN24aHh2MzMkGYbc/FSPx/e3cf00SaxwF8gFDhWN6uhNeCOZRbOAIRPE/ExFUX2IWVa6kXFPElBWEvaWJiwhmMeBExVnP3h4EL/oELelpfcF1PFk5RsotiNEcqIHDgsiuIUktfoVAtHm3n/qgi28JKS+sDzvfzF5lMhm9+feb5MUxnHoPBoNVqp1+Wtbe3RwfFWjwRHxMc19nZafeH3t3dHfPzM8jN1e3jwNi2trYFcrPQYDBoNJqB/oGYjJ/ljAmO6/u+b7GP9rmzHg/v5OfnNzW9zMbmRkjTr1eeo2naZDLNuA+LxTp37pz1dg8PD19fy7ctT05OUhRlvf1DxeFwlDqFxUalThH4caC3t7d9dQgJCfnpxX8sNqp08tDQULsLGxAQoNRY5RwfjoiIsPuY/v7+Sp3i115vn41Tv1B+5P0Rm/12GQqbxkN4ePioXjNpnJz+h4VyXB4QELDYRxTTzovZGAwGk8k0vQ5hYWEznUHy2ODldpcrKChosEtudczhsLCwBfIRmOvg7eOt0ilDfN9+bU2pk/v7+y+QkO+B9Xh4p7l8FdHmRshmsxUKBYfDUalUsz3t6+LikpiYOPdjuru7230ra9FZu3at3l13f+DOmt+8voml1Y/Ud39z4YjY7jrweLyjpaLto7vD/F4v8v6DvKdX3ZWenm53YTdv3lwsPPD57/449caNf//3X2GRoTNe688Rn88Xf/tV6Rd/n3qaSiyp5vF4FiHnXofg4OCk5KSv28/l/F5g3mIwGWrb/vnnAwUfwIhi1HkxGxcXF4s6pKSkfPnyy67n7XGhCeYtSp38u74bB/nf2V0uPp//eUX6lsQdbK/XT2q3PWtVTMo2bNiwQD4Ccx2ysrLEkq+KPv2reSNN0ecl1Xw+f4GEfA+sx4NjDkvb+GaZkydPslisvLy86upqo9FYWFhosQPeLPNOTU1NuTm5a8M2xobEK8bl17ou5QkFpaWl86lDRUVF6YHDmbF/4vhF9Kt+uvHjtYrK8m3bttkdkqbpwsLCG1/f5MZn+3r6dQxJOjStdd/WrVy50u5jjo2NZWRkjD/Rp0Z/4erievvHpld+ups3bwYGvv3fpq3joa+v77O0z5Z5xPxhafKL/+nqu79J+CT+woULi31qYOB5MaMZ3yRy9erVgryCTyMzfhsYI9NKr3XX/qWkaN++ffP5RWVlZRV/+wc3LjvYJ/QHec/3g401Z6o3bdo0v/gOY64DRVFpaWmskV99EpVqok1Njxq8lnpcv36dOQ9RLJRXrOl0OpFI9Pjx46ioqOLiYi8vy/d1oRHOhVKprK6u7unpCQ0N5fP5q1atmn8dHj16JBaLnz59umzZsl27di1dunT+OZubmxsaGlQqVXx8fH5+/vzPN5PJdPny5Tt37hiNxjVr1uTm5lr8+96OOrx8+bKmpqatrc3HxyctLS09PX2eIRcCZp4X1mab+KRS6enTp/v6+jgcztatW+PiHLCidUdHR21trVQqjY6OFggEwcEL6N0UU3UwGAznz5+/d++eq6vrunXrsrOzHfIM5WLhrFfNOfyBDFufI+zv7z9+/LjDYyw6AwMDx44dI52CvCdPnohEItIpyBscHDx69CjpFOQNDQ2VlZWRTkGeVCo9fPgw6RTkyWSyQ4cOOfyw5P+UkEqltbW1pFOQJ5PJLl68SDoFecPDw/P5HvwHQ6FQiMVi0inIUyqVqANFUWq1esZvIDKNRqM5e/asww9LvhECAAAQhEYIAACMhkYIAACM5vjVJ9zc3Hx9fXfu3DnH/dVqtVwun/v+HyqNRqNUKlGHkZERtVqNOoyOjmo0GtRBq9VqtVrUYWxsbGxsDHUYHx/X6XQ21eHIkSMRERG/vI/jV6inKEoikfT09Dj8sAAAADbJzMz09/f/5X2c0ggBAAAWC9wjBAAARkMjBAAARkMjBAAARiPfCFtbW/Pz83k8Xn5+vkQiIR2HmJaWlt27d/N4vL179w4NDZGOQ5LRaBQIBKRTEDM+Pl5SUpKVlXXw4EGGL0nI8JFghpnBzLmdwuEvbbOJwWDgcrkPHjwwGo23b9/esmUL2TykPH/+PDMzs7e3d2Ji4tKlS3v27CGdiJgrV64IhcKUlBTSQYipqqoqLy9/9epVeXn5qVOnSMchBiOBxszwhrM7BeErQqPRuH///oSEhImJCXd3d+u1LBhCJpNt3LgxOjp6yZIlaWlpz549I52ImMjIyO3bt5NOQdLdu3e5XC6LxeJyuS0tLaTjEIORQGFmeMPZncLxD9TbhMVirV69Wq/Xc7lciqJOnDhBNg8piYmJ5qWMjUbjmTNn1q9fTzoRMStWrCAdgTC1Wh0UFERRVFBQkEajIR2HGIwECjPDG87uFASuCAUCQWpqampq6tQWT0/Puro6gUBQWVn5/vOQYl0HiUQiFAq9vLyEQiHBYO+fdSmYjKZpFxcX8w8mk4l0HCCPsTODBed1CgJXhDU1NVM/y2Sy+vr6goICT0/P9PR0Rq2/M70ONE1XVVX19vaWlJRwOByCqYiYXgpgs9kKhYLD4ahUKizMy3AMnxmmOLtTEL5HyGazGxoaurq6aJpubm5evnw52TykdHZ23r9/v6ysjM1m6/V6vV5POhEQk5SU1NjYSNN0Y2NjcnIy6ThAEmYGM2d3CvL3CEtLSysrK4eHh8PDw4uKisjmIeXhw4dDQ0NZWVlTW27dukUwDxC0Y8cOkUiUk5MTFRVVXFxMOg6QhJnBzNmdAu8aBQAARiP/QD0AAABBaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBoaIQAAMBo/wdgJIvkXcFHhAAAAABJRU5ErkJggg==" }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nsamps = 500\n", "ymean = [];\n", "visamples = Array{Float64}(undef, nsamps, size(xtest, 1))\n", "\n", "for i in 1:nsamps\n", " visamples[i, :] = rand(gpvi, xtest, Q)\n", " push!(ymean, predict_y(gpvi, xtest)[1])\n", "end\n", "\n", "q10 = [quantile(visamples[:, i], 0.1) for i in 1:length(xtest)]\n", "q50 = [quantile(visamples[:, i], 0.5) for i in 1:length(xtest)]\n", "q90 = [quantile(visamples[:, i], 0.9) for i in 1:length(xtest)]\n", "plot(xtest, exp.(q50), ribbon=(exp.(q10), exp.(q90)), leg=true, fmt=:png, label=\"quantiles\")\n", "plot!(xtest, mean(ymean), label=\"posterior mean\", w=2)\n", "xx = range(-3,stop=3,length=1000);\n", "f_xx = 2*cos.(2*xx);\n", "plot!(xx, exp.(f_xx), label=\"truth\")\n", "scatter!(X,Y, label=\"data\")" ] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Julia 1.0.0", "language": "julia", "name": "julia-1.0" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.0.0" } }, "nbformat": 4, "nbformat_minor": 2 }