{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "在贝叶斯分析中,计算后验分布时经常涉及复杂的积分运算,比如\n", "$$\n", "P(\\theta\\mid x)=\\frac{P(x\\mid \\theta)P(\\theta)}{P(x)}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们的目标是计算后验分布$P(\\theta\\mid x)$,困难在于计算$P(x)$, 因为\n", "$$\n", "P(x) = \\int P(x, \\theta)d\\theta\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们可能会想到通过Monte Carlo来近似$P(x)$, 但仔细一想,这是不可能的,因为无法从上述积分式中sample出样本来。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们可以构造一个Markov链来进行Monte Carlo近似,这称之为MCMC。下面以一个实际例子来说明如何进行MCMC。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "首先,导入必要的模块。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "from scipy.stats import norm\n", "\n", "sns.set_style('white')\n", "sns.set_context('talk')\n", "\n", "np.random.seed(123)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "生成20个正态随机数,而我们的目标是根据这20个随机数,估计均值$\\mu$的后验分布$P(\\mu\\mid x)$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "data = np.random.randn(20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "绘制这20个随机数的直方图" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#为了显示matplotlib画出的图\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.subplot()\n", "sns.distplot(data, kde = False, ax = ax)\n", "_ = ax.set(title='Histogram of observed data', xlabel='x', ylabel='# observations')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "实际上,可以计算得到$\\mu$理论上的后验分布。" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "## ###############################\n", "## mu_0 prior\n", "## sigma_0 prior\n", "## sigma post \n", "## ###############################\n", "def calc_posterior_analytical(data, x, mu_0, sigma_0):\n", " sigma = 1.\n", " n = len(data)\n", " mu_post = (mu_0/sigma_0**2 + data.sum()/sigma**2) / (1./sigma_0**2 + n/sigma**2)\n", " sigma_post = (1./sigma_0**2 + n/sigma**2)**-1\n", " return norm(mu_post, np.sqrt(sigma_post)).pdf(x)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.10896926852884785" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mu_0 = 0\n", "sigma_0 = 1\n", "sigma = 1\n", "n = len(data)\n", "mu_post_true = (mu_0/sigma_0**2 + data.sum()/sigma**2) / (1./sigma_0**2 + n/sigma**2)\n", "mu_post_true" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "画出理论上的后验分布曲线" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.subplot()\n", "x = np.linspace(-1, 1, 500)\n", "posterior_analytical = calc_posterior_analytical(data, x, 0., 1.)\n", "ax.plot(x, posterior_analytical)\n", "ax.set(xlabel = 'mu', ylabel = 'belief', title='Analytical posterior')\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "下面我们进行MCMC采样" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def sampler(data, samples = 4, mu_init=.5, proposal_width = .5, plot=False, mu_prior_mu=0, mu_prior_sd=1.):\n", " mu_current = mu_init\n", " posterior = [mu_current]\n", " ll = []\n", " for i in range(samples):\n", " # sugget new position\n", " #\n", " # i-th state(xi) of markov: mu_current\n", " # proposal: sample from q(x|xi)\n", " # \n", " # sample u from uniform(0, 1)\n", " # if u < alpha(xi, x) = min(p_proposal/p_current, 1)\n", " # accept!!\n", " #\n", " mu_proposal = norm(mu_current, proposal_width).rvs() # random choose\n", " \n", " # Compute likelihood by multiplying probabilities of each data point\n", " likelihood_current = norm(mu_current, 1).pdf(data).prod()\n", " likelihood_proposal = norm(mu_proposal, 1).pdf(data).prod()\n", " \n", " # Compute prior probability of current and proposed mu \n", " prior_current = norm(mu_prior_mu, mu_prior_sd).pdf(mu_current)\n", " prior_proposal = norm(mu_prior_mu, mu_prior_sd).pdf(mu_proposal)\n", " \n", " p_current = likelihood_current * prior_current\n", " p_proposal = likelihood_proposal * prior_proposal\n", " \n", " # Accept proposal?\n", " p_accept = p_proposal / p_current\n", " \n", " # Usually would include prior probability, which we neglect here for simplicity\n", " accept = np.random.rand() < p_accept\n", "\n", " # if plot:\n", " # plot_proposal(mu_current, mu_proposal, mu_prior_mu, mu_prior_sd, data, accept, posterior, i)\n", " \n", " if accept:\n", " mu_current = mu_proposal\n", " p_current = p_proposal\n", " \n", " posterior.append(mu_current)\n", " ll.append(p_current)\n", " return posterior, ll" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "进行5000次采样后的结果如下" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "posterior, ll = sampler(data, samples=5000, mu_init=.1, plot=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "下面画出估计的后验分布的直方图" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.2380707784151337e-15" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p_true = norm(mu_post_true, 1).pdf(data).prod() * norm(0, 1).pdf(mu_post_true)\n", "p_true" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-14.907254526724241" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.log10(p_true)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2)\n", "ax[0].plot(posterior)\n", "ax[1].plot(np.log(ll))\n", "ax[1].hlines(np.log(p_true), 0, 4000)\n", "_ = ax[0].set(xlabel='sample', ylabel='mu')\n", "_ = ax[1].set(xlabel='sample', ylabel='ll')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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qxZf6f//v//HVV18xbtw47rrrLoYPH87//d//1Xm/yWTi5ptv5oYbbqhxLTQ0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\nwAKcFYd3AI/1bDo5lHLgEPBx4Jaej0/gbK0gQxhOWzXG5AJ/BlqArwF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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plt.subplot()\n", "\n", "sns.distplot(posterior[500:], ax=ax, label='estimated posterior')\n", "\n", "x = np.linspace(-.5, .5, 500)\n", "post = calc_posterior_analytical(data, x, 0, 1)\n", "ax.plot(x, post, 'g', label='analytic posterior')\n", "_ = ax.set(xlabel='mu', ylabel='belief');\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "下面分析proposal width的影响,太大则选出的$\\mu$跳跃太大,太小搜索空间时太慢。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "proposal width较小时" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "posterior_small, ll_small = sampler(data, samples=5000, mu_init=1., proposal_width=.01)\n", "fig, ax = plt.subplots()\n", "ax.plot(posterior_small);\n", "_ = ax.set(xlabel='sample', ylabel='mu');" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.hlines(np.log10(p_true), -200, len(ll_small)+200)\n", "ax.plot(np.log10(ll_small)); plt.xlabel('sample'); plt.ylabel('ll');" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "def traceplot(mu, ll):\n", " plt.figure(figsize=(10, 6))\n", " plt.subplot(2, 1, 1)\n", " plt.plot(mu); plt.ylabel('mu'); #plt.xlabel('sample'); \n", " plt.subplot(2, 1, 2)\n", " plt.plot(np.log10(ll)); plt.xlabel('sample'); plt.ylabel('log prob');\n", " plt.hlines(np.log10(p_true), -200, len(ll)+200)\n", " plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "# small proposal width\n", "posterior_small, ll_small = sampler(data, samples=5000, mu_init=1., proposal_width=.01)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "image/png": 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2mab5mWmaz5mmOdM0zXmmaT4NXAy0BO4s7U5KyQUH2ahZvXwyQbSs730qRu2wEG7oF+vXNWInTPPaft2HK0rarWJ7ceZmfly93+u+HQkp5dYPERGRM1GgB8jH8D5KXDfv32JN/DRNczZwECubhVRB9XxU6MvJtfPE+R1Y/dgI1j0xkjp+pJtzt2JX+c1D/mTpbp/7Rv1nEUeTMzSSLCIiUkKBHiBvANoZhuHez055/5Ykv1YQoMihirqpf0sAQkOCWPfESEf73UOtAiV1wqsTERrCxDHtHPvuHBLnc3R5wQODHY+DAqi2SK9n53idBiIiIiJFC+g0b1g5kP8BnIdTJgvgOsA0TdMzOW0hDMMYCTQEyn9FlQSE8BrV2PX8WMf26sdG8PfeRPq7pYm7pHsMNqB9k0g6NLFKVg82ol0W9b1yWRdi64fzw+39uOS/f5Brt+YGh9co25eV3W4nrHowqZk5jn7UCAlyFDpxNmX1Pi7qFlOm/RERETnTBHqAPB2YD3xoGEY9YCdwPdAfuCD/IMMwFgCDTNO0ObWtBj4FTCAL6Ac8AGwD3i6n/kuAqxNenSHxnolNgoNsXOZWTa9d40jH47Nb1+OSHlbg2Tgq1NF+KCmduGjXCoGl7URqliM4/vWu/nRsagXww9s1JP6xmS7H3vvNGgXIIiIixRTQUyzych5fCHyNVW56BtAZq3DI1CJO3wzcAXwHTMMadf4A6KPCIVISzpX/nB9HR9Qgv0bIrA2H2X3sVJn2Y5fT9ZvVDXM8Dg0J5rIensFwflVAERER8U+gjyBjmmYSMD7vP1/HDPbSNq4MuyVVUGhIELXDQkhMzXLMZQarUp89L5/KCzM388LMzSx6cIhL8FqathyycjM3jKxBVE3XxYQdm0bx3Z/7XNoOJ6UTU6ds+iIiInImKvUA2TCMgf4cZ5rm76X93CJlyWaz8cud/TmSnE7P2LqFHvvJH7t49FzXQo+5uXaCSmEl3+Ekqzy2t6D3ou5NWbM3kbaNIhxFTY4kZyhAFhERKYayGEFeQOG5i/OVT+JbkVLUvF4YzesVHWzudithvcA8wg0frWRg22g+vam3y75Vu45z6btLufasFjx1QQeSM7KZue4Qw9s3pK5bWrrNh5J4bc4WABo5zX3OFxkawqtXdAXg7XnbSM7I5khSerF+RhERkaquLALkG308TxxwA7ALeK8Mnlekwozu2IgZ6w85tt2r6uVnv/h9y1G2HUmhdYOChXyXvrsUgM+W7WZUx0b865u/OZqcQeflUfwyvr/Ldc5/c4njcfMipnDUq1Wd5Ixsjp3KLNkPJSIiUkWVeoBsmuYnvvYZhvES8FdpP6dIRXv+ks4MaBPN7mOneO/3HSzamsC2I8mcysjBaBThcuwrs0z+e00PwAqKnV39wXLH47X7Trrss9vtZDotuNtxtPCKebuOWaPYny/bw9V9WhT/hxIREamiynWRnmmaJwzD+AB4EPAZSItUNlE1Q7iqT3NmOo0iD3/VmmbfOSbK5dj8kebjpzJ57KfCa91k5eQSEmwlm/ltwyGXfed1aeJX3zYdTPLrOBEREbFURJq3E0CrCnhekTLXvXltjzb3kWCA+79dw8XvLPFod/fugu2Ox3/vdb3O2E6NCz3Xef9xTbMQERHxW7kGyIZhhALXAoeKOlakMmoQGeo1F7G7H/7a55gCUZj8BXkA+04UHP/rXf2x2QrPiHHP8DaOx0//WqyikyIiIlVaWaR5+5+PXXWBvkA08O/Sfl6RQDG2c2OPXMRF+fnOs7ngbc8R5bYNI/i/n9ez93gqBxKtbBQPjYp3VM8rjHOWi1y7P4llREREBMpmDvINPtqPA1uAe03T/LIMnlckILinZsvnKwhuUS+MLs1cp2aEVw/mVGYOmw8lszmvMEi+lvX9y2kcGRpCWPVgUjNzqO1WUERERER8K4ssFgFdvlqkrPkKkDvHRPHcxZ2Y+OM6l/YGETUAWPDAYAa/vICbzm7JwZNpLmnjnNWvVcPvvlzSPYbPlu3mk6W7efKCjn6fJyIiUpUFfKlpkcomOsIzgB3ergE2m40rejZj3f6TfLl8j2NfZraVui22fji7nh8LWIvqfAXI9YoRIO9xKliyPzGNprVr+n2uiIiULvNQMuf8x8pw9K/hbbDb4dZBrQirrnAs0JTJHTEM4yrgTqANUM/LIXbTNPV/g5yRalQL5st/9uFYSiZ3fbUawJELOSjIxqSLOjGifUNuzCsessZLlgtfo9BF7XN3Za9mLNxyFIAth5J9BshLtx/jQGIa53dt4kgrJyIipevBH9Y6Hv9nzlYA6oSFcMPZLSuqS+JDWSzSexR4EjgM/IGV1k2kSukXVx+AsOrBzDePcNugOJf9vWLrOh6/dGlnr9cY17sZX63Y69EeVYz5xKM6NnI8PnjSe8npxNRMrv/fCjJzcjmRmsnNA5SF0dlvGw6RnJ7NpX5kJxER8cVut5OQnOHRvmDLUQXIAagsRnHvABYAo0zTzCqD64tUGsPaNWRYu4Ye7bVqVGPjU+eQkpFNg4hQL2fCUxd09AiQHx4TX6znt9ls9GhRhz93n+Co0xtzTq6dl34zaduwFm0aRDgq9K3b7zmaXVWdysjm1dlb+HDxTgBaRYdzLCWTdxdu5/mLO9GmYUQRVxARsazadZxL313qdd/+E2nl3BvxR1kEyJHAtwqORQoXVr1aofPOQoKD+PnOs/n+z31c3rMZ+06kMry9Z7BdlPx5yK/N2cL4oa0JssFnS3fx7kKrCMnF3Zs6jk1Kq1ov27/2nODB79fy8mVd6NQ0iuzcXJZsS6BHi7pM/n2HIzgGuPidPxyPr/5gOSseGV4RXRaRCpKSkc2eY6m0bxJZrPPu/PIvpq096HP/1iMp2O32InPbS/kqiwB5NdCsDK4rUuV0aVbbkQKuU0zRuY+9cR45jnt4On1b1WPpjmOOth//2u94vK+KjWTkB70XuqXf69KsNmv2Jvo874iXr0lF5Mx2w/9WsGr3Ce4b0Za7h7XxeszhpHSumryM4e0bMnF0O9KzcgoNjvMlZ2QTGVp103HuTDjFkJcX0KZBLWbdOzAgPiyUxWqcR4HbDMPoXgbXFpFiGtfb9fOqc3Dsbu+JVOwqKlJocAzW3HIRqTpyc+2s2m0tqXp19hbSs3K8HvfZ0t1sP3qK9xbu4GRqltdv5eIbeU7P8jY3uSoZ8vICwBpNT8/KrdjO5CmLPMgLDcP4B7DMMIylwC7A/f8ku2ma/yjt5xYRT92a1/G62M+b9KxcDp5Mp0kZpYPbn5jG71uOsnzHMeZsOsIb47oyNL7400ZKQ0JKyf8gpWbmcDItq1gLJkWk8soPjvMdOplObP1wL8cddzyesnofk2Zsdtl/7/C2jB/amod/XMc3qwrelxNSMmkVXcqdrqRqBsgARKmPIBuG0Qf4GCv4HgBci1Vdz/0/ESkHpzKyi3X8y7PMMuoJ3PH5n0z8cR0//X2AlIxsbvp4VZk9V1F2Jpzy77jnxnhtn76u6K9NRaRyy8rJZf7mI7w9f5tL+7+++Zvr/reChVuO8vjP60nJyOavPSdYtqMgQH5i6kZHnnuA96/twd3DWhMcZOOpCzvww+19CcqbSbBkW0KV+fbuj+0J7HXK0e88DXBsp8YV0SWvymIO8utAFnABsMg0zcK/qxSRMuWcUs4fP/61n2HxDRnbuXTfqLJzcr3mfH5q6kZi6tTkpv7lk+bo+KlM5mw6zJEk72nv3NlsNnrH1mXFruMu7RN/XMe43s3LoosiEiAmL9rBizM9Bw3+zpuG9XtenvlPlu4u8lojOxSk3axRLZgeLeqSmxcTvz53K6/P3crbV3Uv9ffeQLJ4awLXfLjc5/6tR5LLsTeFK4s5yJ2Bl03TnKrgWKTidWwaxUc39uLXu/pz7/C2gFVsZPsk15HRWwYW5D++88u/SEzN5EBims+5dsW1P9H7AsD/LdnJU79u5JCPPM2l7bw3F1uZK2ZtcWm32TyrIL5ztbWUYvL1Pfnohl4uv7NmdVWVUORM95/ZW8v0+pGhruOUd375V5k+3+k4mXr6WY5u/+LPQvdf1C1w8s2XRYB8BMgsg+uKSAkNMRrQsWkUdw1tzZQ7+rHkoaEEBxWsEh5sRNPSbT5d16dm0+/5eVxbyKf94jh2qvC3hR0JKaXyPIX5e2+i10D9yl7NWPv4SFa6pW47q5VVCDSqZghD4hsQHGSjX5zV1qFxybKKiIjkuydv0MLZmNcXuUzNCARfLt9Dl6dmMfn3Had1neR031P+6oVX5+YBgVMwpSwC5P8B1xiGoVLSIgEmKMhGt+Z1HIsgdj43hrn3D+KjG3r5nIqxctcJcnJLNjduvnmEl37bTFZOrsvoQ80Qz0UY+46XbYq5I8npHunc8j1/SWcivKRY8lbWu3dL6/c0c8MhsnNK/kfMbrfz69oDbDqYVOJriEjZynR7jb92RZciz3ns3PYu2xd1a8rmp0d5PXaI4bkyb+PBJP71zepi9LLsPTxlHQDPTt9U5FzpxNRMskrw3rjq0eGEBJdFWFoyZRHELgbOxcpi8Q6wE88sFpim+XsZPLeIFIPNZiMuuhYAjaO8V/QDq4BIHS/BYlFu/GglAJGhIY7pCw0ja/DL+P70mTTX5diynHv29K8bXYp+OPv+tr4u2xNHx/PcjM3cN8JzZAdcU7x9vmx3iUrErtx1nNs//5OEFGtUfduzo6kWQH8YRASvo7gXdYvhcFIGz7tlpwC4c0gcD4w02HTQ9b3stSu6+nwOX5lwpq87VMzelq7cXDt3f72a0JBgXrq0s8u+lbtOOAYK3M/ZdjSFsW8swmazMe/+QcTUCQNgy+Fkth4u+JbQZoMb+sXSpkEEM9Yf5Lq+sQGR+9hZWQTIc5wefwC4f9Sw5bUFRh4PEQEgvEY13rm6O3d84TkH7nhqZrED5ONOUyp+33rUkc6tTlh1r38UJi/aySNj23u0l9TJtCzemLuV2PrhXoPj/1zRlbGdG3uMWNw6KI5bB8X5vK7zSPueEox62+12LnMrOdv6kRl8eH1Pr2XJRaT8rd2XyPlvef/G6daBrRjUNprRry9ytL1wSSeu6GUt2m0QWcPred74CpCr+/mBOT0rh1Av38idrtmbDvNrXoET5/UpADPWH/QaILd6eLrTlp0hLy9gzeMjqRkSzMjXXMdEf7y9H92a1wHgqj6Budi5LALkG8vgmiJSDsb4SLGz/0SaY6TZH5Omb+J9p7lqKRk5LNpqrfaOrBni8w3dPJSM4SWJfmF+33KUzOxcjzLcF7y1mF3HUn2cBf3i6pXo67xuzevQsn44OxNOkZHt3wLGrJxcgm02Vu9NdElp5Oy+b9ew5vGRxe6PiJSuWz9bxW8bDvvcb7PZaNe4oNz0w2PiHcExQN2wgsEEX99E5asWHMQ/+rfkw8U7XaqcZubkEjthGq9d0cWxcG3R1qMcS8l0fLD/4c993P/dGi7u3pRXL/c9Sl0St35WsJju7z2u+RaCvYz0frTEcxAiK8fO+v1JXqeq1Qkr/jeS5a0sCoV8UtrXFJHyM+vegXy5fA83D2hJ/xfmA/D9n/sY0Ka+16/Aflptlaq+sFtTAGauP+gSHINrZboVO610af/o35KvV+zhfzf04or3lwGwMyGlWAHy0eQMrvvfCgDm3DeI1g0KgvjCgmOA2qfxBj0svgEfLN7JF8v3cPBkOr1i63L7YO+jzm/P38ZLvxWdW/pkXsWtw0np1KgWxMm0LOrXqkF4DS3nECkvR5LTfQbHdw9t7bL96139Wb7zONec5ToCGhRkY+r4/uw9kepz0MHZY+e2d8xbnm8ecUxNA7j3mzXsTEjlH/1bcu2H1nvdv775m2UTh3H/d2sAKzXnpd1j6Ne6vv8/aCHcp5Y8+MNal+1tRz0XVO846j2v/DsLtnHH4NYe7SWZslfe9M4rIi7aNozgifM7uLT9suYAjWuHMnF0O5f2XQmn+Nc3fwPQvXkd/txznHu/WePX8zx2bnsmjo53mXv72uytjOro+w9KSkY293/7t9c/YLd9/ie5uXYu6NqUv/ac8HI2vH5lV+75+m/uGBxH9Woln/P7t1PAP2/zEeZtPsKNZ8d6jIyv3nPCr39a1jcAACAASURBVOA4386EU46SqwDBQTa2PjOaoKDizc3LzsnlqxV7mL7uEK+P60qDCN/zy0WkgPtoKcCE0fHUDAnmil7NXNo7No2iY1Pv2Ww6xUTRKab4mW5ae/mm7o25W0lOd02x9tps1zSVL/xm8nMpBMi/rj3A+C8LXyCYkJLBAvMIGw4kcdugOIKDbCR6KakNsMA8ygLzqEe7e3q7QBT4PRSRCjM0vgHzNh8B4L2FO5g4uh0nU7M4/+3FXNo9ho5OfwD+2nPCr+B42t39HY/dF6aZh5PZejiZNg29jyL3emYOaT7yMm87Yo1qvDZni9f9O58bg81m44KuTYvsY1E6NIn0KD37yJT13D44jtYNanH5u0s9Cot4U79WDZeS1+8u2O6yPyfXzjer9harIElmdi5tH53h2L7y/WXMu3+w3+eLVGWvzvZ8/4hvFMFgo0G5PH+zumFc37eFR+GRj5bsctme8vd+l+3oWv7Pe/bl4yU7eWLqxiKPO5KUwQ15o9whwTa+W7WPrUcKRpWrVwsqMk1doC3I80bLpkXEpyS3UYF9J1IZ9PJ8dh9L5ZXZW1xSt+WPJBelQxPPUZURTvOHR7zmmeAmKyeXCT+s9RkcF2Zg22hevbxLqb4hTxzTzqPth7/2MfzVhZxMzfIrOK5RLYhesXVc2r5ZtdfzuX5cV6y+LdmW4LK94+gpvlm5p1jXEKmqanmZ0tQ3L/d5eXnygo5FHuMegM7Z5HvOtLs1exMZ9soCXpu9hdgJ04idMI0th5OLDI4njo4H4IjTOopJ0ze7BMdPX9iRNf830mUgxN0FXZv43deKpBFkEfHJvajGB4t2kugUFL8xr3hVpjr7+MrROXUaWOmCnKcVPDttE1+v9Awe/fH+tT1KfZV3YdfzNj8vvlEEk6/rydp9J9l9/BQvzjR5/cpudIqJYt+JNNbt9yzBXVLvLtzu0fbQD+s4r0sTwqrrLV/El5nrDzq+GbpvRFsu6taUmDo1K2S08z9XdPV70CHfwi1HqRdenQ5NIl36vDPhFC/O3Mx1fWPpG1ePC/Lywb8+t+D92z3LhLsHRralf5v6MKPQw4iLDqdm9WCvAyFgDQw8e1EnP3+iiqURZBHxqb3TSm2Aj//Y5bLta2HGnPsGsfGpc1j5yHDm3j/I0d4kynt55pvccgm7pguCHQnen8cfZZECCeChUfFe25flrUJ39vP4s2lWN4yxnRtzx+DW7Hp+LKM6NqJp7Zp8fGOvQp+nTYPCs4f8ufs4j/+8noMnrQ8z7dzuWT5f90pELLd9XpDiMifXTrO6YRU2FeDCbk3Z9fxYerRw/ZbpX8Pb+Dzn+v+t4Nw3F9Ny4nSXwY3z3lzMjPWHGDd5mV/P3TkmivO7NOGfTlXtbh0UR4t64YWcZWnXqOD959e7CkaRL+0Rw5rHR7LpqVFeR+kDkQJkEfHpsXPbF3sxxYA29WndoBZh1asRHVGDuOhaxDeKICTYxgPneE951KVZbY9AcY9TForft7gu8vjsH71Z9OAQwArin76wI+0bRzJ1vOvXetueHV2svhfHbYNaMemiTvx059ku7d4W5dWo5jtIrxNWnSZeirSM6tAI8KzklS8tM4cpq/dx7Ycr+GTpbp6bvpn5m49w6GS61+NnbajYwgMilcmJ1MyiDyoHLzoV6bi+bwv+5aU0tTf5i/hOpmWRklFQ3rnrU7OKPPfrW87ijXHdeGRse1Y/NgLzmVGEBAcVGdjeMrCVS3aKZnXDHI8zs3OJqhlS7AXHFalyhPEiUiFi64ez+v9G8t8F23h5lvfFb+68jaz+eEc/ktOzaRjpO5uC+yKYGz5ewT3D2vDYT+s9jm0VXYumtWuy6/mxjrZrz2oBWHMIUzKyubBrkzKtTmez2RwJ7h8d245npm3yetyYTo0KvU5QkI1f7upPcno2LeuHk5Nr50hyOqv3JDJzwyF2H0tl3ubDjkIr+V6dbTJ5UUHu0V/WHOCXNQcc27cMbMVDo+KJyxuNf2PeNu4d0bZcR8ROpmVhHkqmZ4s6leoPo1RNdcOrOwocDWrrWQK6IsRF1+LPR4ez8WAS/eI8s1Sc36WJy+s+X/6i5Ws+WO7S7jxFzptuzWu7TMVyT8f2yU29uT4vtaazr/55lsdcbeciKPVLYRFhedMIsogUKjjIRkqG/4vjOjTx/Io/rHq1QoPjfH8+OtzxeMfRU9zz9d8kpWd7HNe0tvepGgAvX9aZS3vE8Oi5pVeVryg3D2jl0da0dk1a1g/nUT+qA9avVYOW9a2vL4ODbDSOqkmwU0B508erXI4/eDLNJTj2pkFEDZdrAGw4kORx3G8bDhE7YRrz87KVlBa73U6XJ2dx+XtLmbrW8w+4SCA5lpLhCI6v7tOcofHlk7XCH/Vq1WBAm2iP1zNYqSvfubq7R/vfexNZuy+x0PUN//FSAtu5Aqo3g9pGM+e+Qaxyeq8G3xUBJ13UiSFGNOOHeuZCDnQKkEWkSJf3jHHZHmwUjK5MHd+fcb2t/KDX921xWiOU9UphlGFUx8a8fFmXch+xWPjvwS7bb13VjfkPDKZJIcF8Ybo3d517uPd4Kn/tOcHJ1CwuevuPIs/PL4Tyw+19HW1pWTlkOU3ZSMnIdlTMuvHjlS4r42esO3ha2S/+2F4wF/uer4u32EikvP1nTsGCtRvPbhnQach+GX8253Vpwux7B2Kz2RjQxnv+Y1+lsvNd2K2pyzxh8FwP4k3rBrWoX6sGtzqVoG5S2/sAyFV9mvPRjb29VtMLdJpiISJFahVdi09v6u2oWje4bTSvXd6VxLQsWtYP54lGHbi4ewxdYmqf9nNNv3sAY95Y5HP/zf2LfgOvCC3qhXP30Na8MW8bALF+LGgpTHREDS7tEcP3f+4DYMCL84t1fk6uFew6B9pfLd/DZe8upVPTKKbe1Z+7v3ItCJCUblXvO3Eqk9u/sBYsxTeKpEuz4t9Xb4sVRQJVdq7d8bhV/dN77Za1zjG1eXNcN8d2RGgINUOCi5UGc/J1PQErw46z/Klq/ri8VzM+W7abfnH1T6syaaBSgCwifunfuj6jOjQivEY1rusbS1CQzTE/rUa1YHrF1i2V52nvZYoGwNMXdKBxVE0r1VCAum+kQVyDWoRXr1YqpVRfvqyLI0AuTESNaiRnuE5FyS+I4jwS9mNeWfB1+0+y/WiKowhMvnX7TjIkvgGHkgoW+j07fROf3Nibmk6p+NbuS+RocgbD2hXMi07LzGF/YiqtG3gv8nIgMY0XZ27mhrNb0rUEAbdIWcnOyWV1XvXN6/q2qJTz5Rf8ezCHk9JpFBlK70lzfR43YXQ8tw2Kc2xXCw6iQ5NINhxIIr5RRLF+dmt+9AhCQ87MyQgBHyAbhlELmARcBtQGNgBPmab5ix/nxgGvAEOwppMsAh4wTbPoUjEi4iIoyMa71/Yol+caP6Q1b83f5tLWol44AwNk4UxhSqNSn78mX9eTEe0bkpmdy00fr2RxXpGQ3rF1XdLbhVUPJjXTdXRp2CsLPa636VASzeqGueRSXrHzOD2fmc2Gp0YBsPVwsuOr249u6EXrBrUwDyVz86fWPOnqwUF8fnMf3pznev/6PT8PgJ/+PsDGp85RTmYJCMnpWXR6oiCzQ2HrGwJZw8hQGkaGkuM0Eu6sWd2afHNLXxp7yZgz7e4BHEvJINLHPOLC1KxeNmk0A0FleIeaAnQHHgR2AjcAUwzDOM80zem+TjIMowFWQHwEuB7IBh4FFhqG0c00zaKHZUSkQnibr1bnDPwKzx/94uq5zOd11rulNWpfvZoVlBZ2jTmbil6E9+JMkxdneqapO5WZQ9zD05lyRz/ucpqW8cuaA0xdc8Dl6+nMnFwuf29poc/z69qDXN6zWZH9ESlr37gVICrvqnmlzdtCvojQanx0Q+9C10OUxvqPM01Aj4sbhjEGGA7cbJrmh6ZpzsMKdpdijQwX5gGgDjDGNM2fTNP8FRgL1AAeKcNui8hp6tjUswpT/YiqGSBf5rZAMl+/uHo+V467W7nrxGn3IyfXzvlvLWG3U37qKav3uwTH/nrw+7XY7cU/T6S0uadn7FwK6ygqWsemBdPURrRvyMpHhtO6iIJD4imgA2TgIuAk8HN+g2maduATIN4wjMLyJ10EzDZN05FfyDTNY8BU4OKy6a6IlIbeLevy73MM7hvRloaRNejevDYNI4pOE3cm6t3SdUTrw+t7ctfQ1nxyU2+/r/H8xQWlXS/p7hlw1/MxX/olpyIFpe3K95exbMcxNh5IIi3T/8VFImWlsCp1lcnk63ry0Y292PncGCZf17PMqome6QI9QO4IbDRN072U1Fqn/R4Mw6gJxAGeFQascxvkTcEQkQB155DW3D2sDYsfGsoPt/erlAtnSkPDiIKvPpvWrsmwdg25f6RBSDGKoIzuZKW+e+fq7rxyeReP/TPuGeD1PG/BdGlZvvM4V76/jDFvLOLur1cXfYIXHyzawauzPKeESOBbuv0YHyzaQW4JvoE4HWmZOdz5xV88N90aOY6LtjJWPDq2nd9V6gJd46iaDDEaBHSqusog0Ocg1wO8le867rTfmzqAzek4X+eWbmZ8ESl1xQkEz0TO1QBHdmhYyJGFu7SH72C3QWQoDSNrcDgpw9GWv6L96Qs7eq1mWJpmbzyM3W73+IOenpVDWmaO14wgq/eccHw9vvdEGq95KXoggWnfiVTGTV7m2PZWaKes/LJmP9PWHQSsqVzbj54C0CireKgMf3kK+3hZ1EfP0zlXRCQgvHxZF87r0oT7Rxqlcj3nr5Jn3TsQgGcuLJiG8cyFHfk0bwrHNX2aM+/+QdQOs+Y7X9Yjhjn3DXK5XrvGkax4ZJhHdS2AN8Z149zOjRnVoRFPXdCB+0Z4H6Wbt/kIT03dSOyEaQx9eQG3f/4n8Y/NpNvTszl0Mt3j+DV7Ex2Pp+Slr5PAtflQEgkp1gew/i8U5PSetfFwmT6v3W4nIzuH3Fw7drudh35Y59jnvOD0aHKGt9OlCgv0EeRjeB8lzk+46m2EGOAEVgBcknNFRALKpT1iCh0BLq7bBsUR3yiCs1rVcyT4H9G+Ie9f24OYOmEuuahtNhutomvx5c1n8d2fe7l9cBwN3OaDf3vrWUSEWgH0i5d25sHvrVlwsfXCOL9LE87v0sRxbHZOLq/O9vxi8I25W1mzzyqLuyPhFDsSTjn2nfXcXHY9P5bk9Cxe/s1kVMfG7D6e6nJ+7IRpXNYjhqcv7KjRwACzfv9Jzn1zMTWqBbH4oaGuO8twqMput9NyopXsKsgGbRt6z9ENcG1f/wtkSNUQ6AHyBuASwzCC3OYh5w91eP3ezzTNNMMwduB9jnIn4KhpmppeISJVUmhIMKM6NvZoH9mhkc9z2jeJ5PEmHRzbkaHVSEq3ipPkB8cAl/dsRs8WdVi24zhD4j3zVlcLDuLTm3rz1Yo9zFh/yNGe4lboxN2eY9bX8vsT0/hk6W6vx3z35z7qhFfnziGt/c7wIWXDbreTkJJJSkY25765GICM7FwGulWEjI4ou/Rimw4mOx7n2mHzoWSfx5Z3aXoJfIE+xWIKVnGQ89zarwPMIgp+TAFGGIbheMc3DKNu3rV+LO2OiohUJRnZ7munC7SKrsVVfZrTOMp73tWBbaP57zU9uPHsWEdb/lxQXwa+NJ/9iWlF9uv933fQ5clZ7DuRWuSxUnbGf7maXs/OYcjLC1za3cshT1t3kNgJ09h9rPD7XxKHkzyn5nhTWYuDSNkK9AB5OjAf+NAwjJsMwxhiGMbHQH/g3/kHGYaxwDAM9y9qXsZKETfdMIwLDMMYC0zDKhgyqVx6LyJyhro4L8NFSHDJV8o/fl4HnnNKQVcS7Rp7L03+mY9RZil7x09lOhbC+euer/8u9X78d8F2n/tm5829B/jwhp6l/txS+QX0FAvTNO2GYVyIFdBOwhpN3ghcbJrm1CLOPWwYxgCsQPkzCkpNDzRNc0/Z9lxE5Mz28Jh4WtYPY1i7kmfWAIip43v07tqzWvDZssID3V/Gn82J1Ex6PzvXdccZnOFq3b6T5NrtxDWoxcHENNoUMre2Iuw4mlLsc06mZZV6Pw4VMoLcpmEEa/5vJOE1gl0yxYjkC+gAGcA0zSRgfN5/vo4Z7KN9K3BB2fRMRKTqiggN4ZaBcad9Hfevt7vERNG0Tk3uGtqGdo0jubZvC0a+9rvXc+c/MJiQ4CAaRIRy97A2vDF3q2PfUh/luSubT5fuYn9iGhNGxZOda2fR1qPc9PEql2NuHdiKiWPaVUwHvTiR6l+wO/+BwYx7fxmHktILrfSWnZPLrZ/9yf7ENCZf15NmdcOKvPapjGz2HPc+zWZQW2tufFSY5qmLbwEfIIuIyJmrUZRrRoxBRgOXVHDumQc++0dvMrJy6RVb1yXAuWNwHMnpWXy0ZBcAa/MyYlRm244k838/bwCsDxLJ6dm89JtnYZT3ft9R4QHy4q0JzNp4iIdGxXMiNdNjf8v64ex0ykwy2IimZf1wrurTnFdnb+FYivc0a3a7ndaPzHBsD3hxPmseH+lzEebfexNZsi2B71btdWkf17sZ53RoxDcr9/LI2MD5MCGBSwGyiIhUmLDqrn+GvJW9/uH2fqzec4Jr+7agRjXvKdxCQ4J5/LwOLNmWwJbDxf+KPxANf7Vg5Dw/UPbFW6GV8pKWmcM1Hy4HoHZYdcKru96jXrF1+PbWvqRm5hBWPZjDSRk0jLSyRuRnjzjqI0Ces8kz4VSXJ2ex6/mxXvtx4dtLPNrvGtrakUN8sIroip808UZERCrULKcFU5d4yffco0Udbh7Qymdw7OyRse0dj1fvOVE6HawE8lPulbc/tiXQ7v9mOrZ/33KU43kjyM3rhnH3sDa8fXV3bDYb4TWqYbPZaBQV6gjm69eyPhDtPZ7Gr2sPeFzfedqMs4MnXTOaJKdn0WfSHK/H3jG4dfF/MKnyFCCLiEiFatswgjn3DWThvwdTq8bpfbHZ2GnKxkXv/HG6XaswR5L9S1GWb9uRFHJzy75A7K6EU1zw1mJmrreyVFz1wXKX/X/vTeS9hTsA6NqsNveNaOtRWMaZcx7k8V+udtm3aOtR1u33PlXm5d+saRn51fnGf7na64eET27qTc3qKhwjxacpFiIiUuFaNyidTAx13aZopGflVMrKehOcSiIXpnpwEJk5uVzyX+vDwI5JYwgKKrupFpe/t5QjyRnc9vlfdI6JKvRY93vhjXuBjhs/WsGtg+KY8td+vnGbR/yP/i35cPFOANKysjn7hXmEBAexdOIwFm456vX67RoHVoYPqTw0giwiImcM9znMT04trJ5U4Nl0MImJP65j3uaCubeRoa5jWdPvHsC43s357B+9iXRbrLZke0Kxn3PZjmOs3HXco/3nv/dz8yer2HakoALdkeSCucJFLYT0p0peY7dFmvPNo1z5/jKP4HjSRZ147Nz2jGxvpRWcvu4Q6Vm5JKdns8HHKDNQ6Oi1SGEUIIuIyBnDZrPx12MjHNtfrdhD7IRppGZmczI1i8VbE8gph6kIJfXSbyZfrXBN1X9Zz2aOx69d0YX2TSJ57uJODGgTTW23VGUH/Kg26Gzr4WSufH8Zl727lKNOwe/ny3Zzz9d/M2fTYd5xKrjhHqw7G97OdQFc9+Z1inz+asFBfpUFH2xYqdm8TZdwLkrSrG5B2kDnYiAixaUpFiIickbx9tX+6NcXsfuYlRf37mFtXFLJBRLnkWOA16/sSocmkXy0ZCcdmkRxYdemLvsPn3Sdq/zMtE1c0au5X8+VnpXDCKcc0/sT04iOqMGGAyd59Kf1jvaFpjV94c/dx30uBlw6cSiNo2qywDzCDR+tBKw5yP745KbeXrNPOGuQNxpd20sw/alT1cTrzoolKzeXdo0iA66AilQuGkEWEZEzzmtXdHHZzg+OwcqMsL0E1d7K2rzNhz3a+rSsR+sGESybOIyvbznLI5XbgLb1XbaTi5HNYvLvO1y2T6Zlse9EKmPfWOzSfuxUJidOZToCX28aR1kjt4PaRjPpok78cHs/vxfHtawf7nPfOR0asvaJkY5qdw+Nji/0WvGNI7hjcGuGxCudm5weBcgiInLG6dS08AVkd3z+Vzn1xD+LtyZ4VMiDgjRoDSJDCfeS4WOIl7y+dnvRU0g2Hkjig7wFb/m+Wr6HX9Z4ploD6Pb0bL+Cb5vNxlV9mtOjRdHTK/JF1QzhmQs7et1nNIokMrRg1Ng9b7a7zk39G7UWKYoCZBEROeMUlRXDPJxMSkbF5A52N3XNAUehDXf5I6e+XNojhhrVXI8pKifywZNpjHljESfTXEtCz9xwiBdnFlTqCytkBNifDBXFcc1ZLdj1/Fi+uLkP717Tw9FezUtGjhv6xVIzJJhvbjnLY19kTc0cldKhAFlERM5IU8f35zIvhUfy7XGadlGR3pznWgyjZf1wJl/Xk/kPDC7yXJvNhvnMaFY9OtzR1uXJWTw3fRMfLdnp8SHgZFoWL/+2xa9++Vpk9+xFHfntXwMZ27kxAA+MLL353Ge3rk+/1vUc286L7vI9cX4H1jw+kj6t6nnsq6hqgnLm0UctERE5I3WKieLFSzvz3Z/7vO5PSs/y2l7emtcNcymPPbJ9Q0bkpTPzl3t6u/fy5hdvOZzMcxd3BuCL5bt5ZMp6j3N9effaHuw4msL5b7kuoLu6TwsA3r6qO2+NK/0S15GhIdw+OI69x1M5r3MTr8dUzxs1//D6nvzjE2tqysQi5ieLFIdGkEVE5Ixls9l4ZEw7hsU3YMY9A9gxaYxj39xNnoviKkJ6Vq7jsc1mTTcoLl9B6lcr9jryGPsKjn+9q79H2/wHrKqGnWNqu0y1mHv/IL+e93Q9NCqet67qXuQUk2HtGvLmuG5Mvq4ntw6KK5O+SNWkAFlERM5o/xzYig9v6EW7xpEuVeYmL9pZyFnlZ98Ja6rHxNHxrHviHJrVDSvV6w9/9Xd+8DKKHhcdzoqHh9GxaZTLdI5HxrRzySzxztXdHY9b1vOdcaKinNelSbFH3EWKoikWIiJSZZ1My/KrUEVZOXgyjV15c6G7NKtNLS+ZKkrD/d+t8Wh7++ruNIi0Ks21rB/OnUPi2HcijZv6t3Q5blDbaF67ogutoyPKtIy1SCDRCLKIiFQp/xxQEAC+OXcr2Tm5hRxdtg46FfroHFN4arqiLH5oiF/HRUfU4I1x3YhvFOnS/u9z4nn9ym4EuwXBNpuNi7rF0Ok0+ydSmWgEWUREqpSHx7RzTK/4YPFOQkOCeeAco1SfIz0rhy+X7yEtK4dLe8TQMG+kFiA5PYu0zBwaRIZy8Tt/ONqLyvFblJg6YeyYNIYcux273cpmkZaV43HcO1d3p1ds3dN6LpEznQJkERGpUtwXlr01fxsPnGOQm2svlSkEOxNOMeTlBY7tl34z2fX8WACOpWTQ45k5gFVGurQFBdkIwvoZ6oZXZ39imscxvtK3iUgBTbEQEZEqZ7AR7bI9d9NhWj08nX99vfq0r+0cHOf7Y3sCdrud8V8WXP+er/8+7ecqzOU9m3m0jevd3GMKhYh40giyiIhUOa3q12KBedSxnZ9L96e/D3Bdv9gSj7K6V6fLd9Xk5VQLspGd670M9Ll5RTdK0yU9mvKfuVuw22FE+4b0aVmX6/vFlvrziJyJFCCLiEiV06dVXf63xHuat69X7ClxgLxo61Gf+3wFxwAvXNK5RM9XmJg6Ycy7fzDJ6Vl0jqld6tcXOZNpioWIiFQ5w9s15IVLOnnd9+2qfWRkey5u88fBxIKsFEVllbh7WBueubAj2yeNIbyM0ru1rB+u4FikBBQgi4hIlRMcZOOKXs197jcencne46nFvu6RZCtAHtQ2mpg6vgt+zH9gMPeNaMs1Z7XQnGCRAKQAWUREqqzCioRM/HFdsa41c/0hR/q42mHWdZ++sKPXY50r1YlI4FGALCIiVdbHN/ZyPP7tXwNd9m0+lOT3df7YnsBtn//p2M4PvIfGN/A49tGx7YrbTREpZwqQRUSkyurWvA6z7h3IvPsHYTSKcEn/lpCSyV1frWa+eYTYCdMY+soCTqZl8fjP6/nxr30u17lq8nKX7fwAuWntmnx0Qy9edFqE1ygqFBEJbMpiISIiVVrbhhE+901dc4Cpaw4AsOPoKe7/dg1zNh2Gpbu579s1ANw7vK3HeTlOGSuG5I0i7z2RyrFTmYzuWPop3USkdClAFhERyfOP/i1d8iO7m7PpsEfba3O2eLTVq1XDo+3+kaVbzlpEyo6mWIiIiOQZ0Ca6yPRs/ri8Z0wp9EZEKooCZBERESeNo2qe1vlX9mpGRKjv7BgiEvgUIIuIiDgJDrJ5ZLTw1+TrevpM7SYilYfmIIuIiLgxGkWw4pFh9H52LmBVvdt8MIlZG605yDufG8PkRTsIr1GNNXsTybXDiPYNGdG+YUV2W0RKiQJkERERLxpEhLLzuTHYbFalO7vdzi9rDtCqfi1sNhu3DIwD4Oo+LSqymyJSBhQgi4iI+JAfHOc/vqBr0wrsjYiUF81BFhERERFxogBZRERERMSJAmQREREREScKkEVEREREnGiRXvFEJicn07Nnz4ruh4iIiIichuTkZIBIb/sUIBdPLhCUnJycVNEdEREREZHTEokV23mw2e32cu6LiIiIiEjg0hxkEREREREnCpBFRERERJwoQBYRERERcaIAWURERETEiQJkEREREREnCpBFRERERJwoQBYRERERcaIAWURERETEiQJkEREREREnCpBFRERERJwoQBYRERERcVKtojsg3hmGUQuYBFwG1AY2AE+ZpvlLhXasijEMIwb4N9AD6AqEA0NM01zg5dirgIcAA0gAPgeeME0z3e24hsCLwFigJvAX8JBpmn+U9JpSOMMwhgHXAn2BZsBxYAXwuGma69yOHQE8DXQBkoEpWPcn0e04v1+j/l5TCmcYRj/gcaAjUA/rhbC+GwAAIABJREFUd7kOeMk0zRlux+o+ViKGYTyBdW/XmKbZ1W2f7mWAMgxjMDDfx+52pmludjq2Ut1HjSAHrinA1cCjWIHURmCKYRhjKrRXVU9rYByQAsz1dZBhGNcAXwBLgNFYL+47gY/djgvNu84g4C7gIqwX9VzDMLqV5Jril9uA5sBrWL/L+/K2VxqGcVb+QXlv9tOBvcB5wAPA+cA0wzDc3y/9eo0W85pSuDqACdwPjAJuATKA6YZhXJl/kO5j5WIYRgesgYDDXvYNRveyMngIawDC+b9d+Tsr433UCHIAyvufYDhwsWmaU/La5gOtgFew/oeQ8vG7aZoNAAzDuBDrxefCMIxg4CXgF9M078hrnm8YRhbwvmEYr5mmuTyv/SagA9DDNM2/8s5fCGzCCoBHl+CaUrQ7TdM84txgGMYsYCfWNwSX5DW/CKwHrjBNMzfvuIPALKzRjG/y2orzGvXrmlI00zSnAdOc2wzDmIp1H28Bvs5r1n2sJPICmQ+BD4BOWCOGznQvK4ctpmkuK2R/pbuP+qQUmC4CTgI/5zeYpmkHPgHiDcNoX1Edq2ryX3RFOAtohHV/nH0BZFEQfIF1b9flB8d5z5EBfAWMMAwjogTXlCK4B8d5bYnAViAGwDCMpkAv4DPn+26a5mxgP573scjXaDGvKSVgmmY21r3IAt3HSuherNfgI+47dC/PDJX1PipADkwdgY1egrO1TvslcOTfj/XOjaZppgLbcb1fHd2Py7MWCAbaleCaUgKGYUTjej+8/s7zrMPzPvrzGi3ONcVPhmEEGYZRzTCMJoZhPAm0xZo+A7qPlYZhGK2Ap4DxpmkmeTlE97LyeM8wjGzDME4ahvGrYRg9nPZVyvuoADkw1cNaROTuuNN+CRz598PXPavndqw/97Y415RiMgzDBryP9R74cl6z7mPl8S3WiPF+4F/A5aZpzszbp/tYCeS9BicDv5mm+ZOPw3QvA99J4D9YU5yGYE1Zaw8sMQyjT94xlfI+ag5y4LKXcJ9UHF/3xb29OPfW32tK8bwEXAjcaJrmJrd9uo+B70HgBaxpSFcB3xqGcb1pml85HaP7GNj+CfTECqaKonsZoEzTXA2sdmpaZBjGL1gju89izSfOV6nuowLkwHQM759+6ub96+0Tk1ScY3n/1nN6nK8u1gIi52P9ubfFuaYUg2EYz2JlQbjHNM2PnXY5/87d1cX1dVeS+1jUNcVPpmnuAHbkbU7NW6j3tmEY36D7GPAMw6iPtcDqOeCUYRj5C/OqAcF52+noXlZKpmkeylsEnb+ovVLeR02xCEwbgHZe0pR0yvvX25wbqTgb8v51mfNkGEYYEIfr/drgflyeTkAOsNnpOH+vKX4yDOMp4GHgQdM033Db7fV3nqcTnvfRn9doca4pJbcCKwVcNLqPlUEMEIUVIJ9w+u9srN/xCeAJdC8rsyAKRnEr5X1UgByYpmClujnPrf06wDRNc2P5d0kKsQw4hFWIwtk4IAT40altCtDJMAxHInzDMKrnHTvHaaFKca4pfjAM43HgMeAx0zRfct9vmuY+YBVwtfObc16RkaZ43sciX6PFvKaUQN5c1sFAInBM97FS2IY1X9X9vzVYi5CHAO/rXlZOhmE0AkZg/R2rtO+tmmIRmKZjVab50DCMelhfp18P9AcuqMiOVUWGYVya97BX3r+D8r4iPGWa5gzTNLMNw5gAfGwYxlvA91jZKF4AvnfLDfkhVrGPHw3DmIj1NdA9QBPg8vyDinlNKYJhGPdjjUj9CsxxLg4CZOTNowMr2f0s4CvDMN7Hui8vAMuB75zOKc5r1N9rShEMw/gC2A38iVVZsjHW730ocFdeyjfQfQxopmmmAAvc2w3DSMzb77xP9zKA5b0md2BVhD0BxGP9fmsCE50OrXT30Wa3az56IDIMIxKrcMSlWJ+mNmKVWvS12lfKiGEYvl4ku03TjHU67hqsF2xbrD/eX2CVMk5zu14jrEViY4FQrDeWCaZpLvby3H5dUwpnGMYCrOqF3rjfx1HAkxSULv0Ja0rGCbdr+v0a9feaUjjDMMZjVdhqi/UV/UmsUaS3TNOc6nas7mMlk/c6re2l1LTuZYDKG8i5EogFwrHmBi8AnjFNc73bsZXqPipAFhERERFxojnIIiIiIiJOFCCLiIiIiDhRgCwiIiIi4kQBsoiIiIiIEwXIIiIiIiJOFCCLiIiIiDhRgCwiIiIi4kQBsoiIiIiIEwXIIiIiIiJOFCCLiIiIiDhRgCwiIiIi4qRaRXegMjEMIxvrQ0VSRfdFRERERE5LJJBrmqZHPKwAuXiCAFtERERURXdEREREREouOTkZfMymUIBcPEkRERFRq1atquh+iIiIiMhp6NmzJ8nJyV5nBWgOsoiIiIiIEwXIIiIiIiJOFCCLiIiIiDjRHORKYNeuXRXdBREREZEyFRsbW9FdcFCAXAm0bNmyorsg4lNQzUjqnnMnNVt0ISctiZA6TQBI37sB7LkEh9chpF4M/9/efcdHXeR/HH+l9wAJndDL0DvYEBBExY69n3rq6empZzsVe693553tLPeze3axoWJDrAgonUFp0msIgZC22d8f302yNdmFbDYh7+fjkUd25zvf2WG/7OazszOfce3eQXxqJq5d23GXFZOY3Yq4hCSftipKdrH6n6cBbuLTsnGXFUNcHLlHXE5a9+GUrLMkpDcjPr0ZZVtXk9ZlCMWr5pLaeRDuChcl6yzgJiknj/jUTOLiEyhes4i4xGRS2vagZN1SXLu2kdZ9BCXrLLsWfknJ6gXEp2XjKtpO+ba1e/w8ZA6eSEb/caR26INrZz5l29YQn96M5JadKFlncbvKSGlncLsrqCgqwF3hIqlFO9zlpeyY8wGJWS3J6DMagJJ1S4lPy6x6Ll27d+DalU/Z1jXkf/40mQMnULbld9K6DydzwASnTlEBFSW7qs4BcFe4KN+xmYqiAhKbtWHnvGkUr55PUm4ehbM/AHcFzQ46g+ajzqB4zSI2vvw3wA1AWveRuIq2U7p+aZCLngAVrpDPRVKrLmQNO4bybevY8dM7xCUm4y4vBXfFHj+/IuFIyMyl+Zg/kNiiHSntDbjdlG1dw7ZpT1BRVED5jk24y0q8zojz/HbXzeNntaL1ybeR3KpzVVnx6oWkduxXfX/NQhKzWpHYrDVl+et8XrMAu1f+QlqXwQBUlJUQn5RSfe7axcTFxQFxpLQ3uHZtpyx/LUnN20NiEgmpmRSvXkBSbkcAdvz4Nmk9RuIuL4GKCpLb9iAhoznFqxfgLivG7Sqn+Pd5lG5cTpvT7yEuLp6S9UtJadcLgG3TnqRwzgd18tyEw+2um+tQF+IaUmcaOmPM9lhksXBeDCINQ1xyGp3++kbU2t869RHKtq6m7VkPRe0xQnEVFVC05Bvyv/o/Jzj3SOk0gOTWXSmc9T4Bf0jjE+h87ZT67WgdKS/cSmJWbtj1XTvzSchsAcCWD/9BSl5fsgYd7lNnx6z3yB5+bMg2Vt1/DHUVjIhUSunQO+z3jFUPHEt8ejZZAw+n+eizqSgtpvj3ebh2bGL7N69QsXsHOYddStaQiZTv2MzaJ84L2VZii/Z0uOipuvpnNEhbP32Css0rqSguJLFFB4pXzHEC7iio75jUk8WiwFrb3P+YAuQIxCpA1hQLqS9lrgqKyirISErgwyX5DGibTrfcVMY+uRCAF07rwd+/Xscv64qCnj8iL4OCYhdtspLIa5YMQFFpBRsKy6gA2mYlUVxWwbRfCyLuW/+26fRtncbr87YGHBvXI5vtu110ap5CamIcu0ormLFiB9uLXUzo2YxSl5v0pHgS4+N4f3F+WI93+uBcjuuXw7KtxUz+eDUAvVql8tSJ3QEoLHGRkRzPE99v5A1Pn7rmpFDucrNfp0wykhNYtrWYwhIXg9pnEB8Hv20p5puVhbU+9hGmOamJ8by7cBsA3XNTWba1OGT9NplJ5KQn4nK7Wbq5ut6IvAxyM5Jok5nE87M3h/Xvri9xwE3j8xjfMzCtfHFZBalJgUtkdpdVcO+Xa3FVuLl9QkcSEzR40FCsLSjliikruHZse/brlFUvjzll4TamLNzG3Ud04vIpK9i8q7zq2Ii8DH5asyvoeX1ap7F40+6IHmt4XgYPHd0loLzyvTGULi1SGJaXwVvzt1WVnTOsFe8vyid/dznD8zJISXT+r38b5L2hTWYS8XFQVuFmYLt0urZIrbr/sd3OhsIyju3bglX5JcxdH/x9GeC4vi0oLnezq9RFm8wktu0u58tlgdnNerdKY8nm2p+bQ3s246bxebXWi1R9T7FQgFxHYhUgi9SXY/79DfPXRh68AvxyywSapydHdM6MXzfz04ptXDy2O2/OXsMtU4L/sTlqYDseO2MoAK4KN3e8v5ANO4rJSk3i8H5tmdC3TdiPWVHhZmdpOamJCVz9xlzen7suoj7PvHE8ny3exI3vzA84Zu86gpTEhIjaW7C2gA/nr6eopJwTh+XRrlkarbJSAuoVlZbT95ZPqu6nJsXTvnka7102isyU2mfLfbpwAxe9ODvosVuO7ssdHywKKO/bLptF66O7cegbFx/AyU9+H1A+ulcrXjh/JK4KNx/OX8+gvGbcPGUhXy+tDvSvntCLYwe3p3NuRlT7KIHWbd/NFf/7mQsP7kaXlhkc9o+vq44tu+dIEuLr9sNLwe4yTnvqB3q1yWTB2gJGds3l1Zm/B63779OHcMwgZ9pCmauCt2av4fq3A1+vkXrrkgMZ1tn5BqW4zMWvG3dyzKPfBNSbNKQD/zh1cK3tVVS4ifd6nn7bVMgXSzbRIj2ZjjnpDOjQjIwwXtuV3G430xZtpE+7bNo2S+XA+75gc2EJL5w/ktG9WgXU37KzhM2FJXxpN9GheRqH92tLalICrgo3s1ZuY9aqfB78xIZ8vBnXHULHnPSw+9cQKUCuIwqQZV9WUu7C3PRx2PUvGt2Nqyb0IiE+DrcbkhP3LinO5sISRtz9mU9Zl9x0erbJ4sGTBkYcfEeipNzFBc/P4tvftlCxh2+Jp4/syL0nDKzbjvmZvnQzi9bt4MKDu5KYsOfPd2l5BX9+eQ6fLd7Ibcf05dyDurJ1Zwl/fH4WHZqnMbhjc44f0oFWWSms2LKLhesKuPvDxeS1SOPCg7v5BNptslO4/dj+FBaXce2b86rKnzxrGEs3FhIfB/HxcUzo04YJXkFUXUpOiOetSw5kQJ42OY2mn3/PZ9Lj34VV9/3LRtXp9bjohVl8umhjrfWm/XU0Pdv4jmC73W5ufGc+r85cXSd9eeyMobwxezVfWd9vZS4Z253rDjcNZlqk2+3GVeHe4/cKV4Wb7jd+FPJ4ckI8S++euKfdaxAUINcRBcjS0K3bvpvE+DgyUxNJS0qI6I16yi9rueJ/v4RVd0LfNjx9zvA97WZIq7cVsXDdDn5ZvZ3urTI4YWhenY9E1abL9R/u0XmL7jic9OSmse75qa+Xcc9HSwBYetfEqg9Hrgo3i9fvoMxVweCOzQP+/20uLGHmim1c+sqcqPRr5X1HRaXd+uaqcLOzpJxmaUmUllfs9YfPuuB2u+l6Q+hgKZi6vB7hvC4T4uNYds+RYbfz3fXjyMlIJjWp+lsft9vNIQ99xcqtRRw/uD0Hdm/JdW/NC9ZUlbwWaXzzt3G19m9fUfkcxsXBinsb92uupgC5abybizQilR9a/YOLrTtLeOXH3zl/VNegX7t9+9sWznzmx6r743u35tlzR4T9uOu2+85xfe68EZz7fz8FrXvi0A5htxuJjjnpdMxJ54j+baPSfjgePWMIl73yM8M6tyC/qJQRnXPYXebi0kN6cPg/g4+ANk9PajLBMcBZ+3dm7poCRnbJ8QneEuLj6N8h9Khhq6wUjhrYjqMGHsVLP6zipncX7NHjv3vpQRz/2LcB5W63u8GM3oVrQ0Exd364iDNGduLA7rl8NH9DwAeIP43pxg0T+8Skf+WuChIT4tm2qzTic8tcFSQFGb2c8etmzn52JscPbs8/Th1c4zVzu90BI7Xeltx5BM/MWM4vqwv4x6mDau3TZ1eN5urX53Lt4b1p3zwt4HhcXByPnzmMOb/nc8rwjiQnxrNgXQEvfL8qZJspDeADTH369vpxXPXaL/zztNqnkTRmGkGOgEaQJZryd5VSVlHBxS/OpqjUxZTLDvKZz+o98uE/MhPqq7B3Lz2IwR0DPhgHVdn+8M4tePOSAwFnjtw7P69lUMdm/LB8W1VA8/0N42jXLPCPy75u9bYiHvrUMuWXdTx51lAO7NGS/36zgtNGdKJts9RYd69R+XrpZs7578yq+zdM7E2/9s0Y1bMl4Pv/PTs1ka6tMjmgWy7XHW6q5m3eMmWBT+Dy/PkjGRNkrmVD5v3vPOeAziEDsViMjn+3bAsXPj+LYwa1Z9KQDpz61A811r98XA8m9G1bNS93+rVjA+aH+3+QB5h106G0zAycdx9q1PjU4R35fMkmJvZvy53H94/kn7THNu0o5tJX5vDTysBFvo3x/504NIIs0sDtLnUx/u/TfUZpfv59O/t3y2Xx+h1MejxwtMzbSz8E/6N60QuzmDn50Fofv7C4rLovZdX5bePj4zhxmLNSuVNOBiXlFXTJTW+SwTE4I9yPnDaER04bUlV25aG9Ytijxmu/bjk+9889qIvPB8K5tx7G018v5/xRXcnJCD7//I7j+nPjkX3ofbMzd/629xby5TVjo9bnuvb7Vt+sAzWNUoYaja1LlSPwFRVu7vhgEc99txKA//20ml5+83pvmNib4wZ3YF3BbjrlpFNYXE7XlhmUuapzXf/pxdl8fOVon/P8g2OA4Xd95vMBINh6hEozJ4+ndVb9fxhtnZ3KGxcfyMOfWv79xW9V5cmJ8QztFN4ghDQuCpBFGoBlm3cGfIV57ZtzmXrFaCY+MiOgvqvCzVtz1nDdm/M4qEcu3/4WmPoMYGdJedByf6u8/lDffmy/oHWSE+P54yhtWiN1IyUxgXm3HcYDHy9hfJ82Adk/mqUlcc3hptZ2vOePrtiyi10l5RGt/I+lOz8MzBwSyr0fLeHUER0xbaOTQu3571Zy63sLGZTXjP265VYFx5Uqs5z0aJ3JS3/cjzbZKcTFxVV9c1I5AuwdxC/ZUMiXdhNjeraiwu3m4pdCzz2f83s+ny/eyMVjunPV68HXQrxx8QExCY69XTauB64KNwf3bEXXlhkkJ8aTlZpU+4nS6DSOdxGRfdy67YF5J1dv280tU4LP0Vy3fTfXeTIGhAqOAfq1zw7r8Z/4alnV7co0RiLRlp2axF3HD6jTNk968numXnFwnbZZ1wp2lzFvzXamhZGVIT4OKtzw329X8N9vV7D8niN9UoPVZtuuUpqlJfksdt1VUs5H89dzYI+WdPDMw731PSfF4tw1BcxdEzrVY8vM5IimE50XYh1DenICRaXV31ad4MmO4XbDjF+3BD1nRJecoOX1KSUxgeuO6B3rbkg9aFozy0UaqFC5Zt+eE3zr44Mf+DJo+QMnDeSaw3pxy9F9AfhpZT5zV2+v9fE/nL++6nZjW+Qk8tHl1QHx4vU76HL9hxQWl1FUWs7yzTtj2LPgbnx7Pmc/Wz3/2j/v9Y83juflC/Zj+rVjA9IbLt8SfPOLYKbOX8/QO6dx+f9+rirbtquUfrd+wrVvzuPqECO1NeneKrPWOkcNbFdrnQW3Hc6M6w4JKH/8q2WkJQXmEn/45NoX4InUJQXIIjG2o7iMf372a5201bttFpeN68kgr4V5xz32LRt3hN6FrbS8es6gYmNpjPq2zybXb57ygNs+pe8tnzDu4el891vwEclYqPBsfOLtkytHM8CT/eOGib1pk53KQT1a0jk3I2Dq1Yxfw9sRce323VzysjOl4cN5zuPtKC5j6J3Tqur8sHwbxWWuGp+f+08c4BPIHtC99q3J75lU+7cC8fFxtAsxEl25DuKEIR0wbbK49nBTtRZCpL4oQBaJsTmrat/6+F+nD+HXMBKyD8xzAuNebXxHeUJ9zQnwld1Udftxz251Io3N6xcfEPLYGc/8GPZ8/Ghyu9385dWfA8pzMpJ5/MyhPHfeCP40prvPsYxk39HU5/3mBody8hO+G3q43W5OD5KFYuqC9ZwRZOEcwME9W3LqiE50zEnnruP7c9WEXkzsX/vocLO00HNyu7XMqAq4a9vAYkBeMz7562guPaRHrY8pUtcUIIvESHGZi8e/+o3351aPJj1+5lBe/9MB3HSUb87TYwe1JykhnsfPDC+A9V80UtN2wflF1SNUh/RuHVb7Ig1Np1q2vH1mxvJ66klwbreb+6YuCRg9rtQxJ52xJvD15z9doba0jW63mzdnr2Fdge+3RlN+WcfCdYHvA399bW7Itlxe20qetX9nLh/fM+yNez7xy15R6Yz9OvlsT3xon9DbxCt1msSSAmSRGPnP9OU88LHlrTlrABjRpQVHDmjHyK45TBoSfCOOIwe0I9Nrhf5TZw+run3dEb4r/i/zGnXp2Tr0vMEdu52Rtb7tsn0yAog0JkkJ8RzWN3SwVVfTmPbU/35azX++DgzS/zS6W43n3XvCwKqFdOBs6LOrhtHwH5Zv45o3AoPeK1+LfL5x33bhLfINxrTNYuV9R/H51WN48qzqD/b+7zE3H92Hbq0yuGpCYLrEllmBuZFF6osCZJEYmbrAdyTJe7QmNzOFkz1z7j67aozveZ4V+k5S/jb8NPlQnj5nOBeP9v1q9i/je5Du+Xq2xGuesb/KEeQWGUpVJI3bgycPqreNIyL18o++OY4vGNWVDy8fxbW1pLJLiI/j2+vH8cBJAwGYuXIbA2//lBOf+I5Xfvy9qp7b7Wb2qm3c+UF4qePGBfm2aOoVB/PDDeM5emA7RvVoyR8P3vu0jt1bZTKya/W85T7tfNPUdc7N4Iurx3L5+J4BAXlWI0nXJ/sm/e8TiTK3281nizfRvVUG3bxWgG/wWzjnvzr8wZMH8WCQldsdc9J9kuq3ykphQpCRs5TEBP512hAueGEWmwtLArbhnb0qn4c/tazOd3IgN08LvhmDSGPRLC2Js/fvzM0htrCuqHBHlCKtLvVqk8WCtdVTHPp3aEa/9qG35fbX2WtagqvCzexV+cxelc+kIR1IS07gpR9WcfOUhUEeN5OlG30zeXx1zVhyMpMZeNunVWUtM1Po4wlQH63jtQg5Gck8eNJACovLGdY5dKq2KZcdRM/JUwG4+ei+yqgjMaUAWSTKZvy6hQtfcLYnX3HvkVVv+n3aZvP98uocxn+OwkKUyvRRu8tcbC8qo4XXSv9z/zuTQq+vaheuC537VKQxef78kcxauY2/jOvJ4vU7OO4xZyfK1flFAVsf15edxdWvtQEdmnFE/7YRnd89xDSp9+auZeKAdtzyXmBwDPDeZaOqdhoEOH1kJ7q0dJ6Dw/u14ZOFTi7mVy7cL6L+ROrk4R1rrZOUEM93149je1EZfcPM4S4SLZpiIRJlX9nqtEybCkuqbpdXONMeThyax0+TD6Vry7r/w92tVXWbK7b65k8t9JvHGKuRNZG6NqZXK64+zJCcGE+b7OpUYmMe/CpmfVrr2Qzor4f24v2/jIp4vn/lTnX+/vbWfM58+kda+83XPWFoB1bceySpSQl093ofuPeE6hRs1xxWPb0jGu8/e6J98zQFx9IgaARZJMpyM6tHbTcUFFf9wd7sCZaHdGoesFFAXclKTSIrJZHCknI2eq1q31AQmBf52sNq39ZXpLFpCHPri0rLWezJJNO7Xd1vFT1/beC3P5eM6V71bdVLF+zH/VOXBIzi9myTxZsXH0BORrLPFtEiohFkkTpX5qrA7XYHPea9dXRlgByt4LhSG08y/hd/WEXB7jKKy1wc/MAXAfUi/cpXpDFISYx9Zpb8ojIq1+D2arPnAfLkI/vUXgl49Iwh9PR6nHbN0vjnaUM4qEfLgLrDu+T4rI0QEYcCZJEwud1uPl+8kd827aSotJxjH/2Gq/y2al1fsJuek6fS9YaPsBsK2VlSzoOf2Krjc9cU8O1vW9hVUs6uUme3qFBfndaVHbvLAPhu2VYG3f4pR//7G8pcvgF859x0LYiRfdY1h1WnEDv72R8pc4XO6rKnvLPQ+PtySfVmPM1r2ESjNheO7oa96wjm3DwhIK1jpdNHduLoge33+DFExKEpFiJhmvzuAp+0SgDz1hRw9/EDSPOkU3v66xVVxy58YRa/bysKaOdMv12rQm23WleapSX5zH3+bZPvivY7j+vHScNqX0Aj0lh5z2md8esW3vl5LaeEsWisNm63m4mPzGDJhkIAXr1w/6qtmBev38GT05dx1YRe3OSVVSMrde/+7KYkJpCSmBDyfePM/TrtVfsi4lCALBIm/+C40s6SckrLK1idX8QXSzZWlQcLjoNp77UJQDTktUjjV7+guNK0v472+SpWZF80tFMLn/u/by2ioKiMlKT4vdoc5z9fL68KjgFOf/qHqhSMEx+ZATg72HmrbXvlcA3p2CJoef8O4aeOE5HQFCCLhKlbywyWb9kVUP7I50t56YfgwXNDcPrITnzplUmjUov0JAXH0iQ0T/fN8b2+oJjBd36K2w1L75pIcuKeBa33TV0SULa71EVRaeid7upK59zArbWPG6ypFSJ1RXOQRcLkCrHwLtzg2H9HPIC76mHXrwl923D3pMDHaZ0V3akdIg3VW3PWUPlynvzO/D1qY0dxWdDyPrd8zA/LtwU9NirIIrk9FRcXxwmeLelPGNqB+bcdxiOnDamz9kWaOgXIsk94debvvDl7TVQfY7PXPN5I3TNpAD2CJPo3baM/ghsXF8cR/QIzVNiNhUFqizQtb+zh+8bHCzaEPHbpK3OClj/zh+F79FihPHTyID67agwPnzyIrNTYp7MT2ZcoQJZG76eV27jh7flc88Zc1hfsjspj7Cwpp8iTdQKcHajClZWSyBmQIvGnAAAgAElEQVSehTMf/GWUz7ERXUJvu1qXMvdyYZBIY/fmxQfUaXveecW9s2T4a5mZQofmaXx/w7i9mu8cTHx8HD1aZyoDjUgUKECWRu/kJ7+vuv32nLVReYzPFlUvvvvw8lH85+zwR4LeuKT6D3OO11bPp4+sv8wRwXLBHjWgXb09vkisDe+Sw01HBc8jvCDIRhu12VhYHSAf2jf0B+ZZNx3Kt9ePo12z6C7GFZG6pQBZ9in//WZF7ZX2wJWvVec7rinRf8vMZFbed5TPFs8dvLJUeI8gta/nP5h3T+rPScPyePmC/Th5WB43HR3epgMi+4qjBgb/UHj0v7+p2go6XJXfKI3u1crnNe4tW9/ciDRaCpBlnzKkU/OI6v992lKG3/UZs1cFX1QDBOyKV7klq/docKX3PVMo/nfh/rTOSuGaw3r5zA30/oN5ZIg/1tFy5n6deejkQRzUoyUPnjxII1rS5GTXME/3ohdmRdRWabmz2UiH5mkh5/++dMF+EbUpIg2HAmTZp6QnRzZi86/Pf2XLzhIe+mRpyDrTvKZXeKdWeuYPw+mY4xtkVgadrbNTmTn5UC4b19PneGJCPN/87RA+vvJgumt7V5F6lZ4ceg7wwnU7wm7nP9OX8cG89QAkJzjzf4Nt3DFAOYlFGi0FyNKorfbbjGPrrvAzTeTvKq26PXNl4Ajy1Pnr6XL9h1z04uyqsjbZ1X8Eh3ZqwYzrxvHupQfRMjOFG4/sHdbj5rVIp3fb7NorikidiouL44GTBpKbkcwL54/k1mP6RtxGwe4y7vXKf5zimTZ1/4kD8V8rp8VzIo2XAmRp1NZ7rSQH2LqzNERNXx8vWM+QO6dV3XdVuLnh7Xls8lp4c8nLgamaJh8ZOG93cMfm/DR5PBeN7h5ut0UkRk4Z3pHZN09gdK9WAVkl7IZCXBVuPpq/3ucDtLdR93/hc79ZmjO9YnSvVsy+aQL7da2fzDQiEl2NbgWBMaYfcBkwDBgIpABdrbUrQ9TvBtwOTABaABuAD621f66XDktUbdjhGyB7b/saygfz1nHZKz8HlL86czWvzlwNwF/G9Qh67qCOwec4a6RIpPGJ93vZHv7Pr33u33fCAO77eAmPnj6UUT2dTT4Ki313ycvyWleQk5HMJWO7s3j9Dq48NHTqNxFp+BpdgAwMB44B5gCFwLhQFY0xA4GvgFk4QfVmoBOg7Yb2ET8u3xpQtnpbER1z0tm0o5g7P1xMZkoCZ+7XmfTkBNKSE4IGx/7+/cVvmDZZ2kxDZB9WXhF8d8xK17/t7LJ31rM/MiivGaeMCEzNuHKL7zSvsaY1c289TB+aRRq5xhggv2itfR7AGHMlIQJkY0wc8BLwHXCMtdb7nfDFqPdS6sXLPwZu8zx7VT4dc9L521vz+NJuBqgaGY5Ematir/snIg3XScPymPzOgrDqzl1TwNw1gfmSkxIDA2EFxyKNX6Obg2ytDTdqGQMMAB70C45lH3DJS7Ppcv2HQY+VegLbyuB4Ty3fsmuvzheRhi0lMYEFtx++V20cVsMmISLSeDW6ADkCoz2/440x3xhjSo0x+caYV40x7WPaM9krmwtLmLpgg0/ZUQPbkeRJt/TAx84K8zbZKWG1N7xzi7DqnRbk61URadwyakj9Fo5hnbUoT2RfFPEUC2PMSGAS0M1TtBx411r7Y112rA5UBsFvA08DNwM9gHuA6caYQdbaolAnS8O1LsiOV4+cOpgek6cCsMWTyaJdszQ27qg57dv43q35x2mDGXjbpyHrpCbFM/movpwwpMNe9FpEGqK9mQ4xME95jkX2VWEHyMaYBOAp4FzA/x3lOmPMC8AF1lpXBG2OBb4Ms3ora+2WcNumenT8NWvtdZ7bXxpj1gEfAGcAz0TQnjQQv27a6XO/U046iQnxXD+xN/d58pMuWFvAL6u319jO/NsOq9oB661LDuTEJ74LWu/1Px3AwLzIdugTkcbjhfNHcs5/Z0Z0TsvMZJ47b2SUeiQisRbJCPJNwHnAu8ADwCJPeT/gOuAcYCVOSrVwLfG0GY5I0wlUpjf4xK/8U8AFDI2wPWkAlm3eyTVvzPUpKy5zPpOZtllVZWc/W/MXGpeP7+mzPeywzi24akIv/j5tKUkJcZS5qqetZ6Y0xrWsIhKu0b1asX+3HH5YHnrLeX8PnjQo6HbzIrJviOQv//nANGvtCX7l3wOTjDHTPHXCDpCttRuA5yLoQyTm13JcKQoaofEPTw8o21ToTKOoTNgPkF9UVnX7/ctGccM781iw1tlKNjUpnr8e6rsFNMClh/RgaKcW9O+QzeA7qjcRiXT7ahFpfG49ph8TH5kBwHPnjeDc//up6tgnV47miyWbKC5zsSZ/N5OGdOCgHrmx6qqI1INI/vK3xhk5DuVd4KG9606dmgrsBo4E3vEqPwJIABranGnZS60ygy/K69wynbuPH8Bxj30LwEeXHxx03mFCfFzVZgDDO7dg1qp8IPzFfiLSePVpl83PN08gOy2JhPg4Hj9zKHd9sIi7JvXHtM3y+YZKRPZ9kQTIS4G2NRxv56kTVcaYdJygF2CQ5/dEY8xmYLO1djqAtTbfGHM7cI8xZgdOwNwTuBOYC7wW7b5K/di/m7OKvGNOetDj2alJDOrYnD+P7U5KYgLdWmXW2ub/LtqfGb9u4YDuucppKtJEtPCaMnHkgHYcOaBdDHsjIrEUSYB8L/C4MeZNa63PJFBjzBDgz8Alddm5EFoDb/iVPe75PR0YW1lorb3fGFMAXI6zk952nKwW11trS6PfVakPL1+wf8hj90waUHX7uiN6h91mYkI8h/RuvVf9EhERkcYpZIBsjLklSPFyYJYx5lOcBXZuoC8wAWdUNuqbz1trVxKYRaOm+k8CT0atQ1JvXH7bwv40+VBaZflOfxjfuzWfL9lUdT83U4toREREJDI1jSDfVsOxiZ4fb0OBIThTGETq3O6y6gyCUy49KCA4Bvh2mW8mwFytMhcREZEI1RQgd623XoiEoai0vOp2Rkrw3a/uO2EgV772S9X9liEW7omIiIiEEjJAttauqs+OiNRmd2n1CHJaiNRrxwxqT16LNF77aTUZKYl0zg2+cE9EREQklD1K8GqMyaV6hHmFtXZrTfVF6sKukuoAOSM5+AhyQnwcw7vkMLxLTn11S0RERPYxEQXIxphBwL+AUX7lM4DLrbXz6rBvIlVcFW52eU2xSAsRIIuIiIjsrbADZGNMf+AbIBV4D1jgOdQPOAaYYYw50Fq7sM57KU3a6m1FXPTibBavd3bCS4iPIzkhPsa9EhERkX1VJCPIdwBlwIHWWp9tnD3B89eeOifWXfekKbt36mL+M315QHl6coI27xAREZGoiWQYbjTwmH9wDGCtXYCzWceYuuqYNG2bdhQHDY7BCZBFREREoiWSADkD2FDD8fWeOiJ77efV20MeSw+RwUJERESkLkQSIC8Hjq7h+NGeOiJ7LaGGKRRpSRpBFhERkeiJZCjuBeBeY8wrwN04W00D9AFuAA4Drq/b7klT9fmSjSGPVbjdIY+JiIiI7K1IAuSHcLaTPg04FajwlMcDccDrwMN12jtpsmqaRrFjd1k99kRERESamrADZGutCzjVGPMMcDzORiFxwDLgXWvtZ9HpojRFmwpLQh7brgBZREREoiisANkYkwB0AHZaa6cB06LaK2nSPl+8kffnrgMgOSGeAXnNuPDgrlz80hwAiry2nBYRERGpa+GOICfhLMC7AXgwet0RgT8+P6vq9uSj+vCHA7vErjMiIiLS5ISVxcJaWwxsAXZFtzvS1Ln9FuA1T08KqBOvPUJEREQkiiJJ8/YRNad5E9lrpa4Kn/s9W2dV3b756L6kJyfwf+eNrO9uiYiISBMSSRaL64BpxpjncTJa/OoZWRapMyXlvgFy3/bZVbf/OKor5x7YhQQNIYuIiEgURRIgbwLcwCDgLABjjH8dt7VW25zJHispqw6Q37rkgIDjCo5FREQk2iLdKEQ7NEhUlZRXZ6honZUaw56IiIhIUxVJHuRzo9gPEQCKvUaQUxIjmSIvIiIiUjcUgUiDsWVnCYf+fXrV/ZTEhBj2RkRERJqqiOcLG2NGApOAbp6i5Tg76f1Ylx2TpueGt+f73E9J0uc3ERERqX9hB8ie3fSeAs7F2WLa23XGmBeACzxbUotErF/7bKYt2lh1PzlBAbKIiIjUv0gikJuA84ApwIFAc8/PQcB7wDmeOiJ7JDXJd0pFvDJWiIiISAxEMsXifGCatfYEv/LvgUnGmGmeOrfXVeekadlVUh7rLoiIiIhENILcGmekOJR3PXVE9khRqWbniIiISOxFEiAvBdrWcLydp45IxOat2c6z36yIdTdEREREIgqQ7wUuNcYM8j9gjBkC/Bm4p646Jk3LsY9+G+suiIiIiACRzUHuhZPSbZYx5lNgCc7Oen2BCcBcwBhjbvE6x22tvbOuOisiIiIiEm2RBMi3ed2e6PnxNtTz480NKECWGhXsLgsoy06NOEW3iIiISJ2IJArpGrVeSJO2oaA4oOyVC/ePQU9EREREIgiQrbWrotkRabqWbNgRUNa/Q7MY9EREREQkskV6IlFxxf9+8bl/+bgeMeqJiIiIiAJkibF5a7b73D9xaB5XHWZi1BsRERERBcgSY/7p3R4+JSCLoIiIiEi9UoAsIiIiIuJFAbI0GP3aZ8e6CyIiIiIKkCW2cjKSq24/+4cRMeyJiIiIiEMBssRUu2apAEw+sg9tPbdFREREYinsPMjGmOW1VHEDu4HfgU+Bp621u/aib9IElJZXAJCcqM9qIiIi0jBEEpX8DpQDXYAWwHbPTwtPWTlOgLw/8HdgtjGmVR32VfZBpS4FyCIiItKwRBKVXAnkAH8GWllrh1prhwKtgMs8x/4ItAT+AvQE7qjb7sq+pmoEOUEBsoiIiDQMYU+xAB4CXrPWPuldaK0tBx43xvQHHrbWTgAeM8YcABxVd12VfZGmWIiIiEhDE0lUsh8wr4bj83CmV1T6DmizJ52SpqGiws2u0nIAUhQgi4iISAMRSVRSAtSUh2ukp06lFGDnnnRKmobCknKKy5wR5PbN02LcGxERERFHJFMs3gPOM8b8BvzLWlsEYIxJB64A/gA871X/QGBpXXVU9j0l5a6q26lJCTHsiYiIiEi1SALka4AhwD3AHcaYdZ7y9p525gPXAhhjUoFi4LG666rsa0o8o8egKRYiIiLScIQdIFtrtxljRgIXAkcDXYE44HPgfeAZa22pp24xcHbdd1f2JSXlXgFykgJkERERaRgiGUHGWlsGPO75Edkr3lMsUhI1xUJEREQahj0etjPGtDTGtKzLzkjTUlzmHSBrBFlEREQahohGkI0x7YF7geOALE/ZDmAKMNlau7bOeyj7rO9+21p1WxuFiIiISEMRdlRijOkEzMKZW7wceMXzsxw4B5hpjOkYjU7Kvi8+Pi7WXRAREREBIhtBvhNoARxtrf3I+4AxZiLwtqfOuXXWO9mnVS7MG9ChWYx7IiIiIlItku+1DwMe9w+OAay1U4EngCPqqmOy7/t9WxEArgp3jHsiIiIiUi2SALkF8GsNx38Fmu9dd6QpeemH3wFYtH5HjHsiIiIiUi2SAHkNMLaG46M9dUSC+mLJRq59Yy75u0pj3RURERGRkCKZg/wGcJ0xZgVwn7W2AMAYkw1cD5wC3Ff3XZR9QXGZi/OfmwVAYXE5T549jF5tMlm6cSeXHtI9xr0TERERqRbpIr2Dgb8B1/htNZ0AfAvcVbfdk33F/LUFVbc/XrgBgDKXM/e4XbO0mPRJREREJJhItpouMsaMAc4Hjqd6q+lPgHeB56y15VHppRdjTD/gMmAYMBBIAbpaa1cGqdsWuBmYCLQDNnj6e4e1dp1/falb3/22hem/bubSQ3pQ5rWtNEBFhZsVW3YBkJakXfRERESk4Yh0q2kX8LTnJ1aGA8cAc4BCYFywSsaYZGA6kAPcAiwG+gB3AOONMf2ttSX10uMmaMvOEs545kcA/jN9ecDxzxZvrLr98+p8ThyWV299ExEREalJRAFyA/GitfZ5AGPMlYQIkIEDgV7ABdbaZz1lXxljSoFngAOAr6Lc10bl59/zKSp1cVCPvd9B3HtKRTCPfflb1e3D+7Xd68cTERERqSshA2RjzDl70qC19oU9705Y7VfUXguAMs9v/0it8r5Gj71s3VnCpMe/A+Czq8bQo3XmXrWXmVLzZ69VnhzIAEM6tdirxxIRERGpSzVFMc8Bbpx5xuFyA1ENkCPwAzATuM0YsxJYAvQGbgO+Bn6MVccaotveX1R1+72567hqQq+AOg98vIRlm3fy6BlDSUqoOUNgenLN84q3F5VV3U5NjCTboIiIiEh01RQgH1JvvYgCa63LGDMeeBH4yevQx8DJEYxENwmfLaqeE/yvz38NCJCLy1w8/tUyAN6Zs5ZTRnSssb2KMJ/d5IR4EmsJtkVERETqU8gA2Vo7PdoPbowZC3wZZvVW1totEbSdBLwC9MfJvPEbziK9W4EpxpgjrLVlNTTRZLjdbnaXuWqsU+KVhWJrGBt9uNzhbR+dmqTgWERERBqWWC/SWwKcF2bdwgjbPh8n28Vga+1cT9kMY4zFWZx3Og1nOkhM/bJ6e43Ht+4s4Z2f11bdd1N78OuqCC9ATk+O9X9BEREREV8xjU6stRtw5jpHwxCgzCs4rjTL87tvlB630Skpr3k+xMn/+Z7lm3dV3Q9ncNgdotK43q35YsmmqvtptcxVFhEREalv+/L32+uAJGPMEL/yAzy/1yIAJMTXvA7TOzgOV6gR5CP8UrqlaIGeiIiINDCN7vttY0w6cKTn7iDP74nGmM3AZq+5088BVwHvGGPuApbhjBrfDGzEmZ8sQLkrMJgtLnORGmKHu1Cjw952lgTfVDE7rdH9lxMREZEmpjFGK62BN/zKHvf8ng6MBbDW/m6MGYmzKO8moA2wHvgQuN1au7VeetuA2Q2FrNu+O2giv/Ia5hCHM8Vi5optQcsP6d3a5/6SDZFOLRcRERGJrkYXIFtrVxJmbmZr7VLgzKh2qBE7/J9fA3DugV0CjpWVV0BK8PPCyVCRl5MetDzZL6Vbh+ZptbYlIiIiUp80AbSJqvAaIX5r9pqA44s37Ah5bnFZhc/5QYUIouPi4lhw++FV928/tl8tPRURERGpX41uBFnqxn0fL6m6XRhkvvAZT//IyvuOCnruk9OX8eT0ZYzsmsPrfzogaJ2yIPOaK2WmJLLi3iPZWVJOVmpShD0XERERiS6NIDdBmwqLeerr5XvdTqh5xgDlQbbS69E6s+p2XFycgmMRERFpkBQgN0HfLwt/fWK5a8925PYfQe7QPI0P/jJqj9oSERERqU8KkJug/367Mmj5DRN7B5TVtolIKN6p40Z2zeHlC/YLmTZOREREpCFRgNwE7d81J2h5ZmrglPRdIfIZVwqVE7lyisUB3XJ5/U8H0KVlRoS9FBEREYkNBchN0Jrtu4OWZ6YEBsihNvyoVLC7zOd+ZcBcOcUiMSGsjHwiIiIiDYYC5CYoNTH4VIeM5EQeOGlg1f3S8go+XrihxrZ+Xr296vbJT35H1xs+4v6Pl/DyD6sA+Oa3LXXQYxEREZH6ozRvTVCoaROZqYl0yq3e4OOaN+ZSVssive1FpYAzcvzTynwAnvhqWdXxcHbdExEREWlINILcBP2wIngWi6zURFISq/9LvDd3Hd1a1Tx3eGexE2zXNhVDREREpLFQgNwEbS8qC1qelpRAot9W0I99uSxo3Uo7S1xB22yR7uQ4vu2YvnvaTREREZGYUIDcBF17uCEuDs7av5NPeVZqEvERrqkrLHYCY//FevmegLlZujYDERERkcZFAXITdOkhPVhx71HcdfwAFt5+OAd0y+XGI3vTKiulxjnDX1w9JqAs3zMHecfu4KPSWSkKkEVERKRx0SK9Ji4jJZFXL9q/6n7b7NSg9fq0y6Zbq8yA8qJSZ4qF/whypWC5lUVEREQaMo0gi4/4+DguH9cjoPz8g7oAcO8JA3zKd5W4WJNfxPZQAXKQ3MoiIiIiDZkCZAlwwtC8gLJkT3aL00d24oGTBpLlCXw/W7yRUfd/yZRf1gZtK0sjyCIiItLIKECWAHkt0gLKvNO/nTK8I+d6RpQr/bB8W9C2slI1B1lEREQaFwXIEsA/1RtUjyBXSkkM77+ORpBFRESksVGALGFJ8guaU5OCb1dd23kiIiIiDZ2iFwlLckL4I8ifXTWG5IR4DuyeG+1uiYiIiNQ5ff8tYQmcYhF8BPmWo/vSo3UmP00+VCneREREpFHSCLIEdaJfJgv/AHne2u1Bz+vdNgtwdtBLiHRbPhEREZEGQAGyBHXLMX197vtPqcgOkZ0i2AI/ERERkcZE0YwElZrk+18jOcF3SsX5o7oGPS8xQaPGIiIi0rgpQJag/BflJSX6Br4tM1OCnjcor3nU+iQiIiJSHxQgS1Bxcb4BsX/AHMw9kwZo3rGIiIg0egqQJSwZKbVnpGiZmVwPPRERERGJLgXIEtI/Th0EwKF92oS1McjIrjnR7pKIiIhI1ClRrYQ0aUgexw7qEHLaxIlD85i6YD33njCAEV1yaJ6uEWQRERFp/BQgS41qmlP80MkDufeEAQE5kkVEREQaMwXIssfi4uJITtSiPBEREdm3aOhPRERERMSLAmQRERERES8KkEVEREREvGgOcmSyCwsLGT58eKz7ISIiIiJ7obCwECA72DEFyJGpAOILCwt3xLojIiIiIrJXsnFiuwBxbre7nvsiIiIiItJwaQ6yiIiIiIgXBcgiIiIiIl4UIIuIiIiIeFGALCIiIiLiRQGyiIiIiIgXBcgiIiIiIl4UIIuIiIiIeFGALCIiIiLiRQGyiIiIiIgXBcgiIiIiIl4UIIuIiIiIeFGALCIiIiLiJTHWHZD6Y4zJBO4BTgaaAwuBO6y178W0Y/sYY0wecC0wDBgMZACHWGu/ClL3DOBvgAG2AC8Bt1lri/3qtQEeAI4C0oA5wN+std/taZtNmTFmPHA2cADQEdgGzARutdbO96s7AbgTGAQUAu/gPPfb/eqF/foKt82mzhhzIHAr0B/IxXmu5gMPWmun+tXVdWpAjDG34Vy7udbawX7HdK1iwBgzFvgyxOE+1tolXnWb/DXSCHLT8g5wJnATTqC1CHjHGHNkTHu17+kBnA7sBD4PVckYcxbwMvAtMBHnTeZS4Dm/eqmedsYAfwEm4by5fG6MGbInbQoXA52Af+A8T1d57v9kjNm/spLnD8pHwGrgGOAa4FjgQ2OM//tnWK+vCNts6loAFrgaOAK4CCgBPjLGnFZZSdepYTHG9MP5kL4xyLGx6FrF2t9wBge8f1ZWHtQ1cmgEuYnw/Gc9FDjBWvuOp+xLoBvwMM5/XKkbX1trWwMYY47HeRPwYYxJAB4E3rPW/tlT/KUxpgx4yhjzD2vtj57y84F+wDBr7RzP+dOBxTgB8MQ9aLOpu9Rau8m7wBjzKbACZ/T/RE/xA8AC4FRrbYWn3nrgU5wRk9c8ZZG8vsJqU8Ba+yHwoXeZMeZ9nOt0EfA/T7GuUwPhCXaeBZ4BBuCMKnrTtYq9pdbaH2o4rmuERpCbkklAATClssBa6waeB3obY/rGqmP7msoXfy32B9riPP/eXgbKqA7QwLl28yuDY89jlACvAhOMMVl70GaT5h8ce8q2A78CeQDGmA7ACOBF72tqrZ0GrCXwGtX6+oqwTQnCWluO81yXga5TA/RXnNfQZP8DulYNn65RNQXITUd/YFGQ4G2e13GpP5XP9wLvQmttEbAM3+vR37+exzwgAeizB22KH2NMK3yf66DPp8d8Aq9ROK+vSNoUD2NMvDEm0RjT3hhzO9ALZ3oM6Do1GMaYbsAdwGXW2h1BquhaNQz/McaUG2MKjDEfGGOGeR3TNfJQgNx05OIsRPK3zeu41J/K5zvUNcn1qxvOtYukTfFijIkDnsJ5T3zIU6xr1HC8jjNivBa4EjjFWvux55iuUwPgeQ09DXxirX03RDVdq9gqAP6JMz3pEJzpZH2Bb40x+3nq6Bp5aA5y0+Lew2MSPaGed//ySK5duG1KtQeB44HzrLWL/Y7pGsXedcD9OFOIzgBeN8b8wVr7qlcdXafYuhAYjhNw1UbXKgastT8DP3sVzTDGvIczsns3znziSk3+GilAbjq2EvxTWo7nd7BPdhI9Wz2/c71uV8rBWYTkXTecaxdJm+JhjLkbJ0vCFdba57wOeT+f/nLwfc3syTWqrU3xsNYuB5Z77r7vWaj3mDHmNXSdYs4Y0xJnEda9wC5jTOXCvEQgwXO/GF2rBsdau8GzQLlyMbmukYemWDQdC4E+QdKpDPD8DjY3SKJnoee3z9wrY0w60B3f67HQv57HAMAFLPGqF26bAhhj7gBuBK6z1v7L73DQ59NjAIHXKJzXVyRtSmgzcVLAtULXqSHIA5rhBMj5Xj8H4TyH+cBt6Fo1VPFUj+LqGnkoQG463sFJt3OMX/k5gLXWLqr/LjVpPwAbcDar8HY6kAS87VX2DjDAGFOVbN8Yk+yp+5nXYphI2mzyjDG3AjcDN1trH/Q/bq1dA8wCzvT+A+DZZKQDgdeo1tdXhG1KEJ65rmOB7cBWXacG4TecOa3+P3NxFggfAjyla9XwGGPaAhNw/n7ofc+Lplg0HR/h7KDzrDEmF+fr9j8Ao4DjYtmxfZEx5iTPzRGe32M8X0PustZOtdaWG2OuB54zxjwKvImTjeJ+4E2/HJXP4mz28bYx5gacr6OuANoDp1RWirDNJs0YczXOiNYHwGfem4MAJZ65euAk1P8UeNUY8xTOc34/8CPwhtc5kby+wm2zyTPGvAysAmbj7ArZDud5HQf8xZPyDXSdYspauxP4yr/cGLPdc9z7mK5VjHheT8txdmLNB3rjPHdpwA1eVXWNgL35MG4AAAUFSURBVDi3u0HOjZYoMMZk42wscRLOp75FOFtChlpxLHvIGBPqhbXKWtvFq95ZOG8cvXACgJdxtjve7ddeW5yFZEcBqThvcNdba78J8thhtdmUGWO+wtmZMBj/a3QEcDvV26O+izMlI9+vzbBfX+G22dQZYy7D2aWrF85X+AU4I1GPWmvf96ur69TAeF5nzYNsNa1rFQOeAZTTgC5ABs7c4K+Au6y1C/zqNvlrpABZRERERMSL5iCLiIiIiHhRgCwiIiIi4kUBsoiIiIiIFwXIIiIiIiJeFCCLiIiIiHhRgCwiIiIi4kUBsoiIRI0x5itjzMpY90NEJBIKkEVEREREvChAFhERERHxogBZRERERMRLYqw7ICIiwRljUoHrgdOBjkApsBr42Fp7rafOqcCZwGCgDVAIfAPcYq2d59feSmAlcAXwMLA/UAS84HmcROAuz+PlAjOBP1lrF3u1cS7wf8AEYBRwHtAWsMA91tr/hflv6wncAhzqeax1wBvAbdbaXeG0ISISLQqQRUQarseA83EC2H8ACUBPYJxXncuAbcBTwAagO3AR8K0xZqi19le/NvOAacBrwJvAYcDVgAvoB6QB9wEtgWuAd40xfay1FX7t3A9kAE8AbpxA+VVjTKq19rma/lHGmGHAF8B24D/AWmAQcDlwkDFmjLW2rLYnR0QkWhQgi4g0XJOAqdbaP9RQ5wj/EVdjzAvAL8BfgT/71e8OnGKtfcNz/0ljzGzgWuB94FBrrdvTzlbgEZzR4k/82mkJDLTWFnjqPgnMA/5ujHnNWru7hj7/F1gPjLDWFnr1+3PgbZwR8edqOF9EJKo0B1lEpOEqAPoZY/qHqlAZHBtj4owx2caYlsBmnCkP+wU5Za1XcFzpGyAO+HdlcOwxw/O7Z5B2nqgMjj39KACeBFoAY0P11xgzABgIvAKkGGNaVv54+rELZ1RbRCRmNIIsItJwXQm8CMw3xiwHvsQZ5X2/csqDMWYIcCdOUJrhd/6KIG0GK8sPcayyPDfIOYuDlC3y/O4W5FilPp7ft3t+gmlTw/kiIlGnAFlEpIGy1k4xxnQBjgTG4Cxo+yMwwxhzKM7iuK+BHThBssUZgXUD/wQygzTrquEhQx2LC1LmDlIWrF6oOg8DH4eokx+iXESkXihAFhFpwKy124CXgJeMMXE4C+iuA44D2uMEwcdaa7/0Ps8YkwuURLFrfYH3/MoqR4eX13Be5aJBl7X2szrvlYhIHdAcZBGRBsgYk2CMae5d5pkf/LPnbg7VI75xfudeiDO6HE2XGGOaeT1mM+BinMwU02s472dgAXCxMSZgKoYxJtEYk1PXnRURiYRGkEVEGqYsYL0x5j2coHIT0BW4BGcKwvs4KdmKgBeNMY96yg/CmZKxjOi+x28BfjTG/BcnQD8P6ARcYK0tCnWStdZtjDkbJ83bPM/5C4F0oAdwAnADymIhIjGkAFlEpGEqwplHPB5n7nEmTmq094B7rbXrAIwxE4F7gBtxRpS/xZmv/CjQJYr9+xtwME4e5jY4UyfOtNa+UtuJ1tpfPIsLbwCOxRl5LsTZxOQ54PPodFlEJDxxbnewdRYiIiKBvHbSO8Ra+1VseyMiEh2agywiIiIi4kUBsoiIiIiIFwXIIiIiIiJeNAdZRERERMSLRpBFRERERLwoQBYRERER8aIAWURERETEiwJkEREREREvCpBFRERERLz8P5Sz9+ySL2JOAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "traceplot(posterior_small, ll_small)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# moderate proposal width\n", "posterior, ll = sampler(data, samples=5000, mu_init=.1, proposal_width=0.5)" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "traceplot(posterior, ll)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "# large proposal width \n", "posterior_large, ll_large = sampler(data, samples=5000, mu_init=1., proposal_width=3.)" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 6))\n", "plt.subplot(2, 1, 1)\n", "plt.plot(posterior_large); plt.ylabel('mu'); #plt.xlabel('sample'); \n", "plt.subplot(2, 1, 2)\n", "plt.plot(np.log10(ll_large)); plt.xlabel('sample'); plt.ylabel('log prob');\n", "plt.hlines(np.log10(p_true), -200, len(ll_large)+200)\n", "plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, 1, figsize = (10, 6))\n", "ax[0].plot(posterior_large); plt.xlabel('sample'); plt.ylabel('mu');\n", "ax[1].plot(np.log10(ll_large)); plt.xlabel('sample'); plt.ylabel('log prob');\n", "plt.tight_layout()\n", "#_ = ax.set(xlabel='sample', ylabel='mu');" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.hlines(np.log10(p_true), -200, len(ll_large)+200)\n", "ax.plot(np.log10(ll)); plt.xlabel('sample'); plt.ylabel('ll');" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.hlines(np.log10(p_true), -200, len(ll_large)+200)\n", "ax.plot(np.log10(ll_large)); plt.xlabel('sample'); plt.ylabel('ll');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "两者进行比较" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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h4RFN00aH65kyAiGEEGE077yOn7q/2F1MWrpnS2BGipnZk+JIys7rUM9e3sDM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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.distplot(posterior_small[1000:], label='Small step size')\n", "sns.distplot(posterior_large[1000:], label='Large step size');\n", "_ = plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "下面分析自相关系数" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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PAfIrOX8H8LbWerLn87tKqf8ADwFXhKpTslJICCGEqB3hOsKSDtiVUg3LnU/BSLAtrz2w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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymc3.stats import autocorr\n", "lags = np.arange(1, 100)\n", "fig, ax = plt.subplots()\n", "ax.plot(lags, [autocorr(posterior_large, l) for l in lags], label='large step size')\n", "ax.plot(lags, [autocorr(posterior_small, l) for l in lags], label='small step size')\n", "ax.plot(lags, [autocorr(posterior, l) for l in lags], label='medium step size')\n", "ax.legend(loc=0)\n", "_ = ax.set(xlabel='lag', ylabel='autocorrelation', ylim=(-.1, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Python中的pymc3包可以很方便地进行MCMC采样。" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 15000/15000 [00:01<00:00, 14445.82it/s]\n" ] }, { "data": { "image/png": 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OOOMMfv3rX2t1L7zwwiHfn52dTSQSoaqqitzcXABqa2u1oCIrKytuhcSuT92L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\n6C12rK9J1R0918OAP9OzhShMkkCInBkK+dl14hepcry/joS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pymc3 as pm\n", "\n", "with pm.Model():\n", " mu = pm.Normal('mu', 0, 1)\n", " sigma = 1.\n", " returns = pm.Normal('returns', mu=mu, sd=sigma, observed=data)\n", " \n", " step = pm.Metropolis()\n", " trace = pm.sample(15000, step)\n", " \n", "sns.distplot(trace[2000:]['mu'], label='PyMC3 sampler');\n", "sns.distplot(posterior[500:], label='Hand-written sampler');\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考文献\n", "1. http://twiecki.github.io/blog/2015/11/10/mcmc-sampling/" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }