{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Approximate Bayesian Computation: Synthetic likelihood (parametric approximation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Florent Leclercq,
\n", "Institut d'Astrophysique de Paris,
\n", "florent.leclercq@iap.fr" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "init_cell": true }, "outputs": [], "source": [ "import scipy.stats as ss\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from cycler import cycler\n", "np.random.seed(123457)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "plt.rcParams.update({'lines.linewidth': 2})\n", "plt.rcParams.update({'text.usetex': True})\n", "plt.rcParams.update({'text.latex.preamble': r\"\\usepackage{amsmath}\\usepackage{upgreek}\"})\n", "plt.rcParams.update({'font.family': 'serif'})\n", "plt.rcParams.update({'font.size': 15})\n", "dir=\"./plots/ABC_synthetic_likelihood/\"\n", "!mkdir -p $dir" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we try to infer the unknown mean $\\mu$ of a unit-variance Gaussian distribution.\n", "\n", "The data consist of $N_\\mathrm{samp}$ realizations. For inference, we run $N$ simulations per value of $\\mu$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def simulator(mu, sigma, Nsamp=10, random_state=None):\n", " mu, sigma = np.atleast_1d(mu, sigma)\n", " return ss.norm.rvs(mu[:, None], sigma[:, None], size=(1, Nsamp), random_state=random_state)\n", "\n", "def summary_statistic(sim):\n", " return np.mean(sim, axis=1)\n", "\n", "def neg_log_likelihood(mu, Phi_0, Nsamp):\n", " return 1/2.*np.log(2*np.pi/Nsamp) + Nsamp/2.*(Phi_0 - mu)**2\n", "\n", "def sample(mu, sigma, N):\n", " sims=np.zeros(N)\n", " for j_ in range(N):\n", " sim=simulator(mu, sigma)\n", " sims[j_] += summary_statistic(sim)[0]\n", " return np.mean(sims)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "data: d_0=[[1.72558743 1.96316607 3.90707517 1.95831498 1.57465709 0.93464301\n", " 0.23803412 1.5998699 2.56876862 2.08744352]]\n", "summary statistic of the data: Phi_0=1.855755990636889\n" ] } ], "source": [ "# Set the number of samples and number of simulations per mu\n", "Nsamp=10\n", "N=2\n", "\n", "# Set the generating parameters that we will try to infer\n", "mean0 = 2\n", "sigma0 = 1\n", "\n", "# Generate some data\n", "d_0 = simulator(mean0, sigma0)\n", "print(\"data: d_0=\"+str(d_0))\n", "Phi_0 = summary_statistic(d_0)\n", "print(\"summary statistic of the data: Phi_0=\"+str(Phi_0[0]))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Set the prior\n", "mu = ss.uniform(-2,6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate simulations" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Generate some data points\n", "N_sims=100\n", "mu_sims=mu.rvs(N_sims)\n", "sims=np.zeros(N_sims)\n", "for i_ in range(N_sims):\n", " sims[i_]=sample(mu_sims[i_], sigma0, N)\n", "S1_sims=neg_log_likelihood(sims,Phi_0,Nsamp)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(xmin,xmax)=(-2.1,4.1)\n", "(ymin,ymax)=(-5,85)\n", "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot(mu_sims, S1_sims, linestyle=\"\", marker=\"o\", markersize=3.5, color=\"black\", label=\"realizations at $\\mu$\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-synthetic likelihood\")\n", "plt.legend()\n", "plt.savefig(dir+'stochastic_process_simulations.pdf',dpi=300,bbox_inches=\"tight\",transparent=True)\n", "plt.savefig(dir+'stochastic_process_simulations.png',dpi=300,bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The synthetic likelihood as a stochastic process" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the true variance (unity), the synthetic likelihood is given by\n", "\\begin{equation}\n", "-2\\log \\mathcal{L}_\\mathrm{s}^N(\\mu) = -\\frac{1}{2} \\log\\left( \\frac{2\\pi}{N_\\mathrm{samp}} \\right) - \\frac{N_\\mathrm{samp}}{2} (\\Phi_0 - \\hat{\\Phi}_\\mu)^2,\n", "\\end{equation}\n", "where $\\hat{\\Phi}_\\mu$ is the stochastic process from which realizations are plotted above.\n", "\n", "Since a realization at $\\mu$ is the average of $N$ realizations of the summary statistics (themselves Gaussian-distributed with mean $\\mu$ and variance $1/N_\\mathrm{samp}$), realizations of $\\hat{\\Phi}_\\mu$ are Gaussian-distributed with mean $\\mu$ and variance $1/(N\\times N_\\mathrm{samp})$. We can therefore write the synthetic likelihood as a quadratic function subject to a random shift $g$,\n", "\\begin{equation}\n", "-2\\log \\mathcal{L}_\\mathrm{s}^N(\\mu) = -\\frac{1}{2} \\log\\left( \\frac{2\\pi}{N_\\mathrm{samp}} \\right) - \\frac{N_\\mathrm{samp}}{2} (\\Phi_0 - \\mu - g)^2, \\quad g \\sim \\mathcal{G}\\left(0, \\frac{1}{N\\times N_\\mathrm{samp}}\\right).\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def neg_log_synthetic_likelihood(mu, Phi_0, g, Nsamp):\n", " return 1/2.*np.log(2*np.pi/Nsamp) + Nsamp/2.*(Phi_0 - mu - g)**2\n", "# this is likelihood(Phi_0, mu+g)\n", "# equation (17) in Gutmann & Corander 2016" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### One realization" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Get the synthetic likelihood for one particular realization\n", "sigma_g=1/np.sqrt(N*Nsamp)\n", "g=ss.norm(0, sigma_g).rvs()\n", "(xmin,xmax)=(-2.1,4.1)\n", "mu_arr=np.linspace(xmin,xmax,200)\n", "l_mu_one_res=neg_log_synthetic_likelihood(mu_arr, Phi_0, g, Nsamp)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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aWgBAc3MzzGYzLBZLSP03Njaiq6vLe58mTpyIsrKyYWMQBAFarRYtLS0oKSnx6VcikUCj0aCgoMA79Uuv16Orq8tn2tVw125sbITJZAJwbBqc5z5otVqo1eohYwCi85wNJphrGQwGtLS0QBAE2Gw2yOXyoJ9vq9UKlUrlfbxMJhMaGhqGfYyCjc/D8zvjOQ8ANBpNwMfBarUO+3gF8/sVzv0b7ncglPvTPx69Xu/9vZDL5bDZbOjs7PRezzMlM9jXYrCPf7AxD/faHuoxDeZ4zLlTmN1udwNw2+32mFyvpKTEnZaW5gbg/ZeWluYuKSmJyfWJiJLV4cOH3Z999pn78OHDg56zYcMG98knn+w++eST3W+++abPMUEQvMdKS0v9bvub3/zGe3ygzZs3e49t3brV51hPT4/32DXXXON32xtuuMF7/MCBA0He2+BYLBa3SqVyd3d3+7Sr1Wq3yWTyaVOpVO7CwkKf9oaGBrdcLvfrUy6X+/RZVlbmLiwsDDouuVzuLiwsdFssFnd7e7tbLpe729vbg+7fZDK5NRqNT58ajSZgDBqNxl1WVubXrlKp/NoH9mkymdwAfB6TUK6tUqncer3er32oGKLxnA0mlGsN9jgOpru72+9xCtQ21GMUbHwDf4f633bg7TQazbCPVzDPcSTun+f4wMc12PszGLlc7lapVD639/TZ0NDgd+5Qr8Vgfz+CiXm41/Zwj2mwj/lggnmPcLtDyw04nS+GlEolnE6nT5vT6YRSqRQpIiKi1NHT04Nvv/0W3377LXp7e32OOZ1O77FAi73379/vPT7Qjz/+6D126NAhn2Nut9t77MCBA3637ezs9B73zFCIlKKiImi1Wr8F9eXl5SgqKvJpk8vlEATB+001cGzhu81mg9Vq9emzpKTEp8/y8nI0NjYGXSRAoVDAZrNBrVZDpVKhu7vb+812MP3bbDbvSEL/uMxmc1DXB/wLTthsNp/HxPNzWVmZz2MSiWsPFoOnr0g/Z4MJ5Vqh8oxcDYy3oKAg6D6Cja+oqAjFxcU+j6cgCOjq6vKrgNfV1TXs4xXMcxyJ+wcM/jsQ7P0JRKFQoLCw0Of2KpUK5eXlWL58uU8fw70Wg/39CCbm4V7bwz2mkXrMI4lJVAyVlpYiOzsbUqkUaWlpkEqlyM7ORmlpqdihERElvfHjx+Pkk0/GySefjPT0dJ9jMpnMe2zChAl+tz3hhBO8xwc6/vjjvcfGjh3rc0wikXiPTZo0ye+2EydO9B6XSiP3liwIgt8HbA+NRgObzeb3wT83N9fn54EloT19zps3z6ddLpdDLpcH9cHdI9C0pGD7LywsRHd3t3e6ktVqRXt7e1glo+VyOYqLi70/FxUVQaVS+U2zisa1PaLxnEXyWqHw9DthwgRotVo0NjbCZrMFNeUylPg8z0FOTo7POf2fp/6CebyCeY7DvX+DCfX+DGbixIl+bYWFhQGf16Fei8H8fgQTczCv7eEe02g95uHgmqgYysjIQFNTE6vzERGJ4K677sJdd90V8JhSqcQ333wz6G3/+c9/DnrshhtuwA033BDw2Lhx44bsd/PmzYMeC0cwCU3/Dy6h9Nnc3Oxdj+ARyjocIPCHvFD696zpUCgUKCoq8lmHMVKeD6jV1dUwm83eNRsDRePaQHSeMzGvZbFYUFlZCbPZDKPRCAAwGAwoKSmJWHyeJCjSe0AF8xyHc/8G4xlpicaeVp4+B47mDPVaHIrn9yOYmIN9bQ/3mEbjMQ8Hk6gYy8jIYBEJIiKKKs+0moEfWPq3hVqy2nN+QUFBRD7Ij7R/o9EInU6HhoYG73mRKiXtKdrQ0NDgjcdsNiM3NxdyuTysaxuNxiE/7EXjORPrWoIgQKFQ+IzkVVdXQ6vVori4eNARFc9jFGx8nvMiud9UMM9xuPdvMNG4Px6ePoN5XkP5/Qgm5mBe28M9pl1dXSN6zKOJ0/mIiIiSjGeNQ6BvlK1WK+RyeciJkFqthlwu91Yd6y/YdTiR6F+n03mr0nn0/7AXTkJVVFTkt5msyWTyfkCL5rWj8ZyJdS2r1Yr6+nqfNs/6smAShGDjk8vlUKvVaG5u9jtvpL+TwTzH4d6/wUTq/nR2dvq1mc3moJ/XUH4/gok5mNf2cI9ptB7zcDCJIiIiSkINDQ0wGAw+HzA8JYtra2uH/eY20LfQ27dvh9Fo9PvQUllZGZFRkmD7H/gh0bNexWaz+cQ92GL8QO2exfIDyyUPXEMS7LU1Go3PB8uB050CxRCN52wwoVwr2KIG/Q1WBr3/tMyhHqNg42toaIDZbPZ7noxG47BTTAd7vIJ5jsO9f57rB/odGOn98Qg0chbs71D/OIL9/Qgm5mBe28M9psE85rEkcbvdblGuHAd6enqQmZkJu92O8ePHix0OERGN0JEjR7xrTceMGSN2OHFj4N4tnn1ePB86PPsAGY1Gb3EFvV6P+vp67wcjtVqNJUuWeBdw9+/Ts/h+YNWtQKxWKyorK9HY2Oi91sB9gYLp39OPSqXyLlQvLCxEdXU12tvbUVBQAJVKFfB+CYLg124wGGA2m1FQUIDCwkJvn52dnd4Po571UcFc2zOK5anwp1KpkJWV5b0PgR5zg8EQ1ecskr8fRUVFw45mmM1mn32lPI/HwH2DBnuMgo2vfz86nQ5yudx7rmeKV6iPVzDPsadYwkjv33C/A0Pdn+FkZWWhsLAQWVlZUCgUEAQB7e3t0Ol0Pvt/hfpaHOrxDzbmoV7bw/3OBPs7NZhg3yNCyQ2YRImQRDkcDhaXICKKICZRRETHkiitVitq1bp4FI0kioUlYszhcCAvLw+tra2QyWRwOp2oq6tDU1MTEykiIiIiogTANVExVlNTg9bWVrhcLvT19cHlcqG1tRU1NTVih0ZERERECS5QYQmKPCZRMdbR0QGZTObTJpPJ0NHRIVJERERERJTIrFYrioqKIAgCGhsbodVqxQ4p6XE6X4wplUo4nU6fNqfTCaVSKVJERERERJTI1Gq1X2VJii6ORMVYaWkpsrOzIZVKkZaWBqlUiuzsbJSWloodGhERERERBYEjUTGWkZGBpqYmVucjIiIiIkpQTKJEkJGRgdWrV4sdBhERERERjUDcJFGNjY1obm5GeXn5sJuJeXZMnjhxIoBjm3/p9fqgd2EmIqLklMJbHxIR0SCi8d4QN0mUIAiorq5GdXV1wOMajQYmkwkAkJ+fj9raWu8OxYIgICcnBxaLhYkUEVEKkkqPLfEdWLiHiIjI897gea+IhLhJotrb21FWVuYdXepvy5YtMBgMAACj0QgA3gQKAFQqFdRqNSorK6HX62MTMBERxY20tDTIZDIcPnyYa0yJiMjHwYMHkZaWhrS0tIj1GTdJlFwuD5gAmc1mqFQqqFQqAEBDQwNyc3P9zps3bx4MBgOTKCKiFCSRSDB27FjY7XYoFAq//fiIiCg1HT58GD09PZDL5ZBIJBHrN26SqECbgtlsNphMJp/EyGw2B0yUVCoVBEGAzWbjlD4iohQ0efJk7N69G1999RUUCgXS09Mj+oZJRESJwe12w+l04uDBg+jp6UF6ejomTZoU0WvETRLlGWnqT6fTeafxAceSqsF4EidBEHym+hERUWoYPXo0pk2bhgMHDuC7774TOxwiIhJZWloa5HI5Jk2aFPEZCnGTRA1kNBpRUFDg09bV1QUAQ440ec4JpLe3F729vd6fe3p6wguSiIjiytixY3HKKafg6NGjOHr0qNjhEBGRSKRSKdLS0qI2IyFukyi9Xo/29vagzx9qlMqjsrISa9euDSMq8TgcDm7QS0QUpFGjRmHUqLh9iyMiogQXl+8wjY2NAafkKRQKAIETJs8IlOecQMrLy3HXXXd5f+7p6cH06dPDjDb6HA4H8vLy0NraCplMBqfTibq6OjQ1NTGRIiIiIiKKscgVS48gg8EQcI1UMAUjAt3OIz09HePHj/f5lwhqamrQ2toKl8uFvr4+uFwutLa2oqamRuzQiIiIiIhSTlyORJnNZhQVFQU8ptFoAk7zs9lsUKlUSVGZb+DUvS+//BIymQwul8t7jkwmQ0dHh4hREhERERGlprhLogRBGPJ4UVFRwBLnJpMJhYWF0QorZgJN3Zs0aZLfAmmn0wmlUilSlEREREREqSvupvN5kqjB1jaVlJQAODZa1f82giAkxUa7gabuHThwACeccIK3yohUKkV2djZKS0vFDpeIiIiIKOXE3UiUQqGAXC4fcm2TxWKBTqeD1WqFXC6HxWKByWSKYZTR09HREXDq3sKFCzF79mxW5yMiIiIiElncJVFqtRrd3d1DniOXy3024U0mSqUSTqfTp83pdGL27NlYvXq1SFEREREREZFH3E3nS3WlpaXIzs7m1D0iIiIiojgVdyNRqS4jIwNNTU3cWJeIiIiIKE5J3G63W+wgxNLT04PMzEzY7faE2TOKiIiIiIgiL5TcgNP5iIiIiIiIQsAkioiIiIiIKARMooiIiIiIiELAJIqIiIiIiCgETKKIiIiIiIhCwCSKiIiIiIgoBEyiiIiIiIiIQsAkioiIiIiIKARMooiIiIiIiELAJIqIiIiIiCgETKKIiIiIiIhCwCSKiIiIiIgoBEyiiIiIiIiIQsAkioiIiIiIKARMooiIiIiIiELAJIqIiIiIiCgEo8QOIJE5HA7U1NSgo6MDSqUSpaWlyMjIEDssIiIiIiKKIiZRI+RwOJCXl4fW1lbIZDI4nU7U1dWhqamJiRQRERERURLjdL4RqqmpQWtrK1wuF/r6+uByudDa2oqamhqxQyMiIiIioihiEjVCHR0dkMlkPm0ymQwdHR0iRURERERERLHAJGqElEolnE6nT5vT6YRSqRQpIiIiIiIiigUmUSNUWlqK7OxsSKVSpKWlQSqVIjs7G6WlpWKHRkREREREURTVwhJPPPEEbr755mheQjQZGRloampidT4iIiIiohQjcbvd7mBO7OnpCanjrq4uFBUVobm5eUSBxUJPTw8yMzPR3NyM3NxcscMhIiIiIiKReHIDu92O8ePHD3lu0CNRcrkcEokk7ODi0bXXXotdu3ZhzJgxMbke95ciIiIiIkpcQSdRKpUKBoMBCoXC29bV1YWGhgYUFRX5tHd2dsJoNGLFihWRjTZKvvjiC/zxj39ERUVF1K/F/aWIiIiIiBJb0ElUYWEh8vPzfdrWr1+PTZs2BTxfo9Fg/fr1mD9/fngRxsB//Md/4I477ojJtfrvL+VyuQDAu7/U6tWrYxIDERERERGNXNBJVFVVlV9bZmbmkLcJcrmV6J599tlh70ukePaX8iRQAPeXIiIiIiJKJGGVOLfb7UMenzBhQjjdx0ws13pxfykiIiIiosQWVhJ14MABfPjhhwGP7d69Gy0tLeF0L4q+vj58/PHHUeuf+0sRERERESW2oEucB2K326FUKrFkyRLk5OR4i0uYTCbU19ejo6Nj2PKAYhpYxvDzzz/H0qVLIQgCPv74Y0ydOjUq12V1PiIiIiKi+BJKifOwkigAEAQBK1asgNls9rbl5OSgvr4+7qeoDXygrr32Wvztb38DAPz617/GSy+9JHKEREREREQUCzFNojzsdjsEQYBKpYpZkYZwDXygOjs7ceaZZ2L8+PF45plnMG/ePLFDJCIiIiKiGIjKZrvDsVgssFqt2L17N/Lz8+N6Gt9gJk6ciDfeeANZWVkYO3as2OEQEREREVEcCjuJ2rFjBwoLC2Gz2bxtEyZMwBNPPIGrrrpqxP3qdDpMnDgRnZ2dAIDy8nLI5XLvcZvNhsrKSkycOBEA0N7eDr1e73POSJx55plh3Z6IiIiIiJJbWElUR0cHysrKUFtbC41GAwDo6uqCxWJBRUUFlEolzj777JD6FAQBWq0Wer0earUawLGEavny5WhoaPCel5+fj9raWu85giAgJycHFosl7ERqoC+//BKzZ8+OaJ9ERERERJSYwipxbjQa0dLSgsWLFyMzMxOZmZlQKpUoLCyE2WyGwWAIuc+ioiJotVpvcgQAVqvVW/nPc10APueoVCqo1WpUVlaGcY982e123HDDDTjjjDPQ3NwcsX6JiIiIiChxhZVEqVSqQY/J5fIhjwfS2NgIQRBQWFjo024ymXwSsoaGBuTm5vrdft68eWhsbAzpmkMxGo14+umncfToUSxduhRHjhyJWN9ERERERJSYwkqiJBJJWMcHMhgMAZOjgcxmM7KysvzaVSoVBEHwWZ8Vjt/97nfIycnBuHHjcO+99yI9PT0i/RIRERERUeIKa01UW1sbDh48iHHjxvkd2717N9ra2kLqr6WlBcXFxTCbzbBarQCOFYzoP71vqATJsxZKEASfqX4evb296O3t9f7c09MzZDxpaWn4xz/+gbS0NMyYMSOk+0JERERERMkprCSqvLwcc+fOxcqVK5Gfnw/gWGEJq9UKg8EAk8kUUn82m807klRWVuZtUyqV2L59O9RqNbq6ugBgyOIRnnMGqqysxNq1a0OKadasWSGdT0REREREyS2s6XyZmZmor6/Hxo0boVarkZOTA41GA4PBgPr6esycOTPovgRB8P63/5oouVyO4uJiFBUVDdvHcNP4ysvLYbfbvf/27NkTdHz9dXR0IEJ7FBMRERERUYIJK4kCjlXIa2trQ1tbG+rr62GxWPC///u/mDt3bkj9eKrvBZqGl5WV5R2h8pwXKGHyjED1r+TXX3p6OsaPH+/zLxQulwuPPPII5syZg82bN4d0WyIiIiIiSg5hb7broVKpQq7G199Q0/OGW+sUKJZoeOedd3DnnXcCAG6//Xb86le/CljggoiIiIiIklfEkqgdO3bAarVCpVJBo9GEPMoDHBuFCjTC5GnzJEcajQbt7e0Bz1OpVBHfbNfjl7/8JW6++WY88cQTWLFiBaZNmxaV6yQKh8OBmpoadHR0QKlUorS0FBkZGWKHRUREREQUVWEnUTt27EBhYaFP8jNhwgQ88cQTuOqqq0LqS6vVQqfT+bU3NzdDrVZ7k6OioiLo9Xq/80wmk98eU5H28MMP45prrsHFF18c1evEO4fDgby8PLS2tkImk8HpdKKurg5NTU1MpIiIiIgoqYW1JqqjowNlZWWora1Fd3c3uru70d7eDoPBgIqKCuzatSuk/kpKSqBSqWA0Gr1tVqsVZrMZtbW1PucBx/aL8hAEAYIgBEyuIikjIyPlEygAqKmpQWtrK1wuF/r6+uByudDa2oqamhqxQyMiIiIiiqqwRqKMRiNaWlp82jIzM6FUKqHRaFBeXo6NGzeG1KfFYoFOp4NWq/VpG7jOyXOe1WqFXC6HxWIJuaR6pHR2dkImk0VtGmE86ujogEwmg8vl8rbJZDJ0dHSIGBURERERUfSFlUQNVcBBLpePuMBDMKNJcrkcBoNhRP1H0vbt23HdddfhwgsvxD/+8Q9IJBKxQ4oJpVIJp9Pp0+Z0OqFUKkWKiIiIiIgoNsKazjdcwpDsCcXBgwexZMkS7N27F/X19airqxM7pJgpLS1FdnY2pFIp0tLSIJVKkZ2djdLSUrFDIyIiIiKKqrBGotra2nDw4EGMGzfO79ju3bvR1tYWTvdxb9y4cdi4cSOKi4uRn5+P/Px8sUOKmYyMDDQ1NbE6HxERERGlHInb7XaP9MZ2ux05OTlYuXKlN4Ho6uqC1WqFwWCAyWTCzJkzIxVrxPX09CAzMxN2u31EJdk9XnvtNSxYsABSadh7FxMRERERkQhCyQ3CSqKAY9XziouLIQgCJBIJ3G43srKyUF9fj7lz54bTddRFKokiIiIiIqLEFkpuEPY+UWq1Gm1tbRAEATt37oRKpYr75CnanE4n9uzZE9ejcERERERENDIRm3+mUqmwePFinwRq/fr1keo+YezevRsXXXQRLrroItjtdrHDISIiIiKiCAt7JArAoJvqbtmyBatWrYrEJRLGbbfdhnfeeQfAsQp2zzzzjMgRERERERFRJIWVRO3cuRP5+fmw2+0ItLQq2UucB1JTU4O3334bEyZMwIoVK8QOh4iIiIiIIiysJEqn06G2thZqtRoKhcLnWGdnZ0omETNmzMCrr76KM844A5mZmWKHQ0REREREERZWElVQUIDFixcHPJaZmYmioqJwuk9Y559/vtghEBERERFRlIRVWEIulw95fMmSJeF0n1Q++eQTsUMgIiIiIqIICCuJys3NxY4dOwY9rtPpwuk+KRw+fBi33HILzjzzTLz66qtih0NERERERGEKerPd8vLygO1WqxVdXV3Izc31O1ZfX4/Ozs7wIoyiWGy2+9RTT2HZsmUAgEmTJuHzzz/HxIkTo3ItIiIiIiIamVByg6CTKIVCAYVCMewUvv527twJp9MZ9PmxFoskyu124/LLL8f27dvx5z//GTfddFNCVy10OByoqalBR0cHlEolSktLkZGRIXZYRERERERhCSU3CLqwRG5uLrZt2xZSIKlYnW8giUSCzZs344cffsAZZ5whdjhhcTgcyMvLQ2trK2QyGZxOJ+rq6tDU1MREioiIiIhSRtBrovR6fcida7XakG+TjCZNmpTwCRRwbA+s1tZWuFwu9PX1weVy4bPPPkNhYSEcDofY4RERERERxUTQSdTcuXND7nwkt0kVn332Gbq7u8UOIyQdHR2QyWQ+bW63G2+88Qby8vKYSBERERFRSgirOt9wVq5cGc3uRedwOFBVVQWtVouqqqqgkgi3240nnngCubm5uPnmmxHkkrS4oFQqB13j1traipqamhhHREREREQUe0EXlnjuuecAAIsWLfK2DVaxDwBsNltSV+cLtD4oOzt72PVBBw4cwGmnnYauri4AQF1dHX7729+GdT9ixXOfP/vsM7/kLy0tDcuWLYPBYBApOiIiIiKikYtKYYmbb74ZEonEJ4kyGAxQKBRQqVR+53d1dcFmswUfdYLpvz7I5XIB+L/RmNWrVw96u0mTJuHJJ5/ElVdeiRUrVvg8nvEuIyMDTU1NKCwsxBtvvOFzzOl0QqlUihQZEREREVHsBJ1EWSwWv6RouIp9yVydz7M+yJNAAYBMJkNHR8ewt73iiiuwa9cu/PznP49miFGRkZGBxsbGgKNwpaWlYodHRERERBR1QSdRgUYZhpu6lczV+QKtDwplNCYREygPz4gU94siIiIiolQU9Jqokejp6YnaJraRIMaaqMHYbDZ88sknuPDCC0O+LRERERERhSeU3CCq1fl0Ol00uxeVZzSmoqICy5YtQ0VFxYgTqKamJsydOxcLFy6EIAhRiJaIiIiIiCIl6JGooSrxBZLs1fki6frrr8df//pXAMCCBQvw+uuvixYLEREREVEqCiU3CDqJUigUg1biC6Srqws7d+4cdF+heBAvSVRPTw9ycnJwwgkn4B//+AdOOeUU0WIhIiIiIkpFUSlxPlwlvkCSuTpfJI0fPx5msxlTp05FWlqa2OEQEREREdEQgk6i9Hp9yJ0nc3W+SJsxY4bYIRARERERURCCLiwxd+7cQY/t3r0bzz33HHbv3g0A2LlzJ3p6eoa8DQ3N5XJh06ZNOHLkiNihEBERERFRP2FX5ysuLoZKpcLy5cthNpsBACqVCg8++CB6enrCDjAV7du3D5deeilWrlyJu+66S+xwiIiIiIion7CSqNWrV0OlUqG7uxudnZ3w1KjIzMxEVVUVjEZjRIJMNT/88APefvttAMc2NP7ss89EjoiIiIiIiDzCHomqqqpCZmYmAEAikfgc87RTaM4880zU1NRgypQpMJlMOP3008UOiYiIiIiI/r+gC0sEMmvWLJ+fB1ZLt9vt4XSf0m688UYsXrwYcrlc7FCIiIiIiKifsEaiWlpacPDgQe/P/Ueidu/ejba2tnC6T2kSiYQJFBERERFRHAprJKqsrAwzZszAihUrkJubi/b2duzYsQMmkwlGoxEWiyVScRKAV199FT/++COKiorEDoWIiIiIKGVJ3APn4IXIarWiuLgYgiB42yZMmACz2QyJRIKzzz473BijJpRdicXkcrmwZs0aVFVV4fjjj0dLSwvmzJkjdlhEREREREkjlNwgrOl8K1euhFqtRltbG9rb29HQ0ACLxYLOzk7MnTsXOp0upP5ycnJgNBq9CZnZbEZBQYFPggYANpsNOp0O1dXVqK6uhlarhc1mC+euxDWpVIrvv/8eAPDjjz/iiSeeEDkiIiIiIqLUFdZI1MSJE9HZ2Rnw2IoVK1BbWwun0xl0fxMmTPBJhuRyORoaGqDRaHzOy8nJQW1tLdRqNQBAEAQUFBTAYrGEtI4oUUaiAODQoUO44IILsHTpUtx5551+lRCJiIiIiGjkQskNwloT1d3djSVLlmDLli3etl27dqGoqAjt7e0hf9DXaDSYN28eOjs7MW/ePGg0Gr+kyLP3lCeBAo5t7qtWq1FZWQm9Xj/yOxTHxo4di+bmZowaFdZTRkREREREYQprOl9JSQlKSkq808vWrVsHtVoNjUaD7u5u1NfXh9SfSqVCWVkZ9Ho9CgsLA44qNTQ0IDc316993rx5aGxsHNH9SBRMoIiIiIiIxBdWErVp0ybk5+dDqVRi1qxZqKqqgslkwsaNG5GZmYnFixdHKk4vs9mMrKwsv3aVSgVBEJJ6bdRA//u//4vFixdzPy4iIiIiohiKyNBGfn4+9Ho9JBIJ8vPzve0rV67Exo0bg+7HZrN5p+sBgMVigU6ng0ql8h4fjGfUShAEn6l+/fX29qK3t9f7c09PT9CxxZvt27dj0aJF6OnpgdvtxtatW7lOioiIiIgoBoJOotavXz/sOVu2bEFXV5f3Z7PZHFIwXV1dKC4u9kmIcnJyYLFYoFKpvH0PVTyi//UHqqysxNq1a0OKKV4plUpIpccGEltbW3HgwAGccMIJIkdFRERERJT8gq7Op1AofP4bjI6OjpCq8wVSUFAAADCZTBAEAVlZWTAYDCgpKfE5r7GxEUVFRTCZTH7V/DwCjURNnz49IarzBfLKK6+grq4ORqMR48aNEzsc0TgcDtTU1KCjowNKpRKlpaXIyMgQOywiIiIiSiBRqc6nUqnQ0tISUiDFxcUhnT/YdT1T/DwJXKBpfZ4RqKGSvPT0dKSnp4cdU7xYuHAhFi5cKHYYonI4HMjLy0NraytkMhmcTifq6urQ1NTERIqIiIiIoiLowhIjKR2u1WpDOre6unrQ4zabLag9oDzrp1KV2+0Oe/QvkdTU1KC1tRUulwt9fX1wuVxobW1FTU2N2KERERERUZIKOonqXzAiGrepr69He3u7X3tXVxfkcrk3gdJoNAHPs9lsUKlUIW22m2x+/PFHXHvttVi1apXYocRMR0cHZDKZT5tMJkNHR4dIERERERFRsgurxPlwVq5cGfS5JSUlMBgMfu1ms9ln/VNRUVHAghUmkwmFhYUjCzQJOJ1O/PKXv8Tf//53PPLIIyHv0ZWolEql38ib0+mEUqkUKSIiIiIiSnZBF5Z47rnnAACLFi3ytpWXlw96vs1mQ319PTo7O4MKRBAENDY2oqyszNtWXV0Ng8HgN/LkKS7hKSAhCAIKCgoCjlANJZTFY4lg06ZNWLlyJcaNG4enn34aV111ldghRV2gNVHZ2dlcE0VEREREIQklNwipOp9EIvFJihQKBRQKRcB1SF1dXdi5c2dI63MEQfCORnnWQAVai2Wz2aDT6ZCVlQW5XO63n1Swki2Jcrvd+MMf/oBrrrkGp512mtjhxAyr8xERERFRuKKSRHV0dMBms2Hu3LnetksuuQTbtm0b9DYrVqzApk2bggw79pItiSIiIiIiopGJSonzQGtMAq1h6i+U6nwUPfv27cPkyZPFDoOIiIiIKCmEVVhiuMX7WVlZ4XRPYXK73fjzn/+MmTNn4u233xY7HCIiIiKipBDV6nw6nS6a3dMwtmzZgjvuuAOHDx9GcXExfvjhB7FDIiIiIiJKeEFP5xuqEl8gnup8GzduDDkoiozCwkLU1tZix44duO666zBx4kSxQyIiIiIiSnghVecbrBJfICOpzhdrqVBYYt++fWhqasLll18udihERERERHErKoUlcnNzh6zEF8iKFStCOp8ib/LkyUygiIiIiIgiKOg1UYH2axoOq/PFp7179+LDDz8UOwwiIiIiooQUdBLVf3+oaN6Gouu9995DTk4OFi5cyEITREREREQjENXqfBRf3G437rvvPnz//ff49ttvceedd4odEhERERFRwgl6TRQlPolEgr/97W/Izc3F7Nmz8eijj4odEhERERFRwmESlWJOPPFEvPXWWzjllFMwahSffiIiIiKiUPFTdAoKtkw9ERERERH545ooQl9fH37/+9+z0AQRERERURA4EpXi9u3bh8LCQrz99tt4++23YTabkZaWJnZYRERERERxKyIjUT09PT4/79q1KxLdUgy4XC4IggAAaGpqQnNzs8gRERERERHFt7CSqJ07d2LWrFlQKpU+7UqlEuvXr/dLrij+nHjiidi6dStUKhXeeustnH/++WKHREREREQU18Kazrd9+3Y0NDR4RzI8MjMzsWrVKjzxxBO4+eabwwqQou/cc8/F559/zml8RERERERBCCuJcrvdmDt3LubOnRupeEgkgRIot9sNiUQS0zgcDgdqamrQ0dEBpVKJ0tJSZGRkxDQGIiIiIqKhhJVEDfcBu729PZzuSUR1dXV46qmn8MorryA9PT0m13Q4HMjLy0NraytkMhmcTifq6urQ1NTERIqIiIiI4kZYa6La2trw1VdfBTy2Y8cOdHd3h9M9iaS6uhpLly7F9u3bsXLlSrjd7phct6amBq2trXC5XOjr64PL5UJraytqampicn0iIiIiomCENRJVVlaGuXPn4uqrr4ZarYZCoYAgCGhubobZbEZHR0ek4qQYmj9/PsaMGYMjR45g1KhRcLlckMlkUb9uR0cHZDIZXC6Xt00mk/H3iIiIiIjiSlhJlEqlQktLC4qLi7Fp0yZve05ODlpaWjB+/PiwA6TYy83NxVNPPYX9+/fj1ltvjdm6KKVSCafT6dPmdDr9qj8SEREREYlJ4o7QXC273Q5BEKBSqZCZmRmJLqOup6cHmZmZsNvtTPjiQKA1UdnZ2VwTRURERERRF0puELEkKhExiQpNZ2cnpFIpJkyYELVrsDofEREREYkhbpKolStXYuPGjdHqPmxMooL36aef4je/+Q2ysrLw2muvYdSosGaCEhERERHFlagkUc899xwAYNGiRd628vLyQc+32Wyor69HZ2dnMN2LgklUcI4ePYo5c+Z4S9avWbMGf/rTn0SOioiIiIgocqKSRCkUCkgkEp+kSKFQQKFQQKVS+Z3f1dWFnTt3+hUKiCdMooL3zjvvYP78+fjZz36GF198EdOnTxc7JCIiIiKiiAklNwh6TpbFYoHNZvNpy83NxbZt2wa9zYoVK4LtnuLchRdeiNdeew15eXk4/vjjxQ6HiIiIiEg0Ya2J8iz+H8zOnTsxd+7ckXYfdRyJIiIiIiIiILTcQBrOhYbbvyeeEygKn8vlwiOPPIKDBw+KHQoRERERUcyEVWJt165dOPvss33aamtrIZFIoFAooNFoOMKTpA4ePIilS5fixRdfxL/+9S8899xzkErDysmJiIiIiBJCWJ96DQaDX9vy5ctx8803Y9GiRTAajeF0T3Hs+++/x7/+9S8AwEsvvYT3339f3ICIiIiIiGIkqkMHnpLYlHxOPfVU1NfXY+LEiXjttddwwQUXiB0SEREREVFMhDSdb926dZBIJN6fW1pasH79+oDnNjc3+1Xzo+RyySWXoKOjA+PGjRM7FCIiIiKimAkpibrnnnvQ0dGBxsZG6HQ6SCQSdHd3BzxXo9FwOl8KCJRAuVwuro8iIiIioqQ14hLnZrMZjY2N2LRpU6RjihmWOI+8V155Bffffz+2bdsGhUIhdjhEREREREGJyma7A2k0Gtjt9pHePGiNjY0QBAFlZWU+7TabDZWVlZg4cSKAY+uv9Ho95HJ51GOiwP72t7/huuuug8vlwuLFi/HGG29g9OjRYodFRERERBRRYZU4X7x4MQBg9+7dsFqtUKvVmDlzJnbu3ImsrKywR3dsNhuWL1+O8vJyv2P5+fmora2FWq0GAAiCgJycHFgsFiZSIrngggswadIk7Nu3DyeccAKcTqfYIRERERERRVzYC1eKi4uhUqmwfPlymM1mAIBKpcKDDz6Inp6esPoebE2Vp92TQHmuqVarUVlZGdY1aeRmzpyJf/7zn7jvvvvwj3/8A8cdd5zYIRERERERRVxYSdTq1auhUqnQ3d2Nzs5OeJZXZWZmoqqqKqzCEmazGRqNJuCxhoYG5Obm+rXPmzcPjY2NI74mhe/cc8/FAw88wMISRERERJS0wv6kW1VVhczMTADwKX8OwNs+Ep7pgYGYzWZkZWX5tatUKgiCwNLqcaanpweffPKJ2GEQEREREUVEWEnUrFmzfH4eWOhvpIUnqqur/QpJeAyVIHnWQgmCMKLrUuR9/fXXuPDCC5Gfn4+vvvpK7HCIiIiIiMIWVhLV0tKCgwcPen/uPxK1e/dutLW1hdznUCNQANDV1QUAQxaP8JwzUG9vL3p6enz+UXTdc889+Pjjj7Fv3z5cd911fok2EREREVGiCas6X1lZGWbMmIEVK1YgNzcX7e3t2LFjB0wmE4xGIywWS8h9btmyBXq9fkTxDDeNr7KyEmvXrh1R3zQyf/nLX7Bz50643W7U1tb6TfkkIiIiIko0YSVRKpUKZrMZxcXFqKqqAgDo9XpMmDABZrMZM2fODKk/o9EYsJx5f54NXAMlTJ4RqME2eS0vL8ddd93l/bmnpwfTp08PKUYKzcSJE/H6668jMzPTu6cXEREREVEiCyuJAo6VGW9ra0NHRwesVitUKhXmzp0bcj+CIEChUAy7x1Mwe0CpVKqA7enp6UhPTw85NgrPYM8HEREREVEiCjuJ8lAqlVAqlT5t69evx6pVq4K6vSAIMJlMMJlMPu02mw1btmxBe3s7CgoKUFhYCI1Gg/b2dr8+bDYbVCoVN9uNEofDgZqaGnR0dECpVKK0tBQZGRkh9+N2u1FZWYk5c+Zg0aJFUYiUiIiIiCh6JO4IrPTftWtXwPbly5ejubk5rL4lEgn0er1PtT6j0Qi9Xu+XSBUUFECtVge9pqqnpweZmZmw2+0YP358WHEmO4fDgby8PLS2tkImk8HpdCI7OxtNTU0hJVJOpxO33norDAYDxowZA7PZjAsuuCCKkVMkRSqRJiIiIoo3oeQGYY1E7dy5E/n5+bDb7QGrrkWqiEBnZ6fPzyUlJdDr9T4b8gqC4B3NosirqalBa2srXC4XXC4XAKC1tRU1NTVYvXp10P1IpVIcPnwYAHDkyBFYLBYmUQkiUCJdV1cXciJNRERElOjCSqJ0Oh1qa2uhVqv9ijl0dnZixYoVI+5bq9V693syGo2w2WwoKiryJk0WiwU6nQ5WqxVyuRwWi4UJVBR1dHRAJpN5EygAkMlk6OjoCKkfiUSC2tpadHZ24pprrsE111wT6VApSoZKpEtLSzlCRURERCkjrCSqoKAAixcvDngsMzMTRUVFI+7bYDAMeVwulw97DkWOUqmE0+n0aXM6nX7r4IIxevRovPTSSyx3nmAGS6S//PJLjlARERFRSglrs93hCjgsWbIknO4pjpSWliI7OxtSqRRpaWmQSqXIzs5GaWnpiPoLlEB99dVXOHr0aLihJhSHw4GqqipotVpUVVXB4XCIHdKgBkuk9+7d6x2h6uvrg8vl8o5QERERESWjsJKo3Nxc7NixY9DjOp0unO4pjmRkZKCpqQkVFRVYtmwZKioqIjrS8N577yEnJwe33nprwPV1ycizxmjNmjXYvHkz1qxZg7y8vLhNpAZLpKdOnQqZTOZz7kimehIREREliqCn8w22Ca7VaoVOp0Nubq7fsfr6emzcuHHk0VFcycjICKmIRLBsNhsuu+wy2O12GI1G5OTkoKSkJKjbJnK1uEgV64gVTyI98PGuqamJ2FRPIiIiokQQdIlzhUIR1Ga4/e3cudPvw1U8YYnz+PHss8/immuugUajwdatW4N6PiJVdl0sWq0WmzdvRl9fn7ctLS0Ny5YtS6j1fon+PBAREREBUSpxnpubi23btoUUSDjV+Si1/Od//ifGjx+PgoICjB49OqjbJNpIzkCRLNYhpsFGqJhAERERUbIKOokKdgPb/rRabci3odS1cOHCkM6PVNl1sZSWlqKurs5vBGekxTrEFK2pnkRERETxKOgkau7cuSF3PpLbEHkcOXIEq1atgk6nw/Tp0/2OhzuSI/Z6Ko7gEBERESWmoNdEBbJr1y6cffbZPm21tbWQSCRQKBTQaDRxvdaIa6LiV1dXF6688kq8/fbb+NnPfoa3337bbz1eOGtxuI6HiIiIiPoLJTcIq8R5oMXvy5cvx80334xFixbBaDSG0z2lsKNHj2Lv3r0Ajk3ba21t9TsnnLLr/ddTcW8jIiIiIgpF0NP5RqK9vT2a3VMSmzx5Ml5//XVcfvnlePrppzFv3ryA5410LU6ir6ciIiIiIvGElEStW7cOEonE+3NLSwvWr18f8Nzm5mbYbLawgqPUNmvWLHz88cd+G7lGQrJUxiMiIiKi2At5TVRHRwcaGxuh0+kgkUgG/dCp0Wig1+uRmZkZkUCjgWuiEtPnn3+OOXPmhNUH10QRERERUX+h5AYjLixhNpvR2NiITZs2jSjIeMAkKvE8+eSTWL58OR566CHccccdYfUlRnU+sSsCEhEREVFgMUmiAGDr1q1YvHjxoMfXr1+PVatWjbT7qGMSlVisVitycnK8P7/99tu48MILRYwoNBz9IiIiIopfMavO50mgdu3aFfDfli1bwumeyIdarcZ9990HALjjjjtw/vnnixxRaFgRkIiIiCg5hFWdb+fOncjPz4fdbkegAa3+RSiIImHt2rU477zzcOmllybc7xcrAhIRERElh7CSKJ1Oh9raWqjVaigUCp9jnZ2dWLFiRVjBEQ0kkUjwH//xH2KHMSKsCEhERESUHMKazldQUIDFixdDqVQiMzPT559KpUJRUVGk4iQa1N69e7Fw4ULs2bNH7FCGdMMNN2DSpEkAAKlUColEguzsbNxwww2oqqqCVqtFVVUVHA6HyJESERER0VDCGomSy+VDHl+yZEk43RMNq62tDRqNBl999RUWLFiAt99+GxMnThQ7LD8OhwMajQYHDhyAVCqF2+3GCSecgBdffBEajcan2ERdXR2LTRARERHFkNVqxVdffRX0+WGNROXm5mLHjh2DHtfpdOF0TzSscePGYdSoY98FHDlyBHa7XeSIAutfVMLlcsHtduPAgQO49dZbWWyCiIiISES7d+/GggULUFxcHPRtwhqJ2r59O5qbm6HT6ZCbm+t3vL6+Hhs3bgznEkRDmjJlCrZt24aVK1fiqaeewkknnSR2SAENVlTiq6++YrEJIiIiIhFNmzYNl112Gf76178GfZuwkqgHH3wQCoUCcrkczc3NfsdtNls43RMFRaVS4Y033hA1huE20R2sqMSMGTPw5Zdf+rWz2AQRERFRbIwaNQqbN2/GrFmz8F//9V9B3SaszXYvueQSbNu2bdDjK1aswKZNm0bafdRxs93k5Xa78cILL+DKK6+Mein0YDbRHewcs9nstyaKG/ASERERxV7MNtvV6/VDHtdqteF0TzQiLpcLd9xxBxYtWoS777474B5mkRTMJroZGRloampCRUUFli1bhoqKCjQ1NeHEE08M2M4EioiIiCg6Dh06hNtuuw1dXV0j7iOs6XzDfcM/d+7ccLonGpEPPvjAm8A8/PDDuPrqq3HOOedE7XrBbqKbkZGB1atX+91+sHYiIiIiiqyffvoJixcvxuuvv44333wT27Ztw9SpU0PuJ6yRqOXLl4dzc6KoyMvLQ21tLWQyGZ566qmoJlAAN9ElIiIiShTffPMNdu3aBQDYs2cP9u3bN6J+wloTJZVKUVRUBL1ej5kzZ460G9FwTVRya29vR1ZWVtSvE8yaqEhfb6giFiM9l4iIiCgVtLW14YorrsDGjRvxy1/+0tseSm4QkcIS27dvh9VqRVZWFhYtWjTS7mKOSVTqcTgcoic24V4n2IQt1skdERERUaJwOp2QyWQ+bTErLOGpzJefn4977rkHc+fOxbp16/DEE0+gp6cnnK6JIu7999+HSqXCSy+9FPG+PeuaDAYDVq9eHbUkJZgiFiM5l4iIiChZvfPOO35tAxOoUIWVRA2kVCpRWFiIbdu2YcKECVi5cqV3ziGRmD799FMUFBRg//79KCoqwvvvvy92SCPiKWLR32Cb84ZyLhEREVEyqqiowC9+8Qs88MADEa3YHFYS9dxzz/n8/4IFCzBr1iwIgoBNmzZh48aN6OzsxPr165lMkajmzJmDyy+/HABwwQUX4MwzzxQ5opEJpYgFC14QERFRKvvggw/w+9//HgBw//33o6mpKWJ9h7Um6tRTT0VhYSGMRiO6u7tRWFiI8vLygKXNt2/fDrvdHldrprgmKrX09fXhoYcewh133IExY8aIHc6IcE0UERERUfAefvhh3HXXXVi3bh1WrVo15LkxKywhlUohl8tRUlKC8vJyZGZmDnn+E088gZtvvnmkl4s4JlGUiFidj4iIiCh4FosFOTk5w54XsyQqNzcXLS0tw563detWGI1GqNVqVFZWjvRyEcckig4fPozS0lKsWbMGKpVK7HCIiIiIKAxHjhwZ8YyjmFXn02q1QZ2nVqsxd+5clJeXh3M5oog6dOgQLr/8cjz55JO4+OKLsXv3brFDIiIiIqIRevHFFzF79mx8+umnUb9WWCNRgfT09EAQBJx99tmR7DYqOBKV2vbv34+LLroIn332GTIyMvDGG2/g/PPPFzushMWpg0RERCSWf//737jkkkvw008/YeLEifjggw9CnmUUSm4wKpxgi4uLYbfbUVBQgFWrVqG2thYrVqyARqMBAOj1+oRIpig1nXDCCdi+fTuuvPJKPPzwwzjvvPPEDilhE5FARSzq6upYxIKIiIhi4swzz8RZZ52FlpYWXHrppZgxY0ZUrxfWSFRtbS2Ki4u9GZtCoUBVVRXuueceAMD69euHrYIxkCAIMBgMmDhxIjo7OyEIAsrLy6FWq33Os9lsqKysxMSJEwEA7e3t0Ov1kMvlQV+LI1EEAG63GxKJROwwErqaXlVVFdasWQOXy+Vtk0qlqKiowOrVq0WMjIiIiFKF3W7HI488gjVr1mDUqNDHimI2EiWRSLwV+cxmMwB4EygAw1brG8iTQOn1em+b0WhETk4OLBaLTyKVn5+P2tpab5sgCN7zQkmkiAIlUP/85z9x7rnnYsqUKTGLo6amBq2trXC5XN5kpLW1FTU1NXGfiHg29u2fRHFjXyIiIoqlzMxM3H///TG5VliFJRQKhff/TSaT32hRqN/uNzY2wmg0wmazeduKi4sBAAaDwdtmNBoBwOd6KpUq7qr/UWJ65plncNVVV0Gj0eDAgQMxu64nEekvURIRbuxLREREsbRz505otVocPXpUlOuHlUS1t7d7/7++vt67FsqjfzIUDLVaPegCsK6uLu//NzQ0IDc31++cefPmobGxMaRrEvV3+PBh3HfffXC5XPjkk09QW1sbs2snciJSWlqK7OxsSKVSpKWlQSqVIjs7G6WlpWKHRkRERElm586dyM/Ph9FoxG9/+1tREqmwkii1Wo1LLrkEp556KhQKBcrLy2G321FbW4tTTz015Gl1Go3GbzqeZ5pg//LoZrMZWVlZfrdXqVQQBCHk5I3I47jjjoPZbMbUqVNx6623xnQaXSInIhkZGWhqakJFRQWWLVuGioqKhFjLRURERInnhx9+wI8//ggA2Lt3L44cORLzGMJaE5Wfn+/dcDc/Px/AsSlJngIT4a5NMpvNqKysRENDg3fq3lAJkud6giD4TS0EgN7eXvT29np/7unpCSs+Sk6zZs2CxWLBlClTYlpwwpOIJGJ1PuBY/PG+douIiIgS36WXXooXXngBGzZswPPPPy/KZ6Wwkijg2AIuTwIFHJuSFO70I6vVCrPZjObmZmg0Gp9pgp5pfUMlaP2n/vVXWVmJtWvXhhUbpYYTTzzRr23fvn047rjjMG7cuKhdl4kIERER0fD+4z/+A5deeqloFZbDms430MqVKyMyuqNWq1FWVoaGhgZkZWVBqVRCEIRhbzfcND7PdEPPvz179oQdK6WG7777Dr/61a9w2WWXweFwiB0OERERUcr48MMP8dprr/m1i7lFTUSTKE/VvEgqKSkBABQVFQH4v4qAgRImzwhU/6qB/aWnp2P8+PE+/4iG43a7sWjRInz++ed45513cMstt4gdEhEREVFK+PDDDzF//nxceeWVeOWVV8QOxyuiSVQY+/YOKTc3F1arFTabLah1VoNV+CMaCYlEgscffxxyuRwzZszAH//4R7FDIiIiIkoJmzZtQldXF3766Sds2LAhavlGqMJeE9VfuENqWVlZUKvVaGho8GkfWDBCo9H4lFf3sNlsUKlU3GyXIk6tVmP79u2YMGECZsyYIXY4RERERCnhscceQ3d3N/bs2YMXXnhB1Cl8/UU0iQo3MxQEwW+vKeBYoQng/zbXLSoqgl6v9zvPZDKhsLAwrBiIBhOo4qPb7cahQ4dw/PHHixDRMQ6HI2Er+hERERENZdSoUairq8ORI0fi6vNNRKfzBfqQGQq9Xg+tVuvTZjabIQgCDAaDt82zTsqzhxRwLAETBCFgckUUDW63G6tXr8aFF16Izs5OUWJwOBzIy8vDmjVrsHnzZqxZswZ5eXksfkFEREQJ6dNPP/WrfTBq1Ki4SqCAMEeiFixYAIPBgJkzZwIAWlpa/M7ZsWMHTCYTlixZgrPPPnvI/srKytDY2AiDwQC5XA6bzQZBEGAymfxGqCwWC3Q6HaxWK+RyOSwWC0wmUzh3hygk1dXVqK6uBnBsz7QPPvgAo0ePjmkMNTU1aG1thcvlgsvlAgC0traipqaGpdKJiIgooezatQsajQZKpRImkymul+iMOImy2+0oKSnxJlCBbN26FSUlJVi+fDmWL1+OhoaGIc8HgMLCwqCm5Mnlcp/RKaJYu+KKK/Doo4/iu+++w8qVK2OeQAHHNreWyWTeBAoAZDIZOjo6Yh4LERER0Ui5XC789re/RWdnJzo7O1FeXo6NGzeKHdagRjydLzMzE93d3di1axeWLFmCJUuW4M033/Q5p6qqCkajEVVVVTCZTEx6KKnMmTMH//73v/Hf//3fftNQY0WpVMLpdPq0OZ1OTJ06FVVVVdBqtaiqquL0PiIiIoprUqkUDQ0NmDRpEs4///y4X6IjcYdRDaK2thY6nQ65ubkAjk2xa2howPz58wEcezAEQfCOPq1btw733HNP+FFHSE9PDzIzM2G327lnFEWU2+0esnpMpIpBeNZEtba2QiaTwel04rTTToPb7caXX37pbcvOzkZTU1PczScmIiIi6q+1tRXTp08X5TNLKLlBWGuirFard4Nbj5UrV2L+/Pmw2+2QSCQ+G9/G87xGokixWq3QarXYunUrTjnlFL/jgRKfurq6ESU5GRkZaGpq8knIent78cADD3CdFBEREcW1trY2nHjiiQlZZTisJCorK8uvzbPRrSe56p/FxUtdd6Jo+eijj1BQUICuri786le/wltvvYXp06f7nBPpYhAZGRk+t9NqtVwnRURERHHt+eefx5IlS6BQKLB///6wv1iOtbBKnLe1tfm1CYIw6PkDyxUSJZuJEydi4sSJAIBp06ZhwoQJfud4ikH0F8kkZ7B1UkqlMiL9ExEREYXjiy++QFFREfr6+vDDDz/A5XKhr68PLpfL+8VyvAsriSosLIRCocCCBQuwYMEC74fHXbt2QafTQalUeotN7N69GwcOHAg/YqI4dvLJJ+Pf//43rrvuOrz66qsBv0WJdpJTWlqK7OxsSKVSpKWlQSqVIjs7G6WlpRHpn4iIiCgcp512Gv7whz8A8J+pliizZ8IqLAEcW/9RVVUFhUKBoqIi5Obmwmw2Qy6XIz8/H5dccgkmTJgAq9UKi8USVwUcWFiCxBBoTVSkCz9EqnAFERERUbRcd911qKurQ/90RCqVoqKiQpR13KHkBmEnUcGora1FcXExMjMzo32pkDCJoljp7e3F0qVLccstt+Ciiy5ikkNEREQppaury6fgHBCbL5ZDIUoStWPHDlitVqhUKmg0moRISphEUSwcPXoUV199NbZu3Yr09HRs3boVCxcuFDssIiIioqhzu93405/+hL/85S946623cOqpp/ocj6cvlmNW4hw4ljwVFhb6FI2YMGECnnjiCVx11VXhdk+U8I4ePYojR44AODZEHW8jskRERETRsmnTJvzXf/0XACA/Px8ff/yxz2ehgVWGE0VYhSU6OjpQVlaG2tpadHd3o7u7G+3t7TAYDKioqMCuXbsiFCZR4hozZgyef/55XHfddXj++edx4YUXih0SERERUUwUFxfjzDPPBADccccdEfky2eFwoKqqClqtFlVVVXA4HGH3GaqwpvOVl5ejsrIy4DGbzYby8nJs3LhxxMFFG6fzERERERFF1759+7Bt2zZce+21YfcVzXVUoeQGYY1EeTbWDUQulw95nIiAZ599Fg888ABiUN+FiIiIKOp+/PFH9PX1+bRNnjw5IgkUANTU1KC1tTXg3lKxHKEKa03UwLruoR4nSmUvvfQSli5dCqfTCZvNhg0bNvA1Q0RERAmrq6sLv/71r6FUKvHMM89AKg1rvCagjo4OyGQyuFwub5tMJsOXX37pN0JVV1cXtUp/Yd2ztrY2HDx4MOCx3bt3o62tLZzuiZLa7t27vZvuHjp0SORoiIiIiEbO5XLh0ksvxfvvv4+///3vKC8vj8p1lEql9/OTh9PpxN69ewcdoYqGsEaiysvLMXfuXKxcuRL5+fkAjmWgVqsVBoMBJpMpIkESJaPbbrsNY8eOxb///W88/vjjHIUiIiKihCWVSnHffffhqquuwqRJk3DNNddE5TqlpaWoq6vzWxM1derUgCNUHR0dUYkj7H2irFYriouLIQgCJBIJ3G43srKyUF9fj7lz50YqzqhgYQmKB263mwkUERERJYXGxkacffbZmDVrVtSuEWhvqZqaGqxZs8YniZJKpaioqAi6hLoom+12dHR4N9uN9+TJg0kUxaPvv/8et956K/7yl79gypQpYodDREREFJDNZoNcLhc7DACRqdonShI1WCDxnJwwiaJ4Y7fb8atf/QoffvghsrKysG3bNla5JCIiorjz6quv4pprrsGWLVuwYMECscMBEHiEKpSiEqHkBmGtiRqOTqeL632iiOLN/v370dXVBQA4evQoxowZI3JERERERL6amppwxRVX4OjRo1i0aBHef/99nHXWWWKHhYyMjKCn7oUr6CQq1AobNpsN9fX1TKKIQjBr1iy89957WLp0KTZt2oSpU6eKHRIRERGRj3nz5uGKK67A1q1bsXDhQpx22mlihxRzQU/nUygUUCgUQU8t6urqws6dO/1KEMYTTucjongR7hQEIiKiWOrt7YXBYMCtt94KmUwmdjgREZXpfLm5udi2bVtIgaxYsSKk84koMLfbjVWrVmHmzJm47bbbxA4nriRD8hFoMWw0NwgkIiIKRV9fH+x2OyZNmuRtS09Px+233y5iVOIKOonS6/Uhd67VakO+DRH5q66uxkMPPQQA2LdvH/74xz+KHFF8SJbko6amxrtBoKc0q2eDwFjN7SYiIgrk4MGDKCwsxP79+/Gvf/2Ls7f+P2mwJ46kbHmilDoninc//vij9/9nzpwpXiBxpn/yEYvdyaOlo6PDbypENDcIJCIiCtb111+Pbdu2YefOnbj22mvFDiduRLU6HxFFxgMPPIATTzwRdrsdN910k9jhxA1P8hGr3cmjRalU+q0fdTqdUCqVIkVERER0zIMPPoh///vfcLlcKCsrEzucuMEkiihB3HLLLQHbXS4XpNKgB5WTSrIkH6Wlpairq/PbILC0tFTs0IiIKMXNmTMHL7/8MjIzM3H66aeLHU7ciOpmu/GO1fko0X3wwQe4+eab0djYiNmzZ4sdTsxFYnfyeJEMBTKIiCjxffTRRzjzzDMhkUjEDiXmQskNmEQxiaIEJQgCzjvvPOzbtw8KhQJvv/32iL4hSvQP74kePxERUbx4/PHHcfvtt6Oqqgr33HOP2OHEHJOoIDGJokT2zTffYOHChfjoo4/wq1/9Cm+88QbS09ND6iOZRnKIiIho5CwWC3Jzc70/v/POO7jgggtEjCj2QskNUnMhBVESmDZtGt5++22sXLkSzz//fMgJFJA81e2IiIgoPDk5OVi7di0AYPXq1TjvvPNEjii+hZVELViwALt37x7ynB07dqC8vBy7du0K51JEFMD48ePxl7/8BRMmTPBpP3jwII4ePTrs7Vlam4iIiDzuu+8+7NixA5WVlSlbtCpYI3507HY7SkpKhtyzZuvWrSgqKoLb7cby5cuHTbiIKHw//fQTrrjiCixatAgOh2PIc5Oluh0RERGF5osvvkBzc7NPm0QiwcUXXyxSRIllxElUZmYmuru7sWvXLixZsgRLlizBm2++6XNOVVUVjEYjqqqqYDKZYDAYwg6YiIa2cuVKvPnmm3jppZdQXFw85LmlpaXIzs6GVCpFWloapFIpS2sTERElubfeegvnnXceFi5ciPb2drHDSUhhjdO53W7Mnz8f3d3d6O7uRmFhIXbs2OE9brFYkJOTAwCQy+VQKBThRUtEw/rtb3+L8ePHY8yYMbj//vuHPDcjIwNNTU2oqKjAsmXLUFFRwaISRERESW7dunXo7u7G/v37sXr1arHDSUhhbbZrtVrR1dXl07Zy5UrMnz8fdrsdEonEJ3GSy+XhXI6IgjB//ny8//77aGtrw7nnnjvs+RkZGfwDSkRElEKeeeYZnHfeeZg5cyb++7//W+xwElJYSVRWVpZfm0qlAgBvctW/POBwm3YJggCDwQCbzQZBECCXy6HX6719ethsNlRWVmLixIkAgPb2duj1eiZpRP/f6aefHnDPKE+50lhvoMe9nIiIiOKHXC7Hjh07cMIJJ2DUqLDSgZQV1qPW1tbm1yYIwqDn22y2QY8JggC9Xu+zbkqn0yErKwvt7e0+iVR+fj5qa2uhVqu9t83JyYHFYmEiRTSIZ555Btdddx1uvPFGbNy4EaNHj47JdQPtRVVXV8dpg0RERDHw7bff4k9/+hMefvhhjBkzxtt+0kkniRhV4gtrTVRhYSEUCgUWLFiABQsWeEeGdu3aBZ1OB6VS6S02sXv3bhw4cGDQvvR6PfR6vV+bXC5HUVGRt81oNAKAN4ECjo1+qdVqVFZWhnN3iJLWt99+i+XLlwMAnnzySbzwwgsxuzb3oiIiIhKH1WrFOeecg02bNmH58uVwu91ih5Q0wkqiNBoNzGYzMjMzoVQqUV9fj6qqKrS3t0Or1aKtrQ2VlZVYsmQJCgoKcO+99w7aV319vfdD3sBrWK1W788NDQ0+uyl7zJs3D42NjeHcHaKkdfLJJ+Opp55Ceno6VqxY4fPFRLRxLyoiIiJxuN1udHd3Azg2pX/fvn0iR5Q8wp4EqVarUV9f79O2ePFi7/9v27YNtbW1MBqNPuujBgqUGAViNpv9RqyAY6NRgiDAZrNxSh9RAFdffTXOOOMMzJkzJ6ZrohJ5Lyqu5SIiokSWk5ODuro6PPzww9i6dSsmT54sdkhJQ+KOwLje7t27YbVaoVarMXPmTOzatQsqlWrIpClYnuIV7e3tsNlsmDBhAvR6PcrKynzOM5vNKCgogMVi8Znq119vby96e3u9P/f09GD69Omw2+0RiZUoEX3yyScwm8244447opJcBVoTlZ2dHfdrohI1biIiSl19fX1IS0vza3e5XJBKw5qA5iNZv2Ts6elBZmZmULlB2I9mcXExVCoVli9fDrPZDODYN88PPvggenp6wurbbDZ7K/YB/1fxb6iRpoEl1/urrKxEZmam99/06dPDio8o0R04cACXX3457rzzTixbtgxHjhyJ+DUSdS8qruUiIqJE8s033+C8887DE0884Xcs0glUXl4e1qxZg82bN2PNmjXIy8uDw+GI2DUSQViP6OrVq6FSqdDd3Y3Ozk7vYrXMzExUVVV5i0CMlFarRVlZGTQazbDnDlX5z6O8vBx2u937b8+ePWHFR5ToXnnlFe/apE8++QQulysq1/HsRWUwGLB69eq4T6AAruUiIqLEsX//fuTm5sJiseCWW27Bu+++G7Vr8UvGY8JeE1VVVeX9/4FTgTIzM0fcb1FRETQajc/6J8/GvYESJs8IVP/NfQdKT09Henr6iGMiSjbXX389jjvuOJSXl+OFF17A2LFjxQ4pboi1litZp0gQEVH0nHDCCViyZAn+/Oc/Y9q0aVFdpuL5krH/F6+p+CVjWEnUrFmzfH4euLzKbrePqN/q6mqoVCq/AhLBFIwYuDEvEQ2tuLgYV155pd++UUePHk3pDfhKS0tRV1fntyaqtLQ0KtdzOBzYsGEDHn30UdhsNu8bFPfUIiKiYGzYsAFjx47F3XffjUmTJkXtOolcMCqSwprO19LSgoMHD3p/7j8StXv37oCb8Q7HU6a8fwLVv8S5RqNBe3u73+1sNhtUKhUr8xGNwMAEyul04oorrkBZWRmOHj0qUlTiiuVaLs/88rVr16K7uxtutxtHjx5N2SkSREQ0tM7OTnz66ac+baNGjUJlZWVUEyjg2JeM2dnZkEqlSEtLg1QqjeqXjPEqrK+Zy8rKMGPGDKxYsQK5ublob2/Hjh07YDKZYDQaYbFYQurParVCEISAlfc8FfeKiooCljg3mUwoLCwc+Z0hIq8//OEPePXVV/Hqq69iz549ePbZZ8UOKaBoT33zrOWKNs/88kDFUlNxigQREQ3uww8/xFVXXYW+vj60tLRgypQpMb2+50vGVJ96HnaJc6vViuLiYgiC4G2bMGECzGYz5s6dG3Q/giCgqKgIS5Ys8Wnv7OyE1WqFyWTytmVlZcFgMHgLTgiCgIKCgoAjVEMJpYwhUSp5/PHH8bvf/Q4ulwvbtm1Dfn6+2CH5SaYS5FqtFps3b0ZfX5/fMalUioqKipgkc0REFP8WLFiAbdu2AQAWLVqErVu3ihxR8qznDSU3iMhmu21tbejo6IDVaoVKpQopefIoKCiAIAg+U/c8Bo4wWSwW6HQ6WK1WyOVyWCwWnySLiMJz66234qyzzsJnn30WlwkU4FsdyLO41TP1LdESjkDzy4FjU6RTcYoEEREN7qmnnkJOTg6mTZuGRx55ROxwAn6pmQrreSOy2e5g1q9fj1WrVkWr+7BxJIoodNu2bcPFF18ccDO/WAo0epOWloZly5Z595ZLFP3fgKRSKZxOJ+RyOe644w7cfffdSf0mREREofv8888xc+ZMjBkzRuxQUFVVhTVr1vhU60vUWRQxHYkCgF27dgVs37JlS1wnUUQUmpdffhmXX345fvWrX2HLli2YPHmyaLFEsjqQ2NMQOL+ciIgCaWpqwuOPP47Nmzf7VMydM2eOiFH5ClTyHAC+/PJLkSKKjbBGonbu3In8/HzY7faAC6IlEknAKSrxgiNRRME7dOgQZs6cif379wMAHnvsMVGnmUVqTVS4/YidgBERUXJ65plncNNNN6Gvrw+rVq3CunXrxA4poEAjUQAwefJktLe3J9R7Yii5QVglznU6HWpra9HW1obu7m6ff21tbXG7loKIQjd27Fi8+OKLOOmkk3DVVVfh1ltvFTWeSJUgD2fndU8CtmbNGmzevBlr1qxBXl4eHA7HSO8WERERgGMzLjyDFM3Nzfjpp59Ejiiw0tLSgGXV9+/fn9RbdIQ1na+goACLFy8OeCwzMxNFRUXhdE9Ecea8886D1WrFcccd57MvHHBss+2BbdEWiRLk4ey8nkzFLYiIKL5ceOGFePjhh9He3o7q6mrR1yIPJiMjAwsXLsTTTz/t8146atSopN6iI6yRqOE2th1YrpyIEt+JJ56IzMxMn7a2tjacd955fhv/JYJw1lZ5ErD+uK8TERGNxEcffeTXVlpaiocffjhuEyiP2bNn+7WNdJ1yoggricrNzcWOHTsGPa7T6cLpnogSwOHDh1FYWIj/+Z//wTnnnIO33npL7JBCEs7O65EsbkFERKnpp59+wp133omf//znaGxsFDucEQnnvTRRhVVYYv369WhuboYgCMjNzfU7Xl9fj87OzrACjCYWliAK37fffovLLrsMH330EebMmYMPPvgA48aNEzuskIy0OEQybfhLRETiaGhoQHFxMQBg3Lhx+PzzzzF16lSRowpdMhRaCiU3CCuJUigUUCgUg07r27lzJ6vzEaWAQ4cO4a677sJtt92GM844Q+xwYioZ3jSIiEg8brcb1157LRobG/HII49gxYoVMV9jTMfELIm65JJLsG3btkGPr1ixAps2bRpp91HHJIooug4ePIg333wTl19+udihEBERxS2Hw4Evv/wSarVa7FBSWsxKnOv1+iGPa7XacLonogTmdruxcuVKXHHFFbjllltw5MgRsUMiIiIS1TfffIMFCxbgk08+8WnPyMhgApVgwhqJSnQciSKKnjfffBPz588HcGyO965du6BSqUSOioiISBwffvgh8vPz0dnZidNPPx0ffPABjj/+eLHDon5iNhJFRDSYiy66CEajEWPGjEFtbS0TKCIiSmmnnXYapk2bBuDYdPevv/5a5IgoHByJ4kgUUVR9++23OPnkk33aXC4Xent7cdxxx4kUFRERUex98cUXWLt2LWpqaqBQKMQOhwbgSBQRxY2BCRQAPPzww1Cr1di1a1fsAyIiIoqB559/Ht3d3T5tp512Gv7+978zgUoCTKKIKKasVivKy8vx+eef47zzzsPevXvFDomIiChiHA4HbrzxRixatAg333wzUnjSV1JjEkVEMZWRkYGf/exnAIDbb789ITcUjCaHw4GqqipotVpUVVXB4XCIHRIREYWgp6cHL774IgDgueeeG3I7IEpcXBPFNVFEMdfb24u//OUvuPXWWzF69Gixw4kLDocDGzZswKOPPgqbzQaZTAaXy4Xs7Gw0NTVxA18iogTywgsvYOnSpXjsscdw/fXX+2yey03a41fMNttNdEyiiOKL2WzGyy+/jKqqKowZM0bscGLG4XAgLy8Pn332md+0D6lUioqKCqxevVqk6IiIaCh79+7F5MmTMWrUKJ/2/fv344QTTvBp8/y9b21thUwmg9Pp5JdlcYSFJYgo4ezfvx9Lly7Fo48+inPPPRcHDhwQO6SYqampQWtra8B58zKZDB0dHSJERUREw2loaMAZZ5yByspKv2MDEyjg//7eu1wu9PX1weVyobW1FTU1NbEIlyJo1PCnEBFF3wcffOCtYjR16lRMnDhR5Ihip6Ojwzt9byCn0wmlUilCVERENJS2tjZcffXVcLlcWLt2LS655BKce+65Q94m0N/7RP2yLFrTEhNluiOTKCKKCwsXLkRzczNuu+02/Pd//7fP/PFkp1Qq4XQ6/dolEgmys7NRWloqQlRERDSUWbNm4b777sPatWtRWFiI0047bdjbBPp7H8kvy2KVgASallhXVxf2tMRo9RsNXBPFNVFEca+trQ3vvfceli5dmpTJVf83DalUCqfTCblcjjvuuAN333133L1xEBGlor6+PqSlpfm0HT16FK+++ip+85vfBPX+FM01UbFcb1VVVYU1a9b4jKhFYg1vtPoNFtdEEVHSOHr0KJYuXYrrr78ehYWFfhsXJoOMjAw0NTWhoqICN954Ix588EF8/fXXuP/++5lAERHFAavVirPPPhvPPfecT/uoUaNw+eWXB/0FX/+/98uWLUNFRUXEkpxYrrf68ssv/doiMS3RM90x0v1GA6fzEVFce/XVV9HU1AQA+Oijj/y+BUwWGRkZrMBHRBSHPv74Y5x77rk4evQotFotLrjgAkyZMmXE/UXr732s1ls5HA688sorfut4IzEtMdrTHSOJI1FEFNcuv/xybN26FVOmTMEzzzzDkRkiIoqpn/3sZ/j1r38NAJg+fToOHjwockSBxSoBqampwf79+/3aJ02aFPYa3tLSUmRnZ0MqlSItLQ1SqTRu1wZzTRTXRBElhMOHD+O4447zabPb7Xj//fdx6aWXihQVERGlgv3798NoNOKee+6J203iY7UmSqvVYvPmzejr6/O2SaVSXH/99XjyySfD7l/M6nyh5AaczkdECWFgAgUAq1atwhNPPIEbbrgBDz/8MORyeewDIyKipPH5559jxYoVeOyxx3DmmWd620844QSsWbNGxMiG51lvFe0EZLCKsrNnz45I/4kyvZ0jURyJIkpI//M//4O8vDwAx/7gfvLJJ5gxY4bIURERUaJ66623cMkll6C3txc5OTloamrCqFEcbxgollUAY43V+Ygo6Z1zzjmora3FuHHjsH79eiZQREQUlnPPPRdZWVkAjn2Y/vbbb0WOKD5Fs8JgIuFIFEeiiBLad999hxNPPNGnvKzT6cSbb74JjUYjYmRERJRoPvjgAzQ0NOCBBx4IOI2ckhtHoogoZZx00kl++3M8/vjjKCgoQGFhIb777juRIiMionhlsVhwySWXoLOz06f9nHPOwbp165hA0bCYRBFRUvn+++9x7733AgC2bt2KtrY2kSMiIqJ4UldXh3POOQcmkwl333232OFQgmISRURJZcqUKaitrcWkSZOwYsUK/OIXvxA7JCIiiiP5+fkYN24cAGDnzp348ccfRY6IEhHXRHFNFFFSOnDgAEaPHu332n799deh0WhYcYmIKIVt3rwZ33//PVatWoW0tDSxw6E4EUpuwCSKSRRRynjzzTcxf/58/PznP4fBYMC5554rdkgBibnRIBFRsnC73airq8Pf//53vPzyy5DJZGKHRHGOm+0SEQ3gdDqxYsUKAMCHH36Ijz76KC6TqED7b9TV1aVk+VgionDcdtttePzxxwEAf/7zn3HnnXeKHBElk7hcE2W1WpGTkzPocZvNBp1Oh+rqalRXV0Or1cJms8UuQCJKODKZDM888wzOPvtsnH/++bjpppvEDimgmpoatLa2wuVyoa+vDy6XC62traipqRE7NCKihHLttdd6//+TTz4Z9nyHw4GqqipotVpUVVXB4XBEMzxKcHEzEuVJjACgpaUFVqt10HPz8/NRW1sLtVoNABAEATk5ObBYLJDL5bEIl4gS0DnnnIPm5mZ0dnZCKvX9DqmhoQFnnnkm5syZI1J0x3R0dEAmk8HlcnnbZDIZOjo6RIyKiCj+/fTTTxg9erT357y8PPzhD39Abm4uFi5cOORtOQuAQhU3I1FyuRwGgwEGgwFLliwZ9Dyj0QgA3gQKAFQqFdRqNSorK6MeJxEltlGjRmHKlCk+bV999RVuuOEGnHXWWVi7dq1IkR2jVCrhdDp92pxOJ5RKpUgRERHFt6+//hpXXXUVbrzxRr9j999//7AJFMBZABS6uEmigtXQ0IDc3Fy/9nnz5qGxsVGEiIgo0T344IM4dOgQ+vr60NXVJWospaWlyM7OhlQqRVpaGqRSKbKzs1FaWipqXERE8aivrw8XXnghXnjhBfztb3/Djh07Qrq9Zwrf008/7XeMswBoKHEznS9YZrMZer3er12lUkEQBNhsNk7pI6KQPPzww5g0aRL++te/ij4SlZGRgaamJlbnIyIKQlpaGu677z6UlJTgxBNPxOHDh4O+bf8pfAB8plEDnAVAQ0uoJGqo4hGexEkQBJ+pfkREwxk7diwqKirw+9//Hscdd5zPsVdffRXbt2/H/fffH7OtEDIyMrB69eqYXIuIKJG0tbVh+vTpSE9P97bddNNN6Onpwc0334zMzMyg++o/ha8/z5rZeJ0FwG0w4kNCTefzTLMZaqRpqKk4vb296Onp8flHROQxMIE6cuQIbr/9djz00EOYPXs2vvrqK5EiIyJKbQcPHsTq1atx+umn4+GHH/Y5JpVKcffdd4eUQAH/V8hnYF+zZ89GRUVFXBaV8IyerVmzBps3b8aaNWuQl5fHSoIiSKgkaijBlDivrKxEZmam99/06dOjHxgRJazm5mZ8++23AIA5c+bglFNOETkiIqLU1NHRgXXr1qGvrw9/+tOfvH+bwxGokA8AXH/99Vi9enXcJVAAC2DEk4RKohQKBYDACZNnBMpzTiDl5eWw2+3ef3v27IlKnESUHH7xi1+gtbUVixcvxmOPPQaJROJz/ODBgyJFRkSUWs466yysWLECo0ePxu9+97uIrH9PxEI+gUbPWABDHAm1JiqYF4xKpRr0WHp6us8cWiKi4cycOTNg5c8vv/wS8+bNw+233w6dTheX31gSESWi3bt349lnn0V5eblP+x//+EfcddddyMrKish1ErGQD7fBiB8JlUQBgEajQXt7u1+7zWaDSqViZT4iiomysjL09PTgT3/6E8aOHev3Zk9ERKF76KGHcO+996K3txdz587FpZde6j2mUCiGnHE0EolWyKe0tBR1dXU+mwLH++hZskqo6XwAUFRUBLPZ7NduMplQWFgoQkRElGqcTidmzZqFtLQ0nHTSSbj99tvFDomIKClMnToVvb29ABBwS5tU5xk9q6iowLJly+K2AEYqkLjdbrfYQQyk0+lQXV2NwULLysqCwWCARqMBcKyseUFBQcARqqH09PQgMzMTdrs9ZqWLiSh5tLW14euvv8b8+fN92l9//XWceOKJOPvss8UJjIgoAbjdbvT19WH06NE+bRdffDHy8vJQXl4ecsU9onCEkhvEVRKl1WoBAPX19bDZbNBoNFCpVCgqKvImTMCxqXs6nQ5ZWVmQy+WwWCzQ6XRDrocKhEkUEUXaoUOHcOqpp+K7777Db3/7Wzz55JNIS0sTOywiorjyzjvvYPXq1Tj//PNRXV3tc8zlcnn3aiKKpYRNomKNSRQRRdojjzyCO++8EwBwxRVX4IUXXhA3ICKiOHPgwAFMnz4dR44cwZgxY/C///u/mDZtmthhEYWUGzDNJyKKoBUrVuChhx7C5MmT8eCDD/od/+mnn0SIiogofkyaNMlbCGHmzJn4/vvvRY6IKHRMooiIImjMmDG488478fXXX+P000/3OdbS0oJTTjkFjz76KI4cOSJShEREsbNv3z6sW7fOb517eXk5nnzySXz88cfIzc0VKTqikUu4EudERIkg0J509913H3744Qf87ne/Q0ZGBm666SYRIgudw+EIeR+VkdyGiJKL0WjEnXfeiUOHDmHmzJkoKiryHlMoFFi2bJmI0RGFh0kUEVEM9Pb2eudXz5w5E0uXLhU5ouA4HA7k5eX57ElSV1c3ZEndkdyGiJLPjBkzcOjQIQDAgw8+iMLCQkgkEpGjIooMTucjIoqB9PR0bNmyBbt27UJtba1PSV8A2Lx5M5599lm/nejFVlNTg9bWVrhcLvT19cHlcqG1tRU1NTURvQ0RJTa73Y4DBw74tF1yySWYP38+br/9drz66qtMoCipcCSKiCiGfv7zn/u12e123H333eju7saDDz4Ii8Xil2SJpaOjAzKZDC6Xy9smk8nQ0dER0dsQUWL68ccf8cgjj2DDhg0oKiqCwWDwHpNIJDCZTCxXTkmJv9VERCJrbGxEd3c3ACAnJyciCZTD4UBVVRW0Wi2qqqrgcDhG1I9SqfQbHXM6nVAqlRG9DRElpqNHj2LdunXo7u7Gk08+6fdlCRMoSlb8zSYiEtmNN94Is9mMiy66CPfee6/PMbfbjcbGRvT29gbdn2dN0po1a7B582asWbMGeXl5I0qkSktLkZ2dDalUirS0NEilUmRnZ3vLE0fqNkSUGI4ePerzc2ZmJm6//XZIpVL89re/5ebilDK42S432yWiOPbmm29i/vz5OPnkk/HQQw+huLh42NtUVVVhzZo1PtPppFIpKioqsHr16pBjYHU+ItqzZw/WrVuH7du3Y9euXT7JUldXFw4cOIDZs2dHPQ7+baFoCiU34JooIqI49sc//hEA8O233/rtszKYSK9JysjICDn5GsltiCh+rVy5Eq+88goA4Nlnn8V1113nPaZQKKBQKKIeAyt/UjzhdD4iojhWXV2NK664AllZWVi8eLHPsf3792P37t1+t+GaJCKKNM+XImPHjkVnZ6coMbDyJ8UTJlFERHEsNzcXL7zwAnbu3IlRo3wnD6xbtw6zZs3CNddcg6+//trbzjVJRDQSTqcTzz//PC644ALs2rXL59iFF16ITZs24auvvsKdd94pSnyeUfb+WPmTxMIkiogoAYwbN87nZ5vNhk2bNsHpdGLr1q0+6xMyMjLQ1NSEiooKLFu2DBUVFZzuQkTD+utf/4pFixbhvffew/r16/2Oa7VaTJo0SYTIjuEoO8UTFpZgYQkiSkA9PT145JFH8Nhjj+Gqq66C0Wj0Od7a2opTTjkFxx9/vEgRElGi+fHHH3HKKaegq6sLc+fOxf/8z/8EXW0vFgUfAq2Jys7O5pdEFDGh5AZMophEEVECO3ToEA4dOuTz7bDb7cZZZ52Fb775BsuXL0dFRQXLDhORV1NTEx599FGo1Wrcc889PseeeeYZnHDCCViwYAEkEklQ/cUyuWF1PoomJlFBYhJFRMnIbDajoKAAAHD++efj3XffFTkiIooX33zzDWbMmAGXy4WTTz4ZHR0dYX/JEultFYLFhIoijSXOiYhS2PTp03HDDTfg73//O373u9/5HX/55Zfxy1/+Mu6+POIHIqLI6+vr80mSpk2bhssvvxwvvPACfvrpJ3zxxRf42c9+5nObUF+LkdpWIZTrstw5iY1JFBFRkjnttNOwefNmVFVVYeLEiT7Hdu/ejcsvvxzHH388Vq1ahfvvv1+kKH3xAxFR5Ljdbrz++uvYtGkTuru78dZbb/kcLy8vxxVXXIGrr74aY8aM8Tk2ktdiJAo+hHrd/uXOPcmbp9w596ijWGB1PiKiJDVlyhS/suhGoxFutxsOh8PvWLAcDgeqqqqg1WpRVVUFh8MRdqzc/4UosnQ6Hf75z3/i7bffxocffuhz7JxzzsENN9zgl0ABI3stRmJbhVCu63A48Pzzz/u1s9w5xRJHooiIUsjVV1+Nzs5ONDQ04KabbvI5dvDgQfzXf/0XbrjhBvz85z8PeHuHw4F58+bhiy++gEQigdvtxtNPP43m5uawRowiNR2IKNU4nU588sknPq9ZiUSCFStW4NZbb8XJJ5+Mb775ZtDX9EAjeS16tlUIZzpusNf1jFh99tlnGLisn+XOKZY4EkVElELOOussGAwGfPfddzjxxBN9jm3ZsgWPPPIIzj77bFRUVAS8/YYNG/D555/D7XbD5XLB7Xbj888/x4YNG8KKi/u/EIXukUcegVKpRG5uLvbv3+9z7Nprr8Xzzz+P3bt3Y+HChUH3OdLXYkZGBlavXg2DwYDVq1eH/KVKsNf1jFgNTKAkEgk3FaeYYhJFRJSC0tPT/drq6uq8/3/JJZf4HPOsO3j11VcD9jdYe7AiMR2IKNV899132LNnD44ePerz+gWA8ePH48orrwx52q5Yr8Vgr+sZsepPIpFg3rx5fuunojH1mMiD0/mIiAgA8MILL+DZZ5/FO++8g9zcXJ9jb7zxBlasWIG+vr6oXDsS04GIkpHL5cLbb7+NrVu3Yt26dT5fgCxbtgwbNmzApZdeirPOOisi1xPrtRjsdQONWEkkElx11VV+CRSL1VA0cZ8o7hNFRDSsa665Bs8+++ygx//whz/ETaU/omTyu9/9Do8++igAoLGxEYsXL/Y5vn//fpxwwglihCaKYDf2FWvvKkpsoeQGnM5HRERDcrvd6Ovrg0wmg0KhwJw5cyCRSLz/VCoVpk6dCrvdLnaoRAltz549fmt9+q9n+tvf/uZ3m1ASqGSY3uYZsaqoqMCyZctQUVERcHQp0LQ/FquhSOJ0PiIiGpJEIkFDQwP27duHTz/9FPPmzfOZcvPdd9+hpKQEpaWleOmll/zWUxHR0F5++WVUVVXh3XffxXvvvYfzzjvPe2z+/Pm45ppr8Otf/xqXX375iK+RTNPbPEUshsJiNRRtnM7H6XxERCPmdDpxyimnYO/evRg1ahR++OEHKBQK73G73Q6pVIpx48bFNC6HwxEX66viJQ6Kb3V1dVi6dCkA4NZbb43K/mipNr0t2Gl/RP2FkhtwJIqIiEZMKpWivr4e9fX1cDgcPgkUcGxz3/vuuw8LFizAgw8+iDPOOCPqMcXLN+7xEgfFh6+//hr19fVobGzEX//6V8yePdt77De/+Q1Gjx6NWbNmYc6cOVG5fqrtxcZiNRRtTKKIiGjEJBIJLrjgAlxwwQUBj9fX16O3txf//Oc/8cgjj/gc6+npwV/+8peIf8Dx7CPjKcsOAK2traipqYnpN+7xEgfFhxdeeAH33HMPgGMFIu69917vsczMTLS3t2PatGlRu34qTm8LZtof0UixsAQREUXF0aNHce6552LKlCk466yzfD6sORwOZGdno7y8HE888QTuvfde5OXlRWShe7wsKI+XOCh2fvzxR7z44ou46aab8P333/sc+81vfuP9/08++cTvttFMoADuxUYUaUyiiIgoKkaNGoWamhrs3bsXr732ms8xTztwbB8ct9vtHaUJV7x84x4vcYxUMlRyi7WqqipceeWVePLJJ/HKK6/4HFMqlTAYDPjyyy/x97//PeaxZWRkwGw2o6CgAFlZWSgoKIDZbOb0NqIRYhJFRERRJZVKMXXqVJ82QRAgkUh82vqP0jz33HNQq9W499578eWXX4Z0vXj5xj1e4hgJz3quNWvWYPPmzVizZk3ERgoTXXd3NxobG1FSUoKenh6fY/1HmwZ+cQAAJSUlOPXUU6MeYyAOhwMajQYmkwnt7e0wmUzQaDR8TolGiGuiiIgo5lQqFSQSic+eOP1HaV577TXs3LkTO3fuxC9+8QufRfie0Z2BU+U84mVBebzEMRLxtp4rnqoc3nfffXj88ccBHNvD6YorrvAey83NxV133YX8/HzMnz9flPgGE2/PKVGiYxJFREQxV1pairq6Or/yw55Rmh9++AEAMGbMGFx00UU+t/33v/+NxYsX46KLLkJpaSny8/P9+o+XBeXxEkeo4qmSmxhVDpuamvDaa6/h/fffxyuvvIK0tDTvsQULFniTqG3btvkkUVKpFBs2bIhKTOGKp+eUKBkwiSIiopgbbpTmn//8J3744Qd89NFHOO6443xuu2PHDthsNrzwwgsoLCz0OeZ0OvHee+9h3rx5GDNmTMzuz1DiaRQlWPG0nivaIyiHDx/2+x177LHHvOuWWlpafDa/vfjii/G73/0OCxYswC9/+cuwrx8rQz2nifg7SiQ6dwqz2+1uAG673S52KEREFKTf//737okTJ7oBuPfu3etzbNeuXW4A7tGjR7vvvffeqMZx8OBBd2VlpbukpMRdWVnpPnjwYMBzzjjjDLdUKnWnpaW5pVKp+4wzzgh4bjyJp7hLSkrcaWlpbgDef2lpae6SkpKw+r3zzjvd2dnZ7pNOOsntcrl8jtXW1nqv9ec//zms68SLwZ7T7777Lm6eayKxhZIbcCSKiIgSyh//+EesXbsWra2tOOmkk3yOvfPOOwCAn376CZMnT/a77bJly5CVlYULLrgAF1988YhjCHaKWSijKOGMBkR6JCGe1nONdFTM7Xajo6MD7777Ll5//XVkZGT43I/PPvsMra2tAIDdu3f79HfZZZfhr3/9Ky666CJMnz49pHjjdVRnsOeUa6WIRij6OV10dHd3u8vKytx6vd6t1+vdJSUl7u7u7pD64EgUEVFyefPNN9033nije/bs2e7m5mafY3v37vWOLlx88cV+t7Vare6Ojg6/UYlAKisr3VKp1Gd0RCqVuisrK33OC3YUZaiRn+FGvOJp1Cgagrl/P/30k7unp8fndocOHXLLZDKfx73/bdeuXeseNWqU+5xzznG3tLTELNZ4E62RPqJElBIjUfn5+aitrYVarQZwrFxuTk4OLBYL5HK5uMEREZEoLrroIr9CFB4tLS3e/z/nnHP8jt98882wWq2YMGECvv/+e4wePdp7rK+vD6NGjfKWZQ92kX6w61C++uorfPbZZ3C73T6jARs2bEBDQ8OQI17JPpIw1KjYrl27cMMNN6C1tRV33XUXKisrvbc77rjjcMIJJ3g3ve3r6wPwf4/N7bffjnvuucdvPVQ4EvG5iKf1b0SJJCGTKKPRCADeBAo4Vi5XrVajsrISer1erNCIiChOLVy4EF988QWam5txxhln+Bw7evQoPv30UwDA5MmTfRIoAPjDH/6ATZs2Yc6cOdi0aVPQHzwHq0J4ww03+EwHPHr0qE+5d+BYUvbqq68O+6E8lKpr8TrVbCivv/46nn76aXzxxRd49NFH8Ytf/MJ7bMKECfjwww8BAB999BEA3/s4evRov1L6nscmGl+4JmIFvOEqZRJRYAmZRDU0NCA3N9evfd68eTAYDEyiiIjIj1QqxezZs332nPI4cuQI7r77bnz00UcBv4H//PPP0dXVhffeew/HH3+8zwdPiUQCp9OJMWPG4MQTT/S5XUZGBt59911s3Lhx2HUoA/XfD2uoD+XBJnRilAofSv9k57vvvkN6ejr27t2Lt956y2cPsN27d+Mf//gHAODee+/FwoULvcnfKaecAoVCgSlTpiArK8vvPgZKTqM5ypKIozrxtP6NKJEkZBJlNpsDJkoqlQqCIMBms3FKHxERBS0jIwMVFRWDHlcoFJg2bRoOHDiAGTNmQCaTeT94vvbaa3jrrbdw6NAhOBwOn9u5XC5MmTIFEyZMwMUXXzzk6JFHWlqadzTgsssu85mGCPh/KB9qJGHglMFoTjVzu92w2+3o6upCWloannzySbz66qsAAI1Gg+bmZuzbtw/Z2dmora31SXY8U+0AYO/evT7FHE455RTv/7/77rt499138fTTT6O5uRkZGRn44YcfMGrUsY8z9957r3dEsf9jK5FIMGrUKL9RFs/j8+WXX2Lv3r2YOnUqZs+eHTCJCGYUL1FHdRJ1PzMiMSVcEmWz2QY95kmcBEHwmern0dvbi97eXu/PPT09kQ6PiIiSUG1tLQDg0KFD3lESzwfPzMxMfPbZZzhw4ABUKpXP7Q4cOIDe3l58//33Pu9fgUYsJBIJLrnkEsyYMQNKpRI///nPYTAYMH78eNjtdr8k4OWXX0Z6ejomT57sN5Jw7bXX4sCBA7j00kvx5ZdfYtSoUT6JiodUKvUZ1XK73WhpacFPP/2EMWPGICcnx+f8v/3tb2hubkZPTw/+/Oc/+yQR//jHP3DNNdcAAKZMmeLdMBkAPvjgA++0OpfLNeRI3DfffOOTRL377rs+8QHHRgY3bNiA+++/35tAff/994PORFGr1cjJyfFJfjyjVp61aP0fk4EjdMGO4nFUhyiFRK++RXS0t7e7AbgNBoPfMZPJ5AbgNplMAW97//33+1Sf8fxjdT4iIgpXT0+P+/Dhwz5tgiC4582b5546dap7xYoV3nZPFbf+70Wnn366TxU3g8HgPbZ48WKf6nxHjhzxHps/f75fLIsWLQr4fjfwn0Qi8ako6HK5vMfOP/98v36vueYa7/H29nafY2+88caw15PJZO6zzz47YEW4UaNGuW+88Ua/a55zzjkB+zrnnHN8zluwYMGg112wYIFfv4EqLHr+Day0GGw1RiJKbClRnS+QoUapAKC8vBx33XWX9+eenp6Q938gIiIKZNy4cX5tSqUSH3zwAQD4jHZ4Riz+8z//E4Ig4LjjjsO//vUvnxGL/rMlrr76ahQWFnp/3r9/v/f/09PT/a575MiRoGKePHmyz1QziUSC0aNH46effvKbmuiJ26Ozs9Nn5G369OkoKCiAIAhob2/3u61EIsGNN94Io9GIqqoqv5E4l8uFU089Nai4A/nqq68GPTZ16lS/tqGmVA5cd5aIBSOIKLoSLolSKBQAAidMXV1dPucMlJ6eHvDNhoiIKNo85dE9MjIy8NJLLw16/i233IIlS5agp6cHJ598ss+x9PR0PPDAA+jt7Q2YeOTm5qK9vR1ffPGFXwy5ubn47rvvcPzxx+O+++7zm2p22223we12B/yScdWqVVi2bBkyMjIwa9Ysn2PZ2dnYtm0bqqqqcO+99/oVdADgTbpCWTt02WWXeRPRge39zZgxA59//rnfeQACFhMJNKXSY+C6s0QsGEFE0SVxB/orF+ckEgn0ej3Kysp82o1GI7RaLbq7u4MqLNHT04PMzEzY7XaMHz8+StESERHFXqB1PNnZ2VGvxudwOHDOOeegtbXVp33OnDneYhCe84JZO+Tpr3+CNGfOHHzwwQc+53///feYMWMGfvrpJ5/bz549GxaLJWChiMHWRA18nMR6LIkotkLJDRIyiSooKIBKpYLBYPBpr66uhsFgCDiNIBAmUURElMzE2hfK4XBgw4YN3up8l112Ge6+++4RXzvY+/H999/j2muvxUcffYT09HQsXboU995776DXjXR1PiJKbEmfRBmNRuj1er9kqaCgAGq1Ouh9ophEEREREREREFpuII1RTBFVUlIC4Nh+UR6CIEAQBG60S0REREREUZVwhSU8LBYLdDodrFYr5HI5LBYLTCaT2GEREREREVGSS8jpfJHC6XxERERERASkwHQ+IiIiIiIisTCJIiIiIiIiCgGTKCIiIiIiohAwiSIiIiIiIgoBkygiIiIiIqIQMIkiIiIiIiIKAZMoIiIiIiKiEDCJIiIiIiIiCgGTKCIiIiIiohAwiSIiIiIiIgoBkygiIiIiIqIQMIkiIiIiIiIKAZMoIiIiIiKiEDCJIiIiIiIiCgGTKCIiIiIiohAwiSIiIiIiIgrBKLEDEJPb7QYA9PT0iBwJERERERGJyZMTeHKEoaR0EnXw4EEAwPTp00WOhIiIiIiI4sHBgweRmZk55DkSdzCpVpJyuVzYu3cvxo0bB4lEEtRtenp6MH36dOzZswfjx4+PcoQUD/icpx4+56mHz3nq4XOeevicp55Qn3O3242DBw9i6tSpkEqHXvWU0iNRUqkU06ZNG9Ftx48fzxdgiuFznnr4nKcePueph8956uFznnpCec6HG4HyYGEJIiIiIiKiEDCJIiIiIiIiCgGTqBClp6fj/vvvR3p6utihUIzwOU89fM5TD5/z1MPnPPXwOU890XzOU7qwBBERERERUag4EkVERERERBQCJlFEREREREQhYBJFREREREQUgpTeJyoSBEGAwWCAzWaDIAiQy+XQ6/VQqVRih0ZRZrVasXz5clgsFrFDoQiw2WyorKzExIkTAQDt7e3Q6/WQy+XiBkZRxddx6uD7dWryPO8TJ05EZ2cnBEFAeXk51Gq12KFRjDQ2NkIQBJSVlUW0XyZRYRAEAXq9HgaDwdum0+mQlZWF9vZ2/mFOQjabDTqdDgDQ0tICq9UqckQUKfn5+aitrfW+sQqCgJycHFgsFiZSSYav49TD9+vU5Emg9Hq9t81oNHr/tjORSn42mw3Lly9HeXl5xPvmdL4w6PV6nxemp00ul6OoqEikqCia5HI5DAYDDAYDlixZInY4FCFGoxEAfN5QVSoV1Go1KisrxQqLooSv49TD9+vU1NjYCKPRCJvN5m0rLi4GAJ+EmpKX5/09GphEhaG+vh7Lly/3a9doNPxmkyiBNDQ0IDc316993rx5aGxsFCEiIookvl+nJrVaPegoY1dXV4yjoVgzm83QaDRR659JVBgCfegiosRjNpuRlZXl165SqSAIgs+3mESUePh+nZo0Go3flGyz2QwAUZneRfHFarVGdcom10SFwWQyBWy3Wq2cX02UIIZKkDxvvIIgcO48UQLj+zUBxxKoyspKNDQ08G96kquuro54IYmBmERFmNlshiAIg/7BJqL44pnSMVTxCE77IEo+fL9OHVarFWazGc3NzdBoNFGd4kXii/YIlAen80WYVqtFWVkZX6BESYDT+IiSF9+vU4darUZZWRkaGhqQlZUFpVIJQRDEDouiZMuWLTF5Xaf0SJTNZkN+fn5IH5SGGgIuKiqCRqPxqwBE8SPSzzklPoVCASBwwuQZgfKcQ0TJge/XqaukpAQ6nQ5FRUXcHy4JGY3GmK13S+kkSi6XR+wFVF1dDZVKxT/IcS6Szzklh2D2gOKaCaLkwfdrys3Nhdlshs1m4z6ASUQQBCgUipg9pymdREWKpwRy/z/IsZqPSUTh02g0aG9v92u32WxQqVR8kyVKEny/Ti1ZWVlQq9VoaGjwaWfRoOTkWeM4cJ2jzWbDli1b0N7ejoKCAhQWFkbkekyiwmS1WiEIgl8FELPZzBcmUYIoKioK+K20yWSK2B9bIhIX369TjyAIAdfGePYG4/OeXAYrGmI0GrFkyZKIV+tjEhUGQRCwfPlyLFmyBNXV1d72zs5OWK3WqJdWJHF1dnaKHQJFSElJCfR6vc/GfIIgsHJXCuDrODXw/To16fV6vw/VnqqMBoNBpKhIDNH4W88kKgwFBQUQBCHgbuf89jp5abVaAEB9fT2AY78HKpXKu1CZEpPFYoFOp4PVavWunWMClbz4Ok4tfL9OTWVlZWhsbITBYIBcLofNZvN+OcbXefLTarXeKoxGoxE2my2if+MlbrfbHZGeiIiIiIiIUgD3iSIiIiIiIgoBkygiIiIiIqIQMIkiIiIiIiIKAZMoIiIiIiKiEDCJIiIiIiIiCgGTKCIiIiIiohAwiSIiIiIiIgoBkygiIiIiIqIQMIkiIiIiIiIKAZMoIiIiIiKiEDCJIiIiIiIiCgGTKCIiIiIiohAwiSIiIiIiIgoBkygiIkpJVqsVWVlZfu1arRbV1dUiRERERImCSRQREaWkLVu2QC6X+7UbjUaoVKrYB0RERAmDSRQREaWkxsZGLFmyxKfNarUCADQajRghERFRgmASRUREKcdms0EQBL9kyWw2Q6VSBRyhIiIi8mASRUREKcdsNgMA1Gq1T7vJZOIoFBERDYtJFBERpZzBkiWz2YyCggIAx0ariIiIAmESRUREKcdsNvuNQg0cnaqvr495XERElBiYRBERUUrxrIfyFJHwtBkMBgCASqVCY2Mjp/UREdGgRokdABERUSyZzWbI5XKoVCpUV1d7i0g0NDR494jyHCciIgpE4na73WIHQUREFCtarRaCIMBkMokdChERJShO5yMiopTSv3gEERHRSDCJIiKilDHY/lBEREShYBJFREQpw7MeamBlPiIiolBwTRQREaUMz0gUkygiIgoHkygiIiIiIqIQcDofERERERH9v/brWAAAAABgkL/1GPaXRQwSBQAAMEgUAADAIFEAAACDRAEAAAwSBQAAMEgUAADAIFEAAACDRAEAAAwBtLGLldOIiCIAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot(mu_sims, S1_sims, linestyle=\"\", marker=\"o\", markersize=3.5, color=\"black\", label=\"realizations at $\\mu$\")\n", "plt.plot(mu_arr, l_mu_one_res, linestyle=\":\", color=\"black\", label=\"one realization of stochastic process\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-synthetic likelihood\")\n", "plt.legend()\n", "plt.savefig(dir+'stochastic_process_realization.pdf',dpi=300,bbox_inches=\"tight\",transparent=True)\n", "plt.savefig(dir+'stochastic_process_realization.png',dpi=300,bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean and quantiles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean and quantiles of the stochastic process can be obtained using the Percent Point Function (Inverse of the CDF)." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "g_m=ss.norm(0, sigma_g).ppf(0.1) # g value for the 0.1 quantile\n", "g_p=ss.norm(0, sigma_g).ppf(0.9) # g value for the 0.9 quantile\n", "g_0=ss.norm(0, sigma_g).ppf(0.5) # g value for the mean\n", "l_mu_m=neg_log_synthetic_likelihood(mu_arr, Phi_0, g_m, Nsamp)\n", "l_mu_p=neg_log_synthetic_likelihood(mu_arr, Phi_0, g_p, Nsamp)\n", "l_mu_0=neg_log_synthetic_likelihood(mu_arr, Phi_0, g_0, Nsamp)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot(mu_sims, S1_sims, linestyle=\"\", marker=\"o\", markersize=3.5, color=\"black\", label=\"realizations at $\\mu$\")\n", "plt.plot(mu_arr, l_mu_one_res, linestyle=\":\", color=\"black\", label=\"one realization of stochastic process\")\n", "plt.plot(mu_arr, l_mu_0, linestyle=\"-\", label=\"mean of stochastic process\")\n", "plt.fill_between(mu_arr, l_mu_m, l_mu_p, alpha=0.2, label=\"0.1 and 0.9 quantiles\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-synthetic likelihood\")\n", "plt.legend()\n", "plt.savefig(dir+'stochastic_process_quantiles.pdf',dpi=300,bbox_inches=\"tight\",transparent=True)\n", "plt.savefig(dir+'stochastic_process_quantiles.png',dpi=300,bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distribution of the maximum synthetic likelihood estimator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The randomness makes the maximum synthetic likelihood estimator $\\check{\\mu} = \\mathrm{argmax}_\\mu \\mathcal{L}_\\mathrm{s}^N(\\mu)$ a random variable: it depends on $g$ via $\\check{\\mu} = \\Phi_0 - g$, i.e.\n", "\\begin{equation}\n", "\\check{\\mu} \\sim \\mathcal{G}\\left( \\Phi_0, \\frac{1}{N \\times N_\\mathrm{samp}} \\right).\n", "\\end{equation}\n", "As expected, this randomness is reduced as $N$ increases." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def max_synthetic_likelihood(Phi_0, N):\n", " sigma_g=1/np.sqrt(N*Nsamp)\n", " return ss.norm(Phi_0, sigma_g)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(ymin,ymax)=(-10,700)\n", "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot([Phi_0,Phi_0],[0,ymax], linestyle=\"--\", color=\"black\", label=\"$\\Phi_0$\")\n", "plt.plot(mu_arr, -max_synthetic_likelihood(Phi_0, 2).logpdf(mu_arr), label=\"N=2\")\n", "plt.plot(mu_arr, -max_synthetic_likelihood(Phi_0, 10).logpdf(mu_arr), label=\"N=10\")\n", "plt.plot(mu_arr, -max_synthetic_likelihood(Phi_0, 100).logpdf(mu_arr), label=\"N=100\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-pdf of max synthetic likelihood estimator\")\n", "plt.legend(loc=\"best\")\n", "plt.savefig(dir+'distribution_max_synthetic_likelihood_estimator.pdf',dpi=300,bbox_inches=\"tight\",transparent=True)\n", "plt.savefig(dir+'distribution_max_synthetic_likelihood_estimator.png',dpi=300,bbox_inches=\"tight\")\n", "plt.show()" ] } ], "metadata": { "celltoolbar": "Initialization Cell", "kernelspec": { "display_name": "base", "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": "3.10.12" }, "toc": { "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }