{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:12:19.326534", "start_time": "2016-03-02T08:12:19.314282" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import re as re\n", "import pandas as pd\n", "import numpy as np\n", "import seaborn as sbn\n", "from scipy.stats import norm\n", "import matplotlib.pyplot as plt\n", "import warnings as warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "sbn.set_style('white')\n", "sbn.set_context('talk')\n", "\n", "np.random.seed(12345678)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Note: these are my personal opinions and I'm sure that lots of people would disagree with my assessment of available software packages.\n", "\n", "We have been working on getting under the hood of Metropolis-Hastings and Monte Carlo Markov Chain. But there are some very accessible Metropolis Markov Chain software packages out there. These are my personal views on what is available:\n", "\n", "1. Stata (`bayesianmh`)- just available in Stata 14. To be honest, I have never heard of anyone using Stata for Bayesian Sampling Methods although I haven't really looked.\n", "2. Matlab. There are numerous user and Matlab written routines. For example, there is a version of `emcee` that is implemented there (more on this later in the course). Matlab is for people who want to possibly tweak their own sampler code and who need the fastest possible computation.\n", "2. SAS. A decent set of packages, not used very much in the social sciences (maybe in the medical sciences??), but is well suited for big data.\n", "3. R. For a long time R was the de-facto standard and probably still is, with packages like R-stan which interfaces the `STAN` C Library. Also `Jags`, `Rbugs` and `Open BUGS` have been around for a long time. I almost elected to teach this course in R. \n", "4. Python. The libraries aren't as rich as R, but you might view Python as sitting between Matlab and R. Maybe (in my view probably) also easier to code your own samplers than R as I really prefer python syntax to R. Python is the used a lot in many fields including physics and is strong in the big-data arena, more so than any of the other packages mentioned above. The major players on python are:\n", " * PyMC and PyMC3 (in beta)\n", " * PyStan\n", " * EMCEE\n", " \n", "Today, we are going to focus on PyMC3, which is a very easy to use package now that we have a solid understanding of how posteriors are constructed. \n", "\n", "We will start with our very simple one parameter model and then move to slightly more complicated settings:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:15:41.573355", "start_time": "2016-03-02T08:15:41.171536" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAADctJREFUeJzt3X/sXXV9x/FnaYFRjOPHSAtrOpYF3iQzupFBgQxQNsc2xgSEyWj8AYphC9oYNWvciJIo7ZqwuG46jaFDQ9Fk4uqwRmBzPzAERA0bQfOGjZHA1qaBUhRaaVO6P87t8s23hX7P93Pb873vPh/JN3A/355z3yf3fl/ncz/3fD5n3p49e5AkTb4jhi5AkjQeBrokFWGgS1IRBrokFbFgqCeOiKOBs4BNwO6h6pCkCTIfOBl4ODNfnv7LwQKdLszvH/D5JWlSnQ98Z3rjkIG+CWD9+vUsXrx4wDIkaTJs3ryZ5cuXwyg/pxsy0HcDLF68mCVLlgxYhiRNnP0OU/ulqCQVYaBLUhEGuiQVYaBLUhEGuiQVYaBLUhEGuiQVYaBLUhFDTiySNGanrtw4622fWn3JGCvREOyhS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFdFr+dyIOBvYkJmnjB4fD6wDLgJeAG7OzNvGXqUk6YBm1EOPiHkRcR1wL3DUlF99AXgRWARcCayJiDeOvUpJ0gHNdMjlY8AK4FN7GyLidcBlwMcz86eZ+V3gTuD6sVcpSTqgmQ65rANuAS6c0nYasCszn5zSlsAVY6pN0iHk3Y4m34wCPTM3AUTE1OZjgR3T/ul2YOFYKpMk9dJylct24JhpbQvpxtQlSYdYS6A/ARwZEUuntAXww7aSJEmzMetAz8yfAF8HVkXEwog4C7gGWD+u4iRJM9c6seh64EjgGeAu4KOZ+VBzVZKk3npNLMrMfwF+bsrjrcAfjLkmSdIsOPVfkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpCANdkoow0CWpiAWtO4iI84C1wOnAJuDmzLyzdb+SpH6aeugRMR/YAKzOzNcD7wO+GBGnjqE2SVIPrUMuxwEnAQsiYh7wCrAT2N1amCSpn6Yhl8x8LiI+C3wZuIPuBPHezHx6HMVJQzl15cZZb/vU6ksGe24d3lqHXI4AtgNXAQuBS4FPR8SbxlCbJKmH1iGXK4BlmfnVzNyZmRuBjcC72kuTJPXRGuhLgaOnte0a/UiSDqHWyxbvA1ZFxLXA7cAFwOXARY37lST11NRDz8xHgSuBFcALwGeAd2fm98ZQmySph+aJRZl5N3D3GGqRJDVw6r8kFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRBrokFWGgS1IRzYtzaTIMdUu11tuptd7OTTqc2EOXpCIMdEkqwkCXpCIMdEkqwkCXpCIMdEkqwkCXpCIMdEkqwkCXpCIMdEkqwkCXpCIMdEkqwkCXpCIMdEkqonn53IhYAnwOuAD4MbAmM9e27leS1E9TDz0i5gEbgB8BJwIXA5+IiPPGUJskqYfWHvoy4BRgZWbuBh6LiHOBZ5srkyT10jqGfibwGLAmIjZHxOPAOZn5XHtpkqQ+WnvoJwBvAb4NLAV+DfhWRDyZmfe3Fie13sJO9Q11e8W5qDXQXwa2Zuaq0eMHIuIu4G2AgS5Jh1DrkEsCx0bE1BPDfGBe434lST219tDvA54HVkfESuBs4HLgra2FSZL6aeqhZ+YO4M3AG4AtwJ3ABzPzwfbSJEl9NE8sysz/BH57DLVIkho49V+SijDQJakIA12SijDQJakIA12SijDQJakIA12SijDQJakIA12SijDQJakIA12SijDQJakIA12SimhebVH9eLssVeT7em6why5JRRjoklSEgS5JRRjoklSEgS5JRRjoklSEgS5JRRjoklSEgS5JRRjoklSEgS5JRRjoklSEgS5JRRjoklTE2AI9IhZFxJaI+L1x7VOSNHPj7KHfBpw4xv1JknoYS6BHxA3AS8DT49ifJKm/5jsWRcRpwIeBZcAPmiua41ruzKLDg+8RDaWphx4RC4A7gBWZuXU8JUmSZqN1yOUm4JHM/OY4ipEkzV5roL8DuDoitkXENmAp8JWIWNlemiSpj6Yx9Mw8Y+rjiHgKuDEzv9GyX0lSf04skqQimq9ymSozTx3n/iRJM2cPXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqYixLs6lmrylmqpqeW8/tfqSMVYyHvbQJakIA12SijDQJakIA12SijDQJakIA12SijDQJakIA12SijDQJakIA12SijDQJakIA12SijDQJakIA12SimhePjcifh24FTgDeBZYk5mfb92vJKmfph56RBwP/AOwFjgeuApYFRG/OYbaJEk9tPbQfwHYmJnrR49/EBH/DJwH/GPjviVJPTQFemY+Arxz7+NRj/184EuNdUmSehrbLegi4meBu4Hvj/6rMfNWcKpoUt/Xc/H2dWO5yiUifhF4ANgKXJGZr4xjv5KkmWsO9Ig4E3gIuAe4LDN3NFclSeqtacglIhYB3wJuzcw/H09JkqTZaB1Dfy9wEnBTRNw0pf0vM/NPG/ctSeqh9SqXW4BbxlSLJKmBU/8lqQgDXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqQgDXZKKMNAlqYix3YLuUJuLt3+SpCHZQ5ekIgx0SSrCQJekIgx0SSrCQJekIgx0SSrCQJekIgx0SSrCQJekIgx0SSrCQJekIgx0SSrCQJekIgx0SSqiefnciPhV4PPALwNPADdk5oOt+5Uk9dPUQ4+InwHuBv4WOA5YC3wtIo4aQ22SpB5ah1zeArySmX+Tmbsycx3wHHBpe2mSpD5ah1zOAH44rS3phl/uOsC28wE2b948u2d+aevstgOeeeaZWW/b8rySBLPPoCl5OX9/v28N9GOB7dPatgMLZ7DtyQDLly+f1RMfPautOr9x7ydnvW3L80oStGXQyMnAf01vbA307cAx09oWAi/OYNuHgfOBTcDuxjok6XAwny7MH97fL1sD/UfAjdPaArjzQBtm5svAdxqfX5ION/v0zPdqDfRvA0dHxAeAzwHvBBYB9zTuV5LUU9NVLqNe9u8AfwhsBT4A/H5mvjSG2iRJPczbs2fP0DVIksbAqf+SVISBLklFGOiSVISBLklFNK+2eKhExCLgUeC6zPzG0PX0FRFL6C7tvAD4MbAmM9cOW1V/EXEe3SJsp9NNCrs5Mw8472CuiIizgQ2Zecro8fHAOuAi4AW647ltwBJnZD/HsQT4a7rJeruAvwM+MroSbc6afhxT2o8A/gn4fmZ+ZJDietjP63EUcCvdFYDzgL8H/jgzdx7MOiaph34bcOLQRcxGRMwDNtBNxDoRuBj4xCgcJ0ZEzKc7jtWZ+XrgfcAXI+LUQQubgYiYFxHXAfcCU1cD/QLdzOZFwJXAmoh44wAlzshrHMcdwDPAzwO/ApwF3HToK5yZ1ziOvT5M1/mZ017jOFbRrWl1OnDa6P8P+olpIgI9Im4AXgKeHrqWWVoGnAKsHK1K+RhwLt1CZpPkOOAkYMHoJPUKsJPJWLrhY8AK4FN7GyLidcBlwMcz86eZ+V26Wc7XD1PijOzvOI6i+/v45Og4NgPrgbncYdjnOPYanVCvpevVznX7ez2OBN4P3JiZWzNzK/B2utfkoJrzgR4Rp9Gdrf9o6FoanAk8Rtf72xwRjwPnZOZzA9fVy6jezwJfpvtYfz/dm3YSTrTr6HquU9fAOA3YlZlPTmnbu1roXLXPcWTmzsy8ZBTke10K/PuhLq6H/b0eRMTRwJfoAnEma0IN7dXeVwuAZRHxRET8D/Ah4H8PdjFzOtAjYgHdR8kVo7PcpDqBbu34Z4GlwHuAv4qI84csqq/RuOZ24Cq6RdguBT4dEW8atLAZyMxNmTl9Ft2xwI5pbTNdLXQQr3Ic/280BLCWbmnrVYeusn5e4zhWAfdk5kSs8/Qqx3EC3fDLpXRDX+cAvwX8ycGuZ04HOt0Y4COZ+c2hC2n0MrA1M1eNelMP0K0X/7aB6+rrCmBZZn51dBwbgY3Auwaua7ZaVgudcyLiGLovQy8GLszMLQOX1EtEXET35fScHfufoZfpsvXPMnPb6BPsX9AN7x1Ucz3Q3wFcHRHbImIbXe/2KxGxcuC6+krg2NEnjr3m0337PUmWsu+S8LtGP5PoCeDIiFg6pS3Y96Ytc15EnAD8K13v8NzM/O+BS5qNq4FfAraM/t6vAW6MiEm7qu0Juu+XjpvSdkj+3uf0ZYuZecbUxxHxFN2Y7aS9wPcBzwOrRyejs4HLgbcOWlV/9wGrIuJa4Ha6qxAup+tVTZzM/ElEfJ3umK6nGzu/BvjdYSvrZ/QF9deAzcDbM3MiT7CZ+X66sXMAIuJ24NlJuGxxqszcFhEbgFsi4jK6ob0P0Q0fH1RzvYdeQmbuAN4MvAHYQnclxQcz88Eh6+orMx+lu7RvBd01258B3p2Z3xu0sDbXA0fSXfJ3F/DRzHxo2JJ6Oxe4kK6D8HxEvDj6+beB6zqcvQd4nO7T3n/QdYZuPdhP6mqLklSEPXRJKsJAl6QiDHRJKsJAl6QiDHRJKsJAl6QiDHRJKsJAl6Qi/g/xkhOY1cKyEAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigma = 3 # Note this is the std of our data\n", "data = norm(10,sigma).rvs(100)\n", "mu_prior = 8\n", "sigma_prior = 1.5 # Note this is our prior on the std of mu\n", "\n", "plt.hist(data,bins=20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PyMC3\n", "\n", "Let's use PyMC3 to model this:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:15:48.951819", "start_time": "2016-03-02T08:15:48.631621" } }, "outputs": [], "source": [ "import pymc3 as pm3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the model statement describing priors and the likelihood. Here, `mu` is defined as a stochastic variable (we want a chain of sampled values for this variable) and we provide a prior distribution and hyper-parameters for it. The likelihood function is chosen to be Normal, with one parameter to be estimated (`mu`), and we use known $\\sigma$ (denoted as `sigma`). Our \"dependent variable\" is given by `observed=data`, where `data` is generated above and shown in the histogram. In more formal terms, the code below sets up a `basic_model` having the following form:\n", "\n", "\\begin{align}\n", "Prob(\\mu|\\sigma,\\mathbf{data}) \\propto& Prob(\\mathbf{data}|\\mu,\\sigma) \\times Prob(\\mu | \\mu^0_\\mu, \\sigma^0_\\mu) \\\\\n", "Prob(\\mu|\\sigma,\\mathbf{data}) \\propto& \\phi \\left( \\frac{\\mathbf{data} - \\mu}{\\sigma} \\right ) \\times \\phi \\left(\\frac{\\mu - \\mu^0_\\mu}{\\sigma^0_\\mu} \\right ) \\\\\n", "Prob(\\mu|\\sigma,\\mathbf{data}) \\propto& \\phi \\left( \\frac{\\mathbf{data} - \\mu}{3} \\right ) \\times \\phi \\left(\\frac{\\mu - 8}{1.5} \\right ) \n", "\\end{align}\n", "where $\\phi(.)$ is the standard normal pdf. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:26:56.419275", "start_time": "2016-03-02T08:26:47.094910" } }, "outputs": [], "source": [ "basic_model = pm3.Model()\n", "\n", "with basic_model:\n", "\n", " # Priors for unknown model parameters\n", " mu = pm3.Normal('Mean of Data',mu_prior,sigma_prior)\n", " \n", " # Likelihood (sampling distribution) of observations\n", " data_in = pm3.Normal('Y_obs', mu=mu, sd=sigma, observed=data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This defines how the chain will be constructed. We will set startvals at MAP and use a Metropolis step method (which is Random Walk MH that we have studied)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:27:33.174483", "start_time": "2016-03-02T08:27:03.942212" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "logp = -290.67, ||grad|| = 31.153: 100%|██████████| 4/4 [00:00<00:00, 1041.61it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "{'Mean of Data': array(10.69594596)}\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Multiprocess sampling (2 chains in 2 jobs)\n", "Metropolis: [Mean of Data]\n", "100%|██████████| 10500/10500 [00:01<00:00, 5803.08it/s]\n", "The number of effective samples is smaller than 25% for some parameters.\n" ] } ], "source": [ "chain_length = 10000 \n", "\n", "with basic_model:\n", " # obtain starting values via MAP\n", " startvals = pm3.find_MAP(model=basic_model)\n", " print(startvals)\n", " # instantiate sampler\n", " step = pm3.Metropolis() \n", "\n", " # draw 5000 posterior samples\n", " trace = pm3.sample(chain_length, step=step, start=startvals) " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:28:01.191964", "start_time": "2016-03-02T08:28:00.413725" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm3.traceplot(trace,figsize=(20,5));" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:28:03.719675", "start_time": "2016-03-02T08:28:03.710601" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
meansdmc_errorhpd_2.5hpd_97.5n_effRhat
Mean of Data10.6949320.3001450.0050510.12713811.2977214101.01.000226
\n", "
" ], "text/plain": [ " mean sd mc_error hpd_2.5 hpd_97.5 n_eff \\\n", "Mean of Data 10.694932 0.300145 0.00505 10.127138 11.297721 4101.0 \n", "\n", " Rhat \n", "Mean of Data 1.000226 " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm3.summary(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Understanding the PyMC3 Results Object\n", "\n", "All the results are contained in the `trace` variable. This is a pymc3 results object. It contains some information that we might want to extract at times. Varnames tells us all the variable names setup in our model." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2016-02-25T10:04:48.196169", "start_time": "2016-02-25T10:04:48.191151" } }, "outputs": [ { "data": { "text/plain": [ "['Mean of Data']" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trace.varnames" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the variable names, we can extract chain values for each variable:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:28:50.513858", "start_time": "2016-03-02T08:28:50.507305" } }, "outputs": [ { "data": { "text/plain": [ "array([10.47837212, 10.47837212, 10.47837212, ..., 10.99946804,\n", " 10.99946804, 10.56559062])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trace['Mean of Data']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So for each variable, we have an array of values, which is our chain.\n", "\n", "## Diagnostics\n", "\n", "### Autocorrelation Plots" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:28:57.707829", "start_time": "2016-03-02T08:28:57.298767" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm3.plots.autocorrplot(trace,figsize=(17,5));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Acceptance Rate" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:28:59.732848", "start_time": "2016-03-02T08:28:59.723573" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Acceptance Rate: 0.3402\n" ] } ], "source": [ "accept = np.sum(trace['Mean of Data'][1:] != trace['Mean of Data'][:-1])\n", "print(\"Acceptance Rate: \", accept/trace['Mean of Data'].shape[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Geweke Score" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:29:07.296047", "start_time": "2016-03-02T08:29:07.269815" } }, "outputs": [ { "data": { "text/plain": [ "{0: {'Mean of Data': array([[ 0.00000000e+00, 3.98089881e-02],\n", " [ 2.63000000e+02, 3.62035946e-02],\n", " [ 5.26000000e+02, -2.17552281e-02],\n", " [ 7.89000000e+02, -4.24670150e-02],\n", " [ 1.05200000e+03, -3.11835563e-02],\n", " [ 1.31500000e+03, 1.68953273e-02],\n", " [ 1.57800000e+03, -4.88126007e-02],\n", " [ 1.84100000e+03, -3.36627389e-02],\n", " [ 2.10400000e+03, -1.12498869e-01],\n", " [ 2.36700000e+03, -9.30590373e-02],\n", " [ 2.63000000e+03, -5.75132684e-02],\n", " [ 2.89300000e+03, -7.35140470e-02],\n", " [ 3.15600000e+03, -4.69262730e-02],\n", " [ 3.41900000e+03, 2.63093107e-02],\n", " [ 3.68200000e+03, 7.54162558e-02],\n", " [ 3.94500000e+03, 1.94482040e-02],\n", " [ 4.20800000e+03, -1.93971697e-02],\n", " [ 4.47100000e+03, -4.05472731e-02],\n", " [ 4.73400000e+03, 7.72650011e-02],\n", " [ 4.99700000e+03, 1.40478948e-01]])},\n", " 1: {'Mean of Data': array([[ 0.00000000e+00, 5.70312640e-04],\n", " [ 2.63000000e+02, 1.85112715e-02],\n", " [ 5.26000000e+02, -2.74031618e-02],\n", " [ 7.89000000e+02, 4.82398836e-02],\n", " [ 1.05200000e+03, 9.18104690e-02],\n", " [ 1.31500000e+03, 8.91433530e-02],\n", " [ 1.57800000e+03, 1.02104854e-02],\n", " [ 1.84100000e+03, -4.78043809e-02],\n", " [ 2.10400000e+03, -6.67302844e-03],\n", " [ 2.36700000e+03, -7.82674713e-03],\n", " [ 2.63000000e+03, 4.37846176e-02],\n", " [ 2.89300000e+03, 9.97546903e-02],\n", " [ 3.15600000e+03, 1.31289828e-01],\n", " [ 3.41900000e+03, 3.92879936e-02],\n", " [ 3.68200000e+03, 2.38198177e-02],\n", " [ 3.94500000e+03, -3.02272942e-02],\n", " [ 4.20800000e+03, -2.16042161e-02],\n", " [ 4.47100000e+03, -4.52155240e-02],\n", " [ 4.73400000e+03, -3.60629631e-02],\n", " [ 4.99700000e+03, 6.10076770e-02]])}}" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "score=pm3.geweke(trace, first=0.1, last=0.5, intervals=20)\n", "score" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:29:09.089163", "start_time": "2016-03-02T08:29:08.725198" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "score=pm3.geweke(trace, first=0.1, last=0.5, intervals=20)\n", "plt.scatter(score[0]['Mean of Data'][:,0],score[0]['Mean of Data'][:,1], marker = 'o', s=100)\n", "plt.axhline(-1.98, c='r')\n", "plt.axhline(1.98, c='r')\n", "plt.ylim(-2.5,2.5)\n", "plt.xlim(0-10,.5*trace['Mean of Data'].shape[0]/2+10)\n", "plt.title('Geweke Plot Comparing first 10% and Slices of the Last 50% of Chain\\nDifference in Mean Z score')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gelmen-Rubin \n", "\n", "For GR, we need multiple chains in order to test if each of the chains collapse to the limiting distribution which is our posterior. PyMC3 makes it very easy to generate these." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:30:26.899641", "start_time": "2016-03-02T08:29:30.476472" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "logp = -290.67, ||grad|| = 31.153: 100%|██████████| 4/4 [00:00<00:00, 1067.66it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "{'Mean of Data': array(10.69594596)}\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Multiprocess sampling (2 chains in 2 jobs)\n", "Metropolis: [Mean of Data]\n", "100%|██████████| 100500/100500 [00:17<00:00, 5815.33it/s]\n", "The number of effective samples is smaller than 25% for some parameters.\n" ] } ], "source": [ "chain_length = 100000 \n", "\n", "with basic_model:\n", " # obtain starting values via MAP\n", " startvals = pm3.find_MAP(model=basic_model)\n", " print(startvals)\n", " # instantiate sampler\n", " step = pm3.Metropolis() \n", "\n", " # draw 5000 posterior samples\n", " trace = pm3.sample(chain_length, step=step, start=startvals, njobs=2)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:31:09.839336", "start_time": "2016-03-02T08:30:59.876091" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABZgAAAFgCAYAAAA2IxyjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzs3Xd4XGeZ8P/vqMu23B07iSEsSziEFBIggSwECATYBQKhBVja0vsGwi6BAO/SwvKDhZewEMoueZdAYENNSHPixHFix92xbKsd9ToaTe99zvn9cUbSaDS9S74/16VL0syZcx6Nppy5n/u5b5Ou6wghhBBCCCGEEEIIIYQQxWqq9wCEEEIIIYQQQgghhBBCrEwSYBZCCCGEEEIIIYQQQghREgkwCyGEEEIIIYQQQgghhCiJBJiFEEIIIYQQQgghhBBClEQCzEIIIYQQQgghhBBCCCFKIgFmIYQQQgghhBBCCCGEECVpqfcAhBBiJVAUZRw4D/iWqqpfzXD9e4E7gMOqqr64tqMrnqIo24C7gL8DelVVfUGGbcYx/uZ5ccAFPAF8VVXV/iKP+VzgfFVV7ylx2EIIIYQQYoWS82lAzqeFEKuUZDALIUThYsA7slz3j4Bew7GU64PAS4CrgGtzbPdj4Ozk1/nA24FNwEFFUS4u8pj3A1cWP1QhhBBCCLFKyPm0nE8LIVYhyWAWQojCPQy8XlGUy1RVPTF/YTJ74VUYmQgd9RpckTYCFlVVj+bZLqCqqiXl93FFUV4PHAV+ArysiGOaihyjEEIIIYRYXeR8Ws6nhRCrkASYhRCicD0YS9zeAZxIufztwBFgHHjO/IWKorQBXwfeA2wGVOD/U1X1rpRt3gB8CXge0AqMAN9RVfWO5PX/A7Ql9/0BYA1wGPiMqqpqtoEqivI64CvAxUAY+Cvwr6qqOhVF2Qu8PLmdDnxAVdX/KfROUFU1rCjKfwI/VxTl6aqqTiqKsgH4d4zsjR2AD3gU+JSqqtaU5YE3KYryTlVVn5HvNoWORwghhBBCrBhyPo2cTwshVh8pkSGEEMX5HcuX9f0j8NsM2/4P8EaM5XOXAD8HblcU5WMAiqJcCtwDPJC8/vkYmQy/VBRlZ8p+3go8HbgGeBPGSfdPsw1QUZQ3A/cBjwEvBN6JsZTuUUVRWoC3YCzVm8ZYqndXll3l0p38fkny+//DyL54J/AsjJP3qzE+EABcnjzej5M/F3IbIYQQQgix+sj5tEHOp4UQq4ZkMAshRHF+B9yiKMqLVFU9rCjK0zFO8K4DrpjfSFGUZwHvAq5SVXV/8uIRRVGeCXwR4+RYA25UVfXWlNt9C3gfcAHGCSRACPiQqqqR5DY/Ab6RY4xfBHapqvrl5O+qoijvwjiJvVZV1b8oihIAEmnL9YrhSn7fkPz+CHCLqqrHk79PKIpyPckTZlVVbYqiJDCWCNoKuY0QQgghhFiV5HzaIOfTQohVQwLMQghRBFVVxxRFOYyRdXEY46R3t6qqdkVRUje9LPn9oeSyuXktQLuiKJ2qqp5SFMWhKMq/YJwA/y1waXK75pTbjM2fDCd5MJb5ZXMJaVkLqqqeVBTFjbF08C+F/K15zJ8Iu5Pffwa8TlGU/8D4O54DPBsjgySbUm4jhBBCCCFWMDmfXiDn00KIVUNKZAghRPF+B7xdURQTxgnxnRm2mX99fRXGSe7810UY3aMjiqK8DBjCWNbWD3wHY9leukiGy0rRXMF9vSD5/YSiKE0YSxN/gdH5+y8YHxh+l+3GpdxGCCGEEEKsGnI+LefTQohVRDKYhRCieL8HfgB8CKPW2T0Ztjmd/H6uqqqH5i9UFOVG4HxVVT+RzLQ4oqrqG1Oun/+5nA7RpzBOsr+Tst/LgC6gt4z9zu+rFfgk8IiqqmZFUZ4PvAG4WlXVvSnbXQDEU26amnlyaYG3EUIIIYQQq4+cT8v5tBBiFZEAsxBCFElV1dlk5+jvA39RVTWYYZs+RVH+Cvw4udTvBEY2xXeAryU3mwSuVxTlFcAY8CLgh8nr2ssY4neAPyuKcgtwB7AT+E+ME+VdRe5rraIoO5I/t2EsufsKRpOUdyYvn8U4ib1eUZRJjBPvGzCarJxM2ZcPOF9RlHOLuI0QQgghhFhl5HxazqeFEKuLlMgQQojS/A5YT+Zu1/PeibHc71aMJXufB25SVfXbyev/D7AXYznbaeCm5Nc4xslxSVRV/QtGp+x/wDgJ/i2wD3ilqqrRInf3aYyT11lgAKPOWz/wQlVV+5PHmwXeA7wS6MPouN0C3AwoiqLM15f7fnKbU4CtwNsIIYQQQojVSc6n5XxaCLFKmHRdz7+VEEIIIYQQQgghhBBCCJFGMpiFEEIIIYQQQgghhBBClEQCzEIIIYQQQgghhBBCCCFKIk3+hBBCCCGEaDCKolwB3K2q6jnJ33cCPwauAmLAH4B/UVU1kuG2lwE/By4EhoCPq6p6qFZjF0IIIYQQZ5ZVFWBWFKUduByjeH6izsMRQgghhBCNoxk4GziaKSjbKBRFMQEfAH4AxFOu+g3QA5wLbATuBr4KfCXt9h3AvcAtwH8D7wX+rCjKMwppTCXn00IIIYQQIous59OrKsCMcTK8r96DEEIIIYQQDesqYH+9B5HDzcD1GAHimwAURWkDAsC3VFUNAxZFUe4E3pzh9lcDmqqqP03+fruiKJ8DrgX+VMDx5XxaCCGEEELksux8erUFmGcB7rzzTnbs2FHvsQghhBBCiAZhsVh497vfDcnzxQZ2O/Bt4OXzFyQzj1+ftt21wMkMt38O0Jd2mYpRLqOQALOcTwshhBBCiGVynU+vtgBzAmDHjh3s3Lmz3mMRQgghhBCNp6HLPqiqOgugKErG65MlNG7FCCS/J8Mma4Fg2mVBYE2BQ5DzaSGEEEIIkcuy8+nVFmAWQgghhBBiVVIUpRP4NXAx8HJVVa0ZNgsCnWmXrQH8VR6eEEIIIYQ4QzXVewBCCCGEEEKI3BRF2Qw8DmwGrlRVdSzLpv1AevqzwvKyGUIIIYQQQlSEZDALIYQQQgjRwJJlMf4MWIC3qqoay7H5HqBdUZTPAD8D3gtsBx6q+kCFEEIIIcQZSTKYhRBCCCGEaGxXYjT9ezXgUhTFn/x6AkBRlHcritILoKpqBPgH4F2AE/gM8EZVVQP1GboQQgghhFjtJINZCCGEEEKIBqOq6l5ga/LnA4Apx7Z3Anem/H4K+LsqD1EIIYQQQghAMpiFEEIIIYQQQgghhBBClEgCzEIIIYQQQgghhBBCCCFKIgFmIYQQQgghhBBCCCGEECWpS4BZUZQrFEUxF7DdqxRF0RRFWVeLcQkhhBBCCCGEEEIIIYQoXE2b/CmKYgI+APwAiOfZdhNwOzkamgghhBBCCCGEEEKICtJ147tJwjFCiMLUOoP5ZuAG4JYCtr0N+N/qDkcIIc5Muq4z4w5xeNTBH49Pc+9JM8Foznk/IYQQQgghxGqnaTD0MAztXgw0CyFEHjXNYMbISP428PJcGymK8m5gE/Al4As1GJcQQpwxDo06+Npfexmw+JZc3tXRwpsvO5f3vvg8zt/eVafRCSGEEEIIIerGPweR5OeEgB3WbavveIQQK0JNM5hVVZ1VVTXnFJiiKE8Dvgl8sDajEkKIM4PVG+aG/z3BO39xaElweeOaVlqaTPjCce44OMHf37qPOw9P1HGkQgghhBCiHmIJDV2yVs9wepafRdV5zWDpMbLIhVhhap3BnFOyRvOvgC+rqmpWFOUZdR6SEEKsCqrFx3t/eRirLwLAReeu5+Z/uICLd26gq6MVqy/MH45Nc+ehCcyeMF/+Sw8j1gBffv0FNDdJ7TUhhBBCiNXOG47x2ICVszd0csXfbK73cIQ480wcML63tMPW8+s7FiGKVOsazPk8DbgS+KmiKG7gVPLyaUVRXlq/YQkhxMp1fMLJ2392AKsvwtq2Zr553UXc86mX8nfP2kpXRysAZ3V18Kmrn8Wuz72Mq87fCsDtT47x0TuOEYkn6jl8IYQQQghRA8fGnQDMekJ1HokQZ7igs94jEKJoDRVgVlV1UlXVTlVVN6qquhG4JHnVTlVV99dzbEIIsRI9Pmjj3f99GG84zua1bfzuoy/mvS8+L2tW8vqOVv7fP13Oe198HgCPDlj53F3dJDRZHieEEEIUIxxL4AnF6j0MUQUTjgDDVl/+DVeY9pbmeg9BCLHaBeww9oQE0VehhggwK4ryM0VRflbvcQghxGpyaNTBR+84Rjimcc6GDv7w8Su5ZOfGvLdraW7im9ddxD+/yliW9cBpC1+9p0fq8QkhhBAF0nWdh3ot7FWtEmReZcKxBN1TbnrNXuz+SL2HI4QQK8voXvBbYWRPvUciKqwuNZhVVd0LbE35/eNZthsHpPinEEIUqWfGw4d/dYxIXGPnpk5+/7ErOWdjZ1H7+Nw15+MORrnj4AS/PTzJlrVtfP41SpVGLIQQQqwe8ZSVPxZPmA2drXUcjaikaGKx+VYwkoB1dRyMEEII0SAaIoNZCCFE5YzY/Lzv9iP4I3G2dbVz54dfVHRwGcBkMvG1ay/kDZecDcB/7hnmLyemKz1cIYQQQgghhDhjTLuCOGQFhFhl6pLBLIQQogqs/fjGj7P74YN8NjKHt2MTr3/DezhvU0fJu2xqMvGD6y/F7o9waNTJTX86zTO3ruN5T8tfakMIIYQQQgghxCKrL8zxCRcA115yDk1ZeuMIsdJIgFkIIVY6mwp7vgn999IFfBwWX93/8nvYtRkueQe84ovQWXxguK2lidve/QLe+OP9TLtCfPTXx7j30y/lrPWlB66FEEIIIYQQoiTxCHimYcNOaGmv92iK4gxEF37WdJ2mRqgK65mBRAQ2P7PeIxErmJTIEEKIlSoehftuhNteDP33AuDV19CvPZ257VfBhqcb24WccPin8OMXQvdvQdNy7DSzzWvb+K/3vZDO1mbmvBE+9pvjhGOJSv41QgghhBCijhogzCVEYSaeBPMJGN9X75GsfPEITB6EmacgYK/3aMQKJgFmIYRYieJR+MM/wbFfgq7hbT+bG6Mf59LIL3joZX9i+yfug8+egk8fg5d/EVo6IWCDuz8Bv3kzBBxFH/KCs9fzg+ufB8CJSTdfubsHXdfz3EoIIYQQjc4TjHFg2I7VF673UIQQIr+g0/gectd3HKtBPKUWdNhTnWO4Jhb/Z2LVkgCzEEKsNPEI/P69oN4PgPm5H+EK73f4s/YyXv+8ndzwqvON7Uwm2Ho+XP0l+NRheM4bjMtH98IvXgGzJ4s+9D9cfDb/nNz/H49Pc/uT4+X/PUIIIYSoqyeGbNj8EQ6OFD8BfSZzBCJMOAL1HoYQQjQuzzRMH4WRPfUeiagyCTALIcRKoiXg9++HwV0ABF78ed40+FrCeivP3r6O7771EkymDAscN50H77wTrvspNLeDZxJ++Ro4/ceih/DZV53Pay/cDsAt9/exb8hW1p8khBBCiPrSZEVSSSadQbqn3My4Q/UeyhlN0yr/+LV4wuzqmWXKGaz4voXIK9PnuZXKP1fR3UXiCSYcAaLx4ss+iuqSALMQQqwk+38Agw8CoL38i3x48jXY/FHWtDVz27ufT2dbc+7bX/qP8MFdsH4nxMPwpw/B49+DIj5YNjWZ+MH1l6Js70LT4dO/PSEn30IIIYQ4Yzn90fwbiao4MGzn4T4LkXhle4McHnMQiWs8Nemq6H5FFazGCbJErN4jaFgHRhx0T7k5Oi4lNxqNBJiFEGKlmDwMj/278fNl7+Un2ts4OGosZf33t1zMs87qKmw/5z4fProXnvYi4/fHvgX3fLqoE5m17S381/teyIbOVjyhGJ+88ylp+ieEEEIIIWpG03Rs/giRuMaoTUqVnLH81nqPoDJSayH7Zus3jgbnDRmfWe3+SJ4tRa1JgFkIIVaCkBv+9GHQE7D12Qy94Kv8aM8QAO+64mm86dJzi9vfum3wvr/ChW82fu/+DfzmrUU1ynj6ljX88J2XYjLB6RkPX7+3t7gxCCGEEEIIIZaLS1Z8wbR4vUdQGasxE1ucUSTALIQQK8F9nzXqJje3k3jLL/nCX4eJJXTO2dDBl1//3NL22doBb70dXvJZ4/exx+H2vwf3ZMG7uFo5i8+80mj697sjU/z+2FRpYxFCCCGEEKJWnGNg7m7MoJ5zDPr/CnN99R6JEEIUTALMQgjR6AYfht6/GD+/5pvcMdbFiUkj0/iWt1zMuvaW0vfd1ASv/jpceyuYmsHWD/99DUwfK3gXN7zqfF727G0AfPXuHnpmPKWPRwghhEil1a6JT0LTcfgj6GUGnEpuONaIgS4hVquZ4+AYBudovUey3Mxx47tVAszCoGk6p6bdDdP3Ztjq5/Cog3hCGu2JRRJgFkKIRhYLw4NfMH5++pVMPes9fHeXCsCbLzuXq5WzKnOcF/wTvPv30NZldPq9/e/h0E8L+rDb3GTi1ndcyrkbO4nENT5x53E8QWlMIYQQokwht5HFNx9sqbIjY072D9vpNXtL3sfQnI8Hemax+YqoDanrMLIHhh6uaUBdiFXH2m8kZkSLqMcc8VVvPEJUyIjNz5g90DBNJ3vNHizeMINz/noPZcVbTX2MJMAshBCN7MB/gmsMTE3o//Bdbr67h1AswZa1bXz1DSWWxsjmWdfAhx6Czc8ELQa7vgh3vQdC+U9kNq1t46fveT5tzU1MOUN89q4TpWdwCSGEEGAElrW4sVy8Bqy+MGB8kC9V36yXhKYX190+7IGg0wh0eadLPraojHyZ7KYaj2elcwej7OqxMGytQSBqrhci3qJW4lXd9HEYeQy0lRREkkd5o/FFGrPOdGgVBUfroWfGw0O9Fsbsq6NJqQSYhRCiUbknYd/3jZ8v/wh/Nm9m35AdgH9744VsXttW+WNuvxA++jg89zrj94H74LYrYfChvDe9ZOdGvvbGCwF4TLXxk8eGKz8+IYQQZ44zpmREyt95JvzNsVBDB9uOjRuZ7D0zpWeyA0TjGoNzPnzhM3tV16FRJ5F4gl5zdUuoLXnqJBqkQV48aiSKBB1VmyiThA4haswxAuYTFXm/np/QPjXtLntfjUACzEII0age+jLEQ7BmK/bL/4Vv3GfUYbvmgrO49pKzq3fcjvXw9v+B1/0HtHSAbxZ+ez3c/SkjwyqHd13xNN72gp0A/OCRQZ4YtFVvnEIIIYRYWUIuGLi/oInrerF4jUz2UXt5Gbcnp930z3rZM2CtxLBWrPgZXfYlJQClVT4DNRCJs6vXwrFiVkwIIUqn60Zw2TFiTB6JJSTALIQQjWjykFF3EuCar/Fvu6fxhGKsa2/hm9ddhMlU5aVrJhNc8RH4+H7YeYVxWfdv4EeXwpM/MmpDZ7yZiW9ddxHPPXs9ug43/O8Jpl2N0YxCCCGEiMY1Rm1+QtHGzaCtmbAHZp6qbQ1a26DxPVbauYHZHeLUtHtFNJYyu0OLvyTiZ0Z2uqipvlkvsYTGTOpjTaxg8hrR8FJfx4up9X6GkACzEEI0Gl2HR75m/Lz9Yh5uexX3n5oF4Euvew5nb+is3Vi2ng8f3AWv/ga0rjU+jO7+Kvz4hXDwNggvXz7a0drMz97zAtZ3tOAKxvjUnU8RicsHeSGEEFUUcsPwo+CeyrnZiUkXp2c8PD5Yx6zSoNPIfqp3wHFoNzhHa5NNHA0aNbVD5WVaHh13MmYPlN9Yym81/gc10JSIGEkDw4/U5HiiUWV5vpeR4V3tl5C4puEKNki5EbGqjdj8nJ72ZK19L1YGCTALIUSjGdwFkwcB8L30Zm6+2yiNccXfbOZdlz+99uNpaoaX3AD//BS84ANgagbPFDz0JfjBBfDAv8LsySVnuU/fsob/+45LATg57eHr9/bVftxCCCHOHOP7jPILU4dzbjZf/iASr08GrM0XIaLuTi6xPYN6FUweNGrQVijjyxMqo66xrsPYE8b/wDNTkfHkstY/AbpmTNInFsskrJhASixUXCRzrg8mD5cVOD1juKeg7y81m+wo1sCsj8OjDsZXSQOyZQJ2mD1l1MqukZ4ZD6O2VXp/liIRIz62nzH1JKN2P7OezKtkxcogAWYhhGgkWgIe+brx83kv5ebTO7D7I3S2NvO9t11CU1Mduzp37YBrfwifPASXvQea2yHqhyO/gJ+/zGgG+OStxgd84FUXbOfTVz8LgN8enuSPx6frN3YhhBCrWzxSn+NGg2AfhkT+gKfFE+bAiJ3TM8lmZ77ZjNuN2vw8plrxRwqs2Rp01jRAUpLkuUEjiKWW1wg66jIGiyfMgz2Wxg/c+eaMmtljjxe2fSIO1j4jEcE9Xp0xzfWBa6I6+6628f2gPrj4ejF1eLGmawMKJ1cgqnNGGZ2hOR8Hhu1E6zRBVzZdX/paPboX7INGokwNzHpCjNj8S1+DznTWfnSPmY3uXsCoK75i2NQlk4YV0SgrnEokAWYhhGgkp+4CWz8ATz7zM9ybUhrjvC1r6zmyRdueDW/6CdzYB6/8Cmw8z7jc1g+7/w/84ELYdTN4pvncq5/NVedvBeDLfzlNn7m8juxCCCFWH38kzpExJ1ZfeZlLrmCUKWeQhFbDD2bDu2G2G6aPZt1kvm3CjHt53eFYQuPgiIMp5+J1p2c8eEMxjk8UEJT1mmFkDwzcV/TQz0Q9Mx4eOD2LJ1TfgPzhMQexhMbJaXddx5HXfOAtYC/wBinPvSz9OsrimTYC2NNHjaSMFJ2W7M/BhpCIgc9iZPE7R4u7rW8O+u6pe6Zz36wXmz+Caqlh3fZKmjhglKsJe5ZeHqhNyaRghtr/OsaEk2rxNcaqhiL6/LSHbWyc2FX84zlVtnr888+VOtA0nXF7AE+wgJUy9sElv5Z6/tEWccH0MeP93HyivPu0jiTALIQQjSIWhj23ABA5//V85olmAK585hbe86Lz6jmyzNZuhZf9K9xwEj6wC57/fmhdA7EAHPoJ/Oj5NJ/4Fbe+8zLO2dBBJK7xiTuPl7esVQghxKpzZMzBrCfEwZHysklHbH7mfGGGrWXW5y3GfDac11zSzYetflzBKHMZguvhWAH9C+bLbOhGRlwknmDfkI3BueoHgPyROJZyljOXeJ+VY8RmPDaGrQ2eOTwv5DJqZSczdm2+CHtVK1bvGbqMPLX3R0qAuS3ioNVf/XInmUTjGtOuYAFZqSmBJ73IDNbxfcZrTYNkOodXam8V36yRGTp7qt4jWeLwmIMBi5dJZwM2Rtd1mDoC5u5lV221H8GUiBjNYivJPbmY7V8Ho/YAJ6fd7C2kV0N88bV4zB7g/tOzSyaMC7XNdgBc44sX+OdyHzahYfNF0Go5oV4ACTALIUSjOPrf4J1GNzVxk+s6nIEoa9ua+W69S2PkYzLBeVfCG38En+uFV9wMa7ZAIgL33sDmR27ktnc8l9ZmExOOIDf98VRjzNALIYRoCL5w9iWmrmCUk9NuZj2hgvfnXkFNqSq91LzP7MUZiNI/W/0VQ4/2z3F4zMG0q8SgyMSByg6oYCvoHGTsCSPbMpkhf2DEjicU4+BofUp7lCI9o0/XdfYN2XhMtVYsONKk1SB5QdczZlQeHXdyfMLF0fHyGliK4iU0Da1enylmjoPldEV36Q41YHkI36wR8HUMQ6RGk7d1LoEzV+IE3qlpN7qu89Rk9UtCHR5zcmDETm+DrQ6WALMQQjSCsAf2/QcARza+nrunjXIY337LxTxt85p6jqw4azbDK26CzxyH819jXHbi11z6yLv45mt3ArCr18KfnqpPlokQQoiVodfs4diEc6Fe5ZGxMyV4U16wJByrTW3PeEq2pjRlqqICanuvNJ5QDGcgijcUy5i5XysOf4RBi5dQodm4U4eNjErn2JKL7X6j/rvNV9k68DZfmHFHoOEyFLNyT9Wkaea8hKZxctrD6Wl37YPMPovxOLCpZQddXQVOiNYt1Si1v4G+QjPXq2jcEWRXz2zNJ7bnX3dG7TVcsVUACTALIUQjSDbHize188+zrwXgU1f/LW+69Nw6D6xEnZvgXXfBK74EmMB8gneMf5VrlC0AfO2vvSUtHxJCCHEGiPiZGR8klpAPs0XTdbo8g3SEci+vLcew1c8DPZaq7V/UgNds1PusQ3PI1HhpPRe0jTkCeCNx1NkCy8l4ks2qZ44XcZTSw4ITziB2f4RxR73LuRTwTwp7jAD85EGj8WkNeEJxNF0npul4cqyCqYqUsgho5R273NJQefltYB9asU3jlolH2ODupS1S/VUcJi1uvFbmaOQ34QgQiWuLzXvPcBJgFkKIevNZ4OBtAPxX9LXMsZlXP3c7n3+1UueBlampCV7xRbj2VgBMo3v50aa72Ly2DX8kzo2/765tIyYhhBArw+AuNjtP0BpboY2kMokGafNPF197tUgdvjHW+4bY4jhWtWP0mj0rvtSVvpLKZFTDRLLe5+zyuqpnmmAhtc7L5A3HCJV4nEyN4RpOJOW1OlvTtkY2/3oWj4B9uPINKkNusA7UZ0XC2ONGs07nqFHSY2zfsgaZFafrJd+H5nwrYmaOs84/zjbboZL2X4xNzm7jtXLyYN5tA5HFIHR72Ab99y5b7XAmkACzEELUmb73OxAP4dbX8tP4tVxw9np++I5LG7vucjFe8H548ScBWNN9O79+Xg8AR8dd3L7/zHvjFUII0UA0zVjaXe1u9eoDrLU+xXrvYP5ty9ASkSyqopjynGtpWs7stbIOrcXqn1UYcue8OhxL4AmtnJrmjcgTijI45+PwCqqbXbRya/OauzM2kau58X3GpMvYE8XfNhYCS8/SRpTzhh+BuR7abXVsLhh0GCU9/HOLzWGrZXwfDNxnZE/nk/Ya6A5GieZomBn1Vm91TrrOcPJYeRrupdtqP2JMVhS12mF1kACzEELUUcI6iH78DgBui7+R88/bye8+8iLWtrfUeWQV9upvwrOuAeDC7m/xzxcas9O3Pjq0UENKCCGEqDm7ulhbtQyeUJQnh+15t1vrnyz5GJF4Yknt44IEneCrzAdybziGP1LbpeihaIJxe4BYsX93kSKZ6vDqOgzugv6/VryUREvMzznm3WyxHy17X3PeMP2z3qrU6j0x5WLI6i+4TuwS1r6Kjyfd4vxA4yZlOAMrP0AfzpV9HQ22nBl7AAAgAElEQVTCXE/J+7VbZ42Ap2PYeL2qp/kJl0gJjdMmngTbAAw9nHWTFr+5xIFVWLx6tc9D0QQ2yyRxTTMyp0uQLcA87QrSPZl7UqwUvnCM4xOuhTrKjftq0vgkwCyEEHVi90c4fvtnaSLBjL6F6fPfx50ffhEb17TVe2iV19wCb7sdNj0DtDifCfyYDe1N+CNxfrC7utlcQgghRFau8YrsZsjqL3nCtDOYP+gQiSfY3TfHY6rNKE+RiOXPGoxHYWSPkU2WJ1M1n3AsweOqjcfVAjLSKmivauXktJuTU5UPKsy7p3uGXT0WzO7Qkstb4kFjub+ugWeqosdc7xkAdDoiKfendxbG9y8tN1CAQ6MOBud8jNiq1+zJtdKCpNXODC/yf7SqFZjdqWn6stI6D/VaODY6h2P+tbPMesZ1VeZrbM1p1Zm0e3zQyoQjyGQJvXbW+idyXn98wrXk923WA0aW8Ok/FpYtnUX3iSPYzWM8PljKPozHdL0XozQKCTALIUQdHBt38sUf/hdXhJ8E4PB5H+c/33clHa3NdR5ZFXVsgDf8XwBaLU/xk2efAOB/j0yiWuREXQghRAOr0qfHloCFLv9o3u3M7jAJTScYjRu1XPvvNbJrwzlKYqRmqQXyZ1fnYvNF0HTdyEqroflMtpm04G+lpNbNPDpeuezJkmpUTzxp9OUYf3LJxb5wjNMznrzNkd2hOtR3raMxR4CpoZN0eYdqf/DhR+pTTzcHXzjGrh4LfeYSsm/TRBIJ5rwlZrnGl0+0ReMaD/fN8eRw5jIhjlqsZqx23eFU08dh8tCy942GCUL6bdB3t1EXusIiceM1u5TM/Y3uHjqDMwu/h2MJRm3+rCt32qKuxTrHY48vvTIeKax0i2eGTkev0begCj0SbL4I3VPujKsAovHavp/WggSYhRCixn5/bIp3/uIgH4v+CgDP+mfzln/6PM2rpeZyLn/7Srj4egBeMvETLtsYRNPhW/f3rfiGQUIIIVapaBD6/4o+udhUKOeS8YKZaA3lD/z6I3EGLR5aYil1ouc/CGcI5mSipdY31RL1X4peV4vnG4kqnXuMO8podBZdGhRR53xE4gmemnQt23SynOPUi66xwd1HZ2Am/7ZZhGJx+idmsQ4eYb13kPZIkfWNM9XJLYaWyF+3PRoouURAKbqn3ETiCYas5SdtdE+6mXKV+NiaPAie6SUXTTgCROIJHIFI7YNq08eMBnfqA7U7pmvMuA+S2d3BaJwxu79C7xsVEHYb7yElljYp6jg+S1E3aY8svjf1mD2cnvHQU+ykia6nTMLmuW04NfO88PeDaEIrqD79gRE7E44A3RlW4eSexFmZcYG6BJgVRblCUZSsa8EURfmIoihDiqJ4FUU5qijKVbUcnxBCVIOm6XzvoQG+8MdTXM0xLm8ySkNsuPbb0LSKM5fTvfbb0LkJU9TPTzffBcC+ITt7S1qWJIQQQixl8RrZvpXb4SlmHB5O9pzGE4wx6QjyUK+FXnP27GGTFqUpkT34qxUR2NwzYGXd7AG2z+1dkt1VqBl3kO4p12IJj5HHjNIZFWKKh42sW3fp9aVXG5svQnM8wHbL46z3DRGcz5TO01TQFYguyarOJZ7QODFlBJ1NWow5u5OHei30zHjwBAutl53jcaglqhLiaHKNss4/xmZXctJj9iQM3F9Uo7hYXKdJW8wgbkpEiggNUf3AGhiN4ty5l/xXUiVrPbuDZWZnp0zGQTFhuwqbPGyUQZp5quDJuKxSm32Glk/2ZL6NcT/2zXpxBKLY/dWrfVwV7inslkmGrb7SJwbG95d93+dbvbFMaqmVCpc3mnd62sOQtYDXLF1ni/0o+kTKcyIRM1YVJc8D1nvUqoyxHmoaYFYUxaQoygeBh4GMRUYVRbka+DbwdmAj8GPgXkVRttRsoEIIUWHxhMZn7+rmJ4+N0EyCr635g3HFM65aaH53xli3zWj6B+ww7+aDO4ylTT96dEiymIUQIilbQoaiKFsVRZlQFOU5OW77JUVRooqi+FO+rqzuiCtn1lN+OYSKll7SdWY9YeKazvFJ50JQbzjbh0s9wTnm3Zw9+8jyIHMywHhi0l1wjUpd1xeyuja6+4se/qwnjKbrHBpNZnmGl2ZSpTe4KzY4v8bVD75ZmDqS8fqEptc+c2/ycNbxVFKXd4hNzpNL1r57gjHimsYmVw8tceMxUkimtCcUZcTup9/iLeh8aGGfus7Z5kfYYdlDPOhlxOZn76CVR/vnSm6O2JQIQ/+9C+OvZGkUU3oDNfsQxEJgfir/jRPVqwUdT2iM2QOVa2SZzHAuN0jf7qx98EnPMxHSaFpnjhiPoXSVCi46R42SEo4R4/f5740gEQevOX8JkGI/YwWdMHWY8VEVdyjGuL30Gu8Wu4tT0+6CJ88qJaFpTDqDeObLB8WjoO4ystrLpBc4bdIRttIRttIZMi/W6R7dC6N7aXEZ5X26fMNZbz//3hmNa4zbA42TBZ9FrTOYbwZuAG7Jsc1O4HuqqnarqqqpqvorIAFcWIsBCiFEpem6ztfu7eWvJ404wXf+5iTnxpMnPK/+Rt5sllXpsvfAzssBuJE7aELjxKSbYxMFZgQIIcQqlSshQ1GUlwFPAk/Ps5tLgS+oqrou5etgdUZceQXX23VNgDVzwLUSQepMConXtcQXA8cd4cwNsHT0kpoglSNb3Dh9HA+cns2ZnZ2uJZh7BdKeASs9Zg/ecHlZkZ48WZXHJ5w82j/H9PQkk2MDJJzjECiydEIB5u9HkxZnvXeQNcFpWn2TkIgzYXWyd9CKzRehSSsuGOoLLwZfiosFaZgwHphrgktLEzzcO5e1fmku671DS7IAveEsgaGwJ20JfBnntPkavMVC4MgeiClVPKHhCkTpNXs5Ne3m0f4Mz9nJw1lv3+UdZk1gOuv1GdkHjWBXilhCw+oNo6U9UTucla+Tmyoa13IG1bt8w6A3dlALXYOp7P+jZYr97DWTnPwwnyjudgVqifnYajtIa2B2yeUFTRBNHoCJAzB9NO+mnlCUcUegsP2mZWmHyghsjtr9RBNaEeVbKvPZeM4bYdjq59h8fX3bgFGCKLW5b5Vrc5tSnzvzpa2SvRNa7bknjE9Munio18KMO8SxCScnp93sHyqvn0K11TrAfDvGCW/WR7+qqr9WVfW7878rivISoAvoq/7whBCi8n65f4zfHDKWjX7kRdt5m+/XxhUXvRXOfX4dR1ZHJpNRKgNY51a5YbOxbOjnjzdQRoAQQtRHxoQMRVFeDtyVfnkWlwHdebdayRJx4wP1XC94Sq/lWneVnGM2n6AtlDmgDcaEd3rwClh2mabr2bOzS2ByGkHBopqGxcIQdNIZNLNtbj+tUQ97B62L+0y733RdZ9oVwh+J0zvlwOqLYPaEFwNjjhFQH6Q1ujR721Tsx2HrANPq8eQvi0GapngIBu7DfexPOUujZFJu4D2XuKaVVw86n6HdxhJ4v3XZVZquE4pWKHjjHDXKaFSBpsMTQzbGHZlrKrfE/NkzYX0W1ntVNrlOYipmQiERg+mlGfb7h+0cHHXQN5u5ZqzNF2bGXfn/5YM9szzaP4c7mHn87REn587sqvhxCTgwaRV87NeqrrxtMaNc03U8odiSFQe+cKHlaRZttR2mPeJkjW2xZrc3HOPBHgunppfX7l1i/rnnmTay5icPgS/z+8CQ1Y/dHym+5ESFxEssXVVMSalUNp/xnrPw/8g0iWUfXH5Zg+R+zU/+Hht3YvMZ7yuBaG2zwItV0wCzqqqzqqoW/OhQFOW5wJ+A/6OqamOH6oUQIoOHei3c8oAxO3nNBdv50qY9mPxz0NQKr/xqnUdXZ0+7wgiyAx9L/I51BHmk38rQXAWXNQshxMqTLSHjNPA3wG9z3VhRlHXAs4AbFUWZUxSlT1GU91dlpPWU2ggtIu8bADhG8mbNnp4pPDO5IryzbHT3Fn+7gftgZA+bnSdoi3nY6Dpd9C5CqR/EzScgGmCrvYyl0WEvzPUQN/csC1Q3xUMLwYvO0GymWy9KxOlMzWwPupaVKTG2Ky/41hILYNJiS5ZU+8KxjJMMZfMl/+aU8it9Zi8P9xXX4CurmQLKZwDeUIxhq49gLE8QppiAlZ4j2zOlbnRTWvAqb5mTtOZn3uQy/hHb8smdWEJjwhlk1hPG4qlOHd+qraiY62Pt2MNGoH6eYwRGH+Ms65PVOWY1WRZfi0ZtAfYP2+mfNd6DnIEo6pyPAYuXaBErB5q15ZNSYzY/uq4zZs/TTDLVRLLB4vi+5deFF1/7K1YGployPHUKyrqOBmDqKAQrv3KFuV50XccZjJYc8D4T1KXJXyEURXkNxhLAH6uq+p16j0cIIYo17Qryubu60XW46Nz1/OiNO2k68CPjyss/BJv/pr4DbATXfA2a2+mIOLhprdHd+RdPjNZ1SEIIUU/ZEjJUVXWqqlpIZGEHsA+4DXga8AngR4qivLqyI62z4UfqPYLKKOBzanM8NcBQ3gfbbFmapWgP2+gMZu3bbpioTACpLbYYHGmOh1jj7DMCvkVqSgvkpNfRDMcSNMeDafd5UkqjquZEmKVpbkX8X2xLl0Vbp0fY1WPBkp7hXUad17aIi+1zezl79tGFyyYdQfYMWDkwshh88bgdPNE7gdVXoaDl6N6FH8OZguZAs3s85y7CsQTj9gKX8acZtPpwh2L0mZOTTl4zTB9fVo4in548EzGBSJyZtDI8OyyPGfWkAbM7xIkp90IGZbESaTWvU+uiBxspgzEWgniev9HaR1M8yCbXYnYuc8akU0um51kJqjJpkkM0oTHlDOIOGY+r+dIPoyl1iiNVrJV7cMTBgWH78kmMcI5s5/Ta56WY6yu+lnMtjT9pNNYc37/0cl0vqoloRtZ+es1e9g3ZKrrCZ7VpyACzoigfAP4IfFJV1W/VezxCCFGKb9zbRzCaYMvaNn75/stZc+B7EPVBWxe87F/rPbzGsPHpcOWnAPhH/T52mmzc3T1TtewMIYRY7VRVHVZV9eWqqu5SVTWqqurjGFnP19V7bJWm6zr+SDx3NlEitthYJ5Po0gBHczxQ0Q/Qa4Jm2hyZ6yyaSOCxTuTdxw7L3oKPt9DMqMqaEhG22o+w2XmCpnwBphIkNC1rFuoWx1E6PcMw9HDFj3toaJYdlsfYYdm7LBhdqNQa3BmlZdxPubJsn6fu7agte3BubcB4XKXW/5xvTukILP5dQ1Y/JstJDo4Un/HXM+Ph5JS7ck2nkiUOHh+0cXLKxYnJPKUBUpjSAvyxRHJMEwfANQaWU0UNJVMWcap+i5fuSTdWf9pjf/YkaBpHx51ous5ESlawSS88MGxOOw8utmTw/iE7vrTSKyM2Pz0zHmbcocoEqeNRo2zJ3PIVCnpKeZS4pmH3R5dleKcLxeLYfOGSGn6PZZg4m/WEOD3jwRPKPrngCUWLKlEz4w4ybPUzZvMzl2fyQIfc2e9FsPkimFIeBFZfGJs/Qv+sb8nzeYlq1Bb2zlSuceK8Sr5/ZAmib3Ecg8Fd4J7Mu4twLLFQjiLd/OtCNcsazcv3+GpUDRdgVhTlVRgZF69XVfV39R6PEEKU4rEBKw/3Gcsfv/S6C9ju74djtxtXvvSzsHZrHUfXYK66EdZuo1mL8pX2u4gldO44OF7vUQkhxIqkKMoLFUX5QtrFHcDK/LSS1JSIwsgeI4MKI4PsqUk3AxYv/ZYcmVnqA0a2szdP2QJgTWCKHZa9bHEcz7ttodojDtqdapbrnJhilcsorqWsQdRQ7ma9802mcjWeG7cH6J7y0GfO/H9tjZVXEqUpJfBiSiu2GfItjr8tWniAM9U6/5jxQ7bgUqEBtFjup+xghUqK5Qv8ZTNi8xPTNCYrmBUPEImE2WHZQ3zo0fwbF6pK9XmdgQzBy7A74/94bSB3YK455TkVjWd/fuR69DQlIpi0GI5AhKPji39zOJagZ8bDiM1oeLa7bw5N05dkahcd1w27CcXijDsCywLW444AD/dZmHQEmXQGl5eASSzebybdWEfQa/ZyfMK10BS9GLGEhqbDgRE7JyaN5/CRMSeReIKhTNmmCSOwPGT1MzjnI6blDwRrus6sJ4w7FMVXaIkJZ9oqhBLnLg+M2DNOHg5ZfYzZA8smEwDivfcwYZ7DF46hWrw4/IVNmIVjWtYAq7FBBTKhl1h6p2R7fS9n3rcjbDUmLgp4rVMt1S25VWi2faVe32utIQLMiqL8TFGUnyV/vQmjY/aDiqL4U77+vo5DFEKIgoVjCb52rzGb/8LzNvGW5+2A+240PmhseRb83WfqPMIG094Fr/wKAH/PAZ5vGuT3x6ZynlwLIYTIKgB8Q1GU6xRFaUqWnXs7cEedx1WW9d4BI0hkNQLMA7PehfIGoamTy7ZfSPaar2PrGMqbpbkpWee3I7U+bthDoVGBtkju4GqjKDTj9NS0e+G9+KnJAv+24UeNBoxZzDeZmpzP2s1QuuDktHtZ6YpSeMNxes3LSx1sn3scMAJGuTNVCx+DKUP0ozWeZd8BW/4dOkaMzNsKaA5Xt/mZBkbQyZahWVYJunwjNCfCtEVdeYPs8/QMXbkC9aozGw8vKU1SqK329LL7xWmOhzh79hHOMe8GXScQWXyeZ2quNmr3583UzmfA4sPujyxrTOhIBt5PTLmWB+Fjyyen0gO2w2NjeNV9xuPKazZKceThDESx+SJM25yEgnkmPYJOPMHFoGw0btw/8YS2WJ7EOlB+FnCeCbd8NjlOLPycrQkjQDBDM81Ju5eJgeOocz58kXjGLO9Fi4+P/UNWDozYszdltQ0slIIpRb5yPG3R6ryPnpp2LylhAkB0+WOx1EaEhRhzBLj/9CyuHP/Lla4uAWZVVfeqqro15fePq6r68eTPr1FVtVlV1XVpX1VoXSqEEJX388dHmXAEaTLBN950EU0nfgXmZHOS1/0HtLTXd4CN6LL3wlkXAvDV1t/g8Icr1xhGCCFWOUVR3q8oykkAVVX7gXcC3wJ8wK3Ae1VVXR6FXUGa05bRFtNACYwPjUXXmZ3rg6HdRoAjg47g0qzoJTVGU4TKKCGQnu3UpEVpGt5d8v4AesyeZZO4ncGZZduN2QOcnvHkzDbOKJE/Uy44H/ya7S5u3wVZvM+mnEGsaYGS+UaIVl845wf9DZ6BPMcpsm4BGBMWhWQMz57Iv00Oa1L+n+um9y0pE5P+uK0I/1zRZSiAjMvju3wF1J5Ou+s7Issnj0op+1GuAYuX4ExvSeVVWrJNSKRp9puh7x5wjS+5fLG5pF7Q8T2h0gLw7WEbrUErsLQ2NBjlMHIliDTHQ5jUB/Iew927m8GhfqMMzsQBYyVKHpqu05SIcvbso5gG7sNUVGa+TjSu0T3t5tSMxyi7NNdjBFPLVErJj3lrQsVnc89zBqKYtOJLOWx09wAsrwmfavYkzfGlQf/0x0Kq1BI2Y7YAw1Y/U/PlY2pU0zmm6csnO8aeqMmx5/XPehcmNl2BaHENHFeIlnoPQAghVhOHP8Jte4cBeP/fPYPnro/AHV83rrzorfC3V9dxdA2sqRleewv8+jouaxrm2qaD3HloG2+45Jx6j0wIIepCVdW9wLJ6SqqqxkkLr6iq+ivgVym/3w3cXeUh1lRHxAZsLnj79M+sJX2GTWZLZ7PF+RR0ZRhT2sGcgSg7ukoL5hwYcdCRdpkp4oWW5vw3zlG41ROKsq3L2LMObHZ2M7Pm3GXbOQPRCuQS5xBMBgF13cj269hY9i5TA3UbPP0kbJnvh2lXCLqMn9vDNtb5Jwh1nlXiUQu8l0b2lLj/MrnG6AzGCHWeTVusjCXu8YhRt3xN4c/FXDpGdsGa1rL3YwRUlz5TAtE4FPA0qSR/JM7AbO4GgYVIf71KLeXSaT4C6ztg+hise2X5B0q+TrS7h6HJBOc8P/O29iE6Ay42u7rpCrbB9quWXO2PxBnIVa4I2G7ZCzvXpw+isHHmoek6bcmJhnAsQSu5SwykvzzOJps2JjSdcDzBmtYWY+Jk+4X5x5eNrjM5VpnM/lqz+cIMhLL/P1Nrig9b/Qxi4RXKtozbtqa85li8YZqTdbFDsQTP2KqVMlW3jCsQxROOsXNTJy1NBebRRkvJ4F/6WFwbmMTX9Uxo7qIlFqA9knmFSnpm9IjdDzTREi3+9bicSYtqa4gSGUIIsVr89vAkkbjG2rZmPnvNs+HBLxjZKm1d8Npv13t4je1vr4ZnG9WQbmr9X54anZUuvUIIcSbRNaMLfJW0xAK0ptbVrUYTpCwcmWq1ZtEcD7HFdgSTezJ7A6cK8terlEAqy2kj+Dp1qLjbDe02gp4pWlIy61pjXtqsp7PefL60wlb7ETrCcwtlUgqhF9t5LeuOqhwsMAGOETY7u+nyDi9cvKwubh7ecIzJA38gou4Gz/KM91LouoY7GC16RUI5YiUeS9N1PKHoYgkFMtdTrVjTwxTVKPexdu4oZ88+QlMijEmL0enoBedY9kZosyfZ7EpZcZDWrHIirQRDS2x5w1QTy+/7zuBilm6Xbzhvc8tsUjOnfeEi768sz8FIXOPwqCNno8B8YmMHSr5tvRX63uAORYkltKx187PxhmOMVyiLd8RulF8yu2vfbmKTy8j63j63l43u5U0vc9lu3VfU9iYtxsjAqSU12xuJBJiFEKJConGNOw4ZXbuvv/xpbBi+B3r/bFx5zb9B1446jm6FePU30ZtaONfk4MPND/C7I/m7/QohhFgd1gYmwZd/+X7OBkTZaAm2z+3lLOuTdISM5d0L2bN5lBNcKMaMO4gnGGOT6xQdEdvSYE4JEsHSmtQVq9hAJUA4nqDX7FkM0NmTWX5ZypFk35EH5npLjtFmCnitZut9i7VTRzJN4ueImT82YMXqDTI051/evKxEFk+YYZuf/myBqXAR2cApj4HWuJ+NyaBPKqs3zIM9ljz1aDObdgUZsvoX7zeTCbOnNsGskZTasTpGsHtwzruQdZtPpozHFp+ZJi3KBo+6tIZ4AfWOC3m+GcG21P9B5hs1p5TzaI842ODJ3BS1UvyROKM2/9IgdDxCi3t02bYnp9xYvOHMjQJXgM7UfgIpEslyEVoDZMKGosuD2J5wrOT33dSGkzFNx5RtwqKECeb0siDzTFos46M7kad5ZPr7z/xjMxjLHtjv8o3iHjmctSRXvUmAWQghKuS+U2ZsvggmE3zokja4/0bjimdeDS/8UH0Ht1Jsezam5H31yZZ72HvsdFUyQYQQQjSWtoij4MwfLUODobwflBOLgaAtjuKaac2mBJHWufvpDFQmezPTcWY8oYJrseZz8tDurE28Mt1bG9x9SzO8C1RqjelQLIHL7So/gzeRUmc0ZZl8IUx6qQHmbJHY7BHaOW+Y/lnv8hq1RWRCd3mH6PJUZsl9MM//LVvt7XA8UfL/bMDiXRI4mn/sxLIFYjLUaC7U2sDEsssOjjrQdZ0ZV2GB2VTW5MSWt8xsYn8kzuCcr/Cs5AwPjzlvGG+xWbpp3Av/h1Kff/lvtzZQfKLImmDpdYfnzfnCtIeXlioIxeLY/GEGLF6cwSiDc0szsNusywN2qWUN0rfPS1/yLaumxOLzwROKLwmQpuoMzrBjdg/tYfvCZaXWU0/oOqN2v5F1Hi1+siXb++2Mu/jnVSZj9kDFgvq6KUudHFvxExk7LHsyNnTNJK5pDFgyPGZyvOcsPDYz3S6py2esQmmPVLd5a6kkwCyEEBWg6zq/3G90+371c7axc+/njayLjo1w3W1QaC0oAa/4Ilr7BtaaInwk/lvuP1WFZjRCCCEayjabURqhkIyqtrnlzcTGS8hILMU678iSzOJM421JLF+6GktouAL5Gy61+abKG2AKLZFY1sQuV0BinX+Ms6xPgq5nzdQqSDLrdMYd4vRM7gxUTddh+NHSj5VmTXCK1goF6ItSwON2yhUkEI0vf6wWGLBoiXpZ7x1kvW+opImAvOKLjxWTnmA0y+REKTpCFja6ehg0u5ZM2JSjLeoqeNu4pmFeEvxKK92gxegIzZVcniGntAmEAYsXbzhGf556xbnEE/XNPDX+pAqViKmS1Gx9gF6zlwlH6WUF8pWLiGeZJNFzNL8D2Ox8auHnmKbRN+vNmHG+2dlNcyLEVvvhhcvao0aQ0e6PMGrzL2TM5mpemsoRiIL6IFiXNjPM1PQ1VTFlLUrJkm7NUCe+x1xabfP0x8G8aaudSWeg6HrGWTOi03RPuY0JtLT9rw3kf49Pr9e8kkjEQwghKuDouIve5PK+m7c8BmOPG1e8/vuwXhrVFWXNZppecRMA1zc/zqEDj9V3PEIIIWrGUmLwKb07fGnlcYv/UGfNUK5ji+P4ssucwSg6OvmCMi0hewVr8i7fz5aUYEY2m1wn2WHZw5rAFG0hK8yexKTlD44vmDiApukcG3fmLZ+hA4QrFyxd5xur2L4AVIs36zLnlhJrYHrDRdyXKZq1xcd4c6KytbnX+Uah/690eMcBWBOcyZmpm1ozOZEWDAnG4kw6lwagtjiOszYwwXpvkdnXQXvWq4rZ1+iUmaPj2TP+tjiOs8VxjM3O+i47P3f6fs6dvp9CX4uaEtGsz81Kh6jMFcpOrZ76BuWyTZykPo9MGcbYXsSKi2xCsQTOYHShZEu2lStZeYyg53xphs3OzOWZ5p/3zgID2LD89aGQycvmxPL7cspZuZrDmq4zMz2O1Rcpqj8CZA5+57IubSVFa6z8JqCNTALMQghRAb/cb9Ttetu2Kc576rvGhRe9DS5+Wx1HtYJd/hGC686jyaRznfWnDM+V0fFcCCHEilFquYV0nd4xcC1fIl+u9IBpLK5VvI5lak3STEwlZg62xApb4r0mmb22yXWKzbYjmBxDbLUfZdvc/oLLg2QqeRDMELAsqZ52Bel57ktfJE7PjJdQKCVgmrzJ9rknluwpVUus8Ay/9qiLs5bsq7K8ofwB7Q2efgDW2ZevDsjEn5debnQAACAASURBVFKeIf0522/2ZZx4gRKCK84xCJQfgPNG4rRGsx97PsjXGSp81dw6/3jGy9ODiKFo9te0YrMnk7da+Ons2d2cY97NJudJ1nvLqV2cfxzm9HrPBdawz6eYAOvjp4bZf+gQMdtw/o1rLFHDRpVglDRKfwxGYhqhHPV788nVpC+m6ZyadmP3pz23i3wI77DsKWr7ja6eijdC1XR9IYi9tGTR8vcDX3JCcH4Se6v9SFHHWu0B5XQSYBZCiDLZ/RF2982xDTffjP4HJi0OW86Ha39Y76GtXC1ttL/uFgBe0tzLkUf+VOcBCSGEqIVcS3sLzfxsizhZ7+qF6fy1lkOxeElN6ja6jEDcnC+ctwxEo9hURnZmW9RFW8xTcONB09RhOkKWJZfFMiz7DcUSzLjLzExLSVcvtjxGpozCdDFNo6/7cFHlEzYUWE8cjPu2tYDgf2o92/aIo+CgSyiWKOkxnksgV9A0x31aaP3SJUYrs5LtLOt+1gSm2eg6TUfYWvb+1gYmCwqOBrLU1AVjGX0++ScIdNYEp5fUEzfpuvF5xNwNnsImhYr5z+g6ECq8REklTDgCrJ3cQ4f9FNaBAzU5ZnFlWKo4kDStUQ/r/JlXa5RcVj5NthUa6SV+ElVuFLg2MMFW+6GCty+/cMt88Wzj+3zm/qi9tqWXOsK2JaVKurxDrM0yqdVIJMAshBBlerDHgklP8JP2H9MZsUHrWnjHb6C9q95DW9GaL3gD5q6LAbh06FYisdKWlAohhFgd0pfaZtMS96PrRmDG4g1nzRL0jx2h1+zl9Iwnb7f3dKl1FGNFZK415clOLqSxrdkTWlKioOBj6+U1BSuGyTOdsVRIJrOe8NK/p8iARSiaYM5Xmbq+2ejoEMkfYJivnWli6f/HU0AWcSapWd+p2bXr/GNst+w1gogp1vrH2ZRheXulGyanl8DIZtvc/iXB9mICdqmiCY1JZ3Ahm7BQwWicvpTarZtcJ0tqPJdNa6y8oFNC1+k1e3I2/CtlVYdJT7DWPwGOYZg8mHPb+SZzDn9xpQLSVWr1SarURpODc4v3dZEv10Xzh+MFP2e6koFed6i8+y9VvlfArfbiGtXm4wlFl2UmZwtgL6hyYDlVroZ25a4gSj+vmE42AJ2vjV3I3nNNVJbaSNakJ9js7KY16qY9bGe9d7DgRsj1JAFmIYQo030nzfxry++5wtRnXPDGH8FZz6nvoFYDk4mW134dgOcyRs/Dv6rzgIQQQjSCQj7wheMJBq0+pl1BrL4IpgzBwYEJ88LPkbSAbWlL1yn7Q3e+RlKw2NCpWE3F1FGuMS35IT+a0JY0sUrVEZpb+Dk1S+3ohJMjY9kDELn+IzomTFqBgSFfrvIJOnFNy5q9myuAmEtfjkZwLYkgnaHZJU2nmvT4QomTkhSY/ldo0KQt5slaSqIY4/YAVl8Ydc7I9A7myKBO1TfrJViFwGclhWKJohr+FfISs84/VnDpiY6Izdjv/GO3nAafFdY97a5o7d1CTTqDBTeVWxOcznpdJSZ2Nrh7aQ8vrUWeb6KyGHFNY8jqL7lRburjsSkRZkta8LvarSC7p8p7jCydnNRpiflB1+lMW4FTL60xL80ZGgc3KgkwCyFEGea8YTZOPsTHW+41LrjiY1J3uYLOuuhVdHdcAcC5J74Picb9cCyEEKIxZQrubbPmXmJ9vGeg+APpOttstVm6nR6I1nR9SbZfJk2FBlLroMfsIRxLMGjxZQ2MbXEcK2nf4VgCTdcZyBDEM6Fzjnl3QfuJh7IHnOIJLWe5g1wlJcph0hO05agtnE1quZnWaPFNFjNlIntCUfpmK9szYz6zPb08zrSrNgGXzsBMeQH7Oik1UxwAx0jlBlKC9Pj5fAAwPVCZ7/dU7iKa0lWKjl7SRGC6df7xrJNumY9anHKzwVOfm5ucp0ooP2NKq4OcZSstSmdghiZ96WuBpusVW8HS5Rtl+9zjC9nLongSYBZCiDLsO3SI77X8DADt3MvhNd+q84hWn8BLb0bTTeyIm3Hs++96D0cIIUSdjNj89MzkXk6ejTe89DbpAZj0Rlwh62ITqUCksOBgsxamrYRgXSX0mr10T9fn2JUy6QwQzlcruIg6yPMs3jCznlDG7PBisrojObIR05vapQfzK90IslyDc4s1n1NLp/jChd+/6eU5Ru0BgjnqDZdi1OZfNnGSLcs/W2PBfFrimTM3W2IBNru66fKPlrTfcuR6tNS7MWa1lVpSYM6bPcg4XIFAbymyZs/rGp3BGZoS1S3tU0vrfGML2fDFKiSD/xzz7oJ6APgKOD/Idg6x3jsIULXsZeOxXe2c7vqSALMQQpQqGuSFh29gvSmEr3kjTdf/Clra6j2qVeeKK1/OrqarAGg78H2Ir+4TayGEENmF46XV283XoGfcvjQjcj7opOl6wTlhpQZGyqXpeklN3ArJes5UKmSdbyTn8vtpV5ABS/6mdenSJwEy2ejuB8BdZE3jQAH7zse05Pxj6f2SHjIopGlfJbTGfGx09VRsf8XkP6ZP0hRaIz2bPrNn2ePNH4kvy24cmst83xafu2lIz7jsDBgZy82JxVIRzkDjZP+XUn+90HNnTyjK8YnqNO/LFshPl56hOi91kqaW0zWbHZXMZtXZYj9Kl3eYzc5uNjtPVHDfpXEESvtctcm99HVng6evEsOpiHwTekPWyk44tMa8BfVi2GY7mLOedCYbPCqbXKczX9lgE5cgAWYhhCiZ76Fv8IzEOAndxNBVP4QN59Z7SKtSa3MTU5d8Bk3//9m77/iqy/P/468zskMIM+wp3MiSIS4UVFy46qgLrdphW1utbX/VtnZp6/h2aW3rVmxddaHWgXUjQ1FUkH2zQXYEEsjOyTm/Pz5BQwjhnOScc58k7+fjkUdy7vM557zJOCTXuT7X7aNdVSGhz552HUlERFJa7B1C9YtTadVeR1WqdZ7GS3VNmIUbiw7a9dxQMat98XLydtsD3mbr7oomFbyjkVO6PiH3G5U6LyBkVjStUy/ecko3EIxxPmfunnh15Ma3E6+suobC3QcvQtYk+Gey464FZJVtwlenu/1AL1AlKklZE2d2fykS2WejycDWrzo/A6FybwPABqzcXkKESFJeLItmLEJddTcRjHWzx+aou7lmLA5UxMys2E7enpXAwTava9LDxmxTUdNmbjdrDEuCbS1O3c7wYCi24nZjo60yK7Yd8DpXVGAWEWmK7cvI+fRBAKb6zmH4sV9zHKh1O/W48UwPe7OYK2bcAeHU3rBFREQklW0priCUrApGgtUf1ZAoEWBXaRXVNeF9NtZLlES9uFG38NiQaGcyN7Xw1phdn7wY9/tsisyKL8h1+GJGdTN/NtNCJaTX2RjOV/bVGQcFW2eQX9R413u7PQefw9zkjVBrrdwe7y7/1vF8Bt7PflNeSKmMsWjfWhXGaSbzXtF8rwerm7ZJYnOk4sa9KjCLiMQqEoHp1+OPhNgY6cy6oVeTHtTTaSL165zDnIJvAN6ML5a/6jiRiIikqvyiJa4jJEVr7a6OVVbFtn26i2MT/eewsKSS1bWdrPsXteP/tWjKrPF46Lp9TsPr22btczmndEPcH3tP2f7d2DscjadwNfImnuZ/vovFm4r36ehs6AWG+iNvoulObWqBeO/3dXkjM83buqrqpn3v6XP6lV1xfN6IZkROl8IP4vZ4LZkqIiIisVo8DdZ5v2TfVH0FJx3W33GgtuGoY09kZs0IAKre+2tKzp0SERH3ktFdmiw5JesOeN26HcnvmEolNeE6IyvKm3aqcHbZpqiPrVtkyKp3anIiNndMtV9z9o6NSbamzFxv7aKdN10TjlARqmFHcXGjxzVlFnA0M9MbsqqwpNndz1U14QY/Azkx/DynsuZ8dlJpXrhLqw+y70IsiqMYyeIPJ3+PoPSqxn+uXVCBWUQkFhW74fVfAfB2zWhmBw7n6AGdHIdqG04d1o1Hg+cBkL5tAayd6TiRiIhIYjXWjb23kFBW1XoK6rFYuKn4y00KfY5Pj29sTmZT1IQjrIj7CIHE2VGiDZi/kvjvxZY+3qZJ6esUpWvCkQbnYruaSds5hbpXU+kFmeLyKnaVN/7cWB1u+WcKuOJ0T4IDUIFZRCQWH90PJVup9qVxc+hyjhnYhcy0gOtUbUJmWoA+o09lQXggAJHZf3OcSEREWrNQFLvCp4JVLagQGU814QhfRNmtF4pDPS6ZI0lcjYVoqrVttJs+LcYNu+KlpIndwy1VSWUoqrnQrjS2WV9btnJ7Cet3xLYJaaIVH6TgLc2jArOISLSqy+HD+wF4OnISGyIFnGC6OA7VtlxyZB8eCJ0BgG/NO7AjdX/ZFBGRlm3BxiI2F5W7jnFQqdLNGI5E2FGa3E7WbcXRdeuVVbW0glxqfE0lNVU5fvGropmzfovKYtucrLK6hrzdtlmPWV+6isJt0srtsb0olGqjilKdCswiItFa8CSUFhLxBbi34jQAjjddHYdqWwYVtGNn75PZFsn3Fj6e6jaQiIikPl/Tb7p9j079j8bu8mo27Spn7RfJ7WT96vRqVQFEGpNZvjVu91URal6BuaHxFo2pTsCLaDmln+9zOVSTOs8h21NozIVILFRgFhGJRrgG3v8HAEs7ncwmujCwSw69O2Y7Dtb2XHrMITxVcyIANZ8+7nWWi4hIy5XgTfm06VHirdi+J6Vmf0rstu7W71N7BUOtb+RHRuUOfHGeFZ4sG3cldszCnsoQ1Sk0EqmljchJNSn0WkGbowKziEg0lr0Mu9YC8M/K0wE4Qd3LTpw6rBtvZJ5GKOInUFkES15wHUlERJqhfieZpJZmNIBLC7JxlwrMe6VX7SK9apfrGHGVW7KOHpvfdB0jJSW6gC3JFc95+aVVoZQek5FVtolICgVUgVlE5GAiEZjjbShX2fcEXivsDGg8hivpQT8nHTmat8JjAQh/9JDjRCIi0hz+cEubjysiIiJtwa6y1O0o77BrYcwzzRNJBWYRkYPZ8AFsng/AnG6XAZCdHmBc/w4uU7VpU47sw5PhkwHwb/4ENi9wnEhERERE5MBWbNvjOoKItCK+SBhqVGAWEWk55j/uvS8YztOFfQEYf0hnMoIBh6HatoK8TPKGTmJNuBsAkXkPO04kIiLSOpVXp85s0gPpsGuh6whxFe8znhOwR5o0we6K1CkEyb6qNbhXWqpw6jyvqMAsItKYyhJY8iIAoZFTmLN6JwDHmy4uUwnwjaP780TNJADCi56DSnWFiIhI27K5KPFzc5dv3Z3wx2guXyRMTsk61zFS1urCEtcR2o4UmocqB5ZWVbTP5VQegyDSUqjALCLSmGUvQ3Up+IPMbz+JkkpvTqTmL7t3RP+OLOl8OpWRIIFQGSye5jqSiIhIUm0u1sZse+UXLXEdQYS0kIr5LYG+TiLxpwKziEhjFjzhvR90Km9u8DoSTEE7euZnOQwlAD6fj4uPH80b4cMBqPjwEceJRERERERERNoeFZhFRA5k13pYN8v7eNQUZtjtgMZjpJIzRnbnzcxTAcjcvgC2LnKcSERERKR59mhWr4iItDBOCszGmCOMMZsbuf4SY8waY0yJMeYVY0xBMvOJiADw2VPe++xObOp6HCu2eadSaTxG6kgL+Bl53NlsCHtF//K56mIWERGRlm13Rch1BBERaQF8PtcJvpLUArMxxmeM+RbwBpB+gGNGAvcBlwBdgK3APUkLKSIC3gYdnz3pfTziAmas8jaCyM0Icni/Dg6DSX0XH9mPF/zeZn++Rc9AteZRioiIiIiIiCRLsjuYbwSuA25t5JhLgf9aaz+01pYDPwe+ZoxaBkUkiTbMhV3rvI9HTeHd5YUAHHtIZ9ICmi6USnIzggRGX0Yo4iezZg+VC593HUlERERERESkzUh2lWQqMAqY18gxQ4Cley9Ya3cARbXrIiLJsXia977LECo7D+P91V8AcMIQzV9ORRecMI4ZkdEA7Jr1sOM0IiISk0jYdQIRERERaYakFpittVustZGDHJYDlNVbKwOyE5NKRKSemhAsfdH7ePjXmbeuiLKqGgAmDtbJFKmoIC+T9f0uAKBb0SeEtlnHiUREJFrZ5VtcRxARERGRZkjF87zLgKx6a9lAiYMsItIWrZsJpd5IDIafx7t2OwCHds+jW/tMh8GkMceedjFbI9587PVv3ec4jYiIRE0dzCIiIiItWioWmJcBZu8FY0xnoGPtuohI4u0dj9FjNJGOA3hnuVdgPt5oPEYqMz068FH+6QB0WjWNSKjScSIRERERERGR1i8VC8z/Ac43xhxrjMkEbgdeq53FLCKSWKFKWPay9/Hw81m5vYS1X5QCcPLQAofBJBo9T/wu4YiP/EgxK2c94zqOiIhEw+dznUBERESkxfGFKlxH+FJKFJiNMfcZY+4DsNYuAK7C2xBwO9AD+KbDeCLSlqx6GyqKvY+Hncvri7cC0LVdBqN65TsMJtEYM/IwFqSPAqDqw0ccpxERERERERFJDF/pdtcRvhR08aDW2hlA5zqXv1/v+mcAtZ6JSPLtHY/R5xho34vXl84C4JRhBfj96rBKdT6fj5rRl8NH8xla/ilrVi5lwKChrmOJiEhjIgfbA1xERERE6vOROjWKlOhgFhFJCVWlYKd7Hw8/j427yli8aTcApw7r5jCYxGL0SVPYRR5+X4TVr9/jOo6IiIiIiIhIq6YCs4jIXiv+B9Vl4AvA0HN4Y8k2APIygxw1oJPjcBKtYHomG/udB8DYwhfY/MVOx4lERKRRmsEsIiIi0qKpwCwistfi5733AyZCbhdeX+LNX550aAFpAT1dtiSDzvwpIfx09JXw6cv3uY4jIiIiIiIiEl8pNGZMFRMREfA29lv5hvfx8PPZUVLJvHVe5+spQwscBpOmyOzcl9VdTgbg0HWPUVSaOrvrioiIiIiIiLQmKjCLiAAsewVqqsCfBkPO5O1l2wlHICPoZ6Lp4jqdNEH3034GwEDfZmZO/4/jNCIiIiIiIiKtkwrMIiIAi6d57wedDFn5TF+8BYDjBnUhOz3oMJg0Vd7AI1ifexgABUsepqK6xnEiERERERERkdZHBWYRkdIvYM0M7+Ph57OpqJyZKwoBOHtUD3e5pNlyj/8xAEeyiPdmvuM4jYiINEyb/ImIiIi0ZCowi4gsfREiNZCWDWYyz8z7nHAEOmSnceowzV9uyTqN+RqFad6LBBlz7yKSQpsgiIg0xhhzhDFmcwPrnY0x640xQxq57VhjzDxjTKkx5lNjzBGJTSsiIiIibZkKzCIii5/33g8+jZpgNs9+/DkA543pRUYw4DCYNJs/QNkRPwLg+OpZfDpvjuNAItLaGWOGGWMeMMbMMMb0NMZcY4w5JYbb+4wx3wLeANLrXTcBmAP0aeT2WcDLwANAPnAfMM0Yk9aEf46IiIiIpKoUOglMBWYRaduKN8L6972PR3ydmSsK2VxcAcAlR/R2GEzipe+J32GrvxsAkRm3O04jIq2ZMWYSMA/IAY4CMoAewKvGmIuivJsbgeuAW+vd90Tg6frrDTgJqLDWPmitrbbWPgCUAKdH/Q8RERERkRYgdSrMKjCLSNv22X+ACGTmwyEn8Z+PNgAwrl8HDunazm02iY9AGltGXQfA4WWz2bBkruNAItKK3QbcYK29FKgGsNbeCFwP/DbK+5gKjMIrVNe1COgPPHmQ2w8BltZbs8CwKB8/6YKhEtcRRERERKQZVGAWkbYrEoEFtX+nj7iA7WUR3l6+HYCLxx3w7GNpgUZM/g7rfd4s5rLXb3acRkRaseHA9AbWXwIGRHMH1tot1tr9BsZba3daayuiuIscoKzeWhmQHc3ji4iIiIjESgVmEWm7NsyFnWu8j0dfyjMff05NOEK7zCCnj+juNpvEVTAtnZWH/hCAIbvfp2S1uphFJCE2AYc1sD4J2JCkDGVAVr21bLwxGSIiIiIicacCs4i0XQue8N53HcruDsN4aPZaAM4f04usdG3u19ocfvq3WRHpBUDJy7/wOthFROLrduBBY8zPgQBwpjHmDuAu4M9JyrAMMPXWDPuPzRARERERiQsVmEWkbaoqhSUveB+PupQHZq6lqKyajKCfq48f6DabJER+bhYz+14LQLei+USWvOg4kYi0NtbaR4DL8TbUKwVuxtvsb4q19qEkxXgLyDPGXG2MSTPGXAV0AN5M0uOLiIiISBsTdB1ARMSJZS9DVQn4AhQOOJuH7/Yau745vj8FeZmOw0miHH7SRbz34BNMDCyk8rVfkWkmQ5q+3iISP9ba6TQ8hzlhjDFXAD+11h5mrS03xpwG3Af8CVgBnGWtLU9mJhERERFpO1RgFpG2af7j3vvBp/L3ubspr64hLzPI1RPVvdyaHdY7n2s6fp/xRdeQWboJ5t4Nx/0/17FEpJUwxvygseuttfdEe1/W2hlA5wbWQ4Cv3tq/gX/XubwAr3NaRERERCThVGAWkbZnx2pYNwuA7QPP5z8vevsuXX38IbTPTnOZTBLM5/Mx4djjeOK/k7gi+CbhmX/FP+pSaNfNdTQRaR2ur3c5CHQFQsAcIOoCs4iIiIhIY3y+gx+TLFHPYDbG9EhkEBGRpPnkEQAiuQX8ZmlPQuEIBXkZXHlMP7e5JCnOOqwHDwUvojiSjb+6FN75g+tIItJKWGv713vrDXQCXsKbjSwiIiIi0urEssnfBmPMW8aYK40xeQlLJCKSSNXlX47HWNnzPF5fvhOA608dQlZ6wGUySZLs9CAnjR3KXaHzAYjMfwI2L3CcSkRaK2ttCfA74Keus4iIiIiIJEIsBebhwGzgF8BWY8yzxphzjDE6n1xEWo4lL0D5LiK+ANetHAXAcYM6c/6Yno6DSTJdemQfHq05mdXh7viIwOs3QiTiOpaItF4DAe0oKiIiIiKtUtQzmK21y4GbgJuMMWOAC4FbganGmGeBx621sxKSUkQkXuY9DMCi3GNYVtiO7PQAt507Al8qDS+ShDukaztG9unMLRsv45H0P8P6ObDsJRj6NdfRRKQFM8Y808ByO+A44MkkxxERERERSYpYOpjrssBnwGK8bozxwHPGmMXGmMPjFU5EJK42L4BNHwPwpx3HAnDDqYbeHbNdphJHLhrXm3fDo5gVHuktvPEbqK5wG0pEWrrSem8lwHrgOuAah7lERERERBIm6g5mY0wmcCZwMTAZ2An8BzjaWvuZMSaItzP2c0C/+EcVEWmmj73u5Q2+7swJD2Ns3w5cfnQ/t5nEmTNG9uDml5fy++rLeD3jF/iL1sOH98KxP3EdTURaKGvtN11nEBERERFJtqgLzEAhUAM8D5wFvGut/XJgpbU2ZIz5H143s4hIaikvgoXPAvDvqhNJCwT54/kj8fs1GqOtys0IcsaI7jz7SQ2vpJ/G2VXTYeZf4bAp0K7AdTwRaSGMMX+K9lhr7Q2JzCIiIiIi4kIsBeZvAy9Zaw94/rC19nm8ArSISGr57CkIlVMRSeO5molcd+ogDuma6zqVOHbRuN48+8lGfrf7bE7Pm0Wwag+8ewuc/Q/X0USk5RjnOoCIiIiIiEuxFJhfBe4yxqy01v4FwBizHHgTuL6xwrOIiFORCOF5D+EHXqo5hh7de/DdCQNcp5IUMLZvBwZ0yWFNIfyv0xWcueWf8OljMO4q6D7SdTwRaQGstSe4ziAiIiIibU8qnY8dS4H5H8DhwNQ6az8G/gj8Gbg2jrlEROJn7Uz8O1YC8GTkZP789ZGkBZq6x6m0Jj6fj4sO783try3n15uP4fROr+HfuRr+90u48hXwpdJ/2SLSEhhjjgWGAYHaJR+QAYy21n7DWTARERERkQSJpcJyNnC5tfbDvQvW2v8B3wEujHcwEZF4qZj7IACfhQcw5qhJDO/Z3nEiSSXnjelF0O+jqBI+GFi7wd/62bDidbfBRKTFMcbcCswEfofXnPEL4A68ZowMh9FERERERBImlgKzj4Y7nmuAzPjEERGJs91bSFsxHYBp/lP40aRDHAeSVNOlXQYnDukKwF0bBkK/47wr3r0VIpFGbikisp8rgauttT2AjcAEoAB4B1jtMJeIiIiISMLEUmB+BbjHGDNs74IxZghwFzA93sFEROJhx6wHCVBDcSSbvhO/QX52uutIkoIuGtcbgI/W72Lz6Nou5q0LYdnLDlOJSAvUBXit9uMFwNHW2iLgV8BFzlKJiIiISKsTiYRdR/hSLAXm64AyYJExpswYUwYsAUqIcv6yMWa0MeYjY0ypMWaBMeaoAxz3a2PMJmPMLmPM68YY7cYlIrGrCeH79N8AvBacxKXHHuo4kKSqiYO70LWdd/b6o5t7woDaPbtm3A7h1PlPW0RS3hagZ+3HFhhV+/EXeJ3MIiIiIiJxUVqdOmfcRl1gttYWWWuPB4YDlwMXA8OstZOttV8c7PbGmEzgZeARIB/4O/C8MSa93nFnAVfgbSjYFVgFPBRtThGRvVa8/zwda7ynp84Tv09mWuAgt5C2Khjw8/WxvQCY9ulGQsff6F2xfSksfcFhMhFpYZ4CHjfGHId3ht+3jDFXALcDy50mExEREZFWJRxugQVmAGNMAKjE61xeBfiNMUONMUOjuPkJQNhae6+1ttpaOxXYAZxV77jBtbkCeHOfa4DyWHKKiACUvv8wAIuCwznx2PGO00iqu/Bwb0xG4Z5K3i3pC4NO9a6Y8X8QrnGYTERakBuBqUAHa+0M4G68Df5GAlc7zCUiIiIikjANbdrXIGPMZLxfmLvWu8oHRPAKwo0ZAiytt2aBYcC0OmtPAd8DPscrLm8GVBkSkZisWGkZWfYh+CA06hv4/T7XkSTF9eucwxH9O/LR2p08PW8DJ598I6x8Hb5YAUv/C8PPcx1RRFLfodbaW/desNbeBNzkLI2IiIiISBLE0sF8OzAHb5bcgDpv/WvfH0wO3gznusqA7HprGcBsvE7mfOB14GljjKpDIhK1cdtuCgAAIABJREFUla/fR8AXYTe5jDz5ctdxpIW45Aivi/md5dvZlG1g0CneFXP+BpHUOf1IRFLWZ8aYhcaYnxtj+roOIyIiIiKtmC91SqVRdzADg4CLrbVNnR9XBmTVW8vG2ySwrr8Dz1trVwIYY34E7MGb/byoiY8tIm3I5ztKOKzwJfDB5r5nMySj/utYIg2bPLw7v395KbvKqnnqow38v/E/hpVvwJbPYM0MGHiC64giktr6ABcCFwC3GGM+BJ4EnolmzxIRERERkZYolg7meXhF3qZaBph6a4b9x2b0weti3qsGCAPVzXhsEWlD3p3+NL183t/x/U/5geM00pJkpgW+nMX81LzPqe51FPQa5105528Ok4lIS2Ct3WStvdNaewzeGX7TgEuAz40xr7pNJyIiIiKSGLF0MD8L3G+MOR5vg7+quldaa+85yO3fATKMMdcC9wHfAArwRmDU9SpwvTHmf3jzl28HFgMrYsgqIm3UztIqClY9BT7YkjeS7j1HuI4kLcyUI/tw/8w1FO6p5I2l2zlj/HXw9GVeB/Pm+dBjtOuIItIyFAOFwDa8hon6+5iIiIiIiDRZCk3IiKmD+WfAbuAM4Drg+jpvPzvYja21lcBkvC6OncC1wNnW2lJjzGvGmBtrD70Jr9tjNl6BeSBwjrU2HENWEWmjps36jBP4BID247/tOI20RH075TBhcBcAHp+7HswZ0GmQd+WcuxwmE5FUZ4zJN8ZcaYx5BdgO/AavUWKMtXac23QiIiIiIokRdQeztbZ/cx/MWrsQOKaB9cl1Pq7kq8K1iEjUqkJhij/6D+m+Gqr8mWSPOt91JGmhLjuyDzNXFPLBmh2s+qKMQ8b/CF66Fpb+F3atgw79XEcUkdS0vfbtWeBma+08x3lERERERBIulhEZGGMygPOBwXib8Y0ElllrtyUgm4hITF5bvIVTQ2+DH6oGn0V6RjvXkaSFOnFIV3q0z2RzcQWPz13PTadfBG//HkoL4eOpcPLvXUcUkdQ0GXjHWhtxHUREREREJFmiHpFhjOkPLAf+CPwKyAd+CCwxxmggpYg49/Z77zLCvw6A3CMvdxtGWrRgwM+UI/sA8MzHn1NU5YMxtd9Tnz4G1RUO04lIqrLWvq3isoiIiIgkR+oMYY5lBvPfgTeAvsDev6wvwduU78445xIRicn8DbsYXjgdgIqcntD3WMeJpKW77Ki+ZKcHKKuq4bEP1sPYb4LPD+U7YcnzruOJiIiIiIhIG+ZLoV3+YikwHwvcUXezPWttCLgFGBvvYCIisfj37FWcG5gNQMbYS8Efy9ObyP7ys9O5eJzXxfyv99dRkdMDzOnelR896DCZiIiIiIiISOqIpQJTCXRsYH0AUBKfOCIisdtaXEHpktfp4isGwDfqEseJpLX49nH9Cfp97Cit4tmPP4cjrvKu2PwpbPrEbTgRERERERGRFBBLgfkx4J/GmCNrL3cxxpwN3A88GfdkIiJRenzues71vwdATe+joeMAx4mkteiZn8XZh/UA4IFZawj1OQ46D/au/Oghh8lEJFUZY4YZYx4wxswwxvQ0xlxjjDnFdS4RERERkUSJpcD8S+BtYAaQA3wAPAe8WHudiEjSVVTX8OqHSzjJ73WTBkZf6jiRtDbfmzgQgM93ljN9yTYY9x3visXToGynw2QikmqMMZOAeXi/Kx8FZAA9gFeNMRe5zCYiIiIikihRF5ittSFr7Q1AB2AEMBroYK39sbW2KlEBRUQa89Jnmzm28j3SfTWEg1kw7BzXkaSVMd3aceKQrgDc9dYKQsMvhGAW1FTCwmccpxORFHMbcIO19lKgGsBaeyNwPfBbl8FEREREpHVJnS3+YigwG2OGGmOG4s1cjuD90ty3zrqISFJFIhEembOOrwdmAuAf+jXIaOc4lbRGPznJG4uxurCU55bs+eqFjPmPQSTiMJmIpJjhwPQG1l/C+x1aRERERKTViWVExmJgUe37vR8vAhYCC+IfTUSkcR+u3UnN1iUc5l/jLYya4jaQtFojerXnrNpZzHe+tYLKEbWjWLYths3zHSYTkRSzCTisgfVJwIYkZxERERGRViySQj3MsRSY++N1XvSvfRsMTAY+Ac6OfzQRkcY9Mmct59d2L0fa94J+xzlOJK3Zz04ZTNDvY9vuSh7+vBt09GYzM/8xt8FEJJXcDjxojPk5EADONMbcAdwF/NlpMhERERGRBIllBvP6em+rrbVvAD8C7kxcRBGR/X2+s4x3lm7mvMBsAHyHXQL+WF4zE4lN3045XHpkHwDufW8NZcMv8a5Y9BxUlTlMJiKpwlr7CHA5cDpQCtyMt9nfFGvtQy6ziYiIiIgkSjAO91EO9I3D/YiIRO3+mas51reQLr5ib+GwS9wGkjbh2kmDeO6TjeypCHH3znFc7wtA5W5Y9hIcdrHreCKSAqy102l4DrOIiIiISNz4UmdCRvQFZmPMDxpYbofXpTE7bolERA5i+54Knvl4I3cG3vMW+hwNnQa6DSVtQufcDK4+fiB/eWMF93xSyncHnUj7DW/Cp4+pwCzSRhlj/hTtsdbaGxKZRURERETEhVg6mK+vdzkCVAHzgF/FLZGIyEFMnb2O3FARp2R+4i1ocz9JoqsmDOCF+ZtYXVjKXbuO4re8Cetnw8610LG/63giknzjojwuktAUIiIiIiKORF1gttbqr2YRca64vJrH567nosAs0qiBtBwYdq7rWNKGZAQD3HruCC5+YC6PFg7i+ryOZFXthM+eghN+6TqeiCSZtfYE1xlERERERFyKZUTG0GiPtdYubVocEZHGPfbBOkoqq7k4o3Y8xvBzIaOd00zS9hw1oBMXjO3Fs59s5OnKo7nS9yp89iRM/Lk2mxRp44wxI4GrgOFADbAAuNdau9ppMBERERGRBInlr+DFwKLat8X1LtddXxTnjCIiAJRVhXhkzjpG+1YxyLfRWxxzhdtQ0mb98vRD6ZCdxlNVx3kLRRtg/Ry3oUTEKWPMOcAnwMja94uAo4FFxpjjXGYTEREREUmUWArM5wMrgHOATngb/J2AV1T+GTAA6F/7XkQk7qbOXsuO0iouSZvhLXQ20Cva0Zci8dUxJ53fnDmU5ZE+LA738xYXPOk0k4g4dxvwW2vtRGvtz6y1P7HWjgf+CNzpOJuIiIiItCI+fK4jfCmWTf7uAC631s6qszbTGPMd4AVrrX5pFpGE2VVaxf3vrSGbCr4W/BDCwJhvgC91nlCl7Tl3dE9e/mwzz62awHD/OiJLX8R3+p8hI9d1NBFxox8wrYH1J4GfJzeKiIiIiEhyxNLB3BGoaGA9C8iJTxwRkYbd/e4q9lSGOC/9IzLCZeAPwsiLXceSNs7n83HbeSN4OziBqkgAX3UZLHvJdSwRcecl4AcNrF8ITE9yFhERERGRpIilg3ka8G9jzE+B+YAPOBL4K/DvBGQTEQFg464yHv1gPRDhmrz3oAQwkyG3i+toInRvn8UPzjiSd14ew2mBeeyY8widRk1xHUtE3CgGrjbGnAzMAULAaOAI4A1jzDN7D7TWXugmooiIiIi0Cil0RncsBeZrgYeBl/mq87kK+Dvw6zjnEhH50p1vrqSqJszxOevpVrLMWxx3ldtQInVcPK43d8w9ndN2zqNT4UcUb1pJ+56DXMcSkeRLxxuHAZBW+7a89i0mxpgjgBettT1qL3cApgIn4hWyb7bWPnyA294NfAeorrM81Fq7IdYcIiIiIiIHE3WB2VpbClxsjMkHBgFlwGprbUNjM0RE4sJu3cPz8zcC8Nsus2Ar0OVQ6D/BbTCROnw+Hxdc/G123H0nnXy7+eCFuzntmr+5jiUiSWat/WZz78MY4wO+ibf/SajOVQ/incNTAIwEXjPGzLPWLmzgbkYBl1prn2tuHhERERFJTSnUwBxTBzPGmK543RCDgRuAs40xS621ixMRTkTkz68vJxKB0fkV9N/+prd45HdT65lUBOjTtT1L+p5Fpw1PMHT7K7yz7OeceGh317FEJMmMMUcDQ4GMeldFrLX3RnEXN+LNbL6V2o0BjTG5wDnA4Nrmjo+MMU8CV+GdZVj38f14BegFzfl3iIiIiIhEK+pN/owxowELnAFcAuQCJ+P9gjspMfFEpC2bt24nby3bDsDtfefhC4cgsz2MvMhxMpGGHXra9wHo4y/kmWnPsrui+iC3EJHWxBjzV7zZy7cC1zfwFo2peB3I8+qsDQKqrbVr6qxZYFgDtx8EZAN/McYUGmPmG2POjOkfIiIiIiISg6gLzHin6d1lrR2PN3sZa+1VeDOY/y8B2USkDYtEIvzfa97IypHdsjAba8/yHXM5pOc4TCZyYP4eI6ns7NV7Tqx4i7veWuk4kYgk2TeBq6y13ay1/eu9DYjmDqy1W6y1kXrLOUB5vbUyvEJyfR2AGcCfgB7AzcAzxpgRsfxDRERERESiFUuBeSzweAPrD+CdBigiEjdvLdvOJ+t3AfDHQ1fhKy0En1+b+0nKyxh7GQBnBOby7PvLWVNY4jiRiCRRKfB+Au63DMiqt5aNN5N5H9baudbaSdba96211dbaF4G3AXUxi4iIiLQiqTQ4NJYC8y6gXwPrY4HCuKQREQFqwhH+9D+ve/mY/h0Ysmqqd8XgydChr8NkIlEYcQERf5AcXyUn8SG3TV/mOpGIJM9vgb8ZY4YZY3KNMdl135pxvyuBNGNMnzprBlha/0BjzCRjzPfqLWcC2phbRERERBIilgLzPcADxpiL8Irko4wxPwLuBe5PRDgRaZumfbqRldu9pqxbD12Hr7C2QHfcTx2mEolSbhd8g04F4ILATN5atp1ZK/U6rEgbsRk4AlgIFAN76r01ibV2D/Bf4PbaYvU4YArwRAOH1wB/NcYcZ4wJGGMuAY4Enmnq44uIiIhIKkqdHuaoC8zW2j8Cf8Gb55YNPAf8ArgFzWAWkTipqK7hzjdXAHD68AL6L7nHu2LgJOh1uMNkIjEYfSkARweW0t+3hT+8spRQTdhxKBFJgnv4ahzFiQ28NcdVQBqwEZgGXG+t/RDAGHOjMeY1AGvtDOA6vM0Cd+NtLniWtXZTMx9fRERERFJK/W073AlGe6Ax5kLgSWvtPcaYHCBgrd0dy4MZY0bjdTsPwzvV7/vW2rkNHHcucDvQE1gCfM9a+1ksjyUiLdOjH6xjS3EFAb+P3w7eANMXeVdMvMFpLpGYDDoV2vWAPZuZEnibW7d1Z9qnG7loXJ+D31ZEWrICvMLv2ubeUW2huHOdyzuBCw9w7G31Lj8MPNzcDCIiIiIi0YhlRMZ9QDcAa21pE4rLmcDLwCNAPvB34HljTHq940bjdVxcBbQHXgCejeWxRKRlKi6v5u53VwNw4dhedJt/l3dF/wnQ5yiHyURiFAjC2CsAmJI+iwyq+Oe7q6hWF7NIa/c0cK7rECIiIiLSFqTOiIyoO5iBj4HTgeVNfKwTgLC19t7ay1ONMT8BzsI7zW+v7wEPWmtnARhj7gDeMsb4rbX6y1ykFbv/vdUUl1eTmebnhoHrYdEC74oJ6l6WFmjM5fDen8gJ7+HMwFym7ZzAC59u4sJxvV0nE5HEKQJuNcZcDqwBQnWvtNY22IEsIiIiItKSxVJgrgT+Yoz5HbCeejtRW2uPOMjth7D/TtcWb1xG3QLzGOAVY8w7wEhgPvBDFZdFWrcdJZU8MmcdAN8+pg8d3v+Od0WfY6Dfse6CiTRVXg8wk2H5K/yw3UymFU3gn++u4twxPUkLxHICkYi0IB2Bp1yHEBERERFJplg7mD9uxmPlAGX11srwNgysqyNwNV5n8yLgZuAlY8xwa20IEWmVHpq9lvLqGnIzgvwwfy5sr3096uTfgy91TvsQicnh34LlrzCgYilDfetYurMfL8zfxIWHq4tZpDWy1n7TdQYRERERaSMiqdOL22iB2RhTBvS11hZaa2+uXRsLLLTWVsf4WGVAVr21bKCk3lol8Ly19uPax/sN8FO8DujFMT6miLQARWVVPPr+OgC+c2Rnsmf/0Lti2HnQe5y7YCLNNeAE6NAfdq3ll10+4Bvb+3H3u6s4b3RPgupiFmmVjDHH4p2hF6hd8gEZwGhr7TecBRMRERGRViWcme86wpcO9tdtJvtPjH4XaErr1TLA1FszNDw2o+5nyFfnTURaoUfmrKO0qobs9ADf878MpYUQyICTbnIdTaR5/H443GtoHF/2Jh3ZzfodZby6aIvjYCKSCMaYW4GZwO+AfwC/AO4A/oxXZBYRERERiY8UOtu7Ke1TTU3/DpBhjLnWGJNmjPkWUAC8Xu+4fwFTjDHHGmPSgFuAlah7WaRV2lNRzSNz1gLwg9EZZH1cuw/oUVdDh74Ok4nEyZgrIL0d/lAFNxXMBmDq7LVEIhHHwUQkAa4ErrbW9gA2AhPwft99B1jtMJeIiIiISMIk7fxca20lMBm4BNgJXAucba0tNca8Zoy5sfa4l4DvAw/WHnck8DVrrf4SF2mFHv1gPbsrQmQEfVxVci+EKiC7Exz3U9fRROIjK//LLubJ5S+TTQWfbSzm0w1FjoOJSAJ0AV6r/XgBcLS1tgj4FXCRs1QiIiIiIgkUyyZ/zWatXQgc08D65HqXHwceT1YuEXGjorqGqbO97uVbBq0iY3XtCQ0n/wEy2ztMJhJnR/0APryPtKpirs2fwx+LJjF1zlrG9u3gOpmIxNcWoCewAW/s2yjgP8AXeJ3MIiIiIiKtTjQF5iuNMXU34gsClxljvqh7kLX2nrgmE5FW77lPNrKjtIrO/hLO2/o3b3HACTBqittgIvGW1x1GXgTzH+MKXuEOJvK/xVvZXFROj/z6+9+KSAv2FPC4MeZKYDrwrDFmKXA6sNxlMBERERGRRDlYgXkDcHW9ta3AN+utRQAVmEUkajXhCA/OWgPAvV2eI1C8A9Jy4Ky7UmpQvUjcjL8O5j9OdsU2Lsn6kEfLx/PoB+v5xeQhrpOJSPzcCOwGOlhrXzLG3I23wd8O4AqnyUREREREEqTRArO1tl+ScohIG/PGkq2s31HGRP9njCt+w1uc9Btt7CetV+dBcOiZsOxlfpzxEk+WH8l/PtrAjyYdQnZ6UidWiUiCWGtrgFvrXL4JuMlVHhERERFpxVKoOS9pm/yJiOwViUS4f+Yacijnr1mPeIu9xsER33UbTCTRJtwAQMeKz7k4+B7F5dW8tGCz41Ai0lzGmExjzHnGmJw6az8wxrxkjHnIGDPCZT4RERERkURSgVlEkm7eul0s+LyI64NP07lmOwTS4ex/gj/gOppIYnUfCSMuAOBnGS+SSSWPzV1PJBJxHExEmsoY0wdYBjwJdK9duw34B+ADsoA5xpjDnYUUEREREUkgFZhFJOkemLmasT7L5cE3vYUJ10NXzaGVNuKEX4E/jfyaHXwr8D+WbN7Ngs+LXKcSkab7A7ASKLDWrjLGdAB+CvzXWnuWtfZS4P9qjxMRERERiRONyBCRNmrltj3MWraRP6Y9iJ8IdB0K43/sOpZI8nTsD4d7e+X+IO0V2lPC43M3OA4lIs1wKvBra21xnctpwNQ6x0wHjkl2MBERERGRZFCBWUSS6sFZa7gm+CKH+DcT8fm90RjBdNexRJJrwvWQlkMupVwTfJFXFm5mV2mV61Qi0jT5wNY6l08AQsC7ddZ2A5oDJSIiIiJxE0nPOfhBSaICs4gkzbbdFSyf/wHfD7wMgO+oH0CvsY5TiTiQ2xXG/wiAKwOv06vmc577ZKPjUCLSROuBoQDGGD9wOjDLWlta55jjgbXJjyYiIiIirZYvdcq6qZNERFq9f81exS2B+0jz1RDO7+fNohVpq475EbTvTZqvht8FH+WJuesIh7XZn0gL9G/gH8aYS4F7gZ617wEwxhwD3AI87SaeiIiIiEhiqcAsIkmxp6Ka4Ef3MtLvNXD5z/47pGc7TiXiUHo2nHILABMCizBFM5mz+gvHoUSkCf4IvADcBZwL3GitnQZgjPk7MBt4v/Y4EREREZE4SZ1N/oKuA4hI2/DqjPf5YeRp8EH5iMvIGjDRdSQR94Z+DfpPhLXv8evg4/zfnJM5blAX16lEJAbW2hrghtq3+h4EplprFyQ3lYiIiIhI8qiDWUQSrjpUQ78Pf0umr5rdwY5knX6r60giqcHng8l/IuwL0ttfyKBVD7OluNx1KhGJE2vtIhWXDy7NnzrdNyIiIiISOxWYRSThPn3tEY6KeH9fl514K2TlO04kkkK6DiE87ioAvh94iVdnfug4kIhIcvl8KjCLiIiItGQqMItIQkXKizjkU69jeXHWOLodfYnjRCKpJ3jiLykJdiTTV83AT2+juibsOpKIiIiIiIikMF8KzWBWgVlEEmrTC7+mU2QnlZE0Iqf/2RsJICL7ymxP+cTfAnBC5EPmvzvNcSARERERERGR6KjALCKJs2UhPVY8AcALuRczYsRox4FEUleX8VewMv1QAHrNvQlCVW4DiYiIiIiIiERBBWYRSYxIhJL/Xo+fMGvDBXQ69QbXiURSm9/PFxNuIRzx0SO0ke1v3eU6kYiIiIiIiMhBqcAsIomx/BVyt84F4OGcbzNpeG/HgURS37ijT+SV4EkAtP/or7Bnq+NEIiIiIiIiIo1TgVlE4i9USdVrvwJgTs0wRpxwMX6/Zi+LHEww4GfP+BspiuSQES6nYvqvXEcSERERERERaZQKzCISfx/eT/ru9dREfNyf9R3OHaPuZZFofW38SO72XQRA5rLnYMNcx4lEREREpC3Y0v1k1xFEpIVSgVlE4qt0B+H3/gTA0zUncPKJk0gP6qlGJFq5GUEC477FsnAfAMKv/gzCNY5TiYiIpIYdnQ53HUGk1Qr7A64jiEgsfKlzpriqPiISX3PuxF+1h5JIJo9lXcoFY3u5TiTS4lw+/hBurrkSAP+2RfDJI24DiYiIpIiKrALXEURERKQeFZhFJH52byHy4YMAPFwzma9PHEtmml4FF4lVj/wsug4/kRdrjgEg8s4tULbTcSoRERERkcTwkTqdmCISOxWYRSR+Zv0FX00FRZEcns84hylH9HGdSKTFuuq4AdxePYXSSAa+8l3wzh9cRxIRkXrKs7q5jiAi0ipkpqk8JdKS6SdYROJj1zoin/wLgHtDZzNlwgiy0tW9LNJUI3q1Z9iQIfwjdC4AkY8fgc0LHKcSEZG6dnYaS1lWD9cxRERi1qN9lusI+wj4W28H8+484zqCSMKpwCwi8THjj/jCIbZH8nk16ywuP7qf60QiLd6PTxrE1JrJrAl3w0cEXrsBIhHXsUREWr2O2en7XO7dIZvM4AFeOE+hDXZEGjK0R57rCAlVktvfdYQWqUd+ahWYWy8fe9oNSOgj7Ow4KqH3L6krlX4FUYFZRJrvi1VEFj4FwD9C53DVicPUvSwSByN75TPh0J78PnS5t/D5h7DwGbehRETagD0Fh+9zuSAvk4456Qc4WiR1+fCRnRZ0HSOhitsf6jqCSNTyMtPIqPeCZdjX3J/RFKoySpulArOINN+sv+KLhNkc6cis3NO5+IjerhOJtBo/PmkwM8KjeLNmjLfw9s1QVeY2lIhIKxfI23/sRbf2mQ6SiKSWzGCA/Kw01zH2lUotfNJkLfkkvVAw5yBHfPU9OrigHcPrnVXgowX/40VqqcAsIs2zcw2RhU8DcE/oa1x90qH7vSIrIk03vGd7Th5awO2hKYQIwO5NMPdu17FERFo1v3//P5P8BypipUBVJC+jdXeoSuoY3K0d7VOowFyW3ct1BGmBcuP4nFmRWUB1MDem2/hayYsiKfdikzilArOINM+sv+KL1LA10oGP2k/mvDH6JU8k3n5y0mDW0oPHQid5C7PuhD3b3IYSEWnNfC3rz6SGCuIiiRBM4kZsI3vlH/SY6rTWPV86FqU5fV1HaLZtBROT8jjxfMYszyqI4721LLmZ+xbqq4O57Og0zlGa5kvT/6XNktTPnjFmtDHmI2NMqTFmgTHmqIMc/y1jzBfJyiciMdq1jsgCb/byfaGz+OEpw0kL6ElZJN6G9sjj62N6cVfoPHaTA9Wl8O4trmOJiLRqNYHkjMTo2i6jybf9ovMRcUySfLF2XldmdIzquL4ds5sSJykGdI6t0zFeElkY7pLb9O/hxqRH8XdFeVbXhDz2wezsOIrqtHbkZaZGB2fE56ckt19SH7M0Z/+xiN3yGn/e3N51fKPXh9Lc/HxIfBR2HU9FDD+TJbn92NFxTAIT7S/SyAvIaUHvurBfey40RdIqQcaYTOBl4BEgH/g78LwxpsGvnDFmAHBHsvKJSBPMvhNfJERhpD0fdzqLM0fuP69QROLjZ6caKtPyuav6HG9h/uOwdbHbUCIicdCtc3RFw9aqa7tM0pLYFdqS7eg09qDHBHw+2qVI0a8hHXPSGdgleUW0tID3vTWoa7u43af7oTBfqTno7Nv429b1OMqze1Ke1YMBXXLo3yn5GRoS9sc+9iHe2RtrNgr7glSnH7wrvTWL5kWTlizii21UZnH+MCqyuycoTewGdM4hOz1IYZejXUeJQer8/pDM7+4TgLC19l5rbbW1diqwAzir/oHGmADwKPBAEvOJSCyKPic8/wkA7gudyTWnjCSgP45EEqYgL5PvTxzIYzWnsCHSFSJheONXKTH7U0SkOTrV636sSu/gKMm++tUWXpJRPErlERc987O+/NjlvNvCLkcRiaKrbO//ihWZbjpbU80htcXsnIxgVGcaRtslXlcrGScbld15gwmlfzWWI+j37/cc1lR197GpSs+P+QyFcCCT8qzYinUdctIpz+p20OP2tDskqvuL5rfSyozOUd1XU3XXhqxJE8n96vttR6dxzX4ycH02dGZagKHd89RJ30TJ/OoNAZbWW7PAsAaO/QWwBJie6FAi0jSR2X/DH67mi0geCwrO5dRhbXf2lEiyfHfCADrmteO26inewpoZsPJNp5lERJqr/p+jhV0pp8jmAAAgAElEQVSOZkv3k51kqasgL5PD+3aMW/GoMQM6J6cDsjKjU8y3SQ/4yU7zCl9Vcew+jLWTryrG7Ls6jIjpeGh983wHdsklO8YxJLs6jExQmtQX9h/8Z7067atO8JLcPnF9/P6dc74sMhd2HU9lZpeY72NPuwFxzbTXgYrQNYGsBtcbEqntsO7UPoexfTokrJM/1g3nY/k3HEi42SOVWmbDSDijPVm1/z+EYvgcdMo58IuFe1/cjfWFgpLc/lEdV5ke+/+DEp1kFphzgLJ6a2XAPgOyjDFjgW8A/y9JuUQkVrs3E/n03wA8GDqDa049rNXshCuSyrLSA9xwmuF/4XF8FDbe4hu/hpqQ22AiIvHk8xEOpOD8wwT+rpOTEaRjI39w++P02CW5zSs+hX2xn4LvSlMKPjs7jk5Akv21i7Ho25AdnQ6PQ5L9RXwHHi/SMSc9bt+LqagiswvVwf2LnsN65NEtL5P8rH0/NxF/OrQ7ePdvLJpyQmheZhrd22cxrEfyXyCJxHB6/lffsz58Ph8ZQYfdqvW+jzf3aN6LmsXtB++3FtPZvQmsL6fiWI7GagedczMY2SufnvmxzdIvy/5qXOfuvP2/Hnvt6ngYpTm9KcpvqNe1cZ0P8IJzIjuvD/SYqSiZ32llQP2XhrKBkr0XjDFZwL+B71hrSxCRlBSu7V7eGcllSY8LOH5w7K+ui0jTnDOqJ6P7dOCW6su8hS8sfPovp5lERBKtqRtpBeJZDOs6tMHlUBNnwBZ28fY7j0eRJV7/zFG9kjwftZHcFZmt9+y4YMDPyF75dG3X9K7HpnSTd85t+gs3Be0yG9mgsPUWnQGy0oL06pBNVnoDnbG9Gh5j4Uvi58Tng179hnBIDHO2D+2W/GJ0dXr7pDzO3jMuGhMM7Pv1iWb8TmMi/vQGX5yIVuecr150auzFxgMJBVN3Y9O6ou0ybm5RPNLIi6HhQAZFHUY26YyexjqvG9Pazo45kGQWmJcBpt6aYd+xGYcDA4BXjDFFwCtAR2NMkTEmvuefiEjT7NlK5ON/AfBQ6Ax+cuZodS+LJJHf7+P3Zw9nEQN5oaZ2J+53b4OKYrfBRCSujDFHGGM217ncwRjzgjGm2BizwRjz7UZue5IxZrExptQYM8sYc+BWnlQQ/KrIdqBi7aCuTfvDPTcz8R23e/IGxnybjjnpHNKvP2P6dEip36OCDjrdDlSUifjin6UmihEIsWpq51p6wE8wyg7H0pzeTXqM+nq0zyIn/cA/E1H9W7rU/5Me8mL4OYvma1CV9lUhMpmF2lAgK/ZXa4IpcrZF98NiOjynCV309Tu4m61e125Jx9g7ShsSzViYDlnJ/LodvD05Ldi0/6uq0tpTmtOnxWyeWNy+9vmjiXvINLqJZJ3nluoEzVBu6vN9U0Y2fakF7beTzN8g3gEyjDHXGmPSjDHfAgqA1/ceYK2dZa3NttbmW2vzgTOBnbWXNyQxq4gcQGjW3wiEKymK5LB58GWM7du2d34XcWFEr/ZcPK43f66+iIpIGpTtgHdudR1LROLAGOOr/T35DaDuX8AP4p35VwB8HfiTMWa/YanGmALgeeCXQAfgLeA/ic7dLL3GEfalEfZnfNnV26L4Ypv3CTCgcy6DCtrtM26goteEqDfSSqTG5l4mYnTJ9oJjCfvTk7JZdCxFmNwoC3CDEjRHtq6GuvHC/tiLfT6fj0O7N7OTrt73e0YwELexGaFgDoVdjuaLODwPNKUYWhLH+cW5GbE/L8C+84ML8mLocA8k9sW0zrmZ9K234WksXZl7X4QI+v3069Rwt215XuOf/1g27vz/7N13mGNndfjx7y3qXRppei93ys72vuv1ru117/RiCKaZ4mB6KAkBQv0lISEFHDDYJPQACb3bQLABF8ANZHt37bXX2+v0Iun3x52i0ajOaCTN7vk8zzy7c+eV9I5GujP3vOc9J9f7t+L6qnry27HhTFkgOlq9nVMFBC8DzgpZEMnTdMbwgYYrco6N6Q6OB9dyyt+XV/3yYtTezpfLkfu9vNDFtMpZoi5hgDkajY4BlwEvAk4ANwNXR6PRIcMwfmAYxrtLNRchxAINHiFx3+cA+Hzsct50xboyT0iIc9fbLjYYtNfwb5PXmAfu/QwceKC8kxJCFMO7gTcBM6tGhmG4gWuB90Wj0dFoNPo74EvAq9Pc/nrgD9Fo9DvRaHQc+DugbarPSUVSHV4O1l/MwbqLitAoaa5KuvCao3rFvEMdrS2c8c3PDs0kuRlbKWpsDrkaF9R0LCdFY8wawChge//SqcxMselg8oo6H2e8XRyOnAdLkOGdr+SEOrulePMYdLcwbgvONINbaqd93TP/n9DdRX3cppBzQbVTbbrKmM1M4Ml3kWMx8j1Hrmr0zcnePOPpJO5PFxBO/x7qqvZy9ao6Lumrxj4VRE8dmWvHyaTuXHC5pHxEPEsTcEyg5syMn/Tk3qWgoNBb6y1+JnkWK+pylDVJXnBKOictpPxEOi0hV0E/81FnLUPulrzGFvs8M92cMJ5SbuWUv4/z+3PvdGqtchHxLJ96y+mU9LdSNBp9MBqNbo1Go55oNLomGo3+Zur4ZdFo9MNpxt8VjUarSjlHIURmI7/4JyzxMc4knIyueSWtJep4LoSYL+S28daLDW6NXcWeeC0k4vDdN0M8Vu6pCSEW53PAauDepGOdwEQ0Gt2bdCwKpNtP3E1SCbpoNBoD9mQYu3yo87MBszXxqSR+h3VOoGnI1QyR7nnjrLpKbwHZpcNJZRNq/fYlDbwMBPs4FZiXML9o8aQIk9OmFy0TNtPdLDR83BBw0J6x/vDCOfKoFQtmBvOxqo3E6tcz4O1k0rrALGR3BDouLGr5kXp/cYJyx6o2me+NFD7H3CDQdH3dbKU+UmXKjo+pxV3QSuaw6FR7Cw8WjftaOFaVvq5zpoWk0zVbZ/6frfZsOoqizKmtvbYxQL3fkea1OffdM+DrIlBgAF1RlDlleJLrzzstWu5gJuBMVwe7COr8DixaaZckkzNWJz31HA9tYMJSvIW2fDLMk+fgtunEVducZq72HOeoSXct444wI45aJpPKUiy0N8EcVjeKouBKsxtg3BpY/P2nWOzv0Onf86O2qjlljabLAsWzNFAFsy54U3B5x1cqbWOAEKJSDR1Du/82AL7I5bzmkrVlnpAQ4iWbmmirCfLeyRvNAwf/APfeVt5JCSEWJRqNHoxGo6lxMBcwknJsGLNhdirX1NfyGStKwG5RaQm5ZrP2lqDmsq6qdFXPDUz4Csxye7ZuN2QogZFr63qy1OBlewlKSICZJbZUNFWZ1xSsGAJ5Nowat/oZs4dJ+OcHYAticYIjwKGaCxZ3P0kyBW8TU6GGbNu+k4OYY/aqtCsDqc9RW9jN6gb/guurOyzaTO3rEWfNzPFMwbiFLCx4Csw8HnbWz/x/0uoruOzOpGM2J29yAbVnk4O2Nl2l1ufAkvJzXYoysLqm0lPjxaj20Fvnw7qIhqfTr+nm4MJ+1a1unFs+J55nvfaF1uQ1bzv3OR51RIoTmJ0SV3UO1ezMWud/TZN/5nuo9dk57TMYdZjlOqbfn1kXkRSFicbtnAhljg3k07A17fPdugPq1zLeetHMoelFyNEF7KZpyvHaKLTXw7N1u2d2QQRTSo8MOxvmjT9Uu6ug+5+W7edn07WKKnsiAWYhRF5O/uwTWOOjDCQcWLa9ntACtnwJIYpL11T+9uo+7on38c3YdvPgzz8IZw6Wd2JCiGIbBlKv8JyYNZkXM/as0hpy0VFXlbKtvDQZaYklvqxKzvTrrvHSX58706/QmsYJ1ZpX2YVs2a/DzgaerbtkzrFsF7/TUxx2zb8Ynyv395Iu+3UxCgmotS1BdjPA0fAWjofWMW4rbrZeXFvc3/HJAdRcjQpTFzpakur4LnQ35HQW7Jgt82bnTEGZOTWokwK5mer75rsIkKwxQ43hTCqh9vpCZMoiL6S2rcum4ynC7ouY7qA15CLsWVhWemqgeFJf/JqsK88dCulYilQkOpYjYK0qCivqvPTVefE5rCQUjdO+HsatgZka4LW+7D/PlQ3Zfx8tOCvb6oRgG7XVswFqi6YwbvEx4GnnjDf/klIwv351qkznjEw7a3SLnU2d9TQHndQHcr/mE6plJiB9JLI95/hcjw/QV+dFLUH/gnxJgFkIkdvwCRy/N7Miv6Fdzkt2ri7zhIQQ0za3hbhyZS0fnngJZ3DB2Bn43luXVcdhIUROjwMWwzCako4ZJJXCSPKnqa+ZgwxDAzoyjD3r+Nden7VJXWHyv2grZsmBWJpMLldSQM9t0+c0Asumu2aRDd2mJDcbO1y9gxFHTebBaZ6LuowBiqlsNEcNtJ7PodrZzNpgUmBvyNU075aFsuf5nGWSLYss6LKyutGPNjUmsYDGj+mM24Lmc1MG2cp3OG06XREPPTVetDSBsIjHjlVXqU4T7Kv22uiMuGmvcuO06jSHnGlf81mF2hls2sWxqg1pvxzx2OcEDJN/cqnBmiORbZwMrGLEZWYRx7TFBxadltLUkJ6WuohzPLS+qPc/meE56ap246mdGxxPJOBYkR8/l9hU7X7bIgK6AHFr8cpTNAWdeJa4VnKmQP765mBet5/OutVUFcfUa3bEUUtcs3E0snXOOTgbu0UjnKV2cHKGft4hyKTdNNNv2SORbQy7mzkRWgeKyoC3Y0lKZaTKdOav9dlx23TCHvu888qkPrvoOGGdDcAPeto50HDFnGMLVedzmI+7BLuiFkoCzEKInA7+6B+wJ0YYStgIXHQLjiWqfSWEWJj3XNHDkCXIBydeYh6Ifg8e+VZ5JyWEKJpoNDoA/C/wEcMwnIZhbABeDHwxzfBvAesNw7jeMAwr8F7gGeD3JZvwMjdzwdq4Ke/bnAyuWqLZLI7bpmNULz5o0lXtYUW9j/O7wsR0FwOe9A2LMh2v9dlzb+N1h4nrswGTvjzqsRaiqybz89AQyD+oOOhundMcbpquqouqD1toWYUFSdPUKlMGcq7n3+uwzC58pNyFTVdZ1eCjMcOWdJ/DOpMZPFm9hiPVO3JMfNZ0Zn7c6k27mLGywZ9zK3yyCat/Tgb9ycD8BpyLlasWbiwpmBazz5ZqSF5YCjqt815fnRE3tT47HSlb+0cd1Txbt5sDDVcsZtozEmlq4IOZSd63ciP2tq2MJJVBSK0RnlA0aEi/GFBJRmo3Mmar4nhwLR1hd16LlZmCsBGPfUFxvwFPx5wdK5mMOGo5EtmWdcyQM/vCnDO1trGnpojByqT60hY3h2p2mWWYphfhMtzKk6X0zYTVz2BoJTF9aZox5pKpNno6cc3Kkcg2joa3EiskG75+XdbyLMm/JyoorjxDAsxCiKwSg0fxPWhmL3/PfiVXbu4v84yEEKlqfQ7eeEEHX4+dz6/iU+/R778dhk+Ud2JCiGJ6NWDBDBZ/A3h7NBr9LYBhGO82DOMHANFo9BBwDfA+4DhwEXB9mrrOFS/b9velcqxqE0fDW8xPXCGw5lf6YFIvXuZb0Uz9xIux/VxTFdrDbvw5gsSZ6r+ajZpKm9WZKlODNMidqx5PKlFx2t/LoKc9bZZoa5WbgNOK25b/cx7x2NBVhaYCyyosSKQXmC254rBodEY8WDWVxoCTY7XnF/HB8ot+TLrriKep/T0xnQFomX1eqty2rDVvV9T5sv6c8xHX7Fkz9AvJTtensrvTBaaSS9gkVCvHqjYx0bAZ7LOvteRAuUVXaQrNLXfgc1ip9zvTlsNJqEWuy5ppZ5yqMuGunwmipZtLvPsaCORXwqYhj1IDSyVhdXMsvIlRZy1+l4VanwO/wzovE7/KbWNFnY/mkJM6n51ilWJa0xigpqaWmk3Py3qXCVROhNbOK3XjqWqgd2rXyong6pms/GJYbDPPmO7M+prUNQW/w0pTjsW+dA3/MklXl38x2f2F7kyZsPoZtwXY0VlAvWhniEM1s+fh1Brw7WH3/IWFCtq1Wt7f8kKIivfktz5Aa2KEgYSDxiveUXA9PyFEabzqvFa+dt/TvOvEq/ip/Z3Yh4/BD98F199a7qkJIRYgGo3eBVQlfX4CeH6GsR9O+fxOoDJTaguQyHKFndyhvRBBp5WJWJyBscm0X49ptrlpQcmZe+rCArWpWUYjjtoF3U+hzCzCeMG3m3etmseffs0hJ08dn+0t6bXpnBmbpMbngs7d8PhPCp5Hqq3tVdy959ii7yedXMHvuCMIQwNzjk03wkp+fqy6SnvYzcGBCYZGR+fdz8zf0XVrwFsPT/yEpiA0BpxZS3DkQ1MUYtkCDboNdDPAc15nmFMn7YQ9dqyaysoGM2v2D6oHYqn9RMvjSPV50BUgtu+PwFEAwkk9YOr9Dp44Mre0vH2RJRKy8tYxMTHMmGKelm26SmuO2ttmMFxJW/PaZdU4Mzp7HhqzV5HwhGm3aew/MYzPYSH1sis5eJ5vmZwzXgPPwBM0tXXz9J5H8rrNYlS5bVQ5536/fQ3+DKPnW9ng5/gzTvwOCw8/e7rY0yuIqigz2eGqCgdPm+9pq6Zit2jYLRrxIgb3mkLOmYWm9rCb6KEB7BaVkYnYnHGZzhVGVw8cuB/IXFN8oWq8dg6cWrpzQ0+NB4cayznOa7cwv+dxekPuFuKqleCJ2Q1cM+ftdIJtcGIvOIMwkHnYHHruLPeC6rin7DIJuKwMpvy9MmH1c6D+UqoTj0K4vqJSmSWDWQiR0eiRfdTv+RIAP/K/gC0r528HFEJUBpuu8TdX9vJMIsxHx6diUA9+BR77cXknJoQQS+BUYOW8Y+kWwVOvu9rC7uwZvanBguQt+MHWvOs9TtdjVFAIucxgS73fwZHINuz+LBe4S6SxgBIQCxF22/E7Zi+iO6o9dNd4qe/bCvbilLrIVuMzlZJXU0Bz+3h72D3bGDLp55/PNXum2rQ52bxgmQ1MpAsYHaq5YN6xbNI14I470tdiddl06v3O2YClxQHNW7Pev91SpNBBMH0ZlXkUFWyZA7h+p5WdRnGDaFk1bGCkduPMC2N3bw1GlrIr0075ewt6GJuucXFvNVvaQ1nH5ZvJOeDt4EzrFVTX5GqkWRyqorCto4rmAsqUJLNoKjVe+8xiwfHQurxvmyl5PVs98Xylqyee28IDf26bzpomf2GlggIt4GuESA+JDAui4TTniXwoijLzHHizlLHIV6l2tEzoBTRgrV0NLedBS/4le/BUQ6gdwouLk1hUBXfDCrOxYT4UjZH6bVBTWbvLJcAshMho79ffhZVJjiZ8rHn+e8o9HSFEDhf2VLPLCPOF2MU8qEz1+Prum2H0THknJoQQSyzgtOLLs6FSQR3XG9aDZjEvIFWNo5GtjNmyB34A1jT6Wd3oZ0W9dyZQEnBZOW9lV9btsrVptiGvzpH9lzWTsdrcIlzttdMedoOiEJrKpiq4sVoB1JZtuJtWowRako6WbhuvVVfx5ng9DDvNgFvO2tCFCrYWMDjza7G6an5wOJEUAA+5bDlrsMY8dXk9Ft1XgNccG88QmKoqNDBlz1B32FMDvuIEO5Pf8+4yl2ApWJa3Q0HnqHwkLXgtllbibMlRe/YFObMOtYOeWu9Mo7r5YzzU+uwln3uVe3HnltTGcTkpCjRtguo+1rcEURSF3tq570N7tjrxgdRz19zHbwg46K31pq2tHsljAVBPaggadttmAtY2Xc2r7jTMf9usWm3W9s5UviK1HngmExaPmabuqQYt07kkw8+jbg3ULLx2e8RjZ8Xqjai108HizCeHeN2aBT9OKUiAWQiR1sHofXQf+SEA97e8mvb6EmYICCEW7G+u6kPXdN48+iomFQuceQZ+9v5yT0sIIbJamSaIWjPVYMmizg2LHIlsnze2PeyeyQJVfLN1J7WpGyZ3dI94bLisOlUu67yg1HQd0Zl6k3Yf9FxtXkCmcGbJilMUBV1V5wV/PXZL1nJjbpvOysa5z4U+lZaXGkzcaURoCjrpTGrw1V2TcjEd6YHOiwEzkHphfzPVKy9i0N3KGZ+RcR4Lk3RR7K2DSHfRt+62hFxzghTZbG7NvRCQiaYqeTX4SsueZUGggBj76sbsCwsNAQcT1vxLD+RNURizzQ9uF1LCY9JdA01bMg/I9hylPm6Or+/qjtBV7aEtXECm4oLMnUliCeqeZv1e83y4rqmmnukWWHpqPHjtFroa59aYTuhJwUFFgdrVTNrSZ85OL4KVLKCf43XntOo0BZ0z3/e0Cfvs+9+qq2bGfp5BzLy4c+9EmTlXFek0mO2pSA1G1/sdXLaihs58mrx2Xwltu8CXUrO548KUx1dwWvU55+DpHUFtOcrFAGxoDdBf76O3zouiKDQGnVzeX8vu3pqswfTUhZH1LUGsmsr6liCuSAtHw1vn7fjItcCY7lFyGU853xbrPaAqoFV15jfYnt8uqnKRALMQYr5EgmP/81eoSoL91LDt+W8t94yEEHlqrXLxyvNa2ZOo55OT15kH7/0sPHV3eScmhBBZtIScbGkPsat7dkHbrpu1YftTgs8T1uxbhr0dW3G2bSHstuFMcwGoKgo9tV5aki6IJzUnh2p2kVB1dnZF8DmTLk6TLnynM7fcNp3epK3Lk0l1GKsKqbeYhiNDRnJqMNHnsNBb65tTdzbtBa/da2Zi169DdwXQfXWc9veSUDSMak/WpmlF07aLmGN+08ZRb1tBd7Oq0c9lKzI3YAPyzmRPF7GbtLhJKCqrGvxZg1GFBy/yn8O0clTVrPFOv45zvCYaN2WNdo3WbQarK/0XLXOzH3PFrUMuGw6LhtOq40yTfem1W+ip9S66ud9SKfXcums8bGkPsb1j/vvNadPpqvbg7Zy7SBfztzJqr2bA02GWJqnq4FR9asNH87Va7bHRVe1hR9fcnRjjlkWWwmmc3whxMU6H13HK35czAzpZ8iLKYrK9i5oprajEFQujtuyN4tI1R8z73G6xm01tU9n9ZvA5zf12hN20hFwEp35XqqqSM8isKQptYTfOpExzi6amX3SNZC4tU+93cFl/7cxCcEdL87xGoTZdZXdvNeuaAzgsGh2LWICamd/Uz7U55KTKbTN3BZVAaJGZ8KVUmWdhIURZPXjnV+gfuReAZ9e9HY+rBF2thRBF88ZdHdR47fz7xJXst0xdvP/vG2GiMhr3CCFEKkVRiHjsc7bJjgcNrJqKassjAyuZZqG3t5/mSP6ZPpO6ayZ7eU5wOcWqBj89td6Zxk+z34BGZMP1NG+5nqZQhsBaCSVQGQonZV0HWmZKN1h1lc1tIVbUB+bXo84zMKIUmr3pCjHScN6cQ8dqtjNcVfi24kzlA87vClPjtS+49isAisrB2t2ovddkHWbPs8HactNb56W7xsuqbGVZFAX8jdB7XUH3fTy0jmNVG+fUns6HOrXNv7fWu+hGiPkIOK1pOl0uXL3fyWX9tVl3PBQinqO0zfS5NGtwMfV5VFSOV63Pa1eDoih47ZZ59z/irOO0rztnLe957H5zh4i/Ka/h86ae4SXhdbsZcreYjVvTSOjJAVnz590ScuK26dR47Vi0uXesa7M7UqpylIMouJwMWV5yFicH6y7ieLi4Afj8pZ+Y32kt+PvM+/3btsssS5Wn9rDbXDhJ+X3mtOo0BJz01fnwpymFlG9964h37jkr7LbTEnKl/V3UsIB+B7meFqdVZ0Wdj9UNfhIlLDW1EBJgFkLMMTw8SOhX7wPgYUs/Gy+/scwzEkIUymXTedfl3Uyi87rBVxJXNDixB+76aLmnJoQQeYs5QmBcDp27od5s9DRqn81wng5G16epWwzM68ZeDJqqEHRa05ZpUCxOwqGqwutmptLnX7Sny9zM5mDdbmIZtriDWZO5rtFcgLQUu95rniat/nn1j+dkH7urZzKyW1o7ct6f32mlIeCcKSmyUAlVB33uvGL29M3yCpV1bnnUJU5+3VmmXv9jtulM1cUHHiyailHjwe3KY5Ekz1Il00YdNYzZs2dhZpJXYGremIU9H+d1zs/8LYZgUhZiajmHBVnsj9uWX23avCkKg572mVreeeu8qKBgYlyfe77PVDKnp9ZLc8g1rwbxtLHaDfOO6ZrKhT3VbGoLgT5/IaSvzsvqRr+Zke6cf06octtoDbmoDzjM313FouR+r9mLtICRrOi1wPPlChVUXklVzV1JyTug8pHvzoJCnoZqjy1jeaMdneG0AejUvxmUNO9tu0Wb9/ujTD+drCTALISY494vvp/6xGEmEyqua/8RtUK3mwkhsrt6VR0bW4M8kmjly9pUJtbd/wLP/r68ExNCiEJYnaBqEGjmUM1OjofWz3xpVaOfnhpv0rb+FE2bQbNxxtvFiH3pe0nk26Qop8ZNTOpuTvtmtwiH3ea29MYVU1vba1aa/2boOJ9Q9dzxJ1WFQAutYRcOi8aK+vQBaUuBgcTM5s5IURQ6Im46Ix42t5nbs9c3B1E6LqK5fwcEWjDOew69Wy6nuSX/ANTs/Rc2/nDkvIxfi3nqsTSsNjNwKaQMh8nvsGLTNdqrUgO3SZP0ptQ/TcNh1WgPu2kIOKibqhF9yr+CYUcdA3Xza5MvWO1Ks/54xUrzw/U1Fuee883iL/AFFvHYaQ256Kvzzsu0LIu2qRIYiordNRuEzdgEbgkW7BZisHFXXuMsmsrqRj/hPJrPpVW3Bhx+qJ7dZaFO1danui9tIN2ma4TcNjNgmOHcXDBH9p04rVUuvHYLbeHy75xJJ7l0h9de3teQXoKA+XSGfzoBl5V1zfN/nhVxPiiSyjhLCCEqwuPRR9n4zO2gwB9rn8u6vnJtxRFCLJaiKPztVX1c+S+/4gODV3N54D4CI/vhf2+G19wJ2tnzx4wQ4twQ0+deQKuKkrbG8gxnkOG2yxg4cBoSMeKaDTpWwBM/SztcV1VWNiw8qJa6jRYAi6Pw8kR2L4drzOCP7/SjgHlO76n1Ar0Q65w9h9s80DCViffs7yE+WcHvtAMAACAASURBVNhj6XYcFt3cKhx2w/H5Q/KtNzyv3EYOiUQCTVXorZsNbjmsGuu6Z+syK3YfzjSBzmNVG7GPHkFJxPCPHiCYZvtzoSatWTI6FQVbTTfr3WPE4wlGJ+JZ7yvgtHLgxOznEa8tjyBCfimpqQsBkxYXJ0Nr8DvSBJjSZGHmxeKAzt1M7vki+uRQzuEKMORqxjX0FIPuFiILXJQ4vyvMLx47uqDbVjpVUQgllRTINwH5cPVOqg/flf6LDRvMIOhC6DbouQoUDY+m0z/1usr4Oq2UBQdt4e/1IV8H6rFofoMtDui4yPz/4Yfnfi3SAyOnFjyPvDRvhTPPQk0/nDiWcVi6BrnZJGpXwzN3LXJySSyZA+ndNV7cNp1LumtQlBw7OErAbtFo8jnZf2K4rPNI5SpVw8wSkNREIQQAsVicY994Kw5lnJP46HvJx8o9JSHEIvXWeXnp5mbGsPKGgVeYBw8/BL/+p/JOTAghMkhurJRre24iNYMwzZblmTRWRWPQ05Y1G+zy/pqZJn7lFp4KRNnS1fpNXSAMNJsfC3qgbnBHMjZUsqgqNG+bdzyuzJ9X2GOjr87HtjTNxYptzB7mtL+PhKKzqsG/+J+bM02DqzSq3Lb0Cwkp7BaVxmy1OEu0yBvz5C67USyn/H0cjpzHaV9v2oZj+ZrOOG2dzvb2Lz4zOZEm7BFLqmXcEHDgtumLfu3G1eI345q0uBh0t8x8PicwHWheXOBXt4FmBrfawm7aMjQtSyjlCYCNW9Ofryf1lHnm+f6dtC4wGJ+vPBJkm0N5nqu8dWZz1jQlkxYqoagkgoXvBkmr4yLounTm9ZPOdIkju0VL/7usDNpT+ycUajqTP4+yJQu1aqrERsSzwAXCMpIAsxACgLu+9Rm2jN8NwNHN78buKU6tOSFEeb3tEoOIx8bdkwY/dl1lHvzFx+HY4+WdmBBCpGHVVer9DrwOCy05muUlAu1mlpk7YmbiteW3dTqTojUQW0SG3bT1LUFWNvgxaopQqzUbTYfWHVCdPsAMgLd23qFJq5dhZwMjjhomLGbmrzpV8iJb46fpsRWnqrN496VPLw5kudReaNZpAWKqrfA6IYuhKExavWxsCy2qduvqRj8r6n2zr313xHxvz6lpW2AB4pRgUELRORbeBJg13Nc2Bbiwpzp707Jsz2XzNsZsIY6GN+c9pRrf0gePpgNU/RnK32TTV+tjwNNOTLVxMrASrcCfacBlxaIqOCwartSyG3qOc2THhVDVyfHQ2nlfCntsDNZsnG126JhqEphJlgzbRUl6Pcxb7EzDbtFYsfkSfJ4KPQdmlOF7c/jBNjdYay1WmahFcFnNAHBnZGl+d8badpkNc6ez2zOYPpekay6YVtKiY1PQycoGP00VsuBdiLMnF1sIsWD79u9n9UN/Bwo85lpP1yWvLfeUhBBF4rVbeP/Vfbzuiw/w5uPXcq//Xpyjh+B7b4GXfbu0F59CCJGH9S15LnJrFjPolOd5rD1Ddl7Rte2Eo3+GUAfsv2dBd2HVVTOD82D5L9gzORlcBUD48P/lfZtJ3YVl4sxSTSmj2hIE84j0mOVQvPUQOAaDjy79Yy4DHrvOqZHxvMc7rfr896orvwzVfB2LbGVSMx8j7/NNNt5ajk0Fl5Mzo7PxOaz01no5GVjFgSV6S2xuCzI2GTcbwMXqQX/IPG/acy9w+JwWrPWrODTYjU1XsRRY3kBXVfob/CikWbyrXgEjJ8Fdk/7GjgA4AsQPH5g51FvrZdTrI+i2saGrmfvtHtqq3JBc19xbZ5aVCCU1Ba3qgtEz4Ayi7C9iaQS7z8ycnhhjxGEuwo0Fe2D0obRZ5Qpgr2oGlw+e+CkAE1YfjJzkRGA1pSxAciSyjciRX+c32GIHTy0MHMw5tD3s4s+HzBdzPkH3pbCrO8LoRGzpyk7YvOBdl3PYhpYgh06PUu3LMwM9eVeLapnbgNDXCKefLnCi5SEBZiHOcbF4gv1f/EvOV84wjJ2al94qASchzjKXrqjhop5qfvqnw7x37KX8I38P+34JD34VVr2w3NMTQoiFK+BvlpZ5DdaWiN0LjdN9LJbf31QBp5VDZ0bNT5bf9NPSpmsCp7xelGJ8g9N3Ud03e6ymH57OI8BsscPk6OLnkE4l/D1v9xFJJHjqdGzu8SVpGJfl+035UnvEzUPHzWB2sQ0764H86vM6rTongy1w5kTOsQuhKIoZXAZzt4JxGaDk/drY0hbi5PA4QdfCdmWomR5Ht+XMAE3ltOo4p+bhc1q4oLt6/qDGzWbgOrlckqpBk5mt7jnyCIt+tyXfd/suiMXhITP4qvjqoakOLFl+1zj8ZpNWReG44mZ8dIiYvvCSMgsxUWipkJZtMHQM9t6Vddiiaiw7gzBwaOG3n6Kpyvzgcv06OHA/BNvmNK21WZZuAdeqqzTlWw4ltcSLqprlR8YHQbXAxNBMgNmaVGqk1l/a100+JMAsxDnup/9zO5eM3QnAM2vfTldtR45bCCGWG0VR+MA1fdyz5xjfHFnDX4S2snLobvjRe6Dz4vR1S4UQ4iyTSBS4rf4clXxxvpQhyqKVJFkAv8OCze+gSZkNBNktGqMTsZylWfKiavkF8apXwJP5Z4DnctrXg+/0n4p2f4vWsh3l5JMMYIfkvojBVji5z2xSqduA0jbdaq1y4vE78eXZwPKsoRZWB1dV5zYmrHiqmjXbvavaw7OHrficVvLPqU/Rev7ch9RU2sNuTo9MmLtOMpQSaUiuyR7uAqA9McjDB7I3DD1n1K+HQw8Vpeb6PMFW8NSAxYEDs/ng2GSMaq+dJckL9mTIzC+EzT1bguTUbKNVBbikr4bJeGKmxnUlqdw9V0KIJbfvyb2s++P7zP87++m68i1lnpEQYqnU+R2887JuQOF1x1/ApOaA4WPw0/eVe2pCCFF2SqE1XYulZbtZH7Z6RXkefwFSg3Jle+7SmV4wzdC0MOi0oqkKTUEX/Q1+fI7ZzMzzu8Ksaw6wIqVebb4lD1KN1+dRj7cI9bqTDXrainp/i2ZxQKSHtroIkFSXWtWgczc0bV7ChYbM96ugEPbYKqJm7LIyXc+4kAZntsqpOWzVVVqq3ATyrYubTpog/Yp6s7lpujrVK+p8tIbcdKepp9+WtKum1A1mZxpHLqQefO3qos4FMHdzNG4oTnA27f3PZvsaNR5WNuT+vjM1mcyo/QKzMaO/qdDZFcRu0SoyuAwSYBbinDU+McnxL76KKuU0w9ipeslnzVVfIcRZ64bNzezoCnOAMP8ce4558IEvmOUyhBCiwm1IqZVatvxXb13+Y3312b/uqYHeayHSvbg5ldB5nWF2dUfKPY30WnaYNbAjPXOCPY6prdB9dT5WNfjTBhbtFo2GgHPmdrGW8xlxzNbWTZbII6ged89vjlhWrnDx77N5K1hdTDRuzTqsJeRkW0dV5bxuKijomQ8leffFVEC+LMs6beebDTE7d+ce234BBNvMRbRzmN2iUeW2pm18qSgKV62s4/L+2tlSJnmIFaFx4WlfDyN1W+ZlZOfFUoKa9hXgaHgLk1oBz7UzCIGWnLtXirJLpkJJNEmIc9Qv/+vvWD9xPwDPbPkAnvrlc2EjhFgYRVH4f89did9p4VOjF7PP0m5+4ds3w/hQ9hsLIUSZ1fkdeWUdLblQB9StgY4Lc4/NJzN5iRb4l6oiiKYqeO2FlxYoSYUSTQdXFSgKFk2lNeSi3u+Yk6mcsS5sioSzihOhtUxaStQcEij2sonXboHWHRBqN1+zxeatA+MyEpmatU1RFIUqtw2bnj2ItlSvkTk1WT21yyapJjm7uyKmbHVB7SqztEkuziDUrwVraTNzF6LaW75atqqq5N1AMVa3EZwhBiIbCnqMdJnVKCoxV/Xc5nKlVs7HzoeikFiCevGrGv14z9LyPJVwmhJClNhD9/0f5z35LwA8EtxN18WvKfOMhBClUu218+Hr+plE5w2DrySmaHDySfj535V7akIIsTwoihmwc+SxfbbAmqfLSdVUbVZ7jqBhOYXcNmp95Qke2ZMaSOlafoHjI5GtjFsDHA/lF0CyTgWm5tR3xawx2lPrNQOr7ogZXNYzlAVYkoZ7laUl5KLKZaUz4i6svMMC5FUyxt9knj/q1+YcWu93YLdoVHvOjazRcgi6cgT7pss2uNM0FiyBzW0h6v0OVvStgPZdxK15BPiTtFY5seka9X7nnORavVyrFu0XmO+Btl15DbfqKq6phpxNS1RKJJHhvDBdSiRR5NBpBbRgXRJn/28TIcQcp08eI/C9V2JTJjmsRGh/xX9URpdpIUTJXN5fy3PXNfDf98O/TVzNX+rfgt98ytymPdVpWwghhMhmfUuAAydHaLB7YWKg3NOpuL9n/U4rdT4HigJOS36X3RNWP0cj6ctNpNaGBthpRDgyMEq938Ejz56ZOe626WDJM0MuXNxdjJXYS9OqmbV3y6ptJ+y9y/y/1QWNG83/nxrJerP1LUGwBOHEqaWcXUXa2l7FowfPmAsDxZBUGiVhcTJu8WGdOM1kOMdOk8bNMHh44QHmRZ6bqr12qr0LX2BwWHT6633m4oquUetzMDQ2SUOgTJnbziA4NxZ0kwu6I8QSibyzvfM15GrGMXyAk/7+tF8fdjUyEqzlkC1W1Medw7cEjQ3LRALMQpxDEvEYT33mJaxMHGI8oTFyzX9Q7QnmvqEQ4qzzwWtW8OizZ/jXg9dyhX4v7TwD//M6eO0v8tv6KIQQ4qyloJAgQdiTucGdTddoC7vhlAYTJZxcBZh+Xk4GV2PT/mTW3Uyjzl+cAE5DwEF7eH6QzWHVaF5oPc+uS2HkBHgbMg5pD7s5cWKMjhwBvqVr1Ld8dFV7eOzwAL11Phg7PX+Aff4Cgcgu7LFxvicMDxWpGabda9YNV1SIOzka2YI+OUJLrgCfpueup7+MbGxdftf/qqqgLkHe76nACk75e7PubIg7q4hrxV/gOVx9Ppbx0+aOqLOElMgQ4hzyxy+9l5XDvwHggd6/omVNfttShBBnH4dV49Yb1uF0OnnL2GuYRIMTe+Dbf1mZ6UdCCCFKpr/eR3uVe1FZc6VQrjqWTqvOBd0Rzl/TjbbiWmhYv7A70pOe3yyNu+bUEC4Wm9vcpp5lm3zYbcOo8aIlj/Fkr7d89soe3Oqp9XLZiloiWRZl8r2vbBJK5ZakWRa8deCpMRt1KlqJa6yf/aYXwuqLtLhWEopalkWySYubEVd9xe2+WQwJMAtxjth/zzdZ+finALjbcwmbnve2Ms9ICFFujUEn//KiNTxEBx+ZeKF58JFvwr2fLe/EhBBClIl5oWvVVQIua94N8fJR7K3N5eaxW3Ba9cU1qrI6zfrINf1mc8JK1nWpWTs1n9rj5yirvvSv8RPBNcQVCyP+jiV/LCEK1VfnZVd3hI40Oy6Wq8QSJN60FLLzZBkl/pxdv+WFEGmNPHU/4R+9DlVJ8Geljb5XfRalIloRCyHK7bzOMO++vIfbYpfzw5jZVCjxw3fBgfvLPDMhhJgvuWSD3bJMMvmmt786/Ev7OBnKNCy5PMsqNQWd+MuUcZxW8kV7OS/gQ+0QNuYcCroKLwmw5ElwNrdZO7XIvPbZ7GyHNc/3tKXAsiBL3Nhv6c2+PiesPg7W7WYk2FvG+YiCZNmdcLZRFAWv3XI2JeXOUazvqznkZHNbiIt7z64dIVKDWYiz3amnGf/P5+FjlEOJAOPP+098Pm/u2wkhzhmv3N7Ks6dGecevX0OP8hTNHIEvvxhu/CEEW8s9PSGEmOG26ew0IuiqgqYukyvYmlXgqQVnaIkfpx/sPg6Nlbggcu0qiE+aW8+zUFWF/gY/953YX6KJFaBCApDnd4V5+sQIndWFZ/91VXt45uTInIDt4i194N1jt7ClLYSiKLkXjWpWwshJCOXO3h3zd8HAg+YnrefBEz/Le04TFi+O0cN5jy+5szV6d7apXwsn9kJDYQ3tzgrBNji+p2LOrZVGUZSKL0G1EBJgFuJsNnqa07ddh2/yOIMJO79c/+88vy9Hl1whxDlHURTee0UPhwdGed1Dt/A16wdwDx6CL1xjBplzBA2EEKKUfJWUBZsPVS1N3VpVg2Arsf0Hlv6xklns0LKtpA8Z9tg4OjBm1vscOlbSxy5Iy3Z46tcQ6YXDj+Qc7nda8TvN7OV4fDa4686jBrPdonFJXw0ayy+RJJJvoCXclflrVZ1w6inQrNC8ldETOgfi9ajx8bllPfIIzg5421ETE9hHj+Y3r3wkB9psswsI9qSyGoWU2Kj2nH3BqbNOsM38OBfZfWBcZr4fxTlDlhOEOFuNDzFyx3PwDTzOZELl05G/5rlXXFbuWQkhKpSqKvzD81bhaVnLqybexljCYl6o/ed1MHS83NMTQogFyT/Rb/nUOMzXUtSNrBRb2kJcuqKm8hcbPDXQex1Eegq+qaoqrGsOYNR48m6YtWyy+peCww/dV5gfrirzza+oxLWpQKy3HlQdqvNItlE0Tvv7GHEUcWFI1cxmkJEe8DXOHA65bXTXeOmr8+XVzHGnEWFtU4DG4DJqoibOAgs4t1hdi6tRL5adkmYwG4axBrgV6AMeB26KRqO/STPuvcBrAC/wB+CN0Wj04VLOVYhlbWKE2BdfgOPgvQB8RH8tr3v5q1HP5T86hRA52S0a//Gy9Tz/0xO87uibuNXyCSxH/wy3Xw4v/mr56nsKIUQxucIwdHSqdvCZcs+mstStMTNupxU789pTC5hlC+yWhec6KYqCTV/aGtxOq45FU5mMJ4gsJlt0EX1PGgKLqd16Dv7db8kSdG3eAvGYGegtlwx/Rxk1+dUxB3MHR8UvrIjKlO39IUQRlCyD2TAMO/Ad4POAH/gk8E3DMKwp4/4CeBmwE6gCfgp8zzAMybYWIh+T4yS+9jK0p34FwPsnX8YFL3obVW5bjhsKIYR54XL7jRv4k2crb5l4HZOocPTP8JkLYP+8NWEhhFh+mraYgdTW88s9k9ymM1/9TaV5PG+tmQHaew00b4XGzcW9f38TkZ7zGG2+gDVNgdzjc9GTAibpMrbbdi34rjVVYacRZqcRzr/5nKhs5QwuC1EudWvMBdXmreWeiVisCq+/Xsqg7S4gHo1GPxWNRiei0ejngOPAVSnjqoAPRaPRvdFodBL4Z6AJaCjhXIVYnsaH4MsvRHn8xwB8dOKF1F58C9s6qso8MSHEclLrc3DHjRv5hXUHfzH+TgZwwvBxuOMqeOAL6S/ihRBiudCtEGo3awcv0s6uCHV+B+d3hYswsTSq+6BzNzRsWJr7T8fiMLc1e+tAK/KGV0Whqb2H7f0dedUVzinUbs4z0pv+wtsVMhcUdBs0FR4sd1p1vHbJFs3FllQ7OGejPlE4R7DcMxDLWagdui4x6yILsYRKWSKjG3g05VgUs1zGN2YORKN/nzLmasxA9DNLOjshlruRU/ClF8DTZobhJyaew+GVr+Od552jjQWEEIvSVe3h86/YwA23Jbh27P3cYf8HGmKH4Ns3w95fwJWfAPvyayQkhBDF5HNa2NCyxMEfCQpkpmq5s/J89eYHgKLBmRI3QVzOLE4zgSUHl01nRb2PWDxB0FUZTb0qPNGvMIEWiE1U7N9dbVVu9p8YnrPQIIQ495TyDOAChlOODQMZC0sZhrED+DTwl9FoNL6EcxNieRs4DHdcORNc/uDES7mr9kY+cn0/yln115UQopTWNQf57MvX84zWyJUj7+c32jrzCw//N9y6Aw48UN4JCiFEDhZt9nLnnG6AJkzeWmjbaZYBEbk1rAdnyNxin0N72E1Xdf61hJdaR8SNTVcXVz+7GJQihFwUBcJdxa+JXiQ+p4XdvdVc1FNd7qksiPxmyENysz5NSm+K9EoZYB4GUquKO4HBdIMNw7gB+B5wczQa/dISz02I5etoFD57ERx6iFhC4e0Tr+GHnudw6w3rZYuaEGLRtrZXcesN6xjSvLxw6C38i+VGEqoFTu6D2y6Gu/8V4rIGLISoTLU+O/V+B+1hN05rSfubi0rlqpJmV/myuqB9l7nFfpmxWzQu7q1hS3uoOHe4kKQdZxD8zcV5/ArntOrommQwn7XsXgh3Q6gD3EtUEmoZUGQ5IqtSngH+BBgpxwzml83AMIy/Bv4JuCYajd6+9FMTYpl68tdmgOf0fkax8vqJN3Gn4xL+61WbqPGVebVeCHHW2GlEuPWGdVh1jX8YuIhXah9iwtcC8Qn48Xvgyy+AoWPlnqYQQsyjKArrW4KsqJcyE0Kca9Ry71povwBUCbqKs0TNCqhbXe5ZiApWyrPdzwGbYRg3G4ZhMQzjRqAa+FHyIMMwXgG8GdgWjUZ/XsL5CbG8PPwN+M9rYfQUp/Dw4rF3c491K//5yo20VrnKPTshxFnmgu5qPvfyDTgsGj8faGD30Ac51X6N+cXHfwyf2gb7flneSQohhJjhdUhzuook2dMVb7qxo1UyckUFctlkl7KoTCU7Y0aj0THgMuBFwAngZuDqaDQ6ZBjGDwzDePfU0HcBHuA+wzAGkz56SjVXISpaIgG//iT8940QG2d/opprx/6Wx629fP4VG+mprczmD0KI5W97ZxVfeOVG3DadJwc1tjz2Ih7Z8BGzCdDgIbjjavj5hyA2We6pCiFEgRLlnkDRbGgJ0lZVWfVwBWY2q78ZWneUeyYihy3tIYwaD2ub/HOOB5yzDQxlo7woF6PaQ0PAwepGf+7BIi+JxNnzN0A5lbQQWTQafRCY1+Y3Go1elvT/rlLOSYhlJR6DH7wT7v0MAL+Pd/Cq8bdi8VbztVdskOCyEGLJbWgJ8rXXbuHG2+/l0JlRrvq/Zv7fzv/i+r1/jXL4Efjlx+HQg/Dcz5m1G4UQQpRUnd9BnV+yZCuOM2h+iIpnt2h013jh4NxM0RqfndWNfpxWPXP5Dc2a/rioKMs5nqhrKuual/ZcIr9DZi3jl0rJyZ4PIZaLsUH48otmgss/jq3jRePvIVRdzzdfv1WCy0KIkumt8/I/b9hGb62XeALeeucof+X/BJNr/sIc8NgP4Y6rYPBoWecphBBCnLMW0pRO5NQcchH22DIPCHWajSSrOks3KSGKZG1TgBqvnX7pW1A5bEm7kfTK7rMlAWYhloMzz8LnL4PHzZLlt09ezE0Tb2ZnXzNfv2mrrDAKIUquxmfnazdt4aKeagC++sdjXLnvOZzY9j5zwIH74bbdcPLJ8k1SCCGEEGKhbAsoM6Pp0LYTalcVezZCLLnGoJNNbSHsFqnzXDGcQahbAw0bKr6GvwSYhah0hx5i8tYL4NCDxBMKfzvxMj6q3MiHrl/Fp166Fp80cBFClInbpvMfN6zj7ZcYqAr8+dAA5/+6j4c2f8LcInpyH3z+Cjixr9xTFUIIIYQoTKAFwgY0rJeMcCFE+YTaIdBc7lnkJAFmISrY6KM/YPw/LkYfOshwwsZrJt7Cww0v4rs3b+dFG5tQ5A8dIUSZqarCG3Z18IUbNxF0WRkYneSqu6r5qvEJEroDzjwDt18JJ/aWe6pCCCGEEPlTFKjpNwPNQoizVnIDT7FwEmAWogIl4nEe/tbfY/nai7HGhzmc8HOT5YNc+bxX8vWbttARka7gQojKsr2ziu/cvJ1VDWbNtnc+EODDgQ+QsDhng8zH95R5lkIIIYQQQggBW9pDNAQcbGjJ3DSxfqocqVVTsVskhJqNPDtCVJgn9j/N7z5+NSv++EE04vw53sjXV9/Bv7/9lVy7pl6yloUQFave7+BrN23hJZuaAPjM0/W8gXcR0x1w5oAEmYUQFSfkMrOWYpqzzDMRQgghRClFPHbWNQdxWDPXnLZbNC5bUcvFfTUSi8lBAsxCVIgzoxPc8aX/wnHbTjaN/gqA++1bsLzmJ7zxup24bXqZZyiEELnZdI0PXdfP3z9vFTZd5fsD7dww+g4mNAcMPAu3XyFBZiFExagyttLS2sm6zTvLPRUhhBDZ2LzlnoE4R1l1FU2V4HIuEmAWoszi8QQ/uuuX3Pexy3n5Y2+gXjnGGBYeXf03rH3H92lvqC33FIUQomDPXdfAN1+/laagk7snDV48/HbGFAcMHDSDzMeeKPcUhRACJdRGVd8uXE7JYBZCiIrUsB5CHRBsK/dMhBBZSIBZiDL6UzTKzz7+Ai6682ouSPwOgCOuTnj1nfRe+1YUVd6iQojlq6/Ox3feuJ0LuyPcm+jmpaNvZwR7UpD58XJPUQghhBBCVLJAC9StNpsuFomadF9S9kCI4pDolRBlcPL4Ue76tzfQ+qVt7B79EZqS4Lge4fjuTxJ562+x1feXe4pCCFEUPqeFz7xsPW/d3cV9dHPD2DsYwg6Dh8yazBJkFkIIIYQQJRTx2PA6LARdVgJOS7mnI8RZQYq6ClFCsfERfv+Nj9MZvZWdDIECp/FwbO3NtF/2JrDYyz1FIYQoOlVVuPnCTlY1+nnTVyy8bOSd3GH9GO7BQyRuvwLlxV8zM1OEEEIIIYRYYqqqsMuIlHsaQpxVJMAsRCkkEuy583Y8v/oQ6xNHARhJWPlTy0tZ8by/od0dKPMEhRBi6e3oCvOdm7fz+i86edmBv+IO68fwDB4m/rlLUZ97G3RfUe4pClHRDMO4EPh7oAN4GLglGo3+Ns247wEXALHpY9Fo1F2qeQqxLNg8s/93yN/iQgghxGJIgFmIJXZs/5859tU30j10LwCTCZXfBq6g6/l/x9q6lvJOTgghSqwh4ORrr93C+7/j44X3Wvms9e+pnTxB4isvQdn9ftj6l0WtsSfE2cIwjBbg28AtwOeBS4DvG4bRF41GD6UMXw2cF41G7yvtLIVYRix26LgQEgmwSpNHIYQQYjEkwCzEEhmbmOS+r36EtY9/kiplHIB79XXYr/oY21ZtKPPshBCifOwWjY9c38+320O85FtB/in+MVaq++Anf0Nsz11o1/4beOvKPU0hKs1lwEPRaPQzU59/zzCMlHSxMwAAGaxJREFU3wLPA/5lepBhGBEggpnhLITIRjKXhRBCiKKQALMQRZZIJPjJfX/C9YOb2Ra/DxQ4ho9HV72HbVe/Gk2T3ppCCAFw9ao61jZdwzu/Us0Lnv04V2v3oO39OZP/thn9in+A/udKNrMQszRgOOVYHOhMObYGGAC+axjGKuAx4G3RaPSepZ+iEKJyyO9PIYQQpSORLiGK6P6nTvLef/4P+r97hRlcBv7ouxDt5vvYcd1rJbgshBApGgJO7njNTp48/5PcMvlGTiec6GOn4ZuvInHbxfD0veWeohCV4kfAJsMwnmcYhsUwjEsx6yyndgi2A/cAbwIagP8CfmAYRk1JZyuEEEIIIc4ZksEsRBE8fWKYj//gEVoe/TQf0L+BpiQYU2yc3PFBVu18jWTgCSFEFrqm8pcXdXF/59t4xZdXcfPQv7JL+yPKM7+D2y6C3mtg+1ugbnW5pypE2USj0ccNw3g+8GHgU8D3gS8Cp1LG/S/wv0mHPmUYxuuBXcCXSzRdIYQQQghxDpEAsxCLcHRgjH+78wl+8tvf83H139lmeQSAIV8nrpf8JzWRnjLPUAghlo91zQHuuOU6Pvz9bm6/77u8W/8ihvoMPPq/5kfbLth+C7SeLwt34pxjGIYH2B+NRlclHfsN8M8p454LqNFo9GtJh+3AaEkmKoQQQgghzjkSYBZiAU6PTPCZX+7lc7/ex3mT9/Bdy2cJKIMAxNe+HNelH5Vu1EIIsQAeu4WPXL+SX/XX8ur/3sCmwR9zk/Yd2tWDsPdO86NuDWy7BXquAlUr95SFKJUQcI9hGDswG/i9CmgCvp0yzg181DCMh4HHgVsAB/DjEs5VCFEuziAMn4Ca/nLPRAghxDlEAsxCFGBkPMYd9zzJp+7aQ3zkNO/Xv8DzrL8EIGHzolz5CdT+55Z3kkIIcRY4rzPM99+yi498v4bdv93BbvU+Xq9/h1XqHnj29/D1l0OgFTbdBGteAjZPuacsxJKKRqNPGoZxE/ANzGDzA8DuaDQ6ZBjGp6fG3BSNRm83DKMW+GHSuMui0ehQueYuhCih1p0wMQw2d7lnIoQQ4hwiAWYh8jARi/PVe5/mkz97nCMDo1yj/pr32L5ERJkqe9i8HeW6T4O/sbwTFUKIs4jbpvOh6/q5or+Wd3zDxTUnN7BFfZRb7N9nU/z3cHIf/PCdcOeHYe0NsPE1EGgu97SFWDLRaPS/MJv2pR6/KeXzjwAfKdW8hBAVRFUluCyEEKLkJMAsRBaTsTjfefBZ/umnj/PU8WFWKU/wSetX2Kw+ag7Q7bDr3bDljbJNWwghlsjWjip+dMsOPvmzx7nt/1ReMNxHj/IUfxX4OeeN/gJ17DTc86/wm383y2ZsfgM0bpQ6zUIIIYQQQoiC9Nf7eOjAaYwa2SFZCAkwC5HG+GScb/3+Gf79rj08dXyYtcpjfMD6Tc5XH5wd1HUpXPpRCLaWb6JCCHGOcNl03nV5D9evbeCv/+dhfvckvPzEKwhzHe+r/Q2XjHwPy+jx2YaAdWthyxug52rQreWevhBCCCGEEGIZaAu7qfM7sFskibAQEmAWIsnoRIyv3/8Mn75rDydOneRq7R4+af0Zq9S9s4PC3XDh+6D78vJNVAghzlFGjYevvnYzP370MP/vR1GeOAJvPHgpNi7gDVV/4GXq9/GfeQyefQC+8UpwhWHVi2Dty6Gqo9zTF0IIIYQQQlQ4CS4XTgLMQgCnRyb46r37ueNXj9E1dD9v0e7hYtv9eJSR2UHVK2DH281sOFUt32SFEOIcpygKl/TVcFFPNd984Bk+86u9PHZ4kH88tpF/ZAPnW/7EWzw/Y+Xwb1CGjsLdnzQ/mrfDupeb53GLvdzfhhBCCCGEEEKcFSTALM5pTx4b4mt3PcDxB3/A9sT9fF99EJ91eHaAqkP3lbD+RmjdIfU8hRCigmiqwvPWN/LcdQ3cvec4t9/9JHf++Qi/mOjlFyd6aVBewAu0u3ix5ZeEEifgqf8zP+xvh95roO86aDkPNPlzSAghhBBCCCEWSq6oxDkncWo/T9z7E5598GfUnf4D71APQGpCcsNGWHE99F0PnuqyzFMIIUR+FEVhW0cV2zqqODk0zo8eOcT3HjrIb/eq/MPk8/mnyeewS/0DL9R+zi71D2ijp+CBO+CBO4g7Qqidu6HjQmi/AFxV5f52hBBCCCGEEGJZkQCzOLsNn4BDD8LBPzL81APEnvoNnrFDdAKdMBNYnlSsJFq2Y+m+FIzLwN9UxkkLIYRYqIDLygs3NvHCjU2MjMd4YP9J7t5zjHv2hHjtM+sJTxzjOu3XXK79hn71SdSR4/DgV8wPYMLfjt6yCaVhIzRsgEgPqFKDTQghhBBCCCEykQCzODskEjBwEA6awWQOPUji4B9QTj8zM8SZNHw0YeExSzfW9u20r7sYS8smsLpKP28hhBBLxmHVZjKbAQbHJrl33wl+u28jf/vkCU4982cu4F52qA+yUf0zNmUSy6k98Ic98IcvARCzuFHr16LUr4W61VC3BvzNUjJJCCGEEEIIIaZIgFksP5PjcGIPHHkUDj08E1Bm6OicYcmX/k/FIzycaOFxrRNn5w42bbuAlc1hFAkQCCHEOcNt09nVHWFXdwSA0YlN/OHpa/jdvhPcsfcAiad/R28sylr1cdaoT+BXhtAmBuHJX5ofUxKOAErdGqidCjjXrQFfgwSdhRBCCCGEEOckCTCLypRIwMhJOPmk+XF8Dxz9E/HDj6IcfwIlPpH2ZrGEwhOJeh5OtPBovIVHEi0ccnSxub+Vi3qqeV1XFTZdtjoLIYQAu0Vjc1uIzW0huLCTydgOHj14ht/tO8FX9h7j6FOP0j72CKuUPaxQ99Gj7MemTKKMnIQ9Pzc/psQdVSj1q83Ac6QXgq0QaAWHv4zfoRBCCCGEEEIsvZIGmA3DWAPcCvQBjwM3RaPR36QZdwvwdsADfBt4bTQaHSrlXMUSiE3A2ACMD8H4ILHBYwyfOsToqcNMnDlCfPAoDB7BPvQM7uFnsMcG591Fci++kYSVxxINPBJv5pFEK4/EW/hzohGH08265gCb20Jc2xqir86LqkpWmRBCiOx0TWVlg5+VDX5edV4bicQG9hwd5Hf7TnL7vuP8ft8R3Gcep1/dx0plL/3qXgzlaaxKDHXkGDzxU/MjyZjqYNgSYNQSYFJ3kdBsJDQr6DYUfepfixPF4kC1OlGtDjSbE6vDjctXhe4OgzNofth8oKZ2pRVCCCGEEEKI8ipZgNkwDDvwHeBDwGeBG4BvGobREo1Gx5PGXYkZXN4FHAa+DHwAeGup5ipMiXicyYkxJkYGmBwdYnJ0gNjoIPHRAeKjp4mPDsDoGRg7Q2JsgMTU/9WxAdSJQfSJQSyTg1hiw1jjI1gSc7OONcwVBE+OeQwnbOxPRHg8UU803shjiQYeSzQy6WmkPuShKeikKehkR42HFfU+6nx2KX0hhBBi0RRFoSPioSPi4cWbzOavB07t4N59J7j/qZP8z6EB9h0+Qc3oXlaqe1mh7GOlupc25SAOxfzTxhYfwTY2AmPPLno+MVRGdC9jlgCT9gBxR5CEPQjOEKrTj9Vqw2q1ouk6qm5F1XQ0zYKi6SiqDqoOmsVsWjj9uaqDZgWLY+rDCbrd/FeTjW5CCCGEEEKI3Ep55bALiEej0U9Nff45wzDeDFwFfCNp3A3AbdFo9DEAwzD+GviZYRjviEajsRLONy+JRIIfPnyIvceG5hxLJCAw9AStx/8PiJklH0igTP1rfg4k4ubn5g1nvqYw+/9EYvZf8/9x4snHSEA8Dok4SmISNRGDRBz1/7d391FyV/Udx9+zs0+zu+Q5BIny0EP8IhYltgWxAiLkKNUgpICmaUREKlCoHNtQoeUIlIhwpAejQpSSooXQlhMEkpAilmorUB4EPDz5DbVygpREyGbzsJt9nOkf927OZHZmszvPEz6vc/Zk5/7uZO7sd+7Mne/v/u6NvycyIySybjdlRkiQJpkZoYkRklm3WxiiPdNPigE66Kclkaalgn+/3kwbWzNT6GYKW5nKzuQ0ulsOYkf7XPo630V66qG0TZvDzK52Zna18sHONs6c1s7caSnaW7TUhYiIVNfcaSnmzp/LGfPnAuEz/61dg/xmWx+v9+zmsZ5+1vcOMLxjM+07N5EafJPU4DY6h7ppTu8mMTJIMj1IU3qI5vQAycwQrZkB2hgixQDtDJJikFRigGnsojmR3vPYSdJ0DffQNdwDu38N2yr7XIdopp9WBmhlmGaGaSIdf+IIItxO5NyOv4/QxJSONt47dyoJmuIa1Ynwb+csOPlvoOvAyj4JERERERGpuGommI8EXsopc8JyGWty6v0wp85UYC6waR+PkQTYvHlzSQ2djI1bdnLRHU/nPba69ToOSbyZ91g9G4o/O0gQ/6RjDGSa6SVFL+300kZvJsXuRIqBRIqBZAfDyQ6Gm1OMtHSRaekk0dpBU1sHLe1dtKUOINV1AKkpM+nq7GJqqpUpqWbe3Zrcx8zjDNAPA/28taWn/E9cRESkSLObYPYMOGZGK9BKuD5n3oTum8lkGE7D4PAI/cNpdgyn2TUwTE/vIDt3dNO7fSsDu7oZ6e0ms7uHRH8PyYEeUsM76cjsYlpiF13sppk0SdIkY6o3SZrmmOpNktlTnp203kfLgIH4EzTFnwkPIHfC61sKHGs+DI4+e6L/U8myxoc6Qz2+qo+nRURERKT+jTeermaCuRPoyynrAzr2UW/099x6+bwDYMmSJcW0r2htBcrPA2B29RpSM6NfPpX0FRERqb0kDZFDXbsSWFmLR34H8KtaPHCDqMl4WkREREQaxpjxdDUTzH1AKqesA8jdyS233mhieeyOb2M9BZwAvAHU3XIaIiIiIlIzScJg+KlaN6TOaTwtIiIiIvkUHE9XM8H8MnBJTpkBq/PUs5w624F97o7j7gPAz0poo4iIiIjsvzRzeR80nhYRERGRceQdT1czwfwI0GZmlxKuh1wKzAEeyql3J7DSzNYArwHXAne5+0QXDBQRERERERERERGRKmiq1gPF2RCnAYuBbuBS4HR37zWzDWZ2Zay3FrgBWE/Y1K8HWFatdoqIiIiIiIiIiIjIxCQymUyt2yAiIiIiIiIiIiIiDahqM5hFREREREREREREZP+iBLOIiIiIiIiIiIiIFEUJZhEREREREREREREpihLMIiIiIiIiIiIiIlKU5lo34O3AzE4BvgEcAbwAXObuT+Sptx74KDAyWubuXdVqp0yemR0L3OfuB8fb04FVhDhuB65x99sL3PdU4GbgcOAZ4Hx331iVhsuElRjj7wBfAIayio9y902VbbVMVG58s8pnAT8HPubuvyxw398DVgJHAQ5c6O5PVrjJMkklxvgK4BpgMKt4gbs/Xqn2yuTleZ9+J/Bt4ATC++89wF+5+0Ce+84Hvgu8F3iF0I//u1ptF8Wg3pnZh4GbgCOBt4Ab3f27442HzKwNuAU4k9AHV7j78ngsAXyNMD5qBn4AfNndR+Lxy4BlwAHAA8AX3b23Sk/3bcfM5gDPA59393VmdhhwO3As8AYhNuti3YrEXMonfv6tBE4EdhD66wr118ZnZh8CVgDvJvTNa9x9tWLbmCaTY6hUHM1sMbAcOBD4CSEftaWU56UZzBUWP6QfILwgpgPXAQ+a2UF5qh8DnODuXaM/1WupTIaZJczs88CPgNasQ7cBu4A5wFnAjWb2vjz3nwPcC1xBeF38GLi70u2WiSs1xtExwJLsPq3kcn0YJ76Y2YnAo8Ah49w/BawFvgdMIwzm15hZS8UaLZNSaoyjY4DLc/qwkst1YpwY3wn8BphLiOEfAFfluX87oR//I6EfrwDuNbPW3LpSGYpBfYtfeB8gxGU6cDZwfZwkMd54aDlwKGESxYeBL5jZwnjsz4FPAO8D3gP8IXBxfLxPEr4Inwy8C5gBXFvZZ/m2dzswM+v2PcCThL/9l4DVZjY7Hit7zKV8YqLpPuBlQkw/BlwdE5Pqrw3MzJKE2H7d3acQkonfj7kmxbaBFJljKHsc4/+9ElgMzAY2E3KWJVGCufJOA55399vcfdjd1wNPEAZoe5jZgYQzBy/UoI0yeVcSBl3LRwvMrAs4A/iqu/fHmYyrgQvy3H8R8Jy7r3X3QcKJh9+JMyKlPpQUYzNrIrzRP1ed5sokjYkvgJmdBPxLbnkepwL98b19yN2/RxgU/FElGitFKTXGAPNRH65n+d6nW4Fe4Lr4Pr0ZuAv4UJ77nwyk3f3W2I9XAVuBhXnqSmUoBvXtUGC9u9/l7ml3fwb4D0J/Gm889KfA19x9u7u/Qrii4M/isaXAze7+Ruyf1+ccu93dN7r7dsKJofNjckXKzMwuJLxfvhZvvwc4Grg29scNwE+Bz05gDFxszKV8jgMOBr4S4/cicDzwOuqvjW4aIQnYHE8kpAlX142g2DaaYnIMlYjjEuB+d3/C3XcDfw18KuYli6YEc+Ulgb6csjQwL6dsPrATWGdmb5rZo2Z2fDUaKEVZRZgV9VRW2TxgyN3/N6vMCZd85joSeGlPpXAJw68K1JXaKDXG84AO4BuxTz8bzyJKfcgXXwiXiR5O+FAfz159OCr0WpDaKCnGcbB3BPBlM9tiZi+Z2bkVaakUa0yM3X3Q3T8RB9mjFgK/yHN/9ePaUwzqmLs/5+5LR2/HGc0nAAkKjIdinTnsHdfsmObG3IGjYtIk37GphKsRpIzMbB7wl8BFWcVHAq/GZMOo0dgVHAOXGHMpnw8ALxJmPm42s43ABwmzFtVfG5i7byXMLr2bsETCfwGXALNQbBvNpHIMFYxjbj5qK9ATy4umBHPlPQQcZ2Znm1mLmX2csK5Ke069duBxwtmMdxIu79xQYCkNqbF4hiiTU9wJ7M4p6yMkGXN1MvbEQ6G6UgNliPF0wlpGNxJmE1wD/KuZHV3mpkoRCsQXd+929/4J/Bfqw3WuDDE+iDCAv4VwWdlFwAozW1DelkqxCsV4VLwMcQVhsHx9nirqx7WnGDQIM5tKWM7k54RZzIXGQ51Zt3OPwdiY9xG+k7YVOAZ6PZSVmTUTvmt+yd27sw6N1x/HGwOXEnMpnxmEq0LeIiwB9jngW0AX6q8NLV4Z20e4Cr6DcOL8ZmAKim1DKSLHUKk4VmT8pU3+KszdXzGzcwgLb98KPEi4VLMnp979wP1ZRbea2cWEDwmtzdsY+oBUTlkH4bL5UupK/Zhw3DxsUHRKVtF9ZvbvwCcJMyilsakP7+fc/X+Ak7KKfmpmqwmXsD1cm1bJRMV10v+JcLn3Se7+2zzV1I9rTzFoAGZ2OLCOcLXdpwnrPBaK2+gX1hRhk7HsYzA25h3AsLv3m1m+Y6DXQ7ldRViq78Gc8vH6476OQRExL/YJSF4DQLe7j55QfczM1hAmuai/NrZFwHHuvizeXm9m64GrUWz3BxV5f91HHCsy/tIM5gozswOATe7+fnef5e6fJXzZeTan3lkxEZ2tHdAHb+N4BWgxs+xNo4yxl35C2HzB9lQK6+AcUaCu1I8Jx9jMTjGzL+YUq0/vP/bqw1Gh/i4NyMx+38wuzylWH24AZjaDsG7oDOB4d/91garqx7WnGNQ5M/sAYf+Yh4Az4vIJBcdDcUbsb9k7rtkxzY25xbJCx7YD/1eeZyPRp4HPmFmPmfUQZrv+M+HvfZiZZc8sHo1dpWIu5eNAZ5yhPipJyDuovza2Qxg7438IeAbFdn9Qi8/U3HzULMK4uaT3Zs1grryZwONxx/oXCDt+HkLYkTlbF/B1M3uB8AK7jHBG4UdVbKuUwN13mtn9hN21LyCsi/Mn5N/064fADWa2iDAj5ArCjvfP5qkrdWKSMR4BbjKzl4DHgHMIm298rkrNlcr6MTDFzC4C/oEQ1+loZuv+pBe4Nq5h+ABhY8ezCbszS52Ka87dS9gN+4/dfWic6o8AbWZ2KWEn7aWEde4eqnhDZZRiUMfMbA7wb8BN7n7DaPkExkN3Aleb2VmE70KXAJdnHVtmZo8QEiRXEK42GD22Ms66fI2w2/1d7p6u4NN823H3vdbYNLNXgUvcfV2M2d+Z2VWEZR0/AlxcwZhL+TwMbCPkFL4CHAucCSwADkP9tZE9TIjfecAdwImE2H4Uxbbh1eIz1czuJlyduQp4mrCU3Ia4FnPRNIO5wtz9VeBCYA1hPaRzgAXu3mtmK81sZax3B/BNwiCuBzgdOM3de2vRbinaBUALIVm8Bljm7k8AmNmVZrYBIG4+9Cngq4Td0k8FFo23lqTUjYnG+CeENdVXES5nWQYsdPfXa9FoKZ2ZnWtmvwCIM7g+DpwLdBPe5xfmbIwjDSYnxi8DnwGuI2zC+01gqbvn2yxO6sfxhKVNFgDbzGxX/PlPADNbYmYvArj7AHAasJjQjy8FTtfYq3oUg7p3PjAbuCqrL+0ys+WMMx4C/hbYCPwS+Blwm7vfE4/dQlgW8EnCDKxHgb8HcPe1wA3AemAT4TvR6CXhUh2LgPcTZszdDCx299fisbLHXMonjkE/AvwuIX6rgb+Iy/apvzYwd38eOIvw3XI78B3gXHd/GsV2f1HVOLr7c/ExVxHeLw4Gziv1SSQyGeWzRERERERERERERGTyNINZRERERERERERERIqiBLOIiIiIiIiIiIiIFEUJZhEREREREREREREpihLMIiIiIiIiIiIiIlIUJZhFREREREREREREpChKMIuIiIiIiIiIiIhIUZRgFhEREREREREREZGiKMEsIiIiIiIiIiIiIkX5f25hr3r49OYmAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm3.traceplot(trace,figsize=(20,5));" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T08:31:13.671720", "start_time": "2016-03-02T08:31:13.658017" } }, "outputs": [ { "data": { "text/plain": [ "{'Mean of Data': 1.0000182594945974}" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm3.gelman_rubin(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based on Gelman-Rubin and Geweke, we can be confident we have a chain that has converged to the limiting distribution (although perhaps for Gelman-Rubin, we'd want to try different starting values rather than MAP)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# In class excercise\n", "\n", "Team up and modify the code below to estimate sigma as well as the mean: " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "basic_model = pm3.Model()\n", "\n", "with basic_model:\n", "\n", " # Priors for unknown model parameters\n", " mu = pm3.Normal('Mean of Data',mu_prior,sigma_prior)\n", " \n", " # Likelihood (sampling distribution) of observations\n", " data_in = pm3.Normal('Y_obs', mu=mu, sd=sigma, observed=data)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "logp = -290.67, ||grad|| = 31.153: 100%|██████████| 4/4 [00:00<00:00, 1032.44it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "{'Mean of Data': array(10.69594596)}\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Multiprocess sampling (2 chains in 2 jobs)\n", "Metropolis: [Mean of Data]\n", "100%|██████████| 10500/10500 [00:01<00:00, 5263.93it/s]\n", "The number of effective samples is smaller than 25% for some parameters.\n" ] } ], "source": [ "chain_length = 10000 \n", "\n", "with basic_model:\n", " # obtain starting values via MAP\n", " startvals = pm3.find_MAP(model=basic_model)\n", " print(startvals)\n", " # instantiate sampler\n", " step = pm3.Metropolis() \n", "\n", " # draw 5000 posterior samples\n", " trace = pm3.sample(chain_length, step=step, start=startvals) " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2016-02-25T10:37:01.724954", "start_time": "2016-02-25T10:37:01.435545" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "score=pm3.geweke(trace, first=0.1, last=0.5, intervals=20)\n", "plt.scatter(score[0]['Mean of Data'][:,0],score[0]['Mean of Data'][:,1], marker = 'o', s=100)\n", "plt.axhline(-1.98, c='r')\n", "plt.axhline(1.98, c='r')\n", "plt.ylim(-2.5,2.5)\n", "plt.xlim(0-10,.5*trace['Mean of Data'].shape[0]/2+10)\n", "plt.title('Geweke Plot Comparing first 10% and Slices of the Last 50% of Chain\\nDifference in Mean Z score')\n", "plt.show()" ] } ], "metadata": { "hide_input": false, "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": "3.8.12" }, "latex_envs": { "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 0 } }, "nbformat": 4, "nbformat_minor": 4 }