{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains material from [cbe67701-uncertainty-quantification](https://ndcbe.github.io/cbe67701-uncertainty-quantification);\n", "content is available [on Github](https://github.com/ndcbe/cbe67701-uncertainty-quantification.git).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html) | [Contents](toc.html) | [11.3 The Kennedy-O’Hagan Predictive Model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.03-Contributed-Example.html)

\"Open

\"Download\"" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "bdNm3J0HWYcB", "nbpages": { "level": 1, "link": "[11.2 Markov Chain Monte Carlo Examples](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2-Markov-Chain-Monte-Carlo-Examples)", "section": "11.2 Markov Chain Monte Carlo Examples" } }, "source": [ "# 11.2 Markov Chain Monte Carlo Examples" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "izBlOg3zWYcE", "nbpages": { "level": 1, "link": "[11.2 Markov Chain Monte Carlo Examples](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2-Markov-Chain-Monte-Carlo-Examples)", "section": "11.2 Markov Chain Monte Carlo Examples" } }, "source": [ "Created by Xinhong Liu (xliu27@nd.edu)\n", "\n", "\n", "This example was adapted from:\n", "\n", "McClarren, Ryan G (2018). Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers, Chapter 11: Predictive Models Informed by Simulation, Measurement and Surrogates, Springer, https://link.springer.com/chapter/10.1007%2F978-3-319-99525-0_11\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": {}, "colab_type": "code", "id": "wvSaZPPuWYcG", "nbpages": { "level": 1, "link": "[11.2 Markov Chain Monte Carlo Examples](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2-Markov-Chain-Monte-Carlo-Examples)", "section": "11.2 Markov Chain Monte Carlo Examples" } }, "outputs": [], "source": [ "## import all needed Python libraries here\n", "import numpy as np\n", "import scipy.stats as stats\n", "import math\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[11.2.1 Markov Chain](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.1-Markov-Chain)", "section": "11.2.1 Markov Chain" } }, "source": [ "## 11.2.1 Markov Chain\n", "A Markov Chain is a sequence ${x_1,x_2,...x_t}$ for a random variable $X$ that satisfies the following property\n", "\n", "\\begin{equation}\n", "p(x_{t+1}|x_t,x_{t-1},...x_1) = p(x_{t+1}|x_t)\n", "\\end{equation}\n", "\n", "which means given the present state, the probability model for the future state is independent of the past states if $t$ is large enough\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "dJuJ7c2rW8gg", "nbpages": { "level": 2, "link": "[11.2.2 Metropolis-Hastings for MCMC](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2-Metropolis-Hastings-for-MCMC)", "section": "11.2.2 Metropolis-Hastings for MCMC" } }, "source": [ "## 11.2.2 Metropolis-Hastings for MCMC\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[11.2.2 Metropolis-Hastings for MCMC](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2-Metropolis-Hastings-for-MCMC)", "section": "11.2.2 Metropolis-Hastings for MCMC" } }, "source": [ "The Metropolis-Hastings algorithm (MH) enable us to evaluate the product of the prior and the likelihood function without calculating the normalization constant. It is a rejection sampling technique that uses a distribution that is not the target distribution to generate proposed samples\n", "\n", "\\begin{equation}\n", "\\hat{p}(x_{t+1}) = \\int_X p(x_{t+1}|x_t) p(x_t) dx_t\n", "\\end{equation}\n", "\n", "### Algorithm\n", "1. Choose initial state $x_0$ and a proposal density $q(x_{t+1}|x_t)$\n", "2. Randomly simulate candidate sample $y$ from $q(x_{t+1}|x_t)$ and $u$ from $U(0,1)$\n", "3. Calculate the acceptance ratio\n", "\n", "\\begin{equation}\n", "\\alpha(x_t,y) = min \\left(1, \\frac{\\hat{p}(y) q(x_t|y)}{\\hat{p}(x_t) q(y|x_t)}\\right)\n", "\\end{equation}\n", "\n", "4. Set $x_{t+1} = y$ if $\\alpha(x_t,y) \\geq u$, $x_{t+1} = x_t$ otherwise\n", "\n", "Then the stationary pdf for the Markov Chain is the target probability" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)", "section": "11.2.2.1 Implemention" } }, "source": [ "### 11.2.2.1 Implemention\n", "\n", "Following example is using MCMC to approximate a Beta distribution with a proposal density $N(2,1)$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "nbpages": { "level": 3, "link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)", "section": "11.2.2.1 Implemention" } }, "outputs": [], "source": [ "def beta_mcmc(N, x0, sigma, a, b):\n", " '''\n", " Use Markov Chain Monte Carlo to approximate a Beta distribution with a proposal density N(x0,1).\n", " \n", " Arguments:\n", " N: total number of samples needed\n", " a,b: alpha and beta values for beta distribution\n", " \n", " Returns:\n", " states: stable\n", " acc: acceptance rate\n", " \n", " '''\n", " states = []\n", " acc = 0 # number of accepted samples\n", " x = x0 # initial state - starting point for Markov chain\n", " for i in range(0,N):\n", " states.append(x) # append state vector\n", " y = proposal_dist(x,sigma) # candidate sample\n", " alpha = min(beta_dist(y,a,b)/beta_dist(x,a,b),1) # acceptance probability\n", " u = np.random.uniform(0,1) # generate uniform random number\n", " # check if sample is accepted\n", " if u <= alpha:\n", " x = y # generated sample=candidate sample\n", " acc = acc + 1 # update accepted candidate sample count\n", " acc_ratio = acc/(N-1)\n", " return states, acc_ratio \n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)", "section": "11.2.2.1 Implemention" } }, "source": [ "*Note*: The cell below can take a few minutes to evaluate. Adjust $N$ (number of samples) to explore the trade-off between accuracy and run time." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "nbpages": { "level": 3, "link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)", "section": "11.2.2.1 Implemention" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:20: RuntimeWarning: divide by zero encountered in double_scalars\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Number of samples = 5000\n", "Acceptance ratio = 0.27645529105821165\n" ] }, { "data": { "image/png": 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kQmPq3/esb9gHpaVfwNjS9Pcb26HehxZpjiJjBEtLS7nwwgt55JFHuOmmm3DO8ctf/pIf/ehHMdvPmDGDd955h9mzZ9OmTRuGDx+edhKQsrIy1q5dyzHHHENpac338corr2To0KG88cYbjBw5kieeeCIa1HkdcsghCcuOD0oi773Lg9Q3VffLVq1aAaFkO5WVlUm3TXbNRo8ezfLly2vtc8stt3D11VdTUFDA+vXrKSgooLKyktLSUjp16lRr+27dugFw2GGHcdlllzF37tyUgaDftSorK+Ob3/ym7/YvvfQSxx9/PDt27KCyspIWLVpQXFwcPbZXQUEBZ5xxBl26dAHg/PPPZ8GCBdkVCFroCj0JLHXOPZRgsynAjWY2gVBimFLn3CYzewv4nSdBzLnALzNVV0+dM30IERGRejOzQ4Ac51xZ+PW5wN1NXC2RJpGq5S7TOnTowPjx47nkkkv48Y9/zMiRI7njjju46qqraNu2LRs2bCAvL4/S0lI6duxImzZtWLZsGXPmzEnrOLt27eInP/kJl156KR07dowJBFevXs1RRx3FTTfdxOrVq1m4cCEDBw6krKwscPlz585lzZo1HHnkkUycODGalObwww9n6dKlHHvssUyePJl27doB0K5dO9/yjzvuONauXcvKlSvp3bs3zz//PGeccUZa5xqR7JqlahG8+OKLefbZZxk2bBiTJk3izDPPrHWvv3v3bqqrq2nXrh27d+9m6tSp3HnnnQA8/PDDANx44421yn7ttdf45S9/ye7du5kxYwbjxo2jXbt2SVsEAUaMGMGkSZO4/PLLefbZZ7nkkktqbTNy5Ejuv/9+9uzZQ8uWLXnvvfe4+eabk5ZbV5kcI3gq8H3gzHBq6yIzO9/MbjCzG8LbvAmsBlYCjwM/AXDObQd+A3wc/nd3eJmIiIjA4cBMM/sUmAu84Zz7TxPXSeSgdeKJJzJw4EAmTJjAueeey5VXXsmwYcPo378/o0aNoqysjPPOO4/KykoGDBjAHXfcwSmnnBKo7BEjRtCvXz+GDBlCjx49+Nvf/lZrm4kTJ9KvXz8KCwtZtmwZV199NZ07d+bUU0+lX79+3HrrrSmPM2zYMG6//Xb69etHr169uOyyywAYN24cF154IWeeeSZHHHFEdPvLL7+cBx54gBNPPJFVq1ZFl7du3Zqnn36a73znO/Tv35+cnBxuuOGGWsfzSjRGsK7XDOC6666jpKSE3r1789BDDzFu3DggNO3G+eefD8DmzZs57bTTGDhwIEOGDOGCCy7gvPNC+SmXLVuWsNtuZNtTTjmFO+64w7dlz899993HQw89RO/evSkpKeG6664DYMqUKdEAtGPHjtxyyy2cfPLJFBYWctJJJ3HBBRcEPu90WENlz2kOBg8e7OqT9vXUce9yylGdefC7AxuwViIi0tDMbL6mTAiuvv8/AqEunnXtGlqX/USSWLp0Kccff3xTV0MOYBdeeCGvvPIKLVu2bOqqJOX3XQj6f2TGk8WIiIiIiIhkk9dff72pq5BxjTJ9hIiIiIiIiDQfCgTjOOUNFRERERGRA5wCQQ8lDRURERERkYOBAkEREREREZGDjAJBDzM0o7yIiIiIiBzwFAiKiIiIiKTpnnvu4YQTTmDAgAEUFhby0UcfAXD99dezZMmSBjlGz5492bZtW9Jtfve736Vd7jPPPOM7UfozzzyDmTFt2rTossmTJ2NmTJo0CYCKigpuv/12+vTpE53f8N///ne0vt/85jdjyiwsLKRfv37R93PnzuX000/n2GOP5bjjjuP6669nz549aZ9DEPv27WP06NH07t2boUOHsnbtWt/tevbsSf/+/SksLGTw4NQzE40dO5bf//73darTmjVrGDp0KH369GH06NHs37/fd7uFCxcybNgwTjjhBPr378/evXvrdLxkNH1EHDUIioiIiGSZP/SH0i8arrwOPeDmzxKunj17Nq+//joLFiygVatWbNu2LXpD/8QTTzRcPQL43e9+x//93/81WHn9+/fn5Zdf5qyzzgJgwoQJDBxYM8f2HXfcwaZNm1i0aBGtWrVi8+bNvPfee9H1ZWVlrF+/nu7du7N06dKYsjdv3sx3vvMdJkyYwLBhw3DO8c9//pOysjLatGnTYOcQ8eSTT9KxY0dWrlzJhAkTuO2225g4caLvttOnT6dLly4NXod4t912GzfffDOXX345N9xwA08++SQ//vGPY7aprKzke9/7Hs8//zwDBw6kpKSEvLy8Bq+LWgQ9DGWLEREREck6pV/A2NKG+5ciqNy0aRNdunShVatWAHTp0oVu3boBMHz4cObNmwdA27Ztue222xg0aBBnn302c+fOZfjw4Rx11FFMmTIFqN06d+GFFzJjxoxax7z00ksZNGgQJ5xwAo899hgAt99+O+Xl5RQWFnLVVVcB8MILLzBkyBAKCwv50Y9+RFVVFQBPP/00xxxzDGeccQazZs1KeG7f/OY3mTt3LhUVFezatYuVK1dSWFgIwJ49e3j88cf585//HD33ww8/nO9+97vR/b/73e9Gg62XX36ZK664IrrukUce4ZprrmHYsGEAmBmjRo3i8MMPT3q9/c49iNdee41rrrkGgFGjRjFt2jSca5hmn08//ZQzzzyTPn368PjjjwfaxznHu+++y6hRowC45pprePXVV2ttN3XqVAYMGBANwDt37kxubm6D1NtLgaCIiIiISBrOPfdc1q9fzzHHHMNPfvKTmBYxr927dzN8+HDmz59Pu3bt+NWvfsXbb7/N5MmTufPOO9M65lNPPcX8+fOZN28e48ePp6SkhHHjxpGfn09RUREvvvgiS5cuZeLEicyaNYuioiJyc3N58cUX2bRpE3fddRezZs3i7bffTtp11cw4++yzeeutt3jttde4+OKLo+tWrlxJjx49aN++fcL9R40axSuvvALAv/71Ly666KLoukWLFjFo0CDf/ebNm8f1118f+NwBRo8eTWFhYa1/zz33HAAbNmyge/fuALRo0YIOHTpE940/53PPPZdBgwYFDjQXLlzIG2+8wezZs7n77rvZuHEjZWVlvvUpLCxkyZIllJSUcOihh9KiRahTZkFBARs2bKhV9ueff46ZMXLkSE466STuv//+QHVKl7qGxmmopwQiIiIicmBq27Yt8+fP54MPPmD69OmMHj2acePGce2118Zs17JlS8477zwg1OWyVatW5OXl0b9//4Tj1RIZP348kydPBmD9+vWsWLGCzp07x2wzbdo05s+fz8knnwxAeXk5hx12GB999BHDhw+na9euQCiA+vzzzxMe6/LLL2f8+PGUlpby4IMPpjUOsVOnTnTs2JEJEyZw/PHHB+7yOXjw4ITdahOde6JunhF+9/XmM1/crFmz6NatG1u2bOGcc87huOOO4/TTT09a9iWXXEJ+fj75+fmMGDGCuXPncumll1JUVJRwn61btwaqT2VlJTNnzuTjjz+mTZs2nHXWWQwaNCjaXbehKBD00DyCIiIiIhJEbm4uw4cPZ/jw4fTv359nn322ViCYl5cXvdHPycmJdqfMycmhsrISCLVUVVdXR/fxSwoyY8YM3nnnHWbPnk2bNm0YPny473bOOa655hruvffemOWvvvqqb8CRyJAhQ1i0aBH5+fkcc8wx0eW9e/fmiy++oKysjHbt2iXcf/To0fz0pz/lmWeeiVl+wgknMH/+fC655JLAdUl27qNHj2b58uW19rnlllu4+uqrKSgoYP369RQUFFBZWUlpaSmdOnWqtX2kW+9hhx3GZZddFk1ok0z89TQzysrKaiXLiXjppZc4/vjj2bFjB5WVlbRo0YLi4uLosb0KCgo444wzomMWzz//fBYsWNDggaC6hoqIiIiIpGH58uWsWLEi+r6oqIgjjzyyTmX17NmToqIiqqurWb9+PXPnzq21TWlpKR07dqRNmzYsW7aMOXPmRNfl5eVRUVEBwFlnncWkSZPYsmULANu3b2fdunUMHTqUGTNmUFJSQkVFBf/4xz9S1uvee++t1RLYpk0brrvuOm666aZocpxNmzbxwgsvxGx32WWX8Ytf/IKRI0fGLL/xxht59tlnoxlWITSm8csvv0xYj2TnPnHiRIqKimr9u/rqqwG4+OKLefbZZwGYNGkSZ555Zq0Abvfu3ZSVlUVfT506NZrl9OGHH+bhhx/2rddrr73G3r17KSkpYcaMGZx88sm0a9fOtz5FRUX07dsXM2PEiBHRDKzPPvusb1A8cuRIFi5cyJ49e6isrOS9996jb9++Ca9RXSkQjKOOoSIiIiKSzK5du7jmmmvo27cvAwYMYMmSJYwdO7ZOZZ166qn06tWL/v378/Of/5yTTjqp1jbnnXcelZWVDBgwgDvuuINTTjklum7MmDEMGDCAq666ir59+/Lb3/6Wc889lwEDBnDOOeewadMmjjjiCMaOHcuwYcM4++yzfY8R71vf+hYjRoyotfy3v/0tXbt2pW/fvvTr149LL7002uU0ol27dtx22220bNkyZvnhhx/OhAkT+PnPf86xxx7L8ccfzwcffED79u0TjhFMdu6pXHfddZSUlNC7d28eeughxo0bB8DGjRs5//zzgVAm09NOO42BAwcyZMgQLrjggmh33mXLltXqfhsR2faUU07hjjvu8G3Z83Pffffx0EMP0bt3b0pKSrjuuusAmDJlSnTcaMeOHbnllls4+eSTKSws5KSTTuKCCy4IfN5B2YE0Jm7w4MEukqWpLoY/MJ2B3Q/lT5ef2IC1EhGRhmZm851zqSd7EqD+/z8CMLZDKJtiY+0nksTSpUs5/vjjaxY08vQRcnC48MILeeWVV2oFtM1Jre8Cwf+P1BhBEREREcluCtokA15//fWmrkJGqWtonAOogVRERERERMSXAkGPdLIpiYiIiIiIZCsFgiIiIiKSdQ6kPBcidVHf74ACwTj6kyIiIiLSvLVu3ZqSkhIFg3LQcs5RUlJC69at61yGksV4qGOoiIiISPNXUFBAcXExW7dubeqqiDSZ1q1bU1BQUOf9MxYImtlTwIXAFudcP5/1twJXeepxPNDVObfdzNYCZUAVUKkU4SIiIiISkZeXR69evZq6GiJZLZNdQ58Bzku00jn3gHOu0DlXCPwSeM85t92zyYjw+sYLAk39zUVERERE5MCXsUDQOfc+sD3lhiFXAC9nqi4iIiIiIiJSo8mTxZhZG0Ith//0LHbAVDObb2ZjmqZmIiIiIiIiB6bmkCzmImBWXLfQU51zG83sMOBtM1sWbmGsJRwojgHo0aNHvSpiKGuoiIiIiIgc+Jq8RRC4nLhuoc65jeGfW4DJwJBEOzvnHnPODXbODe7atWtGKyoiIiIiInIgaNJA0Mw6AGcAr3mWHWJm7SKvgXOBRU1TQxERERERkQNPJqePeBkYDnQxs2LgLiAPwDn3aHizy4Cpzrndnl0PByabWaR+Lznn/pOpesbVWX1DRURERETkgJexQNA5d0WAbZ4hNM2Ed9lqYGBmaiUiIiIiIiLNYYygiIiIiIiINCIFgh6hrKHqGyoiIiIiIgc2BYIiIiIiIiIHGQWCcZwaBEVERERE5ACnQNAjlKhURERERETkwKZAUERERERE5CCjQDCOuoaKiIiIiMiBToGgh6G+oSIiIiIicuBTICgiIiIiInKQUSDoYaZ5BEVERERE5MCnQFBEREREROQgo0BQRERERETkIKNAMI6yhoqIiIiIyIFOgaCIiEgWMrNcM/vEzF5v6rqIiEj2USAoIiKSnX4GLG3qSoiISHZSIOhhZsoZKiIizZ6ZFQAXAE80dV1ERCQ7KRAUERHJPn8EfgFUN3VFREQkOykQFBERySJmdiGwxTk3P8V2Y8xsnpnN27p1ayPVTkREsoUCQQ9DWUNFRKTZOxW42MzWAhOAM83shfiNnHOPOecGO+cGd+3atbHrKCIizZwCQRERkSzinPulc67AOdcTuBx41zn3vSauloiIZBkFgiIiIiIiIgeZFk1dgebEDFDeUBERyRLOuRnAjCauhoiIZKGMtQia2VNmtsXMFiVYP9zMSs2sKPzvTs+688xsuZmtNLPbM1VHERERERGRg1Emu4Y+A5yXYpsPnHOF4X93A5hZLvB5mg5sAAAgAElEQVQI8C2gL3CFmfXNYD1FREREREQOKhkLBJ1z7wPb67DrEGClc261c24/oYxolzRo5RIwU9ZQERERERE58DV1sphhZvapmf3bzE4IL/s6sN6zTXF4mYiIiIiIiDSApkwWswA40jm3y8zOB14F+hCazi9ewnY6MxsDjAHo0aNHvSpkmFLFiIiIiIjIAa/JWgSdczudc7vCr98E8sysC6EWwO6eTQuAjUnK0YS5IiIiIiIiaWiyQNDMvmYWmrDBzIaE61ICfAz0MbNeZtaS0GS5U5qqniIiIiIiIgeajHUNNbOXgeFAFzMrBu4C8gCcc48Co4Afm1klUA5c7pxzQKWZ3Qi8BeQCTznnFmeqnrF1BqdsMSIiIiIicoDLWCDonLsixfqHgYcTrHsTeDMT9RIRERERETnYNXXWUBEREREREWlkCgQ9jCTpSUVERERERA4QCgRFREREREQOMgoERUREREREDjIKBL3MUNJQERERERE50CkQFBERkcCqqh2bSssp21vR1FUREZF6UCAoIiIigW3btY9h977LlE83NnVVRESkHhQIeihrqIiISHLtW+cBsLO8solrIiIi9aFAUERERAJrnZdDy9wcSsvVNVREJJspEBQREZHAzIz2+S0UCIqIZDkFgh5m4JQ2VEREJKn2+XnsVLIYEZGspkBQRERE0tIhP4+dahEUEclqCgQ9rKkrICIikgXat1YgKCKS7RQIioiISFo65OdpjKCISJZTICgiIiJpUbIYEZHsp0DQw0ydQ0VERFLpkJ/Hzr2VSrAmIpLFFAjG0f9pIiIiyXXIz6Oq2rF7f1VTV0VEROpIgaCIiIikpX3rPAAljBERyWIKBD0McKhJUEREJJkO+aFAUOMERUSylwJBERERSUt7BYIiIllPgaCIiIikJdIiqK6hIiLZS4Ggh5mSxYiIiKSirqEiItkvY4GgmT1lZlvMbFGC9VeZ2cLwvw/NbKBn3Voz+8zMisxsXqbqKCIiIumLJovZW9nENRERkbrKZIvgM8B5SdavAc5wzg0AfgM8Frd+hHOu0Dk3OEP1ExERkTpo17oFZmoRFBHJZi0yVbBz7n0z65lk/Yeet3OAgkzVJSjD1DVUREQkhZwco22rFhojKCKSxZrLGMHrgH973jtgqpnNN7MxTVQnERERSaBDfp4CQRGRLJaxFsGgzGwEoUDwNM/iU51zG83sMOBtM1vmnHs/wf5jgDEAPXr0yHh9RUREJBQIqmuoiEj2atIWQTMbADwBXOKcK4ksd85tDP/cAkwGhiQqwzn3mHNusHNucNeuXetZIU0oLyIiEkT71nns3KtAUEQkWzVZIGhmPYBXgO875z73LD/EzNpFXgPnAr6ZR0VERKRpqEVQRCS7ZaxrqJm9DAwHuphZMXAXkAfgnHsUuBPoDPzFzAAqwxlCDwcmh5e1AF5yzv0nU/WMqXNjHEREROQA0D6/hQJBEZEslsmsoVekWH89cL3P8tXAwNp7NA5lDRUREUktlCxG8wiKiGSr5pI1VERERLJIh/w8yiuq2F9Z3dRVERGROlAg6GHqGyoiIhJI+/w8ACWMERHJUgoE46hnqIiISGodwoGgxgmKiGQnBYIiIiJZxsxam9lcM/vUzBab2a8buw7tWysQFBHJZk0+oXxzYhhqExQRkSywDzjTObfLzPKAmWb2b+fcnMaqQLRrqAJBEZGspEAwnuJAERFp5pxzDtgVfpsX/teo/4Opa6iISHZT11AREZEsZGa5ZlYEbAHeds591JjHb58fepa8c6+mkBARyUYKBD2UNVRERLKFc67KOVcIFABDzKyfd72ZjTGzeWY2b+vWrQ1+/MgYQXUNFRHJTgoE4zj1DRURkSzinNsBzADOi1v+mHNusHNucNeuXRv8uK3zcmnVIkddQ0VEspQCQRERkSxjZl3N7NDw63zgbGBZY9ejQ36eWgRFRLKUksV4qGuoiIhkiSOAZ80sl9BD3b87515v7Ep0yM9Ti6CISJZSIBjHqWeoiIg0c865hcCJTV2P9vl57NyrQFBEJBupa6iIiIjUiVoERUSylwJBD8OUKkZERCSg9q1bKBAUEclSCgRFRESkTkLJYjSPoIhINlIg6KFkMSIiIsF1CI8RrK5WfxoRkWyjQDCOU7YYERGRQNrn5+Ec7NqvVkERkWyjQFBERETqpH1+HgClezROUEQk2ygQFBERkTpp3zocCCphjIhI1lEgGEcdQ0VERILpEG4R1FyCIiLZR4GgiIiI1Ek0EFSLoIhI1lEg6GFKGyoiIhJY+/wWAJpCQkQkC2U0EDSzp8xsi5ktSrDezGy8ma00s4VmdpJn3TVmtiL875pM1tNLSUNFRESCibQIaoygiEj2yXSL4DPAeUnWfwvoE/43BvgrgJl1Au4ChgJDgLvMrGNGayoiIiJpOaRlC3JMYwRFRLJRykDQzPr6LBsepHDn3PvA9iSbXAI850LmAIea2RHASOBt59x259xXwNskDygbhDqGioiIBJeTY7TPz1OLoIhIFmoRYJu/m9nzwP1A6/DPwcCwBjj+14H1nvfF4WWJlmdcXXqGVlZVk5tjGmMotWzcUc6OPRX07da+wcqsrKpm7prt7Kuqjll+UveOdGiT12DHCWLV1l18un4HJ/boSK8uhzTqsZsD5xz7KkPf/7xcDbmWg1MHBYIiIlkpSCA4FLgP+BBoB7wInNpAx/eLnFyS5bULMBtDqFspPXr0aKBqBVdRVc2g37zNoCM78vQPhjT68aV5+8a4dwFYO+6CBivz7SWb+fGLC2ot/94pPfjtpf3TLm9fZRVvfraJ3JwcLuh/BLk5wR9o/PKVz5i7Zjvf7NOF568bmnTb6mrH/qpqcsxo2aJxg6aet79R5+uTzI0vf8IbCzfRskUOb950Gr0Pa9eg5Ytkg/at85Q1VEQkCwW5G6sAyoF8Qi2Ca5xz1cl3CawY6O55XwBsTLK8FufcY865wc65wV27dq1XZerSoLevspqdeyuZvnxrvY4t2eHP01Zw6rh3+fu89ak3zpDd+6sAePR7g5j8k28w+SffoGu7VuwJL0/XhytLuHnip9z08ics2lCa1r77KkLHLA9w7CufmMNxd/yHvnf+h/nrkvUYz4wX5nzR4GWu3bab9q1bsL+ymlVbdzd4+Yl88sVXPPDWMh57fxVV1Q2T4aqq2vGLSZ/yw2c+ZummnQ1Sphwc1CIoIpKdggSCHxMKBE8GTgOuMLNJDXT8KcDV4eyhpwClzrlNwFvAuWbWMZwk5tzwsoxbtWUX33/yI6Z86ht31uICpBldtKGUp2au4avd++tbPWlkC4t38Pnmsuj7mSu3sWFHOXPXNH4gExH5zJ3QrT0n9ujIiT060sqnhW3yJ8WB6lleURPEVVSl+Ywn/PSkKsD3YO22PXz90Hwqqx3FX5Wnd5xmyjnodmg+AEs2Nl7w9PC7K3lk+ip+9+YyVm7Z1SBlluzex9/nFfPusi3MXLGtQcqUg0P7/Bbs3KvpI0REsk2QrqHXOefmhV9/CVxiZt8PUriZvQwMB7qYWTGhTKB5AM65R4E3gfOBlcAe4AfhddvN7DeEglCAu51zGb/z/la/r7GzvIJ5a7+iVYscLh7YrUHKvWvKYuav+woz+MGpvRqkTMm83fsqufjhWUBN185IuNMspxmJq9PNEz8FEndL3bm3gtmrSlizraYly4WXf7V7P0d2DjDmL3whqgO0Sjkc3Q7NZ8OOhgsCXyvawF+mr6JNq1z+etUgvtahdYOVHUS1cxzWvjXLvixjXUnmWgS/LN3LPW8upWVuDr+9tF9M4J128J5Ic/xMS1bokN9SDzpFRLJQykDQEwR6lz0fpHDn3BUp1jvgpwnWPQU8FeQ4DWX0yT0YfXIPLhj/ge+NfkVVNReOn8mQXp34zaX9Ape7N9zi0lBduKRx7Kv0ucF2kR9N97uMHNnblbku3Zr/9t4qHpm+qtby65+dx9w1230DyKpqx7qS3fTqckhMcqSgH+10EypVVTsWbyyNBjt5uTn069aBnPA4xg9WbGN5uMV25ZZdjR4IAuTn5dD7sLZ17pobxMdrt/OvcC+Fa7/RM+bvUyb+rjTl51uyT0HHfEp272fXvkratgryfFlERJoDpbnzYeb/cHzPviqWby7j+TnrosvSuV1KpxWp+Ks90QCyuVmxuYzFG0sDdYvNZn7n52oiwWYn3Srt3lf78+UcSbuTPj1rDWc++B4fr/0q5phBghHnarJABf3ovPHZJi5+eBb/9dfZ/NdfZ3Pxw7P496Iv/ctvgl9KtXMYRqc2LRtkjJRzjg9XbmN7Gq0rlQ0UCDbDj7RkiaPCGYPXbmu8cbIiIlJ/CgQTaIogp6Kqmg07ypm/7itOu286N7wwv9Hr4PXMrDWMnbI4ZtnKLbs45w/vc8H4mcxcqXFETSL80azvdCXVKT7jft+BT9bvAGDzzr2Bytq9r5JHpq/koanL2VK2j5xwnYMGbZFMhOOvOJE/ji4EYNe+moDLe9j6fmXL91exeuuutL77zkFODrTKy2F/A3TRXLqpjCuf+Ihb/l4Ue5yY17H1a6gWwQP8uY5kUK+uoUBwjQJBEZGsoj4cPgzDAdOXbaFH5zYc3bUt4H/z6r152l9Z7ZsWP+gN1m9eX8Jzs9dx/6gBACxY91XadW9IY/+1JPTz4hOiy8r2VnheJ04O4Jzj6qfmAvDcD4dk5RyLfr821wwaBCOfQ+8VNd8ZV5LzC97q+gAkUTAye1UJD7y1PPo+8jGIHGblljJemPMF1c4xuGenWuNyI6WeclSn6DF2lldSuqei1pyJ9f2djHl+Hh+Ek6Qsvfs88lvmptwn0iKYiHMOM+OvM1axausu7ryoL+1bJ57rsbwi9J1Klb3Ve64Z6RqqoFDScGQnBYIiItlILYI+zEI3Qj945mPOevC9wPulSoKRqhXkjYWbANgVDrCa+81YsvpVVTs+WLGND1ZsCzx+rLmJP79nP1zLvHBw3hy7xaZbp1S/lyDFRbZJlDU0vttifCD4yoINPPPhWp6bvY6bXv6E2atKfA/gDbbueXMpA++eGlrt+U7V93fyxfY90dclu/cF2sdR+5winp+9lqP/700WbSjlvv8sY9L8YhYVB5ueI9mpxK9rsBZBdQ6VOspvmUu3Dq3VNVREJMsoEPSR6Pm+781ZTNe0+t1IRW4oIy01zfG2LFkXtYTbOce2Xfv4x7z1LPsye+Yniz+/uzzdZP3OvHx/FU/PWtOgWTF96xXtGlq/clJl+myY8a9xgSAWs7TaEdOKvnhjbKDkTYyTqtWzvt+XyipvUBlsH+dCXXQjLd6LN5aytSwURE5dsplqR8xUGamKTdTiHP+3xfu+srphsoY2w2cbkkV6djmE1QoERUSyigJBP2YZCcKS3Wjd9PInbNsVShARCQRTjeFqasniiJixW8ATH6zh1kkLuW3SwozXq8Gkefk/XLWNX/9rCQ/8Z1lm6pNETatU8Er7dg31vk5SVvyaRK1S8UXE1zNVK1Q06A1SkXp+XeryfXPOkeM5pwvGz+S/n4tPtFxTbspxmZ5yU8mJe3DUkJr3Xx5pjnp1OYS1GZxCRUREGp4CQR9G8BvqmK5picoL0HLjncA+knOiMQPBXfsqufUfn7Jzb/LMh7HJOZIFCrGtK5EEH75TMjRTya6+36lHukG+WrSRO15dlJlK4WkliwuPSssr6HvnW9z5WrBjp+waGqguoa0SBoJx783Md3n8+uj+ka6hZvVuAU3F24016Fev2oX+XhhQHs7yWxROqBNt3XOx2weR9LMX/tkiN/Tn29uSWR8K/qQ+enU5hB17KjSfoIhIFlEg6MPM/8a2rjdK6cZzNS2CdTxgHTw9cw3/mF/MY++tbpDyYlsEHftTBIDV1aHuo+tKdlOewfnY0pF0nFaK7b1TjDQGA7bt2k95RRXPzQ52bL+uoUE/q/ExWaKHFvGLc+J3dEla+/AGvcnXh17X7wvjvR5BH8I4XDR4TTSPoLek1JlaY38mkxs+bsNlDU0/EBaJ6BWeQkLdQ0VEsocCwQRSBS5+Ut08Bb23inaba4K7Mf/MqMFu8pNJdT3/Z2IRg3/7Dmc8MIPrn/s4eMGNJH6OOP9r0ji/r0RjBNMNhIIGJX5emLMuZq67xC2C8WMEoysC8Z5rqgbB+n5dSjznE7So6upw3ax2IBgZu+dio9WkgnznI9u0CEfViRL1NIYpn25kyD3vUJli6oypi7+Mjp2UA1MvzSUoIpJ1FAj6MGBvpd9k27E3XMu/LOP5gK0v6YjcUzXm/V2izIcQ3zLp7QqbpGuoi30dmWMt0Tmt2babYw9vx/FHtOer3fWfmLsheM+vdE9cINjYlQmrqnaU7PK/oU43Z4j393rKUZ2A+K7Oic/yozXbmTR/ffT3mahRqnaLYOw8go7kXacTdYOtKb9hWrEWfBE7VUs6D2EiddtbUfM3Y8/+Suas3g7A2H/VJBkK3NJYKzlM/HrIzW3oFsH097nj1UVsKdvHrn2Jp5L5snQvY56fzy9fyaLxwZK27p3akJtjmkJCRCSLaB5BH2bGsk1lKbf76UsLWLlll2dJ3VtYvJoiWUyysVtV1Y7cWn36kgce8UFEqhbB/ZXV9OzShqrq1NNwNJb47q3pbA/wyRcNPw/kzROLouNJY+YRrEOCI29Lkl+glerj5/2dbtu1jy0793JY+9axZcTtk+yBg59oQBQZiJds22BF+qproF8dThZjxH5fd5bXBEbelrCg4zKDHD9pl1rn+HzzLo7uekh0LGE6grYu12Q6TrxN5HMyv4nnRZXMysvNoXvHfNYoYYyISNZQi6APo+Ym+cjObRJuFxsENpymGCMY4d8i6N/qkjShRVyLYKokMfurqmnZIjc8h2PzGKAU06MvvkoBqnjZXz5syOoAsDFJkJzudfNuH22VS6OIqurY63LThE8C1Cn2gYNLMSF7rfrFl5/0WHV31oPvceyv/h2d2xNgX2UVz89ZFzOWMDR9RM3rVAI/3IlvAfRJShV9eBO37RsLN/Fff/2QkX98n7/OWBXseHWwe18lO8IBdLJr39yzH0vD6dnlENZsVSAoIpItFAj6iEwoHy/V7UxD3e80xY1TfJc9r8RTAyTpGhrz2nnmR/PfZ39lNS3r0HKRSUGzotYsy7yY8WDxYwTTrIC3Rdcv0EpVXqQu3+zThU6HtGT3vsRJfiLj2VIFTbVyyTj/5X7qc/39fp/7Kqv5tHhH9P2fp63kjlcX8dqnG2L2y/FpTU8YuKYcIxgpN3V9E12Tn760gAVfhOod3+U1yLHjXydy4Z9nRl8nnUom7qccuCJTSDSXh3kiIs3d+Gkr+NM7K5rs+M3rzruZCNJCURdBu1tlqiWwoqqakl37qPBJ7JDsBj1RMorkLYJxY5xSnPu+ympatsjJ0JWvm2Stn011n5NoEngj/WQxfl1D0ykhUpdWLXIZWNAhuvy52WvpefsbjP7b7OiynHAgGJ1zLzJG0KUaIxjazszq1H21vryf46/2hJLJ7Npb0+2z2kWSxcTWLWGW05TzCLqU22XqnNP9/HjHgnnr/eTMNazzdA9UUHDwOKrLIezZX8UWJQYSEQnkrcVfUrS+6YZOKBD0U9en+Q10+EQ3+/V11RMfMei373DV4x/VWhftGehzks4TN8asDdAKECrT/3XE3ooqtu3aR8tcY9e+SpZ9WdZsxgmmozHud5ON60v3+L5dQ73rU3yiq13NFt5AaGl4fG3R+h3ROkVbBPHvzpi4juHy09i2LhLt6/0qJmo1jZ57oK6hAevjc5zax41sW7PS7yFPowhX4Yvte/jN60v4v8mfxa+Sg0DPyBQS6h4qIhJI8VflFHRMPAwt0xQINqCg3b5SyVTX0CUbdwLw+ZbaiXDq0iKYrJ7xrWnJTimSTKN1Xi4frioB4JHpKxPv0ARSZXHMtDc/28QNz8+PaY2KYel/bvyCknS6B0Y+F7UDktDPFjkWXRaZ8y7H5y9ObNKbuPqEf+YEmlC+4X8pqbqIh8Y4Bm+RTfk7inQNDXQqtS/IrJXbguzof+iAl+/L0r08/G5sN5bIZ6ky/MI7TqxmOpw6V02yRGQKCWUOFRFJbefeCkrLKyjomN9kdVDWUB9N3T3xozXbfZdvLdtHl7Yta3VDC2J/ZTW79lXSIsfYsaeCb9w7DYC+3drzxDUnJ+0aWLJrH50OaRlan6S7ZAzPytPvnx6dc85vn8gYxOOOaBddljDgaURJu4b6jhHM3J3ur15dFDNvHyQOmoLyjv30+0z5lefdytty7V3uF0zmxLcIJjlGTB0iLYIBksWUV1TxRckeeiRJ8JTqOPG8gZu3BXZL2V7+9M4KSnbvrxkjGKhFMFXX0CDiAnDPTuUJJrVvSJc8MpPNO2O7/sV3afV+nhQAHjy6dcinZYsc1ipzqIhIShu+CvV+U4tgM5P4pjPY+J7ay9OzsLi01rI5q0s4+Z53+Pu89Sn3f61oA4V3T+X7T9Z0AY3cgH77pK9zxZDunNq7C+3z83j/81ALQrIWwcfeX+17nGQ3eN5rER/AbNm5l22eufAirQi5fs1FTSjoPImJeD9H9R0nlWyetpqDpFfm5p17o6/9PvK+3YQ9r0NZQ51n+7ifnte5cclivBcw2YMN7+8g1eOPmyd+yukPTE+xVf05Bx+uLOHFj74I1Ss8oXzM1arn06T4z55v11Cf/eozuXzQPeODQKhpEYxvZd68c69nDlFFhAe6nByjZ+c26hoqIhJAcTQQVItgs5KpZDH1sTbc1WbBuh2MPrlH0m0/+WIHO/ZU8MGKmm5ikdafo7u25UdnHA3Aff9ZxqqtoSCvZh5BR3W148/vpu6amSxQmrO6xH8f5zjl3mkc0rIFn/16JACV4fSVLXzmKmxK6WZRjN8m1F0wpNpBbgOfnsW9Tmd02J79obGY8fymKUgk8nDBiAt6PYlgvF07ofZ8lX7XLKY+qVoEMxxcPPPhWrod2poxpx8drUNFVXVMy15Ni6B/66FXyhbBAF1D46+Jd9v6TC4fG9Sn2c24Orb7p1lo7O/Q303jhG7t61wnyT69uhzCKgWCIiIpFX+1B2jaQLB5NcE0EwkbKOo4BrA+9/8lu+qefc07CXzkBtRvYnjwJosJTej+h3c+j66LHxOFZ9tEbnhhQcJ11Q7KPC1clVU1Y8qaExf4nf8yb0tXfcd9BkuWEvwYeytiw8Y69DaudU6+4+lc7O82xyd4CXJow+rUJTqoZFfud28uY9L84uj7376x1OdcLVCLWnWKaD0aRAeon1+w2VRz9kUOG304YERbAheHxybLwaFnl0NYV7K7Xg8lREQOBsVflZOflxsdftUUFAj6yNT9Zl1aLx6Znv6E0H7HqY4+qa85OcOvdcHVuslNVO36tsZE9o/cMLTwNJll8J4/sPqm8E80bq6hxAdG6dx3xZ+bT49N3zp7jxh7o1d7TJjztC9Gu4aG3981ZTEPTl2eurt1XEKaWuuT7p2+759ypO/yn//j04THzUnjw1rXCeVrr/bfoD5JQ2Mf+KS7b2iHmlbiYGNO5cBzVJdDqKhy0bEvIiLir/irPRR0zM/og+5U1DXUR127hmbiZr+8Iv3kD5FqVFU7SvdU0KFNXrTrVqJGt2ggQPCkJ3U5Xe8+f3xnBTeccXSzHSPoVft36zN+Lj648lzrTLfUmBkurc6htfePN2P5Fi4p/HrMMu9ZeFt/8HQDjen2GfegwXucovU76H1Y25jy3166mWtP7VVzvMj+BG9Zd86l/Uc18rvr2q5Vwm1iEuX4TL1Rl+7DidYnHZ8af1xvverVNbTOu9bq0tocHuRI0+jZOZw5tGR3nRI3iYgcEP7QH0q/SLpJ8b57KLAdMPbimoUdesDNnyXeqYFlNBA0s/OAPwG5wBPOuXFx6/8AjAi/bQMc5pw7NLyuCohciS+ccxfTxOp6n5RoPFRdjjpx3nruGzUg+R6eXb7/1EdMufE0366h3gQX0bFbzicxRYJxY5HtFm0oZW3Jbkae8DXycoMHc3+atoKTe3aiZYvQPt6uoc3hPtIleB2UxYwSbHiJxtMFUasbq8/yn00oqhUIelVVO98b/9hsq5EHELEtgpHtnItdOGtlSfThBfi3ZCc9kXoK/LnzHDfHagc+iZL7pE44Ff5Zq1W+djfchk4WUx+Rvy/ecaNycDo6/HBn+Zc7OeOYrk1cGxGRJlL6BYytnfzRq/jXUzlpYDe49Fc1C8d2yHDFYmWsCcbMcoFHgG8BfYErzKyvdxvn3M3OuULnXCHwZ+AVz+ryyLrGDgLr+jQ7E9MHpBpTlKoekQyk/l1DQ6+XfbmTu6YsrrVvyuOEb/queHwON770Ce8t3xqkcrTMzWFor05A6MY1kizGG6Q2h25kQRJ21KWsj1aX8P0nP+KhqcvrVrEw7+fU2823vmUl3c7zOtINsWaS+Mj4tppxbtHpI3xaBBN91vZ7+jdGtklWvVrTaNTjOuQkGaeaqO5+QeqI38/wLaOuE8rHrIv7LnuDxPqNy/J/4JPOnpGqVDnH9c/MS1S8HMC6tG1Fry6HMDfBNEgiItI85hCEzI4RHAKsdM6tds7tByYAlyTZ/grg5QzWp96a4mF7TPe7gOLruWd/JW8t/hKo3TXUOcdPPIldvJkeaxb6lx15WRae8+/lucmbwL28YxJ3llcAzS9ZTMyNca1W0gB8MmkCjH5sDh+s2Mb4AJlZ05HOmE2/ZCfpljFndQnLN5d59vY5TvhnTdbQ2nWo3bJZ+7qbT6tbqHzXIK1P8d0tU27vuUxmwVvAUmcNdTE/4+tX3/KTH7vOu0brGzl+8VflzF2rQCBTzKy7mU03s6VmttjMftbUdfIa2qsTc9dsV8IYEZEEmsMcgpDZQPDrgHfSu+LwslrM7EigF/CuZ3FrM5tnZnPM7NLMVdO3PnXaL+X4n7qU2QD7POOzFz0AACAASURBVPrean716iIAcr0tguGuoau31aT69vt/O1EdItt2aRsaVzVt2ZZAdQvdvNdMI/DKgg0AtM/Pq6lbypIyL3mLoN8Ywdj3mT6H+LGs9bnnChwAeV7vDY9f3R+focQzWDB6TcLlB4n1/brkJvtOxidrib8M6QS3QccHe691OmOKU/2OgtTUucTt9k114x0/j2AT9VA9mFQC/+ucOx44BfhpfI+bpnTKUZ3ZubeSpZuUMVZExM+GZjCHIGQ2EPS7O0p0e3A5MMk5582M0sM5Nxi4EvijmR3texCzMeGAcd7WrQG6JgbQHIKQiLo84Y+/8V21dVf0daoMh9OWbg584xzZzjssMGiyipqJxeGQVqGhqn3iEoc0tdiAJP0WmkTj5uoiVaAWCurTaBGM29ZvjGAqPzytl+/ymjiwJm9ozRjB2OyifoldYj7zKebmc65hEpPEd2H14zdXYmR50DqU7tkfrD4BtvFLFlOveQS9r9MspjpBS2ai8qV+nHObnHMLwq/LgKUkeNDaFIYeFer6/5G6h4qI+GoOcwhCZgPBYqC7530BsDHBtpcT1y3UObcx/HM1MAM40W9H59xjzrnBzrnBXbs2zMD0xHkp6ncrU5dgoCH28QZnqcaVbSmrPW9hTFc932yZNa9TJauITE8RnYQbh3OOHp3axI5fbGZpBwNlhKwVXGV4zGMDjo2ryxjBRPv7de2MBFjexLCJvk/x3Y9TB8FxLYI+iVWCqkvX0HR6NP9+6ud8Vpxk8HiiFjWf9351baquoZGxzOoJ2PjMrCeh/x8/8lnX4A9KgziiQz49OrVhzuqSRjumiEg2aQ5zCEJmA8GPgT5m1svMWhIK9qbEb2RmxwIdgdmeZR3NrFX4dRfgVGBJBusaW6c67peJ7lB1masvfhdvK0GQOc9S3YMmOg4EuxH13txHxiQ2s7gPSNU1NPX+fue0Z79/NsmGkNZNeK1urD7NSykkStLi4t7HlO8z32CtcuLKjK5O8BlpyI9O0DkBI12tQ8e3tLqHbt21N+G6IA+banrb1v6d1Wcewfh6PPHBaobdO40tOxPXNyJIi+CufZX8edoKNgcoT4Ixs7bAP4H/cc7V6oeZiQelQZ1yVGicYH2mNBEROVAVf1XO15t4DkHIYCDonKsEbgTeItRt5e/OucVmdreZebOAXgFMcLF3EMcD88zsU2A6MM4512iBYCLeGpbtrcj48cw82T7TuNGMv5mcumRz9LU3M2eq6OtPlxfSM34eqJjWGhe/KHCWU+90FdC8uuNGxEyb4eLX+WwfYEzh/f+pX6ZQr9jW3fpNVVHfv0OJJhCvGeMX+un9+HnXe3lvHB3J5wT06xoa9EGG31Z1+YMctEXwm326hI4U8Nc0e1VNa4pfgNjgLYKeY/zxnRX89o2lbCrdS/GOcp79cC1//3h9wn037igPHz/5MR58+3NemLOuznWUGmaWRygIfNE590qq7Rvb0F6dKS2vYNmXZU1dFRGRZqd4x54m7xYKGZ5H0Dn3JvBm3LI7496P9dnvQ6B/JuuWTJCbwcffX11rWeo5wtK7Scsx872xm758C4e3a03fbu2jy6qqQ9MwVFY5/j6vOGGZQe5za89h5r+d301fyq6hhIKiHPO+T12npuA3H17NuuRdZCFuzrzwz0iGVa/bJi1k8icbuG9Ufy47saCOtU3vOjbEJU84bYTPYLPId8rv85fsI+ltEUz02U3nIUkqSaepSNgkGez4OXEPP/x4170wZx3Dju7su403W6r3s1mvMYIJdnWO6PQy3z25u+82Y56fz8zbRgTqwVC+vyrlNpKchb5QTwJLnXMPNXV9/NSMEyyh2WSxERFpJoq/Kqew+6FNXY2Mdg3NWkFu67btDpb0oT5yzP+G/QdPf8z54z+IWfa9Jz7i2F/9h6L1O1KU6RmHl+L4ZpayNcb7E4K3SERvYsMZEJu6adxPgpwlgfmdk1/r0YIvvmJ/VTVLNyV+cu4XhHiXhFqP069kpIo1iUfqFkjEJlIJ//Rkt6zpGBq7Yaruxam6DTucz5Qo8e8DdLeMG8uYDr8J5f1Etkn2e0rnu+T3+UoWCP7r0428MGcd+yrTC8Q2hFv7UnllwYZA3ZOb6XOfbHMq8H3gTDMrCv87v6kr5VXQsQ0FHfP5aLUSxoiIeJXtrWDHnoomnzoCMtwimK0SJ4vxbOO33sGOPfsp2b2fo7vWzoCZ7n16jhnrSnbz4xfmc+zX2iXddnZ4UP5qT4ZQP96uoYlvXl3Cd7Gva59QqvEgkTGBNcliwnWJ2645hIXpBkXxW8e0CCYYDxezfz2bRr17r9++J/r6m/e/y/93fl/O6/e1WvXJMaPKucCtajHfgURjBP2SxeTU3ic6WXytZC+xryN1S5yopuE+LcknlE+wPOC1i//Mp5LsQUTiVnr/FTv27Of/vfwJAD07H8Jp4W6qQcr8zevBe+XXp2uqBOecm0nz+DOZ1ClHdWba0s1UO9NTZxGRsMgD1ubQNVR/m33V/P+6rmRPWmNazv3D+5z14HtpHS1RAJCbYyzasJN/L/qSKZ8mSrgaa9uu5C2V6bR4GJHMov7182/NSV1uaFxXTTe5+gZAmVKXG/EYPn1D/ZKR1PXmuda0C56Lf+aDM6Kv128vZ/46/6fy8YlY6vqr8G0RpOZ3Gzlv7/lHujjGq/WwIWnwXHt1Xab6iEjVTdVP4BbBFOVA6gct3uV+5SVqEayoqlleEXQgb9hWn0zCfv65oDgmiU4izfTrLhkwtFcnvtpTwYr/n70zj5OjqPv/p2Zm7/vIsdlcmwvIRRICBEiCSDjDQ3hQEZBHfETxQsDj9zyKx4M3qI8oinIoj3iCKCpqAEHOcIWEJISQQO772hy7m713pn5/9FXdXdVdPTuzM5v9vnmFmemurvp2dc9sfft78bypbEEQBJFzdh3Oj2LyACmCUryLOmtxIyossoUfh7z8QrqIi+YuzbiaMKXKVaJBsex1dRHidmdutd+FxSg5ViDPljx/tu1XLmQxgu5tslOSWZwcV8p0pXP3A7gX/rK+vddBd/qZ4r1rfMFl2Lb4BmhK3j3uOoJijKC8jzAlTK/0R/AYQWiX3hCLZ6rkUD10kXbo36T6+nHPnMrH6N8NuP1QB3YIlmiCmDfBiHF9JUVRggRBEBb5UkMQINdQKbJ13aRblrouWKQsnnYyDdV+hRzCEN19ek/xw5ZyuunxxfFVfaZcZSmMRaiudctOFmO5TGpLlRv6GyPoFFZX9x00hFaSlYAOVAqClW3Um8U1KmEPFay9LougYrwodQSN/WrX0qiExSPKj9ErH2Fde918LsrzMBVsmVqp+v7pDDlQlrr+KpzE4GF0TQkaq0vwautJuDbXwhAEQeQJu450orgghroc1xAEyCKoTV+KY9sh52m31CKY5kpKdZQYz6etCIaI4E0wEiZPoKucMKYla5gi6CgGQryU7JA80AyDjChSBUajL2mZhQytwAOTkKiki2gRdB3qsxZbDzycsax31q2sKjzv6cnVJkzJCrUIaigeYsxkWJuo41uEZQ1dtrEZv3l1hzNeSH9RksUEZcAliGzBGMPpE2rxUmoqejNV5JIgCGKQs+tIJ0bXlOZFokRSBCVk7bpEXPCLi9IebYtg5hZ5soLVqtp61s0c6hpqLbhjzmdprbg8WKtyj0Li2qchn+59ZE1ZVH3QVUeQMS1F1PvZcbs0t0cZX1TQXAqe+N6yhFoxgsI+yC1+Kdfxwe6rshjB/pBe1lCmJURYZtYP3v8qnn/noP05OEZV/j1UKoKK763u70omoRjBocXiGQ04igo89/bB8MYEQRBDgHypIQiQIihFx81LuiiNOM7DK3bi8p++iIm3LJXuFxelPSFPU53U9MFjMvna3YVXwVMtXO946h28s78NHEDc7DgsD4WVKcl2RfQkvsgnAi2CsjnxbJLkipFa7TKVaTGoG9UYOjGCb+9rw/7WLvW43lfJUE6ZCneyGGl/XtfQANmAcHfnKNObTk1C3SPCLIIp1/dO3Y/VTNZE6RoqUSp/9uxmTPnyY/jnun2BchFEf1g4ZRjq0II/r9qda1EIgiDyAsMiSIpg3pKuRVBnYSvy+Jv78PoOdd2/bJiMo3QpM3RY55IwtdRHXjf+uOu6htp9C/1JD8kDzVAUSy/hiLuRW+kx9skUdSdGMNpKXFRaGPTr0xljuftwYgTdDVs6enHBD5/H1fe94h9f8VBBPA9LJlVBeWO3e6OrjiBXH2uNlomviT+JkT66cbc6dQTttqZUOv2JqCyCsjHf2tsKAHhp8yF85IEV2HmEEr0QmacgHsO/xV/Gk+v3o6WzN9fiEARB5JR8qiEIkCIoRa84dPQVo9+qFEw8jTF+9uxm7bbqGMFwN8iHPjYPRYmYUTScc1sRTGoni3GWuqL7X/6ShmuorBfJgXZsXUCfOtMTJFJocXLF9pseMmrPbT7YriVAW1cvnli3XxjXeLVjBIWRlBGCHlfksHPPbLKYoBhBtVVV5/pE+c2IMaaM67OysTpxtn7F24vMum1dkz+t3IWn1u8niw2RNS6Pv4CevhSWrt2ba1EIgiBySj7VEARIEZSSjnuYQXh8jmt7yIo1as0/vXaCFUmxMBXjx4LWruI+SxHce1TtQig79lcvbcPjpmuaSs6BZM/RTnz696vw/x5eg+5ep2SHyqLm2uZ1DfXEwwHyhXq6eosqWYsM30MI21IXPEaXOQdTRpSr+xasdm/va/PtAxzF3zWeQgZfPJtEiXSNHXwKWnCPwhoFXQXP6vutva2ujLvyPnWSxfi3hcXoAv64TcvtPMqx/SFf64YS2WMG24qJw8rw59fpYQNBEEObtbtaAACThqvXVQMJKYIysqSDRE8Goi9IJt1IbUWQuT8DcqsmB1BZbFQiOdwRXNDewlqErth+JH1Bs8CrWw/hb2v24OGVu7Dp4DF7u+/SaV1Lfzyc7B7IRIwgY8H3V+jiW5EsxjosHouhtasXr22TF6a3jvUnfnEre/64SZmF1Hn/1p5wpcnrmqlj0dbpq7q0wLXvgZe3S48xHpiEf/+svu95bgvue2FLYFvGmDIhjPezO1mMvL/nxCQ01hie43UUtEzocKQGDj0YAy6fMxrLtx3GTqo1SRDEEObFTc2oLy/ElOEVuRYFACmCGSXqIokDOKmh0lUmQiQW4epoq4EaDcWFNAPD4+v24eO/XulZKLprpzVGNHHnqyeoeIqiAuJVRqQF5TX6l7nOZspAEuga6lEQfFlDQ+oAcs7x5T+/if2t3fY+Ufmx3r21p1XajxOLKNsnH7OlsxfLtx1Ge09SeWzQdrs/nfIRkr70k8DotRObWfF5Om29BJ2P6qHCl//ypn8MK8FThBswE7cqGQSHJktmjQIAckEmCGLIwjnHsk2HcNakesTScUHKAqQIStC5NFEKs6uSgXAOFMYZpo2q7PcYmcRZqDF7Yfz4un2K4t8cnIsZEfVWeZmM68oWOq5yQcSFb5d17eUWQbNNxElQWd9kBBVDF/vyu8A6Gx5dsydQHs45vvLXdb5tYv/MYyUNspBabqk3L5qsHhNqRTIdXMqtdhIYPUdmmeKsbutWumSxVVHqCIp43WCthxM600ZunUS6jK4pxbwJtfjzqt10HxEEMSTZsK8Nzce6MX9Sfa5FsSFFUILOAlBaUF7S7mhHDzYeOCbZY7YPGCudZDFhiD0qk8Uo/kZzuBeC/REvTx6E+HC52QW5xEqVYvfns8QvurlPrqzpL8RVhLmGqvQD5nn1opvARnUvWOPKvlOqTJ3WkNbYIyqL1UIo+nb1F8k1VL+tM35m2xlyOMli2rp68dLmQ/Y+J1mM+Vk4Ti9Zk3veg9yW5UdGZ+GUYWkeSRxPXD57NLY2t2PVTnW2bIIgiOOVZRubAQDzJ5MimNdkUkf5ydObQsdSjaebgRPIbNZNb1yXhUwJNKw63FcjbeboqsAxwuTNhyyi4vl6FTidK1NZXODbdsaEOt+2dA2PURLqKG8lXxfy80xXSfBan1wJdBQWQafUBncdKx1T0sHuo524/fEN6OjpCxfa008sgtXObseY1v0qnkeYtT/GmD2ffUn55Mu6CIunBHJjff/UuyY641OU4JDlohkjUVGUwM9DYmQJgiCOR17Y1IyJw8rQUJUfGUMBUgSlaJWPkGyTLbC6+1LK/fYiVjHgf11wYrggEXG7pyniwhTHcs8+mUUoyAVSxJ/gIz9wWVfERbXq2rmODXLNNCgq8H/ltMpHhNyUYUqhV96gDKciljImOzedeLqURMH6+QfnYmytUz/HK7s17d4ahCq8sbQ/fnoTfvbsZvvJW5R7S8fKGXRMEDGdCfPs3trcjk/+9nXXPg4os8V4XUODy2F4PgeLJD1Gl2zURCUGHxXFBfjQWeOxdO0+X4ZhgiCI45nuviSWbz2EBZPzy0OGFEEJmVyydPclA/cHrY8K4hGyhmpKrdPKXoAD2CxmzhQWgVamREs59FoEw576D4Z1YYAeqEVQ1kfVOFGIMocpzvHUW/t9GfvC4usiuQ0GWPdEF9RFU0dgyohy08UxwFXWtiaqE80YLpLuHW1dRtHqrj5FCs0ABqKgvOwY34MFZmx7YeNBvLzlEGRILYKcayTPcb8qZZAem97N6rUEE0OX6+Y3obwogTuf3phrUQiCIAaMlduPoKs35Q4bygNIEZSg8/Ra7gbn39ojWgR97YNdQyMli8lgbJN4Gr2CW5o0U6Zl1JQcGzx2fmqCKndQHetJf5WloEV2f2ervSeJj/xqBT7x25WusULj6zyvMpl4QD/Wcf7dTLnPaxEMi9vzHp8wD+gzaylESUyRXrIYvesTlCzGK6L13Q9y9XQKyjskUzw0trg/ihgpcUR/qS4txLVnjsPStXuxcT9ZBQmCGBos29iMeIxh3oTaXIvighRBTa6ZNzat414w3dNUBMUXRSkfoYuOd5qT6dFrtYBr1el2o3MvSsNdQ+VjhsmWbVSuoTq16XyKvut9gNuohtUtSBEDwi1ZvaZS9Obu4PIOKiuRTJnSUZR8rqGCda+rNymNf+O2Iug6RLugfML84lh9iyOIFm4Z6cQI6iaYEduFZXy1kv+oHjhxSR+AkeBIVY7GPl7TfTuTiBKRLkl8ZP4ElBbEcWdIDD1BEMTxwrJNzZg9phoVkvwRuYQUQQnpKiGyBc6hdnWB9VD3yQiSZFJxUsYIikqgrfgZq1UneYzeIjPKueWKv7/hlEtIJ57K1T5A2cvEwviNXS2B+72xYyHhqb52WvFjklZWgXOvcsJgxL89Iqkp5k8WEyxkWVHC9TluulT3eosnAnju7YO+bcaYMMcKHEoKA4tUUN77HvDPr5EshmtnbbVIpbhtEQ1D5+GG75gM3KxkVSRqygrxwTPH4+9v7MGmA2QVJAji+OZIew/W7m7JO7dQAEiENxmCSNZRXsVFp3xA2P4w19BseE+K56FMEJJyx3VZcPM/oTMba+0Z5Eookq/lI0TB39l/TLY54Nj0VrhOQhY1sumSKR+3XHwivr10g3IMAGg1Y+jcfRmvfoVXrQlGsS7bcX4axzp1Fa22wTGCiXgMDVXF2NvSBQAoMG+u3j7LNdTdPgiXXCH3aFEihu6+VFpJZfwZed2fvd8nV1vvZ2FDMsVDi9Ry3S9pBnGfL2mCBPDRBRPwwEvbcOe/NuHOq2bnWhyCIAg1d8wAWnZEO6bK8SR8ecshcA4syKOyERZZVQQZYxcC+BGAOICfc85v8+z/EIDvAbDMAj/hnP/c3HctgC+b27/JOX8gm7K65NKwVmUqBboRXyQfL0qMYCaVRi2LoLCNQzgHexEfYu3M06yhKrzns2bnUexr6cLIKnWNO5kCkm5soS5XzB0jVwQF49hHfrkCt793JgC5Ajeisgj7W7sxtaHSPi6oWL2FrMk9z2+JfG86rot6MYKA+zwSccPRIcxKKhtT11I9vq4UE4aV4+kNB9IrKO+ZFP/8Mrs0i1ReDjDJxCR5uEWwP7db+r97+frkh8gVtWWF+M+zxuOuZzbj6tPHYp6ktA5BEERe0LIDuFV/TeHlhY3NKC9K4OQx1RkUKjNkzTWUMRYHcBeAiwBMBXAVY2yqpOlDnPNZ5j9LCawF8D8ATgdwGoD/YYzVZEtWL7KFa9gTfCB8kaRyxcqERVA7a6jLEiM/RllH0DemgxXPGFZmIGhbPqC6hrKt33vi7cA2Yl9BsXa2RTDiGltqJQy5pgCwfNthnPP9ZwE45U3EsUfXGKUdSgrj9hnIcpYw5Qc3rrg7Sbyfz7LpiRH0WhNdTTm3M9haWPUb1+5ucfVntQ9C5/thyRxFUTXa6ccfWjGCgW3MV1eCoxRHPCS42ElO5NmuoeSRayiRSW44ZzLG1ZXii4+sRVdvcIZtgiCIwUhnTxJL1+7F2VOGoSCefxF52ZToNACbOOdbOOc9AB4EsETz2AsAPMk5P8w5PwLgSQAXZklOH/IFtpsomQhVcPDgxWaunqIrTo1zd8ySHSfInfOQxcJFUVicvnWFHSDM81l00gg8+ZmFKErE0BVSGkT3FnHaZWCFrJg3lSwdPcY5eOtAGsdw+z73xhhGGUPu1qruJ2rWUC9WrcaNB47hU799Hc++c0D7WJnSKoMx52qxIP9uzzGqvmWuoRxcbonl5m+HNFkMh+7fmbDaktJj9Lr2kXffZyIvKCmM4zv/PgNbm9vxo39ROQmCII4/Hlm1Cy2dvbj2zPG5FkVKNhXBRgA7hc+7zG1e3sMYe4Mx9kfG2JiIx2YFnUWLdF0ccZXEDZ9K5XjZiREM79+brdG7XdxnLyYDYppksWy+xb0kfjIXqMa1FKQPzx+PySMqMLqmJPRYLtknv200TlbTqqq6pskIEyqrfyh98CF5ECDDbQlTx/vZY5rz4S0or0rIwjzfIVHUf6zdiz+s2Ok/yDumx/oYRoyxNI5xH+8a33MPeB+syJCNaiSL0ftZT+crlpEHYGQRJATOnFSPK+aOxr3Pb8Gbu9N3vSIIgsg3UimO+5dtxYzGKpw6fsAcGyORTUVQ6snl+fw3AOM55zMBPAXAigPUOdZoyNj1jLEVjLEVBw/KMwJmgvCYHg0U7nWqRXQk19CMxggqtSGPRdDeLC0oX5Qwbq/Gar/SFJbQIsWB5mPdkeTOBKqrasXKua5VyC2ge4t4k6NkA5VFL8gyxSEqZf0YXNNiZuFLFqMzhEsRVFu6Qt0tXa6hAe00ZPL3rXYN9c5vYPkIr4u58D7JeWjZGdFqP76u1Lc9iMfW7gtvJIEMgkQQX7p4KmpKC/GFR96w638SBEEMdp7feBCbD7bjw/PH52397GwqgrsAjBE+jwawR2zAOT/EObdW+/cBOEX3WKGPeznncznnc4cNG5YRwfWSxeht0+pDMVykZDGez8MrivQaSnAW4GqrhbfuHPO0MbIjDcPPPjAHP7pyVmQx/vT6Lsz95lOhdd8GGqccHpPEfPqjrnx4NnX1JrXcLuWy+GdRNa9BSUeMvoRtwj5RsQ8aK+hWldXPC8peqyofoYyl9fTnuwou5VZ/HoJ+tI3yDs57nd+MoL6918fqX2mh5nL5kimEF5QXv8dCW52HW//1pzdC2xBEVKpKC/D1JdPw5u5W3EkuogRBHCfc/+I2DK8owuIZo3ItipJsKoKvAZjMGGtijBUCuBLAo2IDxliD8PFSAOvN908AOJ8xVmMmiTnf3DYg6Ohf6bhI+Y7gplubSo7IIzg0SKxwRp8BSTocseTbvVYLYbud7l5wgSxMMFw0o8FOPuI6VjNr6OGAOozZQO0a6kbn2uhYor7ylzdD20RBdU11dU2VKqtzvOo70dUrecIf6Bpq9We8Blm45GVc3BujWO91H74YFjtuv4/ad1giJmtjkNuw+P2z2HLwWGhB+cAxBRZOycyDNcB9X2Yq4zJxfHHR9JF47ymjcefTm/DEuvQszwRBEPnCxv1teP6dg/jgGeNQmMi/JDEWWZOMc94H4AYYCtx6AH/gnK9jjH2dMXap2exGxtg6xtgaADcC+JB57GEA34ChTL4G4OvmtgFBTxEM3qajKIYli5G5T6pqkHgVgP4okfbCWbJYVVlbnALz1nbn3PqTNTTVL5/EzGEv+l3bPG18x4j7uOvV4kiHUdOvoiiRkQWyalrXhsbe+I/kEDOaSiyCmm6UslGCrIlei2CYOwVjzOVOphOrGSafTC7vmBYxxrTuZ1ffXmu7R1eOxYx7RfU7w7l83rr7Umg+FvzwRIz7DBI7k7U+g743BAEY36lvXjYdJ4+uwmcfWk2F5gmCGNT830vbUJSI4erTx+ValECyqqJyzpdyzqdwzidyzr9lbvsq5/xR8/0XOefTOOcnc87P4ZxvEI69n3M+yfz3f9mU04/E5S4glkqG7mLHm+giWAqgtDCu3W/oe8WxMqVH3G714yh/QgZDMTW97QYokS9IeIHfL49YwLOf6JaPENP7/3X1bvxp5a40F7gcUxsqUV4cXNKzP2vyKE+iXJlhhSA1rz4+ob7Mf2xAv1Hk554xbddQSSey6+V7dsClb6VNxIcvQcrdse7eSDGMQJhF0O8aGobXPduSJ6xg7dMbDuDSnyxDS2evS3jv/TuyUl0jsz+QHkioKC6I4+7/OAUlhXFc/6uVaO3qzbVIBEEQkTnc3oNHXt+Fy+c0orasMNfiBJLVgvKDFakFy7Pck7mbuVLvS/pVJbFQJ4vxb5e5WRp9uCkSFv9MIY+K9XvlT2KNmCUxTtA5Z++iVJRJnjVUb/n8l9V78MMrZ2u1zSbcY51icGIEb3pwNQDgq5e4y2S6SzG4X8XtTgbW/sspm9YbzpmEHzz5Tlr9Oa6hbuEe/vgZeGLd/sBxg+RzJ07xfrfMsdMsH+FVqqK4huoO1d2bcu79APduEVespGefzO2ac7lF3G6rcC8Ncw39+xt7ARjKfNB1i8cY6ssLQy2MMWu4UQAAIABJREFUOuRpjDyRhzRUleCnHzgFV9/3Cm78/Src98G5A1d7644ZRuHoqFSNBT6zNvPyEAQxKLn9sQ3oTXJcN78p16KEQoqgBK34L9k2n2toWNIGt2XJi2w9d9Oiydh+qB1PrXfXRhO7+OkH5mDNrqN4ZYvhTcuEQXRc36xC6bqZUmUxgqJAJQV+K2a+LgyDknMAoiJjbVcr/94MnNJ+4VYkvApnVGQPFaIrUs6rdc0theTyOY342MKJqCsvimwld8sZML7tGmp8diyCEvdVHq5U6biGyuY9yG07meLCPaEbVyi4k3ouit/izKSu2Kr2gKg468mT4uGlJnRLUUSBXEOJME5rqsU3LpuOLz6yFjc9uAp3XjkbiYFQBlt2ALemUcLi1qrMy0IQxKDk5c2H8NCKnfj42RMxaXhFrsUJJX+jF3OITkxbmJUhTFG0+4U6vki2wEzEGKY2VEr6djq/eEaDK3NgxnQur9WC+RUkSw5DwTE2lhTG8dqXFnmO9SyE82R1GG3h7RRk1z5Gsk20pr7/nldw7g+eC5FSjexeCivVoTpuz9Eu9CWtGEFj20kjK3HCSP8Pm07WTGMcv5unKnFKSvLwQgdvogm3sh58n+kqzb1CTCKD3oONILds7++JlYwm6GvhfXig6luFt+t9rV0+GRLxaLN/1Wljpdt17w+CsLjqtLH48uKTsHTtPnz2D2vSzq5MEAQxUHT1JvGlP6/F2NpS3HTu5FyLowVZBNNFlsQhahchWQdli1JDcWT28d4kLWFKbFAtM/9YHnnhP0c7tkqaLMZhWEWRW3EMGTvfkMn9z7f2457ntwht5K6/4j6/ayh3xVsu35b5nEhRypBwDltIsY5jUnKv+u+PzCzUvHMVZHGzXGvFkfe2uBUaHamc749ejKBoEdTONCrMWEOVO/5OmZFXIr3loq3MPKp5uVOe7+iOwx2+NoURrTCq5u7yJLSgJ/T4yIIJ6Emm8N3H30ZBPIbvvXem1oMtgiCIXPDTZzZhS3M7fn3daSjRzOmRa0gRlCB7eh32BN+LjoHLcgsE1//DJiaX8WYOPHNiHb6+ZLrkGHmUYFT3Q/GcjEMd5c8b5yZukxFFORlQzBP46IIm3PfCVmcz3IqQNXdBNa/CYka92wOtP/2Yr0ysm8IyeEYVL+hcrX27j3YC0JM/qD/RkBD2vQyK4xPpS3FPjKC79djaUjRUFePVrY5iL/ZdWuj+6T31W0955AiuI2jI57WqO8daPL3hAP7jF69Kj995uBNjat1lZu79j1Nw44Or0NWbAgOLbBHM2+81MTi5YwY+2bIDPYnL8cPX34uu1Q/jfwvuRjELSSJDMXsEQQww7+xvw8+e24zLZzdiweTMlV/KNqQIStAqHyHbFuKCxj1tV+04ioaqYkwcVh5NPkliFs6BaaMqMWm4vy+duEDpOD6Lg+ScPFYbLmwPit0qK4rjxJEV2LCvzXVcvnD16ePcimA6Akqtxn6rYZD1JypS19AMLM4tZSroXtrf2g0VQXUj/Q9ZjNcjZg3JuvIiZb9hJViAaG7H4lyVFal/HvtCLII/v3YupoyowPgv/MPpW9AEw661ZT0P+p1RfT+90rwWYGXeebjT9fn8aSNdbuVRYwS17rV8+7IT+YsZs3cT5yh5fgu+8xiwb+TFuO+Dc4Mz8VHMHkEQA0hnTxKf/cNqlBcl8KXFJ+VanEhQjKAE2VLGHyMY3EfY2tPKxLe3pSugfITEMumyCLoVTx1rTbpKoTGezCoIQFRmXCUm1AMkYgyP37wQ3/73GdGEyDKOq6t8u3WmOlOnY+3jAMD8caLpxkzKk8VEcA1VqChBbsyymnZK+ST3rkwGse3wSrUiqIPWVHpiXQFgwrBynDymWtq8vlxYhEpduCXbNOZoyohyXDe/CSMqi31ZelX9eTPSeq/3+Loy3H3NnPDBJf0XRLQI6hSzf2TVbjz51v7QdgRhwRjDx86eiLuunoO1u1tw+U9fxNbm9lyLRRAEgVSK4zMPrcZbe1rx/fedHPjwOh8hRVCCjhuebIEWtt4UDxGTTajlkGwTlvpeRUMldbqJGoJKZjCPXdK7+NS1buWrJ5nvfDyKkEohkh1jflK2Ye4m0nb9QWdxHtZCahHsR6SnyyLom2v3a9AoGsl5PWU8Qixxns7OnzrC1+bDZzXhrqvnuOJjvfeD6rvryCEf/z/PasJXLplq3H9mshjVQwnV/HuNeIwxXDi9Ab/76OnyQb1yCsLXR/yDFmPAU59dKOnTeT+isgi7j/jjEQkijMUzG/D7j56O1q4+LPnJMjz+5t5ci0QQxBDnu0+8jcfX7cOXFk/FuSf51wz5DrmGavCJd01En0dxi6L0yRAzoOks1C28MYIueTS6CUr2EYYxnkwB5lLrRFD/Tj0+93G5RlcO2ULfGzeqe0riNbVIco6YMINRLW4iUWIEvVZfZ3twjKDu3WQrL54x7r5mDj7+m9cBOPPoWAb797SAayjYXitkEB9d2ISGqhLHiihtJbPMiuPJsdrY3yfL0i8I/rFfrwQAjKhU1fdj0k9N9WWK9upefnz1bLy8+RCue2CF1jGxGMP4uuBxXvzvdw9MKQDiuOSUcbX466fOwqd+9zo+/pvX8cEzxuGWi09CsaRMETEISaeWI8WEEjniDyt24u7nNuMDp4/Fh88an2tx0oIUQQnexeDnzz8Btz223rVNallwKWZyhemNXUfxnaUbsOngMXv7h84cj2ffPhgqBwAzVb1li+OefQoLQZrr6KBFsaW8eN3RODhSKY79rV2RFVMA+Pun5+OSHy9LT+AMYNdi89Z507BOJb2KoEQB8d4V7hhBB59SqaugSjdqWARDmtgWQbdJEICe9dfbvXgMAzCqugRedDPMshAZomSd13GjdWzhjjVcxyIYpW/jnIIfqFgxmZYc3lIuXlnSseCWFiZwoqRcjYo4Y1LFnbkeauSpGwAxaBhTW4o/fvxMfPfxDfj5sq14bdsR/OjKWZgyIv9rdhEhpFPLkWJCiRzwxLp9uOWRtVgwuR63Xjpt0P5to8eyGsgubdjCXLV/2aZmvLzlEA62OYk13nXCcJyoWZuNCYtOieehFCZbvRs71AdJkFuK/NvvemYTepMcRQn1E1rV4nR6YxUaJUrBQBOkuBj7/XOXCtA4VHssiw8Dcz1cSIV7DkuR/hBFMLcaCUoC4tKU4+r1r5VLxKM0Bx2jFf7niqUNxvvQJHBsheIFhCuvykvC3G14iAyuPhXJYqL+bbKae632OsSYXN3sjycCQcgoTMTw5Uum4v4PzcX+1i4svvMF/ODJd9Ddp67tShAEkQn+sGInPvGblZjeWIWfXD0HBYPYy4UsghK8SxkdN0DAE4uk6Fu1AKwuLdCUTbBIeCyQ6qQz6SFThlzJYiSui5w79ec+s0ijmKbEqpTLhyoq5cObHVUmozfsU3qpJZY+JunPe39VFCfQ0hmSMl1BFIvY5x5eE9xAELQ/l8l1eopzdyyCwSOF3S9WZlrfuBJ5dJ7oOW6b4mfvb0ZwPyplO2bfX8z+vqnKv9h9hSSLsa2MA/C9isX81lGCyCbvPnEEnvzMQnzzH+tx57824h9v7MF3UifgtFwLRhBDiXRceoFB6dZ77/Ob8e2lG7Bgcj3uvuaUwAzjg4HBLX2W8LtW+Vc26cS0ca62Gn3lkqlYfKfbJVJqaWDiQlRMghGwMFcYAaOu12QZQ60sk2LqmBQHakoLMLyy2NeHd+x8XTOqarRFcw11Xx8ZYsbNINfQurJC7DriTvUvQyZfWM3LKCgtghGPD5LJsQhqxO1pJIuJQpQC6nbcpMxyL2mvoyCJ3wvD2s61T89JXuPebscdavbjkynCgUrX0PQdEQgilLryItzx/lm4bHYjbnlkLa7o+R8s/u3r+O8LT8TYutJci0cQxz/puPQCg8qttzeZwm2PbcAvlm3F4pkN+MEVJwd6vg0WBq8tM4vorFNk+pw7Jky+0FVZZ6aNcn8ZSgriKJc8ZWCC65U3WUxUi2DogkxiqXEZcoT91mLTci0MjYcSLB+R5coijlXFs93TTu4urE4WY8dxeY8x6+B5+/O6hkZJPOOXS+M4xV2y7L/PwQfPGCftP1P+8L5z91gEM8EF04xMXipLnLW1IMHw5ZAaQPb3z3yNMf+8h02N6ty8WWkjuYaqEvo4fth6eGTwMqpK/YAn3XhkIjqMsfsZYwcYY2/mWpZ84ewpw/DkZxfi5sQf8fSGA1j0g+fw7aXrcbRDlViJIAginN28Du+/52X8YtlWXHvGONx55ezjQgkESBGUohfHJHEN9ShmMoIsIX/6xBn2+1VfPU+ZTVRmQQLUi3lxYdgvdz7PWC6rhWAhTHH9xatMqc0HvIvplL3IthsAAC6f3WgrDkmvlh/ysMAZzL8vXSue1HqdVk8Go2tKXUp9rJ/3kjS+1YPvvlZYxo224QXlAdj++zrTOqwiWsmETAaIO10xwSIY5mYa0md/ZYrg9upNsiTrY7AG1OchvwRwYa6FyDdKCxO4OfEInvn8u7Bk1ijc98IWzL/9GXzviQ040k4KIUEQ0Xjqrf1Y3P1tvLP/GO68aja+tmR6pGz/+Q4pghK06giG7Vc0SJlK02WzRvn2jalxXFhkJQXsfXaMoOh6GJDgQ2HFCY29UrhHysdgdhsnrimob79sunJlE1WMoFX3UbYotpQjvx6o6RoKKybMISgDaVTSLU4vIx3r8rVnjPPtdymUvoBM8yXA9dJf51E9PqDv8hnl3lNZj3X6UYkrnheH23U4VB5rbKVBUK8jxz3Vstq7948LcLULe3hFZA7O+fMADudajnxlZFUxvve+k/H4TQtx9gnD8NNnN2P+7U/jO4+tx96WcDd7giCGNoeOdePzD6/BR361Ao2sGX//9HxcerJ/7T7YIUVQgs6aJbSgfIAiGGMMd7x/loYc+hZBrwtZQC4ObfyLN0+yGFN58Y3NubaLWJC1JxfY5SM8QqzZeRQAUFxgfGWsvTHmKAJBJR+4R7mxt5uvKvdIp136ypyOdTFozlXxXbrXqU4oSm7d09fMc9xN27v7XO298gZl5dRVlGyLoGJ/JF3Z8/1jzH/9QmUKGZAx417RCYEMTxajKZMmQRbTeRPqMjMIQWSIE0ZW4K6r5+CJmxfi3SeNwH3Pb8GC25/Bjb9fZf+uEwRBWKRSHA+9tgPn/uA5/HX1bnzyXRPxp8JbMT5iLd7BAiWLSZNnJHX/RKR1BLnhNmnEFAWsbmG6Xqosgpb1TYgjC0oWo3INjbowlCaLsZOoOFbKlIY7m9dKkXeuoZ7PVlYo64dAjOWy3OG8rqFa58QBFrPaOwekWz5ChjebaVRcbn2S62rce9FupvmT6+33e1u6pG7VQQl6dGryiSTiGj6piPidUMXkKfsOb+ct2cB5hHNVWCjTKQNhHAfpcXHGkIgx9EkCnmeNqZb3FXFsIjMwxq4HcD0AjB07NsfS5JYpIyrw46tm478uOAEPvLQND722E4+u2YOZo6tw1Wlj8W8nj0J5roUkCCKnvLS5Gd99/G2s3nkUp42vxbf+fTomj6gAXkkva/tggBRBGWmuWnSyRFoWwf5gLxK9yqZK4evnOBZcNiasxarzXvys7lvudiYbNxd4r5GV7TXmWVTHBNdQnyLoKicSlCwmBrDgGEHx43vmjMaeo/quTf3NGsoUN1M6t7HOMXayGI1+dJOphNX4iWJxFTPkGp/V7pjq8eTYGT7t8wt4wgOhjfDqVTijK4Dek/E2AIoL4jjmseSWFh4fgfPHE5zzewHcCwBz587Ns8dtuWFMbSm+fMlU3LRoMv60chd+v3wnvvjIWnzj72/hkuRH8e+bD+H0plplvGvOGUJp+glioFi98yi+/8TbWLapGQ1Vxfjee2fiPXNG5+/vQAYhRVCCrnVjyaxR+OvqPdJ9sr+4VsyPShH01uVTW/jM/rx6oLK9u9+w9iq2H+rwHetN8c8BM1nMIP/yeMS3dDxZwXEnRjDcNdSL6NooKpJBytt7TmnEmRPrlfv9Y+Q2RpAFHCfD6+oou5eiPkwpiBsW9myshOWZbyXbdPqyHpDYyWL0586ZL68sapmCZVHLKPvbqIoPLC9KUIwgkXdUFBfgQ2c14dozx2PVzqN4cPkO/GPFPPzhvlfQUFWMS2eNwiUzRmF6Y2V+/T0bAmn6CWIgSKU4nnvnIO57YQte2nwIdWWF+MolU/GB08eiuGDoPNgkRVCC7m9+Iua2MqRcFkH5kjOV0oufY/b/FPsgutBl0N3NdZz7wI6ePtdiT9xtLcyt8hFhYwYtTnP5R1e1mE553ADFV2tK9rd2ufsK6F9sYyn9YoKYjzywAo/dtMCVhCddLpk5Ct//5zv25/F1pdgmKPVhuN2Jg91EM4F9X1sPGWQy2Q9D9LKGxmMxO8ttEAxODNx4RVIUv1u0fy7CJAorHwHALCjPQ78P3338bVfMpS9GME3XUPt4X4Ikw6qybk+rp52c7713Zj9GJ1Qwxn4P4F0A6hljuwD8D+f8F7mVavDBGMOcsTWYM7YGX1u7CE9evgZ/WbUbv3hhK+55bgtG15TgwmkjceH0kZg9tua4yhZIEEOOO2ag7ehB/DV5Jn6ZvACb+GiMxCF8IfEErul7CuVPdQFPSY6rOn5d60kRlKD7M+/9eyAW/P7OYxvw/fed7DsmGeAa6vfIUrWzlAPTJUyhvDj9yPtMJ0bQFyfoiePiZkIZ3b7z9U+qzzXUc05MeB1tZnsNixuVYSkyjDGXQr9hX5uy2HwUBWx0TYkvwPnD85vw1b+uc20L6nHt7vCnz2ESnXPicKzeeRQzGsOfSuvc1x09SazaccQ5JqTPsLWbeF+fObEev/rwaThzYh3ufWGL+piAgvdh21QPb5jQ1nioovddemTlLlw6q9HVh6xPHcT4V5WMi04a4VcE88lqMgTgnF+Vaxm0qRqbnkVqgBdfJawHl548CpeePApH2nvw5Fv78dibe/HAy9vw82VbUVNagLOnDMO7TxqBBZPqUVNWOKDyEUQk0nEjPk5diDnnWLH9CB5qvgj/iL0bnX1JTBtViTsWNGHxjFEoTHww1yLmjKwqgoyxCwH8CEAcwM8557d59n8WwEcA9AE4CODDnPPt5r4kAOtu3ME5vzSbsrrl0mvnVRb2tjgWob+u3u1TBJ3SCjoyBCWLMfuD+zUsy6hvu2ZCF4sU54grYvvc5SPC4yCDFqe5XE6qrFCGJVfuojh/cj0SMYaePndWFmnWUN94ftfQ0sI4OnqSSuWmv+vtqAv2Dfva7PfHupyAaZWLsowlsxqxxFRUwvDOlUreV7YcdskRBGMws9xqmAQBLJwyTFtOWWKndK2ljqXZGUOnJ8Pt3BCoMOH2VOj//eL/XFTgj7kM+r0iHXGIMwgXljVlhbji1DG44tQxaO3qxfPvHMTT6w/g2XcO4i+r94AxYPqoKiyYXI/5yamY05scUu5kxCAgHTfi48iFmHOOdXta8bc1e/D3N/Zi99FOlONUXHZKI648dQxmjq6iB5jIoiLIGIsDuAvAeQB2AXiNMfYo5/wtodkqAHM55x2MsU8A+C6A95v7Ojnn4TUWsoDuIs7jGWovDI14JHkfKc7VtbZCPtvbPTFpdr01l1uZ2E/6VkARf0wiExbrzrgpjUyHTkZC482h9m6x47wj5SmJ4bWaVJYU4LCvWLE/WYwX0b3QChGMuyy+butvVGSHRfVs6uxJ2u/buvqkbbz3+5cuPgnfWro+2kAmOw6bbqsh58wjpHiJMRboGhpldq0ztRLQ6FoEdcYTvxc7j3Tg6Lpe7T9UVp+1HiuFGHeog/OQRu5SysBQnHAWvBXFCbR19fU7CRZB5CuVxQW4ZOYoXDJzFJIpjjW7jmLZxma8sPEg7n1+C36a+jIKbn0Cs8ZU4/SmOswdX4PZY2tQVVKQa9EJYkjRm0xh+dbDeGr9fvxr/QHsONyBRIxhweR6fO78Kbjwr3NQevmBXIuZV2TTIngagE2c8y0AwBh7EMASALYiyDl/Rmj/CoBrsihPxvEufHqSxoK5KBFHZ2/S195ym9RZMDGoLSH2VnPlt2L7Efd2b3vljnAZRFLcv/D2KSh2+Qg9youNW7CrN4P1EvqBOkZQHh9nXcsxNSU+RVCcmg5TmZLVEfQq9nGz1IFSWdA6EzVxyQ0RpGz0mPUnThtfi4tmNGiNcWJDBW44ZxJ+8symyPI9/47hYhvmFqmTjMciGyrK586fgh8+tRFjav2xhLLxdGSw2iye2YAjHcb9dMq4Gvz46eB5FJVcBkc5A4Q5zOAklBU5iqD1YEvdfbaiSQli4InHnJjCG8+djLauXqz41iK8cubdeGXLYfzsuc1IPmPEyU8ZXoE546px8uhqnDymGpOHlyMRksGYIAh9OOfYdqgDyzYexAsbm/Hy5kNo6+5DUSKGsybV45PvmogLp49Edan5gPTR7uAOhyDZVAQbAewUPu8CcHpA++sAPCZ8LmaMrYDhNnob5/wvmRdRTrquoZZrYFEihmPdfVIrTlBGTW92zzDFzur9nuc2A4BR60TWXtFPVNxn487CaC311u5uQWmELIGThvsrN+XWNVSx3avceiyCD15/Bg62dWPh95xnG2Jfj67ZIy+2bfbLmOMaGvcohl6iuDLI7sFeSf23IE5rqsXyrYfxh4+foX1Mf5b+pWbNxjC3SM65dhIdy9U6rLmO3Nb8L5g8DAsmDzOPk3P3Nafg479Z6duuktv6Tbl4RgMuFpTuMEUQEKzOzH0WYTF/KryWQbG/C6c14Ll3DmLp2n1IWIpggGsoQRyvVBQX4Jz4apxz0UkAgPbuPqzZeRQrth/Biu1H8I839uL3y42lUElBHFNHVWL6qEpMG1WFqaMqMXlEOYoS5FJKDFEixg+nOMMW3oDlRWdi+cQbsHzrYewxw7Iaq0uweGYD3n3icMyfXI/SQkqDokM2Z0n251+6/GGMXQNgLoCzhc1jOed7GGMTADzNGFvLOd8sOTbjBXN11y1eF09LEbRidLx15QD9rKFAeGyftZhMcuDkMdW4cPpIRT9y19AwMbzjGwtv9zl5T/GZtw/ihBEV2spKYZ4+HfUqBKr6j1a7ksI4xnqyTHLOMba2FDsOd/jiB119MKMfS/Gz6tZkouqDrIt9Lfo1CAHg/z50Kg60+Z+ihV3jKLX53Ady+/igMYLKS3ix5lg5pxkssWEMaLxcOH2krUiLcmYr/tMaWqx9FFUpt+UMUOyqSgtw3fwJWLp2n2MRDBCe4jCIoUJZUQJnTqrHmZOMEj+WxWLNzqNYvfMo1u1pwcMrd+GBl7cDMNYRE4eV4aSGSkwZUYHJw8sxZUQFxtSWUoZS4vgnJH74QGsX3tzTgjU7W7Bq51Gs3nEErd19QA9Qv8mo+fmJCbWYP3kYxteV0t+aNMimIrgLwBjh82gAvqJ7jLFFAL4E4GzOub3a5JzvMV+3MMaeBTAbgE8RzErBXM0bydvMcqErshRBSV25oILy7qf4LDT5i11Imusrl/3BmzGUwR2f+I0l0/CVv65Da1cvKoqDby2rL29iC6Ov3H2RVa6hSe6OrbPeBs07N/efOLICf1y5C999z0x5+QjzfcrUFWWum75srZrI9JuoOk9ZUQJNRf7rKbM6yT7ryCuKZD1cCLMIprg7CjMI7fg4jWZSt0+v1UyMy9UaWX98Gdz+n9+bIESvSwOjJ+tBl1VGR+nBkNGxCWJwwRhDU30ZmurLcNlsI2FWKsWx9VA71u9txfq9rdiwtw0rth1x1SUuTMQwob4ME4aVYeKwcjTVl2F8fRmaeDlqcnUyBJElepMpbG1ux4Z9bdhgfi/e3NOKg+ZD6BgDpoyowOKZDZg1phqn/u08NH1pAyl+GSCbiuBrACYzxpoA7AZwJYCrxQaMsdkA7gFwIef8gLC9BkAH57ybMVYP4CwYiWQGBN3bSu0aarh5SC2CXF14WVcQa7NYeDso7tBtBRStg6E2Qdcn79kYWRgdxtYZZQr6Unq13QBHac53vAq8jruddX3KTSWqpbNX2sZyW7RjBCUWQdG6FuVnT2aV09EDF0yux/9Kyp/ojtGfn2b7AQdC5jeCxTFmaiPKpD0R5NNBlbjJ3qYsH5H+zIk9Sq3XEf9ghj2Isl2ZQ1xDCYJwE4sxTBxWjonDynHJzFH29mPdfdi4vw0b9x/DpoPHsOXgMazf24bH39wneN/ci6qv/RPj6koxprYU42qN19E1JRhdU4pR1cXkakrkLS2dvdja3I6tzcew5WA7Nh04hk0HjmFrczv67IeLDBOGlWHBpHpMb6zC9EbDjbpcfCD9j330RydDZE0R5Jz3McZuAPAEjPIR93PO1zHGvg5gBef8UQDfA1AO4GFzkWKViTgJwD2MsRSAGIwYwbekA2UB8d4yiiHL8epz3ZYiaKZW7026F3ttXX14dM0eNFaXhI4r++yMayoK5meO4OQsutn8hlUU2U9fLE4ZV4OVZjIaacyakKDCsmT1JVOh309rv8w1VGYRGyjU2T3l5qmgubUSwVw6axRWbD9iJtvxJotxPic9iqA4333mvTS1oRLj6tx1AaOiYxGsKE5geGVxYBvVA4b+khK8aIP6TXHYMZZh2FayTGt8qvEUMoQe149pdJezcDqy7lHdrnUfD3kVQXV9VHUpHIIgHMqLEpg91sg4KtLdl8TOw53Y1tyObb+7GdtOvgU7Dndi3e4WPPHmPnsBbVFfXoTGmhKMqipGQ1UJGqqKMTI5DyO3HcbIymIMqyiiUheEnH7W/OzqTWLP0U7sOtKJ3Uc7setIB3Yc7sSOQ+3YcbgDRzqcB+IxBoyrK8Ok4eVYNHUEJg8vx0kNlZgwrIweZgwgWY2k5JwvBbDUs+2rwvtFiuNeAjAjm7IFIS4+zz5BXU8spogRtKxcfUl3XNiLm5oBAPXl8iK03kWvcu1k7kiZP/5CYig6AAAgAElEQVSpVASLoMS9EQB+cMXJOK2pFvNvf8bV9v4PnYo3d7fgAz9/1e2eaP4TFRmrnMaRjl6MrJIruxZWX9YcLphcb++7ZfFJWL71EO56xucJnDO8c2xfK63FvaXYubdXlRS43B9TnoW11fxgWze2NLfj3BOH4xcfOjWS3HLXUP/G+vJCnDy6Cmt2Raw5pIKlH3ZnP+AQ/Wa93TNEGiA0nlF4oBHeV//Hy/RxgPNdZAzSUidRre9hyV+sBxcy19OPLZyAe57fEmk8giDkFCXimDS83EiullgKXPZ7e18yxbG/tQs7D3dg1xFjAb63xViEv72/Dc++fdDMYn4jcPfL9nFVJQUYXlGE4ZVFGFZehPryItRXmK/lhagvL0JtWSFqywpJaRxKKGL2kimOQ+3dONhm/DvQ2o39rV3Y39aFfS3d2NvSib3feNKXPT0eY2isLsG4ulJcNKMB42pLMcF0dR5bWyoNDyIGFkqp0w/85SPcrqHep3TW/v+9Qs/lToV3fZYKCaZSxu74LJD+llUlBZhiZiOVZWkUY+piLiuEWh7AKRsBAMtvORcVxU69pbOnDMPZU4blRBFUl4+Q1xEMtAhayV+Y89nqf/GMBqzeedR0DTXm3rpdxPYA0HzMsNLOGlMd/XzM18JEzH5QIVOfYjGGn1w9Bwu+azwI0Mqe6XIzDmgXUbmxzjvI0s0AvLj5EI529qKmTP5gxS0DtLKGpovvuyRrI7xX6bD9cqkVlFn3QwsD3bT1odZ8O0bQuJ9si6Nw4BcvPslWBBn07ieCGLSkY0WpGhuaKEOHeIxhVHUJRlWXSNOyc87R2tWHfd+Zhb0feAYH2rpxoLUL+1vNBX1bF1ZsP4KDbd22V5OXssI4akylsLq0EDWlBaguKUBVaaHxav0rLUBlcQEqSxKoKC5AWWGcYrjykGSKo62rFy2dxr+jHb040tGDls5eHG7vcf07dKwHh9q7cbi9x/cwGwBqSgsworIYI6uKMXN0NUZVFWNUdYnhqlxbihEVRVQyJc8hRVCCrsub14XRaxH0ullaFh+l8uDZrEp9a/2w2jGCCFa8VFlD3W38i1Drs62YePv0WH3E2McgBenhj5+B2YJSE+aCmA94YwR3HzUyb7ZK4v5ExEW560eUmYqh3cqffMNqbrmIThkpLw8ShHV9Thlbg5e3HDL6U5SP8Fq4c4V9TwVobSkO22VZR0Fm5n+q2Dy7nU4GUq0SE2J7fTKSNdRnEUzTOhnQPwBYDg/WWIG/LflxaxFEdkhHoUvH/S4NGGOGkhbbhRNOGK5sxzlHe08Sh451o/lYt6kAOMrA0Y4eHO7owZH2Hmw/1I6jHb1o7eoNdMyIMcPdtaK4ABXFCZQVJVBu/isriqO00HhfWhRHaYHxuSQ5D6Xr96OkII7iwrjxWhBHcUEMxYk4igpiKErEh0xGVc45uvtSxr/eJDrNfx09SXT2GK8dPX3o6Emivdt5Pdbdh2M9n8KxX76Gtu4+tHb2oq2rD61dvWZ5M/WYVSUFqC0zFP5xdaU4ZXwN6soKMbyiCMOsf+XFGF5JLsbHA6QIStCOpREa1pcX2YqglTHzkh8vAwB8/vwpeODl7bbSoPsDpmpnbXVlDY2pn7gw13u5UmjEFSmOtxQZiQLhuKMxqcVMxpyxNXn/I+4vH+E+p65eo0D8aU21yj64x8KX4o4jrX0NObeVcF+ymJS7n/RmzFQu487RqjKCUfsPUnYYGM6eMgy/eWU75k1Qz5GMlG0R9N9HHzpzPAoTMdxrWpu+duk0vP/UMTjrtqcD+wy73cIUxKiEKYuqWFTdeF55n87Yroc/AcfcdO5k/OhfGwP7VT0gGlNruH+fMaEO7+w/5rtW5UUJHOvuQwktFIiBpp9xTkMRxpitpOnGoSdTHK2dhkJoWZdaO/vQ1mVsa+00FJK2LmNbe08fjnb0YNeRDhwzlZaOnqQnsd6NwAMrQscuiDMUJeIoTMRQ2PVjFH73GRQmYiiIx1AYZyhMxBCPMRTEY0jEGBKe1xhjxmuMIR4zHuwb6xhjLWN56jBA/SPKzb/r3Pi7muLc/pdMGWumvpTxuS/F0bfhCfT1dqMPcfQigV5uvpr/esx/3bwA3Sg03qMAHNEsakWJGCqKEyjnE1HW2oXyogTG1JaiojhhWmwFK25JgWHhLS1AVYmh/JEFb2hBiqAE3dT34mKrKBGzXT8XzxyFzt4knli339XOrhOnTKoQTT4xa2jgsYp9tWVF9vvq0gJ/jKLZqWgR9GavdJc1YNL3muL4uPTkUVi7O0Mxa5qI5TBEUtxd084670SAAs5huOxax4l/7MSMq1av3uQbjqJv7O+PkiAeqypUHwvS7AKQ5xDiOH1CPd649QL9jkxsRZD7s8/eeuk0ALAVwab6Mq0nkrZraCb0Pcnc+BQ/qW+ojrUxfURlVvc37HTpgwzL1dPs17vX3HHiyEq8+IV3o7cvhQde3u6bg799ej72Hu3E6RPqsOdotNqVBNEvMuBySYQTjzHUlBVqueersCxenT1JtPf0ofOOuej46Evo6k2iozeJrp4kuvqS6OpNoavXeO3pS6Hb3NaTTKLntSfQM3YGepIp9CY5epNGm74kx7G+PvSZ25IpjmSKozeVQipl/M21FLUU50iluFGWiJuvcIfDyMLWHcXReI3FmK1UJmIMcfNfIsaQ6KlGfOQ0JGIMBXFDKS2JM1TFTQU2EUNhPGZbPQsTMRQnYih6/psouuBrKC6Io1SwkpYUGp+Nf4bFtaww7ihyt1YBNw7sGooYfJAiKEHXlUp0DY3HmG0RLCuK47JZjYIiaLTp8yz005fPeBVdBwOTxUiOBYxYvGX/fQ4AYHRNKQ60dkmPsxZ44kM7xyrp4E0mEya/Dpm21KRLS2evy6pkSRVYR9CjwHHut+45MYJO8g1vQXmn0Hx0uR2FVVRiJZbdsIcJElT3VX8Rk8WE9WsFmo+uLcUhT5C6SMx8squ6m7xKeX9hknvFNZ5KkH4IwIWTcP8eBPw29PPCNVaXYGtzu9mXe59VO40gCEIFY8x0/TTiEBHbDUSNh199H3Dl97MjYCa5dQlwUxqK2UuPAgt+nXl5CAKIaG8eggQtk0QlIMaMgpiAYSUS463sRai5UAtz+QzDUSzMrKEhulLQYm90TSlG15QGCsDMu8SbLIYxplzQZsLzM5vJPVSo3DBX7TjqWlw7lkP1iVo5fNyuoY7FkXMrIQpzWasStkXQOS5sLKUM5qt4P+q4hvb38kVJDnLmxDrXZzH2NayXAvPJ511Xz44gXebRyiQqvFfd1/2x+orj6LppB+6zLIMhx9jfhSCZMviggCAIgiCIzECKoATdRYu4uE7EY2g+1mO+Z9KsffZxwr6R/UiUkhIWzN4F5AkjnMQiugt8v2uo+xi3Emhtd9kEhf39t0J4XU9zjVsRtLap21tKn6wuoNciCAiuoR5X4v5Yq6xFesKlCMonNXLBcZey4T42SrH3X1/nznVnZw3l4TJZiZnshxkCZ01yFExmuuqE3U9aCl1EpU/km5dNT+u4MFzWZub+/QlMJCXbFiKE93fCsY5nz/JIEARBEETmIdfQEIIWMOLC578vPBGvbjmE8uIEpo+qwrJNB4U+3IsrSzF47UuLUFIYF9rpLZashfzb+9owaXi5kSzGc+iSWaPwuYfXIJnikWMPvTgF7OUuhdax4iI7as0yuTwDv3i0la6QsXUWv5YiI9YRFBfronWQgflcQJ0Y0ODYUi+3XT4DG/a14ZcvbbPljOtYBAMUu2zitZA7DzjCi8UXKILaf3TlLCyZ1YjLf/oiXt9x1IjhgFpB7e8DB7/VzC85Y8Dls0fjy395U10+IkMWQVGgIOts8AMbvfFsV2PS9QiCIDIPJT8isggpghKazIxZ9eVFKC1UJ6IQ16/nTR2B86aOsD8z1xN59wrJOm5YRRHSwarrlwywnDDGMK62FFua25WZQr34FrOepBGiImNtl9sDjWyO/SVo4Z4tAlNhCzqHTtyeN46QeyyChmuoEIOpSBbj1BfUW2lfedpYHGnvMRRBSYwgwDFnbDVe33HUfX6RlRC/TTgTpIT7Oky5kBWj/dQ5E7FkVqNLNt0z8ypNwyv8FntZX17lWmWFD7W29UOZcheU1/zOS/aFieB3DTVedeOUCYIgiAhQ8iMii5BrqISLZjRg87cvxvJbzg3MSBi08PHWGHQd188YQSsdu6U4eIudezvUtwi6GxYkjM9ishOna2sbtz9b++eOq8HkEdFr3snIlWuobMpk1zswFs6OETTaJN0TaDQxAwnFZDFx2yRovDj1JyPI71E+L5rRYO9LpYAzJ9ZLziUaaSYZDUU36RAgVwRlfcVMk6DqflLdZpfPbsRD188LkQKYNqrS9TnsO6cuHxE6lLpPxbwFyRLVbVS2vbHGKCNx86LJQeIRBEEQBJFnkCKoIG7WlwkiaL/o7mbUonE+BymJurIBTkyZsQDUt3mo8J7OCR5lTqyDZ/TE3BZBRemFtAlYuGcL0apy73+cguIC+VdEdIkNw04Wk3K2WXNnGb0YHKuSVfJPjAE1xtKfWOsBxnlTRwIALpg2Ere/Z4bZn0oJEe5Z7ZEMThlXY9eV0+XB6+fhs+dN8W13YgR56DkXxP37Zcq5NcdRicUYThjp/h7IZDqxwdNGKoOzTX1fp//lce4T77UM+p0K+BNg9pHwzLH39EsLE9h222JcMnNUWFcEQRAEQeQR5BqaJmNrSwMTvYgLH6+CpcwaqrlY8lqYVBZB5mkfhrhgvGDaCKGOoDzeCfDECEr6EfniRSfiO49t0JIlqJ+B4vxpI7H6q+fjtsc2YG9LJ86a5FjRdOL2lm87jInDylx1JH3KsqAQqF1DoyvYxQVxvHrLuagV6jstmdWIVTuO4v9dcAJ++dI23zFFBTEUxBl6kxxlReE/DaI4508bifOnjcSV976MV7Yc1pJx3oQ6zJtQ59vuetgQcs5Fcc1i5dpmcdmh4cd6v9Oq8hFZdQ0VrPPvmzsa3/zHerNTf9tvXjYdPX0pTBcsmT98/yypDBXFBfjtR07HY2/uxW9e2UGJXwiCOD64YwbQsmPgxqOYPSIPIUUwDaxEFC9uala2iXusK27FMDMWwZRgEQzO2Cd/728ovvXHGKU8gVDeGMH6ciPmcdZYeQ2gj509ER87e2KAAB5xcrDeFJO5AIZCdask3jEsLqq2rBCH23uw43CHwrVWiBE091t18Lzt0y0oP8LzoKK4II7b3jNT2b64II7Hb16IA63dmN5YqWyXbcRsqWFnbLkvi8iUMKvgr6ouZVC9Sh13TZ1ro2c9zoxF8Lr5TfjZs5txqL1HOofXzBvn23bZ7EbXZ/G4sybV46XNzb7tuuT6oQ5BEISPlh3ArVRwnRjakGtoGnjXjLK1W8zjGiqiriPIfP29+8Thvna2a6i9YJZnBrXG1Y3lUimMTtZQ/4JZrCE2aXg5/nHjfPzXBScEjKIPk4yXL3gTwXi53VS4epMcVmLLlFCHUawFyQB09Tp+o5YrnjWGnZhmANbSE4eV44yJdagoLghta91fPX2pkJbhiNdZVIDDrE+Fiqyh3s7smNYQOaTfZW8iJslx/oRQcjfbMIUooXGRvS7bMhhjOGVcDRgDpjemkW1O1ifkrqJax5IeSBAEQRB5B1kE+8Gk4eWYPbbalS3UwlvH64JpI/Hy5kOYOLwsdEEv7v7ZNXNwrKsPp3zzKV/fTrKYsIx9uq6hwdtV9edEpo3KzKLTYqDVQN3xwgrKlxX5y4K46ggyoKs3acbBAR9dOAGff3gNAP/19VopM8mSWaNwsK0bi4VkMrpYOtiGfa32tkwURI9SPiIhUQSrSx13WLdFMD15dI4TH+5cN79JI4mN/06rKE7gpIZgS+xD18/DuLoyzPvOvyR9WvIastz7wbm+Nh88YxyWbVR7MoiozjsRFFdIEARBEMSggRTBfjCishh//uRZ0n0uZY8xqXuhF2vhJS6mixJxFJW746D8yWIUFkFPv8b7IBdSvzuo+N5vCWWuGMFMw1gOsoZqDuiUdJDvrzGVkfryQkexE5LtDK8owrHuPhzrNt6XCWVKxpvlS5yxMpyEB869MaG+HD+6cnZafZw40lBaRMXgY2dPxMG2bkwaXp62bO6C8tGPf/+pY3zbGHPccfuLTCbRFfx9c0fLj4P6u1RaGMeVp45RegtYnC6JqXRwrPMqvr5kuk8JLSuMo70nGTgu4HggyBL0hEEGQYIgCCJjUG3FjEGKYBqELda8baK69MkWmt9/38no6Okz+raTxRj7VC501iZdS5JKTut4zv35JrNZ5y9XcUU60+VkF5U3PnFkBf7vQ6diTG0p9rZ0AgCaj/Wgvdu4hjeeOxlXnT4WnAMjK4vxxm4jTuEbl023y4P0N0ZQh/5cP6uYe2/ScQ09e8ownP3Zs/spk/s1KuWSRDeOa2hwrzpunzJ0jWSqnnTcYEXuunoOxtaW4t9+sszVh5YMnnH+fuMCLN96yN/OI62TzIgsggRBEEQOodqKGYMUwTR41wnDQtvopm+XIVsQvvcUx8oQj3tcByFX4m46dwpe2tyMMybW4YbfrTJlCRhX2OuNvWIM6E6m0N2btD+LFpZsKG1GMpqBNQnqJCgRCVKezzHjOw+bSWA+9uuVAIw4MMYYGqqccguzxlRjxZcXoa6sEH9etduUxZ01NKMxghlQKi3LUNJbTb2fuArK9/O+Ei3WQYpWkBJVXBDHHz52Bq6452WjL4lMrnIxCplVmUSNz9HmcPFMvyuvmCwmCk31ZWiqd6zQqrnoS6VvESSTIEHkmP5YUGjRTRDHLaQIRuSWi0/USqThUgQ1F0GOUhWMYxF0FAXZMYtnNmDxzAYcMRWRMMTF7Ff/ze3KWhCP4Z7ntviO0YkbTJecuIZqoorbe+7/vcu2lFnMGVuNH105C8dMa+DY2lKpVdnKumpnac2iRfC6+U3Y1tyO/zyrKe0+rPi8vgwrgs41l7s8R+pLsNzquIaqlMXTmmoDjwu6Nu7fAnk7zvunK/UmU3bSnkw9lPGKain86dyHw8qLcN38JoyoLMqEaAQx+Blo17Z0lbl0ZATSL82QzvmRmyBBpA0pgprMGlMDYCsma2TsA4ASIeZr95FOrWMcy0/wQsvyzEqmHEVQu1ZgQLPCRAx/+sQZqC4tdNWfA4CfXj0Hmw4ew21mHUDGmH5Zin6QixBBHRc9Rzlzbx/nie8DDIVpyaxG33YVthsjd1sEM0lVSQHuvCq92EALnQyXujTWONZR0SIYZYQHr5/ne+jhvU6qmeyv5Tno+/fh+U0oLojh1PGOMum9pP01for1OdPJ6qlDXyqVdv+MMXzlkqmZFokgBi/Hu5VtIEszHO9zSRBZhBRBTRbPbMBF0y92lYUIYnxdKRadNAJPrd+PvS1dWsdYC6yLpo8MbGdZBMWsksFJYLSGBwCcMk5u+Vg0dQQWYYStCFr9Ztdix/LXIoj0rSNhMI/SktKwCH763ZPQfKw747IE4bV89ofhFcXY8I0L8d3H38ZvX92OR9fswfZDHZHuXVlxeuuBRkE8lrGHFdJkMa5yMe59500dYWcWdty5/Td2fyx5N5wzCaVFcRQn4lgwuT7tfgAhOZFnuxUKqhMjTRAEQRBE/kOKYAR0lUDAUMwun9OIp9bvtxOEhFGUiGP5LeeixmON82ItxP614QAOd/TgaEev9iK3v25jZ06sw9bmdtSUGu6x2dTTclJQXqNkAZDdBC5Och5rLFPpDNC7Pnd+Zmo3RiHTCkFxQRx15YXo7kvhxt8bMa0njpRb4MuLEigtjEv3iXzzsul4dcthLDppBL72t7fCXUMD9jVWl2D30U7peccjWuR3eb0EQjKklhbG0SHJ7DlhWBmOdfXh5kWTpaU00uG8qSOwbFMzZo2tdm0vMktiZPIBAEEQeQ65XRLEcU1WFUHG2IUAfgQgDuDnnPPbPPuLAPwKwCkADgF4P+d8m7nviwCuA5AEcCPn/IlsypoNqk1lqahAf+E0vLI4tI1VLPqd/W3YfPAYGANmBBSNFpW//uotv/voPHe/WdQErTyPA4luyYJslHSwsLq0yyiYn7OhdOYbnzh7Ii6aPtK2gqpiyp74zEIt19RxdWUed135/aRjeX70hrPQ3p2UKkKikq5zlf64che+c/kMu6+wBxBP3LwQ3X1+RfDpz71LY7RofOfymdLtH1nQhKqSApx3kr9uKkEQxynkdkkQxzVZUwQZY3EAdwE4D8AuAK8xxh7lnL8lNLsOwBHO+STG2JUAbgfwfsbYVABXApgGYBSApxhjUzjn4cWu8ogzJtThK5dMxXvm6MeH6fKnT5yp3TYuxPRk+ml+WBmF/pDXyWLM14FxDc1C1tAM8rGFEzLWVyzGMGFYeA3CxuqS0DZedC5VUJu68iLUKUTTtY4yxvAf88bh169sR1tXn+26Gnafj6kt1eo/m4yuKcVnzpuSazEIgiAIgsgQ2bQIngZgE+d8CwAwxh4EsASAqAguAXCr+f6PAH7CDI1iCYAHOefdALYyxjaZ/b2cRXkzDmMM181PPytjpigvSuAX185FT18KI6vCLY66MAZs2NeWsf5kdPel8ORb+7M6hsjW5nYt99miRAxdvaksWQSNTr/+t7dQUZzAHjvGNP80wW23Lc61CNowAGt3t+CHT73j27dy+5F+9V0Yj6EwEUNPXwrVpcGu3bPHVuPXr2zHn1buQl250TbF+58hlSAIgiAIIgrZVAQbAewUPu8CcLqqDee8jzHWAqDO3P6K51ipWY0xdj2A6wFg7FjySVdxbhbcuS6Z2YDH3tyHglgMp40PTq+fDtUlhTjW3YeP/mpFxvsOor48eCEPAF+/dDr+snp3Viw1U0dVYuboKhxo68IBU88+rakWo6ozp8QPRSaPKMeLmw7hzd2t0v1jakt89TN1ScRjeON/zkcyxVEmKWjvHse4Z761dL1re10ZlVYgCIIgCGLgyKYiKHu+7XWAUrXROdbYyPm9AO4FgLlz5+apI+HxyfULJ+L6hROz1v9NiybjwpAMqtlghEac5hWnjsEVp47JyvhN9WV49Ib5Wel7KPOb67zPofz0x8W5uCA8eQ0AnDq+Fq/eci66eh1P9xhjGF0T3d2VIAiCIAgiXbKpCO4CIK6URwPYo2izizGWAFAF4LDmscRxTkE8hukBSXAIIgrZiGNNF52HDQRBEARBENkkm3nAXwMwmTHWxBgrhJH85VFPm0cBXGu+fy+Ap7mRKvFRAFcyxooYY00AJgNYnkVZCYIgCIIgCIIghgxZswiaMX83AHgCRvmI+znn6xhjXwewgnP+KIBfAPi1mQzmMAxlEWa7P8BILNMH4FODLWMoQRAEQRAEQRBEvpLVOoKc86UAlnq2fVV43wXgfYpjvwXgW9mUjyAIgiAIgiAIYiiSTddQgiAIgiAIgiAIIg8hRZAgCIIgCIIgCGKIQYogQRAEQRAEQRDEEIMUQYIgCIIYZDDGLmSMvc0Y28QY+0Ku5SEIgiAGH6QIEgRBEMQggjEWB3AXgIsATAVwFWNsam6lIgiCIAYbpAgSBEEQxODiNACbOOdbOOc9AB4EsCTHMhEEQRCDDFIECYIgCGJw0Qhgp/B5l7mNIAiCILTJah3BgWblypXNjLHt/eymHkBzJuQZAEjW7DGY5CVZs8NgkhUYXPJmQtZxmRBkkMIk27ivEWPXA7je/HiMMfZ2P8etx9fYYLnHBorB9L0bSGhe/NCc+KE58ZOp31mtv5HHlSLIOR/W3z4YYys453MzIU+2IVmzx2CSl2TNDoNJVmBwyTuYZM1TdgEYI3weDWCPtxHn/F4A92ZqULpufmhO5NC8+KE58UNz4meg54RcQwmCIAhicPEagMmMsSbGWCGAKwE8mmOZCIIgiEHGcWURJAiCIIjjHc55H2PsBgBPAIgDuJ9zvi7HYhEEQRCDDFIE/WTMjWYAIFmzx2CSl2TNDoNJVmBwyTuYZM1LOOdLASwd4GHpuvmhOZFD8+KH5sQPzYmfAZ0TxrkvvpwgCIIgCIIgCII4jqEYQYIgCIIgCIIgiCEGKYImjLELGWNvM8Y2Mca+kAfyjGGMPcMYW88YW8cYu8ncfitjbDdjbLX572LhmC+a8r/NGLsgBzJvY4ytNeVaYW6rZYw9yRjbaL7WmNsZY+xOU943GGNzBlDOE4T5W80Ya2WM3Zwvc8sYu58xdoAx9qawLfI8MsauNdtvZIxdO4Cyfo8xtsGU58+MsWpz+3jGWKcwv3cLx5xi3jubzPORpcfPlryRr/tA/F4oZH1IkHMbY2y1uT2ncxvwe5WX9y0RTNj9zRgrMu/FTYyxVxlj4wdeyoFFY04+yxh7y7yf/8UYO+7Lm+j+DjLG3ssY44yxIZEdUmdeGGNXmPfLOsbY7wZaxoFG4/sz1vwbssr8Dl0s6+d4QvY33rNf+Xcyo3DOh/w/GMH2mwFMAFAIYA2AqTmWqQHAHPN9BYB3AEwFcCuAz0vaTzXlLgLQZJ5PfIBl3gag3rPtuwC+YL7/AoDbzfcXA3gMRj2seQBezeG13wej3kpezC2AhQDmAHgz3XkEUAtgi/laY76vGSBZzweQMN/fLsg6Xmzn6Wc5gDPM83gMwEUDOLeRrvtA/V7IZPXs/18AX82HuQ34vcrL+5b+BV7L0PsbwCcB3G2+vxLAQ7mWOw/m5BwApeb7T9Cc2O0qADwP4BUAc3Mtdz7MC4DJAFZZv20Ahuda7jyYk3sBfMJ8PxXAtlzLPQDzEvY3fkDWyWQRNDgNwCbO+RbOeQ+ABwEsyaVAnPO9nPPXzfdtANYDaAw4ZAmABznn3ZzzrQA2wTivXLMEwAPm+wcAXCZs/xU3eAVANWOsIQfynQtgM+d8e0CbAZ1bzvnzAA5LZIgyjxcAeJJzfphzfgTAkwAuHAhZOef/5Jz3mRHKta0AAAavSURBVB9fgVHjTIkpbyXn/GVu/Pr9Cs75ZV3eAFTXfUB+L4JkNa16VwD4fVAfAzW3Ab9XeXnfEoHo3N/idf0jgHOzZcXPE0LnhHP+DOe8w/wY+rt3HKD7O/gNGA+EugZSuByiMy8fBXCX+RsHzvmBAZZxoNGZEw6g0nxfBUld1OMNjfXIgKyTSRE0aASwU/i8C8FK14Biut3MBvCquekG00x8v+Vqhfw4Bw7gn4yxlYyx681tIzjnewFjsQhguLk9H+QFjKfZ4mI6X+c26jzmg8wA8GEYT7QsmkzXj+cYYwvMbY0w5LPIhaxRrns+zO0CAPs55xuFbXkxt57fq8F63w5ldK6B3cZ86NMCoG5ApMsNUe/L6+D+3TseCZ0TxthsAGM4538fSMFyjM69MgXAFMbYi4yxVxhjx/vDLp05uRXANYyxXTCyIX96YETLawbk7yEpggayJ5l5kU6VMVYO4E8AbuactwL4GYCJAGYB2AvDPQzIj3M4i3M+B8BFAD7FGFsY0Dbn8jKjEPOlAB42N+Xz3KpQyZZzmRljXwLQB+C35qa9AMZyzmcD+CyA3zHGKpF7WaNe91zLCwBXwf0AIy/mVvJ7pWwq2ZYvczvU0bkGQ+06aZ8vY+waAHMBfC+rEuWewDlhjMUA3AHgcwMmUX6gc68kYLiHvgvGb/nPmRlLf5yiMydXAfgl53w0DJfIX5v30FBmQH5nh/okW+wCMEb4PBp5YJZmjBXAWFT9lnP+CABwzvdzzpOc8xSA++C4KOb8HDjne8zXAwD+bMq23zJlm6+WC0TO5YWhsL7OOd8P5PfcIvo85lRmM8nHJQA+YLokwnSxPGS+XwkjZmCKKavoRjWgsqZx3XM9twkAlwN4yNqWD3Mr+73CILtvCQB618BuY96PVdB3uR6MaN2XjLFFAL4E4FLOefcAyZYrwuakAsB0AM8yxrbBiHF6dAgkjNH9/vyVc95rhh28DUMxPF7RmZPrAPwBADjnLwMoBlA/INLlLwPy95AUQYPXAExmjDWZVqIrATyaS4HMeItfAFjPOf+BsF30D/53AFa2oUcBXGlmc2uC8aOyfADl/f/t3T2IHVUYh/HnjyDRGIwxKVK5rpViaSCIlYQtAtpoYbUiNkHsLdKJoCBYaWEnCCLYxCWNoGKTRiVsvsSPmEIEEUkRBBFUjsU5N4zrJrsrZj52nh8Mexnu3n33nbNn5p1z5uzeJPsWr6kLhlxscS1W/nsW+LAT72pbFekocG0xhaxH/xhVGWtuOzHsJI8fAStJ7mlTHVfavluuTXN5iXox9Ftn/6Ekt7XXy9Q8Xmnx/prkaGv3q53fr494d3rch+4vjgFfl1KuT/kcOrc36q+YULvVddtp393j+jTw6eKGzy61ZU7aNMi3qf3ebn/mC7bISSnlWinlYCllqZSyRH1u8slSypfDhNub7fz9nKIuLkSSg9Sbdld6jbJf28nJD9Q1G0jyILUQ/KXXKMenn+vkMoKVc8awUYeiv6XeST85gngeow4BnwfW23YceBe40PavAYc733Oyxf8Nt2jVxZvEu0xdCeoccGmRQ+pzI58A37WvB9r+AG+1eC/Q82piwJ3AVeDuzr5R5JZanP4E/EG9I/T8f8kj9fm8y217rsdYL1PntS/a7WJ1wada2zgHnAWe6HzOI9QC7HvgTSA9xrvj495Hf7FZrG3/O8CJDe8dNLfcuL8aZbt12/J4/qt9Ay9TL+ShXqR90I7R58Dy0DGPICcfAz932v/a0DEPnZMN7/2MGawaus22EuAN4KvW/z0zdMwjyMlDwJl2DlsHVoaOuYecbHY9cmJxfr/ZefL/3NJ+mCRJkiRpJpwaKkmSJEkzYyEoSZIkSTNjIShJkiRJM2MhKEmSJEkzYyEoSZIkSTNjIShNVJL9SV4YOg5JkiRNj4WgNF37AQtBSZIk7ZiFoDRdrwEPJFlP8vrQwUiSNAZJjiQ5n2RPkr1JLiV5eOi4pLHxH8pLE5VkCThdSvHkJklSR5JXgD3AHcCPpZRXBw5JGh0LQWmiLAQlSdpcktuBL4DfgUdLKX8NHJI0Ok4NlSRJ0m5zALgL2EcdGZS0gSOC0kQluRc4W0q5b+hYJEkakyRrwPvA/cDhUsqLA4ckjY4jgtJElVKuAmeSXHSxGEmSqiSrwJ+llPeoC6sdSfL4wGFJo+OIoCRJkiTNjCOCkiRJkjQzFoKSJEmSNDMWgpIkSZI0MxaCkiRJkjQzFoKSJEmSNDMWgpIkSZI0MxaCkiRJkjQzFoKSJEmSNDN/AzBemAawvkFJAAAAAElFTkSuQmCC\n", "text/plain": [ "

" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:20: RuntimeWarning: invalid value encountered in double_scalars\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Number of samples = 5000\n", "Acceptance ratio = 0.20924184836967394\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Beta distribution - target distribution\n", "def beta_dist(x, a, b):\n", " return stats.beta(a, b).pdf(x)\n", "\n", "# proposal distribution\n", "def proposal_dist(x,sigma):\n", " return np.random.normal(x,sigma) \n", "\n", "def plot_beta(N, x0, sigma, a, b):\n", " Ly = []\n", " Lx = []\n", " i_list = np.mgrid[0:1:100j]\n", " for i in i_list:\n", " Lx.append(i)\n", " Ly.append(beta_dist(i, a, b))\n", " t = np.linspace(0,2000,2001)\n", " states,acc_ratio = beta_mcmc(N, x0, sigma, a, b)\n", " # print results on screen\n", " print(\"Number of samples = \",N)\n", " print(\"Acceptance ratio = \",acc_ratio)\n", " # plot results\n", " plt.figure(figsize=(15,5))\n", " plt.subplot(1,2,1)\n", " plt.plot(t, states[:2001], label=\"\\sigma = \"+str(sigma))\n", " plt.xlabel(\"t\")\n", " plt.ylabel(\"x\")\n", " \n", " plt.subplot(1,2,2)\n", " plt.plot(Lx, Ly, label=\"Real Distribution: a=\"+str(a)+\", b=\"+str(b))\n", " plt.hist(states[-1000:],density=True,bins=25, histtype='step',label=\"Simulated MCMC: a=\"+str(a)+\", b=\"+str(b))\n", " plt.xlabel(\"x\")\n", " plt.title(\"Sampling Beta function\")\n", " plt.legend(loc=\"best\")\n", " plt.show()\n", "\n", "# Number of samples\n", "# Set this to be smaller to speed up the evaluation\n", "N = 5000\n", "# N = 100000\n", "plot_beta(N, 2, 1, 0.5, 0.6)\n", "\n", "plot_beta(N, 2, 1, 2, 4)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "90Niq4E6XTH7", "nbpages": { "level": 3, "link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)", "section": "11.2.2.1 Implemention" } }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html) | [Contents](toc.html) | [11.3 The Kennedy-O’Hagan Predictive Model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.03-Contributed-Example.html)

\"Open

\"Download\"" ] } ], "metadata": { "colab": { "name": "11.02-Contributed-Example.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }