{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# LLN and CLT\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [LLN and CLT](#LLN-and-CLT) \n", " - [Overview](#Overview) \n", " - [Relationships](#Relationships) \n", " - [LLN](#LLN) \n", " - [CLT](#CLT) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "This lecture illustrates two of the most important theorems of probability and statistics: The\n", "law of large numbers (LLN) and the central limit theorem (CLT).\n", "\n", "These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeling.\n", "\n", "The lecture is based around simulations that show the LLN and CLT in action.\n", "\n", "We also demonstrate how the LLN and CLT break down when the assumptions they are based on do not hold.\n", "\n", "In addition, we examine several useful extensions of the classical theorems, such as\n", "\n", "- The delta method, for smooth functions of random variables \n", "- The multivariate case \n", "\n", "\n", "Some of these extensions are presented as exercises." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Relationships\n", "\n", "The CLT refines the LLN.\n", "\n", "The LLN gives conditions under which sample moments converge to population moments as sample size increases.\n", "\n", "The CLT provides information about the rate at which sample moments converge to population moments as sample size increases.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LLN\n", "\n", "\n", "\n", "We begin with the law of large numbers, which tells us when sample averages\n", "will converge to their population means.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Classical LLN\n", "\n", "The classical law of large numbers concerns independent and\n", "identically distributed (IID) random variables.\n", "\n", "Here is the strongest version of the classical LLN, known as *Kolmogorov’s strong law*.\n", "\n", "Let $X_1, \\ldots, X_n$ be independent and identically\n", "distributed scalar random variables, with common distribution $F$.\n", "\n", "When it exists, let $\\mu$ denote the common mean of this sample:\n", "\n", "$$\n", "\\mu := \\mathbb E X = \\int x F(dx)\n", "$$\n", "\n", "In addition, let\n", "\n", "$$\n", "\\bar X_n := \\frac{1}{n} \\sum_{i=1}^n X_i\n", "$$\n", "\n", "Kolmogorov’s strong law states that, if $\\mathbb E |X|$ is finite, then\n", "\n", "\n", "\n", "$$\n", "\\mathbb P \\left\\{ \\bar X_n \\to \\mu \\text{ as } n \\to \\infty \\right\\} = 1 \\tag{1}\n", "$$\n", "\n", "What does this last expression mean?\n", "\n", "Let’s think about it from a simulation perspective, imagining for a moment that\n", "our computer can generate perfect random samples (which of course [it can’t](https://en.wikipedia.org/wiki/Pseudorandom_number_generator)).\n", "\n", "Let’s also imagine that we can generate infinite sequences, so that the\n", "statement $\\bar X_n \\to \\mu$ can be evaluated.\n", "\n", "In this setting, [(1)](#equation-lln-as) should be interpreted as meaning that the\n", "probability of the computer producing a sequence where $\\bar X_n \\to \\mu$ fails to occur\n", "is zero." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Proof\n", "\n", "\n", "\n", "The proof of Kolmogorov’s strong law is nontrivial – see, for example, theorem 8.3.5 of [[Dud02]](../zreferences.html#dudley2002).\n", "\n", "On the other hand, we can prove a weaker version of the LLN very easily and\n", "still get most of the intuition.\n", "\n", "The version we prove is as follows: If $X_1, \\ldots, X_n$ is IID with $\\mathbb E X_i^2 < \\infty$,\n", "then, for any $\\epsilon > 0$, we have\n", "\n", "\n", "\n", "$$\n", "\\mathbb P \\left\\{ | \\bar X_n - \\mu | \\geq \\epsilon \\right\\} \\to 0\n", "\\quad \\text{as} \\quad\n", "n \\to \\infty \\tag{2}\n", "$$\n", "\n", "(This version is weaker because we claim only [convergence in probability](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_probability) rather than [almost sure convergence](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Almost_sure_convergence), and assume a finite second moment)\n", "\n", "To see that this is so, fix $\\epsilon > 0$, and let $\\sigma^2$ be the variance of each $X_i$.\n", "\n", "Recall the [Chebyshev inequality](https://en.wikipedia.org/wiki/Chebyshev%27s_inequality), which tells us that\n", "\n", "\n", "\n", "$$\n", "\\mathbb P \\left\\{ | \\bar X_n - \\mu | \\geq \\epsilon \\right\\}\n", "\\leq \\frac{\\mathbb E [ (\\bar X_n - \\mu)^2]}{\\epsilon^2} \\tag{3}\n", "$$\n", "\n", "Now observe that\n", "\n", "\n", "\\begin{aligned}\n", " \\mathbb E [ (\\bar X_n - \\mu)^2 ]\n", " & = \\mathbb E \\left\\{ \\left[\n", " \\frac{1}{n} \\sum_{i=1}^n (X_i - \\mu)\n", " \\right]^2 \\right\\}\n", " \\\\\n", " & = \\frac{1}{n^2} \\sum_{i=1}^n \\sum_{j=1}^n \\mathbb E (X_i - \\mu)(X_j - \\mu) \\nonumber\n", " \\\\\n", " & = \\frac{1}{n^2} \\sum_{i=1}^n \\mathbb E (X_i - \\mu)^2 \\nonumber\n", " \\\\\n", " & = \\frac{\\sigma^2}{n} \\nonumber\n", "\\end{aligned}\n", "\n", "\n", "Here the crucial step is at the third equality, which follows from\n", "independence.\n", "\n", "Independence means that if $i \\not= j$, then the covariance term $\\mathbb E (X_i - \\mu)(X_j - \\mu)$ drops out.\n", "\n", "As a result, $n^2 - n$ terms vanish, leading us to a final expression that goes to zero in $n$.\n", "\n", "Combining our last result with [(3)](#equation-lln-cheb), we come to the estimate\n", "\n", "\n", "\n", "$$\n", "\\mathbb P \\left\\{ | \\bar X_n - \\mu | \\geq \\epsilon \\right\\}\n", "\\leq \\frac{\\sigma^2}{n \\epsilon^2} \\tag{4}\n", "$$\n", "\n", "The claim in [(2)](#equation-lln-ip) is now clear.\n", "\n", "Of course, if the sequence $X_1, \\ldots, X_n$ is correlated, then the cross-product terms\n", "$\\mathbb E (X_i - \\mu)(X_j - \\mu)$ are not necessarily zero.\n", "\n", "While this doesn’t mean that the same line of argument is impossible, it does mean\n", "that if we want a similar result then the covariances should be “almost zero”\n", "for “most” of these terms.\n", "\n", "In a long sequence, this would be true if, for example, $\\mathbb E (X_i - \\mu)(X_j - \\mu)$\n", "approached zero when the difference between $i$ and $j$ became\n", "large.\n", "\n", "In other words, the LLN can still work if the sequence $X_1, \\ldots, X_n$ has a kind of “asymptotic independence”, in the sense that correlation falls to zero as variables become further apart in the sequence.\n", "\n", "This idea is very important in time series analysis, and we’ll come across it again soon enough." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Illustration\n", "\n", "\n", "\n", "Let’s now illustrate the classical IID law of large numbers using simulation.\n", "\n", "In particular, we aim to generate some sequences of IID random variables and plot the evolution\n", "of $\\bar X_n$ as $n$ increases.\n", "\n", "Below is a figure that does just this (as usual, you can click on it to expand it).\n", "\n", "It shows IID observations from three different distributions and plots $\\bar X_n$ against $n$ in each case.\n", "\n", "The dots represent the underlying observations $X_i$ for $i = 1, \\ldots, 100$.\n", "\n", "In each of the three cases, convergence of $\\bar X_n$ to $\\mu$ occurs as predicted." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using InstantiateFromURL\n", "# optionally add arguments to force installation: instantiate = true, precompile = true\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "Plots.GRBackend()" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using LinearAlgebra, Statistics\n", "using Plots, Distributions, Random, Statistics\n", "gr(fmt = :png, size = (900, 500))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "ksl (generic function with 2 methods)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function ksl(distribution, n = 100)\n", " title = nameof(typeof(distribution))\n", " observations = rand(distribution, n)\n", " sample_means = cumsum(observations) ./ (1:n)\n", " μ = mean(distribution)\n", " plot(repeat((1:n)', 2),\n", " [zeros(1, n); observations'], label = \"\", color = :grey, alpha = 0.5)\n", " plot!(1:n, observations, color = :grey, markershape = :circle,\n", " alpha = 0.5, label = \"\", linewidth = 0)\n", " if !isnan(μ)\n", " hline!([μ], color = :black, linewidth = 1.5, linestyle = :dash, grid = false,\n", " label = [\"Mean\"])\n", " end\n", " plot!(1:n, sample_means, linewidth = 3, alpha = 0.6, color = :green,\n", " label = \"Sample mean\")\n", " return plot!(title = title)\n", "end" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "6-element Array{Distribution{Univariate,S} where S<:ValueSupport,1}:\n", " TDist{Float64}(ν=10.0)\n", " Beta{Float64}(α=2.0, β=2.0)\n", " Gamma{Float64}(α=5.0, θ=2.0)\n", " Poisson{Float64}(λ=4.0)\n", " LogNormal{Float64}(μ=0.5, σ=1.0)\n", " Exponential{Float64}(θ=1.0)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "distributions = [TDist(10), Beta(2, 2), Gamma(5, 2), Poisson(4), LogNormal(0.5),\n", " Exponential(1)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is in an example for the standard normal distribution" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ksl(Normal())" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [], "source": [ "Random.seed!(0); # reproducible results" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(ksl.(sample(distributions, 3, replace = false))..., layout = (3, 1), legend = false)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The three distributions are chosen at random from distributions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Infinite Mean\n", "\n", "What happens if the condition $\\mathbb E | X | < \\infty$ in the statement of the LLN is not satisfied?\n", "\n", "This might be the case if the underlying distribution is heavy tailed — the best\n", "known example is the Cauchy distribution, which has density\n", "\n", "$$\n", "f(x) = \\frac{1}{\\pi (1 + x^2)} \\qquad (x \\in \\mathbb R)\n", "$$\n", "\n", "The next figure shows 100 independent draws from this distribution" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [], "source": [ "Random.seed!(0); # reproducible results" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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+vl4ikcyaNevQoUPXhlFCyNq1a2NiYgghOTk5+fn5WVlZ7J5feumlvXv3RkREJCcn19XVyWSyadOmHTlyZOPGjXV1dZ9++qnRaAwJCTl16tT48eMVCsWzzz5LCFm4cKFYLG5sbGT36foQRgEAAOC+/Hr2r7ku4d4JBILHH3/88ccfdzgcv/rVrzZs2NDR0ZGdnS0Wi+fMmSOTyfh8PrtAt7+/P/sSiURy7W2TyUQI4fP5SqWSfTAkJKSoqIi9rdVqOzo6XnrppaEjKhSK62q4xZ61Wq1Wqx16uUAg8PX1/fzzz19++eVHH300KCjov8sjhHh4eLBVjQoIowAAAACEx+OtXLny1VdfraiouHTpUldXF0VRVqv1lVdeuZOX2+32xsbGiIgIQkhNTU1oaCj7uFqt9vb2/uKLL27WNHtrarU6ICDgyy+/vPbBBQsW/PnPf161ahUhpKGhobq6+h727DowgAkAAADGrpUrV3755ZcVFRXnzp175ZVXZs+eHRwcbDabDx8+3Nzc/Oyzz95hEyOfz3/++ecbGhoOHDiwc+fO9evXs48vWrSIoqif/vSntbW1tbW1n376aVlZ2Z2Xt3z5cr1e//LLL9fV1dXU1Hz88ceVlZUqlerAgQOtra379u3bsWPHPbxrl4KWUQAAABi7Fi5c+MUXX7z22mseHh4zZsz46U9/6ufn9+mnn/7hD3+w2+0bNmzw8fEJCgqaOnVqdHQ0+5KYmBgvLy/2tlKpnD9/PiFELBavW7fu0UcfFYvFn3/+eVxcXH19fU5OjkgkKigo+N3vfvfYY48RQpKTk+fMmXNtAampqWFhYextjUYz1ICqUCgWLlwokUhOnjz5u9/9bt26dRRFTZo0aeHChX/84x+fe+65pUuXTpw48e23366vr2c3Htrn4sWLfXx8hvkn5zQUw4xcj2ONRnPw4MHrOu3egl6vl8lkw1qSqykuLsZyoCNmDJ5gMJJwgsHwYRjGYDBIpdIRO+JvfvMbmqZ/85vfjNgRRxetVhsTE2MwGLgu5L7s3r17+/btu3fvpmnaZrN5eHiMzHFxmR4AAAAAOIMwCgAAAHBfgoKC7qonKFwLYRQAAADgvggEArVazXUVoxXCKAAAAABwBmEUAAAAADiDMAoAAAAAnEEYBQAAAADOIIwCAAAAAGewAhMAAADcnt1uN5vNXFcBw8hms3FyXIRRAAAAuI2srKx58+a9/vrrXBfiBAzDDC256eJGvtRly5aN5OFYCKMAAABwGzNmzDCZTFxX4RwXLlzQaDRyuZzrQm7v+PHjmZmZoyU63zP0GQUAAAAAziCMAgAAAABnEEYBAAAAgDN312fUbrdXVlZeuHCho6Pj+eefH3r8q6++OnHiRFhY2MaNG6VSqbOLBAAAAAD3dHctowUFBQsWLHj//fdfeeWVoQf/+Mc/vvzyyzExMeyzDMM4u0gAAAAAcE93F0Znz57d0tKyZcuWoUcsFssbb7zx0Ucfbdq0adeuXU1NTXl5ec4uEgAAAADc092F0f+eXKCiosJkMk2bNo0QIhAIZs+eXVBQ4LTqAAAAAMCt3e88o21tbQqFgsf731AbGBjY2tp6s43NZvOLL754s5m9AgICfvvb3163vVAovM8KRxebzWaxWNxsiYvBwcHjx4/X1tZ6eHhMmTJl4sSJLjJl2hg8wWAk4QSD4cMwjNlsFggwWfi9GEUftTRNm83mkf/QpGnaZrM55bgikWgoJd7M/Z7HIpGIpumhuzabTSwW32xjPp8/efJkpVJ5w2flcvl1f7iFQuFY+1PO5/MFAoE7vWuz2fzee+95enpGRkaazeYDBw709PQsWrSI67oIGZMnGIwknGAwfBiGwQl2z0bRRy2PxxMKhSMfRtkjOuVHdCfF328YDQ4O7urqslgsbAZtaWmZMmXKzTYWCoWrV6/WaDR3uHM+n8/n8++zwtGFx+O52bu+dOmSUChMSUlh7yqVytzc3Dlz5nh5eXFbGBmTJxiMJJxgMHwYhsEJds9G0UctW+rIh1GGYRwOx4j9iO53ntHY2NiwsLC9e/cSQnp6eo4dO7Z06VJnFAZuQqvVKhQKQojFYrHb7SKRyMvLq7Ozk+u6AAAAwCXcXctob2/vggULTCaT3W6fMmWKUqk8ePDgn/70p40bNx44cODMmTPf//73ExIShqlWGI0UCsWVK1cIITqdTiqVenh4mM1mb29vrusCAAAAl3B3YVQul7/33ntDd9nOBCtWrEhJSTlz5szGjRunT5/u5AJhlEtKSsrNzQ0MDKQoyuFwXL58OTw83NfXl+u6AAAAwCXcXRgVCASTJ0/+78cjIiIiIiKcUxG4F6VSuWHDhn/961/19fUSiSQtLW3FihUuMpoeAAAAOIdZIWDYaTSaV1555dy5c6GhoSqViutyAAAAwIXc7wAmgDvk4eExKubRAAAAgJGEMAoAAAAAnEEYBQAAAADOIIwCAAAAAGcQRgEAAACAMwijAAAAAMAZhFEAAAAA4AzCKAAAAABwBmEUAAAAADiDMAoAAAAAnEEYBQAAAADOIIwCAAAAAGcQRgEAAACAMwijAAAAAMAZhFEAAAAA4AzCKAAAAABwBmEUAAAAADiDMAoAAAAAnEEYBQAAAADOIIwCAAAAAGcQRgEAAACAMwijAAAAAMAZhFEAAAAA4AzCKAAAAABwBmEUAAAAADiDMAoAAAAAnEEYBQAAAADOIIwCAAAAAGcQRgEAAACAMwijAAAAAMAZhFEAAAAA4AzCKAAAAABwBmEUAAAAADiDMAoAAAAAnEEYBQAAAADOIIwCAAAAAGcQRgEAAACAMwijAAAAAMAZhFEAAAAA4AzCKAAAAABwBmEUAAAAADiDMAoAAAAAnEEYBQAAAADOIIwCAAAAAGcQRgEAAACAMwijAAAAAMAZhFEAAAAA4AzCKAAAAABwBmEUAAAAADiDMAoAAAAAnEEYBQAAAADOIIwCAAAAAGcQRgEAAACAMwijAMCZ/v5+rVZrNpu5LgQAADgj4LoAABiLDAbD559/Xl1d7eHhYTab58+fP3fuXK6LAgAADiCMAgAHdu3apdPpFi5cSFGUyWQ6duyYUqlMSEjgui4AABhpuEwPACPNZrOVlZWlpKRQFEUI8fDw0Gg0Fy5c4LouAADgAMIoAIw0k8nE5/MpiqJpuru7mxDi4eGh1+u5rgsAADiAMAoAI00ul0skkt7eXoZhrFYrIaSlpUWtVnNdFwAAcAB9RgGAA6tWrdqxY4dKpbLZbC0tLRaLZfbs2VwXBQAAHEAYBQAOTJgwYfPmzSdOnKisrMzMzExPT/fw8OC6KABwsr6+vrq6OoZh1Gq1v78/1+WAi0IYBQBuBAcHL1myJDIyMjU1letaAMD5zp8//9VXX/n5+VEUtWvXrqVLl86YMYProsAVIYwCAACAk/X19X3zzTcZGRleXl6EEJPJtG/fPo1Go1QquS4NXA4GMAEAAICTNTY2+vj4sEmUEOLh4aFQKOrr67mtClwTwigAAAAMF51O19/fTwihKIphGK7LAVeEMAoAAABOFhYW1tfXZzQaCSEMw1gslu7ubszgBjeEPqMAAADgZH5+fsuXL9+9e7dYLObxeCaTadGiRYGBgVzXBa4IYRQAAACcLz09PTo6urCw0GazzZw5E0kUbgZhFAAAAIaFQqFITk622+1IonAL6DMKAAAAAJxBGAUAAAAAziCMAgAAAABnEEYBAAAAgDMIowAAAADAGYRRAAAAAOAMwigAAAAAcAZhFAAAAAA4gzAKAAAAAJxBGAUAAAAAzmA5UAAAcEMOh6Ozs9NisSiVSg8PD67LAYCbQhgFAAB309XV9cknn/T39wsEArPZvHz58vT0dK6LAoAbc0IYPXr06MWLF4fuvvDCCxRF3f9uAQAA7oHD4di+fbuPj8/kyZMJIQaDYc+ePSqVKjw8nOvSAOAGnNBndO/evbm5ufe/HwAAgPvX09MzMDCg0WjYu15eXmFhYWVlZdxWBQA345zL9DNnznzxxRedsisAAID7YTKZhEIhIcRisRgMBj8/P6FQaDAYuK4LAG7MOaPpCwsLX3755XfffVev1ztlhwAAAPcmMDDQaDQaDAaHw0HTNCGkvb09IiKC67oA4Mac0DIaHR0tlUp9fX2/+uqrP/zhDxcuXFAoFDfc0mQyPf3001Kp9IbPBgYGvv7669dtz+fz77/CUcRqtZpMJqPRyHUhzmexWMxms0u9tTF4grkak8lktVpd6qxwIpxgHFq0aNH+/fsDAwNpmr5y5YpcLo+Li3OnM41hGKPRyOONgvkZzWazw+FwqR8++1ErEIyCMdw2m81oNI78UByapm02G8Mw978riURy2xPVCf8SP/7xj9kbzz//fGZm5rvvvvvzn//8hlsKhcKcnByVSnXDZ6VSqUQiufYRm8123SNuTygUisVit3zXIpFIJBK51FsbgyeYq7Hb7UKh0F3/FXCCcSgjIyM8PPzkyZPt7e2LFi2aNGmSm30xYBjGbrePihNMJBI5HA6XKnUUfdQKBAKJRMJJGOXz+U75Ed3JVyZnfi2gKColJUWr1d70YALB4sWLhzqV3xaPxxsVX/uciKIod33XLvjWXK2eMYjH47EnBteFDAucYNyKiIiQyWRtbW0JCQlc1+J8DMOMlhOMx+Ox1XJdyL+54OfRzbCljnwY5f2fETrc/e+iv7+fvaHT6Q4dOjRx4sT73ycAAAAAjAVOaBmNiYnRaDR+fn6FhYWzZ89+4okn7n+fAAAAADAWOCGMXr16tbi42GQy/fWvf42Kirr/HQIAAADAGOGEMOrj4zNr1qz73w8AAAAAjDWjoPcuAAAAwN0ym81OmZwIhtsomGQLAAAA4M5duHBh3759g4ODAoFg7ty5WVlZbja3l5tBGAUAAAD3UV5evmvXrqlTp/r4+JhMptOnT/N4vHnz5nFdF9wULtMDAACA+zh16tSECRN8fHwIIR4eHqmpqfn5+VwXBbeCMAoAAADuo7u7Wy6XE0L6+vocDoenp6fFYrFarVzXBTeFMAoAAADuY9y4cV1dXYSQwcFBhmH6+vrkcrlIJOK6LrgphFEAAABwH/Pnz6+rq6uurtbr9c3NzefPn1+6dCnXRcGtIIwCAACA+1CpVE8//bRYLC4vLzcYDI899hgWKndxGE0PAAAAbiU4OPjRRx+Njo6ePHmyWCzmuhy4DbSMAgAAAABnEEYBAAAAgDMIowAAAADAGYRRAAAAAOAMwigAAAAAcAZhFAAAAAA4g6mdAFyazWarr683GAxBQUEqlYrrcgAAAJwMYRTAdXV2dm7dutXhcIjF4r6+vpSUlFWrVlEUxXVdAAAAToMwCuC6PvvsM5VKFRkZSQix2+0nTpwoKipKTU3lui4AAACnQZ9RABc1ODjY3t7OJlFCCJ/Pj4yMLC8v57YqAAAA53KTltHe3t6DBw9WVlZKJJIpU6bMnTtXJBJxXZTLqa+vLyoqMhgMarV62rRp+BG5OLvdzuPxCCFWq7Wvry8wMJDH49lsNq7rAgAAcCZ3aBk1Go3vvPPO4ODgzJkzk5OTL168+Pnnn3NdlMs5e/bs1q1be3t7eTzemTNn3nrrLavVynVRcCve3t4ymaytrY0Q4nA4CCFNTU0ajYbrugAAAJzJHcJocXGxRCKJjY2VSCQymWzatGkVFRXd3d1c1+VCbDbb7t27p0+fHhMTExYWNnXqVLvdfubMGa7rgttYu3ZtWVnZ+fPnKyoq8vPz/fz8ZsyYwXVRAAAAzuQOl+k7Ojq8vb0JISaTSSAQCIVCmUzW3d2tUCi4Ls1VdHV1iUQiqVTqcDhomhaJREFBQY2NjVzXBbcRHh7+0ksvFRUVVVZWzpo1Ky4uDkPpAQDAzbhDy6hSqRwYGCCEGAwGq9XKMIzBYPD39+e6Lhfi5eXFXpRnex8SQkwmk1wu57ouuD2ZTDZlypS0tLT4+HgkUQAAcD/uEEaTkpKMRmN1dTVN02az+fz585GRkWgWvWwC/MgAACAASURBVJa3t3dISEh5eTnDMIQQvV7f2NiYlJTEdV0AAAAw1rlDGJVKpZs2beLxeMeOHSssLIyJiVm7di3akK7zyCOPEEKOHDly8uTJM2fOPPDAA2q1muuiAAAAYKxzhz6jhBClUvmDH/xg+vTpfn5+gYGBXJfjinx8fH70ox81NDTU1tZmZmZiXicYMWazua6uzmw2h4SE4NcTAACu4yZhFO4ERVE+Pj4BAQFIojBimpqatm3bJhKJhEJhf39/enr6smXLuC4KAABcCMIoAAwXh8PxySefxMTEBAcHE0Jomj5+/Hh0dHR8fDzXpQEAgKtwhz6jAOCaurq6LBYLm0QJIQKBICwsrLKyktuqAADApSCMAsBwcTgcfD6fEGIymTo7OwkhFEXZ7Xau6wIAABeCMAoAw0WpVDocjp6eHkIIwzAMw2i12ujoaK7rAgAAF4I+owAwXPh8/tq1az/++GNPT0+apsvKysaPHz9x4kSu6wIAABeCMAoAwygmJubFF188e/asVqvNzMxEsygAAFwHYRQAhpe3t/fkyZODgoKQRAEA4L+5VZ9RhjAD1gGuqwAAAACAO+VWYbSyv7Koo4jrKgAAAADgTrnVZfpT7ac8PT25rgIAAAAA7pT7hNGK7gqtQSuhJQOWAblYznU5AAB3h2EYiqK4rgIAYKS5Txg9XHOYEMIQprSzdEboDK7LAQC4U2VlZQcPHmxvb/fx8Zk7d+6MGTOQSgFg7HCTPqP1/fWV3f+7xmBxezG3xYxxDoeD6xIARpPq6urPPvssIiJi6dKlSUlJR44cOXHiBNdFAQCMHDdpGT1UfWjo9pWuK1a7VcQXcVjP2FRTU7N3796WlhZPT8+MjIy5c+cKBG5yggEMn/z8/Pj4eKVSSQjx8fFJS0vLzc3NzMzkui4AgBHiDi2jbfq2ko6Sobs2h62iu4LDesamlpaWbdu2BQUFLVmyJD09/ezZswcPHuS6KIBRoLOz08fHhxCi0+kYhpFKpQaDwWazcV0XAIwyZrO5ubm5p6eHYRiua7k77tBwdajmEEMYQgjv/7J1SUdJcmAyp0WNOYWFhREREcHBwYQQLy+vadOmHTlyZPHixWgcBbg1lUrV3d0tk8kGBgakUqler5fL5UKhkOu6AGA0OXXq1IEDB8RisdlsHjdu3Nq1a9lvuaPCqG8Z7TZ2n289z96eP24+e6O4vZiNpzBihlp3BgYG7Ha7QCAQCoU6nY7rugBcXVZWVnV1dWNjo9lsbm9vP3/+fHZ2NtdFAcBoUlNTc+DAgZkzZ86aNWvBggWEkE8//ZTrou7CqA+jR2qPOBgHISROEZcemC4TyQghequ+vq+e69LGlpCQkJ6eHkKIwWCw2+0Wi4Wm6VH0tQyAK+Hh4U8++aTRaDx79mxbW9vq1avT0tK4LgoARpPi4mK1Ws1OtU5R1IQJE1paWvR6Pdd13anRHUYHLAOFzYXs7ezobIpQcX5x7N1re5HCCJg5c2ZLS0tNTY3ZbO7u7j558uSCBQv4fD7XdQGMAmq1etOmTY8//vjmzZuTk9HFCADujl6vF4vFhJDe3l6r1UoIEYlERqPx3vbmcDi6urra29tpmnZmlTc3usPod3Xf2Rw2QkiET0SsIpYQEu8fzz5V3IEJnkaUQqF45pln+Hz+2bNnGxoalixZMmfOHK6LAgAAcH8RERFtbW2EEKvV6nA49Hq9zWZTKBT3sKvW1tbXXnvtnXfe+eCDD377299WVlY6u9gbGMWDS0y0qaCxgL29WLOYvTHed7yIL7Lara361k5Dp9JLyV2BY45KpXr88ceTkpJiYmKkUinX5QCAu7FarTweD8MiAa4zffr0oqKis2fP8vn8jo6O9vb2VatW3cPFSavV+uGHH4aGhk6ZMsXhcOh0uk8++eSnP/2pv7//cJQ9ZBT/Sh+rP2aiTYQQlUyVFJjEPijkCeMUcWyzaGlnaZY6i8sSAe4GwzDs2C+uC4Ebs9vt6HnClY6Ojl27dtXX11MUNX78+JUrVw73pyPAKCISiTZv3nz27NmCggKVSrVy5crQ0NB72I9Wq2UYJjw8nF2/xt/f39/f/+rVq9OnT3d2yf9htH7sWe3WvIY89vai6EUU+ffSeUmBSWwYLekoQRiFUcFkMh06dOjcuXM0TYeFha1YseLe/o7AcDAajQcOHLhw4QJN09HR0Q888EBQUBDXRY0tJpPpvffeCwkJycnJIYRUVlZ+8MEHP/nJTzABFsAQkUiUkZEhlUrVavU9jx42Go0ikYgQYjKZLBaLn5+fSCQyGAxOrfQGRmuf0RNNJ/QWPSFE4alIDU699qnkoGQ2m1b1VBlt99h7F2Akff755zU1NXPnzs3JyfH29n7vvff6+vq4LgoIIYRhmB07djQ0NMydO3fx4sUikWjLli2jaIyqe6iurhYKhVFRURRFURQVFxdntVobGhq4rgvA3ahUqr6+PpvNRtM0TdMMw3R3d48bN264jzsqw6idsX9X9x17e0HUAh71H+9CJpKpfdWEEAfjKOss46A+gLvR19dXVVWVmpoqEokoigoPD/f39798+TLXdQEhhHR2djY1NU2ZMkUkEvF4vMjISKlUWlpaynVdY0t/f79EIiGEGI1Gk8lECJFIJP39/VzXBeBu/P39MzMzjx8/Xl9fr9VqT5w4ERYWFhsbO9zHHWWX6U0m06lTp45ePVpkK1IqleMCxk0PvUE/hqTApLq+OkJIcUdxWghm7AOX1tfX5+npSVGUzWazWCxSqVQul3d1dXFdFxBCSG9vr5eXF0VRVqvVZrN5eXnJZDL864wwpVLJtkZbLBYejyeRSPR6vVKJ8akAzrd48eLw8PDjx4/r9frs7OwpU6ZQFHX7l92f0RRGzWbzm2++yRfwqyRVNE1XVlame6cLeTfoM5QcmLy7cjchpKyzjHbQAt5oepsw1gQEBBgMBpqmbTab0WiUSqW9vb3jx4/nui4ghJCAgIDBwUGHw2Gz2Uwmk5eXV39//6RJk7iua2zRaDR+fn7nzp1jp6opLy+PiIgICwvjui4A9zRhwgR2geKEhISROeJoukx/+vRpgUDgHetNi2m5XB6mCms+2XzDGVmDZcHspE5m2lzdWz3ilQLcBZlMlpaWVlhY2NvbazAYysvLzWbz5MmTua4LCCFEoVDEx8cXFhb29/cbDIaysjKHw5GUlMR1XWMLn89/4oknkpKSamtrGxsb09PTH3nkkRForQGAkTGamgwbGhqCgoJkElmcV1yVsSpVmWpps3R3d99wZGuiMjG3PpcQUtxeHKeIG/FiAe7C8uXLFQpFXl5eb2/vtGnTHn74YXZVN3AFa9asKSgoyM/PHxwcnDZt2rp169j+izCSJBJJdna2RqMRCoVoEwVwM6MpjPr4+HR2doYKQyfxJ6Wp0qQe0nxr/s0mV08OSmbDaElnyYPkwZGtFODu8Pn8zMzMuLi4jo6OEbsscmsMw1y5cqWurk4ikcTFxY3AaMohNE1fvXpVp9P5+/trNBoej+MLOEKhMCsrKyEhoa+vbwQ68gMAjDWjKYxOnDjx/fffDw4OJoR48b0qSyvVavXNwqjGT+Mp9DTajD3GHu2Adpx85D5KAUY7dj6jmpoalUpls9lyc3OXLVs23JMeswYGBv7xj3/YbDZPT8/BwUFvb++nnnoKLZEwithstvPnzzc0NHh5eU2aNAlzBgPc1mgKo2q1+nvf+94333zT19cnEokSEhLWrFlzs415FC8xMPGs9iwhpLijGGEU4M5VVFTU1NTMmTOH7ZYXHR29b9++pKSkEVjl9euvv5bL5fHx8ezdixcvfvvtt8uXLx/u48J9qq+vz83N7ezsDAgIyMrKioyM5LoibthstrfffttsNgcFBel0utOnT69atQpdwAFubTSFUULIlClTJk6cePz48ZiYmNteN0xSJrFhtKSjJEeTMyIFArgDtn82RVHsinCenp5SqbS1tXW4x/gzDHP16tWsrH8vnBYdHV1eXo4w6uJqa2u3bt0aGxubkJDQ29u7devWDRs2aDQaruu6sZaWlrNnz+p0uoiIiPT0dA8PDyfu/Ny5cxaLZegywrhx47766qvk5GQs8wtwC6NpND1LIBD4+fndSQtNgjKBndSpUdfYZ8J6NgB3ysPDg52nore312g0EkJomhaLxSNzdIZhGIZpampibzt9/w6Ho6io6J///Oe//vWvyspKp+9/DDp48GBiYmJERIRcLo+IiEhKSjpw4ADXRd1YWVnZ22+/3dnZyefzi4qK3njjDfYMd5b6+nq2Lxm7eo1MJhMKhZ2dnU48hHvQ6XRFRUWFhYVarZbrWoB7oy+M3jmJQKLx0xBCGIYp7cSKKa6oo6Pj7NmzRUVFw7T6pc1mKy8vP336dE1NzXDEGvfQ1dVVXFxcVVVltVrZR8aPH9/W1jb0Id3a2kpRlEqlGu5KKIqKiYmprv73dGy1tbVDl+ydgmGYjz766ODBgxaLpb+//9NPPz106JAT9z82tba2BgQEEEIGBwcJIQEBAW1tbVwXdQMMw3zxxRfp6emxsbFhYWGpqakeHh4FBQVOPIRUKjWbzYSQnp4ei8VCCGE7QDvxEG7gypUrf/rTn/Ly8s6cOfP3v/997969XFcEHHPzCwfJQckV3RWEkJKOkszwTK7Lgf9w9OjR3NzcgIAAh8Oxa9eu1atXO3cu8Z6ennfffZdhGE9PT51Op1KpfvCDHwiFN1glYSzbt2/fqVOnfH19rVYrwzBPPvmkSqUKCQlZvnz53r17rVarQCDw9PRcv369SCQagXpWrlz5j3/8o6CgwGg01tfXe3t7L1y40In7r6ioaGpqmj17NtsdNjw8/NixY1OnTvXz83PiUcYaf39/vV7v7+/f09MjlUoHBgb8/f25LuoG+vv77Xa7j48PwzA2m00kEgUHB9fX1zvxEImJiWfPnh0atFRRUREYGOjj4+PEQ4x2ZrN5586daWlp7I+Fpun8/Py4uDiX7dcBI8Ddw2hg8hflXzAMU9FdYabNEgHG5LqK5ubmvLy8uXPnshFHr9fv2rVLo9HIZDJnHeLLL79UKpXsHziGYc6dO5efnz9//nxn7d8NlJaWnjt3bt68eWyHtqampo8//vjFF1+kKCo9PT0hIeHkyZN+fn4pKSkjFuLlcvlzzz1XUVFx6tSpOXPmOH1qp5aWFoVCQVEUTdM8Hk8kEvn4+LS1tSGM3o/MzMx9+/alpqYSQvR6/cWLF5cuXcp1UTfg6elps9nYJNrd3R0cHGw2m534N4cQEhUVtWTJkv379xuNRqFQGBoaum7dOifu3w20traKxeKhgC4QCFQqVU1NDcLoWObmYdTPwy9EFqId0NIOurSzNDU4leuK4H/V1dUFBgYONbbJZDK5XK7VauPinLNCAU3TdXV1ixcvZu9SFBUZGXnlyhWE0WtVVFREREQMDa0ICwurqqrq6+tjk5lUKg0PD/f19R3h5mSBQBAfH6/T6WJiYpy+czaOEEJ0Op1IJJLJZFarFVdR71NaWhpN04cOHWpoaAgPD8/Ozk5LS+O6qBsQi8Xx8fGXL19m+34Yjcbq6uq1a9c69ygzZsyYPHlyfn5+ZGSkRqPBSlHXGRoZaTAYTCaTQqFgGIbP53NdF3DJzcMoISQ5MFk7oCWEfF3xdaIyEY2jLoKiKLYTZ29vr1AolMlk7J8n5x6CEELTdHt7+0jO2T6K2Gw2tt2xs7PT29tbLBbzeLwbLrHrNmJiYvbv39/b28vebWxs5PF4ISEh3FY1Aurr6ysrKx0Oh0ajGY5ZEaZPnz59+vTvvvtu3rx5Tt+5E61atWrnzp1Hjhwxm81yuXzRokXO7ZTMkkgkKpUqICAASfS/BQcH22y23t5edkwk+yd60aJFXNcFXHL/MJoVmVXQWKC36ntNvbsrdz+YgNWYXEJkZOThw4eHRszo9XqDweDEyCgQCCIiImpra9VqNSGEYZi6urqUlBRn7d+VtbW1dXd3+/n5BQcH3/qzcPz48YcPH46IiGAHsPf09BBCFArFSFXKAYVC8cgjj3z55Zc6nY7P5yuVyg0bNoxMd1gOHT16NC8vLzg4mMfjnT59etKkSStXrhyOA7l+n2ypVPrkk09qtdqSkpK5c+diPYWRJxaL165du2PHDqFQaLfbaZrOyMiIioriui7gkvuHUS+h1+oJq7dd2kYIyW/InxI8JdovmuuigIwbNy4rK+vo0aMikYiiKKvVunr1aud23lq9evWWLVtaW1tNJlNNTU1gYOCcOXOcuH8XZLPZ2JWTvL29BwYGQkND169ff4uP28mTJ5eUlOTn51MUJRKJBgcHH3vsMc6X3xxuEyZM+PnPf3769Glvb+/ExES3f7/d3d3Hjh2bM2cOm7ljYmKOHTs2efLk8PBwrkvjjLe3t1KpRBLlSmxs7EsvvXTu3Lmenp7MzMygoCCuKwKOuX8YJYSkhaQVtRYVdxQzhPmk+JNfZP5CyHf1r+9jAbve98mTJz09PadNm+b0AacKheLFF18sKSm5ePHi7Nmzx0LnrSNHjnR1dc2fP5/tBXHx4sUDBw5873vfu9n2PB5vw4YNlZWVBQUFarV6aHyr2xMKhYGBgTKZzO2TKCFEq9X6+vqKRCK2Jwyfz1coFE1NTWM5jALnZDIZu0QCkiiHHA5HX18fRVG+vr7cfj6OiTBKCHk48eGqnioTbeowdByuPbx0vCuO9ByDAgMDk5KSPD09hykDiUSixMREmqaHe+kgF1FcXJyYmMj+TaEoasKECYWFhbcIo+xmcXFxVqs1PDx8jCTRsUYkEtntdkLI4OCg3W739fW12+1oFAQY4xoaGnbu3GkwGBiG8fb2fvjhhzkcXOH+rQIsH4nPA7EPsLcPVh9s1jVzWw/AcLBareyg1JaWFkIIn89nJ7Lhui7gUnh4uMFg6O7uZu/qdLre3t4xu3Y8uJmBgYGjR49+9tlnubm5er2e63JGDb1e/+GHH4aHh8+bN2/+/PlBQUEffvihyWTiqp6x0jJKCJkVMet86/ma3hoH4/is9LMXZrzAo8ZKFucc7aBLekvqmXqxTmyymSx2i4W2mGmz2W7Wtmk9xB5hnWFSkVQmknlLvGUimVQklYvl3hJvIQ8dKu7C+PHjGxoa4uPj2aUIGxoaoqOj3b5zAtyal5fXY489tmPHDnZdA4FAsHr1ateclJ5lMBja2tqEQmFISAiWdHcpDofj8uXLDQ0Nnp6eSUlJ7MKnHOro6Hj77bf9/f19fHzY7u8//vGP3XsIprPU1tZKpdKhf8GwsDCtVtvQ0OCs2RXv1hj6PacItS5p3W8Lfks76Pr++mP1x+ZFuvQUJJwzm83FxcU9PT0BAQHJycn3POKYYZgdJTsONh707PL874uDukGdwCxop9v/+4USgWTJ+CVz1XP5FKaguyNLliz529/+dvr0aZPJ1N7ebjKZNm/ezHVRcO8YhqmsrGxra/Py8powYYJUKr23/Wg0mp/97GdFRUUWi2XatGkeHh7OrdOJzpw5s3fvXg8PD7vdLhQKH3vsMczL5iLsdvt7773X3d2tUqlaW1vz8/Odvmze3dqzZ09kZORQM391dfXevXs3bNhwb3szGo1tbW0SiSQoKMjt5z3V6/Xs3BeDg4MURXl5eQmFQnY5X06MoTBKCAmSBuVocvZc3UMI2Vu1d2LQRIUnvkLdWG9v71tvveXh4SGTyYqLi48cObJ58+Z7G+1+oPrAGe2Ze3ihmTbvurLrVPOpByc8GKuIvYc9jDVyufyFF164fPlyXl5eRkZGSkqKK8cOuDW73f7BBx+0trb6+flZrdZ9+/Y9+eST9zzqSCwWh4WFWa1WVz4ltFrtnj17MjIy2GUImpubt2/f/tJLL6F9dIQZDIYTJ040NjZ6e3tPmzaNPesuXLjADn5ntwkPD9+1a1dCQgKHM6PV1dVlZWURQqxWq0gkCg0NPXny5L3tiv0WxC6K4eHhsX79evceWRUcHNzb28uuRsbj8RwOR39/v0ql4qqeMfcbvjB64YW2C9oBrYW2fFb62Y+n/pjrilzU119/HRISMrQ+W3l5+YEDBx588K5naT3Xcm5/9X72tsZXEx8cLxFIRHyRmC/2FHmK+eI2bZtAJPD09dRb9AOWAb1Vr7fo9VZ9j7FHb9UTQtr0bX8989dJqkmr4lf5eWDNxtsQi8VTp041m83p6eljYai4GyssLOzu7h6aj6ytre3TTz/92c9+douX6PX6w4cPV1ZW8ni8lJSUUTePZmVlZXBw8NCCWKGhoXV1dW1tbUNLvXPFbDb39/d7e3u7cpR3lsHBwTfeeEMmkwUGBur1+nfffXfNmjUTJ05saGhgr+rSNM3n82UymUgk6ujo4PBfx8vLy2KxCIXCtra28PBwi8Xi5eV1D/tpamravXt3ZmYme+7V19d/9NFHL7zwghu3j0ZGRkZFRZ04cYJdb6+7uzsxMZHDqxBjLozyKf66pHV/OvUnB+O40nXljPZM+rh0rotyOQzD1NbWzp07lxBit9v5fH5ERMSFCxfudj81vTUfF3/MDqAJl4Y/kfhEkPL675pindjT0/O/l8BxMI68hrx9V/eZaBMh5GLbxbLOsgVRC7KjskfLzFw2m42iKDTqwL2pqqpiW6QYhqEoSqVSlZSU6HQ6b2/vG25vs9neffddkUiUkpLicDhKS0ubm5s3btw4ijoNs+u5E0L6+vokEomHhwefz7dYLByWxDDMwYMHCwoKxGKxyWSaPn36smXL3DijEEKOHz8ul8snTpzI3lUqlV999VVycrKnpye7dFlvb69MJmO7UnD7bWfSpEnFxcVTp04lhNA0XVpaem/r0FZUVIwbN27oW5Bara6vr+/s7OSwpXC4URT16KOPnj9/vqCgQCAQLF26lNseF2PxYzLCJyJLnXW07igh5MvyL6P9onGx/jpshLLb7QKBQKvVhoeH0zR9t2urdBo6txRtoR00ISRYFpzjkyPg3cX5xqN4Weqs1ODUryu+PtNyhmEYq926v2r/uZZzK2JXjJOP85Z4i/ni2+7HTJv19EgPsezo6Ni1a1d9fT0hJDY2duXKley3T4A7x+fz2ZlB29vb/f39RSLRrZfwrqiosFqtqamp7N20tLRjx45ptVrnNlyVlZXl5+f39fWFhIQsWLDAuU0parX64sWLMTExdrvd4XAYjUaj0cjtKJmTJ0+eP39+7ty5YrGYpunTp097eHhkZ2dzWNJwa2hoYEMY2+jo7e1tt9t1Ol18fPypU6eGOorU1dXJZDJuR8ItXLhwYGDg22+/1ev13t7eKSkp7FX7u2U0GtnOBkPfggQCgdlsZp9taWmpr6/n8XgajSYgIMCZb4BTPB5v6tSpAQEBfD6f81mHx2IYJYQsi1l2qf1St7HbYDP8Kv9XC6MXLoxaKOK74pKAJpMpLy/v6tWrQqFw0qRJU6dOHZkv5UlJSVeuXGG/HLOjKJKSkoaeNZvNfX19crn8ZtdEDFbDO+feGbQOEkLkYvkzac+01rTeQxlysXz9xPUZ4Rmfl33epGsihHQaOt+78B77rJAnZAfdy0QyuUQu5ouNNqPBahi0Dhppo8FqMFgNVtra09PT4NmwNnGtp9DzHmq4W0aj8b333gsJCcnJySGEVFRUbNu27dlnn3X9lRLBpUyYMOHgwYNDaa+urk6pVLJjmPr7+48cOVJdXS2RSNLS0qZPn87n87u6uthe3WazmcfjiUQimUzW3d3txDBaVFT09ddfT5gwISIiorOz8x//+MczzzzjxLCYkJBQVFR0/PhxDw8PHo/X09OzfPnyofYqTpw9ezYpKYldRV0gEEyaNOncuXPuHUa9vb2NRiMhpKenR6FQCIVCmqbZ2aAXL1588OBBq9UqFAp9fX3Xr1/PbV8ggUDw0EMPZWdnHzlyJDs7+2YXDW4rIiKitLRUo9Gw85AYDAaTycT2GT1y5EheXp5SqXQ4HPv27Vu+fHl6Oq6mOt8YDaMivmhd0ro3z77JMIzNYdtftf9U06nvxX9vimqKS13Soml6y5YtDodDrVbbbLajR482NzevWbNmBA69ZMmSjz76KDc312g0VlVVqdXqBQsWEEIYhjl8+PDx48fZi1aTJ09euXLldTGLdtDbLmzrMHQQQoQ84Y9Sf+Tv4d9K7iWMsqJ8o16e+fKJphN7ru4xWA1Dj9scth5TT4+p57Z7KGotqu2t3ZCyYbz/sM9+X11dLRKJhpZajo+PLygoaGpqwuLLcFemTJlSX19/9OhR9mKoSCTauHEjIcRoNL799tu+vr5JSUkWi+XYsWNdXV0rV6709/c3GAzsBgKBQCQSGQwG5zbJHzhwYOrUqexHvlQqZRgmNzd33bp1zto/RVHr168vKysrKChQKBQPPfQQ50PpBwYG2H6inZ2d7Aqier2e7TjBbWHDZ/LkyTt27GCbAB0Ox4ULFxITE9mGQ3ZY5PHjx8PCwuLj412ku4KPj09QUNA9J1FCSHJyMnvBmu0Z0tXV9cADD3h4eGi12vz8/Llz57KfcUajcc+ePbGxsVgfxOnGaBglhMQqYl+Y/sIX5V809DcQQvrMfR9c/CDPN2/NhDXhPq6ySl5paanJZJoxYwZ7NyAg4Lvvvps7d+4IXCnw8PDYtGlTY2NjXl7eggULhvp0njlz5syZM3PmzGEvWp0/f/7QoUPLli0beiHDMJ9XfF7VU0UIoQi1IWWD2kd9//XwKN6s8FlTgqfsu7qvSdeks+gGLANWu/W2Lxy6lN9n7nvj9BsLohYsi1l2Vx0G7lZfXx/76WUwGPh8vkQi8fT07O/vH74jgluiKGr16tUZGRl5eXmxsbGJiYnsJ+LFixclEklCQgIhRCaTzZgx47vvvps3b15sbOz+/fsrKyv9/f0dDselS5f8/f1vG+Z6enrY6/vh4eG3/r5kNpsHBwe9vb3ZpiOpVOrv719ZnwqMCQAAIABJREFUWenEt0wIoSgqMTFRIBD4+/srlUrn7vweREREtLS0REdHm0wmhmFaW1vDwsLcOIkSQuLi4pYsWbJ//372mnVKSsq1q7hJpdKwsLDg4GAXSaJOwePxnnjiieLi4oKCgsDAwNWrV7PXE+rr6wMCAoZaWzw9Pb29vZubmxFGnW7shlFCSKRv5EszXzrdfHp35W6dRUcIqe2r/cPJP0wPnf5A7ANysZzrAklbWxt70lssFj6fLxAIvL29Ozs7AwICdDrdgQMHSktLGYZJSEhYunTp/XwvvCGKokJDQ6Oioq4dXXT+/PkJEyZce9GqoKDg2jB6qutUsbmY/e1dEbdiksqZfaK9hF4PJvx7RL+FtgxYBwYsA4PWQZ1ZZ6bNXiIvqUjqKfD0Enl5iby8hF52m/3Lgi+LSbHeomcI823tt5U9lRsmbgiSDte0HUqlUqfTkf9bD0ksFut0OnfqaQQjSaVSxcTEaDSaoU9EdrInQojJZBIKhQKBQCqVdnV1RUVFbdq0ac+ePbm5uUKhcMaMGTk5ObdODCUlJTt37mQvxR47diwhIWHNmjU3S1ps66zJZBKJRP39/VKpdGBgwO1P7JycnLfeestoNJrNZr1e39LSsmnTJq6LGnbTp09PS0vLzc1NSUlxha8EI4CdgEIkEimVyqGzmsfjsQNwe3t7BQKBXC4nhLhTCncdTgijNE2/8847p06dCgkJefHFF0fX6DOKUNNDp09STTpYfTC3Ppd20AxhTjWfutB2YbFmcZY6a1ib0G7L19f3ypUrhJDBwUGxWCyVSk0mk7e3t81m27p1q0gkmjNnDkVRlZWV77///p30SrQzdovjvoam6vV6tVpNCGEzsUgkslqtNE1bHJaK7orSztKCjgI2Fs8Mm7kwauH9HOu2xAJxgCAgwPNWH4d2YtfINMtTlm8v3l7eWU4Iaexv/N2J362KX5XilzIcVcXExPj4+Jw/f55dCKSsrEytVnM+Nw24jYCAAHa518HBQS8vLz6fbzQafX19CSH+/v4bNmyYOXOmp6fnbdtELRbLF198kZ6ezv7CMgyTl5d35cqVCRMm3Owls2fPPnXqFDvqlm1SXb9+vRPfmiugafraGTACAwOfe+65EydOFBYWRkVFrVmz5j7zt91u5/F4rt+2KhAI/Pz8uO2wy7moqKj9+/cPLZKp0+n0ev3I/DF3MI6a3pqLbRe/a/zu5MmTIr5IyBMK+cKh//N5fLvDbqJNVrvVareaaJPZZrY6rM2tzUFtQSoflb+nv5+Hn6/E18/Dj/1PIpAwDMNOUMOyM/Y+Sx+Px6N0FO2gLXaL2WamGdpMm5tbmxO8EkbgnbKckLReeeWV/Pz8X/ziF4cOHcrKyiotLR113xskAsnKuJUZ4Rm7ruy63H6ZEGKmzV9XfH2y6eSq+FVJgUm33cMwiY+PP3jwoFar9fDwYBimtLTU19dXpVLV1taaTKYpU6awmyUmJp48ebK2tjY29lYzw5d3lX9c9HFDV0OaKW2CckKCMmGcbNzd/k0MDw9vaWmJjY21WCwOxlGuLe8L6Hv97OsN/Q0OxjG0WZwi7uHEh+/hLQ8TuVj+/1L/37GGY99UfmOz26x262elnxV5Fy2IWSAXy2UimUwsc9YXDz6fv3HjxmPHjp08eVIkEmVmZmZkZLj+Zw+MFsnJybm5uU1NTRKJxGazlZeXR0dHs2GUdYcnW1tbm1gsHkqiFEUFBwfX1tbeIoxmZWXx+fxvv/22tbU1Njb2oYceiomJuf935AoYhjlx4sR3331nMBj8/f1zcnKSk5PZp3x9fZctW+bj4zNjxoz7+XRra2v75ptv6urqeDze5MmTc3Jy7nlJLfj/7N15eBT3fT/w78zO3veuVqv7REIHAsQN5haHTUJIjI1Tp7EbuzEkjeMmOM2TPk/69OnTX5OmtWvnaVI7cXBpsGOc2Nh1bMJ9CxCnhG4JgY7VStrV3vfM7vz+GLpWxCWE0Eji/Xp4bGk0O/uRdnfmM9/rcz94nndGnQqfQpPQROKRoVeuDn+HQ+LQcp+XdylaUbT7+G6GYSiKisfj69avaw20kiGFilRSlVlpNilNY3IFSfCJlsGWC70XLvddFlbaHogOSLz38K6LxCOuiCvgCrS52kayv8/no2n65rdiIBAoLn3gUyyS7vdvFwwG33zzzePHj8+aNeuLX/xiUVHRZ599tnHjxjEJbpxZVJZvzftWk7Pp/Yb3e/29hJCB4MAvzv2iPLX8ydIn07UitPjq9fpvfvOb77//fltbm9AnvnnzZolEMjg4KExjj0QiPM8rlUq1Wj04eNt5PAPBgd83/r6uv07IINtcbW2uto+aP9LJdTNSZ5RbyktTStWyG/PiecIHYoFANBBkg/6o/4r3CtVFRblonI/HE/HE9MThPx6uDlSH2JDb7nYFXKWlpR3ujqFPl6HJ2Dpv60Sr4UlRVFV+VWlK6VsX37L5bYSQemd9i7cluYOSUerkOq1cq5VrS8wlC7MWKplRLnCtUCg2bNgwffp0oSjI2PwCE1sikTh//vylS5dYli0tLV26dKkwlgPGnMlkeuGFFz788MMrV65oNJply5Zt2LBhFHc7DMMIXZChUCgYDFosFqECp/DTeDze09MTCoWsVmtyFhRN06tXr37kkUdqamqWLVt2P79FLBY7e/ZsZ2enRqOZN2+e6BOVhEx0/vz5Wq12cHDwvffek0qlZWVlY3V8YfX43NzcDRs2xOPxurq6//mf/9m2bdudZ6O73e729naWZfPy8kayakEoFGpsbPT5fGlpaSUlJSh7MRSX4FoGWy73Xa7rr2vvadf16W6uHSWM+B++eOpc0tPXI5FIUlNTj/iOHLlwRNgsjNzgeV6j0ahVar1Cb1aaU1QpZpU5RZViUBho6k5/f5lExlCf52DeqPdS36Xa/tqhk3TFNZJZGWPlfpPR5uZmiqKEO0iKopYuXVpTUzNJk1FBaUrpj5f/+FjnsU9aPxHeEw0DDc2O5pV5K79Y/MXxWRtoqJycnJdffrm2ttZoNObk5AgbU1JS/H4/ISQajQrJqN/vFzqFh4nGo3vb9h7oOCCs9zmML+qr7q6u7q6mKTpdk87xXCAWGPpJ4Hm+r6+vjqob+ij1LHVfX19fX19KSkpFfoUwWYem6DxD3ozUGbyBXzF7xajTOEJIJBI5fPjwlStX4vH4jBkz1qxZM4ZdRRnajB8t/dGe5j2Hrx8e9qMwFw5zYWERgEv2Sx80fTA/Y/6y3GVjMgFryvvwww/r6+uLiookEsn58+fr6+u/853v3LUZKRALXPVfjffEg2wwEAsk//kivmtd16qp6hRVSvKfWWk2Ko13Pr8/JHJycv72b/+2rq4uPT191L3GVquVENLX1yeMhIvFYr29vcKiRU6nc8eOHcFgUC6X+/3+pUuXCuuUJd1nKYdoNPr666/zPG+1Wu12+y9+8YstW7ZUVj6QYTMjdPjwYSETJYSYzeby8vITJ06MYTJaX1+v0WiEKuo0Tc+ZM+fw4cP9/f13GNhWW1v73nvvmUwmiUTyySefCHcdd3iK3t7eN954Q61WKxSKEydOmM3mrVu3CncX165dO3LkiMPhSE9Pr6qqurnIyBQWYkOXHZdr+2sbHA0RLjKKI8jlcqPRKCyXltzocDiuXbsmpK2RSCQrK4vP4D0Rz1X31VsehOd5u93e19fHsqxWq83Jyblru7hBYahMq4xJYssXLWcTLMdzsXiMS3BC21AsHhNqGcoZuUwiU0lVMlomk8haG1vN6eaEPOEKu5L/3BH3YGiQTbAURQ29OktoCaNgKIpK06cxFCPUR5RKpEpG6XV7x7O+zP0mo319fUOXDklJSbHb7bfbORQKPfPMM7dLLNLT0994442hW4LB4C1v94WaHIFAYNh2iqJYlr15eywWI4TcfA/Esmwikbi5/YZl2RnqGeULyv/Y9sdqW3WCT7CE/VPrn05eP7kma83KgpXDLofJuaU3h+r3+29Zzz0YDCoUipsv1TRNx2Kxob9CiA0FYoEBbmDQO9h5tTPBJ4RRHT2KnrdPv200GSWUJNYc08g0hhRD8oEsy3Ic1+Bp+LjtY2FuFiGEItS81Hll2WW0kW4abGp2Nfuj/uSv0BZsu+WQU4lEwrLs0C1CMRilUqnX6/UKfam5tNRcWmIuETL19mB7NBKlyPAXjqbpW75qhBCO45LbeZ5/++23fT6fUIm0qampqalp69atyYuf8KvdXJSP47hYLHbzu4tlWalUOux5N+RuKNAUHGw5SMmpABvwR/0BNpDsrBEewrLs0Y6jRzuOZumyHsl8ZG7a3EQsIZPJbr4MRyIRiURy81+P5/mhv9rQkG5ZuUSo2DTs1W9zt9XZ6672XT0aOiqTyJSMUiaRySQyBaOQ0bJYNCaRSSLxSIgNhblwmA0LKXWPvaf6eHWaJi1dk25VW9M16RqphhASCARUKtXQ9hIuwYW4kDPm9Pf5OSfnj/p9sRtFWX0xX+9gb6om9cmKJ4tNf9ZfE41GKYpKfqacTufZs2dXrVoljPevrKw8derUuXPnhBnfhJBYLDb0V4vz8UZnY429pq6vzuPz6L3D597xPO+P+5sHhs/UllASNa3OMGSkKFNSVCnCf80Ks5yR3+4zJSxnffOrRlHULV+dWCzG8/wtTws8z9+8fzwej0ajN7/xEomEw+G4+QwmHOSWpwVhMSbhfPVnv7VEEolEbj4UwzC3POORP/9MDd047Fd44okndu3aJVSmZll22bJlVqs1EAjs2LFDo9HMmjWL4zhCyMmTJ81mc/LVvOVnSiAkrzeHGgwGhaVDhW+PHz/Ocdy8efNYlpVIJBaL5Xe/+11hYeHQd+awM6EgkUjE4/GRf6aE6k3C/myCZeOsMMbOH/J3R7qprhtxxuPxq76rmfHMfm9/NBqVyWQeytPa21p2tYwQEmbDhCLXQtfCbWGZRCb0xtIUrWAU5P/eYDE+Jgzdi8aj0Xg0Fo/12Ht0Pl3yjVTXUOehPAO2gXAsLJfIGQnTzrS/VfNWMhllCENTdPKNGo1GP/7446KiIp/CRxM6JStlz/E9pgzTjGmfvwrCRMmknTt35ufnZ2RkCDVKampq9u/fv2LFitbW1nfffbe4uDgrK8vn87322mvPP/+80BTd1dV1+PDhrq4uq9W6YsWKYQO9hi78PhRFUbd8daLRKE3TQ8+E0Xi0L9hX31sf4kJnvGcIISE2xBM+wkUSfMLtd8diMavbylCMkFQxNKNklDShJQlJqj7VIDfoFXoVo0q++uFw+ObFrXmeVygUgUCA53lfzOeOuIX0yx1xX+657Ovz3XQ5IhqZJkOdIZVKFRLF0KuVm3PrNXqNavjV3CvxSiSS5FU+HA5fb7u+qGCRVCoNxUNe1tvW1aZWq5PngUQiMaxERXd39+DgoNlspmk6EonU19eXl5cn37HCxUL40xkVxtnW2bOts/P0eRShGoINZsZ818/UDQmilqn1jF6tUGcpssjng3dIOBxmGObm61RfXx9N0zdPUxsYGAgGg7f8mN+rYRedW6KEbppRO3LkyF/+5V8Ko+kJId/5zncYhnnttdduuXNBQcGPf/zj292TqVSqpUuXDt1yu0zuXl27dk0ikSSbFZNsNlswGCwuHj4qYnBwsLe3t6KighDS4+t5v+H9lsEWQgjHcW63e9OcTc/Oenbo/izLnj17dljwghMnTgjrUQ/bLsxJH3YB63B31NhqArGAkAoITURxPn7LX4rjuJ6eHpfLxfO8yWTKysqSSqVGhTFNk2bVWJkoU9Nd42N8yf0LjYXDVq3iCd/l7WoYaKgfqG9ztjkHncm3o1qq1sg0GplGmJwuoSTCKZimaKVUSQiRS+QMzeQackcx6vTOrl+/vmPHjlWrVvn9/ng8bjQaT5w4sXnz5mQTRX9//+Dg4M0tFl6vt6OjY+SNKzzPHzhwQFg8VRCI3chK95/e71A67KE/u62SS+TWuHVV2aqC1IIUVcrQ4UENDQ0Wi2Xkc05tNls4HJ42bdotf5rgE9c81xodjY2OxmEjcYfvmUg4HA6hfeuu1FJ1hi7Db/dnZmXGSExoifRFfSNsKihPLf9KyVeydTeGHAj1SJJFO+rr6//4xz8uWrQoEokI9/0NDQ0FBQWPPfbYsOPY/Lbq7uqzPWeF4VCj0NfXl5qaOuzUppProq7orIJZRalFOfqcTF2mlL5xzr1y5UpmZubIl9vs7OwUVvYd4f5ut7uzszNZOzEpHA6fO3du+fLlw7YLYxNv3v7gxOKxZBLGxj+/sQxxIUJINBq12Wwsy1qtVmHtjmAw+Ktf/eqRRx6JxWIOjyMlJcVmszFSZuWalckDCs0zES4i/AuxoWg8GuEibJzN0GZMM02bZpqWa8hNjtU5ffp0ZWVl8tK7Y8cOmUyWlZU1ODio0+mkUumhQ4defPHFUU/cttlsoVBIuIONxqM2n63H19Pt6+7x9bjCLmF6x50vdpcuXTIYDMncMRAIJBKJO4/CFwwMDJhMprs2FTscDpvNNvQXtNlsFRUVyb+J0NmVvOQJJzSr1cpxXDwel8vlLpfLaDTmZedZ1JZUdaoirvA5fckIo9Horl275s+fL1RLMplMbrfb7/d/8Ytf/MMf/mCxWAwGg8PhSE1N7e/vZ1l2w4YNAwMDn376aVZWFsuycrm8q6trybIlWTk3xksk/2JxPh7looQQnvBh9sbcF6lEqpVphYIjWrlWL9dr5dq+zj4iI3F13Oa32Xw2m982GB4cRY4Ri8V8Pl+yr08qkerleoPCoJaoHb0OYQGyBJ9InrtCbCjOxz0RjyvsumUfYFKqOnV22uyZqTMLTYX308dy5cqVTz/9dNGiRT6fj+M4k8l04dKFktklhRWFrrBrMDx4rf9a72CvsGw+ISQej3/22WfFxcU8z4dCIZ1O19fXp9FrkoMyOY6z99rXVq6dkz4nV587kqvqmTNnZs2adXO7zO00NTWZTKYRXi+EkFiWHfnx79P9toxmZ2c7HI5gMCjcrHR2dq5YseJ2O0skkqVLlwrni8kiS5f1/cXfv2i/+IfGP/T7+wkhNbaax0sf18rGIEse5kDHgYv2iyPcmWGYvLy8vLy8oRuFe8EmZ1MoFIrFYsKlxaAwPF76+IKMBcPe3xShcvW5ufrcDUUbBn2Dxy8eXzxvsVqq1sg1N7drjhuHw6HT6YRWN+EsptPpHA7HODy1kH8TQpwm55w5c+xh+/HO4+ft54UTcTQevei82H65XSaTUYQyKU2p6lSL2mJVW31en0fqsSVsXIKLcJEoF+USXIgNcQlOzsjTNelWjdWqtgrtKDfjEpwz5OwP9vcH+js8Hc2O5qGzHcdKkA22DbYNeAZ66J5R9LE2DDQ0DjTOz5y/afqmm8vn6nQ6oQVFoVAk+62GLsXnDrsv91+u7q4WymglURSVp89L1aSqperkLZBWrlVL1TKJzB1xO0POof98UR+5FV/U5wg5grZgTX8NIUQYdpKtz87R54QD4bgvbo/bhepcITYUZIPC1zKJzKK2WFSWFFWKRW0xKAw3v/PDXNgT9vhjfk/EwyZYFaNSyVQqqUrJKFVS1ViN2+EJ7414fVFfkA0SQsJsONl6JGR+wkbhzoRLcDfGclEkFAsN3RLmwjzh44l4hIskc9CRBuG+8f9IJHKFuWLvsRNhYlMvFQwFE4lET13PSA7jCDlq+2sJITKJLN+QX2QummaaxvJ/1rui1WqFVj2z2cwTXmjaj9ARZ8jJJtgYF+MJH2SDwsj1IBsMxoLJL3jCKxmlglEk/6mkqoAn4A64D/sO9/h6HEEHT+45AcrOzu7o6DCZTDKZLBKJeDyeMeyjJ4SYTCabzSZUdU8kEm6322Aw3Lmwu3ACZBgm+YGlKIpNsL3+3l5/byQS8fl8jXyj8KN4PN5Ct4Qd//dyO0goFGJZNtoYrfHX5BhziJNEY1G5Q84luIHBgUhTpLm5mTbRQToYYAMauSZqjb5z7p3Z7PDbqpHzer0Mw9yuLN+osXFW+PhzHOdyu3q77q1+CkWoPEPerLRZs9Nmp2vGZu5H8mZYGOJCCKF4yig3lqTcuDdwGB0DAwPJuYAOh8PzJ09VblU8Hg+HwxqNxi6x+3y+rUu3CjtEo9ELFy4sKV0yJuFNRvebjE6bNq28vPydd9554YUXurq6jh49+vrrr49JZBPKnPQ5FdaKfzn6L263m0twp7pOPTptjMvBxeKxBkfDzdvlErlWrtXJdXKJXMEoJLREySgZmpFJZEKnRpgN9wX6+gJ9jpBj2E0hQzNV+VVfKP7CXWu4q6SqTFXmg1t6c+RMJpNQiS55mh7zKjIjlGfIyzPkPVn+5Nmes8c7jwtzngQ84YXKT03OJiKUM7Yp7noHaVQarWprmiaNiTBcjLsUu9QX6BsIDjhDzts1f9IUnaPPKbOUFRoLhbwkzIWjXDQaj0a5aCAauMpeLc8vV0lVSqkymSEpGaWMkfUH+u0Bu91vtwfsfYG+27WA0hStkWnUUrVWrjUoDMl2Dp1cp5PrGJo5dO1QdXd1gk/whK+x1Vy0X1yeu7xcWq6Vf34/lpGRodFompqaSkpKKIqy9dq63d1hU/jDpg+7vF3dvm6hMOyf/TUUxsXZixdnLU5V37YxLFWdOt38Z5O12QT76ZFPc0tzXVGXI+hwhByOoGMwPDjsnZ/gEza/zea3nek543K51L3qkcymYmgmRZVCR2gJJZH1yrxRrzfiZRPsnR8lSUiigWiaK40QkpwFqGSUHMvZbLaWiy1KRqmUKoXPr/CvPdBOOklyIJc74vZEPHdu0RlPCoVCGFQjl8uFO9hgMDjyBpWkWDzWMtgidCs5BhzprnSO3PgdvTFvS1dLWixNSLNcLhdtov/fmf836piDwSDHcXdea1k4bd4Y6MLIkp2/N6SQafpp7e3tIW/IqreuW7ouWXVdJVMlk1uhr58MaZlTBVXppnSD2pAcbCdn5FJaKnQi/VmQxcEL5y7YumyUlCqqKJo1a9bQ28Lm9mZCkWQPXjQafa/lvSJlkUajYROsM+y81H0pbdptT9ESiUSr1fp8vmR65PP5MjIyhBt7YWSF8CngOE44u4ZCIaH1URhvI5fLhRmxY9jZJaEkVo01U5tpUpqUUiVN0UpGSVGUSqqiCCX8icJsmI2zsURMaFmPcBGP39Pd161L0XmjXnfYfU8DPbVy7Y2VjBQmYW2jAmOBXj7Gi3BnZ2f7fL5k5200GnU4HMPahoYyGo3RaFR4FYS+fpfLJfqkvQllDFYieO2115588sndu3c3NDRs375dGKA99Uhp6fLs5bWdtYSQ453H109bP7bNh/UD9UILXKo69avlX9XJdUIr0chHECf4hDPkFBLTFluLL+D75opv3uFKPzHl5uaq1eq6urqysjKapltbW3meF7E1XckoV+atXJm3ssPd8f6p94mG+BN+V9h1h97z23GH3e6wu9nZHAwG4/F48ppxM7PKXGYpK00pLTGXJPObm7Esey50bkn5rW+mrWrr0FXJBkODfYG+YxeOlRaVmrQm4d2lkWrucHzB12d+fU3+mo9bP75kv0QI4RLc4WuH/xT6U0VKRar3/95dFJEskJw8f/KjAx9F6SirZHPLc3e37b75aFJaWpleuSR7SUlKySg+QVJaapaZK1Irhl7FecK7w+5DZw7JU+WOmKPL2zUQHBjFC8QluL5AnzDyTMuOtOsjxIYCbIAJMYQQZ8j5+dE4zhFwhHtv0TBpt9vTE+O3OoewKqGSUUolUjnzeVKuZJS3ewnMleaamhpGy6ikKr/fX6AuWFm5MvlWEQ4oZ+RD2yaFbJsQ0uHuaHO1tbvah/41hMHuyQFLer0+Jyenq6uLYRiO49Rq9e1GrYwCTdFpmrQsXVaWLitbl21VW5VSpYJRPKCpb2epsxUVFSOcZPlo6S1aMex2+3vvvdfW1sbzfKgktGXLFmEg6bSvTtu1a1dCn5DSUtmg7Eerf7Ru3boQGxJuw672Xb3ec72o8PNz45LUJQcOHIj3xYXBx0sylyxfspyiqKxI1pUrV4qLi4Uazq3dresXrS8oKODbeDWjTt7qh8NhnVS3uexGsaXkX0xCSYS3TTJ9JITE4jFfxOeL+fxRvy/q80V9/pg/Gohq5JrpqdMztZlZuqwMbUaaJm0UCx55PJ5r0mvJMVdRLuqJerwRb5+nr76lvmJGBRkyZpcQIqS2erk+RZ2SHJ/zQOl0uieeeOL3v/+90WikKGpwcPCxxx67w3IHDMOsWLHi1KlTs2fPVqlUvb29vb29W7ZsEX4ai8Vqa2svXbpkNBqnT5/+cK6BMAbJ6IoVK65evVpXV5eTkzO1V7GptFYKN9OD4cH6gfqK1IpRH0qYJDF0S7KDfkHmgvLU267zdwc0RaeqU1PVqTOtMytUFV6vd9JlooQQhmGef/75//3f/92/f38ikSgtLd26deudO7PGR4GxYH3m+sLCQp1OxyW4wfDgQHBA+HclfkWlVqUYUySURGh3YWhGJVUxNBOIBfqD/UIL6O2avihCmVSmVFWqVWPN0GaUpJRY1ffcCnVXZpXZrDIHTIGZmTPvdRhQujZ929xtHe6OD5s/bBtsI4RE49ELAxc0oT8b5q8p1igKFDzP3zxGXskocw258zLmzcuYdz8rLdySMGoiT5NXllcmdBFGuWiPv6fL29Xt7b4QvaDX6c06s1qqFjrW1bIbX4TZsNC26gw5nWFncj7fUHJGblAYdHKdXq6XSWQhNiTMFQvFQmEuHGJDY/VbCCPwNDINRSiFVEETWs7Ik8O1CSFCwxL5vxY+4VFCO1Nyi4JR0ISmaVpIPaW0dNQDCVxLXXV1dT6fLycnZ+bMmSO/QGZoM5bmLCWEeCKedld7u6u9zdU20D8wbLe0tDSLxRIOh2VSmUFjIP+X/TA0I2fkhCdCBbUbNdV+cmBdAAAgAElEQVSkKqH9Xi1T04QOcaEIG4nGo2EuHOEiYTbc6+hNsIm5xXOztFmZukxxi5Xck3A4/Otf/zorK0sYv+5yuX7961//3d/9nUKhKCsr+9GPftTe3s5xXG5urjDeVCVV5Rpycw25+fL8drZ9YenCoUf72pyvXb16NRAIWK3WZMPbl6d/+YjxyIEDB1ieZRjmexu+J5SYnp6Y/s4775SZy8xms9/vP1d3btvabcsKR79iV2trq1qtHvOp+nJGbmWsVrU1W5Utc8gW5Swa2+OPzpw5cwoKCq5evZpIJPLy8u66qMWjjz6q0WhOnjwZCARyc3O/9a1vCQ8ZHBz8xS9+QdN0KBTavXu30Wjctm3bQ7gu3th8YoX6yGNyqIlMKpHONM68Sq4SQo5dPza6ZPTKlSsfffSRMDhp9erV69atk0qlbJy9MnBF2KEyTcz1TSYCg8HwzDPPJBIJMmRozp1FIpHGxsa2traUlJRxuCNiaMaqtiZTxpnUzLtOYErwicHwoNB13tzTHI6EKwoqrGprqjrVqraO5woao1ZgLHh58ct1/XV7mve0+FtuuU+ywdKgMGTrsrP12dm67Bx9zs3DTB8oOSMvNBYWGgsJIZV05QgnMEW4iCPouNJxhYtzpfmlOrnOoDAMbUq8pV5Hb+u11hkzZvCEF0ZwEmGZsEi47kpd+axyYZUDYX5PhIuEYqEmX9Oc7DnJsihCiZSJ9h4wmUwrV668nyMYFAbh9oMQclxyvLKyUqsa+6H2ApvOFgqFirIn04QEQUdHB8MwBQUFHo+HEFJQUNDX19fR0SGMWNVqtfe04hXDMDeXIaBpuqqqavXq1aFQaOiAzvLy8ieffPKzzz5zuVxqtXrt2rW3nIYLt2MwGObOnTvCnSUSyYoVK26eVPP+++9nZGTk5+f39vZmZ2efP3/+4MGDw1ZSexhMmtvHCaLSVNnh6uAJXz9Q7ww57/US29HR8e67786bN09oYLt48SLHcZs2bWp0NgrDYqwaa5YO40gIGXEaSgjp6en59a9/LSzs1dLSUl5e/hd/8RcTreIRTdEWlcWissxInVEmL7vDbPoJbqZ1ZoW14pPzn0QT0eRcUUJIsgVOySiz9dkPYobfg6ZgFNn67IQpkUgk8s0jnU2vZJQGmeHGqWBIK2Q4HPar/UIqNhTP8ydCJ5bPGr/Z9BOBlJaOT//ppOPz+YSen2SaqFAofL5bT9S7HxRF3Ty1qLKysrKyclgFVBg3HMddu3bt0UcfTQ7VLSgoaGpqQjIKd2GUGctTy+sH6nnCH+88/njp4/f08NOnTxcVFZnN5t7eXrlcvnjx4gMHDnzxi1+80HtB2GFu+khvs0DA8/xvf/vboqIii8XidrutVuvx48cvXLiQrJUKY44iVIW5gqbp3Jzcu+8NALdntVrdbndycAvP8x6PZxTTxe4HMlGxUBRFUZSwIqkwrILn+Yfz5XgYx8nepxW5N5rZT3WfGrpo30g4nU5h8p3BYJBIJAzD0DTt8Xnq+m+UOJqTPmdso53yPB5PIBBIjo6iKCo3N7e5efhi6QDjzOv19vf3h8Njv0oXTCX5+fl5eXnV1dV2u91ut586dermNftgqpJIJEVFRa2trcK3PM+3t7eP7Zpik8XDmIDfpwprhVlpHgwPBmKBi30XF2YuvPtj/k9WVlZ/f7/FYhGmXgYCAZqme6I9wlqAKaqU5KLiMELJeWByuXxor/HDIBwOu1yuWCx2c3UxEFE4HP7d737X1NQUCATOnz9fVVU1tLYCTBkej+fYsWMnT56sr69ftWrV6FaSoSjq2Wefra6ubmhoIIQsX758yZIlE22UETw4TzzxxJtvvnnixAmVSuXxeLKyslatWiV2UCJAMnrPKEIty132UfNHhJBj14/dUzK6cuXK//iP/6BpOj093e/3NzU1bdy48XL/ZeGn6KMfBaPRqFKp7Ha7sBgKz/OdnZ03F/6ZYliW3bNnz9mzZwOBwIkTJ9auXVtVVYUL2ASxZ88el8u1bt263t7etLS0EydOpKSkzJmDTo8pxePxvPrqq8KMSY7jfv3rXz/11FM3F+IaCYZhli9fPp5FuWDiMBgM27dvb29v93q9qampeXl5D+eZHN30t+D1egcHB4WizLe0NHupsHTIVffVYRVl7sxsNn/3u9/V6XSNjY2BQOCrX/3q/IXzhWolBH30o0JR1Ne//vXGxsazZ89evHjx8OHDeXl5U37A6N69e9vb29evX7906dJVq1YdP378/PnzYgcFhBASj8cvX75cWVkpXFHkcnlJScnFiyOtrAaTxZEjR1JTU2fOnGk2mwsKChYuXLhnzx6xg4JJiWGYkpKShQsX5ufnP5yZKEHL6DBut/t3v/tdW1sby7IHDx584oknbnmnq5VrK9Mqz/WeI4Sc6DqxpWTLyJ8iNTX16aefTn7b4GgIxoKEEKPCmKvHdJDRyMnJ+dGPftTc3BwOh9PT0++/7EI4HBYWlpqYeJ4/e/bs8uXLhXHuCoWivLz87Nmz8+fPFzs0INFolBAikUh4nhdK+CgUioGB4atswmTX2dkpDFVXKpU0TRsMhmg0GggEhPo6AHBPkIx+juf5Xbt20TS9du3aQCAgl8t3796dkpJyy5pdK3JXCMno2Z6zG6dtHPWTJte6n5cxb6xuiRKJhNPpdLlchYWFNy8/PiWpVKox6QY9d+7c//7v//b09Hz22WfCUL9kzZiJg+M4YZwoRVHCsslKpfJBrAUDo6BSqfR6/cDAQGpqqjCW12azTdW6dA8zg8EQDAZTUlKEJWw5jkskEvdaTgIABEhGP+dyufr7+9esWSNMgNXr9VlZWXV1dbdMRovMRZnaTJvfFo1Hz9rOKslozkEJPjHmffR9fX2//e1v+/r64vH4wYMHt2zZUlEx+kpRD5WGhoY9e/YsXLhw+vTpJpPp3LlzPM9v2LBB7LiGk0qlqamp/f39aWlpwgqFvb29mH47cTz55JM7duzIzs6Wy+VerzcUClVVVYkdFIyxBQsW7Nq1y2QyabVajuPOnTu3YMGCCXjvCjApYMzo54LBoNCSIZfLDQYDIUSpVHq93tvtvzz3xnjzE90nhtX2HKGWwRahAqFBYcg3jHSR7TtgWfbtt982m82rVq1aunTp3Llz3333XXQRjlB1dXVZWZleryeEyOXyhQsXnjx5cnSv7IP2+OOPX758ubGxsbe3t66uzmazrV+/Xuyg4Ibi4uLvfe972dnZiUSisrJy+/bt6LqdesrKyjZt2nTmzJkDBw7s379/2rRpGzeOvosM4CGHltHPWa3WYDAYDoeVSqWQlfb399+hIN7i7MV7mvdEuIjdb+9R9IziGZN99HPT545JH73dbo9GowUFBYFAgBBiMBisVmtzc/OdK1WCwOVyCZX0TCYTTdNyuZxl2Wg0KrQ+TiiFhYUvvfRSdXW10+ksKCh49tlnhRwaJgir1fqlL33J7/cL6wrDlLRw4cL58+d7PB6NRoPl1QDuB5LRz8nl8i984Qv79u3Lz89XKBQ2m00mk91hXrZcIl+YufBY5zFCyGXP5b8gf3FPT8cTvrbvRh/9WNWjD4VCcrmcEKJUKoUUSiaTCYkp3FVWVtbAwIDBYBBWgXW73VqtdgJmooL09PTNmzeLHQXAQ42maWHMKADcD3TT/5nly5f/1V/9lUajiUajCxcufPHFF+88AWhV/iqhRbPV1+qJeO7pudoG27xRLyFEJ9cVmgrvJ+yk9PR0r9cbjUaF8k48zzscjuxsLKQ/ImvWrOns7GxpafF4PJ2dnTU1NZs2bRI7KAAAgCkOLaPDFRUVFRUVjXDndE16obGw1dmaIInq7uoNRfcw2SXZRz8nfQ5Njc1dgV6vX7NmzZEjR/Ly8qRSaXd3d1paWnl5+ZgcfMqzWq3f/e53Dx061NraajKZnnvuuZG/EwAAAMZBJBKpqak5ceLEwMDAI488IiwhN9khGb1fK3JXtDpbCSH7ru6bnjK90DiiNk6e8Jf6Lglfj+1a92vWrMnOzq6rq4tGo+vXr587dy5No/17pKxW69BVYAEAACaOYDD42muvSaVSmqbb29tPnz79wgsv5OePwQRocSEZHSm73X7y5Mnm5uZAILBo0aLkUMI56XMMCsMAGYhwkZ+f/fmLC16cZpp216N1uDuEbn2tTFtkGuPmt+nTpwsTcQAAAGDKOHjwoEajmTVrVk9PT1pamsPheP/993/4wx+KHdf9QpvZiDQ2Nr7++us2m02hUJw7d+7VV18NhULCjxiaeWnBSxpGQwiJcJHXz77e7Gy+6wEv9F4QvqhMrxyrPnoAmOA4jrty5UptbW1DQ0M8Hhc7HACYZK5evSqsfS6VSimKSk9PHxwcjEQiYsd1v5AGjcj777+/YMGC8vLyzMzM+fPnKxSKY8eOJX9qVVufyn7KoDAQQmLx2C/O/eLO+SjPP6g+egCYsPx+/7/92799/PHHNpvtgw8++I//+I/kPS0AwEio1epYLEYIsVqtEolEuKedAqUWkYzenTA/3WQyURQlLCaXmZnZ0dExdB+T3PT9Rd8fmo82OZtud8BrnmuusIsQopaqp5vRnw4wWfE87/F4HA6HcHm4s48//lin0y1btqy0tHT58uVSqfTTTz8dhyABYMqorKxsaWlhWZYQwvN8bW3tzJkzp0DpL4wZvTulUslxHM/zDMOkpKQQQiKRyM0lVawa6/bF218986o77I7FY78898tvz//2sH0iXKTJ0XS086jw7ey02eijB5ikvF7vu+++29bWFovFjhw5smnTpoULF95uZ57nm5qali9fzvO8sB7ctGnTLly4MI7xAsCkN3/+/P7+/kOHDqnV6nA4nJub+/jjj4sd1Bh4SJNRjuOqq6uPHTsWCoWWLl26evVqpfK2xeVlMll5efnly5dnz55NUVQkEmlra3vqqadu3jNVnfr9Rd9/9fSr7og7Fo/9ouYXC+mFi/nFXd6uBkdDw0DDVffVBJ9I7o8+eoDJ65133uE4bu3atV6vV6PRfPTRRxaLpaCg4JY7UxRFUZSQiebk5BBCEonEmNRdA5gyeJ4/f/78kSNHent7W1tb165di5oCw1AUtXHjxhUrVjidTq1Wa7FYxI5obDykyeh777137dq1rKyseDze3Nzc0tLy3e9+l2Fu+9d44okn3nnnnX379qlUqlAotG7duoqKilvumapOfXnJy6+cfsUVdrEJdo99T+3hWn/Mf/OeOrmuJKVkzH4lABhHPp+vq6tr/fr10WiUEKLRaPLy8mpra2+XjBJCZsyY0draOnPmTOHbtrY2rAE8VuLxOCaETQEHDx48fvz4tGnTjEbj4ODg66+/vn37dp1OJ3ZcE45Op5tif5aHMRnt6+tramqqqqoKBoOxWGzatGknT55saGiYNWvW7R6i0Wi2bt3qcrkCgYDFYrlDMyohJEWVsn3x9ldPvzoYHozzcV/Ul2z/oAiVY8gpSykrt5QXmgonSB+9z+c7d+5cXV0dwzAzZ868Q1IOAIJgMCiTyYRx5ELjjVKp9Pl8d3jIxo0b33jjjWPHjmm1Wp/PZzQaN2y4hzIZcEter/fjjz8+e/Ysy7KzZs3avHlzWlqa2EHBaLAse/DgwdWrVwtDsdPS0qLR6JkzZ9atWyd2aPDATfG0w+PxfPLJJ2fOnKEo6pFHHvnCF76g0+kGBgZ0Oh1N08LKCIQQo9HY399/16OZTKYRdhmkqFJeXvLyq6df7SN9hBCNTDPdPL3UUlqRWiFMcpo4urq63nzzTZ1OF41GP/vssyNHjnznO98RCtwDwO1YLBaO4wKBgEajEeY19vX13WHMKCFErVZ/73vfa2trc7vdZrO5sLAQBSnuUzwef/vtt2maXrt2bTwe93q9b7755ssvv6xWq8UODe6Z0+mUy+VyuZxlWZVKRQixWCw9PT1ixwXjYSono7FY7Fe/+pVKpVq5ciUhpLe39ze/+c2LL75oMBiEFVWSC9cHg0Gj0Ti2z25Smr6/+Pu/8f1m8yOb8035FJmgg8N2795dVlZmtVr7+/szMzOF8TqPPvqo2HFNJolE4u47wdTCMMyXv/zlPXv25OXlqVQqu91OCFm0aNGdH0XTNApSjKGenh6Px7Ny5Uq/359IJAoKChwOR3Nz89y5c8UODe6ZwWCIRCKJREIqlQprFfl8vuzsbLHjgvEwle/L29vbY7HYjBkzpFKpTCabNWuW3++/fv16ZmamwWCor69PJBI8z1+/fj0QCJSUjP3wTZPStMi8KFefO2Ez0XA47HA4MjMzCSHC2hA5OTltbW1ixzVp9Pb2/vKXv3z99df/5V/+5cMPPwyHw2JHBONnwYIFL7zwgslk4jhuwYIFL730EroUxpnH4xGa0BQKhdAaqlar3W632HHBaCiVysrKypqaGmGhNLvd3tPTM2/ePLHjgvEwlVtGnU6ncHpKDvFUq9WDg4PTpk37xje+8eGHH3766ac0TWdnZ2/dulWr1YoarDiE4aHCqlXCQCuO43BBHSGfz/fGG2/k5+evXbtWKpW2t7e/++67zz33HKZIPzzy8/OnQFXoyctisXi9Xp7nk4t+ezye1NRUcaOCUXv88cf37t176NCheDxusVi+8Y1vpKenix0UjIepnIxaLJZAIEAISWZXfr9fWCjUYDA899xzHMfF4/GHOfeSSqVFRUWNjY3CrN54PN7W1rZ27Vqx45ocamtr9Xp9fn6+w+GQy+Xz588/cOCAy+Uym81ihwbwUEhPTy8qKqquri4pKZFIJB0dHUqlsqysTOy4YJTkcvmXv/zlTZs2sSwrDMWGh8RUTkaLiorUavWlS5eKi4uFFafNZnNeXl5yB4ZhMHN8y5YtO3bsOHz4sEql8nq9c+bMWbx4sdhBTQ7CTDhCiEajYRiGoiiVSoVkFGDcUBT1ta997fjx45cvX+Y4rrS0tKqqCmf1yS5Z7BAeHlP5Q8swzAsvvLBv377z589TFDVz5sx169ZNgapZY0uv17/00kvd3d2BQCA1NXXKrKA7DtLT04WqsMI4kHg8HggEhKZ3ABgfUqm0qqqqqqpK7EAAYPSmcjJKCNFoNJs3b968ebPYgUxoNE3n5uaKHcXkM3v27IMHDzY0NOTl5cVisYaGhtmzZ4/5sgwAAABT2xRPRgEeHJVK9eKLL+7du/f8+fNyuXzJkiXLli2780MSicT58+ePHz8eiUSWLVu2ZMmS5MQLAACAhxOSUYDRMxqNTz/99Mj3//3vf9/U1JSenq5Wq6urqxsbG7du3YqVzwEA4GGGqyDAOOnr66utrV22bFlGRobVal20aNHAwEBzc7PYcQEAAIgJySjAOOnr6zMYDBKJhGEYoay50WgUKvcAAAA8tNBNDzBOdDpdNBolQ6owRKNRvV4valCTCcdxV65cqampkUqls2fPTpbzBQCASQ0towDjJDs7m2GYtrY2nucJITabze/3FxcXix3X5BAMBl955ZXPPvvM4/EcPnz4pz/96eDgoNhBAQDAGEAyCjBOpFLp888/H4lE9u7du2/fvu7u7ueff15YNn8ccBx3/vz5kydPnjx50ufzjc+TjqG9e/cqlcpHHnmkqKho0aJFmZmZH3zwgdhBAQDAGEA3PcD4SU1NffHFFwOBQDweH88O+kgk8vOf/5zjOI7jLl68ePTo0a1bt+bk5IxbAPevtbW1oqKCECLUrcjPzz9w4EAikcBaBAAAkx3O4wDjTaPRjPNQ0cOHD0skkiVLlhQWFs6dO7esrGz37t3jGcD9YxgmHo8TQjIzM2ma5nmepmmKooSfJhIJn88nDMkFAIDJBS2jAFNfW1ub0A4qNCtmZGTU1taGw+HkVKqJr6Kiora2duHChUIC2tjYWFFRIXxdU1Pz8ccfOxyOTz75ZPHixZs2bcLcJgCASQTJKMDUp1AoOI4jhKSlpRFChBlUDDOZPv5r1qzp6ek5dOiQVqsNhUJGo3HTpk2EkObm5o8++mjx4sV+v99oNNbV1X388cdPPfWU2PECAMBITaarEQCMTkVFxYEDBywWi5CANjQ0FBcXT65KpFKp9Jvf/GZ3d/fg4KBer8/LyxOaRc+fP19cXKzVav1+P8Mw8+bN27dv3+bNmydXqg0A8DDD+Rpg6lu8eLHNZjt06JBOpwuHw0aj8ZlnnhE7qNHIzs7Ozs4eusXlcgnNvSaTSSKR0DQtkUiCwSAWcAUAmCyQjAJMfRRFPfnkk6tWrRoYGNBqtVlZWcmpP5Ndbm5uZ2dnamqqME7U5/MxDDPqBbNisVhPT08ikcjIyJDL5WMaKQAA3BqSUYCHRUpKSkpKithRjLFVq1a98sordXV1aWlpgUCgra3tySefHF2q3dbWtmvXrlAoRFHU/v37n3766dLS0jEPGAAAhkEyCgCTmE6n2759+9GjR7u6uvR6/V//9V8XFhaO4jh+v3/nzp2zZ8+WSqU8z8fj8V27dv3d3/0duvsBAB40JKMAMLnpdLovfelL93mQ69evazSalJQUr9dLCDGbzXq9vqOjo7KycixiBACA20IyCgBAIpGIsAirVqsVtkgkkkgkImpQAAAPBVRgAgAgWVlZbreb4ziapmma5jjO5XJlZWWJHRcAwNSHllEAAJKenr548eIjR44IS0f19PTMnTt32DJSAHAH4XAY6/vC6OB9AwBACCEbN26cPn16U1MTIWTlypUlJSViRwQwOXR1de3evfvq1asSiWTmzJlPPPGE2WwWOyiYTJCMAgDcUFxcXFxcLHYUAJOJz+d76623iouLCwoKpFJpT0/Pjh07vve976GVFEYOY0YBAABglJqbm4VSGoQQiqLKyspCoZDNZhM7LphMcOMCAAAAo+T1elUqFSFEq9XSNE0IUSgUwhJpACOEllEAAAAYpbS0NJfLRQiRyWQMw8Tjca/Xm5aWJnZcMJkgGQUAAIBRKisr0+l0Z8+eHRgYsNvtJ0+enDVrVmpqqthxwWSCbnoAAAAYJYlEsm3btuPHjzc3N0ul0nXr1i1cuFDsoGCSQTIKAAAAoyeXy9euXbt27VqxA4HJCt30AAAAACAaJKMAAAAAIBokowAAAAAgGiSjAAAAMKHxPN/X19fV1eV2u8WOBcYeJjABwNTk8Xj2799/5swZi8WycuXKhQsXCityA8DkEggEdu7c2d3dHYlELl68uGDBgq985SsURYkdF4wZJKMAMAUFg8HXX389JSWlvLxcKpXu27fP6XRu3LhR7LgA4J794Q9/YFm2qqqqv78/LS3t1KlTaWlpS5YsETsuGDNoJwCAKejcuXNqtbq8vFyr1VoslkceeeTEiROhUEjsuADg3sTj8cbGxpkzZwpNoQzDFBcX19XViR0XjCUkowAwBdlstpSUFEKIUqlkGEYqlWo0GofDIXZcAHBvWJbleZ6iKIlEIlQZlclk4XBY7LhgLCEZBYApyGKx+Hw+QohWq5VKpTzPh0Iho9EodlwAcG8UCkVqaqrdbqcoimEYQkh3d/e0adPEjgvGEpJRAJiCKisr+/v7bTYbz/Msy9bU1JSUlOh0OrHjAoB79tRTTzU0NFy6dKmtre306dPhcLiqqkrsoGAsYQITAExBFovlr//6rz/88MOLFy9KJJKFCxdu2LBB7KAAYDRycnJ+8IMfXLx40e12z5gxY+7cuTKZTOygYCwhGQWAqSk/P3/79u0syzIMg1VgACY1g8GwevVqsaOABwXJKABMZVKpVOwQAADgTjBmFAAAAABEg2QUAAAAAESDZBQAAAAARINk9AGy2+3Xrl3r6enheV7sWAAAYIpIJBJ9fX02my0YDIodC8AYwASmB4LjuF27drW2toZCoZaWlszMzG984xtKpVLsuAAAYHJzOBw7d+4cGBiIRCLnzp177LHHli9fLnZQAPcFLaMPxMGDB+12+9q1a+fMmVNVVRWJRD755BOxg4L70tHRcfny5draWtQ3BwCx8Dy/c+dOvV6/atWqhQsXLl++/E9/+lN7e7vYcQHcFySjD0RtbW1paamwtCFFUeXl5bW1tWIHBaOUSCR27ty5Y8eOq1evHj169Kc//WlXV5fYQQHAw8jlcrnd7qKiIuFbpVKZm5vb0NAgblQA9wnJ6AMRi8WEErqZmZkURUkkEo7jMHJ0kjp37lxnZ2dVVdWMGTMWLFhQUlKya9cuvJoAMP4ikYiwdK5cLjeZTIQQmUyGkaNwZ06ns6mpqaWlZcL27CEZfSCKi4uvX79OCJFIJISQ69evFxYWogbMJNXS0pKbm5t8+TIyMgKBgMfjETcqAHgIWa1WlmV9Ph9N08L1xWazFRYWih0XTFwHDhz493//9/Pnzx88ePAnP/lJW1ub2BHdAiYwPRAbNmz4+c9/fvr0aYPB4Pf7g8Hgiy++KHZQMEoURQntoGlpacmNNI0bOQAYbwzDPPHEE7t3787IyGAYxuVy6fX6uXPnih0XTFDXrl07evTo6tWrfT6fUqkMhUK7du36+7//e7lcLnZof2YMktH33nvvyJEjyW/feOMNNAFqtdof/OAHly9fHhgYMJvNs2fPxlT6yaukpOSzzz7LyckR3tg9PT06nU6v14sdFwA8jCorK61W6+XLl10u1/z58+fMmSM0kcIEEYvFrl+/3tvbm5mZaTAYxA2mra0tIyNDJpMJ31osFolEYrfb8/LyRI1ruDFIRk+dOtXX1/eFL3zh/g81lchksgULFogdxRTE83w8Hh/PZ5w3b15ra+vBgwfNZnMkEolGoy+88MJ4BgAAMFRGRkZ6enowGNRoNGLHAn+mu7v77bffjkajHMedOXNm/fr1K1euFDEejuOEZhSz2SxsoShqnK+hIzE23fRz587F5RketFAo9Omnn544cSIUCs2ePfsrX/lKZmbmODwvRVFf+9rXurq6ent71Wp1UVGRQqEYh+cFAIBJhOO4nTt3FhYWGo3GYDCo0+n279+fm8dnu+QAABB5SURBVJubn58vVkiFhYWnT58uKSkRhpb5fL5IJJKRkSFWPLczNsno3r17m5ubCwoKtm3blpWVNSbHBBiK5/ldu3Z5vd7Vq1fHYrFwOPzmm29u37593LrLc3JycnJyxue5AABg0unv7+c4LjMzU5i0LpfLs7KympubRUxGp0+fPmvWrEOHDqWkpCQSCafT+dWvfnUCjhscg2R0/vz5paWlBoPh4MGDFRUVtbW1t7tmB4PBzZs3327YbGZm5m9/+9uhWwKBwP2HNw5Ylo1Go36/X+xApjKn09nW1rZmzZpQKBSPx9PT0+12+5kzZ5YsWTK6A/I8H4vF8KqNTigUomkaf707myxnsHEQjUYDgQDLsmIHMnXwPB8KhbDG3ITi8Xji8XgsFqNpWqvVxmKxRCLh8XjEPVWuX7++tLS0s7NTLpcXFRUZjcaRxMNxHMuyHMfdfwAqlequw5pHmYxu2bJFOK3813/91zPPPCNsfPrpp+12+1tvvfVP//RPt3yUQqH48Y9/nJ2dfbufarXaYRtv3jIBsSwrl8snRaiTl91uNxgMcrlcIpEoFAqZTGYymUKh0Kj/7DzPy2QyvGqjo1KphLOt2IFMdPgTCeRyuUajwfiWMcTzPE3TGDM6oUybNi2RSESjUeGDz/O80+lcvny56OeB8vLy8vLye3qIkIyOWxvqKJPRbdu2JRIJQsiwTtLCwkKn03m7R0kkktmzZydLRwCMnMViCQQC8XicYRihoIDb7a6oqBA7LgAAAEIIkcvlwsJbVqtVJpP19/cXFBTgOjUSo0xGV69enfy6tbW1uLiYENLZ2blnz55//dd/HZvQAIYwGo2zZ8+urq4uKyuTyWSdnZ0sy86ePVvsuAAAAG6orKzMzMxsaGiIRqOrV68uKSnBYpcjMQZjRquqqhiG0Wq1HR0dzz///Ne+9rX7PybAzTZv3nzixIkLFy5EIpHi4uKvf/3rE3AUNgAAPMxSU1NTU1PFjmKSGYNktLOz8/r168FgsKCgQK1W3/8BAW6JYZhVq1atWrVK7EAAAABgzIxBMkrTdEFBwf0fBwAAAAAeNqivDQAAAACiQTIKAAAAAKJBMgoAAAAAokEyCgAAAACiQTIKAAAAAKJBMgoAAAAAokEyCgAAAACiQTIKAAAAAKJBMgoAAAAAokEyCgAAAACiQTIKAAAAAKJBMgoAAAAAokEyCgAAAACiQTIKAAAAAKJBMgoAAAAAokEyCgAAAACiQTIKAAAPUCwWGxwcDIVCYgcCABMUI3YAAAAwZR0+fHj//v0ej+fIkSPz5s17/PHH5XK52EEBwMSCllEAAHggLl26dPjw4RUrVixdunTdunWdnZ2ffPKJ2EEBwISDZBQAAB6ImpqasrIypVJJCJFIJPPmzTt37lwikRA7LgCYWJCMAgDAA+Hz+YRM1GKxSCQShmF4no/FYmLHBQATC5JRAAB4IPLy8np7ewkhcrmcoiiHw6HX6xUKhdhxAcDEgmQUAAAeiLVr1w4MDFy+fNlmszU3N1+8eHHz5s1iBwUAEw5m0wMAwANhMBhefvnlEydO2Gy2lJSUL33pSxkZGWIHBQATDpJRAAB4ULRa7YYNG8SOAgAmNHTTAwAAAIBokIwCAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGiQjMLDiOf5rq6uq1evdnV18TwvdjgAAAAPL1RggodOJBJ5++23bTabz+ez2WyZmZnPPfecXC4XOy4AAICHEVpG4aGzd+/eUChUVVU1a9asqqqqQCDw2WefiR0UAADAQwrJ6P3yer2HDx8+cuTIsWPHwuGw2OHA3dXW1paWllIURQihKKqsrKyurk7soAAAAB5SSEbvS29v789+9rP6+nqKompqan72s595vV6xg4K7YFlWIpEQQjIyMgghEomEZVmxgwIAAHhIIRm9Lx988EFxcXFlZWVOTs78+fMtFsvevXvFDgruYvr06R0dHYQQISW9du1aSUmJ2EEBAAA8pJCMjl48Hu/q6srOzqYoSiaTEUKys7Pb29vFjgvuYtOmTU6n8/Tp042NjdXV1YODgxs3bhQ7KAAAgIcUZtOPHk3TMpmMZVm5XJ6WlkYIicViarVa7LjgLvR6/Q9/+MO6urru7u7s7OyZM2cK9xIAAAAw/pCMjh5FUZWVlXV1dfPmzaMoiuO4xsbGZcuWiR0X3J1MJps3b9706dO1Wq3YsQAAADzUkIzel40bN77zzjsHDhxQqVSBQGDOnDnLly8XOygAAACASQPJ6H2Ry+XPPfecw+Hwer1ms9loNIodEQAAAMBkgmR0DFgsFovFInYUAAAAAJMPZtMDAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGiQjAIAAACAaJCMAgAAAIBokIwCAAAAgGgYsQMAgMnE5/Pt3bv31KlTFEUtXbr00Ucf1Wq1YgcFAACTGFpGAWCkWJb91a9+1d/f/8gjjyxZsqSnp+c3v/kNx3FixwUAAJMYklEAGKn29vZIJDJz5ky5XK5QKCorK30+37Vr18SOCwAAJjEkowAwUoODg2q1mhCiUCjkcjkhRKPRDA4Oih0XAABMYhgzCgAjlZKSEggECCEKhULY4vf7zWazqEEBAMDkhpZRABipwsJCpVJZV1cXiUTC4fClS5f0en1BQYHYcQEAwCSGllEAGCmpVLp169a9e/eePHmSpumKiorHHntMIpGIHRcAAExiSEYB4B5otdotW7Zs2bJF7EAAAGCKQDc9AAAAAIgGySgAAAAAiGZCJ6OnT58Oh8NiRwFT1pEjR8QOAaascDh8+vRpsaOAKWtwcPDy5ctiRwFTVk9PT3Nz87g93YRORl944QW73S52FDA18Ty/adMmsaOAKctms23btk3sKGDKOn/+/D/+4z+KHQVMWZ9++ukvf/nLcXu6CZ2MAgAAAMDUhmQUAAAAAESDZBQAAAAARDOu64zGYrEdO3akpKSMcH+fz/fWW2+h2CA8CDzPE0JeeeUVsQOBqcnpdHq9XrzB4AFpbm7u6urCGwwekFOnTvX29o7JG+yZZ56xWCx33ocSLsnj49SpUx9++OHI92dZViqVPrh44CGHNxg8UHiDwYPD83w8HmcYVK6BByKRSPA8PyYF9rZv356RkXHnfcY1GQUAAAAAGApjRgEAAABANEhGAQAAAEA0SEYBAAAAQDRIRgEAAABANBN0Ip7L5dq+fXt1dXVBQcFPf/rTWbNmiR0RTHoNDQ2vvfba+fPnKYqqqqr6h3/4B61W+8Mf/vDixYvCDpmZmf/93/8taowwiX3wwQdvvPFG8tudO3dmZGT09vZ+//vfv3jxYllZ2b//+79PmzZNxAhhUvv2t7/d1taW/LaysvJnP/vZhg0bWJYVtjz66KPbt28XKTqYlJxO586dOy9cuOB0Ovfv3y9s9Pl8L7/88vHjx7Ozs3/yk5/MmzePENLc3PyDH/ygpaVl/vz5r776qtVqHdtIJmgyum3bNpqm9+3bt2fPng0bNnR0dMjlcrGDgsntypUrxcXF3/rWt3ie/+53v/ud73xn586dFy9eXLRo0YoVKwghKpVK7BhhEuvs7KRp+gc/+IHwrcFgIIQ8/fTTZWVlBw4ceOuttzZt2lRfX09RlKhhwmT17LPP+v1+4eu/+Zu/qaqqIoQcPnz4f/7nf0wmEyHkrqvnAAxjt9ubmpoKCgree++95MaXXnrJ7Xbv3bt33759jz322PXr1xUKxcaNG7/+9a//53/+5z//8z8/++yzf/rTn8Y4FH7isdvtUqm0p6dH+LasrOz9998XNySYYv74xz9mZWXxPL9mzZrdu3eLHQ5MBa+88spf/dVfDd3S2NioUCj8fj/P8/F4PDU19ejRoyJFB1NHR0eHVCq12Ww8z8vl8t7eXrEjgsmtsbGRoijha7fbrVAoWltbhW/nz5//9ttv7927NzMzU1h51OPxyGSyq1evjm0ME3HMaEtLi8ViyczMFL6dO3dufX29uCHBFFNTU1NWViZ8/W//9m/Lly//9re/ff36dVGDgknv6NGjy5Yte+qppw4dOkQIqa+vLykp0Wg0hBCapv9/e/fzkswWxgF8einth9kYjllt0uEtIqikslwUlEhRBkJQi0joT2jTLtxViwgKoojcZIugRUUYEdTCIg0KohLEMmhRQmHqqJBgzV0MiHg3l5txVL6f1Zwzgs9CHr+cM0c1Gg1aGfyc1WodGBhIroOOj48bDAaLxZJcNwX43x4fH8Vi8d+/f4WhEMDcbndbW5uwq1NRUcGyrNvtzuz7ZuM2/fv7e0VFRXIok8ne3t4I1gN5xuVyLS0tORwOiqLMZnN1dbVIJLLZbDqd7u7u7r//XS1Aqvb29oWFhZqamsvLy+Hh4b29PbQyyLjv7+/Nzc3l5WVhODc319HREY1GZ2dnz87OTk5O8BwI/ERa16Jp+uXlpbCw8LdbWTaGUZqmY7FYcshxHB6FgUy5ubkxmUxbW1vNzc0URU1MTAjz3d3dLS0tBwcHk5OTRAuEXNXT0yNc6HS619fXjY0Nk8mU1spkMhmh6iBPHB0dxePxoaEhYTg1NSVcaLVahmF8Ph8OycFPpAWwSCRSWVlJ03Tq4bnfaGXZuE2vUqn8fn84HBaGXq9XpVKRLQnyw/39/eDg4MrKitFoTLtVUFAgl8uj0SiRwiDPMAwTi8XUarXP50skEsKk1+tVq9VkC4NcZ7VazWZzUVFR2rxUKhWJROhg8EMqlSoUCiUXPoUAplarPR6PMBOPx5+fnzPeyrIxjLIsq9VqhW2I8/Pz29vbkZER0kVBzvN4PAaDYWZmpq+vLxgMBoPBWCzmdDqFu7u7u06ns7e3l2yRkLscDkc8Hqcoyuv1rq6uGgyGzs5OhmGsVitFUfv7+xzH9ff3ky4TclggELDb7cndm6enJ5/PR1FUIpGwWCxyubyxsZFogZBjhBNLHMdRFBUMBsPhsFKp1Ov1i4uLFEVdXV1dXFyMjY0ZjUa/3394eEhR1Pr6el1dXWtra+ZLyUJut7upqYlhGIVCsbOzQ7ocyAfz8/OyFHK5PBAIsCxbXFwskUhYlt3e3iZdI+Sw0dFRsVgsk8lomp6enk4kEjzPu1wutVpdVVVVW1t7fHxMukbIbWtra3q9Pjk8PT1VKBTl5eWlpaVdXV3X19cEa4Nc9PHxkfq12NDQwPP8w8ODRqNhGEYul9tsNuGVdrtdqVQqFIr6+vrf+KQV8Dyf4XibORzHSSSSP3+ycfkW8sbn5yfP8yUlJaQLgZz39fUVi8WkUmnafCgUEn52FCDjotGoWCz+98Y9wE9EIpGysrLUAMbzPMdxqSeZMiirwygAAAAA5DcsOgIAAAAAMQijAAAAAEAMwigAAAAAEIMwCgAAAADEIIwCAAAAADEIowAAAABADMIoAAAAABCDMAoAAAAAxCCMAgAAAAAxCKMAAAAAQAzCKAAAAAAQ8w9fVUnwkDMqQwAAAABJRU5ErkJggg==" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ksl(Cauchy())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how extreme observations are far more prevalent here than the previous figure.\n", "\n", "Let’s now have a look at the behavior of the sample mean" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false }, "outputs": [], "source": [ "Random.seed!(0); # reproducible results" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function plot_means(n = 1000)\n", " sample_mean = cumsum(rand(Cauchy(), n)) ./ (1:n)\n", " plot(1:n, sample_mean, color = :red, alpha = 0.6, label = \"Sample Mean\", linewidth = 3)\n", " return hline!([0], color = :black, linestyle = :dash, label = \"\", grid = false)\n", "end\n", "\n", "plot_means()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we’ve increased $n$ to 1000, but the sequence still shows no sign of converging.\n", "\n", "Will convergence become visible if we take $n$ even larger?\n", "\n", "The answer is no.\n", "\n", "To see this, recall that the [characteristic function](https://en.wikipedia.org/wiki/Characteristic_function_%28probability_theory%29) of the Cauchy distribution is\n", "\n", "\n", "\n", "$$\n", "\\phi(t) = \\mathbb E e^{itX} = \\int e^{i t x} f(x) dx = e^{-|t|} \\tag{5}\n", "$$\n", "\n", "Using independence, the characteristic function of the sample mean becomes\n", "\n", "\n", "\\begin{aligned}\n", " \\mathbb E e^{i t \\bar X_n }\n", " & = \\mathbb E \\exp \\left\\{ i \\frac{t}{n} \\sum_{j=1}^n X_j \\right\\}\n", " \\\\\n", " & = \\mathbb E \\prod_{j=1}^n \\exp \\left\\{ i \\frac{t}{n} X_j \\right\\}\n", " \\\\\n", " & = \\prod_{j=1}^n \\mathbb E \\exp \\left\\{ i \\frac{t}{n} X_j \\right\\}\n", " = [\\phi(t/n)]^n\n", "\\end{aligned}\n", "\n", "\n", "In view of [(5)](#equation-lln-cch), this is just $e^{-|t|}$.\n", "\n", "Thus, in the case of the Cauchy distribution, the sample mean itself has the very same Cauchy distribution, regardless of $n$.\n", "\n", "In particular, the sequence $\\bar X_n$ does not converge to a point." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## CLT\n", "\n", "\n", "\n", "Next we turn to the central limit theorem, which tells us about the distribution of the deviation between sample averages and population means." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Statement of the Theorem\n", "\n", "The central limit theorem is one of the most remarkable results in all of mathematics.\n", "\n", "In the classical IID setting, it tells us the following:\n", "\n", "\n", "\n", "If the sequence $X_1, \\ldots, X_n$ is IID, with common mean\n", "$\\mu$ and common variance $\\sigma^2 \\in (0, \\infty)$, then\n", "\n", "\n", "\n", "$$\n", "\\sqrt{n} ( \\bar X_n - \\mu ) \\stackrel { d } {\\to} N(0, \\sigma^2)\n", "\\quad \\text{as} \\quad\n", "n \\to \\infty \\tag{6}\n", "$$\n", "\n", "Here $\\stackrel { d } {\\to} N(0, \\sigma^2)$ indicates [convergence in distribution](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_distribution) to a centered (i.e, zero mean) normal with standard deviation $\\sigma$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intuition\n", "\n", "\n", "\n", "The striking implication of the CLT is that for **any** distribution with\n", "finite second moment, the simple operation of adding independent\n", "copies **always** leads to a Gaussian curve.\n", "\n", "A relatively simple proof of the central limit theorem can be obtained by\n", "working with characteristic functions (see, e.g., theorem 9.5.6 of [[Dud02]](../zreferences.html#dudley2002)).\n", "\n", "The proof is elegant but almost anticlimactic, and it provides surprisingly little intuition.\n", "\n", "In fact all of the proofs of the CLT that we know are similar in this respect.\n", "\n", "Why does adding independent copies produce a bell-shaped distribution?\n", "\n", "Part of the answer can be obtained by investigating addition of independent Bernoulli\n", "random variables.\n", "\n", "In particular, let $X_i$ be binary, with $\\mathbb P\\{X_i = 0\\} = \\mathbb P\\{X_i =\n", "1 \\} = 0.5$, and let $X_1, \\ldots, X_n$ be independent.\n", "\n", "Think of $X_i = 1$ as a “success”, so that $Y_n = \\sum_{i=1}^n X_i$ is the number of successes in $n$ trials.\n", "\n", "The next figure plots the probability mass function of $Y_n$ for $n = 1, 2, 4, 8$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "binomial_pdf (generic function with 1 method)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "binomial_pdf(n) =\n", " bar(0:n, pdf.(Binomial(n), 0:n),\n", " xticks = 0:10, ylim = (0, 1), yticks = 0:0.1:1,\n", " label = \"Binomial($n, 0.5)\", legend = :topleft)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(binomial_pdf.((1,2,4,8))...)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When$ n = 1 $, the distribution is flat — one success or no successes\n", "have the same probability.\n", "\n", "When$ n = 2 $we can either have 0, 1 or 2 successes.\n", "\n", "Notice the peak in probability mass at the mid-point$ k=1 $.\n", "\n", "The reason is that there are more ways to get 1 success (“fail then succeed”\n", "or “succeed then fail”) than to get zero or two successes.\n", "\n", "Moreover, the two trials are independent, so the outcomes “fail then succeed” and “succeed then\n", "fail” are just as likely as the outcomes “fail then fail” and “succeed then succeed”.\n", "\n", "(If there was positive correlation, say, then “succeed then fail” would be less likely than “succeed then succeed”)\n", "\n", "Here, already we have the essence of the CLT: addition under independence leads probability mass to pile up in the middle and thin out at the tails.\n", "\n", "For$ n = 4 $and$ n = 8 $we again get a peak at the “middle” value (halfway between the minimum and the maximum possible value).\n", "\n", "The intuition is the same — there are simply more ways to get these middle outcomes.\n", "\n", "If we continue, the bell-shaped curve becomes ever more pronounced.\n", "\n", "We are witnessing the [binomial approximation of the normal distribution](https://en.wikipedia.org/wiki/De_Moivre%E2%80%93Laplace_theorem)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation 1\n", "\n", "Since the CLT seems almost magical, running simulations that verify its implications is one good way to build intuition.\n", "\n", "To this end, we now perform the following simulation\n", "\n", "1. Choose an arbitrary distribution$ F $for the underlying observations$ X_i $. \n", "1. Generate independent draws of$ Y_n := \\sqrt{n} ( \\bar X_n - \\mu ) $. \n", "1. Use these draws to compute some measure of their distribution — such as a histogram. \n", "1. Compare the latter to$ N(0, \\sigma^2) $. \n", "\n", "\n", "Here’s some code that does exactly this for the exponential distribution\n", "$ F(x) = 1 - e^{- \\lambda x} $.\n", "\n", "(Please experiment with other choices of$ F $, but remember that, to conform with the conditions of the CLT, the distribution must have finite second moment)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "simulation1 (generic function with 3 methods)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using StatsPlots\n", "\n", "function simulation1(distribution, n = 250, k = 10_000)\n", " σ = std(distribution)\n", " y = rand(distribution, n, k)\n", " y .-= mean(distribution)\n", " y = mean(y, dims = 1)\n", " y = √n * vec(y)\n", " density(y, label = \"Empirical Distribution\")\n", " return plot!(Normal(0, σ), linestyle = :dash, color = :black,\n", " label = \"Normal(0.00,$(σ^2))\")\n", "end" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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+lEgkX3755ejRo48fPy6RSDiOW7lyZVJSEiHkhx9+OHnyJM/zEyZMkK1t4cKFmZmZsncJCQkJCQkpKCioqKh4+PBheno6IWTGjBlPnjz57rvvZs+ezXHcsWPHevfuXVZWlpiYOGvWrFmzZtXU1ISHh48ZM6bF/kOaH0ZGAUCRfHxd+mUPka4q7Rw0VFZWchz3gYOWz3npMkeWxYmj8Dy7k7mDqXJ91wVfO2ay9QvHwkJCQurnwh08ePCpU6cIIbNnz16wYAEh5Nq1a+Xl5Vu2bCGE5ObmhoaG2tnZFRUVxcTE6OvrL1iwoGPHjtHR0fVrk71kZGRECNm5cychJDAwsLKyMjIykmGe/gqNHTtW9kBNTW379u31T1+iU6dOmZmZUqmUEFJeXp6QkHDx4sX6wci8vLzPPvusfiSVEDJ06NBffvnlmZU4OzvL/i3dunVbsmTJtGnTnllAQ0NjzJgxZWVlDVdVWlq6bt26mzdvdu3alRAybNiwP/74o1evXiUlJcHBwcbGxlVVVYaGhrm5ue3bt3/lP0QeoIwCgMK4+oh/UEpKIzalaUzs2LEj7TitbdWqVYaGhl988YWBOjmZxbtboI3Cc/Roy+jI919r3dq8bNOdPn16YGCg7HF9X+zZs6fsgbm5ecPHjx49srOzc3Jykh3X1tDQ6N27d2xsbP3aOnXqJGui9W7cuOHm5tawiebk5CxZsiQ2NlZHR6ewsLCRM2iIxWJVVVXZEXNtbe2pU6daWlqOHTt2/Pjxz50Q7rmnkA4cOFD2YPDgwSkpKWVlZY1565SUFH19fVkTJYQMGzYsNja2V69eVlZWxsbGhBANDQ0TE5NHjx6hjAIANLMvbkoXGKV+v+ibue/Opp2FgiVLlvTp02fJkiXvd9X3T5C6W2AHDs/h0IZxeGnbk3MMw6ioPLtt13+FYRhZ/2uopqam4WN1dfWqqirZ0/9e66OhoVFdXd3wKytWrOjcufPevXtFItEPP/wQExPTmJzR0dENL5YPCgpKTk4ODw9fs2bN1atXP/roo/++739XUp+8urqaZVlZu5WNthJCKisr608tbUhdXf2//2TS4KdECGEYhufleoC8IZwzCgCKIfoRf6+UJIV8/+GHH7Zp04Z2HApsbW3Hjx+/adMmL1v2xmP+QanCfNIAtKiYmJiUlBRCSG5u7tWrV/v37/+ShYcPH37gwIHS0lLZU6lUmpWV1b17d5FIJJFIDh069Mq34zhu586dGzZsqL/tVE1NTXV1tZ2d3dKlS9esWXPr1i3ZFVTl5eUvX1VYWJiseh46dKh3797q6urm5uZxcXGEkOrqatkpCvr6+iUlJQ2/y9bWVkVFRXbnqaqqqrCwMEWfDxl/WAOAYvjqtnSBSdaGo3/JTvxXTp999plscHSmvd4f97n1rkp6IRcI2F9//dWpU6f6p3fu3Hnlt3Tt2tXLy8ve3v7ChQvLly+3t7c/fvz4ixYeN27cuXPnnJycBg4cmJeXN378+Llz5y5atCg8PPzu3bsvOa4tFot79epVVlaWkZHh6OgYHBw8fvx42UsFBQWWlpYDBw7U1taOjIzcuHGjlpaWl5eXk5OTjY3Ntm3bXrROLS2tgQMHmpubX7hw4ciRI4SQFStWzJkzJzQ0NCMjw9zcnBAyePDgjz76qGfPnvb29nv37iWEaGhobN261dfXd/DgwfHx8Y6Ojl5eXleuXHnlD0pu0RnF9ff3T0hI8Pf3b+k3EovFurq6Lf0uIADYVOTcjcf8pNPSUVEfmrQ1+vrrrykmob6pzJ49u2PHjjOWfd7/aG2ml6oajm/Jq5bbVKqrq/X09J451iwMxcXFxcXFDb9ibW2dmZnZrl07NTU1Qkh+fr6WlpbsB1tcXCyVSk+fPh0YGHjo0KHr169bWFjIbg7/5MmT6upqbW3t4uJiMzMz2arKysrKy8tNTU0JIVlZWUlJScbGxk5OTuSfy94dHR21tLSqqqr09fULCgpkXVCmqqoqJyeHEKKqqmpsbNzwmHtWVpaxsXFFRUV8fDzHcY6OjvVnqcr+Oebm5o8fP9bX19fW1m74LcXFxdra2oWFhWlpac7OzvUHfDIzM5OSklxcXGRPDQ0NeZ7Py8urqamxsrJKTU21srJiWba4uDguLs7U1LRz586yhI8fP67PnJGRUf9Da7ywsLCdO3eGhYU16bveHMooACHYVOTe+FPSPqrZP09xuXfvnuwMfVqobyopKSl9+vR58ODBxCu6S7qxEzuijcoplNHWERISEhgYeOLECdpBhIBWGcVeDADkXUwhf+Mxl33oxzlz5tBtovLA1tZ23Lhx/v7+s+zZHUk4bRSUnZ2dnbu7O+0U8EZwzigAyLuvY7iPndjoowVr12yknUUufP/99+rq6qo67PJoSV6lqJ0m7UAA9PTu3bt37960U8AbwcgoAMi1VDF/IZeb11UUEhIiO9kLTE1N27Rpo61CJlixe5IxGxMAKDaUUQCQaz/FcQu6sto4ivM8szthalAAUHjYwQOA/CquJiEpXPxk+Z5Php5B7ZhajvxdwPc2VuCbnAPUu379ekxMzLRp02QzKpWVlQUHB8+bN6/hhEnNZdq0ad9++62tre2NGzeOHz++Zs0aQkh4ePjVq1etra19fX2fueF8TExMWFiYjo6Or69v/VEa2fI2Nja+vr4vuXT94sWLp06dMjEx8fPz09PTq/96Xl5eREREampqhw4dpk2bZmho+OTJE9n9m2T69u3bvXv3JUuWLFu2TMDTzmFkFADk1+ZEzsOSaa9FO4e8+vPPPz3bizE4CoIRFha2YMGC//3vf7KnhYWFCxYs4LgW2cKvXbsmm35z+fLlw4YNI4R8//33S5cuNTAwCAkJmTBhQsOFo6Kihg4dKhKJ7t+/36tXr6KiIkLId999J1t+z549zyzfUEhIyJQpU3R0dKKiogYOHCiRSOpfGjVq1NmzZzU0NE6fPt2tW7fs7OxHjx4tXrz45j/y8/MJIX379l29enVL/BDkBU/Db7/99v7777fCGz158qQV3gUEAJuKHKqR8ubBkvkr1/z666+0szwlV5uKn5/fis++MNxVUyGhHQX+o+U2laqqKjU1tRZaOV2ffvrpkCFD9PX1c3NzeZ5PS0sjhNTW1vI8f+/evX379l26dInjOJ7ni4uL7927V1RUtG/fvjt37jx8+DA/Pz8uLm737t0PHjzgeT4rK2vPnj23b9+WrTk/P//IkSN79+5NTk6WfcXS0jImJubWrVudO3fmeb6iosLIyOjatWv1j69fv14fbOTIkevXr69//OOPP1ZUVBgYGERHR/M8X15ebmBg8Pfffz/3H+Xg4BASEsLzvFQqdXR03L9/f/1LYrG4/nH//v1//PHHBw8eyG4s2lBVVZWxsXFOTs5r/2AbKTQ01MPDo6Xf5b8wMgoAcmpPMtdZrTQ0cMuYMWNoZ5FTa9as2bnlV2fN0iPpGBwFgejUqdOUKVO++eabhl/cuHHjiBEjLl68uHTp0gkTJnAcFxUVNW7cuJEjR546dSopKWnNmjVTpkxZuXLl+fPne/Xq9eeff3p5eV2+fNnNzS00NJQQMmzYsBMnTly+fHno0KHBwcH1aw4NDXVzcyOExMbG8jzv6upKCNHU1BwyZMi5c+dky/A8HxkZOWrUKNlTd3f3c+fOxcTEMAwju5BfS0ur4fIN5eXlJSQkyG4+xbKsm5tbw8V0dHTqH/M8L7uXvkQi2bJly44dO2RdnBCirq4+YMCA8PDwN/3hyiucMwoA8ognZEM853z1N8uxY62trWnHkVO2trZjxoypiQ7YqfPxdFsMLgAhhISHh8vmNH/GuHHj3nnnHXlY7Jkv/teXX37ZrVu3pUuXqqioEELy8/M/++yzGzdudO3ataamxtHR8fDhw6qqqpmZmefOnZPNORQaGmpgYCCbUVNVVfXbb79NTExUU1Nzdnbetm3bxIkT4+PjZSee+vj4+Pn5eXt7y97r5s2b48aNI4Tk5uYaGxvXn5xqamoqm3KJEFJUVFRdXW1iYtLwpdzcXBMTk+cu31Bubq66urrsFFjZYpcvX/7vYvv3709LS/P29i4pKXF1dU1KSsrOzl68ePGOHTumTJlCCOnWrdvNmzfnzZv3kp+b4kIZBQB5dDqbr60sO7l784ULF2hnkWsfffTRyFGjqh2W5FWq4IajQAgxNDSUTYn536/LyWLPfPG/zMzM5s6d+8UXX8jm/o2Li7O0tOzatSshRE1Nzc3N7e+//+7fv7+Dg0PDGTsHDx4se2Bra9uvXz/Z5UQ2Nja5ubmEkF27du3atSs3N7eysjI7O7v+u4qLi2VNUSQSNTw5VSqVamnVna4uEokIIfWvSqVSVVXV/y6vqvqcSy1li/E8L6utz13swoULixYtkvVpAwODM2fOyL6+Y8eOJUuWyMpomzZt7t+///Kfm+JCGQUAebQxXtr1pr+Wm1unTp1oZ5Frjo6OXbt0qX14OCTFZ5kjBkeB9O/fv3///gq9GCHk008/tbOzk/UwQgjfYOpyhqmbybx+qneZ+ovZGYapf8yyLMdxZ8+e/frrr48cOdKpU6f8/Hxzc/P6FbZp00YsFhNCOnTokJ+fL5VKZdUzJydn6NCh9ctoaWnl5OS0b99e9lL79u07dOiQl5fHcRzLsrIvyuryMzp06CCRSB4/fiybPa5+JfWuXr3q6ekZEhIyYMCAZ7536NChOTk55eXl2traT548MTAwaMyPThFhzwUAcif5CX8jt+pSyG+ffvop7SwKYNmyZXlHf8Hd70FIjIyMli9fvnbtWkKIo6NjZmZmcnIyIaS2tvbMmTM9e/Zs0toSEhJ69erl4OCgoqLyzCz2zs7OiYmJsge6urpnz54lhBQVFUVFRY0ePbqmpubatWsSiWT06NGyc085jgsLCxszZoyLi4uOjo5s+cLCwgsXLowePZoQcvPmzfLy8vr1t23btk+fPocPHyaEVFdXR0REyE6Cj46OLisru3Xr1sSJE7dv3z58+HDZ8g2vtT916pSFhYWsc9+9e9fFxaXJP0cFgZFRAJA7vyVw/dIP1jg7P3ekAZ7h7u6+du3anIy0u8W23Qxww1EQiGXLlvn7+xNC2rVrt3bt2hEjRkydOvXSpUsdO3b09PQ8evRo41fl5ub2+eefL168uLa29t69ew1fGj9+vOxETBUVla+//nrmzJmTJ0+Oiory9PTs2rVrenp6v379srOzV69e/fbbb+fk5GRlZZWXl/v4+MiW9/X1nTx5cmRk5LRp07p06SKVSnv16nX9+vWGM5SuW7du+vTpt2/fjo2NtbGxkV0v1a9fv0uXLs2YMYNl2Y0bN27cuFEWpqio6Pz583Z2dnl5eRcvXty9ezchRCKRXL58ecOGDc3xc5VHTMOh71bj7++fkJAg28halFgs1tXVbel3AQHApiI/yiTEaq9ku8XNDtoiOZxyWj43FZ7nP/mbU2XJ171EtLNAnZbbVKqrq/X09Kqrq1ti5XQlJydLJJL6v0ITEhJycnKGDx/OMMzdu3dv3rxpYWExZMgQlmULCgrS09N79eolWzI+Pl5fX9/CwoIQkp6eXl5e7uDgQAgpLi6+f/9+375909PTz58/b2RkNGLEiMuXL48YMeLatWtOTk7a2tqurq7+/v6yvU18fHx0dLSNjc3QoUMZhqmurr569Wr//v3V1NRyc3NPnz6to6Pj7u6uqalZ/74Nl5fdsT8hIUF2rL9eampqZGSkiYnJyJEjZVdlRUVFubi4xMTE1NTU1C9mbm7eoUOHq1evZmZmGhkZDRgwQHbV1OHDh/fs2XPo0KGW/vmHhYXt3LkzLCyspd/oGSijAIRgU5EnmxO5szn8weFyWqrkdlO5W8yPOSlNna6CoVE5gTKqKC5evHjy5EnZxVJv6NKlS9XV1fXH3JvL/PnzV6xY0blz5+Zd7X/RKqM4TA8A8mVzIvdLPzltovKsmwGjr0Yu5fGD2qGOAjTBoEGDBg0a1CyrGjhwYPOg/PgAACAASURBVLOs5xkBAQEtsVr5gQuYAECOnMvhpRwZ0h516nX42LG4jAkAFA7KKADIkd8SuDkWpaiir8cq82xw8J5qKe0cAABNgTIKAPIio4yPSi//waNbXl4e7SwKydpYv/bw2vA0yasXBQCQGyijACAvtt7jXB4E9+/Xr127drSzKCRXV1ezDh1+DDpCOwgAQBOgjAKAXKiWkj/vc1nhmxcvXkw7iwJb8/GyGyEbS2pevSQAgJxAGQUAuXAglbPIPK9CpPVT8MFr8PGcqC7O/fHINdpBAAAaC2UUAOTC5kSOPffb0qVLGQbXL70+kUjk+e77f27+lXYQAIDGwn1GAYC+O0V8ampabcw177C9tLMovP+tnB9oYf13UmbvTha0s0BLkUqlP/30E+0UIDTx8fFU3hdlFADo+z2Bs7nx+8B339XS0qKdReG1baPbfcL8Laduo4wKlbq6+sGDBy9evEg7CDQPiUSiqqpKOwUhhBgaGg4ZMqT13xdlFAAoE0vIwVRu2wyP3t3saGcRiJ9/+Oaj67jdqJBNmDBhwoQJtFNA85DbSYZbDcooAFC2M4lzM2cnDKPw57hQDW3P5FeSu8V8NwOcgAsA8g4XMAEAZQH3uIVdsS9qTixDptkw+x5ialAAUAD4AAAAms7n8hxPBrbDAF4z87Zlg1N4nnYMAIBXQhkFAJo2J3A+Rjmoos2uZ1tGmhE7Z/ka2kEAAF4BZRQAqMku50/dvPerT9/a2lraWQTIq5dV8B+/FRYW0g4CAPAyKKMAQE3APc7qxtZ5c+eqqOBiyuY3p4cR4zxmx85A2kEAAF4GZRQA6JBw5I/4ysxzIXPmzKGdRZhs9Ri7sfM2bQ7gce4oAMgxlFEAoONAKmcYf7Cva28rKyvaWQRr4bhBZZzKhQsXaAcBAHghlFEAoMM/geMvbJ83bx7tIEI23ZatGTDn9y0BtIMAALwQyigAUBBTyKc+SCrKeDB27FjaWYTMUJ0MnjgzPCKioKCAdhYAgOdDGQUACn5L4OzubJ81a5aczMgsYLOcDYyH+sTGxtIOAgDwfLiCFQBaW3E1OZzGbfce17OrDe0swudhxX4wZYPjAJR+AJBTGBkFgNa27T43zpKd4DbEwsKCdhbh0xCR8Vbs3hRMDQoAcgplFABalZQnWxK5Dxyw82k9PnbsnmSUUQCQU/g8AIBW9Vc6116LuBpjBtDWM6w9k1dJEkpwt1EAkEcoowDQqjbd5eZZiWmnUC4sQ6bbMN+FnAkKCqKdBQDgWSijANB6Ygr51JLaz0Y7paen086iXGbYs+cKtdatW4fZmABA3qCMAkDr2RDPDSs4bmNjg1mXWtlbhkxbhz5EXef8+fO0swAA/AvKKAC0kkeVJDyDyzm5DbMuUeFrz7Z9Z/bWrVtpBwEA+BeUUQBoJf4J0nG6Obf+jp48eTLtLMrI146919nr1OnT+fn5tLMAADyFMgoAraFaSv64z+lc2+7l5aWlpUU7jjIy1SR9rNo4j5iwc+dO2lkAAJ5CGQWA1rAnhXMx5MP3Bs6ZM4d2FuU1056tGTgvICCA43DbUQCQFyijANDieEI2xXP9C063a9fO2dmZdhzlNcGKvWfQy9TM4sGDB7SzAADUwdz0ANDiTmXxhJBR3dr3/eYb2lmUmqYKmdiR7eJ/rnNnjEQAgLxAGQWAFve/O9KPurM97XrQDgJkpj37/mXpSieUUQCQF9gfAUDLii3i75eSqTbY28iFQe2YyloSU4hb3wOAvMDHAwC0rB9iuWWOrBp2NvKBIWSGHbPrAS5gAgB5gc8HAGhB6WX86Wxutj3G4eSIrz0bnMIFbPszNzeXdhYAAJRRAGhJG+K5OZ3ZlR/MDwkJoZ0F6tjpMfb6zKFz13bv3k07CwAAyigAtJjiarLrATfXuvrIkSPDhg2jHQee8rNnq3rPCAwMpB0EAKDpZVQsFk+dOlVPT69du3b/neP46tWrrq6uqqqqpqam27dvb6aQAKCQNidyE6zYv08fcXV1bdeuHe048NRUG/aOYb/yyqrbt2/TzgIAyq7JZfTLL78sKyvLz88/ffr0J598EhcXV/9SSkrKmDFjFi9eLBaL4+Pj+/Xr16xRAUCRVEuJfwK3wokNCgry9fWlHQf+RU+VjLUSdRnlExQURDsLACi7ppVRnud37NjxySefaGpqOjk5TZ48ueEcxxs3bvTw8JgxY4aGhoaxsXHXrl2bOSwAKI7AB1yPtsRYUhAdHe3h4UE7DjzLz57NcvIJDg6WSCS0swCAUmtaGS0sLCwqKnJycpI9dXR0TEpKqn/1zp07pqam77zzjo2Nja+vb0FBwUtWJZVKK18M8yYDKDSOJz/GcR93FwUHB48fP15LS4t2InjW2x2YJ21s2ne0O3XqFO0sAKDUmjYDU1FRESFER0dH9lRPT6+wsLD+1dzc3B07dkRERNja2i5YsODdd989evToi1a1e/ful5w7f+jQoUGDBjUp23OVlZW9+UpAGWBTaV5HMlk9kYqzduWHO3d+/fXXYrGYdqJmI6RNZbqVyt+DpgcFBQ0ePJh2FgES0qYCLUrYm4qWlpZIJHr5Mk0ro23btiWEPHnyxMjIiBBSUlJiYmLS8FV3d/eePXsSQj7//HMXFxeJRKKqqvrcVfn5+fn7+zfp3V+Prq5uK7wLCAA2lWbkn1y7uierqsr36dNn9OjRLCuoG3cIZlOZ143feW9m6Np3dXUwdN0iBLOpQEtT8k2laZ8QBgYGJiYmsbGxsqd37tzp3Llz/atdunRhGEb2uP4BACibyFy+uJqMt2Q1NDS2bt0qsCYqJHZ6TCdjrQtFGrSDAIBSa9qHBMMwc+fOXbduXWFh4aVLl0JDQ2fPnk0ImTlz5q1btxYsWLB37974+Pjy8vJvv/129OjRLxoWBQABW39H+lF3lsUfpIrAz54NfID5sQCApiaPWKxevdre3r5bt25z587dsmVLly5dCCF5eXlVVVV9+vT57rvvpkyZ0rlzZ5FItG3bthYIDAByLa6Ijy0kM+wwGqoYptqwZ7O5x1W0cwCAEmN4nsLfxP7+/gkJCa1wzqhYLFby8zCgkbCpNBffSKmTIfNxd8GWUeFtKjMipd01SoaJHvbu3Zt2FkER3qYCLQSbimA/MACg9WWW8xGZ3IIubGVlpYeHh1QqpZ0IXs3Png28nOLl5UVlbAIAAGUUAJrNpnhuVidWX40cOXJEIpG88nYeIA+Gd2DEHXqw6lpXrlyhnQUAlBHKKAA0D7GEBD7gFndjCSFBQUEzZsygnQgahWXIDDum/TAvTA0KAFSgjAJA8/jjHjfCjLXSYR49enTlypXx48fTTgSNNasTe6+Lz4EDByorK2lnAQClgzIKAM2gliO/3OWWdmMJISEhIR4eHvVTtYH866TPWFt2sOrWMzw8nHYWAFA6KKMA0AwOpnIddUkfE4YQEhQU5OvrSzsRNI2fPas2wAdH6gGg9aGMAkAz2HiXW+HEEkISExNzc3OHDh1KOxE0jbcte9/W48LFi/n5+bSzAIByadrc9AAA/xWVyxdXkzEWLCHk5s2bc+bMwXX0CkdfjbxjrdvR/y89PT3aWQBAuaCMAsCb2hDPLXOsm/8TF9Errlmd2K/L+2lq4nMBAFoVDtMDwBtJFfNX8rmZ9tiZKDw3MyZVzD8oxa3vAaBV4fMDAN7I5kRuVidWC6Npik+FJVNt2OAUlFEAaFUoowDw+ipryc4k7r2u2JMIhI8duzuZKyouxlSuANBq8BECAK8v5CHXx4Sx0WUIIVFRUWfPnqWdCN6IqzEjYsiwkWPPnTtHOwsAKAuUUQB4fZsTuA8c6i6c/9///peXl0c3D7w5bzvWYKAnbjgKAK0GZRQAXtPVR3xxDXEzYwghBQUFly9f9vDwoB0K3pSPLXO38/Tw8HCxWEw7CwAoBZRRAHhN/gncBw51d3QKCQkZP348pgAVAFs9xq592869Bh0+fJh2FgBQCiijAPA6CqpIRCbn988dnTAFqJD42LGqmBoUAFoLyigAvI6Ae9wUa9ZQnRBCkpKScnJyhg0bRjsUNI9pNuwdizGxd+5kZmbSzgIAwocyCgBNxvEk4B73/j93dAoMDPTx8cEUoIJhrEEGmat3HzFp9+7dtLMAgPChjAJAk53K5k01ibMRI3t64MABzAIqMN62bPXg9xwcHGgHAQDhw6wpANBkO5K42Z2e/ikbHR1tYGBAMQ80Ow8r9n2tbv1HOtMOAgDCh5FRAGiaompyKoubbvN074EmKjxaKsTdgg1N42gHAQDhQxkFgKbZncyNsWQN1GnngBbmac0cSEUZBYAWhzIKAE2zI4l7txN2HcLnbsHefMw/qqSdAwCEDp8oANAENx/zJTVkaPu6S5ciIyOrq6vpRoIWoiEi7ubs9/vO+vj40M4CAEKGMgoATSC7dEk261JBQcHEiRMlEgntUNBSPG2YWzouERERhYWFtLMAgGChjAJAY1VJyd4Uzs++blh0796948aNwxSgAuZuzsZV6g5zc9+/fz/tLAAgWCijANBYh9O4nm0ZK526MoopQAVPXUTcLViz4TMwNSgAtByUUQBorIa3F33w4EF2dvbbb79NNxK0NE9rJr798LS0tPv379POAgDChDIKAI2SXc7fesxP6Ph0ClBvb29MASp4I83Z2BJ2wlTvPXv20M4CAMKEMgoAjbL3IT+xI6shIoQQnueDg4NxjF4ZaIjIGAvWYIjPrl27OA63HQWA5ocyCgCNEpzCedvW7TEuXryoq6vbvXt3upGgdXhaM1fUnIYPH/748WPaWQBAgFBGAeDV7pXweRVkyD+3F3VwcNixYwfdSNBqRpqzMYX89/5/mpiY0M4CAAKEMgoArxacwk23ZUR1XZS0bdu2R48eVBNB61EXETdzNjwDx+gBoEWgjALAq+19yNcfowcl5GHFHEnnaacAAGHCpwsAvEL0I57nSc+2zKsXBYEaY8FG5nLltbRzAIAQoYwCwCsEp3Az7Or2FRUVFVVVVXTzQOvTVyO9jZnT2dy8efNKSkpoxwEAQUEZBYCXkfJk/0POy7ZuWHT79u2LFi2iGwmo8LBij6TzRUVFhw8fpp0FAAQFZRQAXuZsDm+pw3TSfzoF6NSpU+lGAiomWjHhGZzntOkhISG0swCAoKCMAsDLBCdzXrZPpwDNysoaPnw43UhAhZk2Y6nDtO0z9tatW9nZ2bTjAIBwoIwCwAtVS8lfGdw0m7odxa5du7y8vDAFqNLysGKP56mNHz/+wIEDtLMAgHCgjALAC53I4t4yZNprEUIIz/N79uyZMWMG7VBAjewGT15eXsHBwbSzAIBwoIwCwAsdTOU9rev2EleuXNHQ0HB2dqYbCSh6y5DheNKux9uZmZlJSUm04wCAQKCMAsDzVUvJsUxuQse6S5dCQkJ8fHzoRgLqPKyYo1nstGnToqKiaGcBAIFQoR0AAOTUqWzOyYDpoFVXRp2dnUeMGEE3ElDnYcV+fF169aefcOowADQXlFEAeL6DqfwU66cHT+bOnUsxDMiJgaZMyhP+UbWK7ExiAIA3h8P0APAcEo4cy+AmW2MKUPgXFZa8Y8Yez+JoBwEA4UAZBYDnOJXNOzQ4Rg9Qb7QFE5HJ004BAMKBMgoAz3HgIdfwGD1APXcL9mw2V8ORa9euxcfH044DAAoPHzYA8CwJR8IzuIn/XEfv5+d37do1upFAfhhrkM5tmEt5/KVLlzZt2kQ7DgAoPJRRAHjW6Wy+SxvGQpshhBQVFf3111+Ojo60Q4EcGW3BRmRy3t7eoaGh1dXVtOMAgGJDGQWAZx1M5ervdb9v375Ro0bp6OjQjQRyZYwFcyyT79Chg5OT0/Hjx2nHAQDFhjIKAP9Sy5GjGdwk66f3uvf29qYbCeRNj7ZMaQ2f8oT38vIKCQmhHQcAFBvKKAD8y/lc3k6v7hh9RkZGQkLCyJEjaYcC+cIQ4m7ORmTynp6eJ0+eLC0tpZ0IABQYyigA/EtoGjexY92eITg4eMqUKWpqanQjgRwabcFEZHIGBgZDhgw5cuQI7TgAoMBQRgHgKY4nR9J5D6u6Y/TBwcE4Rg/P9Y45ezmfL5MQb2/v4OBg2nEAQIFhOlAAeOraI95Ig3TWZwghJSUlZmZmAwcOpB0K5JGeKultzJzP5caPH+/s7Ew7DgAoMIyMAsBToWncxH+GRdu0aXP8+HGWxV4Cnm+0BRuRyWtqanbu3Jl2FgBQYPiYAYCnwtL5+hNGAV5ujAVzLAPzggLAm8KnDgDUuVPES3nibIT56KFRurRhVFkSX4w+CgBvBGUUAOocTuMmd0QThSYYZcGcyOIJIRzHZWVl0Y4DAAoJZRQA6oSm1R2jl0gkK1eulEqltBOBvBtlzpzI5Agh0dHRuB8tALwelFEAIISQ5Cf8o0q+rwlDCDl16tTVq1dFIhHtUCDv3u7A/l3Al0lI3759KysrY2NjaScCAMWDMgoAhPwzLMoyhOD2otBo2irE1YQ5n8sxDDN9+nTccBQAXgPKKAAQ0mDipYqKioiIiClTptBOBIphlDl7PJMnhPj6+oaEhHAcRzsRACgYlFEAILkV5H4pP7Q9QwgJCwvr37+/qakp7VCgGNz/uYapa9euBgYGly5dop0IABQMyigAkCPp3GgLVpUlhJDg4GAvLy/aiUBhOLRhOJ7cL+UJwdSgAPA6UEYBgISlcxOsGEJIUVHR5cuXJ0yYQDsRKJKR5ozsSL23t/fBgwdrampoJwIARYIyCqDsSmvI1XzezZwlhISHh48aNUpHR4d2KFAko8yZE1kcIcTCwmLdunVVVVW0EwGAIkEZBVB2EZnckPasriohhMycOXPbtm20E4GCGWHGXs3nK2oJIWThwoV6enq0EwGAIkEZBVB2Yen8hAYTL2lra1MMA4pIV5X0aMtE5WJeUAB4HSijAEqtWkpOZ3PjLLErgDcyypyVHakHAGgqfAIBKLWzObyTAWOsQTsHKLhRFszxLIyMAsDrQBkFUGpH0jkPK5YQkpGRERMTQzsOKKruhkxFLUl+whNCeJ53cXEpKCigHQoAFAPKKIDy4nhyNIOTnTC6efPmvXv30k4EioohZNQ/N3hiGKZr164HDhygHQoAFAPKKIDyuvqIN9FgbHQZnuf37t2L+ejhTbibM8f/OW3U29s7JCSEbh4AUBQoowDKKyytblj08uXLmpqa3bt3p50IFNg75uzlvLobPI0cOfL+/ftpaWmUMwGAIkAZBVBeRzL4CVYsISQ4ONjX15d2HFBseqqkR1smMpcnhKiqqk6ePBknfgBAY6CMAiipu8W8hCPORkxtbe3hw4enT59OOxEovNEWbERm3ZF6Ly8vHKkHgMZAGQVQUofT+IlWDCHk5MmTdnZ21tbWtBOBwhtlzkRk1t3gadCgQU+ePImLi6MbCQDkH8oogJIKS+cmdGQJISEhIV5eXrTjgBA4GTIcT+6X1l1T/8EHH2RlZdEOBQDyToV2AACgIKOMzyjj+5swhJAlS5bY2trSTgQCMdKcOZ7Jd9ZnCCErV66kHQcAFABGRgGUUVg672HFqrCEENK7d29DQ0PaiUAg3C2Y45mYFxQAmgBlFEAZhaZxsuvoAZrXO2bstUd8mYR2DgBQHPg0AlA6hdUkppAfYcbQDgICpK1Cehsz53MxOAoAjYUyCqB0jqZzI8xYDREpLS2lnQUEyN2CPf7PNfWEkMDAwAsXLlDMAwByDmUUQOmEpfMTrBhCyNixY8+cOUM7DgiNuwUTnvG0jFZWVm7evJliHgCQcyijAMqlopZE5nKjLdiMjIzExMTBgwfTTgRC49CGUWVJfHFdH502bdqJEydKSkropgIAuYUyCqBcTmRxfYwZA3WyZ88eT09PNTU12olAgMZZMX+l15VRAwODt99++9ChQ3QjAYDcQhkFUC5haXz9ve69vb1pxwFhGmfJHs14eg2Tr69vUFAQxTwAIM9QRgGUSC1HIjK58ZZMQkJCaWnpgAEDaCcCYRrcjkkq5fMr656OGTMmISEhNTWVaigAkFMoowBK5Hwub6/PmGkzQUFB3t7eLIs9ALQIVZa4mbPh/wyOqqqqTp06dc+ePXRTAYB8wkcRgBIJTeMmdmR5nsd89NDSxlkyRxtcUz9z5sxTp05RzAMAcgtlFEBZcDwJS+cmWDHl5eWzZs3q3r077UQgZGMs2MhcrqK27qmrq+v58+epJgIAOYUyCqAsrj7ijTWYTvqMjo7OF198QTsOCJy+GunZljmX83RwVCQSUcwDAHILZRRAWYSmcRM7YgpQaD3PXFMPAPBcKKMAyiI0jZ/UEb/y0HrGWzFHMzj+1QsCgFLDJxOAUrhdyLMM6W6IkVFoPTa6jKE6c6PgaR0tKSnZv38/xUgAIIdep4xyHJeenv7kyZNmTwMALSQ0jZvUkSkpKRkyZAjH4cgptJJxlkzDI/Usyy5YsKCoqIhiJACQN00uow8ePHBwcHjnnXesrKy+++67/y7w5MkTS0vLzp07N0c8AGgeh9P4iR3Zffv2tWvXDrcXhVYzzpKtnxeUEKKnpzdq1CgMjgJAQ03+TFq5cuX48eOTkpJu3br1ww8/JCYm/neBHj16NFM8AGgGSaV8SQ1xNWYCAwP9/PxoxwEl0teEya/kU8VP+yimBgWAZzStjJaWlh47duyDDz4ghFhbW7u7u4eEhDRc4Pz588nJyfi0A5Arh9L4iVZMSvKDhw8furm50Y4DSoRlyMSO7MHUp2XUzc0tNTU1KSmJYioAkCsqTVo6IyNDJBJZWVnJntrb26elpdW/WlFRsXjx4tDQ0Pj4+Feuqri4+M6dOy961cbGRkdHp0nZAOBFQtO473uLAn8PnDFjhopK037rAd6Qpw276rr0o+51Yx8qKirTpk0LDg7GzW4BQKZpH0tisVhTU7P+qZaWVsPLmFatWjVz5kw7O7vGlNHIyMiXlNHffvutZ8+eTcr2XGVlZW++ElAGAt5UsiqYh0/U3tIs9wsM3L9/v1gspp1IsQl4U2khLtokXawen1dmpV03Pjp58mQfH5/ly5czjJBv74BNBRpJ2JuKlpbWKye8aFoZNTU1FYvFUqlUtt7i4mJTU1PZSw8ePNi1a9d3330XEBAQExNTWloaEBAwc+ZMDQ2N565q4sSJ/v7+TXr316Orq9sK7wICINRNJSKNm9iRj7l1w8TEpF+/frTjCIFQN5WWM9laevyRVv3g6MCBA/X19ePi4gYMGEA3WEvDpgKNpOSbStPOGbWwsDAwMLh+/brsaXR0tLOzs+yxqqrq9OnTY2Njb968mZKSUlVVdfPmTYlE0sx5AaCJDqZynjZsenr6woULaWcBJeVpwx5I/dcNxcLCwlxdXWnlAQC50rSRUTU1tXnz5q1YseKXX365cuVKfHz8kSNHOI5zcnLat2/f1q1bZYuFhYWlpaXVPwUAWrLK+aRSfmh7Ru3dd2lnAeU1uB2TUcanPOFt9eqOy9vY2NCNBADyo8m3dvryyy/d3NwWL14cFRV15swZfX19hmFcXFy0tbXrlzEzMxs1alSz5gSA13EglZ9gxarhvqJAlYghEzuyh9MwMygAPAfD8xT2Dv7+/gkJCa1wzqhYLFby8zCgkYS6qQw4WrvGRTTKXMiXibQyoW4qLe1cDv/J39LrHkp0MwdsKtBI2FQwYAIgWNnl/L0S/u0OaKJA35D2TEYZ/1D8r+GPzMzM0tJSWpEAQE6gjAII1sFUfrwVuydwR1RUFO0soOyee6R+9erVgYGBtCIBgJxAGQUQrINp3JSOzDfffIMpJEAeeFqzBx7+65r6GTNmYGpQAEAZBRCmnAo+oZjXSruirq7eLFNIALyhIe2Z9DI+5cnTwdHhw4fn5+c3Zp4UABAwlFEAYTqUyo+1ZIODAmfNmkU7CwAhhIgY4mXL7nrwdHCUZVkvL6/g4GCKqQCAOpRRAGE6mMp5tK8+fPiwl5cX7SwAdd7txAY+4LkGJ476+fnt2rVLKpXSCwUAlKGMAghQbgWJK+bF18NcXV3Nzc1pxwGo42TIGKiTyNynbdTBwcHExOTChQsUUwEAXSijAAK0/yHnYcUGBwX6+fnRzgLwL372/zpSTwjx9fXFZUwAygxlFECAQh5yE0zLk5KSPDw8aGcB+Bdfe/avDE4sefqVGTNmeHp60ksEAJShjAIIzUMxnyrmx9jrJScna2pq0o4D8C9G6mRwO/Zg6tPBUWNjY3d3d4qRAIAulFEAodmbwntasyosEYlEtLMAPIefPRP47yP1AKDMUEYBhCYkhfOyxa82yK+xlmxiyb9uOAoAygyfWACCkljCl9aQ/qaYjx7klypLvGzZoORnB0erq6up5AEAulBGAQRldzI31VISsHUr7SAAL+Nnz+5M+tcNR+/cudOvXz96iQCAGpRRAOHgCdn3kDd9cGzfvn20swC8jIsRY6RBTmc/baNOTk4lJSWxsbEUUwEAFSijAMJx/RGvypKLh3fh9qIg/97vyvonPD1SzzCMj48PbjgKoIRQRgGEI+QhN97g8cWLFydNmkQ7C8AreNuy1x5xD8VPB0dnzpy5Z8+e2tpaiqkAoPWhjAIIBMeTAw950d8hHh4eurq6tOMAvIKmCpnVid3cYHDU3t7eysrq7NmzFFMBQOtDGQUQiLM5fHstcnwfjtGDwljYlQ18wFU0GAnF1KAASghlFEAgAh9wbiShuLh4yJAhtLMANIq1LtPPlA1OeTo46uXlFRERIRaLKaYCgFaGMgogBGUSEpHJlUYF+fr6six+r0FhfODA/nb3aRk1NDT8+OOPi4qKKEYCgFamQjsAADSD/anckHbsD+vWSiQS2lkAmuAdM6aaI5fy+IHt6mZq+OSTT+hGAoBWhhEUACEITOL8OjE6OjoGBga0swA0AUPIwq6sfyKmqgdQXiijAAovVcwnlvCjLfDrDAppVif2VBaX5GSy/AAAIABJREFUXY6p6gGUFD69ABReUDI/3ZZVw28zKCY9VeJnz26Mx+AogJLCxxeAYuMJ2fWAGyRNLC4upp0F4DWtcGL/TOIKq59+ZfHixRcvXqSXCABaD8oogGK7nMers+SnlXOjo6NpZwF4TWbazESrf90A39bWduvWrRQjAUCrQRkFUGyBD7gx6snp6ekjRoygnQXg9X38FvvLXWn5PzfA9/PzO3bsWEFBAdVQANAaUEYBFFhlLTmcxlVd2OXr66uigju1gQLrrM8Mbs9uv183ONqmTRsPD4/AwEC6qQCgFaCMAiiw/alcH2M+bN9uX19f2lkA3tSq7uxPcZzkn2P1CxYs2LJlC8/jKnsAgUMZBVBgAfe4vo8jTU1NnZycaGcBeFO9jRk7PbL3YV0b7devn56e3vnz5+mmAoCWhjIKoKgSS/hUMX//+C4/Pz/aWQCax6q3RN/FcNw/g6Fz587FZUwAgocyCqCotiRyvuZlERHHpk+fTjsLQPN4x4zRUSVh6XWDozNmzCCE4Eg9gLChjAIopMpaEpzCvdtV/cCBA23btqUdB6DZrO0hWnuzbnBUT09v3759DMPQDgUALQhlFEAh7U/l+hgznY21cEcnEJgxFoyWCglNw4RMAMoCZRRAIQXc4+Z1we8vCNPaHqK1t56eOQoAwoYPMwDFI7t0abQFfn9BmEZbMDqq5DAGRwGUAz7MABTP5kTOz6Ki/EkJ7SAALeWLHqIvGgyOent7Z2dnU00EAC0FZRRAwVTWkpAUTuXStuXLl9POAtBSRpkzeqrkQOrTCZn+/PNPupEAoIWgjAIomOAUrq8x2b8zYMGCBbSzALSgL3qKvvpncPS9997btm2bVCqlHQoAmh/KKICC+fUu16/wrJaWVp8+fWhnAWhBbmZMG/W6CZm6d+9uZmZ2/Phx2qEAoPmhjAIokqhcvlJKru/fsmjRItpZAFrcVz1FX9ziajlCCFmwYAFmYwIQJJRRAEXyawI30yj70qVLmHUJlMHwDoy5FglK5ggh06ZNu3btWnp6Ou1QANDMUEYBFEZ2OX8+hys584evr6+2tjbtOACt4eteoi9vcTUc0dTU9Pb2xmVMAMKDMgqgMH5L4Hw61u7ZuR2XLoHy6G/KdG1D/rzPEUIWLFiQk5NDOxEANDOUUQDFUC0lO5K4BV3YgICALl260I4D0Hq+7iX6+jZXWUscHBy2bdtGOw4ANDOUUQDFsCeF69WW6WasPnbsWNpZAFpVz7aMqzGz5R4mZAIQJpRRAMXgn8At6iainQKAjq96sutjpeW1tHMAQAtAGQVQABfz+HIJGWnO0A4CQIeTITO0A/vbXQyOAggQyiiAAvg5jnvfrqq0BJPRg/L6sge7IV4qlpCamhofH5+amhraiQCgeaCMAsi7VDF/OZ/jr+5euHAh7SwA1HTSZ0aYsb/e5dTU1PLy8sLCwmgnAoDmgTIKIO9+juMWdGW3b908f/582lkAaFrrwm6Il5bUkPnz52M2JgDBQBkFkGvF1SQ4hetZdKWmpmbo0KG04wDQZK/PjLFgf7nLTZw4MSEhISkpiXYiAGgGKKMAcm3rPW68Fbt/x+aFCxcyDC5gAmW3xoX99a60nFfz8/MLCAigHQcAmgHKKID8knDk9wRuZrvCEydO+Pr60o4DQJ+tHuNhxW6Ml86fP3/Xrl1VVVW0EwHAm0IZBZBf+x9ynfTJ1YPbPD09DQwMaMcBkAurnVn/BK6NmY2Li8uhQ4doxwGAN4UyCiC/NsRzSxxIQEDAe++9RzsLgLzoqMtMsmY3xEvff//9u3fv0o4DAG9KhXYAAHi+qFy+vJaMNON//vlnFxcX2nEA5Minb7GuR2ofTPXw8PCgnQUA3hRGRgHk1I9x0uWOrJqq6qRJk2hnAZAv1rrMWEv2F0zIBCAIKKMA8iiplP+7gJ9hh99QgOdb7cz+Ei8txTRMAIoPH3UA8uinOO59B5EmzqMBeAFbPcbdgv09EYOjAAoPZRRA7hRUkQOp3GxrSQkmowd4sc+c2Y3x0rScghUrVtDOAgCvD2UUQO74J0inWrORR/fPmjWLdhYA+dWlDTOsPbu/oM3BgwdjYmJoxwGA14QyCiBfqqRkayK31JH19/efO3cu7TgAcm21C7vxLpk5ew5mYwJQXCijAPIl6AHXy5ipSovNzc11d3enHQdArjkaMH1NWPWhc/bu3SsWi2nHAYDXgTIKIEd4QjbEcyudRP7+/gsXLhSJRLQTAci7NS5sQK7p4CFD9+7dSzsLALwOlFEAORKRyWupkLc0Sw8dOjR79mzacQAUgIsR06UNsR03//fff6edBQBeB8oogBz5OU66zJENDAwcPXq0qakp7TgAiuFTZ9Ff2sPLyspu3LhBOwsANBnKKIC8iC/m75eSKdbM1q1bMRk9QOMNa8+YaDF9Js+9cuUK7SwA0GS4pzaAvPgpjlvkwIp46eeffz5w4EDacQAUyaru7OeSFUGT8KEGoHgwMgogFx5Vkr/SuXldWBUVlenTp9OOA6BgxlmxHCEns3jaQQCgyVBGAeTCbwlSL1vWSJ12DgDFxJD/b+++A5o6FzaAv+ecLAJhyJKhAqICLhQHbqu4RbTOqnXVVRXroq6r91oXbqlVq9faW620ta3WXUXrqAqCogJSVFARAVE2hJXknO+P3I+LVitQ4M14fn8lOSF5gDech/cssqQ1u/6OhnYQAKgylFEA+orVZG8CP7c5Po8A1TfajU0tIlefY3IUQM9g5QdA38FEvqMd62aqwcXoAaqNY0hQK3ZdZP6kSZM0GkyRAugNlFEAygRCQuL4+S3Yo0ePjh49mnYcAD02qQl7t9D0bkLi0aNHaWcBgMpCGQWg7NwzQcKRng7M1q1bZ82aRTsOgB6TcmRuc9Zi0PyNGzfSzgIAlYUyCkBZyD3NvBbsxYsXc3Jy/P39accB0G8fe7HxLoNfZudevXqVdhYAqBSUUQCaHuYJ0ZnCaDd206ZNQUFBLIuPJMDfYi4mH3mIXIbN3bJlC+0sAFApWPMB0LT9Hj/Tk30YH3v79u1x48bRjgNgCOa14GI8Prx67XpCQgLtLADwbiijANTklpHvk/iZntymTZvmzZsnk8loJwIwBPYmZJSHmWfA9M8//5x2FgB4N5RRAGq+us8PasCqMlNOnz49Y8YM2nEADEdQKzbee0ZWbj7tIADwbriMLwAdGoHsjOcP9+ZszWxPnjxpaWlJOxGA4XBTMH28HNp1P0A7CAC8G2ZGAeg4nsw7ykk7G0Ymk/n6+tKOA2BolrRmt8fxZTztHADwLiijAHSE3OM/aYEPIEBtaV2PaWFFvk1EGwXQdVgXAlBwJ0t4lE+GNcIHEKAWLW7NbYrheVysHkC3YV0IQEHIPX6WFxt79zYuRg9Qe3o6MPWkZOi0+SdPnqSdBQDeCmUUoK69LCHHkvmPmpLRo0fHxsbSjgNgyIJasfcsfTZv3kw7CAC8FcooQF3b8wc/3IW9cvqolZVVt27daMcBMGQBjVhZhxEJSU9u3LhBOwsAvBnKKECdUvFkTwIf2JzdtGnTkiVLaMcBMHAMIUHeEssBgdu2baOdBQDeDGUUoE79/Jh3Nyc5sVdyc3MDAgJoxwEwfOPc2aIuU8N+uxQXF0c7CwC8AcooQJ3SntFp48aNixYtYll8AAFqnZglC3wUjkMCg4ODaWcBgDfAuhCg7tzKFNKLiFt+/O3bt8ePH087DoCxmO7BZnT6+My5sPv379POAgCvQxkFqDvb4vjA5uyOz0MWLlwok8loxwEwFnIRCWxr2XLWdrVaTTsLALwO16YHqCPpReR0Cr+jk1gaEoIN9AB1LLA5GxI3wqwR1noAOgdrRIA68uUfmg8as1ZSIpfLMS0KUMcsJWSqB7s5BlcHBdA5KKMAdaFUQ/Ym8IFe+MQBUDO/BXcoiU8vop0DAF6FVSNAXfg2kW9ny3hYMrSDABgvexMytjG7454mNTWVdhYA+B+UUYC68Pk9fqg4Ye/evbSDABi1xa3ZvbHKNm3aJiYm0s4CAP9VzTJ6+/btsLCw3Nzc1x5XKpXXr1+/fPnynxcBGK0LaYJAyNndnxUWFtLOAmDUGpgy/u6mLd6fuW7dOtpZAOC/qlNGJ0yYMGLEiJCQkGbNmkVFRZU/HhYW5uzsvGDBglWrVrm6uh49erTmcgLosW2xmlHSP65evTpz5kzaWQCM3XJvNs4n8PiJEw8fPqSdBQAIqUYZvXr1alhY2K1bt06ePLlw4cKlS5eWL3J3d4+Pj4+IiPjtt982b948e/bsGo0KoJce5gk3M4Xorz8LCgqSy+W04wAYO3dzpo+7lffwjzds2EA7CwAQUo0yeuTIkcGDB1taWhJCxo8f/9tvv+Xk5GgXubq6Ojg4aG83b948Pz+f53ESDTB22+/xwyUJN8Kvz5gxg3YWACCEkH+0YWN85h47fvzRo0e0swBA1U96n5KS0qpVK+1tR0dHsVicmppqZWX12tO2b98+atSovziz9+PHj3/88ce3Le3evbutrW1Vs/0Zz/MoxFAZtTRUckrJ90l8p5//pb3kEkajAcBfFQPQzJz0cLXMHTZ93bp1tXdYIYYKVJJhD5XKXOSlymW0tLRULBaX3xWLxcXFxa89Jzg4OCYm5tq1a3/xOo8ePQoNDX3bUhcXF4VCUdVsf/ZaWoC3qaWhsiue61QaGx0Z/s1Xe0tKSmr89aHu4a+KYQjyYoa0DYxe5rVkyRJHR8faeAsMFagkwx4qMpnsnX20ymXUwcEhKytLe7uoqEipVJZvmtcKCQn56quvLl269Ofp0op69+69c+fOqr57VWk0GuylB5VRG0OlVEO+fKAOkiQP/ewza2vrmn1xoAV/VQxDBznxdZO0+S7K3d2tlt4CQwUqCUOlymXU19d3165d2tuXL192cXGp+D/lvn37tm3bdunSJScnpxrLCKCfvk3kva3JvH7DaQcBgDf4Z1s24FzDJRoi5WhHATBuVT6AafTo0S9evJg7d25oaGhgYODChQtZll27du3AgQPPnj07ffr0/v37//DDDxs2bNiwYUNRES67BkZKIGRrLL+oFdZyADqqjTXTqh7Z/8Bg99UD0BdVLqNyufzatWtyufzs2bNr1qyZM2cOIaRbt25jx461t7dfv369q6trLeQE0DMnn/JyEXnPAdf/BNBdq3y4tXf4YjXtHADGrcqb6Qkhzs7OwcHBFR/p3r279oa3t3cNhALQf5ti+PkeZdX7iAFA3fCxYXxsmO0RGSY3v5s3bx7tOABGCtemB6h5US+Fh9d+3T8ngHYQAHiHNT7sjkT51m3bwsPDaWcBMFIoowA1L/iOiv156bx5n9AOAgDv0LIe08lZ3m3GZ/PnzxcEgXYcAGOEMgpQwxLzhbDDX7vWrzd48GDaWQDg3f7Vlr3YaEyZSv3zzz/TzgJgjFBGAWrY2kglc2Ltpg3B734qAOiAlvWY7g6iDrM3Ll68uLS0lHYcAKODMgpQk1KUwg9fbvbr0bVTp060swBAZX3mw/4i7dbEw3P37t20swAYHZRRgJr0r0vPyYWdG9etph0EAKqgqQXTx4ltNnXjunXrsrOzaccBMC4oowA15nkxCd0RPHHChMaNG9POAgBVs9qHPVTYZOYnizIyMmhnATAuOAkiQI3ZFKOZvHDF+g5i2kEAoMpcFMwHjdnCJgs9PXHhNIA6hZlRgJqRVUq+ecAv72xtYWFBOwsAVMfKttyBh/yjApzgCaBOoYwC1IytsZpRbqyTKa7/CaCvbGVkthf7WTSuVg9Qp1BGAWpAXhn5dwL/aSt8oAD0W1Ar7lwqfzdbSE5Opp0FwFhg3QlQA2buOu797JSLAtOiAPrNTEwWt+JW3OSHDx/+yy+/0I4DYBRQRgH+rtS80h/Xz5vaGruKAhiCmZ5sbI4wdtGaJUuWqFQq2nEADB/KKMDfNXrxBhfP1qMGvEc7CADUAClH1rZjv5P5NWzUaO/evbTjABg+lFGAvyX8XlJ46I4f9obQDgIANeaDxqxMRLrN2bBmzZrc3FzacQAMHMoowN8yZtrcnpMW+jRtSDsIANQYhpAQX253QfNBAcOWLl1KOw6AgUMZBai+Lw/9nPr0cei6hbSDAEANa2vD9HViLcasPXny5LVr12jHATBkKKMA1aRUKhctWDBp1U57M1xyCcAAbejAHXhmFrRm8759+2hnATBkuBwoQDXdyxHEI9Zsn4DjlgAMk70Jmd+Cu5I14vBXI2lnATBkmBkFqKaVcbLVs8dhVhTAgC1oyUZnCpczcAphgFqEMgpQHWdShORCMsMDnyAAQybjyHZf9uOrmlIN7SgAhgurUoAq0wjk00jNlo6cGB8gAEM3pBHbsh6z7o6GEFJYWEg7DoABwroUoGpycnI+/GyPnQkZ2ABb7gCMwo7O3JcJ/PnYZC8vL5x2FKDGoYwCVM2iJcuOX4/Z7svRDgIAdaS+CVnVlvvHY6eBgwYtW7aMdhwAQ4MyClAFN2/e/OHIsVHzP2tZD9OiAEZkugcrZonHlPUnTpy4fv067TgABgVlFKCy1Gr15Gkz2RHr1/ewpp0FAOoUy5A9Xbn1D0yXr900c+ZMlUpFOxGA4UAZBais9evXZ3DWy2eOtzehHQUA6pyXJTPbiztuP8LZ2XnLli204wAYDpRRgEq5ffv25u07LKd9uaAl9hYFMFLLWrO5paTj/J1bt25NSkqiHQfAQKCMArxbSUnJuPEfSsdt+dLfBadzAjBaIpZ8+x63M8N53KyF+/fvpx0HwEDgcqAA78ayrPuYxe27j+3liOOWAIyam4LZ2IHbJJ13c5iEdhYAA4FJHoB3SywSh7uOCW6PDfQAQCY1ZVvZiP5xi6cdBMBAoIwCvINAyOxrmlVtOQc57SgAoBt2deZ+eiycfSbQDgJgCFBGAd7hwEO+UEVmeOLDAgD/ZSUl3/bkJl1WPy4QYmJiaMcB0G9YvwK81enTp7fs+venkZovu3IcdhYFgAq61WeWeXMBZ8s+GDvum2++oR0HQI+hjAK8WWZm5rRp046XuM/0YH1sUEUB4HWBzdl2diLXhaFBQUHx8fG04wDoK5RRgDebPXu2z6CxLxt2W+qN45YA4M12deEyrDz95gaPGjWqqKiIdhwAvYQyCvAGhw4duhMTG9l55X96cDJ0UQB4CxlHfuzNXXT9sEGL9nPmzKEdB0AvoYwCvC4tLW3BggUun3w9wUvewRYb6AHgr7gomEPviaL7hYRHRWPnUYBqQBkFeIVarR47dqzfh4HJ1j6r2mJSFADerZcjE9zFTDn54MJF2HkUoMpwBSaAV+zZs4eTyn/zDvqlB2eCzwcAVM7kpmxSd6+jygMW1na0swDoGcyMArxi+owZ3MxvZzcXd7TDBnoAqILV7bi23frMj7PicS58gKpAGQV4xY4/2GKx+VJvfDQAoGoYQvZ149KLhWU3NbSzAOgTrHEB/icuR9gYoznYA6e4B4DqkHLkZF/RmRRhexyuXA9QWSijAEQQhLi4uBINGXtRs9WXc1GgigJANVlIyOl+3Jarqe17DVAqlbTjAOgBlFEAEhwcvGjRosDrmlb1mLGN8aEAgL/FyZQ5Nco5We4+Ysps2lkA9ADWu2DsLly48MUXXwxe9c31DOHLLjiXEwDUgFb1mNDdW85H3F6782vaWQB0HcooGLWnT59++OGHq748tO15w5/9ODMx7UAAYCj8Gkg27f9h5bLFZyPu0M4CoNNQRsF4lZSUjBgxYs78oODirpvbqjwssasoANSkeb09Jq7YPuT9USmZBbSzAOgulFEwXnPmzHF2do5qHTi0ETOsAQ59BYCat3/R2CY+XdoNn16C0z0BvAXKKBip3bt3R0ZGNpv/dXYZCW6PXUUBoLZEfL+TLc4e/Us6ToYP8EYoo2CkBg8ePG3XycNppj/2FonwOQCAWmNmKn8SfjZfZrvgBmZHAd4AK2EwUsli59VPHI715exMaEcBAEMn5cixvqJLacKWWOwRBPA6lFEwRo8LhNG/aQ69J2phhYOWAKAumIvJ6f7cjnv8t4noowCvQBkFI/LgwYP09PTsUjLgV80qH7aPE5ooANQdRzlzoi/30YhBO365TDsLgA5BGQVjkZqa2q9fv3MXrww+qx7qwkxthsEPAHWtZT1m3fJF8yaOCg27TjsLgK4Q0Q4AUBfy8vIGDRo0feasg5bDW5gz63H4PABQsnBk78yigxNGvm9x7NigHh1pxwGgD5NDYPiKi4v9/f07d+ka3maBpZTZ3YXD5nkAoGj9xL6TN/xn6NCA367fpJ0FgD6UUTBwGo1m/PjxTs7OOcO3MQz57j0OVRQAqPv3jP4Dl+4a4D/k5t1Y2lkAKMNmejBkGo1m6tSphUql3axDz0uZE305Mf7/AgDdcDTo/e7Ksu69+z+9H2tjXY92HABqsGYGQ3b9+vVnqWnywMOZKtGxPiIZ9hQFAJ3BMuS3f47xXhe2MsEC12YCY4YyCoasQ+duZotOqcXyo31EcmwGAAAdI2FJ2BSvmGxhQQQuzgTGC2UUDJZSTfzPqWVi5ogf5kQBQEeZisjJfqLL6cLq2zgZPhgplFEwNIWFhYIgvCwhvU6pXRTMoZ7YTxQAdJqlhJzpL/o2kR/xj51paWm04wDUNaylwaBkZGR07dp17w/HOx9X93Nm9nTlWBw7DwA6z96EnB/I/fa4wKdb74yMDNpxAOoUyigYjvT09N69e7fu3n8VP/DTVuxnPjiJEwDojQamzM0vF5e2G9OqU0/0UTAqKKNgIBITEzt37txp+Ee/dly9t6tomgfGNgDoGTcFE7N/pabNMO8e/dPT02nHAagjWGGDIYiMjOzZs2fHycvPeASe7Csa3BBTogCgl5xNmfhv1xGf95u2ancuLIx2HIC6gDIK+k0QhO3bt/v7+7ecsyO+xaRr/lx7WzRRANBjdiYkfv+KhvMPvD9uSugPh2nHAah1OPUi6L3HKWnNgq8xji5Xe4nMxbTTAAD8bVZSEvlp79HNor7QSPyKiZ0J7UAAtQkzo6DfnhSSC53XtW7meqIvmigAGA5TETkxvL5fY4uOx9V3s3GFJjBkKKOgx64+F7qcUM/yZHd05nDkPAAYGIaQz3y4jR3YvmfUPzzib968WVpaSjsUQM1DGQU9k52dPXTo0MuXLx94yI+4oP6mh2iWF4YxABiska7sr/1FK27xH6zc6du5S2JiIu1EADUMa3HQJ1FRUe3bt2/YqNEpcYfVt/lLg0R9nDAjCgAGro01c3uYqNeyfam+szt27hoaGko7EUBNQhkF/SAIQkhIyKBBg1at2/B08NaoHHFEgMjDEk0UAIyCqYjs6crt+3Qit+jsJyvWjvtwglKppB0KoGagjIIeyMrK8vf3P3To0JGLEZvFQ+1NyLkBImsp7VgAAHVrSCM2NrD1ezuuH0/mPb3bx8bG0k4EUANQRkHX3b17t23btl5eXpuPXB19t+HkpuyerpwYIxcAjJK9CTk80OLodwdVfRb2/GDG00KediKAvwvnGQVd5+TktGfPnjS3vqMua/7Tg+vvjE3zAGDs/JyYJzs+2nBnos8vmhkewuLWnALntgO9hfkl0HVW1jaXrPsE3+UvDhKhiQIAaEk5stJHdGeY6GUJcT+sConj1ZgkBf2EMgo6h+f5Bw8eaG9nl5J+Z9Qx2UJUgMgThysBALzKyZTZ05X7tb/ocMTDBtN3HHnC4/z4oHdQRkG3HD9+vHXr1suXLyeERGcK7X9R+9gwJ/qKLCS0kwEA6Ko21szBXmLzqAMfjXm/zZ4HF9LQSEGfoIyCrvj999+7dOmyYsWK4ODgH3/88av7/ICz6o0d2A0dcHUlAIB3cHNzi426Nm9g20dLu7w/dlKXfX9EvkQlBf2AMgr0xcfHjxo1avz48RMnToyOju7df9DU3zXb4vgrg0XDXTFEAQAqRSKR/HPlytTkR0v6e8V82v09/1F99sfdy0ElBV2HNT1Q9tNPP/n5+XXr1u3hw4fTp0+/X8D6HlMXqcmNAFEzC8yIAgBUjUKhWLpkcVryoyX+bZ9/u7z3afXEy5onBaikoLtwaiegrH///g8ePDAzMxMI2RXP/ytaE9yBm9IU/yYBAFSfQqFYsXzpiuWkQEW2xfHtj6lHu7HLvTkHOe1kAH+CVT7Utfz8fJVKVX7XzMzMzMzsRTEZck79zUP+mr8ITRQAoKYoxGRlGzZhpNiEI01mbJt0MCqrlHYmgFdhrQ91p7S0dPv27U2bNr18+XLFxw8m8q2OqFrXY676i5pg0zwAQE2zlpJNHbnl7aQ/LXzf0XfQtAPh+ap3fxVA3UAZhbpQUFCwb9++Zs2aXbx48cKFC35+ftrHHxUIfc+ot8Xyp/qJ1rTDRT4BAGrR0k9mZaUk/mPCoO+Cxti26zf7wFWlmnYmAJRRqFUqlerEiRNjxoxp0KDBiRMnQkNDjx071rx5c0JIiYYE3+U7HlP3cWIjA0Q+NpgQBQCodVKpdMX8WdkpD5dPGf7N4gn1vHvPCb1RiFlSoAplFGpRSUlJSEhIz549Hz16dOzYsc6dOxNCBEK+T+I9f1JHvhRuBIiCWrEiDEMAgDokkUhWfjI95+n9lR+Pi0/La3xYtfYOn419SYESHE0PNenevXsNGjQwNzfX3lUoFOfPn6/4hCvPhU8jNRqefNOD614fs6EAANSIxeLls6csJyQhV9gQwzc5rBrnzvZQRgzq6iOTyWinAyOCKSmoAc+ePdu8ebO3t3f//v0TEhLe+JzzqULPU+opVzSBXmzkUBGaKACAjvCwZL7uzsUOF5kw6g/mrTS3qd/Df1Ro6Hd5eXm0o4FRQBmF6svLyztw4IC/v7+3t3dMTMzq1asfP37coUOHis/hBXIsme90XP1JuGZqMzZhhGicO4seCgCgaxzlzAZfafbtC+vOJya7DZi+40h950YdOnekDm2LAAAPnElEQVQNCQlJS0ujnQ4MGTbTQzWFhYWNHDnSz89vypQpP/30k1Qqfe0JmSXkq/v8lwm8vQlZ1JJ934VFCQUA0HFmYrLI12aR7+SbmZN23c4/fPzMuiPHvj0fdeT7gw1M8UccagXKKFRKaWnpgwcPWrZsWf5Ily5dkpOTLSwsXnumRiBhqcKhRP7kU36YC/tTbw5HygMA6J12Nsz+Pha7e40JSx195Anf5ojazZzp5cj0dGAV6XdMxYy3tzftjGAgUEbhrZ48eRIeHn7jxo2IiIi4uDhvb++rV6+WL5XLX7monEYgN14IPzzif3jEuyiYsY3Z7Z3E1q/PlgIAgD6RcmRwQ2ZwQ07Nc9cyhEvpwoa7mohfbgsn10oYoU33vl182w3q4tPBu4VYLKYdFvQVyii8wdixYy9evMhxXMeOHTt16rR58+a2bdu+1j61skrJuWf8qRTh7DPeUc4Md2Wv+ovczTEVCgBgUEQs6eHA9HBg/knYkv5Tbr6cfCri7qWLF/cev7Jh8zbh5RPThp49lu5r27qlg5xxlBN7E8ZRTqxljCmKBrwLxohREwTh/v37N27c6N+/v729ffnjU6dO3bBhQ4MGDf78JSUakpArRL0Uwl8I4S+ENKXQ05Ed2IBZ316E3YkAAIyBjCNd6zNdh3qTof/dUp+UqQwLv8M4NXpOmNhs4ddn5EUx/8fBNcUm1qRRWxv3VjYKEyspsZQwVlJiJSEWEsZcQiwkxFxMLCWMhYSYS4i5mLGQEDmKifHB79y43L59Oy4uLiUlJS0tLTExMTIy0srKytfXt3PnzuVltEBFvDr1UqqEW5nCi2LyokRILyLPi4UHecL9XJJeLDRWMG1tmE52zLwWbHMrhkMFBQAwbo1tTBv7d3ntwf2ZDcPDw2+e+k9Cwh+mru6OLX1sPdvYNmtj7dW5QC08LSR5ZSRfRfLK+NxSkq8i+WVCnoqoeWIpIZZSxlpKrKXEWsZYS4mDnKkvJ/VNGAc5aWDKWEiofJdQW6pTRpOTk0+fPm1hYREQEGBqalpxUX5+/rFjx4qKigYPHuzk5FRDIaGycvPyY5OexT9++jglLflpSuqzZ14Dxlu26FqgIvllpFBF4r77tSA5nrF0FNVrqvbuZz58PzG3O1smnIkgJEKVW0oEQszExFRETEWMlZTYmRA7GVNfTlzNGD9H1sOSuCrQPgEA4N2mTJkyZcoUQkhZWVlsbGx0dPStW7cunf3+2rVrDPPfFYlGo5k/f4GDg4OTk5Ojo6Ojo6O1vSMjt8wpE7JLSVYJySoVskpIepEQm02eF/NpRSSlUCCENDBjXMyIq4JpbM64KUhjc6axOSPjaH6/UG1VLqNRUVF9+/YdN27ckydP1q9fHxERUd5Hc3Jy2rdv37JlS3t7+2XLll25ckV7FXKoKQIhL4vJw7TMP56kFkutNJbO6UXC82LyoliI3r/q5YntAmE4a2eZtZOZraOVQyPrRm0FCwdLCdPAlJhLiJmIKFYvEbFEISYsQ8r/szQX/7dfWkoJeiYAANQsiUTi4+Pj4+Mzbdq01xap1Wp3d/f09PSEhITU1NT09PTU1FSVSuXp6Xnz5k1CCCEMIUSlUkVERDg0cXBycjIxMcktIymFQnIhScoXHhUI51OFpALypECwlTHu5sTdgmmsYBqbEzcF09gc06h6oMpldM2aNQsWLFixYoUgCF26dAkNDS0fW/v373d1dT169CghxMLCIjg4+ODBgzWc10CVakheGUl+kf2ysKxQkKhkltmlJLNEyColCTevJV49nfcitehFSll2GpPzjJWYyKwd2kxc3m7AKAc509yK2Jmwpuvn2e8IcrM1x3XeAQBAX0il0rlz5772YFFR0YsXLyo+kpubu2zZsvT09LS0NJlMpp1DdXBw8PLyClm8WPscXiCPcsoiE9MziNmzQnnkS0lSPp9UIEhY0siMaWTGNFKQhqaMg5w4mzL1TYiDnDHDCQB0Q9XKqCAIZ8+eXbNmDSGEYZghQ4acOXOmvIyeOXNm2LBh2tsBAQFDhgyp2ay6KT8/XywWm5iYqHhSqCJKtZDw4OGt23fylcXK4pKsnLyikrKCggJlUZGDT2+HTv4FKlKoJnllQuLJ/ak/B/NqFV+iFEqVRF3GmlpyIon76E/bjJlXT0qsZcTDkrGwLG3oatb4Pb+mLg2auzi5ujQ0MTF5UxDruv7OAQAAaoFcLndxcan4iK2t7e+//669nZ2drZ1ATU9PV6vV5c9hGUKyny4Z0auwsFCpVJaVlVlZWZlKJDK5qYVnqw93/vy0kDwtFKIyyeOU1IRD64pECkFiYmois7CwVJhIzRWmtnb2nh26WUkYuYjIRcSM05CSAinHWFtZag+rMhURSYU9AVhCLCT/26CYWyYIVf9mOYawZYy6lBBCLCTEOK8OU7UympWVVVpa6uDgoL3r6OhY8RJhaWlpFRdlZ2eXlJTIZLI3vtTdu3e1pfaNPvjgg4YNG1Ym0s4/SJH6rUtLSxmpVPUXX64RSMGbvrxMQ5T//7i2ZRJC7v/8ecKhtYQQQRA0ylztUsbEXDZgXvGAf2g3f5twRBMVXRb5k1hmIpbITBUWUolYrrAwc6hva2fnruDNRMRMTCzERO04gJvcw8pU4mBpaq2Qv3oFI/5/N5v0JKRnxWwq1V99R1A9KpUKP1ioDAwVqCQMlVqiUCgUCkXTpk21dyv+kBs1apSUlKS9LQhCbm5uaWlpcXGxWq1u4qQpf1pWlvjHPK+CgoK8wqK84pznmY+UmWUFSmWuha2iU5esEvJURYrUJDUx/tL89wSBVyvztF/ImpgTlpM4ezn86yIhhCckv8Jv2EJcnV3d1AIpUEkYRkUI0R65oa0T5S9oKiYSlohZop3HNeWImCWEEIWYlG8Lfa0la8k4IvsbG0snuhO7N859VZFIJCrfRfitz6nSKwqCQAgpf1GGYXier/iEiosEQRDe/k+CSqXKz89/29KysrLXXvltcksZpeatS8tURML81T8qHEMs3vQzEEtI+ey9iCVmIoEQIsyZKvl4PCHETCxYWlppf/cKMcMRwVLK/+8nPXwYIcPe8oYVvqn6dq8sqNz3C7WE53n8CqAyMFSgkjBUqKt4jcCKvwsrK6vp06e/5Ysq/Mo6eZAP0ysuy8/P12g0HMeZm9fkb7agoEChUJTfLZ8Cy1MRgRClipTxRC0w2gcL1YKK195g1P+fQqkmZX/qQiUakvP22bp3UvFCnY3fqpVRa2trsVickZFhbW1NCHn+/Lmjo2P50vr162dkZGhvP3/+3MrK6i0blAkhpF27dhs3bqxW5lf8q/1fLS0oKFUoanDXZSkhr1/9EgxDWVnZq5PTAG+GoQKVhKFieGxtbWvjZV8bKlJCzEwIIaR+bbyZTqraBC7Lsr169Tp16pT27pkzZ/z8/Aghz549Kyoq8vPzO336tHbR6dOntYsAAAAAAN6mykfTL1++3N/fPz8///Hjx8nJyRMmTCCE+Pr6btu2bdq0abt27ZoyZYq9vf3u3bsvXLhQC4EBAAAAwHBUedfWbt26Xb9+XS6Xd+7cOSoqytzcnBCyc+dOX19fW1vb6OjoNm3aWFpaRkVF+fj41EJgAAAAADAc1bkCk5eXl5eXV8VHAgICtDfs7OwCAwNrIBcAAAAAGAGcIR0AAAAAqDHwMrpjxw6c5g0qY+vWrbQjgB5Qq9Wff/457RSgB4qLi3fv3k07BeiBvLy8ffv20U5BGfMXpwKtPTt37oyPj9+5c2dtv5GpqWlGRoaZmVltvxHoO+1Jc995Yl4wckVFRTY2NkVFRbSDgK57+fKlp6dnZmYm7SCg6548edK9e/enT5/SDkKTgc+MAgAAAIAuQxkFAAAAAGpQRgEAAACAmuqc2qlGxMXFbdmypbbfRXu0AS7IBpWxZcsW7DMKf02lUqnV6jr42wX6rrCwsLi4GEMF3ik7O7ugoMCAh8qECRPeeRlVOgcwqVSqVatWFRcX18EbicXi2n4XMAAYKlBJGCpQSRgqUEmGPVQWLlzo6Oj418+hU0YBAAAAAAj2GQUAAAAAilBGAQAAAIAalFEAAAAAoAZlFAAAAACoMeQyWlhYuGLFim7dunl5eY0ZMyYhIYF2ItBdhw8fDgwM7Nev37lz52hnAR2VmJg4dOjQpk2bjhkzJi0tjXYc0FEFBQUhISETJkzo06dPXl4e7Tigu1JSUj755JMOHTq0atVqxowZGRkZtBNRY8hlNCsrKzMzc+3atUePHnVwcPDz86uDk0mBnrpy5YqdnV1SUhJKBryRIAgBAQHNmzcPCwuztrYeO3Ys7USgo3Jzc6Ojo5s1a3b+/HmVSkU7DuiupKQkhULxxRdfhIaGZmRkjBw5knYiaozl1E4ajUYmk0VFRXl7e9POArqrU6dOM2bMmDRpEu0goHMuX748cuTI9PR0juOUSqWtre2tW7c8PT1p5wIdlZmZaWtr+/LlSxsbG9pZQA/Ex8e3aNGipKREIpHQzkKBIc+MVhQdHS2RSFxdXWkHAQC9dO/evTZt2nAcRwgxNTX18PCIi4ujHQoADERkZGSTJk2Ms4kSipcDrUt5eXkTJ05cs2aNhYUF7SwAoJdevHhR8Q+IlZXVixcvKOYBAIORlJQUFBR04MAB2kGoMbSZ0fv37/v4+Pj4+PTq1Uv7SGFh4cCBA/38/ObPn083G+iU8PBw7VAZMWIE7SygBywtLZVKZfnd/Px8KysrinkAwDCkpKT06dNn9erVAwYMoJ2FGkObGXVxcfnuu+8IIdqtaUVFRYMHD27RokVISAjtaKBbWrdurR0qUqmUdhbQA25ubvfv39feVqvVjx49cnNzoxsJAPRdWlpa7969586dO3PmTNpZaDK0MiqVSps2baq9XVxcPGTIEGtr63Xr1uXm5hJCzMzMxGIx1YCgK+RyeflQIYQUFhaqVCq1Wl1UVJSTk4OhAq/p169fQUHB0aNHhw0b9vXXX9vY2HTs2JF2KNBROTk52pVObm4ux3GYRIc3ev78ea9evYYPHz5x4sScnBxCiIWFBcsa2ibryjDko+nv3LlTvrFe6/Dhw35+frTygC4bN27cmTNnyu9iqMCfhYWFTZ48Wa1Wm5mZHTp0CGUU3sbW1laj0Whvcxz38uVLunlAN33//fezZs2q+EhMTIyzszOtPBQZchkFAKhxubm5lpaWtFMAABgOlFEAAAAAoMYYd00AAAAAAB2BMgoAAAAA1KCMAgAAAAA1KKMAAAAAQA3KKAAAAABQgzIKAAAAANSgjAIAAAAANSijAAAAAEANyigAAAAAUIMyCgAAAADUoIwCAAAAADX/B+BnuCT2CjZ6AAAAAElFTkSuQmCC" }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simulation1(Exponential(0.5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fit to the normal density is already tight, and can be further improved by increasing n.\n", "\n", "You can also experiment with other specifications of $F$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation 2\n", "\n", "Our next simulation is somewhat like the first, except that we aim to track the distribution of $Y_n := \\sqrt{n} ( \\bar X_n - \\mu )$ as $n$ increases.\n", "\n", "In the simulation we’ll be working with random variables having $\\mu = 0$.\n", "\n", "Thus, when $n=1$, we have $Y_1 = X_1$, so the first distribution is just\n", "the distribution of the underlying random variable.\n", "\n", "For $n=2$, the distribution of $Y_2$ is that of $(X_1 + X_2) / \\sqrt{2}$, and so on.\n", "\n", "What we expect is that, regardless of the distribution of the underlying\n", "random variable, the distribution of $Y_n$ will smooth out into a bell\n", "shaped curve.\n", "\n", "The next figure shows this process for $X_i \\sim f$, where $f$ was\n", "specified as the convex combination of three different beta densities.\n", "\n", "(Taking a convex combination is an easy way to produce an irregular shape for $f$)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "simulation2 (generic function with 4 methods)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function simulation2(distribution = Beta(2, 2), n = 5, k = 10_000)\n", " y = rand(distribution, k, n)\n", " for col in 1:n\n", " y[:,col] += rand([-0.5, 0.6, -1.1], k)\n", " end\n", " y = (y .- mean(distribution)) ./ std(distribution)\n", " y = cumsum(y, dims = 2) ./ sqrt.(1:5)' # return grid of data\n", "end" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ys = simulation2()\n", "plots = [] # would preallocate in optimized code\n", "for i in 1:size(ys, 2)\n", " p = density(ys[:, i], linealpha = i, title = \"n = $i\")\n", " push!(plots, p)\n", "end\n", "\n", "plot(plots..., legend = false)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the distribution smooths out into a bell curve as$ n $increases.\n", "\n", "We leave you to investigate its contents if you wish to know more.\n", "\n", "If you run the file from the ordinary Julia or IJulia shell, the figure should pop up in a\n", "window that you can rotate with your mouse, giving different views on the\n", "density sequence.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Multivariate Case\n", "\n", "\n", "\n", "The law of large numbers and central limit theorem work just as nicely in multidimensional settings.\n", "\n", "To state the results, let’s recall some elementary facts about random vectors.\n", "\n", "A random vector$ \\mathbf X $is just a sequence of$ k $random variables$ (X_1, \\ldots, X_k) $.\n", "\n", "Each realization of$ \\mathbf X $is an element of$ \\mathbb R^k $.\n", "\n", "A collection of random vectors$ \\mathbf X_1, \\ldots, \\mathbf X_n $is called independent if, given any$ n $vectors$ \\mathbf x_1, \\ldots, \\mathbf x_n $in$ \\mathbb R^k $, we have\n", "\n", "$$\n", "\\mathbb P\\{\\mathbf X_1 \\leq \\mathbf x_1,\\ldots, \\mathbf X_n \\leq \\mathbf x_n \\}\n", "= \\mathbb P\\{\\mathbf X_1 \\leq \\mathbf x_1 \\}\n", "\\times \\cdots \\times \\mathbb P\\{ \\mathbf X_n \\leq \\mathbf x_n \\}\n", "$$\n", "\n", "(The vector inequality$ \\mathbf X \\leq \\mathbf x $means that$ X_j \\leq x_j $for$ j = 1,\\ldots,k $)\n", "\n", "Let$ \\mu_j := \\mathbb E [X_j] $for all$ j =1,\\ldots,k $.\n", "\n", "The expectation$ \\mathbb E [\\mathbf X] $of$ \\mathbf X $is defined to be the vector of expectations:\n", "\n", "$$\n", "\\mathbb E [\\mathbf X]\n", ":=\n", "\\left(\n", "\\begin{array}{c}\n", " \\mathbb E [X_1] \\\\\n", " \\mathbb E [X_2] \\\\\n", " \\vdots \\\\\n", " \\mathbb E [X_k]\n", "\\end{array}\n", "\\right)\n", "=\n", "\\left(\n", "\\begin{array}{c}\n", " \\mu_1 \\\\\n", " \\mu_2\\\\\n", " \\vdots \\\\\n", " \\mu_k\n", "\\end{array}\n", "\\right)\n", "=: \\boldsymbol \\mu\n", "$$\n", "\n", "The *variance-covariance matrix* of random vector$ \\mathbf X $is defined as\n", "\n", "$$\n", "\\mathop{\\mathrm{Var}}[\\mathbf X]\n", ":= \\mathbb E\n", "[ (\\mathbf X - \\boldsymbol \\mu) (\\mathbf X - \\boldsymbol \\mu)']\n", "$$\n", "\n", "Expanding this out, we get\n", "\n", "$$\n", "\\mathop{\\mathrm{Var}}[\\mathbf X]\n", "=\n", "\\left(\n", "\\begin{array}{ccc}\n", " \\mathbb E [(X_1 - \\mu_1)(X_1 - \\mu_1)]\n", " & \\cdots & \\mathbb E [(X_1 - \\mu_1)(X_k - \\mu_k)] \\\\\n", " \\mathbb E [(X_2 - \\mu_2)(X_1 - \\mu_1)]\n", " & \\cdots & \\mathbb E [(X_2 - \\mu_2)(X_k - \\mu_k)] \\\\\n", " \\vdots & \\vdots & \\vdots \\\\\n", " \\mathbb E [(X_k - \\mu_k)(X_1 - \\mu_1)]\n", " & \\cdots & \\mathbb E [(X_k - \\mu_k)(X_k - \\mu_k)] \\\\\n", "\\end{array}\n", "\\right)\n", "$$\n", "\n", "The$ j,k $-th term is the scalar covariance between$ X_j $and\n", "$ X_k $.\n", "\n", "With this notation we can proceed to the multivariate LLN and CLT.\n", "\n", "Let$ \\mathbf X_1, \\ldots, \\mathbf X_n $be a sequence of independent and\n", "identically distributed random vectors, each one taking values in\n", "$ \\mathbb R^k $.\n", "\n", "Let$ \\boldsymbol \\mu $be the vector$ \\mathbb E [\\mathbf X_i] $, and let$ \\Sigma $\n", "be the variance-covariance matrix of$ \\mathbf X_i $.\n", "\n", "Interpreting vector addition and scalar multiplication in the usual way (i.e., pointwise), let\n", "\n", "$$\n", "\\bar{\\mathbf X}_n := \\frac{1}{n} \\sum_{i=1}^n \\mathbf X_i\n", "$$\n", "\n", "In this setting, the LLN tells us that\n", "\n", "\n", "\n", "$$\n", "\\mathbb P \\left\\{ \\bar{\\mathbf X}_n \\to \\boldsymbol \\mu \\text{ as } n \\to \\infty \\right\\} = 1 \\tag{7}\n", "$$\n", "\n", "Here$ \\bar{\\mathbf X}_n \\to \\boldsymbol \\mu $means that$ \\| \\bar{\\mathbf X}_n - \\boldsymbol \\mu \\| \\to 0 $, where$ \\| \\cdot \\| $is the standard Euclidean norm.\n", "\n", "The CLT tells us that, provided$ \\Sigma $is finite,\n", "\n", "\n", "\n", "$$\n", "\\sqrt{n} ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu ) \\stackrel { d } {\\to} N(\\mathbf 0, \\Sigma)\n", "\\quad \\text{as} \\quad\n", "n \\to \\infty \\tag{8}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "One very useful consequence of the central limit theorem is as follows.\n", "\n", "Assume the conditions of the CLT as [stated above](#statement-clt).\n", "\n", "If$ g \\colon \\mathbb R \\to \\mathbb R $is differentiable at$ \\mu $and$ g'(\\mu) \\not= 0 $, then\n", "\n", "\n", "\n", "$$\n", "\\sqrt{n} \\{ g(\\bar X_n) - g(\\mu) \\}\n", "\\stackrel { d } {\\to} N(0, g'(\\mu)^2 \\sigma^2)\n", "\\quad \\text{as} \\quad\n", "n \\to \\infty \\tag{9}\n", "$$\n", "\n", "This theorem is used frequently in statistics to obtain the asymptotic distribution of estimators — many of which can be expressed as functions of sample means.\n", "\n", "(These kinds of results are often said to use the “delta method”)\n", "\n", "The proof is based on a Taylor expansion of$ g $around the point$ \\mu $.\n", "\n", "Taking the result as given, let the distribution$ F $of each$ X_i $be uniform on$ [0, \\pi / 2] $and let$ g(x) = \\sin(x) $.\n", "\n", "Derive the asymptotic distribution of$ \\sqrt{n} \\{ g(\\bar X_n) - g(\\mu) \\} $and illustrate convergence in the same spirit as the program illustrate_clt.jl discussed above.\n", "\n", "What happens when you replace$ [0, \\pi / 2] $with$ [0, \\pi] $?\n", "\n", "What is the source of the problem?\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Here’s a result that’s often used in developing statistical tests, and is connected to the multivariate central limit theorem.\n", "\n", "If you study econometric theory, you will see this result used again and again.\n", "\n", "Assume the setting of the multivariate CLT [discussed above](#multivariate-clt), so that\n", "\n", "1.$ \\mathbf X_1, \\ldots, \\mathbf X_n $is a sequence of IID random vectors, each taking values in$ \\mathbb R^k $\n", "1.$ \\boldsymbol \\mu := \\mathbb E [\\mathbf X_i] $, and$ \\Sigma $is the variance-covariance matrix of$ \\mathbf X_i $\n", "1. The convergence \n", "\n", "\n", "\n", "\n", "$$\n", "\\sqrt{n} ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu ) \\stackrel { d } {\\to} N(\\mathbf 0, \\Sigma) \\tag{10}\n", "$$\n", "\n", "is valid.\n", "\n", "In a statistical setting, one often wants the right hand side to be **standard** normal, so that confidence intervals are easily computed.\n", "\n", "This normalization can be achieved on the basis of three observations.\n", "\n", "First, if$ \\mathbf X $is a random vector in$ \\mathbb R^k $and$ \\mathbf A $is constant and$ k \\times k $, then\n", "\n", "$$\n", "\\mathop{\\mathrm{Var}}[\\mathbf A \\mathbf X]\n", "= \\mathbf A \\mathop{\\mathrm{Var}}[\\mathbf X] \\mathbf A'\n", "$$\n", "\n", "Second, by the [continuous mapping theorem](https://en.wikipedia.org/wiki/Continuous_mapping_theorem), if$ \\mathbf Z_n \\stackrel{d}{\\to} \\mathbf Z $in$ \\mathbb R^k $and$ \\mathbf A $is constant and$ k \\times k $, then\n", "\n", "$$\n", "\\mathbf A \\mathbf Z_n\n", "\\stackrel{d}{\\to} \\mathbf A \\mathbf Z\n", "$$\n", "\n", "Third, if$ \\mathbf S $is a$ k \\times k $symmetric positive definite matrix, then there\n", "exists a symmetric positive definite matrix$ \\mathbf Q $, called the inverse\n", "[square root](https://en.wikipedia.org/wiki/Square_root_of_a_matrix) of$ \\mathbf S $, such that\n", "\n", "$$\n", "\\mathbf Q \\mathbf S\\mathbf Q' = \\mathbf I\n", "$$\n", "\n", "Here$ \\mathbf I $is the$ k \\times k $identity matrix.\n", "\n", "Putting these things together, your first exercise is to show that if\n", "$ \\mathbf Q $is the inverse square root of$ \\mathbf \\Sigma $, then\n", "\n", "$$\n", "\\mathbf Z_n := \\sqrt{n} \\mathbf Q ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu )\n", "\\stackrel{d}{\\to}\n", "\\mathbf Z \\sim N(\\mathbf 0, \\mathbf I)\n", "$$\n", "\n", "Applying the continuous mapping theorem one more time tells us that\n", "\n", "$$\n", "\\| \\mathbf Z_n \\|^2\n", "\\stackrel{d}{\\to}\n", "\\| \\mathbf Z \\|^2\n", "$$\n", "\n", "Given the distribution of$ \\mathbf Z $, we conclude that\n", "\n", "\n", "\n", "$$\n", "n \\| \\mathbf Q ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu ) \\|^2\n", "\\stackrel{d}{\\to}\n", "\\chi^2(k) \\tag{11}\n", "$$\n", "\n", "where$ \\chi^2(k) $is the chi-squared distribution with$ k $degrees\n", "of freedom.\n", "\n", "(Recall that$ k $is the dimension of$ \\mathbf X_i $, the underlying random vectors)\n", "\n", "Your second exercise is to illustrate the convergence in [(11)](#equation-lln-ctc) with a simulation.\n", "\n", "In doing so, let\n", "\n", "$$\n", "\\mathbf X_i\n", ":=\n", "\\left(\n", "\\begin{array}{c}\n", " W_i \\\\\n", " U_i + W_i\n", "\\end{array}\n", "\\right)\n", "$$\n", "\n", "where\n", "\n", "- each$ W_i $is an IID draw from the uniform distribution on$ [-1, 1] $\n", "- each$ U_i $is an IID draw from the uniform distribution on$ [-2, 2] $\n", "-$ U_i $and$ W_i $are independent of each other \n", "\n", "\n", "Hints:\n", "\n", "1. sqrt(A::AbstractMatrix{<:Number}) computes the square root of A. You still need to invert it. \n", "1. You should be able to work out$ \\Sigma $from the proceeding information. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Here is one solution" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function exercise1(distribution = Uniform(0, π/2); n = 250, k = 10_000, g = sin, g′ = cos)\n", " μ, σ = mean(distribution), std(distribution)\n", " y = rand(distribution, n, k)\n", " y = mean(y, dims = 1)\n", " y = vec(y)\n", " error_obs = sqrt(n) .* (g.(y) .- g.(μ))\n", " density(error_obs, label = \"Empirical Density\")\n", " return plot!(Normal(0, g′(μ) .* σ), linestyle = :dash, label = \"Asymptotic\",\n", " color = :black)\n", "end\n", "exercise1()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What happens when you replace$ [0, \\pi / 2] $with\n", "$ [0, \\pi] $?\n", "\n", "In this case, the mean$ \\mu $of this distribution is\n", "$ \\pi/2 $, and since$ g' = \\cos $, we have$ g'(\\mu) = 0 $.\n", "\n", "Hence the conditions of the delta theorem are not satisfied." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "First we want to verify the claim that\n", "\n", "$$\n", "\\sqrt{n} \\mathbf Q ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu )\n", "\\stackrel{d}{\\to}\n", "N(\\mathbf 0, \\mathbf I)\n", "$$\n", "\n", "This is straightforward given the facts presented in the exercise.\n", "\n", "Let\n", "\n", "$$\n", "\\mathbf Y_n := \\sqrt{n} ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu )\n", "\\quad \\text{and} \\quad\n", "\\mathbf Y \\sim N(\\mathbf 0, \\Sigma)\n", "$$\n", "\n", "By the multivariate CLT and the continuous mapping theorem, we have\n", "\n", "$$\n", "\\mathbf Q \\mathbf Y_n\n", "\\stackrel{d}{\\to}\n", "\\mathbf Q \\mathbf Y\n", "$$\n", "\n", "Since linear combinations of normal random variables are normal, the\n", "vector$ \\mathbf Q \\mathbf Y $is also normal.\n", "\n", "Its mean is clearly$ \\mathbf 0 $, and its variance covariance\n", "matrix is\n", "\n", "$$\n", "\\mathrm{Var}[\\mathbf Q \\mathbf Y]\n", "= \\mathbf Q \\mathrm{Var}[\\mathbf Y] \\mathbf Q'\n", "= \\mathbf Q \\Sigma \\mathbf Q'\n", "= \\mathbf I\n", "$$\n", "\n", "In conclusion,\n", "$ \\mathbf Q \\mathbf Y_n \\stackrel{d}{\\to} \\mathbf Q \\mathbf Y \\sim N(\\mathbf 0, \\mathbf I) \$,\n", "which is what we aimed to show.\n", "\n", "Now we turn to the simulation exercise.\n", "\n", "Our solution is as follows" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function exercise2(;n = 250, k = 50_000, dw = Uniform(-1, 1), du = Uniform(-2, 2))\n", " vw = var(dw)\n", " vu = var(du)\n", " Σ = [vw vw\n", " vw vw + vu]\n", " Q = inv(sqrt(Σ))\n", " function generate_data(dw, du, n)\n", " dw = rand(dw, n)\n", " X = [dw dw + rand(du, n)]\n", " return sqrt(n) * mean(X, dims = 1)\n", " end\n", " X = mapreduce(x -> generate_data(dw, du, n), vcat, 1:k)\n", " X = Q * X'\n", " X = sum(abs2, X, dims = 1)\n", " X = vec(X)\n", " density(X, label = \"\", xlim = (0, 10))\n", " return plot!(Chisq(2), color = :black, linestyle = :dash,\n", " label = \"Chi-squared with 2 degrees of freedom\", grid = false)\n", "end\n", "exercise2()" ] } ], "metadata": { "date": 1591310629.0556972, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "lln_clt.rst", "filename_with_path": "tools_and_techniques/lln_clt", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "LLN and CLT" }, "nbformat": 4, "nbformat_minor": 2 }