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Tidyevalで関数としての確率変数を表現してみる
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Tidyevalで関数としての確率変数を表現してみる" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "目的：Tidyevalを使って関数としての確率変数の概念を掴むこと\n", | |
| "\n", | |
| "遅延評価機能をつかって表現することで確率変数が関数であることの感触がつかめるのではないかと考えた。確率変数はランダムな事象の関数で、「ある値をランダムに生成しうるもの」という理解をコードで表現したい。Rのメタプログラミング機能の練習にもなると思い書いてみました。もし御参考になれば幸いです。\n", | |
| "\n", | |
| "### 独立同分布i.i.d.から確率変数列を生成する\n", | |
| "\n", | |
| "ライブラリーをロードする：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "\n", | |
| "Attaching package: ‘purrr’\n", | |
| "\n", | |
| "The following objects are masked from ‘package:rlang’:\n", | |
| "\n", | |
| " %@%, as_function, flatten, flatten_chr, flatten_dbl, flatten_int,\n", | |
| " flatten_lgl, flatten_raw, invoke, list_along, modify, prepend,\n", | |
| " splice\n", | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "library(rlang)\n", | |
| "library(purrr)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "`purrr`は関数型プログラミングの( https://purrr.tidyverse.org )、`rlang`は、tidy eval のフレームワーク ( https://rlang.r-lib.org )。\n", | |
| "\n", | |
| "\n", | |
| "独立同分布 (independent and identical distribution) i.i.d. からの関数リストとしての確率変数列を生成する関数を定義しよう：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "generate_Xn <- function(sample_size, distribution, ...){\n", | |
| " parameters <- rlang::enexprs(...) #パラメータを...でうけとる\n", | |
| " X <- rlang::enexpr(distribution)\n", | |
| " Xi <- rlang::call2(X, 1, !!!parameters) #パラメータを!!!でもどしつつ、1回の試行の関数expressionを構成\n", | |
| " Xn <- c()\n", | |
| " purrr::imap(1:sample_size, ~c(Xn, Xi)) %>% unlist() #expressionで表現された関数列の生成\n", | |
| "}\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "ここで、i.i.d. 確率変数列の生成の実行例を示そう：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "lines_to_next_cell": 2 | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[[1]]\n", | |
| "rnorm(1, mean = 2, sd = 3)\n", | |
| "\n", | |
| "[[2]]\n", | |
| "rnorm(1, mean = 2, sd = 3)\n", | |
| "\n", | |
| "[[3]]\n", | |
| "rnorm(1, mean = 2, sd = 3)\n", | |
| "\n", | |
| "[[4]]\n", | |
| "rnorm(1, mean = 2, sd = 3)\n", | |
| "\n", | |
| "[[5]]\n", | |
| "rnorm(1, mean = 2, sd = 3)\n" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "Xn <- generate_Xn(sample_size=5, distribution=rnorm, mean=2, sd=3)\n", | |
| "Xn" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "この確率変数列から値を *実現* させる関数を定義しよう：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<ol>\n", | |
| "\t<li>-2.74001766071721</li>\n", | |
| "\t<li>1.83922307560419</li>\n", | |
| "\t<li>0.0681122930732083</li>\n", | |
| "\t<li>2.91183783401362</li>\n", | |
| "\t<li>4.63125140306206</li>\n", | |
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| "text/latex": [ | |
| "\\begin{enumerate}\n", | |
| "\\item -2.74001766071721\n", | |
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| "1. -2.74001766071721\n", | |
| "2. 1.83922307560419\n", | |
| "3. 0.0681122930732083\n", | |
| "4. 2.91183783401362\n", | |
| "5. 4.63125140306206\n", | |
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| "[[1]]\n", | |
| "[1] -2.740018\n", | |
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| "[[2]]\n", | |
| "[1] 1.839223\n", | |
| "\n", | |
| "[[3]]\n", | |
| "[1] 0.06811229\n", | |
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| "[[4]]\n", | |
| "[1] 2.911838\n", | |
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| "[1] 4.631251\n" | |
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| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "realize_Xn <- function(Xn){\n", | |
| " purrr::map(Xn, eval) #それぞれのリスト内の確率変数Xにevalを適用して実現する\n", | |
| "}\n", | |
| "Xn %>% realize_Xn()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "これらの値は確率変数列のひとつのサンプル(例)であることに注意しよう。実世界の問題では、我々は未知の分布からの実現値のみが与えられている。ここでは、我々は正規分布から確率変数を人工的に生成している。\n", | |
| "\n", | |
| "実際、もし別の *試行* で実現させた場合、" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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| "<ol>\n", | |
| "\t<li>4.6722360467119</li>\n", | |
| "\t<li>1.21836674895179</li>\n", | |
| "\t<li>4.78421683455094</li>\n", | |
| "\t<li>6.01917891240497</li>\n", | |
| "\t<li>0.723484011247627</li>\n", | |
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| "text/latex": [ | |
| "\\begin{enumerate}\n", | |
| "\\item 4.6722360467119\n", | |
| "\\item 1.21836674895179\n", | |
| "\\item 4.78421683455094\n", | |
| "\\item 6.01917891240497\n", | |
| "\\item 0.723484011247627\n", | |
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| "1. 4.6722360467119\n", | |
| "2. 1.21836674895179\n", | |
| "3. 4.78421683455094\n", | |
| "4. 6.01917891240497\n", | |
| "5. 0.723484011247627\n", | |
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| "[[1]]\n", | |
| "[1] 4.672236\n", | |
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| "[1] 1.218367\n", | |
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| "[1] 4.784217\n", | |
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| "[1] 6.019179\n", | |
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| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "Xn %>% realize_Xn()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "異なる値の組が実現された。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "それではもっと多数の確率変数列を生成しその実現値のヒストグラムを描こう：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
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BDYSALz/Et/Izk5VgIECAxd4KsZYJ0t\nas4MHZfnVczUl7v+RHJk0rQ6wzP5+Z9vNyvy+KCk7i532+TJSRVH9XmoP02qPSapPt+T3DR5\nUrJ3Uq22feYPnt34nz/Pw+8mtV39gl4FXN1+u87o1M0UJgutvFyyTV721mx0aZ58N2lu7f2y\nPG8uZ3t6nj8iadrOzZM5PK7GbzWHW59Dmywa6/eFctcIECBAgAABAgQI9EbgkBxJ/bLf5H7L\nHFldVtZs95JF250yse4VE+uqKKi7vTXva3usfhdf7vbYJd6zS5Y37bfypD7L09ZnLbsyeXyy\nuD0wCy5PFr+vznI9f9HyffO6aZO3+X5Ks3DRYxVti/ttXp8zsa5MmiKpirJmm3p8WDLZXpYX\nzfrJ24PXNnXVRrOuHn+6Fk7ZVup3bvpv9jlZ5G5pt4dNvK/e31yKuKX3WU+AAIENL+ASuw0/\nhQZAgACBmQmcmJ6qCHt/0nZjgg9meZ25qTNAk62W/+3kgjy/KNl9Ytkb8vwJyYeSKniaVgXX\nPycHJO9oFk48fiLPH5hU/19L6sxVbfeQZPIMR17+4IxQPU7bXpANj0kmL8H7bl7/WfLjydlJ\nte2TKgLn2VbqN89jtm8CBAgQIECAAAECgxGoMyZ1u+0HJXdOmkvR8nTJVpfn1WV6t1lyixtX\n1D/O3SO5W7Lcpd57Zn1z5iZPf6QtPqO2w49sMd2COtN17+TuyXLHM11va7/VtH5rfyT2QIAA\nAQIECBAgQIDAugn8YfZUl3ddnJyaPDiZbC/Pi1pf+XqiESBAgACBVQtshH8pW/UgdUCAAAEC\nG1Lg5IWjrkv1KickdVndFUndZe+nkqYd2zzxSIAAAQIECBAgQIAAgaEK/H0G1pwlWuqxzi5t\nN1QA4yJAgAABAgQIECBAgEAjUJ+3eVzy4eSspG7qcF1Sd2c7Kfk/iashgqARIECAAAECBAgQ\nIDA+gfo+JAXR+ObdiAkQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIEBgZAKbRjZewyVAgAABArMS2DYdPSTZelYdLvRz\nXR4/llwz4351R4AAAQJTCGwzxTY2IUCAAAECBH5UoIqjE5Pv/OiqVS3ZKe9+RPLPq+rFmwkQ\nIEBgRQIKpBWxeRMBAgQIEPjBmaMqjm46Y4ur0t+sz0rN+BB1R4AAgeEK3GS4QzMyAgQIECBA\ngAABAgQIdBNQIHXzsjUBAgQIECBAgAABAgMWUCANeHINjQABAgQIECBAgACBbgIKpG5etiZA\ngAABAgQIECBAYMACCqQBT66hESBAgAABAgQIECDQTUCB1M3L1gQIECBAgAABAgQIDFhAgTTg\nyTU0AgQIECBAgAABAgS6CSiQunnZmgABAgQIECBAgACBAQsokAY8uYZGgAABAgQIECBAgEA3\nAQVSNy9bEyBAgAABAgQIECAwYAEF0oAn19AIECBAgAABAgQIEOgmoEDq5mVrAgQIECBAgAAB\nAgQGLKBAGvDkGhoBAgQIECBAgAABAt0EFEjdvGxNgAABAgQIECBAgMCABRRIA55cQyNAgAAB\nAgQIECBAoJuAAqmbl60JECBAgAABAgQIEBiwgAJpwJNraAQIECBAgAABAgQIdBNQIHXzsjUB\nAgQIECBAgAABAgMWUCANeHINjQABAgQIECBAgACBbgIKpG5etiZAgAABAgQIECBAYMACCqQB\nT66hESBAgAABAgQIECDQTUCB1M3L1gQIECBAgAABAgQIDFhAgTTgyTU0AgQIECBAgAABAgS6\nCSiQunnZmgABAgQIECBAgACBAQsokAY8uYZGgAABAgQIECBAgEA3AQVSNy9bEyBAgAABAgQI\nECAwYAEF0oAn19AIECBAgAABAgQIEOgmoEDq5mVrAgQIECBAgAABAgQGLKBAGvDkGhoBAgQI\nECBAgAABAt0EFEjdvGxNgAABAgQIECBAgMCABRRIA55cQyNAgAABAgQIECBAoJuAAqmbl60J\nECBAgAABAgQIEBiwgAJpwJNraAQIECBAgAABAgQIdBNQIHXzsjUBAgQIECBAgAABAgMWUCAN\neHINjQABAgQIECBAgACBbgIKpG5etiZAgAABAgQIECBAYMACCqQBT66hESBAgAABAgQIECDQ\nTUCB1M3L1gQIECBAgAABAgQIDFhAgTTgyTU0AgQIECBAgAABAgS6CSiQunnZmgABAgQIECBA\ngACBAQsokAY8uYZGgAABAgQIECBAgEA3AQVSNy9bEyBAgAABAgQIECAwYAEF0oAn19AIECBA\ngAABAgQIEOgmoEDq5mVrAgQIECBAgAABAgQGLKBAGvDkGhoBAgQIECBAgAABAt0EFEjdvGxN\ngAABAgQIECBAgMCABRRIA55cQyNAgAABAgQIECBAoJuAAqmbl60JECBAgAABAgQIEBiwwDYD\nHttSQ9stK3ZNtk+uTC5Lrko0AgQIECBAgAABAgRGLjCWM0gHZp6PTS5MLknOTE5PzkuqSPp6\n8qZkz0QjQIAAAQIECBAgQIDAYAVempHdsJCz83hK8oHk7cmHkk8l30hqm4uSX0o0AgQIECCw\nJYGfyQZrcQVC9Vl9awQIECBAYOYCR6THKnyqELrXMr1vyrpDk08ntf39E40AAQIECCwnoEBa\nTsc6AgQIEOilwPE5qrp8rj5vNE2rzyddkbxxmo1tQ4AAAQKjFlAgjXr6DZ4AgaEKDP0zSAdk\n4j6ZXD3lBF6a7U5L9p5ye5sRIECAAAECBAgQIDAggaEXSPXZooOSbaecszqDVEVV3cBBI0CA\nAAECBAgQIEBgZAJDL5COy3zeOXlXcvAyc1ufQTokOTHZKXlvohEgQIAAAQIECBAgMDKBoX8P\n0gmZz72So5NHJecndWvvi5P6rNEuye7JvsmtkmuT5yUnJxoBAgQIECBAgAABAgQGKbB/RvW2\npAqkukvdZOp2ql9NXp3cNtEIECBAgMA0Am7SMI2SbQgQILDBBIZ+BqmZjjPy5IkLL+qs0a7J\nDsmFyeWJRoAAAQIECBAgQIAAga2G/hmktineOgsrNfadk5smGgECBAgQIECAAAECBEZTIB2Y\nuT42qTNGlyRnJnWnuvo80pVJfVfSm5I9E40AAQIECBAgQIAAAQKDFXhpRtZ85ujsPD8l+UDy\n9uRDyaeSuh14bXNR8kuJRoAAAQIEtiTgM0hbErKeAAECBHoncESOqAqfKoTutczR1W2+D00+\nndT29080AgQIECCwnIACaTkd6wgQILBBBYZ+k4bHZl7qBg31ePUyc1RF0UnJYUmdZXpyUmea\nVtrqM04/l2w3ZQf1eahbJq+bcnubESBAgAABAgQIECCwBgJDL5AOiNknk+WKo0nWS/PitGTv\nyYUreF63C/+LZNsp31vzsNvCe+q7mDQCBAgQIECAAAECBOYgMPQCqT5bdFBShco1U/hWkVJF\nVd2wYTXtrLy5S5F1v2xfZ6zGeFfBDFsjQIAAAQIECBAg0A+Bof9CflyY75y8Kzl4GfL6DNIh\nyYnJTsl7E40AAQIECBAgQIAAgZEJDP0M0gmZz72So5NHJecn5yUXJ1ck9aWxuyf7JrdK6vK2\n5yUnJxoBAgQIECBAgAABAgQGKbB/RvW2pAqkuiHDZK7K668mr07qs0PzaHWJXR3TtDd1mMcx\n2icBAgQIbC7gLnabe3hFgACBQQgM/QxSM0l1J7snLryos0a7JjskFyaXJxoBAgQIECBAgAAB\nAgS2GkuBNDnVdWldRSNAgAABAgQIECBAgMBmAkO/ScNmg/WCAAECBAgQIECAAAECywkokJbT\nsY4AAQIECBAgQIAAgVEJDP0Su6dnNuszR11bfSdRfcGsRoAAAQIECBAgQIDAiASGXiD9n8zl\nPVcwny/PexRIK4DzFgIECBAgQIAAAQIbWWDoBdIjMznvTuo22u9L/iaZpn15mo1sQ4AAAQIE\nCBAgQIAAgY0msH0O+D+Sq5MDe3rwVcD5HqSeTo7DIkCAwBICvgdpCRiLCRAgsJEFxnCThiqM\nnrYwSa/fyJPl2AkQIECAAAECBAgQWFuBMRRIJfiF5IVJ3bDh7olGgAABAgQIECBAgACBHxEY\nS4FUA39NckDy+XqhESBAgAABAgQIECBAYLHAmAqkxWP3mgABAgQIECBAgAABApsJKJA24/CC\nAAECBAgQIECAAIExCyiQxjz7xk6AAAECBAgQIECAwGYCCqTNOLwgQIAAAQIECBAgQGDMAgqk\nMc++sRMgQIAAAQIECBAgsJmAAmkzDi8IECBAgAABAgQIEBizgAJpzLNv7AQIECBAgAABAgQI\nbCagQNqMwwsCBAgQIECAAAECBMYsoEAa8+wbOwECBAgQIECAAAECmwlss9krLwgQIECAwPQC\n986mH0+2nv4tU215XbZ6UPJfU21tIwIECBAgMEMBBdIMMXVFgACBkQnslfFumzxuxuN+T/q7\n5Yz71B0BAgQIEJhKQIE0FZONCBAgQGAJgTrb86El1q10cfWpESBAgACBuQj4DNJc2O2UAAEC\nBAgQIECAAIE+CiiQ+jgrjokAAQIECBAgQIAAgbkIuMRuLux2SoAAAQLLCGyfdcclVy+zzUpW\nvT5vetVK3ug9BAgQIDAeAQXSeObaSAkQILBRBOrqhk8k753hAR+Zvu4yw/50RYAAAQIDFVAg\nDXRiDYsAAQIbXOC0HP/fz3AMD5thX7oiQIAAgQEL+AzSgCfX0AgQIECAAAECBAgQ6CagQOrm\nZWsCBAgQIECAAAECBAYsoEAa8OQaGgECBAgQIECAAAEC3QQUSN28bE2AAAECBAgQIECAwIAF\nFEgDnlxDI0CAAAECBAgQIECgm4ACqZuXrQkQIECAAAECBAgQGLCAAmnAk2toBAgQIECAAAEC\nBAh0E1AgdfOyNQECBAgQIECAAAECAxZQIA14cg2NAAECBAgQIECAAIFuAgqkbl62JkCAAAEC\nBAgQIEBgwAIKpAFPrqERIECAAAECBAgQINBNQIHUzcvWBAgQIECAAAECBAgMWECBNODJNTQC\nBAgQIECAAAECBLoJKJC6edmaAAECBAgQIECAAIEBCyiQBjy5hkaAAAECBAgQIECAQDcBBVI3\nL1sTIECAAAECBAgQIDBgAQXSgCfX0AgQIECAAAECBAgQ6CagQOrmZWsCBAgQIECAAAECBAYs\noEAa8OQaGgECBAgQIECAAAEC3QQUSN28bE2AAAECBAgQIECAwIAFFEgDnlxDI0CAAAECBAgQ\nIECgm4ACqZuXrQkQIECAAAECBAgQGLCAAmnAk2toBAgQIECAAAECBAh0E1AgdfOyNQECBAgQ\nIECAAAECAxZQIA14cg2NAAECBAgQIECAAIFuAgqkbl62JkCAAAECBAgQIEBgwAIKpAFPrqER\nIECAAAECBAgQINBNQIHUzcvWBAgQIECAAAECBAgMWECBNODJNTQCBAgQIECAAAECBLoJKJC6\nedmaAAECBAgQIECAAIEBCyiQBjy5hkaAAAECBAgQIECAQDcBBVI3L1sTIECAAAECBAgQIDBg\ngW0GPDZDI0CAAAECjcAuebJn8pRmwQweD0gf/qFxBpC6IECAQJ8EFEh9mg3HQoAAAQJrJfAT\n6Xi/5LYz3MGu6Wv7GfanKwIECBDogYACqQeT4BAIECBAYM0FNmUPZyd3nOGeXpq+Xj7D/nRF\ngAABAj0QcGlADybBIRAgQIAAAQIECBAg0A8BBVI/5sFRECBAgAABAgQIECDQAwEFUg8mwSEQ\nIECAAAECBAgQINAPAQVSP+bBURAgQIAAAQIECBAg0AMBBVIPJsEhECBAgAABAgQIECDQDwEF\nUj/mwVEQIECAAAECBAgQINADAQVSDybBIRAgQIAAAQIECBAg0A8BBVI/5sFRECBAgAABAgQI\nECDQAwEFUg8mwSEQIECAAAECBAgQINAPAQVSP+bBURAgQIAAAQIECBAg0AMBBVIPJsEhECBA\ngAABAgQIECDQDwEFUj/mwVEQIECAAAECBAgQINADAQVSDybBIRAgQIAAAQIECBAg0A8BBVI/\n5sFRECBAgAABAgQIECDQAwEFUg8mwSEQIECAAAECBAgQINAPAQVSP+bBURAgQIAAAQIECBAg\n0AMBBVIPJsEhECBAgAABAgQIECDQDwEFUj/mwVEQIECAAAECBAgQINADAQVSDybBIRAgQIAA\nAQIECBAg0A8BBVI/5sFRECBAgAABAgQIECDQAwEFUg8mwSEQIECAAAECBAgQINAPAQVSP+bB\nURAgQIAAAQIECBAg0AMBBVIPJsEhECBAgAABAgQIECDQD4Ft+nEY63oUu2VvuybbJ1cmlyVX\nJRoBAgQIECBAgAABAiMXGMsZpAMzz8cmFyaXJGcmpyfnJVUkfT15U7JnohEgQIAAAQIECBAg\nMFKBMZxBemnm9qiF+T0nj59MqkiqwqjOJO2e7JMcmRyePDs5IdEIECBAgAABAgQIEBiZwNAL\npCMyn1UcnZi8KDk1aWubsvCQ5DXJ8clZySmJRoAAAQIECBAgQIDAiASGfondYzOXZyT1uFRx\nVNN9Q3JScljy7eTJiUaAAAECBAgQIECAwMgEhl4gHZD5rEvqrp5yXi/Ndqcle0+5vc0IECBA\ngAABAgQIEBiQwNALpG9krg5Ktp1yzuoOd1VU1Q0cNAIECBAgQIAAAQIERiYw9ALpuMznnZN3\nJQcvM7fNZ5Dqs0o7Je9dZlurCBAgQIAAAQIECBAYqMDQb9JQd6PbKzk6eVRyfnJecnFyRbJL\nUnex2ze5VXJt8rzk5EQjQIAAAQIECBAgQGBkAkMvkOrmC8ck70temRyaLD6T9J0suyCpO9i9\nNjk30QgQIECAAAECBAgQGKHA0AukZkrrTnZPXHhRZ43q+492SOqLYy9PZt32SYd1ud60n32q\nY9EIECBAgAABAgQIEJizwFgKpEnmurSu0rTt8uQuydeSq5qFq3z8Zt7/R0n1PU3bPxu9YJoN\nbUOAAAECBAgQIECAwNoJjKVAenwI64tg6/K5umFDFUM7J3+dPDK5WXJ9cnzyrGS1Z5W+nz7e\nmkzb7pcNFUjTatmOAAECBAgQIECAwBoJDL1Aqrv0vSd59ITf7+f5PZKXJL+YfCypgunA5EnJ\n7ZJDk/r8kkaAAAECBAgQIECAwIgEhn6b76dnLqs4+sjC4zPzeGny0eRpyRHJQ5PfSO6TVNH0\nU8kTEo0AAQIECBAgQIAAgZEJDP0M0mMyn5ckj0q+tzC35+Xxfck/Je9cWNY8/GGeHJlUkfS2\nZqFHAgQIECBAgAABAgTGITD0M0j1/UZ1CV1THNWs1tmj+rzRF+vFolbLz0z2WbTcSwIECBAg\nQIAAAQIERiAw9ALpnMxhXUI3eRvtuilDjfuuyeJWZ9TulZy1eIXXBAgQIECAAAECBAgMX2Do\nBVJdSrdbUpfTPS6pO8X9WfK5pAqlX0qaVhZvTurudv+aaAQIECBAgAABAgQIjExg6J9B+qvM\n5yOS+izSgxfm9lsLy16Rx7qt93OS+lzSfZNbJx9O6lbgGgECBAgQIECAAAECIxMYeoFUnyl6\nbFJnj+6fnJG8P/nf5PeS+iLXn03uk3w3eX3y/EQjQIAAAQIECBAgQGCEAkMvkJopfU+eVCbb\nZXnx1KQuraubOZyTXJdoBAgQIECAAAECBAiMVGAsBdJy09vcuW65bawjQIAAAQIECBAgQGAE\nAkO/ScMIptAQCRAgQIAAAQIECBCYlYACaVaS+iFAgAABAgQIECBAYMMLKJA2/BQaAAECBAgQ\nIECAAAECsxJQIM1KUj8ECBAgQIAAAQIECGx4AQXShp9CAyBAgAABAgQIECBAYFYCCqRZSeqH\nAAECBAgQIECAAIENL6BA2vBTaAAECBAgQIAAAQIECMxKwPcgzUpSPwQIECBAYDYC9bP5yOSw\n2XT3w17en2cf++ErTwgQIECgVUCB1MpiIQECBAgQmJvAttnzjyc3zPAIDkpfuyYKpBmi6ooA\ngWEKKJCGOa9GRYAAAQIbW+BtOfw/mOEQ3pK+Ns2wP10RIEBgsAI+gzTYqTUwAgQIECBAgAAB\nAgS6CiiQuorZngABAgQIECBAgACBwQookAY7tQZGgAABAgQIECBAgEBXAQVSVzHbEyBAgAAB\nAgQIECAwWAEF0mCn1sAIECBAgAABAgQIEOgqoEDqKmZ7AgQIECBAgAABAgQGK6BAGuzUGhgB\nAgQIECBAgAABAl0FFEhdxWxPgAABAgQIECBAgMBgBRRIg51aAyNAgAABAgQIECBAoKuAAqmr\nmO0JECBAgAABAgQIEBisgAJpsFNrYAQIECBAgAABAgQIdBVQIHUVsz0BAgQIECBAgAABAoMV\nUCANdmoNjAABAgQIECBAgACBrgIKpK5itidAgAABAgQIECBAYLACCqTBTq2BESBAgAABAgQI\nECDQVUCB1FXM9gQIECBAgAABAgQIDFZAgTTYqTUwAgQIECBAgAABAgS6CiiQuorZngABAgQI\nECBAgACBwQookAY7tQZGgAABAgQIECBAgEBXAQVSVzHbEyBAgAABAgQIECAwWAEF0mCn1sAI\nECBAgAABAgQIEOgqoEDqKmZ7AgQIECBAgAABAgQGK7DNYEdmYAQIECAwKbBLXtx+csEMnu+f\nPjbNoB9dECBAgACB3ggokHozFQ6EAAECayrwJ+n9yDXYww1r0KcuCRAgQIDA3AQUSHOjt2MC\nBAisq8D22dsJyW/OcK/PT18vmGF/uiJAgAABAnMXUCDNfQocAAECBNZN4Jrs6YoZ7u3qGfal\nKwIECBAg0AsBN2noxTQ4CAIECBAgQIAAAQIE+iCgQOrDLDgGAgQIECBAgAABAgR6IaBA6sU0\nOAgCBAgQIECAAAECBPogoEDqwyw4BgIECBAgQIAAAQIEeiGgQOrFNDgIAgQIECBAgAABAgT6\nIKBA6sMsOAYCBAgQIECAAAECBHoh4DbfvZgGB0GAAAECBNZcoH7m7zzjvdSt3uv28RoBAgQG\nI6BAGsxUGggBAgQIEFhS4N5Zc7fkl5fcYmUrzsvbbruyt3oXAQIE+imgQOrnvDgqAgQIECAw\nS4Ht09m5yc/PsNMHpK8/nGF/uiJAgEAvBBRIvZgGB0GAAAECBNZcoC6H+8wM97LXDPvSFQEC\nBHoj4CYNvZkKB0KAAAECBAgQIECAwLwFFEjzngH7J0CAAAECBAgQIECgNwIKpN5MhQMhQIAA\nAQIECBAgQGDeAgqkec+A/RMgQIAAAQIECBAg0BsBBVJvpsKBECBAgAABAgQIECAwbwEF0rxn\nwP4JECBAgAABAgQIEOiNgAKpN1PhQAgQIECAAAECBAgQmLeAAmneM2D/BAgQIECAAAECBAj0\nRkCB1JupcCAECBAgQIAAAQIECMxbQIE07xmwfwIECBAgQIAAAQIEeiOgQOrNVDgQAgQIECBA\ngAABAgTmLaBAmvcM2D8BAgQIECBAgAABAr0RUCD1ZiocCAECBAgQIECAAAEC8xZQIM17Buyf\nAAECBAgQIECAAIHeCHQtkF6fI39Msm1vRuBACBAgQIAAAQIECBAgMCOBrgXSz2S/703OT/4s\nuWeiESBAgAABAgQIECBAYBACXQuk+2XU/zc5N3lO8tnkc0kt2yvRCBAgQIAAAQIECBAgsGEF\ntul45Bdm+9cu5G55fHLyy8kxyZ8k/5S8JflAck2iESBAgEB3gePyln27v23Zd/x41n5t2S2s\nJECAAAECBLbqWiBNkn0hL56fvCA5JKnPJlWx9OjkouTvkr9MvppoBAgQIDC9wC9k0/cks/z7\n8+7p78emPwRbEiBAgACBcQqspkBqxG6fJ4cmD0zqMrsbkjrTVJfdPSc5KvmDRCNAgACB6QVO\nyKZ1Vn5W7Vdm1ZF+CBAgQIDAkAW6fgapsdgzT56VfCr5SlIF0B4Lj3fIY11+V4XTPyZVID01\n0QgQIECAAAECBAgQINBrga4F0uEZzQeTC5LXJXXJxvHJw5LbJS9LzkiqnZn8xg+ebbXVQxce\nPRAgQIAAAQIECBAgQKC3Al0vsasbMVQh9B/J3ybvSC5PlmrXZsXZyalLbWA5AQIECBAgQIAA\nAQIE+iLQtUB6Qw68rok/fcoBXJzt9ptyW5sRIECAAAECBAgQIEBgrgJdL7H70xxtFUd1yVx9\nxqhpt86TtyYupWtEPBIgQIAAAQIECBAgsOEEuhZIVQi9P/lIcvDEaPfP8yctLP+DieWeEiBA\ngAABAgQIECBAYMMIdC2QXpORPTKpS+3+ZWKU/57nhyX/lrwkuX+iESBAgAABAgQIECBAYEMJ\ndCmQNmVk9WWw9eWFdYvv+jLYyfbhvHh8cl3yhMkVnhMgQIAAAQIECBAgQGAjCHQpkG6WAe2Y\nfHSZgX0j6z6T7LPMNlYRIECAAAECBAgQIECglwJdCqQrMoKvJPdcZiTbZt3+ydeX2cYqAgQI\nECBAgAABAgQI9FKgS4FUA/h48vTkifViUds5r9+U7JnUTRw0AgQIECBAgAABAgQIbCiBrt+D\n9NKM7qDkhORlyReTy5K6u919kt2Sv0s+lGgECBAgQIAAAQIECBDYUAJdC6QLM7oHJ69LHpQ8\nNqmbN1Q7L3lh8uZ6oREgQIAAAQIECBAgQGCjCXQtkGp8Vya/tjDQXfNYN2Q4O6nPKG2EVme5\n6ri3T2osdQbsqkQjQIAAAQIECBAgQGDkAl0/g7SY6/Is+HzS9+LowBzjsUmdAbskOTM5Pamz\nXlUk1U0lms9P5alGgAABAgQIECBAgMAYBVZyBukhgXpSsldSt/1uLrHL0x+2t+TZcT98Nd8n\n9bmpoxYO4Zw8fjKpIqkKozqTtHtSZ8GOTA5Pnp3UZ6w0AgQIECBAgAABAgRGJtC1QPrF+Lxj\nCqNPTLHNemxyRHZSxdGJyYuSU5O2tikLD0lekxyfnJWckmgECBAgQIAAAQIECIxIoGuB9IrY\n1Od16mxL3fK7Lllra9e3LZzDsrqJxBlJPV69zP5vyLqTksOSs5MnJwqkIGgECBAgQIAAAQIE\nxiTQpUC6aWDumNRndU7YIEgH5DjrkrrliqPJoVyaF6cle08u9JwAAQIECBAgQIAAgXEIdLlJ\nw3dDUjdj2Eh3fPtGjre+t2nbZJpWd7iroqpu4KARIECAAAECBAgQIDAygS4FUl02V58temLS\n5X3zJD0uO79z8q7k4GUOpPkMUn1WaafkvctsaxUBAgQIECBAgAABAgMV6HKJXRE8PTk5eWfy\nZ8lZSdsZpe9keZ1xmnerSwHrbntHJ49Kzk/OSy5O6mzYLkndxW7f5FbJtcnzkhqjRoAAAQIE\nCBAgQIDAyAS6Fkjvj08VHI9byFJcR2XFy5dauY7L6+YLxyTvS16ZHJosPpNUxdwFSd3B7rXJ\nuclq27bp4PHJdlN2dPspt7MZAQIECBAgQIAAAQJrKNC1QPpsjqWKiS21L21pg3VeX3eyq0sD\nq9VZo/r+ox2Sugvf5cmsW52NenFShdI0bftpNrINAQIECBAgQIAAAQJrK9C1QPrNtT2cdem9\nLq2rVNs6uUNyUXJZMqt2Tjqqzz5N2+6XDU+ZdmPbESBAgAABAgQIECCwNgKrudnCjjmkuyfN\nJWt1G/A+trok8I3J304cXJ1B+sukPj/11aQ+k3RaUp8/0ggQIECAAAECBAgQGKnASgqkfWL1\nD0kVF1VUvDqp9vfJ0UmfLhe7RY7n1OQ3kv2TanXZ28eSZyw8/9c8vjupoqnGUoXTSlzyNo0A\nAQIECBAgQIAAgY0s0LUQqM/WVMFxRFLfFXR20rS6VfaLkv9K6vM9fWgvzEHUl76+IDls4YB+\nK4/3St6c1LoHJzWeOyavS6pwemiiESBAgAABAgQIECAwMoGuBVIVEHVp3SHJXZMqlpp2eJ68\nMrlb8pRm4Zwf67M9ZyZ/nFy9cCx17PV5o2cm31xYVg/fT56b1F3sHpZoBAgQIECAAAECBAiM\nTKBrgVRnVv48+fcWp+uyrG7vXXeFu2/L+nks2iY7rTvvXT+x8zrOc5JrJpY1T2u7uktfnU3S\nCBAgQIAAAQIECBAYmUCXAmmX2OyWfHkZoyo6vrCw3TKbrduqutzv4ckeE3s8Kc/vlOw5sax5\n+mN5cu/kv5sFHgkQIECAAAECBAgQGI9AlwLpirDUJWk/uQxPFVF1iV19PqkP7dgcRN004nNJ\nXVpX7a+TKpzqRhO3Tpp2zzyp4una5N3NQo8ECBAgQIAAAQIECIxHoEuBVCofSn49qRsd7JxM\ntpvnxVuTuhvchydXzPH5Z7LvuulC3c3uE0mdGXpD8qXkgclZyReT/03qUrw7JM9KPp9oBAgQ\nIECAAAECBAiMTKBrgfTb8anP6Lw+OT+5f7J/8t7k68ljkrckH0360ur7j/ZLXpXUJYJPTqrI\n25Rsm9wlqe9wentyQPLmRCNAgAABAgQIECBAYIQCXQuky2J0r+RNyQ7JLZO6TK0Ko2rPTqr4\n6FurM0QvSPZJ6pK72yQHJ3dPqmiqs2FPTP4n0QgQIECAAAECBAgQGKnANisY90V5T122VrfJ\n3jepGxucldSZpY3QrstB1tmvikaAAAECBAgQIECAAIEfCqykQGreXIXGGQtplnkkQIAAAQIE\nCBAgQIDAhhXoeondhh2oAydAgAABAgQIECBAgMCWBLqeQarPHtXnjrbU6oYHFY0AAQIECBAg\nQIAAAQIbRqBrgfTwjOx2WxjdeVlft9TWCBAgQIAAAQIECBAgsKEEuhZIB2Z0iy/Lq9d1V7if\nSI5J6sxRPWoECBAgQIAAAQIECBDYUAJdC6TLlxjdxVn+38kXks8m/5a8P9EIECBAgAABAgQI\nECCwYQS6FkhbGtjnssHZSV2Kp0Dakpb1BAgQIEBg4wvsNeMh1F1y6x9eNQIECMxFYNYFUn0J\n6x7JrP+ynAuOnRIgQIAAAQJLCtwta3ZK6svYZ90OTYd1NYpGgACBdRfoWiDtkCPc1HKU1c+e\nydHJzslnEo0AAQIECBAYrsCOGdoNSRVKs2ynprObzbJDfREgQKCLQNcC6YvpfEt3sasvj/2r\nLgdhWwIECBAgQGDDCnxpxkd+/Yz70x0BAgQ6CXQtkE5K719p2UP9ZXZFclpybLLUzRyySiNA\ngAABAgQIECBAgEA/BboWSE/t5zAcFQECBAgQIECAAAECBFYvsPg7jVbfox4IECBAgAABAgQI\nECCwQQW6nkF6U8Z5yxWM9e/ynnet4H3eQoAAAQIECBAgQIAAgXUT6FogHZAj+4mk7lRXrb6r\n4LJk96Tt7nZZ/IP2qeaJRwIECBAgQIAAAQIECPRVoOsldk/KQK5K6ktgD0rqtt+3WHh8ZB7r\nTjZVDNVZpvo+pCbH5LlGgAABAgQIECBAgACBXgt0PYP01xnNZ5PHJZO34fx+Xp+Y/E/y5eTn\nkzcmGgECBAgQIECAAAECBDaMQJczSNtnVPdN/j6ZLI4mB3teXnwueeDkQs8JECBAgAABAgQI\nECCwEQS6FEjXZkBXJnsvM7Bts+72ycXLbGMVAQIECBAgQIAAAQIEeinQpUCqGzJ8OHlhcp+W\n0eyUZc1d7upyO40AAQIECBAgQIAAAQIbSqDrZ5D+MKP7qaRuxHBSUjdl+HZym+QhyV5JfU7p\nA4lGgAABAgQIECBAgACBDSXQtUA6LaP7yeRvkkOSQ5Om/W+e/EZybLPAIwECBAgQIECAAAEC\nBDaSQNcCqcb2jaRu6V2X590pqVt6fz05P7kh0QgQIECAAAECBAgQILAhBbp8BmnxAOuudnVT\nhu8ldfe6+gySRoAAAQIECBAgQIAAgQ0rsJICaZ+M9h+S+sLYuuTu1Um1v0+OTqpw0ggQIECA\nAAECBAgQILDhBLpeYnerjPDUZI+kbtAwedZoU16/KHlscu+kzixpBAgQIECAAAECBAgQ2DAC\nXc8gvS4j2zGpGzTcNaliqWmH58krk7slT2kWeiRAgAABAgQIECBAgMBGEeh6BumhGdifJ//e\nMsDrsuyo5LeS+yb1nUgaAQIEhizw4xncW5Kuf5duyaQuVV7uS7m39H7rCRAgQIAAgRUKdPmh\nvkv2sVvy5WX2dU3WfWFhu2U2s4oAAQKDELh9RnFQUl+gPctWfdYlzRoBAgQIECCwzgJdCqQr\ncmzfTOp7kP56ieOsIqousXvjEustJkCAwNAE6h+GmpvVzGpsfzyrjvRDgAABAgQIdBPo+hmk\nD6X7X0/qMrqdF+3q5nn91mTX5MOL1nlJgAABAgQIECBAgACB3gt0LZB+OyO6IHl9Ul8Me/9k\n/+S9SX1Z7GOStyQfTTQCBAgQIECAAAECBAhsKIGuBdJlGd29kroBww7JLZNbJ1UYVXt2UmeY\nNAIECBAgQIAAAQIECGw4gS6fQWoGd1GePCN5ZrJv8mPJWUmdWdIIECBAgAABAgQIECCwYQW6\nFkh1i+/vJr+fXJucsZA8aAQIECBAgAABAgQIENjYAl0usavv5agvgP25pIojjQABAgQIECBA\ngAABAoMS6FIgfT8j/3ayU7JpUAoGQ4AAAQIECBAgQIAAgQh0KZBuyPaPW1B7fx5/OqkvSazv\nPlqcOtukESBAgAABAgQIECBAYEMJdCmQamCvTuoMUl1md2LyteTylrwgyzQCBAgQIECAAAEC\nBAhsKIGuN2k4PaO7dIoRfnmKbWxCgAABAgQIECBAgACBXgl0LZB+vVdH72AIECBAgAABAgQI\nECAwQ4EtXWJ3aPb1kBnuT1cECBAgQIAAAQIECBDorcCWziC9Lke+a3K7RSO4e17vkfzrouVe\nEiBAgAABAgQIECBAYMMKbOkM0lIDOzorPr7USssJECBAgAABAgQIECCwEQVWWiBtxLE6ZgIE\nCBAgQIAAAQIECCwroEBalsdKAgQIECBAgAABAgTGJKBAGtNsGysBAgQIECBAgAABAssKKJCW\n5bGSAAECBAgQIECAAIExCSiQxjTbxkqAAAECBAgQIECAwLICW7rNd715t+RVi3q568Lrxcub\nzT6cJx9pXngkQIAAAQIECBAgQIDARhCYpkCq70H6vSUGs9Ty72R7BdISaBYTIECAAAECBAgQ\nINBPgS0VSC/KYd98BYd+2gre4y0ECBAgQIAAAQIECBCYq8CWCqQPzvXo7JwAAQIECBAgQIAA\nAQLrKOAmDeuIbVcECBAgQIAAAQIECPRbQIHU7/lxdAQIECBAgAABAgQIrKOAAmkdse2KAAEC\nBAgQIECAAIF+CyiQ+j0/jo4AAQIECBAgQIAAgXUUUCCtI7ZdESBAgAABAgQIECDQbwEFUr/n\nx9ERIECAAAECBAgQILCOAgqkdcS2KwIECBAgQIAAAQIE+i2gQOr3/Dg6AgQIECBAgAABAgTW\nUUCBtI7YdkWAAAECBAgQIECAQL8FFEj9nh9HR4AAAQIECBAgQIDAOgookNYR264IECBAgAAB\nAgQIEOi3gAKp3/Pj6AgQIECAAAECBAgQWEcBBdI6YtsVAQIECBAgQIAAAQL9FlAg9Xt+HB0B\nAgQIECBAgAABAusosM067suuCBAgME+BXbPzO874AO6Q/jbNuE/dESBAgAABAnMUUCDNEd+u\nCRBYV4E/zt6OXIM93rAGfeqSAAECBAgQmJOAAmlO8HZLgMC6C2yfPR6fPGOGe/799PXCGfan\nKwIECBAgQGDOAgqkOU+A3RMgsK4C12ZvV85wj9+fYV+6IkCAAAECBHog4CYNPZgEh0CAAAEC\nBAgQIECAQD8EFEj9mAdHQYAAAQIECBAgQIBADwQUSD2YBIdAgAABAgQIECBAgEA/BBRI/ZgH\nR0GAAAECBAgQIECAQA8EFEg9mASHQIAAAQIECBAgQIBAPwQUSP2YB0dBgAABAgQIECBAgEAP\nBNzmuweT4BAIECBAgACBzQR2zKtdNluy+hffThe+2Hn1jnogMHiBMRZIu2VWd03qSyPr+1Au\nS65KNAIECBAgQGD+AjvkEN65BofxZ+nzuWvQry4JEBiYwFgKpAMzb89MHp3s2TKHZ2TZR5IX\nJ99qWW8RAQIECBAgsD4Cm7KbNyZ/NcPdHZW+6h9INQIECGxRYAwF0kujUH8xVjsn+WRySVJn\nj+pM0u7JPsmRyeHJs5MTEo0AAQIECBCYj8A3stvPznDX9XNfI0CAwFQCQy+QjohCFUcnJi9K\nTk3aWv1r1SHJa5Ljk7OSUxKNAAECBAgQIECAAIERCQz9LnaPzVzW5XP1uFRxVNNdH9o8KTks\nqQ9xPjnRCBAgQIAAAQIECBAYmcDQC6QDMp91Sd3VU87rpdnutGTvKbe3GQECBAgQIECAAAEC\nAxIYeoFU1zAflGw75ZzVBzirqDp9yu1tRoAAAQIECBAgQIDAgASGXiAdl7m6c/Ku5OBl5q35\nDFJ9Vmmn5L3LbGsVAQIECBAgQIAAAQIDFRj6TRrqbnR7JUcnj0rOT85LLk6uSHZJ6i52+ya3\nSq5NnpecnGgECBAgQIAAAQIECIxMYOgFUt184Zjkfckrk0OTxWeSvpNlFyR1B7vXJucmGgEC\nBAgQIECAAAECIxQYeoHUTGndye6JCy/qrFF9/1F9U/eFyeXJrNt+6bDuirfdlB1P+xmpKbuz\nGQECBAgQIECAAAECKxEYS4E0aVOX1lWatmee7JF8Jbm+WbjKx7qM7znJtAXSHbPtK1a5T28n\nQIAAAQIECBAgQGCVAmMskBaT/U4W/F5SRdIli1eu8HV9luk9Hd57v2yrQOoAZlMCBAgQIECA\nAAECayEw9AKpbtl90y3ANd959JPZrjmzVJ9DqrNAGgECBAgQIECAAAECIxIYeoH01szlPaac\nz7rFd9NenidHNS88EiBAgAABAgQIECAwDoGhF0hvzDQek9QNGd6ffClZ3B6cBfdJXpd8d2Gl\n23wvQHggQIAAAQIECBAgMCaBMRRI/5YJre9DenjykeQNSd3+u2mvypMqkOqM0aw+g9T07ZEA\nAQIECBAgQIAAgQ0kcJMNdKwrPdQv5I1VAP1FUt9z9M9J87mjPNUIECBAgAABAgQIECBwo8AY\nCqQa6dVJ3a3uYcldks8nT0g0AgQIECBAgAABAgQI/FBgLAVSM+CP5Und2e7DyduSuvRut0Qj\nQIAAAQIECBAgQIDAVkP/DFLbFF+ahY9PPpDU55F2STQCBAgQIECAAAECBAhsNbYzSJNT/nd5\nUbcAf2fyr8k1iUaAAAECBAgQIECAwIgFxngGaXK6z8qLIyYXeE6AAAECBAgQIECAwHgFxnwG\nabyzbuQECBAgQIAAAQIECLQKKJBaWSwkQIAAAQIECBAgQGCMAgqkMc66MRMgQIAAAQIECBAg\n0CqgQGplsZAAAQIECBAgQIAAgTEKKJDGOOvGTIAAAQIECBAgQIBAq4ACqZXFQgIECBAgQIAA\nAQIExiigQBrjrBszAQIECBAgQIAAAQKtAgqkVhYLCRAgQIAAAQIECBAYo4DFn//VAAAhv0lE\nQVQCaYyzbswECBAgQIAAAQIECLQKKJBaWSwkQIAAAQIECBAgQGCMAgqkMc66MRMgQIAAAQIE\nCBAg0CqgQGplsZAAAQIECBAgQIAAgTEKKJDGOOvGTIAAAQIECBAgQIBAq4ACqZXFQgIECBAg\nQIAAAQIExiigQBrjrBszAQIECBAgQIAAAQKtAgqkVhYLCRAgQIAAAQIECBAYo4ACaYyzbswE\nCBAgQIAAAQIECLQKKJBaWSwkQIAAAQIECBAgQGCMAgqkMc66MRMgQIAAAQIECBAg0CqgQGpl\nsZAAAQIECBAgQIAAgTEKKJDGOOvGTIAAAQIECBAgQIBAq4ACqZXFQgIECBAgQIAAAQIExiig\nQBrjrBszAQIECBAgQIAAAQKtAgqkVhYLCRAgQIAAAQIECBAYo4ACaYyzbswECBAgQIAAAQIE\nCLQKKJBaWSwkQIAAAQIECBAgQGCMAgqkMc66MRMgQIAAAQIECBAg0CqgQGplsZAAAQIECBAg\nQIAAgTEKKJDGOOvGTIAAAQIECBAgQIBAq4ACqZXFQgIECBAgQIAAAQIExiigQBrjrBszAQIE\nCBAgQIAAAQKtAgqkVhYLCRAgQIAAAQIECBAYo4ACaYyzbswECBAgQIAAAQIECLQKKJBaWSwk\nQIAAAQIECBAgQGCMAgqkMc66MRMgQIAAAQIECBAg0CqgQGplsZAAAQIECBAgQIAAgTEKKJDG\nOOvGTIAAAQIECBAgQIBAq4ACqZXFQgIECBAgQIAAAQIExiigQBrjrBszAQIECBAgQIAAAQKt\nAgqkVhYLCRAgQIAAAQIECBAYo4ACaYyzbswECBAgQIAAAQIECLQKKJBaWSwkQIAAAQIECBAg\nQGCMAgqkMc66MRMgQIAAAQIECBAg0CqgQGplsZAAAQIECBAgQIAAgTEKKJDGOOvGTIAAAQIE\nCBAgQIBAq4ACqZXFQgIECBAgQIAAAQIExiigQBrjrBszAQIECBAgQIAAAQKtAtu0LrWQAAEC\n8xWof7zZesaHsCn93TDjPnVHgMDGEai/A7ad8eFel/6un3GfuiNAYM4CCqQ5T4DdEyDQKnBm\nlu7TumZ1C/9ndW/3bgIENqjAvXPcd0uePOPjPyf97TvjPnVHgMCcBRRIc54AuydAoFXgFln6\nO8knW9eubOE78rYdVvZW7yJAYIMLbJ/jPy95/AzHcb/09Qcz7E9XBAj0RECB1JOJcBgECPyI\nwJey5JQfWbryBd9b+Vu9kwCBAQjU3wGz/Dvl5gMwMQQCBFoE3KShBcUiAgQIECBAgAABAgTG\nKaBAGue8GzUBAgQIECBAgAABAi0CCqQWFIsIECBAgAABAgQIEBingAJpnPNu1AQIECBAgAAB\nAgQItAgokFpQLCJAgAABAgQIECBAYJwCCqRxzrtREyBAgAABAgQIECDQIqBAakGxiAABAgQI\nECBAgACBcQookMY570ZNgAABAgQIECBAgECLgAKpBcUiAgQIECBAgAABAgTGKaBAGue8GzUB\nAgQIECBAgAABAi0CCqQWFIsIECBAgAABAgQIEBingAJpnPNu1AQIECBAgAABAgQItAgokFpQ\nLCJAgAABAgQIECBAYJwCCqRxzrtREyBAgAABAgQIECDQIqBAakGxiAABAgQIECBAgACBcQoo\nkMY570ZNgAABAgQIECBAgECLgAKpBcUiAgQIECBAgAABAgTGKaBAGue8GzUBAgQIECBAgAAB\nAi0CCqQWFIsIECBAgAABAgQIEBingAJpnPNu1AQIECBAgAABAgQItAgokFpQLCJAgAABAgQI\nECBAYJwCCqRxzrtREyBAgAABAgQIECDQIqBAakGxiAABAgQIECBAgACBcQookMY570ZNgAAB\nAgQIECBAgECLgAKpBcUiAgQIECBAgAABAgTGKaBAGue8GzUBAgQIECBAgAABAi0CCqQWFIsI\nECBAgAABAgQIEBingAJpnPNu1AQIECBAgAABAgQItAhs07Js6It2ywB3TbZPrkwuS65KNAIE\nCBAgQIAAAQIERi4wljNIB2aej00uTC5JzkxOT85Lqkj6evKmZM9EI0CAAAECBAgQIEBgpAJj\nOIP00sztUQvze04eP5lUkVSFUZ1J2j3ZJzkyOTx5dnJCohEgQIAAAQIECBAgMDKBoRdIR2Q+\nqzg6MXlRcmrS1jZl4SHJa5Ljk7OSUxKNAAECBAgQIECAAIERCQz9ErvHZi7PSOpxqeKopvuG\n5KTksOTbyZMTjQABAgQIECBAgACBkQkMvUA6IPNZl9RdPeW8XprtTkv2nnJ7mxEgQIAAAQIE\nCBAgMCCBoRdI38hcHZRsO+Wc1R3uqqiqGzhoBAgQIECAAAECBAiMTGDoBdJxmc87J+9KDl5m\nbpvPINVnlXZK3rvMtlYRIECAAAECBAgQIDBQgaHfpKHuRrdXcnTyqOT85Lzk4uSKZJek7mK3\nb3Kr5NrkecnJiUaAAAECBAgQIECAwMgEhl4g1c0Xjknel7wyOTRZfCbpO1l2QVJ3sHttcm6y\n2rZDOvjVZNpL+/Zb7Q69nwABAgQIEFhXgR2zt/o96tkz3ut16e+tSd00SiNAYA4CQy+QGtK6\nk90TF17UWaP6/qMqYuqLYy9PZt1ukQ5/Ldluyo7rsj6NAAECBAgQ2DgCd82h1j+EPm3Gh3z3\n9Fe/t3xoxv3qjgCBKQXGUiA1HPWZq7q0rtLWts7CKqC+m3yvbYMpl52X7X5yym1rs/slp3TY\n3qYECBAgQIDAfAXq88vV7nHjw8z+e1V6avqeWac6IkBgeoGh36ShJG6ZvCO5JKnC6OPJA5K2\nVv9qU9s9v22lZQQIECBAgAABAgQIDFtg6AXSzpm+Tye/mNTZoTqz88DkpKQ+k6QRIECAAAEC\nBAgQIEDghwJDL5B+NyO9bXJUcpukbvldl779T/LC5E8TjQABAgQIECBAgAABAj8QGHqBdP+M\nsm7EcHTS3A3mv/K87mb3b8lzkyqiNAIECBAgQIAAAQIECGw19AJp78xxFUL1/UaTre5c93PJ\nacmrkroETyNAgAABAgQIECBAYOQCQy+Qzs78PiypW3ovbnXDhp9J6nNJxyVL3bghqzQCBAgQ\nIECAAAECBMYgMPQC6aOZxPrOoz9Mbt0yoedn2cOTuvzun5KfTTQCBAgQIECAAAECBEYqsM3A\nx/2GjO9Xk/qs0XOSX07enky2L+fFYUnd/rs+q1Rt040P/kuAwBYE6u+QByez/ruk/vFm6P+A\nswVaqwkQIECAAIF5CMz6l5p5jGG5fdaXvR6c1C29H518P2lrn8vCeydVUD2ibQPLCBBoFXho\nlp6Y1Jcrz7LVZbH3TD4wy071RYAAAQIECBDYksDQC6Qa/5VJnT2qLPcv0l/P+kcmdRvwKqw0\nAgS2LFDfL/ad5KZb3rTTFtdn6+X+vHbqzMYECBAgQIAAgWkFxlAgTVrUL11bavXFshoBAgQI\nECBAgAABAiMU8C+0I5x0QyZAgAABAgQIECBAoF1AgdTuYikBAgQIECBAgAABAiMUUCCNcNIN\nmQABAgQIECBAgACBdgEFUruLpQQIECBAgAABAgQIjFBAgTTCSTdkAgQIECBAgAABAgTaBRRI\n7S6WEiBAgAABAgQIECAwQgEF0ggn3ZAJECBAgAABAgQIEGgXUCC1u1hKgAABAgQIECBAgMAI\nBRRII5x0QyZAgAABAgQIECBAoF1AgdTuYikBAgQIECBAgAABAiMUUCCNcNINmQABAgQIECBA\ngACBdgEFUruLpQQIECBAgAABAgQIjFBAgTTCSTdkAgQIECBAgAABAgTaBRRI7S6WEiBAgAAB\nAgQIECAwQgEF0ggn3ZAJECBAgAABAgQIEGgXUCC1u1hKgAABAgQIECBAgMAIBRRII5x0QyZA\ngAABAgQIECBAoF1AgdTuYikBAgQIECBAgAABAiMUUCCNcNINmQABAgQIECBAgACBdgEFUruL\npQQIECBAgAABAgQIjFBAgTTCSTdkAgQIECBAgAABAgTaBRRI7S6WEiBAgAABAgQIECAwQgEF\n0ggn3ZAJECBAgAABAgQIEGgXUCC1u1hKgAABAgQIECBAgMAIBRRII5x0QyZAgAABAgQIECBA\noF1AgdTuYikBAgQIECBAgAABAiMUUCCNcNINmQABAgQIECBAgACBdgEFUruLpQQIECBAgAAB\nAgQIjFBAgTTCSTdkAgQIECBAgAABAgTaBRRI7S6WEiBAgAABAgQIECAwQgEF0ggn3ZAJECBA\ngAABAgQIEGgXUCC1u1hKgAABAgQIECBAgMAIBbYZ4ZgNmcBYBZ6Wgf/ajAd/8/S33Yz71B0B\nAgQIECBAYG4CCqS50dsxgXUXOCR73DF51wz3/OD0dZcZ9qcrAgQIECBAgMBcBRRIc+W3cwLr\nLnBa9vjKGe516/T1kBn2pysCBAgQIECAwFwFfAZprvx2ToAAAQIECBAgQIBAnwQUSH2aDcdC\ngAABAgQIECBAgMBcBVxiN1d+OydAgAABAgQIbCawbV69NHnGZktX/+L4dPGO1XejBwLDF1Ag\nDX+OjZAAAQIECBDYOAL1u9n1yVdneMiPSF+PTBRIM0TV1XAFFEjDnVsjI0CAAAECBDamwIk5\n7D+Y4aHvMcO+dEVg8AI+gzT4KTZAAgQIECBAgAABAgSmFVAgTStlOwIECBAgQIAAAQIEBi+g\nQBr8FBsgAQIECBAgQIAAAQLTCiiQppWyHQECBAgQIECAAAECgxdQIA1+ig2QAAECBAgQIECA\nAIFpBRRI00rZjgABAgQIECBAgACBwQsokAY/xQZIgAABAgQIECBAgMC0AgqkaaVsR4AAAQIE\nCBAgQIDA4AUUSIOfYgMkQIAAAQIECBAgQGBaAQXStFK2I0CAAAECBAgQIEBg8AIKpMFPsQES\nIECAAAECBAgQIDCtgAJpWinbESBAgAABAgQIECAweAEF0uCn2AAJECBAgAABAgQIEJhWQIE0\nrZTtCBAgQIAAAQIECBAYvIACafBTbIAECBAgQIAAAQIECEwroECaVsp2BAgQIECAAAECBAgM\nXkCBNPgpNkACBAgQIECAAAECBKYV2GbaDW1HgECrwE2z9AnJ1q1rV77wurz17clVK+/COwkQ\nIECAAAECBLoKKJC6itmewOYCh+blm5Ovbr541a/umB4uSD606p50QIAAAQIECBAgMLWAAmlq\nKhsSaBXYlKXfTX68de3KF9aZo+pbI0CAAAECBAgQWEcBn0FaR2y7IkCAAAECBAgQIECg3wIK\npH7Pj6MjQIAAAQIECBAgQGAdBVxit47YdkWAAAECBAgQmINA3VBoj+TwGe/7m+nv5Bn3qTsC\ncxdQIM19ChwAAQIECBAgQGBNBe6R3vdPDpjhXrZb6GuXGfapKwK9EFAg9WIaHAQBAgQIECBA\nYM0E6qY/ZyZ1h9RZtZ9JR//frDrTD4E+CfgMUp9mw7EQIECAAAECBAgQIDBXAQXSXPntnAAB\nAgQIECBAgACBPgkokPo0G46FAAECBAgQIECAAIG5CiiQ5spv5wQIECBAgAABAgQI9ElAgdSn\n2XAsBAgQIECAAAECBAjMVUCBNFd+OydAgAABAgQIECBAoE8CCqQ+zYZjIUCAAAECBAgQIEBg\nrgK+B2mu/HZOYEmB+s6K/ZJZfqnfbunv24lGgAABAgQIECCwhIACaQkYiwnMWWCH7P/P1+AY\nvrwGfeqSAAECBAgQIDAYAQXSYKbSQAYo8EcZ05/McFyfTl9bz7A/XREgQIAAAQIEBiegQBrc\nlBrQgAS+m7FcMsPxXD/DvnRFgAABAgQIEBikgJs0DHJaDYoAAQIECBAgQIAAgZUIOIO0EjXv\nWQ+BXbKTm63Bji5Mn9esQb+6JECAAAECBAgQGICAAmkAkzjQIXw149prDcb2hvT5rDXoV5cE\nCBAgQIAAAQIDEFAgDWASBzqEnTOupyf/OsPxvSp9rcVZqRkeoq4IECBAgAABAgTmKaBAmqe+\nfW9J4IJs8LUtbdRhve8A6oBlUwIECBAgQIDAGAXcpGGMs27MBAgQIECAAAECBAi0CjiD1Moy\n6IX1BaSzbnXTg+tm3an+CBAgQIAAgd4LrMXvFb0f9MIBrsXvP/V9hduuAcD31qDPwXapQBrs\n1LYO7DVZ+tuta1a38Ny8fZ/VdeHdBAgQIECAwAYSuHOOdcekvrNvlu2GdLZplh2uYV9r8fvP\nmTne267BMf9p+nzeGvQ7yC7HWCDtlpncNdk+uTK5LLkqGUPbI4P8YPKKGQ72ATPub4aHpisC\nBAgQIEBgjQTqZkrV7nvjw8z++8n09Obkr2fW41ZbvXOhr1+YYZ9r9ftP/a5WhczJMzzWl6Sv\n6lebUmAsBdKB8Xhm8uhkzxabM7LsI8mLk2+1rB/SoosymE/NcED+wM0QU1cECBAgQGCDCczy\nd4pm6OflySz7bS4vm2Wfa/n7z+kzHn/97qd1EBhDgfTSeBy1YHJOHutfJi5J6uxRnUnaPanL\nw45MDk+enZyQaAQIECBAgAABAgQIjExg6AXSEZnPKo5OTF6UnJq0tbrW9ZCkPqNzfHJWckqi\nESBAgAABAgQIECAwIoGN8iG4lU5JFTt1bexdk6un6KQ+n3R2UmeQnjHF9kttsn9W/Fey3VIb\nLFpet1uvz0TV9tcuWjfLl8ems6ck359hp1Vk191WZv0hzR3T5zXJLD3qTjvXJ7Mcf81d9fud\nZJZtp3RWxznr8dcxNpca1PPVtpr/+v/W+Fcrufn7zb////359/efv/83/3txNa/q53S1Wf/8\n2yi//9TvmG9Jfj3RphAY+hmkA2JQl9RNUxwV16XJacne9WIV7ay89xeT+oMzTatC9RbJLP8y\nbNtvXW747rYVq1hWt6OsSxTrriuzbLdLZ3VJ5HUz7LSuF66741wywz5r/PsmZ8ywz+pqLcZf\nl5NWm/X4N8r8G7/59/+/P//+/rvx74FZ/Hcj/fwf+9//Nd+fm8Wk62MYAv+SYXwpmbZQqTNI\nVyR/kmgECBAgQIAAAQIECBAYlMAvZzR1xuD9ycHLjKzO4NRnkOruJnUW5wGJRoAAAQIECBAg\nQIAAgUEJVOHz3KS+56gKpfOS/0jqu4DetvBYl+BdkNT6+szLcxKNAAECBAgQIECAAAECgxWo\nmyZUQXR+UoXQZKp4+mry6uS2iUaAAAECBAgQIECAwEgF6gzL2NouGXB9/1Hd0eTC5PJEI0CA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBNZPYNP67cqeCBDogcB2PTgGh0CAAAECBJYSuD4rrl1qpeUE1kNAgbQe\nyvZBoB8C/5HDOLgfh+IoCBAgQIBAq8ANWfqryXGtay0ksA4C26zDPuyCAIF+CJyRw7g4Obof\nh+MoCGx4gftlBK9MHrLhR2IABPoj8LEcykX9ORxHMkYBBdIYZ92Yxyrw/Qz8W8knxwpg3ARm\nLLBb+qvLgfyZmjGs7kYtUH+m6iySRmBuAjeZ257tmAABAgQIECBAgAABAj0TUCD1bEIcDgEC\nBAgQIECAAAEC8xNQIM3P3p4JECBAgAABAgQIEOiZgAKpZxPicAgQIECAAAECBAgQmJ+AAml+\n9vZMgAABAgQIECBAgEDPBBRIPZsQh0OAAAECBAgQIECAwPwEFEjzs7dnAgQIECBAgAABAgR6\nJqBA6tmEOBwCBAgQIECAAAECBOYnoECan709EyBAgAABAgQIECDQM4FtenY8DocAgbUT+P7a\nda1nAqMUuCaj9udqlFNv0GsoUH+m6s+WRoAAAQIE1lxg9+yhohEgMBuBugpj/9l0pRcCBBYE\n6s+UK5z870CAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAIFxCGwaxzCNksCoBbbO6A9ObpWclnw10QgQWLnAPnnrUj8/z8+6a1fetXcS\nGJXAfhntA5Ljlxn1bbLuwOSq5FMLj3nQCBAgQIDAygTumLd9KblhIl/I89smGgEC3QX2ylsm\n/zwtfn6n7l16B4FRCuySUX8x+fYyoz8q665Jmj9n9Y8Pv7fM9lYRIECAAIFlBepfuE9Krkh+\nJblD8vTkO8nZyU0TjQCBbgKHZfP6Ze3DyTEt2TPLNAIElhfYLatPTOrP0lIF0sMX1r87j3UG\n6T5J855n5blGgAABAgQ6C/xm3lE/fH5j0TurSGpbvmgzLwkQaBF4fpbVn58HtqyziACBLQs8\nLptckNSfo6uTtgJppyw/MzkvqcvEm7ZdntTyc5PJ5c16jwQIECBAYFmBulb7e8nNF21VlzV8\nN/n0ouVeEiCwZYG3ZZPrk5tteVNbECCwSOCReV2F0UXJo5NTk7YCqdnuj7J+cXtlFlQfP7t4\nhdcEZiVwk1l1pB8CBHolsG2O5p7JV5LLFh1ZXXJ3enKPpLbTCBCYXqD5c1X/kv3E5LnJTyc7\nJhoBAssL1GeIjk7ulLx/mU3rcrpq/3njw2b/bZbde7OlXhCYocA2M+xLVwQI9Eegru+uX+Au\nXuKQLsnyKo7q8xIXLLGNxQQIbC5Ql/3UL3bfSuoyn8mzSHV3yPqsX/PLW55qBAgsEqjP7lW2\n1G65sEHbz7D6+VVt7xsf/JfA7AWcQZq9qR4J9EFgl4WDqMsY2lrzA8aNGtp0LCPQLnBAFtfP\nzfoHiFckd03ulvy/ZP/kH5PdE40AgdUJLPczzM+v1dl69xQCziBNgWQTAhtQoD57VG2pfwRp\nPtx63Y2b+S8BAlMInJFt6rK6+oD4yRPbvzDP689U3X74t5MXJxoBAisXWO5nmJ9fK3f1zikF\nlvrlacq324wAgZ4KfDPHVR9iXepfs5vll/f0+B0WgT4KXJiDensyWRw1x/nWhScHNgs8EiCw\nYoHm0u/mZ9VkR80yP78mVTyfqYACaaacOiPQG4H6IGz9Mtf8IFl8YLW8vg9p8Q0cFm/nNQEC\n0wnU55KqNZcG3fjKfwkQWInANAXS+Svp2HsITCOgQJpGyTYENqbAl3LY9RmJWyw6/Loxw12S\n/0pcYrcIx0sCywg8N+u+nNRldovbnRcW1HqNAIHVCdTPr2oPvPFhs/82y/5zs6VeECBAgACB\nKQR+PtvUZXb1uYjJ9vt5Uct/YXKh5wQIbFHg8GxRf3b+J9k0sXU9PzGpdYdOLPeUAIHlBU7N\n6rbvQap3nZZ8I5k8K7trXtcl5J9NfI4+CBoBAgQIdBOoM8RfTOos0SuShyVHL7x+dx41AgS6\nCdSHwz+WVCH08eRJyeOSf0lq2ZsTjQCB6QWWK5DqTG39uaqrHeof9I5Iavu6hPxeiUaAAAEC\nBFYkUJfXfSi5PqkfNJV/Tn4s0QgQ6C6wW97yl0n9ktb8marb6f9uohEg0E1guQKpevrl5JKk\n+bNWz5+WaAQIECBAYNUC9YWWByUKo1VT6oDADwR2yH/vnuz3g1f+Q4DAWgnUJax3SOo7x7Zf\nq53olwABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgT+/3bomAgAIISB4AyC8G8DRQ8S\nqJ8t0l2TJUCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBBYCOc2b\n1aKVECBAgMBxgTj+330CBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIEDgf4EGop1M\nxsn4k7cAAAAASUVORK5CYII=", | |
| "text/plain": [ | |
| "Plot with title “Histogram of .”" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "Xn2 <- generate_Xn(1e3, rnorm, mean=4.5, sd = 2) #確率変数列の生成\n", | |
| "Xn2 %>% realize_Xn() %>% unlist() %>% hist(.,40) #その実現からヒストグラム描画" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "次に、異なる分布(一様分布)からの確率変数列を生成しよう：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[[1]]\n", | |
| "runif(1, min = 1, max = 5)\n", | |
| "\n", | |
| "[[2]]\n", | |
| "runif(1, min = 1, max = 5)\n", | |
| "\n", | |
| "[[3]]\n", | |
| "runif(1, min = 1, max = 5)\n", | |
| "\n", | |
| "[[4]]\n", | |
| "runif(1, min = 1, max = 5)\n", | |
| "\n", | |
| "[[5]]\n", | |
| "runif(1, min = 1, max = 5)\n" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "Xn3 <- generate_Xn(5, runif, min=1, max=5)\n", | |
| "Xn3" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "### 確率変数列の関数としての標本平均\n", | |
| "\n", | |
| "確率変数はランダムな事象の関数である。よってランダムな事象の関数の関数もまた確率変数である。\n", | |
| "\n", | |
| "標本平均はサンプルから構成される確率変数のひとつである。その変数を生成する関数を定義しよう：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "runif(1, min = 1, max = 5) + runif(1, min = 1, max = 5) + runif(1, \n", | |
| " min = 1, max = 5) + runif(1, min = 1, max = 5) + runif(1, \n", | |
| " min = 1, max = 5)" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# reduce にわたす和のexpressionを返す関数\n", | |
| "expr_plus <- function(a, b){\n", | |
| " aa <- enexpr(a)\n", | |
| " bb <- enexpr(b)\n", | |
| " expr(!!aa + !!bb)\n", | |
| "}\n", | |
| "\n", | |
| "my_sum <- reduce(Xn3, expr_plus) # 確率変数の和のexpression\n", | |
| "my_sum" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(runif(1, min = 1, max = 5) + runif(1, min = 1, max = 5) + runif(1, \n", | |
| " min = 1, max = 5) + runif(1, min = 1, max = 5) + runif(1, \n", | |
| " min = 1, max = 5))/length(Xn3)" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "my_mean <- expr(!!my_sum/length(Xn3)) \n", | |
| "my_mean" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "この`my_mean`を実現させよう：" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "3.50345684420317" | |
| ], | |
| "text/latex": [ | |
| "3.50345684420317" | |
| ], | |
| "text/markdown": [ | |
| "3.50345684420317" | |
| ], | |
| "text/plain": [ | |
| "[1] 3.503457" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# 単一の確率変数Xを実現する関数 (ただeval()の名前を変えるだけ)\n", | |
| "realize_X <- function(X){\n", | |
| " eval(X)\n", | |
| "}\n", | |
| "my_mean %>% realize_X()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "別試行:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "3.40139275528491" | |
| ], | |
| "text/latex": [ | |
| "3.40139275528491" | |
| ], | |
| "text/markdown": [ | |
| "3.40139275528491" | |
| ], | |
| "text/plain": [ | |
| "[1] 3.401393" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "my_mean %>% realize_X()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "lines_to_next_cell": 0 | |
| }, | |
| "source": [ | |
| "この、確率変数としての標本平均はどのような分布を示すのだろうか？" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
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WCdLWrODL0501XM1B93vVPy1KRpdYan\n/f2fi5oFeTwkqbvL3SJ5YlLFUX0f6i+Sao9Mapv/muyY/Epys6Rarfv0q6au/s+r8/AHSa1X\nP6BXAVe3364zOnUzhXahlacrtvZlb81K52Xi0qS5tfcLM91czvYbmf6ZpGk7NROb8NjFr8vu\n1vfQ2kVj/bxQ7hoBAgQIECBAgACBuRE4KHtSP+w3udeYPavLypr1nr9kvU+0lr24tayKgrrb\nW9Nvucfa7tLL3R61Qp+dM79pv52J+i7PctuseRcnj0uWtoMz44Jkab86y/XsJfP3zvOmtW/z\n/aRm5pLHKtqWbrd5fkprWZk0RVIVZc069figpN1emCfN8vbtwWudumqjWVaPD62ZE7ZZ/U7N\n9pvXbBe5q73sQ1r9qn9zKeJq/SwnQIDAwgu4xG7hD6EBECBAYM0Ejs2Wqgg7JlnuxgTvyvw6\nc1NngNqt5r+xPSPTZye7tea9KtOPT96dVMHTtCq4/jPZL3lrM7P1+OFMH5zU9r+Z1JmrWu8B\nSfsMR55edUaoHidtz8mKL0val+Bdmud/mfxUcnJSbbukisDNbLP6beY+e20CBAgQIECAAAEC\nvRGoMyZ1u+1DktslzaVomVyx1eV5dZnezVdc4+oF9cu5n07umIy71HuPLG/O3GTyWm3pGbXt\nr7XGZDPqTNfdkzsn4/Znsq2t/1qT+q3/nngFAgQIECBAgAABAgQ2TOCP80p1edc5yXHJ/ZN2\ne1Ge1PLKtxKNAAECBAh0FliE35R1HqQNECBAgMBCCnx8tNd1qV7l6KQuq7swqbvs3Tdp2uub\nCY8ECBAgQIAAAQIECBDoq8A/ZGDNWaKVHuvs0rZ9BTAuAgQIECBAgAABAgQINAL1fZtHJ+9N\nTkrqpg6XJ3V3to8kv5W4GiIIGgECBAgQIECAAAECwxOov4ekIBrecTdiAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nEBiYwNYDG6/hEiBAgACBWQVum463nrXzqN/lefxA8qOO29GdAAECBNZJQIG0TrA2S4AAAQK9\nE/h4RnSPpEtxs0P6Pzx5V6IRIECAwBwKbJnDfbJLBAgQIEBgHgW2yU49Pzmyw86dn77+7e0A\nqCsBAgTWW+A66/0Ctk+AAAECBAgQIECAAIFFEVAgLcqRsp8ECBAgQIAAAQIECKy7gAJp3Ym9\nAAECBAgQIECAAAECiyKgQFqUI2U/CRAgQIAAAQIECBBYdwEF0roTewECBAgQIECAAAECBBZF\nQIG0KEfKfhIgQIAAAQIECBAgsO4CCqR1J/YCBAgQIECAAAECBAgsioACaVGOlP0kQIAAAQIE\nCBAgQGDdBRRI607sBQgQIECAAAECBAgQWBQBBdKiHCn7SYAAAQIECBAgQIDAugsokNad2AsQ\nIECAAAECBAgQILAoAgqkRTlS9pMAAQIECBAgQIAAgXUXUCCtO7EXIECAAAECBAgQIEBgUQQU\nSItypOwnAQIECBAgQIAAAQLrLqBAWndiL0CAAAECBAgQIECAwKIIbFmUHV3D/dw129ol2S65\nODk/uSTRCBAgQIAAAQIECBAYuMBQziDdNcf59cmZybnJiclXk9OSKpK+lbw22SPRCBAgQIAA\nAQIECBAYqMAQziC9IMf2sNHxPSWPn0yqSKrCqM4k7ZbslTw1OTR5RnJ0ohEgQIAAAQIECBAg\nQKBXAo/NaK5M3p3sP2ZkW2fZ/ZL/Tmr9eycaAQIECBBoC3wqT57dnjHDdF3W/cgZ+ulCgAAB\nAhsk0PdL7B4VxxOSejxujGkVRR9JHpJclDwx0QgQIECAAAECBAgQGJhA3wuk/XI865K6H0x4\nXM/LescnN5twfasRIECAAAECBAgQINAjgb4XSN/Osbpbct0Jj1nd4a6KqrqBg0aAAAECBAgQ\nIECAwMAE+l4gvTnH83bJ25IDxxzb+g7SQcmxyQ7JOxKNAAECBAgQIECAAIGBCfT9LnZ1N7o9\nk8OTRySnJ3Vr73OSC5Odk7qL3d7JTZLLkt9PPp5oBAgQIECAAAECBAgQ6KXAPhnVW5IqkOqG\nDO3UH4n9RvKS5BaJRoAAAQIElhNwF7vlVMwjQIBAzwT6fgapOVx1J7snjJ7UWaP6+0fbJ/WH\nYy9I1rrtmw1+Mdl2ig1X0VbrXzFFH6sSIECAAAECBAgQILCGAkMpkNpkdWldpWlVlNw++WZS\nZ5PWolVB9uBk0gLpDln3lUkdjx8mGgECBAgQIECAAAECmyAwlALpcbGtmzCcmtQNG6oY2in5\n2+RhyfWTOnNzVPI7SdezSnU26GPJpO3SSVe0HgECBAgQIECAAAECBGYVqLv0vTNpf+eo/tbR\nXsnrRvPfn8fXJp8ePf9oHuuudhvZ7pUXay6x28jX9VoECBAgMLmA7yBNbmVNAgQIEJhTgd/M\nflXh8d7kEclvJXX5W92Uoc4YPSZptz/Mk1q/+b5Se9l6TiuQ1lPXtgkQILA2AgqktXG0FQIE\nCBDYRIH/yGufk9QNGZr285moIuhdzYzWY51xOiV5dWveRkwqkDZC2WsQIECgm4ACqZuf3gQI\nEFgIgSoI+tz2zuA+kHy/Nci6pK7OHn25Na+ZrPknJns1MzwSIECAAAECBAgQIDAcgb4XSHU2\n6IFJ+wxS3ZShxl13jlva6qYV+ycnLV3gOQECBAgQIECAAAEC/Rfoe4FUN2jYNalL7R6dPCf5\ny+TzSRVKv5Q0rSzqxg11d7sPJRoBAgQIECBAgAABAgR6JVBFzzuS+s5RkzMzfaPkb0bz/iuP\nb0tOHz1/Tx43uvkO0kaLez0CBAhML+A7SNOb6UGAAIGFE+j730Gq7xQ9KqmzR/dOTkiOSb6b\nPCupP+T6c8kBSf0tovpjrc9ONAIECBAgQIAAAQIEBijQ9wKpOaT/molKu52fJ09O6ixT3czh\nlOTyRCNAgAABAgQIECBAYKACQymQxh3e5s5149axjAABAgQIECBAgACBAQjU2RONAAECBAgQ\nIECAAAECBCKgQPI2IECAAAECBAgQIECAwEhAgeStQIAAAQIECBAgQIAAgZGAAslbgQABAgQI\nECBAgAABAiMBBZK3AgECBAgQIECAAAECBEYCCiRvBQIECBAgQIAAAQIECIwEFEjeCgQIECBA\ngAABAgQIEBgJKJC8FQgQIECAAAECBAgQIDASUCB5KxAgQIAAAQIECBAgQGAkoEDyViBAgAAB\nAgQIECBAgMBIQIHkrUCAAAECBAgQIECAAIGRgALJW4EAAQIECBAgQIAAAQIjAQWStwIBAgQI\nECBAgAABAgRGAgokbwUCBAgQIECAAAECBAiMBBRI3goECBAgQIAAAQIECBAYCSiQvBUIECBA\ngAABAgQIECAwElAgeSsQIECAAAECBAgQIEBgJKBA8lYgQIAAAQIECBAgQIDASECB5K1AgAAB\nAgQIECBAgACBkYACyVuBAAECBAgQIECAAAECIwEFkrcCAQIECBAgQIAAAQIERgJbSBAgQIAA\nAQIbJrBDXumvkpd2eMVL0/eQ5JwO29CVAAECBFYQUCCtAGM2AQIECBBYB4H6d/e45F9n3PYu\n6VfF1e6JAmlGRN0IECAwTkCBNE7HMgIECBAgsPYC/5NN/u2Mm71J+nU5+zTjy+pGgACB4Qj4\nDtJwjrWREiBAgAABAgQIECCwioACaRUgiwkQIECAAAECBAgQGI6AAmk4x9pICRAgQIAAAQIE\nCBBYRUCBtAqQxQQIECBAgAABAgQIDEdAgTScY22kBAgQIECAAAECBAisIqBAWgXIYgIECBAg\nQIAAAQIEhiOgQBrOsTZSAgQIECBAgAABAgRWEVAgrQJkMQECBAgQIECAAAECwxFQIA3nWBsp\nAQIECBAgQIAAAQKrCCiQVgGymAABAgQIECBAgACB4QgokIZzrI2UAAECBAgQIECAAIFVBBRI\nqwBZTIAAAQIECBAgQIDAcAQUSMM51kZKgAABAgQIECBAgMAqAgqkVYAsJkCAAAECBAgQIEBg\nOAIKpOEcayMlQIAAAQIECBAgQGAVAQXSKkAWEyBAgAABAgQIECAwHAEF0nCOtZESIECAAAEC\nBAgQILCKwJZVlltMgAABAgT6IHC7DOI+HQeyR/rv1HEbuhMgQIDAnAsokOb8ANk9AgQIEFgT\ngWdlK49JzuywtVum7/4d+utKgAABAgsgoEBagINkFwkQIECgs0BdUv725MkdtnRR+m7dob+u\nBAgQILAAAr6DtAAHyS4SIECAAAECBAgQILAxAgqkjXH2KgQIECBAgAABAgQILICAAmkBDpJd\nJECAAAECBAgQIEBgYwQUSBvj7FUIECBAgAABAgQIEFgAAQXSAhwku0iAAAECBAgQIECAwMYI\nKJA2xtmrECBAgAABAgQIECCwAAIKpAU4SHaRAAECBAgQIECAAIGNEVAgbYyzVyFAgAABAgQI\nECBAYAEEFEgLcJDsIgECBAgQIECAAAECGyOgQNoYZ69CgAABAgQIECBAgMACCCiQFuAg2UUC\nBAgQIECAAAECBDZGYMvGvIxXIUCAAAECMwvcPz2fm2w98xa22uoO6futDv11JUCAAIGBCCiQ\nBnKgDZMAAQILLHBA9v32yRs7jOGu6XvjDv11JUCAAIGBCCiQBnKgDZMAAQILLnBa9v/5Hcbw\n+A59dSVAgACBAQn4DtKADrahEiBAgAABAgQIECAwXkCBNN7HUgIECBAgQIAAAQIEBiSgQBrQ\nwTZUAgQIECBAgAABAgTGCyiQxvtYSoAAAQIECBAgQIDAgAQUSAM62IZKgAABAgQIECBAgMB4\nAQXSeB9LCRAgQIAAAQIECBAYkIACaUAH21AJECBAgAABAgQIEBgvoEAa72MpAQIECBAgQIAA\nAQIDElAgDehgGyoBAgQIECBAgAABAuMFFEjjfSwlQIAAAQIECBAgQGBAAgqkAR1sQyVAgAAB\nAgQIECBAYLyAAmm8j6UECBAgQIAAAQIECAxIQIE0oINtqAQIECBAgAABAgQIjBdQII33sZQA\nAQIECBAgQIAAgQEJKJAGdLANlQABAgQIECBAgACB8QIKpPE+lhIgQIAAAQIECBAgMCABBdKA\nDrahEiBAgAABAgQIECAwXkCBNN7HUgIECBAgQIAAAQIEBiSgQBrQwTZUAgQIECBAgAABAgTG\nCyiQxvtYSoAAAQIECBAgQIDAgAQUSAM62IZKgAABAgQIECBAgMB4AQXSeB9LCRAgQIAAAQIE\nCBAYkIACaUAH21AJECBAgAABAgQIEBgvoEAa72MpAQIECBAgQIAAAQIDElAgDehgGyoBAgQI\nECBAgAABAuMFFEjjfSwlQIAAAQIECBAgQGBAAgqkAR1sQyVAgAABAgQIECBAYLyAAmm8j6UE\nCBAgQIAAAQIECAxIQIE0oINtqAQIECBAgAABAgQIjBdQII33sZQAAQIECBAgQIAAgQEJKJAG\ndLANlQABAgQIECBAgACB8QIKpPE+lhIgQIAAAQIECBAgMCABBdKADrahEiBAgAABAgQIECAw\nXkCBNN7HUgIECBAgQIAAAQIEBiSgQBrQwTZUAgQIECBAgAABAgTGCyiQxvtYSoAAAQIECBAg\nQIDAgAQUSAM62IZKgAABAgQIECBAgMB4AQXSeB9LCRAgQIAAAQIECBAYkIACaUAH21AJECBA\ngAABAgQIEBgvoEAa72MpAQIECBAgQIAAAQIDElAgDehgGyoBAgQIECBAgAABAuMFFEjjfSwl\nQIAAAQIECBAgQGBAAgqkAR1sQyVAgAABAgQIECBAYLyAAmm8j6UECBAgQIAAAQIECAxIQIE0\noINtqAQIECBAgAABAgQIjBdQII33sZQAAQIECBAgQIAAgQEJKJAGdLANlQABAgQIECBAgACB\n8QIKpPE+lhIgQIAAAQIECBAgMCABBdKADrahEiBAgAABAgQIECAwXkCBNN7HUgIECBAgQIAA\nAQIEBiSgQBrQwTZUAgQIECBAgAABAgTGCyiQxvtYSoAAAQIECBAgQIDAgAQUSAM62IZKgAAB\nAgQIECBAgMB4AQXSeB9LCRAgQIAAAQIECBAYkIACaUAH21AJECBAgAABAgQIEBgvoEAa72Mp\nAQIECBAgQIAAAQIDEtgyoLE2Q901E7sk2yUXJ+cnlyQaAQIECBAgQIAAAQIDFxjKGaS75ji/\nPjkzOTc5MflqclpSRdK3ktcmeyQaAQIECBAgQIAAAQIDFRjCGaQX5NgeNjq+p+Txk0kVSVUY\n1Zmk3ZK9kqcmhybPSI5ONAIECBAg0EeB+rf/IUnXnwHql41f6COQMREgMGyBrh+O86732Oxg\nFUfHJs9LjkuWa1tn5kHJS5OjkpOSTyQaAQIECBDom8C9M6B3JRd2GNi26fuNZL8O29CVAAEC\ncynQ9wLpUVE/IanHH4w5Aldm2UeS+o3ayckTEwVSEDQCBAgQ6J3ANhlR/btXV1HM2n4rHZ8+\na2f9CBAgMM8Cff8OUv1mqy6pG1cctY/PeXlyfHKz9kzTBAgQIECAAAECBAgMQ6DvBdK3cxjv\nllx3wsNZd7iroqpu4KARIECAAAECBAgQIDAwgb4XSG/O8bxd8rbkwDHHtvkOUn1XaYfkHWPW\ntYgAAQIECBAgQIAAgZ4K9P07SEfnuO2ZHJ48Ijk9OS05J6kvp+6c1F3s9k5uklyW/H7y8UQj\nQIAAAQIECBAgQGBgAn0vkOpLqC9L3pkckdwvWXom6XuZd0ZSd7B7eXJq0rXVWaj68uq2E27o\nFhOuZzUCBAgQIECAAAECBNZRoO8FUkNXd7J7wuhJnTWqO/dsn9Qfjr0gWetW239YMmmBdP21\n3gHbI0CAAAECBAgQIEBgeoGhFEhtmbq0rlKtbnV66+Ts5PxkrVrdHOIBU2zsXln3E1Osb1UC\nBAgQIECAAAECBNZBoO83aSiy+g7SXydvrCejVmd4/iq5JKk/dFffSTo+qe8faQQIECBAgAAB\nAgQIDFSg72eQbpjjelxSf9foI6NjXLf8/kCyf3JF8qGkziAdkLwkqTNK9f2hWqYRIECAAAEC\nBAgQIDAggb6fQXpujmUVR89JHjI6rr+dxyqOXpfUsvsnj01uk7wieVrywEQjQIAAAQIECBAg\nQGBgAn0vkOq7PScmf5b8YHRsD8pjfd+ozhJ9ZzSvHn6YPDOpu9g9KNEIECBAgAABAgQIEBiY\nQN8vsavxfS5pXy53eZ6fkvwoWdpqvTOSOpukESBAgEB3gfo7c3+c1E1xZm31B7/ru6Pa/AjU\nFRiVf+y4S8ek/9Edt6E7AQIE1lSg7wXSZ6P1S8nuSd2IoVp9F+nhyR7JWUm73ThP7p68uD3T\nNAECBAjMLHCX9HxM8oaZt7DVVrum724d+uu69gL7ZJM7Jed12PR907e+F6xA6oCoKwECBKYV\nqGKnLq2ry+bq0rpq9UdcP5Z8MLlp0rT6R/zryfeTOzczN+ixLgW8Mtl2g17PyxAgQGCjBB6Z\nF+r6ZxT+I9u4qOMOfyP9K11a7UPtS5dWVyoc0WEDN0nf+vfith22Ud+9bV9ZMcum3pJO9e9l\nl1bf+31blw3oS4AAgfUQ6PsZpM8ErW668Jrkw8kXkjqr9JXk15KTkm8mdYZpz6T+0fnNpNbT\nCBAgQIAAAQIECBAYmEDfb9JQh/ONyS2TI5O6TOOJya8nWyd1av/2yY5JXUe9X/K6RCNAgAAB\nAgQIECBAYIACfT+D1BzS72biOaPUF4Xru0b15dLvJaclXS//yCY0AgQIECBAgAABAgQWXWAo\nBVL7ONVd7E4fpT3fNAECBAgQIECAAAECAxcYwiV2Az/Ehk+AAAECBAgQIECAwKQCCqRJpaxH\ngAABAgQIECBAgEDvBRRIvT/EBkiAAAECBAgQIECAwKQCCqRJpaxHgAABAgQIECBAgEDvBRRI\nvT/EBkiAAAECBAgQIECAwKQCCqRJpaxHgAABAgQIECBAgEDvBRRIvT/EBkiAAAECBAgQIECA\nwKQCCqRJpaxHgAABAgQIECBAgEDvBRRIvT/EBkiAAAECBAgQIECAwKQCCqRJpaxHgAABAgQI\nECBAgEDvBRRIvT/EBkiAAAECBAgQIECAwKQCCqRJpaxHgAABAgQIECBAgEDvBRRIvT/EBkiA\nAAECBAgQIECAwKQCCqRJpaxHgAABAgQIECBAgEDvBRRIvT/EBkiAAAECBAgQIECAwKQCCqRJ\npaxHgAABAgQIECBAgEDvBRRIvT/EBkiAAAECBAgQIECAwKQCCqRJpaxHgAABAgQIECBAgEDv\nBRRIvT/EBkiAAAECBAgQIECAwKQCCqRJpaxHgAABAgQIECBAgEDvBbb0foQGSIAAAQKzCmyd\njo9KrjfrBtLvbsk2HfrrSoAAAQIENlRAgbSh3F6MAAECCyVw6+zt25PvJFfMuOfXT78dZ+yr\nGwECBAgQ2HABBdKGk3tBAgQILIxAnUGqtn/y7aumpv/PEenynOm76UGAAAECBDZHwHeQNsfd\nqxIgQIAAAQIECBAgMIcCCqQ5PCh2iQABAgQIECBAgACBzRFQIG2Ou1clQIAAAQIECBAgQGAO\nBRRIc3hQ7BIBAgQIECBAgAABApsjoEDaHHevSoAAAQIECBAgQIDAHAookObwoNglAgQIECBA\ngAABAgQ2R0CBtDnuXpUAAQIECBAgQIAAgTkUUCDN4UGxSwQIECBAgAABAgQIbI6AAmlz3L0q\nAQIECBAgQIAAAQJzKKBAmsODYpcIECBAgAABAgQIENgcAQXS5rh7VQIECBAgQIAAAQIE5lBg\nyxzuk10iQIAAAQIElhfYdjT7tXm8ZPlVVp27+6prWIEAAQIDFlAgDfjgGzoBAgQILJzADUZ7\nfHYeT5px7+82Yz/dCBAgMAgBBdIgDrNBEiBAgEDPBF6X8bxnxjE9M/0OmbGvbgQIEOi9gO8g\n9f4QGyABAgQIECBAgAABApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyABAgQIECBAgAAB\nApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyABAgQIECBAgAABApMKKJAmlbIeAQIECBAg\nQIAAAQK9F1Ag9f4QGyABAgQIECBAgAABApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyAB\nAgQIECBAgAABApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyABAgQIECBAgAABApMKKJAm\nlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyABAgQIECBAgAABApMKKJAmlbIeAQIECBAgQIAAAQK9\nF1Ag9f4QGyABAgQIECBAgAABApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyABAgQIECBA\ngAABApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyABAgQIECBAgAABApMKKJAmlbIeAQIE\nCBAgQIAAAQK9F1Ag9f4QGyABAgQIECBAgAABApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4Q\nGyABAgQIECBAgAABApMKKJAmlbIeAQIECBAgQIAAAQK9F1Ag9f4QGyABAgQIECBAgAABApMK\nKJAmlbIeAQIECBAgQIAAAQK9F5i2QHplRB6ZXLf3MgZIgAABAgQIECBAgMDgBKYtkH42Qu9I\nTk/+MrlLohEgQIAAAQIECBAgQKAXAtMWSPfKqH8vOTX53eRzyeeTmrdnohEgQIAAAQIECBAg\nQGBhBaYtkM7MSF+e3C25U/JnyQ2TlyV1VumdyaMTl+AFQSNAgAABAgQIECBAYLEEpi2Q2qP7\nUp48O9krOSSp7yfdM3l7ckbyF8ltEo0AAQIECBAgQIAAAQILIbBlDfZy32zjfsnBSV1md2VS\nZ5rqsru6DO+w5I8SjQABAgQ2VuB5ebkbd3jJG4z6dvllWoeX15UAAQIECGy8wKwF0h7Z1ccn\nv5wcMNrtk/NYhdCbkxOSWyV16V0VSKckb0o0AgQIENg4gRfnpT6anDXjSzbfLa1Lqesyao0A\nAQIECPReYNoC6dCIPCV5SFJ9L02OSt6YfCCps0dNOzETv5k8Mnlg8qZEI0CAAIGNFXhRXu6D\nM75kfdb/54x9dSNAgAABAgspMG2B9OcZZZ0Z+lRSRdFbkwuSldplWXByctxKK5hPgAABAgQI\nECBAgACBeRGYtkB6VXb8P5KvTjiAc7LeLSdc12oECBAgQIAAAQIECBDYVIFpv3hbd6ar4qgu\nmdu3tec3zfTfjea3ZpskQIAAAQIECBAgQIDA4ghMWyBVIXRM8r7kwNYw98n0r4zm/1FrvkkC\nBAgQIECAAAECBAgsjMC0BdJLM7KHJXWp3Xtao/xYpuvLvHW3pOcn9040AgQIECBAgAABAgQI\nLJTANAXS1hlZ3ZHuX5PfSc5O2u29efK45PKkbgGuESBAgAABAgQIECBAYKEEpimQrp+RXS95\n/5gRfjvLPpPsNWYdiwgQIECAAAECBAgQIDCXAtMUSBdmBF9P7jJmJNfNsn2Sb41ZxyICBAgQ\nIECAAAECBAjMpcA0BVINoP7Y4G8kT6gnS9pOef7aZI+kbuKgESBAgAABAgQIECBAYKEEpv07\nSC/I6O6WHJ28MPlycn5Sd7c7INk1+fvk3YlGgAABAgQIECBAgACBhRKYtkA6M6O7f/KK5JDk\nUUndvKHaaclzk9fVE40AAQIECBAgQIAAAQKLJjBtgVTjuzh5ymigu+SxbshwclLfUdIIECBA\ngAABAgQIECCwsAKzFEjtwV6QJ19ozzBNgAABAgQIECBAgACBRRWYpUB6QAb7K8meSd32u7nE\nLpM/bm/K1Jt//MwEAQIECBAgQIAAAQIEFkBg2gLpFzOmt04wrg9PsI5VCBAgQIAAAQIECBAg\nMFcC0xZIL87eX5I8NalbftdNG5ZrVyw30zwCBAgQIECAAAECBAjMs8A0BdKOGchtkvpbR3Wb\nb40AAQIECBAgQIAAAQK9EpjmD8VempHXnerqDJJGgAABAgQIECBAgACB3glMUyDVZXP13aIn\nJNP06x2aAREgQIAAAQIECBAg0E+BaQud3wjD95J/Se6X1N9A2n2Z1N3tNAIECBAgQIAAAQIE\nCCyUwLQF0jEZXd3e+9FJnU06OTl7mTw78zQCBAgQIECAAAECBAgslMA0N2mogX0uOWOCEX5l\ngnWsQoAAAQIECBAgQIAAgbkSmLZA+t9ztfd2hgABAgQIECBAgAABAmsoMO0ldu2Xru8Z3Tk5\ncDSzbgOuESBAgAABAgQIECBAYGEFZimQ6sYM/5TU7b6PT16SVPuH5PBku3qiESBAgAABAgQI\nECBAYNEEpr3E7iYZ4HFJ3bmuvme0Q9K0rTPxvORRyd2T7ycaAQIECBAgQIAAAQIEFkZg2jNI\nr8jI6tK6g5I7JFUsNe3QTByR3DF5UjPTIwECBAgQIECAAAECBBZFYNoC6YEZ2KuTjy0zwMsz\n77DkguSeyyw3iwABAgQIECBAgAABAnMtME2BtHNGsmvytTEj+lGWfWm03pjVLCJAgAABAgQI\nECBAgMD8CUxTIF2Y3f9Oco8xw6giqi6x++qYdSwiQIAAAQIECBAgQIDAXApMUyDVAN6d/Hry\n28lOSbvdIE/+LtkleW97gWkCBAgQIECAAAECBAgsgsC0d7H7PxnUg5JXJnVDhkuT+u7RO5K6\nccNuyZuS9ycaAQIECMwu8LB0rZvhdG3bd92A/gQIECBAYEgC0xZI5wdn/+Tw5FeTuqSu2iOT\nc5NnJK9JNAIECBDoJlB/Y67O1J/VYTP15xd+Kqmz/xoBAgQIECAwgcC0BVJt8uzkacnTk72T\nGycnJWckGgECBAisncCR2VSXXzpdkf5VJGkECBAgQIDAhAKzFEjNpuvSuhNGaeZ5JECAAAEC\nBAgQIECAwMIKTHuThoUdqB0nQIAAAQIECBAgQIDAagLTnkF6bTZ4o9U2muX/OMoEq1qFAAEC\nBAgQIECAAAEC8yEwbYH04Oz2rVbZ9dOy/MOrrGMxAQIECBAgQIAAAQIE5k5g2gLprhnB0svy\n6vnNkzslL0vq7FE9agQIECBAgAABAgQIEFgogWkLpAtWGN05mf8/yZeSzyUfTY5JNAIECBAg\nQIAAAQIECCyMwNKzQV13/PPZwMlJXYqnESBAgAABAgQIECBAYKEE1rpA2i6j3z3Zc6EU7CwB\nAgQIECBAgAABAgQiMO0ldtunz3J/dLC2s0dyeFJ/+f0zyby2XbNjuyRVzF2cnJ9ckmgECBAg\nQIAAAQIECAxcYNoC6cvxWu0udvXHY/9mzlzr5hJPT34+qUJuaat9fl/yh8lZSxd6ToAAAQIE\nCBAgQIDAMASmLZA+EpavL0NzReZdmByfvD5Z6WYOWbTh7QV5xcNGr3pKHj+ZnJvU2aM6k7Rb\nslfy1OTQ5BnJ0YlGgAABAgQIECBAgMDABKYtkJ68YD6Pzf5WcXRs8rzkuGS5VpcNHpS8NDkq\nOSn5RKIRIECAAAECBAgQIDAggbW+ScO80T0qO1SXz9XjSsVR7fOVSZ0de0hyUfLERCNAgAAB\nAgQIECBAYGAC055Bem18bjSD0d+nz9tm6Ne1y37ZQF1S94MJN3Re1qvLBG824fpWI0CAAAEC\nBAgQIECgRwLTFkhVcNwpqTvVVbs8qbvA1fd46jK1ldp/rbRgned/O9u/W3Ld5EcTvFbd4a7G\nWIWgRoAAAQIECBAgQIDAwASmvcTuV+JTt8Q+JqnCo277fcPR48Py+JWkiqE6y7R7Ky/L9Ga0\nN+dFb5fU2asDx+xA8x2k+q7SDsk7xqxrEQECBAgQIECAAAECPRWY9gzS38bhc8mjkytaJj/M\ndBUXX0y+lvxC8tfJZre6G1390drDk0ckpyenJeckFyY7J3X2a+/kJsllye8nH080AgQIECBA\ngAABAgQGJjBNgbRdbO6ZPCVpF0dtsio+Pp8cnMxDgVQ3X6izV+9Mjkjulyw9k/S9zDsjeWny\n8uTURCNAgAABAgQIECBAYIAC0xRIdXal/nbQuBsY1Hd99k3qLNM8tROyM08Y7VCdNdolqcsD\nz0wuSNa67ZMN/k+y7YQbHvf9rQk3YTUCBAgQILBQAvtnb++V/KDjXj8z/V/TcRu6EyBA4McC\n0xRIdUOG9ybPTT6UfDppt/ruzquS+v5RXW43r60uras0bY9M1Pel6g/grnRmrFl30scTs+LP\nJ1UwTtJun5X+cpIVrUOAAAECBHoiUDd8Oi/5pQ7j+dP0HfeL2w6b1pUAgaEKTFMgldEfJ/dN\n6kYM9XeDvpJclNw8eUBS3/ep7yn9e7Io7f9mR5+VVJF07hrtdF3a98EptlWGGgECBAgQGJrA\n9zPg93QYdP0brhEgQGBNBaYtkI7Pq98jeUNyUFLf6WnadzPxm8nrmxlz8Lhf9mHHVfaj+c1T\njas5s1TfQzptlX4WEyBAgAABAgQIECDQM4FpC6Qafv1toYcl10lum9Qldd9KTk/qzMk8tb/L\nzvz0hDvUvizwRelz2IT9rEaAAAECBAgQIECAQE8EZimQmqHXXe3qOzZ1erzOttSZmvobSfPU\n/jo787KkbshwTFKXBC5t98+MA5JXJJeOFn589OiBAAECBAgQIECAAIEBCcxSIO0Vn5ckj0nq\n7msfS+pyu39IvpS8OOl6R5psYk1aFUgfTY5OHpy8L3lV0j7TdWSeV4FUZ4zW6jtI2ZRGgMCA\nBeoXRs3lu7My1C+g6jNWI0CAAAECBDZQYNoC6SbZt+OSuqFBnY2pO9c1rf4hf17yqOTuSZ1Z\nmodWRVsVQEck9XeO6g/G/mpyeqIRIEBgPQRem43+rzXY8IHZxqvXYDs2QYAAAQIECEwoUN8j\nmqbVZWjXS+qM0R2SKpaadmgmqgi5Y/KkZuacPNYZrbrTzYOS2ydfSB6faAQIEFgPgfqcrJvZ\n3LRD6nOrziJpBAgQIECAwAYKTHsG6YHZt/pt5seW2cfLM68uU/vt5J5J/QZ13toHskN1Z7u6\n9O4tyc8nFycaAQIE1lrgkmywbmqjESBAgAABAgskME2BtHPGtWvytTHj+1GW1SVttd68tvqj\ndI9L/j15VVLj0ggQIECAAAECBAgQIHDVrbonZai/EfSd5B5jOlSxUZfYfXXMOvOy6O+zI3UL\n8H9JPpRUcacRIECAAAECBAgQIDBggWnOIBXTu5NfT76YvClptxvkyZuSXZL3JovQTspOPnYR\ndtQ+EiBAgAABAgQIECCw/gLT3qTh/2SXzkhemZye3DvZJ3lHUn8s9pHJm5L3JxoBAgQIECBA\ngAABAgQWSmDaAun8jG7/pG7AUH989UZJ3aWpCqNqz0jqDJNGgAABAgQIECBAgACBhROY9hK7\nGuDZydOSpyd7JzdOTkrqzJJGgAABAgQIECBAgACBhRWYtkB6dUZ6afL/ksuSE0bJg0aAAAEC\nBAgQIECAAIHFFpjmErvtMtT6A7APT6o40ggQIECAAAECBAgQINArgWkKpB9m5BclOyRb90rB\nYAgQIECAAAECBAgQIBCBaQqkK7P+o0dqx+Txocm+Sf3to6Wps00aAQIECBAgQIAAAQIEFkpg\nmgKpBvaSpM4g1WV2xybfTC5YJs/JPI0AAQIECBAgQIAAAQILJTDtTRq+mtGdN8EIvzbBOlYh\nQIAAAQIECBAgQIDAXAlMWyD9+lztvZ0hQIAAAQIECBAgQIDAGgqsdond/fJaD1jD17MpAgQI\nECBAgAABAgQIzK3AameQXpE93yW51ZIR3DnPd08+tGS+pwQIECBAgAABAgQIEFhYgdXOIK00\nsMOz4IMrLTSfAAECBAgQIECAAAECiygwa4G0iGO1zwQIECBAgAABAgQIEBgroEAay2MhAQIE\nCBAgQIAAAQJDElAgDeloGysBAgQIECBAgAABAmMFFEhjeSwkQIAAAQIECBAgQGBIAgqkIR1t\nYyVAgAABAgQIECBAYKzAarf5rs67Jkcu2codRs+Xzm9We28m3tc88UiAAAECBAgQIECAAIFF\nEJikQKq/g/SsFQaz0vzvZX0F0gpoZhMgQIAAAQIECBAgMJ8CqxVIz8tu32CGXT9+hj66ECBA\ngAABAgQIECBAYFMFViuQ3rWpe+fFCRAgQIAAAQIECBAgsIECbtKwgdheigABAgQIECBAgACB\n+RZQIM338bF3BAgQIECAAAECBAhsoIACaQOxvRQBAgQIECBAgAABAvMtoECa7+Nj7wgQIECA\nAAECBAgQ2EABBdIGYnspAgQIECBAgAABAgTmW0CBNN/Hx94RIECAAAECBAgQILCBAgqkDcT2\nUgQIECBAgAABAgQIzLeAAmm+j4+9I0CAAAECBAgQIEBgAwUUSBuI7aUIECBAgAABAgQIEJhv\nAQXSfB8fe0eAAAECBAgQIECAwAYKKJA2ENtLESBAgAABAgQIECAw3wIKpPk+PvaOAAECBAgQ\nIECAAIENFFAgbSC2lyJAgAABAgQIECBAYL4FFEjzfXzsHQECBAgQIECAAAECGyigQNpAbC9F\ngAABAgQIECBAgMB8CyiQ5vv42DsCBAgQIECAAAECBDZQQIG0gdheigABAgQIECBAgACB+RZQ\nIM338bF3BAgQIECAAAECBAhsoIACaQOxvRQBAgQIECBAgAABAvMtoECa7+Nj7wgQIECAAAEC\nBAgQ2EABBdIGYnspAgQIECBAgAABAgTmW0CBNN/Hx94RIECAAAECBAgQILCBAgqkDcT2UgQI\nECBAgAABAgQIzLeAAmm+j4+9I0CAAAECBAgQIEBgAwUUSBuI7aUIECBAgAABAgQIEJhvAQXS\nfB8fe0eAAAECBAgQIECAwAYKbNnA1/JSBAgQIECAAIG1FNgjG3tA8ucdNnpF+r4qObXDNnQl\nQKBHAgqkHh1MQyFAgAABAgMTuEXGu3VyTodxPzB9v5D8Q4dt6EqAQI8EFEg9OpiGQoAAAQIE\nBijwlYz54R3G7cxRBzxdCfRRwHeQ+nhUjYkAAQIECBAgQIAAgZkEFEgzselEgAABAgQIECBA\ngEAfBRRIfTyqxkSAAAECBAgQIECAwEwCCqSZ2HQiQIAAAQIECBAgQKCPAgqkPh5VYyJAgAAB\nAgQIECBAYCYBBdJMbDoRIECAAAECBAgQINBHAQVSH4+qMREgQIAAAQIECBAgMJOAAmkmNp0I\nECBAgAABAgQIEOijgAKpj0fVmAgQIECAAAECBAgQmElAgTQTm04ECBAgQIAAAQIECPRRQIHU\nx6NqTAQIECBAgAABAgQIzCSwZaZeOhEgQIAAAQIE+iGwe4bxiuTIDsP5QfoenJzaYRu6EiAw\nJwIKpDk5EHaDAAECBAgQ2BSB6+ZVP568ccZX3z79/ja5UaJAmhFRNwLzJKBAmqejYV8IECBA\ngACBzRD4Rl706BlfeMf0qwJJI0CgJwK+g9STA2kYBAgQIECAAAECBAh0F1AgdTe0BQIECBAg\nQIAAAQIEeiKgQOrJgTQMAgQIECBAgAABAgS6CyiQuhvaAgECBAgQIECAAAECPRFQIPXkQBoG\nAQIECBAgQIAAAQLdBRRI3Q1tgQABAgQIECBAgACBnggokHpyIA2DAAECBAgQIECAAIHuAgqk\n7oa2QIAAAQIECBAgQIBATwQUSD05kIZBgAABAgQIECBAgEB3AQVSd0NbIECAAAECBAgQIECg\nJwJbejIOwyBAgAABAgQIbKbAXfPiO3TYgfPT9/gO/XUlQGCNBBRIawRpMwQIECBAgMAgBbYb\njfpvOo7+yvSvAuv7HbejOwECHQVcYtcRUHcCBAgQIEBg0ALbjEb/pDzWz1Wz5ID02zpptpVJ\njQCBzRJwBmmz5L0uAQIECBAg0CeBOgNUmaXN2m+W19KHAIFVBJxBWgXIYgIECBAgQIAAAQIE\nhiOgQBrOsTZSAgQIECBAgAABAgRWEVAgrQJkMQECBAgQIECAAAECwxFQIA3nWBspAQIECBAg\nQIAAAQKrCCiQVgGymAABAgQIECBAgACB4QgokIZzrI2UAAECBAgQIECAAIFVBBRIqwBZTIAA\nAQIECBAgQIDAcAQUSMM51kZKgAABAgQIECBAgMAqAgqkVYAsJkCAAAECBAgQIEBgOAIKpOEc\nayMlQIAAAQIECBAgQGAVAQXSKkAWEyBAgAABAgQIECAwHAEF0nCOtZESIECAAAECBAgQILCK\ngAJpFSCLCRAgQIAAAQIECBAYjoACaTjH2kgJECBAgAABAgQIEFhFQIG0CpDFBAgQIECAAAEC\nBAgMR0CBNJxjbaQECBAgQIAAAQIECKwioEBaBchiAgQIECBAgAABAgSGI7BlOEM1UgIEBiBw\n14zx5UnXX/78e7bxpwPwMkQCBAgQIEBgiYACaQmIpwQILLTAHbP3P538WYdRPDh9H5AokDog\n6kqAAAECBBZVQIG0qEfOfhMgsJLAhVlwxEoLJ5i/Q9a5xwTrWYUAAQIECBC8+TpoAAAklUlE\nQVTooUDXy1B6SGJIBAgQIECAAAECBAgMVUCBNNQjb9wECBAgQIAAAQIECFxLQIF0LRIzCBAg\nQIAAAQIECBAYqoACaahH3rgJECBAgAABAgQIELiWgALpWiRmECBAgAABAgQIECAwVAEF0lCP\nvHETIECAAAECBAgQIHAtAQXStUjMIECAAAECBAgQIEBgqAIKpKEeeeMmQIAAAQIECBAgQOBa\nAgqka5GYQYAAAQIECBAgQIDAUAUUSEM98sZNgAABAgQIECBAgMC1BBRI1yIxgwABAgQIECBA\ngACBoQookIZ65I2bAAECBAgQIECAAIFrCSiQrkViBgECBAgQIECAAAECQxVQIA31yBs3AQIE\nCBAgQIAAAQLXElAgXYvEDAIECBAgQIAAAQIEhiqwZYAD3zVj3iXZLrk4OT+5JNEIECBAgAAB\nAgQIEBi4wFDOIN01x/n1yZnJucmJyVeT05Iqkr6VvDbZI9EIECBAgAABAgQIEBiowBDOIL0g\nx/aw0fE9JY+fTKpIqsKoziTtluyVPDU5NHlGcnSiESAwTIHrZdg3TH62w/BvlL71OaMRIECA\nAAECCybQ9wLpsTkeVRwdmzwvOS5Zrm2dmQclL02OSk5KPpFoBAgMT+DuGfJdkn/uMPQqsnbs\n0F9XAgQIECBAYJME+l4gPSquJyT1+IMxxldm2UeShyQnJ09MFEhB0AgMUKAuPa6zP3UWadZW\nl+/WL140AgQIECBAYMEE+v4dpP1yPOqSunHFUfuQnZcnxyc3a880TYAAAQIECBAgQIDAMAT6\nXiB9O4fxbsl1JzycdYe7KqrqBg4aAQIECBAgQIAAAQIDE+h7gfTmHM/bJW9LDhxzbJvvINV3\nlXZI3jFmXYsIECBAgAABAgQIEOipQN+/g1R3o9szOTx5RHJ6Ut8NOCe5MNk5qbvY7Z3cJLks\n+f3k44lGgAABAgQIECBAgMDABPpeINXNF16WvDM5IrlfsvRM0vcy74yk7mD38uTUpGurO1g9\nLdl2wg3VbcY1AgQIECBAgAABAgQ2WaDvBVLDW3eye8LoSZ01qr9/tH1Sfzj2gmStW32X6ReS\nSb/7tNNa74DtESBAgAABAgQIECAwvcBQCqRGpr5zVZfWVZZr22RmFVCXJt9fboUJ59UZqfq7\nSpO2e2XFT0y6svUIECBAgAABAgQIEFgfgb7fpKHU6i/avzU5N6nC6IPJfZLl2p0zs9Z79nIL\nzSNAgAABAgQIECBAoN8CfS+Q6tK1/05+MamzQ3WDhoOTjyT1nSSNAAECBAgQIECAAAECPxbo\ne4H0BxnpLZLDkpsndcvveyRfTJ6b/EWiESBAgAABAgQIECBA4CqBvhdI984o60YMhycXXTXi\nrbb6bB7rbnYfTZ6ZVBGlESBAgAABAgQIECBAYKu+F0g3yzGuQqj+vlG71Z3rHp4cnxyZ1CV4\nGgECBAgQIECAAAECAxfoe4F0co7vg5K6pffSVjds+Nmkvpf05mSlGzdkkUaAAAECBAgQIECA\nwBAE+l4gvT8Hsf7m0R8nN13mgJ6eeQ9O6vK7/0h+LtEIECBAgAABAgQIEBioQN8LpFfluH45\nqe8anZo8PlnavpYZD0muSOq7StW2vvrBfwkQIECAAAECBAgQGJJA3wuk+mOvByavSE5Jfpgs\n1z6fmXdPjl1uoXkECBAgQIAAAQIECAxDYMsAhnlxxvi7o4wrCL+VdR6W1G3Aq7DSCBAgQIAA\nAQIECBAYmMAQCqT2Ia3L6FZr9YdlNQIECBAgQIAAAQIEBigw7ozKADkMmQABAgQIECBAgACB\nIQsokIZ89I2dAAECBAgQIECAAIFrCCiQrsHhCQECBAgQIECAAAECQxZQIA356Bs7AQIECBAg\nQIAAAQLXEFAgXYPDEwIECBAgQIAAAQIEhiygQBry0Td2AgQIECBAgAABAgSuIaBAugaHJwQI\nECBAgAABAgQIDFlgaH8HacjH2tgJzLvAPtnBLyXbdtzRyzr2150AAQIECBAYsIACacAH39AJ\nzJnAbtmf7ZOHJ5fOuG+/l34Pm7GvbgQIECBAgACBrRRI3gQECMybwIeyQ5fMuFOPmbGfbgQI\nECBAgACBqwR8B8kbgQABAgQIECBAgAABAiMBBZK3AgECBAgQIECAAAECBEYCCiRvBQIECBAg\nQIAAAQIECIwEfAfJW4EAgbUSuEU2dP0OG7tVh766EiBAgAABAgTWRECBtCaMNkJg8ALbReCE\nZC0+U+o237PepGHwBwIAAQIECBAg0E1gLX6Y6bYHehMg0AeB+iypPCT5/IwDemz6vTrxuTQj\noG4ECBAgQIBAdwE/iHQ3tAUCBH4icF4mz/rJ06mmLppqbSsTIECAAAECBNZBwE0a1gHVJgkQ\nIECAAAECBAgQWEwBBdJiHjd7TYAAAQIECBAgQIDAOggokNYB1SYJECBAgAABAgQIEFhMAQXS\nYh43e02AAAECBAgQIECAwDoIKJDWAdUmCRAgQIAAAQIECBBYTAEF0mIeN3tNgAABAgQIECBA\ngMA6CCiQ1gHVJgkQIECAAAECBAgQWEwBBdJiHjd7TYAAAQIECBAgQIDAOggokNYB1SYJECBA\ngAABAgQIEFhMAQXSYh43e02AAAECBAgQIECAwDoIbFmHbdokAQIECBAgQIDAxgrcNC/3m0nX\nX35/PNs4dmN33asRmC8BBdJ8HQ97Q4AAAQIECBCYReAB6fTs5GOzdB712TePByYKpA6Iui6+\ngAJp8Y+hERAgQIAAAQIESuCs5EEdKI5I33t06K8rgV4IdD0N2wsEgyBAgAABAgQIECBAgEAJ\nKJC8DwgQIECAAAECBAgQIDASUCB5KxAgQIAAAQIECBAgQGAkoEDyViBAgAABAgQIECBAgMBI\nQIHkrUCAAAECBAgQIECAAIGRgALJW4EAAQIECBAgQIAAAQIjAQWStwIBAgQIECBAgAABAgRG\nAgokbwUCBAgQIECAAAECBAiMBBRI3goECBAgQIAAAQIECBAYCSiQvBUIECBAgAABAgQIECAw\nElAgeSsQIECAAAECBAgQIEBgJLCFBAECBAgQIECAwKYK7Dl69ePzeOWMe7JT+l1/xr66ESDQ\nElAgtTBMEiBAgAABAgQ2QWD30Wu+Mo8Xzfj6v5x+952xr24ECLQEFEgtDJMECBAgQIAAgU0U\nOCqvfdaMr3+39FMgzYinG4G2gO8gtTVMEyBAgAABAgQIECAwaAEF0qAPv8ETIECAAAECBAgQ\nINAWUCC1NUwTIECAAAECBAgQIDBoAd9BGvThN3gCBAgQIECAwDUE6pfn17vGnOmfXDp9Fz0I\nzI+AAml+joU9IUCAAAECBAhspsABefEHJt/ruBOHpf+LOm5DdwKbJqBA2jR6L0yAAAECBAgQ\nmCuBOnN0QfKQDnt1ZPru1qG/rgQ2XUCBtOmHwA4QIECAAAECBOZG4LLsyac77M25HfrqSmAu\nBNykYS4Og50gQIAAAQIECBAgQGAeBBRI83AU7AMBAgQIECBAgAABAnMhoECai8NgJwgQIECA\nAAECBAgQmAcBBdI8HAX7QIAAAQIECBAgQIDAXAgokObiMNgJAgQIECBAgAABAgTmQUCBNA9H\nwT4QIECAAAECBAgQIDAXAgqkuTgMdoIAAQIECBAgQIAAgXkQUCDNw1GwDwQIECBAgAABAgQI\nzIWAAmkuDoOdIECAAAECBAgQIEBgHgQUSPNwFOwDAQIECBAgQIAAAQJzIbBlLvbCThAg0EVg\n/3S+a5cNpO8VyduTCzpuR3cCBAgQIECAwEILKJAW+vDZeQJXCfxJ/ntAck4Hj1um7w+Tozps\nQ1cCBAgQIECAwMILKJAW/hAaAIGtto7Ba5LndbA4NX1rOxoBAgQIECBAYNACvoM06MNv8AQI\nECBAgAABAgQItAUUSG0N0wQIECBAgAABAgQIDFpAgTTow2/wBAgQIECAAAECBAi0BRRIbQ3T\nBAgQIECAAAECBAgMWkCBNOjDb/AECBAgQIAAAQIECLQFFEhtDdMECBAgQIAAAQIECAxaQIE0\n6MNv8AQIECBAgAABAgQItAUUSG0N0wQIECBAgAABAgQIDFpAgTTow2/wBAgQIECAAAECBAi0\nBRRIbQ3TBAgQIECAAAECBAgMWkCBNOjDb/AECBAgQIAAAQIECLQFFEhtDdMECBAgQIAAAQIE\nCAxaQIE06MNv8AQIECBAgAABAgQItAUUSG0N0wQIECBAgAABAgQIDFpAgTTow2/wBAgQIECA\nAAECBAi0BRRIbQ3TBAgQIECAAAECBAgMWkCBNOjDb/AECBAgQIAAAQIECLQFFEhtDdMECBAg\nQIAAAQIECAxaYMugR2/wBAgQIECAAAECaylwx2zsZ5LHddjoFen7a8l/dNiGrgRmFlAgzUyn\nIwECBAgQIECAwBKBnfL8rORZS+ZP8/QvsvItp+lgXQJrKaBAWktN2yJAgAABAgQIEDg/BP/U\ngeGFHfrqSqCzgO8gdSa0AQIECBAgQIAAAQIE+iKgQOrLkTQOAgQIECBAgAABAgQ6CyiQOhPa\nAAECBAgQIECAAAECfRHwHaS+HEnjIECAAAECBAj0Q2DrDKNu9rBHh+Fclr7ndeiv64AFFEgD\nPviGToAAAQIECBCYQ4G9s09HjtJl9+6Rzp/psgF9hymgQBrmcTdqAgQIECBAgMC8CmyTHau/\ngfQHHXbwi+l7/Q79dR2wgAJpwAff0AkQIECAAAECcypwYfbry3O6b3ar5wJu0tDzA2x4BAgQ\nIECAAAECBAhMLqBAmtzKmgQIECBAgAABAgQI9FxAgdTzA2x4BAgQIECAAAECBAhMLuA7SJNb\nWZPAUoHrZcY9k7od6axt53Ss/w/PnXUD6bdrsl2H/roSIECAAAECBAiMBBRI3goEZhf45XT9\nm+SK2TdxVXFVBVaXbdSZ4Es77IOuBAgQIECAAAECIwEFkrcCgdkFrpuudYedO86+ia0+n743\nTG7eYRtnp6/LZTsA6kqAAAECBAgQaAT8UNVIeCRAgAABAgQIECBAYPACCqTBvwUAECBAgAAB\nAgQIECDQCCiQGgmPBAgQIECAAAECBAgMXkCBNPi3AAACBAgQIECAAAECBBoBN2loJDwOTWCH\nDPjJSd1oYdZ2n3TccdbOc9Zv++zPQ5LdZ9yvbUf9fKbMCKgbAQIECBAgMB8CfpiZj+NgLzZe\n4IC85KuT/+nw0nunbxUWfWg3yCAeluw342C2GfW7dR4/NeM2dCNAgAABAgQIbLqAAmnTD4Ed\n2CSB+ttDVyZ36fD6b0nfR3foP29d/zk79Fsz7tQe6Xdm0uWP5s740roRIECAAAECBNZOwHeQ\n1s7SlggQIECAAAECBAgQWHABBdKCH0C7T4AAAQIECBAgQIDA2gkokNbO0pYIECBAgAABAgQI\nEFhwAQXSgh9Au0+AAAECBAgQIECAwNoJuEnD2lnaEgECBAgQIECAwPwI/H525Zdm3J26O+td\nk88mdVOnWdtJ6XjErJ312xwBBdLmuHtVAgQIECBAgACB9RW4cTZ//owvcZP0qzvdnpGcN+M2\nbp5+j00USDMCblY3BdJmyXtdAgQIECBAgACB9RQ4Kht/2YwvUH88/QHJc5NZ/2biI9P3zYm2\nYAK+g7RgB8zuEiBAgAABAgQIECCwfgIKpPWztWUCBAgQIECAAAECBBZMQIG0YAfM7hIgQIAA\nAQIECBAgsH4CCqT1s7VlAgQIECBAgAABAgQWTMBNGhbsgHXc3aem/1M6bqNudfnC5D0dt6M7\nAQIECBAgQIDAeIGHZvFh41eZaOnfZq3XTbSmlbZSIA3rTXDvDLeO+T93GPbT07f+LoACqQOi\nrgQIECBAgACBCQTqVuM3TV49wborrVK3Gr9PokBaSWjJfAXSEpABPP1ixnhkh3E+ukNfXQkQ\nIECAAAECBKYTqL/F1OVnt9tP93LWHmKBtGsO+y7JdsnFSf0BsUsSjQABAgQIECBAgACBgQsM\n5SYNdUnY65Mzk3OTE5OvJqclVSR9K3ltskeiESBAgAABAgQIECAwUIEhnEF6QY5t8+W2UzL9\nyaSKpCqM6kzSbsleSd3A4NDkGcnRiUaAAAECBAgQIECAwMAE+l4g1ZfSqjg6NnleclyyXNs6\nMw9KXpoclZyUfCLRCBAgQIAAAQIECBAYkEAVBn1uVezcM7lD8oMJBlrfTzo5qTNIT5tg/ZVW\n2ScLPptsu9IKS+bXpY71naha/7Ily9byaV1m+KTkhx02er30/VHSZT9rrLUPdcvwWdv26fj9\nWTunX5nXNr7XYRt1vLZJLu2wjdqH+v+wyzbqmFyRTPIez2rLttrG5UmX98YO6V/7UNuZpZVl\nvTc2+5jUPtT7o+sxqfd3l/foWh2TOqaz/v/a/H9SFrP+/3rd9K10Oa5rcUzq/7VqXY9J1//X\n6v+T+gytzNLq86LeGzWO2pdZWv1ytD6/uhwTn3/XlPf59xOPen/6/Lvao/5fq8+/Lv+erMU2\n6jP0TcmvJ9oEAoXe57ZfBvfJZNIfHM/LuscnN0u6tJPS+ReT+p9iklb/4N0wmfWHmEleo9Z5\nQfL2SVdeYb2yKacu/7DeKv1PTbqM9zbp/41k1lY/+NV+1PfPZm31A1cdt9Nm3UD61WWe9YPG\nWR22ceP0rRuNXNRhG3un7xnJrD+01UvfOvlmTXRoXbdR/8/dNDm5wz5cP313TL7TYRv1fcYq\nTC7osI2bp+/ZSZcf6PdN/xOTWX+QTtfOx7UK372S2o9ZW/3weYOk3qOztrqcutq5Vz/M9N96\nb9WNfbp+/p2Sbcz6i4TacZ9/pXB18/nXSFz9M4fPv594zMPnX/2cfYuk6+df/QL/9J8Mbaap\nz8/US6deCrwno/pKUj80TdLqDXhh8ueTrGwdAgQIECBAgAABAgQILJLA/8rOXpkckxw4Zsfr\nDM5ByX8ldVbjPolGgAABAgQIECBAgACBXglU4fPMpC4/qkKpLoX6VPKu5C2jx7oEry7bqOV1\nedHvJhoBAgQIECBAgAABAgR6K7BPRlYFUV2/WYVQO1U8fSN5SVLXiWoECBAgQIAAAQIECAxU\noM6wDK3tnAHXF+PrC/ZnJl2+RJ3uGgECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIDClwNZTrm/1xRfYdvGHYAQE\nCBAgQIDAMgKXZd4Vy8w3iwCBKQQUSFNg9WDVT2UMB/ZgHIZAgAABAgQIXFvgksza6dqzzSFA\nYBqBLdOsbN2FFzghIzgnOXzhR2IAfRS4XQb1huQByff7OEBjWniB12UEH07+YeFHYgB9FHho\nBvXUPg7MmAhstIACaaPFN/f1fpiXPyv55ObuhlcnsKzAj0ZzP53H+i2oRmDeBC7ODp2S+Ayd\ntyNjf0pg3+RyFAQIdBe4TvdN2AIBAgQIECBAgAABAgT6IaBA6sdxNAoCBAgQIECAAAECBNZA\nQIG0Bog2QYAAAQIECBAgQIBAPwQUSP04jkZBgAABAgQIECBAgMAaCCiQ1gDRJggQIECAAAEC\nBAgQ6IeAAqkfx9EoCBAgQIAAAQIECBBYAwEF0hog2gQBAgQIECBAgAABAv0QUCD14zgaBQEC\nBAgQIECAAAECayCgQFoDRJsgQIAAAQIECBAgQKAfAlv6MQyjmFDghxOuZzUCmyFQ788rEn8J\nfjP0veYkAvUe9Tk6iZR1NkPgR96fm8HuNQkQWHSB3TKAikZgXgX2ndcds18EInDT5HokCMyp\nQP3Se+853Te7RYAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIElhPYermZ5i2UwM7Z211X2ONLMv/sFZYtnX3zzLhrUn3+a/SYB41A\nZ4G9soWVPmtOz7LLVnmFtXqPr/IyFg9Y4LoZ+52TfZITk88lVyTTNJ+h02hZd1qBG6fD3ZL6\nvKz355nJpM1n6KRS1iNAoDcCr8lIrlwhR084ysOy3o9a26gP4GdN2NdqBMYJ7JmFK70/a/5t\nx3UeLVuL9/gEL2OVgQo8POM+L2m/Tz+T57eZwsNn6BRYVp1KoIqbtyft9+elef6cKbbiM3QK\nLKsSKIEtGBZe4C4ZwcXJ65cZyWeXmbd01oMz4wXJvyYvTuo3qX+UHJnUh/ArE43ArAL1/qz2\nvuSLV01d8z/1g+lqret7fLXtWz5cgUdk6O9MvpQ8JTkpeWryG0n9ULp/Ur88Gtd8ho7Tsayr\nQH123iP5k+QtSZ1F+oPkj5MTk39MVms+Q1cTspwAgV4JXCejqeLogzOOaof0qw/Y05JtWtvY\ndjT/1CXzW6uYJDCRwLOzVv3m8+CJ1r72Sl3f49feojkEfiLw35m8MLnNT2ZdNfXW/Lfet4dc\n9Wzl//gMXdnGku4CP5dN1Pvwr5ds6g6j+R9aMn+5pz5Dl1MxjwCBXgv8VEZXH55/PuMoHzbq\n/6fL9D9itKw+oDUCswrUbzzruxzXn3EDXd/jM76sbgMQqKK9Pj//3zJjvUXmPTCpS0THNZ+h\n43Qs6yrwwWygzrJvv8yGHpB5dWZpteYzdDUhywksI+ASu2VQFmhWc/lSXUp376ROvddvQz+V\nfC1ZrR0wWuHTy6zYzLt7lr1rmeVmEZhEoN6jX0/qrOQTkvqi8ZeTjyR1Cedqret7fLXtWz5c\ngfq8rPaeqx+22iWPd0rq/VpnzyurNZ+hqwlZ3kWg3qMfSr6f1I1u6szRNkl9hn4gmaT5DJ1E\nyToECPRK4E8ymvoNaP2DXo9NLs/0XySrFcCvGfU5OI9L20GZUdv7m6ULPCcwocAOWa/ei99J\nqnBv3p/1WO/Z5ofLTK7Yur7HV9ywBYMXqM/Iei/eKvm3pN6rzXv0bZnePVmt+QxdTcjyWQV2\nTsd6P74qeXRy1uh5zTsnOTSZpPkMnUTJOgSWCNS1qdriCtRtuavVD6A/m9xi9PiVPD4zWe7S\nkcz+casP4GrL3Qr83KsXbbXj6NEDgWkF9kuH+ozZNXlxUr/9vGNS/2Dvk9QPpbsl41rX9/i4\nbVs2bIGbjYZfxdBeyVOTxyfvTH4hOSap39qPaz5Dx+lY1kWgeX/WLyvfkvxdUu/LukFDtX9J\nHnrV1Pj/+Awd72MpAQI9FKgPzqckS69PrsuYzk/qtPy4AqfufFe/jbpzsrTVD7e1rD6UNQKz\nCOyZTvUD532W6Vx3Saz31+HLLGvP6voeb2/LNIG2wLvzpN6DX06WfoZ+ZLTscXkc13yGjtOx\nrIvAgelc78/KE5ds6IGj+fXL0NWaz9DVhCwnQGBQAv+c0dYH67gvcf7RaJ2Dl5E5ZLTslcss\nM4tAV4E6k1Tvzy7fb5vkPd51P/Xvr8AbMrR6Dz59mSH+1mjZXy6zrD3LZ2hbw/RaCtRZzXp/\nnrnMRq+Ted8eLb/BMssnneUzdFIp6w1OoP4n0/opcNZoWM0lIMuN8ozRzOUuc2rmnb5cR/MI\ndBSY5P252kusxTZWew3L+ytQf96g2nevfrjGf+tvz1Tb4+qHFf/rM3RFGgs6CtR764pkuQKp\n5n9wtP3V3qOj1ZZ98Bm6LIuZBK7+fgCHxRS4fnb7s8knkuUK3duNhjXubnbN6fmDR+u2H5p5\nn27PNE1gCoFnZt16/9Xd65a2Sd6fa/EeX/q6nhNoBJrPv/2bGa3Hm4ym/7s1b7nJZhvN52V7\nnWaez9C2iulJBS7Lit9MfirZYZlO9R6tW4DXOis1n6EryZhPgECvBb6Q0V2Z/OKSUdZ3Puo3\nTO9fMn+5p8dnZp2qb59pqtvdfif5XLLanfCyikZgWYG6y1K9P7+YtL/sXtPHjpbdL4//v707\nVnUaDMMADA4qbt6BiIMgungLIuIm6CTiIII3oLOz4igOzk7CWdwcdBBHhV6C7ro4iYi+rxoI\npaftaYqgfX54SfI3yaEPH/9p0qRZ1rZR48v277XdFTict/4x6bfkww3xg8bzzLR2zw8dS6bG\n0CU4XpokcCdbtw7vz+2l9wj3AOrFXP+iRWPoIhV9BAj81wK9UfN70l+he5RcSO4lX5JPSQfR\noXW+A+1s6Pgz7dn99r9LribXkvdJB99FZ1bTrRFYS6DP63iVtL5eJzeSK8nLpH1Pk3Hby0L7\nu87QDlLjwzamBNYVuJkVezKpP9TQD6MXk2dJ6/BhMm7G0LGG+b8hcCR/pLXZenycXEpuJ70s\ntCcxTyZD268+jaGDkCkBAjslcDnvdvwcpB7YvEn6bI9x22/w7DrXk89JB+Gm87cSjcBUgePZ\nwZOkdTnUVw/o7ybzbS8dXWd8gNR11q3xrqsROKhA6+tDMtRn7/14kIy/9czirxNOXWfWhblm\nDJ0Dsbg1gV4m14P2r0nr71vyNpk/gbnsf7wxNGAaAQK7KdDrkTtgHtvw7ffDwKnkTNKzVhqB\nbQoczc7OJicm7HRqjU/40zbdAYE+HuH0hPdpDJ2AZ9OVAr0ktAdBPWDatBlDN5WzHQECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECvwXOZfIjmQEhQIAAAQKrBA6tWsHrBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAIF/XOAnwKNGUaHfUksAAAAASUVORK5CYII=", | |
| "text/plain": [ | |
| "Plot with title “Histogram of .”" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "Xn4 <- generate_Xn(64, runif, min=2, max=10)\n", | |
| "my_sum <- reduce(Xn4, expr_plus)\n", | |
| "my_mean <- expr(!!my_sum/length(Xn4))\n", | |
| "\n", | |
| "my_mean_lst <- c()\n", | |
| "my_mean_lst <- imap(1:1e3, ~c(my_mean_lst, my_mean %>% realize_X()))\n", | |
| "\n", | |
| "my_mean_lst %>% unlist() %>% hist(., 40)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "正規分布で近似できそうな分布になった(参考：中心極限定理)。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "ところで、ただ単に実現値が欲しいだけならば上の例のような関数たちは実は必要ない。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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TMdCBAgMEsCK/mH/iw5OVYCBAj0XeB/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\nrkJggg==", | |
| "text/plain": [ | |
| "Plot with title “Histogram of .”" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "my_mean <- map(1:1e3, ~mean(runif(64)))\n", | |
| "my_mean %>% unlist() %>% hist(., 40)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "こちらのほうが計算も速い。" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### さいごに\n", | |
| "\n", | |
| "今回はわざと実現を遅延させて確率変数を関数の expression として表現し、確率変数の関数、f(確率変数)も確率変数になり分布することを確認した。データを何らかの未知の分布の実現値であると考え、その未知の分布に対してより適切なモデル分布を構成することを目指すのが統計モデリングであろう。データを確率変数列としてモデル化すると、その関数値はすべて確率変数になる。上で挙げた標本平均のみならず、尤度関数、事後分布、予測分布、AIC、WAICなどデータに依存する統計量はすべて確率変数であることを忘れないようにしたい。" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "jupytext": { | |
| "cell_metadata_filter": "-all", | |
| "main_language": "R", | |
| "notebook_metadata_filter": "-all" | |
| }, | |
| "kernelspec": { | |
| "display_name": "R", | |
| "language": "R", | |
| "name": "ir" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": "r", | |
| "file_extension": ".r", | |
| "mimetype": "text/x-r-source", | |
| "name": "R", | |
| "pygments_lexer": "r", | |
| "version": "3.6.1" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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