{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "* スクリプトはここ([Chap08.r](https://raw.githubusercontent.com/whatalnk/stat-model-intro/master/Chap08.r))にあります\n", "* Jupyter notebook のファイルはここ([Chap08.ipynb](https://raw.githubusercontent.com/whatalnk/stat-model-intro/master/Chap08.ipynb) )にあります" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "'Thu Nov 24 17:00:45 2016'" ], "text/latex": [ "'Thu Nov 24 17:00:45 2016'" ], "text/markdown": [ "'Thu Nov 24 17:00:45 2016'" ], "text/plain": [ "[1] \"Thu Nov 24 17:00:45 2016\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "date()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 8章 マルコフ連鎖モンテカルロ(MCMC)法とベイズ統計モデル\n", "\n", "* マルコフ連鎖: 現在の状態が一つ前の状態で決まる\n", "* モンテカルロ: 確率的シミュレーション\n", "\n", "## 8.1 例題: 種子の生存確率(個体差なし)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Loading required package: pipeR\n", "Loading required package: dplyr\n", "\n", "Attaching package: 'dplyr'\n", "\n", "The following objects are masked from 'package:stats':\n", "\n", " filter, lag\n", "\n", "The following objects are masked from 'package:base':\n", "\n", " intersect, setdiff, setequal, union\n", "\n", "Loading required package: tidyr\n", "Loading required package: ggplot2\n", "Loading required package: readr\n" ] }, { "data": { "text/html": [ "
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pipeR
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TRUE
\n", "\t
dplyr
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TRUE
\n", "\t
tidyr
\n", "\t\t
TRUE
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ggplot2
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\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[pipeR] TRUE\n", "\\item[dplyr] TRUE\n", "\\item[tidyr] TRUE\n", "\\item[ggplot2] TRUE\n", "\\item[readr] TRUE\n", "\\end{description*}\n" ], "text/markdown": [ "pipeR\n", ": TRUEdplyr\n", ": TRUEtidyr\n", ": TRUEggplot2\n", ": TRUEreadr\n", ": TRUE\n", "\n" ], "text/plain": [ " pipeR dplyr tidyr ggplot2 readr \n", " TRUE TRUE TRUE TRUE TRUE " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sapply(c(\"pipeR\", \"dplyr\", \"tidyr\", \"ggplot2\", \"readr\"), require, character.only = TRUE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "例題データ: 植物個体の8個の種子の生死を20個体について調べた" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " num [1:20] 4 3 4 5 5 2 3 1 4 0 ...\n" ] } ], "source": [ "load(\"data/chap08/data.RData\")\n", "# or\n", "# data <- c(4,3,4,5,5,2,3,1,4,0,1,5,5,6,5,4,4,5,3,4)\n", "str(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "頻度分布は," ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "data\n", "0 1 2 3 4 5 6 \n", "1 2 1 3 6 6 1 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "table(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "合計生存種子数" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "73" ], "text/latex": [ "73" ], "text/markdown": [ "73" ], "text/plain": [ "[1] 73" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sum(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "図示すると," ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width = 4, repr.plot.height = 4)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(data_frame(x = c(0, 8)), aes(x)) + \n", " geom_histogram(data = data_frame(y = data), mapping = aes(x = y), binwidth = 1, colour = \"white\") + \n", " xlab(expression(\"y\"[i]))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "生存種子数 $y_i$ が二項分布に従うと仮定する.\n", "\n", "生存確率 $q$ で個体 $i$ の8個中で生存数が $y_i$ である確率は\n", "\n", "$$ p(y_i | q) = \\binom{8}{y_i} q^{y_i}(1 - q)^{8 - y_i} $$\n", "\n", "となり,尤度は\n", "\n", "$$ L(q) = p(\\boldsymbol{Y} | q) = \\prod\\limits_i p(y_i | q) $$\n", "\n", "であり,対数尤度は\n", "\n", "$$ \\log L(q) = \\sum\\limits_i \\{ y_i \\log q + (8 - y_i) \\log(1 - q) \\} + \\mathrm{C} $$\n", "\n", "となる($\\mathrm{C}$は$q$によらない定数)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "対数尤度を求める関数 `logL(q, y)`" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "logL <- function(q, y){\n", " sum(y * log(q) + (8 - y) * log(1 - q) + log(choose(8, y)))\n", "}" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "-37.7523669906762" ], "text/latex": [ "-37.7523669906762" ], "text/markdown": [ "-37.7523669906762" ], "text/plain": [ "[1] -37.75237" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "logL(0.46, data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "対数尤度関数は,次のような形になる" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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Gaz2ZrJ6YxLHHq9PioqqsFML7IZcGJiYkFBQUFBQU5OTmpqKqMAfcrq1asvXLgA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\nWMfSUixH0OHh4WTI7PgSABxD4wYcFQ8AePrppysrK8ljhUJRXl7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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_frame(q = seq(0.2, 0.7, 0.01)) %>>% \n", " mutate(logL = sapply(q, function(x){logL(x, data)})) %>>% \n", " ggplot(aes(x = q, y = logL)) + \n", " geom_line() + \n", " geom_vline(xintercept = 0.46, linetype = \"dotted\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$q$ で微分して`logL` の傾きが0になる点 $\\hat{q}$ を求めると," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\hat{q} = \\frac{\\text{合計生存種子数}}{\\text{合計調査種子数}} = \\frac{\\sum \\boldsymbol{Y}}{8 \\times 20}$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "0.45625" ], "text/latex": [ "0.45625" ], "text/markdown": [ "0.45625" ], "text/plain": [ "[1] 0.45625" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sum(data) / (8 * 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "となる(尤度関数の図の点線)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これを最初のヒストグラムに重ねると," ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(data_frame(x = c(0, 8)), aes(x)) + \n", " geom_histogram(data = data_frame(y = data), mapping = aes(x = y), binwidth = 1, colour = \"white\") + \n", " stat_function(geom=\"point\", n=9, fun = function(x, size, prob){20 * dbinom(x, size, prob)}, \n", " args = list(size = 8, prob = 0.45), shape = 21, fill = \"white\", size = 2) + \n", " xlab(expression(\"y\"[i]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "このように,最尤推定法では尤度最大となるパラメータを求める" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.2 ふらふら試行錯誤による最尤推定" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "微分できない -> シミュレーションで近似解を求める\n", "\n", "`q` を離散化して(0.01 -- 0.99まで,0.01きざみ),\n", "\n", "1. 確率 1/2 で `q` を増やすか減らすかを決定し, `nq` とする\n", "1. `nq` の対数尤度 `logL(nq)` が `logL(q)` より高いなら,`q` を`nq`に更新する" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "library(\"R6\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "MCMC <- R6Class(\"MCMC\",\n", " public = list(\n", " data = NULL, \n", " vq = seq(0.01, 0.99, 0.01), \n", " initialize = function(data = NA) {\n", " self$data <- data\n", " }\n", " ), \n", " private = list(\n", " logL = function(q){\n", " sum(self$data * log(q) + (8 - self$data) * log(1 - q) + log(choose(8, self$data)))\n", " } \n", " )\n", " \n", ")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "MCMC.walk <- R6Class(\"MCMC.walk\",\n", " inherit = MCMC, \n", " public = list(\n", " doMCMC = function(start, nstep){\n", " qs <- numeric(nstep)\n", " qs[1] <- start\n", " pL <- super$logL(start)\n", " for(i in c(2:nstep)){\n", " q_L <- private$generate_step(qs[i - 1], pL)\n", " qs[i] <- q_L$q\n", " pL <- q_L$L\n", " }\n", " return(qs)\n", " }\n", " ), \n", " private = list(\n", " generate_step = function(q, L){\n", " nq <- dplyr::if_else(sample(c(TRUE, FALSE), size = 1, prob = c(0.5, 0.5)), q - 0.01, q + 0.01)\n", " nL <- super$logL(nq)\n", " if (nL > L){\n", " return(list(q = nq, L = nL))\n", " } else {\n", " return(list(q = q, L = L))\n", " }\n", " }\n", " )\n", " \n", ")" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "\n", " Inherits from: \n", " Public:\n", " clone: function (deep = FALSE) \n", " data: 4 3 4 5 5 2 3 1 4 0 1 5 5 6 5 4 4 5 3 4\n", " doMCMC: function (start, nstep) \n", " initialize: function (data = NA) \n", " vq: 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0. ...\n", " Private:\n", " generate_step: function (q, L) \n", " logL: function (q) " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mcmc.walk <- MCMC.walk$new(data)\n", "mcmc.walk" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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    \n", "\t
  1. 0.01
  2. \n", "\t
  3. 0.02
  4. \n", "\t
  5. 0.03
  6. \n", "\t
  7. 0.04
  8. \n", "\t
  9. 0.05
  10. \n", "\t
  11. 0.06
  12. \n", "
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"collapsed": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AOAF/SgoX/PP/88EV1xxRXTpk3jXQtAggo2oFm/uLS0VPWTn59PRC0tLf5PRrBY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\n2zZVVY1G4+LFi3nXAgAJCgHdD5fLxU5/nj9/fkpKCu9yACBBIaD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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_frame(nstep = c(1:100), q03 = mcmc.walk$doMCMC(0.3, 100), q06 = mcmc.walk$doMCMC(0.6, 100)) %>>% \n", " gather(start, q, -nstep) %>>% \n", " ggplot(aes(x = nstep, y = q, group = start, linetype = start)) + \n", " geom_line() + \n", " ylim(c(0.25, 0.65)) + \n", " theme(\n", " legend.position = c(.9, .85)\n", " ) + \n", " scale_linetype(labels = c(\"0.30\", \"0.60\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.3 メトロポリス法" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`q` を離散化して(0.01 -- 0.99まで,0.01きざみ),\n", "\n", "1. 確率 1/2 で `q` を増やすか減らすかを決定し, `nq` とする\n", "1. `nq` の尤度 `L(nq)` が `L(q)` より高いなら,`q` を`nq`に更新する\n", "1. `nq` の尤度 `L(nq)` が `L(q)` より低いなら,確率 `r = L(nq) / L(q)` で `q` を `nq` に更新する" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "MCMC.metropolis <- R6Class(\"MCMC.metropolis\",\n", " inherit = MCMC, \n", " public = list(\n", " doMCMC = function(start, nstep){\n", " qs <- numeric(nstep)\n", " qs[1] <- start\n", " pL <- super$logL(start)\n", " for(i in c(2:nstep)){\n", " q_L <- private$generate_step(qs[i - 1], pL)\n", " qs[i] <- q_L$q\n", " pL <- q_L$L\n", " }\n", " return(qs)\n", " } \n", " ), \n", " private = list(\n", " generate_step = function(q, L){\n", " nq <- dplyr::if_else(sample(c(TRUE, FALSE), size = 1, prob = c(0.5, 0.5)), q - 0.01, q + 0.01)\n", " nL <- super$logL(nq)\n", " if (nL > L){\n", " return(list(q = nq, L = nL))\n", " } else {\n", " r <- exp(nL - L)\n", " if(sample(c(0, 1), size = 1, prob = c(r, 1 - r)) == 0){\n", " return(list(q = nq, L = nL))\n", "\n", " } else {\n", " return(list(q = q, L = L)) \n", " }\n", " }\n", " } \n", " ) \n", ")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "\n", " Inherits from: \n", " Public:\n", " clone: function (deep = FALSE) \n", " data: 4 3 4 5 5 2 3 1 4 0 1 5 5 6 5 4 4 5 3 4\n", " doMCMC: function (start, nstep) \n", " initialize: function (data = NA) \n", " vq: 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0. ...\n", " Private:\n", " generate_step: function (q, L) \n", " logL: function (q) " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mcmc.metropolis <- MCMC.metropolis$new(data)\n", "mcmc.metropolis" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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"code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width = 10, repr.plot.height = 3)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8KT9sJbHryd8YimZcC2JdCGczkpw65PjgHLMWZHHed62nsPocFgiIqKyszMbL7w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\n27dvQEAAhse03z333LNw4cJ58+YdP348JSXl5ZdfdvYZd+zYkZu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KRCtXruzQLBSzZ88uLi5WKBRr167t2rWrHVcDAAAAAODqlFIHAJ3B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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d.met1 <- data_frame(\n", " nstep = c(1:100), \n", " q = mcmc.metropolis$doMCMC(0.3, 100)\n", ")\n", "gp1 <- ggplot(data = d.met1, aes(x = nstep, y = q)) + geom_line() + ylim(c(0.25, 0.65))\n", "gp2 <- ggplot(data = d.met1, aes(x = q)) + geom_histogram(binwidth = 0.01) + xlim(c(0.25, 0.65))\n", "grid.arrange(gp1, gp2, ncol = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "メトロポリス法 1000 step" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IlH0CEYjUaDwUDxyOaRt9vtfr9fdqoffPDB3NxcSZJ+85vftLS03H777fPnz+fv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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d.met2 <- data_frame(\n", " nstep = c(1:1000), \n", " q = mcmc.metropolis$doMCMC(0.3, 1000)\n", ")\n", "gp1 <- ggplot(data = d.met2, aes(x = nstep, y = q)) + geom_line() + ylim(c(0.25, 0.65))\n", "gp2 <- ggplot(data = d.met2, aes(x = q)) + geom_histogram(binwidth = 0.01) + xlim(c(0.25, 0.65))\n", "grid.arrange(gp1, gp2, ncol = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "メトロポリス法 100000 step (100 step ごと)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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IYtCKPrIYyiIDS9L6ZlWFC02vNm2i3Z15MwFu2Ql9/0+XyNjY3CPZLnTCY8ZDQQ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\n3LKzs9va2phq5W/iiy++2NjYOHXqVHZSVoZaJXQqu93Oqt21axf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SyoSBqU7jz2J6UZRYCEJ5yRyrbs9bK5fXJ3JRHUVsNtuKFSvk/RMn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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d.met3 <- data_frame(\n", " nstep = c(1:100000), \n", " q = mcmc.metropolis$doMCMC(0.3, 100000)\n", ")\n", "gp1 <- ggplot(data = slice(d.met3, seq(1, 100000, 100)), aes(x = nstep, y = q)) + geom_line() + ylim(c(0.25, 0.65))\n", "gp2 <- ggplot(data = d.met3, aes(x = q)) + geom_histogram(binwidth = 0.01) + xlim(c(0.25, 0.65))\n", "grid.arrange(gp1, gp2, ncol = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "十分長いステップ数をとったときの$q$ のヒストグラムを考えると,求めたい$q$ はただ一つ決まるのではなく,確率分布として求められる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.3.2 マルコフ連鎖の定常分布" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ある変数 $q$ のマルコフ連鎖が一定の条件を満たしているとき,そのマルコフ連鎖から発生する$q$の値はある確率分布(定常分布)に従う\n", "\n", "初期値に関わらず,十分長いstep数をとれば,$q$は定常分布に従う" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "d.met4 <- data_frame(\n", " nstep = c(1:500), \n", " q1 = mcmc.metropolis$doMCMC(0.1, 500), \n", " q3 = mcmc.metropolis$doMCMC(0.3, 500), \n", " q4 = mcmc.metropolis$doMCMC(0.4, 500), \n", " q45 = mcmc.metropolis$doMCMC(0.45, 500), \n", " q5 = mcmc.metropolis$doMCMC(0.5, 500), \n", " q6 = mcmc.metropolis$doMCMC(0.6, 500), \n", " q7 = mcmc.metropolis$doMCMC(0.7, 500) \n", ")" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width = 8, repr.plot.height = 4)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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qmFvlVrP1ll7amwWDiaHL/FXXHwrsQxsdwZOzrvNrmjHEuFnakeiQOTHQADkGQV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\nrrhx4HYAJmfwlgCL8pOG0bxkfulwRtirtD3lcRs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jawXUi+JE8ER+Z3Gtlr/N6/hl3vGkwpgkADVJR8EAACAASURBVDyaH4DVIPo+0ukD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\n8/MvR88+kNVP592DAvvrmz4jsAHX83nZ8ybv1G1FnKxLn/Wkvj12UCjWC00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53xRcvJNd9Yu0WHi8Mui4NVXwWILK9lo2dviQZ/kUfkOq\nBZgLxHdJ/R6rQdgNQITDQD3lt/WCR8q6vSqBPgxotiec2wFEPT9a9qvazIqU80xRK7+DwQbT\n7XgRKFi3Dab6gdYSpexoS01JXF18XfmgxSw483POJLAt26Mr5QyQNYFeBUUOv1lzYSq33J6j\nev9WSUnF9XxGlSVlVYSaSjpWmJPArMNKGCYwNp6U0v6AghXmWO1HDgY7tOlJxSytCewGBGJ4\n4unaE+xQnarW9EyrXr7LfbkY0Gp4OhzeqnrDa0iDVqNzylJtIrujS7jcVqQBWKaJsSJqpfo+\nV/PSHGjqEYEgFfqozWiAHS4rB6Vt82xhnsrgIKWdJQ4FFgsHr9QBBCxhyqcMzOWHjoQvyOOY\nUp46TcHxmpdrInu2aC8pZ1zju2oEOp5dLN+c8yxumFbJtHyXlyEbOC+UMl2WOSq1ynrXQqCr\n+iflz1bi8VWo3Wte9SL/ySGEMH98EP/pfWVeJ9DXhGOpuZKwuZ4KwisxlD4qi81X+3eteEKv\nHypicPIPjRetsSKsVJlXi7OFhaxtAhGrXOLdXUitVqLACatV1X2ANCCoQtjFGxaOgox5uICd\nV2xAtRveFsNNpRjcHekF8on+Zadt9uKssIsr71N+9nxLDtBGTEAfKVHJIcvGjgCtJYAJO1E1\nSpDIx5f/rVfGMgLtL2k3xVfWBbCd3VTU2dS47fPc6kvdBMw1Tc+oO4Fua0lzrS+eNBQb+XQU\nzA4NWDECvbYS5izYTiCvcbJ+qhf33vnFiepQpFLFoipHw+Xjow5p10BP1pAia8uQ0DtLje1C\n16u1+bKTSFvgah+4RjyTPo8MUtsjseKYdHEby7wsFRJWJtD2yBp1w0DdYsJfVd7uRmfQo6jA\nCfc64HBDEtgzF9zlrgfsughuDzVFS3vHo/Lrnwg47ZEhJZVUFuYBu71TWiv3V/T75EFQyXea\nl/LzLwu7UEugC0o7kFfFqNsELniXhI6qYoJAYz4QLC1Jvhq4gkD352Iv5xNFYQN19mDcXY6B\nhUOZXVfRl5gxGpVCQYtFfWFTdwgq8sblC/7HCLRASBohRXukeNwNLm4M3ATUiX4gzq6MZZ1e\nKneIGt3mDu+qvNGGbW1pX6L5YLV1AoYttlua/OJWIVrKjJxzd9eepsC6VAugRLLl8cEOI3Qg\nIvqBOir75j4TSFe8UVZEvDAhlZjD+V5FGCyNMSdLs7Hi2GCNVoZAxD1lbfVgfcYQPwByuS6z\nBCClFxsS5ddKEyjRJsATsAynfSwXlwuk0Hxdp6+87d7t3Ql0+7ZLeWApdlZFMa/KukaJ+Vlj\nWUBddwhf2JzKDYRFeXdixD0BizLkEh3qEl5+ONiBZanTUxFHR9Bo4goRPau9Y06pSaIQkZO5\neFHYUoVJvt1BzbHOGaBGmunasSz8LHx+OxiCsmrhtUSg+2t614EavntYD8sNMX1yTCmaSiYI\nWO1lUnE8F5MeQLuWEmjh8/dZi7R1xXdkMneulhAPcBawcC9w44p3tSwhp87ZHnKsbA5ajOUy\nNa0dq4ojKeVjwyG8oRUG0nT6cM5zSR7Liaa2YV+9GW1brSTSAOr4qDoztUSHW1GUVT/1BNqy\nrNyPD9b1KJz8X8HrBPqa8FJyCvCq+kbXyrv21wI5bgaMxgbnqhVPkOHbszmGC/z9RBvFHVV5\nZlWN3Tn45Nfnh7+THL1z8Mln0kv0O2XEwqFo3VoeCFj4LXZ5CkBfRnXX7bBRf3N+28+cip15\n7m3pyUeBwvzJTZkLUM7fUFaKQFOJuB/OzB3IzL3PteuxwJ5i6lIxPTj+0s9OH/uYTBdxKGzz\nAjhUtnuxzfTYS+/+7IkH7hp8oj8bk8GtTKcCqGlbHzbVmEUlAVrGmzupBwqquDj9tYeMc9+r\nQ3W3Uo5AX8ca1A5rIqQBIqCJmt38nK8ACJDbdgVNS5Xqcynt2FAdgCB+9Bd9qf1A0riYVG4A\nthbKcVbD3QZks598YDgYKalKn//Yk4FCmxO4ZSaiC6VZUYG1maY/O/POO2Y3rUs3Awkjsyrp\nBfrrKKjm3oXC3oXyCNueXzgR0rKaApwMaRldaXMAHMqLgl/KgWnrsioQN2QuADFHGrAVPR7Z\nRKU2f5XD16i7qESgq7sQQMHK/O35937h0kdjxbG/PPvWh0f/cCx76lNn7n56+u/PLjz7ydN3\n9se+fSQbByLWpC4KwJ+8fOsPJj8r439OzdukhADd3SrtdRwlH2CLUoe3Y8Y3Ou+KAjhzzpce\nMadPTTy8K/XER28oLtb1nKmLATtigTcVG32fX3B/Pysl0vTJCUBN5Xad2f7ws5sNWzlQ5xYj\nQ4vTT6H1U/8+/8Hh/ECOoQLvuMBfTwHsdBdVbGEX84kTdiAovL6kod63p+uZ+huAy27ThjYH\nFz3lCcnhKQEN2R7D1toMD9CTaZF9QMo5MBL3AAAgAElEQVRrZLXChCvRVqlncNsJ4LH40U8P\nfRrQRDFojefc5Qwiu2Xu/Myvle9QydYevOxtMxVVnRhVFKQ7nSOuAx0uFTiZYbjA/ef5vddk\n+jabvywd5mXwsioTGXF2hB2tEfqAuLI9xm659pIdCUWgxnZ7GrZ4cFACekpTLsciyTu38Pwf\nRT71UuMFNb/+y0/sftNU3eHMXOHiyxtPffVd5+8Dglb5UW7KOvymC/Dlv3QTi7xQweqd3vQ7\nz720e2qTSgnAcU7+6uLTf3z88YmjPwxeyaQHKz587YW7AUtNl7yjQNjRqqCklKa3Dx98KKMD\ndc42YELfdjhYXpF/0jo46ZHba6on/yZN0Tv1NqCphAY5Nfyi+/8ZyawH+j2jD8YG+rLRi75p\nwJx3rnHfLC8i82Jdmr/VvQG4lDzcF3v4k6fvPBV76vGxv/nn/gfkabKAbH5Wn5/RAafHlpvJ\nwXpTURhM91Xj7lHvMUAsNGrCKe8Z2O4trz7l43jZ2zToDt8/GfzEKH7vO55VH/+yYy9QDNa9\nb+O73rnpPUebe9JS9EN2Lau+aNXddqp0LBUCdld0k+R+4Nfmh9489NRoMe1+/Lueh76iFFby\nLxTC9cNH+ZcHRTYD6JPjgPCXHQCkEGT1QE3EyS03nzqSi90x+OT246e3HD+/f+Alqarepi/m\nTLTnF4A5W/tY49cO119SZqaTx2ekS/w/NX1mJn+JSrA8qDnWOwPUEGirtV32ZNk+l/L8v+y9\nd5QlV3ktvk/FWzfHzjnMTE9O3T1BM6OcBUIgY2FAZGEbjPwMNv4R/GzwI9gYywQ9MOEZYzJI\noBxQntTdEzvMdM59u/vmHCqc98epezvMSKDlB8v+rdlLS1NdVbfuuSd+9Z3v2zt6ib06ljxJ\nwfdx3zzBPwRaeXDmyb3z/66phwyIAKqKMQBPTA1Zf/p9ks+jtLaWm4BtMkQWxBOPuIPjcnBc\nPvGIO7IgAkiOmAa7BVEAGQkFgQeQkaSCyAOQhJN/fe7Erf3pEy++Iz7x3XKR8tGetN3cW9Cb\nRFDK/MemDz60RLQ1b++WZx63/vh7JJVSfvkT5eGf8MuLrLHY/UJwzmwXXqCKAoB4/cT2m1hs\nruC/GK4Y0L8V/kfdzuc23vqV2m7h1UXCfiOYdfJq7O4oGdAaxadn0ZvmoLWxwCtCMt9PDJzN\nRf9xeeCflofO5qJfjwyv/iAzoLcr7q2uqwA0FACQ/T4PgJEcCp4jY+KWR7jDL+d9zxbqI8P/\nDCAbOVmjhmu1CCOwa7VcXkKMGWfn8rEHwkP9Ov2u7xaAhgb+Z2b5pcT0DwrJi+y2q11m+S0c\n0sGnMssvfI1UncnFvhweulhIAnC1OJh7VX4xy0xirVGgei4f7wfQ0fB+Zu4+OvOFcZmOWxBt\nvB6AXggX05Ovq5LJZisAslVJO03rJ2QpJJqeBhBT5AWHA8CS3UYNMtxjW0goWUEAULmgS6oC\nYNS2RMEDuDOYAsAJdk/7hzSjLlX4SF1KvnfBXheWw3PSWMoJQNFxbbDuj+OclaZuWNzWmKl8\ny1zXxlQ1gGFHcH9YAHAskBVovmW8vzs5ZzM0AH8z/YLO4eWAAODXFZJbwLsqAOBMBuM2DcCG\nDLchxwE444zMWsMAnqw6V+Q0ABHLhnJzd5c2QzbJThcvYdX27kDi2cHEr3sjv/jJ1CfGUiee\nCX790bkvTqVPPzL3xacW/mU6c/bx+S+PajKA7cl4bdYLIKNFH537h+HUKwCa7Xts/kMA7DW3\nWdzbAFQkdvJUBFAlWACcrzwGgHKTwsC5zPF/THNTy9lf+oorm+8BcgqARedufN4qTKrySznD\n1wyAW5iFYUi9i1yh6Q0zFYeW3CfcCk0mhKF+AIbTJZ0igUXtExeyFPibWbySNDlfr/bZOd6K\nUlSP3tz6WMD+a69FUesBjFjVKhHvrsCIVdU4CkBq7wMgUKElU3Gnq6FJsrenqgAsWmI9nnEA\ng655Suj9/g4AEgqt2ksApgx5SJMBeI1pDnpbpQJA5zLPWP85nf2pjDAAiIMcoQCFeAFAhhfP\n2avYWshCJ5uzIgHub1IAFCk+PYvjKXxjydR2eV1gZgEhXLNtT1jDRB4ozRKbXEeYAa1DGefe\nA8DB470VAMBxMZDiYVulxKHSOA4gIB5d/dhngw9OGSMPN/aS7J66iPUjQw1hvaCeovb0zo/1\ndygaf0fyWYEaBPSdC8sAKGhj5sGKyb/36qaID+GW3zx8z/aI980jb2Nh0C3qTzguBCAavS60\nuCOyIC7PyFgL9nMCclND8XYABefIRtdBALu9d1RYWqbE/RdVeprfrxPphuoP8US8KN7Y5woB\nKHLa88r8dyqbs3wBgFi4q8661eW/GoBAUVPkZoTOKNlkzzcAOKZMfTE0cDwbGrEHARgGWrQ3\nArAK7kabqZrENOrH0z1PzH95OnP2V1P/+NDU37O8RlkxqpoLWOWB9tWozoAKgDF7jKd7ffSk\nQIoAMsrPABBDcuf2dPru8skNAG7wVLN8lfurAUAj3F+13fgKcX17CUfV90ax92X5/WkBz++5\n/qFAx6P+jZ+XWwEQUIijAGC4oW4eK8hacTNWBQ2ydGGVGqeykZ/MDwgD5/ipcX5szULAwEUj\n4vnTmBwz+s8B4OZmAWjtmwx/BQC90dxkYB5oUCqs8owy/Gtk5FyGm9W2BrVNI+kmAAT4aGG8\nfMPHZo+x16PzqHqkoY/o+lh/HkCWJ7+29h4L/RAlzpC9peATarMbgQoAkw2bFooAcF8lgJWs\nxNWYSPfGsGsab5qnV9lSf1WZvqkh8fb62HsAiEhuUX8GYECowdSEMDaMUqTTbu8bKiwtADpc\nRwBMDyjJsDBxzjpxzpoMC9ODCoBEkABQaNJp/SUAi/BSokIBkK6RnX4NgI4nvqN29+btv9I6\nwhe/WPLg0GzkZMJ9DIBh5/QqgQ+HSCEPoLinGwB0nQuu5FRwsah4to+fmbI8+7gwclEYvSgd\nfxkAOK64ay8AbmmRn5oAYFTXaE1tALj2jZc25RX8F8cVFo7fCiLh9tr824TfTifgcigzj75G\ndvAGC9wC4hqeLPvy9FoAlA+/kF4EMK1m2LTVlw1r1Chb88yi6lL8d/s/Wx9f8iefl+yt+912\nzIACg7arB2RzbJ+Xu25J/NzQMiyc9JvZ4x+0fWBWe9UYazZ9F6nxfHoRQFD0hQUXgk+yq7lI\nj+zsAPCnVdiomA/JR3vmpEBMcAB4JmVy4e7w+oxKnVvUxKEiAMPNGx4+Fz7DBFPclTdWRh8I\nIjtKTFnFRavDTThQIx/tkeyvI7XCuNsn7nCmq2fHih92xK6elOp0+8s+fiC14ZlCyzX/oDvU\n1F1viFdwwPKMBCBstTYkk7XpNAAK47kqDoDTiN28UJN0vkX7gw+Ljg2JxEGcA4DdKTOgdiJl\n304IR+lnB1ztrjOdd18TGqgF4NAUR9oCIMsnqvI2AMcqI15jeioy0am1PJM5trDjwPWuDdW+\nois5aeSGdgjWxza+MWkQADkDLwjqZliqCqblMeIaGmtP/rXY9XSuf3esuSNVE1ErPUZycFVk\nIQAOZI/ifS692FNiuSrn05yPPVk6eApAXk+NJI8CmMwHkzY3gEOx4vun3vD8VeTh4nc1WrgQ\nfwFAq72rqvn9ufo3WSuuNdSE8ciXvAl7PLCcpiNCdiKguv9tx2epNHlVzAYgmxuAAoDWqk90\n5+dUotiNEL9hi94PXoX9grkHR0g9AFIs8uFlYTQPOAAcWHY/2BGmhAjjIwD02gapTwXQkjaq\n8saTMQ5As4xP1eMmF7fk3ZMNvcy06PLX3PTy5CvVWYP5R+9qK3ysCXUyWi20oyXh1Mjzxe8r\n/HZRt21IVXcpynu8bf3n3ACm7WM/rTsz7AgOOef9vHyvt61BsvcGv3Q6OwwJBoQlvgOAT5+w\nCq79O2/7QvKmnLCUTJ8noEeMOw7Xf7PGVm2j6ZmT96X5xP9yPqQS6birftfcMEoGtF0njQX+\n/fWWT49kMsbKWO5J442/ge1gPdgrd42yySq4XoiZKzkbZX/Q+NlNrpeOT6JAsYCbAey1474q\nNFvgEASQI3utvnhsZAfuq6X7G7g+4K3smWWdtgzHwXAD2BdycZQIQR8ASef2Rhy3Z08fTk2p\nRKxLfzwNQBh20sVs8ImvCcM/c77l5+7DMl3aHusGsC3i36+/u4pc/9bU95L8VVnjjVnVpAyP\nLwm17Wt+DrNyWh37LOnNGrCxsfH6pi91+u7a4ro2qycjmWoABvgo17jbe0eldffPZkfjtuXv\ntH0hLtGM4DgqbDlgX9qRaKjI7Kl2dFXU/JXiP0CN/AdsdcfiS+2hKmaojdgXk7p6LLMMheii\nxquCM7v3w5t+5JXqBGKO31ZH1wtL317OTxAQAEPRFyioL3sQgLtSdVeogFIWQXRXqO17iomQ\nGKgvAhhPnpQQ+6j7G7LYPhj8qc79K29YfdmDLfbthyrunc9e2Oq+/nEnloo44sTfzyOu4VHv\nBva9p3JNAHTIT1RYB/ytWAaApzISgA49+a7hc3/ZvAPgoFcDAFUU4txa4gK/3Vn3/YZD/xga\nPJuL9qbNNxlhflbbsn1dtynv59DpCbphExePAtBr6wud+/mloNZitorhclObnWTS/PwsY7Ur\noycbhlEKlNJrAbRY8N7h3obkqUXZXqlmbgmPPthy1UXeEUHXtO3HOb5ojSkA+rzCErd7LHVS\np7QvG8EqDzqA7F338EvBo+4NmAIB7vbj64tYVNGTxs1rZBkxnu6JELMjtWj3sANOvgaAl55S\nlSeB9xfhfsEvHZ6fWWr3RwtzAFrtXddUvX8uM7DVfQOlpgRPJmGG5SRCIqWIJZ0AvJaQpHwy\nQB6ThZfJVY8ujDfK+7idXHL8pX86TvspCIABqUtPfrmYnpTsLcX0pF4IR73PRd40IbbtAVci\n5eR5ddsu6diLpFAQ5mf1+sZ1TcBmtvKBXlGlN7XhxV9D14WpcQB6bUOxaz/p2CLvWJH0uoL/\nLrjigf49YSZ9jukdvIYHmiPm6rg+aoELl8+wg4yhlVWpZtXsvJoFsM8asAqultiSbEDxdTXJ\nqBIB4AzZeE7ez24+L++jhpaL9jEDutLbPVcQAOxfo/C9gq0WN9MtLxfgnNJa/quc8GfhcLsH\nFSIAZCMnzymtq0vr5+VW2WFq4zH386r4DU50SM6OZrF19bdMZs/LLGfxdeYRQuFIpyOVPFYU\nw5HKX3gqvucRThmkEPU9k2hMhJ0P/LReGnCu7EWGWRIJBYCMEj9m3w1gb/Y8MagrXq0UfYQT\n8kUzZr28J60RLm6xAKhP+ZVIZHuhRciVX0EIgJaCCMAAjlbO+vWxUecCgI4q9xGfoG7o6PbJ\nW1scVBq7Yen8pnx0hw0KBwAXrSr7vKmc7Jjt8Fh3twk2Ygw7FgDEwpbebJhFFq4mhNlvqwDQ\nU7o0XtorLwu8rTsI8eY7yZ1pvz/vuCN8lcQp5aut9i5e9tpr7uAEmyhVeOe8hPJW524AuUhP\nG92YEVNPtzwEUqSEZuRFABkeKUGt005vU88G9JGLwkXK9HJLLcrFnZTnAfBzMyzZCMBVS+6I\nxF+0i4yM1nC2clnzA1eFzPCV61y4wwOJg+LrBpCL9QKUWizHJI05+ynoNa1GiwUSwe0eNFdo\nvhp1LHMiqAwC2Jiq2WerqDbsYsoFIGjtyfNqj3c8LeT32QIEuNZedcC11W3MCTRfbj6/PtZs\n26PwTqlyMWE5x6rFgbFa+uQdrrp92vn92WduSPV0FM8AOOpq4BJxkkq6KzTGeXetJjoEwsKm\ny1361dgGXgOmPLWju/zxWsmkvlF4Z7fv9t1mpyMAdlpTrAaOOJxH7FUAJmefkhGupY9kjGBZ\nAC+YH2Y6bRsju1jhPAWhM+yojJl5bNcvWerU1Ob89I7cWF47BMDJPc/6Tr02/oHEA5ww3hmV\nJJ0DIBlcY2ynt/hdmeZl4eVyYXBJQmFeT89lBwE001u0Agegslqwi97d3jtk3lbv6I5xpvGR\nk/a6xMolUsOSRxu8z/DCzwBQEDYKmjNtLbZ9nOh0NfyBu+mdvsA1w7plY6oGQFLMLShRVu2U\nUIu/ACCxJG1xXVetrHj4ypMwa1kKyhkWd64TgC2QWpdD5q5UZatR0VggHE2oS6HCFIAjnvo3\nBRooUSPKCQC+7KE2R5dfbtzhuZknwmYF17jAEbAw9DLVcbkzPFlddyIvrj55SFI/PDPtVddk\n+zXwzWUvCQdyk6PmdkcdgBMkz/QWV+ellSGUThqT42TabHetroE6XVr7JvArcd4aC4OeXZNH\naC4o+ppsnxZLTpyfuS0y8t6F07eHhnlqbJFDAMLYZxA65gi1JWQArwSEMNk3nT7bnw+lDBVr\npylWgBNZDkCrBX7BjBtcR1YTLcxHC3NhYtJouJNmSZS0G4Afxz3oY4FDjwf8/NxMOTSo1dHt\nk+p3eG7hiZCOCWpxTRCRWiDJRcSNSgAO37KhL1jFn/NkWQ09ar2e4+2QLEWx+OWzskn0cV7q\nNsCzRcpc6QiwZ4MRMOcxAHpFFZVlJqbIrUrHXEnNLKfBUQpAr2vQAxVUtqw+Qy2K3rEVlssT\nRl3Bf2VcMaB/T2BMYTJvq7etdxisxuU9wdxl+PMZbS1KO2UE6LYF9GKskLwAwOrfV35aT0bq\nl81sqmmhPcF7E1Pf14sRABfs15hurVcJvuIJ2bs2b7JfWUl0KFPOlaGriULywup7AHTbAmSt\ngCozoLPh4wAUbychfJv78OqPjKd7JX8XgFz4BF4/0stHAciOTdaKI+WTc4LqwLgFkRHrygK5\nWmE7YiVD0h4A3akpdoaRE6+jsmIIKQoAW14CkBhZYxwJIt0QkwFccJG4nPPpExddC4Cposeg\n19SB4wDw87MiwW4bAEREIyqZxn1USofkVLc1wIF0J1WW8aYWuHPLWQBeQWZJRQxsoyBtaBcK\nibyenssOvHb9RPgWAE4ab/NuAiDNL5RVu3girJbJ5BaDRNcBKDVXA9CL0SZLG4ApWyjPqVkp\nrHNFAAslrotrfe8AEMxdzDWsyf/gp3WjshoAPzlN0mYiQXfIJVBy3G0GIpPiipTtgYgZ8VAO\nzWcGtF6IFpIjMb0wnE9sTFcDmLdFBXHNK2dBz8xmzo/bZwFsylR7OIn5ogCklGdWKq3Usdsc\n+wgMrzFlFgOG15hsd+7HJWRYjFqr3Ce3F04AOOpuACAszPECnVc0ANtzIoBux5r1+7JsA6+B\nlBY2SXscqwKg184Pq/+sxHrOx7HEsXUlR4ktDsCG8IrH688uNAjUXAuuCXnYno9OKzSjHYAs\nrESA2PR8cyF4YGnFYdgSPTgrqhSQ+TWBItkkX8yvrC8TqV6D6gB8uasAcJwZMs6QF7cYMA27\npLQFpV01ryB3OTr8uhk8wEaBRZcK+ZUuOpxPJvQi4ygcsy+Wu4JMuPpqAIgvC+uy+b1ynU+u\nX33Gk9/LUxlAyn5alA2by+y9koUyUUOG8RJJSJtjX421wyZ4ItZXAATyh2zCZfYXXm1nr9fW\nui55ritgIZR2J9dEU1iMinUfZA7dLKH9TgsALhJex7CB0qwFgEYjRv9ZAIbTRe2X2T41ausB\nrMtmM+VajDWErYq+WOagZKhURgCkSFsBvvM2v69IARzzSRHSrdHCk7HzACTC71LWVwsbCKzr\nstF9LoPCqgYaS58ASATdAKwG8ZcIPVsyAgAfegRkXXQAwAlnAxeLjsZeAVBpaXWKK2WOX27S\nnjnDG4QHIHlWZsjcsjlMConzhp7tl82uleEck+JGtkix/8uOTbxk9nzGSccCu426ejCy7RKF\n86vlFBq19SBErylxLxKil0LSr+C/I64Y0L8nTKyio3qN2y5lsZA5HSR56Z29GTPgle2UNUsO\nLy/lY2eYR8Pi2QuA+cBOZxDizBx8CjIo7UkHHwUAwp0nmwD4BDS/+tvvXmVN/v6AZSVPX8vO\navml1VcLsdOgxup7yk/QGlcMaL1RBDXysdMAFG8ngE2Vd6/+iGrko7ZKAMX0uF6I4nUitXwC\ngOLrtHpN57FgqZoqjgC0jh8fVVayPRKyReXMUbBoaSgQC4CD0dIO6cK8ppJ0/DJNFrEqABRN\nL6AmsbhmHLkC2pZlDsCJQJED9RrTU7ZQ3iGz5HcGKstMw5alcpdJHpYdZtnG7EsA9io+ohb3\nLSfHbEuUUADhJR7AHsW72jrbqXhEU+w3PJk+xSyV10CEawbQxhcZpzIXDrVaTXOq1rqZSbUx\nMAkGKohS07UgHIAaiweAToxx51LGYhJZzEsA4NK5zrr3AKCgM4Gx1d/IB3WjqgGAOBpHyVSy\na/yWmO2ExwKAyhY+utIL90XMFb1MDqN49phM5NHe07koBdpSVQAu2IOz6posqKnMGZ1qg44k\nAEWTsgk+viwAoFJaEF4q31bu2FXKBrvoLTPYOI1FkeaZk5J5f8uYSPXpVMtFzZT/rWofgGXR\nNqW4ufnZ+SKGFBWAPyUA6LSvMaAv5NYw1/5GjCd7mH+0zd5doOjPAKv6ifkTStMFgSZqz6x7\nwigdLB+X6eHKFBAbojvLV++aWjHUtocCircLQEHbx9zJMr/mPXlrbnI1/0xHZHOeQ0KALJwh\nJL/6zvgqegq2K2IXfDReA8Du0Zj0pnlVWwmYnjPcBiijmtmjeNvsnQqNKzQOYMIW0okBYH55\nhVClNxfmKdeaqQTAEgfNH2LxeCs0AJpKMpcM4XU7gb7sfgA6l5nmngZQppF2+tdkhrFq9MkN\nbqmKgDTb9zCqFkFzl0MFVuPVyFtGuV3rOsOeChu12rqTawyvmLp+Z3Cn4pXAATjhZltnlA+u\noUIj2QyXiK/8PdSPtRRyq8GsN6Lr3NJKvfVlIzAcoGs49ePFNV5q6nDK5Dn2hVHsSRrbARhA\nj5dPoEOD9XhmHsBWi9tC1lRLUsdIHijVDBvdRYpzqyg1xlM9aTQX4AXQlhHLo8ilcdVF4qFn\nAPjQB2DU0gFKJxLHALQ41jRoPLRmA4RhcdkNQKQFCCvi29nCEDvIRfuKRB4RVzxc/VJXLtrH\nLgFQfKWtyFSKJBMovYFo1XUASKHARcIAkMtyscuvWSxx0ygx2Rs+P73ieP7vjCsG9O8DZTqq\n5pKf79Ww2waJAwBHadrZpOggFICDM2cEdvBseuHP5nuCao45DLbnJ7OhV5jiIC95JUcbVmUl\nMtiMFIABqYsaGgDFvflkRgTQ5cCapX4tyo469r2jct3/rH73tLXtpLXjSxVvnQqf/Gl86pOL\nZ9iGXTbSk+DtM1IFAJturqbtwZ/rxbjh4wwHB4DKRK8WCqlhvRgHYPF2AfDat7gMAQBPwUIV\ng5I+acGvXXQ5/Gxy5kfL/Z8y9PXZ4noxtnT+/0vN/2r1SS0fySeG2ZOZAnmKxzNecSjxPIDt\n1vSYoukEAASRUoJoyQkdVioqi/ybQ3JF9gib17j5mURIYHoLzM1pAAWOAkhYzLGT0beMZwIA\nSjEAsDkLrXEdwLFAfAMvCTSvc8ZYo/Hi0ncemv07zTAdOcx4Zb6KsqeK95mG47Aj2KjShqEh\nbmH+QDSTEQrzlhiALZMb3jLX3WVZsy1g5QQWKxm96Og/HeiT33fM+pFR6XqNWAYt98wIXQAs\nvLmYC7w3wdcB2GN1mysrpe35JrOxooHV7hN2bFTXchaP7NgEwK5FrJoMYMQbyihBADyVghIA\nNBY9fkuTXfAB6He9zHoVtRAA0CkVmkluK5c8DABEA08AHFh2/6rS8cfbqoL1tdnJHADDQgDs\njOueovGVwWzLabNWOdEhOTexPtaTDTtVpSrvBjBiDx6LDwOIFuZ/MPWxz84//vnQxSKxnXMW\nDVAA5190zI1YAFh8MQuNWWkUgEy4HYrJEU5Ammy7yxzqPn2CJ0KjfSdWDVhWe0Uju5AdZOyK\nnOjYVughoADe0fHmn6eknnRJXCPDp3/68L7sIs9iPzgKQKM4lca/hfC3ozny9BPcwhy/MEee\nfuSxp0+9cOqsmucunrQvT0vZJD90zP7U4C8fmv07AG6pioZbjr9stxc5XOLR7LSbI9eNwfPR\nH/1w6i8zWuyFpW8/NPuZbG55XloCYIEVwGTmVEJd+veJ+/vjzwBwwN8c2wJAFwsABEoApEQd\ngK0g2owbPDPfq5r5IkfpjtBkbWg/J5qdh5ecO3KT+0MuAClRA7ArVKvB9s+Vb/2ef3tKNonh\nOCRRYvTLUf0TwTOfSVpPy/dU2PfHl0SsslAZWP6rSPMAMhRD+URfNgxgc7ynDi4APm0CQIFT\nZ6whAKllKRUVzj3vOPW0K3rBWZ/1WXQRwLB90V6Keei2BVwBjf116SbSupY1hV2UnsnMyXBh\neoT/Ibs6Lf5qIXeh/CnGstdqNw2pFkdn1HocYKwdIoBClrtw3B6eN63P3TYwA9CpmXQZNj13\ndczytqBLokQkkDkDQLWk1spEr60/kCh5oIl6W1jpnnFG8vrnT0x959Q0yefl555yDF/cTmQA\nJ7wWKssAuPkZfnba8szjXCL+xMUTn+p9OCJyAC76HB/aWtnrlACo1U0jvbb5EUsxz108YV+e\nkYYj+W8/k3s576SCCEB+6tHnXxp+4KnYrX3f+2l0xGR/IhREEyj9zGCqc1i8bZ8cMQ6S/AYA\nWm19PPMoYyKPkM6q1CYAF50kJnEUQgx7hlSKVUoCZZzKQKdAqSdvs8LKASW3dCKb/OUzZ09P\n7B3XvveeBfuWjLglLwAwSlsIh1UIyCpq3R/M796WFpOk/pzLmNcmVjcKA/NAl/em2AGlBIBb\nWMrHTgLgOOt/OD78Vfc7tPRyaPDvoqNfuyjtVImE0lrZL3cO5uU/H00O5uVT8qH/Jf4xY5UV\nFmYB/O+azk8LrSqFUVvaTlyYFUYvWh/6MQvPYA1EeZ5Frxku99O6449GcYe189btb/+LtptT\ntU24gteJ++67j8msHDx48LXvHF+Dyu8AACAASURBVBsbI4SMjY299m3/GVwxoH8fWM5PpLQw\nXjODkMHCYacVAN7gMSOYr3fxEuEBfMBnJn+wg7Sh/TA++Q+hgQuFBICNoaeXzn6URTYrvi7m\nOtpmhb1kiDeqo3sKLwE4L5lv6taqa/qSBn6TSsteq291AXTCPevY8+3qt3+u+t6H3Ie+FJ//\nyELvNyIjP4lPAchHe/qVZpaE8ebEiwAstFg7/tXE9H8A0FpEsPgNDqyohBMUrxlz1szXA6iF\nkyXLTxZGnvJw5214Lvjg4un7Y2P/OzX7i3VlS0x9Pz7+r8FTf0qNle3F5PIx5oa3+rtl5xZO\ndJ624yxmC3oGwNUuZ56nU4oGoKqlIFmMkNUKICsIGVG8LazcteQYVW5d2nQzAC4Rj88ZAESZ\nVrcWAEwpGotUdhvDWYkDoOmNVPcAmFDMjMkL0QwbV0er5g+7GhVdAnDMf+FHUx9/auEr5+JP\nsHIyClUuGkEuu7e00DbWmYbFRfvCoaWU5ZnHxeGhznhOoLjgnAfgKzjetLB3b7ppXVV0Wf3V\neff24S3uqcO+9JuCXPt56c5+6Y0XhYN9lrerxHJ15XsZ/W2D/0/YdvmNrm2Gx8tIlNpCbp6I\nADZPiPKzZglBKQv102rrACj+bgD5SG+r1gJgJBBLWZcA2JSrmKuxTdpGQFgEyAX1Fb1aAKDu\ntjAbml/yculD0HwADEdCrxUAHFh2x0Xuu/WuB6r8rigH4PzOIgDRoJ/tz35wKGt9OM3FTYe6\n1dfN+lhPNrwhXc1sxxFH8JXFYwCeCX718dBjD8RTj+Ydg9IdWV6btoYBpKJCMccBqKm18EQI\naKMAOq1+aZVvrN1xwKtPclQH4NfHGm07Jc4KwCPV+OVGAIcq3iFwEoDh0KO6mgDgbn6Xy4g2\nqcMAep2191UffjFmmHrXwHJ/1PvCkztyYQBvzU67BQD4VRQfm8JX48oji3nLc0/Jzz5xPBgS\n528qnL9usI/MDFkGXnaMn7XODVtS57uW8uOsYAOv2Ivjllsjio3D5pWAIwDwCtikAICfHkur\n0ReXvvuruc/9aOrjTy38yy/HPsWctUfcfwggmB1+dO6LR0P/wXT+7iIfEw0JwFjN/yk/7XgV\nRwkAiCev2TDf2bFMdy0tbQwXmiY/6Q/8OQBeclW0vf1AVPMWRACvNB4F4C2Kudx7nrUd+pb3\n7TP2owCy0phFfAols/UXielvRkcmacWkeHDOuCmX4gF4KldiBph4NYAm9RiBAeC70bG0oQFo\nD/68MPx1tyEEjFEAIs0vWk8BsEddI33WpSk5Mi9uHu64NrQZgEb0SdvyH5EkTwiA/dYAL1Cn\nV8PlJBIZAQiAa6s+QEC8uQMAItajk+nTj8598Zj2Oeb+76MPPDTzGXZn0cjNZvoBlGOcNjgO\nqFw8IQ+gZLFNDyqzFy0DL5tTqsJhpw0A3hwaqiqmAXxw4fz75u23RpR9cXmnDZXkPIBK9ALQ\n6xv3Jucthg6gQV1426LtzpD12y+lvsQ3/ZXROHf0pHTqpPz4w/sTKoBjXrve0AxAmJ+zPP2Y\neLaPO/7iHxenHvQL32pwG07X3+5o+FaD+y82VwCY47ZODShDx+xjp60zFyyDLzuO9nL1c/UT\nfW4z/CC8HJne2bHQviF8bRKkZEAnwC3fHFQ/PlT4fO/GN43cVBHZwaWvBRWCtUJSDTEClgjp\n3h6uAnDePy0iAWCRHI5TBUD3JcK9zFD2CmizAIBAwOL4WYTSidPjytz1R2Y/eH1o73VRyweD\n9j0FEcCcQw1ZdAB7izaFd7ZHProlftMH5h0A/rURBozVjQKgkOVyaR5AfYcZ39KweSXQxe2O\nFpIjAII1H33Q9envOD/6+Ln/iI58Rcst9EvdABQjc2P2pwD65e6vuz/9/bjzQdenvuj5px9k\nW/8lCADc3MyU4r5/wy3/EpGejIOKkh6oBMDPzlie+CVzOlCHU2vvAGBU1xo1dQC0+sYPTeDp\nOF5Ulee8LV+r6/ph1TZcwevBAw88MDAwQCllGiv33Xffa9x87733/q7Lc4WF4/eBiRU6qt/g\ngQbwxSY8FMG7Arjbj5cS+GAlv9Wxb6SQ/JB/Y41oLVLj3Z42hQg/S05fzCd+Ep9ieWPbchPF\n4qKanQXAdmABiATfasUTMXAEt+mzvRnXS3lctHTbmt4ji0qo+WPZ88AlgZXr4ODEb9btGy4V\n4AfhC6eKmaNCoEApgF/BxSRmTmTC73E356Kn+t03AKigxXdGnxJBNuYmRKrlIifQ/qf5m23U\nyxd2SyilZcjOLZxgbtK/aeNXnRN/s7/2T87kT4+ne87HntaIAWA8P7SXGgBykROuprevLhvT\ndmai35ZStEZq8SgAwVIpWhsB1HZ9a3Hmw9CXaq0dXb63HKnc/dF5fKcm/ZdUPrwjV9VcSE7L\ngyP6UL4OwDVx03UU8uyswsMAEvMA4AqozTuygky/kC9EDFoTCd88/mjG8mZrkVcKDp4CwLdr\nnNWFlFPnDi0WAIQs3B2tle/ztv94cedQsecofY4tyWPJE3u8b8RaGilP64ZvtGIsj5uqtKWu\nRPj483cvXXzfdAKUCgPnRJ1uL+KXNad0Tj+yvFnRJX/CB6yJfey2BoZT5nDemK4+7ZkEMCte\nBYCCa6/42M0176m1dkQKs4PCdcgMWjl62L0DIHptgzA27JyPvu/Gb0Zf/LfOSCuPZVIoUFnm\n4lGSy5aLqni74hPfLabHmza/tz9+YUyZLnBpAiy37jRizwHo6PgLAK2OrnOxJybTp9JvtlgG\njcIBCwlr4ogqntXZe51ev5y73i+OCfyMemu0YqNoHVaz83GJUAD4/qbFHWcbSJ6+ezoPABTC\nlFbcyYNtVkx8J5uZPpUNvynVBiArRMNS6pRKAIymTkQ4M/h+WuwG8NO2V76i3sI2ECSL0bSJ\ne3fywX3ZuUlp493uNVFGhyreWTAy3WIgRB0b1YPdvjeWL7277ev9sWduqP7j8VTPRLpvNPFC\nPUA4wdP6gdjo1/86dv+T1Q/8Qt9YJPzPorQgGjlZVwp8RGiuXXjka/GHH/J3fCA1NnXgXc8m\n8KOwmTF2zFV/z9gggHD1VVIBBCQ04QSgqWRpSgLgzG9RjMoDNXcesH9oMMsB2JgR99ohXLJV\n9M/NeDSmtRr0QrQxXJg+uvwDdv5Y9hEAVs1yoOH9T8W/Q0GPh34MoFrZ0O2/+/DFtwDFPJ99\nvu1Bi+HWU/cVeD5lc8TlRU8+H5g1X0ebk6YWYwX3Tn1TrrLpWl1NNj8fAmAQw+n9e40cFihp\nih1BYNEA31PxMA990f7YzaFOqHcnwgI1yInMKu2PZAf7d7Va8lghGdWLAG53b35Cky8W1R/H\nJwGIVO/IT2fyszVOLcydLBKXW5+IW28HbvUU7LGVaGccDncAIJbxP4o98g7J2N3x2dli5jp7\nNQBXhZoIC5d6oGuUjrc1/YNOtSOV77brrdpQAEBUOVo0sn2RX2pS4UzNByTDHbG+kku7KDUI\n4abSp5nMUGspsKfV0X1342e4DFGnTRudpU4Wc1w2yVudOoAvNuLhYP7DJ166Z6n/OW/rHwUT\n520AcKQQPlQvfGnofyh4Y5v+KPCMunWnmM992xM6JjhqR8z6mStWs5F+cjG1CSC6fnBi/is7\nK2dlbqaupmX0IrcwSwwDwMD8WKa+DsAr9YEPd+47mjkDTTvjUmI33hJNeQFQioUxGYBaJFVL\nlQACGXfwhhsqPadHR+edmg3AtqS7WT26oB0uAO3i5Ebr6B2hKmAzgHvHagCActrGG4drhjEN\nH3rncTsp7G5PpwCMevvqeH1S71ziDgFjWLV7WYaps2tf2fPssuGVJHrSoEA27LQBkkH2JSQA\n3jxvFDkAPbLqg1GR56tT4oGr/s/0dBcFvCoXKPIvu2u2AjbeXaWsEImU35caOvIWqwGgbmNe\nKGTUs6MyzbjrRoLTFMBg5T1YAoBjBWMjwEveYek2AHvT00cc1oeABb4xxFUDOCsfKDLHfwoA\n+PnZY04zoeVECnd4oNfW80tBYeQCiyZXN21Rd+5ljPVax1YQCEMDAx2d0SkAuM2D0wktaAjH\n7LV/hCt4Hbj//vsff/xxdvzJT37y1ltv/cY3vnHZOx944IHfQ3muGNC/D7DIuWrLRqvwm3VY\ntijYUgcAdTIOOgDg9pLw6Ts9pn3wkUCHnRc+HjxdoAYAl55pLC4BYI5Y5ilkuM6F68zvvNaR\nwReGkKd8sP0LnXY8GrcA+bKP5DVwm7PutlIB6kTbW6dfLJSycoolN15PLlxIDhpa5ry1BcBe\nUbIYxXeHzeCKXKQHoIaPy91iBi8ySXAWYsFQ6ep6264nACRjAoJgpCUAlgRDJ+ApspE1Cl4A\nLUejZiMnywZ0cukoSpEhAHhf19JUBMCRivccrnwXgF02nKTaEx7tbhssNsNbrX5KL2gh4ZoY\nOMPck4nF7YbLTZLJeNIOwFOpWaxG++5MzSjOx/GQO/xBPZz15pC0uwoF0TASAhm3YsxaAPCx\n/iKA0RrhExXbALQEjgzN95R/TpkiYx2N1B0l0fFGx2hH7LlDMbDdVTYj7+edp4Xkv9cfrci5\nd8ebMsvSOgO6y+o/kTYDSTekqy2E5ClVS+sUsV5r4e2dvrsAfHf6RQD7rNWM9kuvrRPGhrng\n/B7uDbZRphRgcAtzenOrGctBCEszZw5ggNbIfgBZIx0R4VcxZ9EBWHhHrbsTpbjhopGb9Fxo\nunkXAL1ZEkdUogGAEeBTH94MgOgF+WU4E+TPHbs+GD3avewCMGPPPyYFP9fYIg6rYimQW5hU\niztllLQwR+XaHDU2pKsBqPJZAOOCdyk7u5C7EJFNsjYdIoDqAOloWJOrtdd35971u8oAYBVc\nb6j7eOmvNYmDrfYuFi/b6uiaSPdNFUYAyK6tgqVKcm7anDjVTb/+vPb5mKAUQABwrhyW7RGx\nBRltVzK4KxkEsE9Wn4VYzpQ66mpg+Ua6YbqgqG6OI4NFF4HbZNxzd+MnmMUDoDEv7LeSSxl6\ndtuw2yYAf/IIl3ps/h/L3UxlEipaa6XS5hQDSTXELl1V8c7rqu6TnkwCGPGfnbUURivmo3ZT\nti1sVTz5PF8a3ZxuHogzvP/Nf+nx+4uZeTU1BSBnuyDws8OeyJao/8CS95sbFgEE5Yqhik9S\n0Ji1aMmAGiQRFliMGU+LOpEssQAAxW4wsRIGlg/NE/Khhj/JLA9cjI6waW1DYUY2VArUFDFk\nLW4qPgoAJe1ls6IEAxonGjyAGnfwvZHHeMlzl6u+TAbiqdRmhpBP8/ksx2ypMthsAGAH9/5T\nACFIWE8D5swz5f4Wu5rVEgu54VprBxu5Cu+sUTaxSwTkuqoPBjNy/zQyCT6X5lJRc0mNL4vM\ngN5qxdZWi12kdfGpw/GpftudZoOmqd04baf9W9FPVSznJyosLcWDV98I3Aj0z+5i6QUtWXOk\nH3XW3btwGsCBcAqoBHDUZ2sBSEmt7bjL7Con7cJwwLOcyANQCXramuhT4treBcHgARBK+nK2\n666/5WzspJwGgLps7fbcK5NCFYA3OIt3eWs9ETOGyqKbcyO1bR7L/QDAJkvwfAH7I4S9+k77\nH9pmaZrMIIUtwHgVT5nSUxlFw1TTXC3atc8BBBHVMJKjUtI0gkXDLCdnEABDilbF02ti4FJ8\nm3jDdNp0+WzICkPubhhoFbeRVXGI7H1Jseuy1ajvKEUS2s5Y0o+C4yZFHYBgqegtmvb9WbET\ngFJx3RltM4Aj0dCtjpb7AQAsoqNYUoMfziGWVx2hpVfazY1TZlIbtfU43cPmasrzhVveSJlo\n1+Fr2W364WuPhwBAIPhaCz43J3xjCcdTrxE7eQXrwYIx2tvNrfhbbrkFwBNPPMEO1t15//33\nj46Olm/+HeGKAf37AEuBZ3n9/69wwLYq7yc/TkorK+EVi3vXZT+yzQqFQ85ATxqddhyLawB2\nloIHfkt0Wf08IfolIvULanYs3EOJeFFuAHDA2bj6ql6MFlOjksOcH7XcgpqdBmDzX6ZO2h37\nCeEoNVc7nWBJRE0RamZSyy8KlpJWdnJYL6nf5cIn0P4hAIaeT4d6Vz95It2nUw2r6r/bgZNp\nnFxlWZ00rDabek1sZbqPL4t6fVP6YkQzRACeStMh1GXHk3H0yQGNcMIGDVMgFN5crqfKjLaT\nDeyNagBypaTJNud+rMrzmcsO5vSkwjsBaHUN4vDQOhopYW4GAFUUvXWDMGBSKxzw1n0tOQRg\n2LGwO94UXxYMA9yqCKxKwbKtxG7Rmq64x9Hy3eSK8MGJEkW0TmlvNoIS8x0Ara5RBoiqiqdW\nGAP5+Rm9uZWfnQGg+ytYRLhgrReVWjU3X5mKCpykGcUFCTVy63j2PIBWeycLEWm07ZQ4pWjk\nxlInmuy7UCJdMb+udKy3SCAAxbURHwgYscOxQGK8kEo2cr5VAhH8lFn5orVetNadk1slXWjJ\nVACo9kUAGIQ8HPyVQfUwv4b+Zd8lDrD/DNoc+54Jfj1Bs0keHt8+AFb//kJiMB853mWJPSWY\nhl29vLCMDTGhXoMswDRnD2YXgJURccEaiIoKiGpRN1z6RQx1xdsAxEtkcDzFnoIAqK92/zrC\nEIZ2yx526XT0EfOMYz8ohBkNwIj39JyEgnaofH9YsbYjdulzhKmSxKOt1pXuBMBU2Wbdo1ui\n/oPLZnZsWtpRzY8sZC/O2s5sDKcM6phdwKSYBtCsHhuTrm5JVgFwV675FcxFvVl2O3lxvy3w\nzahJnbsjZ3bg2lX0D60eT8SS8uUdAAhH52sWamZM/4K3Ts6OQi/GCsmLjJ8eq0ZufElkCimX\nIrLAAbB7tDpX62hq+dIbxlInaq0djMCkpdTPyyj/nOlBxSi99cUWhZq2lXu0ugbxwgCAkGB2\nUUu+6cziV8o3jKdOMhEQ8+Oldm/LCgKFRnDcZWaeVRT19kxx1CYdl7S3C2JZAO+ox+yBSV39\nbnQl7rMvHt90uQRHhrkFoA0hoZVVIqGimHsbHATAbb6GFsntiSXWfUSY0sYqTgDY7/Q8FsGB\nsApgXqFpW98Rt/1XGRjUAsNVz68XeRnMIW8Aa/c8O+3gCXSKF2bizfplzB2VoxNWLS4aACjF\n+DmptDJgY1Y85t6iEduG/BqtADZq1tERsnlVD1Rmow8DUHz7ykvAoLxXJ8Ki5VAsbwFwIDlb\nMyc0tnVNX9JfKHBqOtJgGMed9eUfldbhqF8Z3UZVDbOe14F53zcrsHHoduAbS5gtYqGIGunS\ne/8b49jSD48t/+g/+ZADFX94oPKedSdHR0cBtLW1Xe4Ta3DvvfeWHdW/U1yJgf6dI6NFl/MT\nAFp+Uwbh68IGyVlOK9yaW5Hrs7i2EW59wB9DmS6NjeTjSQOvouD9GrBzwkbp8qzRJ5LTw3K9\nSgQA3e52Xl5jvpS9xQDysVNmaT2XqROr4K6Q10yIZZY0lg1tPmTVA3PRPuacy0bOGHoBgMVr\nPnki3QvAKriqLObszGK+l1Ww+TGTV/tl76iyZrZVCyTh2RAVmgFwHGUiVShVF9Ofk7Y5iwIP\nwJ/LjZWo8XbHNNkAAFer2QpNtl2rV1yD6kxSBys0UotlNxKYXB+gV9WURXfB83trTUuL8Qzo\nGknH1szRxTznyZUyvSh3WF1jSp7JRTVqABguJlm6Z5mDglZWsxwXsf9M+X4mTsYoOIxVKfys\nVtXomVplM4AFCRbf3qnMGQAtDnMHgCci42pkNQ9AbxDLwQdak9mWhpVQvwCgaVb06MKuqAPA\nsYo4Bc5WrnEb84s6yZlrpsWzd1Bpbs5W8JQDsLG10W1kABzNBovEliJraL86/58a0OW0s6Bk\nUsew3qtmpjolkyfHJ6AjOwiAgouJK6yFu5fGpFVzLSXkpLPugsNDXj1915reBiCxikygOn35\ncV0q3u51hh2ApsAhAC2l/CqJs9ZaN3NLGskaAIb9pwsccvrKS2zYquBy4JY1wmgj4pqUqwaQ\ncp4BkLP3AmhKKzVZGcAiAo22TgBBSZf4XgALJZKeVu0lq8E3Zv0A3IE1BnRvNgyg0+oDsGcV\n5095WvNoUGB2mxZHZ9Zj1rbTp59xrBAhB5pqGU/L6qlGUgzFrmMtJcg6RIIEgLtCK/fhdZhM\n91FqTGVOA2i95B7FbshWA8DC6Ko38LUsEIx4QSdiQjApzAjI+NyKdt14etX0WNJwASBR0pAX\nAIxZvCHJ3CvsTqoAevMxo2qF+ZGx2TD8ID5RPp5bIdi4DIyoFYAlX1U+487fCMCGpW2OasuC\nwBvr642bKYaykwDabLt32U0D+owvAuBGb4vI3NFGwKauJ9NkBqtMsGPVnqedR4cCAAvByzdQ\nyKaphC5LelE0AMxeXKnY9qxAIUSxZ2NkhSxP10gqJgBwre1m3PwcAK2mOh8/ByDsum65dD1P\nrGPCloHCJgACNboSc/zCbLd9vZOIoTdWjIrWi6W5Rac4lQG12WmJZOnVmOlY/DdbfcqvEL2v\nnx7+vzhC+anB2PP/yf9C+anf8utGRkbWnXnggQe2bt16qVv6d4ErHujfOcZSJToqx2/IIHxd\n4AnZa/UxgcBtuQnCidRQsTZ+41J0OnA0hd40pgtYKhhYRRP226PbFhgqJAAI1GBZ7iIhKqV9\nxWyFtQUmKYRn2deVWngcACtbNnzSXn1LauFRe9VNLH5DsNYLSvVlv6LV0bWUHwPAUWIQuiCZ\nD8lFehRvZ3rxKUfN7YxyxDyvRl6c+3IL1yDOPQyAE6yyayt7FOPtarbtJaX0/L125vrE6eHZ\nokf+RkLRiGNJ1nlZ1wssAQmUIiq1xEUFgFMIC9EQdTqF4Qs76pslOIvgTviaNlQEYu5cZTjr\ny+bGFdN2ORhRAeR4NDabZyy8vVbZPJvtB8ATUafqeLqn0tI6lHi+s7pLBoiucUtBvaYul1k8\nN/SNXaGiH7JR26CX2I70iqoaq6tJdkwVUhO2ZcJRapD4suj0rRj98SXTRNWJwVOuMVkBEQBE\nwqnUyBjaYD6xQ/GczIQACITbrXgpxeKkbHXoSlUNPz9r8rzyPHSdW5gnmTQXi6CUQchg9XWn\n5n9ZiJ9rafjD6czZeQlJZ0M2EsdaXrA2R/d46mSZMW1eu0D8snPRCUBrXJlz9CZJCGncRP4P\nXHVs07avIgXgaU/oOq4WBjV9UxT8rDbMp1PBXH31vvNp/WCoCgAhGV9dw87B9AucbdCw1fEt\nbOOeg26Al0DbUwOwXr2ua5GsIfYXtU2S4VoxaYkG8VxBq+Wpi5P6Clyaao2Cutk02qhRTM7+\nwuLZ7hcqw9rSvATV1fry8ve2uHew6y3aw+A/DmC3mF9OP8LhJgPWiNgcUEdZfTrmp7fupKez\nBIBo6CrHn3TWbyk4uCIoVMKaimigAgBKVELFQrTiwZlYW5wHwEKY0q9mAhqGcGHA5g/UKJuY\nWAkPQYcmUL6x7nqsyq9qtu/miSDM5AFQoo97+i1apaG3lb80JwgZUbSpKghAyOomUB7L0DsK\nWDa9wWn7GcKJDuXXwJ8B2B92jNjFt0xXHLC1Tjpfiss6cqpCtGjIwtWRw+Gaetp0mNSw1x7e\nn3swMhLWCvttgZ2Kd6KYQile1pO+WM+RWYMC2Fqa1gjQJLddKAyxbpYOFBEEAEsg/4w8dhsO\nALA6dYtdkZybC4l+MrwkJYvF7WbzuSu1XJq/NI8wMi9RCpdfS8WYAa2W+zAbp+WDsdTJsgDN\nOro08ysq1KUpWVMJAI6DN5OzJtVijiQjIiHw1RS5VANRK2NWu0FWmtiR2QPbj0XIN418Ir+c\nRjMA8HMaHeQIBSVmu3dk+AlFo4ScdDfcvnwBQDexfR8YKsQTdfVHi1GbYTTljSVZACCAaiAs\nBVMk3NZ4fWOwiZWKkRSXD9hE4U94g6mQL+8HYBCNo0JldqtTpR9ZiHJtAbb5w+4EoHJUNAiX\nR3Wy3aHadooH9/mwK64BGPYP+uSGKktVo6yO5UUYPlK8+PnBY/OCd7cj/66anT+P4EchANhu\nw0Lm9NnQC3Koc2fbRq+l6s6ENM0Vpbin3NVXl9PwaQAoO1iUypVsGKjPC1ad+DPvEoNzVFez\nvV+V/FtTtluZi5olqmaWngWI3dEd107IFkfSm3/MeFNH8WxMOYAkCMBRTSfCkOXgYs4HCzZn\nwna9iBw6ucxPYAcgUFUjIgARVAXpUS09zhomjiMSqBR9aRxxQqupFxPxIVvF8cDWN1Kcz+Dp\nBKwc3upDjYSwhqkCUOLvqxBRL2G2iN409jnw65jxNovhl/7/4NCssW7qDLzpP/+Q3/LODRvW\nbOKx4A16yQ757whXDOjfORgDtFuq8skNv/Hm14Vua+D59KJItU35GWfDmxPTP0JJb+LVwF5/\nQyp+FAYAcjnm6d/ie/1si/B2Lv8wtYpUuwHZx+E8J9VVESuAPYpPIJzF251aeJwQ3lF7Z3L2\np/loT6j/04mZH2eqn9Xyi1iJqb0M2h37joV+AGCH1HFGHVqQiLXqpszCo/loz9KZifTiU7lI\nL0tDdNTemZz7eY/d6J3/XJVK7glRADZ/J3PDG1RnzFOr+U98AlotGMujb3Lpb1Mb5yUHAJee\n91Vpy9O83aMBSEWFSMYbl6wAAokB68+fVTdslk6dFGvrdzXcflIOHKtofychMwGxMgxfPrcz\nPdVv76iVcCtbTgJi06rImDZH92y23y74muy7BuLPTqR6hhMvj6aOz1e8772ik6gqPzej19Q9\ncvojz0nP9TXX/3X/nVptveEPUItC8jm9tp4AB5xVU6FUvcXq9GuJZTG2KDR0rNQYsw+iUjpo\niW9J1mlhpaHBNqNmbnfWPZacK1KjJxfeoXiYPsU2i9vKCUvTUv+LDl6gN9W3KCXqOq1jqzBw\njqhF8WyfKRC4Sv+FxaxT4/+y995xklzl1fC5Fbs6x8l5Ns3mOLNBaSUhoYACAiTZBBEswctr\nhF6/5jNgwmcEP4ONhQFZy5JriQAAIABJREFUFgIcMJiMkCwJSYDEos05aMPkHDun6u4K9/vj\nVvd0z8wGSbv+ZNjzx/xqqivfCs997nnOKVSnYgCSPE4RRmAVWp0bSouxQCShTYXzQwGp8Wun\n3nGn84M34b3UwTEfLwazTcL+LB3J3VlbBSAjGHXNLqQSvy9MG3VN/KiuLRGFYZ1kTK5XW7pT\nc2ryj9+6LlLdsyRVC8CunOaE5k2y42UD40KDbC4CYKMJjzE+JXQszQ1M737QdcMBwV4hgqs8\nl5X25rSlYuaDswUJ0h5VeSpjenlthSjvzAGQgdRDPqOWB5AY+sHUkb/k5VBjlS+MqQmb9NOJ\nrx6KPr0p8PZrlDpdHW8MP8bV/YVJxEDmxb9t/bfNo3dXp2+MCG2l68lNTWxNjx7iGn26ui0+\n/F/Bpbs8De3TtXZAtb0sFjpF0zPs/kFj4j0EpN/zVHv8Ls4kR4/b2ikA7PLkr4zLzIuYzMtZ\nC6dOKM8+SWXbols7R7OvusVQS7r6mHyiJV8vSE4AjfZVjFTDqt+EAQ2Aau9xIC1mb2AbGfH8\noCn+Pl6g6ZDsGNcysmSrpvyQpi0S+DGDS5vSgbxxZpjb7AGQlyfy8qSn8R469MNRR7YhY3/r\nhPaNwXWhnASg1v3NfcHsbf3N467JVxoabhvf8M7RLoN7y1jrBIAcr/2jfvi70R4A3wif+quq\nVZaXkxKkRm7klTuXh94x4trUUJjxGyl38z3stbbIe/WpqZM8EVud6/ONZPIYAOxWBmf41Iyc\nCuVdjEehBLrMyGjTS+8hZtL8kFtfIgHwVmkTfXIqKhg6KYlPZxL8wRfcABZvsMQxfdW6S97E\nyGOdwbt2z/wQAJsI54cORp5i93lb2X1egq9Gnxq0aLJNjerG54c5Svt+V3Vowg3g+pUTtmd4\nkDtirkEAvEhTngP28BZmHn7P9D/dcnyrQcj4lrjb63U+nnDlaWOdbabB0a/na1X71rR5yJ2e\nkJyvtKy5NXwGptnpqQamDEr/qVp82F/PU/pXSRHQAVqv7WMVtADuJg03nbmVTYeaCpExUddI\nsE2d6lUIMF473jjeIJvCC0fzLI0x6PlZW/zulkzwk6dG/++ZkDGZMp0EQNjucuXzdl3/acvU\nOwarRZMsm3zf+0/ewpvCu69RbQYADPp/zTJEXimJXIAYgQH82UvZrQB+mKQTeviRKStlu8mp\n/cOpOzrG/7Y9eueekcMtHmfHiHSvL9eUFQHs9uS3xWUC1Lbnx3pkADXVGjIAUFOjxSetThH7\nlQA3RJV3TL3/OGdyL34ipn6VHxO5likAokQdXj2fPD26608AVNd8eKrmeY7yz+C2L/m+ETIn\nbzGrALTboCROHZdXvSpe3UfcALr4NAvPtyVGgA4A16s//5X9bgB3Tx77j5o1ByX/Dk8LgKCA\n1Q78NmGllo2GRuH0ibet/pOxrHtkAo+MW+4wu1L4yZJZH6WSZ1mXCyMR7EvjL4fwXEw/qGb+\nbfVrHA5+U2JT6M43HkAvCEZo7u3tPQeL45lnngFAyt6SixcvfvbZZy9RQvoPocfzJkdvci+A\ntrM7eL9u3Ottuc5m/1/hJyWqeVs/4Gv/kLvxLkfV9nOsstEBjgDAd6cBYImd+F97H+omV/1t\n7sb/HVz2SX/b1syJj8z8ck3kJQD9cu1RRweK8p+epnc6a24MLP+Uo/paAIV0f3ryBQDZ8Cv5\nxAkApbK/+Vjnf9s6/6031T20ueEjAFSOqr6lAHLx49nwTgCZyecL6X4AjprrZdeyERsATIk0\nzxF39bb6NZ9i2xlXT+eMFOb5JrCOxE9Dy1n0vDwz/XD8aOsqNVCvta/LstRFeFTOEi+AgNZP\nUinp5HEA/OT4lsgAgD32GgC/aSUARMP8RHp6u1P/TAM6wxoAx6KKy3pNzQeXe7bf1fx59o3p\nTx8YyBwEcCa106ytR1Fu+RQ9BuCMZ0JdudJoaAIh+Wuu11vbtbUbAXy8btV2Z82nq1exw0tU\nZtRYAD3uODrhOAQgMSN+pmb1dmfNg8GONTYfAJZ7ZhVdLNsXnRABGDqZqd+st7Qb1bX6kmW5\nq69njA758AEA1Okq938pqaZ4x5lvM15JPAmg3r6i3H6lzbmJkRN6U3sn1O6kNv1C238ONHSr\ntzjKOQtmqwQAJq4+5gYQaaCdzhCAo7lY6i02fYmU325nGWthn+rUeACFQYkAi9M1AAINTgBb\nvIsB6JCGxM0AFhX635L97YbsmfdHngM1MzMV9ngAhN4CAGFAh0nLZmoAuLghHZnl2wp91nR2\n5hUARn4mlBgDMMNrp5M7AJxJvhJa8VnZszIlZFfiC7V4wTD+xuDMqLILQEReVFi7qbC+EwAM\n4yPHn78h2vfF4R2bpTyAw+4mm74GgEc/4yXfiTpePB36m9Ohz0+7n32x+rcFQgHcEFUAJAVz\nhy8HQC8sYAgCQBgeBEDyuWv525Z7tt/Z+Nk7hjesjDXexlkkQoGT3t70uZXe67eF/hSAMKQD\nSLkO1Wkci+FUcfhk6HNS9ejijRl6gxz125Pbnbm32PXFUv5ae+4WO+tIIGWYuxMA8rUJV8Od\nVau+5G54e7pqAsA7B5ez6BlAQ3LR9tFlAELZLKG4dWo1AN50NI20AOh2TjyZLFrlAY9HuwHU\nifZGyZGLHTb1zN3R33SpvQ9EngLhgss/7aq/3bfoI1fUf3SV94Y7Gv9a4uwrq2wv1Z7Y7e/5\nhrgfwC+b9gXqCs3LcwDsgU5ncj0xBQBivzU+w54XaiIxM3v12M0PYOhVBYDioDan4RT9tzX8\n1RrfW9/R9P9eXf2BzuA7bm34BFvsd9PfBdBgX8n0Deegti1f1VRwB/RgfWGxN86xnuerFi+L\nnjQAgPKasAyAN6S3NPgB+NSNWwPvWT21HQBPaeRwmB/VSZ4CqMpmfdV6YyADoK3g6FIMALv9\nrfmrrtPbl7R1bPTxMoB/MiMADEIe83MA3ObUMu1XdWafzxyuN45cnSIADGIWgsmWldklmzLB\n+kJi8egv6vcf8PWv7yxonAHAPVgLICFmxjxPALCb3I1TGgB+VBMGdAARRTleVRWuNb67/NfH\n/AkAd/XcwKgdHftUADkBNc2J62o+DEAlkwAodY7TW4qXh3x7xgnAzmG7G1fZjxRMNZS5FoCS\nWhGbFAFsSMrVeR7AEVdhV1OmqqmweGOmsUOtactft1S7048/q8LaZflQY8ETNGpbafv6jGgz\nAdwUUQBQcGOxNACD0yLDGQCekEYIsuGdzNY9PP09ACYxfq+KAGa4mqdilrD6NuQB7JW6eiUP\ngE6faARCAFaN9/xZFW5zzPy18MztytT/Gtt///hBACon/GvtWgBdLovRdzADk0JftuLM0g1j\nshvAt6ZmvRX3pFAwLdpkvYSGomUQS12dyOKVJAD8NnLW8obLYGBxM2NCA3juuedQLCUs4cEH\nH6RFsCV7enouHZ3jcgb60kKnhaHMEVxs/gZDnWj/J3NoJvYyx9tlz8oq38K1g+XwCVhiw2kV\nUR0ANrs54DyudfNh54TvNG4FYBrZv9t7DzX1QakGgdtNcCnCAei0hwDwcqh+y38A0LMsu0lZ\nzZ+pWZ3xc2SgbbzzgcX/AiCrJ8ggR6k5IfPVADULTGmkVD6o+DuF4IZp9SQACoS9ddfe9kqh\nUEgmkyha7/JEbHGuL99+lws/CCMq2gFwoL89/K/2LVvzIX3DDQkApkGGT9kKOSvWCzGLDTUL\nAIaxJTb4tbrOMcgjefy7W/g/HJFM2tTc+eMOgQsbcsYEULdELH8dVtsWfWzZjwH0JHcByBkW\n8W0idybZEPANDwpjI5nkyKQUBqBxevcVjW0cB0BbtU5bZTXrWkfwx81XA5ip1gaPK7ksp6Z5\nxu80dJIMCwB0+T+rHXHgtkKOXG+23tHcBKDLEdqvRvap4QlNZaZ9LIAuFahF0z7fO2f1lMya\nOn5shJ2v3lAxbMJ0uzPTOxQ17nYjySOtxTCvf+IU/TXK4gm1uy+1TzNzACZcg1++8oG/XXe8\nfDFaI8LBI2MIWQqgarG7U5EAFKi5tyXd1REEwDcL4smCVLTQ2TDpqlf9Tt0GINRaA2idoU4h\n8jMdQoE4AFyb6H9X/BRwivkmqtF9nuZ7SnvkUiYXMQGQAuXHDKNRAAA6W6doMX0JQMEPaLhC\nYRthv9aqGThBQdloflKbzofWN9c/v+83zYvpY4vpYyYPADOOHR0z0KgU2fg2p1ejso3kc+2x\n8adi389fde3OFatxCrU5mTNtAFqN8KpwdO+Sz/9OSp0K/Q2AEfL1PrvekRGdOgFw2q712nXC\ngZqITgpshKQcfNG6uWGa/9imH5NE3DnR/cmJO9Q731Za9JrqD15T/UEAXJpyEQNA2nW4RWxO\nZq8EELb/XhWHN9yQdgk2gGC5XQE0cNoSEQBaRW217PlsFAZF2gAgrN1Qt+kKALWbHpc0FQMZ\nR84OwCSUSUn7ChIA0TA9+RwlRV51QQBwxjUR1fMAOBATlE0zL/psZC+AJfnRr458DYDs7hBs\nNXWdlhrGR5d+32pEkIGO7t+kJ8CI8Y3xDc0WK9oW6BRSFieSH7Da1OnTRZlqeRKbEv21szWF\n1kHlCAB/rfUavKnuITZxb8uX2URAaowURtJaFJViw+UQZXPtddYxKM9Zu/Als/ADgDxmzRGy\nbtjgq9ZCTdXTR8BR6W2ub7imrFeZ1MfzgtVnC6qqWu2sscuHRmEWhK0+/5Nh43BeTG/cIm3a\nAmCTPfBCapzJ/wFgEwGjz2nObMk+wmYa038CoNc5dXr9oVtDXZ6Q3rA09/cz4z+rP+Hlpb/y\n3XHEFa1PhByaDGDIeSpq30U5Kup0eYIp5oDVHoTtyqTDYSxrqeb//tVA24bwVl/ealMuawIQ\nmsWPdvwAgEHpoD4IrABQIH4ABCYFlzJtAG724bE2PDu2QzL8rvwKAByVWA2ksygPctqurW80\n1zaqADo2W/6E37IKOsx11ydlWVYUJR43/dX61JDEnhEAKu2y43GATyaDKFZ25orCTYaZBkBB\njvOWASf7Ana54AvU/XMasaKa6sZ6vzndzM9M8aPDX7oJQAj493/t71V6nisQXjF1lRPYh6PT\nidV2AEgaOJXDCkXZseVmDMxunCMwKXImjmVn9ftKYMG3RqEZADCaM4dU8w8hBX0pcf/99z/8\n8MMsIH744Yfvv//+/3+P53IG+tJiMH1IpwWcpUb+jUMNM8/qjWcrHJyPzWXP6Fb3G7oBON4u\ne1YDaC5M+XQrLOYJmSP/ydQb5qzLSz7Zs/y8u7ALnnqlA8CAMcKJc4sXmSzDtDNYVD3CjKti\n1z2pPQCaHWskrqI6aos4W1+9Mj3t1XN6WalcuUqA3W3w/oqc0xXxIUIpgJ9F0WPgkE8Ay2gW\n/4KD3rJwc7S6NjKfRQZKzTPBCACo2YGTP6LFs2CHfTaUimNik1YHOBkWGF8wYt8Zqmau3rMh\nwmZ7CMCEpv4oMWidvj2kF2bLEOfQQ42yoLmcv8GgBKw7uVwbYb7CDLvhe1N7eovnEi9MzuQH\nKxYiIItn20VvEVbZfE5OALA7Y4khGG0VNerLEo7OSD0AwsFbpQOQeVutMVuMZUk3EM5VdxuK\nSuElWA1kTVuXkZvWuWwFZ66wSiotrGWHdNVyLPdpUCodmHtTewgnTTgr5Cljyl6TFMAaiBCj\ndvbmN+qb1jqgcFiSFQDofGaxryonRnkjVSK0h7H5jH32Duy269U2yvju84m8JJPm4pZvMBvH\nEErig/PaDoAwqDHBnqR7f7vzLd78WgAR+84qW7tLOGvNJRWJ0VBGXm+dbZTyBjoQSA05Kty8\ng9kKsUUAZ1zWxbzNPfvEbXYEMa+xlOBZ35nl+iqby9w6RKXendnKpvlhSzkRxUem/OrNuZKB\n2rParJff2xeipMT3Ww+GP5fjKRVN05Gw3jb+dA6Ap0pz+nTmjRcbFtxJ69fgjKN0f7oLeb8r\nz9KoAJZnBQAFikNFy+sFFWaCRl/5v2J8OYBu10TpaQKwJxsG0GkPciBcaNbbNWzf47WFonYj\noKp8GYWUgrDS0sS03Opc3x2c1eopQW+1LuaJXDxD0yCzlXH1dNYmln16elN7/NmtC5bPzkhG\nTDQ3X1gUOcfMMqdtA1AwVhumDUUJjmykwoV+WFwU4yuu22Ynuhp8pHi+jVqqwe9g/qxcPEoy\n1olwY8MAJGpsSo7OruvCRqflHLw7CQC7U+XbxvUeKBwAvJS0vMrLT225Al9lAvP3sctJ6PPg\n8ccfX7lyJXMiXLlyZUkEetu2bf89ws9zcDmAvrToS+1Hsfj94m+dmmp0L8o0jy8E5VWDXW8s\ngEZRmpeArihYUm1LJTeLgcpRrvdszfGtx9klCMrBSuMH0gdsvrnsQ7b3cX42lBvjK5SHBtIL\nO6gvio0GNOvT3pUcAceZNXWzx2af1an1VetmXQWJNqCp7XoKwHemAGBPQAAsXTBhWANgVgmW\nf/U8CERqdFS4T/XJg4zWOjD9u9LMwczBBVdnkGyUScwmwtZ3iykM6Hw6JZ9o9a5yenUA8eKA\n9UZ7gB3NdyI9AJpER0iwJcJC6SuZmBHKiy7Kq8iNurk9n9LNVld2pecrzLBWm8z1nE7sKM3s\nT+2fsxhpLwbQHIwmkSdknRIAcFC1gkKjXqBl2hKEYvtkFQCnVy/xWb3moHVsZqG9MAZAci5y\n1t4AoJDqNQqR0ur80Ownih8u5gWHK3K6ppNo620AuLTJRU1W8GrtHajVKwIvxrAfFwrlMw2i\nJuXjKDaQWarC5HmzplYkWG3H4qwIIO/oJrX1adsEgNo8AOQRTJOWkqgLgB67ttFhKVfMl5Jg\nSinW9NgIAH5iDIDp8VFFwTywXHtBmixIUw7h7YSKACLK7vNqBOlN1q6pjRjVs01iVPGlu31P\nKLGnqkL1LJCrCKBNQvsd0wBqReUOz+xjtckepNQoZfoZlLO/1sr1VTaWCXcQHfaUJbZDDHDF\n1K/Feire5/ksp6YrXn2+mrMOxJW/Pc7rhEUM8GNW23GUenM5v6qS4sPlV1UO8IR0QsCEfTLH\nwBWfvUCan70/KVzxvChbT7ozITLL6/3FEG1BhRm/OSvH5Ci02PRqAD3OyREtO6XnABiUHspG\nSqvXVM8+9inbi23OzhM2LaBWNFlCllileDoutClXjPt+M3+/RlGykwmqcLz1xNkxWo+nS4tt\ncsKkxkD6UEBduB/SY9cJsPHCynJ8VRWPrW4uNmmwoG8BwHFwB3QtO1Lq+jKcECuazy+g1Qa/\nS2krWKMHnUYCgF7s8ZYeLqE4sbkYQNs4rFRg47BCAYCDGQA4UCmpscVleSz8+zQ0al2BEggs\n1+ES9sQvB9Dnx+OPP84YGuUWKjt37nzwwQfnLLlo0SJK6YXI3r1uXA6gLy1YBWGbcwNPLj5b\nppDpNwpxwBLVukCUdOuqJK5NeaNC7qVdr+eKQm+OufatAOzzjvDCj5nRA6bU3kG3d85XjumI\nDeROl+YMFoZ2T/xk79TPk9p0rDAeyY9gIQd1fnRka5GIuTUxalTVULEiMCo5pXmqNKO+cc7q\nXUgDmNQAoLdGAMDFDC5uMLnccqGJBU6nchS4Vz1kBEMAupVZNeje5F46zzKDIV6YPBR92vD1\nAxgfy/an96eiwsyIDCBq22MSvd3Z6a3WUZaBDvByu+wCMKmrhJIbjUWmWZGB07UKUbyMvyXL\n+wFQUTSqalAJxbeeiYXVF0PJgNToleaqqbBWo9RMaFOlmX3pfZSaw5ljTOIAmM1AGzUClQmK\nBPqD2eiO0aRBqcobU7UVzb4x7CAUDVKWjeBH8iMu4xT7aXluUKAGAMW/sXiDUTV6kOQpP2mA\n5V+LEAZ0oV8DhdBfkTQ1WiS9WWCdO2GgkIsdKP+1RaxI6/am9kbzowmzMvUEROw7UTR00Osa\nM3y219tnVtcwc5wuF2UZaNEzbNQ1pG2TAGB26MQRIZ0A6SlmoAuEDip6pxOsTZkhSGkvXCIu\nnLRYMRpnS+XdXDzKjQ4BYBbN82ERoN2HAOQK6wHoXDJpOz7/GZkDo5hlpC1yxXeDm42t++rz\nu6ri5WuVMtACNT35vOHN5jkNQKcSLL0oHJywXPYUUj0lcheDEjjrK2K9PcDGWQTCbbDPBtD8\nqE7KZNfYyaKYrdQLJH8GWhLDpyoMPgQJnsBZM9Al9l1AbvJKcx+HOeBHdVIW1wVVtTweFU1z\nRS5iP5XnpnT2hvHEZu89nlJOnX3qxSEdJm2QMoQiPSncndfr83z3DLhJHcBaxS9VqhbKNOU0\nZ0r/+lXLq7zHMQngO5HuqJ4/lU8wFUvGmVlXL7P9FTg9L+0Y4e49ZtfnDBpE7FaUR000ajdm\n5b5BZ2WcSKA2ccdzMVr0xNlkcJJJCLBK7auihwWKFlVwkNxiEh1XT9vSS6rTC3NSu+1amw3B\nc34qTS0VHfplauwpkn+S48ojTpLTt+b0bQDs0jBvJHLRA3PWPS5X3ORdLiuFs5lavb4uuwGA\nerzU5QYgnDwunjkpnjnJjVvpoS0Jq9h6ncPKPTNWxt4Uojp6K14k6HJaX1v2pXDyWF7ZpZ2j\nIftKdC476zLe5LgcQF9CUNDe1D6cRfnojUNlBC/CKf7z5EXK0SKjSgSALR7ujfsgKcXUcpe9\nmk3Mt29FWQbaXqxxVOblpM8G9gGjoN/P/uJZf8VG7MEuSs2BzAEALXkAKJjqVw+96x+P3fvZ\no13HYy+wxdrnVXAKYyOb41YuYUtyeH6IzFJWALxVWonSoLdYXLzyFx9tswIL4WSBm9ZR6Rsy\nH6WDWe7dDmAwfUhrqNc4Y9A5DWAlWQ8gpYdncgPz103rkc8e7fxWzwd2a18GYCS9P9z5n7t/\n6WWJyYh9p0Pw1SpL2Lc5m+QLOesBZ99LAPeMbr5mzxWndrlYAO2v1TgeKIZ6APJZ7vf/Vfe8\n7zNZzmfWNlSYtQAAONEluTsA1LvWMmfN9oVir5CttZwSsNyzHUBvcu+To1/80onrvjdgMU1J\ni8IkokvxWZc9BOCunm25F9u+9/vsOwZf/r5nFIBB6N76CIDmFN0wNbnqpXHl6TSAvvQ+vzHA\nVMDX81YYpAS6REeLYKsCkIvucz2acP1DTDqY58cNAAnvKwC4lOn854TtxSw9PQJAbbLSZnqz\nUFILEYZ0NbwXZbdcu2tL+RlNqt3H4s8DIEBzHgDsutzm2MACaDXF57OcWdfw6U3/9rnVz75Y\n9zJbt0OLuXUOQCbz5HTyB2ll4kX7XZ/37Pgd+a8IOgF49ITbmATQr+g6QZdrllZUKh7lImHH\nt78pdp8CYLS0v+T5vy/6Phk+nObDMwD0ebc0AKJZ+dGU87DoaE1EPACiyh4K47xVzqVuodk6\n1/jBKBKWzFZhVzEDfbphHIBD0+y6nvUcuXZw+Mb+gVUFK0TudASDvNwmuQBstAcFwhVVKQVH\n1VUABFu1aG/GWaAQfpXNB2CFzeMoG+/iBwoADC7Leggl/xdPUOc4tCYSNd8Ni/+QHjhmB6A4\nDZbf9Veb5OxfwjplGbM9upA6FpbgpxKJe2wAagqZ6nwWQDJkMzkCoGNgxv4fSfdX47VGFkAg\nqwKIeRW9eASUYMrhAMAPaPZfZNbsGF87PbX2+MS3noz/Yi8e/UnC/Q9x8VTBRvg1CrsC3pBg\nQ5G/wW5LiVPajbsAaPYxXooCeCR86oq+X/0+MwVAIvw6ux9AlUMM2xMAhu2DO7nvPRq5qsdu\nZaBVm9URCiuKj0yIMgXgSK0lIIerBgGkJWOwtgBgNFj4QHj3tX0v/OPMyX3Z8PaZ5R87vu6T\ng+53TTk+1nfXNSNf+vNR/ot93j+ZSA79dlvP6cT2gf3e3DoAcpX1BiYBi7bebdc7z5d+7nnh\n6p7fvmN83wcnDtwncnsBjNj0mGgCgH5r3tgGgKM/G/2v7eyOEh2tEoIAXHTRcakLwDZi7W5T\ncTC2tNNNVdYs9viI3adsT/3U9tRPmVuN3tLelRzlQFH2CWATIwU8GbVyHtvdQFHuuvx0NjrB\nV35xS79e5+WCEtdqL1l/Xsb/DFwOoC8hptTejH6u0pM3CDWyF4DsWjafHHxufKgafgH31cvn\nX/R8EGw1rvrbBaX2isYbNymBdsl1vXMBaWfZs9Ie3Cbam2vWfll2L7X51p1bbq8cAblprf9m\nNj1s40T3kuo1fyvam+2hK2T3ipI+68a8q4mf5RvkjPQLE98EEJJb3GKFvwZMk5sYvSv8ah3y\nt2hTzUTTl1fQKgCEmvOK0wzUF5xew3R79CXLqMudv/ZGo6bODARvaAu0yADgFfDWBs4M8ABs\nO1T2Bi15hSyIDs819faOJseaG2r/HEDBVPvahf5AnFXEX9/4INOrLjl+l6M7uatgqigmOAGu\nI/x59pMuRkbdP25zbiSEK6XP48Ww+B5fKyvb35RoBTA9IiamBQD+2oLLX0GujU6IpkFM8FOO\nVdrqhctSva338ZLX1/Leq6s+4BT9m4N3z1+GgGyv+RAbeFnnu3VT4E4AE7kzB8K/AHAi9msr\nxS4R7mqv6ST5tdZF2+qoWmPzrUk0AeAm3fuzkR+2TU0qhV3L0931+wD4VbU2lQYgntYA9KX2\nyTS9WD8SNFL3Nr3NHtwqOlqctTeiyDbRR3pY0s72YgYGBTBW/5jqtKzapENZOVsDIFrza225\nZHp5bbUMWCx2fiCfT50G4G643VV/m6DUrmj+cJtrU7Vt0W0NnwRAQX898RgAryltTMNuCNdy\nNy32bA1bDYT4tDilHp+RdABHFctawh2bAECBCZkkRn6WE+O7bdcDiGPlBLkVwNbESJv6e4HX\nj1fnrnBjhQJZMRWXgTLiuzDYx5RyqWyLLb8mxVcBCPdTyyS8boEAmh/VoFMAafchJbiZubSo\n7hMrPNfWKOfxvDVdHOlywysY6+fKUBTWyKaHK6yW3lrXNBwsvFQbHXHl8FYrFvHmZlobk95c\nDkBbJne9s7ZBdNw+jAi5AAAgAElEQVTiagDwAf8iHy+/29eKYr2X7F7ubb+fl/2+tg+e+3ju\n87d7eel9vorxWZZyznheTbn3o8zDkheoK6DXpNMAvGpONgyOR2NHrqkjJ8q0deVZ088ACOGu\nrj7rfT4HbIjDaBSMRSKAQFb1ZXMAxmVHv8dbHh35w1m3Xw+qKgCjXTxdU6AEIBj0eCdYAD2q\nCScLAOpS6VA2C2BJNOrOawDE0wUA7/W1eXnp/f5FH/IvdhCjWdvjlxturv8/TiFwVfV9/uwW\nADO237UWXuaoAWBGzzES1yrFqxSz10J7NCPkuv0/jJBOAA1pTTRNAONeSsWpjCRMOB0+V4KR\nyLMRd1foXTtaXwnL2mPLRr+xZDgm648uHn05NQngP2L9Y1p2bbwZwOKscEWcB1CdvWV1ygZg\nZVoy8uH4qHVX2Bxme/vLcdvBpPzqnsC7M1L/oGMw7dTvPqf3USHdn0/Nmiy6pG8RLvEbX67b\nrgFI4Z262QxA4ndlyHB6/HkA9kBndWKVYNio755hsR3AO0PCzT7USbit6L5y46JgayF5pTrZ\nUWfN0letpXLFMIVR15C/5i0+WbhXHa4WcWdx3VIQ/E+TAFAj4i/rERDw3hAkgitcWGkHAAeH\nd887tS4X1jmwRMG3lwrT1/l/sd7Nv/Gc1mX8N+KyCsclBCuf4gg/PwN6UcBqbuwLuWGfGw/V\n4qFaeDxCPv+aJTjmo1Qm/6zzrN9gQvjGK59k0y3XvfJad/Hhxf/Wn97/lVdvLsDkur4pOdva\nbrSG55i/rsBJV1938nrO5na7JUm6/9cN0fxYOD+Ehco3+akJomktWvx43bRZ35je+hfz92iz\nm1e+M1r6V739XWwi+54PAQgA+1fPLqy3ClLE4KImANPDmYFz9UttvPMzq3YAMKjG1HnP2Ab0\nt7RiFDbeuaTmxrrwsrHsyZ7k7i3Be+asy042KDc/3PX7l0fNQo5zFNoA1C3NfktsKpjZRa67\nAChOU3GaapqLTYlVzQUAW+yh7mV3FHLk5X0+AFoxM+2v0fUCl5gR4pNWAF3yEJ5ccWuwY2Gb\nLG/r+7yt7wNwO3B746fOdqY31//FzfXWtWUJdUrNSGEEQFqPTKo9LfIqANyfVqfeKpSk72XC\n/TJw005NAVCd8dl1+Yg/NfFpd4covfDCfwA38ZQqug6Aixhc0mTX5COu3HvaPgQAV/6ydAD2\n4Jb0+H9JI1ZHkTWQLqRS7iPHVr2tw7/f/YyTi4Jx8aPCTxz3fbS0rt4qSPvAT1Ohya0LcSWw\nxdNsCZV8YrllEuuVauKFSXabtQhNTfnej6ntLdc9cSLx4vPCNzJSv6PQFpsUpgo/ZssPUssU\nTp2CAozY9OO2VTfF/gXAUdm6S1NoBrAtPtye29/clrj2mjtKh+Sv0cdSfKmBmPiG0dCUvfe+\nSNEDL0IbAFDFbgYWiERYjZrBpzKO0275U1qeALhrzQf9te89WyOWg3+gDkAunUaukjUe4pOf\n9gPYBveZjjvQAQAuIG8/JmfrViq/k6QrgRQA+6T2n81XlVZ8ILDkgYDlg5AN7wagBDY7a25c\ndPNcF+j5uNfbeq+3tWIWtVLOuerpFDkIxmKfMdhggq9aCzFyAkVNPrPkgwVWn9e0XHW73do5\n2ad3NH76jsZPn/eQSgegt4pyC8FBCHkrNJ/gHTM19kM11VffHfX9NC6dKIiD2ta7IvJOA4Bt\nHY5VT5wceAtb2J9XMQ2igWgmAEfx4EoTrB3v8bbeU7wChemPDxonFvnesci1+e83nNby5KVk\nAMCE7cXW/DMt+eeecv6dDnlIy6Cy7PLuja6vO28eTPIUHwbwC6kAwCRkyNFQhe885/s8AF89\n5e1aeFSKTwnvu/6b3fWJ2oZfsdW/3jLEThzAkJYhwNJUHQAC4tckAMTwsZ5xINeas7mERAcA\nrek3N1y3ZvroSyca38N67mOL2ld4rj297EfnvsDsk0cIv+iWHk5kSWDtU8c0bpx0JeRc3hLc\ntIk7QKCpIwAc8orqmarqmZU/WXMvjRMAV9W0/Wll7ijgsu/bBmA2D6W3tKc/9on5B5D+yENf\nq5xTLaJVxkDe8rXd7MImJ04XMw8Kh5dWnPV0JIIXlgOAJFxYPdBlvMlwOQN9CcGSiHVKh41/\n7W4l54Oem2ZCyPPr8/4g0eRYIxAZ81KzzO6uwb5C5GYTBku8s52KBQjQYyMAKC/QssLBN4JS\nETrOR4CuOAwiNjvWAuhP72Nc+VbnBo7wbKSYCfDNQV96L4pDyd7q2SAmorxSMLMoG2VmpM85\nUgOJSnthwlFPyOJi5oplVaVV5gs+vBGEbK1zxgH6F0qxz9k1ARZnqqsEW6vkHE4f7fcc1Srf\nWHp/fEI9jbMMr7MqNGeiYngh7TwCmABSrkOlmXl5Mktf1bKzNHRrGIHClVrLy0HJWRmrASiz\nyAbAPEryyW4jH213dhLCsVGC+LTYl7SkABKcHk4eBoBYE4Buu35M7gIwzddP8RX2v5tTgwAY\nm7kE1qbpmKAXCMoCaJQxcFJcVYE4jfrGBQxXigyHtPMYYOaL5Vae0KViXuaqpgHIE95SJpiV\nCsxfUlfHtewwzucDdW6ULMr1VinlOkwJY71bZxe05Wy6NV1LswtdnjcKbsZgMoh6i2A0iaWv\nq0lI1KagaPrN2Er8sCb0FACAg9Es1tTNvr5og0DFcx1f6UwZ8kZmJHMcZfSw0pPObkIC02fM\n3kudZWWXzGoqgi4AQQHVYzqAuM0WEeunxA4AoNS9zM0obcwle4nsYcNZ81GT87p024I/EfBD\neJes1wEI1HAAsuE99WWFyAsyweaADbravB3F6BkAulwoV62xuw2bOUtGdqg1AMDze6QggDoJ\njRdh5LUC5Yy+rstCdH9MuBxAX0L0pw4AaHe9hgq/C4catQQNzlGr/ocEgUhNjtWYp+TAZBDm\nVMcv9s5mnecXznNjIwDMmlrmGPLGUSqiQllB+oWASVX0pw70pw+iWO/P/k7n+pn0bAl5IzOW\nPVVaoCRmB2Cf/ggAgZOaHMxc2ipRT0UF05j9Es/RcPAEDcJRb7GYPTEj6gWSiVvXJJvkS4nq\ni4LWSgu3vnmKHAse56JUDVMM6E8fAKSYUvF5zvVNMyrIfKEVALJnJSc4nOm15TPTriNsIkVf\noop1gmnnYQDlghumn2M2bM70Wnugc0HFmPIAemnV7QAAqsYO2AVvnWNJVNkNIB0TRvOzImLd\n00/G0glbvgVAj10bEhYneP8xuVJF20y26scBcMkESSVL81mLU4pEWODiUZLNAGD0/ZIeCwiJ\niC1GfUU4boFCGDEApN1HeCmQTtYBcPpmxUwuOhgNxpZuFLpnAyVheIEAWi3We114acR8WGoq\nHLjFzQafzin9AISirkV5bZx/nrjeRYFVs0hgNInlWiVxxWZwBMUWZK8LYsC2Nw/AqOapTBY1\nNsDStYa7SrcUys+GYlMyDGeOGlRH2beGPUGaGMtIFuGhpHBHgM2O2a7sZK47Z6QY877TZV2u\nsKJQwvXZrgLgJDHRK7uDOiuWiE8JBNho92MhMIejs8HMftxarLHe1JL51OnassR/2/kUTlAs\n+3FVbS2f2enEiE3Pc0VNnirdIVjEHl4K2KcpACNUvS/L4XU5754X5UTn83K4L+MPCZcD6EuF\ntB6ZzvVhoQq2iwJWYiwotaJ9oY/lHyKs1GxZ5rI0gD4nzbzEY2WgWVHdnO0IVururCVKrxVm\nlUDt1qN0NgXoBVGyvGZceXaCpaLJ/nRFiNmb2M/EK9gCpTLHvDDdbz4PoMm+upSGZ9lK00Ai\nPPslnpNUZrlnSTFZKVV8WmRm0SXE5ommLXDuF0wCKlUCcFRCcejA0JGOQ9es8NSgGjO8KK21\nNFXLylL70vt86qaI4ijfpjREATgEf7WygFYR4QS7c7OSrbgB0sXEsxrdpzdZ+025DwNgghvM\nqQcEeiMF4EyuZ2Iv5zgjp+hv8F/Ny0zMeD+AZd4tLPlnmiDZ7aUT70m80jsywkRwu+06BTkp\nrn9VrOhjLyscVm2WsrVQplLn9BqslisyJmFkFAAlvF7boOVJOjbbFYyIrQsqQNORCZa2TDkP\nSZ5rmAOct+qc3IU3iKV1AAjl+Zky08czBUunwixFjFY6QLQ3CrbzyFycA0zY26gRpJo1hBPY\nCENJd8U2Pis16IgVZrUydEpNjbEQrKYvm7hwULMgDBYAGDWWrl+ptjIdsvj97Gob9QIVAVh6\nGmwxt+LKKr2lxc5diAyAHywUDx+9qf0AbLyrTulgM60n3TdKKMdR3oQUMPrZT0t5t5+XrDWB\n3uRe3lRiZC2Aa6nJxUwAMbcNQEKoBeBXIgA43lIij05Khk5KRclzsCS1QAFMCfbCSgCqPBRw\n+zNTvwE1S1KYHLjWhTzSGaipg5pGPlpI9wFwVlWw8jY5YRD0KlaL2kOa4rFssxTfen50BEC2\nvokpMV+KALqkDGvn5ups/LFBEATnxYMgvNk5xhcaQJMLxiU93P9B6EvtY7mxCxmZeh1grl1/\nJOlnBpbwixcmGI8WQCnEnNNLaXGvYY67rKiu/CcuEbdSd/MUjl8/iMXcoCIx6l5DVrtkeQ2A\nIzz7hATlZo9YjXlklTPxXQAU3l2nLAPgCeqEowAiyk7rTiurVXUVnRpKdYSmCeZWyKoGUZbD\nZrF4bFJgTADRZtrsJi6AxXFqt/O33w9MDZ2raLIEFve3xh64/XS6Y+az07m+qXDiF4/hqSfw\n8n/6IuPCV07e/LVfP/zyD33ZJA9gRukH0J6t3qiEAPSl9gay28JFbeNhzxkAvhmfZNgWuToX\n9GUA4DVuIpQHoIVUABRG2nVM9qwAUEgPZAODbLF8TRyAGt6bGP5Rz9Ot4Ve/EDn91Un17wA4\n06vs/oUf4Ub7KmbQ0+bcRMAxZ81cdF+s79v8q99LyCc0PgGga/QnVw/uWJq67W1nYsLQ/zM9\nqQPI8xMaPwXguNx1zNYJYHXa0vtbXdiXtk9TtwcAVxZAE2I12eAJ5eVDW2JC47P+L+z6VV10\nwrr+HiECICK2mzVz45ixvR+IPfsFAJQYU/LaM70/UtM8KolAFx18a7suzGbQmR+4tD/nfjjK\nj+juL0fdX46xmJ5lFt9I+hnFBLDRInKCQ3avSLsOo4xWwWgkcVkGQAxqdg8AsL2Y9XwmMvaP\nH+v+1VXZmVd6n1kyvve+5OjPe55unT7+2QvfdT7xat+zy3FqCGVxs14cjCqNSjF3DwjEaCgj\nfRWX5/yWVpqvWi9tZNhr0cHZkZcm8kcpgBkN64/hocl3GlDaXBs5wgMwi6blL5rNf/+rPV95\nfvfLxkCGbiKUbp/wH/jeRvv3U9KBnOczEeW5bHCH8m+/3PeBfg7A9ph1M2hNs4dXekuw6H96\nSPrdD/0bclaJ6grZoiwsF2UAS9K1ACT+KJtZetXAPavHbDhfHfrdzeP77wfgFXxukwdQwwVk\nvqJvPHt9cpP9z68Z/O1VaoT5csNdva18gaU2eAR0F1kc745oR2rvZNMO2sYlEwAOVi8uUODS\nZIiXKvAKALDBySSF/qhx4bHiH0AweTkDfanAEmxeqTYgLSzI+kZAzXw+fhTndMP+w8MidxeL\nk/qS1lA7IwrP1yHmibjK+xYAa3xzBUeZp9TZfNpeN7SVEgCtQ5yrVHROOEV/qcZxqfsKppaF\nYijcW0mD7onvRlmXgHA01KgBmHA/BYAQbrX3xtLCpMhtLQXBqYhg6ARA+9osL1BBoiVb4xK5\nNjwmAfBV6WxOiVm7IEwT472yaZCJvgsiFTbZ1/jl+ub4fYSKTYn3U9Azp6OFHAAYOunvzfWn\n9lfH7qImB8DgMidCDwOQDKE9HZzJDSS1GX92W9huVwVT4/M/XvF1ALwhtMdWnUOCzZ3eCEAX\nEhMN3wGQ8O4yhUJoxV8DAOgU/88URsE2blu7HUA+dTre/21qFuJDP4gPfT/lPAiAM22OzFyR\nFgaBk1Z6r0fxNmOiH2rscHzw3+vyOmBOuCwbtkD2yuXRv+NNezD5Tm26HkBe2bmqsBfAXtu1\nveIKAB8aP7hIjfIwt+ZeSCsTTEiL8fVLYCWhAHKmctjxrhxxpuP84AkFgKSYdXVRADGx2SSV\n1pKFWHriGVdqPQDV3p0w7qWUByCINFB3KTPQHJdpsBKfedtwekuCdXNI1rT/MsPFTC5miL06\nNdR84jheoyHU3F0VLcpZ7tYW6Ey6DgMAhTCkk5wlBN7r9+kcBWC+2gdAOpAnBnwT12Wjh8Mn\nHzb1TGr82Vjv49QsJId/CHoudY5ypMaf5rK8lKlGWUCsLxGpRKiNSOs5QqC4jJINO3tdAKAS\n0RcX9dQbshQ0quzWxLDeKlIHpwn5f1nzRYPTCxJ/vCoEghm7POT1AHBEC6ZGf5PERAERsy5M\nNpeSCKmo9aQH09m6rLMh47pqmo7izqDZc/dgtawR6Xhe3pUjBsT96rKTKwVTeO9gXiJYPFEA\nYPo572JrXImH7lthxbWhJqvsUtdIcLK6WrBJhP8Un7KZBbeR/d/hp9y6VKd6Abjkb4jiNOGw\ntDPDi1QQafOGaZPoACioS3omV+QfOmpu7OBbACwunLWvnp58Qc9N55Nnoj2PAhCVatnVVtH0\nBG/14pC7YAKTktErGU/L6yXdTcAFhq3+9m5HHQA7Z2liXFywAwBwk+/ib/x/Fiil+sUDpZeK\nXXaxcKEZckopIeT+++8vd3/Ztm3brl27enp6XpPXy6OPPvr8888DWLZs2Ve+8pVzLDkxMfHA\nAw88/vjjtbXnGhh6c4JFP5eKvxE7wgYZ/0gqCBmcQqDK1jaV6+tL7+8MvgPFHO2COf4PLfrW\n27XPze+9CGOjAEyff0GftteNwiabvkgyva+5R/rxjp+Nq6cBlIZfAbS7ug5Fnx5KH9FpgVl/\nU2p2x/eg8mTXbE/mM/wm6aGU9m6XGPJJFTWR3iotMi7OKQrkeBpsKFz1rigIRKnEGrTItSxF\n7a3SOAFTg3IyLJgG4fiF32Kl7/QFlhsKnPTZFbt/f7SBWjZp9dGoUErXx6dErlEIqF0Aevz/\ncCb0RYPLGNxjvCmnZ+RxshfgAuoWjeNevb1mMPj1QzO/U4WMojuWhtefwwTENlULmCnX4Qnb\no9H1P1cWXd228qhgqxKUOl0dj+k/P7Jxh1yzNhj6AgBQMxc7AsDIhwFkHJNUMIjOC0MwzsL3\n+bNF345qY+w2YwlUaqj5xEkvoJg4UHdfn++b2wd2AxzJLAFAqGjPdgDghZ1rqX0HbjkjWnou\n2xLD75k8MuyOpIJHdCBbTTynwE9PEl1j9isAGpbk/DXakV870wkxJlrHxNKNvmrdvTKEYRiU\nT4R5b5lPWy56ANR0p9YDwLKmQn49gNZVasuqrChf2k8U/fC14Z5TU/v/PKv0VNV8ifzVn9p/\nkBSG9JINJD+oqXVHqKnhjaUD+MGCJSLZLLBNxW1PFMQZSQsJQzp4wn71b34q81vqSXRJowKN\nG1zMAOBIreSopEaZ/SfNxQ4BMAqxfKpbdi+7kL2rkX3O1DpQgrIA2nRyyU/5QOBQzKvujgoi\nLeXU8lcq2jKJ5Knp50rsr2XttQ9Hm/LCdEfqO2t8b538C3zu8LVJKfrRW679/Pp9i6mWNPwP\nTfHeo/SbUxBMM38a+4olaxF0lr417HnUONqWshgSWyL6M/Xrb1XvuSvyHgAwwY/qALg09aMa\nwLqY3iVDGmISIlLD0py/VjMymk3RRK8VQPuqtSvfGT25yxkelVLT0t4Nt6jUMI5/+mfDP+Wp\n6TTVfzHtOfwZgEVXfsgRpKYRlRTzqndGAYhyffDt/QMn/lmf/oVPHQRACN909a9s3tW3D3x3\nxYlPemmYGirhF3gnl6Jt1kD2hQzev96C0zV6fnn0p1FKE9iXEb5hfBIjvaJhGaPs02UA6504\nZ3Hm68c/tuAv69F0QUNxf8gwDENVL1qBgaIob3IWx4V+7x944IE50TOAnTt3bt269X3ve9+F\n7+/pp58eGhp66qmnnnrqKQCPPvroORZ+5JFHLnzLbyroND+cOYqFJCAuCpjkEyc4Zc/KS7H9\nNy2YJQ1LPBfM7EjmBM7SSyGEWzD3X65dcHFh+rjXoUXEE7HRvqrRvqrcq5KdUekuAjCaOcnk\nrstPlhDYnIZPqmtyrJkTPaMYFmt5ko7zKH5WPUGd4yHKtBQ9o4xcy+CrtqQ5qEmS4bO+v0px\nc0Hl1NQFEVfUqJua1jUKZq9EvBGAywcANO0PZa7jTQeAcffPfQ6fQfJx2z4AsSmhL73Pne+Q\nDD8AXyO/ou4GkxjdgcMAlkc2MTGTBWBQYYQCSLkPAMjLE466G5i7ij1gfYYLYliuWi852xmD\nuRyU0/QGHmVKDvNRfpvZvGtKEQAB6goAzJiyLyGfmL+il+zc7JzdrE9AB1TF1BclFUIJgIwy\nAQCGUc7iAGB3G35HBPPgrdJcAasicE6XRo3skQpVcq4JQKauntWVVjXnL3X0DAAcJyxdodcT\nk8upkT2mj9OXVEQZwoCmhvcA4EWP7O44y1bOD6bsZvp408cDUAJbAKTcBwHw/QUmP2I6SY7/\nZcq1H4Ay0yL0F7VBqORILTDIwETTzgtqFtTofldyAwDNnjR9s19VaudYoaqsmHOKNc0QbzTM\n1k4ACMhNskM3SYEJ1HRr+5JSFEBcmunXD9ichunh1nro9xopc12hp43dRevGCLaWOMSMtdWv\n6NvC1gleOaPrsJP8Vm90YZqEZNL3xgr8+KwPlN1tuGo50VsxuGRzmMH6AoBkRFCoGOTlbHi3\nx8g4TRWAlF8LQFJMT90iQeIlxQQgypTdZgG3f0nTMh8dZJuSPSttvrUgnCO41WOwa3hwwWPL\nzuwq/9cR2jp/GY5guYJ1QfP6AAVwSkWksUM0rGyzVt/MLtTmS1bhx5HL0fMfIy40gP7Wt751\nxx13zJ+/cuXKXbt2zZ9/NjzxxBN3323J0d99990sFb0gnn766Qvf7JsNA+lDOi1gIRHiiwLm\nsaT4NxBycXQk/qdgiWsLgLHsyYwe608dKBbVXehFJqrKRWYAXFz+xkVHo2MVYwT2FBXQupO7\nAAic1LaQ3MSC8FZb7mbM0zs6IQCzhnZzFy4Wk/ECdQU1l9+iUEcnzx5Al5X6lZf9nQPlq7RF\nP8zrLgDLrT4mWRr+JACTy8WVA1dVv1/h3WH7K2yt3tSeQPZKAISDt0qvURY7hcCZ4CEAS6Lr\nBbrwt4ufMEiBoiiyAcBWZDOXD93Y/J0Asc8bzBHtzUabAoDvL5zFWL0ChBMV36z1TH2xDi3i\nmCt8rnPpGhxe568pqoBgowNmfT0A3pQULQggnT9FbTYAQiWLA0DQGJy/d2+1VtKki1c2Rzay\n15myDmxKtgPgRasm7L8HjJvBRE7m6DzyE3pu6igAm38DzuEHeD6wYsHSxgVblWhvYjRoflQX\nexk9WspF96aZSaHuFHbHSqu70uvnb9Oyej0f8okT1MixLaTdx173KQBod3YB6EntQdFGgKE0\n3eVClse4UwbAD2t9Rbm2KLeRECs4Zg/jiKytTFhNvC6u2w3aELuZ5cgXxC3HVFbTee76RUbj\nNg3EZwQjHy2keko/5Y0rAfjO8oZBZcVO6QEsGYGxj9oc6LlJpm9YgmOhDHQJnQ4AoMC+0CzN\n41TdorgOXJbIuIyLjdfwwuru7p4/88SJE1u3LtAjXBATExMA6uqsVNmGDRsAHDy4QL9zYmLi\niSeeeOihhy788N5U6E3uBWDjnfXK8kuweZqLHQRg818Sgbw3M1gGmoIOZg4x/oZD8NXZL2iY\nFQA/MQZKURT/etOCJwLLJ5XqCHsSewA02leVy12fZyMCdXp1AIkZMZvktTwHoHxkvxylUiFX\nQOc4Vq9mrXu27cfLGNLxC9DrmLNYMHs1AHC0aSlERS/NidkOGiS/2LWl1bUhat8NoJDj0gka\nyG4B4PLpvEAJSLurs8d/BICtoDAH9flgVWWUNzPOkwAEeyNLPwNQis8OIbziWw9gvtSGEuhk\n5V9clnLRC1IbKS+DqysG0HHb7jmLqfJ+juquwIb1ZWbCJe9AO9cOIBc9YNQ2AOBG5wXQ8blR\nGi9Ql09HsR3LrzM1C7n4UVd6LQDTx4fTNgCegP4GgtXXDCWwCYCWHTLyM+UCyQBgQhjJo6xF\nXgeIBn7CQKWIpBLoTLmOACAGGGOkUJvR1LG08ziTiJaGZhd2JhcYxChJhZ4bavQAZ8r2dAeA\npO0VoxA77ypnAxuxHE4f1Wm+vIa4P2VNL1fg5HHMKwFwR/Klbp1OpVdVAFBTfEHlAEj5TIl7\nJZp0XcxYHF6gk1BCaFgDQO2cWXWuZ9lZVp2cix9CsWdJqVQwNuDsbxgAor1BUCw2pr3U3IRT\n/BtQlK+Zg5K+obUsr9i85xp0bbUhKADAbrkKnHWf7fE2AuAJNl4OoC/jouJC+SX333//xz/+\ncQAPPvhgaSbjQH/ta187+3oVGB8fB3AhhOZHHnnkc5/73II/PfTQQ0ePWuPabW1tTzzxxAXu\n/Q1ib+xH3zv9ieX+Kx9a98P5QYxJja8ffc/RmRecou++5Y+MaccALPZ1hYJVC23sDUGNnzLy\nUQDVLdd7A4HzLn82EEIEQXA4Fh7Ue3PCD7/rVDBVCH+r5wMmNQAs8XUFy0zXWOmuJEmB4pUx\nXnzW3LuLGgYA6DoA4nD62hct6DTx5sHK0FWnEztOxH/9t6eu/+jqf2Xq1ytCVwZeS4vXtpBU\nFMmwrGWsHG3bMpe0UARuLEHvIQCoaxHZLmpbSGQcybAkksDuZ0k6DncAW2+hR3cQrYA1V9K8\nSgDYXcimkIrYUJD3PU+yaQCQZKy9muZz6D9G1m2nU0NkYghdN9LEzOwqDJx7WpSqpdCkNmyp\nMUaUnTLvWN14ZW/+qicj36SgBMSvbvWr2wDUNAvs8FZWXfWz8BcMYvCU98zI3ApvxfkUTPOx\nCXoqAwCNvHYKfG4AACAASURBVMnlAPjqripdPeq/avQVl6Gl7P5VoZoWAGLbW2Ze/RsAkqOh\nkBkFEGza7m6qMv41CQr3N5PcdT5y+3kuPtd8XeTM1wDIjsaq7AhPYRDwdiv/LSgpXXUBgLiT\nlzx1Lduu0nM7UyqA6+vdDvcK/eUXiVbX3P0VBL8Wxi+4tioM9OaG0/IX99CG4/ZVa8iSZcbP\nf0SnJxVfXOW8NgcKKkwTgVoSqgoAyC/GwDEUctzOnwXXXk3lwwlpd1Jq/FNncj2AadExMywB\nqC228uuAw+F4rS8Np3zjxH4A4Asn/S1vN+vTdCQPGwcCqKYjvlRJtDQcfw/Hxcl2D1lmpz+e\nwdUeovD0/2PvzsPbus478X/P3YCLjQAJ7vuqjdpXk46dNHYcOY2zOMkkzdLGv1Rqm7bxdNq0\nM3WfdNHTdtJVSSet1GkyTprFTtI4jmMmcWI5tmXLkmxZtjaT1MZ9BQFiu8Bdzu+PA4AgRVKk\nRJCgdD6PH/ni8gI4WHj54uA979sRIO8roiM6jk2ST5SSuunv3YRl/esAvaTBoqwom3Nzkaso\ndYxe/Y7LPU9YgiZYqT1W+WV0wRQjmuuKGm5M3YZtyJYo8wbv3nj6B72bDgbJcwBszupEtFeP\nXnFIY5df+n3FWdH0tv9gE+T0ska/OYw2j/ArqSVjye+Llad+xoozhj2vjj97Z+Wmzzt8G3pe\n/bOK1j/wN87sJzqPLeI7H7sCgyZHyIXe6BsA/Gr1WLz3rfDRvz73jt/e+H+bvLt2eyefK7Z+\ntReqYewI4k3vmA6PBeWs5binSL08BAAUqIppACYUQbaoy6DtY8nNgQoAAcdIYawEwLBTLI2a\nAHodYnUs9flQaHIU+a/zxvBXkqEriAWd8LwJQLYXm3o4ntxKqR1AbbOjqGjOlXrj5W8bu/Q4\ngPKm+2zO1B3FKu+ODh9JBF8tKvSBCFePf36k81EiKlVbHkGsC4DiKNO1MWoZnpLdbo+PEDLP\nu7e9KPzD4eTrpv1I/fZHvJt/d/jUaVsxkNjgkupKChb4QqwUn2851iEmk4uu0sjNaqGzECz7\n+eGHH84uMvLSSy+1tbVlh9Q3gEXV2X70ox/V1tay+elrxWKxybRoNLqENVPmr6Vi0ERUnzgx\n/OSb489ee0xX6JWjA9+J6IGh2MUnLn3xrYmXAKz1tediPOHhlwAQInpK77iZ28GSVpxZHgIR\nNvnvAZAwY7qVALDRf0/2AZn3SepyQjOPPEMjYcRjiMegJwGQphYiCCsw+sXYVHwvAIuaVyZP\nP9715yPxKwDWLPIdVVwJAOEJ9HcTAAVFsKmzH+kvJ4oNAMpqkX3dRBynnyeBISQ1jPXjtWfJ\n1QsYuIQ3j6ae6jXbAWByHGePkeAYkhqSGiIhnD9OzrxExodw7hVy5hjG+nH6ecJqbmzYPfXh\nJeQ5CiBUMJUGNur8eWvROyRBXlPYnhTHw7YLAConH3QlGwEUV6aGt7n4Xk2M9Xq7AOCiNuPh\n4EyMvhGBTgGIG4vsnkYA3sqpt4ogSAUV78je6S7eKdl8AGq2fYEIEojgrXwncUmk1g4AUdN6\napwk6PxPuKf8TkFyAKjZ8ZciJVVJAGjw+Vie9/pdMIUwAK/wc2/FrxBBvLdIAeCRyC6vLFbV\nwOEgsc1SqLi673cAGiuYAOAae5caajIHPOaRn1nP/ZwOD4LSEv0CgIoG+CunvWollYQtOIxO\n4twrxPHLcU8kWdH/W87YOgADgsrWtZfV3cjv/rTfrMWwu2ttzmoAkZGXCSFkgxMAWesgTSoA\nd2hXZd/vChERkwZ9KkA7JuhljT4ZoE8H6BWNdkzQJ8fpZQ1HgjPH80aUvhlF1ETcAgCPKNRM\nvb+9VfdQwZosSM/jOsWgfASA3d2g14XSbzerr+rLAAgVHbG1NbE/ke1+AFVbUw3qrx7/k2D/\nMyOdj8Ym3mA3S58N0ssa/eE4ST8TvtfvVJIlAAwlFHOe1+Mjva/9Rf8bX4yMnux7/a8X9UQ1\neLex3K2OK19m57cPNv4vAJRaPeEzP+35V0JIu0/+QXmqbOMDA6Yfx3w4DeDlkEkIGR8kAAZt\n5vZxHcArRdKJIhnA20eMbQEA+FnDN6PKJIA/W6caBBbw5xum4l2y3nHdQbIzw9gAJodfBuAp\nu9NTflfCaAcgySgsm++63sp7AajetXZXTWanp+xOAEZiIh46b2ij/W/8g66NJqP9faf+Ijx8\nFEBB+TvcpW2Z39b534TtPhnA8aDx91V7XnVX/G3dXUeDBoB2n7SwF2Fl3PAv1w3fF3fzFrHC\nkVK6f//+w4cPZ/b88z//801Gz8jK6GBY8gZbYjirj3/84/fdlyrX5Xa7I5HITQ7gulwuF4Am\n5x1u2R/Wx94cPrLGcfeMY94YOpLZfiuQqstba9+Wi+GN9z0HwO7dEE8KSN747auqahiGruey\njlUO/Fr9F9e5385SzJ2Sd0vR/dlPst1ulyTJMAxN0wCQi52SZQGw3vlualcBUFFEy7pE7t82\nN6lG2faHG5/4ce8/ng8+f3I49etQbduyqHeUw0sAJ4C+bgDwluiRSGKug9vfL8QjxFVksntQ\nCwghTkpT12Uy22zD5bMKKzTAQSn6LwJAaY2pOKzeC/L4UOrIgUvTrkIIiuui7e8Xnu/qeHXi\ne2Hv0X34wFnHP8arHlvnfPevNH643PGptd47I5FIpbxRIGLAcdSTWFcWfm/6EUUjEQqgRFzz\n+c1PFQxU4GVYnZH49KdFPjcpAtQjGh8oMDfa6vUfasEzatl92c9e+fYveao/7K54V2Zn0z3P\nJCJXnRX3Nt3TRC3dFCsikQh5yCe+GpN+GIJFY2cD1pr5U2ikpnueMZMTJY3vgVzxUPDkFWNg\nd+MfWWtik+NCaQ2Jic+PjFzaXPUxT8XeSCSy04YftMoVimDFoxGAfGq/8g8aklASlUqyNKCd\nlwTZaboBKPFGSG9ZF84CsJrWtO5yF0MrqTZNA4EhsaTGyDyy9vcLl8/IPeflxIDhSOoASsIu\n9k37mKr6K82mLUmnz7yB3wB2JkwkEjdw0lD9uxPR3on+5/2RCLlHFSqKrGab+GJUehMFk7un\ncnNNSt+MAEBApxM6ANoVY4M3O6OxGa/y+UkRoF7ReLcHgNVk02JZB4gVTe/8yZj/a+NnfypJ\n3rIH/y54+jkADv/u2Fp9VPsjwXTE1Ythz6v+7Z9wn1ovdFH7WGPjR36ajFx2VbxLcf5NMtoT\nuJr61Ru9+iy1NQOwdUYIgIgZvRSkpZLe1+NOFAGI7Rqz3uYrCf2P4bNfNPVwaOA5ALHguVCg\nT1Smfz0yrwb39syvvCI4dhd+1Lu5+ie9B98IPHNu/IVIJLLNbv2lgwQUpTCRvHPc+B59hYjN\n49bOFwPJSCQy3OsAhG5VfyigA1i/2UmTJoaT94wkCQWAN0uOnSh/dkA/8n2//WyBKFs46pc/\n1CTfQylUwdwo43rvDFehCKhJDRODIRFQvDsK6z/WPyYhjoJiMzZvl0dHxYfq73Kr3o3Zv4mC\ns5UIErWM0avPSvbiTFpIMjaUjA0DUHw7ijf+VWzsmLviPk3TFEWJxWJz3cU2mwUgatJniQ9A\np+RG1ASwXTWXIVq4MaIoqqoKIBqNLkPtNtM0bbalbmh+W1pciZBDhw7NKMSxKCxWHhwcnCeL\n4+TJkwAeeOCBzJ79+/d/4QtfyExI33XXXZkfGYYRDAZveDwLQQhhfzZKbc1N7j2nAk+9NfGS\nVq7NOOytiaMA3JI/bIyx6FkgYpVtEwvjllZ09GUAdt/Om7xxm82m63ouRphTItQd3gczF80k\nNTH1EBRFAWBZFntcyqVuCaAOZ3Trzmk5G6vhUTc52ncUXjkffJ69o0rUervlXdTrRSSoLjUe\nSX3R5CrSNG3OAFp2QHZMe2JcPls4kDpFKHYreU1n74LipGiLKaqdpV0CKG2Iubxm74U5IwaX\nzzDMuMOLmhbziQvfhoHLodeuRF41Pa/cXbenqNQowrthQjM1QKpU14+rR+smPsMm3FSXRaR4\nZoQN9t1KQwIvh8mYmRyNWe6p4cndcQB6oxTbIMBKQCxVikoTSQPITtB02orfndQBPX2LSq1S\nWKtpCcHZCiD1VNuBNrngGYHELKszpl2vfyVRW2QHASAV7Ch1bysFYEGQY94yJJJoqN3VULsL\ngE6haxqAO1Ug/X4UEg5bLPUCucPbJseO+ZQPsou2RK3uhkApgMSGzUZlaSEihgUI8FVAN6Cn\nH5nNheq1Ys95nz8TZFAA0EUhZLOvr4t4Sm7wl56dCW/spKEUbAe+F584HY8GiWjHWgIkpSq4\nABY9UxGQCdHo1HpNmvUvQEaN5Fic9Vdn5G4NgN4ox7axtdQGtGkJuKJ7q9oc6Bv9KAAbPh4P\nvglALtguFm4e8//G1Nh2rjMln9AVIIMGzCq5sEbTEvbCncloT+buJ4ePump+XQhb9rFUtoPZ\nGUkW2M3X3wLWgdDEPSXEW1jg/72R8/9MrWTqitQKDr7oLL1n4U9UvXNn5le+wbVdTxgN9t27\nCj/8RuCZkfilkXDPFluJAPO819Y+nFwfTPjpsRpnxekwBhL03FgiHHAB0K2YR6cAqjeo0VAE\nz4JFz0mJDPiujKDsZ4IdwPHCVBZ42XohygIqI4HrLS5VCwgRVGohntjhsr0mF2wz4J4MFgLw\n+BPXfW8oRe80AXPaYaLNs0ELng4PH2XFcESl0ExOAJQ9jbJnm0kKbMX3JXUQQZckaZ57WS9D\nFRC3Zrx9sN2ma1qezhYpisIC6EQiYVkLrT7OrbhlbaTC4uZMzgZbPjgjVeO9733vk2ksWD90\n6NBc6RzLjLVSuxx5lU1/ZlBqsXXTd5Z8MtNOqcqxwS66r72Rm2Row8nIJQDq7dRC5Yaxqs9m\nZXWeZzzPJbvAyFrfnTdwC9llNwrLFld4Ifu6tRtm+YvFandkt4P2leounzFPfbTMIv0G107W\nOO2Hl/7OpAZmq6bS5N4z7nhh1vEwRn0qAmBVzBiSpGI/66mxiLbq8yGp0gTz1LNbEtmPwj25\nPRF8XdBKU5cp0YgDAAgxq66zBNbpNRW75Z8+FziuqpTMWYYl1xz+O8Aqvk1MrRpPFI9RITUe\ns0aeUaBjJgpWjY4hGhUHp8quzUUt3MVKFQU6v0wtA4BatEd2VMmO1HMo2cts7gbaZGN3wRae\nAlCnt5+Mj72M6S8Q25YuJgBozj7iLQRARLvNu3naFRdWCy+jyTV1v5nfiCb3HWyjO/yKU4AP\nnS/6JQBFiWSDFn57gY+d3U73yGz6siQaBwCJoM5u1skQUme/U36prmDrGKYVnCmVUb+Y6UhJ\npqzFoGa+jYiq3bs5GhLZp+vFnmEy1KI9AKJjL8fGjgFwlr4jU4FblAtsnkWsxZcJtlyTol+p\noIpPud4S9u/fzxJR2tvb5z+yu7ubENLd3Z19MeO6V1+I5e5EeN999z322GNs+7HHHsskY6wK\n9a4dAAya7IlOWwU/rF2MGUEATZ49mZK0rO/0ksusSrYXLrSc2e3LNIXBdAC9OpXYG5xSIdtu\n8d5IScRMeQ1FtVT3gkpJZPjSC+pFiVat0a79DMJ6gGfW3asuy+awAHj8c0Zpmd7RdtFV5VwP\n4Njg95FqUb5mxsGN7p0R5aImpXpce4tn3qzlEVjZXfHKVGgl9hqwKACzfokC6HR9NPGqzm45\nR6SsR+EOb6OWbpusy+yhhh+A5fVRx/XX8BUUG/7pHQ3GVIdip86Cxb0HloriWStILkwvthAL\nn4g6zrNts042669TSjcT3QIQe/RU2bV5X2VBdsvuFgCRwacAiIrX5m5G1vmTbdBiiX2DwTp+\nI105JMPQhvRYX/bbTLqsA7ANFwFIlI5l9jumX3HW4hLzqHdvJ+kKKfXu1CC9SlmhrQrApciJ\n8USvlx59qlwEAIptQ+/fXLCxWQWA4SEJwKRkbQwlAZBaOxRCFcKaqAP4uU8ucbxtnEz7bLBz\n8bUp2FklYdxh920hghwakQEQMt8v/vzYs23EehOhNwDYfTuyXqBti61vuPuamStewO7WcPDg\nwTNnzlBKWaLL/v375zl4RouSrq6utrY2mnb06NGbH89yB9Cf/exna2trH3jggQceeKC2tvaz\nn/0s2//5z38+/ws/1zg2sfobF8PTKlayekOECA2uHZk+F6wb85JjbZkktSIzg3I7kM+cth35\nGZk781KYDNmfeVrsuZy9UxwdJoYBwKyoyvkQc4OANKXfSC3ehdaLzOZLB6yZjYUrSE8tF/gN\n2WY5vQYAQiDKFIBitxweE1kz0JmNzH2xilfZG9nT1U2ePQDY9HOmRXk21qM7oKaWGHpnewhs\nmll+LeF4IkriFjLV6+zELFmyKulmnQyAJKnzq5PSxWnvQ6JR9cmIcmrO3Jh5EAPqj6Kuf590\nfDcihK3MyAGo0Za1575mS5QDMMUIAClRC8Ca/mlQ6tYd/xURJqZ97SsMGVveGipIaAD0dG/5\ncdVecM0nkGVDiKgW7sD0cr/x8eMR9+ts26iVjJrUXDJ7Bq7dkF/VHE9EiUaReZUdglV8nVeZ\nNThk08923w4WjWVqEmfaH5o1EgDleML175PORycdY82C7AYgyO6CYFv9pS+MP/950jWaGYwQ\nMOlg0B6pBGDUTYX+mYbk7OrxiVOWPjl65guhq9/MHJOMXBx+/Q+zn4ro8C+GT3/e0IZU0VOh\nrkX6D0rmAPaX5WL4+MXI8SKcOO5FXBIBrB+92xHa9Ol+V0lSlAIygE6HsWfcAMDWaCKrut8x\nvzw2lgyQHQBkpErh7HCao2f+vO/ohwZf/X0jPpj91CVCbw6f+h+J0NkZTyn7BTesxqHAv06O\nSxMjEq7px7QomZeDvUwO/+7MHnXxDd53pD9gutNvjZ1L/2UwtwIefvjhRx55hG0/8sgj2Uvy\nZjh48OCMPZ2dna2tS9x4brkDaACf/exnWYZGJnoG8MUvfvG9733vjCPLy8uffPLJ/OnjLQlK\nnXMrgEuRaQE069pdoa5VRU+zpw0AIUKjKycpFukWKrdRB28Sj9t/+iPl5DHp/Cwd3Rjl2Ivy\n6yftP/1x9k6xvxcAFUWrbGaXvlWk2d0GwCUXVTlvpE9bJqFingYHc1Fdlt1lAvCV6Zl/3YUG\nuyl2EYCnyGAhdWZPZqNmfRyAINKqNRoA1WXanVOh3pqCqS/RMl9SZyu0VRbZasacvwQg26jL\nN1sA3ZAq1ay8FFdOJJCeRJxZb/jmmFUylQFA7tQd/zVtKZJyMmF7UXN8N8KatiyKfFqzvRCX\nupLKCc3+TEwYNQEk21QABGJBaA8ASsyo9zkA9niLRWBMb6Lp+H5YOabZj0xbU6X+JOa7GmNp\nr73F5wBYhIw71MzrsiJYkWwtcAI09R6IB46HPccBQCBmnWzWSFQCgER7aqVmol0FAIJEmx2A\nEKXKS3HlZALpANqoka7b/tPhn/rkqfpTbzNncfuMPak3UsSSupLy2aTzBzGWxeEseUfDlb8t\nGf5o0Zm75REVQHKPCgAUtl8Mp/6Grp16URxFu1nSiK/h/wNAzfjo2b8KdH1l6NQfsBbxAMYv\n/H3w8qPDr/9x+kp08NXfC1762kT3IQAt7jYA1Y5WVfRkbpbNyPRE3zgf+qWfHqPEuuixA2gM\nNp5/2VMzYP/giKMsKgEIiPGamImsAJo9NF0gx4rE1yZLw2gE0ED/g/10c+JooOv/REd+Odnz\n7YmL/5b91I2e+fPgla+z8o7ZXO5LBBaAYGDzW8edqS6nJTf+7pLUctlZx7ZFuUDxrHcU3wG2\n8sE/y5lhfjtdkAgA7EsnQN3BZ6BXP5aM0dzczC7u3bsXQEdHx6xHPvzww48++mj2znPnzq1f\nv8R9OfK6z3geavLs7gq/PGMGmlW5Z/lq6zx3fbDmCx65pNBWueT3Tk1NmzgNwOG/jRKgxYFe\nWBYAqb9H37R19mP6ewAIwQAiYRSmSoQK/b0ArLIKKq7ifo13lnwiZoY2FN197QTtQhCCjXdP\nBkfkiuYbWTi26a7IaJ9cvS4OoGFTXFZQUpMQZeouNCvTNyiI2Pz2cGhMKm9MzcL6SvU1u6KS\nQssbEoIAV6HhLdGJQIurpv2J3e5/78fWHBiL90im8+7S35h1AA81fuXNgheqS8aLy6RZ89j1\nbTZt0lJOasKEJV0xEm9Lh1bzpsYuFpUR+7hHOabJF5LCqClELMuVejnES0kAMKjYaxiNi0sa\nyU6qlk9qbMVTYpfd9Ank0lgy3AlqmWWGSF14CYJlCzdtwLqpptNC2BLGrRm3k0nkDTmHBovP\ni+1d/ae3hh2e6nqtqmUl186yqVkzGUyEO22etZYZS4TeTBTSid0XbE07LQcBEPu4RxwyEm93\nWIUiSdBEu0ptoB5Rb1UgEOXVhDBhipeSaLOz3ijmAtLcXRXv8a//n0asX7AVeetT3+oqnnWl\nW/6OWoY9nbKc3GknMUuIUBI05bd0YdQsa/qrYMH6Qt8nlbgLQNHYrxIqAUhutcmnNCFkqWe9\nAHRlQqxpytydaPOX7/jXZPRqYdNvBbr/jZpa6Oq3AYBasfHj7or7kU6MTkyes/RJQfYkI5fM\nxGhm/30Vn7NLri2+92Q/CrYCx6T6ibH/UpH4qOtbgfIHEUBxWIoHBRDsmVRkiwDwplN3SLPK\nFtElN8jCu51fMsSgLPxM+m8sMP01f0K39TvlypahjkzrF5aCzFDLiI+fBBAPnKDUzO56a0Zf\nKHL8fST5Gc24OzgiUXa/NxFAA6jY8ZVQ73dBLXfFewgRZUdt+fYvGYlA9uefBSqU8G8NuJzA\n75ahRAaA1jkrU3NL7NuBS98JXLr+cfP6aGHDxwobZuzs6uoC0NTUNNs1pvn1X//1p59+esbO\nw4cPt7W1sX4mAJak2gkPoBeHRcmT+uiwdrHU3ghgUh8Z1i4ifYIjRHhX+e/m6N614OvUSiLr\nW8LbgZjuxCb0Xp31ABKPCePpHMQrlzIBtNR7FYBZdb26CfnNLrofqPoTu32hDQiv5a/U/ZU3\n+LfNW6pnlp3ZHFbTtijbbt4enXYXVUl/1bSVtbUbUn/FG7bE0leZWXlKJPKDTX8KYHx8fK7T\nWaN7d6N7N+opMPtDoDLR7nXApPZn4+KVpDhsskSO66xIWzx9vWKWi/LfJAGIV3SrNbUoKZOY\nK125wQCayoTolBgAYLkFq1BI7rZjdxVQBUAALD1pvTIsmKphekVJmnF1AMKwQWIWdQgAhBGD\nRC0Ag7WPGGscZZu/hc1wwirDnJW/lodauJ1VK4sHjts8a7XAa+z7+uS9hcSTejL1DYq+QQGQ\n3JmehH57KvbR3uUgJmxHYtJVQxwyWCLHQj4mEUEpWvMH1+731v9G9kVqJ9p9TgDChCX/TQAU\n6liNtOHPlNcTQBiAYNkAWErSLBWNOlk5nSCmCEDz94M0Z9+Uu+oDbMPu2xofe5laqQ+WWuC4\nu+J+Pd6vx/oAgFraxKuOkndo6VwOLfgGNTWvUva+qj+dMdpKdb1DKogZIYMmAHzUL7RsseNs\nVKSWN5EI2O0sek4KtDGcAIBiGR4JLO1NJNqvqMaghT4kiQ1AuRD9nYbU/PeVM68AIKJKzXgi\n9CY140RUASRCZywzBsDSw8nJC7aCDZnBxAPHncp/OjyJnqG7WfSMm1hBmHquCnfO6K3rqVlE\nD5oZ3pdaOYKHlr6VGTefK4nwkcmZzT0Wa4+zeIFHdnZ2sqnojIMHD7a2tu7duzezfBDp2euP\nfOQjLPWZLSi8+RiaB9CL0+jaJRDRoual8HEWQF8Mn0j/KOezwmx+QpA99oIlTuXJZ2x2GYAQ\nCpJImLpmprOJA31I/ybQnivYtjN1cCwKwKxcrQnQ3MKZDQqejQsRqhxP1R8w666zIu0GWD7R\n8onChCldNvRWGwBh3BTCqYQE6bIOqAu/NSFKWRPy5G6b7cXU3LBRP8s5mchKrPCqa3St0iNm\nrwFMTX4jNeusr1OQCcphRlyv+Yr+cLGPMXcEyWUraNUmXo+PHfPWfYqdzUTFZ/MsNDfJqJds\nRyCELeWEBoCK03p3LxXLJ1heUQia0mVdX6+wxYIZUV8XhAqjXlJOp8Jivcac67shtWgPK9/B\nsIccH39l6tbGXnaUvINVJkWqSslrs865EiLUO7efDT3LLja6dyvrYQqCaFnFsVgg/QH7omp8\noD8JIFVXJMs20gWk1uluts4BOwFY+mRi8iwAb90nJy4eppYeD7zqKL4T0+uHxMZenhZAjx8D\n4Ctz949TUycA7M5Uuhd3m1trL/iAr+7mb2SBR7a0tGRfZMkb10bGTU1N2TvZNHZHR8eM4Hux\neAC9OHbRXWZvGYif7w6/ckfxx5DOhy60VeYiZ2OG2NgrANTC7Ytdlbx6EdMQhqY+zkoDfXrL\nzD+3LNc5pecK+39qupqQ1VuCg1s4o1oEAShYGrRZJtKlj6wAwKiVlAlT6snMOk9FV2KPDorr\npuTOPB5I7FGVVxJEp5g7J0GviGMU9rHKKKWZmoyZYQAQr+rpAFoHEHd2mWLckWfFLtXCXdrE\n6yyCZMs57L7tC3/KjGop9SqfTACwKmWam+Qso0ZUgqZ4VQcgXp02sTqpHnXSt2UH7lZz6Vyn\nY0fR7kDWRS34BjXj2vhUBiDb1gLZe16ZK2mh0bObBdBuyV9ibyAgYY/NG4wXxeJIT7j22pIb\nQiYA2jDzO6vGyHN2WqMRFcCG6M9ZAK1NvMpS0gvqPjXZ85iph+Ljr7AAOpYV6McDx32Nn2Hb\nZnI8Ge4GoPp3FPiNwKCMrGo/3G3uA766mw+gZ8Wyn7u7u+fJ4vjxj38MILvbYnNz89NPP32T\ngfJcbpc4bAk1uncCOBt69pfDX01acTYDXe9chqJyVJt4FWwheV4Sey5LnRcASJ3nxZ4rsCzp\n7Bvi8ODsR1uWfO5Nceg63/WQoUFimgAgigCE/l4SjcinXyPxuDARkN88RXQ9FUCzROehAehJ\nnH3DsMgJbwAAIABJREFUdvpVAJaviDUg5G5tVBWsUgkASVDkIH8jI1XPrt+wHYkJEZpKohAJ\nWGXioetPwpGYpbyiCSGLXddyC1aJaFZL6dufPYC2Gr0AZN1Hv/Fzs78XrNz1gJm5d+WNpHJC\ng0FZSknY/RoRFPv0msQrjlUr02M9RnwwHngV11SLmx91pmpupF7lJU1zz8a+vhB7DSFKxaGp\nlxjApOPl0bN/qXn6LMkAYAkJaW3LXLdj921jHw+IIAOglq4FT8cDJzJ7tIlThjbCSvuzPZlC\npddqSP+VqXdvZ62F4uUKgJJYrGViQrasgkTivVcDImvh0jhzBloPHF+bPMW2N0SeMeIDAGLj\nJ5D6HqDFXrgtewBa4OTUOAMnqaVP9nx77OxfjbzxCEutVgt3ZuLmWSvkcNwSYnEzy4RGevng\njMj4c5/7XKZQHTuyq6tr7969HR0d1/Ywz6xHvGE8gF60RvduAMHk4Lev/PFPBg72RE8DaPLk\nfKYnMdlpJieQXsyeb8hkyPHdb6o/fFw5/pL6w+86vvufyomX1KefUB//BsxZogq564L9xz9Q\nv/MoMeabupAG+gBQSdYbWwBIA732nz5l/9lTtud+pj7xuP0nP5KPvcCmqI11rQBgmuYLz9Hv\nfF0YWN0VoLnFyg6nrltR+IalaksbVO2I2Z+MsGg1uUlhAZZ45frzcGpHzPH9iPrdMDuYReRs\n8FQhZsXsc6rChjWUmAB8Z7aqjw6Albs2KYDkVhsAYcx0fDdif14TxkwAEfdrdu8mIt546nwu\nZMoHBa983dInsfiCQtnNcXIXQLNbJiaUo3FWbZo9yZQYUdfpQNf/6T/xUKzwMoC49yrkOd9s\nouKzedYAcJXdx8pgR4Z+warCeao+CMAyY8HLX2XxKNsTD5zIap83Tb1ru0gkZKcLNosAFNPc\nMjS8YWzsrp7e9/VFAVCngLKZo4qPH9+YPA5AtaKNxnn2DYCWKuu0EyDstWBlUvRYj6ENZUal\nx3onuv5l8NXfH+/80mTv9wBI9hLZWedL5z3f5ApCjluIffv2HThwgG0fOHBg3759C7zi3r17\n29raMiU7Ojo62traFrIecX48gF60rb73bPX9Kmtv8fzI11hXwkz559xhZ7pMOdV8I/X1sFoZ\ntuMvAYBl2U4cA0A0TRwZuvZ4secKAKLrwuB8k9BsdtkqrzSrawEIw0Ni7xUA0sVOYWwEgO30\na6zYc2LTNmqzAzBfOAKAiqJZU69vz6+vsLnc0drtRrNiVknJTQpLZsgFs0JKtquWVwQgd+rC\nsAHAaFFY4CstIICWunUA0mVD7J2qI5Hcreprlfj9jsxM5wzE7QnseDPhGADgCNbT8GQq19lO\ntL0Ofb1CVQGA7YXU2s2w+7U8/KSdKWAfvPxVAESQ2aznwml3pl/lLTZjba6ay5kVIlUIANvL\nGgDqFLR3O/R1SmDXWbGgAkAidKa//J9CBS+HdnTOf1NF6/6ns+TthS2/rxZuBxC6+nVKTQDe\nxn1EUAAEL30VgGQvc1d/CICZnEhMzn6bNtH5/upHNnrftaf4I6k9u8lIpStpFwHUh0MqOxOW\nSvH7nTPyYlhA/ED0G2+3j/2e9i8iNWJjr1Bqsu8B2Oq9VJkUPZQIv5VO1Ca+5lS12cDFfwNb\ngePdbPdt82/4AoDC8mR5Y6J6rVbg5zPQXM4dOnSotbWVtRJsbW1lzaoBtLe3X1v4eYajR4/e\nf//97LoHDhxYkkYqPAd60Wyic3/L13468OUf9P5lRA8AUEVPlSPnq/rYug1bQSubycg3Yl9q\nqR/isRkbYl+PWT4zQTyzNFDq62HB8SwoFfuuAjCqaqzqOgAwTZbRQTJd1uIxAFRWrPJKs6JK\nutxN2drB2vr4g7+2BA+MWyWsUinym57rH3fTYu9zymsV53+ESCy1fNCol8VBQ+w1rtvrWwhb\nwrgJgGU8I12j1/IJ0YeuM3jxw/dEdl+x/QsAwTr7lnR5DQCjTrbcQvQ3POqPo7Zfxln9jYRt\nIGEb9BfdSOvKXFOL9uixXjMRAGD3bhLExRUYs8qW5VUWiFkrS11J9nwadZLlEaKf9oh4Z1Ws\n+dJPtwM06DgSXH+kauO3578ld8X9rHSdWrQnOvJL9sBFpcju3Wj3bY2Pv5L+XnGPWrQrVaVk\n/Bibt77WveWfvbd8qn+CIBPlc3bjOJTvReSkyUau/V4BVciMzxaxsZcBlJt931kjjbzZNxlA\nfPxYInTGMiIAHMVtABxFu4igUCsZHzuWCJ0BYPO02DzrFFdDMnKJjdxT899KN/311AAEbLwr\nvLjnluNuwqFDhzJxc8as0fCMhYNYotJ12fgM9A3Kztmod20TSM4rDbMVhPb8m1VixIHehf+I\nxOPC2CjbFtKR9LWEiXEWKFtV1aa/mE0wz8oqr4AgWFk9JqzKmrkO5ribZNSImRk+VniOZWII\nE6YQnC8NekaEPU/OxqzE6lpdmQAgdE3OKIScnfYddr8GEDXPVhAy2fPi+VyOMzs/JDtvRHbU\nSPay1AUizKi8No/sB6sW7gBI9hJPh3+3IDpsng2YvqZwYUOdGl5m7nwGtlrR5m4WFS+73+Tk\n+ejQMwCIYLN7twAgop2V2ogHjqeWeBbumjHyfFuWynEriAfQN6jWuUVKf8hvyE3X7mxmYlSP\nXQXgWPD5ejllB8TXEnuvYvonP3GwP7NHHOhjuR+zXJGtDhQEs7wKhFw7jZ1hVFYDMLIq1hk8\n+5nLGaoKVkkqwGIFGTKBrNQzXwDNCjtkmFUShAWX7QBAiFbUD8DVVZsqhFw7bRhMxP267KwT\nlcJZb2NlqVlnMMdiVhAus+znc0axvEwSneJqEuWF1ttSC7dlepHYC3dk/k3t8e1AekklW9i3\ncFaxyEqAXzvUjFjgROZe2P1SagYvPwrA7t3IkkkyP4qNPp8IdyL9AmUv9LTnZQIhx60IHkDf\nIIkoNc5NbHsZEqAzFYXycwZaHBrA3F+OkHhcOvcmy1RmhKw5aZJIyK+flN86l/2f2HsFlIr9\nfQDMQj+12QBYc1d0tiqqAVhllRAEAFjl7bu5/JeZoWQbbB4agHg5ee3BJJkq0DFjBvoGlsHp\n1QYAWfMCgEgy5Tsst2AVpeKzsPu1vG1WqnjWCnKqlHtez0DXSOzPIxVhVk17mTKT6IvKMhck\nl+JJdRJm87hq0S5Wo0MQHbaCVqSXVOrRy4Y2soixEhg1mSous7yjTD2UDL+FdAtbm7tFVLwA\n2DLB7EfBBmZoI6y2HXuBMgs9ZUeVrOa8WivHrRY8gL5xje5dAAQi1rsWtw7mBsTHjyOPz18s\nDYOqDrO0HIBZVkFVFYBZ18hq1qpPP6F+/1uZ46X+XgBmbT2Ld+2/+In9ye9l/+f4zteVo8+l\nVhCmEzOMitSkslHXOG2DELOiEgCVZbBZ6rIKKuemDjDHAciKVKY26hVkNSbM5vqXoPsfJ5RX\nE+KAAUBvSb05F9KJegbaMtVaTfMOZn9fb9TLAEwxGnd0Lra6xbIhRGTzoLKjVrKXrvRw5kTt\nxCwVAZhVEp0elGbi/sXmM7D4lQiK3bcVgKgUKa5GAPbC7USQkDU/El9kFsdUJs9sH8m0wMns\ngHhG5sn03JKpbdHmV1wNSAXcPiy+ZArH3dp4AH3jdvkf9Mgld/g/ahdn9sZbculiQ3l6/koF\nxJXV+pYd1K7qW3Ykt+6E6kju3GNs2MRiaLGvh+hJADBNYbAfgFHXqG/cimuqMzLyuTeFiXEA\nRkVq4tmqrjXLKix/ceKevVaB16ypS979Tup06Rs2TRV73rkHqgM783H5FHcr0dcpll806qSs\nEs4SAHHAJMlp38YIQZNNP9uficKgABL3OM1y0ayQFtv6G4Cwbm3U1wXAEhLDJd/K/lFyu81S\njeGyb1Ni5vPkrq/+k6Li8zY8tNIDuY7EHSp1CMndM5de2L2b1aI9srPeWfauRd2gu+pDos3v\nrftkprygr+EhUfEV1H2CXZTVStlRhfSMycIlNytWgZBsVVh9mBnYF5iZgBhAQe3H2WJ0m2ed\ns+TuzJGSWu6ufAAAESRfw0OpHjdE8DY8JNoKb6a3NsfdepagG/gKMgwjGAzm9C4IIUVFRQDC\n4XAikcjpfc3FMmPdTzVRSy/d/EVvw6eX6mYLCgoSiYSmaTd7Q6bp+tL/JoaRePu9yZ13XPtz\nYXzM+dWvAIh96ONmfaMw0O/85n8AiH78IatilqwM+Y1T9p/+KHMxsu/3aYF3gWPxeDyKoiST\nycnJyRt5LPnKbrfbbLZQKLTSA1lKNpvN7XYDGB8fX9UnIkYYNjz/EAQQ/c2CgjvKA4GAZVkA\nlFMJx7enKhVQOwn9RdHCGxbOKjLwVP8rnwbQ8O7Xs7+VGjv/t+MX/kFUiprec34RTREXxu/3\nA4hEIktw0sgnHo9H1/V4prDPiho8+duTvd+z+7bWvv1nN3M7brfbZrPpuh4KhXpeeCA+9rK7\n4lcrdn9tqca5Umw2m6qquf67v8wURfF4PAAyJ41cY7/LS84wjCX8PVJVVZLyulJcXg+OY7TA\na9TSAah5mdcoDA+x/Oa51u1ZhUVQHYjHxIFes75RGugFQCXZKi2f9fjs7ifU7Vl49MxxK8gq\nkahDIDFLumog64PkjKQOo0a6+cg2U2FDC5yQK6cCaFa+Vy3aueTRM7c81MJdk73fS4TetIyo\nIDlv/gapldQCryFfO3BxtxJJklyuJSuze23vwHzDUzhWAZYPJ8gem3vtSo9lFtcNiEEIS8Ng\nmR6pzOay8lTz7WukAm4AWfkbHJfv0mu5xMvTSm3MWFaY6mV4c0RbseyoRbq6JUMtPRUq5XH+\nBjc/NktCLUObOLUkN6gF36BWAvm9ZJO7ZZCls9IP5fp4AL0KxMdPAFALt4Pk4+slsIC4tGyu\ngBgAS9UQBvuF4ISYTpie8xYJMdIV6yxejY5bPdhaLrFXR/prWGHCEoenFbbLFEy4SWxCUZs4\nmdmTmDxvmTFMrzvGrS6Kew2rUhIbOaLHrrL2JQCoNUt1l4XQAieRKva8cakGyXGzopQaSyf/\n8/p4Ckfeoxb7G5m3s0qpFYRV8zUuMSqrFYAkk85//zLbY847tWxWVkuXujB/nM1xeYatIyQa\npX0aXFCfitpeiIMCgFkuioMmBGLWLE19GLVw52TvdxOhM5YZY/382FLjTJEHbjUiRFQLd0SH\nj4x3fmm880uEiCUb/yoR6Qpd+Vb5zkPuivcs9gbZCkK7b2um2DPH5YhpmrdVDnQ+zmhy2RLh\nt8xkEPn6BZwQCpJoBNeLdK2KSuqaqlVC7eqc7bsBAGZTCwSBFnjNkrJ5DuO4vGLWSBAJANod\nB4VyMsGiZ6tYTPyKA4DeJFHb0nw16fDvAfuuP/Aq25NqVurbTATbfNfk8purbG9mm1IzeOUb\nk1cfo1Zisvd7N3Br7GNV3tYF57jVK6+jew7pekZEkNTC7Ss9llkIfT3AVJbzXKgoRT/zWSEw\nzi5aXt88fbkBmP6SyG89DJst1RiF41YDKhOzQhR7DdodF8olErMAxB506dvtVIJRI1kFS/Z+\nVtxrRLnA1EPx8eOO4rchvVgib7+q4hbI2/BpR8ndlhGODv1s7PwXE5Pn2f7FtvgGkAhfYj1Z\n8nP+heNWNR6d5Lv4+DEAtoLWJVmRveSkvh4AVpE/s+xvLlRWzNJy9t/80XPqeKeLSrwZCrfK\nsG4m9K2YeEkHAIHoW22sE4flExfXuHt+6XYY7BShx3qM+AAAtYgXQV/1FFeD3bvZXfn+7J2G\nNpKMXFrU7YSHXwQAIqiL7PnCcdx18QA637EMtrydVRIHegGYFTxTmeOATCu4CUN5PQHALBez\nmwUuLfa9fDxwklKTFbADCK9WdstQ3E2iUpS9Z7GT0OGRl8BaCcoFSzkyjuN4AJ3njPiAEetF\nVtnXvELicWF8DHNXgOa4241Zm/raRLyYxA0161449r28ZUSSk+dZrpfibhKVwtzdI7e8yIyC\nKrHxV+Y6dFbh4ZeQr38+OG614wF0zmkTp64+966JS/+R2RO68o2rz70rPvep0EyM9Tz/3u4f\nN1/+eTvboxbuyPlAF08c7AelAKxKXq2Z4wDAcgtW0dR5ldXlyBHVt5UIMoDY+PF44AQAuy8f\nTxTcDcu8oKzfJKtJtxCTAz9/7fE1Wugt8HcFx+UGD6BzLnj5q9rEqfELXwRSRQ3HLvydNnFq\n4uK/z3WVcP8T8fFjZjJoGREAirtFUiuWabiLIfT3AKAOp+Xlk14cl2I0p+uFicRozOEMNBFV\nW0ErgNjwL5KTF8CLLdxynCV3AyCi3df0WwAS4U4zObGQKw6d++d4qBOghIiO4jtzO0qOuy3x\nADrnWG0pMxFIhrsAGLFeIz6I9JL5ea6iuFtKt/5D2dZ/qmr7znINdnHYCkKzqgaroWkQxy0P\n7T0u8Tcr4h9yh3+nwHLn9hzLVkdEhp6h1EQeL5bgbozdt6X6zv+qvftpV/l9AECthUxCU2pG\nx44DKKz7cPXbfiQ7+DeE3C1i//79rE9he3v7rAd0d3dntzOc67AlwQPo3DK0IT16mW3Hxo8B\niI69nPpRfFCPXZ31WmxZvavsXd66TxXUfUJ25GWGsWkKgwPgvU44bjpqJ+QOj75HNatzXidU\n9bOaGxSAaPMr7qZc3yO3zBzFb7MVbJSd9ZK9FOm/DvNLhM6ayUkApet+m7el5G4ZBw8ePHPm\nDKWUNSncv3//tcd0dXW1tbXRtKNHj+ZuPDyAzi0tcGJqe/w4pi+jZjPNMxixXkMbQrpVb94S\nhgeJaQAweAkOjlshjqz1YY6iXQD/LuiWxdaMLmQdIfsrI4g2Z1E+dg/guBvz8MMPP/LII2z7\nkUceOXz48LXHdHZ2tra2Ls94eACdW9khMjvxscXyzKw1iWJT5ajyOp2RdfCmkmyV8maBHLcy\nRFux7Kxn27xZxq2NJbhrE6eolZz/SPZ3x+nfJkjqcoyM43Kvu7sbQHNzM7u4d+9eAB0dHTMO\nO3fu3Pr165dnSLwTYU5ER34ZGXiqsOVz2sRJAILstvSwHr2ajFxMhN/K7ImPnzC0ocBb/+Qs\nu9dZeg+7LktxU1z1eV6OilWAtsorIIorPRaOu305inaGopcB8C/rb22smAa1klrwjbnqMhna\n0Ni5v4mO/AKAu+SOZR0fxwHfHrG+M2Le5I18tET8WMnM6d2uri4ATU3XyVI7fPhwW1vbww8/\nzC6yZI8c4QF0Tgyf+u96rJed6QB4638j0PllgE50fQXUyuxJhC+Mnf9i6Mo3Jvt/1HT/Wfb1\nK5uBzvfJJErF3qvgFaA5bqWp/rZQz+NEVO3eLSs9Fi6H7N6NRLRTU4uPH58rgJ7oPhS6+i22\nXVB+1zKOjuMA4IpGjwStm7yRPZ6FJkd0dnayqWiGzVJ/5CMfYanPbEFh7mJoHkAvPT3er8d6\nAUz2fp9aOgBP1QfDvf+lx/tDPY8BEJWigpqPBTq/DGpN9jwOwEyMJiOXFFejpYeTk+cxPbUx\nDwnBCRKPA7Aqa1Z6LBx3W/NUPWjEB2zezURQrn80t2oRQVF922JjL2mB48DvzHoMW2Jo86zx\nN37cV/OrhnGzoQzHLcpaBz7gv9kvpdc6FnpkS0tL9sWmpqbscJlNV3d0dGQH2UuIB9BLLz6W\nWiVNrQQAUS6wedar/j167/fZHod/j+JuEm1+MzHG9gCIjx9TXI3xwIlUOarU4vo8Jfb3AgAh\nZgUvkMRxK4mI9qK1f7TSo+CWg1q0Jzb2UmzsZYBeu2CUmnEteBpAQf2nyzc+TIgI8ACaW1Yf\n8Isf8Ofklln2c3d393WzOJYNX0S49GYsDbQXbgcRslMy7IW7ADJjjpkt+2DtCUWbX3E1Lstg\nb5DY3wPA8hdTu32lx8JxHHdbYCvLzWQgGbl07U/jE6fYd56Ooryef+G4G8DiZpYJjfTywRlT\nyx0dHeSarhSZdYdLjgfQS29GmSF2yssOl1l9uhlZzizsZt1V1MKdeV6Ois1Am7yAHcdx3HJR\nC3cSIiI91TKDNv4KAEH22DzrlntkHJd7+/btO3DgANs+cODAvn37Zhywd+/etra2TGmOjo6O\ntra23M1Y8xSOG0An+36QDJ0V1Upv7ceIOK1OkGVEWE9dIshsMoAtnVY8awXJZRkRItjs3k0A\nHOkl8+zIZOSSoY1oE6cA2OdYILLixMsXpd4roFQIjAMweP4Gx3HcchFkt+JuTkxeiAdOuMrv\nCw/82FX2bliJUM/j1IxFhn4GQPVtBeFTY9wt6NChQ6wTIYB9+/YdOnSI7W9vb//IRz7yuc99\nDsDRo0czk9BtbW05baTCA+hFiw4fGTyR6n9DjcnCloezfxoPnGRJzJ7qB0NXv0MESS3cDoAQ\nUS3cER15zu7bwtb62LybiWCjVoIdCdDg5a9ZRhT5uoJQCAYc3/8WsjL0rSo+A81xHLd81KLd\nickL8fHjI288Mtn7vVjFESMxHB8/kX3ACg6P43Lq0KFDmbg5Y0aUnNPSddl4AL1osbEXp7ZH\nX5wZQI8fByAqPv/6PzUTE6r/DkFysh8VrvnvAPU1/y67SASlZOOfR4afLVr7x9Hh5wxtKHj5\nq2y/3ZeP5ajEnqugFIJgFpcCMGvrLW9eV6rmOI67xdgLd+Lyo8lwl5kYARAdfZ6aMQCys06U\nC0Sb31P7ays9Ro67LfAAetHirLkgEUCteOBVahlEmHoatXQSs2Qvq7zjP7Ov6PC3Ofxt2Xu8\nDZ/xNnwGgFq0K9z/pJkIID0znfvHsWhSfw8As7g09qnfXOmxcBzH3Y7S309SMxkEYOmTbH/l\nnq/z1GeOW048U2pxqKlpwdcBuCseAGAZkUTozNRPLZ19laYuchG0wz/VMsrpz9P2UUJfDwCz\nkuc9cxzHrQzZWSepFTN2irZCm2ftioyH425bPIBeHC34OrWSAHyN+9g8cTyraF0idNYyYwBU\n/+Ky0KYVuSvKxx6EJBoRghPgnVM4juNW1LVtCFXfjjwv3MRxtx6ewrE4bIJZEB1231a7b1N8\n/ERksEOylwmSw1F8lzZxEiyJuWDTom7W5lkviA7LjAFkrh6ty0wYHxPHRgBQUTRr68X+Praf\nV97gOI5bQWrhznD/k9P2pGs6cRy3bHgAvThsvtleuJ0Iklq4Kz5+Ijb6Ymz0RQCusvtYSTu7\nbzMRF9dehAiSvXB7bPQFxdUoKkW5GPmiiAN9jm9+NXPRLCkza+sBUE8B9RSs3Lg4juNud2r6\nW0pHyTtiI0dwTVcBjuOWAQ+gF4WyIhvs/OWpfjDU85iZGGM/i47+UpQLAKg3dC7z1n0yETrj\nbfj00o32xomXuqZdHBkiCQ18+pnjOG6l2bybVf8dRnyobMv/7nv546LsyZPvLbnbnCRJLpdr\nqW7t2p6C+YYH0IuQmOw0kwGk1wjaCjY23X8egDZx6upz76KmZpgaFr+CkHFXfcBd9YElHe+N\nk/p6ABgta7V77nd95R8BCKEgALOKJ0BzHMetJELEmrelUjjq73lpZQfDcdnyP+pdQjyAXgRW\noo61RMnebytoJaJKzTgAgKh5uQpwEUxTGOwHYFZUU6fLKvCy6BmAxQNojuM4juOuQSk1TXOp\nbk0UxTwPx3kAvQgsAVrxrBOkaV9SEEFWfdtiY0cBKK5GUVnd7UWE4SFiGACMymoAVmUNC6Cp\nzW76S1Z4cBzHcRzH5R/TNOPx+FLdmqqqkpTXMSovY7cIsbFXADj8s2RoZLqn3gJtVKWBXgBU\nkq3ScgBGuvCzWV6J/P44yHEcx3Ectwx4AL1QRmJMj14BYPdtv/anmaSOW2Axh9DfC8AqLYMo\nArAqq9l+i7dQ4TiO4ziO4wH0wkVHjwEUU51Up1H9d4i2QiLaHaXvWPahLTGpvxdZ6wVNf4nl\nLYQgGI0tKzoujuM4juO4vJDX+SV5heVvSGq55Ki+9qeC5Gq49wSlxqpPgA4FSTQCwExPPIOQ\n2Kd/CwmNOpesPA3HcRzHcdzqxQPohYqOHsW8JeoE2bOMw8kVofcqABAyFUADVJIg8eiZ4ziO\n4zgO4CkcC2QZsfjEadxok5RVhOVvWEV+aldXeiwcx3Ecx3H5iAfQCxIZPUktHYDDv+qLbMxP\nHOhFdv4Gx3Ecx3FcHti/fz8hhBDS3t5+M8csiVWfwmGz2ZbhXiZHXgYgSE63fwsRVuuTJnS/\nJf70KWhx2tBsvO/DgiBIkpR5AoXL3WLHj8jEOABSU788T+ySEwSB/btKxz8XSZJuyQfFNhRF\nWdmRLC1W/N9ms1mWtdJjWXrZJ41bw4wz4a3hVj0TyrJ86z2o7DMhpTTXd7eEvU6W2cGDB8+c\nOcOeovb29v379x86dGjGMfv371+/fj07Zv/+/e3t7UePHs3ReMgyvFq5Y5rmMoxfkiRq6ZMj\nJxORnsK6B3N9d7lj/fu/0CuX2Law7/ekhiZKaeZvvPX/DtOuCwAgCMIf/C/iW5WrIVnvoqXt\nh5QPBEEghNxiD4oQIooiAMMwVnosS0ySpFvyQQGwLOsW+2AgimL2mfDWcKueCQkhgiDceg9q\nOc+Euq6rak5SNA3DyGkjFULI008/vXfvXgAdHR3333//jAiwu7u7ubm5q6urqanp2otLbrVO\npjKU0mAwmNO7IIQUFRURQRacrYLUnOu7yyHTdPX1ZPqgxC+cU2vqEomEpmkAYFmunssE0Nes\nT27fbREBq/ORejweRVF0XZ+cnFzpsSwlu91us9lCodBKD2Qp2Ww2t9sNIBQKrepP8jOwk8bk\n5OQtFpP5/X4AsVgsddK4VXg8Hl3Xl/APfz5wu902m80wjFvvpKGq6ir+QzwbRVE8Hg+AZTtp\n5CiAzqnu7m4Azc3N7GImjGYbTFdXV1tbWyZcbmpqyulfltUdQHMLJwwPsgbd1OEksajY35v9\nU3F8lCQSAPStOyyeAM1xHMdx3CL1dcp9nfJN3khVi17Vos/Y2dXVBWD+ueTOzs7W1lY2Oc3J\nBgYGAAAahUlEQVT28ACaWwJ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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d.met4 %>>% gather(start, q, -nstep) %>>% \n", " ggplot(aes(x = nstep, y = q, group = start, colour = start)) + \n", " geom_line() + \n", " scale_colour_discrete(labels = c(\"0.1\", \"0.3\", \"0.4\", \"0.45\", \"0.5\", \"0.6\", \"0.7\")) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.3.3 この定常分布は何を表す分布なのか?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "この例題では,定常分布 $p(q | \\boldsymbol{Y})$ は 尤度 $L(q)$ に比例する確率分布で,\n", "\n", "$$ p(q | \\boldsymbol{Y}) = \\frac{L(q)}{\\sum\\limits_q L(q)} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "定常分布を返す関数を `MCMC.metropolis` class に追加する" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " object generator\n", " Inherits from: \n", " Public:\n", " doMCMC: function (start, nstep) \n", " clone: function (deep = FALSE) \n", " st.dist: function () \n", " Private:\n", " generate_step: function (q, L) \n", " Parent env: \n", " Locked objects: TRUE\n", " Locked class: FALSE\n", " Portable: TRUE" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "MCMC.metropolis$set(\"public\", \"st.dist\", function(){\n", " vlogL <- sapply(self$vq, function(x){super$logL(x)})\n", " data_frame(vq = self$vq, st.dist = exp(vlogL) / sum(exp(vlogL)))\n", "}, overwrite = TRUE)\n", "MCMC.metropolis" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [], "source": [ "mcmc.metropolis.st <- MCMC.metropolis$new(data)\n", "dd <- mcmc.metropolis.st$st.dist()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`q` のヒストグラムを密度にする関数" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "met.freq.q <- function(vq, q){\n", " lcount <- hist(q, breaks = seq(min(vq) - 0.01 * 0.5, max(vq) + 0.01 * 0.5, 0.01), plot = FALSE)$count\n", " data_frame(vq, dens = lcount / sum(lcount))\n", "}" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width = 10, repr.plot.height = 3)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "\"Removed 58 rows containing missing values (position_stack).\"Warning message:\n", "\"Removed 58 rows containing missing values (geom_path).\"" ] }, { "data": { "image/png": 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UL8t19VprxfEaGpBYOmFgyaWjCmx2Z9EQBgJdiXvQYNGogdRHw9e/aMiYl5+PDh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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gp1 <- ggplot(data = d.met1, aes(x = nstep, y = q)) + geom_line() + ylim(c(0.25, 0.65))\n", "gp2 <- ggplot(data = met.freq.q(mcmc.metropolis$vq, d.met1$q), aes(x = vq, y = dens)) + \n", " geom_bar(stat = \"identity\") + \n", " geom_line(data = dd, mapping = aes(x = vq, y = st.dist)) + \n", " xlim(c(0.25, 0.65))\n", "grid.arrange(gp1, gp2, ncol = 2)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "\"Removed 58 rows containing missing values (position_stack).\"Warning message:\n", "\"Removed 58 rows containing missing values (geom_path).\"" ] }, { "data": { "image/png": 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Xq9JSUl7a7HZrO1OwBVaO57JwiC5mIOP+DgQ1tV6OTT5sD6ioqKfAmMl1BCNoOl\nuvgy9NLTN9AUo+Tmm2+Wvjye7415PB7K7ubOndu/f3/G2BtvvHH48GFpBxKLxfLiiy8yxkRR\nrKmp4VnBqFGjpFU5HI6jR4/Onz9fc9PqdGb8K8b7hcpIP0QlH2hcfXlDUltbS4Nmcd62A2WA\nSsosWLAgMzOT/kMsLS2lzBCgQ3r77bcZY127dv3hD3+odiztYbFYunfvziTzqwNoQqxbCPmg\necbY3LlzFy9e7DuOory8PDc3F//nhYT3TIuHSSzo6lDanZK1lRBK2w9bWlrq6+uTkpKiF2E4\nnE4n5auyNs/U1FQaCcm+nwxXV1fzy+WsrKxPPvlE+hJ64HA4zp8/z+Lj44Pg+GcUKH8LNSGM\nqy9vSLQbeTxosy8oL5Ofn5+Xl8f/38zPz6fHJCkpiVZsI126dPGdwThURqPRbDb77eEfnywW\ni8lkam1t1VDMVqvV6/U2NTWpHYhSNptNp9M1NTU1NzdHaRdut5sWdp80aVJDQ0OU9tKmML9B\nWVlZFRUVTqdz+/bttBqzQjqdjtoG6+rqtDJPqV6vT0pKCv83J2ZMJpPFYtHQwteMMbPZbDAY\nIrIymd1uD/SnWCeESgbWl5eXZ2ZmxjgwrePXnfFwq74dXUZlTeHV1dVxmxBKBxBKtxuNxsTE\nRLockb533kIoCIJs1hBeBi2EGtLmGoPS7EhJo19cfXlDot3IY4zyuuAzwQQqs3fvXsYY/4/y\nV7/6lWxSGaPROGLECF6+oaEh/CtpnU4niqJszuR4ZjabGWNer1dDMXu9Xm0FTLc7oxrz5s2b\n6cdk8uTJKh6ZMHfdq1cvs9nc3Nz89ttvhzQGhA8S83g8Ho8nnBhihs4KDZ3G/CBrKGaDwaDT\n6aIdcEy7jAYaNC8rVlZW1qdPn1gG1gHEz5VZfX09DYejSWX4krLBE0LZuEfV30UQ0ilGZX/i\nCZ60dbSqqopeYrPZunTpEqi8rHKIW20mhNLtbre7zavz+PnyhgqrayhEyRvvI0r/60lnlFFY\nBqBjoyXds7OzNX3m63Q6uvm7du1aGnAOEP9i2kKoZGA9Y2zz5s25ubnLly+np9K+MYyxhQsX\n0jQGjLGePXuGP8KQMhaz2Ww0GsOsKmZ0Oh313Pif//mf1tbWKVOm8KbkxsbGIC3CMVBbW0sP\nevbsmZaWRtOHsksJocVioVu5MiaTSfr0rbfeysrKeuqpp3g+qQo6znQ8jyBFONYAACAASURB\nVBw58uKLL3bp0oV3SerTp4/sUKelpdFiEl27du3Tpw/1IF22bBlNIupwOHr27Ckt37VrV6oh\nPT2dttTV1UXk47NarRqar5Lu2Kl73jLGKioqFixY8NOf/nT48OFBivH/4Ddt2tS/f/8ZM2Z8\n+umn69evf/rppynhl/UB83q9Qd7akSNH+HokTU1NUT0IdJz9TkFZUlKycOFC/vTXv/517969\n26yQ37B0Op3RiJx//cOfYsHvgjexlJeXt2bNGrrMXbNmTV5ensIy9JQPr/CdVAagY3A6nVu2\nbGGM3XXXXWrHEq6srKyjR4+6XK4NGzb8+Mc/VjscgLapP8toeXm579Tbo0ePpjGENMGMNCc8\ncuQIb1TMycmJVBan1+s1NAUtWb58+d/+9jfG2KFDh3gHy5qaGnUzW94tOz093Wg0OhwO2kKN\nYIGOs9FoTElJ4e0Mb775JmMsLy/v2muvjVHcgdHxfOGFF9avX883CoJAb1BaskePHt988w1j\nrFevXhaLpWvXrufPn+eDBtPS0mQX2T179qQaevXqRVuqq6sj8vGFP+987Km+kN2SJUsWL178\nzTfffPrpp0GK8bP0xIkTs2bNys/PnzVr1sGDBzMyMp5++mlegLoMMcacTmeQBQZfeOGFEydO\n8Jpj8OX1e5z/9Kc/LVu2jD8VBIF+W4Lj40Yidd4GEn7lqg/ImTlzJk2oxhjLy8vjXUDnzp07\nevRomqM1UJmCgoL8/PzNmzczxjDAHjqqgoKC5uZmQRBoeXdNS0lJcTgcVVVVq1atQkIImqD+\nVaNsYH1GRoY0/aP7oNL1moYNG8b713Xr1i38wc0mk0kQBI/Ho/oVg3KUVpWWltLT06dP876I\nlZWV0RvwrcTZs2fpgc1ma25uTk1NLSkpYZdaCIMc5yVLlnz00Udvv/02b3Y4efLk4MGDYxF0\nAHq9nvfblq0jb7PZvF6v7FA/++yzGRkZgiA8/PDDzc3NDz300Pz58/lfU1NTBw0a9Oyzz545\ncyY9Pb2qqmrq1KlUwwMPPLBt27Y9e/ZcvHgxnI9PEARqa21paVG9SUQ5g8EgCILqHfrLysoY\nY7R+VJBilZWV/LEoiiUlJadPn6aX0wupQL9+/YqKihhj586dC1Kh9LyK9pfXaDSKouh3aAq9\nd2lUSiI5d+4cPaiurm5qaop4e75Op6NU0O12hznzsCiKqt/ymzlzpu+YeVl257cM8+kpA9Dx\nUH/RESNGKOmeEP+ysrKqqqo+/fTTkpKSIPcEAeJETBNCJQPr2yRdYcnj8YQ/dsXhcAiCoGSo\nT/wwm81Wq5XmpWTfn/7+/PnzvNOmKs6cOUMPTCZTbW0t70hGs4w2NTUFmlRt7NixY8eO3bhx\nI7/KLC8vV/e90Mx1FMOFCxekf0pJSfGNLScn5+WXX6bHtbW1l112mfSvycnJtbW1s2fPlm6k\nSpKTk2+77TZKCMN5yzqdjhLvxsZGGsmpCYmJiTqdTt3Pml1Kb9r8CPj3jpSUlFBD2blz5+iF\nVKBv376UEJ45cyZIhdLzitcQJXQXw+9MZbLTW+HPCP+qtra2nj59OuIroBqNRvoBqaurC/8G\nh+YWfAPoPEpLSz///HPGWIdpT+vbt+/BgwebmprWrFnz//7f/1M7HIA2xLSPlpJB83v37qUO\nM1JKpufuhPgUFLW1tfEzuwMFYDKZEhMTmWTmleCTynDSqTtVfy9SsmCUrBAqKxP8cpkKu1wu\nDbVUdzD0EdfX1wdvq5TNr11aWkqNV7I1GHr16kWtW8FPY+lfVZy5WzafjcKvXpwEDwBat3bt\nWlEUTSbTxIkT1Y4lMoxG42233cYYW7lyJf5bh/gX60E7NGieHvsdWD9s2LDc3Fw+SnDv3r0Y\nQB8Ivxrzer38seoTFfI1J+ipdKk9JS+Pz4SwtbVV1mCi5O3IMsDgCSH91ev14sJaLXTqiqIY\n/MSTfcVOnjwp287X4aTPNMhXUnZeqfjllb1lhZFIiylZYAMAwJcoinRlOG7cuIh3NFDRfffd\nxxgrLy+Xrj8MEJ9inRDOnDkzMzMzPz8/Pz8/MzNTOrC+sLCQHi9YsGDevHlUZs2aNRhAH4jf\nK7CampowB9uEia4Reb7EHwRfmJ6TJlrxc4lZU1Mj67GmpIVQljQGzyH5X1VP6TutNteTYIyJ\noij7gL777jvZq/hXgD7TIB+o7LxS66OX3lEKKRLpgcJ5CwDts2/fvuLiYtaB+ouSG264gcZD\nrlq1Su1YANqgwrR+M2fOLCgoKCgokA6dX7BgAU2zRgouQTYYhN92DI/H8+c//3n06NFHjhyh\nLbNnz77tttv4YgnRRteFfOhgqF1GpZPXx08LoW8kSu5iypLG4PPy8wofeOCBn/zkJ7yHycKF\nC2+44QbeDBXc119/ffnll+fm5tLo/HYoKioaPXr00qVL2/dy7fJ6vXyC3CCNtF999ZWsQym/\n9VteXn7zzTcXFxfTID273U6fePCEUPrU5XK1e6RcQUFBdnb2VVddNXbsWJrsVDnf/brd7sce\ne6xfv36///3vfcu/9957119//fXXX79//36+0e+39R//+If0twgAwNe///1vxpjD4bj11lvV\njiWSdDrdvffeyxjbuHFj/NzgBvBL5Xneod34+u++/vSnPxUVFa1bt44xduHChZUrV3755Zcx\n67FA14U8/evfvz9jrFevXlarVcnLpXlj/LQ5+EaSk5PT5qtMJlNmZiZ/SociEJ49Hj58eOvW\nrQcPHqSnS5YsOXLkyH/+8x8lca5evfrIkSNHjx5td0a3du3aoqKi1157rX0v1y6n08mToiAn\nHu/xPmrUKNmfPB7PwYMHV65cSU30qampdDIHua8h21Fra2u7Owy//vrrTqezoqLim2++ef31\n10O6AeQ3wtWrV9fV1S1evNi3x8E//vGPEydOnDhxQvoT5PegLVmypKioaO3atcqDAYBOpaWl\nhZZ0mjhxomxF4g7gvvvu0+l0brebLskA4pb6y05A+0hnFpWhaeXp+kzWjS0GZGMIb7rppnfe\neUc232YQ0pa3OEwIFy5cqNPprFbr+PHjlbzw3Xff/fbbbxljycnJQ4cODVIyJSWFFrKnp/TB\n8Qwh1C587b4ZSTsKcnZ1VNKkKMjRpgN70003rV+//o477ti5c6esAO9BqmQMIf/TM888Q21x\nNTU1SnojBwqMUL9WvjZpm3gYL730Unp6+qJFi+ikZYy1tLS4XC5Z47bf08NvVklR4dY4AATy\n8ccf00/K6dOnZ82apXY4Eda7d+8f/OAHn3zyyapVq6ZOnap2OAABoYVQq9q8xqKLPH6pF7NL\nfFkLoU6nGzdunPKEUHo1HD8JIR1tQRDuueee++67T/mNzKysrIkTJ06cOPHmm28OXtJoNEqv\n4GmPvNlK4SW1klFwSmpobGwMtDpIRyU9YkGOHh2f7t27p6SkDBo0yLeANCFscwwhP6/GjRvX\n5q6Dk70wpO8OL0znam5ubvCqguR+Um63m3rPxs8XGQDiDQ1wsNlsfDnlDoamljlw4ADv+AMQ\nh5AQahW/xqKp7aUPCF208WIxm7tS1kIYqvicZZSOns1mMxii2Kg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C6FtV8I0pKSnSCVT9Dqf03SMAdAazZs2SPt22bRtjzOFwBOlk3oFN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EhFCj0YwbN06C+AAAAgW76Sajfv8Aga2m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\nVtfd3Nx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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gp1 <- ggplot(data = d.met2, aes(x = nstep, y = q)) + geom_line() + ylim(c(0.25, 0.65))\n", "gp2 <- ggplot(data = met.freq.q(mcmc.metropolis$vq, d.met2$q), aes(x = vq, y = dens)) + \n", " geom_bar(stat = \"identity\") + \n", " geom_line(data = dd, mapping = aes(x = vq, y = st.dist)) + \n", " xlim(c(0.25, 0.65))\n", "grid.arrange(gp1, gp2, ncol = 2)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "\"Removed 58 rows containing missing values (position_stack).\"Warning message:\n", "\"Removed 58 rows containing missing values (geom_path).\"" ] }, { "data": { "image/png": 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Mpc/SERoudCwlwGR95d+aNHM7WFscQ5DyQQdQQTt0T3XIII9q5oJWgR78yRL0xP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CczvLli2rrq6ePHkyycwpJgg5Piu6ZtLh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\nIjOpDADEA6zrPB6PR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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gp1 <- ggplot(data = slice(d.met3, seq(1, 100000, 100)), aes(x = nstep, y = q)) + geom_line() + ylim(c(0.25, 0.65))\n", "gp2 <- ggplot(data = met.freq.q(mcmc.metropolis$vq, d.met3$q), aes(x = vq, y = dens)) + \n", " geom_bar(stat = \"identity\") + \n", " geom_line(data = dd, mapping = aes(x = vq, y = st.dist)) + \n", " xlim(c(0.25, 0.65))\n", "grid.arrange(gp1, gp2, ncol = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* メトロポリス法で得られた `q` のヒストグラムが定常分布になっている\n", "\n", "ということは,\n", "\n", "* `q` は定常分布からランダムサンプリングして得られた\n", "\n", "と解釈できる.\n", "\n", "つまり,\n", "\n", "* MCMCアルゴリズムは定常分布からのランダムサンプリング\n", "\n", "をしている" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.4 MCMCサンプリングとベイズ統計モデル\n", "例題をベイズ統計モデルとして考えてみる" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ベイズの定理\n", "\n", "$$ p(B | A) = \\frac{p(A|B)p(B)}{p(A)} $$\n", "\n", "* $p(B)$: 事象$A$が起こる前の事象$B$の確率(事前確率)\n", "* $p(B|A)$: 事象$A$がおきた後の事象$B$ の確率(事後確率)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "条件付確率の定義より, $p(B|A)$,$p(A|B)$ はそれぞれ次のように書ける\n", "\n", "$$ p(B|A) = \\frac{p(B, A)}{p(A)} $$\n", "$$ p(A|B) = \\frac{p(A, B)}{p(B)} $$\n", "\n", "$p(A, B) = p(B, A) $ なので\n", "\n", "$$ p(B|A) \\times p(A) = p(A|B) \\times p(B) $$\n", "\n", "したがって,\n", "\n", "$$ p(B | A) = \\frac{p(A|B)p(B)}{p(A)} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 例題をベイズの定理に当てはめる\n", "\n", "データ$\\boldsymbol{Y}$ が得られた時の種子の生存確率$q$が知りたい: $p(q|\\boldsymbol{Y})$(事後確率) \n", "\n", "ベイズの定理に当てはめると,\n", "\n", "$$ p(q|\\boldsymbol{Y}) = \\frac{p(\\boldsymbol{Y} | q) p(q)}{p(\\boldsymbol{Y})}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "右辺の各項についても当てはめていくと,\n", "\n", "* $p(\\boldsymbol{Y}|q)$: ある生存確率$q$のもとでデータ$\\boldsymbol{Y}$が得られる確率: 尤度 $L(q)$\n", "* $p(q)$: データ$\\boldsymbol{Y}$がない時の$q$の確率分布(事前分布,不明)\n", "* $p(Y)$: $q$ がないときに $\\boldsymbol{Y}$ が得られる確率.つまり,すべての$q$についての$p(\\boldsymbol{Y}, q)$の和で,\n", "\n", "$$\n", "\\begin{align}\n", "p(\\boldsymbol{Y}) &= \\sum\\limits_q p(\\boldsymbol{Y}, q) \\\\ \n", " &= \\sum\\limits_q p(\\boldsymbol{Y} | q) \\times p(q) \\\\\n", " &= \\sum\\limits_q L(q) \\times p(q)\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "したがって,\n", "\n", "$$ \n", "\\begin{align}\n", "p(q|\\boldsymbol{Y}) &= \\frac{p(\\boldsymbol{Y} | q) p(q)}{p(\\boldsymbol{Y})} \\\\\n", " &= \\frac{L(q) p(q)}{\\sum\\limits_q L(q) p(q)}\n", "\\end{align}\n", "$$\n", "\n", "となり,p. 185 の式になる" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "つまり,事後分布は,\n", "\n", "$$ p(q|\\boldsymbol{Y}) \\propto L(q) p(q) $$\n", "\n", "となっており,$L(q) p(q)$ に比例している.\n", "\n", "いま,定常分布は,\n", "\n", "$$ \\frac{L(q)}{\\sum\\limits_q L(q)} \\propto L(q) $$\n", "\n", "となっており,$L(q)$ に比例している.なので,$ p(q)$ = (定数)なら求めたい事後分布がMCMCサンプリングによって得られたということになる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.5 補足説明\n", "### 8.5.1 メトロポリス法と定常分布の関係\n", "\n", "メトロポリス法で得られた$q$のサンプルが定常分布$p(q|\\boldsymbol{Y})$からのランダムサンプリングであるためには以下の二つの条件が成立していなければならない\n", "\n", "* $q$が任意の初期値から定常分布 $p(q | \\boldsymbol{Y})$ に収束する(エルゴード条件)\n", "* ある$q$が$p(q | \\boldsymbol{Y})$にしたがっていて,メトロポリス法で$nq$ を得たときに,$nq$ も$p(q | \\boldsymbol{Y})$にしたがっている(詳細釣り合いの条件)\n", "\n", "$$ p(q | \\boldsymbol{Y}) p(q \\rightarrow nq) = p(nq | \\boldsymbol{Y}) p(nq \\rightarrow q) $$\n", "\n", "今回の場合は両条件ともに成立している" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 詳細釣り合いの条件の確認\n", "* $L(q) < L(nq)$ のとき\n", "$$ p(q \\rightarrow nq) = 0.5 \\times 1$$\n", "$$ p(nq \\rightarrow q) = 0.5 \\times \\frac{L(nq)}{L(q)} $$\n", "\n", "両辺割って,整理すると,\n", "\n", "$$ L(nq) p(nq \\rightarrow q) = L(q) p(q \\rightarrow nq) $$\n", "\n", "定常分布が \n", "\n", "$$ p(q | \\boldsymbol{Y}) = \\frac{L(q)}{\\sum\\limits_q L(q)} $$\n", "\n", "であることを用いると,\n", "\n", "$$ p(nq | \\boldsymbol{Y}) p(nq \\rightarrow q) = p(q | \\boldsymbol{Y})p(q \\rightarrow nq) $$\n", "\n", "---\n", "\n", "* $L(nq) < L(q)$ のとき\n", "\n", "$$ p(q \\rightarrow nq) = 0.5 \\times \\frac{L(nq)}{L(q)} $$\n", "$$ p(nq \\rightarrow q) = 0.5 \\times 1 $$\n", "\n", "であり,同様に,\n", "\n", "$$ p(nq | \\boldsymbol{Y}) p(nq \\rightarrow q) = p(q | \\boldsymbol{Y})p(q \\rightarrow nq) $$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 詳細釣り合いの条件を満たす推移確率ならば定常分布に収束するかどうか\n", "\n", "定常分布 × 推移確率 = 定常分布なら収束しているが,\n", "\n", "$$\n", "\\begin{align}\n", "p(q | \\boldsymbol{Y}) &= \\sum\\limits_q p(q \\rightarrow nq) \\times p(nq | \\boldsymbol{Y}) \\\\\n", " &= \\sum\\limits_{nq} p(nq \\rightarrow q) \\times p(q | \\boldsymbol{Y}) \\\\\n", " &= 1 \\times p(q | \\boldsymbol{Y}) \\\\\n", " &= p(q | \\boldsymbol{Y})\n", "\\end{align}\n", "$$\n", "\n", "となり,これは成り立つ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### ある定常分布に収束させるには\n", "\n", "定常分布がわかっている場合,詳細釣り合いの条件を満たすように推移確率を決めれば,定常分布に収束させることができる.\n", "\n", "定常分布が$ p(x) $のとき,メトロポリス法の推移確率は,\n", "\n", "$$ \\prod_{x \\rightarrow x'} = \\mathrm{min} \\left(1, \\frac{p(x')}{p(x)} \\right)$$\n", "\n", "であり,いま,定常分布が $\\frac{L(q)}{\\sum\\limits_q L(q)}$ なので,推移確率は,\n", "\n", "$$ \\mathrm{min}\\left(1, \\frac{\\frac{L(nq)}{\\sum\\limits_q L(q)}}{\\frac{L(q)}{\\sum\\limits_q L(q)}} \\right) = \\mathrm{min}\\left(1, \\frac{L(nq)}{L(q)} \\right) $$\n", "\n", "となり,モンテカルロ法のときに設定した $r$ と一致する." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.6 まとめ\n", "\n", "* 最尤推定法は尤度最大となるパラメータを探索する\n", "* MCMCアルゴリズムは定常分布からのランダムサンプリング\n", "* ベイズ統計モデルで考えると,定常分布は事後分布とみなせる" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考資料\n", "* [可視化で理解するマルコフ連鎖モンテカルロ法(MCMC)](http://d.hatena.ne.jp/hoxo_m/20140911/p1)\n", "* [http://bin.t.u-tokyo.ac.jp/summercamp2015/document/prml11_chika.pdf]()\n", "* [http://www.smapip.is.tohoku.ac.jp/~smapip/2003/tutorial/textbook/koji-hukushima.pdf]()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Session info -------------------------------------------------------------------\n", "Packages -----------------------------------------------------------------------\n" ] }, { "data": { "text/plain": [ " setting value \n", " version R version 3.3.2 (2016-10-31)\n", " system x86_64, mingw32 \n", " ui RTerm \n", " language (EN) \n", " collate Japanese_Japan.932 \n", " tz Asia/Tokyo \n", " date 2016-11-24 \n", "\n", " package * version date source \n", " assertthat 0.1 2013-12-06 CRAN (R 3.2.1) \n", " Cairo 1.5-9 2015-09-26 CRAN (R 3.2.2) \n", " colorspace 1.2-7 2016-10-11 CRAN (R 3.3.2) \n", " crayon 1.3.2 2016-06-28 CRAN (R 3.3.1) \n", " DBI 0.5-1 2016-09-10 CRAN (R 3.2.5) \n", " devtools 1.12.0 2016-06-24 CRAN (R 3.3.1) \n", " digest 0.6.10 2016-08-02 CRAN (R 3.3.1) \n", " dplyr * 0.5.0 2016-06-24 CRAN (R 3.2.5) \n", " evaluate 0.10 2016-10-11 CRAN (R 3.3.2) \n", " ggplot2 * 2.2.0 2016-11-11 CRAN (R 3.3.2) 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