11 Kullback-Leibler information.ipynb

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   "source": [
    "# 11 Kullback-Leibler情報量\n",
    "\n",
    "黒木玄\n",
    "\n",
    "2018-06-24～2019-04-03, 2023-06-22\n",
    "\n",
    "* Copyright 2018,2023 Gen Kuroki\n",
    "* License: MIT https://opensource.org/licenses/MIT\n",
    "* Repository: https://github.com/genkuroki/Calculus\n",
    "\n",
    "このファイルは次の場所できれいに閲覧できる:\n",
    "\n",
    "* http://nbviewer.jupyter.org/github/genkuroki/Calculus/blob/master/11%20Kullback-Leibler%20information.ipynb\n",
    "\n",
    "* https://genkuroki.github.io/documents/Calculus/11%20Kullback-Leibler%20information.pdf\n",
    "\n",
    "このファイルは <a href=\"https://juliabox.com\">Julia Box</a> で利用できる.\n",
    "\n",
    "自分のパソコンに<a href=\"https://julialang.org/\">Julia言語</a>をインストールしたい場合には\n",
    "\n",
    "* [WindowsへのJulia言語のインストール](http://nbviewer.jupyter.org/gist/genkuroki/81de23edcae631a995e19a2ecf946a4f)\n",
    "\n",
    "* [Julia v1.1.0 の Windows 8.1 へのインストール](https://nbviewer.jupyter.org/github/genkuroki/msfd28/blob/master/install.ipynb)\n",
    "\n",
    "を参照せよ. 前者は古く, 後者の方が新しい.\n",
    "\n",
    "論理的に完璧な説明をするつもりはない. 細部のいい加減な部分は自分で訂正・修正せよ.\n",
    "\n",
    "$\n",
    "\\newcommand\\eps{\\varepsilon}\n",
    "\\newcommand\\ds{\\displaystyle}\n",
    "\\newcommand\\Z{{\\mathbb Z}}\n",
    "\\newcommand\\R{{\\mathbb R}}\n",
    "\\newcommand\\C{{\\mathbb C}}\n",
    "\\newcommand\\QED{\\text{□}}\n",
    "\\newcommand\\root{\\sqrt}\n",
    "\\newcommand\\bra{\\langle}\n",
    "\\newcommand\\ket{\\rangle}\n",
    "\\newcommand\\d{\\partial}\n",
    "\\newcommand\\sech{\\operatorname{sech}}\n",
    "$"
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    "<h1>目次<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Kullback-Leibler情報量の基本性質\" data-toc-modified-id=\"Kullback-Leibler情報量の基本性質-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Kullback-Leibler情報量の基本性質</a></span><ul class=\"toc-item\"><li><span><a href=\"#KL情報量の定義\" data-toc-modified-id=\"KL情報量の定義-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>KL情報量の定義</a></span></li><li><span><a href=\"#KL情報量の正値性\" data-toc-modified-id=\"KL情報量の正値性-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>KL情報量の正値性</a></span></li><li><span><a href=\"#KL情報量の凸性\" data-toc-modified-id=\"KL情報量の凸性-1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>KL情報量の凸性</a></span></li><li><span><a href=\"#KL情報量が-$L^1$-ノルムの2乗を上から押さえること\" data-toc-modified-id=\"KL情報量が-$L^1$-ノルムの2乗を上から押さえること-1.4\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>KL情報量が $L^1$ ノルムの2乗を上から押さえること</a></span></li><li><span><a href=\"#KL情報量の使われ方\" data-toc-modified-id=\"KL情報量の使われ方-1.5\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>KL情報量の使われ方</a></span></li></ul></li><li><span><a href=\"#多項分布のSanovの定理\" data-toc-modified-id=\"多項分布のSanovの定理-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>多項分布のSanovの定理</a></span><ul class=\"toc-item\"><li><span><a href=\"#Sanovの定理とその証明\" data-toc-modified-id=\"Sanovの定理とその証明-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Sanovの定理とその証明</a></span></li><li><span><a href=\"#Sanovの定理の使い方1\" data-toc-modified-id=\"Sanovの定理の使い方1-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Sanovの定理の使い方1</a></span></li><li><span><a href=\"#二項分布の場合\" data-toc-modified-id=\"二項分布の場合-2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>二項分布の場合</a></span></li><li><span><a href=\"#Sanovの定理の使い方2\" data-toc-modified-id=\"Sanovの定理の使い方2-2.4\"><span class=\"toc-item-num\">2.4&nbsp;&nbsp;</span>Sanovの定理の使い方2</a></span></li><li><span><a href=\"#連続的な確率分布の場合\" data-toc-modified-id=\"連続的な確率分布の場合-2.5\"><span class=\"toc-item-num\">2.5&nbsp;&nbsp;</span>連続的な確率分布の場合</a></span></li><li><span><a href=\"#正規分布による近似\" data-toc-modified-id=\"正規分布による近似-2.6\"><span class=\"toc-item-num\">2.6&nbsp;&nbsp;</span>正規分布による近似</a></span></li><li><span><a href=\"#多項分布の中心極限定理\" data-toc-modified-id=\"多項分布の中心極限定理-2.7\"><span class=\"toc-item-num\">2.7&nbsp;&nbsp;</span>多項分布の中心極限定理</a></span></li></ul></li></ul></div>"
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Base.MathConstants\n",
    "using Base64\n",
    "using Printf\n",
    "using Statistics\n",
    "const e = ℯ\n",
    "endof(a) = lastindex(a)\n",
    "linspace(start, stop, length) = range(start, stop, length=length)\n",
    "\n",
    "using Plots\n",
    "#gr(); ENV[\"PLOTS_TEST\"] = \"true\"\n",
    "#clibrary(:colorcet)\n",
    "#clibrary(:misc)\n",
    "default(fmt=:png)\n",
    "\n",
    "function pngplot(P...; kwargs...)\n",
    "    sleep(0.1)\n",
    "    pngfile = tempname() * \".png\"\n",
    "    savefig(plot(P...; kwargs...), pngfile)\n",
    "    showimg(\"image/png\", pngfile)\n",
    "end\n",
    "pngplot(; kwargs...) = pngplot(plot!(; kwargs...))\n",
    "\n",
    "showimg(mime, fn) = open(fn) do f\n",
    "    base64 = base64encode(f)\n",
    "    display(\"text/html\", \"\"\"<img src=\"data:$mime;base64,$base64\">\"\"\")\n",
    "end\n",
    "\n",
    "using SymPy\n",
    "#sympy.init_printing(order=\"lex\") # default\n",
    "#sympy.init_printing(order=\"rev-lex\")\n",
    "\n",
    "using SpecialFunctions\n",
    "using QuadGK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Override the Base.show definition of SymPy.jl:\n",
    "# https://github.com/JuliaPy/SymPy.jl/blob/29c5bfd1d10ac53014fa7fef468bc8deccadc2fc/src/types.jl#L87-L105\n",
    "\n",
    "@eval SymPy function Base.show(io::IO, ::MIME\"text/latex\", x::SymbolicObject)\n",
    "    print(io, as_markdown(\"\\\\displaystyle \" * sympy.latex(x, mode=\"plain\", fold_short_frac=false)))\n",
    "end\n",
    "@eval SymPy function Base.show(io::IO, ::MIME\"text/latex\", x::AbstractArray{Sym})\n",
    "    function toeqnarray(x::Vector{Sym})\n",
    "        a = join([\"\\\\displaystyle \" * sympy.latex(x[i]) for i in 1:length(x)], \"\\\\\\\\\")\n",
    "        \"\"\"\\\\left[ \\\\begin{array}{r}$a\\\\end{array} \\\\right]\"\"\"\n",
    "    end\n",
    "    function toeqnarray(x::AbstractArray{Sym,2})\n",
    "        sz = size(x)\n",
    "        a = join([join(\"\\\\displaystyle \" .* map(sympy.latex, x[i,:]), \"&\") for i in 1:sz[1]], \"\\\\\\\\\")\n",
    "        \"\\\\left[ \\\\begin{array}{\" * repeat(\"r\",sz[2]) * \"}\" * a * \"\\\\end{array}\\\\right]\"\n",
    "    end\n",
    "    print(io, as_markdown(toeqnarray(x)))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kullback-Leibler情報量の基本性質"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KL情報量の定義\n",
    "\n",
    "一般の確率分布についても定義可能だが, このノートでは簡単のため, 有限集合\n",
    "\n",
    "$$\n",
    "\\Omega=\\{1,2,\\ldots,r\\}\n",
    "$$\n",
    "\n",
    "の上の確率分布のみを扱う. $p=(p_1,\\ldots,p_r)$ が $\\Omega=\\{1,2,\\ldots,r\\}$ 上の**確率分布**であるとは\n",
    "\n",
    "$$\n",
    "p_i\\geqq 0 \\quad (i=1,2,\\ldots,r) \\qquad \\sum_{i=1}^r p_i = 1\n",
    "$$\n",
    "\n",
    "が成立していることであると定める. \n",
    "\n",
    "$\\Omega=\\{1,2,\\ldots,r\\}$ 上の確率分布 $q,p$ に対して, $(q,p)$ の**Kullback-Leibler情報量** $D(q||p)$ を\n",
    "\n",
    "$$\n",
    "D(q||p) = \\sum_{i=1}^r q_i\\log\\frac{q_i}{p_i} = \n",
    "\\left(-\\sum_{i=1}^r q_i\\log p_i\\right) - \\left(-\\sum_{i=1}^r q_i\\log q_i\\right)\n",
    "$$\n",
    "\n",
    "と定める. ただし, $x\\log y$ は $x=0$ のとき $0$ になり, $\\log 0 = -\\infty$ であると約束しておく.  Kullback-Leibler情報量の $-1$ 倍を**相対エントロピー**と呼ぶ. \n",
    "\n",
    "記述の簡単のため以下ではKullback-Leiblerを**KL**と略記することにする. さらに, $q,p$ は $\\Omega=\\{1,2,\\ldots,r\\}$ 上の確率分布であると仮定する."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KL情報量の正値性\n",
    "\n",
    "**KL情報量の正値性:** $D(q||p)\\geqq 0$.\n",
    "\n",
    "**証明:** $x\\geqq0$ に対して $f(x)=x\\log x$ とおく. ただし, $f(0)=\\lim_{x\\searrow 0}f(x)=0$ と約束しておく. $f'(x)=\\log x + 1$, $f''(x)=1/x>0$ なので $f(x)$ は下に凸な函数である. 期待値汎函数 $g(x)\\mapsto E[g(x)]$ を\n",
    "\n",
    "$$\n",
    "E[g(x)] = \\sum_{i=1}^r p_i g(q_i/p_i)\n",
    "$$\n",
    "\n",
    "と定めることができる. ゆえにJensenの不等式より,\n",
    "\n",
    "$$\n",
    "E[f(x)] \\geqq f(E[x]).\n",
    "$$\n",
    "\n",
    "そして,\n",
    "\n",
    "$$\n",
    "E[f(x)] = \\sum_{i=1}^r p_i\\frac{q_i}{p_i}\\log\\frac{q_i}{p_i} = D(q||p), \\quad\n",
    "E[x] = \\sum_{i=1}^r p_i\\frac{q_i}{p_i} = \\sum_{i=1}^r q_i = 1, \\quad\n",
    "f(E[x]) = f(1) = 0\n",
    "$$\n",
    "\n",
    "なので $D(q||p)\\geqq 0$ を得る. $\\QED$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KL情報量の凸性\n",
    "\n",
    "**KL情報量の凸性:** $D(q||p)$ は $q$ の函数として下に凸である.\n",
    "\n",
    "**証明:** $\\Omega$ 上の確率分布 $q,q'$ と $0<t<1$ が任意に与えられているとする. $f(x)=x\\log x$ とおくと, $f(x)$ は下に凸な函数である. ゆえに\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "D((1-t)q+tq'||p) &= \\sum_{i=1}^r p_i f\\left(\\frac{(1-t)q_i+tq'_i}{p_i}\\right)\n",
    "\\\\ &\\leqq\n",
    "\\sum_{i=1}^r p_i\\left((1-t)f\\left(\\frac{q_i}{p_i}\\right)+tf\\left(\\frac{q'_i}{p_i}\\right)\\right)\n",
    "\\\\ &=\n",
    "(1-t)D(q||p)+tD(q'||p).\n",
    "\\qquad \\QED\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "**注意:** $f(x)$ は強い意味で下に凸なので $D(q||p)$ も $q$ の函数として強い意味で下に凸になる. このことより, $q$ の函数としての $D(q||p)$ の最小値を与える $q=p$ とは異なる $q\\ne p$ において $D(q||p)>0$ となることがわかる. より精密な結果については次の節を見よ. $\\QED$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KL情報量が $L^1$ ノルムの2乗を上から押さえること\n",
    "\n",
    "$q=p$ ならば $q_i\\log(q_i/p_i)=0$ より, $D(q||p)=0$ となる.\n",
    "\n",
    "* 黒木玄, <a href=\"https://genkuroki.github.io/documents/20160616KullbackLeibler.pdf\">Kullback-Leibler情報量とSanovの定理</a>\n",
    "\n",
    "の第5.3節で次の不等式が証明されている:\n",
    "\n",
    "$$\n",
    "D(q||p) \\geqq \\frac{1}{2}\\left(\\sum_{i=1}^r |q_i-p_i|\\right)^2.\n",
    "$$\n",
    "\n",
    "これより, $q\\ne p$ ならば $D(q||p)>0$ となることがわかる. 特に $D(q||p)=0$ と $p=q$ が同値であることがわかる.\n",
    "\n",
    "さらに, 確率分布の列 $q^{(1)},q^{(2)},\\ldots$ について, $k\\to\\infty$ で $D(q^{(k)}||p)\\to 0$ ならば $q^{(k)}\\to p$ となり,  確率分布の列 $p^{(1)},p^{(2)},\\ldots$ について, $k\\to\\infty$ で $D(q||p^{(k)})\\to 0$ ならば $p^{(k)}\\to q$ となることもわかる. $\\QED$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KL情報量の使われ方\n",
    "\n",
    "KL情報量 $D(q||p)$ は確率分布 $q$ と確率分布 $p$ の違いの大きさを表す指標としてよく使われる.  一般に $D(q||p)\\ne D(p||q)$ であるが, そうなることには必然性がある. 「KL情報量の意味」は下の方で説明する**Sanovの定理**を見ればわかる. Sanovの定理はStirlingの公式を知っていれば容易に証明可能である. Stirlingの公式を理解しておけば「情報理論」「統計力学」「統計学」などなどで基本的なSanovの定理をすぐに理解できるようになる. \n",
    "\n",
    "* 階乗に関するStirlingの近似公式 $\\longrightarrow$ KL情報量に関するSanovの定理\n",
    "\n",
    "という経路をできるだけ早く踏破しておいた方が数学の応用について楽に考えることができるようになると思う. \n",
    "\n",
    "統計学へのSanovの定理の応用については赤池弘次氏による以下の2つの論説を参照せよ:\n",
    "\n",
    "* 赤池弘次, <a href=\"https://www.jstage.jst.go.jp/article/butsuri1946/35/7/35_7_608/_article/-char/ja/\">エントロピーとモデルの尤度(〈講座〉物理学周辺の確率統計)\n",
    "</a>, 日本物理学会誌, 35巻 (1980) 7号, 608-614\n",
    "\n",
    "* 赤池弘次, <a href=\"https://ismrepo.ism.ac.jp/?action=pages_view_main&active_action=repository_view_main_item_detail&item_id=32568&item_no=1&page_id=13&block_id=21\">統計的推論のパラダイムの変遷について</a>, 統計数理研究所彙報, 27巻, 1号, 5-12, 1980-03\n",
    "\n",
    "さらに\n",
    "\n",
    "* 黒木玄, <a href=\"https://genkuroki.github.io/documents/20160616KullbackLeibler.pdf\">Kullback-Leibler情報量とSanovの定理</a>\n",
    "\n",
    "も参照して欲しい.  「<a href=\"https://genkuroki.github.io/documents/20160616KullbackLeibler.pdf\">Kullback-Leibler情報量とSanovの定理</a>」の第10節には平均符号長とKL情報量の関係も解説してある.  「情報量」という呼び方の由来はそちらを見た方が分かり易いかもしれない. $\\QED$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 多項分布のSanovの定理\n",
    "\n",
    "1回の試行で $\\Omega=\\{1,2,\\ldots,r\\}$ から $i$ を取り出す確率は $p_i$ であるとし, $k_i$ は非負の整数であり, $k_1+k_2+\\cdots+k_r=n$ を満たしているとする. このとき $n$ 回の独立試行で $1,2,\\ldots,r$ のそれぞれが $k_1,k_2,\\ldots,k_r$ 回取り出される確率は\n",
    "\n",
    "$$\n",
    "\\frac{n!}{k_1!k_2!\\cdots k_r!} p_1^{k_1}p_2^{k_2}\\cdots p_r^{k_r}\n",
    "\\tag{$*$}\n",
    "$$\n",
    "\n",
    "になる. この式における階乗の分数の因子はそれぞれ $k_i$ 個の $i$ 達を全部で $n$ 個順番に並べる方法の総数に等しいので, **多項係数**と呼ばれる.  $(k_1,\\ldots,k_r)$ 全体の集合上の確率分布 ($*$) は**多項分布**と呼ばれる."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sanovの定理とその証明\n",
    "\n",
    "**Sanovの定理:** $n\\to\\infty$ で $k_i$ 達が $k_i/n\\sim q_i$ ($i=1,\\ldots,r$) のように振る舞うならば, $n\\to\\infty$ で\n",
    "\n",
    "$$\n",
    "\\frac{n!}{k_1!k_2!\\cdots k_r!} p_1^{k_1}p_2^{k_2}\\cdots p_r^{k_r} = \n",
    "\\exp\\left(-nD(q||p) + o(n)\\right).\n",
    "$$\n",
    "\n",
    "すなわち\n",
    "\n",
    "$$\n",
    "-\\log\\left(\\frac{n!}{k_1!k_2!\\cdots k_r!} p_1^{k_1}p_2^{k_2}\\cdots p_r^{k_r}\\right)\n",
    "= nD(q||p) + o(n).\n",
    "$$\n",
    "\n",
    "**証明:** $k_i/n\\sim q_i$ という仮定より, $k_i=nq_i+o(n)$ である. $q_i$ は固定されているので, $n$ が大きくなると $k_i$ も $O(n)$ のオーダーで大きくなる. だから, Stirlingの公式\n",
    "\n",
    "$$\n",
    "n! \\sim n^n e^{-n} \\sqrt{2\\pi n}, \\quad\n",
    "k_i! \\sim k_i^{k_i} e^{-k_i} \\sqrt{2\\pi k_i}\n",
    "$$\n",
    "\n",
    "を使用できる. ゆえに, $k_1+\\cdots+k_r=n$ を使うと, \n",
    "\n",
    "$$\n",
    "\\frac{n!}{k_1!k_2!\\cdots k_r!}\n",
    "\\sim\n",
    "\\frac{n^n e^{-n} \\sqrt{2\\pi n}}\n",
    "{k_1^{k_1} e^{-k_1} \\sqrt{2\\pi k_1}\\cdots k_r^{k_r} e^{-k_r} \\sqrt{2\\pi k_r}} =\n",
    "\\left(\n",
    "\\prod_{i=1}^r\\left(\\frac{k_i}{n}\\right)^{k_r}\n",
    "\\sqrt{(2\\pi n)^{r-1}\\prod_{i=1}^r\\frac{k_i}{n}}\n",
    "\\right)^{-1}.\n",
    "$$\n",
    "したがって, \n",
    "$$\n",
    "\\begin{aligned}\n",
    "%&\n",
    "\\frac{n!}{k_1!k_2!\\cdots k_r!} p_1^{k_1}p_2^{k_2}\\cdots p_r^{k_i}\n",
    "&\\sim\n",
    "\\left(\n",
    "\\prod_{i=1}^r \\left(\\frac{k_i/n}{p_i}\\right)^{k_i}\n",
    "\\sqrt{(2\\pi n)^{r-1}\\prod_{i=1}^r\\frac{k_i}{n}}\n",
    "\\right)^{-1}\n",
    "\\\\ &=\n",
    "\\exp\\left(\n",
    "-\\sum_{i=1}^r k_i\\log\\frac{k_i/n}{p_i}\n",
    "-(r-1)\\log n-\\log\\sqrt{(2\\pi)^{r-1}\\prod_{i=1}^r\\frac{k_i}{n}}\n",
    "\\right).\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "これに $k_i/n=q_i+o(1)$, $k_i = nq_i + o(n)$ を代入すれば示したい結果が得られる. $\\log n$ や定数の項は $n$ で割って $n\\to\\infty$ とすると $0$ に収束するので, それらは $o(n)$ の項にまとめられることに注意せよ. さらにKL情報量の定義が\n",
    "\n",
    "$$\n",
    "D(q||p) = \\sum_{i=1}^r q_i\\log\\frac{q_i}{p_i}\n",
    "$$\n",
    "\n",
    "であったことも思い出して計算せよ. $\\QED$\n",
    "\n",
    "要するに多項分布にStirlingの近似公式と $k_i=nq_i+o(n)$ を単純に代入するだけで, Sanovの定理が得られる."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sanovの定理の使い方1 \n",
    "\n",
    "有限集合 $\\Omega=\\{1,2,\\ldots,r\\}$ から確率 $p_i$ で $i$ を選ぶ独立試行を $n$ 回行った結果, $i$ が $k_i$ 回取り出されたとき, $\\Omega=\\{1,2,\\ldots,r\\}$ 上の確率分布 $(k_1/n,\\ldots,k_r/n)$ を**経験分布**と呼ぶ.  Sanovの定理における $k_i/n\\sim q_i$ ($n\\to\\infty$) という条件は, $n$ を大きくしたとき**経験分布が確率分布 $q$ に近いこと**を意味している. だから, Sanovの定理は $n$ が大きなとき\n",
    "\n",
    "* (確率分布 $p$ のもとでの独立試行の経験分布が確率分布 $q$ に近い確率) $\\sim\\exp\\left(-nD(q||p) + o(n)\\right)$.\n",
    "\n",
    "が成立することを意味している. \n",
    "\n",
    "$o(n)$ は $n$ で割ると $0$ に収束する量なので, $n$ が十分に大きなとき $-nD(q||p)$ と比較すると無視できるほど小さな量になる. ゆえに, $n$ を十分に大きくすると, 異なる $q$ ごとの「経験分布が $q$ に近くなる確率」の大小関係をKL情報量 $D(q||p)$ の大小関係で測って良い状況になる. $D(q||p)$ が小さな $q$ ほど相対的に経験分布が近くなる確率は高くなる. \n",
    "\n",
    "経験分布が確率分布 $q^*$ に近くなる確率で経験分布が確率分布 $q$ に近くなる確率を割った結果は\n",
    "\n",
    "$$\n",
    "\\exp\\left(-n\\left(D(q||p)-D(q^*||p)\\right) + o(n)\\right)\n",
    "$$\n",
    "\n",
    "のように振る舞う. $D(q||p) > D(q^*||p)$ ならばこの確率の商は $n\\to\\infty$ で $0$ に収束する.  そのとき, 経験分布が $q$ に近くなる確率は経験分布が $q^*$ に近くなる確率と比較すると相対的に無視できるくらい小さくなる.\n",
    "\n",
    "確率分布の集合 $A$ が与えられているとする. ただし, $A$ の内部の閉包が $A$ 閉包に一致するような「良い集合」のみを考える. 例えば $r=2$ (二項分布のとき)で $0\\leqq a<b\\leqq 1$ のとき $A=\\{\\,(q_1,1-q_1)\\mid a\\leqq q_1\\leqq b\\,\\}$ はそのような「良い集合」の例になっている. (「内部」「閉包」の意味を知らない人はこの例を思い浮かべておけばよい.)\n",
    "\n",
    "$q$ が $A$ 上を動くとき, $D(q||p)$ を最小にする $q\\in A$ を $q^*$ と書く. \n",
    "\n",
    "このとき, 経験分布が $A$ に入るという条件のもとでの条件付き確率分布を考えると, $q^*$ 以外の $q\\in A$ に経験分布が近くなる確率は $n\\to\\infty$ で $0$ に近付く. これは、経験分布が $A$ に入るという条件のもとでの条件付き確率分布が $n\\to\\infty$ で $q^*$ に台を持つデルタ分布に近付くことを意味している. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二項分布の場合\n",
    "\n",
    "$r=2$ の二項分布の場合を考える. このとき, $q_1=q$, $q_2=1-q$, $p_1=p$, $p_2=1-p$ と書くと,\n",
    "\n",
    "$$\n",
    "D(q||p) = q\\log\\frac{q}{p} + (1-q)\\log\\frac{1-q}{1-p}.\n",
    "$$\n",
    "\n",
    "**問題:** この函数は $q=p$ で最小値 $0$ になることを自分で確認してみよ. $\\QED$\n",
    "\n",
    "次のセルのプロットを見ればわかるように $D(q||p)$ は $q$ の函数として $q=p$ で最小になり, 下に凸な函数になる."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xt69e11cXG7evKkHg/MAaMSxLOZtdyXvodOdLRQAwD+tSKBXB+jAtRka6Nu3b9++fRs0rly5Uj4dGBgYGBio3qAA0DflYnSnGB8bouQEoWv5BgCAEELoZDZTLUGTPGAVBgA04VgWM8yZNFX2yABkHAB0j5RBy+8z3wdROnCrCQCAJuxPY6Z0Uv5fPBQNAOiebamMhwUa1h5KBgBAEzKqcHoVVkWKgGMaANAxFRK09iEdMxJWXgBA035PZyZ5KO1+E/XBSAMAOubbh3SEK+lrA8MMAIAmYIQOpONoFeybQDDSAIBuyajCe14wj6N046LRAAD1u1mE+RTqaauS7QoYaQBAl8y/Qy/vTjnBlQsAAM34PZ15XzXDDAiKBgB0SEwBfl6JPvaB1RYA0DSRDP2RxUz2VNXuS8g+AOgGKYPm3aY39aV4unS7HACAWh3NZIIdyHYmUDQAYNg2JTOeFmi0Cxz/CABo1s7nzEddVJgl4EBIAHRAvhCvf0zfHQsrLACgWakVOLcGjXJR4XAAjDQAoAM+ucvM60p1NIdhBgBAs7Y/Y6Z5EZQq8wRsuACg7S4V4Eel+MBAOJYBANAsMY0OZTD3xqj2bx1GGgDQarUyNPcWvTWY4kPNAABo3olspqct4abi8UgoGgDQal8/pHvZE8OdYccEAKAl21KZmV1U/p8OuycA0F7J5XjHM+ZRFKynAICWPCzFuTUowlXlRQOMNACgpRiMZt6kv+1Nqe6UawCAftj6lJnlTXJU/5cOWzAAaKltqQyHQNM7Q2UPAGhJuRj9kc08e0sdt6SBogEAbZRTg1c9oOMiODDIAABo2e4XTIQrKTBWx3vBRgwA2mjmTXqRL9XZEmoGAEBLGIy2PWXmquuWNFA0AKB1fnvBFNeihb6wegIA3uBcHmPHR4H2atrAgN0TAGiXQhFefp++NJLDhZoBAPAmPzxhFnRTX7KAtASAdpkRR8/2JrvbwI4JAMAbPC7D6VVovLv6/sphpAEALbL7OVMgQid7wNUfAQBvtv4xM78bqc5RSRhpAEBbFAjxygR6/wAKdkwAAN6oUITP5zEfqvesbEhOAGgFjNDUWPqTbpQv7JgAAChgSwoT3Ym0MlLrm8LuCQC0wpYURiRDS/ygjgcAvFm1FO1+ztwdq+4/cSgaANC81Aq8Jom+HcGhYJQBAKCAHc+Yoe3Jjiq+p2VjUDQAoGEyBr1/g/6uN9XJMC7lVFBQcPLkSZIkx48f7+Dg0GSf5OTky5cvUxQ1YMAAPz8/NUcIgJaTMuinFObkUA0cMQ1joQBo2OeJtJMJYSD3mMjIyOjevXtKSsqDBw+6d++en5/fuM9PP/00ePDg58+fp6en//LLL+oPEgAtty+N6WqN/O00sJkBIw0AaFJsEd6XxiRFquNOM9rgxx9/HD9+/LZt2xBC0dHRW7ZsWbduXf0OL168WLFixYMHDzp37qyhGAHQagxGPzxhtvXTzInZBrFxA4B2KhejKdfpXf05Dmq504w2+OuvvyIiItjpiIiIv/76q0GH06dPDxkyhMPhHDp0KCEhQe0BAqDt/shmrIzQACfN7M2EkQYANGbWLfptd2KUi0EcysB6+fKlk5MTO+3k5FRYWNigQ2ZmZlZW1jvvvBMcHLxixYrx48dv3LixhRkWFRXt27fv9u3b7EMrK6tFixYRBCEWizkcDkHo9mdL07RYLKYonb/Yl1gsNjJS76mBKiAWixFCmv06MELfJJGfd2fEYrqVc8BYLBZzuU2MbnK5XJJ8w1ACFA0AaMa2VCa9Cv8+0LDWQYIgMMbsNMa48Z86TdNFRUXZ2dmmpqaLFy/29PScO3dux44dm5shSZKmpqZWVlbsQ2Njgxm0AQbpXB7CCI1y1lgAhpWwANASyeX4y0Q6LoJjZGB7CB0dHYuKitjpoqIi+aiDXLt27by9vU1NTRFCrq6uAoEgPT29haJBIBC89dZbkZGRDdqlUimPx9ODkQaEEI/H03QgbSWRSPRgKWia5vF4mh1pWJci+9Kf5PNafxQUxlgmk7X66zCwjAWAFhDK0IQr9A99qM6GcY5lfcOHDz9z5gw7febMmREjRrDTz549q62tRQiNHDkyLS2NHQcuKip69epVCxUDAAblfB4WydDYDpr844aRBgDUbe4tuq+AeM/TEEv2BQsW9OnThyAIqVR6+fLl+/fvs+2+vr5XrlwJDQ0NDAwMDg4OCwsbOnTo8ePHP/zwQ09PT83GDICWWPuQ/tKfJDW6raGqtJWYmDhr1qzg4OD333+/uT4XL1709va2srIKDw8vLi5WUSQAaJU9L5iEEvxTsM4f2tY6Hh4ejx8/9vPz692796NHj5yd/7tv9sSJE127dmWnjx07tmjRIjMzs82bN8N1GgBg/ZWPy8VovJuGNzZUNdJQWlrq7u5uYmJy69atJjuUl5e/8847v//++7Bhw+bNmzd37tzjx4+rKBgAtERyOV4eT18P55ga8Bifk5PTnDlzGjSOGTNGPk2S5NixY9UbFADa7ssH9FcBGh5mQKobaRg2bNiyZct69OjRXIcjR474+fmNGTOGz+d/8cUXp0+fLikpUVEwAGiDGimacIXe2IfysdL0eg8A0Cl/5jAimeaHGZAGD4R8/vy5/JLyLi4uZmZmGRkZmgoGAFXDCH0QSw9wIqIN8lAGAECrYYS+esB800vzwwxIgwdClpWVOTo6yh9aWlqWlpa20P/x48dRUVHyh+yJWARBCIXCJs/21i3sJVwYhtF0IG0lFAp1/btACIlEIqlUqtwTq356Rj2voC4PkdTUKHGuLcEYi0SiJp/i8/kcjgHvIAFApxzNZDgECnfViu0NjSUOGxub6upq+cOKigo7O7sW+vv5+a1fv77x2dgIIVNTU13/o6JpmsvlmpiYaDqQtsIYm5mZaTqKtiJJUrlnY98uxj89l90Zw7E3V99F8dhiWg++DgAMmYxBXz1gNveltORPTmOVi5eX15MnT9jp/Px8oVAIZ2MDvVQowhOu0vsHctzVfud7AICu++0F42CMhrXXluyhqqKhqqoqMTExOztbKBQmJiamp6ez7dOnT3/06BFC6N133338+PGZM2fq6upWr14dERHR8kgDALpIwqC3LtNzvEntWecBALqijkZrkpjvemvRGdqqKhpSUlJmzpx5+vRpPp8/c+bMn3/+mW1/8eKFUChECFlbWx85cmTp0qWOjo6FhYVwNjbQS/Nu0w7GxIoeWrEzEgCgWzYlM30ERB+BFm1yqOqYhr59+zZ5W9u4uDj59IgRI+QXkQVA/+x4xtwqxnfHcLRojQcA6IgKCfrhCX0jXLuOWdauaADQGzeL8BeJdFw4x6z1d5YBABiub5LoKDfSW8su6wJFAwDKl1uDJ1yV7QnldDK8W1IBANouqxr/9oJ5Ml7rtjlgVysASlYrQ+Mv00v9qFEuUDEAAFpjaTyzwJdy0r7T8KFoAECZMEJTbtC+NsQn3WDlAgC0xp1X+O4rvEArc4g2xgSA7voikX4pwtv6adEpUgAAHYIRWnyP/rY3aaKVhw9oZVAA6KZjWcx/0vHdMRwe1AwAgFY5mM5IaDTJQ0s36aFoAEA5bhfjj2/TV0dxBMaaDgUAoJtEMrQygTkwkNKGe1M1SUtrGQB0S1Y1fuuKbHd/TldrbV3XAQBa75uHdKgjEeKovWkERhoAaKtKCRpzif6sBxXuqr2rOgBAy2VW4x3PmEdRWv2/DCMNALSJmEbjYmQjnIk5PrA2AQBab/E9ZkE3qp2JVm97aHVFA4CWwwh9FEfb84l1gXDoIwCg9S7m4+RyfGiQtmcSKBoAaL1P79MvqvDVURytPWoJAKD9xDT65A69qQ+l/SdewYAqAK20LZU5mY3PDedo5+nUgFUp0XQEALzJuseMrw2hE9eQhaIBgNY4ncOsSaLPDKNseZoOBTRPxiCPI9JqqabjAKB5mdV4awr9Yx/d+DvWjSgB0CqxRfjDOPrccLgflbbjkKi/I/lHNqPpQABo1txb9BI/ytlUN5JJE0VDUFDQunXrSkpK1B8NANrvSRmecEV2aDCnp61urORKUVFR0atXrx07dtTU1Gg6ln9nsifxn3QoGoCWOpzBFIiQDt2qpolA27dv/+mnn7q6uk6dOvX27dvqjwkArZUnxGNi6J/6UkPaGVDFgBDi8XjGxsYzZ850dnb++OOPnzx5oumIFBXuSj4owflCrOlAAGioUoKWxDPbQyiuztQMTRUNf/zxR25u7pdffnnt2rV+/fp5e3uvW7eutLRU/cEBoFVe16Gw8/SCbuSEjrqziiuJsbFxXFzcs2fPZs2adeTIET8/P3bgQSgUajq0N+BTKMqdPJwJRQPQOkvj6XEdiL4CXdoCaTr3tW/fftmyZRkZGSdPnnR3d2cHHj744IN79+6pOT4AtESFBA2/IJvkSf5fV4OrGOQ6d+783Xff5eXl/f777yYmJuzAw/z581NSUjQdWkve8yRhDwXQNrFF+EIe/qa31p9k+U8tpT8OhzNu3Li9e/fOmjVLJBL99ttvffr06dev3/3799UWHwDaQCRDYy/J+jkQX/Q03IpBjs/nv/fee7///vv48eMrKip++uknX1/fUaNGpaWlaTq0pvV3JCok6EkZDDYAbSGm0ayb9E/BpAVX06H8S81mQIzx5cuXJ0yY4OLisn///hkzZiQkJBw/fryurm7AgAGFhYXqjBIADZIw6K0rMjdzYnNfHdsmUAWZTHbq1KlRo0Z17Njx2rVrixYtevLkye7du9PT00NDQ0Ui0RvncPr06cmTJ0+fPj0xMbGFbmfOnFm+fLlSdn8QCE3sSPwOgw1Aa3yeSPewJcZ10L2NkCYiLi4uXrdunZeXV1hY2NOnTzdu3Jifn799+/aAgIDx48ffunWLy+XeuXNH/bECoH4yBr17lTbhEHtCtfdmteqRnZ39+eefd+jQITIysqysbM+ePQUFBRs2bOjWrdu0adNu3LhRVFT09OnTlmdy5syZ6dOnh4eH+/r6Dh48ODMzs8luOTk5CxYsWLdunSJViCKmdyb3pTF1tFJmBkCbJJXi39OYTX10ciOkiUvZde3atbq6OioqateuXQMGDGjwLJ/P9/f353DgGnhA/zEYTY2lhVJ8ehiHMuyKoaqqysPDw9jYeOLEibNnz/b392/QwcnJqVOnThi/YRfADz/88MUXX0ycOBEh9PDhw23btq1fv75xt1mzZq1evXry5MnKit/DggiwI45kMu930r1tO6BPxDR6/wb9Qx9KYKzpUFqlif/+zz77bOLEiQ4ODs295tq1a6oMCQCtgBGaeZN+KcLnhnO0/4LwqkZR1KZNm6ZMmWJpadlcnxcvXrxxPvHx8Zs2bWKnQ0ND9+3b17jP7t27nZycwsLCWh1tk+b6UF8k0lA0AM366gHd0ZyY6KGrv8MmioZPPvlE/XEAoFUwQh/fplMr8F8jOXyDrxgQQqampvPmzWvjTKqqqkQikY2NDfvQzs7u5cuXDfoUFhauW7fu9u3bbxy0YGVkZHzxxRdbtmxhH1pbW+/du5cgCKFQiDEmiP8NEIVao0qx0Y1cUYCNzhzcQNO0WCxmGJ0JuDlCobD+d6GjRCKRVCqlqNZnhIRScs9zzp0R0poajR2WizFubq8fn89/424E2MsAQBM+TcAPStBfIzmmsIooj7GxMUmSYrGYfVhXV2dmZtagD7tjws7O7vXr14rM09HRMTg4uF+/fuxDExMTc3NzdtrU1LTBH9UsH2ZPFjXAVWfKQJqmuVyuiYmJpgNpK4xx4+9a55AkyePxWl00iGn0cYJsaz+yo52RcgP7V9hiutVfB2REABpakUTdfo0vj+Lq3NlQWo7L5QoEgpycHE9PT4RQdna2s7Nzgz4XL168efPmnDlz2JEGLy+vAwcOjB49url5mpqa+vn5DR06VJEAPvAiPY9KX9dR9vw2LAYArbL8Pu1rQ7ztrqs7Jli6HT0ASrfoHh1XTFwYRlpqcmNAb7311lvscQwSieTQoUNvvfUWQkgqle7bt6+ysr9qW10AACAASURBVBIhVFxcnJGRkZGRER8fjxCKj48fNmyYst7dhofedid/fgonUQB1u1yAT2ThX4J1ZpSrOVA0APA/K+7T1wrx6cG0NdzwWjVWrFhx7969vn37+vn5OTo6vvvuuwghkUg0depU9uov1n+zsrJCCFlZWXG5yhzwWdad3JbK1MDNsoEaVUjQ9Dh6R39KDxIL7J4AACGEMEIL79JxRfjKKA6Plmg6HL3Vrl27lJSUxMREExMTX19fttHCwqKwsNDe3r5+Tzs7u7KyMrZ0UKKO5sRAJ3Lnc2aB7txXEOi6WTfpKDdihLPOHwqKoGgAACGEEfrkDn2rGF8aybHmISVdTwg0jcPhBAUF1W8hCMLJyalBN4IgrK2tVRHA8u7k2Ev0XB/SCMoGoHr70piUcrx3gJ7828JKAwwdg9HMm3RiCb46mmOj+4OH4I162hLeVghuYQXUIL0KL7lHHxhE6c2Z21A0AINGYzT1Bp1WiS+O4MC5EoZjeQ/q+8cMDXewAqokYdC7V+lVAVR3G33YMcGCogEYLnaVfl2Hzw/nmEHFYEgGORH2fBhsAKr16X3axZSY7a1X/7N6tTAAKK5WhqJiZDIGnQrjGOvJ3kbwL3zdi1r1gJFC2QBU42wuPp6Fd4fqy26Jv0HRAAxRjRSNiZFZGhFHh1BwXwnDFOpIeFig315A1QCUL0+IP4qT/WcQpX+HSUHRAAxOSR0adE7W2ZL4fSDFhTXAgK3tTa1OYmplmo4D6BcZgyZepRf7Uf0c9OdQBjlImcCw5Nbg/mdlI1yIrcEUqYdrNPgXetkRAXbEjmcw2ACUaWk8bcMjFvrq59+rfi4VAE1KrcD9z9IfdibXBMA+CYAQQt/0Itc+osvFmo4D6IujmczpXLxvAKWvmyRQNABDcbsYDz4n+7Y3uUhPtwBAK3SzJsZ1IL95CHejAErwvBLPu0MfHawPl4tuDmRPYBDO5DLjYmR7QjmTPOA3D/5hdQC1L43JqIKLNoA2qZKicTH0ut6Uv52+jjIgBEUDMAQ7nzEzb9LnR3BGuujzygxax8EYLfSllt2HIxtA6zEYTblOD3Iipnrp+b+qni8eMHAYoc8T6fVPmLhwTi+9Lv9BW3zSlUx4jW+8hMEG0Eqrk+hSMd7cV/8PllJ50SAWwyFGQDMkDHr/On2lAN+O4HhYQMUAmmXMQT/0IT++TcO1nkAr/JnD/PYCHx/CMYRTuFW4iHv27LGzsxMIBIMGDXr58mXjDkFBQR5/mzNnjuoiAQaoXIxGXJDVyNCVURw7vqajAVovyo10NkU/pUDVAP6dJ2V4xk36xFDKwVjToaiFqoqG7Ozs+fPnx8TElJWVeXp6Llq0qHGfnJycgwcPJiQkJCQkfP/99yqKBBigrGrc74zM14Y4PoSCS0QDBW0JptY9oguEsJMCKKpUjCIv0z/2oQxn76eqEurvv/8eFhbWs2dPhNDSpUu7detWU1NjZmbWoJuFhYW1tbWKYgCG6XYxfuuK7LMe1BwfAxgrBMrjaUHM8iYX3mOODNb/PdOg7cQ0GntJNtmDMKhzslS1qBkZGT4+Puy0p6cnQig3N7dxt8GDBzs6OoaHh6emprY8Q4Zhampqyv9WU1Oj9JiBHjiSyURelu0I4UDFAFphRXcqqRSfyYWdFOANMELT4+h2JsRXBnalOFWNNFRUVHTu3JmdJgjC1NS0vLy8QZ+DBw/27NlTIpF8/fXXI0eOfPr0qYmJSXMzfPr06eXLl//v//6PfSgQCBISEgiCEAqFGGOC0O2hIZqmxWIxw+h8qhIKhZr6LhiM1jyhTuRS5wZJu1iI21JVikQiqVRKUbqdCzDGIpGoyaf4fD6HA7ttmmDMQTtDqMnX6RAHUo+vzwPa7stE+nkFvhHO0e3/nn9PVYnDzs6uqqqKnWYYpqqqSiAQNOgzePBgdmLz5s0HDhx48OBBSEhIczPs1q3bunXrIiMjGz9lamqqB0UDl8ttoWbSFRjjxjuh1KBGit6/TpeJcfw4jh3fqI1zI0mSx+PpQdFAEIRGvg6dNsCJGONKLL9Pbw/R7R8AUJ1DGcx/0vHtMRwTw6u9VTWE6+Pj8+DBA3b68ePHJiYmLi4uzXWmaZqmaV3P0UBTsqpx8BmZwBhdhhMlgDJ8F0hdzMfX4LINoCmXC/CCu/S54YZyukQDqioa3nvvvbt37x47duzly5efffbZlClT+Hw+QmjVqlV79uxBCD179uzo0aNZWVnPnj378MMPnZyc2KMmAfhXLhfg4NOyGV3I7SFwn2ugHBZctD2E+iCWrpJqOhSgZR6Wofeuy04M5XSx0u3h7VZTVZYVCAR//PHHxo0bg4OD27Vrt27dOradpmn5nvs9e/YMGTIkMjKSJMlLly6xVQUAivvhCTPlhuzwYM7HcNgjUKoRzsRIZ2L+HbiRFfif7Bo09jL+pR/Vz8FAKwakumMaEEJDhgwZMmRIg8bVq1ezE126dLl48aLq3h3oN6EMfRRHp1Xiu2M4rmaGuwID1VkfRPU8Kfsjm4lyg5IUoOJaNPY691M/ZOC/B4NeeKCj0qtw8GmZMYXiIqBiAKpiykH7B1Bzb9Evmz4HBRiQSgkacVH2rhszs4uhJxwoGoCO+TOH6XdGNseH3B1K8eHYWaBKfQTEbB/qvesyBo6JNGC1MhRxSRbqSKzoBruroGgAukPGoGXx9Cd3mbPDODO7wE8XqMPKHiTG6JuHOn8NFdA6EgZFXZa5mRGbDOAOloowvJNMgW4qEOKJ12gzLkoYx7GFq+4AdaEIdGgwJ+CUrJ8DMbidoQ9NGxoao+jrtDGH2BNKwXfPgs01oAP+yse9/5SNdCHPDYeKAaibgzHa3Z96/wZdVKvpUIAasRWDSIYPD6Y48Ff5N/gkgFaTMmj5ffqjOPrwYM6K7iQU+3rg8ePHgwYNcnV1jYyMLCwsbPCsSCRatmyZv7+/u7v76NGj5deI06zhzsSHncl3rsiksJvCMNAYTb1Bl9bhY0M4RvA/WQ98GEB7ZVfj0LOy5DL8IJIT6ggFgz6QyWQRERERERGJiYnt2rWbOnVqgw7V1dV1dXXbtm2Li4vr3bv38OHD5Rek16wv/ElbPrE0Hg6F0380Rh/E0sW1+FQYB462bgCKBqClDmUwQadl73QkzwyHi0PrjwsXLpAkuXDhQnt7+7Vr18bGxmZkZNTv4ODgsHnz5qCgIGdn5y+//FIkEj19+lRT0dZHILQnlDqbi/+TDqMN+owdY3gpwn+GcYzhqL9G4CMBWqdaij6+Tce/xhdHcHrawgCDXnn69Km/vz87bWlp6e7unpqa6uHh0WTnpKQkjLGXl5caA2yJlRE6GUYNOS/ztCCCBPDL1ENSBk2+RldLoWJoFnwqQLvcLsbR1+mh7YmEcRxT+HnqndLSUnNzc/lDKyur169fN9mzoqIiOjp6zZo1NjY2LcwwOTk5Ojqay+WyD62trR89ekQQhFAoZO/zqcTgEUJuXPRLbzLqMroyVOys+rvS0jQtFovll97XXUKhUPvvRSym0fu3uRihA8FSug7VNOogEomkUqmu31sRYywSNX3BMj6fz+G8Ie1CVgbaQsqg1Un0rmfMryHU2A6w40w/WVtbZ2Zmyh9WVVU1WRNUV1ePGjVqyJAhixYtanmGPj4+n3/+eXh4OPuQy+XK7wZuamqqij+q8V4oV8JMvMWPDeeYc5U++3+gaZrL5ZqYqL48UTGMsZbfpb1Git69LLPhEQcGUlyy6XO0SJLk8Xh6UDQQBNHqrwNSM9AKKeW4z2nZw1KcFMWFikGPeXh4pKamstO1tbXZ2dmN900IhcLw8HA/P7/Nmze/cYYkSZqZmVn/TT3/TAu6kUH2xNtwMoW+KBOjsAsyNzPi4CC4We4bwMcDNIzGaP1jZtA52Rxv8swwjqNB3qLecERERBQVFZ06dQoh9NNPP3l7e3fr1g0hdOrUqR07diCE6urqIiIi+Hz+4sWLs7KyMjMzhUKhhoNuys/9KCOS+CiOhgtM67oCIR5wVtbfkdjRn4JLOL0RFA1Ak55X4v5nZBfzmfixnOmd4deo/4yNjQ8fPjx//nxLS8tDhw7t27ePbU9NTU1ISEAI5ebm5uTkpKenDx8+PCwsLCws7NatWxoNuWkUgQ4Ppp5V4s8S4CRMHZZagfudoaM7kd8HQsGgEDimAWgGjdEPT5j1j+mv/KnZPnDVJgMSFhaWk5MjlUrlRy8ihFasWMFOeHl5NTgJU2uZcNDZYZzQszIbHrPIF0pe3XOrGI+/LFsfREV7wtenKCgagAY8KcPT42hLI3RvLMfdHAoGQ1S/YtBddnx0aSQVepa24KKP4CZqOuVoJjPvDr1/AGe4M6SgfwGKBqBWdTT65iG9PZX5tjf1QWcYYAA6z9mUiBlJDTxHm3LRJA+oG3TDukfML6lMzEiOnw0koX8HigagPtdf4lk3aV8b4lEU10nnTyID4L88LIi/RlJh52mEoG7QdhIGzb5JJ5XiO2OodiZQMfxrUDQAdXhdh5bco6+9xFv6kmPgjEqgd3ysiKujqaHnaQaj92AHubYqFaO3Lsts+URcBFw7rpXgxw1Ui8FoxzPG94TUjo9SxnOgYgD6qrMl8ddIalk8sy8Nrt6gjZJKce9Tsv6OxLEhFFQMrQafHFChhBI89xZtRKFLsO8QGAB2vGHYBbpMjBZ0g/pYixzKYD65S28Npt52h++lTaBoACrxug6tTKDP5jLf9qamdIIDHoGh6GxJxIZTYRdooRR91hP+nzRPwqAl9+jzefjKKE43a0hFbQW/aaBkUgZtTma6nZCacVDqW9z3oWIABqaDGREbzvkjm5l9i4YLRmpWnhAPOCvLrkH3x0HFoBxQNABl+usl5XtCdjGfuT6a80MfytJI0wEBoAmOxuhGOCejCo+/TItkmo7GUJ3Pw4GnZJFu5KkwygpykZLA7gmgHA9L8ZJ4Oq+a82NfaqQLVPTA0Jlz0bnhnA/j6IHnZH+GceAcY3WSMGjFffpEFj4+lNPPAdKRMsFIA2ir3Bo89QY98qJsvBt5Z7gYKgYAWFwS7RtARbqRQX/KHpTAjgo1eVaBg0/LsqrRg0ioGJQPigbQeqVitOge7X9S5mqGXkzgzvImOfCDAuCfVnQnN/clR/4lO5gBp2KqFkbol6dM6FnZjC7kH0MpG56mA9JHsHsCtEa1FP2YzGxJoSd0JJPf4sL9rAFoQaQb6WFBjL9Mx7/G6wMpLtTWKpAnxB/F0RUSdCuC08kSBhhURU9+vDRGC+7StXDAkeoJZWj9Y6bTUWlGFY4fy/k5mIKKAYA38rMh7o/jpFfiwedl+ULYVaFMGKE9L5hep2ShjuTNcKgYVEtPigaKQKV16L3rNAMro8oIZWjjE8bziDSxBF8dzdk3gIIbVAKgOCsjdHoYZ7QL2fuU7GwupCrlyKzGwy7Itj1lrozifNoD9pCqnP58wLtCqQoJXnyP1nQgeqhKir57xHgckca/xjGjOIcHUz5WUC4A8K+RBFrenTwxlDPvDj3/DgyOtomUQesfM0F/ykY4k3fGwGUY1ER/igYjEp0YyrlUgDc8gaONlOZVLfosgfY4Ik0ux9dGc44MpmDNBKCNgh2IpEhOSR0KOCVLhLMqWiWuCPuflF17ydwby1nkCwMM6qNXB0JaGaGLI6ih5+lqCV4VQGk6HN2WUYV/SGYOZzDvdCTvjeV0hD0RACiPlRH6zyDqSCYz+i/Zh53Jz3tSPMhYiikQ4mX3mbgi/GMfMsoNigV107dP3NmUiIvgnM3D827D8Q2tdLMIv3WF7ntaZsNDqW9xf+lHQcUAgCq805F8GMV9Vol6npTdLoaE9QYiGfo6ielxUuZujp6+xYGKQSP0aqSBZc9H10Zzxl2Sjbkk+30gxxpO1VWMmEZHs5ifkpkqKfq/ruS+AVy4eywAquZojI4Pof7IZt65Sg93Jr7rTdnxNR2T9qEx2pfGfJnIBDsQ98dy3GAzRnP0s1Kz4KJLIzmdLInAP2WPy6B+f4PcGvxZAu12WHogjfnSn0p9izPXh4SKAQC1iXIjn77FseCibiek21IZGRyX9TeM0Mlspscfsn0vmONDqCODKagYNEtv/xk4JPqxDxVoz4RdkC3vTs3vSsLNFhugMbqQh7c/o+8U48me5PVwTmc4vxkADTHnoh/6UNO8yIX36K0pzMY+1Ahng14fMULn8/BXiTSN0XeB1Gi4Pr120NuigTXRgwy0J6bF0qeymT2hlIcF/OwQQii9Cu9LY357gV1N0UddyCODSRM9/yEAoBt8bYiYkZyzuXjhXXqdMfo6gOhpoemY1I7B6M8c5uuHDM2gz3uSUe6wxadF9P+/wsOCuD6aszmF6XNaNsebXN6dMtb/hW5auRgdz2L2pzNplXiSB/nXCKornD8JgPYJdyVGunD2pzGTrzM+ltSXAThIYBCrqphGv6czG58wFlz0ZU8yogOUC1rHIP4/SQIt6EZOcCcWxzM+J2SrA8jJHga0t6JWhs7lMQcz8NVCJqw9udSPHOFMwtXvAdBmFIGmeZHvuOGdqfidq3RnS7SsOzW4nd6mrUIR/jWV2fmM6WVP/NqPGuCkt0uq6wyiaGC1NyUODaLiivCK+/S6R8wqfzLSTZ9LB6EMXchj/sjGF/KYQHviXQ/yt1CupZGmwwIAKIxHoY86MXN8Ob+nM/Nu0zwKLfAlJ7iTenNRBwajK4V45zPmSiEz0QOOrNIBBlQ0sPo7EjcjOOfz8OokemUCs8iXjO5E8vVlDUQIFdeis7nM2Vx8tZDpIyDGu5M/9eXCSVwA6C4uiT7wIqd5kRfz8KZkesk9epoX+VEXUqcvoJJVjfen4f1pjKUR+qgLuSuUa8HVdExAAQZXNLBGuRCjXDixRXjDY+bTBGm0JzmjC9lFZ++nQGOU8BpfyGcu5OG0KhzWnhzvTuwJ5cI1KgDQGwRCI12IkS6c9Cr8ayrT97TM24qY2omMcid16O+2uBYdz2KOZDLPK/G7HcljQyh/O11NvIZJtUVDeXk5xtjGxqa5DmKxuKSkpF27dgShgd9NqCMR6khlVZM7nzGDz8tczYhJHuSEjqRO3OsZI5Raga8X4iuF+NpLxsWUGOFMfBdIhTgQcLwC0HJanhm0nKcFsSGIWtubOp/H7H2BP7krHdKOnNCRGOmivdVDtpC4nMP8mcM8LsPhLuSy7tSw9pCpdJKqigapVDplypSYmBiSJPv373/w4EEer+Fm7/bt25cvX25lZWVkZHTq1Clvb28VBdMyd3NibW9qTS/qcgE+mMF89UDqY0WM6UCOciG07eZMdTRKKsW3i/GtYnyrmDHnEgMciSg34ud+XJ0odADQocyg5YxINK4DOa4DqpBQp7KZ39OYGXF0HwExyoUc5kx4a8G4abUUxRbhmALmYh6uEBuNccNL/Kgh7Qh92h1sgFRVNOzdu/fZs2d5eXkURQ0YMODXX3+dP39+/Q4FBQWLFi26ffu2n5/fqlWrPv744ytXrqgoGEVQBBruTAx3piQMdf0l/jOHGXuJEcnw0PZkiCPRz4HwsSLUf9SkUIaSy/DDMpxUghNKcGoF9rYigh2It92Jn/pynE01nxcA+Fd0LjNoPysjNNWLnOpFCmXoUj5zPg//mMzQGA10IkIciRAHwluNuatAiO++wrdf4VvF+Gk57m1PhLUnDw0mPYxqLczN1RQEUCVVFQ0HDhz46KOPjI2NEUKzZs36+eefG6SGI0eO9OvXz8/PDyE0d+7cNWvWFBQUtG/fXkXxKM6IRMPaE8PaUwihrGp8pRDfKsY/PmFeinB3W6KnLeFrQ3hbEV2sCFulHjEgY1B2Nc6sRulV+EUlfl6Jn5ajolrsbUX0sCV62BLve5E9baFIB7pNdzOD9jPloEg3MtINIYReVOLYIhxXhDc+YYpFuKcd0dOW6GpN+FoTnSwJGyXlriopSqvETyvw03L8sBQnlWKMUJA92UdAfB9IBtkT8rM8qquV845A41RVNGRlZXl5ebHTXl5eWVlZjTt07tyZnbazs7O2ts7Ozm4hNchksuLi4szMTPYhn89v166dCgL/B3dz4sPOxIedEUKoXIwelOKkUnynGO9+zjyvxDSDOpgTbmaEowlyMka2fMKah2x4BI9EVjxEIMQhkTkXIYQqxAgjRGNUJUEiGa6QoEoJKhXj13WoSISKanFeDXpVx3Uwpt3NkacF0cmCCHEkulkT7uYEBaMJQI/oR2bQfl6WhJflf3NXhQQlluCkUnyrGG9PZdKqMEUgDwuivQnhYoYEfMKWj2x5yIZHmHAQ+zdvzUMYowoJQgjV0UgkQ+ViXCpGpXXoVR3OF6ICIc6sxnU08rQgvK2IbtbEbG/C346A4U+9p6qiobq6mt2YQAiZmppWVlY26FBVVeXo6Ch/aGZm1rhPfWlpaV9++eW6devYh7a2tlevXiUIYsGCBVOnTu3evbtSw28CB6FAcxRojpDbf1sqpURODSqoJYpriaI64mkNKpcQFRIkxUS5GCGEaEyIaEQzyIKLSQJRBLIwQnwSWXKxBRfb8lFHPu5jhZ2MUc7DW0+Trn71+coGbyqqUfViKVlYWFhMTIymo2irNWvWhISEDBo0SNOBtMnjx4/37NmzadOmxk/x+XwuVzOHzOlfZlCpa9euxcXFffHFF22ZCdUod5WIiewa4mUtKqglX9eirAqiXEJUSJFIhsQ0QghVSQmEkAUXI4T4FDLmICsusjbCNjzswkd9rBgnY9TBFNvz/3k7QKbZEQXIDNqjjZlBVUWDQCCoqKhgp8vLyx0cHFro0Fyf+ry9vaOjoyMjIxu05+Tk1NTUmGtib5k5Qs7NHv397+yPKyrMy9HIUihXfHy8mZmZrh/xnp+fX15erutfR01NTU6O1v2oDCEzKFFFRUV+fr7Sl8LcHLnbKXeWbwCZQXu0MTOo6pQXX1/f+/fvs9Px8fHsHsr6/Pz85B2eP38ukUg6deqkomAAAFoCMgMAOk1VRcOcOXN+/vnnq1evxsXF/fDDD3PmzGHbBw4ceOfOHYTQ+PHjCwsLN27cmJKSsmDBgvfee8/CwvDu5gaAgYHMAIBOU9XuicGDB2/atOmrr75iGGbt2rWjR49m293c3Ng9miYmJpcuXfr8888PHToUGhq6Zs2almcokUgyMjISExMbtFdVVaWlpdnb26tiKdQmOzu7vLy88dLposTERF0fhCwrK8vOztb1ryMtLa2qqqrJpXB3d2/hwkoqBZnhX4HMoFUgMyCECIxxyz20xNChQwsLC01MTBq0FxQU2NjYyA+t0lE1NTU1NTX1j//SUenp6Z6enpqOoq2KiorMzMzMzMw0HUib1NbWlpWVNXneQVRU1Keffqr+kFQBMoNOgMygPdqYGXSmaAAAAACAZsG1vwEAAACgECgaAAAAAKAQKBoAAAAAoBAoGgAAAACgECgaAAAAAKAQ3SgahEJhKzowDFNbW6uaiFqjrq6OpukWOmhVtM2RyWRisbgVLxSLxTKZTOnxtNobf1T6oblfnX4sPmQG7QGZQbe0OjNoe9Fw/PhxBwcHFxcXf3//9PT0xh0yMjJ69erl4uIiEAiOHj0qb9+4caOtra2Tk9OwYcPKysrUGHITKisrR48e7ejoaGtru3bt2sYdfv75Z09PT1tbWzMzs5kzZ0okErZ90KBBNn8bOnSoeqNuCGO8ePFiW1tbgUAwceLExgmiqKjIpp4NGzaw7XV1dRMnThQIBLa2tkuWLNH4Wb5JSUne3t6urq4uLi6XL19u3KFTp071F2ThwoUIobKysvqNTX6P6rRkyZK+ffva2dmdP3++yQ5VVVXh4eGOjo42NjbffPONvP306dNOTk6urq5+fn6pqanqilfJIDNAZlA6yAwKZQasxUpKSszMzG7cuIEx/vTTT4cMGdK4T1hY2NKlSxmGuXnzppmZ2evXrzHGSUlJVlZWL168kMlkEyZMmDNnjrpD/6dFixaFh4dLpdLs7Gx7e/vbt2836LBv375Hjx4xDFNYWOjj4/Ptt9+y7QEBAX/88UdZWVlZWVlVVZXaA/+HU6dOubm5vXr1qra2tl+/ft9//32DDgUFBTwer+xvtbW1bPu6deuCg4Nra2tfvXrl7u5+6tQptcf+D76+vj/++CPG+OTJk/b29nV1dQ06lJeXs4tQVFRkbW194cIFjHFJSQlBEPKlE4lEGgi9nh9//PHChQtubm4nT55sssOSJUtGjRolkUhycnIEAsHNmzcxxpWVlRYWFpcuXcIYr1mzJjg4WK1BKwlkBsgMqgCZQZHMoNVFw7Zt20JCQtjp0tJSDoeTm5tbv0N+fj6Hw3n16hX7cODAgT///DPGeMGCBR988AHbeO/ePQsLC5qm1Rh4Q3Z2dteuXWOn582bN3PmzBY6L1myJDo6mp0OCAhgv0VtEBkZuXr1anb66NGjXbt2bdChoKCAz+c3fqGPj8+RI0fY6TVr1kRGRqo0zpYlJiaam5vL00Hnzp3/+OOP5jofP37c2dlZJpPhv1ODmqJUWOfOnZtLDQKB4MqVK+z0/PnzP/roI4zx3r17AwIC2Mbq6moej/fixQv1hKpEkBkgMygdZAYFM4NW755IT0/39vZmp21sbAQCQWZmZv0OmZmZNjY28svLe3t7Z2RksC/08fFhG318fKqqql69eqXGwP+hsrKypKREHo88yCaJxeLz58+HhobKWyZNmmRpadm/f//bt2+rPNYW1f9U2aXAjYYTJRKJvb29o6NjdHR0cXExQghjnJmZqeDiq0F6enrHjh15PJ48niYHt1l79uz54IMPKIpiH2KMHRwcHBwcJk2a9PLlS3WE21rV1dWvXr2Srz71Vw15o5mZmbOzs2a/jtaBzIAgMygbZAYFM4NWFw2VlZWmpqbyh+bm5uXl5S13YHdSVlRUyNtNTU0JgmjwQnWqrKxECMmvHLNzPgAAIABJREFUjW9mZtbcnlSM8bx58wQCwQcffMC2bNq06cWLF7m5uaNGjRo1alRRUZF6Ym5S/U/bzMysrq6urq6ufgcrK6u4uLi8vLw7d+6Ul5dHR0cjhNhu9V+owe8CKfCjkisoKIiJiZkyZQr70NTUNC4uLjs7Oz4+XiQSvfvuu+oIt7Wa+9UpvvjaDDIDZAalg8yg4OJrddFgb29fVVUlf1heXi4QCFru4ODgwLazHw1CqKKigh2QUUvITWA3d+RxyoNsbNGiRQ8fPjx16hRJ/vd7CQkJsba2trS0XLFihbOz87Vr19QTc5Pqf6rl5eVmZmYN7gZkYmISHBzM5/Pd3d03b958+fLlmpoaY2NjMzOz+i/U4HeBFPhRye3duzc0NNTDw4N9yOfzQ0JCjI2NO3TosHXr1tjYWI0fRtcCe3t7giAa/+oUX3xtBpkBMoPSQWZQcPG1umjw8fGR374zPz+/oqLCy8urfgdPT8/q6uqcnBz2YVJSEjvY1bVr1wcPHsgb2cNE1Rj4PxgbG7u5udWPRz4iV9/KlSuvXr168eJFCwuLxs9ijCUSCZfLVW2sLfLx8am/FF27dm2hs0QiIUmSHb5r8MImF19tvL2909LSqqurEUIY44cPHzYZD7uTT75h14BEIiEIgsNR1Z3l247H47m7uzf+2OuvU69fvy4sLOzSpYvGomwtyAxykBmUBTKDoplBCUdcqIxIJLK3t9+2bVt+fv6kSZPeeecdtn3Dhg3yA3TZ9vz8/J07d9rZ2dXU1GCMMzMzzc3NT58+nZWVFRIS8sUXX2hsGTDGGH/77be9evXKyMi4dOmShYXF06dPMcbFxcWDBg0qKSnBGH/zzTcWFhaHDx+OiYmJiYlJTEzEGBcUFOzatevp06fPnz//5JNPHBwc2M6aEhcXZ2tre+vWrdTU1M6dO+/Zs4dtf/fdd9mDua5cuXLu3LmsrKy7d++GhIRERUWxHXbv3u3l5ZWamnr79m1bW9u4uDhNLQJr0KBBc+fOLSgoWLt2raenJ3so3Llz56ZPny7vc/XqVUtLS6FQKG+5fv36mTNnMjMz4+PjBw4cOHr0aA2EXs/9+/djYmKcnZ1XrVoVExPDbjefOnVKfjDdunXrAgICMjIyYmJiLCwskpOTMcZisbhdu3abNm0qKCiYNm3amDFjNLkMrQWZATKDKkBmUCQzaG9BhBAyNjY+f/78kiVLNmzY0K9fvy1btrDt8jE6hNDWrVsXLFgwcODA9u3bnz9/nt0r4+7ufvDgwTVr1lRUVISHh69cuVIzC/C3xYsXV1RUjBo1ytzcfO/evezxJgRBUBRFEARCqKysLDAwcNeuXWx/f39/f39/Dodz9uzZDRs2EATRvXv3a9eu2draanApQkJC1q9fP2fOHKlUGh0dPXXqVLadJEl2KWiaXr9+fV5enpWV1dChQ+X3ZZ82bdrLly+joqJ4PN6GDRtCQkI0tQisAwcOzJ8/v3///l5eXmfOnGF/TgRB1P9dPXnyZMWKFfI9fwghhmF++OGH3NxcS0vLQYMGffbZZxoIvZ6DBw8+efKkS5cucXFxcXFxP/30k6WlJfujYjssXLiwvLyc/dXt2bOH3f4zMjI6f/78okWLtmzZEhQUJP/J6RbIDJAZVAEygyKZgcCavp4GAAAAAHSCVh/TAAAAAADtAUUDAAAAABQCRQMAAAAAFAJFAwAAAAAUAkUDAAAAABQCRQMAAAAAFAJFAwAAAAAUAkUDAAAAABSi1VeEBHqgsLDw+PHjCQkJDx8+FAqFt2/fbu6uPAAAwwGZQUdB0QBUKzY2duHChV26dGEYJjMzUyaTaToiAIDmQWbQUbB7Avw7IpFILBYr3n/kyJGVlZXJyckTJ05UXVQAAM2CzGAgoGgAisrIyBg4cKCpqamJiUlERMSFCxc8PDzu37/f8qssLS3ZewUBAPQSZAaDArsngEJEItGIESNEItGxY8c6dOhw4MCBadOmFRcX19XVaTo0AIDGQGYwNFA0AIUcOnQoPT392rVrAwcORAj17t07KyvrzJkzmo4LAKBJkBkMDeyeAAp58OCBQCBg8wJrwoQJmgsHAKAVIDMYGigagELy8/OdnJzqt7Rr105TwQAAtARkBkMDRQNQiEAgKC0trd9SUlKiqWAAAFoCMoOhgaIBKMTHx6egoCA1NVXeEhMTo8F4AADaADKDoYGiAShk8uTJVlZWU6dOzcjIEIvF+/btO3r0qCIvZA+rPnbsWEpKCkLo7Nmzx44di42NVXG8AAB1gMxgcDAAirl27ZpAIEAIURTl6uq6bds2hFBsbGzLr8rNzW38qwsLC1NPzAAAVYPMYFDglEugqIEDB+bk5Dx48IDD4fj7+8fHxyvyqvbt25eVlTVo5HK5KggQAKABkBkMChQN4F/g8/nBwcH/6iUkSVpbW6soHgCANoDMYDigaABtlZ+fn56e3uRTAwYMIAhCzfEAALQBZAa9BEUDaKUOHTp899137u7uFy9eXLVqVZN9MjIyjIyM1BwYAECDIDPoNwJjrOkYAAAAAKAD4JRLAAAAACgEigYAAAAAKASKBgAAAAAoBIoGAAAAACgEigYAAAAAKASKBqAcjx49ys7OVtbc/tVJPQ06p6SkpKWlKSsSAEBbaCozNO4JmUEpoGgALcEYe/zN399/yJAhixcvTkhIaNCtsLAwNDS0tra2jW8nlUoXL15sbW1NUVRAQMCdO3da6Jyenh4ZGWlqasrhcDw9PU+ePMm2Z2RkDB8+XCwWtzEYAEBztDYzlJaWfvjhhwKBgL0RxldffSWTydinIDMoBRQN4A0yMzODg4O/++672bNnBwUFxcfHBwYGfvLJJ/UL+dWrV48cOdLb27uN77Vy5cpffvll165dycnJbm5uI0aMyMvLa7Jnbm5uSEjIy5cvf/vtt9jY2GXLlpHkf3/MERERZmZmO3bsaGMwAIAWaGdmmDp16tmzZ3fu3Pn06dNPP/30m2+++fbbb9mnIDMoh8ZulQWU5PXr13l5efVbxGJxRkZGbW1t22fOMAxC6Pvvv6/fuHHjRoTQnj172IcVFRWmpqbnzp2r36e8vPzs2bNXr14Vi8WlpaX5+flvfK/Kykoej7dq1Sr2oUgksrKyWrp0aZOd33nnnY4dO9bV1TX57Pfff9+5c2eGYd74pgDoKwPMDFKp1MjIaO3atfKWyMjIoKAg+UPIDG0HRYPOO3jwoJGR0atXr+Qt27dvNzU1raysbPvMm0wNGOPu3bv37t1bHgCPx6v//33jxg1ra2tbW9tOnTp5eXlNnjw5MDDwje8VExODEEpKSpK3vP3223369GncUygUGhkZrV+/XiKRvHjxoqampkGHlJQUhNDDhw8VXEwA9I8BZgaMsUAgWLZsmfzhoEGDwsPD5Q8hM7Qd3HtC540fP37BggX79+9ftGgR27Jz586JEydaWFg06MkwTGhoaHPz2bx5c0BAgIJvOmjQoK1btzIMQ5JkXFycn58fj8djn5LJZNOnTx84cODhw4eNjIyOHTv2zjvv9O7d+43zLCgoQAi5urrKW1z/v737Doji2hoAfu/MLLvA0mEpCoggCgoqYAPsoIIQFUyixu6LGo3PqDGJieWpiYmxxFhiEsvT6LPEGrtiBTWKoGLBRhcQlA67lJ3y/THJfgQQV9hl2/n9NTt7mT3D7p49c+fOHReXGzdu1G+ZnJxcU1OTn5/v4uKSl5eHMR40aND//vc/GxsbvkGHDh3MzMxiY2M7d+6s5B4BoGcMMDMghDZt2jRt2jQjI6P27dtfuXLl8ePHZ86cUTwLmaH5oGjQeUZGRpMmTdqyZcvcuXMxxklJSQkJCZs3b67fEmM8YsSI123Hzs5O+Re1tbWlabqiosLc3Dw9Pb1Vq1aKp65cuZKSknL69Gn+hjTvvvvujz/+KJfL37jNwsJChFDtjGZpaVlQUFC/ZVlZGUJo48aNe/fuDQsLu3XrVnR09KxZs/bs2cM3IAjC0dExMzNT+T0CQM8YYGZACPXs2bN3795r1661s7N78eLF9OnTPTw8FM9CZmg+KBr0wUcffbRq1aorV67069dv8+bNnTt3DggIqN8MY6w45mimkpISgiBMTU0RQpWVlVZWVoqn0tLSjI2N3d3dFWt8fHxu3779xm3yG6moqLC0tOTXlJWVWVtb129pa2uLEBozZszw4cMRQsHBwXPmzFm4cOH27dtFIhHfxtjYWCqVNnkHAdADhpYZqqqq+vXr5+XllZeXJxaLs7OzQ0JCsrKyDh8+rGgDmaGZoGjQBy4uLkOGDNmyZUtAQMDevXtXrVrVYDOWZbt27fq6jWzZsqV79+5KvuLVq1c7depEkiRCyMbGpri4WPEURVE0TXMchzHm1yhzMIEQcnR0RAjl5uYqUsOLFy/4lXU4OTkhhGofQLRr145hmOzsbMXKkpISxdkKAAyToWWG+Pj41NTUnTt3isVihFDr1q2nT58+b948mUxmYmLCt4HM0ExQNOiJjz76KCoqqmPHjizLjho1qsE2GONp06a9bgu1OxIbt3///hs3bvzwww/8w06dOu3evVvxrJeXl1wuv3PnDn8elOO4mzdvKr6xjfD39ydJ8ty5c97e3gghlmXPnz8fFRVVv6Wtra27u3vteVqePn1KUZSzszP/UCqV5uTk+Pr6KrlHAOgrg8oMxsbGCKHa00JUVlZSFEVRf/3SQWZQAc2OwwSqQtO0q6srRVFTp05V4Wb5MdJTp06NiYk5efLkTz/9NGbMGIIgoqKi5HI53+bKlSsIoby8PMVfde/evUePHllZWTKZbNmyZUZGRoox0s+fP2/btu2+ffsafLnx48fb2NgkJCTIZLJZs2YZGRk9fPiQf2rbtm0uLi6vXr3iH27evFkoFB44cEAmk12+fNnOzm7y5MmK7Vy8eJEkydohAWCYDCozyGQyiUTi7+9///79qqqqixcvSiSS0NBQxXYgMzQfFA36Y/ny5QihxMREFW6TZVmrWjw9Pd97770jR47UvtCZZVlPT88NGzYo1jx9+pSv5UmSDA8P/+ijjxSpISkpCSF04sSJBl+urKwsKiqKn6ZJIpEcOnRI8dTGjRuNjY3z8/MVaxYvXswfplAU9e6779a+kGz69OmRkZGq+icAoNMMKjMkJCT06NGDPyQmCCI6Ojo3N1fRGDJD80HRoD8mTJiguEK6hW3evNnHx6fOlCmZmZn8N3n+/PmK1LBhwwYfHx+GYRrZWmFhYXp6uuJ4pRGVlZWpqanV1dW1V5aWllpZWV2+fPmtdwMAfWSAmaG8vDwtLa3O5G+QGVQCppHWB6WlpefOndu9e/enn36qkQD+9a9/iUSiU6dO1V7p4uIikUjqN163bp1iyucGWVtbt2nTRnEashEikaht27b8FVwK27ZtGzRoUN++fZWLHQC9ZbCZQSwWu7m5KaaI4EFmUAnMvc3tBIF2cnV1ffHixaRJk37++WfFyGTt8dlnn125cuXmzZuaDgQAwwKZAagcFA36oLS0lL/Zo6YDaVhlZSVN02ZmZpoOBADDApkBqBwUDQAAAABQCoxpAAAAAIBSoGgAAAAAgFKgaAAAAACAUqBoAAAAAIBSoGgAAAAAgFKgaAAAAACAUqBoAAAAAIBSoGgAAAAAgFJ0pmgoKSlhGEbTUQAAtAtkBgBaks4UDVOnTj19+nT99TKZrOWDUTmWZSsrKzUdhQpIpVJNh6ACVVVVLMtqOgoV0I9vR+MgM+gEyAxapTnfDp0pGmialsvl9dfzN11t+XhUi7/lqKajUAH9+EbpzYdKP96OxkFm0An68VHUmw9Vc94OnSkaAAAAAKBZUDQAAAAAQCn6UzTkynS+1wgAoHKQGQBQIS29z/rbkrOo40E6e4zAVE92CAD9VFxc/PPPPycmJpaWlp44cUIoFNZv89577xUXF/PLwcHBS5YsafLL0SzyOUQ/HClwMG7yNgAA/09PfmMFBAqwwzE57HBX/ek7AUD/FBYWZmVlBQQELFiw4HWXSsbGxq5YscLFxQUhJJFImvNyFIFGuRObk5ml/mRztgMA4OnPT+xQZ+JkFvRDAqDVPDw8Nm/ePGbMmMab9erVKyQkJCQkxNfXt5mv+ElH4pfHbCXdzM0AABDSp6LhHVd88jkLVQMAemDixIlBQUFz5sx59epVMzfVzgIH2OI9qfpwyR8AGqcnpycQQm3NsIURTizgAmyxpmMBADTd8uXLfX19a2pqVq1aNXjw4Js3bwoEgtc1fvDgwbhx4xQNrKyskpKSMMZSqZTjOIwxQmiaO/H5Heq9VjU6lxoYhqmurtaDSQ6kUin/Xug0mUwml8tJUrdPdXEc97rJnUQiEUW9oSrQn6IBIRThjE9ksQG2uv2OAmDgPvzwQ34hICDAzs7u7t273bp1e11jb2/vRYsWRURE8A8FAoFYLOaXTU1N+R+qSA+06B59s9Q0pJWO/W4xDCMQCExMTDQdSHNxHKd4X3QXQRBCoVAPigaMcZPfDjWenmBZ9vbt2zdv3mxkZvgnT57ExcXl5eWp5BWHusCwBgD0h0gkEgqFjU95SxCEWCy2+tvrUuHsTsSqe3CLCgCaS109DVKpdNCgQeXl5UKhsKam5uLFizY2NrUb1NTUDBs2LCUlpWPHjteuXZs/f/5nn33WzBft7YDTy7kcKdfKVMeOJwAwHMXFxaWlpQihkpKSmpoaS0tLhNCvv/5qb28/bNiwrKyswsLCLl261NTUfPfddwKBwM/Pr/kvOtaDWHaHvZ7PBdpDcgCg6dTV07B161aCIO7cuRMfH9+2bdt169bVaXDy5MmHDx8+ePDg6NGjJ0+e/Oqrr5p/XxYSo9DWxOls6GwAQEvV1NQEBAQMHz68bdu2vXv37tOnD78+Pj4+OTkZIVRQUBAdHS0Siaytrc+dO3fs2DEzM7Pmv66AQPN9iO+SdH5wAACapa6ehkOHDo0dO5Y/9zNhwoQvvvhi+fLltRuQJGlsbGxkZIQQsrCwoChKJTcCGeaC/5fK/qu9/lwVAoA+MTIySk1Nrb9+69at/IKfn19aWppcLicIQrUnj6e0J1Yk0YkFnD+MlQagqdRVNGRlZbm6uvLLbdq0ef78eZ0GQ4cOPX36dGRkpLe399WrV3/55ZfGB/tIpdKkpCTFCUuRSBQUFIQQYlmWZVnFuNzw1mj6Na6wkrVqYKI57cX+TdOBNJc+7YWuD/bm72XX4NtBENpeVTdyuUSTCUk0z4f4Lok9MFC3B7IBoEHqKhqqqqr4XgSEkFAo5K8aqp2qSkpK7t+/7+7ubmtrS5Lk7du3x48f38gG8/PzDx06FBsbyz+0tLTs0qULxriyshJjrMjvBEJ9JYKDKfIP3HTpp4u/sErTUahAZWWlrg8tRgjJZDKGYXR9RziOq6ysbLA+UObCKr00rQPxfZL8YTHR0Uq3K0IANEVdicPBwaGoqIhfLigokEgkdZLXxo0braysdu7ciRCaOXOmvb39uHHj/P39X7fBtm3bjhs3bsSIEfWfUlxYxRvdjt2dQk7z0aWcCBdWaRW4sEpfmVDoU19yyW32IHQ2ANAk6uql7N69e1xcHL8cGxvbo0ePOg2kUqmFhQW/zF9YJZVKVfLS77gS1/K5In04bgcAqNhMbyL+JXfzJQyXBqAp1HU4PmvWrKCgoA4dOpiYmKxevfqPP/7g17u7u2/cuDEsLCw6Orp///7r1q3z8vLat2+flZVVQECASl7ahEIhrYg/MtlJntp+4hYA0MJEJPqqK7HkNnNmiC51RgKgJdT1s+rj43P27Nlbt25dvHjx4MGDigurJk+e3KZNG4RQjx49Ll++nJqaumPHDmdn56tXr6qwc/5dN3wgXZfGNAAAWswUTyKjHF1+AZ0NALw1NdbavXr16tWrV52VX331lWK5e/fu3bt3V8dLR7gQ064yhdXIRqeuoQAAtACKQIu6EgsTmKuR0NkAwNvRzw58EwoNbk0chM4GAEBDRrsTUhodzoAUAcDb0c+iASE0rh2x6xlkBABAAwiM1vYk599kayBJAPA29LZoGNwKp5VzT0vhtCUAoAH9HXF7S/TzI6gaAHgLels0UAQa1ZbYkwoZAQDQsDU9yK/vMHB5NgDK09uiASE0rh2x85kqbmgBANBHXpZ4eBviuyS4ZTYAytLnoqGrDTYXoKt5UDYAABr2tT+54yn7BM5jAqAcfS4aEEJjPYhdKXCGAgDQMIkx+rwzOe8GdDYAoBQ9Lxo+8MCH0lkprek4AADa6t8diZQydOo5dDYA8GZ6XjQ4meAge+JAGnQ2AAAaJiDQ2p7k3BsMXH4JwBvpedGAEPqwA97yBJIBAOC1wp1xOwu07gEkCgDeQP+LhnBnIluKHhRD3yMA4LU2BpKr7zEZ5ZAoAGiM/hcNJEYT2uGt0NkAAHg9VzGe1ZH8NB4SBQCN0f+iASH0YQdi9zNWBsMhAQCv93ln4kERdxJGRALwegZRNDib4m52+AjcnAYA8HpGBFofSH7yJ1MJBxgAvIZBFA0IoWlexGaYZB4A0KhBrXCAHf76LkzbAEDDDKVoiHQhcmQosQA6HgEAjVnXk9z6hL1bCLkCgAYYStFAYjS1A3Q2AADewN4YfRNATrvKMFA2AFCPoRQNCKEP2xOHM9hCuKMdAKBRU9oTxhSCYwwA6jOgosFWhCJdiP8+hUQAAGgMRuiXYHLZbSazAnobAPgHAyoaEEKzOxIbH7LQ6wgAaFx7CzzPh5wcC9kCgH8wrKLBzxY7mKCTWdDZAAB4g3k+RLkc7YC+SQBqMayiASH0SUfiB5hhHgDwJhSBtvYmv7jF5MqguwGAvxhc0TDSjUgrR7deQRYAALyBrzWe4UV+GAfTNgDwF4MrGigCzepIrH8InQ0AgDf7qgvxqgptg5vXAIAQMsCiASE0tQNx+jn7XAqdDQCAN6AItLMv+WUCXEkBAEKGWTSYC9DYdsRPyXDoAAB4My9LPLcTOQWupADAMIsGhNDsjsTWJ2y5XNNxAAB0wae+RBWD1sMYamDwDLRocDPDoa2IXx9DCgAAvBmJ0a5+5Dd3mftF0N0ADBqlvk3n5OQcOXKEIIjo6Gh7e/sG2zx48OD8+fMkSfbt29fX11d9wdT3RWdiyBl6pjchIlvyZQEAOsnNDH/bjZxwhbkxjDIy0KMtANTW05Camtq5c+eHDx/evn27c+fO2dnZ9dusX79+wIABT548SUlJ+emnn9QUyev4WuMuNnh3CnQ2AACUMqU94SLGixPhCkxguNTV0/DDDz9ER0dv3rwZITRu3LgNGzasXLmydoOnT58uWLDg9u3b7du3V1MMb/S5LzkljpnkSZBYUyEAAHTJ1t5klyN0aCtuoBNkDWCI1NXTcPbs2cjISH45MjLy7NmzdRocO3Zs4MCBFEXt3bs3ISFBTWE0rq8jtjdGhzOgswEAoBRbEfpvH3LiFaagStOhAKAJ6uppePHihaOjI7/s6OiYm5tbp0FaWlp6evr7778fGBi4YMGC6OjoNWvWNLLBvLy8nTt3Xr9+nX9oaWk5b948jHF1dTVFURg3ser/1BsvvcNFOsk1e9TAMEx1dTVJ6vzwiurqaiMjI01H0VzV1dUIIV1/OziOq66uFggE9Z8SCAQEAaflmyi0FR7VFn8YxxwJ1e1PCABNoK7EgTHmuL+GGXMcV/9HnWGYvLy8K1eurF+/PjY2dsOGDWlpaY0FShCmpqaWfzM2NlZJnOGtOQqjk89VsjEAgEH4phv5XMrBXC/AAKmrp8HBwSEvL49fzsvLU/Q6KDg5OXl5eZmamiKEXFxcJBJJSkpK27ZtX7dBiUQycuTIESNG1Fkvl8uFQmGTexoQQl91Zb++i6M8KA12NjAMgxASCoWaC0E1ampq9GAvGIYRCoV60NNA07QevB1ayIhA+weQgcfpXva4qw0MbgAGRF09DYMHDz5+/Di/fPz48SFDhvDLjx8/rqysRAiFhYU9e/aM7wfOy8t7+fJlIxWDWg1vQzAsOv0cLr8GACjL3Rxv6EW+f5GBOeKAQVFXT8OcOXN69uyJMZbL5efPn7916xa/3sfH58KFC3369OnevXtgYGBoaGhISMjBgwf/9a9/eXh4qCmYxmGEvupKLLvDhDurcdYKAICeea8tcS6H+/g6s7OvbndKAaA8dfU0uLu737t3z9fXt1u3bklJSa1bt+bXHzp0qGPHjvzygQMH5s2bJxaLf/zxx5afp6G26DZEhRydyYbOBgDUKzExcfr06YGBgRMmTHhdmzNnznh5eVlaWkZEROTn57dkeG9rfS/ydgEH98AEhkONx9aOjo4zZsyos/Kdd95RLBMEMWzYMPUFoDwCoyV+xMIEZnBrTY5sAEDvFRYWurm5mZiYXLt2rcEGxcXF77///q5duwYNGjRr1qyZM2cePHiwhYNUngmFDoeQwSdoP1sY3AAMAlx29ZeRbgTLoWOZcMQAgBoNGjTo888/79Kly+sa7N+/39fX95133hGJRIsXLz527FhBQUFLRvi22lng9b3I9y8yZTC4ARgAKBr+ghFa6k8sTGBZOEcBgOY8efJEcRsaZ2dnsVicmpqq2ZDe6P22RIgThntnA0MAQ//+X6QLseIueyCdfb8t1FIAaEZRUZGDg4PioYWFRWFhYSPt7927FxUVpXjIX7yNMZZKpQ3OEKMm3/igsIuCbxNq/t1BlXem4Kd9Y1md7wGVSqUt9l6oj0wmk8vlenAxtkwma/ApkUhEUW+oCqBo+Idl/uSs60x0G4KCsgEATbC2ti4vL1c8LCkpsbW1baS9r6/vqlWr6s/gghAyNTVtyR+qA6Fcjz/ooFaivo4qe1GGYQQCgYmJiao2qCkcx4nFYk1H0VwEQejHDC4Y4ya/HfDb+A+hrbCzGP33qc7X9QDoKE9Pz/v37/PL2dnZUqlUUzO4vC1nU7yzLzXmEpMrg9PL5sPJAAAgAElEQVQUQG9B0VDXt93IpXdYGa3pOADQR2VlZYmJiRkZGVKpNDExMSUlhV8/ZcqUpKQkhNCoUaPu3bt3/PjxqqqqZcuWRUZGNt7ToFVCW+GPOxLR55lquHs20FNQNNQVYIsDJXj9Q+hsAED1Hj58OG3atGPHjolEomnTpm3atIlf//TpU6lUihCysrLav3//Z5995uDgkJubq9kZXJrgi86EixhPuwpVA9BPMKahAd8EEIHH6Q87EDYwbT8AKtWrV6+EhIT66+Pi4hTLQ4YMUUw8r3MwQtt6kz2P0b88Zqd1gKMyoG/gM92AdhZ4pBvx7V04VgAAvDWxAB0NJZckMnF5MLgB6BsoGhq21I/c+Yx9VgrfeQDAW/Mwx7v7Ue9eoNPKIYcAvQJFQ8MkxuiTTuSXCTCyAQDQFCGt8BedyagYRgqjqoEegaLhteb5ELdecdDBCABomk86Ef62eMIVmCkS6A8oGl5LRKKvA4hPb8IXHgDQRD8Hk0VV3OJEGCAF9AQUDY35wIPgEPpfCpykAAA0hYBAB0KofancbkgjQC9A0dAYjND6XuRn8XD/OgBAE9kI0R+DyHk3mWv50GsJdB4UDW/QU4JDnIiVSdC7CABoIm9LvH8A9e4FGi7IAroOioY3W9WD/PUxXH4JAGi6fo54uT8ZdpYpqNJ0KAA0AxQNb2ZvjOb6kJ/FwylJAEDTTWlPRLXBIy/QcGcKoLugaFDK3E5Ecgl3+jl0NgAAmm5ld7K1KZ5whWEhlwDdBEWDUoQk2hhIzvqTqYJDBABAU2GEtvchX1VxXyVAKgE6CYoGZYW2wn42eGUSnKQA2q60RtMRgNczItCBgdTRTO6nZEgmQPdA0fAW1vYkNiUzqWXQsQi0V7kcue+X0/B7pMWshehcGPn9PfZAOrxPQMdA0fAWWpvizzqTM69DvyLQXkcy2GAHgoJvtnZzNsXHB5EfX2fO58BBCNAldVNLSUlJQEDAr7/+WlFRoZGAtNwnHYmXlWhfKhwfAC21O4Ud64HVseUePXqsXLmyoKBAHRs3QD7WeG9/auxl+n4R1A1AZ9QtGoRCobGx8bRp01q3bv3xxx/fv39fI2FpLYpAvwST826yxdWaDgWAenJlXGIBN9RZLf0MrVq1+vLLL11cXCZOnHj9+nV1vIShGeCEfw4mB5+BSZ+AzqibXIyNjePi4h4/fjx9+vT9+/f7+vryHQ9SqVQj8WmhbnY4qg3+4hacpABaZ08qF+1GGFNq2fjhw4ezsrKWLFly6dKloKAgLy+vlStXFhYWquXFDMZwV2KJHxl2lsmr1HQoACih4SOS9u3bf/fdd8+fP9+1a5eJiQnf8TB79uyHDx+2cHza6Ztu5Onn3JUXcHAAtMueFPYDdzUOZ2jVqtXnn3+empp65MgRNzc3vuNh8uTJN2/eVN+L6r1pHYgJ7YiwM3QJXPYCtF5j+UUkEo0dO3bXrl3R0dElJSXr16/38fEJDw9/9uxZi8WnncwF6OdgclIsI6U1HQoAf0su4QqrUW8HtQxoqI2iqOHDh+/YsWP69Okymey///1vz549g4KCbt26pe6X1leLuhIhTjjsDF0B98YD2u21RQNN00ePHg0PD2/btu2lS5fmzZt3//79bdu2paSk9OnTRyaTvXHTx44d++CDD6ZMmZKYmNhIs+PHj3/xxRc6d/oj3Bn3kuD/JMJJCqAtdj5lx7hjQs01A8dx58+ff++995ydnX/77bepU6cmJCQcPHiwqqqqb9++ubm56n15/fV9D9LHGg+PgUmmgVZroGjIyMhYtGiRq6vriBEjioqKtm/fnpOTs3r16k6dOk2aNOnKlSt5eXnJycmNb/f48eNTpkyJiIjw8fEZMGBAWlpag80yMzPnzJmzcuVKZaoQbbM+kPxfKvvnSzhJATSvmkE7n7GTPNV4biI/P3/lypWenp6hoaHJyclr1qzJzs7+5Zdf/P39o6Ojr127JhAI/vzzT/UFoN8wQpuDSCshHn2JgWk2gNaqO2KqrKzM3d3d2Nh49OjRH330kZ+fX50Gjo6O7dq147g3/FKuXbt28eLFo0ePRgjdvXt38+bNq1atqt9s+vTpy5Yt++CDD5qxCxpjI0Rre5BT45iE4ZSQ1HQ0wLDtT2O72mBPCzX2M3Ts2LG8vDwqKmrr1q19+/at86xIJPLz86Mo9QzCNAwkRnv6k1Hn6dGXmH0DSFLtJ5oAeGt1j0tIkly3bl1OTs6WLVvqVwy8p0+fduvWrfHtxsfH9+nTh1/u06dPfHx8/Tbbtm1zdHQMDQ19+7C1xSh3ooMl/s9t6E8EGrYxmf24o3pL14ULF2ZlZe3du7d+xcC7dOnSsGHD1BqD3hMQ6MBAqriam3aVgT5MoIXqHhaYmprOmjWrmRstKyuTyWTW1tb8Q1tb2xcvXtRpk5ubu3LlyuvXr7+x04KXmpq6ePHiDRs28A+trKx27NiBMZZKpRzHYayxmnx1F9zzjGCAbXUvu6Z3KTIMU11dzbI63ykplUo1+F6oikwmk8vlJKkz3UeJRUS+TBBsKa09JRvHca876ycSiZrQJfDJJ580OUKgPBGJ/hhEDTlDz7zGrO+p6WgA+Ce19CUaGxsTBFFd/df8R1VVVWKxuE4b/sSEra3tq1evlNmmg4NDYGBgUFAQ/9DExMTMzIxfNjU11eAPlViMfg5mZ8UTd0ZQTb4+nmEYgUBgYmKi0tA0gOO4+u+1ziEIQigU6lDRsD2RmdUJW5j94z/PF9N68HYYIFMKnRlChZ+h595E33bRdDQA1KKWYVMCgUAikWRmZvIPMzIyWrduXafNmTNnZsyYYW1t7enpiRDy9PQ8efJkI9s0NTX19fUN+VtgYKA6Im+aYa6Eny1eAPe6BZpQUIWOZ6l3CCRoeaYUOjaIuvGSW3BbZ4pXYAjUlWhGjhy5c+dOhFBNTc3evXtHjhyJEJLL5Tt37iwtLUUI5efnp6ampqam8sMd4uPjBw0apKZgWsCmQPJIBhcD954BLW5jMjPSjbARajoOoGoWRuj0YOLqSzz3BhyQAG2hrqJhwYIFN2/e7NWrl6+vr4ODw6hRoxBCMpls4sSJ/JXcVn+ztLRECFlaWgoEAjUF0wKshGhXP3JKLFMI96QALUhKo58fsfN9oJtBP1kaoVMDmWv53ByoG4B2UNf1UU5OTg8fPkxMTDQxMfHx8eFXmpub5+bm2tnZ1W5pa2tbVFTElw46rY8DHumGZ1xj9g+A7kTQQrY8Zvs4EO3UeaUl0CxzAXdmCDXoND3nBrO2J1yGCTRMjQcoFEX16NFDUTEghDDGjo6OdYZtY4ytrKz0YMg9QmhFN/JRCbfjqc5fBAF0gpxFPzxgv+gM3Qx6zkqIzodTN19y068yLJwCBRoF6UaVRCTa25/8LJ55XALfbKB2u1PYDhbIz1YfCm7QOAsjdCaMSi7hpl+DugFoEhQNKtbRCi/zJz+4zNRAdwNQJ4ZDq+6xn3eGc2GGwlyATg+mUkq5CVdgnmmgMVA0qN50L8JVjBfcgoFLQI32pLI2IjTACboZDIhYgE4PocrlKOo8A/e1AhoBRYNabO1NHs7gjmfB4QBQCzmLlt5mv/aHbgaDIyTR7wNJAYFGnKdltKajAYYHiga1sBai/QPID+OYjHI4/QhU779P2bZmqK8jdDMYIiMC/T6QdDTGQ87QpTWajgYYGCga1KW7HZ7vS75/EQY3ABWrYdF3Sewy6GYwYCRGW/uQna3xwFP0qypNRwMMCRQNajTXh3AwwZ/Hw7lHoEqbk9lOVrinBLoZDBpGaEMgGe6M+5ygsyqgRxO0ECga1AgjtKMPeTyL258GvQ1ANUpq0LdJzDcB8M0FCCG0zJ/82JsIPM7cK4K6AbQESD3qZSVEh0PIf//JPCyGrzRQga/vMMNcCR9r6GYAf5npTazqTgw+TV/LhyQD1A6KBrXztcbfdydHXmDK5JoOBei41DJu5zN2KYxmAP802p3Y3Z8aEUMfTIdOTaBeUDS0hAntiAFOeNxlmMoNNMsXt9g5nUgHY03HAbTPQCd8egg1+0/218dQNwA1gqKhhazrSRZXc0tvw6BI0ESxeVz8K25OJ/jOgob52+LYCHLNfXZhAgOHJ0BNIAG1EAGBDgykdjzjjmbCcQB4azSLZl5j1vYgjNV1Y9qWVl0Nd5FXPXdzfC2SuvSCmwAz2QP1gKKh5dgbo0Mh5LSrMM4ZvLX1D9lWpijaTR++sNu3b7e1tZVIJP3793/x4kX9Bj169HD/24wZM1o+Qp1mK0LnwygpjQafpouhMAOqpg85SIcE2OKfAslhMUx+paZDAbojrxJ9l8T82Esfxj9mZGTMnj07JiamqKjIw8Nj3rx59dtkZmbu2bMnISEhISHh+++/b/kgdZ0xhQ6GkH0dcfc/6KelcIgCVElf+jp1R7Qbcb+Yiz5PXwinhPrwKwDU7pM/mWleRHsLfbjMcteuXaGhoV27dkUIffbZZ506daqoqBCLxXWamZubW1lZaSJAPYER+o8faW/M9jtJHxhIBdnrw4cHaAPoadCAJX5kK1M8ORYGK4E3O5HFJRZwX+rLLbBTU1O9vb35ZQ8PD4RQVlZW/WYDBgxwcHCIiIh49OhR4xtkWbaioqL4bxUVFSqPWXd95EXs7EtFn6d/ewYDHIBqQE+DBmCEdvYlB56ilyQycAcB0IgyOZpxjflvX1Jvxj+WlJS0b9+eX8YYm5qaFhcX12mzZ8+erl271tTUfP3112FhYcnJySYmJq/bYHJy8vnz5//973/zDyUSSUJCAsZYKpVyHIexbh9hMwxTXV3Nsk3/ye9lgU72x+/GCu69ZBb7MoSG/h9SqVTX3wuEkEwmk8vlJKnbSZvjOJlM1uBTIpGIot6Qa/QlFekaEYn+CKUCj9OtTNlpHaC/BzRs/k0mwgUPdNL5bKtga2tbVlbGL7MsW1ZWJpFI6rQZMGAAv/Djjz/u3r379u3bwcHBr9tgp06dVq5cOWLEiPpPmZqa6voPFcMwAoGgkZpJGf5iFD8cjbxAj79htKsfaSZQVXRvgeO4+iehdA5BEEKhUA+KBoxxk98O+LnSGFsROhZK/ieRicmB0xSgAZdfcKefc9911+0MVYe3t/ft27f55Xv37pmYmDg7O7+uMcMwDMPoeo7WBrYiFBNGORijoON0WjkkHNB0UDRoUgdLfDCEGnuZvluk6VCAlimTo8mxzC/BpLkmjgvVZ+zYsTdu3Dhw4MCLFy8WLlw4fvx4kUiEEFq6dOn27dsRQo8fP/7999/T09MfP378r3/9y9HRkR81CZpJQKCfg8lpHYigY/R5OFABTQVFg4YF2eNtvanIGDalTNOhAG0y+09mSGsc5qzbvev1SSSSw4cPr1mzJjAw0MnJaeXKlfx6hmEUZ+63b98+cODAESNGEARx7tw5vqoAKjHTm9g/kBp/hV5zH4ZGgqaAMQ2aF+GCF3XB0bGCq5HIHm4rABA6ksFey+fujNDPr+fAgQMHDhxYZ+WyZcv4hQ4dOpw5c6bFgzIgfRzwzWFU9HkmoYDb2ps01c9PGVAX6GnQClPb49Ft2CFn6NIaTYcCNC2vEs28zvzWF7I5UBdnUxwbQZlSqNcxOqUMTlWAtwBFg7b4ohPT1xFHnqMraU2HAjSH5dDYS/S0DmRPib6dmABaRUSirb3Jj72JoOM03BAHKA+KBi3yQ0/SzQxHnaer4V6YhmrFXZbl0MKu8MUELWFqB+LkYGrODfazeIaGygEoAXKTFsEIbe9DWgrx+xcZOXyBDU9cHvfTI2Z3f5KEXgbQUgJsceJw6mEx1/8UnS2FUxXgDaBo0C4kRr/1JVkOjb/CwCzTBiW/En1widneh3IygZIBtChrIToxmBrqTHT/gz6TDXkHNEaNRcO9e/f69+/v4uIyYsSI3NzcOs/KZLLPP//cz8/Pzc1t6NChivlegIBAvw8ki6u5CVA3GAyaRe9doCe3x0NaQ8UANAAj9EVnYv8Aamoc83k89HSC11JX0UDTdGRkZGRkZGJiopOT08SJE+s0KC8vr6qq2rx5c1xcXLdu3QYPHqyYXBaISHRsEFVaw425BCcaDcL8eEZIokVdYepDoEm9HfDtEVRyCdf7BJ0OE0eChqiraDh9+jRBEHPnzrWzs1uxYkVsbGxqamrtBvb29j/++GOPHj1at269ZMkSmUyWnJyspmB0kRGBfh9A8f0NUDfotz2p7PEsbv8ACoYyAI2zFaFjg6jRbYmex+i9qZB6QF3qKhqSk5P9/Pz4ZQsLCzc3t0ZucXvnzh2O4zw9PdUUjI4yptAfoVRxDTf6EvQW6q34V9ycG8zRUNJKqOlQAEAIIYQRmt2JODuEWnaHnXCFKZNrOiCgTdQ1fUxhYaGZmZnioaWl5atXrxpsWVJSMm7cuOXLl1tbWzeywQcPHowbN04g+Gsifisrq6SkJEO4Ae6unmjCdcHws/RvgXKh1vdeww1w30q2DI04L/ypO91GUF1RoeKNN/MGuMDAdbHBicOpOTeYrofp3/qRQfY6/70GKqGuxGFlZZWWlqZ4WFZW1mBNUF5eHh4ePnDgwHnz5jW+QW9v70WLFkVERPAPBQKB4s6e+n0DXDFCRwajcZeZUdfJIyGUWLtvXwQ3wFVehRyNjqHn+RDR7dTypjbzBrgAmFDol2DyWCb77gV6siexxI8UwPV2Bk9dHwF3d3fF+YjKysqMjAx3d/c6baRSaUREhK+v748//vjGDRIEIRaLrf5mUKlQQKD/9SfdzHDIabqoWtPRAFWQs+jdC3R3OzzXB9Iw0GrvuBJ3RgiSirgef9APimF0pKFTV8KKjIzMy8s7evQoQmj9+vVeXl6dOnVCCB09evTXX39FCFVVVUVGRopEok8//TQ9PT0tLU0qlaopGD1AYvRLMNnXAfc9QefABCw6jkNo6lWGItCmQK0/4QQAQvbG6PggaqY3MeAkveoeC5eCGzJ1FQ3Gxsb79u2bPXu2hYXF3r17d+7cya9/9OhRQkICQigrKyszMzMlJWXw4MGhoaGhoaHXrl1TUzD6ASO0sjs5vh0RdJxJLoFvrQ5blMA8KuH2D6Ao6GUAumNKe+LWcOpsNtv7OP2kFFKQgVLjYKjQ0NDMzEy5XK4YvYgQWrBgAb/g6elZ5yJMoIz5voSjCRpwkj4UQsHQJF209j57KIOLjaBMYCQi0DWuYhwTTv38iO19nJ7vS87pREDha2jU/obXrhiASoz1IH7rR0Wdp/enwYWYOmbLY3ZjMhsTRtqJNB0KAE2CEfrIi4gfRsXksL2O0feLoMvBsECVqJMGtcIxYdRn8ex3SVA36Iw9qeyyO+y5MLK1KXQRAd3WxgyfDaM+8iZCTtMLE5gquDGvwYCiQVf5WuM/3yEPpLOTY5kaqBy03t5Udv5N9mwY6WEOFQPQBxihyZ5EUpTgSSnqfJi+/AK6HAwCFA06zMkEX4ukqhnU/ySdX6npaMDrHUhnP73Jng0jvS2hYgB6xcEYHRhIrupOTLzCTLjCvKrSdEBAzaBo0G0iEu3uTw50wj2P0XcKodLXRr89Yz/5kz0XRnaygooB6Kd3XImHIymJCHU6JP/lMctCKtJfUDToPIzQMn9yfS8i7Az936dwokK7bH7EfpnAng0jO0LFAPSaKYVW9SBjwqjdKWzPY3RCARQO+gmKBj0R6UJcCKe+TWJn/wlDHLTF13fYHx6w1yKhjwEYCl9rHBtBzfQm3jlHT70KZyv0EBQN+qOjFY4fRmVWoL4n6Ocwa6RGMRyacY05lMHGRlCuYqgYgAHBCE1oRzx+V2AmQJ0OyX98wMJNevUJFA16xdIIHQklo9oQ3Y/SJ59D3aAZlTQaeZ5JKeOuRFAOxpqOBgBNMBegNT3IK0OpszmszyH6TC7MmK4noGjQNxih+b7EwRBq5jVm7g04VdHSXshQv5O0uRE6MZgyh4nNgGHrYIlPDabW9SIXJ1Ehp2Cwtj6AokE/BdnjOyOozArU6xj9GG5U0VLuFHI9j9HDXIkdfUkj+G4BgBBCaEhrfH1w9Ug3YuhZesIVJrMCMpIOg8Smt6yE6FAIOa0D0ecEvSkZroFSu72p7JAz9A89iS+7EDCKAYDaKAJN9yKevCtwFSP/I/S8m0xhtaZjAk0CRYOem9qBuBZJ7Uphw87A6Eh1oVk05wazKJGNCaOi2sB3CoCGmQnQMn/ywUhBNYM6HJAvu8OWyzUdE3hLkOD0XzsLfDWC6utIBByltz2BLgcVy5ZyA07Rz0q5W8MoX2voYgDgDRyM0cZAMn4YlVrGtftd/v09VkprOiYDUEmjOTcYutmj3KBoMAgUgRZ0Ji6EUz8/YkNP0allUDmoxsnnXLejdJgzcWwQZSXUdDQA6A43M7yzL3lpKHW7gPPYL19zH0oHNWI5NO4KU1CFmn8rcygaDEgnK3xjGBXmTPQ8Rn9/Dy6ebpZKGn1yg5l5jTkYQi3oTMAoBgCawMsS7xtAxoRTt15x7vvl3yaxZXDCQg3mxzNFVdy2Piq48BWKBsNCYjTPh4gfRl15wXY9QsfmQZdDUyQWcP5H6ZeV6G4UFWQP9QIAzdLJCu8bQF4aSiUXc+775V8lMC/hDnyqs+Y+ezabOxxKqeSSLigaDJGbGT45mFruT4y7zIy9zGTDAEmlVTNoYQIz9Cy9xI/Y05+0NNJ0QADoCy9LvKsfGT+MKq5GXgflM68zcCK1+f5zm9nymD09RGXJCooGwzWiDZE8knIzQ12P0MvvsDI4ofgm1/M5vyP041J0N0rwflv47gCgem5m+Kcg8tFIgY0Q9TpGj7zAXIUO0SZhOTTrOnM8i4uNoJxNVdYhConPoJlSaLk/mTCceljMtT9Ab3/KMvD1bEhhNfowjnn/IrPMnzg4kITJoQFQK4kxWuZPpo8SDHDEU+KYbkfpXSlsNaPpsHRHSQ0aFkM/KOYuhlMSleYrKBoAchXjfQPIQyHkzqds58P04Qy4LPP/0Sza/IjteFBuJkDJI6loN/jKANBCTCk0w5t4NJL6jz/5vxTWdZ98YQKTBRNKvsm9Iq7bUdrdHJ8LoyxUfQoVMiD4S3c7fCWCWtmd/OYu2+0offI5B1/NM9lclyP04Qw2Joxa25M0g3tJANDiCIyGOuMzQ6jYCKqCRn5H6Mhz9IksDrpF62M5tO4BG3qaXupPrOtJCtTwC0+pfpNAlw11xuHO1OF09qtbzOJEtLALMczVEK8nvPEKLUyk8yrRqu5khIvh7T8A2sfTAq/rSa4IIPensd8mMdOvoYnt8ERPwsMcvqEIIZRWzk2OZVgOXY+k3NX2P4GeBlAXRijajbgTRS3pSqy8x3Y8RG99YkBnE+NfcSOvkB9c5sa1Ix5EU1AxAKBVTCg0yZO4FkmdCyMrGRR8nA4+Tm95zBYb8M0sKmm0JJHp8Qf9jgtxeagaKwYERQN4HYzQO67EjXeoX4LJPzLZNvvkixKZXJk+dwhezOUGn6bfu8AMduKSo/BkT4KEggEAbeVtidf0ILNHCz7vTJzL4dz2y0fEMAfT2UpDuhCM5dDuFNb7EP20DN0ZQc31UXvHMJyeAG/QxwH3caCelHIbH7I+h+iBTsSHHYiBTlhvzllUM+hAOrv2PlvNoHm+xDgPQl5VI1TBzGkAALWjCBTpQkS6oNIa8nAGu/UJ+2EcM8SZiG6Dw5wJU/39iWM5dDSTXZzIWhqh3/qSvR1aKCPr738UqFR7C7whkPymG7knhf3iFlNSjca3I8a1w23NdLh2SCvntjxm//uU7WyNvwkghzhjfmdgHlsAdI6FEZrkSUzyJAqq0OEMdstjdkos09+JiHTBES6EvR5dJl3FoF3P2DX3WUsh+r47Ge7cokkYigbwFswFaLoXMd2LuF3A7XzG9jrGeFrgUW2JkW669J0sl6ND6eyOZ2xyMTe+HREXQbWz0OHSBwBQm60ITe1ATO1AFFejU8/ZY1nc/Hh5O3Mc5ozDWhMBdlh3Tzs+LuF+fczuTmF7SPCvvck+LdW7UJt6i4bi4mKO46ytrV/XoLq6uqCgwMnJCWOdfRsNkp8t9rMlV/cgz+Vw+1PZRYlyX2s8zJUIscU+ZpoO7jXK5OjMc3Z/Gnchl+3nSMzuSAx1IVQyGTt4W5AZQAuwEqIPPIgPPJCcJa/mc2ees1OvMs+lXH9HYqAT7uuIva104+OVV4l+T2P3pLKZ5dwkT+LmMMpNc1286ioa5HL5+PHjY2JiCILo3bv3nj17hMK6dw7+5ZdfvvjiC0tLSyMjo6NHj3p5eakpGKAmAgINdcZDnckqhryYy/2RyX6fZGRhRA9ujQe1Jvo4YG2Y2OBRCReTw53MYm+85Ho74JFuxLY+ArhnhKZAZgAtT0Cg/o64vyO5sjvKq0QXctiLudzaB2y5nAuyJ4LscS8J9rPFIi0byfSgmDv1nDuWySaXcJEuxH/8yBAn3Px7WzeTuoqGHTt2PH78+Pnz5yRJ9u3b9+eff549e3btBjk5OfPmzbt+/bqvr+/SpUs//vjjCxcuqCkYoG4iEoU743BnclVnWWqN+Gw298N9ZvRFztsK81/InhLcWnWTnzeO5dCjEu5qPnc1j7v8giMxCm2Fp3sRh0P1eVSUroDMADTLwfiv7geEUI6Ui8vjrr/k9qWyySWclyUOsMVdbXEXa9zJGrd8umA5lFzCXc/n4vK4C7msMYmHOOPFfmQ/R6w9faLq+q/s3r37ww8/NDY2RghNnz5906ZNdVLD/v37g4KCfH19EUIzZ85cvnx5Tk5Oq1at1BQPaBkYoa42uKsN/qIzUc2gm6+4a/ncb8+4mdcZ/qkuNtjbCntb4nYW2FxF/RBF1ehZKXe/mHtYzN0p5O4UcPYmuJcE93XEi7oSnjBeQZtAZgDao5UpHuWOR7kjhFAVg+4WcgkF3K1X3JbH7KMSzsEYe1uh9hbY0wJ7mGM3M2SDURwMhLsAABBoSURBVN1useYprEaPS7jHJdy9Iu5OIZdUyDn8nbuW+lPaOcxcXUVDenq6p6cnv+zp6Zmenl6/Qfv27fllW1tbKyurjIyMRlIDTdP5+flpaWn8Q5FI5OTkpIbAgcoISf5yTf5zT2ZLuTuF3P0idPo5t/Y+m1LGiUjkZoZbmWBnMZKIsI0I2QiRlRCbUIjvJ7Q0Qhgjfs6WagbJaFRcwxVUocIq9LKKe16BcmRcahnHcKidOe5kjTta4QgXwt8Ww9kHrQWZAWgnEYl6SnBPyV+/0wyH0su5B8Xc01IU/4rbk8qml6P8SoFExDmLaXtj7GiCbIXIVoQtjJClETKhsLkRIjHCCFkKEUKoXI5oFnEIlVSjahYVVXPF1aiwintRifJkKLOCyyjnSAK1t8DeltjLCr/jSvjZYCvVViVqoK6ioby8nD+YQAiZmpqWlpbWaVBWVubg4KB4KBaL67ep7dmzZ0uWLFm5ciX/0MbG5uLFixjjOXPmTJw4sXPnzioNv6VdunQpLi5u8eLFmg6kuUJDQ2NiYhp8ygKhflaon9X/r3lVhTOl+EUlyqkkXlai9BJcXINL5KiSRlUMQgiVyTFCyFzAIYSEJDKhkIUAWRlxNkLOWYR6WLJOxqiNmLMV/nPKqWpU3ry54ZYvXx4cHNy/f/9mbUXT7t27t3379nXr1tV/SiQSCQSaGW8CmeGtGEJm0Fr2GNlbo4G1Rusu/XqFV8/+rp2C8ipRfhUurMEPylGZHJfKcRWLymoQwyGWQ2VyTBLIhEQk5hBCVkIkwJylEZ+7kI+YC7HjWhlzrmJkIfhn7qpB5TVq369mZgZ1FQ0SiaSkpIRfLi4utre3b6TB69rU5uXlNW7cuBEjRtRZn5mZWVFRYWamrUP2lVNSUpKdna3re4EQio+PF4vFSo54NzNDbe3UHVFTZGdnFxcX6/rbUVFRkZmZqW17AZnhrRhmZtBauc8zfbxfhLiZajqQZmlmZlDX4AofH59bt27xy/Hx8fwZytp8fX0VDZ48eVJTU9OuXTs1BQMA0BKQGQDQaeoqGmbMmLFp06aLFy/GxcWtXbt2xowZ/Pp+/fr9+eefCKHo6Ojc3Nw1a9Y8fPhwzpw5Y8eONTc3V1MwAAAtAZkBAJ2mrtMTAwYMWLdu3X/+8x+WZVesWDF06FB+fZs2bfgzmiYmJufOnVu0aNHevXv79OmzfPnyxjdYU1OTmpqamJhYZ31ZWdmzZ8/s7LSym1tpGRkZxcXF9fdOFyUmJup6J2RRUVFGRoauvx3Pnj0rKytrcC/c3NwamVhJrSAzvBXIDFoFMgNCCHOcbty3MCQkJDc318TEpM76nJwca2trxdAqHVVRUVFRUVF7/JeOSklJ8fDw0HQUzZWXlycWi8VisaYDaZbKysqioqIGrzuIior68ssvWz4kdYDMoBMgM2iPZmYGnSkaAAAAAKBZWjPLFAAAAAC0GxQNAAAAAFAKFA0AAAAAUAoUDQAAAABQChQNAAAAAFCKbhQNUqm0CQ1Ylq2srFRPRE1RVVXFMEwjDbQq2tehabq6uim3dqiurqZpWuXxNNkbP1T64XWfOv3YfcgM2gMyg25pcmbQ9qLh4MGD9vb2zs7Ofn5+KSkp9RukpqYGBAQ4OztLJJLff/9dsX7NmjU2NjaOjo6DBg0qKipqwZAbUFpaOnToUAcHBxsbmxUrVtRvsGnTJg8PDxsbG7FYPG3atJqav25a0r9/f+u/hYSEtGzUdXEc9+mnn9rY2EgkktGjR9dPEHl5eda1rF69ml9fVVU1evRoiURiY2Mzf/58jV/le+fOHS8vLxcXF2dn5/Pnz9dv0K5du9o7MnfuXIRQUVFR7ZUNvo8taf78+b169bK1tT116lSDDcrKyiIiIhwcHKytrb/55hvF+mPHjjk6Orq4uPj6+j569Kil4lUxyAyQGVQOMoNSmYHTYgUFBWKx+MqVKxzHffnllwMHDqzfJjQ09LPPPmNZ9urVq2Kx+NWrVxzH3blzx9LS8unTpzRNv/feezNmzGjp0P9p3rx5ERERcrk8IyPDzs7u+vXrdRrs3LkzKSmJZdnc3Fxvb+9vv/2WX+/v73/48OGioqKioqKysrIWD/wfjh492qZNm5cvX1ZWVgYFBX3//fd1GuTk5AiFwqK/VVZW8utXrlwZGBhYWVn58uVLNze3o0ePtnjs/+Dj4/PDDz9wHHfkyBE7O7uqqqo6DYqLi/ldyMvLs7KyOn36NMdxBQUFGGPF3slkMg2EXssPP/xw+vTpNm3aHDlypMEG8+fPDw8Pr6mpyczMlEgkV69e5TiutLTU3Nz83LlzHMctX748MDCwRYNWEcgMkBnUATKDMplBq4uGzZs3BwcH88uFhYUURWVlZdVukJ2dTVHUy5cv+Yf9+vXbtGkTx3Fz5syZPHkyv/LmzZvm5uYMw7Rg4HXZ2tpeunSJX541a9a0adMaaTx//vxx48bxy/7+/vy7qA1GjBixbNkyfvn333/v2LFjnQY5OTkikaj+H3p7e+/fv59fXr58+YgRI9QaZ+MSExPNzMwU6aB9+/aHDx9+XeODBw+2bt2apmnu79TQQlEqrX379q9LDRKJ5MKFC/zy7NmzP/zwQ47jduzY4e/vz68sLy8XCoVPnz5tmVBVCDIDZAaVg8ygZGbQ6tMTKSkpXl5e/LK1tbVEIklLS6vdIC0tzdraWjG9vJeXV2pqKv+H3t7e/Epvb++ysrKXL1+2YOD/UFpaWlBQoIhHEWSDqqurT5061adPH8WaMWPGWFhY9O7d+/r162qPtVG1/6v8XnD1uhNramrs7OwcHBzGjRuXn5+PEOI4Li0tTcndbwEpKSlt27YVCoWKeBrs3OZt37598uTJJEnyDzmOs7e3t7e3HzNmzIsXL1oi3KYqLy9/+fKl4utT+6uhWCkWi1u3bq3Zt6NpIDMgyAyqBplBycyg1UVDaWmpqen/37nczMysuLi48Qb8ScqSkhLFelNTU4xxnT9sSaWlpQghxdz4YrH4dWdSOY6bNWuWRCKZPHkyv2bdunVPnz7NysoKDw8PDw/Py8trmZgbVPu/LRaLq6qqqqqqajewtLSMi4t7/vz5n3/+WVxcPG7cOIQQ36z2H2rwvUBKfKgUcnJyYmJixo8fzz80NTWNi4vLyMiIj4+XyWSjRo1qiXCb6nWfOuV3X5tBZoDMoHKQGZTcfa0uGuzs7MrKyhQPi4uLJRJJ4w3s7e359fy/BiFUUlLCd8i0SMgN4A93FHEqgqxv3rx5d+/ePXr0KEH89b4EBwdbWVlZWFgsWLCgdevWly5dapmYG1T7v1pcXCwWi+vcDcjExCQwMFAkErm5uf3444/nz5+vqKgwNjYWi8W1/1CD7wVS4kOlsGPHjj59+ri7u/MPRSJRcHCwsbGxq6vrxo0bY2NjNT6MrhF2dnYY4/qfOuV3X5tBZoDMoHKQGZTcfa0uGry9vRW378zOzi4pKfH09KzdwMPDo7y8PDMzk394584dvrOrY8eOt2/fVqzkh4m2YOD/YGxs3KZNm9rxKHrkavvqq68uXrx45swZc3Pz+s9yHFdTUyMQCNQba6O8vb1r70XHjh0baVxTU0MQBN99V+cPG9z9FuPl5fXs2bPy8nKEEMdxd+/ebTAe/iSf4sCujpqaGowxRanrzvLNJxQK3dzc6v/ba3+nXr16lZub26FDB41F2VSQGRQgM6gKZAZlM4MKRlyojUwms7Oz27x5c3Z29pgxY95//31+/erVqxUDdPn12dnZW7ZssbW1raio4DguLS3NzMzs2LFj6enpwcHBixcv1tg+cBzHcd9++21AQEBqauq5c+fMzc2Tk5M5jsvPz+/fv39BQQHHcd988425ufm+fftiYmJiYmISExM5jsvJydm6dWtycvKTJ08++eQTe3t7vrGmxMXF2djYXLt27dGjR+3bt9++fTu/ftSoUfxgrgsXLpw8eTI9Pf3GjRvBwcFRUVF8g23btnl6ej569Oj69es2NjZxcXGa2gVe//79Z86cmZOTs2LFCg8PD34o3MmTJ6dMmaJoc/HiRQsLC6lUqlhz+fLl48ePp6WlxcfH9+vXb+jQoRoIvZZbt27FxMS0bt166dKlMTEx/HHz0aNHFYPpVq5c6e/vn5qaGhMTY25u/uDBA47jqqurnZyc1q1bl5OTM2nSpHfeeUeT+9BUkBkgM6gDZAZlMoP2FkQIIWNj41OnTs2fP3/16tVBQUEbNmzg1yv66BBCGzdunDNnTr9+/Vq1anXq1Cn+rIybm9uePXuWL19eUlISERHx1VdfaWYH/vbpp5+WlJSEh4ebmZnt2LGDH2+CMSZJEmOMECoqKurevfvWrVv59n5+fn5+fhRFnThxYvXq1Rjjzp07X7p0ycbGRoN7ERwcvGrVqhkzZsjl8nHjxk2cOJFfTxAEvxcMw6xater58+eWlpYhISGK+7JPmjTpxYsXUVFRQqFw9erVwcHBmtoF3u7du2fPnt27d29PT8/jx4/zHyeMce3P1f379xcsWKA484cQYll27dq1WVlZFhYW/fv3X7hwoQZCr2XPnj3379/v0KFDXFxcXFzc+vXrLSws+A8V32Du3LnFxcX8p2779u388Z+RkdGpU6fmzZu3YcOGHj16KD5yugUyA2QGdYDMoExmwJym59MAAAAAgE7Q6jENAAAAANAeUDQAAAAAQClQNAAAAABAKVA0AAAAAEApUDQAAAAAQClQNAAAAABAKVA0AAAAAEApUDQAAAAAQClaPSMk0AO5ubkHDx5MSEi4e/euVCq9fv366+7KAwAwHJAZdBQUDUC9YmNj586d26FDB5Zl09LSaJrWdEQAAM2DzKCj4PQEeDsymay6ulr59mFhYaWlpQ8ePBg9erT6ogIAaBZkBgMBRQNQVmpqar9+/UxNTU1MTCIjI0+fPu3u7n7r1q3G/8rCwoK/VxAAQC9BZjAocHoCKEUmkw0ZMkQmkx04cMDV1XX37t2TJk3Kz8+vqqrSdGgAAI2BzGBooGgAStm7d29KSsqlS5f69euHEOrWrVt6evrx48c1HRcAQJMgMxgaOD0BlHL79m2JRMLnBd57772nuXAAAFoBMoOhgaIBKCU7O9vR0bH2GicnJ00FAwDQEpAZDA0UDUApEomksLCw9pqCggJNBQMA0BKQGQwNFA1AKd7e3jk5OY8ePVKsiYmJ0WA8AABtAJnB0EDRAJTywQcfWFpaTpw4MTU1tbq6eufOnb///rsyf8gPqz5w4MDDhw8RQidOnDhw4EBsbKya4wUAtATIDAaHA0A5ly5dkkgkCCGSJF1cXDZv3owQio2NbfyvsrKy6n/qQkNDWyZmAIC6QWYwKHDJJVBWv379MjMzb9++TVGUn59ffHy8Mn/VqlWroqKiOisFAoEaAgQAaABkBoMCRQN4CyKRKDAw8K3+hCAIKysrNcUDANAGkBkMBxQNoLmys7NTUlIafKpv374Y4xaOBwCgDSAz6CUoGkATubq6fvfdd25ubmfOnFm6dGmDbVJTU42MjFo4MACABkFm0G+Y4zhNxwAAAAAAHQCXXAIAAABAKVA0AAAAAEApUDQAAAAAQClQNAAAAABAKf8HtrKyI8hYBTIAAAAASUVORK5CYII=\" />"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D(q,p) = q*log(q/p) + (1-q)*log((1-q)/(1-p))\n",
    "q = 0:0.01:1\n",
    "PP = []\n",
    "for p in [0.2, 0.4, 0.6, 0.8]\n",
    "    P = plot(legend=false)\n",
    "    plot!(title=\"y = D(q, $(round(p,digits=3)))\", titlefontsize=10)\n",
    "    plot!(xlabel=\"q_1\", ylabel=\"y\")\n",
    "    plot!(q, D.(q, p))\n",
    "    push!(PP, P)\n",
    "end\n",
    "plot(PP..., size=(700, 500))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D(q,p) = q*log(q/p) + (1-q)*log((1-q)/(1-p))\n",
    "p = 0:0.01:1\n",
    "PP = []\n",
    "for q in [0.2, 0.4, 0.6, 0.8]\n",
    "    P = plot(legend=false)\n",
    "    plot!(title=\"y = D($(round(q,digits=3)), p)\", titlefontsize=10)\n",
    "    plot!(xlabel=\"p_1\", ylabel=\"y\")\n",
    "    plot!(p, D.(q, p))\n",
    "    push!(PP, P)\n",
    "end\n",
    "plot(PP..., size=(700, 500))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**問題(Laplaceの方法の弱形の一種):** 実数 $E_1,\\ldots,E_N$ について, $n\\to\\infty$ のとき, \n",
    "\n",
    "$$\n",
    "-\\frac{1}{n}\\log\\sum_{i=1}^N e^{-nE_i} \\to \\min\\{E_1,\\cdots,E_N\\}\n",
    "\\tag{$*$}\n",
    "$$\n",
    "\n",
    "となることを示せ. \n",
    "\n",
    "**解答例:** $E_1=\\cdots=E_k<E_{k+1}\\leqq\\cdots\\leqq E_N$ と仮定してよい. このとき,\n",
    "\n",
    "$$\n",
    "-\\frac{1}{n}\\log\\sum_{i=1}^N e^{-nE_i} =\n",
    "-\\frac{1}{n}\\log\\left(e^{-nE_1}\\left(k+\\sum_{i=k+1}^n e^{-n(E_i-E_1)}\\right)\\right) =\n",
    "E_1 - \\frac{1}{n}\\log\\left(k+\\sum_{i=k+1}^n e^{-n(E_i-E_1)}\\right).\n",
    "$$\n",
    "\n",
    "これより, ($*$)が成立することがわかる. $\\QED$\n",
    "\n",
    "**注意:** 上の問題の結果の $\\max$ 版\n",
    "\n",
    "$$\n",
    "\\frac{1}{n}\\log\\sum_{i=1}^N e^{nE_i} \\to \\max\\{E_1,\\cdots,E_N\\}\n",
    "$$\n",
    "\n",
    "は<a href=\"https://www.google.co.jp/search?q=%E3%83%88%E3%83%AD%E3%83%94%E3%82%AB%E3%83%AB%E5%B9%BE%E4%BD%95\">トロピカル幾何</a>における <a href=\"https://www.google.co.jp/search?q=max-plus%E4%BB%A3%E6%95%B0\">max-plus 代数</a>の max が極限で出て来る仕組みとしても現われる. $\\QED$\n",
    "\n",
    "**注意:** コンピューターによる統計がらみの数値計算では<a href=\"https://www.google.co.jp/search?q=logsumexp\">logsumexp</a>という函数を適切に定義して使うことがある. $\\QED$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "確率 $p$ で当たるくじを引く独立試行を $n$ 回繰り返したとき, 当たりが $k$ 回出る確率は\n",
    "\n",
    "$$\n",
    "\\binom{n}{k}p^k(1-p)^{n-k} = \\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}\n",
    "$$\n",
    "\n",
    "になる. $0\\leqq a<b\\leqq 1$ であるとする. このとき当たりが出た回数の割合 $k/n$ が $a$ 以上 $b$ 以下になる確率は\n",
    "\n",
    "$$\n",
    "\\sum_{a\\leqq k/n\\leqq b}\\binom{n}{k}p^k(1-p)^{n-k}\n",
    "$$\n",
    "\n",
    "になる. この確率の対数の $-1/n$ 倍\n",
    "\n",
    "$$\n",
    "-\\frac{1}{n}\\log \\sum_{a\\leqq k\\leqq b}\\binom{n}{k}p^k(1-p)^{n-k}\n",
    "$$\n",
    "\n",
    "が $n\\to\\infty$ でどうなるかについて考えよう.\n",
    "\n",
    "Sanovの定理より, $k/n\\sim q$ のとき,\n",
    "\n",
    "$$\n",
    "\\binom{n}{k}p^k(1-p)^{n-k} = \\exp(-nD(q|p) + o(n)).\n",
    "$$\n",
    "\n",
    "したがって, 上の問題の結果の一般化によって, $n\\to\\infty$ で\n",
    "\n",
    "$$\n",
    "-\\frac{1}{n}\\log \\sum_{a\\leqq k\\leqq b}\\binom{n}{k}p^k(1-p)^{n-k} \\to\n",
    "\\max_{a\\leqq q\\leqq b} D(q||p) =\n",
    "\\begin{cases}\n",
    "0 & (a\\leqq p\\leqq b) \\\\\n",
    "D(b||p) & (b < p) \\\\\n",
    "D(a||p) & (p < a) \\\\\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "となると考えられる. 要するに $a$ 以上 $b$ 以下の $k/n$ で $p$ に最も近いものが生じる確率の寄与だけが, 効いて来るということである.  (前節の説明も再読せよ.)\n",
    "\n",
    "以上の議論は少々厳密さに欠けた荒い議論だが, 結論は正しい. 正確な議論の仕方については\n",
    "\n",
    "* 黒木玄, <a href=\"https://genkuroki.github.io/documents/20160616KullbackLeibler.pdf\">Kullback-Leibler情報量とSanovの定理</a>\n",
    "\n",
    "の第3節を参照せよ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sanovの定理の使い方2\n",
    "\n",
    "KL情報量 $D(q||p)$ は, Sanovの定理によって, 確率分布 $p$ の試行を独立に $n$ 回繰り返したとき, 経験分布として $q$ に近い分布が出て来る確率が $\\exp(-nD(q||p)+o(n))$ になるという性質を持っているのであった.\n",
    "\n",
    "これより, 確率分布 $p$ の独立試行によって確率分布 $q$ をシミュレートしたときの, 予測誤差の大きさが $D(q||p)$ で測られることを意味していると考えることができる.  \n",
    "\n",
    "$q=p$ と $D(q||p)=0$ が同値であることも, この解釈をサポートしている. \n",
    "\n",
    "さらに, 最も簡単(で極端)な次の場合について考えてみよう. 毎日雨が確実に降る地域で, 毎日確率 $p$ で「明日は雨が降ります」と予報を出し, 確率 $1-p$ で「明日は雨が降りません」と予報を出すことを $n$ 回繰りかすとき, 予報の出し方が間違っていたことがばれずにすむ確率は $p^n = \\exp(-n(-\\log p))$ になる. そして, この場合のKL情報量は\n",
    "\n",
    "$$\n",
    "D(1||p) = 1\\log\\frac{1}{p} + (1-1)\\log\\frac{1-1}{1-p} = -\\log p\n",
    "$$\n",
    "\n",
    "となる(二項分布の場合の記号法をそのまま使った).  予報の出し方が間違っていたことがばれずにすむ確率が下がる速さは $D(1||p)=-\\log p$ で決まっている. ゆえに, KL情報量 $D(1||p)$ は予報の出し方が間違っていたことが確率的にばれる速さを表していると考えられる. この極端で単純な場合も, KL情報量 $D(q||p)$ を確率分布 $p$ による確率分布 $q$ のシミュレーションの予測誤差を表しているという解釈をサポートしている.\n",
    "\n",
    "より一般の場合には, Sanovの定理は\n",
    "\n",
    "* (確率分布 $p$ の独立試行の経験分布が $q$ に近い確率) $= \\exp(-nD(q||p)+o(n))$\n",
    "\n",
    "と要約でき, 確率分布 $p$ の独立試行の経験分布が $q$ に近いことは, 確率分布 $p$ の独立試行により確率分布 $q$ の予測が間違っていることがばれずに済んでいることを意味していると解釈できるので, やはり $D(q||p)$ は予測が間違っていたことがばれるまでの速さになっていると解釈できる.\n",
    "\n",
    "KL情報量は以上の意味で予測誤差になっていると考えられる:\n",
    "\n",
    "* $D(q||p) =$ (確率分布 $p$ の独立試行による確率分布 $q$ のシミュレーションの予測誤差)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 連続的な確率分布の場合\n",
    "\n",
    "連続的な確率分布の場合であっても, 確率密度函数 $q(x)$, $p(x)$ に対するKL情報量が\n",
    "\n",
    "$$\n",
    "D(q||p) = \\int q(x)\\log\\frac{q(x)}{p(x)}\\,dx\n",
    "$$\n",
    "\n",
    "と定義され($\\int$ は定積分を意味する), 適当な条件と適切な定式化のもとでSanovの定理が成立していることが知られている:\n",
    "\n",
    "*  $D(q||p) =$ (確率分布 $p$ の独立試行による確率分布 $q$ のシミュレーションの予測誤差).\n",
    "\n",
    "正確な内容については「<a href=\"https://www.google.co.jp/search?q=%E5%A4%A7%E5%81%8F%E5%B7%AE%E5%8E%9F%E7%90%86+Sanov%E3%81%AE%E5%AE%9A%E7%90%86\">大偏差原理 Sanovの定理</a>」について検索して欲しい.  (連続的な $x$ 軸を $r$ 個に区切れば, $x$ 軸上の確率分布は有限集合 $\\Omega=\\{1,\\ldots,r\\}$ 上の確率分布で近似できることに注意せよ.)\n",
    "\n",
    "確率分布 $p$ による独立試行で確率分布 $q$ をシミュレートする状況を考えよう. $\\int_{-\\infty}^\\infty$ を単に $\\int$ と書くことにすると, その場合の予測誤差は\n",
    "\n",
    "$$\n",
    "D(q|p) = \\int q(x)\\log\\frac{q(x)}{p(x)}\\,dx = G(q||p) - S(q).\n",
    "$$\n",
    "\n",
    "ここで\n",
    "\n",
    "$$\n",
    "G(q||p) = -\\int q(x)\\log p(x)\\,dx, \\quad\n",
    "S(q)=-\\int q(x)\\log q(x)\\,dx\n",
    "$$\n",
    "\n",
    "といおいた. $S(q)$ は**Shannon情報量**と呼ばれ, $G(q||p)$ は**汎化誤差**と呼ばれる."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 正規分布による近似\n",
    "\n",
    "例として, 正規分布\n",
    "\n",
    "$$\n",
    "p(x) = p_N(x|\\mu,\\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-(x-\\mu)^2/(2\\sigma^2)}\n",
    "$$\n",
    "\n",
    "による独立試行で確率分布 $q(x)$ をシミュレートする場合について考えよう. 予測誤差を小さくするためには, パラメーター $\\mu,\\sigma$ を調節して汎化誤差 $G(q||p)$ を小さくすればよい.  $p$ が正規分布の場合には\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "G(q||p) &= \n",
    "\\int q(x)\\left(\\frac{(x-\\mu)^2}{2\\sigma^2} + \\frac{1}{2}\\log\\sigma^2 + \\log\\sqrt{2\\pi}\\right)\\,dx\n",
    "\\\\ &=\n",
    "\\frac{1}{\\sigma^2}\\int q(x)(x-\\mu)^2\\,dx + \\frac{1}{2}\\log\\sigma^2 + \\log\\sqrt{2\\pi}.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "$q(x)$ の平均と分散を\n",
    "\n",
    "$$\n",
    "\\mu_q = \\int q(x)x\\,dx, \\quad\n",
    "\\sigma_q^2 = \\int q(x)(x-\\mu_q)^2\\,dx\n",
    "$$\n",
    "\n",
    "と書くと, \n",
    "\n",
    "$$\n",
    "\\int q(x)(x-\\mu)^2\\,dx =\\int q(x)((x-\\mu_q)-(\\mu-\\mu_q))^2\\,dx =\n",
    "\\sigma_q^2 + (\\mu-\\mu_q)^2\n",
    "$$\n",
    "\n",
    "なので\n",
    "\n",
    "$$\n",
    "G(q||p) =\n",
    "\\frac{(\\mu-\\mu_q)^2}{2\\sigma^2} + \\frac{\\sigma_q^2}{2\\sigma^2} + \\frac{1}{2}\\log\\sigma^2 + \\log\\sqrt{2\\pi}.\n",
    "$$\n",
    "\n",
    "これより, $G(q||p)$ を最小にする $\\mu,\\sigma$ は $\\mu=\\mu_q$, $\\sigma=\\sigma_q$ となることがわかる. \n",
    "\n",
    "すなわち, 正規分布による確率分布 $q(x)$ のシミュレーションの予測誤差を最小にするためには, 正規分布の平均と分散を確率分布 $q(x)$ の平均と分散に一致させればよいことがわかった.\n",
    "\n",
    "この結果は未知の確率分布 $q(x)$ のサンプルに基いてその平均と分散の両方を推定することは, 未知の確率分布 $q(x)$ を最も小さな予測誤差でシミュレートできる正規分布を推定することと同じことであることがわかる.\n",
    "\n",
    "平均と分散に関する統計学は, KL情報量のSanovの定理の立場から見ると, 本質的に正規分布の統計学であるということがわかった.\n",
    "\n",
    "以上のように, **KL情報量のSanovの定理は, 「パラメーターの推定」という考え方をより普遍的な「確率分布の推定」という考え方に高めるため役に立つ**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**問題:** 上の計算で省略した部分を埋めよ.\n",
    "\n",
    "**解答例:** $\\sigma$ を固定したときの $G(q||p)$ の最小値は $\\mu=\\mu_q$ で与えられることは明らか. \n",
    "\n",
    "$$\n",
    "f(s) = \\frac{a}{s} + \\log s\n",
    "$$\n",
    "\n",
    "とおくと, \n",
    "\n",
    "$$\n",
    "f'(s) = -\\frac{a}{s^2}+\\frac{1}{s} = \\frac{s-a}{s^2}\n",
    "$$\n",
    "\n",
    "なので $f(s)$ は $s=a$ で最小になることがわかる. これより, $G(q||p)$ は $\\mu=\\mu_q$, $\\sigma=\\sigma_q$ のときに最小になることがわかる. $\\QED$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**問題:** 次の確率密度函数で定義される分布をロジスティック分布と呼ぶ:\n",
    "\n",
    "$$\n",
    "q(x) = \\frac{1}{4s} \\sech^2\\left(\\frac{x-\\mu}{2s}\\right).\n",
    "$$\n",
    "\n",
    "ここで\n",
    "\n",
    "$$\n",
    "\\sech x = \\frac{1}{\\cosh x}, \\quad \\cosh x = \\frac{e^x+e^{-x}}{2}.\n",
    "$$\n",
    "\n",
    "ロジスティック分布の平均と分散はそれぞれ\n",
    "\n",
    "$$\n",
    "\\mu_q = \\mu, \\quad \\sigma_q^2 = \\frac{\\pi^2 s^2}{3}.\n",
    "$$\n",
    "\n",
    "ロジスティック分布を最もよくシミュレートする正規分布の確率密度函数ともとのロジスティック分布の確率密度函数を同時にプロットしてみよ. $\\QED$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\" />"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdflogistic(μ,s,x) = 1/(4s)*sech((x-μ)/(2s))^2\n",
    "pdfnormal(μ,σ,x) = exp(-(x-μ)^2/(2*σ^2))/√(2π*σ^2)\n",
    "\n",
    "μ = 0.0\n",
    "s = 1.0\n",
    "σ = π*s/√3\n",
    "x = -10:0.02:10\n",
    "\n",
    "P = plot(legend=:topleft, ylims=(0, 0.26))\n",
    "plot!(x, pdflogistic.(μ,s,x), label=\"logistic\", lw=2)\n",
    "plot!(x, pdfnormal.(μ,σ,x),   label=\"normal\",   lw=2, ls=:dash)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ロジスティック分布の正規分布による近似に関しては\n",
    "\n",
    "* 黒木玄, <a href=\"http://nbviewer.jupyter.org/gist/genkuroki/96b0508a5773035e3a5247beff1d4f99\">ロジスティック分布の2通りの正規分布近似の比較</a>\n",
    "\n",
    "も参照せよ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多項分布の中心極限定理\n",
    "\n",
    "Sanovの定理の証明によって, $k_i/n\\sim q_i$ ($n\\to\\infty$) のとき, $n\\to\\infty$ で,\n",
    "$$\n",
    "\\frac{n!}{k_1!k_2!\\cdots k_r!} p_1^{k_1}p_2^{k_2}\\cdots p_r^{k_r}\n",
    "\\sim\n",
    "\\left(\n",
    "\\prod_{i=1}^r \\left(\\frac{k_i/n}{p_i}\\right)^{k_i}\n",
    "\\sqrt{(2\\pi n)^{r-1}\\prod_{i=1}^r\\frac{k_i}{n}}\n",
    "\\right)^{-1}.\n",
    "$$\n",
    "\n",
    "これを\n",
    "\n",
    "$$\n",
    "\\frac{k_i}{n} = p_i + \\frac{x_i}{\\sqrt{n}} + \\eps_i, \\quad\n",
    "\\eps_i=o\\left(\\frac{1}{\\sqrt{n}}\\right)\n",
    "$$\n",
    "\n",
    "の場合に適用すると,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&\n",
    "\\sum_{i=1}^r\\left(\\frac{x_i}{\\sqrt{n}}+\\eps_i\\right) = \n",
    "\\sum_{i=1}^r \\frac{k_i}{n} - \\sum_{i=1}^r p_i = 0,\n",
    "\\\\ &\n",
    "\\log\\left(\\frac{k_i/n}{p_i}\\right)^{k_r} =\n",
    "np_i\\left(1+\\frac{x_i}{\\sqrt{n}\\;p_i}+\\frac{\\eps_i}{p_i}\\right)\n",
    "\\log\\left(1+\\frac{x_i}{\\sqrt{n}\\;p_i}+\\frac{\\eps_i}{p_i}\\right) =\n",
    "n\\left(\\frac{x_i}{\\sqrt{n}} + \\eps_i\\right) + \\frac{1}{2}\\frac{x_i^2}{p_i} + o(1),\n",
    "\\\\ & \\therefore\\quad\n",
    "\\log\\prod_{i=1}^r \\left(\\frac{k_i/n}{p_i}\\right)^{k_i} =\n",
    "\\sum_{i=1}^r \\log\\left(\\frac{k_i/n}{p_i}\\right)^{k_i} = \\frac{1}{2}\\sum_{i=1}^r \\frac{x_i^2}{p_i} + o(1),\n",
    "\\\\ &\n",
    "\\prod_{i=1}^r \\frac{k_i}{n} = p_1\\cdots p_r(1+o(1))\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "なので\n",
    "\n",
    "$$\n",
    "\\frac{n!}{k_1!k_2!\\cdots k_r!} p_1^{k_1}p_2^{k_2}\\cdots p_r^{k_r}\n",
    "\\sim\n",
    "\\frac{\\ds\\exp\\left(-\\frac{1}{2}\\sum_{i=1}^r\\frac{x_i^2}{p_i}\\right)}\n",
    "{\\sqrt{(2\\pi n)^{r-1}p_1\\cdots p_r}}.\n",
    "$$\n",
    "\n",
    "両辺に $dk_1\\cdots k_{r-1} = \\sqrt{n}\\;dx_1\\cdots\\sqrt{n}\\;dx_{r-1}$ をかけると,\n",
    "\n",
    "$$\n",
    "\\frac{n!}{k_1!k_2!\\cdots k_r!} p_1^{k_1}p_2^{k_2}\\cdots p_r^{k_r}\\,dk_1\\cdots dk_{r-1}\n",
    "\\sim\n",
    "\\frac{\\ds\\exp\\left(-\\frac{1}{2}\\sum_{i=1}^r\\frac{x_i^2}{p_i}\\right)}\n",
    "{\\sqrt{(2\\pi)^{r-1}p_1\\cdots p_r}}\n",
    "\\,dx_1\\cdots dx_{r-1}.\n",
    "$$\n",
    "\n",
    "$k_1+\\cdots+k_r=n$ より $x_1+\\cdots+x_r=o(1)$ であることに注意せよ. 右辺は $(x_1,\\ldots,x_{r-1})$ の多変量正規分布の確率密度函数の形になっている.\n",
    "\n",
    "以上の結果は多項分布が $n$ が大きなときに多変量正規分布で近似できることを意味している. この結果を**多項分布の中心極限定理**と呼ぶ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**二項分布の中心極限定理:** $r=2$ のとき, $0\\leqq p\\leqq 1$, $k/n = p + x/\\sqrt{n} + o(1/\\sqrt{n})$ のとき,\n",
    "\n",
    "$$\n",
    "\\binom{n}{k}p^k(1-p)^{n-k}\\,dk \\sim\n",
    "\\frac{\\ds\\exp\\left(-\\frac{1}{2}\\left(\\frac{x^2}{p}+\\frac{(-x)^2}{1-p}\\right)\\right)}\n",
    "{\\sqrt{2\\pi p(1-p)}}\\,dx =\n",
    "\\frac{\\ds\\exp\\left(-\\frac{x^2}{2p(1-p)}\\right)}\n",
    "{\\sqrt{2\\pi p(1-p)}}\\,dx.\n",
    "$$\n",
    "\n",
    "この結果を**二項分布の中心極限定理**と呼ぶ. $\\QED$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "より一般の場合の中心極限定理の証明については\n",
    "\n",
    "* 黒木玄, <a href=\"https://genkuroki.github.io/documents/IntroProbability.pdf\">確率論入門</a>\n",
    "\n",
    "の第2.4節を参照せよ. 本質的にTaylorの定理のみを使って中心極限定理は証明される. (積率母函数や特性函数の理論(本質的にFourier-Laplace解析の理論)を使わなくても証明できる.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**問題:** 二項分布の中心極限定理を実際にグラフをプロットすることによって確認せよ. $\\QED$\n",
    "\n",
    "次のセルを見よ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binomcoeff(n,k) = exp(lgamma(n+1)-lgamma(k+1)-lgamma(n-k+1))\n",
    "pdfbinom(n,p,k) = 0 ≤ k ≤ n ? binomcoeff(n,k)*p^k*(1-p)^(n-k) : 0.0\n",
    "pdfnormal(n,p,x) = exp(-x^2/(2p*(1-p)))/√(2π*n*p*(1-p))\n",
    "\n",
    "PP = []\n",
    "for (n,p,l) in [(6, 0.4, :bottom), (12, 0.4, :topright), (25, 0.4, :topright), (50, 0.4, :topright)]\n",
    "    k = 0:n\n",
    "    kk = 0:n/400:n\n",
    "    x = (kk .- n*p)./√n\n",
    "    P = plot(legend=l, legendfontsize=7, xlabel=\"k\")\n",
    "    scatter!(k, pdfbinom.(n,p,k),  label=\"Bin($n, $p)\", markersize=2.5)\n",
    "    plot!(kk, pdfnormal.(n,p,x), label=\"Normal dist\", lw=1.5, ls=:dash)\n",
    "    push!(PP, P)\n",
    "end\n",
    "plot(PP..., size=(800, 600))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "data": {
    "description": "11 Kullback-Leibler information",
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   "title_cell": "目次",
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