{ "cells": [ { "cell_type": "markdown", "id": "dietary-sample", "metadata": {}, "source": [ "# Logistic Regression (an example)\n", "\n", "
\n", " このページのオリジナルのipynbファイル
\n", " ホームへ戻る To homepage\n", "
\n", "\n", "これまで扱ってきたデータは、説明変数に対する目的変数の値は、平均値の周りにガウス分布すると想定してきました。\n", "\n", "(参考:PRML 図1.16)\n", "\n", "\n", "\n", "しかし、目的変数に上限、下限がある場合は、平均値が上限、下限に近いときガウス分布するとは言えません。\n", "\n", "典型例としてよく紹介されるのは、学習時間を説明変数、試験の合否を目的変数にとるような場合です。この場合、目的変数は2値ですが、同じ時間勉強しても合格者も不合格者も一定割合ででるでしょう。その確率分布はどのようになるか、また合格可能性を勉強時間の関数とした数値で表すにはどうしたらよいでしょう。\n", "\n", "[WikipediaのLogistic Regression](https://en.wikipedia.org/wiki/Logistic_regression)では、その例が載っています。\n", "\n", "![A graph of Logistic Regression](https://upload.wikimedia.org/wikipedia/commons/6/6d/Exam_pass_logistic_curve.jpeg)\n", "\n", "合格可能性を$p$ とすると合格者数の分布は次のような二項分布になると想定されます。このような場合は、サンプル集団の合格者数分布は合格可能性曲線の上下でガウス分布のような対称な形とはなりません。その意味では「平均」としての合格可能性の意味には慎重な解釈が必要になります。\n", "(この図(ヒストグラム)を作成するプログラムは、下の「参考」に掲載。)\n", "\n", "![2項分布](images/binomial_max10.png)\n", "\n", "\n", "同じような問題ですが、\n", "\n", "この授業では、生態学でのサンプルデータを扱ってみます。\n", "\n", "「データ解析のための統計モデリング入門」(久保拓弥、岩波)の著者ページにリンクがある、著者の講義ノート\n", "https://kuboweb.github.io/-kubo/ce/EesLecture2008.html#toc5\n", "からの引用です。\n", "\n", "上記ページでは統計処理言語Rのプログラム例が載っていますが、ここではpythonで分析を試みます。\n" ] }, { "cell_type": "markdown", "id": "three-pennsylvania", "metadata": {}, "source": [ "## サンプルデータ\n", "\n", "ある植物の種が発芽するかどうかは、植物個体の大きさとその植物に施肥したかどうかによるかどうかを分析します。(データは仮想のものです。)\n", "\n", "
\n", "
目的変数: 発芽した種子数(y)
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各個体からとったN個の種子のうち発芽した数(データではすべてN=8)\n", "
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説明変数
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\n", " \n", "
\n", "
\n", "\n", "まずは、データは、上記ページにある\"data4a.csv\"です。次のURLよりダウンロードし、各自のスクリプトで読めるところにおいてください。\n", "\n", "https://kuboweb.github.io/-kubo/stat/2008/d/fig/data4a.csv\n", "\n", "これをpandasのDataFrameに読み込んで使います。\n", "\n", "(注)\n", "1. Google colabでのファイルの扱いについては、プレ授業用の資料を参照してください。\n", " https://colab.research.google.com/drive/1aFaB9KzxKjkiyiwgME2wKcmpQ7yMFHRs?usp=sharing\n", "2. 下のセルのでコメントアウトした行のようにkuboのページにあるソースのURLを直接指定して読み込むことも可能です。\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "deluxe-semester", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Nyxf
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" ], "text/plain": [ " N y x f\n", "0 8 1 9.76 C\n", "1 8 6 10.48 C\n", "2 8 5 10.83 C\n", "3 8 6 10.94 C\n", "4 8 1 9.37 C\n", ".. .. .. ... ..\n", "95 8 7 10.45 T\n", "96 8 0 8.94 T\n", "97 8 5 8.94 T\n", "98 8 8 10.14 T\n", "99 8 1 8.50 T\n", "\n", "[100 rows x 4 columns]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# You need to put the csv file in your own folder downloaded from\n", "# https://kuboweb.github.io/-kubo/ce/EesLecture2008.html#toc5 \n", "import pandas as pd\n", "#df = pd.read_csv(\"data/data4a.csv\")\n", "# Alternatively, you can use kubo's data directly through URL\n", "df = pd.read_csv(\"https://kuboweb.github.io/-kubo/stat/2008/d/fig/data4a.csv\")\n", "df" ] }, { "cell_type": "code", "execution_count": 13, "id": "2a5d009e-4a77-4ae6-b2d8-1d529f7a44dd", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "plt.rcParams['font.family'] = 'IPAGothic' # Linux上で日本語フォントを扱う場合\n", "# plt.rcParams['font.family'] = 'MS Gothic' # Windowsで日本語フォントが使えないとき利用\n", "df_C = df[df['f']=='C'] # extract df['f'] == 'C'\n", "df_T = df[df['f']=='T']" ] }, { "cell_type": "code", "execution_count": 18, "id": "9e4d3fe0-ab1d-4bc8-afa4-b7059d1cae14", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(df_C['x'], df_C['y'], label=\"C\")\n", "plt.scatter(df_T['x'], df_T['y'], label=\"T\")\n", "plt.legend()\n", "plt.xlabel(\"親のサイズ x\")\n", "plt.ylabel(\"発芽数 y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ready-quebec", "metadata": {}, "source": [ "## scikit-learnでのLogistic Regression\n", "\n", "$f(x)\\rightarrow 1\\ {\\rm as\\ } x \\rightarrow \\infty$、$f(x)\\rightarrow 0\\ {\\rm as\\ } x \\rightarrow -\\infty$のような関数の典型例はlogistic functionと呼ばれます。($\\tanh$関数のスケール変換したものと同じです。)\n", "\n", "$$\n", " f(x) = \\frac{1}{1 + e^{-x}} = \\frac{1}{2}\\left(1 + \\frac{e^{x/2} - e^{-x/2}}{e^{x/2} + e^{-x/2}}\\right) =\n", " \\frac{1}{2}\\left(1 + \\tanh (x/2) \\right)\n", " $$" ] }, { "cell_type": "code", "execution_count": 16, "id": "imperial-narrative", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "x = np.linspace(-4,4,100)\n", "y = 1. /(1. + np.exp(-x))\n", "plt.plot(x,y)\n", "plt.title(\"Logistic function\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "continental-finland", "metadata": {}, "source": [ "この曲線に近似するのがLogistic Regressionですが、上の例のように、目的変数は合格か不合格かの2値であるような問題に適用される場合が多いためか、sciki-learn の Logistic Regression モジュールは、regressorsではなくclassifiersのカテゴリに入っています。\n", "\n", "https://scikit-learn.org/stable/modules/classes.html#module-sklearn.linear_model\n", "\n", "Logistic Regression は、多くの場合、2値問題(ある事象が起こるか起こるか)を説明変数から推定する場合に用いられます。\n", "\n", "ここでの例でも、あるサイズの親から取った種が発芽するかしないかの確率を求める問題といってもよくその意味ではクラス分け問題に属するのですが、データの与え方が異なります。\n", "\n", "各行が8個中何個が発芽したかが目的変数になるので、単純にここで読み込んだデータフレームを渡すと、各行が9種類にカテゴライズされるという結果になります。\n", "\n", "以下ではそれを確かめてみます。\n", "\n", "本来のlogistic regressionを行うためのモジュールはscikit-learnにはないようなので、あとで、もう一つの統計モジュールであるstatsmodelsを使ってみます。" ] }, { "cell_type": "code", "execution_count": 21, "id": "portable-demand", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "LogisticRegression(max_iter=500)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import LogisticRegression\n", "lr_C = LogisticRegression(max_iter=500)\n", "lr_T = LogisticRegression(max_iter=500)\n", "\n", "lr_C.fit(df_C[['x']], df_C['y']) # explanation variables (features) are an array\n", "lr_T.fit(df_T[['x']], df_T['y'])\n", "# warning will be returned but you will get resultant learned machines" ] }, { "cell_type": "markdown", "id": "worldwide-formula", "metadata": {}, "source": [ "本来、予測したいことは、与えられたサイズの親から採取した種が発芽する確率ですが、ここでは親のサイズと8個中何個が発芽するかのデータなので、結果も0個から8個までそれぞれの確率が得られます。\n", "\n", "まずは、確率が最大になる個数を図示してみます。\n", "その値は、predict関数に、引数としてサイズを与えることにより得られます。" ] }, { "cell_type": "code", "execution_count": 25, "id": "opposite-county", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/anaconda3/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n", " warnings.warn(\n", "/opt/anaconda3/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n", " warnings.warn(\n" ] } ], "source": [ "# 親のサイズに対する発芽数予測:predict bud-break number for a given parent-size\n", "import numpy as np\n", "x_test = np.linspace(6,12.0, 200)\n", "predicted_C = lr_C.predict(x_test[:, np.newaxis])\n", "predicted_T = lr_T.predict(x_test[:, np.newaxis])" ] }, { "cell_type": "markdown", "id": "encouraging-things", "metadata": {}, "source": [ "最大確率をもつ個数をプロットすると次のようになります。" ] }, { "cell_type": "code", "execution_count": 26, "id": "nuclear-position", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Predicted value versus the bud-break number in eight\n", "# predicted value is one with the highest probablity\n", "plt.scatter(df_C['x'], df_C['y'])\n", "plt.plot(x_test, predicted_C)\n", "plt.scatter(df_T['x'], df_T['y'], color='#ff7f00')\n", "plt.plot(x_test, predicted_T, color='#ff7f00')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "floppy-joseph", "metadata": {}, "source": [ "確率分布はpredict_probaにより得られます。" ] }, { "cell_type": "code", "execution_count": 8, "id": "periodic-thumb", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/anaconda3/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n", " warnings.warn(\n" ] } ], "source": [ "X=np.linspace(7.0,13.0,5)\n", "prob_C = lr_C.predict_proba(X[:, np.newaxis])" ] }, { "cell_type": "code", "execution_count": 20, "id": "victorian-andorra", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "size = np.linspace(0,8,9)\n", "for i, p in enumerate(prob_C):\n", " plt.plot(size, p, label=X[i])\n", "plt.legend(title=\"親のサイズ\")\n", "plt.xlabel(\"発芽数(max=8)\")\n", "plt.ylabel(\"確率\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "expected-alias", "metadata": {}, "source": [ "発芽確率を$p$とすると、$N$個中$n$個が発芽する確率は2項分布\n", "$$\n", "P_p(n) = \\frac{N!}{n!(N-n)!}p^n(1-p)^{N-n}\n", "$$\n", "になるはずです。\n", "\n", "2項分布をいくつかの確率で書いてみると次のようになります。\n", "\n", "データから予測された確率分布とはだいぶ異なりますが、これはデータ数の違いによるものでしょう。\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "brown-union", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import binom\n", "plt.plot(size, binom.pmf(size,8,0.1), label=\"p=0.1\")\n", "plt.plot(size, binom.pmf(size,8,0.3), label=\"p=0.3\")\n", "plt.plot(size, binom.pmf(size,8,0.6), label=\"p=0.6\")\n", "plt.plot(size, binom.pmf(size,8,0.9), label=\"p=0.9\")\n", "plt.legend()\n", "plt.xlabel(\"n\")\n", "plt.ylabel(\"$P_p(n)$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "addressed-guarantee", "metadata": {}, "source": [ "あるサイズ(横軸)に対して確率が二項分布になることを想定した回帰をscikit-learnで「直接」行う関数があるかもしれませんが、見つけられませんでした。\n" ] }, { "cell_type": "markdown", "id": "changed-financing", "metadata": {}, "source": [ "## statsmodelsによる回帰分析\n", "\n", "statsmodelsはRでの書式を用いる仕様になっているので、Rをよく知っている人、Rと併用したい人には使いやすいものとなっています。\n", "\n", "久保のテキストを参考に、statsmodelsを使ってみます。\n", "\n", "引数 **formula** に与える式がR独特のものでわかりにくいのですが、\n", "- チルダ\"~\"の左が目的変数、右が説明変数\n", "- \"+\"は足し算ではなく、複数の変数をセットするという意味\n", "- I()は独立変数としてセットするという意味\n", "\n", "と解釈してください。" ] }, { "cell_type": "code", "execution_count": 27, "id": "incorporated-drain", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Generalized Linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: ['y', 'I(N - y)'] No. Observations: 100\n", "Model: GLM Df Residuals: 97\n", "Model Family: Binomial Df Model: 2\n", "Link Function: Logit Scale: 1.0000\n", "Method: IRLS Log-Likelihood: -133.11\n", "Date: Wed, 26 Jul 2023 Deviance: 123.03\n", "Time: 11:12:56 Pearson chi2: 109.\n", "No. Iterations: 6 Pseudo R-squ. (CS): 0.9768\n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -19.5361 1.414 -13.818 0.000 -22.307 -16.765\n", "f[T.T] 2.0215 0.231 8.740 0.000 1.568 2.475\n", "x 1.9524 0.139 14.059 0.000 1.680 2.225\n", "==============================================================================\n" ] } ], "source": [ "import statsmodels.formula.api as smf\n", "import statsmodels.api as sm\n", "N=8\n", "# 説明変数x及びf、目的変数yが起こる確率pと、1-pとの関係を二項分布だとしてフィッティング\n", "model = smf.glm(formula='y + I(N-y) ~ x + f', \n", " data=df, family=sm.families.Binomial())\n", "result = model.fit()\n", "print(result.summary())" ] }, { "cell_type": "code", "execution_count": 10, "id": "75bbe022-8eb3-4a00-8ea8-521a80b9124a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model" ] }, { "cell_type": "code", "execution_count": 28, "id": "musical-shepherd", "metadata": {}, "outputs": [], "source": [ "df['predict'] = result.predict() # xに対する予測値を列に加える" ] }, { "cell_type": "code", "execution_count": 29, "id": "linear-newton", "metadata": {}, "outputs": [ { "data": { "image/png": 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Z1R6ydJlnI46aaMaL0LX0kPv+e7jvPsjJqZrqOzERRo82tzQGD1YvDTGUUIhIZHFvgG//A4tnQckWs651OzjkMjjyWujUx9n4osR338Gdd5rBpyodd5y5GjFmjHlOQqQ6JRQiEhm2rYbc+2Dpc+AtM+s69IIjr4NDLoU2yY6GFy2WLDGJxLx55r3LBeedB1OmmMm3RHxRQiEizirMh0/uhu+eAG+5WdfjOPN8RP8zIUZjL4fD4sUmkXj7bfM+JgbGjoWpU6F/f2djk+ZBCYWIOKNkO3w+wzxsWdljY+9T4IQ7zLTgEhZLlsC0afDOO+Z9TIwZxXLqVOjXz9nYpHlRQiEi4bWrGL55FD77J+zcZtalHg2nTDeTcklYbNwIt9xiun+CSSTOP98kEvvu62xs0jwpoRCR8PB64aeXYeHNVYNRdRkIJ98H/Uaox0aY7NoFjzxibm8UFpp1559vrlLss4+zsUnzpoRCREJv3dfw7nWw/hvzPrknnHgXHHi+npEIowULYOLEqnEkBg0yycXRRzsalrQQSihEJHTKSuCj2+HLh8Dymu6f6beacSRaaXaocFm5EiZNquoC2qUL/POfpguoxpCQYFFCISKhsfYLmHsJbPmfeX/A+TD0QWi/l7NxRZGiIjMo1b/+ZW51xMXBtdfC7bebKcRFgkkJhYgE165iWDTV9N7AgnYpMGKWeU5CwsKyYPZsmDzZDJkNMGQIZGXBfvs5G5u0XEooRCR41uTC3Eth6+/m/cEXw6kPQUJHR8OKJmvWwJVXwvvvm/e9e8PDD8PIkXruVUJLCYWIBG7XDvjwFvj6EcCC9t1hxOOw72lORxY1vF6YNQtuvNHc6oiPN11A//EPaKPHVSQMlFCISGD++MRcldi2yrw/5FIY+i9I6OBoWNFk7VrzgOVHH5n3xx4LTz2lgakkvPxKKD7++GNOPPHEOus//fRT0tPTgxaUSETxesyl/KJ88zxAz/Tm0dWxMu7C9bBjM7TtYq4cNBS/P3UtLYIPp5hBqgCSUmHEE7DPsMBjDrSt/dyPxwO5uZCfDykpkJ4OsfUUt1sunF55Ba66CgoKzCyg06fDNdfY671hpz6RWOdIjiua+ZVQDB48mJKSkt3v8/LyGDRoEIMGDQp6YCIRYXkOLJgA7nVV65JSYVgWDMhwLq7G1Bd3JV/x+1PX1R/B3Mtg+2rz/tArYOgDgU3gFay29nM/OTkwYQKsq1Y8NdU8wJiR4X+5cHG7TeLwwgvm/ZFHwosvQt++9ra3U59Iq3OlSI0r2rksy7KauvH06dNZvnw5L1T+RjfA7XaTnJxMQUEBSUlJTT2kSPgsz4FXRwO1/4tUPNk2JjsykwqfcVfnqhm/3bqWFsIHN8Hix8z65B4w8knoMyREMfvZ1n7uJycHRo82vSJqlK4onp1tTlB2y4XL55/D3/4Gf/xhrkRMnWperVrZ295OfSCy6lwp0j6LaGD3/B1QQjFw4EAefPBBhg8fHrSARCKC1wOZver/hg+Ay3zrnbg6sm5/NBp3pWrxg726nvk0vHU5FKwxqw+7CobMgPj2IY7ZZlv7uR+PB3r1qvktt0Zpl/nW+/vv0KdP4+VWrw79JXePB+6+27y8XhP/iy+aZyb82Udj9e7e3SxHQp2rs/uZhTuuls7u+bvJY6T9+OOPbN68mSFD6v9mUlpaitvtrvESaTbW5DZyUrbAnWfKRZJG465ULX67dX1hqEkmOvSCCz+EMx4LPJmwFbPNtvZzP7m5vk9MYL4B5+XBzJn2yuWG+Fdh40YYOtTMweH1woUXwg8/+JdMgL16r1sXGXWuze5nFu64xGhyQjFnzhxGjx5NXFz9j2FMnz6d5OTk3a+0tLQmBykSdkX5wS0XLv7GU5TvxzYWHHwJ/N9PsPdJfofWYAzBKOfnfvJtFl+50l45u/triq++MvNuLFoEbdua5yaeew6acrE3mHGGss6BHC/ccYnR5IQiOzu7wVsdU6ZMoaCgYPcrLy+vqYcSCb92KcEtFy7+xtMuxf42R98AZz0N8e38j6uxGIJRzs/9pNgs3qePvXJ29+evJ56AwYPNiJf77QeLF5vnJ5oqmHGGqs6BHi/ccYnRpIRi+fLlrF69ut4upJXi4+NJSkqq8RJpNnqmm/vtlQ/z1eGCpDRTLpLsjrsx1eJvtK5A264w5P5gRVlTsNraz/2kp5v77b5Gj3S5IC0Nxo+3Vy7YPedLS0130CuvhLIyGDUKvv4a+vcPbL926p2a6kydG2P3M9MoBs5oUkIxd+5cjj76aNq1C/I3FZFIERNruhkCdU9QFe+HZUbWA5lQLW4bYyxXxl+jrj6c/ljo6hqstvZzP7Gxppsh1D1BVb7PzITWre2VC+ZDgPn5cOKJZuRLlwvuvdf0XmgfhEdW7NQ7Kyv8dbbD7memBzKd0aSEYv78+QwdOjTYsYhElgEZppthUvea65NSI7fLKFSL28eViqS0uvEPyICznoPY+Jpl26fCmNdDX9dgtbWf+8nIMCfq7rWKp6bW7H5ot1wwLFlinpf48ktIToa334ZbbgnuNON26hPOOvsjUuOSALuN+kPdRqXZioaRMreugtkjYPNyiGsDg/4O/c8Kf12jfKTM9983J8QdO2DgQHjzTfsDVTWFRsoUO8IyDkUoAhKRMMv7yiQTxX+ZhGPcPEg5xOmoos6LL8Ill0B5OZx8shnASX8qJRKEfBwKEWkBfnkLnjvJJBMpg+CKb5RMhJllwYMPwgUXmGRi7FiYP1/JhDQ/SihEotXix2HOKCgvgX1Og0s+gaRuTkcVVbxeuOEGmDzZvL/+enOlonVrZ+MSaQpNXy4SbSwLPr4DPrnLvD/kUjhjFsTqz0E4lZaaKcdfecW8f/BBk1yINFf6CyISTTzl8M7/wXdPmvfH3w4n3OG7Y7+EhNttxpVYtAji4uDZZ+H8852OSiQwSihEokV5Kbw+DlbkgCvGjC1x2JVORxV1Nm6E4cNh6VJo1w5ef93M0SHS3CmhEIkGu3bAK6Ng1QcQ2xpGz4H9znI6qqjzv//BsGFmNsyuXc3Dl4MGOR2VSHAooRBp6Xa64eUzYG0utGoLY+fC3ic7HVXU+fZbOO00+OsvMz/Ie+/ZnydEpDlQQiHSkpVshxeHwfqvIT4Z/vYupB3tdFRR54svzJWJwkJzRWL+fHOFQqQlUUIh0lKVbIcXhsCGxZDQCS54H7rp+nq4ffaZeWaiqAiOPx7mzQvOnBwikUYJhUhLtLMAXhhqkonEPeDCD2GvA52OKup89pm5MrFjB5x0Erz1FrRt63RUIqGhga1EWpqdbnjhVNjwLSR0VjLhkKVL4fTTTTIxZIi5MqFkQloyXaEQaUlKC6uemUjoBBcpmXDCb7/Bqaea8SYGD4a5cyEhwemoREJLVyhEWoqyEnh5BKz7Etp0hAsXwl4HOR1V1Fm/3lyR+PNPOPhgc5tDyYREAyUUIi2BpwxeOxfWfALxSXDhB5rkywFbt5orE2vWmGnHFyyA5GSnoxIJDyUUIs2d1wtzL4X/zYO4NjB2nnpzOKCoyIwz8fPP0L07fPAB7Lmn01GJhI8SCpHmzLJgwUT48UWIiYMx2dBrsNNRRZ3SUsjIgK+/hk6d4P33oVcvp6MSCS8lFCLN2cd3wjePAC446znY93SnI4o6Hg9ccIG5ItG2rRm0asAAp6MSCT8lFCLN1VdZ8MmdZvm0R+DAcc7GE4UsC66+Gl57DVq1gjfegCOPdDoqEWcooRBpjn56xdzqADjxbjjiakfDiVZTp8KsWWb295deMr07RKKVEgqR5uaPT+HNi8zykdfB4FudjSdKPfQQ3HefWZ41C845x9l4RJymhEKkOdn8C7xyFnh2Qf9RcOpD5uuxhNWzz8INN5jl6dPhiiscDUckIiihEGkuijbBS6fBzm3Q/UjIeBFiYp2OKurMnQuXX26Wb7gBbrrJ2XhEIoUSCpHmYNcOMwrm9tXQsQ+MmwetE52OKup88w2cd57p2XHJJfDAA7pAJFJJCYVIpPN6IedvFZN9dYLz50PbLk5HFXXWrIGRI2HnTjOA1eOPK5kQqU4JhUik+/gO+OVNiI2HsW/BHvs6HVHU2bHDJBObNsGBB8Irr0CcplYUqUEJhUgkW54Dn95tlkc8Dj2OdTaeKGRZcPHF8OOPZijtt9+G9u2djkok8iihEIlUm36CNy40y0dNhIMvdDScaHXffZCdbQauev11SEtzOiKRyKSEQiQSFW813UPLdkDvk2HIA05HFJXeessMXgXwn//AsbpAJOKTEgqRSOMph+zzYNsq6NAbzpkDsbphH27Ll8Pf/maWr75aY02INEYJhUikWXgzrPoAWiXCeW9CYmenI4o627bBmWdCYSEcfzw8/LDTEYlEPr+/9ng8Hq6//nqeeeYZOnfuzAMPPMA5GnNWIp3XA2tyoSgf2qVAz/SmDwrl9cDqj2HNx2ABvU+AXicEZ5CpH1+CL/9lls96DvY6sP7Ywb/6NFT/YLZNuNmI3eOB3FzIz4eUFEhPh9gGqldebsaa+P136NnTTPwVEwMff2x/H4GoL14w69avh82boUsX6N69Kg5/6ygSCn4nFI8++igrVqxg2bJlrFq1ijPOOIOTTz6ZTp06hSI+kcAtz4EFE8C9rmpdUioMy4IBGf7va96VULKlal3uPZDQ2fTC8Hd/1W1YAm9VDMGYfisMHF1/7AkVVyyqx9BQfRqqPwSvbcLNxueakwMTJsC6akVSUyErCzJ8VG/KFHj/fUhMhDffNCdqf/fRVPXF27ni496ypW751FQYOxZmzw5PfCINcVmWZfmzwUEHHUR2djb77LMPAMXFxbRp04aYmIbvnrjdbpKTkykoKCApKanpEYv4Y3kOvDoacymhuooRicZk2z9xLs+BV89uuMyY15t2Ii7aBI8fZk6O+5xuxpv45U0fsdfHR30arL+v/TahbcLNxuea80sGo0ebbp81SlQUyc6ue8KdPRvGVcwC/+qr5lu+v/toqpyc+o/VFKGIT6KX3fO3X89Q/PXXX2zYsIHPP/+cffbZh8GDB7Nq1apGkwkRR3g95htsvSfOinULJppydvb17nWNl1swwd7+qivfZU6O7nXQuR+c/ZKJz2fs9amnPnbqb3dfkcRGvawFE7l+oqfek3PluokTza2CSj//XDVHx5Qp5kQ8YUL9J3hf+2gqj8f3sZoi2PGJ2OFXJpCfn8+OHTuYPXs22dnZDB8+nFGjRlFWVlanbGlpKW63u8ZLJKzW5Na8HF6HBe48U87OvgrXN17Ovc7e/qr78BZY+xnEJ8HYudAm2Ubs9alVnybtw8e+IomNz9XlzqN3jO/YLQvy8sztDDAPX2ZkQHExnHIK3H23+dm6Bg5Tex+BaOxYTRHM+ETs8CuhKCoqoqSkhMzMTA466CCmTJlCTEwMX331VZ2y06dPJzk5efcrTaPBSLgV5QevnN19+Vt25QdVD2GOeh726Of/PnwdP5B91N5XJLEZU0r7xsvl55sT71VXwf/+Z549ePllc6sj32bV7ZYL9T6c2LdIdX4lFF27dgWgb9++u9f16NGDDRs21Ck7ZcoUCgoKdr/y8vICDFXET+1SglfO7r78Kbtjc9VImIePh/5nNu14vo4fyD6CEUeo2Iwpv7Dxcikp8MwzVUnEnDmmB0Xlz+ywWy7U+3Bi3yLV+ZVQpKWlkZSUxJo1a3av++OPP+jRo0edsvHx8SQlJdV4iYRVz3Tz1D++poR0QVJaVTfMxvbVvnvj5ZJS7e3PsmDupVC0EboMgKEP1j1eg7HXp1Z9mrQPH/uKJDY+VyspjdXedJ+zgbpcZgjtzp3hmmvMunvugWOOqSqTnm6uWDS2j/QgNFFjx2qKYMYnYodfCUXr1q25+OKLmTp1Kps3byYzM5OYmBiOOuqoUMUn0nQxsVVdI+ucfCreD8u0N+ZCTCwM/3fj5YZl2dvft4/B/942M4iePRtaJdQ9ns/Y61NPfezUv6Gf2W2bcLNRL9ewTB7ONLHXPklXvr//ftPlsqQEhg6FG2+sWS421nS9bGgfmZnBGe+hoWM1RbDjE7HD7+4Zd999Nzt37iQtLY1nn32W7OxsXMFMq0WCaUCG6f6YVOvqQlKq/90iB2SYbqGV40BUl9DZfpfRTcvg/RvM8pD7zeBV/sSe0LluDL7q02D9XzevYLRNuNn4XDMyTLfJ7rWKpKaa9R99ZHp27LUXPP+8Gbyqtsb2Ecwumb6O1blz1VgUtaWlweTJJp5QxyfSGL/HoWgqjUMhjoqUkTLLdsITh8Ofy6DvcDj/nca/kmqkTN+aOFJmdrYZDdPlgg8+gJNPbvgw4RyJUiNlSqSxe/5WQiESTu9OgK//DW27wv/9CO32dDqiqLNyJRxyiOkqOnWq6SIqIr6FZGArEQnA/94xyQTAWc8qmXBAaSmce65JJtLTYdo0pyMSaTmUUIiEQ+FGePMSs3zkBNhnuLPxRKmbb4YlS6BTJ9NVNE6zwosEjRIKkVDzemHuJVC8GfY8EE75p9MRRaV580yvB4Bnn637IKOIBEYJhUioff1v+H0BxLWBs1+GVm2cjijqbNgAl1RcILr+ehgxwtl4RFoiJRQioZS/FBbeZJZPfQi6DnQ0nGhkWSaZ2LLFPIz5T10gEgkJJRQiobKrGF4fB55d0G8kHHaV0xFFpZkz4f33oU0b89xE69ZORyTSMimhEAmV92+Av1aY8RFGPhXccZXFlv/9zwz8BDBjBvTv72w8Ii2ZEgqRUFjxJiz+r1ke9Ry03cPRcKJReTlccIEZWvuUU+Dqq52OSKRlU0IhEmzu9fDWZWb5mH9AnyHOxhOlpk+Hb76B5GQzo2h9Q2uLSPDov5hIMHm9Zkrykq2QciicdK/TEUWlJUvgrrvM8n/+oy6iIuGghEIkmL54EFYvglaJpotonJ4ADLeSEnOro7wczjkHxo1zOiKR6KCEQiRY1i+GRbea5WFZsEc/Z+OJUrfcAitWmFlEH3tMz8KKhIsSCpFgKC0yXUS95bBfBhx6mdMRRaWPPqoaDfPpp31P+y0iwaeEQiQYPpgMW3+D9t1hxBP6WuyAoiK4rCKPu/JKGK7pUkTCSgmFSKBWLarZRTSxk7PxRKkpU2D1aujRAx580OloRKKPEgqRQJQWVXURPewq2PtkZ+OJUp98Ao8+apaffBLat3c2HpFopIRCJBALb4btf0ByDxgyw+loolJxcdWtjssvhyEa9kPEEUooRJrqj0/g2/+Y5ZFPQby+Fjvh1lth5Uoz1oRudYg4RwmFSFPs2gFzLzXLh14BfU5xNp4o9fnnkJVllp94woyKKSLOUEIh0hSLboNtqyApFYY+4HQ0UamkBC69tGp68mHDnI5IJLopoRDx17qv4atMszzicWijr8VOuPdeM5tot27w0ENORyMiSihE/FG+C966HLDgwL/BPhrswAnLlsH995vlRx+FDh0cDUdEUEIh4p/PZ8CfyyBxDzj1YaejiUpeL/z972aujjPPhFGjnI5IREAJhYh9m3+BT+82y8OyoO0ezsYTpR5/HL74Atq1g0cecToaEamkhELEDq8X5l0Bnl3QdzgcMNbpiKJSfj7cfLNZvvdeSEtzNh4RqaKEQsSOJbNg7WfQqi2coSksnTJhAhQUwOGHw9VXOx2NiFSnhEKkMYX58MFNZvnk+6BDT2fjiVJvvw2vvQaxsea2R2ys0xGJSHVKKEQa894NsKsQuh0OR+hrsROKiqquSEyaBAcf7Gg4IlIPJRQiDVn1ISybDbjMrY4YfS12wu23w9q10KsXTJvmdDQiUh8lFCK+lO+Cdyq+Fh8+HroNcjaeKLVkSdXw2o89Bm3bOhuPiNQvzt8NDj30UL7//vvd7/v168cvv/wS1KCkCbweWJMLRfnQLgV6pjevb9O+4neyXl/+C7b8Cm27wkn3NC3+cKoWgycxhdy16eRvjCUlBdLTHXzmwM+28XggN9f06OjaFW680XSyOe+8msNrVy9XWUeof93HH5sXwAknmFc426O+WPUMiLQ0ficURUVFfP/99/Tv3x+AmBhd5HDc8hxYMAHc66rWJaWasRIGZDgXl12+4t9/rLnd4ES9tv0Bn1SMOTH0X5DQwXfZSGj/WjHEAn0KUvn3gize+CWD1FTzLT8j3L8OfrZNTo7pybFuXc31bdtCZmbD5Tp3Nv9u2VJzXWmpeQaj0j33mPWPPx6e9qgvVsc+D5EQclmWZfmzQffu3fnqq69I87MDuNvtJjk5mYKCApKSkvzaVhqwPAdeHQ3U/hgrujWOyY7spMJn/L6EqV6zz4Jf50LP4+Hij3x3E42E9vcRg9cyMYx+NZs3fzUxZGeH8STmZ9vk5MDo0Wayr/q8/rqJvbFy/qjcZ6j4irXy1ymsn4dIE9k9f/t9eaGoqIiHHnqIPfbYg0MOOYQff/wxoEAlAF6P+fZX78m4Yt2CiaZcJGowfl/CUK9f55lkIiYOTv+P72QiEtq/gRhiXGZd5rCJuDAxTJxoLr+HnJ9t4/GYb/ENJQkTJ8KuXY2X88eECaFrj4bqVLkubJ+HSBj4nVDs2LGD+Ph4VqxYwbnnnsuoUaMoLy+vU660tBS3213jJUG2JrfmpeQ6LHDnmXKRqNH4fQlhvXYVw7vXmeWjJ0HXgb7LRkL7NxJDjMuiR3Ie6T1ysSzIyzP38kPOz7bJza17m6O2vDyYObPxcv5Yty507dFYncL6eYiEgd8Jxbx585g+fTpdunThpptuYteuXSxevLhOuenTp5OcnLz75e8tErGhKD+45cIt0LhCUa/PpsP2P8x9/sG3Bef4oWx/m/tOaV9VLj8cvw5+to3dmFaubGI8DQhVe9jdb1g+D5Ew8DuhGD58OK6KS8Aul4vU1FQ2btxYp9yUKVMoKCjY/crLyws8WqmpXUpwy4VboHEFu15//WpmEwXz0GB8u+AcP5Ttb3Pf+YVV5VLC8evgZ9vYjalPnybG04BQtYfd/Ybl8xAJA78SipUrV3LppZfufu/1elm9enW9Vx/i4+NJSkqq8ZIg65luvknja14JFySlmXKRqNH4fQlBvSwL5l9TNfnXfjbmxI6E9m8kBq/lYm1BGrlr03G5zGRa6eH4dfCzbdLTTc8HXypjHz/elAvWVCqpqaFrj8o6+Yo1rJ+HSBj4lVD07NmThQsX8sQTT7B582Zuu+02OnXqxKGHHhqq+KQhMbHmmzRQ9w93xfthmZE7HkWD8fsSonr9/BqsWgix8XDaI/bOWJHQ/g3EUNnLY+KCTCxMDJmZYRr/wM+2iY2t2S20RumK4pmZ0Lp11SBXwUgqsrJC1x6xsb5jrV4njUchLYVfCUVcXByvv/46jz32GD169GDRokXk5OTsvgUiDhiQYbrfJXWvuT4pNfK7jEID8afBMZMrvuVWXx+Ceu10mx4HAOlToJMf19Ujof19xLDOncroV7N3j0MR9i6KfrZNaan5t/afk9qxZ2SY991r7bZz56qxKKqva1fPnavOnUPfZRR8x+rI5yESYn6PQ9FUGocixCJhpMZAODlS5oJJ8NXD0LEPjF8GrdoEL/5wasYjZRYWQv/+sGED3HWXibexUSU1UqZIeNg9fyuhkOi28UeYdShYHjj/XdhnWOPbSNDddBPMmAF77w0//wxtmpDTiUhohGxgK5EWw+uFd/7PJBP7na1kwiG//goPP2yWs7KUTIg0V0ooJHr98BzkfQGt2sKwh52OJipZlhlNsqwMTjsNzjjD6YhEpKmUUEh0Kt4KH9xolk+4A5I18JoT3noL3nvP9N7w1ctDRJoHJRQSnT68BYr/gi4D4agJTkcTlUpK4PrrzfINN8A++zgbj4gERgmFRJ9138CSx83y6TMhtpWz8USpBx6A1atNl8pbbnE6GhEJlBIKiS5ej3kQEwsOuhB6DXY6oqj0xx8wfbpZ/te/6h8rQkSaFyUUEl0W/xfyv4M2HWDIDKejiVo33AA7d5rxIMaMcToaEQkGJRQSPYo2wYe3muWT7oV2ezobT5RauBBycszATv/+d/Dm5RARZymhkOjx/mQoLYCUQXDY352OJirt2gXXXmuWr74aDjjA2XhEJHiUUEh0WPMZ/PgC4IIzHmtew5K3II88Ar/8Al26wJ13Oh2NiASTEgpp+bweePc6s3zo5dD9cGfjiVL5+VVJxD//CR06OBqOiASZEgpp+b57CjZ+D/HJcPK9TkcTtW66yUwCdsQRcPHFTkcjIsGmhEJatpJtsKjiQcwT74S2XZyNJ0p9/jm88IJZfuQRiNFfHpEWR/+tpWX7+M6KETEHwOHjnY4mKnk8cM01Zvmyy8wVChFpeZRQSMv153L45lGzPCxTI2I65IknYOlSSE6G++5zOhoRCRUlFNIyWRYsmGimJu93JvQZ4nREUWnLFri14o7TXXdB167OxiMioaOEQlqmX9+CVR9AbDyc+pDT0UStqVNh61bYf38YrztOIi2aEgppecp2woKKaSyPuQE67e1sPFHqu+9g1iyz/OijEBfnbDwiElpKKKTl+fIh2L4a2neD46Y4HU1UsiwzIqZlwXnnwfHHOx2RiISaEgppWdzrIbfiyb8hMyBe01g64cUX4YsvIDHRTFMuIi2fEgppWT64Ccp2QNoxcMA4p6OJSm43TJ5slqdOhdRUZ+MRkfBQQiEtx9ov4KeXABcM1zSWTrnrLti0Cfr2hUmTnI5GRMJFCYW0DF5vtfk6LoNug5yNJ0qtWAFZWWY5Kwvi452NR0TCRwmFtAxLn4H8JWa+jpM0X4cTLAsmToTycjjjDDjtNKcjEpFwUkIhzd9ON3x4i1k+YRq00+hJTnjnHXj/fWjVCh5+2OloRCTclFBI8/fpPbDjT+jcD464xulootKuXXB9xdAf119vnp8QkeiihEKaty2/wVeZZvnUhzRfh0P+/W/4/XfYc8+qobZFJLoooZDm7f1/gLcM+g6HfXXT3gmbNsHdd5vl++6DpCRn4xERZyihkOZr5Qdmzo6YOM3X4aCpU83YE4MGwcUXOx2NiDhFCYU0T55yM5somOcmuvR3NJxo9f338NRTZjkrC2L0F0UkajVpup68vDwGDhzIpEmTuOOOO4IckogNi/8Lm5dDQmc4/nano2kSjwdycyE/H1JSID0dYmNDv20gqh93r71g2rSq+TqOPTb0x/cnvnC2i4g0MaG46qqrSE5ODnYsIvYUb4GPKpKIk+6BhI7OxtMEOTkwYQKsW1e1LjXVfMvPyAjdtoGo77gArVvD/feH7rh2OdUuImL4fYHyhRdeAODMM88MejAitnx8B+zcBl0PgEMvdzoav+XkwOjRdU/M69eb9Tk5odk2EL6OC6bL6OLFoTmuXU61i4hU8Suh2LRpE9OmTWPWrFmhikekYX/+DN8+ZpaHZUJsky6yOcbjMd+iLavuzyrXTZxoygVz20A0dNxKoTiuXU61i4jU5FdCcc0113DLLbeQamP6wNLSUtxud42XSEAsCxZcD5YH+o+CvU9yOiK/5ebW/y2/kmVBXp4pF8xtA9HYcSE0x7XLqXYRkZpsJxRvvPEG27dv5/LL7V1inj59OsnJybtfaWlpTQ5SBID/vQ2rPoDY1jD0QaejaZL8/KaXC2TbQDh1XLsiPT6RaGH7evHcuXNZuHAhrlpTQv/xxx88++yzdcpPmTKFSdXmLna73UoqpOnKS+G9it+noydBp72djaeJUlKaXi6QbQPh1HHtivT4RKKFy7IaujPq2zXXXMMee+xhu9uo2+0mOTmZgoICkjSUnvjr8wfhg8nQbi+49n8Q397piJrE44FevczDgvX9z3O5TM+E1avrdncMZNtgxOzrtkKojmuXU+0iEi3snr81DI1EvqJN8MldZvnk6c02mQBzQsvKMsu1Lvbtfp+ZWf+JL5BtA1H9uLWF8rh2OdUuIlKTEgqJfIumwq5C6HYYHHSh09EELCMDsrOhe/ea61NTzfqGxkwIZNtADB0KnTrVXR/q49rlVLuISJUm3/Lwl255SJPkfw+zBgEWXPo59DjG6YiCpjmNlHnbbXDPPdC7N/z3v7BlS2SORKmRMkWCz+75WwmFRC7LgmeOh7W5sP9YGP2y0xFFpTVroH9/2LnTDBA1apTTEYlIOOkZCmn+fn7NJBNxCTAkAsZ2jlI33miSiRNPhLPOcjoaEYlUSigkMpWVmF4dAMfdDMnqcuyETz+FV181s4hmZtZ96FFEpJISColMXzwIBWshuQcc8w+no4lKlUNaA1x5JRx4oLPxiEhkU0IhkacgD3Knm+UhM6B1orPxRKknnoClS6FDB7jrLqejEZFIp4RCIs/Cm6G8BHocBwPHOB1NVNqyBW691SzffTd06eJsPCIS+ZRQSGRZ+wX89DLggmFZumnvkNtvh61b4YAD4KqrnI5GRJoDJRQSObxeWFBx0/7Qy6Dboc7GE6V++MGMNQHwyCMQ17xmiBcRhyihkMjxw/OwYTG0bg8n3eN0NFHJsuDaa01ud+65cPzxTkckIs2FEgqJDDvd5tkJgONvg3Z7OhtPlHrlFTPSZGIiPPCA09GISHOihEIiw6d3w45N0HlfOHKC09FEpaIi+EdFD91bboE0Df0hIn5QQiHO2/wLfJVplodlQlxrJ6OJWvfdBxs2wN57ww03OB2NiDQ3SijEWZYFCyaCtxz2PQP2Ge50RFHp99/hX/8yyw8/DG3aOBuPiDQ/SijEWf97G1a+B7Gt4dSHnY4mak2cCLt2wbBhMGKE09GISHOkhEKcU7bTXJ0AOHoSdO7raDjR6p13zKtVK83XISJNp4RCnPPVw7BtFbTvBum3Oh1NVCotNVcnwPzbr5+T0YhIc6aEQpxRsA4+rRhrYsgMiG/nbDxR6uGHzfMTe+0Ft93mdDQi0pwpoRBnLLwJyooh7Rg4YJzT0USl9evhnoqcbsYMaN/e2XhEpHlTQiHht+azqvk6hj+im/YOufFG2LEDjjkG/vY3p6MRkeZOCYWEl9cD715rlgddofk6HJKbCy+/bHK5R5TTiUgQKKGQ8PruSdi4FNp00HwdDvF4zHwdAFdcAYcqpxORIFBCIeFTsg0+rOjNceJd0LaLs/FEqccfNzOKdugA997rdDQi0lIooZDw+WgalGyBLgPhsP9zOpqotGULTJ1qlu++G/bYw9l4RKTlUEIh4bHxB/h2plke/m+IjXM2nih1222wdSsccABcdZXT0YhIS6KEQkLP64W3rwLLAwPOgb1PcjqiqLR0KcyaZZYfeQTilNOJSBApoZDQW/I4rPsKWrc3s4lK2FmWeRDT64Vzz4Xjj3c6IhFpaZRQSGgVbYKFN5vlk++FpG7OxhOlZs+Gzz6DxER44AGnoxGRlkgJhYTWe5OgtABSBsHh452OJioVFcHkyWb5llsgLc3ZeESkZVJCIaGzcqEZEdMVAyNmQUys0xFFpXvugQ0bYO+94YYbnI5GRFoqJRQSGmU74Z2KKxJHXAPdBjkbT5T67Td46CGznJkJbdo4Go6ItGBKKCQ0PvsnbP3NTE1+4t1ORxO1Jk6EsjIYNgzOOMPpaESkJfO749jXX3/N1VdfzYoVKzjggAN4/PHHOfDAA0MRmwSb1wNrcqEoH9qlQM/0xm9DNGWbv36Fz6ab5WFZ0CYpqLF5PGYuivx8SEmB9GM9xK7zM8YgqxNTOsTWE4LdcsHwzjswfz60amWuTvg7X4c/sYazXiISmfxKKHbu3MmIESN44IEHGDlyJC+88ALnnnsuK1asCFV8EizLc2DBBHCvq1qXlGpO+AMygreNZZlbHZ5d0Hc4DDg7qLHl5MCECbCuouio/jnse/oEurXzI8Ygqx0TQGoqZGVBRob/5YKhpASuu84sT5wI/fr5t70/sYazXiISuVyWZVl2CxcUFPDJJ58wcuRIAHbs2EG7du1wu920b9++wW3dbjfJyckUFBSQlGTjG6sEz/IceHU0UPujrvjKOia77sm3KdsA/PAivHEBxLWBq5dDx95Biy0nB0aPNjkLmGQie4zZNsbV8LahUjum3RFUhJCdbU6qdssFyx13wJ13Qrdu8Msv0Mh/zxr8iTXc9RKR8LN7/vYroajt+eef5+677+a3334LWkASZF4PZPaq+e2/Bpf5Rj9xddVtgqZsA1C8FR7tD8Wb4eT7IH1K0GLzWLH06lX1LTjG5eGPCb3onrSuVjLRSIxB5PFQI6Y6EbjMN/Xff4c+fRovt3p1cG4T/PorHHgg7NoFc+bAmDH2t7Vbp9WrzXu7ZXX7Q6T5snv+btJDmXfffTdJSUncdNNNvPPOO/WWKS0txe1213iJA9bkNnDCBrDAnWfKBbINwIdTTDLRZQAcbaN/oh/Hyc2teeJK75FLWrKvZKKBGIOodkx1IrAgLw9mzrRXLjcIoVoWjB9vkolhw+Ccc/zb3m6dcnP9KysiLV+TEooJEybwzTff8Pe//53LL78cj8dTp8z06dNJTk7e/UrTaDrOKMr3v1xTtln7hRliG+CM/0Jc66DGll+raEr7JsQYZLVj8mXlyuDuryEvvgiLFpnuof/5j/8PYtqNIT/fv7Ii0vI1KaFISkqif//+3HHHHRQUFPDRRx/VKTNlyhQKCgp2v/Ly8gIOVpqgXYr/5fzdxlNmJv8COORS08siyLGl1CqaX9iEegVZ7Zh86dMnuPvzZevWqoGrbr/dDGTlL7sxpKT4V1ZEWj6/EorFixdz6aWX1ljXtm1bioqK6pSNj48nKSmpxksc0DPdPEuAr6+qLkhKq5kE+LvNV5nw50+Q0BmGzAhJbOnp5n585Tfu3LXp5BWk4rX8qFeQ1Y6pTgQuM8z1+PH2yqUHGOpNN8HmzTBgQNNHxLRbp/R0/8qKSMvnV0LRt29f5s6dy0svvcS2bdt48cUXWbFiBcccc0yo4pNAxcSaLpRA3RN3xfthmTUfXPRnm+1r4OM7zLqhD0Ji55DEFhtruiGCOVF5rVgmLDAr6iYVPuoVZLVjqhFBxfvMTGjd2l65QB5czM2FJ580y7NmmWM2hd06xcb6V1ZEWj6/EooOHTrw9ttv8/DDD5OWlkZWVhZvv/02Xbt2DVV8EgwDMkwXyqTuNdcnpfruWmlnG8uC+ddCWTH0PB4OviiksWVkmG6I3SuKvvFLBqNfzWbjDj/qFWS1Y6qUmlqzy6Tdck2xaxdcVXHH6fLL4bjjmr4v8C/WUNZLRJqXgLqN+kPdRiNAsEfKXPEGzMmAmFbwfz9Al/3CEptGyqxp+nQzi2iXLmbMiU6dAttfU2LVSJkiLVdYxqEIRUDSTJQWwn8GmG6f6bfCyfc4HVFUWrUKBg6EnTvh+efhggucjkhEWpqQjkMhwkfTTDLRcW8YfKvT0UQly4KrrzbJxEknwd/+5nREIhLNlFCI//K/h68rnsY77T/QKsHZeKLUa6/BggXmAcyZM/0fc0JEJJiUUIh/vB4z5oTlhYFjYJ9hTkcUlbZvN5N+AUyZ4v/kXyIiwaaEQvyz5HFY/w3EJ8GpDzsdTdSaNMk8ALnvvnDzzU5HIyKihEL8UbgRFlZM+HXSvZDUzdl4otT8+fDMM+YWx9NPm2G2RUScpoRC7HtvEpQWQLfD4PD/czqaqLRtG1xxhVmeOBGOPdbRcEREdlNCIfb8/j4smw2uGDhjVtjHeRDj+uthwwbYZx+4Rz11RSSCKKGQxpWVwDvjzfIR10K3Q52NJ0q98w4895y51fHss5CY6HREIiJVlFBI43Knw7aV0L4bnHiX09FEpeq3OiZNAk2fIyKRRgmFNGzTT/DZP83y8H9DG41y6oSJE02vjn794O67nY5GRKQuJRTim6cM3rgIvGWw7wjYTzM9OWHePDOsdkyM6d2RoHHERCQCKaEQ3z69FzZ+DwmdYMTjGorRAVu3wpVXmuVJk+Doo52NR0TEFyUUUr8NS+DTim4Ep8+E9ns5G0+UmjABNm6E/v3hLj2+IiIRTAmF1FW2E964ECyPGV57/3OdjigqvfUWvPiiudXx7LO61SEikU0JhdT18TTYvBza7mkm/5Kw27oV/v53s/yPf8CRRzobj4hIY5RQSE1rv4DPHzDLIx6Htns4G0+Uuu46c6tjv/3gzjudjkZEpHFKKKTKrh3w5kWABQddBP1HOh1RVHrzTXjppapbHZqrQ0SaAyUUUmXhFNj6OySlwrBMp6OJSlu2wFVXmeUbb4QjjnA2HhERu5RQiLFqEXzziFke+RQkdHA0nGh17bWwaRMMGAB33OF0NCIi9imhENjphrmXmuXDroK+Q52NJ0q98QbMng2xseZWR3y80xGJiNinhELg/RugYA106A1DHnA6mqj01181b3Ucfriz8YiI+EsJRbT77V347knABWc9A/HtnI4oKl1zDfz5JwwcCNOmOR2NiIj/lFBEs+KtMPcys3zUROh1vKPhRKvXX4c5c3SrQ0SaNyUU0cqy4J3xUJQPnfvByfc6HVFU2rwZ/u//zPLNN8Nhhzkbj4hIUymhiFZLn4Of50BMHIx6HlppXOdwsyy4/HKTVOy/P9x2m9MRiYg0nRKKaLTld5h/jVk+8S5I1WAHTpg1y8zX0bo1vPCCbnWISPOmhCLalO+C18dC2Q7odQIce6PTEUWlZcvg+uvN8j//CQcf7Gg4IiIBU0IRbT6eBhsWQ5uOMOoFiIl1OqKoU1ICY8fCzp0wbJiZolxEpLlTQhFNVi6Ez+43yyOfgORUZ+OJUv/4h7lCseeepldHjP4XikgLoD9l0cK9Hl4fB1hw6BUw4GynI4pKb7wBM2ea5eeeM0mFiEhL4FdCsXjxYg455BASEhI4+uijWbFiRajiilxeD6z+GH6abf71epyOqHGeMsg+D4o3w14Hw/Cs8MfQHNstiDweeOUV+NvfzPvrr4dTT3U2JhGRYIqzW7C8vJyzzz6bq6++mksuuYRHHnmEsWPHsnTp0hCGF2GW58CCCeBeV7UuKRWGZcGADOfiasyHt8LazyA+Cc55LfxdRJtruwVJTg5cdx2sX1+17tVX4bjjIKPlV19EooTLsizLTsFvvvmGUaNGsW7dOlwuF8XFxbRt25bCwkLatWt8uGa3201ycjIFBQUkJSUFHHjYLc+BV0cDtZvLZf4Zkx2ZJ8df3oJXzjTLY14Pf4zNtd2CJCcHRo82Y05U56qofna2kgoRiWx2z9+2b3mkpqby9NNP46r4S5iXl0fHjh1p27Zt4NFGOq/HfMOuc1Kkat2CiZF3GX/banjzIrN81MTwn7iba7sFicdjenDUl7JXrps40ZQTEWnubCcU3bp149SKm75lZWVcf/31TJ48eXeCUVtpaSlut7vGq9lak1vzcn0dFrjzTLlIUbYTXj0Hdm6H1KPglPvDH0NzbLcgys2FdQ1U37IgL8+UExFp7vzu5VFUVMSwYcNISUnhpptu8llu+vTpJCcn736lpaUFFKijivKDWy4c3psE+UsgoTOc8yrEtQ5/DM2x3YJozRp75fJbZvVFJMr4lVCUlpYydOhQ0tPTeeqpp4hpoAP9lClTKCgo2P3Ky8sLOFjHtEsJbrlQ+/FlWPwY4IKMFyHZoWSuubVbkL3yir1yKS2z+iISZWz38gC49dZb6devH3fccUejZePj44lvKZMT9Ew3vRLc66n/eQCX+XnP9HBHVtfmFTDvSrM8+FbYZ5hzsTSndguyp56CBQsaLuNyQWoqpLe86otIFLJ9heLPP/9k5syZ3HbbbezcuXP3y+v1hjK+yBATa7o4Art7J+xW8X5YpvPDWO/aYXpUlO2A3ifBCXc4G09zabcg++YbGD/eLI8bZxKH2o8aVb7PzITYllV9EYlSthOKd999l5KSEvr06UNCQsLu16effhrK+CLHgAzTxTGpe831SamR0fXRsuCtK2DzcnML4eyXI+NEHentFmSbNpluoLt2wZlnmllEs7Ohe63qp6aqy6iItCy2x6EIVLMfh6KS12N6JRTlmxN3z/TIOHF/OBVy74WYOLjwQ+g12OmIaorUdguisjI45RT49FPo189cqaj8Vfd4TG+O/HzzzER6uq5MiEjzYPf87dczFII5CfY+wekoalrypEkmAEY8HnnJBERmuwXZpEkmmWjfHt58syqZAJM8nHCCU5GJiISeJgdr7n5bAG9fZZaPvx0OucTZeKLU44/Do4+a5RdegP79nY1HRCTclFA0Z/lL4bVzwPLAQRc6/xBmlMrNhauvNsv33GOenRARiTZKKJqr7WvhpdNgVxH0PhlGPFG3K4GE3KpVMGoUlJfDmDFwyy1ORyQi4gwlFM1RyXaTTBTlQ9f94dzXnRkJM8pt3w4jR8KWLTBoEDzzjHI6EYleSiiam/Jd8OrZsPlnaN8Nzp8PbZKdjirq/PUXnHQS/PwzdOsGc+dCYqLTUYmIOEe9PJoTy4K3LofVi6B1Oxj3jnPDakex/HzTPXT5cujSBd59t+44EyIi0UYJRXPy8R3w4wvgijWDQqUc7HREUWfNGjj5ZFi50iQRH35oxpwQEYl2uuXRXHz3NHxyl1keMQv6nupsPFHot9/MgFQrV0Lv3qZ3h5IJERFDCUVz8Pv71Sb8mgqHXuZsPFFo2TKTTOTlmTEmcnNNUiEiIoYSiki38Qcz4ZflgQMvgBPvcjqiqLNkiRnlctMmOPBA+OQTPTMhIlKbEopIVrAOXjoddhVCrxNh5JPqlxhmn39uenNs2QJHHAEffQRduzodlYhI5FFCEal2FpixJgrXQ5cBcG6OxpoIsw8/hKFDwe2GwYNh4ULo1MnpqEREIpMSikjkKTO3Of78yczMef67kNDB6aiiyttvw+mnQ3ExnHqq6Rravr3TUYmIRC4lFJHGsswDmKsWQqu2cP470KGH01FFlddeM8Npl5bCWWdp0CoRETuUUESaT+6Cpc9WjDXxGqQc4nREUeW55+C888zcHOPGwauvQny801GJiEQ+JRSR5PtnzOBVAKfPhH2GOxpOtJk5Ey6+GLxeuPxyeP55aNXK6ahERJoHJRSR4qfZZlhtgPRb4LArnY0nyjzwQNUU5BMmwOOPQ2ysszGJiDQnSiicZlnwxUPw+jiwvHDo5XDSPU5HFTUsC6ZNgxtvNO9vvRUefli9c0VE/KW5PJzk9cB7k+Drf5v3R1wDw7J0NgsTy4LJk+Ff/zLv77sPpkxxNiYRkeZKCYVTykrg9fPhlzfM+6EPwtGTlEyEiddrbnH897/mfVYWXHedszGJiDRnSiicsOMvmD0S1n0Jsa1h1POw/7lORxU1ysvh0kvhhRdM/vbkk+a9iIg0nRKKcNu6El4cDlt/gzYd4Ly50Guw01FFjV27THfQ1183D12++KLpJioiIoFRQhFO676Bl8+A4s2Q3BP+9i502c/pqKJGSQmMHg3z50Pr1maMiTPPdDoqEZGWQQlFuPw6D147F8pLIOVQGPc2tE9xOqqoUVQEI0eayb0SEuDNN808HSIiEhxKKMLh28dg/jWmW2jfYXDOaxDfzumoosb27XDaafDll2Y+jnfegfR0p6MSEWlZlFCEktcLi26Fz/5p3h9yGZzxGMRq+MVw2bzZXIlYuhQ6doT33oPDD3c6KhGRlkcJRaiUl8LcS+Gnl837E++CwVPVLTSMNmyAIUNg+XLo2hU++AAOPNDpqEREWiYlFKFQsh3mjII/PoaYOBj5JBx8kdNRRZU1a+Dkk2HlSujeHT78EPr1czoqEZGWSwlFsG1fCy+dBpt/htbt4dzXoc8Qp6OKKr/9ZpKJvDzo3dskE717Ox2ViEjLpoQimPKXmmSiKB/ad4Pz58NeBzkdVVRZtgxOOQU2bYL+/WHhQnOFQkREQsvvhMKyLF555RXGjx/Pu+++y1FHHRWKuCKCxwO5uZCfDykppmeAzxkof38fXj0bdhVBl4FmjInkNPsH83pgTa5JRtqlQM90iAnxdJcOHNOvNvXTkiXmAcytW+Ggg+D9982zE6FSWZf1683Dn126mOTlmGPgiy/s1TEU7RHKNhYR8cXvhOKNN95gxowZoYglouTkmGms162rWpeaauZ8yMioVfj7Z2HeFeAth14nwrk5kNDB/sGW58CCCeCudrCkVDNR2IDaBwsSB47pV5v66fPPTddQtxuOPBLefdf06giV+upSKTbWnNQr+apjKNojlG0sItIQl2VZlj8b7Nixg8TERHr37s0rr7xi+wqF2+0mOTmZgoICkpKSmhRsuOTkmBEVa7dMZQeN7OyKP86WBZ/cBR/fYX5wwPlw5lMQF2//YMtz4NXRQO2PoeJgY7KDf4J34Ji227QJPvzQDFpVXAyDB8Pbb5vxJkLFV118qa+OoWiPULaxiEQvu+dvvxOKSr169WqRCYXHA7161f/NE8wf59RUWP17GbHvXgXfP21+cNwUOOkeiImxfzCvBzJ71bxKUPNo5qrBxNXBuxXhwDFtt+lq/y/Nz5sH55wDpaVw6qnmpJqYGHDIPjVWF1+q1xGC3x6hbGMRiW52z99+nP38U1paitvtrvFqDnJzGz5ZWBZs21RIwWMjTDLhioHTH4NT7vMvmQDz/ILPEzuABe48Uy5YHDimnTbNyzPl/PHqq+Ybd2kpjBoFc+eGNpmAxuviS/U6hqI9QtXGIiJ2hSyhmD59OsnJybtfaWl+PKDooPz8hn+elrSWTy4+nk7b3oNWiXDem3D4VU07WFEjB/O3XIQes7E29bccwLPPwtixZiry8883yUW8H3eamsqfGH1tH4r2CMU+RUT8EbKEYsqUKRQUFOx+5eXlhepQQZXic74ui0sPeYpl4/fn0JTv2dWqC1z8MfQb0fSDtbM5OZjdchF6TN9t6n+5ggK46iq45BIzsvkVV8Bzz0FcmDpA261LQ9sHsz38LRto/CIivoQsoYiPjycpKanGqzlITzf3mquPkJ3SbgNvjz2Dp0ZeTlJ8IYs3HU3s37+G7gFOCtEz3TyvgMtHARckpZlyweLAMetr0xpHdEFaWuMTds2bBwMHwqxZ5v3kyWY5nM8EVNbFX9XrGKz2qC+uYO5TRMQfIUsomqvYWNPFDsDlshh3wEssG78/p+87n53l8dz4wQzWnpJL7B5BGHoxJtZ00zRHq/XDivfDMoM7NoQDx6zZprWOWPE+M9N3YvDnn3DeeaYnx/r10LevmYZ8xozwT41SWRd/jlu7joG2R0NxBXOfIiL+UEJRj4wMmPfKn7xz4dm8lPE3OiVs49v1h3H6W99x1A2TyTg7iH+VB2SYbppJtYZzTEoNTZdRh46ZkWG6LdYetTI11Xd3RsuCF16A/faDOXPMM6833gg//ggnnBD0EG2rrIuvKxW1T9r11bEp7WE3rmDuU0TEriZ3G/VXc+k2CsDP2fDO/0HxX3hdrVjW+Xa2DbiJ445vFbpveBops4Y1a8yzEgsWmPcHHQRPPQWDBoU0PL9opEwRiQYhH4ciVAE5qngLzL8Wls027/c8EM56DlIOdjSsaOL1wsyZcPPNsGOH6blx++3meYlWrZyOTkQk+tg9f2tysEq/vm2Gzy7aCK5YOO5mOP52iGvtdGRRY8UKuPxy8+0e4Nhj4cknzSRfIiIS2ZRQlGyH966Hpc+a93vsB6OeC7wHh9hWVgb33w933w27dkG7dub9VVf5P1aYiIg4I3oTivJS+PYx+PQeKNkCuOCYG+DEu6FVG6ejixqLF8Nll5kHLQGGD4f//hd69HA2LhER8U/0JRReLyx7BRZNhe0VEyvssR+MfAJ6HOtsbFGkuBimTYOHHjIfSefOptvjuHHh7woqIiKBi66EYuVCWHgT5H9n3rdLgRPvgoMvhtjoagonLVoEV14JK1ea92PHmmSiSxdn4xIRkaaLjrNo/lKTSKx837xv3R6OuwmOmgit2zoZWVRZuhRuu81MLw6mi+V//wtnnOFoWCIiEgQtO6HYvsbc2vjxJcCCmFZw+P/B4KnQVl+Hw2XFCnN747XXzPvYWPj732H6dIjUHsQiIuKflplQFG+F3Hvhm0fBs8us2/88OOle6LS3s7FFkZUr4c474aWXzHMSLpcZQvuOO2DffZ2OTkREgqllJRRlJfD1vyF3OpQWmHW9T4JT7ofuhzkbWxRZuxbuuQeeftqM2ggwapRJLg44wNnYREQkNFpGQlFeCj88D5/cBe51Zt2eB5pEou+p6jYQJuvXm/EjZs0y40mA6QZ6111wmPI5EZEWrXknFJ4y+PoR+PIhKFxv1iWlwUn3wIHnh34uDMGy4PPP4ZFH4PXXq65InHCCuUpxrHriiohEheadUMTEmSsTheuhfTc45h9w2P9pYKowKCmB2bNNIrF0adX6wYPN3BsnnaQLQyIi0aR5JxQuF5wyHdzr4aALIC7e6YhavLVr4bHH4IknYMsWs65NGzj/fLj2WjMrqIiIRJ/mnVAA7DPc6QhaPMuCTz4xVyPefNP02AAzPPbVV5uhszt3djREERFxWPNPKCRkduyAl182icRPP1WtP/FEuO46GDHCjCkhIiKihEJ2+/NP84Dl55/DZ5/Bd9+ZmUABEhPhggvgmmtg//2djVNERCKPEoooZVnw669VycPnn8Nvv9Ut16cPjB8Pl1wCHTuGP04REWkelFBEidJSWLKkKnn4/POqhyoruVwwcCAcd5zp7nnssdCrl3priIhI45RQtFBbtsAXX1RdgVi82CQV1bVpA0ceWZU8HH20rkKIiEjTKKFoASzLzJtR/fmHFSvqluvSperqw3HHwSGHQOvW4Y9XRERaHiUUzVBZGXz/fc3nHzZtqluuf/+q5OHYY6FvX92+EBGR0FBC0QwUFMCXX1YlD19/bUaqrK51azNfRmXycMwxsMcezsQrIiLRRwlFhLEsMxpl9Ycnf/rJrK+uUyeTNFQmEIcdZp6JEBERcYISCoeVl8OPP9Z8/mH9+rrl+vSp+fxDv34QExP+eEVEROqjhCLMCgvNLYvKKxBffQVFRTXLxMXBoYdWJQ/HHAN77eVMvCIiInYooQix9etrPjy5dGnVXBiVkpJq3r444ggzMqWIiEhzoYQiiLxe+PnnquThs89gzZq65Xr2rNn7YuBAzYkhIiLNmxKKABQXwzffVCUPX35pemRUFxNjpvSuPvpkaqoz8YqIiISKEopGFBaaqwxr11b9u3atmffi++/NQ5XVtW1rRpysvAJx5JHQvr0zsYuIiISLEooGfPIJnHBCw2W6davZ++LAA81DlSIiItHE71Pf+vXrGTNmDN999x0nn3wys2fPpr1TX8G9HliTC4XrYcdmaNsF2neHnukQY+OhhMrti/KhXUqd7SpvTXTsCD16mGcfevSAtDRzu6NTJzjgABg8OMBnIBqJwwkeD+TmQn4+pKRAenrDdfS3vG0R2Db+ClnbiIhEEL8TigkTJjBw4EBmz57NWWedxZ133smDDz4YitgatjwHFkwA97q6P0tKhWFZMCDDv+1rbderF7jdNW9Z5OTAhAmwrtpmqamQlQUZDRwukDjCzd86Br1NKkVg2/grZG0jIhJhXJZVewxG33bu3ElycjIrVqxg77335txzz+Xrr7/mjz/+aHRbt9tNcnIyBQUFJCUlBRKzOdG8OhpoKHQXjMmu/8Tjc/uKiS58bJeTA6NH1x21snJ+jOxsP08STYwjlPytY9DbpFIEto2/QtY2IiJhZPf87ddYiytXriQ+Pp69996bvLw8+vXrx5o1ayguLg44YNu8HvOttcFkosKCiaa87e0tn9t5POabZn3pV+W6iRNNOVuaGEco+VvHoLdJpQhsG3+FrG1ERCKUXwnFtm3b2KNixqmXX36ZSZMm0bp1a7Zt21anbGlpKW63u8YrKNbk1n+bow4L3HmmvF/b179dbm7Ny9Z1trIgL8+Us6WJcYSSv3UMeptUisC28VfI2kZEJEL5PRtEq1atKCsrIzY2lg4dOuD1enHVMyf29OnTSU5O3v1KS0sLSsAU5QdW3u72tcrl29zMbrmmxhFK/tYx6G1SKQLbxl8haxsRkQjlV0LRsWNHSktLmTdvHuPGjaOoqIjy8nI6dOhQp+yUKVMoKCjY/crLywtOxO1SAitvd/ta5VJsbma3XFPjCCV/6xj0NqkUgW3jr5C1jYhIhPIroejTpw/bt2/H7XbTrVs3li5dSs+ePUmsZ+KJ+Ph4kpKSaryCome6edK/US5ISjPl692+7lWVhrZLTzdP59dzMcZs5TLdSdPT6/95HU2MI5T8rWPQ26RSBLaNv0LWNiIiEcqvhKJNmzaccsopzJ8/n7Vr1zJ9+nRGjx4dqtjqFxNrug36PNlUMyyz7pgFu7ennn24fG4XG2u6+kHdk0Tl+8xMP8YXaGIcoeRvHYPeJpUisG38FbK2ERGJUH4/Q5GVlcX69evZd999cblcTJs2LRRxNWxAhuk26OtKRVJaw90Kd2/fvdZ2qQ1ul5Fhuvp1r7VZamoTuwA2MY5Q8reOQW+TShHYNv4KWduIiEQgv8ahCERQx6GoFOKRMn0J+siHETgapEbKDB6NlCkizZnd83fzTihEREQkpEIysJWIiIhIfZRQiIiISMCUUIiIiEjAlFCIiIhIwJRQiIiISMCUUIiIiEjAlFCIiIhIwJRQiIiISMCUUIiIiEjA4sJ1oMoBOd1ud7gOKSIiIgGqPG83NrB22BKKwsJCANLS0sJ1SBEREQmSwsJCkpOTff48bHN5eL1eNmzYQPv27XHVns+5GXO73aSlpZGXl6c5SsJMbe8Mtbsz1O7Oifa2tyyLwsJCunXrRkyM7yclwnaFIiYmhtRUH9ONtwBJSUlR+YsWCdT2zlC7O0Pt7pxobvuGrkxU0kOZIiIiEjAlFCIiIhIwJRQBio+PZ9q0acTHxzsdStRR2ztD7e4Mtbtz1Pb2hO2hTBEREWm5dIVCREREAqaEQkRERAKmhEJEREQCpoQiAN9++y0HH3wwbdq04aijjuKHH35wOqSosWrVKtLT00lMTGTIkCFs3LjR6ZBaLMuymD17Nh07duSrr77avX79+vUce+yxJCQkcMYZZ+weDVeCw1e7+1ovweGrfRcvXswhhxxCQkICRx99NCtWrHAwysikhKKJvF4vo0eP5oILLmDDhg2cccYZnHXWWY2OdS6B83q9jBo1ivPPP5+1a9dyyCGHMH78eKfDarHeeOMNZsyYUWf9hAkTGDhwIL/++isbNmzgzjvvdCC6lstXu/taL8FRX/uWl5dz9tlnM3bsWNauXcuQIUMYO3asQxFGMEuaJD8/33K5XNauXbssy7Ist9ttAdb27dsdjqzlW7FihdW1a9fd70tKSqw2bdpYO3bscDCqlquoqMjyer1Wz549rS+//NKyLNPmrVu3tlauXGlZlmWNGTPG6tmzp4NRtjz1tXtD6yU46mvfr7/+2urWrZvl9Xoty7KsHTt2WIBVWFjoZKgRR1comqhr16707t2bl19+GYCXXnqJgw8+2NbwpBKYwsJCWrVqtft9TEwM5eXl/P777w5G1XK1bdu2zvw7K1euJD4+nr333pu8vDz69evHmjVrKC4udijKlqe+dm9ovQRHfe2bmprK008/vXt9Xl4eHTt2pG3btk6EGLGUUDRRTEwM2dnZXH311SQkJHDLLbfwyiuvOB1WVNh///3ZsWMHr732GpZlcf/99+PxeHZPsSuht23bNvbYYw8AXn75ZSZNmkTr1q3Ztm2bw5GJBF+3bt049dRTASgrK+P6669n8uTJSuxqUULRRAUFBYwbN44ZM2awdOlSbrnlFkaMGKEH08IgISGBp59+miuuuIKEhASWLVvG4YcfTlxc2Oa6E6BVq1aUlZURGxtLhw4d8Hq9+gMrLVpRURHDhg0jJSWFm266yelwIo4SiiaaM2cOffv2Zfz48fTr149//OMfpKamkpOT43RoUWHUqFFs3ryZ/Px85syZw9atW+natavTYUWNjh07Ulpayrx58xg3bhxFRUWUl5fToUMHp0MTCYnS0lKGDh1Keno6Tz31VIPTeEcrtUgTlZSUkJCQUGNd27ZtdQ85DIqLi5k8eTIej4eOHTuyZcsWtmzZQs+ePZ0OLWr06dOH7du343a76datG0uXLqVnz54kJiY6HZpISNx6663069ePO+64w+lQIpYSiiY65ZRTePfdd8nOzmbLli28/PLLLFq0aPd9NgmdxMREPvvsM/7973+zZcsWJk+ezJgxY4iNjXU6tKjRpk0bTjnlFObPn8/atWuZPn06o0ePdjoskZD4888/mTlzJrfddhs7d+7c/fJ6vU6HFlGUUDTRwIEDeeGFF7jjjjvo3r07d911F7Nnz2bvvfd2OrSo8PTTTzNnzhy6d+/Opk2b+Oc//+l0SFEnKyuL9evXs+++++JyuZg2bZrTIYmExLvvvktJSQl9+vQhISFh9+vTTz91OrSIotlGRUREJGC6QiEiIiIBU0IhIiIiAVNCISIiIgFTQiEiIiIBU0IhIiIiAVNCISIiIgFTQiEiIiIBU0IhIiIiAVNCISIiIgFTQiEiIiIBU0IhIiIiAft/6p45FqhpktAAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 描画\n", "df_C = df[df['f']==\"C\"].sort_values('x')\n", "df_T = df[df['f']==\"T\"].sort_values('x')\n", "plt.scatter(df_C['x'], df_C['y'], color='b') # データ点の描画\n", "plt.plot(df_C['x'], df_C['predict']*8.0, color='b') # 予測(推定)曲線の描画\n", "plt.scatter(df_T['x'], df_T['y'], color='#ff7f00')\n", "plt.plot(df_T['x'], df_T['predict']*8.0, color='#ff7f00')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "metallic-kingdom", "metadata": {}, "source": [ "説明のために二項分布の図を載せます。\n", "![二項分布](https://8tops.yamanashi.ac.jp/~toyoki/lectures/PracDataSci/images/binomial4.png)" ] }, { "cell_type": "markdown", "id": "61bdf5f4-a514-4891-9adf-d8f5d411136f", "metadata": {}, "source": [ "# Poisson Regression\n", "\n", "前節で扱ったのは、目的変数の値に上限、下限がある問題でした。その場合、分布は2項分布になることが予想されます。\n", "\n", "ここでは、下限が0で、上限が存在しないようなデータについて考えてみます。\n", "\n", "0付近に多くが分布するような場合は、Poisson分布を仮定した分析も検討すべきです。" ] }, { "cell_type": "code", "execution_count": 30, "id": "4bec0d52-9cc8-4a75-996e-409e05440f18", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Poisson分布の描画\n", "import numpy as np\n", "from scipy.stats import poisson\n", "# 平均値\n", "m=5\n", "# 描画範囲\n", "x = np.arange(0, m*3)\n", "# ポアソン分布\n", "y = poisson.pmf(x, m)\n", "\n", "# FigureとAxes\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.grid()\n", "ax.set_title(\"Poisson distribution\")\n", "ax.set_xlabel(\"$k$\")\n", "ax.set_ylabel(\"$P(k)$\")\n", "# データをプロット\n", "ax.plot(x, y, marker=\"o\", color=\"blue\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "secret-generator", "metadata": {}, "source": [ "## 事例:橋を通行する自転車数と気温、雨量の関係\n", "\n", "次のページを参考に Poisson Regression の例を試してみましょう。\n", "\n", "授業で少し説明しますが、ブルックリン橋を通行する自転車の数を目的変数に、最低気温、最高気温、雨量を説明変数にしたデータをポアソン回帰で分析した例です。\n", "\n", "\n", "https://data-analysis-stats.jp/%E6%A9%9F%E6%A2%B0%E5%AD%A6%E7%BF%92/scikit-learn%E3%81%A7%E3%81%AE%E3%82%AB%E3%82%A6%E3%83%B3%E3%83%88%E3%83%87%E3%83%BC%E3%82%BF%E4%BA%88%E6%B8%AC%E3%81%99%E3%82%8B%E3%83%9D%E3%83%AF%E3%82%BD%E3%83%B3%E5%9B%9E%E5%B8%B0/\n", "\n", "このページのスクリプト例では、\n", "橋を渡る自転車の台数に関するNYCのオープンデータに説明変数の諸量をくわえたgithub上の公開データ(次のURL)を参照しています。CSVデータをダウンロードしておいて、それを参照するスクリプトになっています。\n", "\n", "https://gist.github.com/sachinsdate/c17931a3f000492c1c42cf78bf4ce9fe/\n", "\n", "次のようにURLを指定して直接読み込む方が楽です。(colabでは特に。)\n" ] }, { "cell_type": "code", "execution_count": 32, "id": "edfd986f-f563-48ea-adbf-2c579ef10e2e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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DateHIGH_TLOW_TPRECIPBB_COUNTDOWMONTH
02017-04-0146.037.00.0060654
12017-04-0262.141.00.00202164
22017-04-0363.050.00.03247004
32017-04-0451.146.01.1872314
42017-04-0563.046.00.00280724
........................
2092017-10-2762.148.00.003150410
2102017-10-2868.055.90.002245510
2112017-10-2964.961.03.03183610
2122017-10-3055.046.00.251428010
2132017-10-3154.044.00.002727110
\n", "

214 rows × 7 columns

\n", "
" ], "text/plain": [ " Date HIGH_T LOW_T PRECIP BB_COUNT DOW MONTH\n", "0 2017-04-01 46.0 37.0 0.00 606 5 4\n", "1 2017-04-02 62.1 41.0 0.00 2021 6 4\n", "2 2017-04-03 63.0 50.0 0.03 2470 0 4\n", "3 2017-04-04 51.1 46.0 1.18 723 1 4\n", "4 2017-04-05 63.0 46.0 0.00 2807 2 4\n", ".. ... ... ... ... ... ... ...\n", "209 2017-10-27 62.1 48.0 0.00 3150 4 10\n", "210 2017-10-28 68.0 55.9 0.00 2245 5 10\n", "211 2017-10-29 64.9 61.0 3.03 183 6 10\n", "212 2017-10-30 55.0 46.0 0.25 1428 0 10\n", "213 2017-10-31 54.0 44.0 0.00 2727 1 10\n", "\n", "[214 rows x 7 columns]" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "# data url\n", "url = \"https://gist.githubusercontent.com/sachinsdate/c17931a3f000492c1c42cf78bf4ce9fe/raw/7a5131d3f02575668b3c7e8c146b6a285acd2cd7/nyc_bb_bicyclist_counts.csv\"\n", "bike_data = pd.read_csv(url)\n", "bike_data[\"Date\"] = pd.to_datetime(bike_data[\"Date\"]) # 文字列をDatetime型に変換\n", "bike_data[\"DOW\"] = bike_data[\"Date\"].dt.dayofweek\n", "bike_data[\"MONTH\"] = bike_data[\"Date\"].dt.month\n", "bike_data\n" ] }, { "cell_type": "markdown", "id": "8fea6804-5eaf-4f61-adbf-1572ac357972", "metadata": {}, "source": [ "交通量は曜日によると考えて、\"DOW\" (Day of Week)を入れてみる。\n", "\n", "Newral NetworkやRandom Forestとの比較も行う。" ] }, { "cell_type": "code", "execution_count": 33, "id": "3309804e-1f4a-4090-b2e6-c7a943c9074b", "metadata": {}, "outputs": [], "source": [ "features = bike_data[[\"HIGH_T\", \"LOW_T\", \"PRECIP\", \"DOW\"]]\n", "targets = bike_data[\"BB_COUNT\"]\n", "\n", "# 訓練データとテストデータへの分割\n", "from sklearn.model_selection import train_test_split\n", "X_train, X_test, y_train, y_test = train_test_split(features, targets, train_size=0.8, random_state=0)\n", "\n", "# データの正規化\n", "#from sklearn.preprocessing import StandardScaler\n", "#scaler = StandardScaler().fit(X_train)\n", "#X_train_scaled = scaler.transform(X_train)\n", "#X_test_scaled = scaler.transform(X_test)" ] }, { "cell_type": "code", "execution_count": 34, "id": "7dd0757f-f084-422e-9a51-92e8526f7b58", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (5000) reached and the optimization hasn't converged yet.\n", " warnings.warn(\n" ] } ], "source": [ "# models\n", "models = {} # 学習機械\n", "predict_obs = {} # テストデータの推定結果\n", "\n", "# (1) 線形重回帰\n", "from sklearn.linear_model import LinearRegression\n", "models[\"Linear\"] = LinearRegression()\n", "\n", "# (2) ポアソン回帰\n", "from sklearn.linear_model import PoissonRegressor\n", "models[\"Poisson\"] = PoissonRegressor()\n", "\n", "# (3) ニューラルネット\n", "from sklearn.neural_network import MLPRegressor\n", "models[\"NeuralNetwork\"] = MLPRegressor(max_iter=5000)\n", "\n", "# (4)ランダムフォレスト回帰\n", "from sklearn.ensemble import RandomForestRegressor\n", "models[\"RandomForest\"] = RandomForestRegressor()\n", "\n", "# 学習とテストデータの推定\n", "for k,m in models.items():\n", " # 学習\n", " m.fit(X_train, y_train)\n", " # テストデータでの予測(推定)\n", " result = m.predict(X_test)\n", " predict_obs[k] = {\"obs\": np.array(list(y_test)), \"predict\": result}\n" ] }, { "cell_type": "code", "execution_count": 35, "id": "d9a0b0dd-95fb-44e3-bb2b-6d87b66191cd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "model: Linear, R2=0.356\n", "model: Poisson, R2=0.385\n", "model: NeuralNetwork, R2=0.211\n", "model: RandomForest, R2=0.433\n" ] } ], "source": [ "# 決定係数\n", "from sklearn.metrics import r2_score\n", "for k,r in predict_obs.items():\n", " print(\"model: %s, R2=%.3f\" % (k, r2_score(r[\"obs\"], r[\"predict\"])))" ] }, { "cell_type": "code", "execution_count": 36, "id": "622f4409-2d92-4ffd-97c2-c6e3e5fa62fc", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(7,7))\n", "plt.subplots_adjust(wspace=0.4, hspace=0.4) # これがないと軸ラベルが重なってしまう\n", "fig_no = 1\n", "for k,r in predict_obs.items():\n", " ax = fig.add_subplot(2,2,fig_no)\n", " ax.scatter(r[\"predict\"], r['obs'])\n", " ax.plot([0,5000],[0,5000], \"y\")\n", " ax.set_title(k)\n", " ax.set_xlabel(\"推定値\")\n", " ax.set_ylabel(\"観測値\")\n", " fig_no = fig_no+1\n", " " ] }, { "cell_type": "markdown", "id": "483a861d-0acb-465f-9ab9-844c532ea18b", "metadata": {}, "source": [ "決定係数は、ポアソン回帰の方が線形重回帰よりよいが、Random Forestがもっともよくなっています。\n", "\n", "余裕がある人はいろいろなパラメータ設定で試してみてください。\n", "\n", "このデータでは、極めて少ない通行量(数台とか)の日がないので、必ずしもポアソン分布するデータとして扱う必要はないと言えそうです。" ] }, { "cell_type": "markdown", "id": "likely-commercial", "metadata": {}, "source": [ "## 参考\n", "\n", "上掲の二項分布の作図をプログラムをつけておきます。" ] }, { "cell_type": "code", "execution_count": 43, "id": "lesser-horizontal", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.stats import binom\n", "size = np.linspace(0,8,9)\n", "fig = plt.figure(figsize=(8,3))\n", "plt.subplots_adjust(wspace=0.5)\n", "for i, p in enumerate([0.1, 0.3, 0.6, 0.9]):\n", " ax = fig.add_subplot(1, 4, i+1) \n", " ax.barh(size, binom.pmf(size,8,p), label=\"p=\" + str(p))\n", " ax.set_ylabel(\"発芽種子数 ($n$)\")\n", " ax.set_xlabel(\"出現確率 P_p(n)\")\n", " ax.set_title(\"$p=\" + str(p) + \"$\")\n", "fig.savefig(\"images/binomial4.png\", bbox_inches='tight')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 42, "id": "nuclear-emperor", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.stats import binom\n", "size = np.linspace(0,10,11)\n", "fig = plt.figure(figsize=(8,3))\n", "plt.subplots_adjust(wspace=0.5)\n", "for i, p in enumerate([0.1, 0.3, 0.6, 0.9]):\n", " ax = fig.add_subplot(1, 4, i+1) \n", " ax.barh(size, binom.pmf(size,10,p), label=\"p=\" + str(p))\n", " ax.set_ylabel(\"合格者数$n$ (10人中)\")\n", " ax.set_xlabel(\"出現確率 P_p(n)\")\n", " ax.set_title(\"$p=\" + str(p) + \"$\")\n", "fig.savefig(\"images/binomial_max10.png\", bbox_inches='tight')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "monthly-appendix", "metadata": {}, "source": [ "これまで、目的変数が有限な範囲$[0,8]$を取る場合を見てきましたが、データによっては範囲が$[0,\\infty )$で、値がそれぞれ整数値、連続値の場合もあります。\n", "\n", "そのような場合は、それぞれPoisson分布、ガンマ分布に従っていると想定して分析することが良く行われています。\n", "\n", "久保のテキストでは、前者の例として、ある植物の体の大きさと種の個数の関係、後者として葉の重量と花の重量の関係のデータを扱っています。" ] }, { "cell_type": "code", "execution_count": null, "id": "furnished-tragedy", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.16" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 5 }