{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "dG3tCL-_aQHA" }, "source": [ "# 主成分分析" ] }, { "cell_type": "markdown", "metadata": { "id": "bzqUoCdAaRxG" }, "source": [ "このノートブックでは主成分分析(principal component analysis, PCA)を説明する。 \n", "基礎の理解に重点を置くため、scikit-learnなど既存のライブラリにあるPCA関数を利用するだけではなく、 \n", "定式化とnumpyを用いた実装を行う。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "70ilJPZVd6LC" }, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": { "id": "WEJasJ_KbKVJ" }, "source": [ "## 主成分分析とは?" ] }, { "cell_type": "markdown", "metadata": { "id": "U6D19ywlbNFz" }, "source": [ "まず主成分分析とはなんだろうか? \n", "\n", "Wikipediaには\n", ">相関のある多数の変数から相関のない少数で全体のばらつきを最もよく表す \n", "主成分と呼ばれる変数を合成する多変量解析の一手法\n", "\n", "とある。\n", "\n", "具体例を考えてみよう。 \n", "ある集団200人の身長($x$)と体重($y$)のデータが下のように \n", "得られているとしよう。\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 283 }, "id": "YZT6a_-cd5lG", "outputId": "ce4dfd59-4bc4-427d-c990-fb89f88afc40" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mean = [165, 68]\n", "mvec = [0,0]\n", "cov=np.array([[1,0.8],[0.8,1.0]])\n", "np.random.seed(1234)\n", "x=[]; y=[]; n=200\n", "for i in range(n):\n", " tx,ty = np.random.multivariate_normal(mvec,cov)\n", " x += [ mean[0] + 8*tx]\n", " y += [ mean[1] + 6*ty]\n", "x=np.array(x);y=np.array(y)\n", "xm = np.mean(x);ym = np.mean(y)\n", "xp = np.arange(140,190,1); yp = np.corrcoef(x,y)[0,1] * (xp-xm) + ym\n", "\n", "fig = plt.figure()\n", "plt.xlim(140,190); plt.ylim(40,100)\n", "plt.xlabel(\"height [cm]\")\n", "plt.ylabel(\"weight [kg]\")\n", "plt.scatter(x,y)\n", "plt.plot(xp,yp,color=\"red\",linestyle=\"dotted\")\n", "plt.show();plt.close()" ] }, { "cell_type": "markdown", "metadata": { "id": "RxtGVOUQeVpB" }, "source": [ "上では\"何らかの方法で\"データの分布に沿った直線を描いてみた。 \n", "\n", "この赤色の線を\"体の大きさ\"とでも呼ぶことにすると、 \n", "元々は身長(x)と体重(y)の2つの量によってこの集団のデータを表現していたが、 \n", "集団に属する個人をこの\"体の大きさ\"という1つの量で \n", "大雑把に指定(あるいは特徴づけ)できそうなことがわかる。\n", "\n", "主成分分析は**高次元のデータを特徴づける少数の\"軸方向\"を見つけて \n", "その新たな軸に沿った値(主成分)でデータを表現し \n", "データを低次元空間で近似する方法**と言える。\n", "\n", "\n", "人間が視覚的に理解できる情報は、3次元までである。 \n", "一方でデータを分析していると、多次元(4~数十など)のデータを扱うことが度々あるが、 \n", "主成分分析などを用いて特徴を抽出することで解釈がしやすくなったり、 \n", "大量のデータがあったときその冗長性を削減することができる。" ] }, { "cell_type": "markdown", "metadata": { "id": "LwJ96CHthWmK" }, "source": [ "## PCAの定式化\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "iDqwKCP325Hl" }, "source": [ "主成分分析の大雑把なモチベーションがわかったところで \n", "上の軸方向/主成分の決め方を定式化しておこう。 \n", "\n", "主成分を決める方針は主に、[主成分の分散を最大化する方針]と \n", "[情報量削減(主成分軸への距離の二乗和)の最小化]の2つがある。 \n", "以下では、前者を採用することにしよう。\n", "\n", "\n", "$p$次元の量を持つデータが$N$個観測されているとする→$\\{ x_{ni}\\} (n=1,...,N, i=1,....p)$ \n", "このとき$p$個の各変数について、平均値を$\\bar{x}_i = \\frac{1}{N} \\sum_{n=1}^N x_{ni} $で定義する。\n", "\n", "このとき、$p$次元の成分それぞれの共分散を行列にもつ共分散行列${\\bf C}$($p\\times p$行列)は \n", "$\n", "{\\bf C} = \\frac{1}{N} \\sum^N_{n=1,N} ({\\bf x}_n - {\\bf \\bar{x}})\\cdot ({\\bf x}_n - {\\bf \\bar{x}})^T\n", "$ \n", "とかける。 \n", "\n", "次に、各データを成分にもつ行列\n", "$\n", "{\\bf X} = \n", "\\begin{pmatrix}\n", "x_{11} & x_{12} & ... & x_{1p} \\\\\n", "x_{21} & x_{22} & ... & x_{2p} \\\\\n", "\\vdots & \\vdots &\\ddots & \\vdots \\\\ \n", "x_{n1} & x_{n2} & ... & x_{np} \n", "\\end{pmatrix}\n", "$\n", "と \n", "成分が1の$N$次元列ベクトル$1_N$で以下の($N\\times p$)行列を定義する: \n", "$\n", "\\tilde{{\\bf X}} = {\\bf X} - 1_N {\\bf \\bar{x}}^T\n", "$\n", "\n", "これを用いて、もとの共分散行列を書き換えると...\n", "$ {\\bf C} = \\frac{1}{N} \\tilde{{\\bf X}}^T \\tilde{{\\bf X}}$とかける。\n", "\n", "次にデータ集合をある$p$次元の係数ベクトル${\\bf u}$で$p$次元空間上に射影する:\n", "$\n", "{\\bf s}_n = {\\bf u}^T \\cdot ( {\\bf x}_n - {\\bf \\bar{x}})\n", "$ \n", "これを全データ点($n=1,2,...,N$)に対して行って$s_n$を縦に並べると$\n", "{\\bf S} = \\tilde{{\\bf X}} {\\bf u}\n", "$と書くことができる。\n", "\n", "\n", "\n", "このとき、適当な係数ベクトル${\\bf u}$のもとでの射影方向の分散は \n", "$\\frac{1}{N}\\sum^N_{i=1} |{\\bf s}_i|^2 = \\frac{1}{N} ({\\bf u}^T\\tilde{{\\bf X}}^T) (\\tilde{{\\bf X}}{\\bf u}) = {\\bf u}^T {\\bf C} {\\bf u}\n", "$\n", "となる。\n", "\n", "今考えたい問題は、この分散を最大化するような射影${\\bf u}$を見つけることと言い換えられる。\n", "\n", "加えて、以下ではそのような射影として${\\bf u}^T \\cdot {\\bf u}=1$という条件を課すことにする。 \n", "($p$次元空間での正規直交基底間の変換を探すことに対応)\n", "\n", "そのためには$J({\\bf u}) = {\\bf u}^T {\\bf C} {\\bf u} - \\lambda ({\\bf u}^T\\cdot {\\bf u}-1)$の最大化を考えれば良い(ラグランジュ未定乗数法) \n", "$\\frac{\\partial J}{\\partial {\\bf u}} = 2 {\\bf C} {\\bf u} - 2\\lambda{\\bf u}=0 $から、今解きたい最適化問題は固有値問題: \n", "${\\bf C} {\\bf u} = \\lambda{\\bf u}$に帰着されることがわかる。\n", "\n", "\n", "この表式と上の分散の式から\n", "$\\frac{1}{N}\\sum^N_{i=1} |{\\bf s}_i|^2 = \\lambda$となり \n", "**未定乗数$\\lambda$がいま最大化したい分散に対応している**ことがわかる。 \n", "\n", "最大固有値$\\lambda_1$に属する固有ベクトルを第1主成分ベクトルと呼ぶ。 \n", "第2主成分からは同様にして、第1主成分ベクトルと直行する固有ベクトルを考えれば \n", "分散を大きくする軸を順番に決定することができる。\n", "\n", "\n", "また、$\\frac{\\lambda_i}{\\sum^p_i \\lambda_i}$を$i$番目の寄与率と呼び \n", "各主成分が元のデータに含まれる特徴をどの程度表現しているか \n", "あるいは幾つ主成分を保持しておけば元のデータに含まれる特徴を十分に表現(近似)できるのかの指標として用いられる。" ] }, { "cell_type": "markdown", "metadata": { "id": "H3O1n9lz4XUZ" }, "source": [ "## sklearnライブラリを使う方法" ] }, { "cell_type": "markdown", "metadata": { "id": "nzN4jD9e4dAO" }, "source": [ "irisデータを使ってsklearnで主成分分析をやってみよう" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Zv70QfNg4aRG" }, "outputs": [], "source": [ "from sklearn import datasets\n", "dataset = datasets.load_iris()\n", " \n", "target_names = dataset.target_names\n", "targets = dataset.target \n", "feature_names = dataset.feature_names\n", "features = dataset.data" ] }, { "cell_type": "markdown", "metadata": { "id": "czUhoCKO5OVh" }, "source": [ "このデータには、3種類('setosa,versicolor,virginica)のアヤメについて \n", "がく片の長さ・幅と花弁の長さ・幅のデータが入っている。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "mm9pfNPO5AAF", "outputId": "fea74b6f-38d5-4454-e6c2-7636921675df" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['setosa' 'versicolor' 'virginica']\n" ] } ], "source": [ "print(target_names)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 206 }, "id": "bB57ea0d5dDH", "outputId": "38f05195-5869-4f7f-ae6d-9fc3ec78b600" }, "outputs": [ { "data": { "text/html": [ "\n", "
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sepal length (cm)sepal width (cm)petal length (cm)petal width (cm)target
05.13.51.40.2setosa
14.93.01.40.2setosa
24.73.21.30.2setosa
34.63.11.50.2setosa
45.03.61.40.2setosa
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\n", " " ], "text/plain": [ " sepal length (cm) sepal width (cm) ... petal width (cm) target\n", "0 5.1 3.5 ... 0.2 setosa\n", "1 4.9 3.0 ... 0.2 setosa\n", "2 4.7 3.2 ... 0.2 setosa\n", "3 4.6 3.1 ... 0.2 setosa\n", "4 5.0 3.6 ... 0.2 setosa\n", "\n", "[5 rows x 5 columns]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "from pandas import DataFrame\n", "df = DataFrame(features, columns = feature_names)\n", "df['target'] = target_names[targets]\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": { "id": "7PGbM_BA5sdr" }, "source": [ "\n", "- がくの長さ/sepal length (cm)\n", "- がくの幅/sepal width (cm)\n", "- 花弁の長さ/petal length (cm)\n", "- 花弁の幅/petal width (cm)\n", "\n", "の4次元のデータで、可視化して理解することは難しい。 \n", "そこで、このデータを3次元/2次元に落とし込んで理解することを目指す。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 654 }, "id": "knCm13FX6b3H", "outputId": "5f95b71a-b7ff-4eed-df6b-8fa9a98834d1" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "固有値 [4.22824171 0.24267075 0.0782095 ]\n", "固有ベクトル [[ 0.36138659 -0.08452251 0.85667061 0.3582892 ]\n", " [ 0.65658877 0.73016143 -0.17337266 -0.07548102]\n", " [-0.58202985 0.59791083 0.07623608 0.54583143]]\n" ] }, { "data": { "image/png": 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tycZNNsKBVC+yrVu3pnQ4TExMEAqFDC8yyCycDofDlYhrMyDXTENYbdvp7++ntraWI0eOEIvFii56Z3J6yDc1LPQbW5ZlpqenaW1txel0GtfRB03U19dnTCXKQT4BxUcoydILVVWpr69H0zRDbmAymQqaGFTKSOl6p5yZ0mzdi2x+fp5IJEIsFjMiMrvdTiQSyZu4nn32WT7+8Y+jKAq/+7u/y+c+97mUn09OTvLwww/j8/lQFIW/+qu/4oEHHijo/VaIKw3JqWGm5miAxcVFhoeH2bt3Lw0NDUD+NjOZkGwmWEhqWOgNv7y8zOjoKA0NDWzfvh1Zlo0du3R/dv0bWN+xu5mgaRpmsxmXy2XIDdInBq3nelHKVPFGFvkh1YvMbDYTi8Wor683TBU/+clPEolEeOaZZ7DZbHR2dmY9l6IofOxjH+MnP/kJ7e3tHD16lAcffDClhPIXf/EXvPvd7+YP//APuXDhAg888AATExMFrblCXEnQ3UAtFkvWth2dVI4cOZLSZ7YR4tLTNz01bGpqyis1zFcFr2ka4+PjLC0tsXPnTqLR6JrXpA+a0L+BL126RDQaRZIkqqqqaGxsLHt75/WQ6TNL36XLVBOqr6833FDLrThfqvPoxflkL7If/ehHPPDAAwSDQT760Y/yW7/1Wzz00EMZjz958iQ7d+5k+/btALz3ve/liSeeSCEuQRBYWVkBVh1/czn9ZkOFuK5ATw3PnDnDnXfeueamDIfD9PX10dLSkpFU0i2YC4EoiiwtLTE5OVnQrqFOeLlu2EQiQV9fH9XV1Rw5coSlpSUikci65012A9VrYqFQiIGBAVRVxeVyUV9fX1BfXSlwvXYEs7le6NILm81mdEsUOpQ3GeVGXJlqbiaTiXg8zmc+85l1m8JnZmbo6Ogw/t7e3s6rr76a8ppHHnmEt7zlLfz93/89oVCI5557ruB1vu6JK12blSnSmpubY3x8PGfbTrHCTlVVCQQCxGKxgncN15Mo+P1+BgYG2Llzp5ESFiNrEEXReJC3bt1qNAh7PB7GxsYytuaUMwolv0w1obm5OWZnZ1OkFzqRF/I7LLfITVGUjOQky3LJIu1vf/vbfOADH+BTn/oUr7zyCr/927/NwMBAQet/XRPXetosWZYZHBxEluV123aKibj01FAURXp6egq+MbKRkKZpTE1NMTMzw6FDh1KKqhtpstaJWW8Q1ut76a05NpvNILJSmwmWQ5+hvktXU1PD7t27U6QXuvdWvq4X5Rhx5ep5XA9bt25N2V2fnp5m69atKa957LHHePbZZwE4ceIE0WiUpaWlgsw0X5fEtZ42S/eR6u/vZ9u2bWzdurXku2rJu4YzMzMlM/fTeyRFUcwohL0Wu4PJrTnJmqHx8XFCoZChaFcUpeTXLhalTDczSS98Pt+agSOZpBflRlyZZBWF9LYePXqUS5cuMT4+ztatW/nOd77Dt771rZTXbNu2jeeff54PfOADXLx4kWg0amyS5IvXHXFlSg3TMTk5ec3adjLtGs7NzZWEuILBIH19fXR2dq75lktGsRFHPsdl0gzpZoKhUIhz584Zu3XJTqCFoBzEo7lkDJIkpUSk6U4PydKLGyGHWO882WqW+azTZDLx1a9+lfvvvx9FUfjQhz7ELbfcwuc//3mOHDnCgw8+yN/+7d/ykY98hC9/+csIgsA3vvGNgj+D1xVxrafNSiQSRCIRAoFAwW07+SDbrmGx9bHk9FSvw9166604nc6sxxTbulPswyUIV80EfT4fe/bsIRKJ4PF4mJycBKC2tpb6+vq8hbAbxfXuVUx3ekiWXiwvLxOLxQwxbLEDR3IRTiFIb/mBwj+vBx54YI0u6wtf+ILx53379vHyyy9vaJ2vC+LKR5vl9Xq5cOECNpuNXbt2lZy0cglKN0ImiqJw4cIFYrFYXvY5N7rnUBTFFEtjPRrR7VrMZnNOIWwpcKN7FZOlF4lEgo6ODiKRyBoNXb4TteHaClnj8XjBFtPXGjc9caX7ZmUSEo6Pj7O4uMihQ4cYHBwsqe2LqqpcunSJYDCYddewWA2Yoij09fXR1tZGT09PXjfuRiKna0F46dHI9RDC3mjiSj+P3jeYLr3QJ2rn63pRivVkirhCoVDZiZBvauJaLzWMxWL09fVRU1PD0aNHjZFTpSKu5NTw9ttvz3pjFUMKi4uLeL1eenp6ctazMqGcew7ThbDhcBiPx2MIYWOxGPPz8xsatgHl48eVHuHk43qRPC2o1GLgTBFXufUpwk1KXLl8s3QsLS0xNDTEnj17DLtcYI2TaTHXFgShIBuaQshS01bnMfr9fhobG3PWszLhRqeKhSD5IdaFsCdPniQcDqc4PhQqhC3FF9P1atXJ5XqRLL3Q7/eNNmxnirgikUhZOUPATUhcmqaxvLxsWHVkatu5dOkSgUBgTdsOrJJIsdv2es1pdHQ0Z2qY6bh8yESPEGtrazl8+DDnz5+/bhbM5UB4+sTn7u7uFNlBMULYckoVCzlPNunF/Pw8586dyym9KHY9uttuOeGmIi5Zlo0Wl2xtO/39/TQ1NXH48OGMN8xGU8XTp0/T3NycMzUs5pr65sHu3buNelAxZFIOBFQqpMsO8hXClluNayPn0T8Dq9XKkSNHckovinW9iEQilRrXtUA+bTtut5vR0VFuueUWamtrs56rWOJaWFggGAxy4MCBghTAkJtMNE1jYmKChYUFbr/99pQbaCMklEgkCnK13AyEt54Qtrq6mvr6+pIZCZYiVSx1J0Au6UU+rheZUG4mgnATEFe2th39hlAUxShqHjt2bF3BY6E1ruRdw9raWmpqagp+D9nIMpFIMDAwgM1mMzYPklFsxBWLxThz5gwmk4lEImE0TNfV1ZV8GtGNQi4hbDgc5syZMymN4oUKYUulmyoFcpHfeq4X+UgvCvHiul7YtHdpettO8kOtE0E4HGZgYID29vaMg1ozoZAaV/qu4blz54qK1jIJUPVJQdu3bzduukxrLYS4NE3D7XazsrLC8ePHDZLSG6YvX76MIAjU1dXR0NCwJrVIvlYoJhNJqLjsJsxSeTdVQ6oQdnFxkQMHDhhEVowQtlQR1/VWzWdzvRgZGSEajRKNRpmbm0uRXhRS41rPRBDge9/7Ho888giCIHDgwIE1LUH5YFMS13qWyqIoMjU1xezs7LpK8nTkmypm2jXciAJeJ2BYbUydmppat+WokOvpQlVZlqmrq6Oqqop4PJ5REOr1epmbm2NoaAibzWYMbNWJ68ykj+cGlwBwWE285/ZWmpzlJVDMBU3TUmo/cFUIu7i4mJcQtlQ1rlKg2HafdOmFvmsbj8eNLGVgYICLFy+mWNVkQz4mgpcuXeIv//Ivefnll6mrq2NhYaHgdcMmJK582nZCoRB+v5/jx48XHM6vR1y5BKXFenLpKZ9OLpqm5dVylG+qqHuJtbW10djYyNDQUNbXms1mY36fXifyeDy43W6i0ShuX5j/uKzS3uDEZjXjCyf49755PnLXtoLf941E+n2TTQg7NTVFIBBYk1KVSsdVCpQqbdWdYTs7Ow3phSzLPP/88/zsZz/jiSee4H3vex+f+MQnMh6fj4ng17/+dT72sY8ZXxiF1oN1bBriykeb5fP5OH/+PDabjZ07dxb1y5QkCVmWM/5sPUFpsYV9URSJxWKcPHmyoLQ2H+LSbab1TYlIJJI3uSbXifRhoytCNcroDMuL82iaht1uZ3rFRFxWsJjKo+ZTCmQTwuopFWAYKt5oR9hSu5/qEEWRO++8k5dffpmHHnqIBx98kJmZmazH52MiODw8DMBdd92Foig88sgjvPWtby14rZuCuPJp25mYmGB+fp5Dhw4xOjpatBYrG/nkIygtlrh8Ph9zc3McOXKkoOL+eruRo6OjeL3elMhwI7uDgiDQ3lSLsyZAk9OCBLi9K9iI0/vaWcxmszGQInnk1WZHJiHsxYsXjVSqWCFsqXCtrXH04rzD4WD37t0buoYsy1y6dIkXXniB6elp7rnnHmPoTCEoe+LStVmQeaZhLBajv78fp9PJsWPHDJHiRogr+dh8eg2Tjy10R3JoaAi/38+WLVsK3pHMRkLJds2HDx9e01KyEVlDk9PK/fua+MnFRQBqqqt595UaVzQaxePxGCOvdPlBfX192TXpbgSiKGKxWAxHh2KFsKWSl1yriEtHvsr5fEwE29vbOX78OGazme7ubnbv3s2lS5c4evRoQWsta+JKJBI5fbOWl5cZHBxMEWXCxifu6Mfm22tYzHWj0Si9vb00NzfT1NTE0tJSwWvNREL6buSOHTsMu+b1jin0Wrd3uNjT7Fizq2iz2WhrazN2rPRdO31TIJFI4PF4aGpqKhspQbFILs4XK4S9luZ/xSDbevLtVczHRPAd73gH3/72t/ngBz/I0tISw8PDRk2sEJQ1cUHmKEtVVaNf7/Dhw2s65jcScek6Lr021NPTY+yqrYd8i/N6n6R+bq/XW7SMIvl6MzMzTE5OcuDAgWsuGHRYTThyBFHJ8oPOzk4UReHs2bP4/X6mp6cRRdGIxpxO56ZLK3ORTrIQFjA2ONKFsKV639c64sqXuPIxEbz//vv58Y9/zL59+5AkiS996UsG4ReCsiauTKSlR0GNjY0cOXLkmrTtLC8vF9RrmLzeXNdNrjsl90kWGwXpRKmqqrF9ffTo0Zwi0o2kihtJbSRJwmKx0N3djcViIR6P4/F4mJ6eJhAIGOO/rsccR1VTmQnNIAkSLfaWosijEDmEPmQkXQg7PDxMIBBgaGioaCEsXJ8aV75fhOuZCAqCwKOPPsqjjz66obWWNXGlY35+npGRkXUdF4qNuCKRCIODgwiCkLWXMRdyEWY8HjcsdNLrThuRUcRiMU6dOkVLS0tenlwbSRVLCYvFYii6k3fthoeHicViG1K161A1lacmnuKFmRewmWy8b9f76K7p5rGlx/C95END40jTET518FOYxMIehWJ1XMmRaEtLC0NDQzQ3N2cUwtbU1OSVUl+PiKvS8lMA9BtDURSGhobyHuFVDHHpqWFXVxdLS0tF3ZTZiEuXaezatSujbqVY4WooFGJubo4DBw7knc4mE1e5pGeZdu38fr/RmgIYNaJCSPeJ8Sf41qVvYZWsKKrCF898kf0N+5lNzNJkXa2Jnlw4ybOTz/L2rrcXtOZS+dZnc4TVhbAmk8mIRLP1Fl7rWlmFuIqAPm1n69atebt8pivRcyHZ5ubo0aMoilK0mjeduDRNY3Jykrm5uTVjwnIdtx50+cfi4iIdHR15kxZsDlubbGp+t9tNOBymt7fXeJhzjT97fuZ5bJINq2QFCXwxHwPLA5gFs3GMKIgMeAY4seUE9db6vMmoFALUTG1DmZqkPR6PIYRNn6itf+ldy0EZlV7FArG4uMjFixfZv39/QVIBSZIyjplPR/KuoZ4axmKxDe1I6oQpyzIDAwNYLBZDppENhZCCLMv09/djs9nYvn078Xi8qLVuJiSr+QOBALt37zakB8nWxvX19SnRuFW0omqpv8tGWyOXI5dXR26h4Yl6eH7qeV6ee5nbGm7j80c/v0p066AUvYr5EI7Vas0phHU6nWiaVrChZCHryTTd+kajvFaTBpfLldcAiHTkkypm2zXciJGgHjkFAgH6+/vp6uqira0tr+PyIS59/Jh+3mLGmm0Ge5r1kF7sDgQCLC8vMzAwgKqqRo3o3dvfzaN9j+KP+9E0jRpLDX9y8E/4ws+/QEgJsRJfQdEUXBYXgiDQu9zLN4e+yYf3fXjdNVzvSUGQOaUOBAKMjY0RCARwu90pjeKFPjeKohRdT7zeKGvislqtead8yciVeqWnhun1so1YN4uiiM/nw+12FzSTMZ8al9vtZmxsLKVpvBgS0jRQVO3Kn9c+fAlFJZpQqbJISOLVn5Ur4QnCVWvj7u5uZFk2jPREv8hDrocYZ5w6Rx1v2/k2muxN/F7T79Gyt4W/7/97hrxDBnkICFzwXsjrutd6NmM+EEURl8tFbW2tEXXqQtjx8XEj5c7HERY2Pgz2eqKsiatYZIu4MqWG6Si2UK4oClNTU0SjUe64446Cvu1yRVz6ANlwOMzRo0dTvhEL2Y3UNI0fX1jgiV43i8sxXl48xYH93jEAACAASURBVLG6KHWuGhoaGqivr2fan+AH59zEZJUam4n3HG6jpWZzKd5NJhONjY3GHIHbYrfh8XhWU8u+MRaqF1BllVZLK3tr9zLkGzI+QxWVLmdXXtcpRY2r1DKGbELYZKcPvXaYqSVro8NgrydeN8SVr6C0mF+Q7r5QU1NDdXV1wSF6NrKMxWL09vbS2NiYMkA2+bh8ievclJ/vnZmh0WEiIin0Lchsb+/iwLZqlpeXOX1ugMeHItRV26ivqSaqqHz3zCwfe0MXkpi5c2EzIL1GpKfbg4OD9MR6eEV6hSV5CUEU2OrYysN7H87rvKWocZXKGicbAWYTwqa3ZOneW5mIq5zse5JxUxJXcqq4Xmq4UejN1/v370dRFObn5ze0Xh26x3z6FKJkFBIdDi8EETUFn8eP2STRUF/DRXeIdxxoxel0IrlaqF+apNaiEQqFiEajzMQFLo2LdGxpLNuUoRAIgkB1dTUWi4WDBw+iKAp7vHs4N3uOQCBAu62d5ZlltHpt3dSqlHKIjSLf82QTwuriZVVVsdlsVFVVGZF9NBrNOcvxRqGsiavYG0OPuPJJDYtFpuZrn8+34dadZAlFusd8ruPWXW9kBe9KgN1bG1fti+MKXfVXb8hqqwlBEDFbLTRWOQjHFcyRGHaLxNjYGMFgEEEQmJ+fp76+vqgibrkRnyRJNDc285bGtwBrewztdntKj2Eyyom4iulVTG/JUlWVc+fOGc+M/kU1NjZWUCdDPg6oAD/4wQ945zvfyalTpzhy5EhBa4cyJ65iocshzp49W1CvYb6IRqP09fXR0NCQ0nxdbKuRfrwsy5w/fx5Jkjh69GhJjAR/MbLEX/y/AQIxFYfdxlwgQSiqsq3WxDsOXLWErqsy89Zbmnj2/CKCAKIg8J4j7XQ2OaCjHb/fz+XLlwmHw0xPT68ec+WhrqmpKckDeD2Qi3DSh22k2xrX1NQYqRWU71DZYiCKIiaTic7OTmw2mzHv4JlnnqG/v5+3vOUtvPnNb+YTn/hE1qwlHwdUgEAgwN/93d9x/Pjxotd70xGXqqqMjo4SiUS45557Sp4a6o4Ue/fuXdMcupEeSVVVOXXqFB0dHbS3t+d1zHrENTzr5U9/2IvFZKKhpoqVqIxZEnlwu5nfuG8PFjF1rUe21bKj0UEwJlNrN+O0Xb09BEEweg27u7tTRKHDw8PYbDajyF9uo6ySkW+klMnWeGVlxRCDhkIhRkdH8/aoz7aW65kqrofklh+z2cyhQ4f4sz/7M0wmE1/+8pf5z//8z5yRdj4OqAB//ud/zmc/+1m+9KUvFb3WsiauQr+NdKuYxsZG7Hb7hkgr/QbXNI3x8XGWlpYyOlJA4cTVO+3nZ0OLqPEo7XKY++85jsvlyvv4XMTl9Xp5+pU+JJMZ5xUbhxq7idHFEA93i1TbTMRisTWfcV2VmbqqzDdn+hisTBbP6b2G5TY5qNgUL3kQK6w+pDU1NUaN02q1Gu83XxPF613jKuY8+qCMrVu38tBDD+U8Ph8H1LNnzzI1NcXb3va2m5e4CkH6rmExRXIdOiHoN18ikaC/vx+Hw8GRI0ey3iSFENdLI0t8/slBookEqqJSZZJ4wxts5E9bmYkrISv8YmAM98IC+3bv5JmpCeO9xBMqkijwi1kFaczDbW0OBE1D0cAk5n7Qcj2IyRbPenSSPDlIt7CRZXlDda5S1MhKVWcTBCGlNUcf+zUxMUE4HE7ZsctmonitdxVLcZ5wOFyyCFpVVf74j/+Yb3zjGxs+V9kT13rp0LXYNdRFqKIo4vf7GRgYYOfOnRmN+ZJRiK7qaz+fIJ6IUW0xYbHYWPSHeLrfzYfu6sx7nenXC8USfOr/vMrkikyV3c4WzxL7Wp2cnwus/jwu01Frp3cxzvirU2yrszLri+KNynTWVfEHv7KN5hJM60nvNdQtbKLRKK+99prxUOsTmK83rsX2fvrYr0AgkGKimMnaudwiLlj72RRiabOeA2ogEGBgYIB7770XWBVVP/jggzz55JMFF+jLnrhyITk1LOWuod72Mzs7y8zMTM4G6WTkK0/w+/0s+/xYTWaslqtpWUwurD6WTOrRaJSvPnWKqaBGe6MLURCY80e5d1cj7zq8lVlflGfPz7OjyYHbHaau2sJT/QvsaXawxWllzh/lKy9M8IW370bMIswtNlrRLWzcbjc9PT2GE2quhzoTStVmc611Sclq/q6urjXWzvpotGg0WpJoplS1skzI10QQ1ndAdblcKU6/9957L3/zN3/z+tpVLMahNF8IgsD58+eNBul8bYbzSRX1mYnvOtrFN07OEksoRqp2357Meq1c61RVFY/Hw5m+C7yyKDIXiBOIB+hqcGA3S8z6o/y3nQ0sB+O8NLqM/sxGEgqqBlVWE4Ig0FBtYSEQIxCVcdmvXb+arqWqrq5m27ZtGR9qvch/LQZu3AhBpa5oV6tUBk2DhONhupVuNL+Gx+NhYWHBcLsoN81UIcSVjwNqqbDpiKuQ1LCYmzQYDOLz+eju7i7YCzsXcSmKwsWLF1FVlWPHjnFcELHbrDw9MI/dLHKiVmPvlvw7/P2RBD88O8fwhI9b3SHOBmrwRVabiUNxhUF3gC0uGz2tq+esqzKzvbGK0cUQUVkjGk5gMQmYpdXPJyarSIKA3Xx9veDT21RisRjLy8uGutvpdBoPtSRJ1y3iiikxRv2jiILIDtcOzOLGyHwxsshX+r5CTIkhiiKn1dO81flWDrYdxGq14vF4DM+5ctrYKCRVhPUdUJPxwgsvFL2usieu9HRI10+tlxrqJFLIUIa5uTnGx8epq6tLGb5RyFozIRKJ0NvbS1tbGx0dHcbr3nOknfccWZU+/OIXv8j7OiuRBA9/4wyz3hCKqvFzt4hZ8tNZb2fKJzC/EkNRNaosCW7vWC33i6LAR+7u4qk+Ny/3ezm2q5ETXS5eGPFeSQ01PniiA4spc8pxvZqsrVZrysANvVakjwHTRaIbkSCsR1z+mJ+/PPuXLEWX0NDocHTwmds/Q5WpeE+qs4tniSpRWqpW66T+uJ9fen/J4Y7DKRFo+saGIAjU1dXR0NCQV6N0scj2uw2Hw+vWdm8Eyp64dBSaGhZCXLpneywW49ixYwwNDW3Isz4Z+mAMfSBrLuQbDTzVO82sJ4jDakJRVRAFPKEE7bV2VFVbJR9No95h4f/78SUefeetNDmtOKwm3nu0nW2JSU4c7yAWi3HnjgY84ThtLhttrvJKU9JrRbFYjNdee22NBKGhocEw1VsP+ZDvD8Z+wEJkgQZbw6ppY3CCH03+iP+y/b8U/V5kTU5Zn4iIqq0VoGYzUUxulE725i9V2rvRCT/XG2VPXPrswUAgkDJgYj3obT/rtaboLQ7Jnu0b8eTSobdLeDyevNadLsHIhuXlZS6NXUaUJEwmE0o8jkkAp82ENxzHE04gCVDvsLDFZWM5GGdkMURTht1CQRDY3ljFdvK7MW90y44+cGPPnj3A1aZhXXCcrGzP9Xtf7zN2h93YJJvxWotowR12Gz8v5nM42HiQn8/+HG/MiyRIhBIh7nbcvW4ElU0vp79np9NJIpEgHo9vaEd9vWGw5YayJ67BwUHMZnPBu4aFmAmmD9/Y6JSgZN1X+mCMbNCvmWt46OXLl5mfn+e/3n0rP3v8AtGEiqJoKILGfz3Uxht2NfBnT1ykyiLSWmMDTUPVtJLUra51QbuYemRy03C6sh1WW5Ki9ihz8hwOi4PDTYfzus7eur1c8l2iylSFhkZcibO79uoE52LWutWxlT/Y/wf8dPqnJNQEx1uOY3KbCjYSTNfLrayspJgo6tFabW1tQefe6DDY642yJ66enp6iR3dlIx9N04y5jKU2E1QUhVOnTrF9+3a2bNmS87UjC0Ee+X+DzPqjtNsV/nZvnCbX2l+JoigpPYyiKPLXv3kL//v5URZ9Mm8/tJWPvqEbi0nkc/fv4h9fHGchsGrpfKDdxa1b19pez8zMMDY2ZhSCi22c3iiemniKr1/4OjElxoktJ/jsoc9iN9kR5/sx930TFBl576+jdN2bkzDSle2JRIKXxl/ia699DVmWEUWR7TXb+XjPx9clnV/v+nXmw/OcXDgJwH1b7+PerfcaPy92Z7LL2cWHej5k/H3APbBhI0Gn04ndbuf2229PMVEcHR3FbDYbv9v1dmizfWnqyvlyQ9kTV7FpW7aIKxaL0dfXR21tbdYortiIa3Z2lkgkwp133rmu+6k3HOdD//YagZiMJAj0BmX+2/cG+PbvHk1Zkz4cor29PaWd4nh3Pd/8oIvTp09z/PgO49/v29NEW62d0YUgriozx7rqUpxMVVUlGo0arUuRSITl5WWjcVq/0WtqalLWcS2K82cWz/APA/+ApmlIgsQr7lf4St9X+NOOB7E9+8eAhiZIWOfOEnuDSqLjV/I+t9ls5smFJ6lz1GEz2ZBlmcvhyzw39Bzb1G0MDw8b2rH0nTuzaOYP9/8hD8sPIyJiM6XW/sqpOTr5HOkmitFoNKP/Vn19/ZrSRa6Iq0Jc1xGZCC8fj6tsx+ZC8kBWh8ORl2Vz/8wKCVXFcmV8varApcUQ3nCCesdqBKg3dGcr7GcTvO5pqWZPy9o1xONxent7EUXR8A9Ltj3WhaGzs7MMDg7icDgMTdW1wGuLrxFX4gYxCAicnv4p9pceQ5CjaFWNaLXdaIkQ5gs/IFoAcQEEE0EcJgcCAmaTGYvZQn1LPY2J1Ydbf6j1lqSGhoaUEWDZdhHLqTk61zlsNlvKDq3uv5Us/NVTy1w1rnwtyK8nyp64NuLJpT/U+jivhYWFdT2uoLCIS1fvNzc309PTwyuvvJJXKlFlkVDV1LRD08BullLGj+Uq7BcSBekDPHbt2sXIyEjG9ZnN5hRbl1AoxPLyMhcuXDCM5jYiRUhHnbUOk2gyPgNVjlEXDa1+EAgIYQ+iaEK11YEoFZyiHW46zCvzr1BrqSWuxpEEie3O7Qh+wYg8YDUK12c4BoPBnJEJlE7Eej09vdL9txRFMWQXExMTxg78ysoKTqfTWFdlV/E6Q08VdV8hm81m1IfyOVaW5XVf5/F4uHjxYopEI18ZxsF2F/taqxmYDRCTFSRB4L23b8EsavT29mKxWHI2dEP+pK4P2tAHeIyOjq5LeMkK987OTkKhEBcvXjSkCPq2vC5FKAa/1vlrPH35adxhN4qqYNFUPuMPg9kOSgJQEcLLCBYn8dveV/D5dRvm15Zeo9pczUf3f5RWUytuvzvldVarNWWqdnpkovuOuVwuJKlwAs2Gax1x5YIkSSnk7Xa7WVhYYHp6mmAwiN1u59VXXzWyiHywnongo48+yj//8z9jMploamriX/7lX+jszL83Nxk3NXGFQiHGxsbyKpQnY72IKzmCS7e4ybfR2iSJ/NP7D/Hv5+aY9kWoSXh58HBDXp5cA7Mr9E37cdnN2OXs19I3IVZWVlIGbRRTr0qXIujz/XQbG73fsK6uLm/Rb5Wpin+45x94yf0SUTnKselets98C81kQrPVQDyIVtVE9C1/jdp2GC2DDU8u2E12/mD/H6T8m8/nW9fpIj0y8Xq9KQVvp9OJoigbJrAbSVzpEAQBl8tFZ2enEW0//fTTTExMcM8993DixAk++clPsnv37ozH52MieOjQIU6fPk1VVRX/+I//yGc+8xm++93vFrXem5a4VlZW8Hq9HD58uOAcPVeNK3nQa6YIrhAfeItJ5N1HVrvnT506xeDgIAcOHFjjyaWqGt89PcPTA24CUdkw+lM1DYcW58QdCnZLKlnIskxfXx/V1dUpLq36Gjc6jzF9Wz55LFYh/YY2k403t7959S8td6GO/BQhvLiaLtpqib7jX1Cb92U9vlAUSjaSJK0peM/NzREOhw1PLp2wC9VRlSpVLKQ7JNd5jDFtV6Ltz33uczz99NO8+uqrvPrqqzkjr3xMBO+77z7jz3fccQff/OY3i15v2RNXob9YRVG4cOEC4XCYjo6OogqL2SKu9IGshRybDbpBYTAYZP/+/RmNBP9fv5tvn57GahKZ9ITRNGh0WKhzWBlzhzg96eNXdl51Yw2FQvT29tLd3U1ra+ua861HXHP+KAOzAWRVY3ezg+2NuWscenE7uWak9xuGw2GcTudqk/F6n4u9jvBD/45p7DlQ4ijb7kar2ZrykhvtDmGz2WhqaiISidDT02Nox6anp9E0LSWtvB521tfC/TQZmqZhsVi45557ch6fj4lgMh577DF+7dd+rej1lj1xFYJQKERfXx/t7e00NjYSDoeLOk8mHVemgayZUAhx6dGb1Wqlubk5a0Ptz0eWCMRkpr0Jolesb9yBGHUOCwIQk69Gh3qL0a233kpNzVr91npYCsZ58dIyTpsJSRD45cRqarXVmf+3enK/oT5teXl52SB+vak6uQh89WAnck/m1ppSGQmWivz09MrlchnDaL1e75o6YLb2nHKpk+nnSb//rlWnxDe/+U1Onz7Niy++WPQ5bhri0oll//79hqXuRiZSp48306f5rCfSzJe4dJLt7Oykra2NwcHBHIJZ8ATj2MwiiiYSTah4wwm84ThmUeDWthpDWb+wsGDsRAaiMpc9YcySyM4mh6Hn0iOuTDe8eyWKWRJxWFZvjVq7xqQnTHtNTeYbWdMgHgRzFYhryU0QBBxOBy6Xi5WVFXbt2kUwGGR6eppAIJBiKljq+QDXCtnITy86NzU1pbTn6MM2roXrw7WOuHSCXg/rmQjqeO655/jiF7/Iiy++uCETybInrvU+tGyTnvNp+ckGvcali1Xr6+vX1IlyHRuNyzx5cppZX4RD22p5095Upwm91Sg5KsqVvp3YXs9zg4vEFQ0BMIsgAJ31do52xml0mOnv70eSJGMnctYX5dHnRwjHZVQV9rU6+cM3dGOWxJzXMksiinr1ZwlFw2LKMt3YN0HV99+HEJgFQSJ6/9+kREsvzLzAV/q/QkSOsK9uH++wvWON5CIYDK5pWcmWapWLkWA+ZLGenbUgCMRiMfx+/xqxbyEoZjRZJmR6T4VEXOuZCAK89tpr/P7v/z7PPvsszc3NG1pv2RNXLiRrqNInPW+k31AURaLRKKdPn15XrJoODYHf/95FRpeixGQF+6lpPnBiG//9jTtSGq/TW40yrVc3GTzWVUdHnZ1wQmFhJQYIaGhMeCI0KAn+8xcn2dG5lW3bthnHfvfMNAlZZUuNDU3T6J9d4cykjzu663MS17Z6O6OLYeZWYogCmCSBfVuqEYS1N3LVD34LwT+FgAbI2H78acJN+1Ab9zDqH+XR3kcREamSqhj0DvJ/TP+H41wdSZW8g9fV1bUm1bLb7SmpVilwo8gvk5316dOnU8S+xZgJXsuIKxKJ5P2552Mi+OlPf5pgMMi73vUuALZt28aTTz5Z1Ho3LXHptZxsNjfFRlyapuF2u1lZWeHEiRMFi+8GFhOML0dIKKuDKWKywtdfmuB37+xg6OJ57HZ7xsbrZDJRVY1/eHGcx8/OoGmwv83JjiYHz11chCtkoqgqF+YCzCyqjMXM/O2x1M2CpWAch1Uyzm0SBbzhhPH3bLCbJd60t5FZXwRVg5YaK9VWE4lEIvWFiQiCf/IKaelvQkSc70Nt3MNF70VUTcUirZKzTbIxHhvP+S2eKdVaXl5meHjY0BPF4/GsaU0+KJeozWKxYDabjV7cUChkTJVOJBIpaWW296ppGnE5jsW08RQ702da6KCM9UwEn3vuuY0tMgmbjrg0TWN0dBSv15tTVV4McenNzJqm4XK5ilIMx5TVNC79xv7Fq6e4Zff2jLt8kBpxPXt+nsfPzlBllogrKj8bXsIkCsjqaqpoEgVMooisqFRZRJbDCqcv+7h399XIcF+rkxeHl9laK+KLJBhbCvGzoUU0DZrU1SnFmR7AuKxy+rKPxWCcVpeVzoYsn4HJBpIV5EjKP2vVq3q5OmsdAletehJqAoeYvxVzcqrV0dGBoijMz8/j9/s5e/YsZrPZkFxUVVXlfd5M79kf8+MOu3GYHYz4R3jF/QpWycrbu96e4gqR6xyFIpnAM9lZ62mlLi/RozG9JWk6OM1/TP4H8555WqpaeE/je6ixFL4ZoyPbhJ9ydIaATUBcyTdIPB6nv78fp9O5rl1MoalicjPzli1beO2114pa775mG1zRcglXJkK3VwscO5R7ly854jo37b/yHgR8wQT6PW41i8RklVhCxSKBJIlUmQBBIJ42aOM3D7YRiMqcmvAyuhSiq76KaquJH52fZ4ctTs+etZGPqmn84Jyb0cUQDqtE/2wAtz/GbxzYsja9FASiv/Z32P7j4yCIgIbc/UaUbXcDcMeWO7it4Tb6Pf2grb6/dze+u6jPFFa/iGpra/F6vdxyyy1Eo1GWl5cZGxszvLgaGhrWLXynk86Qd4ivDnwVRVXwxDxomsbO2p344j7+ceAf+eODf0xHdUfKOUrRZJ2L/NJV7bFYDI/HY7QkiXaRF8IvUO+sp9HSyIq8wtOXn+ahXbnnHuZCplpZubb7wCYgLh0+n4/z58+za9euvAp7hURcek1F11EpilJ0fazBYeZ/P9jN3/7czawvzHaXyFfed5SamtzfXMlE21ZrR9NWb271CllIooDTamJZjiOIoCDQ4rAQlWNUm0T2t6WSot0i8Qf3dHOow8W3T03TXrca8ltcVgZm/BkjruVgnPGlMO11qzWWWruJ83MB3rinEXuGO0Xe/QChxr1I8+fQHC0oHXfClfNJgsQXjn+B0wunCSQC7K3dy9LI0tqTFIBk4rTZbGu8uJaXl1PmODY0NGCrsmGWzBnPoWka/3ThnzAJJmpsNbjDbsJyGFVTqbHU4A65+eHYD2m0NdJa1crdrXdjkSwlabIuJGqzWq20trbS2tqKpmkMzQ8RG4nhX/QTj8ex2+1MeaeIJCLYzcXVAjMJWcvVGQI2AXFpmsbk5CSzs7N5jwmD/Igrmy/XRgv73bUmPn/cgsNRx+7du/O6QZMjmnfd3saLw0tc9oSxSiIxUcMqiUTjcWpsEm/uaeGV0SVWojKqovG+nibaajMXdNNNBBOKhkUSWFhYYGpqCovFYjzkmrj2HOvtK2n125HrMw8VkQSJ4y1Xi/FL5CYuTdN4xf0Kw/5hWqpaeNPWNxk1slxI9+KKx+P0z/Tz1Ve/iifmodXeyvt3vp+dW3YCV6P4uBonmAjSZF/d9ZWuyDliSgyHycFceI7F6CJNtiYSWoIL3gt8dP9Hr2tzdDoEQaDR1YjT6aS5qhnPkoeElkCJKvSe7cVuu7qhUUgKnanGVa5eXLAJiAtWb+hjx44V9Itej3zi8Th9fX3U1NSs8eXayE2ZSCSYmppiz549GfsjgzGZxUCM5ise8Mnr1YnWYTXxT+8/yLlpPwlZ4dyYmyf756mqcvCbh7byRK+bYFxFVjVkFf7tl1P85qE2nLa1GrM9LdV01NsZX1rCLfyMmObnsKub5eXV0Wt6u87s7Cw+vx9r3MSlGTN1NVVEZbilzYnTZjJ689aFpmIa+C7SzCm02k7it38YLPl1L3zr0rd4+vLTiIgomsLJ+ZP8j8P/A5O4+jnlSxgJIcH/Xfi/2J12dtftZim0xDfHv8lvLv4miXgCu91u7Ga2VLXgiXqotdbSYG3AH/cTlsNEEhHCcpjbGm7DKlnRNI0L3gvMhmaR1NJMGyo2amu0N3LHljv45fwv8cf9OBwOHtr/EF01XYZ2bGxsjHA4bLQkrWcUma3GVSGuIiEIAl1dXUX11mWDPp0637QzX8zPzzM3N8fWrVszktZ/Di/xZ09cQANEAf7yHfu4e2ejsd7k92gxiRztrGVkZIQ7GmL83n+/h5giMOgO8NUXxojJKmZJBBUWgzFeHffy5p6178VqlvjAnc2899mPs5LwoCDz47iF7bYqDpoOomlaiqf5Lt8KL1yYYXJxmQ473OJYneadb5HW8sL/xHzhh6DKIIiYxp4n/O7HwZRbbBiVozxz+RlcFheSsOrAcMl/iRH/CHvr9qa+WI5hGnsOYWUGtWE3Stc9V+psq1iMLBJTYkYk1exsZiGywI79OwjMBwiHw7jdboaHh3mT6U08qT7JYngRs2Tm47d+3NhMeObyMwCsxFcwi2YEBBRNQdTEkjRHb4T8jrccZ3vNdgaGB9jdsZutV1qj0u2s9a4F3ShS18nV1NRk3NlORiVV3CBK6b6pD2Q9ePBgyXZMkl0Yuru7M77GF07wZ09cQFY1zJJIQlH503+/wNMfO0GN3bzGVSK5SfrQoUP86y+neKJ3DlWDQFTGemWMmKqBisb3z84yvhTmrftb6KhLrXP859xPCSt+FG3VqieuxXls+DHeu/e9Ka8TBIHGOhfvvGu1X1KfMDM7O8vKygqxWIy5ubnsKvdEGMv5x9FE8+quo6Yh+CeRZk+jbLsr52coazKyJhOIBxBFkWpzNaIgklCvyjA0TUNAxfLSXyPNnQXJDJeeQfYMkzj8e8brHGYHqqaiqAqSKBFX4qt6MlMVITFETU2NYa4XDofpWupiemkaSZFoTDTS0NBATU0NZxbOcHLhJJIgIWsy22u20+ZoY2Fl4YalislosjfRYm6h1pp5epQoikZLElz9feqkbbPZchpFViKuMoCqqly4cAFFUTh69GjJWi4SiYSRct5+++3Mzc0Ri8XWvG7WH0EQVpXpoP9fY9YfpcZuTnGVSG+SfmXMw/89N0e9w4IowKRHJK6oaAioV3bsPKE4r4x7OD3p5ZG399CaNGpsyb+0pt4XV+PrvrfkCTOKonD69GlisZihctdrY4byW5W5IgZZPYH+cKuJbJcw4A65CSVChBKhVd2ZYGKHawfba1LrZ7bQLNJ8L5qzdfX8qoJp5Mck9j8E1tUe0iZ7E7/a8av8eOrHiKx+3u/a+S4j5dMhCAIOhwOHw0FXZ5cxVXtpaYnhkWEWvAs0mhqRRZkqUxUW0cJSZKkkoZRLfQAAIABJREFUxfkbYf+cPjEo2ZooFAoxNDSU0pJUiBxiPS+uWCzG7/zO73DmzBkaGhr47ne/S1dXV6Fv18Drgrj0gaytra1s27atJDcMXHUV3bFjhzE0M1t02OK0Ga00qqYRislowOkJL4qq4ffFqJeUjO1Ao4shBAGj13Bns4PxpTCN1RbcvghbXFa6Gx0IAsz5opwc9/IbB1f1YpOTkzSHmjFJJmRlNeIyC2bubL6zoPcqCAKSJNHV1UVXV1dKNDY4OGj0HHa2HcM8dwpUQFPRqupRWm9f9/zfHvk27dXt+GN+AokAqqbywLYHcJhTHxxBu0KO+u9QWJ0huUqaV3F/x/301PXgi/lotjfT6riqn8slQ9AbwEOJEPZf2mkRWohGoyiyQkgJMbkwyRZxy4atZG60/XMyaXd0dHDy5Emam5uNlqSnnnrKMJ9c7xr5eHE99thj1NXVMTIywne+8x0++9nPFu3FBa8D4tIV9ukjyPJBrmJwuquojmybAg3VFv70rbv5X88MEYiuPmQ1VhN/9eNL2MwSZhFaqzQ+cdjLHWntQK0umyFfAPCHE3Q3VPGrPU28fOEyVdVVpC9T98FPJBK8/c6307HcwV+d/iv8cT+32G/h0/s/XdBnkU7I6d/ees/hyY6P0Bm30xAeRqjtQnnTI2BdXxjpj/txmBzUWVd/R4uRRUzSWreCmKMdrXoLQtCNZnEgxFZQthwEW2q6JAgCnc5OOp1XHTaDiSDPuJ/Bp/g4ohzhvq33IQqZH8gqUxUtjhZ8MR8NDQ2EE2HUiIolbllNKyWJeDyeIgotBKVs1SmVNCO5JamtrY0vfOELvPjiixw8eJCHH36YT33qUxmPz8eL64knnuCRRx4B4J3vfCd/9Ed/tKHd2U1BXMW8OU3TiMVijI6OFjRINvmamT5YTdOM0DrdLSIuqzmNBH/9tlb6p1d4sm8Ol92MN5xAVjSimozZDJN+6Is1ck9a/egNuxr45biH0xNefOEEKzEZl93M84NLIAvIURmVVWW9zSJxqL3aCMn1Ibe3N9/O9x74HgAXL17EIpbOiSG555CuLhIHj+L2elleXmZlcIbqaj/19fU5d3kPNR7ipzM/pcHaQEJNoGoqi+FFvnvpu+yr28etjbcCoEkWYvf9T8y9/4bgn0LZdheJ297PGuZOQ0yJ8cUzX2TCO4FZMnN+6DzusJv3735/1vf04Z4P89jFx5gPz2OTbHzk1o/QU9/DhHUCs3m1LqmLQnXPsXzHvJXTpKBM93lbWxtbtmzhoYce4m1vext+vz/r8fl4cSW/xmQy4XK5WF5eLqgPOBmbgrgKhT6QVRAEDh48WJR9RqYBrbqE4lLIwk8ug3h+gA/f1cnu5mo++u1eBmZXMEsCv3uohkwOt8vBOKG4DKKASVqtUxnXkyTQNEaX1nqImSSRP71/N5cWgnz6h+fZ3VKNVR+qMR/mffubWI5o2Mwiv9JVvepZX99Gla0RTVv7TBfrgJovskVjwWCQ3t5eIx1LdkV45453ElfinFo4hVk04zA5eMn9EibBxPMzz/PQroe4vXrVoUOrqid+4hN5r0fTNJ4af4repV5Mmol6qR6X1cWzk8+yrXobESXC9prt7HTtTDmuyd7EZw99lrAcxmayIQmScT6LxUJTU5MhCs20e5f+HtPXVC6TgrL1furFeUEQMk6ZupG46YhLrzt1d3dvaCcy3UxQP++CqZkvvTxltNicnfRdcVQIARpxWePrZ/3cfZufgx1X3UxfHffwyccHUDUNfyRBLKGg9/JUWSREUUQQZPa1XjUpDMcVnjg3x5Qvwp7mat7c04jdLGExre5AhuMKcUWjzWXloTvaWFxc5OlXL/DSchXi3AraeT/Hu+r40J2diEmzFUu2S6vKmM5/H2nuLKqrg8SB3wFbqoNrcjTm8/nYvXs3wWBwTW2soaGBD/Z8kA/2fJCzi2f52vmv0WJfrRvGlThPjD/Bof2Hilpm73Iv/zH5H8iavNpEH3VjMpvwRD08O/ksVsnKz2d/zm90/wZHmo+sWX96nS09QhEEYc2YN73+NzQ0RFVVlfEe9S/RUqWK+vU3glyjyfLZVczHi0t/TXt7O7Is4/f7aWhoSD9V3ripiGt2dpaJiQmj7uR2uzfsyQUwNzfH+Pg4t912Gx/7/hBxWTUK5TFFZWg+iChcvYEUVeO1KZ9BXKqq8ekfnCeuKJglkWqrRDShcqBBICI5cK/EkVWVfY0WHr5j1ZpGVlS+8PQgQ/NBLJLIL0aXGVsOcWJ7HS+PePBFE3hDCQRN5fGzbqq1MHJgmTOBGuqrTdgtqxHZyQkv9+xqZHeGOYuCdwzRP43WsBPNmdmKOhcsL/01pktPg2BCmnwZ09QrRH7jsdUpPVlgMpkyRmPJO5V+UtMSSZAMWUQxD+nJ+ZM02BtYji0TjofR0JgJzVBvrae9enUoSUyJ8ZPpn6whrkxYL81Ljzh154fkqUGl8IkvFdaLuNZDPl5cDz74IP/6r//KiRMn+P73v88b3/jGDRHupiCufMwEh4aGiEajHDt2zJA6lMJMcHBwkEgkYpw300rMkoisqgisfhubJIHG6qvpaSiuEE6skhYaoGnYTfC+e3p46y1bmPFHiYZDhJdmsFzRZ40thRlZCNFUbVmtm2kmfj6yzD+97yArUZkfnZ+nzWWl0Syz5A/ww74Yn/+vR/nnS/3Uma8OPRAFYTU9Tfs8q1/7Go7er6NJZgRVJvrWLyPvKsADPBHBPPw0ms1l7OwJKzNICwMoW4+uea3on8QamQetJ2UdyX5ceqTimHcQD8WZikxRba0mSpQ3tr8x/7WlwSJZQFutow0tDRFQAuxw7cBpuRrdmgQTsirnVTAuJM3L5Pzg9XqNMWDBYLDoMW+yKqNoxd3fydjoMNh8vLg+/OEP89u//dvs3LmT+vp6vvOd72xozZuCuHIh2Uxw7969JTMT1DSNgYEBmpqaUkwKP3RXJ32zK8RlFQ2wSiJ/dG83X31hfPVACbY5Bd56y1UVe7VVoq7KjCcYR0AFAUTRxO4WJ6Io0FFnJ2hWGE1q5VM1jXSWFLRVL66D7S4uL4dpqjYzPz+P01ZFwuLEajbRs8XJkDtAc42VUExBunL+ZFgDkzh7vwaqjKDKgIrt2U8S7Lo3Z7SU9gmlLe7KYrXUz1tYmcH2409D1Me+UBBR7kO5+08yFtOTI5Wt3Vv5ztB3WAgssEfYww7/Dmbl2bzHgl0OXGY2NIvL4uK+tvu44L2AP+bHKTlprWrlo7d9lMdHH2c5uoxNsuGNe7l7y915RQEb2Q3TpwYlEgmj1ufxeLh06RLRaDSvMW+qpnLec54R/wgToQkcyw5uqb8l6w7pethoxAXre3HZbDYef/zxotaXCZuauPSBrHv37s2YLxcbcemTW3b8/+y9eXwkd3Xu/a2q3lvdUkutbUbbSLPvu8crXomxARuzmHDZErZLEkhILvcaSEJeAi+GS+6bS7gkDpshIQFCiNkSOwZDPGDwLB5Joxlto10aLb1IvaiX6lruHz1V05K6pe6WJnj88nw+fJjxdFdXddfvqfM75znP6ehYIZK7bZufv3p4P3/3/ASSIPD2G1s41ubjzp11vDC+gFPSqM3MmUJTyD51P3l/B+//pwuogoiOwB/ds5WtdUtlFLl5p3a/m6YqJ+PhBA6rREJWuKGtmiqnlZZqF3JGYXZuAavVSkq3sP3Ksd55cytf+cU43VMRVFXn5o4agnF5SQRoT86gCxYEQc3yz5UbXkiG0K2F5zkugdWF0n430vCPQLKBmkH3NKLW71/yMtvPP4OQDKM7a8jIAj8c/wGP/+An6BYbr259Nb+9+7fzHn5zxWb+6MjV8ruiKExMTDA3N8epU6dwu93mws+Vjmi6xo8mfsQTw0+Yw1tvbLiRP9j3B3SGOpmbm+OmppvoqOzgHbvewY8mfkQ0E+VY/TFublhd3W9go5qs89k7FzPmbSw2Rv9CP3XOOsJimIGFASqsFWzx5u/aKOZc8kVcv/bjWifySRLGxsaYnZ1dMZA1F+UQ1+XLlxkbG6O2tragf9bNHTXc3LGUKGvcNu7bWw9qhgsXZpf828zMDPLcMD/8nePEVAmfy4bHsfSrXy6jsFlEPvaqnXzjzCQT4SQ7Gzy87vAmBEGgwZpkf2WSCzEPkWSSPU1O3ngsSzhep5V339LGl58bI7QoE07I/OPpSV65r4FjbVdsg71tCLp6JToSQdPQrTZ0d2l9m+mXfQRrZTPS9Dk0bxOZo+9ZEbGJkVH0KwZ337el+V+ODGSioAh8pf8rCILAb+36rTU/y2KxUFVVhaIobN26NW9uzFHp4BsT3+DpyaeRBIlGVyOb3Zv55ewvuaXxFu5rvY9BeRC/I1uCr3XW8pvbS/ew2ig/ruVkUeyYt1llFrfFjSiIiEK2lSmYDJZNXIUirlQqtWGW2RuN64K4crHWQNZclLJVNPJk6XSaY8eOMTQ0VNR74ymF93y9k87JCDrwhkON3NeQJUtd180JQUaOrJAEVr/iFjodSXEpsIjLJnFgs5d333r1Zsx1f/2DB25C0UV6LvbS0bKJihynibFwgkBcNreI6YzKTweCJnFl3I2EbvpTap77WHbLJlpJPvDlbOS0HKqMtfvrSJfP0hHXEXY2ZdttACQbmSPvZLWGHq16G9JMF7rLz3dsKQAsggSCiKIrfHf0u0URl3H9xtSZ5V714XCYr1/8Ol2RLnRFx2qxMp2YxmPzIAkSyStOrRs14mwjWn7WajvLHfOm67rpOTY9M82YPEZTZTZKSypJKqylzw/NPZd817NRw2avBa4r4jLm8rW2tuYdfbQcxUZcxjSfmpoaM09WLOl99Ad9dE9FUK608zzRPYNbtnLo0NUexkOHDhV8Qs8nZP7ke710TkTQlQxVvziHx2FB12HfZi+P/MY2LFK2UGAQ9uHDhxFFESvZ/NlyaLq+JD0mioJpSGhg0L6fwZu/ij0TIYob76IXfzhMVVXVkpvY9ou/xDL8Y3RbBb5IEMdTf0jyVY8VpYYHkG/+b9iffgQxdhmLTUMXhKtODjqmNqoo6Dr2+ATidAzdswm9IiuXMCqVk4OTRKQIsiqjKAoWLIyHxql31eNRPSZp/WeaABZCqVGbIFyd4djU2sTJqZNMhCYIy2G0cY10Is10eprq6uqSdYvr8fD/VeG6Ia7Z2VkuXbpU0qDTYojLsLhZPs0n31DYfDg7voCsXiWFZEbjYjDD6dOnaW9vz2tvk4uPfr+PrskoFXaJqYRMNJzgWJsPt02ieyrCmfEFDja66OzsZPPmzUsUyrAyNwbQ7HMSS2X4YfcCNqtEncfO6w5l5Q6KojA9PY3L5WLvkRNZl9UruZVgMMilS5dM14CaKi+ukWfQ3bUgiMg2BVcqgjR3AbX5xqUXoutIk79EnD6H7q5F2X4/WF3o7jpSr/5bhPgsd557gqHwN5dIG96y/S1rfsfG8d1D38N76WlsEx5AQD76HrTGrLZrKDLEwMIAKTWFQ3IQz8TRRI0mXxNva34b0UCUyaFJM9JxOp1mbkzXdS5FLhFOh/HZfWyr3LYqqWyU53y5BGqTbNzefDsBX4ABdYAbD91IKpEiHA5z4cKFNce8Lcdqo8k2qq93o3FdENfi4iJTU1McP368qHYKA7larHwwLG7yOauu9V4DmyodzERTpi+8TRKosirmYNp86JuJ8el/HyQYlxkLJ2jw2M0bRACiKYUKe1Z6MReOcvZyb8FpRvlajC5OxwgnMjisEmlVIxhPs8nnIJVKce7cOTweD36/3xSi5jYXQzYpGwqF6O3r52Aiia4vYrM74IrkA3HlbWO58G1sZx+7Io1QkYaeJvGK/w/J6gbRgu7dzL7Km/nTth38w9A/oOkar+94Pfe33b/mdwwgRCdwjv+URWctuqcGMkls575Cqn4/iBJn5s7gsXoQEMjoGRySgxpHDX9xy18sUbz39PSQyWSWzHE8nznPC5EXst8HOjc33MzLm19ecNH+Kh1QDUiCRJW1iipbFVbJitVjxePx0NramneitpHkz5ezUlU1r03Ri5W04DohLsOTqtQv0miEXQ6jAVmW5YIWN8VuFf/81bt44xdPo2rZyKXGKXB/h7Mgac3F0vz+t86TzqjYLSIZRWP2iiOqrkNG04kmZKocFpRMBnV+ikM3FbaszqeC//lQGL/bhtefJfnZaJpfDMzQziy7d+9ete8MWDJdR+TtWLr+nowcxSonmXe0Ma/XUi3LV292Xcd27kvo9kqw2PkhMT4vXyD95EMcrj/Bfz/03031+W2Nt3F3691rfq8rrlOOowsSGFtLqxOSIVDTILpwWByIgkirt5W0miapJGnztC3ZigqCgMViYdOmTXg8HhRFYXR2lGdHnsWlurDb7dgddn4+/XNO1J+g0l6Z91yuVX9gqSh0HmuNeausrKSmpoaqqipzV7L8OBvVS3mtcF0QF5TH/vm2iul0mq6uLmpra80G5HwoNuLqqHXzb793A985eR6n3cLrb93PC2dOFXx991SEjKqZts11HjuzsTSXF5IoV3Ra0zGZjKLwjv0OXnX70VWTuPmIy2YRzZwbQDKVZG5mgde+4igul4toNFp0klo7/HZUXyvW2S7GA0mqb30HqUiSnp4edF2nurqaTfHzVIQGQRA55/byWZ8Tq67jEmy8EHiBvzr/Vzxy+JG1P2y186hoRBAkRGUR9EqExTm0yhawZCOIWxtv5YmRJxiLjWERLHhsHh7e9vCK4+QShiiJ2CptVFZWUu+sJ5PJkEwmicQinDl3hi11W/L2G74YIq5ij5FvzFskEjEnJFmtVrP3Mve6ShkG+6vAdUNc5WB51GRMCiqk+8qFJEkrh6DmQTKZ5NKFLl6xb2X+KR9cVsmc4CMIAnaLiNdhwSqJWPUMdT4P0XgcWYPfvOs4krT2jbmchF6xp57//cwQ05Ek8cVFLJrCm+48akZtJfUqCgJq+52o7Xcyc/o0zb563D5MpXts5Cyu5z6FLDqxKAnOk0bRrDgFK7rFgQPoDHYuOd+y4PSxsP+dODu/ghCbQvNtybqeXjnemcAZMmoGkWy1ss3Txi7frhWHMb73yfgkX+v/GhE5wuXFy6TUFI2uRtLWNNs3befmHTcTXYgu6Tc0ttPXE3Etx/LRZ6lUit7eXmZnZ5mamsLr9eJyuUilUmW5n4bDYR5++GFGR0dpa2vjW9/61go7qc7OTt773vcSjUaRJImPfOQjPPzwyofMatiYLs9rjPWolI2oaXJykt7eXg4dOlRUc2cxEdf8/DwvvPACO3bsKIq0AI62+theX0E8rRJJZkgpGq/a34DHYcFlyVZObVYbNputqOvOR0IdtW7+6O4Odntkbml28Ohv3kCjz73qe8qB1WqljiB2mw2pdht6RS0+XULSdZIWLxlVI62mTWth8zOT84jBPkjOl/R5maoOJg99kNT9/wf51g+hu7K/Y0bN8A8D/0C1o5qOyg62ercyHh9nYH4g73Wm1TRf6fsKqqbS6GqktaKVmcQMKSVFR2UHb9nxFhw2B3V1dezatYtjx47R1taGLMv09PQQjUYZGxsjEomU/T1uxFZsI8jP4XDgdDrZunUrR48epaGhgb6+Pt785jdz4cIFPvGJT3DmzJmir/PRRx/lrrvuYnBwkLvuuotHH310xWtcLhdf+9rXuHDhAk8++SR/8Ad/wMLCQknn/ZKPuIzp1Kqqcvz48aLLvmvluCYmJpiamlpVAJsPNovIZ9+wjycvzhGMp9m3uZJdDR7OjJ5ickHDYbdhB157uGGJo0Mh5COhdDrNzKUeXrU/6/hazHvKhe7wcUV+D94m7sos8kMhxaDNkrWH1uAu6S76+/vJZDKIo/+B6/n/ZUYt6VsfQW297YqLaSa/lsz4LF1HEMWs1/wVBJIB/rLrLxmPj2MVrDR5mqiyVbGYWeSz5z9LhbWCE/UneGDLA1hEC7quE8lESCpJ6pxZwa3f6UdD420730a9qz7v92X0G7a2tnL69Gk8Hk/eaCyvF3+Ba/lVRFz5YOS4jDFvL3/5y2lqauKTn/wkW7Zs4fHHH+fIkSNFHeu73/0uP/3pTwF429vexu23386nPvWpJa/ZnuP5tGnTJurq6ggEAiVZ51w3xFXOYlPVrBVye3s7ra2tJT3hChGXpmn09vaa3vXl6F/sVokHDly1Ej51cZhEIokmCKQUDZtV4t7dKxdQPiyvKsZiMbq7u1fIO5Zjo4hLbTqB2nQj0uQvQRBxCAKfPvFJnrdCUkmyu3o3dY46IpEICzNjCOc+QUxyYHG4sQka9pOPklYVbC98EeQ44ZoOLu5+FaLDxw7fDlyW1bcrf33hrwmlQvjsPiJyhPHYOHFHnAV5gR2VO3BanJycPonb6ubelnvRdZ0KawUCArIqY5NsyKqc175mNdTV1VFfX2+6P4RCIfMBmevFVYhYflVbxULHyTcM1ufz8aY3vYk3velNRR9rdnaWxsbsvd3Q0MDs7Oyqrz916hSyLNPR0VHSOV83xFUq5ufnuXDhAi6Xa0W/YTHIp+PKTey3tbVtiJbn7PlevnwmhGR30mJNUVnpJZzI8J3Oy/y3e7ateYxcHVcgEGBwcJADBw6s2tW/kREXokT67k8gTZ0BOYbm34no3cwylRc+n49KKY3b6USzVyJnMizKKpbUAuIzH0f21BF2VfOZaCexF/rRqrfid/r5wP4PmC4Oy3NLiqYwHhun1lGL1+ZlLDZGOB1GQGC7dzsVV+Y5VloruRC+YBKXx+bhwS0P8p2R7yCQlUA8tOWhktTnpnxlWTRmSBGmp6fp7+8v2FP5YsmTGcfJNwy2UJ/i3XffzczMzIr//olPfGLJ340uh0KYnp7mLW95C1/96ldLvo6XJHEZk68PHDjAwMBAWcdYnuOKRqOcP39+zUjGwGo3ZtdkhLOjYfpHJugKasynISHL1DqhErCI2VaiYmBEXEbv5tGjR9fcrmwIcek6YuBitrpX1YradHzNt8h2H4gSoibjcDhxSDqCbiEj2UmqIt9MThOTBOqTi2RsNQSTQU5On+S+1vvyHk8SJLw2LwklgdvqZot3C960lzs33cmpuauV3ZSWosXWcuW0s7/LsfpjtHnbCKfDVNurzRmM68VyKUKhaGwjvOI3qiUn37ms5gzxox/9qOCx6uvrmZ6eprGxkenp6YJzS6PRKPfffz+f+MQnOHHiRMnnfN0QVzGLzRhBpus6x44dQ9f1dflxGRHX9PQ0o6OjRc9iNN6b76b694tz/MXTAySSaeZlsFtE6j02khmNuYRGZTJDRtV52fbivbinp6dxu90cPXq0qMWQGy2UC+uZx7Be/Ha2qqdD+qY/BNGKGBpAr2pB2foKEJdev2pxk7jlw7h//klIpkCUkI++F2vPN6iocCOrMdyqgoaFhUh2ovTw5WEiVRFTF7fcefQ9u9/DZ89/lnA6jKZr3Ln5Th5oe4DJxUmmE9MAuC1uXtn2yhXXX+us3TDCyodC0djMzAyRSIT+/n78fn9ZbTqwMYMyCh0nmUyW5QxhGAY+8sgjfPWrX+WBBx5Y8RpZlnnNa17DW9/6Vl73uteVdc7XDXGtBcOXq7GxkebmZpPo1mskODAwQDweL2kW42rE9fmfXkLPpPF7XUTDSTJqNgJoqnIwOZ/AahF55y0t3F4EcWUyGcbGxnA6nezdu7doIlpvxCXMD2O9+O2s4FSUQJVx/OjDINkBHV0QkMZOkr77k0smTAMom4+TeP03ERJBdJcfrC7ExTmk0Wc4KCoMSir2+gN4nB7klMy+2n2mzbPFYsFut5PJZMwOih2+HXz8ho9zefEyFdYKWiqy4+fev//9DEYGUbTsIFfvFYeKDdsil4HcaCwej9Pa2mqmNAwV/1q5sVwU06hdLEqJuFbDI488whve8Aa+9KUv0drayre+lR3QcubMGf7mb/6GL37xi3zrW9/i2WefJRQK8fjjjwPw+OOPc/DgwaI/5yVBXIYv1/K2mPVEFLqus7CwgMfjKVm1XyixPzY2Rmwxhc9bgSSKiIKAomnoOrjtFmqdAo8+uIdAPM2p0Xn2bvKaQtXlMIbG1tTU4HA4Sr7WdRFXaiGrYDcjKgEhtYDm25KtCuo6lrGfkQkPo9VsXXkAmxvddvVpLp94P2LH3dySmie8OMyz891Y1DSv63gdt226zSTa0dFRIpEI3d3dAGbuqKqiyhxrZsAu2dlbvTfvdb8YFOG6ruPxePB6vSuisYGBAbNSuVo0tpG+9ctRLnHV1NTw4x//eMV/P3r0KF/84hcBePOb38yb3/zmdZ3fdU1cuq4zPj7OzMxMybKE1WBMo7HZbGzbtnaCfDmWE1duJfIVB5r4994AFXYLNW4bgVgaTYe0onF/u5WP/1s/wXi2TclfYeMzr91LtXtpzsog6n379rG4uEgymSzp/MqNuHzz3Tj/6S8gHc2aA4oSWN0IqYXsnwWL8QHogghKkeclCGj+HSBaeDW38OoC5+x0OpEkiZaWFmRZJhwOm+PBvF6vudBXi0JeTMSVex6FcmPG9PV80di1Jq58vbEvFlw3xLX8ZlNVlYsXL2YTrWv4cpUCozK3Z88e+vr6yjpGLnHJskxXVxd+v5+2tjZ27NJw2iz8YjjMpkoHn35oDzVuGzVuG5/49nPMRtP4K7JENRdL843Tk/zO7VfH0E9OTjI5OWkSdSKRKGvUmLGNzmQypo2P8f95r2m2hx2Df43gzDZNo2uIyXn0TBKtsgXBUYUYn0G3OhEyKXRXDVr12iVuITKB/eQnERfG0CrqkW/9EFrN2g8Lm81GQ0MDDQ0NpldVMBhkfHx8SdO4MV7LwIuFuFbDarmx3Ggsk8lcM+IqVzn/n4XrhrhykUwm6erqymvzUi50XWdkZIRQKMTRo0exWq1l+9UbxGX4h23dutWsrtitEr97ezu/m0NcNOOOAAAgAElEQVRGBhbSOjbp6qKySSIz0bR5fgMDAyQSCY4dPYq162tIXV+nMZMh2HIftP+PNYei5iKRSKBpmnmdmqaZizofiUnjJ9F1BazZm1m3V6LbvSTf8E2w2BESIWwnP4kU6EWt3UX61g+bry0INYP9J3+KkIqgVdRDOor9J39K8tVfANtKaUIh0sn1qoKrzqHDw8Mkk0mqqqrMpuJyiEvTNc6HzjMRn6DGUbPCbv9ao1A0FggECIfDLCwslJQbKwYvZttmuA6JKxQK0dfXx+7du1f0QJULVVU5f/48drudI0eOrPvHF0WRUCjE5cuXzVFpxWCrz8LYlIZ6pUE6rWgcaq5EURS6u7vxeDwcPHgQqe97SKcfA1sFOgI1g99EbNmOtuehNT/DyK2EQiHOnTuH1WqltrY2a33scJgkpmkaqqpeJTCrmyXTOzQF7G6wZPMvuquG9G98pqTvSVicQ5wfzSbw1TS6ux6SYcToVHbrWA50HWfoAq0TP6dVsiNvvYd5KpcQ2dTUFH6/v+gm4h9P/piTl0/isDhIq2lsURvHtGNY8tj7FItyo77caCyVSlFbW4uqqiXlxnJRqPWo3BzXfxauG+IykrNr+cwvh6FzKkRGyWSSzs5OmpubaWoqclDEGucZi8WIxWJFaapycVuLHWtlJf/elx3388p99bx8h4/Tp0/T2trKpk1ZM0Bx+BkQrSDZEHQBVbZgGfnpmsSlqqoZZRltF8lkkmAwaLbkVFdX4/f78XiyjqHGljKx5eVIz38ZWzIMgCBZSR//vXK+IhOW8/+IuDCa/YsgosVn0Ssa0Qu4q64aLaky0tjPkMaeRbp8Br2qDQDnTBfibR+m+kqu0hgNb1i8GLmjQoZ7aTXNczPP0eBuQBKywzcuhi8yk5gxZzL+qmD8ltXV1SXlxpYfYz3DYH9VuG6Ia2JigsXFxZLzWca2Ld97jCT3RkVvmqbR09ODqqrs3LmzJNICsEgS77qpid+5PZsbWozH6Dz3worz0101COpV5wpRV9BdhROphsup8XTNXfxOp5Pm5mbT8iQUCjE9PW1Oma6traWyspKRmQjijZ9ih9oPmQSZphvR6/YglpsgTkexnf9HdEclQjqWFbQmQqT3vIG4w8sPBr/JaHyUza7NvHrLq005g6ZrnLx8kqHoEHXOOu7YfAdOixPLxe8gzXYjzl0AeREhNo1Wvw8hNo10+QyKN2v1LYrikuvNNdxzOp1mbsyIVnRdR0dHYKn2TdVUukPddAW7kASJE/UnaK9cuf2/llh+XxeTG1s+UXu10WS/3ipuAJqbm4vymV8OwyFieaVpfHyc6enpDatGptNpOjs7aWxsLEtMCFejQ4skMjMzw8jIyFV31uQ8QngYvaIO9cg7EEd/lt1WqSqytQKOvCPvMQ3SMkSGq21RJElaMoE5FosxOztLb28vVquVzZs3s1i7H6fTiaBp6FeOa2jljAVQlAg2k8huEa1OdIsju/XUdZTW2/hy35cZiY7gtXrpDHUylZjiDw/8IQBPzT5FZ6ITu2RHVmV6wj18YNe7sc/1oHmbEeeHQcsgyHHIJAB9hZYs93r9fj9+vx9d10kkEgSDQVNXZdi/7KveR1eoi0pbJYuZRSqlShbkBX48+WOqHdXImsx3R7/LG7a+gc3u0u/RcrFWVTFfbsyYqG1EYxUVFQW3ir8mrg1AucNdl5sJ5koTjh49uiEtE0Y7kOHzNTg4WNa5GsQ1NDTEwsKCKXoVJp/H+sR7suPENAX1+HvJvOHriGM/YzEeZ8Kyhe2VK4sUxjbPcCIodTiDzWZjfn6enTt3Ul1dTTAYZGhoiEQigc/nM6MxwCRHYAlJFlpYursOzduEuDACFgfoGrrdS6iykbHxMeocdVkJhMXJXHKO2cQssipzeuE0myo3ZbdtmsZkdJjxYA+7syPCUWt2YJn4GSgyQnwOnJWoTTcUdb1utxu3221GK+FwmOnpaRoiDSyySFSJ0l7Vjh8/Q5EhvDYvzitGhiklxXBkuCji2igRbCktP7nRWEtLy5JobGFhgZ6eniXRWDlbxWK8uAxEo1F2797Ngw8+yOc+97mSPgeuI+IqN5mZS3hGk3RdXV3RbhFrVaFmZmYYHh5e0g5ULskKgmCG9IcOHcouel3D+r3fASUNFhuIEtKpv0FrvwNt92tILyyQmZrKe965U59L/f7i8Tjnz59nd4uf2hc+iRAawOPfyebb/xjNUc38/DyBQMA8X6N1xWazrSCxfAQmjf0M3VGFLlqzVcXaPaRe/iksDh8amrk903UddLCIFmQ9q28TEEBTEaMTiKkg4qWn0AQJcWEU3e5Fq9mOroPaeivqljtKnhcJVycHGdHnvtg+QqEQoVCIxcQiMSHGoriIx+oBARRdwS4VF2lvlCRjPS0/RjRmt9uxWCw0NzebwzY+9KEPkUgk6Orq4s477yxanW94cT3yyCM8+uijPProoyssbQz8yZ/8CbfddltZ5w7XEXGVCyPiKjTNZzUYeqd8N5kx4zASiXDs2LElQzzKIa50Ok0wGGTz5s3s2JFTUZMXQY5noxLIbnsEECLj6PV784pJdV1HURTzXIqGrkM6SnghysDoFPv37KT6e29BiExkCwEjP8E+P0L6jd9e4gaaSCQIBALmFqumpoba2lrcbrcps1AUhUwmQyaTQYpfxt71d+jeTai+tmz7j9OPXt2BF7ip4SZ+Nv0zLIKFjJbhcO1h6p31TIlT7K/cT2+yl4pMmlQySJ3TT0v1ToToZdTqbegOD+qWO1A3H1vV26sUCIKA1+vF6/XS1NREd3c3R2qO8J2R7zAdmMZmt1FbUct27/a1D8bG+blvhADVSKPkRmPf+MY3uO+++/j2t7/NBz/4Qb7whS9w/PjaTfTFeHEBnD17ltnZWe69917OnDlT1nm/5IlLFEXm5uYIBoN5p/ms9d58N4chn3A4HBw+fHjFTZhv8s5qMDy0KisrV3bT2yrQHb5sm43FDlp2ArV+Rdy5nCSNymHJUVYmie3f/wf66En8iop/72vRU16E+MxVTZVoRYhOIQQugtWN7vQhuGrMLZZh5xwKhRgbGyM1P02jNoXH7WJcqaGubks2/xeavbKxs2QnBzmqEaMT2TyXaOGh9odo97YzGZ+kwdXA4dqr3/GrGl7JVm0rl0b+jTq3m1fWHMYuWtDtFejuWtRt9xZ/zWXA6A/c27aXpsYmRqIjpBZTeGQPgz2DWCwW/H6/KX7Nh40wETSOcy2scXw+H5Ik8dhjj5mvKQbFeHFpmsYf/dEf8fd///erukyshZc0cem6TiQSMdX1pTak5vPkSqVSdHZ20tTUVFA+kW/WYSHkemhNTEysfJ8goDz4Bazf+a3sRBtdRbntQ+hXdE5GxLVa5bAYWJ7/P2jDz5IRnTg8doTB75OpqM3m1XT9qrhVSWF95v9BECVAJ3Psv6J1XJ3aY7Vas4p2rwXrf3wFOTJLLBanWbIxpf0WszYbdQ4fIqChoiNBcgHF6UfRQCS7kA7XHuZw7WHimThnA2dRVJm68T5aF0bY5qlEqzqCuDiHJtpA17JTgDwFZlhqSlYvpmWwyKtPOFoLuWRRZa/iUO0hyDGYSKVShEIhLl26RCqVWiJ+NfJRG9mqs17iyldVzL0HBUFY8u/r9eL6/Oc/z3333bdu6dF1Q1yl/kCZTHaStCiKtLa2ltVFv9yTyxi2sZZ8ohi/el3XGRsbY25uztR7Fdpi6g37kN91EiE6he6sBtfSRvJSKof5oGkaiYFncYhWHC7XlcK/iBiZQGu9FXHkP7IEJojZqM9egW73gCpjPf0Yct3eFaQhjTyLmpgnpFbg29yMU41SySUm2ceFywm81n20zD2Pze7A4vKiHPuvAGaVUtd1ElqCxy48RlgOIybnERemebv3KLudVUjhS6iVrYixrHWNWn8ArW7fyotTM1gu/jNiqB8hOs2u4DQW5zjqzldn3SlKxFpRjsPhYPPmzWzevNkctBsKhRgaGjLnG7rd7mvWqlMqCpFoIeJZrxfXL37xC06ePMnnP/954vE4sixTUVGR15t+NVw3xFUKjFab9vb2snr5DOQSyeXLlxkbG+Pw4cNrKq5FUVx1QpBR2dQ0bYmH1qrNz1Ynej6nBbJP+XQ6XfSAjVwYBL+3qgWbnCWB7BgiDb2qhczRdyFd/BeE0AC6ZzOW/u+DPetIimTLRmKJACwjrmQ0SDIap6ZxW3b0VSqFVZevaqgOHGB+apDI7CTBtIRrOkGtMo/P58NisaCqKmdnzhJKh2h0NiLFw8xJNp6RJ9kttaBbXehVrcjGRG1b/tK9OD+EOD+MkMkWNzJWT1brZXWh7HwgO5+xBJSyPRNFcclEHWPQ7tDQEIuLi1y6dGlV8et/BgrpuMpZM8V4cX396183//z4449z5syZkkkLXoLENTc3x6VLl9i3bx8ej4exsbF1e3L19/dnewSL3G6ulpzPZDJ0dnaaTde5i6CULSZgzsOrqamhq6sLURTx+/3U1tauaC7Oh2QySXd3N1u2bMG+40/Q/+W3EZIh0EHzb0c5+FYQLah7X599g6Ygjf4UUlFweEFJgQ56xVLSCgQCzCx6Oeh1I+opkDMI6Qhq81XTOEmS8LfsxN+yk/YrmrHA3AyT/aeQkalv2s+isohVsiKIArpkx6IqJK1KdrEpaTRbRUHCMqFkez0FOYrmqEQTYgi6hqDJCOkIeonEtZ5tnjHf0OfzMTo6SmVlJbOzswwMDBS0eL7WyOfpVW61shgvro3CS4a4dF1neHiYcDi8pNUm31DYYiEIAr29vVRXV3Pw4MGSnrT5iMvw0Oro6KC+Pv80mWIToUalThAE2tvbaW9vNyuTg4ODpFIpU2tVVVW14kaMRCJcvHiR3bt3X21OfvifEGe7QbSg1e8z+xCvXpiFzG0fwvof/y/C4hwgkjnxPnBfTfJMTU0xPT3N/tseQg9shf4fgKagHHwbWsvNea9FEAS8Lhtj09/gH0K/IKNruObdHPI/QHA+SMaRAdmCIujca3EjxaZQPZtJ1+xBuOKQUEgzplc0gCCiaypk0ljVOJp3TzYvWKR8Yfn3Xk5eaToxTU+oB4BWWyuSJOVtnO7p6TErszU1NXg8nmvqZqGq6grBdLnup8V4ceXi7W9/O29/+9tL/hy4johrtR9PURR6enryNkmvtW0rBKPE39zcXLInVz7iyvXQMmyIi3lfPhSqHNrtdjO/YrSzzM7OmkMbamtr8fv9LCwsMDQ0xMGDB5due20utObV/b91/w7kBx7LShgcPjPiMR4c8XicQ4cOZQsbm4+ibT6a5yA64qV/z0ZvVhfK3jcQDvXyxcDPcVu9VIkWIvICF5LP8rvHfo9vdH4DRYQ9la+gxtnCTI0fT/MebM6Kgpox4x7QK+rJ7Hk9lgv/hBToRbZWojt8WWJ2lt7mVQ5xzSZm+f7I93FIWUlL71wvR2xXx30tb9XJZDKEw2EmJyeJxWJ4PB6zcdqQ3WykiDWf++mLeYo1XEfEVQhrNUmXE3EZJOP3+8vqYVweOS330FrtfQVvyNg00n98EmFhDBoPo9/4AQR74afi8naWWCxGIBDg+eefJ5PJ0NraWp5tj5JGiM+iW5wmaWmaRl9fH6Iosn///jUXtjT4b1jOfBHdUQlqBtszf0agYSe6KOG44rhQKTmZS4axnH2GP7VV4W3ajdJxN4lMdis63jdYUDOmqqqpY5MkCaFqC/qtj5BJRxk/9TN8u24wh8mWinKIq3+hH5toMwfjJpNJxlJj3Ez+CNRqtVJfX2+OP4vFYgSDQSYmJhBFkZqamg11Rsk34efF3GAN1xlxLV/YBsHs2bOn4DDJUokrd9DrxMREWYvbyFUZHlrJZLKoGYwFI650HOu3/gssBkC0YA0PI0UnkF/1N0V5cAmCgMfjYWZmhsrKSrZu3UooFGJgYIB0Om26C6yVJBZiM1if+ShCIpCVZex4FfKBt9N9/jxVVVUrcnaFIA0+he68Gq0Ru4xPUdA0BUVXsQgiiUwSMSOzU+zGZamDS09hDV/CfePv425rW6IZGx8fJxaLUVlZaT5sjPyk8X0qioJkcZOy+8smLSgvxyUKInqOiZeqF59DyhW/tre3I8syoVCI0dFRFhcX6e/vN4msnPa1QjMVf01c1wC6rjMxMVFUk3Sx2y9N0+jv70eWZZNk8um4ioEoiiiKwrlz5/B4PBw4cKCoBV0o4hKmOyG1cHWh63bEyechHQHH2tN/VVWlp6cHt9ttDtUwdGiqqpo9ebmOEDU1NUu6AQAsz38uu0V010EmgdT591yemKHh6FtpbFo5MbsQdMmKoOc8THSNhobDvMZu5YnZn4Ouk9Gs/L5Uh6tue5acHVUI4WGE+Ay6NxtZm5qxKy6okUiEQCDAyMiI6TPm9/ux2+2m84XFYjFTB5IklUxC5URcu3y76J/vJ5gMZtuDNIVtntItwSHr/NrY2EhNTQ0XL16krq6OUChkXnOu82sxKDTh59fEtcEwRpAZUoK1njLFRFyZTIauri58Ph87d+40b8xi9FiFjhcIBNi1a5fpoVUM8uXjdF1HQ8RiCkGz0s3s1Pu1fz7DOnrTpk153TWWJ4mNLaVhgWwsfpfLhbAwgu6oAjmOMNuDlorRpj6F2C+TafjIymR+Aaj73oj15KOQSYKuojurUdtu467dr6Ftopvzg+e5YfdRWk9/9kqkcsVSZhXrUUEQqKqqMiNvw2est7cXWZZNm+uDBw+acotcZ4u1msINlENcNY4aXtP+GgYWBtDR8Xl8OJT1OZIYWzyfz2duG5PJJOFwmMHBQdLptOnFla84YyBfBPnrreIGQ5ZlXnjhBerr64tukl4ralqt0ldOz2EkEqG3txePx1MSacHKiMusHDYeRK/eihDsw1jE6u6HwL66s+ri4iLnz59n27Zt1NSsvT0SgKrQC1QHL6B5m0i03kMgFKK/v590Os0+oQZPbBQpOYciy1itToTqNoRAL+LEL9C23F7UdWqbjyLf9eeIE78EqxO1/W5w1RAIBAheTnLvTa/FYbejbj6GNPnL7EQgeRGtdjd6RWNRn5HrMzYxMcHExARer5euri4zqszVjBm/c74Efy7KrSpWO6o50XCC+fQ8Tw88TSwd47jnOHurix8rl4t8hON0OpcUZxYWFggGg1y6dMkUvxpToQzky3G92N1P4Tojrr6+PrZu3VrUIjSwWtRkOH/u378fj8dT0nvzwRgcu3fvXkZGRop+X+7n5S4gs3JosZN+zVewdH4VITKO1ngIdfdrVz3WwsICvb297N27N++15YPlZ/8TywtfJivO0rG03YbjgS+YpnsLDV70n/4Z3sV5REEgU9GE6KhGWpxBSJXWSqPX7kKt3WX+/fLly0xNTXH48GFzi6oefDN6VQvC/Ch6RT04fEjd/4hur0BrvRWKyFWNjo4yPz/PDTfcgCRJS5Ld4+PjpvbNsHLOTfDni8bW0yAdz8T5p0v/xPziPFbdytMTT5NW0xyty1N5XQNr5dpyB4YYjfChUIje3l4URTEtbBRFyZvjKtZu/FeF64q49u/fX3IZON9WMbfd5tixYwUFf5IkFSWlMKQAhodW7hO8FBjVyLxyB5sL5fh7izrOzMwM4+PjHDp0aHWTRF1DnOmGdBStohHLucfB4gSLFTQNafQkwvhz6K03I0kSSYuX0d0f4GjyP9BHf0bCXoccmMauxpjPeKlMJssqoxvkcvjwYSRJYjgyzExiBr/Tz7YtdyC0C4ijJ5EG/w3d6UOMjCGGh1COvvuqin/5pek6ly5dIp1Oc+DAgSXdCbnJbkP7NjQ0ZA7WMAoVgiCsiMaMiKwcTMWnSCgJfNbs1s7pdHIueO6aEFcucr3Gcr24pqenicVi9PX1LbElSpbxOxbrxTU+Ps473/lOJiYmEASBf/3Xf6Wtra2kz4LrjLjKmQeYz0jw4sWLAGuOrBdFMTuc9cwkAHftrMVfsTSPYyS+bTab6aFlVBRLhUFc5TZKG778BgmsqvLXNaw/eB/SxM/NCdSoco4ThIguCAiJANoVC5/FxUUOHjmOrh1EsLvxjj8HlW4Wd7+DjHurmU8yIhhj8a92vgMDAyiKYpLLU+NP8c+X/hmE7L/f23Ivr936WsSJ59C9m0CyoVMJkYmstU/dnrzH7e3tRRRF9uzZs+o55GrfNE1jfn6eYDC4wmfMmKAdCATw+/1LxrqVQiA6OrqWdYfQdA2xgDvrWliPgj/XGTUWi9Ha2kooFOL8+fM8+eST9Pf3s2PHjpI+o1gvrre+9a185CMf4Z577iEej5d/DWW961eEcp50y2ccdnZ2Fm0keDma4Xe/fxlFz77ufz8zxLfedZwmX/ZplGvX3NJytapWqq0NZBeb0+k0Pb6MG6vYJ59RFdV1nYMHD655Q1h/9MfZvkNBzCrLbd6srYwcBWsFqCmQrKj1B7h48SKSJF3VaElOlBPvgxt+FxCwCgLNZO21FUUhFAoxNTVFb28vXq/XnCKUS6SapnHhwgUcDge7d+9GEATimTjfGfoOPrsPi2hB1VWemniKWzffyqYrsxyXIM+iN3z/3W437e3tJd0zhkaqkM9YJpOhpqaGTZs2rdhS6rqe1YytkuBvqWih2l7NRHwCh+RASkn8RstvFH1+y69zI/obDamMx+Ohra2N5uZmPvaxj/Hss89y8OBB3v3ud/N7v7f2UJRivLguXryIoijcc889AOvajl5XxFUOjAjI8Lzavn07tbW1a78R+MLzMyQyGtKVGySaUvjsT4b49EN7zePlMyYsNalvLACHw8GxY8dIp9MEAgF6e3vNxVJbW4vX6827EBVF4XwJWioh0It06SlAyA531VSETCzrSOqsQohlPbhSd3yMzrEFfD5ffqLPQxwWi2WJeDKfRMHn8zEwMEBNTQ2tra3mexcziwgI5tgvSZAQEUlkEmhb7kDq/Rd0qwtBTaO7/OYkn9zvobu7G7/fv+RBUg6M7ZVu0wk6gvQP9NPmbUNRFE6dOrWmZsyIxHLJxWFx8LqO1/Hj9I/RrToHmg7Q5m0rcAar41pNsa6rq6OpqYlXvvKVPPTQQ8zPzxf1vmK8uAYGBqiqquKhhx5iZGSEu+++m0cffbQs/dlLnrggK084f/48Bw4cKInlwwllyd91HQIxeYmHVr7jldIsndtzaNyIDofDrIgZEczExIQpsjQiGEmSSKVSdHd309zcbN44a0GIXUa3OLNEpGtZnZQqozUeRH7ocVDSpBWdru5umpsbij7uis/JI1GYmZnh9OnTWK1WvF4vkUjEJOQaRw3VjmrC6TBVtipicgy31U29qx7N24Zuq0AIXwJbBdqmI0ucHYzm9aamprLPdzkWM4v8y6V/YWRyBF+ljz5rH/e23Mueij0rCNlobjc0Y0aucvkgEbfVzV5PtmBS6y3uAZoP14q4IFuNdrvdZveFgfV6cSmKwsmTJzl37hwtLS08/PDDPP7447zjHfkHvayGlzRxGdOpZVnmxhtvLLnr/rYOH72zcbQrJGS3iBysFRkZGSl5ZmK+cysmn5UbwWiaZi6YoaEhrFYriUSCHTt25PU+KvjZ7npAR3fXZpuldR3d5kV+eTa0X0xnI7jt27ebliwbhdnZWfbv309lZeUKQvb7/bxv7/v4Ut+XGI+N0+Bu4F173mUOpND929H9K+2RU6kUXV1dtLe3Fx1NF4Oh8BBDE0Nsb9iO1+slnolzLniOZk/zqpqxmpoaczYlrBwksp4Ev4FrSVyFBKjr9eJqamri4MGDtLdnx7g9+OCD/PKXv3zpE1cpP7aRNLdarbhcrrJI5s3HNzF0OchPxrNDGl6+xcHtTSL79q6e1F8L5bqViqJoCg4NKUddXR1jY2OMjY2ZebFVO/uTYay//GzW2iURyvpaVW9Dvu8voaK+LBlFMYjFYvT09Cxxo8jdUhqao9BwiPvt9+Pflo1g1hodl0gkzC37RvXvQZYMe/t7qamuMZviRURU7WqhJ5KOMBgZBGBb3baCsymNBL/FYiGdTjM/P09dXV1ZCX4DG0FchXYF5bhDFOPFdezYMRYWFggEAtTW1vLMM89w9GjpFVW4zoirWBhPYCNp/txzz5V1HIsk8ea9Lh594/GCHlqlYr0Wy5C1jrl8+fISKcdySxsjL7a8smc591WE6GR2xL2vHSE+jbL39ejV7czNzZmzHDdi1qSB+fl5Uy+Xb0EIgmAS8rZt25YkxVVVNa9lucWLQYYbTbLJZJKuri5O7DjBT8I/IZwKYxWtROUodzTdAUAoFeKbA98kpaUAODVzijdufyPVjuoVsymDwSBdXV1A9t5sb2+nsrKyrAS/gXw+WqVitWGwpQpQi/HikiSJz3zmM9x1113ous6RI0d417veVda5v+SIy5jmY8w4NFCO4tnQcZ0+fZqtW7eWtB3Lh/WODNNzZAmG5snAckubcDi8orJXU1ODNTKRdXYAkKzZvFF8homJCebm5pYIQDcCBhkePHgwPxnqOuL4cwjhIXTvZrQtL8PlctHa2mpavBjDN+LxuJnjkySJgYGBgmRYLoyxbHv27MHr9fKqylfRFehC1mSO1x+nozI7pKQz2ImiKzS6svm0QDLAueA57mq6yzxWrmZs06ZNnDt3joaGBnOLnDubMp9mbLU2pHw+WqWiUNRWzjDYYr247rnnHrq7u0s/2WW4rohrrYVuKNeXT/MpNM16LUQiESKRCDfccENBD61isV7SMvRnVqt1TeuY5f2HRl5seHiYVrmKTYudSBYXoiggKDKXFR/z8/NXZzluECYnJ5mZmVmVDKUXvoSl9wkQJNBV1KlTKLc+Yrpe5DZSGx7uExMTBINBqqqqWLz0C9yx81hEAW3zkaxZYZnaqGg0yoULF9i3b59ZdKlx1HBn850rXptW02b1E7JzHzNqfrGyEcHt3LnT3M4W0oz5/X6sVtn2XlIAACAASURBVKtJYrn5sdym8I0aTZYv4vp1k/V/EgyVdDQazWuvXE7PoeGh5Xa7N4S0yppzeAWGL3xtbW3JZf7cyt62bdtIRHeQ+EkE6+XT6ECw+hjB6qPs3bt3w0jLKIrEYjHTVDAvUhEsfd9HdzeAKIGuI008j7owhu5rW/FyURRJp9PIssytt96KGhhEP/MUl1UnGgJVc99FknUcW28t+cGwsLBAX18fBw4cKGrR7qraRW+4F6uYJeSkkmRH1Y4VrzNIa9euXWZuz7iWfJqx8+fPr/AZy91O5ib514vVIq5ft/xcYxgaJpfLlXfGIZTmyZXroXX06FFOnTpV9rkZOYz15LNyfeHXu1UFcHl98OrPoCyG6em5gMXtQ9M0Tp06tarVc7HQdZ3+/n40TVvbVFCVs5GVESEJAohidgxbHkxMTBAIBDh06BAWiwUxPYfob8DjrkNVVRLhGRYGfsFIwILNa6OhtoFGf+OaOqFQKMTg4GDh7WwebKncwr2t99IV6EIQBF62+WVsqdyy5DWLi4t0d3eb285CyG3JKcZnLJ1Os7CwsO4Ef6GIK5VKrXsbeq1xXROX4X7a0tKS17LFQLHN0oaAsRQPrUIwchbGn8s5Vj5f+I1AWpbpujhES9t2Ghqygy6WWz17PB4zL1bsFrtk1bqrBq1mO2KwD91ehSDH0N216JVLo8rcCG5JV4DVBUq24itJEl6XFWFTC+fUcwwGBpGnZHZLu7nFf4u5dV5eXZ6bm2N0dJTDhw8XXXlOKkl+NPEjxmPjWEUrL9v8MrZXLZVpGLmycgoHq/mMWSwWEokEW7ZsoaqqKq9mrFiLntW2my+W8WmFcF0RV+5CmJ+fNxf1WmXwYgwBDRJsbW0t2Y5mOYxJxdPT03kXSzEwtForfOHXCcPqZrlGK5/Vs7GoDcX7avIERVHo6uqirq6O5ubm4k5GEMnc/sdYznwRMdiPVrudzNH3LBGW5vYzLo/gtIZ9iHM9CJGJrCePtYLvEWUkNkJTZROqrjKcGOaE/4TpuQaY1xmLxZiamuLQoUMlFSROXj7JRHyCRncjsirz9MTT+Bw+6pzZiNiodm5E4SB3q5/JZDh79ix+v5+5uTkmJyeXaMZyE/xGLnWtBH++YbDXcjjHRuG6Ii4DU1NTTExMFDXjENbeKhqVyGJIcC0Y+YidO3cyOztLZ2cnkiRRV1dXlC4JMCt8R44c2dAKn6HRyk0+50NuNWzr1q0kk8kV8oS6ujoqKioQBIF0Ok1XVxetra15pxetCrsX5eY/zPtPRkHCbreb/YxLYHWhHPgvWR9+XUf3NjF8/q/w2XwIgoBFsGARLSzoCxxtO0pbWxuyLBMMBrlw4QKJRIKGhgai0ai5DSsG4/Fx/I6sotwm2RAQmE/NU+esM/3Yis2VFQujz7ajo8MU2a6mGbNarWZy34jIlm8pV4u4XuzkdV0Rl67r9PX1kUqlOHr0aNFbmNUirkKVyHLPz6gcut1uOjo66OjoWLHwjfYQY+Hnvt9wrzx06BCWmU7EoafBVoGy92Fwlz552cB6NFpOp5OWlhZaWlrM/Mvo6CjxeJyKigoikQg7d+5c0bO5HqiquqT/siAsDnT/1aR4g7uB/oV+HBZHtiiiK9Q4rspibDab6Yh65MgRotEogUDArOwZjq+rRck+m4+oHKXSXnnFoVbDaXEuSfBvZJRskFZ7e/uS79h4IObTjK3lM6brOpkro92WY6MmCF1LCGuc5IvqCjKZTLakX6T7qYHBwUEqKyuXJLcNTVQkEuHAgQMFSfC5557jpptuWvMziq0cZjIZgsEggUCAxcVFqquzgkWPx8OFCxdMwpOGf4z93/4QXZURBBHdWU3qTU+URV5GBLd///4Nj+AMconH40tGoK3nc4xtZ319fd7JTashlArxtxf+lvn0PJqucdB/kN/c/ptIgmT6pi0uLq6oohqzDQOBAMFgEMB8wLjd7iX3WygV4onhJ5BVGU3X2Fm9kwPOA1wavFRSgr8YyLLMuXPn6OjoKOnBkE6nCYVCBAKBvD5jiqLQ19dHdXU1fr/fjMRUVeXuu+/mhRde2LBrWAcKLvLrirgg+4OUiuHhYZxOp9l8m+uhlesxnw/PPfccN954Y8HXrEcJbwhFZ2dnmZ2dxev10tramh128PX7ESKTpo+7kEmQuekDWfO8ImHIRJLJ5IbKHeBqJW7//v24XC50XScej5sLP1dLVkr0YUQXZW07ryClpphNzGIVrTS6Gk0ft4GBAVRVZdeuXWv+TsaWMhAIkEgkzAVubCmTSpJQKoRVtCIlJDMfuZHVOIO0SnX9XY5czdj8/DwOhwNFUXC73Wzfvt28f3VdJxwO8+CDD9LT07Nh17EOFPyRrqutIpRnJpir4yrkobXW5+W70dfbviNJEi6Xi3g8bkZ9hlD0RGweqw5G6lTXdZATRR/byA/ZbDb27du3oTmLXIdVY6Hm+jq1t7cTXYwyH54v2poHrmqeivXILwSH5KDVc9UuxzAWlCSpKNKC7JZy06ZNpvdWOBw2t5RGZFlXk81pDY8Mc+jQoXU13S+HcZ+ul7RgqWbM8EHLZDIsLi5y9uxZU0u2adMm3v/+93P8+PENuoprh+uOuMqBkZxfzUOrEAzSWx6tbETP4fz8PH19fUtK5oZQVEs+iND9NTKpBAIagmRhcdNNFPM830hfquUYHx8nGAwWdFiVVZmv9n2VM3NnEAWR+9ru497N9xIOhwta88BVzdNGSz/WYyxoIDdflBtZnj59mnQ6bbYmrUVcGS3D4MIgMTlGo7uRFk/+38YgrW3btm2oO4eRQ7VareaYOiNn+fGPf5wnn3ySpqYm3vWud5n5yxcr/n9DXKFQiMnJyZI9ufKp7tfbvgNr+8KLL/sgmt2Bpf8HaBYnM7t+m7Gwhczs82ZVb3nTMWD6c61nq5UPRk7QGPFVaNv5vZHvcXr2NLXOWjRd43vD32OTaxNH6o/kteZxOp243W4zB7eRi0VVVbq7u/H5fGX5mueDEVnG43HsdjuHDh1ifn7ebG4vJOJVNIUnx55kPDaOTbJxeu40t2y6hYP+g0uOf61JS9O0JekRw0ssHo/z3ve+lzvuuIMf/vCHWK1WXvnKV27Y5280XvLEpeu6ubcvx5NruZRiIxqlR0dHWVhYWN0XXrSg3PQBlJs+AEDNlf8pikIwGDSbjo2F4vP5SCQS9PT0bLjFi6Zp5lZrrW1n73wvHpsHURARBRGraOVS5BJH6o5kLyvHmkfXdaanpxkcHMThcNDb21ucNU8RWE+Cfy1cvnyZ6elpc0ajy+Uym9tzRbyGPMHv9xOQAwxHh4mkIwRTQeySHXlSZn/NftN3PpVK0dnZueG/n5HrVBRlxVZZVVXe+973smvXLv74j/8YQRC45ZZbNuyzrxWuO+IqJcdlLLh0Ok1DQ0NZOYjciGu9PYe5vvC5k2dKgcViWdJ0PD8/v8Tmub29fUMtXgxZQmVlZVGWPrXOWqYXp3FZXKYcodqRP3IIBAJMTk5y4sQJ7Hb7Cmseo+K61tCN5bgWbqgGJicnmZub4+DBgyvEm/lEvIFAgHPnzhFWw/REe9AkDa/dS1yOcz55nrgcx2v3XjPSAhgaGiKTyeQlrfe97320trbyZ3/2Zy967VYurjviKhbGzev3+2loaGBubq6s4xgl4rwjw0pAqb7wxZ6bMRsvEomwY8cOIpEIZ8+exWazmdFLuZUuQ23e2Ni4aktVLl7b8VpGoiMEU0F0Xafd286tm25d8bqpqSmmp6eXqNbzWfNcvnx5hTXPar2HRlWyra1tQ3o7czE+Pk44HObAgQNr9j/ming7OjoIRoP83c/+DlEWmU/Oo0kaLpuLQDKATbfR2dnJzp07TVfVjcLQ0BDpdHqFgFfTND7wgQ/g9/v5+Mc/fl2RFrxEicuYTm14aC0sLJQ15xCy5KAoyrpIy8g7tbS0mL2BG4Xx8XECgYBpHVNbW8vWrVuXuA3oul7yFswwYyy1ubvW4eejDfcwOnsWqaKB9p2vxyotzeGNjY0RDodXdY5YzZrHbrfnJWUjallvVTIfRkdHiUQi7N+/v6xI2efxsdO/k0VlkYyawaE5SKVT9HT1MK6N09rauqG+YpCVASWTyRUj2jRN44Mf/CBut5tPf/rTL/q+xHy47nRcmUxmVRIKhUL09fWxb98+syM/FosxMjLC/v37S/osQ/uTSCTYvHlzSW0hBoy+tVwvpo1Arsp+z549q56XLGcHfAQCAdMdta6urqA0wehnLCcCkF74CpbefwHRCpqCtvkYmZd9ODsC7UqC31hM5S4Yg5QDgQCappldCJcuXWLXrl0bGrUYotVEIrGucwboDHTyg9EfIAoiqq6yzbON5nAzba1tpFIpQqGQSdh+v39dnRwjIyPE43GzemhA0zQ+/OEPoygKn/vc517spPXSEaAqilKw73BycpKpqakVQsBEIkF/fz+HDh0q+nNy2yOMp/38/Dwej4e6uro1tyxwVaS5b9++DX2a5s4k3Lp1a8mi11AoxNzcnClNqKuro7q6GlEUTUeKtfoZ8yIdw/6dt6G7ak1/LSE+i3zv/0TztZtDWnfs2LFhWxNZlpmammJkZAS73W6q3ddjzWPASGrLspy/V7IMTMQnmEvMYdEsLI4ssmf3niXyj1QqZYp40+l0QQvu1TA6Oko0Gl0hOtY0jY9+9KNEo1Eee+yxFztpwUuduAwPqFQqxb59+1YQSiqV4sKFCxw5cqSozyhUOdR1nWg0ytzcHKFQCKfTaW5Zlre4GL7wBw4c2FBhomEqWJILQwEYjqKBQIBwOIzFYiGVSnHw4MHyEvzJMPYn3pmdImQssvgc8p0fo3tWWZeWqhByXUtdLpcpFF1YWKCiosKMXkp1vzWi7eXygY1AIXPB5TAeMoFAgGg0WpTV0NjYGJFIJG9L05//+Z8zMzPDl770pbJmGf4K8NIlrlwPrULRRyaT4dy5c0UpgkupHBpCxEAgsMQBYnJy0uyH28gbpNy8UzEwHDeqq6tZWFgo2dECAF3H+sxHEWfPozsqEeQYmqOaM41vxdfYuuFiWGMIR76m5tyqXjAYLMqaJ/e9fX19iKLI9u3bN5S0jKlEa5HW/23vzKOivO4+/p1x2EdQEJBFWVVEQWo1qK+mmuihVWSJBvUkUQ9ZbK1vTNtoTUwTTWs0TYwx0YSkSQuJiQsDdBQI0bilJkYkQdwQqQiyDTPsCDLr8/7Be58MwwCz3IdleD7n9Jwm4syd6POde3/3+/v+jK2JNIQ3NDR0m+VIPvu9e/fQ1NSEiIiIHqK1Z88e3L17F2lpacNFtABbEi6tVssKi6kZWjqdDpcuXcLcuXN7/RlrnfCdnZ2oq6tDeXk5BAIBJkyYAC8vL2pHRBJMR7uGA3QdLZqamhAZGcn+pSaJFgqFgk20IJ+nz/82qnaIrqRBWHcdugdNaGl7AMfRY2EfmQjtlOU/78SspKGhAf/9738xY8YMk4TV8PP0NjmIYRi2VcrcY3h/ENEKDw+3Og6czHJUKBRQq9VsTr3hEBWGYbB3717cuHEDX3zxhdWTgQYY2xOu5uZm3Lhxw6QMLYZhcPHixV5THmi07+jnwo8fPx4KhQJyuRxKpZJ96I053U2hsbERt2/fpl4rIwV+UsPpbYdJEi3kcjk6OjrYh37MmDG9fh7d9Sy05x+C4/jJcHZyhKC1CppfPgudv/V9cCTgMCoqyqJjOGlzUSgU3Uy8bm5uKC4uhrOzM/UjbUdHB4qKivqNcbaEiooK1NbWQiwWo62tDa6urhg1ahR8fHyQlpaGy5cv48iRI1STQQYI22myBn7O0DI1SLCvv4A0RMtYLjzxI2k0mm7jtcaOHQsvLy+Ti8fGGpppoN+EbXhdboidnR18fHzg4+PD+qtIeJ0xf1VHRwdar5+Fl+cEOLj8f4Ff5ARB4x3ASuGqqalBTU2N2amlhp/HcHJQXV0drl69CkdHR4wbNw4ajYbag076MGnPfwS6LqQaGxvx0EMPQSgUstaRzMxM7Nu3Dx0dHXj55Zchk8msrokOJYadcNXV1bHDUK3d9tLoOewvF14kErETm0nKgEwmQ0lJCVxdXdkbPWN1h4qKCjQ0NPTdGmQB1vTwGfNXyeVyNjpo9OjRkMlkmB0QDseGa11bdoYBo1GCcfG0at36wzJo1WmEQiHc3Nxw7949BAcHw93dnXW7Eye8p6enxdYELkWruroacrm8WxeGQCBgh82GhYVh7969OHnyJD777DNs376d6vsPJsPuqKjRaKDRaMwWGcNAQBqiRQyRkZGRZide6j/0jY2N3dI3RSIRbt++DbVa3ecRzhJUKhWKioqot8MwDAOZTIbbt2/DwcEBjkwHwmRSuOBBVwKtRwg00ZsAkWUhe6S/01IDaG9otVo2K9+wp7Gzs5OtI6lUKpOiefQhomWRtaQfampqIJPJerj4GYZBWloapFIppFKpVaGGycnJyM7OhpeXl9F8rnPnziE+Ph5BQV3TjR577DG8+uqrFr+fEWznqEjC/63B2p5DoKdj3Vz0hyCQqBS5XI6ffvoJnZ2dGD16NHXRItfwoaGhVGOWAbDjtKKjo+Ho6Nj10NdOQHnlNag1Ojh7RcCzQ4XRox3M+vPTN63SFi3SiO3j42P0csfR0RH+/v7w9/dnj/x9RfPoQy5TuBCt2tpatsnb8L0PHTqEzMxMHD9+3Ook1vXr12PTpk1Yu3Ztrz+zYMECZGdnW/U+ljDshMsaaMw5JP4etVpNbfIziUpxdHREc3Mz/P39IRKJcP36dbZdx8vLyyonNXmQaOddAV11uMrKym5heo6OjvAPmgQETTKaaGFKnY/48xiG6eEAtxbSh+nn52fSztPwyK8fzePo6AgvLy82q55L0ZLJZKipqTEqWkeOHMGRI0eQnZ1NZVDHww8/jPLycqtfhwtGjHCRnkMiWJY8BCTymUTe0nyQjHm0AgICoFKpIJfLUVJSApVKxd5QGg7a6Avid7J4XJZOCyhbu8aGGRz1SJ49GdJqDGOJFv3NbyS2BDs7O0yaNIm6aJF5nJZklulH8wBgs+qLioqg1WrZNizaolVXV4eqqiqjoiWRSJCWlobs7GzqPY99cfHiRcyYMQO+vr54++23MW3atAF532FX42IYBiqVyuzfU1BQAA8PD4wfP96i2zlSG/L19TU5KcFUSD9jfx4tsnORy+XdBm30ZUsg031M9Tv14H4d7C6nQNBRD0YggnbGE9D5zeo2pNVSo62+qbK+vp5tnvbw8EBpaSnEYjGCgoKoihZJjwgKCmLHfNGCJOz6+PigtbWVjebpzzpiCnV1deztsuEXhFQqxcGDB5GTk0N9N11eXo7Y2FijNa7W1lYIhUKIxWLk5uZi8+bNKC0tpfn2tuPjMle4SBH+wYMHkMvlUCgUEAgE7FgnUx5m0nTMReqApR4tnU7H9hy2trb26DkEuq7KSQHXoqt9hoHd+V1AZxPg4gloOiFob4DqV6+gpKaZDaajVXfq6OhgTbx2dnbw9/enEipIoJnjboixIbDEOqJQKNDS0mJyNI8hcrkcFRUViIqK6vHnmJOTg3379iEnJ4d6jhfQt3AZEhgYiIKCApr1U9spzpuD/s2hk5MTAgMDERgYyDaykjmHRMSM1QXIMWvatGnUr7Ot8WgJhcJutoTm5mbI5XKUlpayD45Go7HOOqBVAfdrAbf/9/+IHMEAKLv2AwTjplJrPCbY29ujsbERkydPhqenJzucgjQb95Vo0R8k8sZwgjcNiGgZDoE1tI6QPte+onkMUSgU7NxPQ9E6efIk3n77beTm5nIiWv0hk8ng7e0NgUCA/Px86HQ66l8IvTHsdlyAaSPKyM1hf/UsEvkil8vZGpK3tzdcXFzY7XlkZCTVWXkMw7CZVJGRkVQ9WmQ4REdH10QgBwcHtufQbJc5w8Du9CsAwwCOrtBp1GipLEbzL/8X/tN6b5+yBFJ3mjBhQo/MMsNECzIjUH932RfkNpWLoD7S5G3u5GrDaB5jLVX19fUoKyszKlpnzpzB66+/jpycHOpHXsKaNWtw7tw51NfXw9vbGzt37oRarQYA/Pa3v8WBAwfw4YcfQiQSwcnJCe+8845JM0jNwHaOikDfwmWNE16/taWlpQVCoZBtKaK1syC3krSPWcDPouXs7IyQkBAIBAJ0dHT0OCKbM+tQ0HQXovyDYFRKNDU1QDNlOcZGr6G2ZuDnI1xwcHC/D6FhooWLiwsbM2TsOGxpU7MptLa24ubNm+xsSUsxNiTY3t6evfQw/MI5f/48XnnlFeTk5FAPphxi2JZwqVQqo7nzNNp3dDodbt26xX4L1tfXo62tzaRCeH/o30oSYaEF8SR5enr2msKgVCpZEdNoNCY3TqvuN6Gk4FuMD5wMz8Cp1NYM/LwbsuQIp+9/M5YAwaVrvaWlBcXFxUaTKaxBp9OhoqICFRUVsLe3Z29diTH5woUL2LZtG7Kzs/sMFrARbF+4aIhWb7nwpFWH7MTc3Nzg7e1tViIq8Q2NHz+e+tQZpVKJoqIis6Kh9XeXDx486DWwjss4ZCIstBIv9BMgVCoVVCoVpk6dCk9PT6pfElyJFtB1WVNaWsoeD0k0T2pqKs6ePYvGxkYcPXoU0dHRVN93iGLbwkWjfcfUXHhyVJHL5SYnopImbFOOQuZCjkLWFJ0NA+vGjBkDLy8v2Nvb48aNG5zUhkhBm4vdUGtrK65fv87aEh48eGDxxCBDmpubcevWLU5FyzDBFwAKCgrw4osvIjY2Ft999x1CQkLwwQcfUH3/IYjtCpe+aFlaL2pra8ONGzfMHg1lmIjq7OzMOqhJwZ08oFw41klhmGZUChHmqqoqKBQKuLu7w9fXF+PGjaPW2Ewa0y02xPbz2oa7IWJLINaR/prbe4OIVlRUFNXLGuDn22tjN8yFhYXYuHEjsrKyEBwcDABGp6ubQn/9hwzDYPPmzcjNzYWzszNSU1Mxc+ZMyz6U9diWcJGBGTqdDlqt1uJdFkAvF96w3mJvbw8XFxc0NDRw8oAS/5e1heH+XlutVrPCTFpbjEVVm/vaXOxY+kpEJeg3t5Mvm97it/XhUrT6eu2rV6/iueeeg0QiweTJk61+r2+//RZisRhr1641Kly5ubl4//33kZubi0uXLmHz5s24dOmS1e9rIbYlXCqVyuqRYQB3ufBAl3GvsrIS9vb2EIlErFeMRqZWXV0dKioqMGPGDKoZXcDPTntjx5X29na2uE88SqaaeIGu6/07d+4YfW1rMTcRFegSMdKuo/+ZDG9diSByIVpkh2jstW/evInk5GQcO3YMYWFh1N6zL1Pphg0bsHDhQqxZ03VzPGXKFJw7d476YF0TsS0D6uXLlzF9+nSIRCKLG6Xv3LmD9vb2HlG31sIwDBvBMnfuXIhEIrZoTGYcEhGzZMdBegNpZ3QBP4f09ZZ44eLigqCgIAQFBaGzsxNyuZw18RIR621nScTW2PW+tRBBNPe1BQIBxGIx21pEjMlkKvi4cePg6OjImoQHUrRu3bqF5ORkHD58mKpo9Ud1dXW3wEF/f39UV1cPlnD1yrATLqVSiZSUFBQWFmLBggWIj4/HvHnzTH6ISfKnnZ0dIiMjqd42kTQDrVbbLdzNyckJEydOxMSJE6FUKtmHQ6PR9PvA67/2nTt30NHRQS2VQh9ThrTq4+joyH4mlUqF+vp6lJaWGp3bqC+ItMWWxDjTEERHR0dMmDABEyZMgFqtRkVFBZsvVlFRQW3sGdBVnyS1OEPRKi0txfr163Ho0KEBa1oebgw74XJwcMDnn38OpVKJ06dP49ixY/jTn/6EefPmISEhAfPnz++1VqGfC0974gzxaInF4j7nBjo4OLAZT2q1GgqFgn3giWvfMPmBeMuEQiEiIiKoiy3Ju9IXW3Owt7eHr68vfH19odVqUV9fz+ZWiUQi6HQ6TkRLv/GYdp56W1sbGhoaMG/ePNjZ2aGxsbFHooWlFxZtbW24efOm0Vrc3bt38dRTTyE1NdXsAcY08PPzQ2VlJfvPVVVV1EMFaDAsa1yGqNVqnDt3DhKJBBcuXMDs2bORkJCAhQsXst/CXFoSVCoVmwpg6R8yCaqrq6tDe3s7u2sRi8W4ceMGRo8eTT0pgYzhAkB9diDQNQK+oaEBLi4uVjUZG6O2tpYd/ktbEEm9zFgtzvAm2dyWqt76GoGuXe/q1avxySefYPbs2VQ/kz591bhycnJw4MABtjj//PPPIz8/n7O19INtFef7QqPR4MKFC0hPT8f58+cRFRWFiIgInD59GmlpadQtCcT5HRISQk0QyfW9TCaDQqGAq6srgoODqR1TAOPtQbQgE6CVSiWb4kpu88hcQCcnJ9Y6Yu5uqaqqis1apz0jkIiWqUdP/eI+gD5DH0nAoLFb5qqqKiQlJSElJQVz5syh82GM0F//IcMw2LRpE/Ly8uDs7Ix//etfmDVrFmfr6YeRI1z6aLVavPXWW9i/fz/8/f0RHByMhIQELFmyhIqFgPiouPBokWDBwMBAiEQiyOVyNDc3sx4kDw8Pi0WMDMtwd3dHQEAA1XXrp5b2tosjt3nEOiISidgHvr/bxsrKStTX13ebAUkLS4v8BFK/VCgU7Fg6klFPopGMiVZNTQ0ef/xxvPfee1iwYAGtj2MLjEzhqq+vR3JyMrvTunz5MtLT03Hy5ElMmjQJCQkJiImJsSipkvi/uPBRkb/khoZYsmupq6tDY2MjxGIxu2sx9SEmrUekJkUTcvHh4OBg1jBVcusql8v7jKquqKhgB9fSvpwgSQyWzmo0hBz9SRaXSqXCpEmT4Ovr223tMpkMK1euxN69e7Fo0SKr39fGGJnC1Rs6nQ5XrlxBeno6vvrqKwQEBCAuLg5Lly41aedUU1OD6upqTvxfxFXeXysMGTFPdi2mHL1ICoN+PDQtdDodrl27BldXIutyWQAAFQ1JREFUV3bqiyUYxgyRWh9JTpg+fTp10VIoFKx3jfafZ3t7O4qKihAQEIC2tjY0NTXBxcUFlZWVmDRpEp5++mns2bMHS5Ysofq+NgIvXL1Baj3p6enIzc2Ft7c34uPjsWzZsh69f/oeLa6OKsREaa7HS9+1r294JQ8ijZ7G3iAjvsaNG0f1tpZEVZeVlUGpVMLHxwfe3t5WxyDrQ0SLi5tJMr1a/0uIfOHs2rULGRkZ8PX1xTPPPIPHHnuM+peJDcALlykwDIPi4mJIJBJkZ2djzJgxiI+PR2xsLMaOHYvjx48jLCwMYWFh1L/1a2trUVVVRWUXZ5jB5ebmBrlcjoiICOrj3zUaDa5cucLJ0ZNhGJSWlkKj0WDKlCloampiEzpo1Pr0PWADIVqExsZGrFixAq+88goiIiIglUoRFRWFX/3qV1TXYAPwwmUu5GZMIpEgKyuLnSi9Z88ejB8/nuotHJlYTTsNFeh6OIuLi+Hk5ASBQEBl1BmBDJ4ICAiwaFpOX5AiP4Aevjj9qGr9MEH95vb+6CvH3VrITXN4eHiPL4rm5masWLECW7duRWJiotXvlZeXh82bN0Or1eKZZ57Btm3buv16amoqtmzZwtp0Nm3ahGeeecbq9x0geOGylIaGBiQmJmLZsmUQCoWQSqUQCoWIi4tDQkICfHx8LBYxY7YBmpCjJ2kp6Sum2tzPQOplISEh1IfLkp2vSCTqdzSZseZ2Is697VyJcZVL0TKWuNra2oqVK1fi+eefR1JSktXvpdVqMXnyZJw6dQr+/v6YPXs2Dh8+jPDwcPZnUlNTUVBQgAMHDlj9foOAbfUqDiT29vb461//ym7jX3zxRVRVVSEjIwPJycnQarWIjY1FYmIiJkyYYLIAkBs4e3t7TJs2jbr5kwzimDlzJvsA29vbw8/PD35+fmyQIHHNmzOMwprU0v4g/10cHR1N8peRYbqjR49GSEgIe0wuKirqtsMkNUMuRYtYWIyJ1v3797Fq1Sps3LiRimgBQH5+PkJDQ9mom9WrV0MqlXYTLluF33FZAcMwkMlkyMzMRGZmJtrb2xEbG4v4+HgEBwf3+tARH9XYsWMRGBhIfV1VVVWoq6vDjBkzTDo6GQ6j6CummqSWcuFdIxclYrGYfRitgfiq5HI5NBoNHBwc8ODBA/zyl7/kRLSuXLliNHSxvb0dq1atwrp167Bu3Tpq7ymRSJCXl4dPPvkEAPD555/j0qVL3XZXqampeOmll+Dp6YnJkydj37593Zqohzj8UXEgkMvlyMrKQmZmJhobG7F06VIkJCR0m3pNBsv6+flxUswuLy9HS0sLIiIiLLr17Cumur29nbPUUmKnGDNmDHVTLNCVelBRUQFnZ2d2UCuNRFSgSyALCwuNitaDBw+watUqrFmzBk8//bRV72OIKcLV0NAAsVgMBwcHfPTRRzh69CjOnDlDdR0cwgvXQNPQ0ACpVIqMjAzIZDLExMRg9uzZOHToEN555x3q/ZLkBk6tVlObHqQfU11fXw+1Wo3Q0FD4+vpStYKQHei4ceM42Q0Y9jUaJqIaG6ZrKkS0jKXndnZ2Ys2aNUhMTMSGDRuolwMuXryIHTt24OuvvwYA7N69GwDw0ksvGf15rVYLd3d3tLS0UF0Hh/DCNZg0Nzfjww8/xFtvvYXw8HDMmzcPiYmJiIiIoCYwpJitv7ujRWNjI0pKShASEoKWlpZeY6otgXjAvLy8qA8RAbpEi4RFGlun4bgz0o3g4eHR7+dSqVQoLCzEpEmTetT6lEolnnzySfz617/Gpk2bqP+ZAF1WlMmTJ+P06dPw8/PD7Nmz8eWXX3aLwqmtrWWztLKysvDmm2/ihx9+oL4WjuCL84PJqFGjkJmZie+//x6+vr7IycnB3r17UVpaikcffRQJCQmYOXOmRSJG4nRcXV27TSaihUKhQFlZGWbOnMkmIYSGhrI3eWSMlre3t9mRzsQD5ufnx0lQXU1NDWpraxEVFdXrDlEoFMLd3R3u7u7duhHu3r3bZ/IDEa3Q0NAeoqVSqbB+/Xo8+uijnIkWAIhEIhw4cAAxMTHQarVITk7GtGnT8Oqrr2LWrFmIi4vDe++9h+PHj0MkEsHd3R2pqamcrGWg4XdcA4RSqezRQNzR0YHc3FxIJBLcuHEDCxcuREJCAh566CGTjmJklqKXlxcnRyyZTIbKysp+b+AMI51Niakmk6snTpxI3QMGmCZa/aHfCC4UCtkbSqFQyFpBDEe2qdVqJCcn46GHHsLWrVs5E60RAn9UHOp0dnbi66+/hkQiYdNdExIS2PhnQ4j505xZiuZQXV0NmUxm8s0kwbBh2lhMNVl7YGAgJ20u1dXV7K0qrVociXWuq6tDa2srvLy8EBgY2K1BX6PR4Nlnn0VERAS2b9/Oi5b18MI1nCDprhKJBJcuXeqR7kqMpaGhodTNnwBw79491slvzYNvaEfw9PTE2LFj2XoZF2vnMqtLrVajsLAQEyZMAMMwUCgUrFA7Ozvj8OHDCA0Nxc6dO3nRogMvXMMVw3TX8PBw/Pjjj5BIJNSHKDAMg7t37+L+/fvUUxjUajVqampQVlbG1sSMxVRbA9eiRXaJ+jfCWq0Wp06dwp49e1BeXo6VK1di1apVfN8hHUaOcP3lL39h23K8vLyQmppK3S81WOTn52PNmjWYO3curly5gqioKMTHx+PRRx+1egKNvp0iPDyc+o6BuO2nTJmC0aNHG42ptsZTxWXAoEajQWFhIQICAnocbXU6HV544QW4ubnhjTfewH/+8x+UlZXhueeeo7qGEcrIES4yqRgA3nvvPdy8eRMpKSmDvCo6vPbaa1i3bh2Cg4Oh1Wrx/fffQyKR4MyZMwgPD7c43ZVkzwsEgj4HfVhKX/17hp6qsWPHsq59U3d8RLQsHfbRF0S0jF0i6HQ6bNmyBXZ2dnj33XepvHd/TdNKpRJr167Fjz/+CA8PDxw9epST7oshwsgRLn12796Ne/fu4cMPPxzspXCKTqezON3V3N5AcyFprsaSEoythUTXmBpTfe/ePTQ2NnKSikrsGv7+/j0uQHQ6HV5++WWo1WocPHiQynub0jT9wQcf4OrVq0hJScGRI0eQlZWFo0ePWv3eQ5SRJVzbt2/HZ599Bjc3N5w9e5a6S30oo5/umpeXh4kTJyI+Ph6/+c1veux2SJuNm5sbJ9/aZDiEJS1CpsRUcylaWq2WzRkz9JjpdDrs2LEDzc3N+Pjjj6m9tylO+JiYGOzYsQNz586FRqPB+PHj2dw1G8S2hGvx4sWQyWQ9/v2uXbsQHx/P/vPu3bvR2dmJnTt3DuTyhgy9pbvGxsZi1KhRyMnJwfz58znxgJExXMaGQ5iLsZhqoVAIjUbDyfGwL9FiGAZ/+9vfUFNTg3/+859U62mm9B5Onz4deXl5bJdBSEgILl26xMkN7RDAtpzz33zzjUk/98QTT2Dp0qUjVriEQiEiIyMRGRmJ119/nU13Xb58ORoaGhATE4PFixdTf18yWt7Y7EBLEAgEcHV1haurK0JDQ1FSUoKGhgaMGjUKV65c6RFTbQ2kBcnHx8eoaL355pu4d+8e0tLSqF8C8JgO3a+qIUBpaSn7/6VSqUWWgS1btiAsLAyRkZFITExEc3MzzSUOCgKBAOHh4di4cSMcHR2xZcsWBAUFYfXq1YiNjcU//vEPyGQy9LMD75fm5maqomVIeXk5lEol5syZg+joaISFhbEdBAUFBbh37x46Ozstem0iWt7e3j1uohmGwTvvvINbt24hLS2NelItYNoUaf2f0Wg0aGlp6eHeHwkMy6NiX6xYsQIlJSUQCoUICAhASkqK2dOlT548iUceeQQikQh//vOfAQBvvvkmF8sdcOrr63Ht2jV2FBbxbmVkZFid7trY2Ijbt2+ziau0uXv3Ltra2nr1mBF3u1wuh06nMyumWqfToaioCJ6enj2avRmGwfvvv4/8/HwcPXqUepYXwZSm6YMHD+LatWtscT4zMxPHjh3jZD1DANuqcQ0kWVlZkEgk+OKLLwZ7KZzDMAyb7pqZmWlWumtfY+tp0J9oGWJOTDURLWOxOgzDICUlBefPn4dEIqE+vsyQ3NxcvPDCC2zT9Pbt27s1TXd2duKpp55CYWEh3N3dceTIESqhi0MUXrgsZfny5Vi1ahWefPLJwV7KgGJOuiuXcwkBoKysDO3t7Zg2bZpFhXgSUy2Xy3vEVDMMw071NhytxjAMPv30U+Tl5SEzM5OTXSRPn/DCZYgpN5O7du1CQUEBMjMzbfW62WRIumtGRgaamprYdNf8/Hw4ODggMTGRkyMUycSnlctvGFOt1Wrh4eGBsLCwHpOE0tLS8O9//xtSqdTsOZc8VOCFy1xSU1Px0Ucf4fTp0xYVmdPT07Fjxw4UFxcjPz8fs2bN4mCVgwNJd33//ffR0NCA1atX4/HHH6eWvAp0CUdZWRlV0dKHeNhEIhEEAgEbU+3g4AB/f3+kp6fj6NGjOHHiBCeXDDwmYVt2CK7Jy8vD3//+d5w/f97iv7TTp09HZmYmNmzYQHl1g4+HhwfEYjE8PDxw4sQJnD17Frt27UJFRQWWLFlidborwzC4c+cOlEolZ6J1/fr1bsZbkoT65Zdf4oMPPoBKpcK+fftG/E57qMLvuIwQGhoKpVLJXjPPmTPH4n7HhQsX4u2337apHRfQdVXv7u7eTdhbW1uRk5ODjIwMi9Nd9UWLi2ZvhmHYSUJBQUE9fj0jIwMff/wxdu7cia+//ho1NTX4/PPPqa6Bx2T4o+JgYavC1R+G6a6LFi1CfHx8n+muZEAuGfjBhWjduHEDTk5OCAkJ6fHrx48fx4EDB5Cdnd1jWo+1NDY2YtWqVSgvL0dgYCCOHTvWY7gG0BXzHRERAQCYOHEijh8/TnUdwwxeuLjAlAL/SBUufUxJdyWxOhqNhjPR0m8mNyQ3Nxd79+5FTk4O9SG3ALB161a4u7tj27Zt2LNnD5qamox6A8ViMe7fv0/9/YcpvHANFrxwdYeku6anp+Py5cuYO3cu4uLiIJVKsXz5cixevJgT0SouLoa9vb3RBIyTJ09i9+7dyMnJ4aznb8qUKTh37hx8fHxQW1uLhQsXoqSkpMfP8cLVDb44P5zoL5NpOOPg4IClS5di6dKlUKvVOHv2LF588UWo1WpoNBowDIOFCxdS84ORrDE7OzujonXmzBns2rWLU9ECgLq6Orb3cfz48airqzP6c52dnZg1axZEIhG2bduGhIQEztY0nLG5XsWhQlZWFvz9/XHx4kUsW7YMMTExJv0+rVaL3//+9/jqq69w8+ZNHD58GDdv3uR4tYODnZ0dfvrpJzzyyCO4evUq1q9fj1OnTmH+/Pl47rnnkJuba3HfIdAlWiUlJRg1ahRCQ0N7iNa3336L1157DSdOnKAytGPx4sWYPn16j/9JpdJuPycQCHrdVVZUVKCgoABffvklXnjhBdy5c8fqddki/FFxiGHudOLhTlNTE8aMGdPtQaaR7sowDG7fvg0ARofkXrhwAdu2bcOJEyfM7mW1BFOPivqsX78esbGxWLlyJefrG6L0elTkd1xDjOrq6m79cv7+/qiurh7EFXHL2LFje4jKqFGjsGDBAuzfvx9FRUX44x//iB9//BGPPPIInnrqKWRmZvZZByKixTCMUdH64YcfsHXrVkil0gERLQCIi4tDWloaACAtLa1bbhyhqakJSqUSQFcz/Hfffdct/ZTnZ/gaF8+QRigUIjo6GtHR0dDpdCgsLIREIsHevXuNpruS20mdTtejjQcACgoK8Ic//AFSqZSTAMXe2LZtG5KSkvDpp58iICCATXQoKChASkoKPvnkExQXF2PDhg0QCoXQ6XTYtm0bL1y9wB8Vhxgj7ahoKcbSXePi4pCfn48FCxYgKSmph2gVFhbid7/7HbKysoxaIniGHLwdYrhgSiaTKSQnJyM7OxteXl64fv06R6sdGhC7w8aNG1FVVYXg4GAkJCQgNjaWvSm8du0ann32WUgkEkyePHmQV8xjIrwdYrggEolw4MABxMTEsJlM5ooW0FXY3bRpE9auXcvBKocWAoEAP/30EwIDA3H69GmUlZVBIpFg1apVcHJyQnR0NKRSKTIyMnjRshH4HZcNU15ejtjYWJvfcQFd/ic7O7tu7UQk3XXnzp1ISkrCsmXLBnGFPBbA77h4bBtjIX8CgQDBwcHsbR6P7cDbIXh4zCQ9PZ1NYy0oKOj15/Ly8jBlyhSEhoZiz549A7hC24cXLh4eMyFZaw8//HCvPzOSOiAGA164eHqlsrISixYtQnh4OKZNm4b9+/cP9pKGBFOnTsWUKVP6/Jn8/HyEhoYiODgY9vb2WL16dY/WHx7L4YXLRlmzZg3mzp2LkpIS+Pv749NPPzX7NUQiEfbu3YubN2/ihx9+wMGDB/ldg4mMtA6IgYYvztsohw8ftvo19Kc5jx49GlOnTkV1dfWIcHObkrXGM3jwwsVjEuXl5SgsLER0dPRgL2VA+Oabb6z6/aZMpeaxHP6oyNMv9+/fx4oVK/Duu+/C1dV1sJczLJg9ezZKS0tx9+5dqFQqHDlyBHFxcYO9LJuBFy6ePlGr1VixYgWeeOIJPPbYY4O9nCFBb1lrNTU1WLp0KYDuHRBTp05FUlKSRR0QPMbhnfM8vcIwDNatWwd3d3e8++67Fr9OZ2cnHn74YSiVSmg0GqxcuRI7d+6kuFIeG4VvsuYxnwsXLmDBggXdZiS+8cYb7K7CVBiGQXt7O8RiMdRqNebPn4/9+/djzpw5XCybx3bgW354zGf+/Pno54vNJAQCAcRiMYCuo6dareYHrfJYBV/j4hkQtFotoqKi4OXlhSVLloyY20kebuCFi2dAGDVqFK5cuYKqqirk5+ePiMQKHu7ghYtnQBkzZgwWLVqEvLy8wV4KzzCGFy4ezlEoFGhubgYAPHjwAKdOnUJYWJjFr6fVavGLX/wCsbGxtJbIM8zgi/M8nFNbW4t169ZBq9VCp9MhKSnJKtHZv38/pk6ditbWVoqr5BlO9GeH4OEZUggEAn8AaQB2AfgjwzD8tmsEwh8VeYYb7wLYCkA32AvhGTx44eIZNggEglgAcoZhfhzstfAMLrxw8Qwn/gdAnEAgKAdwBMAjAoHg0OAuiWcw4GtcPMMSgUCwEMCLfI1rZMLvuHh4eIYd/I6Lh4dn2PF/P9JtO+CLZx0AAAAASUVORK5CYII=", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.decomposition import PCA\n", "import numpy as np\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import pyplot as plt\n", "\n", "# PCA関数の使用 (3次元)\n", "pca = PCA(n_components=3)\n", "pca.fit(features)\n", "res = pca.fit_transform(features)\n", "print(\"固有値\",pca.explained_variance_)\n", "print(\"固有ベクトル\",pca.components_)\n", "#描画\n", "fig = plt.figure(figsize = (4, 4))\n", "ax = Axes3D(fig) \n", "for label in np.unique(targets):\n", " p = ax.scatter(res[targets == label, 0],\n", " res[targets == label, 1],\n", " res[targets == label, 2],\n", " marker = 'o', s = 20)\n", "plt.show()\n", "plt.close()\n", "\n", "# PCA関数の使用 (2次元)\n", "pca = PCA(n_components=2)\n", "pca.fit(features)\n", "res = pca.fit_transform(features)\n", "\n", "#描画\n", "fig = plt.figure(figsize = (4, 4))\n", "plt.xlabel(\"PC1\"); plt.ylabel(\"PC2\")\n", "for label in np.unique(targets):\n", " plt.scatter(res[targets == label, 0],res[targets == label, 1],label=target_names[label])\n", "plt.legend()\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": { "id": "3O_gzsZv0ARL" }, "source": [ "このように、4次元のデータを低次元に射影することで \n", "3種類のアヤメの持つ特徴を可視化できるようになる。" ] }, { "cell_type": "markdown", "metadata": { "id": "0Kfac71jDg_m" }, "source": [ "## 実装してみよう\n", "\n", "sklearnなどのライブラリは非常に便利だが \n", "中で行われている計算を確認するには \n", "複雑に設計されたソースコードを読み解かなければならず \n", "「本当に自身が意図した計算をやっているのか」が分かりづらい。\n", "\n", "ライブラリを「使えれば良い」と「中身を分かった上で使う」の間には \n", "* 問題が起きたときの対処能力\n", "* 自身で新規な手法を開発して実装する能力\n", "\n", "などなど、様々な面で決定的な差が生じる。\n", "\n", "\n", "以下では、必要な計算をなるべくブラックボックスにしないで \n", "PCAを実装してみよう。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 206 }, "id": "XzrwCPxiENxC", "outputId": "547606c2-6165-4379-985e-6ebd9a1f3d17" }, "outputs": [ { "data": { "text/html": [ "\n", "
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sepal length (cm)sepal width (cm)petal length (cm)petal width (cm)
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\n", " " ], "text/plain": [ " sepal length (cm) sepal width (cm) petal length (cm) petal width (cm)\n", "0 5.1 3.5 1.4 0.2\n", "1 4.9 3.0 1.4 0.2\n", "2 4.7 3.2 1.3 0.2\n", "3 4.6 3.1 1.5 0.2\n", "4 5.0 3.6 1.4 0.2" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#上のコードと同様 irisデータを取得\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "from pandas import DataFrame\n", "from sklearn import datasets\n", "dataset = datasets.load_iris()\n", " \n", "target_names = dataset.target_names\n", "targets = dataset.target \n", "feature_names = dataset.feature_names\n", "features = dataset.data\n", "\n", "df = DataFrame(features, columns = feature_names) \n", "df.shape\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": { "id": "yvMc5aRnEzW9" }, "source": [ "今のデータは、上の定式化におけるN=150, p =4の場合に相当する事がわかる。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "bL_YdesrEh_Z" }, "outputs": [], "source": [ "N,p=df.shape\n", "#データ行列の定義\n", "X = df.values \n", "\n", "#p=1,2,3,4 各列の平均ベクトル(p×1行列)を定義\n", "mv = np.array([ np.mean(X[:,i]) for i in range(p) ]).reshape(p,1) \n", "\n", "#共分散行列Cの計算\n", "C = np.zeros((p,p)) # p×pのゼロ行列を作成\n", "for i in range(N):\n", " d = X[i,:].reshape(p,1) - mv \n", " C += np.dot(d,d.T) / N " ] }, { "cell_type": "markdown", "metadata": { "id": "HuxOkOthHxFz" }, "source": [ "行列の固有値を求める部分の詳しい説明は、それだけでノートブックが複数必要なので \n", "Numpyの中にある固有値・固有ベクトルを計算する関数```np.linalg.eig```を用いる。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "QqPxlliMIBYR", "outputId": "6dabab37-e2b2-430d-bac4-8e5236d591de" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "固有値 [4.20005343 0.24105294 0.0776881 0.02367619]\n", "固有ベクトル [[ 0.36138659 -0.08452251 0.85667061 0.3582892 ]\n", " [-0.65658877 -0.73016143 0.17337266 0.07548102]\n", " [-0.58202985 0.59791083 0.07623608 0.54583143]\n", " [ 0.31548719 -0.3197231 -0.47983899 0.75365743]]\n" ] } ], "source": [ "vals,vecs = np.linalg.eig(C)\n", "print(\"固有値\",vals)\n", "print(\"固有ベクトル\",vecs.T) #固有ベクトルは縦に並んでいることに注意" ] }, { "cell_type": "markdown", "metadata": { "id": "MxWvorgrOokz" }, "source": [ "sklearnで計算された```explained_variance_```(固有値に対応)=```4.22824171, 0.24267075, 0.0782095```と \n", "わずかに値が異なっている。\n", "\n", "実はsklearnでは不偏分散が使われているため、" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "Xi7ViJPcI0Ub", "outputId": "f725627e-41a2-4484-a772-cde66ab75df9" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[4.22824171 0.24267075 0.0782095 0.02383509]\n", "[[ 0.36138659 -0.08452251 0.85667061 0.3582892 ]\n", " [-0.65658877 -0.73016143 0.17337266 0.07548102]\n", " [-0.58202985 0.59791083 0.07623608 0.54583143]\n", " [ 0.31548719 -0.3197231 -0.47983899 0.75365743]]\n" ] } ], "source": [ "#共分散行列Cの計算 (不偏分散, sklearnと整合)\n", "C = np.zeros((p,p)) # p×pのゼロ行列を作成\n", "for i in range(N):\n", " d = X[i,:].reshape(p,1) - mv \n", " C += np.dot(d,d.T) / (N-1) #分母 N → N-1\n", "vals,vecs = np.linalg.eig(C)\n", "print(vals)\n", "print(vecs.T)" ] }, { "cell_type": "markdown", "metadata": { "id": "3jM5vMf-PMTg" }, "source": [ "とすると、両者を整合させることができる。 \n", "以降では、上の定式化を修正して不偏分散を用いることにしよう。\n", "\n", "このように、ライブラリのソースコードを読むか自身で実装した関数と比較することで初めて \n", "「sklearnでは不偏分散が使われているんだな」ということが分かったりする。 \n", "\n", "細かな実装が式と整合しているかどうかを確かめるのは重要で \n", "これを怠ると、再現性が損なわれたりバグの温床になる。 \n", "\n", "余談: \n", "世の中でプログラムを書く人が全員「動けばいいや」の考えだと \n", "それがいつかサービスやシステムを通して社会(や自分自身)に大きな不利益をもたらすかもしれない。 \n", "(たとえば自動運転の車による事故などを想像してみよう)" ] }, { "cell_type": "markdown", "metadata": { "id": "sCnY12i_I0oo" }, "source": [ "各データに対する第1主成分軸に沿った\"得点\"は、 \n", "最大固有値に対応する固有ベクトル```vecs[:,0]```が \n", "射影になっていることを思い出すと、内積を取ればよい。 \n", "```vecs[0]```とすると0番目の行ベクトルが取られて誤りになるので注意!\n", "\n", "各点について第1主成分得点を計算してリストに詰めておこう" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "s87q-rYSI5Pe" }, "outputs": [], "source": [ "PC1s = [ ]\n", "for i in range(N):\n", " x = X[i,:].reshape(p,1) - mv \n", " u = vecs[:,0].reshape(p,1)\n", " PC1 = np.dot(u.T,x)\n", " PC1s += [PC1]\n", " #print(\"i\",i, \"PC1\",PC1)" ] }, { "cell_type": "markdown", "metadata": { "id": "Ahhgln0nJWyC" }, "source": [ "同様にして" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "39Of18TJJXuy" }, "outputs": [], "source": [ "PC2s = [ ] \n", "for i in range(N):\n", " x = X[i,:].reshape(p,1) - mv \n", " u = vecs[:,1].reshape(p,1)\n", " PC2 = np.dot(u.T,x)\n", " PC2s += [ PC2 ]" ] }, { "cell_type": "markdown", "metadata": { "id": "tDgcr88IU8gQ" }, "source": [ "プロットしてみよう" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 279 }, "id": "uel1NAySJlIA", "outputId": "36c11e0e-0709-49e3-9b59-c86ec0f82803" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cols = [\"blue\",\"orange\",\"green\"]\n", "\n", "fig = plt.figure(figsize = (4,4))\n", "plt.xlabel(\"PC1\"); plt.ylabel(\"PC2\")\n", "for i in range(N):\n", " x = PC1s[i]\n", " y = PC2s[i]\n", " plt.scatter(x,y,color=cols[targets[i]],alpha=0.4)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": { "id": "yFZRJdJIVDHD" }, "source": [ "sklearnの出力と上下がひっくり返っている。 \n", "yにマイナスをかけて向きをあわせてみると..." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 283 }, "id": "EpFUgJ2tVUVP", "outputId": "c85ae172-7208-492f-fb71-bdb828a4f06f" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (4, 4))\n", "plt.xlabel(\"PC1\"); plt.ylabel(\"PC2\")\n", "for i in range(N):\n", " x = PC1s[i]\n", " y = PC2s[i]\n", " plt.scatter(x,-y,color=cols[targets[i]],alpha=0.4)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": { "id": "ZLPdJtjsV6Tw" }, "source": [ "sklearnと同じ結果を与える自作コードを作ることが出来ました。" ] }, { "cell_type": "markdown", "metadata": { "id": "snHoZ1M0VbX0" }, "source": [ "上の符号反転について:\n", "\n", "第2主成分に対応する固有ベクトルは、sklearnと自前関数で得られた値で符号が異なっている。 \n", "今のように、分散を大きくする軸を見つける場合、 \n", "当然軸の反転(固有ベクトル全体の符号)の自由度が残されている。 \n", "実装によって符号が異なるのは、固有値問題を解く際に使用されているソルバー\n", "におけるconventionの違いなどに由来している。" ] }, { "cell_type": "markdown", "metadata": { "id": "Oyz3uBo1Pa56" }, "source": [ "# $\\clubsuit$ オートエンコーダ(自己符号化器)\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "wlQDrQiuYVi2" }, "source": [ "上で紹介したPCAは、式(or 直交変換の定義)からもわかるように \n", "空間上に\"平坦に\"分布するデータの特徴を説明するのにはうってつけです。 \n", "\n", "一方、一般のデータは必ずしも直線的な分布を持っているわけではなく \n", "空間上で曲がったり複雑な幾何学形状をしていてもおかしくありません。 \n", "\n", "そんなデータに対して、データの冗長性を削減したり特徴をとらえるための方法の一つが \n", "以下で説明するオートエンコーダです。 \n", "\n", "最も基本的なオートエンコーダは隠れ層がくびれた \n", "以下のようなニューラルネットワークで構成されます。\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "LETpVaUGNKdH" }, "outputs": [], "source": [ "%%capture\n", "#from keras.models import Sequential\n", "#from keras.layers import Dense\n", "!pip install ann_visualizer\n", "from ann_visualizer.visualize import ann_viz\n", "from graphviz import Source\n", "from PIL import Image\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 595 }, "id": "RANsWPX9N7kg", "outputId": "163b4d0d-dec5-46a7-bcd1-ed59f65ac78e", "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "graph = temp = '''\n", "... digraph G {\n", "... \n", "... graph[ fontname = \"Helvetica-Oblique\",\n", "... fontsize = 20,\n", "... label = \"\",\n", "... size = \"15,30\" ];\n", "... \n", "... rankdir = LR;\n", "... splines=false;\n", "... edge[style=invis];\n", "... ranksep= 1.4;\n", "... {\n", "... node [shape=circle, color=chartreuse, style=filled, fillcolor=chartreuse];\n", "... x1 [label=1>];\n", "... x2 [label=2>]; \n", "... x3 [label=3>]; \n", "... x4 [label=4>]; \n", "... x5 [label=5>]; \n", "... x6 [label=6>]; \n", "... }\n", "... {\n", "... node [shape=circle, color=dodgerblue, style=filled, fillcolor=dodgerblue];\n", "... a12 [label=1>];\n", "... a22 [label=2>];\n", "... a32 [label=3>];\n", "... a42 [label=4>];\n", "... }\n", "... {\n", "... node [shape=circle, color=coral1, style=filled, fillcolor=coral1];\n", "... O1 [label=1>];\n", "... O2 [label=2>]; \n", "... O3 [label=3>]; \n", "... O4 [label=4>];\n", "... O5 [label=5>]; \n", "... O6 [label=6>]; \n", "... }\n", "... {\n", "... rank=same;\n", "... x1->x2->x3->x4->x5->x6;\n", "... }\n", "... {\n", "... rank=same;\n", "... a12->a22->a32->a42;\n", "... }\n", "... {\n", "... rank=same;\n", "... O1->O2->O3->O4->O5->O6;\n", "... }\n", "... l0 [shape=plaintext, label=\"layer 1 (input layer)\"];\n", "... l0->x1;\n", "... {rank=same; l0;x1};\n", "... l1 [shape=plaintext, label=\"layer 2 (hidden layer)\"];\n", "... l1->a12;\n", "... {rank=same; l1;a12};\n", "... l3 [shape=plaintext, label=\"layer 3 (output layer)\"];\n", "... l3->O1;\n", "... {rank=same; l3;O1};\n", "... edge[style=solid, tailport=e, headport=w];\n", "... {x1; x2;x3;x4;x5;x6} -> {a12;a22;a32;a42};\n", "... {a12;a22;a32;a42} -> {O1,O2,O3,O4,O5,O6};\n", "... }'''\n", "\n", "dot = Source(graph)\n", "dot.format = 'png'\n", "dot.render('neural_network_01', view=False) \n", "\n", "im = Image.open(\"neural_network_01.png\")\n", "plt.figure(figsize = (20,10))\n", "im_list = np.asarray(im)\n", "plt.imshow(im_list)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": { "id": "nC35twUKT29_" }, "source": [ "上には、入出力の次元が6で、隠れ層が1つ(ノード4)の場合のニューラルネットワークの図を描きました。\n", "オートエンコーダではこのようなニューラルネットワークのパラメータを出力$y$が$x$にできるだけ一致するよう学習させるということを考えます。\n", "\n", "入力層から隠れ層への信号の伝播を符号化(エンコード)と呼び隠れ層から出力層への信号の伝播を復号化(デコード)と呼びます。\n", "それぞれを別々に眺めるとエンコーダ部分はもとの入力の情報を圧縮するような働きをしているとみなせますし、一方デコーダ部分は一度圧縮した情報をもとに元の信号を再構成するような働きをします。\n", "\n", "オートエンコーダはPCAを特殊な場合として含むためPCAの拡張とみなすことができます。 \n", "詳しくは記載しませんが、活性化関数を恒等変換にとって重み行列を直交行列に取り二乗誤差関数を最小化する表式を書き下すとPCAの表式が現れます。\n", "\n", "上では単純な順伝播型のニューラルネットワークを描きましたがオートエンコーダを構成するアーキテクチャは上記のような単純なANNに限らず畳み込みニューラルネットワークを用いた畳み込みオートエンコーダなども知られています。\n", "\n", " " ] } ], "metadata": { "colab": { "collapsed_sections": [], "include_colab_link": true, "name": "Python_misc_PCA.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "name": "python3" }, "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 0 }