Skip to content

Instantly share code, notes, and snippets.

@nyk510
Last active January 12, 2023 10:18
Show Gist options
  • Star 5 You must be signed in to star a gist
  • Fork 2 You must be signed in to fork a gist
  • Save nyk510/d82dfbd4596d61bbf063ad472311ed00 to your computer and use it in GitHub Desktop.
Save nyk510/d82dfbd4596d61bbf063ad472311ed00 to your computer and use it in GitHub Desktop.
GPy と Scikit-learn のガウス過程の比較
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Gpy vs Scikit-learn\n",
"\n",
"Python でガウス過程を行うモジュールには大きく分けて2つが存在します。\n",
"一つは Gpy(Gaussian Process の専門ライブラリ)で、もう一つは Scikit-learn 内部の Gaussian Process です。\n",
"\n",
"この2つのモジュールでどのような違いがあるのか、メリット・デメリットはあるのか等を比較します"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.gaussian_process import GaussianProcessRegressor\n",
"import GPy\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## データ作成\n",
"\n",
"テストデータを作成します。 \n",
"正しい関数は $f(x) = x^2 + \\sin(5x) $"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def true_func(x):\n",
" \"\"\"\n",
" 正しい関数\n",
" \n",
" :param np.array x:\n",
" :return: 関数値 y\n",
" :rtype: np.array\n",
" \"\"\"\n",
" y = x + np.sin(5 * x)\n",
" return y"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"np.random.seed(1)\n",
"x_train = np.random.normal(0, 1., 20)\n",
"y_train = true_func(x_train) + np.random.normal(loc=0, scale=.1, size=x_train.shape)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEKCAYAAAAYd05sAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1119699e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xx = np.linspace(-3, 3, 200)\n",
"plt.scatter(x_train, y_train, label=\"Data\")\n",
"plt.plot(xx, true_func(xx), \"--\", color=\"C0\", label=\"True Function\")\n",
"plt.legend()\n",
"plt.title(\"トレーニングデータ\")\n",
"plt.savefig(\"training_data.png\", dpi=150)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## カーネルの定義, 可視化\n",
"\n",
"カーネルを定義して可視化する難易度を比較していきます。\n",
"\n",
"### sklearnの場合"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAD+CAYAAADbNKXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBUiyF0KIFCDJXgghUsD/B0LaLhqIgFIWAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111c4d748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.gaussian_process import kernels as sk_kern\n",
"\n",
"kern = sk_kern.RBF(length_scale=.5)\n",
"kern = sk_kern.ExpSineSquared() * sk_kern.RBF()\n",
"# kern = sk_kern.RationalQuadratic(length_scale=.5)\n",
"# kern = sk_kern.ConstantKernel()\n",
"# kern = sk_kern.WhiteKernel(noise_level=3.)\n",
"# 可視化は定義されていないので自分で用意する必要あり\n",
"X = np.linspace(-2, 2, 100)\n",
"plt.plot(X, kern(X.reshape(-1, 1), np.array([[0.]])))\n",
"plt.savefig(\"sklern_kernel.png\", dpi=150)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### GPyの場合"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
" /Users/nyker-goto/.pyenv/versions/anaconda3-4.3.0/lib/python3.6/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111c4d668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"kern = GPy.kern.PeriodicExponential(lengthscale=.1, variance=3) * GPy.kern.Matern32(1)\n",
"# kern = GPy.kern.RatQuad(1, lengthscale=.5, variance=.3)\n",
"# kern = GPy.kern.White(input_dim=1)\n",
"kern.plot()\n",
"plt.savefig(\"gpy_kern1.png\", dpi=150)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
" /Users/nyker-goto/.pyenv/versions/anaconda3-4.3.0/lib/python3.6/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1120a35f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"kern = GPy.kern.Linear(input_dim=2) * GPy.kern.Matern52(input_dim=2)\n",
"kern.plot()\n",
"plt.savefig(\"gpy_kern2.png\", dpi=150)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 違い\n",
"\n",
"* カーネルの数\n",
" * GPy の方が用意されている関数の数が多い.\n",
" * `PeriodicExponential` など周期性を持ったカーネルが用意されている\n",
"* 可視化\n",
" * `GPy` には可視化用の関数 plot が用意されている\n",
" * `scikit-learn` には無いため、自分でプロットをする必要があり面倒\n",
"* 定義方法\n",
" * `GPy` においては、カーネルの定義の時点で、入力する特徴量の次元数 `input_dim` を指定する必要がある。実際にはカーネル計算のためのデータがあたえられれば特徴量の次元数は自明に判明するため、やや冗長のようにも感じられる。 \n",
" * `scikit-learn` ではカーネルの定義では純粋にカーネルの情報のみを入力すればよい。 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 予測モデルの作成"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"kernel = sk_kern.RBF(1.0, (1e-3, 1e3)) + sk_kern.ConstantKernel(1.0, (1e-3, 1e3)) + sk_kern.WhiteKernel()\n",
"clf = GaussianProcessRegressor(\n",
" kernel=kernel,\n",
" alpha=1e-10, \n",
" optimizer=\"fmin_l_bfgs_b\", \n",
" n_restarts_optimizer=20,\n",
" normalize_y=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### パラメータ詳細\n",
"\n",
"* alpha:\n",
" * ガウス過程ではカーネルの逆行列を計算する必要があります。カーネル関数がつくる行列は、入力のベクトルの値がすべて異なる場合、数学的にはかならず正定値です。しかし、固有値の値が非常に小さくなる場合があり、この時逆行列の計算は数値的に不安定性となってしまいます。 これを補正するための値が `alpha` で、行列に対角成分に `alpha` を持つ対角行列を加えることで、最小固有値の値が `alpha` よりもおおきくなるように補正し、計算安定性を確保します。\n",
"* normalize_y: default True\n",
" * 予測変数の平均を 0 になるように正規化します。Gaussian Process の計算の際の数値的安定性担保のため行われます. \n",
"* n_restarts_optimizer\n",
" * カーネルのハイパーパラメータを最適化する回数です。 0の場合1回の最適化で終わりますが、0以上が設定されると, 直前の最適化で得られた最適解を初期点として再び最適化を行います. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"GaussianProcessRegressor(alpha=1e-10, copy_X_train=True,\n",
" kernel=RBF(length_scale=1) + 1**2 + WhiteKernel(noise_level=1),\n",
" n_restarts_optimizer=20, normalize_y=True,\n",
" optimizer='fmin_l_bfgs_b', random_state=None)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# X は (n_samples, n_features) の shape に変形する必要がある\n",
"clf.fit(x_train.reshape(-1, 1), y_train)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"RBF(length_scale=0.374) + 0.0316**2 + WhiteKernel(noise_level=0.00785)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# パラメータ学習後のカーネルは self.kernel_ に保存される\n",
"clf.kernel_"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x_test = np.linspace(-3., 3., 200).reshape(-1, 1)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# 予測は平均値と、オプションで 分散、共分散 を得ることが出来る\n",
"pred_mean, pred_std= clf.predict(x_test, return_std=True)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def plot_result(x_test, mean, std):\n",
" plt.plot(x_test[:, 0], mean, color=\"C0\", label=\"predict mean\")\n",
" plt.fill_between(x_test[:, 0], mean + std, mean - std, color=\"C0\", alpha=.3,label= \"1 sigma confidence\")\n",
" plt.plot(x_train, y_train, \"o\",label= \"training data\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEKCAYAAAAYd05sAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111c052e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_result(x_test, pred_mean, pred_std)\n",
"plt.title(\"scikit-learn による予測\")\n",
"plt.legend()\n",
"plt.savefig(\"sklern_predict.png\", dpi=150)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# GPy"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import GPy.kern as gp_kern\n",
"# kern = gp_kern.PeriodicMatern32(input_dim=1) * gp_kern.RBF(input_dim=1)\n",
"kern = gp_kern.RBF(input_dim=1) + gp_kern.Bias(input_dim=1)\n",
"kern = gp_kern.PeriodicExponential(input_dim=1)\n",
"gpy_model = GPy.models.GPRegression(X=x_train.reshape(-1, 1), Y=y_train.reshape(-1, 1), kernel=kern, normalizer=None)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### パラメータ詳細\n",
"\n",
"* normalizer (default False)\n",
" * 予測変数 `Y` の正規化を決定する変数です. `None` が与えられるとガウス正規化が行われます\n",
"* noise_var (default 1)\n",
" * データのノイズの分散を指定します. scikii-learn ではノイズは自分でカーネルに仕込む必要がありますが、 GPy.model.GPRegression ではデフォルトでノイズを考慮する用になっているため, カーネルにノイズを加える必要はありません. "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAI4CAYAAAA/PH0eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCVBCCCEsSQKUEEIIS5IAJYQQwpL+P0IHhTLy10/qAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111c6dac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6,8))\n",
"ax1 = fig.add_subplot(211)\n",
"gpy_model.plot(ax=ax1) # 最適化前の予測\n",
"gpy_model.optimize()\n",
"\n",
"ax2 = fig.add_subplot(212, sharex=ax1)\n",
"gpy_model.plot(ax=ax2) # カーネル最適化後の予測\n",
"\n",
"ax1.set_ylim(ax2.set_ylim(-4, 4))\n",
"ax1.set_title(\"GPy effect of kernel optimization\")\n",
"ax1.set_ylabel(\"Before\")\n",
"ax2.set_ylabel(\"After\")\n",
"fig.tight_layout()\n",
"fig.savefig(\"GPy_kernel_optimization.png\", dpi=150)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Name : GP regression\n",
"Objective : 6.799282795295307\n",
"Number of Parameters : 4\n",
"Number of Optimization Parameters : 4\n",
"Updates : True\n",
"Parameters:\n",
" \u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors\n",
" \u001b[1mperiodic_exponential.variance \u001b[0;0m | 2.85057672019 | +ve | \n",
" \u001b[1mperiodic_exponential.lengthscale\u001b[0;0m | 0.416248308257 | +ve | \n",
" \u001b[1mperiodic_exponential.period \u001b[0;0m | 11.478988407 | +ve | \n",
" \u001b[1mGaussian_noise.variance \u001b[0;0m | 0.00923971637791 | +ve | \n"
]
}
],
"source": [
"# 最適化されたモデルの確認\n",
"print(gpy_model)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"pred_mean, pred_var = gpy_model.predict(x_test.reshape(-1, 1), )\n",
"pred_std = pred_var ** .5"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEKCAYAAAAYd05sAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvXd4XNWd//8607umqcuS3I2NsQ2mGUInlJANgbALm8Zu\nCPGG3YQQwJB8SZyEjUMLSTbZxJv2SyPZFGIWAjGE2FQbNxkb3C3JVm8zGo00feb8/hhJ2LJktZFm\nJJ3X8/h5PHfuPfdzRzPve+7nfIqQUqJQKBSK6Ycm2wYoFAqFYmJQAq9QKBTTFCXwCoVCMU1RAq9Q\nKBTTFCXwCoVCMU1RAq9QKBTTFCXwimmJEEKXbRtGihBCDHj9eSHEnGGOeXxirVJMB6bMj0Ax/RBC\n3Aj8O6AFQsBjUsrNQoi1wD8AQUACSeAhKeWboxj+V0KIf5ZjSPQQQtwCGKWUvx5mv42AEdD32mkB\nXpVS3j1gv9nAz4cYpgh4HbjjhG0/BR4SQuwGHgR8vfvdCFwppfzBaK9JMTNRAq/ICkKI24D3AzdI\nKSNCCBNwxQm7fFZKubV333zgGSHERaMQ7GDfvkKIfwVuB1K972mAf5dS7hnqWNKC3fckYJdS+gfZ\n76O9+8aAxcANwHcH7iSlrAEuE0KcBZQDfTeGjwLHgb8O2L8bWCOEuAxYD7xB+oYHMGuY61Yo+lEC\nr5h0hBAa4LPAVVLKKICUMgI8P9j+Uso2IUQzYBFC6IH/llL+84Ax1wNrpJSdQggn0H7C8T8DfjYK\nE1PAWiHEZ4Ao0MzJM+y+cdt7z30t4JRSPnK6QaWUe4QQSeCLpG8GD0gpXx9wHecCXinlC72bSoB5\nQOEo7FcoACXwiuxQAuzvE/fhEEJcAFiklD29r1uEEHOllEd7XzsBIaXs7D2kFDg2DvuSwDeklP87\njF0a4P8BlwKxXqH/3xPEGSHEecCjgxyuATYJIbb2nk8AnwR2AP8khLgH2AW8JqX8qxDCNo7rUcxQ\nlMArskEp0NT3QgjxMHAxUCilPKN3838LIfpcJYeAT51w/PeBfwPu7X19G/DbE97PB9rGYV8EMJ9u\nh96byv8Ab/faUkf6uu4VQsyTUv4XgJRyG3DZgGMvABZJKVf1vp4NfExKWdu7y+96t18GfFIIcTGw\nDNg6jmtSzECUwCuyQT3pRUMApJT/D0AIcaIvut8HPxAp5VEhhFsIYev1V19O2lfdhxPoFkIsklIe\nEEIskFIeGoV9YU4j8EKIhcAPgPuklFUnvHVECPFvwP8KIb4/kvUCIYQDeAD4jwHbl/X+9xe9M/jb\nR2G/QgGoMElFdmgCFgkhDOMY46fA7b1CuEdKmTrhvTBwPVDR67P/zHCDCSE+LYTYLoR4FfghcJsQ\n4vKBIYy9tAG3SSmrhBBrhBDPCCE+BtAr6sdIR9SMBDOwVkoZO8EWI7AaiAMfF0J8i/Qia3KEYyoU\ngBJ4RRboFeP1wPd6BZheH3P+KIZ5E1gF/AvwiwHvBYCbgE2kfdtLhBAlvecxCCEqhBCVfTsLIRYA\nZwLnSykvAT4ObAcuBJ4XQpw5wH5f78LvmYCVdITO2UKID/VeT0nfesFwSClbpJRNAzbfCvyBtEtm\nF+lQyRellIellA+MZFyFApSLRpElpJRPCSESwMbeWXKYtKtipMdLIcQzwMellHUD3j4E7OybFQsh\nvkn6ZpJPOiqmEfgLUNu7f5j0wu9iIUQD8K/Au1LKnwkhPMBjQoi7pJThQUwpBvKAJ0jfaO4FHhrG\n/MGeCui1VQBXAZ8AvgAc6L3WNiHE7VLK/2+4MRSKPoRq+KGYqgghPgX4pZRPD/LeuVLK7aMY6wrS\nwp4PbCMdRRM7/VEghPgg6egXA7Af+OEJi6UD970A+E/SbpkvSyk3DbKPm3Q+wG7gTinl/Se8dwbp\nePvPAFEp5QdHen2KmYkSeMWUpHc2/mPgpgH+92mDEEKMJRNXoehDuWgUU4reBcjnSS843j1dxR36\nF2wVijGjZvAKhUIxTVFRNAqFQjFNyaqLxuv1ysrKymyaoFAoFFOOnTt3tksphw0rzqrAV1ZWsmPH\njmyaoFAoFFMOIcSIai0pF41CoVBMU5TAKxQKxTRFCbxCoVBMU3IuDj4ej1NfX08kEsm2KYppjslk\noqysDL1en21TFIoJIecEvr6+HrvdTmVlJYMX8lMoxo+Uko6ODurr65k9e3a2zVEoJoScc9FEIhE8\nHo8Sd8WEIoTA4/GoJ0XFtCbnBB5Q4q6YFNT3TDHdyUmBVygUCsX4UQKfBVavXn3KtvPPP5/m5uYs\nWKNQZB4pJS1dEd440sZrh9o40NRFNKEaUk02ObfIOlP57W9/S2Fh4Yj337x5M83Nzdx6660TaJVC\nMXqSKclb1R0cae3GbNCiFYJjvh7eru/ksgX5FOadtp+5IoOoGXyOMGfOHOUTVkx5UinJm0faOdLW\nTXGeCZfFgMOsp8hhxqzX8uK+Fup8oWybOWNQM/hB+MxnPsPs2bPx+Xw0Nzfz8MMPU15eDsCXvvQl\n7rzzTh577DGi0Sgf/OAH+dCHPkQ0GuXhhx/G7/fT1dXFddddx2233QbArl27+N73vkdBQQElJSX9\n5/H5fHzzm98E4M033+Tpp5+mqKio//2NGzfypz/9CbvdTiKR4Mtf/jIFBQU88sgj7Nq1i56env5a\nPvfffz8FBQVDXtP999+P0+lk69at3Hbbbbzwwgtcf/313Hrrrae1fdOmTTz77LNoNBra29t59NFH\nKSgoYPPmzTQ1NbFv3z66uroIhUKsX78ejUbNGWYyh1uD1LT3UJxn4q0aH09XNeDrieG2GrhpRSkr\nZjl55VAb1y8txm0dT891xUjIaYH/2rPvsq+xK6NjLi5x8NUPLjntPrW1taxbtw632017eztr167l\n+9//PgB+v5/vfe97fO9730Or1fYf86Mf/YjVq1dTWloKwL333ss111yD3W7nscce4xe/+AUGg4GW\nlha++tWvAuB2u3n88ccBWLt27Uk2VFdX89xzz7F+/XqEEHR1dfWfb82aNaN20XR0dHD33Xdzxhln\ncOjQIX7xi19w1113ceuttw5pu9vtZsGCBTzxxBMIIdi1axfr16/noYfSLUdfeOEFfvKTn2AwGPjm\nN7/J1q1bWbVq1YjsUUw/AuE4O4758doM/HFnPS/ua6Gv24SvJ8YvttQClSwpcbD5YCvXLy3GpNcO\nPaBi3OS0wGeL2bNn43a7AfB6vSST7y0OJRIJ1q5de5K4A7zxxhv4/f7+111dXbS1tdHU1MSqVasw\nGNKzlZH62Tdu3Mgdd9zR77ZxOBzjuia9Xk9JSQkul4uKigqEEKRSqdPa7na7KSkpYceOHWzcuJFk\nMkld3Xv9ra+//vr+61q5cuVJ7ylmHlXH/eg1Gl54p5mN+1pOeT+elPxhZz0XzFlGazBC1XE/F871\nZsHSmUNOC/xwM+3J4kTfuFarHVRsrVbrKbNwgKqqqjGlwieTydO6O4QQJ914xsNQtgM89NBDLF++\nnNWrV+P1egeNAAIwGAyo7mAzl47uKMd9IXYf7+TZPU1D7hcIx2nuilBgN3KoJUi520KpyzKJls4s\nlMN0EHw+H/F4HID9+/eTnz9sXX3mzJnDpk2b+l8Hg0EAFi5cyOuvv94vfnv27BmRDVdffTU/+9nP\n+o+LRqMnhVGWlJSwd+/ekV3QGG0HaGlp4SMf+Qher5e9e/f2fy4KxYnsbQjQHoyyYXcDKytcQ/rX\nBfDtlw7ywJ/28NX/28cN//U6f9qpnvwmipyewWeLZDLJ17/+dXp6eojH4/0Loafj/vvv5ytf+QrP\nPfccer0eo9HI1772NSwWC7feeiu33347xcXFLFq0CLvdPux4Cxcu5NJLL+XOO+/E4XCQTCb5whe+\n0P/+/PnzkVJy//33YzAY+PjHP87ChQvHdL1D2Q6wZMkS7r33Xux2OwsXLsTrVY/UipMJhOLUtHfz\np10N2E16PnFhBXvqA/xyyzFiyfd6ohu0GuYXWnm38b0JhD8U50t/fgetRsONK0qzYf60JqtNt1eu\nXCkHdnTav38/Z5xxRpYsSrN69Wp+9KMfZdUGxeSQC9+3qU7VcT8/f6OG/3u7ibsum8uKchcArx5q\n45m3GwmE4zjNem46u5QNuxvx9cROGaM4z8SWB6+cbNOnLEKInVLKlcPtp2bwCoVizMSTKd5tCPDa\n4XbmF9hYPssJQGswwvIKJ7dfVInFoKOhM8S7DV2DijtAc0AVfZsIlA9eoVCMmcbOMG/V+PGH4txw\nVjFCCNq6I+TbjNywtIQ5+TaK8kycU+HmmiWF5JkHDzhwmPUEQmp9J9MogR8E5Z5RKE7PhqoGLvrW\n37n0sc38ZW8j+TYDi4sdBCNxrAY9lyzMx6A7WV4K88x87sp56LUnZ2wbtBquXVLInvrOybyEGYES\neIVCMSo2VDXw4NN7aegMA5CS6cXSrdUddEUSrJrnwagbPIHpUxfP4c5L5uA8YSZ//dIirjqjkNqO\nniFdOIqxoQReoVCMisc2HiQcPzkHI5GS/GlXA2eWOvDajKc9/t8vn88D1y/iiVuWYdZrqfeHEUJg\n1GnVLD7DKIFXKBSjorF35j6QznCcxcV5wx5vNmhZXuYkHE9w2cJ8dh7309EdxWXRc6wjpGbxGUQJ\nvEKhGBUlzsHL/ebbjJgNI6stMzvfilaj4eJ56byKVw63IYTArFez+EyiBH4Sufvuu/nzn/88qmN2\n7NjBzTffPEEWDc5Q5QgUCoD7rlmIccACql4ruO+aBSMew6jTcmZJHgJYVurktcPtJJIpXBY9db4Q\nfjWLzwhK4Idg7dq1Ge+wtGbNGq655ppRHbNs2TKefPLJjNqRKWpra/nWt76VbTMUk8yNK0q56ez3\nsk6dZj13XjKHfzy3fFTjzC2wkgIuWeAlGEmw63hnvy9+b0Mgw1bPTKZ8otOGqgYe23iQxs4wJU4z\n912zMGdTnouLi0d9jF6v769Fr1DkAvFkis7emPV1H15KIpXimjOLhjnqVCwGHbPcFgxagcdq4I2j\n7Zw3243Toqe2vYelpXm4VM34cTGlBb4vXKtvRb+hM8yDT6cLcI1V5Lu6uvj617/Om2++SUtLC1ar\nFbvd3l/Dfe3ataxevZp169YRiUQ499xzueOOO2hra+PJJ58kmUzS1tbGhz/8YT74wQ8C8J//+Z/4\n/X7q6ur48Ic/3F/Dvba2lg0bNtDT00NHRwctLS38z//8D1arlRdffJEXX3wRgOPHj/P73/++38Y1\na9Zw4YUXsnXrVmpra1m9ejWXXXYZAH/961954YUXOHDgAN3d3Vx++eU8/PDDp73moRqSAKxfv57q\n6mpisRhSSp588kmEEPz4xz9m27ZtHDhwgPb2dgDuuOMOFi1axO7du/nVr36FRqOhpaWFhx56iPnz\n54/p76HIPTq6Y+ypD1DpsWA36UikJPnDRM4MxcJCO8c7erhgjofn32miMxTDaTFg1Gl4tzHAxfOH\nL/SnOA1Syqz9O+ecc+RA9u3bd8q2oVi17mVZsea5U/6tWvfyiMcYiq9+9auyqalp0O3/8i//Int6\nek7aHggEZFdXl5RSylQqJW+88cZTjt20aZP87W9/2/+6pqZGXn311TIQCEgppfzNb34jf/Ob35xy\n3Gc+85mTXt98883ytddek1JKGY1G+8914nlTqZS87rrrhr3OWCwmb731VhmNRqWUUjY3N590vvr6\n+v7/P/HEE/LVV189yf5169adMmZjY6NMJBJSSilbW1vlHXfcMawd2WI03zdFmo3vNMmKNc/JL/yu\nSv5qS6082NQ15rESyZT8w/bj8mevVcuKNc/Je3+/W770brPc+E6T/OWbNdLfE82g5dMHYIccgcZm\ndAYvhPgEsBgwAAEp5dcyOf5AhgrXGmp7prjvvvuwWE6uYe1wOGhpaeGpp56ivr6ehoaGEY11xRVX\n9NeXX7ly5YgWYb1eLxdffDGQrsPu8XgA6O7u7p+BCyFGVOb40KFDp21Ikp+fz/PPP89bb71FY2Mj\nHo+H973vfacds7i4mH379vHcc88RDodPaiaimNpIKXlpX3pt6qzSPKSUlLjG3kRbqxHML7KzryHA\nbK+VrdUdXLOkCI0QGLQa3mlQs/jxkLFFViGEAWiUUj4gpbwH0AghzsnU+IMxVLjWUNtHw+kaarhc\nrlO2bdq0if/+7//m0ksv5Wtf+xpnn332qM851qYZOl36Pm2322loaCAWi9Hd3T2i/qixWGzIhiTh\ncJi77roLm83GmjVr+NSnPnWSfUN9Rt/97nfZunUrH/vYx/jqV7+qSgxPI4LRBHsbuvBYDeRZ9OTb\njdiM45snznJZSKTgwjke6vxh6vzpptwuq4Ga9h46QyqiZqxkTOCllDEp5d9O2LQX8GRq/MG475qF\nmAf0dDTrtdx3zdjqop/IaBtqPPPMM9x///0sWrSISCTCwYMHx23DaEkmk3i9Xh555BGefPJJHnnk\nkWGPOV1DkgMHDrBixQouueQSLBYLVVVVJx3r9Xo5cODAKWO+8847/Ou//islJSUcO3aMjo6OcV6Z\nIldo9IU42tbNsjInPbEE8wps4x7TZdFjMWhYVpaHVgi2Hk1/XzT92a0qomasTOQi6/uArwzcKIS4\nE7gTGHd0SN9C6kRE0dxyyy188YtfZPPmzej1eh566KF+N8ZgfOITn+D+++/H5XJht9tZsGDkMcGZ\npKOjA4fDQSqV4pe//CXXX389ixcvHnL/0zUkWbJkCb/+9a9Zs2YNFouFioqKk461Wq0sW7aMe+65\nB6vVyg033MD555/PJZdcwj333IPD4aC0tJTKysqJvGTFJPK3/a3Ek5KlZWm3YnFeZp6W5xfaeach\nwNLSPLbW+Lj57DI0GoHLoqe2o4cl3Q48Y1zInclMSMMPIcT7gXIp5U9Ot1+uNvyYqhw6dIg//OEP\nfPnLXwagubmZT33qU/zlL3/JsmW5i/q+jZxkSvLxn77F9lof6z68FJtJx7Vnjj70dzB8PTH+sqeJ\nhs4QP3qlmi9cNZ8lJemyB52hGC6rgSsWFZzUH3kmM9KGHxlPdBJCnA+cP5y4KzLPwYMHT2rb53Q6\nTwl7VCjGSmcoxuHWbhYU2okmkszxjt8904fTrMek17C42IHFoGVrte+99ywGGvxhWoPRjJ1vppDp\nKJolwD8BX8zkuIqRce2117JmzRr++te/UlRURDgc5ktf+lK2zVJMEw42BWkLRrlsQT4SQYEjcy4T\njUYw22vlaGs3K2Y52XW8k3gyhV6bnoM6THq21/i4bmkxWo2axY+UjAm8ECIP+D9gA7Cu91HqiJrJ\nTx56vZ5vf/vb2TZDMU156UALAAsK7Zj1miG7M42VMpeFA81Bzq1088bRDt5pCPT3d7WZdDQFwtS2\n9zA3Awu7M4WMCbyUMgDMzdR4CoUid0imJDuP+XGYdNiMWmZ7bRn3h3tsBjQifQOxGXVsr/X3CzyA\n22pgxzE/pS4zJv3IqlaOh2RK0haMUu8P0RyI0BNLAGAz6ijOMzPLbcFrM+T0usCULlWgUCgmB39P\nlKNt3SwtzSMpM5NrMhC9VkNxnhl/T4yzy528VeMjmkj2d4cy6rR0ReJUHfdz4dyJy61IpiS17T3s\nrvMTiiUxaDVYjTqc5nQUXSyR4lBLkHcbA3hsRs6pcFHoME2YPeNBVZNUKBTD8nZdgJ5okgUFdgTp\n2fREUOGx0BNPcG6lm2gixd4BMfAeq5FDLUGaJihbvbUrwnN7GnnzaDtGnZbiPDMemxGTXotWI9Bq\nBGaDFq/NSHGemWg8yV/faWJrdTuxRGpCbBoPSuAVCsWwvHYkXVCu1GmmwG48paF2pvDajSDTRcgc\nprSb5kQ0QuCyGHjjSDvh2OCZ5mMhlkixo9bHC+82I2U6vn8kbiC7SU9xnpmjrT1sfLeZrkg8YzZl\nAiXwk8hYGn7kOh0dHaxZs4Yvf/nL/PrXvz7pvSeffJLvfOc7Qx6r6slPDZIpyZ76TmxGHVajhnKP\ndcLOZTfqsBi0JFKScypc7GnoJDKg/6vFoCMhJW/VdJBKjT+Px9cT44V3mjjQHKTYbhp16QWNEBQ6\nTETjSV7Y20R7d+6Ec+a8D/6FvU2092TuA/NajVy39PTJGUePHuW+++6jpqbmlPT88bBmzRry8obv\nWTmVWLt2LZ///OeZN2/eKXV0PvnJT2bJKkUm6QrHqe0IMb/ABkJDvn3iMkqFEFR40uGS51a62XSw\njbfrOjl/zslVTzwWA8c7QlSZ/JxT4R7TuVIpyeHWINtqfNiMOorG6Ud3Wgx0RxNsfLeZqxYVUJiB\nLN/xkvMC394TpdiRuQ+qqWt4393cuXN5+umnM966biwNP3KdSCTCvHnzAE6JJnC7x/bDU+QWh1uD\n+HpiXL4wH51G4MxweORASpxmDjR1Ma/AhsuiZ3ut/xSBF0JQ5DDxTkMAs17L4pLRTZx6ogm2Vfuo\n84fItxv74+3Hi82oQysEL+1v5f2LCynI8uJrzgv8VKG+vp6HHnoIl8uFEIJLLrmED33oQ8DQDT9g\n6AYdd9xxB3l5eQQCAZYtW8aLL77Ik08+ybx589i0aRPPPvssGo2G9vZ2Hn30UQoKCk5rn5SS73zn\nO1RXV2M0GrFarXzlK19Bq9Wya9cufvjDH2K320kkEnzta1/D5XKdtiFJVVUVv/nNb9i2bRv33nsv\n8F7Djx/+8IccPXqUQCDA3LlzeeCBB/rteOmll/jtb39LQUEBJpMJk+m9H8Czzz7LM888g8FgQKvV\n8vjjj2M0Glm7di3XX389GzZsoK2tjcWLF/OFL3wBgGAwyNq1a0mlUgghWL58OZ/4xCcAeOONN/j5\nz3+O2WwmHA7zyCOP9JdWVoyc1w+/538vdZnRTHCikdtqAAECWFnhZtPBVkKxBBbDyXKl0QgK7Sa2\n1fqIJVOcVeoc1rZUSlLd3sP2Wh8aMTHRQGaDFonkbwdauGZxUVZr6CiBzxC///3vueOOO7jooouA\n9My2j77aMJs3bz6pz6uUkvXr1/PnP/8ZKSUf+MAH+rsvNTU1sX79eu655x7OO+88Lr74Yl5++WXm\nzZvHggULeOKJJxBCsGvXLtavX89DDz10Wvt+97vf4fV6+4WxubkZrVZLPB7n29/+Nj//+c/R6/Uc\nP36cr3/96/19YJ9//nn++Mc/4nA4eOqpp3jmmWf453/+Z1asWMGKFStYvXo1jz/++Enn+rd/+zcg\n7WP/3e9+17/d5/Px1FNP8dOf/hSNRsNbb73Fpk2bADhy5AhNTU385CfpvLidO3fyk5/8hLvuugtI\nd5365je/CcCHPvQhPve5z6HVavnKV77C6tWr+0s09H2+fr+fV199tX+8lpYWHn/8cdatWzfcn1Jx\nAlJKdh33o9cK3DYDpRMgiAMx6bW4LQbC8STnVrp4aX8LVXWdXDRIaKROq6HEYWZvfRfNgQjnzfYM\nGuGTTEmauyJUHfPj64nhtU3cQjGk1wlSEv62v4VrlxSTZ5nYp56hUAKfIW655RYeffRRtm7dym23\n3TaiGjCna9Axa9YstFotLpeLiooKIpFIf+OMkpISduzYwcaNG0kmk9TV1Q17rldeeYUf/vCH/a+L\nitI9NA8dOsQFF1zQXxO+vLycaPS9NY+xNCQZii1btnDTTTf116k/sbnIiy++yKFDh1i7di0AqVTq\npNn2jTfe2P//JUuW0N7eTmFhIeFw+KT6O33XtWXLFg4ePNg/HnDaaqCKwQlGE9S0h5jjtaEVAo91\ncmajs9xW9jZ0MttrxWszsL3WN6jAQ3omX5xnojMU4y97GilwmJjlMmMz6kmkUrQFoxz3hYjEk9iN\n+gmZtQ+GzagjlZK8fKCFa5YUYR1n3fyxoAQ+Q8yaNYv/+q//ora2ll/84hc0NTXx3e9+97RZbic2\n6IjFYiNq0AHw0EMPsXz5clavXo3X6x3XWoGU8hQbh6owOtaGJH3EYjHM5qF/XB/96Ec599xzhx1n\npHZ84AMf4JZbbhmVjYqTafSHaQqEuXZJEQadBrtpciSj0GHk7fr0d3NlhZuX9rXQHUlgO835nRYD\neVLSE02yu66TdICNxKjTYjPqcFkm/wbvMOvxh2JsOtjK1YsL+5O2JgsVJpkhjhw5gpSSyspKHnzw\nQQKBAKFQ6LTHjKVBB6TdDR/5yEfwer3s3buXeHz42Nvzzz+fP/zhD/2vm5qaiEajLFiwgK1bt5JI\npNOwGxoaTvKLZ5KVK1fy/PPP978+sbnI1VdfzU9/+tN+4Y7H44TDwy+I63Q6qqur+18fO3YMgAsu\nuIA//vGP/dclpaS7uzsj1zGTeONoOykJpS4zJc6J97/34bQYEAhSUnJupYuklOyqG771oxACm0lH\ngd1EkcNEkcOMy2LI2CLqWHBZDAQjcV4/3E4iObnJUDk/g/dajSOKfBnNeMPxyCOP0NbWxpYtW7j3\n3nspKyvj7rvvPu0xx44d48c//jFCCDo7OznvvPOwWoePFx5tgw5Iuyjuvfde7HY7CxcuHFFLvNtv\nv51169bxH//xHxiNRsxmMw8++CAWi4W7776bz372s9jtduLx+ElujUwya9Ysli1bxqc//Wm8Xi/z\n58/vf2/+/Plcd911rF69GqfTSU9PD/fccw9z5sw57Zjf+MY3WLt2LVqtNt04Yv58Vq9ejdvt5nOf\n+xyrV6/G4/EQCoW4/fbbOeecCe0iOe3YVuNDCCh0mCbF/96HQZcOxwzFkpS7LRTYjWyv9XHJFO3P\nmm8z0dgZZluNjwvmeCbtRjkhDT9Gykxv+KEadGSfify+SSnpjibS6e16bU4XpRqMcCzJB773GomU\n5NPvm80Hl5XgnEQ3x/6mAFXHOymwm/hzVQPPv9PE4x9ZlvEqlpOFlJLGQIQzSx2cXe4a1/chaw0/\nFCNHNeiYvnR0R9n4bjMbqhp4emcDmw605lwa+3B0dEep94eZm29Fp9XgME2usHptJvoSVc+tdCEl\n7Do2vJsmVxFCUOww8U5DF3sbJqfPbM67aKYzqkHH9MTXE2Pju839xaoA2rtjvLC3mWvPLJoyM9Bt\nNen48lm78heqAAAgAElEQVQuC8V5pklzK/ThtOjRCEhJSanTTHGeie3HfFy+6PQ5H7mMRpNO0Ko6\n7qfQYZrwKpRK4LOIatAx/QjFEvx9fytmvRb7CTNet9VAIBxn04FWrj2zaFLqmY+XLdUdABTlGSnN\nQtq9XqvBa0v74W1GHedWunn27UY6Q7FJdRVlmnRVSg3xSVhwzUkXTTbXBRQzh4n4nu2p7ySeSmI3\n6WnpilDd1o0/FAMgz6wnHE9QdTz33QyJZIp9TV14bQYcJj1uW3YEtcxlJtTbaOPcShcS2DGF3TST\nTc7N4E0mEx0dHXg8nim3KKWYOkgp6ejoyGhIaEd3lEMt3Zj1Wn78WjVv1aQbRwvg8kUF3LSiNF3P\nvLWbuQU2Cuy52SQC0g22j3WEOLPUgRAia26lfPt7fvjiPDNlLjPba31cdUbh6Q9UADko8GVlZdTX\n19PW1pZtUxTTHJPJRFlZWcbG23Xcj0YIvvO3w7QGI1x/ZhHzCmzsbQiw6UArte093Pv+hTiMOrZV\n+7h+afGk+7VHyruNXXRHE5S7LeTbjeiyFEfutOgRpP3wGiE4r9LN01UNdHRHs1rjZaqQcwKv1+uZ\nPXt2ts1QKEaFrydGQ2eYH79STUMgXYdoa42PEqeZj55fwaIiBz985Sg/f7OGO983h6ZAhKZAmFKX\nJcuWD87rvQ0+ih0mylzZK3ur12rw2IyEY0msRh3nzU4L/JvVHXzwLBVxNhw56YNXKKYah1uD/HVv\nU7+4Q1r0f7nlGFurOzinwsVNK0rZXutna7UPu0nHnvpATq43SSl5u64Tq0GLx27M+kx5lttMdzTt\nh/fajJxRZOeNI+2kcvCzyzWUwCsU4yQcS/JuQ4C3ak9d/IslUzxd1QDAtWcWMdtr5Q8769BqBG3d\nUdqCudP9p4/uaILq9h7mFdgQkPWwznybEcl7Yn7xPC/t3TEOtQSzaNXUQAm8QjFOGjpDvH6knaEm\nlL6eGL6eGBoh+Oh55QQjCZ7b04RFr+VAc+6JVG17D+3dMSo9VvIs+qyHdDotBoQQ/U87K8pdmPVa\nXuutU68YGiXwCsU4eachwPbadM30wShymPDYDDR2hin3WLhwrofNB9sQAo53hOjpdT/kCn3CWeI0\nUZIDbecMOg0ui55wb29Wg07D+bPd7Dru7w+hVAyOEniFYhx0ReK8dridYCTBlQsLMAwQebNeywPX\nLeKKRQWcUeKguSvCdWcWEU+m2HQgLfLHOnqyZP3gbK/1odcKCh3GCc+0HCllLgs90feab188z0s8\nKdnWG4qqGBwl8ArFOKj39bCluoOiPBM3n1PGjStK8dgMCNIt7tbdtJQbV5QihODschezXBb0Wg0r\nyp28fKAVo17DvqYuUqncWDCMJpIcbu1mtseKVqvBmaVORAMpsJtInuADq/BYKHOZ+6N9FIOjBF6h\nGAebD7bT2BnhioUFJFKS5bOcvHrf5dR86wO88cAV3LiitH9frUZw3mw3KSm5+oxCwvEkVcc6CcdS\ntPfkxmJrc2eExs4wc/KtGLXpRhm5QN+Nps8PL4Tg4nleajtC1PlP33dhJqMEXqEYI8FInC3VHWiF\n4NxKF+09MZbPcp62NZvVqGNFuROrUUu528Irh9vQa6CmLTfcNG/2Nvgoc1kodppyJpvcpNeSZ9YT\nTbxXv+WC2R70WsGmA61ZtCy3UQKvUIyR5kCEPfUBlpQ4MOm16DWCeQX2YY+bX2DHZtKzaq6Hen8Y\nXyjO0fbuSSk+NRxba3wI0i3zivNyw//eR5nrvXh4AJtJxwWzPWyt9p20XfEeSuAVijHy8v4WAuE4\n58124w/FOKPEgUE3/E9Kp9VwVlke8/KtGHWadNJOClq6IsMeO5EkU5J9jV2UOs2Y9dqs9DA9HYUO\nE4kBaxVXnlFALJnidRUyOSgZE3ghxFwhxNNCiKpMjalQ5CrRRJJNh9rQawVnleWRkpK5+bYRH1/h\nsWI36zmnwsXO4350GkF1a3bdNL6eKMd8oXSCUxYLjA1F2g9/ssCXuSwsKrLz8oGWSe93OhXImMBL\nKY9KKW8C3srUmApFrtIejHKgKciSkjxiiRTlbuuoFiT1vbP4hUV2IvEUNe091HeGiCaSwx88Qew6\n5ieWSFHhseCxGbJWYGwoLAYdNqOeaPzkz+jaJUX4Q3G2VquQyYHk1l9QoZgibKnuIBCOs6wsj3Ai\nyfzCkc/e+6jwWJntteIw6dhR6yeZgtau7EXT9IUcFjlMlDpzswjaQD88wJISB+VuCy+805Qz4aa5\nwqQLvBDiTiHEDiHEDlUSWDFVebk3cmNxsQOdRpA/hoJcFoOO2V4rS8vy2NPQiUZkL5pGSsnb9QHc\nFgN2k458e26W4i3KMxFPneyKEULwgaXFtASjbKtVs/gTmXSBl1L+j5RypZRyZX5+/mSfXqEYN93R\nBO/UB6j0pGe5c/NtY3ZnLCi0s7g4j3hScqStm7osuWmCkTg17T3pJxGR/QJjQ5Fu1Xdq6OaKciez\nXGY27G5QvvgTUC4ahWKUHG0NUu8Ps6zMSTwpqfRaxzxWvs3IwkIrVoOWX289xpf//A6XPLqJDb0V\nKCeL/U1BgpEElV4LFqMOsyE3e8bajDrMeg2xxMkirhGCm88uo707xiuHlGegDyXwCsUoeWlfKxJY\nVGxHpxV4rGN3Z2g0guZglHA8STyZ9h+3dEV58Om9kyryrx1Oi2Kp05yVBtujocxlGTTufUmJg0VF\ndp7d00R3RMXFQ2bDJNcIIR4HLhRCPC6EuDtTYysUuYKUkm21Psx6LW6rgQqvFe042+79ZutxBq4N\nhuNJHtt4cFzjjoYdx/yYe7NFi3IswWkgJU7zKTN4SPvibz13FqFYgj/uqs+CZblHxgpNSCkfydRY\nCkWu0hWJc6g5yKIiO7GEpNw9/miT5sDgCU6NneFxjz0SQrEER1t7mF9gQ6vR4DTnVoLTQJwW/WBu\neCA9u796cSEb321h1VwPCwqHzyyezigXjUIxCvY1BOkMx1lUbEcI8FjHL4YlzsFdIkNtzzQ17T20\ndUeZk29FpxHYTblRYGwobEYdJp1myNIO/3BWCfk2Iz95vSbnau1PNkrgFYpR8PKBFgAq3VYK7caM\ndDu675qFmPQn/xT1WsEXr14w7rFHwuYDaf/7LJeFojwTmnG6nCYaIQSl7sH98ABGvZZPXzKbQCjO\nL7ccy8m+t5OFEniFYhRsr/WRZ9ZjNWqo9Iw9euZEblxRyrduOgt3b0lcvUbwoWWlXLzAm5Hxh2Nr\nTQcGrYZ8uyHnF1j7KM0zExnED9/HHK+Nm84uZedxP8+83TiJluUWSuAVihHSHYlztK2HRUV2EBq8\nGUwGunFFKb9ffSHvm+8lJdMJVPW+iffBh2IJDjYHmV9gQ6PR4Lbltv+9D5f11Lo0A3n/4kIunufl\nuT1N/H2GlhSesgJ/tK1bpSUrJpW9DQG6ownm5lvRazJfjKsoz8ziYjtJKan19VA9Cd/xo63dtAaj\nLCiyI8jdBKeB2Iw6zDrtaUssCyH42AXlLJ/l5Kltx3luT+OMc9dMWYE/2BykKxLPthmKGURfrZZS\np5lStznjvmqbUceyWU6cFj176gKE4yn8oVhGzzGQTQfTM9tKjwWPzZhzBcaGQgjBrNP44fvQaTSs\nvnQOF8xxs2F3Iz/YfHRGxchPjb/mIHRHEnR0T+yXX6E4kR21fmxGHXaTjrIJinCZl2/njCIH7zQG\nSCSTNHZOXI14KSVbq30YdRrcVgOz3FPD/95HidNMND58WQKdRsOnLprNP62cxd6GAF/asJeX9rWc\nUpVyOjJlBV4iafBPTpywQhFLpDjUEmRBoQ2hEbjHUFxsJBQ5TSwpcZBISep8YQ63BSfMrdAdTXC4\ntZv5hen672MpmJZNXFbDkPHwAxFCcPXiQr7ygcVUeCz874467vvTHn619Rh7GwKEYtNzVp/bAa/D\n0BAIk0rJnA/rUkx9DrcE8YfiXJlvw6zTYp+gZtQOk56lpXnYTTr2NASYU2AjEI73FtnKLIdbgrQF\no1wyPx2tk2eZGv73PmxGHRajlmgiiVE3snDVUpeZe65awNG2Hv5+oJWt1R39tWuKHCZme63Mcpsp\nd1uY5bKctr/uVGBKWx9LpgiE4+k7uUIxgWyp7gCgJM9EidM8oc2o5xfaWFRkZ099gBuWFdPYGZ4Q\ngf/b/j7/uxW3RT9ikcwlyl0WjrZ2Y7SN3HYhBPMKbMwrsBFLpDjS2k11eze17SH2NXX1/60hncg2\nJ9/KkuI8ls9yYsvxJLCBTC1rByCAju6oEnjFhLPzmB+tRuCy6ClxTmytlhKnmcXFDrbX+mn0hzli\n6eGMYkdGbyqJZIodx3yY9BpcFgOlGSi5kA2KnWYONAfHfLxBp2FxiYPFJY7+bYFwnDpfiDp/iOO+\nEIdautle60f7lmB5mZOrFhcwfwTN1XOBKS3wFr2Whs4w82Z4vQnFxCKl5EBzkHK3Gb1Oi2sc1SNH\nQp5Zz5lleVgMWvY2dFHusdIVTmTUhfLUtuPsqPWTkvDYiwf5wtXzWVbmzNj4k4XHakDK9N8oUzfA\nPLOevNI8zizNA9JjH/eF2Frj440j7ew87mdxsYNbziljVo7fGKfsIiuA1aijKRBR8fCKCaUzFKPe\nH6LSY0WvFRPmf+9DCMGCgrSbZnddJymZoqEzlLHxN1Q18PBz+/srWAbCcb71woFJr0GfCUx6LW6r\nnsgIomnGihCCCo+Vf1o5i8duPot/XFnGsY4evvGXffxpV/1pY/GzzZQWeK0QJFIpFQ+vmFB21weI\nJyUlTjMlzszHvw9GqcvC4mIH4XiS5s4oh1u7MxZN89jGg8QGiFIknprU8sSZpNxtJRidHA0w6rW8\nf3ER3/zwUlbN9fLCO82se+EAbcHs9dI9HVPaRZNG4O+JTcgilGLmsqGqgcc2HqSxM9wfSVHoMFI8\nSbXS3RYDi0scmHQa9jYEKHaa6AxlJqBgqDLEk1WeONMU5hnZXTe5T/FWo47bV1WyfJaTn71Rwzf+\nso//uGJezvnmp/QMHsCk09AQmJpfTEVusqGqgQef3ktDZxgJ/dmSxzt6cE3SREKjESwotLOwyE5V\nXSdCwHFfZhpyD9VQe7LKE2cal8WAViNIZaEMwfJZTh76wGLsRh3ffukQu+s6J92G0zHlBd5m1NHU\nGZlxNSYUE8djGw8SHiTL8W/72ya1Vku528KiYjvd0XTW9qGWzNSmWVnhOmWbWa/lvmsWjnvsbKDX\naijOM2et9nu+3cgD1y2i1GnmB5uP8Orh3OkJO+UFXqfVEIknCc7wwv6KzDGUq6IzHJ/UWi0em5El\nxXnotYK36wJE4knausfn6w3FEv1PJM7em1Wp08y6m5Zy44rScducLcrdFnpi2Ss9YDfpuff9C1lS\n7OCXW47ljMhPAx88gCAQiuMwTa1MPEVuUuI00zCIyA/l2pgotBrBgiI7Cwvt7Dzu5/1LCqlu66bQ\nMfZ1gKbOCAea0yUXPrmqkpUVbhYW5ZbfeCx47casP8Wb9FruunweP9h0hF9tOYZRp+H82Z6s2jTl\nZ/AARp2G5i7lh1dkhvuuWYh5QKcmnUZw1+VzJ92WCo+FxSUOAuE4zYEI1e09RMZRJOvVw620BqOc\nXe4iJSUFk3zTmigcJh1Wo45oIrsFxPRaDf922VzmF9r46es1VB33Z9WeaSHwVqOWev/EVd1TzCxu\nXFHKupuWUtq76KgRcOOKEv5x5axJtyXfZmRJqQOzXstbNb500k3H2GLiA6E4bx5Jp+EvLc3DpNNO\nmfrvwyGEoNJjJZgDpYCNOi2fu2I+lR4r61+t5kBzV9ZsmRYCb9Rp6YnGCWfRB6eYXty4opSXv3gp\ndpOOcypcrJrrxWKYfI+mTqthQaGDpaV57Drux6zXsq+pa0yLrcd8PexrClLpsaDXaih3W6ZVob4S\np5l4MjeCLUx6LZ+7cj4FDiPf33RkzDfl8TItBD6NoDOs6sMrMsfh1iDBSIJSp5micfi9x8tsj5Wl\npXlEEyn2NQbpCsdpHWViTTIl2Xq0g4bOMOdUuIglU5TleJr9aPHYDGg15Exmu82o4+4rF2DR6/jO\ny4eykgw1bQReKwStXcpNo8gc26t9ABTlmSiapASnwfDaDMwpsJBvN/Lq4TbsJh1v1/lHtajY4A+x\nrTZ9PSvKXYDEM82K9Om1GsqclpyKqHNbDdx91XySKcm3/3aIQHhys+6njcBbjdoJ7X6jmHnsOJ6u\nIFnsMGY1U1qn1TC/wM65FS4Ot3bTFU7Q0hUdcchkKiXZXdfJ7rpOFhTasBq0FOWZMemnXnng4ajw\nWnLOVVviNPO5K+cTCMX57suHx7VIPlqmjcCb9Vo6emI5XfhHMbU40BRklsuMTqvFkeU64JVeK2eV\n5aHTCDYfasVq1PF2XeeIZvEtwQhv1wVo745x0Vwv3bEkc73WSbB68ukLZc12yORA5ubbWH3pHOr9\nIX6w+QiJ1OTo1LQR+L5SoZ0hVXgsl0gkU1kPXRsLwUicen+YcrcFt9WQ9WbUXqsRr93IinInW6o7\n0GsFjZ2RYRfvEskUO2r9vNsYwKjTcHa5EyGhMIsup4nEYtDhtRuymvQ0FGeVObl9VSX7m4L8aWfD\npJRWmCaJTmkE4OuJTXpCiuJUgpE4u477efbtJl7a10IgHKc4z8SaaxdNiYzJ3XWdxJIpirPsf+9D\noxEsKnJw/mw322v9/P1AK1edUci2Wh+FeaYh3S2HW4PU+0PsPO7nwjkekjKdFJSNiKDJYl6+ja01\nPmw52G5v1VwvXeEET1fVc6ApSLl7Yp+kps0MHsBi0E7ZinjTiY7uKM/taeL5PU383+6G/oWlpkCE\nB/60Z0rUHd9ek16QLHGacmbCMMttochhZmlpHn/b34oAEqkUbx5pJzlI5EhHd5SdtZ28XRcgkZS8\nf0kRwUiceQXT0z3TR5HTDLnloTmJa5YU8u9XzDupi9REMc0EXkdzl2oAkk2CkTgv72/FrNPy0v5W\nYgPikiOJFI/89UCWrBs5VXWdWAxa3FYjjhxJBsoz6ynMM3H5wny6own+frCVo609fOH3bzP3S8+z\nat3L/TfPju4oL+1vQacVvHq4jRXlTgrsRoQQlLmmV3jkQGxGHW6bnlAsd6JpTkQIQYF9cp4Kc+8Z\nZhxoNYJkKkUwktn2ZoqRkUpJthxNZ0paDFp8PYPnJTQFIiSSqaz7tYdCSsnhlu7eDk4abDnkzlhc\n4qApEGZZWR4bqhrQaER/ck9jIML9f9rD/uYuSp1m7EYdL+1rIRRLct2ZxXSF45S7LdMyemYg8/Lt\nbKv1TWtX1EjI6C9MCFEshFgvhHhMCLFOCJGVT9cfys3uKtOd6vYemgMR/KEYX3tu35D75Zn1vNuU\nvfTt4WjtitDSFWGWy0yBw5RT2Z5FDhNmvZabzi4lKTklczOWSPG/2+socpjoiiTY+G4Lq+Z6mO21\nEo4nmV9oy5Llk0ux0wQy96JpJptMT6G+AjwopbwPeAX4WIbHHxajTktTlxL4ySYST7Kj1kcwEufb\nLx0iEk9y+cJ89NqTxVGnEdx0dgl76wNZq989HNtq/UjSkSZFjtzwv/eh1QjOLHWgPc1NpzMUJ55I\n8fM3ajDpNdxyThnReBKzQTtproFsYzfpyXcY6YnmXjTNZJIxgRdCaACtlNLXu+lFYFWmxh8pVoOO\nRn926j7MZKrbumkLRvnvzUdxmPR86foz+Oj5FXzywkrcvRmTGpGOdDqjKA+NgH2NuTmL39Gb8Vnm\nMuO25pbAA8zJt6HVaHAN4YZ0WfR8f/MRjvlC3L6qErtJjy8U46xS52lvDNONhYW2nMpqzQaZnMF7\ngBYhxDwhxF4pZQo4JZpfCHGnEGKHEGJHW1vmi+IbdBrCsVTOLrBMRyLxJLvrOnnhnWYSKcndV83v\nr1J4wRwPj958Fj/5xEoevvFMNBrBz96owW0xcKC5Kycbpu+pD+C1GbAYtDjMuefDNeq0nFWWx5WL\nC095QtII6Ikm2N8U5PZVlawodxFPptBrNVR4p/fi6kCK8swIQVZa+eUKmRR4SXqC1gCsO2HbyTtJ\n+T9SypVSypX5+fkZPP0JCJXwNJnUtHezu66TfU1dfHhFaX9DipSUROLJ/tTsAruJfzp3Fgeag7x+\npB2dRnC4JZhN008hlZIcbUsvsJp02pxdpJubb+PcCjf/fF55/xOSViMw6TScUezgS9cv4qK5XgA6\nQjGWlORh1E3/xdUTMem1VHgsdE1y/ZdcIpPfXh9QIKUMA0/1umyyEibRV3hsqjYRnkokU5K36zp5\ncV8LFR4LVywsAKAzFCMUS+KyGpASGgNh7EYd75vnZWt1B8+83cjKShcHm4MsKcnLmciOI63ddEUS\nlLnMFDlz119t0ms5r9JFJJ7g0ZvPGnK/cCyJSadhQdHMWFwdyPwCO7XtPTizbUiWyJgA97pk4kKI\nvh5V1wJvZGr80ZAuPKYSniaDlq4Ibx7toDMU58PLS9FoBB09UUwGLTcsK+GDy0r4h+UlXHdmMZJ0\nX9Obzy4jGEmw6WAbKSmpbe/J9mX001dxschhpCjHFyQrPFaK88z4egYPKpBS4gtFOX+2Z8bN3vso\nsBsxG7REJ7HAVy6R6Rn2N4D/FEI8ClwE/CbD448Is16LLxQnllCFxyaavQ2dvH64g0qPhSUlDjpD\nMUx6LVcuKux3HUC6CNT7lxSh0wgKemuqbHy3GZNWy7uNgZxJTtte60MrBEVOM3lZrCA5EjQawUXz\nvGg1GoID1jKklDR1RVhQaKfMNXOfZDUaweJix6SX6c0VMirwUspmKeVqKeX9UsovSymzctvsLzym\nGoBMKMFInJf3teILxbjhrBKSKUkknuKyhQWYDafOGG1GHZcsSGdhXrekiEg8xVu1PkKxFO0jLH07\n0bzb2EWpy4xOo8nJBdaBWI06rlhUQDIlaQ1GiCaShGIJGgMRKj0Wzpvt6f89zFQqPFZSMncagUwm\nuZlKmAEE4O+ZmXftyWBDVQNXPvEKv99Zj0ZAOJagrTvK2RXO0/b59NiMnFPh4lBLEJ1G8Ied9Tzx\n4kF+/kbNJFo/OJF4kuMdISo9Fhxm3ZRxa7isBm5YVsKCQjuJVDrW4ZL5Xi6alz+jwiKHwmrUMafA\nij808yZ801bgLQYtDcoPPyFsqGrgwaf39LeNS0n45dZjHGwJsqDQPuzxB5qCPPN2Y68Ypf3yP3m9\nhj/sqJtQu4ejr4JkSZZb9I0Fk17Lyko3H1peyj8sL2F2vk2J+wksLLQTnYG9IqatwFsNOpoD4UGr\n7CnGx2MbDxKOn/xjiSclL+1rGVF9mSdeOnRKin08KXls48GM2jlattWk6+gU5RkpyJEKkorM4LEZ\nKbQbZ1zI5LQVeI1GkJLMuD/oZDBUhFLrCEtEDHl8FpoSn8iuY52Y9Vo81uy26FNMDMtmueieYZmt\n01bg+5iJfreJpniI+PCR5h0MtV+eWX9KNMhkcrAlyGyvFY0Q2E2qGul0o9BhJN9uzOp3bLKZ1gJv\n1is//ESw+pI5DAzMMOk13HfNwhEdf981CzEPkth09RkF1GepjlBrV4TmQIQKjwWPzaj819MQIQQr\nyl0EIzNnFj+tBd5q0NLUGZnxJUMzyYaqBr778hFO/Ei9NgPfuumsEbfiu3FFKetuWkqp04wgvSAO\nUOAwcailOyt/ry3VHUigOM805BOKYupT6DBS7DTROUOe7Ke1wOu0GmLJ1IyvKJcp+qJnOk5o5KHX\nCj5/1fxR91m9cUUpbzxwBQcfvo4Hrl2EWa9ld10nXZFEVpJS3qr2IYCSPDNem1pgna4IITinwk0o\nlpwRRcimtcBDutpZp4qHzwhDRc/8aPPRMY9p0Gk4o8TO4hIHVcc7SaVSWSkzsbuuk6I8EyaD9rRx\n/Iqpj9tqYGGxPWeS6yaSaS/wJp2GxoDyw2eCoYS3sTMyrnHneG0sKXEQjiep84Un3U0Tiyepbutm\nbr4NvVZgHSQLVzG9WFbmRKvR9Fc6na5Me4G3GnQ0qAYgGWG80TND4bYaOKfchd2oo6quk2AkPqlu\nmt31nUQSKWa50glOMz21fyZg0mu5YLabjp7YtF6jm/YCb9BpCMdTMy7+dSL47GVzGRhcYtZrRxw9\nMxRCCJaUOlhS4uDtuk7iydSkRj/1NQovyjNRnDdzC3PNNMo9FuYV2Gibxq6aaS/wAEjw98yMVfOJ\nZGlpHiadpr+LUIHdyLqblo56gXUwSpxmzipzkkhJatp7ONI6eW6ancf8WAxa3FYDLqtKcJoppBdc\nXZgM2mkbGz8lBf7bLx3i/3Y3jnh/g06j6sOPEyklbxztIBRPceu55Tx845m8+IVLMiLuABaDjvNn\nu3BbDFQd7yQYSdAVnvinLikl+5uCzMu3IYRQC6wzDJNey2ULCgjFk9OyZvyUFPi2YITtx/zER1g8\nyGbUZS2BZrrQFU6w65gfgDOK7Jj1moyL4YIiO0tKHbzT2MWjfz3A8q+/yEXf+jsbqhoyep4TqfOH\naOuOUuGx4DTrMeim5E9CMQ7cVgOXLsinvSc2Yk2ZKkzJb/PViwuJJVIcHGE/T+WHHz8tXREONgep\n9FjQaASzvbaML0YWOsyYegW2K5JAAg2dYR58eu+EifybR9L+95I8E0V5KsFpplLmsnDRPA8tXRES\n00jkp6TAr5rrxaDV8HZd58gPUn74cVFV56feH2bZLCfxVIrSCegSZNBp2HX81L9pOJ6csEqTW6s7\n0Ij0zaVwipUIVmSWeQV2LpjjobkrMm1m8lNS4E16LQsKbbxdHxhxNppRr6Fe+eHHRCiWYOtRHxI4\nqyQPrRAntePLJL4hbsITsYYipWRvQ4AylwWDXuC0KP/7TGdRsYP3LcinLRidFjHyU1LgARaXOOgM\nxznWMTLfus2oo94XmtYxrxNFWzDKkbZu8sx6nBY9JU4z+hHUfR8LExVrPxj+nhjHfSHm5lsxaLXY\njB27sBgAAB86SURBVLnfok8x8czNt3HV4gK6JjkfYyKYsgK/qMiORqRTzEeCXqshmkhNSmTGdKOm\ntYejbd3pbNNEilkuy4Sd6/5rFmEYcPMYTaXK0bC1xkc8KSl3Wyh2qgQnxXuUOC1cv7QYnVbQ2jV1\nCxZOWYG3GnXMK7BRVecf1XEzof5EJoknU2w75iMUS7K42IGUEu8Edju6cUUpX/rAIoy9i60Ok47P\nXzn6YmYj4ZVDbUD66aBYLbAqBuC0GLj2zCLKvVYaA1PTLz9lBR5geZmTxs4IrcGR1UIx67XUqXDJ\nUdHRHeNQb7TS/AIbZoMWh2liXRkfPb+CT79vNgDXLy2ekCcGKSW7jvkpdZqwGnW4raqCpOJUjDot\nF831cNE8Dx09sSnnspnaAj/LCYzcTWMz6mgMhKdVGNREU+8PUd3WwyyXGSEEFR7LhLsy9FoNF8xx\n47Ea2FsfwB+O0ZXhTMP27ii1HT0sLEy7+lSCk2IohBDMK7Bzw1nFGHUaWroiU6bU8JQWeK/NSKnT\nPGKB12oEqST4Zkix//GSSkkONHdxzBdiSUkesWSKEufE+d9PZE5+uoTw/uYuIrFExgvGbTnSQTwp\nqfBYKbCrDk6K4XFaDFxz5v/f3p0Ht32eBx7/vj/cNwgQBG9Rog5K1GnJ8hEntpXEdtzGTpx0M9PZ\nTbczOXa33c62abbObLe7nnY3bppk0t3sts2m7aab1NmZ1M4mzeXYjpvYsSRblmVaJyVR4k2CBAES\nAHH+3v0DJE1KpAyQIHHw/cxobIEA+P5E4sGL533f52lkR9DFSDRJKlv5u2yqOsADHGrz0jseK7iW\nhKbBWFTl4QsxlUhzcTRGTpd0N7tBgm+DmlEHXBb2t3rQJfSFZukdi5d0oeuFi+MI8rt22nyOkj2v\nUttMBo2jW33cuzNAZDZT8TVsqj7AH2z3IiW8ORgt6P5uq4lrk/F1HlVtGJ1OcjkUw2zQaK2z4baZ\nsG1QrXSTQeOuuTTNmaEI0RJuWcvkdE4PRGj32bGbjfidqsCYUpyOegcP721CCpiIV+6EseoD/Baf\nnTq7qeA0jdVkIJJIE1dlC97RlfE4V0MxdgSdpLI6bb6NLaW7NeCiu9nN+ZFpUuks18OlSdNcn0gw\nEE6wp9mNALwq/66sQp3DzMN7m/DbzYxEZytyK2XVB3ghBAfbvJwdmSadLXDxVAhCBe682axmkhn6\nw3HGplN0N7vJ5vQNr9XS4LKwby5N8+Xnenn0qy9z95PPr7kuzY/PjqBL6Aw4CLqtGNfp0JZS+6wm\nA/d1NdAZcDIcrbzF15r4zT7Y5iWd1Tk3Ml3Q/e0mA30TarvkrYxFk1wJ5VNZexrdIAR1G5R/n2cy\naOT0/Jt2Ip1f0BqOJNdUfEzXJS/1TmAxagTcFtp8G7NorNSu/K4vP93Nboajs+h65QT5mgjwu4Iu\nbCZDwWkal9XIcGS28Bn/JnRlIs61iTgemynfCMNuwmra+F6lz5y+ue7/WoqPTcRSXBybYXejG6MQ\n1Kv8u1ICmpZvHnKwzctwNEmuQoJ8yQK8EKJTCPG0EOJ0qZ6zUEaDxt4WN2cGIwW9e2pCIKVUp1pX\nMJvOMRpNcmlshu5mN/F0jtZ1qB5ZiPHp5X9Gqy0+9sqVCaYSGbpb3Bg0bcM/lSi1SwjBgVYvh9q9\njE4nK2ImX7IAL6W8IqV8DDhRqucsxsE2LzPJLFcmYgXd32w0lGzRrtaMzyQZjSSJz5UnyOk6DWUq\npbtSkbHVFB/L6ZIf9IwigO0BB60+G5ra/66UkBCC/a0e9rV4GJmeLXtOviZSNJDvF2rQRMFpGrfN\nyLWJmDrVuoy+iTjXwvn8++4mN5KNz7/P++yDuxaagMwzGQS//8DOop/rm8ev8dz5MSTwlecvc2Gk\nsIYxilIMIQSH2r3safaUfXfNhgd4IcSnhBCvCSFeC4VCJXteu9nIrqCr4ABv1DQyOVnTHdVXI5XN\nMRSZ5UooRludDYtRw20zliX/DvniY//1w3vx2PL1byxGjQ8eaOauzvqinue7p4f4kx+cZ/5Tc3Q2\nwxefvbiu7QCVzUsIweH2OnY0uBhdIc24EQoK8EKIx4UQL67w50vFfEMp5deklEeklEcCgcDqRr2C\ng21exqZTjEQLy8/aTAauhgpL6WwWoZkUs+kcV0Jxups9xFPZdS0PXIjHDrfx179xOwfb8p/Sbt/i\no2eosINt877w4wtkcktnUsmMvm6dohRF0wRHt/po8VoLLohY8jEUcicp5ZNSyvtW+POZ9R5koYot\nPua2mrg+mVC7aRa5GoozHJldKE+Q0SXBCiilu8Xv4HB7HYl0jktjM4xEZ1fs/rSckejyL7D16BSl\nKPOMBo137ainzm5msgwnXmsmBw/57ujtPntRxcdyOoxNqxc5QDqrMxBOcG0igdmgsb3BiZSSugpo\nZed3mNnT7KbBZeHFSyEsBo0zg+/8c/7u6SHufvJ5VsqCrkenKEVZzGI0cO+uAGajYcPLDZdym+Qf\nCCG+CNwlhPiiEOLfleq5i3GozcvVULzgf0inxaAW2+aMzySRwLnRaXYEnehS4rAasZvL38pO0wRd\nTW7u2OajbyLORCzFwGSCsemVP/p+9/QQn3u6h+HI8vexmQzr0ilKUW5kNxs51tVAVpfENrBMSim3\nSf6plPL3pZQH5v77lVI9dzEOtnuRFFcjfnQ6VfJ649XoynicZCa/B7672U08laOtTPvfl9Pus3Ow\n1YvTYuTZc2O4rSZO9oVX3An1Zz+5yOwKjZNbvDY+/9i+dekUpSjL8dhMvG93A/F0ltQGNfSuqRQN\nQKvXRtBt4WRfuKD7CyEwGuDaxOauMJnM5BiYStA/dzagu8lDOqvT6K6cAO+ymtgWcHB3p58zg1Ei\ns2kiifSKqZqV8usCePnxYyq4KxvO77RwbFfDhtU/qrkAL4Tgjq1+Lo3NFLwI57WZOT8yvW49F3Vd\nMhVPMxpNMhpNMp3MVMQpt8XGppMg4dzwNF6biWavFSkk3grIvy+2s9HNbVu82EwGvvP6IEGXlZ7B\n6LJv0IEVesc2e8u/aKxsXk1eGw91BzfkbEn5k6vr4I6tPr53ZphXr4V5sLvxHe9vMmikszr9kwk6\nG5wlG0cqm+PKeIyeoSiZnETAwmKf1aSxu8lNZ8BZtj3mi10ancFq0jg7PM3hLXVkdYnNaMBpqaxf\nkUa3lXqnhYe6gzzzxjDnRvLrBS9eCnFoNkNngxNNQF8ozj07/Py/N0aW1AWxGDU++2BXGa9AUSDo\n2ZhPxpX16i2RoNtKh9/Oib7CAjxAnT3fWKKj3lGS9m1j00l+0RsildHxOcyYbvhIlsrmeKM/wpmB\nKIe3eNnR4CrbsfmZZIbR6STTsxlmMzn2teT3vzd5bevef7VYBk2wr8XDzGyGl65M8tTJfv7wV/bQ\n5LbSMxSlZyi6cHLw6BYf3z8zgtAEWV3isZn43Ae6VGpG2TRqMsAD3LnNz7dfHWA4MlvQVjiryUA4\nkmZoKkG7f20t3C6OTnOiL4zXZsJrW/ox7PjVSZ4+PUQ4nsbnMPPogSayev7Tw93b63GUYcY8EE6g\nCegZmsYgBHua3ESSaZorYP/7cjrqHZy6HuHjd7Tz5ed7+cYr1/j0e7bRuKheji4l/+NnlwF44pFu\nrCYDPoeJ+7uCZRq1omy8msvBz7u9w4cQFLzYCvlZ/GvXp1adi5dS8sbAFMevTtLgtCzZXiil5PjV\nSf7ulesLawPheJpvnRigfzLBVCLND3tGCM1s7GGIfGPtGbw2Mz1DUXYEnfm2fBJ8juVz2OVmMRro\nbnbhd1r48MEWXrs+xf85fn3h55bTJX/78jXODEb58KEWgm4r8XSW7mZPmUeuKBurZmfwHpuJ3Y1u\nTvSFefRgc0GpBpvZQCSaoXdshj1FBgMpJaf7I7w5FKHZna9SOJPM8PyFcd4cjDIwlWC5mkPpnM7T\np4f4wkf2E09l+clboxzbHaDZuzHlASZiKWKpLFmjgaHILB+9rZWsrmM2aLislfvrsavRzbmRGY51\nNTCbyfGjt0Y5PzrD9oCTy+MxQrEUjx5s5v27g8wkMzS4LCsuuipKrarZGTzkF1tDsRRXi9gCWe80\n83p/pKgTZzcGdwT89NwYjz/dww/eHMFmMvDgnpXXAuZn9A6LEa/dxHPnxhmc2phSxhfHZrCZDLw1\nV9tlX6uHRCpHo8da0aV0rSYDh9vrmEqkafHacFqMhGZSvHJ1cuFI+C96Jzh+dZLpZJYDbd6KW09Q\nlPVW0wH+tvY6TAbBL69MFvwYk0HDatT4RW+ooFSNri8N7umczn9/4TL/97UBdgVdPPFIN599cBcf\nPdyKz7H8tqjFpQCsJgN+h5mfXRhnOLK+QT6WynJ9Mt+1qWcois9hptljJZHJ0lIFR/i3BRz0jsf4\nxivXlpwOnN80E46n+bvj1xmKJJbk5xVls6jpAG8zG7i9w8fxq5Mkizg55rWbiSTSnOwL37L1Vjan\nc6Jvkp6hKM1uG7FUli/85CJnh6P8+tF2/u2x7UsWeB871IJ5mQMOdpNhyZuJxWSgzm7mhfOhdc3J\nXw3F0IQgp0vOjUyzr8WDEAIB+JyVn84wGjR+em7spiqRi2VyMr+TRs3elU2opgM8wH07A6SyOsev\nFj6LBwi6rFwJxXj5cojZ9M1vDtFEhp+eG+PyeJwmj5VEJseXfnqJ0WiS375/O8e6Gm4KKndu8/Px\nu7YszOR9DjPv3l7PUDTJ11/qW9L9xWoy4LYZee78GNFE6csopLI5zg1PU2c3c3k8Riqrs6/Fg65L\nhBB4bJV1wGkloytUiSz2PopSiyp3Fa1EttY7aKuz8eKlEPfuDBQ8kxNC0OS2MhSZZfD00MKujZwu\n6Q8nuDYR59zIND85O0Y4nsao5WfCv/u+nexpdt/0fJmcjq5LjnTUcec2/5KvBd1WvvP6ID9+a5SH\n9zUt3G43G8nmJM9fGOOhvY0lLfrVF4qTyemYDBpvDkYxaoKuRhfxdJZGj60kZwE2QrPXxtA7lPxV\nFSOVzarmZ/BCCO7f1cDg1CwXx4qrGimEIOC04rWZODc8w4sXx/lF7wSj0STXJuL8w6mhhQXSrC4x\naGJJ0TJdzzf2HpmeJZ7KoiOJJDKMRPN/n/dgd5CjHT6eOT3E+ZHpJWNw20xkczr/dDFUsrr16azO\nmcEIfoclv0A8MEVXkwuryUAik6O1igLiZx/che0WJ4FVxUhlM6v5AA/51IjLauTHb42u6vFmo0bA\nZaHRbaPRbaXObuaZN4ZJ37AIm9UlT8+1gIulsoxOJ+kMOHnkQAsfOdzKBw+08GtH2ji2O0hWl4Ri\n+dSBEILfuGsLQbeVv3m5b0nwh/x+9Kl4ml9embjlmkChLodmSGclZqPGwNQsE7E0t7XXASAl+Jzl\n6b+6Gh861MLnH9tHi9eGIL9g7bWZEKiKkYpS8ykayAfo9+0O8szpIQamEiVpQbdSIbNwPM1kPIVR\n0/jAvqab9l4bNEGL18av7G/ipd4QoViSgNOKxWTgE/ds5fM/usDfn+znk+/etuRxAZeFgXCCU9en\nuL2jbtWLhvFUljf6I9TPBfHX+6cQAg62etFlvl6Ot0ry7/M+dKhFBXFFWcammMFDfrHVYtT4xzdH\nSvJ87hUOAXltJpwWEx/Y13jLgzVWk4F7dgRwW81MJfJvFh31Dh7e18iJvvDCvvR5QgiCbivnRqJF\n9yNd7M3BCAIWauOc7o+wo8GJ22YikcoRdFs2rJSpoijra9O8kh0WIw/sCXLq+hRXJ9bWaDscTy+7\nR95kEHzoUDPv3d1Q0IKo1ZRv5ZXV5UIDgIf3NRF0W/jWif6bcu6aEDS5bbx+fYpzw8UH+YFwgktj\nM/jntkCORpMMRWYX0jPxTJY239rq8CiKUjk2TYAHeLC7EZfVyHdODS5UHCxWIp3lv73QiyS/r31+\ny2Od3cQ/u72Nf/9QV1Hlf50WI3dv8zMRTyGlxGTQ+Bd3biEUS/GPPcM33d+gCRo9Vk5eC3N2OFrw\ndcwkM7x0eQK/w4I2l9450TeJAI5seTv/7q+i/LuiKLe2KXLw86wmA48caOZbJ/o53hfmrhu2K76T\nTE7nf754hZFIkt9573a6mz08vK+JdFYnnEjzq/ubVrWVsd1vZ2u9g5FIEr/TQlejm7u2+fnJ2THu\n3Oq/aZufUdNodFt5tW+K2XSOg23eW6ZVEuksL1wYx6iJhTcfKSUn+sJ0Nbrw2s3oukQT1Zd/VxRl\nZZtqBg9w744AnQEHT53sJ5IorOMT5MvP/u3L17gwOsO/vLtjoTKhlJJQLMXdnX68q+zQIoTgYHsd\nGV2S1fNpmV873IrFqPHNE9eXnaUbNY1mj5VzI9M8d35sxWuZjKV49uwYqUxuSQeZa5MJxmdS3LE1\n/yYXT2dp8thU/l1RasimezVrmuA3795KJqfz9Zf6VmzYvJguJU+d7OfktTAfua2FuzrfnvlPxtNs\nq3ewtX5tuWu31cT+Vg8TsXygdttMfPRwK5fGYvxyhVO4miZo9tiIJbN8/8wIL/WGGAgnCM2kGI7M\ncvzqJD/sGUXX5U2lf0/0TWLUBLdt8QL5AF9JDbYVRVm7TRfgARo9Vj5+ZwcXRmf4xivXl5QIuFEm\np/PXL/Xxs4shHuwO8tCiDlGpbA4JHF7DtsXFdgZdGDWxsIB7z/Z6OgMOvnNqcEkxrRt57WaCbgsj\n0ST/dGmcZ8+O8sKFcfonEzS4LLhvSLtkcjqvXJnkYJt3IaUkpaiK+jOKohRuUwZ4gLs6/Tx6sJlX\nrk7y1Rcuk0jfHEAHwgn+yw/Pc6IvzGOHWvjoba1LAvlkPM3RDl/JSghYTQb2t3mYiOULjGlC8M/v\n2EIsleWZuQNUK9GEoM5uptFtI+i20ui24nOYly058Nr1KeLpHPfuDADM1X8XKv+uKDVmUy2y3uhX\n9zXhNBv59qsDPP50D+/aXk9bnY1kRufscJQzg1FcViO/c2w7+1u9Sx47k8zgc5jXnJq50faAi57B\n6EKdmDafnfd2NfD8+XHetd3Ptvq1NwX/+aUQAZeFXY0uAGLJLC0+W0XXf1cUpXibOsALIbi/q4Ft\nAQc/fGuU586PLXRd8thMfHB/E+/dHcR5Q59UKSXTySwf2NtY8qBoNmrsa/Xw+vXIQg3zRw+08Nq1\nKb55vJ8/fHj3mr7n4FSC3vEYH7mtZWG7ZDKjl+R0r6IolaVqA7zdbCSV1fP9Q9doi9/Bv763c2G7\no8Wo5euZrJBXn0pkaPfbaVinJhLb6p280R8lm9MxGjRsZgMfu72Nv/r5VV68FOJYV8Oqn/tHb41i\nMWq8e0dgye31Kv+uKDWnanPwXY0uosnCtzkWwmzUFoqJrRTcdSlJZnIcvCFlU0pWU76p9OSirY9H\nttTR3eTmmdNDRW3vXCw0k+LVa2HeszOw8KkkmcnhshlxWKr2vV5RlBVUbYBvrbMDAr0E1RWLMRVP\n09ngpG6F9nulsiPoQkoWrk8Iwa/f0U4mp/OtE/2rOon747OjCCF4YE9w4baZZJYOv0rPKEotqtoA\nbzMb6PDbiSZL3+1oJbqUpHOSvXOHnNaT3WxkR9BJeNFsPei28thtLZweiPDy5eI6VA1OJfh5b4j3\n7KhfcuApp0uaqqj+u6IohavaAA/5fePJTGmaYBRiKp5ma70dj31jthPuCrrI5PQls/X37Q7S1eji\nqVf7GZq6dSejeVJKnjo5gN1k4NGDb5fVzeo6BgP4HSr/rii1qKoDfL3TgsNqKKqh9mrlZ+86e1vW\nf/Y+z2s301pnYzr59h59TQg+cc9WrCYDX/3Z5VsegJr3894JLo7N8KGDLUt2BMWSWdp99qppz6co\nSnFKFuCFEB8XQjwphPiyEOI/lep5b0XTBHubPERn1z9NE0lk6Kh3rLrezGrtafYQv+EQltdu5t/c\n18lUIs2fP9+77CGteX0TcZ462c/eZjf37lq6c2Y2o9OuygMrSs0qSYAXQpiBYSnl41LK3wM0IcTh\nUjz3O2nz5RcI13OxVUpJMptbKDC2kRpcFnx2801t/DoDTj79nm30hxN88dlLjM8kb3ps7/gMf/58\nLx6biU/cs21h3zvkP5EIIW/ZlERRlOpWkgAvpUxLKZ9bdFMPUFwt3lWymQ1sCzgWuiKth8hshvY6\n+0Lt940khGBfq2dJM+95h9rr+K37OgnNpHji++d4+vQgV0Ixesdn+Par/Xzp2Us4zAZ+7/07cd7Q\ngSqWzNLssRVVu15RlOqyXpuf3w380XJfEEJ8CvgUQHt7e0m+2c6gi8vja+vStBIpJbOZHHtbN372\nPq/Fa8NmNpDK5LDcEJD3t3p54pFu/v5kPz96a5Qf9uQbixuE4OhWHx870nZTcId89cjDHXUbMn5F\nUcqjoAAvhHgceGiFL5+SUn5m0X0fAHqklMv2lJNSfg34GsCRI0dKklfxOy3UOy3Ektllg9laRGcz\ntHptZT3paTRo7G/xcuJamKZlZtw+h5nfvn8707MZroRiGA0abXW2FdcL8umZfI9XRVFqV0HRUEr5\nJPDkO91PCHEHcIeU8o/XOrBi7W3x8LML4yUN8FJKEpkc97Wt36nVQm2pt3Oqf2qhCNly3DYTh9rf\neVY+k8zSWqfSM4pS60q5i6Yb+BjwJ6V6zmI0e204bcaSbpmMzGZo89orok6LxWhgb7NnycGn1Uqk\ns+wIukowKkVRKlmpdtF4gO8BEvj83HbJT5TiuQtl0AQHWrwlW2ydz73vbytf7v1GO4JOBBTUhWol\nmZyOxaQRVLtnFKXmlSSfMZdv7yzFc61Fu9/OqX6NVDaHxbi29EM4nqbD78BfAbP3eVaTgb0tHnoG\no6vOn0dm0+xp9qjeq4qyCdTUq9xk0DjUVkc4vrZZfE6XZHSdAxWQe7/RzqALId5u61cMKSW5HHT4\n1eEmRdkMairAA2ytd+CwGJlNrz4XPxlLsafJg6cCW9hZTQYOtb/dnLsYkdkMrT5bRV6XoiilV3MB\n3mjQuK29jnAitarHJzM5DAaNPc3uEo+sdLY3uLCZtaLexOZ3BO3bwFo6iqKUV80FeIB2n51mr63o\nBVcpJZPxNHdu9VX0FkKTQeOOrX7CiVTBdeGjsxnavLaKWlNQFGV91WSA1zTB0Q4/yUyuqB0nk/E0\nHfV22qugAUZrnY1t9U4mC1hvyOmS2YzOwQL2yCuKUjtqMsADeOwmDnfUMTaTLGiWG0tmMRk0jnb4\nV2zXV0mEEBzuqEMT4qZCZDcKxZLsa3WXpZaOoijlU7MBHmB3o5vOBhdjM7fOxyczOWLpLPftCpSk\nifdGsZuN3N/VwHQyQyq7fD4+HE/jsZnLUglTUZTyqukAL4TgaIePRreFkejssjP5eCpLJJHhWFeg\nKvPTAZeFe3cGCMfTNzX/CMfTGA2C+7saVixvoChK7VqvapIVw2zUuHdXAyf7wlwJxbCZDNhMBrI5\nyUwqg91s5IG9QRpc1Vt4q93v4AP7jLzUG2IkmkQAOpIWr42jW31LujgpirJ5bIpXvsmg8a7t9ewI\nOrk0NkM4nsZpNbK72cW2gLMmZrf1TguPHGhhIp4indWxmgz4HeaqWE9QFGV9bIoAP6/BZa3qmfo7\n0TRR09enKEpxqn/qqiiKoixLBXhFUZQapQK8oihKjVIBXlEUpUapAK8oilKjVIBXFEWpUSrAK4qi\n1CgV4BVFUWqUKLSe+Lp8cyFCwPVVPrwemCjhcMqpVq6lVq4D1LVUqlq5lrVexxYpZeCd7lTWAL8W\nQojXpJRHyj2OUqiVa6mV6wB1LZWqVq5lo65DpWgURVFqlArwiqIoNaqaA/zXyj2AEqqVa6mV6wB1\nLZWqVq5lQ66janPwiqIoyq1V8wxeURRFuQUV4BVFUWqUCvCKoig1quo7OgkhfhPoApyAFfhdKeV0\neUe1OkKIjwN7ADMQlVI+UeYhrZoQohP4M2CrlPJQucdTDCFEE/CfgWkgC/xHKWX2lg+qQNX8M7hR\njb02NixmVf0iqxCiSUo5Mvf/DwPNUsqvl3lYRRNCmIH3SCmfm/v7E8D3pJSnyjuytRFC/KWU8l+V\nexzFEEL8BfAfpJRhIcRDQKOU8n+XeVirVo0/g8Vq7bWxkTGr6lM0i/6hNPLv8L8o74hWR0qZnv8F\nntMD+Ms1ns1q7vfIIKUMz930LHB3GYe06dXaa2MjY1bVB3gAIcQngVPARSnlxXKPp0TeDZwo9yA2\nIT8wJoTYLoTokVLqgF7uQSlLVP1rY6NiVkXn4IUQjwMPrfDlU1LKzwBIKf+XEOJvgE8KIT4ipfyH\nDRtkgQq9lrn7PgD0SCmjGzK4IhVzLVVIAgIYAj6/6DalAlT6a6NQGxWzqj4Hv5gQQgB/JaX8VLnH\nslpCiDuAB6SUf1zusZRCteV/5z42/+X879Dc3/9CSvnp8o5s9artZ7CSWnttwPrHrKpO0QghfEKI\n9y26aRswVq7xrJUQohv4GPAn5R7LZjWXkskIIeZzvA8BL5dxSAq189rY6JhV1TP4uXe/3yL/jyTJ\nbzn6XDVukxRCeIDXge8CmbmbL1fjjiAAIcQfAAHg/cBPgUEp5VfKO6rCCCEaeXubZAb4IyllrqyD\nWoVq/hksVkuvjY2OWVUd4BVFUZSVVXWKRlEURVmZCvCKoig1SgV4RVGUGqUCvKIoSo1SAV5RFKVG\nqQCvKIpSo1SAVxRFqVEqwCuKotSo/w9xsYX09eJHHAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113802438>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_result(x_test, mean=pred_mean[:, 0], std=pred_std[:, 0])\n",
"plt.legend()\n",
"plt.title(\"GPyによる予測\")\n",
"plt.savefig(\"GPy_predict.png\", dpi=150)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Posterior からのサンプリング\n",
"\n",
"#### Scikit-Learn\n",
"\n",
"そもそもサンプリングする関数が存在しない。(共分散を取得して自分で `numply.random` を用いてサンプリングすれば出来る)\n",
"\n",
"#### GPy"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
" /Users/nyker-goto/.pyenv/versions/anaconda3-4.3.0/lib/python3.6/site-packages/GPy/core/gp.py:500: RuntimeWarning:covariance is not positive-semidefinite.\n"
]
}
],
"source": [
"posterior = gpy_model.posterior_samples_f(x_test.reshape(-1, 1), size=30)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(200, 30)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"posterior.shape"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEKCAYAAAAYd05sAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAd4YYxrq/70ygczjgZXgAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1137b6a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i, pos in enumerate(posterior.T):\n",
" label = None\n",
" if i == 0:\n",
" label = \"posterior\" \n",
" plt.plot(x_test[:, 0], pos, color=\"C0\", alpha=.1, label=label)\n",
"plt.plot(x_train, y_train, \"o\")\n",
"plt.title(\"事後分布からのサンプリング\")\n",
"plt.legend()\n",
"plt.savefig(\"posterior.png\", dpi=150)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## まとめ\n",
"\n",
"### 事後分布平均と分散\n",
"\n",
"事後分布の平均値と分散の取得はどちらのライブラリでもかんたんに取得することができます。\n",
"\n",
"### 手続き的な違い\n",
"\n",
"GPyではインスタンス生成時にデータ X, y をわたし, `model.optimize` メソッドの呼び出し時に、カーネルのパラメータを最適化します。\n",
"一方で, scikit-learn ではインスタンス生成時には何も行わずインスタンス変数の初期化のみを行い, `fit` メソッドでデータ X, y をわたし, ここで同時にカーネルのパラメータ最適化を行っています。\n",
"\n",
"### 可視化\n",
"\n",
"可視化の面から言えば `GPy` > `scikit-learn` といえるでしょう. \n",
"GPy にはカーネル関数はもちろんのこと、予測モデル自体にもplotする機能がついています。\n",
"このため 「今回のデータにはどういう周期性を持ったカーネルが良いか」 などの検討を用意に行えます。\n",
"また `model.optimize()` を呼び出す前後での model.plot をすることで、最適化の妥当性のチェックをすぐさま行うことができます。\n",
"\n",
"### 事後分布からのサンプリング\n",
"\n",
"scikit-learn では一つの点での平均と分散を得ることはできますが、事後分布から確率過程をサンプリングすることはできません。\n",
"一方で GPy では `poseterior_samples_n` を用いれば、指定した場所に対する、確率過程のサンプルを行うことができます。\n",
"言い換えると、事後分布から得られる関数系列を得ることができます。\n",
"\n",
"そのため欠損値の補完であったり、学習データに即したような擬似的なデータを作成したい場合に、 GPy は優位であるといえます。\n",
"\n",
"### その他の違い\n",
"\n",
"GPyにはシンプルなガウス過程を用いた回帰問題以外にも, 損失関数をポアソン分布に変更し、二次の意味でガウス分布として近似してやるポアソン回帰モデルなども作成することができ, 拡張性に長けています。\n",
"\n",
"> 参考: https://github.com/SheffieldML/notebook/blob/master/GPy/Poisson%20regression%20tutorial.ipynb\n",
"\n",
"\n",
"一方 scikit-learn では 回帰と分類 のモデルのみで, 複雑な目的関数を扱う枠組みは用意されていません。"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment