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hands-on/04_training_linear_models.ipynb
2016-11-05 14:26:29 +01:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Chapter 4 Training Linear Models**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_This notebook contains all the sample code and solutions to the exercices in chapter 4._"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Setup"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# To support both python 2 and python 3\n",
"from __future__ import division, print_function, unicode_literals\n",
"\n",
"# Common imports\n",
"import numpy as np\n",
"import numpy.random as rnd\n",
"import os\n",
"\n",
"# to make this notebook's output stable across runs\n",
"rnd.seed(42)\n",
"\n",
"# To plot pretty figures\n",
"%matplotlib inline\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams['axes.labelsize'] = 14\n",
"plt.rcParams['xtick.labelsize'] = 12\n",
"plt.rcParams['ytick.labelsize'] = 12\n",
"\n",
"# Where to save the figures\n",
"PROJECT_ROOT_DIR = \".\"\n",
"CHAPTER_ID = \"training_linear_models\"\n",
"\n",
"def save_fig(fig_id, tight_layout=True):\n",
" path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
" print(\"Saving figure\", fig_id)\n",
" if tight_layout:\n",
" plt.tight_layout()\n",
" plt.savefig(path, format='png', dpi=300)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Linear regression using the Normal Equation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"X = 2 * rnd.rand(100, 1)\n",
"y = 4 + 3 * X + rnd.randn(100, 1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure generated_data\n"
]
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x110ec2e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X, y, \"b.\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.axis([0, 2, 0, 15])\n",
"save_fig(\"generated_data_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy.linalg as LA\n",
"\n",
"X_b = np.c_[np.ones((100, 1)), X] # add x0 = 1 to each instance\n",
"theta_best = LA.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4.21509616],\n",
" [ 2.77011339]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta_best"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4.21509616],\n",
" [ 9.75532293]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_new = np.array([[0], [2]])\n",
"X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance\n",
"y_predict = X_new_b.dot(theta_best)\n",
"y_predict"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure linear_model_predictions\n"
]
},
{
"data": {
"image/png": 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1P4qi/dpNTo+iaG2FTZsSh+u2bk1tN2FCYkA6/XSwnJOUQNMQn4hIFjobzsv62s3+/ceK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\n5N75sqXLAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113fc55f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
"plt.plot(X, y, \"b.\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.legend(loc=\"upper left\", fontsize=14)\n",
"plt.axis([0, 2, 0, 15])\n",
"save_fig(\"linear_model_predictions\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 4.21509616]), array([[ 2.77011339]]))"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.linear_model import LinearRegression\n",
"lin_reg = LinearRegression()\n",
"lin_reg.fit(X, y)\n",
"lin_reg.intercept_, lin_reg.coef_"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4.21509616],\n",
" [ 9.75532293]])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lin_reg.predict(X_new)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Linear regression using batch gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure gradient_descent_plot\n"
]
},
{
"data": {
"image/png": 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vJQyxC8ie69CdgHIbu9jNtHM8h02bEpCQkBD0/rlBNaoEjEjT6PXXAxMnJuDj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\nEEIIIcTg/wOhp6W3A90xkAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113fc57b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta_path_bgd = []\n",
"\n",
"def plot_gradient_descent(theta, eta, theta_path=None):\n",
" m = len(X_b)\n",
" plt.plot(X, y, \"b.\")\n",
" n_iterations = 1000\n",
" for iteration in range(n_iterations):\n",
" if iteration < 10:\n",
" y_predict = X_new_b.dot(theta)\n",
" style = \"b-\" if iteration > 0 else \"r--\"\n",
" plt.plot(X_new, y_predict, style)\n",
" gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
" theta = theta - eta * gradients\n",
" if theta_path is not None:\n",
" theta_path.append(theta)\n",
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
" plt.axis([0, 2, 0, 15])\n",
" plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)\n",
"\n",
"rnd.seed(42)\n",
"theta = rnd.randn(2,1) # random initialization\n",
"\n",
"plt.figure(figsize=(10,4))\n",
"plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
"plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
"\n",
"save_fig(\"gradient_descent_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Stochastic Gradient Descent"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure sgd_plot\n"
]
},
{
"data": {
"image/png": 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TQnJLVNTX83MFBRSi06cpNCtXUowuuIDtgZ56CvjNb2jtVFV5ve5Gj+Zn9+yh1bVsGR9n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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114e5fd68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta_path_sgd = []\n",
"\n",
"n_iterations = 50\n",
"t0, t1 = 5, 50 # learning schedule hyperparameters\n",
"\n",
"rnd.seed(42)\n",
"theta = rnd.randn(2,1) # random initialization\n",
"\n",
"def learning_schedule(t):\n",
" return t0 / (t + t1)\n",
"\n",
"m = len(X_b)\n",
"\n",
"for epoch in range(n_iterations):\n",
" for i in range(m):\n",
" if epoch == 0 and i < 20:\n",
" y_predict = X_new_b.dot(theta)\n",
" style = \"b-\" if i > 0 else \"r--\"\n",
" plt.plot(X_new, y_predict, style)\n",
" random_index = rnd.randint(m)\n",
" xi = X_b[random_index:random_index+1]\n",
" yi = y[random_index:random_index+1]\n",
" gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
" eta = learning_schedule(epoch * m + i)\n",
" theta = theta - eta * gradients\n",
" theta_path_sgd.append(theta)\n",
"\n",
"plt.plot(X, y, \"b.\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.axis([0, 2, 0, 15])\n",
"save_fig(\"sgd_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4.21076011],\n",
" [ 2.74856079]])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.1,\n",
" fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',\n",
" loss='squared_loss', n_iter=50, penalty=None, power_t=0.25,\n",
" random_state=None, shuffle=True, verbose=0, warm_start=False)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.linear_model import SGDRegressor\n",
"sgd_reg = SGDRegressor(n_iter=50, penalty=None, eta0=0.1)\n",
"sgd_reg.fit(X, y.ravel())"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 4.23166744]), array([ 2.79099659]))"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sgd_reg.intercept_, sgd_reg.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mini-batch gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"theta_path_mgd = []\n",
"\n",
"n_iterations = 50\n",
"minibatch_size = 20\n",
"\n",
"rnd.seed(42)\n",
"theta = rnd.randn(2,1) # random initialization\n",
"\n",
"t0, t1 = 10, 1000\n",
"def learning_schedule(t):\n",
" return t0 / (t + t1)\n",
"\n",
"t = 0\n",
"for epoch in range(n_iterations):\n",
" shuffled_indices = rnd.permutation(m)\n",
" X_b_shuffled = X_b[shuffled_indices]\n",
" y_shuffled = y[shuffled_indices]\n",
" for i in range(0, m, minibatch_size):\n",
" t += 1\n",
" xi = X_b_shuffled[i:i+minibatch_size]\n",
" yi = y_shuffled[i:i+minibatch_size]\n",
" gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
" eta = learning_schedule(t)\n",
" theta = theta - eta * gradients\n",
" theta_path_mgd.append(theta)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 4.25214635],\n",
" [ 2.7896408 ]])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"theta_path_bgd = np.array(theta_path_bgd)\n",
"theta_path_sgd = np.array(theta_path_sgd)\n",
"theta_path_mgd = np.array(theta_path_mgd)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure gradient_descent_paths_plot\n"
]
},
{
"data": {
"image/png": 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Y2dnx2WefcevWLQ4ePMjGjRuRUmJvbw/A3bt3adasGXfv3mXixInUrVuXmzdvsn79eh4+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eAAAH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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115c53470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(7,4))\n",
"plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
"plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"Mini-batch\")\n",
"plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"Batch\")\n",
"plt.legend(loc=\"upper left\", fontsize=16)\n",
"plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
"plt.ylabel(r\"$\\theta_1$ \", fontsize=20, rotation=0)\n",
"plt.axis([2.5, 4.5, 2.3, 3.9])\n",
"save_fig(\"gradient_descent_paths_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Polynomial regression"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import numpy.random as rnd\n",
"\n",
"rnd.seed(42)\n",
"m = 100\n",
"X = 6 * rnd.rand(m, 1) - 3\n",
"y = 2 + X + 0.5 * X**2 + rnd.randn(m, 1)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure quadratic_data_plot\n"
]
},
{
"data": {
"image/png": 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jv3/z+OZGbTOgWrDKit2HWc17rxBpYwNRoj4w9g3Z2O/fXmx+UNsMqBbs98Lcbypj1WmO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\nklQlA0qSVCUDSpJUpf8PlEA9SmpE4QEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114c7f780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X, y, \"b.\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.axis([-3, 3, 0, 10])\n",
"save_fig(\"quadratic_data_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.75275929])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.preprocessing import PolynomialFeatures\n",
"poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
"X_poly = poly_features.fit_transform(X)\n",
"X[0]"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.75275929, 0.56664654])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_poly[0]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 1.78134581]), array([[ 0.93366893, 0.56456263]]))"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lin_reg = LinearRegression()\n",
"lin_reg.fit(X_poly, y)\n",
"lin_reg.intercept_, lin_reg.coef_"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure quadratic_predictions_plot\n"
]
},
{
"data": {
"image/png": 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MS3zq0QOmTHEVySVuxXWAqkxxEPph6UZeqnchvTe+7q64+GIYO5bcgjR96xIJ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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115eaf048>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
"X_new_poly = poly_features.transform(X_new)\n",
"y_new = lin_reg.predict(X_new_poly)\n",
"plt.plot(X, y, \"b.\")\n",
"plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.legend(loc=\"upper left\", fontsize=14)\n",
"plt.axis([-3, 3, 0, 10])\n",
"save_fig(\"quadratic_predictions_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure high_degree_polynomials_plot\n"
]
},
{
"data": {
"image/png": 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OILlhMp+P/rzUs64qqKrK0EnLyVqgIaeXP7Qy22iyFyoqEt8//zwcOwZny1bk\nqArkNW1A1NhbRA36nDml2/SPTigrkgBISSFky7vo9DrC7cwplTpJOBBgXxQuZxfqzlIUZeSl7xXg\nZmCOqqquN5mXSCQSL/LNrm8I9A/kRN4J7l18L0Y33Lbu+O92dn97G6rRj8JCytYnnT0Lb70FY8dC\nbCyMGAFbt4r3GzYUxQ033cQzPz/EJz88DW+/DdGW0deZXh0sysxJSanQTcLkJGH63h6+1rTVmYW6\nccB/EX2cAKYCR4HXPDguiUQiqTI6vY7nVj/Hm1e9yeJbFnPk/BEmLZpUJZH6vzk5HH/9IgDzPoIJ\nnVPhxRfFhFd8PCxaJFbn5ueXdSO85x544AHRrqJjR8LqNyxzk7CKik70aFtqc2SiIkfzOpviU1U1\nS1GUJ4BGiqK8BlwErlFV1eDx0UkkEkkVeG/Le3Rr3I2BLQYC8Putv3P1N1fzwJIH+Ojaj1wqbCAl\nhfnzYeaUMD7hY94d+AOdZy2B48fL9vP3B4NBLJJt1w5Gjy7tm2RO/dBdHMw5KF5YCVRhSaFlio+K\n/fhKBUpR6mSRxHueHkhNxtxKv6a0lJZIJI7JKczh1Q2vsvautaXvhQeFs/S2pXT7sBubT2ymf/P+\ntg827y4LotLu4EGu/WIJ2awknAJYbzppuIiWxo+H1q3h1CnLUnCzvkkApKQQnXrMrh9fob6wXARV\nUcuNOhtB1XWsrfTXrZMiJZH4Av+37v+4vsP1dGzQ0eL9iKAIru9wPX8c+qNMoKwFafVqiIoSVXeL\nF8M2UQ8WZ36iwYOFU/jNNwsjPlOUZBUt2Vos68gw1rzVhglnIihFUVyOoGp6tCUFqgK8bZkikUiq\nztELR/ls52fsfnC3ze3D2w7nhdUvMD1lunhDo4G+fWHVKiFK334r5pXMSUzkSMMgll/WkAdDB1sK\n0dqyKM0ZV3BHAlVYYunFBxULlKnluysRlC8su5ECVQEmy5S9ez1vmSKRSNzDi2te5IGeD9AksonN\n7QNbDCR6804uDEkj+q8NQpD+7/+EIauJiAgxjzRuHFy8CC+/zJMLxjKu0zj4+YDlCc1FyAl7oYoi\nqHJFEgFOFknUxTmouow3LVMkEknVybiQwa///kr6I+mWGzQakZb75x9CFi/mu+9KqPdJsuU+8fFw\n1VUQHMz8fh8SFKxw663AjBkYjAY0GRrmjpwLKVbC56LnncMISl9IVHCUxXumhbr2kHNQdRhvWKZI\nJDUVXyvMcRm2AAAgAElEQVQSenX9q9zX4z5i/t4lhKOgQKTuZsyA06fFF1APKAryJ3jENWA0wkcf\nifbowI5RM7j7HgVFgR49oENKCqlnU4kLaEXGnngiesZTlR9FdEg053XnbW6rTIqvtkZQsuW7k+iN\negxGWVkvqVt4u69SldBoOJF3ggVpC5ja4mZ44w245hqxYHbUKNixQ4hTZCT07AnAR4PCULt1E/tc\nEqcPP4QnFqegqvDKK6L3HykpLNuznpy5v7nlZxERFEFhSSF6o77ctkoXSVz6zx6+KFwygnKSF1a/\nQOOIxjza99HqHopE4jVqdJGQeeWd0QjffMOeeans3hJA7NPd0BLBHpJJJoDIJk1E+ff994vFs0OH\noq5ezRvRn3PlhJvpmCZsiObMEf0AIYXZs03fC37feJQLx+MxuOFn4af4US+kHrm6XGLDYi222Swz\n93fBScJBis8XCiPMqXMCVdn87LHcYzafdnyJEkMJz6x6hsf6PUazqGbVPRyJD1DjioTMRemPP+DC\nBVF19/vvcOYMIy7tpvWPZpBhNWlKEklx51j38WEit6yyqLxTNBqGtxnOikMr6JjyOGfPlm1+7z2Y\nPLnssiWGEvbwPR06vsqB/e75WZjmoawFSqfXlUvxySKJOkBVfKiyCrII8g9y42i8z8Gcg7y/7X2+\n3PUlH1zzAWM7jq3uIUlqONVeJGS9Pum334RaLl4MK1cK1wYzjiY2JKHPlezp9QhpT3ZGb/Rn74Wm\npMU0pR+rLM+dksLwhll8+s+nPN7vcRo1gmXL4N9/RZcLc7af3k6rRnGs3xDgtp+FvUKJQr1tJwm5\nUFdil8yCTJ8XqPScdAYnDGb6kOnctvA2VhxcwezhswkPCq/uoUlqMF4tErIWpL/+gpCQsgWzu3ZZ\n7t+0KbRvz/mxI5n3y7NMWLgDopqSrIWkV86wN6dxWbSjS7E8NiWFYYXnmfjbRHR6HSWFQhRuuKH8\nsFYfWc3lLS9368/CrkCV2HaSqIsRlCyScJLM/EyyC7OrexhVIj07nXYx7ejXrB//3P8PecV53Lbw\ntuoelkRShkYjqg8WLhTO32++Cf37w8svl4lTx47C4+6mm1CPH+eLN++gQ+FrDGwxiKZRTYFLkd9n\n6axda+b+YqMUvH5ofTo37MyKtI0Oi0H+yviLoa2GuvWj2hMoWyk+p50kZARVN8kqyCr3R+NrpOek\nk9xQrPuICo7itSteo+8nfat5VJI6jSliysgQUdJXXwkx0pvN99arJyyFxo0TLc8vdZ/NfuoRbvrq\nCi7oLrD01qX0PGCpKpEjB5Fkp0S+qEi4GY0YAcPbDGfB6jTS0i4vVwyi1cKOncVsOrSHH2+soJe7\ni0QHu5bic8pJopZFUFKgnCC/OJ9CfSHZBT4eQeWkc32H60tfN41qygXdBbRFWiKDfWCBi8T3MQmS\nwQCbN8Nzz8HJk0KgzGnWDK6+GgICYO5c0dQPYMYM9mbuZc7mOZzNXcC1iTN4pO8jBPgFgNXaWXs+\nmvn5ol3TypXwzTcwfNBwvt/xKElJj1gUg5QdH0Bg4zX4PxkNlrpRJeythbLpJFFH223UmRSfVgsF\nh7uSf9H1j5xZkEmTyCZc0F3w6bVQ6dnpJMYmlr72U/xIjE0kPSfdwVESSRUxuXnn5QmxufNOaNwY\nBg6EDRuEOEVGwo03wpgxkJkpWljMmyea/F0Sp3VH1/FUyVIu/+JymkU14+PZ6UzpP0WIkw1slchn\nZ8OwYaIAMC5OZAt7N+lNkX8Wb36/xSIlWHa8H0VnWpOW5t4fS/3Q+nbnoCpdJCEjKN/D9CR0ePfn\n3LlUz7bNrlXgZBVk0TiiMTq9jvO688SFxVV8UA2joKSAc/nnaFGvhcX77WLbcSD7AD3ie1TTyCS1\nDvNCh8OHxWrXl1+GNWugpKRsv+hoUSZ+++2QkCCUQ6MRymHi0nky8zO57rvreGvcW2R0vqXcDdwW\n1iXy9eqJ+8C+fdCihRCp9u0B/Hms72N8uPt1frzxR4vj23fUk5ZmoEMHxe0l9tEh0ezP2l/u/UJ9\nFZwkalkEVSsEymTFoisItLnd9CSEMZDD6f4uL7DLzM+kQVgDtEVasguyfVKgDuUcolX9VuWeNtvF\nCIGSSCqNuSDp9fDll6Jee8kSoQ7WXHFFmQnrmjXl21OYc+m8X6R+wZgOY5jYfSLgnP2SeYl8p05C\n//btE6K1YoUoADRxd/e7eXHtixw5f4RW9VuVvt/jzm9oUZDJgsenur3E3mGRRCWq+BQUn2vpXhE+\nL1DmeeaGLW9k1Cuvl9vH9CSVuqeY1okGkpJcK3bILMikQXgD8oryyCrIoj3t3TV8r5Gek05iTGK5\n99vFtmPl4ZXVMCKJz2JdCr58OZw9KwRp6VLIySnbFhQkHMKvvx7atoVz5yyb+a1ZY3luG5V2qqoy\nb/s85o8Rx7nSo828LHzePHjmGTHvFBNjtV9wJPd0v4e3/36bOSPmoNXCgMsM7Em7hQ4djfC4Ez8X\nF3FUZu5ykYS5k4SdFJ8vRlY+Nwel1cKmTWVloOZ55rMZMWQfa1zuGNOTVOsnJvLFosMuPwllFWQR\nFxpHbFgsWQVZbvgU3ic9275AyQhK4hDrjrAaDRw8CG+9JcKS114TTfu+/rpMnPr1gzvuEA4P06eL\nsvHXXoOWLS3P5YQL+JqjawjyD6J/M9Fc0NbckjN07y4CO2txMvFo30f5MvVLLugusGcP7N0HGIM4\ndCDE7fNPYFugTG41gf6W2SCnnSQqSPH5WoRVLQKlKEqioiiFiqJ86cpxtowrTdFRYCA0aplDbIsz\nNo+NjISwVrsIjzC6PN7MfBFBxYXF+exaqPQcywIJE+1i25Gek+6TT1cSL6HRCDVYswb+8x/hA5SY\nCE88IRbSqqqYQ7rySvjiC3jhBfEU+cUXIp1njhPN/KyZt30e9/W8r/Tmav5v3p32S82imjEycSQf\nb/+YxA5F+DXcT0Cg0WMWT7YEylb0BC6025BFEm7hPWCLqwfZM6405ZnX5P/IqWL7v8TKklmQSev6\nrTlfeL7aIqiqtjxIz0nnluRbyr0fGxaLn+JHVkEWDcIbuGGkklqBRgNdu4r03c8/iwWzFy+WbQ8O\nFiI1ZoxI4b36atk2Ry3PXeyblFWQxdL0pbw38r3S9yqyX1JVscbp8stduhQAT/R/gtHfjyZQH0PX\n2w/w6pWv0qePZyyebAqUjQIJqLsLdb0eQSmKcjNwHqyNsSyx9TO29+RkyjOHhJeUP8gNZBVkERdW\nfSk+d7Q8OJB9gHax7Wxuk2k+SWka799/hRjdfLNoQXHrreLJ6OJF8fqmm0SZuFYLu3fDrFkQanVD\nrUSUZI8vU79kVPtRxIRa5uVM/+athaOoSBQFDhsGn3zi+vV6xPegZWhnnhjfi51v/h9PPlnpoVeI\nrXVQtgokoO4u1PWqQCmKEgXMBJ4Ax77vDzxgWZEKZU9OFvYlXsBUJBEXFlcti3Urm3M3oS3SkqvL\nLbWBsUYKVB3EJEglJSLcmDZNVNZ16ABTp4qiB39/GDpUdJg9cACysmDBAjGPFGg2R+JGQTLHVBxx\nX8/7nNo/J0cM9ZtvIDxcNMetDDfGzYSsThj0fpX69+Ys4YHhFBuKKTaUtZl3lOKri2Xm3o6gXgQ+\nVlX1VEU7zpsn1vEVn29o8b69JydnqczThanMPC4sjqxC70dQVc25H8w5SJuYNqVVPtbIUvM6gHmh\nQ3Y2vPOOiJIaNBC5sM2bIT1dGLN27iz2e/JJEbbHx4t0ngkPCZI1646tw0/x47Lml1W476FDMGCA\neHht0kQ8wF5zTeWuO3F4b7okB7p9jssaRVGIDokmV5db+p4tHz5w7CShqioqammZeW2KoLw2B6Uo\nSjfgCqCbc/vPYMsWYGtffg1NpevjXas+hko26ypN8YXGVksEVdWWB/ZKzE20i23H92nfV3GUkhqF\neSm4qsKPP8KWLcIRfONG0eDPRFyciI7uuguaNxeCpdGUzSVZV/F5SJCs+fSfT5nUY1KFlWeqKjKR\n//4LXbqIwsFmVWh35s0WI6Z5KNP8ry0fPnDsJGEuTjU1gtJoNGis/46cwJtFEkOABOCYIv7iIgB/\nRVE6qaray3pnf/8Zwi9ShY/f0vH8o+BXDTWHJYYStMVa6ofWFxFUNRVJVMXmPz073e78E8gUX63A\nem3SqlXC727xYrE+6dChsm2mG/7w4SKtN3aspSCZzmfCS4Jkzdqja3l20LMV7qco8PnnMHMmfPwx\nREVV/dreajFiXShhq9UGOE7xmQokoOaWkaekpJBi9nc0c+ZMp47zpkB9BHxn9vo/CMF6wNbOJosS\ng99FnnnlLH5+bbwxxnJkF2YTExqDn+JXrQJVFdJz0hnUYpDd7W1j2nIo51BpHlviI5iLkkYjcsEm\nB4dffy11/S6lSxchSHfeCdu22RckqDZRMpFdkE1OYQ5tY9o6tX+nTmJ6zNewFii7Kb5L66BUVS0n\nQqYCidLXMsXnOqqq6oDSRwBFUS4COlVVc2ztbwqx7918JZcN/dBbwyxHZn5mqbWRydzRYDTg7+df\nbWNylQPZB7i7+912t4cHhRMTGsPx3OMkRCd4cWSSKrF6tZhDWrwYPvsMXnzRsvy1QQMhSOPHCwPW\nF18s27Ztm+W5vDSv5CzbT2+nR3yPWv/AVC6CspPiC/ALQEFBb9SXW8Rr/mBZU1N8laXarI5UVXUY\n45lCbP+dBd4akk2yCrJoECbywwF+AUQFR3FBd4HYsNhqHZcrVDQHBWVpPilQNRiNRjTvW7vWUpRM\n+PlBq1aiOkBR4O23y7Y5Wptk63U1s+3UNnrFl8v8c/iwiJSmTfP8GKq69tAZGoU34ljusdLX9srM\noSzN51CgHBRJ+GJk5bOPJx99JCpfPY2pxNyEr9kdXdBdQKfX0TiivAWUOXIeqgZiSruZ/Oseekg4\ngF91Fbz7rmhsFBYmFtQOGQLnz4u5pnfegfr1Lc9VwwXJmm2nttGriaVArVoFvXsLP72vv/bs9d2x\n9tAZLm91uYUXpr05KLBfKOFKBFXZQrHqwicFasUKsU6qTx+RcvckmfmZxIWWuZf7mt2RyYOvoslT\nKVA1AJMgqWrZItj+/UXvpIkThRW3Tifmkp55Bu65R/RY2rlTCI55dYCPCZI15gKlqjBnjqjpyMmB\na6+FUaM8e/2qrj10lmGthrHh+AYKSkSmyF6KD+wXSpiczMFxBOWL+KRADRggzJFzc0U24+WXLatm\n3Ym1BZCvFUrY8+Czpl1sOw7kSIHyKuaFCTqdsD54+GGRpuvSRfjcbd4s0nVtLhUJPfaY+OO/8kpo\n1gxtgb8wT+4zzPLcPiZI5pzLP4e2WEvr+q0pKIAJE2DKFFGUOG2aqP9wR6WeIzzl92dNvZB6dG/c\nnTUZwtXdXpEE2BcocydzOQdVA4iMhJ9+EkVKM2aIrtFbt0K/h4Pcfq3Mgkzax5a114gN9a0U34Hs\nAxXOP4GMoLyGeeXdkiViUmXxYtF/PD+/bL/wcPF6/Hho3Vqk9axKwbUF/mZtJwaxbpD33FVMpJ5J\npXFEYxpFNHLbObef2k7X6IFs3qyQkCACxPBw4T17ww1l+3lyjsiba6Gubns1yw8u5+rEq+06SYB9\nR3Nn56B8EZ8UKNMf5pQp0LOneMLauhV6FgW4PSbMLMi0WMleXXZHlSU9J52rWl9V4X6toltxMu8k\nxYZigvzdL/R1FusFs99/D+vXC1HaYsMvedAg0eb1lltEMYSDUvA99QfZNE/2BrvP7ubppS+zYuNJ\n7h3Rjw9vKN+HrbJsOLiLva99xOBjQhy++kp405pHMa70hKos3loLNaLtCMb/NJ63eZtCfSHhgeE2\n93OU4pMRVA3B1h/mtm0iN73RUEDWecfH51/0Y9Ph8k9dmfmZPPfXc3x03UcW+/t8ii87ncm9J1e4\nX6B/IC3qteDw+cN0iOvghZHVUqwXzK5cCQUFZQtmT5yw3L9tWyFId9whVMZckNautdzXKm1n3dLc\nU2koczLzM3l0+aOs2reFwC82oWTE8dnS/bx2pUpUlHsm4NdszSbnWCMMl4S3uBh69LDcx15nA1+k\nW+NuaIu1HMo5hE6vs9ux217LjdocQfncHJStP8w2bUR1jwnrpoYmDLow7hrVxmZlzvG843y287Ny\nfwAmHz4TsaGxPlUkkXEhg9b1Wzu1r0zzuQGNBk6fFvNJo0eLJn3XXAMfflgmTt27Cx+8W28V/ndL\nlgiXcGsqKHSoDvPkj3d8TLGhmO8G7+ZcRkP0ej9KzrZl0fpDFR9cAWfPiqzmoYDfSGyvdzj/4605\nIm+gKArD2wxn+cHlDlN8DoskTE4SPlalVxE+J1AV/WEWFwSXlocOHGhZfaM71ZbDB4JtVuYUlBSg\nN+pJy7Qs18ksyLR4ovGlCEqn15FblEvD8IYV74wUqEqh0YjU3Y4dwmtn3jzhVjppEixaJJ6kGjcW\nZeAffiia+e3YAd99Z2nACpWqvKuqebKrbDi+gds630af7mGl/w5jW5wj3f/XKp1XoxG6fde9Bej8\ns/h7Y5BD4a2uzgaeYkTbESw/tBydoeJ1UNaUc5KoRSk+nxOoiv4ws4/Gl0ZYe/aIUnSTBUpIk4O0\nbldkU9xMZZ7/nP6n9D1VVckuyPZZgTqZd5ImkU2cXo2fGJMoBaoiTPNABQUi8nnySeHY0LOnSM+d\nPi3aVJg6zk6ZIt7TaOD++8t88MDnSsGNqpGNxzdyWfPLLP4dfvrLAVYc/6lS5zQYhK4PGyZ+TPsO\nFtI99jKiopQKhdfb4uxJrmx9JWsy1nBBd8F+kYQdR/PanOLzuTkocDx5GZtwujQvHxYmStFvvlks\n8lOSjHz+20H8sjqXq8wpFagzZQKVW5RLaGAowQHBZecP850U34m8EzSLct7WuVX9Vizcv9CDI/JR\nTPNKJ0+KZn5vvin+oAoLy/Zp0kQs0MnLg08/FX984NbustXN3sy9xIXFlVbsmf4dFhsGcuey/Zy5\neKbCBeHmnD4tCpz++kvo9nPPgZIyFz3JnvoINZbYsFiSGiax+shq7ux6p819qlok4YuRlc9FUBUR\nFFZU+mR37Bi8/76oAPr4Yzj46recPhlo86mroKSA+Ih4C4Ey9+EzERcWx7mcQptzXDWNE3knaB7V\n3On9W9dvzZHzRzw4Ih/BFCUZjWWmqj17ih4OS5aIr8LCso54990H994rKu/aty8TJ/C5KMkR64+t\nZ2CLgeXeD/IPYnjb4fx+4HeXzvf660KcGjYUi+9nzYJ/zm0t5yBRVxjRZoR4KK6Kk0QFEVRNdTu3\nR60TKCh7souKggcfhL//FveNotNt+fB12094BSUFDGg+gNQzqRiMBsDSh89EoD6GnLm/MXiw6lEL\nFHdwPO+4SxFUQr0EjucdL/38dQbz8u38fOGjNWmSEKTevWHNGjFvFHAp4XDddSJ99+23MH262H/m\nTCE+tUiQrNEc2E7j89fb/Ju/rt11LD6w2KXzzZolfsypqWLdsaqqNi2O6gpXJ14NUDUnCVlm7nt0\n7SoehFuN+ppnXukORJfbp6CkgCaRTWgY3pD0nHQ6xHUo58MHsH9vAGR2RG9USgstkpI8bypZGU7k\nnXDYB8qa4IBgGoY35ETeidptGmtdCv7bb8JGaPFi8UhfZPaUGhkpnkJuvVW0Oj95UvjimZ/LnFok\nSOZotbDwP1NQz3Vg2Zzy878jE0fy0O8PCS85O04I1oSHi5oSE6e0p9Ab9S5F/bWJnvE9iQ2NrZqT\nRC2bg6qVEZQtIiKgyU2vExOnt7m9oKSAsMAwesT3KC2UsJXiS06GoMaHCAg00qkTtGjhHVPJyuDq\nHBSINN/h84c9NKJqwlpEVq8Wi2Sffx66dRNGbw89JIwdTeI0dKgoavjtNxElffON8NRq2dLyXLVU\nkKxZ/XcmJWfaotf72fSmiwmNoXt8d/468le5Y41GOHWq4mtsP72dXk16+Vwayl34+/mz7LZldG/c\n3eZ2p4okalkEVWcEykT+Rb9y80cnT0LOhRLCAsPo3rh76TyUrRRfZCR0mTaZuT/uYd06OHrUO6aS\nleF43nGXn0ZbRbfiyAXvzEPZW6/mdjQauHgRfvlFGKy++Sb07Su8slJTxT4dOggH0p9/FoL011+i\nLHzoUMtz1eIUniPOR60jqtkJh+uORrUbxaJ/F1m8d+wYXHGF+DEWVNA5Z9upbfSM7+nGUfsevZv2\nLtdOw4RTRRIygvJdDLowJo62XKhrMIg1kvMmPcSZtES6x5cJVGZBZjmBAmgUE0Z8h6NERtbsBYM1\nOYLyeDsDjUY8PcydK3oz1K8vWpt/9pmYZ4qKEvNLr74Kzz4rUny//Sb2scaHK+/cxY7sNUz9ZJHD\ndUfXtb+OJelLMKpGVFV453XuLALWCxcqbo9jiqAktnHKSaKWRVB1Yg7KhO5UW44eCLGIdkJD4fhx\nyD0Ty4cP34zhoXx2NL4fVVXJLMgkuWH5klfztVDeNJV0hSJ9ERd0F5xepGuiVXQrlh9a7qFRleF2\nqxqNRijdli2iyu7998Vd0ZxmzUTPhsBAsd2USvKxZn7Vwfrj63n36vH0cxCQt4ttR0RQBCt37ua9\nF7qyZIl4f9QoUUXb0MGfoqqqbD+1nQ+u+cC9A69FOOUkUcvSo3VKoMRCXR1H0sPo1AliYkQBhU4H\nip8BVVWYNzcC/zgNC3udI6sgy6YvlrXdkbdMJV3hlPYU8RHxLrem90QEZct1uso+cqZCB60W/vhD\nlISdOiVam5uIiBCCpNeL2XjTHXLGDJ9eMGsLTzp7a4u07M/a71T6bWjLoSxYfoIlS7pSr57onXj7\n7ZY/blucvngag2qoswUSzuC0k4RM8fkm/iEFfP7bodI0hUYjxAlANfoxdtI+kpPBkNWGZWvPlfPh\nM+FtN4m8PNXluRpXS8xNtKrfyq1roeyl8ly2qjEvdMjIEKm5q66C2FgYN07MJWVmQr16ZcaMjz0m\n7tjR0ZaP77VAkMzxdLr075N/0yO+h8WCdXv0b9afgsSveP11ERXfcUfF4gSixUaP+B61LgJwJ8EB\nwegMdatIok5FUADhEUa6thXfX3sthIQIkfILLGb0hFOMfyeJMU//StMrUlm1u3yZOYhV34fOV90c\n0xk2HtzNsJQg9GfbkZSkOO07Vpn5J4DGEY3JLcolvzif8CDbtv+u4CiV5zDyNC8FNxjgyy/Fas7F\ni8tXojRvLvK0Dz4obIeGDrXsnVTLS8HFz1hFr1c84uy9/th6i5YzjujfvD8vaF7g+6muXWP76e11\nvkCiIupikUSdEyhzmjSBQ4dg6VL49OKtNG/2MMHBcPe9JXy9e4fdFJ+32r6rqsrk+R+gOz0HjK7d\nfFx1kTDhp/jRMrolRy4csTn/5ioupfLMRWn5chERLV4sfkHZZj/voCDRg2HMGOF5N3JkuWZ+FqJU\nywTJmmNBS9HHNiUgpzOdOvm5vVBnw/ENPNb3sXLv790L27eLFJ6JxJhE8ovzOZl3kqZRTZ2+xo7T\nO+xa/EgEjooknFmo64vCVacFCoRI3XsvfPzJCcIChUVN9/juPLzsYYoNxUQGlYUr330nSmXbXO6d\nFN/P+36mJO4fopufRnuyGZ06+Tt98zmee5y2MW0rdV2T5ZE7BMphEYn1gtmFC0WqzrRg1vofWt++\n0K6duCNu2OCwmV9tFyUTJ/NO8tjquxn3xkjOZTRgyWOvunUOSm/U8/eJvxkwbkDpe4WFokL/9ddF\n+s70awHxBN+/eX82ndjEuE7jnL7O9tPbeXvE2+4beC3EHQt1fa0dR50XKBOmhbogbtCFJYU0CGtQ\nmhM/fx4eflg0Ruzepyfnh9X36HgKSwqZ+sdUPh/9Oft6reXXden8/PCLTt98TmhPkNIypVLXbh3t\n3kKJ0lSetSD99Zdw/l6yRIjSvn2WB7ZoIe58EyaI1ugzZ5Zt27DBct9aNq/kDAajgdt/uZ3JvScz\ndcBU2r3XjrTc6+kX6b783p5ze2ga1ZSY0BhAZFkfekj8OkDYEDawyoL3b9afTcedF6gzF89QWFJI\ny+iWbht3baQudtStU0USjjAXKD/Fj+7x3S3Se9HR8O670KgR/LMlnIxXFzJ1qjCv9gSzN82mV5Ne\nDG01lKs69Wdv8GdERDj/h1fZOSi4VCjhicW6Go0o/f7+eyE6r78uZvZfe61MnJKS4PrrYfx4sY5p\n5Uq4887yM+11UJCseWX9KxhVI88MeobQwFCmD5nOtFXT3HqDSj2TWups8MYbMGKEEKfkZNG5/qOP\nxBIzcwY0H8CmE5ucvsaO0ztkgYQT1MV2G3VOoOz98swFCqB74+4WBRKKIuzY9u+HBx8ygOrHm2+K\n99zNybyTvLX5LV6/8nUA2tRvg1E1uiQax3OP07xe5Up23VZqbkq7pafD7Nli5WZsrHD9/uYbUZ0S\nEyPCq9mzRb+FPXtEqq+DVdt5KUgWbDy+kXe3vMvXY78uXUpwV7e7OKU9xcrDK912nV1nd9G1UVcA\nbrgB4uJEAeWOHXCZnbqJ3k16k3o21eZ8iS22n5IFEs4gI6hajqP8q7VADWwxkDb125TbLzoa3p/r\nT8TkofTpV8Lzz7t/nE+vepr7e95Pq/qtxLgVhcEJg1l7dK1TxxcbiskpzKFReKNKXb/SdkcmQSop\nEd8/84yosGvXTjT2y8gQ80oJCfDAAzB5sih+2LRJNPbzN1uzJQXJIQ8seYD3r3nfIkoO8Avg5ctf\nZtqqaRhVo8vntGU9tevcLro06gJAq1bCuuipp8RaZ3uEB4XTPrY9O07vcOpaO87soGcTKVAVEeAX\ngN5Y3ku0Ni/UrVMC5QhrgRrXaRwfXvuh3f0bJZ7kq8UZ9O3r3nGcLzzPb/t/4+mBT1u8PzhhMOuO\nrnPqHKe0p2gc0djlRbomTGuhKnwSMy9MOH9e5EBvvVWsORo6VNyBTpwQOaBbbxU2QtnZQqg++EA8\njmlcoakAACAASURBVJsjLYWc4njucU5pTzGmw5hy227oeAMKCj/tda3Drflaql69YOdOUUWaeia1\nVKBAOK84g6M0n/W6ra2H99MjvodL462L+Pv5Y1DLt8KRC3VrOSWGEgC7Jo22iAuLY1/WXpvbMjOF\n8XV+vutjWXZwGSktU4gMtqyGGNRiEGuPORdBncg7Uen0HkBUcBQhASFkFmSW32guSj/9JCYmUlLE\nTPnChaLU8cIFkcoDuOsuUV0yaZIwZjOfsJBRUqVYdWQVw1oPs7gpmVAUhVlDZ/HahtdcOqf5erUD\nB8SSsrP5ZzGoBppENnF5jP2b9bcrUJZr41QuHG9qM1shscRf8bfZq602p/hkFR+QX5JvET05w5R+\nU7h/yf38tO8nZqbMpHX91qXbXnhBGGHPnQtPPw3du4uuDtYVeLbsaRb9u4jR7UeXu15SwySyC7I5\nrT1NfGS8w7Edz62ci4Q5pnmohlv3lglHSQl8/jksWiQq79LTyw4wpRauukqk9G64ofzaJGukIFWK\nPw//yRWtrrC7/YrWVzD+p/GcLzxP/dCKq021WmH0bjC793XrBjtO7KZro66VShv1b96fp/58ClVV\nyx1vvjauWRstTbsE1brUlCewF0HJIolajnV6zxnGJ48n/ZF0EmMS6fNxHx5b9ljp083NN4s0yenT\nwm1n8GARPJhX/Nmypyk2FLPi0AqubXdtuev5KX4MShjEumMVp/lO5J2gWWQlBUqjQauFyHNXsffE\ncbFI9uuvRVVdgwbC0eGtt8rEqXNnIUaLFok2FStWiFSfLfGRglRlVFUVAtXavkAF+gfSv3l/p+Ys\nDQbo0UMUVKqq+BVt3y4ysGnZOy3Se67QKroVeqOe43nHy20zt7m6fc48+rbuVKlr1DXqYgQlBQoh\nUOGBrtv6RAZH8sKQF9j/8H5+T/+dnWd2AjBkiGgz/+KLZfsePSru3SZsWQCtyVhDh7gONIqwXdww\nqMWg0puOo15KLpWYWy1w1S7fwKDeOta8MJ03hiahff0DsTD2hx8gN1fsNGAATJwo3t+1S6T6ri0v\nqlKQ3E9aZhrhQeGlBTT2SElIQZOhqfB8/v5w223Qv79YWrZ6tRAssCyQcBbT3+XFi4qYhzpuO81n\nWhuXlrtZVvA5iaMIqtRJwkEE5YvCJQWKykVQ5sSFxZESfx1fLDlQKhh+fvD44yLA8PcXwceIEWXH\n2OojtejfRYxqN8rudUyVfI7MQbVa2LktlLgAxzewUjQaYRv055/w2GPsmbuGtH/9MBgDOahrQxpJ\nonxr+HARSU2fLu5kn30GrVtbnsuFOSWvNSusJjz1+SpK75lIaZmC5qjGqXM++6z4lQ4YYPm+eYm5\nM1j/XfaIGVLheqjtp7fLAgknsVfFZ+EkUUEE5WupVClQVF2gtFpY+dwLvPfQuHKO3Rs2iAWNhw5Z\nzkGZ0hwrV4pUR0SEyqIDixjV3r5AdW/cnYwLGWzcnmezi6/pBrF2xixevPNK2zdHU8SUlSXSdT/8\nIGrnr7wS3nmH5IubSFL2E0gxjaMOkTRluFiZuXy5eNQ2p5JFDh5vVljNePLzVZTeM9GrSS8O5Rwi\npzAHg0HUrtx2W3n3KBAPSdb3rWJDMQeyD9CpgfPpN+usQIOLKWw8vtHu/tkF2WQXZJMYm+j0Neoy\nTqX45BxU7aOqArVnD5w6HI1qCGTvXtXCbNuUyrBlURQZKXL9114LHy44TIAS6PCGEOgfSN9mfbkQ\nud5mF1/TDQJjIBkHw8rGodGIO9OePcJELTlZhHR33ikcHAoLxetbbiFy4o2sy0niuxWZMO1GIqMc\nODhUMoVnK71Zm/DU5ysxlLDu2DqGthpa4b6B/oH0ix/EjDkZJCWJKv9vvxWts5xhf9Z+Wka3JDTQ\nybpyymcFxg5pz97MveTqcm3uv/30dro17mazGlFSHqeKJOQcVOVQFCVIUZRPFEXJUBQlV1GUHYqi\njKj4SM9TVYES/zAV8C+mVaLOaUPX3FyRWVu3Dh66pQ0X567m668V1q+3/9Q9uMVgtmWvttlLKTkZ\nOnYyovgV0akjJLUtEnekp54S6bjOnWHVKnHHDAoSFXcjRsCRI3DunLiDtWhBZLQ/o4Y15Kz+IPpB\nAy0H4IZ5JVvpzdqEpz7f3yf/pm1MW5sO+9Z8+y1sffpb3n2mB//+Cy1bwiefwOWXO3ctV9N7UL7H\nV8OYUMZ0GMMH22x3yf1o+0eM7TjWpWvUZWQE5VkCgGPAIFVV6wHPAz8oitLCi2OwSVUFyvQP87r/\ne4NJ733ptKFrvXoie/a//0FAZDbn0ptzxx0iLTRwoG2RMlXyWURml9J2kZGwYH4qsxOuYn3CBCJb\nxYm5o61bxeLYsEuf8aab4IknYNo0YUXdsmXZBS4JUKB/IE0im3C0u5NzWS7gcrNCH8NTn8/Z+ScQ\nS9EunK1HcONDfPmlWNt0zz2OHSDM2XXW9QIJKJ8xeHrg07z999sUlhRa7Jd2Lo31x9Yzqcckl69R\nV3FYJGFykvAxt/KK8No6KFVVC4AXzV7/rijKEaAnQrjchqvtr6sqUCCuc+NVzVl0YBFwv9PHRUXB\n7ZNP8LqxLxNzjjF7tnB/2LfPdu+nPk37EL15J4V3For0i6rCggWwcSMsXkyHv/+mo6qCyamoYUMR\nHd1zDzRtKsoJ58+3PyCzCMlkedQmxv2LKB02K6wFuPPzmf6el6dtYNaIp5w6ZuJEaNhYz8R9Pbhm\n3BECA2Ncumbq2VQe6fNIZYZrQXLDZHo36c3nOz/nod4Plb7/v/X/Y0q/KW5pillXsBdBlXOSkCm+\nqqMoSiMgEXDrDERxQbDLE9TuECiAIS2HsPboWpf/QBb/u5hrOl3OjBn+dOlimRrSamHT3B1otSIl\nGBoQxo2n63Pou/eFl13LlmJV8LPPwubNqKYHqJEjRRnhggWi8u6TT0S7CvNoCRym7BJjEtmftd+l\nz1IbsFWBV11Vh2UFFypbXnqTrvVFytVgEB1Kxo8XRZjWhIbCuLEBXJbg3HooayobQdli2sBpvL7x\n9dIKtPTsdP449IeFYEkqJsAvoM4t1K0WJwlFUQKAr4H5qqoecOe5s4/G220xbg93CVSLei0IDQjl\n3+x/6RDXoeIDgL2Ze5m9eTavXfEakZGi4i8tDZJy1gGDGDQI0nZ3Jen9EsbovmNIzi/ckZdJ4FKr\nntrdukH79izsHU7kP3sZ/vXvZdsq2V22Z5OeDquwaiMmQTA1WFx3aV209XveSkuWFVwoKJkd2bY5\nkN27RZuLI5ei5NGj7bvqp7QU66Fs+fbZ41z+OQrzAziR1pz6nav+Wfs3709CvQS+3/M9E7pM4JX1\nrzC592SigqOqduI6hr+fv12z2NpaJOF1gVJEsvRroAiwm0OYccki58y2M2xtuJWuY52bsI1NOO2w\nxbitX567BApEFGVacFsR83fO5z8r/8OrV7xaegMpTQ1N/5NN5xqStrsteqM/e/fq+ZD36cffAJyh\nIdr4DoRMvJnmAWdKm/mtX/444/da/cOvZOVdn6Z9ePvvutXl1FYFnqqWf89b6UlTwcXutBLConSM\nHh2I/tI9qlUrYXN49dX2jx/acij3LbnPpWtuPpSG/pPVDJmluE2Qpw2cxpN/PMnAFgP59d9fSX8k\nveKDJBb4K/4YVWM5+yhfiKA0Gg0a667XTlAdEdSnQBwwUlVtxKuXMAnULx/+Qu8BvZ0+eVBYkd0W\n4/YWqRWUFBAdEu30NRwxJGEIfx7+k/t72Z+Hyi/O56GlD7H15FZW37latFbXaETBwl9/CZ+7L74g\nuXA2SaxjLx3pxH46tipiT9sp7EzVc/u5d+A0NP8KMu6aUZqr3Z+1H/1g91TeJTVI4uiFo2iLtOXM\na2sr5j5x5g84jh56PImp4KL7rIlMaDadWVMiue460a1k+HDLDiW26BHfgyPnj5BdkE1sWKxT1/xz\n8xkKTw3CaHCfIF/V5iqC/IMY/f1oJvWYVNqhV+I8iqKgoGBUjfgrZb94CyeJGhpBpaSkkGJ2H5pp\n3h3bAV4VKEVRPgQ6AFeoqmojc+4eXJ2gLigpqJRjsy0GJwzmhdUv2DTJBBHB3bbwNnr8m8erD2/l\nyIYCtEfnE/ne/7d359FRVdnix78nA3MIMSBKgIAEhIQZwhyIgIBMypNhCQioiM8WXr9umrYVfWL3\naxH9obbIE7FtcWpoEEERQUBMiAwyKQJBJglzMyYkJMSEcH9/nAyV1JCqpIZblf1Zq9aSmu6plHX3\nPefss89cnWlnMaEQVqcOKS1mcDCkA3FfziPsjh8IB9rOmcOsnMEMTF9GpzYRBHVOBCAjN4Ntp7fR\n4ffL3fJZQoNDad+wPXvP76Vfs35ueU+zKwoIZS9w7F30uFtGht4M0DIdPD/kKhdqbaZf+yWMOwBt\n2jj/fqHBofRu2pstJ7cwqs0op15zJSyZRncN4kJapNsCslKKZ/o8w6TVk9gw0cnFWMJKUSZfMCUB\nqlQlCUeljkzYsyqP1wJUYTr5NCAXuFB48jaAJwzDWOqtdtiSned6NXN7WkS0wMDgl/RfSme/JSVB\nYiIrDi4n5Mef+G1KS/rNO8PBG82JoyMpnCOMPF0IbcQIOHcOFi0iLCiIHnPmwB0W2U6JiSReOUz/\nu1bzSKdHgERAJ1vc0/we6lavy4IFsG+f3rw2MbH8K2174hvFs/PsTqsA5WqmpCXDMFi8ZzEnMk5Q\nM6QmtUJr0bBOQya2n+hw0WZljllk4c6FzNs6j1aRrYhrEEfc7XGMaDWiVIV4Wxc4nsw6zM7WNXmX\nLYO1a3VVhwsXdIYnwNep2+D9FAb9NaRCQ26J0YlsPrHZ6QB1KHMnH645Qc30SLcG5NGxo4mPirdb\na1KUrziTz+L37MoclL+loXsti88wjFOGYQQZhlHLMIywwltdXwcngJyb7puDUkrRL7ofh1e+Y3GA\nHHjnHW48NpmE3uP5dN4JUrdlcvBGc25SjVRidc273/1OB6fERGjUSBf0A5slhXo36W2VwLAidQVj\nYscAsHgxvPceDBwId94J06bpYrW2Mr4ciY+KZ9e5XaXuq2wpn1e3vcqCnQsIrx5OgVHAxeyLzN8+\nn/nb5tt9jTvKB33+8+e89N1LrBy7kj/0+gNNw5uSlJZEn/f7cDbzrOtv6AZTp+qVAGPH6u208vJ0\n4dYLF0qes3rLMXLONatwZYohMUNYd2ydU0M/N/JvcPjKYbo1b2O3AkpFKaVoVq+Z+96wCrK1Fsof\n5qAqSvaDouLVzK0U9pL6Rvcl6IM34VYLnQv8zTeQm0tNoCZAWBhtsw4QV+88qZlRxDbPI27MSJj7\nrO33tTGH1KtJr1Ir9K/lXiMpLYmPRn0E6OzypUv1VfmxY/Duu/q2f7/ugTgrvlE8z39bel97W4kE\nzvYuPtz3IQt3LWTro1tLVVyfcW0G8e/G07tpb3o16WX1usocE2DPuT1MXTOVr8Z/RXyUntMcEqML\nmbyy9RUGfjSQ5CnJ3F77duff1A1yc/X1S/fuMGaM3qolKqr0cw4FreCulo9z8lhtl4bcinqccXHt\nyb2Zy5ErR7i7/t0OX5N8MpnOd3aW9UkmFRIUYrUWKpCz+KQIFpXI4ivcO2n7dsi6dgs++QReeIEp\njy5gyJpDeiZ77Vp9FgK2x9Qgf+qj8PnnhL0wk5RT0WzZGkLKD3UIq16ma1NOYkP7hu05de0UV29c\nBWDNkTX0a9aP8BrhgJ7M/8tfdAWBffv0JoojR9o+uRkG/PAD3Lpl/VjLyJak30jnUnbJ7roVLeWz\n/th6Zm2cxboJ66y2A2ka3pS/j/g7D618iCs5V6xeW5nyQaevneb+ZfezePji4uBk6Y+9/8iY2DEM\n+mgQ6TfSnX/jcuTl6WuWP/0JVq60/Zw5c/Ta6R07YOZM6+CUfiOdEzk/8f22ai5VprDscfbtqxgY\nNYq1R9eW+7p1R9dxX4yDtEDhU8HKOtW8VCUJP6tWXh7pQeFCgCrsIRXJWpNEwiOdOHiqNnFBh0m5\nuYwwrlOj8PHzUeH8UDebX0YkkP/jHjosWkVo88LZ7+Tk0vMaLmbahQSF0C2qGzvO7GBoy6F8mvpp\n8fCeJaWgfXt9s2f/fj311aABDBgA99yjbzExeqPELo26sPvcbu5rqU9c9hIJHNl9bjcPr3qY1eNW\n2y2IO+LuESSfTGby6sl88dAXpeajHB3T0dxUTn4Ow5cO5797/LfDOZgXE1/ket517vvkPjY8vKHC\na3ROn9a9182bdamj7Gx9//33630dy4qJcfx+KadS6Nm4J7fVC3Wpx1i2xzneGMNXR//M73v+3uHr\n1h1bx79G/8v5AwmvsjXEZ1VJIoCG+KQHhYsB6vRpXYJ86FAOvLGJg2k1uXkrhNSbMXoeqWtXvWpy\n4kTuPJNBt93nyRw+kK6NutK/uUVqVgW3qrDUq3Evtp7aSuavmWw+sdnhVh2OnD8PTZrApUt6SPCJ\nJ/Su7aNH68fjG1nPQzmq0l6kqHd5KT2X8SvHs3DoQno37e2wLXMHzOXKjSu8tv01q8dsHbO8uam3\nd71N83rNmdlzpsPjKqWYP2g+Xe7swoAPB3A557LD55f1681f2Xh8Ixt3pjFrFqxbp4NTbKzuGf3u\ndy69XbGktCQSmyW6/LqyPc6H7+3MzrM7yfrV/uTd8avHycrLouMdHSvWWOFxtsodBfIQn/SgsA5Q\nxVfk6SmEDemti61++aWexLHI329LHeJCjpJa0IrYqOvETRgBL8/WDxau46pfqz7PJjwLBWXmVdxQ\nFbx3097M2zqPL498SUJ0QoXXcg0erIeZDh/WV/5JSfrWrp1+PL5RPEv2LSl+/q5deuiwa1fdAwgO\ntu7FWFZkiIzOoMvszoyNG1tuW0KDQ1n64FI6v9OZCe0mlMqus8XR3NT1vOu8uu1VNk3a5NTQh1KK\nt4a+xezNs+n7fl82PLyheCgyN1e//969+vNfvgzvfZLB8oPLWXt0LUlpScQ1iOPIhdP0HPk1vxnT\nhv79FY0quXoh+WQybw550+XXWfc469CzSU82/rLRbgXxdcfWMSRmSMANEwUSSZKogooDVFISWV0S\nSehVwMFDEBd6OynVowm7dqbkyaGh0KIFjBxJWEEBKS/EFZ4EIgmbn1/yPDf0kMoTF96DHdsVNQpW\nM66z9fCeK5SC1q317Te/0fNShVNnxEfF89RXTxWv7fr4Y3iz8JxZs6Zel5OWBpmZJaWALAPHhRMR\nPN7kDafb0qxeM6Z0nMLL373M3+5zXMnC3sJa0Cnlic0S9UJop/8OipcGvEREjQgS3k9gzeiNPDQk\nhkOHdP27kucZJL3aiYFtujEubhz/GPkPImtFcuzqMcZGjuXz6i0YcdvfgXCnj11WRm4GR64csTlv\n5oyyqfFDY4ay9shahwFqcofJFTqW8A67PSikBxWYkpLIyc+hzvkr8MorHLj6OQcPzNPp3wXNOJgb\nRY/oYJ3+nZ6uc7erV9evnTPH/jySBwKSpawsGHFvPXL3f8361am885N7dy1RSgcfgCZ1m2BgcCbz\nDE3Cm9Cli55T2bMHzpzRvYoiRb2Ytm0hNtZg/8GbhNfP5fCeO1iVpZMAoqKgYUMIcfB/39O9n6bN\nwjbM6j3LKqHCkr25qcxfM5m/fT7JU5KtXnP6tO4xnj6tb2lpesfjFStK1h7N6j2LiJoRDFjam6zz\nB7hlRNIwOoM7Yi7wS61/ER8Pf5u6nrZ3ls6Ki7kthm2PbWPm1zPpsrgL6yeuJ+a2ciaa7Eg5mUL3\nqO5UC65WodeXNazVMF7e+rLNReQ38m+QcjKFj0d97JZjCc+w14OyTJKQHpQfq7NtNzzYSV8O79wJ\nzz9P0tF0Ip7uBEBbUohjMqnEEssh4h7tAY3DddZAUlJJcAKv9JLssdw9V12O5dwvoTT1UIa0Uqp4\nHqpJuN6zatIk/Vh6Onz/vd7N4+LFkl5MWBjMfHc1c1asoMnOj/nTn0q/Z1CQ3kX+3nutj/fPf8LF\niw3peu5dJs/ZzLTuk6hWDfr1g9tsVMjZsQPOntWBMidHz/1sOHiIPoPG0qaBddmFAQPgqI1ScMeP\nQ6dOJf+e2nkqvZr0YmPsLq5XP8y53GPcuHmDJd3/y+E8TY2QGiwctlAXRf3qKdZPWF+hYbPkk8kV\nmn+yJ+a2GOpWr8sP//6Bznd2tjpWhzs6EFEzwm3HE+4XEhRilcVXqpKE9KD8jEXmXa3cAup/sALW\nbNVL9y/p1Ol2gFGtGiovj7D7B5AS/SkH7/4P4k6vJ2yug6EpLwaksoqGtg6m3uKuljeJi3NyJ7oK\nim8Uz66zu6yGhyIi9Ka8P/9cuheT+Wsmz343g6XTl3JkUxBxcbq3cvasvl28CPXsTJm99ZZOrgCd\n9ra58P5t2/Qi1rKef14HydK6s+xR2/NXnTvrQNekCTRurHcgadFCbzpcVmyDWGKHxgJDbTfWgZk9\nZ7LkxyWsPbqW4a2Gu/z6pLQkXh/8usuvc2RYy2GsPbLWKkBJerl/KDdJwlGpIz8MXAEXoGJ+OgOW\nv7NVq3Qe9Zo1JG0+QGjB/pLH6tWDjAz+2TGY8cP/qM+gS5YQBvQAmPNF6Tf3YUAqq2RoK4i4uJoe\n3/4hPireZmadZXss5ztmfzObQS0GkRCdQMJjuodlKT+/pFBGWePHQ3y8ngPbdmIv2Tm3aF+/a6ne\nk2VSxqBBcPfdesPg2rVh18VkcoLP0bvtQzbff9ky5z5zZUsrhQaH8vrg1/nt+t8WF0t11plL10j9\nIZw2Y7q5fmAHhrUcxuzNs3m+X+nF15Je7h/KTZIor9SRnyXA+H+AKrM2qeW+03pTpS+/1FUcUlOL\nHysuXzVggD6jjR5N9sav+G3EEsbP+ktx5l0xEwUkW7y5K22bsG7s2K649sAtwus6Xp2QlJbEqp9X\nsf/J/Xaf42jr8enTS/77Sk40rd5qxWuP7+KuCN3FsbVnU1EAOZd1jvZvP8iOqTtoXImC2Y6O4Yr7\nWt7Hgp0LeGvnW+WuQbI8dt++kHt0PQO3h7p1/6mE6AQOXT7EpexLNKjdAJD0cn9irwdVXM3czwJQ\nefx/HVRSkt5qdvlyBr34Mf1X7tVnlnnzSoJTbCyMGsXM/2zO+d9Pg02bYOFCuOce8m/ll6SY+3BO\nycyysmDUkPpkL/6K+J65DuvgXc+7zqOfP8qi4YvcMp8RWSuS6fHTeeabZ4qvDG2llheZ/tV0nuz6\nZIUTE4o4OoarXhv8GnO/m1uqGkd5x047WgujILTSxy6rWnA1BrUYxOTVk1l+cDmZv2ZapZf7avdg\nUT5ZqGt2RZteHT8Ob7wBH3ygJxTGjaPN+t1UyyvQEyPdu8P8+fDcc/oX/tlnJHe0nvTI6NHRfoAS\nQOmEjKOHQ9j3k/WunkWe2fQMCdEJFZpzsefpPk9z4OIBPvpJ1xm0V/ZoZepKDl0+xHN9n6v0MStT\nWqms1vVbM6HdhFI1DR0FgdubXUQ1+JnQUMMj+08tHr6YB1o/wJIfl9D4tcbMSZpTPP/kjqK8wnNk\noa4J1d62C0bG6V/07Nkl+cGWmjblp86NybiZRd8v9uk8abAatsvq1QXLqfPL3dpS+0spjOlIyVoj\ng+p3nmZD1mf0YZbV85wZ2quIWqG1WPbgMvp/2J8ejXvQKrKVVWp5+o10ZqybwfIxy6keUr38Ny1H\nRco5OfJCvxdovbA1T3R5gpg6nRwOH35yZBGT3rjME9FvemT/qYiaEUzrMo1pXaaR+WsmW05u4d67\ndDplZYvyCs8KCQqpUgt1zd2Dyshg8O4MombP0wtn+vbVqVynT0N4uC79PGoUXLkCJ0/y7dNjya5b\nsyQ4gVWv6HqvrqX+7c7t3gNV0cl6yxbFzq3VeXv/Kxy4eKDUcy5lX+KxLx7jneHveCRVuV3DdryY\n+CLjV44nryDPquzRrI2zGNV6FH2a9nH8Ri5wppyTsyJqRvBS/5d4cu2T/LT/lt3hw7yCPBbtXsTM\ne6a5fbsLW+pWr8vwVsOLg7o7e47C/YKDbBeLDdQelHkDVP/+0KABr7x3ipo/H4OrV0sWwUyaBDNm\n6KJx7duXWhxzrH2ZRZ3lDNtJgHJO0cm6TePGzB0wlymrp5BfkM8t4xaL9yym7dttmdhuIsNaDfNY\nG57s+iSN6zZm9jezS93/zS/fsOH4BuYOnOuxY7vDI50eIUgFsefmB3aDwKepnxLbINal6hfuVHIx\nUvHEEOE5dpMkZKGul337LSjF2dtCibqar1O7IiP1sv8lS+y+zCpAlUMClOse6/QYK1JXMGPdDH78\n948EBwWzYeIGOtzRwaPHVUrx3sj36PROJ36+8jPnss6RlpFGXkEey0cvr3AFcm8JUkEsGr6IgR8O\n5Pv1I7iQVt9qCO9v3/+N2Qmz7b+JF3gzO1S4xmaShCzU9YEHH4SYGP4nbwV/DbqXO/7fAn2/m1PB\nJUC5TinFuyPe5YFlDzC923SmdJzicKt2d4qsFcmmSZv48d8/0rxec5rVa0b9WvX9Jr22fcP2TGw/\nkT9/P4v373+/1GPfn/meS9mXGNbSc71Q4d8qs1DXH5k3QH36KQC7F62DYxb3uznTTgJUxTQNb8re\nJ/aW/0QPaBXZilaRrXxybHd4MfFF2ixsQ8rJFBKiE4rvf3Pnm8zoNoPgoGAHrxZVWWUW6vpj4DJv\ngLJQKrFBApTwc2HVw3h98OtM+GwCCdEJ1K1Wl7DqYaw7uo6FQxf6unnCxCrbgypa0Osv/CJAZfeq\n2HYDzpAA5TmVLRUUyEbHjqZGQQN278sl/LbT5Idc5cNRH1Z4Ty93k+/OnOylmRdXkvCzAFQevwhQ\nniQByjPcVSqoMsc38wn2+nXF85MSffb3ccTX352wz1aauVUliQBKkjBvmrmXSIDyDHeWCnKVP1RD\ncPbv44uyQ7787oRjTlWS8MO5JnskQEmA8ghfLvj0hxOsM38fXwVaWaxrXk5t+R5APSgZ4pMA718H\nhgAABrtJREFU5RHuLhXkCkfbwJuFM38fX5Ud8uV3Jxyraj2oKhegyl5deCNAmX0+xFN8teDTX06w\n5f19fBloZbGuOTm15XsA9aCq1BCfrcWc2fnZHg1Q/jAf4mm+mEdxZx09X5GyQ6KskKAQqx6UVSWJ\nAOpBVakAZUtOfg61Qz1XzdyT8yH+sG+PBOjKCYRAK9wnWJVTLFZ6UIHF00N8nppw9pcTvz8kLAjh\nL4KVE5UkpAcVODwdoDw1TOMvJ37JCBPCfYKDnKgkYa/UkR/2rCRAeSFJwhPDNP5y4g/0eRR/GGYV\ngcNeD8rZShL+UlS5iAQoP00z96cTf3kB2l9P8v4yzCoCh60elFUlCRniCxz+GqAgMCbQnT3JmzGI\n+cswqwgc5c5BSZJE4DAMg5z8HGqG1vR1U6osZ07yZu2p+MswqwgcttLMJUkiQOUV5BESFEJIUJVb\nr2wazpzkzdpT8adhVhEYbBWLlR6UmyilIpRSq5RS15VSJ5RSD3nz+GX58/BeoHDmJG/mnkogDLMK\n/2E3SUKVJElID6ri/g/IBRoAE4G3lVJtvNyGYmYMUElJSb5uQoVUZo6o6CS/Z0+S3ccDuafir9+5\nO8hnd43NJAnLShLSg6oYpVQt4D+A5wzDuGEYxlbgc+Bhb7WhLAlQ7uGuOSJHnz2Qeyr++J27i3x2\n18hCXc9pBeQbhnHc4r59gM8GbMwYoPyRWeeIhAg0lVmo64+8GaDqAJll7ssEvHpNbHl1IQHKPcw8\nRyREIHFmy3dXelBmD2bKWw1USnUEvjMMo47FfTOBvoZh3F/mueb+qwkhhKgUwzDKLWvhzfzqI0CI\nUqqFxTBfB8BqQMiZhgshhAhsXutBASil/gkYwONAZ2AN0MswjENea4QQQgi/4O0086eAWsBF4GPg\nPyU4CSGEsMWrPSghhBDCWaYtdaSU+kgpdV4pdU0pdVwpNdvXbfIGpVQ1pdTflVJphZ99r1JqiK/b\n5S1KqaeUUruUUrlKqX/4uj2eZLbKKt5Ulb5nS/L7du28btoABcwFmhuGEQ7cB8xQSg32cZu8IQQ4\nBSQUfvbngeVKqaa+bZbXnAX+Arzn64Z4gakqq3hZVfqeLVX137dL53XTVkk1DCPV4p8KyAcu+ag5\nXmMYRg7wZ4t/r1VKnQC6oP/HDmiGYawGUErFA1E+bo7HWFRWiTUM4wa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"text/plain": [
"<matplotlib.figure.Figure at 0x1161a9a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn.pipeline import Pipeline\n",
"\n",
"for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
" polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
" std_scaler = StandardScaler()\n",
" lin_reg = LinearRegression()\n",
" polynomial_regression = Pipeline((\n",
" (\"poly_features\", polybig_features),\n",
" (\"std_scaler\", std_scaler),\n",
" (\"lin_reg\", lin_reg),\n",
" ))\n",
" polynomial_regression.fit(X, y)\n",
" y_newbig = polynomial_regression.predict(X_new)\n",
" plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
"\n",
"plt.plot(X, y, \"b.\", linewidth=3)\n",
"plt.legend(loc=\"upper left\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.axis([-3, 3, 0, 10])\n",
"save_fig(\"high_degree_polynomials_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure underfitting_learning_curves_plot\n"
]
},
{
"data": {
"image/png": 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XrnaVfNZZNhzvO+/YVfL06dGNpOZqrsLfOx+eJuFVeS/oqppVnp3X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\ndmCrufZzz57KiNc551wMVXeSqg9sKbR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"text/plain": [
"<matplotlib.figure.Figure at 0x114c85518>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.metrics import mean_squared_error\n",
"from sklearn.model_selection import train_test_split\n",
"\n",
"def plot_learning_curves(model, X, y):\n",
" X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
" train_errors, val_errors = [], []\n",
" for m in range(1, len(X_train)):\n",
" model.fit(X_train[:m], y_train[:m])\n",
" y_train_predict = model.predict(X_train[:m])\n",
" y_val_predict = model.predict(X_val)\n",
" train_errors.append(mean_squared_error(y_train_predict, y_train[:m]))\n",
" val_errors.append(mean_squared_error(y_val_predict, y_val))\n",
"\n",
" plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"Training set\")\n",
" plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
" plt.legend(loc=\"upper right\", fontsize=14)\n",
" plt.xlabel(\"Training set size\", fontsize=14)\n",
" plt.ylabel(\"RMSE\", fontsize=14)\n",
"\n",
"lin_reg = LinearRegression()\n",
"plot_learning_curves(lin_reg, X, y)\n",
"plt.axis([0, 80, 0, 3])\n",
"save_fig(\"underfitting_learning_curves_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure learning_curves_plot\n"
]
},
{
"data": {
"image/png": 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TJzWpNGmiVYDNm2tiOuccaNo073Ym56BxY01WAJ99Bj17Fnn4xpgoU+QdJ/w5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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114c7fb38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.pipeline import Pipeline\n",
"\n",
"polynomial_regression = Pipeline((\n",
" (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
" (\"sgd_reg\", LinearRegression()),\n",
" ))\n",
"\n",
"plot_learning_curves(polynomial_regression, X, y)\n",
"plt.axis([0, 80, 0, 3])\n",
"save_fig(\"learning_curves_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Regularized models"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure ridge_regression_plot\n"
]
},
{
"data": {
"image/png": 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ZIgjuxo4dZmkKoGxZY8FJY9s2aNuqNGH1wwo8bOXKRbxEpbU+o5R6BrhaKTUZ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\npfN/hqqy05/IFPIAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1161ddc18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import Ridge\n",
"\n",
"rnd.seed(42)\n",
"m = 20\n",
"X = 3 * rnd.rand(m, 1)\n",
"y = 1 + 0.5 * X + rnd.randn(m, 1) / 1.5\n",
"X_new = np.linspace(0, 3, 100).reshape(100, 1)\n",
"\n",
"def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
" for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
" model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
" if polynomial:\n",
" model = Pipeline((\n",
" (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
" (\"std_scaler\", StandardScaler()),\n",
" (\"regul_reg\", model),\n",
" ))\n",
" model.fit(X, y)\n",
" y_new_regul = model.predict(X_new)\n",
" lw = 2 if alpha > 0 else 1\n",
" plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
" plt.plot(X, y, \"b.\", linewidth=3)\n",
" plt.legend(loc=\"upper left\", fontsize=15)\n",
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
" plt.axis([0, 3, 0, 4])\n",
"\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(121)\n",
"plot_model(Ridge, polynomial=False, alphas=(0, 10, 100))\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.subplot(122)\n",
"plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1))\n",
"\n",
"save_fig(\"ridge_regression_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1.55071465]])"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.linear_model import Ridge\n",
"ridge_reg = Ridge(alpha=1, solver=\"cholesky\")\n",
"ridge_reg.fit(X, y)\n",
"ridge_reg.predict([[1.5]])"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1.55071465]])"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sgd_reg = SGDRegressor(penalty=\"l2\", random_state=42)\n",
"sgd_reg.fit(X, y.ravel())\n",
"ridge_reg.predict([[1.5]])"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1.55074549]])"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ridge_reg = Ridge(alpha=1, solver=\"sag\")\n",
"ridge_reg.fit(X, y)\n",
"ridge_reg.predict([[1.5]])"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure lasso_regression_plot\n"
]
},
{
"data": {
"image/png": 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O1kUpFRo0riil3KJbNYSh/Px8Hn/8cbp06cLo0aO9dh59bcKLbtUQ3nwVV3xBX//AEDBd\nVCo4zJ49m8mTJ/P6669TWFjo7+oopUKAxhUViLwyi0oFrrFjxwKwbt06/1ZEKRUyNK6oQKQtOEop\npZQKOeHVgiMCZftVnb7soQ0bNjBv3jw6d+7MunXruPvuuxk4cCCHDx+madOmRERoPqpUQAnwmAIa\nV1T4Cq8EJ4AtX76ce++9l+XLlxMdHc2OHTtITExk165dzJkzhwkTJpSUzcrKYvz48SWD4MoOhise\nHCcixMXFMXHiRJ8/FqVUYNC4osJZeCU4p38zcvqy29UyjB07lhkzZhAdHQ1At27dSE9PZ/Xq1dSv\nX79c+ZiYGGbOnOnIuZVSHgjQmGIPpXFFhTdtmwwAy5cvJzU1lWuuuabc9bGxsTz33HPcdNNNfqqZ\nUipYaVxR4S68WnAC1P79++nWrRtRUVHlrhcRhgwZQvPmzctdf3pTcmW0KVmp8KVxRYU7TXACQP/+\n/Tlx4kS565YsWUJERATt27cnPT29XDDSpmSlVHU0rqhwpysZB4iXX36ZPXv20LFjR3Jzcxk0aBB7\n9+5l0aJFDBw4kHHjxjlyngULFvDJJ5/wzjvv0K5dOxITE5k4cSKdO3d25Phlhcpro6zMTEhJgd69\nITa24u26knHgCcW44guh8voHqrfegrZtoXt32LHDezFFExzlNfrahI7MTLjkEtiyBeLiYNmyigFJ\nExwVKvT1956dO+Gcc6BTJ9i0CSIibILjjZiig4yVUtVKSbHJTX4+bN1q/1ZKqdp6+224+WZ44QW7\n7FNBQfmYMvnzyfx79b8dSTB1DI5Sqlq9e9uWm61boVcv+7dSStXW22/D3/5mY0qnTrBrV2lMWfzD\nYp5a8RR1Iupw2VmXeXwubcFRSlWQmQkrV9rfYJuOly2DpUtdNyUrpVRVMjNtcvPTTzB4sI0hn38O\nDRvauJItadz6/q0ATEuYRo/mPTw+p7bgKKXKqWy8TWwsnH++v2unlAo2xTFl82Zo2hRycmw86dwZ\nYmLg6LFC7lx6KwdPHGRIpyE8cNEDjpxXW3CUUuXoeBullJOKY0phIRw/Xj6m9O0Lj372LEt2LuGM\nBmcw9/q5REZEOnJeTXCUUuUUj7eJitLxNkopz/XuDV272r9Pjynx8dDkwLUMaDOA2dfNpm2jto6d\nV6eJK6/R1yZ4ZWaWdlHVdLyNThNXoUJff+f98592zM2CBeVjyrx58NFH8Pr8ggotNwE1TVxE6orI\nqyKyW0SOi8h6EbmikrJjRCRfRDJEJLPo92An66OUck/xeBt/DybWmKJUaNi4EYYPrxhT+va16+E4\n1S1VltODjOsAPwGXGGP2ishVwFsi0tsY85OL8t8YYzwKQB07dkQkKL40hp2OHTv6uwoq+Pk8poDG\nlXCnsct5334L991X8foePexU8ZMn4bQN7j3maIJjjMkGppe5/LGI7ALOwQYpx+3evdsbh3VLdUvZ\nK6Vqxx8xBQInrmhMUaHg2DHYu9e+jwG2HNxCrxa9EBHq1oVu3eyEhgEDnD2vVwcZi0groBtQ2TyM\n/iJyUES2i8gUEQnaQc/F0+AGD7a/i9cPUUo5R2OKUsFnzRqbvNSpAxtSNzDwlYGMWDiC3IJcoLSb\nymle+/CLSB1gHjDbGPO9iyJfA72NMS2BXwE3A/d7qz7eplNrlfIujSn+rpFS7vn2Wxg0CPZn7uea\nN64hJz+H2LqxREVEATbB2bjR+fN6ZaE/sZ3X84BTwD2uyhhjdpf5e4uITAf+BDzlqvzUqVNL/k5I\nSCAhIcGx+jpBl7JX4SYpKYmkpCSfnEtjisYUFbxWr4aRo7O5dsG1/Jz5Mxe1v4gXrnqhZJxb376w\nZInzMcUr08RF5DWgA/BLY0xuDe8zErjfGHOui9uqnNIZKNyZWqtUqPDmNHGNKRpTVHAyBlq1LmTg\njJF8snshnZt05ts7vqVFwxYlZTZvthtwpqSUv29ATRMHEJEXgR7A8KoCkYhcISIti/7uAUwB3ne6\nPr4UKFNrlQolGlM0pqjgtWcPRNTP4kjePhrVa8RHv/6oXHIDcMYZcPiw8+d2tItKRDoAdwIngbSi\n5icD3AUsB7YCPY0x+4ChwGwRaQikAXOBJ5ysj1IquGlMUSq4ffstXDCgEa+P+YLv0r+jV4teFcoU\nJzjGgJOrMwT9SsZKqcAQSisZK6Wc8cc/QsuWMHly1eViYuDAAfu7WMB1USmllFJKAaxdCwMHVl/O\nG91UmuAopZRSyjFbD20lryCPwkI7/bt//+rv06yZJjhKKaWUClCrf17N+a+ez6/e+hXbdpykSROb\nvFRHW3CUUkopFZA2pG5g2LxhZOZm0rBuQ1I2RtWo9QY0wVFKKaVUANqQuoHL5l7GsZPHuL7H9cy5\nbg4bkyM1wVFKKaVUcNp6aCtD5wzlSM4Rrj77ahbcuICoyCg2bKjZ+BvwToLjla0alFJKKRUeOjXp\nRP82/YmtG8ubN75J3ci6ALVOcHbvdrZemuAopZRSym3RUdF8ePOH1ImoU5LcpKZCXh60a1ezYzRr\nBuvWOVsvTXCUUkop5ZHoqOhyl4tbb2q6MrHfxuAU7fHysIj8T0Salbn+BhH5zNkqBbbMTFi50v4O\nV/ocKOWscP9MhfvjDzb5hfnVlqlN9xT4KcEpSmjOMcY8CnQEBpe5eQR2z5ewkJkJl1wCgwfb3+H4\nYdTnQClnhftnKtwffzAxxvD40se5Yt4VnMo/VWXZoEhwgERgnoj0BboCq8vcdimwzNkqBa6UFNiy\nBfLzYetW+3e40edAKWeF+2cq3B9/sMgryON3H/6OKV9N4ctdX5K0O6nK8kGR4Bhj3jTG7AFuA740\nxuwHEJHuQCvCKMHp3Rvi4iAqCnr1sn+HG30OlHJWuH+mwv3xB4NjJ4/xy/m/ZOaGmTSo04B3RrzD\nsK7DKi1//DikpcHZZ9f8HE2a2Na7ggIHKlykNoOMbwSml7l8KXDYGLPVueoEtthYWLbMfsOIi7OX\nw40+B/ZDmJJiA3M4Pn7lrHD/TIX74y8WqHElLSuNS2dfyneHv6Nlw5Z8ePOHnNf2vCrvs3499O0L\nkZE1P09EBDRuDEePQvPmHla6SI0SHBFpCrSlfPdUArDCmWoEj9hYOP98f9fCv8L5OSgeL1AcjJct\nC6xg5A979sAXX/i7FsEtnD9ToI8/kONK8+jmdG3WlbqRdVl08yI6NelU7X3WrYNzzqn9uYq7qXya\n4AC5RT8GQES6Ab8EHnWmGkoFB1fjBcItMGdlwddfw5IlsHgxHDkCiYn+rpVSwSuQ40pkRCTzfzUf\nQYitV7Osa906GFZ5D1alnB6HU6Np4saYE8CdwGQRmQT8CYgljMbfKAXhOV6gsNAOGHzySRgyBNq0\ngaefhtat4fXX4cAB+1sp5Z5AjyuN6jWqcXIDtovKkxYcp4gxpvZ3EpkK/AFoY4wpdK46lZ7PuFNP\npbwhMzP0xwukpsJnn9kWms8+s6uMXn65/VZ26aUQE1PxPiKCMaaGy3r5l8YUFWgCIa5sPLCRpg2a\n0qFxB7ePkZFhvwQdPw51armU8Jgx9kvU2LH2sqcxpaYL/T0qIr8s+luAUcAzpyc3IlJXRF4Vkd0i\nclxE1ovIFVUcd4KIpIrIsaL7Rbn7QJTyleLxAqGU3Jw8CZ9/DvffbwcH9uoFixZBQgKsXg3bt8Nz\nz8FVV7lObrxFY4oKF/6MK8YYXlz7IoNeHcSIt0eQW5Dr9rE2bLAxpLbJDdgWnCNH3D51BdVWQUSa\nAw8AdxRd9SdgDzCjkuP9BFxijNkrIlcBb4lIb2PMT6cddxgwCRgCpALvA9OAB918LEqpGjIGtm2z\nLTSLF8OKFTYoJSbCSy/BwIHuBSgv0JiilBcdzTnK7z78He9seweAPi37UOhBx4y7A4zBthQ72UVV\nbQgzxqSLyB+BViIyA8gCrjLGVJitbozJpsxUcmPMxyKyCzgHG6TKuhWYaYzZDiAi04H5aDBSyisO\nH7atNIsX2wHCderYLqc774QFC+w6FIFGY4pS3vPlri8Z8/4Y9mXso1G9Rrx09UuM6j3Ko2OuWweX\nXebefc84AzZu9Oj05dToO5ox5t/uHFxEWgHdAFdrU8Zhv2EV2wi0FJGmxpij7pxPKVUqLw9WrSpN\naL77zo6fSUyEyZOhW7eab4QXKDSmqHBXWGiXZVi82LbERkXBdde5N+tqU9om9mXsY1DbQcz/1XzO\nanqWx/Vbtw4eeMC9+zo9yNhrjdAiUgeYB8w2xnzvokgMcLzM5QxAsLOzKgSjqVOnlvydkJBAQkKC\ng7VVKjT88ENpQpOUBF272laav/0NLrgA6tZ17lxJSUkkJSU5d8BqaExR4e7NN+GRR+zneNQoqFfP\nDuq9+WY7q/HJJ+2XmJq6d9C9NK3flN/0/Q11IjxPBzIzYe9eO4bPHXv3JrF2bRJlPpoecWsWVbUH\ntQOR38AGnGtddWeJSDLwmDFmYdHlM4CDQPPTv23pjAelXDt+HL780iY0S5ZATo6d7XT55balpkUL\n39XFm7OoNKaocFZQYFtF3nsPZs60SUzZ1teCAli4EO691yY5t93mn3ouW2YnKqxa5d79k5PtTKri\nbipPY4q3WnBmAs2BX7oKREW2APHAwqLL/YA0bUpWqnIFBbB2bekiexs32paZYcPg7rvtehrB1u1U\nQxpTVFg6dQpuuMHOdFy92nbjnC4yEkaOhPh4O9Nxzx7KtYJ88eMXHDt5jF/1+pVX67pmDZx7rvv3\nD/guKhF5EegBXGaMqWqu2RxglojMBw4AU4BZTtdHqWD300+lLTRffAFnnmkTmr/8xS7v3qCBv2vo\nXRpTVLgyBu64w3ZFvf++HW9TlR49YOVKGxfat4erR6YxcclEXt/8Ok3qN+GiDhfROqa11+q7YgX8\nyoMcqlkzZ6eJO9pFJSIdgN3ASaD4W5YB7gKWY79h9TLG7Csqfx8wGaiP/db1B2NMnovjanOyChsn\nTpTfCiE93c5KGDbMdj2deaZv65Odl03KwRQ2HthI8oFkktOSGdp5KNOHTC9XzhtdVBpTVDibPh0+\n+siOp4uOrvn9Urbmc8H/vYQMnUJm/jHq16nPw4Mf5v4L7ycq0jtLQxljF/hbtQo6dXL/GA0a2A03\nGzQIsC6qonUpqlo8sNFp5Z8BnnGyDkoFm8JC2LSpdHDw6tV2HYnLL4e5c2HAALvTrj+8u+1dbnr7\npgrrYjSo45tmI40pKly9/z689ppNGGqT3AD8Y8edZF06C/JhSPthvHLd83Rp1sU7FS3y44+2q6xj\nR/ePIVLaTdWuned1CoylvJQKM2lppS00n31m16BJTIT77rOrB3t7NdOCwgJ2HNlR0ioTFRlVoUUG\noEvTLghC75a9iW8VT7/W/ejXuh/xreK9W0GlwlhaGvz+93ZQcWs3epTuHng3SbuT6Jf2dyL/dx1d\nfuv9gXkrVsBFF3k+BrBRIzsbywlemUXlNG1OVsHu5EkbAIpbafbsgaFDS2c7de5c9f0zM+2Ow717\ne5b8/HT8J0a8PYJNaZvIyc8pub5NTBv2T9xfoXxBYQF5hXnUr1O/2mPrXlRKec4YuPZa+1n/61/d\nP05+YT55p+oQH2+Xibj22oplnIorAHfdZaeHjx/v2XHOOQdeftn+DqguKqWUZYzdv6nsVgi9e9tk\n5j//gfPOq/lWCJmZdtBg8UZ8y5a5DkbGGA5kHSD5QDI7juzg3kH3VijTIroFa/avodAU0r5R+3It\nMsYY5LSvX5ERkURGRLrzFCil3DB7tp1YsHBh1eVO5p/khTUvMCJuBG0bta1we52IOtRpAK+8Ar/5\njW0Zbty49PaaxpWaWrECfvc79+9fLDoasrM9Pw5ogqOUYw4fLl1hdMkSO25m2DC4/XaYPx+aNnXv\nuCkpNgjl58PWrfbv4lVLjTH8+Ys/sz51PckHkjmUfajkfrf0vYWmDcqftEFUA5bftpzuzbvTrEEz\ndx+qclNODtSvH7JT+ZWHDh+2690sWVL5opz5hfnM2TiHaV9P46fjP7E9fTsvXfNSpce89FI7dfzB\nB+H550uvryqu1NbRo7ZVOt6BnmtNcJQKAMVbIRRP4d6+HQYPtq00kybB2Wc784+sY7dMOnYTfvqh\nIb16CXFJ8csMAAAgAElEQVRxpbeJCO9ue5cdR3YA0KR+E+JbxRPfKr7SHYEvaH+B55VSNbZuHUyc\naN8f6enQv799f9xwgx2UqVSxBx+0KxT361fxtoLCAhakLGDa19NKPu99Wvbh2h4u+p5O89e/2ink\nd99NSfzo3dv+vXWr7VoqG1dqa+VKu0FvddPYa6JhQ+cSHB2Do1Qt7NxZfiuEs84qnb594YV2vQpP\nfbXrK1bsXcHGNDsA+IcjP8CpGF48bzm/HhpfoRn5rS1vUS+yHv1a96ND4w4Vupl8RcfgVDRnjk1u\nnn7aTvVv3Ro+/BCeesomv59+Wr7bQIWvtWvh6qttIuxq49sfj/7I2f86mwJTQNdmXZl66VRu7nMz\nEVKzKZbPPGNj16efll6XmVnaReVJ99RDD9kW60cfdf8YxUaPhiuusL89jSma4ChVhePH4auvSmc8\nZWeXJjSXXQYtW7p33LyCPPIL82kQVXG69fVvXs/720v3jKwbWZdeLXrxdOLTDD1rqLsPxes0wSnv\nmWfg3/+203179y5/mzF2Wf1vv7XvK3e7L1VoKCy0X5DuuqvqbRamfDmFs5qexa3xt9Z676jcXPs+\nfO45m0A4afBg2/rkxHHvvNOuhnznnZrgKOWoggLbpVCc0CQn237p4qSmT5/adztlnMqwC+QV/WxM\n20jKwRT+deW/uPOcOyuUn7txLhsObKB/6/7Et46nZ/OeXlucy0ma4JTavh0uvtguXV/ZDDljbOvO\n0qX2p7ZrnajQ8cYb8I9/2IQ3Ky+DjFMZtGvkwEIwp1m0CP78Z7vFS00nOVTn2DG7anJamjPv4fvu\nswsF3nefJjhKeWzv3tJxNJ9/blfjLE5oBg/2fCuEh754iL8urzjf86FLHuKxXzzm2cEDiCY4VkGB\nTW5uucWOeaiKMXaGS9Om5QeAqvBx6pQdH/PUC3tZE/EcL69/mcSzElk4opppVG4wBn7xC9v9c/vt\nzhzzrbfgv/+Fjz925ngPPggxMfa3ThNXqpZOnLDfmIvH0hw8aLubrrjCfotqW3HGZQW5BblsO7St\nXKvMxR0udrlY3sC2AzmnzTkl07H7t+lP31Z9aVSvkYsjq2D3zDN2ptTvf199WRG7bEC/fnDllXYM\nhgovk55bRe41z/KbNQvJL8wH4HDOYfIK8hxvuRWxu43/6ldw883OtLh89JGdpeUUHWSsVC0YU7oV\nwuLFdiuEAQNsC82wYbXfCuGj7z/ihjdvIK+w/BZHl3a8lKSxSc5WPohoCw5kZNjm9dWroWvXmt9v\n2TIYMcJ2ibZq5Xi1VIDam5ZFx+fOxNTNJFIiubHXjUy8YCID2w706nlvvNHOenrgAc+OU1BgB86v\nXevZFg1l/fOfdh2gf/5TW3CUciktzW6BULwVQmysTWjGj4chQypfKG/3sd0lrTIA04ZMq1Cuc5PO\n5Bfm061ZN+Jbx9uxMkUtMyq8vfqqfZ/VJrkBu+DaLbfY6eP//a936qYCz3+eiaFf7gQSE04y7rxx\ndGjcwSfnffxx2416xx127yd3rV5tExynkhtwdh0cbcFRIeHUqfJbIezebfuaExPtP5yzzqr8vvsz\n9zNq4Sg2pm0k41RGyfXNo5tz8E8HK0y7LigsICc/h5i6MV56NMEp3Ftw8vOhSxd4+227UnVtZWZC\n9+7wwQf223W4KSy0/zA//BC++85ubxIRYWfUXHyxTQKdWGfF1/IK8lj03SKa1G9SbhZkaqqdnr1p\nkzMbS9bWH/5gxxf+4x/uH2PKFNuK88QTztVr7lwbw+fO1RYcFaaKt0Ionu20fLkNFpdfbgdrlt0K\nIT07nS9+3Mj29O2MO29chWM1j27Oqn2ryCvMo1XDVuW2Lyg0hURK+dXYIiMiNblRFbzzDnTo4F5y\nA7ZV8fHH7eyR5cvDZ7VjY2DBAju7p2FDGD4cRo60/3xzc+3MosmT4dAh26Uydqwd4xToth7ayqwN\ns5izaQ4HTxzkkg6XlEtwHn3UTgn3R3IDMHWqjZl33137FsdiH33k/OB4bcFRYenIETvLqXjGE5TO\ndho6FJoV7TxgjGHa19NYl7qO5APJ7MvYV3KMtD+l0bJhxcVrlv+0nK7NutI6xo2texUQ3i04xsCg\nQXbmx3XXuX+cwkLbenP//XZF21C3YweMGWMTmX/+07bSVOabb+Cxx+x9Xn/d/UTS237O+Jkb3rqB\n1T+vLrmuV4te3DngTu4ddC8iws6dtv7ffQfNm/uvrk88YcfPvPNO7e+7a5d9r6alObsi9//+B88+\naxck1BYcFbLy8uy3t+KEZuvW0q0Q/u++HHKbpBDXshcN6zYsdz8R4a0tb7EtfRsADaMa0rdVX+Jb\nxZNXkOfqVFzc4WKvPx4VutautdswXHONZ8eJiLD/6MeMsVs5VLYfUSj47DM7Xfkvf7HdJdUN9L/w\nQvjkE9sFeM01cM89NqGszQQBX2gd05p9GfuIrRvLqN6juL3/7ZzX9rxyXd2PPGIXevRncgO2tbBH\nDzvIvark0pUXXrDvU6e3G4mOtjNdnaAtOCqg/Phj6Tiar76yi6QNGwZnDlpBVrMVbDlsty/Ynr6d\nQlPIV2O+IqFTQoXjLEhZQIRE0K91P7o261rj5cyV+8K5BedPf7JdKk4sVQ+2VfKmm5zZnTkQvfKK\nTWzefNN+aamtn3+2s846dYJZs3yfCBYUFvD1nq/p3bK3yxbh5APJnH3G2URHVZyHvXmzXZZixw5o\nFAArRbzxBsyYYcc/1XSM04kTdmDx6tVVj290x9q1domFtWs9jymORn0RGScia0TkpIi8VkW5MSKS\nLyIZIpJZ9NuNt7kKdhkZdlDluHHQpWshF15yilWr7DoN330HGzbYdRuW5v2Th5IeYP7m+Ww9tBWA\nns17kpOX4/K4o3qPYkTcCM4+42xNboJYMMSUwkK72NnIkc4dc9o02x1z6pRzxwwUc+bA9Ol2nJE7\nyQ3Ytao+/9yO1bjqKjtA29sKTSHL9izjnk/uoe0/2jJ0zlDmb57vsmy/1v1cJjdg922aPDkwkhuw\nXaEtW8Lf/17z+8ybZwd+O53cQGDvJv4z8CgwDKhu/ddvjDGa1ISZggJYvx4+WpzNB6s2s/1oMs17\nb6ROu2QOjt3E3y6fwbjzKi7/Orz7cFrHtC4Z/Nu7ZW+X+zhlZkJKit1zxZPN41TACPiY8u23duVV\nT3ZjPt0FF9gdnl97zXbfhIp337UDhb/80s4480SDBrBwof22f9VVduyGt7a7mL/2Q8bPeYX0mK+g\nXhYAXZp2qfVkg2++sdskvPWWN2rpHhF46SU7W+366+1MvqoYY/ez+te/vFOfgE1wjDHvA4jIQKAG\n68GqcLBvX/mtEFq1gtjhT7FxoF3192eAQlt217EfXR7j1vhbuTX+1irPk5lp+5GLd8ddtkyTnGAX\nDDHlzTdt643Ts56mTbMtmb/9rTO71PvbmjU2Gfnf/6BnT2eOGRlp/znfdpv957xokfPPVWYmPHLr\nL0j/bhhRrX/g7v+8weiB13JOm3MqLCFRFWPsmKFHHgm8WWCdOtkuwzvusEMDqtqn6vPP7binIUO8\nUxcnVzL2Z9t9fxE5KCLbRWSKiPYjBLuCwgK2HdrG7HVvMOLlyXSacgUtRk6hXz+b3AwbZldq3bIF\nHhp7Lr1b9uaWvrfwdOLTfH7L5xy6/xBPX/602+dPSbHHzs+3A5K3bHHwwalg4POYUlhoB72OGOH8\nsc87z27uGgoL/x08aJO1l1+2K4c7KSICZs60XT6//rVtJa6tIzlHmLdpHpM+m1ThtpQU2L0jGgrr\nwqGejGr1KOeeeW6tkhuwiV1aGtxa9fc0vxk3zraK/d//2WTMlWPH7LTyv/zFe8sYODnIGGOM4z/Y\nJuXXqri9E9Cx6O84YAvwQBXlTTl6OeAuv/jZEhM1tYFhKsaAYar96fvshT6rT0aGMfHxxkRx0sTH\n28vePJ+r83/zjTEZxPjkfIF2uehzGlYxZdkyY/r0cf/+1V1eutSYLl28d3xfXM7NtZenTPHu+U6d\nMiYhwZgJE2pWfuvBrWbG8hlm8KzB5WLWnmN7ypXPyDAmng0mKsqUxhU36te7tzHvv1+7x+frmHL8\nuDH9+7u+vaDAmKuvNuaee7x3fmOMKSiwlwsLPY8pfpkmbozZXebvLSIyHfgT8FRl95k6dWrJ3wlF\nP8r7jDEI8PH3H5N8IJm8wjymYr+RFW+FMAf466SO5F2bQ4uojsAeHrn0kdLtC8Z39kldY2Ntt9SW\nRpcSt2yVT7unynWPsYxlmaHfPZaUlERSUpK9UObz6Q/+iinvvGNnO7HZjTvXwCWX2KXw2emd4/vC\n1KnwON5/i9Sta8f4XHgh1GRx3msXXMuOIztKLl921mUMP3t4hXE1sbGwjEvYsjSTuDj3P9dNm9pF\nDGvKHzGlUSM7FZ82dlubyZOhTRt72+TJtgXn6acBL42/KRtT8qZM9fyAnmRHlf1QzbctF+VHAmur\nuN2oikqy+4zqy9ZWWlaauWzOZab5jOYl32yYiqn3SBPTr3+hadLEmOuvN+Y//zFm505jCgoLzJHs\nI85XJEh8840xderYLyJRUcasXOnvGvkefmzBcVHeJzGlZ09j1q515FCV+vhjY/r2Naaw0LvnMcb5\nmLJ0qTGtWxtz4IAzx6uJH380pk0bYz7+uNBsObjF/Jzxs8ty05KmmdHvjjZvprxpjuUc81p9srKM\nadvWmG+/rd39/BlTUlONufdeY5o2NeaSS4yJjTXmqquM2b/fN+dv1syY9HTPY4rTQSgSqA/8FfvF\nvh4Q6aLcFUDLor97YL//TKniuN54DoNacXdMnTqmfHdMDR0/edws3b3UvLjmRVPoInKeyss1dafX\nM0zFRE1paiJ/O8S0HjPBDP/LbJO0NM82O6sSJd1jUe69HqHAGwlOIMeUn34ypnnzoiZ1LyostO+p\njz7y7nk8jSmnO3bMmE6djPnwQ2fqVxNpWWlm/qb55pcv3WYi/tTWMBUzPWm67yrgwrRpxowYUfv7\nBUJMSU01ZtEi23XlS+3b28+XpzHF6S6qKcAjgCm6/BtgmojMArYCPY0x+4ChwGwRaQikAXMBB7fr\nCn2uBtSef37V93ly+ZOs2b+G5APJ/Hi0dLbS8O7DaRPbhqNHy26FEEWjVv9jaP+zuP4X7UmcICVb\nIaiKSrrHimZwhXr3lA8FbEz57DO7YJu3V9IVsd0DTz1lp0N7izsxpSrjx8MVV8DVVztXx6rM2jCL\n3y76bekVMRCZ05JTp/w3f2X3bjulet262t83EGJK69aer87tDqcGGutKxkGquH9261a7XsayZVAv\nOpdth7bRtVnXCtsXAPR9oS+bD9rBAvUi6xHXojdtIuLpsu8vfLu4I1u32sWbivd36tEjfDb8U54L\nt5WMR42yn5XbbnOoUlXIz4ezz7YLrF14oXfO4SqmuPtP9X//s7NtNm2yawQ5JScvhz3H99CjeY8K\ntyUfSOaCmRdwSYdLSDwrkcu7XM7sGX3YkhLBJ59UPfXZW264wc4amzLF9+cOZgMGwKuvwjnneBZT\nNMEJYl9/v573l+7gUEwSW46vYsvBLeQV5vHZLZ9x2VmXVSg/f/N80g4WcmRrPJu/6sHXX0XRsaMN\n0sOGwUUXhcZ6G8o/winBKSiw6zklJ/tuN+j//McO6v/gA++dIzPT8xaDzEy70ObMmbaFyxPZedms\n3LuSr/d8zdd7vmbVvlWcGXsmu8bvqlC20BSSW5BL/Tqli8zk59tWr1697B5fvrR4sU3ytmwJvHVv\nAt3FF9sV7C+5RDfbDGnGGPIK86gbWXGzlRc3/40FPy8od12Xpl3IzitdJSkz0y7ctGQJLF78azIz\nbevMjTfASy/YIK2Uqp316+1nx1fJDdiWounTS1tYvCE21rNuKYA//9kmNp4mN1m5WTSf0ZxTBaX7\nVQhCk/pNyDiVQaN65fc6iJCIcskN2FabBQvsTu99+thFE30hO9tuBvrss5rcuMOp1Yw1wQkguQW5\nbDm4heQDySQfSGZjmt1YclrCNMafP75C+au6XUVs3VjiW8UT3zqe+FbxNIyKZf16ePxxm9SsX28X\nDBs2zC5I1rdv4O2+qzynW1T41pIl9ouCLzVoYP9pzpgBs2f79tw19c038N579r1YE3uP72XF3hUM\n7z68wt5NMXVj6NWiFyLCpR0vJaFTApd0uISmDZrWqk5Nm9oVjgcPtnsnJSTU6u5umTIFzjnHd+OP\nvMVfccWpMTia4ASQGStm8PBXD1e4vuxaDWWN7jua0X1H8/PPNuD+e7EdJNyypQ2+kyfDpZd6b38W\nFRh0iwrfW7LEtlT42t13Q9eusGeP3c05kOTlwV132a6gppXkIJvTNpO0O4lv9n3Dip9WsDdjLwBf\n3volQzpXXPv/2zu+JSqyhltcV6FHD7tr9siRsHRp9fsteWLZMttqtNlLayP5ij/jilPbNWiC42WF\nppBdR3eVtMYkH0imb6u+PPaLxyqUHdBmAN3P6F6yoWS/1v2Ibx1Pm5g25crl5NgP6eLFNtCmpsLQ\nobaV5m9/g/btffXoVCBwevaLqlpODqxda4O/rzVtavcLevpp72126K5//MPGnptuqrzM1K+n8u62\nd0suN67XmAvbX1hpEuNEclNs6FD461/tmJyVK6FFC8cOXeLECduV+MILcMYZzh/fl/wZV5zqotJB\nxl6UtDuJ4W8MJzM3s9z157U9j2/v+LbGxzHGvtmKE5qVK6F/f0hMtEnNOefYTedUeHJy9osnwmWQ\n8dKlcP/9dhdxf0hLs5tVbtsWOGPotv9wikHXbmD8377lh5xvGd59OKN6j6pQbnbybL7a/RUXtb+I\nC9tfSK8WvYjw8TaEDz9sV+v98kto3Ni54xpjZ9bFxNgB1sHOn3Fl/HjbnXjffTqLyi/Ss9NLWmSy\n87L5y6V/qVDmx6M/0uW5LrSJaUN863j6tbItMgPaDODsM86u8vgHD9rupuKkpmFD2+00bJjdxbVR\noyrvrsKME7NfPBUuCc4TT0B6Ovz97w5Xqhb+7//sP9Inn/RfHQA++v4jpn89nbX7kjEReSXXj4kf\nw+zrZvuvYlUwxo5l2rTJTmd3qgt/xgxYuNAmwKEysNhfceXPf7b/4x58UBMcnzmSc4Rb3ruFjQc2\n8nPmzyXXx9aN5djkYxW+iRSaQg6dOESrmOq/ZuXmwooVxbOd4McfbSJT3ErTpYvjD0cpR4VLgnPV\nVXD77XaNE3/Zs8euFfLDD5WPd3GCMYafjv/E0ZNH6de6X4XbP/zuQ4YvGA5G6NmiJ+e3G8SgtoMY\n3HEwPVv09F7FPFRYCGPHws8/w/vve/7P+9NP7Xti9WrfzqwLVY8+CqdOweOPa4LjmOy8bFIOprA5\nbTO/7f9b5LRV7goKC4h9Ipac/BwaRjUs1yoztt9Yl1O5K2MMfP99aQvN0qW22bm4lWbQIIhyrvtZ\nKa8LhwSnsNCOrdi+3f/dQ3fcYTdCfPRR546ZlZvF5z9+zrr961ibupa1+9eSnp3OoLaDWHXHqgrl\nfzp4nHOuXse8GecyLCG4mpULCuyg7fXrbZeVu2NyliyB0aPt7LGLLnK2juHqH/+Affvgn//UdXA8\n8uyqZ/n2529JPpDMd4e/o9AUApDYJZEOjTuUKxsZEcmimxfRqUknzmp6Vq37jo8etf2+xUlNQYFN\nZm65Bf773+AflKZUqNuyxf4j9HdyA6VTkcePh+bNnTnmgawDXP/m9eWua9agGa1jWmOMqfCl72+P\nNubavr9gWIIz5/elyEh48UU7Jueii+Ctt6BfxUaqKn38sR1UrMmNs3QdnBoqKCxgx5EdtGvUjpi6\nFdcMn7NpDutT1wMQKZH0btmb+Fbx5BXkVSgLuFwhuDL5+bbJsjihSUkp3QphwgTdCkGpYLNiReD8\nI+vUCUaMsDMnn3qq8nKFppAdh3ew4cAG1qeuZ8OBDew8spMf7v2hwpe0Lk27MLz7cHo278k5bc5h\nYNuBdGzcsUJiA7BqlR1zUtM1bwKRCDz2mG09T0yEhx6Ce++tfq2w3FzbcvbKK/DRR3atMeUcnUVV\niY0HNvLN3m9KFsrblLaJnPwcPvn1J1zZ7coK5edvns/J/JPEt4onrmVchZUwa2v37tKE5ssvoUOH\n0r2dLr44dAafKXW6cOiiGj3ajo27/XYvVMoN+/ZBfLyd6eKqVckYQ+u/t+bgiYMVbttxzw66Nuvq\n1nlzc23r0YMPws03u3WIgLNzJ9x6K2Rk2ETnppsqzk7Nz7fxfcoUO9bmlVfshpTKWQsX2rWE3nkn\nDLuojDEUmALqRFSs/tMrn2bepnnlrmvfqD1ZuVkuj/XrPr/2qC6ZmZCUVDo4+Phxm8xcdx08/7y+\n+ZUKJcuX2y6NQHDwxEG2ndpIz9uTufTZjXw++UnaNSo/wlVE6NykM/Ui69G/TX/6t+7PgDYD6N+6\nf4WytVG83taoijPBg1aXLvb1/d//bOvMPffABRfYBPLkSTh0yMb4zp3tMgE336wt8N4SdisZv77p\n9ZLF8jambWTShZOYeOHECuWGdRlGhEQQ3yqe/q37E986nmYNmjlWj8JC2LChtJVm3brSrRDefNN+\nGHQrBKVCz969NuieXfUKD143/tPxvLX1LQ5kHbBXNLS/Fq0Zwd1DKyYtSWOTPG6ZLmv7drta8bp1\nofcPXgSuvNL+7N1r1zravNmOu+re3U5f9uYqyMoKu5WMR783utzlbenbXJfrO5prO4+2+2c0h9gG\nnp97/36bzCxZAp99Zt/siYkwaZLdCqFhw6rvr/sEKRX8vvrK/nPLyvLe5zgtK43NBzezKW0Tv+j8\nC5dTs7NysziQdYCGpjVn5Q7n/AExHP2hB+8835+7h1Y8ppPJTX6+7cZ59NHA2yrCae3b258bb/R3\nTcJP2I3BuW7BdeVaZSob+ObE/hk5OfZ+xa00+/eXboWQmGjH1dSU7hOkwkUoj8HJzLRdGIcP212p\nnfwcL0hZwMwNM9mUtqncWJknhj7B5IsnVyi/88hOsjKFW4d3ZutWIS4OvvjCLqP//PPe3QT0scdK\nt4kJtdYbFTi2bLED6LduDZMxOO+NfK9G5dzZP6N4K4TicTQrV9rpgomJ8OqrcO65pYPNMjPt7TVt\njdF9gpQKfikpdgwG1O5zXFBYwA9HfiDlYAqtY1pzUYeKU7B+zviZz7etgoO9iWkXSXyHs+jTsg/n\nnnmuy2N2adaFld/ZehTHlR077LiYCRPsui716nnyaF3bsAGee84eX5Mb5U1h14JT03rWdP+MQ4fK\nb4VQv75toSneCsHVHiXutMYEyj5BgU678YJfKLfgHDtm16mKjKz+c7zm5zX8a/W/SDmYwtZDWzlV\ncAqw3edzr59bofzGPT9y3bAz2LezEb16wfLl4lZciYmxkxv69LEtLU46fhwGDoSpU+HXns3L8CmN\nK8EpLc2+jw8d8iymODocVkTGicgaETkpIq9VU3aCiKSKyDEReVVEHFm3NzbWftiXLi0fhHJz7Wyn\nBx+0LTLdutlBwQMH2rI//mh3gL3uuso3YHPVGuNufVSp4mA9eLD9nZlZ/X1UeAiEmAK2m7pDB/j6\na8PCT9P49tDnLP5hscuyh3MOM3fTXDYc2MCpglO0b9SeK7teyXlnul4sJXv/Wezb2Zj8fGHbNnE7\nrojASy/Zqctr1njyaMszxk6LHzo0+JIbjSvByalBxo624IjIdUAhMAxoYIz5bSXlhgGzgSFAKvA+\nsNIY82Al5Wu9ZoUxttm27FYIZ59d2kpz/vm13wpBW2O8Y+VKG4Ty8+1rsnSpduMFI2+04ARCTNl7\nfC9jZz7B5rQtFJ6xhcM5hwHo37o/6+9aX6F8enY67257l94te9OrRS+a1G9S5fGdjitvvGFbcNat\nc2bdrWeegXnz7BTqYFrHS+NK8CoosK+ZMQG4F5WIPAq0rSIYvQ7sMsZMKbo8BJhvjGlTSfkaBaPi\nrRCKx9Lk55cusnfZZc5shRAIuzaHGk0cQ4M3u6i8GVMOnTjElkNbOJB1gFG9Ky7ssvf4Xjo8Uzqz\noHG9xsS1jOPcNufy7JXPevrQAGfjijEwcqQdxzBrlmfjZd5/H/7wB/jmG7v+SzDRuBLc6teHU6eC\nM8FJBh43xrxddLkZcAhobow56qK8ywQnP982xRa30mzebJdRL26l6dlTB8MFC00cg5+fE5xax5TB\nswaz9dBW0rPTATudOuvPWURGlF++1hhDp1HPce/NPRj5izjaxrZ1OYMzkJw4Yf+5jxwJDzzg3jGW\nLrVTpD/5xHbrByONK8GrWTM4ejQ4Z1HFAMfLXM4ABIgFKgSjsnbvLl2T5ssv7ToFw4bBtGn2Ax1M\nTaiqVGysNh8rj9Q6pizdsxSA2Lqx9GrRi7gWcZzIO0GjeuV3xc7LE9I/Gs/vX6t+zatA0bAhLFpk\nP1NnnWW3HaiNb76x95k/P3iTG9C4Esyio22vjCf8leBkAWWjSGPAAJUOAzvvvKns3GmXzL7gggRu\nvTWBf/0L2rhsgFZKeVtSUhJJSUn+rkaxWseU0YdH0zy6OY0KGzGk6xASEhJcltu82SYJwZLcFGvX\nDj78EK66ClJT7dYDNWl4mjsXJk6EOXNs175SvlI2puTkeH48f47B+dEY83DR5aHAXGPMmZWUN08+\naUhMtOvT6FYIqjI6LdR/AmAMTq1iSk1j34svwurV8FqVc7gC1+7dcPXVdrPfJ5+EJpWMeT50yE4D\n//RTmxjFxfmyloFLY4p/9O8PycmBNU08UkTqA5FAHRGpJyKRLorOAW4XkZ4i0hSYAsyq6tgPPAAD\nBmhyoyqn00JDjzdjSk2tXWuXkwhWnTrBihVw6hR07QqPPALJyfbzkZ1tZ0c98ogdsxgRYcc1anJj\naUzxn+hoz4/hdLowBcgGHgB+U/T3QyLSXkQyRaQdgDFmMTAD+ArYBewEpjpcFxVm3FmnSAU8v8eU\n9bSaM0QAAAzXSURBVOvtl6tg1rixnVG1apXtrrrlFmjd2s4snTDBLmS4ahX861/OzDYNFRpT/MeJ\nBCfkVjJWNRdqTa86LdS/QnEl49xc26WTnu5MwA0kxpSuEeOkUIorGlP859prYdGiAOqiCmfFe1QF\nSxNmKDa96qrRymlbt9r1X/yV3Hgzroh4J7kJpbiiMcV/nBjUrwmOA4LxQx2qTa/F00I1ECknbNhg\nBzv6g8aVwKAxxT8CcQxOWArGD3Xv3nYgYVSUbXrVQYVKVeTPBEfjigpnmuAEiGD8UGvTq1LV82eC\no3FFhTMdZBxAdElwFe5CbZBxYaEdYLx7t1023h80rqhw9cYb8OtfB+BeVE4LhgRHqXAXagnOjh2Q\nmGgTHKWU73kaU7SLSimlXNiwwa6crpQKTprgKKWUC8nJ/ht/o5TynCY4Sinlgj8HGCulPKcJjlJK\nuaAJjlLBTRMcpZQ6zYEDkJcH7dr5uyZKKXdpgqOUUqfZtAni4+12Bkqp4KQJjlJKnWbjRujb19+1\nUEp5QhMcpZQ6TXELjlIqeGmCE2SCbddypYJROLXgaExRoUoTnCASjLsLKxVscnPtKsbBsPeTpzSm\nqFCmCU4QCcbdhZUKNtu2QefOUL++v2vifRpTVCjTBCeIBOPuwkoFm3Aaf6MxRYUyRxMcEWkqIu+J\nSJaI7BKRmyspN0ZE8kUkQ0Qyi34PdrIuoSg2FpYtg6VL7W/dXViFA1/HlXAaf6MxRYWyOg4f7z/A\nSaAFMAD4WESSjTHbXJT9xhijSU0txcbC+ef7uxZK+ZRP48qmTXDffZ4cIbhoTFGhyrEWHBGJBm4A\nphhjcowxK4APgFucOodSKrz4I66EUwuOUqHMyS6qs4E8Y8zOMtdtBCrr1e0vIgdFZLuITBERHQ+k\nlDqdT+NKWpodcNu2rbvVVUoFCie7qGKAjNOuywBc9ep+DfQ2xuwRkTjgLSAPeMrB+iilgp9P40px\n641u0aBU8HMywckCGp12XWOgwsoKxpjdZf7eIiLTgT9RRSCaOnVqyd8JCQkkJCR4VFmllGeSkpJI\nSkry9mm8FldcxZRNm7R7Sil/cTqmiDHGmQPZvvIjQFxxc7KIzAH2GWMerOa+I4H7jTHnVnK7caqe\nSinvEBGMMY62fXgrrlQWU8aMsYve3X67I9VXSnnA05ji2LgXY0w28C4wXUSiReRi4Bpg7ullReQK\nEWlZ9HcPYArwvlN1UUqFBl/HFW3BUSp0OD2wdxwQDRwE5gG/N8ZsE5H2RWtStCsqNxTYJCKZwEfA\nQuAJh+uilAoNPokreXmwfbsudqdUqHCsi8qbtItKqcDnjS4qb3EVU7Zsgeuvh++/91OllFLlBEwX\nlVJKBbPNm7V7SqlQogmOUkphx9/06ePvWiilnKIJjlJKoQOMlQo1muAopRTaRaVUqNEERykV9o4d\ngyNHoHNnf9dEKeUUTXCUUmFv82Y7PTxCI6JSISPoPs6ZmbBypf2tlFJOWLMGWrXSuKJUKAmqdXAy\nM+GSS+x6FXFxsGwZxLrack8p5XPBug5OZqbtmjp61M6i0riiVGAIq3VwUlJscpOfD1u32r+VUsoT\nKSlw+DAUFmpcUSqUBFWC07u3bbmJioJevXRJdaWU53r1smNvNK4oFVrq+LsCtREba5uPi7uotBlZ\nKeWp9HRo0wYWLtS4olQoCaoEB2zwOf98f9dCKRUqNm2Cfv00rigVaoKqi0oppZy2aRPEx/u7Fkop\np2mCo5QKa7pFg1KhSRMcpVRY27hRExylQlFQrYOjlApcwbgOTlYWtGwJGRlQJ+hGJCoV2sJqHRyl\nlHJSSoqdGq7JjVKhRxMcpVTY0u4ppUKXowmOiDQVkfdEJEtEdonIzVWUnSAiqSJyTEReFZEoJ+ui\nlAoN3owrOsBYqdDldAvOf4CTQAtgNPCCiPQ8vZCIDAMmAUOAjkAXYJrDdfGJpKQkf1ehUlo392jd\nAo7X4kogThEP5NdY6+YerZt/OJbgiEg0cAMwxRiTY4xZAXwA3OKi+K3ATGPMdmPMcWA6cJtTdfGl\nQH5zaN3co3ULHN6MK8bYBKdPH2/U3H2B/Bpr3dyjdfMPJ1twzgbyjDE7y1y3EXC1s0tc0W1ly7UU\nkaYO1kcpFfy8Fld274aYGGje3KmqKqUCiZMJTgyQcdp1GYCrnV1igOOnlZNKyiqlwpfX4kpyMvTv\n70QVlVKByLF1cESkH7DcGBNT5rqJwGBjzLWnlU0GHjPGLCy6fAZwEGhujDnq4ti6CI5SQcDpdXC8\nFVc0pigVHDyJKU6u/vA9UEdEupRpTo4Htrgou6XotoVFl/sBaa6SG3A+aCqlgoZX4orGFKVCn2Nd\nVMaYbOBdYLqIRIvIxcA1wFwXxecAt4tIz6L+8SnALKfqopQKDRpXlFLucnqa+DggGtssPA/4vTFm\nm4i0F5EMEWkHYIxZDMwAvgJ2ATuBqQ7XRSkVGjSuKKVqLSj2olJKKaWUqo2A2KohkFdArmndRGSM\niOQXfaPMLPo92Iv1Gicia0TkpIi8Vk1ZXz9nNaqbr5+zonPWLXoOdovIcRFZLyJXVFHeZ89dberm\np+dubtFzcVxEdorIQ1WU9etK5RpT3K6bxpXa10tjivv1825MMcb4/Qd4o+inAXARcAzo6aLcMCAV\n6AE0xjZF/zVA6jYGWOrD5+w6YDjwPPBaFeX88ZzVtG4+fc6KzhkN/AVoX3T5Kux04g7+fu5qWTd/\nPHe9gPpFf58NHACG+ft5q6SuGlPcq5vGldrXS2OK+/Xzakzx2QOp5gU4BXQpc91/XVUeeB07DbT4\n8hAgNUDq5vM3R9F5H63mw+7T56yWdfPLc+aiHhuB6wPpuatB3fz63AHdgb3AgEB73jSmOFJPjSue\n1VFjSu3r5XhMCYQuqkBeAbk2dQPoLyIHRWS7iEwRkUB4fgN91Wi/Pmci0grohutpx3597qqpG/jh\nuROR50XkBJACPG6MWe+imL/fcxpTvM/fr3F1/Pa8aUypdZ28FlMC4cMSyCsg16ZuXwO9jTEtgV8B\nNwP3e6letRHIq0b79TkTkTrYWTmzjTHfuyjit+euBnXzy3NnjBmHfV4uAx4TkYEuivn7Pacxxfv8\n/RpXxW/Pm8aU2vNmTAmEBCcLaHTadY2BzBqUbQyYSso6ocZ1M8bsNsbsKfp7C3ajvxu9VK/a8PVz\nVmP+fM5ERLAf9lPAPZUU88tzV5O6+fO5M9bXwNvYIHg6f7/nNKZ4n79f40r563nTmOI+b8WUQEhw\nSlYqLXNddSuVFqtyBWQf182VQFgt1dfPmad89ZzNBJoDNxhjCiop46/nriZ1c8XX77c6QLaL6/39\nntOY4n3+fo1ryxfPm8YUzzkbU/w1oOi0AUTzsYOIovn/9u4ftIkwDuP492cVRacidpDaglCsoJN0\ncxAVFNHBxeIgOPhncXAoTmIXdemog4OIIJ119M/SQTrYqQhOog7qqEKxW30d7oYg0Sahl8u9fj8Q\nCEkgT94mT3+5yyVwGPjO3494+ArsB4YpPkl9Z0CynQRGyvOTwFvgZoW5hoBtwF2Kb3DdCgwNyJp1\nmq2va9Zyvw+ARWD7OrerY+06zdbv59suYBrYQfHG6ATF0T9Tg7BubTLYKb1ls1d6y2andJ+r8k6p\nbFG7fKDDwFOKzVCfgOny8j0U+9pGW257neJQsh/AQ2DLIGQD5spcK8B7YLbdi28Dc80Cv4C1ltOt\nMtdKzWvWUbZ+r1l5n2NlttXyflfKv+P5up9vHWSrbe0o3v0tAN8o/iG/Ac60ey3U8Zxrk9dO6S2b\nvdJ9Ljult2yVd4rfZCxJkrIzCJ/BkSRJ2lAOOJIkKTsOOJIkKTsOOJIkKTsOOJIkKTsOOJIkKTsO\nOJIkKTsOOJIkKTsOOJIkKTsOOJIkKTsOOJIkKTub6w6gvEXEFYofVdsHPAHGgRHgAHAjpfSlxniS\nGsZOUaf8sU1VJiIuAcsppaWImAJeAReBn8Bz4FRK6UWNESU1iJ2ibriLSlXamVJaKs+PAWsppWfA\na+BIaxFFxN6IeFRHSEmNYaeoY27BUV9ExD1gNKV0ts1114BDwHhK6Wjfw0lqHDtF63ELjvrlGLDQ\n7oqU0n3gcT/DSGo8O0X/5ICjSkTEpog4HoXdwCQtZRQRM7WFk9Q4doq65YCjqlwFXgITwDlgFfgM\nEBGngXf1RZPUQHaKuuJh4qrKIjAPTAPLFOU0FxEfgQ8ppfk6w0lqHDtFXXHAUSVSSsvAhT8utoAk\n9cROUbfcRaVBEeVJkjaCnfKfc8BR7SLiMjADHIyI2xExUXcmSc1lpwj8HhxJkpQht+BIkqTsOOBI\nkqTsOOBIkqTsOOBIkqTsOOBIkqTsOOBIkqTsOOBIkqTsOOBIkqTsOOBIkqTs/AafiIX7zWkEJAAA\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113fdd828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import Lasso\n",
"\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(121)\n",
"plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1))\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.subplot(122)\n",
"plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1)\n",
"\n",
"save_fig(\"lasso_regression_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.53788174])"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.linear_model import Lasso\n",
"lasso_reg = Lasso(alpha=0.1)\n",
"lasso_reg.fit(X, y)\n",
"lasso_reg.predict([[1.5]])"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.54333232])"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.linear_model import ElasticNet\n",
"elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
"elastic_net.fit(X, y)\n",
"elastic_net.predict([[1.5]])"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure early_stopping_plot\n"
]
},
{
"data": {
"image/png": 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93Tp47bUAls9kc9ZZZ9GmTRvatWvHkCFDeOWVV/jzzz9ZsGCB36+V1kknHDod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\ngpQxxpiQZUHKGGNMyPp/NURcxehDL9kAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11487f748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rnd.seed(42)\n",
"m = 100\n",
"X = 6 * rnd.rand(m, 1) - 3\n",
"y = 2 + X + 0.5 * X**2 + rnd.randn(m, 1)\n",
"\n",
"X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n",
"\n",
"poly_scaler = Pipeline((\n",
" (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
" (\"std_scaler\", StandardScaler()),\n",
" ))\n",
"\n",
"X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
"X_val_poly_scaled = poly_scaler.transform(X_val)\n",
"\n",
"sgd_reg = SGDRegressor(n_iter=1,\n",
" penalty=None,\n",
" eta0=0.0005,\n",
" warm_start=True,\n",
" learning_rate=\"constant\",\n",
" random_state=42)\n",
"\n",
"n_epochs = 500\n",
"train_errors, val_errors = [], []\n",
"for epoch in range(n_epochs):\n",
" sgd_reg.fit(X_train_poly_scaled, y_train)\n",
" y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
" y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
" train_errors.append(mean_squared_error(y_train_predict, y_train))\n",
" val_errors.append(mean_squared_error(y_val_predict, y_val))\n",
"\n",
"best_epoch = np.argmin(val_errors)\n",
"best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
"\n",
"plt.annotate('Best model',\n",
" xy=(best_epoch, best_val_rmse),\n",
" xytext=(best_epoch, best_val_rmse + 1),\n",
" ha=\"center\",\n",
" arrowprops=dict(facecolor='black', shrink=0.05),\n",
" fontsize=16,\n",
" )\n",
"\n",
"best_val_rmse -= 0.03 # just to make the graph look better\n",
"plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
"plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
"plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
"plt.legend(loc=\"upper right\", fontsize=14)\n",
"plt.xlabel(\"Epoch\", fontsize=14)\n",
"plt.ylabel(\"RMSE\", fontsize=14)\n",
"save_fig(\"early_stopping_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(239, SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.0005,\n",
" fit_intercept=True, l1_ratio=0.15, learning_rate='constant',\n",
" loss='squared_loss', n_iter=1, penalty=None, power_t=0.25,\n",
" random_state=42, shuffle=True, verbose=0, warm_start=True))"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.base import clone\n",
"sgd_reg = SGDRegressor(n_iter=1, warm_start=True, penalty=None,\n",
" learning_rate=\"constant\", eta0=0.0005,\n",
" random_state=42)\n",
"\n",
"minimum_val_error = float(\"inf\")\n",
"best_epoch = None\n",
"best_model = None\n",
"for epoch in range(1000):\n",
" sgd_reg.fit(X_train_poly_scaled, y_train) # continues where it left off\n",
" y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
" val_error = mean_squared_error(y_val_predict, y_val)\n",
" if val_error < minimum_val_error:\n",
" minimum_val_error = val_error\n",
" best_epoch = epoch\n",
" best_model = clone(sgd_reg)\n",
"\n",
"best_epoch, best_model"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
"\n",
"# ignoring bias term\n",
"t1s = np.linspace(t1a, t1b, 500)\n",
"t2s = np.linspace(t2a, t2b, 500)\n",
"t1, t2 = np.meshgrid(t1s, t2s)\n",
"T = np.c_[t1.ravel(), t2.ravel()]\n",
"Xr = np.array([[-1, 1], [-0.3, -1], [1, 0.1]])\n",
"yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
"\n",
"J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
"\n",
"N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
"N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
"\n",
"t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
"t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
"\n",
"t_init = np.array([[0.25], [-1]])"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure lasso_vs_ridge_plot\n"
]
},
{
"data": {
"image/png": 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qBktLceWbeq61uDJKrZVZY2WSCPSqy4q3BivyyvB2QLTRqxasrCWfbFrpTj0W\n1Ml917prYAtKG/YcINxHpkS3ZI9qLR8nlfUbpFRAzSmQ9SNk/RTd2NZEiysA2WZh/cT96TRuNXt8\n9BVrrzmIum+jGxGeaHEFsOovG9P+dSVXvTiHCZ+8xQsXnkDleu2adsSLNwJjt+/GCRfezosPPc0B\nQ1Zw3ZSLaWpO19m68Ly/5mBW13Vh1lFPMahgE48tGYtMYHKBkjLY2SfiF15ouYSVu1Ou5G9Xf95z\n3sBNKTfymeUQrU1NevRODWzv4irkOgkQV4mOWumFKawUfBs/JYKSkiAzbNo5JSVbsNu7Ybe7DNH8\nIlI6VAQrmp3DOtJYTy5daaSYZiD+3UMvoRxdQ+kCskeOCLtGoK6BEmV4cCNQAEQSd1AjegWeLoIx\nDnf0J9QwYWcuVJ8BqVshbz5E0iMgmPNz1JdiyxkZu51RzLrKHr6Nfs/8iP3p3bG/sBuRyMNg4srh\nWIjNdnC05kbEzimBkkMv+IPjJixizvjjWPl9r7jWdjh+x2bbVwUrFXxT23xTANNS27jv1tfYb/Aa\nLrzhGjZsjm8oscOxHJttj7jWiITOGTW8eNTT2JvyuO67i2lyxi4OY7U5lmjWvu7lvOicwn+sY3nM\n8n9xDSVuzxGs5+T5QHKlBnr9UTQD7P1JdGpgoAhWMoirSPyRkcSV1y9p6Y+0JBK7wwmoRKfOl5eX\nIcRBQWwxrvhS8x5JZDTL7CIYIZGKKwnYyWQ9ufSldru48mKk1EBfJFCD0i2wmMSKKzXrrsINE06p\ng6I5IK1Q+X/gCpN1p2XdVTROruHHTiw/4SiKzlxHnxk/I2yhT9YjcrVrvZXg+5eH8PIVx/N/T/yX\nIy7+DeVO059Q9VWtbancdM/5/Oe9I/j4pfs4dNjfepgYNVub8zn905upa83k4zH30zNbi3aXofGt\nzYqU3y17MDr1aY5yL+I5591kyObwJ3VQkrVrYLKIq4BrVGvXyS9RkSsjzLXy1lm11xoru92xyxfs\n6Jwb6CvRFBTYg9oRyPb2SDLVZXWICFakRcVuYAO5tJBCP2pIw739PTWiV1rNvHKhNLOwAvlEljqn\nVtdAr7hyXxx/BCuaXUYJNI6AxqFQ8D6kBXjeJ6qpRTRYMpz0mfEzad2bWH3JCNrsu/Z1NIa42pnC\nnrVc8tInbPyzM2/fehSuVn2yi32FVSQcMmwZT017npkvjeWlt44iusRSvZBcPOhLrtlnHld9czkL\nyrWPnvmC+TLxAAAgAElEQVQTSyTLJlt5wPUYg+U/XJhyD5tEl6iv294jWHpFrzpSaqBvBCtUNkS8\nJFJcgb7CCtpXKmAwAWLUZk6xYLfvnHFi5AhXLCQikhVvBKvDCKxwjq0VC2vJJw0XvandJbRnpMYW\nvs6uFUVcZXm+Ir0T1IxelWyIbrhj0LVicIYtA6B2DOR8BZl/+q2nQ91VZEi6XrucTuNWs/rSg2n8\nrchnfeOJKy9pma2c+9j/yOvSwEuXnEDd1qxEmAdEL6x86dltG7MffZIlf/Xhtgf+j9a2cP00jcEh\nXZfx1OHP8/gfY5m9LPHiMBaRhZRc7H6fq11vclXKHSy0RJcS2p4F1mT5REzn6j1QOJnEFSi+yHKt\np+FSkketvOghrtpTnVUgQdWexFQktEfBpbXIMlMEwxBJUXEjqaykkDxa6BNEXMVLpI0tQs3B8k8N\nbEIRV3lANtGJKzVIZGpgMNJXQeF/oGEE1B4N3l+FSIYJRzt3RL2dREHZzEGsv30oA175gaLT13nW\nj0xcqTkLI5o27K1Nabx8+Rj+/qovN8x/g177lkd1rVjmYPm3W4+FjVs6ceKFt5Gb08S7zz1Mp6LQ\nQ4n9UXsOVqT8UDaIE+fdzv/t/g2PHPIKaZbI2/2rYXMs6YIIwSzraVybcivPOu/hAteH0E438RKB\n3qmBztf+ie1cA8y7SjZx5euP9G6/Hk3LdaPOZgqX6qf2XMZEEI/NwVIKE4FW94jR0wXbvcCC0KmB\nlaSzhnx6UkcXmoKKlHijV8q11Jl5JVG6BDagzLeKphRe7dRAI8wlSa2E4lfAWQxVZ0F5Y3zrhUJN\nZ1f7v26sOG0kXa9fRuHNvyGsbkNGrnyRUvC/xw7i3TuO5PJXP2LY6drVN6k5x6qpOZ3LJl7J1wsH\n8+mcexiyZ4y9/hPMhoZOnDj3NvJtjbxz3CN0yohOHMZLTCIL+M6yPyemPsE49yc85JpBqox/FlxH\nRc/UwHiIN3oV17WTTFztdB0dUwKTuc7KvwZJ73opI+P775LsdVtGFlntOkUwVNcmCWwmhzrS6EcN\n6UEiTEZKDQQQ/3SnGiValU/0Clnt1EAv8aQIqpUnLwWUDwf2huLpkLo5/jW9RNvUIhqsea30mLkQ\nm83B6it2w1WjfX2TGgOEuwys5JLZH7P0s/58fO+huF3q7NfEG7EKx3EjF/PQHXO469F/8/6nydH9\nSuDmhn0/4azdvufir8bzR2WfhF4/pnRBIEs2MdP5AEXUcknKFCpEYcjjzRTBHZipgTGcXw3umYKu\n56r7uaa9i6tkTQf0FwWmkIod3xTCZEwf1CJd0EwRDEMgceVEsIp8WrAykKqQ4ipe1Jx55f6nOxVA\nKkob9ljElRqonRqoltMSEiwfQ967UHUbtKg0s9U3F14Ltqy0sv6ivjT9ncmgeX+SPjC6aEG0qCGu\nAMpXFvHomLPptmcFl736IRl58d9gWosrgP+WDuWMK27ipis+4s7r3sZicYc/SWckFqb/fhKTfzqL\n146ZwSn9fkzo9WONZDWKTC5JuYvvxX582jaevd0rNbCu/aF3amC8XQPjIR5xpQWJEFd6dgmMJh3Q\nKARL/TOJnWSPahkxktWuBVYgcdWMlRUUkomT/tSQEqbtdKJTAwPVYNnboPWf7lShDA/OJfZydzWi\nV6BuaqBaeB1h5gIomA6150H9STvqsvyJpAZL6x3F7Q8Dl2DT3b0pm9GD3d/7m/xjq4KeE08+s1ri\nyktTTTrPnnsy5SuKuHHem5TsFvxTSKj8cW+tlRrpgJGwYnUPxoybxODdN/Dq44+TlxO8VlOvGqxA\nfLp+f874783cvN+HTDrgHSwisDjUwuZYRZYUFh5JuYApKVfyuvNWTnZ9pbpt7REjpAY6fiqN/Fwd\nW7JrNecqUeIKIL+pVLuLBLyuOumAiarBCpb+FysdrQYrGtSu1UrUPWK0DYJ2LbD8qcHGKgrpSiPd\naQgpUowSvSpvhYbKHOpQola7NvWODK1SA+NFLcfl7wjT1kLxXeDYB2rGgzuOiLfW4sr3oVD5bidW\nnbcHve5dR9frNqHm3Cm1xZUXt8vCh1OP4LPHD+Ta999lr3+tidIu7aNWgaiuzeacayawal0X5r5y\nLwP6GOvhHIzl1T0YM3cSexetY87Rj5Obpm3E05d4/o/mWw7nzJSHmeh6iTucz2ORxtlpNBLx+B41\nfE6s0StoX3VXiRRXekatjEywRhUmiUGvphjxUFKyxTBRLN0FlhBivBDiZyFEixDipTDHThBClAkh\naoQQLwohIuq3LIEysthEDv2pppDI8hj0aGyRPXLE9r+7XIK6skLaqnIjHh4ciPaeGujFfz1rLRTd\nD6IFKu9UmmD4YssZGdpGDeuuQjm4xt+zWTZ6MHlH19DvuX+wZO5sRCwT0bUSV778/M6ePD/uRM68\n/yv+de1P+ItDm23nlt1qdAiMF5fLypTpZ/Pk7NG8/8JDHH3Ykl2OsdkSP4cqHNWObM793wTW1JUw\nb+w0BuSV7fS+1jZHG8XysszSnzGpTzFEruAV5yRyZYPKlsVHIvxRKNSYt6hmaqDtwJGRnRuHj1Gj\n7qo9iCubbaR2F9t+TfWbWMTij8KRiBRAf3+UDOhls7/QihYt7pFwGEFk6S6wgM3APcCsUAcJIY4F\nbgGOBHoD/YGp4RZ3IVhLHvWksTtVZOIMa5Ba0at4Gls4Wq2sWNsJYXVThDJEOB46QmpgIIQT8l6E\nzG+gcjI4BkW4poZ1V5HsHrZtTWPF6XvibrKyx0d/kdYj9k8wiRBXXtb/1pXpY85i8DGrueDZ+aRl\nBG5HpmaHQDV465NDuWDCNTx4+xyuvnAeakYOtcIpU5i86Bye+vN43j/+QY7q8UdCrhvv/1eVyOOc\nlAdZL7oxr208A6ShdqQ19UeREG9ji5iuGUfXQDU60xqp7so7P1GzAcU61VsZPWqldgqgifr412gZ\nFaPUY+kusKSUH0opPwaCF50ojANmSSmXSylrgbuBC0Od4MDCSgqwIhlANalEXsyuRvQqFhpKF9DQ\nYGPN2k5k5DWSX5cV13hRI0avQLvUwEAIIOtzyH8Waq6ExqOVj8/BarASkbYRiZOTDgvrJvSj4s1O\n7PHJX+QcrLTojiafOZHiykudPZsnTjuD1uYUrvv4LQq61wE78sf1jloFY/HS/owZN4njR/7GM/c9\nR0a68m9npBqsQLz5z2Fc9NXVPDziFa7eez4gNbe5pGRrzFEsAKdIYVLKNTxt/Tfvt03gKPciFa2L\nHS39UTjUSA2MZ1MvUGpgpDVYeqQGalF3pcVw+p3WD+FbHI5Sja6pbev1eOtr9EoBNGuwYifatEE9\nZqUZQWTpLrCiYC/AN39nCdBZCFEQ7ISVFFJMM72oi/gH1bMtu5RQW5vBxs0FZHepIjO/MS5x5cWI\nM6/UJFKHaPsbiu6BpiOh9iKQIcKCmje1iBjB1lldWXvtAPo9u4pOF5QTaXRFD3HlxelI4fUJx/Dz\n23syYe6b9B++yWOTMcWVl/JtBZx66URa21L4aNb9dO9SobdJEfHL1gGMmTuJ0b1/5ZkjnsMWxVDi\neIhHZAG8YR3NxSlTedg5nfGuN1SyKiFE7Y8iwSipgRGfq2NqILQfcaXdNY0btTJrq5KbeNMGE4He\n930yCaxslPm6XupQghM5wU7oQy2daFZFpERKrGkabjdsLsunafCx9O+7jbTM1riKjUG9xhYQ3Am6\nXFAf4exTtXccQ6UGBiNlGxTdDe5saLhvJK48vzV1Tg0MRv13eSw/cS86j7Mz8PEuiNTQ0Vg9xdUO\nBKUvDOW1645l3DPzGHaW0zApgaFwtKZy3ZSLeXf+wcx95T4OH54cY5nKmwo49dOJtLmtfHba+3TP\n0nZoj1r/jz9bBjM29SnGur9VZb0EEbU/CoUaM69iIVxqYKgarPaSGmjfZgxxpWYNViIHBkdbX2MU\nYWXWYKlDJCJLjxosX/SKYhlm0LAQ4h6gu5TyoiDv/w5Mk1K+63ldBGwFiqWUuzxuhRByn/MPJL9P\nEQDp+Rl02bcHfUbuBsC60n8AdnpdTyupI08DYGupsjnZeeSQqF4zcjCVDN7ebt3btCLU67Y2C2ve\nXUqK1U2f0/emwiVxvqbY53Vw3lSNSF+Xf6+87lLgef8vz/t7Rfe6ppfyOv9bz/t9PO+vK8XZCg1Z\nI0lLg5anBVlnfk3uoB3v+x9fXQ9dMjyv7Z73S2J7Xb7C8/NJz/uedD9v44pwr1vqS2k+FFovGEnB\nTJB/lFJdBSJ9JCWuHekaXqcX7+vy8i8Ve7sM9Ly/0PP+wVG9zig8kL5PrKJ+7WK2PNydlJbDdzne\nbncg5SIKCuzbH8je1AI9XtvtTeR3Xcg59y3CKvbkvUn70NSw0vP+Hp7jlxvy9TFHOJl59yyuvfMg\n/vftvrrbE9lrybHdXuWEPr8wZ9U1/LR1N82uV1Oj3H/5+d7/z+juD4DW1iU4neVYcNPU8oUhBg0n\n0h9V42BT6SqqGRC1v+k8cghbcbG+VEnDjcTf+L5uPGQE1n+6R+1fHD+VUt0au38p/1l53SXT834A\nfxHstb0a5KZSCuoC+4ey1wSFR3+9/bX/+76vayzK63zv+hH6j2he2+0gW0opcKvnT0K9tttdSFlK\nQUFl1P5Fy9fV1W0IcRAA+fkfe97X3z+Zr9V7XVNzIgD5+Ys97xvj/isvV/xTly6jPO+Xet4fudNr\ngNbWUpzOdQC0tLwSlz9KJoH1GrBGSnmn5/Uo4FUpZbcgx8vJ8omIr69G96ZY8uCbmlPZsLGQgoIm\nOhfXs+nLBaQdMcIw0atgbdmbGqC+BvIKIT0TyqYKrJdK0jMgJx+E3y2pRfQq3rUc9aXIkSOpvRBy\nX4O6D7VNDVRrJ9HRuoC+t/ek6N/bWH3RQJr+zPa5jhEiVzvwTQl0i6Vc9lIDmfltzL50GPUV6Tpb\nFxmFeQt5/8V5LFy8O5MfPps2Z4reJoXF4VjOMX2dzDx8Fg8tPpnXVh6h2bXs9s6UlGSqslZZ2ahk\nEViq+aN4o1fxzrwK5WscP5UGjGLFE73Sumtg2WuCrueG/1yTqE6BkfoUh6M07iiWHimBDsfCkBEK\n38iGUfwSKKLAiBGhUCSDzXZ7LwBKSnbMxgl3jyQCu70bJSXRtYsrKxNx+SPdUwSFEFYhRDpKo7wU\nIYRNCBHoX2EOcLEQYpAnz30SMFtNWxLdlr26JoN1G4ro2qWWkk7120WJGuJKDQIVIEsJddXQUAeF\nnRVx5aW4BNpaoXqbkvLoj56pgcFI/xUKH4CakyHjIpAa/EaoKa4AkIItj/Rk45Te7Pb6cgpP3rlO\nyChOzL/eqq0lhVkXHcQ/C4q5Yf439Ni7Rk/zIqZsawFjL7iDrp2qeeuZRygqqNPbpIj4ZstgTpk/\nkcv2+pz7hr9KigjfQbWjk2h/pNfMq0jEVTiSOTVQa3Hl2ykwESQyJTBSjJIKaJJYjFyXlehUQd0F\nFopjagImAud6/n6HEKKnEKJeCNEDQEr5GfAQ8DWwFlgN3KWGAYkeKiwllJXnsnVbLv16V5CXqygi\nexukHTEizNmRoUXtldsFVdugrU0RU6l+g7ksVkV0WVOholw5DtTPlwd1HKM3naPqVxDXQttuUD0N\n3Fnxr+1Fi19o705QzfwiVp45iO4TN9L99g3Yt7UYxokFamZhs+2BlIJPHx7Eh1MHc+XrC9jvpE16\nmRgxNtseNDRmcOGNV/Pj4oHMnzONwbuv19uskHhT+dbUdWHs3NvpnlXNW8dNp9CmcjtQD/E2uzAQ\nCfdHejS2gMjEVbDoVTJ3DUyEuILoxVWs0Su9G1n4RyaSRVgZPRIUiGSx2V9k6R29An1+PwyTIqg2\n0aQIJrJzoMsl2LCpEICePapIse7494+nm9P2NVQoPIZdUwPb2pTIVLAUwLKpgq5Tdvws3hRCaQOR\nYqzUwF3W9Ow0SivUXQ6OYVA4GVI2xrtuYhxfSmEbPWauwN1iYfMEK656ffdNIu0U2G3PWi55aRGL\nP+rOvAf3RLp1zwyLiLFH/8z9t/6HOx48l48/P1BvcyJC4Gbi0A84pd8iLvrqav6q6qXq+mqlCRol\nRVBtAvkjNRpbxCKw4oleGTk10Eu4FEEtG1okulOg3uLKF6OmAproR6B0Qb2JJlUw6VME9SaR0asW\nRwqr1nbGZnPSp1flLuIKiHjuSCjUasvupaUJquyQnQu5BbuKq0BkZkNBJ5AtkFWtzthWNVMDQanB\n8k3jEC7Iexqy34LKR6HloPivkYi5I5uXufnp+AHI8lb2mFeLrb9+cx9CiSv/2Uxb/s5j+ugj6LN/\nFZfO/pH0nMS0Fo8Wf7vnfjGMs666kTuufZeJV72PEJHP10sU/jZLLDyw+DTu/fV03jx2OmP7/KyT\nZSagjt/ROnoFgf1RsqcGGlVcRTMHy0gpgQ7HwqSIWPljlJlS0ZBsNnvvh/JyY3WITVSqYIcXWJCY\n2qu6+nTWrCumc3E93brUBhQpRmlsAYojlFJpwV5brYilzOzw5/lS3QQiE1osUGNVR2Sp6Ryrg4wS\nzfwvFEyG2gnQcFZsdifqF9jr2DoXbWTjpCzsz2awxwe15B3VmpDr72xL9DOuGqtsPH3WIVRuymTC\n3G/o1K9BK/NU5a+VvTj+vDs5cN9/ePnRJ8nJTo4UuY/XHsjZn93AnQe8wy1D30dEMXw9FPEOHu6I\n6NXYQs+ZVzGdq2JqoFHFVXTXMlbUqrq6LamElUniKSiwG6YmK5G/Nx1aYCUieiUlbN2WzeayfPr0\nrKQgf9cPIb6zSELNHUkEXkfodkNNBTialXqrtBgjvF2qocipDIipSIFYy+zVjl7BjpbsgUhbBsXj\noeUwqLldSXWMFK0doH8+s69jq3g9ndUX59D74Qa6XNWMOrI2PJGIK29dkD9up4X37hhC6XMDuO7D\nbxl0pIbDyGIgmN1VNTmcddWNbLYX8Mns++jb0zh2B7MZYGlVb0bPncTwkpXMHvUk2anNCbTMRO/G\nFtHg9Ud6zryCjiGuIqnBMoq48q2z6tKlq662xEqy1DP5kow2g2J3SckGw4gsSMwmeIcWWKBt9Mrt\nFmzcXEBdfQYD+m4lMzO4hzNS9KpoDVTaQVigqASsMXSl9k3pEECeCzLcUJkKrTFmtKrpICMZKGyt\nhKIJSupgxWPg6hz5+olwgMEeVg0/p7JsbB4FJzjo+1QDlgxtRVYskatALHy9Dy9dchBnT/+No678\nh0SJw3hoc6Zw+wPn8eIbR/PhrAc44uClepsUEZUtufz7s5soaypg7th76ZtrHHHYETByY4tgxNPY\nQs/UwGQQV5FdyzjiSrHDjFqZRI8RRFaifoc6rMDSOnrV2mpl9bpihIB+fbaRmho4Fcd/V1GNGqxY\nsdeDrIHKcsjMUmZcRVJvFQxfpyaAbDfkO6E6BRqjuPO0cpD5TaVhjxGtkPcgZHwFFTOhNcxnm0Ts\nivjnvAeirczK8lPyQMLuH9SS2k0bu6IRV/51QYFY81MRj449nKEnbeK8J34lNV2/ejIvkdj9n/dH\ncuktVzJjyktccd5/0VscRmJzmzuF2xaex6y/j+bD0Q9wRLfkEIfJTDJFr0DxR3qlBnqJ59mvRebD\n9rVVFleharCMIK68USt/YZVsdUFektHuZLQZdthttBbuWn9e67ACC7SLXjU2prF6XScK8pro0a0a\nS5h/ZSNEr6QEWQbib8gvhqzc2MVVqF1Hm4SiNmiyQm0EdVlaOMho55MIIPsdyJsO1VOgaUzo4xPl\nBMPtHsoWwdqrs6n6yMagubVkD1O3iYRakSt/arZk8vgphyEscO0H35HXNTlS2H76fSAnXHAHpxy3\niJl3v0i6LfF1cLHw6oqRXPb1FTx22EtcttdnxCMOzTqs8HSk6BVo3zUw6PkatmNPVOTKKM0sjDbA\n3iR5MYrISsTvU4cUWFpGryqrMtmwqZAe3aopLmoMKVIC7SrqUYMl3VD+uyKwikrAlh7/mqGcWgqK\nyHIJqEoh7L6sVqmB0c4dSf8Ziq6HhlOh9lqlrfvOa6s8UDgINTVDo3B0AvszGay7IZv+s+opPked\nKdSxiKtQdUH+tDWnMGf8/vw+txs3zvuGPgdolOMTAdHYvbm8iJMvvpUUq5v3X3iQrp2DdFLRmGhs\nBlhk352xc2/n9P4Leeywl7BZoxfjagvt9oYabdljIdboFUDNPiNjv64KjS1iPj8JxZW/PzJy1MqX\nZK4LUgu7vWmnL61oL//WRhFZig3a7ZJ0SIEF6kev3BI2l+VTWZ1Nv77byMmO7MbRO3rlckDlT0Ar\nlBRCSmpc5kS862gBCpyQJpW6rLYAQlSr9I54HGPKZii+VqnHqnoIXHnK9xPdNTBa6krTWH5yHiWX\nt9Dr3gZESvxRCu0/UAu+fGogb960L5e8tIjh56zT+Hrq0Nxi46o7LmP+V/sz95V72X/vVXqbFBGb\nG4s5ad5tpFvbeO/4B+mSqeKEcJO46UjRK4hfHCWTuNr1OsYQV4oNHTNq5S+aQn2VlGzd6QvWRXxu\nR8UI95XWv18dVmDFg/9uotNpYe36YtraLPTvsw1bWvinb7BdxUTWYLXVQuUCaMsGMYiwqYxqI4Ac\nF+Q4lUhWc4Dra9nYIpq5I75YGpU27ql/QeVT0NZf+X6inGF+/scxnedYY2X52FzSerrZ7Y06Ugpj\nb9Edi7iKpC4oEH9/1YWZpxzGUVeu4rRpS7CkJHbuVGx2C558eTS33DuO2Y8+yVknfqe6XaGI9d+6\n2WXjitLL+WzDfswbO42hnVTqnGOSlG3Z8z8uje1cnRpbJGPkyovXH+ktriKJWvmS7HVBkYqmUF+B\niPTcaERXsv9b+2O0zoJq0+EEVjxpGr54HV5zcyqr1nYiK9NB755VWK2RRwb0jF41b4GqnyFnEFh6\nQ5eNcZmi2BNjznyGhEIn1FuhzlOXZcTolS/CDbkvQc6LUHG/RP5LnXVD4XV68eCqt7DqghwaF6cw\naH4tGXtG1zjf63gSzdbVOcwYczjFvZu48vUFZBUmx0P5y++HcOqlExl//qfcfdPrpKTEOqggkQie\n+GMMExeM4+VRT/DvAd/rbVCHRa/UwGRubKEFHSVy1RGiVl4RU13t2CkbIxLRpAWRiK72jt4iS6sM\npA4nsOLF1+HV1GawdkMRXUtq6dK5PuKmEKEcn9Y1WFJC3QqoXwmFB0JdlqaXi5hUT/OLNqF0GZRC\n+7bs0dZgBSKjFMTlbiy3SOovzEXG0XUxFL4PoLjzsN2Czfdnsen+TAa+VUfBmMgebvE+6KOtC/Kn\nuS6N588fzoYlBdww7xu6DaqNa71IidfuVeu6Mub8SfTrZee1J2ZQkKf9MOV4bQb4YtMQTv30Fq7e\nZz5TD3wDq9C/o2NHRM/UQNteI2M7V4fGFlptyiVKXNXUHKZcRwdx5TvXKlpxZfS6oGCRqS5dShIu\npiLFX+h5ba+pGaizZbER6h7RW8xr+fvWoQSWGs0tACrkYMrtuZRvzaVv7wrycqPf7tMjeuVug+pf\noa0GikdAaq7yfbXu73gFkRUlkuVoAtkJnGmqmLUdLRyk3e6iS/UWiq6207q3jeqpxbgztVFZaj+I\nqj+y8c85ufSY0kS3m5tABI++Jq7uKjTSLfjk3r2Y9+CejH/7B/Y5Xt+ZMJFS15DJuOuv489lfZg3\nZxp7DNikt0kRsaq2G2PmTmJAXjmvHzODApv24tBEoaNFr9SYeaV25KsjRK7a41wr/+iPHpEptQgm\nttpTZKu9pgp2KIEF8TW32IoLpyuF9RuLaGpOY0DfbWSkR5liFcbxaVWD5WyAioVgzYTCYWBJUyeV\nQ20EYKmFPDtU9gdHdvxrBmvLHmsN1o51dyxqrXFTeMs2rJUuKmeW4OwWw3TmoNfZOTVQzTzspj9T\nWDY6j5wRbfSfVY8lO3h9U7zOKda6oEAs/rAHz5wzglPv/pPjb1qGCCEO40Utu91uC9NmnsHDz57M\nO88+zPFH/qrKuoFQ89+6rjWT8764jqWVvZg3dhq75yeHOGwP6N3YwvFXafTn6tDYQotZiYkWV/n5\n72l7oYDXjj8l0Ch1QaGbTuyKms/IRJGf/21AsWV0Ir1H9BJZJSVbNEkT7DACS43oVZMjk5/XHk5q\nqpO+vStIibHYPtHRq5ZtULkIsvtC3p4gfP7X1diwUmPncftanjSPzCooWA81PaGhWO+xrcHx3XEU\nTsh7vJrMD+upfLwzjqG2uNdPxAPHWWFh5Zm5OLdZGPRJHbY+Oz9o9Kq7CsemP/OZfvwRDDx0Gxe9\n+BO2LHXnfGnFB58O59xrJnD3TW9y42UfIURim3bEgltauOeXM3nkt5N49/iHOa7XYr1NateY0aso\nztVoViJ0nMhVshJMVHUEklFohSKZ78NgdBiBBfFFr8oaivht3YEUFzXQvWttTEN4I3F8atZgSQkN\na6D2TygYCpk9fWwxYPTKi3cnMq0JildBcwHU9iSm+qZQQ4XjqcEKtduRNbeR/LsrqZlYRMNp2XGL\nQ/8HjxY577JNsH5iFltfTmePj2rJPVwZkqvmQ1uNuiB/6ivSefLMQ2ioSmPCJ99S1LtR9WtoYfcf\ny/owetwkjhj+Fy889AyZGerMJ/Oihc0A7685mP/7/HqmDX+dCUM+RmB8cZis6B29guhrsPRqy65F\nU4xEiyub7WBtL7j9utF1CQxHomuwgqX/RYtWz0gtCWRzMgitaO6R9pQq2CEEVjzRKylheUUvFm0Z\nRM+edRQWxHfzqhG9igTpgpol0FIGxQdDWsGux6gVvVLLuQXaibS2KSJLCiVl0BXnnC41CbXraPvT\nQdE1dpr/lUXtLYXIGOxO/INGsO2VdFZfnkOfxxsoubQZkIbfEXS1Wnnr5n35fk5frv/oWwYeZmx7\nvWyrzOP0y2+mpi6LT16+j17dNarSV5klFX0Z/ckkjuzxJ88f+QyZKeqKw46OntGrWLvSxtuW3UiN\nLWN7EpIAACAASURBVEJtyql3DX0iV8kctWovNVVa4S+0khE970st0gQ7hMCC2KJXTreFn7bsxYa6\nLgztu4iszFYNLNuZSGqwwjlBVzNU/qj8vWg4WDN2fj8Zole+CAn5GyC9FioGQGtmZGuFc5Sx1mBF\n+kuYstVF0fVbkWmCyhmdcRVZo75WoAeO1jnvDT+msnxsHrmnNHPQ6/WI+DMdAa1z3gXfv9yPV648\ngPOe+JUjLl6NWomlWtrd2pbKTfecz3/eO4KPX7qPQ4f9rcq6WtcXbG3O5/RPb6GuNZOPx9xPz+zk\nEIfJgl7RK38iqcHS25+o3W1WL3HlcCzU+LraiCut/ZEa0apAJGMNViQ2+7d6NwLR3iPtJYrVYQRW\ntDS12fh63f64pWDvPotIT41vlzaegY/b14jAhNZqpZlFelfIHwIiyGd6o9ZeBUMA2dsgbxNU94Gm\nABG5RBLpzqOlRZI/rZL0H5qpeKozrYMia42o9wNm42IHCw+zYcmA3d/NJLVEo/7zKrNqYSdmnHA4\nB521nnNm/IY1gqHf+iOY/fYorrrjcp6c9gIXn/UFxq063EGrO5Ubf7iAN1Yexidj7mNEl+T7wGI0\nkjF6Be0jehVolIfamJGryNFKWHUUkjWalUz3aDjavcCKZbBwRVMeX64dRo/crQzvvhSrxR3XjmI0\nhKvBCuUEmzZC9WLI2xuy+xFTnVi0qLl7GMla6fVQuBoaOkNtt+AfQyPZiYylBiuWELIAst+oJ29G\nNdV3F9N0TGQhuGAPmkTlvBfnbGPNFS3Ufu5k0LxMsvaL73GRqJz3qo1ZPHbS4diynFzz7vfkdo5v\ncyRRdi/4ZQ9OuPB2zj75O6bf+TJpqbF/Yk5cfYFg1rKjufrbS3n6iOcYv/8nJIM4NDKJjl6F2rgL\nV4PVXtqyJ6KpRThxpVUNlpr1VoFQ2x8lqmlFe6nBCoVRolmx3CN6bTKrmSbY7gVWtKyp7sYPG4dw\nQNdlDCpezzYVhmvGs7O4fY0QTlC6ofYvaFgLRQdBeqcQ68SRK7/TOgmMXvmT6oDif8CVBlV9wR19\n5l1cxLr7mL6ohcIbt9JwTi61V+Yjg/z26R298n8Ql81sZf3tLQx4JYOiM9RrP68lrU0pzL5sGH9/\n2YUb5n9Dr31VvGE1ZOOWTpx44W3k5jTx7nMP07m4Rm+TIuL7sj05cd7tXDrkMx45ZDppFu3Tqdsb\n8Uav1GpsEfW5Sd6W3QjiSptr7mhmkQz4CysT9Ui2aJZe96zav5/tWmBF09zCLQWLyweyorI3R/b5\nha45O57eakSvInV+oWqwAjlBdytU/azUXRUfDCkqzI2KlERHr3yxuKFgHaQ2K3VZbek73os01SPa\nGiw1djZSNzgpvtqOq1cKVQ90wp0T+Fcw1ANGy5z3YAOFa//nYsVpzXS9zkbPu2zKVOgoSXzOu+B/\nj+/Ou3fsw+WvLuSA02J7aCfa7qbmdC6beCVfLxzM/FemMWTPtVGvoUd9wYaGThzy6sPk2+p557ib\n6JRRlXAbkp1EZUp4CZd2HqoGqz20ZTeSuFKzBiuRKYHx+iP/VMBE0V5rsIKhp8iK9R7Re7M5Xtq1\nwILImls4nKl8u34/GlozGdX3Z3Jt6t2AakSvgtFWBxULIDUfCvYHS5hOdWoVI+sZvfJFALnlkGOH\nqn7QkrvjPa0cpho7HJYGScEdFaSuaqXiqRLa+uz4jzPCAyWYk2v5x82yMY2k725ht/9kYM1PsGEx\nsvSzrjxx2qEcd8MKTp78Jxar8VuLS2lhxgsnMunhc3j18cc59XhtC+DVorEtg0u/msI3Ww5g/tjx\n7FO0Qm+TkgIzepW4c3dZywDiSt1rJke9lVljlXiSKZJl9Ps3Etq9wApHTUs2X6wdRkFGHYf2/J00\nq3P7e1txJTR6BYFrsALtMjaXQ9VPkDMQcnePvN5KrXtWz+iVPxk1ULBWqckqz4q8AiSaGiy123cK\nN+Q+X0v2nFqqHulEy4gdrR7DPVi0qsGK5KHrqoV//q+Z5mVuBs3LIn1g5I8QPXPey1fm8uiYI+i2\nZx2XvfojGXmRp7Dpafd/S4dyxhU3cdMVHzH5+rewWiO7D/Ww2W7vTElJJhILj/4+jjsXjee1Y27j\nlH5fJNyWZMRo0SsIXoPVXqJXRhJXatRg6SGuovVHRhFWHaEGKxB6iKxEz0ozCu1aYIWLXm2q68Q3\n64cyuPNqhpSswmLgRmneXUYpoX4l1C+DwmGQ0S2y8/Vupas1ac2eeVlFkLa3NnVZWuxCZn7RRMEd\nFdRenU/5KZkxDVNWk4icnQs23e2gbIaD3d/LIP/Y5KjLaqpJ49lzD6Z8RQ43zvuGkt3q9DYpIlas\n7sGYcZPYa+BG5jw2k7wc9Ycpa8F/NxzKGf99hFuGvsykA57DokI9a3vEjF4l7lwvWncMNCNXgTGC\nsDJJnkhWSckGXbJ61NpQb9cCKxhSwtKt/fi9fHcO6/UbvfN2fdrG4/S8xJIe6F+D5bvL6HYqXQId\nVVA0AlLzols7GQYLx0PFZhC/gKUNKoeDMyP08bHOwVKbtBWtFF9tRx6Sie3JXNzpodWhFjVYsTxo\nK991suq8Znrda6Pr9eHbzxsh593tsvDh1L357PHduea97xl8TFnYc4xgd3VtNudcM4FV67ow95V7\nGdAnXD2H/jYDLK/ux+hPnmLvon+Yc/Qd5KY16G2SITFi9AoC12Ale/RK67qrWMVVPDVYeoqrSPyR\nXnVWoTDKMzIa1LQ5kSJL61lpaqLmpkiHE1htLisLNu2DvbGQUf1+ojAjuLdIdHpgMEpWg7MRKheC\nxQZFB4JVpeGveqNmqiFAFyfk/QWZGxWR5SiMf0273aX5TmTFsmbERZsRjU4qZ+6Ps0t6+JNUJhbH\n1/i7m2Wjm8gblUK/59KxhBG1RuHnd3rxwvnDOeO+Jfzr2hUkQ2txl8vKlOln8+Ts0bz/wkMcfdgS\nvU2KiGpHHuf870HW1vVg3tjxDMgz7g57ojGjV4k7FxLT1ALMyJUvZtTKuCRLJCtZ6VACq6E1g6/W\nDSPN2sbI3r+SkWK8VsKBarAcFVD5I2T2gry9QET5v9bemluEQwBZGyB/CdQMgcZegT8+xzIHS0u6\nFG4gb/pyMudvoXLm/jiGBO4iocXckXho2ypZcXoT7ibY4+NM0noEznM0Ws77+t8KmT7mCAb/q5zz\nn/2FtAxnwOOMZvdbnxzKBROu4cHb53DNhfMIdHcn2ma7vXPI913Syp2LruapP8/i/eMnMKrHjwmy\nzPgYNXoFu9ZgJXv0CrSvu4pVXMVSg2UEcRXMHxkxauWL0Z7rkaCFzYn4v4n3M4sRmn/FgiEElhCi\nQAjxgRCiQQixVghxdpDjzhdCOIUQdUKIes+fh0dyDXtDAV+uPYB+BZs4oOsyrJbgO9ZqpQfGG70q\nbwb5O9Qsgfx9Iat37MOD22NzC18C5dTbqqDoR2jqCbWDiam+Se3mFoGvsePhIYCsDzeRf//f1Nyx\nF40ndU9IbCXeh6x0wLoJLVS82cYen2SSc3CCh5PFSJ09gydOP5S2ZgvXffwtBd2TYydv8dL+jBk3\nieNG/sYz9z1HRrr+DqikJPwA7Tf/OZ4Lv7ybh0Y8ytV7v4ERI4eJ8EcQf/QqHjpy9EorEuErdr6e\n/uIqGGbUKrnwDiM2Ika8vyPFEAILeBpoAToB/wc8I4QYFOTYBVLKXClljufPb0MtLCWsrOzJos2D\nObjHUnYr3BSRSEn0rqIXbw2WdIL8EqxLoOhgsBXFtl57b27hS6CdyZRmRWTJFKg8EFw+qZWR1mAl\nIt3D/yFi+62aout+pWlsd2pv2AOZuuOmNXI+89ZZbay9toV+z6TT6YKd5wYYNefd6bDy+oSh/Px2\nLybM/Yb+wyt2et+odpdvK+DUSyfS2pbCR7Pup3uXHXYb1WaAX7ftxZi5TzG693c8fcS9ZFijCKkk\nBs38kT/x+Bk10s/D4VuDlczRK6PWXfkSTQ2WkcSVrz8yetTKFyM/I4Ohtc1aiSwjf2bREt0FlhAi\nEzgVmCSlbJZS/gB8BJwX79out+Dnsj1ZW9ONo/r+TOcsFXPcQhDv7qKrASrfAtqgaDikhN8YDola\nzS3UQu30wHA7kxYX5P8OtgqoGA6tuaGPNwopZS0UXfMr7pwUKh/eD1dB+EYS0aLFA7X+OxfLT2qi\n87hUej9kQ4SZz2YMBKUvDOC16/anf9YzHJIylcEVDzK44kH61r7B4IoHKax5RW8jd8HRmsp1/8/e\nmYc3UW5//DNJ03Rv06ZNy44gmyC7UAVFcQVEEUHlKoqo1x0RF67AdUEUF0QFl6sCole9uKGiuPGT\nKioooiJg2RcBaWi6N2nTNHl/f6SBtCRtlpkskM/z5IFJJjOHkMyZ855zvufByby/Mp9Plz7GoL7R\nMXeqyJLNZZ/Pp96h5qORU2idrHB6wUeU9EfuhCt7Zaw98bJX0RBc+Xe+yAmu3IllraKb2P+Z/IQ9\nwAK6ADYhhPtlfyNwipf9+0qSdFiSpK2SJM2UJO8dSQX7+lNvV3NOx19IifdtlTQcs6/ckdoOw/Rf\nqG8HuSeDKoIUsCO1PBBadp4SkLoL0guhbABY8lruwQqFuEVLtcWqWju6Rzaj/bUM0wsDqOuSKnsP\nlhIXVus+QeHFFuL0El3eSyROL0VFzfu273I49L6Z9/b/xVe27Xxl284v9gN8ZdtOq/qicJvnBYlX\n3rqAux68nleeeJlrxhaE9LNuqf/KG7V2LXeumc7y3cNZMeoOTjP8IbNlAaGYP2pKpGev4GgPVjRn\nryA6gitferAiMbjSavtETdbKnWjwR01R2malSgWDvWcJl1x7sERCgJUCNB1IUwmketj3W6CnECIH\nGAtcBdzr7cC5KSXkt9mERhUd81csW6DsQ0g/F6SBgfdbuQhFeaAQUBc911QSDkPmz1B9MlR2jYwO\nkJacpSQg9Y09pL24g7LHelNzjkGW8ypdc+0ww67JtVR9b6f750kk9YqEy03zVFW9SaLWs/iNwxHZ\n9bbfruvJpZOnM/nKVTz+rzfRxHkW7VACX/qvPCPx8ubxTF1zL6+e/bCsNgWIYv5IDmLZK/9Quu8K\nYpmraAyuYjRPpPZjhRI5eiojIT9SDTQt2koHjrmbEULsdfv7FkmSHgHuAZ7weOB7b2FLh1wANBnJ\n6Pp0JmeYc/jw4QKnxLH7dhl2dA3b1QU/ApAy7HS/ts1nOLddvVQuVcDmtoUDyl8toO5vSBkCFW2G\nIX4pwPr30RVEVy28P9vCArlJDdt7G17v4P+2sQwy/izACmgNDa8bCxB1YN4+jPpy5+dt3lVAcqej\nr9Nkf4By1TAMJWCtang9teH1ALfLLQ3bDf1UrqxUc9uaakhbXUCF/nfq+99FxkawmRvvX1T0f85/\nFF0a3r+24fV8WbehX8P27w2v9/G6rfo/yDxoofSycmrVZSSu/JsEjff9W9oWwkpurqFhe2vD691k\n3/776TqK/28LiUMPktn5XEqX1yt6vkC3a2vX0bt3PfwJBTgZxtG/W+IrcBEJ9nra3rO/G6Oum8E5\n+Y9x/y2P8NJ/76GkLC0E5/f/++eirm4jH20pYtX2nsD3hBnF/NFP1z1JcodczDiwZnQmsU+l3/6F\nM05HvaO1X/7FtS3qAF3Dto/+BKC83TDE1gKsh/33H+XpDdte/EFz22XlIGU2bAfgH8pKQUoYhsHu\nn3/wdbuszE5urnz+wWbbQkrKDR5fLypytvbl5uY1vB7Y703O7bIyK5LUi4yM7xqeC//1z59tm+0v\nUlLOjxh7fNl2Pafk+QyGwxQVGbFatbJ9X6qr30ej6RzU8YQ4BJzZsK3U/RjU1a0lPv4AtbXBz5yR\nhAjvGn5DzXspcIqrLEOSpDeAA0KIB1p47xXAvUKIAR5eE+PF137ZIkd5oL/qgY4aKPvU+XfdKLBt\nKqD81GFBrTQesaVKueHCtnIo+xYS2kJqHyh6R0KlFaQPhoQ2zRyrWH71wEDLP2rrCrCeOgxrNuh+\nBY3Z/bihKw/0d0WyNm4T5seuQaoXZMzZgsocWKbCaLSEdtUxdzu9lveldIWNg3PrwBG6U7dETU0B\nPXrswmAwoF6zhvdMRwUjCnAGWpdnZfFj/JNhstA/6uoKmTmlkMtHruX6abezeVt7Rc5jNOYEkb06\nlkOHhiNEIHqf8hAKfxSon3FlrwIpD3RJs/vrV6xbCihvNyxgPxLMYPpAfcWhDRJ5/UVQvqEllOi7\nslrXei0TNBqtEZW5cs9aWa1bo7LcLhrtDpXNrrJvua7tVuvvMki1t8NgCN0AWKOxFQ5HXFD+KOw1\nO0IIC/Ah8IgkSUmSJA0BLgbebLqvJEkXSpKU0/D3bsBM4KNQ2isnNhOY3gKNHjLHgioRj3OwAkHJ\n8sDa/VC6ClJ6QVq/o3O5dMOg4meo2uwsHYx0EuKHkb4VUnZD6WlQmx16GwJxmgn1vcj810bUBy2Y\nFvanvq18N7iKUtSFwpEWkvuqOXlpIuoIEBux201otW/Ss+cecnNzKSoqwmZrXIc1rOFPW30dFz+w\nBamZEQ+RQnx8d5586TJmPzeed154htHn/Rxuk6ICpf1RsCNAQj1YuOkcLH8IZ+9VtAVXQFQGV0DU\nBSkuotHuUNks98Kr3H3j0UIklAgC3AYsBg4DJuBmIUShJEltgS1ADyHEAWA48LokScmAEafTe1wO\nA+SafeUrtTuh4ktIPQuS3BYz/RkC2RJyZ6+EgOrNYNnpDKbi9Y33jdeD/kIo+w7qyyA9v7FIhxLZ\nKzlIOghx1VDWF+r/guq1dsK2hO4jkl2Q/sIOLBfmUfJMP9KfLiThJ98/3JBnrxqoLxXsuKqGNg9p\n6f5ZMjuus2DdFZ6AxW430a/fBmprQa93BldWq5XixESu0Grp0qULarUau93O9u3b2WXWMahfKTcu\nWccbtw+gtiry5RFXfD2Q3fsMLJ63kB5d9vPkS2NwOORZVwtU3CIKUNQfRfJg4WPeG2QVRDjnXilJ\nqPuuIoVYv1WMGL4T9gwWgBCiTAgxRgiRIoToIIRY1vD8/obZIgcatu8VQuQ2zBzpLIR4WAgh2zpV\nKNQDhYCqtVCxCnSXNQ6uAMQvBbKUB8qNwwbla8D6tzOIahpcuVAnQdZ5IKmh5Cuor1bWrmBWKd3n\nYMVXgH4t1OaAOFMiu9Wh4I1rhmAcp3v/StIXh9A9+AcVU7tRfVX7iBDt8IarzlvUw/6ZVoperKPb\n8iTSzwn9UGK73UTr1p8xYEAX2rRpQ0lJCXl5eeTk5CA6dmSzXs83DgcbdTo+KCnhi9ohlKbdx4tX\nnkHJgSSmfvot2Scp/OUOAvea/S3b23HRNbMY2HsnS+YtJCW5RrbzyFkeGCko5Y+ClWYPdfYKQGwt\nCPic4UTJ7JVSwVXTOViRJmrhLbiKxnlSEJ12h9JmORUF5ZiDFY1KghERYJ0oOOqgfAVYd4P+aojP\nU+Y8cpcH1lc7gyVJA1nngrqF3j9J7cxeJXaEki/BGhkjblpEbYWsnwEHlAzKoT5B2Rt/uRxn/J+V\n6G//hdoh2ZQ/cApCGx0/a9M7NnZNrqX90wnk3ir/jC9v2Gw7GDhwHe3bZ6JSqbBYLLRv3x4hBPHx\n8VitVjIzM8nJycFoNHLgQBeSk0cC4KhX8cGM3hT8pzNTPvqO7mdHx5e7tDyVK26dxkGjjs+WzuGk\ndpEqOX98E23Zq4DfG4beK1BWNVAOVTHfzxUdwVWMGDG8Ex13YgoTivLA+gooeachSLkC1Cme95MG\nDAvaFpCvPDBjizNISuoE6YOdwZMvSBKkdIeM06H8eyjaEHklH57mYEkOkL4XJP5tpmSwgToFhvsG\ni6d6ZrXJStbUX5HsAtOz/bHneG8GDZcEq6f68er1dgpHWtBdHEfHFxJQBS/c0yw22w56995A377O\nsUYOh4NbbrmF6upq4uLisFqtZGVlkZ2dTXFxGTt2nEVKyuhjjrP27Q4smjyIq+b9xjm37iAyBP+P\n4umzrq+P44G51/DKW+ex/LUnOCt/c8DHl1vcIoZ3gh1cH0xFhEuFNoYTJUsDXT1Y0RZcRWMvE0Sn\n3eGwWY77hRO1BysWYDWgZHmgdT+UvO0sB0y/ECQvnW/BzimREyFAbITyH5xBUnK3wOZyafMg63wQ\n+6FiHwiZlOOUamI2Gp39Vyl7q8nYVEJZHz3mtsnyn0gBpDoH6U/8SeI3RZieH0Bdz3Sv+0bSSqTt\nkGDrGAsI6Lo8CU0rZTrgXMHV4MGnoVKp6NChA0VFRaxcuZJ//vOflJeX43A4iI/Xsn27lR07RqDR\nnOz1eHvWZ/HMqDPpN/oA1yzYgCYhOubtvbX8LG687xbmP7iYf179JZEWHB6vRMNgYRfROFhY6exV\nqPquIHqCqxjHN7H/9+CIBVgKIgSYf3OWBWZcBMn9Ww5S3OePBIIc5YGiHipWgNjsDI60QZYyxqWC\nNAjsNijZ4fwzEnDvwXLH5Ui1JVayfjqMpX0qFT10yCUeHawqVHP1zBKQ8t5+0ucVUvZgLywjWwV8\nHrlprn5c1MKe22sp/dhG90+TSDlN3vJM9+BKo9HgcDi46aabkCSJ+vp6XnzxRfR6PXV19fz0U09K\nS8eiVutbtLv87ySeGzMUSQV3friG9Dz5+puCoaVa/Z9/78LF183gsovW8fwjr5HgZbiyJ2LZq9AR\n7sHCrnlWfr83TOIWSi26hQKrdW1E9Zj4GlxFYy8TRKfd0WgzyNODFY3EAiwZ8OQEhR0qvwbL75A1\nAbQdQmdPMItf9mooeQNqKkAa5wyOgsVY7Mza6TqBNgVKtoItSgaFx1nqyVprxJ6gpnRgNnZNdPxk\nEtaXknXXBqova0vFHV0Q6kjXRXRifMnG3mm1dHotAf0EeVT6mgZX48ePx2g08uqrrzJ16lSysrLo\n0aMHf/9dzJYtg5rNWnk8fk0cb9zWn98/a8Xdn35LhwERVgvrhYNFWVw6eTpxagcfvvoEeTml4TYp\nhgdCnb0KhuMte6WUJLsnyspsDecKf/YqlrmKESN4ouNuUUHkGC4MjZ2g3Qwl74LdAln/gLiMlt/v\nWm0MZu5IsNj+BtOroD0JpJGQK6NYhqHEmb1LbQ2pbaB0B9QEeD8nlzP11IPlCZVdoPvVRHyZlZLT\nDdhSwyvP7Ws9c9zBGvR3/oI9J4HSJ/tgTw+33b7Vj1eutrP1UguGmzW0m6P1WlLbEna7ifT0z+jT\np3FwtWjRIqZOnYoQggceeIANG37l4483s3nzOR6DK9/slvi/F7qw7N4+3LD4JwZftTcwo2XC18+6\nplbLrTNuYuU3/fl06Rz699rZ7P6x7FV0IJc0u7bDML/ffzxlryA0wZXRaEWSBkVlcBWNvUwQnXaH\ny+Zg+7BiPVgxZMFmhJL/grYt6C4BVeRpJHikZhOUvgVpF0DqsMD6rXwlUQeZJ0PVQag8GNhQYqVK\nQbw5UwlI3VFJ6rZySgdmU5OrsBqDTKjMdnQP/oFmSwUlLwzA1smLukqEYd0t2DrSQnxbFSe/k0hc\npn9fSLvdxNChO7n88h4MGtQ4uJo8eTLvvvsuycnJVFWZWbu2ByUlo4+UBAbDn9/k8vyYoZxz607G\nProRVZxMTYeKIrHw9RHcN2ciS55ZyJWj13jc6zieexWRhFPcIkZoVQMhlrmKEZnEvguBEwuwZKSm\nEErfh9SzIXVIYEFKMD1YgfRfCYezlLHqG8icCIk9Aj69X2iSIKsb2KqhbBc4wqAP4K0HqzkSi2rI\nXF9MVdcMKk9O91seQI4ae3/rmSUHpC3eTepruzA93pu0ceHJQPhbP26vgp3X1WD+1U73lUkk9vDt\ncmW3m2jXbhVLl85HpVJ5DK5sNhvr1v3Mxo39WywJ9Nfuw7tSmT/yTPTtLdzy9o8kZ4a+ryKQWv3/\n+743l914P7dd9zmP3PM2avWxP8pY9iq0hFvcwp8erONRmj1U2SsIf59KoMFV9PYFRZ/d0WgzhP+7\n7S9GYysMhuD7wE/oAEsueXbVttZUfgdVayBzPCR28fMYQZRzNMWfRTBHLZS94ywN1N8IGkODPUE4\nyqY0V1ev1kBmF1DHg2kr1Mv4OSiJpspG1o9GbLp4yvrpcfjZ3xSulcrEgsNIN/1E1U0DqZrUTzbR\nDkVxwMHH6zjwuJUuyxLRjWy+XtBm28FZZ23iggtOIzk5GZVKFVRwFSg1lfG8cu1g/tqo4+7PvqVV\n9wpFziM3O/fmMXLiTE5qZ+Tthc+gS3cOU45lr0JLuMUtog25KxpCpRoYKZLsscxVjBjyc0IHWBC8\nPLvDIlG2HGyHnMODNdmBHcflEEPVg1VvAtNroM6EzKtBpeDCdHPBmiRBejtIyYGSbVDbwn2onKuV\nvvZgeUJtc5C5vhh1rR1TvoH6pAAbhQIgmHpmaVslWbevoK5XLmUPn4sjKXR9WcHUj5d9XM+OCTW0\neVBLq3vjnTWbTbDbTZx66u8sWfIyGo0Gs9nMddddd0xwtXbtBr+Cq0DtFg6JFXNO4bMnenDbuz/Q\ne8TBgI4TCMF81pXVSUy8awqbCjvw2RuP0q3zASCWvQo1kSBu4WsP1vEkbhGu0sBw9akEG1xFYy8T\nRKfd0WgzxHqwYgSA9VAcZXOzUWdA5uXKBilyUrsDSpZAyumQfpHvw4OVJCnbqTJYsQ+qi5rvy4oU\nKV5JQPqfZSTvq6JkUA5WfYL8himAuryWzPu+QF1ipmTBKOpbp4XbJJ+wbHJQOMJC6ulqOi1KQNUw\nnsxuN6HXF9Cly2ry8/uTnJzMddddx4MPPoher+eOO+7g7bffZuPGP/n44x1s3ny2YpkrT/z6URte\nmnA6lz60mYvuKUSSIn/ulMOh4tHnx/HUy5ey7MV5XHvlr+E2KYYPyCVuEQjHk7hFqLJX4c5cuYhl\nrmLEkJ9YgBUgVX9o2TFXT9L51aQPly9ICbQHyxfnKARUf++ccaW7EpL6BXQqxYhPAX03qCmD3f29\nsgAAIABJREFU8r3yDSX2RtMerECdavJ+M7rfTZT3zKS6Q6riY1vlqGeW6h2kP7eWpOV/UvLsSKz9\nlZ+XJUf9eL1JsH18DfXFgu4rklDnlTB06E7Wrn2Jc8457Ujmqn379txxxx08/fTTvPrqq3zxxU/8\n8EN/Skou8FvMQg67D2zK4JkRZ9FlSDHXv/Yz2mRlh8HJVav/8uujGXnNQ8y+5wWm3bQUSYoG0Y7o\nJpLELQKdgxWthCp75akXNxx9KkajJejgKnr7gqLP7mi0GaKvB0suTtgAK1B5diGg+PMUDizRkX5z\nKSkGXVB2yNl/1RzCBuUfQu2foL8B4tt6sSdE/VfeUMeDvisgnCWDdt/nn4aV+LI69OuM1OQlUdEr\nE6GKhgYnSP50GxmPfEP5fWdSPfYUxYNDORA22He/lYMLDtGu7f+xdOn8Rv1WDz744JEg65577mH7\n9n389de5sqgEBkOVKYGF44ZQXRLPXZ+sIau9Oaz2+MoBY29GTHyBMwdt4NUnHyYpMTKGKR/PhFvc\nwq/3HmfiFqHIXjnPExl9VzFixFAGvwMsSZLaS5L0siRJcyVJeleSpGQlDItEHFaJ/a/qqPg5kU6z\nionvLM/dv/uKoxI9WPYKMC0GJMiaBOoQVoQF4jwlFWR0hASdU/yirlp+uyC4HixPqGvt6H86jFBB\nyaAc7Fplai/lrmfWbjKSdccKas7rTMV9QxEapeyWr37cbjfRw1jI2T0HkJzsvAS591s9/fTTzJw5\nk9GjL2f16jZBBVey2m1Tsey+PvzwRgemfvIdXYYE0YDSDHLY7D7zqrgkk3E3P015ZSorXr+Ddq1D\ncxMaw3eCXazzdL8fyBysUCJneWCohS2aEso+FTlFLaK3Lyj67A6XzQbD4aAC8lgPlg9IktQB+BD4\ntxBiOrAOeEx+syKPulI1u+c6b9JO+lcx8Zlh0BUPgLq/nGIWib0gYwxI4Z016zOSBCm5kN7eKeNu\nMSkrxysXkkOQsbGUhCILpvwc6jKODkKTQ6JdKeIOm9FP+RShUVPyzAjsWZE758tdht1VEggcKQt8\n++23WbduM5988lfI+618Q+L7pSfx+s0DuGbhL5w1eRdEWO7Qk2pgnS2ee2ZP478fjOKTxXdyxsDf\nwmDZ8Y3RFlz2KtSzr8IlbiE3oS4NDHf2ymlDrO8qRgwl8TnAkiRJA7wPPC+EcP0y/wIuUcKwSMK8\nI55ds7NJP62GtjeWoYoPvk7eG4H0YHkr77BsgLJlkH6JU9BCyeHBSpGQDlldncIXjjLIqZfv2IHM\nwfIFCUjZU0X6ljLK+uqxtD6a5JXDsSpVzyxZ7WTMKSDhx32YFo6mrnuAkphekKN+3DVA2CXD7hKz\ncAVZer2ewu1Gfv11ICbTMFnKApWqe9+5Npv5o85k0JX7mDD/N+K08t3kBWOzK7jyrBooseTdS7l1\nxgxeeHQO11+xnEgLDmP4R3Plgb70YIVD3MJolF/cItylgaHqU5Gj78qd6O0Lij67o9FmkOe7bTS2\nk8ESX84jXz+6Pxmsu4Bc4C2359KBtpIUCTp0vuNP/1Xpd0nsW5hJm0llZF9U3ShICbZOXqn5V8IO\nFZ9B9TrIuh4SOvtoTxCrkUoSl+AUv8AOpaXgiJI++4TiWrJ+Pkz1SalUdMuIirlTEpDyzh+kP/cj\nZY+ci+V8H788CuOuFOieuXIXs5g5cybnjr4M07RTSRsQHXObSg8k8+zoM4lPquf2974nLScyhsG1\nJMn+4y99uXjSAiaM+Yx5s54mXhMlzZIRTGz2VXgIp7BFqIn1XcWIZgwGbYjOI09I41OAJUmSFrgP\neE0I4Z5D6O7PcaIJUQ8H/5uO6YsUOk03kXqqMhfHpk4x2B4suxlK33T2XeknQ1yWn/aEUeCiOVRx\nIGWBRgMmE9hkyCC6erCUrL2PM9ejX2vEnhyHOK8VDk3w87JCUc+csG4/mdNWUj2hNxW3DJJFtCPQ\n+nFX1sqlFNg0c+USs9i69TC7Nw/H+GIqnZcmkjVOntlkSte919XE8fo/B/LnNwbuXvkt7foEv9IR\nqM3ufVctsf/vPEZPWkBaqpn3/zON7KzSgM4Z4yiRMPvKneZ6sI6n2Vfhzl6B8td1pYYJR2MvE0Sn\n3eGyOdhB87EerOa5CsgEljV5/gygSgihrOZwiKmvUrHnGT02UxydZhajzZOxLk1BbEVQ8hpo2jpl\n2FVhHsskV7DmQpIgLQ1SU52ZrJooETNT1Qt0G0xQYsWUPxBbSnTowmj+qkB/+wrs7dIpnXsBjrTQ\nrB65aJq1cikFespcDRs2hjVrOqNW66n4ys62sTXkTdHS5kEtREV+XeKrZ7vx/oxT+eebaxl4eehT\nCoE4UUtNIjfd/29Wrx3I52/cSu8e0VnCcqISjHogRP/sqxMpewWxvqsYgRMbNO8/vgZYlwK1wDxJ\nkj6XJGmlJEmrgIHARsWsCwM1++PYOTubpI51tL+zBHVSaPsLAp2DVbPFmblKHQ5pw51KfMcriYmQ\nmQmVlVBV1fxQ4uZQqgfLExKg2lBC6o7dlJ7Wl9qcwHuDgq1n9udGWlVdh27G12h2lmBaeDG2DhkB\nn9ef+nFPWSvAa+aqqQx77Q4HhSPNJHZV0eWtRNSBmx3SuvfNX+axYOwQLpi6jUv/vQmVOrB6WH9t\nbr7vqnmEUDH/1YnMfOp2/vv8A1x20dd+H+NEJ1LLA0+EOViRkL0CZXuwlCwNjN6+oOizOxpthtgc\nLK9IkqQCzgI+FEKMEEJcJIQYAcxreP83CtsoK4fxvmJV8UsCe57Sk3tZJbnjKr0GKcEqPclJUQUk\nvQ5VX0Pm1ZDo/2ivqESjAb0erFYoK4uevqzEQ0Z0v2ykonsXqjp3DLk8QCA30JJDkPbKelLe+I3S\npy+i9nTlm00Nhs3HZK3gqFLg3LlzueiiceTn33Ikc9UUewXsuKYGy58Oun+WTEKX6Fh1KNqexjMj\nz6JVj0r++d+1JGUo298UTHDlzhcFQ7j8n/O45+alzJryH1Qq/7IDoWpijlQixaf4wvFQHhjLXsWI\nEcMdOQUuwLcMVmucYhbrmjw/Aqd81PsAkiSdJknS3ZIkPSRJ0leSJJ0pq6Uy0lTgQjjAuDyVQ8vS\n6TithIzByteeeRO48KcHy2EB8QLU7YOsG0GTJ49tkYgnx6pWQ1YWqFRQUgL1flZyyj0Hy1fiK6vQ\nr/0Fa5aOsj49caj9q2ELVz1z0qpd6GZ8TcXtg6m6uo/foh0t1Y+7SgJ79FhH69Y1HrNW0KAUWOij\nUqAdDjxi5dB8K10/SCTjAv/7ssJR924pj+flf+RzaGsad3/6LYaTK/16v682yxVcudi2qyMjJ75A\nz647+e/zD5Ce6lsN2okeXIUDX8oDm+vBivbyQIic7BUod12XWzWwKdHYywTRaXc02gzR1YMll8AF\n+BZgGRr+/NP1RINq4DjgOyHEFkmSEoFLhRDPCCEeAl4BPpckKeJv+e01En+9kEl1oZZOM4tJbB+6\ndrJgyjrqi6BkJpAOmRNBHWRbT6QqCLrjybFKEqSnQ1KSM8iyRsZiYYuo6+rI+vk3VLZ6Sgb3pz4x\nzA1zPhK/zYT+9hVYB7amfNbZOBLkEZJwLwlcteoVBgzoFlDWyhsl79ez85oa2s3RkndXfMtviAAc\ndhUfPdyLL5/ryp0ffs8p5x1S5Dxy19aXVaQz4Y657NjTjk+X3kbnDvua3d8VXIVKISrSiNTywOOZ\nUGavwjnzKqYa2HjhLj39M9LSltOp03v07v05WVlfYrebwm1ijBYwGttFpX/wJcCqx5mpKnJ7bgSQ\nDcxq2O4M3C9J0kkN218CiThFMCIW62E1ux7LRp3qoON9JjTp4a8z86UHy/oHlMyCpAtBNRHkEsmX\nW5QiVEgSJCdDRgaUl4PZ7FtfVih7sDwhCUH6lq0k7T9IyeD+WDN1Pr0v3PXM6tIasu75HMlio+T5\nUdTnpvj0vubqx91LAgFuuOEGZs2aFVjWygvm3x0UjrCQPjyOk/6TgMrHuCLcde/r32vHKxMHM/7x\njZx35zZ8mTvli83+KAb6i92u5sF5t7FwyQQ+fPVuzh26ttn9o9F5ykmklgd66sE6XoYLhyp75StK\nXdeVLg0M5ProHvTo9QV+Bzm+vt994W7RohkMGZJJfr6eYcMGkJOTxKWXdqFfv1+iJsgKty8KlHDf\ns4QLX5afXcsv7gVYdwOvCCG+BxBCbJIk6QwhxO6G19vivAvYIZulMlO9Rcv+V3XkjK4i6xxzuM3x\nCSHA/BmYP4GMqaDtAdVBqkApQbicqFbrLBksK3PKuKenR/5wZQlI/usgcdVmynufQsrufSTtO4DS\nZjtvrgN3vJLNQfrT32O5tAclz48iY04B2o1FLb/RDbvdhMGwmZycBDSaoyWB4MxaTZkyhQsvvJz4\n+LYUF9diNPYMenCw7bBg2+UW2s9NoNvHSeycVEPdgcgflLvvt0zmjTyLyYt+pnWPCt6e2o+6msCz\nh0oGV+4sW3EhO/a049WnHuL1d3ezYMkEcPt2x0oDw0M0qgcqMVxYSWLZK8+4gp6lS18iOTkZs9nM\ntddOZc0afLq+N31/YWEht99+N5BLcbG9kZ9wLty9hMlk4u677yYzMxOdTsf06dNZv349AwcOZNas\nWezZs4bKyjEK/8tjnGi0mMESQpQCPwLdACRJuh6IB6Y02c+9R2s6ME8IEVEKg4exYxI9MX2VzP5X\ndbS9udTv4EppgQtvPViiDipegJrvIGuOM7iKZMKVDYuLcwZZQjhLBu3NOORw9WB5QltaTta6DVja\ntKKiZzdEM5FhsPXMct1YS0DyR3+S8fi3lM8YhvmS7s3mVtzrx5srCXSh1+upqMimsHBwwFkrTwgr\n7J1ai+l/Nrp/mkRqfvMp4Eipe680JrJg7BDqatRM+eQ7dK2930A1Z3OogisXv27uwciJL3DhsB94\n6bFHSUyobbDjxC4NDJZQlAc214MVrSg59zAYlOhTCYWwhb/Xx6bVCsnJycyePZV27Vb5lNFyf/++\nfftYtGgRn3zyPosXP8Qll7RnyJANR0r/cnISMJlMLFiwgI4dO7J3715mz55NcnIyw4YNazj3bHJy\nomORPRy+KNgZWBAdPVhGYytZ+6/Ad5n2m4AbJUl6ETgVOFsI4VHaqiEA+1sIcZ9MNsqG3abi4OIM\nyr5PptPMYlK6KavOJRf2Uih5yBlkZT0CcdnO541VJ24NfXOoVM5yQa3WOZS4Ljr+m4mrqSVr3QZE\nXBwlp/XDro2OXiHtb4fImvIZllFdqbj7DISm5ctKSyWBrlVNo1E5WczDi2zsvqOWk15OIPs6jWLn\nkZN6q5q3p/Zj/bvtmPrpt3Qa7F9pixzOMhCKirO57MZnqbNp+HjRFLRxTkd2ogdXkaRIqzSRVB6o\nNOFWDozU7BVATk5Co2oFV5BUULCcVateYe3alxg6dKfXIMv9/a+//joPP/zwkSBq+vTpfPDBMtat\nW8zQoTsxGit47bXXmDx5Mhs3biQhofG5wRngpabGZjw1RzhnYEVzlYNPAZYQolAIMVoIcasQ4q5m\ngquRzt3FdEmStJIktffl+JIk6SRJWi5JUrUkSXskSbqqmX2nSpJ0SJKkckmSXpMkyac7o5qyeH5/\nYiB2q4pOM4qJ14ev1qC5lcemPVh128H0AGgHOMsCwz08uDkcqyQslsi4sEuScyBxerqzZNCTWeHu\nwfKEym4n4/fNaE0lmAYPoC4t9Zh9IrGeOe5QFVl3fIojVUvJUxdh1yUes497/XhTJ+teEjh8+E0B\nCVkEQtUaO1tHW8iZqKH9k1o8XU0ir+5douDVzrw1pT+T/rOeIdfupmlfliebXZmrcDlLa108Ux68\nn/dXnsuPn4xj9IWR9z2G0PijcOJPeWDTHixjWfjKA+UgVOIW4JtyoDtyX9dDJcvu7/WxuLi2UbWC\nK0jyNaN1+PDR9zscDpKTkxsFWlOnTuWaa64hMbEGSTrAli3bmTdvHhkZGRw+fPjIewsKCgDnYp7J\nFOvBUpJgv9vRuhAn22AYSZLOwqk4uFKSpFzgIiDXx7e/iHOQcTZwNfCSJEndPZz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IGWCQqgqks6tblJZP5cjKY6MFlwJVc1nY716UaO9cknH6X/LY9i63oO+tt+QVWZholxAdXeh3LV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tu5Ezr0KdnAT8LvBlgy8LfC7tX78L/M7Avw6QzoCwkpqIkn7t/85O7V/fngLnlxIpgODxTu1Y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59o5x9PvclH951FY1XsaJBSUxq5bsZ/ueDaNwOep2Z08ch+X9PqTOZXS2SDM+Ue/Di15Uu2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\nNnctAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114cc9f60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.1, n_iterations = 50):\n",
" path = [theta]\n",
" for iteration in range(n_iterations):\n",
" gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + 2 * l2 * theta\n",
"\n",
" theta = theta - eta * gradients\n",
" path.append(theta)\n",
" return np.array(path)\n",
"\n",
"plt.figure(figsize=(12, 8))\n",
"for i, N, l1, l2, title in ((0, N1, 0.5, 0, \"Lasso\"), (1, N2, 0, 0.1, \"Ridge\")):\n",
" JR = J + l1 * N1 + l2 * N2**2\n",
" \n",
" tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
" t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
"\n",
" levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
" levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
" levelsN=np.linspace(0, np.max(N), 10)\n",
" \n",
" path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
" path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
" path_N = bgd_path(t_init, Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
"\n",
" plt.subplot(221 + i * 2)\n",
" plt.grid(True)\n",
" plt.axhline(y=0, color='k')\n",
" plt.axvline(x=0, color='k')\n",
" plt.contourf(t1, t2, J, levels=levelsJ, alpha=0.9)\n",
" plt.contour(t1, t2, N, levels=levelsN)\n",
" plt.plot(path_J[:, 0], path_J[:, 1], \"w-o\")\n",
" plt.plot(path_N[:, 0], path_N[:, 1], \"y-^\")\n",
" plt.plot(t1_min, t2_min, \"rs\")\n",
" plt.title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
" plt.axis([t1a, t1b, t2a, t2b])\n",
"\n",
" plt.subplot(222 + i * 2)\n",
" plt.grid(True)\n",
" plt.axhline(y=0, color='k')\n",
" plt.axvline(x=0, color='k')\n",
" plt.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
" plt.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
" plt.plot(t1r_min, t2r_min, \"rs\")\n",
" plt.title(title, fontsize=16)\n",
" plt.axis([t1a, t1b, t2a, t2b])\n",
"\n",
"for subplot in (221, 223):\n",
" plt.subplot(subplot)\n",
" plt.ylabel(r\"$\\theta_2$\", fontsize=20, rotation=0)\n",
"\n",
"for subplot in (223, 224):\n",
" plt.subplot(subplot)\n",
" plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
"\n",
"save_fig(\"lasso_vs_ridge_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Logistic regression"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure logistic_function_plot\n"
]
},
{
"data": {
"image/png": 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JBUARici6dT74PfcclJRAWpq/o8f06dC9e9DViYhIXSgAikiNnPPz9j3wACxf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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114cda198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(-10, 10, 100)\n",
"sig = 1 / (1 + np.exp(-t))\n",
"plt.figure(figsize=(9, 3))\n",
"plt.plot([-10, 10], [0, 0], \"k-\")\n",
"plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
"plt.plot([-10, 10], [1, 1], \"k:\")\n",
"plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
"plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
"plt.xlabel(\"t\")\n",
"plt.legend(loc=\"upper left\", fontsize=20)\n",
"plt.axis([-10, 10, -0.1, 1.1])\n",
"save_fig(\"logistic_function_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['DESCR', 'target_names', 'data', 'feature_names', 'target']"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn import datasets\n",
"iris = datasets.load_iris()\n",
"list(iris.keys())"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iris Plants Database\n",
"\n",
"Notes\n",
"-----\n",
"Data Set Characteristics:\n",
" :Number of Instances: 150 (50 in each of three classes)\n",
" :Number of Attributes: 4 numeric, predictive attributes and the class\n",
" :Attribute Information:\n",
" - sepal length in cm\n",
" - sepal width in cm\n",
" - petal length in cm\n",
" - petal width in cm\n",
" - class:\n",
" - Iris-Setosa\n",
" - Iris-Versicolour\n",
" - Iris-Virginica\n",
" :Summary Statistics:\n",
"\n",
" ============== ==== ==== ======= ===== ====================\n",
" Min Max Mean SD Class Correlation\n",
" ============== ==== ==== ======= ===== ====================\n",
" sepal length: 4.3 7.9 5.84 0.83 0.7826\n",
" sepal width: 2.0 4.4 3.05 0.43 -0.4194\n",
" petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)\n",
" petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)\n",
" ============== ==== ==== ======= ===== ====================\n",
"\n",
" :Missing Attribute Values: None\n",
" :Class Distribution: 33.3% for each of 3 classes.\n",
" :Creator: R.A. Fisher\n",
" :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
" :Date: July, 1988\n",
"\n",
"This is a copy of UCI ML iris datasets.\n",
"http://archive.ics.uci.edu/ml/datasets/Iris\n",
"\n",
"The famous Iris database, first used by Sir R.A Fisher\n",
"\n",
"This is perhaps the best known database to be found in the\n",
"pattern recognition literature. Fisher's paper is a classic in the field and\n",
"is referenced frequently to this day. (See Duda & Hart, for example.) The\n",
"data set contains 3 classes of 50 instances each, where each class refers to a\n",
"type of iris plant. One class is linearly separable from the other 2; the\n",
"latter are NOT linearly separable from each other.\n",
"\n",
"References\n",
"----------\n",
" - Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n",
" Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
" Mathematical Statistics\" (John Wiley, NY, 1950).\n",
" - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n",
" (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.\n",
" - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
" Structure and Classification Rule for Recognition in Partially Exposed\n",
" Environments\". IEEE Transactions on Pattern Analysis and Machine\n",
" Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
" - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\". IEEE Transactions\n",
" on Information Theory, May 1972, 431-433.\n",
" - See also: 1988 MLC Proceedings, 54-64. Cheeseman et al\"s AUTOCLASS II\n",
" conceptual clustering system finds 3 classes in the data.\n",
" - Many, many more ...\n",
"\n"
]
}
],
"source": [
"print(iris.DESCR)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure logistic_regression_plot\n"
]
},
{
"data": {
"image/png": 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s2VI8PT2lUqVK8uSTT8r58+dz8B0vfMX1s1nQEhJE3n1XxNNTpF07EbO5YO6D\n8cebTevccXaHtJzbUpiMMBm5//P7Zc/5PTa9h6aVFmn/P7PNU+51ZNuSIzkba5MjInJLKbUamKqU\negFjdlU3wFrH9BJglFKqExAGvAxcxphxVeps2bIFb29vfvrpJ0sXR/oVUKOjo+nTpw/vvPMOvXr1\nIj4+np07d96zzsGDBzN69Gg++eQTPDw8AAgPD2ffvn3MmTPnntdOnTqVGTNm8MEHH6CU4uzZs/Tu\n3ZuRI0fyz3/+k4MHDzJq1Kgsq7Rmfp6YmMjbb7/NggULcHFx4bnnnmPo0KH8+OOPVq9Zv349PXr0\nYNy4cSxYsACz2cyGDRswm82A0ao0depU7rvvPq5cucJrr71G3759bf/XgVZgXFxgzBh47jmIiyu4\nLSHu/D+yhYs3LjJ201gW7V8EgK+nL+8++C59G/bVKxVrmh3laFsHGxsOzAcuAVeAoSJyRCnlBxzG\nmHl1TkQilVLPYkwfrwiEA90l03gcW1BTCuaHkEyy3Q9RNzc3vvjiCxwdrf+TXbhwgZSUFHr37o2f\nnx8A9evXv2edffv25d///jdff/01Q4YMAeDzzz+nXr16tGnT5p7XPvPMMwwaNMjyfNy4cQQGBvLe\ne+8BUKdOHY4ePcobb7xxz3pSU1OZM2cOtWvXBmD06NEMHjz4ruWnTZvGU089xZQpf+fe6d/ngAED\nLI/9/f2ZPXs29evX58KFC/j6+qIVH5UrG4c10dF3f60wJaYkMmvXLN7c+ibxSfE4Ozgzuu1oXu/w\nOh7OHvYOT9NKvWxnVymlDiilyqU9Ppj23OqRkxuKyFUR6SkiHiLiLyLL0s6fFREvETmXruy3IlJH\nRLxFpJNkWkunNGnQoMFdExyAxo0b07lzZ4KDg3niiSf47LPPuHLF2GXj7NmzeHp64unpiZeXF2+/\nbayp6OnpyZNPPsn8+fMBo1Xlq6++siQ899K8efMMzyMiImjZsmWGc61bt862HhcXF0uCA+Dr60tS\nUhLXrl2zWn7v3r106nT3TQrDw8N5/PHH8ff3x8vLi5YtW6KU4syZM9nGohUPf/1lLCrYrx+cO5d9\n+YKyNnItDT5twGs/v0Z8Ujw96vbgz2F/Mr3zdJ3gaFoRUajr5BRVtmxxKSjZzaAymUxs2LCBXbt2\nsWHDBj7//HNef/11tm7dSnBwMPv377eULV++vOXx4MGD6dixIxEREYSHh3Pr1i2ee+65fMeTU5kT\ntztN+3f14BSxAAAgAElEQVS6n3Lj1q1bPPzww3Tt2pUlS5ZQqVIlLl++TIcOHUhKSrJJvJr97doF\nSUnw5ZfGKspjx8Lo0eCWy0WC87pOztErR3nlp1f48bjRpXpfhfuY9fAsugZ2zV0AmqYVuFyNybHl\n+BytYLRu3ZrWrVszYcIEgoODWbZsGdOmTaNWrVpWy7dv3566desyb9489u3bR/fu3bOdTWXNfffd\nl2W6+65du/L0Hu6ladOmbNq0yWqXVkREBDExMUyfPp2aNWsCcOjQIT0mooTp0QOOHIFXXzVmY02c\nCJ9/DgsWQG4mVeY2uYlLjOPNLcaU8GRzMl4uXkwJmcLwlsNxcigCO45qmpZFnsbkKKUCMaZyAxyR\njIv7aXawa9cufv75Zx566CEqV65MeHg4586dIzjY2jqLGQ0cOJC33nqLuLg41q5dm6f7Dx06lJkz\nZzJmzBheeOEFDh06xNy5c4GMA4dz8ovlXmXGjx9P9+7dCQwMpG/fvpjNZjZu3MjQoUOpUaMGLi4u\nfPLJJwwfPpw///yTiRMn5un9aEWbvz8sXw5hYfDyy3DoEOQhN88Rs5hZtH8RY38eS/TNaBSKIU2H\nML3zdD0lXNOKuFxt0KmU8lFKfQscA75NOyKVUmuUUgX0I6b0yq4FIv3rZcuWZfv27XTr1o2goCDG\njBnDxIkTLWvd3Mvzzz/PrVu38PPz4yErq69lN0MKoEaNGqxatYrvv/+eJk2aMGvWLCZNmgSQYRHB\nnLSq3KvMI488wjfffMP69etp1qwZoaGhhIWFYTKZqFChAgsXLmTNmjUEBwfz5ptvMnPmzGzvpxVf\nISEQHm4kOw0b2r7+Xed20fbztgxcM5Dom9G0rd6W31/4nf91/59OcDStGMjVisdKqW+AOsC/gDt9\nEa2BT4HjItLL5hHmLC652/vQq8raz6xZs5g8eTJXr161dyhFkv5sFrzr18HdHayN2b/XmJyLNy7y\n+qbXWbh/IaCnhGuaPRTWBp3pPQR0FpEd6c5tV0r9C/g5P4Foxd+cOXNo2bIlFStWZMeOHUybNo2B\nAwfaOyytFBs+HPbvh48/htDQjK9ZS26SUpOYtXMWU7dOtUwJ/3fbfzOuwzg9Y0rTiqHcJjmXgZtW\nzt8CYvIfjlacHT9+nBkzZhAbG0v16tUZNmwYEyZMsHdYWikVFwc7dsCJE9CpE/TuDe+/b4znsWbd\nsXX83/r/41jsMQC61+3OB10/oHb52tYv0DStyMttd9VgoB/QX0TOp52rBiwEvhaReQUSZfZx6e4q\nrdjRn82Cl5BgbPQ5YwbcugWurjB+PKRfozIyJpJXfnqFdcfWAcaU8I8e+oiHahfj3UE1rQSwRXdV\ntkmOlQ06AwBX4Hza82oY+1GdlOw36CwQOsnRiiP92Sw8584ZU86/+gpeeQU+/BCUq4IHwKmDk2VK\n+OSOkxnRaoSeEq5pRUBhJTmTclqZvdbR0UmOVhzpz2bh+/VXqB9s5vvTi3nt59csU8IHNR3E9E7T\nqexRBPaK0DQNKKQkpzjQSY5WHOnPZuHbfX43I38cye7zuwFoW70tHz/yMS18WxAfDx56bLGmFRm2\nSHJytU6OpmlacfRX/F8MXDOQ1vNas/v8bqp6VGVxz8VsH7SdFr4t2LwZataEOXMgxeZbAGuaZi+5\nXQzQWSk1RSkVqZRKUEqlpj8KKkhN07S8SEpN4v3f3ifokyAW7FuAs4MzY9uN5eiIo/Rv3B+TyfgR\nuGoVxMYaU86bNTMWF9Q0rfjL7eyqd4CngbeAmcAbgD/wDDBBRP5bADHmJC7dXaUVO/qzWbDWHVvH\nKz+9QmRMJADdgrrx4UMfWp0SLmJs9jlqFJw6ZZx78kn4z3+gkl7YWNPswh7dVU8BQ9OSmVRgjYi8\nBEwCuuQnEK34CA0N5aWXXirw+wQEBPDhhx/mu54tW7bg4OBAbGxsjq9ZuHAhXl5e+b63VviOxRzj\nsS8f49EvHyUyJpK6PnX5sd+PfNfnu7uueaMU9OwJf/4Jb75p7Gj+66+539lc07QiRkRyfGAs+lcj\n7fFFoHna4wAgLjd12fIw3oZ193qtKHv++edFKSXTpk3LcD4sLEyUUhITE5PjukJCQmTkyJHZlhsw\nYIB069Yt23JXr16V+Pj4HN8/vZdeeknq1Klz13rd3Nzkf//7n4iIXLlyRW7fvp2n+6SXnJws0dHR\nubomISFBLl++nO9730tx/WwWVXEJcfLqhlfFaaqTMBnxestLPvjtA0lMScx1XWfOiGzZUgBBapqW\nY2k/I/OVH+S2JecM4Jv2+DjGNg8AbYHbeU+1tMyUUri5ufHee+8RExOT5TV7SE5OBsDb2xt3d/c8\n1TF48GCioqLYtm1blteWLFmCo6OjZVNRHx+fDJt73i2e7Dg6OlIpl30OLi4uVKhQIVfXaPZhFjML\n9i0g6D9BvPvbuySbkxnUZBCRIyIZ1XYUzg7OVq9TSt31/5KfHzzwgPX7JSbaKnJN0wpabpOcb4DO\naY9nAVOUUieBBYBdVjsuyUJDQ/H392fq1Kn3LLd161batGmDm5sbVapUYdSoUaSkTREZOHAgW7Zs\nYfbs2ZhMJhwcHDhz5kyO7j9w4EC6devGu+++i5+fH35+fgCEhIRk6K5avXo1jRs3pkyZMvj4+BAa\nGsrly5et1tmoUSOaN2/O/Pnzs7w2f/58nnrqKUsClbm7ymQyMWfOHHr37o2Hhwfjx48HYO3atdx3\n3324ubnRqVMnli9fjslksrzPLVu2YDKZLN1VCxcuxNPTk19++YWGDRvi4eFBp06dOH36tOVed8qk\nt27dOtq0aUOZMmWoUKECPXr0ICkpCYClS5fSqlUrvLy8qFy5Mk899RQXLlzI0fdZy7sdZ3fQel5r\nBq4ZyF/xf9Gmeht2D9nN5z0+z3bNG/m7JTjHkpOheXNjgHKM3shG04q8XCU5IvK6iExPe7wS6AB8\nAvQSkfEFEF+pZjKZePvtt/nss884efKk1TIXLlzgH//4B82bN2ffvn3Mnz+fr776itdffx0wdgJv\n27YtAwcOJDo6mosXL1qSlZzYsmULBw8e5KeffmLTpk1Axpak6Oho+vTpw8CBA4mIiGDbtm3079//\nnnUOHjyYlStXEh8fbzkXHh7Ovn37GDJkyD2vnTp1Ko8++iiHDh1i+PDhnD17lt69e9OtWzcOHDjA\niBEjePXVV7P8hZ75eWJiIm+//TYLFixg586dXLt2jaFDh971mvXr19OjRw8eeughwsPD2bp1K6Gh\noZjNZsBoVZo6dSoHDhxg7dq1xMTE0Ldv33u+Fy3vzsedp/83/bl//v3subAHX09flvRcwm+DfqNl\ntZYFdt9ff4WICGOqeVCQnnKuaUVefvu7isKBDcbkGPMrsh62Kp9b6cfHhIaGSp8+fUTEGJNjMpks\nY3LGjRsnQUFBGa5dsGCBuLq6Wsaz5HVMzoABA6RSpUqSnJycoVz6+sLDw8VkMsmZM2dy/N7i4uLE\n3d3dMvZGRGTYsGFSv379DOX8/f3lgw8+sDxXSsnLL7+coczrr7+e5boZM2aIyWSS06dPi0jW79mC\nBQvEZDLJsWPHLNcsXbpUXF1dLc8XLFggnp6eluft2rWTvn375vg9HjlyRJRScv78+buWyelnU/vb\n7eTbMm3LNCkzvYwwGXF500XGbxovNxJvFFoMBw+KdOr09//5Ro1Efv210G6vaaUGdhiTg1KqmVJq\nkVJqT9qxWCnVLBfXl1NKfaOUildKnVRK9cnBNZuUUmalVKlcvPCdd95hxYoV7N27N8trERERtGnT\nJsO59u3bk5SUxPHjx/N97wYNGuDoePfN6hs3bkznzp0JDg7miSee4LPPPuPKlSsAnD17Fk9PTzw9\nPfHy8uLtt98GwNPTkyeffNLSZZWYmMhXX32VbSsOQPPmzTM8j4iIoGXLjH+5t27dOtt6XFxcqF37\n75k2vr6+JCUlce3aNavl9+7dS6dOne5aX3h4OI8//jj+/v54eXnRsmVLlFI57hrU7k1EWH1kNfVm\n1+ONzW9wK/kWvev15sjwI0zrNA0P59wvVXyvMTn30qAB/PyzsbaOvz8cOGDsjaVpWtGT28UA+wG/\nA1WBdWlHZWC3UurZHFYzB2NDz4rAs8CnSql697hnX8CRjJuE2tzd2mZsVT4/WrZsSa9evRgzZkyO\nrxERmwxQzm6AsclkYsOGDWzcuJHGjRvz+eefU6dOHQ4ePEi1atXYv38/+/fvZ9++fRm6gwYPHsyu\nXbuIiIhg1apV3Lp1i+eeey7f8eRU5sTtzvfqTvdTbty6dYuHH34YDw8PlixZwp49e1i/fj0iYhmz\no+XdgegDdF7Umd7Le3Pq2ikaVmrIpuc2sfKplQSUC8hzvXf+0ssLpaBXL2PK+eefw1NP5TkMTdMK\nUG5bRqZjLPrXRUQmph1dgQnAtOwuVkqVAXoBb4jIbRHZDqwBrA7iUEp5AROBnP92L6FmzJjBtm3b\nWL9+fYbz9erVY+fOnRnObdu2DRcXFwIDAwFwdnYmNbVgF6Ru3bo1EyZM4Pfff8fX15dly5ZhMpmo\nVauW5fD29raUb9++PXXr1mXevHnMnz+f7t274+Pjk+v73nfffezZsyfDuV27duX7/WTWtGlTy5ik\nzCIiIoiJiWH69Om0b9+eoKAgoqOj7TYLrqSIuRXD8LXDafrfpmw+tZnybuWZ8485hP8rnE4Bd29V\nK0xubjBokJH0ZJaaWnB/+GialjO5TXIqAsutnF8B5GSObhCQLCJR6c7tB4LvUn4GRstPdG6CLIkC\nAwP517/+xaxZszKcHzZsGBcuXODFF18kIiKCtWvX8vrrrzNy5EjL9Gt/f392797N6dOniYmJyfNf\nr9bs2rWL6dOns2fPHs6ePcuaNWs4d+4cwcF3+yf928CBA5k/fz5hYWEMHjw4T/cfOnQoUVFRjBkz\nhsjISFavXs3cuXOBjAOHc/Ke71Vm/PjxrFixggkTJnDkyBEOHz7MRx99REJCAjVq1MDFxYVPPvmE\nkydPsnbtWiZOnJin96NBcmoyH+/6mDqf1GHOnjkoFCNbjeTYyGO82PJFHE137z4tSt57Dzp1goMH\n7R2JppVeuU1yNgMhVs6HAFtycL0HEJfpXBzgmbmgUqoFcD/G7C0NmDBhAo6Ojhl+efv6+vLjjz+y\nb98+mjZtypAhQ+jXrx/Tp0+3lBk9ejTOzs7Ur1+fSpUqcfbs2XzFkf7+ZcuWZfv27XTr1o2goCDG\njBnDxIkTLWvd3Mvzzz/PrVu38PPz46GHHsryenYzpABq1KjBqlWr+P7772nSpAmzZs1i0qRJABnW\n2MlJq8q9yjzyyCN88803rF+/nmbNmhEaGkpYWBgmk4kKFSqwcOFC1qxZQ3BwMG+++SYzZ87M9n5a\nRiLCmog1NPi0AS+vf5mrCVd5sNaD7B+6n48f+ZjybuVter+8jsnJieRk+OwzYw+sJk1gxAhjbyxN\n0wpXtntXKaV6pXtaFZgMrALu9JG0weiCmiwic7Kpqwnwq4h4pDv3b+ABEemR7pxKq3+0iGxTSvkD\nUYCTiGQZNKGUkju/2MBYxyUkJOTOazZtudCKvlmzZjF58mSuXr1q71DuSX82//bHhT/494Z/s+W0\n8bdSkE8Q7z74Lt3rdi+23X6xsTBpkjHN3GyG8uWNLSNefNF695amlXZhYWGEpdsdd8qUKUg+967K\nSZKT05GYIiIO2dRVBogFgu90WSmlFgHnRGRcunJlgRjgEqAAB6AC8BfwZNpYnvT1yt3eh/5FUvLN\nmTOHli1bUrFiRXbs2MFLL71E//79bbLvVUHSn004e/0s438Zz+IDiwHwcfNhUsdJDG0xFCcHJztH\nZxsHD8LLL8PmzdC1K/z0k70j0rTiwRYbdOZqF3JbUEp9iTFT6gWgGfA9cL+IHMlULv0YnxrAbowt\nJa6ISEqmsjrJKcVGjRrF8uXLiY2NpXr16vTp08fStVeUlebP5o3EG7y7/V3e3/E+CSkJODs481Kr\nlxj/wHi8Xb2zr6CYEYHVq40FBBs2tHc0mlY8FNckpxwwH2PX8ivAayKyTCnlBxwG6ovIuUzX1ARO\ncI/uKp3kaMVNafxspppTmb93PhM2TyD6pjGf4Kngp3ir81vUKlerUGO50w1WFP4NbtwAzywjEzWt\ndLNLkqOUehR4DaiP0SLzJ/COiKzLTyD5oZMcrTgqTZ9NEWFD1AZGbxzNoUuHAGhTvQ0fdP2A+/3u\nt3N09nXmDDRqBC+8AOPGQbly9o5I04oGWyQ5uV0McAjGJp1RGInOWOAk8I1SalB+AtE0rWTafX43\nnRd15uGlD3Po0iH8vf35uvfX/Dbot1Kf4AD8+CNcvw7vvw+BgTBzpt7pXNNsJVctOUqpY8AsEflP\npvMjgZEiEmTj+HIal27J0Yqdkv7ZPHrlKON/Gc+qI6sA8Hb1Zlz7cYxsPRJXR9dsri5d9uyBMWOM\nKecAAQGwaBG0b2/XsDTNrgq9u0oplYgxM+p4pvO1gcMi4pKfYPJKJzlacVRSP5vn484zZcsU5u+d\nT6qk4uroyv+1/j9ebfcq5dyKTl9MURqTA8bg5HXr4NVXITLS2DKiTh17R6Vp9mOLJCe300/OYAwY\nzrzzY1fgdH4CKSg1a9YstutsaCVbzZo17R2CTV29fZV3tr/Dx7s+5nbKbRyUAy80e4FJHSdRzaua\nvcPLoqgkN3coBY8+Cg89BLt36wRH02whty05/8JYgXgh8Fva6XYYe0+NFJG5No8wZ3HdtSVH07SC\ndTv5Nv/Z/R/e+vUtriYYCzD2rteb6Z2mU7dCXTtHV7IcOwY3bxqrKGtaSWev2VU9gX8Dd3YOPwK8\nJyJr8hNIfugkR9MKX2JKIv8L/x8zts3gYvxFAEL9Q3n7wbdpVa2VnaMrmXr2hG+/haefhqlTjXV3\nNK2kKtQkRynliNEttUtEYvJzU1vTSY6mFZ6k1CS+2PsF07ZN41ycsaRV0ypNeavzW3QN7FpsuoeL\n2pic7JjNMHq0sU1EYiI4OMDAgTBxIvj52Ts6TbM9eww8TgDuE5FT+bmprekkR9MKXnJqMosPLObN\nrW9y6topABpVbsSUkCn0qNuj2CQ3xd3Zs0YrzhdfQGoq+PjAuXPgqiesaSWMPZKcXcB4Efk5Pze1\nNZ3kaFrBSTWn8uXBL5myZQpRV6MAqFehHlNCptC7fm9MKlfLbWk2EhlptOIEBsL06faORtNszx5J\nziPA28Ak4A/gZvrXRSQ2P8HklU5yNM32UswpLD+8nKlbpnI05ihg7A4+qeMkng5+GgfTPffj1QqJ\niPVdzc1mMOn8UyvG7JHkpN83Kv2FihzsQl5QdJKjabaTlJrEov2LePvXty0tN7XK1WLiAxPp16gf\njqaivfFpThW3MTm5IQKdOxvT0MeNgxK2WoFWStgjyel4r9dFZEt+gskrneRoWv7dTr7NvPB5vPfb\ne5yNOwtA7fK1GdtuLM81fg4nByc7R6jl1KFDxn5YIuDoCAMGGIsM6rV3tOKk0JIcpVQZ4F3gccAF\n2Ai8JCJX8nNzW9FJjqbl3Y3EG3y651M+3PGhZWfw4IrBjO8wnieDnywxLTelTUQETJsGX331d9fV\niBEwa5a9I9O0nCnMJOc9YBiwBEgA+gGbReTJ/NzcVnSSo2m5d+XWFWbvns2sXbMsi/g1r9qcNx54\ng+51u+sBxSVEZCS8+66xF9bbb8OoUfaOSNNypjCTnCiMWVVfpz1vBWwHXEUkNT8B2IJOcjQt56Ji\no/hwx4d8se8LbqfcBqCdXzveeOANHgp8qNRMBS/JY3KsOXcOvL3Bw8PekWhazhRmkpMEBIjI+XTn\nbgNBInI2PwHYgk5yNC17O8/t5P3f3mf1kdVI2ryBR2o/wqvtXqVjzY6lJrnRMkpNhR49jNWU+/YF\nNzd7R6RphsJMclKBKiJyOd25G0AjETmZnwBsQSc5mmadWcx8d/Q73v/tfbaf3Q6Ak8mJZxs9y6i2\no2hQqYGdI9TsbfVq6N3beFyhArz4IgwbBlWq2DcuTSvMJMeMMdg4Md3pR4AtwK07J0Ske36CySud\n5GhaRvFJ8Szev5iZO2dyLPYYAN6u3rzY4kVGthpJVc+qdo5QKyqSk2HZMpg5E8LDjXNOTjBpEowf\nb9/YtNKtMJOcL3JSmYgMzE8weaWTHE0zHIs5xuzfZ/PFvi+IS4wDwN/bn1favMKgpoPwcNYDMu4o\nbWNysiMC27bBRx8Zm4AuXgz9+tk7Kq00s8su5EWRTnK00swsZn46/hOf7P6EH4//aDnfvkZ7RrYa\nSa96vfQ0cC1XTpyA6tXB2Tnra0lJ1s9rmq0VyyRHKVUOmA90AS4D40TkKyvlngNeAuoA14GvgNdF\nxGylrE5ytFLnWsI1FuxbwOzfZ3M89jgAro6u9G3QlxGtRtC0alM7R6iVNDdvGntlPfywMXanVSvr\nW0pomi0U1yTnTkIzCGgGrAXaisiRTOX+BRwCdgEVge+B5SLyrpU6dZKjlQoiws5zO5kbPpdlh5ZZ\npoDXKFuDYS2GMaTZEHzK+Ng5Sq2kWrcOHnvM6NoCaNrUGKTcpw+4u9s3Nq3kKXZJTtrKyVeB+iIS\nlXZuIXBeRMZlc+0rQIiI9LDymk5ytBIt9nYsSw4sYe4fczl8+bDlfKeAToxoOYJudbsViy6pKVOm\nsGrVKg4cOJBt2dOnTxMQEMCePXto1qyZzWO515icgIAARo4cyagiunLeyJEjOXToEJs3by70e0dF\nwX//C/PnQ0yMce6ZZ4yVlTXNlmyR5BT2kqZBQPKdBCfNfiA4B9c+ABzOtpSmlRAiwrbT2+j/TX98\nP/Dl5fUvc/jyYSq5V+LV+18lckQkm57bRM96PfOV4AwcOBCTyYSDgwPOzs5UrlyZTp06MWfOHFJS\nUmz4jmDMmDFs2ZKzLe5q1KjBX3/9RZMmTWwawx0iUqwHHdtrXaPAQGMF5XPnjMHJ999v7I2laUVR\nYf/p5wHEZToXB3je6yKl1CCgOTC4gOLStCLjzPUzLDmwhEX7F3E05qjlfNfArrzQ7AW61+2Os4Nt\nR3526dKFJUuWkJKSwuXLl/nll1+YNGkSixcv5pdffsHNRivElSlThjJlyuSorFKKSpUq2eS+WlYp\nKSk4Oub9V4CrKzz7rHHcLVf86CMIDoZOncDBIc+30rQ8K+yWnHjAK9O5ssCNu12glHocmA48LCKx\ndys3efJkyxEWFmaLWDWt0NxIvMGCfQvotLATNT+qyfhfxnM05ihVPaoyvsN4Trx0gp+e/Ykn6j9h\n8wQHwMXFhYoVK1K1alUaNWrE//3f/xEWFkZ4eDjvvvv3MLjk5GRee+01/Pz8cHd3p3Xr1mzYsCFD\nXUePHqVHjx54e3vj6elJu3btOHzYaISdMmUKDRs2tJQ9dOgQDz74IGXLlsXT05OmTZtaWnpOnz6N\nyWQi/M7iLcDWrVtp06YNbm5uVKlShVGjRpGcnGx5PTQ0lOHDhzN+/HgqVqxI5cqVGTNmTJ6+Jzdu\n3KB///54enpStWpVPvjggwyvnz17lp49e+Ll5YWXlxe9e/fm/HnLovBZ3ivAwoUL8fT0zFJm2bJl\n1K5dGy8vL3r27Els7N8/6sxmM6NHj6Z8+fL4+PjwyiuvkJqacTedn376iQceeMBS5uGHHyYiIsLy\n+p3v5ddff03nzp1xd3dnzpw5lC1bltWrV2eoa+PGjTg7O3P58mVyylqj0uXLxs7nXbtCQABMnGjs\no6VpdxMWFpbhd7lN3GmyLYwDKIOxwWdgunOLgBl3Kf8wEA00z6Ze0bTiJiU1RTYc3yD9VvUTt2lu\nwmSEyYjrNFd5ZuUzsi5ynSSnJhd4HAMGDJBu3bpZfa179+7SsGFDy/O+fftK27Zt5ddff5WTJ0/K\n7NmzxcXFRQ4cOCAiIhcuXJAKFSpIz549Zc+ePRIVFSVff/217N+/X0REJk+enKG+hg0bSv/+/SUy\nMlKioqLk22+/lZ07d4qIyKlTp8RkMskff/whIiLnz58Xd3d3GTZsmERERMjatWulSpUqMnr0aEt9\nISEh4u3tLZMmTZJjx47JihUrxNHRUb7++uss7w2Qu/3s8Pf3l7Jly8pbb70lx44dk7lz54qzs7N8\n8803IiJiNpulSZMm0q5dOwkPD5c//vhD2rRpIy1btrTUkfm9iogsWLBAPD09M5Tx8PCQXr16yaFD\nh2Tnzp1Ss2ZNGTp0qKXMO++8I97e3rJy5Uo5evSojBw5Ury8vCQ0NNRSZtWqVbJ69WqJioqSgwcP\nytNPPy21a9eW5ORky/dSKSUBAQGyatUqOXXqlJw/f16GDh0qjz76aIYY+/TpI71797b6fcmNmBiR\nqVNFAgJEjLYe4+jSRcRsznf1WimQ9v8zf3lHfivI9Q3hS2BpWsLTHmMgcj0r5ToBV4D2OajTZt9U\nTStIqeZU2X5mu7y07iWp+n5VS2LDZKTD/A7yvz/+J9duXyvUmO6V5IwdO1bc3d1FROT48eNiMpnk\n7NmzGco8/vjjMnz4cBERGTdunPj7+0tKSorV+jL/4vfy8pJFixZZLXvnF/OdJGfcuHESFBSUocyC\nBQvE1dVVbt++LSJGknP//fdnKNOlSxd54YUXrN7jbvz9/aVr164Zzg0ZMkQ6dOggIiIbNmwQR0dH\nOXPmjOX1EydOiMlkkk2bNll9r3fizZzkuLm5yY0bNyznpk+fLnXq1LE89/X1lbfeesvy3Gw2S1BQ\nUIYkJ7P4+HhxcHCQ7du3i8jf38uZM2dmKLdnzx5xcnKSCxcuiIjI1atXxc3NTdatW3eP707upKaK\n/PKLyPPPi3h6igwebLOqtRLOFklOYXdXAQxPS3AuAUuAoSJyRCnlp5SKU0pVTyv3BkbX1jql1I20\n19baIV5NyxcR4ffzvzN6w2j8P/Kn3fx2fLz7Yy7GX6RWuVpM7jiZqJei2DpwK0OaDaGsa1l7h2wh\nIuSHXxwAABo2SURBVJYBrnv37kVEqF+/Pp6enpZj3bp1nDhxAoB9+/bRvn17HHI4AGPUqFEMHjyY\nzp07M2PGDI4ePXrXshEREbRp0ybDufbt25OUlMTx48ct5xo1apShjK+vL5cuXcpRPOm1bds2y/M/\n//zTEouvry9+fn6W1wMCAvD19bWUyamaNWvikW5r8PTxxsXFcfHixQzvWylF69atM9Rx4sQJ+vbt\nS+3atSlbtixVqlRBRDhz5kyGcs2bN8/yvEGDBixcuBCApUuXWrq7bMVkgtBQWLAAoqNhxgzr5TZv\nhhUrID7eZrfWtEIfeIyIXAV6Wjl/lnTjdUSkU2HGpWm2JCLs+2sfyw8vZ/mfyzlx9YTlNT8vP54K\nfoqng5+mhW+LIr37959//kmtWrUAY2yIyWRiz549WQas5nVg8qRJk3j22Wf58ccfWb9+PVOmTOG/\n//0vA3IxXSd9Igbg5OSU4XWlFGZzljVEC8ydWEwmU5bZW+nHD91hi3gfffRRatSowdy5c6lWrRqO\njo7Uq1ePpKSkDOXcrSxmM2TIED7++GPGjh3LF198wYABAwrsM+nmdvddzqdPh02bjAHNjzwCTzxh\nrMnjlXkUp6blQtFfWEPTiokUcwrbTm/j24hvWXN0Daevn7a8VtWjKk/Wf5KnGzxNm+ptMCl7NKLm\nzqFDh1i/fj0TJ04EoGnTpogIFy9epGPHjlavadq0KUuXLs3VzJ3AwEBGjBjBiBEjGDZsGPPmzbOa\n5NSrV48VK1ZkOLdt2zZcXFwIDAzM3Zsj+72rdu7cmeH5jh07qFevniWWCxcucObMGWrUqAEYrSkX\nLlwgONhYEaNixYpER0dnqGPv3r25itHLy4uqVauyc+dOQkJCLOd3796Nr68vALGxsRw9epTPPvvM\n8u8SHh6e4+n//fr149VXX2X27Nns3buXZcuW5SpGWxAxEppbt2DHDvjmm/9v787DqyrvBI5/fxAg\ngSwECAkgSAy7BiolgkBlUaf4UCpUKYqtYmfGKbSoNY57Z6Qu6Gjr0ilTt6otpa5TtXaswiNhsyiK\nirKWRYEkYCIBskDW3/zxnoSbm5vk3pDcJDe/z/Oc5957znvOefPy5ubHu5zXbV27wgcfwJgxYc+S\niRAW5BhzGorLinl7z9u8vvN13tz1JkdOnJoVkxKbwpwRc5h39jwmD5pM505tdw5taWkphw8fpqqq\niry8PFatWsXSpUvJyMggMzMTgKFDhzJ//nwWLFjAww8/zNixYzly5AhZWVmkpaUxe/ZsFi1axBNP\nPMHcuXO58847SUxMZNOmTYwaNapON9LJkye5+eabmTt3LoMHD+bQoUOsX7++TjdRtUWLFvHYY4+x\ncOFCbrjhBvbs2cPtt9/O4sWLiY6ODvlnri+4qbZx40YefPBBLrvsMlavXs3y5ctZsWIFABdddBHp\n6elcddVVPProo6gq119/PePGjasJRqZOncqRI0e4//77ueKKK1i9ejWvvvpqyPm84YYbeOCBBxg6\ndCjp6eksW7aM3NzcmiAnMTGRPn368NRTT3HGGWdw8OBBbrnlljotRPVJSEjg8ssvJzMzkylTpjQp\nYDxdInDjjW47eNAFOK++Cjt2uCnoxjTZ6Q7qaQsbNvDYhNGXR7/U3276rc5aMUuj742uNXh4xH+P\n0NtW3qYbD2zUyqrK1s5qUBYsWKCdOnXSTp06aZcuXTQpKUmnTZumy5Ytq5mdU62iokKXLFmiaWlp\n2q1bN+3Xr59eeumlunnz5po027Zt05kzZ2pcXJzGx8frpEmTdOvWrapaezBuWVmZzp8/X1NTUzU6\nOloHDBigP/7xj2sG4frPrlJVXbdunU6YMEGjo6M1JSVFMzMztaysrOb4tGnTdPHixXV+vvoGVtcn\nNTVVlyxZovPnz9fY2FhNSUnRhx56qFaaAwcO6Jw5czQ+Pl7j4+P1sssu0+zs7FppnnzySR08eLDG\nxsbqlVdeqY8//nidgceNDU6uqKjQm266SRMTEzUxMVGvv/56XbRoUa2Bx6tXr9b09HSNiYnR9PR0\nfeeddzQuLk6ff/75esvS19q1a1VEdPny5SGVU0srLg68/+BB1eHDVTMzVVevVvWpAiaC0AwDj20V\ncmMaUVpRyrr963jrH2/xtz1/Y1te7YGlE86YwOzhs7l0xKWM6DOilXJpTNO9+OKLLFy4kJycnCa1\nioXbU0/Bdded+tyzp1s09Ac/gJkzWy9fpnk1x7IO1l1ljB9VZW/BXt7e8zZv7X6Ld/e9S0l5Sc3x\nuK5xXHTWRcwYMoNZw2bRL65fK+bWNFVjY3I6ghMnTpCbm8vSpUu57rrr2kWAA3DttTB8OPzlL/Dm\nm65b64UXIDnZghxTm7XkGANkH89m9RereXffu7y7791ag4YBRiePZkbaDC4ZegkTB05skacOGxNu\nS5Ys4b777uOCCy7gtddeqzWVvT3ZvdsFOxMnwnnn1T3+xz9CdrZ7+vLo0W5au2n72t0q5C3FghwT\nqvySfLK+yKoJanzXiAJIjE5keup0LhlyCTOGzGBA/IBWyqkx5nRNmgTvvefeJybCt74FU6bA/PmQ\nktK6eTP1syDHY0GOaYiqsu/oPjbs38D6/evZcGADW/NqL2gf2zWWC868gOmDpzM9dTqjk0e36dlQ\nxpjgvfIKvPUWrFoFvs9H/OwzOOec1suXaZgFOR4Lcoyv8spyPjn0CRsOnApqDhUdqpUmOiqaSQMn\nMT11OtMGT2Nc/3F06RzclFsTGWxMTsf0xRewdi28/z78+td1u65UYc4cGDkSJkyA8eOttae1WJDj\nsSCn46oeJLwpZxObsjexKWcTH+V+VGugMECf7n2YNHCS2wZN4pv9vkm3qG6tlOv2RxUOHHAPatu4\nEW66CXxWNDAmYuzdC/6PCjrzTNfF9fvfB15x3bQMm11lOpzs49m1ApoPcz6k4GRBnXTDeg9j8sDJ\nTBrkApthvYe16eUT2pqyMvj4YzeO4Z133P96T56EqCj3Onq0m+FiTKRJToY33nDB/MaN7onLX34J\nffsGDnCOH4ddu1y3VzuZnNahWJBj2qTyynJ2fr2TLYe38OmhT9ny1RY+OfRJnW4ngOQeyWQMyCCj\nfwbj+o8jo38GST2SWiHX7ddXX7lWmjVr3LiFnTvdF3Zpqdt8BVj+yJiI0aMHzJrlNoDKSti2DQoL\nA6dft84tSREVBaNGwdixbps8Gc49N3z5NoFZkGNaXV5xHlsOb3EBzeFP+fTwp2zL20ZZZVmdtD2j\ne9YEMhn9M8gYkMGAuAHWShOCykr4/HPXSrNqFWzYAEePQrdu7ou8uue3rG7xRxQbk2OC0bkzpKfX\nf7y83AU3O3bAli1ue+45uPpq8BZ3r6WoCLp0cb9vpuXZmBwTFlVaxf5j+9mRv4PtedvZnr/dvc/f\nTn5JfsBzzko8izHJYxidPLrm9azEsyygOQ2qEBcHxcVuwGVTFudu6nlt0a23wgMPtHYuTCQoLnYB\nzubNbrv4YrjiirrpHnwQ7rwThg1zXVznnOPW5xo/Hs44I/z5bsts4LHHgpy24+jJo+w5soc9BXvY\nmb+zJpjZ+fXOOoOBq8V2jSW9b3pNMDMmZQzn9D2H+G7xYc595FN1XVLr18PKlfDRR6eOFRcHd43u\n3d3j87/znZbJYziNH+/GWhgTLpmZ8Mgjp1pMq/3yl25Av799+9xYoEGDOt5DDC3I8ViQEz6qSm5R\nbk0gU/26+8hu9hTsqbUKt7/kHsmMTBrJyD4jGdFnBCP7jGRk0kjrbmpFqm7QZHXX1bp1cOgQxMS4\nZvVALTY9eriptzbw2JimOXECtm+HrVtd1/HWrXDzzeAtYF/LD38Iy5e77q2hQ2HIEEhNdb9/DXWj\nRQKbXWWaXXllOdmF2ew/tr/O9uWxL9lXsI8TFSfqPT8mKoa0XmmkJaYxtNfQWkFNYkxiGH8SEwwR\ntwbQ8OGngpaCAjebau1a19rz2WfQtStUVLgv58rK1s1zc7ExOaa1xMScGqDcmNhY6NcPcnNdQPT5\n527/t78dOMh59FE3kSA11U19HzjQdYPFxTXvz9BeWEtOB1JcVkxuUS65hbnkFuWSU5hDTmFOrUAm\npzAHpeGy7B3TuyaQSUtMY0ivITWfU2JTrFUmwlRUnBqovHIlfPghvPiiWyfIGBMe1VPV9+51XVhX\nX+2CH39jx7rHP/hbv94tb+Fv0yY3k3LgQEhIaFvPAbLuKk9HDnIqqyr5+sTX5BXnkVeSVxPA5Bbm\nklOUUyugOV56vNHrdZJO9I/rz6CEQW6LH1TzfmDCQFJ7ppIQnRCGn8wYY0yoXn7ZTXnfu9c9wPPg\nQfe6fTsMHlw3/ahR7hi4FqaUFLetWBE4fXY29OwZnkdJWJDjiZQgR1UpKS+h4GQBecV55Jfkk1eS\nVxPA1Lx67/NL8jly4kijLS/VunbuSr/YfvSP60+/uH70j+1fO6BJGET/uP62vIExxkSQ6j+PgVpp\n5sxx098PHKg9+SA3N/ByFoMGubSxse54cjL07g3PPAN9+tRNv3s3xMdDr17uWUKhsCDH05aCnMqq\nSorKijh68igFJwsoOFFQ632t15PeMZ/95VXlId+zV0wvkronkdQjiZTYFPrHekFMXH/6xfareZ8Y\nnWhdScZ4bEyOMaeouudkHT7stvPPd88I8k8zfLhb5NT/IaHHjrlgxl+vXm6cH7jusN693bZypfvs\n74033AzOnj0hI6MdBjkikgj8DrgYyAPuUNU/1ZP2Z8AtQAzwCrBQVetEAU0NclSV8qpySspLarbi\nsmKKyoooLCvkeOlxCksLKSwrpLDU+1xW2OCx+qZJBys6Kpqe0T1J6p5En+59SOqR5AIYL4jxf+0V\n04uoTjZ+3BhjTHiouqCmOiD6+muYPbtuS1FVlXsOUF4eHDlSe7ZmeXndlh1VNz7o1INI22eQUx3Q\n/AgYC/wVOF9Vt/ul+zbwHDANyAVeA/6uqncEuKbet/a+WsFKsFulNu9UEUGI7RpLQnQCidGJJMYk\n0jO6p3vvfa6z32dfdJQtfmKMMSayVFW5J6vn57uWnfHj66apqIB581y6ggL4+ON2FuSISHegABil\nqnu8fc8D2f7Bi4j8Edinqnd5n6cBK1S1znhyEVHubmKmKgXKo6C8s7dFQVkl/zR1IvHd4onrGue2\nbnGnPndz++K7xTN98mIoPQPKoqC0i7uGCnAA1Y1BlssEINCSzsFd43TPB7juugfYtetknf3DhkXz\n5JO3he0akaI5/k169ryYoqLedfbHxn7N0aMrGz2/U6eJqA4IkLdsqqreCyoPzfFztJVrnG552u+I\nMeHVHp+TMwworw5wPJ8CUwKkPRvXeuObrq+IJKpqnWWnb598O927dA9pS+h+LVS9GuDWc3n76ZeD\n+4lyRgKB0s4N7nzAfXmfzjVO93zYteska9bcHeBIoH0td43Icfr/JkVFvamsfCHA/gDPig/ABTh1\n86AazrrZdq5RtzzF2z8vqPPtd8SY9ifcQU4s4D+P+TgQ6DFFscAxv3Tipa0T5Nx/4f2h56aqgz0j\nO2hZwNRWzkMkycLKszll0TzlWd2KHVzQGKmysrKYGuhRu6ZJrDzblnAHOUWA//jrBCDQIvb+aRNw\n30oBF7y/++67a95PnTrVKtlpycL+KDenLKw8m1MWVp7Nx/4oNy8rz6bLysoiKyurWa8Z7iBnFxAl\nImk+XVZjgK0B0m71jr3iff4GcDhQVxXUDnKMMcYY0774N1AsWbLktK8Z1v4aVS0B/hf4hYh0F5HJ\nwCzgDwGS/x74ZxEZ6U07vwt4Nny5NcZENqF6XI4xJjK19nNy8oFbVfVFERmIa70ZpaoHvbQ3ArcB\n0TTynJxw5d8YY4wx4dGuppAbY4wxxoSLTS8yxhhjTESyIMcYY4wxEcmCHGOMMcZEpHYR5IhIooj8\nWUSKRGSfiFzZQNqfiUiuiBwVkadFpEs489oeBFueInKNiFSIyHERKfReLwh3fts6EfmJiGwSkZMi\n8rtG0lr9bESw5Wn1s3Ei0tWrZ1+IyDER2SwiMxpIb/WzAaGUp9XP4IjIH7w6d0xE9ojInQ2kDbl+\ntosgB1gGnASSgB8A/yMiI/0TeYt63oJb1PNMIA04/Yn2kSeo8vS8p6rxqhrnva4NWy7bj2zgHuCZ\nhhJZ/QxaUOXpsfrZsChgP/AtVU0Afg68JCKD/BNa/QxK0OXpsfrZuKVAqleelwCLvbpYS1PrZ5sP\ncrxFPb8H3KWqJ1R1A/A68MMAya8GnlHVHap6DPgFcG34ctv2hVieJgiq+pqqvgEcaSSp1c8ghFCe\nphGqWqKqv1DVA97nvwL7gG8GSG71sxEhlqcJgqpuU9XqVWsFKAfyAiRtUv1s80EO9S/qeXaAtGd7\nx3zT9fWezWOcUMoT4FwR+UpEdojIXSLSHupMW2X1s/lZ/QyBiCQDQwn8lHmrnyFqpDzB6mdQROQ3\nIlIMfA7cp6qbAyRrUv1sDwXeXIt6GieU8lwDnKOqfYHLgCuBf2/Z7EU0q5/Ny+pnCEQkClgOPKeq\nuwIksfoZgiDK0+pnkFT1J7j6dxFwr4hkBEjWpPrZHoKcFlvUs4MKujxV9QtV/dJ7vxXXPHh5i+cw\ncln9bEZWP4MnIoL7g1wKLK4nmdXPIAVTnlY/Q6POGuBlXEDor0n1sz0EOTWLevrsa2xRz2oNLurZ\nQYVSnoHYYj9NZ/Wz5Vn9DOwZoA/wPVWtrCeN1c/gBVOegVj9bFwUUBJgf5PqZ5sPcmxRz+YVSnmK\nyAwR6eu9H4Erz9fCmd/2QEQ6i0g00BkXQHYTkc4Bklr9DEKw5Wn1Mzgi8ltgBPBdVS1rIKnVzyAE\nW55WPxsnIkkiMk9EeohIJ28G1VzcZBh/TaufqtrmNyAR+DOuueoLYJ63fyCuX+4Mn7Q3AoeAo8DT\nQJfWzn9b24ItT+AhrywLgd3AfwKdWzv/bW3zyqUKqPTZ/sMrz0Krny1TnlY/gyrLQV5ZlnjlVOj9\njl9p358tUp5WP0Mrzz5AFm4mZQHwATDLO9Ys9dMW6DTGGGNMRGrz3VXGGGOMMU1hQY4xxhhjIpIF\nOcYYY4yJSBbkGGOMMSYiWZBjjDHGmIhkQY4xxhhjIpIFOcYYY4yJSBbkGGOahYhcIyLNts6Rdz3/\nxWT902SKyL5G0pwpIlUiMrYJeYgXkUMiclao54Zwj64ickBExjSe2hgTCgtyjIkgIvKs9we9UkTK\nRGSPiDwkIt1DvMYbTcxCcz5d9AUgmOCi5p4N5L2p+boFWKWqe5t4fqPULQ3wK+D+lrqHMR2VBTnG\nRJ6VQAqQCtwJLAL+q1Vz1ASqWqqq+c10uZAXRhSRLsC/Ar9rpjw0ZAVwsYgMDsO9jOkwLMgxJvKU\nqmqeqmar6gvAcmB29UERGSUib4rIcRE5LCIrRCTZO/afwDXATJ8WoQu8Y0tFZIeIlIjIPhF5UES6\nBpsp7/y3fD7/i3eP7/vsWycid3jvF/h3f4nILSKS6+X9OSDW51i9efcMFpF3RKRYRLaKyEWNZPli\nIBpY7ZeH4SLyuogcFZFCEdkgImd7x54Vkb/45POoiNzvLT54j4h85e3P9L2mqh4GNgFXNFaOxpjg\nWZBjTOQrBboBiEg/YA2wBRgHXAj04NSqvw8DLwGrgGSgH/Ced6wIWIBbgXkhMA/XUhSsLGCiiFR/\n70wB8oCpXt5igAxOBRVK7a6o7wP3AD8HxgK7gJt8rt9Q3gHuBR4FRuMCij810o33LeBj9Vngzyu/\n9bhFQy8ExgCP41ZMr3YBMNj7+f4NuBX4G+77diJwN/BQgDE4H3jnGGOaSVRrZ8AY03JE5DxgPvCO\nt2sh8Imq3uGTZgHwtYiMU9UPReQE0F1V83yvpar3+XzcLyJLgUzc6srBWA9UBzLv4/6gPwz8yDs+\nCSjHBSCB3AA8q6pPe5/vF5FpQJqXv+JAeRep6an6lar+n7fvDuBq4BvUDoR8DQX2++37KS7Ym6uq\nld4+//E6R4GfeMHRLhG5GUhS1eqAcLeI3IYLkj71OW8/8N168mKMaQJryTEm8lzidaOcADbgWkau\n946NBaZ4xwu97qD9uBaTtIYuKiKXe91Jud55jwCDgs2UqhYDHwFTRSQNiAd+AwzyusumAH9X1Yp6\nLjES2Oi37+/B3h/4zCcvOd7bvg2kj8cFNL6+Aaz3CXAC2ebb+gMcBj73S3M4wL2PAwkNXNcYEyJr\nyTEm8qzBDZitAHL8/iB3At7EtcD4D8Y9XN8FRWQ88Cdcq83buNaKS4GHQsxbFjAdyAfWqWqJiLzv\n7ZsKvFX/qaetPMC+hv6jdwyfMT+ncR+tZ5//veNx5WqMaSYW5BgTeUpUtb5nx2wG5gL7G2iNKKP2\nGBNwXUkHVbVmmnMTZwJlAYuBAu89uKBsJm6M0K0NnLsdmAA857PvfL80gfLeVLsDXP9j4CoRiWqg\nxampzgT+0czXNKZDs+4qYzqW3+C6RF4SkfNEJFVELhKRJ0Skh5fmC+AcERkmIr1FJAo3yHeAiMz3\nzllI02YCrQe6AnM4NcA4C/g+ruXpgwbOfQy4xpuVNUREbgfO80sTKO9NtQ44V3wG9QDLcK07L4vI\nOBFJE5ErRGT0adyn2nnA2ma4jjHGY0GOMR2IqubiWmUqcV1DnwO/Bk7iZmEBPIVrNfkQ+AqYqKpv\n4rqmHsENlr0QN8sp1PtXj8spwrWKgBtnUwG811DriKq+hJuZdC+uReps4Jd+yerkvfr0QJdsJLsr\nceUy3ScPObjZU12Ad718/NTLfyhq3VtE+uJasl4I8TrGmAZI7fFxxhhjqonIPcBZqnpVC98nE5iu\nqjNb8j7GdDQW5BhjTD1EJAHYAUxqqaUdvAcq7gZmqeqnjaU3xgTPghxjjDHGRCQbk2OMMcaYiGRB\njjHGGGMikgU5xhhjjIlIFuQYY4wxJiJZkGOMMcaYiGRBjjHGGGMikgU5xhhjjIlI/w8OtsfgAxIZ\nawAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f8eef28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"X = iris[\"data\"][:, 3:] # petal width\n",
"y = (iris[\"target\"] == 2).astype(np.int) # 1 if Iris-Virginica, else 0\n",
"\n",
"log_reg = LogisticRegression()\n",
"log_reg.fit(X, y)\n",
"\n",
"X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
"y_proba = log_reg.predict_proba(X_new)\n",
"decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
"\n",
"plt.figure(figsize=(8, 3))\n",
"plt.plot(X[y==0], y[y==0], \"bs\")\n",
"plt.plot(X[y==1], y[y==1], \"g^\")\n",
"plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n",
"plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n",
"plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")\n",
"plt.text(decision_boundary+0.02, 0.15, \"Decision boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
"plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n",
"plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n",
"plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
"plt.ylabel(\"Probability\", fontsize=14)\n",
"plt.legend(loc=\"center left\", fontsize=14)\n",
"plt.axis([0, 3, -0.02, 1.02])\n",
"save_fig(\"logistic_regression_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.61561562])"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"decision_boundary"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 0])"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"log_reg.predict([[1.7], [1.5]])"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure logistic_regression_contour_plot\n"
]
},
{
"data": {
"image/png": 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goDC39BfuEepRj1nMIooomSBLL7X7Z5EBOZushftnkQE5m1zBuK5wxXuHd5n3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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114b74780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
"y = (iris[\"target\"] == 2).astype(np.int)\n",
"\n",
"log_reg = LogisticRegression(C=10**10)\n",
"log_reg.fit(X, y)\n",
"\n",
"x0, x1 = np.meshgrid(\n",
" np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
" np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
" )\n",
"X_new = np.c_[x0.ravel(), x1.ravel()]\n",
"\n",
"y_proba = log_reg.predict_proba(X_new)\n",
"\n",
"plt.figure(figsize=(10, 4))\n",
"plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
"plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
"\n",
"zz = y_proba[:, 1].reshape(x0.shape)\n",
"contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
"\n",
"\n",
"left_right = np.array([2.9, 7])\n",
"boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
"\n",
"plt.clabel(contour, inline=1, fontsize=12)\n",
"plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
"plt.text(3.5, 1.5, \"Not Iris-Virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
"plt.text(6.5, 2.3, \"Iris-Virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
"plt.xlabel(\"Petal length\", fontsize=14)\n",
"plt.ylabel(\"Petal width\", fontsize=14)\n",
"plt.axis([2.9, 7, 0.8, 2.7])\n",
"save_fig(\"logistic_regression_contour_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Saving figure softmax_regression_contour_plot\n"
]
},
{
"data": {
"image/png": 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SlgvfwH/TCnaP/S8lbTs6PR9daRE+6Sn4pv2Nb+oadG6FFF/ZhqODIynt2wrppnOoP2mT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\nM0TkJxH5UkTOj/S4mjoRedF/4udPIrJDRO6M9JiaC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"text/plain": [
"<matplotlib.figure.Figure at 0x1148abc88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
"y = iris[\"target\"]\n",
"\n",
"softmax_reg = LogisticRegression(multi_class=\"multinomial\", solver=\"lbfgs\", C=10)\n",
"softmax_reg.fit(X, y)\n",
"\n",
"x0, x1 = np.meshgrid(\n",
" np.linspace(0, 8, 500).reshape(-1, 1),\n",
" np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
" )\n",
"X_new = np.c_[x0.ravel(), x1.ravel()]\n",
"\n",
"\n",
"y_proba = softmax_reg.predict_proba(X_new)\n",
"y_predict = softmax_reg.predict(X_new)\n",
"\n",
"zz1 = y_proba[:, 1].reshape(x0.shape)\n",
"zz = y_predict.reshape(x0.shape)\n",
"\n",
"plt.figure(figsize=(10, 4))\n",
"plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
"plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolour\")\n",
"plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
"\n",
"from matplotlib.colors import ListedColormap\n",
"custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
"\n",
"plt.contourf(x0, x1, zz, cmap=custom_cmap, linewidth=5)\n",
"contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
"plt.clabel(contour, inline=1, fontsize=12)\n",
"plt.xlabel(\"Petal length\", fontsize=14)\n",
"plt.ylabel(\"Petal width\", fontsize=14)\n",
"plt.legend(loc=\"center left\", fontsize=14)\n",
"plt.axis([0, 7, 0, 3.5])\n",
"save_fig(\"softmax_regression_contour_plot\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([2])"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"softmax_reg.predict([[5, 2]])"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 6.33134078e-07, 5.75276067e-02, 9.42471760e-01]])"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"softmax_reg.predict_proba([[5, 2]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercise solutions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Coming soon**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"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": "3.5.2"
},
"nav_menu": {},
"toc": {
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
"threshold": 6,
"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 0
}