{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Machine Learning and Statistics for Physicists" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Material for a [UC Irvine](https://uci.edu/) course offered by the [Department of Physics and Astronomy](https://www.physics.uci.edu/).\n", "\n", "Content is maintained on [github](github.com/dkirkby/MachineLearningStatistics) and distributed under a [BSD3 license](https://opensource.org/licenses/BSD-3-Clause).\n", "\n", "[Table of contents](Contents.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from sklearn import preprocessing, pipeline, model_selection, linear_model" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import tensorflow as tf" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import edward as ed\n", "import edward.models" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "from mls import cv_summary, create_param_grid, estimate_log_evidence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Selection With Cross Validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that there are three main types of learning:\n", " - Learning model parameters from data.\n", " - Learning to predict new data (unsupervised learning).\n", " - Learning to predict target features in new data (supervised learning).\n", " \n", "All three types of learning require an assumed model with associated parameters, and predicting new data is only possible after learning model parameters from old data.\n", "\n", "Since all types of learning assume a model, they must all solve the meta-problem of comparing competing models. The Bayesian evidence $P(D\\mid M)$ is our primary quantitative tool for comparing how well different models explain the same data. When we are primarily interested in a model's ability to generalize and predict new data, **cross validation** is a useful alternative.\n", "\n", "The basic idea of cross validation is to:\n", " - split the observed data into separate training and test datasets,\n", " - learn the model from the training dataset,\n", " - measure the model's ability to predict the test dataset, and\n", " - repeat the steps above with different splits and combine the results.\n", "\n", "Comparing with the Bayesian evidence, cross validation:\n", " - is generally much easier to implement,\n", " - has less statistical power because the data must be split, and\n", " - does not account for priors on models or model parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Overfitting and Generalization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate some data consisting of 2D points along the path of a projectile, where $x$ is measured with negligible error and $y$ has a known error $\\sigma_y$:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "xlo, xhi = 0., 1.\n", "poly_coefs = np.array([-1., 2., -1.])\n", "f = lambda X: np.dot(poly_coefs, [X ** 0, X ** 1, X ** 2])\n", "sigma_y = 0.2" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def generate(N, seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " X = gen.uniform(xlo, xhi, size=N)\n", " y = f(X) + gen.normal(scale=sigma_y, size=N)\n", " return X, y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare results with different numbers of samples from the same model:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "Xa, ya = generate(N=15)\n", "Xb, yb = generate(N=150)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plotXy(X, y, ax=None, *fits):\n", " ax = ax or plt.gca()\n", " ax.scatter(X, y, s=25, lw=0)\n", " x_grid = np.linspace(xlo, xhi, 100)\n", " ax.plot(x_grid, f(np.array(x_grid)), '-', lw=10, alpha=0.2)\n", " for fit in fits:\n", " y_fit = fit.predict(x_grid.reshape(-1, 1))\n", " ax.plot(x_grid, y_fit, lw=2, alpha=1)\n", " ax.set_xlabel('$x$')\n", " ax.set_ylabel('$y$')\n", " ylo, yhi = np.percentile(y, (0, 100))\n", " dy = yhi - ylo\n", " ax.set_ylim(ylo - 0.1 * dy, yhi + 0.1 * dy)\n", " \n", "_, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n", "plotXy(Xa, ya, ax[0])\n", "plotXy(Xb, yb, ax[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The family of competing models we consider are polynomials of different degrees $P$,\n", "$$\n", "y(x) = \\sum_{k=0}^P\\, c_k x^k \\; ,\n", "$$\n", "each with $P+1$ parameters. The true model that the datasets were generated from have $P=2$.\n", "\n", "Use sklearn [LinearRegression](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html) to implement this fit after expanding the features with [PolynomialFeatures](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html),\n", "$$\n", "x \\; \\rightarrow\\; \\{ x^0, x^1, \\ldots, x^P \\} \\; ,\n", "$$\n", "and combining the preprocessing and regression steps into a [Pipeline](http://scikit-learn.org/stable/modules/generated/sklearn.pipeline.Pipeline.html):" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def poly_fit(X, y, degree):\n", " degree_is_zero = (degree == 0)\n", " model = pipeline.Pipeline([\n", " ('poly', preprocessing.PolynomialFeatures(degree=degree, include_bias=degree_is_zero)),\n", " ('linear', linear_model.LinearRegression(fit_intercept=not degree_is_zero))])\n", " return model.fit(X.reshape(-1, 1), y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare fits with $P = 0, 1, 2, 14$ to each dataset. Note that $P=14$ is an extreme case of overfitting to the smaller dataset, with the model passing exactly through each sample with large oscillations between them. Similarly, $P=1$ underfits the larger dataset:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtwAAAEFCAYAAADQcDATAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzsvXmYXGd95/s559S+V6+SurXLKsmrZEte5N0Yb8LAzYUAASaBwIRJnmSyPEnInczcZZIZAmEmM3eGOwmMB4ZAGCAQb9hgsI032ZJt2VosldaW1N3qvbr29Zz3/nGqqrfq6q7qqu6S9H6ep5/uOuv7nqp+63t+5/v+fooQAolEIpFIJBKJRNIc1JVugEQikUgkEolEcjkjBbdEIpFIJBKJRNJEpOCWSCQSiUQikUiaiBTcEolEIpFIJBJJE5GCWyKRSCQSiUQiaSKWlW5AsxkdjdechiUYdBGJpOo6nxCCC+/8WwDW7fw3dR2j2czXv9jwa0wO/hxv560Eex+o+bjZ1CDD4W9gc65m1bbP19W2ofA3yKUG6d76Wezu3qrbXnj3SwgjR+/1f4qq2YGlvXfzoRdSDBz+a1TNSe/1f7ykY5WvcddtBHveX9O+zehbrWTiZxg59fcAOP0hOjd9rGHHboX+LYV07BSjp7+Lw7uZri2fnLGu3r51dnqVRrXvUqGeMbvEpf4Zqobs26WJ7Nulx1L6VW3MlhHuClgs2ko3oaks2L+W+IpfuBGKYvZDCL28rCnvnTBKJ2zkQWveo9mfy8WkCBWla9EELuf/u8u5b63E5XydZd8uTWTfLj2a1S8puCUtRUn0KYsQt2XBbRSa26aiOFYu43+X1ORxBg5/hUy8r+p2029uJBKJRCKRLI7LV0FILlFKUdZFRJPVoiOq2SKwHOFu4L9Li9WbyibPY+gZsskL1TdsYoRbIpFIJJLLFSm4JS3G4gV3JUtJU2io4C71q8UUd7E5QlR/WjDTUtJifZBIJBKJpEWRglvSWpR8xLVYSposuEsiU2mEub0l/PGVMK/7gvYcaSmRSCQSiaRmpOCWtBgtGOEutamRlpIWZaFr2cxJkxKJRCKRXK5c/gpCsuwsxWggatlbLc4kbvakyVKEu6GWktaifN1lhFsikUgkkoYjBbekYTRESpYdJS0U4S5HdVtTLDeSmjzc0sItkUgkEsmiuOwL30guNa4MS0lNkfzlQFT3cI9Mpnns6WO0a2EeDC1nwyQSiUQiufSREW5Ji1GL4DbvF5dt0uRlbCkpT5qcJ8L92NPHOHFhEgXp4ZZIJBKJpFak4Ja0FjVkKZnycDc7wn0FWUrmiXCfHogCoCktFpmXSCQSieQSQApuSUsxVdWxdSwljYxwt6xkL1lK5rmWm3v8AKjqlOBuOVuMRCKRSCQtihTckhajBT3coglpAUWridXqHu7P7t3O1rUBLGqrtVsikUgkktZHTpqUNIEliLKyuF140ynB3dy0gA3NUrIYq8wKUHrH5ruWXQEnX/zkjUQGJoiPLFD+XSKRSCQSyQxkhFvSQBopJhfj4S7eLzbZwy1o5KTJVkVWmpRIJBKJpFnICLekxajFUmIK4GXLw91Qwd1i1gxRPUvJ1GYyS4lEIpFIWpNSCtvTA1E29/j57N7tdAWcK90sQEa4JS2GKAq/xRW+Waa0gDXcBCxMa1pKSiwc4ZaCWyKRSCStSSmFrW4ITlyY5LGnj8277chkmi99520+/+UX+NJ33mZkMt3UtknBLWkx6pk02WwPd+km4HL+d6mepaS8lbSUSCQSiaRFKaWwne/1dGoR543gclYQkkuSGqLJyjLl4b4SLCWl9iwQ4ZaWEolEIpG0KqUUtvO9nk4t4rwRSMEtaS1qKHyjqMuUh7s0abIh/y6taSkpXXYhCmVbT+UNp1/rVrtpkEgkEsmVTCmFraYqbF0b4LN7t8+7bS3ivBHISZOSFqMV83CXItwNFMstp1WnNUjooFQeGoQs7V4ThckIkZ8/R9JpxfXIhxc1N0EikUgk9VFKYbsYPrt3+5wJls1kxQR3KBRSga8BNwBZ4HPhcPjUtPV/AHy8+PIn4XD4/w6FQgrQD5wsLt8XDof/bBmbLWkyU5UmF2bZJk020sNd7lirKe5pFSRFAWW+oUF6uBdFPhIh8szTRF96EVEoEHM62fTgo2CRMQ6JRCJpBWoR541gJUf/DwOOcDh8WygUuhX4KvAhgFAotAn4JHALphJ4ORQK/RhIAW+Hw+FHV6jNkmZTDnAv3sMtmu3hLkd1L19LyfTKl8LQQZtvMxnhXojsxQH6/vqPEQXTD++5aRdbfv2TpKTYlkgkkiuWlfwGuAN4FiAcDr8eCoV2TVt3AXgoHA7rAKFQyApkgJuAnlAo9AKQBv4gHA6Hl7fZkuZSu6Wk6VHXJkyabLX49nSqZn2REe6K5MfHmHzpOdgAhfEJhK7j2bWb9g98EHvvWtydXlKj8ZVupkQikUhWiJUU3D5g+pRQPRQKWcLhcCEcDueBsaKF5CvAwXA4fCIUCq0C/n04HP5BKBS6A/h7YHe1kwSDLiyWecJ1Vejs9Na8D5gRQLPwtVL3MZaDSm3Tk3YmAZfTVlfbU7EYQ4DFotbd9/6iqaSjw4dmsVXd1mJ4GD8HNtvMa93o6y7SNiYAZ53XZQZZBxHA6bDWdaxmfabigxZSxb+DATsOd+XzTPRN3QjZbJaGt6eV/2cqkRkepv8HP2Lk+RdQemzYNqzG1hbk2v/8p7jWrZux7aXWt5Wi3jG7xOV8nWXfLk1k3y49mtGvlRTcMWB6j9RwOFwOrYVCIQfwGBAHfru4+E2gABAOh18JhUI9oVBICYfD8wYMI5HUfKvmpbPTy2id0aipDA+i7mM0m/n6l0xkAUilc3W1PZdKAlAoGEu+fmPjCVTVWnXbdDwHQCaTKZ9vKe/dfCQS6eJ59CUfOxHPAJDO1H6Nm9G3Eplsrvz3+HgUW8pRcbtcLjft70JD29PM/jWa3MgIE08/SWzfq2AYoCi4tm1HZxLrml6SziDJaX2pt2+X65dZNeoZs0tcSp+hWpF9uzSRfbv0WEq/qo3ZKym4XwUeBb5f9HAfLq0oRrYfB54Ph8N/NW2f/xMYB74cCoVuAM5XE9uSS4+pSZM15OFu+qTJYlrAhlhKWtTDPY2q1SavcA93bmjIFNpv7DOFtqriu+122vY+iu5KMHr6uyvdRIlEIpG0ICspuH8MvD8UCr2GqUI+EwqF/hA4hTll627AHgqFHi5u/2fAl4C/D4VCezEj3b+x7K2WLIKl3APVkRZwuQrfXAJiuW7EzCwl829mTH/RzBa1FNnBQSaefpL4/tfNfqsqvtvvpO2RD2Dr7gYgHTu1wFEkEolEcqWyYoI7HA4bwBdmLT4+7e/Kz7Rhb3NaJFk6DRCk5cI3izibujxpAcs3AY2sNNlyYnV6lhI5abJEdnCAiaeeIH5gv/meaRr+2++g7eEPYO3sXOnmSSQSieQSQeapkrQorVP4ZspS0oAbikug8MmiI9yXMdn+C4w/9QSJt96cEtp3mBFta3vHSjdPIpFILjlGJtNzCs10BZwr3axlQwpuSYuxeEvJcnm4m5EWsPWYFnGvYtFp/tOElSVz/hwTTz9pCm1AsVjw3XkXbQ/vxdrWvsKtk0gkkkuXx54+xokLkwCcuDDJY08fW9bCMyuNFNySlkFMs1ksJpq8bBHuYuEbpSGFb6aO2kqIRXq4L9dJk5lzfYw/+TjJdw4CptD233U3wYf2Ym1rW+HWSSQSycK0egT59EC06uvLHSm4JS1EbSJUUUuTJqsIxEYgGunhvgQsJVWu5+UW4c70nWX8iX8ieehdABSrFf/d99L20CNYAoEVbp1EIpEsnlaPIG/u8ZfbV3p9JSEFt6QFWZwoVZTlmTQproQsJVxZEe70mdNMPPk4ycOHAFBsNgL33EfwwYew+KXQlkgklx6tHkH+7N7tcyLwK8VKPA2QglvSeOp1S5QjyYsUtstkKYFG5uFuUcTispRc6pMm06dOMv7k46SOHgGKQvve9xF88GEsPt8Kt04ikUjqp9UjyF0BZ8tE3FfiaYAU3JIWooYJk0x5uJs/abIJaQFbzMM9neoR7kvTUpI6EWbiycdJHXsPAMXuIHDf+wg+8CAWrxTaEonk0qeVIsitzko8DZCCW9Iy1FRlkuXzcJfTAjbEUqIUj9mAQzWUeiLcLdeJOaSOH2P8ycdJh80U/6rTSeB99xO8/0E0j2eFWyeRSCSNo5UiyK3OSjwNkIJb0jrUaikpZw0RCGE00fLRjAh3q7Gwh9vMZNL6lhIhBOmS0D4RBopC+/4HCN7/AJrbvcItlEgkEslKshJPA6TglrQQtVpKFNPHLXRzMl+TBLFoSh7u1ooOT4+4i3nzcLe22BZCkHrvKONPPk7m1EkAVJeb4PsfIPC++9FcUmhLJBKJZGWeBkjBLWkhahPcYPq4hdARooDSrI+zaNykyYZUq2wKi4lwt6bgFkKQOnLYFNpnTgOgut0EH3iIwH33ozlbJw+tRCKRSK5MpOCWtA5lS8nid1EUDUExKqs1pVVMRXZbVSw3gkV4uFtswqQQguThdxl/4nGyfWcB0Dxegg8+RODe+1Adyyu0JxM5AI6cnWD/G2+3XNEJiUQikVTHyGbJDKdAdTX82FJwS5pAfXaJqfh2DRFu1QJ6c1MDlqowNtYj3lqWkum0eoRbCEHynYOMP/k42fPnANC8PlNo33MfqsOxIu362f7z3LseQLRk0QmJRFKd2bmZP3TnRh5/+WzLVm6UNAZhGKRPniC271USbx7AyGRY+2d/jnPzloaeRwpuSeNYsl2idksJy5EasCw0L+dKk60f4RaGQeLg20w89TjZCxcA0Px+2h58BP/d96Da7SvavovjSVg/9brVik5IJJLqzM7N/F/+8RDprF5+LW+ipxiZTPPV77/L8b6JS/ZmJDc0ROz1V4nte43C+Hh5uXf7NqydXQ0/nxTcktah5iwlU7m4q+aOXiKiZClpWf91A5gxa7K1ItzCMEi8/SbjTz5BbqAfAM0foO3hR/DfdQ+qzbYi7ZrN6vaZkzJbreiERCKpzuyb5JLYnm/9lUyrl5GfDz2RIH5gP7F9r5bn/ABY2trw3boH32176Lk+xOhovOHnloJb0kLUN2kSqmXWaADNsJS0XiLuMvNFuOfadprbB2EYJN48wPhTT5AbHADAEgwSfHgv/jvvQrW2htAu8cDN68gP7wcUtq4NyKITEsklxuzczE67NkN0y5voKVq9jPx0RKFA8vAh0zLy7jugm++pYnfgvWkXvj2349waQlGbm/pXCm5JC1GH4FbNj3BTy7tfAZYSMSNLyTzXcpki3MIwiB94g4mnniR3cRAwow9tD38A3x13olqty9KOxSCEQC8Y6LrAZVWJAtvWBti1eztCCKKRFAAB/6X1qFUiuRKZnZu5kodbYtLqZeSFEGT7zhLb9yqx/W9gJBLmCkXBdc21+PbcjmfHjctqRZSCW9IyTE1OrMXDrRb3beKkSUppAVtTLC+Vkck0g6MJOoqTsvP5XMXtmnpTAwhdJ7bvVcafepL88BAAlo4O2h75AP49d6BYGj9c6bpBOpUnk8qRTuVJp/Jk03kymQLZTJ5spkAuUyCX08nnzN+FvE4+Z6AXdHR96kals2OCm2+CwQuTHPinN2acx+O182u/dQua5XIuniSRXNpUys28/ZPBFWpNa/PZvdv59s9OzPBwtwL5iXHir+8j9tqr5IYulpfbNvTiumM7aq8Lq7sN76pbl/07XQpuSQtRu0VBWc5Jk42wlLSgZn/s6WPctUaHouCOJtKsrbRhkyLcolAg9sY+zj/7NJmLptC2dnbStvdRfLfuqVto5/M6iWiGeCxLIpYhEcuSjGdJJrIkEzlSiRyZdH7J7dc0Bc2iYrWZn0WLpuL12VHUqTe7d30bqtaCb75EIpHUQVfAyZd+545FeZ1nZ39p9ARLI5Mh/tabxPa9Sjp8vGzZ1Lw+vLfehnqDk1T6EBlOQxyIg2bz42nf0bA2LAYpuCUtSC0e7qKlZL7MGktkZDJN38UYqzzwvedPs/eengYNFK3j4T49EOXunoWzlMyOcC/Vhi4KBWKvvcrET54iPzYKgLWrm7a9H8B3y22LEtqZdJ5oJM3kRIpoJE0skiY6mSY+mSGdWlhMKwo4XFacLhtOlxWH04rDZcXhsGJzWLDZNSxWC1abisWmYbFoWKwqqkVF01QUTQEUEIJ88gypwXfp7PHxyK6dM87T2eklHk3jtGuX7ZMSiUQigbkCO1fQ6btoCvNGTbAUhkHq2HumL/vttxA588msYrHgvGEn7ptvw779arLx48QHnwAULM61qFY/udhhJvp/SlZdi2rxlJ+ul1BtFpKZPA6bhtZAX7cU3JLWYUlZSpoTfX3s6WPsWWX+I18YSTZgoGg9sTXbe2e3VlbSjbrGolAg+uorTPzkyXIqJmv3KjZ84qOwfQeKNrOCkRCCdDLHxFiSidEUkfEkkbEUkYkUmSqiWlUVvH4HHp8dt9f8cbptON1W7C4bdqcFi80cAnUhMAzzRzcEQsz0tQPoxZ+sboBe4Vpk8qhAQTeIpWbacrRohshkCqum0uF3Yrc1rUqTRCKRrCizM5jMZjETLHXDnBujF8fk0ticHewne+ANcm+/gYhNHUdZvxl1x27Ua3dQcLqIAoxfRBn/CQpg+O4l574ehEDJxlGyfSQuPoMIPjpHc2ixLJHJNKqi0OZz4HE2Zt6QFNySFqKOPNxqcy0lpwei3L66eAqhtPRM7Hr57N7tDLz3cvm1Y76xZYnX2Mjnib3yMhPPPEVhYgIA26rVtD36Qby7b6Gr28/QUJTJkQRjwwnGRhKMjyQYH03OK6wtVhV/0IUv6MDrd+D22XF6HTjdVmwOqymSdQNjVgRDABlDQGbplpJayOsGw5EUazrcWDTp55ZIJJcfC31PblrjI5vXKegGBV2g6wYFw/xdEtkzJvIn4hiH3sJ4Zz9isH/qQG0daDt2o+7YjdLWMfMkRhYl8hSKKCCc28F1nblcURD+98Hot1GyZxCZE+AMVWynIQRjUVN4uxxLl8srJrhDoZAKfA24AcgCnwuHw6emrf888FtAAfiLcDj8VCgU6gC+CziBQeAz4XA4teyNlzSF0j9YTZUmm5yHe3OPH1Ux22UIpWEzsWdHT1eSroATvc1JPl0aJCsL63oj3EY+R/Tll4g88zSFSAQA25oegnsfpbDxGgaHEoz8/BSRsRTDA9EZExFLWG0awQ4X/jYX3oATt9+B02fD6rDOEdMABpAptFYp+hKGEEzEs5dckQiJRNIYGulpbrY/uh42rfFxsn9+0Z3I5DnaN0Gbd/4MISKfR4SPoB/cjzh5DIzi94/DiXrtTlNkr980r0VPib+KokcQlg6E/76ZUWzNi/DdiRL9BUriDYQzxEQ8yxOvnKV/JMGGNX4euXVduX3jsQxOu3vJdsCVjHB/GHCEw+HbQqHQrcBXgQ8BhEKhVcDvAbsAB/BKKBR6Dvg3wHfD4fA3Q6HQFzEF+X9ckdZLGs+SLCXNEVfTo7+9XV4+dN/SZmLXcjOxYggdIcTcwaV0jRWt+Hf1mwYjlyP60otMPPMT9OgkedVGcu0OsqHdRAw3I6/Gyb/w1pz9PH4HwQ4XvjYX3qATl9+BzWWpONhVEtuXApls8wo1SSStzmyR+Mef3sWVZLJqZNGYWo/VSIFuGIJsXidfMIo/OsORNIkFnhxeHEvxxCtn+Y2Ht81YLoRAnD+LcXA/xpGDkEmbK1QVJXQN2s6bUULXoiyUGjY/AqnDCBRE4CFQKmzvvBoR/SVKYQKhp3jilfOcHzZTB54ZiM5on26Y/bNZl/YpXUnBfQfwLEA4HH49FArtmrbuZuDVcDicBbKhUOgUcH1xn39X3OaZ4t9VBXcw6MJiqf0idXZ6a94HzCigWXRaqfsYy0GltulJO5OAy2mrq+3peIIhQLOode2fSaa5CGiatuj9U6NOkhPgcVvK+zTyund2elHHPKTiUf7lJ3bh9i2t3GtEdzAG2G2WutrZrM/U6CmF6UNkR7sTVZs5SE0KO6OAqmoYuo5tnj7omQxDP/0Zp/7pZ4zlnESc24lv7iWuFCsx9uUB8wvC63fQsdpLW5cHf6ebtk4Ptnk9La1NPuEgFQGrRcMdcM9ZH5y1rK3dg6ZeAjdgy0y9Y3aJVh53l8rl0revfv/dGSLxb753kC/9zh01H2doPMnffO8gx/sm2Lahjd//+E5Wtc/931tpZr9vlYrG1Pve1nqs2df+2z87Ub72811PIQT5gkEur5PN6+Ty5t/R0rkVFdWqYrdaePypY1wcmzIeOGwamdzcgFj/SKI8JhbGRsnsf43M/n3oxQn0AJbedThv2YNj1y2oXt+irocQguS5l9ER2IK7cXaun3fbRKwHPXUOj22C/pHEvO0D8AfdS/Zyr6Tg9gHTPyl6KBSyhMPhQoV1ccA/a3lpWVUikdodJ52d3rrLek7NdhVNKQ3aCObrXzKRBSCVztXV9lw6CYBeMOraP58xP/C6vvhrl8maj5lisRSMxpf03s3brrwZjZyMpElll3bsVCwDQDabr7mdzehbiUJ+5oA4OhJBtcyMeqQmzfdXFAsA5XKFGe2JjUY5+dzr9IcvMmFpJ9P24Iz9VU0h2OnG3+Em0OnG3+nG4ZoawIIBN5HJJMlM5TzgLU8mgwrkCzqR4rUqUepbCU1VmXAsLCovF4FVC/WM2SWa+T+y0lxOfTveNzHndT19+8p33i6Lx6NnxvnKt99sufLild63SkVj6n1vFzrW7Ij2qf6ZkxinX/vZ1/Pf/Y/9fO4D28nljYo2yNnjGkDf4MwbgGxOZ123pxw9LrGxzcrYc8+ZvuxzZ6ZWeP2oO3aZEyC715AFsjow6zzzkg6jpi8gVCcZ201kquyXyXfg4hy/eOU1rJYtZPNTtsneLs+MvrkskE4sbcxeScEdA6a3TC2K7UrrvJghsdLy9LRlkpajvsf85ZuVWurelPNwN/MRfSPzcF8aEc1KnviSbUdRVAQgDMHZE2OcPzXChfAQ8awK2MG5AQCLBsHVPtq6PQS7PfjaXWhyoiAALrucry65cpktErdtaKvrOK1YXnwxdpnZFS2XUjRmoWPNtpzMLle/cY2PRDpPNqfPEePnhmJk87XZNXu7Zorrtd0efuPhbUzEszz58mmsfSfYnT3HurPn0PXi94zVhnr19aYve/MSSqwbeZSYaQEV3j2gOqpu/tIxhYe2wLpgjGzewG5VyReMsoe7hFVTsS7hqVuJlRz1XwUeBb5f9HAfnrZuP/CXoVDIAdiB7cCR4j6PAN8EHgZeRtJCNEZM1jdpsomVJsXlXWnSZFYWD2Pu9Sxd43weNAUG+yd548CR4loVzcgRFDHaN6+i/drN+NpcM4q/SEw0VSVYZbKQRHK5M1sk/v7Hd05NiquBViwvPlvg/s33DvJHv3rDjG0qVbSshZKoP9U/id2mkc0bbJnHjz37JiST09m0xkffxRi9XR4eumUdY1HTKz1bLPd2eeae3MhA5jRKfoRkLIGSnQTFAqobNC8fuXU1P3rDxfnhFL1dHj54+waMwQv43jnAJ959C5LF6LuioGzaakayr7kBxV5dHC8GJXkAxUggLF3gvGbB7Q+es/LAJljtTWDVdPIF+PNf3zUnct/uX3rbYGUF94+B94dCodcwldpnQqHQHwKnwuHwE6FQ6D9jCmoV+FfhcDgTCoX+AvhWMYPJGPBrK9V4STOoPS3gcgjuqXZdvtHZ2Y8LSxHuXLbAhbMRzp8eJ5c4wfatkE3ruFyAAH96mLbUIO0+CN69B+2qWy7zG5Ol4bBZ6PA7UOWNiOQKZrbg7Gx312WpaGSkuFHMFriz7TONYLqoL0WrK02YLOgGG1Z7OT0QKy9b2+XhUw9srXjcD96xsZypo7fLwwfv2GiuEAKyZ1FShyF7DqX41LfA3G9rH+/y6ztsCG0d+mkV41s/pjA8VWKdzm4zld8Nu4hobvN8h4+Uz1ctc0lVCpOQMCfhC/89i3oi3d3u52LcQ48/Qa8/jm7tnbHeoql0+B04bI2RyismuMPhsAF8Ydbi49PWfx34+qx9hoGHmt86yYog6sjDXRLcFSKyjWIqwt1Iwd1i2TXKl14FYXDy6CCnTg5w8fwkhmGuXLfWFOFq8TFgIDPMbmsM7cMPo2y66rIU2qqioCoKiqqgKuZTjtJvheLv4usCVtKYjx/dHvsM+1B3uwuXhYY8lpRIJCZLjRQ3g0bZZaoxn3XmVP8kiXSeTK5AJmfmuX741vWVRXQF2rz2OZlDyF4wU+zlhwDMzB+2dQj7ejz+bhIZm5m1Sk9CdgQldhTFmkQpnELpFeixHIW8F3VrMZVfz7ryd8UTzxwvR9TPDyd44pWzFUX/YkS4EnsJBR2c27E6e82xWp0an1UAxRzTwVz2qQdCnHrvOD0k2LEuw9XXhwh6HXQGnThUsFnVhn6vSSOhpIWoIy1gkwvfmMcuebgb8Y/XmqLU0M3rVyioWDSDd/f3MRn1gQKBDicduWF64kcBO7Z8GrChrupB/dynV7TdtaAqCpqmoqlK+Ued9ltVZv5daxQ6LUzBbdFU/J6ZXxBel41MMtvA3kgkkkbQ6DzWjbLLVGO2qC/R2+Up20NKlER0Kc/01350eHFCVk+iRJ9HyZ4GQKhOhHsXOLeD5gLA6nUj8nFE3ymMgwcwjr4DuSyK34p2UwBtmxfLdX60620I/3XgnJkxpFJmkCdeOTtDhD/1ah9f+NA1xbFanTFuj8cy/M9nj6Nl+/jETWcQig1/xz2gqhiGQBQM87cQlMo7lJSCooBfU9lx1XXkIn3cuC6H12VD1Q2cVo1cE6oBS8EtaSHqsZSYH2FpKamd8ZEE4aPDnD0xxs5rMnjcUCgoWDToWO1k7dZu2s4fxHLgl5DLou3wA3aUQAcQQ3E6WyZOryoKFk3Fopm/teLfmlp8rSqXZQReIpEsjUbmxIbG2WUqIYSZ9/oj92zmu8+d4NxQHJtVJVcwWLtA9Hq2kK2UB7t4Eki/Z0aMRRahWBHu3eDeAaptarPRYRIvvUP+jdcYanyWAAAgAElEQVQgGikvV9ZuMCPZ192IsGYg/hJK9hzK5DOIzFmE/x4U1YmmKqzr8tA/nMCKKUZ7gi4mhhOsAiwoaIA2lODNn58il9XJ53XyOfN3Ia+Tzeq0qzp37jkLwPHjPZx59mhN19Rmy/H+eyGb7OfJv92HECoWq8r/9qkb6eiu4GFfAlJwS1qGUpaSWoTR8k6avPQtJWOjCcJHTJEdj0xFQkqX3GKzA3k26WfQ//EHkDNT9ClXbUO9dTNwDOxOyMfmHrzJWFQVq0U1hbVFxaqVRLYqPdESiaQuFpPpZCWrORZ0g3S2QDqnk8kWMITAoin8s4cqlyOfj0rR5DkYGZTJ56ai2vYNZhl0zUwaJ1JJjMNvYxzcj+g/N1W7IdCGumM32o7dKB1d6AWDdCpPPukgn74Ha+E4fsebqJnj5GLnOXZyB2NjDjozBTqnB7ImMngrBLbOna7sg1eA7aHTeNxpYgkXJ86tIeCzo2mqaQMsPq1EmbL/Qcm9KhCGqTtSGTcuR5LVq/NEY15cHjs2u4xwSy5r6hChZQ93E9MCigamBSxF75dJbwshGJ9IceLoMH3hMaLjUzmOrXaN7nUBVm0I4rK+C3oaLZsFB4jj70Iuh7L1arR7H0JduwHib0ACmhnpV1CwWFRsFlNcWy0q1qLAVmWEWiKRNJjFZDqpFgVvhhjP5nRS2QLpbIGhSKouT/NsFsxAku1HmXzWzPKh2BC+e8G5DaEXEO+9i37wAOLEUdB1dEUj7e5ED+0k2bWJnMNHJpknvT9CKj5MJj270qQdt2snO68/jt+f4Lptr3P4vasYGOzG4bTidFlxOM0foSmEB6KMJ7IE/U7uurGH9qATm03DZrdgsWpYrSpWm8b3f/ocG9YNUTAUvntoK77eIL9bx9OJ8fNDJMcPcu+DPnzdtzUt570U3JIWpLU83KI4I7shZdmXQTMahiAaz3Dq2Chnw6OMX5waOCxWle51AVZvDNK+xoeqKohYFCYSYAcRS6A47Chr12F56AOoPVO5SJVG5iPHjFjbrGZ+U5tVZc0qLz57YyepSCQSSTUWk+mkWhR8thj/4n/bx9a1gRnCeyFRbghBJquTyuZJZ3X0oud7Ip7l608cLRdkqWoFWYCqGUgS+1ESr6MgENZVGP6H0AcjJA/+E4nTF0gJOymrn9Sq95N2tpGlaC2JAbEMkJlxLlVVcHtsuL1288djx+WxYXNfD+o+tNwxdlwX5vZ7PLT1PoiizpSiDy+iP3o+zt0bjoIBz5/cgC/QW3eWGrurh+T4QXLpobr2XyxScEtaB1HHpMnlSAtYblfjIruVqnYthYJukMzkOX96gjPHRxk6F8EozhJRVIWutX7WbArS2eNHs5j9ENEIhZd/gfHma9g+sRrFbgWbEzDQ7rgHXOtmnqR8jUuP2hbfB6umYrNq5o9FxW7V5thAbFZNim2J5AphugjdtqGNTz+wddlsGtNZTKaTalHwShaU2VHw2aL8vz1+BKumcnogyrpVXh69fSNBj23OcZ545eyM6ocwjxVkEVTMQKKnYPJZ1Nx5AMYmt9B3JEg8doi06kIo66F9bml0VVXw+Ox0dHlwuKx4/Y7yj8fnwOW2VbH5fZTE2NtM9D9Dcvwt8qlBOjZ+BIs9uOi+GHqW0bM/ACONw7uJ3/zYJ5f03VE6t55rbi1FKbglLUNJhLZa4ZvGWkoaR75gkMoWGB1JcObYCAOnx8kkpx7lBbs99GxuY9X6ANZplQ3FZAT9pecw3toHxewkis0GCJSuXsidn6dy5+Kug0VVsdk07FXEtURyJbOSnuBWYboIPXpmfMmTFZtJtSj4fBlDpgvx2aK8b9pTx76LcR5/+UzFqHUlcW0I+OYzx2u2lgghyKYLxCdSxCbSkD3Huq63sduyZHNW3j0cYnSsmMJQA4TAZSkQ7PTS1tNGoM2FP+jEH3Ti8dlRVbVu64Wn40ZsrlWMnv0hufRFLoa/TrDnAdxtNywonPVCmtHT3yGXGkSzemlf/6ElB2ostgAAhVxzK5VKwS1pIZbi4V4OS8nKC+58wSCVyRNL5rhwepz+k+MzLCNOj42ezW30bGnHNWswFpFx9F8+h3HwDVNoKwrqtTtR73kQlGfAiJsVw4Cp5EnTD1CKtExdBwUFm9UU1faiyLbI8u0SSVUanRnjUqQVy7LPR7UoeEmMzxbdpSi4rhtsWOXl9OD8E83ni1rP9l2XWMhaIoQgk8wTHU8SG08THU8RG0+RyxRQFIPQVX1s2tCPosD4hI9jb/Vii8XZoA/SsSbIqp3bWbXrWqyOuVH3RmFzrWF16POMn3+cdPQEE+ef4O13fsmRiZ185P27K96A5rMTjJ35PvnMCJotQPeWT6NZvUtui2bzAQp6PtbU+WBScEtah3osJSXvV8WIbINoYB7uqej94m8uTLtIgYwR5/TpMS6cGKP/1Dj5YoUxVVNYtT5I71XttK3yzLnbFxNj6L/8GcbB/WY+WEVBve5GtHsfROlabW40XLr21a6neR00TcMAbBaN7m6PnMwokdRIq4nNeiPuS4nUL2ay4nI/CajnfCUxPn3fTWt8fOx9WxieSBHN6jx821TxGatFnWMTqVhCnZm+a2PWV8Z0kZ7LFoiOJpkcSxEdSxIdM8X1bNqCCa6/+jhuTwphQOKtDI4D57hzSxrfg3vw3LQbzeVa5NVaOqrFScfGj/G/nn6SGzqPsKEtyvrgi/QdOYxr+x3Y3WtAgK6nSIy+SWryPUBgsXfQteVTWGy+hrRDUTQ0mw89F6WQjwGLt7fUghTckhai9Uq7CzF9lFs+YakbpshOpvOkswVGzk8yeDrC8LQvKG/QydqtHazZFJxhGSkhxkfRX/wZxrsHpoT2jt1odz+A0tk9e2vzV1lwF60mKDhsGg6bRi6tkk6Bw24nlQJVRYptiaQOFiM2l5N6I+5LidRPt2mUPNyNPH49LOV8nX4Hv/e/X0ciUyCdKSAQDIwn+cnTx+gbjNLb5eG3f+U6vvajw3P2nS9/9nTf9TenVWV0AOs9Dg690sfkSJJkbG5RLZvdQucqDx1tNjyx87jEAaybDRRVwYjmEW8V6N56K76/3IO1s3NRfWwGiqLwi/e8vKzdxP1X9XFDzwir3ONMnH+8wtYq7rbrCay5H83qbmg7LLYAei6Knp0E5vrWG3KOphxVckVT/4TApQjuxlbymmKqTc2e0GcIQSpTIJnJk8nqpFM5LpwwI9rZlOnNVjWFNZvaWBvqwN/uqtgmMTZiCu1Db5pCW1VRd95sCu2OruqNUKwAOKwQaHNhnzaRcXy8lCddWkYkkqWwmMwYy0m9EfelROqn2zTm8wIv95OA2cc/1T/Jl77zdtWIdyZXIJHOk8qYObKnU6nYzGybyLpuT1UvtmEIomMpdnV6CUQyaDkdCwrEcwzEzfzUqqbQ1umhe42X1b1+OjudqGePEXv9ebKDfVhuDqB4LAgB46csdG35IGv+cGG/9HJRugF98r2reO7ERu7dnuSurTH0fALdEETieY4N+xjKbuMTD96IZm38Uw6LLUCWcxSaOHFSCm5Jw1hq2rypaHINxykL7iZZSho+YXJu39JZM5KdKhY1mBxN0ndshKGzkbLLxu23s21HD8E1norRbAAxMmRaRw69ZdpzVBX1xltMod0+fwTDoqkIxby18LqdJFJgtwgctpnnKd/UKI0vCCCRXEksJjPGclJvxH1tt2fGBMC1Da7Mt9xPAmafz27TKka88wUzK1Qinaegzwr2CAF6DArjdFpPsW5jHrtFRwgFQyjsvrqHN08mOT9q4HAFuXf3zGiqoRtEx1KMD8WZGEowOZpEL5jnMGW5gsNlpXO1l1W9fnrXBehc5UVVFdInTxB//SeMvb0fZa0F7QY/1vYOACYiVh4PhzgXDbA1Z/DFna0htmHmDei61R3cffud5RubL33n7WnvSZZ0k55yTE2clIJbcgVRT6VJmjRpsjlVJkEYgkg8SzKdp2AYGIZgqC9C33sjRMeKxWkU6F7nZ922TtpXe2kLeohMJuccyxi+iPHiTzGOHJwmtG81hXZb+5ztFRQcdg2nzYLTbsFqUekfMgW3qlqL/a40abJoM5ERbonksqLeiPvskbrREm65nwTMPt+pChHvoYkUmdy0AI8QUIhA9ixK9izkR1CEWaH30WsqnCR3nrvXU3YtiOSrGEkf6ayXyKST0SEr0ZiLVMpB6Yq6/Q46V3tZvTbAug0Bgm3m082RyTT/64f78Jx4lx2Zs3jb8qgbXFg/1oXiML8bNYuXHx5cw6HBDkTxeK1STXP2Of/yn98655zL9ZRDk4JbcmVRh6WkOGmyeWkBS9GLpX+VGEKQzpntzOQLpJNZ8tkC50+Mcf7YKJmibcRq11h7VQfrtnXg9FR51Dg0iP7Cs4ij75gLNA31plvR7nw/SrBtxraaquKymwLbYdcqeK9LObuL17PCTG0Z4ZZILk/qjbjPzqBRKaPGUpivXY0Uh9WONTO6ak5uLIttIw2pYyipwyh6ZMYxhepiYNLJaEwjmbeSzVuwWmBXqAOnzUDPxilkYqgihs2aQWMSj30STzesLU6vMQwVQwlgd7Xh9HRgsQpULYuqRkkMpUifPcnQe++x15FGvduK0tmGYp0Khthca/B23owrcDXpQ4cQ1F9Ns1ks5pzL9ZTDYpeCW3IlIWr3fi/XpMmlRHWzeZ1EKk8yk8dI51ABvWBw/I0L9J8cLz8udPvtbLi6i57N7eXiNJUwLvajv/BTxHvvmgs0DXXXHrQ770cJTM2utlo0XHYLLocFu3VxIlkpR7grCe5ZEe5lKk8vkUhak5Wa/NlIcVjpWH/yiZ0k0nn23raeTK4wszpjYRIlcQDSx1GK6VOF6gT7BoR9I9h6QHPz2LNvljOLKIAPaLetYmwgRmLSC6wBQNN0bK4UnrYMV22AoC+FakxAIY7KBHp6gkT61NyGOyFwkxWwlhcNx11ctWUnTv827O6e8vJqTwpKNxyz0xouR+acxUSvl+spR9lSkpWCW3JFsJRKk63l4TaEIJnOE0/lyRWmbgZS8SweIDKc4NyxUQDaV3vZeE0XHT2+qnaa/Pk+8k/8GHH8iLnAYkXddRvaXfej+MzBwm7VcDmsuIpWkcX3sxThLgruSrlIy/YaGeGWSCQrN/lzMUJtsVHwShMlL4wkEAi8LutUrutCFCXxIoweN0ugA8K+HuG6Duwb5zz5W9fuIjGWIoCCD9BQ6Ds6AoBmUWlf7eXUZIq+uEE27oa4m61GoHzjYBQy5DJjZAZPcuLAfvyFcaxWgWJVEAIsbj+DuofD8QDDKQ8jcTdrurvYfdfcG49qTzAqiW1Ynpunajdsi7GbNBIzn7eKUUhg6PkFt68HKbglLYOow1JCkz3ctVpKcnmdeCmaXRSxQggmhhOcOTwMmQvcssvcds2mNjZe04WvvXreU6P/HPoLzzIRPmousFpRd9+Oduf7ULx+HDYziu2yW5ZQdKYUyS9ZdOaPcLdaxU2JRLIyNHPyZzXBvJjI+mKj4JvW+DjZPyW6e7s8MzNtGVmUxH5IHkTBwDDgZKSHjrV3EfBPpVcVQhAbTzNyYZKR/iid4xk6pxUJc/ntrFoXoKPHR9dqH163jWf+66tMn3JZEv/5SIT46/uI7XuV3OAAgeL6Iaufw77NhH2b+A//6gM4JtO8+PQxzkXmv+FZ6Maj0s3K1rWBZbl5qnbDttwWF0VRsdj8FHIRcpkI0IRMKA0/okSyxKyANU2aVJttKVl40qQQgmSmQDyVI5vXZywf7Y9x+tAQk6PmZMfuLvM4bd1u2q/bUPXcxoU+06N94j1zgc2GevMdaHfch7OtrQEie1ofir9VGeGWSCQtQDXBtZjI+kJR8HzBDI48fOt6si+fmWkbAfOpX/oYSvxlFCMNwLuDnbxwaj2TaQe8eQG7ZQB7wWCt00YAyKWnxs1SFHvD1k7cbQ68PgdupxW3w4LVYo6hW3oD5T5ajTx3Wcfp/w9fIXXsvfJTR83jJRzYxCv0MGRvB0Vh61pTgi/mhmch4Tr75mXr2sCyZdCp1v6VKA6l2QIUchGy6QmgZ8Hta0UKbknjWPK8wjoi3OUIgmhOLu6yr3yuqC3oBvGUmRpKN4xpuwiGzk1y+tAQ8QlzoLbaNdZv72Lj5gAkDqFq6rz3Jcb5M+jPP4s4ddxcYLOh3nInqz/0IXSrA5ejMSJ7BmLWpMmqHu6S4JYmbolE0hyqCa7FCM1KUXAhBOlsgXgqT7o4+THgsc0tkZ4fR4k9j5IbAEBY1/CNlzsZiHpRgAAQRCFQEFhQIV0gB9hdVvzdHsKRFGcn0/TmCtx9dRc+m4atwjyazzwc4qnv/pzgmUNsS57HoudJAYrFgvuGHfhuux33tdfhTeQ59PQxRuuw7iwkXFstJ3yJlZgfYLEHyCYgl46AQwpuyWVN7YJ7NJpBN1Q01eCv/+Et/vBTtzB7WDP0LCOnvo3TdxX+1XfX2KK5Ee5MrkAslS9XEytvawgu9kU4fWiIxGQGALvTwsZrulkb6sBi1SB7bt5zGX2n0Z9/BnHmhLnAZse652789z+ItyPImtX+isUhGsPsLCWV0gI2Oie5RCKRVGapgmu6kNy0xsdH793MwFhybt7s6YiCOSEycQAFA6E6Ed670K1bcXGMTWQJYPqxS6QRRIAogj/46LV869kw5yfNQMu54TjfevoYf/SrN8w4TXZwkPjrr5F8/TXunJgoL3ds3oLvtj14d9+C5p6qpNgVsNQddV7oOrZaTvgSK3EjYLGZ1yabnsDuaMLxG39IiaRORO2TJh97+hi/cpWCpsLZwQh/872DMwa3kck0P3nxJe5bP0g8PkrGsZvuYHXP9Mw2lUSmQiKdJ5bMzZgEaW5iCu1T714kGTVL7DrcVjZdt4reLfNlHJnyd4uzp9BfeAZxtjgT3e7Aedd9tD/wIK7g8pZ8VoqVJqkY4ZaWEolEsjwsVXB1BZz80cd2EE/liKfyCER1sZ0bRJl8rpziT3dcy2jsOgaPpxi5cJhAwaAUDEoiiBSFdqa4+4bVXrqDLvpHZqZGPN5nCmo9Hid24A1ir71Ktu9seb2lowPfrXvw3bYHW/eqmvpYjZJ3+1T/JE67RjZvsKWFItgLsRI3AhabmeUrl45gDy6wcT3Hb/whJZL6KEWLa6lYeXogir7F3F5TjfLgVuKxp4/hEeMA2LU8P/7Ffr7wkXsWfXy9GOkt6DAWTc9srzCL1Zx8Z4hk1Bx2nR4bm69fRc/mNtSKto9S3wTG6bBpHTl32lzjdOK99346HngQi6exFdsWZuEsJQI5aVIikSwPSxFcmVyBWDJHKruI7FVGFiX+CkrqMAAF4efswHWcOWGhkB8ob+bvcLFqQxBHh4ufHRxgaCSBzaKi5A229Pr5zQ9cjcthneHL1oTOPc4oA//lP5E8fAh0cwxVnU4s1+3k57lVvJH0sDkZ4LN2P1119dZk9uTIXEEvVwFNZ/Vl9WZfqkyPcHubcfwmHHNBQqGQE/h7oAuIA78eDodHZ23zFeAOzDb+XTgc/nooFGoDTgDFvGj8OBwO/6fla7mkudTuCd7c40c3TAGoqYJtG2YWfDk9EOXuTdnya2XaAFqNfMEglsyRiCVRoFyhC0yhPXIhysmDF4lHTBHudNvYfMMqera0o6rz3zCU8nqLgX4K33/JbJPLReD+B2i7/wE0Vw3R90ZSbNdEwvxCmIgl+Z/feXvmjHYZ4ZZIJC2KEIJU1hTa0yevV9kBMqdRYi+gGEmEUDh7fj3hE70YhgoY+NqcrNoYZPWGIC6vWYRMVRR+d2M7Hpe1Yn2Dzzyyjcf/4QX8pw9xTbIPWyFLEkBVcV93Pd7b9uDZcSNf/sERTkw0LgvH7MmRs1mOSYcrQSOLIGn2UoR7YoEt62OlItz/AjgcDof/r1Ao9HHgz4F/WVoZCoXuBbaEw+HbQqGQHTgaCoV+CNwI/EM4HP7dFWm1pLmU9fbiI9yf3budsfDzQI4tazz8i4/vhGkTGDf3+PE7MuXXV69OVT1eNqcTTWanRUaMYmtUhBCMX4xz4u3Bcvl1h8vK5htM60jliHaxa0IgTh7DOPQM2u0aIptGdbsJPvAQgfvuR3M2t4TuYvn+C318eCtYVGPOl8DcSZMSiURSG5UEUmdn/fFEQ4iy3a+qZWQ6hUmMieex6OcBiEx6OXR0K4mEG7fPzupNbazeGMTjnzLyOmwWPE4rLoelQqVeyI+NEtv3Gql9r3HPyHB5uXvjRly7b8F7y61Y/IHy8kZn4Vho/+UqSrTcNDJ9oGbxgKJRyCcx9ByqZmtkU1dMcN8BfLn49zPAv561fh9QrFeNADQgD9wE3BgKhX4JjAC/Fw6HL1Y7UTDowmKpXSDUOwAIYXABAGVJg0izqdQ2PWlnEnA5bXW1PZ1IcRHQtPr6rhbsjAMOx+LP39np5ciwm2wqxRd//SacHveM9X/86V288/K+8uuN7TE6OjxzUg8m03ki8QwZA+xOO3anGc0opO0kx0AIhYO/OMNwMV+rw2XlmpvXsuXa1VWrQgohyB05ROLZJymcO4va4wDW4FjVzdXf+AoWV21Cu1mfqQvFu53TgwkoCm4wB/HSOS8qpqnE53MzDlisWsPb08r/MwsRVZyMAjZb5etyKfdtOal3zC5xOV/ny6FvX/3+uzME0rd/doIvXdU1o29D40n+5nsHOd43wbYNbfz+x3eyqn3m2K4bgmgiSyKRRagaXu/CY2kuk2T8zAs4xGEsqkE+rxE+uZHh8XWsD3WzcVsnwa6p7wdNU/C6bPjctopZRgqpFOOv7WPkhV8SO3K0vNwaDNB515103XcP7g0bKrZl24Y2jp4Zn/F6Ke/v7ONtXRvAatVmXMPOWdewEaz0Z7LSjctS2jTibCObGsXnyeP0tC+1eTNouuAOhUK/CfzBrMXDQOkqxYEZt17hcDgDZEKhkBX4FqalJBEKhY4Db4XD4Z+HQqFPAv8v8JFq549Eqkc0K9HZ6a07G4Qop5ETTcwosTTm618yYVovUulcXW3PZ8xrretGXfsnY6Y9I5Mt1LS/UbSUTIzH6PF0z9hXA1YFCug5MKtIJbnYfw6ro72cPzuazJEvVH4EmZ6YxA1Ex9MM90ex2DQ2XdvN+u2dWKwasUS64n5CCMTxw2YJ9kHzFkzz+vDefTsZwqiBIJFkAZKL7+dSPpcLUfLPr+02H6mVBPfmnqnMKLpuRv3jiRwAhbze0PY0s3/LQbr4+c3l5l6Xevu20l9mK0E9Y3aJS/0zVI3LpW+z59mUXk/v21e+83ZZlB89M85Xvv1mOWpZSscaT+XKxcWqIYRgYihKZuQgXYH3cNnyoMDAxS4m0jvp2tbDttXeshVwMprCbtXwumy4LRZEvkB0csoLLnSd1LGjxF57jcTBtxB5syqhYrPh2Xkjvtv24Np+DYqmkQLcwNGTI3Oi+p9+YOuMZZ9+YGtd72+1yZEzrBVGfd/L1WiFz2SlLCxLaZOieYFRRocGcPprv0GpNmY3XXCHw+H/Dvz36ctCodCPoOxJ9wJzDEehUCgI/BB4MRwO//vi4ueB0mj8Y+D/aUabJSvD1M1KbQm9qxW/EcJAz8UAcPq2kI6dIJM4R9rwVn0EmUnlOfXORRKjZ9hzs9mmTdd1s+nabqz2+f9thGEgjh3GePFZjIumX1zz+Wh7aC/+u+8hlxskcypcU/+WheKl//TDV5M++yyqCqG1Pj4zbUa7mJUWUMg83BKJpEYWk+6vUtSyoBtEEzkS6fyixp5MMkf/qRGM+BHWrTlLZ5cZUIolAySVW+i8biurp0WtFRQ8Titel7ViNDt74QKxfa8Se2MfenSqfc7QNny37cFz0+55rYHz2R4aMYlx+rGvxMmRjU4f6PRvJZ8eRLMFFt64RlbKUvIq8AiwH3gYeHn6yuKkyl8AXw2Hw9+ZtuobwD8C3wfeB7y1LK2VLBOl8uI1Cm6lJLjnzkjX83FAoFrc2L2bSMdOEBk7jRHYUvFYhbzO2SPDnD06gl4waG8z2+Rrd+PfPn8ifGEYiPcOYfzyp1NCOxAwhfZdd6Pail6w3JKrAzUJs59dARf9mhVh5Pnjj18/08MmPdwSiWSJlATSqf5J7DaNUwNRvvhfX+HTD2ydt3T7um4vA6PJBYW2YQhG+6MMnenHbTnBut4hHF3mE7ls3ofhuQXPqqvxTPuOiaXyPPHKWfouxtjSG5gRGS5EJ4m/8Trjr7yCMdhf3kft6CJ4++34btuDtaNzwT43s2riSlRkbCUanT7Q23kzG7ffy9hYsmHHLLFSgvv/A74VCoVeAXLArwGEQqEvY0a1bwc2AZ8PhUKfL+7zGeCLwGOhUOi3gSTwueVuuKSZ1BfhpiQAK0S4C7locRMfk7kOc7Nc/5zthCHoPzXOyYODZIvlebvX+dl+gx9yh1A1reJQLwwDjr6D8eJP0YfN6QSWYBttDz+C7867UK3zTbpotejwVHsURUOQL97ATLV/MWXuJRKJpBolgfSlWbaR2aXbv/HUe5wZiNLb5WHvnvVVxXY6mWPw5CC5yRN0BIe44aoIqmpunxcB0o5d/OM7GhdGkvR2hfngHRvpaXfjddn43i8OcWbQfAp64sIk33ziMF/YZhB77TVSRw+XMzilVRvHPBs47NuMd8sWvvjoTYvuczOrJq5ERcblppGZSBZDs77jVkRwh8PhFPDRCsv/pPjnfuA/zrP7vc1ql2SFWYQfrxLlCPes6oiGIYjHxgAoKB6E1o6i2FH0OKIQA4sPgLHBGMcP9BOPmNlM/B0utu3upa3bY1aGnIDZpd2FrqO+ZwrtwvAQAJa2dtoe2Yvv9jtRrda6+rLyKChKqdrkrCcGpRsaGeGWSC5rlkPgzBeZzRd0FOChW9bxxCtn6R9J8MQrZ/ngHRtpK6bmAxB6lujFPtLjZ3BYhtjcGUPtLhUUU/W0fEMAACAASURBVNCtm1G8O9Bsvfzw2TDnh82CNOeHEzz7xnn+j0/dNHVeIVibGeHa+Gm2nTnH0EumLxtNw33d9Xx32M8JVw96cewbKQr0xdLMqomtWpodzM/R3z5+hLPFfOAbVnv5woeurfmz1MhMJCuJIuoUOZcKo6Pxmjr4tXcf4+j48SWd80+DHoQQfHmy8Y8kmsnNdiv3uuzsz+R4IZ2ref82VeHzfjfjusE3YrVPfLrBZuEht4N3s3meTWUX3qHIr7gdXGWz8KNEmpOz8q/e6rByt9POG5kcL6Zz5W2fTGY4FbWz6vx2fFGz3EDOlmJobZhY28VykH2TReOjXidn8gV+kMigGIJQX4abj6YIxs1zxdwq+69xc2yjA0OrHp1fa1H5Na+LC3md784z4XIl+NOgWWjnryIJfsvnIqCp/G00yaRRKkYEf1L8XH8nnuZTPhcDBZ2/j7dOH1aajRaNX532WZnOztXX8rnt/6zmY3Z2elvVg9Q0ah2zp9MKk7iaxXL2bXr0GWiKL3j2Obb0+vnnH7iaRMYUu9985jgXhuN4HTmCzgybVwnu3O7EyE2gZ0awqvEZRYmFgLyyGotvGziuAm2qpsFffOtNjGmfKk1V+Pqf3EtueIhn/u5HrB54j0BhqkKkfcNGfLftwXfzrWhe75Kux5X8mZx93aC+z9Lnv/wC+rQ3sPT+NYulvGfVxmxZaVLSctT6bVuS2FoFK4pPNSPTseI/60BB5yqbhS2pDpQjO1CEiq7mGV1zmvFVfQh15iTK0oAuBFx9Os3uoykCxeIwkx6VA9e4Ob7RgVGl2M1S+rYSlOLa0+PYpfj+IspJSCQrQiOCJZIiq8G5eurlBeB3nv9e085hA9BUfnxEpUNTCWoqH75OxX+DgjZdVSfNcUnTwDAUJhNOLuYEJ7QYfWTJipMQOTnnVPbd0/7OGVx1LsuLX/wOa8YKlOLBcZfK8Q0Ojm10EPEngefgwHNz2gpNuh6XI7OuG9R37Wy75i77neefqb9dC1BvgGQhZIS7AktNC3jhnX8LwLqd/6auYzSb+foXG36NycGf4+26lWDPAzUfN58Z4+Kxr2Gxt7Pm6t+pef/46JtE+n+Cp+Mm2tbuXfR+Y30/IhU5AoEH8a/eRWTakwVl4sco2XMYwUcRtk1E+g7Q4XyNgcEu3jm8jd6r2tl64xrszsoWECV1AiX6E4z+PLnHzfR+1q5u2vY+iu/W21C02uwVmcQ5Rk5+C7t7Ld1bP1PTvs2KlAhhcOGdvwAU1u3811w8/nfk00OsCn0em8scLQ09S/+hv0JRrXRt/hTDJ/8HNncvq7Z+tmHtuNQjQenYKUZPfxeHdzNdWz45Y90S0gLKCPcikYL70kEB1lk0Nlk11lo0ujW1YjEZgGRBIZ1ykE16SCadJFNORshy1jNMNDC6qCk/qi5YfzHH9rMZNg5ksRTjKjmLwqm1do5tdNDfbYUaJ+xLLk+WIrhlhFtyiVDbpEkhBPF0nlTW3M+oMGkS3RQ5saiFw/vDONVJOm4E5//P3ntGx5Ged76/quqckCMjwNCMQ3JmyGEazYw0msQZjrLHsr22Zcu+2mR5be+R79p7fc/1nqOjXXu9d32OvVeWrrxr6SqO5AkiJyem4TCHIZsECYIAiZw6p6q6HwrdaAANoLvRDTaA9/eFYHVVdb3V3W/966n/8zxO2PvcBipqsrdSV3QV86VTRK6+ibLfiR6LY25spObAc7h37c5baJc3E/WNJE/1cI+XBFxM4xYsJv7ltq8s+Ju2mZjPsaU83MWwA2SSiA7g7z9FcOgSkjZuO9SR0U21YK5BN9Wi6h5u3khy9UIAk2bMR0l0BoEvfm4z2zy2rPt3WE14nBZsFhO6rhPruIX/2FECJz9EDY6dO0nCsXETnr37cN3/AFusVj5T8Ihmpxy/k8WyDM02tmJ5uEvFdLkKpfrMhOAWlBG5Ce5Uw5qRQIykpiGlzCR6YvKKkDSSWz58o5dk0oSzyUi6qaqzoGcR2yY0zOdPEnrrMJGhIeS1ThSc2Fa30vi5ryLJc81eLsMISlpvG8eWtcxiuiRgxvgX+dMxgWCpkqokMtk7e61zhL6RSN6CKR7uZrT3CJGRK4Ax0wyFbVzuqaV9qAKTfTkvPL6RkD/KrUt93GkbQk1qmDARQacPnQHAbJaJSRKZ7UgkJBw2ExVj3SATQ0MMnTiG//gx4t130+tZmpvx7NmHe/dezFVVczg7C5/5KiVYX2nnz39z5+wr3iPmOxlTCG5B+ZAScDM81gtHEwwHJ3aG1GUHEiBp4wl8mqbTda2L1RVJEkkFVTOx5r5G1mxohNGzoE1MCrWgYTp/kuCbhwgPDxvLmpfhenwnYS5grq0rgtjOGGpZubknnveUqE5HtTP+liSF4bGOpDfv+vneqTMlL9EkEAjuDZNLzgF5iRI1GWHkzhuEhs4BoKOAfSPfeUeha9RF6ibfTYjTb92gr3Nc+MUsMmu2NvLL83eJJY05KpbQeOlIO7/19AYkJJx2ExVOK0oyTvCjE/QdP0r46pX0tURxu3Hv2o1n7z6sK1fl3eNhoTNdBHcplBLMhfmuYS4Et6BsSIlQKUsUOBpPMhyIEUtksY3IY5Fq1fBuD/eFuHziNlKij9V7IZF08PBnNuH02CA51lZYNwS3DQ357HECb76GOmpMQJblK6h57iCuHQ8QGr5I+PYFihWZLsfpfqr4H7uxyBDc4yUBZV451sETLYZMX8glmgQCwcx85cBGvvH3xycsy1WUhIYuMdR1GF0NoyODcxu68wFQXMi2qzAapApoRMKFRF/nKDowgE4vOpG4xkjXCIlJ3YC7+oJ4HBbcdhPx6z4Gjh8lePoUetyY0yWTCef2HXj27sO5aQuSaenKnOkiuOVcSnA+me8bj6X7TRSUIVOjvomkynAgRjg2tYtkGsV4wKglg5x88zptl4y62CtWGiLRXlGDnvL8SYalRNLjOM4cwf/mYVS/YTuxrlhJ9XPP49q+IyOanep+WazodjlKboP0jU66dXv2CHdXfxBaxrdbap3NBIKlQn2lnfUrKvMSJbqWpP/2L4kOj0W1LcvQKz4FpmoA1KTGQ80V1AxEMKnG/Gq2mli5oZYXz98l89ljV1+Q5fWudA1tgO2VKurrL9H54XGSY08jAWxr1uLZux/3gztRnJmmk6XLdBHcYndnXKjM942HENyCElCgXSLDS5xUNUaCMYKRxExbGJtJRoQ7NDRE26UeJFmiZXM969bpRj9SxZNe1yrJJAA9HmL4xR8by1a3UPPsQZzbtk995JhOFixy56ly8j/r2S0lE44xHe2WWV5n1OxOnaml+jhSIFgK5CNKouFh+tt/gh7vQUdBr3gU7FtAkkjEVW5f7efWx33Eo0lMgN1loWVzA1seXEEgFKWxxz9BXC+vd/H8w6288c4VXDcv8EC0g6q2PlIy21xbh3vPXjx79mGpr09vN9+dCcsVYR2Zmfm+8RCCW1A0BgOGt7d3KML//H4h3t5xn56/P5STzznkj3L9VB/3bwSzOUb9sgq8O5txVdqR/G3GXhUPNj2JfPoogTdfx/QbtUgmCVtrK9XPHsS5ddu03r5UlFeiSIK7LAPck86zNNVSkj4Pksyze1cT7z4KGNntS/VxpECwmJhOpE4nSjLXb2328IX9lVhGf46khdEVN3rVc2CuJxZJcOvjPm5f7SeZMOYRT7Wd1q0NNKyqQpYlTGYjUfvg/pZ0d8mVtXZeWBbBceif+Myli6AaTyxlux33zl149uzHtnZt1rl7sXQmnCvCOlJeCMEtKBo/e/cGz60F0POe5HRdJ5YwbCOxhIpun1lsa6rGzUu93DjfA6iwEWzWJJ/8/BZG/WPJk2MlAa3ttwm+8jO0kOHxNqt1IMOyP/ljFHP2soDjB5aKcBdLKZel4h5jLMLNVEtJZqS/ym2ltxtamz3sfWzpXcQEgoVErtHefEVq5vrhQBd6/+tIpgS6ZTl61QEiEYX2M510XhtAG7OOVDe6aN3aSG2zO6tQrnJZ+M3NNhT9EvFzp9GOhwgDyDLOrffh2bsf57btyBbLjGMudjLcQo2YC+tIeSEEt6Bo3O4NwNrx/+c6yUViRkJkPBofk3ozi9LhvhCXjnUQHDHaZy9bU4suWZGIgWYss6pxkqN30K0QfPc4eiiGbe06ap57nhH9TdSEH31yGcEspBtDFdtSUk5VSvRJ5RjT7TWzebiLfR4EAkEpyVVIT56vZysB2NZl7HNV1Shfvv9jrCYV3dpKyPQpbp7op6ttEH2spGD9igpatzZSVZ/dW60O9KO+/x76hVNoA/2kZmbripV49u7DvWs3porc7RDFtlKIiLmgGAjBLSgaKxvcE/4/2ySXSGoMB6JZEiKzC+5kQuXambt0XOkHwOG2snnPCmqbPdDnADWGEh3CdvQjgu++hfmFeiQUrPWrqP2Nz2L3bkCSJPxXPkBNGN0TZyUlNMs6Mj1XUjcVY/+kywJm3hSkxHfmeSijmwaBQJCVXKO9uZYAjCdUhgIxlte7SIR70mL75mAjgdGt3Gnzpe/hm1ZX0XpfA55q40niUCCWtoy0VJt5rsqP/coZBjpupPevVFTi2b0bz559WJevKGjMxbZSzHf5OMHiRAhuQdH4/KNriHe9C0gzens1TWc0FMcfik/0ac9Qh7v/jp/Lx24TCcWRJGjZ3MDa7U0oprGYuGQHhhn4f/6a5M1RMElIDgWQWfFv/3TC40tJNh5H6loOgpsSJU2WEePx7dQ5So1VRLgFgoVOrtHe2UoAqprGSCBOIGLUEfnM3irso29jNal09tVz5dw60IeRJGheU82arY24Kid2hHz5gxuY2q/zbOAG69o6MesqOiBbLDh33I9n734cGzfNuedBMa0UfSMRLGaZSGy8JK1IPhQUghDcgqJR47bRDTRU2/nG/uyTXTCSYDgQQ9W0LK9mKQsYS3LlozvcaRsEjGSbLftWpVuyK+EQykfvE1PaUNY40Ewqjo2bqTjwCMORw5isVVO8grJilAbMJcJdfKFZjpHyyZaSqY1vKJm1RiAQlJJco73TlQDUdZ1AJMFIIIaWmgfUIJWRV5DNcfoHqrh4bj0SEs1rq1lzX6PR82AMXdfRe+6gnT3Jcx+ewKVG06/dtjey84UDrH7iMYZDM5R+LTL5eLK/++qVCWLbblVE8uEiItt3oa7OPfuGBSAEt2BeiMVVhgLR7I1rpmAIv97OES4f6yQWSSDLEmu3N9GypQFZlpBCQZQP3yVy5F30eBzT/hoAmr/4LI6WpwiP+uAmmCyVU/c+Jrh1NT7ltank1m5+QTOpRKGUpUpJZllAgUCwcMgn2jtZnP/aE+vpHgwTz+jsGwmEkQZ+isMWYHjEzZnzm2heUzcmtK3p9fTAKNr502hnT6L3Gi3WXcCg2cMl9xouu1tobF3O4/vux+SwQyhQ1HHPRD6e7Mn2kXhCWxAJk4LcyPZd+Kuv18+yVWEIwS0oKaqmMeyPEYzOnqAojYnbpKpz6f1b3L1pdIWsrHOydd8q4/FkIIDy4TtEj76PnjAEs3Prfdh2rSUUO4dSYUyEyZhRqdVkrZ7yPvKYpUTLwVKiL4U63CmkiRHu6coCCgSCxUlKnCdVjZGAMW+npHY0nODGhW5qrB/Q3DhCOGKla2g/ew+uSke09Xgc7coFtHMfobddHZ/n7A4cD+5C2r6LFy9GuHHXP220fT4qguTjyc5myVmoVUsEU5lPf/6sgtvr9X7O5/O9WLIjECxKdF0nEE4wEsx4DDn7VgDcvjLA3Zs2ZEVi/f3NrN5YD0E/0muHiJ84QjxhiHfn9h3UPHsQ2+oWgoPnCN0+RyIewAok48YEabJOH+HOK2mySEJzOGjcJNzqDfC904XUKi8FE6P4KS939rKAEos62i8oCuK6sTDJNm/Ho0luXuql40ofras6aF7Vj6opaFXPs7m1GV3T0NqvEzl5Aj4+h1k15mddVlA2bMa1Zx91D96PYjED8I1tMx/DfFQEyaeKSTZLjqhasniYz+ZAuUS4f9fr9X4F+Jc+n+92yY5EsGjQdZ27g2ESyVzsIwaJuMpw5wiNVUY1kqp6J1v3r8KhR5AOv0j85FFIGh4/5477qXnueWwrV6W3V8xG98NEzHgsmY5wW6qmvFckbojnX7zn427cMovoTYnR4gjul46081QroOdfq7x05ND4Ri92i3vBIkdcNxYYsbjKgD+anreTCZVbH/fRfqmXZEKjvnYQ77pb6IBUcwB70ETyzVfRzn0EI0OYx/Zz11rLRU8r4TVb+aPf3odJyW/OKGXEMRWZbusawW5ViCU01s5SxSSbJUdULVk8zGdzoFkFt8/ne8br9X4JeMvr9X4H+C8+n2/+shsEC4ZURCSp6uh5iO2Bu34uHr3NquYIVEHtsgrWVNfCey+TOH08LbRdDzxIzbMHsa5YOWUfimlMcMfHBHc8ZSmZKrhPXRthRwOYleSsonc8abI4Ud3OviC0jrs3ymGiTovpVIR7xrKAQnALZkdcNxYOqqYxHIgRjBiRaU3V6Lw2QNv5HuJR4yNrXqWwbcN14/WRZpL//HP0ro7xnVRUcUxeziV3K0MWI0KoDCXzFttQ2ohjZmQ6ElNZv6KyoICHaJm+eJjP5kA5ebh9Pt+PvV7vIeA/Aae9Xu+/8vl8R0p7aIJ7R/7iMhCOMzwczmsbNanhO30nXVfb6jC+jpWD7ST+58tGK19Jwr1zF9XPHsS6bPm0+0pFuJOxALquo8bGLCVZkibvDiXZ0QBWk3FTMKPoLXKy4PL6/GqVzyuSKAsoKB7iulH+BCMJhvxRNF1H13W624e5dvYukYBhfausc7JuWw3V2s+RiZO8GSZ5aOwjtFiRN29H3rELafUaOl67zlDveOJjoXNbtohjsTzT2Zr7fPVb7+S9T9EyXVAIOQlur9e7BdgLeIBlwC+9Xu8Pga/7fL78VJaxPzvwT0A9EAB+0+fz9U9a5yWgBkgAEZ/P97TX610LfA/jGfgl4F/5fL5s9eUE80Q8oTLoH6s+ous5y9LRgRDnP7hFaDSGJMGa9RU0qacA0Dpvgabh3rWb6mefw9q8bNb9ySYHIJFMhFATo+h6EtnkSJcAzKTKbYjzlOCe6cKQrhNeJKH5/P4W4nc/QIIZa5XPL5MtJWMe7mxVSoTgFuRIsa8bguKRSKoM+mNE40YEe+CuH9/pO/gHIwA4K2ysW2Wm9s55lBvXMa23o40miL/Vzy17Ez3LN/PIrz6JZLEiIeFxWvj9z2zme7+8OmcRmi3i+M3vnymKZzpbcx9Vy9/eJ1qmCwohl6TJEaAbOAK8DfyfQAfwdeCnwDMFvO/XgIs+n+8vvF7vC8CfAX8waZ21wGafz5epBv4a+DOfz/eu1+v9e+B54OcFvL9gjmi6zkggRiCcmNi8BpipA6Gm6dy82EPbuW50HZwuE1u067gOfQC7K2FZJdaVq6j/3AtYmppzPh5JkpFNDrRkiFjoDpDdvw3wyAMtJHrPYTWps4veIltKqt1WeoAVDW6+8Ui5TNiTkiazeriFpUSQOyW6bgjmiKbrjAbHm44FhiNcPXWHgTt+AKw2hTXOERpuHkY+3YPkdWF6sB4tqXP0eDUfNj9E0ORABh61WHHYzFS7rWnrSKlEaLE805mRaVWbeJ0qB3ufYHGTS4R73eTo8xh/7fV6f7fA990PfGvs70PAn2e+6PV6G4BK4GWv11sJfNPn870CPAC8l7HdEwjBPe+Eo0mG/FGSU5rXzCxKw4EYFz64xXBfCICV5kFaLxxC0ZIgy1iWLUMjhGfXHiwNuYttMJJhBoMKVTY4evoMG2qy+7cBqtxu+npha4uLx5+Y5QJRsoYvZVQWMH0okywlmRFuURZQkB+luG4I5kAkZszbCVUjGo5z/Ww3XW2DoINJ1lmV7GDFx0eM+RiQmisxP1YD6LzfuZl3peq0YmiscdBQ5cBunZ/KwsXyTGdGpjOj5nPZp0CQK7kkTWabNFN8drbtvV7v7wB/OGlxL5C6nQwAk7/pFuCvgP8GVANHvV7vSUDKiHhn224KVVUOTCZlttWmUGinIV3X6ARAKlm3omKQ7djUoJURwGG3ZH09qWoMjERIIOH2TPW6qfEYwX5QZBl3pTO9XNd1bl3t46N3bpCMq1ilBJvuvEN1+C6SolD3+CdZ/oXPMzB6kr7bH+By2/I+d3/14/PsqJKpsoHbZHxlPZUNWfcTtlbR1waylJz1fUJ9CkHA7XYU5fMM+/30ACZFLmh/pfhOxcIJ7gLK2DGpITuj3WC3m8bfL2ZhCLDbrVRVOekFTKbCxjAT5fybmY1RyU4/YLEoWcexkMeWL3O5bhQ6Z6dYzOe5kLGpms7gSIS4rmKzWWg/3cXHp7pQkxoSOssC12jpP4NFi4HJhHX7TmwP7SJhO4kWH8RcsZWbo81AKL1Pp83MyuXZAxqFMtPY/uQ3HuRvfniWq7eG2LC6mq+/sIO6Gue06+dCKfY5HeI7ufAoxbjmdHvq8/l8OazzHeA7mcu8Xu+LQGo0bmBk0mY9wN+PZbX3eb3es4CXzCyu7NtNId9EPjBOdH9/YV2vxis76AXvo9RMN75QyKhLHY7Ep7weCMcZDsxSUzsZQWYs633EmJwTsSSXT3TS3W5UDakL3mJj33HMJKn4xCNUP/0s5ro6gkA4Yrx/MBhDzvPcXb01xDqH0dCm0W28d1x1ZB1nYizzPhGLzPoZRdPHFIcifJ7xsPF9TCa1vL8fc/lezkSqlKKqGd/ZUMioVhAOx9LvF/Abxx2NqQwPG+c3mVCLejylGt98EfEb/td4fOp5KXRsi/FiNtt1o5A5O0XmeV5szUkK+Q6FogmG/DGSqsqdG0Nc+6iTWMy4jNYFO1g7eBpHwo+0qhV5xy7kzdvRbXaio68jRQbRlSpitofp6rswYb837/rn9bevAH/0pYwC3lr+8+d87DMbC31em4nFOra5jGumOftedZo8iuHhOwk8DXww6fXHgX8NHPB6vS5gC3AFOOv1eh/1+Xzvjm33zrwd8RIlkdQY9EfTyTX5MNwb5Nw7bUSjGoqWYH3/hzSF26l8+BNUP3MAc03tNFvm75des6yCYMwQ3Ips3BRM5+FOJVLm1Wmy6M1eyshSMsbUsoDZWrtLGdVMBILypRybk8zXTUBS1RjyRwnHkgzd6uPK8Q78MeOpgTs6wLqBj6iyJ1Ee3oe8fSdSdcZcHL6MFLmCjgm96gBmi53W5graMjzOwn4hEOTPvRLcfwf8o9frPQLEgS8DeL3ebwE/9fl8h7xe75Ner/cERlT7f/f5fANer/ePgG97vV4LhgD/6T06/kWPruv4Q3FGgvEsSZGzc/2Ij7a2ICDhjg6wpf8oTXt3UP301zBX10z3pkBh0vYrBzZy9PjNCcum83CnOk3qajyHPRe54Us5itUpTy2ylAUUHm7BAqMcm5PMx01AMJJgcDBA8PwFfJcG6dVrAAVrMsQa/0WaW2tQnv5VpJUtU5PBE/1Io28bf1d8kqrq5XgcZn73uU2iDJ5AMEfuieAeKwn1xSzL/33G31/P8vo14JHSHp1A1XS6B8PE82hek0k0EKGtLQRIrBq9zPYtFdT9wX/EXJWj568AUVpfaeeJ3RsYvPXx2D5kFHP2RzuSZAIkdD2JrqlI8gx+0SVRDi+VGJqKcGcrC1iq5FGBoDQUuzlJMaLTpbwJSCRV+i58TPDDE7R3xuhwbUCTa5C1JFXRLtY+sIKq+7+KZDZn34EWQxp+FQkVxbWVhlW70tVHci2Dt9hsPAJBMblXEW5BGZKKZIciCXRzfmJb6+qg//gHNO0HDRlLMsIDTUG2/G+/hqlyavOZUpDqNglGw5vporGSJCErVjQ1iqbFUGTHtPtMN3xZApaS9LOFdFnA8WPM1vimHEcgEKQodnOSYkSnZ7sJmEmw9gyG+M/fPzPlte4btznxg1dounuFhKWattqdRD3GXKjHR7kqmxl1rGTlkIvfmk5s6zrS6BtI6giKtR5Tzaf4Lz88l7dwLkcbj0BQLgjBLQAgllDxjyXL5YPW2U7irde4PuJksKmVJgZQJJ0v/M6DVDTV5bm3uUm4VLdJmN6/nUKSraBGDVuJaXrBnbZVFC2yW4aWkinnPYuHO6O1ezmOQCCYTLGbkxQjOj3bTcBMgvVvfng2/VrHrT7e/vYl9qqdRNuus8pSybW6vQw7mgBwu02cCsTxW8af8nX1Bac9Lin4EVK0DUm2Ut/6Rf7qZ20FCedytPEIBOWCENxLHF3XGQnGudXj54avl13L4FL7IE2tMardU7s0ptA6bqK+fYhwxx0uNT6Cv7IOJ0Z1AWeFowCxnUlhkm5ChHsa/3YKWbGiJmZPnExXnSlH73WRmDzG8Sh2lsY3i/g8CBYfuq4R7P8Im2cNZtt0Sdq5MTk6bTHL9I1E8rJMzHYTMJNgvdY+wJrQHbYEbrAu1IlJ1wjKZtpqH+JOxQaQJBK6zl1J5/c/u5W213z4e8dF9vJ6F9kwJztQg8cAqF39Ocy2Gm7cmViVJFfhXGwbj0CwmBCGzCVMLKFydzDMaCjGPx9pZyRoiE9/KMFLR9qzbqO1t5H47t+S/Pbf0NsT4eTKg/htdThdZj79mc3AvYvhSooVSTbuIU2WmW0skmJUNNHVWSqVpC0lxf2pFJKIWmqkKZaSqVVKRNKkYCERGrrI8J3XGGj/WUbJ1sL4yoGN2K3j+R6RmMp3X70y10OcwGSBuqbZQ/R2B30//AH/uuNnfLH7bTYGO5B1jav1D3J8/Ze5U7kRXYJedC5KOrYGF5IscXB/CysbXMgSrGxwcXB/y4R9S0hUWIJog78EoKLpMewV67IfR47C+SsHNrJ+RSWKLM3exVcgWGKICPcSRNd1hgOxdHtfMB43Ll81vk7m40dd19Hbr6O+fRj9VhsaMm0Ne+h0ewFYtbaGTz279HYDogAAIABJREFUAVkK0D00pyOby8ZIkoTZ4iYeHZ49wi2PlQacTXAX2VJSfC94Mcje2j17WcDM81B+Nw0CQSbhkcsAJKK9xIK3sLkN0VlIcl99pZ14YmJ33WJbJlKWk56Obh6W7rLtaju3370LgBXwO6o449xArHo9JlWCJLiq7XSg0zUcZnn9uLCudlv5rac3ZH0fu9VEpS3OwI0fo2sx7JUb8TTsn3Ic+frfi23jEQgWE0JwLzHiCZXO3gCjoYlCc/LjxuX1LkNo37iG+s5h9I4bAESdNVxa9SSjcQuSLLHnsVbue3A5kiSRmL2s9cxMaTGePzZnPfHoMGZ7w4zrjdfinrk0YCoqVvTIbjlp1bzLApbjTYNAMBEtGSEaGC8V6u87kRbchSb3ldIyocVi2K6e5df7jhFuvwy68auTXS7cux7CsnMfN65G0T7uw6SCxWbC+8Aylq2t5uEcrV6yJFHtseEwq/Re/yFqwo/FuZyaVZ+ZUCJQCGeBoPgIwb1EyKyrXVk5NUnw4P4WbvoMG4nHYeazzjjJb/8N+u0xa4ndwfCOJ7g4UkMiruJyW/n0ZzbRWFSPXspLXPgeWrb+Kr3ddzBbq2dcT5Lzs5QUTWSWtVYVZQEFi4fwqA90DbO9iUS0j6j/Oono4JhHubDkvlwjv7lG0HVNI3LNh//YUQKnT6HHogBIJhPObdvx7N4Lazfw8ZUBrrzWRThoBAhWemtZf38zZmvul3CnzUy1x4qkJ+m/8UMS0T5MtlrqWn8VWZ6mekkBiNKAAkF2hOBeAiSSGgOjEWKJ6Uv9VbutVG+og4CPjf6bJF9/25C/dgfy3k9y07WBG5cHAJWVrdV86rmN2OzZJ+lC/cnjWxWuSk0WJ5axTP2ZyLXbZOkavpRViNv4R8qvLKBAUM6ER4ya/K7aHcTD3YQGzxLo/5DqFc8UHKnONfI7WwQ93tPNyIfvEuo9j5aIgCIhb7Jilppxb9qL58HdSA4nnXdH+eifr9Lf5QfAU+Ngy54VVNQ6cz4PiixT47HisJlRkxH6bvyAePgOitlN/ZpfQzEVVwyL0oClRdzQLFyE4F7k+MNxhv2xGUWwruvovkvQ+R7yFgWCfnC6UPZ/kuS23Zw90cPA5QEkCXY+3ML9e1ZO7VBG8fzJ8xEEHk+anKXbZNEb35RjiHvid0OapSygQFDuaMnomJ1EwlGxEatzJaHBs4SGzlPR9FjRa3RPJlsEXQ0G8Z88TuD6cdS6EPIqB8pKBwoTnzgGpJPEuvu43b2McydBTeqYzDLb97dQu8KDJOc+h7hsZqo9NmRZQk0E6Gv7PoloH4qlkvq1v47JUlF0ASdKA5YWcUOzcBGCe5GSVDUG/VEiseS06+i6jn7louHR7u5C2VEB1CC1rMX8+Bfx+5Ocfb2dSDCOzW7m089vZPnqma0ac2P+or45J03qExMKFyNTniykb6amlgUUEW7BQiBlJ7G6VqOYnShmJzZ3K9HATcJDF6ivf6ikIiUVQVd0lTWhO+xO3ubGH/8Tpr2VmHZVoOAEDSzKcs71WhgYTWA3J1hdPUqdK0I82Eaju41P7LExGFxDzdo9NC1rYHgklNP7G1FtGw6bcYmPBtoZ7PgFaiKAyVZL/Zpfx2TxAMUXcKI0YGkRNzQLFyG4FyHhaIKB0SjaNGWwdE1Du3zeENo9d4yFLg+ydwvQjbxsFZ23glw+cRtN06lvdvPkZzbj8tjmaQSlF7c5J00uBUtJOjF09rKAwsMtWAik7CSOqk3pZY6qrUQDN4kG2nHXP1Sy99Z1nX+xxcb5a2dp7r6GXYuBWcL8VAPKKgfoEp76h3E37EQxO/nZt95B1XRkYBkSKy1xli/rY/XKbhyOKA7HZfTAdaJ9D4KyERT3jO+fGdXWtSQj3e8Q6DsOgNW5gtrWX0HJaPZVbAGXz9MDYY/IH3FDs3ARgnsRoek6Q/4owUj2jpGG0D7H0PtvkOweE9puD8onPo384B6k2AUIdDNw18/FEx0AbN7RzL5PrUUxlVZo9Y1EuNw2wJoqOPThbR7ZV9qJVxqLcM+eNFnsZMFyjJRPspRkKQuoFzt5VCAoEZqWIBq4QcpOksLmMuqeRkMd6LpW9JvoxEA//hPH8R8/RqK3hzVjyy2rVmB6sgLNHEZW7NS1/gpW18r0dmuWVdDbOcIqJKxIxOJWdMcDKMsa0LROpNBppPgdYoPHkDgO1hZ0xxawrgBpPI8mM6qtJSOM9p0m0P8hWjIESFQ0PYKnYf+UcRdbwOVT4UTYI/Kn1HYoQekQgnuREIur9I9GSKralNd0TUO7dBbt3dfQ+3qMhZ5KlE88jvzAHiSzMWknAyoWwD8UQVEkPvHkejbcN3sCYjH47qtX2OiJQRX0DIVLPvHKYx7unJMml5R3OTXWTCGerTxiGUXpBYIxtEQIdA3FXIFiHk8uNFkrUSyVqPEREpHenJKrZ0ONRAiePoX/2BEi13zp5UpFBZ5du3Ht3kNIP0t4+CImSxV1a39tQgWlYDDKOlmmYuw3lzDJ7HhkNStWpBp3taLbWtHjd7HGLxIP+JBiN5FiN9FRwNII5gbMZhsOu51ovx9/pJtEuAddN+yEZnsD1SuewepckXUM91LACXtE/oiSjQsXIbgXOJnl/iYnRuqqinbxDOp7r0N/r7Gwogr3088S3bAdyTQeHfH3h+i/1s+6VrBYFT77G/dT1zjzo8ticuPOKBs9E/9fSiQl1wh3iVqaz7HrXVHR82h8I+pwC8ocTY0AIGepvmFzrSY0dI5o8FbBglvXNMIfX8Z//CjBs2fQ44YtTTKbce24H8+efTg2bUZSFIIDZwh3XkSSzdSteSEttnVd5/L5bk68c5NELIliklm3o4lVG+uRsyVFWppx1K8jNtiHHvkYKXIdkn1I8TsQv0MS8I9M3MTmbsFdvxebuzVrknuKYgq4fC0iwh4hWEoIwb2ASaoaA6NRovGJiZG6qqJdOI367msw2G8srKxGeeQJ5B27cNRWEBtLvtF1nf72Yc4e6WD1SqNs4PrNDfMqtmFsopUm/b+EjCdNzlalpMiWkmIL96IwXVlAkTQpWHhoyTHBrUzNObG6VhEaOkcs0AH1e/Lab6yrE//xo/hPnEAdHReJ9vVePHv24npgJ4pj3BsdD/cw1HUIgOoVBzDb6gAIjEZ465c+ujuMfdQ0u9myZyUOt3X2g1Cc4NqJ7tqJzZTAKfeiJ4bRtDi6Gkc2GWVRLY6mCT7tuZCPiM7XIiLsEYKlhBDcC5RsiZG6qqKd+8iIaA8NGAuratJCW1KUCfuQdLhx5i7XLhrR76YVhsg1mSeuNx985cBGPj57DoCGKieP7i/txCvlainRF7+lZHKsPV0WEJE0KVh4qGMR7myC0+bOz8edHB0l8OEJ/MePEuu8nV5urm/As2cvnt17MdfVTdlO11UGO34Ouoqz5n6c1feh6zqXztzhxLs3SSY0TBaFjTuXs2xt9YwR6MlISFR5rHgcHqAm5+0KJR8Rna9FJBVdr6tz098fKM4BCwRlihDcCwxN1xn2xwhExiOzejKJdu4k6ntvwPCgsbCmzhDa2x6cIrQBTLrOyTdv0HvHj2KSefSp9TTW3WTk7nyNZCL1lXaU1mpCQ108s2cVrhJnqsu5Jk2yFITmmD97clnAzAh32ssuTd5MICgrxiPcU+cQk2V2H7cWjxM6dxb/8aOELl8Czfjuyw4H7p0P4dm7D1vrmhlFcnDgNIloPyZLFVXLn8Q/EuGtV6/S02kI0IaVFWzavRKbI78Oj1azQm2FHXOJk9gzyUdEC4uIQDA9QnAvIBJJlb6RKImkYf3Qkwm0MydR338DRoaMlWrrUR59Ennr/VmFtixJSLEkb7/4MaFADKfbytOf30Jdoxt/7835HM4UxoP1ZVQWMG2lKO4xFdqNsyRMrjU+q4dbIChfxj3c2cuYZvNx67pO5Po1w5d96iO0iLEPFAXn9h149uzFed92ZPPsAllNhhntfheAymWf5tLZXj585ybJpIbZamLz7hU0rq6cdU4ZCsR46Ug7XX1BGmoc2C0mbnX7Wbu8cl7L5+UjooVFRCCYHiG4FwiBcJyhsY6ReiKBduaEEdFOZcrUNaA8+hTy1h1IcnZRZLeaGLnj57XDZ0kmNRqXe3jys1twOC3zOJLyQJJNhnjUVXQtafw/KykxWhyhWaxunCUhHeAWrd0FC5eZItwANvfqtI87zhr8x48SOH6MxEB/eh3r6hY8u/fifughTG5P1v1Mx2j3e2hqFJNtJa+/Gqa706gM1bi6kk27V2C15RbVfulIO7d7gwB0D4TTy+e7fN5MIjqbv1tU0BAIsiMEd5mjaTqD/iihaAI9EUc7dRz1/TchYDzWkxqakB99Ennz9mmFtoREpdvC1dN3OHPM8CFu3NbEw59eV/L62vkxv1FfWbaiqRE0NYYyjeDWl0Rkd3I3zdRYRWt3wcJjpiolACbZ8FxHBq8x/M3D6a+/qaoa9+49ePbsxdq8rKD3jkf6CA6cQkfivffqGRnxY7GlotpVee2rqy847WvzWT5vpiomoo62QJA7QnCXMbGESv9IhEQkinbqKOr7b0HQD4DU2Izy2FNIG++bVmgDWEwKlQ4z7x+6Rvv1ASQJnnh+My3e2qLbJIrFfB2XpFhBjaBrccCZfaUSWUrKywA9e1nA7Dce5TQGgcAgW4RbTyYJXbpo+LLPn8P8QhNyhRm5yYVr1Tbce/bi2LBxxrk0FwZvvwno3L7dxMiII+eodqZ9ZHm9i8883EpLs4cbd/xZ1y8Xb7Sooy0Q5I4Q3GWKPxxnaMCPevII6pG3IGhkcEtNyw2hvWHLrBeHCqcVRdN45YfnGewLYbEqPPGZzdy/a1WJM8ILFWLzH+FWAW3GxMniWkrSUeRy0qpTypRM39pdkuQyLW0oEBikI9yKnWjHLcMy8uEJ1MDYnCdJyCEbVKjU/t4XqVz+yJzfU9d1rl+8jE1tQ1Vl2jtb2f5IC00tE6Pak4X1wf0tVLutE+wjt3uDHDrRwVef25y2a6xocGExKWXnjRZJkgJB7twTwe31eu3APwH1QAD4TZ/P15/x+lPAN8b+KwH7gS2AHXgZuD722t/5fL4fzddxzweaptPfP0LwvbdRj7wNYaNetrRsJcpjTyJ5t8wabVVkmdoKG/7BMId+dpFIKEFFlZ2nv7CVqpri1GbNTrGE2PwIuly6TRbdu1yGWlVPd5Eci3BnLQtY7Bb3AkFpUOOGcO35+28T93Wll1uamvHs3Yf7oT3EpW4Gb/2MWOT2dLvJmUg4znuHr1HteI/GBugfWc1Dz2zHmqUCyWRh/dKRdn7r6Q1T7CM37/qnWDnKsXSeSJIUCHLnXkW4vwZc9Pl8f+H1el8A/gz4g9SLPp/vMHAYwOv1/glw1OfzXfF6vb8L/LXP5/ure3HQpSbiD9Lz2mskPsgQ2stXoXzyaaR1G3OyNTisJmoqbLT7Bnj71auoSY3mlZU8+dnN2Oz5laBa7OTUbbJkHu5yDHHnUhZQCG5BeRK50cal//4SiftHkBwm4p3dKC437od249mzD+uqVek5VE4aFUxiodtoWgJZLmxubL8+wHuHfJjkYTbtG0TTFeo2fHJCF99MJgvr271BvnfoKo01Du5mJEYWGinOt9PjXBFtxgWC3LlXgns/8K2xvw8Bf55tJa/Xuxz4DWDn2KIHjMXe5zGi3F/3+XzldctfAGo4TO/hwwTfeRMixqQrrVhtCO21G3IS2qlmCG67mTPHOjj5wS1gLDnyiXUoygIQSvPc7jzdbXKa0oC6rjM1oXCulGGIO83kTpMZn8eEG49yulkQCAwGfvYTItd8WPe0AND021/DtXU7kmnqZU4xOTDbm0hEuokFb2P3rMnrveKxJEffauPqBaMCye6HjAYGknMrmFzTbre83pWOcKe43RtkdaOL9Ssq5xwpFkmMAkH5UnLB7fV6fwf4w0mLe4FUdkUAmO52/t8B/9Xn86VCkCeBf/D5fKe9Xu9/AP4P4I9nev+qKgcmU/6dE+vqCmttrusanQBIs+4jGQxx5+VXuPvSK2hhQ2ib16zD+fRBLN7cItoAZrNMY40TRYJXfnyBC6e7QIJPP7eJ3Z9ozbqfbMemBq2MAA67paDxxyIJ7mJYWgrZPtBtIgx4PHaqCzz/kPtnF+pzEh4BpyP78WZ+lvX1+ZUGm454JMldQJZn/35ko9Dv5UyMYqMfsFhM1NW50TWVLoyodur9en3GutXVLtA1egDFVNjnPBOlGN98MSrZx86jknUcC3ls80mhc7bz33yNwM02uuK/RJbNtD7+2Izrx4a99N7qRla7qKvbnvP73G4f4hc/OMvIUBhZkXhwfyU1th6QFDzNn0A2T5OADfyLZzbxg9d93JyUXNjZF+IX//ngrO8923coWxLjQvneLZTjLAQxtoVHKcZVcsHt8/m+A3wnc5nX630RSI3GDYxM3s7r9crAs8B/yFj8c5/Pl1r358B/n+39h4fDs60yhbl45fR0VFCfdh9qMMjwm68z/OYb6FEjwUdqWYvy2FPQso6wJBEeze24XXYzbquNvu5RDr94ie7OUUxmmccPbqJlXS0DA1NLS003vlDIuK8JR+IFjT8ZM2wwqqYVtH0smgDAH4iimgo7//l8drGxwLZ/1A/WqdvoWtL4Q5KK5p1Mxo1zpBVwjkrl4YyMfdfiCZX+/sD4d1jX6OvzI0kSqmo0WxoejqDrxnlRk4V9ztNRjh7VfIj4jd9yPK5OGUehY1usF7OZKGTOBsBeSeVD2+n64JdIin3W860rywEY6vVhrZo9cVJVNU4f7eDM8Q50HdzVdrY9vBoP70IUdPtmRkMyEJp2HzLw659exz8e8tHRO358a5ZVzHq8uXyHsiUxLoTf1EL/7c+EGNvCYy7jmmnOvleWkqPAMxgR66eBD7KsswW46vP5IhnLXvN6vf/G5/OdBD4FnC75kRYRNRhk+PXDjLz9Jlo0CoDUuh7lsaeQW9bmtS8JiZoKGy67mdHhMK/+5CKjQxGcLgtPf2ErdY0L+UI9T0mTY75NXUtkfT2dTFhU33L5W0omPhHRAWlC8ug8O38EgpxRE4ZYn64GdyYW1wqQFBKRHtRECGWGyPTIUJi3Xr5CX7dxEW7d0sDaHU0ouh/6r6Ejo7sezOkYHTYzv//8Zr536GrRkw1FEqNAUL7cK8H9d8A/er3eI0Ac+DKA1+v9FvDTMUHtBSb3Gv8a8LderzcO9AC/N3+HXDjJgJ/h1w4z8s5b6DEjiiyt8RpCe3V+3kEwamvXVdowmxR6ukY59LOLRCNJauqdPPOFrbg82VsazxsLRJBJslGlRJ+uvfuSaHozTZt5STbGr+uGDl8i50KwsEmmBPc0XSYzkWUzNtdKooF2osFbOKs2T1lH13WuXujhyJvXSSY07E4LWx9eRc1YQEMaOYWEjm7fCMrMtrNUno3HYcw7xfBWi06PAsHC4Z4Ibp/PFwa+mGX5v8/4+yfATya9fgbYW/IDLBLJ0VGGXz/EyDtvo8cNUad4NyE98iTyypaC9um2W6jyWJEliRtX+3jr5Suoqs7K1mo+/fwmLNZ7WFp9jsHbrMKvhEhjEW5tmgj3uMgs56h0EUhV/Mv4ACVkdDR0NCQU0fhGsCDIJ8INYHO3GoI7cHOK4I5GErx32MdN3wAAza3VbHpoOebUHKsGIfIxOswa3TYpMnWVdqzm/L3pMyGSJAWChYNofFMqdGj/0z9JC237lvvQHn4CfdnKgnYnIVFbacNpM6PrOudPdnLs7RsAbNpuVCKR59glrVyQ5s1Skopwz6elJLXzchKrKcWdcd4l2VicLg2YWRZwkd+ACBYs+US4wRDc8BZR/010XU/bqe7eHuHNl68QCsQwmRU27V7OsjU1E7aVQqeR0NBt68BUPe17OGxmaj02ZLn4vxvR6VEgWDgIwV1EkiPDDB5+FbyGWNPjcZzbd2B7/GmClU0FR3DNJoX6MQuJpukce6uNi6fvALD70Va2P7SibNu058U8i9BUhFtX59FSMvY5lZPczno0k7tNCkuJYAGQEtyKkputzmxvRDa5UBOjxEOdmB3LOXWkg9PHOgCoqndy38OrcbitEzdUwxC+CIDu2jl5t8CYhcRtxeO0FDia2RGdHgWChYMQ3EUgMTTE0KFX8X/wHnoyic3bioTEij//C0IVDQSiCQqVWC67mWqPDVmSSCZU3nz5Cu3XBpBliU8+u4F1mxqKO5hyYJ5uHqTZItzF7jJJuceGMywlkmwEuMfOQSnOhUBQbMYtJbl11JUkCVfNNvy9RxnuPsXxEwP03PEDsG5bE63bGrNGpqXgh0h6Et3aAub6Ka+b5DELiaW4FpLJiCRJgWDhIAT3HEgMDhpC+8j76EmjVJrzgQdQGQYJhp11xKPT+INnIbMKCRh+wkM/vUjPHT8Wq8JTn9vCslVVRRvLUkROe7iniXCnW5uXQiaXUYxbz2IpSY9ZRLgFC4dkwihqlauHG8BZswN/71Eiox8z0OvB4XKwdd9qqpumaWCTHIHwReOG1L0PgKFAjJeOtNPVF2Rlg5uvHtxccrEN89vpcb67WAoEiw0huAsgMdDP0C9fZfToB6CqIEm4d+6i+tmDWJqX0Xnu/wIgnlQL2r9JkamvtGMZS7AJjEZ55ccXGBkM43RbOfClrdTUTd/NbOEyz5YSZeaygONCdHGXBcxmdUpFstMR7rSHu/yOXyBIka+HO5lQOf7uAC6lgtqaUTZtCVK34X4stukvjVLgmOHdtm8Ccy0ALx1pT3eQvNUT4B8PXV10yYsiQVMgmBtCcOdBvL+PoVdfwX/86LjQfmg31QcOYm1uBmA0aJT9K1Q6Oqwmaivs6ceYA71BXv3JBcLBONV1Tg58sQzK/s3KXIXz4rWUlDMTxPTk9u4lufkQCIpL2lKSg4d7eDDEG7/4mMH+EMuam6mtGWX5sm70GcQ28V6k6DV0FHT3nvTirr6JDcaudY7QNxJZVBFgkaApEMwNIbhzIN7bYwjtE8dA0wyhvWcvNQeew9LYBICm6wyNRglG4gXXtKhy26jISLC50zHM4RcvEY+pNK+s5KnPbcZqMxdhRKVirkL5XpUFFJYSg4llAcGIbBudJ6euIxCUG8kcywL6Lvbw/uvXSCY0PFV21jy4Dy12EznZzz+8+C6KvZGD+1uozkyW1DWkwPvG387toBi1uM0mhdZlFbR1TRSgiy0CLBI0BYK5IcJVMxDv6ab7H/4Ht/7sT/EfOwKAZ+9+Vv/lN2n6nd9Li+2kqtE7FCZYoF9bliQaqhwTxPaNq3288uMLxGMqazbU8eyX7itzsV1MyqQsYEki3OUoWGerUpK68ZAnVMOZ77rpAsFM9I1EGB41BOHfvdRG30hkyjqJuMrbr17l7VevkkxotG6oY/czXpzVLj7uawRg18o73O4N8tKRdsDwZ3/v0FWOH/8ZUvwOGrZ0ZRKnzUxTjYPffXbTlPdabBHgrxzYyPoVlSiyxPoVlSJBUyDIExHhzkK4s4vu//X/ETj5oRH9UxQ8e/ZRfeBZLHUTM9JjcZW+kQiqpk2zt5mxmhXqKu2YlHFRd+nMHT54/ToAW+5fxr7H15akhmvZMc/6LV0WcNpOk6kDWiL3pdLEKiVg3HRMvvEQPm5BOfLdVz/mSxuM3/LljvCUCPPQQIjXf3GZ4YEwJpPM/Z9ooXqFJ30T+d61GjbW3mbbsn56Ak4+vL0cMPzZHqmdfS130DQ4fHMrTzfZJ5T8q6+0s35F5aKOAM9ngqZAsBgRgnsSgVMnufY//i4ttCv2PUz10wcw19VNWTcYSTA4Gi040ue2W6j2WNMTvq7rnDpyi1NHjRqwuz7Rwv17Vi6OGts5kD6P8zTcccGdmND0YpwSVuYox8Y3E058RoR7qXTcFCxobncPY9qkk1BlkpoyIcLsu9TD+68ZFpLKagcPPr4Gs2PiE0O7q55/vrSOz913jSc33MJud4MaplK+yXOb2wA47Gvl5G0rp25+xNrllRMqdYgSfQKBYCaE4J6MDiaXE+f9O6l+5gDmmtqpq+g6w4EY/vB03t+ZkZCo9lhxO8YtJJqmc+SN61w+exdJgk88tZ5N25oLHoZgdiRJRpJM6HoSXU8iSRMvwOOR3SIKzTIUrXo28S9llAUUCZOCBcCGFYbwjSSMy9qaZRUkEypH3mzjyvluANZuqse7czlalp/hwf0tvHQEDl9N8NSGdh5edRGp7yKfu894/UxXAydvp3J2plbqEBFggUAwE0JwT8K9cxetz3yK/v5A1tc1Tad/NEIklixo/4pslPzLrNGqqhpvv3KFtiv9KIrEp5/fRMv6qRH1pcJ8WhYk2YyuJo1uk/Ikj3yWZMLFjJTVUqJnlAScJLjLKUgvWPJ86dFlxO8agnv9ikq+tL+FF//XGQb7Qigmmd2PraFyuQdtmqdL1W4rv/X0BmADeuA4UvBDdMlEQm7gfKeT16/UMnkuWGw+bYFAUDqE4M6DRFKjbzhMQi2eXzsRV3nt55fobB/GbFF45gtbaV5ZWaxDXmDMv4KTZAuokayJk7qeHFtnsf9MstxYSNksJfKU1QSCcqHSodMHrGyq40sNK3hnrMJTRZWdh5/xopmVacX2ZHT3HnTHFpAdmCSFx9fY+PwBC9/8/plF7dMWCASlQzwjzpFoPEn3YKhgse22W2isdkwQ27Fogpd/dJ7O9mFsDjPPf3n7Ehbb94ZU85tspQFTIlyaHPkuCuUUHs7S+GZCWcClVY9csDDRkkZVkpEhjdd+fpl4TKVlfS2Pf2ELqlnOP9dGcSPLpgkVpESlDoFAUCiLPXRXFALhOEP+WEHJkdn82gChYIxXfnSBof4QLo+V517YRmW1o1iHvDC5BxaOmUoD6loqwl1MwT2WIFvEPRaPzAj32N+TygIKBOVKNGzYAPv7EkgS7H60leb1tYQLtP8P6E52AAAWZUlEQVSZFZn6Kgdm0/j3Xvi0BQJBoQjBPQNzTY5UZJm6Shs2y8TT7B+J8PIPz+MfiVJZ4+C5X7lvAXSPXJzMVBpQS0W4peIJ7rJ0Y6STInMrC5ix4XwcnUCQE20fd9JYCzpWnvvVbchOS8Fi2241UZfR8VcgEAjmihDc06DpOgMjkYInbAloqploIQGjnfDLPzxPKBCnrtHFgS/dh31S9HvJM4+VPDJLA05G141lckk83OUkVrMdywwe7vK8bRAscWrqTKCD975VxG1mYgm1oP1UOK1UZXaYFAgEgiIgBHcWEkmNnsEw8WRhE3aKyWK7vyfAKz+6QDSSoGl5Bc98cSsWq/gIxpl/EZqylGhZLSWl8HCXn1gdN/JMTZoUHm7BQqGySiY0BFHVglZAIzIJiZoKGy77UunoKxAI5hOh9iYRS6h09QUKFtsVLivZCgr2dI3y6k+MVu0rWqt58rObMZuVLGsK5pMZI9ylTJosqwD3VO98Wlzr+niEuwxvFgSCFPF4CABNyj86na1cKxjt4ic3s0k1uhEIBIJ8ECGrDMLRJD2DYVS1sOTI+ko7la6pk33XrWFe/tF54jGVVm8tT39+yyIX24WqyflPmpTSSZPzVKUkPbSyUtzGP5mnPbMsIKLxjaC8GQ7EiMfDxn/k/PJhLCaFphrHFLEN8N1Xr3CtcwRV09ONbgQCgaAQRIR7DH8ozlAgWtC2JlmmvsqOxaxM6drX0TbIaz+/hKrqrN/SwGPPeJHlxSpc5iaU70W385kj3KWrUlKeZES409VUhKVEUL7ous7AaJRQNIGUummWc49AO6wmaivtyNPkjUxubCMa3QgEgkIRghsIRhIFi22rWaG+yo6SRUTfuNrHmy9dQdN0Nu9o5uEn1hW3TfgiZT47TcpyLnW4F/vPJM/GNwJBmTDoN8Q2gO56AKs0QNRUk9O2uSRHrllWIRrdCASConBPlYTX6/0s8EWfz/flLK99Ffh9IAn8pc/ne8Xr9dYCPwDswF3gt30+X3gux6BqGoOjhYltp81MTYUta3REB97454/Rddi2azl7HlsjxPas3ItOk2MRbnVqhLsUZQHLkiyPFrK3dhffX0H5EI4mCUYyfrf2DdgrnURHQjNul09y5FcObJzi4RYIBIJCuGeC2+v1/jfgSeBcltcagX8LPAjYgCNer/cN4D8CP/D5fN/zer3fwBDk/3UuxxGJqQU1tKl0WbP6tdPoho55YO8qdj68WojtfJjHUyXN2PgmVRZwcXeaTB/JhO9oKpo9U4S7fMYgWHqEY1N/s7MhSxJ1lXbsOVaHEo1uBAJBsbiXz4iPAV+b5rVdwFGfzxfz+XyjQBtwH7AfODy2ziHg8bkeRCKZX/koCWPCnk5sXz57J/33Q4+0sOsTLUJs58y9SJqcwVKiLxUPt3Hes5YFzNr4phzHIFhq5Dt3mxSZphpHzmJbIBAIiknJZx6v1/s7wB9OWvzbPp/vR16v99FpNvMAmdkpAaBi0vLUshmpqnJgMk1fEcRssyCbp56GqkrnlGWKItFU48Q2zYT94fs3+eD16xx4EpDgyYNbZju8e0ZdnXvKMjVoZQRw2C1ZX5+NeFTlLiDLckHbD91SiAGVlQ7c1flvnyKf9zZpHoZug8WsT9lu6JZxQa+q9szpeDJRk3G6MCRrIeeokG1mQwtZGAHsGZ97pN9KCHA5LVjtNvoBi8V4PRqK0g0oSmGf80yUYnzzxahkHztPStZxLOSxzSezzdkpkpJMKDI1yp1t7rZZFZpqnCjKws5DWMzfITG2hcliHVspxlVywe3z+b4DfCfPzfxA5mjdwEjG8kjGshkZHp7Z4h1PqAxP8vxVVTqnLDObFBqq7AT8kax1ts9+eJsT79xM/18C+vuzrXnvqatzZz22UCgGQDgSL+jYk6k6uJpW0PaJsc5wIyMRomph5266sU1HJGi8ZzQSnrJdPGZ4+0f9iYKPZzKaakTSdV3P+xzlO7ZcCQaNcUYiifT+IzHjvAQDYSJxw3YTTxifayJqfM6qWtjnPB2lGt98EfFHAIjH1SnjKHRsi/ViNhOzzdkpwqE4w5OS3bPN3U6bGbfVxtDQzN7ucmeh/z5mQoxtYbJYxzaXcc00Z5frs7WTwH/yer02wApsBC4BR4FngO8BTwMfzPWNLGYFl81MMDq9H9BuMVFXaUeWsz9KP3O8gw/fawfgkSfXF+Owlij3MGlyvhrflLO9KNNRklEWMJVUKcoCCsoJt8NMIBwnoU5vLZmpEoloaiMQCOaTsrqCer3ef+f1eg/6fL4e4P/GUK5vA//B5/NFgb8EXvB6vUeBPcDfFuN9q6fJWJeQqHBaqa+aXmyfPnorLbYfe8bLxu3NxTikpck9yMGbqbW7VspOk2WFKAsoWHhIkkRDtQNrliZisiRRW2GfseyfaGojEAjmk3sa4fb5fO8C72b8/68z/v428O1J6/cCTxX7OFKTs9tuIRJP4nFZIJnEYTNjNk0vMk4ducVHR24hSfDYgQ14tzROaXwjyIdUR8P5T5rM3mmyFEmTY/suowof+gyt3SeWBRSCW1BemBSZxmoHkZhKNJ6kwmVFUlVcdvO0QZIUoqmNQCCYT8rVUnJPsFoUrBaFuioHUlKdcd2PPmjn1NEOJAk++exG1m9umKejFBSTnMoCFrEOdznXsp54ZLmUBRQI7j2SJOGwmXDYTNRV2SGZzGk70dRGIBDMJ+IKmie6rnMyQ2x/6jkhthcyuXWaXCKWkswnC2N/Zy8LmNqsfKL0AkG+fOXARtavqESRJdavqBRNbQQCQUkREe48+ejILU5niO11myaK7b4Ro1KBrsM3v39GJOLkgX5P6nCPRbgndZrUdRXQjGMpSWS3nMTq9JaSCR7u1OvlnPgpEOSIaGojEAjmExHhzoNMsf34wU1TxDbA//vL8cSbJZuIM8fI53zKOUlWMH4GGro2biPK9G8Xt3HRQhGr44I7dSMkqpQIBAKBQFAY4gqaI6eO3uLUWILkp57byNqN9VnXW9KJOHMVplmS9+YDSZmaOFlyO0lZBbinWkrSSZPCwy0QCAQCwZwRV9AcOH2sg48+uJVOkMwW2U4xOfFGJOIUwDwHgbOVBiyZ4C7DAHdWK0/aUqKnPdxCcAsEAoFAUBjiCjoLZ0/c5uT7Rp3tTx7YMGuC5G8/M554IxJxFgbZSgOmxLdcsoTJcgpxT2W8LOB4hLucK6wIBAKBQFDOiKTJGTh/spMT7xrt2h87sIH1Wxpn3aa+0k4nxtN5kZCTL/fIUpKlNGDpLCXlKFrHPNoTji2jLCAiwi0QTEZ0qhQIBPkgrqDTcPFUF8fevgHAo0972bB1drEtWJhkKw2YFtzSErgnzerhzqEsoECwhBGdKv//9u4/RvK7LOD4e3Zv70e5445614BnTKSUJ43VKiL9YaE0QdqjNkGjCZbEACpNMDFcY9DGxEpCxIpF5Q9iFC6awB+opNZw/IgGiS2UqIC/Qn3ONrGeJcC13u/bu92dGf+Ymb2529m5m9n5/pjZ9yu55Ga+O7PPZ2f2+T7z2ef7+UgahWfQAb721HM8+XfPAPCGu1/NjTe/ouKINpuyZ7h7LSVlzHCvfoeCnndC+nq4vWhSWmtTXyAvaWSeQS/z3LMvcviv/g2AO970Kn7wR7+34oimT81LyTUGtpS0i9rWvb4tJQxoKWm3W+tu7V6n7emlsnmBvKRRWHBf5vTJ8zQacNtd1/NDr/2+qsOZKhsuJSvaubBXVLeaJS4LWCcDlmO82D6ydllAL56U3KlS0mg2QYPqaG56zX5uv/NVnDq9WHUom85quV3yToZzQy+anP1fkYEfc/p2mmy33fhGupw7VUoahWfQAbZtn/0iq556q2WUa9iygJOe4Z7srpWT0iuoB2x8c8nW7qYLSZLG4RlUNVTVTpNrZ7iLW4eb1Znj6g3q4e79/2IPtxdNSpI0Hs+g2vRK3WmyjgbU/QM3vqnl7LwkSfVnwa0aqfaiyYE93I1NUHCzdh1ulwWUJGlyPIOqAGMWzhevmpxUIFfl4rKAfauUrC4LWGQ/f11aSnr6ergvWRawfcl9kiRpNJ5BNUEbLZRrOMNdSEtJvVozBq6n3bjYw73+DHfdPjBIklRPLseh+il9WcC1W7sXtUpJLfWW/WNQS8mgrd3r9YFB0kXfPbHIocNP8+zzJ7l+/27ede+NXLdnR9VhSZueM9za9AbuNFnCKiW1myF2WUBp6h06/DRHjp6g2Wpz5OgJDh1+uuqQJOEZVLVSp5aSInu46zZDvP7W7p2Gk8tnuCXV1bPPnxx6W1I1Km0piYifBn4uM+8fcOwg8Lbuzc9m5vsjogH8L/Bf3fufysyHyolW5Sn7osm1LSWlLAvYpia199oPOgNnuC8vuGs2QS8Jrt+/myNHT1xyW1L1Kiu4I+KPgLuBfxlw7JXA24Fb6JzWn4iIx4BzwNcz874yY1U5Bl68V4LVrd2bJS0L2KBexeqg1WEG9HCvtpzU4kOCpEHede+Na3q4JVWvyhnurwB/DTww4NhR4J7MbAJExAJwHvgxYH9E/D2wCBzMzBz2TV72smvYsmV+5OD27ds18mOgMyN4FIDG2M9RhkGxNc9s4wRwzY6tY8W+fKHN88Dc3Hhj/+6ROVaAa6/dyY6d4//sRv3ey0sNvvVNgOXVx37nP5sAfM/ePWx/yWRfx6M0aAN79+1kbsSWlSLeU+eObeEMsGvX9tXnXzxzjm8D8/OwdWGO88Ce3TvZvW8XFxZX+BYwPz/593idf2eu5GRjB8eArVvnB45jmsdWpnFzds8s/5yvZmz79u3i0fdeV0I0k7XZX7dpNatjK2JchRfcEfGLwMHL7n5nZn4qIt446DGZuQy80G0h+RDwjcw8EhEvBz6YmX8ZEXcAnwB+fNj3P3783Mgx79u3i2PHTo/8OOjfrrs99nMUbb3xnT17AYBzi0tjxd5cPgtAqzXe2FdWOjOpx//vLGcWx/vZjfPa9VYkaa1cHPfKcudncfzEElvOTfZ17L1DXjh2eqQe8Y28L4dZXOy00pw5cwG6z798vvN7s7KyAkud4ydPnWeJ06wsnQGg2Zzse7yo8ZVl8dQiAEtLzTXjGHdss3oyG2acnN0z7e+hYRzbdHJs02cj4xqWswsvuDPz48DHR31cRGwHDgGngfd07/5nYKX7vE9GxP6IaGRmnf5Ar7H1djws97s2Gp1fg3Z7hXa7RaMxR2t145tNsCzgqsE7TfY+RK69aNJfO0mSrkYt1+Huzmw/DnwxMx/pO/Qw8CLwexFxM/A/FtuzqOSLJhsNGnMLtFvLtFvLNOa3lbIsYJt2Pdqh22u3dh9+0WQtopYkaWrUquCOiAeBZ4B54E5gW0Qc6B5+CPhd4BMRcS+dme53VBGnilLdZ6fG3NbVgrs9twDtZvfA+L2k636vbg93fQyKpldcty4uC+gqopIkjaXSgjszvwR8qe/2h/sOb1/nYfcWGJJqofwZ1P6lARuthdX7GiXvelmtK81wb6afhSRJk+OUlQTMzW0DoN280LfpTcH92+26zHMP2PjmkmUB1+vhliRJV8MzqAowZiFZYQE6v7ATgOby6WLX4O48cTHPO6b2gJ97r32kjVu7S5K0UZ5BNUETKiQrKEjnt3Z2Y1tZOlXOLpM1dEn7TO//7Rawzk6TkiTpqngGVW1UtdMkwJatLwWguXySVnuzFdzDWkraqztN2lIiSdJ4PIOqdhoVXDQ5v9ApuPtnuEfdBXJ0NenhHtRSMnRZwNUHFhyYJEmzwYJbon+Gu4yWknr1cF/UH9ewZQHrGr8kSfVkwa0aqfKiyU4Pd3PpVHmrlNTGoI1v+orqVm9NctOFJEnj8Ayq+litt6u4aLLbUrJ8inZrqRNF4QV3PVoy1u2dX20r6X4AseCWJGksnkFVPxV0LMzNLTA3vwPaTVaWTnTCaBTVw91bAaSgpx/T5b3zq0sDdmf8bSWRJGk8jUFr8EqSJEmaDGe4JUmSpAJZcEuSJEkFsuCWJEmSCmTBLUmSJBXIgluSJEkqkAW3JEmSVCALbkmSJKlARe3sMRUiYg74KHAzcAH4pcx8pu/4LwMPACvABzLzM5UEOoarGNtB4G3dm5/NzPeXH+X4rjS+vq85DDyemX9cfpTjuYrX7gDwcPfm14FfycypWFD/Ksb2a8DPAy3gdzLzsUoC3YCIuAV4JDPfeNn99wG/RSefHMrMP60gvJkwq7l7lvO2OducXVdl5ezNPsP9VmB7Zt4G/AbwaO9ARLwc+FXgJ4C7gQ9GxLZKohzPsLG9Eng7cDtwG/DmiPjhSqIc37rj6/MB4NpSo5qMYa/dLuBDwE9l5q3AfwN7qwhyTMPGtofO79xtwJuBP6wkwg2IiPcBHwO2X3b/AvAHdMZ1J/Dubo7ReGY1d89y3jZnm7Nrp8ycvdkL7juAzwNk5leB1/Ydex3w5cy8kJkngWeAaUpuw8Z2FLgnM5uZ2QIWgPPlh7ghw8ZHRPwsnU/cnys/tA0bNrbbgX8HHo2IJ4DvZOax8kMc27CxnQWeA17S/dcqPbqNexb4mQH33wg8k5nHM3MJeBJ4famRzZZZzd2znLfN2ebsOiotZ2/2gvulwMm+282I2LLOsdPA7rICm4B1x5aZy5n5QkQ0IuL3gW9k5pFKohzfuuOLiJuA++n8KWgaDXtf7gXuAn4dOAC8NyJeXXJ8GzFsbNApKr5J58+uHykzsEnIzE8DywMOTXs+qZtZzd2znLfN2ebs2ikzZ2/2gvsUsKvv9lxmrqxzbBdwoqzAJmDY2IiI7cAnu1/znpJjm4Rh4/sFYD/wReAdwIMRcU+54W3IsLG9CPxTZn47M88A/wD8SNkBbsCwsR0AXgH8APD9wFsj4nUlx1eUac8ndTOruXuW87Y525w9TSaeRzZ7wf1l4C0AEXErnT/79Pwj8PqI2B4Ru+n8eeE/yg9xbOuOLSIawOPAv2bmA5nZrCbEDVl3fJn5vsy8pXsBxJ8BH87Mz1cR5JiGvS+/BtwUEXu7swy30pldmBbDxnYcWAQuZOZ5OsltT+kRFuNp4IaIuDYitgJvAJ6qOKZpNqu5e5bztjnbnD1NJp6zN/UqJcBjwE9GxFeABvDOiHiQTt/O30TER4An6Hww+c3uG2parDs2YJ7ORQDbuldPAzyUmdNUAAx97aoNbcOu9L58CPhC92v/IjOnpZiAK4/tTcBXI6JFp2fubyuMdcMi4n5gZ2b+SXecX6CTTw5l5vPVRjfVZjV3z3LeNmd3mLNrrMic3Wi3p2JlGkmSJGkqbfaWEkmSJKlQFtySJElSgSy4JUmSpAJZcEuSJEkFsuCWJEmSCmTBLUmSJBXIgluSJEkqkAW3NKKIOBQRD3f/f0NEHImI11QdlyRpMPO2qubGN9KIImI/ne16DwCfBN6dmU9WG5UkaT3mbVXNGW5pRN3tXf+cztbRB03aklRv5m1VzYJbGlFEXAe8BTgLHK04HEnSFZi3VbUtVQcgTZOI2AN8DvhtYB/wCHBflTFJktZn3lYdOMMtXaWIuAb4DPDRzPw08DHghoi4q9rIJEmDmLdVF140KUmSJBXIGW5JkiSpQBbckiRJUoEsuCVJkqQCWXBLkiRJBbLgliRJkgpkwS1JkiQVyIJbkiRJKtD/A4/SLGCUgZ8sAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n", "plotXy(Xa, ya, ax[0], poly_fit(Xa, ya, 0), poly_fit(Xa, ya, 1), poly_fit(Xa, ya, 2), poly_fit(Xa, ya, 14))\n", "plotXy(Xb, yb, ax[1], poly_fit(Xb, yb, 0), poly_fit(Xb, yb, 1), poly_fit(Xb, yb, 2), poly_fit(Xb, yb, 14))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Train-Test Split" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [train_test_split](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) function picks a random fraction of the observed data to hold back when learning the model and then use for latest testing.\n", "\n", "Note that since train/test splitting involves random numbers, you will need to pass around a random state object for reproducible results.\n", "\n", "The plots below show 20% of the data reserved for testing (red points) with a $P=2$ fit to the training data superimposed. The primary sklearn test metric for regression problems is the [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination) $R^2$, for which the goal is $R^2 = 1$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def train_test_split(X, y, degree, test_fraction=0.2, ax=None, seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " X_train, X_test, y_train, y_test = model_selection.train_test_split(\n", " X, y, test_size=test_fraction, random_state=gen)\n", " train_fit = poly_fit(X_train, y_train, degree)\n", " plotXy(X, y, ax, train_fit)\n", " test_R2 = train_fit.score(X_test.reshape(-1, 1), y_test)\n", " ax.scatter(X_test, y_test, marker='x', color='r', s=40, zorder=10)\n", " ax.text(0.7, 0.1, '$R^2={:.2f}$'.format(test_R2), transform=ax.transAxes, fontsize='x-large', color='r')\n", "\n", "_, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n", "train_test_split(Xa, ya, 2, ax=ax[0])\n", "train_test_split(Xb, yb, 2, ax=ax[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is no rigorous procedure for setting an optimum test fraction, and anything between 0.1 and 0.5 would be reasonable (and the sklearn default is 0.25). A larger test fraction improves the reliability of the test metric but decreases the reliability of the model being tested. As always, more data always helps and reduces your sensitivity to the training fraction." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def test_fraction_scan(degree=2, seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " test_fractions = np.arange(0.05, 0.6, 0.025)\n", " R2 = np.empty((2, len(test_fractions)))\n", " for i, test_fraction in enumerate(test_fractions):\n", " for j, (X, y) in enumerate(((Xa, ya), (Xb, yb))):\n", " X_train, X_test, y_train, y_test = model_selection.train_test_split(\n", " X, y, test_size=test_fraction, random_state=gen)\n", " fit = poly_fit(X_train, y_train, degree)\n", " R2[j, i] = fit.score(X_test.reshape(-1, 1), y_test)\n", " plt.plot(test_fractions, R2[0], 'o:', label='$N = {}$'.format(len(ya)))\n", " plt.plot(test_fractions, R2[1], 'o:', label='$N = {}$'.format(len(yb)))\n", " plt.xlabel('Test fraction')\n", " plt.ylabel('Test score $R^2$')\n", " plt.ylim(-2, 1)\n", " plt.legend()\n", " \n", "test_fraction_scan()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### K-Folding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cross validation goes beyond a simple train-test split by repeating the split multiple times and combining the (correlated) results. There are different strategies for picking the different splits, but [K-folding](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) is a good all-around choice:\n", " - Specify the number $k$ of splits (folds) to use.\n", " - The data is split into $k$ (almost) equal independent subsets.\n", " - Each subset is used for testing once, with the remaining subsets used for training.\n", " \n", "The result is $k$ different train-test splits using a test fraction $1/k$. For example, with $N=10$ samples and $k=3$ folds, the subsets are:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(0, 1, 2, 3), (4, 5, 6), (7, 8, 9)]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kfold = model_selection.KFold(n_splits=3)\n", "[tuple(split[1]) for split in kfold.split(range(10))]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [cross_validate](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.cross_validate.html) function automates the k-folding and scoring process, and outputs both train and test $R^2$ scores, as well as CPU times, for each split:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def cross_validate(X, y, degree, n_splits):\n", " model = pipeline.Pipeline([\n", " ('poly', preprocessing.PolynomialFeatures(degree=degree)),\n", " ('linear', linear_model.LinearRegression(fit_intercept=True))])\n", " kfold = model_selection.KFold(n_splits=n_splits)\n", " scores = model_selection.cross_validate(\n", " model, X.reshape(-1, 1), y, cv=kfold, return_train_score=True)\n", " index = [tuple(split[1]) for split in kfold.split(X.reshape(-1, 1))]\n", " return pd.DataFrame(scores, index=index)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
fit_timescore_timetest_scoretrain_score
(0, 1, 2, 3, 4)0.0014240.0008620.4040380.731105
(5, 6, 7, 8, 9)0.0011260.000506-2.2328600.632223
(10, 11, 12, 13, 14)0.0006710.000285-0.3525040.518438
\n", "
" ], "text/plain": [ " fit_time score_time test_score train_score\n", "(0, 1, 2, 3, 4) 0.001424 0.000862 0.404038 0.731105\n", "(5, 6, 7, 8, 9) 0.001126 0.000506 -2.232860 0.632223\n", "(10, 11, 12, 13, 14) 0.000671 0.000285 -0.352504 0.518438" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cross_validate(Xa, ya, degree=2, n_splits=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With enough data, you can use a large number of K-folds but remember that they are highly correlated so you are not increasing the useful information as much as you might think. The sklearn default number of splits is 3." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
fit_timescore_timetest_scoretrain_score
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)0.0013620.0006910.5742210.613270
(10, 11, 12, 13, 14, 15, 16, 17, 18, 19)0.0007040.0003640.6440160.608664
(20, 21, 22, 23, 24, 25, 26, 27, 28, 29)0.0006470.0002920.5598570.614704
(30, 31, 32, 33, 34, 35, 36, 37, 38, 39)0.0004980.0002700.3820870.619587
(40, 41, 42, 43, 44, 45, 46, 47, 48, 49)0.0004840.0002670.7413440.601154
(50, 51, 52, 53, 54, 55, 56, 57, 58, 59)0.0004810.0002740.4158990.625590
(60, 61, 62, 63, 64, 65, 66, 67, 68, 69)0.0005080.0002700.6751240.601310
(70, 71, 72, 73, 74, 75, 76, 77, 78, 79)0.0005490.0003940.7454600.599734
(80, 81, 82, 83, 84, 85, 86, 87, 88, 89)0.0005660.0002760.3667920.618551
(90, 91, 92, 93, 94, 95, 96, 97, 98, 99)0.0005030.0003720.4982760.614549
(100, 101, 102, 103, 104, 105, 106, 107, 108, 109)0.0005050.0002680.7520760.595514
(110, 111, 112, 113, 114, 115, 116, 117, 118, 119)0.0004970.0002670.6041960.610233
(120, 121, 122, 123, 124, 125, 126, 127, 128, 129)0.0004940.000269-0.2926030.630345
(130, 131, 132, 133, 134, 135, 136, 137, 138, 139)0.0004950.0002770.5290280.616538
(140, 141, 142, 143, 144, 145, 146, 147, 148, 149)0.0004910.0002690.5135200.619319
\n", "
" ], "text/plain": [ " fit_time score_time \\\n", "(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) 0.001362 0.000691 \n", "(10, 11, 12, 13, 14, 15, 16, 17, 18, 19) 0.000704 0.000364 \n", "(20, 21, 22, 23, 24, 25, 26, 27, 28, 29) 0.000647 0.000292 \n", "(30, 31, 32, 33, 34, 35, 36, 37, 38, 39) 0.000498 0.000270 \n", "(40, 41, 42, 43, 44, 45, 46, 47, 48, 49) 0.000484 0.000267 \n", "(50, 51, 52, 53, 54, 55, 56, 57, 58, 59) 0.000481 0.000274 \n", "(60, 61, 62, 63, 64, 65, 66, 67, 68, 69) 0.000508 0.000270 \n", "(70, 71, 72, 73, 74, 75, 76, 77, 78, 79) 0.000549 0.000394 \n", "(80, 81, 82, 83, 84, 85, 86, 87, 88, 89) 0.000566 0.000276 \n", "(90, 91, 92, 93, 94, 95, 96, 97, 98, 99) 0.000503 0.000372 \n", "(100, 101, 102, 103, 104, 105, 106, 107, 108, 109) 0.000505 0.000268 \n", "(110, 111, 112, 113, 114, 115, 116, 117, 118, 119) 0.000497 0.000267 \n", "(120, 121, 122, 123, 124, 125, 126, 127, 128, 129) 0.000494 0.000269 \n", "(130, 131, 132, 133, 134, 135, 136, 137, 138, 139) 0.000495 0.000277 \n", "(140, 141, 142, 143, 144, 145, 146, 147, 148, 149) 0.000491 0.000269 \n", "\n", " test_score train_score \n", "(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) 0.574221 0.613270 \n", "(10, 11, 12, 13, 14, 15, 16, 17, 18, 19) 0.644016 0.608664 \n", "(20, 21, 22, 23, 24, 25, 26, 27, 28, 29) 0.559857 0.614704 \n", "(30, 31, 32, 33, 34, 35, 36, 37, 38, 39) 0.382087 0.619587 \n", "(40, 41, 42, 43, 44, 45, 46, 47, 48, 49) 0.741344 0.601154 \n", "(50, 51, 52, 53, 54, 55, 56, 57, 58, 59) 0.415899 0.625590 \n", "(60, 61, 62, 63, 64, 65, 66, 67, 68, 69) 0.675124 0.601310 \n", "(70, 71, 72, 73, 74, 75, 76, 77, 78, 79) 0.745460 0.599734 \n", "(80, 81, 82, 83, 84, 85, 86, 87, 88, 89) 0.366792 0.618551 \n", "(90, 91, 92, 93, 94, 95, 96, 97, 98, 99) 0.498276 0.614549 \n", "(100, 101, 102, 103, 104, 105, 106, 107, 108, 109) 0.752076 0.595514 \n", "(110, 111, 112, 113, 114, 115, 116, 117, 118, 119) 0.604196 0.610233 \n", "(120, 121, 122, 123, 124, 125, 126, 127, 128, 129) -0.292603 0.630345 \n", "(130, 131, 132, 133, 134, 135, 136, 137, 138, 139) 0.529028 0.616538 \n", "(140, 141, 142, 143, 144, 145, 146, 147, 148, 149) 0.513520 0.619319 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cross_validate(Xb, yb, degree=2, n_splits=15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hyperparameter Grid Search" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [GridSearchCV]() function puts all the pieces together to scan a grid of one or more hyperparameters for a family of models. For example, the polynomial degree $P$ corresponds to a pipeline `poly__degree` parameter, which we vary from 0 to 5 below. The full output from `GridSearchCV` is detailed but unwieldy so we use the MLS `grid_search_summary()` function to create a summary table and plot:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def compare_models(X, y, max_degree=5, n_splits=3, seed=123):\n", " hyper_grid = {'poly__degree': range(max_degree + 1)}\n", " hyper_model = pipeline.Pipeline([\n", " ('poly', preprocessing.PolynomialFeatures()),\n", " ('linear', linear_model.LinearRegression(fit_intercept=True))])\n", " kfold = model_selection.KFold(n_splits=n_splits)\n", " cv = model_selection.GridSearchCV(hyper_model, hyper_grid, cv=kfold, return_train_score=True)\n", " cv.fit(X.reshape(-1, 1), y)\n", " return cv_summary(cv)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With a small dataset, a polynomial fit is very prone to overfitting and the training score continues to rise as $P$ increases. However, only the $P=1$ and $P=2$ models look at all promising on the test data, but are still worse than guessing the average $y$ value (which always has $R^2=0$):" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
mean_testmean_trainpoly__degreesplit0_testsplit0_trainsplit1_testsplit1_trainsplit2_testsplit2_trainstd_teststd_train
1-0.7270.62720.4040.731-2.2330.632-0.3530.5181.1090.087
2-1.0490.57710.4740.621-2.8190.628-0.8010.4811.3560.068
3-3.6080.0000-0.0480.000-7.5490.000-3.2260.0003.0740.000
4-11.5890.7324-1.7430.857-5.0190.714-28.0060.62511.6850.095
5-17.1660.65630.4080.740-51.5810.708-0.3240.51824.3370.098
6-158.5380.7875-0.8370.895-316.8560.716-157.9210.749129.0150.077
\n", "
" ], "text/plain": [ " mean_test mean_train poly__degree split0_test split0_train split1_test \\\n", "1 -0.727 0.627 2 0.404 0.731 -2.233 \n", "2 -1.049 0.577 1 0.474 0.621 -2.819 \n", "3 -3.608 0.000 0 -0.048 0.000 -7.549 \n", "4 -11.589 0.732 4 -1.743 0.857 -5.019 \n", "5 -17.166 0.656 3 0.408 0.740 -51.581 \n", "6 -158.538 0.787 5 -0.837 0.895 -316.856 \n", "\n", " split1_train split2_test split2_train std_test std_train \n", "1 0.632 -0.353 0.518 1.109 0.087 \n", "2 0.628 -0.801 0.481 1.356 0.068 \n", "3 0.000 -3.226 0.000 3.074 0.000 \n", "4 0.714 -28.006 0.625 11.685 0.095 \n", "5 0.708 -0.324 0.518 24.337 0.098 \n", "6 0.716 -157.921 0.749 129.015 0.077 " ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEJCAYAAABhbdtlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzt3Xl8VNX5+PHPLMlMNkI2QthB5Mi+gxHct1qkLq1ttfqrS11a/Vq1Ll3120VstRWXarVWUbTW2qoVd/0KVGWTLRC2AwECQvYQIPsyM78/ZjKZLJNMwszcmczzfr18mXvv3HufE+A+c5Z7jsnlciGEEEJ0xWx0AEIIISKXJAkhhBB+SZIQQgjhlyQJIYQQfkmSEEII4ZckCSGEEH5FRJJQSs1VSq3sYv9CpdR6pdQapdSNBoQmhBAxzfAkoZS6F/gbYO+wPw5YDFwAnAncpJQaHP4IhRAidhmeJIC9wOVd7B8PFGitq7TWTcAXwOlhjUwIIWKc1egAtNZvKKVGdXFoAHDMZ7saSO3pei0tDpfVaglSdEIIETNMXe00PEl04ziQ4rOdAhzt6aSqqro+3zArK4Xy8uo+nx+NpMyxIdbKHGvlhRMvc1ZWSpf7IzlJ7AROVkqlAzXAGcAfjQ1JCCFiS8QlCaXUVUCy1vqvSqm7gI9w9528oLU+bGx0QggRWyIiSWitC4FTPT+/6rP/HeAdg8ISQoiYFwmjm4QQQkQoSRJCCCH8kiQhhBDCL0kSQggh/JIkIYQQwi9JEkIIIfySJCGEEMIvSRJCCCH8ioiX6YQQQvTNuh2lvLemkKLKOoZkJLIgdxRzJ2QH7fqSJIQQIkqt21HKs8u2e7cPldd6t4OVKKS5SQghDOZ0uThe18Tx2ibvvkPlNazYfJiKo/Xefa/+326efivfu/3W5/u6vN57aw4ELTZJEkIIEUSHy2s4VF7j3S6qqGXZF/vZW9S2PM4/l+/h/ue/pLnFAUBNfTN3PPEFL3+kvZ/ZWVjFyx9pCkvapv/ee/g4eQUVuFwugHYJxFdxZW3QyiPNTUKIfuNE2uddLhcuwGxyr71TcOgYDU0tTBqTAUD50Xo++vIgp4xIY9YpgwB467N9fLaliPu+N4PB6YkA/HbpBnLSk3jgutkAlB6p4z9f7McWb+GkIe5106qqG6k83kB9o4M4q4Uku5UZ47I4aWjbumqTxqRzU9IExgwZ4N33k+9MJc5qweSJcUhmEofKOyeEnIykXvzWuidJQgjRL/hrnz9cXkP6ADtnThuCyWSipr6ZpR9pRuekcNHckQB8uO4g/1pZwJ1XTPUmhRc/3MXx2iae+LF71eT6xhaWbzqMyWTyJgmLxYQ93kKLw+m977kzh5GSEO/dPmlYKnd/d1q7B/fN35jofdADWMxmbrt8crvy5GQkdXrYJ9rj2m0vyB3Vrsxt+0cG8BsLjCQJIURUqKpupPxoPaNzUoizWnC5XCz9SDMgMZ7LzhjDe2sKuzzv/zYeoqHJwakTs7HHWzGbYMOuMlpanFw01/2Z9AE2ThqaSpy1rQX+gtnDaWp2eLdzMhL5zfVzSE1uSwDfmDeab8wb3e5+V5w1tt32gMR4JoxKb7fPN0GciNZa0ntrDlBcWUtORhILckfK6CYhRHTr2LSzpaCCmvpm5k3OAdzt+i+8v4s54wdx4ZwRALyzupCVmw/z2xvmMDQrGZPJxPqdZaSl2LjsjDEUVXS9dHFTs4ObFk7AYnbfK8FmZfH/zCfR1vb4mzM+mznj2z9Yz5g6pN12nNXCsEHJQSl/MM2dkM3cCdkhW7JVkoQQImjqG1s4VttEdloCJpOJhqYW3l97kKxUO6d7HrrLNx3in8sLuPWySUw5KROANz/bR9nRem+SMJtNHCytRg0f6L325DHpJNmtJPg83O+/dhZJCe4mmCGZiV22zw/JTObUiYO92yaTidSk+E6fE12TJCFEPxbMF612f3UUh9PF+JFpAOwrOs67qwuZN3kwM5W7jf65d3aQV1DBEz8+neSEOMwmE++uLmTiqDRvkhiQGM/QzCQs5ramnUvmj6bF4cTlcmEymRicnshf7zmrXbPM9JOzmH5yVruYBqUlen8OR/t8LJIkIUQ/5a8j1+VyMXVspvcbeU19M+t2lJKdluDttP1w3UE+3fgVt39rKsM9TSxPvZVPoj2Oh246FYDGphbyCioYkZ3sTRITR6eTkhjnHaIZH2fhvqumkzbA7o1j1imDvB2/rWaMa//w70ubfTja52ORJAkRM0I9fUGwtX6rBne7+tGaRhLtcSR7mlcOllZTebyBSaMziLOacTidfLrxMAOT45kzPttvR+6LH+zC6YJn7z4Tk8lEXUMzf/9kN/MmDfYmCRfuPoPGpraO24tzRxEf1/btf+ywgfz5jtPbNf+cO3NYp/upEWkn+JsIXKjb52ORvEwnYkLrt+pD5bU4nS7vt+p1O0oDOt/hdNLQ1OLdbnE4OVhaTVlVW2dpUUUta7aXUFXd6N23fNMh3l1d6N0uP1rPX/6zjc+3Fnn3fbjuIL/62zqKKtra0+/68xc88MKX3u1dB6v46bNr+WxL23kfrDvIk2/kU1PfDLi/fb/26R5Wbj7siafrjtxmh5OJo9K8wzbTUuzccslEbwcxwEVzR/LHH81j7LC2cfvnzx7OmdOGerfjrGYS7XFBG6kjIpMkCdFvOF0uGn2GLFbXNZFXUEFxZa3fb9XvrSlk8etbeO3TPd59G3U59zy9ql0CefSfW/jRo595H6y19c3875L1vPHftmkRtuyt4Ll3dnCgtO0b7H/zivhg3UHvdmOTg/W7yjjg8xZtfWMLR2saaWppi31EdgpDs9pG0mQMsDN/cg5DM9vGzc8dn823zx6LLc4CuEcK3Xb5ZC4/8yTA3ZHblaGZyfz4CvdLWeB+2M8Znx2RI3eE8aS5SUSc8qP11DW0MHJwCuB+2K/KL2FIZhJTTnI3h3y2pYjV20q45kLlfXD+5KlV2OOt3jbzr8pqeOLfW7l0/mi/36qLK+soqqijrrHZu889UtLkbVcHGDNkAHFWM06nCyxgt1k5b+Ywb4wAE0elk/A1K8Oy2h7k1150Cg5n23UGZySy+LZ52OPb/ulddsYYLjtjTLu47rhiarvtoVnJXL9gfLt9007O7FQe37Z96cgVwSBJIkYFu33e6XRR19iC1WLyPgALDh2jtKqOuROysVrMNDY7+Psnu8nJSPS+6boqv5h/rSjg+187hemeB9wzb2/jq7Ja/nrPWQDUNbbw+ooC5k/J8SaJo9WN7P7qKNW1TeBJEqeMSPOOuwcYnJ7IFWedxMnDB7JBl/mdvuAX18xs9xLV9HFZ3lhafdPz7byVLc7CVeePa7dvRHYKI7JT2u0bnTOg3bbVYiY12dbNbzJ4pCNXBIMkiRjU3fTC08Zm8lVZDSmJcWR75qLJ31eJPniU82cN8z7g/vjaZpLscfzw0kkA5BVU8Oc38/nuOWO5wNO2/fGGr9iwq4xJYzJITYrHYjbxxdZixo9M8yaJ+DiLe6oBn2btueOzUcObcDpdmM0m0pJt3P7NKWQNbBsh8/XckVw8b1S7pHDzNya2K2f6ADsXneq+T3ffqm3xlr79IqOAdOSKEyVJIgb5b58/QE5GIote2ch5M4d5vynvLKziwy8PMmNcljdJlBypIyWx7YWkzFQ700/OJCM1wbvvzKlDmDQ6HZtnRIzVYuahm08lyWf+mdmnDGJ2h+GQF/h0oII7kXRsWrFaetedJt+qhegbk2+7a39QXl7d5wLFwrctp9PFTY+swNnFb8liNvHobfP46MuvOHlYKlPHuh/MpVV1VNc2MzQryTvc0Xd4ZrSJhT/njmKtzLFWXjjxMmdlpXT5D1pqEjGksdnBn17Lw2Ix42xxdjqek5FESmI83zqrfft7dloi2R2GukdrghBC9I6hSUIpZQaeBqYCjcAPtNYFPsefAOYBrenxEq31sU4XEgGxxVnIGpiA0+ViX9HxTsdl1IsQoiOjaxKXAnatda5S6lTgT8AlPsdnABdqrSsMia4fqKpuZNu+Su+8Odd9/RSsFrNndJO0zwshumd0kpgPfAigtV6rlJrVesBTyzgZ+KtSKht4Xmv9gjFhRieXy8XTb+Wzr+g4I7JTGDk4xdvhK6NehBCBMPqN6wGAb/ORQynVmriSgCeBq4GvAT9SSk0Jc3xRqXUwgslk4rvnnczVFypGZMvbtEKI3jO6JnEc8H37yKy1bp0gpw54XGtdB6CUWo6772JrdxdMS0vEau37uPesrJSePxTBNuws5eX3d/Kbm3NJTbaRlZXCqT2cE+1l7gspc/8Xa+WF0JTZ6CSxClgIvO7pk8j3OTYOeE0pNQN3jWc+8FJPF6yq6nr6hUD0h6aXnXsrOFBynLVbDneafrkr/aHMvSVl7v9irbwQlCGwXe43Okm8BZyvlFqN+53b65RSdwEFWutlSqm/A2uBZmCp1rrzK7OCg6XVDBuUjNlk4oLZw5k6NqPTAupCCNEXhiYJrbUTuKXD7l0+xx8GHg5rUFFmVX4xL7y3k6vOH8e5M4dhNpskQQghgsbojmtxgiaNTmf0kAGMzI699lchROhJkogyDqeTd1cXetcjSE228YtrZrZbHEYIIYJFkkSU2Xv4OG9+to9//3evd59MkSGECBWjO65FAJwuFw6HkzirhXHDB3LDgvFdLjgjhBDBJjWJCFdT38zif+bx9092e/fNm5zTbrptIYQIFalJRDh7vIXjdc1YLGZaHM5er6MghBAnQpJEBDpe10RxRS1qRBpWi5l7rpxOkt0qfQ9CiLCTr6URpsXhZNHSjTz5Rj5HaxoBSE6IkwQhhDCE1CQijNViZkHuSGobWhjgszyoEEIYQZJEBNAHq1ix+TA3LpyAxWz2rv0ghBBGk+amCLAyr4j1u8ooOCSL7gkhIovUJAxytKaRgck2AL53/jjOmzWMk4bIW9NCiMgiNQkDrNh8mHv/sprdXx0F3B3TkiCEEJFIkoQBhmUlkZpk864gJ4QQkUqSRBg4XS5WbD5MTX0zACcPG8hDN5+KGpFmcGRCCNE9SRJhsG57KS9/pPn3yrZJ+eTNaSFENJCO6xBpbUoymUzMnZBNUWUt580abnBUQgjRO/J1NgSO1zXx5zfz+W9eEQBms4lvnnkSqUnycpwQIrpIkggBh8OFPniUvIIK6ZwWQkQ1aW4KkrqGFmoamhk0MIG0FBu/+H8zyU5PlDmXhBBRTWoSQVDX0MwDL6zjz2/k09ziBCAnIwmzJAghRJSTmkQQJNrjmDI2k5SEOCQvCCH6E0kSfbSv6Dg7DxxhQe4oAK4+f5w0LQkh+h1JEn3gcrlY+uEuviqrYca4LHIykiRBCCH6JUkSvdDc4iDOasFkMnH9gvHU1jeTk5FkdFhCCBEy0nEdoE83HuKnz671rhY3IjuF8aPSDY5KCCFCS5JEL7Q4nJQfrTc6DCGECBtpbvLD5XKRt6eCqWMzMZtNnD1jKHMnZJOcEGd0aEIIETZSk/Djwy8P8uSb+Xyy4SsAzCaTJAghRMwxtCahlDIDTwNTgUbgB1rrAp/jNwI3Ay3A77TW74YijnU7SnlvTSFFlXUMyUhkQe4o5k/O4UBJNbPUoFDcUgghooLRNYlLAbvWOhf4KfCn1gNKqcHA7cA84ELgIaWULdgBrNtRyrPLtnOovBan08Wh8lqeXbadHYVV3HLJJDJS7cG+pRBCRA2jk8R84EMArfVaYJbPsTnAKq11o9b6GFAATAl2AO+tKfSz/0CwbyWEEFHH6I7rAcAxn22HUsqqtW7p4lg10ONC0GlpiVitloADKKqs63J/cWUtWVkpAV8nmsVKOX1Jmfu/WCsvhKbMRieJ44BvqcyeBNHVsRTgaE8XrKrq+qHvz5CMRA6V13ban5ORRHl5da+uFY2yslJiopy+pMz9X6yVF068zP4SjNHNTauArwMopU4F8n2OfQmcrpSyK6VSgfHAtmAH0Dr3Uuf9I4N9KyGEiDpG1yTeAs5XSq0GTMB1Sqm7gAKt9TKl1BPA57iT2S+01g3BDmDuhGzA3QdRXFlLTkYSC3JHevcLIUQsM/W3ldPKy6v7XCCposYGKXP/F2vlhaA0N3U5S6nRzU1CCCEimCQJIYQQfkmSEEII4ZckCSGEEH5JkhBCCOGXJAkhhBB+SZIQQgjhlyQJIYQQfkmSEEII4ZckCSGEEH4FlCSUUok+P2eELhwhhBCRpMckoZR6EnhVKbXIs+u3oQ1JCCFEpAikJpGqtb4U+EIpdX+oAxJCCBE5AkkSTQBa6/eBg8DFIY1ICCFExAgkSSxp/UFr/SLww5BFI4QQIqL0mCS01qs6bL8XunCEEEJEEhkCK4QQwq+Ali9VSmUDtwONwFNa60rP/gzgG1rrJd2dL4QQIjoFWpP4BzAXGAr8Syl1ulJqOVAMXBui2IQQQhgsoJoEMFRrrQCUUhOA9cBfgO9prYtDFZwQQghjBZokalt/0FrvUEod1lrfHaKYhBBCRIhAk8RYpdQrwHbPf02hC0kIIUSkCDRJLABmeP67ClBKqVLgS+BLrbVM1SGEEP1QQElCa/058HnrtlLKDkzFnTSmhyY0IYQQRgu0JtGO1roBWOf5TwghRD8lL9MJIYTwS5KEEEIIv3rd3KSUugqYCDwIfEtrvTToUQkhhIgIvUoSSqnfA8OAmcAfgOuUUlO11j/py82VUgnAK8AgoBr4vta6vMNnlgEZQDNQr7W+qC/3EkII0Xu9bW66ELgGaNBaHwfOB07kof1DIF9rfTqwFPhlF58ZC8zXWp8lCUIIIcKrt0nC6fm/y/N/m8++vpgPfOj5+QPgPN+DnokFBwLvKKW+UErJgkdCCBFGve2TeB34J5CulLoDd63i1UBOVErdANzZYXcpcMzzczWQ2uF4PPAn4HEgHVillPpSa13m7z5paYlYrZZAQupSVlZKn8+NVlLm2BBrZY618kJoytyrJKG1/oNS6kLgADACeEBr/W6A5z4PPO+7Tyn1JtBaqhTgaIfTSoBntNYtQJlSajOgAL9JoqqqLpBwupSVlUJ5eXWfz49GUubYEGtljrXywomX2V+C6W3H9RKt9XXAR32OpL1VwNdxT+9xET5vdXucB9wGLFBKJQOTgJ1BurcQQoge9LZPYpLnYR0sfwEmKqW+AG4Cfg2glHpYKTVHa/0BsEcptRb4GPi51roiiPcXQgjRjd72STiBg0opDdS37tRan9OXm2ut64Aruth/r8/Pd/Tl2kIIIU5cb5PEvT1/RAghRH/R2yTxGXALcK7n3BXAk8EOSgghRGTobZJ4GDgZeAEwAdcBowFpEhJCiH6ot0niAmC61toJoJR6D8gPelRCCCEiQm9HN1mBuA7bjuCFI4QQIpL0tibxd2CFUuofnu0rgX9083khhBBRrFc1Ca31IuAJ3G9bjwZe1Vo/GIrAhBBCGK9XSUIpdTtwr9b6HtzJ4lal1E0hiUwIIYThetvcdBMwF0BrXaiUmol7neu/BjswIYJtQ2keHxUup6SujMGJg7hw1DnMyp5mdFhCRLTeJok4oNFnu4m2acOFiFgbSvNYsr1twuKi2hLvtiQKIfzrbZL4D7BcKfU67uTwTeDtoEclRJB9VLi8y/0fH1ghSUKIbvS24/o+3H0RChgDPK61/lUoAhMiGFwuF/uPHaSotqTL48W1pWGOSIjoEnBNwrMq3A6t9b+VUg7gBqBWKfW+1ro5ZBEK0QfHm6r5smQTa4o3UNJNIshJyg5jVEJEn4CShFLqbuA7wPeVUlOAV4AfA9OAR5BpOUQEcDgd7DiiWVO0nvzKnThdTqwmCzMGTSHTns7HB1d2OueCkWeHP1AhokigNYlrgFytdZ1S6vfAMq3135RSJmBH6MITomcltWWsLd7AupKNHG9yr8w1NDmH03LmMGvwNJLjkgDISRrMSztf8x6/YOTZ0h8hRA8CTRIuz9oPAGcDTwNorV1KqZAEJkR3Gloa2FS2lTXF69l37AAAidYEzhx2Grk5sxmeMrTTOXNyZvCqfoMRqUO4a/qt4Q5ZiKgUaJJoUUoNBJKB6bhXiUMpNRJoCVFsQrTjcrnYe6yQNUXr2VS2hSZnMyZMjE8fR27OLKZkTiTOEtftNewWG/UtDWGKWIjoF2iS+D2Q5/n837TWxUqpbwOL8Cw5KkSoHG08xrrijawpXk95fSUAGfZ0cnNmMTdnJun2tICvZbNKkhCiNwJKEp4RTauBTK31Vs/uGuAHWuuVoQpOxK4WZwv5FTtZU7yeHZUaFy7izFZmZ8/gtCGzGDtwDGZTbycxdtckKhtqQxCxEP1TwENgtdZFQJHP9vshiUjEtMM1xawpXs/6ks3UNLsf5iMHDCc3ZzazsqeSYE04oevbLDYaWhpxuVyYTKZghCxEv9bbN66FCLq65no2lOaxpng9B6sPAZAcl8Q5w08nN2c2Q5IHB+1edqsNFy4aHU3YrbagXVeI/kqShDCE0+Vkd9Ve1hSvZ0v5NpqdLZgwMSljPLlDZjMp4xSs5uD/9bRb3Imh0dEoSUKIAEiSEGFVWV/F2pINrC3ewJGGKgAGJWaSmzObOYNnMNCWGtL7tyaGhpYGUm0DQnovIfoDSRIi5JoczWwt38aa4g3oqgJcuIi3xJObM5vcnNmMSR0Ztv4Bm6cm0eBo7OGTQgiQJCFCxOVy8VX1YXcndGke9S31AJyUOorcnNlMHzTFkOYe3+YmIUTPJEmIoKppqmV96WbWFK/ncE0xAKnxKZw+8mxOzZlFdmKWofHZvM1NkiSECIQkCXHCnC4nO4/sZk3RerZW7MDhcmA2mZmWNYncnNmMTx+HxWwxOkygrSYhzU1CBEaShOizsroK78R6RxuPAe6pt0/Lmc3swTNIiU82OMLOpLlJiN6JiCShlLoMuEJrfVUXx24EbsY9R9TvtNbvhjs+0abR0cRmz8R6BUf3A2C32Jk/9FROy5nNiJRhEf2SmjQ3CdE7hicJpdTjwIW454bqeGwwcDswC7ADXyilPtFay7/wMHK5XOw/fpA1RevZWJZHo6MJgHFpY8nNmcW0rEnEW+INjjIwUpMQoncMTxLAatxrZ9/cxbE5wCpPUmhUShUAU4D1YYwvZh1rrObLko2sKd5AaV0ZAGm2gZwz/AxOzZlFZkK6wRH2nrcmIUlCiICELUkopW4A7uyw+zqt9T+VUmf5OW0AcMxnuxro9m2rtLRErNa+d5JmZaX0+dxo5VvmFqeDzcXbWLFvNZuKt7lXdzNbOW34TM4ecxqTB52C2dz7ifUiRYs9AwCT1Rlzf9ZS3v4vFGUOW5LQWj8PPN/L044DvqVOAY52d0JVVV13h7uVlZVCeXl1n8+PJhtK8/iocDkldWUMThzE3JyZ7nWhizdR3VwDwPCUoZ6J9aaRFJcIQGVldM+gWtvoXv7kaG1NzPxZQ2z93YbYKy+ceJn9JZhIaG7qzpfAg0opO2ADxgPbjA0p+m0ozWPJ9le920W1JbxV8B7QurrbPM/qbkOMCjFk7NLcJESvRGSSUErdBRRorZcppZ4APgfMwC+01rJizAn6qHB5l/vTbAN54NR7elzdLZrFm+MwmUwyukmIAEVEkvAsXLTSZ/tRn5+fA54Lf1T9V4mnE7qjY03H+3WCADCZTCRY7TK6SYgARW8PpOizwYmDutyfk5Qd5kiMkWC1S01CiABJkohB5404s8v9F4w8O8yRGMMeZ5OahBABiojmJhFeiXHuJUCT45Kob6lncFI2F4w8m1nZ0wyOLDwSrHZKHRVGhyFEVJAkEYM2l+UDcMuUa5kzdlLMDRVMiLPR4mzB4XREzMSDQkQqaW6KMS3OFrZW7GCgLZWRA4YbHY4h7FY7IMNghQiEJIkYo6v2Ut9Sz/SsyZhNsfnHn9CaJKTzWogexeZTIobllW0FYNqgyQZHYhx7nEzyJ0SgJEnEEIfTwZby7aTGpzAmdaTR4RgmQZqbhAiYJIkYsufoPmpb6pgaw01NAAlx7iTRKM1NQvQodp8UMWizp6lpegw3NUHb/E31DpnhRYieSJKIEU6Xk7zybSTHJTF24GijwzFUa3OT1CSE6JkkiRhRcHQ/Nc21TMuaFNNNTdDW3CR9EkL0LLafFjGk9QW66YOmGByJ8Vrfk5DRTUL0TJJEDHA3NeWTFJfIyQPHGB2O4RLj5D0JIQIlSSIG7Dt2gONN1UzNnCjTUNDWcS01CSF6JkkiBuR5mpqmSVMTIH0SQvSGJIl+zulysrk8nwRrAirtJKPDiQgyukmIwEmS6OcOHP+Ko43HmJI5AatZJv0FsEtNQoiASZLo59pGNcX2C3S+rGYLVrNVkoQQAZAk0Y+5XC42l+djt9g5JX2c0eFEFLvFJs1NQgRAkkQ/drD6EEcaqpicOYE4aWpqx2axSU1ChFVBwR42bdrQp3M3bdrA/PmzqKurC3JUPZMk0Y9JU5N/dqtN3pMQYfWzn/2E/fv39uncyZOn8vbbH5KQkBDkqHomSaKfam1qslniGS9NTZ3YLDYaHY24XC6jQxEx4kT+rsXFxZGRkYnJZApiRIGRJNFPHaoppqK+kkkZ44m3xBkdTsSxW2y4cNHkbDY6FGGAdTtKuf/5dfzgDyu4//l1rNtRGtL73XbbTZSUFLN48SN861sLmT9/Fi+++De+/vVzufvu2wH4+OMP+P73v8vZZ+dywQVnct99d1JZWQF0bm6aP38W77//DtdffzXnnjuPG2/8Pps3bw5J7JIk+qk877Tg8gJdV2yet66lySn2rNtRyrPLtnOovBany8Wh8lqeXbY9pIli0aJHGDQom5tvvpUHH3wEgNWrv+CZZ17gRz/6Mfn5W1i06NdceeU1/OMfb/LQQ39kz57dLF36gt9rPvfcX7jxxlt45pklxMXFcf/994ckdkkS/ZDL5WJT+VbizXFMzFBGhxOR7JbWqTlkTYlod8/Tq3nm7W3e7Y26jBt+9zFf7mx76D/3znbueXo1LQ4n760p7PI6r68o4J6nV7O98Ih33+LXt3D/8+u828WVtdzz9OpexzhgQCpms5nExEQGDBgAwLe/fSUjRoxkzJiTsNls3HffL/na1xYweHAOM2fO5vSB0ajjAAARI0lEQVTTz6SwcL/fa15++bfJzZ3PySeP46qrrmH37t00NTX1OraeyJCXfqi4tpSyugqmZ00m3hJvdDgRqXX+JhnhFHuKKroeIXS0ppH0FHvY4hg6dJj353HjTsFut7NkyXMUFu7nwIFC9u/fy+TJU/2eP2LECO/PiYlJADgcjqDHKUmiH5IV6HrmrUlIc1PUe+RHp7XbnqkG8bX5J1FeXu3dd+PCid6fh2Qmcqi8ttN1hmYm85sb5rTbd+e32z+kczKSOt2vr2w2m/fn9evXce+9d3DuuRcwffoMvvOdq/j44w8oKNjj93yrtXNfYygGYkREklBKXQZcobW+qotjTwDzgNY/8Uu01sfCGV+02VyeT5zZysSMU4wOJWLZLFKTiFULckfx7LLtXewfGdL7djcy6e233+Scc87nl7/8tXffCy/8NaTxBMrwJKGUehy4EMjz85EZwIVa64rwRRW9SmpLKa4tZWrmRO/iOqIz73ThUpOIOXMnZAPw3poDFFfWkpORxILckd79oZKQkEBhYSHjx0/sdCw1NZXNmzei9S4SEhL44IN3Wbt2NRMmTAppTIEwPEkAq4H/ADd3PKCUMgMnA39VSmUDz2ut/Xf3CzaXuTvwpklTU7ekJhHb5k7IDnlS6OiKK67kyScX88knH3Y6dsMNN/PQQ7/htttuxGazMWnSFG699Q6WLHmOxkZj/46GLUkopW4A7uyw+zqt9T+VUmf5OS0JeBJ4FLAAK5RSG7TWW0MXaXTbXL4Vq8nC5MzxRocS0eySJESYLVx4KQsXXtrlsfT0DB555PFO+6+88moAZsyYxRdftE3p4ftz63Gtdbt+mGAJW5LQWj8PPN/L0+qAx7XWdQBKqeXAVMBvkkhLS8Rq7fvqa1lZKX0+12jF1WUcrilmxpDJjMgZFPB50VzmvsrOSAPAYoud8sdKOVvFWnkhNGWOhOam7owDXlNKzcD9Tsd84KXuTqiq6vsEWFlZKSHJxOGyvHAtABNTxwdcjmgvc19kZaXQUOMeKnjk+PGYKH+s/TnHWnnhxMvsL8FEZJJQSt0FFGitlyml/g6sBZqBpVrrzsMSBOBuajKbzEzJnGB0KBHP29wkHddCdCsikoTWeiWw0mf7UZ+fHwYeDn9U0aWi/ggHqw8zIV2RGJdodDgRr3VajkbpkxCiWzItRz+RVy7TgveGdFwLERhJEv3E5rJ8T1NT5zHYorPW6UqkuUmI7kmS6AeONFRRePwg4waeRHJ8ktHhRAWzyYzNEi/NTUL0QJJEP5BXLi/Q9YVdljAVokeSJPqBzWX5mDAxNUuamnrDbrXLtBxC9ECSRJQ72niMfccKGTtwNAPiY+/loRNhk5qECKOCgj1s2rSh5w/2oLi4iM8/X3niAQVIkkSUa21qkhXoes9usdHsbMbhDP4c/EJ09LOf/YT9+/ee8HUWLfo1W7b4mw81+CRJRLk8aWrqs7Z3JYK/mpcQHQVrrYdQrBnRnYh4mU70zfGmagqO7mdM6kgG2lKNDifqtC1h2khiXILB0Yhw2lCax0eFyympK2Nw4iAuHHUOs7Knhex+t912EyUlxSxe/AgrVnzKr3+9iMce+yNr164mMTGB3Nz53HbbnSQnJwPu9SVefXUpZWWl5OQM4ZprruOiiy7mwQf/l7y8TeTlbWLlyk/597/fCVnMrSRJRLEt5dtw4ZKmpj5qrUnUtzSQZnAsInw2lOaxZPur3u2i2hLvdqgSxaJFj3DttVdx2WXf4pJLLufee+8kMzOTZ599gaamJp566nEeeODn/OlPT6D1Lh577BF++9vfM3bsOFav/oJFi37NpElT+PGP7+arrw4yduw4brih0+oKISFJIoptLnO/ZT0ty/iFSaKRb01CRKc3C971/jvwZTGbcDi7bpY51ni8y/1Ld/yTt/d+ENB9pw+azOVjLw44zgEDUjGbzSQmJlJQsIe9e/fwxBPPEB/vfqnzgQd+x6WXXsS+fQWUlBRjMpnJzs5h8OAcLr/8CoYPH87AgWkkJydjtVqx2+2kpYXnq40kiShV3VTDnqP7GD1gBGn2gUaHE5Vkao7Y5HB1PVDB3/5g279/Lw0NDSxYcG6nYwcPHiA3dx6TJ0/luuuuYvToMZx22uksWLCQlBRjRi9KkohSWyu243Q55QW6E2CTJUyj3uVjL+7yG31302Y/uO5RimpLOu0fmpzDz+d0XBct+BwOB4MH57B48VOdjqWnp2Oz2XnssafIz9/CqlWfs3r15/zrX6/x8MOLmTVrTsjj60hGN0Wp1ir29CxJEn0lNYnYdOGoc7rcf8HIs0N6X5PJBMDIkaOpqCgnMTGRYcOGM2zYcKzWOP7858VUVVWxadMGXnrpeaZMmcYPf/g/vPzy6yilWLlyebvrhIskiShU21yHripgRMowMhLSjQ4nask617FpVvY0rpt4FUOTczCbzAxNzuG6iVeFdHQTQEJCAoWFhYwbpxg9egwPPPBzdu3ayZ49u/ntb3/F4cOHGDw4B7vdzpIlz7Fs2VuUlBSzbt0aCgsLGT9+guc6iRw+/BXl5WUhjbeVNDdFoa0VO3C6nDIt+AmyS3NTzJqVPS3kSaGjK664kiefXMy2bVv4wx8W8/jjf+T222/BbDYxffosfvWr32KxWJgwYRI//emveOWVF3nssUcYODCN7373eyxY8A0ALrvsmzz44P9y7bVX8s47n2A2h/a7viSJKJRX5l7ie5o0NZ0QqUmIcFq48FIWLrzUu/3gg4/4/exFF13MRRd1PXoqN3c+7777f0GPzx9pbooy9S317Dyyh2HJQxiUmGl0OFFNhsAK0TNJElEmv2InDpdDmpqCwG61A7LwkBDdkSQRZWRUU/BITUKInkmSiCINLQ3sOKIZkjSY7KRBRocT9Vrfk5CahBD+SZKIItsqd9HibJEX6IIkzmzFYrJIx7UQ3ZAkEUWkqSn4ZAlTIbonSSJKNDqa2F65i+zEQeQkZRsdTr9hs9rkPQkhuiFJIkpsr9xFs7OZ6YMmh/21/P5MahJCdE+SRJTIk6amkLBZbDQ6GsO+2pcQ0UKSRBRocjSTX7mTrIQMhibnGB1Ov2K32nC6nDQ7W4wORYiIJEkiCuw8omlyNDF90BRpagoym7wrIUS3JElEARnVFDre6cKl81qILhk6wZ9SKhV4BRgAxAN3aa3XdPjMjcDNQAvwO631u2EP1EDNzhbyK3aQYU9jeMpQo8Ppd7wv1ElNQoguGV2TuAv4VGt9JnAt0G6pJqXUYOB2YB5wIfCQUsoW7iCNtOvIbhocjUyTUU0hIVNzCNE9o6cKXwy0/uu0Ag0djs8BVmmtG4FGpVQBMAVYH74QjdXW1DTF4Ej6J7t3ao6Of/WEEACmcA39U0rdAHRcQPY6rfV6T43hA+AOrfV/fc65Gpistb7Ps70UWKq1Dt9k6kIIEcPCVpPQWj8PPN9xv1JqMvAacLdvgvA4DqT4bKcAR0MWpBBCiHaM7rieAPwL+I7WeksXH/kSeFApZQdswHhgWxhDFEKImGZ0n8RDgB14XCkFcExrfYlS6i6gQGu9TCn1BPA57k72X2itpfFYCCHCJGx9EkIIIaKP0UNghRBCRDBJEkIIIfwyuk8iIiilzMDTwFTc7238QGtdYGxUoaeUmgv8QWt9ltGxhJpSKg54ARiFexDE77TWywwNKsSUUhbgOUABDtxDzvcaG1V4KKUGARuB87XWu4yOJ9SUUpuBY57N/Vrr64J1bUkSbpcCdq11rlLqVOBPwCUGxxRSSql7gWuAWqNjCZOrgUqt9TVKqQxgM9CvkwSwEEBrPU8pdRbwKP387zV4vxA8C9QbHUs4eEZ/Eqove9Lc5DYf+BBAa70WmGVsOGGxF7jc6CDC6F/Ar3y2+/3c4Frr/wA3eTZHAqUGhhNOfwSeAYqMDiRMpgKJSqmPlVLLPV90g0aShNsA2qpqAA6lVL+uZWmt3wCajY4jXLTWNVrraqVUCvBv4JdGxxQOWusWpdRLwJO4y92vKaWuBcq11h8ZHUsY1eFOjBcCtwB/D+bzS5KEW8c3u81a637/TTPWKKWGAyuAl7XWrxodT7horb8PjAOeU0olGR1PiF0PnK+UWglMA5Z6pv3pz3YDr2itXVrr3UAlELTVyfr1t+VeWIW7/fZ1T1Ut3+B4RJAppbKBj4HbtNafGh1POCilrgGGaa0fwv1t04m7A7vf0lqf0fqzJ1HcorUuMS6isLgemAz8SCk1BHfLSHGwLi5Jwu0t3N8+VgMmIGgjA0TE+DmQBvxKKdXaN3GR1ro/d26+CSxRSn0GxOGeQFNmLOh/ngdeVEp9AbiA64PZEiJvXAshhPBL+iSEEEL4JUlCCCGEX5IkhBBC+CVJQgghhF+SJIQQQvglSUJEHKXUKKVUYRf7Y24onlJqtFKq07K/IbzfSs88T0IAkiSEiHQjgZOMDkLELnmZTkQdpdTnwG+01p8opUy4pyU4E1gNvA6c7/no9VrrzUqpscBfgAzcbx7/j2f/i559Y4F7cc9v1NX5ZwIPAonAQOBOrfXbXZxvB34CJOCejvx6rfVqz5u/m3BPJGkH7gN+DEwAFmutFyulkoGngEmABfcU7v8AngDGKKWe0lrfqpT6KfBtz2c+8lxrJO4JKiuAeq11a/wopTYBN2qtN3qmDj8AzPD8vjrF6nPeWcD/ts4s6inrSq31i0qp/wfcgftL5kbgVnlJr/+SmoSIVEOUUnm+//kcewH3NOcAp+NeD711xs9arfV04H7gJc++l4B7tdYzcM+K+prPtSq11uO11u90c/7/4F5jZAbwA+B3Hc8H3sM9udrFWuupwMPAz3w+Z9JazwHewJ2MLvfEfr/n+C+BjVrrmcAZwC+UUmOA24ENngTxNWAmMBuYDgwFvuc5XwFX+yYIj5eBKz0/nwNswZ1MuovVL6XUROBG4DSt9TSgDLg7kHNFdJKahIhURZ6HkJdPn8TrwCLPZHXfB170+dhfAbTW7yilXlJKDcP9UF2ilGr9TLJnTQmAdR3u2/H8TNxrUVyslLoCOBVI9vn8Os/nnUqpy4CFyn2js2g/T9IHnv8fANZqreuAA0qpgZ795+Ge7vl6z3YSMBGo9rnGecBc3N/ewV0LOAh8AZRprQvp7B/AGqXUPbiTxSsBxNqds4GTgbWe32c87lqS6KckSYioo7WuVUq9D3wLOBe41eew75w1ZtzNMg2+CceTOI54NjvO3dTxfAfwOe7ZY1cCnwK+M8jWe66ZDHwJvAJ8BmwFbvP5XJOfe7Sy4K4JbPJcL9sT47wOn3lMa/2o5zMDPdfK7KIcAGitS5RSGnciOA+4LYBYwT0HkMlnO84nhte11rf7lFueI/2YNDeJaPUC7n6CDzq0h38XwPNNeafW+gCwRyl1tWf/+bgfjP60Ox/3g3Ic7mahD3Cv7Gbp4rxxuB+si3AnlMv9fM6f5cAPPffOwf3gHoE7CVh9PnONUirZs17Af3Anyp68jHu1xRWeGkwgsVbg7guxK6XScTeNgTtRXqaUGuTpD/oL7v4J0U9JkhBRSWu9CveDbkmHQ/M8/Rd3426KAne7/Q+UUluBh4DvaK39Dadtd77W+gjuWTa3404aKbibhTquy7AFyAN2eT5bjrtDOVC/BhKUUttwJ4N7PetR7wQGKqVe9vSbvIG7iWub534v+bugj7dwNxG9EmisWuvtuPtZtuNe1e9zz/4tnliXe45ZgN/3opwiysgssCLqeL7BTgKWejqZW/cXAmf5aZsP5LondL4Q/ZHUJEQ0ugP38M+O7ehCiCCTmoQQQgi/pCYhhBDCL0kSQggh/JIkIYQQwi9JEkIIIfySJCGEEMIvSRJCCCH8+v8E1YH5yBc4LwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "compare_models(Xa, ya)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With a larger dataset, the training score is stable over a wide range of $P\\ge 1$ and the test score decreases very slowly. You could make a case for either $P=1$ (less overfitting) or $P=2$ (better test score) from the graph below:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
mean_testmean_trainpoly__degreesplit0_testsplit0_trainsplit1_testsplit1_trainsplit2_testsplit2_trainstd_teststd_train
10.5670.62020.5930.6100.6000.6110.5090.6380.0410.013
20.5550.62330.5630.6190.5900.6120.5120.6390.0320.011
30.5370.56710.6070.5360.5900.5400.4150.6250.0870.041
40.4990.64040.5750.6200.5840.6120.3370.6880.1140.034
50.4970.64250.5690.6230.5860.6120.3360.6890.1140.034
6-0.0140.0000-0.0170.000-0.0230.000-0.0010.0000.0090.000
\n", "
" ], "text/plain": [ " mean_test mean_train poly__degree split0_test split0_train split1_test \\\n", "1 0.567 0.620 2 0.593 0.610 0.600 \n", "2 0.555 0.623 3 0.563 0.619 0.590 \n", "3 0.537 0.567 1 0.607 0.536 0.590 \n", "4 0.499 0.640 4 0.575 0.620 0.584 \n", "5 0.497 0.642 5 0.569 0.623 0.586 \n", "6 -0.014 0.000 0 -0.017 0.000 -0.023 \n", "\n", " split1_train split2_test split2_train std_test std_train \n", "1 0.611 0.509 0.638 0.041 0.013 \n", "2 0.612 0.512 0.639 0.032 0.011 \n", "3 0.540 0.415 0.625 0.087 0.041 \n", "4 0.612 0.337 0.688 0.114 0.034 \n", "5 0.612 0.336 0.689 0.114 0.034 \n", "6 0.000 -0.001 0.000 0.009 0.000 " ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "compare_models(Xb, yb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison with the Bayesian Evidence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function below estimates the Bayesian evidence for the data $D=(X,y)$ given a polynomial model of degree $P$, using the same MCMC techniques we saw earlier. The evidence calculation requires an additional ingredient that we never specified for cross validation: a prior on the $P + 1$ polynomial coefficients, which has a similar effect to a regularization term in an sklearn linear regression. We adopt a Gaussian prior on each coefficient with the same scale, chosen to be large enough that the likelihood will dominate the posterior." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def calculate_evidence(Xdata, ydata, degree, sigma_y=sigma_y, coef_sigma=10., n_mc=5000,\n", " n_grid=50, grid_fraction=0.1, seed=123):\n", " # Use sklearn fit to initialize MCMC chains.\n", " fit = poly_fit(Xdata, ydata, degree).steps[1][1]\n", " coef_init = fit.coef_.astype(np.float32)\n", " if degree > 0:\n", " coef_init = np.insert(coef_init, 0, fit.intercept_)\n", " print('Best fit coefficients:', np.round(coef_init, 3))\n", " P = len(coef_init)\n", " # Build the graph for this inference.\n", " graph = tf.Graph()\n", " with graph.as_default():\n", " # Build the inference model.\n", " coef = ed.models.Normal(loc=0., scale=tf.fill((P,), coef_sigma))\n", " X = tf.placeholder(tf.float32)\n", " XP = [ X ** p for p in range(degree + 1) ]\n", " XX = tf.stack(XP, axis=1)\n", " y_true = tf.reshape(tf.matmul(XX, tf.reshape(coef, [-1, 1])), [-1])\n", " y = ed.models.Normal(loc=y_true, scale=sigma_y)\n", " # Prepare for MCMC sampling.\n", " mc_coef = ed.models.Empirical(\n", " params=tf.Variable(tf.reshape(tf.tile(coef_init, (n_mc,)), (n_mc, P))))\n", " # Prepare to tabulate log_likelihood + log_prior on a coefficient grid.\n", " coef_in = tf.placeholder(tf.float32)\n", " y_in = tf.placeholder(tf.float32)\n", " y_true_out = tf.transpose(tf.matmul(XX, tf.transpose(coef_in)))\n", " y_out = ed.models.Normal(loc=y_true_out, scale=sigma_y)\n", " log_likelihood = tf.reduce_sum(y_out.log_prob(y_in), axis=-1)\n", " coef_out = ed.models.Normal(loc=0., scale=tf.fill(tf.shape(coef_in), coef_sigma))\n", " log_prior = tf.reduce_sum(coef_out.log_prob(coef_in), axis=-1)\n", " log_numerator = log_likelihood + log_prior\n", "\n", " with tf.Session(graph=graph) as session:\n", " tf.set_random_seed(seed)\n", " # Run the inference using HMC to generate samples.\n", " inference = ed.HMC({coef: mc_coef}, data={X: Xdata, y: ydata})\n", " inference.run(step_size=0.02, n_steps=50)\n", " ##inference.run(step_size=0.01, n_steps=5)\n", " coef_samples = session.run(mc_coef.params)\n", " # Build a parameter grid for estimating the evidence.\n", " coef_grid = create_param_grid(coef_samples, n_grid=n_grid)\n", " # Evaluate log(likelihood) + log(prior) on the parameter grid.\n", " log_numerator_grid = session.run(\n", " log_numerator, feed_dict={X: Xdata, y_in: ydata, coef_in: coef_grid})\n", " \n", " #sns.pairplot(pd.DataFrame(coef_samples))\n", " #plt.show() \n", " return estimate_log_evidence(coef_samples, coef_grid, log_numerator_grid, grid_fraction=grid_fraction)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-0.31]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 24s | Acceptance Rate: 0.994\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Ea_P0 = calculate_evidence(Xa, ya, 0, grid_fraction=0.5)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-0.31799999]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 25s | Acceptance Rate: 0.991\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Eb_P0 = calculate_evidence(Xb, yb, 0, grid_fraction=0.5)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-0.87699997 1.14699996]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 26s | Acceptance Rate: 0.999\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Ea_P1 = calculate_evidence(Xa, ya, 1, grid_fraction=0.3)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-0.74699998 0.84500003]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 25s | Acceptance Rate: 0.839\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Eb_P1 = calculate_evidence(Xb, yb, 1, grid_fraction=0.3)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-1.13800001 2.39599991 -1.20200002]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 23s | Acceptance Rate: 0.990\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Ea_P2 = calculate_evidence(Xa, ya, 2, grid_fraction=0.02)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-0.92500001 1.78699994 -0.92500001]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 24s | Acceptance Rate: 0.856\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Eb_P2 = calculate_evidence(Xb, yb, 2, grid_fraction=0.02)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-1.24000001 3.37700009 -3.49499989 1.48000002]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 24s | Acceptance Rate: 0.981\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Ea_P3 = calculate_evidence(Xa, ya, 3, grid_fraction=0.0005)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit coefficients: [-0.89200002 1.44000006 -0.097 -0.54000002]\n", "5000/5000 [100%] ██████████████████████████████ Elapsed: 25s | Acceptance Rate: 0.805\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "log_Eb_P3 = calculate_evidence(Xb, yb, 3, grid_fraction=0.0005)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Summarize these estimated log evidence values, $\\log P(D\\mid M)$, for the four models considered, P0-3:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
P0P1P2P3
N=15-16.83-7.74-9.22-10.47
N=150-61.2822.9626.8224.74
\n", "
" ], "text/plain": [ " P0 P1 P2 P3\n", "N=15 -16.83 -7.74 -9.22 -10.47\n", "N=150 -61.28 22.96 26.82 24.74" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results = pd.DataFrame({\n", " 'P0': [log_Ea_P0, log_Eb_P0], 'P1': [log_Ea_P1, log_Eb_P1],\n", " 'P2': [log_Ea_P2, log_Eb_P2], 'P3': [log_Ea_P3, log_Eb_P3]},\n", " index=('N=15', 'N=150'))\n", "results.round(2)" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Use the table of $\\log P(D\\mid M)$ values above to answer the following questions:\n", " - Which model best explains the $N=15$ dataset?\n", " - Which model best explains the $N=150$ dataset?\n", " - Which pairs of models have a Bayes' factor $> 100$, indicating \"decisive evidence\" favoring one model over the other?\n", " - Does \"decisive evidence\" that favors one model over another indicate that the favored model is correct?\n", " - Are the model comparisons based on evidence substantially different from those based on cross validation in this example?" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The $N=15$ dataset is best explained by the P1 model (since it has the maximum value in the first row of the table).\n", "\n", "The $N=150$ dataset is best explained by the P2 model (since it has the maximum value in the first row of the table).\n", "\n", "A Bayes' factor $> 100$ corresponds to a difference in $\\log P(D\\mid M)$ of $\\log 100 \\simeq 4.6$.\n", "\n", "Here is a table showing which model pairs pass this test for $N=15$:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "solution2": "hidden" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[False True True True]\n", " [False False False False]\n", " [False False False False]\n", " [False False False False]]\n" ] } ], "source": [ "row = results.iloc[0].values\n", "print(np.exp(row - row.reshape(-1, 1)) > 100)" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "And for $N=150$:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "solution2": "hidden" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[False True True True]\n", " [False False False False]\n", " [False False False False]\n", " [False False False False]]\n" ] } ], "source": [ "row = results.iloc[1].values\n", "print(np.exp(row - row.reshape(-1, 1)) > 100)" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "We find that, in both cases, the P1, P2, and P3 models are all \"decisively favored\" over P0 as explanations for the data.\n", "\n", "The Bayes' factor is calculated for a pair of models, without considering the range of all possible models. A high value can either indicate that one model of the pair is particularly good or that the other model is particularly bad (or some combination of these). In this example, P0 is particularly bad. In general, the Bayes' factor compares models relative to each other, but does not offer any absolute measure of how well either model explains the data.\n", "\n", "These evidence-based model comparisons are broadly consistent with the earlier cross-validation comparisons, but with some differences in the details. The advantages of using evidence are clearer for the smaller dataset, where the cross validation results are difficult to interpret and priors have more influence. Ideally, you should use both methods and compare." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }