diff --git a/docs/source/notebooks/bayesian_neural_network_with_sgfs.ipynb b/docs/source/notebooks/bayesian_neural_network_with_sgfs.ipynb new file mode 100644 index 0000000000..e86b49c22f --- /dev/null +++ b/docs/source/notebooks/bayesian_neural_network_with_sgfs.ipynb @@ -0,0 +1,618 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "# Bayesian Neural Networks in PyMC3 with Stochastic Gradient Algorithms\n", + "\n", + "To learn more about using bayesian methods, to train deep learning method please refer to this post by Thomas Wiecki http://twiecki.github.io/blog/2016/06/01/bayesian-deep-learning/. This notebook\n", + "follows a similar structure." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Stochastic Gradient Fisher Scoring\n", + "\n", + "Author: [__shkr__](www.github.com/shkr)\n", + "\n", + "```\n", + "Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?\n", + "```\n", + "\n", + "\n", + "Stochastic Gradient Fisher scoring is an algorithm which at high mixing rates (or epsilon valuees) samples from a normal approximation of the \n", + "posterior, while for slow mixing rates it will mimic the behaviour of SGLD with a preconditioner matrix that is as parameter `B`.\n", + "\n", + "The mixing rate is controlled by epsilon which is $ \\epsilon = 2^{-\\frac{t}{step\\_size\\_decay}}*step\\_size $\n", + "\n", + "\n", + "Here we run the sampling algorithm with a minibatch of the training samples of X_train.\n", + "The `total_size` is `X_train.shape[0]`. If the preconditioner matrix is not specified, an identity matrix is used.\n", + "\n", + "Reference: https://www.slideshare.net/hustwj/austerity-in-mcmc-land-cutting-the-computational-budget" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Generating data\n", + "\n", + "First, lets generate some toy data -- a simple binary classification problem that's not linearly separable." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/shashank/.virtualenvs/pym3/lib/python2.7/site-packages/sklearn/cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n", + " \"This module will be removed in 0.20.\", DeprecationWarning)\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "import theano\n", + "floatX = theano.config.floatX\n", + "import pymc3 as pm\n", + "import theano.tensor as T\n", + "import sklearn\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "sns.set_style('white')\n", + "from sklearn import datasets\n", + "from sklearn.preprocessing import scale\n", + "from sklearn.cross_validation import train_test_split\n", + "from sklearn.datasets import make_moons" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "X, Y = make_moons(noise=0.2, random_state=0, n_samples=1000)\n", + "X = scale(X)\n", + "X = X.astype(floatX)\n", + "Y = Y.astype(floatX)\n", + "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.5)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": 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ze3DHjFy88lAeJgztpThO+f6p2km+rtGBc03sPdz2cq7R4Vc+NTInDZNG9kH3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\n7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.scatter(X[Y==0, 0], X[Y==0, 1], label='Class 0')\n", + "ax.scatter(X[Y==1, 0], X[Y==1, 1], color='r', label='Class 1')\n", + "sns.despine(); ax.legend()\n", + "ax.set(xlabel='X', ylabel='Y', title='Toy binary classification data set');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Store training data in Theano shared variables" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "ann_input = theano.shared(X_train)\n", + "ann_output = theano.shared(Y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Model specification\n", + "\n", + "A neural network is quite simple. The basic unit is a [perceptron](https://en.wikipedia.org/wiki/Perceptron) which is nothing more than [logistic regression](http://pymc-devs.github.io/pymc3/notebooks/posterior_predictive.html#Prediction). We use many of these in parallel and then stack them up to get hidden layers. Here we will use 2 hidden layers with 5 neurons each which is sufficient for such a simple problem." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "n_hidden = 5\n", + "\n", + "# Initialize random weights between each layer\n", + "init_1 = np.random.randn(X.shape[1], n_hidden).astype(floatX)\n", + "init_2 = np.random.randn(n_hidden, n_hidden).astype(floatX)\n", + "init_out = np.random.randn(n_hidden).astype(floatX)\n", + "\n", + "with pm.Model() as neural_network:\n", + " # Weights from input to hidden layer\n", + " weights_in_1 = pm.Normal('w_in_1', 0, sd=1, \n", + " shape=(X.shape[1], n_hidden), \n", + " testval=init_1)\n", + "\n", + " # Weights from 1st to 2nd layer\n", + " weights_1_2 = pm.Normal('w_1_2', 0, sd=1, \n", + " shape=(n_hidden, n_hidden), \n", + " testval=init_2)\n", + "\n", + " # Weights from hidden layer to output\n", + " weights_2_out = pm.Normal('w_2_out', 0, sd=1, \n", + " shape=(n_hidden,), \n", + " testval=init_out)\n", + "\n", + " # Build neural-network using tanh activation function\n", + " act_1 = pm.math.tanh(pm.math.dot(ann_input, weights_in_1))\n", + " act_2 = pm.math.tanh(pm.math.dot(act_1, weights_1_2))\n", + " act_out = pm.math.sigmoid(pm.math.dot(act_2, weights_2_out))\n", + "\n", + " # Binary classification -> Bernoulli likelihood\n", + " out = pm.Bernoulli('out', \n", + " act_out,\n", + " observed=ann_output)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "scrolled": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/shashank/.virtualenvs/pym3/lib/python2.7/site-packages/pymc3-3.1-py2.7.egg/pymc3/step_methods/sgmcmc.py:107: UserWarning: Warning: Stocastic Gradient based sampling methods are experimental step methods and not yet recommended for use in PyMC3!\n", + "100%|██████████| 5000/5000 [00:10<00:00, 488.84it/s]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 13.3 s, sys: 443 ms, total: 13.7 s\n", + "Wall time: 13.7 s\n" + ] + } + ], + "source": [ + "from six.moves import zip\n", + "\n", + "def train_sgfs(model, B=None):\n", + " \n", + " # Tensors and RV that will be using mini-batches\n", + " minibatch_tensors = [ann_input, ann_output]\n", + " minibatch_RVs = [out]\n", + "\n", + " # Generator that returns mini-batches in each iteration\n", + " def create_minibatch(data):\n", + " rng = np.random.RandomState(0)\n", + "\n", + " while True:\n", + " # Return random data samples of set size 100 each iteration\n", + " ixs = rng.randint(len(data), size=50)\n", + " yield data[ixs]\n", + "\n", + " minibatches = zip(\n", + " create_minibatch(X_train), \n", + " create_minibatch(Y_train),\n", + " )\n", + "\n", + " total_size = len(Y_train)\n", + "\n", + " with model:\n", + " draws = 4500\n", + " step_method = pm.SGFS(vars=model.vars, \n", + " batch_size=50, \n", + " B=B, step_size=.1, \n", + " step_size_decay=100, \n", + " total_size=X_train.shape[0], \n", + " minibatches=minibatches, \n", + " minibatch_tensors=minibatch_tensors)\n", + " trace = pm.sample(draws=draws, step=step_method) \n", + " return step_method, trace\n", + "\n", + "%time step_method, trace = train_sgfs(neural_network)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "A smaller wall time than mini-batch ADVI" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[,\n", + " ],\n", + " [,\n", + " ],\n", + " [,\n", + " ]], dtype=object)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+p5544olZm9DPR6lUmrVm2DRNfN/Hsub0cTlvPpAtVUgFFchlmKxOr11Sw3tx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gD+sWwDMz80YVjeU4j9wRNPPJH/WWvNu+++i23bJYxICCGEKDChOvbYYzn22GNJpVI8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\nE0KI/kR++hJZry6eUA1oSahU81pTpqVT7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pm.traceplot(trace)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 500/500 [00:00<00:00, 1846.49it/s]\n" + ] + } + ], + "source": [ + "# Replace shared variables with testing set\n", + "ann_input.set_value(X_test)\n", + "ann_output.set_value(Y_test)\n", + "\n", + "# Creater posterior predictive samples\n", + "ppc = pm.sample_ppc(trace, model=neural_network, samples=500, random_seed=0)\n", + "\n", + "# Use probability of > 0.5 to assume prediction of class 1\n", + "pred = ppc['out'].mean(axis=0) > 0.5" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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on6wCFk7cT6+iMPoU8wkgddut9rtZ5TO7hIFojnYzeO9dy8SzBvjO8QxIzWKY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\n550HHDnCvo4aN7LO8VJTA2zZIv/L6ovSUmDBgsRF35o14n3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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n", + "ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n", + "sns.despine()\n", + "ax.set(title='Predicted labels in testing set', xlabel='X', ylabel='Y');" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accuracy = 96.6%\n" + ] + } + ], + "source": [ + "print('Accuracy = {}%'.format((Y_test == pred).mean() * 100))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Lets look at what the classifier has learned\n", + "\n", + "For this, we evaluate the class probability predictions on a grid over the whole input space." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "grid = np.mgrid[-3:3:100j,-3:3:100j].astype(floatX)\n", + "grid_2d = grid.reshape(2, -1).T\n", + "dummy_out = np.ones(grid.shape[1], dtype=np.int8)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 500/500 [00:01<00:00, 279.21it/s]\n" + ] + } + ], + "source": [ + "ann_input.set_value(grid_2d)\n", + "ann_output.set_value(dummy_out)\n", + "\n", + "# Creater posterior predictive samples\n", + "ppc = pm.sample_ppc(trace, model=neural_network, samples=500, random_seed=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Probability surface" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": 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GIMsR5jXVfHVEMQiA3XYuJdXtxB8XHZWhbxJprOst8dxa66VUmDVYmQazCpoI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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cmap = sns.diverging_palette(250, 12, s=85, l=25, as_cmap=True)\n", + "fig, ax = plt.subplots(figsize=(10, 6))\n", + "contour = ax.contourf(grid[0, :], grid[1, :], ppc['out'].mean(axis=0).reshape(100, 100), cmap=cmap)\n", + "ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n", + "ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n", + "cbar = plt.colorbar(contour, ax=ax)\n", + "_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n", + "ax.set_title('$B \\propto I_t $')\n", + "cbar.ax.set_ylabel('Posterior predictive mean probability of class label = 0');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Uncertainty in predicted value\n", + "\n", + "So far, everything I showed we could have done with a non-Bayesian Neural Network. \n", + "The mean of the posterior predictive for each class-label should be identical to maximum likelihood predicted values. \n", + "However, we can also look at the standard deviation of the posterior predictive to get a sense for the uncertainty in our predictions. Here is what that looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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OBlx8zc8LhjBYL2DHgC9p1J5VGsN5wRDebBPwYftwL6CuGJesErt0nER9Dn36\ny42/rZOGjl52wtajH7zqZOJ9LsjnH0h2o0F2RNC2g4ddM0fnMhpkR9Aw8eMuf/jDH/Dggw9i+fLl\naY9xHJfsM2RFUQmhfIu+uLUGWtGQqQ/JaX8ir0Se3Yu3JCt45ZMB9MfMI0L6UnOzcnovytKThmdZ\nSjE8R+VENRiJ7T0cLhoDw47XRrhpkLbjbwKshdPiWcG0aj430M83y5dGiSTc/J4iRYMy9QZ5jRti\nKNcpMbc5vK8710soGB588EEAwD333GNryKqeohJC+VCy7RVmX5iZRowynROWSYSKdKF2K22TioJq\nUcGcanKpubacvnNAQrVPwUmTSnHp7CCO9EmJqJHN5xmV0yu7tPj51A7WoViiszUJs47XVudxC5rI\nmRYz4dQxIOO+97rRM6h4mi4bCdgdn6HFzB/kZTRIxa4IyjfR40WEh43YsM/SpUsRjUaxePFiLF68\nGGPH2ruGFJUQAryNBOXrrDO9AHS6PtLzy5awzFTEmkUfqkUZN02Joy5gLBS05fT7Pz2EMhFYGwHu\ne69H520ZY9r0EAAkBY58PpW+RGfrLoIYInW8dnoepxVfZpGz48f40o5pJpwAoHswYZzORrosX8n0\nOyUTEeQm2RBBQOJ55YsYYmmu/OGVV17Bvn378Pbbb+Pmm29GdXU1Lr74Ynzta1+j2r/ohJBX6CMW\nXoshJ3O6nAoJ/b65iqp5NT+sJ87Bx6eKILPhqfUB4J2BSlNvi5nwdOLzUaM6MysV/K0j/XFSx2s7\n5+lsbkNV4xhbxmVSQ0p9I8rqIIcyP4+tbTH8ZU8k5ZhmwomEm4NjgfwXQVrsCiI3TNFuRoPsUuiN\nE5kIyj8mT56MG264ARMnTsSKFSvw3HPPMSHkNtmKAmVbcKk4FVJerM/JWpzODyOdOyonptCTukuQ\nLtbai5hdnw8pqjOuRMZAPCHgtFEeLU78RLTGZZqGlGojynd3hrGmJWJ4TL1wqgpy6AqTS+jdHBxb\nSCLIbbLdM4g2GlQo4odU4UV6nJE//OlPf8Jbb72FrVu34stf/jKWLl2K+fPnU+/PhFAeYdSVGsiO\nELMjQLxajxoZie5oI6axjNYXEDnMKo3hw4H0iygpmgIYpxTNvDpWF2u7Ph9SVKcrBpxeK+HMhjhK\nBGBQSggmbbrL7nnsiDvahpRVJYlIEAntMbUdvIMihx+930MUrPVVAUw4vhGRPXuIxyxm7HyerKJB\n0yZVZdyu3osKAAAgAElEQVQ7yG3yvTpML27yoQ0Bg54333wTl1xyCX7yk5/A56P81auBCaEc4bSP\njtEXplvpLNoxDW5D63cx6rIMAIuH7iIdw4xIXMH+Tw8lzcZmXp0qn2w65b1MTBwjQsjS6SNTZlGd\nHb0cFE5AU4j8etj1E9GKO9qGlKqwoa0iUzt4AzBMl508owYBn4BAHld5uYmTz5LXF2gvokH53CyR\nFN1hIqjweOqpp7Bx40a8/PLLWLJkCbZs2YJTTjmFev+iEkJulXV7TSaixShdRhvNoTFVGx3Ly9fT\nrq/G7hwuEpICvLCpf8gz40sRG0ZT3mdXKUQPy6EdbQjFgL8eFRCRyYJDH5nqiIAoZIDE/X/r4FNu\na18Ps0n0pAiYmXDSVnzZaUhpt4pMRZ8uq68K4OQZNfjmuZMAjIy0Vq7GaeS6SswJXoigTNJbbCRG\n/vHb3/4Wq1evxpEjR3DBBRfg3nvvxeWXX46bbrqJav+iEEJOyrqz6b/Rk8nYDdpBq5ls40WZvBlu\n98/Rl6UbkRBfamSCSxEbRlPe9dElSVbw27VHsb1HRFeMM5xZw0PGWfUS2iOJqNG7hwVs7zY2Bau+\nHD3a14N2jQBMhZO2V5JVpRegaTLpsP+SfuBt4lgx9O/abXjOYiGTzw9NpMKpPyhffUG5qBCzGl4L\nsIGp+cZrr72Gl156CVdccQVqamrw8ssv42tf+9rIEUJO0jj51muItloqG5VqtNsYrcVJTxun/XOs\nMFsLjfiiiS79du3RlEiWkXyQweOJZhExhYOfVxCRzV8co+NoXw+7ETCScDppUmkyQgOYl8irlPo4\niEPn0Ud3ajRVY1Zo02VavBjomuumitn40eXUF8REUDq0KTMWHcoPeJ6H3+9P3g4EAhAE+qKLghZC\nmQoar6NCdnv7eJGSon2OmXqWnPa0AczTNrWlAiYdV4f+lkPUa6NZC634Uj1DJKFxaEcbtvfQf4Si\nytBAVYPUGaCgQlBwXJWC5hCH7jid/4c2AkYSTmNmpfft0YobUmTo8x4JK7cM4Jp5ZQbRHWfixYu5\nZPr5Y7mgmERQNnBbAJEiPE4EjFGkiImh3POFL3wBjz32GMLhMFavXo2VK1fitNNOo96/YIWQU0Nv\nvs/tcnMt2jlTXn8ZZzIjiyZtE7BRPUezFhqzMUlQnTSpFFfKCgSeMxVTTumVOOzsBUpFoDue/rhR\nBZwKTUROK5xI4lsVN4tnBXHfe93Jxoda9JVmRtEdO3gxl0w/f6xQycTA62aFmJfRIK8iQEavnZMB\nqDRpM0b2ueuuu/DSSy9hxowZWLVqFc466yxcddVV1PsXpBByEjUxEyZeC4V8NW1nivq83PD40KRt\naKBdC43ZeFVruqDSXpjNxJQzuOR5umLAuBIZYQlUFXCZROSMIpHhuIIegggC3O35Azgb6GqHQjZg\njwQRlGvseH60fYZYJCi3tLa2Jv995pln4swzz0zePnLkCMaNG0d1nIIUQnaFhRveF7sUmvgx8ylZ\nPRc3PD5kv0sIAj8cCaARuzu3tlGvxcxsbCao1AvzmFljMfvQEaKYcoOwBNzWGMeglBrhIX1pZzq1\nniSGnFaFOcG0FD8sQxo7ETj6uWvnY9jDqwoxN6NAVo0QabATJWIiKPd8/etfB8dxiEQi6OjowIQJ\nE8DzPD777DNMmDAB7777LtVxClIIeUkuq8kKFbs9bczQ+13sjhmx08fHzGzcFbXuuyMePELsXXRc\nZSKK8ulQDyAOgAyzaIYCEB7vjnEYlKxFpBdT6wFz47RZVZgTzERXfWUANRU+BGqH01uFHOGxQyaV\nYlbRIC/8QXaiQW6IICZGRjZ//vOfAQB33HEHrr32Wpx88skAgK1bt+JXv/oV9XEKSghlS6Tk63BV\nOzjxQtmNBqnHtNvTxohMp6hH5UQ6i7aPjwrJbFzpA6pFBV0Ew7KPlxH77AhEwVxMfWVsolfQr/aI\n6JHsiwZaEWnaLDHGoTsKjCoxP4ZR1DSTqjASRhVhZqJLbbQ40ig0EZRr3PDuMGFVmLS0tCRFEAAc\nf/zx2Lt3L/X+BSOE3Cx5py1XL8TokJUXCnBH4OnPY6enjX7fo01tjv0tgMYf080RhQsABHgZi0Zb\np4jU4/3xkACjVjoRmceqVgFLxktJ0UMSU34e8PFAyIEIAlKFm1YkqqgeBXOvEocPOgQsHisZikyz\n90wmVWHaknWairAU0RWWUV+Z2mjR6NjFSD6JIK/SYm5MknfLuMwEUGEzZswY/PznP8dFF10EWZbx\nxhtvYPLkydT7F4QQqp46KqP9zTooa/Gyv1A+iSojQaQXiHbWS9vThvQavxeu1DQ2HPa3yDLw1WOs\nxYveH0MiKnPojwNBQXsfwE8YBfnzIymC49UDAjZ0mx9vYxePPb0cZlebCzZaQ/VMfgAH5AD6waMC\nEqYJESwe6yOaoCfLFTjL1wttRfmUMgVd3eRjf9zFoalHRLduiKukJJ5/JE7ulq3FblVYYOpUHOoc\nRM3UqQj4BDz7h82WFWF60TXh+EbDSJBdEZRvwsns+yCfRJAdnJik3RBDmcJEUOHzxBNPYPny5fj3\nf/93AMCXvvQlPPLII9T7F4QQygbZGClht6+QF7jVfdpoG6ueNnpTbiSuGA4D/XsnD2VIYBkJDTN/\nTOq6FJQNvdslJSG+NrVG0bmtG9U+Menr2d5D7t+TTiL6RGNInlquYGOX8ZFEyDgo+9EHHuWQMIWP\n4CxfLwSulli51oWEcLjqOB9WtSZEUkJokb1GEZlPeqZUkbmnj0tUpG3rQm2pkFG/Hm26S+QTZfCb\n3t6YjPwcP8ZnOJz1w32DuHR2EKUa1ayKLpIIcipm8kkEAcafHysR5HR8BuBMBHldKZZvTRMZhUlV\nVRV++MMfOt6/IIRQ954jGNtQ79nxsz1Xy0tyMSfMLtq1tEeA7hjZCCODw986hGS0CUj3EdH28onI\nPNZGKnHNvDK8sKk/JTrRFeOxrsP58yEZkvWRnACvICYrkAmCLw4BvUP/7oOILbIIPgZ8zUTk7eOD\neP2ggo86nXlnWgeH12HUr8eqwzMp3VXq4/B5j5Ry7DV7IobrGIwDL2zux7e+UJH2WKh5V7L/T74J\nGS/IRASZ4TQKlK2Bqm5C2+eHiSCGloIQQsDwBd7tFFM+DmrNNHKUD8+BFprU0fYeDotGD83nGhIW\ntaUCZpXGsGi0RN3LZ1NrFItnBS2nq9uF1CJAn65LRGQ41CKGKDj0QYAawyFFcXZJJdjW3InuGPkH\nQFeMw7aQi08Cw20BklEdiw7PpAaIRnrSaHYaADQdiRmm50aCAAIy97q42S8IyI4I8qKDtPp/o9eT\nCSAGCfcagWSBzua2ghVBdsvA8w23/VNRORENAhKmYDO6YhxWHUwIi64YDwUcOgZkfNguYG2k0nL/\n5HEGZBzoiVtOVzeGfB59dZdZui4ODlP4CAAOCjiQRBAA9IHH67Ea+AzkQ6WooNcwhacAUFAtygjw\ndK8NMNwWQBU4HQMyFAxHjFZuGUhua9YAkYTZK94dTkSeipFsfJbdnCgPWIugOeNH550IAtJ7AOlF\nDxNBDCMKJiLkBk7HcrgFbbWadtt8wo1oHMn8e1ylgtNqJfyzkzfot8NhW4is2Te1RvHAefXAuvah\nY/JDfXvSqfLJKGvvQLVPRFeM9jeAghqfgpmVCqISsJFgotaX5Zul60IQsFe2qGUHAHDoN/l4TpHD\n2IsAQoRtanwKbpwcR10gUf1mZSRP7lfKIyhyVB2ezRogkqgt4dAfUxAhWKncbs6YD9j5nORL52jA\nuwoxIDt+IKNuz0wE5RZZlnH//fejubkZfr8fy5Ytw6RJk9K2ufnmm3HOOefg6quvxuDgIO688050\ndHSgrKwMjz32GGprU/+OM2fOBMcNf9eKogie5xGNRlFeXo7169dTrW9ECKFcC6B8OKdbZCqGSB2Q\n13UAJ1dLmF8tG1ZrkRokAokoRl9UwY0LR+HQjjbwE0bh3Z1hrGlJ96XMrlJQLhr3PCJxUo2M08NH\n4RsARh9bi6Bo3SLALN1XLijok+xd9H2QUAIFfRCSFWVn+XrBx4BNUvpHeHaVgrHBxL9JbQ2CQqpH\nSGXeOD/CccW4w7NmrIZZA0QS849J5A0zbc6onxmWj6kzLz7fTvxB+dIrKNuGaG3ndb0AcjJfjJE5\nq1evRjQaxcqVK7F582Y8+uijeOaZZ1K2efLJJxEKDef7X3zxRUyfPh233HIL3n77bTz99NNYunRp\nyj5NTU0AgPvuuw/z58/HxRdfDI7j8O677+KDDz6gXl9RCyEvy+FHGm58uZuljDZ086gQEikdo3QR\nCTWaoDZ2xMEjuKAUiNWT+xIBwKLREtZ3cojI6WKAG0p/afc5vDvxGG2LALMGk30Sp/EG0REHj8v8\n7RA5oIyT4Bt6ec7yJSzWLVIAvRqRtHjscJ6OtGaBMxgme0Ip4jJQE+TQGU5foTZyY9YAcUKVgAhE\ntIciqAmmN2DMpDmj1kANIK/M1E4+I16WytvFbV9Qrsvi2Syw/GHjxo1YsGABAODEE0/Etm3bUh5/\n5513wHFccht1n29961sAEnPEnn76acPjb926FQ888EDy9qJFi0y311NUQsiu8CnkyEwhYl7hxaHX\npPFggFeIHaPnjfOjv+VQyn1WgqU/nugrREIBMKdSxpUTpGTPIf2XqVWLACA1EpOIDKnn42yJIACo\ngIQqflgAqfAcsNDfizOUXvQrQlIkHd5tvWbt6zPpuDEIiBwkWcErnwxgIEZeoT5yY9Z1Oi4DPYPB\ntIozp80ZteTbRHmn3yOZiCArct00MdciSEUvhlQjNRNI6cwYU4+qQHr1phU9kV6stdDkfX19KC8v\nT94WBAHxeByiKGLnzp146623sHz5cvziF79I2aeiIrGesrIy9Pb2ph1XJRgM4pVXXsGFF14IWZbx\n+uuvo7q6mvo5FIUQylbkh6bRoNFaCkV0ZTrmwoxMprWfXKOA46ThKEaQx4nj/DgvaFw6ZSRYrDox\nbwsJqD5s3BuI5jVSxdi5o4AffyqgD+kpPw6KRhQZvybThEiKCIopSBE+Pg6o5lLXavfLvndQxm83\n9uHj1vR+PyUicMbkkrTIjVnXaYGHYQNGu80ZjbAjiLyKHOWjCLKL272C8kUEqeiHFHspgpjIIlNe\nXo7+/v7kbVmWIYoJ+bFq1SocPnwY3/zmN3Hw4EH4fD6MHz8+ZZ/+/n5UVlYaHv+JJ57Agw8+iGXL\nloHneZx++ul4/PHHqddX0EIoEwHk9AvMiQjSPpavgkhvYlbL02nHXNBgljJKRUlWRenTWpIiYHtP\nYiL55s/CiFUJttdIs47tPRxOrQHqAsNih2T0NhsF0rqrE92ygD6QS+AVAJf5OrE6VoVewkeRg4Lj\n+YFkCkxWgLWxCrRIAYSGUmET+CgW+kIIEASZ0Zey9nl0xTjwzR2mQ2HLfDyWzDVutuiWsFHRChuS\ncNH3N7ISN/pUmltiyEsRZIXblWJukW8iKJu4Ne6jGJk/fz7WrFmDiy66CJs3b8b06dOTj911113J\nfz/11FOor6/HmWeeid27d2Pt2rU4/vjj8de//hUnnXSS4fFfeuklPPvss47XV9BCyKh5IA1Omg46\nFUH67fJRDOlNzB0DMj4cSNw265pMixpFUed9betWOzinX1xrfApua4xjUEqNuqxqFfC3jlSjNU1n\nZxKLx0oIS4lRGaQ1dMU4/GSXDzUasUMyehudX/1S9ENCOWRiRKgSEo4RYjhWjhBNz8cLAzjHPxwO\nXhurwCZpuOFhL0R8KovYFSnBHCGcNnYDAPbv7ETZpNqU11H/PKzszl3hYZN0NtD6gGjnldXMmk4U\nOFaiKl9x2kHaq5QYTTQoX0VQtiI0LBJkzHnnnYd169bhqquugqIoePjhh7FixQpMnDgR55xzDnGf\nq6++Gt///vdx9dVXw+fz4Sc/+Ynh8desWYPbb789pYLMDgUthABrMaQVHTRDVvX70ODW+XOFmYmZ\n1DWZltoZYw0Hqs6sVPD3TvJB1equcs270+01ChywZLyEPb1Gg1oT92nnnu3opTt/667OlOhNn0G7\nLjXlZWR6Vu8HEumwFolsTIqBxyapDBGFw5m+EKIQEISEj+JD0aNmISnoFo2WqEaSaMlFebveFA2Q\nGziu3j0If201bpyVnv7KJyO1W+RCBOUrWuFBisYwYZI/8DyPH/3oRyn3TZs2LW27W265JfnvYDCI\n5cuXUx2/uroaF1xwAWbPno1AYPh7knbeWMELIRI0Q1bdSmPZETeZdsf2KppkZmImdU02Q/96GEVR\njBr9GU2J74jA0Ftkd40qfh6YVangI4qI9rYQh5BBA0Pt+dUvZH30ZhgFlTqhY2R61tKvCAgRokpa\nPpWD2BEJQgHgg4wY0l/3sEQ3kkSLnfJ2rzBr4LihuQvXLpyQnE2WDQGUC29QrkRQPo3RMBI3TPSM\nbC677LKM9i94IUQSIm4IBtr97c72yiSd51VKzcw8rO+abIV2jYkoDvktZtQXSD8lPuln6Ta+ENtd\no5Yz6iV81ElOj2npjXOoFBWiGFLPr17kzKI35ZBwTaAdpYQAC8n0rFLGSaiERGygOMxwRVrMQDS1\n9HKoFhWDKJgWBbUlPOYfE7BV3u4VZg0c20MRdPXGMKY2O6m7XHqDSIyUSBATOwwjLrvsMnR3dyMc\nDkNRFEiShAMHDlDvXxDtXKunjiLeTxPVsfsYYP+LTj/6IxOvUS5QzcMk9F2T7UA7EFWLXtSoEaWu\nuLFYyWSN1f6EJ4lmXbSvkVn0ph8CohaRHRI+LpFKy5SeOIdp5dbPd1RAwfeOjeCaeWWOJtJnij4t\npjZwJFET5FFTkaqEvYoGFboIsks+VYoxMzLDiJ/+9Kc455xzcMEFF+Caa67B+eefj5/+9KfU+xdM\nREgb5cnEa+O2CHJr31xD6kBM6ppsB7NIk1FfIK2oMPMFJWZpKZhT7WyN2hJ4mkq2yXIYl47zQeDI\nr5H2S9oselMBCWUGUR9gOC1CurCoqbTtUokjMaWe/5SBdrSWjMKhQS7NKM0DGFOi4N+OjcPP2xsL\nYxcaI7N6v1kDx3nj/Ijs2YPMZaI3eF0lZodCjQYxGGa89dZbWLt2LR566CF897vfRWtrK1asWEG9\nf0EIoe49RxDoHO5vYlW9Zfa49ou9kIWL29B2TbaDWZl6Wl8gn4JpZUqKP8gsosQBuGlKPDlKghaj\nWWdfqpPwaShxX+J5J4RajU/BZDlRkSVwtcTXSH+hU6M3pEqwKbqeQFq03hCSIFK9RKfLvVgTq8Rn\nsn+oGo0+YjNNiODvUgVao+l/3DmVEi4/RkoxqQP0IigSV3C0XwKURAQnHFcMmyZa9f4hCSOzBo7F\nAskfZCSC3I4GOfUCuRUNsjI/MxhGjBo1CuXl5WhsbERTUxPOP/98PPHEE9T7F4QQsoMdbw8jHZqu\nyXYwizQJHLBodKIsvqWXw8ZuHi39XPJxK+9SnYN1Gs06O6Newp0z4kmBA2jFjg/A8Jc0zWukrQQL\nQUiO1dgjBcBHE49LgKE5WqVlf0/KhUa9UDaiB1PAYWvFKHweNO6g6oOEOPhkJdrpYi/+J0Lua3Qw\nzFmK30hcwdE+CeCAhjIh2ZH6xc39+Gh/BIPx1O3rgjzmjU+IFYHnkj2AItt3omF2opeIKnr0/YH0\nmDVwzBZOfkCp3YytsCOCnOBFNMjNlJi275X6fyaIGDSUl5dj1apVmD17Np5//nmMGjUqZW6ZFUUn\nhBj5hVWk6d3DAjZ2GffmMYooOfEFmaXatrYrmNfXCR8HqKejMWcafVGr0Rs5AmyRy5Im5l6I2CSJ\nOCD5EAGPEARUQkJ9fwizQTbtGVURiVBwYu9h+GQZbYFyhAUf1FltJVIMswIxnC72IoxhsdUtG/uX\nzKrvJFnBH7b0Y92+YbFTIgKnTwqA44A/E4bcAkBHOFHirkABBy61B9Anm5PRHKP+QCR/ktsNHPMB\nuyIoH6JB2fAF0YpIxsjmoYcewttvv41LL70Ua9aswb333ovbb7+dev+cCKEtW7bgxz/+Mf7nf/4n\nF6fPKvneUdotrMZOkKIoNL2B3PQumaXaeiGgXxFSqras2uVbfUHHFGCvTA4dHYV/eF0QESpLnGdu\n/1HTY8bBISKICEhxiFDAD+0zq78dEUGEKEmICwICUhwzJiVa0gcw/JzM/Euk6jv1/btyywDe350q\ndgbjCQEUoNAkWgEFDPcAUiH1BwISs8mKHa8jQUBhzxJj0SGGFaNHj8aNN94IALj77rtt7591IfTc\nc8/hjTfeQDBo09yRZ1iVzOsfz3dPktP12R07oSUUM+4N1KWJTrjlXbJKtR3bWEV1bNovZJreP1ra\nAuWY1d8OkTCWVQawvawBbSUVCPMignIcYwd7Mbv/KHgkokOilPDRBSTjXtE+DggY9JIOCumvrer7\n2XiQ3MMHACIUmlSfMlP5+GAEnIHHaVNrFEvmlua8h5GKF59fJ/PE7ESD3J4oD+SugzQrn2fomTlz\nZko3aVEUwfM8otEoysvLsX79eqrjZF0ITZw4EU899VTKfJF8xW6lTL52jqbFiRiyM3ZCT4mQSAWR\nLss8Euml9siw+MnUu2Rm3jZLtanRrv79nYZeHhJ0vX+GCQu+oahO+uDT7WUN2FNWm7LtHsookpaY\nAgwadM0YiANt4cR8NYED3gtXYtO73egw6N/jBl1hBSAIPwDoGvBmtIeVF0lPpgLIbiTDrZRYvnuC\nGIxMaWpqAgDcd999mD9/Pi6++GJwHId3330XH3zwAfVxsi6EFi1aZKvRUa4odFED2EvLdTa32Z48\nn+nYi0HJeM6VDOC/dotpg1ftDFclPR99qk01EZ/c1wutIRoYjnZtbVeGvDz1yY7QNK11zKrHSASl\nGAJSeugkDg5tJRXEfcyiSHqjNZCIUvUaeYTiw/PVggLQOpheqk4iIFhHhUpEclSoJsiBA4eOcPo7\ngTTaI5Ou0WazyrzqlWQmglr296SlOt1CFUE+KYbKaD9C/jLEBIddRxmMPGfr1q144IEHkrcXLVqE\np59+mnp/ZpY2wO3+KblIi9Ge02l6K9PRHJU+oFpUhoav6hkeaWF3uKr6fNTBrtp+Q1rz9u5dPSkV\nW+pFSzVorolWYJOU6uVRRc1CzTBUI1r29+AY9KCnrCFpZg5KMfhkCSF/emp4bKSPeDGMCCLCPPmj\nahZFUtegFUPmUarh17uLfDgiX5qc+CMTq8aGxIasKERD9fzxiX2N+gPpIzaZNEo0mlUGeONFMhNB\nu/b3EFOd2LnNsBkCbTRo7pjJ4GUZF7esxdyjLaiOhNAdqMQnDdPwxrSzIPPD4tJOWszraBBLfTGc\nEgwG8corr+DCCy+ELMt4/fXXUV1tXE2rhwkhC0hignbIaqHgNL2V6WgOPw/MqbZuZqiyvYfDuaOQ\nNpVezxutAtZpptR3xxPPR1GAy8Ynnk97SyeqDfZv3dWJiAxsk8g+thYpgDOUXqp+QKqZeXp/B0K+\nACpjEfggJy6CGnE0NtKH2QYproAUR1COD1WFpWIURTLCbpTKDLVq7OoTE92nv3Z8WVofoaDIIRxX\nUO7nwHOcaQ8gL/sDmc0q88KLZJUOM0p1Vo6biobWPRmf/+KWtfjygU3J23WRUPL2qsaFAHIrgpjo\nYbjJE088gQcffBDLli0Dx3H40pe+hMcff5x6fyaEHGB3vlg+k0l6y6nnRktaqio5zyt9TV0xDj/d\naZ4ui8rAhi7y89nQxeErY+nSfmtilYgZeGlIFWYqevOrmclZrfQySotovSI+pRTh0cekbePrOIKm\n1kPJ26SLmz4qpO9xZKchY00J8G+nV8Incsk+QioBkcMxVYmvFElW8OaOcFoa6oHzqtAXTW+06HV/\nILNZZVZeJLveOSsR1Lw/hLa6KcTHBqrrILftA6+krtVONMgnxTD3aAvx8TlHW/D21DMwY2L6e8mI\nYhNBVtWgjMJj/PjxePbZZx3vnxMhdMwxx+Cll15y7XhaUZItMVIsHaozTW9lWt6u7zNUIgA/3yUa\nVJNZp8s6IiCO7gAS93dEgLFB8/4kMQX4XPYTHwMSg1NJYzJiCtAv+FKEjZXJmZTSIpll64eiBAPV\ndYj7AxCjEZR2dyTv1+5LEkPN+0OICCJmjS+Fj0uIobgCfCLbi7rMGu3HlLpEZCoSV3CkTyIKF6M0\nlL+2GpdPIufdMukPZGWAVmeVkYzfJC+SV7Ts70FE8BmmOuP+ACSfH3x0+LWzI4IAoDLaj+oIuZlc\nTaQXldF+6vUWmwjKlzUw3OWDDz7Ak08+iZ6eHijK8I/K999/n2r/ookIZSpGnAqafBZBNObnTNNb\nbo3m0FaF0cz+UqExZRuh7U8SU4a7PJsZigFgAh9NSYvJCrA2VoGmqB/h2tHJqM+M/nbbJmejiiEO\nQEPrHsht+yD5/BBi0WTUQOb4lPvUY8wZPzotIrWuP46Z/igUAJ/I9nwxAQG4fE6ppenYLA21obkL\n1y48HpE9mad/AGAgKuOFzf1oOhJDV1gxNEBbzSqzikDRfj/QVIiZpTrFaARCbPi1c9I4MeQvQ3eg\nEnUEMdQVqMAxk6eA5mdKtkSQ1pvHYDhh2bJluPvuu9HY2JhSTk9LUQghJ2KkEKrCnKbf9Obn2lIB\n88b5cV4wlGZ+diO9pR6n0ufOnDI76TJ91KouAAR4IELIggR4pI3lkBRgTbQimSaqhIQpfMTQUOyH\nhIW+1AvM2lgFNkllULWTGvWJcbwtkzNNEz1ekZPRAgVA+7ipQ1GiEojRwWSUiBs6njJ9TlpEapPk\ng8+wXs+YiAQ8tCaEUh+Hz3s0UTid6dgsDdUeiqCrN4YxMxozMj6rYuzDfYOGjRr1BuhMZ5VlGv1V\n06YiFIwd7E35u6iUdnckBa7TUvmY4MMnDdNSPEIq2xqmQRKNo50qXoggK5HIBBHDKTU1NVi4cKHj\n/bzQA30AACAASURBVItCCDnBy6naepyk7jLxIOnNz8mLw7GVuGZeWdpxMk1vmVWdSYq5OCJFreyk\ny/RRKz8PnFwjp5ilVU6ukdPW8GabkFYZtkUW0QByRGO2MIiA5hgxBWiK+kEKIB31l1qanDPpINw+\nbipCGt9QPBBM3m5o3QOZ43HIICIVs/AFjSuREZbUhpfD23YMyOgw2Ec1HZumoYI8pM/3Y/de44Gs\nNOhTb6S1LJ4VTBn8mumsMrPPn9VFXu8dU43xn4lBYqoz0xEab0w7C0DCE1QT6UVXoALbGqah5cyv\nWe7rRXUY6wrN8JKTTjoJjzzyCBYsWIBAYPjX7imnnEK1/4gVQirZTm3R9vZRDdl212dmft64fwBn\nl4TSxECm6S2jqrM9fVzyYlopJsTRpeMS5maakn2adBkpanXxOAkcRxZ22i/kmAJsHSQPIB0EjxOE\nfuyVAuiFkOw3pBqNVfoVwTDqMyj4MGGwhzgUVW9yJqFPeekfG6iuI+6nGm4ln99wbUYGaR4KTq2T\ncek4CWEJ+OlOMenLskJrOjZKQ5X6OPzo/Z6M+viYpd5UOgZk3L+6G92EdJldL5LVZ9CuCAIS1YTc\nzm2YYPI3poXUOFHmeaxqXIi3p56R7CNkxyCdbVgUiJEJW7duBQB8+umnyfs4jsPvfvc7qv2LUgh5\nZZ52c24YzRqdnCcT87OT7s1mwqt1cFihhOIc/tYB7O/ncFtj3HbJvp2oFUnYtbd04vDu1O3MRmD0\nQcBJ4gDO9PWaTog//HkXgnXVBn6PQQjN21AxdjL66kZDERIfN26o3D0xHjUdq5QXAEg+P+L+EuLa\nVcOtEItCjA4iHqAfZ3NarYyvDrUYGJSAXkoRBAybjiVZgQIlpYliiQjUl/KmKTVazFJvWhJdq52f\nxw1PkNUIDW2qU8XN7tExwYexx84Abdw7F52jmQhiZEqmc0uLTgiRZnwB7piptf/OV4GVqfnZLh0R\n43lhJFoHebx6UMDOXnsl+yRxAwBdUetBr0YXK7PmghVDlWE+DsQyeSBxkRMBU7+HoMjgACji8Auv\niL6UFJYeq5QXAFORoxpueUVGaXdHyrHSSYiFyqGI1xcGhjtsm72XSKim4xc29RMHtLYbiBe7fXzM\nUm9m0J6H9nOYSbrH7aGqepxMk3eClQHayb7FzEgZwp1tNmzYgF//+tcYGBiAoiiQZRmtra3485//\nTLV/0QkhUo8fN950To9B60Fy64PhlvnZCm33ZrtsD3HoM4g00EStavx0nbCtvozNmgtOEyKmc8W0\nv/RVv0dK9+iOI6gf8ulYpbC0KRHa7c1EjtZwW9+6B+A4hBrGAYRqipJ4DFeU9qCKT494mb2X9Hxp\nUiL1ZJa2Mhq82mlzpphZBZhfAKIG1jarfkFuX5yMokFuiaB8mCifiRgcif18mADyhqVLl+Lb3/42\nXnvtNXzjG9/AX//6Vxx33HHU+xedEALy482Wy+7TmZqfadCntuzQH094hkjeE5qoFU1ajfYLWttc\n0MwLBBhf2NTu0doGiar/J06RwtKmRmhSXur2NL2FOAANB1tQWxbEPkLUalykD/UVxu8L9T2jjish\nJfNqgxy+Pr8cAs+hY0CiSltp4QD8X1MY508vQW2pQBUZSqsAC/KYOUrEkjmleGhNKOf9goywEkGZ\nmqS158mn8RkMhpeUlJRgyZIlOHjwICorK7Fs2TJ89atfpd6/oISQF2kuLW4JFK+Pb3XuzuY2V3r7\nGGHmC6Kh2qdgZqWCvxHKj6yiVpkOetXDc4m5YWcoxl4gK5+HigglrUEiTQrLzvZNB3YB8rBwmQsQ\newulPc+d2zB1+hzyWI/61Iug9pe6NiX58gEBH3eni9/54wNJ8WKWtgr6eYSj6ffLANbujWDt3khy\nNpmVgdqsAsxJvyC7n00n3iA3RZCb0aBszBAzer1GYlSI4T6BQADd3d2YMmUKtmzZgi9+8YsYGBig\n3j+3P49s4lbJe2dzm+0ZYrSQ0nJG5/MC7XlUjwyNMLDz3M0M2TTMqlCwoE7C6bUSanwyOCio8ck4\no16yjFrRmMGd4OOAakJ6KFPUFBYJbQqLZvtw694UEQQkLp7b2/bAFx00rTrikKhSOrtzH87t3Iuz\nO/dhbv9Rqi8ASQH+eEjAvkjid5O6T10pj3OPLUnpwxMQOZw4jhzS++IEHxZODZieUzU2r9xC9yWm\nVoBpBc6VJ5Ti3GNLUFfKgzdYpx4773+rifK0wlmLW5Egu2RrkKqR2GEiiOEG119/Pe644w4sXLgQ\nq1atwle+8hXMmTOHev+CiggBwx4gNyrDjGaGZYLTsne70HSNtoOd9ZqZaHkokAHU+BQcV6lAUoBP\nQ1xyPlhQSNz+W6cvGRlaUBdHtZ/uedCawWkauHmF/pc/7XgMIGFdVgBw8RjkoSozxGOIH2hBrHmj\n4TnVC6lVpEAftYqDQ7dsXBUHAK8fFPBRpwDVWK3KrePH+IhVWEr62LQki2YE8Zc96VPo9WQyCDXT\nfkFOMRNAZtEguyKIJhpEkxbLdjpM28lde5vByJTTTz8dF1xwATiOw6uvvop9+/ahooLcQ41EwQkh\nIF3AZJIy86KxopciiKb/jteYmWhPrJKxcJSEOk0kShVta9sF/K0j1dvzt47h9Eum554sh9Heku7t\ncZM4OOpBqSpm4zH0tI+bit4hA3Tyz+nzA1DMFcYQnxzaZ3qhVL0jKaM3BkVUcsPeKDUjJSnAqlYB\n/+gke8G2HoohEldSREYkrmBLGzkst6UthkuOK6Wq+OoakHG0X4Jf4AyFjDpfTJ1wr9/OqF+Q0Vwy\nmh8wRuLaqQiyi5UIovUF6UUQH4vC39eDaHkVZJ915+lMYAKI4RZtbW1QFAU333wznnvuueScsYqK\nCnz729/GO++8Q3WcghRCRjiNxBRSSaPd/jteoTVkd8U4BPhEV5xNPTz2DnAp4kwdv9EUMvb2nDsq\n0beGJsJFMoNPlsNEg3MmaC9uZlPk1eVaXfBIPWO0fHLkc5TMmEdMHQmjJyC2c1Naaox4HAoxpB+9\nEYKYrJ5b6E+8jm+2pQpXPaQqLKsp7+G4Yujh0eITgJ9/0IvOcHrjRXW8xscHI+gMK+CR+PvUBXnM\nG2/sL0qdkSbZ/hHhJMKYTV+Qk5J5TpYwbfUrqN+5BYGeTkSqatE+/QS0nLsECu+sGEKFCR6G1yxf\nvhz/+Mc/cOTIEVx77bXJ+0VRxJe//GXq4xSkEHIrepOLqfVG56dZh12jcCZjOqzQmmhfPSBgQ7e5\nODPz9nTFOPx0p5hMn1ldnCQFOKNO0oknH1qdj65KQf/rPg4OWytGpXSIVueJtfcNEHsB0aK9EHKl\n5eBKyA3/uJIycCVBKAN91Mc1unCajd5okQI4Q+nF/p2d2C6NMj1HlU9Oq8KimfJ+5QmlCMdkrNtv\n3B06IgGRcOIY+oaI+vEa6pk6wuaNE1P342z9iLDyBXmNV+boaatfwYT1w71Wgj0dydu7z78ieX82\nI0YMBi2PPPIIAOCXv/wlbr75ZsfHKSizNA20IimXIkjvcdI/ZoSZmOiJ8eAnjEoe2+z4bvuiWvqN\nxZlaJKR6e8hwCMV5KODQFePxYbuAN9vSf42qqZonmkU81uzDz3eJ+LBDSAqmTH+B6o2uMoBPyhrw\nft0UfF5C9lMMVNdB5px9jPTRAGUwDGWwn7itMtgPZTCc0fFVzEZv9EJAv5L4z8oQP7tKSUtZqT1+\nSKhVWwKfKLevDdrL5W5qjaJ3ULYcr7GpNYpIPPW9ZtbfSPs+JeHUa+ZWNMjtfkEqfCyK+p1biI/V\n79wCPhYFJ0s49k8v4Qv/7wGc+vS9+ML/ewDH/uklcBSRSQYjWyxatAhvvPEGFEXBvffeiyVLlmDD\nhg3U+xekEMq0CkubCsumCCKJEG1VmZVfyUxM2OmR4uZzpq3iUr09tJAuTmpasCtmLZrcYHtZA/aU\n1WJQ8BGbEQLDvX3sQrwIyhKkw58nbwZiEYzpbkMgFknc7+DiQzqPWqJPQu2oXcZJqAD5fDwUnF5r\nXOFHU7UVEDnMH29vnkvngIy9nTHLPkVqyk5LImVHXq9ZtWGmIzSMoBFBc8dMxtwxk+GTYqgLd8Mn\nGZdEOkmL+ft6EOghP79AqBP+vp5kxCjY0wEeSjJiNG31K6bHZmkxRja555574PP58P7772Pv3r34\nwQ9+gMcff5x6/4JMjaloL+h2ohy5ToOZnV9bFaffzswoPG+cH/0th6CPJ3hdwWZnpIfe21ORbKqY\nvq++wzRNWrC9xXmVmPaCFgeHfsGHVoP0kRZSLyAzrC6AseaN4GUJN+/5AKft34yG0FEcDVZjXbAO\nz46a4yj6pE+TmXWl1nbUNuq6fWrd8DwyErRVW2lNEUt5BEXgQIgsdBQAv93Yh4Bo3KUaSP9R0Nnc\nBlkGqn2irdEzmYggN6rEeFnGxS1rMfdoC6ojIXQHKvFJwzS8Me0syLz994HeIB0tr0KkqhbBnvR2\nDZHKWsQDQdOI0Z6FlxLTZEwEMbJNJBLBhRdeiP/8z//E4sWLcfLJJyMeN/mS0FHQQkhLvhmdM/Hn\nmJX1G3WNPi8YMjyWGZmU4av7zqpQ8BHhmqFvjqj6is4dBbSFgboA8EwL3cXJKvK0e1cPqjOMb+oN\n0TSQegFpsd0fRlFw019/g0u7WpJ3jQl3YUm4C1AUPD3mBHvHM0Bf0h+U4hgb6cNZdcOi7ixfL8pq\nSmx3KNdWZemrtvQVW1rBFBQTk+nN6DL3WAMYTsHpe2q5NXomW2XyF7esxZcPbErerouEkrdXNS5M\n3u+0VF72+dE+/YQUj5BK+/QTIEbClhGjwZqGlPtJIog1TWR4jSAIePfdd/GXv/wFt912G1avXg3e\nxo+FohFC+YRbs85I0RzS8FEnfYQyKcPX71slKhhXIiMswfSCSTpnUAC6CBF//cXJLPKkpnOcol7Y\n1FSYJYoy1AuondgLCHDeIC8gx3F6byvxsdN7W/F29WQc8pchQinUtOvRRoX0Jf1zG6ohQsHe/uGL\nJm/zvZZalTVc7fXtKxLi7bmXtqQ9duUJpcky97ZQnHqQaokIlIocOgc1VWOaY5I+c7SjZ7zwBNl9\nPwTkOOYebSE+NudoC96eegZigs9SBFn1Cmo5dwmARIQnEOpEpHK4aoyTJNOIUbQ89dhGIkj9f7GL\nIafVx9noO1fs/OhHP8JvfvMb3HvvvRg1ahTefvttLFu2jHr/ohRCbpTDZypmMn1jW+2vdo12ilUZ\nvlmkSL9vd5xDdxz4Yp2Es+rjafuY9RHqioFKRJn9orcakGqGKoLi4NBGkQoDgPKOQ2g40GIaCTIj\nIMdRGx9Ep1iSJmhq44MYFSebosfEw3hu7/s4IgbxUcU4PDt6rq1UGamSTC3pJ/VEUjF7r2mjl/pq\nrmS110uJ9ArxMQxXeFmV1GuJxoF7zq6EX+AM+wjpsfoRkasGnCS+WFOP6mZylLcm0ovKaD86NFWM\nTlF4AbvPvwJ7Fl6aVhU2dkYDwl84FcH3/pi2X/gLp2LMcWMsBU6xix83YCIoc2bMmJGsIAOAn/3s\nZ7b2LzohRGq0CNC/2dyoqMr3N7aZ32ZbNwdZFrCjlxwpMtu3KcRh8djhi0tYSnQlbulLDOw0ukSF\nJeC2xrhlHyG3+wdpUxwRQTROhw016RKjg8mO0E50F6/I+JfDn+D03laMioeJgqZTLMERMYixBDHE\nARAAjI2HsWQodWaUKjMSW1Y9hpxiVpW16WAUioHQUjtIA8DWVvr5KDWlPBrKhkdr6CWs2a9svbBz\nQwC5GQ0CgJC/DN2BStRF0sVQV6ACIX8ZVUqsZX8PVQdp2edPS3MBwNGrvgEAKN+0Ab7OdsRq69E3\n7+Tk/UzoDJPv3/sMY4pKCJmJGFKEx+0y8kLB1G8T5/BR57AS0UeKaKrEavyJqNH6Tg4RefhYRjGH\n7hiHQck6wkX+Re9O/6CAFEdQjiMspLtmg1IcdTu3WM7zAhI9ej7tOQLwQlqV178c/iQpYACyoInw\nIj6qGJeynRGn97bh16NmpwgdGrFlB6tf/FEZ2Lm1DaUTGwyruTrDsuHfXlvh1RGmj7CZDVBVyaRT\ndC6ZO2YyYgA+aZiW4hFS2dYwDTMmphvdjaAVQ0QEAUevvR7tl18N39GE2Is1jAYEbyo1GYxcUDRC\nyK6oGakiCLCaFTbcoE6LWplFUyWmT51ZYVS1Y4T2F73dC1lMAfoVAYc/70p584tQMHawl+gR8nUc\nRiBiPgRUQWI8RndFFUpKyqAM9kM6/HliPpiiWHh/UgXNs6PnJu9viA9AAKmuDmiID6A2Pog2f3ny\nPhqxRUIdvQGkXzhJYijNJ9bShYDIE6u5aoM8FCjoDKfLoUSlGIej/ZLhew8Aaks4dA8qqNH4gHKB\n3anymcwRe2PaWQASnqCaSC+6AhXY1jANLWd+zdYxnZL8u0sS6l9+ERUfr4fY2Y54bT1655+SiAox\nQcTIEw4cOIDdu3djwYIFaG1txYQJE6j3LSghZPYLL9MIjxczx+ySrSaPZn4bowuRtpzdrPoGME6d\nGXFcpb2qHRU7IkhWgLWxCrRIAYQgIFhXnTYiY3b/UQBAW6AcYcGHoBSDr+OIoSFaS/u4qQiNPiZ5\nLK60AvyU4wAAsaYNpt4fvaCROR5PjzkBf597EerCPfj2ltdQF01P/x0VS9EpliRv04otmvSYlRgi\n+cSMmDc+4TkheYCCInD/6m50h42SZwluP7PSdO5YNvBaBOmReR6rGhfi7alnoDLaj5C/zFYkSCWT\n4aqtuzpxwj/fQK3GJ+TrOJq8ffTa6x0fmzFykGUZ999/P5qbm+H3+7Fs2TJMmjQp+fjvf/97vPrq\nq+A4DjfeeCMuuugi9Pb24s4770RfXx9isRjuvvtuzJs3j3j8P/7xj3jmmWcQDoexcuVKXHXVVbjr\nrrtwySWXUK2vIIRQ9dRRqG2oB2DfCG3Va0h/nFykzNyqMrMDyW8zs1JB84APnYQUhTZqY1Z90xU1\nTp05JZMSf5W1sQpskobHLqgjMgBg7pAA4of+Pau/HRFBRMvnrVSGaJnjMVBdR3xMnRFm5v05Kpai\nnxcxNtqHseNnIDaUnosBOFRej09GHUtMkTSPmYHp445NXnDtiC0S2qgQYCyG+uLA1m7y37hEBMp8\nPLrCMjF6o/YMqg5yiEqKYc8gLbVBLsUP5BZ6Ia1GC8s4KcV8b1QubySCnAogI3EaE3zoCFY7appI\nEkF2xmXwsSgqPl5PfKx80wZ8Mu8CyD4/8woxTFm9ejWi0ShWrlyJzZs349FHH8UzzzwDAOjs7MSL\nL76I1157DZFIBF/5yldw4YUXYsWKFTjttNNw/fXXY8+ePfiP//gPvPbaa8TjP/fcc3jxxRfx9a9/\nHXV1dXjttddwww03FJcQ6t5zBIHOmGXO30pA6EWRV9El9fg068pVBErvtykTgXcPCxiIkS9M2nJ2\ns+obs9SZEZ/0cDhvNFCuezcalfif3HcUhJmahsSUxAwtEm2Bcszqb0+pmhKhoOmzA9Rt1z/tOYIS\nX4CYvlJnhEUGJEPvT58g4leffZhomnfg72lN84xSJOr96gXUJ8VwZP8HhmJLGz1ygjw04mRrNzfU\nCDOdRDVXBTF6o+0Z9MemAfx1L10jyvnjA5YiSN+fyI43SB8trISEaUIEZ/l6sfczeyLIKV4MVNWL\nICcDVv19PRA7CeFfAL7OdmIvIQZDz8aNG7FgwQIAwIknnoht27YlH6utrcWqVasgiiIOHjyIQCAA\njuNw/fXXw+9PCHVJkhAIGJtIeZ5Hefnwj7xRo0YVbx8hNyMlXvd60Iopu6Irm30lVL/NqlayryfA\nKzilViY20SOVVZul3RJOmvQLWiieGLp6fHVqHyOjEv9+oSI5Id0M9Zd8v+BDqFYgGm3Cgg8RQYSo\nGV9g5yL3yaF9AC9AGewHV5pefq/OCEtElhT08yJK5YSRpp8T0eYLolFTGURqmkdKkcQIpu6Y4EPz\nmJkYS4gefVQx1rB6TOZ4SD4/hFg0LSqkZUN5g6X3S1/NpScgJsrdN1vMC+OAlF5DRpB6F80qjWHx\nWBj2w9JHgvTRwhBEbJJE9IQimGu6ynQyTYfp8UkxVEb7IcRrIIn0o1xIkSDaAataouVViNfWw9dx\nNO2xWG096k6YDMXkAmUEF4lA7OlCvKrG0f6MwqKvry9FqAiCgHg8DlFMfCeJoojnn38eTz31FL7x\njURFYmVlJQDg6NGjuPPOO3HPPfcYHr+xsRHPP/884vE4duzYgRdeeAEzZ86kXl9BCaFs4oZAoY0s\nOY1AuZEyUo9j5OsJ8gouGmPdZFGLPnVWJSqYWqagpY9Dj0SMmyAUT+9jZLQmdUK6We8gbTrDvCIs\nhoA07PC1LYKA5Iww1ROkRZ0RljAxp3qNypU4jolHiMfWNs1TUVMkZmijR9WREI6KpfioYmzSgK1F\nNXgnukuXJNsDyP8/e18eJ0V5bn1q6W16lp7u2YcBZGQRGLYookFxCCQuCeIGGKNG782NMRqjWfg0\nLvlcE/VGvX5Rc2OiicGocbt6XRIxiAhBRARZZBsEBhiGmenZuqfXqvr+6Kma6ur3raWXWaDP7+dP\npqtr6Znqfk8/z3nOQTClGhaTzGm/9Ka5ZNKy8VAEPeSXDQAocTL4ydnFptphJO+ij/oSZI2UKE9q\nh1mpFgKDUw1Sx2uURnoR3OrB/rrJ2DDrAmr1Rk8LxMaiKNu1mbhNLy6janIVemedlqQRkhGYeap1\nEiMIKH/hubzwehhidG0RytzW9WTtQQDkJBYFhYWFCAYHAqBEUVRIkIzvfOc7WLJkCb73ve9h/fr1\nmDNnDnbt2oVbbrkFP//5zzF79mzq8e+88048+eSTcDgcuO222zBnzhwsX77c9GvIEyEdkPRF6VZr\nzOxn9rhyy+iLPhv8fSI8NtG0KzQJuqn28eTMLzVoRIzWOktUnfSvZXs3g5kBP4ISh85YGfl6waFF\ntKGajZkyUtSbCKuOBJSFLi0S1I/Yrk8BJDRBjGZqTE/E7BTJlZF0TfO01aN/dbZTXah3ecpgU+WN\nxR0u9FSOwurWQ2hkklPrjNLoPU4Gp45yEKs3ctvq77tCWLVPhwHJz49J+HBfJOlYkbiEtoAAMFAI\nUiQu4dMDfSBlR8tTjkaGiUGJQw/IC7DVamE61SBaS0wbr1EU7ETDzrUAgI9PXaQ8bkYIzYgCxr/7\nPJw91uIyZBh5CVlB+QvP5YXXJyBmzZqFVatW4fzzz8fmzZsxYcIEZdu+ffvwm9/8Bo8//jhsNhvs\ndjtYlsXevXtx00034dFHHzWs7rz00ku4+uqr8ZOf/CSt68sTIZNIl/yY3d/K8QdaRgk9TyKFPbGN\n9C3YCFaCUwHz8Rza1plcKRrQmJDDVoNsQrBaDAE9hFuUAfBy1Juk5TDSDJEmwqojAeXxjL/lSxJi\nOzcitvszME4XpHBI8RHSEzHTIJvmpQu5ehTp7iI/geXAVZLHS/s8PsS7+5IqIXIaPenvUcyL+L8L\nfShyJhOS5LaV0P/XNmauYWFgwmzp9AK8sCWItfsj/aP5EhyshFNLJXzVJ6ArRvZd0Ib20iYM9e4z\nK9XCbJIgmxCjxmuMad6BjTPOTWmT6Qmg61e+gprP11OvgxSXkQSVl1Am7SwmEtEVXrdfenm+TXac\nYuHChVi7di2WLVsGSZJw//3345lnnsHo0aPxta99DZMmTcLSpUvBMAzOOusszJ49Gz/4wQ8QjUZx\n3333AUhUlWSBtRatra1YsmQJTjrpJCxatAhf//rX4XK5TF/fcUGEshGpkW3kahQ+KgJf9NlAGnQn\nfQs2A6uBlEbxHDSoQ1d/s5snCm7l3DAbQ08/l/oXU1nLAcBQM6SdCHMI8bQqQYDBoicKsAe6klyd\n9SbGwv2kTItt5fVEHZBVNFSNJV4v43SBcZKJVtzuUCoh8uSY3t9jmkdC7EAroGnvJretGN3xeBI+\nOxJFnz+IdX51xYZBRGSwtiNh+G2GwOvZLOi9rnSrhWagJ44ujgbhIThKA0BhsAsFoV70FvlQP6bE\nUADNxqLUBHkZ7ROmG06PAYDkcCBWUWX4PBr47k5d4TXf3ZnR8fMYvmBZFnfffXfSY/X19cq/b7jh\nBtxwww1J22mkh4Tly5dj+fLl2LhxI95++2088cQTmDZtGh566CFT+x8XREjrATTUhCiXYme2rgL+\nbeRv+dpvwVZgNpBST7tjlogV8onF0yg3TI7OkKd5GAyQIDVImqH6MSXEsWceUtrCaCPouTrTRMwb\nqqZAYhjqRFiuIIVDVIE3H40kVUJkyH+P/ayLeI+otW56kRtm0dEnYFuUXkHa0cPglBIJ/0rNBMVY\nMYT2JnPRK/NsvejuiaRdLczENJEEvXiNgNuDPtfA34wmgGYEAXvOuxz2QDc1QV4C0NIwRwleJUEm\nkdkYj4+XlOoKr+MlpRmfI48TF5IkIRaLIRaLgWEYZeLMDI4LIiRjqAmQjFxeh9h8DB4bj85YKtsw\n69BM0vbojcSrn28mYkNLxEjn0xKvIlWbSwbLJCo9c6VetIg2vBwlfxj3gkNQ4uDpT6Cn+b5okQ4J\n0lv0aK7OPnex7gi8yLKGE2GZgFgV0hF4F3R1YOeRoylO0/LfIyb1wj3OSxTpy2SoOyxSIze0cPIg\nOlIX8xJ1TB9ImDie5YuDY/TvIyN8ebAbDUBa1cJskyAg0dY8clIDfP2aIDUO1E2GwNsTfw+dak/N\nZ2sgMcCXjYsRKS6Fi6APChd7see8b1PF12qoq2rpkiLJ4ciu8DpNDOZUbj5ZfnBwzz33YOXKlTjl\nlFOwaNEi3H777brj9locV0ToRIDVNpYaZrQ9al0P6fmTiiXTeiKj8y2uERLCaDbVxE4NGwNUszGq\nlkNupwFDR4L0BNHyBJjeCLyZibBMQCJDWoG3LRZRQmX1YGOA6EE/7JQF0b+rBSX1VfAWsOgg5HFw\n+QAAIABJREFUkCEWiWqEPB4vQcL7e1NF1FNKJHzRTXet9vASPPbU+wgAeiQObtDvKRK01cJsw2zY\n7dTaSmyovgBAQhNUGOxCwO3Bgf6pMRl61R5WElH36WqA5RBzFhCJUMxZYKolpoVR/pwesim8TgeZ\nDr1YRZ4EDQ7Gjh2L1157DV5vevdlnggNATJ9E5ptY2lhVdtDev6/OoAap4hOwnqhJWJG5zuyxw8b\nA6WSowc9LUc9F8FBivFdNmDmW7+eINob6UFJpBftBV7EOBt67O6cVX/0kEKGNALvcSUVSU7aevlj\ngP6CGGw6ipk1xcRYjXn1DnxjgksxP2zb2YJIGZkwHwjy6CJUiwBgqkdCe1NigbcxQDEEojHimXwv\nQtAn2yRks21qlgTJkFgOH5+6CBtnnIuCUC/6XEUpAuloYQkiJV64ugm9wX6U7dqcEFMR4BQiqB3t\nhuRwEFtgetqqtMlQloTX6WAo/dryyA1efPFFLF26FN3d3Xj++edTtmt1RzTkidAQIRM9k14biwar\n2h6957dHgDNKBewM0ImYmfNZhVoz1AsuqQ3ypfXDmYLZ1oeeIJoFcHbzZ3h9fKPiDeOJ9KDLUZzi\nIi0b6OWKJNHaZFJfAGwx2a4gXSx09QAnFyuxGurIje49RxEEEAT9fg7EgV5KgcbOiPhGpQC1NRPN\nGHG74EQULIoh4CQugplcH4rYBCmiVRA/P9IGwe4EF4tSY1bM3htWSJDWzFLg7egtIse3iDY72idM\nT9IIaeHo7aQSIVtnhyJQJpGamvFey6HGZmFGeJ1toqL1a8uToJEPiXJvW0WeCA0BzLpOG4Hk7Ewj\nWFa0PVEROBAENSYjKrGISQJ+NjFOJWJG59u7pxsek9Nt6gwoWTOkzoQy2w6zAqvajwjL4+PCKizu\nIlOyyR2Jx88+MqDpULtIv1E/j0qSJteZM9vMtIJhJoxVC73KAMcA5xb0YP64hMjfKP5Cvp8FVZRH\nL9GAE4hJDIJx9c90Y8Rov09QD3hsEXhsEQqUatEodCe5EIkAtrvL0XzK6CSTybIj+5Jk+tl2kAaS\nSRAXj1IrQerKXNOCS8AIAmo+W0MkbJGihACZ2BozIVAeygyxXBAV+bM3T4KODyxbtgwAUFtbi4su\nuihp24oVK0wfZ0QRITOhqSMFWjIkP5YtyMc8+kULemKAkzMeNdZqehJTWmQ0BRPHoU2oGXkTuTXt\nMFLgpV4GlIe17pdkFukucq96T8aFXV8SnXJKI71oaCd7w0xtawIrikSSVG1nsa56cdJiSFskp9ZW\nmiJDtJH6dGHUJrGzAA4fUypARtC2VEmQ71lZKqdnjJgKRqkWtRdWYlrgmCKO3u4uTzLelE0mAaC8\nXztl5XdnRRcEJMwPZ296C2Obd8Ad7ELQneworW1PSiyHPeddDolBQhOkQfv4BnDRCFxbU32EsiFQ\nHolRGSN1zcgjFc8++ywCgQBeeOEFHD58WHlcEAS8+eabuOKKK0wdZ8QQIVoExXAZmU8H2rH/bH5T\nGTCzc8LfJ8Bjk+DioKvtoeWNkWA0qm8k6rb1r4g0srNssg0v7IgRWx3AgG9QOtWgbBvjyWi3ueCn\njD33ONwojgSI+3kjPZjVSa4kTdj3KWqONmH/6Cn4ZMa5OG3zu9RFEhhYUNOtDqVTFcom9FqqamjH\n4/WMEfXQ7CpBu8ON6nAvJgbbcZAnm7D1eXwQW/Zje4u+kDwdqCtBsze9pThIA8mO0u2X0AXFTV9f\nArBcwk+ox49IsRcxhwtle7bC2eOHYHcADAM2GkHMV565QDkflZHHMMCYMWOwffv2lMftdjt+9atf\nmT7OiCFCRhjJ5c5c9MG1ZnadMQadsYTQOSQgRdtjdgGSYWcTifV60BN1c0ziW/eK7WSyI+4I4ktK\nq8NM1thgQyYPW4PNSdEIMrb66jGl40siSQq6iuEOkce9GQBFfV1o2LkWVa37UN45cK/QYhcA89Uh\nKyAJprMNvZYqIKEQAsYTxuP1xPS6YBiEOBv2ub04FoogbncSnxa3O7Cj+5i1Y5uAth02tnkH8Xlj\nmndgY1MbxtaTYzAklsPery/BvsbFsAe6Ubd+JUZtGqgQcdHEVF64phYHb78PUgE9yNYM8lEZeQwH\nNDY2orGxEeeddx4ikQgmT56M3t5ebNu2Daeeeqrp42QQ1Tk84N/VklJZGQx4J1Yr/w03HP2ipT+D\nKRUhAbhpfBzLJ8bws4lxLK5JjLLrL0CpiIgM/t6q/81PFsH+bGLq+YDEt//9LPkbeJPgpLY6ZN+g\ndJBtcgAktz/eqJ+HD0bNRLujGAIYtDuK8cGomXh9fCO2ltcT9w87ChB0G4/Oe7vI1z6meQe4eKp5\nIS1FXnvNWqirYmZ+X9nUkcgtVRIKIeI7jnY02smRKvNsvZjJBVGMOBhIsMFa+zRU5FEIgxZiKAgp\nGgVTUAiY8N0xA+3fpyDUC3eQbJYqO0obQbTZES0sga9pG3G788hhlL+cOl1jBUZRGUzEOE8ujzyy\niddeew0PP/wwACAUCuGJJ57A448/bnr/EVsR0lZR5EpILltlw5H0kGAkVA4LqS0tPU1PQimU+rh2\n2owWwkoSdRtdZxAsCiEgoOMbZLUtZjQJlA1zPG3oqXr66436eZgSPJpU1QGA8q6jaCutRpGBgIY2\nvaSOXdAi25WhXFeF9Fqq47kwCnS+uqkNOIMSBxcErIv3t10lDmD0ib5gd6CwoxUBR+r7XIpF4fzq\nBWCcbth7/Sg5+AVam/ciwtBJkR7ZJJHUPlcRgm4PioKdKdtkR2kzv/+EvxB9pL7ws41oW3olVdNj\npPuxGpWRn9TKI9f44IMP8D//8z8AgIqKCjzzzDO46KKLcOONN5raf0QQIc+4iqSfaW+mdN9kmbTV\nhuMb20io7OQSI/BqwqK3ANEg64RK7eZCWK1cZxEEnMRGsEUk+wZZaYuJAFZLbvTpTAJl2yGYZJDY\nUO2Dc2Oqrw4AOCIhbJ8wB6MP70RhsIsouBYZFhyBDGljF8zCrGha7SdEQrZiGOTjnCoBQa6IaJNA\nEtVrofamarT3oubAYYQ4HvucHhx1FCLM2YikiI9GUHaoCawgJIJn7Y5EJSgWBVfiAysKuHb1H3F6\n0waU97ShzeXBWqcXT1U2QGQyL64LvB376yYnaYRkHKibTG2LqcHGomBjUUQLS+AMkL8o8F1d5Fwv\nHd0PE48r5MhKVMZI+fKYx8hGPB5HOByG252QWcRi1oxRRwQRkpGLqap0MRwJkAw9UuPigMf28ETC\notb0JMiJvFhQnH37J3fSDWG1swnRaydSwz+VVPkY2TfISjVoteRWJn+A1EmgXIxCazG1thIFvR30\n1kdfN7adcjY2zLoAX13/Cibs35zynK4iH3w9qYuPHLugd+5Mq0Jac0UARINFNcwSI+1+2sqOmxHA\ngT5BSGqTyWg60A0eQJEQw/RgG6YE2/F5UQWaCS7eBV0d4CQR5Uf2QWzZD8Fmx84j++D8asLN+drV\nz+DCz/5XeX5VqBOXhBLVmyeqpicdy2o1SIbsHK12lO6ZOA3B2Y1gY1GqE7Q2fFXQcYyO+chj8zTd\nj2vXDvDBYBI56p3xFXjffzflGHqTaMP5MzOPkY1ly5bh4osvxvz58wEAH374oemJMWAEEaHhQoJG\nypuZJFR2ccCR8MA3Vy1hMZMOr8aUEkk5BwlGIaxH9vgxr98zkER2SAuiVd+gz4+0oe+U0cRtfR4f\ntm5OHTnOFYxaHyFHAU7d/C6q2w5AAiAxLCCJiYkfAKU97YjwiX/b4hEE3KUpsQs00MgQrSpEmh7T\nVoZohEiGGWJklAwvV3ZWRclmicDABKEZ8JAwo7cV3T0BperDR1OjRVhJxPaDO8EUFIJxuuGIRXB6\n0wbiMc/sbcEfKqYgwvKGlUI9EgQkO0pP8ggY9ckqlO3dhppNH6Yky6uhDV9lY3SdDoms6Ol+XAf3\nK/+WyZF/wbnwLzzfdFTGSPnczGNk4rvf/S5mzZqFjRs3gud5PPTQQ5g8OTVHkYYRQ4SyiRPhTal1\n63X2V4JI0BKWsAD0UkmQhGJewjRPopLUGbUewqpe/GhkRw2zMRxabDvcCsHu1J0EYpwuSH3ksXYa\nrI6Xy4ufUevjK5+/l7SN6W+DsSoBryOe+PeRaXOw59xvQ7TZMa5/W7rGkpn6ChkRIhlWXYrlNpgd\nAtUsUW+CkPb7YIGkqo+ee7QUDkEKB1EaDaCcUI0DgPJ4H7zxMMpGT82aM/jY+nKM+sdLSd5AcrI8\nRAGHTl+AaGEJRJtdN3w1ZndAsDvhCPYi5qOTFT3dDwmFmzdh/33/aRiVcSJ81uYxdFi1ahUaGxvx\n+uuvA4CSNbZ7927s3r0bixcvNnWcEUOEhst4/EjzLZKFyu0R84RFT7tTzEu4ZUIchbzxc7UhrAB9\nMbRCdurHlBgu+nL1g4tFwUfDiDtSp9PEUBBSmJwPlg2Qvv2TWh8H6ibj02kLsfTv5qccSg/sSXlM\nJiLZcto2UxVSwywhMoLWWyohmtefINTeO3q/A/neYCURbJSs2Rq4GAFCazM6R9WjrbgcVT2pI/Rt\nfAG6ODv+fc8q3fgUo2qQDKNk+dpNa1D76WpESnxonzAdh75yNjV8lYtFsenqn6N8fLmu6aGe7ocE\nW/sx8P52xKprDaMyzGKkfbbmMfTYunUrGhsb8fHHHxO3Z0yE+vr6UJCh1wQJoijil7/8JXbt2gW7\n3Y57770XY8aMyfp5co1M3rRDQeqKbUAJLxGTvEv4ZMKipzGa5pEUEmT0XNmoMVd5RWbASiIKujqS\nNEIyhNZmQLRWaTJTDdJb8GhhmlMLQ3DqTPpo4ejxwx7oRrg0VUBLI4q58BYiIdPJMm1mGGlyUIY8\nQag9Pw1mX7+6Qhbb9SkCANaPmYHFW/+R8tx1RdX4ad/hJP8odXzK6+MbTZ0TGCCRRsnyQHKFiBa+\nGin2IlxabkhWJIcDvbNOS9II6YEBUPreOzh21b+ber4R1HKFPCHKwyx+9KMfAQAeeOCBjI5D/YS5\n8MIL8cADD1gyJTKDlStXIhqN4sUXX8TmzZvxq1/9Ck8++aThfuo3hVbjM1hvmExzarRv9sF8o9tZ\noIAHMcm7gE/V8cgao21dDLriDDy8hKkecsK9nnFiLkiQ2WqQDFn7odaEhI58idiuTy2dV0uCtG0Q\ns9/4geQwzfoxJRj1ztsUSToZkWIvooV0smGmapYujKbIMoFeZhgJ6gnCbFbCkiBJiO3ciN8yRRAq\nJuFM/0GUx/vQxhdgXVE1nik/BX868CHxWFPbmvDWuLmm2mRq8mgmWV5G2d5t6KifmmSgKKN9wnRU\nTTZXsZFbZmrdj+B0wnXoIPH57s83g4lEshKtoQ1EBYZPFyCP4Yv58+eDodhiMAyDlStXmjoOlQjd\ndddduPXWW7FgwQLcfPPNsNvpUwhW8Omnn+Kss84CAMyYMQPbtpGNv9To2ncMlZ6BKQfSm2awkA0S\nNBSIigkzRRJCQmI7SdSsPzeWAC09HMhugrWZhY70jZ9BqibEalSCmgSxokgMSG2qvixFxGoEuQ1C\nM8CjoX3CdOoEkfrY2t+ZWdG04pTd/xipRSYfL5vQzwwbMFq0QcQULmx5gtAIelopUZLwhG8y/lA6\nAd54GH7eiQjL45wSDzy7Ux3DgUTGXHE0iOqTJ1q6DjPJ8jIcPX4cmt0IieuP2OjuQLTQg46TpyJ2\n8SLzZIXj0HbFd5N0P7y/Ayfd+mPi+5/kGZQJhsIYNxPkidrQ47nnnoMkSfjtb3+Luro6XHzxxeA4\nDm+++SYOHTpk+jhUIjR37ly88cYbeOyxx3DppZfizjvvRE1NjbJd/W8rCAQCKCwsVH7mOA7xeBw8\nb02ulGsylM2bfDiExVpJnwcII/Fx45F4mnFiNsiQ1SoQCbImJFPPoEVNq4ltEN+mgpSoCz2YaYNo\nITIsjsw8C00LLjF9Hi1oeWTa16n+PdEyyLJdHdLPDBu4f2Pg0NMTwZfBwSFBakRYHi32xGdYQ9VY\n9AgxdFEy5jodRRg19iRDj2tSK1H+G8v5YQBDFHXHfeXwzqxHU2k5IAoo37UZjkAXaj5fB2z+KDHy\n/pXZaL9oCfhAD5rbQSXRNeO9kBwOhdzEvT7EfeWmPIOyhaH8omsVeTI0tKitrQUA7Nq1K6k9du21\n1+Liiy82fRxd9uFyuXDTTTfh6NGj+MEPfoDi4mJIkgSGYfD++++ndeGFhYUIBgcsdEVRtEyCZJh9\nw5jtOeeyNDvUbxYroma93DHSSDzNUTpbyFWLxwxI7bCGNnKK/JjmHdg441xdTx8SrLRBDs86C3vP\nvdz0sfVaZNnSDGWTDFnJDGtxFOKUYLuSHG+EbIftyvdGjLNha3k9MWOu5aQGy/eDDKP8MBnyOPy0\njW/Bq06gFxOkyeZvh/e9t1GyZhXYSBjVxfQx/JRr0NEOZSO9noZsVt7T1XFmch1WzpHr85woWL9+\nPebMmQMAWL16NTgL4b+6nzYffPAB7r77bsydOxerVq1KquSki1mzZmHVqlU4//zzsXnzZkyYMCHj\nY+oRFivfLHJ1Mw7FTa4lJ2ZEzTLMVo8EyZyjdCbVoHTbYTRkap5YHA3CQ/jmDwCFwU5q1IUMLh7F\nJG+C/Mjf7fXaIDG7E1wsgohq8bKKbJEhK8n06QqmRSnRALNBRAzMQDeMoAMIcTZEOB68QHaRzaUw\nXPt7eKN+HoCEJqg00otORxG2ldejyYTHk9HvSbTZES4tx95vLBlof/X4EVelyOv5AMng+ickZZG1\n2+PUDUiVozbaL1oCAKY9g4YSmeo4AfNazmydw+g8eRjj3nvvxfLly3HsWGKqs7a2Fg8++KDp/alE\n6Ec/+hF27NiB++67D2eccUbmV9qPhQsXYu3atVi2bBkkScL999+f0fHUGWPaG2mklFezCT1yoidq\nVsNs9YjmKB3sDFsyuaMh25WgbMRo9Njd1DaIBBZTv/gQ609dpHzTlhc5rfOv1hxP2waRic+X874F\nW19A8YxJF3qj9bmaJrPy95Ovb3WsCJtVE2N64jSXEINDSFX/W30tucyYm5qlgFYgtUIk3xM1HAe+\no82SDxCQIDbtlyaqi0leQJSojf13Pwg+0KM8j4lEwHe06Y7lDwWySVDyGBmYPHky3nzzTXR2doJh\nGHg8xiHWalCJUHl5Od54442sj9CzLIu77747q8ck3fhDNVk21DCKu5Cdo1tCQLULSaPwMsxUj/Ta\nZ3omd2Yx1CSIBr02CAcRU3avh9g/Iq/+pq91/lVGnwHs/foS6iIHAALBA4kErXMzqRKnrT5Y/T1b\nqQpZQdOBbsTBYKfPB6pWWoPqSMB0W4yGwciY04NRNYikr5MrRDKO7PGDjQF1Xh9sHebJkM3fjoo/\nPw33zh1JhAeSCO/KgfgM2U0aQKKCJAgoX/EsMZMMFtoRww00EpRutUav9TWSdFAjAYcPH8btt9+O\nw4cPY8WKFbjqqqtw//33Y9SoVNsUEqiKjjvuuCMnPkKDBf+ulhOG/Mgw0vYc7gNeOczhsT08/vtL\nGx7bw+P1IxwEwlryrWoBc8sElNpEMJBQahMxt2ygqqTXPpNN7tKFlcU5V+0PvQWv6ezLsG3CHAiU\nt8/Y5u1ocAXAxqIAoGuOV7Z7i/I8YGCR01Z/asZ7iREV8uO0bWZhSuPDcmAKCrH1WHPKpmz8HSIc\njxBL+W4mSXAKMUCS4IpHMS7ox5RgqoA3l23SdB3FM4FRW7lmvBc140rQ8Nm7YIPWHNJFuwOetath\n62gDI0kK4Sn5iBw7U/jZRjCRiJJJpt2v/IXnLJ3/RAJNuySvUSfaWpVt3Hnnnfi3f/s3FBQUoKys\nDN/85jexfPly0/uPGGfpdHEi3WB65KQzxuCRvTaoew164ah6I/GAcXK81uTOLHJBgrK54E2trYQE\nYPspZ2PybrKbaWGwC6f9/h7F+fewjvOv1hiRjUVTKkJAYkFUEx5ZvxE3GI3OZGJPGalnGNgmfgVc\nZR0YpxtSOIi23m6UHdlnyfvICA4hDpcYR4jgueMSYpjnP4A4x8EhxImVoMEwizQLMyQoXdNJLcHV\nhqXKkH9DotMJLkxy0CZX01iK27rN3w5bWytViyS32oZTm8wKaFWadNcQs1WfE2mNyhU6Ozsxd+5c\nPPzww2AYBkuWLMGKFStM73/cE6ETCW4esLMSIiJpeaIvWXrhqKSReFmIPalYwr8Ig05qk7tcYSgq\nQerFTS9Alen/T25/MYK+82+0sMRQQwT0k6FxJUT9RjbaEjStkG3iV2A7aSDAkCkoQk9BEYCEP5OM\nTKfHeEioDvdinzu1klUdCcABEQ6BnAk2FLogGgaTBOmJpONeHw7dciti3jKUvfZSkti5b9Ip1MoP\nDTFvGQBQtUjZ9hUaCmjJS6YkJd8CGxw4nU4cPXpUMVfcuHGjJe/DEUeEhru6fiiv7++tHCKi9fl1\nWjiqFiQhdjmiCINFQJMcn0vkqv1hlgQB+gGqWviatqH95KlJAZoyZOffgt8+pashkqH99p+i3yAg\nIx8nlgNXWUfc1OfxQWzZn+RtkykZkttdLY5ChDgbXEIM1ZEAsQ2mPqcVZEsvRkIuSRAJemGpfFcn\nJLsdUkFBklGi4CoA390F947tsBH2FZ0uZcJMjcDMUxErr6RmkuXKV2iwMZzXlzzIuPXWW/H9738f\nBw8exIUXXoju7m489thjpvcfcURouN+kQ3V9evogI5DCUUkgCbEBO6ZzQXyF7yMmx1vBUI7KWyFB\nMrQBqgwkYt3N0ePHodMaAZZLmQprWnAJaiIRVO3bSjxH5ZfbEBp9jTKlU/RUem0JGhkyiuJgnC4w\nTjdxW9zugGCzpwSXZuI6zQJoCLbhlGA7IhxPbYNpz2UG6RIgs9WgXMWO6EEvLFVLTCSeh+e9d5Vq\nouhwEo/Z/dV5AMuSx+U5bkh8hUYq8tWgwUFHRwdefvll7N+/H4IgYNy4ccd3Reh4QC6qRnr6ICNo\nfYRIOLDbj8/DZcRtXwoOnG3LbErMDIaCBOlBHaBa1OvHN1Y9g6K+rpTnRYq9iBZ7qVNhHVv2Y7yJ\ndoPet39bR5thW8JMZUjbHpPCIUjhIJj+VpgafDQCTiX01iKT6hAPieoPpD6+WQwXEpRJNYgkfrdi\neKitJspVH8HpAhuNpBAeddSG+jikTDKrvkLDvbKfC5yIr3mw8NBDD+Gcc87B+PHj09o/T4RUyHUU\nRi6/HeiJl8mQUErxEdLiyB6/bgaUPCXmSVMgnW1kkwSZWeAE3o6u0irsHz2F2CpT54JpR5+BhLmi\nmW/1et/+JYZB6bv/i2NXXKOrFSKRIb2qUENFHXa2NoNVaYRkhI58SYx8UCNXmWQnGgnSgxlioqcl\nEt1uHLz9HsTKK5MIjzpqIwmETDIrlSD5c9Cqe/PxQCSOh9cwHFFXV4dbb70V06dPh9M5UOlcvHix\nqf3zREiFXCcg51I4p+f9o4WDlXD9uBjKnfqRGOoFUy8DKpMpMRk5Sw7XQaYkSLuwddR9G80rHcT2\nlx5Em93Ut3q9b/+sKKL0n/+AxPG6bsHpILbrUwAAV1kHJ8fD4z+M9kAAsaat2CpJpghDNmM4ZBIk\nMqwSomtEyKxisNphbCwKZ2eC2JJsE2ToWiGYICa8vwM8gUADAN/pT2iJLLa1qETJAJl68owk5MXS\ng4PS0sSXxS1bkm1K8kQoTZASkEcKGdI6R9tZECfITvOKqDWwiNJWDfQyoAZjSswMsimCtUqCALrz\nrx7kBa5tnLl2Q9uyKwFBgOeD98CKqYt/ybZNEMbcDP+B1Gk2s9C2xxoqx2D7FxvwvdV/xJmBFlRE\ngzjGu7CuqAZPVTZQE+ozBa3qIwForxmHPo8PcbsTfDSMgq4OeFv2Q9QQo1wKo61Ae78wooD69/6G\nqs/Xg+/XWMXtDhyddgaaFl6WlAFm5AelWCmUlFKJiee9d6hzo2ZEzupzDKYOyDuxGgiHwR46DLHM\nNyIrKto1ZSS+huGOBx54APF4HLt27QLHcZg4caIyQWYGeSJEQS5v1FwdW+v94+aBV3fGsJ916UZq\naEHTkcjTYE2CA70ZTonFJCAocXAzAg4ezFwknWtzPDXMZkORQF3UTHyrlxej7vkLUbrqH8TDsK3H\nwLZ3wDux1tJ9pm2P2YRYUlTELwIHcI5/r7K9Oh7CJZ2J8NknqqYDMHadVv8NSUTTbLurvWYceioH\nHGPjDhd6Kkeh11cJieMVYnT0s1WmjqdFLpyztahf+QrqNn6Q9JgtGkk8xrDKpKAuCaJEYWitFJhI\nBEVbNlEPE5w2g05uTJ4j2/BOrAbicbgfeQyODz8Ce+wYxIoKdDfMAobYwTrd8fp8dSh3WLduHX7+\n85+joqICoiiip6cHjz76KKZNm2Zq/zwROg6h9v65YooNUTFuKR2eJqplGaDR3ou5Uq9CYqxWgkQp\nkSfVJDjQAw4uIY5qtx1Tgm1Um/NsewZlQxdkFWZdnontBu1iVOqD6HASR5zFygqIZYnQV9o3z5rx\nXhzdcZRYtWJEAbM3vYWlzTtQEOxEl6MY230nYUrHl8TrPbO3BX+omIIIzRFafW2qVla6f1ORYdHn\nIYfaSnxi9FEmRraJX0Fs58a0zpMtKCG7sajye2ZjUZTt2kzdp2zXZuxrXAzRZleMNEkwa6WgJ7KX\nAHQuPI96LenYNZgFrcokkwX3479FwUsvK49zR4/CezQ7584E+WrO8MP999+Pp59+GpMmTQIAbN26\nFXfddRdeffVVU/vnidAJAJIpohHMLNzpeNOsjhXhM1WoZoizKQZ6DTpeMSSoF1azyPTbfjqCVytR\nFySkLEY64ZqRs+YCKrFgChnqJ1Xj+klVWKVjqh9TgrJXnksSfPsiPTj7yBbqAHt5vA/eeBgt9kLq\nNdFaWek4Uws2O+J28ti3FlxlHWK7PwNE8/q1bBknyoTy5JadKQaZ9kA3HD30946jtzPx+ky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Vsd0l53V1d6vl0nMmpqavDss8/i0ksvBQC8/PLLqK01P2GbPZVjHsMabkaAx0b+Vl8EAY22Hszk\ngihCHIDUH7IpoRhxzOSCmGfrxTxbL2ZyQRQjDkazLZvgYlGIIXLJnhakmU0SlA14J1Yr5ojc0aNg\nRFFpZbn+9jLESvr1COXlAKSEFqpfDyUWuiH6yFUysbIio4kyoF90O30Wcdv+uinYP3oKcZuaZJhp\nS7KSiOuPbsEfmt7Dn5r+gT80vYfrj25J22FajacqG/BKaT1a+AIIYNDuKMYHo2bq6oHUSPceEW12\ntE+YTtzWUzEKTf1Cab3WV9WWdYAoUI9jxbDQLGShdbrnkxwORM6eS9wWn3921q83WzqaXOpxvBOr\nLR9/uE/OjQTcd9992Lx5MxYsWICvfe1r+Oyzz1I0SXrIV4ROENgYYKwYQidSR4bruQgcbGLya67U\ni6DEwQ4BUaR6BamfQ/IRsjItRjNS3N6yD7YSr6IJUoPkHp0pCdJ+y8+0GiS3w6jmiOv+hciZc5L0\nPjJEhoHt4EHlZ661FQUvvQzn/75NHKsHrGWOqaF8+MqTP1s+TdBfhgUkMeGGPHEGOhZcovxN5TFy\nbfSGDKPxdz2n5yeqyCTALESGxZoZF2K9JineDKzeI1rIjtGJllcHooUetE+Yjr3fWKKMztsD3XD2\nUFpf0TCmr38drdddh2b5OD1+xH3lOc3XytQgsfkbl6AOqboz4cYfwsvzWV3gZY2O9phWdDuD1c7K\na4cGFz6fD48++mja++eJ0HEGmvEfkMj5cpc6ldyxIpUPkAwbA0X0XIDsxVVoYeQmLbtEZ+oerbfA\nkRa3rJAg9JsjHjtGfA7begyhJZcCPJ9YQI62QnI4wIbDYCkTcayGBEkAxOqqtDLHgOQFQDv5w/RX\nZ9rHNyhj39ox8o2dIcvtJiOn5z9UTMmoTSbfCzHOpmuUqEa2AnclljN0kvZNH4t4qQ82mhbri+1g\n4nH0/fA6NNOyv7KNTF2eOQ7N5y8B87ULk/dvakuqjuRSv2NWxEyq1GTj+mj2AHkylHt8//vfx+9+\n9zvMnz8fDJOqgX3//fdNHSdPhI5D0MgQywCzg204f6IXe/d06zpDkyCbLmZqqGgqUsOEe/RgRWjQ\noFcCF8t8EMvLwRGcosXKCoiVlQPC5cNHUPq96yydWywvg/+Pvwc85hZ8GvQmf8r2bsO+WBSiza5U\n+uQx8olF9L9jQ9VY7D6yN0UDpDfZVR7vgzceNhXoSjqfGaTT+rJ6r9CcpGvGeyEBidDbteTQW77T\nrwiM08nXoganmkDptLHw70qfcJGuV62hGe6C4lxd33B/3SMd99xzDwDg0UcfhY8iHTCDPBE6DmEU\nkdDe5IcnDXWY1nSRZKho1BYzIkFm3aOzPSZvFbo6gHgc7id/B6aXrJ1KamX1/58JkQkCDWyHH2wg\nCDFNIiR/W9Wb/CGNfauhzSADAFYUsahptWK8qE5715vsauML4Oett/dyaZ6ZrXtFXWU8dsU1KPp0\nAziCzi1tgbHJ4FQ95HKhHgoSYLZyRHuuFdA+C/LkJ/eoqKgAACxfvhzvvPNO2sfJE6HjDNlIiSch\nJoFqutgkOFBz4LCSIk+ClWBVI6RLgoxgpi2WToK8DLGgAOFvnp9WKyvlWFkQSHsnVqMzEqFODkWK\nvcrYN2BO/7WoaXXCaLEfWg0QbbJrXVG1pbZYrt3Ds0WCtJAKCtB9VqOlBHejSo/V4NSRACuVFCtj\n9GoylG0ClC3i4xlXkZXjnEiYNGkSXn/9dUybNg1OlV6ypqbG1P55IjRCoBf4mSvyo0ZQ4qimiz0S\nhwjHK2nyamSTAJkFjQRlsriZngTREUlL7gIEr7k6xQVarK2B5HSCCdMjIbRIVyCt9TQqnTaWGtHQ\nrhr7lqElQ+qqkE2IoaEtleQAAxqgpyoblJ/L433wc06sK6pWHjeCGQJkS0MsrYbV+0RPlwekEhnT\nAmVtpafUh74Jk+A/71uIe33gQn0QXAXU1mbRxvXoWHQxxKLipMeHe7tG/V6zqrMx89x0X7feZ0C2\nfpfeidVoaSNXaPOgY8uWLdiyJXkik2GYvEboeIP6w1ZbuciEEJlJkgcS4/fFENBDuGVcQgwOITXY\n0grMetAMtzF5LXRF0m3t8F55DSLzz0mOxXA6ET736yh4/Q3ifmJBAaTiIrDH2iBWVgwIpK1kjsXj\ncD/+W2I8h3Dnz+BH6sLct+xKYJ95X6jiaBCeSA9xm1oD9FRlA1hJwlcDR+CLh3F64CiEVhZPVTZQ\nc8tMjeZr2nJyHtob9fMgsuZ6wemQIPX/1e9BRhQwbeNbKHoqtWVlRqCcUunxt6Nk/UcoXj9AtOOe\nUvAU3xm+04+xd/wMvaedkXAPj8fBd3ei08AxWotMtEdWYbXKog1wzRUGIwLjeI/ZyCWMIjiMkCdC\nIwhGrRsrhMiq8NnGJMbsSYaK1ZGAblvMCJkEbZqF0QKXrSgNvXBTBgDX3k6MxQj+5GbYtu8gxm6E\nv3m+4gYtlvkAnk8lNV89A6HLLk0EtxJIkbZdp43nEO6+Ffs/35/Rgtdjd6PLUQwfgQx1OYpRXTsR\nLW2HcV3rVlzUtU/ZZjRCb7YNpm3LyXlovsICfHzqIlPHaDrQnVHlUH0fla94VrdlpSeI1hOxq9+e\nNh3zPaZ/u/e9t+HatQN8MGhNQ5QF7ZEVWK1UDRYJko9Puz497yCrr8W/qyVvqJgGuru78dBDD+Hg\nwYN47LHH8OCDD+LWW29FcXGx8c7IGyqOOERFoD2S+D8NNeO9hgu7LHxOVHiYfuGzG6tjRdR9SIaK\n44J+TAmm6kvMIpskKN1qUFbzxPrDTY3gWPMRoG6F8Ty6/vh79F1yEYSKckgsC6G6Cn1LLk1Uf/rd\noOF0ko0aX3kN3mVXwLvsOyi85z5AnSGl52mkuo7SaWOViSUZ2t8NSSMk/95jnA1by+tTtgMDxouz\nymt1R+gdYnJl0SwJ0mvLjWneAS4eNXWcbMEoh4uJRHT31xOxpwPXwf2wdbSBkSSFkJW/8JzuPnJF\nyup+6SJdY8HBdJKmibBpMFvlyZsqZoY77rgDDQ0N6OrqgtvtRkVFBX7605+a3j9fERohECTgzRZO\n8QDy2CRMKZHwrWoBHKGCo1cVMhI+05LkWSbZULG1uTMjgbRVEqS3KFr1C5KRi1DV4I0/BAQBrtf+\nBwwl74YYi8HzCP70FgRvuJ7e8tIhNQwSBoyut9+F44MPFWG2kaeRpXgOA8gGi1PbmlAa6U1Jey+O\nBk2P0FsRROu15QqDXSgI9RLT4+V7I91omCN7/MR7KNMcLr34CxIkJFeKzEAvGDWTQNVciYi1GE7E\ngTaRlsfg4NChQ1i6dCn++te/wm634+abb8aiReaqwEC+IjRi8GYLh4/aOXTGWEhg0Blj8VE7hzdb\nUkvURq0xPeGznCSvBxsDdDT7B21KDBh6EmTpQ5fnEVq2FNAJ/RPLfGlNfemRmqTn9fWh4KWX4X78\nt0q7jngdqukzM6/RqG0ksixeH9+IX59+Ne6fcw1+ffrVeH18o6LRkdtnJMgj9A1VYy1PhekdN+D2\noM9Fr3QCidcl/5cNyESGBDNj8nrxF0SY1ECpIRMyEswQORL0TAuHM4yu0cxrsFotsnr8POjgOA69\nvb2KqeL+/fvBWnhP5InQCEBUBD5vJ5OOz9slHNjtx5E9A/8ZQRY+k6BNkidB79vztsOtpkiQlWrQ\nUJMgGVbIkFjmg1hF/8afMvUVDoM9cBDuh38D7+VXwrv02/BefiXcjzwGxAfaRXqkhgTHmkT1iNau\nS3v6TAPt30F2d9ZObem1z3ZVTcSEmpPTOr/ecQ/UTYbA24nbshESTHrPZZrjBSTiL7q+Os+U+i5e\nkBqdYwQ9QpYOkTMTiDrYsJL9RXueNpZDD3KLK51WVzo5ZXkkcOONN+LKK6/EkSNHcP311+Pb3/42\nfvzjH5vef8S3xk4EG/OeGAwrOB4D8qKGnvBZnSSvRaZmiekg2yQoF60wIvq1QiQ/odj4kxH88Y8S\nP6inuY4eTWpvaAXNRsclQW59yd5FciZU0vQZ9EmedjzcSp4cCUbts3QwtbYSTdWXwbepQMlDC7g9\nOFA3GRtmXZD2cc2C1CIjjckHp81A1/yFYMxMbnEcjl3173B/sQ02PznZXoYt0IvQ6LHggkHYOtog\nsSwYUUTMVw7B7Ybr4P6UffQImUzkrPgdDbf2kNkxfL3nWckxy8Z1AnkfoXRw9tlnY+rUqfj8888h\nCALuvvtu00Jp4DggQsc7CQKAYhuoo+tmKjgkyPliTYIDveCIuWMyzCx6VkhQNgTSQ0GCrH7IJ5GP\no60Qy3wJ8nHzTcroPM18UQ3Hmo8Q/MH3lcqNctwPVoM91qarDVFaXzw/EOlB0B9l4wOe5DRNvKb+\n9tlb4+Zm5PejPi+QmofW5yqiVoJkZNM4McXeQp3j5e+A5713ULRlEzyr3jM9gSU5HOj9yulEQqIF\n19eHA798QPEX4kJ9iQlAnkf5C89ZDlbVEjmZPLd94xLqPjQSMdif05lUgeT3QjZJ3XAiiMcjli5d\nihdffBHnnHMOAEAURVx44YV48803Te0/4onQiQA7C0wrY/ARoWWvV8HRg1b4TPIRyjRFnoRstcSs\nYLAJkAID8qEnfFaDbT0G9vARwOFQjhG8+SYEr7ka3iuvAddOny5KaX3J02cE6JEhs1Uhs2QIsBaO\nSgKNDMt5aEZI1zPIqP2srQ5JDgc8//wHvP/8u/KYFffnJELS0QZIEpH82vzt4EJ9ighbbaTYdsV3\n0bHoYjgOHUBk1JgUk0UZKeaPV3wXwm03J9+/JknNcPuSalTt0T7XaJvZY+WRO1x11VXYsGEDgIS7\nNMMwkCQJPM9j/vz5po+TJ0IjBN+qTlR9Pm+XDCs4VqBOm1cjG9qJwUY20+Sz+sFGIR9mhc+S0wnP\nT34Otq0tyQgRHg8i88/JapyHFfO8bJChdJGJcWa24zPYWDQlcV5NhjKZwAKQVFmyH25G7WMPwUYQ\nK1M1P2b8gAQBdX9/JdGibW1Neo7/QCe8ExP3b67ITTpu17TpNKsEx8x+Zo+Vx+Diz3/+MwDg3nvv\nxe233572cfJEaISAY4DFNQLOrwL27um0nBw/HJAtz6Chdo/OFvTMF9Vg+/qAvj4AqbqhFO1PRQWi\ns2YicMtNAMcpLTmzztNewkIoL5akKInBIENTayvBxaOm2116yIQEaV87IwqoX/kKynZvgaPbj0iJ\nF+0TpqNpwSWQ2IF2l5kJrHhJqT4BFQSUvfzXBJmhTGwFZp6aOOaxo0mtsbKX/2qYRVb+wnMo0HnO\nYBgWpruPFTGz3nn12mFm9EV5DB1++MMfYt26dTjzzDPxu9/9Dtu3b8dNN92E+nryAIUWeSI0wmBn\ngckTEx/mg5ExNlSgtcWs5ojRfF70MGgfbjrCZwmAWFUFpqcnQYQ0UOuGUtpvJOdpuYrEk9/yWq1S\nNoI7tWQonQywhuoyzNnwGsY070BBqAd9rmLsr5uMj09dlEQ2hgL1K19B3ScD1v6u7g7l571fX6I8\nrucJFCv1ofTd/0Xhls903Zu1cRsyJACxUi8C078CSCJOuu1m8B3tiXF6UUS81Ac2lHr/AAPVKACZ\nVawGCbTWbTb1PNpjGRE00vY8ORp8/PSnP0VjYyMA4N1338XVV1+NO++8EytWrDC1f358fhBghrCk\nQ2rMOEgPFxhVgxxiHNXRABxi3DIJGsng/t+jiH//exCqqwbcpC9eDP8Lf0HXw7+mBrHK02AKjJyn\n+z2FiAiH4Vi9hripcNMnSS7IbCwKZ2cb2NiAU7NelWVqbSVYUcTiPavwfz7+E25b/0f8n4//hMV7\nVoHV8VkCEiRo0TuPY8ru9SgM9YAFUBjqwdTd67HoncfBiOQhgWz6AdHAxqIo272FuK1s12bUjh4Y\nZ9cbpRfcbpT+8x+67s16rTWwLGydfpSs+xDele/C1tEOBgAjiomIjc4OcGGygaVcjUrXMyhdpDMm\nbvT8bDpSy4+nWwXTc6Am/ZdH5uju7sZ3vvMdvP/++7jooouwePFihELk+56EIf2LuuYAACAASURB\nVKkIvffee3j33Xfxn//5n0Nx+kFHrshKripCVvRBmXoGsZKI61q34szeI6iIhxJBmcHmlKDMdP2C\nhj14Hp3fvQpYtiRVUB0OU1tnaiPEJBjEaainz2Sw7R1gW8l/R1tHW8IF2VeO8heew7hNn4DraKe2\ngUi4pvUTNBAywADg9fGNxH2m1lbi9A2vobyTvFCUd7ZgzsY38K/ZFyU9rr4XMnWN1oM90A1HN/n9\n5+zxo+LPT6P12uuUqg4xcX7aTBRt+ZR4DHUlRo+oyM7lXFQ/soMEtaaIWrEyYf5oFbmK0TCr9RnM\nSI4Twd5lOEAURWzbtg0rV67EX/7yF3zxxRcQBPPT1INOhO6991589NFHOOWUUwb71MMaZslSrtth\n2SZBRriudasSuAmYWyTVyLZp4mCXtXt27Un8gySo1mmd0YwQ04nTEAvdSitFC4llIbgKUloz2jYQ\njXTYwwGcdGAr8Xpmde7Hl5WlRM0PF49ibPMO4n4yxjTvwIZZFyj70+4FIxG90XuKdB8xETcEXxlY\nAnlgAHjWroZY4B5oK6pH6VWaoNJV/yCeUx3DYTVuwyzUfkBWPYNkDGYyvVlkQjzSEW3n6lryMI+f\n/exnePDBB3Httdeirq4OS5Yswa233mp6/0EnQrNmzcKCBQvw4osvDvapRzQGQw+UCxKkVw1yiHFq\nAOfUtia8NW6urpYk235Bw7G3b2SEqIWeAJtWRWIDQWocCCOK4Lu7qK2Zst1bsK9xsTItJYunGVHA\n7E1v4aQDW+EOWc8AKwj1ooCyX/JzEgLqSV4gGosq16EH7f2Rzv2iZzgog6SvUSfO62qHVJUYyeFA\n7/RZSeP3ViE4XRDdbvCdfqKPkHDnz+AHzHsNDXIyfa4xHN/7eZjHGWecgQkTJuDzzz/HypUr8cQT\nT6CsjOyMTkLOiNDf/vY3/OlPf0p67P7778f555+Pjz/+OFenzSNN5KJ9YKQL8sbD1ADO0kgviqNB\nyz4zI6EKZAlGXkRapFFFEst8iPvKYOtIbb/EfOWJy6C0Zhw9ftgD3QiXliuP1Y8pQdkrz6Fh51rd\nl6aXAdbnKkLQXYqiIF2fEnB7MOWLD1Hfukd3aksGqQqUSdu6bdmVYENBlHy0murroxeuasW9uWvh\neSj9598tB6vK6D6rMakalVK94fmUipVehUdbIcyGuH6okK33f74NNnRYs2YNbrvtNsyYMQOiKOLO\nO+/EfffdpwiojZAzInTZZZfhsssuy9Xh88girJKgbKXK+3knjvEuVBPIUKejCD32hOCUpA8a0bog\nswiHFfJTPL0hZbPSVtMgdaS+HNFZMxH83r8lHVMhRU4nYl87BzYCeQrMOg2x8kpq5SJS7EW0MPlv\nwcaM21qAfgaYwNuxv26yPplyuzF193rlR9rUlgxSVTWdqUIFHIdjV/473Du2w0Ygimb0NUTtEKES\nE/f6EC/1wtZpXBmWgKSIjYCqUkMjZfICrq5Y0ZCxL9IwRyYi6TyGBo888gief/551NXVAQCam5tx\nww03DD0RymP4I50qkB4JsuoTFGF57KqahGqVkFY5T3k9tS2WzZbYsKwGqfPHjh2DVFsL8fxzIdxz\nV9L4e/HE8QAIhEiuIv3Hv6PwN4/BvmkTnO/+HY4PPgQAMKEQxMpKRM6ei+ZvXJJoZdz4Q4Q7+wYW\n5FIfQuMnomf2GbC1tVJbM+0Tpqe0o+yBbriDXcSXJgEIuorx5ZgGwwywT6ctxIS9G+GIpwqBY3YH\nbKEgcT9tu84ImZChRATGbGpVB0j4+lArLATtEOl5ksOBwMxTUfpPsqZIje6vzkPbsisHIjZMkhKz\neh8zU2ZGZCpbyLQKQzNlHEwMt4y2kYh4PK6QIACoq6uDaDCVqkaeCA0DZKNMbxVaEhQHgwjHwyHE\nwVPyrnPhFmwUwJnLkfl0P3zMWutTiYoMUnUGqZ4+THMz2N/9HgAgPHBPwlyx9RhQWQEUFKB44nji\nOdz//TRcb78zcByVH5E8Ul/e2ZcwzGtqA674LtovWoKKv/wRRRs/RvH6j1C8PjGBJjqcCNWNAdfX\nB1tnB2LeMrSeNBVNC1Jzp6KFJQi6PcS2VsBVjNcuuAlRZ2HCJDHYRTVJdEX6YItHUx4HAC4WpU5K\nkdp1RsiEDMnVm6JNG8D7OxD3+tA749R+X59bqBoaLfEwIg/HrrgGzr27iQGqEoBYWcVANYnjqDEa\nKbCo9zGrbco11EaKmVRxsi2QzmPwUVNTg2effRaXXnopAODll19GbS05SoiEISFCp59+Ok4//fSh\nOPWwBMmxd7AgAtjuLkeLswghlodLjKM63IspwTZLJlPpuEY3VI2FCFADOIdrS8wsgerZtQfFE8en\nEiJNxSfJ8DAep46/s2+/C8TiYN9bCebwYaJRonwu9PWBN5FjVrJtE4QxNytEzP3IYyhY92HK87hI\nGK7mA+ic/3V0nvtNxEtKcfgguSIj2uzomjwTRSqzQRn7xzQgZnfh9I1vYGzzDriDXQi6PdjfnxKv\n1vYkdEJkQiXwNthiZJJEatepQYrEyMqXEAmAJAES4NqzM4mwJGloll1pmnhoydLBux5A+YpnUfjZ\nJ7B1JWwNAtNmomvheYh7fWm1pKzqfdJJph/OGE6xIf5dLejqyq5v04mA++67D/fccw+eeuopSJKE\nOXPm4O677za9f74iNExg9EGcK7K03V2Ofe6Bc4c4m/JzQzDxjS/XuVFAagDnYJCgwShJy+RHIShI\nrfioYzNCl11KHX9nmpvB//EZ4n7Bm29KPp/dZirHLGmkPhyG40OysaKMwi2b0Lb0SkgOB2rGO6j3\npFwpkuMnAm4PDvSTndmb3krS/hQFO5WfPz51kfK4nk6Ip5AgAOion0psi9WMK0HBU79PicTou+57\nuq/ZCClEwt9O1AwBCQ0NBME4gFWnStN21b+hfel3Mh5bZyIR2NpaUfTpBuq10vQ+ZrVNucJwbyWl\nS4LySA8+nw8PP/wwdu7cCZ7nMXHiRDCM+dGCPBEaIcgFCYqDQYuTPLXT4ijEKcF27Dysn4MFpF8N\nIsFqhIYaGQlfcwyFoNTVUis1jjUfIXjN1fT8MYrXD8kosaflKHx2O9WZWoZ6pD5hrKhPnnh/B1UD\noq207P36EuxrXKw8tudISNcfaEzzDvgXLcWeIwPieVlHNGnfp7BFB14L7SNOAnBodqpAsma8F+Ur\nnoWXEInh9zjTnnTSdX0mwNbRbkpobFSlMdNKU19jEmnSkCxI5Fa4rt7HpLaJhExbUVZI0FBNclkN\nj82ToMywdu1aLF++HBUVFRBFET09PXj00Ucxbdo0U/vnidAwwWC2xmR9UITjEWLJt0CIsyHCGd8e\n2QpSBTIjQSMFgX9tgFfP8DAQpI6/07x+kqo6/W0359vvgjUgQUDySL1Y5oNYWQHuKL0CGPf6kjQg\nNeO9aNnVRg0fFW12RatTP8aOY9v2UYXUhX1dsAe6UT8mWdvjH7UUwlM7kogQDeESHyLFqT5BuZp0\n0hMOkxD3eMBTJr/UAazZuFZvfTncj/8WtvdXJ1WVIInwrnzXcH8zeh8rhExGpou+2kE6nSywPI4/\nPPDAA3j66acxadIkAMDWrVtx11134dVXXzW1f54I5RhqgkOrVuSSBKlF0VpC4RDicIlxhAjTWS4h\nBocQ1z12uiSIVA0abBI0VKV1scwHsbwcHCHSQqwoh1jmSxl/l0bVQlz4NbB/Xwnm0KHU/VRVHW3b\nTQv5u79YXZVqzOh0InL2Wbr7986arSzCcmtl5gevo+STgSqX3hh71cRRiJR44erugBYkbQ8jChj/\nzvNw9JjTTZCm2IDcTDqxvT2wtRxJjLX7U18PCYGZp6Jwy2e6QuNMr1W+t92PPEYM0hWcLtPXOhR6\nH7MVozzJyUOG3W5XSBAANDSk2o3oIU+EcoihTofXToZpf+YhoTrcm6QRklEdCei2xbLZDqMhHRJk\n1B4bcm2B0wmxuIhMhIqKlOqMbKJYXFykTIeBv0OZHlNDruoU19XC9i8Ds1KWRddjv0F86pTEj0db\nk6bWgjf+EBAlON96G4wqtFB0utA9NzGWDUFA+fN/QsnaD3SrTqQxdtFmR/uE6Ump7TI66qemiJjr\nV76Cmq3rU56rHI9hAUlEpMSnVKFIyOqkUzSK0ffeDuehg9QqHQCERo9NTNn52yFWVqB76iy0LbsS\nEsfrCo2zcq3hMGzvryZuYikhrBIAMExCgD2Ieh+A/L48kVpGJ9JrzQWmTZuGX/ziF1iyZAk4jsNb\nb72F2tpafPJJorJ62mnk0GMZeSI0hBhqogQAU/oF0S2OQoQ4G1xCDNWRAKYE22BsiWceeiQoHWG0\nlawoGUNOgoDEyHxvgLiJ7Q0A4XCC1KjE1TKEe+5KPO+dd8EcPgKptgbieeeCu+cuoOnLRNvt8GHd\n04uVFYhPmgj3k79LTK21tkL0+RLTZzfflPAg+smPEfzhdWAPHwEiEfS09CBWXqlUB8pXPAvv+8at\nFdoYe5KQusePSFEpYs4C+PZuRe2mDxEpLEHbxOn4snExNeFdxuFZZ+HQ6QuSyBMJ2Zx0Gn3v7cQR\ndpHlwPz/9s48PKry/PvfmUwWMtnZiyRWlKVVBFxKq1gUEMW2gJKAIJZ6tYo/RbG+yIWvIiIGWxpF\ncCmiL8riC1Gq9XVFFEFQkbJoqQaBKspidiCZkExm5rx/TGZy5sxZnnPmrDP357q8JDNznvPMdp7v\n3M99f29wMYnDrkAgLodGKdE40bk2HDiB9Jof0U3Flh0Q3vY8+ud5Me+1lZAwIFg5fDjcr/Jvf/tb\nzO3Lli2Dy+XC6tWrZY8nIWQgVmyFqcWNcHXYIF9djI+QGZViesGaIG0H4zLZpqg18U1R+f5AeQPO\nQ3DxIwg+OC/qI3T6h2PA4W8ByPcZi9A24nJ4V74QW7VWV4fsf7yO9H/vx8n/szJcip+VhVC/cwAA\n/rTOBcnV1iZZZSQkmJ4Jf3ZO3O2cOy0mkfqsnZvRd3dn9CKr+ST67t6Kgm8PIEuiwzsH4MTg4Th8\ndZloO40I/M9GIpVOkYTjUFoasn44Iv6YUBCnL/0lqmfcBi47OzxPMTdnhkTjRKuy5KJKoawuSBOJ\nCrlbfMjf+qGpkaAIqSp6+NcjigppZ82aNQkdT0LIZMwUQZEGmCx4wMETbDd4RuwcPnLKkPwgq8UQ\na1NUMYPEmFL8n54d/xiZPmOh7Gy0/mYcfLf+EUU3zRCdW/rBQ/AuXQbf//pzzO38C7Sa5OB0fyvO\n2fr/RNtdAOFtMn9OProd2i96f27Dj2hPz0R6e7xxYmteEQ5eM1VWBMWhIEBEnZWFZey5eZJVVi4A\n+Z9/Ci49AzU3/1ExqiKWaMyfg9aqrMjYUlGlU5f9GnC7kf/xlhhBlNba6th+YXLoYZxqFkUDeqOt\nVrrRNBHLXXfdhcmTJ+Oyyy4TvX/r1q149dVXsXz5ctlxSAglMXq30IhgRqWYkVgqhjQ0RRUSMWoU\nQ6rPWPM9dwM5OXAfPQZ3tXTEKOvtd+GbeSuQEx/JAXiRBkYxpNTuIqP5lGTUB4Ck6KgbMESxhYZU\npDBOgMh49sSVsZ9W/k7l79gKb9V/0DTsUvZu7DJz0NquQi6q5AoEkLv7c9HIUDL0C9MDitDoRygU\nwoIFC3DgwAFkZGRg0aJFKCkpiXlMQ0MDbrzxRrzxxhvIzMxEMBjE4sWLsX//fvj9fsyaNSuud9ji\nxYvx1FNPYdGiRRg4cCB69eqFtLQ0HDt2DPv378fo0aOxePFixfmREDIZs1ykjRJBWlCbJK1Eol5B\neoggqbYWLETFipizNCOS51boVh/q1hVcZpakv5D7zBnkPPEkmh/839Hb+IuBXG8tMZTaXfhz8tGW\nk4+sZvGS+rSAH8cHD0fhkYPhfKK8ItmkaC2fDUnPnmAQuV/sUT2eC2G/IDXRFUO6uctEwDz1tfA0\nile6JdIvzG7tKqzeCpfDznPTm82bN8Pv92PDhg3Yt28fHnvsMTz77LPR+z/++GNUVFSgtrZzK/ef\n//wnAoEA1q9fj+rqarzzzjtx43q9XsydOxd33HEHPvvsMxw5cgRutxtDhgzBo48+iuyOLWolSAgZ\ngJTQiVykjRRDRgsgtdEgtUnSEfRqrGrkxSYRMQSgox0DJxn1iEGsL5lErzIA4RyfsyR67Sg4rmbs\n2RtN2hajdsp0IBRC/o6tMRVIYqMG0zPRLpInFCGUnoHaARfG5AjxacvvioPXTA3PS1BRFiERYexu\nOo3cf4lXpeXs3QVPgu0OWKIrRndzF9uCM6JfmDDfBbBWEOnx3aeokD7s3r0bI0aMAAAMGTIE+/fH\nboe73W6sWrUKN9zQ+QNn+/btOO+883DrrbeC4zg8+OCDkuPn5ORg9OjRmudHQkhn5AQOv7lq5OKt\npyByUhTI6SIoEeJabFRXx7XKiCLWl+zyXwFwIXP7jviIkkf+K+2uq1d0m3bX1EaTtkUXgbQ01E6/\nBXVl05BeG/78FHy4SbQzerq/FT+VyRMCgMNXlyH/h8PIq4n3SOL7AolFlVg/E5Luyrs+g+ekhMHh\nyUYECgqRLmGAyAJLdMWKbu56VtHJfc/UCgmpsfQYQytGiCE7XpsKzumBou7dVB/HktPU3NyMHN52\ne1paGgKBADwd1yuxHJ/GxkZ8//33WLFiBXbt2oV58+Zh3bp1qufHAgkhCzAiGqRFBKlFr9wgrXlB\naltoGJkLpDkS1Noq2VRVrFWGaF+yV2PdUsV6jkkRdo/uKVtZxk/alluYuMxM+M8qBgDUTpqKvE+2\nIU1EZCnlCXHuNJxYvASBdZ3NRFv12gKTyL1hcVdu79odvsFDRAUeKyzRFau6uevVL0xPkcB3jeZj\nZISJP6bY553lnFqPE+Pkf5V7BDqNnJwc+HydTZpDoVBUBElRUFCAkSNHwuVy4dJLL8V3331n2PxS\nQgiZ1YPKTmXxLBi1JaZ1OwxwZmNVNciWz1cLyudlRJMYYkIqDplk7QisSdt8PM2n4W6Lr+4C5POE\n3O1+9O0GBAKBuGaiwu72eub/BBkiHhFRwKV5kPuvz+BpbJDscSY3Bkv1mCXd3BPoF2Y0UoJIiUS/\n68LrRSLCS068SV2XknUbbtiwYdiyZQvGjRuHffv2oX///orHXHTRRdi6dSvGjh2Lqqoq9O4t/d4+\n/PDDmDhxInNvMSEpIYQAezfkTBSjo0FmRYKMaqyq9aJqBKzl84C8aBIjTkhJ0Jms/THcP1ZHm7mG\nevViTtoWbhfIRTX4rTMijVnbs3Nw/hfvy1ZJ/eQ89kVZrPRdLvdGSrQBAOd2o3HkmGjFV92kG3H6\nl5ejz5NLkH5KPmdIzJ1ZtCxfgJHd3JW2drT0CzMLoWAwI2fHiG0wFjGUrCIIAMaMGYMdO3ZgypQp\n4DgO5eXlWLVqFYqLizFq1CjRY8rKyvDQQw+hrKwMHMfh4Ycflhz/wgsvREVFBRoaGjB+/HiMHz8e\n3buLF2iIkTJCyCrMqhJTC2s0yE4iCEi8YsxyVJTPsxgk8hEKKUmElWU5XribfeJJ14zIRTXq+l8I\nLi0N526qRLdvvkDW6QaEMrNiSrc1V0nJlJ3L5d7IRnY44OQ14a733de9GB07lKn82rR37Y5j98wN\nuzN7PJJziyupVxGdUZtHY7cFVu02F+vj1P7Q0et1UTqv1Hns8MPMLNxuNxYuXBhzW79+/eIe9+GH\nna13MjIymErfAWDChAmYMGECTpw4gTfffBNTpkzBueeei9LSUqYk6pQQQmYtnnzRY9Y5jUyQNqOf\nGGC8CLLbBSfO66dnj/gGqADTNhYf1VtavMqyUEFB+Da5SjQFpKIaLVOmY/D6NSji9RcT86+JHKum\nSkqu7Lxu0o2SUSo52ruG83KEY0fmHMzqAnfrGVEx1TzskmjeVPd1L6ouibdzdMZpmCEAtUZ0Ur23\nmhH88MMPeOONN/DWW2+hpKQEY8aMwTvvvINNmzbhr3/9q+yxKSGE+AijM3oLFuF4dosGWSGCtFSI\nCUkWEQRA0euHj6houqyjamzHDlkhpaq8X6w67bJf4kzpJIR69mATRRJRDbktKiFqqqTkxs3/eAvq\nJpZJRqnkaB56MQBIjh3yevH9vAUo2PoB8r7+Eu7qmritLKNL4sVIpoU00efiFBEkTNQmZ2ltTJky\nBfX19ZgwYQKef/55/OQnPwEQjhRdccUVisennBASYlTukB1NE50YCUoqASQkKws5o0aG/93SEts/\nLIKMaPLdMVNWSKmpbBOtTtv4GrpsfC02d6ij0kNNzomathzthV2Zq6Tkxk1rPYMe61ah+paZAIDc\nPZ/DU18nGsUJud1wceFIUETMpNfXwiMRSfI0NiDvZyUIXP0gGgQRNNeX38FTXwuX329YSbxUzptT\nRJBR84zk3Bj9OiTyuqdKTpDZ3HLLLbj66qtjbjt27Bj69OmDTz75RPH4lBNCem5fWRXtcdJ2mBUt\nNJzE6f98De/yp5H16U64jh0D16cPCsddg8abpsZ6AokZJMqZJqpBpjrNhfjyfLUXcLlEaiFBrzcu\nUiKVbBwetyvS68UFR3bVV3AFAtEoVY/Vz6NgR7xx48mRY3DymutiPIYK330zmkQuJCYXK/IeBAJI\nm78YP43kAxV2jcuDiqBXSXwyL6Ran5veeT+spfNazss/hyN+uNmQEydOgOM4LFu2DBdccAG4DnPa\nYDCIP/3pT3j3XXmLjAgpJ4QAfbbDkk0EaU2K1to+w8hokJMQRmJcP/wA94qVKATQOONmU+bAWp3m\n+XAbGkeNB1Ru6cglUgtJ8/ngamuLNT2USDbmMjPhG/RzFGwXd6VOb6yPRl64zExU3zIToWyveGUW\nL3m5+/o1st5BYrlY3uVPI5ufDyQTATO0JJ7QFaEgMkKwkAjSzrJly7Bz507U1NRg2rRp0ds9Hg9G\njhzJPE5KCiEhfFHDsviSCAqj1T2aRFAHMpEY9zvvIu/BeUB2dmJtPBhgrU5Lr69F1n+/Qes5/dUt\n5MEgEAohmJUFN89wUWybKiJeAvmF6LHm+RiRI5ZsXDP1D8j9105RI8e4yAtDZZZcbg/nduPMhN/F\nJ7W3tiL9A3ExFszqgpDXC09DAwIFBVHhZYcWFHaCNaqSiFO1Hp5Aes1LjMjxJxNs65JKRKrKnnvu\nOdx6662ax0l5ISQUNSw5Q1aUxJvhHK2GRFpoKJESIgjykRjX0WPhnKGfnp14TzMlGKvTOJcLff+6\nSL4MXITu69eg6AO2EHV7YVcUvPsWcvftlsyxydmzK5pszGVn49SIq1SZEQpzmPiLnPvoMclmpABw\n5sYpcW1M3HX1knN1t7WiaehF8H79VTi36KsvkfneRvj634GGw9Jbha62NnQtSo/mHiW7YFLj3iwW\npREen6gAUooAid2vJIZSyUDRbCZPnox169bh5MmT0e0xALjzzjuZjk9pIWS3ii4xEhVA5/fpaVg/\nMSPQQwQ5JdSsZK54+nQT8jr+NloMxVSnnfhRNFrj7siXUeP5o6ZiDAjnCBV9+J7sY9Lra9FjzfOo\n/sPMcJRHULYfKCyCb9DPUTdRur8ZH36Ohtx70l7UDfUN7eB8sZU+9Q3tyJPIgQplZqHg086oXyTf\nqrWxBRB77fjbgY310T5yDWNvYBKdyYpcgrJcjo1eURqpCJ7wfjXXHhJB+jF79mzk5ubivPPOg0uh\nqbQYbgPmZHuOH2xgao4qhxlRCyf1D2NF7xYajqYjEiNGJA/F6G0xtLbCffQYEAiEE6FfXoOG9WvR\n3u8cxUNz9v4LLhmHZkC+sosD4C8sAud2w9+tBxqvuhqe5mbF87oAFGzfiu7r14Rv6Njy+m7hX3Hq\nlyMADsjfsQ0/fXAOuq97Mbw1p0B0UZJ5T8QiTJGea03DLlE8Bx+p1y7iXZReXwtXKBQVTtHnSuhu\nxMg6ltx4as9FIkhf6urqsGzZMsyaNQt33nln9D9WUjIipLS1pSRy7FgaL4YdO8vLkUh3eTu10VAD\ni7miIWJIzDeoo0Q+1LMn3L4WxSFYysBlG4p264EjD5Uj7UwLAvmF8JxqRMGW95mfgtCPp9trlTFV\nYVrdqoXvCUu7CzEzyZYBg5D/yTbRx4u9dizeQwBi8ptSJddIS2m82b5KVP1lHYMGDUJVVRUGDhyo\n6fiUFEJA56Kr1mDR7ttpRjVSjWBUlViiETbHXoBUmCvqiahvUMffZ0onMVWRsZSBKzUUDeXmIZQb\n3gBUU2YPxIoJFhFROPhs0YUx7rPT8Z4cHTWeud1Fw4ETcYnYAJC3dxdcLfGiMpSRGffayUXPItuB\n3q+/iqugK/rZWbLVTckikqxuVcEiOllzhJLJ/NIOHDx4EBMnTkTXrl2RmZkJjuPgcrnwwQcfMB2f\nskIogtQCbHfBI4YdcoHEokFGiCDHCh8p9PIEYkGmWi3z4+3w/eH3TFVkrGXgrA1FOZcLaIuv/pIi\nIsSKBvQOJznLGBh2LUpHCPECQTa3RKHdhdjCxk/Elts2dLldKOzfCw1HOiuE5IRgKDNLsoIuuHCe\n6JyIePSIoGkdw4oGsqnCU089ldDxKS+EhNhBANk1N0jLllgy5wTlDTgv+m/Dc3l0RK5azV1dA3ez\nT7KKjAMQ6t0LbSMuR3DWHYBM5VMUxoaixYseQHpzU9ztQU860gLtcbe3DBwEILzAuNqkE5bbi7qJ\nNqPVKhqkjhMubJ5TjXCdEe+p5mppgbuuHkUD+kSPUeO3FCFn77/w3ZffRV9Ps4WQ1ZVQVrpraxEy\nJHz0ZcuWLbjyyiuxa5d4NLhPH7YflySEeKSKCNICuUdL4yQRBChXq4W6dRXPXfqVyt5jAuQairqb\nTiPr6Pei97mCATSOHA3v/i+R3lCHUEYmAA7527fC+/VX0S0iKRERuOqKmPkK+zsZRe4lgxDq2VM8\nsuZ2o8v6DfDNvitmQU0010iurFvKoTsR7JQXwyIyEnGA1mMsQl/+/e9/6v8AZAAAH4RJREFU48or\nr8TOnTtF758wYQLTOEknhNSaI4odZxVmiSA9K8VIBDlLBAGQ9Q3iuybz82RyLxmkS+4SfzEGOhN/\nM48eEW1nAQAujkPTL36J2ht/H9cmIyYhWkREBK66IirqxBauhBdyQa8xvqhpONKItAuGoejHeHHm\nCoWQvfE1IC0Nvnvu7jxOJHoGAN6qrySjXWJ5WjHPKxBA37crkf7BVlGH7kTRQ1hqia4YnQdlF4FH\nSHPXXXcB6DRW5NMqYrIqRdIJIT6sDVVTSQRpQUtXeSD5HaQdKYI6YKlWA3hRHBERpGrxEbTLCGVm\nAeDgbm1FoGt3NF9wIeByATwztOgc3G60nVUCICwIxIgkRPNFBF+8KSW4xix6ra3o5g2FPYNEnKfd\nR48hVJAP78oXRKvuYhKop0wHgkEUfPR+1IeJT+bH2+G7/baoiIocJ4yeySWcS0V3Is+579uVMaJX\nazUdC3pGXIw4FytKc6JokL1477338PTTT6OlpQUcxyEUCqG1tRWffvop0/FJJ4S0LKxWOEXrjVFN\nVbVWiRmNnULyjsTkarWIP04EfjPS9PpaFH60Ge05uaI5Qm1nFSOUm4f0mh+ZOrpHRAQ/ERlgWHAF\nlgJ5hV07IycdzyH/33vgrqkBl5UFN68aTNiYln8+7vY/wLVFvHeZu7om/Pp3JMpLLbCsCedCXG1t\nkonxQvsBK7Br+b/w+iJlnGi3eacqS5YswaJFi7Bq1SrMnDkT27dvR2Mje6uSpBNCTqVfSb7mqJBT\nRVCi0SASQzqgsVpNzQLA6i7NZWbhTEEhMo8fhSsU6ogEFeP7BxYBUPAkYijlV/q8CC0F+JETADH/\nFiuJB2IjPBFC3bpK5gqJuVWLwphwLsRzqhHuavHrA4sPlJHY/bvLspWajDYFTiQvLw/Dhw/Hnj17\n0NTUhFmzZuH6669nPj4lhBBL3lAyRIX0xMheYoCzt8Tk4FeSieG07TQ9Snzl/HH4pDfW4+jcpQh2\nyUbm0SNoO6sk6jEEKHsSJRTZkLEUyNmzC2npbCb8wggPANmcLLXzDnshsT9etiS/Zw/m7UM9cbp4\nkBLUVA5vHVlZWfj222/Rr18/fP755xg+fDiamuKjy1KkhBASLrpaE6r1JtG8IKPME+0eCbIzThM6\nLCT6y53VKDES1eEyM3Fm0AWiC2Zt6VR0OfBVuMIsFALcbrSeVYza0qlMc5FaxOQsBdIZRFyESNWd\nEC1u1VKoWXDlxCM/Md5sB2anQ9FoezF79mwsXboUS5YswXPPPYcNGzZg0qRJzMenhBCSw4ookJkC\nCNBfBLFEg6QSpfUUQXQhcgas/jiR6IicN0z3V15Gl++/67wzFEKX779D91deZk78FVvElCwFACDt\nR+XvHV9cxCCRk8X/NrCWfxcN6K1KDMlV0yWDKLEKo167gnN6GDJuMlNYWIgnn3wSALBx40acOnUK\n3377LfPxKSeEnL79ZQf3aDtAIsha1G4DCBfjUEYmXG4XXGfOINSrZ9SgscgTe0nin4OljQbrNlOc\nGJLZvgrl5qL9wguR/erG+Puys+FqbY2pupPteyeTk8X6mvLFUORvWaTyi1jMMG2KkdtrViZCFw3o\njRO17BHIVGf37t0IhUJ44IEH8Oijj4LrqDoNBAJYsGAB3nvvPaZxUk4IORktIkjv7vKJRIP0gkSQ\nA+Etxl2L0qPbR2oq1mR7cWlI/BWKId+sO5C+dx/SDx6KHfvgIbRfOBgtZZPg+XBbWMhFhM+tf4S7\n8aRpPeLEYBUFcoaWdsbM77vV15aGAyeAonRL5+AkPvnkE3z++eeoqamJRoQAwOPxYPLkyczjOF4I\nqe0i79SkaDNEkNEJ0olg9QXKSJzaqkMN/PcvBP6C7QZ8jUxtKxKtGlMkEIC7qVn0rswdn6Dh5TWA\niN1AyOuNm7NWlKJCSmMnY1m3VD6OEc/RDq/byf8qNzwmwsyaNQsA8PrrrzO7SIvheCEkh9rO8smE\nWZEgM3qJkQhyHnLvmVRZstJxhlaNgaEHW0c1GJPdgMBxWg1SYkjN98AoQaT2fdULOwgUwr6sXLmS\nhBArVkeCjPYJiqBnQ1W5KBCJIP1IJhEEaK+qETtOqRcXa/WVUrQl1K0rQt27I03Ed0eqGiwOgSkj\n33EaHm2XWyMjTHrOQ+u5qOycSJS+ffti3rx5uPDCC5HF++GRsr3G7Iqd+4jZ1T06VUQQC0J/IjsI\nJ6UFTCrKk1DEQyTxt3Dw2SgCW9RA8hyBALzProBLwnsklJPDJGSEpoxijtMs6PnZ10toyIlbNeNb\n/b0m4ZV8FBaGt8W/+OKLmNtTRgjZOefH7P5hZoogLdEgNVuTekUT7A6roDl94GCMGMobcJ4txBAL\nch3RhbdLIVy8Iom/Yi6/Uouc3OdDKGCEpB88BO/yp+XFjIwpo+fDbYDAcVoPWF9DPcVQIjjt+0k4\ng0jT1VOnTiE/X/3axGaXSqji8JFTuokgI8vlkyUS1HDgRGfHb5N/6eUNOC/6n9HYUfgI3ytXWxvS\na36Eq60t7rHC94ZfAq7HuZVul0RGwPDJ/Hg7Gr/8TvJ+JVPGpl1fq5uXAvzX0+4CJdH3WmpMuxF5\nnvz/1BxDaKOqqgrXXHMNxo8fj+rqaowZMwb/+c9/mI93TETIrlEfIzHKORrQzziRFSMT1a28gPAj\nNWZEaewqhhq+OhrTXT5Q1K2zYWlaWvSxiUTt1ESRxKJD0c7xggRmOQHDx11dA8+pRjQciDd9BORN\nGXWpahOg5vVQs21oVDWW3BzVRqwSaX6q9fmx2BSoHZvEjz488sgjePrpp3HvvfeiZ8+eWLBgAR56\n6CG8+qp0lJePqRGhpqYmzJw5EzfddBMmT56MvXv3Mh1X/d1Jg2emL2YkETsJtSLIafv3dhQnZtP3\nvY0oev9tpNfXwsVx0Yal3deviXtsIu+v2l/ORQN6o6hfd3Rf9yL6PTQHRZOnoujG6fA+8SQQCADo\nFDBKhHr2kBczHaaMYjQPvRiFg89mnjcrLK8Hq0kjf0wrMCI6qBdGGDjKOagT6jhz5gz69esX/fuy\nyy6D3+9nPt5UIbRq1SoMHz4ca9euxeLFi7Fw4UIzT+8o7B4NYt36SxXLgtMHDioKIrO20ExHrmHp\n3n8xbZPxbxf7LxG8y59G0ftvI+3HH+EKhaIJzN7lT4cfICNg+Jw6f5hiib5v1h1oKZuEYO9e4Nxu\nBHv3QkvZJE09xfTA6MVVjTBNKJld57lohUSQPSkoKEBVVRVcLhcA4I033lCVK2Tq1tiMGTOQkZEB\nAAgGg8hM0PfDjuiRG2R1XpBe7tGpIoLUEhFDyRJJUsqNEXN8ljPIE253JLS4MSYwC5uich1bZ/wW\nILVjb1A+H0NPMbNINPJm58XZTJNFI8bV5bNNRFmwYAHmzp2LgwcP4uKLL0ZJSQmWLFnCfLxhQuiV\nV17BSy+9FHNbeXk5Bg8ejNraWsyZMwf333+/Uae3BCtEkF1baCQigpL14iCs/EoWlBqW5l4yCA1H\nGgFoMwVMBJYE5twRQ8UFDBAnZpgXRJmeYnZE7LVW0/tM6zm0jhV5rB55TVa6cdtZbDqJ4uJiLF++\nHNnZ2QiFQqivr0dJSQnz8YYJodLSUpSWlsbdfuDAAfz5z3/Gfffdh0svvdSo05uO2SLIiFJ5JRFE\nPcQSJ1miQDHINCyNdGNX897qaYOgOoFZIGCEYsYpn1E9t3D0GMuo100PAcT/m4SJM1m9ejVee+01\nvPbaazh27BhmzpyJGTNmMPcbM3Vr7NChQ7j77ruxdOlSDBw40MxTG4oT/IKUsLpCzCkLjNE4yR8o\nSiAAhLhwJ/aWFgAAl52N1nHXRLecLENGpOnRliMZMOO7l2jLkERQG4VUE+FSemwy9n6zI5WVlais\nrAQA9OnTB//4xz9QVlZmTyFUUVEBv9+PRx99FACQk5ODZ5991swp2BYj84KAxD2DjI4GOdEM0Qgs\nF0EaemR5lz+N7Fc3xtzmamkB3G5VbSUiC4venwNh/k+kc3xw1h0o0tj2wu6oWaSl0LrlxXqcUjsV\nNee1SmjJzZdEkHm0t7dH848BID09XdXxpl4FSPQkjhXRILIDSAG09siSSUbO/Hg7fCrdlFkXZ1WL\nnEQCs91JVBQm0sokkQovo7eYpPKZAGt+UIk9X/pRZy6jR4/G73//e1x77bUAgE2bNuGqq65iPj45\nfw6ZhNnu0SSCCKPQ2iOLtWO73mha8ByWwAzov7AbLYL0Ru15zBQg/PdGytySokFhQqEQFixYgAMH\nDiAjIwOLFi2KSWaurKzE+vXr4fF4cPvtt+PKK6/E8ePHcd9994HjOOTn56OiogJdunQRHX/OnDl4\n9913sWvXLng8Htx8880YPXo08/xICGnESSJIS2d5wPh+YoRNSCCqo1QxxtSxXQWp9ks70eer5XiW\n7R459NraityuV6J9Is+J5Xyp9tlUw+bNm+H3+7Fhwwbs27cPjz32WHSHqLa2FmvWrMHGjRvR1taG\nqVOn4rLLLsOLL76Ia6+9FtOmTcMTTzyBV199FdOnS/tx9evXD926dQPHcQCAXbt24ZJLLmGaHwkh\nDThFBMnlBemVHK2X8KGLiHUkFNVhqBgzEiuTcI3Gyuehd6m73NhK46htIyLmki13DuHj9drao2hQ\nJ7t378aIESMAAEOGDMH+/fuj93355ZcYOnQoMjIykJGRgeLiYlRVVWHQoEH4seMHVnNzM3r16iU6\nNgA8/PDD2LJlC/r27Ru9zeVyYfXq1UzzIyGkEhJBnZAI6sTJJomJRnWkkpGNrhhT6veUDJ8ru6Jl\nkU/UAFFLtEftPLU8L7F5kQiKpbm5GTk5OdG/09LSEAgE4PF40NzcjNzc3Oh9Xq83KnwqKirw5ptv\nwu/3484775Qcf8eOHXj33XeRpfGHFwkhFZhdJq8Vu1eIJSNOFEBREo3qWJCMnGhFFJEYrFETufdB\nq+hQOwejScSM0k7knHM28n6i/nvTlJuj+JicnBz4fL7o36FQCJ6OIgzhfT6fD7m5uZg/fz4WL16M\nESNG4KOPPsLcuXPx3HPPiY7ft2/f6JaYFkgIMaKnCLK6hYYcakTQ8YMNukSFqHTeenSJ6qhMRpZb\nKPReQAnzMHJbTc0YZpSvyz1XJ4ohoxg2bBi2bNmCcePGYd++fejfv3/0vsGDB2Pp0qVoa2uD3+/H\n4cOH0b9/f+Tl5UUjRT169MDp06clx8/Pz8d1110X3WKLsHjxYqb5kRBSwMookNlVYloiQSSGkgSP\nBz+MK4Nr1Hh4TjUi95JBhkZ1WPJCtG430OfIHIQLvVkCSAkrKtqkctVIDIUZM2YMduzYgSlTpoDj\nOJSXl2PVqlUoLi7GqFGjMH36dEydOhUcx+Gee+5BZmYmHnzwQSxcuBChUAgcx2H+/PmS448YMSKa\ng6QFEkIyGCGCjDZO1ApthxGRi3Z7j16O8NkhrMduolOPcnu97ANIAHXidruxcOHCmNv69esX/XdZ\nWRnKyspi7j/33HOZk50nTpyY0PxICElgtQgyopeYnbHbBTVVMfPXtNqtMS3HJApFKtWhlKhuxHaV\nFQaKYreR8DGfgQMHwuVyRf92uVzIy8vDr371K8yfPx8FBQVM45AQEsFpIohVAOnZTywC+QYhpqO8\no5OmTUZqa8EuJnqi5dglhY5ypzYDMQGgJCDlBJFSlEbL50PPJrTC+URuJzFkPlVVVXG31dXVobKy\nEgsXLsTjjz/ONA4JIR5G5QPZQQTpid7ix6m/uPkCiH8biSH1sH4GjOpHJiRuQQsG0X39GuTu2QVP\nYz17C5IkR8mfR+l9Ym2NoYexpJJgYzVclBqHsAfdunXD//zP/+C6665jPiZ1v8ECrBZBRm+F6ZUk\nTSKok4jgoYiQuVjRTLPvexuR/f7b0b9ZW5AkO2ojO2LwI29WXA+0bNEqHUdYj5rGqySEYL0/kBHV\nYRH0rhLTEyeLID4kfpKT6OdT58ayyYjW77KaTvV6n1sJsa1b/m20FWZfNm3axJwfBJAQMlQEWe0X\npLcIIidpIhWxqrFsKqLFNsGIzu9S+WuUPG8vrrrqqphkaSDsYl1SUoIlS5Ywj5PyQsgorOwoD9hX\nBBGE0zC7sWwqweJFpDbyIiVWtLphU2d5+7JmzZqYv91uN/Ly8uD1elWNk/JCqF9Jvu5RIaO9gpSi\nQXqKICMEEP2qIhyFxY1l7UoilVx8WI5Vm5cjVcavdTtLz15itKWmH3366BOJdesyisPRM1cmmbyC\nKAqUGGJVZXan4cAJW1+kI/Mze46+WXegpWwSgr17gXO7EezdCy1lkwxvLGtHxF5/u35m1CZxG2mU\nGCmxVzpPwTk9NI1PaCflI0KEsaRyKJmSqJMICxrL2pVkiGjIldPzH6MnTn/NkhkSQrCmasyoaJAR\npol6kQwX0FTAztuWls9NZWPZZMXs90GP7Sy141mVF3Tyv+KJ+YRxkBDSEas9g/QWQYk2VJXz4CDs\nCb0/hJ4otdxQelwi21BK52KFchqTn5TPEdIrGmS1CCL0IW/AeYbm9jgxb4ggEkXJgVrp32owqucc\nRbOTl5SICEXEjlEGglb7BQHO6CNm5P673hjVKoPyhginwhrd4aOmIkzsXHqdQ+rxRokbcp92Fkkt\nhITRnsNHTsWIoUSjQWoFkNV9xMxupREJKWtpymgHqG8YQYSRitQYFX2RQu/z6SVY7H4tI+RJWiEk\nJXKEYkgrdhJBekeD9IwEOe0X0ekDB2O2r/hiSGxbi4QSoQUt0RWrSLSxqtR4aiNBWl4ro19nJ7x/\nhDJJK4SMMEqM4EQRxCr+yDtIWtyQ6CH0wkkLqFy1p1nPQ040Sc3BzCiW0vkJe5O0QsgojBZBRmB1\nc1UhTloECIIQR+v3OJGcHjHU9icjgUIISeqqMSkBcPjIKU3RIqNbZwD6RoP6leSTCHIgRlWWUcUa\noRVh13Wrv8dGO1uzPke157XDa0fEk7QRIStMEoUYGQ1iEUFqSXRbjCol9MGoLTja2iMSwYwFnKUJ\nq5HnlrqNJcKkNFehmKTrpH1IuoiQ1miPEmZsibGaJhohgswiWb/8FG0hnIydfHIiURM1PcGU/k4E\nNY1epUQcX1DxhRNFh+xBUkSE7BD9SRSr22fwo0HHDzbE3aYGpV87TiidV0NEBEX+T5EXwkkYKYDM\niO5IjasUXTLqeUsJHWHyNr8Bq11EaKqSFELIaOyQIK13dRgfqhRjgyXqQyKIIMxBq1mjmuMTQc5H\njX8/fy4kiKwhKYSQk0vlAeVokNkiSIswkgpNO8kvRQmhx5DwPoJwIkZ+N+34vTczIq0kbIRzKRrQ\nG2216UZPixCQFELIKOxWJWZH1CQIJgNCMUQCiCCcQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cmap = sns.cubehelix_palette(light=1, as_cmap=True)\n", + "fig, ax = plt.subplots(figsize=(10, 6))\n", + "contour = ax.contourf(grid[0, :], grid[1, :], ppc['out'].std(axis=0).reshape(100, 100), cmap=cmap)\n", + "ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n", + "ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n", + "cbar = plt.colorbar(contour, ax=ax)\n", + "_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y')\n", + "ax.set_title('$B \\propto I_t $')\n", + "cbar.ax.set_ylabel('Uncertainty (posterior predictive standard deviation)')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Next steps\n", + "\n", + "This section was added with the introduction of the first approximate MCMC sampling algorithm in pymc3, Stochastic Gradient Fisher Scoring.\n", + "The file [sgmcmc.py]() defines a BaseStochasticGradient class that can be extended to other approximate algorithms by only implementing `_initialize_values` and `mk_training_fn` methods" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.13" + }, + "latex_envs": { + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 0 + }, + "nav_menu": {}, + "toc": { + "colors": { + "hover_highlight": "#DAA520", + "running_highlight": "#FF0000", + "selected_highlight": "#FFD700" + }, + "moveMenuLeft": true, + "nav_menu": { + "height": "390px", + "width": "252px" + }, + "navigate_menu": true, + "number_sections": true, + "sideBar": true, + "threshold": 6, + "toc_cell": false, + "toc_position": { + "height": "913px", + "left": "0px", + "right": "auto", + "top": "106px", + "width": "212px" + }, + "toc_section_display": "block", + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/docs/source/notebooks/sgfs_simple_optimization.ipynb b/docs/source/notebooks/sgfs_simple_optimization.ipynb new file mode 100644 index 0000000000..e4b4b70645 --- /dev/null +++ b/docs/source/notebooks/sgfs_simple_optimization.ipynb @@ -0,0 +1,266 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "*Example Notebook* for using Stochastic Gradient Fisher Scoring Step Method - It is based on [this](https://github.com/ferrine/pymc3/blob/a62b4fa98e75c392e634546d29cd5f2266007c46/docs/source/notebooks/simple_stochastic_optimization.ipynb)\n", + "\n", + "The goal here is to learn from small noisy samples of a quadratic function and estimate the parameters of the function." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import functools\n", + "import numpy as np\n", + "from theano import theano, tensor as tt\n", + "import matplotlib.pyplot as plt\n", + "import pymc3 as pm\n", + "np.random.seed(42)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Quadratic problem\n", + "Consider a simple quadratic problem with unknown parameters. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "def f(x, a, b, c):\n", + " return a*x**2 + b*x + c\n", + "\n", + "a, b, c = 1, 2, 3\n", + "min_ = np.array([-b/2/a])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### True data\n", + "Generate the quadaratic data with noise" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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DFxGpCPXQRUQqQgE9IpIfJWkkJ/NuS9pI/h7JfyR5nuQXSd6Qd5vSQnI/yX8i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\nRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "batch_size = 10\n", + "def xy_obs_generator(batch_size):\n", + " while True:\n", + " x_obs = np.random.uniform(-5, 5, size=(batch_size,)).astype('float32')\n", + " result = np.asarray([x_obs, f(x_obs, a, b, c) + np.random.normal(size=x_obs.shape).astype('float32')])\n", + " yield result\n", + "\n", + "x_train = np.random.uniform(-5, 5, size=(batch_size*100,)).astype('float32')\n", + "x_obs = pm.data.Minibatch(x_train, batch_size=batch_size)\n", + "\n", + "# xy_obs = pm.generator(xy_obs_generator(batch_size))\n", + "y_train = f(x_train, a, b, c) + np.random.normal(size=x_train.shape).astype('float32')\n", + "y_obs = pm.data.Minibatch(y_train, batch_size=batch_size)\n", + "\n", + "# Example observation\n", + "# obs = xy_obs.eval()\n", + "plt.plot(x_train, y_train, 'bo')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Final task\n", + "Our task is to find to estimate the quadratic function. We will test this by calculating L2 loss of the generated samples from the trained model to the observed output" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 1500/1500 [00:00<00:00, 1707.10it/s]\n" + ] + }, + { + "data": { + "image/png": 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3E5GJIoEVS8doCbSwEF9gOjrNdHSazvpObG1zeuI0+1v301bXRspO8cL1F+hv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\nHWZqKV5yX+F4Kq/9HBucNl8PEimboZlw0QDA+dF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "burn_in = 50\n", + "draws = 1000\n", + "\n", + "with pm.Model() as model:\n", + " abc = pm.Normal('abc', sd=1, mu=1, shape=(3,))\n", + " x = x_obs\n", + " x2 = x**2\n", + " o = tt.ones_like(x)\n", + " X = tt.stack([x2, x, o]).T\n", + " y = X.dot(abc)\n", + " pm.Normal('y', mu=y, observed=y_obs)\n", + "\n", + " step_method = pm.SGFS(vars=model.vars, batch_size=batch_size, step_size=1.0, total_size=draws*batch_size)\n", + " trace = pm.sample(draws=draws, step=step_method, init=None) \n", + "\n", + " pm.traceplot(trace[burn_in:]) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Inference results" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We don't have exact function as our observations were noisy" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.99199537, 1.98098698, 3.16144194])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.asarray(map(lambda t: t['abc'], trace)).mean(axis=0)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.13" + }, + "toc": { + "colors": { + "hover_highlight": "#DAA520", + "running_highlight": "#FF0000", + "selected_highlight": "#FFD700" + }, + "moveMenuLeft": true, + "nav_menu": { + "height": "12px", + "width": "252px" + }, + "navigate_menu": true, + "number_sections": true, + "sideBar": true, + "threshold": 4, + "toc_cell": false, + "toc_section_display": "block", + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pymc3/sampling.py b/pymc3/sampling.py index 511f343abe..6655ce3042 100644 --- a/pymc3/sampling.py +++ b/pymc3/sampling.py @@ -8,7 +8,7 @@ from .backends.base import merge_traces, BaseTrace, MultiTrace from .backends.ndarray import NDArray from .model import modelcontext, Point -from .step_methods import (NUTS, HamiltonianMC, Metropolis, BinaryMetropolis, +from .step_methods import (NUTS, HamiltonianMC, SGFS, Metropolis, BinaryMetropolis, BinaryGibbsMetropolis, CategoricalGibbsMetropolis, Slice, CompoundStep) from .plots.traceplot import traceplot @@ -20,7 +20,7 @@ __all__ = ['sample', 'iter_sample', 'sample_ppc', 'init_nuts'] -STEP_METHODS = (NUTS, HamiltonianMC, Metropolis, BinaryMetropolis, +STEP_METHODS = (NUTS, HamiltonianMC, SGFS, Metropolis, BinaryMetropolis, BinaryGibbsMetropolis, Slice, CategoricalGibbsMetropolis) diff --git a/pymc3/step_methods/__init__.py b/pymc3/step_methods/__init__.py index a14715d79e..67212508d3 100644 --- a/pymc3/step_methods/__init__.py +++ b/pymc3/step_methods/__init__.py @@ -12,6 +12,7 @@ from .metropolis import PoissonProposal from .metropolis import MultivariateNormalProposal +from .sgmcmc import SGFS from .gibbs import ElemwiseCategorical from .slicer import Slice diff --git a/pymc3/step_methods/sgmcmc.py b/pymc3/step_methods/sgmcmc.py new file mode 100644 index 0000000000..402c3e8e20 --- /dev/null +++ b/pymc3/step_methods/sgmcmc.py @@ -0,0 +1,295 @@ +from collections import OrderedDict +import warnings + +from .arraystep import Competence, ArrayStepShared +from ..vartypes import continuous_types +from ..model import modelcontext, inputvars +import theano.tensor as tt +from ..theanof import tt_rng, make_shared_replacements +import theano +import numpy as np + +__all__ = ['SGFS'] + +EXPERIMENTAL_WARNING = "Warning: Stochastic Gradient based sampling methods are experimental step methods and not yet"\ + " recommended for use in PyMC3!" + +def _value_error(cond, str): + """Throws ValueError if cond is False""" + if not cond: + raise ValueError(str) + +def _check_minibatches(minibatch_tensors, minibatches): + _value_error(isinstance(minibatch_tensors, list), + 'minibatch_tensors must be a list.') + + _value_error(hasattr(minibatches, "__iter__"), + 'minibatches must be an iterator.') + +def prior_dlogp(vars, model, flat_view): + """Returns the gradient of the prior on the parameters as a vector of size D x 1""" + terms = tt.concatenate( + [theano.grad(var.logpt, var).flatten() for var in vars], + axis=0) + dlogp = theano.clone(terms, flat_view.replacements, strict=False) + + return dlogp + +def elemwise_dlogL(vars, model, flat_view): + """ + Returns Jacobian of the log likelihood for each training datum wrt vars + as a matrix of size N x D + """ + # select one observed random variable + obs_var = model.observed_RVs[0] + # tensor of shape (batch_size,) + logL = obs_var.logp_elemwiset.sum(axis=tuple(range(1, obs_var.logp_elemwiset.ndim))) + # calculate fisher information + terms = [] + for var in vars: + output, _ = theano.scan(lambda i, logX=logL, v=var: theano.grad(logX[i], v).flatten(),\ + sequences=[tt.arange(logL.shape[0])]) + terms.append(output) + dlogL = theano.clone(tt.concatenate(terms, axis=1), flat_view.replacements, strict=False) + return dlogL + + +class BaseStochasticGradient(ArrayStepShared): + R""" + BaseStochasticGradient Object + + For working with BaseStochasticGradient Object + we need to supply the probabilistic model + (:code:`model`) with the data supplied to observed + variables of type `GeneratorOp` + + Parameters + ------- + vars : list + List of variables for sampler + batch_size`: int + Batch Size for each step + total_size : int + Total size of the training data + step_size : float + Step size for the parameter update + model : PyMC Model + Optional model for sampling step. Defaults to None (taken from context) + random_seed : int + The seed to initialize the Random Stream + minibatches : iterator + If the ObservedRV.observed is not a GeneratorOp then this parameter must not be None + minibatch_tensor : list of tensors + If the ObservedRV.observed is not a GeneratorOp then this parameter must not be None + The length of this tensor should be the same as the next(minibatches) + + Notes + ----- + Defining a BaseStochasticGradient needs + custom implementation of the following methods: + - :code: `.mk_training_fn()` + Returns a theano function which is called for each sampling step + - :code: `._initialize_values()` + Returns None it creates class variables which are required for the training fn + """ + + def __init__(self, + vars=None, + batch_size=None, + total_size=None, + step_size=1.0, + step_size_decay=100, + model=None, + random_seed=None, + minibatches=None, + minibatch_tensors=None, + **kwargs): + warnings.warn(EXPERIMENTAL_WARNING) + if model is None: + model = modelcontext(model) + + if vars is None: + vars = inputvars(model) + + self.model = model + self.vars = vars + self.batch_size = batch_size + self.total_size = total_size + _value_error( + total_size != None or batch_size != None, + 'total_size and batch_size of training data have to be specified') + self.expected_iter = int(total_size / batch_size) + + # set random stream + self.random = None + if random_seed is None: + self.random = tt_rng() + else: + self.random = tt_rng(random_seed) + + self.step_size = step_size + self.step_size_decay = step_size_decay + shared = make_shared_replacements(vars, model) + self.q_size = int(sum(v.dsize for v in self.vars)) + + flat_view = model.flatten(vars) + self.inarray = [flat_view.input] + self.updates = OrderedDict() + self.dlog_prior = prior_dlogp(vars, model, flat_view) + self.dlogp_elemwise = elemwise_dlogL(vars, model, flat_view) + + if minibatch_tensors != None: + _check_minibatches(minibatch_tensors, minibatches) + self.minibatches = minibatches + + # Replace input shared variables with tensors + def is_shared(t): + return isinstance(t, theano.compile.sharedvalue.SharedVariable) + tensors = [(t.type() if is_shared(t) else t) for t in minibatch_tensors] + updates = OrderedDict( + {t: t_ for t, t_ in zip(minibatch_tensors, tensors) if is_shared(t)} + ) + self.minibatch_tensors = tensors + self.inarray += self.minibatch_tensors + self.updates.update(updates) + + self._initialize_values() + super(BaseStochasticGradient, self).__init__(vars, shared) + + def _initialize_values(self): + """Initializes the parameters for the stochastic gradient minibatch + algorithm""" + raise NotImplementedError + + def mk_training_fn(self): + raise NotImplementedError + + def training_complete(self): + """Returns boolean if astep has been called expected iter number of times""" + return self.expected_iter == self.t + + def astep(self, q0): + """Perform a single update in the stochastic gradient method. + + Returns new shared values and values sampled + The size and ordering of q0 and q must be the same + Parameters + ------- + q0: list + List of shared values and values sampled from last estimate + + Returns + ------- + q + """ + if hasattr(self, 'minibatch_tensors'): + return q0 + self.training_fn(q0, *next(self.minibatches)) + else: + return q0 + self.training_fn(q0) + + +class SGFS(BaseStochasticGradient): + R""" + StochasticGradientFisherScoring + + Parameters + ----- + vars : list + model variables + B : np.array + the pre-conditioner matrix for the fisher scoring step + + References + ----- + - Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring + Implements Algorithm 1 from the publication http://people.ee.duke.edu/%7Elcarin/782.pdf + """ + + def __init__(self, vars=None, B=None, **kwargs): + """ + Parameters + ---------- + vars : list + Theano variables, default continuous vars + B : np.array + Symmetric positive Semi-definite Matrix + kwargs: passed to BaseHMC + """ + self.B = B + super(SGFS, self).__init__(vars, **kwargs) + + def _initialize_values(self): + # Init avg_I + self.avg_I = theano.shared(np.zeros((self.q_size, self.q_size)), name='avg_I') + self.t = theano.shared(1, name='t') + # 2. Set gamma + self.gamma = (self.batch_size + self.total_size) / (self.total_size) + + self.training_fn = self.mk_training_fn() + + def mk_training_fn(self): + + n = self.batch_size + N = self.total_size + q_size = self.q_size + B = self.B + gamma = self.gamma + avg_I = self.avg_I + t = self.t + updates = self.updates + epsilon = self.step_size / pow(2.0, t // self.step_size_decay) + random = self.random + inarray = self.inarray + gt, dlog_prior = self.dlogp_elemwise, self.dlog_prior + + # 5. Calculate mean dlogp + avg_gt = gt.mean(axis=0) + + # 6. Calculate approximate Fisher Score + gt_diff = (gt - avg_gt) + + V = (1. / (n - 1)) * tt.dot(gt_diff.T, gt_diff) + + # 7. Update moving average + I_t = (1. - 1. / t) * avg_I + (1. / t) * V + + if B is None: + # if B is not specified + # B \propto I_t as given in + # http://www.ics.uci.edu/~welling/publications/papers/SGFS_v10_final.pdf + # after iterating over the data few times to get a good approximation of I_N + B = tt.switch(t <= int(N/n)*50, tt.eye(q_size), gamma * I_t) + + # 8. Noise Term + # The noise term is sampled from a normal distribution + # of mean 0 and std_dev = sqrt(4B/step_size) + # In order to generate the noise term, a standard + # normal dist. is scaled with 2B_ch/sqrt(step_size) + # where B_ch is cholesky decomposition of B + # i.e. B = dot(B_ch, B_ch^T) + B_ch = tt.slinalg.cholesky(B) + noise_term = tt.dot((2.*B_ch)/tt.sqrt(epsilon), \ + random.normal((q_size,), dtype=theano.config.floatX)) + # 9. + # Inv. Fisher Cov. Matrix + cov_mat = (gamma * I_t * N) + ((4. / epsilon) * B) + inv_cov_mat = tt.nlinalg.matrix_inverse(cov_mat) + # Noise Coefficient + noise_coeff = (dlog_prior + (N * avg_gt) + noise_term) + dq = 2 * tt.dot(inv_cov_mat, noise_coeff) + + updates.update({avg_I: I_t, t: t + 1}) + + f = theano.function( + outputs=dq, + inputs=inarray, + updates=updates, + allow_input_downcast=True) + + return f + + @staticmethod + def competence(var): + if var.dtype in continuous_types: + return Competence.COMPATIBLE + return Competence.INCOMPATIBLE diff --git a/pymc3/tests/test_sgfs.py b/pymc3/tests/test_sgfs.py new file mode 100644 index 0000000000..89f7eb3a20 --- /dev/null +++ b/pymc3/tests/test_sgfs.py @@ -0,0 +1,35 @@ +import numpy as np +import pymc3 as pm +from pymc3 import Model, Normal +import theano.tensor as tt + +def test_minibatch(): + draws = 3000 + mu0 = 1 + sd0 = 1 + + def f(x, a, b, c): + return a*x**2 + b*x + c + + a, b, c = 1, 2, 3 + + batch_size = 50 + x_train = np.random.uniform(-10, 10, size=(batch_size*500,)).astype('float32') + x_obs = pm.data.Minibatch(x_train, batch_size=batch_size) + + y_train = f(x_train, a, b, c) + np.random.normal(size=x_train.shape).astype('float32') + y_obs = pm.data.Minibatch(y_train, batch_size=batch_size) + + with Model() as model: + abc = Normal('abc', mu=mu0, sd=sd0, shape=(3,)) + x = x_obs + x2 = x**2 + o = tt.ones_like(x) + X = tt.stack([x2, x, o]).T + y = X.dot(abc) + pm.Normal('y', mu=y, observed=y_obs) + + step_method = pm.SGFS(vars=model.vars, batch_size=batch_size, step_size=1., total_size=draws*batch_size) + trace = pm.sample(draws=draws, step=step_method, init=None) + + np.testing.assert_allclose(np.mean(trace['abc'], axis=0), np.asarray([a, b, c]), rtol=0.2)