{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian Coresets using Edward\n", "\n", "*(Better displayed in [nbviewer](https://nbviewer.jupyter.org/) as red warnings in font tag may not be displayed on github)*\n", "\n", "In this notebook we try out Bayesian coresets \\[1\\]\\[2\\] exploiting Tensorflow/Edward \\[4\\] for the definition of models, for their derivation, for posterior approximation, and for sampling. We rely on the code made availabe by Trevor Campbell for computing coresets \\[3\\].\n", "\n", "The notebook is divided in three parts:\n", "1. **Setup**: defining the data and the model;\n", "2. **Bayesian coresets**: computing and visualizing Bayesian coresets;\n", "3. **Bayesian logistic regression**: evaluating classification on the original data and on coresets.\n", "\n", "**ISSUES**: still to correct/review: (i) Low acceptance rate of Metropolis-Hastings; (ii) proper way to handle coreset weights instead of upsampling.\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Setup\n", "\n", "In this first section we define parameters and auxiliary functions, we generate and show the data, and we define the statistical model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Importing libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as stats\n", "import matplotlib.pyplot as plt\n", "\n", "import tensorflow as tf\n", "import edward as ed\n", "import bcoresets as bc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setting a random seed" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "np.random.seed(742)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining the projection code\n", "\n", "We copy the code from bayesiancoresets.projection \\[3\\] and slightly edit it to make it work with Edward models.\n", "Specifically:\n", "\n", "- **ProjectionF.\\_\\_init\\_\\_()** now receives:\n", " - *data*: as before\n", " - *grad_log_likelihood*: an Edward model for the gradient of the log-likelihood \n", " - *projection_dim*: as before \n", " - *approx_posterior*: an Edward model for the posterior\n", "- **ProjectionF.\\_sample\\_component()** was changed to exploit Edward objects. The posterior is sampled using *.sample()*, while the gradient of the log-likelihood is estimated using *.eval()*. Notice, though, the use of the iterator because the *.gradients()* function in Tensorflow defines automatically a sum over the gradients.\n", "- **Projection.\\_\\_init\\_\\_()** was changed only to manipulate Edward objects.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "class _Projection(object):\n", " def __init__(self, N, projection_dim, approx_posterior):\n", " self.dim = approx_posterior.shape[0].value\n", " self.x = np.zeros((N, 0))\n", " self.approx_posterior = approx_posterior\n", " self.update_dimension(projection_dim)\n", " return\n", "\n", " def update_dimension(self, projection_dim):\n", " if projection_dim < self.x.shape[1]:\n", " self.x = self.x[:, :projection_dim]\n", "\n", " if projection_dim > self.x.shape[1]:\n", " old_dim = self.x.shape[1]\n", " w = np.zeros((self.x.shape[0], projection_dim))\n", " w[:, :old_dim] = self.x\n", " w *= np.sqrt(old_dim)\n", " for j in range(projection_dim-old_dim):\n", " w[:, j+old_dim] = self._sample_component()\n", " w /= np.sqrt(projection_dim)\n", " self.x = w\n", " return\n", "\n", " def get(self):\n", " return self.x.copy()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "class ProjectionF(_Projection):\n", " def __init__(self, data, grad_log_likelihood, projection_dim, approx_posterior):\n", " self.data = data\n", " self.grad_log_likelihood = grad_log_likelihood\n", " _Projection.__init__(self, data.shape[0], projection_dim, approx_posterior)\n", " \n", " def _sample_component(self):\n", " sample_post = self.approx_posterior.sample().eval()\n", " \n", " sgll = [self.grad_log_likelihood.eval(feed_dict={X:self.data[i].reshape([1,self.data.shape[1]]),\n", " theta:sample_post})\n", " for i in range(self.data.shape[0])]\n", " sgll = np.array(sgll)\n", " \n", " return np.sqrt(self.dim)*sgll[:,np.random.randint(self.dim)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining the params of the simulation\n", "\n", "We define the parameters of the simulation, including the number and dimensionality of the samples we will generate (*nsamples*, *ndims*); the number of random projection dimension and core samples for coreset computation (*nrandomdims*, *ncoresamples*); and a grid step to plot contour plots (*gridstep*)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "nsamples = 200\n", "ndims = 2\n", "\n", "nrandomdims = 100\n", "ncoresamples = 20\n", "\n", "gridstep = .1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data generation\n", "\n", "We generate data from two Gaussian distributions. We use two-dimensional data for ease of visualization." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "mu1 = np.array([2,2])\n", "sigma1 = np.array([[1,0],[0,1]])\n", "mu2 = np.array([-2,-2])\n", "sigma2 = np.array([[3,.5],[.5,1]])\n", "\n", "pdf1 = stats.multivariate_normal(mu1,sigma1)\n", "pdf2 = stats.multivariate_normal(mu2,sigma2)\n", "\n", "X_pdf1 = pdf1.rvs(size=nsamples)\n", "Y_pdf1 = np.ones(nsamples).reshape((nsamples,1))*-1\n", "X_pdf2 = pdf2.rvs(size=nsamples)\n", "Y_pdf2 = np.ones(nsamples).reshape((nsamples,1))\n", "Xtr = np.vstack((X_pdf1,X_pdf2))\n", "Ytr = np.vstack((Y_pdf1,Y_pdf2))\n", "\n", "permutation = np.random.permutation(nsamples*2)\n", "Xtr = Xtr[permutation]\n", "Ytr = Ytr[permutation]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data visualization\n", "\n", "We plot the data we generated." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xmeshgrid, ymeshgrid = np.mgrid[-7:7:gridstep, -6:6:gridstep]\n", "xymeshgrid = np.c_[xmeshgrid.ravel(), ymeshgrid.ravel()]\n", "\n", "ycolors = np.array(['b']*Ytr.shape[0])\n", "ycolors[Ytr[:,0]==1] = 'r'\n", "\n", "plt.figure()\n", "plt.title('Data')\n", "plt.scatter(Xtr[:,0],Xtr[:,1], c=ycolors)\n", "plt.axhline(y=0, color='gray')\n", "plt.axvline(x=0, color='gray')\n", "\n", "xcontourgrid, ycontourgrid = np.mgrid[0:5:gridstep, 0:5:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf1.pdf(xycontourgrid))\n", "\n", "xcontourgrid, ycontourgrid = np.mgrid[-6:2:gridstep, -6:2:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf2.pdf(xycontourgrid))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining the model\n", "\n", "We define our standard Bayesian regression model as:\n", "$$\n", "P(Y \\vert \\theta) \\sim Bern (p = \\sigma(X \\theta))\n", "$$\n", "where $\\theta$ is the two-dimensional vector of parameters and $\\sigma(x) = \\frac{1}{1+\\exp{-x}}$ is the logistic function.\n", "\n", "We also define the log-likelihood of the models and we use Tensorflow for the definition of the gradient of the log-likelihood." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "X = tf.placeholder(tf.float32,[None,2])\n", "theta = ed.models.Normal(loc=tf.zeros(2),scale=tf.ones(2))\n", "y = ed.models.Bernoulli(probs=tf.sigmoid(ed.dot(X,theta)))\n", "\n", "log_likelihood = tf.log(tf.sigmoid(ed.dot(X,theta)))\n", "grad_log_likelihood = tf.gradients(log_likelihood,[theta])[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Bayesian Coresets\n", "\n", "In this second part we compute and plot different types of coresets (GIGA, Frank-Wolfe, OrthoPursuit, and Random Subsampling)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Performing Laplace approximation\n", "\n", "We rely on Edward to compute a cheap posterior approximation, using Laplace approximation.\n", "Notice that we need to define the additional hyper-parameter of the number of iteration (*n_iter*) for the computation of the Laplace approximation. This value was set by hand here-- setting this value too high causes the computation too fails due to NaN values in the computation." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fmzennaro/miniconda2_1/envs/bayes3/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " not np.issubdtype(value.dtype, np.float) and \\\n" ] } ], "source": [ "qtheta = ed.models.MultivariateNormalTriL(\n", " loc = tf.Variable(tf.zeros(ndims)),\n", " scale_tril = tf.Variable(tf.eye(ndims,ndims)))\n", " \n", "inference = ed.Laplace({theta:qtheta}, {X:Xtr,y:Ytr.reshape((nsamples*2))})\n", "inference.run(n_iter=15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Performing random projection\n", "\n", "We discretize and random-project our log-likelihoods." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "randomprojection = ProjectionF(Xtr, grad_log_likelihood, nrandomdims, qtheta)\n", "vecs = randomprojection.get()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing the coresets\n", "\n", "We compute the coresets for our data." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "bc_giga = bc.GIGA(vecs)\n", "bc_giga.run(ncoresamples)\n", "\n", "bc_fw = bc.FrankWolfe(vecs)\n", "bc_fw.run(ncoresamples)\n", "\n", "bc_op = bc.OrthoPursuit(vecs)\n", "bc_op.run(ncoresamples)\n", "\n", "bc_rs = bc.RandomSubsampling(vecs)\n", "bc_rs.run(ncoresamples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the coresets\n", "\n", "We finally show the coresets." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2,2)\n", "axes[0,0].set_title('GIGA coreset')\n", "axes[0,0].scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_giga.weights())\n", "axes[0,0].axhline(y=0, color='gray')\n", "axes[0,0].axvline(x=0, color='gray')\n", "\n", "axes[0,1].set_title('Frank-Wolfe coreset')\n", "axes[0,1].scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_fw.weights())\n", "axes[0,1].axhline(y=0, color='gray')\n", "axes[0,1].axvline(x=0, color='gray')\n", "\n", "axes[1,0].set_title('OrthoPursuit coreset')\n", "axes[1,0].scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_op.weights())\n", "axes[1,0].axhline(y=0, color='gray')\n", "axes[1,0].axvline(x=0, color='gray')\n", "\n", "axes[1,1].set_title('Random Subsampling coreset')\n", "axes[1,1].scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_rs.weights())\n", "axes[1,1].axhline(y=0, color='gray')\n", "axes[1,1].axvline(x=0, color='gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Bayesian Logistic Regression\n", "\n", "In this third part, we perform Bayesian logistic regression on the original data, the GIGA coreset and the Frank-Wolfe coreset." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing MAP estimate for the original data\n", "\n", "We first compute the MAP estimate for the parameters, $\\hat{\\theta}_{MAP}$, and then we plot the MAP discriminator." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fmzennaro/miniconda2_1/envs/bayes3/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " not np.issubdtype(value.dtype, np.float) and \\\n" ] } ], "source": [ "map_theta = ed.models.PointMass(tf.Variable(tf.zeros(2)))\n", "inference = ed.MAP({theta:map_theta}, {X:Xtr,y:Ytr.reshape((nsamples*2))})\n", "inference.run(n_iter=5)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mapx = np.linspace(-6,6,500)\n", "mapy = -(mapx*map_theta.eval()[0]) / map_theta.eval()[1]\n", "plt.plot(mapx,mapy)\n", "\n", "plt.title('MAP Discriminator')\n", "plt.scatter(Xtr[:,0],Xtr[:,1], c=ycolors)\n", "plt.axhline(y=0, color='gray')\n", "plt.axvline(x=0, color='gray')\n", "\n", "xcontourgrid, ycontourgrid = np.mgrid[0:5:gridstep, 0:5:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf1.pdf(xycontourgrid))\n", "\n", "xcontourgrid, ycontourgrid = np.mgrid[-6:2:gridstep, -6:2:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf2.pdf(xycontourgrid))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing the posterior predictive for the original data\n", "\n", "We then compute the posterior predictive via MCMC, and then we plot the contour plot of the posterior predictive." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fmzennaro/miniconda2_1/envs/bayes3/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " not np.issubdtype(value.dtype, np.float) and \\\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "10000/10000 [100%] ██████████████████████████████ Elapsed: 5s | Acceptance Rate: 0.001\n" ] } ], "source": [ "mc_samples = 10000\n", "qmc_theta = ed.models.Empirical(tf.Variable(tf.zeros((mc_samples,2))))\n", "proposal_theta = ed.models.Normal(loc=tf.zeros(2), scale=tf.ones(2))\n", "inference = ed.MetropolisHastings({theta:qmc_theta}, {theta:proposal_theta}, {X:Xtr,y:Ytr.reshape((nsamples*2))})\n", "inference.run()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_post = ed.models.Bernoulli(probs=tf.sigmoid(ed.dot(X,qmc_theta)))\n", "\n", "ppc_samples = 100\n", "probs_BLR = [y_post.eval(feed_dict={X:xymeshgrid}) for _ in range(ppc_samples)]\n", "probs_BLR = np.array(probs_BLR).mean(axis=0).reshape(xmeshgrid.shape)\n", " \n", "plt.contourf(xmeshgrid, ymeshgrid, probs_BLR, 25, cmap=\"RdBu\")\n", "plt.scatter(Xtr[:,0],Xtr[:,1], c=ycolors)\n", "plt.axhline(y=0, color='gray')\n", "plt.axvline(x=0, color='gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Upsampling the data for the GIGA coreset\n", "\n", "We rely on an upsampling trick to manage the weight of the data provided at the end of the coreset computation-- this solution is far from ideal, and a better approach would be to redefine the model to take into accoun the weights." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "Wt = bc_giga.weights()\n", "Xwt = Xtr[Wt>0]\n", "Ywt = Ytr[Wt>0]\n", "Wt = Wt[Wt>0]\n", "\n", "for i in range(Wt.shape[0]):\n", " np.vstack((Xwt, np.tile(Xwt[i,:],(np.int32(np.floor(Wt[i])),1))))\n", " np.vstack((Ywt, np.tile(Ywt[i,:],(np.int32(np.floor(Wt[i])),1))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing MAP estimate for the GIGA coreset\n", "\n", "We now compute again the MAP estimate for the parameters, $\\hat{\\theta}_{MAP}$, using only the coreset data, and then we plot the MAP discriminator." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fmzennaro/miniconda2_1/envs/bayes3/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " not np.issubdtype(value.dtype, np.float) and \\\n" ] } ], "source": [ "map_theta = ed.models.PointMass(tf.Variable(tf.zeros(2)))\n", "inference = ed.MAP({theta:map_theta}, {X:Xwt,y:Ywt.reshape((Ywt.shape[0]))})\n", "inference.run(n_iter=5)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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2Vnw0uiU/TmxPam4hI77cw9yt4ehVOGCFQnEHUcJ+G+jb2IdN03syuIUfszaHMfrbfUQkZld1tRQKRQ1BCfttwt3Rhrnj2/Dlg22ITslh6Be7mL87EqMKB6xQKG4zlSbsQgitEOKYEGJNZZVZHRjW0p9N03vSLcSL99acYfz3+7mcqsIBKxSK20dl9tifB85WYnnVhloudsyf0J5PRrfkdGwmg2bvZMnBSyqgmEKhuC1YVUYhQogAYCjwAfBCZZRZ3RBCMLZDHboEe/LyHyf474qTbDqTwEejWlDLxa6qq6e4S8jJzCU2Ip74yETiIxNJvJRMWmI66YmZZKfnkJeVR35OAXqdAYPegBACK2stVjZW2DvZ4eBij7OHE+4+brj7uOEb6I1v/Vr4BfngW78WVtaVIgmKKqayvsXZwH8A5/IMhBCTgckAdevWraTT3n3U8XDgtyc78/O+KD5af44Bn+/kvZHNGd7Kv6qrpviXkRSTwuk95wg/cpGI45FEnbpMany6hY2Dsz3uvm64+7jiXccTB2d77Bxs0VpbobXSgASD3oCuQEdeTj65mXlkJGcRfSaGtPh09Lri9RYarQb/YB+CWgUS3CqQxh1DaNKlIfaOquNxt3HLwi6EGAYkSimPCCF6l2cnpZwHzANo3759jfZBaDSCx7rVp2dDb15ceoLnFh9j4+l43h/RHHdHm6qunqKKyEjO5NjWkxzZHMrxbaeIj0wEwNrGisDmdWg/qDV1GtWmdgM//OrXwrd+LZzcHP/x+YxGI6lxacRHJRF3IYGYsFiiz8YQdvgCO5ftA0xi37BdEG37t6Rt/5Y07doQaxvrSrlexe1D3KqfVwjxP+ARQA/YAS7ACinlw+Xlad++vTx8+PAtnbe6oDcY+W7nRWZvCcPNwYaPR7egb2Ofqq5WjWXBggUATJw48Y6cLykmhZ3L9rFn5UFO7T6HlBIHF3va9G1Oix5Nad6jCUEt695xMc1Oz+Hs/jBO7jrLiR1nOLc/DKPRVLeOQ9rS/b5OdB7WFlt72ztar5qOEOKIlLL9de0qcwDP3GN/SUo5rCI7JeylORObyQtLj3MuPoux7QN4c1hTnO1Uz+hOcyeEPT+3gJ3L9rHl150c//sUUkqCWtaj28iOdBjchobtgtBaaW/b+f8JORk5nNh+hn1/HWb/X4dJT8rEwcWenqM7M3BiH5p3b4wQosIy0tPhgw/g3nuhZ887VPFqxo0Kuxop+ZfQ1N+FVc90Y86WcL7dcYE9ESl8OqYlXYO9qrpqikoiLjKBVV9uYNOCbWSl5eAf7MPDb95Pv4d7UDvEr6qrVyGOro50HdGBriM6YDAYCN1xhs2/7GDHsn1s+Gkbgc3rMHzqPQyY0Bs7h7J78T//DLNmwR9/QGTkHb6AGkal9thvFNVjr5gj0Wm8tOwEkck5PNYtkFcGNcbO+t/Vg6uu3I4e+4UTUfz+yUp2/L4XodHQfVRH7p16Dy17Nr1uL/d6GAxG0lJzSEnOIjMjj9ycAnJzC9DrjOh0BjQagdZKg42NFY5Otjg52eHm7oiXtzOOTra3fP783AK2Ld7N6q83EnEsElcvZ0Y+O4ThT9+Di4flXIqoKHj8cXjoIXjiiVs6bY2lSlwxN4oS9uuTW6jn4/Xn+HlfNEHejswa04o2dd2rulrVnsoU9pjwOH56YzE7l+3D3smOYU8NYNT0oXjV9rzpsoxGScylFC6EJxARFk90ZBKXL6UQH5eO0fDPfsP2DjbUDvAgoK4H9YNr0aCRHyENfXH3uPkBWSklp3afY+mnq9i/5ggOLvaMfXkEo6YPVbNqKhEl7NWEPRHJvLzsBPGZ+UzrHcJz/RpgY1U9I0F8+SUsWwY7dlRdHSpD2HMycljw1u/89c0mrG2tGD19GKNfGIazu9MNlyGl5FJ0Cgf3hhN67BKnQy+TlZUPgLWNljp1PQmo64l/gDve3i54eTvj4uaAk5MdDg42WNtoTX56KdHpDBQW6MnJKSA7K5+01BySk7JITMjgyuVULkcnEx9XHInUP8CdFq3q0qZ9IB06B+Pi6nBT138xNJqf/+939q46hIefO09+9BD9H+55y28HCiXs1YrMfB3v/nWGP47E0MTPhc/GtqKJn0tVV6vS2bkT1q2Djz6qujrcirBLKdm2ZA/fvrCA9MRMhkzqz4R3xuLu43bD+SPC4tm+5Qy7tp0lLtY0Zz2grgfNW9WlWYsAQhr6EhjkjVUlD65mZ+VzITyesHNxnDpxmVOhl8nMyEOjETRrEUDPfk3p2acJHp433jid2nOO7178mXMHI2jRswnPfzOZek0CKrXeNQ0l7NWQzWcSeHVFKBl5OmYMaMjkHkFYaatn772q+KfCnp6UwZyp37N7xQEadQjmua8n0bBd8A3lzcrMY9O6UNauPMrlSylotRradqxPl+4N6dQ1hFo+rjd5FbeO0SgJPxfHvj1h7NlxnqiLSWg0gnYdg7h3VDs6dglBewPPntFoZMOP2/jhv7+Sn1PAEx8+yH3PD0GjUc/tP0EJezUlNaeQN1aeZN3JeNrUdeOzsa2p7/XPF6koLPknwn50SygfPfIF2Wk5THj3Ae5/cRha7fV71HFX0lj62z42rwuloEBP0xYB3DO0Fd17N8bFxb7CvEajJCY5g8j4FOJSMolLzSI1K5eMnHyycvPRGYzo9AY0QmBtpcXGWourgx2ujvZ4uzni5+lCbU9XQvw9cXe+vqslOjKJbZtPs2HNCVKSs/DxdWX0A50YPLwNdjcwLTctIZ3PJn/L/r+O0Lpvc1799Tk8fNWY0c2ihL0aI6Vk9YlY3lx5ikKDkVcHN+GRzvXQaJQP81a5GWE3Go0s+WglC95cQr2mAby66HmCWta7br642DQW/rCTvzefQqvR0G9QC0aMbk9IQ99y82TlFXA0PIZjEVc4fiGWsJgk8ktsnm5rrcXTxREXBzucHWyxsdJipdUgJegMBgp0ejJz8knPySc1Mxdjid+9l4sDTer50CakNm1DAmgW6IO2nB61Xm9g3+5wli/Zz+nQGNzcHOg/pDPd+3SgWbOKBV5KycaftvHVcz/i4OrAm0tfoHm3xte9X4pilLDXAOIz8nlleSg7wpLoFuLJJ/e3orZbxT09RcXcqLAX5hfy6WNfsf33vfQZ340Z86Zcd/ZHTk4Bvy3YzZ9LD6LRCIbd1477x3fCy7vs8ZKk9Gw2HgljZ+gFjkfEojcasbbS0qyeD03q+tAgwIsgX08CvFxxd7a/4cFJncFAYlo2l5PSibiSTPiVZEIvxhGdmAaAq6MdXZsG0qd1MD1aBGFbTmCwk8cv8cM3uzlz8iL5hS6Mn9CPqc9cfwpn5Mlo3h49k4SoJF74fgoDJ/S+oXorlLDXGKSULD54mffXnkErBG/d25T72wWoGQj/kBsR9uz0HN4a+TEnd57lyY8eZuzLw697v/fuPM8XMzeQkpzFwCEteeypPnh5l46ZpzcY2X4ighW7T3Hw3CWMUhLi70n35vXp2iyQ5oF+2NncnnWFKZk5HA6LYc+pSPacjiItOw9ne1sGtGvI2F6taBjgXSrP4cMwbEgU9Wtvxsk+gbYd6jP9lSH4+VfsZslOz+G9sbM4uuUkE997gAdfG6We2RtACXsN41JKLi/9cYKDkan0b+LD/0a1wNtZxfG4Wa4n7DkZObwy8D0uHI/i5QXP0Hd89wrLy80p4MvPN7J5XShBIbWY/spQmjSrXcour1DH8l0nWfz3MeJSM/H1cGZYp6YM6diYQF+PUvZSSmKzsjidlEhkWhqR6WkkZGeTkpdLWl4+BQY9BXoDWo3ARqvF3soaTwd7vBwc8Hd2Icjdg2B3d5rX8sHZtvRzYjAaOXjuMmsPnOHvYxHk6/R0aFSHRwe0p2vTehYivHIlpKYa8XQ5yo/f/o0Epk0fyD1DW1Uo1rpCHbOe/Iatv+7i4TfvZ8I74yq8lwol7DUSo1Hy455IPtl4HidbKz4Y2ZzBLf7dS9X/bVQk7HnZebwy8D3Cj1zkrT9eosu9Ff++oi4m8c5ry4iNSWP8o9146LEeWF+zglhnMPDn7lN8v24/KZm5tG1Qm4f6tqVny6BSfu64rCx2REeyIyqKo3FxJOXmFB3zcnDAz8kZLwcH3O3tsdVqsdFqMUpJocFArk5HSl4eybk5xGRmkqvTASCABp6edPAPoHdgfbrUqYODtaWvPDMnnxV7TvL79uMkpGXTOtif5+7rTuvg0g1UYnwGn76/muNHo+k3sDnT/zu0wsFVo9HI55O+ZcNP25j43gM89ProCu9pTUcJew0mPCGLF5ae4OSVDEa09ufd4c1xdVABxW6E8oTdoDfw1siPObzhOG8ue5Hu93WqsJwDe8L58P/+xM7ehtfevY9WbUoPqp64EMsHv20hIjaFtg1q8/TwbrQJsRTL9Pw81oSF8efZMxyLjwPAz8mZzgEBtPL1o6WPD0HuHriU0esuDyklCTnZhKWkcCI+nqNxsRy8EkOeXo+tVsuA4BDua9yEHvUCsSrRuOj0BlbtPcW8dQdIzshhWKcmzBjds9SsGoPByJKFe/j5hx2ENPLj3Y/Hlul2uorRaOTTx75iyy87eXH+NAY91ueGr6WmoYS9hqMzGPl62wXm/h2Op5MNH49uSe9Gtaq6Wv96yhP2r577kZVfruf5byYz7KkBFZaxeX0oMz/4i6AQH979ZCzetSwHRwt0er74czeLtx3D192Zl8f2pnerYAu3RWRaGj8cPczys2coNBho5OnFiMaN6Vs/iAYenmW6OPINhSTmZ5JamE2+QUeBQYdGaLDVWuGgtcXbzgVPGyesNKWnYhbo9RyKvcLmCxGsCTtPWn4+fk7OPN6mLQ80b4GjTfE+AXkFOn7ccJCfNx/G0c6GNx7sT7+2DUqVuW93GP97eyXOznZ8Ovdh/ANKu5SuotfpeX3Y/zj+9yk+2fwWrXo3q/Ae11SUsCsAOBmTwQtLjxOemM34jnV5fWgTnGxVUM/yKEvYty3Zw4cPzmb09KFM+WximfmusnHtCWZ9+Bdt2tfn7f+Nwd7BcuOUmKR0/vP9Ws5dTmRc79Y8O6IbDnbFNlcyM5m1bw+rzp3FWqtldJOmPNSyFU29LRvlLF0eR1IjCU2LJjwrjvCsOFILc7geGgS1HTxo6OJHI2d/2noE0dS1toXYFxoMbIu8yILjxzhwJQZXW1umdejEo61aY2tV/OxciE3m7YWbOB2dwLjerZkxqgc218ygiTgfzyvTF2Fra8XMLx+pUNxzMnN5ttOrZKfn8M3RT/H0U/Pcr0UJu6KIfJ2BzzeHMW/XRQLc7Zl5fys6Bd18IKqawLXCHheZwOSWLxLcOpCZf79d4Z6gu7af473X/6BN+/q8+8lYbG0t3V9Hw2N44dvVALwz4R56tSxemaozGJh35DBfHtwPwITWbXiiTTu8HYsXn2Xq8tgSF8rGuBOEpl/CII3YaKwIcqpFA2c/6jh4mnrlts7Ya22w1VhhRJJv0JGjzycpP5OE/AyicpIIz4ojJjcVACcrO7p7N2awf2s6eoWgFcXul+PxcczZv48d0VHUc3Xjvb796F632K2k0xv4YuVuFm09Sutgfz6fOgLXa6Z9XghP4D/P/Yq9vQ1ffP9YhWEJok5f5tlOr9K0a0M+2vimmilzDUrYFaU4FJXKi0tPcDktlye61eelexqpcMDXUFLYpZT8Z8C7hB26wPcnZ1Grbunpflc5cyqGl5/5leAGPnwy9+FSA4Y7Qi/wyvdr8fd04YunRxLgXRw/5mJaGjM2rONkYgKDQxrwWo9e1HYpdt9czE5g4cWdbI4LRScN1Hf0prdPMzp5NaCFWx2sNf/sDSy9MIfDqRfZlxTG9oTTZOnz8bZ14f66nRlTrzNOVsUCvSs6ire3byMyPY1HWrbitR69LHrvGw+d562FG6nr7cbXz43C281SvMPOxfHi0wupU9eTWV89WupNpiRrvtvMnKnzbsjtVdNQwq4ok5wCPR+uO8uiA5cIqeXEZ2Nb0TLgxoJU1QRKCvtVF8z1BCYzI5cpE77HykrLF98/hpu7ZYiH/Wejef7rVTSs7cUXz9yHu1PxIrKtFy8wY+N6rDUa3u/bn8ENGhYdS8hL58uwjWxZMgdUAAAgAElEQVSKC8VOa82w2m0ZVrsdjV38S/Vks3XJpBZGk1EYR5Y+EZ0xH50xDyG02GjssdE44mrth5uNPx62gdhoLBeyFRr1LNx/jo0ph4i2DseQbU/Bll78PKUr7VqbBDxfr2Pm3j38eOwozWv58N2w4fg5Fw+KHjp/mRnfrMLXw5kfXhiLm5PlOQ7sjeDNl5cwcEgrXnr93nLv59UGNeJoJD+Hz8XFs/yB15qGEnZFhewIS+KVP0JJyi7g6T4hPNs3BGsVUKxI2MePG8/jTabj5O7I14c/Ljf2i5SSd19fzv7dYcyZ9xgNG1tOLz13OZEnZi2ltpcrP8wYg0sJN8VvJ0N58+8tNK/lwzfDhuNvFkmjNLI4ai/fRWxGSnigXlceqt8dN5viBsMgdURlH+RC1m5ickPJ0icUHRNosNbYY62xQ0ojOmMeOplvcdzbLoQ6Dm1o5NIHd6sQRo6E7dvBaARR+wq1H96CW6fz6OO9WDDiflq61y3Kf7UxcrS2ZuF999PAs9itd+j8ZZ798k8a1anFvBn3l1q1umDedhYt2M0b742iV7+m5X4PkacuMaX1SwyfNoinv3i8XLuahhJ2xXXJyNXxzl+nWXHsCs1ru/DZ2NY09KnZvaOrwu6S4c03MxbwyZa3aNO3Rbn2u7af493X/uCJqX154JGuFscyc/J56H+L0BuNLHxlPN6uxe6JxSdDef3vLfStH8TcwUOxN88dTy/M5a3Q39mfHE5378a81ORe/B2KBxEzdQkcS13Oucwt5BsysdO6EODQCn/75njZBuNm44+TlRdCWDbSemMhmbo40guvkJB/niu5J4nLO4MRPdrc+vz5xTB2LRmErqB42qRrh/MEPr0KO58MpjW8h0fq9yh6UziXnMSEP1eYruX+MQS5Fw+Kbj0azsvfr+H+Hi157cF+FvUw6I08/9QCEuLSmb9kaoXBzmY/9R0bF2zj5/C5FbrBahJK2BU3zIZTcbz+5ymyCvS8NLAhT3QPQltDA4otWLAAKSUb3thHnUb+zPz77XJtCwp0TBjzNW7uDnw1/wm012yA8sr3a9h24gI/vDCWlkHFPfnNFyKYsmY1vQLr883Qe4t81bG5aTxzeD4JeRm82GQY99XpWCSk+YYsDiT/QmjaKkAQ7NyNJq4DqefYHo34Z+MkeYYMwjK3s/bYRhz9w0hP8GTt509waNUAQGBrC+Mezcd/2gq2xp9isH8b3mw+qmgGTURqCuP/WIqN1orV4x/C06F4PvvsFTtZuPkIn0waSv+2DS3OezEigamP/cDQ4W157uXB5dYv8VISExo8y5BJ/Xn2yyf/0TVWN25U2NW7t4JBzf3YOKMnvRt68+G6czwwbx/RKdefOlddyUjOIjUujTEvlu8HBli78igpyVlMnT6wlKjvPhXJ5qPhPDW0i4WoR6Wn8eKmDSb3SwlRv5KbyuSD88jU5fFNx0mMqtupSNSjcw7za+STnEhbSVO3QUwMXsiQ2m9S36lTKVGXxixk4VFk/t/IvJXIvDXIgl1I3Tmk1FvY2mtdaeU+AvZ/xbxJM0mP9+ahjz5hyvf/xSsgmTfegJ++tePDVuN5KqQ/62OP8Wbo7+iNBgBCPDz5ccQoUvJymbFxPQajsajsZ0Z0p3GdWnyydDvZeQUW5w0K8WHo8Las/+sYCXHp5d7fWnW96f1AN7b8spO87LwKvwuFJUrYFQB4Odny3SPt+GxsK87FZzF4zi5+3R9NVbzRVTVpCel41/Gk/aDW5doY9EaW/bafVm3rlVpVqjcYmbVsB4G+Hjw6oF1RulFKXt60ESuNhq9LiHquvoAXjvxMvqGQrzs8WeTPllJyJGUpKy+/iq3GiXGBX9LPdwbO1sVz2qWUSN0pjJnvYUy+F5nYHpn6ADJ9CjLjP8iMF5BpTyBThiMT22FMfRSZMx9pSC4q46mnBCnhrfl24lyWvfMcQe1O89If03jyhXNoNCCE4ImQvjzfaDBb40/xdfimorwtfHx4p3dfdl+K5ucTx4vSrbQaXn+wHymZOSzYVPrtfPyEbgAs//1ghd/F0En9yc3KY/efFdspLFHCrihCCMGotgFsnN6TdvXceWPlKSb8dIj4jPzrZ64mGA1GstNy6Dm6c4WbZezfE05yUhb3jelY6tiGw+eITkzjmRHdsC6xhd3yM6c5Ehdbajrj/06vJDonmQ9bj6ehS3Hv/kDyQnYnzaOBc0/GB36Nj52lS0Pmb0SmjECmjILc30HjjXB6FuH2HcLzD4TXJoTXOoTHYoTrLLC/H4wZyKyPkUk9MaY9g9RH4ekJp07Ba68J/A3DcTv7Fd6eNvwZ8x/i8s4Une+h+j0YXacTv0buYkdCcfrYZs3pVS+Q2fv3kpiTXZTeLNCX/m0bsmTbMdKu6XF713Khe+/GbF4fSl5eYbn3uWnXRnj6u7N31aFybRSlUcKuKIW/mz0LH+/IeyOacSgylYGf7+DPYzE1ovcujZJadb3o93DPCu22bDyJh5cTnbuVXkq/ZNtxQvw96dOqeAGS3mjkiwP7ae3ry6gmxbNB9iadZ2PcCSaF9KOjZ0hR+vnMbRxI+YWmrvcw2P91rDTFg5rSmIEx/UVk+rOAEeHyf4hae9B4/IhwegZh1wdh3RJhFYiwCkHYtEPY34vG5U00XqsQXuvAYQIU7jM1DLm/4ekpefNNWLoUJj1Yj7H1ZmOvdWNNzNvk6FOKzj2jyVAau/jz8ZlV5OhNLhYhBG/16kOeTsf3R45Y3ItJgzuRW6Bjzf4zXMvQEW3Jzsrn4N6Icu+zRqOh87D2HNl0Ar1OX66dwhIl7IoyEULwSJdA1j/fgwY+zsz4/QRTfz1KSnbB9TPfxWittfjU86ZB26BybQoKdBzaF0H3Xo1L+dYvxCZzJjqBkd2aW8w13xARzpWsTKZ16ITGnG6URuacX08dB08eDSpuSNILY9kaNws/+2b09Z1hMcNFGq4gk4dD/nqE0/MIz5UIh4cQmhvfF1VYhaBxeQXhtRas2yEz30ZmzEDKYh+5k7UXwwLeodCYy4bYD4sadRuNFS83HU5yQRa/Re0usq/v7s7Qho1YciqUrILiZySkthct6vvx177TperRonVd3Nwd2b39XIX1bdu/BXnZ+Zw7WH4DoLBECbuiQgK9HFn6VBf+O7gxf59LZODnO9l4Or6qq1WlnDsTS0GBng6dS29Wved0FAADrpkJsvr8OfycnOhbv7jBOJIaSWR2Ik8E97VYPbov+SckMNj/DbSiOF3KPGTaNJBZCM8lCKenEeKfx/0RWl+E+3yE0wzIX4fMnmtx3Mu2Pj19phCTe4KL2XuL0lu41aW7d2NWXD5YNJAK8HDLVuTodGyLirQoZ0C7hkTEphCfmmWRrtVqaN8piBPHKh7LadGjCQBhhy7842utaShhV1wXrUYwpVcwq5/tho+LHU/9coQXlh4nI09X1VWrEs6dvgJA0+al45EfDosh0NfDYkl9gV7PrugoBgSHFPXWAdbHHsPZyo6+vs2L0jJ1CYRlbqeV+wicrS3nbsusmaA/h3D7DGHdslKuRQgBjlPAfjTkfIUstBzobOY6GFdrf46kLrVIH1mnAykFWRxMKe5Ft/Xzx9vBkS0XLQW4Y6M6ABwOv1zq/E2bB5CWmkNifEa5dXT3ccPD140LoVE3e3k1llsWdiFEHSHENiHEWSHEaSHE85VRMcW/j8a+Lqx8uhvP9Q1h1fFYBs3eya7wpKqu1h3nyuVU3NwdcXF1KHXsYlwKja/ZQi48NYUCg4EO/pYNwZHUSDp4BmOnLY4rE5m9H5A0c7Oc3y0NSaYBUvvRCNvelXYtYBJ34fIWaDyR2d9YHNMILU1cBxKXd4YcfVpRekdPU7CwY6lRJWwFbf38OJWYYFFGkJ8nVloNF2NTuJa6gaZVq1diUiuso1+wD4nRNe9Z+6dURo9dD7wopWwCdAaeFkKUv1ZYcVdjY6XhhYGNWD61Kw42Wh6Zf5A3V54it7DmDGwlJ2VRy6f0BtQGo5G41EyLAF8AF1JNotXQ06soLUuXR1xeGk1d61jYXskNxdnKB3ebAMvC89cDhQjH27NQRwh7hMNDULjL1IiUoJ5jO0ASl3eqKM1Oa00DZ1/OZ8Va2Db09CI6PR2dodhFY6XV4O/pwpWUzFLnreVjGhtITCh9rCQefu6kVDDnXWHJLQu7lDJOSnnU/HcWcBYo/Y6qqFa0ruPG2ud68ET3+vx6IJohc3ZxJLriXld1ITe3AAfH0jsW5RbokBJcHCyPZZgHE93ti5fPp5ljp3vZWoZwyNYn42rjW6psabgIwhm09W+5/uVi3cr0ryHKItnF2lSfbF2yRbqnrTPp18SAd7e3QwLZhZZTGJ3tbckpY1rj1SiP+ddx69k52lKQW70H7iuTSvWxCyECgTbAgTKOTRZCHBZCHE5KUq9U1QE7ay1vDmvK4kmd0RslY77dx//Wn6VAb7h+5rsYo0GiKSPkgtFoGgC89tjVFZlWJdIN5hko2mtiuhilHk1ZA6LCAWT+7Y1PLswByqSlgGqFyVVkkJbiayW06IyGa2xN16MvsQoVTAOlhmvSADTmwHPGMo5Z2AkN0lj9p9tWFpUm7EIIJ2A5MF1KWeq9Sko5T0rZXkrZ3ttbBfSpTnQO8mTD9J6M61CH73ZcZPjcPZy6Uv5g2N2Onb11mT1MB/PGGjn5lj3Tq/uRZuQXC6aLtan3nqHLtSzDysNi3vhVhHAGdEjjbbyvevOgp9bSPZRtro+jleXmLOm6HFytLccZssw9dWdby3jrufmFFjtFXSXf3IuvaMNrgIL8Qmzsy4/hrrCkUoRdCGGNSdQXSSlXVEaZirsLJ1sr/jeqJT9N7EBabiEjv9rD3K3h6A0V98TuRjw8nEhJziqVbm2lxd3JvtS0vgDzKtOo9OLBR3cbR1ys7QnLirOwrWUbQkpBNJ/OyaBHD2jZErp0gVlze5kMchdX8tWYkFIic38zuXq0pf3+AN52xQuoDNJIRFY89ZwsO2mRaWl4OThgZ1Us1FJK4lKzqOVWeueklGTTSlX3CnZVAkhPzMDVq2ZHHr0ZKmNWjADmA2ellJ/depUUdzN9Gtdi04yeDGnhx6zNYYz+Zi8RidnXz3gX4VvbjaTETAoKSvfaA309iLhm9kcT8xvqiYTi+f8aoaGFW10Op1womsOdmQnzP+qKXqdl08kt7N4NJ0/C/v3w2v81ZdP2HmTEzycyovS0wVsmb6lpKqXj5FIhf8OztuNi7YuHTXFM9vOZseToC2jlZhknJzQhnmbX7M8an5ZFTn4hgT6l9zC9ctk0LuPnX/H+ponRSXgFqO0cb5TK6LF3Ax4B+gohjps/QyqhXMVdipuDDV+Mb8NXD7blUmouQ7/YxQ+7Lhb5oO92Gjbyw2iUhJ8vvVCrdbA/Z6MTyC3hjnGxtaO1ry9bLl60sO3v24LYvDSOpkaSnAxt28IvX4Vw5WwwXcevQGtdXIZOB8+8+hYGvST7yjSOH6u8xlIWHkZmvgs23cF+pMWxK7knick9QSv3kRb+/b9ijmCrsaJHrcZFaVHpaYSnptCjXqBFGUfCYgDTvbmW82disbO3pk7d8kU7LzuPuIuJBDarU66NwpLKmBWzW0oppJQtpZStzZ91lVE5xd3N0JamcMDdQ7x4f+1Zxn+/n8upudfP+C+naYsAhIBjhyNLHevUuC56o7FoBepVhjRoyKnEBM6WmDjQz7c53rYuzAvfSv/+cOkSFBQI1s55HI/aCQx/6XuLMi5E1WP8lNk0Co7ASTeSxCvHbuk6pDSaIj2mTgStP8Ltc0SJMMAFhmy2xM3EycqLFm7DitKT8zNZG3uUfr4tcLYunumz/MwZBHBPcAgl2RF6AQ9nBxrULj22dvxIFI2b1i4VmqEk5w+Z3moqCvOgsEStPFXcVmo52/HDhPZ8Mrolp2MzGTR7J4sPXvrXBhSTUpKbmUdKXFq5Nm7ujjRtEcD2LaUDW7VrGEAtNydWXxMbZUzT5jhYW/Plwf1FaXZaGx4M7Max9EgS3M6iM3t2wva2Y/vPo+j16J90GLHJopzNO7rTf8xCtMKAhxiPMfMDpD76Jq/RiCzYg0x9BJn1Mdj2QHgssYg3Y5QGNsV9TIYujkH+r2OtKd7Sb27YBgxGI0+G9C1Kyy4s5NfQ4wwIDrGIXJmWnceO0IsM7ti41Gyhy9EpREUm0a1nowrre3RLKBqthhY9GldopyhGCbvitiOEYGyHOmyY3oOWAW68uuIkjy84RELmvy8csL5QT8SxSDYv3FGhXf9BLbgUlUzYOcvBT61Gw33dmrPndBRhMcW9c1c7O55o05b1EeGciC/OM7ZeF0jwxXfqcmy8ihfgrJ45mbD9rRn/wUw6jV5vcY5d+zvQqu9fLFx6PzL3F2TyAIwpDyNzfkIWnkDK0vPFpTEdmb8NY9anyKR+yLTHQB+OcPkfwu1rhLbYFaIz5rPuyntczN5HL59p1HYo3hpwzZWjrI89zoSgXgQ4FOeZe2AfGQUFTG1vGcZ40dajGIxG7uvWnGvZsOY4Gq2ge++KBfvg+mM07dIQR1fHCu0UxShhV9wxAtwdWPRkJ96+tyn7LqYw8POdrD4Re/2MdxBrW2vsne3YvWJ/hXZ9+jfD1taKv1aUsYlEnzY429sye8Uui/RJ7Trg4+jIa1u3UKA3rdRNiLXi/Lvj0VjrCXlzERoHU2Nn1Fvxw7T3CNvXhvHvz+L+t+ZgY18c0zwr24npb73P+oPbTUG8jEnIrP8hU8cgE1pgTOiAMakvxsSeGBNaIxM7ItOfgpwfwaoewvUzRK1dCIfRFr7zlIJolkVP50L2HnrVeppW7sU+99C0S3x8ehXtPIJ4PLhPUfrJhAR+On6Mcc2a08q3eHFVSmYOS7Ydo3/bhgT5WfrQ8/N1bFx7gq49GuHlXf5sl7iLCVw4HkXXEaXj3ivKRwm74o6i0QgmdqvPuud6UN/LkecWH+Pp346SmlP+Zgt3Grdarpw/dIGLoeW7OByd7LhnWGs2rz9J/DVL3V0c7Zg0pBP7z0az40RxQCwnGxve7zuAs8lJvLNjGwAxMSBSvLnwyTgcguNo9MFPaJ1MAl6YZ8+8KR/y9/wxdB23hv+snEzLAbsAkxuroADCL/ginKai8d6I8N6FcJsLjtPAfhhYtwXbrmA/FuH0MsLjV0StI2g8FiDshyFE8QrZQkMu+5IWsDhqCtn6JO4NeI/WHvcVHT+aGsnzh3+ilp0L77caV7TvaVpeHtPW/kUtR0f+062HxX347I+d6AxGpg7rUur+rV15lIz0XEaNrViw18/fikYj6DW2dBmK8lHCrqgSgryd+GNKF16+pxGbTscz8POdbD2bcP2MdwAPHzesba3584uK5wA88EhXNFrB/G/+LnVsXJ/WhPh78uHiraRmFg8Y9wsKYmr7jiw5dZJ5Rw5xNaRKxoEmRHzwIA7BsTT5/Bvs6pruhdGgZfXMp/hq4kx0hTY8/sU7vLR8Cp1GrcfGIYcSIVkQWh+E3T1onJ9H4/J/aNxmonH9CI3LawinSQibjgiN5YKi9MIr7E36kR8vPMTBlF8JdurOQ/V/IMipc5HN6pjDPHf4J7ztXPim45N4msMg5Op0TFmzmqTcHL4acq9FyIStR8NZf+gcEwe2J9DXw+KcmRm5LF64hzbtA2nRui7lkZeTz/r5f9NxSFtq1fEq105RGiXsiirDSqvh6T4hrHq6O15ONjzx82H+88cJsvKrNhyw1lrLkCf7sXnhDuIiy29svGu58MDDXdm+5QyH9luGqrXWann/scFk5ubz6o/rLBZqvdClK8MaNuKj3bvYlXOkaNA0fV9Tzr/6OFYO+TSd8zW17t0HGlO+C4da8enIefz26stY2+oY/8Es3to2Focu73MqfR2pBZcsNsooD72xgCu5JzmU8htLo5/n54sTOJSyGH+H5oyr9yWDa7+Oo5VpTnlaYTZvnFjC+6dW0No9kHmdJlPLzjTAmqvTMWn1So7ExTJz4CALF0x0Qhpv/7KJ5oG+PDGodI983pdbyc7KZ8pzAyqs65pvNpGemMG4V0ZWaKcojaiK2Qnt27eXhw+X9k0qai4FegNztoTz7Y4L+Lna8+mYlnQNvvO9tAULFgAwbOBwJjZ4ls73tuONJS+Ua19YqGfqxB/IyS7gu4WTcHWz7BGv3neatxdu4t4uTfm/hwcWzQzRG408v34t6yPCEcfacfGXHmA09bOsPTKp/8JyXNuFkxNWm8s/DCbrZMmpfpLA1mfpPGoTvcftId9omsGjFda4WvvhbO2DjcYBa40dUhopNOZRYMwivTCWbH0yV105XrbBNHLpQyOXfhax3wuNev68fJDvI7aSoy/gieA+PBbcpygOTFxWFk+tWc2ZpERmDryHkY2Lg7kmZWTzxMylZOcVsOi1h/DzsIyCuWfHed5+dRkPPNKVJ6b2pTwyU7OY2OBZGnYI4aMNb5RrV9MQQhyRUra/rp0SdsW/iaOX0nhx6Qkik3OY2DWQVwY1xt6m/E2lK5urwj5x4kQWvr2UX95dxuc736V59ybl5ok4H89zk3+ibYf6vPPxWLRayxfhb9fsY97a/TzQuzUvjeldJO4Go5H3d27n5xPHKbxYh/ifB2HIuDqQKPHoFUqdJ9dj45VJZmh94pf3IONwAzBq0Whg3DhYtEiSXhhDbN4pUgsvkVEYR5Y+EZ0xH50xD43QYq2xw0bjiKu1H642/njbBuNv3xx7K8vt9DIKc1kbe5TfIneTWJBJe48gXmp6L0FOPkU2O6IieWnTRvL1OmYPGkq/oOIGJyUzh6lzlnMlJZPvpt9P80DLKJXxcelMe2w+vv5uzPluItbW5X+vXz3/I6u/2sC3x2dSv3n57pqahhJ2xV1LXqGBjzecY8HeKIK8HJk5thVt61a85LyyKCnseTn5PNlsBrb2Nnxz9BNs7UuH6r3K6uWHmTtrAyPHdGDa9IEWM02klHy+fCe/bj3K0E5NeOvhAVhbFYvab8dO8/qWv5EGDSmrepJ9oDlIU35ho8N70CH8xuzExisTXaoTKdtbkXe0KZt/qkvrFrfW6GXq8jiQHM7m+FB2J55HLw20cQ/kiZC+dPAILrqO9Pw8PtmzmyWnTtLQ05MvhwwjxKN4psulxHSe/fJPkjKymT11BB0bW4pxZmYe059aQFpqDnN/eJyAOpZ+95Kc3nueGT3eZNiUgTz31e2JP3+3ooRdcdezJyKZl5edID4zn6m9g3m+X0NsKlihWBmUFHaAI5tP8N973mfkM4N5+ovHK8z77ZzNLP/9ABMn9+ahid0tjkkpmb/+IF//tZfWwf589ORQi6BYfx9JZ8KvG7EOvELBJR9SV/cgP6IOYBZ4Kz2uHcLw6ncU147n0VgbcNTa0tK9Ho1c/Gjg7EcdB0+87Vxwt3FEc028F51RT1J+FokFGURmJxKeFcfp9BjOZ8ZiROJh48Q9fq0YWrsNDV2Kl/4X6PX8djKULw/uJ7OggCfatmNG567YWhWHFt5zKpI3FmwAYPa0EbQKsgwdkJNTwGszFhN+Po6PZj9IyzaW8WUsbDNymNbhvxh0BuaFzsLB2b5c25qIEnZFtSAzX8d7f51h2ZEYGvs68/m41jTxK717UWVxrbADfDNjASvmrOX1xdPpPa5buXmNRskn761i68ZTTJzUi4ce61HKZuOh87y7aDN21la8/ehAerQodmVEREiGvniW/La70bplkx/lR8bW9uSeCgapwdkZbGzgx9/ycG55gQMpEYSmXSIyJ7EovjuAQGCntcZWY4URSYFBR4HRcocrRytbGjn709ajPp28GtDMNaBoCiNARn4+i06GsuD4UZJzc+lapy6v9+hVFNAMoFCn59s1+1iw6TAhtb2YOfle6tay3D0qJ6eA115YzPkzsbz+3ih6VLAYSUrJu2NmsXfVIWb+/XbRJtaKYpSwK6oVm88k8OqKk2TkFTK9f0Oe6hmElbbye+9lCbtep+fFPm9z8XgUM7e/Q6P2weXmNxiMzPzgL7ZsOMnIMR2Y8uyAUnFQIuNTeeWHtURcSWZQ+0a8cH8vvMyrKqWE3ft1vPHbaaI8j6B1z8CY6YhzbBOm9m3CpJFeWFtbLs0vNOqJyk4kNi+dxPwMUgqyKDDqKTDo0AiBrdYaB60N3nau1LJ1oa6jF/727qU27SjQ69l9KZo/z51ly8ULFBoM9KxXj6fadaBzQB0L+yPhMXzw21ai4lO5r1tzXh7bBzsbyw1CkhIzefPl34m6mHRdUQf45d1lLHx7KZM/eYQxLw2v0LamooRdUe1IzSnkjZUnWXcynjZ13Zg1phVB3hXH8b5ZyhJ2gNT4NJ7r8joFeYXM2fM+/sGlt6+7isFg5Psvt7L89wO07xTEq+/ch4uLpUuhUKfnp42H+HHjIWyttEwY2IEH+7bB3rY4jrneaGTrxQssP3uG7VGR6I1G/Jyc6FkvkE4BdWjj60ddV9d/vKtSgV7PueQkjsbFsftSNPtjLpOn1+Nhb8/wRo0Z07S5RQ8d4FJiGl+v3sumI2H4e7rw6gN96da89HZ9p09e5t3XlpOfV8gb74+mQ+fyG0OADT/+zawnv2HgxN68NH/a7d0p6i5GCbuiWiKlZPWJWN5adZoCvYH/DmrMo10Cy9yq7p9QnrADRJ+NYUaPN7F3smPW9nfwDaxVyqYk61YdZe6sDbh7OvHft0aU6VuOik9l9opd7Dx5EQ9nBx7s24ZR3Vvg5mTZEKTk5rLl4gV2REex+1J00Z6irra2BLl7UN/dHT8nZ7wcHHCzs8POygobrRajhEKDnlydjpS8XJJzc7mckUFkehpR6ekUmlc41XV1pXdgfXoH1qdbnbpYay0HZcNikli09SjrDp7F2krLI/3bMXFgB4uGCEyN2rJF+/jp++34+Ljy7ifjCAyqeMe0rYt28cmEubTp3/L/2epxZCIAACAASURBVDvv8KiqrQ+/Z3oy6b2RkAqkkNB77yIIgoiin12v9SoWbNdrF6+9d0WwIKJSRZDeSyAkEBLSezLpk8n0cr4/Ilz0kmQSsMG8z5PHxOyz50yY+e09a6/1Wzy79mFk8rO0BnQBuITdxQWOpsXEou+y2H6yjuGx/rx0RSrhPud+0NaRsAMUZBTz4ISnUHu7s3jTv4iID+1wvpM5VTz/xA9UVzUxe95grr9l7OkGzmeSWVTFB+v2sz+nFJVcxtRBvZkxLJG02LD/2b3aHQ7yGhrI1FRzvLaW4qYmSpqbqNXrsXfyflZKpUR4eRPj60uMrx+pISGkhYQQ4vG/fi1Gs5WtRwtYvfc46XkVqBQyLh+Zwg1TBuHv9b+GXKXFdbz6wnpOHK9gzIRE7lt0CWoP1f+MO5Ofl+7g5RvfIWV0Is+uewSVe/uZRy5cwu7iIkAURZYfKufZdSeQCAJPzEhk7oCIc/oY35mwA+QdLuSRqc8hCPD0modJHJrQ4ZxGg4WP3tnC2h8OExjsxS13TGDsxMSz3mdBZT1fbc3gp/RcTBYb4f5ejO8Xz8jkaNLiwv5nJ30mDlGk2WSi2WTEbLNjttuQCAIKqRQ3mRx/d3fUcnmHfx+t3sTe7BJ2Hy9me1YhRrOVMH8v5o7uy+UjUvBS/69Q6/Vmvlqym++/OYCbu5I775vM+MnJHT6OKIosX7yKTx/7irTxyTy9ehFuZ5nbxa9xCbuLi4byRgP3f5vJweJGJvYJ5vnLkwny7J5IOCPsABV5VTx6yfM0VDXyz/duZfJ1Yzud+3hmGW+/upHCfA29k8K57ubRDBgcc1YBNJgsbM0s4McDuaTnlWOzO3BXyukbE0q/uHASI4OJjwgk0Fvd7YXMardTpmkiv7KerKJqMgoqya+sxyGK+Hq4MTY1lulD+pAWG37WUJfRaOHH1RksX7qH5mYDky/py813TMDXr2N7XZPBzBu3f8jmZTsZf/VIHvj0DuSKjptZu2jDJewuLiocDpFP9xTzn40nUSukPDc7hUtSOg6TnA1nhR2guU7Lc/Nf4+i2bKbfOonbX7uuwyImaItB/7whi88/2kF9nY743qHMv2Y4I0b3areLkN5k4UBuGQdzy8goqKSgqp5Tb1sPNyXh/l6E+nvh7+WOl7sKT3clCpkUuVSKQxSx2h2YLTZaDCaa9UbqmlupamihulGH1dYWY1cpZKREh9I/LpzhST1Jigpp99xC22xg3Q+H+X7FQVq0RtL6R3HznRPo1ed/W9/9loq8Kp658lWKs8r4vyfnseDxOa6D0i7gEnYXFyUFtToWrsgkq0LLZWlhPDUzCZ+zxLTboyvCDmC32fn0sa9Z8dJqIvuEs2jp3SQM6DgDBNo8Zjb/dIxvlu2lqrKJgEBPps/qz+RpfQkK8e7wWp3BRH5lPfmV9RRVN1Ld2EJ1QwuNOgMtBhP2dnrLquQyvD1UBHp7EOrvRbi/F7FhAcSHBxAd6tdxmMchcuJYOT+uyWD7lhNYLXYGD4vjqv8bTnJq5yX/oiiy9r1NfPTQMuQqOQ8vu4fB0/p1ep2LX+MSdhcXLVa7g/e2F/Lmlnz81ApenNuXcb06zmA5RVeF/RTpmzJ55aZ3adJomffgTK5+bI5TB4F2u4MDewtY8106hw+2NbtOTIlg7IREho6MJzSsa1YKoihiNFux2h1YbXYkgoBcJkEhl6HsYraJ3e4gJ7uSvTtPsn3LCeo0Lbi7K5g4rS8zZg/oNNvlFBX51bx150cc2XyMgVNSuf/j2wkIb795tYv2cQm7i4ue45VaFq44Sp6mlasG9+Cx6Yl4KDsWt+4KO4CuqZX37lvCz0t3ENIzkH+8ej3DLxvkdKihurKJ7VtOsO3nbIoLawGIig6g34BoktN6kJTSo8NuQ+eK3e6grKSe45nlHMss4/DBIlq0RqRSCQOHxDBuUhLDRibgrnYuc8XYauSbF1ez4qXVyFVybl58DZfeNskVejkHXMLuwgVgstp57ec8PtxVRISvGy/PTWVITPu7xXMR9lNk7TzBW3d+TEl2Ockje3PTCwtIHtG1RsyVFY0c2JPPgb0FZGeVYza3WQL4+qmJ6xVCdEwQEZF+hEf4ERDoSUCgF4pOFi1o29G36kzU1+moq22hoqyB8rIGCvM0FBVoTj+Of4AnaQOiGDYygQGDY/DowmG0zWpjw8db+OKZlTTWNDNhwShufela/EL+GCO3CxmXsLtwcQaHShq5f0Um5U0GbhwRzYNTeqE6i23s+RB2aIu9b/hkK8ueWkFjTTP9JqQwf9Es+k1I6fKO1Wazk3+yhpzjlRTk11BwsoaKsgasVvuvxrm5K/DwUOLmrkQmlyKTShABm9WO1WqjVWdG32r6n+s8PVX0jA0ivlcIcQkhJPftQUiYT5fv02Qw89OnW1n5ylo0pXUkj+zNLS9eQ+KwXl2ax0X7uITdhYvfoDfbWLwhl2X7S4kL8uDVean0jfi1adX5EvZTGPUm1r67ke9eW0djTTNx/aK57M6pjJ0/4pyKcex2B7U1WiorGqmv09FQp0PXYkKvN6HXW7Db7Kdj7DKZFLlcitpThVqtxMdXTWCQJwFBXkT08MPbx/2cwiOa0jrWvb+JDZ9sQVuvI3F4L65+9HIGT+vnCrucZ1zC7sJFO+zMq+OhlVnUtZq5c1wcd4+PQ/6Lodj5FvZTWMxWNi/dwQ9v/khJdjmevmrGzh/JxGtG0Wdowt9OAM1GM3tXp7P5ix2k/3QUgKEzBjJ34QyXK+PviEvYXbjoAK3RylNrsvk+o5KkMC9enZdGrxDP303YTyGKIsd25bD2/U3sXXUQi8lKWGwwI2cPYcTswfQaHIe0g7TDPxODzsihn46yZ9UBDqw7gkFnJDDCn4nXjubS2yYRFOlcloyL7vOHCrsgCFOBNwAp8LEoios7Gu8Sdhd/FX46XsNjPxxDZ7Jx/+QEFMW7EPj9hP1M9C0Gdq3cz45v93J063FsVjuevmrSxifTf2IqKaP7ENk7/E/bzVtMFnIPFpC5PZsjm7PI2Z+P3WbHO8CTYTMGMuGa0fQdk4hE8vs2P3HxX/4wYRcEQQrkAZOACuAQcJUoiifau8Yl7C7+StS3mnnsh2NszNYwz6uQmEA1/7jlpj/0Hlqb9RzckMGRn7M4sjmLuooGALwDPEkYGEtsWjSxqVFE9AojPD70vPqqiKJIc62WirxqynIqKMgopuBoCYUZxVgtNgRBIH5ADP0npDBwahrJI3ojlf01P1Vc6PyRwj4MeFIUxSm//PwIgCiKL7R3TXR0tPjvf//7nB7XhYvzTX2rmab6OgC8/AII9vrzTKnMRgt6rQG9Vo9RZ8JkMMMZb9X4/tG4nae2cdVFGurKG07/LJFKcPNQ4e7lhtrbHbWXO9IOGk+7+OO44YYbnBL282F8HA6Un/FzBTDkt4MEQbgVuBUgPDz8PDysi78bdpu97ctqx2azY7c5cNjs2O0OHKe+HA5Eh4jDISKKIohimy/KmRsQQUAQQBAEBImAIEiQSAUkEgkSqQSpTIpU9st/5dK21D+5DEknHZcCPJRYdTKMVjvF9Xqa9BZiAj1+9z6rZ0PppkDppsAvpC1rR3SImAxmLEYLZqMFhZvzNgmd4enngVwpb3tMdwUK1fmb28Wfw/nYsV8BTBFF8eZffr4WGCyK4t3tXeMKxVw4iKJIk6YZTWk9deX11Fc0UlfRQJOmmYbqJpo1WprrWmhp0OGwOzqcS66Uo3JXIFcpUChlyBSy04J8SpRFUTy9CFgtNmwWGxaTFbPBjElvpqPXs0Ilxy/EB79QXwIi/AmODCAoKpCw2BDC4kII6RnIF19+AYC09zieX5+DTCrw1MwkZvf782LdLlycwtlQzPnYsVcAPc74OQKoOg/z/n0QRdiyBcrKYPJkiIj4s+/ovOJwOKgrb6Ayv5qqQg2V+dVUFlRTVVBDdZEGi8n6q/EKlRy/UF/8Qn0Jjw8haXgvvAO98PL3xNPPAw8fNR6+ajx91ah91Ki93FB5qM45G0QUxdMhjNZmPa1NeloadGjrdbTUt9Bcq6Wxpm3BKcosYf/a9F/du1Qmpd8t8ajUCuIq0nkuKYwlNRYWrshkY3YNz81OIcDD1QjCxV+f8yHsh4B4QRCigUpgPnD1eZj378PDD8M777R9L5XCkSMQ27nD318NURSpK6+nMLOUoqxSSk+UU5pdQUVe1a8EUKGSExYbQnh8KAOnpBESHURIzyACe/gT2MMfT1+PP2V3KwgCKnclKncl/qGdl6+f+rRRVaihqqCG8pNVlFsKMOpMLHl5edsYQSBiTH9+djjYfaKGu9OCuGFmaqf2vC5c/Jmcr3THS4DXaUt3/FQUxec6Gn/BhWJUKjCb276XSOCxx+Dpp//4+1i9Gt54A5KS4MUXwd293aF2u53K/BoKjhRRkFFMYVYp+YeL0DW2nh4THBVIVFIEPXqF0+OXbIywuBACwv0u2BS3U3ns8+ZcScnxMgoySsg/XEj6iWqO9I7HHOyPd04RY01ahoxJZPAl/YhN7ekK07j4Q/gjQzGIovgj8OP5mOtviVr9X2FXKMD3TzA7ysqCq68GgwH27QOTCT766PSv9Vo92XvzyN6TS86BfE4eLMCgMwJtse2eSRGMnD2EuH7RxKb1JDolEvfzlHXxd8Td043EYb1+5XPSWN/Cc98c4Xsxmo0mM4c+2o768a8JCPdj6KUDGDNvOCmj+/xlC4xcXDy42oGfD778EubMAbsd+vaF22774+8hN7ctDARgMlG/P5Osr3ZxfHcu2XtPUnysDFEUkUglxKZGMWHBKBIGxZEwIIbIPuGuzvBO4BfgxSt3juX/yptZuOIohVdOYbSPjMjDx9m8bCfrPvgZvxAfJiwYxZQbxhGV2KPzSV24+B1wWQqcL4xG0GohOBj+hI/l+sJSMvtNJt3ozVGHP+WiBwBuHir6DEsgeXhvkkb2ps/Q+D+sabDRaKG52YC2xUhLixGdzohOZ0KvN2MwWjAYLJjNVsxmG1arHZu9LQXyzJekVCpBKhWQy2UoFFJUSjlu7grc3RR4eKrw8nTDy8sNHx93fH3V+Pq4IzuH4hlnLQVMVjsvbzzJJ3uKifRz5/kZfbBlFbH1690cWH8Eu81O4vBeXHbnVEbPHepaOF2cF1xeMRc4oiiSf6SIgz9mkL7pKDn783HYHagUUlL6RdBv7hjSxiUR0zfqd6kStFhs1NRoqapuoqZGi6a2hdraFuobdDQ0tNLYqMf0m2yZM5HJJLi7KVCq5CjkMhQKWVvuuVSC9Jdem6LYlpFjszmwWu1YrDbMJisGo+W0b/hvEQTw8/UgMMiT0BAfwsJ86RHhS2RkAFGR/rh1kv/dVa+Y/UUNPPBtJpXNRm4dHcN9ExMwNrX+soPfRFVBDUGRAcxfNIspN45HoXQ1bXbRfVzCfgFiMVvJ3HacfWvS2bc2nfrKRgASBsYyYFJf+k/sS+LwXudVPHQ6EyWldZSWNVD2y1d5eQM1Gu2vdtZyuZSAAE8CAzwJCPDEz0+Nr48aHx93vL3bdtVenm54eKrwUCtRKM5tB2u3O2htNdGiM6HVGmhuNtDUpKehoZW6eh21tS1UVTej0WhxnNEDNDzMl/j4YBISQklKDCMhPgTlGX+v7piAtZptPLc+h68PlpEQ7MGr89JIDvfG4XBw8McMvl78Ayf2niQoMoBr/z2PydeNuWAPn138vriE/QLBZDBz8Mcj7Ph2H4c2ZGBsNaFyVzJwahrDZgxk0LR++AZ13PzYGURRpK5Ox8m8avLyNRQUaCgqrqWuTnd6jFIpo0eEHz16+NMjwo+wMF/CwnwIDfHB11fdblf7PxObzU5VdTOlpfWUlNZTUKAhL78GjaYFaPvk0KdPGP3Sohg4IJpDBzcjCN0zAdt2spZFK7No1Fu4Z0I8t4+NRS6VIIoih3/O4vMnlpN7sIDEYQnc/c7NxKVFn+dn6+JCxyXsf2MsZivpG4+yY8Ve9q1Jx9hqwifImxGXDWLYZYPoNz75nMu+zWYruSerycmp4kROFTm5VTQ0tKU6SiQCPaMCiIkJIiYmiOiebWGMoCDvv6R4d4emJj05uVUcP15BxtFS8vJrEEUYkGbD08uNaVNn079/T6Sd2BD8lmaDhSdWZ7Mms4q+Ed68Oi+VuKC2PqUOh4Ofl+7g40Vf0NKg48pFs7juqStdhlounMYl7H8zRFEkL72QjUu2s335bnRNejz9PBg5ewhj548gdUziOQmAxWIj+0QlRzJKycwsI/dkFTZbW4l/eJgvvXuH0qdPGH16hRETE/ir8ER3novBYqVeZ6BJb0BrNKE1mGg1W9CbLRgsVsxWG2abHbvDgd3RdmB6yv9FLpWikEpRyWW4K+V4KJV4uSnxcXfDz8ONAE81fmo3pOcxnKHTmUg/XMyunT/S0mLkSKYMX181E8cnMv2SNCIj2++TejbWZ1Xz+Kpj6C12HprSixtHRJ9eFHVNrXxw/1I2LtlGyqg+PPrVPwkI79r8Li5OXML+N6GpVsuWL3ay8bNtlGSXo1DJGXn5ECYsGE3/iSndzqYQRZHikjoOpReTnl7MseMVWCw2JBKBhIQQUvtGkpIcQWKfcHx82i9kOhsOh0itrpXS+mbKGpqpamqhqrmFGq0OjbaVOp0ek/Xsh5sAEkFAKZehkEqRyyRIBQmC8MthqShiczgwW22YrDYc7bw+pRKBYC9Pwv286OHnTUygHzFBfiSEBBLi3f3K1yVLliCKIrFxw9myNZu9+wqw2x0MGhjNNQuGk5LsfApjrc7Eo98fY3NOLYOj/XjlilR6+P33b735i5288Y8PcfNUsXjjv4jpG9Wte3Zx8eAS9r8woiiSvSeXNe9tZNfK/disdnoPiWfK9eMYe+VwPHzU3ZrXZrOTlVXOnn357N2XfzqOHBUVwID+PenfL4rUvpGo1c6Xw9e1tJJbXU++pp686joKaxsprmvEeIZwSyUCId6ehHh7EuztQZCXB/4e7vh7uOOndsPb3Q1vNyUeKiVqpQKlTOqU8IqiiMlqQ2+20GI002Qw0qQ3UtvSSl2LnqrmFiqatJQ3aGloNZy+zk/tRmJ4MP2iwhjQM5zUyBAUMucWyN8enjY2trJ+QyarVh2mqdnAgP49ufGG0fTpHebUfKIo8u3hCp5eewJRFHn80kTmD+px+vmXZJfzyNRnMenNPLvuEZKGuxo/u2gfl7D/BbGYLGxbvofv31hPUWYpam93Jl83lktumUjPpO4Vs1gsNg6lF7NjZy77DxTQ2mpGqZQxoH9Phg2NZ9DAaIKCvJyaS2cyk1VWQ2Z5NcfKazhRpaFe91/BDPbyIDbYn9ggP6IDfYny96WHvzfBXp7IuhiLPt80G0wU1TaQW11HTlUtx8prKKhtQBTBTSFnWFwko3tFMzEpDl91+xW17WXFmExW1qw9wvIVB9BqDcy8tD833TQaDydrAiqaDDy0Mou9hQ2M7RXIi3P6nvZ715TWsWjyMzTXanlj73NE9bmwTORcnD9cwv4XoqVRx9r3NrHqrQ0012rpmdSDWXdPY/yCUd0qFnI4RI4dK+fnzcfZufskra1mvDxVDBsWz8gR8QzoH41K1XmMvNlgIr24goOF5RwuqeRkTd3pWHdMoB9J4cEkhgfRKzSQhJBAfNzPrbBJFEXMdhtWhx0HIg5RRCq0hWLkkra4+vlEazRxuLiSPfml7Mwtpqq5BalEYFhcFJcPTGJCYtz/LEidpTsaDGY++3wXP6w6jK+vmkceupT+/Xs6dT8Oh8iy/aW8sCEHpUzK05clMTM1DEEQ0JTWcdeQR3D3VPH2wcV4+nqcwzN3caHiEva/AI01TXz78lrWfbAJk97MoGn9mLtwBv3GJ3crBlyj0fLTT1n8tOkYtbUtuLkpGDkinvHjEhnQv2enFZc2u4PMsip255WyJ7+EE1W1bTtauYzUyFAGREfQPyqM5IhgPFTOhWsMNgsVei2V+maqDC1ojDpqja00mPU0mY00W4zorGZarWZM9vbj7gByiQR3mQJvuQofpRt+SndC3LwIcfekh9qHaE8/oj398VJ0fYERRZHc6jp+yspjfWYu1c06Qn08WTAsjXlD+qJWtmUZOZvHnnuymhdfWk95eQN33zWJy2b0d/peiupauf/bTDLKmpmeEsozs5LxUys4se8k941+gsnXjeX+j2/v8nN0ceHjEvY/keY6Lctf+IG172/CZrEx7uqRXPngZUSndP1wzG53cPBQEavXHOFQehEAAwdEM3lSMsOHxXdaSWm0WNmdV8KW7AJ2nixBazQhlQikRoYyLC6KobE9SI4IQdHJotBqNZPbXEuetpaT2joKWuop0TVSY9T9apxEEAhQqvFXueOnVOOjcMNTrkQtV+Auk6OSypFLpEgEAQEBURSxinYsdjtGuxW91UKL1USj2UCDSU+NUUej2fCrxwh19yLZN4T+AREMCYwkyTcUWRcyZOwOBztyi1m65wiHiirwcVdxz+ThzB2UwrKlSwHn8tgNBjPPPr+G/QcKuXr+MG6+aYzT92CzO/hgZxGvb87D203B4stTmJgYzEeLvmDFS6t5bdczJI/o7fR8Li4OXML+J6BvMfDdq+tY+epazAYzE64dzYLH5hAeF9rluVr1JjZsyOKH1YepqdHi7+/B9GmpTJ3al5DgjguSLDYbO0+W8GNmLjtzizFabXi7qRjTO5qxfWIYFheJl1v7u16bw0FOs4aMhgqONlRxrLGaYl3D6ZabHnIl8V4B9PT0I9rTj0gPXyLcfQh19yRA5dElkXUGs91Gub6ZEl0jhS31nGjWcKyxmtLWptP3MzokholhCYwPi8OzCzv6rPIaXv1pF4eKKkiJCGGMvBU3hdzpAiW73cEbb21i3fqj3Hn7BOZcPqhLzy2nuoX7vjlKbo2OKwZEsGhiHLf3vodeg+N4du0jXZrLxYWPS9j/QOw2Oxs+2crnTyynua6FUXOHcv3T84ns3fXero1NelauPMiadRkYDBb6pvRg9qwBjBge32mo5USlhpWHjrMh6yQtRjP+Hu5MTIpjcko8A3tGtHvAKYoiedo6dtUUsa+2hPS6clptFgACVWpS/cNJ9g0hyTeE3j7BhLp5/iX8x+uMrRysK2N3TRFbqwuoN+lxk8qZGZXEtXED6eMb7NQ8oiiyPvMkL6zdRn97IzGBftx3p/OhELvdwVPPrGLP3jxefflqUvtGdul5WGwO3tiSx3vbCwn1dmOyoYndzy5naeHbhEY79xxcXBy4hP0PInNHNu/c8ynFx8pIHtmbf7xyHb0GxXV5nsbGVr5avp/1Px7FarUzZnRv5s0dTK9eHe/2DRYr647msOLAMXKqalHKpExMimdm/z4MjY1sV8xNNit7NMVsrspne1UBtaa2qtNYT3+GBEUxOCiSAf4RhLp7OS3ioihichjQWRsx2HUYbK2YHQasDjM20Xq6H6kgCMgFJXKJAjepJ2qZF54yHzzlfkiE7u32HaLI0YZKvi06ypqybEx2G2NDY1mYMpYk3xCn5qjT6Xn5rXdoNVsYNW0G84emOv34RqOFm279BLlcykfv39gtL5wjZU08sCKTono93odP8Oj0RK68d3qX53Fx4eIS9t8ZbX0LHzy4lJ8/30FwVCC3vnQto+YM7fJOtrXVxDcrDvDdD+lYLDYmTUxmwVXDiIjw6/C62pZWlu3JYOXBY7SYzPQKDeSKQSlMT+vVbpjFYrezs6aQ9WUn2FKVj95mOR3GGBMSy4iQaELdO0+NbLU1ozGWUWuuoM5cQaNFQ5NZg9Zaj1W0dOn5n4lUkOErDyJQFUGoqidhbjFEqfvgLvPs0jxai5EvC47w6ckDaK0mbuk1lHuTxziVdfPpZ59RWNvAqmYp7103i9G9nfdz2X+gkEcf/5YHFk7jkmnOLwpnYrTYefGnXJbsLcHLYmbJvePoH/knNG5x8ZfEJey/I9u/2cNbd32CXmvgigdmsuDxOajcu9YD0253sGZtBp8v3UWLzsT4cYnccN0owsM7fhNXNGr5cPtBVh85gcMhMjEpjmtH9KNfVFi7i8rJ5lqWF2WwtjSbJosRH4UbkyN6cUmPPgwJjOpQ8KwOC5XGAkr0JyjTn6TKWITO1nT690qJO/7KEPwUwfjIA/GU++Ep80Ut88JN6oFK6o5cokQmyE/vxh2iA6towWI3YbS3ordpabE10WTR0GipQWMqp8FchYiIgECwKpI+XoPp7zceP4XzoYkWi4nFmVv4pugoyb4hfDRqHkFuHS8SS5YswSGKrNfJqWpu4ft7riXUx7mFRRRFbr71U+RyKe+/e73T93k2bp7/FruDw7C4q/jHmFj+OTEepctT5qLnD22Nd7HQ0qjjrbs+YfvyPfQeEs/Cj/5BdHLX4qkAx49X8PpbGykqqqNfWhT/uG0c8XEdhwtqW1p5f+sBvks/jkQQmDsohetH9aeHn89Zx1sddjZVnGRZQTqH6spRSKRMCu/F7J4pjAyJRi45u0iIokituZy8liMUtGZSos/B9ssuPEjZgzjPVEJV0YSooghUReAp8+1+vL2DVHuLw0SloZBifTZFrcfZXruSbbXfEuvRl9GBs4n16Nvp43opVDw/aDpjQ+N44MAartn2JV+PvxZ/VceVvRJB4LUFlzLztaV8uO0A/5490amnIwgCkyYm8eHH22luNnTZquFMertLaVm3jajFt/Du9kK25tby6rw0EsOcKzZzcXHjEnYnOb4nl+fmv0aTRsv1z8xn/qJZXTblMhjMfPDRdtauyyAo0Isnn5jFqJG9OhQok9XGpzsO8cnOdGx2B3MGJXPbuCEEe5+9gMVst/Ft0VE+yN1HlaGFSLUPD6dOYG50X3yV7QuNxlTK0aadHNfupdGiAdqEfLD/ZGLUyd0KiZwLComKaI8koj2SGB88j2ZLPUeatnKwYROfrdNyegAAIABJREFUFT9FjEcKcyLuwkcR2OlckyN68bHiSq7f+TV37/2eL8dd0+miEOnvw6wBifxw+AT/nDLS6eKsU1YDefk1DB4U49Q1Z8MhOpDb7bx0RSpTkkJ4+PtjXPbObu6dmMBto2P+9EpfF39tXMLeCaIo8v3r6/lo0RcERwXw5r7nSBgQ2+V5MrPK+M9L66nRaLliziCuv25Upzno23IKeWHtdiqbWpiaksC9U0d0uENfUXSUd07sRmNspb9/BE/2n8K4sHgk7YiY0dZKRvMODjduocZUggQJsZ6pjAqcTS/P/ngrArr8PH8vfBQBjA+ex+jA2aQ3bmZTzRe8m/8gV0U9SLRHUqfXDw6K5PG0ifzr8E/8XJnH5IjOPVlmpPXm24PHyCitZFwf5/7Nff3aPg3ofmkU3l3qyhvwD2sLy01MDObnKF8eX32clzaeZHOOhleuSCUm0FWd6uLsuIS9A6wWK6/d9gE/f76DEbMG8eBnd6L27ppBl8Mh8tXX+/js852EhPjw+qsLOnUI1BpNPL9mG+uO5hIX7M9nt8xlcEz71+zRFPPU4Y0U6hoYEBDBy0MuY1hQVLu70mZLHbvrVpPeuAWraCbcLZZLw24mxWc4HrKzLxwdIYoiOOrAXg2ORhCbQLSAaAVBAoJH25c0FKRRCJLumZwByCRyhgZMI84zlWUlL7Ck+BnujH+ZIFXn/irzYvrxad5BPj653ylhT4poC4/lVNU5LeziL92azuXoShRFSo6XM2ha2un/56tW8M7V/ZmSVMW/Vh3nkjd38fDU3vzfsJ4XjEe+i/OHS9jbobVZz1NzXuLotmz+79/zuOaJuV3PeNGbeH7xWvbvL2T8uETuv29qp7v0Q0UVPLxiA3U6PXdOGMot4wYjb+dws96k55mMTawrO0Gkhy8fjryC8WHxHQh6PVs135DRtB2AVN/RDA+4lDA35zM/RFEEWz5Y9iNaj4MtF+ylIDq/QxUl4aAYiKAcA6opCELXvd8DlGHcHPM0b+bdy8ryN7gtbjFSoePQmEwiYXxYPMvy07HY7Z1myZw6rHQ4HE7fV1V1MwAhId3valV4tITmWi1pY5P/53czU8MYEu3Hou+yeHLtCTad0PCfuX2J8O1+PN/FhYdL2M9Cc52WR6Y+R8nxMhYtvZuJ14zu8hz19ToefmwFpaUN3H3nJGZd1r/DhUEURb7al8mL67fTw8+Hr26fT3JE+weqe2qKWXhgNS0WE/9MGsVtfYajlJ79n9PmsLK3fh3bar/FIToY7D+ZUYGznIpPt92bA6wZiKYNYN4K9oq2X0iCQNYbFEMRpJEgDQOJP0h8QVCCIAfRDqIexBawVYC9FNGaA5bdiKbVoE8Ar6cQFAOcupcz8ZT7MiX0Wn6oeJdKQwGR6s534T09fLE47DSY9Z2mdjbp2xYrZ31zALKzK9s6UPXsfhhr61e7kEglDJrW76y/D/ZS8dn1g/jmUDnPrDvB1Nd38cSMRK4YEPGXKBxz8efjEvbf0Fyn5YFxT1JdpOHp1YsYNPXsb66OqKxs4v6HvkanM/HCc1cwcEDHO2K7w8Fza7bxzYEsxvaJ4cV5U9sVE1EUeSt7F29m7yLOK4ClY66ml09Qu3NrTKUsL32VWnM5vb0GcWnYTfgq2h//68cygeELRP0X4KgClKAcjqC+FZRjEKTOWiX8soDI+wIg8MtiYf4ZseV5xMarENV3IvH8p5Pz/ZdYj7Y5q03FTgl7s8UEgK+ifeveU2SUVgGQ0sO5AieHQ2T7zhz6pUU5bef7W8xGM5s+386IWYM67GUrCALzB0cyIi6AB77N5KGVWWzKruH5y1MI8jw3F04Xf3/OSdgFQXgJmAFYgELgBlEUm8/Hjf0ZGHRGHpv+AtVFGp7/8TFSx3Z+KPdbajRa7n/oa0wmK6+9cjUJ8R2Lgt3h4PGVm1iTkcONowdy35SR7cZMbQ4H/zq8gRVFR5ndM4VnBkzDTdZ+GONY8x6+r3gHhUTFNT0foY+Xcz4momgH4/eIrW+CQwOK4Qhu94FyAoLk/BzYCYIEVFNAMRJR+zDo30N0vwpB6tyic3oeurZD3V9bSqSHL6oO/m6nWH3kBD7uKlIinMud37c/n6qqZq67dmSX7ulM1ryzEW29jsvumubU+B5+7nx9y1A+3VPMfzaeZMprO3l2VgrT+3bdn8jFhcO55kz9DCSLotgXyAP+tq5FdrudZ+a9QkFGMf9acX+3RF2nM/HgQ8sxGMy89OKVnYq6KIo8s3orazJyuGviMO6fNqpdURdFkUUH17Ki6Ch3JI7gpcEzOhT1ffU/srzsFUJUUdwZ/7Lzou5oRWy6AbHlMZCGIvh9icRvCYLbZedN1M9EkKgRPO4AHG1hni5SrM8GIFTV+TlBWWsT+2pLmBGZ2OnYwtoGtuUUccXgFKe6L9ntDj5fupvQUB/Gj+t8/rPRpGnm6xe+Z9DUNFLHOP/6k0gEbh4Vw4/3jCTSz507vzrC3V9n0GzofhWwi7835yTsoihuEkXxlMn2fuBv2/pl2ZPfkr4xk3veuZmhl3Y93mu3O3j2+dVoarU8/8wVnRYcAXy59yjfHjzGLWMHcfuEoR2OfSt7F6tKj3Nv8mjuTxnbYSz1uHYf66s+obfXIG6KeRovecf2BKcQ7Q2IjdeAJR3B63kEv28QFF1zK+wWtsK2/0qdP8SFtrODrZoVBCl7EO7euT/PMxmbcJPKuTq2c+/0p1dtwUOl4NoRzvmsf/vdIQoKa7nlprFIu5FjLooir//jQ0wGC7e9/H9dvh4gLsiT724fzsJJCWw4Vs3k13ayLbe2W3O5+HtzPqscbgQ2tPdLQRBuFQQhXRCE9Lq6uvP4sOdO1s4TfPX890y+vq1NXXdY8e1BDqUXc8/dk0lO7nx9y62u4z8/7mBCYiz3TBrR4dj0unLeyN7F5T37cldixx/zW6yNfFf+Fj3cE5gfuRCZxPmME1H3AtgKEHzfQ3DvehZQdxBtBYi6xSCNgC4sIqIosq7qYxotNVwSdn2nGTHL8tPZWlXA3UmjCOnk0LS6WUd6cSUPTBuNv0fn2SY5OVV8tmQnI4bHM2Z093qWrvvgZ/auPsQNz8wnKrF7bRIBZFIJ90yIZ9WdI/Bxl3PDkkM88n0WreaOm5y4uLDoVNgFQdgsCMLxs3xddsaYxwAb8GV784ii+KEoigNFURwYGOhcNsYfgbHVyEs3vENoTBB3vXljt8SsoqKRJUt3MWpkApdektbpeIdD5KkfNuPj7sbTcyZ3mIdsdzh44vBPhLp78dSAKZ3e3+aar7GLNub2+CdyifPZHKKjFUwbwe3ytjTEPwDRvBex4WpARPB5ty3u7sx1osgWzXIONf7MmKA5xHt2fMC9tSqfpzM2MT4sjhsTBnc4tklvpKJJy6Vpvbl8YOfhkPp6HU889T0B/h48cP8l3Xr95BzI5717P2PQ1DTmLLy0y9efjeRwb9bePZLbxsSw/FA5U1/fyf6ihvMyt4u/Pp0GD0VR7HALKwjCdcClwATxz3AUO0dWvrqOmuJaXtn+FG4enWdKnI0lS3cjk0m5567JTo3fnVdCVnkNz86d3Gmp+t7aEk5qa3lt6GW4yzrOgXeIdrKad9HPdxz+SucyOX6NHYTfP1FKtJ5EbH0FzNvbCpZ8P0GQOee5Y3GY+KH8XbK0u+nvO55JwVd3OH5NaTYPHVxDH59gXh86G2kHTUA2ZxdQWNuAh1LB05dP6lSkm5r0PLhoOXq9mcWvX4O3V9dfP2W5lfxrxgv4h/vx8LJ7kJzHJiVKmZRHpvVhUp9g7v82k6s+2s+NI6J5cEovVHKXodiFzDm9igRBmAosAmaKomjobPxfjZZGHStfWcuI2YPpO7p7B16VVU1s35HDzBn98Pd37nDxq31HCfRUMz2189Zn68qy8ZArmRLR+dh6czVW0UJPdddbqgkSj7acdNM2RGt+l6/vDFE0IZo24Gi6A7FhJliOIHg8gBCw1mlRrzDk837BwxzT7mFyyAIuj7izXfG1Oxy8nb2b+/avop9/BF+OXYBa3v7CuPrICe7/aj1qpYKEkACU8o4XuIaGVh5ctJwajZYXnr2C2NiuN8SoLtLw8JRnkEglLN74OF7+v48Xz8Cefmz45yiuGRLFJ7uLmf7mLjLL/7bJay6c4Fy3Z28DSuDnX95g+0VR/Mc539UfxOalOzHojFz7xBXdnmPr1hOIosjls5w7cLXY7BwoKmf+kNRO+4wCFGjrSfULa7f46ExOxZltju7FUwXPhxCb70FsuAxRfSOC+mYESdctBuCUzYAGzLsRzVvBshdEA0gCQX1Ll+Y22HRsqvmC9MbNeMh8uC768Q7DL7VGHfcfWMNeTQkzI5NYPPjS9ou37A5e/WkXn+8+wpDYHiRIWjrc1QOUlTWw6NFv0GqNPPv0XFJTu+7wWZZbyUMTn8JisvKfzU90q31iV3BXyHhmVjKTk4J5aGUWl7+3lzvHxnLX+HgUMpeh2IXGOQm7KIpdbxX0F2LDJ1voMzSe2NSe3Z5jz958khIjCAx0zk61QFOPxWYnLcq5N7LWanKq+QWAryIYf0UoGU3bGOQ/yalrzkRQDoXAnxB1/wH9h4j6jxFliaBIRZD2BGkkSHxA4kmb5661zQ/GoW3ziHHUINrLwFbaZjXg+CWmKwkF1SwE1RRQDEbo5KDzFHpbC3vr17G//kcsDhPDAy5lfPCVqKRnP9B0iCLLCzN4+dg2zHYbiwdNZ250aru7+somLY9+u5H04koWDEvjwemj+XLZsg7v6cDBQp5fvBaZVMLrrywgIaHrIa/svSf596wXkUglvLL9qW5ZP3eXUfGB/HTvaJ5am82bWwvY8osdcK+QP86508Xvz0VbeVpdpKEku5zbX7u+23PY7Q6KS+qY7eRuHUBvtgLg7aQNbA+1D0W6RqfGSgQJqT6j2Fq7gmztfpK8O06hPBuCxA/BezGi+/WIpo1gOQjGNYiizskJvNoWAOVYBFmftkwXWe8uHSrWm6vYX7+B9MbNWEUzSV5DGR98JSFuUe1ek1FfydMZG8lqrGZIUBTPDphGjJf/WceKosgPh7NZvG4HAM9fMYXL+nccirPbHSxdtptlX+4lNiaIp568nLDQrn+a2f7NHv5z/TsE9vDnufWPEhH/xxcSebvJeXVeGlOSQnj0+2PMeGs3CycncMuoGKQuQ7ELgotW2LN2ngBgwOTutTADaG42YLXaCQ1x/g1+ykfbaLE6NX5AQA9eP76DgpZ64rw69x8ZEzSHXF06K8peY1bE7fTzHev0vZ2JIO+NIG+L1Yui2ObYaCsHUQuOVtqKjWVtfjCCN0j8QBqIIOleGzejXc/x5r0cbd5Bif4EUkFGX5+RjA6cTZCq/fS/443VvJm9iy1V+QSq1LwyZCaXRSW3u5Dk1dTz/JptHCquYFB0BM9dMZlw344Nu8orGnnxpfWcOFHJtKl9ueeuSSiVXTMus1ltfPLIV6x8dS3JI3vz1A8PnZ+YutUKu3dDv37g07WFZkpSCAOifHnsh2Ms3pDL5hMaXr4ilZ4B3XffdPHX4KIV9oqTVcjk0nPaMQmndjdd2OQkhAQgEQQOFVU4ZQV7dVx/Psrdx2OHfmT5+Gs73fnKJHKuj36Cr0tfZmX5mxToMpkYcpXT/jBnQxAEEPxA4Vyhk7O0WBvJ02WQ23KIPN0R7KKNAGU4k0MW0M93XLuFVaIocrCujI9y97OtugBPuZKFKWO4Ln4QHvKzp3g2tBr4YOsBlh/IxEOp5N+zJjB3UErHqaZ2B9//kM6nS3aiUMh47JGZTBjf9UP22rI6XrjmTY7vzmXmHVO47ZXrUHRxYWiX22+HL7+E2Fg4frzLlwd4KHn/mgGsOlrJE6uzmfbGLh69pDfXDG3f9tnFX5+LVtgbNc34hvh0uQvSmXiolUgkAvX1rU5fo1YqGNWrJz9l5bFw6qhOO+H4Kd15NG0ij6b/yCvHtndadQqglnlxQ8wTbNWsYFfdKrKad5HsPZwBfhOI8Ug53Xv0j8Zg01Gqz6FYn01BayYaUxkA3vIAhvhPIdVnDOFuse0+v1armTWlx1lWcJg8bR2+CjcWpozh/+IG4qk4e2hLazSxZNdhlu3JwGy1ccXgFO6ZNBwfdcepiVnHynnz7U0UFdUxdGgsC/85lYCAru2wRVFk8xc7eeeeT3HYHTz61b2Mm99xMdqvqKwEQYCwsPbHtP7y2tPru3RvZyIIArP7RTA0xp+HVmbxr9XZbDqh4cU5fQnz6V4KsIs/l4tW2EWHeM45wwqFjPi4YNIPF3PTDc5b+84dlMLdy9bwXfoxrhzSeShoXkwaWY3VvJezl1arhUfSJnSaJSMVZEwKuZrB/lPYU7eGw01bydLuxlseQJxHKtEeiUS698ZXEXzehd4hOtBa66kzV6AxllFtKqbKWESduRIAmSAnSt2H1JDRJHj2I0TVs8O0xQN1ZawqOcaGihwMNitJPsG8MGg6MyKT2vXLqdPp+XJvBsv3Z6EzmZnWN4E7JgwjJqjjTx0Wi43qGi1Lv/zS6faFZ6O+qpG37/qYPasOkTyyNw8tuYvQmC6kRL78Mjz+eNv3ixfDvfeefdzHH8PMmTC669bSvyXU242lNw7mywNlPLc+hymv7+TJGUlc3j/ctXv/myH8GTVFAwcOFNPT0//wxz2T9+//nHXvb2KNbtk5CfyyL/fw+dLdfLH0H4QEO9dcQRRFbv7kOzJKq/jy9vn0Ces8TOIQRZ4/upnP8g7S2zuIFwZPp69fBzu532B1WMhpOUhW825K9Ccw2tt2egqJihBVFP7KUHzlQXjJ/VHLvFHLPFFK3JBLlEjOyGKxOSxYRQtmuxGjvRWDXYfO2ozO1kizpZ4mi4Ymiwar+F8DKm95AKGqnvRQJ9BTnUi4WxxySfs55TaHg/T6cn4qz2FDRS71Jj0eMgWX9OjDFTFp9PNvX2hOVtfxxd4M1h3NxWq3MzEpjn+MH0rv0I6rnRub9Hzx5R5Kig8AkJwyhquuHNppY5TfYrfbWfvuJj57/GtsVhvXPXUlcxZeirSTph7/g48PaLVt3/v5QcMfWzVa2qDn/hWZpJc2MTkxmOcvTyHAw/lKZhe/D4IgHBZFcWCn4y5WYV/7/ibevOMjlha83bWd1G/Q1GpZcO37zJjej3/e41zlKbTFfOe+9QUCAh/eeDlxwWfP4Pgt26ryefTQj9SZWpnWow+39R5Gsl/XzgkcogONqZRKYyHVxmI0pjIaLRparA2IdO/14Cb1wFvuj68iGD9FMAHKMAKVEQSpeqCWdZ6uqTHq2F1TzK6aInbWFKK1mFBJZYwLjeOSyETGhca1uzs3WKxsPJbHykPHOFpajZtcxsz+iVw3sj9RAR0f5tbX6/jm2wOsW38Uq9XO2FFygoO9ueWWm7r8N8jckc37Cz+nIKOY/pP6cs87N3c/Pz01FbKz//v94cPdm+ccsDtEPtldxMsb8/BUyXhudgpTk7tT0ezifOES9k4oP1nJjX3u5e63b2bmHVPOaa633vmZVasP89br15KYGO70dXk19dzy6XeYrXZevXo6w+PbT+c7kxaLiY9O7mdpfjqtVjP9/MOZH9uPiWEJ+Ci7HxO1OazobE3obS0Y7C1YHRasDjN28b8FTzJBgVyiQCFR4S7zxE3qgYfMp8Md+G8RRZFKg5aMhkoO1ZZxoK6MgpZ6APyVasaExjIhLJ5RITHtVos6HCLpJRWsy8jlp2N56M0WogN9mTsohdkDk/B26zidtLyikW9XHmTjpmPY7Q4mTUhiwdXD2bx5DQDXX3+908+nsqCajxZ9wZ4fDhIY4c8t/7mWsVcOP7fwRUUFLFoEEgm8+GLHcfbfmTyNjoUrjnK8soXZ/cJ5cmYS3m7n6fDXRZdwCXsniKLIHQMXYbfZ+eDoy+f0JjQYzNx48yc4RJG337iWoCDnCooAqppauP3zVRRoGpg/NJV7p4zA08lWbDqLie9KjvFlwWGKdA1IBYGBgZGMCYlhcGAUyX4hyCV/rieIQxSp0DdzUlvLiSYN2U01ZDVWUWdqO+xTyxQMDOzB0KAoRgXH0MsnCEkH8fajZdVsOpbPz8fz0bS04q6QMyk5njmDkukfFdbhv6PDIXIovYjVa46w/0AhcrmUKZNTmH/l0NM56UuWLAGcE/b6qka+eHolP326FblSxvxFs5mz8FJU7hdeyMJqd/D21gLe3lZAoIeS/8zty+iEv46Z38WCS9idYM27G3nrro95ZftT3faKOUVhoYZ7F35FQKAnLy2+sksZFEaLldc37uHLfRn4qd25a+IwZg1IcspyANoWqczGKrZU5bOlMp+T2jYPbjepnETfYBJ9QkjwDiDK04+eHn4Eu3kiO49mUyabFY2plWpDCxX6Zir0zZTomijSNVCsa8Bga8vZlwgCsZ7+JPmG0M8/nDT/cHr7BHd4L60mM/sLy9mRW8SO3GIaWg0oZFJGJvRkakoC4xJjcVd0vHtsbNKzceMx1m84SlVVM76+amZMT2PmzP74+f46Z9sZYW+obuLbl1az9v1NOOwOLrllIgsen4NfSPdy+P9OZFU0s3BFJgW1rVwzNJJHpvVBrbxoczD+cFzC7gQmg5nrE+7GO8CLdw4tRtaJ8VNnZBwt5bF/rcTDQ8WzT8/ptIPSb8mu1PD82m0cLa0mwNOdq4amMW9wCn5OeIKfSb2plYN15aTXlXOssZqT2lr0tv8eZkoEgUCVmgCVB74KN3yUbqhlCtQyBUqpDJlEgvSXTBmHKGJ12DHZbZjsVvRWCzqrGa3FRKPZQKPZQIvV9KvHF4BwtTfRnv7EePrTyzuQBO8gevkEdupQabXbOVZew8GiCvYXlJFRWoXN4cBTpWRkQk/GJ8Yypnc0amXH81gsNg4cLOTnzdns21+A3e4gJSWCy2b0Z9TIXsjbcTfsSNirizWsfGUtGz7Zit1mZ8KCUVz77ysIje7+Gc3fEZPVzssbT/LJnmIi/dx5+YpUBvU8vzUOLs6OS9idZM+qgzx5+UsseGwO1z8z/5znKyzU8Ni/vkPbYuCWm8dy2Yz+XeqoI4oie/PLWLrnCLvzSpBLpYzpHc20vgmM6tW5oJ0NhyhSY9RRqmuktLWJGmML1YYWGkwGmswGmixGDDYLBpsVs92GTXT86nqZIEEllaGQyvCQK/GUK/GSq/BTuuOndCPIzZMgNw9C3byI8PAh1M0LhZNZIC1GE8crNBwtreJwSSWZZdUYrW0x/d6hgYxM6MmIhCj6RYUh72ROu91BZlYZ27bnsHPXSXQ6E76+aiZOSGL6tFQiIzs/oD6bsOccyOf7N9azc8VeJFIJE68dw1WPzCYs9uI+SDxQ1MADKzOpaDJy66gY7puU4LID/p1xCXsXePnGd9m4ZFvXC0jaobFJz+IX15F+uJg+vcNYeN9UYmO6XvlZWNvAigPH+OnYSep1BuRSKYNiIhiV0JMhsT2IC/bv1ImwO4iiiEMUkQjCec1fbmw1kFdTT251HTlVtZyorKWors0HRxCgV0gg/XuGMygmgkHREfh2UkQEbTvzIxml7Nmbx969+TQ1G3BzUzBieDwTJyQxoH/PLi2sp4R9wdUL2PXdAVa99SM5+/Nx93Jj+i0Tufze6QSEO5fBdDHQarbx3Pocvj5YRkKwB6/OSyM53Lm0XxddxyXsXcBitvLw5GfI2Z/Ho1/dy6g5XTfP+i2iKLJl6wneeW8zOp2J8eMSuWbBcCJ7dF0U7A4Hh0sq2Z5TxK6TJafF0FOlJDkimMTwIPqEBREb5E/PAB+nmi//XpitNqqaWyhv0FLW0ExJfROFtY0U1jbQ0Ppfy/4Qbw96hwWREhFC3x4hJEcE49VJJssp6ut1pB8uZt/+Ag6lF2MyWXF3VzBkcCyjRvZi6JBYVKruZW18+P6HNFY3c/iDPJprtYTFhTD77kuYfP1Y3D1dVZjtse1kLYtWZtGot3D3+HjuGBeLvBu9X110jEvYu4iuqZXHZywmd38e97x7C9Nv7brt7dnQthj55pv9rFpzBIvFxuhRvZg9awDJSRHd3g1XNbeQXlRBRmkVxys05GnqsdnbwicSQSDMx5NwP28ifL0J8lIT5OWBn4c7vu4qvN1VqJVK1Eo5bgo5Momk3ftwOETMNhtGixW9xUKryULL/7d35/FR13cex1/fTDLJ5L4vcpCTI4QAAQQRPEBA8V6x0m211vVqy4Kra23p8ajbdu2qFWu1q21R69FWvFAriFaQW0AgCUkIRyD3TSbXTDKZyXf/SGRFgRyTZJLJ5/l45KFJJvP7fB/MvH/f+R2fr7UDs8WK2WKlocVCQ5uVuuZWappbqW5qob7l7PVW/L2NJEeGkhwZSlpUOBNiwkmPjujTWqJfsFg6yM0r48DBEg4cOEXxye41c8PDA7h4bipz56QyfVoiRuPAdmjWtnZ2vPUZH76wha7E7vr9Tody3X1LyF6cNairGrkzs8XGz9/NZ8OhSqbGBfHE8izSoqQd8GCSYB8Aa1s7/7X8CfZtOsTSOy7n+0/fOWiXrjU2trH+jb28949DtLV1kJgQxqKFGSy8YjLR/egOeS42u4MTtQ0U156muO40pQ1mKk43U2FuoqHVwoX+iZUCL4MBw5cOuzi6unBofWZncSFBJp8zO4/ooABiggOIDQkkISyYhLBgQv1M/d6BNTa2UVBYSX5+OTm5ZRQdraKrS+PlZWBKRhyzZiYxa2YSycmRA945OhwOcrYWsOW17Wx7Yw+WFisxyVFkfDuR0Ohg7rrnrgE9r4AP8qpY83YebTYHDy2ZwHfnJV2w2ZroOwn2AXLYHbz8i/W89uu3SMyI48E/f48JswZvPRGr1caWrYVs+jCPw/nlAEycGMPFc9KYc1EKycmRg/omsDu6aGi1cLrN0jPTbqeto3v23d5px2Z3YHPYQXefZNUaDAaFQXng7WnhZe1QAAARdklEQVTA6OWJycsTP28jft5Ggnx9CDL5EOJnIsTP1OsJzd5YrTZOFNdSVFRF4ZEqCo9UUlXVvWybp6cHkybGMjUznunTEsnIGNfvdrlf1tXVRcGuIrb+fRfb3thNY00TPn7eXLr8YhZ/5zIy50/ipZdeAvp3g5L4utqWdn78Vh4fF9YyOymUx2/OIiGsf1d3ia+TYHfS/s05PHbHMzRWm1l29yLu+NUKAkMH92NldbWZT7YWsn3HUYqKqgAICjIxLSuRzMw4MiaNIyUlEk8nOlCOFA5HF1VVZkpKGygpqedEcS3FxbWUlZ+mq6v7NRgREcDECTFMmjSOjMmxpKdFOxXkAJ22TnI/LWD3u/vZtWEfdeUNGH28uGjZDC77xjxmXz3jrE9l/blBSVyY1po3Pi/nkfcKcGjNT5ZNZsXseGko5gQJ9kHQ1mzhLz9/nXd+vxG/QBPLH7yeG1YuxeQ/+CfRTp9uZd/+kxw8VMLBQyXU1XWvWOTlZSA5KYLU1CiSkyJJTAwjIT6MsDD/EfcGsdsd1NW1UFPbRGWlmYrKRioqGikta6CiopHOTseZx0ZHB5E0PoK01CjS0qJJT48mop9tcc+nuaGFfZsOsevdfezfdAhLixVvk5HsxVlcunwuc66ded4ToRLsg6/CbOWhN3LYebyByyZE8Jt/mUpUYN9OlIuzSbAPohM5p1i35jX2fnCQoPAAbly1jGvvXTxkq8prramra6GgsILCI1UcP17DsePVtLZ2nHmMt7cnMTHBREUGERkRQHh4ACEhfoSE+BIU6EtAgA8BgSZ8TUa8vT0HtBOw2exYrTZa2zpobWmnpbWd5mYrzc1WzGYLjY1tnDa3UV/fSn19C42NbWdm3wAGgwcxMcEkxIcSHx9GYkIYiQnhJCSE4ec3eLfdd9o6KdxzjAMf5/L55hyK9p1Aa01IVBBzrpnJ3OtmMmNRJt6m3rcpwT40uro0L+8p4b83FuLtaeCR6zO4LuvCLSDE10mwD4GCPUd55ZH17Nt0CKOPF1esuISldy5k8tz0IX+Baq1paGiltLSB0rIGKqvMVFY2UlvXQn19C2az5bx/6+GhMPkYMRoNeBk98fT0wGDwQPUs/aTR2O1dOBxddHY6sHXY6bB1Yref/+SpUhAYaCIkxI/wsADCw/2JCA8gKiqIqKggYmOCiYwM7Nc15H3lsDsozi0hZ2s+h7YcJvfTAqyt7Xh4KCbMTmXWkulkL8li4uzUfl/RIsE+tIrrWnlgfQ4HS81cnRnNL2/IJNSv/zfdjVUS7EPoZF4J7zy9kU/+uoP2tg7iJ8RyxTfnc9k3LiYu3TVd+Gw2O01NFhobLTQ1W2lpsdLS0k6bpQOrxUZ7Rye2Djs2mx1Hl8Zud5z1956eBgwGD7y8DBiNnnh7e+JrMmLyNeLn642/vw8BAT4EBZoI7PkaitA+F2tbO4V7jpG/4wiHdx2hcPdRrK3dbQzi0mOYdvkUZi6ZxrTLM/ALcm69Tgn2oefo0jy37QRPfnSUIJORR2/KZNHksdWWYaAk2IeBtdXKp+v3sPnFLeRtLwQgeWoiFy2bwZxrspkwO7X/CyyMcZ22Tkryyzl2oJiifSc4svcYJ/NK6XJ0oZQiKTOBjHkTmTJvApkLJhMRN7h3gUqwD5/Cqmb+4/UcCquauTk7jp9dO5nAAd5YNlZIsA+zuvIGtq3fzc4Ne8nfWUSXowv/YD+yLs9g2uVTyJw/ifFT4iXov6TV3EZxbgnFOSUcP3iSYweLKS0ox95zktU30MTE2alMnJ1GxryJZFyc7vSMvDcS7MPLZu/id/88xrNbjxMd6MNjy7OYlxru6rJGLAl2F2ppbGX/hzkc+DiXg//Mo6ak+05J30ATE2alkp6dTFp2CslTE4hNjXbrsLd32qkpqaPyRA0Vx6qoOFpFaVEFJfllNFQ2nnlcUHgAadnJJE8dT9qMJFJnJBObEjXsd31KsLvGwdJGHng9h+L6Nm6fm8jDV03CZHTf98VASbCPEFprqk/Vkr+ziMM7jnB0/3GKc0tx9Bzj9jYZSZgcR+LkOBImxjEuLZrY1Giix0fiHzy0s9PB4HA4aKw2U1d+mrqyempO1XUHeXENlcerqT5Ze2asAL4BJuImxHaPd1IcyVMTSc5KJCwmZERcISHB7jpWm4PfbDrCi7tOkRTux+PLs8hOdP8e9/0xrMGulHoQeAyI0FrX9/b4sRTs52Jrt3Eqv4zi3FJO5pZwqqCM0oJy6itOn/U430ATkfHhhMYEExYbSnBEIEERQQSFBxAQ6k9gWAD+wb74BfliCjDh4+eNVy+LTpyPvdNOe1sH1tZ2LM0W2pqttDa20drYSqvZQsvpVpobWmiqb8Zc14y5tonGajPm2qazLnH8ou7YlO4dVGxKNOPSYohNiSIuPYaQqOAREeDnI8HuertO1POf63OparJyz6UprF6Uhrcb3KQ3GPoa7E63AVRKxQNXAqXOPtdYYfQxkp6dQnp2ylk/t7RYqTxRTeXxampK6qktqaOuvJ6GKjNlWw5jrm2ms6Pzgs9t8DRg9PHCy9sLT6MnBoMHBk+P7usTAbTGYe/CYXfQabPT2dFJZ4f9rFn1+fj4effsXAIJHxdKenYKodHBhMeFET4ulIj4MKISI0bFJw0xcl2cEs6m1fP55fuF/GHrCbYcqeW3t0xjcmzfl5wc6wajv+uTwEPAhkF4rjHNN8BE6rQkUqclnfP3Wmva29ppqm85M4NuNVuwNFuwNFtpt3TQ3tZBZ7sNW4cdu81Ol6MLh+PrlzZ6GDwweHme2Qn4+Hrj49f95Rvoi2+giYAQP/xD/Hv+6zfgTwNC9FeAjxe/uXkqizOiePitPK5/ZgerF6Vzz4JkPKUdcK+cCnal1HVAhdY6p7eP10qpu4G7ARISEpzZ7JillMLkb8LkbyJ6fP8X7hBitFk4KYrNq0P4yYbDPPZhER8V1PDELVmkRPi7urQRrdddn1LqY6XU4XN8XQ+sAX7Wlw1prZ/XWs/UWs+MiJDVzYUQfRPiZ+SZb87g6RXTOdXQxrLfbeeFnSe/dm5H/L9eZ+xa60Xn+rlSKhNIAr6YrccBB5RSs7XW1YNapRBizLs2K5aLkkL54Zu5/OK9Ajbn1/DY8qnEhUg74K8a8MEqrXWe1jpSaz1eaz0eKAdmSKgLIYZKZKAP674zi0dvyiS33MzStdt5fV8ZrrhseySTsxBCiFFFKcWtsxPYtHoBGbGBPPRmLv/20n5qm9tdXdqIMWjB3jNz7/UadiGEGAzxob789a45/PSayew4Xs/itdt4P7fS1WWNCDJjF0KMWh4eijsvSeIf/z6fxFBffvDaQVb+9SCNbTZXl+ZSEuxCiFEvNdKfN++7mAeuTGdjXhWL125jy5FaV5flMhLsQgi34GnwYOXCNN75/jxCfY3c8eI+Hn4zl9YOu6tLG3YS7EIItzJlXBDvrpzHvZem8Pr+Mpau3cbuEw2uLmtYSbALIdyOt6eBh6+ayPp75+LpoVjxxz088l4B7Z2990RyBxLsQgi3lZ0Yyger5nPb3ETW7TzJst9tJ6fM7OqyhpwEuxDCrfkaPXnk+im8cudFWGwObvrDLp7YXITtAou1j3YS7EKIMeGStHA2rV7ADdPG8fQnx7nx2Z0UVbe4uqwhIcEuhBgzgkxePHFLFs99O5ua5naufXoH//vpCRxu1lBMgl0IMeYsyYjmw9ULuGJiJI9uPMItz+3mVH2bq8saNBLsQogxKczfmz98awZrvzGNYzUtXPXUdv6y+5RbtAOWYBdCjFlKKW6YPo4P71/ArKRQfrYhn9vW7aXSbHV1aU6RYBdCjHkxQSZeumMWv7xhCgdKG1mydhtvfl4+atsBS7ALIQTds/dvzUlk46r5TIwO4IH1Odzz8ufUt3a4urR+k2AXQogvSQzz4293z2XN1ZPYerSOxU9uY9PhKleX1S8S7EII8RUGD8VdC5J5f+UlxAb7cO8rB7j/74dosnS6urQ+kWAXQojzSI8K4O3vzWPVwjTezalkydptfHq0ztVl9UqCXQghLsDL4MH9V6bzzvfmEeDjye3r9rLm7TzaRnA7YAl2IYTog8y4IN5beQl3zU/itb2lXPXUdvadOu3qss5Jgl0IIfrIx8vAmmWT+dtdc9BobnluN7/+oHDEtQOWYBdCiH66KDmMTasWsGJ2As9vK+bap3eQV97k6rLOkGAXQogB8PP25Nc3ZvLiHbNobu/kxmd3svbjo3Q6XN8OWIJdCCGccNmESDavvpRrpsaw9uNj3PTsLo7VuLYdsAS7EEI4KcjXi7W3TufZf51BeaOFZU/v4I/bil3WDliCXQghBsnVmTFsvv9SFqRF8KsPClnx/B5KGyzDXocEuxBCDKKIAG/+eFs2jy/PorCqmaVPbePVz0qGtaGY08GulFqplCpSSuUrpf5nMIoSQojRTCnFzdlxbLp/AdMTglnz9mG+88I+qpvah2X7TgW7Uupy4HpgqtY6A3h8UKoSQgg3MC7YxMvfvYhHrs/gs5MNLH7yU3Ydrx/y7To7Y78PeFRr3QGgta51viQhhHAfHh6K2+aOZ+OqBcwcH0pKpP+Qb1M5c9xHKXUI2AAsBdqBB7XW+87z2LuBu3u+nQAUDXjD3cKBod/1DQ93GYuMY+Rxl7G4yzjAubEkaq0jenuQZ28PUEp9DESf41drev4+BJgDzAJeV0ol63PsLbTWzwPP97a9vlJK7ddazxys53MldxmLjGPkcZexuMs4YHjG0muwa60Xne93Sqn7gLd6gnyvUqqL7r3RyO9rKYQQbsrZY+zvAFcAKKXSASPu83FJCCFGpV5n7L1YB6xTSh0GbMDt5zoMM0QG7bDOCOAuY5FxjDzuMhZ3GQcMw1icOnkqhBBi5JE7T4UQws1IsAshhJsZ9cHubi0NlFIPKqW0Uirc1bUMhFLqMaXUEaVUrlLqbaVUsKtr6g+l1NKe19NxpdTDrq5nIJRS8UqpLUqpwp73xSpX1+QMpZRBKXVQKfW+q2txhlIqWCn1Rs/7o1ApNXeotjWqg93dWhoopeKBK4FSV9fihI+AKVrrqcBR4EcurqfPlFIG4BngKmAysEIpNdm1VQ2IHXhAaz2J7ntMvj9Kx/GFVUChq4sYBE8Bm7TWE4EshnBMozrYcb+WBk8CDwGj9oy21nqz1vqL5dv3AHGurKefZgPHtdbFWmsb8De6Jw6jita6Smt9oOf/W+gOkHGurWpglFJxwDLgT66uxRlKqUBgAfBnAK21TWttHqrtjfZgTwfmK6U+U0p9qpSa5eqCBkopdR1QobXOcXUtg+i7wEZXF9EP44CyL31fzigNxC8opcYD04HPXFvJgK2le7Lj+vXmnJNM942bL/QcVvqTUspvqDbm7HXsQ26wWhqMBL2M5cfA4uGtaGAuNA6t9Yaex6yh+5DAq8NZm5PUOX42Il9LfaGU8gfeBFZrrZtdXU9/KaWuAWq11p8rpS5zdT1O8gRmACu11p8ppZ4CHgZ+OlQbG9HcqaXB+cailMoEkoAcpRR0H744oJSarbWuHsYS++RC/yYASqnbgWuAhSN1J3se5UD8l76PAypdVItTlFJedIf6q1rrt1xdzwDNA65TSl0N+ACBSqlXtNbfcnFdA1EOlGutv/jk9AbdwT4kRvuhGLdoaaC1ztNaR2qtx2utx9P9IpgxEkO9N0qppcAPgeu01sO/Jphz9gFpSqkkpZQRuBV418U19Zvqnh38GSjUWv/W1fUMlNb6R1rruJ73xK3AJ6M01Ol5L5cppSb0/GghUDBU2xvxM/ZeuLKlgTi33wPewEc9nz72aK3vdW1JfaO1tiulfgB8CBiAdVrrfBeXNRDzgG8DeT2ttQF+rLX+wIU1CVgJvNozaSgG7hiqDUlLASGEcDOj/VCMEEKIr5BgF0IINyPBLoQQbkaCXQgh3IwEuxBCuBkJdiGEcDMS7EII4Wb+D0bqNiaxWYEqAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mapx = np.linspace(-6,6,500)\n", "mapy = -(mapx*map_theta.eval()[0]) / map_theta.eval()[1]\n", "plt.plot(mapx,mapy)\n", " \n", "plt.title('MAP Discriminator on the GIGA data')\n", "plt.scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_giga.weights())\n", "plt.axhline(y=0, color='gray')\n", "plt.axvline(x=0, color='gray')\n", " \n", "xcontourgrid, ycontourgrid = np.mgrid[0:5:gridstep, 0:5:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf1.pdf(xycontourgrid))\n", " \n", "xcontourgrid, ycontourgrid = np.mgrid[-6:2:gridstep, -6:2:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf2.pdf(xycontourgrid))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing the posterior predictive for the GIGA coreset\n", "\n", "We then compute the posterior predictive via MCMC, and then we plot the contour plot of the posterior predictive." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fmzennaro/miniconda2_1/envs/bayes3/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " not np.issubdtype(value.dtype, np.float) and \\\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "10000/10000 [100%] ██████████████████████████████ Elapsed: 7s | Acceptance Rate: 0.001\n" ] } ], "source": [ "mc_samples = 10000\n", "qmc_theta = ed.models.Empirical(tf.Variable(tf.zeros((mc_samples,2))))\n", "proposal_theta = ed.models.Normal(loc=tf.zeros(2), scale=tf.ones(2))\n", "inference = ed.MetropolisHastings({theta:qmc_theta}, {theta:proposal_theta}, {X:Xwt,y:Ywt.reshape((Ywt.shape[0]))})\n", "inference.run()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_post = ed.models.Bernoulli(probs=tf.sigmoid(ed.dot(X,qmc_theta)))\n", " \n", "ppc_samples = 100\n", "probs_BLR = [y_post.eval(feed_dict={X:xymeshgrid}) for _ in range(ppc_samples)]\n", "probs_BLR = np.array(probs_BLR).mean(axis=0).reshape(xmeshgrid.shape)\n", " \n", "plt.title('Bayesian Posterior Predictive on the GIGA data')\n", "plt.contourf(xmeshgrid, ymeshgrid, probs_BLR, 25, cmap=\"RdBu\")\n", "plt.scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_giga.weights())\n", "plt.axhline(y=0, color='gray')\n", "plt.axvline(x=0, color='gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Upsampling the data for the Frank-Wolfe coreset\n", "\n", "We rely on an upsampling trick to manage the weight of the data provided at the end of the coreset computation-- this solution is far from ideal, and a better approach would be to redefine the model to take into accoun the weights." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "Wt = bc_fw.weights()\n", "Xwt = Xtr[Wt>0]\n", "Ywt = Ytr[Wt>0]\n", "Wt = Wt[Wt>0]\n", "\n", "for i in range(Wt.shape[0]):\n", " np.vstack((Xwt, np.tile(Xwt[i,:],(np.int32(np.floor(Wt[i])),1))))\n", " np.vstack((Ywt, np.tile(Ywt[i,:],(np.int32(np.floor(Wt[i])),1))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing MAP estimate for the Frank-Wolfe coreset\n", "\n", "We now compute again the MAP estimate for the parameters, $\\hat{\\theta}_{MAP}$, using only the coreset data, and then we plot the MAP discriminator." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fmzennaro/miniconda2_1/envs/bayes3/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " not np.issubdtype(value.dtype, np.float) and \\\n" ] } ], "source": [ "map_theta = ed.models.PointMass(tf.Variable(tf.zeros(2)))\n", "inference = ed.MAP({theta:map_theta}, {X:Xwt,y:Ywt.reshape((Ywt.shape[0]))})\n", "inference.run(n_iter=5)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mapx = np.linspace(-6,6,500)\n", "mapy = -(mapx*map_theta.eval()[0]) / map_theta.eval()[1]\n", "plt.plot(mapx,mapy)\n", " \n", "plt.title('MAP Discriminator on the Frank-Wolfe data')\n", "plt.scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_fw.weights())\n", "plt.axhline(y=0, color='gray')\n", "plt.axvline(x=0, color='gray')\n", " \n", "xcontourgrid, ycontourgrid = np.mgrid[0:5:gridstep, 0:5:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf1.pdf(xycontourgrid))\n", " \n", "xcontourgrid, ycontourgrid = np.mgrid[-6:2:gridstep, -6:2:gridstep]\n", "xycontourgrid = np.dstack((xcontourgrid, ycontourgrid))\n", "plt.contour(xcontourgrid, ycontourgrid, pdf2.pdf(xycontourgrid))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing the posterior predictive for the Frank-Wolfe coreset\n", "\n", "We then compute the posterior predictive via MCMC, and then we plot the contour plot of the posterior predictive." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fmzennaro/miniconda2_1/envs/bayes3/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " not np.issubdtype(value.dtype, np.float) and \\\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "10000/10000 [100%] ██████████████████████████████ Elapsed: 7s | Acceptance Rate: 0.001\n" ] } ], "source": [ "mc_samples = 10000\n", "qmc_theta = ed.models.Empirical(tf.Variable(tf.zeros((mc_samples,2))))\n", "proposal_theta = ed.models.Normal(loc=tf.zeros(2), scale=tf.ones(2))\n", "inference = ed.MetropolisHastings({theta:qmc_theta}, {theta:proposal_theta}, {X:Xwt,y:Ywt.reshape((Ywt.shape[0]))})\n", "inference.run()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_post = ed.models.Bernoulli(probs=tf.sigmoid(ed.dot(X,qmc_theta)))\n", " \n", "ppc_samples = 100\n", "probs_BLR = [y_post.eval(feed_dict={X:xymeshgrid}) for _ in range(ppc_samples)]\n", "probs_BLR = np.array(probs_BLR).mean(axis=0).reshape(xmeshgrid.shape)\n", " \n", "plt.title('Bayesian Posterior Predictive on the Frank-Wolfe data')\n", "plt.contourf(xmeshgrid, ymeshgrid, probs_BLR, 25, cmap=\"RdBu\")\n", "plt.scatter(Xtr[:,0],Xtr[:,1], c=ycolors, s=bc_fw.weights())\n", "plt.axhline(y=0, color='gray')\n", "plt.axvline(x=0, color='gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "\\[1\\] Campbell, T. & Broderick, T. Automated Scalable Bayesian Inference via Hilbert Coresets arXiv preprint arXiv:1710.05053, 2017.\n", "\n", "\\[2\\] Campbell, T. & Broderick, T. Bayesian coreset construction via greedy iterative geodesic ascent arXiv preprint arXiv:1802.01737, 2018\n", "\n", "\\[3\\] [Bayesian Coresets: Automated, Scalable Inference](https://github.com/trevorcampbell/bayesian-coresets)\n", "\n", "\\[4\\] Tran, D.; Kucukelbir, A.; Dieng, A. B.; Rudolph, M.; Liang, D. & Blei, D. M. Edward: A library for probabilistic modeling, inference, and criticism arXiv preprint arXiv:1610.09787, 2016" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 }