{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "\n", "\n", "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", "\n", "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "\n", "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# In Depth: Gaussian Mixture Models" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The *k*-means clustering model explored in the previous section is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application.\n", "In particular, the non-probabilistic nature of *k*-means and its use of simple distance-from-cluster-center to assign cluster membership leads to poor performance for many real-world situations.\n", "In this section we will take a look at Gaussian mixture models (GMMs), which can be viewed as an extension of the ideas behind *k*-means, but can also be a powerful tool for estimation beyond simple clustering.\n", "\n", "We begin with the standard imports:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Motivating GMM: Weaknesses of k-Means\n", "\n", "Let's take a look at some of the weaknesses of *k*-means and think about how we might improve the cluster model.\n", "As we saw in the previous section, given simple, well-separated data, *k*-means finds suitable clustering results.\n", "\n", "For example, if we have simple blobs of data, the *k*-means algorithm can quickly label those clusters in a way that closely matches what we might do by eye:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Generate some data\n", "from sklearn.datasets.samples_generator import make_blobs\n", "X, y_true = make_blobs(n_samples=400, centers=4,\n", " cluster_std=0.60, random_state=0)\n", "X = X[:, ::-1] # flip axes for better plotting" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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NHX/LXduMjAxeeOEFZsyYUatgDDffuDvZlNH3MWV09Wt1q7tPZ5LP8f3mZRQ7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\n2qkiyS239RV69fnKf69Z8TZ9O8wntpv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/Pz2PffpPjre1u3zW5ISZbx+aVftC3SJZmWmc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\n7cVXE+ZRcNyJQlLglJ2Ymqt47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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the data with K Means Labels\n", "from sklearn.cluster import KMeans\n", "kmeans = KMeans(4, random_state=0)\n", "labels = kmeans.fit(X).predict(X)\n", "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "From an intuitive standpoint, we might expect that the clustering assignment for some points is more certain than others: for example, there appears to be a very slight overlap between the two middle clusters, such that we might not have complete confidence in the cluster assigment of points between them.\n", "Unfortunately, the *k*-means model has no intrinsic measure of probability or uncertainty of cluster assignments (although it may be possible to use a bootstrap approach to estimate this uncertainty).\n", "For this, we must think about generalizing the model.\n", "\n", "One way to think about the *k*-means model is that it places a circle (or, in higher dimensions, a hyper-sphere) at the center of each cluster, with a radius defined by the most distant point in the cluster.\n", "This radius acts as a hard cutoff for cluster assignment within the training set: any point outside this circle is not considered a member of the cluster.\n", "We can visualize this cluster model with the following function:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "from sklearn.cluster import KMeans\n", "from scipy.spatial.distance import cdist\n", "\n", "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n", " labels = kmeans.fit_predict(X)\n", "\n", " # plot the input data\n", " ax = ax or plt.gca()\n", " ax.axis('equal')\n", " ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n", "\n", " # plot the representation of the KMeans model\n", " centers = kmeans.cluster_centers_\n", " radii = [cdist(X[labels == i], [center]).max()\n", " for i, center in enumerate(centers)]\n", " for c, r in zip(centers, radii):\n", " ax.add_patch(plt.Circle(c, r, fc='#CCCCCC', lw=3, alpha=0.5, zorder=1))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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otG40Go3ExU2kpKQEo9EXeh5r8c0+vYem2k+QJAXNMB1np51Lly6i6zqq6kVV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\nfSxO4ysiCAIJCfdWNiotLQFAUWSioqIeuSDL3bi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dOokgCGg0GsaMGcuoUf2fW7PZmcal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\nKT9Z+gJrZjzCT77zE468cRqlW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PcFt1FfX4/DYSc+PgFBEPjpl7V88et2GjQxCC4baeoV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kmeans = KMeans(n_clusters=4, random_state=0)\n", "plot_kmeans(kmeans, X)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "An important observation for *k*-means is that these cluster models *must be circular*: *k*-means has no built-in way of accounting for oblong or elliptical clusters.\n", "So, for example, if we take the same data and transform it, the cluster assignments end up becoming muddled:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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Bslln8KIY1FCAvLT4blLh8XhiLc0rqVymqiotLWdpbKynvb2d3t6eWCv6XA3w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\nTTz/wKuUf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.RandomState(13)\n", "X_stretched = np.dot(X, rng.randn(2, 2))\n", "\n", "kmeans = KMeans(n_clusters=4, random_state=0)\n", "plot_kmeans(kmeans, X_stretched)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "By eye, we recognize that these transformed clusters are non-circular, and thus circular clusters would be a poor fit.\n", "Nevertheless, *k*-means is not flexible enough to account for this, and tries to force-fit the data into four circular clusters.\n", "This results in a mixing of cluster assignments where the resulting circles overlap: see especially the bottom-right of this plot.\n", "One might imagine addressing this particular situation by preprocessing the data with PCA (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), but in practice there is no guarantee that such a global operation will circularize the individual data.\n", "\n", "These two disadvantages of *k*-means—its lack of flexibility in cluster shape and lack of probabilistic cluster assignment—mean that for many datasets (especially low-dimensional datasets) it may not perform as well as you might hope.\n", "\n", "You might imagine addressing these weaknesses by generalizing the *k*-means model: for example, you could measure uncertainty in cluster assignment by comparing the distances of each point to *all* cluster centers, rather than focusing on just the closest.\n", "You might also imagine allowing the cluster boundaries to be ellipses rather than circles, so as to account for non-circular clusters.\n", "It turns out these are two essential components of a different type of clustering model, Gaussian mixture models." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Generalizing E–M: Gaussian Mixture Models\n", "\n", "A Gaussian mixture model (GMM) attempts to find a mixture of multi-dimensional Gaussian probability distributions that best model any input dataset.\n", "In the simplest case, GMMs can be used for finding clusters in the same manner as *k*-means:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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+X7z0f0Rvu4TNJAhvE0TPEZ1Z9/tm4vemgwoi2wUzeepL1G9U36m9/xn1Asdm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nMPq3btp8YFsQY1F5w1nLGnndbm129NosXIgRBTtvp2i8ccrmFlbjkYY/C5XVidJdx+y5Ud9tpC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\nU1FJdHQUKbERHCwJzGpVFIUec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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.mixture import GMM\n", "gmm = GMM(n_components=4).fit(X)\n", "labels = gmm.predict(X)\n", "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "But because GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments—in Scikit-Learn this is done using the ``predict_proba`` method.\n", "This returns a matrix of size ``[n_samples, n_clusters]`` which measures the probability that any point belongs to the given cluster:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0. 0.475 0.525]\n", " [ 0. 1. 0. 0. ]\n", " [ 0. 1. 0. 0. ]\n", " [ 0. 0. 0. 1. ]\n", " [ 0. 1. 0. 0. ]]\n" ] } ], "source": [ "probs = gmm.predict_proba(X)\n", "print(probs[:5].round(3))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We can visualize this uncertainty by, for example, making the size of each point proportional to the certainty of its prediction; looking at the following figure, we can see that it is precisely the points at the boundaries between clusters that reflect this uncertainty of cluster assignment:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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DiIh/nenz36dT68OYDG7+3FEXtekWevTqe7GrV2UqlYro+g+xeNXrDOpVhEql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jP7UHNgMxEZPVHpWiNLq/dtJCw+jbCUrtgAmwTPfbUZh9PFpZMuBCAmPAyl3hfQb0VRiGojmCYY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\nSy+8gKVPvYG7vtqv7jE0B4ZZ0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "size = 50 * probs.max(1) ** 2 # square emphasizes differences\n", "plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', s=size);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Under the hood, a Gaussian mixture model is very similar to *k*-means: it uses an expectation–maximization approach which qualitatively does the following:\n", "\n", "1. Choose starting guesses for the location and shape\n", "\n", "2. Repeat until converged:\n", "\n", " 1. *E-step*: for each point, find weights encoding the probability of membership in each cluster\n", " 2. *M-step*: for each cluster, update its location, normalization, and shape based on *all* data points, making use of the weights\n", "\n", "The result of this is that each cluster is associated not with a hard-edged sphere, but with a smooth Gaussian model.\n", "Just as in the *k*-means expectation–maximization approach, this algorithm can sometimes miss the globally optimal solution, and thus in practice multiple random initializations are used.\n", "\n", "Let's create a function that will help us visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from matplotlib.patches import Ellipse\n", "\n", "def draw_ellipse(position, covariance, ax=None, **kwargs):\n", " \"\"\"Draw an ellipse with a given position and covariance\"\"\"\n", " ax = ax or plt.gca()\n", " \n", " # Convert covariance to principal axes\n", " if covariance.shape == (2, 2):\n", " U, s, Vt = np.linalg.svd(covariance)\n", " angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n", " width, height = 2 * np.sqrt(s)\n", " else:\n", " angle = 0\n", " width, height = 2 * np.sqrt(covariance)\n", " \n", " # Draw the Ellipse\n", " for nsig in range(1, 4):\n", " ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n", " angle, **kwargs))\n", " \n", "def plot_gmm(gmm, X, label=True, ax=None):\n", " ax = ax or plt.gca()\n", " labels = gmm.fit(X).predict(X)\n", " if label:\n", " ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n", " else:\n", " ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n", " ax.axis('equal')\n", " \n", " w_factor = 0.2 / gmm.weights_.max()\n", " for pos, covar, w in zip(gmm.means_, gmm.covars_, gmm.weights_):\n", " draw_ellipse(pos, covar, alpha=w * w_factor)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "With this in place, we can take a look at what the four-component GMM gives us for our initial data:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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/y6bNc5k9d/mI2jUtD0k7T1NLB1MnNaBppfUdkEhKwRErvs3bmxFxpcihyHBN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SeeuHplfLrDQ0tbcNQ1rP+0p7ljXFWSqdSfjOEFuP/mB5A3y2w9vZ84GaqEj/tnf4q50+bR2t6J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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gmm = GMM(n_components=4, random_state=42)\n", "plot_gmm(gmm, X)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Similarly, we can use the GMM approach to fit our stretched dataset; allowing for a full covariance the model will fit even very oblong, stretched-out clusters:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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SYwkMx6F3Bf/mZ3fw8HceRM/VuuR33L2D7e9/iU/+xZ/WHafpOkXLYmAkQm+X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\n3ClIquFiZFyUoBSEN8IhB99bb72Vvr6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6WlvaEsmxinQ7SyRHCNN6OrDKk5egNE2DjrCP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\nsBUHw6MxbLt1EpThcDEwmqJY2v/aS4493rHJOjQ0xBe+8AVuvPFGLr/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sh8OB0xCcd/Ip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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gmm = GMM(n_components=4, covariance_type='full', random_state=42)\n", "plot_gmm(gmm, X_stretched)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This makes clear that GMM addresses the two main practical issues with *k*-means encountered before." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Choosing the covariance type\n", "\n", "If you look at the details of the preceding fits, you will see that the ``covariance_type`` option was set differently within each.\n", "This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem.\n", "The default is ``covariance_type=\"diag\"``, which means that the size of the cluster along each dimension can be set independently, with the resulting ellipse constrained to align with the axes.\n", "A slightly simpler and faster model is ``covariance_type=\"spherical\"``, which constrains the shape of the cluster such that all dimensions are equal. The resulting clustering will have similar characteristics to that of *k*-means, though it is not entirely equivalent.\n", "A more complicated and computationally expensive model (especially as the number of dimensions grows) is to use ``covariance_type=\"full\"``, which allows each cluster to be modeled as an ellipse with arbitrary orientation.\n", "\n", "We can see a visual representation of these three choices for a single cluster within the following figure:" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "![(Covariance Type)](figures/05.12-covariance-type.png)\n", "[figure source in Appendix](06.00-Figure-Code.ipynb#Covariance-Type)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## GMM as *Density Estimation*\n", "\n", "Though GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for *density estimation*.\n", "That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.\n", "\n", "As an example, consider some data generated from Scikit-Learn's ``make_moons`` function, which we saw in [In Depth: K-Means Clustering](05.11-K-Means.ipynb):" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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IbsADuHwGpojXO8SJZv4Q3IAHpHP5DN3qSFc2PzP0DrmP4AY8IJ2Z5xw4ka5s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\nAwS7zXKJEUjLAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_moons\n", "Xmoon, ymoon = make_moons(200, noise=.05, random_state=0)\n", "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "If we try to fit this with a two-component GMM viewed as a clustering model, the results are not particularly useful:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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JayeBMArp6kuRKXiYVrzuPcXFLpKLCH3k9g/ffA8rtLGFQ5IWPpTv0Se30Su3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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gmm2 = GMM(n_components=2, covariance_type='full', random_state=0)\n", "plot_gmm(gmm2, Xmoon)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "But if we instead use many more components and ignore the cluster labels, we find a fit that is much closer to the input data:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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QHHzuCK6vJKK0DBGN4hjPC1DmHXtg3yH+5St7+fZdNZ7cfZDe/oi+gdmuYVEU\nzNzYl4WAMPQxdUF/TwlNU9mz+wCf/LjC7kevY2z0JRw6+Coef/gwL3npBMWiRRRF7WsUEIUePXmL\nbJf4bTZnoSgahVyGOPKJQp8gDFFVDUVRCKOAjKHQN2cIx5c+/xi7H72u7Ty2vYkw+A4XX3oOWcsi\nl7XI5yy+8nePs+ext7TtG0VbsTL/xSt/YjWoCgoK/YO9bD1vkh/8xxF879Ud11mZ2MNP/JTCyMgg\nA4N9bDt/ksD/DrnCHrad/x+88xdyXP2WH6d/oLftONPU8f2Q/XsP8rmbsux94i1Mjl/Iswdfye4f\nPcfZ5xxhzZr2JkqqqhGEIQoCPUWMk88lRiFG13VUzaRWr7WNMX2xOFF/e6cKcn0rl3z+6IykaaSr\nfAXjOC7jlRaGmcV1XSp156gyxx3X4fnDZRQjj24uv/bW8yOsjNY2XOTAvkPc/On87BjMPbD3sZ28\n/7cOzcS99eXW+wqIQh/LVOnvLzE3GnDHbemjMb919618+PfOx/c9Gk0bPxQomoGlKVPnWII7XFEo\nTk29i+OYZrOF7bjkshaleeNtu030mr9dQWFyPF3M6rUSfaXkYSOIQkQM5563lpe98gW+e3/n/mFY\n5L47jnDueUnt9ZZtG9myLcl6932PIFp4jbvuHqU8OS+zffIyvnXXzfzYj13Qsb+q6jhe0tVtvkUO\noGk6tusn40x1HdQME5MVmW0ukRwjUrhXKJ7vM1puYphZbMem1vBnapEXI45jarUGdcdHMfJH5d5+\neu8hHtgxyuR4noGhFhdvH2Fg9RBxFDP3NLO12rNUy5fxwI6bZ4Rb046+TWYY+mQMlb6+ImpKLL2b\nYE7XmZumRX+vSRS6qCIiQk1i20fpwo2FoJQ32bhmACEEjZaN5yehBsMwu070Stvebd+RETdxRRsw\nd1XXv20j3/vuPYRBZ4e38fGHUs+1lIBY18z2ie5eEU0zcLwARVVSY966btJoOvT1FtE0jVrLo683\nOikuc4nkdEEK9wokjmOOjFcxzBy241BvBuhLLDvyfI9600UzLPwoPKoOak/vPcTNn8lRmUx6ZT/1\nBOzdvZO3/+Ihzr3g7LZ9X3gm/av1wqHkhh34Ln2lhcdsTiOimDgOsQyVvt50wZ6mmwhO15mHgU/e\n0ujpH5ix1OuNBrbj4IcCw8oubH0LQRT49BQtCrnZ+FR/bxICCKOIZsvmmjeP8MhDO5mYE2MeHNrF\nNdet7Thn6jXVAAAgAElEQVTlNdet5ZGHdnXEw9P2Bdh2/kZe9oqv84P/7OzwNjT0b6nHqKpCHApU\nTemIY1/9lvWctW41g0M2e1OOHRxsdf88SMTbtj20vJoqyKpu0mi2KBbymFaWcrXG0ED/gueUSCTd\nkcK9AjkyVkYzkkEh9aaPtoQGHwCNVhPPT9pU1huttulQS+GBHaMzoj1NZfIyvnf/33YIt+OMpp5j\neuSmqrJguZaIBVEUoGsquYxOLlNibjXV3AS04RGHa69fy7YLNnLt9ekieNWbRiDyGerLd3QxKxWL\nlIpJT/dao4HnRQRCwZznwYiiAFMVDA33pCaoAeiaRm+pyEU//XL6P7uPf/zyrRw+bDE4ZHPlG1ex\n9bytHcdsO38jH/ujA9x5+60z67nmurVsO39j18/nf7z35TxzoD35bWBoJ9vfmF77rmk6Qrjs33uI\nz92UnXGJ7wWe3L2LX/7wQS69coTHH/kW1fLlM8f19n+L11+7mqbtkMtmkszytPPrJs2WQ6mY73jw\nSeLd4Ps+pmnienHXdUkkksWRwr3CqNXr+EIn8jxqDW9Joh3HMZVaHVQLTVcJwxA/Bv0ovZXdBlzU\nK0XiMADdmhHXTDZLWjvTTC6LEALL6HzzOIwRIsTQVSxTI5ttj19PM52ANjeW/chDu/j4Jw+w7YKN\nfPyTB7jjtlsZH80yONzijW9ezU/85PlkrIU/K03T6O9NEreCIKDRaOEGEZ6bZM73lXJkM0sfXXrh\nS7dw06e3zK5PxNiOg+f5BKEgiGIUVcPQTbadv3FBoZ5Pmthfee0IazemW+mqqqKQHseeHL+UXXff\nwrt/+eW8/0PP8cC9N1Mez9E32OTqN6/l3PPOAeBHP9zD1//pCQ48pYMosHmrzzt+7lzOPS+5blU3\nabZsioXO74mmGbQcH8MwCGMp3BLJsSCFewURRRGVhk8sFCoNd6Zs64ndB7jjtmcZO5JleJXDtdev\n47wLkpvptGtcN2ajpJ7voy8je3xgqMVTT6Rtt+nrKRCGMX4QEQs4a12O558ZZro157Q7d836HIHr\nkC1m2Lf7Kb519xiT43mGR2yuefMaLnz5VhboUwJ0T0C747Zb2XbBRrZdsJEt565HI6SnmCOTOfrM\nTcMw6O/vJQg8RgYsanUNxwsJAh9jiR6O+aiKSiGXpzAnZOz5HrbrEYbxVHlYTEzStU5bJHkvTexr\nje7DRlRV6RrHnhjPEceCdZvO4ud+5Swylk7Wmn1I2bfnIJ/+oyqN2muYfhj74fdh/757+Z9/cmBG\nvGNFw/VcMlbnA46qGTRbNpZ56o4AlUhWAlK4VxDjk1ViFMo1eyYR7YndB/jkx2B8Wsgehkd+uIuP\n//EBzt60ipYTohvzXL7x8kr3L94+wt7dO6nM6bDVN7CTi7ePoGsqlmmRB+Io5oprRnjqieeoTF7f\ntu9l24co5VUqo2X++lMFJsbfCMCe3fD4o7NW80IslIAWhSEqEb2FDLns8sdMBmGILgJWDZRYt3Zw\npo7UdhyaLQfPj/HDGMPMHNM0LMu0sOblJ4RRhOclXevCKOlaF0aCWIBAQVWTWHKau17XNLr9dhWF\nBeLYTRRC+kp5dLXztnDvnYdp1Hpp96BArXoFd93+Jc792JTVrai4foCuhx0Ph4qiEISCjLS4JZJj\nQgr3CsH3feotj7oTtWWP33Hbs7OiPcX4+KXc/v/ewvs/OISeYh1GESjLSOrdtHU97//NQzyw4wuU\nx3P0DyVtTTdtXY+mK0wrhqqpXPDSLXzw4we5784vMjGWY3A4aWO6cfNGSnmDf/j8kwtazQvRPQGt\nRX/RWpaFPU0YRSixT38xS6nY2/F6Lpud6dcdxzG1egPH8xJPg6JhHmXzmjR0TUPP5UkLTIRRRBgG\nBGFIGIVJLkCciDqAoYY4foCqJr9gIRLBVhSwdMHPXNHHnnmzwIdGvs11b9tAqZhHVdJvCRNjOabb\npc5nfF57VU0zaNkePcXOcwlFWXTSnEQiWRgp3CsAx3U58MyzjNYiTDOLqsUzVt7YkXTrc3Q01zYk\nZN+eg+y44wUmxnL09Da4+MpVbNra2Ud8mrSyr01b18/8m0sUhZhGHt9vt/W2bNvAlnn9xqPAwbKK\ni5ZtLURaAtrwqm/znvdsWbZoR1GEiDz6SllKxaElHaOqKn29PUxXJTuuS6NpHzdrPA1d09A1jYWW\nWak20Lo8QGRfbfG7f/g8d93+JcbHsgwNO7ztnZtYu34dTTv9gQhgcNiG3ekhgqHh5LhYxDiuRyyS\nhxrP88nnM+SyGRQUhBDohGRzvbiud0wPWBLJmYwU7lOUKIqYrNTxgoggFDwz5pHJ9+JFArvaQlcF\nhXwS0+bhzuMHh2dvwvv2HOTPP2lQnrhxZtveJ3by/t88xKat6ztEeusFgru+tqmj7Gt6//nEcYhp\nmvi+t+Ca5ialLVa2tRCbt67h4584yDfvuJWJiTyrVrn893ds4MKXnbPosZ3XHiNCj1LBordnePED\nFiCbycwkr8VxTKPZxPE8gkDghzGabr4ok7JMUyOMRWpZm6opnHvexhnXNkCpJ0u95qAqSlc3+xXX\nrObhH07QqLUnHJZ6dnDVm9fQsG38qWEqU2+EHfiogcB262iagqWEbDp7Daqq0pLCLZEsGyncpxhC\nCCbKVRx/ymLTY0bHRtEzSbxWUZSZm2O14fL6Kwd55Ie7GJ9jffYP7mT7tWfN/LzjjhfaRBuSMq4H\ndnwBoKM2+6Hv3T0187lz/zTh1lRlSZ3HwsChrz9xP3cr27r2+vSs6DAMUEWcdEvry7P2opdz0UWL\nvmVX4jgmClx6ixY9pcGldU47ClRVpadUYrrBqxCCVsvGdj38IMaPYsRUydnxfu9cNku51sRIsboz\nlontBqgpcWzD0HD8CC0ljrJl2wbe/p4X+Nrff5N64/+iKkU2bG7yrve/lL6RXkKhohvt59R0A8/z\n0TWFjKZQLPYxNlmjVMiQsSyaLZtCSm94iUSyMFK4TyGCIGB0ooZqZDDMxLU4NlEhxkjtB60bJus2\nr+c3P/4Md339ZiYmigwO22y/9qw2F3USn+xkcjyXWpvt+1cxPbd5LuWUjGQhkvGeixHHMVlTnxGp\n+WVbQ3Nqsed+HpoisAyFnp4smeMwGjKOY+LAo5A36B8eOu6i2Q1FUSgU8hTmlEoFQUCzZeMFIUEg\nCKIIgYphWMfkYlcUBUNPX5ehGyik9302dAPXC1Oz+vftOcj/948bqFaTUrIYGD3yZf75/+zFcQYZ\nHnG44tqzZmafCyEIPBddiVi1qh9ruoxO06i3AlqOSzFjkM8t0vBGIpF0IIX7FKHRbFFpOBhzeo1P\nTFZQjSyx2wTSM3pUTac41Mf7PriOjJXuehwctuf8NDvHuTx+kFazm3u4MxHJtA7xd39pt8W9120c\noVBc3GqKQ49Cf0/btunSrZl9opjA9zA0FUOHvt4cpnl8RkGGQYBKRDFv0DN8/C3s5WAYBn297Z9J\nEARJrbfvE0aCKBIEcYyIFTTdWLKrPZfJUG+56CnzxC3TwPXj1IcD09DwQ9HRaOXeOw/P89rsoVHb\nwKMPvQuAp/bAnt07+eXf2sc5564lY+r0D/WgqiphFDL3m6kZBmBQabpE8ShrV69a0pokEkmCFO5T\ngHK1RsuL20S7Uq0RKSbaAnFHgFq9gW4WcFx/qsFIpyBtv/YsHn9kJ+WJtcyd41yeuBbD/KvU85rm\nIfw5hlmh9GUOHXgFjdp2YDbu/b4PHmLgVZ0DKOYSxzEZU+sQyziKicKkO5ppKFg5nVy2L7XpynIQ\nQhD4LhlTZag3Ry639AEsJwvDMOhJmVsdRRGO4+L6PmEUE4ZJzXckBAgFVBVdM2Zajuq6TrdW8JZp\n4notoFO4LdPE822Y11Wv02uzm/mjRcsTl/HdnX/HT732wrbtfhiTE50xd93KUHdcDo9NMjzQK/uX\nSyRLRAr3SaZeb2K7oq1sq9Fs4UWzfZ9VRSFKUe9qrQ6qmdwQNZNGy6aY7ywi2rJtAx/46FP85U1f\nZ3L8o22vBf7lmObdU+7xhL6BnVz9VpO9u2fLvpr1Frt/9K62YyuTl/Gd+27mFa9aeI1x4JHtKRD4\nHqoCmqpi6ApWVieb6+3aRnO5RFGECH1yWY3Vq/tPC0HQNC1xtacUicVxTBiGeL5PEARJeVgsyFqC\nlt1CUTUiIRBCJA+BAhABjuOjaRq+q+AHU4mFigIixPOjmTIyVVEYHG4mWj1DuidkIqW7nqYbOK47\nU0Y3F1UzCCKVIxM1BnryMmFNIlkCUrhPIi3bpmb7Mx3QAFzXpeWEba1MNVUjiAVzrelavZGI9pS7\nM2luEZPclecKoaDZshlZu5r+wQaT4/OvYhvDZ+1gzfovUJ7I09tf5/VXj7DhnFfyUxcns7ZRVf73\n7z+ZuoZKuYiIRVJXHARThcPJDV9TVBQ1piev0F80sTLWcRfpuQSBh65Cb95ccknX6YCqqpimiZmS\nAzDd6jaNSq2Bohr09mYpl20Eibg//tgYX/3HA4yP5hlZ5fDGt6zjbe/YxJO7dzE+Np1MGKSeM61a\nQFEUfD8izeGhahqO79FbKjJZtymFYWrLVIlEMosU7pOE63mUa05bM5UgCKg0nI5OZ9msRaPcnGm1\nWW80EOgzoj2NqhrYtjvjEhZCJAKvWai6Qv9QC1Jalq5Zn+fGD/w4AIoIKM27cQZhyPAqm6f2dB47\nMtIiZykMlDJkNbUjbhr5DiNDfScspjxtXWcslYGBQtc4/5lKMZ+jXHdS27QWchnqtj/ViS35vT32\n6H4+9mHB2Oh7AXj0YXj4oV383h/Du258nn+89VPU6/1kMi/guTVarffOnK9/cCdXvfmsjvcBUFR9\nZsjIfKJYIQxDdMOibgdEUZ3entLxWL5EcloihfskEIYh4+UG+pyYthCCyUod3exM9FJVFVNPYt22\n3SISWupkLUVV8QOP3NR7NFo2qj77EHDJG9Jbll7yhpHZc6Toq6HrXPmmtZ0dt4Z2cd3bNpLLZjAt\nE8cJ246L45hcxjzuoh3HMWHgkTFVinmLYuHUSDY7FdF1HUtXiFJizIZhoCvtGeZf++pBxkbbQyLj\nY5fy5Vs+zcEDr2B8LHnNbiU13C9/9afwvHUMDTtcce1qztnaPiVuGlVTCcKItMIA3TCxHZdSsYBu\nGDhBRFyp0d/X07mz5IxACEGj2aTp+DRdl4nJJqoCuq5QymcopIQEzySkcL/ITM/SnivaMJtB3o3e\nUp5nX5jAjzW0hTKLFQ3bbuEGMZrebrlv2no2v/Bbz3D/PYlbvH+wxSVvGGHT1M1WCNF1sMWWbRv4\n0McPsuOOpIXp8EiL69+2cWaYSRoi9Cj1H5+5y0ndtYdhqJSyBqVTJDN8JVAq5pmspHdTKxayhOGs\n2/vI4fTv4L4nFarVS9u21Wvbgb0MDTuMjWW5947DaGrMy16xLfUcUdS9R3kw5zVV0/AiKEvxPiNp\nNFtU6g6aYaFqGXQzg5WJZl4vNwLqzUlWDfUd986EKwUp3C8yoxMVtHmiXa3XiRVzwfhvGIaJlb3I\nfIYgimm2HIql9Bvepq1nzwj1fKIoJLNA5vV0C9MwcBnqL7HQGK8oCigWjs1tHUURUehjGSo9OVNa\n1stEURQylo4XdpaAqapKPmdQqbromsaq1emd6wTpA1se+1GJMHwPMFVo+MjOroNiohjiKEr3Fint\nrnRV03BDQaVWp0+6zc8YxibKeKGKYXW/DxlT5YTPHZlkzcjpkXx6tJyZjysniXq9STQvG9d1XRxP\npN7MponjmFrDJl/IU8gZRGF6YpDnuTheiKIuXPv89N5n+OJn/5M/+/huvvjZ/+Tpvc8AoCEWfYIV\nQpC1dBabvamJkHzu6NxZQgg8zyEKXFTh0ZvX2LBmkLNGBigVi1K0j4FCPgdxeuOVTMZEV5PEtLe+\nfQPDI99ue3145Nts3ZZ+bBi2C/rk+GXcedtzqfvqhoHnp59H03U8P+jY5vhT1ROS0xohBEfGJvFj\nHT2lHDINw8pxZKyCEMubdriSkRb3i0QQBFSbbtuTZBzHVOp2h9t8LkIIKpU62lQSm2WZqIpKs+Xx\n9P7neWDHGOXxPL0DdX7ikn42bd1EFKXfHCER7c9/erbFKTN9yA+ybdu6RdcRhR6F0sIWUBh4DPYu\nPlJTCEEQeGiAaapkLI1Cf9+L0s/7TKRUyFFtem3DZ+a+Vqk3eMmFm7npM/v52le/zOiRLCOrHN76\n9g3ASzn49NysctD1ewjDzhr+bgNkAj/Aj3ziGCxDR5/XXCdMcaVruk7LD6EmE9ZOV4QQHB6dBD2D\ndpQP54qRYaJcZWigb/GdTyPkHfJF4sh4tcP9U67UFhRtgGq9gTIvy9wwdSb2P8cXPpOnPKdd6d7H\nd/KeXz/E2g2rCcMg9QZ9/z2dLU4rk5dx/zf/lle+csuC1xJFETnLYCFrO45jspY65c5qRwiB73vo\nSiLUlqlS7O+VQv0iYRgGWTNIdZkrikIpn6PWdHjJhZt5yYWbO47/0z/fz9e+8mWef8FkaNhmcmKU\nh3/4ho795peExXFMvWETo6AK2LvvIHfd/iwTozlGVtm89Wc38ZKXnkMsFKIo6nB96lPirdYblErL\nn7EuOTUZnSiDvrye/Yqi4Phx14qF0xXpKn8RqNUbxEq7kDWaLSKxsGDZjkMktFSd3HHHC5TnZIcD\n1MqX8d37JtA0gzAIOw8CyikNMgCqkwUWc38rIiC/2FCIyKO3VJoa6+gSeA5x6KHhkzMi1g6XWL9m\nkFVD/fT1nhjR9oOAcrXOWLnG6GSNiUqdcrVBy7YXP/g0p5DPoYj0UIuu6xTzGcIo/bsDgJL0FTB1\nnZ++ZJCBoZ1tLw8O7eKaeYNi6g0bVANV1dn75DP86e9rPLjzRnY/+na+/a0b+dhvR/zg+4+jGyau\nlz5hTtd1Gm6E7Sw+PU6ycqjVGwSxfkxhMMPMMFltHMerOvWRps4JJo5jak2PkeKspeD5Pg3bxzAz\nXY8Lw5CmHaB3eYoc7zI4pFrOgQjwAp/nDr7Ag/dNUh7P0z+UZJB3q+UeXuUuuI4oDOgppHkHBEEQ\nEHoKvttiqMfA0gLMjE4u++Jb0y3bST43w2Su4SaAlhthuzXyWTO1i9eZQm+pwGS12db4ZxrTMMhn\nIlpuiK7N/u4ee3Q/H/nNsK1UbOj7u3jne5/nkYduZWw0y/CIwzXzBsX4np9Y2lM/3/Z/djMxvgW4\ng6SJywVMjl/G1//579hwzhpKOYN8Lv27rRsmlbqDoeupHh3JysLzfaotH3OB++BSCWONlm13/e6c\nbkjhPsGMT1baXORCCCrVBkZKvfZcavUWutk9K3to2CalHwpDww7FQo6nnjjMLX9RojxxXfLCE7D3\nsZ1cdUPAk4/tpFqeW8v9LS6/ehVxPBtjjONoKulDgABDCdBVE4SPpiioCiiqgqFpZEoFhod7KFkq\nI0PHp/xrOQRBMCPaaSQuWG1GwHsKuTNSAFRVpZizaDhh6oNVxsoQxw6OPyveqfXd45fy8ENf4sO/\n97qOc0zjerMjRPftOcjuR18GzHWv/+vUuXIomkWlbpPLuORy6Tdz3cwwNlln9fCZWwp0OiCEYHyy\njrlIqHCp6IZBo+VK4ZYcO47j4scq+pz7S6VaX7BeG5LOaGjp4rPviYPsuOMFDu5vpPYYv+TKpJnK\n/fdMzIr29HuXL+OZp57ht38/4J5vfJGJsSwDg02ue9t6tp13zkwvawXQdRNVTTqhhb7L6qFVC3rS\nA89haKB3wXWdaGqNVkfXuTRUNRHwSt2mmLfIZo79iX+lkclY+EFAEKfXFyYeCQfXD9E0vWt999iR\nhT+7uZ1677vzMFF447w9XgfcxtBw4gJXVJ2GExBGIaViIfWcupVlbLLCqqGBBd9bcuoyPllBXcLf\n6tHgBTEipdHQ6YgU7hNIudYuJC27hRcp6F1mJQN4nocXgGZ07rPviYN85pMG5fHpm98eTPOvGVmT\nY826iEuunG2mUp5If/KcGMux5bwNbDlvA3EY0FPILGh1RlFEqZBZULSjKKKvlCPwT94fjOt5xBhd\nhp+mo+kW9VZAEESUimdeJ6ZSsUC11uhaTpPLZlFVl5YTdK3vHhpeOG8gFmLGTd5tLryuN7nqzWsA\nEIqComp4gaBcqdPfl55JLlRLNmhZobRsGy9U0VPucceCpps0mq2uD3ynE9LXdIKoN5qIOfXUURRR\n61KKM00cx9SbztS84k523PEC5fG5CWnb8P1fZc26iBt/48fbGqsMdLmhzszmFmDqyqKuYk0JyS8y\nDlMVwUkv1fG8YFmNGHTdwAuT0apnYj1oT6mAiNKT1SBxmxdzJte/dU1qffcbr0/vTT7N3M90sMt3\n8sJX1Dn3/CQurqoaYRigaBoROuVKeg23qqo4oUKj2Vrw/SWnHpWaveRa7aNB0zRst3sp7OmEFO4T\nRKPltQnJxGS1bd52GuVKFTdIXL6VSotKtUW90ZrJEO+WkDY50Wkt/syVq+gfbM/47R/ayfZrkxtt\nHAaUCgs/mUaBy2DvwhZN6LsMD5x8qyfs4vJdCqqqEWNSrp55jT4URWGgr0gUpmdzA5imyWv/24X8\nr08Jtl/5ZV7xqn9m+1Vf5qbP6FyYUjY2//zTXH7VMANDu9peHxzaxTt+7tyZn1VVJZ6aYauoKpHQ\nujZg0XWdesvH79LURXLqkQw9OnFlW54fnxEP4NJVfgKYb2237BaqYdFtFCJApVKl3AiSRDZFZfpw\nATRsj6wZMziYbl0MzNv+9N5nuP+bo+SLGpp+E/l8lnUbCmy/9qzERR6FFPPmIu7vgJ5iFkVdoK1p\nENBbzJz0OmwhBGEYs4AzY1EURUFgMlmpMXCGuV9VVaW3mEsm0+npN1VVVXnta1/Gy16+BT+MZzxH\nru/htUJUPd3bMTfcuHXbej7yiVHu/vqXGB/LMjTscNWb18xY2zBloc85RtE0gghqtQY9PZ013Lpp\nMVFtcNawjHef6gghqDW9BduZHiu6adFoNikVT+96fyncJ4B6y0Obim0LIag3XAaG86QJt4gFlXqD\ncr37F1rVDJwg5CcvLrL7kZTpXlfOTvd6eu8z/O2f5dqarERDO9l+bcCW8zYgYoFlqFgLjL+M45iM\nriyYtCWEwDLEKTE7OQgCUI79q6woCrEwqFTr9PWeWV26dF2nlLeoN72uWfkAxUKOIAiwbY8QlYxp\nUW+40CW7QJlS4TAMKOWznHv+xjah7nJQ+4+ahhcJ6o1mavxS0SzK1Rr9i3iHJCeXSq3eNsb4RKCq\nate2uqcT0lV+nKk3mjDH2q5U6x1DRaaJ45jJSoOmHaCk1NTOJQgjhtev4Rd/y+YnX/cFtpz/FX7y\ndV/gF3/bbott3//N0TZhByiPX8aOO14AASohxcWaqMQBvSnWTfsuLoP9JzeLfJoo7uwEtlxUVSUU\nGvX6mdXQAcAyTUoFizBc+MZnGAY9PQWKWR2iAE2JuronFQRR5FPImgt6b6YRQqCm7KdqOo4vcJzO\nfgOqquL4Atft7u6XnFyEEMl97kXI+A7C5YfNVgrS4j7O1JrezFOl53l4IenZkwIqtRZCUfFDgWYs\nLDyu66MbGVafvYobfyN9uhekx7sB/uvfY/7ypu/ytndsom8BUQ59l6H+hUU7DDyGB0qnTNmFiI9v\nCYiqJpOp1JadDOc4g7BMk15FodpwUhu0zMU0TUzTxDA0xqpNRKwSC8G0hmuagmVAzly6VyZ5AEj/\nXWq6kXizNA1zXp9z3TCZrDU5yzr+898lx86LYW1PE4Snf4xbWtzHkVq9gaLN3lCq9VZXt2O5luzb\naDloC7gmAVzHQZlK6AiCaMF958e7p3Hsfr57//v4w4/BE489nbpPHEUU89aCMesoiijlDKxTqC9w\nLOLjfrPWNJ2WG50Rbrf5GIZBXym3YMLaXHK5LBlDp1DIUSrm6Skl/wr5HKVCDrHExEERC0QcoWnd\nv3+aYVGtt9qaBc2+lgyckJx6HK21HQYhtVqTWq2JneJlWQhF1fC6tM49XZDCfRypt/yZTPJGo4lQ\n08Wt3mgiFB3X8xDK4iVMfhihKMmvSlF1PK+7mFxy5Qh9Azvnbf1XIJniND52Kd+47dmO4+I4xtTi\nRS1MXQnoOcUGPZyoJFJdN6g27DMiS3U+uq7TW8wRBku7aZpdPEamZREtUG4GyQNjpdqk0nCo1Jo0\nm06St9AF1chQTulNrSgKfqzJErFTjHqjgdol6XE+nuczNlllrNrEFxq+0Kg0fEbHK0Qp0+PS0A0D\n5zQPm0jhPk7U6rNfziiKaDjpdcW27RDEGoqq4Lge6gLWBSSJV2Lur0lRCKPuVvemrWfzi7+dxMGz\n2S8AtwHDwLaZfUaPdMbcldhfNCEr8ByGz7TxeXqGiXLtZF/GSUHXdQb7SojIS7Vw52KZRuo+iqKg\nawvfZlq2h2qYaLqOaWWI1cQlbtvdB4oIdJopAq3rOrWmu+j1Sl48mo6/pB4Ltu0yWbdRNAtjTphG\n0zRUI8PoZA1/gQe6aRRFSR0RezohY9zHiabjo+pJDOf/Z+/NA+yqy/v/11nvfme9s2RfyEYSomit\n1VoFogbZlICItopaW/2Wb22/at2wAhVRKl392SpClaqoNQgoizhJ1Nq6sIZkyL4RklnuzJ2Zu9+z\n/v44M3fuueecmUkEMpnc9z+Qc+4299zzeT7P87yf93tkNOtrIGKaJoWSjqSqDpFGnH5+SdN0RMn9\nONOcOgNctnIxy1Yu5uv/8Ct+88vNnvOdXe4F0dQrdE4jV2oaGqmW+BmtD63pGvliBdOyEQUBQYBw\nSCYanno8xbRlSoXCWdfvBmcRbG1Oki8UKVW0wNZPNBIhmx9FDHl/96osok2xjprAoT1HePRHfWTS\nUTq6y7zlrfNZsWoh+lieE8cGuff7z1X9wa98+yLWrFtGvlxBVXVPv1sJRciMZmcNefJshqZp6Aao\n06MQxgMAACAASURBVMTtXD5PrmS6AnY9FDXMyGiBztT017URuBuYFuVKBdt2fpnlchndlny/2LFc\nEWm8N1wqV6qBfiqYlk19Nd2GaTV5LV3jsrfN49C+raQHL6oeT3Vs5YrNCydf36jQ2hybel7bNImH\nJSKR2anpLcsSZX1qZrllW2TzZSQ55NKOL1VMSpUc8XCIUChghlkSKZQMFEWbVb39lxLxWBRF0cgV\nnO+wHoIgEFJF/GpBkVCIcr7k2YBO4MCeo3z5i1EyQ38KwJ5e6N2xlY999hi2ZfGFvxUYG30PADuB\nx3/zKJ+//RBr1i1jNFsg1dbkuRcqhkCpVJ61v9mzBWO5AqrPZq4WxVJ5PGhPf2/ZokwuX5h2DNWY\nJrk509EI3C8AsrkC0vhOcSxfQvYJyIViCVuQEXDMR+qz7QnRlOGhGG3tBS54SydLVyzCsmyeP/Ic\nv3x0iJGhKC3tRf7wTe2sWLXQN4gc2neUbT8+wdhoEx2dBd79fpUdT32jmq1csXkha9YtA5wsujkR\nQZ1CftC2bRTBoLnp9Ll+TQdFljHNUmDg3rHjAP9x5176B2J0dZW46prFrB1X/JowHMmVNAzLJBZg\n9ykrKmO5IqlW5axlLYdUFVVRGM3mMCzJQ2JMxKIMjXpd7SRFZqpJsJ4HB8gMfcB1bDh9Ed/75r8A\nMDb6l65zoyNv4oa/uZnP3QZr1i4lm817xFlkRWEkV2wE7tMI27YpVUymGk4wTYvRXGlKi+NaSJJE\nrlgmFo1MvVG3GoHbA9u2ufHGG9m7dy+qqnLLLbewcOFkFveNb3yDH/zgB7S2Oov9zTffzJIlS16Q\nDzzbYFkWZc1CCUGxVML2EaKwLZt8Qa9mteWK5sq23aIpe9hPL4/97wir1h5g3e+p/OTe1Yxlxp2+\n9sKB3T28/8NHWbN+het9Du49ylf/PsJI5oMA7NkFu3du5W9voRqsq5/bMIiHFcJTCLEA2HqZjq7Z\nrUrl9M/8S2M7dhzgr64v099/nfNv4KkntnHLbQerwdt5DYWyZmLouUDynSSHGcvmp51xn8sQBIGW\npiTlcoVCuYIgTo5fKYpCgIAah/Ye5b57+0kPREl1Fl2KacNp/+xp51NNhML++uaZofl89hM2N33h\nMCtXLyCseashgqQyls2SSp291+t0IpfPT0tKGx7xthV37zrE/VuOMdAXobO7xDvffQ6Lls6vnpdk\nlUKxNGXWPcfj9qkF7p6eHjRN47vf/S47duzg1ltv5Stf+Ur1fG9vL7fddhvnnnvuC/ZBZyvGsrnq\nfKJTRvTuHLP5AtFEHCpl32zbEU1xgjYMApsxDXh2B+zf/SC6tsD9npmN/Pwn/+4K3Jah8/OH+xnJ\n/JnrsQ6L/BuuwG1ZFuGQQDw+dc9Wr5SY39ky6zNMYbxf7Ydv332I/v53uY4NDlzID753tytwg5N9\nm7bIyFgucNa9rNtUfILE2YZwOEQ4HCJfKFLWDETJCeCxSIhc0UCsycZ7dx7kls+qpAffWz226+mt\nfPymw6w6dynt7Vn2+ryHYcShciLgE+RID17Ivd//Jp++eRlj2SId7e5rIooi+ZKGOQWZs4EXDw4p\nLTiTzuXzWILsSnV27zrEzZ+G9OB1AOzcAY//9lusWPk05VKKzu7xquGa+UxlAmZjY72AwkyzDaf0\nVz3xxBO87nWvA2DDhg3s2rXLdb63t5evfvWrvPOd7+RrX/va7/4pZzEKZQNBECgUi77ZtmmaaDX9\nlrKmj5dnJzEpmtKL4088CV27ZPy4GyPDk7tNS9eIRVVGRvyDTS2L3LIsQpJF0zTWd4ZeoaM1cUqO\nW6cDUkAttu+Ef0XBj1kP47KnyI4Zgg8URSWbD2Y7n22Ix6K0NSdQJQvb1FAkESzD9Zgt33vOxbMA\nGEpfxI/vfR7b1LjymsXI8sN1r+yMMKpqYfz/6885QXpwwLmOgqSSy+c9n09Ww6SHz86pgNMJwzDQ\njeDzlmWRK3onb+7fcqzut7KH0cwiHvv19ezccQ09j1zHzZ+GZ3YennJyQBDEOb1hO6XAnc/nSdSI\nuMuy7PoSL7nkEm666SbuvvtunnjiCX7+85//7p90FqI43rcGyBcqSD4uF/lCsXrc1A0syxtgJkVT\ngnrN3uPNbQVMXUdGp6U5jqoqgd7IEyxyZ1bbnLbUaxgazXEnozpTIAak3N3z/Oc565n1rtcSRQxb\nJu8TCAAQFLK5xqzwBARBIB6L0tqcoL0lTiICllFG18oYukZ/wOYpk46STMR5+fmrWbdhB87o4gPU\njjCuPDdJsvlI3bnjwIUAdHQ611EQRYpl03cxrxgOgbSBlw5jufyUpLSxXN5XmW+gr35D7U1m0oMX\n8eB9AxSmGBcURQndmGLncIbjlErl8XicQmFy4aovSbznPe8hPm4Z+frXv55nn32W17/+9dO+7pnW\ni+ob0OiINFEoFEi2JD27R8MwKGnhqvesKNs0NXsz3Ys3L2Df7h4yaf8ZRUU9il6judLc+lPeeEk7\nixa0usrYV75jCbt3bmWoZsfa0bWdd73nHBKJEKpo0j7d2JdpEg9HTskh63RePyUkoJnefeiH/u+5\nPPbb7fT3X1A91tW1nes+sJLmlmnGwAyLcMR5zdY2dz/N0DVaWiKn3RnthcILee1SqQTP9WWcmWzL\nYtlyk2ee9j5u4WKT5ibnGnzgL36PGz8hkB68cPJ1Orbx/g/9HgB33/EsTz0Wd8rnvBxYTWfXdt79\nvhXV14AIAgatrT69T1M749aXk8Fs+9vKeoWY5L9hsyyLQrlCVPWen79QZ+eO2iP+yUxmOEY0FqKl\nxb/PbVkWzTFx1olFvVA4pVXn/PPPZ/v27WzatImnn36alStXVs/l83kuvfRSHn74YcLhML/+9a+5\n6qqrZvS66fSZY+xgWRbH+7OooQgD6RFExbu7HM3m2LvnOI88cIKRoTixxAgXXjrPZQoCMG/hPP78\nI0d54Lv72LPrYUzj4uq5lrYeLrsmxO5nvsbIUJS2jiIXvqWLRUuXkC+4s4j5i+fx158+wiMP3MnQ\nYJSOzgJXXbOU+Yu6KWZzhFuayGSCM0XLslAEnWh760lfi1QqcVqvX7FYolCxPT2tpUsW8HdfzPCD\n791dZdZfdc1iFi9ewOhI8I69d+dBfvC9o/T3hThnucXV71jChg3nuB4zNtJPe+uZ70j1Yly7Ur5E\nvuCUKq++ZjG//h/35inVsY1L3zqP0THnGpyzahF/fcN+HnngLoYGo7R3FHnLW+czf7FDYPvk5+az\nb/dhHrrvOEODT9Pe/kuueedSFi6ZX30NcCYlNM10cRBaW2MMDpcwKuk5yTI/3fdePSzLoj+dIxTy\nz3gzo1lMFCh7779Lrujmid/WjrD6JzNt7QXSQ3mkKVwBtYKBNssLLae64RLsU9BzrGWVA9x66630\n9vZSKpW4+uqreeCBB7j77rsJhUL8wR/8Addff/2MXnc2/fimQ2Z0jLIhUSwVyRctFxkHnGz7scf2\n8I+3Rsik3TacE45efiNggOdYfaAHxwu7tSk2ZbMjJNpEIiFkdNpmIEZhG2XmdZ4ag/x0Lx6WZTGY\nyfkKOIxm89jCzM26e3ce5NN/YzI4MJn9dXVt55++HHYFb8syiYVFogEjZGcKXoxrZ5omfekxlPFy\n6TM7DnDPtw7TdyJEc2uOze9Y6pl0yIzmqpr81SA9EKW90wniK9e47UAlWyeZnKxgmabplEdNjZam\nRFW1raurmUymgG2U6UrN3rHGU8Xpvvfqkc3lyJXxJYbZtk3f4Gj1d+GHKqu8P0I4fIwD+85jJPOm\n6vlUhzMps3zFPOZ1NAeSZ0OiQespVA5fSrykgfvFwmz68U2H5/uHkZQwA+kMouJduEezOf75tsf4\n763v95x79R/dwQVv6RwfAfMP6tPBNHRaktFA4RTbsonINomoPKMfr6mVmNfZesoszNmweKQzY4g+\n5blsLu/s8GeIm27Yxk8eerfn+GWXf5vbbn+T65hhlOlo9QqAnEl4sa7d8MgoBl72fTaXRzMl6kcB\nisUSZR327z3K398kM5yebPm0pbbysc8aruBtmzqJWAhRFNENA8sWkEQJ09RpiocIKQq2bZNsCpHP\nVZAEaE2E5lzWPRvuvVr0pzPYon+ZPJvLUzbEGd0vEwH86OE8uWyReLyTJcvtqhaFruu0N4VRAyY8\nFEGf9ep5pxq45yZX/kWGpmnYiJRKk+S0WliWhWZAetB/3Gp4KObrmz0yvJHtDw3M7EPYIATYHwLo\neplERHxJgvZsgRz0+U8yqPYHMM6PH/cGf0kKkcv7kwLPdrQ0JdErXpOSRDyGoXtrmNFIGNsyeOi+\n466gDY4gy0P3HXcdEySFbK6IpusIgow0Pq0hSQr5gvO+TtatYFmODOZY41q96KjowWzv0vgUznSY\nGAvreeQ69u+9nv6+v2FsbIFLQEqW5bPSvQ8agfuUkCsUkRWVQsmfSV4olpGVYJZ3W3sh0Dc76Hg9\nbAiyLcbUdcIytLZMbwhiVEp0d7Sc8UEbHP9nP4hTyXb5oCuAcd6eKmLjLlAJgkBJM85KB7HpIIoi\n0ZB3nFAQBKJh2WvrJghEQjLpAf+N01DdRtiyLIoVHcFvDNMWqGiT/VFBELARKZQNCsVG8H6xUCgU\nA6Vty5UK5gxDjncszOtsKAgC1tyd+JoSZ/5qfRpQ0Zyxk6CdZUVzfk2bLp9Ha8ptsdnS1sMFb+kM\n9M1ubg0YQfKDTzwydZ1EVCEejQQG9gkYWpnujuYzZlZ7Oqiq4ju7KUsSVsAd3rvzIDfdsI0P/emv\nuOmGbfTuPMhV1yymo3Ob63Edndu46tolvpaRkqSSzZ3EdTuL0NyUwND8s27T8GZL0WiEVIf/vdFe\ntxHWdB01FPUNxJKkkC+631cQBGQlzGAmezJ/QgMngUKpEjhpUSiWUaaQV66Fdyxs/HhdNcwieMN8\nBnevpsXcmGV5CaFpGoYtUMwXfPV1y+UyjJfsVqxZwkduOMKPt3yNkZEEzS35KtlM13R27/opY5k3\nVp/b1NrDqy9ontZABPxjsqFVaI5HUEMqljk1nVKvlOhONc2ZcSaAcCjEWK4EdRuRUEglV8x7hG8m\nSWhOP3sH8MRjPdx8q8Att8lVJvrCRRqXv20Ba9cvRzN0NF1DrTFEEASBsm6RmMNKTacKURSJqBJa\n3W9aEARiYZmSbiHUfWeb376I3md6GK4hdbaltvKWt07KXmqahig6v92KbuMnJ2TaoPuogBiWzFg2\nS1NyahvbBk4eZc1fm9y2bSrj0tAzQWd3qW4sbPx4XTXMOksrXdKNN9544+n+EBMoFmd/v2Ism8cW\nVcayBd+SULZQQqjx2G5LNRONFUn350gPRhk4PkI8WaZ7yXyWrhrG0P+bSGw3y1b9msvfJbFkxRIs\nQ5t2Z2pbFpGIOv7/NoKh0dIcrz5PwCIWQMIxNCdoz3T3OxPEYqFZcf00TafeTk1AoKxpCHXH/+1f\nn+aZp9/qOlYsLqNY+hmXXLGGN21axSWXL+Syt64hOT4PKooSlUqFaJ04jSjK6Fr5jBKtmcCLfe1C\nIZWxbN7TVlJVlUKxiCC6N4+d3e0sXd5HRf8lsfhe1qz/Ldd9MF4lplmWhWGaHNj7HPfc9SyP3D/C\nU0/sJ5WC9o7J9pAoShh6hZbmOOXyZNlckiQKhQLNyfgZTSqcwGy59wzDIFuo8GzvEf75H57kW3cf\n57e/3k9Hh0UsEUG3xCk3tqZpkc3lyRYqJJs0dj71PMXi5ORBqmMrf359E6maa2xbZuA6Jwv2rCci\nxmKntl7MnXTrJUJZM9BNExPJ02cwTRPTBKnmxP7dR/jKl5KMDDsmIfuB3bt+ynUfPsHi5YtY/KFF\nnvcwanaRfiNjy1Yurmbcpq4TUiDZ5CahBUmAGlqZjrbkCxq0ZxMUWaRieCsWsiB4bEiCSGjpwRiG\nLZPL50nEfXI5QaFQKnmcxCq6jWEYc6qK8UJAFEUSUYWij/VqMhZmrKB5gvorX3UuS1cuqrru1ULT\ndQ7ue55//JxCZsiZ2piwAr3hc4dZvXaSeV4xLF/+gS067Y25KtBxOlAoltiz+xgf/WuDgf4/rh5/\n/LHtfObv9rF63arA5xq6yUi2gKSoyAqIssK8hTvR9QOIYoFzVlq8+/0v94wQnqUJdyNwnwwMw0C3\nIF8s+3rHFoolpLqA+MgDJxgZdo+EjWXeyC8f/RqLP7SIowe9lp0Ll3SDDYf217qGOUF/b28PH/zY\nUZYun4ehVUjGQoTD3l2lXyahayU6WhNz2iAjFo1QzOSR666PJAnUq2F2dZXwqcbR0elYhBqWTLFY\n8CisiaJIqVIhGgm7mP2yopLNF2ltbpRg69GUTFIYzIDo/q2GwyEKxbKnUymIIsl4mFxRq1a29u0+\nzIP3Pk96IMLw0HNkhtzVkqH0RTyw5RuuwC3LIfKFAvXNJVlWGM05DlON9sYLA003+O53jrqCNsBA\n/wXc+/07+VRA4LZtm5FsvrpJ27/nCLd/TiGT/qvqY44c2ur73Llu3xmERuA+CWTzBVQ1TGW0iJ9b\nnW7Y1E+HBY2E9T1f4Ku3/ZQDvS/DNMcdvcYtO6/7yxNE1yyucQ2bxMjwRrY99DXe939aaW/pDlx0\n5LqMW684QXs6G88zHaIo1re4AVAVhXJRR6ppY1x1zWKeemKbS2ilPbWVyzYvrL5WxbQol718AVFU\nKRRKxGPu66sbNLLuALQkomTymue7aWlKkB7JebJrVVWJmhZFzeDA3mPjs921m+AeYBuwAEdha62X\nkS4IFMsmquS9HrrpWOxGZ3k59UyBZlj09fmvL4ODwdMy2XyhKrwD8Mj9J8ik3cmOn8vhtDjzuyCB\naKwuJ4GyZlIxDE8PFUDXdfxI+qmOIns8R/eQ7lvJiaNl4GLXmbHMRv7zy7fS0l5i4MQYjtXnatdj\nRoajtLU0BQZty7IQ1clzhlaio23uB+0JKJKIUbcRV1UViu4AvHb9cm657SDf+dZdpAdjdHSWuGzz\nQlafu5Q9zx7mR1uOMTgQYd78EpuvWcz6GhtVh5BmEsP2ZN25QpGWpkbWXY9IJIxSKGLXLTuiJBIL\nK5Q0E6Fu1xWJhDGNPA/98DjD6ffVveJGYAy4fPzfv0ANHQN+z/Uoy/bfTMlqiJGxPJFwaE70uk8n\nbNtGN226u/1JsV3d3skCcErkFc1CViavTVCyE+TodzaiEbhnCNM0MUybSkX3lGEBSmUNQfYG9E2X\nz6N3Rw+ZoUmGrKL2oGvX47gdeZEZWktmaHIxcjAZvDu7KoFuWOBIcYZU58dvaiW62l9YItpsRySs\nMprXXNk1gCziKcmuXb+cj93QiSCq1WD9r3/fy/Fj51CpXAfArh3w1GM9fP5LB10e3pKkks8XPH1w\nzZjbXsC/C1qbk/QPZT2Sl/F4lHJmDHxmsuOJOEODQVlx7e/6j7B5mrJWwbadcSBZFJHlMMV8nmTc\n/XsQEKgYNuWKRuQMJBXOJhSLJSRJ4dp3LeHxx7YzUKNL357q4YrxKlY98sWiZz11Jzt7cBzCFNID\nR9m9q33GWfdJyjecUWiwymeIsWwOSxifDfXJuPPFCoLoPd6WambVuRly+a2Eo3tYturXWLZKbux8\nYBdwrs+71R5fDPy8+u/WVA/v/kCMjs5mQqp/MDYNnWQ8Oq493vqSlG1nC7MVxlnDpVJ1XGgCpmVh\nmE62bFoGuXyeilahkC+xb89Rbv2sRO/OKxnJPI9pXuF6brG4jHL5Z1xwkXvR0E2TcEhxZWyiKGPo\n5TOmwvFSXjtRFLEtHc308jDCqkouX0D0KWs//cRBDh14mc8ruu+h1rbDbLx4Afv3HOU/v7ab+/5r\niMd/s5emZo1Fizo9z7YsEG2TaPTMLZfPhnsvVyhgCwqdXa287OVjVCq/IJncy8vPf5L3/HmYdeet\n8DzHMEzyJQ2xrsrS2m7y9BNHKRU1YBCnKrmKfP61PP6bw6xdP1JlltuWSTzmvXa2bRNSBEKz/B5s\nsMpfZFR0E0GUMUzLxRoHpwxnTyFAunjZPK7/xHwGh7JIcphv/9uTnDgKsBYno671m/3F+PFJJJuG\nmL/oHto7imy6fB4rVi9BEoNJGaJgI1gVujvbztoSoCqJ1EuuRMIhRrIZsnkN3QRFDYEAFUtky/eP\nMZQe5xoE6Jr79e8kSaVQKHqy7rJukZzBPP7ZiKZkksLAMKh1pD9JJBkLkysbnmrJ265exM96HsYw\naltL3nsl1VFi3+7DfOGzEsPp9wLw7E546vEevvgP+9jwspWux8uyTL5cprnBS/idoBlWtVO4fsM5\nrB8348kXChQCJCUKpZJv9XLFakf/4p8+fx/pgU+4ztX3uoNuL8MwkE8xKJ4JaNTyZoiKbmFZFqZP\nvCyVKx53sFqUNR1FUYhHQph6iddsbKGptQen/N0BbEGSv0Gi+e/G/+3uaW94pcxNt7+M//vx17Bi\nzRIsy0L2yUoALMMgIpt0d5y9QRsgGglhGG5LQE3TSWdyIIdQQqEqeUVRFDJVqdk9wAHf10x1VigW\nvXKoFcP2SKFKkkq+0JDWDEJrcxxT91NOC6MIlmfOZ+XqRWw4vxfYgtNiugs4Tu290pbayiVXzufB\ne320zoc28p3/POj7WQzTYUQ3cOrQA1QkdSO4ZaRNoWm+YvUS2lL+Zksz6XXbtoU6h9uDjS3mDFAs\nlRAlhWKphOxDJ9cMy0OqmYBt2UyocMqKSnOTSmS1ynv/8ij//ei/MTIcp6WtwOvf3Iosncsd//g8\nI8OTi1FrqodNl89zvaZlmciytzxkGDoRFTpmoFE+16GqKqLgDrKDw2PEYnEMy3Zt1WVZoj1VYB97\ncEpzb6G+EtKe2srlmxdSMQzqqTOiqFAolohHJ88IgkBZM2hMCfsjHAoRVstUTO/C3tKcID085vK4\nNy2LP3n/yzl62Bn7crAHVf0y3QsiLF4Kl21eyMo1S/nGwIjvew4MRNF0A1WpI8fJCrl8ocEuP0Xo\nul5Vi/ScMyy/ziKGYU47g+1P7HWrpwWlJrZlzhkpZz80AvcMUCpXkGUFPV9EFN27ONM0sWw/So2D\nYqmMWCcuEQqFWXveKtae5338Bz92lG0P3cHocIyOrpJTGl+zxPUYwbY9i52ha8QjMtFImJDSuKwA\nIUVmYlNfKBYxkQmHZMZyRc+8/Zsu7eLxX/WgabXe8VsAhY6u3Xzgw+ewaMlKEJwNXK0HtyAIVHTT\nK7spyJRK5Vmv3nS60NrcxInBYRDdGZQgCLQ2xRkeK1RHxCwbVq9dyg2fO8wDW75BeiBCqrPEpiuW\ns+rcc1zPT3UWYaf3/do7iuimhaK4G1uSKFHWjAah8BRRKpeRfcyWAAzDQvFZHEvlim+ZvBabrphH\n784eMjXSt6mOrS6iW5CtsYAwpyuOjRV+BtB0CyTHFrA+QpfK/g5htc8VfdjmfqiqpA1G6eousuny\n+Z6gDSDJ7h+koZdpioeJRiJolRKRiJ9y89mHeCzCYCaHooRcBgd+LmKr1y6hc/4Qxw5XjzBRhm3v\nKLJy3UrGiib54hjJuOIK3A4kyuWKS/JUFCVKFa0RuKdAqiXJYCaPrLr7kbIi0xQPky1UECQFezzQ\nrl67tCqwYlkWZZ8S9yVXzmfnjq0eP+9Nl3U5myzNIFxH7DQsR5HtTCEUziZouokgeNfAcqUCon+I\n0QwDQfQG7v17jvDI/SdID0ZJdRR5+x/Dnl13MTwYo7O75LL1hGDnv7m+/2oE7mlg2zaaYaFKjqB9\n/e/BMC0QAno4Fc2lWz4VDu1zq6Qd2APP7urhIzcc8QTvCd9py7IQzAqplmSVWCMKNLKGcYiiiDIe\npHVzkjwTUiTKdeYWiqqyYKFRE7gn0d7hlOYkWQIkhkbLWPogXV2pauYmihJlTfNolTdGw6aGoigk\nIgr5ioFUxxMJh0MYhkm2UEbyWeR106h6cNdi5ZqlfOKmwzx473+QHozQPb/Cmy/r5pxV56BXdGSf\nFFAQJfL5UiNwnwKMmnurFpWKjuJT/bPGpzuUuudMKqaNy9gCvTt7+ORNBuvXn4PskwAFjcWerJXv\nmYZG4J4GhWIRabyv7deS0XULKaDio+umx9giCH4qaZn0Rh554E5P4JZEAUPXCCvQ0trqOifLjQBR\ni3BIplixME27ugsPhUIUy3lPMHjzZZ3sfdY9c9/a3sPFNa5UAGo4TF4zON43xFB/hvu3HKe/P0Jn\nZ4H3vn8lL9swOfoiyyr5QolkYmY+62cjksk4paEMfstRPB6lWCpSsUyPu5uzIfK/v1auWcrKTzuZ\neTIRIptzqM2GZaKKKpphoNZsFCRJplAq0v4C/U1nEwzT9kzaABiWhV8TsVyuIPkYNPkppmXSG3nw\nh3dxns84GYAY0OVuBO6zHOWKPvkjq4vcmqb7zm5PQLesKc/XYnjIf2EfqlMRMg0TUbFoikd9yrWO\nalgDk4hFoxRKY55qiSKLHtORtRtW8KGP7mf7I19nOB2lLVVk46WdrFyz2uPtbFpw8GA/f3+zQmbo\n3dXjTz+5jX/5/w6wYXwcxul/NxjL0yHV2kxfehTZxyo3kUhgjhUxLaFaJbECgsJ0sLERBMeJqn71\n00xmZKnbgBuGaeMThzFN25+YZvpvuIIU04KOQ2Cxc0qBqrmARuCeBrrh7WtPoKLrgf1r27KxLHx3\non5oay+w3+d4e8fkSJFlWZiVHPMWLHRJBFbf07ZR1bnLpDxVqIrocUuLRMKM5UrINSQ1URRZuWYR\nkizS8+MBhtJRen48QCQcYt7ibtfzRUnkwR8+T2bIXSUZHLiQb9/9bTbcPkmYsmwRXdfPKvW6k4Uo\nijQnwozmddc1AWcyrKU5wchoDtOSEUQRwzQQRWnceOQ46YEoqc4il1w5v2r/OXFueDhGW1uBS66c\nz9q1DrHJz5tCEGXKlQoRH9OeBvyh67rHT30ChulPTDMt25cOHsQiT6WKvhm0ZVlIqv97B7kjpND4\nMwAAIABJREFUzhU0AvcUsG0bTXf6234wDDOQBVEue60Kp8IFb+lkb28PI8M1ZdqaUTBT11Flm9b2\nFt+g7XwenXCyUZKtRyIWxTSHqG2hSqKI7ENSO3boOP96a4SR4T8FYB+wt3crf/HxIyxftaT6OEEU\nSQcYJ5w44S7By7JCoVimuakRuKdCLBpF17OUdNOlpjVhy1kbvC3bZv8et9AKO2Hnjq189DP7sWyL\n2z8XJjNxDufcp246zKtetRZRED3lcllRyOUKjcB9EghilFuW5dtaBCeg11J/Jghpzx2RUENfRqts\nZIIYqoYeZP35/m6HpmmiKv4z3X739lxCI3BPgVLZPcpVz0au7ZvWw7RMTubrXbZyMR/82FG2P3QH\nI8NROrrKbLp8HuesXoxRKZKMRQlHwoi2HvgatmU6ZhoNuCBJEqqMpzQeDskUyu55z0cfHGRkeMLM\nwtFJHk4rfOW2Z/k/f4MreLe2533fr6U16zlW0et13BrwQ3NTEm1oBMsWEQRhPGhP3nfV4G0Y40Ir\n73U9fzh9EQ/edyeiIJCpMyVxzt3Fq161FkEAq65cLiA0rtNJwjAsj7QwQEXTPaOzE7BrbsR6QpqD\nB3F0FNrQKmu55z/CrFxxyMeL2/RVuzNNEyU8tzfJjcA9BcpltwWhJApVGU3DMLADGiz7dx/hgS3H\nyAzFaWsvcMFbOln/cn9yRS2WrVzM4mXzaElGEcYJaJKt0drWUt1xKlOQz9R6mmYDVcQjKiMld5BW\nFZVSuUBtL2TSFnJCjGUzAEODl/OFTz1I5/ytLFwcZ+OlnVx4SRd7e91ktrZUD3/05lYyo2O0NjdV\nj4uS2pjpniFSbc30DWaQ1Ihvz7mlOYE2lGFwwP+7HE5HA7O92iqJX7lcN4PVvBrwwqw3uR+Hrusu\nFvjuXYe4f8sx+vsiNLfmuPit81mxeokvIQ0uwdFQGL/30qt9LT1FISATN3TC4bldeWwE7imgm5ar\nFxNSFXLji3+l4ng77999hEcemJw7XHsefP8/F5MZcnSv9wN7e3v4q789wryF8/zfqAai4Mj12ZpO\ncyKCWjPfahoG4WjwuIraYJQHIh6LMFIsUk9YCKsyJX1yXCvVWWL3TnAciTa7Hqtpl3Ds8BaOHd7M\nnl09XP+JEh/+ZJGtD9/F0ECE9s4SF1/RzbJzzmG0YGAYI3S0Oyp2oig2ZrpnCEEQ6GhrYmA4C6Ls\nWZwt2yIRTzBvXplnfYRWUuPje3790u4ae0nbR7pLb2TcJwXD9FefMmt2Rbt3HeLmT0N68LrqsYlR\n12DimTtj9pM5lQNHLO05rZoGjcA9JXTDcrElY9EoY/kMkhTBtCz27znmmTv8zS8nejSTGBneyE/v\nv5P3XD914LZtG9usEJZDxJubvectA1X1F9E0DINkvFEmD0JzMsGJwTym6c66Q6EQZa3AxCDqxVd0\n07ujh+F0UKnNOZ4Z2kjPj7/Oh/7fK1m3wW1cgW1jmBYlXaJvcIjuDmfIyPATum/AF7Is09YUo29o\nDLFO3tdhJQtcfe0Sdjy1jfTghdVzDi/EIRLuesatutWe6mHzNYsmX0gQHJZ5ze7cFuUGkfAkYFo2\nfjGydlN0/5ZjrqAN46Ou999JqsN/gwXulmCtzOkE/ISUYO4T06BhMhII27YdTes6REPy+DmLRx44\n4VoYALRKzcLAHiZMEZ55coRD+44Gvp+ulxHMCl2pZuJxf+WzqcrktqkTjTaM5oOgKAqxmAq2dzQr\nElKcfifO/O9H/1ano2t3wCtNLijD6SiWn+CyIIwTcCQ0W+F4fxrHhkRy1KQamBHC4RDxkIxhuq+Z\nNX5fnrtuGZ+7TeBNF3+TdRvu4Q8vuIO//lSJFWuWsmLNUj56g84fXXQX61/2PV77hq9x8xcFzq1V\n3RJEdMOdYSuKQqnkHv1rIBiWX78Bd8Y90Oe/Lg2lo2y6Yh6tqR7XcUH8CbWubx2d2339vKWAjHuq\ndXKuoJFxB6BULvuKBDQlEwykM1imHVDmmVjY3T3S7Cj8+9/38MGPHWXZSsf1xrIsLKOCIou0JKLY\ntk00HBx8Fb/ZinHIstiYP50GEUWiooBWZ2yhqirlymTWvXLNUv760/Clm3sYdm3M3DaSbamivyoP\nDnERnMXFtEIcO5FmQXc75UpDVvNkkEjGMMYKlPRJq8/avve565Zx7rplVDQDENixYx+3fOo+Du2X\ngQRLzynxgb9YyOpzX+nJxPwIarIkoxnBBNAG3AiI29g1E1+d3SV27vA+5vhzx3nkfkfWtHfHnQyl\no7SniqzdAL07nmco/RRtbXne92drWLTULYKk6waqalEoFhEEZ9xTVVUEQZjzjHJoBO5AVCqaL2NR\nEASak3EGMn0Bc4drUdUH0bQy9T3SkeGNbH/oDhYt60awTcIhhUgiORlwLT1QNN80DCKN/vbvhEhY\noWIrlLN5RDFUd06lUDaqY0hO5n2Yh++7i+eOCJw4VkDTJsdUWtt72HhpZ/CbiSK6YaDIMqIoYAsR\njp1IM78j+WL9eXMWTckk1liWiuEEb9v2+jDbts2eZ4/wd58cZHT0NUw4u+14Am78+KPc9MUjrD53\nMfUNWb+4YzZaGjOCaZqByYJVU0K/YvNCdjy5lfRgrdXqL8iOXcp/b1tN784ePnKDzorVS6pnL9zk\n/FewdRYvTNHXn6GimZiWjW3alLUyHW3NSJoFmNiWhW0XEEWB1qhjYDOXExnpxhtvvPF0f4gJFIte\nf97ThXyhhBWgvKLrBoIoE4uXePrJ5ykVJ8tvramnufJPDnNobwmt8krPcyPR3bz50nnEYzEURZn8\ncdmgygKqGjBCYWo0Jf1L6KZpkogogc99KRCLhWbV9fNDKKQyODyKLEsYppuRKkkSmq67pJjaUi28\n+nUL2fyOc1iwrISmPYvA0yDcj1Y+zG9+KfLsMweYt1CiLeW2UhVFESyzqtUsCCBKCoNDGdqborOq\nhzqbr51TyhaJhEPoWgXDsjFML9NcNyzu+vddPNsbBy52nSuVdJ56/Gf88mdFnnz8AKkOi1THxPWy\nUepElEQMEvEzh5V8uq6frusUyoYvESxbKFUrJKmOFtauH0HXf8Fw+jdUKkeBpUxsgkvFZejaL/j9\nP5wsh9u2TbFUwtANdNOiVLFBkBAECUGSkESBRDyKKAqIoogoSUiSjGGYRCMRsrk8shS8ns4WxGKn\nVn1rBO4AjOVLCAHONsVyGUSFBQs7WblmkFLpZ0Rje1h17q9513sVVqxdwvFjg5x4zhu41254jD/4\noyWe46au0ZyIBe4SZdEmGvG/yKZeob01eVp3mLN58Z+AIAjk8kXUUJRSqeyRXZQkkXJZc4l/OLAx\nRRE1WuLXP7PJZ89H19+LVnklg/2v5vFfHWTN+hFP8Ma2PAuHooYZGh6iORnzreicDszma2eMB26A\nSDiEVilTqZiea6TrJj/8/hCDAyFgVc0Zp2WVz7+TwYF1HDzwMn7zv4dZv2GUVEcLtu0N3AIGyUbg\nnhalchnd8m/RZfNll2lMqqOFP3zDEv7nF4OkB68B2nGuzc+BA4yOHGf1OoVYIkq+WKZQ1NE0nUQy\nQSQaRtfcXARJtHxbTpah09KUQJIV8oUSigzqLNok1+NUA3ejvhoAwwie5zRrZj03vHw1n71lI1++\n4zXcdOsbec1rz6O9Oclbr17sIV3UKqHVQ1GEwDK5ZVmEppAyVZRGf3umCI9/j9Gw4plBlSXJ+Z5r\nCGe2BZlsASUU4bFf5Cjk4kyUYScwNrqJ+//rmEtYAoJLroIU4bm+TIOodgpobW5CFg3f+WGHeVzf\nn+6l/nqlBy9ky/eeC3wPP75hA16Ypr/rncMo9/8SU1UJ51oO0OVkRz/Kl25W2LXrKLagICkKiiL7\nWojYBBPTapnmihpmaMRfJOlMRyNw+8AwjGD1etyMyXoICEys1wsXP0Gy+Uskm77KK179ZaeP4+Ov\nbRsm0SlkFi1DIx4NzgBCM/T7bgBamuJo5TLhcBjBh2EejYSxaljMxVIJYbwfnknHqZ8vncDwUIzB\n4TEKxcmxlSBxCsO0UcMxjvVl0LTZmenOVpiWSVMigWjrVCoammGiGSaGYXDJlfNpai7gkAgn4H+9\nBsaFdvxmuee6s9QLhSBGue1HQhjHpW+bR2t7D34bqtHMG/n5Twad1wDkAKMHU9eJhP0z1XpGuSCF\nGMvmgv+IMxSNwO2DYqmErATPRAf9YMH50R7Ye5TbP6ew4/GPkx39KNmxP+fooTVTvKO3pFoLRRZ9\nRfnB2WREAkroDXgRDodRJOf6RcMqpukV3IhFVKzx45phVp2G2lIFvBmdg9b2IpIaolCySQ+PoWsG\niKJ/8JZEdE1DCcc4emIIXW+wmIMwsf4bhoGm61iWjQ20NCUJqyKWYSEIIogiq89dxo1fnMf5r/oN\nTc1foqn5q7S2+Si0AJ2d3rlgcMRd/HyfG/DCdxRyGqw7bwUf/kSRRDLtez6TdiZ1TF0L1IwXsHzb\nTLZto0j17S+JQnnubY4bgdsHuhHMloRpMm5R4Kc/GvDMdw8NXsQjD5zwPsGGSCi412lZFuEpzmPp\nDVOEk0Q8qjjth1AIUfAGbkVRkAQbbNu1SXvDxZ3Ek/UZHSSaHuENFzsMc1EWEeQQmbESxWIF02e0\nSJZktHGrTyUc58jxtO8GogFnXMshDTokJEEQqsG8KREjEZUxtEpVRGX1uUu55fYr+e6P3sZ3f7SR\nG255FanOba7XTHVscwux1MAwDCKhxv00EwQFbmcUzM8UxCJXKNLS2ca5L/PfHLWmnFK6qgiBlY8g\n4RVD13y1LAxj7vU+Zgc7ZpbBMP1t58Cx65wOQ+mZeWvD+I8tETwiZBoaMR8VtQmEGvrkJ422lmYy\nRwcIRWLEwiGyRc3jcBSPRRnLFVyLx7KVi/iLT8KPv/c/HD30WwQSLFpW4tJrlrFspTsQSKpCWTcZ\nGBplflenx4ymdvOnhOMcPtbPskXdvj3DsxWGaWJaeL4TgckOaiwaRpYl+tMZJNU7dbFm7TI+/w/H\nueeb32CgP8S8eRWuesdilxCL67Vta87LZb5QsCx7Rqmfbdvk8kVKZQNRUVEUlTds6mRfnRuiqj7I\nyrU2pq4TTwRvnurJhBMQBH+pU3MO6s83ArcPDNMigFCOYRoIfu7wNWhPFfyP13hrA062rUqBmwRw\n5rMDZ7tNk8QpshLPZoiiSDQsYQKKqqKUNQ+VRhAgFg0xMua+lstWLuIvP+OfrXneR5YwbJn+9Ajt\nrQnUGjvWeuKaFHKC99KFXY3gjfPbtiwQJcE7/lVXDQupCp1tzQyNFbBs2cM4X7t+OR/7zHxsyyQU\nUgCn3O53VzWMemaOoBTGtu3quVK5Qi5fRpAUpPH2oyI799Glb/8t37vzy2jaIkBH09Zy33cknvzV\nTzGNpbR3FHnzZd28/PdWV1/b0HWamv31zZWzQHhlAo1fqQ+m6mFruu4zLuTGpsu7PIzy9o6tHka5\nZehTzovatk1YnaKMbmjEokEi/Q1MhbbmBFrFkbaMx6MYurcPpsgyIUXACiCZzQwCkhomnclTrJHS\nNC3LRYwSBAFRjXH4WL8vYepsgm3bmJaNIDhM//rvQ6wL3LZtI4gCzYkYEVXA0Mq+36Ew7iYljEud\nmpbl2hAYhk4yHg3iVTVwErAsi8xollxRQ5RV1/ccCqmYhs6+XgFNux64HIddvprc2CZ6n17Fnl3X\n8stt7+cfb1HZ23u4+lxJCK6IyEEiVHPwgjYCdx1s2w6U8YPgEYharF67hI/coPO6i+5kzfp7eN1F\nd/LpW3Axyi3TIhZVpsy2Db0yZWAOh6TGGNgpIhqJoIhOQBZFkUhY8iWSJeIxsLVTDqYTV0dWQ4xk\nK+SLTtVFlGT0us3CRPA+enzgrA7eRo0il+PJXTe2J0tomo6mG1Q0E92wEAQJw3D86Fua4thmGU1z\nE9Bq+66CIGJaNpblcAtsbBTJRp2ClNpAHQJ+ooVikaFMFgvF16tbkR0OyXBAS7F2EiAztJEfbTlW\n/XdQcNZ1jUjI/9pJc3CNbJTK62CaJoIYnFHPhEkpSSIr1iypBur9u4/wox8c48SJQVIdRTZdPo+V\nq+YTCU+dLYeUqcvkscjsFRY4E9CciDCcN5BlmWgkSqWShTop1Fg0ggEUCgUE5RTaEjWLhqyqjOU1\nLLNAMhFD10xUtf7hApYY5rkTAyye33UKf9WZj9ppIidw155znNcsy0KSFVcytfvZI2z5/jH6+yN0\ndZW44soFLFjaQbksYJqmh+QpCCK2ZaMZBjIGbeMWrHNwnX9JUNE0RsYKWCjI09wr8ViE1rZswFk3\noTM9PrpnGDqxIAdEyyQUQCqU5bl3QRuBuw6ViuZR1KrFTBKhSEilnCshyQr7dx8Zt/68DnBkB3p3\n9HDj59O0rPe36AQnMCfjwYYjpqGRiLdN/2EaCERzU5L0aB/IDqkpHouQLZSR5cnFQRQFFEkkFouS\nLxSQlJkzjm3b9jBjZUUlX9YxzRxtTf7XVxRFDDNEX3+a7q7UKfxlZy789K9rv0JNNx12ed33uvOZ\nA9zwcRgceA8AO4CnntjGLbcNsey1XRzL94GpouuA4LDTbctCkSxCkkhzU1M1Ixen0HBowAvbtsmM\nZilpFooSQmLKQiLgjGldeuVC9u92E9TqjXwAUuOje4JtEVL9NwRTGYvMRbewufcX/Y7QDX/t3ZOB\nLMtMaAf4WX9mhjbywL3HfJ45CcE2CAWUfsBRAGuUyX83CIJASzxc7WErikJIEj1lalUVHUJbJIKp\nzVztzAzwdZZkhbIukB4eDXyuJEnkNYGhzMiM328uwG9fPPE718eDNnj73N/7zlEGBy50HRscuJAf\njCuktbY20ZxM0N4Sp7M1Tqo5SqolxvzOVpqTCSzTxhwvm08bdRoAnGtVLlfoGxxBt2SUmix7JmvT\nyjVL+X83aPzhhXeyet09bHjFv5BoOsKEhjk4Zj6XjVt6KlMQB4OCs6M6Offy07n3F/2OmIqYBgRT\nKeuQiEUYy5YCrD9hoD84m7Zte9rZ7li4USZ/IdDe1sLI0T7U8HjWnYiRGc0h1WTdsbDKUCbnlNSj\nYYqlMqKscnj/MX728ADD6RhtqQJvuLjTNRYmit5Rpuo5WaJckegfHKarw79yoqgqI7kyqpInmfA3\nmJlrcDZNXvvNCe7JRKItCgK1ne/+Pv9KSH9/BEl0+qrO6zv3uKJImKYxuREQhXGmv4naEGCZEUZH\nsxRNBdmnCjXTnGLF6iUuV7D9e47wkx/dydBgtMoqX7V2NWOZHImk/zXWtUog01zXK8SirTP7MGcQ\nGoG7DlOJqziYWeRWZJmmZISOjoKP9eeErnLAZ9ArJJqCZ7dNvUKivVEmfyEgCAItiTDZslmttCSi\nIXIlrerHHolEsK0RQEaWZRLxGDuf3sPX/qGZ0cwHADiwG57d8QiLlj5MpbKY1lSeCze1s27DqqC3\nBlHAQGVwaISO9hbfhyihMP3DeVRVOWt9vEVBoGJYrraDosiUKnq1rdXV7X8/dXeV2NN7hDu+uof+\nvjBd3WWuuXYx689bjiS6M0NRFNB1jXjk7NgknSoMw6A/PUJRE5ADqoJB3JypYOMN5BMQRTvQUU/E\nQq0ni4xDlYQ5OZffCNx1MC1rygbCyXB9FVnm6ncsZfdOtxdtqmMrV2xe6Hrs7l2HuH/LMQb6InR2\nFbjuvStZv+Ec39dVG6YiLyjaW52sW5KcBVtRVUK6QcVwgrmAQFiVmFAwFwSB/9k6ymjmKtfrOKMs\nBWAz7IYDz/bw4U8eYbnPQgSAbSOKIpopkx4aJdXuv1lTw1GO9WdYtqBjTi5C00FRZEpaxcU9cTJl\n5240TJMr376Ixx/b5iqXd3Ru45W/r/ChP8vT3/cn1eNPPL6d224/yIYNS33eTcC0LOSz8HueCXL5\nAsOjRZRQBFEqBz5OEgSCtACdEnsZ3TSxTMfIxxyfrJcExyYiGlarrl6WZU05Fqso/tfKsiwS0blZ\nmWwE7jpYlj2Vvwg+lbwpsWbdMv72lkM89MC3eP6YQmdXiSs2L2RNjXLT7l2HuPnTkB68DoCdO2Dn\nju3c/k8HPMHbsiwSjTL5Cwq/rDsWi6KP5WDckz0Ri5AeKSKP7+z9VPAcuEdZHv3x13kT8OiP+3j+\nqEQhP0A0FmbhkjgXXpzi5eevQpREKobN0PAY7W1N/q8ainH0+CBLF3addZs2URSxHTUW13FJEMbn\n4eG8DefwhdsP8v177magP0JnV4m3X7uY73/HoL/vAtfzBvov4Hv33M15G5Y5M+C1WbfglMwl0ev5\nfTbDtm0Gh0YoG6CEnDbfVN+PKArUCpbt23OEh+97nvRAlJb2Ahdc3MWyVYtBAkHyBqJ8UUNVdOLR\nKJbhL2UKYBoG8Zh/tm3oFZo62k/q7zxT0AjcdTAt+wX/UtasW8arX7uWsTH/ct79W45Vg/YEBvov\n4J5vf8sTuI1GmfxFQXtrC6M1WTdAMhFjZCwPRFFVBVmcrLe0dxTZ2+v3Su5RlueP5vnnW0Nkhv60\n5ugveO5wB7ufeZ6PffYQa9adgyhLlHSDzEiW1pYACVw5wvH+NAu6O07575ztEBD8CWp1m+kdOw7w\nrbsP8vzzIbq6y7ziVTJP/Nagvy9CV7cTtNetX86/9A/6vk9/X5iQqqAbpkvRThAcjWzDMFGUxvII\noGka/UOjCFLYNUc91b4mpMqU8hqCIPLMM/v46peSjGb+rHr+wO4ePvCR5zxSwYf2PcfPHhkgk47R\n0pbnLVd08erXrPLVPgewLZ1IxH86JxKau5XJxi+zDtOJZIkCLlKMq8Td7c2mZ4KBPv/dZH+ft6cZ\nabDJXxQIgkBrMsJoaTLrFkWRZCyMMW4UEo0o5CuOAM+bLu1m984eMkNTj7KMZPrJji4EHsAJ6mtx\n7Ay3kBnezMP338madc7mTJJlChUdcTRHc7N3MRJFkYouMziUoaN97hFuYIKI5j0uC2L1vtux4wB/\ndX2F/v7J8vejD/8Ey1rMBCP5yce38YXbDwb2vru6ytUZcdO0kKRJkhqcXEtsLmMsm2MkV0ZRvRWm\neoKgC4LE6FgeJJXtj2QYzWx2nR4Z3sjPHrnDFbgP7XuOO26PMjL8geqx/c8+yoJ/HWDxkgW+bzOV\nIEtra7Aq5ZmOxjhYHaa9YWuC5kSJu+eR69i54xp6HrmOmz/tHD8ZdAYtLt3u0SND12hKNCROXyy0\ntjRjGe6+naKqRFQRy7KIx2JYhqN2tnz1Ej78yQqvveDrrF73Hc47/589oyyxxDcp5F6HI+c4Ies4\niDPN75TU60vukqyQLZtks3nfzygpMqMFg9GxIPGKMxuiKPpOdojy5Jjet+8+TH+/u/xtWW/G8Xh2\nMDhwId+/5yhvv3YxXd3bXY/t7NrGO/94CeBs2CYU82zbrnpAC4KAcRY7ttm2Tf/gMKN5A0X1Tyz8\nEgjDMBgezTGSKyFKErKikAlQSJuw8JzAzx4ZqJvphtHMm9hyz1Hf51uWRSSg9y1hzWnXxFPKuG3b\n5sYbb2Tv3r2oqsott9zCwoWTZKtt27bxla98BVmW2bx5M1dfffUL9oFfTDgG8FM/RhSEanT3K3Gn\nBy/i/i3fOKms+4rNC3n6ia0MpScJbJ1d27n2XUtcj5MEx4qygRcHgiDQmggzUjRcfr/xeIx0Jgco\nREMyFcvpfy5fvYQP1RDPDu45wqM//jrD6SjJ5iy5bIndz7yn7l2cbHsCqc4S+3Yf5sEfHic9ECXV\nWeSSt81n2fL5yEqZaMS7+KihMOmREqqiBPb+zlQ4wcBLJAmrCqVyCUVR6DsRdA+4uR8D/RHWrV/O\nv/77ce78mtP77uoqcc07F/KKV05usGxbcMbNLAtZnnxt0zw7SWqmaXJiYBhBjiArU/SxBZjwyrFs\nm7Fsnorh6CHIIkhyGRtoTRVgt/f5I8PP8aXPCLSmCrxhU2dggA8a9TMNjViLl9Bp2zaxyNwuJp/S\nX9fT04OmaXz3u99lx44d3HrrrXzlK18BnB3XF77wBe69915CoRDXXnstF110Ea2ts7+0Z9v2tLyz\nWuGHoBL3VDPaflizbhk33rKXh3/0Lfr7QnR1V7j2XUtc/W2HIdnQUX6x0dbawkj2RFVNbQJNiTij\nYzmakgn60iPIqncxqQ3k2Wye2286EPAuBeBVtLb1sO7lAl+8UWY4/T7n1E7YtWMrH7/xOCzvokuS\nUFUvGVEJRzg+OMKyheqcY5rLkujxCxBFsSpq1D0vSATHzS+YGLnc8LIV3Pz5+c5B2+tvL4oClmXj\nnWA6+1pS5UqF/vQYSmj6yp4wnsQUS2VyxQqyHKJ2YisSCpMtVHjDpk7211l4CsJPGB58G8ODq2E3\n7O/toXuhf6Wyq9ufva5IAVm/VqZ5jvOATqlU/sQTT/C6170OgA0bNrBr167quYMHD7J48WLi8TiK\novCKV7yCxx577IX5tC8y7FqR5ADIslRV2goqcU81o+0H09D4/Vev5fO3beSu/3wdn79to5dNblRI\nxBvzpS8FOtqS6HUKaYIg0JSMY5llYmF5WhMQQRBoaa+3d90DbEEQx2hN/ZALLtvFzicthmsqLQDD\n6Yt48IfHkdUI/UNjgaJASjjOsRP+5KszGZIk+TqyRUIKtg3vevdSurrc5W9R/Am1/IKOzm28/drF\nntcQsFFkb75i23jkaQXByT7PFuTyBfqGsjMK2gC2bTE0PEa+ZDra5HVLp6IoiFgsW7mID3ykyKv+\n6A7OWfNt2jpuxbYn+QjAeFAv0dLmdlVsbe/hqncu8by3aRhEI97Ki2VZJGLKnLfGPaWMO5/Pk0hM\nkmdkWcayHNJO/blYLEYul/vdP+lLACfjnjpwK4qMXdBAFLli80J2PDn9jPZ07xmSherMYhAaEqcv\nHZKJOCPZgofvIIoiTYkYNkUKmaIn63ZK5X0MDUZpacuzfI3BgWd7GM1sxAnag8BmbAvHv8c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AEeeeAuivkYqXnFa+BVODctL6/o174kymGKJf+QuRIOc2SiyJrlQ2dE3rYTsUiEWAS0ZhPDsLAd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\nnFlVe1Xly/na3/9Xi2iDJ/47t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gmm16 = GMM(n_components=16, covariance_type='full', random_state=0)\n", "plot_gmm(gmm16, Xmoon, label=False)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Here the mixture of 16 Gaussians serves not to find separated clusters of data, but rather to model the overall *distribution* of the input data.\n", "This is a generative model of the distribution, meaning that the GMM gives us the recipe to generate new random data distributed similarly to our input.\n", "For example, here are 400 new points drawn from this 16-component GMM fit to our original data:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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Zj3QbKMrgJvIhHzTY1dWCL3zhRr8SP8We/0Y87lrlm3A6f4CeHvEamUwtkI48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\nKEbkN6o339yOiYkyAMvQ0zM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Xnew = gmm16.sample(400, random_state=42)\n", "plt.scatter(Xnew[:, 0], Xnew[:, 1]);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "GMM is convenient as a flexible means of modeling an arbitrary multi-dimensional distribution of data." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### How many components?\n", "\n", "The fact that GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.\n", "A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the *likelihood* of the data under the model, using cross-validation to avoid over-fitting.\n", "Another means of correcting for over-fitting is to adjust the model likelihoods using some analytic criterion such as the [Akaike information criterion (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) or the [Bayesian information criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion).\n", "Scikit-Learn's ``GMM`` estimator actually includes built-in methods that compute both of these, and so it is very easy to operate on this approach.\n", "\n", "Let's look at the AIC and BIC as a function as the number of GMM components for our moon dataset:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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F2WJjXIQPd16TRGKkr6NLE8NIYbPZbI4sYKz+Vf+X/Jc51VrE07MeJdAzoN/9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\nLctGjaFH68z2i14MagqrWN1Z+IN+HK85hYMVh3G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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_components = np.arange(1, 21)\n", "models = [GMM(n, covariance_type='full', random_state=0).fit(Xmoon)\n", " for n in n_components]\n", "\n", "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n", "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n", "plt.legend(loc='best')\n", "plt.xlabel('n_components');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The optimal number of clusters is the value that minimizes the AIC or BIC, depending on which approximation we wish to use. The AIC tells us that our choice of 16 components above was probably too many: around 8-12 components would have been a better choice.\n", "As is typical with this sort of problem, the BIC recommends a simpler model.\n", "\n", "Notice the important point: this choice of number of components measures how well GMM works *as a density estimator*, not how well it works *as a clustering algorithm*.\n", "I'd encourage you to think of GMM primarily as a density estimator, and use it for clustering only when warranted within simple datasets." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Example: GMM for Generating New Data\n", "\n", "We just saw a simple example of using GMM as a generative model of data in order to create new samples from the distribution defined by the input data.\n", "Here we will run with this idea and generate *new handwritten digits* from the standard digits corpus that we have used before.\n", "\n", "To start with, let's load the digits data using Scikit-Learn's data tools:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(1797, 64)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.datasets import load_digits\n", "digits = load_digits()\n", "digits.data.shape" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Next let's plot the first 100 of these to recall exactly what we're looking at:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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e2fn5eTBY9cLR0FK8dSXGCsa8TOKc6BvO6v7+fgDMT58+2bt37xLTpkql0lwp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_digits(data):\n", " fig, ax = plt.subplots(10, 10, figsize=(8, 8),\n", " subplot_kw=dict(xticks=[], yticks=[]))\n", " fig.subplots_adjust(hspace=0.05, wspace=0.05)\n", " for i, axi in enumerate(ax.flat):\n", " im = axi.imshow(data[i].reshape(8, 8), cmap='binary')\n", " im.set_clim(0, 16)\n", "plot_digits(digits.data)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We have nearly 1,800 digits in 64 dimensions, and we can build a GMM on top of these to generate more.\n", "GMMs can have difficulty converging in such a high dimensional space, so we will start with an invertible dimensionality reduction algorithm on the data.\n", "Here we will use a straightforward PCA, asking it to preserve 99% of the variance in the projected data:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(1797, 41)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.decomposition import PCA\n", "pca = PCA(0.99, whiten=True)\n", "data = pca.fit_transform(digits.data)\n", "data.shape" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The result is 41 dimensions, a reduction of nearly 1/3 with almost no information loss.\n", "Given this projected data, let's use the AIC to get a gauge for the number of GMM components we should use:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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WtBDt6TeD1d+P1Kt6UFVTxxd5pWaXIyLSLOeqanl5eTbvbzlCRHgQT81IUuD7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\n6gXOOmr4ZGcxG3Z9/Xh9d24c2UvH60U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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_components = np.arange(50, 210, 10)\n", "models = [GMM(n, covariance_type='full', random_state=0)\n", " for n in n_components]\n", "aics = [model.fit(data).aic(data) for model in models]\n", "plt.plot(n_components, aics);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "It appears that around 110 components minimizes the AIC; we will use this model.\n", "Let's quickly fit this to the data and confirm that it has converged:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n" ] } ], "source": [ "gmm = GMM(110, covariance_type='full', random_state=0)\n", "gmm.fit(data)\n", "print(gmm.converged_)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Now we can draw samples of 100 new points within this 41-dimensional projected space, using the GMM as a generative model:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(100, 41)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_new = gmm.sample(100, random_state=0)\n", "data_new.shape" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Finally, we can use the inverse transform of the PCA object to construct the new digits:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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BJ+rXGw6RKlDWP7WBoEliaySO1Gq10Df59PT0T0OYitypBdZ4rCZqaUkVzqzZ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\nwevBls0zd7H2ztp0eY6IAsmInBRGqSqU9pGh8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "digits_new = pca.inverse_transform(data_new)\n", "plot_digits(digits_new)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The results for the most part look like plausible digits from the dataset!\n", "\n", "Consider what we've done here: given a sampling of handwritten digits, we have modeled the distribution of that data in such a way that we can generate brand new samples of digits from the data: these are \"handwritten digits\" which do not individually appear in the original dataset, but rather capture the general features of the input data as modeled by the mixture model.\n", "Such a generative model of digits can prove very useful as a component of a Bayesian generative classifier, as we shall see in the next section." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "\n", "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }