{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Plotting Examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we demonstrate how to write a simple [`Model`](http://python-qinfer.readthedocs.org/en/latest/apiref/abstract_models.html#qinfer.abstract_model.Model), run an SMC updater for several experiments, then plot the resulting posterior distribution." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Preamble" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before anything else, it's helpful to take care of some boiler plate. First, we want to enable pylab inline mode so that the plots will be associated with this notebook." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, it's a good idea in any Python 2.x program to turn on the `division` feature. This ensures that the `/` operator always returns a `float` if its arguments are numeric." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having set things up, we can now import the parts of **QInfer** that we will be using in this example." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from qinfer.abstract_model import Model, Simulatable\n", "from qinfer.distributions import UniformDistribution\n", "from qinfer.smc import SMCUpdater\n", "import scipy.stats" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Model Definition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this example, we'll be using a very simple likelihood function,\n", "$$\n", " \\Pr(0 | \\omega_1, \\omega_2; t_1, t_2) = \\cos^2(\\omega_1 t_1) \\cos^2(\\omega_2 t_2).\n", "$$\n", "The model parameters for this function are $\\vec{x} = (\\omega_1, \\omega_2)$, and the experimental\n", "parameters are $\\vec{e} = (t_1, t_2)$.\n", "\n", "This likelihood function demonstrates many of the core concepts we want to explore here, but is simple enough to implement quickly." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# We start off by making a new class that inherits from Model.\n", "class MultiCosModel(Model):\n", " \n", " # We need to specify how many model parameters this model has.\n", " @property\n", " def n_modelparams(self):\n", " return 2\n", " \n", " # The number of outcomes is always 2, so we indicate that it's constant\n", " # and define the n_outcomes method to return that constant.\n", " @property\n", " def is_n_outcomes_constant(self):\n", " return True\n", " def n_outcomes(self, expparams):\n", " return 2\n", " \n", " # Next, we denote that the experiment parameters are represented by a\n", " # single field of two floats.\n", " @property\n", " def expparams_dtype(self):\n", " return [('ts', '2float')]\n", " \n", " # Valid models are defined to lie in the range [0, 1].\n", " def are_models_valid(self, modelparams):\n", " return np.all(np.logical_and(modelparams > 0, modelparams <= 1), axis=1)\n", " \n", " # Finally, the likelihood function itself.\n", " def likelihood(self, outcomes, modelparams, expparams):\n", " # We first call the superclass method, which basically\n", " # just makes sure that call count diagnostics are properly\n", " # logged.\n", " super(MultiCosModel, self).likelihood(outcomes, modelparams, expparams)\n", " \n", " # Next, since we have a two-outcome model, everything is defined by\n", " # Pr(0 | modelparams; expparams), so we find the probability of 0\n", " # for each model and each experiment.\n", " #\n", " # We do so by taking a product along the modelparam index (len 2,\n", " # indicating omega_1 or omega_2), then squaring the result.\n", " pr0 = np.prod(\n", " np.cos(\n", " # shape (n_models, 1, 2)\n", " modelparams[:, np.newaxis, :] *\n", " # shape (n_experiments, 2)\n", " expparams['ts']\n", " ), # <- broadcasts to shape (n_models, n_experiments, 2).\n", " axis=2 # <- product over the final index (len 2)\n", " ) ** 2 # square each element\n", " \n", " # Now we use pr0_to_likelihood_array to turn this two index array\n", " # above into the form expected by SMCUpdater and other consumers\n", " # of likelihood().\n", " return Model.pr0_to_likelihood_array(outcomes, pr0)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we've defined a model, we can make an instance." ] }, { "cell_type": "code", "collapsed": false, "input": [ "m = MultiCosModel()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The prior we take to be $\\pi(\\omega_1, \\omega_2) = 1$ for all $\\omega_i \\in [0, 1]$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "prior = UniformDistribution([[0, 1], [0, 1]])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can pass the model and the prior to the updater. We will use 2500 particles." ] }, { "cell_type": "code", "collapsed": false, "input": [ "updater = SMCUpdater(m, 2500, prior)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's run a few experiments." ] }, { "cell_type": "code", "collapsed": false, "input": [ "true = prior.sample()\n", "for idx_exp in xrange(50):\n", " # Use the variance in the posterior to set the time we evolve for.\n", " # Note that this is a slight generalization of the\n", " # particle guess heuristic introduced in [].\n", " #\n", " # We slow it down by 30% to ensure unimodality, since we\n", " # don't have an inversion argument here.\n", " expparams = np.array([\n", " # We want one element...\n", " (\n", " # ...containing an array.\n", " 0.7 / (2 * np.pi * np.diag(scipy.linalg.sqrtm(updater.est_covariance_mtx()))),\n", " )\n", " ], dtype=m.expparams_dtype)\n", " \n", " o = m.simulate_experiment(true, expparams)\n", " \n", " updater.update(o, expparams)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:15: ComplexWarning: Casting complex values to real discards the imaginary part\n" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the [`plot_posterior_contour`](http://python-qinfer.readthedocs.org/en/latest/apiref/smc.html#qinfer.smc.SMCUpdater.plot_posterior_contour) method of `SMCUpdater`, we can quickly produce a contour plot of the current posterior distribution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "updater.plot_posterior_contour(res1=60, res2=60)\n", "plot(true[0, 0], true[0, 1], 'r.', markersize=12)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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0uJB6+RGfBNFxcPwsnEsBf1+o6getasPATlC9Yr7eziXx8ans3n2GyEgjcBvPCRw9eo4y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\nhqPIx0NFNv9L5PQOZTdqQYayE7XKahZmivzwpuK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PPPJIg2o1hxr9zZtfKjAwatQopk+f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\n", "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using [`posterior_mesh`](http://python-qinfer.readthedocs.org/en/latest/apiref/smc.html#qinfer.smc.SMCUpdater.posterior_mesh), we can also get to the raw mesh of kernel density estimated points and feed it to other plotting functions, such as [`imshow`](http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.imshow)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "w1s, w2s, Z = updater.posterior_mesh(res1=60, res2=60)\n", "plt.imshow(Z, origin='lower', extent=[np.min(w1s), np.max(w1s), np.min(w2s), np.max(w2s)])\n", "colorbar()\n", "plot(true[0, 0], true[0, 1], 'r.', markersize=12)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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6b5LIho45DL3d2kkbkmWlSLYVmlrnGHd6UFbens92491MvO2Kl83lWpa+/Mfr\n1NZC11n+1V/9Ff/wD//Al7/85aHGD4Tlnj172LBhA+eeey4AN9xwAzt37uyB5cjISOf59PQ0a9as\nGTBjWX9JAwcABUKBVF2jrYJeMj5aPJq8SIgGYBp06zAbwDQwUxxlCfCOESW0G5+pgpFFvFSpYoyy\nrE/XvQ5AFJ9FWPff+RiyiJsK/TjH4LQAroqkVl7cQ8/vpMwVt0ufXFC6MJwvAeOC2D237Hz3F+nh\n6nVytJB1lrt27eK9730vDz/8MNVqdahzBl593759rF+/vvPz+Pg4jzzyyJxxn//85/mDP/gDfvKT\nn/CP//iPA2b8G7qm4guBF80dYvI/Rbc2VhTHSmAZvUlku1RRoRNCs8UxQ2/LSrsHb6fnr4BE6sfU\nwDOANC+y8rmGaSdhVABEBNrFl0G5590xUEX3M3X+RojevxNm6Wa7OKc0k471aAPKZL36QXEQyMpA\nZ8c2XViWQdJD02uuJicnmZycXPB5y8qChtGNN97Iww8/zP79+1m/fj07duzg3e9+N+12u5PoueKK\nK/jgBz84cJ6BsBRiPstE69prr+Xaa6/l61//Oq973ev4z//8zz4jX4f+Mpp+lSUyTYjqdFfxnAGs\nLp7b1TNuP98W2rpsoIHZorf8qGc1kNCAakm9GqgtNLQSpWOfaQGAvCyLLkDKIgElSnI7wqqRF91K\noZ5qIaE/Z0tAowg5JOYPSVl5jvtvoeifDHLHzQdNM3+ZG16WAHLjux6UXl1t2bKFLVu2dH7esWPH\ngsx7rG74Aw88MOe1m2+++ajnGQjLsbExpqamOj9PTU0xPj7ed/yVV15JmqY89dRTnHHGGSUj+sXi\nLJmOZ3VgObAKWAOciQZmWbmheUzQoDTF7DN0rcwG3VrNhAKsQh9NegvgzW26FUDuxzAQLEuKK9Gb\nDDfhTROqNR3dQqGXb7aNRecWmdsmq6uMuRaoraOB2KB/F3uefrWrHpheJ1an9HLHTZs28fjjj7N3\n717OOeccHnzwwTmU/uEPf8izn/1shBA89thjAH1ACd1YXFnZTXEIqQFSERqYI8WxDG1p9gCJridq\nvqtVpQ8FMskR7RyZKERbkbcFeVui2hLVEHBEwBH0ow3WWeYu6nGZYFuT7mEbhhm9JaXz1nQbApuG\nHi4s7RuxG3/Ya8xDeik/H9Rci3JQsNc+x01mDZKHqdfxabGXOw6EZRiG3HvvvVx11VVkWca2bduY\nmJjgvvumY9jRAAAgAElEQVTuA2D79u185jOf4WMf+xhRFDE6OsonP/nJATPaNHEDfcXrUmoXtWhv\n2UnuLCsOO0ENXR5kQKy6sKzkCDIClRGSInJF1g7IWgFZO0RNSzggusch4DDdSia7/NEusSzry9GP\n/SZ+afjlLoLp4aCwJjMQdEuNzF8HcxgomliODUoTpHWXbrpLOG0I24/meT/IuRCXfca783l5HZsW\nG5ZCKXVS/g/W8c+vob9cxg+1d3AsjlUhnB3AOnMAZ6MfV9F1pdvM7Y07omBFDitzWJETRQlRlBCG\nCYHMSFoxSSsiaUXkhwP4uYQnpX58GjgAHCwebbbY4EyZyx3XwmxZR0IvIN0VjLNoSB8BjqjiBRN0\nbdNLVfNXodOzzjpMhsjdoiKll/j2XxrhzG3HJN219bnzXlnXpX5wLVtF5XWylefvHDoPsZASQnC8\nmBFC8Hz1L0ON/TdxxXFfr0wnOQhgU8VYQU4zCCF10iQUvQ3Iq+i8kPm3Nt8/u++F2UqnyKiLmkLW\nMsJqQhBlqLYgb0He1parKpIqqq2KjDjdeCb0Jp2NO24vITeP0GtNGji6C3b6hRd7jMfiRFVh7qoj\n25y2A6LGdTcdjMz7htQmHuB2YC9LGtnPyxI6pTdtjXNl/pp4UHodn1pUFvX6ixQxteNyTvMJUcQt\nHe+8w1R7bzEDyxSdnJHoXpgVqWGphE5Yx4pAZOQyJQwFSklEpFdK5pFAhbLX4qswt2rGGHABXaDa\nTdANK4zr7VqcZaFH2yOW6LIiJfWNAd1lmDaIBrnNBq42OFO6+63bh3u+uWnXaiwrrLf/cUwmzMRM\n3Xinl9fCaLHd8EWEpakRMit4bF+VomibXljauz2A/i436WbBheh69VGg2VtRBFlOQEYuJSqQKJLi\n0gIVBYgIlNOwvYcFCu3l2vXidr9hmyHQy7VhYGl/zrz4HyIPQLnWoHImGBQ8Nb8gO4ZpiG9nx1yL\nsMzNNrL/gpTFKN3mHl5eC6clCEu75sbQyV7ZI0rzPj3rws00ZtdYs3pHoZtsxAIiEBWBrIPMcwKR\noaRAhUIvBY8ERAEqyrUhZ1uVxgO2uWMnZ4yHaxtVtgxDbOCWJbRdyzJEr0hS5qK2/w/d7Lg9iZui\nt3uEulvy2il4N/FjA9S1LLHOE85z94Pbj15eC6cltq1EYUEGIcgQgkAfkSwOdE3lOuAs4EyQZ2QE\nqzLkygy5PEekCjKFSEFVBZkMyYKATISosLAsAVqQtwKSVohoxWQtQaYCchWQKUmeB+RKoISYWwNZ\np5cHbl7DXqEJvR5smdfqrux0Y5o2WNsUK4uUXlWkCsAp6Zxo+/82ME0tlXnPTdS4JUH2Bytb7mSu\nY9dKufLJG68Tr1O6zvKEXE7IApABhIHenKxe1FTWhYblWcWxFuSajHB1m2hlm3BFgsgVMssRuSKv\nBbSDCm1ZJZcBKhfdnhgtyNuStB1Cu0LaDlAIciRKCfJcopAoacHSJJLsukqYmxuxS38Mb+ykD9a5\nopgbenljwgpuxVAnDCiK9eoFKJUxae1N2Gzg2dnysvpKl+RYr5dl0F3T19zkoNIgL68TpyXmhhfL\nXYJQw7ISwEjQXfu9gu5qnTOBtRCckRGtblNZ2SBe0UKqDKlypMrJ6iFCKnIZ0JaxTrpYm5vlLUnS\nishaAtkuftGFF6mygFxJlBCaQ8ayrNFrVBnP12aJ3UXNruYxFTy2pPVoW5AmCmFHIGxLM0W3mcuL\nE4SyrEuzD5ABmkvusjIe1+Qtsyztw56nLH1vNKhkyMtr4bT0YCkK17sSQF3CcqGXMa7Rh1ijEGfk\niDUKuSYnXt2isrxJdWSWSrVJQIYkR5KTBhF5FpCqkFDEpLMKmhLVFKiW0FajEBqKeYAQSh8oDZ9A\nzd3dwYT83I7sdk4qoTeRb5cQDeKRHVp0V/rYCSwTYswoenUa0tr/XGUAc2sq7RsqixG4tZP9aivL\najFteVB6nXi12sfWSGOhdJJhGWlYRqF2v5ehLUrL9dZud0J4RkK4OqE62qA6Mks1bFCh2QGlJCcJ\nUrJKSLosJJUhshqTNQPyZkjWDBHLFaKukJUcEeRImSOkQsoclUmyWEIlR1VBmdIjUyZke6QGhGYd\nuA0zU6FjxzFt5vRL7tgQti1NO3xY1IGCKLLj0Gua2iaxqWcyh+uGl5G77Od+4Bv0vrcuvU68snRJ\nxSxjXd4TBVCTMCp6YXkOyDU50ao2lVUNKquaVCoNqpUG1ahJhZaJOiJQBDIjrWpQppUAmjmiEZM0\nBDQDqCtkLUfGOTLMkDJHFtBUuYQ4IK+EUFE6g25AWNbazV6FaCeaFb1Zc+OWD1PtY5I9brVPp/i9\nODEv3PCOdWfqL826cHPSLN0UfVkR6HyQHAQ7Nz5qv+7KF6F7LbyydEm54VEBy1DDcpnotmDrwDIj\nWqljlPWVR6iKJlVaVESTCm1EAUqBIgxS0iAkrYQkBKgWMCvIGgE0QMQKUcmRcUYQ6EMGOUGQkSsN\nSlnJdVLH7o9pqnUMtBTd+KLZ0setr7QTPXaLSQNamAtKA0vjgkvnuik6Zpm6LreZzAaYMX8zussk\n+8UE5kv89JNyHucb5+W1cFpisLS+bHYcMFIaQjUQ1ZwgTonDNhXZIiJBkhX2kgaA5owiRyLJiUWb\nGrMEQUYcJ8SqTSJaiChDRDmEOdKAUmbFap4AYoEYEaAga4WoI5I81FnyORwx67ordHtc2OFAe6mk\n7XbnznN7BSL09sEwWXO3vlQ4h4TOnkKKIlsOurK+AiopJrJT9Pa6UHevdJOZMjdWVjpkbqzs39N9\nzwa1HfcsK0gte+7lNVdpsqRgWZhZokiw9JTRKKgqZCUjCFMi2aZKq5PQUQgyp69ZB5a0EeTEMiGN\nWqQ0dfInEJ1DSTqgDMhQUiIqxWyhIm1EZLUQwkhfx/VOTQmQ6Vlsf7dtUMb0wtJO/JjMusmY2ywy\nvwu7rNHt7WvXaJpKItM3M5egQlBFSl+Z9eAuKDtt4untShLSBWbinFOW0LHDAm6hum2B2mZ3v/c8\nKL3mV54dO67uuusu7r//fpRSvPGNb+Qtb3nLUc+xCJal9eUw++2ESrdXqyhEnBNGKbFMihhl94uU\nFWaWsoBpYBnRJpcBWRiQBSFZHpCIiFSEJCIkF7IDylCk5IEsXGoFNYWYzjVjItktfjXfcX0h/duq\nMjckZ0BprE5b9iofY1lC1xo1zDBwNPPaqz/tVUD2Ip1c9HrgKoS8Uszhrge3V+UYWEbWo9ts00DT\ntghdsLmQcxt/mDE2KAfFSD00vQboGN3w//iP/+D+++/n0UcfJYoirr76an7913+d5zznOUc1zyLB\nkq5lGYAIFcQ5opITxglR2KYim9RoWLlvfWTWc6DnXSEyRKCQ5ARIROECaqMuICTtHEqIAjrFPdUg\nrwRkUTh3PzXobZBkJ2bsqpqyhTJYY8oWwNhj3Qx5Wd9LO3veAa4orh+AMP+kpomGa1Xa1A6tRxeU\nbevnsn6Yrnvupv3tDyj6nGePMfMMkofpklbz2HD1/e9/n8svv7yzMdmLX/xiPvvZz/K2t73tqOZZ\nnFy89cUXgUKGOTJOkdWUuNKiGjapBQ1GmCEjsBAXohCkhCTEZIUbLlAdV72zSqcYlxHoGCQUEM2I\nOuaduR2FkgFZGJFWlF5NZO+ZYxI8xk3O6W5bcZhu42DzvGyloKnRdPfiMauGTJLJNAly2WUXt5et\nN+/JGDm/ZFJrInNjdoF7aD2P0GayeTTQdYGL9dgJpFo3VFYCkDuv44wdVh6aS1Jpn9f3TMKjk31P\nu+iii/ijP/ojnn76aarVKl/4whd4wQtecNSXXzxYWiCQUUYQpwSVhDhuUQ0b1OUsI8yQEtImJiFC\noEgJyZG0iUiL2zfZccDKlfeC0wA1JC2FZSYjkijT2fEaXW6YzkImG26MMheW9mHzQtLNoFs9jrvd\nkazXbM/Ztmzt0iKXSdjPbTdYOo+dICfdZZMpvYS2q/LtzYXsbkWu7Jhl2VFmTdpueVmss5/cmKfX\nklI/WP7SFn0YfXBHz9vnn38+t912Gy972csYGRlh48aNSFnW42CwThnLMohTomqbuKLLhGpCw7JN\n3HGzc2QnC94mHmprTBudxrIMSTsWqRmTypgwTBGxA0uTGDbQMqVF/WB5mF7QGRiasqMaXWvSQNS2\nJCN6E9O2dQkDLEuYC0bbqrQ7mhvr0vjyppWbu1lQmXvdD3xz0vWUJ3TKgOtao/3kk0FLWv1gOYRu\nvvnmzo6Of/iHf8gv/MIvHPUcJxmWVRASogjqIawQyBU58WibamWWWjDDMnGEETFDBV02ZFAHOvvd\notJxyo1bbqxHIwPBgKw4UiJSKrSo0Cqy56pzbo5EBjmiohAj6F0l3f133LyEAeY0MKv0drqJ6jIo\nFMVeQqK7f9Ay9J5Cdbr7otutPEUx35Hi0SSMzJHRC2KTyG4X56b603cacHRu1nWh3a0g7PIe446X\nmbWU/CLceKNr8g4bj/TymkfJ/EP66cknn2Tt2rX86Ec/4nOf+xyPPPLIUc9xkmFZ1/WBcQijIayU\nyFUJ8WiLkcoMy+RBVohD1JmlKpqd+KINy7iwKSOSTkzSTvjY1mJA1smUx7SpdB5bHVBmBNrKLGCp\n9/GhN+5o6ryNNwrdxsMdWOaQFdAJpG45VxPdLX1XFsdy9AZsZiM2N+N9uHjvMHO3KrJbUpoSJDue\nCQXz7ISKnf22s+Ou3OVI9mFbiW6Sx7UcvbxOkLL5h/TT9ddfz1NPPUUURXzwgx9k+fLlRz3HSYZl\nTX+fKhJGJKwSyFU5ldE2I5UZVshD2rJEW5Zh8aV2YRmRdLPaRTzSWKCycBO1261hW6VJlSYRCREJ\nMUkHlCmhzrEHuV7xY+CmL9zlzWxxGDaYrSzM1rltBVkGIteNQmK0VTkievc/X4m2MJcXh1tLOULX\nVbdjmzFzOxo1rfNsfnVYaL/gFqD3c5ftVH9ZgLQMmEcf//HyOmodhxv+ta997bgvf3JhWYs1L0cV\nYqXuLhSekVBZ1qRenWVZMN0BZVD8GbETMzmSCi1qNArI5SSF3ZgUBY5mvEBRZ5Yas9pSpVnEK7Vr\nbixSDcxAL4espgSjKYFKO3MBkFJsRyFQqUAFRamOAWbbcsFRupuRyaobq9J0VlpFF5QGlvpiek4b\nnm5nIrOBo126aFu/9nNVAK4nH6LQu7TZdZNuPZMbdywD5iDZFmaZy+5jjl7HqObiXv7kwvIsEHVF\ncHaqj3NSamfNUF0xS7XWoCKbHWsyJaRJtSezHZBRLToPVWmSEBXo06mb3tyqooJeV66tyl6zLC3g\nqt1xQRI0SSoxaR6RyrCTSxcoSAUJEamKSNMYVRXdpI2AXuCIwgWXXYtyNXr9u7EsR+hakO7KQFNO\nVKPr+tsZcruuvKwzkl1PngfoXdlEscJH6sfc1EDZVqIt83oZOO0bxhpTZn2a5+42vGWxTlceql6O\njsOyXAgNBctdu3Zx6623kmUZb3jDG7jtttt63v+bv/kb3vOe96CUYtmyZXzoQx/ikksumTvROqAG\nwbqU6OwW8dktamtnNCirTarFWnCgE4+0M9mSnBoNqtafGBOhtJ8bt93YnDFtAlLLrgxoUelJ8KRB\nk6QSFY05gt76zUTQymu0UsjaRXu5iK5V6FpgkdRd35eLubBcQW9tJfRahLH1fpve5d12nXnZsm/j\nQQfo5FIaFGMC3RMzK4CJYG4Gy1YZDO3F6rbcbLg53/4L0GPyMheELjA9KL1KdKrDMssybrnlFnbv\n3s3Y2BibN29m69atTExMdMY8+9nP5mtf+xorVqxg165d/PZv/zb/+q//Oneydei9vM/OiM5uUzln\nlupZM1TFLFXZoFIkdexCdBObtBM25jAlQGZdj3LQaq/YEShaRYqnRUWvD0d04JkEEUkQkhZ79EjL\nUVeJRKSQJQGyVSEzBeQ9lmXxhRdSg6qGtixX09PcmGX0ZrhtSzGlF5a2VZnRW/JYtvTbrjFPBCQB\nJLK4vcKfV1I3FO5Zd+nCqd+SItey7Oeeu5l227LsB0IbtF5eJTrVYblnzx42bNjAueeeC8ANN9zA\nzp07e2B5xRVXdJ5ffvnl/PjHPy6fzLieRZZXRYI81DWTDWocYRnkkOQx7SwmyWNCmRIFbUKZUJEt\nlnGkkyWvM1ugTyNQIYvUT9SJYRqAdqBYvNfqFBJVivRPlbaKSVREokJCAVLkCKGQQYYIc70s09RN\n1tHZ7OV044ltdDu1ZcXntPfYsfMshh8Jc3MvJpHUoGtZ2pU9MJdF7tGTqyniq0oWyyEjK59jbsqt\nh7QnsFf6ZHR7yRnCU3Kue3P2c6OjiYGWPfdacjqO0qGF0Lyw3LdvH+vXr+/8PD4+PrBG6SMf+Qgv\nf/nLy9/83p+Qh4rkiRSpXkB08UYSIhpUCVimXeJc0kpqtNo1WkmVMGoTRW2iuE1NzqIQnQYbFZqM\nMsMI04wyTUZQgK9Gk2on+WNWATU7efEqDWrMMNI5e1bVmc3qNPIarayCCgRS5oSB7nYhhNLGWYi2\n/EzyZjUangZ6GdrVrtGNMRZ7AtFkbrF5m94G561inP1od0xzDbbMubYbwxTFPSuhYWlqMTs35rZ4\nd2FpF3aaIvay+GRPJom50HTndelPyXP3Gu5zr1NRk5OTTE5OLvzEx1E6tBCaF5ZCDGsBwFe/+lU+\n+tGP8o1vfKN8wP/zJ7pf5fOayPMb5LJZwLKGKlblJHlEMxmh0dRHVG0R0SIOW9SZpkKLFRwqkjza\n0lzJAVZykJSQGUaZKVz0GUZ0YqZIFtmg1DnyegeWDVWjkddopDWaaRWhFGGYoqRACtVrYBnLchk6\nJlmhNwRoLOgyWNqeq0DDsEHXmrRiktd89wv87iN3U01bNEWFuy/4XR5a94r+SR47jml4YkKUqohh\nSrsLh124OYxlaSd+sMa7Jm0/UNqg7ed2u+DsB2OvU1Vbtmxhy5YtnZ937NixMBOf6m742NgYU1NT\nnZ+npqYYHx+fM+7f//3feeMb38iuXbtYtWpV+WQCEEJvRZsGpMWe3gpJWlh+7VaFxswojdkRGjOj\nREmLSLWIZJO2iFgtnyYVEVIoKqJFnVmWq8Os5mkSIl1yJOgsiTTLJI2V6brfs0pDs5HXaKUV2u0K\nSRITqZRMJORBgKSAZahbyIl6DssF6gygKTQEbXjFzmFyIj01kIUa6FrN6eKxYMs1//kF7vrSWzjv\n4A87Q59z6IewCR5a+4puktnupZkryFSRR1EgRcE7G1DmuV1HCf3Le9y4pfkLYC+pLANoGSjdeXHO\n6SdvTXpx6pcObdq0iccff5y9e/dyzjnn8OCDD/LAAw/0jPnRj37Ea17zGj7+8Y+zYcOG/pPNACnk\nhwKypyP4OeS5zlMHIkOKjKwZkcxUyGZDmIF8VJK19N7fyUibPIogFsgo1/FMlRCrhIpqI4UiFhqL\noUjnrAG3V+2kKizik5GOVSYxaTsia4bkrZAsj0hERCuIyQJJGgaoikKOpASJQCWSXEhUVUJb9MYM\n7eRwiHbXl6FjnKbfpfnum5VA9qIb4Hf/z909oAQ47/APefMP7uGhs1+hX7CbeswCedY9yHWySUht\nTWai66oD/Vu3lb02jIVXBshBtZX2LwrmwtPLy9GpblmGYci9997LVVddRZZlbNu2jYmJCe677z4A\ntm/fzu23386BAwd405veBEAURezZs2fuZDOgEg3L9KkChEmEkDlSKITIyVsB2XRINqNhqRqSrB2h\nEkk7TcjqIUoJZGDBMm9TyVsalrJNLBMikXQqMKELSnvlTqIikjyincckSUTaismaEaoR6hRSECOj\nnDwICliCFKm2qWQIVchWSkhVLytS0U3egHbZzWHvDa7otpOEbv5DQDVvlf571PJmN8yY03XvZxWo\nXP+ClaleD3QWXIS61rKn8blbOuTWQrrJmUHALINjP1CWgdOD0msIneqwBLjmmmu45pprel7bvn17\n5/n999/P/fffP/9E00AsyA9K1IjU2zi0tfGjvTwFTYGaFh3XNG8FqFSSZSGJSslUBIEgqOpVPbFK\nqORtKlkLIZVeDil0TtzA0rYsO6CksCpN5j3VlmXeiMhnQ7IgIo0zRK70LIHU215ESbEFBqgVAtFU\nqNz6sis0uBpCW3spveu7jddqDpP0MfAratubQaX0V9iIql233mTUW+hrdV5ogsp05rsTa5QOp8os\ny7Li8WGBifNev/HuObY8NL0G6HSA5YLpaYrSG4EK0WUts+h9tkx9oEmGmIoWqfTywRBUpMgCSSIj\nmqKiEzWizowYYUaOkgm9lUQuJHbvykqxiqcDSSKqNBkV0+RCIqQiCWKyKCKrRmREyEqKjFKkTBEi\nhwCUEMUhyWRIHkVklXAOB1RVoJoSVS+WR0YCIvRjAUtVdDfPlSRPA7I8IBdBxzO9+1d/l+cc/iHn\n7e+64v91xnO454o3a3e+TbfFG3SXWtrudKcA3SU0dGFZFp8sO+z5+1mNrlt9NG72fFlwryWvU710\naEH1c5xibrQFaTeNsHMOVV3ETk0nVUQ9I6sImmHMjBjhCMupiiYV2SIWbRDQFFVSEfYUsdd6lkbq\nQyEIREYs24yIGdI40it8wpCsEqIqgrwCeaghKVAIqTpJqlwE5IFEhd0VLQLtjmdRQF6VZCMBeSZR\ngdSbpoUatqjC1lVCF8OLCu2oQl7rzvXQulfAKnjzF++hljZpxFXu+ZU389D6V8B+NCyP0JtAAuZa\nd/3cabseCXoTOe58bhJokNVow9lNKPUD36BMt4elV6FTvXRoQbWf7h42xuubodvb0SpY7ywHrCpE\nTYOSWkZakbTCmBlR57BYRoUmcdAmUnrL3ExoGAIdWFZpFE55t3mGENplH5EzGqQiJAsCsoq28pIg\nIpF6VU8mAl2groomHRJUILT7HWsYiAIaAkizkDQvDqU3S8tlkRDqrDLS5zWjGiKErBKQjMQ9LHro\nqlfw0Mtf0S1zPAL8DA3KBt2tKDqwtKHjLjM0SxzNa2WWpZvZ7lfq4wITa0w/q7SfBoHSHeO1pHWq\nZ8MXVIfSbmNcWXyR2kK7laN0v9MVhYiBUYUcyZAjKbKWENXaetvaMGRW1plmlKpo6uWPot1p6mvv\ntVOhhWkObD9GJNrKE0XyRwrysAvTZrEKvUGNNrFeNmln2BUIWWxnobp7mYMiiWISEelmciLq1Hoa\n67anOYjMEIEgj6VOXuUClUnyXJdY6SJ20a3csUuNajgNPQr1sKXM0nT30oFeKJqxpuFG38mZH5YG\nwO7687I5PBS9BmhJxSw5jC6OjvRObTMRxEF3e9kYxIhCrMgRq3PEqpx4eYtoWYu41qIWzVANmjrG\nWBSzz1KnRoMZRlCIzprxmHYnrWOvH4+Kxhr2bo+mHZwNsSMs6xxNqp2S9got4rxNlGWEWUqUpYhc\nu99C6cd2FNEOY1phRDOoMF3MM80oLSodIOdIKkGbStymmjcYkTO0sgrtLKaVVUizEIXUbrsq4GNq\nyu2kkannNB2F8gCUorcFO/S62DY4bRfZPLr1lXadpXIeB1mZRrJkjP2eC2X7XjxEvVhiMUsOARLS\nGrSqMBtAJdA1iAUsGcmRyzPk6hS5NiOuNajVGtSqs9SjGSqiBRLaIu6A0tiA3e6UupWbbWWa1hym\nHyZgrQpvdUqMjA6wigOs4mlW06DGKNPFWp8ZaqpBNW1TS1pU221EliOs0GCrGtGqxDRlxExQZz9n\nsp817GcNM4x02ntkBFSDFrW4SUvM0IyqTKejzKQj5KkiS2uQKVQa6HKkIqlNRDdMYYAZoWspMwnK\nJJ1syNkyLnlZYbq9mseMdaHpAtPcWBloXYuyn5VaFtN0VxZ5LWkdR8zy4MGDvOENb+C73/0uQgg+\n+tGP8sIXvvCo5lgEy7KoS2xJkBX9RTeZ7wqIukKsyJBnpARrEypRk3o4w2h4hJFwpgPBtogLy7JG\nlbqOXRbJHElerB/vblAWk1ChTZtG4VZnnTXlo0x3OhOZqOLPOZMnWUudWWYYYQUHWcEhVnKQZWqa\n0bTBSKvBaLOBTPOeypum0qBsxjGHGeXHrKfOLJKcQ6zoZOQTIhLZoB3FJFFMK68QpG1UomglEa12\nBO2iRlLJLv9Mz0vXskz0OL2I3QDMTbKYgHFAF5hlAHNdafNYZlkq5zw77lkGzH7ylqXXAB2HG/6W\nt7yFl7/85Xz6058mTVNmZmaOeo6TDMsimxwqqxmFQqxSiDNz5FmKcG2beFWTeFmTuNZkWXCY5fII\ny+VhRsV0B36mLMi0ZjN7iZsGbsbdNVtNREVPy6rSTnmkEkbULHU1wwizhCrrRDVBkciYRMRkIqCq\nmqxIDrGyfYiV7YOMNmaoH27q40gL2c51pU6RM4mXR1SXh7SXR0SjCY3aCI1ajUathgzzoiOntokR\nOtsOkAtBmGbIPC8K2/XqINUSqBbaDTF8ci1LU5aZS0gN1GyL0EDMrZE0z92seWq9X+aOmxuBuVAT\n1nzmZ/t9nNdL/j8ZalzZWK9nrI4RlocOHeLrX/86f/3Xfw3ohTYrVqw46nlOMixDXYFeCWBUwmqB\nOFMh12UEYynyFzKqZzaoL5uhVp+hHuh9eVYIfYwyDXQTKaaxrwambs/WosIsdQIy7J3DAzJi1SZQ\nOYHKiFVCNW91DqnyTsQSoB60GA1mSIKIOG+zYvYwK44cYfnhGeoHG8T7E8KfZ4j9qgMylYLKQK7M\nCVdliFWQrW4xeuYMK848zGz4NIQQsAzTOMQUzXe2sMgEKglQzYC8EUJLFAfF+m+62+pWnUMVq3QS\nYxHaHYPcbLabiHGz51jjy5I2Rm623MxlZGKRg6DmWraudQqD5/DAXBLqF7P8yaQ++uh//ud/OPPM\nM7npppv49re/zWWXXcZdd91FvV4/qssvDizjAEYFrAKxVjcDDsYSwl9IqK6cZSQ+wrLKYZYHh1kp\nDmGb4u8AACAASURBVLJSHGAVBztt2DK6uzLqLui6WUZa9Kk0LrXl7BKSUVUtqqpJJddJmjjLiLJM\nJ2mU6vlq1iLd/i2TkkreYvnsEZYfmGbZz2eo/rRF8EROsC+HJ5QurE+KI0XvLbQGwjNy1DrJsuYs\ns+FhWitj8prerKKNjrmauKqRygSqLVGNADUbQEtblrRFtxdmGSxNOKMtCsbY3YJCyreDsJ/bq3gM\nDO2suG2hSuu8spika5UOUhkY+1mW/dz0snO8nnEqXwEMq7fow+ixHT1vp2nKY489xr333svmzZu5\n9dZbueOOO7j99tuP6vInGZZRF5b1AFYKxBmKcE1KtLZNvK5JfXSaZRxmpTjASnGwSLNoWI4wY21s\nG2P25TFueKvwRU2XIZ29blJFIlWOVA0qWYtl+RGqaZsgVQQJyLQApWU8VUSbumyQKkmUtxltzjBy\naJaRJxtE+xLUXsj/L6R70UsNTfPeFORahTgrQxwC2oL66CzL1xyhnerce0KkOx4x0ikl0rAPCVVG\nkGXITCETpTdLy5S2OEGvegpAmTZxI6K7p08utPveKuLCxqoUoY5lGs3xwg0s7RimXZ9py45hliWE\n7IldN7yfBkHQu+BehY7RDR8fH2d8fJzNmzcDelvcO+6446jnOcmwHAEEhDFUQqgLZD0nrrYYiaap\niyM6iVJYkis5wHIOs4zpzg6NGowRdld048ba8cyQtKiS1BnvUabJ0pAoyViWzBK0FbIJoqUQLXrK\ncVQFMEsbkfrICuuuCdksNBvQnIHWLIQtiBVUBFRiEFX0lrqjIEYVUS2lGuvlle2i5lLHUpVuD1fE\nL2epk0chWS0gUyFBlJImIVka6COTKFXUYOYSNSPgoEQdFjAt9HYWQbFkMlY60SMkCNFlV6fEUkAW\nQBZaXrdbbO6uF3djnsbVtzPirgtfVi40n6U4n9vutSR1jKVD69atY/369fzgBz/guc99Lrt37+bC\nCy886nlOMizrxfcr1LCsSWQ9pVJpMRLOsEJ2XW7zaMp19BYSbZICjsZ6zIt6xdyKo5n4n11WtFwd\nIcwyRtuzqGaAbICcVQjTeLeKLoyX+rleuq1d5lwVa7zboJqQNqAxC4dn4fAMVFNYFoIMoBqBKHZn\nFKMglinCakI1ajIiJWlhSQpUp0HxLCPMUqcqWuRhQFoLSIMQUctpZ7Fu9pHHpFlIlkmyNCDPAvIZ\nqTdCOyJ185FQFh6yKHZ/kN2CdtPOzXRDahcJJBUWe/K4heN2Ebt7lMU73cz7IFD2g6U5z7zngell\n6ThKh+655x5+8zd/k3a7zXOe8xz+8i//8qjnWBxYhkIvEywsSw3LaVbKg6wWB1iJsSwPFnt/a+iF\npLSodGCZWnuGm1Uy9vrvWqe4qMGMOshoOsua1kHUbEAwo2AaxDR6NcwIujFPUSCvhCAvmmYoJVGZ\nRCUCmoJsFmZn4cAs7J+FUaWNt2oI0tRAOpZlJWqSSw0P0+SjQosZRpmmwTQjulg+CkiLZZeoInOu\naghVQ2QxIg0hCVGpQs4G5EcKq3IWDUezfUSIld8pEj/21hWisAoz41a7ZUSDrMuykiIXoPYc/QrR\nyyzLfq6915LXcZQOXXrppTz66KPHdfmTDMvA+g7qL7DKBHkuyVTYScUY6Bnr0cBRoDjMcg6znEOs\nYJZ6T82iHf8z46Vuj0FKRJYFGngtELPotdaHiyOhW+xdhyDPiPOUat4iaGfEM23CQxlyvyJ/GlqH\nYbahV3ASwGgIWQ1dYL8cvQ/PShArFEEtoxIkkIJogcwhyjNqeYsZ2WAknGE0HGEmmCYUKUGQFrWh\nrZ59gpp5lSSNaAcxSRqRjsZkKxTpGYKsWQCy6HDEDL0cS9BLJRt0rc8cbV1K6HQoUm6ixbb0ylbz\n2PHNMgDacxm5UDWvlcU++83jobrktLSWOwIUVk7RDCJvCNrtCrNZnUAt76zAiYoli02qnVikQnCI\nFZ1jlnqPJQkgO6jMEYWTHpASqpQwy5CJQpjO4tNoUB6gsw2tqIKqQZRk1OImoqLImgHVwy0q+xPE\nT3Pyn0FyCBpNmM4hqkC7CukosLI4VulDrISglhPJDJFo1z9MFNUkod1uMFqZpVGr0qhVmQ1qnXZy\nZqWR+eNQpcksdVqyQjOs0pIVWvUa7RWgWgFZFnUz5DV6tqggRzchMBszUryWiCJRXkDSgFJ1/tP9\nN+sAMqQXmDAXoi4InX//Hjfcfm5bre4SSjcrZcZ4YC4ZLa3ljkWiwdrAK29IWu2YmbSOUnkHlBXa\nVJ02IxkBh1jRAUiTaqfw3GTGY92+oqi/NJalLlkP8gyR5IiW6sLyEBqWGR3QiDqElZRaqojyFNUQ\nBIcywqcypIHlEWg0YFrpstFWBTIDywKUrAZWKoKq7gQfJhlRklFtJmSNgLwZ0KpHtFREK4xpVuPO\nGnS9GqnBCDOdnyuiRUPWiEWbhqoR1BWsCEizWDOjRpEhLz6bvZHZDM5eQALaStdwSqktffPvU/bv\n1knm2C64gaVtVQ4CZdmcZa67+dkFpHt4LSn1Kx06SVoEy5JuQ+8GqIYkaUY0kjpZKgiylIrQYKiI\nFu5WEIdZ3mlw0aK3m7jZItd0BjLgjdD79IRZSpBmBSTodvA5gv5umhKcaQiTjDDJqJj7PAjqKVBP\nQvIUtJvQbOmm6CMBJDHkVWuO4hA1CMK8a91lqQb1DDALSRbQiiPa9ZAmUc9ntbskZegstxTGalbk\n1ZD2aBWpsmJVlOhal9P0brNrGqabxTkJGpTN4r1MdJZVagvTtRLtFUEu4MqsSvuw6yjd99xzcuv1\nsr6ZJgllQ9VrSWjJueHm//diOwTVEGRHQtIDMeyHRpJwJE4IKllnCZ+xHDMCZhihQY0WFZJi969u\nd8gWIYne8ZHDLOug9TDLxBFqskEUJMhIdftA2saR2Z7hMD3f43wGWk9A6yloTcOBFhxJIMlAKB2D\nFPZ2t9PAQTqVUro7PN3Nytp0Ng9L8ohZVWda1TnMCD9lHT9lHT/hbPazhkOFFX2Y5TSod2pMU0Iy\nKXWX+UqOTFNUIiHVmXtMezfDkgRteVrX7hhnAdAMoBVBSxU8si09e68eG1b2oznHjmcG1utlBe42\nKG2XPreel9VsuquK3PXn3up8RmppueGFjGXZBjUryI+EJAcg+3lAmOeEo3o726wSdMqABAqF6FRO\ntqiQEmJWwJhxESk1ZlnOoS4oC1u0JhvEYRsZ5d2FLeb7ZuKoBpbGfU0gPwLNJ2D6KTgyAweKWGU7\nL77yBSyFacp7BA3LKvp7a2AZM6cBUJJHzKg6B1nBU6zip6zjCc5hH2M8ydrO3uYzBShNqVRGQF7A\nUlRyRJ5BqlCpRKSB7tBmeJcX164yF5QCnS0PAz0olXp/8Q6UlHWSveNZWXbchpdZPSSssa4L71qX\nRmXNN6QzRxmkvXv+jNaS6pRuZFzBlnbDsyOC/GAAI0pvXgaklYCWijpup+k5aZpkaHDIDijNksHI\nsiyXd0A5zTKmu5ZlmJdblgaWQfFYHOogtH4Ch5+Gp2bgUBtmFCSqa1nKItNNg65lafYUsvcQj3qP\nVIXMqjoH1Up+zpn8jLN4gnOYYj1Pstba47xiZfi1rZ1JiQoVVHIEqYZcCiozrrT1uzbLIe2ev8a7\nDtD/SSQ0zF8Ru0DdlBal1iT2P6aZzIVh4LwHvXAcFOc08BvUsaifG+6B+YzU0nLDZ/X/x+1A97I8\nHEBF6A2+Yp2ZTfOYVjtDpYosDZAyI5A5MshBKlIZkgYhqQxREgKREcoUhHHHlQWUrjqr+kxC19Qh\nljXlscFZlBepGV2Qrgojy3RKq6IXy4QpSLPToomFmj2FzPrtXNdvZhVJVgnIRySH68t4Kj6Dnwbr\nmGKMfckYP03O5ufJWp7O1nQ6rScihACCMCUIM8IwRcliS+AooQJkaUSWReQK8uKfVpkst9sk3bDP\nlEwFQmfFhflt2b8k+3+TfskY16q0rU7XJBgUa3Tjk2XPfZJnSWppwfKgTiC0Y5iuoJe6hN1qFCBv\nSdLpCI5AfihAxjkiUshYQaTIK4IslmQVgYxyRKBQCg1TodA2VkiLmJhKp1y9Klq65ZoMUcX66s5h\ne40Bc0tsUggzqCgd9jP/ZuYrX88hziAoQgu00LHLJhqYZk4giyTtekxrZURrZcxTo6v46chZ/Che\nz/+oc/l5cy0/P7KWA9NrONJcQSYDUhGSyQBRyYlG2qiRBBFoszYIMmJaBCIlzTISlXfaWioh0Ysq\n6QLTQLJlfcaB3LETPOZnG2BlsLStyn5z2nKz3m67uLLXPSyXnBY5ZinnHwK7du3i/PPP57zzzuPO\nO++c8/73v/99rrjiCqrVKu9///sHzHQI8kN6QfV0G57O9Y6PPwN+CjwB+Y8l6f/f3rnG2lVd9/43\n53rtx3nbTgDbLWAnyEBsF8FN6KUNCLXIJKFIaXWJrqJUohGiTav0Uyv1A4kqpanSLzR8SKS2ifpK\no9tc8VCgVRNhqS3BpHBDriAiwIXUuGB8fM4+5+zXes15P8w59557nX3sY+f4mOA9pOnlvc/aa+y1\n1p7/NR7/OcbxiOwnNfr/r0n3J1N0T0zTeWuazuI03VaTfrtO1kvIswhVSFAM3HFtC1Jk1n313dhM\nRJQyQEsxCpL+/PaL9ACUIEoIFMQK6no04T2FeS8uIXAg5IYjgWcMQn0qlKT1iO5sndVdTU7Pz/NW\n8z0cj/bwmr6KE/09vL1yGcsnF1g7MUvnxAy9/2qSvtkgO1UjX00o+iGlNtnxICiJw4x61CNJUqJ6\nRjCVI6ZLxHQJU8p80QajDeH8LpsbYs84APQvUNWN9t3roLK//2RaZ/OzHhCrK4fc/30A9T8/kXe9\npJscF0jOalmWZclnPvMZvvOd77B7925uuukm7rrrLg4cODDYZ8eOHXz5y1/m4YcfPsvRVkAHZl1y\nGUG/bp4W3qTVfUnRlibJ4hqZOVSa0ohMQVkiRImWpsIQEoRWCMGgeo9fncjEOBMKaTLIKhR2tQuj\nW///ntUlSgiVCTnWpbHa3BwVGmoaohJEDtqj6whXsNdVLBOgQkFRC+lPx3Tm6qxE0yyJeROv1JfR\nTqfptGfoLE3TX6lDIEwnyQDCQiKTEtkMUeQEQhGIgkCWSG2KIJdSkochQgbWipSmKLH7Xj3vesN6\nHNIbZberSRS/SlF1H//zvsteReVx2+o69IkLPhEr73Q3/JlnnmH//v1ceeWVANxzzz088sgjI2C5\na9cudu3axbe//e2zHC3DzNQClDO18Hh/GNe1mngZuLcCXQqEljZ/EaB0gAoCVBTYlmTS8hPNAdw6\n7EjkSOtLKy0oMoGYA5mCKLTR5ywvPxkTgoggrEGtCcxgWuHmhjKZ5wZMy9xwLztAMG2Sy0ET5AwG\n6Bvm2EGgiVVOo9tHrMB7kkXa0XHKKCQOMlr1BVpz87TUAu2pabIgJpNmiIYinMmIasbtdgWOwdKr\nlESXgSkenAWmJmZHmrjrCrDkjRaGjN+yo6MgVaB89BQMnxx+giZj1Cx35qnf/Mxtq9bpmahH4wDw\nTCBZ/f8ERN/V8k6nDp04cYK9e/cOXu/Zs4djx46dp7q/ACSoOojbgI8OY2gZQ56im3+Oj+ne7wPa\nlE4TUqJlgJYWKOuBzZkPARP0OrDUiaaUUJYSmWootKH+OIqPszC9zLUDS5ogMxACyj5kPZPYEcqA\nZaqhqyAuQIcgGhWwrIMMFXGZQU8TtQre01ikaEREomAqXGOxtotTs+9hMdrF8twCHdGkI5t0RJMy\nlgT1nCApCESB9MBB4xf8CNFpiO4L6IghWC4DpzGhjxVvrGJ4UGlhngDrwHKcO+5bkX4wtPT232ho\nbwvjAbEKeuMs0jO9P5GLJUePHuXo0aNbf+B3OnVIiI2ylucj/8Oq3GmG0qNZWecq+oaKA8oY40IK\nAVKaBoaRQscBqh6gtBwBSlWxLENyZGAsyzISFEIYoNPWqvRNfAecFcsyaJrYpBC2tGUBUR9wYGkz\n4qoEEUDYwBTV8OKFBixzol6BUimUglAUTEer7BRv82btCuaiFlPTazRU29ReEnMICmNdWmaAEKOF\ndZW1LFURoPIAnYVoV35uTRjrcQkDlG9jQNIVEuloY1GqApTjVDpgGylf5L2uWpQF6931Kmncf38j\nq/BM75/N8pzIO0FuvfVWbr311sHrz3/+81tz4He6G757926OHz8+eH38+HH27Nlznupcxy3bg4Hc\nTNDCoY9cn3Ly6S4aM/nrAjqga5KyFlDUI/I8piBCyQCEQAjTI7xOj2lMUeGG6BLLFCkMz1LX9bBV\ng4svOtCu1HGQztqsQ5xDkpqSbA3Ltom0sTCVNmE/bTneg4SKtVSF0ASFfUj0ShpFF60gUhl11SMI\nFWFYEMY5cWBSU5KSEmmKAyMGYQalJKqUaCUpi5BiLaZsh+i1AL0iYBEDjqcw/19k6Ia3tbmWPW1M\n4hE+ozSxBn84kBQB6Mg8EXQJ2o+jRAxjjc4CdUDqW5Y+Kx5G45rj5Exg6FuqZzrGRH7m5Z0Oljfe\neCMvv/wyr7/+OldccQXf/OY3+cY3vjF2X63P9kN1Z+uZkToyZOoshL7l+lW9PWec+JZmD3RXUNYD\n8n6E7msyHVMGAYSaMCgMUOpVFlhip15kWrdpqB6hLkxCyPWyadqv5UC5zxA8C4Y4YilAMoY4Mp0x\ntKUU+rZXIE1tihFDzBlj2jtuAWFakqQZ2hYjzhsxuimRzZIoMM3YSiQpCRoxSFrlhBRFSJlFlGlI\n2Q/JWzFFK0YtS+Nyn8K43Yt2u4R5fxXoW5As/SWMlj0qMPchMFY80oGmfTKUwtyzMjSJOtOHl9He\nO+5p4y2FImAYePL3w9PvZ7o3K37iqWq1TuRdI+/0mGUYhjz00EPccccdlGXJvffey4EDB/jqV78K\nwH333cdbb73FTTfdxOrqKlJKHnzwQV588UWmpqYqR3OTyUsZ68hMuExAT9pJyijf0Q0/q9sFXROU\nDeNuln1JLmJUJBHSUGpqus8Mayzo0+zSp0h0SqIzQpUb0noIItFDY6dvdfSsjozRBSsWS2QMcWiA\nUvrZcXuoQIC0rW/WMWdcHLZr9AQ9RdLLCDslSTuHeUFAQRL3SZI+ioCUmA5T5EQDwCwIycqEoh9T\ndGKKdky5GKAWA9SiHAKkGy1sjFLb5ZwaitIDS4/yI+wDKxCmUHMg7Hv2/dzuq0P7eQeY7mHoxxB9\noMy896sFM5z4FujZZNw+E6B818p5Wpb9fp8Pf/jDpGlKlmX82q/9Gn/yJ39yzsfZFCn9yJEjHDly\nZOS9++67b/D/yy67bMRV31gcWHpZGx3ZHtkB9KPR0FjMaF7BzTsbw9RdQdkLKPsC+gFZEFGKwLab\nLUlIaeo287TYwRJCKaRSSKVNN0dpjiMkNh7KECyddekA083twABh5LYSSmlDfsKMALsYpko9FMPT\n132gLZB9RZwq6OXUugKkJqjl1GZ6BOR0aLLCLKfp0GaKVCf2SprQQ9arkbdr5K3EAKTjrJ5iNPu9\ninG9O3arq/xF19zM9u0JGBYS9rmoEvOPCmxTNBfg9cGyes+rMU7nujuwO9vSxjMB5wQwJ3JmqdVq\nPPnkkzQaDYqi4JZbbuHf/u3fuOWWW87pONu8gseBpZfR0Zlx57KIgWnmRGFifm4+SwyAJXh4K6Ar\noCNRMiITCb2objv3NOmIKdraFKKIRE4kTMk2lB6SWPsY99TF+E6a19rSa/SaDc8VdvRBd0EUpj+Y\n1OZwSpmzCwsIVkGcxODIzHCoSKCmJGVdUi5IdChQsURHgjIJWJ2bYrU5zUo4zSI7OM0OlpljhVnW\nymk6xRS9vEFaGIJ6uRKhWnKYwHFu9yLQ0ub9NYbUoMInVToLLjAn4pY8uorrjhHgE9cVw5Md4ULC\n+tgJjAJkycZrTH/aJI3/wxm31mKSMb+UxfUIz7KMsixZWFg452NcBLCEIdJZsCxiTEqZ0UnpXGD3\n+w6GH3O8SxO/lNDRqCAkDxN6tQZtpmg7oBRTg4Zg0Dd11ZUyx3A9eBzIvA2cNECpLQ9RtW2iuDRb\nCkNAl4XhU2phDDWtzVcNcpAOLAF22W0COhYUzYAsCcmTgDIMKIPANCoLQlqNWVqNWZajWRbZxRI7\nWGaBFrOsqhl6aZN+r0nWr1OuRJStAN2S64HyNLZlhjajX0JeQOFii94ieRGYQGskvMEQLP3QY4k9\nUd86dTfIAu+IKe04YD5YBpW/4930s/EpzyZnskInMc13pxy1Y2NRSnHDDTfw6quvcv/993Pttdee\ns5ZtBksX/PPSzspOXmWLQ/rzyhmiMJzbzjUe8DKFif/FgjIKyWoJvdJYlm2m6IipQQdFwPYZz4b1\nKzsMrTLfsrRkbdUC3Tb0w7I0Q2ibxLEGmZAGO7BgKQoQq9YNd95mgrEsZwXFVEA2H9Kfj8nD0Kz9\nFiG5iGgFMywF85wOFjjFLmtZzg8syzRr0O82yNbqqJZELwtYFkOw9AGzra3rrU3xTZWDTs0DamAy\n2oBqYEHSkfJ9sHS3baRvmW8tOhByFl11VY9/U6ttKXyS+lZalxvJBCh/dmWjDM9/t8PJeqqSlJIf\n/OAHrKyscMcdd3D06NERetNmZJvBcuDHMUKwVA48c4NEAmOulVjE8Ya/LHEwoY0lVCYhaSOhkzcJ\ny4xlMc+i2MEMqySkzIoVShEipEbTJ8wUUUchV0rEMugl0BYw1RqoVTu6NibpvnoAIjZ0Imk7OlAO\nDS1VQtEdsmuCGGQCgaUR6aZGB6CntCmsQUwqEnrUaTHLEvMsspNFvZOlYoGVYpZ2MU2v0yRfqZG3\nYsqV0NCDHKm8ZbdrDClBfW3I5plN5gweUm4BratGbClbkRj0Th8pJeesSod7I7jm3x+fRzlO/P3G\nAeb5im/Z+tuN9pvIz6b89Nyh2dlZPvKRj/Af//Ef73SwHOd2+XygAFRoEj7YNLOQJu1cBjYL6x3K\np+dEUNYD+v0aQTqNygRvB21qMiWQJYUM2SUW6ctFSiGZYY16nkE3I2gpWDZdG9US6NNQ9qDsQpka\n19slbIIAgghkDUQdQza3SRtRgM5Nncs0hdQS1JPY9OlJFEg0YayIZ8yOhTTFPfrUWBPTrDDLEgss\nspNT5S5a3XnanRn6nSbZSo1yOTK1P5cZtKYYtKnoMCzase4a+xSe3F40axW6FL5LqtWG13TwC6kW\n3RgLesLbqbqqp+qunwk0NwtqG8UhN2NhTuRnT86PO7S4uEgYhszNzdHr9fiXf/kXHnjggXM+zjsA\nLB0fyM5GFRpg1IFNM0fWZZbD1T1jgJIIikZIv19HpZDmETXdJwxLtBDk1norpSTQdqlg3iPoapKV\nHJYsWJ6G8rQJ7RWZGao0We8osGu+Y5B1EE0QU94p2O9X5NBLoV0YC3PKGlxRZtaGBzMl0Xs0oijp\nRabpWl8asGwxNwDLRbWL5e4Ca8uz9Jaa5KdrqKUAtSTRS2LIBfXoVKR4htpGQOkTyK0laGlRgx4+\nfilLTQUsheVLuZvgyOcO8PzhdG+UDHKZO59GVKUOnS0OOY7gPpF3n/TO61Nvvvkmn/rUp1BKoZTi\nk5/8JLfffvs5H+cdAJbOPbQ+ng6h8AiKBYaDGQWQBkMjxIGkK3qRQNkzlmWWhYi8TkgBQpDLiJQE\nJSSBKKnRIxYFQaFJurlxZ1uglqFchmLJWIe5MkNj+JSxhCCEMMF0gZzC9Al3dCMLJnkOvQzWusYL\nFkBUgOpBGGuCXSW0S2QOQawoCeiLGmsYy3J5YFnuZKU7T3t5mv5bTbK3k1HuZJUD3mW4IgltQhrr\nANOBpgMwCzTumtprOULhcjjobpveyDL0d6pWVq9allWL1AfKzcpGcc4JYL475fwsyw984AM899xz\nP7X2ixCz9C1KR1b2J3U4OrQGJQ2A2oJFI/N9pMyhMHirBJSSPIjp6RptpqjRZ5l5GnSo0SOQGplA\nfSpDz0nkaol0bq0tYyZDA446grhuYo7Sut7Crfeu2/1Xh0MGpv5lmBqrlAzyttmtXAJxGuQiyFNA\nJlD1kLwekwYJ3bzJWjHNSjHPanuB7tIU2WIN9bYcZrjtevRB8tnHKOz7wlp/eWi7Slo2vHYo6AKQ\n9mFVCGO9dy1Z1CfTO4qVA+JBF0hX4LdKCSqGxx307ynGjOpqHR+E/feqvx//ZCdy6cjFXe94kRI8\nfl+DjFHrp7LsRVvXXMeG0JiLUW/Sy9BqZ/UoU1Qi1xE9XSfSOSEFDbqDHtxRUFKLM2abbdScIGyD\n7ILogegbUFR1iOqgGxBOQzAFYtrGKv1amKsMrb0AhIIghahtuZepNT4L4+JHpyFahOgUoCVKBeRh\nRD+p0S0atHszrPTnWWnNky4lZIsJ+m27hNHxQp336oMaDAEUbE8dbMBVGdQXuXWh3f0oTHa8dJZ7\nYIDTvw0upDxodia8YwjvfvprOl0s2n+q+UDpPuMXBKmCZNVC9OlFE7n05OKud7wIYAlj3e/BZKpU\n19YhlImZ7AV2mZ5YP+8cdUcJY4kqTa4i+rqOq6Jep0dMRkhBTWbMJmukzQQ9KxAdA5b0QPZBWxK5\nnjVbMT8c1LxTEhiaTo1BCE5kINsQhlBqjGVpyezKUnyCRRCngFBShiF5IyalRjdv0u7PsLpmwFIt\nSbOE8W1pQHlgRXuXyRXq8MOICFOYJBZ27aX9wDrL0prpBYa3quUw/+OGo1n5lqWSDPuL+/fOBTb9\nUlLVm+WvHPKtRR8wxwGi8rYTwLz05JKyLF3pLzeR3MRwFomfUXDoZyeV1mdNqgoJSI2QCiGVSagL\n0288J6KH4V8uM0cz6LJQa7EyPcNaPkVZSkNWDxVBvUTPStSMsFtJOS9RcxI1F0AMUimENssng0QR\nBAoZlEipDGUR2/Y8tlE5m3SmCboGOjLVz0sRkIrYfDc9RSdv0u006LXqpKdrxpp05dR6DC1a6yLX\niAAAE7tJREFUl4jxCxa7pYkuXBELs7ZbwmgQ0h3EgpszBB0YFt6fQ/uev05ewaB7JHj3q5pMcv67\n/75PHauu3qneWHdsH0An8chLVy4py9KR9arL3XyQ9P1In44iGFTD8d1Pj28pYo1MFDIpkElBHGVE\nQUYsM7PEEdNKt8MUK8Esp+vzzMztpBm2mUlWqU/3qe/qUVvpkzdCskZM3ojIGhFZIyFtJqTNGEJB\npDNinRPpnBqpGXFKrZESTEMyB+yAaMUYdW7IXYLwauDnBMXlgv58THeqwWpsMuGddIp0NaFcDMxq\nohaGEuSeLTVMfcwmQ6Cs2WuwxjAE3GO0PcbgurqsmJ8hi4bsAweezs13VfV8oFSWfT8gprtwii0H\nNRhugX2VQuQP992o/H8cd3MClJe2nF82fKvkIoKlbzn41qTPtxtDIXFz3gdKV9E81si4JIgLwiQf\nAGUsTGEz4xFHdGiYlTKNeaaCNvV6l2w6ZGbnKrqvCPsZ/SiiF9foRzW6UYNO3KQTNenETZBQ131q\n9KjrPtNhm+m4TdAsqc2mhBYog/cYUrtrekYJLIC+WsBeSX65IG1GdOI6a/E0LT1HO52iv1YbBcsu\nQy83AWaBecY3ILNu/0gBDOGupV+hpHIBlQNKMTT+q7UvfHxzS5bWcWV9oOwzapL6SR1/fbr/UPR/\nG2KDMZFLUy4pN9wvAgujs9C5YG7G+9aEN0F8ap+/iicegmWYFERJRiRyYmH6PEY2PpoRowgIg4LT\n9Q61eo+IlFKD1ppIpzR0m1REdESNtpga8B9XmKXFHABTtJm2iyrLuiRoKupzqSm7tgMC19umzUjI\nrpyFfI+g2CsoLg/oRxFd6qwyzXI5Rzttkq4llKctWLYZUoJCDDjOYIrN274+2I7CjhxPl9HGayNg\n6Vbt+BcwtF70+dJ2qpZln43B0gdZd0PdTfXDMhsBJkwA81KVS8oNr/ZnceJbFT54+hNLmfhlLsx6\n8I4wCQ+X3AhNHFBFIWWsIRaEkSKLSsKoRISakIIAiaKgT40OU7SYIyEdENf7JHREgx51eqJBT9Tp\n0mDNVjHq2+yOa7ubE1LImG7UpKXmeEt0yVVEHsRktYiyF1jL0sZcmxq9AKqh0QL+s/w5Xi3380b5\nc5zK3svq6jzdlSblcmhilW4tfPXZ4fIz7vfjQLKNccfXNHS1WepY2mu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