{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/colin/.venv/bayes_talk/lib/python3.6/site-packages/IPython/html.py:14: ShimWarning: The `IPython.html` package has been deprecated since IPython 4.0. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.\n", " \"`IPython.html.widgets` has moved to `ipywidgets`.\", ShimWarning)\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pymc3 as pm\n", "import scipy.stats\n", "from sampled import sampled\n", "import seaborn as sns\n", "import theano.tensor as tt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# plt.rcParams[\"figure.dpi\"] = 600 # for presentation figures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define Bayesian linear regression model:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "@sampled\n", "def linear_regression(X=None, y=None):\n", " β = pm.Normal('β', mu=0, sd=10, shape=X.shape[1])\n", " σ = pm.HalfNormal('σ', sd=1)\n", " X = pm.Flat('X', observed=X)\n", " y = pm.Normal('y', mu=X.dot(β), sd=σ, observed=y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate synthetic data, sample from model, and plot posteriors:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using ADVI...\n", "Average Loss = 159.48: 5%|▌ | 10797/200000 [00:00<00:14, 13503.19it/s]\n", "Convergence archived at 12100\n", "Interrupted at 12,100 [6%]: Average Loss = 244.14\n", "100%|██████████| 1000/1000 [00:00<00:00, 1289.89it/s]\n" ] } ], "source": [ "X = np.random.normal(size=(100, 4))\n", "β = np.random.normal(size=X.shape[1])\n", "σ = np.random.normal(size=X.shape[0])\n", "y = X.dot(β) + σ\n", "\n", "with linear_regression(X=X, y=y):\n", " posterior_trace = pm.sample()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { 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CEASsqy+CLANnetibpfyVMGQjkQi+//3v46tf/SruvvtuvPnmm+mqi7JE9+AU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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = sns.distplot(posterior_trace.get_values('σ'))\n", "ax.vlines((σ ** 2).mean(), *ax.get_ylim());" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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iujYWqx3F55twoqwBucV1aGy9tGZuZGgAJo+OxYT0aBgC1DCZglBX1ypzWupO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\ntuPYvKcYXVZeKo/8F998on7DanPgkyP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=len(β), sharex=True, sharey=True)\n", "\n", "for ax, weight, true in zip(axes, posterior_trace.get_values('β').T, β):\n", " ax = sns.kdeplot(weight.T, ax=ax)\n", " ax.vlines(true, *ax.get_ylim(), alpha=0.5)\n", " ax.set_ylim(bottom=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Inverting the CDF" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 4)\n", "y = 1 - np.exp(-x)\n", "plt.plot(x, y, 'k-', linewidth=6)\n", "\n", "z = 0.75\n", "z_inv = -np.log(1 - z)\n", "plt.hlines(z, 0, z_inv, linestyles='dashed', colors='steelblue', linewidth=6)\n", "plt.vlines(-np.log(1 - z), 0, z, linestyles='dashed', colors='steelblue', linewidth=6);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Rejection Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a pretty general implementation, and a vectorized one for plotting." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def rejection_sampling(pdf, q, k, size):\n", " \"\"\"Rejection sampling\n", " \n", " Args:\n", " pdf: A (possibly scaled) pdf. Eats vectors and returns floats\n", " q: A scipy random variable with methods `.rv` to sample and `.pdf` to get the pdf of a point\n", " k: A scaling factor to make sure `kq(z) >= pdf(z)` for all `z`\n", " size: number of points to sample\n", " \n", " Returns:\n", " points: numpy array of sampled points\n", " draws: number of draws it took to get this many points\n", " \"\"\"\n", " draws = 0\n", " points = []\n", " while len(points) < size:\n", " proposal = q.rvs(size=1)\n", " draws += 1\n", " accept_prob = pdf(proposal) / (k * q.pdf(proposal))\n", " if accept_prob > 1:\n", " raise RuntimeError('k isn\\'t big enough at {}'.format(proposal))\n", " if np.random.random() < accept_prob:\n", " points.append(proposal)\n", " return points, draws" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def two_gaussians_pdf():\n", " pdf_one = scipy.stats.norm(2).pdf\n", " pdf_two = scipy.stats.norm(-2).pdf\n", " def pdf(z):\n", " return 0.8 * pdf_one(z) + 0.2 * pdf_two(z)\n", " return pdf\n", "\n", "def rejection_sample_plot(N):\n", " \"\"\"Hard codes rejection sampling for the above \n", " pdf using a hand-tuned normal distribution\n", " \"\"\"\n", " one_d_unknown = two_gaussians_pdf()\n", " one_d_wide = scipy.stats.norm(0, 4)\n", " k = 1.02 * one_d_unknown(2) / one_d_wide.pdf(2)\n", " new_x = one_d_wide.rvs(N)\n", " new_y = np.random.uniform(0, k * one_d_wide.pdf(new_x))\n", " extent = max(abs(new_x.max()), abs(new_x.min()))\n", " if N > 0:\n", " x = np.linspace(min(-8, -1.1 * extent), max(1.1 * extent, 8), 1000)\n", " else:\n", " x = np.linspace(-8, 8, 1000)\n", " fig, ax = plt.subplots()\n", " ax.plot(x, [one_d_unknown(j) for j in x])\n", " ax.plot(x, [k * one_d_wide.pdf(j) for j in x])\n", " ax.fill_between(x, 0, [one_d_unknown(j) for j in x], alpha=0.4)\n", " ax.fill_between(x, 0, [k * one_d_wide.pdf(j) for j in x], alpha=0.1)\n", "\n", " accept = new_y <= one_d_unknown(new_x)\n", " ax.plot(new_x[accept], new_y[accept], marker='o', color='green', linestyle='None')\n", " ax.plot(new_x[~accept], new_y[~accept], marker='o', color='red', linestyle='None')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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s4aGHHkLTNJ5++mk2btxIbm4ugUCATz75BK/XS2lpKQA/+tGPePTRR3niiSfY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\njPRX1OQWgrJIkkREqAFbo4O0U1WuDqfbulsPv7+GTEqSxLW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rejection_sample_plot(50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Concentration of measure" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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jQelOf72XUS1E13FvuRYVDmG8chyGxxY4LhjWzqZGS9MuIcSWJeEsys4eHMRL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\nLUvXSNZVk6yrpmfNNdOWwXBzDNo9DNm9OBQSzpQrNbToS2j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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for N in (2, 4, 8, 16, 32):\n", " x = scipy.stats.multivariate_normal(cov=np.eye(N) / N).rvs(size=10000)\n", " _ = sns.distplot(np.linalg.norm(x, axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Sampling from a donut" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def jointplot(ary):\n", " \"\"\"Helper to plot everything consistently\"\"\"\n", " sns.jointplot(*ary.T, alpha=0.1, stat_func=None, xlim=(-1.2, 1.2), ylim=(-1.2, 1.2))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def metropolis_accept(old, new):\n", " \"\"\"In log space -- the proposal should be symmetric!\"\"\"\n", " return np.log(np.random.uniform()) < new - old\n", "\n", "\n", "def normal_proposal(scale):\n", " \"\"\"Make a proposal for metropolis hastings from the normal distribution.\"\"\"\n", " def proposal(x):\n", " return np.random.normal(x, scale)\n", " return proposal\n", "\n", "\n", "def metropolis(logp, n=1000, step_size=0.15, init=np.array([1, 0])):\n", " \"\"\"Implementation of Metropolis-Hastings.\n", " \n", " The proposal distribution is hardcoded to be a normal distribution, \n", " but it will sample in whatever dimension `init` is from. Also prints\n", " the acceptance rate at the end. Optimal is ~0.234.\n", " \"\"\"\n", " proposal = normal_proposal(step_size)\n", " accept = 0\n", " old = proposal(init)\n", " samples = []\n", " for _ in range(n):\n", " new = proposal(old)\n", " if metropolis_accept(logp(old), logp(new)):\n", " old = new\n", " accept += 1\n", " samples.append(old)\n", " print('Acceptance rate: {:.2f}%'.format(100 * accept / n))\n", " return np.array(samples)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def donut_pdf(scale):\n", " \"\"\"Sample pdf for visualizations. \n", " \n", " Normally distributed around the unit \n", " circle, and the radius may be scaled.\n", " \"\"\"\n", " def logp(x):\n", " return -((1 - np.linalg.norm(x)) / scale) ** 2\n", " return logp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we actually sample from donut distribution using the handwritten Metropolis sampler above" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Acceptance rate: 23.90%\n" ] }, { "data": { "image/png": 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eS5qmzC7V8f3uP4vrOcwu1UnTdNcdXoU4rlrTdLZl4zoWlgVJpiCmHZQsiw0l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\nc5wIAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samples = metropolis(donut_pdf(0.1), n=1000, step_size=0.37)\n", "jointplot(samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now see how bad the sampler does with a smaller scale on the donut:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Acceptance rate: 25.60%\n" ] }, { "data": { "image/png": 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+PhWLReXzee3du1fXXXddtYZaFVdddZWGhoY0MjKiXC6nPXv2aMWKFdUeVs3x\n1RHS+di2bZs6Ojq0evVqbdy4URs2bJAxRg899JDq6uqqPbw51dfXp0cffVR9fX0Kh8NTVxo+88wz\nuv3223XzzTfrvffeU09Pj4LBoB5++OGzrsK7mN16663avXu3ent7ZYzR1q1ba+r1l8rPwZo1a9TT\n06NwOKw1a9bommuuqfaQPfH6668rk8lo/fr1euyxx3TvvffKGKN169Zp0aJF1R5ezeFu3wAAK9T8\nKTsAgB0IEgDACgQJAGAFggQAsAJBAgBYgSABAKxAkAAAViBIAAAr/H8sEhBnz83wtQAAAABJRU5E\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samples = metropolis(donut_pdf(0.01), n=1000, step_size=0.03)\n", "jointplot(samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do the same thing with PyMC3, but we will want the pdf rewritten with `theano`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def tt_donut_pdf(scale):\n", " \"\"\"Compare to `donut_pdf`\"\"\"\n", " def logp(x):\n", " return -tt.square((1 - x.norm(2)) / scale)\n", " return logp" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "@sampled\n", "def donut(scale=0.1, **observed):\n", " \"\"\"Gets samples from the donut pdf, and allows adjusting the scale of the donut at sample time.\"\"\"\n", " pm.DensityDist('donut', logp=tt_donut_pdf(scale), shape=2, testval=[0, 1])" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1500/1500 [00:00<00:00, 8950.14it/s]\n" ] }, { "data": { "image/png": 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O0WiEECCK4YUpr+X3Fu0jteyEEB1z3+3XV9cheYpBR19NZDiSzTCqFKFSmLq+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\n3XRXUwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with donut(scale=0.1):\n", " metropolis_sample = pm.sample(draws=1000, step=pm.Metropolis())\n", "\n", "jointplot(metropolis_sample.get_values('donut'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PyMC3 also does poorly on a smaller scaled donut (because the problem is the Metropolis sampler, not my implementation!)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1500/1500 [00:00<00:00, 9002.16it/s]\n" ] }, { "data": { "image/png": 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bNqmqqmpMBgoAKGxZL9m1tLRo0aJFkqS5c+fqwIED/dscx1Fra6seffRRNTU16bXXXhv9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\nAAAmECQAgAkECQBgwv8HHpsVRseQE8IAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with donut(scale=0.01):\n", " metropolis_sample = pm.sample(draws=1000, step=pm.Metropolis())\n", "\n", "jointplot(metropolis_sample.get_values('donut'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sample the same distributions using the Hamiltonian sampler in PyMC3. It has no problem with either:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1500/1500 [00:02<00:00, 520.08it/s]\n" ] }, { "data": { "image/png": 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82JhlFtR8bKmvKDLYcOPYItaDKQqEcMkHTwqcT2HRslCUZipIeUeO8nPmNTPf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\nLl3q0ir7l74o2Y2NjeHo0aMtr/3yyy/Yt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with donut(scale=0.1):\n", " nuts_sample = pm.sample(draws=1000, init=None, step=pm.NUTS())\n", " \n", "jointplot(nuts_sample.get_values('donut'))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████▉| 1493/1500 [00:20<00:00, 63.19it/s]/Users/colin/.venv/bayes_talk/lib/python3.6/site-packages/pymc3/step_methods/hmc/nuts.py:448: UserWarning: Chain 0 reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n", " 'reparameterize.' % self._chain_id)\n", "100%|██████████| 1500/1500 [00:20<00:00, 73.96it/s]\n" ] }, { "data": { "image/png": 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0yjiYFexPx42jmdUUWUKWfPevpdaa9H16M2Mlh/cPm+/1sQ/iv/s6731cKfVd7VPqW5Ua\nptXYs1ptU457h9WKVd2TaEU3DAxeMwyWrR5IGFcCOiJFmpAYTSBgrSZLDS4qzpctm7bndFkTQqRp\nHC4E3j3d8vorc+pOFkCIF48EkvguVz2CGALr1jH0jsGHccNq3eNDoHXjm6rWmkgEDb2PpJklAFbD\nrEohRvLMUGUJ+3sZ0yLleD9nWo69imEc1SMxmvk0u9HzIkop9iYZ05BgjKK97DUVmeHhsqHe9igU\nTd8xuAAopmVGjJHMJOzPMsoiIYRx4/C2diybjuDCkzJL664ns4r7x1PytGFSZjKMJ14YEkgC+FbJ\nnm3d4wKcLRrqYeDh6RZjDHmSMJ8m9IPHxUjwgYDB6HH+o8zsWGQ0M7igcHgmWaRIStJEU+Ups0nK\n0Tzn5aMpkzJ9skQcwGh9a940tR4XcWilKYuUe0cVpxdbTlcNTd1zvu24WHfEoLEWlIIiM9w7nJJe\nFpcNIbJt+ssCshFjDN4Ftu3A195dsah7Hi0KPnY8ZVqmJO8zhybErpFAEjw82/B4WfP4dEvTR5wb\nmJQ5qVX0LpIR6bVjtR0n/Dd1S5paVBznO4KPTIqcItUc7uVkqWFWJiTWMKsSgCeLAqwxT94Q3zuk\nddtMypRN3dNd9mzuHE54+c6ELDXUjWO56Xj70ZZ2GMgzi/eRLBtr4Bk1Vm/QShHDuEfLu0A9jKWS\nnHO0fSD4yHLTsmkcqQVrDHuT9HLxh4ST2D0SSLfMk+G4GAH4xrsLHl3UvPNoDKUYIm3vmZYt870C\nozRDCCRK0wyOu/OCbdeTaI0xdtwsmqXsz3OsMdzfz7GJZnZZhFT89yZlSvU+CyayJGE+zXnl7pT1\ntqf3kbYbh01TMxZltVbx+GxDkhi8D3Qh4L0nSwwhQmYNm23P+aYluEieWfLUcu+wwPvIpMyYFpbE\nGo6OZK5J7AYJpFsixsiq7vA+EqLCZi0PTlecr1r+97tLHp5s2XYDPka8j7RDpHOeO/MJibUEPw4T\neQ935hP2KsNsUtD3A70DiKTWkKX2Rs8DfdS+14IJawz7s+LJTUTdDPR+rEJ+Z7/i4X7N+apn3fWE\nxpMYTXZZD3JwHqUU23oYdxmbcRHFelszn1acXNTs7xUkRmPyBHonPzdx7SSQboGrmnLtENAKrFY4\n5/jamwv+14MLThY967qHCDZR9IMHetIkoxkc0yplUiZ4H5lPU1CKKjMkVmNNRsm4B2hWpdIregau\nQmtaZd+2BP3//Mw9vvbWOYttzyJp2A6RPB03APdDAG3oXEeRG7QaDyo884HlxqMUeCJ39kqWq5bc\nKKh7CSVxrSSQbrhN3dMN4+F1TesYvOPR+ZZ/+tpjHp2sOFl1NF0H0aCUxrtxw+jgIn0/nh00DgMF\nyiwBFJPccPdg8j3PNRLPxnt7VJMy5dOvHnC6aDivcrZdh1YWo+Fi3dF0A8ZoEq3YbAcG54kozpYN\nSiu63nN60fJagFePcnwIlLm9URWmxYtFAukGizHSucC2dXzz0ZK2D5wtG7rBEZQGfXk+0AAqDiTp\neAzE1TlFSmtSC9MqYZKnHM4Livdsuvyo9vmIpzcpU6oi4ZW749Hqq7qn7T2LdYcymjKzGKNxrkdr\nTV33RAVFnoCB00VD6x/z+HHO4bykbj1HezlVkcjNhnjuJJBuMB8C623PetuwagaaZuBk0YIa54iK\nVJFllkkYS+E451DaUCUp0yLl3mHGj376Pp+8P0VpLW9OO+pqvmk+NexNsrGnkxkeXdQMPrLa9Gyb\nAbft8CgSq7BousGPm56jwQVwIbCuO7p+oCpS8ixBK+R0W/HcSCDdMO+dAG97x8miHo+B2Pb0MeCj\nhzBWm45Ro41idtnjGfcUwZ1Zxmya8fpL+9w7KLFWfk1eFFfh9MqdGYMbC+BWmSG3ivmsIK17lDYE\nFXBDRAFVaWh7T9s7Hp6PRWEPL0sRhajoLuvmSSiJZ03eaW6QqzI/623HYjugVKTrPeeLmnXjcX4s\nOGq1IU0NhMgsT9E6YpSmzC/fzI6n3D+uuDMvpCbaC+yTL80vj4x3zKcpJ4uGs4VBWcPFpiP6gay0\naDRReao8YdM4FIrFpmPwgSpPMWY8lr26rLguxLMigXRDXIVR3fS8e76lHyIqBlZ1T0QT40D0immW\n0TvHXplStwMaKJKEO3uGewfVeGhdmVGkVsLoBphVOdMycjwvKR4siRHq1jMrEvZyg7KWxFjSzAKK\nCKyalqELLNaWadlhk4RpMW5y3qvy6/6WxA0mgXQDXC1eaNuBi03Lct2zbXs6F1ltOwxgjIaomVWW\nZa1BK6aVZV5lHOxlfPaTR5RZIjv4b6CrxSevvbzP0V7BNx+vuVh3bDtH33lms5RUjwVdg/csNj2J\n0bRuoPcBYwbqblzmLxuexbMkgfQCu6oF5/xYYft0VeNcZN12eA9ajQe5xThW5e6dJ0syXjrOOJrn\n5NpytJdQlDlHs0yW+94Cs0nO/1FlOO9Z1R3r7cC6i1wstxhliGFcWaeVIQSHUmasc9hpto1jsW6Z\nTaRgq3g2JJBeUJu652LdcrbsWG0bztYtTRcoU8NiNVBkBptolBqP0C6znOWmZ3+aYpOE/VnOLLWU\nxVgfTcLo9lBKkVjL4cxyMI3YPOHdBykhwtuPFD5uudh0gCYqR6IVSgWabuDBeU3nxqoQVnpM4iMm\ngfQC2tQ9756ueXBWs9x0NL2n64bLQp0ZUUHfB2KIWKOJAarCcjwvuHNQEEPk7p0ZQ+dkSe8tp5Ti\nYFawvKjZdg6lFUpBZtW4V0kpFLBYtzjncGGs+GDMWOF9fzown9zsY0PE8yOB9IKJMXK2ajhdtuPR\nA0oRlSLNLHXX0rb9eE6RAZsY5mVGCIFJkZIkhnmVkSWGj9/f4+xsI3e3Ahg32Ja5pe0GhsEBEBh/\n39p+wA0eO8lwIWJjxA+REAYUkCWaGKMsghEfmgTSC+Zi1fDuyViZO3gYfIQISmmKPCWx4/lE1miq\nImNWpexPM7LUUGSWw71inOQ2t+f8IfGD0Vozn+Ss64FhCGx7P+5rs4ZpZckTS986ug6cD9T9QKoN\nzgeml6vvJJTEhyGB9AK42uz65oMVb7y74JsnWzb1gNaKNNWkSUKaaNJkPPhtf5biXUQbxbRMxgrc\nhZEjrcX3NatS9qqMIk/Ybju6IdL0A03n8W48nDECF5uxh26UxujIfDIwLSxKKRm+E09NAmnHXe0v\nenRe87/fPscrRZFZeudpB0/XBAofSUyKUTApEw5nBbMqY14lFEWC1bJoQfxglFLsTzO6wTO/PIL+\nYttxctGwrmHo3GUVEA9K44lcrAeW2yUBz0tHFT/0yv6tOgFYfHQkkHbYVRjFGKm7nnXrQYF3Aa01\nVkVQAT+Mn5MXKXtVznyasy8TzeIpTcoULk+zjSiyxDKfZISgaLqebTuMvfYQ0Qo6PJmxPDpvx9/X\nAHcPJ7JgRnxgEkg7apxMdvgYcX6s5BxCxFiNsZpZamjMwOA988m4sfXOQcG0zOTuVHxo7z3N9nCW\nsal7fFjR9Rmr7YAyhrYd6+JprTFaEULA+8DFpuPuQUXvAhupgSc+AAmkHRRj5K1HK77xYEEMikjk\ndNERI4wj+JAmYz26oXd84u4eP/TKHGPMNbdc3CTvPV5kWmV8/O6MKjUYA03neeckoK3Cak0/BDwB\nFxIW24HFtmVSZDS9I03GfU9ykyS+HwmkHRJjZLXt+f/eOOHNhxuW9UBmDZPcMnjP4D1gMVZBZDw0\nL0+5f1xJGIlnblqNm2AXW4/34yF/Wo1zk4pImSdURcq2GXjj3RV160Br5pOUO/OSl44q6S2J70kC\naUeMlRc6Hpys+K83F7QuoI2idQ6/9RSpIbUGa8a6dEYrZkXGS0cV9w9l9Zx4PiZlyuc+fcQ7pysC\ngbb1tC5Q5oa9SU7bOZq2R18ekV4kGgWcLrd4H3jlzkSWhu+An/zcy9fdhPclgbQDNnVP1zvOljXf\neLRm03hCDKSJvjxO3OO7yH6V88mX97h/VGI0JNqQpTIUIp4vpRSvHO8xKzPeeLjifNnT+4gbPCoG\niiwjjNvjcIPntBvou8DFuqN3ntde2pNQEu9LAumaxRg5X3W88WDFg9M1jxc129aT2LEit7GRPLVo\nrakKw7RMSK1Fa0Umq5jENZpVOZ+8pyizGh8jbedYbhzrbc8QPG07sGgH6sERgiLdjPNNe5NM9iuJ\n9yWBdM1W256HZxvqfiDJDCaxGBfohkCMkCaaRINWioNpwf2DkqpMpdqy2AlXPZ1u8OiZYlK0vKM8\ni7Vjue1YbnrawTP045aF7aan6Qd+9NP35MA/8V1kt+Q1ijHSD45m8GOPxxgyM5b4sVYx+IDrPCFE\nJrnlEy/NmE1yWdYtdsq0yshTS1SKxBiKJGGzHbhYdWzqgbod6L1HAY0LvP14w9uPliw33XU3XewY\n6SFdIx8CnQ9oIs4FktRwOE05XUN0EZ3C4X7Bq3emvPbSHvdk8YLYUVf7luaTFK3hrcdLfAw0/UAE\ntNEorXA+sqo7vvF4y+G8wGgl80niCQmka7Kpe7rB887jNY+XHV03gFbkxnB3P2OYpUzyhNdfnnFn\nv5IXrdh5Sik04x65V45mPDyvGQZPiIAaw6htO5RRnF3UfPPRBh/g1bsynyRGEkjX4Kok0NmyxTnI\nEoVRCSFEIKKU5t5Bwd39ktdensvwnHhhhBgvK89byjwhz1LqbsD7sfJI9IHEGtZtzzcfb+hcoBs8\nn/vUHfk9FzKH9LyFEKg7x2rT8ubDJZu2xwdo+oHOebI0wWrDJ+5Nef2VfXmRiheKVgqjFfNJxt39\nikmiSbQitZHgPdooUqNJtCUwzpO+/XjDYtNcd9PFDpAe0nO0qXvOVi1vP16z3PQ8XmyZFBlJYiiy\nBBMjLx1VVHnC0X553c0V4gNTSpFaTVUkfOLulBjhrYdLFuuGxGjyMqWwllmVonWk6z0aqFvPfBLl\nBuyWk0B6TjZ1z2Ldsq471nXPqu5oOk8MLbOqIEk1LgTazjErU6wcFyFeUFfVwqeTjE9/zLBXWS7W\nHW88XOF9JMsSEqvphoAPPXliqbuewXsSYySUbjEJpOdgHKYbWNQ9zkeM0UQUeWZpB4due+ZJhtWG\ndvDkuZxfJF5skzKlKhJWdUdiNXnasO0cm+0AGup2QGkNMaJSeHTeYLRlr0rJEiOLHG4pCaRnbFP3\nNL3nYtVxvurIE0OeGpQeD9pzIdI5T/CQ5VBmCXf3q+tuthAfmlKKvSpnWqSXvZ7IWw9XPFo0WGvJ\nUw0hUKaWtve8e7rB+4I8Hd+WJJRuHwmkZ+hqNZ3RCm00WilcCESgyhJCDOSJITGaO/sVeaaZT8eN\nr0LcFFprDmc5kyKhzCyKc3w0KBUYfCTPLF3nWW4GnB9LZW0bzw9/XCo53DYSSM9IjJHOBRQQIuSX\nJYA8CqMNe1Vkse2JGlJryDPL/jRlflnnS4ib5Gpe6XC/4tXOExVYAyeLjn7wOMDo8Y/zntNVw71N\nwXyaX3fTxXMkgfSMhBjZNgM+RGIcVw/lWUrT9XQ+Miky8jQhSzXTMmNWpeQydi5usEmZUuaWrnc4\nH4kh8vCsxUWAiA+Bphtr3nkXuVh3TwqxittBAukZqZsB5wNaf6sI6mySUGQGBUwnCYkxpFZTFokU\nSxW3gtaag2nOYtPRdg4UBBeIMZClFm0UIUSsVrS942LTsD8p5LVxS0ggfcRiHO/0usFjzVguRevx\nxaSUwhjN8V4mFbvFrXU1CtCmhvsHFY8utjRDIE0MbeeJIRBj5N3TzVgL7y5kiZXRg1tAAukjdLWI\nYbnpuFi3aK1JLMSoKfIEpSAxiqpMZeGCuNWuloUn1pAYxemqpR0iMTouNh1t70lWLe+ebVisOn7o\n5b0n/0/cXBJIH5H1tqMbPG3nOFs0nG46YoA0VewVKbMyYVKmY+Vj6RUJMS4Ln2RoBYMP1Oc1devo\nBk9iNF3vWW49q+05F5uW116aS827G04C6SOw3nY8XrQAfPPRChciiVF4FfAe2sHz6KKlKhKyRHai\nC/Fe0yrj1XsTusETfKDtPE3nqLsBZTTew8Vm4K2HK+7sl7x8PL3uJotnRMaNPqRN3dMOAYh477hY\ntaybnrpc7zNCAAAgAElEQVT19C7QtgMxwrbr0TrKkIMQ72NaZlhrCTHivKduHcpojFbECG7wbDvH\nw7MNIYTrbq54RqSH9CFc7TXqesfJsmGxajldd2SpIU89+9OcoDWJVRTaUuYSRkK8H6M1R7OM5SYh\nzQ26GQgush4Gmn7Aoti2PVliuXNQ8bE7s+tusngGpIf0IfgQWG17FpsOFcfH8sQQQqBpHU3nyBKD\nC5Es1SRGLrcQ70cpxcEsZ17lVIlhcJ66d9R9T3QBYxQKxemy5nRR8/Bsc91NFs+A9JCe0njiq+N8\n2bCpO1AGYxSTzLLqBryLxBCw1mAUHO7lUjBViO9hUqZ86mNzQgi882hD03XoqElzTZZYeh/wm443\n3l0RIpSZZTaRSg43iQTSU7ha3r1tHG89XHGyaVE+olAc75cczwoG75mWOUVqmZSG+4eT6262EDtv\nUqZ89oeO2DYD//Ptc85WHUprmmZgCBFrNV9/sKbpBg4m402ezMveHBJIH9DVvFHT9PznWxfUnUMF\nRQCcj5ytau7sV3z83owiMxzOcvJUikQK8YNKjOalOxPqfiBgWLcdgUhiDVqNr8HFZuDNhwuMMVSF\nvL5uChlD+oBCjGy2HW88WnNysSUAViuy1FBkhiQxl6dgRoo0JU8TuYMT4gPQWjMpLLMiZVZZXB8w\nRqPN+PHBjdVQ3j1vWawbvKy6uzGkh/QB1c1A7zxd74koEquBiBsCSkFEU6SaO0cVd+eV3LkJ8RTu\nHU6pW8di0xMj+BBxvccaTWY0UWmW255VO7CuO/an5XU3WXwEJJA+gBgj7eDZtoFt29M7jwsRrTV5\npqjyFGsNx3sZxzMpCCnEh/Hay/tYq1jWHSeLhrbz2HQ8Pyz6QNM4LpZbzlcVVhumVXbdTRYfkgTS\nB/DgfMN/vnFB0zrOVx2LTYe5PM8oSRImpSI1kcO9HGPMdTdXiBfex+7s8fG7WzbNQASU0nSdIzIe\n5BeioWkH2iFD1b0Mj7/gJJB+QI/ON5xd1Gzagbb31L1ncI7GR/JUkRNwQ8/8YM5rL+9fd3OFuBGU\nUnzmE4ecrxtOLhq2vUdrKPOUu/sVWWrpnKfrHVorqsuzx8SL6akDKYTAb/3Wb/Ff//VfpGnKV77y\nFT7+8Y8/+fhXvvIV/vVf/5WqqgD4oz/6I6bTF7MGVQiBTe3YtJ71tmfbOobBk6QpiQvsVYb9ac4P\nv3rA3aPqyYF8QogPbz5J+cT9OfuznJPzFucDRW7JMosbAqk1dEMgSyMhRoy89l5YTx1If/u3f0vf\n9/zFX/wFX/3qV/m93/s9/viP//jJx//jP/6DP/3TP+Xg4OAjaeh1ciGwrnsenm1Yrlu2ncf7QJIY\nIhFtLAd7BWlqCEFeFEJ8lLTWHM/zsTAxilU9oLWibgcyqxl85GLVQowc7clG2RfZUwfSv/zLv/AT\nP/ETAHzuc5/j3//93598LITAm2++yW/+5m9yenrKl770Jb70pS99+NZek7Z1nCw2fPOkflKhwUco\nQhyHDPphnGhFyfESQjwDdw8mxLhm3SSEqNk2PXtFgjaaxxc1bvB0w4DW8MmX5tfd3Gv3k597+bqb\n8FSeOpA2mw2TybeqDxhjcM5hraWua37pl36JX/mVX8F7zy//8i/z2c9+ls985jP/7dfb3y+x9vks\nBDj+AOXrY4w8WjdkeU5i1xRFigPCEKj7gTRNSNKU2SzjYL/g/vGEvRdktc8HuQ43lVyD0YtwHY6P\np7y6adnWPQ/Ptzw+b3l0vmFwgSSx6CThrO54GZ7qiIpduwZVmT51ubFd+15+UE8dSJPJhO12++Tf\nIQSsHb9cURT88i//MkVRAPDjP/7j/Od//uf3DKSLi/ppm/KBHB9POTlZ/8Cf3w8Db729hODJrOZi\n2TM4TwwRgsLqiA6ehydrjqcZfd1zUvfP8Dv4aHzQ63ATyTUYvWjXoa47mu3Auw+XuBBJE01qFdu6\nw7vI/9s9wP6P8IHezJ/XNfggQbH9EO8ju/zz/F7X4KkrNfzoj/4o//AP/wDAV7/6VT796U8/+dgb\nb7zBL/7iL+K9ZxgG/vVf/5Uf+ZEfedqnujabuud83bHeDtRdYFZlHOylHM8L5lXKbJowKRMO9wuO\n5xVH8+K6myzEjTcrMyalRRnNpErIsm/dVyutaFpH7/w1tlA8rafuIf30T/80//iP/8gv/MIvEGPk\nd37nd/izP/szXn31VX7qp36KL3zhC3z5y18mSRK+8IUv8KlPfeqjbPczd1VANTGGMje4JpCmBmv0\nuP8hTyAEXj6uePnOHnmaXHeThbgVlFKkiUYrvm01a4yR1BhQAPHa2iee3lMHktaa3/7t3/62x15/\n/fUnf/+1X/s1fu3Xfu3pW3aNrgqoXv2qH0xzusETgyVPLFpHlNJMJzlH+1OqIsEajZHjJYR4Lg6m\nBbMyYds6lFaAIjWGJFGk1pJa2WL5IpKf2vsIMbKte3yEEMEmhlmVYa3D+xytAjZJubtfUBUpiVHM\nJ5nsPRLiOdFa86mPzXnr0Ya696gIykBqLa/ereTssReUBNL7qJvhskadou/G8egYYVZY7u2X7E/T\ny7BSGD2eEislS4R4vu4ejKt8V9sB58EamFXJk8fFi0cC6TvEGOl9JEsMi03LcusIcRy+28RImljS\nxFIVCSFGtFLSMxLimtw9mHA8D7gQsFp/W88oxiiv0ReMBNJ3CDES47iM/dFFTdv2gCW1UJYZxigu\nNh1VkcickRA7QGtN+h2vxdWmpRk8CoU1mtTKybIvAgmk76CV4nzZsG66cdNdAOcaEmsp254yt9Rt\n4P5hwEpFbyF2zjfeXXCx6QhBYQxMsoTDecFGqoHvPAmk94gxstx0tL3j7UdrFquBznl6H8gSj3cJ\nj85qjvcLNk3PfCL7joTYJQ/PNjw8r8dRjjgu/u56B8DBvJBq4DtOAunSuO/Ic7ZsOVlsuVi1uAjO\nR6wxeOdxwbJpOg6mKd4jVb2F2CEhBB5etOPpsi4yhECMkQZoes/eNJPCxztOJkH41ibYGKHpBs6X\nHZ0HRcRYRaIV1mqGIaCBJLWEOM43CSF2w+A93nkGFxiC52pzrFLQtI513Unh4x1363tIV5tgtRpr\nYT083bKqO+rW4X0ApcgyUMqQZ5oiT5nmiVT1FmLHjKvpxu0YXe/x8XLMTvFktZ3Ybbe+h3S1qm7b\n9Hz93SXn65Z+CLjB0TmPD5528EzLhFmVc7SXgVIUiZbhOiF2iDWGIrPE6CFevjYjeBcpzLgkXEY1\ndtutDyStFG03ULf9uOu7i9Sdo/eBYRgLNLohkFnFrLTs75VMCsP0BTliQojbQinFy8cVRimSVENQ\nDD5gDexNc1Z1h9xC7rZbP2QHcLqsefPhkgenawIKhSJNLFp7yjzBas3H7k54/ZUD8kTCSIhdVRUp\n9w8nnK8boo9EFYgBFpuetnU8nG156ejFPCvoNrj1gfTgbIP3cLbsWdYDzgXQijyx7M9yyizh/mHB\nq/f2OJzlUiNLiB2mleLOQcGqHhhCi/egNDjvcRbOVi3TIpWbyh11q99dQwjUrWexbjlb1agILkZ8\ngLZ31G1P2w0cTEoSa6WgvRA7TimF1jA4R2oNqVVopXEhUNeOR2c1dTcQZS5pJ93qHpILgRAi58st\n23YgzSwuQAC89/RDwGjFncMMrZWs0hHiBVDlyZOVdiFGun6gdxFjFKt6oCoseWbZq/Lrbqr4Dre6\nh2S1JkRPM8QnZYDSTJMaRZZZUqOYVzllnpJZWVUnxItAqXEBUmo1zgfafiy+2g9jr6gfAst1x+ZD\nHBEuno1bHUhaa0IYd3FXeYrWitRqslRRZpYstdw7LCgzKzWwhHhBGK3Zm+QQoO89IQIBYvBYEwk+\n0jtoBy9DdzvmVg/Zbeqeo3nOXpkyOE+ZWnwIZDajKg2p1bz+ypyZdO2FeGEopTiYpkwnCZ0PXJys\naXpH9JE8S4lhy9E8Z1qlUkpox9zaQLqq0ND3gXuHE7SG860j+oHEJExyzcfv7fPKndl1N1UI8QFV\nZcrBtODR6RatILcWnSq0Uazaga+/vWRW5ei53GzuklsbSO89pvzuQYlSMJs4hiFgNHzi3h6v3pvK\nvJEQLyCtFMf7Of/rHYu2FpRHa4PVYIxiOzi27XDdzRTf4dYGkgKGEDFaUeSWO/slbe8IASDwyp1K\n5o2EeEEppYgKqixhr/R0vSOEcb7IGs0kTwgofJBzzXbJrQ2kCCRG40NAqTGU8sziQyQxikrCSIgX\n2sEkJ0sNWaop0vHoCWvU+Dr3kEoO7ZxbG0haKarcsm0dgwuMI3OKIjXkmZU9R0K84Iwx3D8qqbue\niEbpsecUfGCSp+RpgpHKKzvl1gbSthmo3xNG1mgmRQJAKnuOhLgRXnt5n6bzvH26wfWAikzLhI/d\nqdifpvI63zG3MpCuDuSblCnbuqN1kW7wKAX7k0zmjoS4QX7ktSNeuVOxbhxdP0BUBBS9C2zqXl7v\nO+TWBdLVcm8FrOuewY3VgJWKECPVZS9JCHFz7E0KtOo49xEfIjFGVvVAYhwAx9fcPjG6dYEUQmTb\nDKy2PRfrhhAiaWKoipSm98zqTmpcCXHDxBhZbDqcH0+HvqrPMPjAxabjE1KxYSfcukDatAPLTcPX\n3l7Sdh4FaK04mObcOSxZrntmZSZjy0LcIMtNx8mypR88gwtYDUWRkBpNmiR4H667iYJbFkgxRr75\naM1bj1acLWrGX0FFZg3v9muMgUmRyt4EIW6Qqznj1bqjD4Gud7ghkqQ980lKam/eBtm//+o7T/7+\nk597+Rpb8sHcqkBabjoenW5YbAZOli3eR5SCPEmYlpZhCGzrDphcd1OFEB+Bqznjrne4GNhse9Zt\nj3cQgqdpc472cjZStWEn3JpAuhpDfnRec75qGLwHFBYIBHofWGw77h5WsgdJiBsixIj3gboPGAWn\ni4ZNNxB8JARoe0+VW04vGmaZkaH6a3ZrAsmHwGLTQwhcrDq63jM4j0JjrSfPEkIM7FWpnAwrxA1R\nXy5g2mw7Hi8btt1Y9TsSQY83qufrjsW6pkoqGaq/Zrdmm3KMEecDZ5uBITh8AJTCx0DdDTR1w16Z\nURSp9JCEuAE2dc/gI3miQUWCi/S9Y2Bc9q0VRBSD95yvOjkbaQfcmh6SUgpNoK5b8iTF+x7vFMZo\nUgsRzbS0VKlUaRDiRXc1d6SVoiozsrrHRYhKUTcDBNBGYbW//PxrbrAAblEgGa2p8owhaoiQJ5Zg\nAQ2ZHQ/jS5KEaZVdd1OFEB9SiHEMmct7y/v7JV+vEh6faogRYw1ajTekdT9Qd73ciO6AWzNkp5Si\nzA2TzDCpUozRGAWJhjJLOJyXvHp3SpBbJSFeeFop9HvyJSrNvXmB1pEqTUkTjTUaRSSzltVykG7S\nDrg1gRRjpCxSqjKhrjucc8To0UqT54aXDiuyVKp8C3ETKKVIrX4yL6QVzKYZkyohLQxFYkmsJs8T\niiKh8Z63T7bX3Gpxa4bsQox87a0LYlTUbqBtI1op0uDQy5qjT98jT2TZpxA3xaRM2dQ9nQvEOA7N\nH89LpkOk6QaCi2ijyFNDlVm63rHedjJsf41uTQ/p0dmG803LYtOxPyk52iuYlimTMiXLUh4vVpT5\nrclnIW6FSZlyMM3Yn6Z84v4ed/YLQvAQx0UNxmqMhuk0xVpDMwRZbXeNbsU7cAiBdePAQ9sMpIkl\nSYA4Vv6dFyn9oOgGR5FJKXohbhKlFOZy5OO1l+ZcrDrOY48GlNEkWnM0ryBEFONoipGRkmtxKwLJ\nhYBCUeQGZSAO37oDskaRJAalIMiNkRA3VoyRJLF86mMHPDhbE4LCB4fWhqbpSYA00Wgl1f6vy60I\nJKs11mqmZcIkz9iEFpQa/4RAliqqIiFPZJe2EDfV1VLw4/0SgNNVjXMWpTVJosm1RsXxeBo5tO96\n3Io5JK01VW44nFfcPSzonaftPE0zYJXiaFbyyfszjJQNEeLGeu9S8KN5QWoMoIkh0g+BYfCURXq5\nCEKGS67DreghAdw9mPCNdxe89vI+fTewqgcyaziYZRzPCz750vy6myiEeIauloL3LrCux42wkyKh\n7hxZYmhbx8PTDZMqYz5JZR7pGtyaQIoxMpvkHB6UTDKLih4XNakBpcf9CrLkW4ibbVKmPDxb883H\nG06WDV07gIIks+gQUNoyOE/dDLL8+xrcmkC6Gj9WSmG0QitLchlAPkRZWSPELbCpe7ph3IMYnaPp\nHCjFNx+sSDTcOSjZn6T0PspN6jW4FXNIMI4ft93A+apjte1Ybnvqy0O5lEIqNAhxw8UYaS+PMF9s\nGpQ1GKtRWuNCZNs6luueSZ4QI1JG7BrcmkDaNle1qiLxsuJi7zzbpiezUuFbiJsuxIgPEEJkGAKK\n/5+9e/mRLLsLff9dj/2ORz6ruqra3e62MdfnGB9jBkdXlgELIfEP2HJbggEjLIEQSIgJA4QsBEie\nwgQJIQ8wRh5aQgKJg2VgZMmHy7nXD+x2u7uqOisrXxE79mu97mBnFt1+dld1VWRlrI9U6s6MVOaK\nHZnx22ut3/r9IE00eSrJMoWWAucDxtl4k7omG7Fkd1GKXghB01sWqx4YzxxM85SqSNY8wiiKHjcp\nBFoCBNJU44JHWUfTO5rOYYylNY5vvnrKs/tTdmfxPNKTthEByYfAqhlwAXaKhGGSvSGtM+4fRdEm\nEEKQJYo8VaSJwAcFAc4aQ6IkWiVkiSLRiqa3HBzXXN+ZrHvYG2UjApIAjB83Mt15OQZ5fiDBuIsF\nvCiKrrqLA687ZwP3zla07YAKsDMrCd4xr1KqIsU6WDaW/S2PlBuzs7F2GxGQAmCMp+3HrpHLuiVP\nNUU2lqCPW5dRtDkmZcqH3rfH11+RvOICxguyRCIQ7MyL868a95us96QxID0xGxGQmtawbHoOzxo4\nbmlbQ5ZK3rU/49lnpnHzMoo2zL2TFWmi2Nsq8CEwnWTYwdJ2hiJPAIGSY9mx6Mm58gEphMDtw4bj\nRcdgPGWZoIzDBzheNlzfzRGxmGIUbYzlqqfuHEqNB+JXrWE1nOIcFLnm+lbFtNRMSx2X656wKx+Q\nrHMcLlpCgIDEew8EPFB3DiFilYYo2hQXZ5FA8O3bp9w/bTlrBowNmNaws12SSbi+vRsTGtbgygck\n5wNHpw2LxmCMJS0SMI7teY4QEut8zLKLog0xHnYV3Dlccrbs6I0jUYJZlbEUgSyTXNuuHsye4o3q\nk3XlA9LRaUs/OOqmx7hA6qHvB5rBc3O3QisZ95CiaENIISB42mZgMJ7FasCHQNN7us4R6FluG6Tu\nublXoWMHgCfqSi+Qeu9pegdA21ma3rBqDO3gOF22eGMoUhXvgqJoQwghQEi8EBjr8T7QG09vLD4E\nWus4qwec89SNWfdwN86VDkjWe5wb25RrLQCBD54QBEKAY9zEjKJoc2xPEqSEJFVoOb4JFlkyvhc4\nj3WW4ALWh9gX6Ql76Hdj7z1/+Id/yDe+8Q3SNOUzn/kMzz///IPHv/CFL/D5z38erTWf/vSn+djH\nPvaODPjt0FLig2fRGaRS5Ml4Uts5T5opAgrrPEmMSVG0MYSU7M5znA0Y43ChR0pJ3xvyPGFSZmSp\nflBgNe4vPzkP/Vb8j//4jwzDwN/+7d/yta99jT/5kz/hL/7iLwA4PDzkc5/7HF/84hfp+55PfepT\nfOQjHyFNn2xbYCklIsBq1WPd+MvlEThjyXONkPHuJ4o2jRSCF27MaTpHMziMdahMUWU5e/OS2SSj\nLBICscDqk/bQAemrX/0qH/3oRwH40Ic+xH/8x388eOzf//3f+dmf/VnSNCVNU5577jm+/vWv88EP\nfvDRR/w2LFc9p/VAAAYz9j2R1hKCx3SWbEeh1ZVetYyi6PuMnWMV774+QUmY5Jqi0jSNpcgU8/Py\nQkUSuwA8aQ8dkOq6ZjL5rzx9pRTWWrTW1HXNdDp98FhVVdR1/WO/3/Z2idbvXEbLohmwAtIi4dlr\nUw6OGpZtTzsYEqXonGM+y3nm+nxjD7/t709/8hddcfEajDbtOuwD2f2aNkBRGrresjVLmU4SplXC\n9d0pN/fWew6pKtNHem/6lf/73e/cYJ6Qhw5Ik8mE1Wr14GPvPVrrH/rYarV6U4D6YU5Omocdyg8I\nIXC87LHWcXjcYKzHuvFfQDAYi3Ge1w+X/D/ffJ2bu5v1xwjjG9Dh4XLdw1ireA1Gm3gdQggslj2l\nFPQEdrZyFmcttgOfKLT3j+WavJ3Av2qGR/pZl/U1/XHX4KHD74c//GG+/OUvA/C1r32N973vfQ8e\n++AHP8hXv/pV+r5nuVzy7W9/+02PP24X7cqVFAjhEfK8Nx8QgsC6gAiCo2XPt753cl69IYqiTXHR\nksZ4MCbQD46m85w1A8eLNnaLXZOHniH98i//Mv/yL//CJz/5SUII/PEf/zF/9Vd/xXPPPccv/dIv\n8au/+qt86lOfIoTA7/zO75Bl2Ts57h9LCoEU4JFslwVHi466HzDWo5Uk1ZosUQQCt48ajpcde/Py\niY0viqL1umhJc7boaQbDLNckiUAIyaIx3DtecWNv81ZO1u2hA5KUkj/6oz960+fe8573PPj/T3zi\nE3ziE594+JE9gnHTUtIbx95OwcFxDcGhpCRJJBJBliqUkFjj6fqBEIq4gRlFGyIASgiOVi3BA6uB\npjUkUlAWCcvOcd3HXkhP2pW92pMyJUsUWgmmk4ytSUmeaWZVSpZIEDBYT6oFQqo4RY+iDSKFIBBo\nG0vdGup2YNWPVVxAIMJ4sD56sq70kdBJmZJnCms937t7RttZ+t5inaNQKWmimE9SMq3ieYMo2jAn\nixbnPVIKJJBIidaSrreIWeyFtA5XOiAB4zKdllzbKTDeYYXAdQ6pBFWq2NsqyZJYzy6KNslZ3YOQ\nVEVK01mElFgXSM5PnhSZist1a3DlAxJA3Q7oRLM9LeldoPYDSgSqXHFtu6IsknUPMYqiJySEwGAd\nCMGNvYrj0xaRKKxWBAF5ori+E5Oc1uHKByTnPcYFCONBs5mWaBmQQpBlKd6HuFwXRRvEh4AQkkwr\n6nZAakmRKfwg0Vpxfa9CxdnRWlz5gBRCYLmySClp2h7pFCGAThSrztB0llVrmJRPts5eFEXrIYVA\nSUGqBKd1y9lyQGWavjXkSnBzr4pL+Gty5W8DVp1BykCWKqwHF8D7QNcbslSRpYqTuo9l5qNoQwgh\nSJTgbNXhbSBNFdMipcw1RZZyvGhZrvp1D3MjXemAFELAOZhVGVKMZw/KVJNlmiJV7M8LlJL0g8fF\nFM8o2hh5puisRyhFpjRZIpmWKVtbOc3gaXobb1LX4Eov2fkQCAi2qhTvHGWiKYpkrLsnBZMiRYx9\n+6Io2iA+gPewXHV0Q6DyDmscxgTyXON8iL2Q1uBKB6SLEkJlkY57Sa0hzxTBalKtKIuxCVeqZNzE\njKIN0veW+ycrTusBrSXGKIbBsQgtkJNqGZOd1uBKB6SLEkKD9QgpmVcpXiqCd4Qg8T6QacHWNIub\nmFG0IUIIfPv2gmXnaK0j9I4gxLhQMgSSmSCNvZDW4spPCyZlirGWzjjyPMMDvQk0neXgqME4HzPs\nomiD3DlaclK3zMqUvWlOniq8DxhjKVLFzmwsMxY9eVf+qocQ0FqzPdHcO26YlQlit8IHIAR8gIPj\nmus7623GFUXR4+e9Z9VaEq0xtkcqyaxMyIqUvu3Z2y6och3LBq3Jlb/qF72RQgi01qGURAhQkvOE\nBkndutgTKYo2gPUegcR7j0LgvUdIQaIUHjCDY1bpWDZoTa78Vb9IbHA+EPx4h2RswDmP9yAYZ0mx\nsm8UXX1aSpQCBCSZxNtA01qarkdIwc68jKsla3Tll+wuEhu892OKp3EcHte4IKgyhVQgkXGKHkUb\nQErJcmVY1gM+CKoyYQrMtzIyqXj+xjyme6/RRrwLT8qUZTMQvKc1hiAg1YqA4OSsJUug6ey6hxlF\n0WP2+tGSVTfQDp5VN9APliBgd3YxM4q1Ldfpys+QYFym80Hw3I0tjpueuu5ZtQNCgM0kRbpFbz1V\nCDHVM4quqOWq595phw+wv1UwWIdzHq0FSo37SYmK6d7rtBEzJOv9mFUHDL1nsew5WXWcLXuOlh13\nj2pWzRC7xkbRFRVCoB0s1l5U+ld4P3aNrleG+6cdgzXMqngEZJ02YoakpURJOD5teeX1MxbNgAtA\ngMbAa4cLhBQ8ey1uZkbRVTSWERsFoF4NSAWlTnAuUOUJVZ7Gyv9rthEBSUpJkUqOFg2L1jFYTzhP\n+dRacbQ0TMv+vJ3xRkwao2ijSCE4WbTcParpe8dpY9AS5tOUVCkmVcq0zOLS/ZptREAC2JnneARD\nP9ANjgCkUpAphXOezjicD8TesVF09dw7WbFsHEWmWNQ9vTEsB8ei7ri2VTItUtrOkGVJzLJbo40J\nSFIIylwxKRO0HntRCCEIBEQISAEy/g5G0ZXjvWfZWNJUYmtAnR8HSTRSCrJC03QGBbjWsDvL1j3k\njbUx61NKSnKdMC0ztJT4AMY4hsFhfaDK07hcF0VXkPUe58E7TzsYUqVItEBrQaYlmdYs2uG8asO6\nR7vZNmaGFIBn9ioGKVgue0xwKCHIMs21acHOLKftLNNKrXuoURS9g7SUaAXHZz0nZz39YGkGj3ee\nREvKXHHNT8a95rhkt1YbE5CkEEzLlJ8uE9pFQ28LQggUuWJSZOxMMwYXCHFDM4quFCklgkDTdZwu\nO1xg7AjrAqmGziQ455iVCQjiwdg12piAdFFCaGuasT0raXqLtw4vBXkiqMosdomMoisohEBVZngk\nCKibAWP9WC5MaurGEICmM2xP83hDukYbE5BgLCE0uIBOJO2ZZdn2KCEx1mGc5z3P7sS7oyi6YnwY\niyknSjItUurGEVTA+/GwbKokaSpxHqoi5tmu00YFpBACaaI5W/acrjoCAofHNgOrzpCnmt3ZtXUP\nM2E477YAACAASURBVIqid5AUAinHGdCqMxS5AqEggPOeNFUEL6hyHVdI1myjApIPgWXdcVb3KCXG\nteTGMFiHEJIQztibZ9zcn697qFEUvUOEEORaIiUIKfHOIoMAAVmiUVogRSBcscKq/+trt3/o53/x\nQ7ee8Ejeuo1KchTAqusxDrI0wduA8R4QeB9YNh137jUcHNfrHmoURe+gskwpsxQtBTIIvPMoISnz\nhHmRkWUpaRILq67bRs2QApAnCik8IQhOVwPWOurW4PGUreburKa1lv2tMp5LiqIr4ui0pcgUVZGg\nJAQEWgiKXLM9yZhPEuZVvu5hbryNCkhSCHbnE2aTnIPjFYenLW07MFiLB6pC80xd4mzgtcMlz12P\nS3dR9LRbrnpuH644Whqsc3gvEEIym6aURcL1nZx339ymX/XrHurG26gpgDg/CPvT79qi6SxmGGh7\ng3MBJQIEwcsHNa1xHJ31+NjWPIqeaiEEXj1ccVL3TCvN9iSnyBO0CtS9ZZIr3nNrh1ms8H0pbNQM\nCWBWppS5JE8VOhlPcCdpgtYKJWDVDTS9wTqPcY4sLttF0VPLOkfTDgTOD8dPMqoyxbuAc47rOyXT\nMqZ6XxYbF5AA0jRlWibsb1WEIOh7R9c7gveIEFi1luDjie0oetqNjTkFWgmcH6uwSDn+8wESrYlt\nOS+PjQxIRSJJE0WRKpSUCOVIEISgEAH63nFwUqPV9XUPNYqiR5AoSaJBBAg+4Pmv0mB5qphXabzx\nvEQ2cj1Ka8279qcIAYmWaKWQjC0pskSSpgprHXfvL9c91CiKHsHhacPhacP3Xl/w6kHNwdGKYXDM\nCs2zexV5qmOq9yWykQEJ4Gfeu8/zz8xItSBLNGkimU8ybuxNuLFbkWUZZyvDMmbeRNFT6eC45tWD\nJUWe8czelKpMEEKyansCcHN/EtuVXzIbuWR34Rc+9CzOOe6fDQzGorWizBKmkxRrPVpJWuOZxArg\nUfRU8d6zXBmawQGSSZkwKROcC4Tg2Z0XlPlGv/1dShv9iiileM+tbRK1pB0CSoOUAuc8syJFKYWA\nWN8qip4y1nvunTYcnnYoIRASMq2ZT1OsBesE1nvSmEV7qWz8q/HirW32tkoCjmHwdL2lSjU39iuy\nRI4ZOTEYRdFT5ei0wRiLECAEIKC3lrPlAEKQ6LFxX3S5bPQM6cIH3rOH8457Jy1SCDxwthx49lpF\nqkRcrouip4j3nvtnA70LLJsB5zypVhSpxjnDzixjViaxNNglFF8R4OU7pzS9AyHpLSxWhsOzFd99\nvWawnroZ1j3EKIreopNlz8miJdOKvXlGpjW9sZy1Pc57bu5VXN+ZrHuY0Q+x8TOkRd3x+tGKIMaN\nz643LBpDvbJ0vWWSC4o8I4TAtMrWPdwoin6M5arnP1895ZXDGgEoAfNJwq2iIgDTUnNjt1z3MKMf\nYaMDUgiBVe8YHKQJhAAn9cCdgxUrMxCs4+5xw7VZznuf2+H568SgFEWXVN0MvHZ/SWscWspxuc4H\nlk3PrLLszAvKPDnfVIouo40OSD4EBOHB72fTG753e0FrDP3g8CKQdQN3vce4wPWdAtGIeHYhii6Z\nEALdYOl7j/MeJUEJiRceHySr1rA1yZgWsTLDZbbRAUkKQZqMZ4+6YWC56lgZQ28cq86QKMmiNrTa\nE/y4HCCloornkqLoUvFhbLbpAvTdQNNapIRMjdvk0zylKlNCLFx3qW10QBJCkGrFM9s5d448be/o\nBkM/jK2Mk0ThwzhzEgTuLzqmVRHPJUXRJSOFIFWSxbKlsR7rHN3g8IwV/VMFW9UWeabj3+8lttEB\nCXiw/Ga853SZUuQavMWFsbbdYB0B6K3n/knD/rxibx47S0bRZSKEYLCOZjDU9YDxkKQaARSpYmta\nIIRAxXOFl9rGByQYg1KZa5wLvH6/4bt2CRacDYBAiECRarreAYFVa+I+UhRdIstVz8FxhxQKFwLO\nOpASoQWJVMyqlBACqZZxuf0SiwHpnJSSa1sFL9za5u5ZR3AWJwIKKIqxf5IPgapI6a2P+0hRdEks\nVz2Hpy13DxcsGkuaKBI1Vlkp85QQPAjBrMooi9iM7zKLAekNZpOcZ3ZKbu1PGDpD3bvxLIOS5Fqi\nlKbpDJMyi+vQUXQJLFc93z1Y8M1XT3j9cIUNAYIgTyXzac60TNFS8K69kkkZM+wuuxiQvs8Lt+bc\nPWo4WnRQt3QmkClBWWYgYNH0KCXZncXzSFG0TnUzcLRo+eb3Trh9WLMaHMGPzfj6IeACzMuE7a2C\naZWRxeW6Sy8GpO+jpOTFW3O2ZxnfuS0wzhFCIBCQwMlZj7WeZ/dj6ZEoWpcQAseLnn5w3DvtGKxH\nBLDOIYREBcGqMZSpYn+7IktU3Pd9CsSA9H2EEGxNMqwLbE0zlo1hcI6mG3DWQwgsO8P01RN+6rmd\ndQ83ijaS857BeYwPrJY9vXdIKZFS4vGkWQoB9nYq3nVtEgupPiViQPohJmWKdZ77hQYEr7x+StNZ\nEIKz1pAqSZVrlJK8eGtr3cONoo3U9oZvfOeQk1WPC+PNZJZIUq3QSlJoyf5WFoPRUyS+Uj/CfJKx\nv1VQNz3WBZJEI85bURjnOa0HTuqORd2te6hRtHHazvLdO8ecNAadSIQIeD/2MzPWoZVke6tge1qs\ne6jR2xAD0o8ghGBeJbS9AQHGuwdlR4oioe0swcFq8IRYjySKnphx/6jDWEEAqjwlSRRSCaQGpQSz\nMuH9z2+jlVr3cKO3IS7Z/RhZljCrUhoTMLbHM55X8g4Gb7E+IAkxBTyKniBjLbfvL+mNxVpLkggq\nNEII/Hlm3c4s49beJGbVPWUeKiB1Xcfv/d7vcXR0RFVV/Omf/ik7O2/e4P/0pz/NyckJSZKQZRl/\n+Zd/+Y4M+ElKlWR/p6IbDGYQSKURUuCtx/pA11vqzlK2JraliKIn4OC45uvfPeblOwu+e3dBZx1Z\nKtFSk2WC3XnBLFc8d21OFbPqnjoPFZD+5m/+hve973381m/9Fl/60pf48z//c/7gD/7gTV/zyiuv\n8KUvfempvkNRSjEvE5azkhAEde+oe4sd7FjGXkucdRgXqJshppVG0WN0cFzzvYMlp3XP8cpggwME\nvfHILDAYS9P0fOD561zfq+Ih2KfQQ+0hffWrX+WjH/0oAD//8z/Pv/3bv73p8fv377NYLPiN3/gN\nXnrpJf7pn/7p0Ue6Js/fmDMrErbnJVUqyaTgxnbFi89uoaVAKUHbGXob95Ki6HHx3rNYGU6WA9YF\ngvfMJgVaS7wPGONIlaIqU95zaysegn1K/cQZ0t/93d/x13/912/63O7uLtPpFICqqlgul2963BjD\nr//6r/Nrv/ZrnJ2d8dJLL/HBD36Q3d3dH/lztrdLtH4yG5D7+9O3/LUhBHSW4p3jzv0V3WAZjMc6\njw8BmWiclmxtFexulSj19OSJvJ3rcFXFazC67NdhGCzloiM/TbAByrInBEGRp3S9IdGS569N2JoV\nbO9W3Nybve2fcdmuQVWmjyVl/bI9zzf6iQHp4x//OB//+Mff9Lnf/M3fZLVaAbBarZjN3vzi7+3t\n8clPfhKtNbu7u7z//e/n5Zdf/rEB6eSkeZjxv237+1MOD5c/+QvfoG4G2sHRtQNHpy02AAScC6zq\nMS38+GjFu5+ZMZ9kT8Wd2cNch6smXoPR03AdvPesFh1NM2CtxQwWqSSEQJpIJqmkKhIkAWHc234+\nT+oavJ1gsGqGxzKGdb/WP+4aPFT4/fCHP8w///M/A/DlL3+Zn/u5n3vT4//6r//Kb//2bwNjwPrW\nt77Fiy+++DA/6lKYlCl5Ml4qB3g/BiOlBEKOfVja3nL/rOO1ezX1Y/pFiqJNJaVkViXkiSRPEyZF\ninMOQiCRUFY5earYmxdoHZOHn1YP9cq99NJL/P7v/z4vvfQSSZLw2c9+FoA/+7M/41d+5Vf4hV/4\nBb7yla/wiU98Aiklv/u7v/sDWXhPm2mV4YLHeRiM42TVEQI0/UCiFEWeIqXA+EBvHMQkhyh6x4QQ\n2N+uaDrLK68vuLZdAoHOOrarjJ1pxu6s4L+/uLfuoUaPQIRLshP/pKaRjzI1DyFw+7CmGzyLVQeM\ns6OqSPABZmWKD7BVJSAEO9PLu3z3NCzTPG7xGowu+3VYrno6Y/EBhsFRNwYTxl5leSqYTDJ2J/kj\nzYwu45Ld3/3D1x/LGH7xQ7cey/d9q37cNYhz27fhovBqN1gQIIC6HQgBUiUQ55+7OKAXD8xG0aM5\nOK45PO2wzlN3Bms8RaYp84Q8T0i1oErTuEx3RcRX8W26WIbLBkc3ODyQK0GRJ4QA2Xm9O0GI5yCi\n6BEsVz33T1tWrWGwgeNlRwhhvCFEMCkTrA+c1D1VkVza1YjorYsB6SFMypSqSFg0PXkt6W3Anwej\nskgJIcRzEFH0CEIItIPj3kmL8QHvoGkNidb0eJarjr2tAqUE/eBx3se6dVdADEgPaSy+mjMrMxZN\njz0PStY58tgMLIoeiQ+BRd2x6ixpIrlYI7fB4Y0k0fL8IPr5Onl0JcSA9IguAtO48eoBgXGBxaoj\nzzT6vGlYFEVv3cHRWCbo4KRFAFki8EGCcCjlUSpBCM73byUq/o1dCTEgvQPqZsC4gD6v0nBwvGSx\nGkiUpCgSpkXCzb1pXMKLorfg5Tun3D1ace+0ZbCOEALWS1IdEAEkgiofM1gTCVuXOJs1entiQHpE\nIQR66x8kMPz7t+5xtOxYNpbVqhsP620XvLq94gMv7salvCj6MRZ1x+2jGmcCWaLYqlKWrcMFgw9w\nbbsgkZqbuwXzKiWLy+NXSgxIj8iHwMVS9it3TzlatCwax+3DBV1vQQTunrZcW7TMq4R3XZ/FP6Ao\n+iFCCHzvoObgqEUgWLaWRMHOJKG3CqUE17YmzErNs9cnJErFmdEVEwPSI5JCIAV47zipBwbnuXu0\npO4M3gVCCDR9T9cN/JsYs/BiimoU/aC7xzVNP4AQSAVZKjGDo8dRZimJhv2tnNkkj8Hoioo7gY9I\nCEGqJb0d62r1g2fVWpwLBDwIiRQCLyT3jlbcvb/ibNWte9hRdKl47zk66emNw3hD0xqCDySZQkpB\nmsD1nZJZlcUjFVdYnCG9AyZlivMOIQUKjzEGIQUBRfBgnUd7aAbB68c127MUKQSzKl/30KNo7UII\nHC1b7p3UtMYTvKTrBmyQ5LkihECZJFzfnsQ9oysuBqR3yHxS8K79Cf1gKG4v6azFGAd4lBIkWhFc\nYDg/7Kekou0t13cm6x56FK1N3Qx0g+Vbr55wthrI05R5kZFISd9bpBQ8u1/ygRf22ZrmcWZ0xcWA\n9A56z7PbNJ3l2s6Cg/tLnAKBHE+X94YqH4uvNp2lNxbRCspVz7TK1j30KHri6mbgZNnR9GMnWKRg\n2fVM84z5NCNUKYOxvPvGnO1Zse7hRk9ADEjvsJ957z5Fpvi3/+8udw5WWO9pB0eWJEwnGWfNgJCw\nv13gPDRDwqQM8c4v2ighBF67t6IzhmFwtIOjTBMEhkUzsCUzhIQiS7i2Xa17uNETEgPSY/Ded+1Q\n5oqvffOQO8cNJ4sOnWjyRKOU4Hgx8J3XTtmqMvJUkaeSedxPijbIWd1zXLeEANZ6rHUsnGNaZBQp\n7M4LEg1aSRIVc682RQxIj8n13Snvf8GTZQm705yzZsC6QG88xjiO6rHTZddZjPGc1T2zKo0zpejK\nCyFwUg9jJp0QdL3FeVj1lm7wbFUpSkGiJXvzPJbe2iAxID0mUgjKIiFLU8oSTmqDtZamc1jrMMYh\ng6AbDvEEqjzBeU+qYxZRdLU5Pza49EDbDxAE0ypFCOgGh9YSrWBvnseknw0TA9JjIoSgSDWTQiFl\nwnyScVZ7aAYyLdFaMbjA4VmH/c599uYFzs+5tl1Sx/bn0RW2XA28ftTQGcfxckALQZ4qqjIhTxX/\n13NbbE1yducxkWHTxID0GM2qnHnV4bxHyLE9RZElaK1w1tF0BmNhcC0r4/A+oCTszEuqEBMdoqtn\nueo5WXQPbtiq3OGdx4WxcOrWJGdrkoOQsePyBoqLs4/ZCze3uLlbsVvlVLmmKlKqTDM4MNaNZYcC\neBs4WfX8v989wTuPD2HdQ4+id9Ri1XH7fs3hWY8QHus8aaIosoRUa4pccW27REqJEMSOyxsozpCe\ngBt7U4pUIb8Dq86x6geGwxUgkBKUEmRaEYLgtO44XbXsbcXliujquHt/wct3ao4XDa0BKQJajhW9\nhVBAoMxSZlUCEMsDbagYkJ6QrVnJs9cG7h6vUEJQlJrgAkLCYDwnqx7VCowx/Oerp7xrf0KWxqy7\n6OnmnOMbr57w7dfOGKxncB7vA5MywQ4erQPbkwTjAtMyocoTUi3jHuqGigHpCXrh5hZFprlztKS6\nn9J3hmVjCDKQBMHJomdwlq+/csL9s473PrvFB17YoywSpBAxOEVPhRACPgReuXvGy6+fce9+y8mq\npyxSpnnCahioG5iUY9X73VlOkWnmkzwefdhwMSA9Yc/sTri2XVKmKf/724cMdizKerYaMM4yzTOS\nNKG3jjsHSxZ1z08/t8OkSsm0imWGokutbgYG63nl7hkHJyuO6wEbAoPzhHYAYJqnLFuLHTwyGTNO\nd2ZFnBVFMSCtg5SSn35+h4PThpNFj5CCZT1Qpilpqmg6y6I2DBPP4VlHQHBrf0ZVaJrexLMZ0aVy\nMSNqWoNxgbrpeeXeEuM8TWsQwZNojfOOZTuwPc2YqYStMmV7lvHuZ6Yopdb9NKJLIAakNfEh8P7n\nduh6Q9N66mYgIAgBvHP4IHA+YAL0bjxICDnBB8osFmSNLoeLGZF1nrPVgHcW4wVtMxCUxLqAdQER\nPFIKrBkr3kslmRSKm3tVDEbRAzEgrYkUAq0Vz+xMOFk0lCeawXmsDVjvyRINQmIGS7PqOTCe5Wpg\nPslQ55u+ca09WqeLYNT2lm5w3DtqOK1brA3UvSPPBUmq8YMZy/+4QFCQaMHOLOP5G/M424/eJAak\nNbnoNPuu6zN8CORpTbfqsc5RpAmTMuG07vEh0LkA1qO0x3jPYtWzaNJYkDVamxACvfV0vaU3jqOz\nhlcPT1msPIM19INjsJZplRGSBElAJYFb04z/8VPXeHZ/GmvURT8gBqQ1mpQpdTPw3PUZVZ7wn68d\nc/eoxQdB2xuEgN1ZQZElQMD5ACHgPRjjCbGaQ7QmPgScdRwuVjSt4RvfO2NRdxgXsNajtaTtHO3Q\nsj8vqPKEnUnGz/70tdjbKPqRYkBas0mZUoWAVpLdecGqGTg4XbFsBu6f9bS9Be+RQlKmCqkUSgSM\n9zjv0XH9PXpCLpIXpBAcnqz49mtL7p2seP2kZrEYKKoM1w9Y79FhbEw5LTXP7JTsTFOu70zZmsZZ\nffSjxYB0CQghmE8y6maAKmMPwWCWbFWMFRykoMoTyjzBDBaTapYrgxKSIo2p4NHjd7Ff5AMcna3o\nB0/vDK0xdIOncx7X9EgpSaVCJ5JECaoi4dp2yaxM2Z7Gfc/L4H997fZj+b6/+KFbj/w9YkC6RC5m\nS/MqYVZq6mbsnun8uDTXDxavJd57jA3UraFuTUwFjx6ri2AUQmAwlrv3V1g3HkkYzJhhJ5XCOk+m\nxqZ6kzyFANMiYValJEpSFsm6n0p0ycWAdMkIIdBKkSUaUUm0kpw2A/3gaHuHVoIiT6iK/3rplq0l\nXTZMywwlYw2w6J1zkbxwdNLw2mHNK4dL7h01qODpAlzfLki1BuEZTEAJiSdQZIpECt59c8b2NCcQ\ni6VGP1kMSJfURcJDyBOupRrrLPPzpTml/usPu+kMx4ueo9MVW5OcLNXszvK4jBe9I3wIfO/ugjv3\nlxyetpw1A50xBA+tsYgQyFJNmSryNCORAhcCRSq4tT/nxu6UEEIslhq9JTEgXWIXS3g+BAQZR4ue\nZTM8ePz4rOP1o5pFYwgE8rRjWmgOJxnPXZ/EZbzokdVNz8FJzb3TjrPacLzoGKxDSiCAGTxpEjDW\n88xuyVaVo6Tg2Wsl+zvjkYYsFkuN3qIYkC45IcSDJmV5Ilmef77pDCfLlmVnCMEjxNjKojMBVgMH\nRy1ZoplPMoQQb8qQineq0VvhnOPl1xecnvUP9iqt9ySJxhg7NlNTELxgMsv4H+/dJ8sUe7OCaZnF\n37fobYsB6SkyrTKa3rBsLavO0fUewvm+k1YIIXDBseocRzKQJArnx03nRGt8ACkg1ZL9dT+Z6NLy\n3nP7qOb+ccPLd045bQaccwTGJTycRyeKItVMM0WZJ9zcKZlPMmZl9mA2FLu9Rm9XDEhPmes7E7K6\nxVjLIlN0VuJcIE3G80h9b/EOtBQszyuIS6HYnkKZj1lOg/Us3rD0F0Xee6z3HJ223L634t5px+17\nZ5y1BusCfT/+t0gVxo3txpUI5EXKziTnxt6E69tlrEsXPZIYkJ5C8yrHuYC1gYBn1VoAAoF2cAgB\nLiS0xjI4gVYWYy3XdyqyRCGlpO9trPQQEULgtYMFt19fcP+k4XjZc/+0pbeWZnA4F0iERJUZp4ux\nEgM+oFPNfFZwa7dkZ6vgxm4MRtGjiwHpKSSEIEs025Ns7MJpGvrB4lxgMIGdKmVSpGSJ4vis5eC0\npTeOmzsV8zLh5rUZ860c6xyJUjEobai6Gbhzf4XKFPeOa753sEIKwUnd0w2ePFekCLreUKQJW9OM\nSa6YT1LmZcpsUlAWCTvTjGd2YwJN9OhiQHpKXazT+zCeWzqte7yzCCnYmhVMC83B8Yqvf++E/rzu\nnSZgbUVrjjB4tssErSR5omOa+Iapm4FusKx6S1t3vHav5vCkI0kUgxkLpGon0VqQek2mJamUlLni\nuWvbPHt9QpZpqlQym8RyQNE7Iwakp9ikTKmKhJv7JSEErPN889UTQHK66HjlYEE3uAdLc61x4x2x\nAuMl8yIhSRWzMmGr6pnPcnIt0Tr+Wlw1IQSc98B4QLW3HhcEdw9regLGBmwArEcIGExgUoyJCVoK\nJkVCqjU39gv+53/bRyoVM+iid1x853nKXVR2ANAqsDMtOVt13D/r6AaHkhJCQCrJYDztYCjS8c0E\nIbDG8X++c4Zznq1JwaRK2Jnm/PcX99b8zKJ3St0MHC86euPhPMtyrBofWHUDaT722MoTST9Y8jxl\n1Q04Y0lUSp5pdqY5O7OUZ3YnJEksARQ9HjEgXSFCCLanGYMzaCnGwqzeo7QgUXKsiWc8AcngHIfH\nPbePGprOUOYapRTTacrh6Yr//U3Pz7x3L/asecrVzcBrB0uWrSEgSBKBtR5rHcYFQhAMvUEgmJQp\n3oPwjmd2KxI1FkjdmZbMphnP7Ja8cHNr3U8pusJiQLpiJmWKcTmzScqsSRFiOH8jUrjejodog8dY\nR9NZ6s4ihaDpDPdOaprBk6WK1+43FLlkUmXc2JnEpZmnzMUS3TdfPeZbt08xxuM8JEqwVeXkeYIU\ngfk0ozOe02VLoiXzKkElgr1Jzou3ZmxNM/IsJdMyZtFFj10MSFfQ1qTgxl5JCIKTRcPpytBbi7ee\nPNHszFIECuN6Lhr/SSFZtQ4XWq5vl/SD4/X7HZPOU68sN/eqWP7lKXFRnfvu/SX/5ztHnK0MwNhD\nywYWK8O1ec7+3oQMQTVJAUeuNEWREILn1m7FCze3441I9ETFgHQFCSF4dn+GFAIpBXk2YJxH4tme\nF3TGce+sR0kIHhCCNBEYB9bCaT3gvKduB7JcsWyh7cc3tRiULqeL0lBNa86X4jxHpx3LztD2Fgdo\nJRicY9kEklRyA7h1fYITEt87yjxBSNieZLx4Ky7NRU9eDEhX1KRMubk3ZWdW0Fs77hEUCQLBd+6e\nUnce7z2zMqEbLFmiMdbQW4fsAmWRcNoOtNZTZZoyT6hyR5nrB60E4t3zer05CHkG61g2w/lNRuCk\nHug6x+DGfUQQSCUx1tN3hjzXpFpSzQpwjkmpqfKEWRXTuKP1iAHpCrtIC//+IpcvPDMny1MODmve\nfW3Gd+6csmx6OjOQ64Q01SitOV32KGk4xjMtE44XklVn2JuXCBHIdOxW+6R9/0yobg3LpqftPELC\n8aJFCJhVKVoJtJZo53EmQArCB4SAIk8oMk2RJ2xPc6R3zMos3mREaxUD0hX3xmrhF2aTnGJaUC87\nmt5zY6diZ5YyzTPKXLEynra3SDH2GJBKcLrsyQvN6TLgXKDIUwSxW+2TdLE3VDfjEqw6r1e46i3O\nB7TkvIDu+HkpoMg1LoSxDl2uECQoYH9ePAg+WaaZx1lRdAnEgLShbu5N6J7boektLni61nJ32nCy\n6Fm2DSIEALJEkaWKzjgEglRJjAtUAkCwbAxF2r3ptH5sdfHOu6isYD2crgaa1tJ2A8f1QJIIpmWK\nVwolBYGA9TCf5vTGYa1nCJZEaYpEcn234uZuyfXt4rxCd8rhql/3U4yiGJA22bQaWwX4EBDbIJUk\nSxTTKuF4MdANZgwo56f1hZRwHmBW3YD3YF0ghA6AskioG4PzgYB40OqizDXWe7SU8VzT23BRgVsC\nr96r6Yxl1Vju3K/REsoio+sHjJNIAVmanFfj9nTWkWrFzWsT5tOUrnNjy4gsYWuasj/P2ZrGWVF0\nucSAtOHeuKS3O8upm57OjkFJiIBSgqpIGMyYuZUlcuwYKhRSCpSCfjB893VL15nxxH+q2JrmFJnm\ntXs1xjnyLEVJqHIVl/jegoPjmlXnqJuBw7OGVevYneec1R0+eHoPohtQWuO9p+09WnkSnSAE5OfF\nULenGU074ALk2Viho0hj7cLocooBKXpgWmXsb5cEOspUoZXA+0CqFSL48xmUpu0dUo5daJ31NCYg\nhOe0MUxyTWcsp3VPCIKAR0iJEONMqW4tHNfsb5UPZk3ARs2gvn9J8/s/vghG/WDxYWwPHoLnbDHQ\nDR7nQCWSzo0ZkMYIOmMRQZMmCiUVRSrGEkFCsD0rfmhySxRdNjEgRW9yfWdCmSUcL/uxQ21rMyL1\n3gAAEBRJREFUEALmk4xucPSDIU0UPgS0VDgZGNyAEvJB99rBOvrO0lnHte2Spnec+Ja61RS54s5h\nzdmqR6A4q1sCkq1JBgKmhb5SrQwult20lAghWDQ91o5VE7QSGOve1M1XS6jbMeAPLjBu5QkSpWh7\ng5CgtEAL6F0gTRImpWDVDGxNcqo8IU8029OUskjeFIBiB9fososBKfoBF3tLb6wOfXH2aLnqOTjp\nkGMCHsZKpBhnNuPkJmDtWC/PmoGmM7gASqW44Dk4alksBzyS4BzWO4QQNP3ArMxY1C1nq54Xb87R\n39er6WlLlriY6Tg/LmtaG1B6nHUqAZxfw+1p8aCbbzM4Vu3ApEwJAaQcr7vOJMZ7vA8QQEtJViqu\nb2dIKdmfFzx7rWRaZqjz4BdFT5sYkKIf6o1VxN9oNskRQtAZjxQQgGU7liDKtT5fpgMlOa8m7skz\njRDQNAPHy4EQ4PS0ph7c+RtsQCeKs6yjGQLWGO4dt1zbrri1P5YsqpthzBjz4ywiS9QPrRrxk5bD\n3vjxw7r4HgLw59mI3x8EXj9asmzsONMZDMYGjs5WpDqhyBN6Y+kGS5El9L3jhVtbCCFIlMCef28p\nQAhJkSnawZKnmnmVsGwN3o/nwBACKSTXtjO2p+VDP6cougxiQIretmmVIZqB3noSJVBCoqVgOte0\nnaHuQGtBmaUoNZ5zCQGWnR271EpFYzzLxoxnaJwDH8hSPX6t9xyetSglCd4znyYMFpwf3/zHN26L\n95481+NSlBiXrQZ3Xsnag/CeLBuDlpICY+2blsfyyQC8vZnXRWBcNIa6GVOl0zShTCXb05yqSDit\nW759e4kn0PWOph9bftSdw3nDDVUhhMD58bmsBsdy1TOb5EgpKdME58dra1xga5rjFw3BC1Kt2aoE\n0zJja5ojBJRpPKAcXQ0xIEUPZVKmVCGwNUnJUsX9RYcxgSTR7E4FeSrZqjLunba0wxgkvPPkSUII\ngrbr8WFc3vMujK3YfYcPBUrC4VmHkpL7Zx1ZIphVKWWRkihFmWteP2549cBRZgkWR9c58lxx93CF\nsZ5la8A7JmXOB17cBcaqBZkO5JmmGwyHh2ccnjRMigQpNUqOiQBvTAAIITxIvV60A8vlwPHK0rYd\n7eAIQJWndLnm6KynyBTLzrCoe8T5MmYIYy1AYzzOBdrBUZ2XYBqbJ3K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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with donut(scale=0.01):\n", " nuts_sample = pm.sample(draws=1000, init=None, step=pm.NUTS())\n", " \n", "jointplot(nuts_sample.get_values('donut'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Also note that PyMC3 will make good choices if you just call `sample`:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using ADVI...\n", "Average Loss = 23.675: 1%| | 1929/200000 [00:00<00:10, 19286.52it/s]\n", "Convergence archived at 2200\n", "Interrupted at 2,200 [1%]: Average Loss = 27.687\n", "100%|██████████| 1000/1000 [00:01<00:00, 613.70it/s]\n" ] }, { "data": { "image/png": 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VhqCkc9gNYx/WWlxNC3iagKq6wrOBjyj0cDXJYIwTr1laQAggDDwIuKTbk4G/aHEXwLuX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\nRP1wsWtGYDAUSjUFhELUisos3PDr9GpSWpPlmiQOGU3sgwcq6Rc0/cg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with donut(scale=0.1) as d:\n", " nuts_sample = pm.sample()\n", " \n", "jointplot(nuts_sample.get_values('donut'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$H(q, p) = -\\log \\pi(p | q) - \\log \\pi(q)$$\n", "$$\\frac{dq}{dt} = \\frac{\\partial H}{\\partial p}$$\n", "$$\\frac{dp}{dt} = -\\frac{\\partial H}{\\partial q}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example:\n", "\n", "Let $\\pi(q) = \\mathcal{N}(0, 1)$, and $\\pi(p | q) = \\mathcal{N}(0, 1),$ so \n", "$$ H(q, p) = C + p^2 + q^2.$$\n", "\n", "We can manually compute the gradients for these distributions in order to plot the HMC paths in 2 dimensions: 1 for position, 1 for momentum." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gen_data(position, momentum, n=10000):\n", " \"\"\"Generate a background density plot for the position and momentum distributions. Not used for sampling.\"\"\"\n", " q = position.rvs(n)\n", " p = momentum(q).rvs()\n", " return np.column_stack([q, p])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def leapfrog(q, p, dHdq, dHdp, step_size, n_steps):\n", " \"\"\"Perform the leapfrog integration. \n", " \n", " Similar to the implementations in PyMC3, but \n", " returns an array of all the points in the path\n", " for plotting. It is a pretty general \n", " implementation, in that it does hardcode\n", " the potential or kinetic energies.\n", " \n", " Args:\n", " q: current position\n", " p: current momentum\n", " dHdq: see Hamilton's equations above\n", " dHdp: see Hamilton's equations above\n", " step_size: How big of a step to take\n", " n_steps: How many steps to take\n", " \n", " Returns:\n", " (`n_steps` x 2) numpy array showing the \n", " path through (position, momentum) space \n", " the Hamiltonian path took.\n", " \"\"\"\n", " data = [[q, p]]\n", " p += 0.5 * step_size * -dHdq(q, p)\n", " q += step_size * dHdp(q, p)\n", " data.append([q, p])\n", " for _ in range(n_steps - 1):\n", " p += step_size * -dHdq(q, p)\n", " q += step_size * dHdp(q, p)\n", " data.append([q, p])\n", " p += 0.5 * step_size * -dHdq(q, p)\n", " return np.array(data) " ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def leapfrog_paths(position, momentum, dHdq, dHdp, n=10):\n", " \"\"\"Get a number `n` of paths from the HMC sampler.\n", "\n", " This is not quite as general -- I hardcode a step \n", " size of 0.01 and 100 steps, since a path length of 1\n", " looked pretty good (and *not* because it is the best\n", " choice). Returns an iterator of plot data.\n", " \"\"\"\n", " q = position.rvs()\n", " p = momentum(q).rvs()\n", " for _ in range(n):\n", " path = leapfrog(q, p, dHdq, dHdp, 0.01, 100)\n", " yield path\n", " q, _ = path[-1]\n", " p = momentum(q).rvs()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we write down the distributions above, and manually compute the gradients needed to use the above two functions." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "position = scipy.stats.norm(0, 1)\n", "momentum = lambda q: scipy.stats.norm(0, np.ones(q.shape))\n", "dHdp = lambda q, p: 2 * p\n", "dHdq = lambda q, p: 2 * q" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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88npd0fDbZ/Ezy4B2m3eHVJzBKpqMbRyvPU5DXfWOpPjWi8noj1Jh330pCCkV\nN08dreFWv4c3Lj7kqWM1eyZKEkIqMgoto0lvCKNRybuMUkWkxjU8wz48I/NEtqjckhUJe4UVR4UV\ne4UFW7kFk9WQVZqsqtxCIPCoWFYxUuk4uXIvtaIsrAXxhqbwBCeZjU0yL00TMayNpjQlzpxjgjkm\n6PJewD7ipkU5yKmGU9TVVeU9tbf899GhYBGTkFLxUmYzcqLdza3+WS7cnuT5x+oL3aS0EEIqIopB\nRgB2i5FAcKuTd/osi8hqkPE89DE1OEdwPrzhayUJHG4bzho7zmob9gpLwca/pJ5gnRipcbiAwyuP\n+WML9E73MxEawiONEVVTBCWB3z7LHWbp9nyE82EtR6zHebz9NDa7Oa/ttC8tq1GoVJ6QUvHydGcd\n3YNevv3hIOeO1WA0FH/FnRBSkVDoMR757jNaFpEciTPZP4tnZB5de7QETlFlyusdVNSX4ap1oO6B\ngwbAbijj8YYzwBl0Xccb8XDf08NQqJ8FwwwsBUS6rONzTHCZCa72vU9T9CBPNZyjqbEur1FTIfuY\nhJSKE4fVwOOHqvioZ5q3r4/x6aeaC92kbRFCKgKKoYAhnyLSdZ3FST++YR+Ls48WCsiyRHl9GVXN\nLly19qIY/5MLkiThNlfhbqziHM8TiC9yd7qL/kAPi8bZldfFjREGjXcYnOumcqSRJ93n6ew4lNf9\nL5SYhJSKk6eO1XDzwSxvXBri+cfqsJoNhW7Slki6rmc5ciMzwpE4wWBpjfS2Wo0571MhZbRZVGSz\nmrJK2Q2NL+AbW8A76CXsf/R7sZVbqGktp7LJhWrc3UjIZjNt04e0M8yFPdyausZgvIeY+ujnly1W\n83jZec4cPoGiZi6m7f5WkVjyd7Vb0dJyijUXKeXjuCpGKsqtab92ZiaZYZjyBplbzO13+9HdKd67\nNc5PP93CF59vy2lb+aCqyrHpc0JIOZAvIRWTjCBzIemaTtf1Mab7Z4kF15ZqS5JEZbOT2g43jor0\nD8h8UyghLaPpCXpn73Jr7goLxplHnnf4qzjrfJbThzsz6jdL92+1m2LKVUpCSPkVUiyu8dff7Sae\n0Pl//uN5HNbCRrBCSDtErgdOMcoI0j/J6brO9Mg8dy4PE1kXESkGmdp2N3UdboyWwqcJCi2kVCb9\nY1ye+IBpw8OVvqZlyhfreK7mZQ63tqbVx5TJxcOylGDnxZSLlISQ8iskgKu9yX6kzzzVzM+/1JHz\n9nJBCGmfplFHAAAgAElEQVSHyOXAKVSqLp3ihXROcgveID0fjTA7sbjmcdWoUH+oktoOd1EVKBST\nkJbxhme5MPouE+oDkFIOQ02iwd/Bqwc/RVVVxZbbyCa9ulvRkizLQkgpFFJI8YTGX3/3LtFYgv/7\nPz5d0H4+IaQdIlchFaOMYOuTXCya4P71MR72TJP6y5FVmYZDldQdqiwqES0zMLlILLr5tEOHm127\n2Jq1DM9NcMPzPlPGoTWPKzEjxxNneenEcxhNG0eZ2fb3FbOUhJDyLySAG/dnePPqKJ98oolffOVg\nXraZDUJIO0S2B04hoqNMyro3O8lNDs3RfXmYSGo/kQQ1bRU0HavBaN6dos3eYV/G72lrdG154p7K\nYLmHnZJXv2eIa3PvMG+cXvO43V/JKzWf4VBr6yPvyVZIULxSEkLaGSElEhp//cZdIrEE/++vP4Ot\nQBV3Qkg7RC5C2i0ZZTO+aP1JLhKK0X1pmMmhuTWvc1bbaD1Vj9WZ38Ge2wmnJosTaC4n7lQ2Elc+\nBeXzRxhc6OFW6H2i6upnSZrMweApPn3qVczm1ZN7rvtVjFISQtoZIQF81DPFezfH+fJLHQUbl7SV\nkMQ4pBImH4Ndp4Z93P5wKLm0wxKqUaHtdD3uJmfeBneul1A20tkNNmpXattzlZPLbuK0/RSNi+3c\nnPmAQfkOSDq6rNFnv874zYd8pv5naG1uyulzlkldFBB2VkxijFLheazdzcXbk/zk2giffLKx6Oa4\nE0LaZXYrOspVRol4grsfjTLSu7ZE2dXo5NDjDXkZR5R6Ii9WAaVDatuX9ylXMVU5HJyVX6Et3Mll\n7w8JGJPb9dtn+ab37zg9/SwvnX42p89IxWSQ11Th5RsxcLY4MBtVjrdVcOO+h+t9Hp48Ul3oJq2h\nuPQoyAu5ymjBG+TCd++tkZFqUml+spFj55tzllHvsG/lxF1TYdnTMlrP8v6k7mO2OG1G2t0H+Ezd\nL9OhnQY9GY1qapxr5nf5+4/+gYX5QD6aDSR/Lzu5dPryhVihp8na75w5VAXAm1dHCtySRxER0i6y\nGwdirjKaGPDSdWGIRMrVclmtnbrjtbjLcxNHqURE6bC8f/mImCrsFh6XXqQx2MHlhe8TVpMSmiwb\n4C9u/Dk/XfdFWpoac280q1LaqdTdcqQkKBzuMjMttQ76R+eZ9AapLeCA9fWIX8Yus5PpulxkpGs6\n966McuPdgRUZyYpE3fEaGk/X501GpRYRbUe+IianzcihqjY+XfXLVMcOrDwetPr4pufvuXLnJvms\nT9rJSAlElFRoOluT49su3pkocEvWIoRUIuQio3gswbW3+hm4PbnymLXMROv5ZiqaXbjsppzaliqj\n/cr6iClbqsvKeLH2C3RKT6+k8BKGKO9q3+WHV97OywXP+kKHfFPIJVYESQ41ujCqMhfvTKLtTqF1\nWgghlQC5yCgciHLpjXtMj8yvPFZ3oJxnPncUc5k55w5oIaNVUqWUi5hcdhPPND/H89YvoMaTFwu6\nrHPbeoF/++hbxKKbr4ybLrshJRElFQ6DKnO42YV3IULvw7nt37BLCCHtEjtVXZeLjBbnQlx8o4fF\nlKXD207U8sxnjzI+F8qLjPZbim47Ur+PXKOlI9UH+WzNL2ONOlceG3J08w9X/5FwKPexKzstJUFh\nOd7qBuDincltXrl7iIGxOZDJAL6dEFIuMvJN+7ny4/sr0+lIksTxZw6glZkwGFSsxuyvVYotKurq\nn8ZoUIjGNp86KF1OduSvTHZ5kG0uBQ82mwnvwjzfGfgX5oyr/QEViw384omvYLPn/jeIxLQdK3LY\naMCsGBi7cwNjU9F1nb/+7l3C0QR//BvPYtqlKb/EwNgSJBcZzU4scvXN+yTiSUEqqsyZl9sJLi0U\nV1VuyXki0kLJqKt/esPHO5pcBHNMEQ1NLa7Zfq5yqqmwMOUN0Tvsy0lKJsXMz3V8lR8Ovc6o3A+A\n1zHG39/+Bl/p/CUcZbac2gnsaOWdoDBIksSxlnIudU9xo2+Gc521hW6SENJusFO58mxk5Blf4Oqb\n/WiJpIyMZpUnXj3I/JKc8pWm2w02kk9LzeZXX7nSUuNgShtiUnuAETMXHpZji9VzqqMu623mqzxc\nlhQ+0/JF3h7+Pg+4A8C8Y4p/6P57vnr8l7A7spfS8qDZnZDScl+SGCxbGDpbKrjUPcXF7kkhpP1E\nPtN12eb0ZycWuPrmfbREMktrshh46jOHmF2aFihfBQw7wW7LZyMSepyu+FskWCoasIOKkanxJlyR\nNs62HMt6KqV8REuSJPGJ5p/CMGrknnYdWJLSnf/OV09+DZste5ns9EwOgsJQUWamzm2le9DLvD+C\nM8eK2lwRRQ17jGxTdXPT/qXIKCkjs83Auc8ezruM8hUddfVPr7lBUkCpt91GkVRsUvmax+JEmTc9\n4GHZm3xn+v/jveELxPXYJlvYmnwUO0iSxHONr3BUfnzlMZ9jkn+69Y9Ewtm1K5WdKnAQFXeFo7Ol\nAl2HD28XfkySENIOsxMHWiYy0nWdiUEvV3682mdkshp46jOH8SwtI1FMMiomAW3EOfVnOa1+ijb5\nFBbK1jwXUX1M2a7wbc/f8tboT4homZ+881EaLkkSzza+zGHp9Mpjs2Wj/Mv1fyWeQ2FHLpP0boUY\nl1RYOlsqMKgy794YR9MKOyZJ+b3f+73f240Piic0YnmociomDAZl232KxBJ5O+CWr05VJf200HDv\nDF0fDK1ERkZzck66qCThtBkxbzAvndGopv23yoeMuvqnmfIGmPIGaKlx4LKbch6Mux6Dcfu/VTpI\nkoxdcuGWGzkgH6dSbkRCIqD70En+nXUpQcgwzf3QLRLEKVeqUKT0s+N2iwG7xUAgFGd2PkzlFst7\nbPa3kiSJA2Vt+ObnmCM5J6Hf5GVmaJEjDYeyTi2qisR8IIY9z8vSS5K08ltM57jai1gy+M6WqwwD\noRjhLRaWzAeqIrMQjDI4sciBWgd17tyLYLbCZtv82BYR0g6Sz+go21Td/Exw5f9Gs0rj4w2Y7Ka8\ndCLnKqONoqG9hCRJlMu1HFdf4EXDL3FEOY+F1X3QpDg9oY/5vu+/0hu6TkLP7MSSawov2af0WeoS\nqwv79Ttu8vaND7PaXio7kboTabvCceZgcsLVt6+NFrQdOQnp1q1bfO1rX8tXW0qSfKYjskmZHDxd\nT0OHm45TdbQ+24LFmfvsC5AfGcHeFNFGGCQTLcpJnjP8AieVl7Gn9DVF9Qi3gu/zY9/fMxl9mNF2\nc50LT5Zkfqr1i7hiqyXq19X36OrtyXhby+xE6k6k7QpLlctCY5Wd7qE5JmbzN4N8pmT9y/qbv/kb\nXnvtNSKRnRm0tdfZiegoGyx2I48934qpvgzVqBRcRuujolJDlmTqlQ6eUb/ESeXlNf1Mi9oc7y9+\ni0uL3yesBbfYyqPkEi0pksrnWv4HLLHk960rGm/5v8vE1MZjttJFzOBQWjxxOBklvXExs4umfJK1\nkJqbm/mzP/uzfLal5Ch0dLTMw8nkqO9ikBGUTlS0FdKSmJ4zfJnDynlUVr/7kWgfP/R9g5FIX0bb\nzCVasqhWfqrh51ESyX6MmCnMtwb+jVCWy5/vVJQk0naF42CjkyqXmct3JwsWJeU0ddDo6Ci/+Zu/\nyb/8y79s+9pwJPcJH/cKHt9S8YGa+0E7MrWI3ZK9SO6PJE9cVTkuHwFw+4EHgKbqzGVyrWccSM6Y\nsBtc6Xqw5fNPnmzflXYsE9aC3A59yEi0d83j7dZOzpd/EoOcWRHHyHTyIuNEe2VG77s3fZcfzPwb\nLNU0NPiO8muf/GpWRQ7+UFIeTXm8uIjHNSpdpTkjhNmUfmFLPJ5AVRXGZ/zMzod3sFVruTMwyz/8\n6B4vnmnkf/vq49u/Ic/s6sDYUpufarM5t2JLlXW5ZjOXUyIBPbsNpUZGmUwFZLOZHnl9amQUyPCq\nOjUyynX6HoCbPUPbvuZwc8Wa+1abcc1nX7y6dXRy6mhLNk3bApVOXqRabac7/j5h/AA8CHYzFR7j\nacdncalVaW+twp68SLn9wEMsmth2MG0wEqdveI6GqnqOKU9wV7sKwJizh7c+usj5k09kvEcSyXnu\ncp1mKpXlxftK7VwBmQlpbi6Z0vV6g/h2aC67jWgoN1PtsvDe9VFeOdNAfWX+K+7EXHa7SL5TDtmm\nRoopTZdrem69gNbLJhu228b6z8yXoKrkJp4xfImexEXGtaQU/ZqPt+b/mSfsr3DAdCSj7TVVOxgY\n9W07w8MbFwaZmA0iAU8dP0aFcQyvOgESXIq9Rdt0CzXVmUVby+RzSiFN0/D4Qlg3GI4g2HkkSeKZ\nE7V864NBXv9ggP/lCyd29fOFkPLIsozy0XeUS4dxMcgol8KFnRBQpqz/zNQ25Song2TipPoSlYlG\nuhMfkCBGgjgf+X/IfNzDCeszGaXQ0pkPT1maOFcHLt+Z5uWzL/Nx/F+JqxHixgjfvv86v1r+H1Az\nnPFZTClUenQ0OKlzW7naO0PfiI9Du5RmhxzLvhsbG9PqP9pPFLqQYS/L6GbP0MqJ/3BzxcqtGEht\ny3I700kdbkW9cpDzhi9gY/WAvxe+yiX/90nomfe5blWJ96mzzdS5V5c/+PDGHGdtr6zc9znHebcr\n9/FJ+UIUNxQOSZJ4+UwjAP/4k75dXVFWDIzNE/ku896PMgKKSkIbsV6UuYrJLpVz3vAFqqTmlcdG\no/d5f+FbxLTM+w42k5LdYuBnnm3FYU1W2UViCfp6LTRrh1dec0u+xMRk5qXgJoOc1xLwfBQDCXKj\nvtLG0QPlPJzyc2EX57gTC/TlwHJRw06k6rIVUj7mpTMYFWLRxK7IKFVEuSKRwKSEMClBjHIEVY6g\nSHFkKYHRIBGLaWi6gqYrxHUjMc1IJGEhkrAR17P/3nqHvSv/zzadp+sa9xKXeKjdWXnMHK/gU1Vf\nxiRvPnWQzWrasMhks8X/xmb8/Nu7qxWIz56u5Lb070TVZCd65UIzv3Lul1eKC9Iln4v42WwmQqFY\nyS1JUWwL9G3HQiDK337vLjazgT/4n85hyaAoYyu2KmoQQsoBq9XIxEyyWiqf89UVUkYAbY2unCrp\n0iU3GWnY1XnsBi92gw+bOo9ZCSJJ2f2cY5qRYLyMQMzJYqycxVgFcT2zUuxcxaTrOoPaLfoSH608\nZoqX0+z/BKfbmzZ8z2ZCgs2l9GHXONd6k/PbGVSZ58/LXIy8sfL88/pnOXcis5Lf5X6kfEhpWUiQ\nn2i/WNhrQgK4cHuCC3cm+fRTzXz5pY68bFNU2e0w+Z48NVOWU3W5kK8Br+mQrYgUKUqFaYpy4yRl\nRg+qnL+xbQY5itPowWn0rDzmjznxRWvwRmoJxstYGbyzCan7s7yPmYhJkiTalFMYMNKd+ACAiDrH\niP0d6H+Z0x0NaW8LNl9j6VxnLYPjC3gXI8TiGg/6bdTVtTChJtv8Ufg9TgSOZbR+Ur6LGzRNyzhK\nE+Sfs0druDPo5cdXRnj2RN2OlIGnIiKkHAhGEytjjnIl21RdPvqN1stos6tuXdeZ7vWwMOmn6qAb\nV0PZjstIQsNlnKLKMoLLOI28RQSk6xDVLEQSViKambhmIq6paCgYDAai0TiypKFIcVQ5ikGOYJJD\nmNUAirT1xKehuJ2ZcCMz4SZi2uYptPVkGzWNJu5xJ/Heyn1rrIZG/4vIKGuWTt8qQlpmyht6JEoa\n9wT413f6V+6/fNbN5cQ/oylJyR8JPMHPPPVTabcX8pe2Wx4HJ8uyiJAKHCEB3B+d51sfDHD0QDn/\n+y+cynqm+GVEym4HmA9EMRgUIpHcFz2DwqTqNouKNjrJ6brOxJ0pfKMLAJgcRgK1yQNsJ2SkSlFq\nLEPUWIYwKhsfkP6wytichUmfmZlFE16/kbi28Xe43C925uTRDZ7VMckhrIZ5HOocDqMXu+rbMP2n\n6RLeSB0TwXYC8fTLYbMR00ji7kqkBFArt+OcPYuEtCKldIQEG0vp7Wuj3B6YBcBhNXD0pIfb2iUA\nlLiBr9b/GrUZjE3KV9ouVUhQOmm7vSokXdf55vsDDIwv8D//bCdnj9bktD0hpB1gPhDFYjHkZZR6\nIaKjrVJ0G53kpvs8eB6snlQTbjN6hTnvMlKlCPW2fmosDzeMWhYiDjwBN7MhN8GYhe3SaMtYrUau\ndD06aeTGggJFiuE0zlBhmqTcOIkiP9oWX7SSUf8R/PHyDbawMZmKaSBxg77Exyv32+TTGGeTbT7Z\nUZ2RkGBtf1I4GucbP7hHaGm9nSePVdJvfp2wmuwXbVw4zC+e/3JGV8T5iJJSZwoppShprwoJYG4x\nwn/5fg8Oq4H/9Gu5FThsJSSxQF8WzAeiaJqW0UJ2W+EPxYtGRgBGw9r9mhuZZ7p3tW9FcxjQKy20\n1JZt9PZHSEdGMnHqrf0ccl7DafSuSc1F4gbGFhro9RxidKGJhYiTmGYgXRlBctG3coeV6grHym3G\n62diyrPmVleTnL5HRyGUcOCN1DEZbCWUsKNKUUzKaj+fWQlSbRnGqizgj7tIpFGpV+m0UOm0MDsf\nYtLjo7Zq6yjLJdUSI8y8nixCmNMnabDXkAjamPIGaKpxpvUbXF7wL3WxP1WRMRkVBieSUe+0N8zZ\ntibGEslU3qJhjsZYBy5nen9ngISm57x4X+pxJUkSkVhiw4Uk9xrFukBfOlhMKpquc390Hl3X6WzN\nvip2qwX6RISUIakl3hvN+ZYpu52qS6d4IfWqO+AN8vDj0eQQf0Czqmj1trzKqNw4SYvjzpqTPYA/\namNkvpGZQCV6mkPmNDSicoiIFCYmR4hLMTQSqEYZS8iFI7G5ALr714632Ch6sqrz1Fsf4DaNkRo4\naLrMeLCDsUAHOumfPJcjpq2iJU3XuB7/IR59BAAFlXPqF5idMWA0KBw54E7rszaKkjRd5x/f7MOz\nNIFnZ1s5HuePWTAkU3m1C2187Xz6k6/mI223/rgqlShpL0dIALG4xn/+fg+BUIz/6398itqK9Pcn\nFZGyyyPL0RFsPAlpJux2qi7dSrplIcXCMQYuDJNYukLTjTKJJgctdfmRkSpFaHXcwW0eX/N4IGpl\n0HeA2aCbraIgHZ2Q7GdB9eJXfASUBcJyAH2LwofHFp/Dotm3bft6OcFaQZkVP422XirXtT0Yt/Ng\n4XTe+5dieoRLsW8RZB4AGy7OG77I9FyMaCyxptBhKzbqS3o4ucjrHwwAIEnw8rNGLkS+k7yvSXzJ\n9R9obW5Me39yTdsJIRWnkAD6Rny8/uEgJ9rcfP3nT2ZV4CBSdnkiVUZAzim7bFJ1APP+6I7JCJIp\nu2gkzvC1MaKBZNGGrkgkGh20NDjT+rztZOQ0TnPU9REO4+qMArGEygNvG32zBwnFbGwkIx2dBWWW\ncdMAg5ZuJsyD+AwzBJVF4nJ02yxeTbQZQxrji1JTexul96qqG/BG6pmLVGNTFzAqyQjDIEepMo+g\nI7EYq9hwH9aTThpPkVQqpHrGtT50NGKEiRLiRHUnM3MhprwBaiq2L8m1Www8nPSvSd05bUbGZgIs\nLF0wGiUHmKaIKEGQYG5mkcea0p9kM9e03frjqlTSdns5ZbdMRZmJsRk/faPztNSVZRUlbZWyE+OQ\nCkQuY452UkbLzPTPEppLnmR1QKu10tKYnoyW2VhGOo22Xhpt99c8OrlYw4O5VuLaxgdtRAoxbRxh\n2jhKTN76itGomTBpVgyaCVU3oKBiVFWsIRdWLbuZxzs76tbcv961ugT4h7j59FONNNt6UOQEsqTT\nbL9HOGHDG6lP+zMON1fQO+zddAyTQ67gqPLMSjn4qHaPpmgHLTUNDE0t0tU/nXaklIokSZw/XrtS\nBt477OMTzee4GPkuAJO2AcYnp6mvTW/by1MJ5XMGcDEmqTiQJImXH2/kv/3gHv/4k/t0tlRgyONU\nTyJCSpP10RHkFiHlEh1lcqWYjYwi8xGGb6ymojS3mQMH0y//vdkztKGMFCnGIedVaiwjK48FIwr3\nZo8xutCIpj+6X0F5kSFzDwOWbhYNXrR1lXeKZqA8XkV1tJnGSActoaM0RNupjjXijtdRHq/GFa+k\nRq1FiWY288JWpEZP014//WNx7k/aqS6LYDcnx/LMRyszSt3B9tGSQ3ITYA6/PgfATHyUBvkwbrsN\nXyCaVqQUCMWZnQ+viZIcViPjngALS32kVtVJzDBGVAmDrOOfjnKsMf2lMXKJkjY6rkohSiqFCAnA\najYQiiboH5vHZlbpSDNrsoyIkIqM3SpkyEZGWlxj8MqqMDSLSvORzGS0EQY5xBHnx9gMCyuPjcxa\nGAmcJKY9uk8RKcSIuQ+PYfyRrJdBMxIbU5GmzWjzBnxI+JgD5ta87uzjp9Nudy6kRk+vX1PpqFnE\noOj0jAc5leVyMqnRUmqkJEkSx5TnmNMmiRAkogfpTVzmhPoiLTUOhqa2n7VjeQaH9Zw9WsPIdLLk\n+96Qj2fOP8GV2JsAjJh7SWgJFLkwQhBRUnHxdGct3YNevnthiGdO1OVcWbmMEFIabBQdZctuTw+U\n6VRA030eIsGlfiNZov54Vdodl5v1G5mUAMdcl9ZU0V0fcrHIcdbbRiPBuGmAMdMAurTuO58zIo1a\niXtMyLrEY0daYW0mbQ0fX7ux8n+DQSEWS+y4pI62r6boNH1iJbW32XinrdhMSkbJzDH1OW7EfwTA\nmNZLg3aYCjn5ZaSbuls/pVBDlY2aCitT3iAJTSc0V4PRaiEqh4ipEfoWejjqOp5W2/OdthMUFxaT\nyvnOWt65McZ3Lwzxi68czMt2hZAKQLarwGYaHWUqo5AvjPfhapFBRXs5apoD4DaTkVnxc8x1cWW2\nBU2XeOduFart8PpN4FfmeWDpIqT41z7hMSEN2pEWDUkJpVflnHztEstLmKdKCnY2ikqNnLIV02ZS\nqpFbqJFamNKHAOhJfMjT0s/lFCVJksSZQ5X84PIwAN0PfJx+7gzXFy4AcMN7NW0h7QSapjEfyLyg\nR7AznD5YyY37M7x9fZRPPN5ATQZVhJshYuBt2IsLhW20QNt26LrOxN2plfsmlxlrdWY/sEciIznI\nUdelFRkldJnv36yld2Jt2biOzpjpAd22S2tkZEuUIV2rQO4q51TDoTWCyZbHjrSuuX187caa206x\nLKfrXT1rCiLSIXXtpVSOqM+gLF1TLupeRrV7K88tzzGYKe0NrpX0SzASx7TYirQUxY4Gh5mNeLZ6\n+yPkc50kQXGhKjIvPFZPQtP5ZsqSJrkghJQGe3FpiUyjo/mxBcLzSXFIskR5e3lGqbr1MlKlCEdc\nlzEtlUMndIXvXq9leNa2JnKIE6PPep0Rc9/K+CFZV5D6HATfsyDNG/Mios1IlROwo4Lq7KhbI6ZM\n2EhKFsnOYfMTK/f7E9eI67GMlgBZf/GiyNKaUfj3B8McsKwuO3Bn7lba2842E7AVy1GSoDg41ORa\nWe58ecaPXBBCKjGyiY60uMbY3dUr6vIWF6ols1RdKhIJDjuvYFEDye3rMr2+Jxmfs66RUUQK0W2/\nzJxh9bPtcRf6pXKkURunjrTtqIzWsz56AnZETstiyjRa2qhyscN8ChPJqroIQYZTFvjbLkra7KKl\ns7VipWdvZNpPo7paXXfXd5tMx9KLKKl0kSSJFx5L9pt+873coyQhpC3I97Lk2ZBNMUOm0VH39VGk\nxFJ0YpSpaE2vVHnjfiOdVsdtHMZkxZuuw/2FM7x7bW2qJygvcse+NkVXF2kl8IEJKazuqog2Y6fT\ne9lGS6kXAapkoENZXUxvMHGLuB7NeAn5VBxWIwdqV9+/MOnCJCV/U4vxBUaDw2lvayeiJNibqfRS\npbnGQWutg7tDc3QPebd/wxYIIW1DvtJ1sPPFDNlER129U8hzqwNNy5qdyGkMdNusiKHaPEx1yjij\nh/5jvHUl2a7lE3BAXuCu7aOVAa6SLtEePMnUhRDScvVcEbJZ9JQLmUppoyipQT6EhaRAYkQY0TIT\n3Ea/myMHVmcw7xteoC2lCOXefHdG2883+TwmBfnhueUo6d0HGUfQqQghlRiZREdd/dNI8xEkLfkD\nUswqtur0V4Rcf3K0KIu0OFZTRjOhRiZDbcDqiTck++mxXSEuJ0vLZV3hSOBJqmLJ1VCLVUbr2Sxy\nyoZspJQaJcmSQpuyWi04lOhC09MbTLnZ76Wt3rkyAn9uMYJbb1t5rm/hXkYnneUS8HwjoqTiobbC\nypFmF0OTi1zvy6zwJRVR9r0L7MY0QZlGR13906DpGBaiLF9vljU5kOTtCxk2KmKQ0Ogou468NHYo\nGHcwuHiC612rlV9RKUKP7WpyzjlA0VWOBJ7EkXBlfTK/dPnixk9IErLFimy1IhuMqEaVeDRO5+Ej\nqPE4SjyWweIVW7Ms0Vv3Blf2I9Ny8s6OOrr7k+OWshmz1CAfoj9xNTlYliCT2gAtNQeznk7IoMq0\n1Zet/K58kzbMTithLUgg7mciNEa9Nf0JV/ONGChbfDxzoo57wz6+c2GQ04cqkbOYeFUIaZfYqVx6\nKpn2HVVKMr6l5QIUk4K1avvoaLOZGOqt/SuzMGi6zP35x7nalZyvrrOjDo0EfdZrROWknJOR0RNr\nZJRJdJQqojMnj6LJCpGyciJ2F1Gbg5jZChucsJYnRNITCeK+OSoUGUvQjyXgR8kxFbReTNlKKV1u\n9gzx9BOHgGSU1Kx0cj9xBYCH2h3qldwGK3Y0OFeENDC2SHNtO32B2wD0L/ZlLKSdGCgrxiUVD+4y\nM0cPlNPzcI4bfR4eP1yV8TbEJcY+pKt/GnQd//hqQYG9fvvoaKvBrw0pk6UO+48QSiT7NJbTUUOW\nu/jV5NIJ6HAweApHojxjGV26fHFFRqdPHuXos88w23qMiRPn8LYeJVBVR8xq31BGqUiKgsFdyaKr\ngun6ZobaDnPXYidgc5DreizrU3mZkk7qbqO+pEb5KNLSIT2vT7Oozab1eTUVlg0j7AO1DpSl38Ts\nQkFbDsQAACAASURBVJgq+cDKc4OLmVVU7VQJuKC4ePp4LZIE37kwiJZFX5IQ0ibkc7qgbMg0XZdu\ndLRcClxnMRFfmiJIkiVsNVtHR1stJ3HA3r2SqvPHXEyG2tacVD2GcaaNo6uvDx+lPL6aRspERpAU\n0eEXX2Tq2BN42zsJu9wbCkiORTEEFzEt+rD6fZgWfRiCi8ixR/seJEXB3NzCVOMB7tc2cu3ho8ud\nZ0pq8UO6rJ9VPBNMkoUaefW7HNV6s94WgEFVaKxeXTsqMle+Iryp8ATBeCCn7QtKD3eZmaPN5YxM\n+7nRN5Px+0XKbh/SUuPA27d69WyttqZVWbeRjJzGacpNScnpOgwsnmB5frrOjjoiUohBy2pVljta\nR200eaWdyYn60uWLnDl5lIjdyXRjO3HLowI1BBcxz89hDMxjDPqRE/HVfbQa1ywQqSkKUYuDqL2M\nsLOCmHW1zFl1unC99CqX/vkbkEgWB5w/93TabU3lsSOtWaXw0u1LutL1gM72ppX7jfIRJrVk9DKh\n3efF6nNZ9yMBtNQ6VoYejE1GqG6vYyoyBsBwYIgjzs6MtifSdqXP+eO13H04xw8/Hubxw5n97kSE\ntMNkOztDumRSzLAcHWkJjZBntdDCVrv1Cqqb9RuBTpNttWhhOtxMMO7ielcPmi6h6RqDlm4SUlIM\npoSFttDxlaloIL3o6NLli5x6rBNfYzuegyfXyEiKx7BPjVBz9wrVvTcpm3yIedG3RkYbIScSmP0+\nyiaHqe69Sc3dK9inRpDiyahR1ROc7jy0IoXUVGGmZBoppRslbXSB4JbqMZGc8ilKGK8+lmYrN6Y5\nZTzT2EyAetNq2m44kFkUKdJ2+wN3mZm2+jIejC1kPHuDEFIRkulg2EyKGVpqHIRmQ+hLpd6qVcVg\n23zq+K1SdeXGKeyGZL9QQpcZDSTHqgQ0Gx6thhsLU/gMS2G7Dh2hx1bmXkv35Hzp8kUUh4OZw6cI\nVK3OpC0l4jjGh6jtvoJzfAg1Ek5re5uhRsI4l7ZXeb+Lqt6bK9o8c/JozmLKJn2X6YBZAEmSqZVX\nS7QntYG03rdZP1K5w4TNnPybRWIJLPHVjurRQPoDZAX7iycOJX8nP7k6ss0r1yKEVKTkOwWROo1M\nyBNc+b+1yrbpnHVbL0OuU59SyDAVaiGmmfn41n0Cuh2kBJGa1eipJtqMI1G+ZgvbRUeXLl/EUFlN\n9c98aU1UZPZ5qOm5RtnUCLKW38XLZC2ByT+PshQppZKrmDKpIsylLylVSNPaQ/QcyjQkSaK+cvW7\nj/jKViJcT2SaSGLr1Xs3QoxJKn0O1Dpwl5n5uGcanz/934gQ0j6ipcaBltAIz61GE9bKrWf03lhG\nYFfncBiSV9SaLjMRbAcgoNkBCbVmGNmU/BxVM9AUPrTy3nSjBENNHe5Pfw5NXYrgNA3X8H0qBntQ\nNihM2C3WiykTlqvvdhKXVIOR5GqwUUJElLlt3rE1qUKa8caoMKxGSZOh8Y3esikibbc/SC5lUkVC\n03nvZvq/ESGkPUw2ax5FfGGWL5gNVsOmk6hu3m+UpNa6+rwn3LAUHfURwQRyHLVucOX5xkgHKmvT\ngttFC1f6+nB/8jPoSnKFUjkWo+p+F7bZybwNaM2VbKW000iSTKW8WujgN2QmjfXUuleFNOkNUmWq\nXbk/FU5/3JRgf9HZUo4iS1zrTX8pFFFltw/o6p9emWwzNToyV5i3fN9m0ZEiRakwrZ6IJkNJuQR1\nGyChVI0hGZIRjFEzUx1t2mgzmxJXVVwvfxpdSf485ViEyvu3MUS2TvV88P47mz63vGLsMs89/9KG\nr4tpMp6IA5Mco9wYZLvB5mdOHuV6Vw+XLl9MuxJvOUrarupueUbw7art1i/eB+CWGhknmVINqlMb\nvOtRlvuRUleRBah0mpGkZBXlvD+KU1mtnJoOpbdtwf7DaFA4UOtgYHwBjy9EpWv7i2chpCIj26XK\n02WNkMo3FtKVrq0HPbpN4ynjjpwE406u3rpHWK8CdNSa1eqr+kgbMsrK/e3SVTrQ73BhtCZTiVI8\nRmX/nf+fvTcPjvS87zs/79V34z4GGAww98EZDucgh8ObFHVLlmQrjpU49tJOJS7v1laqrHKuP/xH\nNlaSTSlJ1VZtNutdy0piryS6IsmWKZmURYs3KZJDDmc494GZwX0Dfff7vs/+8aL7fQF0N7rR3UAD\neD5VUzXdePvF2+i3n+/zu0uKkVeIii3yuYmxuWvwvsYrTnfi7cxmHYtgNhtjd3iS1boprUWUasWx\nfZ2cuzS64vl2dScs6m/KmOLD6yM8sMa4lK6ptDUFmJpz7h017Q5YnEivbRBgPZDp343Hvt5mbg7P\n88H1ST754OobU+mya0DK+VKVm+7tTWYwUyZW2lmlFFXBF/UXfV0x6wigPeC6gCZSzk2WFgFARW2e\nRA04SROa0OnM7Fzx+lLuutn2Tnxdiy4hIWi/dQkjlSh6fE5Yzpw+WXadT+7Y3PGvvvJy/jy66sYj\nZjIRbix0Y4vVnYSVuu/qHUsKKOF8B3Abk5RWeSd4Lx3N7uYlG3NdeNPpSWyx8TEcGUdqTPbvdDYv\nH14vr+GqFKRNTLnxo5y7LrPgZrv4mnwFWwWtFjvSlTRNhlNUKwRMp51dd0o416J1uHUvnZm+fJp3\nOWR8PqZbO/KPm0Zu44/NFT3+1VdeLkuIVNumZ2KCg2Oj7JqZoimZcC4eVgjTrtAUHX7XSp03g9yK\ndVBOF5S1NEWtJy1qd/7/Kb28NkLFaGtyBWlhQRDUHFGyhMV8tvhnJNneREM+ulqDXL4zS9ZcPSNW\nuuy2EZl5NzOtlHV0bF9n3r21nBb/eD6uspBtJWsH+MWHV8jSBaqJ1uJaZF2Zpc03V7MIpjp7UBaT\nGIz4PJGxe0WPLRUvWs7A9BRHxpYG39OazlBLC7faOkj6fHlRev1V57z7HvoKI0knTX02G2Y4mWVn\nqDwrYyNcd4VoUjoZ4ToAqXIz7Yoob6vnfplZSNO8o5Wk5bQOmklP0+JrLfg6iaS7Jcj4TJLJuRQ9\n7aVblEkLaRuRiXkFaW2+9maf259qNuPswDPCWazU5kkUzXGdBK0IIXvl1NJi7rpkMEQysni8ELTe\nvb5qNl25Ljq7QJ87v2Wyd2qSZ65f4cjoCOqiyyd3zhu/+AHdAXfnP5pqZiFbXMRzNJKV1KS4btd0\nGS678Lt/y/3f+9/R//aFFT9ribjvfT6eoUl3Ex9ms9WllUu2Ns2L904uBlkKKUjbBCEE2YRb7Okr\nEKdazV0H0Gy4vuC5jONeywmS1uKKVVu2m0qYbXNrW0LT4xjJ4o07K7GOAAZb2zh/YD9XO7sYbmom\nrbmOAVUI9k1N8PjN6wQzjmDnROnWu98nqueSKRQG4x3YZbju1FCYjK88wa9nHCniEaSMNrfqUL3Q\nhXfQzAzGm38DscWWL8JEN4dpDrnbg/l4hojmJjYsZCtrDyPZXuRi4hNSkLY33nRvK20hLGdBUnUV\n1Vf4oy+VzACA4pwjYUaImy0IIcjgAwRasytWLWb5TRWzhm+JdRQdW70lTUWzhhSFydYWrnbt4P1d\nA7x06Ahv9+9hOugWBTelUzx26zrhdNpzfsH4hb/IZxSmbYPJ9Eqrb8l7CYTo/Orf4+7AfhaaWkoe\nW07nhlzq91rwEUTHWQxsxSQliieHANiR5vz/1XHHxRlJ/Iho4vu0mn+Db7EBr2ULfLiuFylIklI0\nR5x7cHJ29Q4dUpC2CWbSbTaqh/Si7YJW4/LsWe7EjnBp9hFAIZ62EagoviSKz1nMNaERsZpKn8iD\nd+H2z09X3ZduVRSFiWiUN/bs43zPTqzFv0XANDkzeAvDdP5WZ06fRJgJegOuu2s02VzSSrIMH6gq\niqoy29ZR/MB1QFEUQor7OcSt0skHZpMbB1IWnPesW06dkc+8TZtHixXLTXKQYygkpYgEnaL4+TLa\nO0lB2oSspUODmfIIUqB4M9XVSJjNDCf2k7WdBWku7pxXjbiLXcRsyc/NKYd4k7szD0+tY6GlonCn\nrZ23B/ZgLopSOJvh/pGlHbI7Awvoix3Ls0JnNlO83ZIvPg+L8aisP4CpaUWPLZdq4lJB3E7uCbt0\njZsddsVLiTvH2qqrQp1R1+Ursq5LMmGWtrwk2xvTcr4PPmP174IUpAaikqF8lWKlvYJU/SKZ4/pd\nJ26khFy3Tdgq7arykjV8ZH1ODEpkswTm1z9APh2O8EFff/5x7/wcHTFnQT5z+iSvv/ozOgPuYj6d\nKT6uQ7VtfAn32HSwdK/A1ahkpHkh/IrrWkvapS0Z2zvWI+5ME7YVd+PTHHBrfUTW3dQkrfIFKZ21\naz4PSdLYZE3nvvFLQZLkyBXEAmi+2gmSJRZ7zQXdceghu/R8JS9Jz4KdGRtB2aAiy9GmZu62uC6r\nAxNLLbV2n7uYz2eDJYtlfXGPIPk3dvH1eQQlI0r78G2veC4WIwvFdc2F/O49ZGXdxJCMXXnHb8n2\nIWPmLKTV5UYK0jbB8vRxU2spSIttgRS/u9gFrdK1Bl7SSwRpZQuc5VSaYVcJV7p2YC+67toTCSKe\nWJZfMwmojg9coBA3i6eAGylXvLL+1VPF64mB+/vTdunYnO1zxUdZfO9CcS32oOERJNNdOtYygkKy\nfchZSAHf6mWvUpC2CXbWtTy0Go4AsAsIkk+UbxXk3HUA5vTq7UWKNUWtBSnDYCzqxlG655dmj0UM\nd+FNmMVdq5qn756prz1eVwsM3Os0RemgsjA87ymbE193EfFp7j1kWeTnIgkElqjtXCrJ1iGWdGKP\nueSGUqx5ZbJtmz/4gz/g137t1/iN3/gNBgcrG2e8HajHILK1Yltuapii10aQbFsgUEGxULTFHnlC\nQRflL8JZzyJozW98C5qxiBvEb0ssjbkENHdBT9nF36N3VtNGC5KquIJiipVDB70IT30W2cVjFdea\n1lT3HrIsljTNtWo8KFGydZied6ztnvbV46lrXpl++tOfkslk+O53v8vXv/51/u2//bdrPdWWph4D\nydaCsNzdrVqgc8FaMHMip7sLnSaM/M551WsCLN1dBK3ExmdrzQVd6y6cWeqK8qnuopu1i7s9VdNN\nILG1+n7+F25MlPy5VzQEq8TnPBmBSr5ZqXv9qqfxrBACVXF/Zq927jqjqqrs9N2gTM8736Md9RSk\n9957jyeeeAKAEydOcOHChbWeSrIOLCnSL/GpX7kzXfY5rcWTKp6FSqP8+JQCGIuLvj+ZANtacxFo\nrUh5LBqftXTXrynu+yyV1OBNzBBK/Tcky2chLbkWz+Zg9VHmnve0+NkKz3Ped1xOs9nlpLOyI/d2\nZHohRVPYR7iMcpM1N1eNxWJEIm42laZpmKaJrhc/ZSi0eXYwiYyFXoa7JRwuHrT2xTKEg+W/Z8NI\nljxf/jifRji0+nE+Q2N4OsH+XS0owl2OQmEfWoEUzEcfPJifhRQqY7dpq4uWgOKuTqqiFv2cDUNb\ncd69U8PMB8M0peIcePZpXnnl1VXvE8PQOHf+PI898uCq1+ilnPeke4L1yuJrDEMjFPKRTumwmECn\nasXfp72s6LjU782du+jPfSv/Zssp9XNfVoPFBEhNK33faH73fld1lXDYj2apsOiBVFX3nvEtC1CH\ng34Ceul7UiQz7Oou3ekif74yvgdeTNPeVOvLarS2htB1jSxKfmryZiRr2szFMty3t53OztU/+zUL\nUiQSIR53fey2bZcUI4BEYvVK3UYhm7VIp0v73MNhP/F48QyjTMYiLsrPQMpmzZLnyx+XsYgnVj/u\n8EA756+Pk4hnluyNk4ksql7Y55/NOM8X6/btJZVLJfdYC7awi37O2axV4LwZggsJsuD8y1qr3idn\nH3mSV195uaxrzOEd0FeKsCezLqNq/O0rbwPOvZvIeO5vu/h12p5YjGLbRX/vh5dvceb0yZLvN5sp\n9DdbSqmfp2z3Z8Ki5H3jSyTzDYEsVJLxNMFsNm/z5rKlACzLWpLIkEqZWGrpezKTtcu6v1f7XhVC\nVdWGX18C/vKX25kZx309PZ1gdmHzZjGOTicQQFdLgIkJZzdXSpjW7E84deoUr7zyCgAffPABBw8e\nXOupJOuAt1XQak02y0VbnKck7MaJJVRLU8oVpMRig9RcZp83bmSoxYP4XkHSNjjYbwlPQbSyisVv\nuceyuLlUPK/PWu7nrKkKNp7aNmXz7uIl9WNisX/drs7yahPXLEif+tSn8Pl8fO1rX+Pf/Jt/w7/4\nF/9iraeSrAPeYXzCKi5IJ47sXjVQnkPXFs9peTK5lGwZsYraUI9O2Z0xt6j14tz8kjTzpOW6hPxq\ncev50j23nkrzJDhsBCau1bCaIKneJI58Or77PjOWJ+NOdzceuqIvSXCQSHKM5wSpqzxBWrPLTlVV\n/tW/+ldrfbmkCg71t1TUz+722AIBrTxBqgRVcf7ZtoawVBTNRig2FiY6a093fv/8pVX7tz3x5DM1\nL5LVLYteT+r5VUvg7ccd8xTDhvXi7iE96vbmM7JrdyNdvD5S9XylLJ4pwZ6uC4VQPO5K4XeOVTy1\nS8mMKzoZjyvQp64eu5EJDduTnIW0s7O8Ynm5rdniHN/vjIFQPbVHtlmbxUFRFAI+FVAQWXexy6hr\n79Zd6aTVWlpJbYk4+mK687gt2PP40/mfpS2d1KKFpCAI68X9+npbe/7/Rnpj/f/edkF+tfQGJjHt\nqQMLOCm6qicGGkt7XJGGa/n5tdJCl0P2sNt+TMym6GoJltWlAaQgbRuWCFK2dFzjoeP7yk7/Di7O\nVRIpt8YgpRZv4vnh5Vtlnbcccu60WolSzOcno2pkheCvTRs8cbfpjLvDixpJVKW4lWl0usMJ/an6\nFUeX8xl5ZyAF1NK7VN3T8kiEHReL4hG0+aQnA9FwXXlBrboGspKtSSKVJZk26e0ov5WYFKRtQsJT\nGGtlahdoD/uduIJIuTddQis85qCioXplUktRSvj9/PtEhv+QttnxuBs7sgVMpNzMIG+j1eWcu3IT\nI2chCUEgVbjYt1bC/NDxfSV/Ppd1rZ6QWjrt1ki6n5tYHEWhejqET8Y8iQseCzGkS0GSrGRqsSC2\np6P8+0MK0jbg+P4uhMdCMtO1E6RI0Fmk7IS72MW16iaIPnL20YoKZGshSu+8d4533jtHGji1rF/e\nZDpKVjguB12xaCkhSP6d/XnLyp9KotrF3aP1EOjlZFW3C3tYLT000Ui4n5toagaRQVlMahBoTC24\nVqGtu5ZTxCivtkiyvZhcHFne2y4tJMlyPC2MrNTqmV8njuwuyyXUHFoUpJg7A2lBm123TLsc1YhS\n7jVPPPnMiuatpq0ynHTfW3dgDrVIk4b3z18isMe1WMKxjR3tnRGpfG2Qhk5QLZ3p5Iu5k3FFcxuq\nZ6CfSYScke3TVdK4ohzVSwudTGjYnkwt9rCTLjvJCoRHkLzjzKslGtTQVMdllxvaZqoZEmrp6aT1\nwCtK5QiT97hCXcSFgMF4e37mk0816QoUf19qKIR/56784/DC2pvFVjuYDyAm3GGHUa215Nj6ifE5\nfIsuO6GqiOZWNNu9/rTtLirhoEHccsW2ybf6QEaZ0LD9mFq0kHa0le+yW3Pat2TjGZtOlp36ffRw\nN1fuOe6bbDKLsMWS2qS1oioKLWGdqQUTa74dvd2pwZnVJwhnSu+cS/HI2Ud58603Kk57zgnLq6+8\nvESUDEMjWyCZo9Q4i7FUE7NZdyHuD00VTWZ4//wlwicfzLvrAokYRrZwrVK58aNqU74H54dgcS1o\n1jpKHuufn8r/X7S0g6qhZl2LKeZJ6mgK+ch4NhzNhpvmLpHkmJpP0Rr1E6ygQ4UUpE1KrhapXDRD\nQ+gKiilAgJnMYpTR2+3KnWkO9beVPKYjajC1YGLPdcKiIE0bY+zMrAy4nzl9knfeO8cDh/es+Fkt\nWS40oZCvotYyk+kIQ0n3fXf652n2Fc6Ye//8JRTDoOnoA/k+FU0zpd2d1caPysqw01wLqUXvLHls\nYHY8/3/R4WQJarb7+qmEu8uNRgzuZNzf3+p309wlEoB0xiKWzHJ0T+m1YznSZbeNEH43SyoTK92n\nD0p3kfbS1ey46qyZToTtWAhxfY6UUv04ifXu/i0EjCWbGIy7FkVET9EXKi0ABz/zBezFJphGJr0u\n8aPVPp+k7g48bNO7SxwJwRlXkOzOHgA0y33PQ7NurVE4YpJdLIwNaAFCMu1bsoypCmYgeZGCtI3o\n7nVdK5kaNmwMBzQiAQ0sH/a8u5CP++5Wdd5Ki2SrxbRVbsU7uOexjIJamn2R8ZKJDGokylyr+75b\npsbLnAhVPzIiSWYx21FBpbWEII1NJ2lPuO2i7O6dIGw023XjXR/3dAIPuZl7Hf7OkrEpmdCwPckn\nNFSQYQdSkLYVwRZ3l5uer21n5N42x/1nTuzMPzfmu1u02WoldTjrYSXNZYJcnOtlJuNmooX1FAej\nY+hq4feQu67+z34RsTj00JdKEikx+TbX4bveTAs3KaJN70ZXSnjnbRt19J77sGcXmj2Nstg81SLC\n+OJbUhUF0+e6ijsDpS0vkAkN25HxGce93VdmU9UcUpA2OWMVjEkPtQTzU9bMRLasAtly0793tvkA\ngT3bhR13khmKDeurZEFeDyvJEgo3Y52Ywl20O/wLZYnRfZ/9IsnwYh2OEHSMDVdtHdWih93tuCv4\nXUZfyWODs+Moi41VRaQJos1o1lj+5wuWazG2RH1kDTe2VI4gSbYfo9MJVAV2dUtB2jYc6l893daL\nqqtLraTZtfecW47fUPErKRAq6Y8fJjj0AEdjZ1FrcItVWihbKSoiPw3WUEz2RsYZCJfOqAM4+fSz\nTHXuyD/fPDNFoESroFp1Z1htgyCEIKa7FlK3MVD02LHpJOHxO/nHVt8eUBR0y+1YPrbguno7moOM\nJIfzj3uCvRVdu2TrY9uCsZkEOzsj+AsMAi2FFKRtRsRTpJaaqZ0gAZw84DRyRWjMDPVgpUs33ax0\nga6XKCkKHGke5kB0lKMtQ7T6CidjvH/+Uv4aHnr8KcZ29oPHVdc6OVbwdV5q5a4rldCwIKYxNadw\n1VB8dOg9Jc/VM+9x1/U7mZG66YrO9Qn3nmlpFcwvtiMyFIOOQFfF1y7Z2kzOJTEtwZ6eyjt4SEHa\nAlTitot42sAnZ1IIu7yOCuW47VrCOsbiuAMB3JosfmylC3POdVcvUTJUmyYjhbaKVfTI2Ud56LEn\nGOnbjbU44l61TLqH76LWaPBhtYzZN/P/32HsRi01PM+2Ue/ccB/u3o9iL6AJJyFCoPPRXU+X76jr\nrtsR7C05mC+dtWX8aBsyPOVs6Hb3VF6HKAWpCM1hH6q6vn+egR1R5ioYyw2Vu+0CTX70gLPACNMm\nPbd6tl256d8AEU/vtPEFmEvWbpGutygVwmsVPXL2UUxdZ2TXHrL+xdlIwqZ76O6qc4/KTWaotkOD\nEIK72ev5x32+A0WPHZtOEp64m5+DZDe1INq6MEw3OzJud5FarBAIB3QWVNeV1xfur+paa8V6f08l\npbk14mxmjvS3Vvxa+UluMxRFoWmHG2hMTBRvFLoWHn5gP35cV+DVMbCLWA5nTp+s2G23XqK0XIge\nOfsoaX+Aof69ZBeH1yEEXcP3CCZL/w0rfY/VJDTMi8l8ureOQY9vd8njdy+48SN73xFQFAzTfe7e\nvFv0uqM9zIwYyj/uDxePTa03zWUUeUvqj2nZDI4u0N0apLuClkE5ZKeGLUKxNkJqbI7oGy+S7e4j\n8cAjADT1RJm+7aTuJqeS2JaNqq2+NymnawNARF0gbfsBhVga7s1AqZd9ePlWRZ0bcqL05ltvANW3\n2PHiFTpvht9CUwuT3b359G6EoGvkLpEyC2DXI9UbYMi+kv//Tv/+0mPLhUC78lH+obX/PhDWEkE6\nf8+NA3R0CM5nnNokXdHZGWoMC0nSONybiJExbY7vK92qqhhSkBqQuXimoh1fqTZC0bd+SujKObhy\nDrO9m0zfXoLNAXxhg0w8i7AEyckk4e7SBWwnjuzmg0u3y7qehx44yKsf3CEunMXs5iS0hQSRwMqE\n6FwrobWwXJigcnEqZGl5hcjSNCa7eok3uZlmimXRPXyXUCK24rXLqXXd0ZU700VdqKbIMmxfyz/e\n47+v6HnGppMEZ0ZRZx2BET4/9u4D6NZQfuSESZSPh5zPTAGU5glyxm9fqB9dLb58rFdBrKqq0jpq\nIG4MORu04/vX1k5KClKDMbAjyuBo7Tpl23430y146T0yfXtRFIWWnc2MX3WyDuKjsVUFKUe5VlJI\niaP6oiyknXY8F0fg9IBAL9DyoNr+dl4B8YqTl2LNVZe/PodQFOab25jp6Mq3BAJnJHn38B18mdVj\nb5WKUbXxoxH7OiZOLCuittCpl64/2jvtxpqsA0dBN/Al3QSHsWQPucK1ztYgMeNGXpD2RovHpnLI\nhIbthW0Lrt2bxW9oHOyrLLadQwrSKqiqil1iyNpqpLM2fqP+obqclbTcbZc6+ACRD14HIHj9AvNP\n/hLCH6Clr4mJa1MIIcgsZMgsZPBFS+80K7GSTj9whHc+vIqqdGILSGTg8ggc7RVFW81U6rorRLFC\n2lDYR6KMhBFbUVlobmGurQPTWPr3iM5O0z4+iipWvx/WWnO0VvejEIJB23W/7QscL9nSB9tGv/h+\n/qF136lFd52boffhkBuU7usOcC3mvqd9ZQhSvZHJDI3F7dEF5hNZnnygB0Nf22cjP9ESVOsKqGaH\nWGm2XTGyXTvJtjvFm4qZJXjlAwB0v05Tj5vcsDBUvlVWTgo4ONNVw7iuxIkY3JoqfGzOkqhV8Wgl\nCCAZDDPR3cvgvkNMdfcuESM9k2bH3dt0jg2vKkYfXr6Vt4zWK24EMCnu5ucf6RiruuuOWOMoi/Ev\nEYpg7zmIbt5FFY4JZBHm3ZvufjXQMYUpnDlaHf4uWv2VdXGuNTkxku66xuH8TefL/eQDO1c5GRZZ\nbgAAIABJREFUsjhSkBqQgR1rGwl9qL9lZU2SopA49lD+YeijtxwfGtC2290BJycTZQ3uqyQF/NTx\nIwTVFEHFzUIbnIKhmeJZd1AbURKAKNDERygKWcMgEYow29bBaG8/g/uPMNK/h4WWNoTHPaeaJm3j\nI+y6fb3seJH3fVRCOe2Cim0EhBDcsNw43J7AMXxq6aJk/YO38v83j50GTcOfvZx/bjixC1s4f7+O\nlgDxgJvocKi59HWuV/xIilHjEE9muX5vlr7O8JoKYnNIl906sFa3XaXJDcVIHj5J9I2/Rs1mMKbH\n8d25RmbgIMHmAOH2EPHFQrb5u/O0HSxv51tuLOnU8SO89+ElgsEw04sNEK6Og6oKepqLx5Oqcd+l\ngiFGe/uxdR3FspyCVQVslCWCUwwjk6ZpZoro3EzZxa7ViFElFNoQTIkhZoVTH6SicihwquQ5jMQ8\n6rWL+cfWiYdR7CSG6W4E3rzpfra7e4NcXnCTJQ43Fbe+ctQzfiRddY3HhVvT2AKeOrGztKt4FeQn\nW2fW+sWspZUkfAGS953OP468/0r+/x373IUnMR4nmyx/TlK5rrvTDxxBTY0R9WzaL4/CvTpZSrFI\nE7a+WPyraVi6jqXpJcVIy2Zpmpmi985N+m5do3l2uiwxqoWLrppmqkIIrlm/yD/e7T9KSCt+74xN\nJzk4egFl0fVo9e9DtHfjy15GWezMnqKTj4ecpUFVQG8fxRJOQkhXYAftgdLD/uqJdNU1HpZl8/61\nCXyGytmj1TXblRbSKjSHfczFM1UlNlRDrayk+AOPETr/Noqw8d+7iTF6h+yOfsLtIULtQRJTjojN\nD87R3LF6xl0lCQ4AqiLwZ8YQ/m5iiwlq18YhbQr2drBiV5Vb3HMp4ZVYS01zM6RCYTL+QH6keB4h\n0EwTI5vByKTxp5IEkgmMTLqiLt1esazGKqo2s24oe5054QzXU4TKfcEzJY9XzQz6OTcT0XzwcRAC\nf+ZC/rmPJ9zsvF1dUSZU92dHW45Xdb21QIpRY3FpcIaFRJZPPthHOFCi7q0MpCCtE2tx2601BbxQ\nxp3V3Eby4HFCi0kNkbf/hpkv/xYA3Qc7uPWm0y4mOZkkOZME3+qurZwoleu6e//8JQLZMdRAN4vz\nu7gzDfE0HOkRGFppFx6UJ0y+TJq+wRtOHElVsRWVYMggHU+j2HZV4yFqJUReyrGOClmjljC5kHTF\npTV9qKR1BNB+/RzKYkdyu6Ud+8AxDPN2vnedjY+/uehuSHb225xLOs1XVVTua7m/5PnrGT+SrrrG\nQwjB25fGUVWFzzxUfaG0/ITLpJovQ7X+9LVm3C133cUefBqxaDEE7lzDN+QsrsGWIE2eQOT4pUlE\nBY1Cy3XdnTp+JG8peQdJTsXh3cHife+87rCci6wcd54CqLaNbpkYtoVahRh5f2etMugqddUtjx/d\nsj8gYTtCotl+nux5quTrxycW6L36dv6xeeYpUFX8mQ/yzw0l9hJftGCjIQPaB/M/O9B0mLC+uvVc\nz/iRtI4ai+tDc0zNp3jkaDftzaUTacpBClIZ1OpLsJbdYzWxpOVYbV0kD53IP46+/pN8xl33oQ6U\nxaLV9EKG2PDqWWVQeTzp1PEjKIpATY6yy9N7MZWFc3fg5oTAKtKBPCcEaxGntVIPIYLqXXVxMcdN\nyxWSjuTxVTPr2q+fQ1lwRkeIcBTrgTNo5iiG5YyaEKi89LFbYX9gIMyF2fP5xyfaTrNRyI4MjYcQ\ngrc+dkaufO7h2vQ1lIK0TjSMlfTwJxGq447zjd0lcPVDAIygQcd+1/U2e3sWM7V6GjisVZQgPT/K\n0V7ItdETwOA0/OI2TMVESSutlDhVK1DLz1PrmqKcGJVrHS1vFySE4IL5c+zFEeNNSictmX0lzzE+\nPk/3hdfyj7NnnwHdIJB5L//cdHaAO1POpsTQVTr2TpK1nfuu3d9Bf3g3paiXu0666hqT26MLjEwl\nOHWwk94y4s7lIGNIFVBt1wbYmFiSF6uplfiJx/KZdk2v/4T0niMIn5+OPW3MDy+QjmVQBAxfnGDX\nqR1lpXHm4kmVpIOD00uuBQ0z2MnconYms3B+CFpDsKdD0Bws/fsLicXy/nilWgeVe85qqVSIijFo\nX2BGOOdSUGibO42yyt6y6/JbGCnH6hWRJqyTj6JZ4/jM285zwE8vu4P8Duxq4sPZH+cfn25/uKz7\noF7uOmkdNRZCCN644JQa/NKju2t2XilIZZLLtquGHW1BRisYprectWTcFUpwiD30NMHL76MlYmjx\neSJv/w0LT3weRVXoub+b24sJDmrS5M6VSQYOl5fmW6kogZvsoKZHOdi9g5sTYC5q/kwCZu5AS0iw\nqxXawyuz8YqxXFBCIR+JRG26X1SK1z1XqRgttzpjYoarlhsHOhg4jTLTxvH9xSe3qvEFOi66yQ/Z\nxz8NhkEw4Z5n1hzg0vBiqreqsOe+GLcmHPdeUAttWHadtI4akztjMYYm45zY37HmsEIh5KddIbX4\ngqxnLCmH13UnfAEWHvtc/nH4w9cxxpxMqlBLkJ5DrgCpkykyC+Uv5JW678BZpE8/cITZyVFaGKe3\nmSXJB7MJ+GgI3roFtyYFiUxjTGYtB69VtFYxyv1NLWHygfnTvKsuqrRxOFA6zRtA/9sX0EznM7Q7\nurEeOINuDuXHTAjgry+57V4O7Grig3m3k8Pp9jMYaul03npm10nrqPF4fdE6+tLju2t6XilIFVCL\nL8ZGxJIKJTgkD50g3efEHRQhaP7pn4PlxIx67+si0OxMRFWAsYsT2BW4u9YiSpDLwrMxY6O0qhN0\nNy0VplQWbk/B27fgnVuC6+OCqbjAtBpPoC5eH8ln0VXjovPGjj62XiMmnL+pisZx7Vlu3VsoaR0Z\nI4O03/ww/zj77JdBUQmmXs8/N5Xdy2WPddTeP8N02ukE71P9nGp/iHKotbtOWkeNyZ3xBe5NxDi+\nr53dOyofU14K+Ymvgc1oJa3o4KAozH3il7F1Z+drTI8TffMlwHl/fQ/0oC527FVMm3sfjVeUCl6N\nKJ06fgRdsRDxUdrUCXa1wvLmwfEM3J2B8/fg1evw9i3BxWHBzUnB8KxgMrYxQpUTotx7WSvLExnu\nWB8vGb53RHuUqLqKW9SyaH75B+7Dg8ew9x7Cl72Mbk8AIND4iw/d2NGh/mZui3fzj0+3nyGgbdwY\nCWkdNR652NGXHquuM38hpCBVyGa1knJ4RclqblviuoucexXfHadnmS/so/d+tw2ImjC5e3G8ot+1\nVlECV5g0xSI9P0orTkZeR8RpZ7OcRAbGF5zmrVfGHBffmzchu06itFyIqhUjL9P2MJcs16LpVQ/Q\npx7h9ljpRJfI+z/HmHLScoXhI/vsl1FEmmD6zfwxg/FDSzLrmvvHmMk4v9+v+nmo4+yq17tezVQl\nG8+9iRh3xmIc29PG3t7aWkcgBWnNbFYrCZaKUuL+h0n1H8w/bnnxe/lalaYd0SW97tTZDINXJiv6\nndWIEriLu6LAxNgoanKUdmWM+3dCXwtE/BQtdjVtx81XT2opRLAybhQXc5wzX0Qs9plrUjo4qj2R\nT+44faS34Hn0yREi77ycf2w++VlESxuB1Nuowvn8LcL8+S/cz/fovmaum+/kHz/c+VjZ1pF0120P\n6mkdgcyyWxObNeMOCqSCKwpzn/oqxv/3fzhZd8k4wR/+V2Jf/m3QdDoPtJOOZ1gYdVKG1Ykkg9oU\nAxWMKPZm3znXUPksneULfW70eAgIqrCrbweJDCQzkDLBtKAtDNECY9NrQTWZc4VYLkQ57lgXyOK0\nTvAT4qT+GTTFKG0dWSYtLz6PYjtxP7u3H/PBJ9DMUfxZd4jfO8NH8n0FoyEDpfs68ZQzKiSiRznd\n/nDV76sapLuusRiejHN7dIEjA63s72uuy++Q25AqMM3qXRUbkXG3PJ5kh6LMfubX8m2F9KHbNL3y\nIxDOdNedx3cQbHG6ACiAOppg8EZlFs+JI7urtpa85KyRnPV0b2iU6YlRknOjiPgox/sU+lprL0a1\ntoiguBiBYxEBGAQ4pX+WoBLJi1GxZIboG3+NMeXsZIWuk/ni10CxCad+lrcmF6yd/PVH/vxrzhzp\nZsx2p8U+2f2JVTPrQLrrthOvX3Du+y89trtuv0NaSGukOewjkSk/86wQG2Ul5RibTubrkzJ9+1h4\n5DM0vfETAMIX3sFs7SRx4jFUTWXX6Z0Mvn3XKZoF1JE4g8DAvsqsnVpYS8spZD0tb81j+DQO9hfP\nRitFra2hHKWEKMdO7RCtag8+AuiK+1kXEyP/rUv5kfUA2Wd+CdHeTTD1OprtTJQV6Dx/bjc5Z+fe\n3iZ2dUeJWwPMZKY42HS4orqjevaukzQGQxMxbo041tGh/tbVX7BGpCBVSS26N6yFtXZvyJFz3XlF\nKX7qCYzJYYJXnf5lTa++gB1pJrX/GLpPo/+hPgbfvksmkXVFSYiK3HfgLsCVFtGWSyHR+Ojy1ar6\nx9VDiKC8CbwhxQ0e3x4rnuatzU3T8tLz+cfW/vuwTj+Gbg4taaD60dSxJYkMpw855/t07xd4vPsZ\nQlqoqiFr1WKatnTXNRivfeRY3F9+vD6xoxxSkKqgoyXIyER5TUhLsdaJsjlRWuuXd4UoKQqzz34V\nIzaHPjyIgqDlxe8xHQiS6duHEdAZONPH4Dv3XFEaTTBoCQYOdVT8+73C5FxPbYXJy8Onj5GoMu5X\nLZUK0XJKiZGSzdD6V/8dNe3M9ciEmrC+8DUUkSacfCnvqovZvXz/Xbfv2OPHewgHjbwbuJxu3jmk\nu257cHc8xuDYAkf3tHFw18qaxloiY0g1YCNHU0B1aeArimZ1g+RXfxuzxbF6FMuk9Uf/DWPEqeo3\nggYDD+/CH3FEUAG0iSR3LlRWp+QlF1+6cmc6/28rkXtPufdZazFC2DT/9M/zcSNb1bB/9bcgGCKU\n+imqcBIVbAL82bt7EIvy1NcZob+7unikdNdtbYQQvPaR41n4Sp2tI5CCVDUbOZoCqk9wgJVJDiIU\nYfpLv4UVdlxFajZD2w+/5YpSQGfg4V35RAcAdTbN3XOj3B6eW/N1LE982OzitFyIKkYIkh+8R/NP\nvsOjUx+BKHyPRN98ieB1d6rrvYc+h+jtJ5B5D5/pzjN67e79DM84YuTTVT710C4URalpL7Jqkene\njcWtkQXujjtdGfbtrE9mnRf56deA5rBvU1tJsFKUrOY2pr/y21hBx4WjZtO0/fCP8d1zMrF0n8bA\nmT6i3ZH8a9SEiXYnxu3BmaquZbklsdnEqWohArAtoi8+z4kPXmDH6DWi7/wN+uTYisOMc28Qee/n\n+ccTh87Q+Yln0M1BAmm3eeq95GF+9rGbVfeJ031UUzJcT3ddR4u0uhoB2xb8/MMhFOCrT5Ueb1Ir\npCBtAWq1w10uSmZbF9O//A89opSh7S/+BP+Ni85jTaXvZM+S4lnFtNHuxRi8PLFmF56XUuLUaALl\nvaY1CxFwd2iK9hf+lN4Rt1WQ2dSGFV26Qw1c+4jAi/8j/3iu9wCRr/wdVGuGcOLFfNwoIbr59utu\n4sl9u91MqWruHemu29p8PDjNxGyKR4/tYFdXZPUX1ICqkhpeeuklfvKTn/DNb36zVtezqak2426t\nyQ1QfYJDjkP9LdwcXaBtMUZktu9g+lf+EW0/+GO0+LwTU3rhz5h/8oskHngERVHoOthBoMnP8Edj\n2KaNIkCbTHE3Pkrv0U70QG1yZwot8rmEiKXvoX7JEYWoNlnBy8jtYc6890OaFtyOGIkjp5h/7HOI\nQCj/nP/WZVpe/C7Kop0Tb+9l8Ilf4SAZIokfoeJYzCZhvv32frKWI0/tTQGePrmzKotaDuLb+piW\nzWvnR9A1ha88sXfdfu+aV4p//a//Na+99hpHjtQuHXYzU233hmprknJUW5sEcP++Dt6/NJZPBzfb\nupj66j+m7YffQp+bQkHQ/Mpfos+MM//EF0HTaNoRJRD1c++DEVLzTvm/mjQZeW8EuyNI/8H2uqQS\nLxcAb41TjnoJVC2F6PbYAs0zwzxx/sdoCTedf+HMJ4ideRY8fzv/7Su0vvCnKIubn1RTOzef/nsc\n2NNKJP4DNDEPOPVGP/z4OGNzbtzoC4/uxtA1SFsNaR3JdO/G4L2rE8wnsnz24X7amwOrv6BGrFmQ\nTp06xSc/+Um++93v1vJ6tj21sJJqIUreFkPdbUGs5jamfvV3aP3L/4ZvzBngF/7obfTpcWY/8zXs\ncBRf2MeeR/oZvzbJ1E0njqQIJwvv3vwIXYfa8Tf5i/7OWlBMoAyfRnaxkLkagVoudrUQIoRg153z\nHLn8Sr7dj1BV5p7+CsmjDy453n/zEq0//rP8cZlICzee/QfsP9BNJPkCuu00wBXAa/dO8tFdLf/a\nz54doDXqb0jrSNI4JFJZ3ro4Siig8/mzA+v6uxWxiqP/+eef59vf/vaS577xjW9w/Phx3n77bb7z\nne/wH//jf1z1F6XSZnVXugmYnHUsHH35rIQKuDu2QCRYnZhcuztLZ2ttdrAf3XBcR7u6FnfT2SzB\nF76DcdkttLTDUZK/9A+wBvbnn4tNxbn13hCphfTSEzb52H28G98G7oR/cf5GweeP7Vs5GffCjYkV\nzz10vPoA7/W7jtjr2RRnb72GcdmdWWQHQyS//D8t+XsCGBffI/BX30FZzLbLRFq4/bnnOHx8L9rs\nC2ipq/ljL8+f5DtvujVFz5zexSP39zAx49yjB9ZYTxJLZthVZap4IXJtuLZyQkPAX/7+3zQtdF1j\neCLG1Fyqjle1kr949QZvXRjlH33lGF96Yn2SGXKsKkilqFSQNmqEdL0oNBZ7Lp6pKo6Uc9ut1UrK\nUU08KRz2E4+7QuK1lAAQgvC7Pyf61kv5GIZAIX76SRYefhY054tnWzZTt2aYvDGNsN3bTACiyYfd\n6md3nQvtcoTCvlULYwvFo6q1gAqR60X3YDBG80t/jr7gNrvNdvYy8/lfx2rytGcRgvC512h6/cf5\np9KRVq5/8je4//R+xNQL+LOuGN2O38efvObp4r2njWdP96EoCnPxzJpddTnrqB7uOlVV8/frRo6b\nrydtraHVD1pkYsK5R8amE8ws39TVkam5FH/840t0tQb53/7hw+ha7eN6nZ3F7z/ZqaHBqFUsqVZJ\nDlC4o0P8oafJdu+k5cXvoSXjKAgi7/0c/+BVZj/5VczOXlRNpXN/O807mxi/PMH8YsdwBVDmMyjz\nGe5MpbBb/RDQ2V2HnXcl1EN8vOSESDMzPDJ+jvCHby75efzYGeaf+ALonqamtkXTKz8i/JGbwp1s\n7oTf/J/ZG46gzf4EzSNGI6mD/MlrrpgNdEd55pQrRtVSLzGSNAYvfzCEEPB3n9lfFzFaDSlIdaAW\n/e2qiSV5qUU8CQr3vsv0H2Dya/8rLS89j/+e4wYzJkfo+O7/Sfzk4yyc+QQYPnxBg76TvSRmk4xf\nnSQx5QiuAiixLGosi/BrDM6lEREfaMqGi1OtyYnRQ9oUTa/95RKryPYHmfvEV0jtv3/Ja5RUgtaf\nfAf/3ev552Kd/Wi//o8g4CecfBHNdN2PY+n9/N8/7yTXNLW7LcTnHx1AU10xqsY6qmeat0xm2HgG\nRxe4OTzP4f4WTuyvvBVYLajKZVcJ28VlB9W77cBx3dVCkHINWCv5wi932S1npQvPJvzBG0TffBHF\ncmOFZrSFhcc/T2rf0SVZYvGpBJM3polPJQqeP9QaZL7ZgALvf61CVY7Lrh7khCgUn+GhO28RuH1l\nyc9TA4ecUfKRpdM39YlhWl/4U/R5t8h4ZuAogb/7G6AJIokfY1j38j8bS+/n//p5N0Ispnc3B/g7\nT+8j4NNrIkZQX+vIe39Kl936u+yEEPzXF68wNp3kD557kN07aj8NNod02W1SamEl1TLzLsdKF55K\n/OTjpHYfpvln/wP/8G0A9IVZWn/8Z6R7d7Pw2GfJ7ugHINweItweIjmXYvr2DPMjsSVFtImZJL2d\n4SUFtwDnr48XHEzXqNbU7bEFfOk4ZyY/InThnXyaNoAdCDH/+OdJHj65RKwRguDFX9D8yo+WiHv2\n8U8TePzTKCJBJP4jdNutUxpKHeL/+XlHvkddW9TPLz+5l4DP/Xo3ohjlkNbRxnPlrvN9fvi+7rqK\n0WpIC6kKSu3kamUlQfUJDlCZpbSahZTDO3nWay0FP36f6Bs/QUsttYBSe46wcOYTmF07lzxvpk1m\nh+aZG14gvZBGM1QGHt5FILp6ivj56+MFn18uUuttIQ3fGWP3rfcYuHse1XTnqAsUkvedZv7RzyKC\nS3fMSipB88s/WNKXztJ9mF/6+9iH7kezJogk/irfLBXgduI4f/JqFDxi9CtP7yMccOJQ1SQxQH1d\ndYWsI5AWEqyvhWTZgv/3rz5mIZHlD//xWbrqnOlYykKSglQF9RYkqJ3rDsoXpXIFKccKFx6gpJJE\nfvEzwuffXGIZAKT6DxI//QSZnXuXWgc4mXmKqlRVRLtcpHZ3R9dNkMZu3mVg8Bz9Qx+jeIQIIN27\nm/knvrBCkMEpdm3+2ffR4vP555LNnSi/9tuI9i6M7DXCyZ+h4FhNAoUPJk7ww/fd1O6O5gC//ORe\nQgGjajcd1D9u5M2s8yIFaX0F6dy1CV569x7Pnu7j1z91sK6/C6TLbsOoRXJDLuuuFqKUW5zWElcq\nRW6EhVeYRCDIwhNfIHH/WaJvvUTw2vn88YE7VwncuUq2o4f4/WdJHTyO8DnWkFqDzJ7lYxrOXx/H\nZ2hksk4xac1dfLZN7OIFdt39iIPjN1kupdn2HSw88mnSuw+tEGAlmaDptRcIXX5/yfPmyUfg2S8h\ndI1g6jUCGU+dEj5+dvskr11xs/F62kN8+fG9+H1azcSonhQTI8n6Ylo2b14cxW+o/NKjuzf6cqSF\nVA2r7eRqaSVBbVx3OUqJUqUWkpeCbjxAnxwl8ouXCVy/kK9dymEbPlIH7id56CSZnbtBqX26aTjk\nJ55IF3TxrVWgfLMT2B+9R+/QZYKplbGtbGcvsQefJrXvvpXvSdgEL50j+vqPl7g2s4Ew9hf/LvaB\nY6j2POHki+iW2+U7SzPPnz/K1RH3fHt7m/jc2QF0Ta2pGK23qy6HtJDWz0LKWUefe7ifX31m/+ov\nqAHSZVcnyhEkYNOJUjWClKOYMGkzk4Q/eI3Q5XMrXFoAVjhKau9RUnuPkNm5J19kWy05QVpOuTEo\nAIRg+toNOsdv0j16nWhsquBrU/0HiZ98jMyu/SssIgBj9A5Nr/xVvgVTjpmB+wh85dcgFMHIXiOU\n/Nt8k1SAOWsXf/zGAHOe0NxDR7o5e7QbVak+tRs2XoxAChKsjyBZls0f/ehjkhmLf/+7j9K0Thar\nFKQ6Uc4Xp1ZWEqyfKNVCkHIUEyYllSR06T2CF3+BMbOyPQ84llNm5x4yffvI9O4m29kDqlbw2NUo\nJkiFyIuUEITiM7TODNM2dZf2qbv4M4VT1a1AiOThUySOncFqLVzDoc1MOO5LT9ICQCbUzL2HPkvP\no2dQ7CSh1Cv4TLf2SKBwde4Y33mrKZ9Jpyjw9MmdPHJ8J/F4uiZiBBsXN/IiBWl9BOn8jSl+8s4d\nPvlgH3//k/WPHeWQMaQtQi6eVKuiWahfXCmHd0T6cnGKn3yc+InHMMbuEbz8PoHrF9CSbgaZms0Q\nuH0lX7tj6wZmZy/Zzl6y7Tsw27qwWtqxg+GClkglKOkU+uwk+swEj02NYUwMY4wPoaaLd80Qmk5q\nz2GSB0+Q3n2wqDWnzUwSefdlglc+QPHs/4SqMXbkLOPHHufAnk7HKkq9iio8M6mI8pOrR3n3lnvu\noF/n848M0NfpzKjZSmIkWR9sW/DWx6PomsLnHl7fBqqlkIJUZ3JjKWplJdVDlGBpvVI4XJ+O3MXE\nCV8H3U9/mfknv4hv+DaBm5fw37qMPr+0s7ZqZvGNDOIbGVzyvG34sCPNWOEodjCM7Q8ifAGEbiA0\nDRQVn6GipNIopomSTaOmU6iJGGoihhabRU2X18DSCoRIDxwivfcw6f6D+WSMQhhj9wi//wqBGxeX\nCBFAcv8xbt33NJloK0d2QijxIwzrzpJjJjL7+O9v7WAu6YptT3uIz50dIBpyFvZcs9RaiFE9kWLU\nWFwbmmM2luHpE720llFesV5IQdqE1FuUJmaShHz17WO1XJzyk2pDvXCsF449S6+awH/3Or7hW/iG\nB9FicwXPpWYzqDMT6EVcfznWMtXFDgTJ9AyQ6d1Num8fZmdP6aQLyyRw4yLh82/iG7mz4sfp/gMs\nnP0U94x2NLKc6LqEP/4BCq4gWIR57c5RXr60dAE/faiTR471oKmOQM3FMxiGXjMxqnfcSNI4vHvZ\ncUt/6qFdG3wlS5GCtA7U2kqC2jVhXc7AjijhkJ+PbzqdANZjV+sVpxxX7swybIdg53HnH6AnFwhN\njdCZnkafGkOfnUSbnULNVu9jF7qB2dSK1dJBtq0Ls6OHbFcvVlPb6u5AIdAnRwhePkfo8jnU1Mo4\nU6r/ALGHPkG2d4Dx6RjdvisMhC+iZtzPUKAwmj7Ad97pWpK4EA7ofPpMP/2eRIucm+7ArpayY2OF\naIQkBsn6MjwZZ2gyzvF97fS0h1d/wToiBWkdqUVdkpda1igtpx4thyqhkEhBC1fuRJkHyI1pEQIt\nk2KHkXZccMk4aiqJkk2jmFkUywIEhqGTsQFNxzZ8iEAIOxDCCkWwI03YwUhlcSgh0KfGCNy4SODa\n+YKJGULVSB44TvzkY5idvYxPx+mIXeCB6EcEtDje7PeU6OTHV/bz4eDSpI3D/a08dbJ3SRugWsaM\nQIrRduPdK4519OkGs45ACtK6Ue2I82LUW5SgfgkPKxAC7b3XUWensPp2Y/fvh9DSHVwxa2qIIERa\nwInzL8nog8qy7IqhpFP4hm7hv3MV/+DVJY1PvZjRFpL3PUji6EPY4SiKyELsA040fYzUBT5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# First plot a KDE of the joint pdf\n", "X = gen_data(position, momentum)\n", "g = sns.jointplot(*X.T, kind='kde', stat_func=None, xlim=(-3, 3), ylim=(-3, 3), alpha=0.5)\n", "\n", "# Now plot the Leapfrog paths on top of that\n", "for path in leapfrog_paths(position, momentum, dHdq, dHdp, 15):\n", " g.ax_joint.plot(*path.T, linewidth=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Volume of an N-dimensional unit sphere\n", "\n", "It is pretty small:\n", "$$\n", "V_n(r) = \\frac{\\pi^{\\frac{n}{2}}}{\\Gamma \\left(\\frac{n}{2} + 1 \\right)} r^n\n", "$$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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/IpRzvVhp/nhFiZAFgGyV8yEbmA4rFjdzatFTEscrAkB2y/mQHVlY9OSryL2ebIm7QLWV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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.special import gamma\n", "n = np.linspace(0, 50, 1000)\n", "V = np.power(np.pi, 0.5 * n) / gamma(0.5 * n + 1)\n", "fig = plt.plot(n, V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# In 20 dimensions, how many samples from an enclosing cube fall inside the unit sphere?\n", "\n", "This actually samples from one \"hyper quadrant\", but by symmetry, the probability will be the same." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.random.random(size=(20, 10000000))\n", "((x * x).sum(axis=0) < 1).sum()" ] } ], "metadata": { "kernelspec": { "display_name": "bayes_talk", "language": "python", "name": "bayes_talk" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }