{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## GPy crash course" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial I will run through a few basic features of GPy." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import GPy, numpy as np\n", "from matplotlib import pyplot as plt\n", "np.random.seed(1)\n", "%matplotlib inline\n", "#%config InlineBackend.figure_format = 'svg'\n", "#import matplotlib;matplotlib.rcParams['figure.figsize'] = (8,5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic GP model\n", "### 1D model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "GPy handles the parameters of the parameter based models on the basis of the parameterized framework built in itself. The framework allows to use parameters in an intelligent and intuative way. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.random.uniform(0, 10, (200, 1))\n", "f = np.sin(.3*X) + .3*np.cos(1.3*X)\n", "f -= f.mean()\n", "Y = f+np.random.normal(0, .1, f.shape)\n", "plt.scatter(X, Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A simple GP regression model with an RBF kernel can be constructed in the following way." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "m = GPy.models.GPRegression(X, Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Details of the model can be shown in a ipython notebook with pretty printing in the following way" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: 198.414142406
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve
Gaussian_noise.variance 1.0 +ve
" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or on the commandline in the following way" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Name : GP regression\n", "Objective : 198.414142406\n", "Number of Parameters : 3\n", "Number of Optimization Parameters : 3\n", "Updates : True\n", "Parameters:\n", " \u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mGaussian_noise.variance\u001b[0;0m | 1.0 | +ve | \n" ] } ], "source": [ "print(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that there are a number of parameters of the model. Each one is a object itself, can be accessed seperately, in two different ways. Directly or via a regular expression" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "" ], "text/plain": [ "\u001b[1mGP_regression.rbf.lengthscale\u001b[0;0m:\n", "Param([ 1.])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.rbf.lengthscale" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "
indexGP_regression.rbf.lengthscaleconstraintspriors
[0] 1.00000000 +ve
\n", "\n", "\n", " \n", " \n", " \n", "\n", "" ], "text/plain": [ "\u001b[1mGP_regression.rbf.lengthscale\u001b[0;0m:\n", "Param([ 1.])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m['.*lengthscale']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the current model, with its default parameters in the following way." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /Users/alansaul/anaconda/lib/python2.7/site-packages/matplotlib/figure.py:1718: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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qcxVDho3Gp53Y0odjTR2K1T0E3EPIzS0iFg7gr9+Cr2YD/r3fgI5RVHQya9eu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\nUVpaylNPPcW6det59NFHycvLZdiwfKq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_ = m.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course the default parameter values are not the optimal settings, as such we need to optimize them.\n", "\n", "Note that all of the parameters of the model are restricted to be positive, as such we have a positive constraint on each of them (indicated by +ve). This is done by allowing the optimizer to optimize the parameters in the real space, but a transformation of $\\log(\\exp(theta) + 1)$ if performed before the parameter is given back to the model, gradients are transformed appropriately.\n", "\n", "To find the optimal parameters we must optimize the model. A number of optimizers are available, such as 'scg', 'lbfgs', 'org-bfgs', 'fmin_tnc', as well as stochastic optimizers if a dependency on a package 'climin' is satisfied, such as 'adadelta' and 'rprop'." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Widget Javascript not detected. It may not be installed properly. Did you enable the widgetsnbextension? If not, then run \"jupyter nbextension enable --py --sys-prefix widgetsnbextension\"\n" ] }, { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: -151.496450286
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "
indexGP_regression.rbf.lengthscaleconstraintspriors
[0] 1.00000000 +ve
\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
rbf.variance 0.130864941346 +ve
rbf.lengthscale 1.36805842166 +ve
Gaussian_noise.variance0.010323494102 +ve
" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.optimize(messages=1, ipython_notebook=True) # Messages indicates you wish to see the progress of the optimizer, needs ipywidgets to be installed\n", "m" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IhYWFjB8/npiYGJ555hmcTic+n499+/a1aq54OvQ4D6oRnVZDZa2DWINWDkvI\nhKWwsJD169ez8Le/w+72889XT0q/Q8m3K+0qdhTHoFUruWvK6GDYLjs7m927d7f7adHl9uDzeklJ\nNLa75p1apSQ5yURyEtTZnJRV2UCpRN9GIduW8vhG0g01eA1pFFXUs+XLI9xw2fCI5zHotRRXWRme\nltiu8XYndBpFh6Tgp3L+9rJw4UL69+/PE088wZ133klMTAwXXHABS5YsYdy4cdTW1jJmzBgkSeLW\nW29lyZIlYc/VXkl5UlISb7zxBvPmzSMnJ4cZM2Zw2WWXBd+/8cYbsdls3H777RQUFBAXF8c111zD\nLbfcEvI6TV/fcsstVFdXM336dEpKSsjIyGD9+vWkp6fz73//m4ULFzJ48GDcbjeZmZnNRB+nS7fs\nB1VQYWvXvkII7HYHI9KT2iUZljn7WLp0KUuWLOHeBx5EZzCSl5fH3LlzGjwd0awlRXZ2NkXq8zhR\nVsf0a0Zyy6TMVuGzpj2XTp7nJEIIrDYnfeK09I03nnbOSqXFRoXFicGgi/AZb34fffr04eqrr2bj\nxo2MvTSLGuP56LUqnl1wDYmxkY2l3eGmf6KOWGP3LSQr94PquUiSRMv53W53cs6gpN7XD0qSJDRa\nLUUVdQxM7tlN2GQ6h0WLFmEur+DVf72LUhIRpd9lzhhOVNXRN97A9ZcNA06G7cxmM5IkBY9NSxvQ\nSqjg8frwuNwMSY1Fp4mOV98nPuCBHS+1oFCpQzZUbPTypk2bxo4dOygrK+PAgf2BtvKfb+Gim0Zh\ntsH697/n1z+/MOL1DHoNZVW2bm2gZM4eerSBgkBYxO7wUmd1Eiu3D5AJgcuvQSm1fuJuqrrz+hV8\nXmZEqYGZU0ajVXdMqOB0e1DjZ8TAxKhn+qtVSoalJVJUXofD6ULfomJCU3GGEIK77prJnj17gYBX\nqDHZqXJq2fZNIdeOH8y5g9roBaVQYKl3Eh8jf59kupYeKZJoiUGvpajSiq+NhWCZs48nnnyKN9/+\nd8gcoqZ5T0nnTEapMTB8QCwTR3dMVeV0uTFqFGSkdl4pLkmSSE+OI86gxu5ovtbSVJwhSRKaJt7b\n7t27Wbd6JYPjApXL17yzB59fhBWIAOh1Wsqq5XYcMl1Pj/egGtHrdRSaa8lIlWWyMie5ZupN+DQx\n/GJ2wONpKv1unNhLKq28979jSBL86qYLOmRkHE43sTolKWeo4GpyogmlwkZVvQtDi2oYZrOZxx57\njD179pIQFlxKAAAgAElEQVSZOYL8/EPk5+czduwYHnvg58xb8RHHSmv5z67jlOz/hJUrV7F9+3ZG\njhxFXl4eX331NX/84x9JTk5GqVZRVWunT7zxjNyXjEwoeoUHBQHpucsnYamXmxzKBPB4fcQm9OMX\ns39BpJp0G/9zAJ9fMGncQAanxrf7/M4zbJwa6RNvJClGg72Fam3Lls3s2LGDMWN+1Gx7RsZgtBoV\ns6YEtm/8zwFun35nYI1qz17y8vLIzMxkx44dwdqBOo2ailqn7EXJdCm9xoOCwAJvSZUVk0HT46sz\ny5w+pS36PYXiaImF7XuLUCkV3HbVue0+t8vtQaeWzrhxaqRPvBGfT1DncKPTBWTooaqxjxs3jry8\nPNLSBjBrVg6ZAxPJL6jmX/89zMiRo4JrVfn5+WRnNxeQaDRqyqttJCeZzvwNysjQywwUnAz1DZZD\nfWc1Xp8fm8uLyRhZTbfhg0Di4pSLB9M33tC+c3t9KISf9OSu/YwlJ5lwm2txe7wh1X3jxo1j4cIF\nJCYGwpqSJDFzymgWv/Bf3vo0n8JP/x3sawWwf/++Zsdr1Cqq6h30iTd0q7JigwYNOqtaTvQm0tMH\ntr1TE3qdgVIpFdjdEhark3hZ1XfWUlJZ32Z/oP3HKtl9yIxOo+LmKzPbdV4hBC6XixHpbSjhzhDp\nyXH8UFSNV6Fg/csvtaoFmJjYvBbgOYOSuHhUKv/bV8KwiT8j/9OXyM7OZv/+QIPG3NzcZvvrdBpK\nq+pJ60Czvs7m+PHjXT2EsxohBPkF1RgMuk5/UOh1BgoCob7SSisxek23evKTOTN4fX5sDi8mU3jv\nSQjBKx8EPIZplw8jztS+Znc2m5OhAxK6VWL44P7xHCqsYcqULCAQ6isrM3PkyNGGbaJZ88Q7fzKK\nXQdKcWoGMOPu+/n1r2YCJxssNkWtUlJvdePx+lrVCJQ5Oykqr0OjVZ8RL7bXzt46nZbiCrkR29lI\nWVV9cF0mHF/nl3HwRDWxBg03NCTltoXd4aJ/HyMadfeaqJVKBYP7x2I0xQXl5lu3bmHHjh0sWbKY\nv/wl0Dzxsccew2w2k9rHxOU/SkYAdbpA+aNI3X/1Bi0llXLdSxmoszqxuXyoVWfGt+m1BkqlUmJ3\n+7A6Oq8+l0z3w+fzU+/woorwtO/3CzZ8eACAn03KpM5SHTYnqBGP14tBo+i2YWOdVk3fOB3Ohl5p\nOTk5EVV6mvqD+D1OvjlUzh+ffj5i91+lQoHd5cXp8pyx+5Hpfnh9fooqrRgNZ+470GsNFARaCBSV\nW2Wp7FlEaVU9ujaKq+7cX8Lx0lqS4vT8ZPzgNlu1CyFwuzyk9Yvt7OGfFn0TjCglEaxcPnLkqOB7\nLVV6v7p7VjB59+tCWin4WmI06CiSvaizmhNltRjOoHGCXroG1RSNVk1plZXULpIDy5w5Gr0nk1Ef\ndh+/X/D6JwHV2s1XjECjVraSZ7es12e1OxmSEtsjlGODUuI4VFjNG29sDHpO4VR6qfpajlSr0cb1\np8oduUuwJEn4/JJcUuwspbzGih8JTZhOwZ1Fr/agANQqFRabWw5PnAW0x3vadbCU46W1JMbquOrC\nQW2e0+3xkmjU9JiWLkqlggF9TPx48tVMmDAh6Dk1hvsayzzl5ubyWt4GDPYfAPiuTMWcuffzt7/9\nNWxLe4NeQ2mVXALpbMPp8lBZ62rzu9UZ9HoDBWAy6Cgsr+vqYch0AoWFhSxduhSv10ed3cv69evC\nTrBCCF7/+CAANzV4T9C8aGzTen1CCHweT49LVI016cgY0J/FS/7A3Llz+M1vFvLiiy8yd+6coEov\nK2sqEyZM4Iev38Njq0JtTGJ/sZuXX14fdi0KQKlWUWFpXzscmZ6PEILjZbWYuqi6fa8P8UFD8y2l\niooaG30T5NpivYn169ezZMkSCs0WNIYYNoZoxd7IVwfLOFZSS0KMjmsuyghuD9eq3WpzMjglpkeE\n9lqS1i8Wm9MTtgJ7cnIyK1c+x1/+soxNH2+jz9ibiR1yOVmXnRtxLUqrUVNZ6yAptnsl70Ybl9uL\nw+nB7fPh9wmUSgU6jRKD7uxKXSksr0Ot0XTZd+CsMFAQqC1WWesgIVYvl0HqRTT2e1r/5ruoVVLY\nfk/NvafhzaTioVppeLw+NAo/+jbk6t0VhUKif5IJs8WJQR/5HuzmA7hqS9HG9afU2XYoXK8PpHAM\nTOk+ybunixACS72T6nonbo8fSaFAqQz8SJKE3+OjxubB67OhUoBJr6FvvKFX54ZZrE4cbn+rosRn\nkrNqptYbtBSaa7t6GDJRxi3UqFXhP8pms5k/r1zPkWIL8SYtZQf/GzYM2IjL5Sa1T/dW7bVFfIwO\njVLg84duQ5Obm0teg8cZ4zwMwLFaAy+seSnieVVKBTa3D7vDHdXxdgV+v6Cssp78gmoqrW40Wi0m\nkx6jQYtOq0atUqJSKtCoVeh1GmKMevR6PS6fxOFiC8dKanB5vF19G1HH4/VRUmnrUuMEZ5mBUioU\nuHyBZDOZ3sGTTz7F62+9y/Tpt7fq99TI5s2b+exAIGk7QZTw9+fD5/wAOJwuUhIM3apaxKmS1i8W\nhz10LmBW1lRmzryLOXPuI2/NX+ij96BQ6/AnjGy1b8v+Ua9vfJWvv/+hcwffyVRabBwqrMbmERiN\n+pBdkMP1zVIpFcQY9ShUGo6U1FJUXovf33vEIyfKas9ovlM4zpoQXyNGvZbiShsmg7ZXTEBnO1dP\nvQlvmH5PjZx3aRb//uFLfC4r//3Pmoht34UQSMJPQmx4qXpPQq1SkhijxepuXVA2OTmZefMeCL5+\ncPY1/G7lp3y0u5ifX22nT5w+WGGiMVespqYGCNT58/kgc9hA+iX0LBGJy+OloKwWoVBijJCSAIS8\nbyD4N8nJySHGqGP1i2uZPGkyF/5oOMY2QqrdnZLKeiSlqlvMj2edgYJAblRJZV23KoAp03FcHi+x\nickN/Z4CtBRHCCF45b3vAKg7/j+E38u+ffsoKzOTkpLS6pxWu4shKT07tNeSfolGLAXVISueN2Xo\ngARSTW5KrBoeXvEGw2MqgxNyqFyxe+6ZTVWtk3iTvtuVfwpHpcVGucWJydi80KnZbA4aHDhZ+ilc\njlxubm4rw6VUSPRN7k+SSdPjlJ+N1Ntc1No9mLqB9wRnq4FSq6izOXG6PD0mv0WmNSUV9RjbiJF/\ne7ic42YrPreN/vp6UjMz2bNnL48//jgrV65stq/X58ekVfa6z4QkSaT2NVFcaccYoj9W08l50T1T\nmLfsQ8qcJr75eENEbxPAYNBRYK5lWFpiZ97CaeP3CwrKLHj8EjGm1l5TOE8p3L2HT+6WqHO6cZTU\nMDAlvlt4Ie3F4/VRWFFPjKl9bWfOBGelgQIwGbQUmOsYMbB7tE2Q6Rh2hxunV2DShJ8Amir3TK4T\n5B8M9H4aO3YMDz/8cKv9nQ4Xw9N7Zx+xGIMWtdKO3y9aTZpNJ2choL7IQkz6OOKH/Ti4T9NcMQhM\n4AkJgVYeQlK0mcJRWFjI+vXrWbRoEQBPPfUUM2bMID09Pfo32wKn28Ox0lp0Wi06TWhPL5Kn1PK+\nVSoVJpOJpvnKNps9+LtOq8Hj9XG4sJqhaQk9QjUshOBYiQWjoXuFts9aAyVJEpJKRXmNtcfF0GWg\nuLIeo751GKKpN7D3SDn5BdUYdSrGJOnJ/zKwz6hRo0hJaV612+3xkhij7RGTyamS3i+WH4otQQ+i\n8W81a9YsqqtPTs5KrYm49PMwJJ/Dm5tzm63rtcwVg8CEXFHrIM6kCxvqa8xXq6ioAGDFihUALF68\nuPNumIBUuqTSismoP6VcnlD3bbVaWbXqeYBgKalNmzaRljYgGGJWq5QoFFoOF9YwdEB8tw+BFpXX\noVSru53Hd9YaKGiSGxWj79X5DL2NWqsTISlDTjiN3kB1dQ3f1fYH9CgsB3ntnddCPv034nZ76JfS\nvcNUp4tGrSTWoMLj9aFSKZv9rXbv3h3cb/Q5Q5h0ZSZvbTvMqB/fyZQpV4TMFWuKyajjRJmFYWmJ\nIf8vixYtoqKiImiY5s+fH/SmOgtzlZUam7tdIatIHmLr+xZYLLVs2rQpWEoqISG+lThHqVBgNOr4\nobiGwSmx3TanrrrOgd0tMOi7X2j7rDZQAIaGUN/QAb0ztNPbEEJQWmULq75qDNX8870vSL7wTlSS\njz/Nn84nP0oK+fQP4HC56Rd/ak/YPY3+STEcKqrBpNK3CmtlZmYybtw48vLymDBxFyZ9X6ocUFIn\nEUJP0gxJklCo1BRXdL34SAhBobkOl1e0WyodyUM8HSRJwmTUc6ysnoHJJkxdnFfUEofTTVm1PeS6\nXHeg98Yz2olSocAnJGrqHF09FJl2UF5tQx0iX6UpQkDckMsBGKCvJWNgKjk5szGbyxtamueQnNwv\nmNMivD6S4rrPwnBnolQqSIrV4nK3rhgxbtw4Fi5cwNy5c5h2fRY3XzkCgFfe39euHB+NWoXN7cdS\n3zrP8KmnnmLFihXMnz+f+fPns2LFCp566qnTv6EW+Hx+fiiqwYuETqcJm8fUkpMeogRI5OTMDtm8\nEQLe1qZNm4CAUc/Ly2PVqufD5tZJUkCYUWC2Um/rPv3pPF4fx8rquq1xAtmDAkCv01BabSPWqD2r\n6mz1NLw+P9X1LkwRvlC5ubm89d4XJF8U8J62v/siuQMCE04opZbb4+d3D/zyTN1Ct6BvvJHqumo2\nvLq+VVgrMfFk6HNKYh82f3mU46W1bN9bxBXntS1oMOi0lFbZ0GmaqyFnzJgBEAzr9e3bN7gtWjjd\nHo6W1mLQ61A2tIUIr85rXauxvWRlTUUIQU2NJViJY9q0aa0Ufy2l62++kceVP76KsecO7vLGl36/\n4Ehx9xNFtEQ2UA3o9ToKzbVkpMqhvu5KcUU9uhAhkqYTwXXXTeH9A+AGbr16NPXD7m4Wvmmp1Jpx\n5x3EnWX9jSRJIiXRyKSrrgXCh7W0aiW3XXUOq976hrz/HGBoPxUfvL+1Va5QS0/DaNRxtKSWEQMT\ng6KT9PT0ZoKIaIsj6qxOiiptrcQQbfX6CkW4nKjG+0xOTmb27NksW7YseIzR2NoDD2cc+/abDiJQ\niqorEEJwtKQGrVbT7UQRLZENVAOB+mLIDdm6KVaHC7vbh8nQOrzXdCKwuHW4VamoFX6yJg7FMOmc\nsOd0ewT9k87O6vbxMTqS+yRFFD4ATDp/IJs+O0xxhZUXXvuYLa+27Y1IkoTRqOeHohqGpyV0elTi\npBgiOt5Ae7yuSKKKRiLlSpXV2PH6fPSJP/Ofv+MlFhQqFaoeIAyTDVQTAmWQrBj1Z1dJ/e6OEILi\nCiumMOGIphNBv4tmoEuAn181CoOuuTFrOqkIAWtWr2ZAgqrTpc7dldS+JooqQifvNqJUKrjj2lE8\n8+oODlXruPX26WzYsAGAc889l1mzZhFY22nuZSgUElqdlh+KahjWSUbK5/NzoqwWL1JYMUR7DElL\n2uN1na6owmjQUVXvwucXJCeeuTSX46UW/AolGlXPmPp7xijPIDq9jqKKegb1olYCPZ3yahsqddsS\nWG3iIHQJA1FJPrImDmn1ftNJxWpzkmBQRn0dpCdh0mtRKe2B+oMRFIwTRvYnXufF4lTx1dGTCakH\nDhxg2bLlSFJoL0OlVIBOy+GiQC5QNFM5bA43BeZAyFffwvg1DdFNmZLFV199zfTpd5CSknxK6jwh\nAg9JL7100gi3JbuHto2jQa+l1u7G463tdOWjEIITZbX4ULRZ8qo7IXW39s2SJImCiq7t2GlzuEiJ\n13dZjFjmJE63h6MlkZVGzz77N9ate5nRWQup8+qxHP6Um64Y2qwQalOEELjdbobJqQU4XR6OldVh\naqNo6vdHy/njms/xe12Ufv53hmWkkp9/KPh+dnY2Cxcu4KWXXmq1LuX3C2x2B4OSY0+7kGrAm66j\n3uENO+bc3LWsXLmqmWGYO3dOg5Iz8vpS0+PHjh3Dnj17AYK/N56nPbTnWgAutwel8DOof+eURvL7\nBcdKa0Ch6pbGyW53cs6gJIQQrW6++422G2DUaymttmEyaHp1ZYGeQEFZXZvtpoUQaBMHUefVo5J8\n1BfsQojWHlQjdoeLgX3l6iEAOq0anVoRsgRSU0YP6Uucoo5aVSzxwydz/mgDWq2WvXsDhXh3797N\nsmXLg6q2ppO4QiERYzJwotxKvFFN/yTTKeWcWeqdlFbb0GjUEQ1qpBBde9aXGj2sWbNmBe9pz569\n7RJYNKU9XhYEuhR7vD4OFVYzJDW6VSc8Xh9Hiy1otJoesebUkqjMvpIkXSdJ0kFJkg5JkvRgmH3+\nJknSYUmSvpUk6bxoXLcz0eu1nCiTmxt2JWWV9ShUquBkFi6nZd68eQy/+GcAVB76jOzbfsYDD4T3\nnlRKqc0us2cTA/rGYnNE7pGWm5vL/m0vI+HHmPoj/vXedvbu/Y7s7OxguZ+8vLyIk3iMUYfDIzhU\nWE11O/MOhRDU1Dk4XFhNea0Dk1HfYS+gMUSXm7uWKVOygn3DGsNvLcfbaFgaP3eSovX12ptf1d79\n1Coler2OH4otUcvJrLM6OVxkQafX9UjjBFHwoCRJUgDPAVcBJcAuSZI2CSEONtlnCjBUCDFckqQJ\nwN+Bi0/32p2JUqHAg9Rja/V1ZXHOaGBzuKmxuZs9KTc+/RYVFXP8+DH27NmLEIJKu4o6byw+j4P6\ngl0wcWDY89odLgb163n/z85Eo1Zi0qrw+vxhIwbBuntp5/LGJ/kMvSSbC5LKeOCBeTzxxBPk5+cD\nAWOwdu1apk79achEV406EGaqrHdRbrFj0KiIM2nRa9WolAqEEHh9fhxODxabC6fbh6Jh8m4vjWs/\njWG5vLw89u/fF/y8hMPr8/PdkQq2f3uMbw8WYnUr8PiHkH71g0j4+bSwnsNPvs61l59P8cEveOkf\nbSsaO5KHFfA09VTUuaipd5KeHHtK63Y+n5+iinqcHn+3TsJtD9EI8Y0HDgshTgBIkrQRmAYcbLLP\nNOBlACHEDkmS4iRJShZCRO673cXotBoq6xzE6DXdto5WOLqqOGc08Pn8FJjrWyXkhirNU11t4dMj\nKnQJsQyJc3DlbT8Lq9Rq9J562v/yTJDaN4bDhTVhk6AbvQqX28snuwuorIXMCdfz0ksvsWnTO8DJ\nqgoQkJpHWqvRawP/A79fYK514fPZg8ZDISlQKhVoNWqM6o7/ryKF6IBWwgWtKRFT+oV89NUJrI7G\nChsnp0bh84JShUofh9kG69/bB8QxKus3/Os//8ZRnt/ME2u69jRr1iy2b9/eoTwsvU6Dz+/nhyIL\nMQYVKUkx7Vpq8PsF5dVWaqxudHptt6yt11GiYaAGAIVNXhcRMFqR9ilu2NatDRSAyaDjuLmezPTE\nbp/U1pSuKM4ZLY6VWkIm5LYkPz+f4xUuki+8A7XCz5O/nYFBpw6r1JLXnsKjUiqIaVJINhxajYpZ\nWT/i//J2suHD/Twy49p2VVUIh0IhodeqgY5NppEECCfXfgQtl7qysqY2GM8cLFYXhZ5UPjmhw388\n0L4+vV8MF49KZf/Xn/L+O6/hd9vJzr6d++c9wAu5r5JxzoUcKXOw60AZ9W4dfc+7BXe9GYvbF7xG\nU0//2LGjwXU6aN6WIxJKhQKTSY/H5+dQYQ1atYI4o5YYgwaN+mShZJfHi93hoabeidvrR6PVRKy0\n0tPoliKJZc88Gfx94qWXM/HSK7psLJIkodNpOV5qYYis+up0iivqQKEM+cTYGLrJzs5m9+7d5Ofn\nEz98MgA/v3oUhgbPKNSTu7z21Db9k2I4FMGLamTi6FRGD+nD90creXbjdpY/mMOyZcuD74eqqhBN\nzGYzjz32GDt27KC6uiYYvoP2JdPOnJnD1i+P8coH+3C4dCgkuHxMGtdfNoxhaQmAYNl3W/G7A2ri\n3bt389yzfyMvL6AGXJAzm9UvruXVf++k/6irICaZ7+tg3lOv8fT8m1t5+gCZmSPIzz/Uqi1HW6iU\nimCYzmL3Ulnnwu/3N7wrUCgUKJVKdFot6u5VhzYiX37+X778/DMAPB5v2P2iYaCKgaZB/7SGbS33\nSW9jnyALf78kCsOKHiqlAqdPQVllPSl9Yrp6OO2iaXFOCIT4+vbt2y1DfI3rZffc9wB1Di9vvLYh\npBy30SsSQpCfn8+543+CLa4/Xmc9NUe+gB+HrxrhcLpJ73N2Vo1oL0qlggSTBpvHG1GIIEkSd18/\nlgV//Q8FdVpm3vd79n/1KRCQY7cnGfZ02LJlMzt27GgWUhw7dky7kmkvuvQqHlz5EUdK6wEYl5lM\nrOMQt026hOTkwANoqAeh/PzmYbwbfjoVlQKm33kTmz47zOsfHaC4XsuCZz9mwa0Xthpzfv6hsG05\n2otWo0Kr6ZY+RYeZeOkVQcfDbneycsUzIfeLxt3uAoZJkjQIKAVuB7Jb7PMOMBd4TZKkiwFLd19/\naolOo6bW4UJX7+wR+VFnojhntFi/fj0P/+lJiqo9aDWKsAvJjaEbs9mMQGJ3TRq2KhvjBiq44afh\nv/RCCBSSkL2ndtAv0UR+YXWbSrmBybHcMukc3vgknxrtOaD4jOzbbm2WCwXtzwXqCDk5OVRX1wSN\nE8DIkaNa7ddS5j3k/Gt4Ku9bHC4vXmc9o/vaEAXf8/KmTZg0PmbPnk1ubi4XXTSeuXMDa1iRBCCN\n57518rlcNiadFa9/xQ9FNfzhH/+lan8+t9+ezTff7A4eL0kwe3ZjxXSZ9nDaBkoI4ZMk6X7gAwKy\n9ReFEAckSbo38Lb4hxBiiyRJWZIk/QDYgPYnE3QjDHotJVU21CrFaSccdjadXZwzmsyZt4DCKjf/\nfPM1IPRCctOJLjm5HwW1GkqrbKT2MfHwvGkRS+nYHW7S+sreU3tQKCSSYrXUO1t7US2NjbXgS7SS\nAYxJxA25HElqLY7ojGriAPv37wv+3uhJNa3E3hSfz89LW79n8xdHALh4VCqUfsHrG18N7lNTY2HZ\nsmUNSb2B8eXmrm0iABkRNIhffvk/Vq/+B3DS4KYmJzP/xkyWvfIpRy06EkdO4dvSQvLzDzF27Bgy\nMgZ3umfZG4mKvyiEeA/IbLHthRav74/GtbqaGJOe42V1DB0Qh66NvkRnEp/Pj9Xhpt7uwu0V+PwC\n4RdBZZQkSUgKCaVCQqWUiNVrMOg1Xd6KuqbOQUm1HZ028jiaTnQ+IfFtSV+UWrjj2pFt1nlTKkS3\naxTXnekbb6S6oLUXFcrYaOIGkDJhJnFDLuHNLS93oGDqSTrqZeXm5rJnz17Gjh3DyJGjAg0WJ0wI\nGTqzOtz8JW8Xe34oR6WU+MVPx3Lt+EEsX749uE/TUGHT8WVlTeWrr75ix46dzapmfPPNN8FK5k0N\n7vvvb+XT11dx9c33cNjaB7s2nRGT7ub5pb9Ao1aSljYgKk0QzyZ6R0DzDBNj0nOkuJbhaQldOsG7\nPT4qa+1YHR68foFKpUSrVqPWSBE1UUIIKurdeGrsKCUJrVpBrFFL3Bnuh1VWWY/F7uGfb+S1WdCz\n6UQXO+Qy4ocNZnhaQuBpOAI2h4sBZ2nF8lNFkiT6xuuptnmaPYS1NDbTpk1jwIBUNANG8Na2wwy5\n9E4mX30JcNLozJo1i7aqqXXUy2q5tpSYmBDSoBVX1PPU+v9RUmkl1qjh99MnMHJwH3Jz1zYrGtw0\nVNiy7t5zzz3HnXfOCIbpMjNHcP7540Ia3JN/n9VoE9JJHX8HTnU/7n/6LZ59KCCeiEaI82xCNlCn\nQGOHzB+Kahhyhj0pIQQ19U6qah14/QKdTtuhJEZoUCZq1c0aylVb3Zhr7KiVErFGDYmxhk4r8+T1\n+Skoq8UnKTAadB2qDK3QGIjNCOR433XdqDZL5igRxESo1i0TmqQ4A5WWKojw2TYaDcyePRuPV7D7\nUDnHS2t5+38lPJDWP2h0tm/f3qyeXcfaUoSmPSWEvjlk5i8bd2F3ehiUEsuiGRPplxBQFzb9vK1d\nuxYIVGY/cOBAs6ReOCnIaSQ//xAWy8kKM/v27aOszExKSkqz67tqChkTV8K++gFUOtTc98RrjIw1\nszFvQ9gxy7RGLjR3ikiShKnBk7I53J1+PZ/PT0llPQcLqqmyutHpdZiM+qgZEW1DfTOtTke908+h\nohp+KKqmvMaK1+dv+wTtpLrOwaHCGiSVOmjYm7bbNpvLG7b1o2lpmEZl1bif3I1CpcVR8QM7t70b\n8Vp2h5vkxLOjlXtnkJJoxOE82aK8qWy7sVxQbm4uapWCBbdeiFatZNs3hfznq+Pk5OQwfXp2cKLP\nzs5mzZo1zJ07p1PDXEII3tl+mCfXfYHd6WHCyP4svffKoHGC5p+38eMnMGHCBNatW0d2dsCDb1p3\nz2azBcff+L7ZbCYzM5PMzEz27NnL448/HvLvs+n1l5mYWo9a8mHxGPjooI/bsztWz+9sR/agTgNJ\nkoiNMVBQXk9KgoGE2OgnyHm8PkqrrNicXrRaTdgimdFUSzWWowGoc3iprK0JeFYGDfGxOrQdroUW\n8PoqLXZQKiOWXwkX7snKmkq1Q8nnRYGs+qwL+5KVNSXidRX4iW2j0KxMeOJidJhrTnYWiOTpanBw\nbmId35qNrHl3L9/t2tYsKTWUgKKRU+nZ9P333/P888/z3HPPAnD//fO455f38tlhD5/sLgDg1snn\ncOvkcyIm2O/atZMdO3awfPlydu/e3er9W2+9DZPJFLxntVrFrl1fceDAASDgFT788MNh/z5TplxH\n3cuv81V5Evq+wzhYb8Pj9Ue19UhvRjZQUcBk1FNe66Le4Satb2xUKk64PF7KKq3YXD70ei0mY+Qw\nYrTVUk0NnlajJDc3l2t/MoU4WwIKQKNSYNCqMOhUaDVq1CpFMNzm8/nxeH3U291YHW6cbj8qjQp9\nmIaDTQkX7vH5odQ/ELAw7fJh3HFta1lxU+wOFykJsvd0ujRtahgptLZly2beWb+K8TfMo8wZy7Yj\nSsFlaigAACAASURBVMp2fBLR6DQamYcf/gN+v2D37q+577772tWz6fnnn2fHjh3ceWcgdeLwsSIq\nX/0ajypQDfyBWy7gkh8NaPP+QpXPGjduXLPxNh3zAw88wLJly4IGatSoUaSkhH8IfP3119j0+npu\nuHUm39dqqXYbmbc0j/FpbmbPjp70vrciG6goYdBr8Hh95BdWk5poJO4Uc6Xq7S7MNXY8Xj8GvY4Y\nU9tydrPZjBCC7OzsZgvYoWqDQfu+EJE8mcZz2T0+nv3Haq655hr69unbcKQASUKhUKBWKdFotLTj\nFsJis9lZu3YtqSMncbTEgk7l5/KR7ajoIfzEmWTv6XRpb1PD4ESft5J+F2SjS8zgnKvv49450zCG\nKT/VaGR+85vfAjSs9UisXLmyzXE999yzQfGCOiaF9Mt+iUdlIClOz0N3XszQAfGndL/jxo1j4cIF\nQeFFSyJ5e6G+MzNn3tXQQyqHI8UWFj3/CeVOIxv+8x0WS2sloExzZAMVRdQqJWqVHnOtA7PFTlKs\njoQYfZselcvtpbLWTr3DgyQp0Os0aLXt98K2bNnMqlXPk5l5Uul//PixZu931LsK58nk5ua2lhqr\nIhcG7QihJgCFWk/G5DhASeHX/+KjD2sjXs/hdJGSICv3okVaHxNHSyM3jQwi/FR++0+GXzOPereG\nJ176kj/mXBLy/9XUyEDAe2kM2bUHAZjSxpGQeQ1CqSJzYAIP3nFxhxLpn3322WDVCAgo+jQaddhm\nl5HCnKG+Mz//+a1s3boFgKED4rmwv5VdpbHEZlzMu59/SP2JnR3uM3U2IRuoTkCvC6jGamweymsc\naNQK1EoFWo0ShSQhELjcPjw+gcfjQ0gSWq0GY0MIrKMeT05OTjO1VOPibW5ubkOIovkXJzs7m1mz\nZpGbu7bDoYWOKq46SssJID4+ni+PQZVPiaPqKDdOPr/N6wm//5Q9WJnW6LRqjDoVPr8fpSK0KKfl\ng8Vrb/2DYZPvI7+gmsdf+oIlMy/BqDt1tWvL78TNt9yOPXYMiYMCod76wt3U1tbgsp9L7psb2v3d\nCdV+I1JLjvY2IWyk8eGx8YHu9Q15TJvxa74xm0jIvAafyxrx+LMd2UB1IlqNGm2DUk0Igd3txy/8\nSJKESqlCrZQI1U3gVDyejIzBQQM1btw4rrpqctg4fqTup40TgRAi2FOneRZ85z7ptZwAJky6gX//\nsB3h91Fz4AOkzGsjHu90ukmWvaeoMyBCOw6z2UxZWRkTJoxn/vwF5Obmcs7QNDK0xykxjubgiWru\ne3oTD06/iFEjBgWPu//+eeTn5///9u48POrqbPj498xMZpJMMslkJwv7KrIquGAr1rqBFWvrEi1W\n3Cruok9b5bW1tdW2z1OkrdjWtqQuBVSqRStYV9TSGgURECEgCAQkAySEZJLZf+f9Y5KQQJZJMslM\nwv25Li+TyWTmDJn53We5z32aRv5lZWXcfvsdrU7xNf9M1AasBAvPx27PJNFq5pZLJ/Lcn95k7ty5\nnf7s3HnnnQSDwRYdrrYOu+xIa6P/W2+d25Tx2Pj46al+3n7vTZyjvk72+Ev5+2t/kwoTbZAA1UuU\nUhGfatnZ3feLFy9mxYoVzJo1C7s9uaFcy61Nvcb2il9edNEMSkoWNz1+Y5XoWbNmNR34Nm3atKb0\n4K5kXHVW42srvmY2j5a8C5gZYK3kK5ee3+HzGUaoT9RK7GssZhNpKVY8rRSSXbnyVf7+9xeBcA3I\nxim7zZs3c9mVs6k35+H2W3n4mbXce7WVKWMGADB37lz8fj9nnHE61103hzvuuJ3CwkJcLtdxI545\nc+ZwsLKalWtdpA6aSoLdxKA8B/cVT6UgO5WvNgS1k08e26Mj/NY0vl8vumhG0+hrxoyZDVl8M1iy\n5G8t7h/uOCp0zlBe/c9OCqZew/gpcX/IeEzEZYCq8/jjvtZdrDXvKR46dAiA/Px8rr9+Djt27GTK\nlKNHch17gFvzjYfHTkGUlpYyYcJ4VqxYAYQ/4M0LXHZmU21nNR+9PfHE73l9w2F8yUPx17qYPDGB\nG2+Y1+7zyeipZ+W1UUi2efHWxvfWVVddhVKKpUufQVlsjLvgVqoDyTz6zAecPamIa847iZNPPpkz\nzzyDRYueoLq6mmHDhrFkyVLy8lqOon2BEG+v3cW6w0U4Bg9Ba4P8xGp+Mfcbnd7ycKxodLhaG7U1\nptQ3r1rR+DOLxUJqairXzRjH4Vof/9m0j8dXfMYvC/Ja7Nc6EQSCBstXb2vz53EZoO757dvcdfmp\njB2aFeumxEQkH5rWzpyprq7mscceo7S0lFNPPYWTTz4ZODptVlKymKVL25+CaL5ZsTWdnYPvjMYP\nenFxMcMnfBVf8lC0YTC1KMCNN3wPaD8ZQ0ZPPctkUuQ6k6ms8ZHYiVOJddDHWEcFI0+7hGdf/4x3\n15ezZuM+zpk8kLOnf4OqquNHPIah+XzfYT7Y/CVvrd1Nbb0fsJBq8TLUXskrL/yVJUX6uPdDZwNO\nNDpc7c14tPb4brf7aEDT4K0yAYN5+K9reOR7Xz1hKp98eaiWx55by4591W3eJy4D1KEjHn70l/f5\n5ldHcuW5Y0iwnFgFL7ryoWle8LKtJIjWNxK2nIJoLPPS3Sm8rqS2N37Qly1/mQFn3IgZOLLjXVJy\nBrX5O40kc693ZDiSqDzSMu28pKSk6b03atQoysrKWLZsGUCL99FtGU4eu/Nylr6xhTWb9vHGR7t4\n46NdmNVgcqdcS8hfx5aaXH7w+3f58qCbOm+g6XmLcuzkml3cf/s1KKUYmJPc6meis5+d9jpchqEJ\nGQaGoTGbFGazqcPSWpE9viYQCDQFtCuuuob9Vge7K2p45OkPeOiGs7DFuIhzT9Ja89a63fzllY34\nAiGy09rODo3LAPXtc0bx4uoyXnx3G5u/OMS9V00hK/3EGfpGMkpp3lM8tuBlW0kQrT1ua1MQp512\nGvPmzQPAYrHgdrsJJ/VGvqmwqxuHtYbMcZdgtqVg8hxgxmmDIguSkrnXawqzU9nlqm2qajJjxkxq\na2ubKi6UlJTgch0gJcXOHXfcARwNFLlZqdxbPJXLv1bD6vV7WPn+Zvzais0ZPs+00g+V5eH3TI4z\nmckjczl7UhEjizKagoPLFT5K7mg5rNaOew/rTMfKMDQenx8MA2uCGatFkWQzYzaZCQYNfIEgvqBB\nIGRgSbA0lerq7jShxWTw/757Bvf/4T3K9lSxYNmHfP/q03q1cHNvcXv8/P6l9fz30y8B+MqEQmaf\nN5pV/9f6/eMyQF193klMGpHDgufWUraninsff4e7Lj+FyaPyOv7lE0RrBS9nzZrF1q1bWz0BNJLH\ngeY9zvDFIDU1lUWLniAQCPdmIw00XUlHLykpYdW6AzgGn44yfJR/uJQZN8zusH5bvcfPgAwZPfWW\npEQr9kQLwWAIi8VMbm4ud955V9PPr7/+huN+59j3y8BcBxdMyuaFRc/iqjzCkNGTqK3zUet2M2xQ\nPgt+8VOcqbZWRyzRrpoSCIbw+fwk2ywMzLJ3eLClYWiOuL0cqvEQMhQXXTSj4fkjG7W1FdAevO7b\nzH/yPT7aUsGTL2/glksndnrEFs827zzEwhfWUnnEQ5LNws2XTODsSQOpr/e2+TtxGaAAxgzO4te3\nn8NvX1jHx9tc/Oyp//Lt6aO48tzR/bJn0Vwk02PNe4pTp57GunUfM3/+fBYsWNAiCaIjHfU4Owo0\nbbc1p5OvGjKHTsUx2InZpHjopnP5cFR9RKM1EyEcUjWiVxVkpbJt72FSLEktsthWrnwVCHd8Vq1a\n2e7fb+XKV9m/fz9Op5MdG9cAkJWVRcmip1Gq7c94tPbihQwDT72PtBQrg7KdEV9XTCaF05GE05FE\nvcfPPmVwVfF3aOzUdRQo2+oU5uY6uH/26fxk8Rre+GgXmY4krjh3dKdfV7wJhgyee2sLL767Da1h\nRJGTe66cQl4Encq4DVAADruNB649gxff28ayNz5j+eoytu6u5J6rpuDsx9M5jT3EvXv3sWvXF2zY\nsLFpzr+1D3xjwcubbrqxw6MN2tNasGnsHXbU1mN7s263u8UO/SVLlpKQ0PYO/U+2u3j2zc8BuOHi\n8Ywdks3YIR23u67eR2F2SkSvT0SP2Wwi15nMoRpvq0drrFmzpunrtt5/rR3dnpmZ0fONJ3xOmM0c\nvlh250SA5CQrI4oyqTxSj+uwB3tyYoeVY9rrFI4ZnMXdV07h/5aUsuytLTgdiZw3ZXCX2xdrFZVu\nHntuLdv3Hkap8PLNFV8bHfG/ufmhhx7q2RZ20k9+8pOH7vn+/KbvlVKcNDiLMYOz+GS7iz0Hanlv\nQznDC539NiVz0qSJuN1uli9f3lDafyROZwaLF5eQkGDhtNNOa/X+b775FhBOknj00UexWhOYMWMm\nKSmRXcBfeOF5Fi16gtLSUj7/fAeLF5fw/vvvs2bNGq6+uphx48Y1BZpJkya1eO4lS5ayadOnXH11\nMbfeeiulpaVs2LCRcePGAeHCoCaTiUsu+QYQDn75+fmkpKSwvbyKnz/1X/xBg4unDePb54xqsd7w\nwgvPM2nSxON+T2uN1iHyMiRAxUKSLYHDtV4mTz6Furqj7z8I/90a3wuNI4vWPPLIIw1rnOGRxN69\n+9i4cSMzZ7Y/RbZ4cUmb78n2hAyDujoP+Zl28jJTo1LYGSA5MYH0FBuV1W4MVLdmeQpzUnHYbawr\nc/FxWQUDslIYlJcWlXb2Fq01735SziNPf8CBw/VkpSVx/+wzOPeUQcf9mwcCQR5f+Cseeuihnxz7\nOHE9gmpu3LBsfn3H13hs2Ud8+sUhfvyXf/OdC8Yy66zh/WqeFsIX87fffqfp+7KybU1HTtvt7Q+L\nzUlpVAeSeHPtbtKGTuOdTVWwqQprgomUJCuZaUkMyLST67Qf9yFqXjJpw4aNTRlZzZMmIk3DPXaH\n/oQJ41m/fj0PP/yzFqPCKm8CHx9Ix+sPcfbEIq67aFyLv2d76w11Hh+DcyQ4xdKgXAfby9tOE25P\nSUkJFRUV5OXlcc4557B06VKKioqYO3duu7/X1dRwrz+ASRuMLMrokcM4EyxmhhdmUH6gBq/PT6Kt\n63s5Lzx9KDV1fpa9tYXfPL8Wk1JMG18Yxdb2nDpvgCf/8Qnvb9wLwJknF3DLNyeS0oW9rX0mQAE4\nUxP58fXTWPpmeD7z6VWfsm1PFbd9a3K36nzFmwcf/BEVFRWkp6dTW1tDqOHAwFGjRjFjRsvKD7/7\n41PsqTL4dKfBkAt+SEib2VwDm1/6pN3nSLRaGJRrZ9/29Xz3ihlMmzycJc8+zeDBg5umZsrKyigu\nLubee+fhch04ZvpvcVNl82MXfHfs2Mnjj/+uxVHfJ500lpNOGtsiHXmHy8fm6lRM5hBnjivgtm9N\nPq531fbxGwaJFkVSJ/bjiOhLsJhZ+vST/G3JMiY2VB6ByKaYZ8yYidvtxm63M2fOHJzOdNxuN9nZ\n2a3ev1FXMvXq6r047VZyM3t2JKKUYmBuGgcOuzns9pGc1PU9TVecO5qgYbD8nTIee34tJpPijJM7\nPkIkljZ/cYjfvrCOg9X1JFrN3PCNCXxt8sAuDyL6VICC8Nz3dy4Yy8giJ79d/jEfbP6S3RVH+P41\npzMozxHr5kXF73//BNddN6epQkSjsrIyHn74YT76eBMvvbuN1ILxeHT4A5eU7SSkIT3FhjnkZuSQ\nAnIz07A27KfwB0PU1vnZ8NnnVFTV4yWNsvIjkDiURS9v5fcvf4b7wCE8B3czcsw4tm3ZBMAnn4QD\nXXvHb8DR3uyOHTspLS3lxhtbroctXRqu69dovz+L+po8TGZFkcPLNdMHdqpXW1/vY0Rh145UENF1\n8/XfIajNXHrZZbz22iqgZZJEW3Jzc0lJSWmqJAHh91VqamrUNoBrrXHXeSnMsvdqIk2OMwWzqZ4D\n1Z42DxmNRPHXx2AYmhff3caCZR9x39WK007Kj2JLoyMQDLH0zS2seH87Wocrt99z5ankZ6V263FV\ne5V7Y0EppfccrOv4jsD+Sje/+lspuytqsCWYueWbkzh7YlEPt7DnaW20OIbA6XRSWFjIls/3MnDi\nBQTsA1GmhhFjyE/dgW2cNXEIt3z3MrI73C+mWbBgAcuWv4wtvZABQ8ZRRyq2tKNveq01Zt8hDn3x\nMfWurcy96VrmzJnDggULWoxkwtN+x/aMdIv7FRcXM2/ePdx++x2UlpZy6RWz+WiPGbOjAK01CdWb\n2fnRioYzc64/LlHjtttup7S0tMUIbe7cudw451oKc/rWvHx/FgwZbCs/HNmRHBxNyGksv9U4sm77\nfdW1Nvm8XobmO5s6ar3tcI0HV3U4eaKrtNY8/dqnrHj/c0wmxW2XTeacyQOj2Mru2eOqYeHza9m1\n/wgmBZdN71wiRH29l9GDMtFaH/dH73MjqOYGZKbwi1vO5o8rPmH1+nJ+8/xaynZXMmfmuD59pPLN\nN3+PsrIyhg0bypEjNRzxKuqdU8k/6xsElUIBnkM7cO9dj+fg5xRfdQX33nUNnflQG/46PAfKSHCC\nq6wMkzWFs2dezUGPjSPBZIzEbDLGXEDGmPP5rM7Bq//ZgS/U+X/TxqO+5/3P/fzxhff4pDoRs0Oh\nAx4OblqB99AOJkwY3xSQjh2plZaWHrcGdvbZX2NAZvd6ZiK6LGYTBVl29lfVR3Qxbvw7V1Ud5sMP\nS5tu1xoWL17MzJkXd+uEWX8giA4FGVmUGbVEiK5wOpLQwIFuBCmlFNdeeDIWs4m/r97G75av44jb\ny6yvjIjp+rthaFb+dwfP/GszgaBBboaduy4/hdGDMqP2HH06QAHYrBbu+Hb4H+XPr2zktdIv2LGv\nmvuunhrBaCL2WkvtHjAgj/XrYcIpZ1DucVLhTSWgTCg0tfs2ULu7lJSEIJ6Gi/hnn22O+PmabxLc\nvDlc1mjChPGMHTuWJUueZMKE8ez9dCtJ2SMYeep51Bqp7Piylh1fbgIGMfqi/yEtwcNLb/wLu+Ov\nfO/GOW0+fkgrXnztv+zyPcchXzJef7h3nZtYh8f1PuWHdgDg9weoqHCRl5fX6ppT8x518TWzSU+y\n9Pu9cH1RWkoidd5AqxXPj9VaLclRo0Y2jaQai612hdfnJ9GiKMxzxkUCVYYjiVDI4HCdv8trpkop\nrjl/LA67jZJXN/H0a5vZd9DNzbMmxqQU3N4DNfzhH5/w2a5KAM49dRDXzxxHki26uQB9PkBB+I93\n/tQhDM1P53+XfMj2vYe57/F3uOuKU5k8suu9sN7Q2trO926Zy1cuvYUPD6VgsthQSjPI4WXNy3/k\n69PPYGOlmYqKg4wfH854a344YUearxlVVLh4+OGHefDBB8nLy21aPzo6nbaQm2+5ldGnnsc763by\n6c5K6kNW6kNWsiddwb92wrs/+jsD89LJzXCQaLNQZQxixDk3sS9hBHtcNeScOoS9tQAhJo/M5cpz\nR7PwFw/y6YZ1TecAbdmyhYcffjiio76NYJBsp0ztxav8rFQ+31tF0GTq1JriqFEjmzJVZ82a1eUj\nMurqvWSm2siOs7qM2U47vsARPP5AU4mkrtSr/Ma04WQ6kvjt8nW8tW435QdqmHfV1F7bcuMLhPj7\n6jL+8d42giGNw25l7jcn9di6WL8IUI2GFzr5v9uns/D5dazf5uJnf/0PF08bxnfOHxuzOeiOHNuT\nHDP1QtZWFXCw3oPJAp6D20n37yQjKR/D72b48OHceeddLQJL4xs7Es0zoPLy8loEhR/96EctPjBH\nd7jn8tWJRQSCBr958llWvfsJRaOm4A5a8QZNbNtbw7a9NUefJCGHL/YfATT+GhcnD07jzusuIT8r\nBZfLxciRI/F46tm4MZyIMWbMGB588EGg/bpmdfVe2ZTbBwzNd7KtvBJTUlKb02vt1ZK02zt/sY1V\nMkRnFOak8cW+wwSCIRIs5i6XbDpzXAG5Gcn84tlStpUf5r7H3+Z7syZy5riCHhsxaq0p3fwlT7+2\nmYqqcI7AeVMGM/vCsV1KH49UvwpQAKnJNuZfewYvvbeNZW9u4Z9rdrBpx0HuuXIKA3PjN8vPmlaA\nc9TXqUsvpK7ag7/WRXXZW5h9Lg7W1bN9c8uzmZoHlp44ibOiwsXatesaKkkcLch5362zMXkPsmTJ\nrwHFN6+czcxLr6Ta7cMfCAGw+q1/sfrNVQTcBym+8lvMm3cLjVN0K1e+yjPPPNM0egJISLCQm5tD\nSclipkyZym23Hb/HJRgySEwwkdKNtF3RO0wmxbACZ1PSRGsXzbZqSTYeuNmZCijBkIHX62NovqNp\ndBKvBg1IZ3t5FWZTYrdKNg0rcLLgjnP43fKPWbu1gl8v+4j3N+7lhovHR3VpQ2vN+u0HWPrGZ03H\nYgzMdfC9SycyJoprTW3pdwEKwh+Qb00fxfjhOSx87iN2V9Tw/UXvUHzeSVx85rC4Wr9Y9ORT/GuT\nh7zTrgMg5HNT/fm71O3bwKhRIygrq++1tjTv0TWuT82f/0DD+lRj7675B0iTZA4wcUQOoHC5XLz6\n6j/JtNbhP7IPgLq6lu1vvhm40caNm5rS0sPB6fg9LrVuDyOLnD3zwkXUJVjMDCtIY+eXR0ixHx+k\nmo/kZ868uGHNqfNnMnn9AczaYGRh5LX0YslkUgwtSGdb+WEcqV1PP4dwZ/z+2afz+oe7ePq1T/nw\ns/2s3+Zi5pnDmHXWCNJSut6ZCxmadVv3s+L9z9myO7zOlJ5q4/Lpozlv6uAe2ejcmj6dZh4Jjy/I\n4lc38tba3QAMzU9n7jcnMqwgthe7Om+AF1eX8cqazwmGNFaLiW+cNZw3n3uMTRtabrItLi5GKZqO\ncm9+Ae/KPHbbWqaIN1aSgKPJCiUlJSxa9ETLc34a2lRSsphFi5447ndbtlnz8MM/azqxt/naQ1sp\nxh6fnwx7Alnp8bWuIDrm9QfYsS8cpCLNpov0PV1b5yUzxUpuZt+b9q2t8/Howj/wlz/9sdXPUmcd\nqq7nqVWfsmZTuGOYYDHx1YlFTJ80kNGDMjFH8G+vtWbX/iOs2bSP9zaUc6jaA0BKUgKXnT2Si04f\nis0a/TFNv00zj0SSzcJtl03m9LH5/HHFJ+z8spofPLGamdOGc+XXRpPcyxUofIEQr32wkxff3dZw\nSiicPbGIa84/iVdeWsamDZ+0uLjn5eUxb949KKVa7Vl29+iB5hcDrTWbN7efEdhemZk5c+awd+8+\nVqxY0VSFwulMb9HmkpISVqxY0eraQ2sMQ2PShgSnPirRmsDIIic79lVjs1mxRLD9o6P3tD8QxO8P\nMCgnFXsPrn/0pFS7jW9fchEWk4mbbgq/rq6c5tsoKz2Ze4uncslZVTz/9lbWlbl4a+1u3lq7mzS7\njTGDMxle6CTXmUx6SiJmsyIQNDhS52P/ITe7K2r4bNchqt2+psfMy7Bz0elDOffUQb1+nWzU70dQ\nzXl8QZa9+Rmv/mcHhobUZCuXnT2SC08f2uMnWAZDBm+v283zb2+lqiZ8/smYQZlcN3McIwrDozmX\ny8VPf/pTSktLKS4ubjrdtv1elY5wA23rGkc9x6adA8ekoEfSu+u4Lc0D4uLFi3niid+3WHs49jnc\nbg/DC9P79L42Ee5o7Kmopnz/Ad55+40ORketv48MI1yF3JFkJj/LEdP9TdHy+d4qLFYrZlN0p8z2\nHazlrXW7+e+mfbgOR75MkOFI5JRReXx1QhFjBvfOHrITegTVXJLNwpyZ4/nKhCJKXt3Elt2VPLXq\nU15Z8zlXfG000ycNjHq2X229j9c/3MWqD3Y2BaYhA9K45vyTmDQyt8XcfG5u7nGZdJ3J0OuM5jv5\nq6qOLtROmDCeP//5z7hcB1pkCkbSu4vkZNHOrD14vX6y0hIlOPUDJpNicL6Tkj//gd/8oYRDlYcx\nmyIb8Wsdns6zWUwMy3dg62CPVV8yeEB6pypwRKogO5VrLzyZ2ReMZd9BN2V7KtlVUcPB6npq6/yE\nDAOL2YTDbiM7PYlBeWmMKHRSmJMaF3vHGp1QI6jmtNZ8vM3F317/jF37jwDgsFs5f8oQpk8eSH5W\n1+e1tdZsKz/M2+t28+76PfiD4WKvBdkpXHXuGM44uSBqPZPmIyCIfB678feKi4v5+OOPj1tr6kqp\nmWiuhwVDBjoYYGiM1wpFdGmtueeeeTzxZAlJjky+M/u73HffPVjMRzshje/Ny68sJhgI8vTiJ/nB\nvXfw4wcfiGHLe06120vFYQ/2EzRDVUZQrVBKccqoPCaNyOU/m/bx0nvb+GL/EZavLmP56jKGFaRz\nyqg8xg/LZmhBOokdLA4ervWyvbyKDZ8fZF1ZBQeaDasnj8xl5pnDmDA8p9XA1J0Le1ePHjg2xXXU\nqFFMnjy50ym+0XgNrfF4fIySrL1+SSkIeI4Q8BzB7D9MoknjC/gJGeHO8nlfPxdfvZsf3nc39iQr\nA7NszJ49O8at7jnpKYnUuH0Eg6GI1uhOJCdsgGpkMinOmlDItPEFbNlVGZ63/fRLduyrZse+ap5/\neysmBbkZdnKcdhx2K4lWCyHDwOsLUVnjwXW4jupaX4vHzXAkMm18IedPGUxBdvt147qT6NCVowda\nM3nyZObNu4eMjK4t1HY3WQOOBrlvXV7MwBw7v/zlL5g9ezZFRX2/ALAIe/TRR1m4cCF33303AAsX\nLiQvN5sHHjg6OhpW4OSMSWOavm/+s/6qMMdB2Z4qUqI81dfXnfABqpFSipOGZHHSkCxuvmQCm3Ye\nYv02F1t2V7LHVcP+yjr2V7Y99ZhkszA0P52Th2YxcUQOIwozIp7G686GvUhFUiU8I6PzI6dGF100\ng3//+98t1rI6Oi7+WCtXvsrvFv0B195dWE0hFi5cCJwYF6gTReNI6P777wcgOzu7X4+OImUyKQpz\nUth3qK5blc/7GwlQrbBZLZw6Oo9TR+cB4dRwV1UdB6vrcdf78fpDWMwKW4KF9FQb2enJZKcn3O4V\nBgAAEZJJREFUxyyrKJLptUiqhHcnGWPlyldbbL7dsGEjK1e+yvXX3xDxY1x9zWz2793DE7/9XwDu\nvvvupguZ6B+KiopadDik83FUarKNZJtXpvqakQAVAVuCmYG5jh4rlRRJ9lt7Iplea69KuMvlAiA3\nN4fmZY26c9xBZ/kDQZQOkWgK9NpzChFvCrMdbN1TFfWsvr5KAlQc6GqiQ6PuThFGY/1oxoyZrFmz\npsUpupG+hkAwhA4Fee6pPxy3PpGdnS29bHHCMJkUhVl2vqzyYE8+MbP6mpMAFQeilegACkwmfAGD\n2lovJtPRZPG/PvUUTz2zhKuuvAqT2cSSJcuaRmnRWANbtWolGzZsbDEKXLVqZYevJRAMYgSDDM13\ncu21s1FK1ifEic2RkkhVjYdgyOi1mnfxSgJUH6a1xusLULK4hD89+SdmX3MVZoIs+vXDFDoTWow8\nbp1zOakWL/f9z/fxB0KkJydw/tfPpb7eQ8iAkNG9tnRlFOjx+bEqzZCC8MFysj4hRFhhblqPbODt\na7q1UVcp5QSeAwYBu4ArtNZHWrnfLuAIYAABrfXUdh6zVzbq9mWNtcgSE0xkpCVxpPIAzz77bNPI\n49FHH+1UevbPfvYIP/n5L7nh5ltRZisvvvR3brv1lh45xqORu95Lhr1vFvoUojccqq6jqi5Akq1v\n1huMVHsbdbsboH4JVGqtf6WU+gHg1Fr/sJX77QRO0VofjuAxJUC1wecPEAwEcaaETwyNJGuwvLyc\nZ555pt3g1fw+hqH5yc9/yYUzL8WZmUOC1YItimfsBIIhfD4/hdkppMocuxDt2l5eiS0xMa7KD0Vb\nTwaorcDZWmuXUioPWK21Ht3K/b4ATtVaV0bwmBKgjuEPBAn4A2SnJ5HhaP0AuLY88sgjzJ8/v0Xi\nwc9//vOIps8MQ1Pt9nK41os/YGCxWrp8IFwwGMLj9ZNmT2BAZmq/KPQpRE/z+gLsrKgl1d5/90b1\nZICq0lpntPV9s9t3AtVACHhSa/2ndh5TAlSDkGHg8fjISLGRk2HvUi9Ka828efOaNr3efffdLFiw\noNOPZRiaGreX6jof3kAIjSLBYsGaYG7zsQLBEH5/EKUMUpOs5DrtfeJQOSHiyd4DR/Abpn5bNLlb\ntfiUUm8AzTfEKEAD/6+Vu7cV7aZprfcrpbKBN5RSW7TW/27rORf86udNX58x7SucMe2rHTWz3/F4\n/ViUZnhBfBw1YTIp0h1JpDvCi7b+QAi3x4/b4ycQ0hiGprGzYzIpzCZFSqKFtIzUHjnkTIgTRX6W\ng7I9lSSkRO8o91j775r3+O+a9wEIBIJt3q+7I6gtwPRmU3zvaK3HdPA7PwZqtdYL2vj5CT2CMgxN\nfb2XvIxknI7uZ/B0Z4pPCBEfqmo8HKrxkpTY/9Zte7Ka+cvAdcAvge8CK469g1IqGTBprd1KKTtw\nPvCTbj5vv+QPBDGCgage0Ce1z4To+zIcSVQeqUdr3a8TJo7V3RFUBvA8UATsJpxmXq2UGgD8SWt9\nsVJqCPAS4ek/C/A3rfUv2nnME3IEVefxkWIzUZDtOKHegEKIyPTXhIn2RlDdWrHWWldprb+utR6l\ntT5fa13dcPt+rfXFDV9/obWeqLWepLUe115wOlHV1nnISUukMCeNvXv38sgjj6B1eE3nkUceoby8\nPNZNFELEWKItgdREM8FgKNZN6TWyeh1DWmvcdV4G5qaQ0nCa5jPPPMP8+fM5ePAggBw5IYRokp+V\nSll5Fan9KGGiPRKgYsQwNHV1Hobmp5FoO7q36P777+fgwYMt0sLlyAkhBIDZbCLXmUxlrZ+kxP5d\nYQK6OcUnusYwNHUeDyOKnC2CkxBCdCQzLRmMEN3JH+grZATVywxDU+/xMKLA2WqmXmtHYsuRE0KI\n5opyUtnlqiXF3r+LyUqA6kWNI6eRhRltltGXtHAhREeSEq3YbZZ+f/put9LMe0J/TTNvTIgYEcU9\nTkKIE1coZLBt7+E+P4rqsTRzEZlwcPLETdkiIUTfZzabyE5LxOPzx7opPUYCVC9w13kYkufAmiDB\nSQgRPVnpdgj134QJCVA9rLbOQ1F26gmREiqE6H1FOanU1Xtj3YweIQGqB9V7fAxwJpNq738FHoUQ\n8SEp0Yo90dIvK0xIgOohXq+f9OSEqFQkF0KI9hRmO/B6fbFuRtRJgOoB/kAQW4IiNzMl1k0RQpwA\nTCZFXoYdj7d/JUxIgIqyYMhAh4IU5Thi3RQhxAnE6UjCrMKHh/YXEqCiyDA0Pq+XoflOOTJDCNHr\nBuY6qO9HCRMSoKKort7D0HwnJpMEJyFE70uwmMnqR3ujJEBFSa3bw6Bc2eskhIitbKcdZYT6xVSf\nBKgoqKv3kp9px54ke52EELE3KC+9X+yNkgDVTR6vD2eKlfTU/nUMsxCi77ImmMlOS8Tbx6f6JEB1\ngz8QJCnBRG6GpJMLIeJLttOOCU3IMGLdlC6TANVFgWAIZYQoyk2LdVOEEKJVg/LS+nRWnwSoLgiG\nDIJ+P0Py02PdFCGEaJPFbKIwK6XPrkdJgOqkxr1Owwpkr5MQIv45UhJxJCfgDwRj3ZROkwDVCY0n\n4g4vzMDcxom4QggRbwZkpqBDwT63HiVX2Qhpramr9zI839nmce1CCBGPlFIMGZCOp97Xp86Okitt\nBLTWuN3hE3FlI64Qoi8ym00MGeDAXeeJdVMiJgGqA4bRcFx7oVOCkxCiT0u0JVCYlYK7jyRNWGLd\ngHgWDBn4vF5GFmXItJ4Qol9wpCQSCBkcqvGRnBTfh6lKgGqDPxBEh4KMkIQIIUQ/k5mWjGFoqup8\nJCfGb5CSANUKr8+PzawoklRyIUQ/le20A1BZ68WeHJ+l2iRANaO1xl3nJSc9kax0e6ybI4QQPSrb\nacdiNrH/cD2p9qRYN+c4EqAa+ANBgoEAQwc4SLQlxLo5QgjRK5yOJBISTOxx1WJPToqr8+zicnHF\n6/Hirvf2yqaykGHgrvNgT1CMLMqQ4CSEOOGkJNkYUejE7/Pi8wd67Xl9/mC7+7JUvG3aUkpprTW+\nQJADh+uo8wYBE0mJ1qhG9pBhUO/xk5SgKMxxkGCRFHIhhHBVuqms9ZGcbMNsiv4YxjA0Hq8PkwJn\nio3MtGTMZhNa6+Mu8HEboJqr8/ioPOLF4w9ioLBZE7ocULz+AEF/kORECwMyU2RvkxBCHMMfCPHl\nwRrq/UZUApXWGo/XjzYMkm0WcpzJLWarlFJ9N0A15wsEqa71Uu8NEggaBA2NyWTCbA7/1zjK0hpC\nIYOQESIUMjArhS3BRJrdRlpKYlzNswohRDzyBYK4KsMzWSaLiSSbNeLMZp8/SCAYxIQm0Woh05GI\nPan13+83AepYhqHx+YP4/EH8oRDBUPh3TUBCgplEqwWb1SIbbYUQoou01tTW+6iu9eEPGgRDBoaG\nxlijUaA1JhUuqWQ1K+xJVlLtVmwJHefi9dsAJYQQovdprQmGwolsSinMJtXlfaNtBShJMxdCCNFp\nSqkeTy6TeS8hhBBxSQKUEEKIuNStAKWU+rZS6lOlVEgpNbmd+12olNqqlNqmlPpBd55TCCHEiaG7\nI6hNwDeBd9u6g1LKBDwOXACMBYqVUqO7+bxCCCH6uW4lSWitywBU+6kbU4HtWuvdDfddBswCtnbn\nuYUQQvRvvbEGVQCUN/t+b8NtQgghRJs6HEEppd4AcpvfBGhgvtb6lZ5o1EMPPdT09fTp05k+fXpP\nPI0QQogYWL16NatXr+7wflHZqKuUege4V2v9cSs/Ox14SGt9YcP3PwS01vqXbTyWbNQVQogTSFsb\ndaM5xdfWOtRHwHCl1CCllBW4Cng5is8rhBCiH+pumvmlSqly4HTgn0qpVQ23D1BK/RNAax0Cbgde\nBzYDy7TWW7rXbCGEEP2d1OITQggRU70xxSeEEEJEjQQoIYQQcUkClBBCiLgkAUoIIURckgAlhBAi\nLkmAEkIIEZckQAkhhIhLEqCEEELEJQlQQggh4pIEKCGEEHFJApQQQoi4JAFKCCFEXJIAJYQQIi5J\ngBJCCBGXJEAJIYSISxKghBBCxCUJUEIIIeKSBCghhBBxSQKUEEKIuCQBSgghRFySACWEECIuSYAS\nQggRlyRACSGEiEsSoIQQQsQlCVBCCCHikgQoIYQQcUkClBBCiLgkAUoIIURckgAlhBAiLkmAEkII\nEZckQAkhhIhLEqCEEELEJQlQQggh4pIEKCGEEHFJApQQQoi4JAFKCCFEXJIAJYQQIi5JgBJCCBGX\nJEAJIYSISxKghBBCxCUJUEIIIeJStwKUUurbSqlPlVIhpdTkdu63Sym1QSm1Xin1YXee81irV6+O\n5sPFlLyW+CSvJX71p9cjr+V43R1BbQK+Cbzbwf0MYLrWepLWemo3n7MF+aPGJ3kt8ak/vRboX69H\nXsvxLN35Za11GYBSSnVwV4VMJwohhOiE3goaGnhDKfWRUuqmXnpOIYQQfZjSWrd/B6XeAHKb30Q4\n4MzXWr/ScJ93gHu11h+38RgDtNb7lVLZwBvA7Vrrf7dx3/YbJIQQot/RWh83E9fhFJ/W+rwoPPH+\nhv8fVEq9BEwFWg1QrTVSCCHEiSeaU3ytBhalVLJSKqXhaztwPvBpFJ9XCCFEP9TdNPNLlVLlwOnA\nP5VSqxpuH6CU+mfD3XKBfyul1gMfAK9orV/vzvMKIYTo/zpcgxJCCCFioV+kfiulfqWU2qKU+kQp\n9XellCPWbeospdSFSqmtSqltSqkfxLo9XaWUKlRKva2U2qyU2qSUujPWbeoupZRJKfWxUurlWLel\nO5RSaUqpFxo+K5uVUqfFuk1dpZS6p6FIwEal1N+UUtZYtylSSqm/KKVcSqmNzW5zKqVeV0qVKaX+\npZRKi2UbI9XGa4na9bhfBCjgdWCs1noisB24P8bt6RSllAl4HLgAGAsUK6VGx7ZVXRYE5mmtxwJn\nALf14dfS6C7gs1g3Igp+A6zUWo8BJgBbYtyeLlFK5QN3AJO11uMJJ3tdFdtWdUoJ4c96cz8E3tRa\njwLepu9cw1p7LVG7HveLAKW1flNrbTR8+wFQGMv2dMFUYLvWerfWOgAsA2bFuE1dorWu0Fp/0vC1\nm/BFsCC2reo6pVQhMAP4c6zb0h0NvdivaK1LALTWQa11TYyb1R1mwK6UsgDJwJcxbk/EGrbYHD7m\n5lnAUw1fPwVc2quN6qLWXks0r8f9IkAd43pgVawb0UkFQHmz7/fShy/qjZRSg4GJQGlsW9ItjwH/\nQ3jvX182BDiklCppmK58UimVFOtGdYXW+kvg18AeYB9QrbV+M7at6rYcrbULwp08ICfG7YmWbl2P\n+0yAUkq90TDf3Pjfpob/f6PZfeYDAa31khg2VQANWwuWA3c1jKT6HKXUTMDVMCJUtLGVoo+wAJOB\nRVrryUA94WmlPkcplU54xDEIyAdSlFJXx7ZVUdfXO0RRuR53qxZfb+pow7BS6jrCUzFf65UGRdc+\nYGCz7wsbbuuTGqZdlgPPaK1XxLo93TANuEQpNQNIAlKVUk9rra+Ncbu6Yi9QrrVe2/D9cqCvJuN8\nHdipta4CUEq9CJwJ9OWOqUsplau1diml8oADsW5Qd0TretxnRlDtUUpdSHga5hKttS/W7emCj4Dh\nSqlBDdlIVwF9OWNsMfCZ1vo3sW5Id2itH9BaD9RaDyX8N3m7jwYnGqaPypVSIxtuOpe+m/ixBzhd\nKZXYUKj6XPpewsexI/KXgesavv4u0Jc6di1eSzSvx/1iH5RSajtgBSobbvpAa31rDJvUaQ1/1N8Q\n7jT8RWv9ixg3qUuUUtOA9wgfxaIb/ntAa/1aTBvWTUqpswnXm7wk1m3pKqXUBMLJHgnATmCO1vpI\nbFvVNUqpHxPuNASA9cCNDQlGcU8ptQSYDmQCLuDHwD+AF4AiYDdwhda6OlZtjFQbr+UBonQ97hcB\nSgghRP/TL6b4hBBC9D8SoIQQQsQlCVBCCCHikgQoIYQQcUkClBBCiLgkAUoIIURckgAlhBAiLv1/\ncyOw93sQR9cAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_ = m.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course you may need to change the parameter settings such that the optimizer starts in a more sensible location. You can access the parameters with standard dot notation" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: -81.7521034055
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
rbf.variance 0.130864941346 +ve
rbf.lengthscale 0.1 +ve
Gaussian_noise.variance0.010323494102 +ve
" ], "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.rbf.lengthscale[:] = 0.1\n", "m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or you can set several parameters of an object at once, i.e if we wish to change both the lengthscale and the variance." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: -112.008504113
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
rbf.variance 0.3 +ve
rbf.lengthscale 0.3 +ve
Gaussian_noise.variance0.010323494102 +ve
" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.rbf[:] = 0.3\n", "m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also make additional constraints on the parameters. We may wish to fix some parameters, and fix the range of others." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: reconstraining parameters GP_regression.rbf.lengthscale\n" ] }, { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: -92.1828527437
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 2
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
rbf.variance 1.0 +ve
rbf.lengthscale 0.3 0.1,0.5
Gaussian_noise.variance 0.01 +ve fixed
" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.Gaussian_noise[:] = 0.01\n", "m.Gaussian_noise.fix()\n", "m.rbf.lengthscale.constrain_bounded(0.1, 0.5)\n", "m.rbf.variance[:] = 1.0\n", "m" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Widget Javascript not detected. It may not be installed properly. Did you enable the widgetsnbextension? If not, then run \"jupyter nbextension enable --py --sys-prefix widgetsnbextension\"\n" ] }, { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: -139.107192827
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 2
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
rbf.variance 0.051783879034 +ve
rbf.lengthscale 0.499999991553 0.1,0.5
Gaussian_noise.variance 0.01 +ve fixed
" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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82/Fs3ryZoqIiPvtsJ+XlOygpKUm43cbR0JXg3LjxpUitPr3rAMH0SbzzaX3k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\n1CIJrZTw2LPvcOCYmdx0M9ecP7TJ56FMiCZTMk888pt2fZeKjiEvw4J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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.optimize(messages=1, ipython_notebook=True) # Messages indicates you wish to see the progress of the optimizer\n", "_ = m.plot()\n", "m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see that the optimizer was not able to go above the bounds." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of constraints you may wish to set a prior. In this case we will have a constraint where we need to consider the prior of the hyperparameter during optimization. HMC is available in GPy which allows hyperparameter integration, but here we will show a simple MAP solution." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: reconstraining parameters GP_regression.rbf.lengthscale\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/alansaul/Work/Code/GPy/GPy/core/parameterization/priors.py:301: RuntimeWarning:divide by zero encountered in log\n" ] }, { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: 199.465650082
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraints priors
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve Ga(3.2, 2.1)
Gaussian_noise.variance 1.0 +ve
" ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PENTAf5QL6QRMZDLLOYgrALZtizZAkTwTeUIfun0rAP/kWI2itlMV7MtFPMpQ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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Reset model\n", "m.unconstrain()\n", "m[:] = 1.0\n", "m.constrain_positive()\n", "\n", "# Make a gamma prior and set it as the prior for the lengthscale\n", "gamma_prior = GPy.priors.Gamma.from_EV(1.5, 0.7)\n", "gamma_prior.plot()\n", "m.rbf.lengthscale.set_prior(gamma_prior)\n", "m" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: -150.515620364
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraints priors
rbf.variance 0.12881177115 +ve
rbf.lengthscale 1.36155433892 +ve Ga(3.2, 2.1)
Gaussian_noise.variance0.0103243560503 +ve
" ], "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gxowZc0qNnBhK5OePjr1RBIPGQEEo1FfT1M6EkRkDvRTBIMbqiN53L3JKbkND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\nFJe2mPRcOWUEM88dGSqXFg8GhEBBoF3HXd+ZyMiiDF5+p5x31+ykYm8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.optimize() # Messages indicates you wish to see the progress of the optimizer\n", "_ = m.plot()\n", "m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Core GP model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A GPRegression model is a wrapper around a more flexible 'GP' model that expects input $X$, output $Y$, both of which must be 2d numpy arrays. It also expects you to provide your own likelihood, your own kernel and your own inference method. We will look at alternative models shortly but for now we will show what the wrapper is doing" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: gp
\n", "Objective: -151.496450286
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
gp. valueconstraintspriors
rbf.variance 0.130864941346 +ve
rbf.lengthscale 1.36805842166 +ve
Gaussian_noise.variance0.010323494102 +ve
" ], "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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WVofJqGvV0bZp5Qiz2cyWLZuDobXc3FxShk/g1Y+OYnd5SYzVMXvqGCaOTm3xVNy8U24j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\ncyOw93sQR9cAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rbf_kern = GPy.kern.RBF(input_dim=1, lengthscale=1.0, variance=1.0)\n", "gauss = GPy.likelihoods.Gaussian(variance=1.0)\n", "exact = GPy.inference.latent_function_inference.ExactGaussianInference()\n", "m1 = GPy.core.GP(X=X, Y=Y, kernel=rbf_kern, likelihood=gauss, inference_method=exact)\n", "m1.optimize()\n", "_ = m1.plot()\n", "m1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2D model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly for a GP over two dimensions very little needs to be done" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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S2e/g4GCSkpJwcXHBycnp2jqop59+Gp1Ox8qVK3nllVe4evUqvXr1on79+qSn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\nwHW33Ua7k092XbNm1SrGjBjByuXLWbxwIV98/jkpHtxvpdi7YwcHEhK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1sn5377kheRw0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PUMIF9SOOm0AAldPtC76/ccRsgF7m+h6Qto+hyCVbL5Vj8E9IMlgASg/51g6OD7DPmg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3n4+VNXmyjt9yi+/nlrTl9tt1cIyP+7uRn5amr2NjdWj+fL9yRdg6e7ZGVKumvYtK8KLpgdQj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\nLn/Rurv6iY2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dCD3fhqsePLsHOb4GNn0ACb9D8/uh9RCo3Kh0Y7kckPqHIaukn6DqNVDt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\nwZWVRf6iReS5CYugIMKaNCGsQQN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# sample inputs and outputs from 2d model\n", "X2 = np.random.uniform(-3.,3.,(50,2))\n", "Y2 = np.sin(X2[:,0:1]) * np.sin(X2[:,1:2]) + np.random.randn(50,1)*0.05\n", "\n", "# define kernel, notice the number of input dimensions is now 2\n", "ker = GPy.kern.RBF(input_dim=2, ARD=True)\n", "\n", "# create simple GP model\n", "m2 = GPy.models.GPRegression(X2,Y2,ker)\n", "m2.optimize()\n", "_ = m2.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Kernels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will now dig into the details of what each component does and is capable of, starting with the kernel.\n", "\n", "Kernel construction is modular. Kernels can be created seperately and then easily combined with simple operations such as addition, and multiplication, including over difference spaces. Lets explore" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "d = 1 # input dimension\n", "var = 1. # variance\n", "theta = 0.2 # lengthscale\n", "k = GPy.kern.RBF(d, variance=var, lengthscale=theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A summary of the kernel can be obtained using the command print k, or k in the notebook." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "
rbf. valueconstraintspriors
variance 1.0 +ve
lengthscale 0.2 +ve
" ], "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \u001b[1mrbf. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mvariance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mlengthscale\u001b[0;0m | 0.2 | +ve | \n" ] } ], "source": [ "print(k)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also possible to plot the kernel as a function of one of its inputs (whilst fixing the other) with k.plot().\n", "\n", "Note: if you need help with a command in ipython notebook, then you can get it at any time by typing a question mark after the command, e.g. k.plot?" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simiarly to the model its parameters can be modified" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Osr9640p/fm8VxV4/N13Tmu42nVFU6dWxMTf0aklRiY8/v7fa6TjGQVagjOss3rCHhev3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\nR9CCAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k.lengthscale=5.0\n", "k.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute the covariance function of the kernel on some set data, we just call k.K(X,X), or equivalently k.K(X)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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FV/3Qv9tu9bPVP/8SRoW+/4X1+Qafn91fWH2j8sw2/MHv4ccjf8Wvj6bPzTjQxgngL2iC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\nWiaFMXzjEs2H/dW86/yEoCUXyHQE/Icm/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.matshow(k.K(X))\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Combining kernels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In GPy you can easily combine covariance functions you have created using the sum and product operators, + and *. So, for example, if we wish to combine an exponentiated quadratic covariance with a Matern 5/2 then we can write" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \u001b[1msum. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 2.0 | +ve | \n", " \u001b[1mMat32.variance \u001b[0;0m | 0.5 | +ve | \n", " \u001b[1mMat32.lengthscale\u001b[0;0m | 0.2 | +ve | \n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kern1 = GPy.kern.RBF(1, variance=1., lengthscale=2.)\n", "kern2 = GPy.kern.Matern32(1, variance=0.5, lengthscale=0.2)\n", "kern = kern1 + kern2\n", "print kern\n", "\n", "kern.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or if we wanted to multiply them we can write" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \u001b[1mmul. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 2.0 | +ve | \n", " \u001b[1mMat32.variance \u001b[0;0m | 0.5 | +ve | \n", " \u001b[1mMat32.lengthscale\u001b[0;0m | 0.2 | +ve | \n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kern = kern1*kern2\n", "print kern\n", "kern.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A range of kernels are implemented, and it is relatively straightforward to implement new ones.\n", "\n", "* RBF (exponentiated quadratic, squared exponential, or any other name you wish to give it)\n", "* Linear\n", "* Bias\n", "* Matern52\n", "* Matern32\n", "* Polynomial\n", "* Brownian\n", "* MLP\n", "* Exponential\n", "* Standard periodic\n", "\n", "A full list can be found by doing ``GPy.kern.``" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AVswIR74WyOuB7caYVb3vEJFbhxWRctWR+lZqGttIHZlA9tgU1+KYlZOBCOwr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\nPV1xjlg4nTOOWlDu5VgKiOll/o9FJNPmUkQuwHBXrYgsF5FXReR1Ebna5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, axes = plt.subplots(4,3, figsize=(10,10), tight_layout=True)\n", "kerns = [GPy.kern.RBF(1), GPy.kern.Exponential(1), GPy.kern.Matern32(1), \n", " GPy.kern.Matern52(1), GPy.kern.Brownian(1),GPy.kern.Bias(1), \n", " GPy.kern.Linear(1), GPy.kern.PeriodicExponential(1), GPy.kern.White(1), \n", " GPy.kern.StdPeriodic(1), GPy.kern.Poly(1), GPy.kern.MLP(1)]\n", "\n", "for k,a in zip(kerns, axes.flatten()):\n", " k.plot(ax=a, x=1)\n", " a.set_title(k.name.replace('_', ' '))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Active dimensions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It may be that you only want one kernel to work one set of dimensions, and another kernel on another set. That is the two kernels work on different domains of the input. In GPy this capability is provided with active_dims argument to the kernel, which tell the kernel what to work on. Lets return back to a two dimensional example." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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peYI8heD1Jfrzb49pbsos2Lyg9SQ4twoO/Jn281O04619eP4/Q1AKFyhpofhQ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\noF9CxFzXC5+Nfxi3cXGryO8lRSIuGFt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MgEA/3acOT4Rd/eDWRVDS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\nuHChtHuKjcVxExO037ULFbt21Xq8XFdf9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# sample inputs and outputs from 2d model\n", "X2 = np.random.uniform(-3.,3.,(50,2))\n", "Y2 = np.sin(X2[:,0:1]) + np.sin(X2[:,1:2]) + np.random.randn(50,1)*0.05\n", "\n", "# define a sum kernel, where the first dimension is modelled with an RBF, and the second dimension is modelled with a linear kerel\n", "ker = GPy.kern.RBF(input_dim=1, active_dims=[0]) + GPy.kern.Linear(input_dim=1, active_dims=[1])\n", "\n", "# create simple GP model\n", "m2 = GPy.models.GPRegression(X2,Y2,ker)\n", "m2.optimize()\n", "_ = m2.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to plot the marginal of the model where we fix one input to a certain value, we can use \"fixed_inputs\", the format for which is a list of tuples, where we specify the dimension, and the fixed value.\n", "\n", "Here we fix the first dimension (the domain of the linear kernel) to 0.2" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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zeP2U1bZhMBqwmPs/Y62nDp1qYPWGfRyvbAEgO83KrVeNZOolBWj7aGgr3jZV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\nZpYkB5SZmSXJAWVmZkn6L5P0tLT+tfGAAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_ = m2.plot(fixed_inputs=[(1, 0.2)])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then lets fix the zeroth dimension (domain of rbf) to 1.0" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rnM6VJctonINS0X9iDDvbsp0wp45uPzsPNERSwGvqaW6PaXGuYMakgsiy3awy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\n6pIUD2swdwN7R+vJMiJAAWuBv0/1IIY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_ = m2.plot(fixed_inputs=[(0, 1.0)])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we would expect, the data doesn't necessarily sit on the posterior distribution, as this is a projection of all the data onto one dimension." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Non-Gaussian likelihoods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considered the olympic marathon data that we use as a running example in many of our other notebooks. In 1904 we noted there was an outlier example. Today we'll see if we can deal with that outlier by considering a non-Gaussian likelihood. Noise sampled from a Student-t density is heavier tailed than that sampled from a Gaussian. However, it cannot be trivially assimilated into the Gaussian process. Below we use the Laplace approximation to incorporate this noise model." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Download the marathon data from yesterday and plot\n", "GPy.util.datasets.authorize_download = lambda x: True # prevents requesting authorization for download.\n", "data = GPy.util.datasets.olympic_marathon_men()\n", "X = data['X']\n", "Y = data['Y']\n", "\n", "plt.plot(X, Y, 'bx')\n", "plt.xlabel('year')\n", "plt.ylabel('marathon pace min/km')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We might want to use a non-Gaussian likelihood here. This also means that our inference method can no longer be exact, and we have to use one of the approximate methods. Lets use a Student-T distribution that has heavy tails to allow for the outliers without drastically effecting the posterior mean of the GP." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "GPy.likelihoods.StudentT?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Laplace" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: gp
\n", "Objective: 0.155064820671
\n", "Number of Parameters: 5
\n", "Number of Optimization Parameters: 5
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
gp. valueconstraintspriors
sum.rbf.variance 0.247079340096 +ve
sum.rbf.lengthscale 18.0531700475 +ve
sum.bias.variance 5.77057683482 +ve
Student_T.t_scale2 0.00664234394947 +ve
Student_T.deg_free 2.27411786114 +ve
" ], "text/plain": [ "" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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0hFPDPFNRFGVoUspsgOrVY3IciV3gqiYVoPrZ3hTm5ntfwLQcTj1mPp8+dfFE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\nN+zlPdftwiQ+92rmm5VX99FxjKkgMi0MpUhL996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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_distribution = GPy.likelihoods.StudentT(deg_free=5.0, sigma2=2.0)\n", "laplace = GPy.inference.latent_function_inference.Laplace()\n", "\n", "kern = GPy.kern.RBF(1, lengthscale=5) + GPy.kern.Bias(1, variance=4.0)\n", "m_stut = GPy.core.GP(X, Y, kernel=kern, inference_method=laplace, likelihood=t_distribution)\n", "\n", "m_stut.optimize()\n", "m_stut.plot(plot_density=False)\n", "\n", "m_stut" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### EP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we instead wanted to perform classification, it might be that we want to use Expectation Propagation (EP). Currently EP only works on a couple of likelihoods, namely the Bernoulli likelihood" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from matplotlib.patches import Polygon\n", "from matplotlib.collections import PatchCollection\n", "import cPickle as pickle\n", "import urllib\n", "\n", "urllib.urlretrieve('http://staffwww.dcs.sheffield.ac.uk/people/M.Zwiessele/gpss/lab2/EastTimor.pickle', 'EastTimor2.pickle')\n", "\n", "#Load the data\n", "with open(\"./EastTimor2.pickle\",\"rb\") as f:\n", " Xeast,Yeast,polygons = pickle.load(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will create a map of East Timor and, using GPy, plot the data on top of it. A classification model can be defined in a similar way to the laplace regression model, but now using GPy.inference.latent_function_inference.EP(). A wrapper for a classification model using EP is given by GPy.models.GPClassification()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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svNrH3Xlw9HNoeZ/xNKWEtX+D91MgbQGc9w5ctgqShhr3A7V4db0Npu6D5LHw\nwxT4zxDICCARoLBAu2dg52Pmk1wCRE2F/PfNtz9tqO1w4HQ6uXrKZBKshTxzefeT7YSeWlFYQKpz\nl/ZNwe7K54EHHuDrr78mM/tENTW02+3miSee4OVXXsNaQ40049IufPvNfPbt22usYnK5wI/x2VdU\nhNDLSqiBs4sg2vevO0FEN4P8I+baOqKUd4geLHa1OOjCi+6jkSUg9FxJCzCOfM7B/04/l8AqvxWi\nduB/VPUSqEXfilLB+YMFfYLQiXVAoh0MtwdoDqIGufqKoWwdhA6qPdSxr1RKDX/Sw865sGseTFwC\nF86HZoMDj7S2hUCXW+HaPdDpJlhwMWRuMN8/YZzysMr4xHyf8HHg3AauOqYQP2Wofq9Wr15Nr+5d\nObRjHa/d0Ae7TX2fUlpA6NmdKp0WLBbB81d244cv5zH1qsk8+fSzvPrKy7RKaUF4WCgOh4Mv577F\nqmfGlz+mys1KTFgQd41N5esvPkcaPUO3W2UlNIAsLsYSZlY7cLYRRLO2kHMUyuqQkjkqMQCCiASX\nQQU74UcFhQ/9aOQS9GMN8jEmCDOqoEC9kSoI4o+OIMypjoxcWV1oE0RB+fEa9gS5DYRGTY6SFapO\ngpaaMeMzaHa58RRLsmDlAzDyfWjU3ritGVhsSvU07DX4dgIU69fSqAYhIPU52PVXZXcz1ccBkVMg\n/4M6T/fUQeJ0Orn80ksYMGAAXRMsLHliNI3Cqz5jI881gUCetMP0atWYtc+O5fAbl/PghK5c0COJ\n40ePEBUk2PPyJH55egxdk2MrLl0Nt5yXyvGMA+w3KmPndpuTIAKodHTGCEII0VUIsUYIsUEI8ZsQ\nopdBW4sQ4nchxPx6XdRqhaatIWN34H1DY8BdCi4Tftr+CMJiN/5gpFFxIiOCKMB4sa4wJhvBTJsK\nSP48BBGMOYKwok8QehJEJprJ+OR2EB1rHy9epK1ecp2A3NWQMN54iivuhXZTIKGncbtA0eYyaD8V\nFlyi7YGjhbghENYWDr5j/jpR1yuCCEQ1dcoh8Hq9jBw2hGO71pHx1pW8eWMfLJaaO3gDzzUhkDqO\nC01iQmkWE0pSXASPX9qdpjGhlVXjNKSEyFAHU/on89OSpXRq346tW7fWrh7ncvmXIIqKsPwRCAJ4\nHpgupewOTAeMyiHdhSqBVn8ktYPDGkVm/UGIcinChB0iyI+KSfhTMRlJEEbVx+qrYvKhpAyzKqYy\n1Cv0P5DSNtMkAAAgAElEQVTmod6osEP4g5EE4UTbFqOTrVVu0yaIksUQNrL28aNfQONRYDP4wA/8\nAEdWQr+n9NvUB32nQ2gCLLnNvIdS6kzY/Qx4TEruwZ3B1gRKfqr7POsJCRw7eoQYbxbzHxhGVKje\nztzofTA6L0BKIoJt5BSaI9t2TSO5YkBLRrQKonPnzlgsFkaPGsV1117Njh07TKmYfMXFfxiC8FG5\nmkWjqtPUghAiCRgLBLAFMUBSKhzaWbe+UYmQbyIjrCMSXH5sEP68nIxsEIYqJqMIbH8qpsLysY1f\nsurt/wzSA5hXMRkZqZ1oG6mNCKKGislzXBUJCtYQqI98BokG6iV3Mfx8Kwx/A+zm9cwBQVhg1Edw\nfC1setlcn+ge0GggpP2f+etEXQd579ZtjvVEWloaY8eOxeUq451b+lfWJteCtCB0bRBUM1RXPy6Q\nPh8FpW5sVi27ggb5SggJsjNzck8OvTmZ1c+OpwUZrP5pAT26d8NnUoIQfxAbxD3AbCHEQZQ08YhO\nu5eABzDnYuIfyZ0gvY6urrHJkG2isElIHJRm65+3hoHXQFUlbOhH9hp5OJVhXOJTz9Wy6vlAFnwj\nj6o/GhyYM1Ib+aLrpdPIoFZsiiwtD5KrYSMo+h5CR9R+xqUZkL8e4sfqT23Vw5A4EFqMNvwF9YYj\nXBm+1z4HB3401yf1Gdj/d3CZrA0feaVStXlMeg6agJSSggID1S+wePFienTvSvOwUpJiIggNMlN0\nM3AHDZ+UfL3uAIeyCxmYqhVzpDGmlFCu4ooJC6JLi1heuvZcfp91EZ1SEvCWlvqXIEpKECHmywCf\n1pKjQohFVHfKr1DIPQacB9wlpfxKCHEp8B4wskb/C4DjUsqNQoihmHgSVUvyDR06lKFDh1Zv0KYX\nvPdQ4D8GIL4tZJqwX4Q2hWIDg7Y1VLm56qUFF8Eg9XazRiKtB+NHql2DuRJG0oneeP+rZUUDhZF3\nUlV40Jew9FR8aUCNYj5yE4hUEDWef9F8iJhQe4iMedDkErDpPJ9DS1QA3JQthrM/ZYhMhrGfwYLL\n4LLlEKPhqlsV4W3V/PfOgg6z/I9vjVaR1blvQuMZ9Z6u2+1mwvixfPfDYlauXMmAAZUxJj6fj8cf\ne5QVy5exdt16nrq8B3dMjMHiM+GxJXxIqZYll8fDNS8vZ+XO49isFh64sDPTuni49pXlzLiiDy3i\nwnjnp118umo/gxsV0j7cQ+umsXRLqeFWLmWtlc7t8VFW4iJMR60X6rCpQDqb8ZIunU5W7t/PbzVK\nl+rhtBKElFJDkaoghJgjpbyrvN1/hBBa8uQA4EIhxFjU1jhCCPGRlLJmrceTqFmztRaatoKSfMjL\nhOgAF7fGbWHjf/y3C0+EYoOdjxCqWJAnD6waQW2WEPDqqah0RFbAmCAk+jryCgRCEBL/hPNHgpHx\nuSrc6BOEnhdZOrWC4eQ6qOmX4StTevcmb9VoK+HwR9DpFe3Lugph8fUw/C0I/i8GLDYbrFJ0zL8Q\nLv/F/7Xb/hWWdSGNccS36EGYP1VHzDQ4OAJiHwFL3e1cPp+P0ecNJzdjD7Ou6s1D99/DitW/njQK\nv/XWm7z7xiv8ZWRbXrroAto3i0ZYDyK9ZhLa+QALLo+HIdO/Byn5+sGRfLYmnXd/3s2d3aDE7aXL\nvZ9jtQgiQx38ZVR7BkXlIQsyObe1Xl2GSobYdjCHnzdl0O3IcRp53Dj3ZdGjVfV+yzen4bIKLr5w\nHBFNmvLehx8RoiEpSKeTwd26Mfayy04ee/LJJ3V/3WklCD/IEEIMkVIuE0KMAGptzaWUjwKPAggh\nhgD3GZGDKQgBrXvCnvXQO8Aq5AntzEkQYYnGEgQognDnQZAGQYgQkMe0+wmLgYHbiCDcqF2y0SMv\nwbzKyFk+1h+lOJA/+DM2VsDoHmsRhBfN0q1yPYi+1Y+V/AxBXVV9hKoo2ASeQojViIsAWPEAJA2H\nFAP10+lCpxvgxBb4/nK46DvlEquD3YeKWbc8iKKCwTzzVSKz//4SkyZN0h87qAME94C816BR3ept\nSym57bZbyTq4m+8fGUGow8YHyxdy8UUXcvHES/n0449YuOhnvnt0NIM7VKoBhdVVnSAcYSqPVa3o\nZ4lPCvo/voAQu5X5D48iJiyInq3igF4EZX/Ev+8dQXaRh+yCMtolRiGEwHZ8F98vO0bzWI0NWZWI\n6cISFwvXH8TnkwgkHgk/b8ogKS6c+KjqBGD1SQ7v30b+7q3cctP1fDRXI/7E6UQEm9/UnUkbxE3A\ni0KIDcAzwM0AQoimQohvT+uV2/SCvesD7xffBrL2ludEMUBIY3DmaobSn4Q9WpUd1YIIAZ9eQjij\nna4H/QXbzG4/EAnCn73jj4YKgvBn6tKTICTaTgJHUT4YNe6rXAeihhtq0XwI13BhPTwHkq7Sdn0+\n8COkfweD/+5n3hpwl8Fvc+Gz2+DAusD7V2DQbEDAiurR3W63m6eeeorQ0BAGDxpIu3bt2LwzhuvP\nc3D78EiumnIljz/6sPHYCS/BiWfBfTDgaR06dAiLxcKcD97no9sGEBMWRJDdytf3D8V9dDtTp04l\ntuwQS5+8oBo5AGB1gdcBjjBsbYZhb3ce9vbnY03qUcMN1cfKHVmEBdn4/rHRxITVlHRUJcG4iGBS\nm0VXurJKibAICsuMswinHS/E5ysPtpMghSK9tGPVbSn3X9gFG/DslF6sfGos//r35+Tk1Lb3SKcT\n4ScdR1WcMYKQUq6WUvaSUnaXUvaTUm4oP35USjlOo/0yKeWFp+TirXvCnjp8EEHhENYI8g4Zt7NY\nlStgsY4UAGCPURKEZv8QZcTUPokxQeipP8wQRCnmF/1SE+P9kSAwJ0XoEUQp2mlO0qlV3lWWqLri\nonP148U/QVgNA7PPo+wPSVfXvqQzHxbfqPIrBQWQ1TU7Db5+GJ44B36bAxEJ8M4l8H/DYfsPgaf8\nttiUPSJ9IWypVI89+MD9vPfq37m0dxJFx/azafYlPDHxXHzuTtw3oZR9r0zizddfZfHixfpjO9pC\nzF1wfJrpeRUVFXHpJRM45xxVWfGOMe1pm1h5fxIbhfGvuwdTNHcqb94ygF6taqt5hM2F9DiwNe+J\nCC4nfSGwxDTHEldZ7vez1Xs4nu/ko2mDCQ/W+/a0TaeNwoPYkF57ERdVJIiw4EqJTCBPbl+qHgco\ncbqxCWgcHUp0WBB9UpuxZMmSWmP/YQjijKJtb9j1a91y38e3g2MmMsKGJUKRQQ1se4y+R4cINSic\nYkXfw0npQ7XhxH+8QiAE8WeTIMA8QWipUfLQdjHWSMYnNyrvpaoGancG+HIhqFP1tlmLIOQcCNcw\nAi+7C5LHQAtdU18lXCWwdh68Mhqe76UC3e5ZCdN+gLHTYcY+6Hs9fPUAzOwCq942FxRagaBouPAb\nWPMEHFrC7t27ef/dd/jqgeG8fvNAVswYTasm6v64XR2wWLOIi8rnlevOZcyY83nh+Vm1A78q0OhB\ncO2Bwi/8TmP+/PlERESQs28De1+exGX9W/HFrwfM/45yCKsTKUMRobXtKpYIJW1c+8oyNqRlMaJT\nEi0aa1ULVGohPY+k6PBgNqVlsyMjr9pxNQHVJyUhkoRoJX0KCRJBdHgQ7ZqpeS3ccIiLXlzGmz/u\nwAfsOqoki8QoB5mZmbUv63KZLhYEZytBJCSDzV63gLmk7nDIRBrkqNaQb1ADO6gpOHXsFNZY8OrV\nrTBKTW3H2FXTnxOYPy+oqjAy1v5RYUSwoNQFemq4bDRjHdgJ1KhfLVeB6F/9WPFCCB1ZW4106F1o\nfn3tYXd9AkfXGKuWpIR9K2HeTfB4Evz6IfS5Fp45BBNfgoS2lW2tdjj3Knhkkzq35Rv4awv46iHI\nManeiWkLo+fCj9fw5j9mctOINrRpqiXZ2HA7e+II/pVxPZNY8PAonp/5NKltWzNz5kyysrKqN7cE\nQZN3IPMOVa9dB2vWrOGaKZN5+Yb+zH9gGE1iQnnh6t4czC5i5Q4DaV4DIqgIWRaqWdfFVVbMgMe/\nYd2+bB6a0J6YMD27nReJVTsHlvTRrlkMoQ4rs76q4nYvZbV8SxaLYNKgVgzo0JTY8CCaxoVz5ZA2\n2G0W0jILufTFnxg28Qa2btwENht3f/gbc5bt4evf0khOTq59XZ9PZZQwibOTIISAriNgYx0iNVv0\nhoMm1FMx7SDXwKAdkgSlOhKGNQ68enEUUShdtxaCUPmAtGBUq6ACXswbnQMhkz8CJP4JwoW6j1o7\nMJ10GuwEasQ6+FaBqJHKu/h7CK/hNOHMUjWnm11R/Xh+mpIexnyiHxBXcBye7QSf3AyNW8OjW5S0\n0PtKcBjYmYSA1PPgL/Phvl+UHe1v3eGdS/3aKZxOJx8syeDn9HC6Fc3lsr7Jum097pYgrdjsexmQ\nmsDWFydwfZ9Y3vjHLOLj47nxhuuqF9gJHQDhEyGzdhbbvLw8Zs+ezfgLxvDWTX25bljbk7r+uIhg\nEhuFsWa3yfxR5bAEFeJzhuE9sb/acenz0vOmv5Nb5GT1s+OJjbQg9TZK0qMbsySkT6mihYWJfao4\nMPh8tTK2Bjts9G/fhA5J0ZyTEEFYuSrrtR93cfddd/LYY4+R2rYtFquVceMv4ta3V3HbtDs5//zz\na0/J50MYZYSteR9Mt/yzodsI2FQHgjinl0mCaAt5BgQRnARlOlHZtsbgzdI+J6JAGhGEXvyEUbWz\nChil+KiJPyNBCIylLL1AONCOli5BFXBqWeUyEuRqsFQhCOnWtj8cngNNLqpdNW7x9dDrIYjvoT0V\nnxc+uBK6TIDHtsHIh1Q24kDRuJWSJp5KhzZD4fUxSiLRwJYtWwgODmb2kw9x94cZXNLVTpcEIxWV\nwFXWB0fQ74CT8GA708Z0ZMdLl7Bx9iUsWzifC8dfgNtdRSJuPBOKf4biyuC8jz+eS3x8Yz596++8\nc2NvLuh5Tq0rJTYK43i+nk1PCxIRVIh0RuA7th3v4Q34Co/jyz3E9pUL2LMvnRtHtCMq1IHAhZTa\nKhshPUi9oFafyrcmpawejGdU80HKahLm2rQ8zhs5Sv3D6wWLhQ/nzsPlcjF79uxKg3i169YmICOc\nvQTRdThsXqpubCCIawnOIrVDM0J0W/8SRJmeBBEL3hydeAcjCcKBvgRhlHWyAgYpPqpB8ucjCDPS\nUwmBEcRuoBXVVXF7gGAQzSsPla4Be0uwVXF5lhIOvgvn3FB9yGO/QUE6dLtbf5rfzVD/HfdU4Cm+\ntRAcAUOmwTVz4Z2JcHhTtdNlZWWcN3woM6/sza/PjGXNcxOxNBqMo2i1flJKiw1ieuN1dMcRXj3N\nWusmkfz42Ei2rv+Fm2++mfz88vfdGgFN3oCjN4OviPffe4/777ydbx46j2XTRzOya5LmpTomRbP5\ngMliX4CwlygXV596br7cg3jTf8F7+HdaR6n1IjqsnBSEG3QIQkkQOu9UuQTh9UmC7FXaGC3gVQLo\n/rV6P9sOZDFs2LDKfuWqI7tRNHUDQZhEbCLENIH9GwPrJ4Q5KSK6DeTt0Q9qCzZQMQk7WMJ0auJG\nYqxi0kv8ZUbFZFaCqEg38Wd6ffypl8A4UWIWtaPKt1PL/uBbVV16AGV/qKleyvtVSRaNasQ+bHoZ\nuk5T6gktbPsefnkfps7Tb1NXdBgNl70Mr49V7t7luP++e8nMzuHOsZWJB32ORLz2ZjhKNL4TWxC2\nNsOwJnbG1+RWbLYDWOOq6/Hjo0L48LYBfPDBB0RHR1NYWG53Cz+ftMxz+Pmzflx/ww18etcgnVQV\nlRjfszl7jhmn2KgKS1g2slQ76M9SvrgePqESDwrhQkrtBVngQeptoqTvpDTg9ckax3VI3adSbRw+\nUcxD835nztyPCQ0tfx/LJQi/aCCIANCtjnYIMwQRFKmS9hXpGKKDm4LzuH5KY2tjbTuEiAKp97LX\nhyDM6OAr8GeTHsCc9KSnYtIrCLSDWvYHubq2/aHoewirThBZ6//GC59mMWb0efTu1YtOHTswok87\nCjd/yjurfeTn5zN37lxee+01nM7yZ55zEOZeB1M/gUi9srP1RI9JMGY6vDIS8jJYu3Ytr772OgBN\nbvyY7Ycrd+qusF5YXRlYXNW/AUtsS0SFHcQagTf6ShwsUobyKujVqjE7/3kZE/u34bZbbgJgwYIF\nXDBlA91TdvD5XztruqjWRHJ8BEWlbspcxjEHFbDFpOPJra2qqorLByi1oRBuXRWToQ3C50VaLLRo\nHM5rP+ysclwi9RZwn49tGfmM+dvP3H7XPUycOLHaOTPG5wYbRCDoeT78FkDN3Aqk9IN9K/y3i+0I\n2TqJAS0OCIqHUp2YClsTcGuRSxyQpeOiG4Z+bWU7+uqnQGGWSP5IMEN6eskOc1AuvzXdfrcCNdJ5\n+5aDqCIVuA+rILCQPicPHdy/FVvW12zZE8bA2AKCiw+TElLEI/3yWHcknJvueJDo6GjuveMv3H77\n7Vw0fix7tm8he9ZQ3IPvhNY6EdenCgNvxtP3Ro7/tTujB53LQxO6kv/RNXRLiePl77ZVtrM4cIX3\nI6hodbXofxEUjsvjZfOBHI7klOALH4GUHpbsWsPeo9Wl46TYMF6/oQ+/rfiZRlERjBs3jgcv6EFI\nzkAmTDgEwr+KOCU+grjIYP721SbDdh6PDxGcizXiCJ7cZM02Pp8PISCnqJyURRlIbfdxId1IoWfA\n9oKwcnn/FLYerOLu7tOvBbPrcB7fbs7k1XfnMH1GjXTuPgPJo9p1A3Pt/7NtAwND95Hw4jWQfRji\ntPWXmmg9RBkBXaXgMIgFiO8Fmev1UyCEp0LRTghNrn3OngLu9NrHRRgqQC2H2rWjY1AFf7QQitKh\n60GgXgejYLuqODXJdf93YCZOJA9oo3E8A6j5/uQDx4AqrqTyMHCieoBc0bcQPhaEDSklP/30Ewtf\nH8/AVMHrN6r4hrvHdQLpJjTnP5RGX0DR3Ejyip1EhwVRWOpm0j+Xs+KOLoTb4YZXn+V45t2VqofT\ngPnz53PRRY/zxnkO9twURXDvTmCxMK5HEh+vrO7143Uk4bPH4yjeiCu8t/rJOcf5cHUeUkqcHi9u\nj494e18ubPExfe7dxcYXLie0SiBYaJCNRY+NoPW0f3HLyFQu69cSb67EF7sXe/w23Me7qIa2YKzx\nbRDBUciSXLxZe05mM/jblN7c+Ppy5q87xMLHRhMdZsdRnthu8ebD3Pr2Go7mFrPsI8GWj6OY2lk7\nCHTO8r1IyUn3XYsowSe177XwOXVzSAmvB6x2Lu/fnEc+XktaZiEp8RG6koDPJ9lzpIChI89n0BiN\nFEFGxu2q17VakQHYXf9s28DAYHdA34tgpYkEfFUREgnNuvqXIhJ6QaaBKiq8vSIIzbklg1sntbhI\nKl9saqIR+gQRhFKjGMVJ+IujODkBE23+aNArF1oBiX49jQygppfQJqAT1fZgviUghlbfIRbNh3CV\nIGDhwoWMHDmSO8b6mLfMwayvKu1jtrK9eO0JSKsKNosuT+kQEWJn0dRmTOkaybSVVoqKS3jppZfM\n/GClt968FL76pyrFCxw5coSrpkxhwwaVyTQvL48775jGq6++Sn5+Pm63m0ceuJd/XNeXKddcQWRc\nHEG7l4LPS6PwIJzu2jY3Z9i5WJ37sLiVyvSiR9/FVXCcaWM6cOPwdng8HgY3aUR8eArPXu3g2leX\n1RojNiKY0CAbU4dWEK7AdbAv9ibbEI5CsFixtRqk1FdhsVgat8bWatDJRfOi3i344fHz2X0kj5a3\nf0ajqXPJLiij2wNfMuH5xdx+fnv2fNSDJrFW7pqdh8ujrY76Zp2KCSlzeVGp990gdTIKSCeyZrbe\nk/feg7TYiAx10CMljns//FUFCurYEv7y7q94hJ1+g3SkQ5MEgdXqP1VQFZzdBAEwaBKs+Ffg/VJH\nws5Fxm0SesFxI4JI9UMQ6Todm6FdXykGJVloQeBfijCqQ1FzrLNNgqhwH9ZaDPQIomv1Q3IJWIZX\n/ttXhCxZyUtvb+fll1/m6ilX8q/7O9M8NogBbbvx3pJyQ7D0YS/djjukRpQ1YCnMxHFoI94O55FT\n6mPh4+fz+OOPM+22W6u7iJ6cg4Rdv8Fb98DUc+Cte8hduwjvTan8cmlrrujZio/nzaNHjx5cOnEi\nTZs24aevP+G9f84kOjqaKZOvIC7IzQ3D2yEsFlytBoCwELR3Jd1TYjl8opCfttRQjVqCcYWdS1DR\nKpBeTuSXEJv9O759K4g4sZkHOxwnJbgQj6sXVw1zsT3jEG3v+He1Ie58bzVlbi/xUZX3X7oicB/r\nhOOcX7BENa20a5RDBIUjIipzLD335SYiQ+0nvZ2Sb/uUlgmRHHpzMnePb0vLrjtoUnIeIXY7X+pE\nX+eVuJg6rB1JsWEIUYKUIehtmITPidSTIHwesKrNw6f3DuP3/dnM+PdGhM+HrCFBbEo/wZIdWUwY\nfyE2h8E7aoYgLJaAPDcbCKLbCFWjOjPAZGBmCCKihar5oGeoNiQIHRUTgGimI0GEoaQEPZ9vfwQR\niATxZyQIoxQEFaVYtT5CLYLYCHSv/KeU4PsJLMot8ejRo7z09Pn8uKKQt//vFb567yVuGJrChL4l\nuN3tuKxfK4pKXTz+yTqsroNISzA+e3UvKeEqIWj3UpytB/DvjdlEhTro2yaejbMvYeFXnzFr1izK\nysqJLX0rfPgY3NAaZl8NoVEcvWMO9wcPp9HMBcTNL2DNgeN831uysi+suakTZQfWM/Py7vz23IUs\nnz6Kbx4eRZPSPXzwl35V6idbcLYZgnCV0NW9i8cnduPaV5bVsiV4g1LwWcKwl24lPMhGVkEZsjQX\nWXAEq1SbEq83lG3pzXh+KkSFVao584qdzFuxj68fGnky7UQF3Mc7YnEUY43QdikXNvVM1+w+zvcb\nDvO3KX348oHzOPr2FP7v+n58dvcwYsKCcCRuwFuQhNXZhGGdmvHpqv21xvrblxv5ZXcm947rWP7T\nS5E+fRWzMJIgfEqCAGgUHszjE7vxwZJd5RJEdYJYufMYo0eNxmGzniSVWjBpW2hQMQUKmx36XQwr\n/+2/bVW0OBdy0qGwdr6TkxDCWM0UngqFOnmdjFRMJIHUkiAExmqmUJQnjh7MEsSfEf4kiFy0a3X7\nUBlbE6sccwPbgC5VjqWh1FipHDp0iIsvvpiuKfuRxS1ZO3Mc8+8fwl8npmKzH8Tjbk1UqIP7xndm\n3qp92Eu31pIejuYU4t68CE98W7wxzdmUnkNiozBsVgutm0QyZ9pA3p35BE93CmHLIEH27X147f/+\nwbzkCXhe28qu3pPpfP7F/PjFx6ydNYE37xjO2KvHwGWX81lBGAkZacxPzub2RDeUe0kN65TIc1f2\nrJVmGquNstQRWAqOc08nN71bN+aReWurtxECV3hfKNqKqzSbUnftReqJz9bT76F0RnSxsf6FylTo\n364/REJMaDV31qIyF1NfWUr0tXMYelM+zpCvEKJG6hzpw1egUmwczCqiReMIrhnSGlCqueuHt8Nu\ns2AJycHWKA1XhsquO6l/Mos2ZzB7fqWDyVdrDzD7my28cE0fWiZElv+kEqSO/QGMJQi87mqLfYnT\nwzmNI5SRukqJ0zKXh7eX7GfU2HHg8eh7KgWiYmogiAAxaBIsnReYhd9qU9Gl/qSI+F4quEkLwYkq\nrbdLI++SvTl4j4NPw21VJAF6GWUboa9mCsOYIGycnRKEB/V7jHw2KiSISsz7eC79+rUiK6tmIaZd\nKIlCJXA7evQor79yCXv2JfHqa6/yxeef88itkxnWu5jhQ+5HhDYCwObYg9fT/KROu9TlYUwHG8Ln\nxOuoElgnJau+/Zqlu3N5cIUywrZNjMLlqdQtdwtysX+UgzuGpkD/AYzbF82sg4Ip0/+O3eGgfWoq\nd49ux5qnx9C+WTQX9DyHpNgwsFi48NLBdPrJyermnRH5eYTO/xzHr6sRBQZ11m0OytqPwpG9n+kD\nQqplKc0pKqPr/V8y4/NdLE5L4I1JkrvGdKg1xGV9Uyh1wZ1veckuWUpF5P/nv6RxXmcloXk8PjLz\nS3l14Xa+XnuQEZ2b0T2hA3c+68HjeRqrZRaQjfQ48RxaDx4lQYU4bBzIKiS3uMb3ZHXiaLEK15Hu\n4FH3/YIe6l7P+FdlzrUbXlvOoNQm3Dqq0m3ZYsnH59Mv0askCG37hPB5kJZKKamozE1okA3h9SGr\nSBD3f/w7qV16ccUVVyjyMIptMUkQDRJEoOg6HIrzYecvgfXrfCFsmW/cptkQOLxU+5wQENkd8jWS\n/wmbiq51aSQUFG1A6kVpN0Wld9CCkXQBikDMZPC0oVRZfxaSqMhia/SBnaCm19iWrdto0UKwfPkB\n2rRqiRACIQQPPjicAwcq1UE3Xn8d8fGbePrZdWTs20WTCCvDO+UiZRxYmmJt0hGQ2O27cbsqA+uW\nbj/GTec6cYd0rGbYth3bQa9YD+mxPXll4Q6O55VQ7PRgKa9XLPLzCF65jLJBQ4kYNoSWXdrw0xOj\nWPTEWC7u25Ipg1oREx7EnWNrxGiUo1/bBB66qCsXvLme/F79KB03ARkaSsiP32PJ1kkBA+AIoaz9\nSPraDpJgLT0Zd/DYvHXsO5bPSwu2Mu6Vw0SHOYiUeyEoopwc1by7pcTyzcOjmLdcciCrDJtd2WA2\nH8ylaXQILo+HTvd9Qatpn/H0fzby1OU9+fz+85h5ZW82bIgmrn8x3qwy7JY7ELnPIwsqN1FdkxsR\nbLdy0axFlVljbaUEt12Ir6QJPjkaS0J7RGgjHDYr/7lvBMDJfFBen48SV/WF1WLNwufVj8MQvhKk\nRVsFJTwupK2SIMKCbJQ6PeD1nCwbOmfZHhZuyeTDufOUSs/jURqPekA4HOAy7+7eQBCgxK4L74Sv\n/hFYv3YjYPcSY8kjcQBkb1RlIbUQcy7k6kgYQZ3BqVFjWKSC1LFd0Bx96SIWlXVUD+Hox1FUmwDm\npVG1TWoAACAASURBVI0/AvRzLKnFxIdWttbRo0fTq1ccEWUOLu0ayUW9W/DS1L5MuaQx9933KQ89\n+CAtWpzDtk1rmDDWzsDYnsy4ejAX925OaPBafL5+AIiQSCyWEyAkHncc2w7l0uTGjyksOE6fZAue\n4NYnrylcJTgObeSyH600jYtiVNfmDHvyez5bvZ+x3ZtDWSnBSxfj6t4TX5PEavNtFhvGnGmDSYgK\nIT4qBKtBwNT53ZMoLV8QZUgo7s7dcPYbQPCyn7Cc0H+HZEgknuRezBkpaXX7PLYePMG3vx/iqwdH\ncuL9q9k0+xKatRmLw7kV+zmdsLUahC115MmaC8M6JbLw8fP568cO7EEbABelLg/PfL6BuOs+pkl0\nCPteuZz3bhvMdcMrXYiHdUqkpAwufziP0h0XYAnLIqTDV1gj1bfQonEEq2deyNaDOXR/4CuySrIJ\nafc93oKW+EIfxZrYFWt8W+UJ1bg153VREkuFLaJZo3ASoqsu9hKrLROfV6dssZQIbzHSovFeSanc\nb62VNi+LRZBdUHpSjTTj88089u8tfPvdQho1UhImHrdxzWkTGhARHIws08vXVhsNBFGBkdfBxsWB\nGasbtVBFhI5t129jD4WEcyFjufb56N6Qt1b7nB5BkAB4QWrt5poBenUo4jg1BAGnNvDuTEM7hXdF\nRbJevdrgdtuoaaPo3bs3o0a1oW+XUcx46G4+mXENN41sR5eeDia16cLzL7zAwYOHWPl/3aE4iinn\ndkaW5gI+LJZf8fn64vNJ8rKOIax7+W1XJJNeWkKfR76m2Olm4Z1N8YV2qBaNaz+yFU98azxBEaRn\nFfH2XwaQmVfC2r1ZjOvalOClP+FJbomnlVa8hkKz2DCExVgdUVTmJizYRoij8treZs1xntufoKWL\nseTopaMHT+PWHCiy8lQvSd9Hv2FAahOGd0rEarHQMiESR1I/vM0nYNv5ulpI7SFYm1cmHkxuHMGS\nLS4KihOwB20GCQ9e1IWwYBsfThtMfFQIk/q3rFagp1frxtitFn7YeJgvV+Xg3DcC16E+OJqvJajV\nYoSjgLZNo8h+7yoaxZYR1ekH3Fnt8HmvQNirP3trfDtsdgfxUSG8+oP6tgtKXVzaJ/lkG2HJQ8qg\nWjaIzPxSMk4U4/O6lIbAouH44CvP0VRFXeT1SQ5mF+Eqc7Enu4R5qw+xZdsOevasUnXQayBBCGGe\nIJx62RZqo4EgKhAaASOugW9fDaxf22FKijBC0jDIqO3bDUD0uZAXqAQhVMEZqWXg9idB6H/YgRGE\ngz+zBHHs2DHap7YjLiaSQf1bseDbX3juuefYv38/x44dY/bs2dx0042ktgsh2JKECInGmtQDW3I4\nvsIgLujUkrwPr8Fhs1AYuR/v0XId+tFtCN92lEorifm/7qX7tU+R79zJtf/MoMzlZeaVvfj2/v4k\nhubgDq4sFCRcJdgy9+JO7MTg1ARe/3EHWw/l8txV5/LkpJ4MytyJjIjE3aU7enC6vXzx6wE6/j97\n7x0eVZn3/7/OmZZJ7z0hJCGh14D03pQqCIoNFNeOYBf72ta6K7bVVddeQMUG0jvSeyBACAkppPcy\n9ZTfHydtkpkQXZ/vb59n931dubiY+54zZ86cc3/uT3u/YzpWoIsP9cVib1/yLMfF4xg8FNO2zQhV\nniRzBR4/6s2i3gaOLh/MV0vHNoe/AETfMJT42eCsQSzWnh3BK6B5Rx0b4sOYXtFc/XItesM5YkIc\n3DqxO0XvX+demAd4f9MZuscE8uic/jzVmDuQa2OxZsxCqY/A3GMthugj6P3K2fKRynN/F5BKe2lE\nhG0h6sFg5vL+sZzM075jTYOdYakt9CU6XQmy1OI92J0yK3dm8cnmM3y5PZPVu0/gVDsKL7kajnc3\nneWl64ew59RF1qcX8+XKb4iOdvUAcTo9VzF1kpRRMJn+60H8bsxYAhs/BFtHidw26NYJAxF5GRTv\ndz9m7qLREFjdVCWZenvwIOggzBTHfz2I3wKp8c+EqqrU1dWhKAqPPHgfz963mIvbP+HVJ24gNSqR\nTT9+zYrXX+fdd9+loaGBJUvmoSpemnZxI3RxEkqJtuisO5qPQ1IITCxBLmpMMttqUWtWIVV1Qco/\nzFtvvckto1TKagx8uXQ2a5ZP5p4rejMpqQqnVzcUjJwvquHI+TKknGNIYUmoRm+emj8AnSgy88WN\njO0ZySOxdgSbFfvQER0uFk+uOkJmYQ1/uW5Ih1fFoBORZKVZD7k15PgEHIMG47VtI0KNe9ncChsc\nMvSkr/UUguS6Y1WdFhD1yN3vRnf+E7BXalU9SotB+uvCIWxNr+K+D518/6iOiMCOY+/7z5Xy0V2j\nuX50MtnFNXyzp7FMVdXhLOmDNWMmoqkOr5T1NFwYxIovnDgkGdXipqBDsoOjnqRIf2RFxSFJGHQi\nmYUtSXqdrhRFbjEY+86UkFfWEkbWqRaK6zz8DpJreAmgsLKetYfz2HXyItcsvIkxY8a0f58sQUdM\nrZ30IJT/GojfiahE6DUKtnza+fekjIOsHR13J0YOgdIjLg9AMwTBsxdhSNRov2U3D6FHDyISzQi4\nW7wD0XbLnnb+TVxOnUk+/+/1IGwuD0gTQ6tA2sAB+Pv7o9PpKC2r4OZZ2kMqeEvEBUVz+223ERQc\njF4nIggCEWE1iEqsy4Is+hcgF2sG4nxxLclJEBgESlVTgltFH3ABqTgYR3kex84Xc8tkHd3CB9I9\nprFKSrGht5/HaujO17uyWL0nm/0ncjCUn+egXWv8Cvb14virVzIjrQvff7oBXX4utjHjOyRskxWF\nL3ae451bhhPla0SXmY/xx1/x+mAN+gOnwdHye4b6eyEIAlYPBHdyQiKOAWl4bdnotrpJLwpccPoh\nhSViOv+ry+KllGWBIqP6JaJET0af+Q/k0rMuzMep0YGkxgTyyyFfooNiMJk9bLCAMxerEQRIjQ4g\nzN+L5Vf256Z3dpK69Jtm8kDV6YM9ZwyW4wvwdaQS4m+m933fkXvmBGqDKxeSdPEYqCpS4zP9+c7z\nmAw6hqe2eAyivgS5lYHILXXNMfobnZTX69xeP0Fu70HoRZGdp4u5Yd4cohKS2r0H0AzEH+BB8N8Q\n07+AOQ/ANy+Bs5MXMTAGfMMg/7DnOaZA8IuHMg/U4kHDoNKNEIsgamEm21E3Y71BdUcEqEeryXfX\nCSqihZk8aVkY0Bb+znhQHTHH/ntBlmWeffZZRg4bTFhIEGazGX8/X15++WUcjiqqqyV2797NyNGa\nQdDrBD566Cot/i6oCF4Sb67ORPQLJy05HElWSI70w2zORicnQFO5ouBA8ClCLtUI/T7dcY7p0+Dr\n1Q6S7/6Gbvd8w/S/fUV+RT397t7BhmP5BPuKxIZVIkktutUGawaSMYET+VYulmse3UjfUo5bgthy\nuooGW8tC/umsrtwVbuWfhkQweaB8aMSJ9AKuN8vMPnMW71dXYvj1JEpEIM6x/dFdKMb79W8xrj+A\nUKmxBRv1InVWz5sAuWsSzn4DNCNR77pA2iUZq0PGGTcAwdGAvhU9uGqtxpm1HaX8PM6AYVCThXDR\nlVU5p7SOU/lV/PzIFER5FDpdWXNVU1v8bU06o3pGNzfvPTqnP5/dMxa9KDB0+U9kl7RiP27UeOga\n5kdhpYUxT/zEka0/IGXvRso7iPPMBtTG3onF47Xw3pNfH6ZPl5Dm4wtiDaCgKi0a5H7erjv7ILOD\nBsmESd/eYAuSHVXfks+6UFqHU1b4/PPP6d4lFkweeiucHSSpBaFTFBqC2Yxi6bzW+H8NRFv0GgFd\n+8LPb3X+PX1nwYkfO54TNwHyPVCLh06A8s3ux8zDNUGZthDSQD3sQW8iFa0W3x1i8RyCAs2AeOqj\naI1LNd39e8DpdDJl8mReefF5ZiQJfHHnMHL/fg33TEnh4Ycf5sCBLcyfv5hRo0bxxhtvsHBcdyIC\nvNl7WrtGgpdERaWESWdgcNdAJg9IwNukp8ZiIyikCLkqVAtJyE5UaQ8XzkqE3vAl/e5fTW55A0sX\nezPEewiPz+3Pi9emcefVXpw4EUBeeQM3vbOTxZOMyFJUC5+PYsdgO4vTuw/FVdqD7C866Oddxe76\ncGRFobxW84DE8jLM+3/lY30XlqxKbynfbES9xUH9+SIM24/h9Y+f6ffDdmYFG5B6d8Wy7CpsN12O\nNLQXcnIs9vnjsN42A1Wvw/zhWkxfbmZGgJ59baQ688vr2ZFeyMFzpVjsElJSN5w9e2tGwtJyPzic\nMvGhviDqsCeNwpB7iG2HM1s4juz1yEUnkQvTsXsPwdhwoLnnJ6e0jjFPrqFnXJDWm4EBm3UsRtNB\nBLG9N11V7yA6yHVRvXJIAidem8OAxFDe2eBaRPL5ziyO55Zz4MVZTO4Xw23v70FtqECtKdRCXY0I\n8fPimasHUW9zcsv4lqS/Xp+D7EygdVn00NQI9PqW5TTEbCckOMIl99IEwWlFNWi/d155PWOeXsfj\njy3nuuuuA2sdmD30VkhOjT/OHUSxUwZC9PNDre9sGPn/RwMhCEI/QRD2CoJwVBCEA4IgpHmYFyAI\nwjeCIJwWBOGUIAiXuZv3h+LG52H1a5pL1xn0nQ0nfuh4TkcGInAwWPM0fYi2MA8H66/tXxfC0Poa\n3PVDdEfTQnZ7InhOYsOlS2GbYEQr//z3DDNZrVYWLlxISnIip44dYO9z07n78l6M6B5BiJ8Xy6/s\nR+2Xt3BZWg/emp3IV8vGkRwdzP3Te3Lv9N78+V2ts/6irYr8ApnFV00lOsiMGBjNgH59CY6so6xM\nj/PkDpwnf8KZ8Qui+SSfrirF5pS5fEAMIWEy8V0lEoRUFo1LYe7QBOZOVpjYZRTHX52DqsLyq7yQ\nnC1lrAbbaSRjHKrOr5lWYpRfKUcswdQrBnSiqIV/amsw7diKfehInEEh2CWFtUe031WSFbZty8Cw\n4lv0q7aRca6EylH9iL4A5hsnIfdNArMJSVY4mVvBjpOFZBXWoPj74Jw4CMuyecjd41kRJTJkzU7E\n/Rlgd7L/bAlf7zjHgcwStp+4yCdbzlBrcSCl9kBKTsFry0ZoDN8lRfrx1voMrnp1C9f/8xh/3uvE\ndH4Pcbd9RY9l35F410pCb/qMJR/+SnqxEdkYi9FyGItNYtKz6xiWGsGuZ6ZrF0UQEMKGIwVej1fA\nQcRAV4GgaYPi2Jp+sZ2B1IkiVwyIZf2xi9RaHOw+XUzfB75n6Ud7eem6IfSMDWLuZV1aqLvdYOvJ\nQiRFZePxphyhit6Q4+LxAUQF+3Dj+FTSuoXTJyGExFCVrjHuNSUEpw3VYMYhyQxZ/hMLF9/Ks8+9\n0Hjj1oG3v9v34XR4rmL6DQZCqfNQcu9ufqdn/vF4GXhKVdUBwFPAKx7mrQB+UVW1Bxr7mQduij8Q\nXftAaBwcuUSXdBO6DIGGCig953lO7Fgo2tvc2ekCUQ8hY6HMjQHxbvQg3HkK4hBQ3FVA/asGoqNK\npyZ0hvzv/z0qKysRBAFvb28+/fRT5vUPIv3V2SSEt9+VGSJjEGvKiQkwMSOtC8denklihD9XDevK\n6TNn+dPyV7AJVeiVILylGtT6MpSKXBpqKoiILGb116eY9+SnDH/sZ3LL6iCihp/WaPH4ijoHC+bp\nKM8KB1ULM4je5aCKKNZgYoK9SYxUUdQaZKmRKlxxYLCexumtUXT0SQimW4iOXuZqfq3X4t/De0Ti\no0p4bduMs98A5Ng4lk3vQ8+4ILKKtFDK0eN5DN97jD2hYbyZ0oMfgsP5qcxOoL+ZvDJt9yjJCl/v\nzGLdoTwOnC3h+73Z/NLIVIpBjzQwBb8H57OkUsRyJh/zim8Qtx9zySXUW50cOqdRzTh79UGK74LX\n1o3gsPPB7aPYfrKQHRmF1NlkjimxDE8KYt1NCdw9tQfXjkxiwagkPtp2jsuW/0ih1Audo4Db3vqO\n3nHBfLZkTLMUpy66L7rwFNTAaaimJIzehxACW+jVF4xMpKTGSllt+2frtkndSQj3o+tdK5n50kau\nH5XEqb/OZfEELXwUFeRNea2VExfc3/PbT2kstweztXFBrAZBctsgF+Lnxbi+MUwdGItJaEDRuV/o\nmzyIHw7kkpiYyCuvvtYyeCkPwpOB6CRLq+jr+7/GQChoAsugZU/blfEIguAPjFJV9SMAVVUlVfUo\np/bHYtJNsPnjzs0VRehziTCTKQBCekPRHvfjoROh3I1B0keBLtBDR/UQUD0ZiLO4TzZ3VOUEnTcQ\n8O9kIF588UUEQaBbUkuC79grV/LU/EEutfytoYuMRS5ubyxD/bw48OJsvtywj4hoE1TZUW1NiViV\noV3MDOgPX3+VSVZxDUVVDcz/+zrqFCtHj1qZN6wrG44XMH2ajDOvS/NxNaWyBEDruL55okBucQRN\nj6HBdgbZGNNM6W3U65gXW0NtYBJDenVh4YRUhqaG47VzK1LXRKTklkYxp6zia9aD3UGvrQc5HhTE\noeAWhbv8snq6RQWy8bj2258tqKao0jVEmJFXSUlVy+/pkGU21ymoCyZQeO0UUqqrmVRS5GIkKuta\ndt/OvgNQwiPw2rWDxHA/XrguDZ0o8PmSMXy5bDxCjzGMNBVw99g4nluQxps3D6fq4xsRgLXHinl1\nuzcvXG5l5bLRGjEdgCAiBjXuxAUBOeR2RFsGBu+i5s9dcygfVBW9rv1yFuhjYs0jk9n3wkwy35zP\nQ7P6EtkqHJUSHcDMtC5MeX4DkuS6wP55lZZXnD6oC+ZGY6U35CC1CS+1haDUo4pentXknDasGHhm\n9Ukef+qZZhlTACx1Wsm9Ozg7MBCd9CCE/0UexL3Aq4Ig5KF5E8vdzOkKlAuC8JEgCEcEQfiHIAgd\nKPT8gRh9NRzZAHWdFDvvNxtOfN/xnPiJkOch1xA2Cco2uS9VMw8HqxvD4tFAhKAlkYs8jNnR1NHc\nIQBt0e9MCeuluJ3+30BVVZYv126fYYl+LJ6QytCUcJKjOq71FyNikYvdG8uEcF96dI+kpsZCkNE1\n7lsuFVJXp5CTU8/yK/uR/fbVPLusG7t2WFFVLf6d99FsRg8zEGhpCkWo6IIvIFVq/z90vpSrRsiE\n+DQS+qkKetsZF1I+wVqLoaoAv9RBDE4JJzzQG11eLigKzj79Xc5pWLdQNh0pwGvlNioD/dgR5io5\najLomDEoll1ntB1/RZ37UseKVuGWQ+fL8TMbMBv1+EcH8V33VBLr65hQUtx8n8a21pIWBBwDB4Mk\noT9zitsn98TLaGDzCW3vp3oH4ojpgylrd/P7D2WXoQJ3fbCXp9dUEhIUjq/zlMsxXRZj0YwU9gD6\nhpWNyWJ49eeT3HV5b4J9PZMtdosKINSvfRLfqNfx9z8Nx8ek45EvXZ+ljIJqZg5OICrITIifiabw\nkt2W4PFzAES5BkXXwb3nsPHKumzSho9i3rx5rmOXzEF0YCA6wbH0b5WDEARhkyAIJ1r9pTf+OwO4\nA1iqqmo8mrH4p5tD6IGBwNuqqg5EW7ke6egzn3766ea/7du3//6T9wvSJEm3f9G5+d3GQVEG1Lhb\nlBsRNxHyPIStfLpp3ZX1biJo5hFgdVflNBDUU6C6e9i74z4aJ9BxmElE05XojBfR5EH8z3IylZSU\nsG7dOhYtWsSTTz7JmNGjWLLkbh599FGunj+veQeW8/bVrLxvAskR/tglD7spQUQMSUSXNBzRPwil\nxj0BXU5pPSNGJXPsUC4hdlcjUi3m8N132ZRUWzh9sQZBEJgxLYBk4jDoRKYPikMfk4dSHAOKtosU\nfcpANqDaNMGhN9ZvBoyY9FqoQue8iCp6o+iDmz/HWHAMZ1RPaKp4URSMJ47g7D+wXVnj6YJqntfX\noXoZkacPR2yzm07rFk55nR3fRqW2mJD2FBCCIBAd3LK7Lqy0oBO1fgidKDJmSFe+Sk4hpa6WsaUl\nxIb6MjC5jQ63KGIfMQrjqZOIlRWM7B7O561U5qSonoCKvpF9wN/cYnx9vYwcKOuGwXYGQWpMRisy\nSq3rM6Uau+IUxmIyb+f0xXIyC6u5c3J3lzmCTwj6xBHou09GFzcI9J4rvLyMeh6fO4B3N54h8a6V\nvL9ZC8/mV1joEx/EZclhHDpfzuV/+ZyLlQ0E3riWqc+v93g8Qa5F7cBA2Brq+DXXwocfuSmn/1dC\nTJ00ELvz8lzWyY7wPyo5qqrqJE9jgiB8pqrq0sZ53wqC8KGbaQVAvqqqTXzZ3wIPd/SZl/rCvwkz\n7oa/LoIr7ri0ILjBBP2uhIOfw8QH3c+JGg612VBXAH5tJCoFAcKvgJK14NeG6dJ7PFQ8357SV/AG\noQ+oe0EY1+bD+gFHgQluTiQRyALaM2pqiECTy4zyMN4EI5rBsdFej/lfR3V1Ne+88w6PPfYYANEh\nfozpGcm+veexl2QhqQL947UHcWr/WMIaaagVVcVqd/+w6LoMQfSLQAzyRm1woE8ahXRue7M0ZRME\nYPy4VE4cymVSXweqrRZdRHcEvzD693WwcmUQax+fxujUUBAV1LAa5tx/jutGJyOKIvq4HJxZLWR4\n+pDzSJWJzf+/YZzCsfPhTGyUrNZbzyK17ppuqESsKcSeOKzlGOfPoZp9kNtwLKGq3G2rIsbkj33O\nKLro9VwzuhvHssuxO2VSYwPpFR9MfmVDs4eQGOlPry7BnMrVKtYEQWBUr6hmpTqAvgkh1FgcFFVZ\niAv1JSkqgJgZfSnMi2HYL7sZrrfhdFPGqfr6YR80BNOvO7lzwhCm/GUTNoeEl1Gv6UckjcR8ci1y\nYCy94oJYNLYbH28/R1mtjd3n6pmY0g9Twz5s/lO0sFLBUVAVxIBoUGTk8vMo1SGIZn+O5W9k8YTu\nLmEjTL7ouw5vJjgUAmMRvPyRznluaG0yjL3iAnnki4NsTS8kI7+SVfeNJybYG39vIwNSjvHJljpS\no73ZfbqYz3dmcf3o5HbH0kkVyAb3z46iqAgOCwvueh5/fzc5ioZq8HVHK4+WpPYkGNTZHERgIEMF\ngatarZN//vOfPc+/5BH/53BREIQxAIIgTMBNOY6qqiVAviAITcHWCUAHxEd/MHqNhMAI+PW7zs0f\nthj2fOC5o1FngK4z4Pxq9+PhV0DpL+1fN6aAYAT7yfZjwkRQ3IWt0gBPanYpQAcJdWLwzAjr8uGA\nP/DHpoUcDgfvvPMOQUFBvPXaX/jm/gnUfrqQzBVzef+2EVR+fCNbnpzKjqemsOKmodw5tRdOueXh\niAryptxNCEXwCkD000Ivor8ZpcaKYDAjBrevNtHrBMaN7877Xx7grg/2gNOKYPJD1RVhd8D1E2cw\n4fJZCIKAFFzD0RMNzO6XzFuLhyOYLIiBlc30Ggiyln+oaDIQdq4YpLLk/dLG4Tp0UhmSqaUyxph/\nBGdMH+2eAXA6MaQfwzEwzXWToKrsf3Mt3UWZHodrqG/0nGJCfJg2uAtzhifSK17zSmYO7kJ1vZ2h\nD64me1sms3LKWX44j8c3nOL+GgtDg11LRd/deJoh3cKJaxVG8jLqSUyOQF40Ff3hTPQH3RdDyF0T\nkYOCKNq0gyuHJmrGoemUzf44Yvs1hpoUNp/Q7rUesYG8+vMJ6sVkUOzoHI16KIqEnH8Y58mfcWb8\nglJ6FhBY+LrM9MFOnrraNZwmBsW7sN8CCF7+zbTq7vDAJ1oj3h2TexIZ6M3Ph/PY/ufpjcpxAtPS\n/EiKbODey+dx8KXZQEsCuy1EqRxZ31YvXsNXO04jAjffdX/7QUVpzEF48D6cjkuXuV7CSIjBwSiV\nnSljb5zf6Zl/PP4EvCYIwlHgOeBWAEEQogRBWNNq3j3AF4IgHEPbFr/w//Qs5z8C377UOa2IxMZd\nS7abstQmJM+FLA8GJ3Q8VB8CZ5uwhyCAzxXQ4MZ4iBNBdWcgegN5gLsQSjfgPJ7lRaOAUjRK70sh\nwMNn/D7IssywIWk8+8QjvH/7KM69cRWXD4hzW0/ehMFJIWSXtuRCJveLobLO1k7VDEOjlyMICL5e\nKI1GRHATfrCYjVRWNDA+KZRv9mRzy8o8dp8t4WjlcbIy/RjQNRTBNwyMPlT5lbB5o5Un52mEc7rY\nXOSi2Obwki4gH8UajOrUFlq9IQdViaXBpmPWSxvR2zKRTEnNSU2xtgSxoQoposWjMJw+hRIRhRLs\nuvBkr9pNeHE5D+mCCAr24/3N7vtfhJJa/HZmsT/Ym93FtfD5fhAElIVDcTw/C6PZiPnJNZje2o54\nXiOBnDEonvRc96FG1d8H2w2TMexOR3+s/WZjz9liunyaz3h/J3+fGgsGM2JoMmJIIuiMSJE9QBDR\nF2UwIDGEblEBbHt6GgICB7IrcPgOw9hwCBTPubB95+rYejSRkKD9tG7aFDwlkAX3y90PB3PJbuyE\nDvU3sfHxqWS9OZ/+XVuutcGYjtPRA62ZFF698TJ2nXFTlq44EGQLqq69FyDJCl9vP40aFIfB6Gah\nt9SC2ddztKIjAyEInQoz6YKDkf83GAhVVfeoqpqmquoAVVWHqap6tPH1IlVVp7ead1xV1cGqqvZX\nVXWOqqp/3GrUGQyeBg4bHPWQXG4NQWj0ItxFyxoRPwnKjkNDcfsxvQ8Ej4AyN5/leznUr3PzmcNA\nzQC1bTLdgCZ56S6J7YPGy+SJudaIVljmqeO6NfzQEtWdFyHxhCNHjhAeGoJoreD0X69kwUgPlANt\nkBThT2l1A/U2bTEJ9DExf0QSE59dT2YrI6E2lIMiIfiaUK0OaPQ6lLr233N/rZ28jELevmU4qx+a\nSLeoIHadLqJnTwupvi2huWqrE6/4OrZtbJF51cflIOVr3oAY1AVDlzpU81z0yWMRvALQG8+hSiks\nvaIXJ/PKMdjO4TQ3GgNVxZh3BGdcf638GRCsFgxnT+Po50rCV7L+MD7p55lTrmftc7PQ6USXDaQu\n/SLGT/ZhfuA7vJ5bh5hdRkFqBMkqrBiZjPOqgSipEahhfjivScPy16uQk8Mwvb0dr2d/Ia2ifDnu\nkgAAIABJREFUngarE6eHfI4a5KcZiS1H0J1yVT+8+8N9TLksieDLJxGafgRDzGB0Ub3QRffBkDoR\nwRyIPXkExovpPDgxntyyOv6x6QySrDAyNQLFEI5siMFo8cA+AKRG+fHtXgVZisXktZ+mXJhS3b7w\nQHVYUBvaG7slH+7h+hVa6Gl6WjwpUQHEhPi4hKwEoQ69vsBFq2PGoHhKqy0cyXbtGRKlCi2P5MYY\nvbvpLD1jg/GOSW03BkB9Ffh4CC8BOOyeDQRoXdaXMBCCnx+qzYbaSU2I/3ZSXwqiCPMehm9e7Nz8\ny27UqpmsHsIuei9IuALOe2isC78CSte2f917HNgPg9zmuIIJhBGgbndzsKGAmy5sQAszeRIdAo2u\nozNhJh0ayd/vDzNZLBYWLVrEoEGDuHNiEtuemIRB3/lbs2+XYCRFpaCipUTzH7eOYPqgeMY+1epa\nKhJS/mFEPxNKrQ1UBbk0E7XelTZ99YELJPeNJT+jEEEQGNk9kofHh3Lv/Bh8Dd54o4Uq8i8WcdMH\n32KXZXbt1wyRYG5A9K9BLo5G8A5GF9sVUXcaRRmOYA5AHxOJINiQ5WiC/by4YbABRR/UnNTUVV9E\nkGxIYS3G0ZB+HCkxGdW3JXmpS8/GvPck9+qCePfByQAUVTYwsocWbtGvP4Xxk32oob7Y7hmH9Y35\nOG4dxbMldVSJAs9d46Yv1WxAmtoL6ytzcU7ugfWbI1wwipi3nQW7+4ZINTQA2/WTMK3bjy5TK3xY\nvS+HoqoGnrtmEGpUNEr/0ei/f6/FC9cZECN7oHr544jtT7ea43gbdUzsG40Kzcp4Dp9B6O3ZiE73\njZtpSaHklTfgsA1G0FVjMu9k5a+n2XroNFLuQVR7Pagqan0Z0oW9uCumWHskn5jG0NrXy8a75GCa\nr7/pJE5nCq3p3g9nl6OoKl5G192+TqpAcRNekmSFNzec5c7r5yAExbUbBzQD4RvkfkxRNK2Ijsj6\ndDptTgcQBAExKAjZExNvG/zXQHQGYxZA4TnI9KDb0Bp+4ZAyHg5/7XlOR2GmiCugdF37xjjRWyt3\ntbjxLkRPeYhhaAbCXXjsUgais3kI+FfCTPn5+fj4+PDJJ5/w5dJxPDK7bzPnTWdx7EIF3iZ9C9kd\nmgBLYrgvtRYHpTUtu3u1thjBR4czfQfO0xtQSrRKr20nC1n8zk56LPuWP723m+HDk0hq9XSodSV4\nm0+hVEagqipvfbeDtGsfZewEM6VnTMSEaOEjXewFpMI4UHWIAdGI4k4UZTBNSXydbRey0A8QSI0O\n4MpeDTi9Gnemqooh7zCOuIEtCdaaavR5F3D01sphz1ys5m+vrqX2m51Myld544EpXNZNa6IblBTO\nl7vOo9+RiWFDBrZHpuCc1hs1Prg5b6EXBW6b1B1/7w52ojoR5+AuDHDIHJzcE11GEd73fYt+3Um3\noVY1IhjbggmYfvwV4fxFHv7yEE/OG9i82CpXLIKqEsRDLY2gTQJBUmR3ciss/HNmMH0acyWb0htb\nokQv7L5DMdVtbye9+8n2TN7deJaR3cMBPbaGKyiplhk7YD/Pfb+RK5/4BClzC86TPyHl7AF7+9LO\nb/dmY3fKXKy0eCyRFQQLekMOTodrQYfFLhHk60XPWNcFXcs/tKnsAtYfKyAsIoqekb4Q+DsMRBPN\nRkfPhl5/SQMBWpips3mI/3sGoqijLuHfCb0B5j4Inz7euVzEiFth19ue5yZcDqWHoMFNkssnGQyB\n7kWEfKZBnRuJU2EyKOvcfF4SWp4hp/17mg2EpxsqAq3UtTOEfE0G4reXu/7www/0Sgin7rOFzBzc\n0lSGICKGJqNLGIYupp8mzOQBNVYnAwcNRt91OLq4QZq2AJAU6Y8ggK+pZdclhkWC3YZSnk9pZQ3B\niz7F9/qPmfHiRlbvv0Dv+GDWvjGfzNNFTHxiDfvPlSJJCiU1FsSIWhyHz7Ho7gd55Y1/sP6h0Tx8\nZzw5x/V4NyZh9fE5yI3hJVWREMVtKEpjhZliR2zYhSRpBmFogo4uQfD491qyWleeDYIOuVXS3Hjs\nMM6efcBk4lR+FZc/+gN31JXzc49UbrrmMkJaLWyje4QTmVGI4buj2B6ajBra/ppZ7HKH/QJNePbb\no4DAxPkDsS8dj/WJaRh2ZmH42R1BJCgxYdjmj4WvtzFIL3PL+JYwiuqoR77mXnTrPoVKLZzXRLNd\nWmtjwXqZGWFViLY6uoT5UdGqI1o2JSAb4zHV7Wq+vyVJ4cHPDnDHlO48OLMPALllVvouLeGnfVFs\ne85AYvRFEu9ayaNfHmTJh7/y+hpX2vx6m4Ml/9zLE1dpYbtXb3TP4GMwHUVyJEMbbYcrL0ugos7a\nLEmqfSkVUSpFMbgaiHqbk2dWp3PHkmVQmQtuiiK0iR0YCIcd3OUtWqOTBkIMCUGp6Fwz7P89A3HV\nENh3CX2G34MrbofyAthziWY4gB5TAAFOugkVgaYyl3wVZHzsfjz6arj4VfvX/edB/Y+gWF1fF7SH\nBPV4mzcIwETAXe9FIJqEpqdqJgNasrozCnumxr/f7kU88vDD3DgyoZ3XoItPQxfVC9EvHDE4AUPS\naDC6Z7mcNPkKxk6YRIXqhxgYiz55NIKXPzPT4jHpdRzPa3kY9F27I13IpNbi4LLlPxET7ENkoJmH\nZ/ej6pMb+ea+8YydM5BeVgfDu0fy3sYzXPnKZm7/YTcnz1QRMOcTvt2bzWf3jKFPd19EfxtSkS81\nFgeCby2Cdz1yaWOJo/UQAvWoqvb7iJY9KPoEFKu2qHg5znKgOJTX1pzScg8Fx3F0GdS8SxSLixCr\nq3CmagYlv6KeZ0LAd1h3rlkwjNsn93C5boPK61lWXo/twcmoHpoE662OSzJDv7/5DH/feIb7ZvRt\nliVVI/2xPTwZ/a4s9BvdFxLm+/qxIE/iizAFg9QSkpIL07EGhGMZPhP9t2+h2huQizXP7eZ3dhEZ\nFYEc1xdTzl5uHp/CX35wXcwdPmkIqg299RTVDXaGPPoTAvDQrH4E+ph45PMD9Lr3O5Ii/ZnQaxiq\nYwav3uTLx0t1pOdXsvN0Cc9+d4xaS0vcff3RAow6sZEMEOYN64qqqhzPKWfVrix+3JdDeX0WOn0h\nDrtrUyLAgawyjG16TQRFC7Oqomv56l3/PEBcSl8WL14MZecgrH1pLAA15RDQ3vvQLoJdK6XvCAaD\n1m19CegiIpBKOpNf/L9oIF7+DO5bAP/8a+d2+52F3gB3vg3/uPfSgkKCAFMegw3PeT6H3rfCyffd\ncyzFLIDClaC2STjpo8BrENS3qWYSBBDnguIubDUJ9wYCoD/Q1qi0Rlfcex/u8FsoOjRkZGTg66Xn\ntkmuTU4YfRD929SR6wyIwQntD6I3oQTEoihqC7VyYzOcIAiM7xvLl7saaaJ1evRxSUg5Z3n0y4PI\nisLhl2eT9dbVzTtJMcIfwaBDLqhkXK9Idp4p5tezxbz9zDA+/Pgcy6/sT8VHNzAsJQJ9QiVSfiBj\nekRTVW8jz3RU8x5U7bHSB6bjLE9GqS1BtdUiVv2Is7bxeyl29I5cIqMHEOznha66AFVnQPHXiOhe\n/eEYlVt24Oif1qwBEFJv4UpfsI3o2+4y6I7mM2F/DouDfVHjPOxCAWdj05sn7M0s4ZEvDvLCtWnc\nN72Xy5ga6I3t4SkY1p1Cv6P9xmL2K5uxJsdi7puI6ZcW/Yaq8mLCRi1k+EfHKCwo0FQbHdozdCCr\nlD9NSNUa6Jx27h/shdXu5JlvjrQcWBCx+43BWX2MuS98RWZhNWZTS9nsl7uzeXPxcLY9PY3ECH9U\n1R8cs5jUL4hNf5Y5/trljOwRxYwXN6EoCuuP5XPT2ztJjg7kgU+18xQEgZ2nith4JJ/c0jpySirw\n9ztAfnE/tKINV3SPCSTQ18QrP7V4VDpHEbIh2iUMtGpPNtsySln17Wp0Oh2UZUGYBznYmjLwb8/x\nBGgG4hJ07hiNnTYQcrGbIhk3+L9nIEZMhG/2w89fwL0LwPIHUkH0HQs9R8DKTlTa9p8D1mrI3Op+\nPCJN42fKdzPumwpe0VC+vf2Y/wKo/bL96x4NRH+gGvcLfX/gGJ5DQ13QKLI6w9gajEbf0UkGXGDD\nhg2M7R3TjkNH0HuIB7t7XWds3kWbWycMG+fqRQFJ1r6f2mswZ46ks3pbOp/vyuLze8Zi8g1CDE5o\nrpE39o7FeUqLgV8+II7iKgszh3YheYAfywf358GZTbtqFX1yOdK5ULJL6lBVhcjeRUi5jb0OohN9\nUA5ScSxy7gHk86tBKkN2aAZAbzuHbIwlJiyEmgY7DVmNXdOCwNJ/7qX0cDoXqmysONUYO1dV/LYe\nZlNoBHo/13CHLv0ipg9+5bsxKWR54J1qwuDkMDY08jGpDon8vdl898Y2nvn8AE+tPMyC17fz4Kx+\n3Dw+1W0uSA31xfbQZAzfHUG3P4fyWhu/HMlj4VvbKa+18sldo3FMTkMsqkCXns3ra9Lpe/9qHA4H\nJ06e4lh0CsYTR1z0IworLSCIOJKGYy44zGMzevDL0RZqNockcc2bB7nlK4VNd5nIfmM2VrvE2iN5\nOCSJynobVw7p0uZMDdit45HlKMw+a/jorh4UVNTz7LdHeeizQ1wzMokfHpxIQUUD141KQpIVjp5v\nSYaPH1hMXokPO064v55h/l5cN6obH2xtMZQ6Z6FLg5zVIfHIV0f5+NPPtKY4aw04LOAf6e6QUNuB\nB2G3eW6Sa/7KBuhEdZIuIgL5P9aDAIjpAl/tBi8zzB8Kue6FRn4XbnkV1r0HBR0leNEEyScthw3P\nux8XhEYv4h/ux2OuhUI3YSa/OVqiWm7bKzEEqHWjMieihZk2uvmQeLTF39NuwgsIp2P21ybo0HIR\nna+xPrBnF2NS2zcvqdYqVKl97kOpdT3PzMIaftx9EktdDSoqVQ0tD4daW0RJtYXNJwoYmBiKGBaJ\nPaIrI2cs56Z3dvLun0YybvxE9N3GoYvphz5pFPpegxF8TUiNzJ694oLwNunpPzwIuQL8BGNzP4Yu\nuhbVoUep9GHhWzu5YVYg/mYDSpX2gOsDc5Hrw1GdWgjDYDyL5OwGiKAqGGxncHr1IMTPi7tHR6M0\nVGEPiGf5FwdYe+A8r/TWkxHTnWe+1co8hTN5eDscVPRIcLkGYkYRpnd3YVs6jrIwP0pq2oQfW19X\np8wIncCssnoqn19Pye1fkfH2TpwHcrlqfQb2n9Nx1lpZPM7DDrfpOFEB2B6YhOmz/Tyw7Bvm/3Ur\n3++/wPrHp+Jt1HPbP/dybEhf5J/28N63h5k5uAuf3TNWYzsd0RNnzz6Y9mkqc7EhPjz9jUaKp/iG\nIod0ZWF8FdklNVhs2mZjzitbOZpTwdUTx+Pln0ic/jD3z+zDkyuPoBdFBDSJ1PYQcNoH4LANJjZi\nJ/fMMLPp+EUulNaw4qZhWBwSJgO8cF0ygi6Xwd2LmD48n4VTz9O7azXrD0RjdaPL3YRl03pRWWvl\n+/05oCronMUoxhYDsS+zlOCQUGbMmKG9UNoYXvIU46spA/8OQkyXMhCd9CD0kZH/wR5EE7zM8Jd/\nwrV3wtXDYZuHfMBvRUg0zF8O7y65dAhr8LVQkQPZHhhcU6/VuJkspe3Hoq+Gou9BbrNQ6oLAe6yW\ni2gNQQRxDijuurQn4z7MJKD1HnquNf+fCjOpqsrRo0dJjnQTK1dV5NwDqI7GstWmctQ2nDz3fLSP\n61ZsY+C1j1FWWkagtxFUBaX8PEpVHt/szcHmlLlhXCqmoRN4YvkKrrsslt3PzeSaCf0R28SCDV29\nkbLrXX7X2yZ1Z+zUSKQ2l0DfrQwpU3uYQ/296DuiirU/GzlzUTPc+tBMpPKmhdaJ3pCN5NAIATTe\nJS8UgxZOeHiQwN9PQugtX/LZjiwOXJuIMTYGc0wk/j4mkGWqv93FslIIaJVgFs+W4PX2dmx3j0FJ\niWD2kC7UWR3YGmUuVUnGcbaE+u+PU/XCBsru+IoBxwowq+AzrTeP9o7m6fhgpn9wHckvzea2QfFs\nF+D9u1ay8Dk3PTetf6L4YH4cl8rbTplDNw7B39vIR1szSVn6DV/sOs8dv5zhlUq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2LNaTmeWmO0IKjrVeW0FkQXI9ZC5ccmqJTjZouVB+dEIVWBtZ6FQCrLRXRNQja7Itcq/QmyOQ9N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\nAPP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64TN+PAo9zW1GTk7YTZyI7bhx5O3YQdbixax6GI98vzGnfR25lfmCx0nk+sM0zEyM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\nCEmC4q4ArFoVrigG4joPnYFQqdWyVjYYjUa7rgUnJyd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ep = GPy.inference.latent_function_inference.EP()\n", "kern = GPy.kern.RBF(2, lengthscale=0.6, ARD=True)\n", "bern = GPy.likelihoods.Bernoulli()\n", "m_ep = GPy.core.GP(Xeast, Yeast, kernel=kern, inference_method=ep, likelihood=bern)\n", "\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "for p in polygons:\n", " ax.add_collection(PatchCollection([Polygon(p)],facecolor=\"#F4A460\"))\n", "ax.set_xlim(124.,127.5)\n", "ax.set_ylim(-9.6,-8.1)\n", "ax.set_xlabel(\"longitude\")\n", "ax.set_ylabel(\"latitude\")\n", "\n", "m_ep.plot(ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we optimize the hyper-parameters" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [], "source": [ "m_ep.optimize()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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BipoON/A8cjwA5lme2bIXdqHKc95hcPItqGRuN+Df7rAZRRCT0B942g4hBFOn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34ZZ80dxj2Pr0VRNM6fVsTeuk6u+scXZLrsLJpk6FCVlmZw4EAr+e5Eblo8Bmd+Cg+/sImFv1/O\nozvrqd3TxENv76AG6GzqplbR6AgpuARoiQ6S/QGeu+scTkqTKC0dyqJhdp64+iyccheamoIkdzA2\nawhud5in3q1F2P0gR3l3SzX7t0rYs4IIm7HIuP7ZjaxZ0czKp06n88Wfcvkpg2sMXXpyKf6wQnt3\niEisF7NwguwWaIEy5MKTkDLKQDIh53XS0Bpk3064YMYQ5LQWNm2Gp24aiR5JBM2CM6ETtzOfq88Y\nxahsnVElQzGFugwDoesIvw/dmdjjYnrhs72YvEFmXHA+O77ew/888AAppcPQdZ2VK1dy6w03kJI1\n+HdlTU0l7PWiRo93YTUQ4c5O2rZvJ+s4GET3jh0kjh17wn/j39xAKEbmzHeBpsGtlxjuoe9qHA5j\nyhy45i649hyjjuJYmLoYvM2wb/Pg7488Hb75pO+YEJB/CtR81nc8aTx0xmWQWEpAqQMtrlhOFIEe\nH6twA/0yonBiFMv1h5ESa3ck4g32MwaaBtLAlfFguPv1bX3Yh9cf5sKHV3HmH1eQ+Yt/kfzTF3n1\n80pC4Sj/s3wPz14zmz1/O7+nmE4PdaK1V/c5pu5rQY/FOQJhhRue28jFi6eid/XzVVhkpBQHanMX\nwgaqquOjG91n5ZaLc9mxU3Dfh8uprLJxoHkfb6wPMrVApywjnd1tOo0HanlkzSGa/VF2fH6Q7ToM\ntZpI1XSkglQsyQ4ObTpIucWEqmmY2nzMm288JPeWNzFi+OAPnQ+21pCrayyeU8roob3X5qdnjcVu\nM/Pk0m3MKMvk9An5fLKjjrr23ntrSFEaNTXtKLEq5oULhvOjsgxGF6Rw1cJRNABacze5Q9M5qyiN\nA8AtUwoR+SlILX6jN3NEQ0Sj6JixoJBosRqRKFVB1638dMnJQBamYSOpqHLwyq7NNHQEmTE0B6U2\nGVOxwSI2V3po3h3EUiSO2jPKYpKpfPwCzCaZ8be+R0RRMA8XqO1FyO7hSElZyJnDMZXMxDymkcf/\n1sld543HktKN3y+or4f5U2VUn3GtJLkVTc3AaZeRtW6jO17A6JYnAn50ixVMZkSXn2+6Ivz91W2Q\nlcVzr7+JEAK1rQ053ei/vmDBAqZOnHhEn79ssZCQnY2vpubIH/AYqF2+nKxZszAnHlsNomvLFpKm\nTDnmvP749zYQSvS7G4h/PGjUO9z60PdzTodxyXUwciLc/vNj10rIMiy+Ft5/bPD3R54Bez4ZOJ6/\nAGr7ZUAljYeuHb3bwgzmEojsi5tUBByK207GMAbxq6FEDBnw/jADCmlpaQQi/Q2EanyWY8DrD7O9\nspVHf27kftd5/My6+0NkSTBnZBbjCo3A9wtrK+gKRQkrGvNHZ5Pv7vtDUut3oFStR23ag3LoSzrL\nP2fEjW8QCCtc9+wGKhs7uf2n89C8fQ2EnJ2M2tJtCMM54WClj8kTEtA6bdjcXmZmjeK2i7J5ZGkr\njZ1VrNgWZWSWzg/H5TFuTBmn51rRgoJQZgpXFqVy9ZJxmAtSmKrqKCOz0HWdQ5sOMvLkUjp8YYYI\nwSkLhuP3h2lq7qK4ePB+3m2NnaBoXH7u+D7jkiS495rZfLrxIJ9/VcPZk43gdiju+jscFtLSEqir\nN1w/hcMzEe0BNj14Nvf/eDIJxW7GmyRGjs9jcrKdZpuZHxalGZIbdUZvZqnZi5acalRUJ6Qh+z1o\nJjeS4kG3FGN2qljNZVy10IXLOgl7icqhli4uml2CUpmGqcQD6HQHwjzwwg40P8jHUMPOTHaw/K4f\nYDPLPPTJLkxDBJq3L+OQ0lsQJhPvv9+N1x9Bdrfw8aeGy1VObEXzZQA6styKpqYjqV502QnChBTw\notuTjQpqp6EMoHf4uHt5BQ/98lqscW4btbUV2e3u2daiUcRRgsJJJSV0VR698v1oqP7gA4qOo+FQ\npLUVxevFMXRwEcej4d/bQKiKkQr6bbH1C3jlf+CRN8D8HY4zGISA3/4P1FbCM0dq1x2H0y6HLR9C\n+yAyBUUnQUcNePvFEvJPgdrP+orxuSb0ZRAA1lEQjlNZF0NAPxQ3Qcbo+xD/ID2SgTABChkZGYSi\n/Qyfqh6z6XpjR4A/vrOTzJQEslMcaJrO1NveRRKC56+dw8d3nM7635/FhgfORI65r6wmiYJrXueT\nbbVosVqTT7bVMvPuD3hvzVdorRXo3U2U13dQ6/GTcfnLvLGhirduPRWb243W2bfQzpSbghp7kGoJ\nGru+aWfmSUloXjtSiiEfXTwkyG9Om8+CcSb+9MMZBNQEwm0taJYkLLLg/rmlFI4rQmrsJOSPYhri\nplhRMRe5aatsxWQxccmScfxoeBYJaQkkuuzs399CSXH6oPGHZo+f1KiKL9GGxSzztw93s+VAr8aU\nw25CSXVw6yOr+a/nDHdjdr9OZyUlbqoqDSboznERCUXp9PiRJMGoyYUUajpSeiJqq48WhwWl3hsz\nEF60zFSk5na01FTkjnbUhDQkvwfNlGYYiITRiEglul6MJFWRqp/OxRf4aPvnTxidn4LWlgA6SOl+\nbGaZMQUpKIdALjrq7QAYTOKMCXkUz3CiNieCEp+ZqCNnrEWpHEGizYzdYkJyN/PpGo3L5pXGEgky\nEFIXOiZ03YEUbUU1GQ96EYzJmHd3oTmTWLrpIN7GDpxlo1k4ajQU9KbXqq2tSDEGAaBHIkhHeS4k\nlZTQ+S0NhKYo1HzyCYWLFx9zbtfWrSRNmnTM39Zg+Pc2ENp3dDH9869ww28h8/j11U8INjs88Q48\n/zB8seLoc50pMPsCWPbUwPdkk9Efonx53/GkArCmQtuu3jFXjEHEsxbrSIjEG4iifgYCIA2j13TP\nCXE0F1NFRQVF7r4pxvoxGIQvFGXaHe/zxPI9/OZsI+/74Y++xmYxseuv57LkpN7uXGOL0jj09x+T\nnGDlqatnc8nJpVz0yGqSLn2R4Te+ycWPrqa6uZuLHjF6CrR1h6jz+CnKTOL3F07mm4fP45QxOUiu\nNLTOOMMnYgwiZiDMLomW+hDd5i4jxTXZg9aZhLD4cFut+II2du+rpLzJjN7Vws597ahpbqSGNnTZ\ngpblIlrTjsh0IumQkJHIoY0HKZo2BCEE5xenMX22sfIr39tM2fCBS2pN0/n9019w7qnDqWz3Mf++\nj7jrta8456GVPTpUv3x6I3W+CJPG5zE7PZG7zxuP29n3+hcXu6msMgyEEILC4VlUxwro5swYghv4\n+JAH4fEjsl0xA5FsMIisFKTmDrTUNKR2D1qiG8kXZyAsxYiwYSCEqEIPDUNXbTjyDivpCpRKN6Zi\nD4Gwwu6aDqIHdUx5GOGsY+Cik0s464J8Nn3YV5lXJFYh5BDRAyYUVcPjC0FqI5+vh9/+pAwhNPSI\ns4c9AEhKG5rJDdEQQlPRLQ5EdxdrawP86vnNpEqCR994D5qbILu3oFNtbe1xMQHox2AQru/AIJo2\nbiQhLw9nwcBeJv3R+S3dS/DvbiC+SwyipRE2r4FFP/5eT2kAsvPh4deMOMexgtZnXm8Eq6ODpM8d\nyc1UsABq4hoLWbMBAaE4tmEZ2ZdBkAO09VN5dQPxqqg2jJTW/kE4w8W0b88uRuT060KnqkeNQfzt\no2+wW0x4n7+U8vouLvzbav783i6ev27OoPOTHBamDU3n4+31/OGiyXieu4QVd5/B5JJ03v31qRx4\n/ALj01zxCkXXvMZPHl0DOty4aDSFsZ7CkisVPc7FJKUlooei6AHjGktOiHbpWFLDaH4ZYQ0j9DBa\nIJWQ0kB5tY0Cl5/WbitmNJS2TlrMiUjNHdClopW4iR5sIyIJ6qwmdhz0cGhzNUXTigCo2FFH6Xgj\nEL93bxMjBjEQ73y2j0AwyjU/nEh2soN9DV6+/MPZTCpOZ/qdHxBRFLZWefjV4tE8fvN8inNcbPzy\n0AAXX0lxOlVVvbGkwrJMqvcajDQhNQG7DodCCgkRhd3BCEpjJ1quyzAQGSlITe2ohw1EHIOQFQ9q\nwIaIVKFrRQhRDWgoNeMxlfS6LpWDqUSz2nAmGffAL5/YgFIDjiVgPxdsp4JlGphHgVwAUgo9qi3j\nZqdQsbeLT1buQ23Y1ZPYIKevIbq3ACIhfj6vlI/27CWkh9i7F9KzumLxB4Ekt6CqRixCVlrRzOmG\ndLk9GYSgqaaZl3Z52PLhB8iZOWRkZ0NzM8R1hNP6GQgtEjlq3cF3cTEdr3sJvn38Af5jII47KDoA\n778Mp50HCf8HcuFTT4Zf3g1XLTYkPI6EotFGO9K1rw58b+TpsO9To/YjHgWnQvWy3m0hwDUROuNS\nYK2jIBynCitkoACIN1jpGL2peyZhsIj+7TvMQIS95XsHpC6iKgjTkSn5ip31zBmZyR/e3clLa/fT\n0hnk9ZvnMWdE9hH3yUqxU9lsnIMkCWaUZfLyDXOZMzIbm8XEM1fPRkNnfFEqM8oyeODCSb072+wg\nBHqoV1ZEzklBqe9NeRVOiHarJKcJhMmH5k1BTmhD86cjpCaqmxwUJftQgoK6qIM8LYgnINCTE5Gr\n21GzXei+MP6OAE12M5u/qMTmtOLKSTbUW/1hsovSCIWi1NV5GTq09wEEcLDeyzNvb+fuq2ZjkiWS\nE61cevIwRuWn8O6vF5CbmkDOFa/S0O5j/ugchBD818+mUVvn5bLpfauPCwpSaGrqIhwr/Cooy6R6\nr7EiF5IgYDXRUu8lmmDBFFaQEq0oEc1QCtAlRCSKbrYiggF0yYJQo+iq4ebT6ncDFgi3o+suNM86\nonucyOlNRkYT0NyssPKzLs5aYvymXlpbQWQzBF6H0CcQ2Qlaq3ELmQrBMh0c5xkv6zRBw6Ygz6+p\nQPMcNJR6O94GmonuMdiwpztM6aggn63VKHAnICc29w1QK+mgRRCq39BgigWo231hfK3t3PCnxyl2\nmI1Fm3HCEFfnoHo8yGm98SE9GkUcpYAtuayM9j0n3iBT13UOvvsuRWeddVxzuzZvxjV16gn/Hfh3\nNxAnkDUzAB+9Bmde9P2ez9FwyXVw2rlw2WlGWu2RcNE98MrvjAB8PFzZkD16oJup4FRo+hIicfGC\n1NngiZP8sAwHtaOfJtNY0OKlxIcA/aqwyQL6x0QclJd/xb6KA7y0toKz/7SCF9YY3Wa1gA/hGGhw\nn/l0L7Pu/pBtVa288nklT67cy9L/OoXP7l3IyaOO7t47b9oQdld7aPYO3hnvx7NKePfXp7GvoRNJ\nkjlnSu9DU3KloXV3IRdNx1Q6FylzhFH/EFedLCXBmm8q6WqRadbq0LxpSAltqH43TkcHAZ+JkCKT\nTpi6sINsPYhLEah56UT2NfN1mx/TkDSa9rXwpS/MfJuJ4lijpL1baxg+qQBJEuzb10xBQSp6XGV+\nIBTljkdWc92FkymMSW7cdd54nlxZTlTRkCTBu79ewH+dNZZP7jid3JgM9fJdDQQSrGz6sronawnA\nbJbJykqiPtZ4J7Mgha52P0G/sahoUDQWlmaguOwkBaOYcpJR671G86D6zlgcwmvUeHR0oCWmIfvb\nUU1upGgLasSFdvAttI4ERPgrUM0oh0owlewF4L0t1bz2ko+H7inijnPH88Ftp/Wcmx4ErQWUSoju\ngPDnEPrYMB6BjyDwts5Yexqerli2nRbFPPIAkV3ZoBvXbNGkfBbMh09XwV8unYbsbELzZQFhJKkb\nTUuLuZfSDD2vQDuaI5Vr//klQx2CSYt/BI21kBUzEJ42iGcMXi9SfI8HWT6qvlrqqFGEOzrorq4+\n4pzB0LLZyFZMnzz5mHP95eXICQknrOJ6GP/eBkLX+uokHS8OVUBzvbGy/7/ETffDtPlw+ekQPEIr\n0DEnQ9YQ+PT5ge9NvhC+6scuzAlG0VxDXHc69zxoW927LSRwzIJA3BxpAujxwexioD9dzgb6F9kl\nkpCgE1E02v0K7iQ7t760mR/992eEfLG0S4tRm6LrOr964UvufO0rHGaZFXefQecLl1D7jwuZPuz4\nmr3PG53D2MI0bnvlK4Q9BblwKqahJyNljuhZHMwdlc0Tv5jJrkN9g9Fyei5gR9Q6W20AACAASURB\nVHJmIGwu5OyhSK4EtDYjtiISQA/D8GEWlq318EXjHiIeF1JCG3rIghAWJuaZOeRNpMDixx820W22\nkxUMoWWkoHr8PL9sDy8d9NBZ1YarMI1IRStDphvideVbqxkxpZDWziCvf/INXbLgiY++Zs3uejRN\n40//3Mjo0gwWzSntOedFEwvQdbjrta1Mv+N9TJLgtiXjmFRiBF29/jC/+ddmfnn2GLLSEnjr0719\nPnNhQSo1MclwWZbILkqjPuZ2Clhkgh4fkjuR5FAUOcdlSH/nJSPqO9CyUpGa2tFS05DbPUag2teG\nZnYbD17VjSy3ovrdSAkGE44eGIG5eD9ICpfNHcay5d0opgh3/aKUeaNjxt/iQMoaiZw7DpHYl0EB\nEDIMiEmW0IHaNh9yThfCrKJW9xY+uhxmTj3FMBALp6YizEG0QCqyqRVNdQMSstKKao7FIvwdbGvR\nqD7Ugjk102hP3FjbyyA8HohjDFpXF5KrVxlAmExoypHbAgtJouAHP6Bm2bIjzhkM+158kbJLLz1m\n/weA9lWrSJk//4SOH4//GAjxLS7Bx6/DD84/rpTM7xVCwG1/gfQseOXvR553yf3w6gMD3UkTfmjE\nIfq3Ic1fADVx6a7JUyBQCZG44Kx9NgTWxZ3LxH4GooTBDUR/HadE3G477mQnb/5qHs9eM5tXbpxH\nozfESXe8T/WhRt7+2sPE37zHogeX8+oXB1h170JW3HMGM8oy+yhiHi8umlVCY0DGVDILKSkbYU9G\nzhjWR3vJbpGxmvseW8rIR4/T2ZESI+gBK8iH+xmD3gXX/7iYPHM6UyZKrNjQgUBHUn1oSgYjM0Lk\nZA0hyxJhUqYLZ1EeprpWUGV2S4If5iazX9FQoip1la18HY7iSHHQ1e6nrbGTouGZvP/lIVrqvDjT\nE1FVjS37W/ifpTuoquvglp+eNODzTi5J54lle9hd094jhAgQjChMv/MDhmYnc/3C0dz4k6k8/95O\nvN29saT8ghRqanoZat7QdOoOtKLrOvVRFXtIoVFAoSxhyj1sIIzuclpWKnLMQEjtbUagOpbqKitt\nqKrb6NbmT+8xELo/CdWTjqmwCpNJAl3QuiMJU2ksFmJLwlw6Dzm9FCm1CNOQGQMkUg4jO8XBlKEZ\nPPDWdszjGojszOlhDwByRiPBEOzbB49/sYZl61Wm37OCqFaPqhoLDinaimZKB11H97XzkxfKefSO\nGxF5sXaeTXWQFSvObGuD+LTWri6kOFE+IcvoRzEQAPmnn07tcRoIXdP46sEHOfjOO5T97GfHtU/H\nqlWk/m8bCCHEMCHEZ0KIr2PbY4UQd33rv/r/FWjfkkF8/Dos/NH3fz7HAyHgpgfg2b8cuYhuxHQo\nHAXLnuk7nuiGITNg1/t9x/sHqiUzpEwHT5xBsM+EYJwqrJgA+ra4bKcsjLTW+ArlHAZjEBZLmECo\nN5C+YGwub/3XKZRmJ3OouoHPKrtJTbCwcX8LxRlORuV/t85bnYEIEydOGrAYkJyZYDHcLi+srWRo\nVt8OeFJCAnqo11UnnBG0bgtIhl9ZzgS1DUrLzEzPzqOoSKeqwYMacLO2fBcPvduIiDaTbHaAM42M\niB8tKQURCFG+vYGNmk5+IMJN546HrCQmAhtVnWZvgL1f1TBsQj7eoEJru5+wL4wjlpba0RHgrRXl\nPHjDvB4ZkXisvOcM/vSTqZTlJuOIyWJ7ukNc9dR6BII19y0EYEhuMqdOL+bppb2GPp5BQK+BiKoa\nzZqO5A8zcVIBdl+ISgRqjEFIdd4eBqGmuXsD1b42w8WktKEpaUhyB1owGcnaDZJxbaMVIzEPLeej\nbdWAjqMxG1O+F8wKcnppz/U+DDl92BEXdi1dQc48OxF0gVrnQtN0lu+o4/dvbcM6dht332fMO2mm\nixFTb6Bo+Hh21pRz/9Jmbnr+S4i08MePGpl/xxs0+jX+9d5KTi7JgdxYbUVTvIupH4Po7BzAIDhG\nz4f8006jfvXqYwr3hb1ePjnnHKo//JDztmwh8Thah+qaRsfataTOm3fMuUfC8T4dnwZuJ5aSouv6\nLuB/OX3n/wDfhkEc2GPEACYdW//kfw1lY4xq62OxiDceHJjRNJibKWMS+GrBHxcvSJsHnjW927YJ\nECnvragW2RgB59rYBAnDzRQfhxicQchykEAojKb1ptKmJ9lYest8ZuY5ePJXZ/DpPWfw6M+n4/FH\nUBStp37h2yAQPnLwW8TqYKKKSmZy37apwm6LMxA6kjOC1haBsOFikgtBqQYpOQRqmM4WO6qljftf\nrCM/3c/m8iA1bSFe/GArEYcbqbUZEZGodyRQ82U1KcMyEREFW1RlxOQCpqU4qJUFdouJ8i01jJhc\ngM0s4/f4caQ4kGJsYNv2OhbOH0Z+/yB/HA61diPFuSDm3PMhn+6s57Wb5vaZ95PFo1m56SB6zNDn\n56dQXdPRs51Xkk59ZRtmWSIzPwVPQyclI7MplCV+u+4ASoMXNScZqaETLS0J0dGNbnMggkF0YUbo\nGkLR0IUFoQXRtUQk0YUWSkZyGC49rSUbJI2KyD5mDM/GptlQG5MwFbcjzIM0iZLNIA+eHZSTamfa\nkigHPnVyzTObSLr0BS5/6kscY1U0IbP0bbj+uuuYOwWKRvyMN998jWkjrKgF56G73DR4I6z3ZnH/\ndZeQO3UR06ZNg/r9hrQ+GAwiOx8CAWNx5Og9P62rCxHPII7hYgKwp6eTPGwYTRsGaewVQ9uOHSyd\nPJmkIUM4e80aEo+zbWj3zp1YMjKwZh85iSO8bZDGYXE43qejQ9f1/joOR//k/3+A9i0MxEevwxk/\n/HbM4/vEtfcYLMI/WDEaUDrJ6BWxvV+l9Nhz4MA68MX52yUT5M0ziuYOwz0XPHFxCMlu1EOE4m4o\n0T8O0d/N5AI0+rIKBxAmwWGjOzRQh0bzdSElGquwc6YW4fWFSLnsRXKufJXia1/nF//4fMA+sZNB\nJOUgZZQN8FOv3dNIYrhlwB56xM/7X+zktpc389nueq44paz3aI5E9GgEtf5rUKMIqwqqRnS/kd0l\nZQAR0IMKwqwi7J3s3CWYNAraW60UZUrcvXAYW2pNlNqD/O6DgyAEoqWbNd0q0yRYMmco5iFu/NXt\nWLOSCHWHEC4HJlWj4WAbJWNySbSbMYeiJKYbwftoVMXnC3PRD47eYvKnJw/lUEsXdR4/qqbh9Ud4\n+ppZjC3qW4WdnuJA13U6fYY70uWyYzHLeDwGO3WmOLDYTHgauwjaTJiDUSypDpKBDYfaUDQdLaqi\nJ9kQngBaWhJSW1dPoLonDmFyI0XbUNV0JLkVtTsL2XW4L4WgZkshY+c28svTjMrkaIUbc2kbmn+Q\n7y3cDUpowDjAvbcUUF0bYviPV2IbOpPNmzfT4W3nrjsUxoz/AE3TefS/fwOaF6yjsQZ3YUoezYMP\nPc5Tv/sFrrLTWLbiU04bmYmUH6tIr9/fyyAaaw0X02H2EDPCuqah+3xIzl4WejwuJjDcTDWfDJKC\nDux94QU+OPVUpt5/P7MeeQT5BOS6jyf+ENq48ajvH+9Trk0IUYIh8o8Q4nwGLg1PCEKIcUKIjUKI\n7UKIzUKIQUPyQoibhRBfCyF2CSH+JYQ4MUHzo0HXjt6vYTCs+RBOXfK9ncK3xrDRhjT4Px488pwF\nP4Xl/dxMNieMXgxfvtB3vOgMqIpzPbkmQ7AeAnFaMfbZEIg3GtNAi5cSHw58HbctMNJhD8WNSQjh\nZNb0Mho7Bgbatc52pGTjIea0m5k7MhuzLPHpvQt56qpZfLS1hpfWVvTdSQhMxTMwFU4xtHeGzEDO\n6+0Ql+KwUn2wErXpG0OgEdADHbz40itc9LfVPL5sD0MynH0yoqTkNPROD1prhaEm69+BUttsiAdi\npFka7CFoVFAnt7Py8yCzJ8r8+YKpWKRMxuUonD1zMnPyTHS1BfmiHaS6FtY3BrBbzURaujENScN3\nyENUlgg7bTjtJvZsrqZkTC6WmHso0Obj5OlDKEh3kmwzU5KfQk7a0dOrRxekYbeaaesKsau6HR34\nwdiBbgkhBLkZSew60MpbG6p4ZkU5tiQbVXEB+9xiN6vWH2DzQQ8Wu5mwL4w9PZFiu4VwaoLhZspP\n6XUzNfcGqo2CuTZUUzpyLFAtya0orWWY3RUgRdE0jdOurGTeHIl5U2PtOlsSjaeN/BW6rze1W1fC\nqIP1WQeQVUad7uc3tzWxbds2nnr6WaZMmQLa0yDyQJxqzPOvAMd8Y3HoWQtpRh2N1LQJV9npRpyr\nbgfkjjPm1+0zDEQ4BN1ecGdCezuk9vYy0YNBhMWCiIuRSTYbWjBOw+wIKDn/fCpefrmPm0kJBllz\nxRVs/8MfOHvNGkovPHGdN8+yZaQtWHDUOaH1g7QCiMPxGohrgSeB4UKIeuAm4Jrj3PdIeAi4V9f1\nCcC9wAA9CSFEDnA9MFHX9bEYZTHfr2vrRAxEh8fIYBo37Xs9hW+NW/8Erz9lnNNgmHsRfL0OWvoJ\ngs29AdY91lc5tfgcqF4O0dhDWzJB1tnQGCcjnngG+ONWOuIU0ONiF0wE+vWYoBTY328sjZmzhg9u\nIDzNSCnuHob28GXT0TSdIemJLBiby53nT+Cu176i3de7ghRJOYgEd5/jSCkFCJtB98+dVsTL6ypQ\nWyqIln9CdM/HKJXreHnldmaUGcJ3j10+o9/+bjTv4YekjpyRiBqrp0CAqSDOQHQYBsLTLFCjFiS6\njJVytBk9YgaHi8tGpfBhbZhodQu2qMA6KpvoQQ9SjgvVH8HnD9PtsLC/oZNdG6oYO9PIZOroCNDe\nHmDRnFJ+NGcoaTYzo0v6ftYjIRRRSHVaiaoagiOT3lSXjfc3VFHV2ElHdwjFJLFsQ1WPmymrMI26\nKg+5aYkkpTvxewJYM5wkhaJY8pKNgrm8ZKT6DiPVtSdQ3WsgNHM6ktKKqmYgyy3oESdqVzYm937q\n2wNUNQSQ60ZgLj0s6y6I7s3APKwJ5eAGohWrUaq+QNm7HD3oHfAZ/KEor7Vt5PMvQrz99gEmTIgt\nEPROUH8L8l97f+v+jyHRiMPQ9hm4TzH+37gecmKu47rtkDfBaAngqYesYmhugIwc40J2dEBKb2xM\nj0QQ1r7K0CaXC6Xr2M2/0saOxTVsGJVLlwLQWVnJOzNmEPX5OG/LFlJHjTrmMfoj0tJC15YtpJ56\n6hHn6LpOaM2aox7nuAyErutVuq4vwKiGGq7r+ixdH6C1cKLQMHwQYKi91R9hngwkCCFMGP6J/lHP\nb49jieD1x5erYfJsOMGuTEeFqkJtLXz+Obz2GrQepRCuPzJzjOZED9w4+GexJxod5/pLgRedBM5M\n+PrD3jFHOmROgUNxBiD7fGh8M+54cyC8G9RYEFNMBf0A6IcfpMMw5Dbi00WHMdBAuJk4qYhm7yCr\nKyWK1t2JlGK4iVx2C2aTRH27YUyuOW0444rSuPIfX/TsctgQDEBsPDfV0aPLhK6DGqXZG2BLZQtX\nLDDcSoK+109KTkPriH0OAXJGEmqTYSDkTNB8sHJDHR9V7uPmR3YQsrVBVCXclWLINkSdCF1B7+zm\nvf1h0ro7qPdqlId0fjUqF31oOtGqNiImiYTCVLy1XgqGZZBlNdNa72XoOMPP/PU3jYwcmY0ciz9U\nVLdTWjiwPepgiERVnHYzk4vT0YG1ewbR6QKESaLb15vxZk204mnzURdzM2UVpmLyhekORklIS8Dv\n8WHLcFIgSQST7bFAdSyTKTu1b0V1otsQ7ZNTkRQvupqIkMIggkSbR2PO3ENumo1Em5lv1mVjKqwE\ns3EuysFU5NQAlqk1mIdUIKUeQErxg0WBuO9L13V+/c4mzvuJnUWLPyU73ueuPgjSYpBibECPgv8z\nSDgd1CB4txgMItwFnZWQPh58bRDqgrQh0HAAMovAZIbmOsiMsTCvF1y9NQ96ODzQQCQloXT2LxQd\nHGNvvpldDz9M1Tvv8Pb06Yz4xS9Y8MorWJzOY+88CBqef56Mc8/FdBSl12hFxTEzMY9qIIQQv4p/\nAVcBV8RtfxfcDPxFCFGDwSZu7z9B1/UG4K9ADYYB8ep6nyXrd8eJMIgNn8KMo1O2QeHzwapV8Nxz\n8Nv74LKfwSnzYGgxJDpgxjS4/TfwwvMwczqcSPn9pTdCbRWs/nDw9xf9ElY8OzDl9eQbYM0jfcdK\nfwgVb/Rup58Cvr0QjPmKJZthJPyxuIawgJgN+mG3kwyMpy+LGIrx9cUHy90MKU5GO4KB1toakdKN\nlb3DZqIsN4XbXjF8/7Ik8eCFk/i8vKmnyEsPDF44eHh8d00HI/NT++SNf7Stloiicd5JRYzIS+HV\n9X1lTKTktB4GIaUmovvDEEt5PRyc/tWLWxg23Myc0gzq6mH6aBMWJRNJboWQjmrOoP5gFWsrA+Qk\nWXj2vAnkTBhCTpsPxZ2IkCUCngAJRal01HawozvETKeVkVMKewT5li7bw3v7mim94U2eWLaH/dUe\nhhUOrubac/00jXqPHyEJVuyoJxBRiCoaLsfgC5ukRBvBYG88yOq0EuoO91zfrMJUfM3dhMMxA9Hu\nx5bpJEdAq90SYxCHVV0NF5PuTDIqqjGhSzIiEkSTXUhKB6qajiy3oAXc6GEn5rRqkhxWDtVqKA35\nmItj8huaRHDVUDSvDWGPYhrSjuWkahxnf43jgp3YFpZjnVNJTe43XH2nFbv9Mmy2orgb4CBoz4J8\nf+9YcIMhYW/KhPYNkDQWTE5o2mQka8gWqN0OeeMNplC3DwZLce3HIIhE4FsyCICixYtp3bqVFeef\nz8IPP2T0tdceV53DYNA1jbqnnyb3yiuPOi+0di32uXOPOudYDMIZe03GcCnlxl5XY/gTjgohxMpY\n7ODwa3fs3zNjx7tR1/UCDGPxz0H2TwbOBgoxciYThRDfY/nyCTKIb2MgIhE4bQHceTusWW0ExmfN\nhtvvhGUrwNsFtfXwxQb4ZBncciucPBu2bj32scFgM3c/Cr+/yfCR9kfeMBgyDj5/s+/4hPOheR/U\nxwn1lSwxZDd63EwWyDxroJvJF8cypFNAi7fZU4AtcdtWjFum9wGs66nk5tkpyR585a+2NiG7e1eB\nty8Zy46DbT0uj1H5KeSmJfLQ+8a5691NaN6+BFRt2d8TL5g7KovyunbUuEyoP7+3i6IMJ0IIZAEv\nrztA4k+ep6q5CyQJkejqEemTM5NQD7ftlMCUD2o1JNpMDBtu4eyT0iixDeGyRalIYQe6bkOOdLCi\nPEq63sWS0QXIOTmY6lpJLstDaugkFNUwl7jxH/LgKEzFW+fl5d0NjATGxNxLmqbTcMhDeXeI634w\ngtte3syBWi/F+YN3wwPoCkQovWEpZTe+SVTRuP+t7URVDatZ4rnV/ZmcgRGFqQTjEgasiVai/gj5\nscC4M9mODiSbZcNAtPmxZSRRYjHxXq0XtbELPTsJ0eYHWUa3WxFeP1pyClJH+wA3k6ZkIMlG8Dna\nNBpz5teUZiXywtpKlP2jMJXuBWG4P3WvA2V/BpFteYTXlRD6ZAQtL43iyrMDzF9czmuvdLJ0TTPZ\nOYuwWvt1clRvB/nGWMZdDL6PIWEQ91LDesiOuZdqtsDhGpm6vZAXk/RuqoPMWAZRpxeS+zGIfp6F\nE2EQQpK4WtP4eUcHmd9SFuMwOtasQbbbcZ00sEYmHqE1a7B9FwOh6/pvdV3/LZCHEQe4Rdf1W4BJ\nGNHHo0LX9VN1XR8b9xoT+/cD4Ke6rr8bm7cUGOyqLACqdF1v13VdBd4Gjto+6b777ut5rTmGf83A\ncVrp2oPg7zaCwyeCO+8w9Fo2bIIXXoTf/g4uvxwWLIChQwesOrjqKnj877B4ISxfPvgx+2PWaTB8\nnJHVNBjOvA4+eLzvmMkCs6+BtXE9JAZzM+X8EBqX9m4nnAH+Zb0S4WIBaPFNh6YB/brXUUa8m+mx\nx54iGIhw0rjBc7m11l4GATClJB2vP0xFo/GQFkJwy+LRvLiut6+kWrsV5cA61LodRPev6tOidHRB\nGlaT3OOmqvf4qfX4+cNFxkPgqatn9ayub3xuI1KyG93f1ROjkbNcve6lbCMBRg/C+NF2vO0akrMD\nzZuCZG9HhBU0NR0RbeGzHe1ETXZmpppQMzKRa1vQdRNKrotItQdTsRt/tQeRaEVymHEKkDWdgliV\neG1tB6okePrGedy4aDQ/nlpEUNf5pnZwxhSKKMy46wMmFrupfPwC6p68kGZvgE37WrjtnHE8t3o/\nXv/ALn+lBSnYZAln7BoU5KagRlXUGIMQQqAl2SixmWMuJj+2jESKzBIv7q5Dbfejazp6ptNId81O\nQ2ry9IlDyL42NFM6crQ1xiAMV6ralYsQOrdcmMpnu2rxtyahd7kw5R8a9DMCPPju16zZHyUlfR6P\nL5VB/IzCwocwPNCHb6KNRgKF1K+/e5/4wypwx7J84uMP1Vug8LCBiGMQzfV9GUS8gThSDOI4DQQY\n19mSdOTU5eNF3ZNPknfVVUdkIGvWrOHee+/lwfff5887dw465zCON0idSV8fQSQ29l1QL4Q4GUAI\ncQoDHdVg+CamCSFswvi0pwDlg8zrQbyBmHsM63hC2LQKpp9yYi6p5cth6Zvw3PMntt8558Bb78DP\nLoXHHj2+WMnt/w3P/23wgPWURdDRBHu/7Ds+80rYvhS64nzTpRfA/rg6CfcC6P6mN5vJUgxyMoRi\nbiQxGugC/TBDGAYEgHh9mWGAIeng9Xq54/bbsXQHkd2D+1d1fzcgEInGj+Unj61lamkmxZm985ec\nVERbZ5C99b0BSz3YgdZR3VOnEA+rxUR7d5jrnllP2Y1vMr0sk4UTjYKnsYVp1D91EU9fPZvtB9sx\njz2J6IGYiJokkNxO1BbDOB3OXgIYMkym8ZBASvGg+a3oUQeS6EBVUkHxYg1FSMrOR25pRjPZidos\nbF99gK1CUL21hoOSINweIBBWqIqqTHNYGDN9SE8b1p076/AIQVay8eBbODob2WrimqcHzzy54OFV\nZCU7ePn6k8lMdqBoOoqqM7E4jatPG8Hskdks/uPKAftlpCbg84e56vSR3HzOOC49pYyM9ESam3vd\nI5ZUB7ZghAR3AoF2P9YMJ1J3iPTkBDpsZpTm7r5upsY4yY3DmUyHGYSajiS3Y2TKCzZtzGTIyIOo\nms6m/S1E94/CVPY1gzH8QFjhudX7Wb1mHe+++y6btmzjnvt+1+8GUkG9CeTfg4gzGsEtoHrANgWi\nncZ9nTLdUH5t3gxZseSTmi1QEEuqrNsLuXEupsMMwusdaCD69X4wuVyoXV3o36GG50QRbmrCs2IF\nWRdffMQ5c+fO5c6LL+Zml4vfPfLIEefB8RuIF4HNQoj7hBD3AV8CLxx9l2PiCuCvQojtwAPAlQBC\niGwhxIcAsdqLpcB2YCfGcn+QhgffBcfpZtr5JUw8geI4nw+uuQqeeqZPOtxxY+ZMw+308kuw5Bwj\n7/poyCuC6++DWy6G/n1uZRl+eBv8696+484MmHYZLHugd2zYj6B2FfhjWcyyFfJ+AtVxgW7nBdAV\nMyJCAmkJaIddWAI4Ffg47g+NAA6had2ce/Zizp5ShKO1G/PQI68x1MZq5NwiAA42d3PbOWP7yEY4\nrCYWTirk3tf7Z00NDoNB+PnX55WUZCax8u4zBsw5e0ohP/rRqXgUGWWf4b6S0hLRuoIQVUECOQfU\nWG3gmUsSeO99L1JyOyKqoPqNHH89YqIj7GBahoRuS0FEIoimbvaY7aTXe6lJTSClPcCWmnbkzCS8\nDZ1URlWGmGSGju0tgnrt42+QUhxMjHWQq6rtYOG0IvbUeXlzQ9+YiaJobNzXwsM/PQmrWebLihZu\n/OdGUp02MpMdmGSJF687mZrWbp5Y1ldB9P9x995hUpTZ+/enQufuyTkPQxgyCJIxgICuGHZNsLoG\nzNnFnFDXsK4J1xzALMrKKmJAQUUlSpCcBiYwgck9sXNX1ftH9TDdk3F3v7/d976uvqb7qae7q3qq\n6jwn3PeJcZhpavEhCMKx3zghwU5dfTtTvyKgkmGUscRYcTe4kYwystVEfrSJBpsRpaoZNSMWobwx\n1BuiLVFdh2pLQHQ50bAhaAqC4kdVo6lvreD8Z3/glNsO4ohxM3aoQLTViFKlexVScmQ9SiCoMu0v\nKxk5fBgZPTGJ1TcBI4iXtI9pGtTcCgmP6WrEtashfqoum1LzKzhywBIPTZXg90BCP/09ZQcgK8Q5\nCc9BtLSAI2y1LwidFnKiwYAcG4v/eApP/kWUvfgiKX/8I4aY7sOQAJ6vv8Z6xhm95jn6WsX0OHAF\n0BB6XKFpWg8F+H36zA2apo3VNG20pmkTNU1nXGmaVqlp2uyweY9omjY4FJq6TNO0397luxOOY1W/\nazMMPw5N9YcWwEknQw9lZr0iLw/Wrtf/jhkN69b1PP+SGyEuEV56pPO2mfN0d3lvh9XnzHthy4fg\nClUmmaJ1I7E7zA7n3ASli0AJ5TiiLtYNhBYiAYlzQP047EPPAr6izfhu2bKLlpYMXnrxKipLCnj5\ninEopfUIURaEmC6YsoBSXoycocfiW70BMkJKpOG4fuYg1h/sTKTqCFVVaWj18sZ3BwgoKtueOhcE\nATFxAHL/U5BzJyE4krE6bDz19G3c/udnjoXQpOQo1NBKWkwCtRlOuudrht6zhLxhAmMSUtGCUcjJ\nDrCMRZRaET1ejrbaGJ+sgReUxCQChyo4ZLKQ6XTRLIu4rAZMrX7csRYaShtIyUuktbaVhJAqq8vl\nA7efHXWteEJ9GwqOODl7Uh5XThvEAx9vo7iq6Rgb/ZRHviI11sqg9Gh8AYVZj62ksLqFpy9pP2cT\no8zMmzaIr36NLHu2mmUCQRV/oL3sOT7ehjO8Z3V2LL4WL5YYC94mL5qqYUq0Y/MGaHaYcRbWEWzr\nDZEch1jdgBYdg+BygyagGm189uMOCurNPPjeV7y/xsOmwl8oq2thx1Pnr9ovkQAAIABJREFUkRgY\ny5+vUDlS1woI+A8Mx5C/O2I/3/juIK2alY+Xfdb9P1urBuVBkF6NJME2fwSaH6Iv11/XfA1JoVBT\nxU+QcYr+/EjIexAEvbzVbAVHaIFXXdHuQbS0QEdSXBeyGuaMDHzl5Z3G/xMItrZS/sYbZM/vvX7I\n/dVXWM88s9d5fdViykLvSv9Z6FEfGvvfR1/CNx43lBTA4JF9+8wtW+CjJfDMs//avoGehH72OT0v\nceH58Phj3eu7CAL89S1Ythi2/By5zWCEuQ/C+w9GjjsSdeLcpnfax0bcCHveOEYqwz5Q7xFxdKn+\n2jQIDBng/iH0vVP1C1NrUwYdgk5Z2clHS5Ywbtw4br75bfIHNLHsjhmYM0cgZ09CqVQxDO5aNkCp\nLEOMSwSjCVkScHXBuh6ZHY/LG6DZ3bOOjcenEFRVftxbyeoFZyBLIlLaCKSUIQiWaAR7InLOBIwn\nTuPglh3s3Na+wpaSolBq9DiykqLw6tsHqG5w8f3iCYiVscyYnY8WGIwgFSOoMWjGXEStlRh7Ioqq\nITqbUBMSsVXW41Zkmi0G7K1+auNs2BrdiGkxNJY1MHZkOmga9mhd7mPX7qOMHpGO1WqkrN6Fqmoc\nLnWSGG8lPdqMx+1n6v1fkH/TUvrfuJR9ZQ28e9NJGGXde3CYjWx64mz+MCE34rdw+5X2kt8QBEEg\nym48xqYGiI+z4axv56lMGZGB5g8iyRJGmxFvixdzgp0/DEpm6eFaln+5m6lvrKf1UA3nLf4Fd4uH\nVz7fSYPJxuG9RfxcobB1+16W7/AyKUdj0SqJWSd4WP3gqWQnOgjWDeKMKSJvr9OLM5SyXARbC2Kc\nvvr2+oP8/duDfLT0H6T3JDWh3A7iPBDDcoWqC2rvhqS/60ZDU6FmZbuBKP8R0kPKzKVh+YfS/ZA5\nJPS5CjhrIDGU8G5pgfASUknq8ro0ZWTgreiugv/fi6NvvUXsKadgzcvrcZ7a0oJ30yYsvZDooO8h\npq+AL0OP79FLUrrmhv8voQu3sEvs2w79hx6Toe4RgQBcezU89UyE0uO/jNmzYcs2+P47OH2mfoJ2\nhYRkeGwR3HUpNHcgFE2/FOrKYOeayPGp18O619q16xOGQUx/KFrePif3Jih5tf111CXQ9IH+XJBA\nvBCUNi9CAGbT1LSEG2+8gdevmcJLv5vMjNPS6D/pdMSEPAR7Apo3AzkrAUxd6CQpQZTqCnZ4dA9j\ncEZnl9lqknFYDOwt76E/BrB6z1GCisaGx8/WZcJFGTE2cn0jWI3IqZls+fzLdgn/UP7hike+JvXq\nD2mJ9bNiRRlf3DOD3HFeDJWZSLF1aN4cBOEoeFrQTAORAtVobo0NlUBNNRomtDgH+QGVI/F2Ep0u\nauOsOBo95A5Lxd3oxq9o1AO+0Cp++/YyRo/KwGyUqW70UF7dTJTdxNaiegTgyukD6ZccRW2zl5xE\nG0vnT2d0bgKaprF0QzFmU9eNasbkxvFrUT3Lt0T2IIi2myMMRFyclfowD0I0S1hCl4olxoK7wY0p\n0c6oWCvTpw3k7Ow4rrv4RIzeAKLbT6XJzKHtxawodvHOso0s3d3Kg7MyuOX30zh3lIVvHzgPqyGP\n+JiQdpdqoKYkh4vOdlFa1wqaSODgMAyDdC9i8ZoCho8crWsjdQf1B1DXgbQgcrz+KbBMAWsoRNy0\nA+RosPXT8w9H10N6qCtheIK6dJ/egAugrhqiYts5UK2RHkR3BuL/yoNQg0GOLFxIzh139DrXs3o1\n5kmTEHvgSLShryGm4WGVSAPQK456FvH4X0BfDcSuzTCij6Vnzy+EpGToIUn0m5GeDqu/h7R0uOP2\n7uedeiacehY81IHsLsnwx4d0LyL8uHMngtECBT+0j424EXa+3P468XTwlEBrqJYgag60rtBXZ9Ae\nZjr2ub9DEFbRL1Fm7pQ8hICA2mxCjA/TjlJE1GYzhmFdr3iU8mLMuQPITYrCKHdN6FFUDaPU82lc\nUe8iJcbC4PSQkRHEyPCDAFJGHMGSCjKiDDS4fcx/ZxN/+e4ghw5Vs3xDIc/Pn4C7Ncj9M0cxaKgR\nJBW1LhrBfBi8FjQtE9FXiCYkgSASFXCxtQa0piaEOjdqbiqjfUHk4WmkNHmwD0zC6gtiNBuITosh\nz24iaDHw53c2oaoqu3ZVMGJEGr6AvuIvOOJkYHY85XX672c1ypw1JpP7fj+Ss0/IYkYod7FqZwWf\nbS7huwdPP3Z4hZVNrNlVwa+FtZxzYjb3nzeaa15bi9vbrhMUbTfRHO5BdAgxCUYZMzopzRJjxdPg\nxpRgw1vbypw/jMLodPHHkwZgyk1g2Zwx5AzP5sUzBjH3nPHcd1I6l589iVilSe9RrTSDGiDgH4Zs\n3E+brFtScCwX/Q7uXarrbQVLBiAl1CCN3EhTym6eXXg2aEfaK+jCofkgeD3IL+qNOtoQOAINL0HS\n39rHar6G5JD3ULsDHBl6BZ+mQenW9hLXsv3t+YfwCibQc4zhISZZ7jLEZMrIwPt/YCBqli3DnJnZ\na2krhMJLs2f3Og9+Yz8ITdN+BXrfk/969DEH0VcDUVgITz8Fr7x6/BpPfYUkwYsvwepV0JOO/F1P\n6Yn1LR3E7U6eCy1O2BZWQisIMOU6WBvmIeT9HhoLoC6krSTKkH4xlL+vv5aTwTIRWj4PfcZ49M4t\netnc99/vZ88uD6tfnnCsKkepdSBGRbJ51TorhpwoEDv/Xns376D/iCE8eOGYTtva4LAYKK7pxpsK\n4erTBuLxK/ywJ5T0VPxore29l8VEB/iDBIv2kZ3ooNLp4s3vDjB8TDZ7fi3jk/nTuWROHpl+B2Pz\nEpH71RMsioegC8FYAj4PmjYAwV+gE+SMKVi8TlpboThoRCqrRclKxnColv7jc7GpGif2T8SWGUvj\n0SZiM2OoKHXiNkgs3VDE/oPVxMRYuG3JVqIsBiYOTNINRE4csfbOXmysw3zs+WurD3LuiVnHemp/\nt6OcTzcUsfVQDd/vKOfDHw8x79QB9E+N5rkv22P8UR0MRFyc7ZhgH4DFYkQBfB69X4W70YMpwY6v\nrhUx2gIBFbXVF6pkCiWqaxpQY+OI97UyfEh/BJ8LFAVVjkMM1qKpMahKIrIhVK4ctKA05HDiuGrd\nk1JkPD/PZPNOLxMmRjN00AoITIKAHQIjIHABBO8H5V1QbgBhCIgd+jTX3A1xt4AhzGPsmH9IP0V/\nXl8CsgliQppcZWEhpvD8A3TKQSBJ0IUw3/+FB6FpGiVPP03OnXf2PldV+5x/gL7nIMIZ1XcIgrCE\nf6fkxf8rCELXq5GO2LcdhvbKC4QHH4A/z4d+/f71fesJUVGw+G248gpdpqMrmC1w0wJ45u7ItoeS\nBJc9Dm/Oj2RXn3gJFP4M1SEPQTLoXsSWsFqEzCugdDEoofdFXw6Nr+vPBQHES0F9A1VVuXre5XgO\nxeAYqoe51uw5yrQr/gmOShDaLyTNI6I0uJD7de4U9sWGg+zatpczLz2/25/ij1MH8MDHv/YoB26U\nZYyGyIZAwbJtqC01YJCQEhz4d29HdRaTl+zg1asnowGTpvTnd5nRnDosDTkDlHJA0JCzGwgWxyHG\nNKC12hAC+9CCSXp5ZdUeFNWGOegiCYjvl4VYXosmyGh2E/7qFgz9E3EV12Pvl0BDqZPYzDg+++Eg\nRzwB/EGVJ9/eRFRqNCu2lvLXi09ElkQKSnQG9dQhqUhhokqSKDJ1iM4ZUVWNzYeqOTvUNrXJ5WNH\nUR3hcLZ42VVcj6aBQW43yg6rkZawXE5MjIXGMCmUOLsJL7Bxz1EsMRY8je6QgXDpZMPUKL2SKT0G\nsaKxXZMpJhbB5YKg0t4fwpCMFNB7XQf8wzCY9qIr74C5aTTXXgQ5N71PUFFRG2O57n4vBsvbYPgB\njBVgqAHpXRDPA8EE2irQykDuULLpWgXeXyAu7Mbpq4GWfXpbXdAr9o4lqDe3h5c0TQ8xhXsQSWHt\nbV0usLV7KoLJhObrzDExZ2fjKSrqNP7vRN3Klag+Hwl9uOn7Nm1CTEjA0Md7VF89CEfYw4Sekzin\nj+/974Ug9h5i8vugogRyB/U8r6BAzw/cdPO/bfd6xKmnwq23wQXngbdr6WPOvVTPiaz4MHJ84rm6\nvv0/nmwfMzvglFvhmzBZglG3QvkaqAlJekcNg6jhcDRU4ur4AwSKwRNifUs3gPoR/1z2JprfxXjT\nIMRYD3U0cN4z37H+lyI2bKqn2K0ngbWgj2DpNgI7j2AYltHJi3D7gjx+73NIqZkYhoymK9x77ghE\nAV74em+3P5WqqjS7fCRFt6+0CXpRSjYimlsJHNiOUqIrhAqCwJ9OHsBr100lqV8CSk2zHrEwgVoP\nUmozaosJzWVCSqlAqUlGEA+gFO1D8cUgtBSi+WU8phjGx4A9KhrNYUE67EQZloZ/fxXG/BRaD9dh\nz0uk4YgTe0YUsRq8d98snpg7lpbKJs6YpstLnzo0FU3TKDjiZFB2HLkpUVw6fRAT8lOYkJ/CZacN\nIic5Co8/yIn3fE5QUTltmL7SbWj1HWOfh2PnkXoKq5q4clr+sTGTUcLvbw+RWCwGgkHlmNxGcrQF\nq83IXz/5FbPDjLfZiynOht/pQtM0pCQHwZoWvIl2tPIG1KQYxDo9ua/GxCA2OFEciUgtNaiGZKSg\nbiBUJRlNtSDJek5E80cRaErlxj/Ch2sP8/P+KvwYmDmzvT81gl1veSvN0fMN8odgWAXhdTOqC6qu\ng+RXQQyrlKtaAUmz9PLtoE9vtZsZYlOXbIKcUI6jsUZfPMaGCJu1lZEehMcDlvb+IWJUFGoXshr2\nIUNo3bevy//DvwOaqlL4wAPk/eUvCH1oQdD68cfY5/Rd77SvBmJfG6ta07THNU37EL2W8X8bffEg\nigsgI7d3gb6/Pakbh98orvWbcOddkJUNN9/UtaETRVjwIjxzj55Ua4MgwA0v6+zq0jDe4cm3wP5v\noSo0ZrTDuPthQ5hMVr/bofBZ/fsEA8TeCs5QtZaQAuK5mA2LueKkXCbdt5LHnz7K181bEQSofPNi\nDv9ci1PZgnfvKl2Zs/koan0raqMbuQMv4stfy5mQHY33hxXIA4Yj9+vcA8Egi5wyLI2tHVbKoMtO\nxF/xPlGXvodfUTkaVpUDIMYlISanE9jbmUtxwe+GUXi4loufWk1rjB8l5C9L2Q0Ej8QCGnLOIZSK\nNARBRVSbUYJ6fF10+fCY4xgfDT9vrUDJTELaU4EyLJXAwWoM+cm0FNZi7xdPQ1kDHqsRO5CTHc/I\nFAeiBjmhvg2CIFDX6EHTNBLj9BtdQpSZqUNTmTo0lfhQeOnj9UXUt/ooe32O3roTSI61HnsejqFZ\ncQQVNULd1WiQIspcBUHAajXq5bYhpCTacTZ6+LGoFl+LF8liQJBFgq0+hEQ7e7eV8s7+Kjwl9Xyy\nuRTFYUWob0aNS0Csr0N1JCG21KDIiYjBOt3jos2LaCfGRbvGMf9ygTs+2MCba4q4+vobEY+3/0rd\nw3oI1H565HjVckg5V39euR7ihoI5pKlUHGYgjuyFrKHtoeKao5EehNcL5vYFh2C1ogUCaB04SMak\nJARJwl/VtVDiv4qaTz8FUSTp9723INAUBdcnn2C/qO/dMPv6q3cS0utm7H8LYh88iMP7oP+QnueU\nlMCKz//vvIc2CAIsfgs2bYQ3uuEPjpoAk2fAq49FjidkwMUPwwtXt4egLFEwbT6sDGOmDrsGGg9B\nWajyKXEGIEDtKv11zFW6Kx8I1daLtzNpwnb+uuJX9hypY6JhGJdeEkfBa+fhsBhI89nIybUhWFwR\nv31gVxmGoekQSjhX1LvYV+bkxLwENI8L7w8rMIyacIw8F45Gl5+4LmLzX/9aii+g8NYNJzF1cCrv\n/hRJ1jeOmUJg1yYIdi6h9cVY+fmnAvaWN7EzUM8TL+3gzR/2IqU3oRyJRUysgqABggGU1iREqQ58\nBj2+3lKH3RZDXQBS3T7UlHjEwloC2XEo1c1osRZUb4CgJGIwG4g1G2kGPEGFTb8coRJ4cvku4h1m\nlqw7TEFJPQOy43okNT26bDsPXzAKo9xevWQxypw2MiMiJDUwPYb0OBuCINASJtBnNEjHKqjaYLOZ\ncLnaw06x0VaGpERT6Q3ibda9Vt2LcHM4qOI/2kSjxYDVH+RoRQOVRhNidQNqfIhR7UhEaq0DwYgq\nRiEGdfKnEsxEQEGUdHKm5o0lRsjgqvNh+cZDzJt3ZbfH3SW8v0LTe5C0MHLcVwvOn9vzD0dWQVbI\nMwn44OguyA4xqEv36m172xBuIIJB/ZoJY04LgqB7EV1Ia9iGDKF1b/ce7m+FpigULlhA/8ce65Ow\nn/fHH5HS0zEMGNDn7+hNzfUMQRBeBNIFQXgh7PEO/3/oKNdWE90TDu+FAb3osT/9FFxzbaS643FC\n0zR827ejNHbWuu8RDocuy/HQg9Bdd6g7noRlb+neUDjOvF4//pVhxuXkm/RqpsrQCS0ZYcKjsP6e\nkNcgQN7tUBjSfZKi9VyEMxT/FYexZZuuEjL/rOFMzMrAWBtPymjdgymuamHFsnLMgyJPPdXpQq1v\nRR6gexGLvtM5Fec/+z3r9lehtTTi+/ErTBOmIbbVoodQ1eghLbYz4e7DdYVMH57GBRNzuXLaQL7d\nWUFZqApIyswDg5Fgkf49a/YcZcJ9K3hmxS4+WneYfT4Fod7Fjud/z6knpVC0x83PDQdZs66Jm17Z\ngiH3EIHiAUj2WhRXPKLYhOD16Y1xWmrBrbKpUaC/34sWFFEzYgmUNmLIS8R1pIEqm5Frn1xNvVFm\nz75KGgUIqhp1pU4qgZe/2Uez289jy7Zzz9sbUXuo1FJUlbpmDxdO7FwNNjwnnmvPGMI5E3K5bPog\nzpmQyzs/HSbWZjqWyAYwGiV8/shL2mYz0trq4+d9ldQ0eTCYZfYV1zF1VMYxA2GMt+FzuigKqjhc\nPjRBoN5mIr7VRxEyYnXDMUY1BguabELwNKEY05D8bYQ9gYB/KEZTe7OpYNVIHrlRZsKJI0lM7Jyf\n6hZaECqvhsS/gZwUue3AfZB5JRhCXQZKV0FWiMhasRMSB4ApVPp5pAcD0eY9dLgpi9HRXRoI+9Ch\ntOzY0fdj6CMqlyzBEBdH/KxZfZp/vOEl6N2DOApsBbzoGs5tjxVA3/bqvxmCEJnA7QqH90FeDx7E\n0aOw9GO47c+/aReCVVU0Pv005UOGUH3uuZQPHkzLBx8cX8xy4EBY9BZcdAFUdtHoLzEFrrkHnuiw\nj6IIN7+hl726Q/FTkx2m3wFfh7GxB80B1Q+HP9Vfp8+F1n3QFBL6irsVmt4BRb84XnrZwsJHrTwy\nR88bBA8kIQ+sBUFj3IBEXnp1H1IOnc4+/64yDEPSuPW9X3j2y928ed1U7jxnBFeGej+ozhq8m9di\nPuUs5IGTEOz6DWBkThybD0fKGQSDKgWVzcwcmYEgCJw7LpuJA5OZeP8XIIoYR0/Cv20daBpef5C5\nz68hN8nO05/v4vb3NzNlch5XDE9BSgHBKfDK5ZNY/NehNBc4+HRbAWrSEYKl/RDtNeA2oipxiIE6\nNNWGZjAhOhspcEtIHh9iWTPK0DT8B6pozYxl4RvrWVnTyiCjyNZGN4+/t5mk9Fg0X5DmRg9fPXE2\nh168kLLX53LjGUMRgypf7TlK+jVLuPzlnyKO8+DRRhZ8vA2LyYDV3DX3wWY2MDA9hqQQa93tC9Ls\niSQXmjqEmAAMJpn5b23kwud+oN+NSwkIYBUEVJOMtyXcg3ChxttwhLyNOruJhBYfjXYbYo2znVEd\n8KOG8hBB8yAM3kP6eQUEA/0QxEZEMdSn2p1AQYnEC09M7PKYuoXz77pWWPRlkeONW6H6Sxj0sP7a\nXQNNRZASKsYMzz8AHNmjh5jaUFMJSaGFidcbkX9oQ3cGIvWSSyhduLDP0t99gRoIUPTww+Q9/nif\nvAfN78f12WfHFV6C3tVcd2qa9i6Qp2nau2GPTzVN65md9L+APnkQvYSYFj4Hl14Gx7HK0TQNz08/\nUfX731M+eDCBAwdIXLSIzJISkpcvp+m556g85ZRe+8VGYPZsuPIqPWnt7typjT/dDKWFsKqDTEHO\nMBgzC5Y/3z429QYoXAulbYJ8Ikx8HH55SFc4FY2QczMUhmrLDVlgmwmNr+P1evn621ZEvw0pUydB\nqQ1WtFYTUnYDg9Ji0Frh4IFm5JwOv0ujm00bCkkYncWb101l7pQ8bvndUJwtHvaU1iNYYpCiBqFU\nNmMcOQJ50FTEhDxmjUhjw8Earn1j7bGk6qUv/4TFKHNRSDpbEkX+evFYmlw+Xis2cPBAMWp1OW5v\nkBPuXo7JIPLK1ZO5/NQBzD5rBMFGD/gVpAwIVgCyQkyuh5kJw3n14RS+/0GkqNyFaGpG8HtRlQSk\nYC1Vla38UKrgrzhKS3MQJS0eqbAOdWASZZuKmbdqH8MlgRmnD+Gk5Cjuu2oyl47J5MIZg9i2rZTR\nozMYmhVHaqwVu9nAPeeOJNFsYOndM/notlNZvbOCy1/68dhvdtVr63n3p8M8FSap0RsWnD8KURD4\neX/7YqJjiKnB5WNzcT1+X4Cily4ixmbCrWoMTHawprAOX4sPTdUwxtnw1bsZPjIdOagiBxTqHGYS\nW72kDM1ArG4AUUSNjUV01qOE8hCa5EAxpCH72sQlJQL+IRhMeunthoPVPPOulTE5q9slXXqDvwic\nf4WU1yNX95oKu2+C/MfDvIfVkHGyXq0HofxDyFhoWmSIye+H1iaIDRFfvd7OKsyEDEQXEYCYSZOI\nP+MMCvpAYusrKhYvxpKXR9zJJ/dpvvvbbzHk5yNnZh7X9/QWYmrrHrO9Q1+HXYIg7Orpvf8T6C0H\noap6M57s/l1vd7ngnbf1aqI+QPP7afnwQyrGjqXummuwzpxJVmkpiYsXY548GUEQMI8fT/qWLdj/\n9Cdq5syhavZsfNu39+14HlwAef3hvD9Ax5I7o1GX4XjoOjjaoQXpnx6FFS9AdYhda7LB2U/Ckqva\n5TZyzgCDAw6GKqJyb4S6NfrKDCBhATifZsVnbzFhcAbKvhMwDt0OYigRuTcF47BKEDTuPGcEl137\nM8JwDSGssOjlb/Zx+fVLeOSBM7loml41ZjHKxNnNFNe2IiYNBFFCbfKgVDdjyEtEyhrG6Sdk8dYN\nJ/Hhz4X84ZnV7Cmt59vtZbx/08kkhHEENA2GDEjnyusvZO4Vj3PHe5tIv3YJmgabnjiHWJuJopYA\nr77yR8Sd+m8kp+nlrVJ6E0qtHfwys8/18eIbAe789Au8zbF68xu/HU00s2PnYb4+4CbQ6iYpCM/v\nqsF/qIZAShRmp5sJ0/PJ9iucde5IGkqdxOfG42/0kJIZx959lYwcESkj4XL7qW/yMCY/mZOGpLJ0\n/jTWHqhmzsIfePfHQ2wvqmXj42dx2SkD+3aOoHsUg9JjWLaxOGK87ZbqbPVx2iMrkWSJe88ejtUs\nkxxjZVNhHck2IxsP1yEbZQLeAMZYC4FGN0Oy4hATbOTbTIjpMQwzyQwblYPg9oHXjxqfoEt/O5KQ\nWkK9ICxDMXj2HVukBf2DkKRKBKGZ174vZMJp9yGah8ChWDgyFapvgcZ3wLtT7wwXDk2Byssg/j4w\ndrhej7yhs/0zL28fK/4ScsPIYkXroF+Iad1YA6IEMaEQVX01xCe392wNBCLyD22QUlIIduXBAwOf\nfZbG9espfeGFLrcfDwJNTRQ9/DAD/va33ieH0LJoEY4rrjju7+otxHRr6O9s9Kqljo//bfTmQdQc\nhehYsHQtKMeyZTBxEmRn9/g1alMTjU8+SWm/frS89RaxjzxCxv79RF1/PWIXVU+CJBF11VVkFhRg\nOeMMqmbPpvr88/H3lugSRT1pbbXCJRd3Ju6cMAnm3Q5/nhOp+JqSC2ffonMj2jD+UohKgdVPhXZK\ngKnPwIYHIOjRu3ANegT23q7feU2DwTEHse4hbp01ALU2FbUlBjlPj/ErlQ40n4yc4+QP43JIVq0s\neb8IY2jRpqoqj3zyK5eOyUQsd2IcEbnScXuDCIZ2t15tcKFUNmHon4YQ2y7d/cOeSibc9wXXzBzC\n8A6tOfOzE9mx+hmsFQXkOQQWf1/Azb8byr6F55EaawVR4LnX/siqf2xDrW9FjNcJupoL5KwGlNJY\nBHsztjgPH/3xEub9XmLXHpveQc6joMjJjIj2c8uM4TRao7llWCIXTRtGiaIx/9GVbAHyDBLGBBuK\npuF3+bEn2qk72kRCahS1ta2kpET2Azhc3kBuesyxRPOU/BS+uncWX24r5ebF67lmRj6ZCb1LJnTE\n7bOHsWpnO5VJUTREUaC22cu0h78mymrkzDGZxyKwN87Kp9Tp4tfCOmaPycBgM+J3+zFEW/A36XwJ\nS0o009JjOPGkAUQ3eUEQUBNjdMJcXDxSfR2qNQYh4IGAF9WQgCbawnIRBgKBfAzGPXy6oYALLrgQ\nMlZAXgkkPKw3AnevhqNzoCAaSsbq+YaGV6D2XkCE2A6LNW8lHHwQRrzezp5X/HpjrNzQLcxZCgEv\nJIWSt+ESGwC1VZDQ3p8ERQG5czhPzspC6YaXZIiOZvRXX1H85JPUfvFF7/+gbqBpGoULFpAwezZR\no7su/e6IYHk53rVrjzv/AL2HmNrM4Q2aph0JfwA3HPe3/bdBEHvOQZQVQ2YPhJJvVsK5vZeXVc+Z\ng3fLFlK+/JK077/HNnt2n2qWBZOJ6BtvJPPQIUwTJlA5bRo1l1xC4PDh7t8ky7DkI53pefVVnT2k\nK+8ARww8/0Dk+Pl3QdEO2BpiZwsCzHkdfny+PWGdNhmSx8KOUJOhzHkQcEKVzqZW4xdw0pg6po/V\nb+T+XWMw5u8O9RgW8O9MwzC8ElHWuO3MYdx8+0Z8soLcD97/+TAOs4HbzhyGf3c5clY8Qki47g8T\ncnlt9QHU1sg8g9roJlhSgfmUMxBjExmcEcf0cQP5+dWrefK+izG9XPK9AAAgAElEQVSMGI9p0gzM\nsy7AesE1WM+/CjE6iUDBPt676SQa3r2Uv1w05lgM1zg6m6rKJr7+hx5aCw8vSSktBMujkbMKUUpz\nEaQgs6YqlBZK7CvT2LJnH4drJBwGSFEV0vJzsNY1kG4yYx+WxihvgE2SwDijTNTAJJxHnMRlx+Fq\n9iIZJKwOM/X1LuLjI2/2haUNDMiKLH7IT49h4eUTkESBBef37SbREaNz4yOaBymqhl9RmfnoSpKi\nzHy/4HRkWTrWhW/etEHcd/4JXDK5H3eeMxKj1Yjf5ccYYyEQItRJiXaUulbUlCjEmmbQNNQknVGt\nxCcg1teDIKLYE5FaQkQ5y1AMnvaFT8CvCx9mJIhkZYV4DVI82KZD/B2Q9iH02w8DaiH5RTCPBu92\n8O6A1HciJVQA9t4GWdfoHJ42VPwMsYPAFrrpF66DvCntYanSvZH5h7oqPY/XhmCwy17OcmYmwe6I\nq4AlJ4dRn33G3nnzaO5rVCAMAaeTXRdeiPP77+n/+ON9fl/L4sXY58xBDCP29RV9LXPtSrO6s6D+\nfwMC3ZDGuoIoHusa1iXKiiCjGwOhKDoxLpzA0wXcK1cSLCwk+aOPMI0a1fd9C99Nq5WYO+4g8/Bh\nDPn5VEyYgOvTT7t/g8kEn34Gu3bCWx06uYoiPPUufLEEfgzr2WA0w3UvwGs3tzOs47Jg9mPwwbz2\n32nyX+HXp8FTr8tvDHkW9t8Jqp/KGj/PvS0Tk6ef/FpzrN5jOCTbrNY40FpNyP3qmTAwiQsm9mfC\njC9pGeDj2e93M2dKnn6z9gfx7ynHOFr3zNJjLdQ2e1FrCiIkMrSAh8CuH/Fv/gnL7y5ib/HXvP/Z\n3xk1+wwMqZmgqSiVpShVLQQO1xLYe5RgaTNyzmS9OisMUmYcDVEWfn/hm9w+W785SOmgVISHlyTk\n7EKCR/pzyP0r36yD3MQAX29VGJLk5eXlBzjgMmNw1qHJFrQoG2JZI4ljMpkuS6xRNITyBqIGJeMs\nricuJ566yiYSUqPxegP4/UEcjsjY9qFSJ/2zOvcTkUSBtDg7MbY+CEh2AbNRJqi0L46aPX4+2VhM\nQpSZbx6YhSiKSKKAEjbHbjcSFRIBNFo7exBSgh2lpgWsRjDKCE0e1OQYxOpGvUe11wM+H2pUMmKz\nHmZSjJkIqhcxEJJt18xsOhjNons7c14iINp0nkPsDZD6JmStAmOkci3VX0PjNhjYYTFU9Dn0C+P5\nFq2DvKntr0v2dKhgquzsQXRnIEpLO42HI3r8eAa/+io7zj77uDSa6r/7jo0jR2LOyGD81q2YkvvW\nr01TFJoXLcJx7bW9T+4CveUgrhcEYTcwqEP+oRj478xBHNnc97mi1HOIqayoew9i+3ZIToYeGpdo\nwSD1t99O3DPPdOpX+1sgOhzEPvAAqatXU3vddXjWru1+stUK774P992j8zTCEZcIz34I983Tm6C0\nYdyZ+srpn2GtSyddreck1oSS2LGDoP8FsCW0gkmaCbYBUPIK7733Hgf2ZiOaWpGi9M8N7B2NIfcQ\nglUvL/XvTMMwrApElRfnTeCKMQN55pk9vLloMjZTmBTGoWpEhxkpNZomt59oiwHUIMHi9QQKfiBY\nuJbggdVo3maU8iJcS1/HvWwR555yKbdddh/+jd8R2L0FpaYOVBME2//PgmxCjG0PYQl2E6Zx/Zg7\ndxGNjW7K610INhAtoNaB3M+D1joaeXA0aCbUxjjyh1Xz0RcynkA5XreNKJuVS0cnkpvXD7HBCS0K\nSkYiUmEtgWgLsgCHgeaD1TgGJVNfUk98TrweXkqLpq7eRXy8rVNFyuGyBvpndS6f3lBQS2LUbzMO\noPfTDqoqjS4f1Y1u3lx9AIfFwLf3zzpGSpNkEVVp90Blg0QwlMg+ZiCiLARbvGiqipSkexAAanIU\nQlXzMQ8CUTzWglQJy0MgiAQsgyO8iOe+MHFq/1Lw/wt1MEEX7L4BRrwKUljFkaZB0Qrod3b72OG1\nugfRht48iJ4MRA8eRBuSzz+fzJtuYsdZZxFsbe1xruL1cnD+fPZefjlD33qLQQsXIoUR9HqDe+VK\n5LQ0TCP72KqgA3rzIJag5xpWEJl7GKNp2iU9vfH/GQ791PucNvQaYiqCzNyut61eBTN69h6a33gD\nKTUV61n/3nSNafRokj78kJre8hLDhsEdd8K8yzsf54kn6ZVNf54bmau49nlYvrA9YS2KMPdNWPXX\ndp2m8Q/B/vegKZTkHPIM2qEneOnZh7ln9lD85WMxZmwFVDSvlUBhPoahuleh1ttQG6zIA3RP4NoZ\ng7m1/3DsNpkL/pTTvh+qhn/7EYwn5DAoI4aicEE+Xwua20lEN8BggMZmPUYeIQ0udXMTbfMgRAHT\nlIGUrz/Epl+KyUywc8d7mxFSNIJHQUzMREpuRAtOQE4/gOo5AzFew2IJ4mlIYHQ/lTMHp6IZUxgT\nHyTeEY3qiNJbbibFIdS04q1z4c1LJA1QBAFTvA1nST1xuSEDkRrNd1tKCHTgOqiqRlFZA/0zOxuI\nB/4wkn3ljWwr/G3dyixGmeRoKz/vq+KihWuIthqZO6V/BGNZEoUILyPCQNiMBFx+RFlEshoJtPh0\nD6I2ZCBSohCrmlGTQwZC01DjEpCcdaj2BER3Ayj6eRc0DUAKVCEoLewormf1Dida8mwo6dBH/XhQ\n8AjETQkRO8NQtwtEA8SFKhPdDeAsgYyQd69pOgciJywkVddFDqIrA5GV1asH0Yacu+4iauxYds+Z\ng9qFyB9Ay+7dbB43Dm9pKRN27iT+NzQfa3n99d/sPUDvOYgmTdNKNE2bG8o7eNCvSvt/bcOgwl66\nroWjtxBTRQl0wdwF4IfvYXr3DTdUj4fGRx8l/tln+1SnfLywzphB3HPPUTlzJr5dPThz80NJ5IcW\ndN527b1gtcPjYYm95Bz4/Xx49tJ2hnFiHpzxELx/mf572ZJh9HxYc4P+2Y4hNNtP57krNYZnx6E0\nZ6FpsRgHNCDGZhIoGIGUXIkYr8ed/TtTMQ6tAlOAr34tJf+WZfzt/j2MOD0WISxHq5Q3oLp8nP/n\nGVj7EEp5/qs9DM2O5/qZ7RpDWmuNrvnfAVqznl4zjsrCWdNC1ml/Z8bIDFbeN4u9ZU6qbC6UcpD7\ng+bKBFVGjNqA2nwyxpRSgvUDSIxqZl8ZpFtdqGI8orcFodmHmpCEVFaLhoyaFYu/sI6UsVlMMssc\nMkgE3H5anW6+OFRL7dEm1pY18Ow/d7CtvJET7vqMkxZ8ycIvd1NZ14rDZsLRxbHnJDmItho5/fEe\nFH17QUqsjee+3ENBZRNnnZCJoYMshyAIEXwcSZZQArrBMFgM+ENcCkO0hUCTRzcQIQ9CS4lCqG4G\nmwUkEaHFjRIfr+chJAOqJQbRFQoXigYC5gEIrr2c8/T33P/AA5iGLIDiF3VP4Hjh3Ajl78HQ5zpv\nK1yuew9t12ThOr28ta3c1VkZWcEEei+I+LDXqgpd5BDFhAQ0vx+loXfPRxAE8l95BU1R2HXBBShh\npemaolDyzDNsmzaN7PnzGfHJJxjj4/t06OEIFBfj3bjxuLkP4eirmutZgiAcAoqBn4AS/lsbBh3Z\n3Dv5rQ29VTF11IBvQzCod42bNKnbt7a89Ram8eN/c96hL3BcfDHxCxdSNWNG95wJSYKln+gd7t57\nL3KbKMLfl8K6b+GbZe3j598NFjssCus5cdKNuhTymhBjesyd4KlD2/0a7733LhMu+45pw0UkuQQ5\nZzKKfCey40ekjBTkzJPwbx+HaewGEBW0RiuBonhMk45wz5ItzJ2Sx+sXTyGwA0yTiTgrfT8fRPYF\nWLfxbup76fuwetdRjtZ3cNnVIMEjW9ACIWVSJYBydBeapxExJRopO55TZr/MzWcM5bWrJ5OT5ODl\nWyYTm2nisxVHkOIOojYNR7BtQ/PmQDAK0bSVYH1/zh4foL4xmSSzE80j6aGT2hqUmFgElwexzoua\nl0iwpB5DbgLjZYkii4G64nqKFJXrF61n7/5KXlh7mCFJDi6dkU9echQxViMP/+NX/vTsd2SlRnU6\nzjZ8de8sPH4loq/D8WB0bjzbi+t48LxRaJqG3RoZBvUHFAxhCrgCoIW8Ntkko4TE/Qx2k67H5DCh\n+YNo/iBqkgMx5PXpYaZGlLh4/FVVLPh4K+uqRXZt28Gb3x1gR3E9Kw86UFoLGD64H/fcex848nXF\n1dLFx3dQgWbYfgkMfxVMSZ23F36mS9m3oeAHGDit/XVHBjVAfU2kgeimOZAgCBiHD8ff04ItDKLB\nwKjPP0d2ONh66qn4a2rwlJSwddo0alesYPzmzaRdfvlvXmA2vfACjiuv/E3J6WP72Md5jwETgAJN\n03KB6cCm3/yt/0lYoqH2UO/zQF8pdGdMNE0vc01O77xt507IyupWWkMLBGh66ili7v3Py1XZL7yQ\nxHffpeqcc3CvXt31pKQkWPEl3HUHdMxb2KPg2SXwyI1QGYqfShLc+SFsXQmr39HHRBEuXgSrnoCa\nQ/qKa9b7BH66m5cfuYErJmZiYhomy+YQtyEVRbkAWX4ZwRaH2jwOtSUaQ75+8QR2piGIKtfcYuOe\n34/EYpQJFoLWCsZwm6pqBLcd4bknvyF59kjk3O4JiWeekElts5edJfUR41prDcEDqwkcXE1g/7eo\n9cVglDFNzOO7t9ZRWd3MY3PH4LAYQIBr7hnA/p+beOzTbQi2ItSmfKTon1CbT0YUt6D6U/l8fSUz\nRgeIM6ajiRak5gbUqBSk2hrwCSgZiYhFdQQzYlAa3AQTbWS2+sg6MZv6wjqa7CZGZcToTXjMMmMz\nYxmYHccnt0/n87tn8NB5oympaKKiycvnm4px+zobgYFp0aTGWvlwXQ9VbT3g9tlDGZwRw8OfbOdQ\neSOOjgbCH8RoCCvnDLtPyUaZYEiaQ24zEIKAFGNFcbrREh0I1bqBUBJj+GXdQU544if8Hj9OMY2r\nlteQJ9TwyppSpjz4BbcsLWGfO4dlj4XlBgbco0u6KMdReLLnFkiYDqldVBdWrAOvE1LDFnYdDUTp\nXsgeFvk+Zy3EhRkIWe627a9x5Ej8O3f2eXdFo5Gh775L/KxZ/JSczKaRI0mcPZuxa9Zgye0mvN0H\nKDU1tL73HtE33fSbPwP6biACmqbVA6IgCKKmaWuAsf/SN/+nkDO+74lqsQcPoqFe5z+YO1Pq2bAe\nJk3u9mNblyxB7t8fcx+6O/07YD39dFI+/ZSaiy/uvrppyBB47wNdjqNjmeyIE+Gy2+DOP7Wf+PYY\neHA5LL4TCkJkuMT+MOt+nUCnqhCXz+LdqXw6T+DGWflIQjJBaQJy/ct6zFn9HaAiit8gmBz4fx2P\nof8BhKgG0AT2/TOBuX+MIXlIe98B3y8gZYGUErmLn3yyjV8W/YxhaDoV2Qk8+I9teDtoB505Wvf2\nrn6tq+S9Bn73MQVR0/h+KEfqWbRkC1MGt/dYMJ6grw3SKu1MPFWm9rABzVuPYN2N2jIRQV1JoDKd\nfZXbKa91MDpFQzGkITVXooo2NLMZsbIJNTMZsagOv0HGkBnL9q1l+IBTp+RRV1SL02wgWlVJzYjl\n6KJLCHoDxMXpK71thbVsLqjGLgkkxVspqGjk21+7jm3fc+5Inly+6xiD/HiQmWBn3aNncc1pg9h6\nuBaTMTKuHvArGDuMtaV9JKNMMGS0ZJuJQKjZkBhn03W1knUP4vZ3NjL/mwKKdpdy892PEDV2Om/f\ndzOHGjUSRkyj4JOn2L9/P0VHyhh33VLiSz9oDwnGnAjxJ8GqJNh0Ohx+Chq3dBkyBKBiKTRshKEL\nO29Tg/DjjTqXRwwdU0ut3iQoK+xW1rGCCfRe1HFhC5NumgMBmEaNOi4DAbrn0f8vf2Hinj2cuHEj\nOXfeidBFjuN44FywAPullx43c7oj+mogGgVBsAM/Ax8KgvB34DcEB/8PkD0eSn7p21yhhxxExw5S\n4Vi3rlsDoakqjU8+Sex99/VtH/5NME+ZQuo331B34420vPNO15NmzoQHH4KzZ0PHOOnVd+l/Fz3d\nPpY9FG5+HR4/T2eXApxyCwT9sF5vFPTR7igkyYjBo5eyBrxDQW1BbP0OkAgGb0SSPgZfIZrXhn/P\nCZjGrgdU3v6miAdubcY8vgwhKmQk/ODbCMaJ6J1HQkiMsrBs1X7+dutH7Klu4bKHz+bixRv4fnc7\n2csVMhjVTd4eGwjJ/RIRHWb8O0qZMSKdTQVVoXGQ0sC3HhLsZm6+JpU7Hz9Ibd0ilKo0godWIYqH\nUJwZnDPeg6DmI/krUMR4BL8HocmLkpSCVFaDGhOFEFTwNbiRc+Mp2VxCocVAbpKDusN1NNiM5FiM\nJKTp0g9Op5u4kJz3/rJGnC4/ZkHAYdcrVgorm/EHO5+rl586gMx4G6PvXv6bEtayJDL/rOEoQYU/\nvx953fg7GIjwUIdslFBCCWvZoXsQAGKsFaXBzTcFNTR4A6zZWsUfH/kbV0way0033YQ4aBwc2qJ/\nyNTrYe2r5OfnI0mSzrFxZMPhf7bvxAkfwPQSyL4WvOWw4wr4NgE2nwWFC/X+0poK7lLYczOc8CHI\nXYRUdr4MlkQYcEH72KEf9fJWKcxL6uhBBALgaoGYsFLjXjwI33EaiDbYhw7FPqQX5eg+wL97N65P\nPyV2QRd5x+NEXw3EOegJ6j8D3wCF/LcyqXPG9d1A9BRi6thBqg2apnsQU6Z03ga4ly9HjIrCPG1a\nl9u7Q8O6dWyZOpWd551H3bffovU1jxIG0wknkPrjjzQ89BBNf/9715Ouvx5mnQ4Xnh/JppYkePp9\nePs52LWlfXzyH2Dan+CJC/SktSjBJW/BVwvwVBxg1979VIvjMHj262J13hb8wllIjR9AsBbIINg8\nBWPKt4BGsGggqBJy/4PsO9rKspW1rHgHzCcXgUG/6NRqCJaAaTwIUcnIuRN5+K5b2Fhr5f53f6H8\n691kuH189PlNvLn7KJ9s0Dt23fXBVoZnxZEUbeHsp77r8vAFuwnj6Gy8Gw6DqvHx+iIm5acgJoBx\nNHh/AvyAKciI0Ub2/KLRkrCfYHE2smMPwYYcBKGF1DgNlCRExQkuBSU6Bam2GiUhUdcfcmso/RIJ\nHnFiyIlHKm3AmWDH7XSjqCoHGj1EKRqJ6TFomkZ9veuYB2GQBDLirBBU2V+jC7yJooDYRSxaEkVW\n3j+LU4emMfOxb1gY1ka0r4i1mciKs1HW4GFLmOihPxDEq6jsKK6npKYFty94LGktmdo9iLYcBIDX\nauDDL/Yy94WfCGZlcfDrlUy67Goo3KdfawNOhILQ+TX8LKgvhoqwfT5hPvz6bCTB0xinh4yGvQCn\n7IFpBZDxJ3AdhG0XwbeJsOEk6PdniOkisOGqhC2PwSkvRWo0dQwvtVUwhXsQDXUQHReZlO7BgzAO\nH05g3z60brb/p6FpGvW3307sggVI/4K6dBv6ZCA0TXNpmqZomhYMifW9EAo5/WYIgjBCEIQNgiDs\nFATh85CH0tW80wVBOCAIQoEgCHf3+sGZJ0DVvr4R5nqqYuou/1Baqp/oXcQHNU2j8cknibnvvj4n\nlvy1tey++GJ2z51LxrXXEj9zJofvvZf1/ftT9OijuI+zXaFx0CDS1q6l+ZVXcD74YNeqsM88q4fO\nrrs20kCmZsKCl+COi6HR2T5+ySOhpHVIbCxlMJw6n7oXzmVoRgz901Px2cdhal0LagCltpGALx+p\n4gkCB77FfzgRJD9ywkFAwLd1EvLg7VQFqvnb089w52MlBI86ME0qBkHf38BOEB0GjCckI9iTOPfk\nUax86S6qVzzKldMGYi6pw7ytmCXvz6MqPZa0a5awv9zJC/Mm8vjcMewrawRZRLCbEOPtSOmxCLmJ\nNI7I4sWF31FVUsfS9YVsLqzlstP7Y5qqey5aSHBTzmpAORqFxeEjPTOIUpWGnHCYYH1/DIYCPlgj\nYlSqUeVEpKYalKhUpJpqNNWAmhCNWOpEzUskUFyHnB1HcpObAwaJuqI6trf6qGhwkyQKJKZF43b7\nEQSwhnIAo/olkJtgRxYFDhzVd2h4dhxyN0l6i1HmhXkT+PzuGfz1s50RXlWfoWqo6D2+QVeJ3Xq4\njnmvrWPqgi+Z9vgPzHt1Lat2HuWMp37igw3FHDji5FBlE5LNiL/FywMfbeP5DUfISciisrKKpAkT\n9T7t9ihd6K6sCAaGDISm6XmsSVfButfa9yP3LD1PcHR99/tqSoK0C2HEazDtIJy8C0a8Af3v6nr+\n2jtgyJUQlx85fvB7GDS9/XVtGZht4AjzFpy1keEl0D2IbgyAaLcjpacTOHiw+/3/D8L91VcEy8qI\n+hdKW8PRG1GuRRCE5i4eLYIg/KvatYuAuzRNGwl8BnT67wqCIAIvoUuLDwXmCoKQ33FeBIxWPVZe\n2QM/oA09EeU61j63YetWOHFcJy14AP/27Si1tX3mPdQsX87GkSMxpaUx+cABUi+5hIxrr2X8tm0M\nX7oUf3U1m8ePZ/PkyZS98gr+us5d07qCnJVF2tq1uL/6iob77+88QZJ0OY5DBXDN1ZHu8u8uhOnn\nwJWnQ0tT+/w7PoAtX8GaJfrYaXdSU13Fayfrv59i6odiSMbU8iNoKgFPPgTdGIRfABFfyVSMadsR\nrXVordEc+nEAy/+pcPHFs/ALZj59Q0UwqBhGhm5uKgRLRiIlHUSMOwJoRFkMRGe0t35Va1tQvtvD\n704bzP5Dj7Ls0+uZfMMpnPXgWRQf/RuWP4zFPH0IVTkJbAiofLS/itcWreP9xesZctsyblq8gZev\nmcTZt2QQPMixrnEAcr96gsVxPL8gnrc/VJj/jy9AE1BdsciGIt7/USRR/v/Ie+/wqKr1/fuzp8+k\n9w4hhJDQe++9iiLYEEWsx94L6hErIuo5ggVBwYJIUUAp0qSE3gIhgUASEgLpvU0v+/1jBzKTTAqW\n73kvf/d1cQFrrz2zZ2bv9ayn3XcuNlU75JV5iIIHokqNvLAaR5sQ5Jkl2CJ9cZQbMFrslAsCXRJC\nKckoJkcQiAv3Qa63EBThS0WF4br3ABAf6UefmEDJYMhkDO4UxqjuTYQ7nTAkPpT3Z/Xj7sV7qTZY\nWpx/DXaHg4pqEzbgnZ/P8M3edHq/uAmNxostO3bgcDgoKi3n5/XrGTthAq8tWkpQl6GUGGT0fGEj\n9319hI0HLrE93cB9r8xjQIcOBAQESNrsOZelN4ntLDEjB0aAQglFdeODHoRTP4K5LmItk0PPZ+C0\nmxLVpqCNkBo2BTdx+6xfofAo9H/ddbw0C0xVEN61fiwntXGCurKssYHQapuW+QU0gwdjSkxs/fX/\nRXDo9ZQ98QQBixcjuCETdIsWrrOlPggvURS93fzxEkWx6fq71qGDKIrXmhZ2A7e6mdMPyKjjf7IC\na2iNFnZED8hthUBHczmI8hLX0rZrSD4DTZSu1qxcidd997XIs2StrCT13ntJf/55uq9fT9yiRcid\nBdAFAZ++fYn/9FOG5efTbt48Kg4c4FBsLKenTqVw7VrEJmKg1yAPDiZs5070v/xCxYIFjSd4ecG2\n7XA5G+be5+pJvPgBdO0LD04GfV3ZqJcfvLYBvnwKss9itFgZu7aajlo9igJJY9riMQAQUelPADLM\nxhEoVBeQy/MQTb6YrwxEHbMX5CYyj0SQmOhLgPc9zLn/Tn5PKcKUGIOiTSWKGMk5FS1e2LIGIQvI\nRtH2BMjNEr2Hk3FWWh20zyjE80wO36w4RPq2FEy7zxEU9BzfP7OG3t3epkevd9nwn91EXynj+fgg\nfn9jImabgyX3D+KuZ9ohVoP1fP3HlwXXIOis2As86TW8jGEewxnYv5KC7CjkiitYbf5UVNrwkZfj\nsHmDQoWstBJ7eATyywXY2wQju1yGWSFH0caP6otFnAbG9YigJLOEPKWcOwe2o7pcj3+INxUVRvx8\nXQkhPZRyYiJ8sQKDEkJdVOGaw9xRcQxJCCP+6Z+YvWRfq84przLh5aFi1tBYNh2/zEs/nubIkSN4\nq1S0i6/fj9nNZjx8fBg3bhwzb7+dwYOH4HA4+G7tWqaMHs35ixkkDB6MvaQuTNWmbX0Xf2wnyUBA\nvRcB4BcJMUMgaW39BXWaI2lFV7SyGrEpGMtgzyMw9htQNshLnPsNOk10DR1dToF23VznVZVLISZn\neHpCMx3Q2rFjMezc+acu/Y+g4s030QwejO5GGuqWfdns4RsUev1LcU4QhGs1bbcB7jgrIgDn3vXc\nurHmEdlKAyGTN20gyoob7xwAzpyB7o0NhMNkovbHH/G8997G5zi/7M6dHO3WDbmnJwOTk/Ed3HQ1\nFEi10kGTJ9Ptxx8ZevUqIbfdRs5HH5E8YwZ2ffN1AvLAQMJ27aLm66+pWrKk8QRPT9i8FbKz4FWn\npLogSFrWMR3hXzeBqS6B3K4bPPwJvDOd7T/9SGzbcGxdxqHMS0VefgUEGWav4cgtucjNWYiiDrNx\nOCrtAQShFntlNPaKaNTtEjmbU0bS2ZkgJPDis0lsPJXDqH/v49T3fqh65iELqsVRlY9o9saWOQzR\n7Ikybh8oL7ilaJdXGDh9OJsffjmLYLDQPyaQOZ8lcqWkhpMLb2bhrL4MiAtGLpNRVGlEq1Iw++H2\nCB5gdirYFrxMqIdkYznWBnlIAaJJR5x3BNPHwrqtMpSqDFKyg3h4sAy7Jhp5ZQE230jkhfnYQ0KR\n5ZYgCiocIV5Y8ytRtAtEn13KJZmML7aeIze9mAybnVHtAvEL9kKukFFRYcDXz7VarrhcT3S4N5W1\nJnq9uAnfe77lhe9bl1tb98xI5k3vwbZTV3hqxeEW5xeX6ZEp5fxw8BLdu3XlUlY2/fv3p6q4GJ/g\n+k2S1WRCWUfzIMhkiA6HtJkJD0cwmSTZzaCgegMRHQ05dR35HTpDRp1XH+eUqAYY/BAcclI1VHpA\nl4fhjJNGyR/Bviegw+0QMbTxsfN1BsIZl1MguqvrWKUbA64CoOgAACAASURBVKHRSBoRTYSZtGPG\nYNq37/80D2E+c4bab78l4OMb8LzKy2Hb1man/K0GQhCEXQ04nFLq/p4KzAUeEwThBOCBlBr805g/\nfz7zN5xh/te/sG/fvuYny5tJUt+gB2H45RfUPXuibIL621ZbS9qjj3L+gQfo9PXXJHz2mYvX0Boo\nvLwInz2bvgcPovD25sTw4Zib4J+/fk54OGG7d1O5aBE1K1c2nqDVwoZNsHEDfOm0m5DJ4O1lEBQG\nj00HSx2B38i7oP9U+icuIflSAQ6VB+b4UagvHUJWWwoyNWbvEahrjyHYKnHYQ7FauqDW7QPsWPJ6\nI8jshMZn0H/AYJAvR6fVkpU5nv5jb+buBUnUHohCPTQL0ZCCo/wyOMBe2AnLhRgUbTJQ9QPciKcN\n6BDIiSwpDPfLi2M58u5NXFw8k3B/1+/ZR6di0tQIhBgR836g7hYQNFY0IzOxnonAnu+Dol0GtuwO\nKPyz2HNEID2vFJmskhPpWu7rL2LTxCGvyMXuHYasrBTRpsAR4IMspwJHbDDWrDKU7QIozyolzWYn\n5Uwugo+GrGWzUBktBEVIFUwVlQb8GkimFpcbiAjyYsn9g5g7sgNrnx3Nij3pDHh1swsLqzsIgsDj\nEzrxy8vjWHckG0sLC9XXuy6QXabn0KFDnEk+S0hICLUVFai0WlROvD82kwlFAwMBoPD0vM4pJA8K\nwuFiIC5L/47tLCWqwdWDAOg0ASrzINep+qf743DxR8kL+CPI+BmKT8EgN6ynFiNcSoSEBlQ5bg1E\nmWsFE0gbKE9PSQ/GDRQhISjatsV84oTb4381RLud0ocewu+995AHu1mzGmDfvn3SOjnrLuZHNl8G\n+7caCFEUx4qi2M3pT9e6vzeLopguiuJ4URT7IoWOLrl5iTzAmdIjsm6sScyfP5/573/M/K6VjBg2\nrPkLbDbEVAx+DTyI0lKJRjs6utH0a+Eld6hOSuJo9+44jEYGpKT8IU4VZ8hUKjp/8w3B06ZxfMAA\nalKar1xRRkcTtmsX5a++Su369Y0nBAbClm3w1nz4zalBXi6Hhd9K/SBP3V5f9TT3A4K8dPw7VlqM\nHJ6BmNsPRn1hD4K5FociAItHHzQ1e8FhxWbpjOjwQKWR8hG7tnRk4kg9t01Ug6AExTq8vfL45GNP\nOnTpyYKlV7CmhqIZnom9KAnr+W1Yz23FdvY8xq0iyEA7CWSBrh9j3/lCJveQHFGZTKBrW3+0qsaW\nxCtMyVfLhjB8zDaSL9YtQAo76hGXsGUFYMsKALUReXABtivtUARmkHQqgOjQfI5e8GFvUhJ6ixzR\noZPoNfR2HAGByK+W4ogORZ5RjD0uGNvlMmThPlBlolghY1ZcMF37RqNTKyjJqyIoQuKMqqwwNAox\nFZfpCfb3YPbwDjw+sTPje0Sy/60p1BjM/HjQ3aPSGIM7hhAZ4Mkba5OanLN0ZxpbTlzhjtmzGTiw\nXt6zsqgI3waModYmDITc0xP7NQMRGIi9vFw61qYNXL0qbcLaJ0DWhbpKpj6QmVSf+5IrpGS1sxfh\nESp1PKd80arP6gJDsdTzMO4bULrRcsncDxHdQedU5WOzQl46tGlQZuouxAStCjMZ/4/CTNVffIGg\n1eI1d26r5o8YMYL5b7zB/Lxc5i92E1lwwv8sxCQIQlDd3zLgNWCpm2kngFhBENoKgqAC7kAiDmwe\nngGg9ZVK6JpDc0lqdx5EcjJ0794oQW27ehXziRPobmncvSmKIucfeojoV16h88qVKH18Wrz81kAQ\nBGJef53YBQs4NXo0pTt2NDtf1bEjob/9Rtnjj2PY6satjI2FnzbAnHskptprUCjg4x8lYrVX5krh\nHYWSzBnvck+oA3muFAG0+7fBGtEFTdpusJmxaTpgVwSjrj0EIpiNg5HLC6kxn+PuT5I4V/UW8pJH\nwHAYBA9QbEVwbGDFiv4s33uJI9vAXuyJeki2JDl5rTnKBpajYDkN6mGQ6V/Biz8co9eLmyio0F+X\nGG0KNaIF9TBI+aWCcymVvLvhLAgi6qHZOMq1WNOiEHwjUcYVY8tvg0xZg6Aw0cE7nntHwZwlRczp\nK7Ik0YYhLxO7bwTywgLsYRHILxdibxuCLLMEW4QvjkoDZruILtwHlVpJnEwgqIO06SjJq7xuICoq\njW48CD3B/q5jXaL8GBwfxg+JmWw6kdNic5wgCMwdFcey3Rf59UROo+Mbjl3m1TVJ3HbLdDp2dd05\nVxUX49PAQNhMJpTXtJibMBCCUonM0xNHRYXknfr6QmEheHpJlUy5l6UqIb8QyL1Q/+ID73dNVoNU\n8pr8KZgb6zw3CVGUOMIS7oGwJvSs3YWXci9CUBtQN2iMdRdigpYNxLhxTTMb/IWw5eVR8eabBC5d\nemOUHEePSmGyFiRL/5c5iDsFQbgInAfyRFH8BkAQhDBBELYAiKJoBx4HdgLngDWiKKa16tUjukNe\nCw0rMpn7hhdRlOqf/RpsUc8mQ7fGtLm1q1fjMXMmMjdC5hV79+IwGIhopXW/UYTddRfdN2zg3Jw5\nZL//frP9E+ru3Qn59VeK77uPmh9+aDxh4ED47AuYMkm6ga5BpYLF6yErDT6Rmm8+/OobZp4B9dFD\nyIolEj5bWCfsPmFoLu4Fhx2LZ38Eew1K41lAhUE/Aq3uFK8+NpIxU+ZB2PeQd4sk+CIEgnIHwQEr\n2fbbHO5YfJCsndKDqRmbjuBjdLlU+1VY8uwFCjHyzMeduWtaDMlLpuMTrEIWpEYWqkAeAfJoiXBP\nmQDKblDUVc/uzQXYrkh2/sD5fOidBSJY03qhjB+PIqonynbpiLbbUQRnYivrwKXiVK6UyPn56YlM\nSJCx6iRoyy5hC2qPPD8Pe1AIsrxSHB6eEhNttQlFG38MuRUoI3wxmq2Y8yoJ6iBtOkryKq83yVVU\nGPD1db13yiqNBPg0vp8eHRePTC7noS8OMOfzlpmL546M447B7VmwyZUfKPF8Afcs2cdPP28Aq5Ww\nNm1cjlcUFOAX6lrFZzUYrnsQwPVckNzD47qBACnMZL9WcdfWKVHdvhNkOuUhLjjdY+6S1QGdJd2G\nle1gz7+g6GTzEsEAF76H8vMw4C33x0URUrdC50mu4+7CSwDVFeDt23jc2xuqmjZcmiFDsKSk1Odj\n/gaIokjpI4/g/eijqBJa0M9oiKVfwAMPuq3GdMb/zEDU9VJ0FEUxXhTFeU7jBaIoTnH6//a6eR1E\nUXy/1W8Q1lnqh2gOTSWp9TWg1kgLozMuXID4xlW2+o0b8Zgxw+1bXP3sM6KeeKJVCnJ/FH5DhtD/\n+HFKt2zh9OTJWJq5KTX9+xP+++9UvPYa5a++2tigzJgBS5fBtKmSpOr1E7WwfBvs3ACfvY1Oq2X8\n2J6YBg9Dk7gXWYFUI2qJ7ouoUKPOPAjIMfuMRjBmsPPwbga+doznV4fx1NAjUHUaPMdD6BdwdaKk\nMyxEg3InfXuu47MvJjBryWHM+9pjy/ZHOyYDZdcCkNVf76e/XCDj51qiyj15/aNudHnAB+14Leqh\nGtT9fVB29UERISDzBzSQW6Lno49S+XhRGsczS/Hx0PDfJWEYFAbMB2KQh/cCmQKZ/0ZEhxZscSj8\nL2MriWNinxqKytsR51OITRVNr2AFdosJh6gD0YFQZcYR6o/8UhmOhFBsWWXIYgK5kprP8rN59Avx\nRqmQ4xnkid3moLKklsAwyUBUV5vwaWAMzFY7GnXj8FiPdgEkvjWZlY8N49DF4hbvDbVSzr0jYims\nqGcLLao0cOfiRJYsWcKUKVPITksjpsECU5CZSWj79i5jhooKdHXNVw6LBVnd8yEolS4JWZmPD45r\ni2dkFOTVRYWvhZkA+kyEI5tcL3bwg3BouevY6C9hVjJ4RsC222B1Dzj9ifvcRHkaHHgOJq4FRROa\nCYVpkuRoRIONXnYyxLipTqytBi83Xn9gEBQ3/f3LtFo8pk2j1t1G7C9CzfLl2PLz8XNXyt4ccnNh\n6xbJQLSA/6UH8fcitBMUtGAgmmJzbcqtTL8IcR1dhmz5+VjT09G6cdVMubmU791L2N1/v3SGJiqK\n3nv34tWjB0d79aKimfpmVdeuRBw7hnH/fopmzMDRMNk2dSps3wnPPQOLPqjftQUEw7e/w68/8JSn\njfc2JFOg88M0bCSaQ4nIc+sqmWKHIlj0qHJO8uPhAuLerGVAWAGfzZvGO8tPIev+JRybDLUXwWu6\nJB15dQKYU0HoBIrtTJ28i36D9YCALSMI47Z4ZP56tBMvIAvQYzDZyCurYUzXcGzZYNwAllMDsaaP\nw5YxAlvWEOx5I7BmdsRyHKynYfzdOzn+eyl7U3J5edVxtq/pRJduKop/iwJBi6DSIfPbjNx3N7a8\nl5HJduGw9UJwmGgb7ODYBS0KUzo2bUde7q9he5EHirwr2KPaIs/Mx94hAnlaAfaEUCpS8/m9ykjm\n2TxSDBamhPsQ0jEYQRAoL6rG21+Hoo4ptbraiLe364JmsdpRKd3U9ddhTLcISquNLSagARIi/Cip\nNrL6gMTB9d9taUyZchOPP/44VouFvOxsoju63tcFmZmEdejgMmasqEDnLz0XdrMZuVriQhEUimYM\nRCTk1YlStU+AS3UBgP5TIWU/1FbWv0GniVB51bWzGsArCvq9BnMyYdh/oegEfNNeMhg5O6RNntUg\n/X/QexDoxhO4hpRfocvUxjvnrDMQ40ZUp7ZaavRriJAQKCpq+n0Ar7lzqVmxwn2z6p+ENTOT8nnz\nCP7++xsXI1v8CdxzrxT+awH/YAORAEUtRKOa8iCaSkxdvAgNHiTDr7+imzTJbWNK7rJlhM2ahcLL\n60au/A9DplTSYcECOi1fztnbbiPr3XebDDnJg4MJ//13ZD4+5A8diq3hzd6zJxw6ItGEP/xQfYI6\nKBS+/Z32Sft43MvBoQtFOIJDMI0cg+rYYeSXs0CuwNRxNPr8bFKPHOCNj1YS9q9khvELIfoTEDYd\nEhbAkdFQmw7eMyHkY7g6DsxpIOtOWsYHvPVONbJgaXERjSrM+9tjSQ1FPfwSZ/1O07tjIFGBdQ34\nghzBs3FZssw7DIDiKiN5ZbV8+/gwIgM8eefNMNp2tTFhQja+Ki3YLAjem5H7b8Z65U2w+SCX/4at\nZhAKVRrf7VUyKUFAlOlw4MUgPz1Lz9qRX72CLSIKeUYuttgIZBcK0bcPxJ5VSqGXmlCLnSpPDVWX\nShFCpIWmJL8+QW0227DbHWi1rvdPSwZCrZSjUytIvVLZ5Jxr8NIqGd89krd/Ok2l3szqQ9m88prU\nOHbu5EmiYmNRqV01JwoyMgiLjXUZM5SXo3XyIOTXPAi5HNFuv74QCj4+OCrrrisyUtqxAsTE1xsI\nDx/oPhKOOaUU5QopF3G4gRdxDYIMokbChFUw9zJEjoTDr0ohqE0TIKArdH6g+S8j5VfoelPj8awz\n0M6NgdDXgIeb5zckBEqa9+A0w4bhqK3FktR0kcAfgWizUXz33fj9+9+obpS7qaoKVq6Ap55ueS7/\nZAMREg9FF5sXBGqKi6myDHwa8JhUVUlJqQjXNgz9pk3obr650Us4LBbyli8n8tFH/8jV/ykETphA\n/1OnKN28mdR77sFhcV9BLKjVBK1Yge6mmygYOhRrQ2nSyEjYfwAKCmDypPqYa2gEwnd7eCZQztHv\n9pFZWI0jIBDTqPGokk6iyMrk4KUKun1n4NUBGu7topHiyVN/hd1zJdH4qHuh41twZFSdkbgTghbC\n1TFgvkjXbnO57wFPlP0SUbTNQKIRFbDn+GPc2okKq4Fte8KQhdY19IsOsFtpBJuZ/HI9Dy87RMcI\nP7q0CSB500BeeioCEuMpL7dTUm1CEZ2O3P+nOuMQjEx2BNERgi2/HIUyh1+OaglWXsamiUdRlk25\nMoC8whpMldWIci3Y7IACRMirNuEQwA7Y5TIyq41QXMO+UslTc84/VNeY8PbWIggCxZUGfk/OZefp\nq5gtzRsIgJ7tgnh42aFmiQmv4Zb+bTFY7CzYlMrUm6bRubPEN7RxxQomz5rVaH5BRgbhDT2I8nL3\nHoQguHgRcl/feg8iwslAXAsxXdtRD5kJBxpU1Q2cCyd+kJh3m4PaF7r9C+48CTdthrbjpHBUczH1\nwgvSmtBhhOt4eSFYLRDkpuTzT3gQgkyG15w57svL/yBEUaTizTeReXvj/UeovL9aDuPGS7mhVuCf\nayA0XuAZJNH5NoWmuJgqyhqXuF68CHFxLjego6oK0+HD6MaPb/QSxRs24JGQgGcrk0dWg4FDzz7L\nwSefJHvTJsyVLe8Mm4MmIoLee/Zgr63l9KRJWJtIqAmCgP/8+Xg//jj5Q4diOd8gLOflBRs3SbmX\nkcOl5hqAsCjOPPMRL/rBoe/2sTc1H9HPD9PocchPneC/S7fTd/Rk/F89gvDTk5C+F0L7wYQfYesM\nKE6CNnPrjMRoqM0An9kQ+C5cHYPMdonkM1qyfxmCokMa6qG7ruta708q5r45uTiS2qIecAXVgMug\nsmIvbayLYC/J5IEvD5JXWcMPzw1BEVuKrmsZlr0dKCqyoZALBCbkouxyGtPe0VjPpWEvSkNmX4sl\nJxIlZ7BZoxjfOQh/VQ02VVsURRcJSejJ8vERrL5i45P/bqc0PAh5WhGOhFA8imoo8fNAV22iXKfE\nC/AC9hVIv4FzBVN1lRReulxcw6q9GSRllnDmUgk2u4P0/ObvgR+eHE5eWS0H0gpbvB+GJoRitNj4\n8fBl3l/0EQCG2lp2//wzNzVo7tRXVWHS6/ELC3MZN1ZUoHUyEDInr8PZQDQZYvIPlDZlpXUL64Cb\nIDXRNczk31ai7D/tlP9qCUHdpRCUqhlPXRRh3WMw8d+gbKDQl50shZfcGZemPIjglg0EgOe991K7\nZg2OZqg5WgtbYSFF06ej37iRoJUrbzyvabFI4aXnnm/1Kf9cAwFSmKk5Tqamylwry8CvgcTfxcb5\nB8OOHWiGDkXmJoR09fPPiXrssVZdZvXly2wcNAhjUREekZGc++ILvo+K4ud+/Tj68stc2bEDawtd\n0+4g1+no/vPP6Dp25OSwYRgbeghO8HnySfwXLKBg1CiMDUWFFAr4ZDGMGg2TJkCZlCC86dGnOPTw\nW0ytLufXz3ey7nAW87ZdYotvR9b0UfLz+68ji+oBc9fCitvh6mloMxpGLYVfJktJxTZzoeOb9Z6E\n7xwIfANr1nB8PCtR6oMx/T4FR0ko2jGbsUal8MKqY9w9vAOKEj+MWxLAKkd30znU/TeiiH0fZfxC\nlAnvoez0Ftop29mfGkTqpWgSHrqMMqEI0++xiHo1e1PzuWOmQMigs5gSxyLW+oC5BsH2G4jV2CuC\nUaguYLMk8NRwOcuPiAj6CgSbBbt3GENkVUybNZbxGpEP0sqv5x+0eVXQzh+PKhMEe3Fn+0CqPNWI\ndQ90aX4VQeGSgaiqNuHtreFIWiH2Ok/A4RCRyQQOpzW/AAV4aejaNpCtSVebnQdwOrsMg9nGks+/\nIKSufHXHunX0GjqUoAaGoCAzk7DY2EZlk4by8utJarvFct2DgGYMRESE1AtxDc55CJ03dBvhGmaC\numT1Mv5SnFoL+jJJGbEhsppIUIsiGGqbDjEVt2wglG3bou7Zk6r//KdFepymIIoiNatWkde9O6rO\nnYk8dQpFRMuEEo2wZo20ye3Vq9Wn/LMNREg8FKc3fbypRjl3OYisS1KvgBPMR4+iHdq4jd+YnY3+\nwgWCbnIT62yAsrNn2TRkCB3nzGH0qlX0fPFFpuzYwX2lpQxctAiZWk3Su+/yTUgIGwcP5tirr5K7\nZ0+r6cAFuZz4Tz8l/L77ONavH4Vr1jQ51+vuuwlauZLimTMlJlhnOnBBgEUfwshR0K/P9V6Ju15+\nnZDtKXyYEELt+kQ+35rC7PUZpE+dB29OhbP7IG4k3LEUPp8gaQDHToehi+DnUVLp4jVP4vAIqbrJ\n9wEuls5kzzd2gkMMIMqwXujG12/Fcc6exNoNtTw3q64E0ybHcioK47YETPvaY9oZg3FLDIZNHTH8\n3IVnbrGTEHkFw5qeGNb1wLi5M2KNlBAePbWaDz8QGTDSzL8+lqprFIHpqCJOYsoaiVyZg+jwxGHz\nxtORzVdHBcS8c9hCOiIrLgSZDI+AADph5cusGmpOXMbcMRRrRjHdRsYRIwj4tQ9icJAnxRoF/ToE\n4XCIlBZUXQ8x1daY8fRUU+VErndNC7qqhY5pgIfHduT7xEy3sqMWm501By/x4JeHeXl9Glu2bOGu\nu6RwkiiKrF68mNseeaTReVdSU4lqENu2WSyYa2qu5yBstbUodA2a0K7lIDw9Ea+VvYaHS30Q18JK\nMfFw2emZHDwDDjUQueoyBUovSRVHfwVqy2DDM9I9KHfTgp912r2BMJskYkF34j1RURKzcyvg/8EH\nGDZv5mp8PNXLlyOaW/5dr8GWm0vR1KlUffABoVu34v/OOwgN8kWtgtUK77wFL9+YTs0/20AExUJJ\nM3KMMvfaslRVgHeDHERODrSNdhkyJyWh6t270emF69YRcuutyFpgVMxPTOTXMWMY9NFHdH/6aZcd\nm1ytJnz4cPq9+SY3JyYyp7iYvm++CYLAoaeeYsv48dRebXnnCNKC0/bpp+m1fTuX3niD1HvvxVZT\n43aubuJEIk6fxnzyJPmDBmFJT3d+IVjwPrz3PkwYB99/D4CqYxe8d17goUljMczoT1l6Gn0fnQ8v\nr5V0JI5thh7T4Z5VsHy6VIcef7cUM/5lElzdA23ug66fwtHxUHYAecAjvPKxAk2Hnch9L7PhaBZP\nL0kj/achxBoHEDPtMKoex0AhLayiQYVYo0HUqxGNKrAowCanrb8XVYaGuQkRZUIyUf0v4XXqFpbd\ndTOrD6RToT2OMvQspvSJiEZfVKqzWMzdUZouIKoj8VHrUFTkYg2OQ5lxEWtcPIr0XGSxETzdLZIi\nEbq/tY3q7DLeO3kFRWktQ0bF4WW1k1Jtpk/7QKrL9Wg91KjrktIGowUPnYq2wfW7VJlMQKmUE+zd\nRKmmE6b3jybIW8uPhxp3V689lMUDSw+wPaWYpOQUJk+efP3YsT17sFmtDJ4wodF5WUlJtG9wX1fn\n5+MVGoqsbrE0V1SgdtIbEG2264UaglaLw1jXt6JWg05XL1DVLg6ynKiw+02B5D1gcvKQ5UroPwcO\n36AedVP4+WnofQe0G+D+eGYSxDZ+jjGbpHJ3d4iOlnIrVjd5rwZQ9+xJ+KFDBH39NfoNG7gSE0Pl\nhx/iaOIZBMmAVy9fTm7Pnqj79iXi5EnUff6EiOeKFRDdDkaPbnmuE/7hBqIDuIlLX4e8iRBTdUXj\nJHXOZZfEjuhwYDlzBnXPno1OL1q7lpDbbmv20rI3bWLHjBmMXb2a2Ntvb3YugFKnI3LMGPq/8w4z\nT58mfMQI1vfuTfqqVa0uo/Pu1YsBSUnIVCqO9uxJ1XH30qyKsDBCt23D8777yB80iOqlS13f4/bb\n4fe90o7kqSelh8TbF/WK7SiGTkB1zyipY7b7SHhzKyx+EPb+AAlj4ZHN8MP9UiIy5iaYtB5+uwMy\nN0rVTb1Ww8lbKTv/LXsOe2C+NAox+BR+nRNZ+lgPbhvUHvuVDhh33AwKG9rxm5BHXOa6FmYDdAjz\npsbonKQXUfU4jjzyMqa9kxD13sRH+PDTIi9MuouYLk5CNHsjV+QgiioctiAUxvNYtF15qofA9nw1\ngs2OvLAAW7sY5Gk5ODpH83pMAAFDY7kz3JdSPx1f77qAqdKANtSbmqIa1AGePPn1YQ6cyCEgrD7p\naTRY0epUDOscRqgTZ5ROq6JrVOsEX3q2C+TL3Y31B77aI7Gh5ublERTkmlP79sMPmf3ss8jcxLEv\nnTpFTIMwRFVuLj6R9Xya5spKVwNhtSIopN25oNEgOsfcQ0MlLwIgOs7Vg/Dyg/gBcHK760UMnAvH\nv5PUC/8MUrdC9mGY8o7744ZqKM2FKDcqAhYzqJrYratUkneU07hD3R0EQUA7bBhhv/1G6NatmE+d\n4kq7dpS/9lqjZjprVhYFY8ZQs2wZ4Xv24PfGGzdeyuoMg0F6Vt9974ZP/YcbiFgoboYyuMkQUwV4\nNagRzslx4WCyZWcjeHsjD3TtttZnZGAuKMCvGR6o88uXk/joo0z57Tcix4xpzSdxgUyhoPerrzJl\nxw6S3n+fnTNnYmylVoTcw4NOy5fTYeFCzkydKpXCuvGiBEHA59FHJfGh5cspmjrVtRS2Sxc4dgKy\nsmDMKGkBkMngyfmSvvXsEXDlEnTsB+/9Ditfhi2fSwnIJ/fAr6/AvsUQORxu3i5x55xbAUFjoN9m\nOpo+ZGBcOY8tzuCxl4M5cgZm3ZeCIjgVcIBFg+XkYMzHhqPqfAbNsJ2oup1A2fUkyi5JKDudRpmQ\nTFnocea9KEPR4RyK2DTUA/ch8y3HtG8CokkHOFC1PUTfbg7ufEqHaNUBIip1MlZLdxSmTBzKIETB\ni0khes4TgSIzA1ubaHAg0WvERSFPzsVzcHue7BBE/LBYXh0cQ7rNAQjUFNXw89uTiQr04oMfTnCq\nqIbfU6TmMb1B8iA8NEpmj4zjnlEdmTUijvYRPtisrQsjLpk7gMIKPasS6zdDPx/NJqvURHl5OboG\noaCM1FQunjnjtnrJbreTnZzcyECUZmbi7ySS5exBiKKIaLdfNxAyrRbR6NT57lzx09BAAAyaDocb\nhJmCO0jNriktM+s0CWMVrHkE7lwO6iaIMS+dkTqo3YWemjMQAO1jIePGKcnVPXoQ8uOPRBw9ir20\nlKtxcZQ+8QTWrCyqPvmEvH790I0fT/iRI6i6NtPT0Vp89ikMGAh9+97wqf9sA+HfFmoKm1aXaypJ\nXVPp6kHY7VI3qJMAuPn0affew7p1hMyY4VZ0XBRFTr3zDqfff59p+/cT5CY8dSMI6tmTGSdP4tWu\nHeu6dePyli2tPjfk1lvpf/Ik5bt3c3LUKExNhKtU6i9EGAAAIABJREFUCQlE1N2oeb17Yz55sv6g\nry/88quUvO7fF44ckcbveQIengd3j5DCCW07w8L9sOEjWLtAKh545gAkfgZb34CgnnDrPjj2Fpxa\nBH79eezbtix5SIGnRwar9mfz3pewflUXiuwZaBI2I9NJuy5HaQjGXVOx5bTHYdSBRQ02BYgCyOxo\ndA46t9cg0+mReVbhqPbBlDgWrGoQbKhj9iEoDaz6NhajUYlkHE4iiirs1jCUxlSs2q4oSrNIKhPo\n2yUGRWY6tg4dkV+8ir1tCILJhqy4RmJwvViEKiGUqZF+pIsi325NQeWhQqlRcmzBTURplCSX6Zm2\ncBdlNSaMBgtaXf3uMMRPR3iAB/4+WsqrXOlFmoK3TsWLN3fn3Q0StUyF3syLq0+zZdtv+LmRnfz+\n44+54/HHUWsah0/y09PxCQ7Gs0ETVWFqKqFOi5WLgbDZEOTy6yFSoaGBcK74aRMD+VdcQzMDp8HJ\nbVKpqTMGPQCHv2rVd+AWm16UKDU6NiP/e6mJ8BI0H2IC6NABLjUToWgBythYgpYuJfL8eQSdjtwe\nPahdv57wQ4fwffHF6wb3T6GiAj5cBG834UG1gH+2gZArwK9t06R9TXExNcxB5OdLjKdOySFLUhJq\nN9UATYWXHHY7B594gks//cTNBw/i26DG/I9CodEwaNEixq5Zw8Enn2TvAw9gqW6d2J8mKoreu3cT\nOGECR3v3psgd0ysgqFT4L1hA4JIlFEycSO26dfUHZTJ4Y77E4XTLNFi6VEpI3vEQPP023DMS0lMh\nLAY+PAj7foAVL4FfG8lIpG6BdY+DTyzMPAjnv4GDL5F4upzSsjG8dZeG5E/86dfBi7sWJdH3DjMv\nfGxC0e53VFFHQWYBUY4tJxZbRmesF7tivdANa1oPrOd6cfVgAvc/YcGS3A/LmQFYz/UChwJkFjSx\nu0GUYb40mtlDO5FTUoVZ3IdMXozJMBqF+TKi3EuSFc0/x2epcrxLCxG1Whz+ASiT0rH1iEWenIe9\nSziiw4E1pxxVbBCmqxW07x7Jb4mZeIXUh5R6B3ty+1gpnLHmUNb1HERD+PtoKa9unYEAiXNJb7Lw\n3oYzvLT6NLfMmMmgQYMazSspKOD3jRvdJqfBff4BoDAlhdAu9WprlspK1HVGRLTZXBYzQattHGIq\nqgsxqdSSlG+u0zPpHwZRCVIuwhndp8OVk3DBvb54s7i4B85tg5s/aH5eZhLENlHV05IHEfvHPIiG\nUISFEbBwIdGlpYQnJqJq0Iz7p/DhIrhpmluKoNbgn20goPkwU1Od1DWVrgRdOTmNGkvMZ86gaqAL\noU9Px1pW1kgESHQ42HvffZSnpjJt/348GpQV/hUIHzaM25KTEWQy1nXvzpUW2F2vQZDLaffKK/Tc\nsoWMV14heebMJnWwPW65RaINf+EFSp94wjXJNmUKHDgEn38KDz4AZjNMnwMvfQhzxsDRvdJCsHC/\nRLHw4T1S3fqTe6VS5JW3gzoAZiRiztrJoonVeGt8UTpupX1ICIc/sFL9wwCSP5xOSW4U8ZNFEBxo\nO29C7nuZpnIQtw1sR3mN0aWZTFDVoOm4HYfZG3P2MBDleOtENswTEdFjMowDUYnSeBartivyyjxy\ny41cdXjT3VCELS4eobQSobQKe8co5GeuYu8eiTWjBGWkL4JGSe3lMoQwb7wtdrxD6w2EzGDhzgmd\nWP/saP699hRbjufw+e60RnmkQF8dRWWtL23WqRW8OK0b/92Swv6L5Sxc5F44ZvXixUyeNQvfgAC3\nxzNOnKB9g42PKIoUnD1LmJMHYSovr/cgrFYXJgFBo2k6xAStDzOptDDraylM9On45sPFzjBUwOr7\n4fYvQNsCe3LmKWjfOBIASB6NspnYf89ecLgZ7ewbhKBS/bWcbXl5kmLcv9/4wy/xzzcQAe2gvIlE\nUlNcTA27J/PzISzcZYo1LQ1VXTfqNZRt307AxImNfuTTH3xAzeXLTNq2DfVfRPftDiovL0YsW8bw\nL78k8ZFH+H32bAytaOYB8OnXj4Fnz+LVvTvH+/Yl/YUXsLpp1lP36EHE6dM4amvJ7dIFg7N+RIcO\ncOSY5NaOHyvpZ0y9Cz78AZ69E775r0T1/P5eib77lVHSLu2x7SBXweKRYLVxJuYjgjxkBJr3gsOB\n1dwXi3EcanUGQQG7+eyBjtTUCjz4uog5aziq8DMYwzZzoPxXduZtQRGUhsI/E7lvDqXiJcYNVCPX\nVSMo9ci9c9HEb8VW1h7LlYGADEFWgdZjC9lFAqmX+gJKFOZMREGDXRGG8koS/z2v4sn+oShrqrC1\nbYfyxEVsPePA6kB+vgBbzyjMKXmouoRjN1oxl9RSplHiZ3fgFSJVKNlsdmorjfgEejKxVxTfPTEc\npSCwL62IZbsvuHzPXeOCOH2hdb/dNRxOL8ZgsfPLlm14ezfu/q0oLeWnZcuY88ILTb7Guf376dwg\nf1Z55QqiKOJbx/gqOhwYCgvR1W10bDU1yJ17gWQyV9ZV/4D6BkuANu2l/JQzBkyD41saMxt0mwav\np0H8WPhoIGyd33TIGKTzv7tXotPoOqXpeQCGGkkb2x2LK0ifQWhmiRw8WFob/gIv4m/BKy/Dw4+4\nhMZvFP98A+HfFsovuz/mjmpDFCUD4dwcU1gATrt+h9GIvaAARQPhoLIdOwhs0FUtiiIXVqxg0Ecf\noWxYN/43IWrcOG5PTUUXFsbaLl04+8knOFpB6ibX6Yh57TUGpqZiq6zkcMeOXPn0UxwNSvnk/v4E\nr1xJ4FdfUfrYYxTPnl1P7+zhAet/giFDYWB/OH8eBo2GdUdh47fw4r2AAC+uhh5j4NmBUJQD966C\nhAnw0QAiNTYmf2mjxOSJtmorMls5Doc/JsNkbNYYvLx2cXBBCLtTcriQqWHonQqeW1xOYmo52WXl\nyDRVyLwLUPhfwjPyPAtfsKGJ2YsmfiuqNscwZw3HVtwZEJArstHqtlNZ05nHvnDQuU0AiFaUhjNY\nPHojL78MMhk/Z4qMspdgTegMdgeKs5ew9YmTvIcOweCpxpKSj6pbBFVZJdR6a/jx6GXaqOTXPYiq\nUj1efjrkcumxm9yrDf1ig/DWqnju22NkFNR3u3eOCaKgpKZVeYjiKiOT3t/NrydyWLlyJb2byG19\n9/HHjJs5k/AmaBZqysspvHSJ2AbJzJwjR2g7cOD1HIOxpASVj8916m9bdTWKBgbJxSPy86svcwX3\nBiKig8TPlHmq8YXJlTDmeXj5NOSfhfe6QloTYjy7PwB9Kdy8yP1xZ1xKkmR0Fc2VozdTIahQwG23\nw+q/j7H1D2PbNkjcDy+/8qde5p9vIAKim/Yg3FFtmIySW+ncw1BQIJW01cGakYGifXuXuKvDbKbi\nwAH8G9QZl509i8NqJejP1DD/ASg9PBj4wQfcfOAAOVu2sL5nT/JakmCtgzosjE7Ll9Nr1y5Kfv2V\nI127UrJ5c6MwiG7sWCJTUpAHBZHbpQu1P/4ozZHJ4J134d/zYdQISaUuMhrWHJKEh+4cAgVX4Z63\n4fZ58NJwSD0Ak+fD5Lfx+eZmZnfVYfXsi1XbDU3VTlT6EyDasFnjMepvol2IjIMLLby2diNFlRae\nGHQzU9pM5fVPZPz6awRLVwSTeqg3/e+0kn1kJMbzt2BMuQ1j6q04asMAB0r1CVSaU5gM41jwk55u\n0YHo5CY0lb9hV0XhkAeiunIaY0RP/GxGwkxV2GLjUJzNwtImhFKZAsXxy9j7tsVeZcReUouyfRCJ\nv19kb7mB+AgfIpXy6zmIypJafIM8Xb5Du93BhhfHoFLI6PnCxuvj2SU1KD00PLJ4P59tP4/J4t7A\nW2x2Zv43EZtnBKWlpcyZM8ftvIrSUn768kvuf6XpBePc/v3EDxqEokH/zjUDcQ363Fw8nUpe7Q0M\nhCAIDTwIf6ho4EFcdRPG7H+T1DPTFPyi4MENcOt/Yc3DUnd+ZX798fS9sO8TmLsOFK0oC714XJI/\nbQqtEeC5a5ZEaPk3MLb+YRQXw0MPwDffScJGfwL/fAPh37YZA+Gmiskd90pBAYTWexDWCxdQNkj6\nVB4+jGenTij9XTuwL61fT8yMGTem9vQXwi8+nik7d9Jn/nz23Hsvu+68k9pr5GktwKtbN3rt2EHH\n//yHjJdeImncOAyZrlUbMg8PAj7+mJBff6Xivfekcthrrz97Nvy8ER6YK3HAaLTw0Q8wdRbM7A8n\nDsC4ufD8KnhvBuxdDf3uZrXuVj4ZaCHEkINNE4vBbxo4TGgrNiE3X0WU+WAxjcBkHMja57Vc+NyP\nTpFKukcH0Kd9ELf/Zw8vrTpOzxc2Uqm3MKyTq/ANggmNbhdyeTlG/RQcjgBkgkCUZzXyss3Y1DFY\nPAagKE5H1HiRbfXi2bYO7B3jQaHAfCCF9TYVq7alYj+TS267QMl76BSKoJBBXhX6AB2rnxyJvrj2\neoipoqQGvyDXe8tud6BUyukc5Yevh7SoXS2tpe/Lv6Bt04Faq463N54j/OEfeWLFEY5nFmO1Oagy\nWDBabNz60V4qrCr27k8koIm8ArTsPQCk7N1LlxEjGo03NBC1ubl4OBmIRh5Ew3vd3981xBQV09iD\ngDoD0Yqy1i6T4dVzEBgL73eXyqUrrsI3s2D2d5L4UGuQfkISLmoOLS38ffpIc5yr+/6XEEV44H6Y\nfQ+4+S1vFP+PGIjL7o+564PQ1zRmb8zPdwkxWS9caFRpULZjB/7jXEXQRVHk0vr1tJ85849e/V8C\nQRBof+ut3JGWhk9sLOt79OD0woXYm2B5bXhu4MSJDDh7loAJEzg+YADZCxc2Cjtp+vUj8tQp1H37\nktevH6ZrJa+DB0u04V9/BY/+C2w2mPssfPAdPDkDNq+GnmNgwR745hVY8y6+vafwr9MhKPPPobp8\nAgQ1Fq+hWAImoLKmonWkoIzpQ9vYCQi2W3E4fNF6bkLrsYkvHq1i06tKyr6LI2dZZxLfiUejLkGQ\nVSJ4eqGMikDnswtRG4/JNBFEKUzy1hQPVtxh4fZvrKRWRILDjjL3LJY2vcjOLmBaMNjiO5F76hIW\nk5VMrQdxhdVc9dOxKbUA89k8VF0lfhxlUTXhXcIxVBiul7gCVBTX4Bfc2IOQyWXIBIFKvYW8Mj1D\n3/iNefPm8cWqH1BZLFRVV7N23U8UKtswav42/OZ8R8RDqwmauwq9KohjJ06iaqaRqjXeA0gGouvI\nkS5jVqORwnPniHLygPV5eXg4cQG5CzE18iAaGoi8y43Du/EDoDRPCjm2BJUObnoXnk6E5I3wVhwM\ne1Rqxmwt0v8CD0IQJC/i/y9hpi+/hIJ8eLMJRb0bxD/fQHiFgLnWVev2GtzlIBrmH6BRDsJ68WIj\nD6Js585G+Yeys2dxmM0E/4EGlb8DSp2Ofm+/zfSjRyk4cIC1XbuSs21bqzqxZQoF0c89R/8TJ6jY\ns4djfftSec0I1EFQqfB74w2Cli+ncNo0auqoOIiOhoOHJWqCSROk5PXgsZL40Mfz4PN3pF6Jj4/A\n4Q1MztzI1rPF6DtPQmYoR5OyDZm+HKHjDGz9FiN6tEV5+hWUjhwEXRBWc08MNTPYlxzPvO/NtA9K\nQC7TEeYnMjDBhEp9Bo3HfrTyr1FWf4zNfy6O8CdRtB0Aog1V7RGUpvNoIm7hUoU3fV7axHerN7Ej\n20Kh3QPxbAqH8QW1Gm1SOicCAkAQ6HmlnDNt/KkxmDGl5KHuGo6lyojWIVKjUVJdWO1S4iqFmBp4\nEDYHFbVmTmWVMqlXFKsOZDJq7HjefOvt6yI+Oenp3HzzzWzbvhNRFNHr9djtdmprazl2MonABs2a\nDdEa76GqpITSK1calbhePXmS0M6d67WokTwIzwYehLw5D6JhDkKrk6oEi/Nd58nl0G8yHG8mzNQQ\noQlS4+UTv8O4G+AZqiwGfSWE/wXl5nfeBWvXSJuf/yUuXIA3Xofvf2ishvkH8c83EIIAvlGSC9oQ\n7nIQhlrQNYjbFRdLpXp1sGZkoHQi7rNWVmLIyMC7n6u7mrNlC9E339yq8JLNbObryZP5uHt31s2d\ny6HPPuPykSNYDC3w4v8B+MTGMmnLFgZ99BGHn3uOjYMHk756NfZWkIhp27Wj5/btRD//PGdvu43T\nU6ZQ3UAQRTd5MuF79lD59tsU33MPjupqiTZ80y/Qpy/06gE7d0JcF1h7BHb/As/eBTpfWLgfnc3A\nzr5wPrsMU8I4bKEd0aTtQnF6PYgi9nZ3YO31HrLSY2hKf0awVQBq9qSYKKoIoI1/T6yWrljM/TAb\nR2AyTMTi/QbWNj9gjVqF6CH1B8jEarRV2xAcJow+kxHl3nzz+AheGtuG2e2MLDyrYt3OZIap9ehj\n4xHKqwktq+CMrz8BtWZCq0xcCPMhsNKIzEONPNiL2swSyn20XC6rpaao+np4CaCqXI+Pv2tHr9nm\n4OYPpDr/bUlXefun08yZK4neCILA2BkzWPvFF67fr06HTCbDw6OJ7mAnFOfn89OXX/LAvOYXzzM7\nd9JlxAjkDZqzsvbvJ3rIEJexmqwsvJyMjbWsDKUz7YbdLj1b1+DtDTU1rpuxyHZw1U1/Ur+pzech\n3EEQIGaQ63u2hIvHoEPf5s+RK8DWMtcScXFSBZ9zf9D/NWpqYOat8O6CP9zz4A7/fAMB4BsBVfmN\nxwVZ4xij0QA6pwfP4ZB2P065BVtOjksFU9WxY3j36dOInC93926ixrbs8oqiyMbHHkOuUjHzq6+I\n6tePguRkNj3+OPMDA/moa1fW3HsvBxcvJvvQIcxOAvF/BtFTpnB7Sgrdn32WiytX8l1UFIeff57K\n9PRmzxMEgbC772ZwRgYB48dzesoUkqdPpyalXipS1aULEadPSx2i3btjOnhQ2iEueB9Wfisl0V6d\nB4EhsDpRehjvHAIV5Qivb2JXoZUeKQeRVZRjC+6Asd/dUF2I8udnEArOgS4CW4+3sPn0QVu1HaU+\niQBVNQZDjfu4sayus12QgcOGLHstiuS3sHj3wew1AmQqEEW6yPJZ0KkIZdwAYqIjGFR5mcVXZMS0\nC0W5Pxljn3hEjYq+2aUktfXHJpfRo8aErn80ANUZxSii/TmfW01NUY1LD4S+yoSnb/1OfNLCPWSV\n1vLaa68hiiI/rPqeBx98gIkTJ16fc//LL7N11Spys5to9mwBn73+Orc++CBhdSWqTeHoxo30dyN8\nlb5jBx0beMYVFy7g56RzYi4oQO3kYYsmEzInjwOZDLRaiRPoGkKjoMhNLqzXWEg77Ere93cg7Qgk\nDGx+js4DDK28jn/Ph7ff/N94EaIIc++DgYPggRYU9W4Q/28YCJ9wqMprPO7OgzAaQONUjlpVJZVu\n1i3+DqMRR1UV8tD6xGfVkSP4DHBlirTq9RSfOEFYM5xM13Do00+5cuwYd37/PVF9+zLwkUeYsWwZ\nT586xVsVFdz+7be0GzKEovPn2fzMM7wVGsovTz2F8U+KCoEUOmo/YwZTd+1i+uHDCHI5m4YO5ZdR\no8hcu7bZPIVco6HNE08wJDMT3yFDSBo7lrO33349kS3z8CBo6VICFi+maOZMyl99VaIQHz0aTiZJ\nTUa3TpfU2BZ9dz15bT++n9cz4KsaHzR7dqK4mIZot2AbdD+2/vei2PMf5AeWgrkWqxCK0fcmBNHE\nw/0q+f1fRij4FlnJRtTVe1HqT6IwpUPBITCVINTmoEh6BVn1RSxd38QuCwdBQDDXojm/A0VpNsYu\nk7EFd+DtoWGEY2Jhpp04uYgiMw/FsK7cPTCGnvmVFPVpy8hu4UTmVqLuI+2oa9KLad+nLQXl+joP\not5A1FYZOZxdRo3Rymc70khMuUL/QYMYOUzSM79r1t0sW+YqtxkQEsKdTzzB5//+9w3/tulnz5K4\ndWuLuQez0Ujyrl30meLaN2CsqiL/zBlinO5hh91OVXo6vk67VEthISpnA2E0IjSk8fDwAGdNk7ax\nkO1mI6Lzlnb2yXtb8Qn/BC4cgfgWDITWA4ytNBCjRkkd46tX//lru1F8sFASZVry6V/+0v9vGAjf\nCKh0ZyDcVDEZ9VKM9BpKSyWajTrYrlxBHhnp0gxXdfQoPgNdb7aCgwcJ6tULlRsxoeXLvqRfr24M\nGzyA4W0j2fLaa8xavx61m5I0hVpNZK9e9H/wQW5dupQnjx9nXk4OVpOJRQkJnPzuu79MFN0nNpaB\nCxcy+8oVOj/8MOeWLv3/2DvvqKjO9mtfZwozdFCkiYggqCjYC2LBktg19orRFE3UFE0xMYnRRNMs\nUWNijRpjiZrE3ks0KqJiQQEVC116b8O08/tjEGEYFCxv3vfLt9diMcx5Th3muZ+77c2v9eoR+tFH\n5N41UXVSCqmFBfVnzCDwzh2smjfnQkAAp2fNYtXKlaxdu5bigAC2BQeTd+GCgUL81i3DMz181PC7\ncyDEx5Pcdwza+T8jnT6K6Y5yph1Poct5gdjQcNi/F134IXRWDqgHfIFYUoBs21SkKbcQpZaorToi\n1hlItDiAwOXWdF+az5k4CxDMkGjSkGf8hfzCe8guf4ze9QU0npPRptwGUUSWdhvza3vR2bmiatYH\n0dwG9HpcboVzsbYnttbmWJy9hqaDLyjMcIpIQurrQp8+TWmukINeROZRC71aS2FcFp4t3chXqclL\nzS8LMd1JzKa4RMvoH0/h8vpm5u+KJCQkBEtbW0oeIwb18nvvce7oUaKvXav2Z5mfm8u3777L5M8+\nw/oxzZnXjh+nQYsW2Boxvt45cYL6HTtWzD/ExaGsUwd5ufCWKQ9CKO9BgIHyu/x9NmkBUVdMX1Db\nvgZupucFnRZuhxmS4o+CRQ0MhCDAnC8MrKnVoAB/Zjh0CH5YBjv+qEAF9KzwjxkIQRD8BUEIEQQh\nXBCE3YIgVJodBUFwEwThhCAIkYIgXBcE4e0nOpltFQZCkFROUquKDCuHB8jMhHLlg9q4OGRGtN+5\n589jZ+RBJB47ZpKpdcigAXw+60M+6uHES65qOmakE2opxaVJE9asXlWt27GsXZthq1YxYfduzv7w\nAyu6dOF+eHi19q0OpAoFDUeOZNBffzHo77/RazT82aED+3r3JuHIkSoNkszKih/SUng5I4PIr78m\n4+1pzHj9derUqcMXPyzB89gx/pAI3O/UyUAhLpfD6jUUjxhJZmMfhri6Iu/Wj8BYDa+Za0gf4EFQ\nOx/G3bPi0ws56Hf/ieTIZrQx5ylx8qbEKxCzuAsook+CxtBQ1tyjNme/Gkr3lv70/T4ajYU/autO\nqOz6UGQ/lCK7EZRkqtDGhiIUZKC4dQJZchTFvr3Q1PUv65yV3bqB3tKKjTElvNrMCUlMMpr2TUAU\nkR+7iaanIcRScjEOZZv6CIJAQWwm5q62mFspcbE1JyMxB2VtC0RR5N0155FYW6PVagkJCSElNY2A\ngACUlpaoHmMgLK2teW3WLJY+xhMAuHfjBvOnTqVPgwY4ubkxdNKkx+5zfteuKsNLPqbCS0YxbrWx\ngaiOB9GkBdy8avqC2vaFiweeX29BzDVwqGegGn8UzEtDTNW9jq5dDZQ8D4oznjfu3oWJL8PWbQbl\nvueAf9KDWAt8KIpic2An8KGJMVpghiiKTYEAYKogCDXPwDwqxFTJgyiq7EHULudBGBmIwlu3kNeq\nhZmjY4XDJJkwEAcOHCA8LJSr3w4gqJET2tAYXhzekr3fDmTh+PZ8Pf/LGt2We7t2vBUaSqvgYFa/\n8IIh7FSF9vSTwr5RIzouWkRwQgINR44k5P332ebnx42ff0ZrpLMriiLr161n8ug21HkniEHdfdhl\nZ86BsW1JXTuWY5/35d2LYaQvX07e2rWkjR6NtqiId+7dZbpCymkbBZGDm/P+uNb0yTIjLDyBz/NT\nOPVeN7oN70Gr0yJFCUkoD+5FkpmB3taFYv9B6BVWWFzdheLGMeRxl5Bm3EOVl0nrBib6AgQBEJFm\nxqK8tge9hT0qv/6Ilg9zTEJeLmaR11C3aUd0SgGv6PPRdGwGZnIk0Wmg1aH3NUyIJRfjULQ1xPfz\no9Ow8XZEIhE4/H5P1BIYvOQUe8PiKS6G+k2aIJVKCQgIwLx0ha2wtERVjZzS8MmTuXfjBmGnTlXa\nptfrObVvH5NffJFXu3XDrnZt/oyI4KuNG5E/RrRKp9Nxcc+eSgZCFEVuHT5MI6PS7ewbN7Az0lmv\n5EEUF1f2IIwNhLsX5GQZfoxRr/T4Cc9IUc4Y1ck/gCFnJjczNM9WF3O+gPlfGvSfnycKC2HoYPj0\nMzChavms8E8aCG9RFM+Uvj4GDDUeIIpiiiiKV0tfFwA3gJqbyqpCTKb6IIoLQVHun9vYg4iPR1Yu\n4ZcbGlop/1CckUHevXvUKVfeumTxQoYOGcIH/RtjoZCxe81Z6nk70rZnYyQSgU5NnJE9AVGXRCql\nw6RJfBAVhaa4mIVNmnDp11+fWdjpAWRKJY0nTmREeDidlizh3p9/ssnDg3MzZ5IVFQVATEwMVkoZ\n7/RrRu+2HjQIbo/P64GY748gZvNF2tSz551+fmw8fQrXM2cQJRJOu7pw9+hexk3ryqbO3jgfvYHL\nvmv8+EYXxmZKOS8oMF+1h17aIhS1bFmmcUPj2wzlyWPIr4QBApr6bSj2H4jWyQekMmSZcUxxTeJE\njwyU4bsxu3sWWWo0QmEWgiofRfRJzOIvU9KoOxr3Vg8T2Dot8ohrmB85gLplG3RW1tQtKsStoABt\nW8O6RH4kiqyOXkxbH8oL7+7kfmIOPTdfYW9YHHnRaVj7GBYKFioNzu61uHQvnY9+u8Jr48ZjXa4S\n7gHMrawofoSy2AOYKRRM+/JLFsyYgbq02qwgL49NS5cywMeHlXPn0j84mMNxcUz94gscXV0fc0QD\n/t6yBWcvL5zKaT0ApEdHo9docDLiG8uOiqqQoNYVFaFXqZCVq2LSV8eDkEigkT/cNOH5CoLBi7iw\nv1r3UGNUJ//wABZWhsrG6iIw0KBdv3LF48c3MM0VAAAgAElEQVQ+KUQRXn0FWrSEKdXTvX9S/JMG\nIlIQhAeizSOAR7Y/CoLgAbQAztf4TNZOUJBm4qAmqphKVIaO3wfIzTHoHpRCl5yMrNyXryA8HOty\nuhB5eXnsXb4c6tcnv7CQ4uJi3pv+DnPnfM78US0YHehJ1MU40hKz6RPcrqwEtr6DFfcSTBixasLS\nwYFhq1fz8q5dnFm6lBVdu5JcrqroWUEQBNx69qTf/v0MOnUKQRDY27Mnf7Rvz5116zBmm7Jv7kaL\nrwahzVdx9aNdDLVXsmXTrxw9dYqphQVcspaxJqeAmLN3iTWTsraLN45ZRTTZGMonL/rS71wqWaN6\nID0XyVxNNgOaOqJr4EVRv0FI8nJRHt6PkJONqLDkepE1w3Zk8N2dOvhvl3DHawBqz47oLWshyUtF\nGX0S8/Dd6M1tKfYfiN661OsTRaRxsZjv3YUkK4PiXv3Qenkz4YeTLLXToX+hDchlSGIz4VYqgSfv\nEi86sWrISOpOnMhr781m7JK/SA5PRFbqteSl5lPLxRYQiU/NoaWfHwoT+ajabm5kVFM6ts/o0dRt\n0IApffvy7bvv0qdBA8JDQpi/cSNbLlxgQHAwZjWIQ+emp/PLBx/w2rJllbZd/+MPmpoo0U4PC6NO\nObbX4nv3MG/QoMI4fU4OEmMdCrlZ5QofryZwryJJYRla94bLVfAtPS2izkLTTo8fB1CrDmSlP35c\neSxZCvPnwa3KKn9PDZ3OQMKXEA8rVlavme8p8AwUKaqGIAhHgfLLJoN/D58ArwA/CILwGbAHqNIn\nK81P/A68U+pJ1AzWjpBv4kM2FWJSl4B1uaReXp6hjrsUutRUpOVWggUREdTu3Zv5X85l7ZrV5Obl\nM1QuoFdpeK30SzKogxenPu+Nl7MNRQUlHNx4nhFvd0Nu9vDxRyRkodPpiY2NxcOIBLAmcG/XjrfO\nnyd09WpWde+Oa4sWtH75ZfwGD8asGnXzNYF9o0Z0+OYb2s2bR+KxY2yf/i5vZ+dx7ucQWo5ohdLa\nsIqU2yjxfqMzORH3ubchlC3OFkzo348UrY7OE9qTJ0jotOUi1xs5ctPTgU0BnvS4kcwbJ2/xS5Ga\nu8jRvBhA0qojvLTnb9QDOqLzdiO3QxcuHQqh7Z49nJI58dqxFDLVcCQ8iZfaN8DdyR49oLeuAw+K\nzkSxwpdKkpmB2aWLoFVT0iEQfSmlyo6Qe3jHJVHXyw5dC0PPi2RbGF9JZHQeMIQ1q9eS4OmJ4+7d\nvNmiBS0sLLjzxmTafnWMga3r4h6TQXhiLs5Ozsz5cj66kpIycrvycPbyIvp89dY8EomEeRs2MOf1\n1zFTKNhx9SrOT8HUuW7GDLqMGYO3iUbO8O3becnIcGgKCsi9c4fazZuXvVcYHY25kbaJPiOjUiMp\nUmllA+HZCGKqmET9g2DBWENOUPkMSS4zEqE4H9yqqbng6GJo6PNu+vixD9CoEcyZCy8HGyjwHxPm\nqzauXIE3JxtKhv/cZfj9nPFcDYQoio9rAugFIAiCN9DP1ABBEGQYjMOvoijuftw558yZU/Y6KCiI\noKAgUFiBqDN0U5eXHjQVYipRVRQJycuDcvkFUwbCsmlTFo0awdcj/WnZwIHUHZfxDPRiUWt3Cks0\n2FqYla2wDm+6QNN2Hrj7PDxmiUbHm2vPM2PG9KcyDg8gkUrp+OabtJ04kag9ewj75Rd2v/UWzQYP\nps2ECXh06mRSi/iJzyeT4d67N6ErG9K/U22k8dnsmbmLlsNb0bCrN4LEcO92zVxp8dVA/l5zlmW3\n0lgFNK1nj9zOgoNdGxIUGkutnGJCW7hxtKkrNsCxXeGoLsdz19eFj7MEblqZ8eX2kxwqlvBanJpi\nEWZ29yAwM5akHhJuFsD5AinjB3gYSnSNO0ofqJ4VFyG/ehnp/SQ0zVui9WxYoWnqjyMRbLEH6cgg\nREFAvH6f1JupXHvhRXasXUfxwYNInZxQlGqCuKSlYffqayzs2JFLl8LQR++kw6AebN28GYlEQshP\nPyEzsbp3adiQlEdUiBnDwsqK77ZurdkHZAJXDh/mxpkzLIuIqLQt7dYtCtPS8DDSNUkLC6O2vz/S\ncs+06PZtLH18KozTZWaiNO7ulkori3N5+MA5I5GgB7CwAc+WEHkaWvcyPeZJEHkWfDtVf+VdxwXS\nkmt+njfehL17DZ7EnLk13788Cgrg89kGOo+vvoEJE57Kczh58iQnHxB3GhfpGOG5GohHQRCEOqIo\npguCIAE+BVZWMXQdECWK4tLqHLe8gSh3MrByhIL0igZCYqKKqUQFZuVWerm5Bu3ZUmhTUsp6INTp\n6ehKSljw8xoUUhjbuSGCIBAVk0nbce2QyyTYyR5OCrfDE4m7lcqbXw+qcMrLMRnILGxZsGBhdW6x\n2pArlTQfMYLmI0aQl5zM5c2b+XPKFDRFRbQeP57W48dT29PzmZ0vPj6Oes3daRfkg1eXhoSuP0f0\nyWgCXgmgVn1D6EUvkTAxKoVJnRsSfPoOjhfjmXQvg2sxmfyokDIrOZfAtHxu9vIl2c+V1w5EEnIx\nDpd7GawY2ZrxG8+zw0xgQz0p8U0VBKfCZ68EkVekRmMmweV+Cvc3HEcdfg3rgmz0NrbonJzROzmj\nq+MEEgnym5HIb0ah8fKmeODgSqIwydlFTCrOJrejD/YOtiCKZKw+zSdaPeu2bkMQBPJWr8a6XIVQ\n1okTuE2axJjBgxkzZgx/nD5D4NtvlxlijUpVpQeRcvcuoij+xwgdiwsKWPHGG7y5ciVKE17ltR07\n8Bs2DImRbG7a+fM4tm9f4b2i27exNfJA9BkZSIyJA00ZiAaP8CAAWr1oCDM9SwMRdab64SUwGIj0\nJzAQggA/r4PWLaF3H+jwmJLaqrBnD7zzFgR1g2sRYFSK/CQoWzgDbF3Jo8zXP5mDGC0Iwi0gCkgS\nRXEDgCAILoIg7Ct9HQiMBboLgnBFEITLgiD0fqKzWTtCvlEewlQfhLqkog5tuRCTKIro09LKPIjo\nw4e5WVTEvt/WceCjngiCQHZaHjqNDqtSWuesfBVpOUWoitTsW3eO/q8EoFBWdDkz80twc6v7TFf1\nxrBxcSHo/fd57/p1gnfsoCgzkx/at2dF166c/fFHbh0+TGpUFKpqypWaQkF+IVZKGSUaHefS8rnZ\nvC6xtubsn3+I0F9CURepeX3VacxkEqZP7MDHShmXztyl3+00ggMbUN+tFps9HfijREevE7eI/Csa\n0c0e1Zx+6F1tGbvvGunTuuDgaMdm13pY9e/AAVcB+alwbJQyBJkMS3c3bjs1ZNA1OUXDRqNu3Q7k\nZshvRGGxczsWO3cgycqiuFd/NC3bVDIOQlYeOT8fxFsOC3Ih+IeTfPbBLooK1CxMSMTGxgZtUhKq\nv//GatQoAPRqNTlnz2LftWvZcXLv3sXGy6vsb61KhdyEgbCwsUFhYUF2SsoTP/eaYuvs2fh27kzL\nXqYn3vDt2/E3QTCZGhqKk7GBiI7GwijEpMvMRFodD6KeJ6QmGb5zpvDAQDxLRNbQQDi6PpmBAAN/\n2/KfDKGmmrIfJCTAkMEw8wNYtwHWb3gmxqECiovgx0dXTv5jHoQoisuAStkxURSTgf6lr88CUuMx\nTwTrUg+iPEz1QaiNQky5uVDaaKTPzQUzM4r1egZ27USt0AsMcrPlr88MkbSPNl3g5KEoPvd1psOs\nPVjJJXRp7IyFQoYQlYK7jyMN/SoXYaXnqXB2qSZF8VNCEATcWrfGrXVr+i9axI39+7mxbx8RO3eS\nm5hITkICUpkM23r1sCv9sa1XDzs3Nxx8fHBr3drkRAeg1WlRa/X8dS2JGwkGcrai+rUodrbBIjGH\n+A92kpCv4rtpXVGayZjyUgs+2X+d5U1c6HI7gyYzuqN0sqHDrD34utnR82Ic+XYWiFIJmpFt0DV3\no9bq0xxys8f39B0cbS2YP3kAil1nkN5OQNvKB523G60a1OJaXCZIpegdndA7OqHxaw46LUJRMaKJ\nZLFQUIT872tII2I4mKLh23QRR7GIHt17MCvuAOoVC3EprTXPX7cOy5EjkZQ2NuZdvIhFw4ZlVO8l\nOTno1WrMy32htSoV0ioSyA+8iFrPQYrWGLcvXuTvLVtMhpYA0m7epCgzs1J4SRRFUs+fp+PiilKm\nRbdvY2EcYjLlQchklQ2EXA6u7gbq74a+lS+mYWvIug/pCVDnyXMtZUiLh+S74FWFBrUpOLpAeM3r\nYsowZAgcPgQe7uDvD37+0MwP/PzA17dCfhMw5Gl+XA5fzYdpb8HW355LAxwAm5ZDywA4+0eVQ/4x\nA/Efh6VDZQNhimrDWKi8IL9MdKPk/n2oVYvdu3dTmB7Pwh7emFsYxqblFvPziWi6Ar/dTCVRLsXB\nWslPR24wrmU9rGMyUZfy9RjDXC4l9xnQZtQUMjMz/AYPxm/w4LL3RFGkODubnISEsp/chATu/PUX\nIT/+SOqNG7j4+VG/Y0c8OnakfkAAtnXrEhMTw+2YBFztAzgdUZH3SlTISG/mSpqlGS9eiEN+IJI0\nOwum92/G9P7NAEg+epPrcw/gPaULU3v78t4voUxt60Gfi3HkrTqDzSsB6Bs7UzxvEK4bQ0l3taH9\nkUhc7c2ZEvwi0ogYZLfiMTsaxhC5ghyJHlQloCz3WUpllYyDkJ6D/FwkshtxFDZtQK8cS6J1sGH7\nKoYNGwZLl0BcLLzyKgD6oiLyVqzA+dChsmNkHjtWQSgqLyYGa6PKHlGvRyIz/XWr17QpseHh+Haq\nwcr2CaBWqfhh4kQmLl6MTRUMsJc3baL5iBGVvNn82FhEvR7rcjkyTXY2uoICFOWq+kS9Hn16OlLj\n1a4gmI531/eG2NumDYRUCr1eg2WTYM4+w99Pg/UzYfD0R+tMG8O5HtyvBv34o7BylYF++/p1iLgO\n50JgzSq4ccNQQu/b1GAsvBrCz2sM7LenzxpIAJ8XstJh7QLYchqW/38DARb2BjHz8hAkVJIU1Ggq\nShAWFaFVKujZpROyqCjeysxm7NixrHmjM5KbKchdDN7FmmM3aVTXjvG2SqKB9r7OFBRrWLTnOonh\nifh51CY5X4VGq0cuq/jlKyjRoDSvKDT0T0EQBCxq1cKiVi1cy1WrPIC6sJCEsDDiQkII++UX/njj\nDcwsLXFr1452UilH/76DXCpUKknLLixhWVg8a6d2oZFax98/nsKleV1q9WiEtaUCtxcaY1HXlugf\nT9FjgB++de1YfO4ebqNa43Mvk/uf7eV0gCfpUgkNWtajr0dtwnaFM2rrRQa1caeunyc6P0/QaMk4\nfo0Of0diseR3dA1c0Pp5ovN2A3npv7soIolLQR4SieR+Btq2TUh/fQA9Fp/Gr0N3/vp1s0Ff4c4d\nQ5Lx7LmypGDeypUoOnRA4e9fdm+ZBw/iNX9+2d/5sbEVJlIAhY0NBWkmSq2B5j17cmbbNvpOfb41\n7Vs++4y6jRvTZfRok9t1Gg0X161j0rFjlbbF7dtHvRdfrGD08i5dwrplywq0M7q0NARrayTG8rpq\ntemVsKu7QV2wKrw8Hz55ATZ9Di/Pe/QNPgoRpw3lre/8XLP9vJvCnSiDcXvSELAgGHianJ2hPHmn\nXg+xsRAZCTei4OIFeHcGjB373MtXWfwJDBoHXo/uO/6XGwgTqxqtpqws7dq1azjGxPD6qJGcionj\n2zbutHJSEvtWVxysldy4EIvMWsGui3EsPRDJuwP8kYcnEjyyFaczCknLKUat02Oug333MmhgYYZM\nWvmDT8wsxrNJNcvu/mGYWVri1bUrXqXxdlEUybh9m9iQEOodPsSdg5FYSCXoPGsjc69VVsF04Goi\nHRs781I7DwCKnawJXXEaMTKZ3Lb1qedqx5COnvjN6cfN70/wtiDwkYWcV/s2Iz4tj+vrQ+mw9zqn\n27pzQ60lt7Ylwe/15KevDnF64THqzh8IEgHkMu7VceAjlSURs/shuxGP/NItFHtD0DZ2R+/qgOzK\nbQS1Bk1AM0qGB6ESYfjik9Rv0pLNv203TIJ6vUEJb9YnBipnQF9QQO533+Fy9GjZ81BnZlJ44wb2\n5Vb/BfHxFeiwAZS2tmRUIW7fvGdPVr75JlqNppLc57NC5OnTnNq8mSXh4VUmw6P27qW2lxdOvpVX\n87e3bqX1p59WeC/v0iVsjPQjjJkGylBSYlqjwMUdUh5hIKQy+GgbvNMGvNtAx8qUII+FTger3oFX\nvqt5yaytvUFA7H68QTb3WUIiAU9Pw8+AAc/22I9CxCU4sQcOVdGDUg7/DrI+qNqDMG6U0xo8iO3b\nt9O8eXNkxQW82tWFGf39uBubhcTSDIfS+n5NnoprGQWMW/oX44N8mPWSfxmDZ7tGjtiYmzGtty8e\nSjkyWyWX47JMfjmPR9wn7ymSw/8kBEGgjo8PbSdMoPHb7xDr58bod4KwzVWhPnELq6wierV0Iyaj\nkKHtDROHRqvnxI0UsgMaoDOXY//3HRLjMrkak4GyjjV+s/siaHXMVmlRZRYQEZ9NVMM6nG7rTueL\n8fjeTuN+RgHpzjaET+qMa3IOikXHDI1sQC0rBYUqDSgVaFt6owruRfGUl9A71UIal4KmawuKpw5G\n29qHu5lFOLyyCWzr8fufux5+Pj/9aJhY3npI/5W3fDnKoCDM/PzK3ss8cgS7rl2RlFsd58fFVTIQ\n5nZ2qKqgQbGtUwdnLy9uhYY+k8/EGMX5+SybMIE3V62qRMhXHqGrVtF+8uRK7+fFxpIbHY2bEXV9\nXlgYNkZa61UaCFMlxwAu9R7tQQDYOcKs3+GHSZDw+EmtEo5tAIUFdBlZ833BoFty23TO5n8Ooghf\nvgXT5xtEmx6Df5eBKDYyEKYa5UoNxKYNP7P81Y7UNpPyQrv62FrIsUZEsHj4T67JU9HGvy7W5mas\nPBzFlVspaEu0mNuZ417HmrFB3nT0roNEq2N4jyYoFJVXh6IocuVeOuPGBT+Pu/6PomXLllxPzMPd\nx4mpX/Rn3NvdUKTkceqn0zTQaGnrZZicMvNVlGh0IBHIb+GGyt2eWqfuEB9lqOSRKuV0/qQ3EeZy\nTn+wE+l9w8SaUseaA0HeeCRk0+liHGKJlo7t6zPSUsna5Fzk3x9HOXsvgfFZ2CDSZuYuClSGYJdo\nbYG2gy/ZAzox60oqB64kMm1tCM3f/5N+fftw4tRplEqlQftj9Wr4Yi6sXVcW99bn5ZGzeDH2RmXU\nmQcP4lBOvwFMGwilrW2VBgKg5YsvcvXI8+kcXv/++zQLCqLdI1apmffukXT5Mv7DhlXadnfbNjyH\nDkVq5N3kV+FByE0ZCM0ThpgeoFE7mPA1zBsMRTVYTBXmwsZPYfLSJw/beDeD6P9HDMSezYYw+tCJ\n1Rr+7zEQ5lV5EMYGQotWgNDzF+jWzAVKdGAmo24tSyQqLZIKBqIYC3tLwhcOxsfVlnnrQzF3sCpb\nhTrZW+DvYI1jXTvy1FqcbCpX/xy9loS/rw8BAdXkhvkvRoMGDSokNz2aODPx0968GNwWX7WOY8v+\nIvJ8LNZKOVJp6ThBoMjbkfzmdSned534MENC0MHGnPtN67Lb0RrbA5E4l3oHN4rU9MhVEZ6US9T0\n3wn+/AB/zx/AXI3IhiEt0QxvhdmtVG5qtXybW8z0j/ag1+n4OyqZF+Yfw/HVTXy/L4IRi49zu8Se\nc+fOsW/nLqT798OI4eDpAUePGOiTy+mO5y5dikWvXpiV6xAW9XoyDx+uZCAK4uKwqqGBaPGcDMSl\ngwe5euQIr37//SPHnV+zhlbBwSYr1G5v3UpDo7yFJisLdUZGpQombWwsMiNeJ6BqD8K5HiTHP/5G\nAHq9Cs26wuIJj23wKsNv8wy8Tt6tHz+2Kvj4QfSzp635j6MgHxbMhM+WVTuf8u8xEBb2UGjEHCmR\nVC6902q4fuMW9pZmuNe2BI0WzKRYKGSY6/QIFoZVlE6tRdTpkZrLcbQ159jsPlirdVxIyye78GFd\nd/r9HBxcbckpUqMz8U8dEp3O4OGj/2NNUs8TXl5eJKbnkpL9UDlMEARSZFIOWJrRZ1w7zu67zsYv\nD9BAFCsQCiq86xD0Xg8u/HKeyAMRRN/P4dDleD6Z+SLNP++Ld1IuTSOTScosxM3Zlnaf9+VOg9rM\njssk+K3tpOcWkVWsRudXl5JpQZQsHEbn3k2Yk1NI+mub2fX1YXoPm0hKSgp6vR6xpIQzc7+kw68b\nwd0NFi2Ani/AvVjY8buBurkUuvR0cpctw/7zzyvcb/7Vq8js7TE3SkhXFWIqzjZaoJRD48BAEm/c\nICv5CWvuTSAvI4OfXn+dt9avx8K4nLIctCUlXFy/ng4mqMGzoqJQpafjYsQYmnfpEtYtWlRIUANo\nYmIqqC2WoaochFNdSE+p/D2sCm8shaxk+KMaTaXxUXB0PYyf//ixj4JPM7hVfS2O/1r8+AV07Gko\nba0m/j0GQmkDJUasmaaqmHQ6Ll29QjdfRwQ9BrdUIiGoqQtCiZabGYaGF12RGlk5Co1aVko+fKEx\nRXIpO0IeykPmZRVi52BFRx9HLt3LIC23InVwbUsz0lOf3aTwT8LW1pYJEyey5GBFmma9CHnFGryb\nu/H6F/3pPqwVqWHxON7LpI1XHXq0cOPl7o1wa+xM78/7cufvO+xYdJzGdW1xsbfA3MWWtvMH4qGQ\nMSAxB71Gw8jFx3nvXibviiJrzGS8W9cez3LqbdgoMXupBSPq2vM6At8HdGD2jm04/bYVYdxYcHGC\nObPB3R3OnYdTp2HSJEOJYTmIokj6pElYT5hQQYccIG3nThz6VWSI0Wk0qHNzK/RAANjXr09OQgLa\nKmig5WZmDJwxg/dat+bK4cM1ffSVUJCdzffjxtF5zBj8HnTNVoErW7bg4u+Powkt4xtr1+Izfnyl\nrursU6ewN0Ezrbl5E3kjEwUXD3TJjWFmBpZWkFu18awAuQJm/gZ/fAdJppP+gEGy9KvhMOEbqOVc\n9bjqwMcPkuIgK+PpjvNPIuwM7NkEH35Xo93+PQZCYQVqI2EWE1VMep2W33dsZ0CruoZVTWlJqo2F\nGX4utpyMNpQq6lRapEYd0dH3MkhXazFXSIksbRQryCnGys6coR0a0M7bkTdWn0Ff7pwSCRQ+I43p\n/wa88GJvwmIrxogb17VDIhHK6CQatarHa3P6Ya6QkXAoiqZ17VCWEhdaOVhhM6IVRWkFdIrLYtlu\nAx201FxO4xk9sLNS8FpmEYX5JXRp4kSoCMc6ejI1v5iOYfHosh5+xn+ejyU8Loufo+9gcSYEliyD\nsDDo0hUiogzlqzM/AlMhkVIU/PIL2rt3qTWvYomlqNNxf8MGXF9+ucL7xWlpKB0cKq2szSwsqOXp\nSWpkZJXnGj1nDlNWr2bV1Kl8PXgwqbGxVT/oKlBcUMCO+fN509sbB3d3xs1/9OpZr9dzauFCgj6s\nLMeiLS4meuNGfE15Fka9H2Co8tKlpCAv10FehuzsSsa3DHa1ISfzkddZAU71YfhH8OMU02I+ogjL\n3zRUPfV6tfrHrQpmZtCuK4RULv/9n0BBPnw4HuauNGjA1wD/LgNRYjQRm/AgcrOzqWMppauvM2j1\nIH34iNxslMTnGkRydMWaCgYiOjmXo+djae3rwowN5+k4azdX7maQdD8XhaUhOffBQD9ORNxn0LcP\n/9EaudoRce3ZqcH907h27RpN61bk93GyVSKTSAi7+3AFJpNLGTatK7a1Lfn1myMUlwvLKa0U/KKQ\nolHIKPz9CqFXDUlMiVyK9ag25JrJWCyT0Nnd0DtyKKOA/BndkVgryJy1h4Lfr5CRns+7v1zkwIED\nBgJEQYBeveDXTTB5soEG4THQxMSQ+cEH1Nm0CcEowZp1/Dhmjo5Yl+uHAChOTcXcSDzqAeq2akXS\n5cuPPGfb/v1ZFhFBwzZteL9NG7Z98QUlxY8XrFGrVOz5/nvebNiQ+IgIvgkJYerq1Y8tmw1Zvhyl\nrS3eRpM9wJ3t23Fs1w4bIwOqyc2lIDIS244dK17DjRvIGzVCMG5o0+sNjAR2VVTN1NRAAAx6B3LT\n4KQJ4sLDP8PdyzD1p2fXT9CpF5x9TvTjzxtfTYcO3aHnoMePNcK/20CUkvXp9XrWr1/PrFkfk56a\nwqSeBtI9dGIFA1FHKSOzxKA3qyt5aCD0ej0DvzlKEwcrQhKyKVFrkYgwf8cl7ifncjI6lfTcYl5s\n7kbU98M4czOF1UcNYZjOTZxJTEzg1vPgjv8HUKdOHX4+GsVn2x8aPYlEQgMnGz7afJGPNl/k4h1D\nR7tUKmHgax2p5+3I+nmHyM8pQqXW8vm2K9R3tuXbVaNReDsSsug4Hd7egf97f/LuxvMcd7VB8HSg\nxdl7uEjgamwmtZ1ssB7VhtrzBqBJzSPz/Z3Mb96S3kalmdWFqNOR/vLL2M2cWaEp7gGS1q/HdWLl\nSpCi1FQsTAgDAbi1akXiYwwEgJlSyfBPPmHx5cvEXb/O202bcmHPHpMiUFqNhsOrV/OmtzcRJ08y\n58gR3tu6lbrV6MJNvHyZY/PmMXrTJpM5sMgVK2j65puV3s8+eRLbgACkRgltTUQEZs2aVT5Rfr6B\nmroqY/UkBkImh7dWwdr3IL9ceOruVdjwMXy8A5TPkN6+04tw5sjzk0F9Xji2G87/BbMeXaRQFf49\nBkKuBK3aIFj+AKVVTJs3b+a9d6aSc2Ufde3Mad3QED8WdHrEcgaiuFCNtjR0oCvWIFEawiJrj98C\nRDxtlGRodLzcpSEu9haciEimIFeFWiLhdKQhz+Bay5Llr3bks98ucSryPmYyCbZWSoqrsUr8b4Ra\npSI+MpLQXbvYuWAB2rAwvgoOZuPRG2w4+TBG/N24Nly+l8HWM3fp+cUB/iql4xAEgfpBDfFuVY91\nXxxk6R9XiM8s4PCnvZBIJMyY3Zf6Xb15s0TDxFZuDAloQFhsFt9mF5Fc355vRYGRjZ2xK/XSkoCm\n4UnMrOPAAImURH9/ivbvr7HCXu6iRTu+WhUAACAASURBVCCRYDt9eqVtmuxsMg8cwGXMmErbilNT\nMa/CQFTHgyiPOu7ufLhjB1NWr2bjzJl82a8f90ub7XQ6HSc3bWJakyaE7NjBzN9/Z9bu3XiYMGam\noMrPZ/OoUby0bJlJRt/0K1coun8f9759K23LOn68UngJQB0ZiVlTE7oJ2dlQ6xFMAU9iIAAad4CO\ng2HDR4a/C3Ph6+HwxjJwb/LofWsKD28Dn9SdqGd73OeJjFT4/A34biNYmcj/VAP/nk5qQTBQfasL\nwdxAj5GQdB+bnGw+fO9dNk7tTLdmrpgvi0P1YDWlqxhiKiwoIUejQ63VoldpkChkvLTgGMfCE3ml\ne2NKIpLwrGfPxTsZTAjyJimrEPmpO/x+JYGXHR52cI7t0pCEzEKGLz5BUYmWZk18aGZq5fVfhILs\nbG6cPcv96GiSb9/m/u3bJN++TU5qKnXq18fV2xsXb28atGzJ/ehoXjBTsHVDKE1tlLRp6UbnJs5o\ndHpifhzBl79fYczSvxjXuSH7LycQn1HA0A6evPFiE3Ztuci0/s2wUj6seBn6WiC3vepw9c+rTPjw\nBbo3c2HwN0d4L6eI7hKBqRH3yb+bQYmjFUFzDuLr14JtBw5ib29P0f79ZL7/PtJFi6i9cCGKVpWJ\n2vT5+Wju3EETHY3m1i000dEUHT5M3bCwyuESIGXrVmr37l1GzlcejzIQri1akHztGjqtFmkVvEym\n0LxnT74PD2f/smXMDAig86hRRJw8ibmNDVPXrMGvW7dqH+sBdk2bhmeXLrQoZaQ1RtTKlfhOmlQp\nOQ2G/EOzX3+t9L46MhKbKVMqH+xR+QcAu1qQ/QQGAuDlr+ANX+jxMuz6Hlq+AEGmqUSeCoJgCDOd\nOVIz8aB/CqIIn74OQyZC68DHj68C/x4DAWBmaRANMreloKCAsWNG8UujIpaM60K3ZqWEY+UVx3R6\nKKXGWHYwiob3cxnXzQczmQxVoZp915K4ba1kdCcvZg325+T5e/i0dScsNA4BqGtrTqEAqQUqfjx8\nk2n9H67u3hvgx4I91wgICGDr1q3IajBh/CchiiLH1q3j148+wrNVK+o2aoSbry/tBg3Cxdsbx/r1\nTU52Y+fNY3i7Nvy05ix1bJQ0beOOlZkUiUTC5yNao9GJ/BWZjEIuZcXrgXy8JYxj1xJx1YsMP3mb\n5PYeuNR/yAjq3c0HqULGsW+P0PuzPtxcPpK2M3fhGuBJ02YuRC08ykcFatr16cWefQfKQiaW/ftj\n0bs3+T//TErfvliNHYtgZoYmJgbtvXtoYmIQi4qQN2yI3NsbuY8P5j17Yjd7tsmGL1GnI+HHH2m0\nZInJ51WckYHSmMm0FEobG2p5eJBw4QIeRvH7x0FuZsZL779PlzFj2PP994z/9lta9+37ROXRF37+\nmYSLF3nn4sUq7+Hujh2MNJFQL46LQ52ejnWpUNIDiKKIOjy8Qpd5GTIyKui6V4KNPeRVs4rJGFZ2\n8OpCeD8QGraC9ysbrmeGLn1g/WKYWNmr/K/D0tmQmQbL5jzVYf47Z6XnBZkCVWEuZjbOvDpxPB28\nHajvkIlja3fT40XKjMU3f17hrKstUTZKJq86Q6PkXHJUWgrNtMwf1ZqgOQeZUahmxfFbBPm7IZdJ\nUau1CFIJg9o34LdzMRUOLZMKaPUiu3btwrGKpOY/jYzERH56/XVyUlP54vjxaocvAMytrPjx4GGG\nDerH3eRELu+5Rg+phG3bLtGzZ2Pmja5I0TA60Iv2H++GWpb0H9KcTd8eZcz7Panr+ZB11LOjJ5pi\nNccWHKPP532JX/lwpbjzaDSf3M3AP7By6aUgk2EzeTIW/fqRs3AhEktLLAcORNagATJPT6SOjtWe\naJO3bEFmZ0etnj1NbtepVMgeIQXZZsIEQlevrrGBeIBarq5MWLDgifYFSLh4kQMff8yUv/+uUoL2\n+tKleA4bhqWJRH7q9u04Dh5cybPSxsWBKJqm2UhIALdH0HUrlFDwFFQzXUfB1WMw+rOKYl/PGkH9\nYO4UQ1e1z3+xx799LezbCttCTPee1AD/nhwEkFdUQvNmvrg4OXL53N/M6NeESn0Q5SGKIEBukZoi\ntRZrpZw1J26x+fQdrsVm0t7HESdbC4J/OEl8Rj5S4J3+fiye2IHXezWhazNXFAoZgzo0QCIRuBr7\n0I1Wa/XodHosy31JE6KiuHzoEHfCwkiNjaW4oKDGsfNnAVEUOb5hAzNatqRRQADfnT9fI+PwAPXr\n1+fCles06zWAa2YyFn3zEiUlWj6etZvly0+RlvawL0Umk+DhaE23Zq74tvNgwKsd2bzwGAm3KzKg\nNurRmPpt63Ni0XG0JYZ80u6LcfyRpiLw8hXS9+4lfMgQtCa4rWRubjgsWYL9p59iNWYMyoAAZE5O\n1TYOerWae59/jvfXX1e5j16trlL3ATDIwO7eTVFWVpVjnhcK0tPZOGwYQ1etMtnzAFCSm0vkihW0\n+ugjk9tTt2/HaWRlTiPV2bMoAwNNP5eEeEO/SVUwUxioOJ4UEglMXwfOVZcrPxPI5TD8ddjy0/M9\nz9Pg70Ow5FNYcwBqP/3C819hIHbu3IlXAw8SU9JYO7kj34/159LX/bCxMDNtHypMygIJGQVodSKX\n72WQll/ChCAfNFo9tW3NGdfZi+vx2TR0tkEqwIxB/jhYK7FUymnkYotCIaNbMxe8XWzp9Oleou/n\nMmfbJWpPNLjC5Q3E2nffZfOnn/LT5Ml82rUrE5ycGGFuzqv16jG9ZUs+f+EFFo0ezc/Tp5N1/z7P\nA1n37zN/wAD2LlnCnKNHGTl79lMxjAqCwMJFi1FrRRwdrRk/vj1Lvh+Gi6stX39zhOxyXdf+9e35\nK+I+97MK8WlZj8GTO7F18XGS7lZsUGo5ohU2Ttac/ulvtFodc/6IYO36X3Bo3Jg2J0+icHbmfLt2\nFEQ924Ri0tq1WPj4YN+lS5VjdCUljzQQlg4ONOnfn7Bffnmm1/Y46LRaNo8aRauxYyvofxgj4scf\nce/TBxsTieuiu3dRxcdXUM57gJKQEBRVeUXx8VDvMQaiKlW5/zaMnAT7f3s6j+d5IeqKod9h+Z/Q\n4NloSfwrDMSQIUMIdJdTv441bRrUYlDb+kglEkCoXLZWfgVU6kE0c69F2s/j8HW15cScvrzV1xcX\nWyX21gp0ehEvZ1tiU/KQSCVlKyidXk98ah5IBCSCwOFPe2NnaUarD3fyVwKMGTOGdevWVTh1ZmIi\nb2/YwOJLl1gTF8e2wkI2ZWXxzdmzTPv5Z1764APalBKufRQYSNIzLI0VRZG/fv2V6S1a4NWmDQsu\nXMDTKM78pJBKpZgr5UhKqb8tLMwYOqQFXbo05LsFRykqMqweZ75k0J9o/M7vdJt7gFwrBQNe6ci2\npSfIM6LvCHg9EE2xhr0/nERiZkGfUj4kiUJBkxUr8Jg5k7CuXUn9o2oxlJpAV1TEvXnzaPiYxjNd\nSUkFZldT6PDGG4SuXPkf9Q4PzpqFIJXS68uqJSY1hYVcX7qUlh9/bHJ76vbtOA4dalL4SBUSgjKw\nimRodTyI/xUD4VwXAnrArueY63gSJMXB5AEwdwW0erLwpSn8K3IQTg61eKdfM5RZZ1GXJ+d7VGRB\nYYXUyRXMQpG6NMMiLZpiuRSpVEojVzum922GOqeYI9fv4+duh75ER0mKQRUuPbeYP87eIzc1F1WJ\nll+O32JYoBeD2zUgWmXP6bMhJl3xzMREatetKEmqsLCgjrs7dcp9wbqOGYOHvz+fdO3KrN278THS\nCa4pspKTWTF5Mmmxscw+dAgvE5U+T4Pi4mLkJqphXhrkT15uMYsXH+fDD19AaSbj4jeDyCks4aXv\njvLJb5c5/Ekv0u/nsG3JCSZ80ht5ace1VCYl6N1u/PLen4z2b1npedadOBFrf3/Chw4l78IFvObP\nr1LRrTpIWL4cu8DASuylxnicBwHg0bEjUoWCOydOmGxQe9YI37GDazt28E5YmMmqpAeIWr0al86d\nqWVCDwIMBsLHRHJen5+P5vZtFC1bmj5wfDyYyk08wP+SgQAYMwW+mAZjpzx/YZ/qIDcbXu8Lr74P\nvYY+00P/KzyIia+8wtT1FxEFI4lRQajM5gogkSP36oxg7YwglSJx8ELmGWjwKEqfmKgXESQC91Ly\neLFFPYa2defBkY9eTSS/WI2oExEkEtJzizkdlUx0aiHBL08waRyK8/PRabVYVtVtaoQeEycyde1a\n5vXvz/W//qrhEzEg+e5dfnj1VaY3b45H8+YsDAt75sYBICkpiay8wkrvC4JAcHB7bO3M+fGnv8so\nSOwsFXw2rBWR8Zlcjcmkfd+m2NexZu+6c2X7/nj4Js5TtzE3X0W9e7Hc2b690vFtWremfVgYeZcu\ncaV3b7T5+ZXGVAearCxiFy6k4SNW3w9QHQMhCAIBb77J2eXLn+h6aoKUyEh2TpnC+D/+wPIRlURa\nlYrwhQtp9cknJrcX3rpFSWpqBWGkB1CFhqJo1QrBVEJUFA1J6nqPSFL/rxmI9kGG3+dP/pNXYUCJ\nCqYNMTTyTXj3mR/+X2Eg5n/9LVqFPcm5qsohJWMvXwCJjQtIzQweRul2QWkDUvnDvwVAFGnRwIH5\nf1xFpdWAaAjVJJUS+pUOYkdoLKO/P0GaSsqoKurOdTodUpmsRmWLbfv35+1ffmHF5MloNZpq7wcQ\nfeECszp1wrF+fb45d46xX36J/CkrHqqCRan8pHFIJT23mPCYTPoMbk5Bfgk7dlwp29bDz5VGrvb0\n/+YITq9tZmOeiqS76URdiCUmLZ8vfr/KD8t/Ysn69Qw8cIDTU6eSfbOymIyZgwMtDx1CWa8e18eM\nQawua2gpRL2eiPHjcR0/HssqErvlITM3R1tU9NhxrYODSY2I4MpWE1QRzwgF6emsHzCAAYsX4/YY\nw3992TIc27WjThVeQMLy5bi+/LLJvpDio0dRVtWLERdnaJIzliA1xn/DSry6EAR45T1YPvef7axW\nl8CUweDgDDOrwW77BPhXGAiJRMKyn1YRn1FU8QM19U8pCKUcTRia5HR67qTkcet+rkE8RmdY5Qoy\nCaJOz5rJgVgoZCw7dAMzwbA6tC3t6hWkEkStnqxCDXZ2dpw4dQZbW1uT12hpa4u6uLjGE32bvn1x\ncHfn+Pr11d7nwt69zO/fnylr1jBy9mxcTJGrPUM0btwYuVzG1jN3y947dzOFDcducuxqAjtDY/Fo\n70HIuRjOnbtXNub4531IXDWa8IVDOHcnDbfujTiw8TxbTkQzcuRIJk2axMsTJuDQogUBCxawv29f\nikzoPktkMpqsXo2+qIgbU6eizqg+K2fsN9+gzcmh4ddfV2u8hbMzRSkpjx2nsLJi3I4d7H77bdKe\nA81KVkwM6wcOpOWYMbQOfrQYVXFGBle/+47233xjcrs6LY3kzZtxf+cdk9uL9u3DsioxomvXwO8x\nFXDqEpA/n8XJc8NL4w2dyqefnnn3iaBWw1vDDEy4C34tE7Z61vhXGAiAgIAABKmUqMRyDTmC6SS1\nmJdqeC2VoirRsD3kHltO3SQpOw+VylBaKUgl6LV6rM3lbH47CEEuBb3I1tO36dzUxeAJyAx8Ttn5\nxez480/c3NyqvD5BELCyt6fgCcofx331FdvmzqWkGivXQytXsmLyZD7dv5+2/fvX+FxPAplMxvr1\nG/h27w3i0vPJL1ITcqPiJJqSr2LQqNb8svE8MTEVu2rr17Fmen8/pvx5lZA8FVf3X2fo8BEVxjSe\nMAGf4GAODhyIxsRzkMjl+P/+O9qcHM56eREWFET80qUUx8VVed2Zx48Tv3w5ftu2IalmJVd1DQRA\n3RYt6DVvHptGjEDzjKhWirKz2ffBByxt0wbf/v158YsvHrvPpS+/pOGoUdiboukG4n/4AacRI1A4\nV6bN1ty9iz47G7OqPJSI6/C4Eml1iSHM9L8Emcywav94Ilx9PlKxVUKjgXdHGvS6F20xXMtzwj9m\nIARB8BcEIUQQhHBBEHYLgmD1iLESQRAuC4Kw5ynOh2vdehyNSDXaYmQgJAKiKh9d4hXO3LyPWqUm\nMDCQ4OBg4jIL2Xsh1jBMJkXUGrwJt9qWbHm3O1pg44lomtSzJ7ibD618nECvp0QU6VANxTjr2rXJ\nz6w55YBPu3b4dOjA/kfEtEVR5NdZs9izeDFfnT6Nd9u2NT7P02D48OH4turAljN3Sc0pRq+v7Jrr\nlXImTgzg+yUnyDXSzZg1pAVJq0aT5GhDA4mUhiYm7LZz5mDn7c3xcePQmwglye3t8f/tN7qkpOA+\nYwb5V69yvnVrQlu35t68eRRERpaFwVRJSUQEB+O3aRNKo8KBR8Hc2ZniahoIgA6TJuHUtCm73n77\n8YMfAa1azemlS/muUSNUeXm8FxlJj08+qaDwZwrpV65we/NmWs+ebfq4+fkkrliBx/vvm9xetH8/\nFn37VqI3L8O1a9DMRHd1efwvGgiAbv1g3hpD9dDhZ1Mt91ikJcNbQw2ccku2VU2A+IzwT3oQa4EP\nRVFsDuwEKhPSP8Q7wFMXtbvWrcvF22nkPKCWFoRK9kEUBAS9SOztKF5+/0ukCAQGBuLr64t/q1Zs\nO3OPiIRsQ/hI9zDB3a2ZK1K5FItS7iYnewuCWrgh0Yv4ejgRWg1Beuvatcl7AgMBBmqL3QsXUpCT\nU2mbRq1myfjxRJw8yTchIc89pGQKZmZmvDt9BssO3iSnuMRkrsXR1pz27Tzo0rkhS5b+hVZbcZIP\nu5dBskpk1Lp1/DF5MurCiolvQRAIWruWkqwsQk3oGzyA1Nwcx4EDabp+PV1SUvBZtAh1ejpX+vQh\npFEjbs+cybXhw3GfNo1a3bvX6D5r4kE8uOahq1YRc/o0lzZtqtG5wGD4r//5J4uaNiX68GHeOHGC\nYatWYWNitW+MorQ0Dg8eTJcVK7Coops/cfVqavXsiYWRWFLZMfbtw+JRnmh1PAiN+n8vxPQA3frD\nusMw7x34eeHzy0mo1Ybj9/cDL1/44fen7pKuDv5JA+EtiuKZ0tfHAJP1WYIguAF9MRiUp4KZmYJ2\n7dqw8dQdAEQEhEoehISdobF0mn2QN6dMwcpcWZZktXdwIHjMOD7+LdzgaWgrVkDJFTJuxj0MYcnk\nUnQ6PW087AkPf7zmQ5369Tnz228VBIWqi3pNmtCmf392GdEwFObm8mXfvpQUFvLF8ePYODhUcYTn\nj+7duzNl2jQ2hyTQ1qfihORa2xJfdwOh25AhLbCxVrLhl/NlK3qdXs+UdRdZvGQZncePxyMwkEOf\nfVbpHFKFgt47dxJ34ADXq1ElJJHJqBUUROOlS+kUF4ff1q0Icjl2gYF4VNFN/CjU1EAAKK2tGbd9\nO3unT+fkggXcPHSInMTEx/ZJxJ8/z0+dO3N07lwG//QTrx44gHM1SR91ajWHhw7FJzgYr+HDTY7R\nl5QQv3gxHjNnmt6en4/q3DnMq6AdQaWCmBh4XHL/f9WDeICmrWD7Odi1EeZOBa328fvUBKcPwwB/\nOHfCQJ/xwTf/sef1TxqISEEQBpa+HgFUFaD/HviAR3JiVBOCwICBL7H+dKzhy1daiVQeGr3I0n3X\n2brjT2bNmWuI9z3Y3cyMQf36kalVMmfXdfRGK1yJmRR5ueMJgoCZQkbojRScq7Gie/2HH4gND2dW\n586E7tqFrgYVN5qSEqxr1+a4UfPd2rffpo67Ox/s2IHiERxB/ym4uLqh0ero2syVsUE+dGnmyqAO\nDRjdxRtZqfclkQi88UZnbt9O4+xZQ9J65dGb2Dq6MX78eAAGfv89V7ZsIfl6ZTF5hb09/Q4c4PL8\n+aSeP1/taxMEAZvWrWk4bx4+CxZUHTZ5BKzc3MiPjUVfw0nC1d+f4B07yE1K4tTChSxt04bPbG35\nvmVLNg4bxr4PP+TcqlVEHz1KbEgIm8eMYePQobR79VXevXwZnxroXoiiyN9vvIGydm3azp1b5bik\n9eux8vPDporKpqKDB1F27IjElJQoQEQENGz4+JWuqtjAx/S/DJd6sPUMJNyDV16E5ISnP2ZCDLz5\nEsyZAjMXwJr9z6xDurp4ro1ygiAcBcpzHz8oHP0EeAX4QRCEz4A9QCUyFkEQ+gGpoiheFQQhiEe3\ntgEwZ86cstdBQUEE/V975x0eVZX+8c+bmfQCCQlJ6B2CSAkgVUAsrCIgCLKItN/qAht1pbn7KIoF\nBFlUFAVUFpVFAVFwQUCaBnDpndBEECFAEkoICenJ+f0xE5gk0xIyySDn8zzz5ObOuee+99zkvvc9\n5fta5uPNyyGqWXMM3v5sP5FEi3A/vPMV+fnqxipfD6MHXh6YHuje3qbQrsAePz+MOTns2X+I9p6e\nZAUX/qOuXMUf49VL7D99mZZ1THPOc40GLiZe5X4nFkQFhoQwOTaWbcuW8e1bb7HgxRfpNWYM3YcN\nw9vGNEGlFDu++47Pxo+ndrNmTNm8udD3Bk9PGrZti8FFsxxKyq+/HKNJhElepFoVf6pVsS4Y5+vr\nyV+f6cy7724ktFZl3l5xhC1bd9xUaQ0Npev48Wx44w2GLF1a7PigunVp99ZbbB07lsd+/rlUqqel\nwS8igqB69TgfG0sNW2/WNqjfrRv1Lf5e05OTuXzyJJdPnuTKqVPE79rFgcWLSUtKovmAAQz49FOb\ngnv22DN5MpcPHqRPbKxNJ5ibmsqp11+n1apVNutJ/fxzAp56yvaJtmyGzsXFE4uRfAlqFpf2uO0I\nCIJPVsEnb0Pf1vDKLOhZXLfKIRnp8Mk0+PIjGDEWZi4uUwcaGxtLbGysU2Vd6iCUUo5ea3oAiEhD\noKeV7zsBvUXkEcAXCBSRBUqpobYqtHQQxcjLQQxeDP/LSAZPn0JuWhonusCsVYcZ38sUmiekZtGx\ndSuaN29uih4yM28cLv7+5F+/jtFoJKxWTX47k0gLi+r9g/0I9hC8jDf/6ZKy84iqXo1QJ7t2DEYj\nnZ94gk4DBnDk55/574wZLJ40iR6jRvFITAyVLXINnD54kH+/8AIpSUmMnjuXllbeIqvWqUOSnZk6\n5U31mrU4emyzze+VUvyacI3Ywxf48chF8jw8eOKllTz7ykSaFlnh23H0aKbOmEFCXJzVrpVGQ4dy\n6IMPOPXNNza7UVxBg0GDOLFoUYkdRFH8goPxa9OGmm3aOC7sJMe++IJj8+fTb9s2PANszgvh9PTp\nVHnwQYJszE7KPXeOrO3bCf/mG9sni42FwXYcSAGXEqGV40kctwUGA4x+ybRwbfxg+Ol7mPQhBFqf\n3l4IpWDdMpg2Dpq3g//uN0UmZUzRF+fX7USRFSa1ISJhSqmLIuIBTATmFi2jlHoJeMlcviswzp5z\ncEh+LhiMjBs/nnbt23PlzEl8vo7h3e/jeLZHE3y8jCSm5dCjl/lBazRCXp7pYzDg4e+PMg+M9hr0\nJNlvv32j6tzcfIwBPkR4G1m99yxNawSTmJLB1XzFv16zfQNsISLcde+93HXvvZw7fpwV771HTJMm\ndOzfn25DhrDpyy/Z8d13DJw0iR5//avNBDRhtWuz74cfSt5WLqJp07tYMj+l2P7rmTn8a2Ucc9Yd\nIzs3jw5tW9O1x5MY2l3Fe8ECxo4rPovGy9+fLmPHsmHyZJ5avLjY9x4GAx3eeYfYp5+mTu/eDlc4\nlxUNBg7k6xYt6DJ7drmd0xniN25k+4sv0ic2Fj87XZ6Z8fHEz55Nu337bJZJXbAA//798bC1AC4v\nD37eAp986tiwy4kQ4p6S96Xm7jawfC9MnwC9W0CfIaZVz5kZkJVhihIyMyDT4ue1q+DjC1M/g/Yl\nTwLlCipSi2mQiMRg6nJappT6HEBEIoFPlVJlP0k/LwcMnhiNRpMHTWuJWjGWyMhQxv9nJ+sPnudT\nnyxqhpizX4mAjw9kZYGf340IAmDIqFGsevttLqVmkpSSwf2vr6ZTRg7+BmHOuqMM79aQR6dtoEez\nZmSVcmZSAdUbN2b03Lk8+eabrJk9m5lDhtCub18+OnaMAHuZuoCqtWuTdPr0LZ2/LDl79iw+xsLd\nPUfik3lk6gbqNWjEylVruM9iVa5Sipi1a7lw+DCVrKiFdvzb35hWvz6JR44QbkVDqEb37oQ0a8ah\nWbNoaWOqZlkTUKMGIc2aceaHH6jbp+SJ4l3B5UOHWD9oED2++YbgKPvpOE++8grVR47E14bAnlKK\ntM8+I8yeIu2BAxAZCTay6xU2LglCnSh3u+HnD6/NNg0y790KwaHg42dyAr5+4G3+6eN7c7tuY5eu\naygxSqk/zMd0OXaY2lKpM3tu/n49Ral+gWrhwoUqMjxMAepCvw5KrV12s0yVYKUuX1ZKKXXljTfU\n5ZdfVkoplZuWplaCqh7ir/y9jWpUj7vUnr90UB83CVfNa1dRRg9RDevXUz9On66+e/55+3a5kKTf\nf1f/V716hZ2/KLNmzVL1IoNV2sLhKm3hcLV9ah/l6+2ppkyZbPOYZdOnqw9GjLD5/capU9XCQYNs\nfn/l2DE1PzRUpV+8eEu2l4S4OXPUuoEDy+189kiNj1cLatZUv3z1lcOy1/btU7Hh4SonJcVmmYyf\nf1ZnGjdW+fn5tit69x2l/jbaOQPbhih1Ocm5spoyx/zctPpMvWNWUgOmCMLDcmGJSaxv8ODBnE9I\nIjMzk4gaNQonLymIIKBQBOHh54cRCPb1ZOm4+5kxpC3+lf2I8DaydUovnurSgJ6PPkpwrVpcc1Hu\nBmcIqVaNlKQkcrLcQwwtNDQUby/TPbiUmknv6RuZNn0GL71kXSQO4L6hQ9m2bBnpVpIAAXSMieHX\njRutzmgCCG7cmAZ//jO77fS1ljX1+vfnzJo1ZJdSILCsyL52jdU9e9IsJoaGg+znalZK8cv48dR7\n9VWMQUE2y6V+9hmBI0bYH/iPjYWu3RwbmJNjyq1QqXh+b03Fc2c5iNwsMFr0CXt4FFJz9fb2Bs8i\nypK+vmCWbvAICiI/xdR/LiLkeh4UhwAAFOFJREFUeHsT7uNNl6am1Iz+VfxJu2gS6msYWYkjhw/j\nFxHB5ZM3NYjKG4PRSOMOHdjsQlG4khAUFERWjmkKaMz8nTz8aB+ed7CKuHJ4OI3atePgjz9a/d4n\nMJBOzz3HtrnFhrFu0PqVV/hlwQJy0tJKb3wJ8A0NpW7fvmwrp24ta+RmZLC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "for p in polygons:\n", " ax.add_collection(PatchCollection([Polygon(p)],facecolor=\"#F4A460\"))\n", "ax.set_xlim(124.,127.5)\n", "ax.set_ylim(-9.6,-8.1)\n", "ax.set_xlabel(\"longitude\")\n", "ax.set_ylabel(\"latitude\")\n", "\n", "m_ep.plot(ax=ax)\n" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: gp
\n", "Objective: 31.0040772275
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "
gp. valueconstraintspriors
rbf.variance 2.23903462364 +ve
rbf.lengthscale (2,) +ve
" ], "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m_ep" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" }, "widgets": { "state": { "01ff0618fd22414daaa993b7f03a32d7": { "views": [] }, "04a380d351324581b67d8e09b73496a2": { "views": [] }, "099d951ace4949059037ff993425cbc7": { "views": [] }, "0b6c83c714164c88806966305769d6ff": { "views": [] }, "10ac41e0175647f19a2cdb68d0c61a35": { "views": [] }, "1d510e76d7d3477d83889920a8d3a8ca": { "views": [] }, "1ffe6ded0c23423288b7c711bda4ce33": { "views": [] }, "21183fbd44474501b112e406373ec9e0": { "views": [] }, "356310f7e33b496c9ff8a914b052bbcf": { "views": [] }, "39b3e1034334478c9e0876fb550c4ade": { "views": [] }, "3c4523035fe845379af5ad22c54372dd": { "views": [] }, "422fad2c92fb483fa557f4487b4bdb3c": { "views": [] }, "46c6a7e73c804f4ebb83c987be6359dd": { "views": [] }, "525ca851d5f9421c968f27d26457c821": { "views": [] }, "550a2154e3814825a3936d0a8539f880": { "views": [] }, "5b290f0d85a048acb539158bc397985f": { "views": [] }, "5cfa7da50be64fbcb06bce262dae9dc5": { "views": [] }, "6b24697472914e73a732a96c1c7d4dbc": { "views": [] }, "6cd03708b7ef4e529adf4d976f4798d7": { "views": [] }, "7006c3fe9c334e7ca4f1da23f5be340d": { "views": [ { "cell_index": 26 } ] }, "70d5c20b7c7144e995918160bd7d8331": { "views": [] }, "7575138884934f7999f2f09a3f0c15a1": { "views": [] }, "87770c3907684cfd8960664cb653b67a": { "views": [] }, "89958e05221c4c758646e56e10747822": { "views": [] }, "8a528f965e7f435b9399d825801c9b07": { "views": [] }, "8cee2dff5a57488a87decce48486fb54": { "views": [] }, "8d4c95b26eb642bf96e8be75a6dc45e6": { "views": [] }, "90cd257a85904c7781eb8c15267fc6fd": { "views": [] }, "982868bfe87f407386b375bb7c4fdde9": { "views": [] }, "98758342aa5a45c4821b534b017511af": { "views": [] }, "a975b20d8b5246149215e3c0ef9662a1": { "views": [] }, "accf8efa4aa34b6a8abf9305a9c65ee0": { "views": [] }, "b05e4b5c936442c3869fc3aebc443421": { "views": [] }, "bc10c6db25a84c649ec9819ad8406ea0": { "views": [] }, "c0398e92c7dd4438b59b63ca6026480c": { "views": [] }, "c3011d42b39c4fed900a10962ae235ca": { "views": [] }, "c644745eace34a53910bb7b6e3f0ebca": { "views": [ { "cell_index": 18 } ] }, "caa970b8fd3142a794048625379b074b": { "views": [] }, "db1d4650ac4448bbb6212470b42a0e58": { "views": [] }, "dbbb11131b37488196a24f149c0b73a3": { "views": [] }, "e238dc0de69b44cebfaff04c4990f147": { "views": [] }, "e4b1197aab2348feb35f19b9e02072cb": { "views": [] }, "e640d4bd445741d28163606dc8a8f152": { "views": [] }, "f1197f6a511641b3a17da1c451b75e96": { "views": [] }, "faad52a8a6c04afd8404e82042a8e6a2": { "views": [] }, "fb3b73c8d9c9492087b8e4cfe7977136": { "views": [] }, "fe6bf7438f9a4dfb95b4ba2df8d8d147": { "views": [] }, "ff10b6b99168448084545c6132de1736": { "views": [] } }, "version": "1.1.1" } }, "nbformat": 4, "nbformat_minor": 0 }