{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Line search in gradient and Newton directions" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from scipy.optimize import minimize_scalar\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Demo functions" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f1(x):\n", " return x[0]**2 + x[1]**2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def grad1(x):\n", " return np.array([2*x[0], 2*x[1]]).reshape([-1,1])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hess1(x):\n", " return np.array([\n", " [2, 0],\n", " [0, 2]\n", " ])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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Wrb1n42Mh6fxFhBB8Fx7GqiuXGezjy+ohwxsV+69Uqfnx5BXWn7iCs7U5n0wZ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UAIGJsQwyXnpHDB6OQT/nl1JhOv7szhzfw8lG7uPDx5KtemjXRY1KWUvFeew5J960nwDeHVidfZ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\nxMlZzv8Ddm0sw6lYpTMAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10000, 2)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.c_[X.ravel(), Y.ravel()].shape" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f2(x):\n", " return x[0]**2 + 10*x[1]**2" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def grad2(x):\n", " return np.array([2*x[0], 20*x[1]]).reshape([-1,1])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hess2(x):\n", " return np.array([\n", " [2, 0],\n", " [0, 20]\n", " ])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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VQtC0DSpuBNaO0GpWi4rR6ERrFbNBxWi4ot4g36oyXss4Qm+cP49DkWRiWoC4HiKuhYjr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\n/ahHkDw559/Vs2T1HFkjR0bPkTFyZPQsrp4lYyjt6tn0WgZXz+DoGRz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + 10*Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gradient descent with step size found by numerical minimization" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [], "source": [ "def gd(x, f, grad, max_iter=10):\n", " orbit = np.zeros((max_iter+1, len(x)))\n", " orbit[0] = x.ravel()\n", " for i in range(max_iter):\n", " res = minimize_scalar(lambda alpha: f(x - alpha * grad(x)))\n", " alpha = res.x\n", " x = x - alpha * grad(x)\n", " orbit[i+1] = x.ravel()\n", " return orbit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gradient descent with analytic step size for quadratic function" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gd_alt(x, f, grad, hess, max_iter=10):\n", " orbit = np.zeros((max_iter+1, len(x)))\n", " orbit[0] = x.ravel()\n", " for i in range(max_iter):\n", " p = -grad(x)\n", " alpha = (p.T @ p)/(p.T @ hess(x) @ p) \n", " x = x - alpha * grad(x)\n", " orbit[i+1] = x.ravel()\n", " return orbit" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [], "source": [ "x0 = np.array([4,3]).reshape([-1,1])" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [], "source": [ "orbit1 = gd(x0, f1, grad1, max_iter=5)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "image/png": 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fC43OX0QIwZrIcFZFXGKAjy+rBw5pVOy/QqnihxMRrD8egbO1OZ9OHEgHn8bl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MgvokOrJzLAh5snjeH6jBQCvPrOI7H3PP8qPMSzO7djRfL41OnckjrG4SVglUbFA1kfUqftYHna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\nIREYYoiLnP8H8rX35TPLmJIAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.plot(orbit1[:, 0], orbit1[:, 1], '-')\n", "plt.scatter(orbit1[0:1, 0], orbit1[0:1, 1])\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/site-packages/ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in true_divide\n", " \n" ] } ], "source": [ "orbit1a = gd_alt(x0, f1, grad1, hess1, max_iter=5)" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "image/png": 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fC43OX0QIwZrIcFZFXGKAjy+rBw5pVOy/QqnihxMRrD8egbO1OZ9OHEgHn8bl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MgvokOrJzLAh5snjeH6jBQCvPrOI7H3PP8qPMSzO7djRfL41OnckjrG4SVglUbFA1kfUqftYHna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\nIREYYoiLnP8H8rX35TPLmJIAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.plot(orbit1a[:, 0], orbit1a[:, 1], '-')\n", "plt.scatter(orbit1a[0:1, 0], orbit1a[0:1, 1])\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "orbit2 = gd(x0, f2, grad2, max_iter=5)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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VZymQJRldktFPodUVQmDYNQquB1b30EpWlUKt0vDWCmaFQq3iinqFdLXIUGnGEfrakeM4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + 10*Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.plot(orbit2[:, 0], orbit2[:, 1], '-')\n", "plt.scatter(orbit2[0:1, 0], orbit2[0:1, 1])\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": true }, "outputs": [], "source": [ "orbit2a = gd_alt(x0, f2, grad2, hess2, max_iter=5)" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "image/png": 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VZymQJRldktFPodUVQmDYNQquB1b30EpWlUKt0vDWCmaFQq3iinqFdLXIUGnGEfrakeM4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\nKSwmnnGeGasQG0Pr2T1GP/FdhBB/BDwcyIffBv4m8aPAEyGE+HXg1wG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + 10*Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.plot(orbit2a[:, 0], orbit2a[:, 1], '-')\n", "plt.scatter(orbit2a[0:1, 0], orbit2a[0:1, 1])\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Line search in Newton direction with analytic step size" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def newton(x, f, grad, hess, max_iter=5):\n", " orbit = np.zeros((max_iter+1, len(x)))\n", " orbit[0] = x.ravel()\n", " for i in range(max_iter):\n", " x = x - np.linalg.inv(hess(x)) @ grad(x)\n", " orbit[i+1] = x.ravel()\n", " return orbit" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "orbit3 = newton(x0, f1, grad1, hess1, max_iter=5)" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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fC43OX0QIwZrIcFZFXGKAjy+rBw5pVOy/QqnihxMRrD8egbO1OZ9OHEgHn8bl\np6tDJldwPjKFI2duEhmTgVIl8HKzpVfn5nTr6Iuft+Mjdzg2lqKSKi5eSeNceDJXbmSiVAm83W0Z\n0COAQb1aYWfzYA5XKa6qYfHvJzhzM43OzT1Y+uxA7C0aN9fOmzeYf+o47Zyc2Th8FBaGmj1QZCol\nr4RtI7wojbWdJ9HTqbnaPgmViSxPWEk76yDm+L7yr2L5RIpAdm0Oi+OW4GXiyTz/d9TuBNQr5Tx3\n/hcSKvL5qds02tmqr+IKtwXg84vn+OHqZca0bMWyvgMaVW4qv7yKeVsOcTU9l2EhLZk/uvd9C1u9\nm+y8MnYfieHImZtUVtfjYGfOgO4tGdCjJc08NBO9J4mKqjpOhyVx9GwcNxJy0NWR0Dm4GaOfCaJD\nW6/7LnRCCHZHxLJ83xmM9PVZMmlgo3cQDiUn8ebRP/GztePnkWOwMdbMMV0jlzLtws9kVBXzS/fn\naGWt3id1JP8Y227tYLz7WIY4D/rH50+cCEiVUhbFLaFGUc0nrRZiZdCwSa8SgrejdnE0J45VHccz\nwFWzOm9CCJZeOMvG6CtMad2WRb36NqrKb1hSJvO2HEaqUPDhmL4MC9G8zpym64yOzWL7gcuEXU1D\nV1eH7h18Gd6/DSGtPZ/YJ762ZOWW8eepGxw6HUtpeS0eLjaMHxrMoF6tMDS8Pyc+3SGtoJT3thwi\nMbeIl/p15NWBXRrlNDyTkc7sP/fjbW3NllFjNRaCwvoqJp7ZiEIo2dHzRZzVlDYXQrA2dT1XSq8y\nv+U8mpv/d8n+J04ENqb9xPnii7zb4i1aWarfmlsdd4r1iec1dqjAfwvAtDZBLOzZR+t3TiEEG09F\n8c3hi/g42vLV9KF4O2hfi+BeqFSC81Ep/PpHOAmpBVhbmjByYFtGDGiLnfWTf95gY5HLlZwOS2Tn\nwSskpBZgZWHMuCEhjBnUDjPT+2d91csVLNt9mt2RsXRu7sEXUwdjZap9Hsf5zAxmHtyntRAkVRby\n7NmNeJjasKXHDEzUpLnXKmr5+OYnKIWST1st/K/Q4idKBMJLIvgudQPDXYYyxm2U2r6Hs2/yVtQu\nxni249N2wzS+kb8Ku8i3UeGNFoB6uYKPtx/jcEwig4JasGh8f0zu09NICMGFqFQ27rhISkYRbk5W\nTBrRgWd6tXokHv3HFSEEMXHZbNsXxaUraZiZGjJxeHvGDwm5r8FJuyNiWfLHKZyszFjz/Ah8nLTf\nPTifmcHQYyUBAAAgAElEQVRLB/fiZ2vH1lHjND5G7lx+MrPDtjHAtSVfdRir9neaXpPBp3FLaWvV\nhtd9X/2r/RMjAsXSYj6KXYSLsQvzW85rMCQSbm8FPnt2E/6WTmzuPl3jY6Q3XIni84vnmNCqNUv7\n9NdaAIora5izaR83swuYO7gbz/duf9881zE3s/huyzluJuXh5mzNjHFd6NvN/4EX3nzSSUwrYNOO\nS1y8nIq1pQnTx3ZmRP+29y0Y6VpmHnN/2k+9TMHKaUMatd17Mj2V2X/up52TM5tHjMFYw12DjUkX\nWXnzBG8E9OHlFt3Vtj+Sd5RtWTuZ4TWdXg49gCdEBCKjIlmesJKMmgw+DVyMg1HDTq5KWT1jz2xA\nqlSwq/dMjWMBdt68wfsnjzHUrwVfDxis9Xtean4Js3/cQ3lNHcsnD6Z3oPq4BU3IK6xg7c9nOBOe\njL2NGc9P6Mqg3oFPb34tiU3KZcPW81yNzcLDxYY5M3rRJVj7o+b/jfyyKl7btI+U/GI+HNOXsZ21\nL0N/MCmBN44eoqenN98PHaGRE1oIwXuX9/Bn9g1+6DqFUMeGf3MqoWJl4tckV6ewJHARjkaOT4YI\nLDm4lG23dvCC9wx62HdrsL0QgtfCd3CuIJlfuj+n8U7A6Yw0Zh7YS1d3D34YNkrrIpIx6bm8unEv\n+nq6rH1hJK3cGy4CqQlSmYLf9kby655IdCQwZVQnJg1vf98dXf9LCCEIu5rGms1nyMotI7S9D3Of\n742LY9NPeKqpl/H2r39yMSGDVwZ0ZtaAzlpbgVtvXOOj0ye0skRrFTImnt1IUX0Vu3u/rNZRWCor\nZcGNj3ExdmVBy3no6uhqLAK6ixYt0uiL3E/Wrl+7qKJHNW2sWjPBXf17z+aUMLakRTKv9QCecWul\n0Rw3Cgt4ft9u/Gzt2KSFKXaHCwkZvLpxL3bmpmx6ZRy+jXgv/DvX4rJ5e8kfnA1Ppmen5iyfP5rQ\n9j7oNSG77SkgkUhwd7FhRP+2mBobcPjMTXYfjkFfT4eA5s5N2k0x0NNlYJAfeWVVbDkfTVlNHd1a\neGklBG0cnVCqBD/FXEVHIqGTm/qHmL6OLp3tvdmWfpnLJZmM8GjbYAVjY11jrA2sOV5wAmNdY7Z+\nuSVv0aJFGzRZ3yOxPYtlJejr6DPDa5rai3mjLIevbp6kn7M/U306aTR+fnUVMw/sxdrYmI3DR2td\nMPLE9WTmbNqHt4MNP782oclFLWvrZHz1wwle/Wg7SqWKrz8eyydvD8PhMY7qexLR19fl2ZEd2bJ6\nBh3berHu13PMWvAbabeKmzauri5LJg5ges8Qtl+8xsc7j6H8z8EumvJm566M9g9gVcQlDiYlaNTH\n29yOT9oNI6Y0m7UJZ9W272rbmXZWQfyRvUertT2S1wG7lnZiz7m9dFfzGlAjlzL69PfIVUp295ml\n0bmAdXI5E3ZtJ728jN/HTcLfTruAmiPRibz/22EC3Z1Y99LIJhekuJmUxyer/yS3oJyxg4OZ+Wy3\nh5Y0ow21NVJKi6qoKKuhuqqe2qp6pFI5cpkSwe3fiJ6eLgaGepiYGmJqboS5pQk2duZYWBmj85iV\nPRdCcOpSIl//eJLaOhmzpvRg7ODGhQbfPeb6Y+GsOxbO4Hb+fDZpoFY+HKlCwdS9u7hRUMD2MeNp\n66TZOZkLru5jT2YMP3WbRic15fHKZGXMv/ER69uvfbx9Ar5tm4vkmCS1VsCHV/ezJzOGn7tPp72d\np9pxhRC8cfQQB5MS2DBsJH29tXPiHbuWxHtbDtHWy4V1L4zEtAk3q1KpYsueSDbtuIi9rTkfzhlE\nUCvNfBkPCqVSRU5mManxeWSmFZKdXkxedil52aXUVksbPa6eni4OLlY4uVnj5mWHh7c9zVo408zP\nCSOTRyt4ZRU1LP/uGBeiUukY5MWHcwZhY9W0smM/noxk9aGLDG7nz9JnB2rlbC6prWXUzq3IlSr2\nT5yCvan6tdQqZIw5vYF6pZy9fWZhqeZhGFV6mY62HR5vEVCXSgxwOi+RV8K3M9OvG29qkGoJsDH6\nCp+dP8PbXbrxagfNXh3ucOZmKm9uPkhrDyfWzxzVpASgsooaFq86xOXrmfQN9efdl/vf16AWTZHW\ny7kZk8n1yHRuxmSSFJuD9D9pvTo6EpzdbXDxsMXJ1RoHJyus7c2wsjHD3MIYEzNDDI300TfQuy3W\nQqBQqJBJ5dTVyqiurKOivJbSoipKCivJzykjL6uU7Ixi6utkwO13dU8fB1oGudM6xIugTj7Y2D38\nVyAhBPuOXeObzWcwNzFk4RtDCG6tfSnxu7kjBKM6tmLRuP5aWRjxxUWM3fkbTiZW1OW7kVdej4uV\nMe8ObMHIdq7/2udGWQ6Tzm5ksFsgK9qPVjvHE7E70JAIlMvqGHZiHXZGpuzo9ZJG8QCROdlM3r2T\nvs18+G7wcK0cN5EpWcz+YQ9+znb8MGtMk3IA4lPyWLBiP+VVdbzxfB+G9Wv9UMuIFeSWEX4mgYiz\nCdy4kolcpkBHVwcff2datnWneUsXfFq64OZlh8EDCERSqVQU5VeQlphPSnwuiTeyib+eRU1VPQBe\nvo507NmCzj398W/j9lBfI1Iyivj4ywNk55fxytSeTBgW0qS/zdojl1h/PIIpPdrx3vCeWo318dFL\nbEkMQ1VlDVW3d52M9XVZNrr1PYXg2/gzrE04y5pOE9SWMH/iReC9y7s5nH2Tnb1eoqWV+grBJbW1\nDN32K0Z6euybOAULDaOz4HYJqufW/o6TlRmbXx3fqDDROxw+HcsX3x/HxsqUpe+NwK9Z07cUNaGk\nqIrTf17j3LEbJMXmAODmZUeH7n4Ed/YlMMQTY5OHb4ncQalUkZaYT0x4KpcvJnHjaiYqpQpbB3O6\n9Qukz5C2+AU+nDMWautkLP32MGfCk+nfvSXvzx7Q6O1ZIQQr9p1ly/lo5g4O5cW+HTXuG/r5KXJk\nOVBvDroKkN/+3blaGXPx/X8/UUuuUjLhzI8U1Vexv+8rDVbOeqJF4Fx+Mi+H/cYr/j2Y01L94SIq\nIXhh/x7Csm+xe/yzBNg3fFjD3eSWVjL5m23o6ery65wJOFk1zlRVqQQ/bLvAr7sjCGntweK3hmJl\n0fTa9w2hVKqIOp/EoV1RXL6YjEqponkrV3r0D6Rr35a4eqqvxvSoqK6sI+p8EudP3CTqfBJymQIP\nHweeGR1C/xHBmFs82HMXhBD8ujuCH7ZdoKWvM8s/GIm1ZeP8BCqV4IPfjnAoOoGlkwYyrL363BeV\nStBs/iFA3BYAqxwodwWlPhIg/fMh9+ybUJHPuNM/MMy9DUtDRtyz3RMrArUKGcNOrsNYV5/dvV/G\nQFe9ubop+gpLzp9hUc8+TGurvijDHarqpExds53Cihp+nTOhUfHhcDvP/7M1hzl5MZFh/drw9kt9\nH+i+f3VlHYd3XebAjnAK8yqwdTCn37B29B8RjJvX43vj34uaqnrOHb3B0b1XSbiehaGRPr0GtWHU\n1K54+T5YS+pseBKfrD6EjZUpKxeMxtOtkRWGFEpm/7CHK+k5bJg5mg6+93YAF1dLeXNHDOeT/7Nt\nqSND4pABckNEiQeuVib3tATu8PXNk2xIusDmBnYLnlgR+DL2BD8mX2RL9xmE2Kl33CQUFzFy+1Z6\neHrx/dARGpuTSpWKVzfuIyLpFutnjqJT88Y5iWrrZHywfC9Xbtxi9tQePDuiwwMzactLa9j9ywUO\n7oiktkZKmw7eDJ/Ymc69/NF7BMU7HwSpCXkc3BHBqT+vIa2X06lHC56d1ZsWgQ+mUAtAXHIe85bt\nQaUSfPnhGPx9tTug5g6VdfVMXbOD4soatr/xLO52/4xWDEstYe72aCrq5IwMcmVfTA71ChUYV6Bj\nnYdujQNfPNPnnj6BO9Qr5Yw4+R06Eh329Zn1rw/LJ1IEUiqLGHVqPcM92vBZ8L3NnDvIlEpG79hK\nQU01RyY/h62J5ub3yv3n+PnsFRaO69eoeHC4XfzinSV/kJRWwPuvPsOgXppFMmpLVWUdv286x/5t\nEUjr5fQYGMi4Gd3xbdn4YqiPO5XltRzYHs7erWFUVdTRsUcLpr/WDx9/zfbVtSU7r4w3P/md8so6\nln8wiuDAxj0UskrKmbRqG7bmJmx9feJfDmaVSrD2dApfn0jCy9aUtZODaelswd7oHL44mkhueR3G\nDvnI9SvZN3GyRq+0FwpSeOnSVuYG9GZWix7/+FwbEUAI8dD/hYSEiLtRqVTiufM/i04HPhel9TVC\nE74KuyC8V68UR1OSNGp/hz+vxIvAt74Sn/1xSqt+d1NWUSOmv7VZ9J7wlTgfmdzocRpCJpOLP365\nIMaELhHPtPlQLHtvh7iVVvhA5npcqa6qE9s2nP7rGqz44HdRmFf+QOYqLK4Uk1/fJHpP/FpExmQ0\nepyI5Fui7Ttfi9c37RMqlUoUVdWLKT+GC895B8Xr266Kqnr5v/Yrra0VHX/4TjyzZbOQKhQazfV6\n+A4RtG+JyK355zUBLgsN78fHQgRO5MQL/92LxJaUCI2+fFxRoWi+5ivx5pE/NWp/h+S8ItHh/W/E\n1G+2C5mGF/rv/CUAE78WEdHpjRpDHVcuJYsXh68SA1svEPNf3ixSE3IfyDxPClUVtWLj10fE0JCF\nYkTHxWL7j2eEVPrvN1NTKC2vEdPe+KnJQvDzmSsi8K2vxMe7LooOS44LvwWHxLaITKFSqRrsdyIt\nRXivXilWhV/UaJ7smjLRdu8S8U7kH//4TBsReOSxnjKVkhWxx/Axt9fo1FalSsUHJ49haWjERz00\nO5ocbpcEf+vnPzE2MGDltCGNOlmoukbKW5/s4lZuGZ/PG0nHIC+tx2iI8tIaPp+3k/kvb0ahULL4\n26l8tn46zVo8GDP4ScHMwpjn3xjID3tfJ7iLDz+tPs6r49YSF3Prvs5jbWnC6sXjcXey4v3P93At\nLrtR40zuFoS7S3N+jixFTwf2vhrKxI4eav1Ffb19GN7Cn3VRESSXlKidx9XEihnNu3Aw+wbRJVmN\nWis8ogSiu9meFsWtmjLmtdas4OfWG9e4XpDPxz17Y22s+VbS8r1nyCgqZcWUQThYal+qq14qZ96y\nPaRlFfPZu8PvuwCcOxbLy6NWc+H4TabM7sP3u+fQqUeL+zrHk46Tmw0fr5rMp2unIZXKeXv6D6xf\n/udfUZD3AysLE1YtGo+jnQXvLdtNUlqBVv2Lq6U8tzmKuCIJFvr1GMszcbHUPPr0o+69MTUw4MPT\nx2+b6mp40a8b9kZmfBGrWft/45GKQLVcyneJ5+hi34zujr5q2xfWVLPy0gW6e3gytLnmN8ixa0ns\njozlhT4dGrUToFCq+PjLA1xPyOaj1wfft6IVcHuLbMX831n6znYcXKz5dscrTJndB4On9QXuSYfu\nfqz/Yw5Dxndk79YwXpuwjuS43Ps2vrWlCV8vHIupiSFvfbqLnPxyjfqFpZYwePV5ItNL+Xx0a7a+\nFEppVTWLfz+h8Q1qa2LCvNAeROXmsCv+ptr2pnoGvObfi+jSLE7mJWo0x995pCKwOSWMclkdb2uY\nG7D84nlkSiWLe2l2tDNAYcXtP0KguyOvDOyi9RqFEKzedIpLV9J488W+9A1tOFxTG1Lic3lt4jrO\nHL7BlNl9+PqXmXg1fzhRhk86JqaGvLZgGEu/f466GilvTf2e/dvDG/00/DuOdhas+ngcKpXgnc/+\noPI/Jzv9GyqVYM3JZCb/GI6Zod5f5n9rT2deG9SV49eTOXAlXuO5xwUEEuLswoqL56mUqk/sGu3Z\nDm8zW1bHnUIptEtxhkcoAmXSWjanhDHApaVGddaj83LZkxDHC8EheFlZazSHEIJFv59AplCybPKg\nRvkBfv/zKnuOxDBpeHtGP6N5MJI6Du+K4s2pG5BLFXyx6QWmzO7z/81+/8MkuIsv63a9RlBnH9Yt\nPcjn83ZSV9v4jMi78XC1Ydm8keQXVjJ/xT7kcuU/2hRXS5n+UyRfHk9iWFsX9s/pRkvn/zvK7rle\nIQR7u/D5njPkl1dpNK+ORMLCnn0oravlm4gwte31dHSY07I3KVVF/JkVq/kXvDOf1j3uE5uSL1Gr\nkGkUGiyE4NNzZ3AwNeWV9ppnBx68Es/5+HTeGNINL3vNhONuoq5l8O3PZ+jRqTmzp/bUuv+/oVQo\nWbv0AKs/2Ufr9l58u/NVWrVTnyb9lHtjYWXC4jVTmDG3P+ePxfL29B8ozNPMhFdH2wA3PnjtGWLi\nslm16dR/ffZ383/VhCDMDP87cEdXR4clEweiUCn5dNdJjS2VQAdHxrdqzS/Xo0kvL1PbfqBrAP6W\njqxNOItCy4Inj0QElELFb2mRPOPaCl8Njg77MzmRmII83u7SDVMNqwQVV9WwfN9Z2nm5MCk0SOs1\n5uSX8/FXB/F2s+XDOYPuy4EfNVX1fPTqLxzYHsGYaaF8unYaVjZNy21/ym10dHSY8EJPPvl2Kvk5\nZcx9dj0J1xvvMb+bAd1bMmVUR/Ydu8b+49fvaf7f6xXV3c6KOYNCORefzqFozd/b3+ociqGuLssv\nnlPbVkci4RX/ntyqKeVQtnbWwCMRgRJpDbVKObP8/xnp9HfkSiUrL13A386e0f7qkzPu8MW+c9RK\n5Swar12uN9wuBvrhyv23DyyZN/K+1LQvKarinRk/ci0qnTcXj+Kldwah+7Sy8H2nfTc/Vm15GSNj\nfea9uImo80n3ZdyXJnWjY5AXKzedYcza8/c0/+/Fs92CaOPhxIp9Z6iorddoTntTU14O6cix1BSi\n89Q7Pvs6++Nn4cCGpPMajX+HR/IrLJXW/LVgdeyMi+VWZQXvdu2mcQWXyJQsDkUn8Hyf9jRz1P6E\noDWbT5OcXshHrw/G1anpFWvzskt5Z/oG8rJK+eTbqQwcFdLkMZ9ybzyaOfD1ry/j7m3PorlbOPVn\nTJPH1NXVYfCoruS5exGTXcmioS3/1fy/Z38dHT4a25fymnrWHL6o8bzPtwvB1tiElWEX1L5K6Egk\nzPTrRmqVdjUVH9nrwIt+oWrbSRUKvo0MJ8TZhV6emh0SKVcqWbr7FK42Flrld9/hbEQye49eY9Lw\n9oS2b/oZAzmZxbz73I9UV9Wz/MfnCemq/tTZR4lSoaQ0v4z02FvEhSdx9eQNrp64ztUT14m9EE9K\ndDr5GYVI6+6P8+1BYWVrxvKNz9OqnSdfzP+Do3uuNHqsO+b/zK3ROFiZ4JSdQXqk+u27v+Pv6sCk\nbm3ZGXaduGzN4g9M9PV5tUMnwrKzuJStPjhqoGsr3Ey0e3A9kjOubA3NCLJRnxm24+YNCmqq+XLA\nII23BHdeuk5qQSmrnhuGkb52X6+4tJrl647SwseRmc+qP/lFHbm3Spj3wibkcgXLN75AM7/GZag9\nCGRSOSlX00iJziDtWgZZSbnkpRZQnFOqsfPK3NoUp2aOuDZ3xjvQA5+2nvh3ao6lnXrz+GFgambE\np2unsfiNraxatBeJBAaM1M4Kuzv1d0SQC5+Nas3ug2Zs+O0CXYKb8YyWiWOvDuzK4ehElu89w+ZX\nx2v0u54U2IYNV6JYHRFGV7eGIw/1dHR4I6APJ7RY0yMRASdj9T8SqULB+suRdHBxpYsGddoBKmrr\n+e5YOJ2au9NHy5OChBB8vu4oUpmChW8MafJxVkX55cx7cRMymYLPf3z+kQuAEILkq2lEHY7h8rEY\nEiNTkMsUAJhZmeIR4Ebb3q1w9LTHxskaS3sLTMyNMDQxREdHghAgl8qpraqjuqyG0vxyirNLyE0r\nID4siTPb/8/EdW/hQlCf1nQc1I6gPoEYPcKqRoZG+ixcNZnFc7fw9cK9GBoZ0PMZzTJH7079/Xx0\nayZ0cEcikTB5ZEciojP4euNJ2gW646iF6JkbGzJnUCiLfz/B8evJDGjrp/476Okxq31HFp09RXh2\nFl3cGw54G+KuXWZsk0VAIpG4A78AjoAANgghVjd13L2J8eTXVLO8/0CNrYBNp6KorKvnXS3rvQEc\nOXOT8Oh03nihDx4uTTtpuLK8lgWzfqamup4Vj9ACEEKQEp3Oqd8ucP6PcAoyiwDwa+/DyDmDCOja\nAr/2Pti72Ta5DkJNRQ2p1zKJC0si9kI8x38+w4HvjmJkYkinocH0HB9K56HB6Bs8/EhIQyN9Pl41\nmQ9n/8wX83dhbmlMcJd7R6j+PfX35+c7/pfzT1dXh/mvPcP0tzaz8vvjrJg/WqvrN6pjK7aej+ab\nQxfpHeijUfzKhFatWRsVwforkWpFQGs0zTS61z/AGQj+z/+bA0lAQEN9/p5F+HeUKpXo8/NGMey3\nX9RmXt0hv7xKhLy3Wnyw9bBG7e+mqLRKDJz6jZi94DehVGo2372Q1svEG1PWi6EhC8W1qLQmjdVY\n6mrqxf7vjoqZQW+LfpKx4hmDCWLB0KXiyE+nRGnBg0nF/TvSepm4fCxGrJr1vRjr+ILoJxkrxtjP\nEN+9tVnkpRc8lDX8naqKWjFrzBoxouNikRyX869tNE39FUKInQeviNDRX4hDp2O1XsuZm6ki8K2v\nxI6LMRr3+S4qQnivXiluFOSrbcujTCUG9gH9G2qjTgSOpyYL79Urxf7EeA0uzW0+3XVCBL27SmSX\naP8j//jLA6L3hK9EZk6J1n3vRqVSic/n7RADWy8Q547eaNJYjaGipFJs/ni7GG03Q/STjBWzQ94V\n+9cdEZWlVQ99LXejUChE5OGrYvG4lWKg/gQxQHec+GT8lyI5+uGLZHFhpZjSf4WY3G+5KC6s/K/P\nLqUUa5X6q1SqxKwPtorB078VFZW1Wq1DpVKJaWu2iz6Lvhf1Ms3Soivq60Xrdd+INzRIoX9kIgB4\nAbcAi4baqROBSbt2iNBN3wu5UqnJtRG5pRUi6N1V4pPfT2jU/m4uX88UoaO/ED9uv6B137+z7Ycz\nYmDrBeK37083eSxtqKmsFT99tE0Mt5gq+knGio9HLhc3zsdpbEU9TAqzisWG934Vwy1vr3Xh6BUi\n4+ath7qGlPhcMbzDIjH32e+EtF4mlEqV+OZEkvB+/6Do/cVpEZdbofFYyemFosfYlWLF+mNaryMy\n+ZYIfOsrseXcVY37fHL2lGi+5iuRV1XZYLtHIgKAGXAFGH2Pz2cCl4HLHh4e91x8XFGh8F69Unx/\nOVLjC7Pkj5Mi6N1VIq+04Qvzd+QKpZgyd5MYN3uDqK+XadX371y5lPxXBaCHdfMplUpxdPNpMd75\nRdFPMlYsHrdSpF3PeChzN5Wqsmrxy6KdYoTVNDFAb7z49vWND9ViuXDiphjYeoFYtnivxub/vVi9\n6ZToNuYLkZiq3kz/O8+t3Sn6LN4gpHLN5r1VXi6arV4pvrzU8ENLGxG4L3ECEolEH/gD2CqE2H0P\n38MGIUR7IUR7e/t7hwpvvXENQ109xgUEajR3cVUNeyJiGR4SgJO1diXD9x27RnpWCa9O79Wko8GL\nCypZ/v7veDSz542FIx9K/fzM+Gze7rWQL2asxcHTnjXhS/l459t4t34y8hDMrEyZunAcm5O+YfCL\nfdm/9gjPt3yDU9vUB8XcD0L7BtBhcig/lqoITy2+Z+y/JswY3wVLc2NWbzqt9dpf6tuRwopqDlzW\nLMvQ3dKS3l7N2H7zOjLlPxOaGkOTRUBy+xe/EYgXQnzVlLFqZDL2JcQx1K+FxgVDfjsfg0ypZEYf\nzWoq/jVXrZSfdl4iONCdHh3V1zK4F0qlihXzf0daL2fBlxMf+Nl7KpWKXV8dYHa7d8m8mcXbP85m\n9cUl+Hd8vIOQ7oWVvSVzv5vJ2svLcfS0Y9nk1Swe8wUVxZUPbM47wT9by1UY6enQLDyO7o4mjRZv\nc1MjXpzUjWvx2VyIStWqbxc/DwLcHPjp9GVUKs0EZHKbthTX1nI8NaUxy/0H98MSCAWmAn0kEknM\nf/4NbsxAB5MTqZHLmRio2T5nrVTOjkvX6BPoq3WW4PYDlymvrOOVqdpvJ97N7l8ucj0qnVc+GIJH\nM80PPmkMpfllzB+8lO/f+YUOg9qxMW4Vzzzf57E7Ebgx+AZ5s/rSZ8xcMZXIQ9G8HPQO0adu3Pd5\n/p76e/D1bpjLZHwxfxdKReOfrEP7tsbdxZoNv51HqdQ8i08ikfBcr/ZkFpdzNi5Noz49PLxwNjNn\nZ9z9uT5N/vUIIS4IISRCiDZCiKD//DvUmLF+v3kDX2sbgp00K6d98EoclXVSpvUI1mqe8spatu+/\nTK/OzRtdZx4gI6WAX749Qde+AfQfod0atCUhMpnZIfOIPR/P3O9msmj3u1g7Nj2v4XFCV1eXce8M\n55uwpZiYGzOv/6fs/GLffXs9+LfUXy8PW+Z8OJyEG9n8/pN2iTd3o6erw4sTQ0nPKuHEhQSt+vZv\n0xxna3O2nI/WqL2ujg7jAgK5cCuTnMqmW0yPzSMkvbyMq/l5jA0I1OjJLIRg+6XrtHR1oJ23djX4\ndxy4Qr1UzgsT1ecv3AulUsWqhXswMTPk9Q+1OwBVW05uPc9bPRdiYKTPmvClDH25/0M95PRh49vO\nm7WXl9NjXGd+mLeFFc99i6xe1ujx1KX+9nymNd0HBLJ1/WlupRU2ep7eXVrg42nP5l1hKLSwBvR0\ndRjfpQ2RKVmkFagvMAowNqAVAtibGNfI1f4fj40I7E2IQwIMb6FZ+a7o9FyS84qZ0LWNVjdEZXU9\nuw5dpU/XFni7N/7YrgPbI0i4kc2seUOwstW+cKmmbF++l8+nfkNAFz++jVj2xDj+moqxqRELtr3J\nc59M5MSv5/hg0GfUVNZqPY66yj93eOWDoRiZGLBq8d5GWx46OhKen9CVrNwyTl3Srt7fqI6B6Ovq\nsuPSdY3au1lY0tHFjb0J8U22lB4LERBCcDApkc5uHjiZaebh/yMiFlNDAwa1064i796jMdTVy5k6\nunNjlgpAWUk1v6w9QXBXX3oNatPocRpCCMGP729h4wdb6fNsN5YdWfDYJOY8LCQSCZM/HMMHW17n\n5p+RTNoAACAASURBVMVE3uv3iVYOQ00q/9zB2taMF996hrjoW5w82PjU4+4dfPFys+G3vZFa3Zy2\n5ib0a+3LgSvx1MsVGvUZ3sKf1LJSEoqLGrtc4DERgbiiQtLLyxjq9//YO+/4KKrvfz+z6b33hFRS\nCEnoTbr0qoKAUkTsFbFgwYaKvaHYBRFEeu8dpAUIIQESQnrvvW+yu/P7I8QfXz5AZiaLAeV5vfhH\n596d3cw9c+6557yPtAVdVadmT2wiIzsHYW4iPRrf0Khh3Y5oenTyIcCnZUWj6/Hbwj001Gt46tXR\nN8UtF0WRn19ZzupPNzP2yWG8uuy5Nsm5v1UY/GA/5m98hfQLmcwd8h6VpTfW6pOr/NPM0PGdCero\nyeIvd1NTLU3442pUKoEp47qTnF5E1LkMWWPv69mRqjo1+84lSbp+REB7DASBrYnKVIabuSWMwK6U\nJFSCwHB/aUd1+84lUd+o4d4e8so49x+7RGl5LQ+Mk3eceCUpCXns3XyWe6b1xstXuSG5EX+8v451\nX25l/DMjeO67R/8V0f/W0nN0V97f8hpZl3KZN+pDaq+j/ivV/b8WKpWKp98YQ1lJNWuXKA8SDusf\ngr2tOWu3R8sa1yPACw97a7ZJVCa2NzOnt2c7diYntmpLcEs8XbuTk+jp4Ym9mbSmotuiE/B2tCWs\nnfTIviiKrNsRjY+nPd3Cle+rF3+9G0trU6Y8qh/h0avZ+sNulr27hmEzB/L0wof/1QFAuXQZEs6b\nq+aQeCaV+RM+Q3OV2yzH/b8eQR09GTgynI1/HKekUFnk3djIkPHDIjh+JpWs3JZFQptRqQRGdQnm\nRGImxZU1ksYMD2hPRkU5iaXSAorX/FzFI/VEWnkZyWWlDJPoBRRVVnM6JYtRXYJlLZBLKQVcSing\n3hGdFS+s81FpRB9PZsqjA7C0lt79SCpn9say6LnF9BrblRd/fvKOB3AN+ozvzku/PkX0vvN89/wS\nQLn7fz0eem4IGo2W1YtbFvi8HuOHRWCgEti6T1qgr5kxXYLRiSJ7JG4Jhvo16WbsS1WeONTmT9nB\ntKYEicE+0kRA9p5LRhRhuAQxhivZuv88JsaGDOsfIvsem1nx40HsHC0ZM1m67LlUspPy+GDyV3iH\nevHGitkYGN7pQXA9hj00kMlzx7Ptp72s+HaXYvf/erh52jNsfBd2rjtNcYEyb8DRzpI+3fzZeSgO\njYwkJD8XBwJcHdgdK00g1dnCknAX17/XkRLa3AgczkjD384eLxsbSdfvO5eEv4s9/q4Okj9D3aBh\n39GLDOwViJWFqaL7jI/JJOZUKvc/3A8TU/0G6RrqG3h/0heoDFTM3zQXM0v9exn/Nh5e8ADe9/fj\nnUtVnEwpaVXu/7WY/OgAdKLIuqXKYwNj7g6jrKKWE9FpssYNC2/P2bQciqukbQkGevtyNj+Psrrr\nd0m6EW1qBNQaDadycujv7SPp+vKaOqLTchjcUV6u/7GoFGpqG2TrwV3J2t+OYGVjxqgJ3RXPcT1+\nfW0FqbEZzF36DG6+d9qQtYROJ/L9oVQO+PljqNMRvvco4zs46TV+4uphx6CR4excH0VVhfz8BICe\nnXywtTZj91/yEnoGhwUginA4TmIasbcPInBCghDptWhTIxCVl4Naq6FvO2mBuiMX09DqRAbJ1A/c\n+9dFHO0t6dJRmlbh1eRmlRB5KIHRk3rovUDozN5YNn6zg3ueG0nP0XekyFvi6uj/0omhVEYn88Oc\n3/X+Wfc91Bd1fSM710cpGm9oaMCQviEcj0qhuka6OnOgmyMe9tYcjJNWjBTu4oqVsQlHM+UdSTbT\npkYgMjsLA0Ggu3vLysMARxMysLc0I9RT+tuyplbNyZg0BvcJUtzsY/ua0wgqgbF6jgXU1dTz1eM/\n4RXkzmOfTNPr3P9GrhX97zW4I/e/PI6di/frveDIL9CV8O6+bF9zSlZR0JUM6RtMQ6OWY1HSqwsF\nQaBvsC+nkrNo0LScOGSoUtHDw4PInGxF99jmRqCjswuWElqL6XQikUkZ9A70ltVR6NiZVBoatQzs\nLS+Q2EyDupE9m87QZ3AIDs76zdj7Y/5aCjKKmPPzkxib3twS5NuZlqL/M969H3d/FxY+9QsN6ka9\nfvaYyT0pyC3nzHFp0fqr6dDeDWcHKw6ekJfQc1eQN3UNGs6mSWu53tPDi/TyMvKrpTU9vZI2MwJq\njYbzBQX08JDmBSTlF1NaXUev9vKUVo+dTsHOxpyOgfKKjJqJPJRAVUUdoybqNxaQnZjLhoXbGT5z\nEGH9lJ9Y/NuRkvxjYmbCs4seJScpj03fKCpgvS59BoVgY2fBno3yEn+aUakE+nb3J+pcBmoZBqpH\ngBcGKoGTydL6KXa/vI6iJbQr+597lD1CT1woKqBBp6WLm7TFefryj9GzvfR9vUar42RMGr27+ilu\nKLpnUzROrjZE9PBTNP56/PTyMoxNjZn14QN6nfffhJzkn+7DO9FrTFdWfLCesgL9dCQGMDQyYPCY\nCCIPJVBRJi1afzV9uvlTr9YQHSe9QaqFqTGhXq6cSpI2poOjE6aGhkTdTkYgJj8fQLJ2wJnUHDzs\nrXGzk+6SX0zKo7pGTe8u0lqYXU1FWQ3RkSkMHh2h1+ah8ZGJRG47wwOv34u9q/yW6f92lCb/PPH5\nDOpr1az+dLNe72fI2M5oNFqO7VdWtts51AsTY0NOxaTLGtfNz4O47ALqGlr2IIwMDAh3diU2P0/2\n/bWZEYgtyMPN0hIni5Zbc4uiSHRaLl18PWR9xqnYdAQBunZU1qzh+P54dFod/YfL6+jSEn+8txYb\nRyvGPztCr/P+G2hN7r9noDt3T+vHth/3UJovPV23JfyCXPHwduDIHnktv5sxMTYkIsST07HpssZ1\n8fNAo9VxIUta38JwFxfiigplaw+2mRGILyqko7O0KH92aQWl1bV08nGT9RlnL2QR6OeCtZWy5Jvj\nBy7i5mWPX5D+Ogglx6RxelcME18ceycp6Cr0kfv/4BsTaKhvZOM3O/V2X4Ig0HdIKLGn06iqVJaQ\n0y28HenZpZTI2FJ08mnykmPTpbn4YS6uNGi1pMisI2gTI6ATRdLLywlxlKbJF5fZZAnD2kk3AuoG\nDfFJeXQOVZYbUFerJuZUKr0GyKtRaIl1X27FzNKUMU8O09uctzv6zP33bO/GXff2YPtPe6irUVYO\nfC16DgxGp9URdVRaOu/VdLr8HMZelH6MZ2NuSjtHW+IkegIhjk1VrQnFt0FrcrVGg04UCXaUVoob\nl12AsaEBAW7SU4UTUvJpaNQSESLt9OFqYk+l0digoUd/eaIlN6KsoJxDq44zYtZgLG1b3gb9F2iN\n+389Jr44lqqyGvb/oTzl92qCOnpiY2fBqSPKjECgrzNmpkack2EEAEK9XIiT2Mbcx9YOYwMDEkrk\niYy0iRGo1zYlQAQ6SFvUl3KL8Hd1kNS4sZn4pKYASccgeVuIZqIjkzExNSK0i/7kvPb9cQStRsvo\nx4fobc7bGX24/9eiQ+9AfDp6sfu3A3q4yyYMDFR07uVPzMkURbX7hoYGBPm7EJckL3AX5O5EXlkV\nFbUtezWGKhV+dvYk3Q7bAbVGi5FKRTsbaWq5iXnFBLrJ0wO8mJSPq5M1djbK3rgxJ1MJ7eKNsbH+\nurfvW36Y4J7t8e6gbIvyb0Hfpb9XIwgCIx4eTMKpZDITcvQyJ0Cnnn6UFVeTkaJMjLRDgBtJaYU0\nNkoP3AW5N3nLSXnSXPwAe3uSbwsjoNXQzsYWQwn18hW19ZRU1RLgIn0rAJCUXkh7X2V9AKoqaslM\nKSS8q4+i8dciMyGH1HMZDH6gr97mvB25Ge7/tRgwuQ+CIHB4zXG9zRneremoOe6sshz99r7OaDQ6\n0nOkL1J/F3sAUgtLJV3va2snW4a8TYxAg1aLt0QvIO3yl/e9/GNIoV7dSHZemWIdwfjYpgSNkE76\n6wN/ZF0kgiDQb4L+tQhuF26W+38tHN3t6dg3mCPrI/U2p5uXPbb2FlyMUVat1/xSSk6Xvmd3tbXC\nzNiItAJpRsDHxg65m5U2MwLtJOoHZBY3ZX95y+gwlJlTiiiiWFI8OT4HQRAIDJWXl3AjTu44Q1B3\nfxw95Hk0/wZutvt/PXqP607a+UwKs+RFy6+HIAgEdvQkKV5+Vh6Ap5sdhoYqMrKlewKCINDO0fbv\nddASUnU5rqTNjgjdraS5gJnF5agEAQ8ZmYLpOU1W08dTuvdwJckX83Bv54CZuYmi8VdTWVJFwslk\nuo/orJf5bif+Kff/WvQY2QmA0zuldfaRgn+wG1lpRdTXyW+GYmigwtPVjoxsaW/1ZrwcbCQbAQ+J\n6+pK2ixZyE1if4G8skqcbSwxkiG3lZPXlC3mobBNV3pyAb6B+hP3OH+kqUFEl6E3p0fBrco/6f5f\ni3Yhnjh62BNzKE5vc/oGuqLTiWSlKfMuvNzsyJaZzehhb0NeWaWkUwlnCwtUMj2sNjMCLpbSuvbk\nl1fjaiuvw09eYQVO9paK2o03qBspyCnDW4/NReOOJWBkbEhgN3liKLcrbeX+X40gCITeFUS8zG5A\nN6KdX1OcKStN2QmBu4sNeYUVso4ZXW0tUWu0lEtIfjJQqXAyl3ci1mZGwFlCzQBAYUU1zjbyjEB+\nUSWuTspczrzsMnQ6EU8f5S3KruZSVAr+nX0xVmCUbjfa0v2/FiE9AynMLKassEIv83l4OyAIAjnp\nyiS+XZ1tqFdrKJeRfuxi2+Q1F1ZWS7peSj3OlbSZEZDaY6CkqhZHK3lfqrCkGicHaduNq8nPaXLV\nXBXGE65GFEVSYzPwj/DRy3y3Mm3t/l8Lv4imZK9UmcU718PIyBBHF+u/nxO5ONk3vdCKS6UtaAAH\ny6a1UlIlTevQwUxeTUqbGAEBsDBq+a3YqNFSVa/G3lKawWimpKwaBztlSUKFuU0BGBcP/bT9Lskr\no7q8Bh+F+oa3A7eK+38tfMOajnnTL0iv5W8JF3dbCmQ0FbkSx2YjUCbdCNhbNRsBacVHdqbyjECb\nmGkDlUrSA1JR17QHsjGXLhOubtBQV9+IrbU8w9FMaXEVKgMVNgqNyNXkpTTlfXu0V5a+fKtTXK1m\nzuoYjiQVM76TOwvuDWvzt/+V2DhaY25tRm5Kvt7mdHC2JvmismNC28tNa+RsB2zMmp7/yjppYqU2\npvJk9dvGCEh8Q1TWNn1pazPpR3WVl3vU2SjsEFRWXIWNnbneRETyLweQ3Pz+fVLiJ1JKmL3qLBV1\njXx8XxiTu3vdEm//KxEEAXd/V/IUBvKuhZ2DJWXF0t/kV9L8XFbIMAJWl5//Sgn1AwBWxvKOttvE\nCEg9wqhVN53FWsgQ4ay+bDgsFZ7xV1XUYW2jzIu4FiWXjysd3P89CkI6nch3B5P5al8iPg4W/D6r\nR5sG/1rC3s2W0jz9SY5Z2ZhRW6NGq9HK7hRlfvlZrpH4Voem/AJTI0NqJSgMAZgZyVvWenndCYIw\nQhCES4IgJAuC8FqLHyrVCFz+0mYy2nLX1jWNMTdTFomvqarHwlpZl6JrUV5QjqmFCWYKOx/datxq\n0X8p2Dnb6lV3sLkPZXWVfL0CAwMVZqZG1MpMNjI3MaJWolCpuYR425W02hMQBMEA+A4YCmQDpwVB\n2CKK4nUF2aS6jA2Xe7iZyLBsDZc71ZrKMBxXUl/XgIVCJaJrUVNR+6/RDrgd3P9rYWlrTq1CRaBr\nYWrW9DZX1yuTNzcxNkTd0HI/gSsxNjT8ez20eK2BvGWtj+1ADyBZFMVUAEEQVgHjgesbAYkTN17+\n0lKqDf8ec7lM09BIWUNPtVqDnaP+dkn1tWpMLfSTftxW3G7u/9WYWppSX6NGFEW9GK3m8nKlRsDI\n0EBWOTGAkYFKshGQs15AP0bAA7jy/CUbaKFUTtofQnc5q8pAhlx48xilEuM6rU6vysKaRi2GetQk\n+KcpqVbzwi0c/ZeCkbERoig2/W310O3Z4PILRmlXIgMDFTqdvFo/A5VKcpah1MB7M//YX1MQhMeB\nxwGsvJRJft3hn0clCOSU1d1W7v8d5KEPI5ADXJkJ43n5v/0fRFH8GfgZwDHAX5JJa37gdDLyrJuD\njnIt7d+fqRLQ6ZRZ+Gvej4EKrUZ/8/3T2FkYs3tOf4z06B3902gux4kEhd7h1eguewCKvU2dKPte\ntDqdZAOslSl/po+/7GmgvSAIvoIgGANTgC03GiD1FpsfPI0Mt8vQ8PIYifunqzE2MaRBLS9ocyPM\nLEyp16PqbVtwOxsAgPqapriMSuZe+Xo09ztUWgvS0KjBWOa2RKPTYWQo7f41Ml9irfYERFHUCILw\nLLAbMACWiKJ4w9pNqXub5h9KLWNBG18+SZAbfW3GxNRIccDnWphZmVKjsL/9HfRDbWUt5no88am/\n/HyYmio1AlrZ2pXqRq1kw9Eos/mIXmICoijuACR3gpTqqTfnB0hpw9RMc36A3HPYZiytzBQXh1wL\nW2cbaivraKhvuNN5uI0oK6zA1lm+4s71qKls8uzMreTnfuh0InX1DZjLNCB1DY2S82XqNPJeYm2k\nLCTNXTG/7G7V1ktf0OaXUyxrapUZASsbM6r0+Oa2d20qRCrN11+yyh3kUZpXhq2L/oxAVWUdJqZG\nipSo69WNiCKYy8ho1elE6hsbMZdoBGobbwsjIM0VsG4unKiXnmJpc9k6V1YrSw6xdbCkvKRGkbb8\ntXDxaRInyUuV1kDiDvonL7UQNx/9icSUFVdh5yBP46KZiubaFhleRFW9GlEEKzNpY6oa5L0A28QI\nSI1eNlcPSi2cADAzNcbE2FBWldaV2DtYotFoqSzXjzfg7t9UOJSbrL8qtjtIp7q8hsqSKlz1WMBV\nWlSFnaMyI1Be2fRc2VhJr0+pvFxNK7WQrkot/aUJbegJ1ElwWUyMDDE3MaJU5lvd3tZCVuPHK3Fy\na3LfC/VUcOLczhFTCxPSZfSmv4P+aP7dfRT2pLwWhXnlOLsp05soLm16Lh1llKo3P//2Eg1HaZ28\n9dJmZz9Sb9TB0pxiiWIKzTg5WFJUWqXktnD1aKr2y8/WT3BQpVLhG9aO1HPKGlbcoXWkXf7d/cL1\n00NCq9VRmF/x93Mil+bn0lHGdqK48rLhkGwE5HmxbWYEimulLWwnawsKK+TVbrs4WlNQJK8LSzPu\n7ZpkxXIy9KNVD9C+ix9JZ1LRKsxduINyLp5KwtbJGieFPSiupiCnDK1Gh4e3sv4R+UWVGBkaYC+j\nPV7z8+9kLW1Mce1tYgQKaqQtbBdbK/LL5b3V3V1sKCiuUpQwZGZugpOrDRmp8jq73ojQPkHUVdeT\ndl5Z55o7KCfu2CU69AnSW7pzcx9CL4Ut7vIKKnB1tpaVbZhfXoWhgQoHy5aNgCiKFEpcW820mRHI\nq5a2sN3trCkor0YrIwvKw8UWnU4kV6HCrLe/M+lJ+ovmh/XvAMDZ/ef1NucdWqYws4jc5HzC+oXo\nbc7m56JZelwu2fnluMs8rswrq8LV1kqS4Siuq6VRZsZgmxgBFYLkpoleDjZodDpZ3kC7y0rBmTny\nOr004x/sRmZq4d/poa3FydMBn45enNqlv044d2iZUztjAOg+Un+dn1IS8nDzssdCYaJQZk4pPjJb\n0WWVlOPlIM1w5MpsRgptZASMDFRkSbzZdo5NUdiMIunR+uYfOS1LmTZ8+w4eaDU60hL15w30HNWF\n839dpEqGyuwdWseJradx9XGiXbD+ekomxucQEOKuaGxeYQXqBg3entKNgCiKZBSX/70OWiKrUr73\n2yZGwMTAkIwKaYva17nprZ4msTUzgKWFCa5O1rK6v15JSETTcVJcjP4i+v0m9EKr0XJ882m9zXmH\n61NdXkP03nP0m9BLb/GAksJKCnPL/34+5JKc0fQ8yumWXVJdS1Wd+u910BJS19WVtIkRMDY0IL28\nTFLmoIOVOVZmJqRKbM3cTICPE0kKFWYdnK1x9bDjQrT+jEBgN39cfZw4tPqY3ua8w/U5uuEkmkYt\n/e/vrbc5z59JByC0s7ei8clphahUAn7tpJ9UND/3Uo1AWlkZLhbyEpnazBOo12jIrWp5SyAIAu3d\nHEnMk/dWDw5wJTO3lOoaedlTzUT08OPcqVTF6jFXIwgCd0/rz5k95/TWKvsO12f30oN4BbkT1D1A\nb3PGnEzBwspU8XYgPjkPX08HTGWUICfmNj33gW7SDEdyWSn+9vK6Z7WJETA1bCq8SCyRtmcPcnMi\nMa9YllBI6OVmHxeT8+TfINC5lz/VVfUkxf2PPopihs8chCiK7F5yUG9z3uF/ybiYzYWjCQybOUhv\nWwFRFImOTCGiu68i+TmdTiQ+KZ8OgfKa0FzKLcbe0hxHCTkCOlEkpbSE9vbyAo9t4wlcNgKXSqS9\n3UO9nKlVN5JeJH1LEBrojkolEBufregeu/QOQKUSOHVEfx1t3fxc6DGqM1t+2E2DjMrIO8hjw1fb\nMDY1YsSsQXqbMyO5kMLccrr1DVQ0Pj27mKrqesJlBikvZOXTwVNaTkJ2ZQU1jY0EOchLjGoTI2Ag\nCHhYWXOxSJoR6OjlCsD5TOlFOOZmxgT6OhOj0AhY25oTEtGOyEMJisZfj4kvjqW8sIJ9y//S67x3\naKKsoJy9y/9i6IyB2Drpr3w48nDTc9Czf5Ci8Wfjmp7DiA7S9TVr1Q2kFpQS1s5V0vUXi5vWU4ij\nvByGNksWCnVy5nyhtCM4X2d7rExNiM2Q59p3DvXiQmIudQrfun0Gh5B6KZ9chUeN16LToI4EdvNn\n5ccb/9a+u4P+WPv5FrSNGia+NFav8x7bF0dQR08cnJVJrZ85n4mLoxVuMsRNzmfmoxNFyUYgrrAQ\nA0Eg8HbwBADCXFzJqCinor7lMmGVSiDcx43oVHn78+4RPmg0OsXeQN+hoQAc2XNB0fhrIQgC09++\nn/y0QvYuO6y3ee/Q5AVs+X43g6f2w1OPDWDzsktJis+l37COisZrtDqiz2fSPcJHVowiOi0XQYBO\nPtICkbEFeQQ6OGImswNRmxmBTq5N1i22QJqL39XXg5SCUkqrpRdHRIR4YGJsyMmz6UpuERd3O0Ii\nvDiwLVZvIiMAPUd3IbhHAEvfXk2dQvGTO/wvv725Ck2jlqlvTtTrvAe2xSAIAv2GhSoaH5+UR3Wt\nmh6dfGSNO5OSTaCb098NSW+EThSJyc8nwkWa13AlbWYEIlzcUAkCZ/Kkvd17tG9K0IhKkf5WNzEx\nomtYO45FpShexEPHdyEjpZBEPZ4SCILAU1/NpDSvjD8/3Ki3ef/LJEWnsmvJAe55bqRevQCdTsfe\nzWeJ6OGLi8KmssdOp2BgoKJHhI/kMepGDTHpufQIkJaYlFRaQlWDmq7u8rMj28wIWBobE+LoxOkc\naYsr1NMFCxNjTiTKq8Tr082fvMIKUhSWBg8YHoaJqRE71+k3069D7yDuntaP9V9uJeOisu3KHZrQ\narV88/Qv2DhaMe0t/XoBMadSyc8pY9g9XRSNF0WRo6eT6dTBE0sZ7ehi0nNRa7T0CJAWSIzKbVpH\nXd3k5zC0qaB8Tw8vzubnoda0HCAzNFDRI8CL45cyZL3V+/doOuo7dELZUZ+FlSkDR4ZzcMc5qvXY\n1BLgic9mYGJuwtdP/KTXhif/NTYv2kXCqWSe/HKm3pu/blt9Chs7c/oOUbYVSMsqJiOnlAG92ssa\ndywh/e9nXgons7NwtbDE20a+4lGbGoFenp6otRpi8qVF/fsGe5NbVikrhdje1oLOoV7sP35J8ZZg\nzOSeqOsb2b0pWtH462HnYstTX83kwtEE1n+5Ta9z/1fIuJjNkjf+pPvIzgx+sK9e5y7ILSPy4EWG\n39tVcaORA8cuoVIJDOwlL7/g6KUMOvu4Y27Ssky9KIpE5mTR01NZm7g2NQI9PLwwEASOZknL0e8f\n4gfAwbgUWZ8ztG8IWbllJKQoE/ts38Gdjl282bziOBqZ3WRbvLcZA+h7X0+WzPuTxDPyvtd/nYb6\nBj588GtMLUx46den9N4ncdOKEyAIjJ3SQn/d6yCKIrv/uki3MG/sZXgoWSXlJOUVMzDUX9L1CSXF\nFNfWcpeXMgm1NjUC1iYmdHJ146+MdEnXu9pZEerlwsEL8hbLgN7tMTYyYNeh63ZLb5GJM/tRmFfB\noV3nFM9xLQRBYM7PT2DnYsuCKV/dKTWWwY8vLSM1NoNXfnsGBzdlQbvrUVFWw851UQwcGYaTqzJR\n0XMJOeQVVjC0vzxRk4MXUgEY1NFP0vVHLq+fu7yUFTa1eZO5Ad6+nC8soEii5uCQsADOZeaTXyZd\nZMTKwpR+PQLYc+Si4vZkPfoH4hfkysqfD+tdK9Da3oo3Vr5AYWYxH0z56o4WoQS2/bSXrT/s5v6X\nxtJzdFe9z79h2THU9Y1MmtVf8Rzb95/HzNSIAT3lxQP2xCYS7O6El4M043M4I41AB0fcrKyU3Gbb\nG4FBPr4AHEpPk3T9sIimvdXuc4myPmfM3eFUVddz+GSSvBu8jEqlYuqTg8nJKObgDv16AwAd7wpm\n9g+PE733HD+++Lte8xL+bcQcvMCi5xbTfWRnHvl4qt7nryirYcvKSPoP74hPgLJ+BdU1ag4cv8SQ\nviGYm0lvP5dfVkVsRt7fz3lLVKrrOZ2bw2AfaV7DtWhzI9DByRk3Syv2piRLur6doy0hns7siJaX\n0981rB0errZs3Klc4qv3oGD8g91Y/v1+GhR6FDdixKzBTJgzhk2LdrLyozv5A9ci8UwK79zzKZ6B\nbsz7czYGBvK6+0ph1S+HUdc3MvVJ5QVIOw5eoF6tYfzQcHnjzjY918M7STMCB9LS0Oh03O13GxsB\nQRAY7h/AkcwMaiS2TxrTJYT47EJZpwQqlcCEkZ05fymXBIXdgFQqFY/MGU5BbjlbV0YqmqMlHv9s\nOndP68dvb65k07c7b8pn3K5kxGfxxsgFWNlb8tGuN7GQIdstldysErauOsmwe7rQzk+ZorBO2MQC\nRAAAIABJREFUJ7Jh51nCgtwJDpCewSeKItuiEwj3dpMsJ7Y7JQlnCws6uyrTOIBbwAgAjAgIRK3V\ncCA9VdL1ozoHYaAS2HT6hh3Q/3fcoI6YmxmzamuUktsEmkqMu/cNZMVPBykr0X8QT6VS8cqSZ7jr\nnu58N3sJGxZu1/tn3I6kxKbz8uD5GBga8Mnet3CSodMnh58/24mRsQHTnxmieI6jp5PJzi9n4mh5\nCUbx2YUk5RUzpkuwpOtrGho4nJHGML8AVK04GbkljEBXN3dcLCzZnigtocfR2oL+IX5sPh0vqxe7\npYUJ44aGc/D4JfIVypEDPDF3FA31GhZ/tVvxHDfCwNCAeavm0Pe+nvwwZynL56/9T8cI4k9c4uVB\n72JkbMjnB9/FI0B/acFXcvpIIpGHEnjwiUE4OCkLsgGs3BKFm7M1A2TmBmw4eQETQwNGSTQC+9NS\nqNdoGBMo7frrcUsYAQOVilHtAzmUniapqhBgQq+OlFbXyj4uvH90FxAE/myF4KenjyP3PXQX+7ac\nJfa0NO9FLkbGRry5ag7DZg5k2fw1fPnYjzQ26EcC/Xbi8NoTzB3yHtaOVnx15H28gvSnHHwl9bUN\nfPfhVjx9HLlnmnJdwtj4bM4n5DB5bDcMZSgQ1aob2B6dwNCI9n834m2JrYkJuFpY0k1BvcCV3BJG\nAOCe4A406LTsSJYW9e8b7IObnRVrjsuL1Ls4WjNqUEe27jtPUYmyfoUADz4+EDcve75+dxP1dTdH\nJcjA0ICXFz/N1HkT2LXkAHOHvEdZKzyY2wmdTsfSt1fxweQv8e/sy9dHP8DFW1nDDyks/XYv+Tll\nzH57PEZGhornWbLmOA62Foy5O0zWuG3RCdSoG5jcJ0LS9SW1tRzOSGdcUHCrtgJwCxmBjk7OtLd3\nYF28tNp9A5WKSb3DOZmcRXK+vOKgGRN6ohNFfl+vPLhnambMC+/eQ15WKUsW7lE8T0sIgsDM96cw\nb+ULJEal8FSXV4g5qD99g1uR0vwy5o3+kBUfrGfEw4P4bP872MkQ45DL+ag0Nv8ZyZjJPQnr5qt4\nnugLmZw5n8mD93SXJSYqiiIrj8YQ7O5EhLe0rc7mSxfR6HTcG6KspuFKbhkjIAgC93foyNn8PBJL\npC3qCT3DMDE0YPlhecd+bs42jB0SxtZ958nJV96CPKK7H+Me7MWWPyOJPiHtiFMpAyffxcLjCzC3\nMmPukPdY/PoKvXVIupWI3HaGJzq9wrnD8Tz//WO8+OtTivP2pVBTXc/nb67H1dOOR+YMUzyPKIr8\ntOIITvaW3DNM2tu8mROJmSTnl/Bgv86SUp9FUWRN3HkiXFxl6wlei1YZAUEQPhMEIUEQhHOCIGwU\nBEFZfuVl7g3ugJFKxao4aT377CzNGNe9A1vPXPy7fbNUZt7fG0MDFT//eVTJrf7NrNnDaOfnxGfz\n1t2U04IrCejky3dRnzBi1mBWfbKJp7vO5cIx/WogthVlhRV8PP0b3hr3Mfautnwf9Qljnxym93qA\nKxFFkW/e20xRQSWvLJiImbn0Ut+rOXIqmbjEPGZN7oOJTKO19FAUjlbmjO4iTb/wbH4eiaUlTAqV\nt+W4Hq31BPYCHUVRDAcSgddbM5mDuTnD/duz4WIcdY3S3nIzB3ZDq9Ox7C95FX6OdpY8MK4b+48l\ncD5BuWCIqZkxr386mZqqej55dY3e+hRcDzMLU1785Uk+2PY6ddX1zOn3Fp8+vIiSvLKb+rk3C02j\nhg0LtzMreDaH1xxn6psT+PbkR3h3UNblRw7bVp/i8K7zzHh6MB06KSu+AWho1PDdssP4eNozcpA8\nCbK4rAJOJGYytV9njA2lxSJWnI/F0siYsa08FWimVUZAFMU9oig2p85FAtKlVK/DtPBOVKrVbEmU\n9oZr52jL8IhA1hw/R0WttJOFZqbe2wMne0sWLjnQqsXrG+jKs/PGEnMqlWWL9imeRw49R3Xh1wtf\nMnnueA6tPMbDQc+z9O1VVJYqD3b+k2i1Wg6tPsbjES/zw5ylBHb358eYz5n53pSb6v43c+l8Nj9/\ntoPu/QKZ9Ijy+gCANdvOkJNfzuxZg2WdCAAsPnAKK1MTptwlPSC4PekS94Z0wNJYejryjdBnTGAW\n0OoUt+7uHgQ7OrE0Jlry2fijQ3pQo25guUxvwMzUmKdmDCAhpYCtrWwbPuyeroyc0I3Vi//i4PbY\nVs0lFTNLMx79eBq/xn1FtxGdWPHBeqb7PcOvr/1BcY7+FJL1SYO6kV2/HeSJiJdZ8MDXqFQC8zfN\n5eNdb+Id0up3iCSK8it4d/YfODhb88qCiahUypdBQXElS9eeoF/3ALrLkA8DSMwrZu+5ZB7o2wlL\nU2lbkT8vxNKg1TI9vJOCu702LX57QRD2CYJw4Rr/xl9xzTxAA6y4wTyPC4IQJQhCVNEN+g0IgsCs\nTl24VFIsWWcg0M2RoeHt+eOvs5TXyFP/Gdo3mC4dvfhpxRHKKuTFFa7m6TfGENbVhy/f2cjF2KxW\nzSUHd39X3l7zEj/Hfk634Z1Y+/kWpvs9w8fTvyHm4IVbQrUoL7WApW+vYrrv03zxyPeoDFS8uWoO\nP5/7gj7jut/Uvf+V1Nc28O7zf6Cua+Tdb6dhbWveqvm+WXIQUYTZChqdfL/7BJamxswYIC2zUK3R\nsPxcDAO8fQmQ2WXohoii2Kp/wEzgBGAudUzXrl3FG1Hf2Cj2+OUHcfqGtTe87kqS8orE8Je+Ej/b\nfFjymGbSsorFgZO+FN/6fIvssVdTXlotzhz5uTip/wIxM7Ww1fMpITclX1z0/GJxvO0McYgwUZzq\n85T440u/i/GRiaJWq/3H7qMgs0hc//U2cXbfeeIQYaI4VHW/+PqoBWLUnhhRp9P9Y/fRTGODRnzz\nqd/FkRFvipGHE1o934HjCeJd930mLlsfKXtsTHqu2PHFL8Xvd5+QPGbV+VjRd+Hn4pGM9BavBaJE\nietREFuRjioIwgjgS2CAKIqSO4Z269ZNjIq6cf7+T2dO8cmxI2yeMo0wZ2nlnG+t2sP26AS2vTYT\nd3t5TSKWrY/k5z+PsuCVcbLTPa8mJ6OYF2f8gompIV/8/jhOrjfvjPtGqOvUHNt4igMrj3JmTyya\nRi22TtZ0HR5BxIBQOvQJwivIvVXu8JWUF1UQfzyRC0cvcnp3DOkXmrwhv3BvBkzqw5Dp/XH2av2R\nlhJ0Oh2fzVvPwe2xzH57PCMndm/VfBVVdUyb/RvOjlb89NFUWbEAURSZ9cM6UgtK2fnGw5IkxLQ6\nHUP/WIqlsTGbJ09t0XMSBOGMKIrdpNxPa41AMmACNG9AI0VRfLKlcVKMQJVaTd/ffqG3lxc/jh5/\nw2ubyS+rYszHvzEkvD0fTx0paUwzGo2Wx19bQWFJFcu/noldKyvUkuJzefWRxdg7WfHJ4kdalYuu\nD6rLazi5PZrTu84StTuGiuKmAKKZpSm+Ye1oF+yBm78rrj5O2LnaYutkjZmVGSbmJhgYqBBFkYb6\nRuqq66kqraY0v5zi7BJyU/LJScoj9VwGJblNJxRGxoaE9g2mx4jO9Brb9aal+kpFp9OxaMFWdqw9\nzcznhjDlsYGtmk8URd79ahuHTybxyyfTaO8jr9rw4IUUnv9tC/PuGyw5ILgtMYHnd21n0cgxjGrf\n8lHiP2YElOIf3kFMOdey1NdXkcf49lQk2x+YToiTtB/6mx3H+GX/KZY/N1ly55ZmUjOLeHTuH3QL\n9+aT1+9t9T71wpl03nx6GU6uNnz866w2NwTNiKJIdmIuFyOTSDqTSsq5dLIv5VJWID8l2dTCBPcA\nV/zCvfEL9yGkV3sCu/phbKqfyHVr0el0fLdgG9vXnmLSI/15+Pmhrf677joUxwff7uTxB/syY0Iv\nWWMbNBru/Ww5BioV61+ehpEEPQStTseoP5cBsOPBGRi04LmdKkqnp7PvrW0EzALcxfiz5/C1urFr\nWFFfT7+lv9DHsx0/jpHmDdSqGxj78VIcrS34c/YDLf5gV7N2ezQLlxzghUcGM3GUMq35KzkflcZb\nzyzHwdmaj36eibNbq/Kpbip1NfUUZhZTXlBBeVEl9TX11FXXw+VHxNjMGFMLE6zsLLBztcXB3R5b\nJ+t/LKgnF61Gy8L3N7NnYzSTZvXj4dmtTz7Kyi1j1ivLCPR14Zv5k2S3Kf91/ykW7jjGD4/dS99g\nH0ljtly6yAu7d7BwxOgWcwNEUWTCwZ/ZePeTko1AqwODSv6Z+buL885slhQM+ebkcdF34ediTH6e\npOtFURS3n7kodnzxS3HVsRjJY5rR6XTiKwvWiwMnfSleTJb+mTfiQnS6eF+f98WpQz4R05ML9DLn\nHW6Mur5BnD/7D3F42Dzx90V79RKIrFc3ig+/9Ls4csa3Yn5RhezxuaUVYvfXvhGfXyLt2RdFUWzQ\naMSBS38VR/yxVNRK+A5H85PF4A3vygoMtkntgJ2JOVsyY8mrbdn9fLhTV+xNzfj02BHJeQMjOwfR\nM8CLhTuOyU4nFgSBec+NxM7GnLc+30pFVesbjoR29uazJY+g1ep46aFfOBclTU/xDsqoKKvhjSeW\ncvzARZ56bTQznhmiF2/l68UHSEwr5I1nR+LiKC/wLIoiH208BMCr4wdKHrfuYhwZFeW83LuvpGrB\nnxOP4mwqb9vZJkbA0cQSEVicdKzFay2NjXm2Ry9OZGdyKEPa4hEEgTcn3o26UcOHGw/Ivj8bKzPe\nf3kcxaXVvPvVNjR6SAX2C3Ljq2WPY+dgyeuP/8bO9crVje5wfdKTC3hh6o9cupDD659OZvyDyrUB\nrmTznli27jvH9Pt60re7tH4AV7LnXBIH41J4elhvySdX1Q0NfBV5jK5u7gz2bVlDMKo4g1PF6cxq\n30fWvbWJETBSGTC+XQRr06MpqKts8foHwyLwtrHloyOHJSsJ+TjZ8dSwXuw9l8zec/IVhkMD3Xjp\nsSGcjs3gh+X6aSHu6mnPV8sfJ6KHHwvnb+L7j7bdFMHS/yrH9sfz4vSfqa9v5LMljzBghH4KbGLj\ns/lq8X56dfbl0Sl3yR5fVl3HhxsOEurlwrT+0uNMP505RXFtLfP6DZTkyXyXcBgHEwsm+ciTYG+z\nUuIng/ohiiI/XjrS4rXGBga80XcAyWWlrDgvPSX3oYFd6eDpzAfr91NSJb2leTNjhoQxYWRnVm89\nw6bdMbLHXwtLazPeXzSd+2bcxZaVkbwy81cKcm/P4p9bBU2jlp8+28H7c/7Ew8eRb/58kuBw/RQg\nZeaW8vonm3BztuHtF0bLDgSKosiCDQeorKtn/qShkvMJsioq+CU6inFBwXRybVlj4GRRGpFFaTwa\neBdmhvJqL9rMCHha2DHBpwvr0qPJqml5EQzx86evlzdfnzxOSa20BW1kYMCCB4ZTVdfAu2v3KtLp\ne+7hQfTu4suXv+7nxBn9SIkZGBrw+MsjefPLB8hKL+KZ+7/j8K7W1S78V8lOL+bFh35m4/LjjHuw\nF1/8/pjijkFXU15Zy9wFG1CpBD6fNwFrS2myX1ey4+wldscm8vSw3gS5S1dG+vDoYQwEgVf7tFzc\nJIoiX8cfwMXUigd85SdBtamoyFNB/TFUqfgm/mCL1wqCwNsDBlHX2MjHx/6S/BkBro7MHn0Xh+JS\nWXtCftMQQwMV818cS4C3E299saVVZcdX03dIKItWP42njyMfzV3Nx6+uobJcvsfyX0Sn07FlZSTP\nTPqO3MxS3vziAZ5+bQzGxsqlwa6kplbNyx+sp7C0mo9evQcPBYYlu6SCD9bvp5OPGw8PknZaB3Aw\nPZXdKUk83b2XpK5CB/IuEVOazdPBAzAxkP/929QIOJtZMcO/F9uyzxNXltvi9QH2DjzWpTvrL8YR\nmS29QGd6vy70CfTm082HZUuRAZibGfP5mxNwtLPklQ83kJwuOUO6Rdy9HPji98eY/szdHNl7gcfv\nWchfu8//p9WFWyIrrYi5sxbz/Ufb6NjFhx/XP0ffoa2X2WpG3aDh9U82kZRWyPsvjSUsWH7GY6NW\ny6srdiIg8PHUkZK3AXWNjbxzaD8BdvY81qVlw6HR6fgybj++lg7c591Z9n3CLSAv9mjgXdgZm/PR\n+d2SHvxnuveknbUN8w7sRa2RFlRTqQQWPDAcC1MTXvx9OzX18oVB7W0t+Pqd+zEzMeKF+WtIzZRv\nTK6HgaEBU58YxLernsbJ1YYPX1nNvCeXkpWmP2Pzb6CuVs2ShXt4asIi0pMKePH9+/jghxk4usg7\nrrsR6gYN8z7dzNm4LN54diR3dZN/EgCwcPsxzmXk8fbEu/Gwl147svDkcbIrK/lg8FCMJWQTrk6L\nIrW6mJdCh2CosAakzY2AlZEpszsM4kxJJrtzW04lNjMy4v3BQ0grL+Prk8clf46jtQWfThtJRlGZ\n4viAq7MNCy9nic1+V7+GAMAv0JWv/3iCp14bzaULOTw54Vt+/GT7f36LoNXq2LM5msfGLWTN4r8Y\nOCqcnzfPZtj4LnrNVlQ3aHjzs81Enk3jlSeGMXxAB0Xz7D2XxO+HzzDlrghGdJYmGQYQW5DPr2fP\nMCU0jB4eLWsrlDfU8e3FQ/Ry8mWwm/TPuZo2NwIAE326EGTtwqfn91KnaVlWrF87HyZ16Mgv0VGc\nzWt5G9FMz/bteG5kH3bFJMqWI2umnbs9386fjEol8Pw7q0lMLVA0z/UwMDRg/IO9WbzlBYaN78KW\nlZHMHPUFK346SE2VPOWk2x2dTsex/fE8c/93fPnWBhycrfly2eO8/MEE7B31W4dRV9/A6x9v4kR0\nGnOfHMY4mT0Em0nJL+GtVXsIb+fKK+OkKxapNRrm7t2Fs7kFr/UdIGnMoosHqWqs5/Ww4a0yhreE\nETAQVMyLGEleXQU/JbZ8ZAjwRr+BuFpa8vLeXZL1CAEeGdydIWEBfLn1CMcS0hXdbzsPe759bzLG\nxoY8985qYuOzFc1zI2wdLJn9zj18v+5ZIrr7sfy7/Tw08gv++OHAv94z0Gq0/LX7PM9O/p735/xJ\nY6OG1z+dzNcrnmiVFuD1qKyuZ85764g6n8HrzwxXbAAqaut5bslmTI0N+eKhMZI1AwG+OHGUpNIS\nPh4yHGuTllWG4srzWJkaxRS/bgTaKOuc3EybFBBdr5T4tahN7Mg+z8bBT+Jv3fJxyvGsTKZtXMv0\n8E7MH3i35M+vVTcwY9Eacksr+eP5yfi5KFNpKSiu5MX31pFXVMm7L4ymv8w+9HJIis9lxY8HiDyU\ngImpEUPHdWbMlJ6KW2ffilRV1rF3czRb/owkP6cMD29HHnxiIANHhGFgqP/uw9D0N3xlwQaycst4\nd85oxVoSjRotT/6ykbNpuSx5eqKsCtbI7CymbljDA2ERfDCo5R6IWlHHg4eXkFNbzo4hz2Jt/L9H\nl7d8KfH1jECJuobRexcRYO3Msn4zJeVKLzhyiMVnz/DzmPEM8QuQfA95ZZU8sHAlpkaG/PHcFByt\nlekHlFXU8upHG7mYnMezDw1k0piuN7WqLj25gA3LjnFwxzkaGzSEdfVh+L1d6TskFFPzW6N8Vw6i\nKBIXncHuTWf4a/cF1PWNdOjcjvum30XvQSGyk3PkkJCSz6sfbaRe3ciCV8bTLdxb0TyiKPLW6j1s\nPh3Phw8MZ2w36bGE0rpaRv+5HHMjI7ZMmYaFBPHQP1JOsuDcLj7rdh9jvK6dFXnbGgGAdenRvHV2\nK/M7jWGSb8vpj2qNhvvXriS7qpJtD0zH3Up6pPhCZj6zfliLr7M9S566HwuFNfD16kY++GYHhyKT\nGD8sghdmDcbI6Oa8uZqpKKthz6Zodqw7TV5WKWbmxvQeHEK/oR3p2ifgH1HsVYooiqQk5HFkzwX+\n2n2evOwyzMyNGTgynDGTe+IffHMajl7JoROJfPDtDmyszPhs3gT82ilXPFq06zg/7T3JU8N68fRw\n6bUKoijy+LZNHMnIYP2kBwiVoKCVV1vBmP3f09nei1/6XF9h6LY2AqIo8vDRZVwoz2XL3U/jbt7y\n8UpqWSnjV/1BsKMTf943SZJQQzN/xafy/G9b6O7vxXePjpe1j7sSna6pA82KTacIC3Ln/VfG4Whn\nqWguOTS/SfduOcux/fFUV9ZhYmrU1EK9XyBdevnj6ml/0++jJWqq6jkXlcaZY0mc/OsSRfkVqAxU\ndOrhy+DRnf4xT0ar1fHrqmMs33CSDu3d+OjVe3CwU64itfJoDB9uPMi9PUKZP0meYMmv0VF8ePQw\nb/UfxMOdWq4pEEWRx4+vILokk013P4WXhd11r72tjQBAdk0Z4/f/QCcHL37tM03SD9ssv/Rwpy68\n1V+e8uvm03G8uWoPQ8IC+Gz6aNna8Vey/1gCH323CwszE959cQydQ29+E41mNI1aYk6lEnkogZOH\nEyjKbyrVdnG3pWMXH4LCPAkM9cA30BUT05vnKeh0OnIzS0m+mMulC9nEnc0g+WIeOq0OE1MjuvYJ\noOeAYHoNDMamFQtQLmUVNby/cCenYtMZOySMOY/ejXErmo9uPXORN/7cxcBQP756aKys5+ZUTjZT\nN6xhiF8A348aK+kZX5sezdtnt/JmxEim+vW44bW3vREAWJl6mvdid/BWxCge9JOWD/3e4QMsjT3L\nV8NHMT4oRNY9/fFXNJ9sPsyozsF8+OBw2YpEV5KSUcSbn28hJ7+ch+/vzYwJvW7q3vZaiKJIdnox\nZyNTiD2VSnxM5t9t0lQqAVdPe9r5OeHezgFXDzucXG2wd7LC1t4CS2szzC1MrvtgNqgbqaqsp7Ks\nhtLiKkoKK8nPKSMvu4zstCIyU4tQ1zed2BibGBLU0ZPQLt506R1AcLiX3lJ75XDmfCbvfb2dqpp6\nZs8azHiZ/QKvZndsInOX76C7vyffPXoPJjKMSX51FeNW/YGlsQmbJ0/FSsJpQHZNGeMP/EiYrTtL\n+s5oMV52yxuBkE4dxIsxN04ManZ9okoyWD/oCfxakCKDplTN6RvXca4wnzUTp9BRokpxM83ST2O7\nhvD+lGGtMgS1dQ188fM+dv8VT3iIB289Pwq3m9hZtyVEUaQwr5zki3mkJOSSmVJEZloRBTllfy/Y\nKxEEAWMTQ4yMDVGpBERRRNOopaFBg1bzv/oKKpWAo4s1nj6OePk64xfkin+wG94Bzq1q9d1aGho1\n/LrqGCs3n8bLzZ75L42RLQx6NXvPJTF3+Q7C2rny4+P3YS4j/qLWaJi8fjUppSVsmDSV9g4tn0xp\ndDoeOrKUxMpCNt39JB7mN65jSK5Kpr11+1vbCDiGOIoHIw8RZnPjvm2F9VWM3/8DbmY2rBrwCMYS\niiOKa2u5Z/Uf6HQiGydPxcVS3r78530n+XbncUZ2CmLBg8NlxReuxZ6/4vnil33odCLPzBjAuKER\nqFS3jiafKIqUlVRTXFBJaVEV5aXV1FTVU1Ndj7peQ2OD5u/sSkMjA0xMjDA1N8bK2gwrW3PsHS1x\ncLbG0cW6TRf7tUhIyeejRbtIySxm3NBwnps5ELNWCqDuiE7gjZW7CGvnyg+P3Su5cxA0/dYv7N7B\n1sQEfho9nqH+0k6zvrt4iEUJh/m0272M9bpxDkOdto43zr/N150/v7U1Bl07uIovnn1FrNXUtqiZ\ndiA3QQze8K64IHZni9c2E19UKIZ+v1Act3K5WNPQIHlcM4v3nxI7vvil+NzizWJ9Q6Ps8VeTV1Au\nPv/OavGu+z4Tn31rlZiVW9rqOe9wferrG8Tvlx0W+0/8XBz/6A/i0dPJepl33YlzYthLX4ozv1sj\nVtepZY//OvKY6Lvwc/H709KblZwuShc7bJgvzj29QdL1S9OWiQ+dfOTW1xh0NHGkpKGU1VnrWrx2\nkFsQ0/x6sDzlJHtyLkqaP8TRiYXDRxNXVMjsXdvQyGzDNWtwd964dxAH41J46peNVNWpZY2/Gldn\nG75+535efWoYiWkFzJizlMWrjqFWS890vIM0jkWlMO2F31ix6RQjBoay/OuZiouAmhFFkV/3n+Ld\ntfvoE+TD94/eI/s4eV38BRaePMGEkFCe7HrjoF4zJeoaXjq9Hk8LW96OGNXi9RcrEzhQeIhhLi0n\nHF1JmxgBE5UJw12HcrDwEOfLL7R4/SsdhxJm58686M1kVJdK+oy7/fx5Z8Bg9qel8vbBfbILhh7o\n24mPp47kbFouM79bQ0FFtazxVyMIAmOHhLPim1kM6BXIb2tPMHX2bxw4fulO2bAeSM8u4eUP1vPq\nRxsxMTbim/mTeP2ZEVhZyBcCuRKtTsfHmw6xcMcxRnUO5tuHx2FmLO9k5VB6Gq/v30NfL28WDJZ2\njKgVdbx8ej0VDXV83WMSFkY33nbUamr5JXUxLiYuTPC8V9b9tdnpwPFTJ3gn7j1qNbUs6DgfS6Mb\n791zasuZcOAnXM1s+HPALMwNpVniz48f5fuokzzTvScv9e4r+16PX8rgxd+3YWFqzHePjCfYo3VB\npWaiL2SycMlBUjKKCAv24Mmp/Yjo8M905f03UVxWzdK1J9i67zxmJkbMvL83E0d1xlAPaca16kZe\nXbGDQ3GpPDSgKy+O6Sc7nhOdl8uMTevwtbVj5YTJktuJfx23n58Sj/JB53FM8GlZJ+CX1MUcKz7B\nWx3ewN/S79Y/HWg+IsyoyWB+/AI623bi2YCnWrSQRwuSefz4CoZ7dODL7hMlWVRRFHnjwF5Wx53n\n1bv68YREV+xKLuUW8cyvm6isU/PRgyO4O0x6evKN0Gp1bNt/niVrjlNSVkOvzr48MqUPIQE3P2Pu\ndqesopaVW06zfsdZNFodY4eE8cjkPq1uH9dMbmklz/+2haS8Yl69ZyAP9pXfCjy+qJAH1q/B3syM\nNROn4GQh7d525cQx59Q6Jnp35v0u41q8/mTJab5P+ZHx7mO5z/Me4DY4IrwyT2B73k7WZK3jYZ8Z\nDHRuuYTy18RjfBG3j9kdBvFkkLRSTa1Ox5zdO9iWdIl3BwxmRoR8BZaiympe+G0r5zL7iVp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MgvokOrJzLAh5snjeH6jBQCvPrOI7H3PP8qPMSzO7djRfL41OnckjrG4SVglUbFA1kfUqftYHna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\nIREYYoiLnP8H8rX35TPLmJIAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.plot(orbit3[:, 0], orbit3[:, 1], '-')\n", "plt.scatter(orbit3[0:1, 0], orbit3[0:1, 1])\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "orbit4 = newton(x0, f2, grad2, hess2, max_iter=5)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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5EMiSjC7J6BfR6wohMByTsheBNSO0qt2gbNZb0VrZqlM2656o18k1KgxXM67Qm6fO41Ak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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = X**2 + 10*Y**2\n", "plt.contour(X, Y, Z, 10)\n", "plt.plot(orbit4[:, 0], orbit4[:, 1], '-')\n", "plt.scatter(orbit4[0:1, 0], orbit4[0:1, 1])\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }