{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we initialize our variables:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x,y,z=var('x y z')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we define our function $f$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(x, y, z) |--> x^2 + y^2 - z^2 + 1" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x,y,z)=x^2+y^2-z^2+1\n", "f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we plot $f(x,y,z)=0$. Note that we want to name it something ``manifold_plot`` for example..." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5U1mNIXJJGQiyoCFSi3LayMp7tA1GE/cFIoq/Cw1d8KYyMxakAF8ErOGcQfkS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\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "manifold_plot = implicit_plot3d(f(x,y,z)==0,(x,-5,5),(y,-5,5),(z,-5,5))\n", "show(manifold_plot,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's choose a point $p=(x_0,y_0,z_0)$ at which to compute the tangent space. It's important that $p$ is on our manifold, so we need $f(x_0,y_0,z_0)=0$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0,y0,z0=(0,-sqrt(3),-2)\n", "f(x0,y0,z0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's add it to our plot, so we can see where it is (we add the options ``size=5`` and ``color='black'`` to make it more visible). To do this, we type:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p=point([x0,y0,z0],size=10,color='black')\n", "show(p,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, we'd like to see where it is on our manifold, so we should ask sage to show both the point and the manifold:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5U1mNIXJJGQiyoCFSi3LayMp7tA1GE/cFIoq/Cw1d8KYyMxakAF8ErOGcQfkS\nqm8BoKjhhDOoRM/uVjI1io2adz5I6mKBLVRdKhkueakW3SEjG9gjhRc4mfZSNu3IG7kbnYm/Pre1\nhHrImB7IswruGhYO5E/iScct2gyjEHGLIF2M3BrX+/IK4EqYD6HRgvJEq2KqCQ0wirjEmK/sr0j5\nvl/8zW/+ERoQX/rSl375y1/u3r27hn2omfdo48aN6FasqweZyeO9770H+E8RJ5ri8zWlTJY+GPMJ\niUm/QNw5CEIZ8zFxKlkbWfjHT3EA4LEYUwgKt/BCrPhWboEw5ltWTMngaROFfGlIILzZUMEvvSwX\n01ZcCkvq8rVYhIB0jSBfpjhLJL/rPeGg3FEqkrqifSWJSuWLknsbbpOJEBgiUElVF9wnX5Gge1lB\nogA2/wvKCwGGOLoys5f7oVXxjUj88gWbxNBI5Zidt1Nmdt5DJc+s7KDcLqZw9yT0fSr1Vi0+LK4C\n/zSUeldd1QsNhfHx8W9/+9sbNmy46667MGatIaY6cn/kkUfuvffe22677Z3vfOdUnvfM4vd+7x8t\nKy7eKmI3yi+CsoXuIX4qmtElmCuEYbUcR/MtoeKOluXIPwl5lSXeSKTtvcytFeY0yVoBm9ws1lCo\njnq6ovvzT/SonOisXWVGUhQiWhAf4b+RFXqhLMgoh+iCDPD9I+00OuOTMI2KwyPsj5JnMcgl6JZE\nKdyOzmdKgXzkUXIHAkrFLai3yDeE0pLiIBJzaHlU7kpfQ5XZoZr4HnyqhO1aUE/l+y8EnEYJ3tes\nWfP1r39dqA5r1qyprbB8Sr+lM4APfvCDaEV/8cUXp/jUZwqrVz+O+qb4FirT0/Enio+c+JXl8wxD\nEROHCKDwB+ZT6sqhGeOr+Ui/Q78S7wiBQtqiUC2m9VRHNj8jFafTR/0odzYTuWJUpfjFKsdGBhBM\n5+VwzIt6PRNdimqhUuOgM3v4oqLLDPAdFPGEhrtKxB86qktBBV15xI16GgjyhzwCsMQL+fI1ZldP\nyhjzfVe67QwkT3rUUcFdJSTaPyr++hhWI8UzRlHkUeR1+RRRHhuRVvUVZg8fXs4ZSMxevvB3vOPP\ntbtXR9i+ffuaNWvGx8c3bNgg68mf/OQna9grmHpZpq2tbenSpRi2ozIjj3UNgd27DwAApb5lAWdt\nW9IoMKBjEpV7XIgXkSYFkH01PoCNvzWJrRiXFIAxyqN1wh/kqZSBZExa2AFPqwkvup7jaYvqEY1E\nlIwuqh+6gKNU5aWMqVVodMmF37pIu6S8QLYq4yhXUSHYZ1F8GnygXbX4yK+g2lMxsMpwO6ZRAAAg\nAElEQVTPN1GNU723VfQc8ejM061iFA/4Tn7m492vOHBKZErlj5QYGS0x4W572ElKxRblBqqpBcXx\nwv+TD/DlG6JXtpFeU3wmkLfwm+PrTyH1g4mJiQ0bNmzYsCHSxbd///7a6hNTHbkDAErtAHDjjTfi\nWIeFHRoC73nPPwiGFd85DEzCX3csdyV+CRjFY/pIyKYRcZOwl6iWNkZ5DOtT6lHqYZiDv1sRVSFR\nQPmRVhzoM+ahN4MfojvwQsEdbuNvLUnbIeFhQEjAQRWUCtG0LN9XZF5pZ5WFGWPy2UUjkUF9Bet6\n8BFX4ZXBLOKkIP1pwhcSOcu0fF3i8SxSNVKquEi9Ank7/5IIK63Fhx+9qZNukeURkexl4RgieOBg\nLGJSqzawyaK/vD9jjPp+Qb4ipn2b8Q/Ev416UoGKB1/s7fXX/79QT9i0adP27dtbW1srCS8bN25c\nsaJmBXMQtSzmIIA3aM2aNXWeXC0WwfddnD2E7hE5IGXMo1Ssd4oqqsXJDoSXg0c0xLZlHRyjbzkY\n9+VlNLS3VN4ZgFEKPK8b7CMtlBykKzUpRs+IljOrvLdMM7nL2Vc9KRc8Ouh3j59OoWyq+3A4IUaO\nEER0T7pjRHLKB5/zG17+EyhGeKUSMgA+PwF/6iISKRE+YAMfO1WS5d1TriPCXx+pMolRH4IbGKkp\nKR5/pkl8UGmGarhXqhyP1yXJ78ohqtVdc0OKIF1805QzynE6Y0xWePRPZQtN8DfduXMv1AdwqupJ\nxfT9+/fXXJCoAblXkqLqn+Lf975vQ+B4saVAkkk/i6D2EyZCGfMAYmF+L5tJfL+IjkD0lTPma1YT\nFn5L5XIxlPrCKIlMp0gffDyQNoR4GalEVUv4tcjMpUsiqigfpbr4egKW0ggVJVKxkUyfLLyClaWN\nKOq/uuAjJzYjrwtjZNxNYm0LQBZqgmKc0oAk/jpE1ovlm8Ai6pRFDlryUYFurmhEWvuEsZIYoqQn\nD6UPNMzLEVUNwm/D5yDg+wqzl+RrF8+jUveVMjWhJKpinFeYndKidAk4OwwDeXrFFTcdOPAjqB2q\nizB1iBr43MfHx2ESxRk2bdo0f/78urqP73znBkGm0sSlmGIsEZSKP07bDnw1eKflnbmzJfjlWFYs\nPAtJrhiDdGbL/M4rjvE9mGqD0Xz0EGV711fvi9wHT8GknoSgL+XBn2+A03HQZ1kPwWmopDxttaxs\nVChUoLKP9JElHy53gpO+rz1nCIaqJKDL4kOwUdGv8YVCcME1B9wEgt+5Iqec6CTzSAGIniOtUF09\nFMtT6mqdD63hp49JlLr8kjGG0Mv2uiLoVrqq94q/FcqPUttAVL4k3H1Q1gaF8Aj8Zr78cs3MhWvW\nrFm5cuXka1ht37695txVA809k8mI+jBVcMMNN/T09NSVHE+ph19l+WmYUs/zCoqpi79gKBpSqi5U\nL3YIt1/C1FZUGqos6QCUzZdhnUGEaXJAysJbPGGTEE/3CuHKzyLiKvh1iUcK3djnKyq22JlTqlgB\nyhYiMn4DJbIIXBzcOR6owOK/KmJ6ZY5m/FaAYhGReSfqQH12EkRF2RExNZdxCCG2ZeGQHPwFNdFc\nZXb9FNwiWZaqKliSmLhGfgOrCPREzxyEzTn4OChyDD5jPorp4lzK4UqvpBSRz4Ifg87sZR1GSkUE\neSPJ+e4DwHe+8zhMLTZt2oQUtGHDhlOqTlhzZoeakDtIOdXqEPmKNWvWbNq06Sx36iT41a+KIlRh\nzBMREJIOT3Lid1E3/zI+2U8OnUJ8jVt4pEO5mVLxnxEAGmZeZX0JNdiUHorLkioEcS7KQbK6LdK5\ngt+p4lET++i3iPcTw3DRuOBxkGo6RhwdxdrykCkOjNxTlRfe5kciYAyzlVLPS3hP9UbkexgQLo6s\nECRIiTbSBHvq3nwpei2nIqWBFiAUQZPIgSScVg0yB+FLpqIYA49LihhqyANk6IgoDwzeNMZ83y+G\ngx61DgF36aAMVeZxSku+n5c7hgPAzp0vwVQhm82uXbv2hhtuOA2vep2EpHWRUD0pBMXj8ng1WTDl\n1lu/xd3c+PX1fZ+KZZXwV8EYSD/gskzBJ6aKDJhv23H+KwIAP2pn8dYlJIazkyQ1I+SklORpWWon\nIjIV1WMIwYgyJg0JhFJf0X+4UVJkCwDAC8s1RMu+AgAlxJGEb8bvjCU3Lp4MJKIMJOZKM1R5O+XN\nWkAdWNEr1HZnivQUHMNnSOoWlLCAwwTl8esVewrKC3WJRU3oDXceb68X7hhTlFIStdy2NnsoUIFI\nMCUqdDrZsiVa5aem0h+LoCDDyi5eJfGri+l60ZiAo3HOE4RAw39uN8z7vvQUFToRN4YxAFi6dCGc\nfeBSP7fffvvtt98+Bac7e6gNua9YsWJ8fPxUs8lI8RMTE2vXrp36dc2XLLli9+4D3HIusl4lfEsI\nEeYTxhhjJcticgUuhYIp9QkR+4NCO1qOUbZ++4xRiwv+eDbLItKvWE6cEtFaONdKeU4YeJfKsjhH\nObJkDDupUCoBAFyWRCI7H13/4WsRw1KZaCzLFiQCwCp5bHS+k+5JueyM2EFPz4oRhQ+QomPlRxw5\nyhakpgg4YnZSqOlQOCzuT+RjTagyIv9TqqMUpSVl3pkSX0dtYUItFP9K0jkeEpSMF7Qbtcxe6Ko1\n7lbnKGmHhwYhpZNiHA373+VPKX6RpJoEDB+IcRfG2I4dewDO4praO3bs2L9//8qVK6eYW84SaiPL\nXH311ZOR3SPR2tqKI+ratWvXrl2bzWbPaNeqgPDHw/KECyFZiOl8Ym/hRud7qsEX/3n7jHm+Xwx/\nqkiZgobKFgV8EZyKllD24fq+x7X7wIEuslX8X48LPsGUVG6BUHrIr5yIXx1wScESqVqZ77huUEXq\nLV8jFzRCKq2+p545lG+LSAlENqJHuNKxuoE9eKELJpH+RW04BCn8VPaskrAt69ThqRIWL46mzAjT\nu6GXQFB89CJrAhCl/ADn+krMHpb7xEMMSjcepZ6UZS23Jr+VvpChxhmjvu/ygQGHaZ/SkuflPC/n\n+0XGSoyh+E6XLn0HnB3cf//9a9euXbZs2fXXX/82mX379u11Us62ZrLMJGX3SmhpaUGK37RpU09P\nT09Pz9kebBcvnrdr1z4Ivo5Fy3J43B143dD7LHs8OM2hH8Cm1MMwX3wqG8Z9v2BZMWGe4eJMOTUq\niy2aRV2O1gPViJ8rGAC41TI6wsVDKhQCw5OKSF7OmornlXLgz8K10kQHlEiC90eBzlz4nM6IJqqI\nXSTRCWNw0WfKWbIcIPNLKLvalV5pOWEi8bWqvei9EfYP7Sr069KvOpQvgTIPisGG+b5a/TF8CaJA\njd4INqQPwEzvc1RkDVzoA01MV4Sj0KUhd4eHjSAZi85ITv2KkycCN9985if033///X19fWdQgenr\n66uHbCo0iuZeBbhc6o4dOx555JGzuhw2pZ7vFyWt3EdaYawsiTDGcJaTxLNCe8GYhYmKY0yt4FgW\ncPl0RFkrYJIQQfAHqa28ESAsgwg2V8k0it/VuomW5SiSRWQVAQXh3UKCsugM/qto/byf5buH6UeU\nLzT/pT7IKQwFfETBwSmiz5pQEyHN8y6FspFIWNrYEOj7ssShPJ1A1NMGhArCCB5UC7tLGpd4aolY\naU97cgqlCqI4NPR314s7ysOb1nn18UV6isXEO6PUte2E645TWmSM8upJp4ydO3/3oQ9dchoHRmLt\n2rUAcMaF9bcZtp5B1Izcz+zc3GXLli1btgwT3D09Pddff/0ZbBzxpS/93g9/+BBKooTEkL+kmYrl\nSTeUlgihYlW8MDn6vAWLZzJtifI8LPEo0kqExERdGsH7+FaPZxnz5JVXw7F/ECspUr6my2GuNaK8\niXQWQb5UYg29HTnAD0YOLvSH5BF8npAr83BCp1rCNtwRbtCMLC9TqewMcpPWIJEaVEc4WZ0X/eHs\nrT4/aVetjH+Cf5VwWzYRUukFkQ6kEnEHz1KUMnHTIOBlVcTnfca3anq2csEvAJDl++CKtAmuPlf5\nSxAE9V6xeMKyYq47AmcUZ4rZMVpfu3ZtOp0+Iw3WJ2pG7ldfffXGjRvP7ExU1GpQPjsbFL9kSc/u\n3ajMlAixKA1cK/jziMWS2qOusH/YEr97ADGR5Aw7VQS/l3eWrRMQolHC1DmoesiplDOLCN7DmVUi\nRf3BDkowKz3RM2mLyu96TA1lmkPJXlwRCY8xsgyigEoJ6sjsqziRz/ugFlDTGLyc45V3k/w8ESfS\nFowWVycbfhhwC4p0aaCFuoLu1VPwZyl5DqqefSVSI6r5XaSaK8zR1TtTXsGDv1UmlHq+7+LGbPaw\nZTml0gQAhFcdqV/s3LnzLAV/dYharsR0GoaZUwKOzytXrly6dOmZavMd7/hzHk0jMdnohuQ/Icuy\n4uL3JiapW5YtU7ZcbZEQosxxVdbOVhYtQjlb7IAt4yf4K5VlfQgUnlB0qe1gy9YafQfgs2pl3Vlb\nz0+tMo8t84HBwmiURZWJ53tKXaxQMJJvJDqLKV4gWamQRkrQLOQRa1lAmQqJsh2CYFnUXAup85GF\nlEUsL4nOrjRmYLitLGUHTFvujie9lQm3iiNFWXpJFG2PaFZ0BspjGMP9fb9o24lCYYAx5rqjlLpI\n6JYV97xxqBH+6Z/ueDuR+9l7ppcxMTFRE6N2JGpJ7lNTzH7nzp0PP/zwmXoEw9LSyOm4hRDLthPi\nNnIeF3N2yjlM206KX7jskoSg8IDFSV+l13BqFAgpf0oIQRFfznyGhwpLW1LDlsI9QkioQekQ4BE0\nZlLLuV8I6DhUDVgZRfCkfB0SFmZblbXlojqS1EOi3FyVvq7BM4cmcMsZEdXxwg+JWF4DNGVcYmd9\njVPCWCnKTeNFbVRNhLpVCd1NykkVGxKlRVmiAW6IlN564fEYPK+Ab1131PPyhcKgbSdddxQAYrFk\nPn/M9wtQr3j11S2nd+DU0Dpi06ZNmAWsB9QyoTp//vwpOMvSpUuXLl2KFP/2/8aUliwrxpgvUqOM\nUc8rWBbGv4TXeQ/YkBAQVVMoLfI1sjFZCiLk5/Gdzz3IJDyPSajnwo5iC1mDUldZSA9zvADC9BYq\nws6YR0icf4oSBModQrLwlVQtzzTKcn+o9Dnhk92ljQyARVVPjDQ1ypab8lk1Zz2rHNQzaeKMfkYi\nBArlGEKCo3RVXzYUyinlqFMrJZrROapuFPyr1XcjqAMJ8Vpjdk9jdnmAQQdL2aHreXnfz7numG2n\nxsZeicVSxeIwdtR1T2j9bwAsXXrlqR6Sz+dvv/12xthUzkXq6+ubsnOdFLUkd1ySaWqAFA9v2/m0\nb9/3V626a8+elwHA9wvcEIksFkSvSFX41IxCDQ/uGFcnKM8iBpKOcCJyri8xRm3bkYkSQNgkqDBB\nI5QcoJhaJUYOQmTyssSsV4SoYyw16CvxfpRMTPkYQIQtRHoIEGyrrPgR8sPIGzVSVoV7iVhZVFAf\nyezBgZWeUNHaoSds5QLlok3G1Lg7svNEWw8LoDxRgF8XkfUlEowgRBq9yikNuX3Py5ZKWdcdicVa\nHCd94kQfAExMvMEY8/1c5DU2OpYuvfKnP/3GKR2ybt06ALjtttvOTo8aA7WUZaB2TzHr1q3r6elZ\ntWrV6R3e0/MnKFUTvsIcFy6EEB+TGY2Xe0TNpFzG3bIcWYvXtRpZEgmr9qq2rrCzItzz/SsejtJ/\neIulVFoPt4kdi2m0KJyL5QOjdHYiNy4xmkqykjgTIuiwBFSmb2nKD1Haj+J9JlUhJhqfKh1RFzDC\n7ZL2XZaAKC2rNEIUCs9RCnYTf3wAKJXGKfVisXQ+fyyXOzo29koqNTufP4JNOU7L+PjvtA40PyYv\nyOzatevhhx+Gc57WETX2udfqKQb/9g888ABmXK+66qpTOvyee9b/6Z9+k9cAwOgYLAswSmXM931f\nVthxggbSpWSPIZSWRLyPUZvsXUEzjGQ+K9l2QlCwkDLwrea6UVaMEyqN2L8UnlGlm+5D1eeR+8L8\ni2GsqCLAMLSVzZ1SZ1SLOgb1cvKzgsGGWRaRjCjCP17W7rnGJa5UTqIyyVCoetgp9cJuS7lBeTVB\nIZ1Z0lNU0OfwdFDGGMGZ9LzZ4IXrjjJGS6XxXO6I42TS6e6BgR3Z7FvoNiEESqWIXGU+f1S8LtSv\nHn4WcfPNk9JR8/l8zWm9Hsr8yqhx5F7zBcKBUzwArF27NpVKTfKop58+/Kd/+k0kMiHOAFiW5YSt\nLEFlMR7XMx7Xl/OTUm7WRiuO7B8Ph6g2j0wtXgagvDyTZowhIvbHBvF5Qs5YytF6VPAux+Yk6hTA\nLy0UqhOiOmciTTJRcbpI/xKRVKjkZBd0r+vglW0wROJlpcRjcJlRWVDA7ChXxgK47mgslnTd0YmJ\nt1pazgeAUmnsrbf+PZ3uzmYPx+OZbPYwbozqvMGkMJmwvU5EmLqyykDNyb2uxrpdu3YBQE9PzyQp\nft68PybERmWcR99oESmvuYF8ynWVsupi2wlFt5Fex+UEqSa/lG0qhFhc/xHCjmqjFC3jdCH5LUTQ\nvep4iZJ3yhOjhJyika+8jhI2JfttQDi4sX2uqIj4WjazU95ghJiOc5307UK/rsT7Wt3HcsfGx1+L\nx9sBwHVH4vH24eGXWlvnHjr0ry0t58fj095884lZs9577NhzAOA400ql0aizG5wBnFRqRxHmNJ68\nzxLqIVSVUWNyh/ob7jAKmGQU/5nP3Llz528tK8ZrQ6JjnXEhHjkdnS2WstASxvtCYQiTcky2MEqF\nJwOClp2XEtcTAGLbCf4OV0AVRYkDm3lYzSBy6hXKpsxK6rxsmwFtH9nvqIgzjD9GWOFQ2tZZWyqB\nKe8ZochH5mbFEZiHxHmS8Xj7xMTrADA+/sbExOutrRfiazQCInAHgzpBlZi9UCjcdttt9UPriLry\nQUI9kHu93RGBdevWTebbc+edj9933z8TErMsh5AyLyOPY3CKjB/F78Fa2/wQhd9RBCCWFQsH4LYs\n3eipVKHp4xAS1uKZWPYvfCLgh5AKbM6E+qycEUJPDOLrZEl+TeEmtCAs1ygRvdwNRerBboyPv+66\nI5nMRQAwNvZaJjPXdUddd3RoaE883h6Pt2O4/cYbjwIAvtUaN6h3VJmvhLQOdSDCKJiYmACAuopT\na0/u9fYso2Ayct53vvPYD37wvywrZllxLn1YwvmO0bFE3JZtx3k1V5AWXA3p9XxOU8Chmq8mJqUx\nwbbjssggapNxLpbZHPsj2JnwMUYO/y2FqXU2j5rFKm8h2CvxngssVjb7VmvrhRMTh+LxaRMThzo6\nFpZK4wDkyJFfip1dd2Ri4g0k6+HhPYajzyns3LmlvT36o3Xr1l133XVLliyZ2h5NCjt27Dh7VQtP\nD7Un97qS3SNRKBS2bt0KAFWskyMjsHTppyGQFCzGqG0nYrG0bScY81CiicXSnC6FVm7JoavO73JU\nK8+JlSsWKGI67qJE35oPUgn2rShjpRxlE9/PO05bqTTmuuO53OH29t7R0QPTp/ceO/Y8AGSzhwmB\nlpYLT5zY29p6wcTEm62tF8Tj7SdO/BZDacPOBidFJZF99+7dW7durVtaR9RhkFp7cq/Dm1IJGMX3\n9vZ+9rOfjdzhjjv+5Qc/uL9KCzjHx7JiWNsdZ51YVjwWawUAx2mh1HOczMTEG7adaGk5r1TKAoDv\nF1KpmSjgcAV5WqEwkEjMSCQ6isXhYnG4vf2KYnG4UBiKxYIqC6OjB9rbe/hba2LijVisxfOynpdN\npWbl88c9byKTuQRZ3vNy+fyRWCzjOK2l0kQNS4gYnJuIZHak9XXr1iWTyZr0avKoQ3m59uQOdXlf\nqmDz5s379u2rJNSclN8NDAwU3Hzz9X/1V59QNtazCKOj3owhUCfk3kDBu4x169YRQr71rW/pH116\n6X8FOJ3lCAwMzinEYi0HDvxY3lIsFm+77bZ169YlEokadeqUUZ/haV2Qe33emkli9+7dOAdK0Wqe\nfPL1m2/+ao06ZWDQAFByp7t370bfeqNE6wJ1mE2FOiH3JsDmzZv7+vp6enoUir/88lV6tW4Dg3Mc\n73zn1T/84ddEEe5vfOMbANBY0bqMtWvXTmXtyUmiXsi9DhWr0wB+RwFA1mr+/u+fuPfe/79GPTIw\nqDdYv/71P4vfOkZFkdpmA6E+tYd6Iff6vDunBxQNIRyJzJ//+VIpa4R4g3MWsVgmleras+cOfLtn\nz56tW7c2Oq0jstlsS0tLrXuhol7IvUFzqtWBgfx11123ePFiANi2rf+WW/6H7xcpPSfr+xmcq7Cs\nhG0nr7nm2h/+8Abgv4vmoHWoV2aH+iH3ZorcFTz44IP79u3r7e39zGc+AwDz53+BMZ9S12jxBk0P\n204nk52EkF//+u9d1926deu+ffu+8Y1vxOPxkx/cIKhb7qoXcj8XgAHLrFmXHjgw9vOf78DCkLj+\nmYFBM8GyEi0t53lezrZT73nPNd///icwxBFPsc2E+symQl2Re90+3ZxB7Nmzp6+vb9++fc8889qx\nYw5jNB6fxphXKAzUumsGBmcG6XR3KjXb9wuxWOojH7lkxYp5WDyg+WgdYSL3k6Nu79HZwIMPPvjk\nk9s2b37swgv/gNKiZcVtO4m1AWrdNQOD04HjTEsmZ+BiYa472tkZv+KKUmdnSgiSzYq6jUrriNzr\n9unm7MF13U9+8r/s2vXbROKKZLLTtpNYptF1xxjTl+s0MKg7WFYymewEYOn0bNtOMkZHRw8sXWpf\ndNGMT33qU4sWLap1B88u7r///uuvn9RCgFOPGq+heo4jHo8/8cQjAHDZZYuPHt3f2npRKtVlWQ4S\nfbE4GLmupoFBzZFKzY7H23y/aNsJ2045TitjNJs9HIvtuOaa+X/2Z19selpH1GoV6Mmgjsh9/vz5\n9TmLdwrwyit7fvWrXR/60B+OjPTFYumurmWO0wpgZTKXYsHefH7AdU3q1aDGsO1kOj2nre3ysbFX\nfb8Uj7c7TsZ1Rw8demJs7NVVq1bccss/niO0jujp6al1FyqijmQZqNcSDVOJ229/YMOGrxFCEonO\n6dN7YrEUY5BItBNi23YSgOVyRz0vZ0Qbg6lEJnMxY5DJzB0Z2R+LpWOxVDLZyRhz3dE33/xZLndk\nzpwZd9214SMf+VCte2pQRn2R+zkou0di3rwbjx37le/nk8mu6dMXUFqKxVoIgVRqlm0nAYBSz/Ny\n2eyhWvfUoGmRSs3x/UI6PTudPq9QGPD9IqWu47TF49MwLTQ2dvDo0ecYY7/4xSPveteVte6vgYo6\nkmUMBF5+eeP119/11FOPAMCRI88AkNbW87u63lkqZUulCcb8VGpWPN4Wj7+DENv389nsYUpLZlaU\nwdtEPD7dtpOJxPRUapZtJyYmDvl+MZt907LiLS3djFFcsvzIkV+Ojb3iumNr1vzdX//1p2vd65qh\nbn0yiPqK3A1kfPe7T953309LpYlicaRYHM5mD7e2XpjJzLXtJCFWPN7u+0XHabHtJC6S57ojxeKI\nZcVdd4TSYq27b9AwsO1UZ+dV8Xg7ADDmlUrZsbFXMEeayVwMwBhjAKxUmjh06PFcrp8x1tGx8MEH\nN7/nPemTNt7EqHOloe7Ivc4Hw6lHb+8tuCaq644OD79UKAw5Tktn51XJ5ExCwHXHCIklkx2W5dg2\nFikjAMz3i6VS1vMmSqUJE9EbKEgkOmw7lU7Pse0Ecjqlbqk07rpjAGBZTio1E4N0XEfXdcdfffV/\nAbBSaTyTufirX/3Gl770+7W8gPqAIfdTQ53fr5ogl4Nly/4U186m1B0a+nU2+xYAdHYuzWQusqy4\n5+VKpbFYrDWRmB6LBatN4qrc+LpYHM7ljgIQszjquQnbTrW0nAcA6XR3IjEdABjz8befyx2ZmHgj\nkZieSEyPxVptO44f4ULtExNv5nJHjhx5JhZrOf/8DyWTXS+88Fe1vRaDScJo7g2AdBr27bu3t/eL\nlhW3LGfmzHcVi/Oy2TcHB3cODu5sb+9ta7s4k7nIdUcLheO+7zpOazLZaVnAGCXEJsRKJDoSiQ4A\nACCWFSsUhnK5fsuKU+qWSmM1vjyDs4CWlvM9L2/bqVgs1dZ2CebhOVixODox8Qa+bmu7LB6fZttB\nJS/GKIBFCHPdsYGB7YODuwDYrFnXdHS843Of+9gXv1i/zr8pRv1rDHUXudf/LashfvnL47fc8k2U\nX0QqNZt9q1AYBCAzZ74rk7mIENvzsp6XIyRmWbFkstO2EyKERyDj42vfdwGgWBwqlSYAoFA4PuWX\nZXAGkEjMAIBEoqOl5fxYLGXbKQAAoCiX4z6l0nihMJjPDzhOJp2e7TgZxnwABkAIsRjzRcq0v/+p\nwcHdAHDBBR+JxVKJxAwTsCuof42h7sh9x44dPT09ht+roKfnZstyLMuxLHzwIr5fPHz4F56Xi8Va\nU6mZ3d3vBwAA5nnZfH7AsmKJRAfakwEINkJIjBAQbwGAEAvHAN8v4r/Z7FuuO2aqz9chbDvt+7m2\ntnktLecVi8NtbZdyBifSv5Qx6vvFUmm8UBgqFAZbWy9MJjssK4E7c1UdGKPI8qXSxCuvPFgqjTtO\n6+zZ721ru9T3i4zRF1/8ei2usq5hyP10UM/lGuoHN954z65dfZblICNjMP7WWz/3vJzn5R2n5cIL\n/8BxphFilUoThcIApV4slrIsx3Ey8XgbAKBEE26VWJYtMT5BFiiVsrFY0nVHAWBi4hAA+H7B9w3p\nTwUSic5YLAUAsVi6o2Nh+EP8+VLlV8yY7/vFYnEIaT2TuSiZ7AIghBD84zJGASgeL2i9r+8+PPyC\nCz7S1nYJY5RS96abPmGkmEjUP00Zcm9gPPfc8Be/uI4Qm0fxlmXFxsdfHxnpKxSGACCTuWj69AXp\n9BwUYYrFEd8veF7WsmLx+PREogOA4YG8SSbxuxzUA4BFiAVACN+MAf7ExCHfd2qCKNMAACAASURB\nVG076bojvl/w/fxU3oFmQkvLhTiUtrZe4Hn5adPmSR8ySV1h0lZgrLxwI6VF3y+Ojb0GwJLJGYlE\nBzdQgfwz51IMBuwslzs8OvrywMAux2mdNu3yjo6FsVia0tLnP//Jm2++4ixecCNj586dS5curXUv\nToJ6TKjWcy2eusJ739uxd+89CxasZszyfWpZMd+nra0XZjIXAbDx8TdGRg4cOvR4JnNxR8dCx2lN\nJNrxQJRcCoUBx8nYdjKZnCGJ8oxSjxBCSEzwO4aHAIwQm7FgIxLHtGmXA4DYmRDwvAIA+H7BdUfi\n8fahoT0AkE7PyeWO2HbSdU9M2f2pN9h2OpmckUx2el7O83KxWBoZPBZLAzDGqEiEyCMrfoQv5E1C\nVCmVxrLZ/kJhEAAcp7Wj40pCCKfv8m4g0ToAMEZHRvYfOvQ4ALS1XTpnzvva2i7FEheM+UZhr46+\nvr76J/d6jNwbYlSsK/zjP267776fWlacEIsQS2g1AGR09EA+PzA+/loqNWvWrHenUrPwEFTYKfXy\n+eOl0phlOa2tF6IbR8SJPO8qEw1w3hdvxQs13gcApBLslbzV8wq53JFYLDk29rtEYnos1jI29gqm\nAXO5w2f25kwBUAFPJDoBIJmcMTHxZnv7FQCktfVCAIjFUp6XR96s0ECIggUwyantGmhihcIgErpt\nJ9rbexjzRZwOZb1FIMisMsYIIdnsW6+88iAApFKzZsxY3NZ2KWM+AGHM+8///KplgUF11L/gDvVJ\n7ganhwULViO/IwNbVhxVFEJivl/s7386nz8OADNmLEwmZ7a1XQIAloURN8nnj1mWk88fx1RtOj0H\nw0n0URBC5K8JIYRTubwR/488rnypMKhXKV4GTrIVECpEsXgCydH3i62t53tefnj4JdtOtbScPzZ2\nMJGYUSwOAUA2+1Zb2+XF4nAslva8XDI5o1AY8rx8a+v5hcIQbvS8kGTU2nqB+AgAPC+HW/DYZHIG\n7t/Scj4hUCgM45b29is8L1coDGIAjqXMZUdK6JYE18uifmUigpaPFRvxdXAgamG+7xYKg9nsYQCW\nSs20rHhLy/kAgInT8N3zpTPiyMHwrzAysr+//6lSaTyVmj179nvT6dmC9H2/YBKnk4Qh99OHkd1P\nD88+O3DLLestK2ZZDrI2CuiEEMtyPC9/4sTeEyf2ApBUaub06e9oa7tETqtS6gFAoXDcdceR4i3L\nicXSlhXMh5K+LRSA8OcDJlKvILluoqCncKXPygNG9HeSEAvAIiTiI/lrTIhNIncq7xkYS6oMNnxf\ncVFETkiGd6j2C2KM8gMjexIRsAu2FbNGKXULhcFEYoZtJ5LJTsfJYIOK6gIAPEKnjAEhoZFjZOTA\nG2/8CwC0tV2eTs+aMWMJ7x7z/cKSJVd8//srqt4NgzIagqDqlNwbYmCsTzz33NDNN6/jXsnASMNj\nZxu39Pc/UygMel42lZrZ0bEwk7lYcUb6vsuY57pjrjsai6Uty8lk5kZRNiHEFsTFpXn8IFaJYWWX\nPT9QpApJ9QAfe4hXAVKEKz6SOqZqRISQKPUjkuIjY23eLt8/UkuRmqAa71vinmif4uhoYUZ6aGiP\n47QVCgOO0xaPt2Uyl2j6DFPEHE70TIwlYvAYGTmA0brjZK644ibGKD6KMeZRWqLUe/75rxsp5pSQ\ny+XS6Xqvq1On5N4QA2M94667nvnBD36KLhoeSlsAgCoN/vgHBnYUCoOo1XR0LOzouJJbJAGVWZwn\nZVnOxMRbqF2kUjOx8Ih8rsqhekD9EneHPtI2yg2qWr+yC8jGnUo7EStsBIo+HQBwNQmq0HpU+9Ed\nQJ4lBMJaFnZbKC3y4wUBgImJN7PZQ5aVAIC2tksBIB7PRDkdMVMa4nqtz4HgPjCwo7//aQCWTnfP\nmXNtKjULRwVKPUo9AHrTTZ8wlphTRaOEnnVK7rlcDgDqf2yscyxYcKtlxTBytywbVXgImCXYx/fd\nN974V1yYO5WadcEFH3GcVuB8QQgRSgilpVzuqOuOEUJisZZYLI3lShBcvldAuEAvA9tmepCOIgZP\nw9oSfxLpQKiUp62AYFSrDsaAm0yqtKnqMGIQIoTgiIjRNCEWvg13PnSs7xdPnNhHCHHdMduOZzKX\nxuMZLSkqYnNZQ2f81PheVtgDD/vAwI6RkQO5XD8Au/LKrwJQSkuYZcUAnzH/V7/62klvi4EOQ+5v\nFyZ4PyN49tmB1atvw8gUjS7IwspkJd8vnDixd2zsd56XTaVmz5ixKJ2ejSwPXGMRAXihMEiph5nM\nWKwlHm+3LCeRaOehegRhWFaMSyhqGjacmxUvhCxOON0TbvYIImIeC8sKjDKXh4kzSqMU4eSI+wAX\ndkQLlqSwB/V5oLIIg7sRYuuGxXBPIJ8/TmnRdcdKpbGWlvNdd6yl5TzHaVWUfQjmGWFszuRxQpP4\nGaUhS0yxODo4uGNgYAcATJs2b+7cj6H8ggMA9pAx/6abPnbzzfMjL8fgpGgUaqpfcm+U4bEhcNdd\nz9x330NYV5KnJS101GAAyBgjxPb9XD5/fGzsd+PjrwGQtrZLZ8++hlO8JZRuDsKYVygMYW1hy4pn\nMnMtK27bSaQpOcqGCPVGniSlR/cgse1JM59C5ZBjZH0fkOQgqLInhDKoOqWqkAT08lEA4Lpjvl/k\nBd2Ktp1IJruSyU6Uv6LSoeVe8TEDL5ww5injYjhgp5R6R448g7SeTs+ZM+f30+k5vFZMMGWJUo/S\nkrHEvB00kFG7HicxIep55dmGw5e+dO2OHS/t2rXfsmKWFScE03Hg+0VCbHSwMObZdqqt7dJM5pLh\n4d8cP/782NgrKNd0dFw5bdpllNJwLpQRYuP0V993XXcknx903RE06iUSM2KxkKomiExX2xkDAC8c\nwocMgnyCT0WKZ8xnDLhrU0lUymdhjHlSPrZiRjRQjvjAVGk3rREGwCYm3ioWh1x31HHabDsRj7e1\nt/c4Tlu4J1SI7wBMmE3Rby7lXVmU01HkToO4vr//qWy2P5frnzZtXmfnknR6DgBQ6uMOlJawlsDn\nP/9JE7C/TTz88MONQu71G7k30AjZQLjxxnt27tyLk5W4wZExBpblCELhNkrI548fPvwfPJU6a/bs\n30ulZhIS0+JoIgvuudxh3y+57ggAaW29wHFaxdwoAOCnqxRVMN1BHzqT5rQRB0qPCNVa4DuD7F2J\n3Cdsr9QTvIwxhgWTs9nDAOD7Rd8vxuOZlpbzhdgiPQGg9E8ije0AQTEArRN+eB9hcwxuwuuvPzoy\n0gcAmDJNp2eJ3QAIYyi1+4yxF174WtV7YjApNBAv1S+5Q0PdxwbCj3/8izvvfJR74S2ecUUmikkU\nHxT49rxsPn+8v/8pfDt37ifS6dk6yXLVpcyAlJZcdySfH6C05Dit6fSsUmkCJ22Kc/GvH+XaN2Cw\nWSVID0+hopHf3wo6D+g6DAb74QCfaSp8AN93keUHB3elUp3I6S0tFySTnSijixZEAQD5VBAo+OqI\noukzgYoitUAwVSt3fmRk/+HDT5ZKY+l0d1fX0ra2S7leT/E5hlIXG7nppo8bS8yZQkOYIBF1Te6N\nkrhoOBw9OvzlL9/329/2owaN/I6yNSExwWtyPE6Inc8fO378+Xz+GG6ZN++PJalB5D8jbJFiCW9c\nSAQAUqlZuB5QlQlHmlNetsoQACoonjMmk1OvACAZHIGbuyO1eCJkfYl8g1OXSuP5/HHXHaO06Psu\njnktLeclEu22nZTNLVAOmSNAqS86IGWJxVFqKjhslGQ4vwz7AwB7994NwNLp7ssu+6wYijBO5zsz\nAPje975y1VVgPOxnEIbczwxMTvWs4i/+4v/793/fQwiG8FhJJob2Fa7MBOG8OMSybM8rvPbaVq7F\nL2pvn48Kr0wxSi0B/BQ35vPH8vljvu/adjwen+44rcnkjEquds3wzqQAP9glnObVg2LKpx2dRKjB\nGaG4xkWpNHbixD4se2nbCcdpw4Lp4mmGXy+xLJs7IEO0Hv5V6XpLKDbnFSMsaaMYpUC2xPT3Pzky\nst91x9rbr+jsXNbS0k2pz4v3Up5iZYwx3y/cc8/Xly2retEGp4gGYnYw5H6O48c//sUddzxk23HL\niqM4gxWACQFCHBH22nZc/p7gkmyvvfYwRvHp9JzZs38/nZ7NPyecBxlnsUBvkbnY90uuewKJPpmc\nYVmJdHq2EggHzZ1sQhOXVkKIMqSrpQtcd9z3C7YdP3GiTywjblmJVKorHp+G6VDeWHXDDPpbInV5\nVV3hH1Bt54jEKQ4MIyP7S6Xx/v6nAcBxMt3d729vv4I71kG8QFMNxu8vvPDXlXtrcJpoLEaqa3KH\nRhsqGxFHj574+c933nnno4TYlpXAOJeQICAVyVVRugA4WWNSdGjopeHhl0qliXg8M2PGkhkzFpfn\nHQWriARmPnFGefIRNlUsDnteNpc75jit8XgmFmtNJjugPCqoRykNitNp6coQfN/N5foJsTAkLxQG\nLCtu2wnbTqTT3fgi3KCFDyJV7p5eRUA8KIispmLDj0qcMq2dwOmYy/X39z9dKo277nh7+zyM1nEu\nkhhycFyh1MXcqaH1swdD7mcSjXU3Gxc/+9nOO+746eBgQYjvfDor4xoLAR6zI0ROtVSaYIwdPvzv\n+fxxx8nMnv1eAGhru0zM7okkZX1GK6Wu77sTE4dsO1EsDltW3HFacLVPaZrPSWelEqTvUmkc1yGy\n7bjrjuNn8XjGshK2HQcgWBezEqS0qnxG4d8vB+MA6vRXTJCGjerl7cp5OLMrp4ZSaby//6kTJ4K1\nDRYt+kt+lzzugKR8rmlgiVmyZP6993686s0xeFtoLIuHIXeDMo4eHV616rvHj4+h/i4iWZ4mDeYT\nyUZGHAyQ48bGXnnrrZ/j5ra2y6ZNu6yt7TJxuKacEKlZAClOJ4QUiyOEWOPjr6NagiF2JjM3FmuV\nc7al0rjvF32/UCqNW5aTyx21LIfSEva8peV82074fqGl5XyRD+CnYoRYYpquqKUlZqXyTgrhuyz+\nRGZNWfkioucl4dmVm4Cudjm6x5B87967XXcMALq7l6fT3Riti8aFdV3wO6WecTqebTRcTZR6J3dj\nmJliHD06/Hd/989PPvmyWGzPsmJS3QLAcD5sZSGc4gEA8vmjpVL22LH/UyplHad12rTLZs9+H5TT\nhqIGixyMR9gW0c5IaQn9IbncUVy4ORZr8bwcpS4APl5AMjkDACh1LSueTHbyxws5Gcs03zoJzwKV\nCz2eVFsvFwkIfxRdfiBc5IvwpwEcJERpBMIYPXFib6k0fvjwkwDgOJmenpt5g0Q2vGOVGN5bumjR\nxd///srKfTY4M2issB3qn9yN5l4T/N3f/XTTpmcsK27bcQgmFmGW1ZZo3RIzQpGIJY4mnjcxNPTr\nfP54LncEAKZNu3z27Pc5TsaysD4lcpMv2E0+Vu6JbJih1B0Y2BGLpTo6FhWLw47TattJZWBA2USK\nj4neZiVUEXyiSF8Ot/X6vcFxwpSpNRWampTNvnn48FO5XD8AdHcv7+xcKgZC4OE88NypZInJv/ji\nmslcmsHbhyH3Mw8TvNcEe/b87jvfeeill95EI41YrwOkKaw842oJ7Ti83DYQQsbHX3/zzZ/h22nT\nLk+nZ3d2LpOKKcrnFC574P+ikMIsy2GMel72xIl906f3xmKt4cP0EsFBI9xXXqWGcMgJo8tHWoaW\n8bCd4oWjwqMlA9hkZpwCwMTEm4cPP5nLHYnHM47TNnfuxx2nVbiMpMQpYHoW5XVK/Xvu+VpDUU3D\no+Ek4vqtLSNg1suuCRYvvmTz5q/97Gfb//IvNwIQxhzMslpWDCfUYKFHnLSJFE+IxRgQEiy+inJE\na+vcBQtWe15+dPSVo0efHR09ODi4e86c329vnw9gCfbjarYnqzRizWhUPEZHX3GcTDw+TZoKFOyG\ne+p1vvg+jPfZliu882cOALAl77lcMECIMMoZgQdGorgY5ZI6USQgfoi8ODWDYMW7JzHZO316z9y5\nn+D7lIN0cRXYPqWeqSVQK1QtVlGPaIDIveGehpoMR48Of/azdw4M5JCyxRQnkVnlzkjhi0dfjSNJ\nIgxlegA4evS5wcFdAOA4rRde+ActLeeFKw1UjKApLQ0N7WlruyyVmlkpBufHnjxkqW65kWWWqFoI\nVeT1iNWXOF8Tzg/Edcdef/3hbPaw42Ta2+efd94HcQqSOEZMMcXXqK3joPW5z/2BKf419di1a9dV\nV11V616cGhqA3I3sXg/48Y//Y9Omp48dG8cSY5zKMd2KZMqwUo04hPspyxsAwLbjpdJ4NnvkyJFn\nMFM6Z87vt7Scl0rNlk9HgvLr5dlJY2OvFovDHR2LbDtOiCWdNHK+Eomkb9nKUslVWSGnKtzr0RlX\n7kqUA3yh3pQxMnJgYODFiYm3HKeVEHLZZascp41Xg8FpUGW/DaW+JMtQ33dNtd5awZD7WUHDOZCa\nGHfc8dDGjU+hMRFAlH9Big/CdkGayjQoAVGBcnBw95Ejz+LGeDwzbdoV3d3LoeyJpILffd8dHv51\nItGB689B+XGhWpAuLPaSaR20hC2OIiS8jwpeLli4120hyEB5zFDEeiqY3XXHR0b6Bga2u+6Y47Q6\nTubyy1eJA8VyHJSW+LE+lhzA2UmM+XffbRT2WmLdunW33XZbrXtxamgAcgejzNQT9ux59S/+4kfH\njo3GYkkAYttxrjwQwdpchS8r4FFVJIMpr0eOPJtOzz506AlCiOO0zZ37h+l0d3hPMjHxVj5/dObM\nd0qxM5FEc1EkMkifSgUPAMplhOWZR8LAXlb2IagVQ3GKEM/BMq6nizL0YgpupZ+POuMUfeuO09rV\ndXVX19VYkSbsbhQlYhhff5X5fpEx/wtfWPknf3L5Kf6VDM4wHnjggVWrVtW6F6eGBkioAkBfX58h\n9zrB4sWXPvXU7Xfc8dCmTdvQ3EKIjYE8Yx4AplKp7xdxmSeRY9Rc5z6ljBBrzpz3AcDChV8aHNw9\nOLj74MEH4vFMOt3d1bUsne5Goszl+hOJDkn0EBOLgl6FzZTAQ+Yym6NVX7kWPvAQeQtXdTCdgPyL\nmoxoTa8iUJ6MKtN6Nns4mz18+PCT8Xjb9Ok93d0fjMczjDFZUmeMMeZJr328M1gl5t57/6rRxACD\neoGJ3A1OH1/+8n2/+MVvbDsBwHjpMbAsG52LAABAlIItUt4VAIAxJjnfWak04bpjb775b6VSlhCY\nNm1eZ+dSxvx8/ngmc3EiMV2vGg+Sn1IW4iuA8CQwLcs/vBHpLeNsHpG55fNCoz5hFIB4Xq5UGjt4\ncBNumjnznd3dHwAA1JeEj4h7eAJ5hydOMaInn/vcR2++2SxGZnD6aAxyN1b3usXPfrbzK1/5kWU5\nWDlSUDmupCochDysJqjkSEoIcEknVE03lzs6OLhrbOwgAHGc1kzmkvPO+6D4ODxhCuQkJABICQAV\nIvVaebUmRVEh0ixWOZsqCkzK5QoYABw/vr2//0n8WXV3v7+ra5nse+GNWvJZMHFKCMGF8Xy/aBKn\ndYVGFNyhUcgdGlPzOkdw9OjwT37y5KZNv7TtJOYnRYF4Xh2M8GKTFp9zT/nsJznuthXOLZUmfve7\nfy4WRwBYIjGju/v9LS3djpMRYwNvkIkXMi8Lpyb6xLmcAjIvY1k0rrNj1CyKDAv7CvCWLbwQ6VcT\nHOK64+hbl2i9/KwpKi7wgl9ixqlYwJpgWccvfGHFn/yJWTWpvmDI/eyiEa1I5xSOHj3xla/8+Ne/\nfs2247gACI95Y3K6UvaZMIbl4wk3jQAE1WzKa32Mj78+Pv5aS8t5b775b7ilq2tZOj1n2rR5+FZ3\n48iYxDIduFvFfSo5IwEIY4Gocvjwk9ns4VyunzHW3f3+rq6rsVQDXppkYGdy4lQ8Jfh+EYCZmo51\niwYln4Yh9wYdPM81/OQnT37nOw/bdoIQC5UZHrMHyUxCiLwMiPQp4YlWxtOwFgAbGtrT2jo3Hp8G\nAMPDL42OHszljjhOJp2e09W1lPtqiLb2kyBQfpKo2mQVqrGX58dW1dZxlumBN974V9za3f3+6dN7\nHKdNDBVcYQ+KyQiFHZOoIn0KAM8//9VTus8GU4Z8Pp9KpWrdi9NBw5B7gw6e5yZ+8pMn/+EfHueL\nsgZULpkmAcpudyyEa3MNhwkFw7Ls0dFXPW+is3Mpxsio54yN/W509JXR0QMA4Ditc+YsR60G+CRY\nDjUdKpsmq1Z/FKbJspNdfCTovr//6YGBFwHAcTKdnUu7ukIr2uFapvIWcV1ClmHMp9S76qr59977\niVO4uQZTjgbl94Yhd4PGwh13bNm4cZttx1FbR/kF/e88bGc84haidsha43m5sbFXU6lZra0XKI0T\ngo6U7MGD9wOA47S2tHRfeOEfClLGkYMFhdeD8l7C9i7NfbUAqEiWoo9F/kXwFIKwpQMAvPzyxlzu\nML6eO/fjQiDiMrrPHz5sAMAIHT9CPwwhBOcoLV586fe/v+IM3nODs4HG1QwaidxNTrWxcPTo8MaN\nT//612+89NKbluXEYikkWcty5JmlluWIJTsY80VadWRkP6Wljo6FEET9etFHQog9OLgTFxcFAMfJ\nXHbZqng8A6qjRhQFC0GeWiWXdlF+FBjm53L9AwM7c7n+UmnccTJz536CLxvLeO34UBlIXvmLz20N\nZp8ySr0vfOETX/iCmZfUGGhccrfXr19f6z5MFj/96U8/8IEP1LoXBpNFa2vqmmt6W1riR48OHTt2\nQtSSBKCUulyNEdlUm88VIoSA7xeLxSHHaUkmO7kjhXLBRNRDZ4z5qdTs2bOvyWQuKRSGisWhwcEd\nfEYVI8RmrIS0W0GEwaIufqUQB8+bzR5+443HhodfyuUO23Zi1qz3XHjhx+LxDFd+LGFO54cAYyW8\nRghY3kdap9S7556vfuxjM87SPTc442hvb58zZ06te3E6aKTIvXGHUIOjR0/ceeejv/jFS4TEuGMS\nqxTEgROitNgTjI+/4fv56dN7w/534JYbYUYkGC+jDOJ5E6+//hgueeE4rXPmXIuaCa9nqZSZlBdI\nEhNTRWGcwBzZ3//kwMAOAHCczOWXXx+LtYbHidB0U+A2GHxowMXwsDVKS5SWtm9fewbupoHBJNBI\n5N6gaQ0DxNGjJ37+851///ePK+v28ReBr5wQu1g8kc8fS6VmJhIdklm+DDTYSGRNhD3GsmKoxWPJ\nSQCIx1FCmSML6JWyqaK4IyHk4MEHcJxob5+P5RC0laxx8pHNPTBldw1jHs5IQgM7Y/7zz/91o9UD\nN2hsKbiRyB0a/F4bAMCePa8dO3biL//yJ1h5xrLiwg7P5xN54+OvA5COjoW8hBaVxHGZIIltO1FM\nTVBwHxjYLuT4rq5ljtPa2XkV8CIwWqmZ8nSkI0eeHhk5AADpdHd7O5ZACAqHhUN71GEAgKLoJMfp\nwg9z771fN7UzGhQNrRY0RuEwAbMqU6Nj8eKLAS5etOjir3zlR7/97RHfL1iWY1kOY57vU8ty8vkB\nxlhr63mUumKCK5pVeKQvZo1Sz8vz0B6ksmLoIvc6O5d0dS0bGNg+MLBjYGA7APT3P33hhR9rb78C\nABhzoVyHgAJANtvf3/80RuvxeFt39/tR1eGTrQKTD6Uu9zUCY+iHofjYIUs9yO+mkIBBrdBgkXtD\nD6QGMlCl2bjxmcHBPACJxdIAUCyeKJXGE/+XvXePsuOo7oX3ruruc86MnrbHlmxexpaxJOs1kNwL\nccDJt8KXC7lZxMbI9phnwBAcknwhL4KMbRB2iIF74cYEHEwCRLJByEAg9g0xIBsIEMyMLUcSmHeC\nGTEjIdl6zJnz6Pr+2F3Vux59ZiSN5nFO/5aWVk93dXV1n3N+tfu3H1VZXq2eSSa5lBWzEBLFxRs2\n50CMhMjr+vLIRVLSJyZ+Pj7+0OHD36G/Bwaes3LlC4BNCd///l3Hjj1OxviaNdfTeJx3AhPxQn8a\nO53GQ5GOSrVJkylpvcTcYoGReym7dxn27z/013+981//9VEh4jRtTU4ekrLa338uAEhZgyw4Ek1c\noxG1jVeWgWg6IpvaE7izwgaPP/7F8fFvUeNzz/21Wu3s0dGvkLUOABdf/Lo4XgRg1vnjS7AqFtKj\nTBUwpVIy3mmB08HB1WUVge7AQk+cXGDkvm3btssvv7zk9y7D6OjBW2/d9vDDPzh8WAoRS1mhAJgo\nog86s9z1n8q4LvVK3Jafk7y1Xr0BUzlSIYqDBx8ZH3+o0XiCgtb7+8972tNeFEWLzIRh1vdI0xYn\nekTRbk/ykPY0bQCgUu1Nm5712tf+dimvdw1Kcp9tLPQnXqII+/cfete7dnzxi98lWkekRZH4Ihso\nZawL0ehdKHSN31yTMVwsRKxLMAoTNEk2uFLp+Pi3Hn/8ixdd9KpFi57CR0KCvhP/biLiaUh8Sbx2\ne/Kb33xLGQzTZVjo4RsLzKEKAPfcc09J7l2JFSuW/6//dd3+/Yc+9rFd//iPXwVQVC9MqTYltaZp\nW6k0TSe5ba5U2m43AMAkvlKADWTKe0spJUQiBAJIw78k6MfxEsRocvJQrXa2fgmgFCQ3l5X2U2xP\nmraValH3Gzee/7rXvaT8PnYlVq9e2IulLDzLfaFPpyWmg/37D/3pn378kUd+ImVFFyCTVKgAUZqK\nMSTg0FLULFoGvNQnAABWmyxrfODA8OjogytXPp9CJKlgADlm9apSUZq20rSpQ3RSKs8Lenr45jf/\nYjYfS4kS08fCs9xL9AJWrFj+8Y//wb/8y8P33//oF76wG1FKmbTbRL6JiZZJ05YQUogE0Sn5my3S\nTfHpphCj1lKykJtq9UxEsWjR04SIvMWhVJo22+1JfaHsRCGSdrs+OPisv/3bl5z2p1Bi7tAFsRsL\nz3KHUnbvMezff+iv//qeRx99/MCBCYpQJMqWsmJUFCEiz4maL2ztL41NEsHNwQAAIABJREFUDY4d\ne/yHP9zxtKe9aOnSi6gxRaynaUsrP0KnI6WIotU6/oEP/EXpMu0FdEHU9YK03Pft21eSe+9gxYrl\n733v7wLAm9/8kd27fzo+fhwAaCHWKKqZheuUaoBeWo+cq0aoUaohZWLWcSW+RhSt1jEAOH7850uW\nXIAojZ0OWYBjs9U6bv4sy8KUWFhYqOQ+10MoMQd4z3tes3//4d27//MLX3jkX//10SiqNptHSQEX\nggrHZ4tQI6KUVb6mEsksOtaF9PREB8W3yfVKbSFbDE9RUOZrXvPiclHTHsRb37rg5/IFSe4L3Ytd\n4qSxYsWyFSuWvfCF6wHgYx/78vbt/z46eiBJlgCoVuu4DpgRadpK06Og17/W9eKzhVspGCZNG08+\n+QOl0jPOuITKD0C+noZstxvl0nc9i+4QfhckuZcoAQCveMWvveIVv7Z//+F3v/tzY2NHfv7zJ8bH\nj7fbk0JIKWt8pQ4qtk7rtepKMgJALV+++tCh/2g2jwqR0BvAv//7X87hHZWYJ+gO4XdBkvvQ0FAZ\nEFmCsGLFsne/++W0vX//oW3bvn7//Xt//vMntEcUlWrrlZJAr72XBREkyVKl0l/6pQ1vfOO1C/+3\nXGLG0B3C74Ikd+iWp19iZrFixfI3v/lFb37ziwDgkUd+gije+9779u799ubNL0HEL33psauues5z\nn/vfLrggM+r/7//91he/ePC2266d01GXmHe4/PLL53oIM4AFGQoJ3SKKlZgF3H777VdeeeXZZ5/t\nH9qzZ8+OHTsW0EqTJWYH9Xq9Wq3O9ShOFWLqJvMS+/btm5iYmOtRlFgAeOCBB4oOrV27djZHUmJB\nYNu2bV3A7LBwyX1oaOiee+6Z61GUWAB4wQteEDTbQRdzL1GCo2sk34VK7iVKTBN79+4dGxsLHupg\n1JfoWXRNpHVJ7iW6H+Pj48H9e/bsGR4enuXBlJjnKC33EiUWDIq09fHx8SeffHKWB1NiPqNery/0\nkjIGC5jcL7/88tKnWmJKrFmzpkiWIezatWu2xlJivmPnzp1zPYQZwwIm93379i30mpwlZgHj4+NF\nDlXCmjVrZm0wJeY5ukaTgQVN7oODg1u2bJnrUZSY7xgYGOh8qDP1l+gpXHHFFXM9hBnDAib3EiWm\ng7Vr1+7Zsyd4qMjRWqJEF2Bhk/vWrVvr9fpcj6LEvMaePXuKHKqXXXYZNZjVAZWYr6jX65s2bZrr\nUcwYFja5A0B35JKVOH0YHx8vcqh+4AMfgDJPtYRG18TJEBY8uZdxyiU6Y2BgoEh+eeMb3whltEyJ\nLsWCJ/eyCEGJKVFE7rS/jJYpQegmbyp0AbmXATMlpgRp6z5Ktb2EQb1e75rCA4QFT+4lSnTG2rVr\nizT3MhSyhMHOnTu7zIG34Mm9yz6PEjOODpI60Xrn/NUSJRYoFjy5Q+lTLTEVOtvmZbR7ia5EN5D7\nP/zDP8z1EErMX3TgbjLqO6SwlugddN+azN1A7u9///vnegglFiQoTmbv3r1zPZASc4yRkZG5HsLM\noxvIvUSJDlizZk3nSPaiWJoSvYNuKgZp0CXkvm3btrkeQon5iyLhhWz2MiCyRFeiS8i9RIkidKgu\nQLJMWX6gRJelLxG6hNzLJMMSHVC6TEt0RjfVCzPoEnLvys+mxEyhKBSSFsgu49xLdCW6hNyhS/3d\nJU4du3btKlLVywzVEtC9JUy6h9zLgLYSQaxdu7ZIlinTl0pA94q63UPu3bT4YYkZxNjYWJFtfuWV\nV87yYErMQ1xzzTVzPYTTgu4h9670d5coUaLEyaF7yL30qZYIYvfu3aXLtEQRtm/fPtdDOF3oHnIH\ngHI91RIcY2NjL3vZy66++uqbb7759ttv9ym+XIOpRBf76qK5HsBMYvPmzZ/97GfnehQl5h5jY2Mf\n+MAH1q5d+8lPfhIALrvsMtpz2WWXrVmzxkjwl112WZmeWqJb0VXk/ju/8ztzPYQSc4/rr78eAG68\n8UbuRz377LNvuummsbGxm2++ec2aNdSmtNxLdGuoDACgUmqux1CixMxgx44du3btuvLKKzvXAtuz\nZ8+uXbvGNci6L9GDqNfrXbzaT7eR+7Zt27qvLnOJKbFnz54dO3a88Y1vnH5G0q5du2655ZYf//jH\nn/70p8vyMr2JkZGRLg7E6CpZBspo994DKS0DAwOG2e+99+ubNl30znd+dP/+g9RmdPTgz39+GFGu\nWHHm6OiYUu0VK8763d/9rV/91V/7r//atmPHjr1795Yx7z2Iffv2dTG5d5vlvmXLlq1bt871KErM\nEm666Sb6f3T04MjIY/fe+/X77vsmAAAoAJSyghgBKETkZymlhIjStPnkkz984onHnv70307TwytW\nLH/ggQ/NwT2UmDt0tyzTbZZ7iR7By172soGBgde//vfvuOO+Cy64EgCESKSsRFGt3W4AQF/fCgCQ\nskLtW63jSrWjqB9Rmp1Hj/40jhcjijhe8YtfiNWrX9duN5RqP+c56++668/m6M5KzB66mNmh+yx3\n6PbZuMTtt98OAJ/5zENLl547MvIYACBGUVQDgHa7gSiiqC+OlwghzSlSVqOoL0mWpmmj2TzWbmf5\nEP/5n//cah176lNfnKaNNG0KkaRpQ4hkcvIXSrXf8IZr3vzmF83FLZaYDXS34A5dSe6lMtOt2LNn\nz/vf/8EHH/xpo5EgCgAgKpeymqZNRCFE0t9/bpq2lUrb7Qml2lJWk2RJFPXzftK00WgcSdPG6OgD\nR4/+1yWX/KGUyeTkL9K0CSCEkK3WRKt1rNU6rpRqNp+84ooX/tVfvXKObrrE6ULXE0Upy5RYALj/\n/gc/8pF/Hhl5rNGIABIpqwAgRJwki4VIlFIACAD9/eciRlJGABBFNURZrZ7Rbk8qlfLehEiWLLkg\nTZtPPPG9Y8d+RlZ/tTowOfmLdruulIiimpQJACiloqj62c9+7TOf+Uq7PfG975WrOXYPurXSr0EX\nkntZQaybMDp68Atf+No73/nRdlsAREIkiNmXVsqqEAkAtNt1KSt9fSv5iZXKGUmyFACkrKVpo9k8\nSvuFSCqVZXTikSM/dk5ptycmJw8hxoiyWj2r0XgyTRtxvDhNJ4WQa9a8odk8UlJ8d6DrxdsuJPcS\nXYM77/z8Rz7y+f37D1IRJCn7aL+USaVyBqJUqq2UqtXOjqI+fmJf30qy7gEAUUpZE6KiVFvKhGid\nUKksU6rNT5SytmjR4nr9oFItAFGtntVuT7bbE2laSdNGu91IkqUXX/yaNG3t3v2xbieHbkbXC+7Q\nleS+adOm0qe60HHnnZ+/5ZaP0jaiVErF8SLi6yjqS5Jl+hBI2RfH/QDQbjfStCFE1N//VL9DIeK+\nvqemaavReMLsbDSeqFbPrNXOqdcPCBFLWaFAmjheUq8foDZxvLjdnjCGf6NxWMpauz2xYcOrAHBk\n5O/7+ryLlSgxD9BVVSENuttP0t24887PX3DBlcTsUlalrEVRf7V6ZhT1IQopK8TsiIAIUdRfqSxF\njISI4rivVjtnyZILnah2AIjjRRQZKUSUJIvN/iRZ2mg8IUS8fPnaJFliQiQRRaWyjHy2ACBlLY6X\n0HalckYcL0qSZbXaCkQ5OPi7q1Zde5ofSYkSJ4MutNwBYPXq1XM9hBInjDvv/Px9932dohsBhFFa\n4ngReUSlrMbxYgAg9o6iflLVEbOIryjqkzKRMknTlvGj1moDXIoRIqlWz2w0nkjTVqPxpBBxpXIG\nANRqKyYnD6ZpUykFoISIK5Xl9XqW4yplRalaqzWhlIqivjRttVrHarWBVut4FPWvXXt9o/Hk9773\n8Vl5TiVKTAtdGAoJZaj7QsPo6MFLL30DZApMiiikrAGAlAlt6KDGzGaHjKPPYn2oJFmurfLMcm+1\nJqKoL44XBS+apo1HH33fkSM/vPTSD5qd9fp4mjapQwBQKjX8DgBp2mw2jwKkiCJN283mEQDQs0ja\nbB697ror//iPf3NmHkqJEqeG7iR3KPl9gWB09OCb3vTekZHHAASRshBSiBgAEUWlspxoFFFUqwNK\ntalsAFE2Yp6mhCj7+8+lTbOzWj1TiKTVOu6EQiJKKZMo6rv//s3nnff/PPOZL6X9SkGaTk5OHjLt\nEWWaNlut44iCLpemk43GEQCFKJrNY+32RJq2W62jadoGSFutCaXSjRsvuPvut5zW51aixJToTs0d\nAHbu3DnXQyjRCaOjB3/lV95w6aVvGBl5DAABEBGlTKSsSFmVstrXtzKK+qWsSVmp1c6WMomimhBx\nkiyr1c6O48WG3KWs1mpnp2mbWyqVynJSY6KoT8oKXYL+RVEfaT6I8sCBYWqvVJqmDQAgqUeIJI4X\nU15rrTZgriVEJY77ESUAxvGiKFokZaVSObNaPVPKWpIslTLZvfsnF130yq98ZXQWH2eJE0AXL63H\n0bXkXpaHnM+4996vX3rpG3TVRiFETNwdx4uk7BMiqVSWGz6N48VCxLSNKJMko3UpK1LW4nhRtToA\nAABKqXaatpRKaXowl6P+dW+LzPbSpauazSNKqXa7kaZNkmIQo0WLnhZFfYhIvlnEqFo9w/QmZU3K\nKr0iRFGN2ggRVSrLSDsSIo7jxdddd+NFF73igQd+etqeYomTRI/45LrToQo98/ktOAwPP3bLLR/V\nXlMAEFJWhZCIkZQVMr2TZAlj9n4nMt32jkZaeY/StKFUSgQdRbV2uy5ErCNeUIhYiMgwvlIp/Tvr\nrEEpK0qlSrWpmAE1SJIljcZhACDuVkpIWWm3J+loFPWlaZMuF8dLSIine2m360myrN2eUCoWIrru\nurcNDj7rrrv+/HQ8zBInh66PcCeUmnuJWcK9936d1VgXiEKpNkWXI0ZxvIiM7jjuIycqAERRjcrC\nKNUmOSVJlvA+k2Qpt9CJ2anQoz+AavWsNG2223XznX/ggVdXKmf89//+HqXSNG0KYdk67Xaj1TrK\n99TrvzBJT0q1ms1jWp1PjRCvVLvZPAYANNkolbZax9rtepo2y9TW+YDeYYaulWWq1erIyMhcj6IE\nAMDw8GO///vvfdOb3quZXQoRASBiRPRH9rLN7IgodcEvBVklGYvZ43ixzeyIGFUqZ3JHqz4gkmRp\nmrYAkBv+ALBkyQWIkrR15yxyuvI91eoZiJJs+Sjq7+tbGUU1UvBrtQEhYkSJGFFSlRAJvTrE8aIo\n6o/jJatWvfw977nvZJ5giZlD7yTBdK0sAwA7d+7skfeveYvR0YPvfOdH77vv62YPYoyIAChlAqDa\n7QZp7kJEiDJJloNWQiqVMwFAqRYAKJVWKst5z0LENvMiAEiZUFiLUi1jYpPgY+wYxEhKMAILoqTC\nYQAQRX2t1nH7KglAvgcxqtXObjafNHviuL/VmgCQiDJJllApeRoeFZUkwSeKau32ZJIs/bu/+9QH\nP/iPpQk/h+jiFbEddDO5l5hbDA8/xqx1Apm9SLlIQkghmmnaFCJGREomIhg7msqEVatnICJp3JRk\nxBsbZo+iRewsVKpF6zE51jpiJERKhvyyZReb/ULEQsQ6zp1aikrlDKo9QC8ESqVcfKdXh1ZrArJC\nZjFpMlLWqJ8oqlIsJqJstY5Tnu2znvWakZGPlHULSpxWdK3mDr1RG2h+Ymxs7KUv3fL444fs3eQ7\njeJ4sVItpRRtTEyMJ8nS/v7zSL9GRCmrvAK7lBWaDAiISPEzSqUmql2IyBScYS0hivqKv+DqS1+6\nplI589JLb+d7Gw1jmCtEgRhRghJNKvR7aTaP0CuFPsX8iRQXT/tbrWOUk5WmTcp1arWOKaVaraOI\nstk8mqatH/zg7imfZ4kZRKm5dwNKZp99jI2NXXPNnz/3udfbzC6lrMbxIiFiMnWVUqRHC5FQNKFe\nfAMBBGd2ROkwe6VyhpRVRIkoTRWZILMLUdEqkAuSwgGwWj3TOWRidRClEKTzRELEAKmxhPiQACBJ\nFptCxCxEB6KoX2dmke5ES4tUKpUzEAXF0V9zzXseeOC/pn6yJWYC27dv7xFmh+4m9xKzibGxsT/7\ns1svvfT3vvnNH5qdiJEQFVNoV8oKWdyIkvlCkWxYYmHHscnrfAEAsa3uXCBGiFipuL5QXXymigjU\nhgqN6X9IOvuyZat9cocsFr5ix1zGjp/W4Xcj3EMWrpPNKBRnqUcu9QquGMdLhIijqDo8vO91r3vr\nVVfdGnqoJWYYe/funeshzB66nNx7JBVtzjE2NvZHf/SenTuH2+0srpziUsj4pRBDih4BAICUpGcA\nQJS12oDuBnkUIyLGcb+xiBERUeoiYrnUEseLhaiYP4m+AcDUcUREkuD1n5J7Yvkh04ASZekvpVpp\n2gIQUbTIdE4nkvsXAAAE1SOLopqU1SiqVasDcdwvZSVJFifJUiEiKZM4XoQoyA0AAFHUJ0QlSZYk\nydKHH/7BqlVD73nPvSfz9EtMG73jTYWud6hefvnlcz2ELseePXv+8i/f+R//YZyQlOKfEuEiSkQB\noKSsksWKKISoCVFBRCGiKFqEiPX6gVbreF/fiijqA0Cl2kqlQiQm4J1gSoAZtV3KRMoq8T4nfSkp\ncdQQOiJGadrUkTM56vWDUlZ0AhRJMREASFnRaas5KEcJEUieIf9Bmjb0hRTiJAD1I+J4caPxJN07\nVRYDACHOICFeiKjZPEYFLIn6hYjuuGMHovzjP/5/Z+jDKeGipwihmx2qJU4rxsbGbrjhHV/+8s+0\ntU7I7HFEgUjquSKpnUxyksuJhZNkKe08evQ/W6362Wf/smFnSmsCAL6HxblnrB3H/UJUhMgEE+L3\nKOqj0mP+mIVIuNX/hS/8zjnnPG/Dhj9VKm23J4WQtDAIxS8CAK2yzX8iaTrZbtdZvLwiBs+urxRx\nNzVut+sUHImIrdZx3WczTRt0483mEaXSVuu4jgoFSncaHFxdlh4rcYroclmmxOnAnj17brjh7f/j\nf7zq/vv3h5id4tZjqrJC8roWYYSUiSnGYhSYJFmqVCtNG+YLGUVVilhHjKhKl8/spOADpGnapOxW\nRIEYC5EEmZ1idZyykVmPKISIAUSattK0aWLkSUfiagyt2MfkeGTiOyKiHedTZdXNanojNqmwUtaE\niJJkia5XA1HUH0W1kZHvrlo1dO+935jikyhxIuj6FbEddD+5l3mqM4ixsbHbb7/95ptv/tSnRg4f\n7rcPkqneF0U1IYzdTaW1MnNe70RSLcyZtdoKAKTy6FRt0SZopBVTteZDXQjuw4SsrGNLCEnlw4ju\n6X/QQSxKKXpvIExMHKjXDxCbCxEp1fKKA0dG0KeilfzWzEi4c5hCOc3ROO43gUBRtEgvBlvRUTQU\nh0OFFqrUM00ecbz4D//w9g0bXjmtD6bENNBTgjt0veYOZZ7qDGFsbGzHjh27d3/na1/7ycRExfnm\n6MDESIhYqTZRM8U16rBCwd2YTiAKsWGzebRSOUuH1iDrXBjD30Sa+4Y8AERRH+kqAKBUmwxwpdo0\nNpM+CkAZTACgqPwk9U8ZTI5QadKajLmNKOK4n5KVqDchYu13BZZ8a6qM1SjynVzEzeZRABVF1Xa7\nYZ6VUm0hKrRULJXcabWOxXH/5GRj1aqhTZvO+OQn/8+0P6sSYfRaMcHu19x7J2fh9GHXrl0f+MAH\nnvrUZ3/mMw/ZRxBASEkxMCKKamnaNFExFNxN7agUO22TFmG6iKJ+IZJf/OLRZvPIOec8L0mWcl8o\nMGleX1Hx3ngek+2AVcZmdzJUQVP/t761pVY7e8OGP2X7s6rudD5kzlhBOagcrdaxNG2bjFkA0G8e\n2dmUuKRlGdVoHKHA/DRttVoTdEqrdZxiQFut4wCoVNpu12nkStHSH/QK0mq3Jy+9dMVHPvIeIbr/\nbbvEjKD7LfdqtVry+0ljz549u3bt2r37Ow8/3P72ty1mpyBFE6oYRTWlFBnvRIhRVFVKAWAU1ciT\nSTJ6FPXpyBYlJR2C/v6Vhw8fkTJ2mN0ETdI1IZPOSSqx7BLO7LoTBFCG2XkyE6JMU/Xkk99vNA5T\nM71fGFOdOiF29svOSFlL0yPaNkIAiONFzeYx85KhA3jMjVBBAsWcDRhFfe32JIBKkqW6/7TdbgiR\npGkjimpp2pJS0aGvfW3sec97zfve94f9/fEll1wy5WdXosfRE1ZAuSrTyeH666/fu3fv+ecPeo5T\nNMtlmLWqIVu8ok/KRIg4SZaSN1UX9c1yUE0+KknVUdQnRCREltN09OhPHUGGRS4aCz02uUimJdfB\nzX5KVjK5Sw5IJjrnnOfpzrN/2oWb3yZrYEAzE4+vR0pKIoWKzuV5T2w1KLp0tjCI0d+lrFEhTAr2\npwei81qp9mT/oUMwNHTbJZdckqaWb6DElKjX63M9hNlGT5B7iRPFTTfddP3111944YbHHjv+pje9\n1ztOOUoUeSIo2VKIKI77KSpRexSRwmPMaSxsJlvhyHSYJMuEiJzSj3G8SNvUGbFGUdUEPpp+oqhG\nDczaSfoo0XTgS+64Z72jEWIkRMR7I0EfALRsonTuq6DFRgCElH3sFJSyxq+uxSgKqumjhjqLCs1M\nRouKUBQNCVB6jkwoXWDVqmsnJgQA3HjjjY8++mjwFko46J1KvwbdL8uUOCHs2LFjbGzsyiuv/MY3\nfnTLLR/1GxAtkheUitlqb2SiKVuaiEOKiTSncqLni6BCZqTXDh/+bl/fuUToZiYgM5kY0E5ByhfU\nVkp5NWSyyyGiUmhrOIInvvr3KERESzuZBiS/CBG3Wk3j1KW74Kt/AICUNSPgIGIUVY3CLmVFZ0UZ\nu76tFK3r1EjTJu3U64CnVIGH/tcKPkSRbLcnBwdfnaaNkZFtixbBJz7xic2bN/t3UYKj1+IgoUcs\n9yuuuGKuh7AAsGfPnuuvv35gYOC5z/2N6677PwXMTiZtTGGIRnlgpQXArC/qcHEUVZ1+2J8ijhcv\nXvwMs0PKitErTBtnsQ59ORqJy9E8UJKS/s1fZqjLl6+enDzknEuSEaKwfx1KqRaA0sE/ZLFLHcXP\nyxJI+04lD643+hVoHYZONClRUlbYZCn0GxJQhTWSfaSskhW/adPQrl3/RcxemvCd0YNet54g92q1\n2oPz9vRBtL5r167bb7/9U58avvLKt9pF2AEydTiTCDRvopYRyDx3zG3LF8rZ39R95NW1ALBSWdZu\n1wEAkSvUhhb7lErTtE2SiBGvdScWQfvhMZrfqeJNhsOHv1OtnsUGBsY3AABk+Otg+TbbSXZ3xNJx\nybdsOqGy9aYWQtWMkEJCSUkXIorjJTRZShlTIR1S2zWhU7dUayw1D1/KWIhEiCSK+l7/+retWjV0\n1VW3rFu3DkqKL8HQE+QOPflSNh3s2bPnsssu27Fjx5VXXrlv3+Sv/Mob+KpJBLKyjZ/QVNTSEZBo\nBBkhEl1ARkZRPy2upFk4t5v4duaJFBXQNnijcViIhH0zURdVz7hT11Vvc2Nc/58Nw1kNVXckKJLH\nP6RpVDBVXVG9MKXatqSDuv5XDiM36b6FVxVnMU2B5F6WMi+QEEX9FJZDfI0YCZFI2SdlRYiKfoyR\nji5N9A3GUVQVIqG1AIeHv0t1JYniP/GJT/j32MvozQKCvULuPehOmRK33nrrv/zLv3z4wx++6aab\nvva1n9x339c9gx0RY+MXVSqNoiqRo66oHumomEiIhLIxKfRFr3gnaBkNM0NQqUjQPNhuT4yPf+ux\nxz7y2GMf+cEPtjcah48e/U87qDETOngMDG1ImSil0rStF9XLpHl/DVV9nvAP7d//VdC8D9pOpz4B\nFMXA2J3I0CVyNieJnsqikQTEwoHykHwzzZgULcjeYADYNCNEFEV9QkjScMjBALqAME0AVMaS6kq+\n+93/DAAk1LTb7YJPvufQU5V+DXrFodpryWlT4hOf+MRb3vIWADh6FDZv3vrQQ4/Yx1ELy+TGTJRS\nUiYAAhGp5qJSKdfNubzODWe77jkarUap9IknHvvFL3bTgccf/1KrNdFu03p1tWc969VPecpvVKtn\nQxZwmSnd7HJVY5pQRipAGwCEqOhSXyZyBnWIfazbk9WvlFKVyhntdkOXBQYWmW7mkgiAiD5X4YVI\ndD6qbo1SiLjdblL1R7rTVquuXcEghFQqMmchSoAmIiqlpKy123VSfkxAvclcpRkiTZtRVEvTNs2j\n7fYEYtJuT1JIj1Kq3a5LWf3Qh7YD4J/8yYsAQEoJAO12mzZ6Gb1WeIDQ/RmqJRyQQUc/+BCtg4nM\nozQcrWujXnAjRoyVahPL0wkUM0P0JGWfiVZEjCi5iZQNnlnaak08/vgX2+3jjz/+pcnJX/jjXL58\n7fOffwdY00NWWRcAzHKpwMRuIWLN4MpJceKrfFD+JwA8+OBrn/70337GM15iLHGqNuyMRFcycPQc\n5aWtKr3aaua/VapNXgRz3XZ7wvziKO8UdChOq3VMXyJttbKzTC3iNG3SkrC6ck7TFKHUI1RKtdrt\nOt3dHXdsveyyp5lL33jjjTfffLP3jHsCPZvD2CuyDJQVxHRYtJRSSllgsAOAIJuX2DCO+0l+IcMc\nEY39y6IJJVthQzJmlzqoJtMfuMRRrx/swOwAcOjQnu9//25WkYbHj/NwFGDbvCaBFR7DVXKjhNTr\nB37yk3+yDwWMXDugM29rx2UqpdIoqhk3A2hznl/XXlck0lUnSemqaEevNK8+PKhUv4KQXBOT95XU\nfBNxr8X6+Lrrtlx99bvMtW6++eZHH330xhtv9O+uRLeih8i9zFO9+eabyeEGABs2XFnE7FSkRefU\nZBW1yLo0rGpscCozYE4vqg6mNegcTzzxWKs1UcTshNHRB0yyqNkpZUWISGcAAdvP11fKKxD4K+SB\nlpwAYPXq6xAFWhB2S5rtrIQmfcjJaZKGr+2HgOxPyZ+DcauSLqR1eaRkJfIkU04vm9KyDabLx1Im\nUdQvZY3SqaiczvDwvlWrhsy11q1bRxTfa+7WnvW39RC596zs/sO94TtYAAAgAElEQVQf/pD/+eUv\n/+SCC64MthQiFkJqE1JqhT0zNlmh2tw45dVuObMDCM5imrnyo5OTBx5//EudR64VeU6OEavOyC/G\nJxKzkelLob5pPx4+/B3nAE9MFUKapNcgv9MqS+RG1qfEWBBL4w0VAahAgjB1GugGdZJqQq5Xiq6h\nOsAUg0Rl8XVIvonFlCYmR4hYiIqUtYsuesVVV/2Vufq6des2b97cbrd7h+J7Ns2lh8i9B0E/4Gc+\n85lmz+bNW1/72j+xW5GFS/EepsyWKdUr9QpKFSHy9ZXIAqUyMiazScc+CkQZx3m1d10phZeC6Vu8\n+JnkPu2Mgwd3W2O1eNNoL2gizR36DckppqtwWCRkBG2FxCCCrjFgQKs1KVrnD5i/1wm4JBcoAOh6\nMlRJLaJnSA/QuH956iwXZ/SN0zQgDfVrA1+yqssUTJnQLCVE8vDDj61adS2/QSnl5s2bH3300TIu\nvovRQ+Q+NDS0bdu2uR7FLIG8pk5W+gUX+FJM5jiVskLMjohkdFMUI4U86uJfEVsigxjfxP8Js+qQ\nDieXWtpGISqmDqK+rmD10DtBOz8p+5+LHnlXWqZwz0WMaEIKdYxFzJ51KhL/uO4tJQcmZDfLX1Cy\nAgyOmc/MeaEXDc9nHa3UA9hmPkW46/155qpZ8cN8IlJmbE4fHKKgS0hZk7KCGEtZuegid92PdevW\nrVu3rtVqQfeiXq/37Ct7D5F7j2D37t27d+92ot9uu+1zQSmGuIOUX2IKInqiZlPB0TCR0a8RLRGG\nJaYi5ksRmXpYCYtSz9ZjOu+8X+/vf8qUt3PmmRtAJy4xbySX4BMMETV3S3qBLnmwZrU64B/VM1PO\n2koBxdQDIEW7aNM+i/pn56IxutmwlHGBapE9cu7CbNMq4ezuTPxl5DTWkr0wBX+I0GkuoZcDRCll\nJtRcdNErj1t1i+lyEQDcfffdu3fvdo8tfOzbt683Q2Wg18h93759cz2E047169evX7+e7/nkJx/6\n4Ac/5rdEjAFSISqGFxAlJcWQFkzNTBChHfuRh6OQQ9Js80VEIS/Ga14RskKJUdS/ePH5ne/lvPN+\nw2xLSQHsKa2QpyUOUWCYgy2q8OAZS6sp8KCaDdTrZWd5UpTWRO837FGA81MyNXuNLW/yeE0DXnPG\nrn5jFcZhmU3SZAWbznU1BUmMr2md6hPQB0q5YxGV69m06dUPPrjff1xXXXXV+vXrd+/efffddwef\n5wJFL/zki9Bb5N6tfvO777676OX6gguufMtb3mXvy8M/2O8/i4pBFGRmUlMe5sgMxoizj6m4C8zp\nqlta6Z3Uv4lUufDCazrf11Oe8kI2DKnJUQGkJNcgCqUCqRq+V9MEz7BivwiAP/rRpx2nqy5vQJI6\nslI2qO8iQjf8hipQon1FoSNtzAO0ahLoMgmmeE7NfnT0tClOpqJvgj4pRcILZJNTZMQ0KiFpHK3a\nQ1vR6cGRlJXrrvvLa655T/CBr1+//qqrrtq9e3d3azU9gt4i967E3XfffdVVV9HLtYPbbvuct08C\npGTWaWsddFBjvrgEi/3ICV3rCcglBcdTaoIUIatLziPBgekziCiWLLlg+fK1Rfe1fv2fELnb0ZY5\nhIgABLGwLihGAj0CCL2Sak78Jopc71AAsGLFrwKk2kIn8PJkVratYWq/MBm4Ye8ArOoOewJWG62r\n+KFHoEvNSK3RZ5EztKwVEbeUVe3KJkLnkzSyiPisGJnpbWTku9de+7+Ln/z6KIparVYXUPw110xh\nQHQxSnJfwCCd9Kqrrgoe3bx5q6PGkPGrq7uYMltZrRIm6WYERKo6RUOyemE1XV8li/ow/RtzPiSV\noPB8oVImz3/+HWvXvslpGseLNm58y6pVL9dX95mUrmLNZyq34ZFySqmaY5q26J9SbUShVEupVpo2\njx/fr1RaqSxP0zYtZBq8Cp+6+H2FapOhHhI9W+UI92DPoLTDKC2Q+6IjXR7SpDVhFJl1TniKU2w+\nU4pWMot76Agc8qnkZZn1fBAND+9bvfp1BbcMABBFURRFC1qL78HVlzh6rvzAyMjIpk2b5noUp4rd\nu3c7wroD232akzixpTbrlBAVRFQq1Z5SMj9N8V4jRJiqh3mxcqVS8qOahaSZVoN2aUZkYTZGZUYp\ns9WIJibGf/CDuycmxp/61N/s6zunXv/FsWM/XbXq5aQ2BM12k2DFgVmdr6IARyrSm+n1hw9/5xvf\n+JOLL37tM57xEtDEnabhYltp2vRnrDRterUKFE0nvPhBu90wFYMJ9nKsqt1u0NsDTQl2VYOUShRA\nVr2AtpHmJ336JN0Xr1UAWRG0JjVQiupoKroRPe01lIJ9+z4UvGUOejucstl8w/bt20vLvYew0OvD\nTUxMAMAJMbtOZUSllHltB1CUo2Qi87TZaNZ3zpidOfSMmQlgr5knhIyiflLzsx12gLkx/FlXNWMr\n12oDl1zyB//tv73rKU954RlnbOjrW2FOLCreG2R2AKHH4EIzez6GZcsuNv+bVxmdtYTGMaBPD8TL\nB2sSAIBX1sbNj3XyuWgJDqPpc38GQO4xtssk5Kts81gm/fxNBeNsRXIpEwqm1JFR2TIjQkSrV1/n\n35oDYvYFZ8Vffvnlcz2EuUTPkfvQ0NDUjeYldu/e/fWvf71Wq3Vu5jG7pMx47SZF8z+FV5tIbR6y\nzR2qNAeALSmgtcAQssozWZC1cWBqrdtxb0Y2BSNPPa1WBwDg6NGfkIDg3SLyCi3mPsGaCRBcihf2\ndnb0xz/+jH3IcYqivilHTtEd5fxOLwTK5IuyTtxz6VFr8kVvtFYkJS9goGv10KUrRqihz8cQPUVA\n8uHRhyVl1ZQg1tGTkZTJy1/+N/6t+aCImmazOZ3G8wG9HCoDPUjuALAQU5mazeb69euf+9zndm7m\n2+wUPqGdezKKqozi8/okkBOBYkHrggkygjsDDZtrJsqjIXWZLTTmP1+KKBuWlyKkCVEBqGr1LAA4\nevQnQXs5WChG98D18bxB0MSu1w8AwIoVv6rDEHk4jdWySOeB3Jq2xBkeA0Pgkf5gyUc8ysgasL4p\n84SBt6RcXMbdFdS1FphPVbLBoBBS56mZ5bap5r4cGXnsa187VHSPDuI4BoAFETHZs+lLhF4k94Vl\nvL/tbW8D/YvqjM2brUBPY5rpJHXUaoaSkr+/G/415rljj9N2riTYqgJ4EdxWeEkU9Tl06TG7W7UR\nQEVRX7CWi5PbCZrZOSmbIgTa8nVVeGpAxeJpsQ4b/D0jF2fslxWALHu2TS83Pps7swI9YUO+TLnK\n+Z3dL7LsXys8SQdBZh+fTiHO1vQgscVY8TpDOOIvH2bqBRB6Jlavf/2Na9de7z2KQpBQ87a3vW3e\nGvIjIyM9m75E6EVyX1iW+9vf/vbpNGP1e7OfPRloTBMQ2lo3VWSlF9VufKeoF8yjM3mxFEtjcUJZ\n+BqqkBETqcm5cOwEF4IVSGOBRTeaDsPrTrA3DGe/a86bBvX6AQA8//ygLGtGi/ZZ2buIrvCuyCLW\nqjpnc3/DN88lb+MnZPE6MzptmKrHJKbAA5sXsyrN5LvWxX9qVMPABE1qA1/qxy5o5qau3ve+B0NP\noxBvf/vb4zh+5BG/vOjcY6F7104dvUju879K3COPPHJCr71f/vJPNLObBCWpl3kjz1vKdBhDJZF+\n64+1h61mvK8sV15w2ddOtZdOkSzHgLXFcXTeAHSHroAOgOec89wjR35k/iaKD0WX01XM5OT2o3Om\nLFondK42zLO3ICs/QIQOOpQejF3vRDd692UEk9xrqtskaIVXOn8S+eY1I80V+XTIymTmY9Yft4m1\nJ1+xoAJwLJtM8Eniwx/+9Pvf77/KTIENGzYAwHyj+IX1gn460IvkPp+n9Gaz2Ww2N2zYMP3Is9tu\n+ycq9Gi8o/S/Usp4MnWSOkqZMB6XkFVgJ2WmYpIqWYS1MPsxK0eVZ3jyeHkAoLnBDEyb7eZPR3kA\n/RLgU7LURQv4TioGYGz51DSmr3GwcJjfuYZYvnyN7jYA6pblNJlYRjR2enE4DfKd9Bx1eRzXs2rs\nbmO/61Mo0IUvHpu9ImiyNi8recasefGylSXJn4ZOa6qYFFYTV4MoPvzhewqe2BTYsGFDs9mcbxTf\ny+hFch8cHJyfyswjjzwSx/F05HWOD37wHyFTz/NIRGDirE50jKiuC73j07nM6ENm9CVsvyEONAVM\neFSMHgWipyo4q2dwWjRcpj2BwFoKKZOJiTEA4JUjnQgZpQDAUHwKkOr80vwMLiXZzwwRBTlUh4ff\nqYdNGa1ZIV+z4nYoEUSEJBT07XeaR6nomG4WMTan+7KKGQiR6BB+NNdiV+Gfl/WR8W0AUEoZS9+j\nftBOdUpxSliOqwDA9ev/2LvlaSGO4/lpxfcmepHc5yHox0A/jBPC5s1bmR1NhEt1cYUd15z9kvWq\n1lngoPnZ8zU3uHXJ2d+pGkZZTiaezymc4q+Ex2QKpTv3K6rTLAVnnLEOsmVFs5Z2I+MyjSCvHJDy\nUgSIqAuNpXqJUWXqExgSf8YzXqKbtZVqAaQ2mQpvhGAepi2y+/Hs5rE7Ye/GwZtb60wrM0qaac/X\nIeEJBGiLM3lck+nQhFSacB09R6IR38xjlLJC8zqiXL/+/4NTAFnxp9LDKaJcUxN6ltznT4yU0WFO\n4tzNm9/50EOPgiYF4gUv0lEgglF7eewjrxVu+vS2uR/VMBr4BMQFFs+MBVsoMHv8oMY8t37x4vPH\nxr7BWhrjN79skX+VfbHNStnGDEcecLl8OSUx5dJH50FiXoDMqQoJwNzL2u+aQkD5cR3IuuqLsPfk\n7fmHgro2JxNnUE913EI3Yj19iLm7lVaaNTUktP2eFSowq/T9zd/8e/DJThPmBfSuu+46lX5ODuWa\nmtCz5L5mzZq5HgI88sgjjUbjJHQYwpEj8NBDu4lG9Vo/wvOaRro0Ll9wGSCnIUtOMTHRkFGSCRqR\nPMWUJxzRTiYukxXfwWwH3T9p1srvh9BqHaPqwWaozhPw85uMs9FPCtUNXDlldPSr5h79S/Bu9UY+\nDdiyTx6qCLq0pB6nX6LSzagycSysgeDTmD021G4GcpNm7hZKYqDoHZ2hZhZ7EmaD1s9iqzhlxYd1\noCSFw0d/93efajSCz+PEcPXVVzcajVkWarZs2TKbl5uf6FFyr1arc1tU6IYbbtiwYUOShMM/poNN\nm67StE5Uq4xWoJ2osSa7TCg3ZWl19krm5ITstMym04ZeTsc8GRX0W7w56hX2IoqnLfo/9u1c1r8y\n/XANpFY7+8iRHznSB7uGy8Vc2Sh6aNwMJ8195cpftW+z8CxOvn5v5ta0DqPslu4PTX8oDssDez4x\nm1bypCQ6S8rYuEClrIH27vLPwtSK4Mv1sRcvOrdKNoHxtNNMo5QSIvrlX/7z4AM5USRJsmHDhkaj\n8fDDD89Ih51RRrgTepTcYe5iZm644QYAeMc73nEqnVx44TUAFBiTx0IwK8y48hQvG8uC303113wF\nTgp21rIvX87CsnYdO9TxByJbLtUwE69Io/dUbQbOqjnyXYsXPxO8ojT5ddwU/9w/WfTQjGeY91av\nj+sOJBRMJJDZs/4hLs4os5BIKG1KOgNDa+WTbOT6LrKnZ6vtFOSer4jNHN3OUn+5KG/amK5M8CXT\ncMwXhhZWzOoJ04Ve85qPBh/ISSBJko0bN8IcCTU9iN4l99lXZshsOUVaB4AjRzL3JhWN0cqMsamF\neePWi3Ail9qZGzNfDIgbwnomyGJCeMV2h3HAohL604kGQS/UPZAyagQZvmJqrXY2ZD5Vex5QLoMX\nK+YcQktBWWPS3A8d+o7dg1WKgF2CizD80tIMG3OYijHOAPIBIwKFq/Inw3lZN5PmHUjopbR1J5zQ\nc91GiDxj1kj5tshm7PeEnZtXRDD2uxDRww9/7/bbHyp+qicDEmoaMyL6lChG75L7bIJoncyWU8fr\nXvdX2lon/jVLZdIKecpwhJbCLamdGdR5ICNPUpUyLw/Ag9wR3YpdTty6Y0Lqnq08TDK63ehHtFyj\nFDtINSz9SERW3zE7mfcTemDZMBzp/PDh7wDA+ef/DmdGu0PQZGdM3fyQicMxcpB9S7nzOR9c5vwU\nugdlK1q5e9Oca+ZmumXuS7AfGnLvNxPokGsy+kaQbUh2CFnNSGE2TjryvQOSJEmSZNaEmt5ESe6n\nHXfddddM0ToAvPvd9w4P79UKjKkugDrOPTVv9zxWnVmCVgYjgcsmzHxzOVfPIjyAzy0a44yWlWLP\npWSH2blowEHE9+ST36d19bRn2KJRe2pxwsyLDmUnUu3J/fu/4r9G+IPRZ4GWX1LW2J/Sct60h5H7\nA8y6IvasgM5d0FsU2yP4fOC8A7EZWrCr55fQ34Q82pIVeTYCDtkN5oNGIaJvfvO0xDWSUHPXXXdt\n3759BrvtggUbZgS9S+6z4HIhq+Tqq6+ewT7vuOMTRjHX4rhi1qWpBRhrK14YfyCjCR4QyV/YObm4\nuja37tHKYMr66RgTYtq4POuHh+udCAAHDz7CYhlT53SWHOTErpgNDBYgA4BabQAA6/WD/iFn/uAB\n8qHG4TcGXboHuMhDYpqVauXW1eGhR0Za4de1niFfu5V9BBQUm9E05SfrEnLkWZHagyqo9BjbkNrd\nGmnDH9/4xlPVEjvg6quvvuaaax5++OHJyclT762McDfoXXKH0xkvRZbIDBrshIsueiVzozmrNFh0\nANkaW/5KDnl76scu9+jEU+fkztx9dJRXSqEG7gqidnEVauPG1Xi2an51AKjVzrF3CtAlAXQFAqXX\ngQpEnetxFlriAEBFCDTyiHiTpGp8AHxg7M+AAh5sbJyl9BHxZsGwd/16RHusOCJ7OrQWnzJ+dfKW\na34XvMakbmx9N7I3tax6c0R1x3SGcwyAz3722/wbnEFs3LixUqlMTk6eolBTRrgb9DS5n45UJqL1\n07S4l4lENj9RClmjo/ZvlXyheSCzedHmlqz9js/JGh2T0ImfISpnb+4dVoLmQjCNOd/vOVcpni/b\nuWTJBSZJFWwCNfIGVSAwNWdYViqRsrXyNf1P7ScmxgFg2bKL2bl5xEvRrAOMW+3ZLhBpY5yrqGvL\nUA1Oh9/5DKQlNf60wVGZIKtJwA12NEodr/JmB61yRc7MNMZ5k20wWSaX/rQ757SjUqmsXr36hhtu\nOGmKn/9lAWcNPU3uM4vt27ef1jUbH3hgP+TMYnxfQiewULCz0I411I5HI6FkZrIOcjeSvXGWOkRv\nCNQ1S3XOOkJORq4f1bOXUWdUGStYeUqO6TDbuWTJBQDQbB4Fm6fsvn2pR+l/qDcy7tbGfhtAUZz7\noUPhxXr02IJWPwZfCIJRmFQKwjb/0Xe3GtvZtPD8GdabE0t6Qj3XGl8Idx3ndgCFxkP2JbBqFYB+\n22OnKBZmA/R9e85z3h58VjOLSqXyjne8Y/Xq1Sen0sznsoCzjMKg4F7A0NDQxMTElAvXTQmyMk73\nUrzXXfeX2v2lWDwDucV4+lL2m0SMyEq1q4OZT5zL7ihEVVuXwAUf1NVizTB83dyv2WtXoQGwiC8z\n3hFdOcI7F6g25MGDj6xY8StstLw5FiWjmoejt52oG1dVt880TgiHl00DqSuLBffn0FVunGZC94za\nZYKIEe+TXCbUGyIoJRAjgJbxxAoRmeW8KUnVXFqIxCyrLUSUpk2lsheCdrtBlxAiTtOWjkdK9Z4G\nndJuN0mlSdOWEJGO9Zw9W7BSyb5Uk5OTZns6KCv9GvS65X7PPacU5rV9+/Ybbrhh48aNMy6vOxga\n+t9mUQgTvMwLefMNzpvcELYFmZhRWGTMcG3CGx+gG8pi8l3NDj/ewyFclujkR7BYgd5+rhAZ76wa\novVYOhT1DfppzaXN+Mmt6gksnWEcG94B29g3RBxSbLjjOjjg3JoGTd+gPyPMyvEXZpOxOVJwIYhZ\n6JkCQ/I6jdcsDqU3BLffEeWHPjTbdjEx+8yG0/QIep3cTwUkwpx6UtJ08O1v/wdf0h7yX29OvkZL\ntYsFOuFxRBYWB9kWtFVh3EwkuhOXfE3opKEwHj7vbZh+eBJs5sa0XywyzqvVzmm1jtP7ivdUCp2l\n/jjZMLKcnVptAABIebf53XXJFs0fwZ8P2cJ+SIwXSmTKwmSPTinfAWutnoroFmhz3of4ti0c5ZGR\nZmlsyGtBC0Qq+WsK0fCKNAnNoCQE3XnnZz/0oe8UPI3TCHotnjICYn6W8p4r9Dq5n5xPlcKtTrcO\nY/Dgg2NackWukCqVR7UHQxuNZ5JJ6giAdmC7VZaLV+nCLKEJjQTE6hHStdwoQ1+Q4Ynyppmn5ChW\nGwf4JX7+839rtY7n7RjDT0+Q8Q9lPZPmfviw0dwzTgydw6c37vw06azAYniKjHq/GA7PxlK6cyeK\n33yaqDnaek+yKwBHZsoH1yubr6tlgiAh99w4ZWcs7Z5iOqlgpDPZzzK2bt0KpRU/bfQ6uQ8ODp5Q\ne6L1Wc6SeMMb3sYzTXhsg9lPRWJ1NBuAncnJZQ070MKKxXaI3q5tYmrG5haut0KpG+ruKB6mWWgF\nDGpmwhCzBk996m8ePz7qP5NiQQaDjk1zaeeslSufz44WBoTY3kUwzk+Szpkun03AoVcKZBE1yPmX\nWfno3BcZ+OxNS4ViUrlrgecDo64+hNp/ng+bNQP9yuVGzZrXMl1HWiKKO+/8TNFTmh1cc8019Xq9\nrPs4JXqd3KePkZGR7du3z0nymzaySOzOC7+wDfoRWgEwZvk0EusxW0c0Cok2xmRz6p9whnKJ208r\nZVVrzPQgfcYMrdHhh5ooHd/iBrArFRiM/azC0GZv1g/VlmFHUb+jFJydlZHhi344vlbOuYHMKf8N\nJjRgd3KiqHN7j5OYarWXMtblaMzy2fRRCl75mW3nUg8rXOEWktQFZ1yHypygWq1u3bq1Xq9zHaZe\nr5feVI6S3Kel0xGtz5oOw/GKV/ytfpVGZpibCuDANHe+shIPdrbWWeZ+VH4hk5uue7AKfjFtnRq7\nkYJeImXgEvpE36o1ZO0sWhQtXXohABw/PqqZ1ElZ8rrv5A7t7Ckt9BDonagDS/KRQO4EDrygeBOk\nM3lQJ8Kf6RwDnz3GTC6zHz7yfAWdXCr0a4SJgLSkITsCKi8waV/CvAsiG7y4447vhR7RbKNarQ4N\nDY2MjFD57jII0kFJ7lPI7rMsr/v49rf3cI3bWNn8hVof5TEz2VG+uqbZiVkCer5AhHl/p3bBEu38\n75DZ7jr3QsK63zO1dJV6AODRIE888T3dg8Kswks4QrGIwb3KMxnIfveUbj3iXHJRer3W3HXMThHa\n8LfedQxR5rtyUSUXYhCdejtZdDzboZzHay/VBPpCginp+e3YohyPqAn4Y1klIsPplqcHEf7+7z8P\n8wabNm2qVqvbtm279dZb53os8wsluReSO1n0c16EiFnreVwaIppoZWrmlAow5/KQbW/Jzeyny8WT\nkDqBjhXv693MHuf2r8OzKGUcqvIYiHY3gXoAEMeLKOBdXz3bz9ZNNYVfFF8CifemB6OY0Y0AMDr6\nFbDFFpPCalcHA2+Gw+B+WxB3nqrRu52wekRd2hcyChaeFGN5OwAscQbRKiMBdsySHWAjmZ2ef+7s\ni5SnUJjKdCbxjRbvRhRpCvMKq1ev3rFjx1yPYn6hJHfwk5iGh4dhfmRDfPWrh0w2o8lN9X+QwV8p\n2Pa1baYJh4N44IfNtn4Bd18Ulr49XrAGHhndyt4dLAuTO13PPHPjwYMP69YdBJlM2HFIXxN3m1cm\nUCo9dGgPACxbdjGd5RNu8IqeC8Hwu19Gxr0pHR8ZcBiYBAUekO5ITLavwszKaFR15+2EX8WJnIG8\nFIHxuGartUAeIkn87hS3yPTAeVWpd9u2bScaGdELKMkdQLM56EDa+fNF+b3fu1k7x6SpkKUNwNw0\n5rxvx07klh1nGadAmE1MkcNfIXZzSIdHaAT69PsxxO2HTurThWkWx4vZHU1R78WDKygZI3rZstXg\nErHVsPio+0ai/w+4o00RNz6lBeUjx+eh9zhXdPLFrFcob9XyyG6cp/iagmKYlS4wAr1vImT3hWg2\nBKJ805veH3gwc4Ft27bNBztsHqIkdwCAffv2AcDw8DAF0s4fmNhk+t0KEWs1VghRIduK3pRJlOA8\nS9Y02k5XyIPczcRg6bNazc9+7b7Z7q9v57FnsL65W0USQsap2e/saTaPQnGMoxOR6Q0P/W3QEe5U\n1b3g3LCC74kzwf3WGPx9nfNRAYBXcjYXMkuOYI5A2R92FcdgR/3eFrHXvnwwfEkTrvhhljeX158p\neuCzjJLZO6AkdwCAtWvXfvWrX50/BjsDctHDDoaho8J486geN/2AdbQMgiu/OgamUyeAx9ihH7fu\neeoC62wEf/kFwrpr8oNHkUopCpip18cLqLaQZVgeAPrNli9fqy8d7tZ53QmN3Le+jT/ACn4P8b4V\n7mK4W+8x7laLrCGLXCx8XIjh9W/1NyRfrcn+mEzEDvJ4VuawMewfORtziC1btpTM3gEluQMAbNy4\n8dnPfvZcj8LFq1/9EWC/KzsHVW+ynSx2TbIXbcF5xFlz2SFr5/vgMLLuyjQGPVtk+/Qe12Fowjft\n+8uEFy1Z8IJZ/KLZWUycAbtBkX1dSM10nDJUa7Wzgi8P2kTtNHMUHZrKE5vBiS6lffQGZl/IjfNx\n/Lehj8m6CnOooFOghnfCpwy9P2IftClgkH2af/AHXyp6ArOAer0+396z5xtKcs9AblUjvs8HfPvb\ne9hrsvCsJ8WC1vnrOeoqNKCrkWgj27a2vD+tyEVO5ZBJNOE1g3SDQJ8ARn93BBlnMIrWTS1+38cD\nBwIfjRNrb6PzMh1B3Vz3Wmwas/ZOxLqpKmz42ukz0I+303oCxt3COiRy9xOD/TcwyF+uChZdsWuN\ncfqOWUSNtVgjBVOSU+Thh78fejKzgW3bts3CSmoLHSW5W6dVsYkAACAASURBVBgcHJw//E5v0rTp\nr8jBY+OMGgO2AG2zAE9GRydd0ydlVv0RASzFRuv4uVlnhhGKAwkwbPClXtuS3IrPDNVlyy4KFQ4L\nqPN6fydmRxSIpLnjxMQBzebW3XW8Bdqh9GjdPNXgS0NBkhcff1Zv2V+TxHYqFHkpON0jskruzufi\nxVAFhBqd5ww68U1qCc7E0c+Z5j48PFyqMdNBSe4uBgcH50ltORZ8Zpidr8PATXW3ahjRL5eGnQBH\nKRMdeOf0BqBlem050j+X+8xLQ95pKMIv6EcNUYOyx6DYUtQIWZJqB73CuW6HL3YmUDiuVKLCginB\n2alYZhPvIfu/2FEcnNLc1FzPL5JrbgYOvaIVn4rkgbcbFBZA5glxPBnV1CZiVjz/ps1NEYIy6nH6\nKMk9gKGhoTnn99tvpxcIZL+x/KfFvGqOA42qNtK2lV8ekhrMz7hQWzeX0zagsfR9B2lAedBjcCT4\ncNHEIK/STLBkyYWNxhG9SN4URQg6M7s5Srmp+/c/yI8FDVKKYmSX5kTs1GAAYyx3HhufI/2ZgNW1\nz1/IdDMTRerEyTjxSNbH4UwPPANW++SFtveldiYLMzam85hI3MBa56cbZWzMCaEk9zBokaY5HMBr\nXzuof11SS6eJDoKMjTeM/551OQGCQMtd1iFCztfi8xnCdKB/8FkD32z36d6eUbi/NGjVugYsMAZp\nNo/SYnugqRZRmogUTrvcTxi6Sn5pstxXrHi+s2CIk61qgl6KdJ6iyMgC6YkvqQrFsxT67gTf+vbM\neauGhKfGmBBY4utcbeeuXVYpDI33ld8OT5175BH/Fk8XSmY/UZTkXoharTaH9vuHPzyMLBDCcKIm\nLzK6Iy6j650ANrM4Bp1fdFB3i15j6sqtM8Ma5LlINveZrjhZK2Qh1fYlAjUUOXmdddYg5BVmLJrT\nZnUed+Olp5o1r0EfVTpDlRyhpgJlvr5raDAdDFXfg1rY0uSj2auqThn2DuYjYnu4FINm2ub8znvg\n6Q56+hf+qwYrX8Er+OevbsHA1tOKMurxJFCSeycMDQ3NVdnoD394p6OrsA1jQfMfZKxfmc06edQe\nubsV3B+8MfSyny79sHmpK4d2uW3I9rnWq5ZZ3JY+A3puWGPjW+pQHC+iwu5F4onuytXH2f9o/+ne\nltkqPhoOzikK2gkZ7/wlwBLKvGfoTMN0YmBl7Y6TCvqLW4H+EO2FPqzc5tDHhIz0s9no4YfHiy89\nY9i2bVsZ9XgSKMl9CmzdunV4eHj2TfjXve6ljMRNEhMysYXHNnARRnIVxTbWnHBGZK/qdKHYoe6O\n4Y+gX+SD61yHhXUWA252Ol/CsNUZx4ubzSP+ftaPP+vwg52+6v4EFvzTvB559Fdo1zO5ib8ZWHmn\nuqXxfvveEV5C0nlDEt5IInvMVgMpK6wHI+6ZAXCfiu/UyacKSlv9h3+4L3jXM4hSjTlplOQ+NQYH\nBy+//PJZDpG8887PGs+V2cnfl5lQI2zrzDLnOVl4y3H45cMco95VS+ycUtTNXEHGT1sFVsmAV+vt\nGFhi2dfN5pFm86i/grYZ6zSldn4GAFSrAwWSt5G5OvC+w/LTkWXMaANnFRfk8aX8vI8if7i5BEsi\noy9MOOzdEc14+I0W34X+kmQBka961Yunecsnh1KNORWU5D4t1Gq1WQ6RNG/uLNTdyRdHr7Fpb84V\nOpCR/lnh0kWZL+Z/T1Vw69BCoD67oouyrpwR5i2hk9mOpg1h5coX0KuI1w83qN0jQSub/1mvH/Q7\ntAcf7DZ0gi0u6dieoL/UmdWczzrrwR4tt74TFsOa9cY75/oJZKScv8w54+HfClsd4t89SndCRF5K\nHj/60dNouW/ZsqVUY04FJbmfAGZfgjdvx3bkWW5h2SUE0MlPYdouOgmozpJ4IevbFVv86o8hCz2g\nCzu0ZSsGoL2g/EKu1gwAzeaR48f3kzITuqg/SaB3KCwlBzsE176e1imQu3bzKxa9VQTDbPzgUW9h\nFpfrAXy/BbDM0sCn6dUI4hJf/magV2rk9j5tcz//aUGps586SnI/MWzdunW2+N1KKDUCC6JgdcQs\nn5utjUpHgYGcrZCZjWGaDuWaoicRFMkp4CzIUaClcCNRsQoEYefkwMBz/J2mq6IDJrKowNx2U5lC\n5xYdyjYBgAViumvmGWlkmm8ABdOJP63666U4NXn4jaMeg/9GSNt5M0TUWRTIu0UEVlkanO/PzGJk\nZKRUY04dJbmfMMjFerqvwk11Hq1ov0Rzc9jJprHYxwmZMImItMf3mvoWWXBdPY+J+Ik8eNwqdKVP\nl14zokLBSom5weBByz2kg/M/i4BQXGwy9EITaODVHgAnudRsBLvyniGtrlW4zom9r2j2zf70khvM\n1yljbfadMYKb0P0Ycs9ndC7anL6qkFu2bJnz5c+6AyW5nwxmoQSNbXf7rI3aj+q8TWfH+CEd3cgt\nbrQbO2/0bvjjNPNRhXC8oGGqsu+uk/mpO8mquMTx4sOHv+sOophlOrpYs0try92nTvcFxU5uUkW0\nb56nZ8K7S4pr8HCavLnbKHCbvNQEXcJynLL6E9lxXsPduQqidBytpgHPfrILWkQbN67yRnVKGBkZ\nKdWYmUJJ7ieJ0+1fHRxcQxt2UBqX1GNtD6LtKbX0GdrBOjZR8IFZAYBEfNePCsDVhiLKFmBPGxB4\nnwi8c7CjUPCFRABUimT3n2ljmf6JYEEx/9L+hUZHH/CuksPwOHON8opm1u14/ReJ9W7oS1EnRYGk\nzl2w52lOtNbaDgYC8Q6LHa2WCmdr9Hmpmd27f+iP86Sxbdu20mafQZTkfvIYGhoaHh6u1+un8yI5\nQwWXwIbM8SXpp84kF9Cv0nkGObikjL4B7th6kEn/4Oyc0rQ06+g5JR7tSxSa7TZDZfv7+lY2m0fs\ns5QDgJRJJargHwKolSufr9vQKalN4k4lL2R/TS37FE0t3MVtbiE01aH9lAz5ot0m34N5fbfO4gxP\nRBI8OhbtUMiQiM9vDQHEpk0XB2//JFBGPc44SnI/JQwODp6mt8i/+ZuXAAhhBbbzmlO+ne47ykAH\nJnOFwVKE/RBpx5D094DmcW9RUADLKgQ/TF6PMGDAcqdraC4BAHja037LVJgJXhTySQWLmR1oo14f\n90g8qG5ng9ZzoRkSgvdZ2GMOHLJzmljfoZY2m/vGNQA4c7kR052xOyY5D2dyvhLSrieTf7VMnrOp\nSQAAGzZc6N37yaBUY04HSnI/VdCXcsbt9yhyZHcrTcnWTMPWPcXY2Hq9ZRojRg5Z+NmnXhyhVcs7\nj/gLyyw8GCYfVagl+i39nqn8gPapuqoxv49iR2jAVaD7CdMxOxM8Fg6eYqYowdpkUEoFJ7xp6DCZ\nV3mqKjT+VIFOmRqnroMzP3mpbfnMYb5OxtUxNFTzh32iKNWY04SS3OcpHnoIeDC7MRidNBObzflL\nOjrpqR4vcOdYLuCA1SIQEGkTAZ8AXLPdPtFk9ATMbTtS0HkhyFv29a0EgEbjiObo8DzRIcSFT4rL\nlq322Lkzv3e4Ylho0n9y1QgKLhH2DBeI5oXijN7jKmmOB7tjlVB0jHejyzvylD/ak0Cpxpw+lOQ+\nM6BFv2YwBP45zwEAI4zykpA8PNmYYEF2dt7orfV9/FqPofBHl7MKMvV9VgobyHZBRFXUmJroNPd8\nzEmy2JxQTC4dmN1SOfbt+9A0T5xem6AIg2DrV2wkHXpA74Fbrz7+6U5yLKIrztiBj+g/cz8rQo/f\nMgJYeC56ycknjDIH9bSiJPeZxOlIceLRMvyV2bHE7SRDl3CnXBfNC7hGISKHlLwrclkWeCRJsJRY\nqJK7AlAhRUJ5rwjZRhwveuKJxyCT1P1LdBJknKuvXv36gpYQtKyLD2WXZn+ZZaScG8nfDIomP/9C\nwYIzIWpGf48daO84SB2txvLD85Aq541wprJSS2Y/3SjJfYYx0/zOtVSi7DxWgbdzXrSLYmDIZ+hn\nJIVUDp/F/NB7n6yDJwI3+mxLFvWJ4YhGB319505M7LcvZy4QFvS1yeke+tGP7vGGAQV7jCzRaYJE\nRE3ryvY2+88q/OZhW+UqtNPA/bzsZfboRGmGzu4hv5ozrXIzgg3bdJ5bGPRN2LDhAv8WpomyusAs\noCT3mcfWrVtnKATeqa/rmO35Z6eXPPWlGwBtXDs/bN5AyoT9qhF0LLz9Xu96X6EgQalAO7aGZNRn\nz2fIi7mbc/MW5577a37nuk2R1uFsZFi58vm12ln8EDLo/e7E4ClCihE68H6s0YXlrCIvtDvVhYz3\nwEzj8Lv/TSDznJO2ZwTwdwunzFy+HXT/Th9lFd/ZQUnupwVDQ0MjIyOn2Mm//dsf6U00vk3N4HlB\nAjs2OW+p91gOWB5eaU7xrhzY42fMhmSWIrXBJRG9v6jer6lMkOUQQSbEiyRZeuzYz1hbiiGBoG3O\nGoS/5xMTB4Bxuj0GdDaAUThPVdXN3AmG28vFbzPuwJRSIR9GkN/95+9KQLxEqB5kUVoDtc8rPoIb\nfOXKOCdnudfr9ZLZZwcluZ8ubNq0acuWLTMVIsnVZKecgLawkP2e+Yl+Koof/ui+4Guq4mf5Q+oQ\nvWcJL0G2KoArCFBXZg28RuNJT8DpRN/FpA+HD+/reKLuPYe1UmtoqOBcis8QBcNwlXrOrXZXgn3K\nZmeQ8f0T8z4dLV7bDWhyoLyM5XyETurc1Vef2GJ7IyMjW7ZsodCDErOAktxPI7Zu3bpv375T7qYT\nX3uB6o4f1V+dw+nKJ5GANR0KzygUZLQtGxBY/B58/b3IX8cHNj7+LSfj1I41dE8NdlitnlWrDdj5\nram9Lra5kYBLoNgeL7pft2Ck2a+vYvYUTZwWTQfH4Av0oc9O6qsAol+zk6tSfFLJzwXP5TMd7N27\nt9TZZxMluZ9ebNq0qV6vn4oEj3qlBf1nxH9+vp1lW2WdrHjdGxREJVr6u3teYALIf/C2NzHAU0Wi\nbUG4i9L9Q5IsNuvtsXHmt2CXIgDO+z7sSwTou5jBzS37O6H4Z+Xwu6mFEOgkGO84vXnXlWt8LZ5F\n0LoKm52jgLYuny+1umHDMwvuMYyyiu/soyT3045qtTo0NHRy/P6Vr1xfIKC7kqhNo0TKbkUw89vG\nLIrRr+oeFMED1r0/VLOAA+TqhNLuQadl0O6zRuKdkrfv7z+X14YMFjMoGjkf4eTkwYmJ8aKWTsp+\nqOdC3g+WEwDX0PaLN/gDKHry/NyAP8PPeHDSrITgOQTomedgf+sk90qQLn/LLSdA7iMjI2UO6uyj\nJPdZwsnxO/3MtGtO2Ha69ePnnlV6Ny8q/MTa+BKNHw8TCJrUE4BFMeHhey2hQNKBbKWLIo5Gbmgv\nW/YsdgimwaQ+hLdMBwa3iyR7009wb/DqOuw9+JYwdRlIvTOYweR7gzvsQfsVLXAtIyJp6SZfAKDj\nq0kAZXWBuUJJ7rOHk+P3V73qt/TmFPK63jRSaQ5utus94aV8WOGt6UQ6ZoKJk/7KLgGsVhfwAXh/\nhiNquNVJ/N7Xd+74+EP6ULgkgLmF8AFEADh0aO/y5auDp4QGGab+ggu5dj1XgYrTU33W9jtXoWkj\n8Bw84cuNX3RO0WI9sj8jfS1+O4FvVweUUY9ziJLcZxUnsQrrq1+9AgAc7nN01VBxxyliZpia4eiw\nBDdHVF8okE1a4ALN5xHn0gXJpahC7tCOYTCFzF6gaQCy4l/1+ni9fqCg28Ben7LNweCf5v69++rw\nSjGdBx70nfgrgfg34l7Xo3vJ2zgd8oX9Pve5ywrGb6Fk9rlFSe6zjZNLYbV/h1kBd2NMMUvT+MfM\n0WAxgEKJhtndgZf9EI8LLTU4p/tWf2B9VG3SZvunw4NLlz4LQsoDH2eQ2dmAM+iS7s65YXTUZ7hm\nzR22JzBjOcJ3QWMjjPjNXIUqZM5H3kky1ADZq5uvUHXWqTKUHtQ5R0nuc4CtW7eeUPz7+973WvaL\n4to6+Aaak1ho22LcKOOnSO+bgL6JXRD3EhTQRYHZHmAH7arLw13YIT9/Misfxgu7e22c/jmz51vn\nn//S0dEHO58b6rwIGZ8r55kVnFLM72A+Mt1b4M2gYH0PX66ZIhA+5I/137T4ufhP/+TOiD5KD+p8\nQEnuc4NqtToyMjJNit+4Md+2A5lRCMlrN/o+Sd9sD2k4ufdM7zR9Kt7MG5qj5GQ7i92DAabzr6X5\n3RWF+Ul+P2xI/CzrUvzQ6OgD/lim6pxFjWQDzmPti8ZT7CUOXiALe7fDSf2p1zWrISzX+JEwRXFK\nerhs9VTdHr2jnVB6UOcJSnKfM2zatGnfvn0nmMKKdgwyZ0znT2otbDIKqiXmZ2z2ODyuIEQcEGAK\n41+1ejZD580KetAtskUt8gQik/cPgP39542Pfyt4on1Fdwf/Y/nyNSwUcpqTB43BWk+VdVCopAcP\nFfkqANDTcqawr1mfU4ZFTm28O/zOJcHbbntu8LqEer1eqjHzByW5zyWI36cjwX/5y6+ALA6ddjjv\n5uhtALCfuqF4R3nArFg8sNP9VSOKfIyBUmJQwNdecE4wdKTITgfO7wC4dOlFjcaT9krZgUvbFOmO\nanT0wWc+8wp2ObQtcT8fKjBO9y6LQzkN7BP82VF5rYouGnApBz3JvjFeEEyVf4ucz8X8uWqVP7Ac\nW7duLW32+YOS3OcYmzZt2rp163SqjIXUZEui9fQWdx0l32yfTnEScyHlycmhlhEPpjSnn4jp6khP\nbm8AkCRLjh+n8mFmSMbS54zP2dn5BwBqdPQB1iwtzl91h+fvK2rsN/BeEVDfiFOQx79sMMLdhUPl\nwe58icz5LjkKVZGkxlFW8Z1vKMl9XmDTpk1ThsB/6Usv5w7JaZQWcD5cN1qO/uTabugs9GqP0Lmu\n4As5gxgyLRoJQXk0lw/V6Zh1ld1mo3Gk0fCLEECQg0IDUMuXryk6xbGyQ0RblL8asLqxoGCkOeoH\nnmJWAdTpybfKg0udgBMu5W2bNmiua5vz6EdGCSE/85lCTaaMepyHKMl9vuBEQ+CdtPug2s6b+64w\nY8izQuSuRMMvAdp4Lyouxk8nhZyN0x+/LAh4F8Xp+1nFq76+c9nuvPJMgXUZNjknJsar1QH2AIuU\nk0IRpqBz5PE5/gbk70DKo3W0P1CX373y9/5O2iOcB+IHwtt3aiQ753g+nvXrC+sNlOugzk+U5D6P\nMGUI/P33X0UbXr0wt5DAlEXbp1l3sGB9Plcgcs4CAKbiZOEfzoWKzPZQPCKnbwCAJFnc33+uVmbM\n6UU+xvD+Wm2gXj8QJHQ+zuD+gnEaZHa3b3rbgo/F4x36CQ3JCqYJjaRIwwm8Bun9RS4BBMCbbjoz\nOMRSjZm3KMl9foFWceoo0fAfofVCzWQEx0gPVPq145cBphflRidqdds54ua7g0uOXKsRbCcbaKcl\nfiymO3bsZ6Y2ZLFx3YmdDx3aW3wtq4/izqeU2jMY3b8oazQ41RnW9gI63VEFFfriyBlLjbFP4u9k\n9E0TAHDttc8O3le58sZ8Rknu8w70ayni9/vv3+xZ5ZaY63svQxEUwT35GdmuggQlvZHzcoHy28nA\nt/2uU0grlFHFb+u883792LHHoZPZOwWY5l6EKbm70OSnp6QUdPbNFl8rl1Ps/VzpclQ4n8rDvgR7\nTzB5jf8pAeDyy93hUiHrcuWN+YyS3OcjOvP7e99LPzUEyFdaYGa7X+7ViZkRiNKIBiRw215TQ7Wu\neeip7UqPJMBNpj6tF2ZjCoEBc736Vq3Vm4NG40izeaQgiyq/04IOAQBHRx9cufIFHRp0HkBH6jdi\n+vSr5XQIEBLO+idF81+IqTu72X3jHfysq9tuc832er2+c+fO0maf5yjJfZ5iaGioyMV6ySX8L0eQ\n8TNUXfHdr+AYDCbxZP0iszpMygUh5+h1mx2HbFUN6MDRTtXfZvOIZ5xOnR6lh4HV6kC9Pl7UYKo9\nuXZhYoScoHso1m0K9vvvAR0UIT8eBkI6e2De9WPYQ4GSOS7wlkrdunVryezzHyW5z2sUhcB/4QuX\nQ6isq5fW5P62iR69eJBg1LNvdYZXAvIpCQMLCU0hTfC0ex6ZXpSXFMeL7VBI50KdFBUacK02wDNU\npwF/IslfOwpaTsfzzBFwUfCYzM5dBacM/U7muKztLgJve1mbT31qvdO49KAuFJTkPt9RFAL/ylf+\nplfc0WX2aeSaBt7c2c7c3gavILi+UDAYJtBSKT+qp7C9zT/cHFZ6fkJEPHz4O6EhdXZ1Zoe8xTrM\n0eC5ytaX3OAfm9DzfoocD8URop2fZzDWhe8MlJfw3rpc4x28J0bF3K+91mL2LVu2lNUFFhBKcl8A\nCOozQ0O1V7zihXyPF9rsr6Upda4pP8n9DgT9qEWhk9OLGOH04ZvwDv3lynKQv4hk43ixUqqv71zP\nXdmhhheAzWK1Ws7voSVVXaVlGjfr6yr+KxQG+VRf1++ELt1Z+/J91LyZ+xj9UFQ/d2H9+me+5CX5\nn/QGWVYXWEAoyX1hgEIknZ3XXJNs2HABZkVj/BylcNQdgYgglNkUzL2cjg9Qh7WHMlrBmx6Y2R5Q\n/O2rB6I+ALC//zyy3P2CAaF6A4op+0opNTExNjEx5p2rQtNPfuXCA8Vh705wYWgb7Ckk3ElInDGd\n8Ol6WiuSh97hrC/DDTf0m+2RkZG9e/eWaszCQknuCwbBVfre9S5aKI4bYlkSKWuFkP+8OTUEjcFp\nrdtZ0NJNo8+vZJELZ89AoSvdfxGTZlqQIXfQKo3usAhWh4cP7+PRkJqdsegWmA1e0HvxgDsmSfnT\nSZGSE9RhhD8rdKz27ruCnfEAAHzyk84ChFCqMQsOJbkvJBC/O1WC77vvxdOxyxy+QARdAEDZzdz2\nBepwUS2woCcWijixI4OHTzSnsGWyp7hK8Gi1ekIO1emoT535nf/JH3vRYwzuDz4WNx8tOD1Mo/pQ\n1j9ndkqpK9WYhYiS3BcYhoaGdu7c6fD7u99tie+22EJme+z94IVvt3VW23nefJEtP23GV9q/Gqaw\nYn9jfhcmSdWnvNAo3A6r1bOC3Tpdedv+n9OE8ZQ6ztIppzfeOJBB5hWNof875HYVeVYBQGzYYNWQ\nueKKK0qbfYGiJPeFh6Ghob1793J+X706r+tUXM0VWOJS5/SW/HTnnUAXDgua7aKAepxIcLO/8AY7\nElP+jV227OJG40n/0DSLAtTrB2iZvc6ZtEVjLDwQvrxyMmztroqM9CKBa1rpWsXlB6w2fMDr1j3t\nrW+t0PbIyEiZg7qgUZL7gsTg4GC1Wh0eHjZ7br31QgAILnHnezIpQ9VrFuSeabFG6HS/jMzUPYc6\nnyInSJcP62Czh6+1fPnqc899QQdHqLnsVPuLhCM/ralQeZ/eIwXI5ld/P4bEGZ/czZfBUe0BANat\ne/pb35qY/atXry5t9gWNktwXMAYHBzm///M/v7BARSVz2+wL5iKZ+uzcbHfXXwUARBmql1JET+Hq\nj2z1D1/095nLlEOwLhHHi/v7z9PGeweCDn/Jq9WBZctct6F/B1M1MM3ykTvl7K12JyLCOJRtHntw\nQioQxPzsJP+KiCiGhi5861uzj5tW9y1t9oWOktwXNgYHB3kIzec//+v2cTcdCUJ5rfZvvlNMd7Gj\n7wTKwnTYTxctqLQVOGVg4Jf4oeCQg1dBxHp9vF4/MA2zvbM4gwXh8Cd24x2GGtoOht8EjfeAL4Gv\nqG66+5//M2+xd+/ektm7ACW5L3g4KU6f+9xlZpv/jL0Ml9zYLCg92GGJHwCLgosiZxymtsx2/4q8\nzXSWuwOA48d/NtVK2YUW7ujog1NV/e1AxEWFB/hVCkWY4v1TKGMFIfOBHgoWYDHdWOdu336+2R4e\nHi7VmO5ASe7dACfFifg9SBbFLjX0mk394k/MW1yEPVDwi3oKdljEekqZ9VFdG/ncc3+dLdnho9Mt\nVKsD5577guJzs4szEneu7qpYoWudWFxNgd5iXSXPZTqB1cl9sS7X2bdvfwZt1+v14eHhwcHBExpz\niXmLkty7BENDQ1x//9znLgv9zoVPSaE5AI1Sb+0qsOWD9nXx4tcnKuDwrtwKARQK2Ww+aWq/0Fjo\nn98nfxvwCof59B3MAPD/PNHImaJwI9AiT3B/uJ9Qy6Bi4w9NAMBb3pIdosCYktm7CSW5dw/Iv2pC\nJD/72UvXr6fXbWPrSYB8dVO9p4N1P6WrMwx/uU7dG0Kh2d6BBwuvkyRLQ/sp7jBs7BscOrS3Xh8v\nOFrEvEVHT0xJL94frJ+MTpXNYnFGmR5ChT8trFv31O3bn07bpRTTlSjJvaswODjIQ+Df8Y5zTfy7\nJ55kEetOD55RaQLbgxVLilbmK6pFU8TgwekkO1hwiXzwfu3fApPWQrU6UFAYsgNmRmnRh3haQOeI\nyUJ9qSAYKbi4dv5M1q077y/+ItseHh7et29f57sosRBRknu3YXBwcOfOnUaiecc7Vr785c9DhOIV\nk52d068t41RanyKwvSDwoxOwcDrIrz4w8Mte4d8pyJE6rdUGChyqJ0bfU541zZudqj0WTZkFGpGv\nI2V7rr76vD//c+tYabZ3JUpy70IMDQ3xEMmXvhRe/vLnea0EgFsVYPrMHtxv8leD+6ctHOcBhcUr\nz+VUdezY4+Pj/2532EEfz49OTIx7KzGdsGE+bXTudlo6T/F7T7BxUN4R69ad9+IXZ38PDw+XHtQu\nRknuXQseInnFFfDpT1NIOPDaI+7ipgXLewKANw0EahWE/vTbT6cCIrXp/OXM+kmSxXG8mF1oWsxO\nCK2R3ZnfT+Vo6ATrMU79ZhNccdDTu5Dtt07/+MdXGpt9YmICAEpm72KU5N7N2Lp1Kw+BN/xul2Hh\nzlUXdi0wp1iV37iooJgTkJOHrEx7tWgo8NBCHC+J4yWszXTptV4f96pCdnCZTnk0cHU7VH/6ES8d\n9iMAhmL/A+KMLbKf8/GPn2P+JJ29ZPbuRknuXQ4ncuSKNAAADmlJREFUBP7Tn/6lUOyESWp3EawY\nU1B4Fvxs2IJOTJuiyD/exh+S9aXt7z/v+PHH9aHizrxhVKsDzHL3FW33DYDKrunia+FYF7DXA+k0\nmvC1Or8GZf0XpKc6LQkCEdatO+fP/iw/NjExsXr16pLZux4luXc/nBTWe+55zrXXbnTa6Nruzs4o\nyGLTkOYLC9Lap0yxny8H6G1kTZYtuxgAms0jnc324LU8zd09iZ3u9NbxtMJpcjrPoUic4Z/OlP7t\nPJbmne+0mH3btm3/f3vnE9tGlcfxn2kb1U4aBbVFJA1CFtpsXLuoiuNeQKJSS1uEqGQLkaY4hisS\nuyBO4IlYAR2HXlDR3qBFbeK0KSpxL5E4bI49bIMjpCZMNhwQglQrWomqjuOKLp09PP8Zz7w3dhzb\nMx5/P6pa5/2PG3/nl9/7vd9zu91ut1u0eOAYIO5tAbPfiyE04TB9883B8hxSLp2hKQowFzwGjI4U\ntVAudEcITFutCObt32IqLtFoDx9mxLl2hb1yuTuF6czUupBHgf3RWuX8CPrC9+3SfkEV9J0jzZpy\n7cOytCTTQWh0dM/o6J6nniqV5HK5SCQi/D6Bs4C4twss3I1tozGuXTt49uxBylvoDK1U8bMXiJOS\nG1HFt+jlZc6o77wkB8W/XTx3h+rx7OOuSbMMPoULsjmbCtq3ojCp6KyT0EFvfLZtNixSDPeMa6lE\nlvecOEEnTpTqFhcXZVmGzd4+QNzbiKGhodnZWW2WgmeeoWvXDj777NOGtnzTkKuDon1Uk41HkQ9H\nYESbWd9E1NGx66efUuLzqNwdSCKiQspfXcoBfXfRvFXU8jqYXTJFhTXo2uueEOxf/jGFQGD3pUu7\n+/vLytkOKm64biuEP/fAqeRyudnZWeO5lddeWy6+drm2Cw6v6rwHzD7dxt1jZLkNjFW8u6Jcmiou\npeeBUeWz2dt37ix4veHytelf6zrOzR3t7X1haOhDwYy6cUxSvmx6T1iU8F1VVaJHVZarKhE90n1+\nR0d7jh/Xd8/lcjDY2xBY7m2H2+1mF23ryr/+2n/gADPh9X5eIjKY23ldM3GqixwvRkzDIsm8isjV\n0dGtKxG8LqOnxxjkrh+5UoMa4cUgsbQw/EnF2SJLb0sg0HPxIkfZtXvpoK2A5d6+TE9Pc8+dj4z8\np2CSk8bsNZrtrHybQHq2adqUtdd21zaozWwnemxjY2119ZLf/3ZHR7eJsuv63rjxd7d7r6nlLoov\nNNbWbLzra5k9LmjPNd5VVX108WIPdxbY7O0MLPf2RRciWeTq1b9++ukAaYxu8SWfxmOu+fbaLzV5\nKM13ICsHtnNTw7MN1Wx2jdtdxIMHd3gnVMtGFpe4CgHvosb8KkOwjaF1uT1eNh/PeD9woFuk7IuL\ni7Ozs+KFAYcDcW9rdEdYi3i9dPXqwOuvD5SLchG9RutOwxtliOm7MbCPSmY7339t6pAprWHHju5C\n+jB+bkVjWoKdO/caTqjqh2XL0+h4Pm6yOFilY00luBfPCpwwgjWV76wGAru++mrXe+8JZ8QN120O\nxL3dEek7EZ08STMzA6dP/0XsCNZSTGPAfqi4lq+qaSxKZlDxOaFPP+lyUUfHLnaayTACd6n5Lwuh\nkJzm5Zqen6UQY87twxuJs+aqML/SpKKss4xgcMi0ORB3kNd3bYiklpMn6coV7+iot1BQNNvL7HfD\nHa1laMIldbHkZLLxI9qrVVXVONHa2rxmhVrTW6i7vb0v8CYVNa9YaxL6Kawy6WUsOnWq01zWiyC7\nAIC4AyKiM2fOKIoi0ncieuUVunzZe/p0XuIFpiX3IqGKXgsWVKMXfZPznMVepFHbjo5duiriK3up\nxJjPvYpDRqWHmeHMqol5bv6NVP7FKBDwXLjgOXaswuLYQxrKDgjRMkBLLpeTZbniUZeff6YrV+jW\nrV+IqFxJi3dt6/3dgszsZeWGw5zbeF3yExVLWKc//sisrl4KBN7Wzm6u7PPzpx5/fH95tIyZtqtq\n6UEi/tQIt4WJSFU5YTCsRvN32YxEj86c8fT2ClelhT2boeyAAcsdlHC73ZIkGUPgdTz9NL3/Pk1M\nPHX6dClxictFmk1Rtby88q17PLe4Ps0AryRvPmezaw8f3i90LFSbGi4PHtzRXbOn0W6OYa579HC/\nI5PpyOzRwQki8vt3Xriw88KFapV9fHwcuR6BFljugMOmfrWfm6PLl3/V3NFaJlWGS1lLbYq2ubGB\nYFfWpanS9/j++4TXGylkFDD21c7iIlLn50f373+r3O1uXGcp9ka3xsLnhhucYxb2Lv7E5Z9en3yy\ns0pBL7K4uOjz+bCDCrTAcgcchoaGqj/Z+PLLND3dPzXVGwhoNakYPCNSdpOfPdG1TSLj10VEe/ce\nMgl1N6TPdZHe527mFjdOqwuONK5nE2MVOH9+5/nzm1b28fFxRVGg7EAHLHcgRHSE1ZyzZ2lp6b/s\nteD0k0vjk8lHuWtrBZeBmJntRPTjj5M9Pb4nnjhk6EjGKYhobu7I0NCHBcvdXI755ZU+OiYWepnL\n6Pz5DvOBTKjt/wi0AxB3YMb4+HjNqQR/+YUk6Q43xlx3BWt5G20eeZ3omyWfuXdPoXyix8rKTkTz\n86eee+6fBbd7LeJOhV1WwWfIzDnj9+94912TOatieno6EonAZgdcIO6gAuPj45IkbUVBfv2Vbt2i\nmZm7RGQ026ncGy6+w094oxPrtbb2r2x2bWDgjUre9jxzc0e83lf373/LRNkLQZxVfUZ4nyR90cjI\n9qNHqxmsMtPT09hBBSZsr9wEtDfsiFMkEqlZR/r7qb+fXnppDxF9+y3NzPyua6Cqquauok3DevX0\n+H777d9VKjujt/eFiiEuhY6VYx8FO65ERF9+WecPGrwxoCKw3EFV5HI5RVHqbie++ea94uvya56M\nZru+sFTpchFRNru2unppYOCNzs5+bZ2ucfHVjRt/6+s77PW+Klpb+dkrk3zunFq/fxsRvfOOaOwt\nsbi4ODg46PF4GjI6cAqw3EFVMLdM3U8/ajMafvYZLS1leK20GmruT1e1ym7OvXs/9PUdFtUaTtUa\njXdO7cjItiNHqpy/RpLJJOGkEqgCWO5gE6TTaUVRotFooye6fZuWlmhmZp30ETJ6S1wr7qurlzo7\n9+3b92Kxjjd2aUM1GPyH6MoOQcqEUlS73//Y8vKjL75oajBxMplswpsPnAEsd7AJgsGgz+dLp9PB\nYLChE/X1UV8fHTvWpS28fZuWl2lmpnjHtz4h144dxfQyFd33rgcP7v7++w86cWehLzplZzr+8ceP\nPfmkbpCmKrskST6fr3I7AIgI4g42i8fjCQaDkiTJstzkqZniv/giP27n3DlaWlp7/vmjH33Uce4c\nLS8/9Pt3BAJ09epDbbNAYPvS0v+IaPfufZ2dHadO5U/JHjlCn39OIyNERAYRJ8uP+0mSJEkS/Oyg\neuCWATViib7XkRYKOEmn07Ozsy39boPmg/QDoEZkWZYkyepV1I6iKFYvoSqYEwzKDjYLxB3UTqvr\nu/1hsTEA1ADEHWwJWZY3NjYg8Y0gmUxGIpFG710DpwJxB1uF7fKl02mrF+IoWGwMdlBBzUDcQR2Q\nZdnn88GHUC9gs4OtA3EH9cHj8USjUdjvW0eSJCg72DoQd1BPWAi81auoCnsGAafTacSzg7oAcQd1\nBiE0NcP8WlB2UBcg7qD+QN9rIJlM+nw+eGNAvUD6AdAQWIgkjNAqSafTkUgEbxeoI7DcQaPweDyw\n36uBnUGFsoP6AnEHDUSW5WQyubGxYfVC7IskSXDFgEYAcQeNJRqNKoqCEHgurZ58DdgZiDtoOMFg\nUFEUuGh0SJIUj8etXgVwLNhQBc2A2acwVIuk02m8FaChwHIHzSMSicB+J/jZQVOAuIPmwfKSt7m+\n49cX0Bwg7qDZtLO+Q9lB04C4AwtgIZLfffed1QtpKlB20Ewg7sAaotHoyspKNpu1eiFNAsoOmgzE\nHVhGNBpNpVLtoO9QdtB8IO7AStrhiBOUHVgCxB1YzPDwcDgcduoWK5QdWAXEHVhPZ2enI0Nopqam\noOzAKiDuwC44TN8lSRobG7N6FaB9gbgDGyHL8tTUlNWrqAPwxgDLgbgDezE2NiZJUkuH0EDZgR2A\nuAPbIctyIpFoUX2HsgObAHEHdoTpe8u5aOLxOJQd2ASIO7ApsiyHw+EW0vd4PJ5IJKxeBQB5IO7A\nvnR1dfl8vgbdaKGqah1Hm5qagrIDWwFxB7ZmeHg4EonY/MaieDyOqEdgNyDuwO4MDw/b2f8Obwyw\nJxB30BqMjY3Z0H6HsgPbAnEHLUMikYjH4+vr61YvJA+UHdgZiDtoJRKJRCKRsIO+Q9mBzYG4gxYj\nkUgoirKwsGDVAtbX1xcWFqDswOZA3EHrEQqFVlZWrNL3VCoVCoUsmRqA6oG4g5aEhR42P4QGUY+g\nVYC4g1YlFAo1+Qgr/OyghYC4gxamq6trcHCwOSGSUHbQWkDcQWvD7PdG6zuUHbQcEHfQ8oRCIRYC\n36DxoeygFYG4A4ewWX0Ph8MV22QyGSg7aFEg7sA5JBKJhYWFKkMkU6lUNW2g7KBFgbgDRxEKhVKp\nVF1cNPF4PBaLbX0cACwB4g6cRiKRGBwcnJyc3Mog8MaAVgfiDhwIs7jN7ffBwUFRFZQdOACIO3Am\nsVisBvs9k8lMTk5C2YEDgLgDxxKLxWKxWPX6nslkUqkU/OzAGUDcgcOJxWJc/4zRLTMxMQFlB44B\n4g6cDzcEfmVlpfj65s2b8LMDhwFxB20B0/dMJsOtvX79OpQdOAyXqqpWrwGAJvHBBx+Ew+FDhw4R\n0f3797u7u5lHHt4Y4DxguYM2YmJiIpVKMUG/fv06ESmKAmUHjgSWO2g7Jicn0+n03bt3jx8/DmUH\nTgWWO2g7YrHY4cOH//zzTyg7cDD/B4hQJnZ3BYDQAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(p+manifold_plot,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's compute our derivatives,\n", "$a=\\frac{\\partial f}{\\partial x}\\rvert_{(x_0,y_0,z_0)},b=\\frac{\\partial f}{\\partial y}\\rvert_{(x_0,y_0,z_0)},c=\\frac{\\partial f}{\\partial z}\\rvert_{(x_0,y_0,z_0)}$,\n", "evaluated at $(x_0,y_0,z_0)$.\n", "\n", "To get the general expression for $\\frac{\\partial f}{\\partial x}$ (written as a function of $(x,y,z)$), we type:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2*x" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(f(x,y,z),x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the general expression. To evaluate it at $(x_0,y_0,z_0)$, we need to substitute $x=x_0,y=y_0,z=z_0$. We do this by typing:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=diff(f(x,y,z),x).subs(x=x0,y=y0,z=z0)\n", "a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute all three of the numbers $a,b,c$, we type:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0, -2*sqrt(3), 4)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=diff(f(x,y,z),x).subs(x=x0,y=y0,z=z0)\n", "b=diff(f(x,y,z),y).subs(x=x0,y=y0,z=z0)\n", "c=diff(f(x,y,z),z).subs(x=x0,y=y0,z=z0)\n", "(a,b,c)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equation for the tangent space at $(x_0,y_0,z_0)$ is then the zero set of $g(x,y,z)=0$, where\n", "$$g(x,y,z)=a(x-x_0)+b(y-y_0)+c(z-z_0).$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(x, y, z) |--> -2*sqrt(3)*(y + sqrt(3)) + 4*z + 8" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(x,y,z) = a*(x-x0)+b*(y-y0)+c*(z-z0)\n", "g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the tangent space. We will make it red by typing the instruction ``color='red'`` and semi-transparent by typing the instruction ``opacity=0.75``." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ho6O1pUUT/0FrfdfUmSkRtofD4U3cb1XlUdz5nDZrOpjKsw1QO3bsCAQCTPQ1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\nDz+sx1lEQ5M3eIbEnTvY1TKv72Im7FhJ33MUBMIlBFR28P6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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tangent_plane_plot = implicit_plot3d(g(x,y,z)==0,\n", " (x,-5,5),(y,-5,5),(z,-5,5),\n", " opacity=0.75,color='red')\n", "show(tangent_plane_plot,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's a two dimensional plane! We should be happy, because we showed in class that the tangent space to an $n$-dimensional manifold is $n$-dimensional... so this is the correct number of dimensions! It also looks like a vector space, and we showed that the tangent space is a vector space... Yay!\n", "\n", "Ok, but it's a little unsatisfying, because we don't see any direct relationship between it and the manifold.\n", "To show them both at the same time, type:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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C+kgtKNJGVt6Dw2A0cV8gIPm70NAFbyo7Y0Ey8IXB6vcZlG6hcgkARQ3H70El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\neidcr6xnLyh4h9CB0FFgUZPTt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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(tangent_plane_plot+p+manifold_plot,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the tangent space touches the manifold at exactly that point.." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ok, now let's try plotting some curves and their tangent spaces. Let's consider the curve:\n", "$$\\gamma(t)=(\\sinh(t),\\lambda\\frac{\\cosh(t)}{\\sqrt{1-\\lambda^2}},\\frac{\\cosh(t)}{\\sqrt{1-\\lambda^2}})$$\n", "for some fixed constant $\\lambda$. Let's choose $\\lambda=\\cos(\\pi/6)$, since this will cause the curve to pass through our previously selected point $(x_0=0,y_0=-\\sqrt(3),z_0=-2)$ at $t=0$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t |--> (sinh(t), -sqrt(3)*cosh(t), -2*cosh(t))" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = var('t')\n", "lam=cos(pi/6)\n", "gam(t)=(sinh(t),-lam*cosh(t)/sqrt(1-lam^2),-cosh(t)/sqrt(1-lam^2))\n", "gam" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot our curve, we use the command ``parametric_plot3d``, we'll also add the options ``color='green'`` and ``thickness=4`` to make it more visible." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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mjtAq8kftTX2HL335S7fccItTXxWJZosJqBXLMiIRTp48qe0t3Lt3r9ljMUz1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\nrfVAJIGEewLV1dX19vaaPQpxXQkqy3ge8ZAN2fr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7yUdV1dXVVV/y3X5iIwHEOktTM9dO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\nQmCC\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gam_plot = parametric_plot3d(gam(t),(t,-1.75,1.75),color='green',thickness=4)\n", "show(gam_plot,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot show it along with our manifold and the point $p=(x_0,y_0,z_0)$, we type:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/+9tSZimCAIBtJ6KE68hntSQjSw6FjNraeNopQvf8QDQMJs4Sd4pcUog+jJap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\nQmCC\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(gam_plot+manifold_plot+p,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the tangent space to our curve $\\gamma(t)=(\\gamma_x(t),\\gamma_y(t),\\gamma_z(t))$ at $t=t_0$, for some fixed time $t_0$ (say $t_0=1$, for instance). To do this, we first need to compute the derivatives $$v_x=\\frac{\\partial \\gamma_x}{\\partial t}\\rvert_{t=t_0}, v_y=\\frac{\\partial \\gamma_y}{\\partial t}\\rvert_{t=t_0}, v_z=\\frac{\\partial \\gamma_z}{\\partial t}\\rvert_{t=t_0}.$$\n", "we do this by typing the following:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(cosh(1), -sqrt(3)*sinh(1), -2*sinh(1))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t0=1\n", "vx,vy,vz=diff(gam(t),t).subs(t=t0)\n", "(vx,vy,vz)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equation for the tangent space to our curve $\\gamma(t)$ at $t=1$ is given by\n", "$$\\sigma(t)=(\\gamma_x(t_0)+tv_x,\\gamma_y(t_0)+tv_y,\\gamma_z(t_0)+tv_z).$$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t |--> (t*cosh(1) + sinh(1), -sqrt(3)*t*sinh(1) - sqrt(3)*cosh(1), -2*t*sinh(1) - 2*cosh(1))" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gamx,gamy,gamz=gam(t0)\n", "sig(t)=(gamx+t*vx,gamy+t*vy,gamz+t*vz)\n", "sig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the tangent space and the curve at the same time:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LstOQxmKdRu4SaGhoCAaDBg7Vg8GgCLOpMEvPfRSsUXP27NnTp0+z67B5V0TEEggEDLys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\nCWDw6tTcnNy0tLTVW1dnIIPdjj3YfF/GuUzu2O2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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tangent_line_plot = parametric_plot3d(sig(t),(t,-1.75,1.75),color='purple',thickness=4)\n", "show(tangent_line_plot+gam_plot,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, it so happens that our curve $\\gamma(t)$ is actually inside the manifold $M$. Moreover, we made the choices $\\lambda=cos(\\pi/6)$ and $p=(0,-\\sqrt(3),-2)$ so that $\\gamma(0)=p$. This means that $\\gamma(t)$ represents a vector in $M$ at $p$. To understand what this means, let's plot the tangent space to $M$ at $p=\\gamma(0)$ and the tangent space to $\\gamma(t)$ at $t=0$. First we need to compute the tangent space to $\\gamma(t)$ at $t=0$ by setting $s=0$ in the previous code:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "t0=0\n", "vx,vy,vz=diff(gam(t),t).subs(t=t0)\n", "(vx,vy,vz)\n", "gamx,gamy,gamz=gam(t0)\n", "sig(t)=(gamx+t*vx,gamy+t*vy,gamz+t*vz)\n", "tangent_line_plot = parametric_plot3d(sig(t),(t,-5,5),color='purple',thickness=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now let's show both tangent spaces together, along with the point $p$:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OHTu6urpyeK9EKkQkkVDNSKLEK344FiUJu3fn/FYxNzFpNEmaB7CHYTK3jWRJbi58agLA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\n1mjtfXo/TvHPUmjnfvefz/xQ72WWBzuo2oDIXRU8Hs/8/Hz6QdkIhav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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(tangent_line_plot+tangent_plane_plot+p,viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, since the curve $\\gamma(t)$ is inside $M$ (i.e. $\\gamma(t)\\in M$ for every $t$), the tangent space to $\\gamma(t)$ at $t=0$ is a subspace of the tangent space to $M$ at $\\gamma(t)$.\n", "Let's show both tangent spaces, the curve, and the manifold, all at once." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bzS5ZsmRWSFqId7zjG1JmKYIAgOsm44SbkM9qSUaOHAoZt7XxdKIM3fMD8TAY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\n9ejCBQAHq9bY3arDuxAeZSwQiWy0nCL4+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