{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "###### Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2019 Lorena A. Barba, Tingyu Wang" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Eigenvectors for the win\n", "\n", "In this third lesson of the module \"Land on Vector Spaces,\" for learning practical linear algebra with Python, we focus all our attention on eigenvectors and eigenvalues. We do so emphasizing a geometric point of view to help develop a lasting understanding of the concepts, and computing with Python instead of tedious manual techniques. This way, we can quickly get to some applications and realize how important and useful they are.\n", "\n", "The eigenvectors of a matrix are the special vectors that don't change direction after a linear transformation. _They don't get thrown off their span!_ This is so cool. The eigenvalues represent the scaling on the eigenvectors by the transformation. And that is a surprisingly useful fact. \n", "Let's get eigen-cracking.\n", "\n", "As always, start this lesson by loading your favorite Python libraries, and our custom plotting functions to help us out." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy\n", "%matplotlib inline\n", "from matplotlib import pyplot" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import sys\n", "sys.path.append('../scripts/')\n", "\n", "# Our helper, with the functions: \n", "# plot_vector, plot_linear_transformation, plot_linear_transformations\n", "from plot_helper import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometry of eigendecomposition\n", "\n", "When you know the eigenvectors and eigenvalues, you know the matrix. Many applications of linear algebra benefit from expressing a matrix using its eigenvectors and eigenvalues (it often makes computations easier). \n", "This is called _eigendecomposition_—matrix decomposition is a central topic in linear algebra, and particularly important in applications." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Eigenvectors revisited\n", "\n", "In the previous lesson, we saw that a unit circle, by a 2D linear transformation, lands on an ellipse. The semi-major and semi-minor axes of the ellipse were in the direction of the *eigenvectors* of the transformation matrix. Now, you should know that this only happens wiht _symmetric_ matrices, but let's revisit this idea.\n", "\n", "\n", "We'll work with the matrix $\\,A = \\begin{bmatrix} 2 & 1 \\\\ 1 & 2 \\end{bmatrix}$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 1]\n", " [1 2]]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A = numpy.array([[2,1], [1,2]])\n", "print(A)\n", "plot_linear_transformation(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in the previous lesson, plot a set of vectors of unit length (whose heads trace the unit circle), visualize the transformed vectors, then compute the length of the semi-major and semi-minor axes of the ellipse (the norm of the longest and shortest vectors in our set)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "alpha = numpy.linspace(0, 2*numpy.pi, 41)\n", "vectors = list(zip(numpy.cos(alpha), numpy.sin(alpha)))\n", "newvectors = []\n", "for i in range(len(vectors)):\n", " newvectors.append(A.dot(numpy.array(vectors[i])))\n", "\n", "plot_vector(vectors)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_vector(newvectors)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Semi-major axis 3.0\n", "Semi-minor axis 1.0\n" ] } ], "source": [ "lengths = []\n", "for i in range(len(newvectors)):\n", " lengths.append(numpy.linalg.norm(newvectors[i]))\n", "semi_major = max(lengths)\n", "print('Semi-major axis {:.1f}'.format(semi_major))\n", "semi_minor = min(lengths)\n", "print('Semi-minor axis {:.1f}'.format(semi_minor))\n", "\n", "u1 = numpy.array([semi_major/numpy.sqrt(2), semi_major/numpy.sqrt(2)])\n", "u2 = numpy.array([-semi_minor/numpy.sqrt(2), semi_minor/numpy.sqrt(2)])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A scaling transformation\n", "\n", "OK, cool. In our first lesson, we saw some special transformations: _rotation_, _shear_, and _scaling_. \n", "Looking at the effect of the matrix transformation $A$ on the unit circle, we might imagine obtaining the same effect by first scaling the unit vectors—stretching $\\mathbf{i}$ to $3\\times$ its length and leaving $\\mathbf{j}$ with length $1$—and then rotating by 45 degrees counter-clockwise.\n", "We have also learned that applying linear transformations in sequence like this amounts to matrix multiplication.\n", "\n", "Let's try it. We first define the scaling transformation $S$, and apply it to the vectors mapping the unit circle. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[3 0]\n", " [0 1]]\n" ] } ], "source": [ "S = numpy.array([[3,0], [0,1]])\n", "print(S)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ellipse = []\n", "for i in range(len(vectors)):\n", " ellipse.append(S.dot(numpy.array(vectors[i])))\n", "\n", "plot_vector(ellipse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A rotation transformation\n", "\n", "We figured out the matrix for a 90-degree rotation in our first lesson. But how do you rotate by any angle? You never have to memorize the \"formula\" for a rotation matrix. Just think about where the unit vectors land. Look at the figure below, and follow along on a piece of paper if you need to.\n", "\n", " \n", "#### Rotation of unit vectors by an angle $\\theta$ to the left.\n", "\n", "$$\n", "\\mathbf{i} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} \\cos{\\theta} \\\\ \\sin{\\theta} \\end{bmatrix} \\\\\n", "\\mathbf{j} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} -\\sin{\\theta} \\\\ \\cos{\\theta} \\end{bmatrix}\n", "$$\n", "\n", "You now can build the rotation matrix using the column vectors where each unit vector lands.\n", "\n", "$$R = \\begin{bmatrix} \\cos{\\theta} & -\\sin{\\theta} \\\\ \\sin{\\theta} & \\cos{\\theta} \\end{bmatrix}$$\n", "\n", "Great. Let's define a matrix $R$ that rotates vectors by 45 degrees." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "theta = numpy.pi/4\n", "R = numpy.array([[numpy.cos(theta), -numpy.sin(theta)], \n", " [numpy.sin(theta), numpy.cos(theta)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can apply this rotation now to the `ellipse` vectors, and plot the result." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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3GLxsOwDNKxZlSMsaRvfdf+FWRWgndWpApzplja6TVDE+dOkWA9cewz8oFCd7G2qVkMV/SueGpElpPP9XRjhuBIL/AO+LvuTJmo4McWx+6cmTNR15sqaj11x54y2Vox0mahWOttZYmpsRFWGYvThk2Q4+BofiYGPFzB5N47xm3wWbefz6PeZmpmwc1RkrC3OD8cev39Niwgq0Won82TKwaoiHkW952qZDLNh1HICeDSoywr220eskVYxX/XmarrM2oNFqyZQ6BYdnDOCZnz/vPgbRtW78XUe+JD79Z0JYyALBV+bFuwDaTFmZYNianud+/nj+eRqAIS1rsHFUZwrmME4R/+vaPdZ6nwPkuhEuKR2M5mw5fkmZ80fnRhSIdZ2QsAgajlqMvy5aYveknthYGVZ+W3PorGKFNylfmPl9WhqJY1LEWJIkJm84QKcZctxytjSOHJnWh5yZXCibLwfLBrYxiAgBuPf8LYMWb8P7km/Cb9pPjLCQBYKvSFR0NC0nLMc/KATbWGIXF1M3HiIyKppUjnb0qF8BGysLXDMY1iCOitbQU2dFF3bNFGf42nM/f7rP8QLk4kL9m1YxGJckiY7T13L90QvUahVbx3Qla1pngzkHL9yg84x1AJTP78qGkZ2MRDMpYqzRaOm3cDOLdp8EoFy+7AypXYi0TvKXiJWFOYV18dKRUdHsOXOVpXv/4vjfd2haoTA1iuVJ9H37WRGCLBB8RUat3MOZmw9JaW+T6GN3bOtYb63GdnMs2fcXvk9eoVKpWDLA3UgkNRp5A+5jcCgp7W1YG0cs8fTN3kqCyMzuTakSqyLchVuPaKqLR86bNR17JvcySolOihiHR0bRZvJKdvwlJ/40q1CExX2bc/P6NYN5T968Z8X+U6z88wxvA+SaI2lS2LNkgPsv664AIcgCwVdj/7nrTN/sDUCKOLLYYhPbOo4Lv08h/LHpMADd6pWneK6sRnNmbj3M/67J0RCev7cz6lN36OJNxQ3RploJ+jc1bO907/lbgyy8Q9P6GWXhJUWMPwaH0nDUYuVeejeqxNxeLQgNlWtAaDRa9p+7zpI9Jzl40ddo09NzcDucHUTqtEAg+Jc8ffOBdn+sUn6OK604JvFZx7FZ6H2FkPBIUjnaMaVzQ6Nxn7tPGbVyNwCd65SlUTnDztH3X7yl1URPJEmisGsmlg9qa2CBvv7wkRpD5ipZeIemGWfhJUWMX74LoNaw+dx49BKQQ+mGtqqpvFaURkPfRdtYf/RinOvsXKdsnGF1vxpiU08g+JdERkXTYsJyAoJClWMp7BIW5KRYx96Xb3Pq9nNAdjPEbrMUEhaB+2RPojVaXDOkZk6v5gbjQaHhNBy1mI/BoaRytGPXxB4GURefgkOpNXQ+T958zsKLXesiKWJ859lrSveZxo1HLzFRq1k9tD3DWtcyEH4zExMW9W3BljFdjdaZxcWJ2T2bGx3/FREWskDwLxm2fCcXbj82OOZoG3+ERVKs47CISAYvl90MpXNno231kkZz9D3vTE3UeI3sjK3V57RnrVZLuz9Wcevpa0xN1Gwf141MaZyU8YjIKBqNWaJk4W0Z09UoCy8pYhyzfZS1pTnbxnajdknjRBSAwz636TrLy+CYSqVi7bAORinbvypCkAWCf8GuU38zZ/tRo+MJuSySYh1P3XiIJ28+YKJWMbtHY6ONrj2nryo978a3r08xtywG45M3/Mnu03Jm3NxeLQzSk2WxXs2Jv+8CchZevVhtnJIixjHbRznZ23Dgjz6UyJ3NaC2SJLHxtC+ex68jSRKpHO2oWjgXm45fZGCzqiJ1OgbCZSEQ/AvsrC04u3Coke82vk29pFjH91+8ZeqmQwA0LelG7lhuhNcfPtJ5phyeVi6/K0Nb1TQY33vmKmNW7wWgY60y9GxYURmTJIkBi7YqERcTOxpn4SVFjFf9eZqGoxYTFhFFFhcnziwYGqcYh4RF0H76elYcu4YkSRT5LTM+y0bSp3ElcmdOy6ROxn7xXxlhIQsE/4KqRXITFhHJsStyPYrJnRpy7MqdeC3kxKxjSZLoNW8jkVHRZHB2xKOCcY2J9lPX8P5TMA42Vqwf3tEgDO7Os9e0mSJvLpbIlZVF/VsbWNfTN3szf+fnLLyRbQyz8BITY0mSmOL1J6NW7gGgQPYMHJzWl7ROhpEdAI9evaPh6MXKRl+LikVYPawDVhbmpHK0Y8PITnF2G/mVEYIsEMTi7rM3/JYxTZLjYfecuUpgSDgmajUda5ehT+PKXH9o3CE7KdbxtpM+HLksi/u0Lg2xMo80GF+w8wSHL8t97pYMcFdKb4K8Sddg1GKCQsNxSWnPjvHdDQRv7aGzDFu+E5AL0cfOwktMjDUaLX0XbFZKf1YqlJNdE3rgEMeXz1GfW7SYsAL/wBBM1Gq6VyvIlJ6tlE1FS3MzCrlmiu8t/WURLguBIBa/L91OcFhEkufr05VrFMuNS0oH7KwtKZMvh9G8xKzjwJAw+i/aAkDtEnmpW9LQOr7x6AVDl+8A5HjiVlWKK2NarRb3ySu59/wtZqYm7BjfwyB87eCFG3SKkYXnNaqzgWWdmBiHR0bRfPwyRYybVyzKwal9jcRYkiRmbz1CjSHz8A8Mwcnehl3ju9C0pFuiX3D3nr/l1fuPCc752REWskAQg7+u3WP/ueu8+xiUpJ3/V+8/KharRw3jer96kmIdj1uzj9cf5N53C/q2MhCw8MgoWk/yJCIqmsxpnFjYt5XBuWPX7OPAebmb86J+rSmd93PExMXbjxPMwktMjD8Gh9Jg5CKl00efRpWZ27u5UTZgaHgEXWdtUMp6FsiegV0Te+JsaxFvZ/GHL/3YetKHLScukc7Zkf1Tesf7Hv4KCEEWCHRIksSQZbIF6vcxiGzpUiV6jtfRC2i1Eo621tQvUyDeeYlZx9cePFd8uyPca5EtXSqCgoKU8WHLd3Lz8SvUahUbRnY0sEx3/M+HSesPANC9fgW61C2njMXMwsuYOgUHY2XhJSbGL98FUHPoPG4+ljtIx0740PP0zQcajVnM3/fluOkWlYqycrAHNlYWBusAueLctpOX2XrSB597TwE5Fvn47EFGIv+rIQRZINCx468rSjyxn66+QkJIkqS4K1pUKhrvBlVi1rFWq6Xn3I1otHKCx+BY9YmPXrnDvB3HABjpXpuy+VyVsZuPX+IxdQ0AZfJmZ17vFsrYG/9P1Bgyl/efgklhZ4339P4GdTISE+PbT19TY8hcnvsFYKJW4zm4He1rGj8FnLx6l2bjlvH+UzAqlYqpXRoxuGUNA9F++ymEBbtOsufcDS7qCuzrsTAzZcf47qS0t+FXRwiyQIBcpW2E5y7lZ7+PQQnMlrly7xm+T2TL0aNGqXjnJWYdrz54lrO+DwHZ3RBT2D+GhNNj5T4AirtlYXS7OsqYf2AIDUYtIiQ8gvTOjmwf313pIBIYEqZk4Vmam7F/Sh+DLLzExDh2wsf2cd2MOo9IksSi3Sfov3ArGq0WR1trNo3ubNR95Pytx/RY4U1AiGF9Zz1LBrgr1d9+dX7t5wOBQMeK/aeVjs8AfgGJC7LeOnbNkJqSccTgQuLW8ftPQQzRbdS1qFSUakVzK2OSJDFj3wXeBgRhY2mB16jOSjNQjUZLq4krePTqPRZmpuya2FOpkRyh69N39cFz1GoVW8Z0MfApJybG+85eo8qg2cqm3PFZA43EODwyik7T19Jn/mY0Wi15sqTj0tIRRmIMUDJ3Vtb1rstvGVIbjXWtW44OtcrE+d79iggLWfDLExQazvh1+wyOJWYhR0ZFs/GYvHnlUaNUvBEEiVnHw1fswj8wBDtrS6N6Dmu8z3P2rhzDu6BvS4MmpCM8dymbiUsHtlEy9bRaLR5TV3P87zuAnIVXv0xB5bzExHjlgdN0my13+Mji4oT39P78ltGwPvOLdwE0GbNEcT00LleINQmkPz9+84FhXie59+K9wfGiOTMzr0/LOM/5VREWsuCXZ9bWw0YWcWIW8p8XbvAhMASVSkXbasZ1JiBx6/ic70M8D8jjEzrUNyibeefZa4Z5yskXDUrnN/Ddbj5+USnz2bdxZWVMkiQGLt7GlhOXlWt2rvN5gy8hMZYkiUnrD9B5ptzho0D2DJxdONRIjM/ceEDRbpO5eOcJKpWKiR0bsG1ctzjFWJIk1h46S5l+s/DViXHTCoUBcLK3Yfu47iIxJBbCQhb80rzx/8TMLUeMjvt9THhTT++uqFQwp0HRnpgkZB1HazT00HX4yJ8tA70bVVLGIqOicZ+0krDIKJztrJjXq5ligV998JyO09cCULHgbwa99WZs9lY2/7rXr8Cotp/9zQmJsUajpc/8TSzZ+z8AKhdyY+eE7kYxxsv2/o8+CzYTFa3B3saSDSM6GdXA0BMQFEL32V5KinYKG0uWD2pDg3KF2Xu2LxtHdTZIahHICEEW/NL43H3KvN4t+BAYzNDlO7E0N8MlpX2CLov3n4KUmN/4NvMSs44X7jrBNV0235IB7piamChjY9fs5cr9Z6hUKoY3KkVKXSnP95+ClPoRmdKkZOvYbopPeZ33OYbGyMJbGCOOOSExDo+Mwn2SJztP/S3PrViUdcM7YBHDco2MiqbP/E0s338KgJwZ07B7Uk/cMhnW2NBz8upd2k5ZxYt3AQDULJabrhXcqFo0F2ampqwb1oHqv3CbpoQQgiz4pamjK4o+aPE2AIr8lok9k3oxUPdzXGw6domoaA02lhY0Ll8ozjkJWccv3wUwepXsjuhcp6zBhtvJq3eZtknnjmhYgcJZXQDZom4+fjlP38q1i3dP7EkqR7m7xqGLN+k0Q7aay8XKwktIjGMnfPRtXJk5vQwTPl5/+EjTscuUKJC6pfKzYUTHONOlI6OiGbN6L9M3eyNJEpbmZszu2Qz3SoW5cuWKMq9F5WLxvre/OkKQBQLg0t0nABRzy4KTgy2rh3rEO1fvrmhaobBBDWI9iVnHg5ZsIzgsAid7G6Z2aawcDwgKoe2UVUiSRMEcGRnVppbSi27w0u1KuUzP39spdSAu3n5Mk7FLidbosvAm9VT8sgmJ8Yt3AdSKkfAxtWtjhsSKHb5w6xGNxy5V0plHt63DuPb14kzeuPPsNe6TVnLl/jMACubIyMZRncmVOa1RYoggfoQgC355ojUaJWOsuJvcsy6+jDHfx6+UufG5KxKyjo9cvqVsuk3r2gQnB1tA3gDrPtuLF+8CsDQ3Y+OozljoYoo3Hr/M3O2yb3hQ82q0rloCkMt0xs7C03cVSUiMYyd8rBzcDo9YCR+rD56h+xwvIqOisbWyYN3wjkYlRvX3vXzfXwxYvJWwiChUKhW/N6/GxI4NDNwegqQhBFnw06DVav/RebefviY0XK6qFrvQe2zWep8FIHMaJyrEUVg9Ies4IjKKXvM2AlAqTzY61PosgusPn1c2wGb3bKZYlndffaDfGlmMqxbJxdSuskUtZ+HNU7LwDk3rp2ThJSTGZ28+pO6IBQQEhcaZ8BEVHc3AxdtYuOsEADnSp2b3xJ7kyZrOaK3vPgbRecY69p6Vrfj0zo6sG96RyoXdEnwPBfEjBFnw06B//P5SLt5+Ash98LInUL8iWqNhg65wTtvqJeO0ohOyjmdsOcz9F36o1SqW9HdXzn/06p0i1HVL5ae77jy/gCBGbzlFRFQ0WdM6s3l0F0xNTJQsvMev3ytZeLmzyIKZkBjvPXOVFhNWEB4ZhbODLQf+6GPQxdovIJBm45YpPuWaxfOwcVRno15+IPutO0xbwxt/ORqlSfnCLB/UNtH0Z61Wy41HLzl25Q7XHr5gSueGRk1Vf2WEIAt+Gk5cvfuPzlP8xzmzJFgi8qjPbV5/+ARAuzh63CVkHT969Y7JG/4E5M2zAjkyArLIt5mykuCwCFKnsGPl4HaoVCoio6JpO20t7wJDsbYwZ/fEnjg52BIRGUXjMXFn4SUkxp4HTtFt9ga0WinOhA+fu09pNGYxz/3kyIihrWoyuVNDgxKdIEdlDF22QymEZGNpwYK+LWlfs3S8793jNx/Y5/OABcd8OXXzEe8+BmFlYcbx2YOEGMdCCLLgp0G/6fWlXLwjFxSKaS3GhX4zr3Se7LhmSGM0Hp91LEkSfeZvIjzau7f7AAAgAElEQVQyinTOjoxvX18Zm7zhT875PgJgzdD2ioAOWLSVc7fk+1rSryX5s2dQsvCOXZGz8JYO+JyFF58Y6xM+9C2dCubIyJ9T+xh0+PA6coHOM9cRHhmFlYUZq4e0jzMS4sajF7Se5Kk8iZTIlZUNIzsZZBACvPUP5Pjfdzh25Q7HrtzmyZsPBuMmajVbx3aLN938V0YIsuCnwD8whCv3nyo/S5KUpPPCIiKVFkPFcsZf4OZTcKjSNDSuzbyErOPdp6/y54WbAMzp2Rx7G7kj9Tnfh0xYtx+A3o0qKb5czwOnlELwrcvmplHZAkZZeOPb11fKbMYnxhqNlt7zN7E0RsLHrok9lNeP1mgYumwns7fJiTFZXJzYPbGnYr3r0Wq1LNh5gqHLdxARFY1arWKke21Gt6ujxEHH5KzvQwYv3c7LeIrNLx/Uhrq6cEOBIUKQBT8Fhy/7Imk/i/CDV+/JlSvx864+eE60Rt4MTGhDb+tJH8Ijo7AwM6V5paJG4/FZx8Fh4fRbuBmAakVz0axiEUCuxuY+eSVarUTuzGmZ3q0JIIt0r3mb5PlF3OhYSRaumVsOG2Th6au+xSfG+oL2u3QJHy0qFWXtsM8JHx8+BdNiwnLF2q5S2I0tY7oqUR96Xn/4SPupa5S6GVlcnNgwolOcHVH0NCpXCAcbK2oOnUdUtMZgbFKnBnSsXTaeMwVCkAU/BQcv+Br8fOzKHepVKRfP7M9c0hXIyZAqRZyNOvXooysali1o1MA0Iet44roDPPcLwNzMlIV9Pzcc7btgM49fv8fczJSNozpjZWHOq/cfaTJ2KZFR0bhmSM3KQW14ePcWm05cVgrnNyxbUMnCi0+MA4JCaDBqMad0m3P9mlRhds9myibitQfPaTh6seJKGNisGtO6NTbIFgTYc/oqnWas5UNgCABtq5VkQd+WcSaF6AkICmGk526W7vvL6Cmlc+3SjHCvHc+ZAhCCLPgJ0Gq1HLp00+DY0ST6k/UVy4onYB0/eOnHmZtyplpc7or4rGPfx68Ud8DQljWUTbStJy4r/ug/OjeiQI6MRERG0WTsUl5/+IStlQW7J/bE0daKiw9eMXLzXwCUzZeDjbosvPjE+MW7AGoOmafUaZ7WtbFBsfitJy7TYfoaQsMjsTQ3Y8XvbWkTqzhSSFgEAxdvVVKlHWysWDLA3aCHX2wkSWL94fP8vnQ773Rp57kzpyWFnTVnbj6kXK6MzOjSKMmNY39VhCALfnj+vv/cqDqb7+NXPPfzJ2PqlAmeGzNDLz7W6cTTJaW9Qb1iiN86liSJnnO9iNZoyZbOmeHutZT53WZvAOS44v5NqyBJEr3mbeL8LXlzb/2IjuTOko6TV3wZu/U00Rq53vDeyb2wsjCPV4xvPXlFzaHzeO4XgKmJmpWDPWin+wLRaLSMWrWbqRsPAZAxdQp2TehJkVh+c5+7T2k92ZN7z98CckPUdcM7JlgIyPfxK3rO9VLC5awtzRnnUY/+TaswdvU+JK3EqEbFjCI2BMYIQRb88By8KFvHarWamKkhe85cpXejyvGeFxAUogiPPkMvNlqtlnWHzwPQplpJo8f6+Kzj9YfPKwK1sG8rrCzM0Wi0tJ2yio/BoaS0t2HtsA6o1WqW7DnJSp2oj/WoS8Oyhbj/4i1Nx3sSHhVNemcHDk2Xs/DiE+MzNx5Qb+RCJeFjx/juSrH4gKAQWk/y5NBF2a1TPr8r28Z1M6iDrNFombHFm9Gr9hCt0WJqomZChwYMaVkjXiENDgtnwtr9zNl+VPHDNy5XiLm9WyhfhOULuNK9bmke3b0d7+cg+IwQZMEPz9uAQA780YfFWw9wQHb14jnInRc632d8XL77OSqjyG+Z4pzz1/X7PH0r+1pjuyvis44DgkL4fel2QBYoffTEzK2H+d+1e/L9/d6OdM6OnLp+n74L5E2/+qULMKZdXSUL70NgCHaW5uwa15UMqVLEK8YJJXz4Pn5Fg1GLePjqHSBHc8zu2cwgOuK5nz9tp6xS7s01Q2o2jupM0ZxZ4nxPJEli9+mr9Fu4WYlbzpbOmQV9WlG7pGFnkZrF84paFl+AEGTBNyUyMpKxY8cyY8YMHjx4QJYsWf71Nef3aYlKpWLZ9oPKsTJ5s+PmlnAKr35Dzy2TS7wbVXpfb2HXTOTNmt5gLD7reKTnbt59lNsuzdU1HfW5+9SgwlujcoV48S6ApuPkwkBumVxYP6IjwWER1B6mz8IzZXKrCrhlcolXjFfsP0X3OXLCR9a0znhP76fESO869Tft/lhFcFgE5mamLOnf2ijCYcvxS3Sf48XH4FAAutQpx+xezeIsmgRygkuf+ZuUMD5zM1OGtarJsNY1sbIwT/D9FiSOEGTBN+PJkye0atWK3377DY1Gk/gJSUS/UWRi8mUbRvqEkGLxWIIhYRFs14lgUq3jS3eesHSfvAk31qMuGVOnJCQsAvfJnkRFa3DNkJo5vZoTHhlFo9GL8QsIwt7Gkj2TemFhZkqd4Qv4+76chbf697a4mEXgMW0du87I9SL0YpzK0Y4Ja/czds3nhI+D0/riktIBrVbL+LX7lRjndM6O7BzfnRIxEjECQ8LoM38z6w7LXzhO9jas+L1dnAWEQK7DMX2zN1O8DhIeGQXIPvBF/VobdRUR/HOEIAu+GcHBwaxfv54XL16wbt26r359k3gqtMXHJZ3LoniuLHGO7zx1heCwCExN1EYRBnFZxxqNlh5zvJAkiTxZ0tG/aRVALrd59/lbTE3UeI3sjI2lBR2mreHy3aeoVCo2juxMjvSpcJ+8UokLXtLfnTol81Jv2Dz+d0suaakXYyd7W3rO3RhnwkdgSBhtpqxk39nrgFzEaMf47gYhfWdvPqTNlJU8fi23VapWNBdrhnYwaCEVkyOXb9Fr3kalCWxaJwfm9mpBs4pFRNTEV0YIsuCbkTevvMn04sULo7HgsPB4H5P1xHVeTCLC424zHxcv3wUodX7js5D1m3l1SuZTisFD/Nbx0r3/U0pzLhngjpmpKXvPXGWZzmIe374+xdyyMH/HMcUVMqljA2qXzMfAxVvZfPwSAOPa16NrvfI0HrXISIztrC1pOm6pkjXYsnIx1gxtj4W5GXefvaHh6MXcefYGkN0PC/q2VJJBojUaJq0/wMT1B9BqJczNTJnapRH9mlSJs1DSq/cfGbh4q5IdqFar6Nu4MuPb11ey/QRfl+8myBqNhpCQhDddfgRCQkJ+irV8y3WEhsr+yuDgYGXD58KdJzx89Z7WlY2z4PRkzJgx3jEAsn6uvxAaGprgZtJfV+VdfzNTE7KlcTSa++JdgGKtNi9fyGB8wtq9REZF4+xgS5vKhQkKCuJtQCAjV+4CoHXlohTM6sL9py+V/nelc2ejZ90yHDjzt9KNpGHp/PSuX5bJ6/Yp9Y471izFgEYVaDxqkeKmsLe24MqSoYSHh9Fw1CKlxkXP+uWZ0rEekRHh7Dl9hS6zvAgMDcfM1IQZXRvRsWYpIiPCiYwI5/GbD3SZ7cXFO/IXRq5MLngOcidf1nRGn3m0RsOy/WeYsvEQQWERABR3y8zs7k3Iny09aKO/aKPuZ/odsbOzS3ziv+C7CXJYWBi3bt2KtxD4j4JWq/0p1vIt13Hvnrybf/PmTd6/lx+bn/t9pL/nYayjg8joZJ/Q6fETIzPs/v37BAbG36h0/1+yhZk1lQO+N64bjXud8kWSJOytLEhlEoaPj+xL9vsUwlpv2XJuWtyVO77y5taUXWf5FBKOraUZTQtn4tLlywzzOsmHwBBsLMzoUy0fh06eottybzRaLVlTO9C1Qk6mrt7BH7tla7msWwZaF8tM/eHzFcvY2tyUVd1q4fP3VYZsOMGTd3K1uW5VC9K0YHp8rlzB65Qvq09cR0JuJjq+eVnypTLHx8cHSZLwvvaY+QcvExYZDUCj4r/RrWpBIv1f4+P/2mDdvs/fMefAJR6+lZ8e7K3M6Vq1ELUKZSMq4A0+Pm8S/Rg+hYbz6O0nHvt95LHfJ8rkTE/edA4/xe+Ii4vLf/oa302QraysyJ07NzY2CddPTe6EhITg6+v7w6/lW65DbyHnzZuXzJnlxIRUfv6EL/mTmQeucGxmP6VbRkxu3044lnXE8h3smiM/Xru6uuLq6hrv3Am7ZfdAuYJuFClSxGBMkiS6esoZdi0rF6Vk8c/+44FLdxCl0eLsYMvYLs2wsbTg1I0HHLn+BICJHepTtXxpluw7xaWHstjN792cSiXzUn3IAgLDInC0tWLXxJ48ev2eGfvklOhSubOyY3w3us/dpIixvbUFK7vWxDldBtynrefl+0+YmqhZ1LcFrSoVJSg0nB7zNrP3nNxwtbBrRryGtye9zhccEBxK/0XbFUs7taMdi/u1oHoR4yIfHwJDGLfuAGsPX1COtatWnPEedXCytzWaDxASHsHtZ2+5/fQ1vk/fKH/HbBA7pVN92lct+tP8jvzXfDdBNjExwcbG5j9/BPgW/Cxr+VbrsLaWQ8xsbW2V10oryZbT9cevmOjlzbw+LY3OSyyMLUWKz7V1ra2t412HVqvlygPZH10mn6vRvAu3HnH/pRy327luBWX8uZ8/645cBOR6wS6pnImMiub35bsBOduvT5Nq3Hr6ijFr5AiHNtVK0KFOedwnreT641e6GsZdidSqaDt1nZKFd2BqX7rN2mAQTXFlyVAOnDhDF8+VfAwOw8bSgu3ju1GzeF4evvSjwajFSoq0R41SLB3YRumnF7vzc91S+Vk5uJ1BMoj+vVh98CxDl+9Qalbkz5aBJQPcDZqvxubAues0HbdMibiIjUqlYsWgtnSqU5agoKCf5nfkv0Zs6gmSBbYxCvLM33mcKoXdlFq/ScU0iam5D16+41NIGBB3hp5+wy1X5rQUjZFaHFdkxextR7j99LXSBSRKo6H1JE8ioqLJnMaJhX1bMWvrETYdl4V8WtcmZE3rTJk+0wkJjyBDqhQcnCaLcew44+OXffl9/XEiozU4O9jy59S+FHPLgvdFX1pOXMHH4FBM1Grm9GpO70aVlML2MTs/W1mYMatHM7rXr2AUEXHtwXN6zPVS6jHbWlkwsWMDejeqZJSRGJs6pfJzbNZAKg+cRURUtNHn4DWyc5xV8QQJIwRZkCwwNzPF3MyUSN0vd4fpa7m6IlOitShiktSwN338sY2lBW6ZDH2CEZFRbD4huzM8apRSRCyuyIqnbz4osb49G1SkSM7MDFi0hZs6S3jDyI5cuP2Yoctlt0SrysVxr1qcMn2m8+5jEI62ci+8QYu3GYnx7tNX6THXS+7wkSYlh2cOIEf61EzfdIjhnrvQaiWcHWzZNq4bFQvmBIw7PxdyzYjXSLnzc0yCQsMZu3ov83ceR6PrQ9iiUlFm9WiWpA4e4ZFRrNh/iqmbDhmJsaW5GTvGdzfK2BMkDSHIgm9GZGQk1atX5+NHecOoZcuWZMyYkW3b5KgDOysLPuh+wf0DQ3CfvJLjswcmaq3pUauTFhOrz9ArmjOzUZ2GfeeuExAUilqtoo2uuzPEbR33W7iZsIgo0qSwZ2LHBnhf9FWiJUa61yZtSgeK9ZiCVitRMEdGZvdsRu3hMXvh9Wb82n0GYnx33QSW7P0f49bsA8DVJQV/TpM7fLSauEIJQSvkmpFdE3qS2cUpzs7Pg1tUZ2LHBpjH8MVLksS2kz4MWLxVCflzzZCaRf1aGxVNiouYQqw/39REjYWZGSHhEdhZW7Jvci8q6L4gBF+OEGTBN8Pc3JyTJ0/GO25nban4MQFOXb/PxHUHGN+hfrznxCTpFvITIO4Kb3p3RdXCuRRrMS7reN/Za+zR+Xtn9WhGVLSG9tNWA3IpzwHNqlK+3wwCgkJxdrBl69iutJmyUsnC2zS6M/N2HDMQ49trxjN2zT4lbrliAVd+r1WQ8MhoyvSZxrWHst+7dZXirPi9LdaWFknu/Hz/xVt6z9ukFJq3NDdjZJvaDG5RXYlTjo/4hNijRmlGuNeiw7Q13HzyCu/p/eKtfyFIGkKQBckGO2vDxBAHGysmb/iTSoVyKo/lCZGU8o5R0dH8rXukj10D+a1/IAd1NRpipkrHto5DwyOUgkCVCuWkVZViNB6zhDf+gdhYWrBhZCe6zFzPzcevMFGr2Ty6C2NX7zPIwtt49KKBGF/zHE3PeRuVhI9WlYuzoFcT1u7xpt2iOfjrrPbp3ZowsFk1VCqVUefnphUKs2ygYefnsIhIpm48xNRNhxR3UK0SeVnYtxXZEuiwDYkLsf78dM6OLO7vTp6s6RJ9/wUJIwRZkGyws7LEysIME7Wa4LAIRrerQ6+GlQjUbcAlRlIs5BuPXip+z9gW8sZjF9BotdhZW9KwrLyhGJd1PGrlbp68+YCZqQmL+rXG88BpxVpe0Lcl2076sOOvKwDM6tmMA+dvKJt649rX46jPbQMxvrB4OO6TVypF8Ps3rcLM7k2ZsekQI9efQCtJpLCzZsuYrlQrmtuo87OtlQUL+rYy8HkDHLxwg97zN/HolRzrnSFVCub3aUnDsgUTTHlOqhDrWTm4HdaWFnFdSvCFCEEWJBucHWzZPbEn2/7ng+eB03gdvcCg5tWVUK7EMFElLsh6/3EqRzsypzEsuq53VzSvWFQRmNjW8Z1nr5m+2RuA35tXR61S0X/RFgCalC9MKgdbOs2Q63R41ChFZFQ0c7YfBaBr3XL4Pn5lIMYn5gyi8Zgl3HoqxyzP6N6Ung0q0GHaWtYfkRNQ8mROy94pvcmWLlWcnZ+9RnYie4zOz8/9/Om/cAs7df30TE3UDGhalTEedRNMT/9SIdYjxPjrIQRZkGxY3L816VOlwNzMFM8Dp/n7/nNuP31tFCUQH0lxISv+45yZDazEaw+eKz5avbsitnVsbWlOr7mbiIrWkDmNE0Na1qDq73MIi4givbMjg1tUp/qQuUiSRNGcmSlfwJVO02VxblCmAP6BIWzXWc4ONlbsndyL+iMX8eKd3OFj1RAPKhbMSfl+M5WaGBVyZ2TT2B6kcU7JvO3HDDo/j2pTh1Ftayu1jaOio5m34zjj1uwjJFxOeS6X35XF/VsblQ6NyT8VYsHXRwiyINmg30Qrn9+VDKlS8OJdAF5HLzCpU8MknZ+UaAx9yyZ9AXc9eus4Wzpnyuo6Kse2jjcfv8Txv2U/8Pw+LZi2+RA+9+SKbUsGuNN+2hoCQ8JJncKOfo2r0GH6GkCuzWyiVhuI8foRnWgwajEfg0OxsbRgx/juWFmYUaTbZN59DEKlUjG2bS3KZ3EgOCyC9kPnJ9j5+dT1+/SY46UkiqRytGNm96a0rV4yXveEEOLkhxBkQbJDrVbTqnIxZmw5zMZjF5nYsUGSyjwm5kMOCYtQBCtmhbeo6Gi8jskpw+2qy37Y2NZxtEbDwMVbAahXOj/2NlZM2yS7LgY2q4rngdPcefYGUxM1kzo2oPscuZ9e7sxpcXawVdwHDjZWzO3VnObj5Sy3VI527J/Sm8t3n9Jv4WaiNVocbKzYNLozZXNnYZ7XHubM2YN/kJxuHrvzs19AIEOW7VC+UFQqFd3qlWdK54aksIs7TVkIcfJFCLIgWeJetQQzthzm8ev3nPN9lGAar57E4pCv3H+GVisXIIq5oed96ZbSJLVdddldEds6HuG5izf+gVhZmDGxQwPqjVyIJMnxxZbmpkrY2ai2dRi5cg8h4RGkd3YkW1pnZcPPwcaKkW1q02nmOqXDx77JvZiz/ZjSUy9X5rTsmdSTdE6O9JnnxWpdISMHGyuWDnSnZWW5roZGo2XFgVMMX7FL6fZR2DUTSwa4G1n/eoQQJ3+EIAv+NVqt9qtX8cqfPQN5sqTD98krvI5eSJIgJ5Y6rc/Qy+LiZFDfeK233IivfH5XsqZ1NrKO7714y8LdJwBZcKd4HeS5XwCW5mZ0rFVGCYFzr1qCtd5nlSy8vFnSsf+8XPjHwcaKznXKMmSZnLVXyDUjqwa3p/PM9Uq36QZlCrBueEfuv/Cj7ohJSgPWMnmysXF0FzLpNiGv3HtKjzleij/cwcaKyZ0a0r1+hThD/4QQ/zgIQRb8a15/+MTUTYcY1qpmklJvk4JKpcK9aglGeO5i68nLzO3d3KAxZ1wk5rLQR1jErF/hHxjCXl13Df1mXkzruFvdclQbPBetVsItkwsuKewZeVLOlvu9RTVGeMo1kIu5ZcH38Ssev/6ApbkZhXJkxFvn83WwsaJe6QLM2ipXkKtS2I1hrWpSa9g8JYZ4XPt6jGhdi1nbjhh0fm5fIR8z+rTB0dGBj8GhjF61h8V7TiqWfptqJZjRvSkuKR2M1iuE+MdDCLLgX5M+VQoszEzJ0WYU/ZtWYWirmjjG0zT0S2hdpTgjPHfx/lMwhy/dok6p/AnOT8xlEVeG3pYTl4iMisbKwoymFYoYWcebjl/iwm3Zsh7ZpjY9524EoHrR3Gw6dongsAjSpnTA0syUS3eeoFarKOyaiRNX7wJgb2NJqdzZ2KALYWtVuTjlC+Sg9vAFREVrsLO2ZP3wjhRyzUi1wXMNOj+vGNAaKdAPtVqF15ELDFqyjbcBsoC7ZXJhcf/WVCpkXAHvawuxRqPlU0gYH4ND+RgcSkBQqO7fYRTJmZmCORJpHCBIMkKQBV+F4a1rseLAKaZuPMSyfX8xwr02vRtVSnIMcVxkdnGibL4cnL7xAK+jFxMV5ITikN9/ClJ6yMXM0NNvhjUuVxh7GyuGr9ilWMdNKxSmcNdJgNwqafGekwSFhpPa0Y5orZaHr95hbmZKvmzplQiIQtkzctZXTvCwt7bELaMLhy75AtC3cWUio6LpMUcWddcMqdkzqRfXH74gf6cJSgW6LnXKMadXc7TRkew8dJ+xo5by140HAFhZmDGmXV0GNqtmUKcCvo4QS5LEqJW7OXD+BgE6AQ4MMW6NpVarmNSxodxBRPDVEIIs+Co4OdgyrFUtRnjuIiAolMFLtzN/5zEmdGhA22olk5TWHBdtqpbg9I0H7Dl7NdG+eyYJhL3p3RVqtYrCv2UC4O6zN4r161GjlJF1PGHtfgKCQrG3sSS9s6PS865iwZxs1bktKuR3VcQ4d+a0+OjSsu2sLXFJaa9Y5WM96nLsyh1O64S1dom8LBngzuhVew06P3sObkfDsoUIDY9g/Lo/mbfzBNG6imwNyhRgbu8WZHFxNljb17SIVSoVI9xrc/nuUyUuOzZpnRzYPLoL5Qv8luTrCpKGEGTBV6Nfk8os2HWc1x/kNkPP/QLoMG0NM7ccZmrXxtQpme+LuxQ3q1iUPgs2Exoeye7TV2lTrWS8cxMKQ76k6yWXO3NaRdT11nF6Z0cqF3Kj74LNinVcIHt6Bi/dDkDn2mWVKm41iuVRxLh0nuwc8ZG7mGR1cVay7WytLLCxtODeCz9MTdSMbluX5fv/4qVOLEe2qU2NYnmoOGBWnJ2f9565St8FW3j69gMAmVOnZEG/VtQrXcBgTf+Fj/jBSz/Wep/jrm5DMTZVi+TCa2Qno0L3gq+DEGTBV8Pa0oLx7evTddZ6g+O+T17RdOxSpnRuxIBmVb9IlFPa21CreF72nr2G19ELCQtyApt6+ggL/YaeRqNVUpPbVi/Jqw8fFet4UPOqSiPS/NkzsPPU32i0WrKlS8Vf12Ufb86MaRTXRDonBx6/kYXVxtICE7WKN/6fsLG0oEf98kzx+pOIqGhsLC1YOaQdt5++puKAmUrn52ldG9O3cWWe+fnTYOQiJYTOzNSE5iXdmNWvDWmcP6d5f20h/hgcytYTl1nrfU5ZU2xUKhXjPOoxsk3tf/y0I0gcIciCr0qHWqWZtfWwgYWV1smBK8tHxRkJkBTcq5Zg79lrHLl8m7f+gaRJGbd1Fp8PWZIkJUNPv6F34uodpb2RR41SBpEVGq3EzcevUKlUZHB25M+HLzA3NSE8MoqwiCicHWx58NIPkN0Mr3RPBNYW5kRrNISER5PK0ZbKhdyYqYusyJbOmYV9WjFxwwGlQ0eeLOnYOKozbplcmLbJm4nr9xMWIbdEqlzIjeld6hP09gXWFubA1xXiaI2GI5dvsdb7HLtPXzUoNJ/WyYE2VUsQEByK54HTpElhz8ZRnY1Kegq+PkKQBV8VUxMT/ujSmMZjlijHXn/4RMsJKzjwRx9srL68EE290vmxs7YkKDScLScu0bdJlTjnxWe5PXvrryR+6Df09O6K4m5ZsLG0UKzjrnXLMWXDQUAOT/tTV44zs4sT91/4YW5qQnBYBBqthJ3V5/rNVuZmhEVGIkmQOY0TLk72SjH5akVy0aBMQZpPWE5wmFxjom/jykzt2phzvo8o0HkCd57J3ZxdUtozu2dzWlYuRnBwMD5vXxAeGcWance/ihDffPyStd7n2HDkvBJyB3J95IZlC+JRoxRVi+TC1MSEvvM3U7Hgb2wa3eUff5kKvgwhyIKvTsOyBSmZOxvhkVF0rl2W3vM38b9r96gzfME/EmUrC3MalyvEWu9zeB29EL8gx+Oy0FvHFrqIiKDQcCWV2aNGaQPr2PfJS0LCI0hpZ6NsyGVKk5L7L2SL2MLcjKDQcKzMzQgKC1euG6Zr9umWyYXg0Agu3JJdJH0aVeLVh0/0nr8JgDQp7Fk91INCrpnoMnM9XkfllG21WkWvBpWY2LG+khYdHhnFzgt3ab1gP6914vlPhPjdxyA2HbvIWu9zSnsnPWXyZsejRmmaVSxiFKrYqFxB5vRqLlwU3xAhyIKvjkqlYlrXxpy+8YBejSoB/GtRlrPgznHxzhPuv3iLa4Y0RnPii0O+qIukKOSaCTNTUzYcuUBoeCTmZqaUy5+DAboaFfVLF1BSmFM52nL3+VtsrSx49tYfkGOKA0PCMTNVKwJsbmqiPO7nzZqOBy/9CI+U45oHNa/GmkPnFNdIvdL5WTagDTtOXaHlxBVKOFlxtywsGeBO4d/khqp618QfXn/+YyGOjIrmwPkbrPU+y4HzN0rSkCYAACAASURBVIjWaJWxzGmcaFe9JO1qlCJHjLKdsYkrxlnw3yIEWfCfUL7Ab0p42dcQ5cqF3HBJac8b/0A2HrvIWI96RnNiWsiSJCn/VvzHuoJCendFvVL5Wbr3L9k6drDluK6jR1YXJ8UHrhdbOysLAkPCUatUREXL4mZqoiYyWgPIlrG+RnGm1CmpXMiNyRsOKp2fZ/dsTqEcGak7YqFipaaws2Zql8Z0rlMWtVodp4/YRK3CvUoxxrZvkKgQS5KEz72nrPU+x6ZjFw3aYdlYWtCsYhE8apSifH7Xr57qLvg6CEEW/GfEjBn+t6JsYqKmZeVizN1+DK+jFxjTrq5RtEbMWhb6bsoajZbLd+WQt+K5svD49XslG652ybxKkkbBHBk54nMbE7WK5zqL1sbSnJDwSCzNzQjS+X61OqE3UasUqzNTmpSKD7i4WxbCIqJYo6uPUcg1I4v7u7Pm0Fl6zt2ofFG0r1ma6d2akMrRTifEJ418xK0rF6VGLhfqVa2And3n2huxefX+IxuOnGet9zkl9A7kJ5XKhXLiUaMUjcsV/kf+e8G3RQiy4Jvxb0XZvWoJ5m4/xv0Xfly++9SoBVNMq09f6+Hu8zfKRlqxnFlYf1gOdUvlaMfF20+IjIompZ2NItL2NlYEBIViZW5GSHgkJjrL1eB1VCo0uuuntLdWXBqVCuXknO9DwiOjUalU/N6iGjkzpKH+yEW8+yhvKubNmo7F/d0pl9+V8MgoFiSwWZfKzhIfH58434uwCDkue633OY743FLWC/BbxjR4VC9Fm2ollIJEgh8DIciCb8q/EeUiv2UmZ8Y03H3+Fq+jF4wE2SSGxazRWaIxK6LlSJ9KyYqrXzo/qw/JVqyzgy3+QSHYWJoTEBSKWqVSfMR6S1uPSiVbySZqNaYmavwDQ7EwMyVXZhdO/C3Xr0jv7MiEDvVZ432OGZsPA7LLYHyHevRtXBmNVkpQiPWuiaCgIIPXliSJMzcfsNb7HFtPXjZIaXa0taZl5WJ41ChFiVxZvzgBR5A8EIIs+Ob8U1HWV4Abs3ovm49fYmaPpgZdQgxcFjp3gj5lumjOzJy79YiHr94BEBQaTmRUNPbWltx7IfuLQ8Ijgc9uibiQJDlhIypag0arxUnX4fnqAznNuFHZgqRzTkHXWRsUMW9aoTBzerXA2cGWpXv/+uLwtadv/dm583+sO3xOuX+QfeY1i+fBo0Yp6pUu8K/qhgiSB0KQBd+FfyrKrasUZ8zqvbwNCOT4lTtUL5ZHGVPH4UOOmaGn38zLlcmF3bqi8Xr0IqtSyaIbH+amJspGXjonByUpxNbKAo8apdh9+iov318FIHu6VCzs14qKBXN+cUJHUGg4G45eZNmeE1x76mcwlj9bBjxqlKJ11eIiPvgnQwiy4LvxT0Q5e/rUlMydjfO3HuF19KKBIJsY+JC1RERGKQVy8mfPQLfZckp3CjsbIp+9wcrCjMBQfeRE4mJsFiOqIqWdtSLGBbJnwMHWikW7TwJgbmbK8NY16dekChuOXKDTjHVJEmKNRsvxv++w7vA5dp76m1CdxQ6yz9u9anE8apQW5S5/YoQgC7jz7DVdZqzj6et3OKc4haOdNXZWlthaWWBnbSn/sbLEztoCZwdbWlcp8dWSBf6JKLtXLc75W4/YeeoKSwa0VtrQx0yd1mglrj18QZROQD98CiYwJBwTtVoJgwuPlEPa9C6KhMRYrVIRpdFiolajUoF/UChqtYpy+Vw55/tQEerqRXMzq2czTvx9l7wdxydJiO88e63LnrugxCyDbI2XdE1HrybVaFShaKIF+uPj/acgnr31J3UKe1I52GIhXBvJFiHIAtwypWXzqI54TF7OsRtP451naW7Gzgndv3rm1peKcvOKRem/cCvBYRHsO3udFpWLAWBi8nkjS6uVFP9xWicH9p2Tu4JkSOXI07f+mJqoidZoUQEJ6PDn60lyIaBIXVxymhT2mJmqleiM9M6OTO/ehPcfg6kxZF6iQuwfGMLm45dY631W2XjUU9wtCx41SlOneC4e37tNkSJ5/rEYA9hZWdJr3ialVZSDjRWpU9iR2tGO1Cns5b8d7Uil+7tOqXwJljkV/HcIQRYAcjH1kY1K07RySQYt22XwuKynXP4cpHf+Oi2aYvMlopw6hT3Vi+Xm4IWbeB278FmQY7gsorVaRejyZ8vAER+5ZrG+BKY+hjgpYgy6JBCdGGdO46SUxjRRq+nVsCIZUqVg8NIdCQpxVHQ0hy76stb7HPvOXVeuB7Kgt61eEo8apXDLlBaQoyweJ/H+/s/eeYc1dXdx/JOEvVUUBVHEASpOlrgHgqNu60LF0bqrtlrrqnVWbeterXuh1q11i6N1ICDujQMHAgKKhA1J3j9uuBABBcX55vM8PkLuzR0Bvjk5v3O+53Xo6siY+W0Hmo+eR4Z6+sfLxGSxHTyThtUr8tvATlox/ohoBVmLiEQiwaeZG41rV6HrlBVcua9pUH70/E1qfDMVp3LW+Hi6072pG2VLFl6da0FE2aeZOwcDr3Ew8BoxL+VYmptq1CErlEoxNYFKhVKpQl9Xh9T0jDfminMjQ6HEQE8XlUolinGdKvY0qlGJDUfPvVaIL919zLrDZ9l0LEg0OQJh+kfHBrXx9fagaS3HQvvkER79guDbYQTdDCP4dhjBt8LEaSS5UdXO+q39qrUULlpB1pIDxzKlCFw2jtHLtokLVQ62VqSmZxAWGcu1B08Zt2IX41bsokH1ivg0c+Prxi4UVZeAvQv5FeV29WtgZKBHUkoa206GMLhdY40IWZ6cKnbP3VT/n64Q8rwFFWPI6toDwXLT27UqJy7dZvbmQ0BOIY56Hs/crUdZdzggxxtbw+oV8fX2oHMjZ8yMDQt+Mdl4IU/k/O2HBN8KI+jWA4JvPxTfHF5FIpFotJRn1kv7etfVGgh9ImgFWUuuGOjpsnhED5rVrky/39bhVM6GbZMHEnD9Pn7+gfx9IpjY+EROXQnl1JVQvlu0hZZuTvh4utOmbnUM1R6+b0N+RNnE0ID29Wqy6VgQfv6BDG7XGJ1sOeQ7j6JE8Xn0TOiky97Nll8yRSxTjOtWted+RAybjgUBmkJsbWnBP2cvM3zRFg4FXddoKrG3tqS3lwe9vTwoV8oy13O9ieTUNC7dfSxGvkG3HuRIO2SiqyOjun1p3BztcHW0w82xHBuOnmP25kOYGRswrkdLhndsKi6Iavk00AqyltfSoUEtalcsw7zt/kgkEuo6laeuU3nmD+vCkeAbbPQPZM+ZSySnprP37GX2nr2MqZEBHRvUwsfT/a0/iudHlH083dl0LIgz1+4RFhmjkbK4pTYHMjc2fO3H9dchlUpEEbextCA1PYOzanP5TCEe16MF0S8T+P3vI2w5HkxcQpL4fDNjA7o0dsHX24N6ThUKlA7IUCi4HhbB/gv3WH/uPpfuh3P1friGa1t2HMuUxNXBDrfKdrg62FGjgm2ORpGz1+/xfWdPJvRsRTFzk4K+HFo+AFpB1vJGypYsxryhXTQe09XRobVHdVp7VEeelMLu0xfx8w/iaMgN5EkprDscwLrDAZQsakb3pm74eLpTu1KZAonSm0S5uUtliluYEh0nZ5N/EC1rlBOfe1vdfZecmnNxMr9k5p319XTFxcBMIe7TwoP/LofSetwijekoUqmE5s5V8PX2oF29GvmKQFUqFQ8iYtRpByH6DbnzMNeFVYDSxYtoRL7OlcqIHsqvO4ffhP7YlihagFdAy4dGK8ha8sXrhNTUyIBeXh708vIg6nk8f58Ixs8/kKBbYUQ+j2fedn/mbffHwdYKH093ejRzo/xrfHiz8zpR1tXRoWsTFxbvOoGffyCta2UJcmj4M0Ai1ge/DcIUkHRS0zPQkUnxaeZONXsbDgZdo+GIPzTysVXKlsLX2wMfT3dsir++EiXqeby42BZ06wHBt8I0rDKzY2qgh2tlO+o6VcTVoSyujnaUKmZR4HuRSCRaMf4M0AqylkLFqqgZwzs1Y3inZoQ+iRJzvKFPnnH7cRST1uxl0pq91Klij4+nG12buFLcIm9rSXi9KPt4urN41wluPIzgbjafh9iXiWDwdh/LZTIpCoWS5LR0dGRSvFyqYKivx45TF1inNicCYQBrj2Zu+Hp74FypbK5vWvKkFELuPCTo5gN13jdMdId7FUN9XWpXLCNGvpVLF+fF0zBcXFxea7+p5ctBK8ha3hsVS1vxi28bJvX+ivO3H+LnH8iW48FEvYjn3I37nLtxn5GLt+LlWgWfZu60r18zz2aQvETZvXI5ylsX597TaPYHXC2U61YolOjIpDiVsyE6Ti7O1QMhZdG6TjWhcaNONfR0s/6EUtPSuXI/XCPyvfkoUiOSzkQmleJUzho3x3JqAbajajlrDbMkuVxOSETejTpavjy0gqzlvSORSHBV5zz/GNyZ4xdusfFoILtOXyQhOVWsJzYy0KND/Vr4eLrR3KWKhjhB3qLco5kb0zbs58C5a7mdvkBIpRIszU149kLOpbuPxcdrVyyDr7cH3Zu5UdzCFKVSye3HURqR7+V7TzSaPbJTwaaExqJbrYq22goHLTnQCrKWD4qOTIaXa1W8XKuSlJLK3rOX8fMP4lDQNZJS0vDzD8TPP5DiFqZ0beKCj6e7hr9vbqI8b2gXpm3YT9SLl+90bTKpYDyf2bxRsqgZPZvXobdXHcyNDQm+FcYffx8h+HYY528/RJ6UkutxShY104h8XRzsCqVGW8uXj1aQtXxQdu3axYwZMzA0NEQqlbJ06VL++XUYMS/lbDsZgp9/IGeu3SM6Ts7iXSdYvOsE5a2L06OZUKnhUKZkDlH+fslWalaw5dK1m+90bQp1VUVLdydqVyyDQqkk5M4jmo+eT9SL+FyfY2pkoBH5ulUuh42lhbbjTctboRXk/yNS09I5ffUuKlR4Olf54OcPCgqid+/enD9/HgcHB9avX4+3tzc3b97E0tyUwe0aM7hdY8IiY9jkLywG3ngYwb2n0UzbsJ9pG/bjXKksPp5udFP7V2SKcvl8TGJ+HXYli2FpbkL0Szm7T19i9+lLOfbR09WhZvnSuFUuJ4pwpdJW2oGhWgoNrSB/4TyMjOVgkJCjPXbhFslpaVxfM/mjXMvs2bNp1aoVDg4OAPTs2ZMxY8awbt06hg0bJu5nV9KS8T1bMc6nJZfvPcHPP5DNx4IIj4kj5M5DQu48ZPSf22lW25Gezd3ZeDRQY5JGfsk0pQcIi4wlLDJW3CaRSKhStpSYdnB1tKO6fWmNRbyPQUpaOjKp5J3c37R8umh/ql8YmVFwpghnn0IMUM3ehouhj7lyLxwdmRSZVIpMJiUtNZX79yJI0AnF1MQYHZkMWeZ2qUT4XipFJpOo58nJkEmzfa1+PHPWXOZxBf9g4eP7sWPHmDhxongtUqkUZ2dn/P39NQQ5E4lEQs0KttSsYMusbzvy35U7+PkHsf3fEF4mJnP0vJCi0JXJRJ+KgpCerUa5rFWxbM0WdtSuVBZTo0/P9UwC1Pp2OjUr2NKhfk283apq3dm+ICS5leS81xNKJDpAya1btz6uVq0aJiafdwtnQkICV69e5WPfy8PIWGZvPoT/hVskp6R+tOvIDYlauDPS0tDT00VfTw+ZTIpUKiUpIYGM9DSsrKzUoi4T3wSkUgk6UkH4pTIpivR0ZDIpEiTEJ6UQK0/kuTwpy0MzNQku7hG+rtUO9HPvXjPQ18WqiBkli5hhXcyCUsUtMDcyQKo+r3B+GTKpMBZKJpWiI5Vqbs/2ZpX5RpR5TzpSiXpfqcabmEwqRSqRiG9gmfeXdVwJsmxvdElJSbn+bq3af5rJa/cCQhqlQfWKtHCrSnPnKp9kS/Sn8jfyriQkJFC5cmVbIFKlUuVeTvOOfAxBLg08fuOOWrRo0fJpYqtSqZ68ebeC8zFWI0p+hHNq0aJFS2Hx3jTsY+SQowFKlizJunXrKFOmzEe4hMIhOjqaLl0E051P+V5UKhXXwiI4duEW/hdu82NXTxpVryhu/1D34ebmxqBBg+jXr5/42MCBA9HR0WHJkiUoFEruR8Rw5UE41x485cqDp9x+HIUiD4ezHOSSssg+dgkAiQQ3x7J8VccJb+cqmBkXTv5VqVSiUKpQqoT/FYrs3ytRKFQolEqUKhUZCiVKpRKlUoVCpSJDoRC+Vm9XKJQ8fxHHlKlTAQnff/89RS0tUSpVZCgVhNx5zKZjwRrnNzcxpJ5TeRpWq0B9J3uKmX0aqYHP5W/kTWTeR2RkJKg17H3wUVMWN2/exNHR8YOevzB58uQJtrbCBODP6V7kSSkaC1Yf6j46duyInp4eW7ZsER3Oajf2xrlxCzIMixBy5xGJeeS/9XRkbzYKSkmAc5uFr+t0F70sapa3pXalMuw+c4nn2Ux89HR1aF2nGj7N3GjtUT2HXeXHJK+fiUqlov53v3H2+j1cHMrS0s2Jlu5OuDmW+yRN5j/Xv5FXyX4fvMeUhbbK4v+Qj1E98OxFPPXb9WDcr3Np9N1MbjyOJuZlAti4cDw0BogR9zU3NqS8TXHS0jMIffKM1PSMt3Jts7G0IDwmjkv3HmNuYsjdDdM5dTUUP/8g9p69TEpaOrtOXWTXqYuYGxvSqWFtfDzdaVSj0icpbgBRL+IZ2KYhO6cOxqqo2ce+HC2FjFaQtRQ6CckphNx+KHj7qj1+M+fQYe3Ef9eyRnfq68pwriSUm5UubsHd8Gj2n7vKhTuP3vk6wmPimODTihl+B/j38h06TFrG/pnf0bZeTeITk9l16iJ+xwI5duEWLxOTWX3wDKsPnsHG0oJuTV3x8XSnZgXbT6rrrmRRc3p7e3zsy9DyntAKspZ3Ii09gyv3n2SZq98K48bDiFwdzqRSCU52NmKtr1vlclgXM2fHfxdYdziAwJuaM5azN24UFFNDA+QqUKpULB7ePYchkZmxIb4t6uLboi4RsXH8feI8fv6BnL/9kPCYOOZsPcqcrUepXLYUPp5u9Gjm/tajl7RoyS9aQdaSb5RKJXeeRGXNdLv5gEuvcTizt7YUTHbUbca1KpTB2FCf9IwMDgffYMbG/ew9e0Xj+ebGhiiUShKSU99ajAEcSlty/nEcm44FcX/TDCDvySOlilkwsrMnIzt7cvtRpGBwdCyQ+09juPkwgomr9jBx1R7qOZXHx9Odrxs7Y2mu9SfWUvhoBVlLrqhUKsJj4rLsJW+Gcf5OGPGJuTucWRUx02gzdnWwy9GkcPnuY9YdDsDvWKDoqAZgoKeDk50NDyJj8pycUVAq2QiC/DAqlrPX7+V7mrVDmZJM7deOKX3bEnjzgXqg63mi4+ScuXaPM9fuMXzRFlq4OeHj6Ubbuvkb06RFS37QCrIWAR19MLVk2YFzhG04RtCtB0Q+z9vhzMWhrBD5qgXYtkTRXHOtUc/j2XQskHWHA7h8T3Nhur5TecpYFeXExTucvyMYsUskUBiFP0VMDKluX5or95/g5x9E/WoV8y3KwnVIqFPFnjpV7Jk75Gv8Q27i5x/ErtMXSUpJY1/AFfYFXMHEUF/t4exOM2fHHB7OWrQUBK0g/x+SlJLKxdDHYuQbcP0u1O8NwMJ/zmrsq6erQ43y6nHyantJB9vXO5ylpqXzT8AV1h0O4GDgNRTKrDpie2tLujd1QyaVsvLAaU5fuweAVCJBJpO+U5oiO0qlCh9PN64sf8LWk+dZMKwrero6BRLlTHR1dGjpXo2W7tVITE5lz5lLbPQP5EjwDRKSU9lw9Bwbjp7DqoiZ6OHs6mj3SS0Gavk8+OB1yJmcPHlS5ezs/NnPCpPL5YSEhPCh7yU1LZ24hOQ3lj5lKBRcf/A0W8XDA649eKohkplIAAdbK9yr2IsG69XtbdDPR32uSqUi6OYD1h0OYMuJYF7Ik8RtpkYGdGnsQremrtwIe8rsLYd5qp7iLJNKsDAxElMVErKsKQpMaiIEbAJg1JyVjOjZgbLdxqFSqdg7Yyht6tYQd12y6wTDFgo1y41qVHqjKOfGsxfxbD15Hj//IM7duK+xrWLpEqKHc8XSVrk+X6VSvVa0P9bvVmHzJd2Hqanpe32X1UbInxlKpZLNx4KZuHo3B2cP1xBklUrFvafRGjPdLoQ+Ijk1PddjlbEqKka+TmWtUMljaFi3ToH+aJ5Ev2DDkXOsO3yW24+jxMclEgnNnSvj6+1BC7eq+PkH4TtrjYYQV7Cx4s6TKI288duIsaG+Lsmp6VSwKcFd9WNKpQrbEkVpWL0i/16+w8ajgRqC/DaR8quUKGLGsA5NGdahKffCn4kDXW8/jiL0yTOmrNvHlHX7cHO0w8fTna5NXDV+Xn7+gRjq6dKpkfNb3LWWLxGtIH9GHD1/gzF/7eDS3cdYW1pgbmzI3jOXCL4tTDU+f+ehRidadoqaGWukHVwd7DTEQYhi8jcCKTE5lV2nL7LucADHLtzSKHGrXLYUvt4e9PR0p5i5CSv2naJa/6kaQly3agWuh4Vz+3Ek8PblbZkjl0oWMedBZAw1K5QWBVmhFK7Jx9Odfy/fYe/Zy8QnJmNmbCg+vzBEOZPyNiX4ufdXTOzVmgt3HgkezseDiHweT5C6JPCHpdvwdK6Mj6cb7evXwtzYkLYTljCobSPmDvkaQ329Ap9Xy5eFVpA/Ay6GPuKn5TtE/1+AiNiXWHcek+v+RgZ61K5YRp12KIubYznKlbJ8p5ymUqnk1JVQ1h0OYNu/ISQkZ7U4FzUzpntTV3y96+LiUJbU9AxW7DvFrM2HRCHWkUlp41GDx9HPOXU1FBCEOEOheOu8caboxiclA1DD3pbt6m0Z6pRM50a1GbZws9iV59uirsYxClOUQfhk4OxQFmeHsvw+qDMnLt3Czz+IHf9dQJ6UwuHg6xwOvo6h/kZcHewA+HPvv5y5dpe/Jw2gctlSb3VeLV8GWkH+hHkQEcPEVbvZdCwox7bMqFQmlVK9vI264kHI+1axK1Voq/33wp+x/sg51h8J0JiooSOT0sq9Gr7eHrSuUw19PV1S0tJZvOtEDiHu3swNPR0d1h46K+aui5oa81wuRPNSiQRlAdcyDNTnq2hTgtDwZwDUrCh6DaBUn6eIqTGt61QTu/JeFWQofFHORCaT4ulcBU/nKiwd2YN/zl7Bzz+Qg0HXSE5N578roeK+V++H4zxwOou+606/VvW0C4L/p2gF+RMk9mUCMzYeYMmek3k2XQAM69CE3wZ2KvSPui8Tktj2bwjrDgdw+updjW21Ktri61WX7s1cKVFESHmkpKWzaOfxHELc28uD2hXLMHPTQcLVj5ewMEWelCKKMVAgMZZIJMJimPr7OlXKERr+DF0dGZXLZLkiKpVZx/Rp5sauUxc5duEWkc9fUrKoeY7jvi9RzsRQX48uTVzo0sSF5/GJrNx/ip+W79TYJzk1nW/+WI//hZv8+b3PR/HG1fJx0QryJ8j1sKdUtbNmsm8bnsXF8+yFnGdxcvX/8UTHJaBQKlmx7xS+3h64qD/6vgsKhZKgu09ZcuIm+85dIyUtayHQqogZPZu74+vtQTX70uLjKWnpuaYmfL3r0qOZG7//fZjVB88AgltbxdJWXA97Knz/qi1mPhBqlFWYGRkQn5SCVCrB3FiYClKzgq1GNUj2KpLWHtUxNzbkZWIyW44HM7KzZ67Hf9+inIlSpWTLieA8t285HkzQrQesGuVTqOfV8umjFeRPkIY1KtGwRqU8tyuVSl7Ik3gWJ+ddP9lef/CUdYfPsuHoOY1GEH1dHdrVq4mvtwderlU0UiCvE+JRX3uy9d8QWo1dSKpacF0c7HgS/VwUY2NDfRKT8z9mKrNZRCqRoFCpsLG0IP5RJM2dq3DzkTAz0PWVN6Xsgmygp0unhrVZffAMfv6BeQoyfBhRDn3yjP4t6yNvnII8KQV5UiryZOHrhORU4bHkFL6du4lOLuWpXbt2oZ1by6eNVpA/Q6RSKcXMTd56flrMSzmbjwWz7nAAIeoOuUzcHMvSr2V9ujRxoYipsca21wnxeJ+WhD55RpsJS8QJ0NbFzHF1tGPv2SuoVCr0dGRIpRISk1PF1MOb71WCUqnCxFCfhORUipkZc+eJkDPu5VWHIfP91Ndtp/E8hVLz2D6e7qw+eIbztx9y53EUlWxzrw2G9y/KHlXL41G1/Bv3y6zf1eaT/3/46IKcmprKr7/+ysmTJ9HV1SU2NhY7OzvmzJmDvb39x768fPP8+XPmzJmDv78/Ojo6xMXF0blzZ8aOHYvOJzCyPS09gwOBV1l3OID9565qVDaUsSpKl0a1qV7CgPZeTTA1NSU0NJTW3r7o6elx6MjR1wqxnq4O3y/5m+3/XgCEhcbe3h5cvPOQPWcuA1CqqBkR6gi8IOmKzFxwZgrFo2p59gVcwczYACc7a9Fbw9XRDsiKig8dPkSjf3eydOlSqlatSqMalbC2tOBpTBx+/oFM6dv2tef9UOmLvEhLS2Py5MnMnz+fy5cv4+Tk9EHOW5hs3bqVlStXkpaWRmRkJA4ODsybN++z+rsG2LNnDytWrCApKYkTJ06cBgyB2SqVamthn+ujK8WLFy9YsWIFFy9exMrKCqVSSbdu3ejatSvBwXnn2T41jhw5wrZt2zh79izm5uY8ffqU2rVrk5aWxtSpUz/KNalUKi7cecS6wwFsPh4kGMKrMTbQp1PD2vh6e9C4ZiUSExMJCQkBYMOGDSxduhSJTIdwLCjvMyFXIbYtUYRFO0/wy9q9YhlcPafyNKnlwJytR8WGlEqlS4hRrbGBHokpaRrXmZmSyIyaM6PizEqKslbFeBgVS3ELU8IiBSP7Lo1duHJf8MYwNTLAwbYkBw7sF4/ZrFlzWjpa4u3tzc2bNzE1NaV7U1fmbD2Kn38gk/u0eWPk+bFEOSwsjO7du1OuXDmxWuRzpGfPnuzbtw8PDw+Cg4NZtWoVLVq04MqVKxgYfPghCW/LsmXL8H4JYwAAIABJREFU6NGjBx06dMDU1LS+RCJpA+yWSCQ3VSrV1cI810dfyC1atCj79+/Hykr4CCmVSmnQoAF37tz5yFdWMIoWLcqoUaMwNxdW8K2trencuTNbtmz54NcSERvH71sOU63fFFwGzWDRruOiGDep5cDan/oQufN31o3rS9Pajjl8KUzNLejywxQuGThyV1KCpzFx6Mik9G9Vn9vrp7Hyx95ExL7EeeAMRi3bRkJyKpbmJiz4rhtFTI2ZvuEAyanpWBUxxa5kMVGMzYwNc4ixTCpFpRKEPjOtoVSqMDbQIyUtHX1dHSJihTcDH093rj0Q8tC+3h4E3xLSLc6VyiCTSVm6dKl4XIVSSc+ePcnIyGDdunXi8wHuPY0m6BXv5bwY2qEJi4d3BxBFuSD577chISGBDRs20LNnz/d6nvdNu3bt8PLyAoS/6wEDBhAaGsqFCxc+8pUVjBkzZtCjR4/sD51E0M4KhX2ujx4h6+npUatWLfH78PBw1q1bx4gRIz7iVRUcLy+vHC3HBgYGpKWl5fGMwiU5NY09Zy6x7nAAR87f0Cj7qli6BL29POjVvA5lSxbL8xhpGQr+3HeK+TtPqSNiCRKVin6tGzDepyX21sWJjpPTb/Za1hwSTIgkEgkDvmpAs9qOfLdwC1EvhLREg2oVuHI/nKgXcqQSCSZG+sQnJovRL2R16GXOy9ORScVRTZnRdc0KpQm8GUZxC1PSM4Q0R3nr4tRzqsDoZUIbiJtjOQDOnDkj3otCqUQqleLs7Iy/vz/Dhg2jZgVbKpctxc2HEWz0D8S9Sv4+On/oSDkzPfG5BSWvsm3bNo3vM6PiD/U3UVg4O2e1tkskEl3gR+AGcLSwz/XRBTmT8PBw2rZty/Xr1xk1atRH+5hfmAQEBPD111+/t+OrVCrOXrvHusMBbD15npeJyeI2c2NDujV1xdfbgzpV7F/78TwlLZ0/953it82HiZELx9CRSSlnmE4R+SNW/rgCpVLJ8n/+Y+yKnaJxUK2Ktswb2pWd/12gy5TlgJCSaOVeje3/XRBK1IwNUCiUxCemoK+rI1ZeGOrpkpyWjm624aWZ06VLFTMnIvYl9qUsuXhXSEuM+ro5c7YJv/+9vTxIz1Bw6e5jQMgfx8bGIpdneSxnin7JkiXF1JdEIsHH042Jq/bw94nzzB3yNbr5zO9/7Jzyl0BQUBDW1tbUq1fvY1/KW/HDDz+AMHH6OuCtUqkSXv+MgvPJCLKNjQ0hISE8ffqUdu3a8ezZM1asWPGxL+utOX78OI8ePeLAgQOFfuyHkbGsPxLA+iPnuKvuUgOhIqGFa1V8vevStl6NN05RflPVxNTxPxImT+di6CMGz/MTRyyZGRswvV976lerQO+Zq8U0gqujHcXNTdj2r5CLtitZjKcxcaRlKISRSsnCApypoT7y5FQNu83M2mLb4kV4HP0CAKdyNtyPiKG4hSn21pZExwmC29u7Dlfvh4vi7uZoR1JSlrscZLVO6+vra2zr0cydiav2EB0nxz/kJi3dq+X7dX+TKCckp2Bi+PnkRj8kaWlpLFiwgIULF6Kr++lM9y4Ic+fOZeXKlcWAX4AzEomkjkqliijMc7y3HLJEIpkskUhUef1r0qRJrrkka2trZs6cycqVK7l+/fr7urx8M3nyZCQSSZ7/zMzMuH37tsZzwsPDGTRoEHv27BFzyu9KQnIKaw+dpcn3f2DXfRyT1uwVxbiavQ1/DO5M+Lbf2D9rOF2auOQQY437kOkgKe2EYeM+DF+0RRBjpZJ69sUIWTaWlT/2xt66OGlKuEtxXAbNEMW4RzM3bqyZjEKppM7QWVx78BSpVMLwjk1JSUvnQOA1AFwcyvIw6jlpGQqKW5iIYlzE1Ai5OgebGbOXLGpGfJIQQccnCfu1rVuDQ8HCz39MN2/+PnEeEKwy7UpaEnw7DIASRUyxLVEUIyMjjfvNrENOTU3V2FaulCV11SVnfv45W9LfRF455cfPnjNycaEvun8xzJ07l/bt29OpU6ePfSnvhEqlUgCTEX59fyjs47/PCPkP4M+8Nu7YsSOievXqKBRChCTL1njg4OAAwI0bN6hatep7vMQ3M3r0aAYNGpTn9oSEBB4+zKrlff78OW3btmXp0qUFKuj/99JtPKqWR08360eiVCo5cfE26w4HsOPUBZKyLYhZmpvg4yl0z+VnMvLo0aPp068/fsdDWLz3FJHqEUo6MildGtakf3MXVEkvKVeyGCqVii3Hg9n9VJdkSRFQqnCwtWLpSB8cy5Skz+w1otGRXclijOzkydQN+3gen4hEAk1rOXLswi1AKKl7FPUcEDr+MnPMZsYGxCemUKKIqdiQUrtiGQJu3MfUyIAipkakpWdQ3MKUrk1cmLBqNyAs5gHiopybYzkkEgnFihXD1NRUTFuo1CmLyMjIHGVWPp7unL1+j92nL5GYnFrgtENukXJzl8qsOXSGH772pIqddYGO96Xzyy+/IJPJmDRp0se+lLciLS0NPb0sewKVSqWUSCShQJXCPtd7E2R1fiXPHMvJkyfR0dFhw4YNxMTEMHr0aHFbRITwKcDa+uP/YpuYmGBikncDhlwu58mTJ+LXbdq0YdKkSXh6Ct1gy5cvZ8CAAXk+X6lUMmvTIf7YeoTne+cDcOdxlNg99/jZC3FfXR0ZbTyq4+vtQUt3p3znP1PS0llzJCjP1IS9dXGxCSH0yTPGrFyhFlQJUpWSad90ZFSX5hwMukb1/lNE/+JezetQxa4Uo5ZtQ6FUUsTUCDdHOw4H3wCgctmS3HwoWGxmT0XYWFoQHhOHkb6eWLHgUdWegOuCyfuor5vz66aDgBAd/6MehGpkoEdntXdwZoScvUOvXr16HDp0CBAiZJVKxYULF5gwYYLG69GliTMjFm8hMUWY/tFDXX1REF4V5X8vCwtw41fuYvf0oQU+3pfK7NmzefjwIaNGjUIikYilldkXyj51ateuzbVr1159uBRwJpfd34lPIoe8evVq+vTpg6WlJSkpKUybNg0nJydcXV0/9qXlm5SUFLp06UKdOnWwsbHh/HnhI/Zff/2VpyBHx8np9etqDgdfp6xVMf7c+y/rDgfkmD7h6miHr5cH3Zq6Fqg77005Ynvr4uK+SalprDp+mb8D/hbzuqUNlVgnhTGiUzOGL9rC8n2nAGHBcNF33TgScoNxK3YBUNWuFMUtTEUxdnMsR9AtIYotb11c7N7LXpNsW6Iotx9HUtzChLgEYTGxZgVbIl+8FKPjwW0b0fSHOQB0bFALUyMDEpJTuPFQeNN2q2wn3sOQIUNEQc5QqvDz80Mmk+Hr66vxuliam9LCzYl9AYL72tsIMsDgdo24EPpI9OsA2HPmMmeu3qVetUKviPrs+PPPP9mwYQPz588nNDQUmUzGiRMnsLOz+6wE+caNG+zfv5+GDRsCIJFIegIOQN6R1lvy0QW5WbNmhISE4OXlhYmJCQkJCVStWpUDBw5ofEz41Fm/fj0nT57k5MmTzJ079437n74aSrepK0QXtIdRsQye5ydut7a0oFfzOvT2qlPgj8AFEWKAfQFXGDZ/Ew+fCamF4qaGlIi/S8yFEK5LDCneciDJEuFn0bB6RWYN6MiwBZu5EPoIEPK9EbEvOXlJiBKbO1fmaIiQ0qhcphS31Eb0TuWsxQXARjUqiVFlu3o1Wbn/NBKJhCl92vC1umJjTDdvHkc/J+hWGJCVrrhw55FYReHiUFa8j+zlkyEhISiuH+fw4cO5TkDx8XRjX8AVDgffIDpOTnGLgo0Wunr/CR1+Xia+0WTnp+U7OLVwzFu3PKelpeHl5cXz58LPo2/fvtjZ2eUoI/uUkcvlDB06FKVSSfPmzTW2rVmz5iNd1duxYMECZsyYwYwZMwgICDiLMNimrUqlOl3Y59LO1HtHCjovTKlU8sffRxi/cneOuXYGerp0bFALX28PmtWujExWsDXXggrxw8hYRi75m92nLwHCBI4RHZowtX8HDPR0+W3LYSat2UOGQomOTMq0fu1wr2xP16nLiY6TI5FI+LFrc/acucztx1FIJBI6NqjFjv+Exdrq9qW5+SiC9AwFlcuWIvRJFBkKJfWrlSfg+gMUSiV9WtRlu9rwfsBXDdCRyVi65yTFLUx5sOlXpm/cz6xNhyhdvAhhm2cik0n54+8j/PjnduytLbnn96t4P0+ePMHWVvBErv/tz5xannfpZFJKKlYdR5OQnMri4d3FFERBCIuMYdLqvWz0D8zhy7Fn+hDa1qtZ4GNm50uaRfel3Id2pt4XROzLBHxnrWH/udy7LQ31dRnesWm+GxYyKagQp6VnMG+7P1PX7xMXChtUK0+/Bo50atGU2PgEev26WjRQr2Rrxcbx/Qi6GYbXj/PIUCgxNzZkRv92zPA7SETsS3R1ZPT0dBcbRpwrleHO42ekZyiwL2VJTJycDIWSiqVL8CQ6DoVSSZWypYhPTBY7/Ya2a4zrkJmAEB0b6Omy4cg5QMhXZ75BBasj5lcd3rKT2xDX7BgZ6NOhfi02HD2H37HAtxJku5KWrB/fj9FdvRi3YqdYYQIwbsUuWtWpVmiDArT8f/DRW6f/Xzh34z61B07PVYwN9XUpVcycUkXNmbRmr9gq/CYyjeHL+0wQy9debXF+VYxPXrpNzW+nMXb5TpJS0ihRxJSN4/uzb/pg7Iqbs+PURar3nyqK8YCvGhCw+Cf+3PsfwxZuJkOhpHLZUiwa3o3xq3YTEfsSUyMDBrVpJIqxm2M5nkTHIU9OoWRRM0wM9Yl+maA2BLIhLDIWPV0dhrZvws5TFwH4bWAn/tp3SiN3fPziLTGlk5muAMTcdGaHXm7kxwMis5U64Pp97mWr5y4o1cuXZv+s4ZyYN0p0nbvxMIL1hwPe+pha/j/RRsgfgITkFK4/eMrsAR2xMDGiiIkRFuI/Qw1j9fxQ0IgYIOp5PKP/3MbGo4GA0LU2pF0jpvdvj4WJEeFR0fy66yxHr4QBUMzMmJU/9sbVwY5WYxeJdcjt69ekQ/1afPPHBtLSMyhZ1Iw+Leoya5OwmOZR1Z7oF3KiXsRjaqSPq4Md/wRcQSKRMLhNI2ZvOQzA1D5tmbfdHxAMiZrWcmCQOoc+pps3xob6rFMLmnvlcjiop4FEx8nFUVKur1huZudV+83caObsSIkipjx7IWfTsSB+7v3VG5/zOhrXdODc0nHs/O8C41ft5pe1/9C9mZt2eKmWfKMV5A+AiaEB/VvXf+fjvI0QKxRK/vrnP8av3CW2Vrs62rFspA/O6gWxs9fu4TN9BWHqemEvlyqs+akPYZGxuAyaIdYJT+nTFgsTQ/rMXotKpaJi6RL4eLozee0/ANR3qkByWhp3n0ajp6uDr3ddFu86AcCoLs35S12l4elcmZS0dO6GP0MmlbJ0pA+/bTmiER3HJyaz85SQi84eHWemK6RSCbUrlsnztXpTykJ47WR0a+LKwp3H8fMPZGKv1u/sPSyRSOjUyJm29Wqw+sAZdvx3gZ7N67zTMbX8/6AV5M+AtxFiEMRr8Dw/0YTewsSImd924NvWDZDJpGQoFExbv5/pG/ejVKrQlUmZ2qcNY3q0ZNWBMwxdsIn0DAWmRgZsGNeXwJthjFi8FxBEvWODWmLZW4PqFTHU0+X0tbtIJBLGdm/BjI1C23jHBrU4fzuMuIQkipoZM9m3Dc1GCZUoIzs3o4ipESsPCAvWmdHx6gOnSU5NR09Xh65NssofM9MVVe2sX9vQocxHhAxC2mLhzuPcfhzFhTuPxDepd0VXR4eBbRt91vaZWj48WkH+hHlbIX4hT2TCyt38+c9/4uq/r7cHvw3sJA4mvRf+jJ6/rhZrniuXKcmoVrVo37wuQxds5s+9/wLCgt72yQOZu82fteoccUt3JzxrOzJK7bbWsHpFShcvIk7HntS7NYt3nUChVOJUzpqaFWyZtEYQ8hWjejF9435S0zOwsbTgF982jF2+UyM6BsR0Rdu61SlqljW5JDNCfl3+GLK8LN6Eq6MdFWxKcDf8GX7+gYUmyJm8am2qRcvr0AryJ8jbCrFKpWLDkXOM/nO7aMRT1c6apSN7iDP6VCoV6w4H8N3CzaKp/PCOTZnQ3YvT5wL5auIyzt0MA6B1nWosH9WTb//YIFYQ+HoLk6RHLP4bEOqJXSqVFZ3YRnfxYs+Zy8TGJ2JhYsT0fu35espfAPRvVR+VSsWhIMGjYv6wrsQlJOWIjh9ExIiLir7edTXuL0issHi9cOY3Ms10gJuybh9bTgTz+6DOBS431KKlsNAK8ifE2woxCMNKh8z3E4XMyECPyb5tGNm5mdhi/Tw+kUFzN4pubFZFzFg7tg8t3Jw4eeE6A5cfEu03J/RsxfCOTWkzfrEogmN7tMDG0oLvFgqm+41qVKJ1nWqM+WsHIIh1eMwLLt19jFQqYe1Pffhp+Q7SMxRUsCnBtH5tcR0k1A17u1alU8PaDFuwOUd0vP6IEB2XKGKKt2uWXcDDqFjRaN+t8usj5PymLEBIW0xZt4+I2JecuHQLT+dCtyjQoiVfaAX5E+BdhDghOYVp6/czd9tRMtR+wh0b1GLe0C6Uscoyoz9x8Ra9Z67hidpPok3d6qz60ZfiFqasPXSWQXM3kpqegbGBHmvH9sXFoSwNRvzOHXXDx/yhXZBJpQxbuBkQxLhvi7r0/U2YxtHK3YnKZUsydrmQU571bUcOBV/n9uModGRSNk38hrnb/AmPiUNfV4fFI7rzJPpFjuhYpVKJguzTzF3DryNIHbkb6OniVO713YuZr0V+qFjaCldHO4JvheHnH4SncxWi4+SYGxtqmD1p0fK+0f62fUTeRYhVKhW7T19ixOItogFRuVKWLB7enVZ1sjx+09Iz+Hn1Hn7/+wgqlQpDfV3mDenCgDYNyVAoGLFoCwt3HgfAuogJO6cOwsDAEI+hs4h8Ho+erg4bxvUjOk6uIcY/dvWi4y9/olKpcHO0Y1CbRrSfJIxQ6tbUlUqlrcTIeXKfNsJ5twllbmN7tKCCTQmGzt+UIzo+ffUu958Kc/OyV1dAlqFQrYq2bzRWUqgKtpjm08yd4Fth7PjvAjP6t6fV2IUc/m0kVkXNCnQcLVreBa0gv2cyFAoUCqVGrfG7CDHA/afRDF+0RWwy0dPV4adu3ozzaalR83rrUQQ+01eJnhO1KtqyaeI3OJYpRXScnC5T/hL9J5rWqsSI5tWIeZlIj7GLiU9MwdTIgN3ThnDzYYSGGM/8pgPePy0gLT2DSrZWLBnZA68f56NUqqhZwZYZ/dvjru64q1+tAj91a0GTH+agUCopb12csT1a8vjZ8xzRMWQt5tUoX5oaFWw17jvTcvN1HXqZ5DdlkZCcQmpaBl2buvDDsq3Ik1KoNWAaz17IkSenYIVWkLV8OLSC/B5JTUvHZ8Yqfh/UmXKlLN9ZiFPT0vn97yPM2HiAlDRh5pync2WWjOhBJVsrcT+VSsVf//zHD0u3kpyarvac8GJav3bo6epwMfQR7X9eKvoUj+nmzbiunszz282s3btJy1BQsqgZB2eP4MzVuxpivGREdzxHz0OeJHTh7Zw6iO7TVvJCnkQxM2N2TBnIkPmbiFF35m0c35+N/oGcvnoXgMUjumOgp8usTYdyRMdJKalsPSm45L0aHSsUSkLuCG8sb6qwgPwv6kklEhqN/IOHUbHiY8/UXtFytVm+Fi0fCq0gvyeSUlLpOOlPDgdfZ1q/dizaefythRjAP+QGQxds5s7jKECYOzd/aFe+buys0cwQHSen/+/r+OfsFQBKFy/C+nF9aVLLEYBN/oF888d6klPTMdTXZfUYX7o1deP3zQeYtv0MKoShqId/G8mBc1c1xHjt2D54/TifyOfxmBkbcHDWcCav/Yer98ORSaVs/WUg+wKuclg96WPZSB9MjQz48U+hPK5zo9q0cHPKMzreffoS8qQUZFIpPZppWmLefBRBYopQFfK6Dr1MMhT5i5CNDPTZMulbXAf9miOq1gqylg+NVpDfAy8Tkvhq/GIxKqw7bDZxCcJct4IK8dOYOH5YulUcYZQ5LmlKn7aYGRtq7Hso6Bp9Zq0Vp3J83ciZv0b1pIipMRkKBWOX72TOVqE8raxVMXZPH0KN8qUZv2IXM9WG8M6VynBw9gi2njivIcZbfxlAm/GLCX3yDD1dHXZPG8LBoOts/1foppsz+GtKFDFlzFghb+zj6U4PT3cGzd1IzMsEjA30Gd7Kjbp16/JQrzRpEguN6Biy0hUt3Z1y5G4z648tTIyoYPPm160gDRlO5WxYMKwrA+du1HhcK8haPjRaQS5kouPktBizQMzbAsQlJBVYiDMUCpbsOsnPa/aIwuBR1Z6lI32o+UpuNTk1jbHLd4qLcyaG+iwe3p3e3h5IJBJiXybQbdoK/NUexU1qObD1lwGYGxvSd/baLM+ICqXYPX1QDjHePW0IPWasJOhWGBKJhA3j+pGcmi6OVert5cGANg1wHzKT1PQMyloVY8mI7gTeuC+a2retZs2YEUPJkOkToc7LZo+Ow6Nf4H9BuL5X0xWAWHrn4lA2X80WigLayn77VQP8Q26KJYGAOAdQi5YPhVaQC5Hw6Bd4jp7HrUeRObYNbd+EeUO75MsrIeD6PQbP8+PyPWE0VFEzY34b0Im+LevmEKMr957QY/pKrocJxu91qtizcXw/ytuUELe3/3kpDyKEyoWRnZvx+6DOpKZl0G7iUg6qGz56NHWhb90K+B0LZvRfQulaoxqV2PfrMIYt3Czut2BYV2pWsMVt8K+oVCpcHMry5w8+jF+5i6v3w5FKJWyc0A8TQwMGz/dDpVLhVM6abg2q0WL6KKp3GowqQZojOt7oH4hSqaKIqRFtPKrneE2yOvTs3vj6Qf68LLIjkUhYProXwbfDRPOizMYZLVo+FFpBLiTuR8TQ/pfl4h/zqyzYcYz4xGSWj+6Vp0du7MsExq7Yycr9WYMI+reqz6wBHbA01zT2ViqVLNx5nJ/UbcdSqYSfe7VmYq/W4vG3/xuC76w1JKWkoa+rw/JRvejt7UF0nJyvxi0So85xPVoytmszfv5zCwsPZk133j/zO2ZsPCBG0GN7tMDX24M6Q2fxMjGZEkVM2Tl1MKeuhDJ/+zEAxvu0on61iizaeZyLoY8BWPa9D/WrVeTxs+eEJghvKNmj48zuQYBuTVxzuN+lpKVz+Z5wrPzkjwGUBahDzsTCxIjNP39Lg+G/kaFQalMWWj44WkEuBB48i6P7on2iK5qhvi5V7aypVs4Gp3I2VLO3wamcNSWLmucaISuVStYeOsuYv3aIA0Sr25dm2fc+1HUqn2P/pzFxOSY/bxzfX5zjplAombRmD7/6CXnh0sWLsGvaYFwc7HgQEYP3mPmEPnmGRCJhwbCufNexKXO2HMwhxqsPnhFzy77eHkzv145Ov/zJzYcR6MikbJ88CEN9XXxnCSN53BztmNS7NRGxcUxcLaQz+raoS/1qFQGYtekQSiToqjI0ouOQOw+5qZ6Rl1u64vLdx2KjR2lzA3Go7KtkDseF/Nlv5kadKvbM6N+en5bvRJ6kjZC1fFg+miArFAoSExM/1ukLjbDwKHYF3aZXMxdqVSxD5TKlsLMqmqsfQkJCziHc1x485ftlOwhUR6smhvpM6NGCgV/VQ0cmE8faZ7Lv3FWGLdrKc7mwSNi9iQu/D+yAmZEBcrmcuIRkvpnrxxG1WHtUKceGn3wpUcSUM5dv0WnKCqJeyNHTkbH8hx50rF+TOVsOimkKj8p2bJnQh+0ng0S/iubOjswd2IGfV+1iz5nLAPz2bQdq2FnR49fVRD6Px9hAj79GdiclOZkRizYTn5iChYkhP/t4C5O5o1+wcr+QT7ZRxqLMSEMuF6aVrPhHMDKqaFOcyqUtc9zzf5dvCV+kJuJaPX9tzQqVMsdx8svAVh4cDr5G7Mv4tz5GYZCYmPhF/J18SffxvkdQfTRBTk5O5saNG5+9G5ZSqWRA46oYGRkhlaYRF/GQSxEP3/i8pNR01py8ws7AOyjVC1CNq5ZhiFdtipsZcfnSJY39k9MyWHI4hP0X7gFgrK/LD1+50dSpLKE3hTKzsOiX/LzlP548F0SknUtFhraozeP7d9jzIJKft/xHUloGxvq6TOvakLKGCiYu2yxGxk6lizGhrQub9x3jJ78TqFQqHG2K8b1XdZb+vY+Zf/8HQOta5alZQo8WfUcS8Fz4FUq8dJRajkvAwhpqtgYgLuQIR/ZXwcHBgfn7g0nLUKCHApP4x+I4+HSFgi3H1ZG5gzUXLlzI8VodPad+LeJzDhTNi4wMhXiOt2Fo06r8c/7uOx3jXVEqlV/E38mXdB8lS5Z8r+f4aIJsaGhIlSpVMDY2fvPOnzCJiYlcv3493/eiUqnYdeYy41buI0Kd4rAvZcmcQR1pVssh1+dcCH3M8Ll+3A0XBKleVXuW/9AD2+JFxH32nbvKd2v8SUhORU9HxpxBHfH1EozRd56+xLhN/5KWocCqiCk7Jw+gWjlrlu8/LYqxR2U7xrdxxqBICSYv2ke6QkkFm+IcnD2M6LgEZs/fAwgua2snDuBR1HMuJRoC6XjXrsSi5T+SrlDSZsoa7kc+p0a5Umz9ay/Fi1sS+ULOwUtCtF3VLAPjDGNxDPw/AVeJT05FIpHwg08bSme7p0zCVgqleiP7+zCw5cI8X9vIyEiaNBFm4ylVvPOoeQ83V0xe47n8vino79anypd0H++bjybIMpkMY2Pjz3oKbSb5vZfQJ1EMW7CZI+dvAKCvq8OEnq34UT3Q81UUCmWuk59/7OotpkSUSiVT1+9jyrp9gNAwsmPKIDyqCrnnhTuOMXLJVlQqFZVsrTj82wjsSlqyZNcJjWqKLRP6cPLMOb6ZvYF4dRfekd+/x8LUCK+xS0hITqVUMXN2Tx+KmakJA8YtJTk1HWtLC/wmDaKYuQkz/Q5yP/I5UqmENeP6U0k2yB3qAAAgAElEQVQ90WPiuoOkZSgobmFKZdM0wl/KxNdq63/CTL2mtRyobJ9zAsjLhCRC1W9ErRu64ujomOfra2JiIn6tVCrf+XfrU/jd/FL+Tr6U+3jfaBf1PgDJqWnM2nSIWZuFdmEQmh8WfddNLE97lUdRsTkmP/tN6I9LNh+H+MRkev26mr1nhbxunSr27JgyCGtLC1QqFeNX7hJn3bk52rF/1ndYmpuyZNcJjTrj/TO/I/r5c8ZsPEHUCzmmRgYcnD2CMiWK0mZCVjPIzqmDsba0YPyKXeIUkvVj+1LM3IQHETFM2yC8KQxr34RaajF+tSvv2sFN4vVHx8lFP47cFvMAzt/OSv+45MPDIjtKpfKz/ois5f8PrSC/Zw4GXuW7hVu491SI8koXL8KCYV3p0KBWnjXJW44HMWiunzgDb8BXDZg7pIvGyKI7j6No//NSsTqhf6v6LBnRHX09XdIzMvjm9w2ijWUrdye2/jIQY0P9XMUYoPPUVTyOFRb79kwfQs0KtkxYuUusP14yojt1qtjz76XbzNosiPzorl40c64MwIjFW0hOTadkUTOm9m0rXmemZ4W5oR57ls0k9NZNUlJSaNy4MaVcm5OhUGJiqE/HBrVzfS0yHd4q2VphYWJUoNc+Q6FETypFpVK986w8LVo+BFpBfk88fvac75dsZcd/wiKVjkzK9509meT7FSaGBrk+Jz4xmWELNrPh6DlAmPy86kdf2tWvqbHf/oAr+MxYxcvEZHRkUhZ+141BbRshkUhITE7l6yl/iULap0Vdlo/qia6OTq5irKcro/3EpYTceYQEWP5DD5rUcmTbyfNi2dzgto34pnUDXsgT6TVzNSqV4Oo2vV87APaeuSR6Z8wd0gVztXBmj44n+rZldNfFGvfhPGA6AJ0bOec5Hy9rQojda1/vI8HX+S9YcyH03tNoft9ymJ97f0W5Upavfb4WLZ8CWkEuBI5fCxMXkNIzMliw4ziT1/4jmuHUr1aBZd/74FTOJs9jnL12j56/rhI76jInP1tbWoj7qFQqZvodZOLqPahUKkoUMWX75EE0qC7U+UbHyWk9bpHY1TbepyXT+7dHIpHkKsZGBnr0+22dOJ5paAtnOtavyZV7T+gze6147fOHdUWlUjF4nh+Pn73AQE8Xvwn90dfTJTE5leGLhAW7prUc6dY0ayBpbo5umVx7EC62l+eVroD8d+i5ONjRcuRMjceq9ZtCuVKWWjHW8tmgFeR35K99p1l25CI/+nbi1JVQBs/zE9uYi1uY8vvATqKnRG68OvlZT1eH2QM6MrxjU438Z0JyCn1nrxXNfFwcyrJz6mBsSxQFyLPhA8hVjI0N9Rm/Ypc4uPSHTk1p41SS5/Ik2v+8lKSUNGwsLdg+eZBgUn8kQDQ4mjP4a6rYCRM7Zmw8wMOoWHR1ZCwZ2V28z7wc3TLJ7Mwra1WMhuo3lFeJiI0TJ5y8aWRTUTNj6lSx5+zZrMcUSiUt3Zxe+zwtWj4ltIL8Dmz/N4QxK3YjlcCg+ZvZpK6nlUgkDGzTkBn922tMTH6Ve+HP8JmxisCbWaPtN038hurlS+fYr/3PS7n2QBD63l4e/PmDj2hGf+nuY1r+tECc8LFxfD++buwC5C3Gi3YeF7vwent58EvvVgSfP0/f3zfwICIGfV0ddk0bglVRMx5ExDB0gXCM1nWqMbidEO3efBjBH1uPAILoOpYpJV7z66LjDIWCjeq0TG+vOnkuvGVGxzoyaQ5Dpdxo4VaVsys1H2vpXvWNz9Oi5VNBK8hvyb+XbuMzYxUqlQqFClGMa1csw7LvfV4b0eU1+XnWgI4aEz8Ajp6/Qdepy3khT0ImlTJn8NcM79RUjESPX7hF+5+XIk9KwczYgD3Th9K4plDPnJcYbzt5XuzCa+nuxMofe5GSnMwK/8ucUE8QWT6qF66OdmQoFPScsQp5Ugolipiy6kdfJBIJKpWKIfP9SM9QYFeyGON9WorX/Kbo+Oj5G2Kbee/XpCsy88fV7UvnWhb4Kt6uVZiU7XsDPV3xtdCi5XNAK8hvwdX7T2g3calYwpbJwDYNWTKix2vHyL9u8nN2VCoVc7Ye5aflO1AqVRQzM2brLwNpWjurDvfv48H0mrma9AwFpYqZc3DWcHHsUV5ifPLSbXr+KizMuTrase2Xgejq6LD+3wv8HSC0W4/o1EwUyl83HuTsdaE7cM2YPqJP8Sb/IHH806Lh3TEyyBLd10XHkJWuqOdUngp5lP1BVoScX0Mha0vNppLGNSvleIPTouVTRivIBeRRVCwtfloolqRlZ8X+Uxgb6DO1b9tcqwZOXLxFr19XE66eGpJ98nN2klJS+eb3DWw+HgRAzQq27Jo2GLuSWYtTC7YfY+QSIcp1sLXikLrhA/IW48t3H9Nu4hLS0jOoWLqE+PiFOw8Zpl6Ya1itAr8P6gTAuRv3mbpeqC0e2r6xODw1LiGJUcu2AdCuXg2+ymaX+aboOC4hid2nhWoIX++6eb7OKpVKLHnLr+Xmq7Ryr/bmnbRo+YTQCnIBiH2ZgPeYBeIYpkwM9XRoWL0i3m5ONKtdGUN9zY/XaekZTFy1mz+2Hs0x+fnVxb6HkbG0/3kpl+4KdpPdm7qx8sdeYgSqUqkYt2IXs9W1wO6Vy7Fv5jDRnjMvMQ6LjKHl2IXEJwpdeId/G0lxC1Oi4+R0mLSMlLQMrMyNWTumF7o6OsiTUvCZsRKFUknlsqX4fVBn8Rp/Xr2HqBfxGOrrsmBYN43rf1N0vPXEeVLTMzDQ06VL47xbm+89jeaF2kApvxHyq7R01y7oafm80ApyPklKSaXNhMXcehSJro4Mjyr2eDpXxsOxDMhjcHdzzbUt9ObDCHxmrBS9gbNPfn6VExdv0WXKcmJeJiCVSpg9oBOjujQXRft1DR+QtxjHvBSmmETEvhS78MqVsiQ9I4MuU/7iUdRzDPV0mda1AZbmQvvx8EVbuP80Bj1dHTZN/Eb86B9y+yFL95wEYFLvryhbsph4/W+KjiErXdG+fk2xXjk3MidMGxvoU6WsdZ775UUZq6KvTYdo0fIpohXkfKBUKvnj76PUd6rAL73bUL9aBVFs5HI5ISHPczznTZOfX9130c7j/LB0GwqlkiKmRmz5+Vu8XLMqBBKSU/h68l8cChKc3fq2qMtf6oYPyFuME5NT+WrcYm4/jkJXR8buaUPEioXRy7aLeeDF33XB3kRwndt28rxYDvfrN+3F/RUKJYPn+6FUqqhcthQ/fN1c4z7eFB2HPokS89Gvqz2GrA692pXKvDYnnxcN1N7QWrR8TmgFOR9IpVIm+X6V7/2fvYjnmz/W5zn5OTspaekMmrtRjBydylmze9oQDY+LVxs+JvRsxbR+7cTIOS8xzoyAA28+EGfhZS4Krj10VpzB92NXL75uVJuQkBCeRL9gwBxh2Gez2o5839lTvI4V+0+J17B0ZA+NN5b8RMfrjwilbqWKmdPc+fW+xkE3hfO8bf64YfWcxv5atHzqaAW5kDkYeJW+s9flOvn5VZ5Ev6DjpGWiyHVsUIt14/pqtFbffxpNi58WiA0fC7/ryrAOTcXteYmxSqVi4JyNYhfe/KFd6Kruogu6+YBB6gnLXi5VmPltR5KSElEolQycv5m4hCSKmhmzbmxfsUb42Yt4xq0Q3OF6NnfPUU72puhYqVSKqZaenu6vjXrTMzK4eFfo4ntTy3ReuL+lkGvR8jHRCnIhkZyazoQ1W1i0K/fJz69y+moonX75k2cv5EgkEqb1a8t4n1Ya+14MfUTLnxYS9UJo+PCb0J/OjbIWwvISY4CJq3azRp12+Kl7C4Z3agZA5POXdJy0jNT0DOytLdn887eiOG4NuMWpq0JKYcWoXthk8yYe89cO4hL+1959BzZVrnEc/3ZSKG0ZpeyyLCKCyJAhICB7I5S9hwVapiCytyxB9t6CiJQtU0HLlKsU2VCQTaGUQkv3SnL/OO2h6Unb4AUae5/PP5rkJDnp+PH2Pe/zvNG4OGY3usAH5o2Oj124wf0nytROWqsrkruzXbn7mJi4BCDjCr20ZLPLeN2yEJZGAvk1uPUkFO/1C7iWtNt06p2fU0qeWx686AcSdXqcHR3YMq4fzVPttHzU/xqfTVxusuAD0g/jJbt+VRsD9WhUg5mffwYoqz3aT15JYEgYjg7Z2D3NW60kPH/rIet+VaZY+jarRdtPXnZfO37hhjql8nXfNhTI42J0rhmNjuHlxbzKpYvxfgnTF+nmbz9CJQ93tRF/XmdHiqe4aChEVieB/Iqu3XtMQqKOD0oVQa/Xs2TPMSZtOEyCTm9y5+eU4uITGLxoK6uT9pYr416A3dO8edfdeFuYrb/+QY+Z69WCj0OzhxqVU6cXxtuP+avNfppUfZ81X3ZXR93DlvzIyUt/A7BxdC/Kl1ReMzo2jr5zN5Oo11OyoCsLBnVQ3yshMRHvBUoP48qlizEgVeCaMzqOjIlVe3BkdDGv4cgFlCykrKcuW7wQB85c4vLdR4zq1FhaaIosTwL5FUREx9J24nJGd26Cq0tOo52fi7nlYcuEz03uEg1Ko5x2k1bw+5XbALT6uAKbxvbB2TG70XGpCz4OzxlmtLQsvTD2S1HO/VGZ4vhO7q+uwli97wTL9yqbiY7r1ox2KaY+Rizfzs3Ap1hbWbFmRFejOewF249y5e4jrKysWD68q2bu15zR8c7jfxEVG4edrQ2d639k8hgAt1xO6PR6bj4MBuDExZucuHiTpUO7SBiL/wsSyGYyGAz0mbOB6/eD2HD4NCOW+/IsXNljq1GFEqwb04/C+fOZfO6Zq7dpO3E5j5+9AGBSzxZM7NHCqKmOwWBg9KqdzNl6GFCmPfbNGERel5fbEqUXxhdvPdRU4SUH6+nLt/BZqIxym1cvz5ReLxvI7z11nhVJQd27bnmqlH65jdKD4OdM3vgTAANafqIp0DBndAwvpyuaVy+vFrCY4pbLWXOfRxE3Pm9RK83nCJGVSCCb6VvfX9Q/u5PX7ro4ZmeBdzuK59DjnMN00/m1+0/ivXAL8QmJ5MyejU1j+9CmVkWjY1IXfDSvXp4fJ3oZBVx6YXwv6BlNvlqoqcIDeBQSRrtJy0lI1FG6aH42j+urjnKDnr+g7zffAVCjbAk61zJeijZsyY9Ex8aTL5cTX/dro/ls5oyO7z95xm/nA4CMpyvccmvDeka/z9RRvhBZnfykm+HY+QC+WrnT6D4rKyt+mNCPWmWLm9wqPj4hkeFLt6lVbe8UdmPPdG+1j3CyyJhYPCet5PCfSsFHn6Y1WTmim9EcdHphHPIigsajFqhVeAdmDVEbssfFJ9B24nKCnofjlMOB3dO81W2Q9Ho9vWZtIORFJM6ODqz+ogtPH9xR3/PAmUvsPKFsQDp3gKdm2Z65o+NNv5zBYFCaI2XUW8ItVU+Pau+VoN0nprd2EiIrkh0gMxD4NJQOU1eh0+uN7jcYDDQfs4Spmw+iNxiMHgsODafByPlqGDetVo4/V4zVhHFwaDj1hs9Tw3hct2as+bKH2WFsqgoveXNRpT3mFrXX8uaxfXiv2Mty7SW7flPfd/mwrrgnNboHZVPWwYuV9/zkAw+6N6qu+bqYMzpObjMK0KV+NU2FYmqpmyzN6d9O5o7F/xUZIacjPiGRDlNWERwaYXR/gTzOtK9ThQ71KlPe3Y2//vpLfcw/4B5tJixTd7oY06Up0/q01lwMu/3oKY1HLeTvQKXgY/HgTvh8Vs/omPTCOFGno+PUVWrgpqzCA1i+5xjrDp4CYEqvVrSq+XJfvst3Ahm1cgcAXRtUo0uDakREvPyMM78/yO1HIdjaWLNsWFdNKJo7Oj5z9bZ6gS6j6QoAeztbcuXMQVhkNC1qfMAnFUpn+BwhshIJ5HR8uWK72nvBLbcTnp9UpkPdytQq76EGbMog2/Tz73jN20xsfAI5HOxZP6oXHepV0bxuRgUfkH4YJ1fh7T9zCYAFPh3VKjxQ1g0PXbIVUJr4jO/eTH0sNj6BLtPXEJeQSLH8eVk6tLPR+94MfMrspAuLX7RvaHLNsDmjY3h5Me/94oWolOJiYXrccjsRHh3DrM/bmnW8EFmJBHIafjj6B1uO/kH/lp/QoW4V6lQonWa5r06vZ8zaPSzdcxyAEgVd2T3NW7MVE8AR/6u0nbhCLfjYO92HOqnKkNMLY1DaXyaPfkd1asxQz/rqYw+Cn+M5eSWJOj1lixXkuzF9jFZzjFm9k0u3A7G2tmLT2D5GHdcMBgMjV+wgPiGRom65mdCjueb8zR0dx8YnqHvw9UxnT8HU3HI5UavcO2kWjwiRlUkgm6DX6ymWPy+Pd3xjssAjpWfhkXy5+Tf+uvMEgAaV32PrhM+NlqslS1nwUcg1FwdnDdGEdkZhvHTXb3y9+QCgVOHN8no5koyJi+ezCct5GhaBi2N2dk/3xinF6o+f/7zCgu1HARjbtZm6W3Uyv6v3+e3CTQAWDupktB45mbmj472nLhAWGY21tRXdGlZL87jUiuXPy5TerTI+UIgsSC7qmWBtbc3H5UplGMbn/35AnS8WqGE8okNDDs4eYjKMF2w/Qudpa0hI1FHGvQCnF3/1ymG8/Zg/gxcrUxGNPzKuwjMYDHjN24T/jXvqChCPIvnV54a8iKDnrPWA0kFtYqrRb3h0LEsPKcv6mlUrR5taH5JaRqPj6Ng4jiUtcdt4WOmj0ahKWQrmzZX2FzGVCd2bUyRf7owPFCILkkA2U6JOp3ZlA2W0+/GgWdwPDsXe1obVX3Rh7sD2mhDX6/WMWrGd4Uu3AUrBx8lFo4yq7yDjME65qWqVd4uxfUp/o/W5C3ccZfMv/wGUHsZNUywxMxgM9PvmO4Keh+PokI3N4/pq1vbO2HKYZ5ExONjbsnhIZ5NTDBmNjkMjomk5bin7f7/I4T+vAuZdzEspdRm5EP9PZMrCTDO/P0hgSBiVPNwZu2aXWlFXxDUXE9pWp6OJ7YgSEhPpO+c7NiVted+ixgf8OPFzow1BIeMwvnjrIa2SqvDeKWxchQdKI6KRy7cDSrvPrzo3MXr9NftPsufUBQAWDe5oNHIGZaS/Yp/SX2Nk+waULKStODRn7jgsMoaI6FhajF0CKLs+Fy/gyv7fL1K9bEmTfzkIIV6SQDaDf8A9pn63j1KF8tF8zGJ1/W6dCqVZN6IL92/d0DzHnIIPyDiM7wU9U/fCy5/bmcNzhuKW+2WJ8Z3HIXRMWiddvmRh1n/Vy2h0G3A/SO2N0bZ2RXo3rWn0/nq9Hu+kXUCK5HFiaFvjpXfJzJk7Do2MMrodG59ADZ9ZfFa7orpBqhAibRLIGYiNT6DHzHUk6vQEPHhCwANlvnhI20+ZO9CT2JgY7qd6TnBoOM3HLOZswD0AxndvztTerTTTABmFsbKp6gIehYQl7YU3xGj0GhUTx2cTlvEsPIo8zo7snuZt9Pz4hES6fr2W6Nh4CrnmYtWI7ppzWH/wtNrwaGizKmQzUbxh7sqKsEjtTtwlCrqyblRPKfAQwgwSyBkYv3Y3V+89Nrqvdc0KzB3oiZ2tLbGpjk9d8LFkSGe829TVvG5GYRwdG0eLsS+r8HZOHaBW4YEyL9z3m41cuPUQa2srfpz4uWaqYfKGn/C/ofyj8N3o3popg5AXEYxapRSItK39IVVKaTdeBfNXVoRFRhvdtrezxXdSf7VcWwiRPrmol45j5wP41veI5v49py5QttdkApIa0ic7d+MeHw+azd+BwWSzs8V3ktc/CmOlCm81Z64qI9fvxvSmQao96L7Zelhd5/tNf0/N48fOBzDrh0OAsvqjfuX3NOcxetUunodH4ZTDgZl9TC81M3d0DMpFvZTme3eg8rvF0jxeCGFMRshpCI+KodfsDRhS9anwKOLGgJZ16Nm4BnldcqqVer+dv0HXmRuIjInDxTE7e6Z7awo+IOMwTq7C2/e7snvHfJ8OdPq0qtFrHPrjMqOT9rfr2qAaw9s3MHo8NCKK7jPXYTAYqFCqCF/31XZqO335FmuTgnZq71YUzOvCo7var4O5o2MwHiF3rFeFga3TP14IYUwCOQ1fLPPlbtAzAGxtrGlT60MGtqpLvYrvauZDj166y+y9/1ELPg7NHqLuxpFSRmEMMHH9XrUK78uOjRjmaRy2fwcG03naGgwGA5U83Fk90nhe2GAwMHD+9zwIDsXB3o4t4/uRzd54f7lEnY6B878HoEKpIgz6rB4x0cajW3i10TG8HCF7FHEzOV8thEifBLIJP52+wNoDJ3HPnwevFrXp07RmmsUNS/YcY/pOpQiijHsBDs0eqlljDOaF8bLdfkzftB+A7g2rG1XhgbJjSZvxywiLjCZfLid2TRtI9mz2Rsds/uWMOpUxd4CnpsMcKJ3eLt5+CMDy4V2NVn48j4jGxs6eHA7ZXml0DMoIOZudLdsm9dfshCKEyJgEcirPw6PYc+oC+2YMoknVckb9KxJ1OvwD7lGtbEn0ej1frdrJ3B9/BqBqmWIcmDXU5Fpbc8J4xzF/9ZjGH73P2lE9jHpQ6PV6es5az5W7j7CxtsZ3khfu+Y2D/87jEHwWKq/RrFo5k/PXgU9DmbBuDwD9mteixvvGW079cf0uh85eZ3Kvlq80OgYIi4ph8ZDOfPhO0QyPFUJoSSCnktspB2u+7GHysWW7/fjj+l0qerjT95uNamXcx6ULs3PagH8cxsfOB9AlnSo8gBnfH2RXUsP4BYM6aOanE3U6un29lojoWNxyO7FuVC+TUwYjlvsSGRNHXmdHkx3Vrt57zLqDpzgbcO+VRscALaqX16xzFkKYTwI5lbTmPR8/C2P8uj042NvRcuwSfj6rlAb3aFiVHtVLkiPV1AGYF8aXbj+k9fhlaVbhgTKFMnH9XgB6NfkYnzba4o0Zmw+qrULXj+pF/jza/el+OXtVnc6Y7dXO5D8gV+8pK0eSpzTKuBdg1b7jFMmXm/Z1ta1EU+rdtKbMGwvxP5Blb2YasWw7EdGxPA2LUMN4QvfmLB7UARtr7ZfRnDBW9sJbxIuoGNxyO2mq8ACu339Mtxkvd5JePlzbMP7M1dtM/W4fAD5t6pqsiouNT8B7gbLRaY33S9K76ccmP2fqNdcnLt5k5pZDlC9ZOM2vTTIJYyH+NxLIZjjqf40ffv3D6L4y7gVoU+tDkyFkThg/exFJk68W8igkjJzZs3Fw1hBNYceLyGjajF+mlk3vnDoQh1QrJiKiY+n69Rp0ej3vFSvINwM8TX6Gb7Ye5u/AYGysrVkxvJvR/HSyRJ2eG0k7fCRzcczO4TlDKeNuumhECPH6SCBnIC4+AZ+FWzT3X78fRP0R8/np90tG95sTxtGxcbQct4Tr94Ows7Vh17SBVCptXECh1+vpNmOdWqm3Y8oAk20phyzeyu1HIdjZ2rBlfD/NqguAW4HBag/lIW0/Ndk4H+Dh8wjiE3Xq7RwO9uyfOdioQlAI8ebIHHIGvvU9ovavSFYwrwtftG+IV4vaGBLj1T31zAnj5Cq85P4RG0drq/BAKXtOLg5ZPLgTNcu/oznG1+8sGw4pS+5mfv6Z0eqGy3cCec+9INbWVgxZvJW4hEQKueZicq+WaX7WO8Fh6v/b2dqwa+pAk+/7qp4/f86iRYs4cuQItra2hIWF4enpyejRo7G1lR9BIZLJb0M67gaFMG3TPvV2qUL5GNWpMT0b1yCbvR07jvnj7GCHHbBq/0lGrlSq59IKY4PBwIBvv1eD9lvv9nSub1yFB7DrxF9MS1qP7NWiNv1NrHJ4EPwcr3mbAahfqQzDUxWQrNh7DI/C+SnqlpsD/7kMKKXM6a0PvvNECWRrayt+GN+PRh+9n+7Xx1wHDhzA19eX06dP4+LiwqNHj6hUqRLx8fFMnTr1tbyHEFmBBHI6hi7+kZi4BCqUKsKYLk3xrFNZXZeckJjI2LW7+fTD0tgnxrDooLJ6Ia0wBpi0fq9arvxlx0YMb99Qc8yVO4/oMXMdAB+/X4pFgztpjtHp9PSYuY6wyGjyODuycXRvzZzw0XPX2Xj4dzWAG1Z5j/YmejandOfpCwDWfdmTdnXSP/ZV5M2blxEjRuDi4gJAoUKF8PT0ZOvWrRLIQqQggZyGvafOExoZzYFZg2lStZzm4t26A6e48eAJD4NDiY6LB9IP4+V7/NRRb7eG1TRVeKD0oGgzYRmRMXEUcs3F9in9NWXPAPO2/YzfeaUH86ovulE41dxy4NNQric1PoqMiQOgTc2KXLj1kBIF8hptbJrS7SdhzPFqQ88mpldg/FNNmzbV3Ofg4EB8fPwrvc7Dhw/Tffzx48fpPi6Epcu0QNbpdERFRWV8YCZ5p2Ae9k8fAEBkZKTRY1GxcUzaoKwLTg7jiqUKs3VcL/SJ8URExKPT6dXR9N7TF9UKuk8rlmbBgLaaz67T6ekwbS1/BwZjb2vDpq96kNPehoiICGLiEtAb9Dg6ZOP8rYeMT6q069GwKo0qlVYbHCXb//t5zefxWbiFKqXd8Z3YF2uDTvP402ehNKlQgu71Kmle7004efIkrVu3fqX3KlrU/ArA6Ojot/I53qSoqCiL/z0xR1b6HE5OTm/0PTItkGNiYrh69arJ5VeWIjh15/kkm49f5kmo8S/7X7cCqf/FPLp/Uo4KxdzYdPwKXg0+5MK9YL7c9CsGg4F3C+VhZJMKXLp4QfOaq4+c58i56wAMa1YF68gQ/P1DADhx7QH3QsLxrP4uXisPkZCoo3CenHSqUgx/f3/Na+389YzmvuoehZjYrjp3bwZw18RnSkhMpE2l4m/le3Lu3Dlu377N+PHjTZ7/63Dz5k3Cw8PfyGu/LXq9/l/xe5KRrPQ5ChR4s3s+ZlogZ8+enbJly+Lo6JhZp/CPPAuPZNucHZr7C+VxZlDbBnSuV4XlP51gr//f9Gldn0m+O0nQ6SlRIC8HZg0mXy7lX9ig5+FcfxBE3Qql2XnyPFtOKcUmXs1rMvbJYPwAAAd6SURBVL6f8XTG4l+vcsQ/gAidDQ+ehWNjbc2msX2pUlq7HM1gMHB56X6j+7o3qMpCH890d9GOioriypUrr/Q9mTFjBrNmzUr3GD8/PypVqqTefvToEcuWLWPHjh18+KF2Z+v0XLt2Ld3Hg4KCqFdPqWL08PDAw8PjlV7f0vyT74klykqf403LtEC2sbHB0dHxjf8J8LpN+u4gEUnzsgC5cmanU40yTPHqiJtrHuLiE1iy9zhRsfE0G7uMhEQdbrmd+GXucEoWdlOft3D3cfzOB+BewA3vRcqed5984MGSYV2N+lhEx8Zx6M+rRMfGs+3YOQCm9G5JvcqmV0AE3A8iMOSFejut7aNMedXvybhx4xg6dGi6x7i6uqpL254/f06XLl1YsWIFtWvXNus9UipTpky6j+fM+bIUPEeOHP+6ny1T/q2/J6lllc/xpslFvVdwNyiEpXv8AGVH5aHt6uPdsia3A66RPZty8W3TL2d4FKIsH0tIKrJYNKiTURWeTqdn1b7jPAgOpfGohUTHxlPULTe+k7VNhfafuUR0rPHFrx3Hz3H9fhCTe7akVIqQB2V1BZDu9lGvS86cOY1CMD0RERG0bNmSiRMn0qCBskRv1apVeHl5vbHzE+Lf5t87oZMJJq7bS6JOR99mtbi5eTqzvNqSO8WKBZ1Oz5ythzXP6zRtNXWHzeV5uPInz8E/LvMgOBSAJ6HKPOf6Ub00fSwAtvmd1dx340EwrT6uoAljgKPnrpHNzpbtk/u/0TB+FbGxsbRq1Yrq1atTuHBhzp49y9mzZ1m5cmVmn5oQFkVGyGa6eOshkbFxXFo7yWTTd4CdJ85xM1UvCFsba0Z0aMSE7s3V5XAr9h7TPLfByPl8WrEMvpP7k8dZmWeLjIll/xnj0uwy7gXYOXUg7xXT9pbQ6fScv/WAX+YOp/YHljN/unbtWvz8/PDz8+Pbb7/N7NMRwmJJIJupREFXdk4dmObjBoOBmVsOGt1Xp0Jplg3rYhTg94KeqZVzKXVtUI3FQzqR2+nlRY99v18kJi5Bve1ZpxLrRvXCKYeD5vkAQc9fsGe6D+VKZNyZ7W3y8fHBx8cns09DCIsngWymtEIw2dG/Avjr5gMA8ud2Zt7A9nRpUFVzMW31/hNGG6fmcXZkxfCuJnsNb/NTloTZWFszp387hrdvkO7FucL5cmuKRIQQ/x4SyK/Jt9t/xdraCu/WdZnWpzW5TFTDJSQmsmb/SfV28+rlWT2yu8n9+sKjYjhw5hL5czvz48TPTe5gLYTIWiSQX4MrD54SE5/AH8vGUvndYmket+fUBZ6EhpMzezbm+3Sgb7NaaY54fzp9kcqli+E7uT+FXE1vsCqEyFokkF8Dp+z2HJk9mFy5XNI9bvmeY9T+wIMNX/XSNKNPzdUlJ7/NH4G9nXyLhPh/Ib/tr4G7q4vR7tSm3At6RrPq5RjWrkGGxwI0rvp6Wl8KIf49JJDfEvf8eRjRoVFmn4YQwoJJYchbIhuACiEyIoEshBAWQgJZCCEshASyEEJYCAlkIYSwEBLIQghhISSQhRDCQkggCyGEhZBAFkIICyGBLIQQFkICWQghLIQEshBCWAgJZCGEsBASyEIIYSEkkIUQwkJIIAshhIWQQBZCCAshgSyEEBZCAlkIISyEBLIQQlgICWQhhLAQEshCCGEhJJCFEMJCSCALIYSFkEAWQggLIYEshBAWQgJZCCEshASyEEJYCAlkIYSwEBLIQghhISSQhRDCQkggCyGEhbDN7BMQWV9cXBwzZszAz88POzs7nj17RvHixZk3bx4lS5bM7NMTwmLICFm8caGhoaxevZpt27Zx5MgR/P39sbOzo2PHjpl9akJYFAlk8cblyZOH/fv3kz9/fgCsra2pXbs2N27cyOQzE8KySCCLN87e3p6KFSuqtwMDA9m4cSNDhw7NxLMSwvLIHLJ4awIDA2nVqhVXrlxhxIgRTJ069ZWe//Dhw3Qff/z48f9yekJkukwLZJ1OR1RUVGa9/WsTFRWVJT7L2/gczs7O+Pn58fjxYzp16kRgYCCLFy82+/lFixY1+9jo6GgiIiL+yWlaDPnZsixRUVE4OTm90fewMhgMb/QNRNZlZWU1GZiUwWEfGQyGsyae2wD4BShnMBiumPl+r/LDWtRgMKQ/pBbCwkggi3/MysoqJ5Azg8NCAAOAwWDQpXhuUeA+0MFgMPia+X5FMjjEBsgHBAFBBoMh0ZzXFcJSyByy+McMBkMkEJnRcVZWVr0AV2BuirsLJv330Su8nzkj3nvmvp4QlkZWWYi3pY+VlZUrgJWVlQMwAbgM/JmpZyWEBZERsngbjgKVgZ+trKwiUaY5rgDNDAZDfKaemRAWROaQhRDCQsiUhRBCWAgJZCGEsBASyEIIYSEkkIUQwkJIIAshhIWQQBZCCAshgSyEEBZCAlkIISyEBLIQQlgICWQhhLAQEshCCGEhJJCFEMJCSCALIYSFkEAWQggLIYEshBAWQgJZCCEshASyEEJYCAlkIYSwEBLIQghhISSQhRDCQkggCyGEhZBAFkIIC/Ff89dHdoi2M+IAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rotated = []\n", "for i in range(len(vectors)):\n", " rotated.append(R.dot(numpy.array(ellipse[i])))\n", "\n", "plot_vector(rotated)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Composition of the transformations\n", "\n", "It certainly _looks_ like we recovered the picture we obtained originally when applying the transformation $A$ to all our vectors on the unit circle. \n", "\n", "But have a look at the two transformations—the scaling $S$ and the rotation $R$—applied in sequence:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformations(S,R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observe carefully the plot above. The scaling did stretch the basis vector $\\mathbf{i}$ by $3\\times$ its original length. It also left the basis vector $\\mathbf{j}$ with its length equal to $1$. But something looks _really_ off after the second transformation. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**What went wrong?** Let's investigate.\n", "\n", "We know from the discussion in the previous lesson that the vector that lands on the ellipse's semi-major axis doesn't change direction. It's _not_ the basis vector $\\mathbf{i}$ that lands there, it's the vector $\\mathbf{v}_1$ that satisfies: \n", "\n", "$$ A \\mathbf{v}_1 = s_1 \\mathbf{v}_1 $$\n", "\n", "Recalling the process we followed in the previous lesson, we find that vector, and plot it together with its transformed version (also called its _image_):" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A_inv = numpy.linalg.inv(A)\n", "v1 = A_inv.dot(u1)\n", "plot_vector([u1,v1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Right. The unit vector that was aligned with the 45-degree line got transformed onto the semi-major axis of the ellipse, without being rotated. This is the effect of the matrix $A$ on $\\mathbf{v}_1$: _it is just scaled_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's look at the sequence of transformations $S$ and $R$ applied to $\\mathbf{v}_1$. We apply the transformations by matrix-vector multiplication, and in the second step, we use composition of transformations." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_vector([v1, S.dot(v1)])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAFkCAYAAAAXG0EgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAewgAAHsIBbtB1PgAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAHDpJREFUeJzt3X90VPWd//HXnYRIMhnTAjYRCCo1JUa0QloUFUMsBWUlyBYVaVa2nq9Kq345K66rX6mwtFg4tXbVLUXB2hjxeKCergqutVhjV3GLBLUlyUq2HMWERBDQJBOSgZn7/QNIjZIfk8zcz2dmno9z5pg7d+79vD/mzot37tzkOq7rCgBgns90AQCAYwhkALAEgQwAliCQAcASBDIAWIJABgBLEMgAYAkCGQAsQSADgCUIZACwBIEMAJYgkAHAEgQyAFiCQAYASxDIAGAJAhkALEEgA4AlCGQAsASBDACWSDddAFKD4zizJd0k6RRJmccfq1zX3WC0MMAiDjc5hRccx3lJ0tOu6z55fHmWpP+QdIHrun8xWhxgCQIZnnAcp1jSu67rHj2+HJDUIunvXdf9rdHiAEsQyPCc4zhDJP1Q0nckXei6bpvhkgArcA4ZnnIc5xeSviupRtKMaMLYcZzRfbwkTdJpkpolNZ/oxoFEQYcMzzmOkyZpqaQFki5yXbepn9tFc7Dmu67bMJD6AFOMBfKmTZvcrKws+XyJfeVdJBJRe3u7En0uXs8jEono+uuvV2lpqRYuXNivbUpLS/u9/2eeeUa5ubkDLc8KHFt2iUQiuvzyy514jmHslEVmZqaKiork9/tNlRATwWBQNTU1CT+XeM8jFAopIyOj23PnnHOODh06pOLi4n7to66urtf1zc3NXaFdUFCggoKCgRVrCY4tuwSDwbiPYSyQ09LS5Pf7FQgETJUQM8kyl3jOY/z48dq5c2e35/bt26dLLrmk3+MVFhb2uj47O7vr66ysrIT/fkgcW6kmcX9+QEKpra3V5s2bu5afeuopvffee1qwYIHBqgC7cJUFPPHQQw9pxYoVWrlypcLhsBzH0fPPP69LL73UdGmANQhkeOL222/X7bffbroMwGqcsgAASxDIAGAJAhkALEEgA4AlCGQAsASBDACWIJABwBIEMgBYgkAGAEsQyABgCQIZACxBIAOAJQhkALAEgQwAliCQAcASBDIAWIJABgBLEMgAYAkCGQAsQSADgCUIZACwBIEMAJYgkAHAEgQyAFiCQAYASxDIAGAJAhkALEEgA4AlCGQAsASBDACWIJABwBIEMgBYgkAGAEsQyABgCQIZACxBIAOAJQhkALAEgQwAlkg3XQBSx4YNG7Ru3TqFw2G1tLRozJgx+ulPf6qxY8eaLg2wAh0yPFNeXq4777xTr7zyiv70pz8pEAjoiiuuUEdHh+nSACsQyPDM7NmzNX36dEmSz+fTbbfdpvr6eu3YscNwZYAdCGR4ZuPGjd2Whw4dKkkKhUImygGswzlkGPPmm29q5MiRuuSSS/r1+oaGhl7XNzU1xaIswBhjgRwOhxUMBk0NHzPBYDAp5uL1PDo7O7Vq1SqtWrVKHR0d/TqPnJ+f3+/9t7e3q7W1dTAlGtfS2sqxZZFgMKhAIBDXMYwF8uHDh1VbWyufL7HPmkQikaSYi9fzWLlypS688EKNHj1a1dXVMd9/fX29WlpaYr5fr/xv8yHt2f+pJp01gmPLEpFIRHl5eXEdw1ggZ2ZmqqioSH6/31QJMREMBlVTU5Pwc/FyHkuXLlVubq4eeeQROY7T7+3q6up6Xd/c3KzS0lJJUkFBgQoKCgZVpyn1jfv1//7tea37p+uUebSNY8sSXnT4xgI5LS1Nfr8/7j8CeCFZ5uLFPFatWqW9e/fq6aefls/n6+qOi4uL+9y2sLCw1/XZ2dldX2dlZSXk92PPRwd09dJHtf/TNk0cd5b+939qObZSCB/qwTNr1qxRZWWl1q5d23Wp26ZNm3TmmWf2K5CT3UcHWzTtzp/rw32HlP+VLyvHn2m6JHiMQIYnWltbdeuttyoSiejiiy/utu6JJ54wVJU9DrUGNeOuf1N9wz5J0nlnjTJcEUwgkOGJQCCgcDhsugwrtR3u0N/d84je/evfLusbTyCnpMT9yBNIAh2hI5rzw1/qzZrd3Z4/byyBnIoIZMCQo+Gwrv/RWm2p/uLVI3TIqYlABgx5b89Huuz8At1xzbe7PZ/m86lwTHyvd4WdCGTAkHPPGql/uubb6ggdkSSd9qWA8oadqoLRX9HQjCGGq4MJfKgHGPThvoNa9+LrkqS75s1Q8dfG6LFN/2W4KphCIAMGrXz6JYWOHNVpXwro+2Ul8meeooLRuabLgiGcsgAM+Xx37M88RZI0+rQvmywLBhHIgCGf744BAhkwoKfuGKmNQAYMoDvGyRDIgMfojtETAhnwGN0xekIgAx6iO0ZvCGTAQ3TH6A2BDHiE7hh9IZABj9Adoy8EMuABumP0B4EMeIDuGP1BIANxRneM/iKQgTijO0Z/EchAHNEdIxoEMhBHdMeIBoEMxAndMaJFIANxQneMaBHIQBzQHWMgCGQgDuiOMRAEMhBjdMcYKAIZiDG6YwwUgQzEEN0xBoNABmKI7hiDQSADMUJ3jMEikIEYoTvGYBHIQAzQHSMWCGQgBuiOEQsEMjBIdMeIFQIZGCS6Y8QKgQwMAt0xYolABgaB7hixRCADA0R3jFgjkOGpUCike+65R+np6Xr//fdNlzModMeINQIZnnn//fdVUlKivXv3KhwOmy5nUOiOEQ8EMjzT1tamyspKfe973zNdyqDRHSMe0k0XgNQxfvx4SVJDQ8OAtu9ru6ampgHtN1p0x4gXY4EcDocVDAZNDR8zwWAwKebi5Tza29slHeuYW1tb+71dfn5+VGNEs+9oLK94XqEjRzUiJ1vll0+M2zgcW3YJBoMKBAJxHcNYIB8+fFi1tbXy+RL7rEkkEkmKuXg5j127dkmSdu7cqY8//jguY9TX16ulpSXm+933aVAVv/tvSdLcSQX6n5qdMR/jBI4tu0QiEeXl5cV1DGOBnJmZqaKiIvn9flMlxEQwGFRNTU3Cz8XLeZzokMePH68zzjij39vV1dX1ur65uVmlpaWSpIKCAhUUFAy8yB7cseZZHQlHNCInW0tvukb+ofE7XcGxZRcvOnxjgZyWlia/3x/3HwG8kCxz8WoeWVlZkqTs7OyoxiosLOx1fXZ2drcxYj2PD/cd1JO/3yZJ+pfrr1DeaSNiuv+T4dhKLYn78wPgMa6sQLwRyEA/cGUFvMBlb/BMKBTS9OnT9cknn0iS5s2bp/z8fG3cuNFwZX2jO4YXCGR4JiMjQ1VVVabLiBrdMbzCKQugD3TH8AqBDPSC7hheIpCBXtAdw0sEMtADumN4jUAGekB3DK8RyMBJ0B3DBAIZOAm6Y5jAdcjA59Adx4/rujoaDqvzyFGFjoQ17NTE/WND8UAgA59Ddzxwv35pqx594Y/qCB1RR+iIOo8c1eHOkILtHQq7v1HHkSOKRFyNyR2myntu1GVf/5rpkq1CIAOfQXc8ODdMv0h/fHeXnnhpa4+vKf/2hfr3/3u9crKzPKwsMRDIwGfQHQ/cXxv3aeNr1Xrnrx+edH2Of6jW3FGueZdP8riyxEEgA8fRHUfvRAhvrKrWjvo9Pb7ugjO/ovU/vFlFY8d4WF3iIZCB4+iO+6e3EP7KlwP6+ykTFQ5HtHbzf2lIepqW/sOVmpwfUP5pXzZUceIgkAHRHfelPyF8TUmxLvt6gdLT0nTXmt+o6IzTtX7J/9FXc7+k6upqQ5UnFgIZEN3xyUQbwp912de/pn/9XpkyT8mI2125kxGBjJRHd/w3gwnhz7pq8vnxLjUpEchIeaneHccqhDF4BDJSWqp2x4SwnQhkpLRU6o4JYfsRyEhZqdAdE8KJhUBGykrW7pgQTlwEMlJSsnXHhHByIJCRkpKhOyaEkw+BjJSTyN0xIZzcCGSknETrjnc3faz/fOF1QjgFEMhIKYnSHf+1cZ+eenmr1v/+TdU3Heq2jhBOXgQyUorN3TGnI0AgI2XY2B33FsKn5WRr8tl5uunqabpi8tcJ4RRAICNl2NId97cTnjA2T+++846K6YhTBoGMlGC6Ox7I6Qj+bGXqIZCREkx0x5wTRrQIZCQ9L7tjQhiDQSAj6cW7OyaEESsEMpJavLpjQhjxQCAjqcWyOyaEEW8EMpJWLLpjQhheIpCRtAbaHRPCMIVARlJqOvBpVN0xIQwbEMjw1G9/+1utWLFCmZmZ8vl8Wr16tc4999yYj7P2xTf67I4JYdiGQIZntm3bphtuuEHbt2/XuHHj9OSTT2rGjBmqq6tTIBCI6Vi/+ePbUnrmF7pjQhg2I5DhmVWrVmnmzJkaN26cJKm8vFx33XWXKioqdNttt8V0rCNHwzptxLHumBBGoiCQ4ZlXXnlFS5Ys6Vr2+XwqLi7Wli1bYh7IkvSNcWfoskU/JYSRMDwPZMdx0iXlbdiwQY2NjcrOzva6hJhqa2vT/v37E34u8Z7HoUOH9OmnnyojI0MNDQ1dzwcCAb377rvdnutJU1NTr+s/+uijvy10tus/X/vvrsXhX8rWlZPG66qLzteFRWd1hXBzH/s0iWPLLm1tbTrnnHNGS2p2XfdoPMZwXNeNx357HtBxRkv60NNBASB28l3X7buDGABfPHbahzwDYwJArMQtw0ycQ94vSXl5eaqoqNCYMWMMlBAb+/fv17XXXitJCT0Xr+YxadIkLVy4UDfeeGPXc7fccovS09P1i1/8os/tm5ube12/a9cu3XLLLZKkp556SsXFxYMr2CCOLbucmMfxY3B/vMYxEchh6diba8yYMSosLDRQQmxkZ2d3hUQiz8WreUybNk179uzp2r/rutq1a5fuvffefo3Z12v8fn/X16NGjUrY74fEsWWbz85DxzMsHkycskCKuvvuu/Xiiy9q165dkqT169crLS1NCxYsMFwZYAcue4NnJk2apIqKCs2fP7/rN/V+97vfxfyXQoBERSDDU3PmzNGcOXNMlwFYiVMWAGAJAhkALEEgA4AlCGQAsITnH+od/5VDp6qqyh01apTXw8fU6NGj1dLSourqaiXyXJJlHqeffnrX13l5if0LocnyPUm2eQQCASee49AhA4AlCGQAsASBDACWIJABwBIEMgBYgkAGAEsQyABgCQIZACxhPJA7Ozu1dOlSlZSUaNq0aZowYYLmzJmj3bt3my4tKgcPHtSyZct06aWXaurUqbrgggv04x//WEePxuVeiHFXX1+viy++WFOnTjVdyoB897vfVUlJiWpqakyXMiChUEjLli3Tt771LX3wwQemyxmQDRs2aPr06Zo1a5YWLlyo8vLyhHtfS9Jzzz2nq666SrNnz5bjOK87jlPtOM618RjL+J/fPHTokNauXau3335bubm5ikQimjdvnq677jq99dZbpsvrt5dfflkbN27U1q1blZOTo71792rixIkKhUJavny56fKiUllZqdWrVyvt+J2ZE8Xbb7/d9fX69eu1bds2zZgxQ3V1dQn1N5fff/99XX/99TrrrLMUiURMlzNg5eXl2rRpkyZPnqy33npLjz/+uK644gr9+c9/1tChQ02X12+//OUvNX/+fM2ZM0eBQOBSx3FmSfoPx3HqXNf9SyzHMt4hDxs2TJs3b1Zubq4kyefzacqUKV13lUgUw4YN0+LFi5WTkyNJGjlypObOnatnnnnGcGXRGz58uF577TWdffbZpkuJyurVq7stl5eX6+jRo6qoqDBU0cC0tbWpsrJS5eXlpksZlNmzZ2v69OmSjr2vb775ZtXX12vHjh2GK4vOihUrNH/+/M8+VaVj2RnzN4jxQM7IyNCECRO6lhsbG1VRUaFFixYZrCp606dP73bzTkkaOnSoQqGQoYoGbubMmcrIyDBdRtTeeOONbss+n0/FxcXasmWLoYoGZvz48Qn3j+HJbNy4sdvyia440d4TxcXFSk8/djLBcZwhkv5ZUq2k38d6LOOBfEJjY6OKi4v11a9+VTNmzEi4H/NP5s0339Q111xjuoyUcODAAbW2tn7h+by8vIQ8b5mMtm3bppEjR+qSSy4xXcqA3HHHHdKxO05/S9IM13XbYj2GNYE8atQoVVdXa/fu3Xr55Zd10003mS5pUP7whz9oz549WrJkielSUkJ7e/tJnz/llFN6XAfvhEIhPfTQQ3r44Yc1ZMgQ0+UMyIMPPihJwyW9IukNx3FO732L6MUtkB3HWeY4jtvTo7S09KTnkkaOHKmf/OQnWrdunRWfkC9btkyO4/T4OPXUU/Xee+9126axsVELFy7Uc88913VO2bSBzCORZGVlnfT5zs7OHtfBOw8++KCuvvpqfec73zFdyqC4rhuWtEySI+mOWO8/nldZPCBpTU8rn3322abzzz9f4XBYkrp9oj9u3DhJUm1trc4999w4lti3O++8UwsXLuxxfVtbW7fLkg4ePKiysjKtXr1aEydO9KLEfol2Holm+PDhCgQCXzht0dzcrLFjxxqqCpK0dOlSpaWl6b777jNdyoCEQqFun6m4rhtxHKdeUlGsx4pbh+y6bpvrus09PYYNG6b09HRVVlbq5z//ebdtm5qaJB3rlk3Lzs5WXl5ej4/c3Nyuf0xaW1s1a9Ys3XfffZo2bZok6bHHHjNZfpdo5pGoPn9u0nVd7dixo+t7Ae+tWrVKH3zwgRYvXizHcVRdXa3q6mrTZUWlh8bqdEl7Yz2WFeeQf/WrX+njjz+WJHV0dOhHP/qRxo8fr29+85uGK+u/jo4OlZWV6aKLLtKoUaO0fft2bd++XY8++qjp0lLGD37wg27L69evV1pamhYsWGCootS2Zs0aVVZW6vvf/37X5W4vvPCC/vKXmF66G3e1tbXavHlz17LjOOWSxkmK/fWUrusaebz66qtuS0uLu2fPHve2225zJ0yY4E6ZMsWdMGGCW15e7u7Zs8dNBC0tLe6rr77qPvDAA66kkz4SwYl5tLS0uM8995xbUlLi5ubmujk5OW5JSYm7bt060yX26cMPP+z6fz5x4kT3sssuc3fu3Gm6rKh1dna6JSUl7nnnnedKcr/xjW+4c+fONV1WVFpaWlyfz3fS98MTTzxhuryoPPzww+7kyZPdyZMnu5K2SnpD0t+5cchFx3XdmId8f1RVVbnFxcUJ9RtUJ9Pa2qrq6mol+lySYR4NDQ3Kz8+XJNXV1amwsNBwRYOTDN8TKbnmwT31ACBFEMgAYAkCGQAsQSADgCUIZACwBIEMAJYgkAHAEgQyAFiCQAYASxDIAGAJAhkALEEgA4AlCGQAsASBDM/U19fr4osv1tSpU02XAliJQIYnKisrdcMNN8jn45ADesK7A54YPny4XnvtNZ199tmmSwGsFc+bnAJdZs6caboEwHoEMhJGQ0NDr+tP3BwXSFTGAjkcDisYDJoaPmaCwWBSzMWreRw5ckThcFitra1Rb3vi9kz90d7ePqAxbMKxZZdgMBj3W1AZC+TDhw+rtrY24T/kiUQiSTGXgczj17/+tSoqer/x7po1azRu3Liu5QMHDnTdYy2e6uvr1dLSEtcx4i2Vjy0bRSIR5eXlxXUMY4GcmZmpoqIi+f1+UyXERDAYVE1NTcLPZSDzGDdunJYsWdLra4YPH6709PRuy8FgUMXFxVHXWFdX1+v65uZmlZaWSpIKCgpUUFAQ9Rg2SeVjy0ZedPjGAjktLU1+vz+h70J7QrLMJdp5DGS+Q4YMUVpa2oC27esu0tnZ2V1fZ2VlJfz3Q0rdYytVJe7PDwCQZAhkeOL555/X1KlT9dJLL+mdd97R1KlT9fjjj5suC7AKl73BE2VlZSorKzNdBmA1OmQAsASBDACWIJABwBIEMgBYgkAGAEsQyABgCQIZACxBIAOAJQhkALAEgQwAliCQAcASBDIAWIJABgBLEMgAYAkCGQAsQSADgCUIZACwBIEMAJYgkAHAEgQyAFiCQAYASxDIAGAJAhkALEEgA4AlCGQAsASBDACWIJABwBIEMgBYgkAGAEsQyABgCQIZACxBIAOAJQhkALAEgQwAliCQAcASBDIAWIJABgBLEMgAYAkCGQAskW66ACS/gwcP6uGHH9aWLVuUnp6uTz75RHPnztXdd9+t9HQOQeAE3g2IuxdffFEbN27U1q1blZOTo71792rixIkKhUJavny56fIAa3DKAnE3fPhwLV68WDk5OZKkkSNHau7cuXrmmWcMVwbYhQ4ZcXfllVd+4bmhQ4cqFApFtZ+GhoZe1zc1NUW1P8A2xgI5HA4rGAyaGj5mgsFgUszF63m8/vrrmj17tlpbW/u9TX5+fr9f297eHtW+bcSxZZdgMKhAIBDXMYwF8uHDh1VbWyufL7HPmkQikaSYi5fz2LFjh3bv3q0lS5aouro6LmPU19erpaUlLvv2CseWXSKRiPLy8uI6hrFAzszMVFFRkfx+v6kSYiIYDKqmpibh5zKQedx///1auXJlr6+pqqrSxIkTu5b37t2r1atX69lnn9UFF1wQVY11dXW9rm9ublZpaakkqaCgQAUFBVHt3zapfGzZyIsO31ggp6Wlye/3x/1HAC8ky1yince9996rRYsW9fqaESNGdF3advDgQc2fP19r1qzRlClToq6vsLCw1/XZ2dldX2dlZSX890NK3WMrVfGhHgYsOzu7Wwj2prW1VbNmzdJ9992nadOmSZIee+wx3XzzzfEsEUgoiXtCBwmjo6NDZWVluuiiizRq1Cht375d27dv16OPPmq6NMAqdMiIu8cff1xVVVWqqqrSgw8+aLocwFp0yIi7W2+9Va7rnvQB4G8IZACwBIEMAJYgkAHAEgQyAFiCQAYASxDIAGAJAhkALEEgA4AlCGQAsASBDACWIJABwBIEMgBYgkAGAEsQyABgCQIZACxBIAOAJQhkALAEgQwAliCQAcASBDIAWIJABgBLEMgAYAkCGQAsQSADgCUIZACwBIEMAJYgkAHAEgQyAFiCQAYASxDIAGAJAhkALEEgA4AlCGQAsASBDACWIJABwBIEMgBYgkAGAEsQyABgiXTTBSD5dXZ26v7771dVVZWGDBmiAwcO6Mwzz9TPfvYzjR071nR5gDXokBF3hw4d0tq1a7VhwwZt2bJF1dXVGjJkiK677jrTpQFWIZARd8OGDdPmzZuVm5srSfL5fJoyZYp27dpluDLALgQy4i4jI0MTJkzoWm5sbFRFRYUWLVpksCrAPpxDhmcaGxtVVlammpoaLV68WMuXL49q+4aGhl7XNzU1DaY8wDhjgRwOhxUMBk0NHzPBYDAp5uLFPE499VRVVVWpqalJ8+bNU2Njox555JF+b5+fn9/v17a3t6u1tXUgZVqDY8suwWBQgUAgrmM4ruvGdQAkL8dxlkla2sfLvum67vaTbDtN0u8ljXddt6af40VzsOa7rtt7Sw1YhkDGgDmOky0pu4+XfSzJlSTXdcOf2TZf0h5J17quu7Gf443u4yVpkk6T1Cyp2XXdo/3ZL2ALziFjwFzXbZPU1tfrHMf5R0kjJD3wmadPP/7fvVGM15+O94P+7g+wDVdZwCs3Oo4zQpIcxxkq6YeSdkp6y2hVgEXokOGFVyQVS3rZcZw2HTvNUSNppuu6IaOVARbhHDIAWIJTFgBgCQIZACxBIAOAJQhkALAEgQwAliCQAcASBDIAWIJABgBLEMgAYAkCGQAsQSADgCUIZACwBIEMAJYgkAHAEgQyAFiCQAYASxDIAGAJAhkALEEgA4AlCGQAsASBDACWIJABwBL/H2yoyS8QmxPYAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_vector([S.dot(v1),R.dot(S.dot(v1))])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is definitely _not_ what we expected. Oh well. It seemed like a good idea at the time, but the scaling $S$ and the rotation $R$ applied in sequence are _not_ equivalent to the transformation $A$. \n", "Our visual intuition was not able to get the whole picture." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Complete the composition\n", "\n", "OK. This will blow your mind… to get the same transformation as $A$ we had to _first_ rotate 45 degrees to the right (which leaves the plot of our circle unchanged even though the vectors rotated), _then_ scale, and finally rotate 45 degrees to the left. \n", "\n", "We will look at this sequence of transformations via matrix multiplicaton. But first note that a rotation by a negative angle $\\theta$ is achieved by the matrix:\n", "\n", "$$R^T = \\begin{bmatrix} \\cos{\\theta} & \\sin{\\theta} \\\\ -\\sin{\\theta} & \\cos{\\theta} \\end{bmatrix}$$\n", "\n", "Check using a piece of paper that the columns of this matrix make sense for a negative angle $\\theta$, and notice that it is the **transpose** of $R$, i.e., swaps rows and columns.\n", "You can compute the transpose of a matrix in Python using [`numpy.matrix.transpose()`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.matrix.transpose.html). Try it with some sample matrix, and print it with its transpose to visualize what happens." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 99]\n", " [ 2 100]]\n", "[[ 1 2]\n", " [ 99 100]]\n" ] } ], "source": [ "B = numpy.array([[1,99], [2,100]])\n", "print(B)\n", "print(B.transpose())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now look at the result of the matrix multiplication (equivalent to the transformations in sequence, right to left):" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[2., 1.],\n", " [1., 2.]])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R @ S @ R.transpose()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's certainly the same as $A$!" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 1]\n", " [1 2]]\n" ] } ], "source": [ "print(A)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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isoC1Kzbw/qYlMy7f0tLCbbfdxp///GeSkpLo6emhrq6OP/zhD+zYsSPo7WpacL/q27Zt45VXXgl6vWf6y0kr//zyMD+6aAnnlaQvej3R5nE7Ge0/zPjAMQwOxROmCr66cwtlWYs6IB1zvvXmKPtOWHnuqipSdGc9DIZ1HI3aEdEH3Zu4t7GE+pzkaIUAQJfJxYOvGmIilliLZ75YHnjgAV767ctkZbYC4HQ62L9/P01NTWRn53D33d+kurp63u1kVmyYd5neKQ+D9z5JWuPOmP9czuV4YikWl9Ed1e1HwvtWLY12CCHzy24zZpeXm5fnRDuURVFKYZk4gaG7FbtlguzCSn6lreMvFh1fWVYy6+uee+45bDYbl156KQB2ux2A22+/nby8PH7605/S0NAw7/b7+4M7ILpz586glpvNrmNGVuansrE47azWEy1ej5vxE22M9h9GeTzklTfxb0dzWVuZnTBJ6KjNzbO9Fj61Mi8USWjYRS0RHSYbXUY+6dnR/cHr3A6GscVELLEWz3yxfO6LX+NzX/zaqfvTe/K7Hn58QXvytdnzH/2wTzhwkxQXn8u5HE8sxZLmdkR1+5GwqSQ+k4Ezub2KhztMXFmVRXlm9HfuFspqGsXQ/RZTkwYyckuoW3cF9tQCHn++n0+uyCF1jrMDd9xxB3fcccep+9Pj6Pe+970FjaOVlUFNET0rB8fsvDVq594tJUEfgY0VSnmZHO5ipOcAbqeNvLIGiqubeXHIw4B9lPubcqMdYsg82mkiJUnjhqXxsVMnc0SFECJOxVsyMJvf9E9x0urmo43xlQw4rEYM3a2YRvtJzcylevUOsgoq0DSNBw+No0+CG5YGP00p1u1uM1KdlcyOioxohxI0pRTmsQEM3a04rEZyimsoqV1LakYOXqXY3TbIRWUZ1OekRDvUkLC4vDx53Mz19dlkJUd/6lgwJBEVIXH77bfz2muvnfp/U1MTjz32WJSjEkLEOq9S7GqbZPuSdBpy4yMZcDmsjPQeYPLkcfSpGVQ0bSO3pO7UjsGUy8sTx828vy6HnBRd0OuN5XG02+Rk3wkrd2wsIilOdoCmJocxdLdgNY2Smb+EiqZtpAecgXt5yEa32cUd5xVFMcrQ+vlxE06v4qZl8XE0FCQRFSHyve99L9ohCCHi0CtDNrpMLv5tfewnAx6Xg9H+w4wNHiNJl0xp/Qbyy5eTlHR6svnzLhN2t3fByUAsj6N72o0Up+l4d3VWtEOZl90ygaGnFfPYIGlZBdSsuYys/LLTllH+HaB1hamsKUyMKS5Oj2Jvh4n31mRRlB4/6V38RCqEECLh7G6bZE1hKuuKoj/fejanClz6DqOUh6LKlRRWrUSnf+cRXKdH8UiHiatqsijJSIyvWIPVzfO9Fj69uiCmi1+cdgsjPfuZNHSTkpZF5Yrt5BTXzDiFpXXUwYExB9+7oDQKkYbHc71mJhwePrI8vqa4JMZfiRBCiLizf9RO65iD+7eVxuR8V6W8TJ48zkjvQdxOG/llyyiuaUafMvtli57vszBm9/DROEsG5rK3w0iaPon318fmfFe3085o3yHGh9rR6VMoa9hM/pIGtKTZ50juaptkaU4yFyyJ30tQBfIqxZ52I5dWZFKdHV8Ff5KICiGEiIrdbUbqc5LZXhZbyYBSCvNoP4aeVhxWE7klNRTXriU1fe5T7V6leKjNyI7yDGoTpPjF5PTwi24zH2rIITPGil88bhfjg0cZ7T8CQHF1MwUVTej0cydiHZNOXjlp4xubimNyB2gxfj9opd/i5p7Ns18qLFZJIiqEECLiukxO/jRk5c7zYqv4ZWpymOHuFmymUbLyl1DRdMFpBS5z2Tdopc/i4hubYn++a7CePG7G7YUPNcTOEV6v18PkUCcjfQfxuJ0UlC+nqHo1+uTg5no+1D7Jkgw9O6sywxxpZCil2N02yeaSNFYWxO4Ul9lIIiqEECLidh8zUpKu44qq2Ch+sVvGGe5uxTJ+gvTswhkLXObiK34xsqEojdUJUvzi8Hh5tNPE1bVZFKQFX/0fLkopTCO9GHpacdot5JXUUVy7lpS04H+HTky5eLF/is+tKUCfFDs7QGfjdYOdoxNOfnjhzN27Yp0kokIIISLqpNXNC/0WPttcQHKUi1+cdguGnv0YDd2kpGVTufJCcoqqF3zK9s0RO0cmHHx/e+IUvzzTY8HojH7xi1KKqYkhhrtb/F2rKqhaeTFpWfkLXtfedhPZyUlcUxeb810XY1fbJE15KWyO0wYXkogKIYSIqL3tRjL1SVwbxWTA7bQx0neIiaEOf4HL+eQvWTpngctcdrUZWZ6bwtbS2Jrvulger2JPm5F3VWRSkRW94hebeYzhrhamJk+SkVNE3bqdZOQubh7khMPD0z1mbm3MJV0fW/NdF+vohIO/Gez8x/nxO99VElEhhBARY3T4il8+sjyXjCgUv3jcLsYGjjI2cARN0yiuaaawookk3eKTrbYJB68N27hnc/wmA2f67cAUJ6xu7tsaneIXh9WEoacV00jfO7pWLdbjnSY04MY4aX0ZjN1tRioz9VxWGb/zXSURFUIIETE/O25CATc2RDYZ8Ho9TAx1MNp7EI/HRUF5o7/A5eyLO3a3GSnP0POuOE4GAvmKX4xsKU2nMT+yxS++rlUHmTzZiT4lnYrGreSW1p91gm91eflZp4nr6rLJTY3+fNdQ6DO7+N3AFP+2oTCmCv4WShJRIYQQEWFz+5KBa2qzyYtQMuArcOnB0LMfl32K3NJ6SmrWkJwWmqRxwOLit4NTfGFdIboEKX55ddhGu9HJj9ZGrvjF43Yy2n+Y8YFjaDodJXXrKahofEfXqsV6utvMlNvLzQl0fdeH243kp+p4b018z3eVRFQIIUREPNNjwezycsvy8B8NVUphmTiBobvVX+BSSdWqHaRl5oV0O3vajeSm6Li6Njaq/0Nhd5uRlfmpbCwOf/GL1+thfLCN0f5DKI+HwsoVs3atWiyXR/Fwh5Erq7JYkiDdrkZtbp7ttfCplXkx3e0qGInxExFCCBHT3F5f55crqjIpzwxv8YvVNIqhu4WpyWEycovPqsBlLuN2D8/2WPjkijxSdYlR/HJozM6bI3bu3VIS1vmuSnmZHO5ipOcAbqeNvCUNFNc0k5yaEfJtvdhvwWDzcGtT4hwNfbTTRHISXB/mbldulyMk01fmIomoEEKIsPtN/xQnrW5ubQzf5Y0cViOG7lZMo/0hK3CZy2OdRvRJcMPS+D41Gmh3m5HqrGR2VIQ+IQR/16qxAQzdrTisRnKKqympXUdqRniOknv9810vKsugPkG6XVlcXp48buaG+hyyU8IzxcXrcTE2eIyx/iM0XXBjWLYxTRJRIYQQYTXd+eWCJek05IY+GfAVuBxg8uRx9KkZIStwmcuUy8vjx828vy6HnDAlA5HWY3Ky74SVr20MT7erKeMwhq4WrKZRMvOWUNG0LeiuVYv18pCNbrOLr21MnG5XPz9uwulV3LQs9Mm78nqZONnJSO8BPG4n+WXLQr6NM0kiKoQQIqxeOWnjuMnFl9eHNhnwuByM9h9mbPAYSbpkSus3kF++PGQFLnN5qsuM3e0NSzIQLQ+1GylK0/Hu6tDOd7VbJjD0tGIeGyQtK5+a5kvJzC8L+6WufN2uJllXmMraovi82PuZnB7FI50m3luTRVF66FK4t7tW7cdpNy+qa9ViSSIqhBAirHYdm2RNYSrrikIz18zrcTN+oo3R/sMor4eiypUhL3CZi9Oj2Nth5KqaLEoSpPjFYHXzfK+FT68uCFnxi9NuYaRnP5OGblLSsqhcsZ2c4pqIXWu1ddTBgTEH392WON2unus1M24Pbbcry8QQhu4WbOZxsgrKqVp50aK6Vi1WYvwFCSGEiEn7R+20jjm4f1vpWScgSnmZPNnFSK+vwCW/rIGi6vAUuMzl130WxkKcDETbIx0m0vRJvD8ExS9ul53RvkOMn2j3d63aRN6ShogcqQ60u22SpTnJXFCWGN2uvMpX8HdpRSbV2Wdf8Gczj2HobsEy4etaVbv2cjLzIp+0SyIqhBAibHa3GanPSWb7WSQDvgKXfn+Bi4nckhqKa9eSmh750+LTxS8Xl2dQlyDFLyanh6e6TXyoIYfMs+h25XG7GB88ymj/EQCKq5spqGhCp498i9BOo5OXT9r4xqbiuL7Ye6DfD1rpt7i5Z/PZXQHCYTMx0rMfo6GX1IwcqlZdTHZhZdS6gkkiKoQQIiy6TE7+NGTl389bfPHL1OQwhm5fgUtW/hIqmi4Ie4HLXPYNWumzuLhrU+IUvzx53IzbCx9qWNwRXq/Xw+RQJyN9B/G4nRSUL/d3rYrevMyH2owsydCzsyqRul1Nsqk4jZUFi5vi4nbaGOk9wMSQr2tV+fIt5C2pR9Oie+kxSUSFEEKExUNtRkrSdVxZtfCCB7tlguHuFizjJ0jPLqBmzWVk5ZeFIcrgTbe+3FCURnNhYhS/ODxeHu00cXVtFgVpCzt1/naBSytOuyWiBS5zOTHl4oV+C59bU4A+QbpdvW6wc3TCyQ8vXHi3K4/byVj/EcYGj6Il6SipW0dBeSNJuthIAWMjCiGEEAnlpNXNr/ssfLa5gOQFFL+cXuCSHfECl7m8OWLn8ISD729PnOKXZ3osGJ0Lm++qlGJqYojh7hZ/16oKqlZeHNECl7nsbTeRnZzENXWJc33XXW2TNOalsLkk+B0gr9fDxIl2RvoO4fW4KKxcQVHlSnRhvkD9QkkiKoQQIuQe6TCSqU/i2iCTAbfTzkjfQSaGOvwFLpvJX9KAlhQ7HYt2txlZnpvC1tLEKH7xeBV72oy8qyKTiqzg5nHazGMMd7UwNekvcFl3OZm5sZOYTzg8PN1j5tbGXNL1sfO7czaOTjj4m8HOf5xfHNQOmVIK43AXht4DuB1W8pYspbhmTcSL+oIliagQQoiQMjo8PNVl5pbluWTMU/zicbsYGzjK2MARNE2juKaZwoomknSRL3CZS9uEg1eHbdyzObhkIB78dmCKE1Y3922dv/jFYTVh6GnFNNJHamZu1AtcZvN4pwkNuHFp4lzfdXebkcpMPZdVzj3fVSmFZXyQ4e4WHFNGcoqqKGm+lNSM2L66gySiQgghQurx4yYUcGPD7MnAqQKX3gN4PC4Kyhv9BS6xddpw2u42I+UZet41TzIQL6bnu24pTacxf/bP3Ne16iCTJ/0FLo1byCtdGnMJKIDV5eVnnSauq8smNzUxul31mV38fnCKL68vnLPgz2ocYbj7LazGETLzSilfv5WMnPgoqJNEVAghRMjY3F4e6zRxTW02+TMkA74Clx5/BxcLeaX1lNSsJTktdhO8AYuL3w5O8YV1hegSpPjl1WEb7UYnP1o7c/GLx+1ktP8w4wPH0HQ6SurWU1C+PGYKXGbydLeZKbeXmxPo+q4PtxvJS9Hx3pqZp7jYpyYxdLdiHhsgLSuf6uZLyMovj8kdhdnE7m+UEEKIuPNMjwWzy8sty08/GqqUwjJxAkN3q7/ApZKqVTtIy8yLUqTBe7jdSG6Kjqtro1sNHkq724yszE9lY/HpxS9er4fxwTZG+w+hPB4KKpsoqloVsa5Vi+XyKB7uMHJlVRZLEqTb1ZjdzXO9Fv5+Zd47ul257FMYevdjHO4mOTWDyhUXkFNcG1cJ6LTE+GmJqPnlL3/JT37yExwOBzabDZvNxpe+9CU++MEPRjs0IUSEub2Kh9uNXFGVSXnm23M8baZRhrtbmJocJiO3mLp1O8nIPbuLckfKuN3DMz0WPrEij1RdeIpfIj2OHhqz8+aInXu3lJxKXJRSTA4fZ6TH17Uqb0kDxTWR71q1WC/2WzDYPNzalDhHQx/tMKFPghsCul25XQ5/16o2dLpkSpduJL9sWcS7VoWSJKLirDzwwAPcdNNNfPSjHwXg2Wef5dprr2XFihU0NzdHOTohRCT9pn+KIaub+5f7qqgdVhOG7hZMo/2kZuZSvXoHWQUVcXXU5rFOI/ok+MDS8F0KKNLj6O42I9VZyeyoyPB3rRrA0NPqK3Aprqakdh2pGfFT7ONViofajVxYlkF9gnS7sri8PHHczA31OWSn6PB6XIwNHmOs/whKKYqqVlNYuSLN3eCpAAAgAElEQVQqXatCTRJRcVbuuece1q5de+r+jh078Hq9dHZ2SiIqxDlkuvPLBUvSqU13c6L9LSZPHkefkk5F41ZyS+vjKgEFmPInA9fVZZOTEr4jTpEcR11exb4TVr62sQibyYChy9e1KjNvCRUbtkW1a9VivTxko8vk4qsb4qM4JxhPdZlwehUfWprF+Il2X1Gf20l+2TKKq1ejT0mMS4iBJKLiLG3cuPHU/10uF/fddx8rV67k8ssvD3odAwMD8y5z0uxZVHxCiMh45aSNAZOVLyyZpPNvx9F0OkrrN5BfvjxuTxs+1WXG5vZy87Lwnu6N1DgKYHR62ZxqY43lDXr6BknLyqem+VIy88vibkcBfDtAu9omWVuYytqixOh25fQo9rabuKzQhfHwr3HazTHTtSocopaIlmLGY53AFuXDyh6rK2ZiibV4FhLLN7/5TZ599lkaGhr41S+fQKcc2MyOoLazfcuG+RcqqkSPN+4+l3MtHvuUG6/HjX1qEps+uvu59ik35MfOhbYTmdfj5i8HW/hCeheZRj2FlSsorFoZ8wUuc3F6FI90GLmqJouSCBW/fPrTn2bv3r2sWrWKF198kays4JOOqqqqeZcprKwiCfhU6uu4bbkx1bVqsVpHHRwYc/DdbYnzt/7kkT6GJibYkd5GSkExVSsvJC2rINphhY2mlIrKhp98+v9UXU4yaWGa/B0su8dLt8lFLMQSa/EsPBbFiRMnGBsbo6lpBcnJwSVFb775xvwL6VP5yn17+OXub8fh53LuxNPlSOXLg3V8u6Kb+tTgdkTCGcv7dn4gfr9hgxOdAXx648rL5Mkuujpb6BozU161jM2rN8ZNgctcftlt5u43R3l8ZwV1EZx36PF4uOuuu9i9ezevvfYaZWVlQb1urmQyKzONqy/bzGVXXcYdd/8vr7/yW5ZUxu+R6kC3v3ySE1Y3j11eMed1NuOBzTzGya4WPnkwg6VZSXx3Rx2ZeTGRYIf1g43aIYsH3Zu4t7GE+pzoHsHpMrl48FVDTMQSa/EsJpa69YrLLruMd787iS984QtBvSazYv4jor1THoz3Pkla4864/FzOlXhcRjepEyaqVl5EfW50j4i6jO6obj+RnSpw6W7FYTVyyFHEH9PW8NMNy+M+GQB/8UubkYvLMyKahALodDruvPNOdu3axf333899990X1Ov6+/vf8ZjyurGN92Ib78XtVeyZLMebspfy6hWhDjsqOo1OXj5p4xubiuP6985hMzHSsx+joZc33aWM6wv5/oU1ZOYlxlSD+UTtm2KYbHQZ+aRnR7eLhs7tYBhbTMQSa/EEE4vT6SQl5fSBOiOniL++eTDoSe+1QSxnn3DgJiluPpdzNZ40t4MknZW0zLyYiEWE3tTkMIZuf4FL/hK8lZv4wSs2/v28orhOBgLtG7TSa3Fx56bIFL+cOY4mJSWxbNkyjhw5EvQ6KisrT/1feb1MnOxgpP8gHreT0pqVvGCr4m8mW1iLriLtoTYjSzL07KyK3WYIc3E7bYz0HmRiqAN9Sjplyzbz0pFMtpQlsarw3EhCAaJ/XlHEtQ0b3nk0c2hoiPLy8ihEI4QIF7tlgt6Dv6dn/0t4vV5q1lxG7Zp38ciAjpJ0HVdWJUYRxXTryw1FaTRHKBkI1TiqlMJo6KHzjWcY6nydrPwyGjZdTX7tBvZ2O3hfbRa6xNhX4MSUixf6LdyyLAd9nHW78rhdGLpb6fjb0xgNPZTUraNh09V06qo4Ounk1sbYb/IQSlI1L87KkSNH+NWvfsV73vMeAB5++GHa2tr48Y9/HOXIhBCh4LRbGOnZz6Shm5S07NMKXIatbn7dZ+GzzQUkJ0iG8+aIncMTDr6/PXJz80IxjlomhhjuasFuGSe7sIKqlReTlpUPwJPHTRidHj6yPJc9YXkHkbe33UR2chLX1IXv+q6h5vV6mDjRzkjfIbweF4UV/q5Vyb6zR7vbRmnMS+H80nPnaChIIirO0n//939zzz338O1vfxuPx4OmaTzzzDNs37492qEJIc6C22n3dXAZakenT6GsYTP5SxrQkt4+kba3w0imPolr4ygZmM/uNiPLc1PYWhq56zSezThqM4/5ulZNnCQjp4jadZeTmft2Eu3x+ua7vqsik8qs6M9pD4UJh4ene8zc2phLuj72T+wqpTAOd2HoPYDbYSVvyVKKa9acVtR3dMLBXw02vnV+cVxfxWAxJBEVZ+Uzn/kMn/nMZ6IdhhAiRDxuF+ODRxntP4KmaRTXNFNY0USS7vQkxujw8IsuMzcvzyUjOfaTgWC0Tzp4ddjG3ZsjmwwsZhx1WE0YeloxjfSRmpFL1aqLyS6sfEfcvxuc4oTVzX1b46OlajAe7zShAR9cGtvdn5RSWMYHGe5u8XWtKqqipPlSUjPeeV3ah9qMVGbquawiPue7ng1JRIUQQuD1epgc6mSkz1fgUlDeSFH1KvTJM58mfPy4CS9wY0NsJwMLseuYkfIMPZdXxm4y4HJYGek7yORQJ/qUdMobt5BXWo+mvXNnQCnFrmNGtpSm05gf/cLKULC6vPys08S1ddnkpcZu4ZXVOMJw91tYjSNk5pVQvv5KMnJmLn7rt7j43eAUX1pXiC7O5ruGgiSiQghxDlNKYRrpxdDTitNuIa+knuLaNXN2cLG5vTzWaeKa2mzyYzgZWIhBi4vfDk7x+bWxmQx43E7G+o8wNngULUlHSd16CsqXk6Sb/Wv8tWEb7UYnP1q7JIKRhtfT3Wam3F5uXhabO0D2qUkM3a2YxwZIy8qnuvkSsvLL5zzCvqfNSF6KjvfVJs4Ul4WQRFQIIc5BSimmJoYY7m7Bbpkgu7CSqlU7SMucv2L3mR4LZpeXW5bHZjKwGHvajeSm6Li6Nraq/71eD+ODbYz2H0J5PBRU+gtcguhatavNyMr8VDYWJ0bxi8uj2Nth5IqqLMoyY2u+q8s+haH3AMbhLpJTM6houoDcktp5p3iM2d0812vh71fmkZIgBX8LJYmoEEKcY2zmMYa7Wpia9BW41K3bSUZucHMI3V7Fw+1GrqjKpDzGkoHFGrd7eKbHwidW5JEWI8UvSikmh48z0nMAt9NG3pIGimuag+5adWjMzpsjdu7dUpIwxS8v9lsYtnm4tfGdcyyjxe1y+Ir6TrSh0yVTunQj+WXLgu5a9WiHCX0S3FB/bh4NBUlEhRDinHFagUtmLtWrd5BVULGgROU3/VMMWd3cvzwmWg+GxGOdRvRJ8IGl0U8G3lHgUlxNSe06UjMWdvR5d5uR6qxkdlTEf7tV8He7ajdyYVkGS3Mj2+1qxng8LsYGjzHWfwSlFEVVqymsXIFOH/zOmcXl5YnjZm6ozyE7gRoNLJQkokIIkeBcDisjvQeZPOkrcKlo3Epuaf2Cj5T5LvY+ybYl6SzLi34yEApWfzJwXV121LsOWY0Ghrtb/AUupVSs30r6LAUuc+k1u9h3wspXNyZOt6uXh2x0mVx8dUNkul3Nxte16jgjvfvxuJ3kly2juHo1+pSFX+7rqS4TTq/iwzE63zVSJBEVQogE5XE7Ge0/zPjAMTSdjtL6DeSXLw/6tOGZXjlp47jJxZfWB9e+Nx481W3G5vZy87Lone71Fbi0YB4bJC0rn5rmS8nML1v0KfWH2iYpTNNxVXVszXddLKUUu9omWVuYytqi6Mx3VUphGu3D0N2K024mt6SOkpo1pKQv7ii606PY22HiPTVZFKef26nYuf3uhRAiAZ1Z4FJYuYLCqpVBFbjMZXebkeaCVNZHKRkINadHsbfdyFU1WZRkRP7r8PSuVVmnda1aLIPVza96LfzT6vyEKX5pHXVwYMzB/duiMx3EMjGEobsVm3mMrIJyqlZeSFpWwVmt81e9ZsbtHj66PHbmu0aLJKJCCJEglPIyOdz1doFLWQPF1cEXuMzlwJidllE7/7UtcYpfXuizMGr3tb6MJLfL37XqhL9r1dJN5JU1LPpIdaBHO02k6ZO4vj5xTvfubpukPieZ7WWR63YFvqI+Q3cLlomTpGcXUrv2cjLzzj4Z9irFnnYTl1RkUJ2dGAV/Z0MSUSGEiHNKKcxjAxi6W3FYjeQU11BSu3bBBS5z2XXMSF12MheWJU7xy+42IxeXZ1CXE5n5rl6Pi7GBY4wN+ApciqtXU1CxsAKXuZicHn7eZeLGhhwyE6TbVafRycsnbdy1KXLzXR02EyM9+zEaeknNyKFq5UVkF1WFbAfsD4NW+iwu7t5cHJL1xTtJRIUQIo5NGYcxdLVgNY2Smb+EiqZtpGeHdg5nl8nJn4as/Pt5iVP88scTVnotLu7cFP7iF1+BSycjvQd8XavKllNUvRp9SminODx53IzbCx9uSJzTvQ+1GSlN13FFVfjnu7qdNkZ6DzIx1IE+JY3y5eeTt2TpjF2rFkv5d4A2FaexsiAxul2dLUlEhRAiTvUd+oO/wKWAmjWXkZVfFpbtPNRmpCRdx5URSAYiYbr15YaiNJoLwzff9e2uVftx2s3kldRRXLt2zq5Vi+XweHm008T7arMoSEuMSwENTbl4od/Cv6wpQB/Gblcet4ux/sO+rlWajpLadRRUNM7ZtWqxXjfYOTLh4H+2J063q7MliagQQsQph9UYkgKXuQxb3fy6z8JnmwtITpDil7dG7RyecPD97eErfrFMDDHc1YLdMk52YQVVKy8iLSs/bNt7tseC0Rn5+a7h9HC7iSx9EtfWhef6rl6vh4kT7Yz2HcLjcVFY4e9alRy+I5W724w05qVwfmliFPyFgiSiQggRpxrOuxotKbxzAfd2GMkMYzIQDbuOGVmWm8LW0tAXv9jMYwx3tzA14etaFaoCl7l4vIqH2oy8qyKTyqzEKH6ZdHh4usfMrY25pIe425VSCqOhG0PPftwOK3lLllJcsyYkRX1zOTrh4K8GG986vzhhCv5CQRJRIYSIU+FOQo0OD7/oMnPTslwyEqT4pX3SwavDNu7eHNpkwNe1aj+mkV5SM3KpWnUx2YWVEUk4fjc4xQmrm/u2BtemNR78rNMEwAeXhq7g7h1dq4qqKGm+lNSMyBxFfqjNSEWmnssqMiOyvXghiagQQogZPX7chBf4UAJ1ftndZqQ8Q8/llaFJBlwOKyN9B5kc8nWtKm/cQl5pfUgLXOYyPd91S2k6jfmJUfxidXn5WaeJ6+qyyUsNzXxXq3GE4e63/F2rSihffwUZOZGrWu+3uPjd4BRfWleILozzXeORJKJCCCHeweb28liniWtqs8kPUTIQbYMWFy8NTPH5tWefDHjcTsb6j/gKXJJ0lNSto6A8PAUuc3lt2Ea70ckDaxOn+OXpbjMWt5ebQ7AD5Ota1Yp5bIC0rDyqmy8hK7884qfG97QZyUvR8d7axCj4CyVJRIUQQrzDMz0WzC4vtyxPnKOhD3cYyU3RcfVZJAPTBS4jfQdRHg8Flf4Cl7PsWrVYu9uMrMxP5bzixCh+cXkUezuMXFmVRVnm4ue7uuxTGHoPYBzuIjk1g4qmbeSW1EVlbuaY3c1zvRb+fmUeqbrEmOISSpKICiGEOI3bq3i43cjOykzKzyIZiCXjdg+/7LbwiRV5pC2i+EUphXG4C0PvgYgWuMzl8LiDN0bs3LslcbpdvdhvYdjm4dbGxc3bdLsc/q5Vbeh0yZQu3Uh+2bKQdK1arEc7TOiT4Ib6xCn4CyVJRIUQQpzmpf4phqzuqPX2DofHOo3ok+ADSxeWDMxc4HJZSLtWLdbutkmqs5LZUZE43a4eajdyYVkGS3MXdoTZ63EzNniMsf7DKKUoqlpNYWXoulYtlsXl5YnjZm6ozyE7JTGmuISaJKJCCCFOUUqxu93ItiXpLMuLzunmULP6k4Hr6rLJWUAyYDUaGO5u8Re4lFKxfivpOeHvxBSMXrOLPwxa+erGxOl29fKQjS6Ti69sCP4z9nWtOu7vWuUgv2wZxdWr0adEti/9bJ7qMuH0Kj6cQAV/oSaJqBBCiFP+ctJGp9HJF9clTvHLU91mbG4vNy8L7nTv6QUu+dQ0X0pmfllMnf5+qG2SwjQdV1UnTvHLrrZJ1hamsq5o/vmuSilMo30Yultx2szkltRSUruWlPTYOf3t9Cge6TDxnpositMl3ZqNfDJCCCFO2dVmpLkglfVBJAPxwOlR7G03clVNFiUZc3/luexTGHr2M2noIiU1M+xdqxbLYHXzq14L/7Q6n5QE6XbVOmrnwJgjqOkglomTGLpbsJnHyCoop2rlhaRlFUQgyoV5vs/CmN3DRxOo21U4SCIqhBACgANjdlpG7fzn1sQpfnmhz8KIfe7Wl6cVuOhTKFu6ibyyhqgWuMzl0U4Tafokrq9PnNO9u45NUp+TzPay2U+p2yzjGLpasEwMkZ5dGJGuVYvlVb5uV5dUZFCdnRgFf+EiiagQQgjA1/qyNjuZi8oTp/hld5uRHeUZ1OW8c76r1+PyF7gcQSlFcfVqCiqiX+AyF5PTw8+7TNzYkENmgnS76jQ6efmkjbs2zTzf1WkzY+hpxWjoJTUjh6qVF5FdVBXTO0v7Bq30WVx8c3PkLpofryQRFUIIQZfJyZ+GrHw9gYpf/njCSq/FxZ2bTi9+8RW4dPoLXJwxV+AylyePm3F74cMNiXO696E2I6XpOq6oOn2+q9tpY6T3IBNDHehT0ihffj55S5ZGrGvVYiml2NVm5LziNFYVJEa3q3CSRFSctccff5yf/vSneDweTCYT1dXV3HfffdTX10c7NCFEkB5qM1KSruPdCVL8Mt36ckNRGs2FaaceM430YujZj9NuJq+kjuLataSkRf89BzOOOjy+blfvq82iIC02pw0s1NCUixf6LfzLmgL0/m5XHreLsYEjjA0cRdOSKKldR0FF5LtWLdYbI3aOTDj4n+2JU/AXTvHxUxUx7ZZbbuG5555j586deL1ePv7xj3PllVdy4MAB0tISo+BBiEQ2bHXz6z4L/9xcQHKCFL+8NWrn8ISD72/3zSG0TAz5C1zGY7LAJZhx9NkeC5POuee7xpuH201k6ZO4ti77VNeq0b5DeDwuCiv8XauS4+uo4q5jRhrzUji/VL7/ghHbx7dFXLjmmmvYuXMnAElJSdx22210dHTw1ltvRTkyIUQw9nYYydQncV1d7Fz65mztbjOyLDeFdRlWeg78lt4DvwMtidq1l1PTfGlMJaEw/zjq8Sr2tBt5V0UmlVmxO4d1ISYdHp7uMfOhhmwcYz10vv4Mw11vkV1YybLN11JavyHuktBjEw7+arBxa2NuTM9hjSVyRFSctSeeeOK0+9N7706nM6jXDwwMzLvMSbNn4YEJIeZlcnr4RZeZm5blkpEgxS/tkw6OnhzjjsqTdLcM+QpcVl1EdmHsFrjMN47+bnCKwSk3924pmfH1wYyjseZnHUbqGOXCqYMMjvq7Vq2+lNTM+D3iu7vNSEWmnssqMqMdSkgopcL+NxO1RLQUMx7rBLYoVyd6rK6YiSXW4llsLG/97WU2rV/FxrUrsJnH5l1++5YN86+0qBI93rj+XMLFPuXG63Fjn5rEpo/uvmWsxUJ+bF7aJZY83mnCC3woQTq/uJ02/vLWq3w6pZdSlUPJ8i3kLamP+QKXM7366quUl5dzwQUXnJrvuqU0ncb8mY8QVlVVBbXeFStWhDLMRZsYH8Z9/BU+nm4iPbWckqYryMiJ7wrzAYuL3w1O8aV1heiSYnOHZyGU8vLi4U6uXL08rNuJ2jfF3+lfx96WTJcuuoOD3ePl7/SumIgl1uJZTCxKeUm19XD/1z9F34GXgnrNNz530/wL6VP5yn17sLf9Ji4/l3Dqd6TisNbRf6SV5FSHxBIQy7rKD0Q1hlhnd/uKX66pzSY/Nb6LXzxuJ2P9RxjqO0KyyUVKZTPL1q+LmwKXQA6Hg/vuu4/vf//7JCcn89pJG+1GJw+sjf/il+muVb0D3WiOZOrPu4Sa8uqYPVK9EHvajeSl6HhvbfSL386GUgrzaD+Gnlb+rzMvcRPRB92buLexhPqc6B5R6jK5ePBVQ0zEEmvxLCaWf/u3r1BSUszVHw0iufTLrJj/iGjvlAfjvU+S1rgzLj+XcHIZ3aROmKhaeRH1udH90o21WMTcnumxYHJ5uWV5/B4NnS5wGek7hNfj4pBWxSNJZfx8XT1JMbCjuBif+tSnuOGGG7j++usBX+vLlfmpnFc8e/FLf39/UOuenocaaS77FIbeAxiHu9Dp03jsWCY5BVXUVtREJZ5QG7O7ebbHwidX5JEap793AFOTwwx3t2AzjTKQUsXxpLKwbzNq3xTDZKPLyCc9O7oTkXVuB8PYYiKWWItnobF8+ctfxmL38N07vrmgvdva7MJ5l7FPOHCTFJefS7iluR0k6aykZeZFPZ5Yi0XMzu0vftlZmUl5ZvR3qBZKKYVxuAtD7wHcDit5S5aiL13FD383xidW5JGmj89k4Mtf/jJ6vZ577rkHgMPjDt4YsXPvlrm7XVVWVkYqxAXxuByM9B9mfPAYOl0ypXUb+M0Pfs+fU+t4bGtetMMLmcc6TeiT4ANL47Pgz24ZZ7i7Fcv4CdKzC6lZcxkPHk2iLtcV9m3H3zkLEZO+853v0NPTwyOPPIKmabz55psAbNy4McqRCSFm8lL/FENWN/+1bebil1illMIyPshwdwuOKX+BS/OlpGbk8v8fGkenxW8yMNM4+t99yVRnFbCjIr66XXk9bn/XqsMopSiqWk1h5QqMd/+QR2z5bDZ00LTy4miHGRJTLi9PHDdzfX0O2SnxNcXFabdg6NmP0dBNSlo2lSsvJKeomh6zi30nBvn6xqL5V3KWJBEVZ+1HP/oRe/bs4Sc/+cmpS40899xz1NbWSiIqRAxSSrG73ci2Jeksz4v+Uf1gWY0GhrtbsBpHyMwrpXz9VjJyfF+UVn8y8P76bHLiLBmAmcfRh5//PX8uuYTvXpEbN92ulPIyMXTc37XKQf6SBoprmtGnpGP+30f4/Qtv0Xv5h/jMoT+RlJ0YleU/7zLh8ChuiqOCP7fTxkjfISaGOtDpUylrOJ/8JUvRknxnEva0GylO03FlBBpcSCIqzorZbObTn/40Xq+Xbdu2nfbcgw8+GKWohBBz+ctJG51GJ19cFx/FL9MFLuaxAdKy8qluvoSs/PLTTlU/1W3G5vZy87L4u/TPrOPou/+B1ddcyFVx0O3KV+DSx3B3K06bmdySWkpq15KS7js6bX36JYx3fZ8n3vdxVhgGWBflOeSh4vQoHukwcVV1JsXpsf+efF2rjjI2cARN0yiuaaawookk3dvTcwxWN8/3WrituYCUCDS4iP1PTcS07OxsPB65xqcQ8WRXm5HmglTWF8V25xdfgct+jMPdJKdmULniAnKKa98xV9LpUextN3JVTRYlGfH3tTbTOGqwurn61/380+r8iCQDZ8MycdLftWqMrIIyKldeSHpAwwD7y28w/tm7OFxaxdGSSr7+0mPot4a3EjtSnu+zMGb38NHG2J7v6vV6mBjqYLT3IB6Pi4LyRoqqV6OfoWHA3g4j6fok3h+hBhfx9xcrhBBi0Q6M2WkZtfOfW+cufokmt8vBaN8hxk+0+Qpclm4kv2wZSUkzn3J/oc/CiD2xWl8+2mkiTZ/E9fWxe7rXZhnH0NWCZWKI9OxCate+i8y804+yOw93MPaJL4HLzRNrt1MzOcLmvg70N78rSlGHjlcpHmozcklFBjXZsVnwp5TCaOhhpKcVl8NKbmk9JTVrSE6beVqEyenhqS4zH16WE7EGF5KICiHEOWTXMSO12clcVB57xS9ej8tf4HLktAIX3RyNI7xKsbvNyI7yDOpyUiIYbfiYnR5+3mXixoYcMmOw25XTZvYXuPSQkp5N1cqLyC56Z9cq98AQo7f8C8o8RU9+MX+rWsa//vFpklDo62Ozyn8h9g1a6bO4+Obm2LsQv1IKy8QJDN2t2C0TZBdWUrX6EtIy5z5y+8RxMx4FH2qI3E6dJKJCCHGO6DI5+dOQla9vLIqp4hfl9TJxstNf4OIkv2wZxdWr0aekz/vaP52w0mtxceem8Ff3RsqTXWbcXvhwBJOBYLidNkZ6D/oKXJLTKFt2PvllS2fsWuWdMDJ687/gHR4F4Mk1F1A8ZeLi44cA0NcF1wkqViml2NVm5LziNFYVxFbBn9U0iqG7hanJYTJyi6lbt5OM3PmvjnGqwUVdFgVpkSv4k0RUCCHOEXvajJSk63h3jBS/KKUwjfRi6NmP024mt6SOkpo1pwpcgnn9rjYjG4rSaC6M7fmuwXJ4vDzaYeK9NZFNBubiK3A5wtjAUTRNo6R2LQUVTbN2rVI2O6Mf+wLujh4AhrNy2be0mU/+9TfolRcAfW18J6JvjNg5MuHgB9tjp42ww2rE0N2KabSf1MxcqlfvIKugIugpOM/0WDA6PdwS4YI/SUSFEOIcMGx183yfhX9uLiA5BopfLBNDGLpb/QUu5VStvJC0gAKXYLSM2jk07uD7MZQMnK3neixMOj18pDH6R0Onu1aN9h3C43FRWNFEUdUqdDMUuExTHg/jn7kT5+sHTj32i9VbyXQ6uKLNd1kqXVkJSRnxveOwu83I8twUtpTOf9Q+3FwOKyO9B5g8eRx9agYVjVvJLa1f0Bxwj1fxcLuRyyszqciK7HxXSUSFEOIcsLfDSIY+iesiVAk7G5t5DEN3C5aJk6TnFFG79nIy8xaXSO5qM7IsN4WtMZAMhILHq3io3chlFZlURTgZCOQrcOlmpGc/LoeVvNJ6imvXkpw697xipRSTd3wX2/P7Tj1mTE3nxaYNXH/gL6S7fV169PXxfTT02ISD14ZtfOv84qgW/HlcDkb7DzM2eIwkXTKl9RvIL18+a1HfXF4amOKE1c1/RqHBhSSiQgiR4ExOD7/oMnPTstyIVcKeyWEzMdKzH6Ohl9SMHKpWXUR24TsLXILVPungLydt3L05uslAKP1ucIrBKT6wtO0AACAASURBVDff2RKdble+rlUnMHS3YJ+aJLuokurVl5KaGeTRWbeHrL+7nuxPfRgtJZnJb/yAvX1OAN53+K+nFtPXV4cj/Ih5qM1IRaaeyyqic0F+r8fN+Ik2RvsOo5SHosqVFFatRKdfXLGe8hf8bS2NToMLSUSFECLBPd5pwqPgxobIXwoosMBFn5JO+fLzyVsyc4HLQuxuM1KeoefyysTozqOUYtcxI+eXpNOUH/lkwGoa8Re4GMjMK6Fu3RVk5C6sGlxL1pO8rA4Az/Ao4y+9wjPvv40r2t6isKIYd1cfAPq6+K2YH7C4+O3gFF9cV4guKbI7QEp5mTzZxUjvAdxOG/llDRTXrAmqqG8urw7b6DA6+XyUGlxIIiqEEAlsuhL22rrsiBa/eNwuxvoPMzZ4FE3TUVK3joLyxlkLXBZi0OLipYEpPr828slAuPx12E670ckDF0U2GXBMGRnuacE8OkBaZh7Vqy8hq6D8rI8ym3/yGC/WNTOVksp1B1+l4Mn/xvqLF7H876NxfUR0T7uRvBQd76uNXMGfUgrzWD+G7lYcVhO5JTUU164lNT00O5a7jhlZlZ/Khig1uJBEVAghEtgzPRZMLi+3LI/M0dDpApeRvkN4gyxwWaiHO4zkJCdxdQSTgXDb1TbJyvxUziuOTDLg61p1AONwl6/ApWkbuSV1IZnm4DVZMD78S35x1SfYcfwg1euXk7KmieSVDbgOtcftpZvG7G6e7bHwyRV5pOoiM8VlanIYQ3cLVtMoWflLqGi6gPTswpCt/+CYnbdG7dwXxQYXkogKIUSCcnsVe/yVsOWZ4S1+mS5wMfTsx+2wkrdkKcU1a+YtcFmocbuHX3Zb+HhTLmn62LvY+2IcGXfwxoid72yJQDKgFMNdbzE2eMzXteosClxmY3noKfaV1DGSmcP1B/5C9gNfA0DT6yn40d0kZcfnDsRjnSb0SXDD0vAX/Nkt4wx3t2IZP0F6dgE1ay4jK78s5NvZ3WakJiuZi6PY4EISUSGESFAv9U8xZHXzX2GshPUVuAwy3N2CY8pITlEVJc2XkpoRnssP/azThE6DD0Zhvmu47GqbpDormUsqwpcMeD1uxgeP4bSbGT/RTlHVKgorV87ZtWoxlN2B6Sc/48mLPsjm/g6WV+aTeuGmU8/rCvNDur1ImXJ5eeK4mevrc8hJCd8UF6fdwkjPfiYN3aSkZVO5Yjs5xTVh2UHpNjnZdyL6DS4kERVCiASklGJ3u5FtS8JXCWs1jjDc/RZW4wiZeSWUr7+CjJzwtTu0urw8ftzEdfXZYU0GIqnX7OIPg1a+sqEwLMmAUl4mho4z2ncAt9NOki6ZZZuvOesCl9lMPflrXksvpDevmNtefo7sb/xDQlzV4OddJuxuLx8O0w6Q22lnpM/ftUqfQlnDZvKXNKAlhe+o/552I8VpOq6McoMLSUSFECIB/eWkjU6jky+GoRLWPjWJobsV89gAaVn5VDdfQlb+2Re4zOcX3WZsbm/EO7+E0552I4VpOt5TE9rTvUopzKP9DHe34LSZyS2ppaR2LfqUe8KWhCqPB8sDD/PkmstZYRhgbYYi/aodYdlWJDk9ikc6TLynJouSjNCmTb6uVUcZGziCpmkU1zRTWNFEki68U2kMVjfP91q4rbmAlCg3uJBEVAghEtDuNiOrC1JZH8JK2MACl+TUDCqaLiC3pDYiR7xcHsXeDiPvrg59MhAtIzY3v+q18I+r8kKaDExNnmS4q8XftaqMypUXkr7ArlWLYXt+H/utGkdKq/j6S4+RddstaLr4P3L9fN//Y++846Sqz/3/nj67O7uzvXd2qUsRBEEUEREUFXtHNKZcc0013l8s0XhNjEGTXOONJDcxCc0KCvaooCgqkbZ02N7b7M7u9H7m/P5YFkHKtpmdM+t5v168XszMmXOeOTP7nM/5fp/n+3Fg9ggsH5cYsn0GgwI9bVV0NRxAEPwkZ48jNb8MdQib+s7GC1VWYtRKrouwwQXIQlRGRkZm1LH/WCfs70LUCRvwe+lqPEh3a0Vvg8uYGSRllYa0waU/3mt0YHILLJeA9WWoeKnKhk6l4Pri0Ez39ja4lOPobiMmPoWCKQsxJI3MclCiKGL/0xrWT5lLgaWT2W4zcTdcPiLHDidBUWRNhZWLc2IpiB/+KKUoitg66zHV78PvcWLMKCK9YCoa/cith2vzCWyss3NLSULEDC5ORBaiMjIyMqOM1RVWCuM1zBtmJ2xQCGBuOYq56RCiKJKaV0ZK7oSQN7j0G8cx55eLsmMpShiae4zUsPsENtTauGlMAnHDFAM+tx1T/T6spnq0MfHkTbyQ+NT8Ea3N9G7bSVVzNztmjeW+T98g4bs3o9CP/ML8oWZri4tGh59fzRpe7bMoijh6WjHV7cXj6CE+JZe8SfPRx4VulHWgrK+xEwjCLSXSuKmThaiMjIzMKKLW5uOTYXbCisEgPe01dDbsRwh4ScoqJS2/LGy1hf3xaauLBoefx2amRuT44WBDba8YuLV06KOhx12r2qtRqXVklZ5HUuaYsDa4nAn7n9awYcpc0pw25ptqMSz//YjHEGpEUWRVhZVz0/RMSh66qHbbuuioK8dp6SDWmEbRtEXEGiNj49pncLG00DCiBhdnQxaiMjIyMqOItRVW0mNUXD6ETlhRFLF1NWKq24vPY8eYXkR6wRS0MZGrI+sTA9NT9UxOiYzzS6jxCkFeqrJxZYGBFP3gL8O9DS6HMTcfQaFQkF4wheSc8SFxrRoKvv1HadxbxdabLufbOz4k8farUSZE51qhJ7Kr08PhHi//e0HGkN7vddkw1ZVj62pCF2ckv2w+huSciK4i8Ga9A6tP4I6x0hgNBVmIysjIyIwaOlwB3m108MPJyWgG2fzi6GnHVNfX4JJN3sQL0Y9Ag0t/lHd5ONjt5Y9zhyYGpMjb9Q4sPoE7BlnvekqDS8540kLsWjUU7M+tZWPZHOJ8Xi6rPUD82l9ENJ5QsbrCylijltkZg5sJ8HtddDbsx9Je0+taNW4OxoziiC9jJQRF1lVaWZgTR45hZMtrzoYsRGVkZGRGCS9UWYkdZCes29GNqbYcR09vg0vh1EuJS5SO6FtVYaXEqOX8zMiUBYQaISiyptLKJTlx5A1QDPS5VnXW78PvdWHMKCa9YMqINricCX9tI+0fbueDm3/MdQe2k3rtQlQZ0V9CUdHj5d8dbn5zXtqABaQQ8NHVdIju5qMoVKqwuFYNh83NTlpdAX4XRoOLoSALURkZGZlRgM0nsLHWzq2lA+uE7W1w2YvV1IAuNoG8ifOIT82L+KjNiVRavHzR7uZXMwcuBqTOlhYnLc4AK2b3LwZ6XataMdWX43FYehtcyi6OSIPLmXD85UXenjATUaHgqsM7MDy7KtIhhYTVFVayY9VcktO/2A8KAbpbK+hqOoQYFEjJnUBK3kRUauk01onHGv7mZITP4GKoyEJURkZGZhTwarUNQey/E/Z4g0tbFWqtnuyx55GYOQaFIvLLuHydNcfEwKK8yI/8hYI+MXBeegzjk84uBly2Tkx15TgtJmKN6RRNW0ysMXyuVUNB6Oii6/UPePO6H7C4Yg+ZC2ejKc6PdFjDptnhZ3OLk/83LQWV8sw3QKIYxNJeS2fDfgI+N0lZJaTmT0aji5xv+5nY3uGm0urj/8JgcDFcZCEqIyMjE+X0dcJeXXTmTlgh4MfcdAhzy1EUCiXphdNIzhkXsQaX/mh1+vmg2cn9U88uBqKJLzs8VFh8rLzwzGLA67Riqt+LrasJfVyiJBpczoTj+Vd4v2gyTq2Oaw9sJ379M5EOKSSsrbSSqFVxVeHpG65EUcRubsJUtw+vy0pCWgHphVPRxYbH/jMUrDpqZVKSjukhNLgIFdLMQDIyMjIyA+bNegc2f/C0nbDBoEBPayVdjQcRBD8pOeNJlUCDS3+sq7SRoFGy9AxiIBpZXWFhYpKOmemnigG/10Vn/T4sHbW9DS7jz8eYXiRJAQoQtDmwrN3ExiXfZn7NAfKnlaKdOiHSYQ2bbo/AW/UOvjMhEZ3q1FkCp6UDU105LlsXcUmZ5Iw/n5j4lAhEOnAOHDO4eGp2aAwuQo305mJkohKfz8eDDz6IWq2mvr4+0uHIyHxjCARF1lZauTQ3juy4r5pfRFHE0lFL9c436ajdQ3xKLqWzriGjeLrkRWi3R2DTMecXvXp0XKYOd3vZ2enhznHGk8SA4PfSUbuHqh2bsHY28vHOKqZcdAsWt1KSoqEPx5rX2ZpeRGdcAtfv/4L4e++IdEgh4aVqK2ol3DDm5IY/j6OHhgMfUb/vQ4LBIAVTLqFwykLJi1DorXctMGiYnyO9kgGQR0RlQkB9fT233norY8eORRCESIcjI/ON4sMmJ22uAL8/1gnb2+DS0uvg4rSQkJpHetkCdHHSWTewP16ptqFSwE0l0p3qHCyrKizkGzRcfEwMBIUA3S3HGlzEIIrYTO756aMUFo3B6/VFONqzI3q82P72Chvm3cSspirG5iahmzcr0mENG6c/yPoaO9cXJ5Cg7S1x8XkcvSPVpjq0+nhyJ1xAQlqBpG8STqTO5mNrq4tHhmFwEW5kISozbBwOB2vXrqW5uZk1a9ZEOhwZmW8MoiiyutLK+Zm9nbAuaycddeW4rCbiEtMpOmcxsQnSanDpD5c/yKs1Nq4tjj8uBqKdBrufj1tcPDQ9BQUiPW3VxxpcPL2uVQWTOVpZw9//sSoq8qhzw3v8OyaFhsQ07v38HeIf+17UCLOz8VqtDU8gyK0lCQR8HroaD9LdVolKrSWrZBZJmSURca0aDmsrraTph2ZwMVLIQlRm2JSVlQHQ3Nwc4UhkZL5ZfNHuptrq4/7xMTQe3Ird3IzekEj+5IsxJGVHpTjYWGfHFQhye2n0jOD2x9pKK8k6JfPieqjZtRWvy4YxvYC0wqnoYnpHfaMlj4qCgOPP69gw5VImmJqZog8Sc8XFkQ5r2PgEkRerbFyWF4ui8zBVTYcBSCuYTErOeJQq6SwAP1BMrgDvNji4tywZ7SANLkYSWYjKRJyBJN52uzzlLyPzdV490s5dhmpi6kx4dXGSb3DpD78g8kKVlSX5BjJiR8flqdMdYH9DE/cnN9F+1IYhKYuc8XNDXls4UgLW/e5W9rkUHM7I49EPXybh3ttRqKJ/5PqdBhsddicXGsrpbHSSnD2W1Pwy1BrpdZkPlBerbMSolVxXHDmL3oEQsb/0DOwIrh7c6sjeZQguv2RikVo8g41FIXgoyEkj4LHhtpsHfJwLZk/vf6PUXNQEJXFePM4AQSGAx2nBrY78xVJK8UgtFpKk4xAUDubYPqHAGEPmmHNJyiqVjIPLUHmv0YHJLbB8kNaXUsXj6Gb7zn9zi6qdAkMm2WMWYkgKzzqOeXl5A9puwoShd7aLooj9ubWsnzKXAksns91m4m5cMuT9SQFRFOlqr+G57V1M07gZn5lGWuElaPXSncoeCDafwOt1Nm4pSSBuAAYXkSRiV4pvqXfiqdBQe5rlEUYSjxDkW2q/JGKRWjyDjUXntvP4fbdhb9pJbcf+AR/n8ftu63cblUbHz59ai6fig4iflyavDq+riKbDe9HovBGNRWrxSC2Wabk3RjSGcFOlKeL6C85Ho5GOg8tQCYq91pcXZcdSlBDdn6fXtWofPR11dNrUqLNmUTpjUtSOVPfh3baTqiYzO2aO5b5P3yDhOzej0Et7BYavEwgKHOlqZ1dLPQ2t1aQ7TbT6k2kLzGDFvGJy8qRlfzlUNtTYCQT7N7iQAhETov8MzOSpcekUJ0R2dKvW5uef202SiEVq8Qw2lh07dvLoH37J5s2bycnJGfBx4nL6HxFt2LoXi/9l9OMWRfy8+K0BdD028ibOo9gY+RFRKcUjtVhGO1MnzhgVIhTg01YX9XY/j54bvT7lx12r2qtRqXVUxk3mn90JvDElP+witKmpaUDbLVq0aMjHsD+3lg1T5pLmtDG/owbD8t8NeV8jgRAMUtndwa7WBna19f4rb28iS6XgptREJsToaA6IHEg4nwuMicwYJSLUKwR5qdrG0sIzG1xIiYhdKTqIRxWbREx8ZO+mVAEvHbglEYvU4hlsLKJKT0NLJ2p9wqDqnwoHsG37H98kIIgoVXHExEe23kUf8KJUudDHJUb8O5JaPFKLZbQj5U7YwSCKIqsqrExP1TMlJfpq8oSAH3PzEczNh1EoFKQVTMaQOY4fvt/OkoJYUvThv9Tm5uaGdf++/UdpLK/kk5sWc/eOzSQuuwalUTq1h0ExSE1PJ7taG4+Lzj3tjTh8X+WBDI2ab6camWmIpcXnZ53Vw38s+A9e3+fngVFSDgK9BhdWn3BagwspEvnhHBmZfhB9frw79gHgLT8El8+OcEQyMtJAI+FO2MFQ3uXhYLeXP86NrpreYFCgp62KroYDCIKf5OxxxxpcdLxWY8PiE7hjlAgc+3Nr2Vg2h1ifj8tqDxC/9heRDuk4jdZuLnvpWY50tZ/29USVimuSE7jIaKAnIPC3jm7q0fDxHffxzKEgY40KZmfEjHDU4UEIiqytsLIwJ44cQ+RneQeCLERlho3P52PRokVYLBYAbrnlFvLy8li/fn1I9u/dvgfR5e79/xd7ZCEqIzPKWFVhpcSo5fzM6BADoihiNdXTWb8Xv9eFMaOY9IIpaPRxQK8YWFNp5ZKcOPIGKAbCnUeHg7+2kfYPt/PBzT/mugPbSb12IaoM6ZRQ5BuT+XT5/Xz3nbVsqth3/PlYpYIrkhJYlBiPXxR5pcvCZqudTEMSH9/xUwSFkX93tPKb89Kivn63j83NTlpdAZ6eEz1lBrIQlRk2Wq2WrVu3hm3/ng8/O/5/7xd7EEVx1CQNGZlvOpUWL1+0u/nVTOmLAVEUcfS09rpWOXqIT8klr+xi9HGJJ223pcVJizPAitkDFwPhzqPDwfGXF3l7wkxEhYKrDu/A8MdVkQ7pFFJjDay66i4W2p5hX3sjlxoNXJmcgEah4F8WO+/22HAHRfISkvh42X2MSU7joX+byI5Vc0lOXKTDDwmiKLK6wsqcjBjGJUW+bGygyEJURtKIooh78+fHHwdNXfgPV6OdVBrBqGRkZELFmgorWbFqFuVJWwy4bF2Y6vbgtJiINaZRNG0xscZTXav6xMCsdD3jo0gMnAmho4uu1z/gzet+wOKKPWQunI1mTH6kwzoJT8DPyl2f8NvP32O8Bp4qyCJRrWKr1cGmbitWIQhAXkISW++4j+KkNJodfja3OPmvaSmolNK+ARoo2zvcVFp9/GVqeJYICxeyEJWRNIHKOoTGVkj56g/L8+E2WYjKyIwCWp1+Pmh2cv9U6YoBr8uKqW4vtq4mdHFG8svmY0jOOePo7Q6ThwqLj5UXRpcYOBOO51/hg6IynFod1x7YTvz6ZyId0nGEYJB1B77k0U/eIlVwc1+akWythi8dLl4zW+nwf7VyRn5CMh/f8VOKk3pvHtZWWjFqVSwtHB0NfwCrK6xMStIxIy26Gv5kISojadwffHbqcx9+RsJP7o5ANDIyMqFkXaWNBI1SkmLA73XR2bAfS3sNal3sgF2rVh21MCFJy8z06BIDpyNoc2BZu4mNl9/N/JoD5E8rRTt16AvihwpRFHm76gAPfbwJv8PM8hQjpfpUDrk8/LWjm9SULBQ6P/htQK8I3XrHfRQl9da1dnsE3qp38J0JiegksH54KDho9rC708NTs9MlX+LydWQhKiNpPB9uO+U5f/lhhE4zqrTQWuTJyMiMHN0egU11du4eb0Svlo4YEPxeupoOYW45ilKlIaN4OknZYwfkWnW428vOTg8rolAMnA7Hmtf5JL0Ik8HI9fu/IH7lw5EOic+bqvn5lo00mBq5McXItJx06r0+nmox4Y9J5Kkr7+T68dOZ9Y/f0u6wUWBM5uNlX4lQgJerraiVcMMY6Sw/NVxWV1gpMGiYnxMb6VAGjSxEZSSLYO7Bt/vgaV/zbP6CuFuvGuGIZGRkQsUr1TZUCripJCHSoQAQFAJ0t1bQ1XgIURRIzZ1ISt5EVOqBGwasqrCQb9BwcRSKga8jerzYnn+V9RfeyKymKsbmJKKbNyti8RzqbOWhjzfxRe0hrksx8t38TDr9AVa2m2lCwy8vvoFvTT0fzTHfe51KTYGxdyS0MPErEer0B3m1xs51RQkkaKW/2PtAqLf52Nrq4hczUlFG4Q2QLERlJItnyxcgiqd9zf3hZ7IQlZGJUlz+IOtrbFxbHB9xMSCKQSztNXQ2HCDgc5OUVUpawWTU2sEtJdVo9/Nxi4uHpqdEpRj4Os4N7/GlLomGxDTu/fwd4h/7XkRGeRut3fzyk7fYeGgHVyTFs6IgC2cwyJrOHso9Av91/mJ+PGsBsV9zGBufmsm6a751kggFeL3WjicQ5LZSadwAhYI1lVZS9aqoNbiQhaiMZPGc0C3/dbyffIno8Uadz7GMjAxsrLPjDAS5vTRyi72Looi9qwlT/V68LhvG9ALSCqeiixmaQFlTaSVZr+KKguif7hUFAcef17F+6qVMMDUzRR8k5oqLRzQGs8vBbz7/F8/v/oSLE2J4qiALgDe6bWy1u/neufN59fzFpMSeXnytvPxWtKqTJY5PEHmhysqSAgPpsaND/phcAd5tcHBvWTLaKDW4GB3fhMyoQ/T58Wz995lfd3vwbt+D/uI5IxiVjIzMcPH3iYF8AxkREgNOSwcddeW4bV0YkjLJGT93ULbEX6fTHeCdBgffn5QYtWLgRNzvbmWfS8HhjDwe/fBlEu69HYVqZEaunT4vz+zYwu+3f8AMvZpf56URp1Syxerg7R47N5Sdx8F5V5JnTD7rfr4uQgHea3Rg9ggsjxLry4HwYpUNvVrJdcXRewMkC1EZSeLdvgfR4TrrNu4PPpOFqIxMlPFeowOTW2B5BKwvPY5uOur24uhuJSY+hYIpl2BIyhr2fl+qsqFVKriuOPqne0VRxP7cWtZPmUuBpZPZbjNxNy4J+3H9gsDf937O49vepoAAD2UmkaZR87ndyetmKxcUl7H9+quZmJY9pP0Hj63vOj87lsKEgdf9ShmbT+D1Ohu3lCQQp5FOw99gkYWojCTxfPgZypQk4v9zGYHmNnizdxknVW4mKf/zX9h+/zyeDz9D/M39o6I7VUbmm0BQ7LW+nJcVS9EIigGfx4Gpfh9WUx1afTy5Ey8kITU/JLnD7hPYUGvjxjEJGKJYDPTh/WwXVU1mdswcy32fvkHCd24KawmUKIqsP7KbX2x9E73HxvdTjBTotOx1uvljWxdFGQW8efu3OT9vzLCOs7XFRaPDz+MzpWNNOlw21NgJBOGWkuge4ZWFqIwk0Z43jYSH/hNlbAzWJ5776gWFgpiFc9Ffcj6eLV8Q7LGhSo7uP0IZmW8K29pc1Nv9PHruyIiBgM9NZ+NBetqqUKm1ZJXMIimzBIUydILxtdpeMXCrRLr/h4v9T2t4bcpc0pw25nfUYFj+u7Ada0vdUR74aCPm7jZuSjUyMTmNKo+XXzd3oItP5S/Xfo8lJWXDvmEQRZFVFVZmpOkpS4n+9V0BvEKQl6ptLC00kKyP7u5/WYjKSJLYqy456+uKY4JURkYmOhBFkVVHrZyTqmdKmMWAEPBjbj6CufkwCoWCtILJpOSMR6nShPQ4PkHkxSobVxYYSI2J/supb/9RmvZUsPXmxdy9YzOJt1+N0hj62sM9bY088NFG9jdXcWOKkZl5GbT4/DzT1km3OpbHF93G7WWzUIXohmF3p4fDPV6evSAjJPuTAm/WO7D6BO4Ic72rKIphn3WM/r8cGRkZGRnJU97l4UC3lz/ODZ8YCAYFetqq6Go4gCD4Sc4eR2p+GWpNeKaW326wY/EJ3BGBetdwYH9uLRsnzyHW5+Oy2gPErwntAvbV3SZ+sfVN3q8o55rkBG4ryKInIPC8qZsjfnj4gqv4/ox56NShvWFYVWFlrFHLnIzBLcklVYSgyNoKKwtz4sgxhPZcnYjLaqKjrpyiaYvDdgyQhaiMjIyMzAiwqsJKiVHL+ZmhFwOiKGLrrMdUtxe/14Uxo4j0gqlo9HEhP1YfQVFkTYWVBTlx5IVRDIwU/tpGOjb/m/dv+hHXHdhO6jWXoMpMC8m+2x1WfrXtXdbt+4xFRgNPF2bhF0Ve6bKw3enjR+ddwttzLiVBF/rfRkWPl393uHliVtqo6SfY3Oyk1RXg6TnpYdm/x2nBVLcXu7kZvSEpLMc4EVmIysjIyMiElSqLjy/a3fxqZmjFgCiKOHpaMdXtxePoIT4ll7yyi9HHJYbsGGdiS7OTZmeAJ2eHRwyMNI6/vMhb489FVCi46vAODH9cNex92rxunt7+Ic9+uZm5cTp+m5+JRqHgXxY7H1od3DHtAlZdcAUZhvDV166usJIdq2ZhbvhuSkYS8Vj3/5yMGMYlhXak3+9xYmrYh7WjDo0+jtwJF5CQVhDSY5wOWYjKyMjIyISV1RUWsmLVLMoLnRhw2bow1ZXjtHQQa0yjaNoiYo0jIwr7ml9mpeuZEGIxEAmEji66Xv+AN6/7AYsr9pB5yXloxuQPeX/egJ+Vuz/hyc/eY7wG/jsnlUS1ik+sDjZ127hs3DnsvnkpJcnh/b6aHX42tzj5r2kpqJSjYzR0e4ebSquPv0zNDNk+A34vXY0H6W6tQKXWkjnmXBKzSlAqR6YJShaiMjIyMjJho9Xp54NmJ/dPDY0Y8LqsmOr2YutqQhdnJL9sPobknBGddt1h8lBh8bHywtCJgUjieP4VPigqw6nVcc2BfxP/6h+GtB8hGGTdgS959JO3SBHc3JdmJFurYYfDxQazlal5Y9my9PtMzxq6yB0M6yqtGLUqlhZGp/Xl6VhdYWVSko4ZacNv+AsKfswtRzE3HUYURdLyy0jOmYAqxDW6/SELURkZGRmZsLGu0kaCRjlsMeD3uuhs2I+lvQa1raa9vwAAIABJREFULpaccXMwZhRHpO5v1VELE5K0zEyP/qWAgjYHlrWb2Hj53cyvOUDBtBK00yYOah+iKPJO9QEe/GgTPruZ5alGSvWpHHZ7+GtTNynJWbx40x0sKBofpk9xKt0egTfrHXxnQiI6VfSv7wpw0Oxhd6eHp2anD+t3LwaD9LRX09mwHyHgIymrlLT8MtTayDRzyUJURkZGRiYs9HgF3qi3c9c4I3r10MSA4PfS1XQIc8tRlCoNGcXTScoeO2LThl/ncLeXnZ0efjtMMSAVnGs38kl6ESaDkev3f0H8c4PrlP+iqYaff7SR+o4GbkwxMi03nQavj6dbO/HqE1hxxZ3cMGH6iJ+rl6utqJVww5jotb78OqsrrOQbNMzPiR3S+3ub+how1e/D57GTmF5EWuFUtPrIjhjLQlRGRkZGJiy8Um1DCdw0ZvDNKEEhQHdrBV1NhxCDAqm5E0nJm4hKHVl7xtUVVvIMahYMUQxICdHjxfq3V1h/4Y3MaqpibE4iuotmDei9hzpbeejjTXxRe4jrUox8Jz+TTn+Ale1mmtDw6EXXcfe0uWhGyKP+RJz+IK/W2LmuKIEEbXQv9t5Hvc3H1lYXv5iRinIIot7R04apbi9uuxlDcjZ5E+eNSEf8QJCFqIyMjIxMyHH5g7xabePa4niMuoGLAVEMYmmvpbNhPwGfm6SsElLzJ6PRRV74Ndr9fNTi5MHpKUMSA1LD+dp7fKlLoiExjXs/f4f4X36335HLJms3v/z0bV47+CVXJsWzoiALZzDI2s4e9ngC3D9nMT+etYA4beSauF6vteMJBLmtdHS4XQGsqbSSqldxef7gRi/ddjOmunIcPe3EJKRSOPVS4hKltbC/LERlZGRkZELOpjo7zkCQ20sHtti7KIrYzU2Y6vbiddkwpheQVjgVXYx0xMTaSivJehVXFkT/dK8oCDhWrmPD1EuZYGpmij5IzBUXn3F7s8vBk1/8i7/t+oSLE2J4uiALgDe6bWy1u/nuuRfxyvmXkRIb2WlenyDyQpWVJQUG0mNHh8QxuQK82+Dg3rJktKqB3QB53TY66/dhNTWgi00gb9I84lPyJFlOMjq+JRkZGRkZyeAXRNZVWbk830DGAMSA09KBqa4cl62LuKRMcsbPJSY+ZQQiHThd7gBvNzi4Z2LigMWAlHG/9wn7XQoOZeTx6Icvk/Cft6FQn/pdOX1e/rjjI57e/j4z9Gp+nZdGnFLJFquDd3rsXFd2HgfmXUm+MTkCn+JU3mt0YPYILA+z9eVI8mKVDb1ayXXF/d8ABXxuOhv209NWjVobQ/bY2SRmFqNQSLdhSxaiMjIyMjIh5V9NDkxugeX9WF96HD101JXj6G4lJj6ZgimXYEjKGqEoB8eLVTa0SgXXD6HeVWqIooj9T2tYP2UuBZZOZru6iLtxyUnb+AWBf+z9nMe3vUMefh7OTCJNo+Zzu5ONZivnF0/i8+uvYVJadoQ+xakEjy32Pj87lsKEyNYShwqbT+D1Ohu3lCQQpzmzmBQCPsxNhzG3HEGhUJFeNI3k7HEoVdKXedKPUEZGRkYmaugTA/OyYik+gxjweRx01u/DYqpDq48/7uAixWlDALtPYEOtjRvHJGA4ixiIFryf7aKqycyXM8dy36dvkPDdm1HE9C5FJYoiG47s4eGtb6Dz2LgnxUiBLoG9Tjd/bOuiMKOATbffzdy8kgh/ilPZ2uKi0eHn8ZmpkQ4lZGyosRMIwi0lp7+pCwYFelor6Ww8SFDwk5IzntS8Sag00WO0IAtRGRkZGZmQsa3NRb3dz6PnnioGAj4PnY0H6GmrQqXWklUyi6TMEhRKaYu712p7xcCtJdE/Ggpgf24tr02ZS6rTzvyOGgzLfwfAlrqjPPDRRszdbdyUamRichpVHi9PNJvQxqfw52u/yxUlkyV5w9DndjUjTU9ZSvSv7wrgFYK8VG1jaaGBZP3JDX+iKGLtqMXUsJ+A10Vi5hjSCqZIoqlvsMhCVCYkbNy4kSeeeIKYmBiUSiUrV65k0qRJkQ7rtOzvaKbDaeOigrFoo2DaQkYmWhBFkVVHrZyTqmfKCWJACPgxNx/B3HwYhUJBWsFkUnLGo1SNrIPLUPAJIi9W2biywEBqTHjzxUjkUdHro2n3UbbevIi7d2wm8far2efu4YF3/sm+pkpuSDEyKy+DFp+fZ9q6MKti+NWiW7m9bBYqCd8w7O70cLjHy7MXSKsjfDi8We/A6hO444R6V1EUcXS30FFXjtdpJSE1j/TJC9DFRm9NrHwVlhk2O3bsYPny5ezatYtx48axZs0aFi9ezJEjR4iPl153aYExhYvW/gEhGGTxmIlcWTKZJSVlpMVJL1YZmWiivMvDgW4vz8ztFQPBoICl7ZiDi+AnOXscqfllqKNo2vDtBjs9XoFlYW5+Gak8Guy2sPHiOcT6fCyu2c/PbynilX/+lmuTjdxakIUlIPC8qZsjfnjogiv4/oyL0I+w5eNQWF1hZaxRy5yMyLgDhRohKLK2wsrCnDhyDL3n32XtpKNuDy5rJ3GJGWSfM4fYhOgvQ5Du7Y1M1LBixQqWLFnCuHHjAFi2bBmBQIDVq1dHOLLTY9THcN95l2D3edhwZA93vbWajP/5f8xd9RS//fxfHDS1IIpipMOUkYk6VldYGZOg4fwMPVZTHTW73qKtZieG5BxKZi4lc8yMqBKhQVFkTYWVS3LjyI8PrxgbiTwaqGsi4HTz/rjpXHV4B++MNdDtbeV3hdnMio/l1S4Lj7V2cdGUi6i+99f89LyFUSFCK3q8bO9wc+c4oyTLBobClhYnra4Ad44z4nFaaDy4lbq97xMUAuRPvpiCKQtHhQgFeURUJgRs2bKFX/ziF8cfK5VKZsyYwebNm/nBD34Q0mP5AgLl7Y3D3s+FeSVoVWp8QgAAEZEvmmv5ormWBz/eRFFiKleWTuaq0snyFL6MzACosvj4vN3FbyYGqSt/D4+jh/iUXPImzUcflxjp8IbElmYnzc4AT85OD/+xRiCPmp9bg0MXQ5JCwSUxrRy8agaLNSret9j5wOpg2dQL+MeFS8g0RNc07+oKK9mxahbmxkU6lJDQV+IyK0WNwbSb2o46NLpYcifMJSGtcNSI7T7kq6vMsDCbzVitVjIzM096PjMzk507dw5oH83NzWffwG4//t9Wh4WFz/9m0HEOljpLF/+782P+d+fHxGv1J03hw+hYFkRGJpRsPFTPt3WHyO50ojSmUTRtEbHG8Au4cCEe6/6fla5nQlJ4R3FHJI863Tje+gh7TCzzUnpwFhTyqdvDphYbi8edw+6bl1KSHH3fV7PDz+YWJ/81LQWVcnQItM9abBwy9fBwWhUOc4CMMTNIyipFqRwddqVfJ2JCNAM7gqsHd4SH/QWXXzKxSC2egcRi626nICcNg16J224+/nx6soFEg/ak587EBbOnn/X1GRoDmemlCEolm8/JokAXHNwHGTYCO2sPsLP2AL/6UMWVE+cTCEzE47TgPs0C0CONxxkgKAQkEY/UYiFp9DQuSBWvy0Zt5W6KO2tJSUyioGw+huScqB+12WHycNTiY+WFmf1vPExcLhcAOt3Jglen0x1/rT/y8vLO+vo5k4opu/17CH+uZUlTOb/S2FBNm8rmpfcwI6tgaIFLgHWVVoxaFUsLI+voFAqCgh9zy1H+tN1KoVLBRaVjSM2bgEoC2iScKEa6Fk6hUOQCTSWlRQS8noj79Yoi+IIiWqWCSOdNURTxen2gUqNVK6Pj3Ijg8XrQaDSoVF/drfn9foLB4CmJ9XR4PJ5+twmgxNRlJT0jGbVipIUoqBS934dKqcQvKujwa8nQ+NAoIltLKooiTq+fHkUcGRo/2ghXfUvl3PSdF1NHF0CeKIr9DBdFF315FKC0tBR1BES/KIoIfg9CwIdfVOAIasgwxEQ8jwYCAaqqqoDhnZt2V4CgCNlx4T+3giBQWVlJdnY2RuNX0+JtbW243W6Ki4v73ceRI0dO+7xWoybBEItGq6ZLjMXf1UZMWhJp8QnERVG97ukQRGhy+EnUqkjUDT35heo3MxyEgA/B78EbVNAZ0JIRqyZOE9kR0BPPC2HMoxEbsvDf/mtWXzOZWcWRdWWotfn5f9tNPDUnneKEyN51dHR0MP+GZXDt/ayKonMza9Ys7rnn+9x997eOP3fPPfegVqv505/+1O9xOjo6zvp6Z2cn19zzMxA6eOLll5meO/z6JbvXy3feWYc/GDjt67nxSVxcMJaLC8dxbnYBmhOmRCqsAe7+3MY/5iYwzhjZUb+Ojg7mXr8cxdUPs+r6cZxfHNkRQKmcm77zQq8QHdV89NFH5ObmjtjxhICPrqZDdDcfRaFSEZs1iWV7Y7hjXBLfnZg0YnGciebm5uOjg0M9N4e7vSz/qJXfzk4fsbrDxMREfvrTn3L//fcff+6KK65Ao9GwadOmft//9an5gMeOq6san6MTlS6eLY4sfvpJG/zuNip3lY/obyZcrDzYzcvVNt5ekkeCduiiLRS/maEgiiK2zgZM9fvweewY04v4gymfepeCDYtzIj4YdeJ5CScRu1I0uDWI2oSI+wmrAl46cKOKTSImPrJ3h2qrm4Z2C0TZuSmdMJVt23dx7497E6goinzw0Wc8/PDDA/oMhf1so9Y309rRDaJISWou04uGP430q23vUO12H3+sVCiYk1PMVWOncGXpZCamZp1xalEf8KJUudDHJUriN9Pa0Q2+ACptXMR/M1I5N8fPi0zICAoBulsr6Go6hBgUSMmdQEreRP5W4UTEyk2jwPqyj9UVVvIMahbkjNzi4AsWLGDXrl3HH4uiyJ49e3j44YcH9P4+8dTnWuU01aHVG8iZsgBDaj4PvVkDNe+AcPqb72jD6Q/yao2d64oShiVCI4Wjpw1T3V7cdjOG5GzyJl5Ie9DAtoMt/GJGasRF6EgS+QI3majngQceYOHChVRWVjJ27FheeOEFVCoVd955Z6RDOy1Wj5s/fLmFeK2ey8ZM5MrSKSwpKSM1NvprjGRkQo0oBrF01NJZv5+Az01SVgmp+ZPR6GJx+YO8Wm3j2uJ4jLroEwOno9Hu56MWJw9OTxlRMTDcPBrwe+hqPEh3a2Wva9WYmSRmlaBUqtjW6qLBFYR/vxHmTzFyvF5rxxMIcltpdN0Aue1mTHXlOHraiUlIpXDqpcQl9s5krdnVSapexeX536xrkSxEZYbNrFmzWL16NbfddttxR5D3339fkovZAzRYzay/7rvMKyiVl2WSkTkDoihiNzdjqtuL12UlIa2A9MKp6GK/uvBvqrPjDAS5vTS6lvs5G2srrSTpVFxZMLL5a6h5NCj4MTcfxdx8GFEUScsvIznn5AaX1RUWJiQoOdB8+jrSaMMniLxQZWVJgYH02OjI4V63jc76fVhNDehiE8ibNI/4lLzjM28mV4B3Gxz8Z1kSWtU3ZzQUZCEqEyKuvfZarr322kiHMSCmZER/bZSMTDhxWjow1ZXjsnURl5RJzvjzTyn78Asi66qsXJ5vICNKxEB/dLkDvN3g4J6JiRERA4PJo2IwSE97FZ0NBxACPpKzx5KaV4Zae7LP+r4uD3vNXh4o1fBqOIKOAO81OjB7Tra+lCoBn5vOhgP0tFWh1saQPfY8EjPHoFCc3Fz1UrUNvVrJ9cXRNcIbCkZH9pCRkZGRGTYeRw8ddeU4ulvRG5IpmHIJhqSs0277ryYHJrfA8nHSFwMD5cUqG1qlguslXO/6VYPLXnweB4npRaQVTkWrP/107uoKK8UJGmYljw63uD63q4uyYylKkO6azkLAj7npEOaWIygUKtKLppGcPQ7laWbhbD6B12pt3FySQJzmm2d4KQtRGRkZmW84fQ0uFlMdWn08uRMuICGt4IwNe31iYF5WLMUSFgODweEP8lqtnRvGxGOQqBhw9LTRUVuOx9FNfEoOeRMvQm8480oFtTYfn7a5eOzcVJQK6whGGj62trhocPh5bKY07S2DQYGe1ko6Gw8SFPyk5IwnNW8SqrMslbWhxk4gCLeWjJ6busEgC1EZGRmZbygB37EGl7ZjDS4ls0jKLEGhPLsQ29bmos7u55FzpSkGhsKGGhu+oMitJdIbDXXbzXTUlePsaSc2IZXCaZcSZ+x/qbbVR62kx6hYnGegoy36hWif29X0VD2TU/T9v2EEEUURa0ctpob9BLwuEjPHkFYwBY3u7CsveIUgL1XbuKrQQLJ+dDT8DRZZiMrIyMh8wxACfrpbjtDVdBiFQkFawWRScsajVPW/lnKfD/Y5qXqmSEwMDBWfIPJilY2rCgykxkjnsuh12TDV78XW2Ygu1kjepIuIT8kdkGtVuyvAv5oc/HhyMppR0vyyu9PDoR4vz14gHcc0URRxdLfQUVeO12klITWP9MkL0MUObHTzrXoHVl901LuGixH/izu2Mr/i3A114td9db/p5ObmcuTIEZZtaT3Fc/ibTN95OWdymXxevob8mzk9fedlfJJudFyBv0ZfHgUGVfgXDApY2qrpbOxrcBlHav4k1JqBC8ryLg8Hur08M1c6YuBEcnNzGaxj4NsNdnq8AsskIgb8XhedjQewtFX3NriMm01iRvEpDS5n44VKK3FqJdcU9Xbd952XiRMnRu1i9qsrrIw1apmTERPS/Q7lNwPgsnbSUbcHl7WTuMR0ss9ZTGxC2oDfLwR7S1wW5sSRa5CejecJ5yWseVQ6t34yMjIyMmHh1AaXYtIKp5yxweVsrK6wMiZBw9zM0IqBSNFX73pJbhz58ZEVA0LAh7npcG+Di1JFetE5JGePPW2Dy9mwegU21tm5Y6yRWInWuw6Wih4v2zvcPDErbUAjwuHE47RgqtuL3dyM3pBE/uSLMSRlDzquLS1OWl0Bnp6THqZIowNZiMrIyMiMUkRRxNnTRkddOR5HD/EpueRNmo8+LnFI+6uy+Pi83c3jMyMvBkLFlmYnzc4AT86OnBgIBgW6WyroajqIKAgk5x5rcFEPrRHslRobInCzBOtdh8rqCivZseoRs1w9HX6PE1PDfqwdtWh0seSMn4sxvXBIfwt9JS6zM2IYlxRZh75IIwtRGRkZmVGI226mo7Ycp6W3waVo2iJijcMTW2sqLWTGqlmUFzkxEEr6ml9mpeuZEAExcLzBpX4fAZ+bxMwS0gom99vgcjbcgSCvVNu4ujCexFHidtXs8LO5xcn9U1NQKUf+Bijg9x5zrapApdKQMWYGSVmlKJVDP7//7nBTafXx56lySZUsRGVkZGRGESc1uMQZyS+bjyE5Z9gjmK1OP+83OfnZ1BTUERAD4WCnycNRi4+VF46sGDilwSUtn/TCaSe5Vg2VN+sd2P1Blo0dPaOh6yqtGLUqlhaOrPVlUPBjbjmKuanXtSo1r4yU3JNdq4bK6gorE5N0nJs2Ohr+hoMsRGVkZGRGAX6vi86GA1jaextccsbNwZhRHLIp9HWVNuI1yhEXA+FkVYWF8YlaZqaPnBhwWU101JUfa3DJIOecOcQkhGYZrEBQZG2llcV5cWTHSa/5ZSh0ewTerHfw7QmJ6NUjU+/a61pVQ2fDfoSAl6SsUtLyy1BrQ1MXfajby65OD0/NTh81JS7DQRaiMjIyMlGMEPDR1XSI7uajKFQqMoqnk5Q9dljThl+nxyvwRr2du8YZiRkhMRBuDnd72WHy8NsREgO9DS7l2M0t6A1JFExeQFxSVkiP/UGTk3ZXgDvHSXNFg6HwcrUVtRJuHBMf9mOJooitqxFT3V58HjvG9CLSC6agjQntsVdXWMg3aJifM/QSjNGELERlZGRkopSupsPHG1xScieQkjdxyA0uZ+OVahsK4CYJW18OltUVVvIMahaEWQz0ulbtx2KqRas39OtaNVR6610tzM2MocQ4OtyunP4g62vsXFsUT4I2vPWujp42THV7cdvNGJKzyZt4IXpDcsiP02D383GLi4dnpKKUR0MBWYjKyMjIRC2munISs0pIyx9eg8vZcPmDvFpt47rieIyjpPml0e7noxYnD05PCZsYCPiPuVa1HnOtGjOTxKySkI5Un8jn7W5qbH4eOGf0uF29XmvHHQhye2n41nd1282Y6spx9LQTE59C4dRLiUsM34jymgoLKXoVS/JHT4nLcJGUEA0Gg8yePRuTyUR9fX2kw4koFquVx/64ks2bN6NWq7FYLNxwww088MADqNWS+tpGhA83b8br83L7smUYHCZWrlzJpEmTIh1WRHn11Vd5/vnnscWmcmTGMn70xm/5y3//nOLi4kiHJhkUCsUPgWeBi0VR3BrhcELOmHOvOqXBJdR5dFOdHWeYxUC46O7u5tlnnz0lj4qLv0eSTsWVBaGf7g0KfszNRzE39za4pOWXkZwTmgaXs7HqqIUpKTqmpZ65+3/jxo3U1dVx4YUXolQqJZ1He92urCwpMJAeG/prns9tx1S/l/qKcqrqmtm+t57yw3Xk5+fz9NNPhyWPmlwB3mlw8J9lSWijyO0q3HlUUormueeeo6qqCqMx+hJeqPn0k09Yv349X3zxBUajkdbWVqZPn47P5+Pxxx+PdHgjyo4dO3jg5z9Hq9Hwwrp17HjrFRYvXsyRI0eIjw9/3ZBUWbZsGW+//Tb5My9i2eYW4lo2c9lll7F//370erkT02QyAdwf6TjCyem6rEOZR/2CyLoqK5fnG8gIgxgIN+++++4peXTa3Plo4y/iicWTQyoGehtcqo81uPhIzhpLan4Zam34/xb3dXnYa/byh/Mzzjjlv2PHDpYvX05OTg7btm1jzZo1ks6j7zU66PKE3voy4HPT2XCAnrYq1Fo9j/3uH/y/R1bw158uJhgMcvfdd4ctj75UbUOvVnJ9cfSUuLS2tkKY86hkqs5bWlr4+9//zve+971IhyIJEhOT+NnPfnb8YpKdnc0NN9zAyy+/HOHIRp4VK1Yw76KLjtvbLVu2jEAgwOrVqyMcWWS5+uqrWbRoUe8DhYLbb7+dqqoq9uzZE9nAJMKvf/1rgCcjHcdIEuo8+q8mBya3wPJx0Tk4kJKSckoeHXfH/XSb2rk+RPWuoihiNdVTvest2qp3YEjKomTmUjJLzh0REQq99a7FCRouyDpzV/eKFStYsmQJWm1v/aiU82if29VF2bEUJYSm3lUI+DHV7aVqxxtYTfWkF06jZObVJGWVsmjxYgCUSiU/+MEPwpJHbT6B12pt3Dgmnrgocrv64Q9/CGHOo5I5Gz/60Y948skniYkZHbZxw2XevAu5++67T3pOr9fj8/kiFFHk2LJlC5PLyo4/ViqVzJgxg82bN0cwqsizfv36kx5rdb1Tct/E38jXeeutt/pKWP4V6VhGklDm0T4xMC8rluIQiYGR5vLLLz8pjzr8QeoTS9Af3YYhBGLA0dNGXfl7NB/5DG1MPGOmX0HO+LlDsk4dKrU2H5+2ubhjrPGs9a5btmxh5syZxx9LOY9ubXHR4PBzZwhugIJBAXPzEap3bKKr+TDJ2WMpnXU1qfmTUKrUp+TRvlHQUOfRDTV2AkG4tSR6bureeustNBoNhDmPSkKI9l00Lr/88kiHImm2b9/OjTfeGOkwRhSz2YzVaiU19eQC/MzMTGprayMUlTTZu3cv2dnZzJ07N9KhRBSn08nDDz/MAw8+GOlQRpRQ59FtbS7q7H7uGh89F87+eK3GhsXh4tZhWl+67Wbq92+mYf8WFAolhVMvpWDyAvSGpBBFOnDWVFhJj1FxWd6ZxW9fHs3MPHnhfinm0T63q+mpeianDH1EWRRFLB21VO98k47aPcSn5lE66xoyiqej0py5jnb79u0hz6NeIcjL1TauKjSQrI+Ohr++PPo///M/YT9WxIt+HA4HDz30EB988EGkQ5E0H330EY2Njbz77ruRDmVEcblcAMenk/rQ6XTHX5PprU/7x9//zrPPPtt3B/uN5ZFHHuGee+4hPS0t0qGMGKHOo30+2NNSdEwZhhiQEj5B5H+/rEd56FN+89eHh7SPXteqfdg6G9DFGsmbdBHxKbkRW5S83RXgvUYHP56cjOYs9a59uVKnO1mASTGP7u70cKjHy7MXDK1z/RTXqtQ80ssWoIvr/4bK6/Xy9NNPhzyPvlXvwOILfb1rOOnLo1lZWWE/VthGRBUKxWMKhUI807/du3Zx8ODBEf2wUuCxxx5DoVCc8d+ECRNwOZ0nvaelpYV77rmHN9544xvXyBUb27skzdenSbxe7/HXZKChoYHFixdz/fXXRzqUiFJeXs6XX37JPffcE+lQQkJ/eVShULBr166Q59HyLg8Hur3cNT4xJPsLNf3l0b7zciKr9zRwsLaRF39y66DzqN/rorXqS2p2vYXb1kn2uNmMOfcKElLzIuqM82KVlTi1kmuKzt5s1JcrvV7vSc9LMY+urrBSatQyJ2Pw5SUuayf1+z6k8eBW1BodRecsJm/SRQMSoQD/8R//wQ033BDSPCocc7tamBNHriE6BglGOo+Gc0T0d8BfzvTilKlT28ZPyOVXH33E7t27j9dp1NfX097ezvz58ykpKeH5558PY4gjz/3333/WL7fKLvCTvV8li+7ubpYuXcrKlSuZPn36SIQoKVJSUjAajXR1dZ30fHt7u7xM0TF+//vfo0icw09+8pNIhxJx3n77bdxuNwsWLMAVnwHQ1933jEKhsADfEUWxOnIRDpqz5tG2tra21NRUvv3tb4c0j66usDImQcPcTGnW7PeXR4GTynm6zGb+a8M2rj5nHFfMOWfAxxECPsxNhzG3HEGhVJFeNI3k7HEoVRGfTMTqFXi91s6ysUZi+6l37cuj7e3tJz0vtTxa0eNle4ebX89KG5TA73Wt2ovd3IzekEj+5IsxJGUPah99SyM+8cQTQwn9jGxpcdLiDPDU7PSQ7jecnJhHjxHWPBq2vyZRFB2A40yvn7uhDrVKxb59+056/rHHHmPVqlVs3bo1XKFFFIMBGvvXAAAgAElEQVTBgMFw5loei86LQtEKgN1u56qrruLRRx9l4cKFAPz1r3/9xq0ssGDBAg4ePHj8sSiK7Nmzh4cfHtr02mhixYoVtLS0UDC116ll9+7dAMyYMSPCkUWGRx55hEceeQSAoz1eJiS/egtQB/wkGtcR7S+P9hHKPFpl8fF5u5vHZw5ODIwk/eXRE7Hb7Vz0vZ+Tevm9/HLRRKD/PBoMCvS0VtLZeJCg4CcldwKpuRPPWls40rxaY0MEbh5gveuCBQtOGiWWYh5dXWElO1bNpblxA9re73FiatiPtaMWjS6WnPHnY0wvGvTvdsWKFdTX1/Piiy+GNI/2lbjMzohhXJJ0fjv9cWIeBVAoFGHNo5JoVpI5Fa/Xy9KlS5k9ezY5OTns2rWLXbt28X//93+RDm3EeeCBB/jk008RxSAAL7zwAiqVijvvvDPCkUWWv/zlL6xdu5Y7li/H5XJx8OBB3nrrLQ4cOBDp0GSimDWVFjJj1SzKG5gYkDIej4erli4leN7VTEtU4ao9cNY8Kooilvaa4w0uCX0NLkXnSEqEugO9zS9XF8aTNEC3qwceeIB33333eJmT1PJos8PP5hYny8YaUSnPLiQDfi/tNbup2vkGDnMzGWNmMGbmUhIzigctQvvy6I9//GP27NnDrl27QpZH/93hptLqC0n3/2gm8vMLx2hvb+eWW245aUrprrvu4q677op0aBFhw2uvsXXrVrZu3cof/vCHSIcTUWbNmsVvf/tbfnzv9487K73//vuSXIR5pLDb7dx7770Eg0Fuu/VWuGsFN/7859BRxz//+c9IhycJfvPkk3DylNJRURRviWBIYWe4ebTV6ef9Jic/m5qCuh8xEA38/e9/55M6M3R7OLpyGa81nF5cnLbBZfIlpzUMkAJv1juw+4MsGzvw+GbNmsXq1au57bbbjjsrSSmPrqu0YtSqWFp45pHuoBDA3HIUc9MhRFEkNa+MlNyhu1admEfPP//8k14LRR5dXWFlYpKOc9Oit+HvWMlXWPOoZIRoZmbmqJ2OHwq333Ybv7r3W5EOQzJcunAhOq2OF9atY3wUTXGEi/j4eARBAHqnoJdtaWXdz4/I5+YEHnrwQdY89djsSMcxkgw3j66rtBGvUZ5VDEQT9957L4cmX4fNF2Ttk/tOO1rmsproqCvHZe0kLjGDnHPmEJMgXb/2wLHml8V5cWTHDU6AXXvttRQVFbFt27YwRTc0uj0Cb9Y7+PaERPTqUydqe12rao65VnlJyiwhrWAyau3waphPzKOh5lC3l12dHp6anS7ZEpeB8Mwzz/DMM8+ENY9KRojKyMjIyESOHq/AG/V27hxnJOY0YiAaOdLjZYfJw5PnnVrvenKDS9KQGlwiwQdNTtpdAZaPHdryRlLk5WorKgXcOObk0VlRFLF3NdJRtxef244xvZD0wqloY6Qxins2VldYyDdomJ8jrVUJpIgsRGWGTVVVFXfeeSdarVYe1ZaRiVJeqbahAG4OkfWlFFhdYSU3Ts0lJzS/9Da47MPSUYtWF0fuhLkkpBVGXIAOJI/2LvZuYW5mDKWJ0el29XWc/iDra+xcVxxPgvareldHTzumunLcdjOG5GzyJl6I3pAcwUgHToPdz8ctLh6ekXpWtyuZXmQhKjMs1q5dy8qVK1GposMtQkZG5lRc/iCvVtu4tige4wCbX6ROo93PlmYnD05PQalQEPB76Wo8SHdrBSq1lqwxM0nMKkGpjPznHWge/bzdTY3Nz8/PSRmhyMLP67V23IEgt5f2NvS4Hd2Yastx9LQRE59C4dRLiUuMrtHfNRUWUvQqluSPjhKXcDM65l9kIkZKSgqffPIJJSUlkQ5FRkZmiGyqs+MMBLk9ipxf+mNdpZUknYoluXo6Gw9QvWMTPW1VpOWXUTLzapJzxklChMLA8+jqCitTUnSckxq9zS8n4hNEXqyysqTAQKLCTfORbdTufhefx0HexHkUnXNZ1IlQkyvAOw0ObitNQHsWtyuZr5BHRGWGxZIlS4a9j+bm5n63abeHp6BcRuabjl8QWVdl5bI8A5mxo+OS0OUO8E6DjfvyrDTs3oEQ8JGUVUpaftmwG1zCwUDy6H6zh/IuD78///TNLwPJo1LjvUYHJrefxdoOqndWotbqyR57HomZY1AoonOc7KVqG3q1kuuLR0+JS7iJWNbJwI7g6sE9xGUXQoXg8ksmFqnF43EGCAoBPE4LbvXZfyqJBh1pSQbcdvOgj3PB7P4do/wp+YA4oFjCzWDOyzctHqnFQlJ0jaZEgn81OTC5Be4cPzpGQ0VR5N0DR/i26iBjXQKGjCLSCqei1Uf3NOmqo1aK4jVcmHX65pe8vLwB7WfChAmhDGvI+P0+/lbeyBS6MNo7SC2c1jtKLQHXqqFi8wm8Vmvj5pIE4vpxu4oWDrebmZgZ3lKQiH3j31LvxFOhoVYV2S/LIwT5ltoviVikFk+TV4fXVUTT4b1odN6zbnvpzFy8U9Kp3fPeoI/z+H239btNqyKRXz69hqbDn/YbS7gZzHn5psUjtVim5d4Y0RikTlAUWVNhZV5WLMUJ0d/84uhpo6VmD4a2DtQJmZTOmB01DS5no9bm49M2F788N/qbX/pcq94+VEe9NYP7pydQOnG2pAwDhsqGGjuBINxaEv03dX6vi86G/fzvfhd/vmFB/28YBhETov8MzOSpcekUJ0R21K/W5uef202SiEUq8fzpT8/x3HN/wp+ST9fVD3PPMyvQmBtP2mb9+g2UlU06/vhv6x+ipaWFNbcO3u88Lqf/EdEaJyh/v468ifMoNkb2jtlvDaDrsUkiFqnFI7VYZM7OtjYXdXY/j5wr3XUzB4LbbqajrhxnTzutYgIvCefw59mT0cdE7jf42GOP8d///d9n3Wbnzp2ce+65/e5rTYWV9BgVl+WdeVS3qalpQHEtWrRoQNuFGlEUsZrqMNXvw+9x8barjNn5ycyfOrCRXKnjFXrdrq4qNJCsl0bt8VAQ/N7/396dh8dZ3ufiv6XZ91WjZTRabdmWJVs2eMHYgO1goCGGhD1sTduTQ0/Spk04bZKei1KSkzRtQ9M05He1OWklY5YAYQthS0gIKVBWybtG20gabbNp5p19eZffH5LAxvZIGo1m3hl/P9eVPyAjzYOWV/e889zPF373CQQm++HnVXgns37Vn7Nov6Ue6CBRm6DSFfdVkIRNwYOEKNYilvX86Z99FXd+4YsYjHD48vsx/OjO57BWd+YvltVqhfS0t15D0RR8wShUuuXfwm9awsckgykAFVBqjEX/PinZFColcVGsRWzrEdtayPnNHQXEoMuiwCZLaZZfUokwfKNHwHjHoFDrUbt+D/7yHeDyRg2sRQyhAHDvvffinnvuyfoYq3XxFwAzcRYvjUfxlU4zZFnKL/X19cteYyEsTK3yuvqQjIWgtzrgr9kNly+KH24sn/b/L0ajCKU53FmihT+eYzE75YR//AQEgYO1vh2/mK2FUZ1c9ecu/u0cIjparRZarRYhRQoyWRpVVitqaGIPIWWlz5/C0UAK/7yr9PbRsukEfGNHEZweglSu+qjg8owrimA6IIowsHAdXalHBxlopJW4vln8h7h/UpzxzU+t8kJjtKG56yqoDVX4h9/PYK1BjkuqxVccywU3P+1qv12Dem3x31ldDkHgEZoZhm/sGNh0Yq7U19iJqCDH831u3L1u9X+XKIgSQsgFqNsZQqtehktrSycMcGwaAfdJBCZPoaJCAltzF8x1cwUXXpgLA/vsGjToSisMnA+T4vDMSAS3txmgLqHyy5lTq4xo6NgLrXluatVAKIW3PQl8e/vZ065K1WuTMUzGWHxvp63YS1myualVbnhH+5CKh2GwNaKqaTMUqrm2/xMng6gAcHMBBlxQECUr8vzzz+PBBx9Ef38/kskkrrjiCtx555344z/+42IvjRByHoOhNN6cSeCBbVUlUX5ZKLj4xo+D5zKw2NfD6th4RsHlN5NxuKMs/u/20gkDC853HeUv+Rx4ALesKY2jgOamVh0F4xmBTKGGff0uGGzNZwTO7n4GdWoprjxt2lUpEwQB3f0MdthUWF8i7xzGQh54XL1IhP3QmmpgX3/pGdvqEiyPxwfDuL5ZB2MBBlxQECUrcvDgQRw8eLDYyyCELMOhgRBq1FIccIg7DAiCAMYzAu/YUbCpOIw1rahq3ASZQn3W43qcIWy3KdFuLo0wcLpzXUcTLI9rX3TjuiYdTCKfdsVlUvC5T2B2sh8SiQzVrRfBVLv2rIEBk9EMfj0Zw72bLZBUiv8F0FK840ligEnj/7uspthLWVQyOguPqw/R2SmodBY0btoPran2rMc964ogyvK4fW1hXgBRECWEkAvIVCyDV9wxfHWTGVKRhoGFgovH1YtUjIHe6oCtcx8U6nPvV3vPm8SpYBoP7RF/GFiq50ejiGR43NEm3ruhPMdidrIffvcJCIIAq2MjLPXtkJznDOyHBxjoZZU42FTaZ7qertsZQrtJgYurxFv4Syej8I4eAeN1Qa7Uob59D/TWhnNujWB5AYcH5gZc1GoKs8WFgighhFxADg+EoZNV4jqRll/mCi4fIs74oDFWo27LJVDrs7fLu50hrDfKsd0m3jCwHAth4CqHBnUFCgPLIQg8gtPD8I8fBZtJwVSzBlWNnVmnVs0mOTw/GsUfbzBCKS2d/a7ZnJhN4X1fEv+w89zTroqNTSfgGz+O4PQgJFI5atfsgKmmFRWV5//6v+KOwpPgClJSWkBBlBBCLhDBFIfnRiO4e50BKpGFgTMLLiY0dO6F1lS36B/4U8EU3vUm8d0d5VN+edUdw3ScxYNt4jrRYK7gMg6Pqw/pRAQGWxNsTZshVy3+oubxIQaSCuCmVnG+AMpFjzOEBq0MV9jPPe2qWDg2g8DEKQQmTqKiogJVjZ2w2NejUpL9RQ0/f6Tbnlo1Wg2FG3BBQZQQQi4QPxsKowLALQVowi7VXMHlCBiPCzKFGvUbLoW+qmnJobLHyaBeI8X+Miq/9DhDuLRGhbVG8Uy7igZn4HX1IhEJQGuuRX37HqiWOLUqluHx5HAEn2vRQS8X937XpRqLZPDbyTj+5iLxTLvieQ7B6UH4x46B4zIw162DtaED0iVOrfqv6QRGwhl8c2thB1xQECWEkAtAPMPjiaEwPtusg0EE5Rc2k4J//Dhmp5xZCy7ZjEcyeG0ihm9stYgmDKzUmzMJDIcz+Ost4jjsPRGdhdfVi+jsNFQ6C5o2fwoa4/L24j49EkGC5XH72uKf75ovh5whWJQS/EFD8fe7CoKAsG8UXlcfMqk4DNUtsDVugky5vBdn3c4QNlsU6LIWdosLBVFCCLkAPOuKIMbyuL3Ih73zXAaByX4E3CfnCy4dsNRvOG/BJZvDAwxMCgmubSynt3sZdJoV2FLgMPBJ6URkvuAyCrlKB0f7ZdBZHcve/pDmBDw6yOAPGrWwqcsjcvgSLF4cj+FPNxohzzLtarUJgoBocGpualU0CJ2lHo6OvVBqjMv+XH3+JI4GUniwCAMuyuOnghBCyHllOAGHB+easDVFCgMCzyM4MwTf2FFwbHpugktDR9aCSzb+BItfjEXxP9uLGwby6WggiV5/Et/fVbzyy9zUqmNzBReZErVrd8BU24qKitz2FL88HoUvWbqjL8/lscEwFJIK3NBSvC0u8bAfXlcvYiEP1IYqNHcdgNqQ+xm6PU4GLXoZdhdhwAUFUUIIKXOvuKPwJjjcvb7wYWDubcMxeEePIJ2MwGBrhq1x05IKLtk8NhSGrBK4oaV87oZ29zNo1smwp7bw5Ze5gstJBCZOoaKiAramzTDb16NSkntMWCi/XF6nRrNePPtdVyKS5vDUSBg3t+qhKcK0q1ScgdfVh7DfDYXGgIaOK6A121f0wmWYSeP303H83bbi7HelIEoIIWVsIQxcVqtGS4HDQDQ4Da+rb77gUgdH+x4ol1hwyfp5MzyeGo7gxhY9dGVSfhkJp/HGdBx/e3Fhw8DC1Cr/+HFw55lalavfTcUxFs3g/m2FLb+spqdGImB54LYCHfa+IJOKwzd2FKGZYUgVatjXXQJDdUte7pz3OBlUqyS4ylGc/a4URAkhpIz913QCrkgG/+eiwoWBRCQwV3AJzswXXK6Expi/vWc/Hw4jzQv4fIHDwGo65GRgU0lwdYHCgCAIYLwu+EaPrKjgku3zd/cz2GpVotNSHue7pjgejw2GcW2jFhZlYeITl0nB7z6BwGQ/KiUyVLdshamubVmlvmymYxm87I7iL4s44IKCKCGElClBENDtDKHLosDmApRfUokwfKNHwHjHoFDrcy64ZJPmBDw6NBcGrKry+BPmibN4aTyKr3SaISvAftdIYBLe0V4koyHorLkXXLL50J/EiWAKP9wtrrNQV+KF0ShCaQ53FuCwd55jMTvlnJtaxXOw1rfD4miHRJrfdzUeGQxDK63E9UUccFEev8WEEELO0udP4WgghX9e5Sbs6QUXqVyFurYdMNbkXnDJ5oWxCGbLrPzyyCADTQHCQDzsQyYVw/jx30JjtKG56yqoDVWr8lzd/QzWGuS4pLrw5ZfVwPECDg0w2G/XwKFdvWlXgsAjNDMC39hRsOkETLVrYG3ohEyR/33DoRSHZ1zFH3BBQZQQQspUtzOEVr0Ml65SE5ZjMwi4TyAweQoVFRLYmrtgrlu3ooJLNrwg4OEBBvvsGjToxDf6MhdMisMzIxHc3maAepXKL6kYA89oLyL+CQiCgIaOvdCaF59alauBUApvexL49vbymXb12mQMkzEW39uZezM9G0EQEAm44XX1IRUPw2BrRFXTZihUq7f95InhMADg5iIPuKAgSgghZWgwlMabMwk8sK0q7+WXhYKLb/w4+DwXXLL5zWQc7iiL/7t9dcJAMTwxHAYP4JY1+Q8DmVQcvtEjCHlG5gou63dBrtRCZ7Hn/blO193PoE4txZVlNO2qu5/BDpsK6035/xmPhTzwunoRD/uhNdXAvv5SqHSrO9AgwfJ4fHBuwIWxyAMuKIgSQkgZOjQQQo1aigOO/IWBhYKLd/QI2FQcxppWVDVuWpW3Dc/13D3OELZVKdFuXt3AWyhJlsfPhsK4rkkHUx7DwOkFF8kqFFyymYxm8OvJGO7dbIGkSOWXfHvHk8QAk8aP9yxvotRiktEgPK5eRGenoNKZ0bhpP7Sm2rw+x/k864ogyvK4XQSFPwqihBBSZqZiGbzijuGreWrCCoKA6OwkPK5epGIM9FYHbJ37oFAXbp/me94kTgXTeCjPYaCYnh+NIpzhcUdbfsIAz7GYneyH330SgsDD6tgIS317TlOrcnV4kIFeVomDTcUffZkvPc4Q2k0KbLPlp/CXTkbn7lR7XZArdajfsBv6qsaCbWNgeQGHB+YGXNRqir/FhYIoIYSUmcMDYehklbguD+WXOOODx/Uh4owPGqMNdVuuglq/OgWXbLqdIawzyrE9T2Gg2Fh+br/rgXoN6lYYBgSBR3B6GP7xo2DTybmpVY2dOU+tytVsksNzrij+eIMRyiKWX/Lp5GwK7/mS+N7OlU+7YtNJ+Mbnp1ZJ5ahdsx2mmjWoqCzs1+oVdxSeBIe7C9D+XwoKooQQUkaCKQ7Pja68CZuMheB19SESmIBSa0RD515oTatXcMnmVDCFd71JfHdH+ZRffuWOYTrOrmi2tyAIiPjd8I4uFFyaYGvavOKpVbl6fIiBpAK4qbWMpl05Q2jQyrDXnvv2E47NYHbyFPzuk6ioqEBVYycs9vWolBT+buTCgIvdNSq0GsQx7YqCKCGElJEnhsKoAHBLjk3YTDIG79hRMJ4RyOYLLgZbc1EDYI+TQb1Giv1lVH7pGWCwq0aFtcbcwkAsNAPPSO/c1CpTbUEKLtnEMzyeHI7gcy066Mtk2tVYJIPfTsbxza2WnAp/PM8hND0E3/gxcGwa5rp1sDZ0QLrKpb5s/ms6gZFwBt/cKp5pVxRECSGkTMQzc+WXzzbrYFhm+YXNpOAfP47ZKedcwaX1Iphq1xak4JLNeCSD30zG8PUtuYUBMXprJoEhJo2/6lr+ftdkdHa+4DINlc6Cxk2fgtZU/H2zT7siSLA8bl8rjrd78+HhAQYWpQSfblzeHV5BEBD2jcI7egTpZBRGWwuqmjZBriz+vtkeZwibLAp0FWDAxVJRECWEkDLxrCuCGMvj9mUc9s5zLAKT/Qi4T0AQBFgdHbDUbyhowSWbwwMMjHIJrl1mGBCzbieDTrMCW5YRBtKJCLyjR8B4RyFX6eBo3wOdtUEUWxXSnIBHBhhc06CFTV0escKXYPHLsSj+dKMR8iVOuxIEAdHgFLyuPiSjQegs9XBsvCLvU6ty1edP4kggtaLtIKuhPH5iCCHkApfhBBwenGvC1iwhDAg8j+DMMHxjR8GxqbmCS0NHwQsu2QSSLF4Yi+KL7UsPA2J3NJBErz+J7+9aWvnlo6lVM0OQSBWoXbsDpprWghdcsnl5PApfksNdIim/5MNjg2EoJBW4oWVpW1wSYT88rl7EQh6oDVVo7joAtUFc5932OBm06GXYvUoDLnJFQZQQQsrAK+4ovAkOd6/PHgYEQUDYPw6vqw/pRKToBZdsHhsMQ1oJ3NAivrXlqsfJoFknw57a7OUXjs0gMHESgYlT8wWXTfMFF3H92V4ov1xep0azXhzll5WKpDk8NRLGza16aBaZdpWKh+F19SLsd0OhMaCh4wpozXZR3Kk+3TCTxu+n4/i7bVbRbXER1080IYSQZVsIA3tq1WjJEgaiwRl4XfMFF3MdHO17oNSaC7jSpYvOl19ubNFDVybll5FwGr+biuO+i84fBnieQ3B6EP6xY+C4DMzzU6uKWXDJ5ndTcYxFM7h/m3jKLyv11EgELA/cluWw90wqDt/YUYRmhiGVq2BfdwkM1S2iC6ALepwMqlUSXOUo/j7VT6IgSgghJe6/phNwRTL4PxedOwwkorPwjvQiGpwruDRtvhIao7j2iX3S0yNhpHkhaxgoNQ87GdhUElzTcHYYWJha5Rs9gkwqDkN1C2yNmyBTivekgIXRl1utSnRaxFN+WYkUx+OxwTCubdTCojw7InFsGn73CcxO9KNCIino1KpcTccyeMUdxV/kacBFvlEQJYSQEiYIArqdIWy2KLD5E+WXuYJLHxjvGBRqPRztl0FndYj2rs2CNCfgkcEwPt2oRZWqPP5MeeIsXhyP4s87zZCdtt91bmrVFLyjvUhGQ3MFl469oim4ZPOhP4kTwRR+uFvcL2qW44XRKEJpDnd+Yr8rz7GYnXLC7z4Bgedgqd8Ai6MdEqn4tyM8MhiGRlqJ6/Mw4GI1lMdvOCmK2dlZ/PCHP8Svf/1rSKVShEIh3Hjjjfj6178OqZR+tAgphD5/CkcDKfzzaU3Yjwou04OQypWoa9sBY00rKirEU3DJ5pdjEcwmOdy1jPa/2D0yyEAjrcRnTwsD8bAP46f+G+6RUzg15MbbR0ZxashdMtfRHieDtQY5LqkWV/klVxwv4NAAg/12DRzauVMjBIFHyDMC3+hRsOkEjLVrUNXQCZki9wPuCymU4vCsK4K7VjjgYjWJ+6eciNqLL76IJ598Em+99RYMBgOmpqawdetWpNNpPPDAA8VeHiEXhG5nCC16GS6tVX2i4FIJW1MXzPZ1oiu4ZMMLc2Fgr12NBp04jpBaqXCawzMjEXx+rQFqWSVScQZeVx/Cfjdm/CE89PDL6H70afy50Vgy19GBUApvzSTw7e3lM+3qtckYJmMsvrfTNje1KjABr6sPqTgDfVUjbE2boVCX1laRJ4bDEADcnOOAi0IQZzwmJcFiseBrX/saDIa5uxZ1dXW48cYb8fjjjxd5ZYRcGIaYNN6cSeAP1+oQnOzH0LvPwu8+AXNdG9Zuvw7Who0lFUIB4LeTcbijLP5wnfjfml6qJ4bC4AHc0CDFlPNtDL//AhLRWdjX70Ja1YKDN94Bo3Huv7dUrqM9TgZ1aimuLKdpV04GO2wqOCpCGO17Be4Tv4NUoULL1mvgaN9TciE0wfJ4fDCM65t0MC5zwEUhldYViojKNddcc9a/UyqVSKfTy/o8ExMTiz5mJsIt63MSciE41B/CHqUXrZ4+eNJxGKtbUNW0uWTeNvykhf2u26qUaDeLsyW+XEmWx2ODDPbpw/AfeQuVEtkZBZdr/qDlrI9ZretovkxGM/jVRAz3brZAIsLySy7e8STRH4jjPscMRo+MQak1o3HTfmhNtcVeWs6edUUQZXnc0SbuAF20IFqNCLh4EIkiT+/g4hnRrAUAkjEWPMciGQshUeT9QbmsZdh5DH90161IRAJLfp7dO7cu+piMpQGAULJflwtlPWJbC0zlU6I4l9rp3+JKdRJqXRNsTfug0JT2nsr3vEmcCqbx0J7ij6zMB55jcfh9J3zBJD6lH4HVsRGW+vZFp1a9/fbbuOmmm5b1XA6HY0mP27Bhw7I+77kcHmSgl1XiYJP4jgLKRToZxY/fGYSdi2GDJIDqNbuhr2os6S0HLD9X+LvaoUWtpvjZJpui/aX4gvQ9JJ0yjEiKuzsgyfH4gjQjirUAgDulQCreDPfJPsgUqZJaSyQSxs0HNmPjxg0Y+fClJT/PA1/9/KKPmaow4m//8RDcJ98oua/LhbQesa2lq355f8xLDVchQ8fFV8BkLo/A3eNksM4ox3ZbaR8FJAg8QjPDmB49isNDduyrVuLSS69d0tSq3/zmNxgfH8eLL75YgJUu32ySw3OuKP5ovQFKkZZflopNJ+EfP453XeP4MNiEb22xYm3nLlFNrcrVq+4YZuJsSUy7KloQ/U92G/5hnQ0t+uIm9ZFwBv/5tlcUawGADMNCEQzD0X4ZWgzF+fb86EcP4aGHfoSMpQH+6/4G9/zge5AFxs94zJNPPoWOjo0f/bPH68X/uutuPPjg97G2vX1Zz6exL35HdOP6rYAAACAASURBVDgGVH7/cFG/LgvE8D0S63rEtpZyJ19zBUxmcR5Iv1yngim8403gOztKt/wiCAIifje8o31wDfXjB2/N4E3Dbvzu3q/iX7xjZz3+vffew8UXX/zRP09OTuKee+7Bc88999He+6Vyu91LetyBAweW9Xk/6fEhBpIK4OY14n67NxuOzWB28hT87pMAgFf5Tqyt1uG6TeI/2mwp+PktLrtrVFhjEP/xUkX7S+GBDhK1CSpdcfcBSdgUPEiIYi0AoGRTqJTEodQYi7aeP/2zr+LOL3wRgxEOX34/hh/d+RzW6s7c6Gy1Wj86WmR2dhY33HwHvve97+GiHXuW/XxNOsuij0kGUwAqivp1WSCG75FY1yO2tZS7W9aI/27HUh1yMqjXSLHfXprll1jIA4+rF4mwH1pTLbbsvRUyTRp3Kyrx7S//9zk/xmr9eADB7OwsDh48iB//+MfYunXxF+efVF9fn/Palyo+P+3qsy066Etw2hXPcwhND8E3fgwcm4a5rg1x83q885oP39xqFN3oy1y9OZ3ASDiDb24tjWlXxb+dQ0RHq9VCq9UipEhBJkujympFjencoSISieAzn/kM7rvvPnzqU58CAPz7v/87vvjFLxZyyYRckAwibsIuhzuawWuTMfx1V+mVX5LRWXhcfYjOTkGls6Bx06egNdXgzek4JtIe3HdJDWqqsr8lXyrX0addESRYHnesLa0XQIIgIOwbg3e0D+lkFEZbC6qaNkGu1OLbH/hhVkrw6UZxHvaei25nCJssCnRZS2OLCwVRkrNkMomDBw9i586dsNvteP/99wEA//Zv/ya6CyghRLwedjIwyiX4TFPphIF0Mgrv6BEwHhfkKh3q2/dAb2346K3dHieDTrMCWxYJA6VyHU1zAh4ZYHBNgxY2dWlEB0EQEAtOw+PqRTIahM5ih6P9cii1JgCAL8Hil2NR/OlGI+SS0noBdD59/iSOBFJ4cFfp7BsvjZ8mIko//elP8frrr+P111/Hgw8+WOzlEEJKUCDJ4oWxKP5He2mEATadgG/8OILTg5BIFahduwOmmtYzCi5HA0l86E/iny6xLbrnsFSuoy+PR+FLciVRfgGARCQAz8iHiIU8UOutaO46ALXBdsZjHhsMQ15Zgc+1lO5+10/qcTJo0cuwu7Z0pl2VfjWMFM2XvvQlCIJwzv8RQshSPDYYhrQSuLFF3HdDOTYD7+hRDL77HBjPCKoaO7F2+0GY69ae1bLucTJo0slwWd3i57mWwnWUnz/s/fI6NZr14i6/pOJhuE++gZEPXwKbSaKh4wo0dV11VgiNpDk8NRLGTa06aGXlEYWGmTR+Px3HXW2GktrvSndECSGEFEV0vvxyY4seOpGWX3ieQ3B6EP6xY+C4DMx162Bt6IBUdu598yPhNH43Fcd9F1lLKgxk87upOMaiGdy/Tbzll0wqDt/YMYRmhiCVq2BfdwkM1S3nvSP91EgELA/ctra87oZWqyS4ylFa57tSECWEEFIUT4+EkeYFUYYBQRDAeEfhG+1DJhWHoboFtsZNkCmzt/ofdjKwqSS4pqG0wsD5LIy+3GpVotMivvILx6bhd5/A7EQ/KiQS2Jq3wGxfh8rK87+wSXE8HhsM49pGLSzK8ohBM3EWr7ij+EqnGbIS2OJyuvL4DhBCCCkpaW5u8sunG7WoUonnT5EgCIgGp+B19c0XXOrh6NgLpca46Md64ixeGo/iz0owDJxPrz+J47Mp/HC3uMovPMdidsoJv/sEBI6DpX4DLI52SKSLbx14YTSKUJrDnSWy33UpHhlgoJFW4vpmcW9xORfx/PYTQgi5YPxyLILZJIe72sQTBuJhP7yuDxELeaE2VJ2z4JLNI4MMVNJKfLYEw8D5dDsZrDXIcUm1OMovgsAj5BmBb/Qo2HQCxpo1qGrshEyx+H5cAOB4AYcGGOyza+DQFn+ITT4wKQ7PuCK4s80AdQnud6UgSgghpKB4QcDDA2HstavRoCt+GEjFGXhdfQj73VBoDGjouAJas31ZU3bCaQ7PjETw+bWlGQbOZSCUwlszCXxrW/GnXQmCgEhgAl5XH1JxBvqqBtiauqBQL29bx2uTMUzGWPz9zqW/wBC7nw2HIQC4pUSnXVEQJYQQUlC/nYxjPJrBt7dXFXUdcwWXowjNDEOqUMO+fhcMtuacQtcTQ2FwQumGgXPpcTKoU0txwFHcaVexkAdeVy/iYT80phrY1++CagkT+T5pYb/rdpsSG84zpKXUJFgejw+GcX2TDsYSHXBBQZQQQkjBLISBbVVKtJuLEwa4TAp+9wkEJvtRKZGhumUrTHVtWQsu2SRZHo8PhXF9sw5mZWmGgU+ajGbwq4kY7t1cvGlXyWgQ3tE+RAKTUGrNaNy0H1pTbc6f711vEs5QGj/eU5PHVRbXc64IoiyPO9pK9wUQBVFCCCEF8543iZPBFH60u/Bh4KOCy/gJCAIHa337kgsu2Tw/GkU4U9ph4JMODzLQyypxsKnw7f90Mgrf6BGEvC7IlVrUb9gNfVXjircHdPeHsMEkxzab+Nr/uWB5AYcHw7jaoUWtpvhbXHJFQZQQQkjB9DgZrDPKsaO6cGFAEHiEZobhGzsGNp2AqXYtqho7IZWvvIDD8gIeHmBwoF6DuhIOA6ebTXJ4zhXFH603QCkt3H5XNp2Ef/w4ZqcHIJHKUbtmG4w1a3K+U326k7MpvOdL4ns7F592VSpedccwE2dLZtrV+VAQJYQQUhCngim8403gOzsKU34RBAERvxve0T6k4mEYbI2oatoMhSp/dy5/5Y5hOs7i+7vKp/zy+BADSQVwc4H2u3JsBrOTp+B3nwQAVDV0wmxfD4k0f8G+2xlCg1aGvfaltevFjhcEdDtD2F2jwhqDuKddLYaCKCGEkII45GRg10ix37765ZdYyAOPqxeJsB9aUw3s6y/NqeCSjSDMHQW0q0aFNmN5lF/i89OuPtuig36Vp13xPIfQ9BB848fAsWmY69rmp1bl9275eCSD307G8Y2tlrKZdvXmdAIj4Qy+sUW8066WioIoIYSQVeeOZvDaZAx/3bW65ZdkdBYeVx+is1NQ6VZecMnmbU8Cg0wa/7urfMovz7giSLA87li7em/3CoKAsG8M3tE+pJNRGG3NqGraDLlydfajHhpgYFZKcG1j+Zzv2uMMYZNFgS7r6r0A4tg0Au6TsDV3rdpzABRECSGEFMDDTgZGuQTXrlL5JZ2Mwjt6BIzXBblSl7eCSzbd/Qw6zApssZZH+SXDCXhkkME1DVrY1PmPB4IgIBachsfVOz+1yg5H++VQak15f64FvgSLX45FcU+7EfIymXZ1xJ9EXyCFB3dVr8rPN89zCE4NwDd+HDyXoSBKCCGktAWSLF4Yi+J/tBuhkOS3/MKmE/CNH0dwenC+4LIdppo1qKhc3ZLN0UASH/qT+KdLyqf88tJ4FN4Etyrll0QkAM9IL2KhGaj1VjR1XQmNYfXHhj42GIa8sgI3tJbPiQY9TgYtehl21+Z32pUgCGA8I/COHQWbin80tWq1URAlhBCyqh4bDENaCdzYkr+3Rjk2g8DEKQQmTqKiogJVjZ2w2NejUlKY5nqPk0GTTobL6sqn/NLjZHB5nRrN+vyVX1LxMLyjfQj7xqHQGODYeDl0lvqChPdImsNTI2Hc1KqHtkymXQ0zabwxHcf9F1vztt9VEAREZyfhcfUiFWOgtzpg69y/7KlVuaIgSgghZNVE58svN7booctD+YXnOQSnB+EfOwaOy8Bct26+4FK4spArnMbvpuK476L8hYFie2MqjrFoBvdvy0/5ZW5q1TGEZoYglatQt24njNWtBb17/NRIBCwP3FZG064OORlUqyS4ypGfLS5xxgeP60PEGR80xmrYt1wClb6wBSgKooQQQlbN0yNhpHkBt61dWRiYK7iMwjt6BJlkDIbqZtgaN0OmLPz4yUNOBjaVBNc0FP6w99UgCAK6nQy2WpXotKxsvyvHpuF3n8DsRD8qJBLYmrfAbF+Xl7NAlyPNCXhsMIxrG7Wwqsoj6szEWbzsjuIrnWbIVrjfNRkLwevqQyQwAaXWhMbOfdCYaouyzaQ8vjuEEEJEJ80JeGQwjE83alGVYxgQBAHR4BS8rr75gks9HBuvgFJjzPNql8YTZ/HSeBR/locwIBa9/iSOz6bwL5fmvmeT5znMTjrhdx+HwHGw1G/Iy9SqXL0wFkEozeHOEj/s/XSPDDDQSCtxfXPuW1wyyRi8Y0fAeFyQKdQFKfUthoIoIYSQVfHLsQhmkxzuasstDMTDfnhdvYiFPFAbqtDcdQBqQ3EPjn9kkIFKWonPriAMiE23k8Eagxy7apZffhEEASHPMHyjR8GmEx8VXGSK4u2d5QUBh5wM9tk1cGjLY9oVk+LwjCuCO9sMUOew35XNpOamVk05IZHKUdN6MYy1+ZlatVIURAkhhOQdLwh4eCCMvXY1GnTLCwOpeBheVy/CfjcUGgMaOq6A1mwvejs9nObwzEgEt63V5xQGxGgglMJbMwl8a9vypl0JgoBIYGJualWMgb6qAbamroIVXLJ5bSKGiRiL7+4sn2lXPxsOQwBwyzL3u/JcBoHJfgTcJyEIAqoaOmC2b8jr1KqVoiBKCCEk716fjGM8msG3tlct+WPmCi5HEZoZhlShhn3dJTBUtxQ9gC54cjgCTgBuXVM+b/cecjKoU0txwLH0vbYxxgPvSC/iYT80xhrYt+7K+9SqXC3sd91uU2KDqTymXSVYHj8bCuP6Jh2MiqXdwRR4HsGZIfjGjoJj0zDVrkVVQwek8vwe+ZQPFEQJIYTk1UIYuLhKiY3mxcMAl0nB7z6BwGQ/KiVSVLdshamuTRRvGy5IsjweG2RwXbMWZqV41rUSU7EMXp2I4d7NS5t2lYwG4R3tQyQwWfSCy/m8603CGUrjx3vKZ9rVc64IIhket7ctfjf046lVR5BORlZ9alU+UBAlhBCSV+/7kjgZTOFHu7OHAZ5jMTvlhN99AgLPwVrfXtSCSzbPj0YRzvC4M8f9rmJ0eCAMvawSBxeZdpVORuEbPYKQ1wW5UiuKgsv5dPeHsMEkxzZbeUy7YnkBhwfDuNqhRZ0m+9vp0eA0vK4+JCIBaM11cLTvgVJrLtBKc0dBlBBCSF519zNYZ5RjR/W5w4Ag8AjNjMA3NldwMdWugbWhuAWXbDhewOEBBlfWaxYNA6ViNsnhWVcEf7TeAKX03Ptd2UxyvuAyMD+1ahuMNeIouJzLydkU3vMl8fc7y2fa1avuGGbibNZpV4lIAF5XL6LBGaj0VjRtvhIa4+pPrcoXCqKEEELypj+YwjveBL6z4+zyy1zBxQ2vqw+peBgGWyOqmjZDoSp+wSWbX03EMBVn8U+7yqj8MhSGpAK4+RzlF47NYHbyFPzukwAgyoLLuXQ7Q3BopdhnF+cLmuXiBQHdzhB216iwxnD2uwSpRBi+0SNgvGNQqPVwbLwMOouj5EI4BVGSs1Qqhe985zt4/fXXIZPJEAgE0NTUhO9///toaWkp9vIIIUXQ42Rg10ix335m+SUW8sDrmi+4mGpgX3+paAou2Qjzoy931ajQZsx/+aUY19F4hscTw2F8tkUH/WnTruYKLoPwjR0Dx6ZhrmuD1dEBqVz8b3OPRzL47WQc39hqKZtpV29OJzASzuAbW86cdMSmE/CNHUVwen5qVdsOGGtaUVFRmic5UBAlOQsGg/jJT36C3t5eVFdXg+d53Hrrrbjlllvw3nvvFXt5hJACc0czeG0yhr/u+rj8kowG4XH1Ijo7BZXOjMZN+6E11RZ5pUv3tieBQSaN/921OuWXYlxHn3FFkGB53LF27u3ejwsufUgnoyVRcPmkQwMMzEoJrm0sn/Nde5whbLIo0GWdewHEsWkE3CcRmDyFigoJbM1dMNetQ6WktKNcaa+eFJXZbMYvf/lLVFfP7UWprKzEnj178MorrxR5ZYSQYnjYycAol+DaJu0nCi46URdcsunuZ9BhVmCLdXXuChb6Oipg7lD+axq0qFJJEJ2dgsfVOz+1yg5H++VQak2r8tyrxZ9g8cuxKO5pN0JeJtOujviT6Auk8OCuaggCj9nJAfjGj4PnMrDY18Pq2AiJrDyOp6IgSnIml8uxZcuWj/55cnISPT09+MpXvlLEVRFCiiGQZPHCWBRfaNNg1vUBgtOD8wWX7TDVrEFFZem9bXgskMSH/iT+8ZLVK78U+joazfDwJjjcXC9g7OhriIVmoNZb0dR1JTSG0im4nO7RwTDklRW4oVXce42Xo8fJoEUnQ0fFFIbeOwY2FYexphVVjZtEW+rLFQVRsmKTk5M4ePAgTpw4ga997Wt44IEHlvXxExMTiz5mJsLlujxCSAE86gxCSMewJfAuGKmAqsZOWOzrUSkRd8Elmx4ng0atDJfXrf4f/kJcR3lBAJPicI1iFvzAm2A1Bjg2Xg6dpb7k7lQviKQ5PDUSxk2temjLZNrVMJPC6+4Q7rFOYHpgGnqrA7bOfVCoy+fosNMVLYhWIwIuHkSiyC28ZIwFz7FIxkJISIufy8W0nqWuxaxX4r9efxVerw9f+tL/wr1/+SV8axkX0d07ty76mIylAYBQUl+XC3E9YlsLTKV5h6eU8DyHSfcgHj4SxX5dEPX1rbA2bIRUJv6CSzaucBqvT8Vx30XWgpRf7HY7PvjgA0xNTeG6666D1+vFT37ykyV/vMPhyPr/G3Rq7LzlTqRZDtdqZ1C3bieM1a0lG0AX/HwkggwP3LbM0ZdiFWd8+Jc3hqHNAHstPOytV0Otty7+gSWsaH8pviB9D0mnDCOS4r6CcacUSMWb4T7ZB5kiVdS1iGU9U1NTmJ6ewlSFEUH5Prz85CM4KoTOeMyGDRugVp89Eu5vvnwjBgcGcPKtp6FULm2U2ANf/fzia6ow4m//8RDcJ98o+vdJDN8jsa5HbGvpqr+pqGsoZ3MFl1F4R4/gyRk5OIkDX967HTXG8rhr8/AAA5tKgqsbcivs3H///fi7v/u7rI957733cPHFF5/x7+rq6vDd734XV155Jf7iL/4CGzduzOn5F6hVCvzB3otw4LIt+A/5Xihf+RWuveyqki+4AECaE/DoYBifadTCqirt/55kLASvqw8uzwzeCK7Dn3WasKZrR8m/UFiKon3n/pPdhn9YZ0OLvrh3RDMMC0UwDEf7ZWgxFP8HWQzrqVkfRzwex1BUwKNHBezYdCvWaM/8ZTCZTB/9glSetvdrZmYGt91zP37wgx/gql1XLen5NPbF74gOx4DK7x8WxfdJDN8jsa5HbGsh+ScIAmLB6Y8KLgpTPV4XGnD9Oh3sZRJCvXEWL45F8eVOc87ll3vvvRf33HNP1sdYrVZw3Ny2I4nk42OU1q1bBwA4efLkkoOo2+0+458FnkMi6EYi4IIgcBhRtCI2VgWTUl4WIRQAXhiLIJjicEcJT7vKJGPwjh0B43FBplDj94qLYDbIcVtH6Z0Hmqui/TR6oINEbYJKV9zWl5JNoVISh1JjLPpaxLIelc4CC4BYMAW5cwq19XVwmM5eS3d3N/x+P+69996P/p3v1DDGJn2oqm1c8hmBTUt4XDKYAlAhiu+TGL5HYl2P2NZC8isR9sPj6kUs5IHaUIXmrgN4dVaFYMaPu9YZi728vHlkkIFKWonPNed+FJBWq4VWu/jd1HNdR6enpwHM3R1dqvr6egBzLxRCnmH4RuemVlXVt6GqsRP/8V4Y7TYOR6XlEW54QcAhJ4P99Ro06EpvHzKbSc1PrXJCIpGhuvUiVJpb8PLLU7izTQ91mex3XYoL57+UrIr/+I//gN/vBwAkk0l861vfQkdHB7Zt21bklRFC8iUVD8N94ncY6X0ZbCaJho4r0LT5AJT6KhxyMthrV6OxBMPAuYTTHJ4eieCmVl3BwkA+rqOCICDsd2P4gxcw5fxvqPRWtF78GdS17YArIcFbMwncXcJ3Dj/ptYkYJmIs7s4y+lKMeC4D3/gxDL37LILTg7A6OrBm+/Ww2NfjSVcMAoBbymS/61KVx/15UhT79+/HBx98gAMHDkCr1SIajWLjxo148cUXIZefPY6MEFJaMqk4fGNHEZoZhlSugn3dJTBUt3z0luFvJ2IYj2bwre1VRV5p/jw5HAEnALeuKUzAycd1NM544Rn5cG5qlbEG9q27znhH6pCTQa1aigOOs/f1lyJBENDtZLDdpsSGc7xbJ0ZzU6uG4Bs7Co5Nw1S7FlUNHZDK57oUCZbHz4bCuL5JB6NCsshnKy8UREnOHA4H/vVf/7XYyyCE5BnHpuF3n8DsRD8qJBJUt2yFqa4NlZWnjYOcDwMXVymx0VwaYWAxSZbHY4MMrmvWwqwsTBhYyXU0GQ3CO9qHSGASSq0JjZ37oDHVnrG3cCqWwasTMdy7+eNpV6XuXW8SzlAaP96zOtOu8unjqVVHkE5GYLA1w9a4CXLVmds+nnNFEMnwuL3twrobClAQJYQQMo/nWMxOOeF3n4DAc7DUb4DF0Q6J9Ow7c+/7kjgZTOFHu8UfBpbq+dEowpmPR1+K1ZlTq7RZp1YdHghDL6vEwabSGde5mO7+ENYb5dhmE/cRYdHgNLyuPiQiAWjNdXC074FSaz7rcSwv4PBgGFc7tKjTlMcWl+WgIEoIIRc4QeAR8ox8VHAx1q5BVUNn1gku3f0M1hnl2FEt7jCwVBwv4PAAgyvrNbBrxRkG2ExyvuAyMDe1qnUbjLVrzrhTfbrZJIdnXRH80XoDlNLyqIScnE3hPV8Sf79z9aZdrVQiEoDX1YtocAYqnQVNm6+Exnj+M41fdccwE2dxV4ntd80XCqKEEHKBEgQBkcAEvK4+pOIM9FWNsDVthkKd/e3B/mAK73gT+M6OKtGGgeX61UQMU3EW/7TLVuylnIXnMghM9CMwcRKCIKCqoQNm+wZIFhkI87OhMCQVwM1lVH7pdobg0Eqxzy6+MZepRBi+0SNgvGNQqPVwtF8GnTX7MUyCIKDHGcKlNSqsMVyY3QoKooQQcgGKhTzwunrnCi6mGtjX71rykWuHnAzsGin228un/NLjZLCrRoU2o3j2u84VXAbhGzsGjk3DXNcGq6MDUvnid6HjGR5PDofx2RYd9PLyKL+MRzL47WQc39hqKci0q6Vi0wn4xo4hOD0IqVyFurYdMNa0oqJi8bvQb84kMBzO4Otbynt6UjYURAkh5AJyZsHFjMZN+6E11S754yeiGfx6Moa/6iqf8svbngQGmTTu7RLHftePCy59SCejMNqaUdW0GXLl0vd5PuOKIMbyuF3k+12X4+EBBiaFBNc25n6+az5xbAYB9wkEJk+hokICW3MXzHXrljUwoLs/hE0WBbqs4nkBVGgURAkh5AJwZsFFl7Xgks3DAwyMcgk+U1blFwYdZgW2Wou/3zUanIZnpBfJ6Cx0Fjsc7ZdDqTUt63NkOAGPDDK4pkGLanV5/Jn3J1i8MBbFPe3GnKdd5QvPcwhODcA3fhw8l4HFvh5Wx0ZIZMsLk0f8SfQFUnhwV3XZbHHJRXn8hBJCCDknNj1fcJmeL7is2Q5TzRpUVC6/vBJIsvjFaBR/ssEIhaQ8yi/HAkl86E/iHy8pbvklEQnMTa0KzkCtt6Kp60poDOcvuGTz0ngU3gRXVuWXRwfDkFdW4IbW4u13FQQBjNcF7+gRsKk4jDWtqGrclLXUl02Pk0GLXobdtao8r7S0UBAlhJAyxLEZzE6egt99EgBQ1dgJi309KiW5N8IfHwpDWgnc1CqOt0bzocfJoFErw+V1xSm/pOJheEf7EPaNQ6E2wLHxcugs9TmHYl4QcGiAwWW1arToy6P8EklzeGokjJta9dAWYfSlIAiIzk7C4+pFKsZAb3XA1rkPCnXuQX8knMYb03Hcf7FVVPtdi4GCKCGElBGe5xCaHoJv/LSCS0MHpLKVve0cy/B4cjiCG1r00JVJ+cUVTuP1qTjuu6jwYSCTisM3fgyh6aG5gsu6nTBWtyyp4JLNG1NxjEYyuO/i8im//HwkggwP3FaE9n+c8cHj+hBxxgeN0Ya6LVdBrV/5JLGefgY2lQRXOcpni0uuKIgSQkgZOLvg0oKqpk3LKrhk8/ORMFKcgM+vLZ+jgB4eYFCllODqhsKFAY5NI+A+OVdwqZTA1rwF5rq2ZRVczmdh2tUWqxKbLMXf75oPaU7Ao4NhXNuohVVVuMiSjIXgdfUhEpiAUmtCQ+deaE11edm+MRNn8bI7iq90miEr8n5XMaAgSgghJUwQBMSC0/C4epGMBqGz1MOx8QooNca8PcdCGPiDBg2qChgGVpM3zuLFsSi+3GkuSPnl44LLMQgcB3P9fMHlHFOrctXrT+L4bAr/cmlue0vF6IWxCIIpDne2FWa/ayYZg3fsKBjPCGQKNezrL4XB1pTX/cOPDDDQSCtxfXP5bHFZifK4ohBCyAUoEQnAM9KLWGiu4NLcdQBqQ/4PZH9xPIpAksNd6/IXbovtkUEGKmklPrfKYUAQBDCekbmCSzoBY80aVDVmn1qVq24ngzUGOXbVlEf5hRcEHHIy2GfXoEG3utOu2ExqfmqVExKJDNWtF8FUu/a8U6tyxaQ4POOK4I42A9RF2O8qRhRECSGkRI18+BIUGgMaOq6A1mxfldb3QhjYa1ejcZXDQKGE03Nh4NY1+lULA2cVXKoaYGvqWnRqVa4GQ2m8NZPAA9vKZ9rVaxMxTMRYfGfH6k274jkWgcl+BNwnIAgCrI4OWOoXn1qVqyeGwxAA3FJG065WioIoIYSUKPu6S2CoblnV4PH6ZBzj0Qy+tX3lBQ2xeHI4ApYHbl2zOm/3xhkvPK7e+YJLNexbLoFKv7rloR5nCLVqKQ44ymfaVbeTwXabEu3m/B/2Pje1ahi+saPg2BRMtWtR1dABqXz17iYnWB6PD4VxXZMOJkV5FP7ygYIoIYSUKGNN66p+GrY2rQAACitJREFU/oUwcHGVEhtXIQwUQ3IhDDRrYVbmNwx8suDS2LkPGlPtqt+hnIpl8OpEDF/bbIG0TKZdvetNwhlK48d78jvtShAEhP3j8Lr6kE5GYLA1w9a4CXLV6u/XfH40ikiGxx1tdDf0dBRECSGEnNP7viROBlP4193lU355fjQKJs3hjjyOvpybWnUUIe8I5EptzlOrcnV4IAy9rBLXldG0qx5nCOuNcmyz5a/9Hw1Ow+vqQyISgNZcB0f7Hii15rx9/mxYXsDDAwyucmhQpymPLS75QkGUEELIOfU4GbQZ5NhZXR7lF44XcHiAwZX1Gti1Kw8DbGZ+atXU/NSq1m0w1q7Je8Elm9kkh2ddEXxhvQFKaXmUX07OpvCuN4m/35mfaVeJ6Cy8I72IBqeh0lnQtPlKaIyFfXH1qjuGmTiLu9eVz4u6fKEgSggh5Cz9wRT+25PAd3aUT/nlVxMxTMVZ/NOulZVfeC6DwEQ/AhMnIQgCqho6YLavXsElm58NhSGpAG4u4ujLfOtxMnBopdhnX9nJAulEBN7RPjDeMSjUejjaL4PO6ij4z7MgCOhxhnBpjQprDOUx7SqfKIgSQgg5yyEnA7tGiv328im/HHIyuKRahTZjbvtd5wouQ/MFlzTMtfNTq+TFOTw+nuHx5HAYn23RwVAm5ZfxSAa/mYzhG1stOU+7YtMJ+MaOITg9CKlcibq2HTDWtK54alWu3pxJYDicwde3lM+0q3yiIEoIIeQME9EMfj0Zw191WSApk/LL254EBpg0/q1r+eWXj6dWHUE6GYHR1oyqps15m1qVq2dcEcRYHrfncb9rsT08wMCkkODaxuWXhzg2g4D7BAKT/aioqIStqQtm+7q8TK1aie7+EDZZFOiylkfhL98oiBJCCDnDwwMMjHIJPlNG5ZfufgYbTQpstS7v7uVcwaUXicgsdBY7HO2XQak1rdIqly7DCXhkkME1DVpUq8vjT7k/weKFsSj+Z7txWdOuFqZW+cePg+MysNjnp1bJih/8jviT6Auk8OCu6rLZ4pJv5fHTSwghJC8CSRa/GI3iTzYYoZCUR/nlWCCJD/1J/OMlSy+/JCIBeFy9iAXnplYVo+CSzUvjUXgTHO5aVz53Qx8dDENeWYEbl7jfVRAEMF7X3NSqVBzGmlZUNW5alalVuepxMmjRy7C7tjwKf6uBgighhJCPPD4UhrQSuLG1fOZg9zgZNGpluLxu8YCSiofhHT2CsG8MCrUBjo2XQ2epF9XdLF4QcGiAwWW1arToy6P8EklzeGokjBtb9NAuMu1qYWqV19WHZCwEvdUBW8c+KDTiCuUj4TTemI7jby+25rzf9UJAQZQQQggAIJbh8eRwBDe06KGXl0f5xRVO4/WpOO67KHsYmCu4HEVweghSuQp163bCWN1StIJLNr+fjmM0ksF9F5dP+eXnIxFkeODza7PfDY0zvvmpVV5ojDY0b7kKar04p34dcjKwqSS42lE+W1xWAwVRQgghAICfj4SRZHncVkZzsB8eYFCllODqhnOHAY5NI+A+icDkKVRUSmBr7oK5rvgFl/MRBAHd/Qy2WJXYZClOWz/f0pyARwfDuLZRC6vq3F/3M6dWGdHQuRdaU52o7lSfbibO4qXxKL7SaYZsGftdL0Ti/E0jhBBSUAth4NONWtjKpPzijbN4cSyKL3eazyq/LBRcfOPHIXAszPXzBRepuN/q7vUncWw2hR9cKp79qiv1wlgEwRSHO9vOfms9k4zBO3YUjGcEMoUa9vW7YLA1izaALnh0kIFGWonrm8tni8tqKY+rDSk6nuexc+dOeL1ejI6OFns5hJBlenE8ikCSw13rjMVeSt48MshAJa3E504LA4IggPGMwDt2dL7gsgZVjZ2iKLgs5Tra7WTQqpfh0pryKL/w8+e77rNr0KD7eCAAl0nB5z6B2cl+SCQyVLdeBFPt2oJOrcoVk+Lw9EgEd7QZoF5kvyuhIEry5KGHHsLg4CAMBnFtFieELG4hDOy1q9GoK4852OE0h2dcEdy6Rg+1rPKjgovH1YtUjJkruHTuh0Itnm0Ii11HB0NpvDWTwAPbymfa1WsTMUzEWHxnx9y0K55jEZjsR8B9AoIgwOrogKW+OFOrcvXEcBgCgFvKaIvLaqKoTlZscnISP/3pT/HFL36x2EshhOTg9ck4xqMZ3F1Gd0OfGo6A5YFb1xgQZ7wYPfIqxo+/DqlMiZYtV8Ox8XJRhdClXEd7nCHUqKU44CifaVc9TgbbbUpsMMowOzWIwXefg2/sKAy2Zqzdfh1sTZtKKoQmWB6PD4VxXZMOpjKZdrXa6I4oWbE///M/x3e/+1288847xV4KIWSZBEFAt5PBxVVKbDQX/wDwfEhxPB4bCuOaOimiQ7/HdGACSq0JjZ37oDHVivJu4mLX0alYBq9OxPC1zRZIy2Ta1bveJPpDafxDh4Ch93+BdCICg60JtqbNkKtKc2/l86NRRDI87mgTz4scsaMgSlbkF7/4BaRSKa655pqcg+jExMSij5mJcDl9bkJIdu/7kjgZTOFfd5dP+eXpgQB8DINL1SeRqlSgfsNu6KsaRRlAgaVdRw8PhKGTVeLgeaZdLeU6Kjb/7+g06vkAbDNOyC11cLTvgVJrLvaycsbyAh4eYHCVQ4M6Tencxc3GH0/Dql7dAl/RgijPsUjGQkhIi5uFkzFWNGsR23oWW0s8HscPH/wefvrT/4dEJACNohJ1NhMSkcCynmf3zq2LPiZjaQAglMTX5UJej9jWAlP5hKvV0uNk0GaQY2d16Zdf2EwKnrHj+PcPMtihSqNrfReMtWtEXXCJRqP45je/iVdfffW8jwmmODw3GsHd6wxQSc+9o87hcCzp+TZs2JDTOvMpEZ3Fm8eP4a0JDf66KYrmrk9BY6wp9rJW7FV3DDNxFne1lf51RxAEhH2j+NG7o7j/2r2r+lwVgiCs6hOQ0lNRUXE/gL9d5GHbANwOYEgQhIdO+7g/FAShaZnPt9QfwrcEQbh0OZ+bEEKKga6jhCwNBVFyloqKCi2AxUZB+AF8AIABwM//uyYANQD+G3MX1j9Z4vPVL+VxgiCU3ntPhJALEl1HCVkaCqIkb3J9JU8IIWQOXUfJhYaObyKEEEIIIUVBQZSsWEVFRU1FRcXrAP4QQE1FRcXrFRUVf1jURRFCSAmh6yi5UNFb84QQQgghpCjojighhBBCCCkKCqKEEEIIIaQoKIgSQgghhJCioCBKCCGEEEKKgoIoIYQQQggpCgqihBBCCCGkKCiIEkIIIYSQoqAgSgghhBBCioKCKCGEEEIIKQoKooQQQgghpCgoiBJCCCGEkKKgIEoIIYQQQoqCgighhBBCCCkKCqKEEEIIIaQoKIgSQgghhJCioCBKCCGEEEKKgoIoIYQQQggpCgqihBBCCCGkKCiIEkIIIYSQoqAgSgghhBBCioKCKCGEEEIIKQoKooQQQgghpCj+fwUrCWUimPSHAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(R @ S @ R.transpose())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have some explaining to do. Let's visualize the transformation $R^T$, adding to our plot the unit vectors that were aligned with the eigenvectors, $\\mathbf{v}_1$ and $\\mathbf{v}_2$. You see that they land on the coordinate axes after the transformation." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "v2 = A_inv.dot(u2)\n", "plot_linear_transformation(R.transpose(), v1, v2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's visualize applying the scaling transformation to these vectors, and applying the rotation matrix $R$ after that." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "e1 = R.transpose().dot(v1)\n", "e2 = R.transpose().dot(v2)\n", "\n", "plot_linear_transformation(S, e1, e2)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(R, S.dot(e1), S.dot(e2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Satisfied? The vectors $\\mathbf{v}_1$ and $\\mathbf{v}_2$ are first rotated to land on the axes, are then scaled, and are finally rotated back to their original direction. This has the same effect as the transformation $A$. In other words:\n", "\n", "\n", "$$ A = R\\, S\\, R^T \n", "$$\n", "\n", "The equivalence above shows an **eigendecomposition** of the matrix $A$. \n", "The scaling matrix $S$ has the *eigenvalues* along the diagonal, and the rotation matrix $R$ has the *eigenvectors* as columns. Let's check:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.70710678 0.70710678]\n", "[0.70710678 0.70710678]\n" ] } ], "source": [ "print(R[:,0])\n", "print(v1)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-0.70710678 0.70710678]\n", "[-0.70710678 0.70710678]\n" ] } ], "source": [ "print(R[:,1])\n", "print(v2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Symmetric matrices, orthogonal eigenvectors\n", "\n", "In our example, we figured out that the matrix that undoes the effect of the positive rotation $R$ is its transpose, $R^T$. But in general, the matrix that has the effect of undoing a transformation is the _inverse_ of this matrix. In fact, $R$ is special, because\n", "\n", "$$ R^T = R^{-1} $$\n", "\n", "##### Definition:\n", "\n", "> A matrix $R$ whose transpose is equal to its inverse is called **orthogonal**.\n", "\n", "The columns of an orthogonal matrix are orthogonal vectors of unit length (a.k.a., _orthonormal_). For our example, it means that the _eigenvectors of $A$ are orthogonal_.\n", "This always happens with _symmetric matrices_. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.70710678 0.70710678]\n", " [-0.70710678 0.70710678]]\n" ] } ], "source": [ "print(R.transpose())" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.70710678 0.70710678]\n", " [-0.70710678 0.70710678]]\n" ] } ], "source": [ "print(numpy.linalg.inv(R))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can check visually that $R^T$ is equal to $R^{-1}$—but if we try a logical expression, it will give `False` because of floating-point errors. To check for the symmetry of $A$, we can use a logical operation:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ True, True],\n", " [ True, True]])" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A == A.transpose()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And to confirm that the two eigenvectors are orthogonal, we take the dot product, which is zero for perpendicular vectors:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v1.dot(v2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Key idea:\n", "\n", "> A _symmetric_ matrix, $\\,A = A^T$, has _orthogonal_ eigenvectors, and can be decomposed as $A = R\\, S\\, R^T$, where $R$ has the eigenvectors as columns and $S$ is the diagonal matrix of eigenvalues." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Eigendecomposition in general\n", "\n", "Up to this point, we've been playing with a symmetric matrix. The geometric insight we developed showed us that the eigenvectors landed onto the semi-major and semi-minor axis of the ellipse coming from the unit circle. But most matrices are not symmetric!\n", "Let's work the general case. The eigenvectors of $A$ get scaled after the transformation, i.e., land on their span:\n", "\n", "$$\n", "\\begin{align*}\n", " A \\mathbf{v_1} = s_1 \\mathbf{v_1} \\\\\n", " A \\mathbf{v_2} = s_2 \\mathbf{v_2}\n", "\\end{align*}\n", "$$\n", "\n", "The two left-hand sides are matrix-vector multiplications, each giving a vector as result. The two right-hand sides are scalings of a column vector (also resulting in vectors). We would like to combine the two equations together into a matrix equation, leading to the eigendecomposition of $A$.\n", "\n", "Our first idea is this: matrix-matrix multiplication is the same as applying a transformation via the matrix on the left, to the columns of the matrix on the right. So if we make a matrix with the two eigenvectors as columns, and multiply it with $A$:\n", "\n", "$$ A \\begin{bmatrix}\n", " \\mathbf{v_1} & \\mathbf{v_2}\n", " \\end{bmatrix}\n", " = \\begin{bmatrix}\n", " A\\mathbf{v_1} & A\\mathbf{v_2}\n", " \\end{bmatrix}\n", "$$\n", "\n", "We can now re-write the eigenvector equations into one matrix equation by matching columns:\n", "\n", "$$ A \\begin{bmatrix}\n", " \\mathbf{v_1} & \\mathbf{v_2}\n", " \\end{bmatrix}\n", " = \\begin{bmatrix}\n", " s_1\\mathbf{v_1} & s_2\\mathbf{v_2}\n", " \\end{bmatrix}\n", "$$\n", "\n", "Using $C$ to denote the matrix of eigenvectors, the left-hand side of this matrix equation is $A\\, C$. We can express the right-hand side of the combined eigenvector equations also using $C$, by working with each column:\n", "\n", "$$ s_1 \\mathbf{v_1} = \\begin{bmatrix}\n", " \\mathbf{v_1} & \\mathbf{v_2} \\end{bmatrix} \\,\n", " \\begin{bmatrix}\n", " s_1 \\\\\n", " 0 \n", " \\end{bmatrix} \n", "$$\n", "\n", "$$ s_2 \\mathbf{v_2} = \\begin{bmatrix}\n", " \\mathbf{v_1} & \\mathbf{v_2} \\end{bmatrix} \\,\n", " \\begin{bmatrix}\n", " 0 \\\\\n", " s_2 \n", " \\end{bmatrix} \n", "$$\n", "\n", "Matchng the columns, and applying our first idea for matrix-matrix multiplication: \n", "\n", "$$ \\begin{bmatrix}\n", " s_1\\mathbf{v_1} & s_2\\mathbf{v_2}\n", " \\end{bmatrix}\n", " = C\\, \n", " \\begin{bmatrix}\n", " s_1 & 0 \\\\\n", " 0 & s_2\n", " \\end{bmatrix} \n", "$$\n", "\n", "Using $D$ to denote the diagonal matrix of eigenvalues, this all comes together as:\n", "\n", "$$\n", " A\\, C = C\\, D\n", "$$\n", "\n", "If we right-multiply by $C^{-1}$ on both sides:\n", "\n", "$$\n", " A = C\\, D\\, C^{-1}\n", "$$\n", "\n", "A matrix that can be decomposed in this way is called **diagonalizable**.\n", "Multiplying on the right by $C$ and on the left by $C^{-1}$:\n", "\n", "$$\n", " C^{-1} A\\, C = D\n", "$$\n", "\n", "\n", "If you go back to the previous lesson, you will find an expression that looks like this for applying a known transformation to a vector in a new basis. Review that section if you need to.\n", "\n", "Applying the transformation $A$ to a vector in standard basis, $\\mathbf{x}$, is:\n", "\n", "$$\n", " A\\, \\mathbf{x} = C\\, D\\, C^{-1}\\mathbf{x}\n", "$$\n", "\n", "Viewing $C$ as a change of basis, the expression on the right means we change $\\mathbf{x}$ to a new basis of eigenvectors, apply a scaling by the eigenvalues in the new coordinate system, and change back to the standard basis. The effect is the same as the transformation $A$: the matrices $A$ and $D$ are called **similar**.\n", "\n", "##### Key idea:\n", "\n", "> Similar matrices have the same effect, via a change of basis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's visualize the eigendecomposition of a non-symmetric matrix $A = \\begin{bmatrix} 1 & 0 \\\\ 1 & 3 \\end{bmatrix}$. The red unit circle below represents a bunch of vectors of different angles whose tails sit at the origin and whose heads land on the circle. Each point on this circle corresponds to some vector $\\mathbf{x}$. The second subplot shows the change from the standard basis $\\mathbf{i}$ and $\\mathbf{j}$ to the new basis $\\mathbf{a}$ and $\\mathbf{b}$. Notice that the red circle representing $\\mathbf{x}$ does not change, however, the vector $\\mathbf{x}$'s new coordinates are now $C^{-1}\\mathbf{x}$. The third subplot demonstrates the stretching effect coming from the diagonal matrix $D$ in the new basis. The transformed vector's coordinates are $DC^{-1}\\mathbf{x}$ in the new basis. Finally, we change back to the standard basis by multiplying $C$ as shown in the subplot 4." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A = numpy.array([[1,0], [1,3]])\n", "plot_eigen(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Challenge:\n", "> What is the relation between the new basis $\\mathbf{a}$, $\\mathbf{b}$ and the matrix of eigenvectors $C$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compute eigenthings in Python\n", "\n", "You can compute the eigenvalues and eigenvectors of a matrix using [`numpy.linalg.eig()`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html). It returns a tuple: its first element is an array with the eigenvalues, and its second element is a 2D array where each column is an eigenvector." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3., 1.])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.eig(A)[0]" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0.89442719],\n", " [ 1. , -0.4472136 ]])" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.eig(A)[1]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.0 [0. 1.]\n", "1.0 [ 0.89442719 -0.4472136 ]\n" ] } ], "source": [ "# display each eigenvalue with the corresponding eigenvector, side by side\n", "eigenvalues, eigenvectors = numpy.linalg.eig(A)\n", "\n", "for eigenvalue, eigenvector in zip(eigenvalues, eigenvectors.T):\n", " print(eigenvalue, eigenvector)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the `for` statement above, each iteration picks an eigenvalue, and the corresponding eigenvector. Note that when iterating over a 2D array, the natural order advances over the first dimension: the rows; to get the columns, we apply the transpose of the `eigenvectors` matrix. Here, we used the [`numpy.ndarray.T`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.T.html), which has the same effect as `.transpose`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To create the diagonal matrix of eigenvalues, use [`numpy.diag()`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.diag.html): if you give it a 1D array, it returns a 2D array with the elements of the input array in the diagonal. \n", "\n", "The eigendecomposition is shown below: " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0.]\n", " [1. 3.]]\n" ] } ], "source": [ "C = eigenvectors\n", "A_decomp = C @ numpy.diag(eigenvalues) @ numpy.linalg.inv(C)\n", "print(A_decomp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way to compute all the eigenthings is to use **SymPy**: the Python library for symbolic computations (a.k.a., computer algebra system). SymPy has a [`Matrix`](https://docs.sympy.org/latest/tutorial/matrices.html) data type with many advanced methods. \n", "\n", "You will create a `Matrix` from a list of row vectors, and then use the `diagonalize()` method to obtain the matrix of eigenvectors, and the diagonal matrix of eigenvalues. \n", "SymPy can display beautiful symbolic mathematics. Check it out." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "import sympy\n", "\n", "sympy.init_printing(use_latex = 'mathjax') #configures the display of mathematics" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}2 & 1\\\\1 & 2\\end{matrix}\\right]$$" ], "text/plain": [ "⎡2 1⎤\n", "⎢ ⎥\n", "⎣1 2⎦" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sympy.Matrix([[2,1], [1,2]])\n", "A" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A == A.transpose()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}1 & 0\\\\0 & 3\\end{matrix}\\right]$$" ], "text/plain": [ "⎡1 0⎤\n", "⎢ ⎥\n", "⎣0 3⎦" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C, D = A.diagonalize()\n", "D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With SymPy, you can also get just the eigenvalues using the [`eigenvals()`](https://docs.sympy.org/latest/tutorial/matrices.html#eigenvalues-eigenvectors-and-diagonalization) method. Its output will be in the form $\\{s_1:m_1, s_2:m_2\\}$, where $s_1$, $s_2$ are the eigenvalues of the matrix, and $m_1$, $m_2$ are the _multiplicities_. A matrix can have (multiply) repeated eigenvalues sometimes. In the case of our matrix $A$, both eigenvalues are unique (i.e., have multiplicity $1$)." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left \\{ 1 : 1, \\quad 3 : 1\\right \\}$$" ], "text/plain": [ "{1: 1, 3: 1}" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.eigenvals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But think of the identity matrix: it has $1$ along the diagonal, and the two eigenvalues are the same, $1$. We can create an identity matrix in SymPy using `eye(n)`, with `n` indicating the dimension." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left \\{ 1 : 2\\right \\}$$" ], "text/plain": [ "{1: 2}" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.eye(2).eigenvals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we try with the _shear_ matrix from our first lesson, we see that it also has a repeated $1$ eigenvalue." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}1 & 1\\\\0 & 1\\end{matrix}\\right]$$" ], "text/plain": [ "⎡1 1⎤\n", "⎢ ⎥\n", "⎣0 1⎦" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "shear = sympy.Matrix([[1,1], [0,1]])\n", "shear" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left \\{ 1 : 2\\right \\}$$" ], "text/plain": [ "{1: 2}" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "shear.eigenvals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's have a look back at the equation for the eigenvectors—on which the effect of a matrix $A$ is just to scale them—and rearrange things a bit:\n", "\n", "$$ \\begin{align*}\n", " A\\, \\mathbf{v} &= s\\, \\mathbf{v}\\\\\n", " A\\, \\mathbf{v} - s\\, \\mathbf{v} &= \\mathbf{0} \\\\\n", " (A - s\\, I) \\mathbf{v} &= \\mathbf{0}\n", "\\end{align*}\n", "$$\n", "\n", "The last form represents a homogeneous linear system, whose solutions are the _nullspace_ of $(A-s\\,I)$, as we saw in our second lesson. We can compute the nullspace using SymPy; let's try it with the shear matrix:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left [ \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right]\\right ]$$" ], "text/plain": [ "⎡⎡1⎤⎤\n", "⎢⎢ ⎥⎥\n", "⎣⎣0⎦⎦" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(shear - sympy.eye(2)).nullspace()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [`nullspace()`](https://docs.sympy.org/latest/tutorial/matrices.html#nullspace) method of SymPy matrices returns a list of column vectors that span the nullspace of the matrix. In the case of the shear matrix, only one column vector is returned, which means its nullspace is a line.\n", "\n", "The shear matrix has one repeated eigenvalue, and a single eigenvector: we cannot build a change of basis with its eigenvectors, which means it's _not diagonalizable_.\n", "\n", "If you tried to use `diagonalize()` on the shear matrix, you would get an error message:\n", "```Pyhon\n", "MatrixError: Matrix is not diagonalizable\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Applications\n", "\n", "### Eigenvalues in ecology\n", "\n", "A neat application of linear algebra is _matrix population models_, used broadly in ecology and demographics. One type of model considers the age distribution of fertility and survival in an animal or plant population. For example, an insect population may have different probability of survival depending on the stage of development, and only be able to reproduce in an adult stage.\n", "\n", "Here's an example, from [$\\S$5.6](https://textbooks.math.gatech.edu/ila/stochastic-matrices.html) of the open book _\"Interactive Linear Algebra\"_ [1]. \n", "We take three age groups in a population of rabbits. Of the newborn rabbits, 50% survive their first year. The survival of the second age group is also 50%, and the third age group all dies off at the end of the year. The annual fertility of each age group is 0, 6, and 8 rabbits, respectively.\n", "\n", "A population vector $\\mathbf{p}=(p_1, p_2, p_3)$ contains the abundance of rabbits in each age group. We can use the fertility and survival of each age group to predict the abundance of each group after one year:\n", "\n", "$$\\begin{align*}\n", " p_1^{n+1} &=& 0\\,p_1^n + 6\\,p_2^n + 8\\,p_3^n \\\\\n", " p_2^{n+1} &=& 0.5\\,p_1^n + 0\\,p_2^n + 0\\,p_3^n \\\\\n", " p_3^{n+1} &=& 0\\,p_1^n + 0.5\\,p_2^n + 0\\,p_3^n\n", "\\end{align*}\n", "$$\n", "\n", "The superscript $n$ refers to the year. The coefficient matrix of this system of equations is:\n", "\n", "$$ L = \\begin{bmatrix} 0 & 6 & 8 \\\\\n", " 0.5 & 0 & 0 \\\\\n", " 0 & 0.5 & 0 \\end{bmatrix}\n", "$$\n", "\n", "This matrix represents the _age transition_ year on year. Multiply this matrix by the population vector to get the age-structured population on the next year. Let's write a bit of code to see the population in each age group grow over 10 years. " ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0. , 6. , 8. ],\n", " [0.5, 0. , 0. ],\n", " [0. , 0.5, 0. ]])" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L = numpy.array([[0,6,8], [0.5,0,0], [0,0.5,0]])\n", "L" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "p = numpy.array([25, 10, 5]) # initial age-structured population" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "N = 10\n", "pn = numpy.zeros((N, len(p)))\n", "pn[0,:] = p.copy()\n", "for i in range(1,N):\n", " pn[i,:] = L.dot(pn[i-1,:])" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.figure(figsize=(4,1))\n", "pyplot.plot(pn[:,0],)\n", "pyplot.plot(pn[:,1],)\n", "pyplot.plot(pn[:,2],)\n", "pyplot.xlabel('Years')\n", "pyplot.title('Population in each age group');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nothing to see here: the population in each age group grows over time. But one question ecologists may need to answer is whether the species reaches a stable growth pattern, and what is the _stable age distribution_. That occurs if the percentage in each age group remains the same, i.e., $\\mathbf{p}^{n+1}$ is a multiple of $\\mathbf{p}^n$:\n", "\n", "$$ \\mathbf{p}^{n+1} = L\\, \\mathbf{p}^n = r\\, \\mathbf{p}^n $$\n", "\n", "We have on the right an eigenvalue problem, and the stable age distribution is an eigenvector of the age transition matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A classic example in this field is the hypothetical beetle population of Bernadelli [2], also separated in three age groups, and with age transition matrix:\n", "\n", "$$ T = \\begin{bmatrix} 0 & 0 & 6 \\\\\n", " 1/2 & 0 & 0 \\\\\n", " 0 & 1/3 & 0 \\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "T = numpy.array([[0,0,6], [0.5,0,0], [0,1/3,0]])" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = numpy.array([25, 10, 5])\n", "N = 24\n", "pn = numpy.zeros((N, len(p)))\n", "pn[0,:] = p.copy()\n", "for i in range(1,N):\n", " pn[i,:] = T.dot(pn[i-1,:])\n", " \n", "pyplot.figure(figsize=(4,1))\n", "pyplot.plot(pn[:,0],)\n", "pyplot.plot(pn[:,1],)\n", "pyplot.plot(pn[:,2],)\n", "pyplot.xlabel('Years')\n", "pyplot.title('Population in each age group');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, the initial population distribution repeats every few years! If we look at the eigenvectors for the matrix, in this case ... gadzooks! They are complex numbers.\n", "In Python, complex numbers are represented as the sum of a real part and an imaginary part, using the symbol `j` for the imaginary unit corresponding to $\\sqrt{-1}$." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.5+0.8660254j, -0.5-0.8660254j, 1. +0.j ])" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.eig(T)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Markov chains\n", "\n", "Population models are one example of _discrete dynamical systems_, where eigenvalues and eigenvectors play a central role. Another example are _Markov chains_, of broad application in economics, genetics, game theory, and more.\n", "\n", "This example is from Ref. [1]. A movie rental company has three offices in a city. You can rent movies from one office, and return them the next day in any office. Suppose the 3D vector $\\mathbf{x}$ represents the percentage of the stock of \"The Matrix\" in each office. \n", "\n", "From historical data, one could build a matrix $P$ with the probabilities that a customer rented \"The Matrix\" from office $j$ and returns it at office $i$ the next day. Say, \n", "\n", "$$ P = \\begin{bmatrix} 0.3 & 0.4 & 0.5 \\\\\n", " 0.3 & 0.4 & 0.3 \\\\\n", " 0.4 & 0.2 & 0.2 \\end{bmatrix}\n", "$$\n", "\n", "A customer must return the movie in one of the three offices, so the probabilities for the three offices have to add up to $1$.\n", "If $\\mathbf{x}_k$ is the movie-stock distribution on a given day, then $P\\,\\mathbf{x}_k$ is the per-office distribution on the next day:\n", "\n", "$$ \\mathbf{x}_{k+1} = P\\,\\mathbf{x}_k $$\n", "\n", "##### Definition:\n", "\n", "> A **probability vector** has non-negative components that add to $1$. A **stochastic matrix** is a square matrix whose columns are probability vectors.\n", "\n", "> A **Markov chain** is a sequence of probability vectors $ \\mathbf{x}_{k+1} = P\\,\\mathbf{x}_k $, where $P$ is a stochastic matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's play with with the stochastic matrix $P$. We can visually see that each column adds up to $1$, so no need to compute that. But let's get the eigenvalues and eigenvectors using SymPy." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "P = sympy.Matrix([[0.3,0.4,0.5], [0.3,0.4,0.3],[0.4,0.2,0.2]])" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left \\{ - \\frac{1}{5} : 1, \\quad \\frac{1}{10} : 1, \\quad 1 : 1\\right \\}$$" ], "text/plain": [ "{-1/5: 1, 1/10: 1, 1: 1}" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P.eigenvals()" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left [ \\left ( -0.2, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}-1.0\\\\0\\\\1.0\\end{matrix}\\right]\\right ]\\right ), \\quad \\left ( 0.1, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}0.5\\\\-1.5\\\\1.0\\end{matrix}\\right]\\right ]\\right ), \\quad \\left ( 1.0, \\quad 1, \\quad \\left [ \\left[\\begin{matrix}1.4\\\\1.2\\\\1.0\\end{matrix}\\right]\\right ]\\right )\\right ]$$" ], "text/plain": [ "⎡⎛ ⎡⎡-1.0⎤⎤⎞ ⎛ ⎡⎡0.5 ⎤⎤⎞ ⎛ ⎡⎡1.4⎤⎤⎞⎤\n", "⎢⎜ ⎢⎢ ⎥⎥⎟ ⎜ ⎢⎢ ⎥⎥⎟ ⎜ ⎢⎢ ⎥⎥⎟⎥\n", "⎢⎜-0.2, 1, ⎢⎢ 0 ⎥⎥⎟, ⎜0.1, 1, ⎢⎢-1.5⎥⎥⎟, ⎜1.0, 1, ⎢⎢1.2⎥⎥⎟⎥\n", "⎢⎜ ⎢⎢ ⎥⎥⎟ ⎜ ⎢⎢ ⎥⎥⎟ ⎜ ⎢⎢ ⎥⎥⎟⎥\n", "⎣⎝ ⎣⎣1.0 ⎦⎦⎠ ⎝ ⎣⎣1.0 ⎦⎦⎠ ⎝ ⎣⎣1.0⎦⎦⎠⎦" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P.eigenvects()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the largest eigenvalue is $1$. This is true for _all_ stochastic matrices, in fact: they have $1$ as eigenvalue and all other eigenvalues are smaller in absolute value.\n", "\n", "##### Key idea:\n", "\n", "> Stochastic matrices have $1$ as the dominant eigenvalue: if $s_k$ are the eigenvalues, $|s_k|\\leq 1$.\n", "\n", "Think about it: multiplying a matrix by the vector of ones $(1, 1, 1)$ adds up the rows (linear combination of the columns, each multiplied by $1$). For a stochastic matrix $P$, the rows of the transpose $P^T$ add up to $1$, so: $P^T \\mathbf{1} = \\mathbf{1}$, which means $1$ is an eigenvalue of $P^T$ and $P$ (a matrix and its transpose have the same eigenvalues)." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}1.0\\\\1.0\\\\1.0\\end{matrix}\\right]$$" ], "text/plain": [ "⎡1.0⎤\n", "⎢ ⎥\n", "⎢1.0⎥\n", "⎢ ⎥\n", "⎣1.0⎦" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "one_vector = sympy.Matrix([1,1,1])\n", "\n", "P.transpose()@one_vector" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P.eigenvals() == P.transpose().eigenvals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see what happens to the vector $\\mathbf{x}$, representing the percentages of the movie stock in each office, after several days." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "P2 = numpy.array(P)\n", "x = numpy.array([0.1, 0.4, 0.5])\n", "N = 10\n", "xn = numpy.zeros((N, len(p)))\n", "xn[0,:] = x.copy()\n", "for i in range(1,N):\n", " xn[i,:] = P2.dot(xn[i-1,:])\n", " \n", "pyplot.figure(figsize=(4,1))\n", "pyplot.plot(xn[:,0],)\n", "pyplot.plot(xn[:,1],)\n", "pyplot.plot(xn[:,2],)\n", "pyplot.xlabel('days')\n", "pyplot.title('Percentage of stock at each office');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can try it with different initial distributions of the movie stock, and you will see that the long-term distribution is always the same: the long-term behavior of a Markov chain is a **steady state**. This steady state is aligned with the eigenvector corresponding to eigenvalue $1$. Let's check:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}0.667424016931347\\\\0.572077528097156\\\\0.476731038919718\\end{matrix}\\right]$$" ], "text/plain": [ "⎡0.667424016931347⎤\n", "⎢ ⎥\n", "⎢0.572077528097156⎥\n", "⎢ ⎥\n", "⎣0.476731038919718⎦" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "steady = sympy.Matrix(xn[-1,:])\n", "steady.normalized()" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}0.667423812471915\\\\0.572077553547355\\\\0.476731294622796\\end{matrix}\\right]$$" ], "text/plain": [ "⎡0.667423812471915⎤\n", "⎢ ⎥\n", "⎢0.572077553547355⎥\n", "⎢ ⎥\n", "⎣0.476731294622796⎦" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "evec = sympy.Matrix(P.eigenvects()[2][2])\n", "evec.normalized()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The normalized steady-state vector and eigenvector corresponding to the $1$ eigenvalue are the same, up to a small difference that will diminish if we add more steps to the chain.\n", "\n", "How can we explain this? First, remember that $ \\mathbf{x}_{k+1} = P\\,\\mathbf{x}_k $. So, $ \\mathbf{x}_2 = P\\, \\mathbf{x}_1 = P^2 \\mathbf{x}_0 $. In general,\n", "\n", "$$ \\mathbf{x}_{k} = P^{k}\\,\\mathbf{x}_0 $$\n", "\n", "Second, the eigenvectors form a basis, so we can write any vector as a linear combination of them. Let's call them $\\mathbf{e}_1$, $\\mathbf{e}_2$, $\\mathbf{e}_3$:\n", "$$ \\mathbf{x}_0 = c_1 \\mathbf{e}_1 + c_2 \\mathbf{e}_2 + c_3 \\mathbf{e}_3 $$\n", "\n", "Multiply by the matrix $P$ on both sides, and on the right side use the definition of eigenvectors that $P \\mathbf{e}_i = s_i \\mathbf{e}_i$ (where $s_i$ are the eigenvalues):\n", "\n", "$$ P\\, \\mathbf{x}_0 = c_1 s_1\\mathbf{e}_1 + c_2 s_2\\mathbf{e}_2 + c_3 s_3\\mathbf{e}_3 $$\n", "\n", "If you multiply $k$ times by $P$, you get:\n", "\n", "$$ P^{\\,k}\\, \\mathbf{x}_0 = c_1 s_1^k\\mathbf{e}_1 + c_2 s_2^k\\mathbf{e}_2 + c_3 s_3^3\\mathbf{e}_3 $$\n", "\n", "The only term in the linear combination that survives long-term is the one aligned with the eigenvector corresponding to eigenvalue $1$. The powers of other eigenvalues for which $|s_i|<1$ all tend to zero as $k$ increases.\n", "\n", "##### Key idea:\n", "\n", "> A **steady state** of a Markov chain is an eigenvector of the stochastic matrix, corresponding to eigenvalue $1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Perron-Frobenius Theorem\n", "\n", "> A _positive stochastic matrix_ (all positive entries) has a unique steady state vector to which all initial states converge.\n", "\n", "Here's another way to look at it (see $\\S$6.6 of Ref. [1] for more discussion). The eigendecomposition of $P$ is formed with the two matrices returned by `diagonalize()`: " ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left ( \\left[\\begin{matrix}-1.0 & 1.0 & 7.0\\\\0 & -3.0 & 6.0\\\\1.0 & 2.0 & 5.0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}-0.2 & 0 & 0\\\\0 & 0.1 & 0\\\\0 & 0 & 1.0\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡-1.0 1.0 7.0⎤ ⎡-0.2 0 0 ⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎜⎢ 0 -3.0 6.0⎥, ⎢ 0 0.1 0 ⎥⎟\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎝⎣1.0 2.0 5.0⎦ ⎣ 0 0 1.0⎦⎠" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P.diagonalize()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The matrix $P$ is _similar_ (has the same effect via a change of basis) to a scaling matrix which, when repeatedly applied, shrinks al components _not_ parallel to the eigenvector corresponding to eigenvalue $1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Google's PageRank algorithm\n", "\n", "Web search today uses a variety of technologies, but the original algorithm that rocketed Google to the top of search engines is the _PageRank_ algorithm. Google's own description was:\n", "\n", "> PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. The underlying assumption is that more important websites are likely to receive more links from other websites.\n", "\n", "(Cited in the Wikipedia entry for [PageRank](https://en.wikipedia.org/wiki/PageRank), from an archived Google web page.)\n", "\n", "A web page's rank of importance is computed from the number of links to it, and the importance of the pages that link to it. The rule is that a page linking to $n$ other pages passes to them $1/n$ of its importance. A page's rank is the sum of all the importance it gets from other pages linking to it.\n", "\n", "For a network of $n$ web pages, you form a matrix whose $i,j$ entry is the importance page $j$ passes to $i$.\n", "Here's an example from Ref. [1]. We have a network with four web pages, connected by links as shown in the figure below.\n", "\n", "\n", "\n", "#### Example network of four web pages, from Ref. [1], $\\S$6.6.\n", "\n", "* Page A has 3 links: it passes $1/3$ of its rank to $B, C, D$\n", "* Page B has 2 links: it passes $1/2$ of its rank to $C, D$\n", "* Page C has 0 links\n", "* Page D has 2 links: it passes $1/2$ of its rank o $A,C$\n", "\n", "The importance matrix is:\n", "$$A = \\begin{bmatrix} 0 & 0 & 0 & 1/2 \\\\\n", " 1/3 & 0 & 0 & 0 \\\\\n", " 1/3 & 1/2 & 0 & 1/2 \\\\\n", " 1/3 & 1/2 & 0 & 0 \\end{bmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This would be a stochastic matrix, except for the column of zeros, due to a web page with no links. Fix this problem by replacing the zeros in that column with $1/n$. This _modified_ importance matrix, $A^{\\prime}$ is always stochastic. Now choose a value $p \\in (0,1)$, called the _damping factor_, to build the **Google matrix** as follows:\n", "\n", "$$\n", " G = (1-p)\\, A^{\\prime} + p\\, B\n", "$$\n", "\n", "where $B$ is an $n\\times n$ matrix with $1/n$ in every entry.\n", "\n", "##### Key idea: \n", "\n", "> The Google matrix is a positive stochastic matrix. The PageRank vector is the steady state vector of the Markov chain with this matrix.\n", "\n", "Let's play with a network of four pages like the one illustrated above, but fill the column corresponding to $C$ with $1/4$. Choose $p=0.15$ for the damping factor." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0. , 0.25 , 0.5 ],\n", " [0.33333333, 0. , 0.25 , 0. ],\n", " [0.33333333, 0.5 , 0.25 , 0.5 ],\n", " [0.33333333, 0.5 , 0.25 , 0. ]])" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Amod = numpy.array([[0,0,1/4, 1/2], [1/3,0,1/4,0], [1/3,1/2,1/4,1/2],[1/3,1/2,1/4,0]])\n", "Amod" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's write a Python function with the PageRank algorithm, taking as inputs the modified importance matrix, the damping factor, and a tolerance to exit the Markov chain. The function initializes a random starting vector (normalized), computes the Google matrix, then applies it repeatedly until two successive state vectors are \"close enough\" to each other (i.e., by less than the tolerance)." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "def pagerank(Amod, p=0.15, eps=1e-3):\n", " '''Implements the PageRank algorithm\n", " Arguments:\n", " Amod numpy array, modified importance matrix\n", " p float, damping factor\n", " eps float, tolerance to exit the iterations\n", " \n", " Returns:\n", " v (normalized) numpy array, PageRank vector\n", " '''\n", " n = Amod.shape[1]\n", " v = numpy.random.rand(n,1)\n", " v = v/numpy.linalg.norm(v)\n", " G = (1-p)*Amod + p*1/n*numpy.ones((n,n))\n", " vold = numpy.zeros((n,1))\n", " \n", " while numpy.linalg.norm(v-vold, 2)>eps:\n", " vold = v.copy()\n", " v = G.dot(v)\n", " \n", " return v/numpy.sum(v)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.2193081 ],\n", " [0.17521869],\n", " [0.35582464],\n", " [0.24964857]])" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = pagerank(Amod)\n", "v" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result above is the PageRank vector for this small network of four web pages. The largest vector value is the third component, corresponding to page $C$, the highest-ranked page. Page $B$ is the lowest ranked (second component).\n", "The interpretation of this result is as a probability distribution for the likelihood that a person surfing the web will randomly click through to arrive at one of the pages in the network. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise\n", "\n", "Build the Google matrix with $p=0.15$ for the network illustrated below, then find the PageRank vector. Ponder the result and identify the highest ranked and lowest ranked pages.\n", "\n", "\n", "\n", "#### Example network with eight web pages, from Ref. [3], $\\S$4.5." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. Dan Margalit and Joseph Rabinoff (2018), [_Interactive Linear Algebra_](https://textbooks.math.gatech.edu/ila/index.html), an open book under the GNU Free Documentation License, Version 1.2.\n", "\n", "2. Bernardelli, H. (1941), Population waves, Journal of the Burma Research Society 31, Part 1. Also in _Mathematical Demography, Selected Papers_ (1977), pp. 215-219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81046-6_24\n", "\n", "3. David Austin (2019), [_Understanding Linear Algebra_](http://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/ula.html), an open book under CC-By license." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Execute this cell to load the notebook's style sheet, then ignore it\n", "from IPython.core.display import HTML\n", "css_file = '../style/custom.css'\n", "HTML(open(css_file, \"r\").read())" ] } ], "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }