{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Algebra II\n", "\n", "In this set of notes, we'll consider singular value and eigenvalue problems. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd # for pagerank example\n", "from matplotlib.image import imread # for image compression\n", "from matplotlib import pyplot as plt # for image compression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SVD\n", "\n", "There are lots of circumstances in which we should compute the singular value decomposition (SVD) or eigenvalue decomposition of a matrix. SVD is somewhat more general. \n", "\n", "
\n", "\n", "As you may remember, a *[singular value decomposition](https://en.wikipedia.org/wiki/Singular_value_decomposition)* of a real matrix $\\mathbf{A} \\in \\mathbb{R}^{m \\times n}$ is \n", "\n", "$$\\mathbf{A} = \\mathbf{U}\\mathbf{D}\\mathbf{V}^T\\;, $$\n", "\n", "where $\\mathbf{D} \\in \\mathbb{R}^{m \\times n}$ has nonzero entries (the *singular values* $\\sigma_i$) only along its diagonal, and where $\\mathbf{U} \\in \\mathbb{R}^{m \\times m}$ and $\\mathbf{V} \\in \\mathbb{R}^{n \\times n}$ are orthogonal matrices. The singular values $\\sigma_i$ collectively give some measure of how \"large\" the matrix $\\mathbf{A}$ is. \n", "\n", "Numpy makes it easy to compute the SVD of a matrix: " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4, 2, 1, 2, 2],\n", " [3, 4, 1, 2, 2],\n", " [2, 3, 3, 4, 4],\n", " [3, 2, 3, 1, 3],\n", " [2, 2, 1, 1, 4],\n", " [1, 1, 1, 1, 4],\n", " [3, 2, 2, 2, 1]])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = np.random.randint(1, 5, size = (7, 5))\n", "A" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "U, sigma, V = np.linalg.svd(A)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([13.81539265, 3.72603666, 2.44819628, 2.09949877, 1.36015318])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sigma # singular values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the components of the SVD to reconstruct the original matrix $\\mathbf{A}$. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[13.81539265, 0. , 0. , 0. , 0. ],\n", " [ 0. , 3.72603666, 0. , 0. , 0. ],\n", " [ 0. , 0. , 2.44819628, 0. , 0. ],\n", " [ 0. , 0. , 0. , 2.09949877, 0. ],\n", " [ 0. , 0. , 0. , 0. , 1.36015318],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "D = np.zeros_like(A,dtype=float) # matrix of zeros of same shape as A\n", "D[:5,:5] = np.diag(sigma)\n", "D" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4., 2., 1., 2., 2.],\n", " [3., 4., 1., 2., 2.],\n", " [2., 3., 3., 4., 4.],\n", " [3., 2., 3., 1., 3.],\n", " [2., 2., 1., 1., 4.],\n", " [1., 1., 1., 1., 4.],\n", " [3., 2., 2., 2., 1.]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U @ D @ V # == A up to numerical precision" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[13.81539265, 0. , 0. , 0. , 0. ],\n", " [ 0. , 3.72603666, 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# low-rank approximation of A\n", "D = np.zeros_like(A,dtype=float) # matrix of zeros of same shape as A\n", "D[:2,:2] = np.diag(sigma[:2])\n", "D" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[3.2096557 , 2.65898671, 1.68173466, 2.08466542, 1.67933816],\n", " [3.42226876, 2.85044822, 1.82194842, 2.24275516, 1.88861276],\n", " [3.0260681 , 2.95788871, 2.43342142, 2.55390929, 4.46809998],\n", " [2.57181111, 2.39956408, 1.85323727, 2.02138112, 3.06622612],\n", " [1.58786939, 1.76571022, 1.67849578, 1.61885415, 3.71096771],\n", " [0.68832846, 1.11390247, 1.38277045, 1.15648122, 3.83777171],\n", " [2.98553926, 2.40609154, 1.43791263, 1.85137671, 1.13203631]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U @ D @ V # close to A, using only two singular vectors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Application: Image Compression\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To illustrate the power of SVD, let's use it to *compress images*. In general, storing an image with $m \\times n$ greyscale pixels requires storing $m \\times n$ numbers, which can be quite expensive when $m$ or $n$ are large! SVD can be used to compress images by treating them as matrices and discarding the small singular values. Let's see an example! \n", "\n", "We will use an image of Maru. Maru is a Cat On The Internet who is famous for doing stuff like this: \n", "\n", "![](https://media2.giphy.com/media/9NAXEP3RiJjm8/giphy.webp?cid=ecf05e47dbjp1upvg5ovlw54yn1j9zrhaa73vg4x5m4er4ow&rid=giphy.webp&ct=g)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 639.5, 412.5, -0.5)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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43H+Gtw0yeISQZNmQLEkIQNuUlNMK23jaFvaf/sDx0R6bO3cQ6vQeA6GLIbnIuVwevbHRF75/3wj3VY/52kj3fbyIV4XLVYK6no6+1ysjRFy3pRtCdA1JGQk3TXO2d3ZRKmF//5CydWiToLXCtRbnGpq6xrpA6wJN0zCvaubzkqZtkVIxGg2ZVyU//XiXspzw5MljNrdvMByMcd7R1DV1U9M0Ft9ZuXfufEqSaMYbW2iTLMb2RYn37GeX98azWqJiNVTr/A1Foo0tfBzlfMq9u1/xj//1f+Xu9//M7OSAtpojCAzygjxLET4gfbxrs7JEaodzjqa1TCcTpocH1NMJwTtQ6uc7XB7dhc71VfAuSBFnwyNf5JA760i8LNaW7i8Q1zvZrSQvnInpvK69aZOQZgU2eIKXTCdzUJpBMSArBkilCN7T2pamrnC2ZTabYZ1DKUOa5jRty97eHsNhwWhjRMBS1zMOjx4ymT3De3De4Z0FJCbJYmgagrqc4H3L51/8nps3P0QqvfD4n10ew9nC4z8vRN5PtN47+igBISRKypVLKXrtABaxsh6Cp23mPH3yE1/98z/x17/8bzx9dJ/Z5AgRPEWWoZVECUFwHq00RVHEfWiDa1Mqk+DaBonEtxbX1nhnUSb52bW/eCzzm8N1O+5e5nR7XaxJdwWva52/C5b99R/D6e2HcM0WrwDdaa7etTRVhUeSD8ckRqOkjGFlAqRWYAUKjdIarTWJSXCZxfkc7y11U7GdbLG1tYXSAiE8bTujbmqUNgihCNbibcD6Fh8Cx4f7TCaHVOUxs08PUSYjyTLSLCdLM0aDEUHKBTmGLlTLect8OkNKRZpkaKMJgLWW6ckRxyeHAKRpymi4wWA4Qiodc/REgCA73vVd6FzD0cETvv7qz3z15V/46d43HO8/oSmnyADGJCgEeZqjpUIKQds4GmUJQmCtxVuLFJI2BLxtkX3tYnl+OcmI1ZDAC962Sw6Kd8HafVO4NtJ9FwjosnjdY75OSeXduJ5v/hiEkGRFQVpktDNomzkeh8cxKad4BEIptDa44PDOIegIxlu0FuQyJc0Mea5omgajJcUgQxBQKr6mlCQvCrQ2TE8meOfxvkFKQQg189kBDx98x2x2RJIVmCQmaYzHW3z66W8ZbW6hVUIInrqqmE6OmU5OePrkMUjJ9tYOW1s7IAT7+0958ON9Dg/20EaTZTl37nzMB3c+YXPrBkiJkGJhaYbgsbbi4U/f8ff/+f/D11/+mcnJIU05JzMKbRO00uSDQRwnIY4X6z0mMSitcc6DD3jnIHhs20AIWGtRWqLEi0j38vg1kehlsbZ0rxiXr+7/7hL9aXTh99fuPPs5ss6inASPdy2JSPGuIRBQ2iCFJLiW1jY0TYu3Du8tHk+WJSQqRUgoBgbrWtIsoyhSsixFq4SqKqmaCqkUVVVSzmdkWcZgMMBaT5I0zGZTZtMDRuMC031nf1by5OlPHB7t88mnX5DnA6aTE548fsjhwR5VOaWuJiRpxtPBmKIYcXR4zP0fvqdtKpJEkmUZQij29x/y5MlPfPabP7CxtUOeD1BSQ3BMJ0fcv/cNf/5v/4m73/4TR4d7XU84kFYjiHmBSZKSpkmM8hCCprFdZEYX+YEk+EDwASkUIbTYtsE5e4H5dDUk8GIEvS5wcz7WpPuaeNWg6ovgomFkZ8vnXR9+TrjX/UAFH9AmJSsGGKMWBW8EoJVCpwbVpQWLBpq6xNoKoUBJAcKRpAYpBUlWkGQpSZKgO/lBCIW2hnpywslkwnQyxdmWW+lNNjbGKJOg9hRPnj5hOpsyHA8YDDOca3C+BiTPnj3i4OAp8/kUgidRgqYpsbZBCkfwLZPJnAcPvuP+vfs8ffqYnZ0tNjZGKL2B94HZo0OePfuJ/YNH3L79EXmXrtxUJY8f/cRf/vxfONp/QqoFWkhs27K1tYWWEmctSmkQkiTNSJMEKTVt63DOd2PEo4SCIPHeIbriP9GKtoTnFCrqdWpYjZy4ep33MpbxqzRX7fdxkc9fhSH0IqxJ9y3jKm7yq3//ed8L/NyaubpMs0tBCNIsZ3N7l70fDFLGa+acg6ZCKYGXsaVPXc1wrkabSLhKS0yqyHKDMYbx5ma31HbUdU1T1bTWM5vNeLa3z8HhIU1TMyhSRuMhxSCWhBwMc/I8Z+/ZMyYnJ2xsboDQGGMQQpJoxcnJEccHT8izhGSYI0KNlp7ReIiUCQ8fPmH/8Ig0M2xujhiPhqSJoanL7lLHaIsnT+5xePQU7wW2tVTlnKdPH/PsySOE9+RJyiDLGA4zhoMhaZpSVxUCwWA4RCmNdaCl6qQLTVlWWFtF2ULISHCIRexznmeI52i654+t63GuXZR4Lxs5ctljeF28bBuvRLq/5HCwtyEPXMV24rZOx3FeDKtOkueVJXzRQ3bd3m1Bmg/Y3r2J0gZCSyB2Bq7alsY5qEqsa6nqCh88aZZgXUsxHJFmCUqB1BKl1eL+SimZzSdMZ3OquuH4+Jj9vQOkDNza3WaQZVTzGUpphnnGeFgwn+YUeUFiUhwKIcH7gFKSNNFoBRKHlgISRdt6TiYnzKY1X331LUdHJ4zGG4xHA/I8YzQa4EOgdS0Ej3eetp7ibE1Zxnjh+XzG0eExs9kUKRTlvERsbjEejxltbKB1H5/cTZRSkqU52iR450mTlKZuKa3HOsey6SdIIcmLAeOt7a6r8vXgIiR5NhLkZZ99n/FKpPtLJVx4O+d2NcR7Ng33ZQOzJ8vz68vGB+Us8f58u29G4xVkeYHUhtC2QEBISXBQVg02WKxrsN5iMkNapGTZBqPxiLZtmM7mUDXUrWU0HHWyQlxaO9dQlyV1WWLbmq2NEbdu7JIahRRRwjg6PqEqSzY3t9ja3kXpAolikKa41tJUJa6pKeczXKIZDAZ4HyjLkocPH/L0yT6T6Zw8L9jcGCJEoG5KTCVj5MKgwHvPfD7Htg3eBQgNtp4zmx7T1iWjwRCCRCvNYDDCB0FV14zTFJOk5PkAIRTz2QxkJOKyrPABhJRY52hb21m5DolDSkEx3KQYbv7svr54YXM1GWhn33/fyfSiWMsLV4irJuyL6lF9VtPKK+d86nm1EZ5fPKRv4b36LJx9OK79ORGAkAzH2yiTUTclrrH4ILBeEBAoZVBaoIJiY3uTza1NlFZY52msp7YOpSXWB6wPiBBo6orWW1zwVE1J21QUqWFrY0SWKqTyGJ0gJJTlnDRLGQy3GI42EDojz8fkec58NmU6OaEs50gBeZIRvGf/2TPufn+Xk8kUKSW//+1v2N3dRQjB0/19ptMJra0ZjcaYRCGAQZGjpeBkOqWp5ygZGA1yhnnBcLiBVjFKQQlJ8I4QJDYIpFAomTAabVDkY+bzOT5ItE4pZzMQgiDBAXiPICCCR+uMjZ1bpMWYIBRBxMSLPm7i+dlop42EqyLLd5V4r3plvybddwAXcYK96Ma/bDz8nJSvDtcep4tASE0+3CIbjanmJzS1pawbnBAoo9FSsbGxwWA8ZDgeoY2irCtmsxOqOjq70iRF64SmbUiMJkmSWNNBRO10PpuQJoad7Q2KIkGKQCDgnCMvCrJixMb2LUbjXaROSZIcKSXOB5yPWV6JThgNhkwnU+7fvc/TJ0/55LNP+OyzT9nc3MBay8H+IXVVxnCttuX46AijJJsbG2RZyrDISRLD1Gjm2jCbzQge0kSjlMKYBImiqSvqukaVCSJIjt0EaTJGozHSJLStRWvPbFrSNNGJJoWI7em7kDKpNMPNHXSSdTy6CFLrr/zP7gX9J15xOF0Fsb5pcl59dq6CgNek+w7g9eWFVe/y5cvevfizKwVWVj6zzES7/owlIQSD0Zjh5jbTgz1UW2NtxbxpUJlmI9ugGA7Z2t5BJ5qjk2MODvdp2galI1k57zB4vIP5fE5mDInWDLKM0SBHK0liNIM8xygNQRK8wLrAcLzFeGOXfLBJkm0gREwFttbGTDIVLdU8z7HWsre3x97eHjdv7vD5Zx+ztTVGKkE1r9nf3+dgbx9jUpRWDEdDEmNIjEYrRVmWaCUZFBl4h5RQziuEBGtbbNuSmBSpVTyvtqWVGlOk1HWF0gaTpDjf4moHQdJ2YXTB+y6NOMpKJsnYGG+jVUK0f/sIhhfdz1+uP+ciOHvu11pPd423iRdZFs+TDS7y/qtbLKsP5nVaHn25QZMkse4roIwhSVMqb8nynLTIkVpjXUtbNrRtAwSMitXBtEli4fOmRkvJbDal1RqtowMsSxMSrcjTFGMM3nmcdShjSLOC4fgGg/EOKinQuiAEifcecEgpgUCapwjfcnJ8zMHBfnTI3dphPCpIjKKqK6azKQcHB0wmM4So2NjcIDEJ1jrKsuLw8IjpdEIxyBkMBow3NGlaI4SkaRzWtmilaGyNtZ4szchT3SWEBLQUeGcJ3pAkCSeTcpEM0TYNwntUp4V7FIPhmM2tXaSQUXognsvi7v5M170KZ+/zx8mbjOu9qtCwd6rgzRoXx1l54eI3c0moP7dyz2q8P9/eRcfL9UsIL4LAA9PZjHv37jI5OSFLc5I8YWhAZwahAkILmiZGL0jhMUYxn9XM5nOci5lnw+EAlSfkqYldJlwgSTSJUaSJIU00wdv4XoA8LciKMXmxSZIMkToHEUs8KuWxUqKUJk0z5MYm1XxC3TzFuprbt2+ytbGBFALXttRVzeHhEVVdx5oQRrGxtcloYwxCcDSZQAAvBIfHExrr2BpvMhjo2DnDzxC5JEkM3kPTWEJwtE2Ns47QEWtejNCbiiTLSTPD7LjBd+m/QtDF9cbU6sFwk3wwjtr9as2Hflw9pz/aebHp76IW+yK8idCw52FNuu8gLn4zV5f3YeXfZ5eJrz7AVoPjzxzlYvvX+cCF7rxm02OePn6ILY/JhlksVdgGPJ4QWoJvCUJSVyWT2YzZrOTx06c8fPyUqmpJ05TxaMyNG1t8dOcWWxsjmnoOzpEazZ0PbqGUwtqWqizJpUIg0SZDJzlSpR3h9tEaEq0TTJozGm9RlQLbtmhtGA6H3L65y7AokF0xG28dTVVS1xVaCXZ2N9jd3WQ8HiKlwllPURRMphNaZ2mbhsl0xubGmMFoSAC8i9qxtQEpoJyVTOopUgjSNENLg9CGPB+ws3uTnc0bXUxyhQ8OKTxSClAKY1K2b9wiLUb4RUx2gJeunM4fn1dlpb5q5bb3CWvSfQ9wPgeftXLhRRbtz8fnxbTYpX57FtcfthAIBO9wbUs5m3Dz1g0UY1Awq0rm9Yw0SQjecnSwR/Ce+bzk4OiYvYNjDo6mPNs75OR4ipAx3CpNNR/c2uXv/vYL7tzeRaeGQZGjxDZN08TGltaitMFZj9YJShlCpM+VBz3W8E2SFJ8PcK4my4eMNzbBtxR5hhACpRSJMSgV+7lVZcXm9jYff/whRZGitSLPB0CULLQ2OB8QKLx3zGZzhBBoozkpyxjPKiVNU+NcS5IYsjRDCRXD9wBbN+w/eUoiFK5taJsaRMAYjRIBlKYYjrnz8afkxZBFQbNXKGxzlXhfSfSyWJPuO4CXyQkXkxue50A7P3zseU63V8HVWx1dXzQC1jsOD5+xt/eIwWjAfF4zr2dUbQMi4L2lnNdMmoamqanKlqPjGY+fHbG3f8y8anFeoIKk9YG2qflm8gN7T5/y+999yt/+/nNu3txhOBjQJgllWVJWFeVsxmBUI4KAIGGlIMyyhU8stGOSFJNkZEXB1vYOw1xj6zlSCLSWOOuoywpbN4wGBZ98/BE3dndASExHyFIpprM5jW1jPC2gjaG1Du89SinSLENKgVaaqixp6xpPLA9ZFDlSqFhvQQiMUcymR+BtDA9TktRopLfIJOPG7Y/46LPfoZIU34WQ9df+xff69e7s+2yhXhXemYy0X3KW28tw+fM+z8pdfS9imaG2WqC5j799nYF/vRloEAnXBc9sOuHe91/z8OE9ZuUJJ9PjGKLlPeV8SiMEWoJrLd46yumMyfGMw4MTyrJiPN5gOBqglMRaj3NRsy3nc/78529p5hX/6u/+wMef3GY8HqC1om2q2LbdeaSIqbPnxawKIZBSo3VKkQ1xTUWaZbh6grMtQUBbC2zrmB5PyJKUv/njH9m9eZMkSRFKEUKgquY4ByeTGcfHx8znJUmiMUbR1g1NY9ncGjMYFMQOnYEbt3YphwWz4wl4R9PO0dKQJmmMumhL8C1KSpJEYZQgUQpEQOUFH3/+ezZvfkgQBoFY7ba2ch9+HsnyalmPp6/ZVeB9Ju53JiPt10q4r4/nOc+6d1cekn6cLuN2X3XgnvfdqwsdCwFC8MynU+59/zU/3v1nHvzwLU+e/kjrarI0waQJWZqSaolWiratsJWlySxts09rK373u4/4+ONbaC1pnWdj4yZJOuKHn75n/+kjjvdP+P7ejwRvyVLF559/zMbGKOqpszmqkxaEED9rXLM6iSmp8cogpaauWpq6wVkLAqwQNHVLniWMxx8zGI/RiSYQYuWyskR3lrI2CikVIUBdN5wclzR1jfcB51qkjDWFT45O2N7aIktT9MYYZy3CA97T1DOUNAgk3gVMkjIcFEjhCd4hhGbzxi0++d3foLIx4aXpuct78ibCAy+K99liXssL7wVefUJaJYfla6+7z/NTh68CfSRHW1f8eP87vvzLP/D4h3/myZOfOJkcsXtzi9s3b5DlGUJ4tBQYpXDWUZU1o40ZD5895fPf3ODf/Q9/ixQ186rEeoNSko2tLf71zT9RV7d4+vCAv/zDX3n48BHffb/BzVs77OzusrG9iQ0BKSP5+xAQPrCop9hdn9AvyYWMzSuTmDTRJjltNQMCAjBGsbWzRZqkCKlwBKzzCCmQUiFCTNCwjSOGbcUohfFojFaK+XxOVc2ZzWZkSUJRDKnr2JpIC0mRpogAddVivcM6CF6gpUFJh1YCicRh0WnKR7/5LVu3PgJlLnDfXpgPfO79e1lY2PtKlleFNem+F7iMhXH2IYl/n3amXXR75ztWzn9mwopF/WoPVQhA8HjrePb0Ife++2ce/fQtDx/eYzI5ZDwquLW7w2iQoROFbX0sPp6nDAZDmsZSDE7Y2MwYbRQMCkvTVKRpYH4y5cs/3+V/+p9+xwd3xrSt4NZOjggV/+3vv+KHB4/4Yu+AzZ0tBsMh1jpsW2HbmsR7UGEZCxKWXv44SUAQCqnSGILlKmSwiOBQ+Jhe29UCbqqaWVkxLSumZc1kVmFtQCcZw/EWxWBMUQzwwaEkSCR5XjCbnTAvZ7E55yBjOp0yOT5BATNt0MTr4X1M/02TFKkSrPN451AyIKVg68Ytvvjj35Hk4043PzsuTv97vQC9eqxJ9x3B8zXtV9F7u3+91gMTdd/TRW+e88kzHPsqcb2Rx2Jng72nD/jLP/yvfPPVf+WH+18xnx+xuTHizq0bJErhrSUoCHiaOhbgliZlNBpiMs1vvviIppkQQo1UAiNULPvoJ9TNDwi1SabmEEo+/90W+wc3+fbrhzx6ss9nn3/CRjFiNB5T1S5WNFsJY11mD0IIkhB8PHYh0SYlH2wgRWA4GCF8i62nzKZHHB3u8+TpMx4+eMrTvWMOTqZMy5q69QQkaV4w2hizu7PDBx/c4vbtGxR5SlvXtG1DAAaDIUZHCSJNM9SWQgqJrS3CCxIJVdkSW68pBArbVkhhUUksgvPxF39k5/bHoLp+bGF1Qj7f6Xr6Pq0lhtfFmnTfEbx6fvfLH4LrHpdnD/XyhBsIHpxtOHj2hH/8r/+Zb778b/z0w7c8fPwAqQS3bt+iKAqUjDULyqpEGQ0e5rMTpvMKD4xHQ37z+WfsPf2R1KguGaHF24YP74zZ3W1R4oAQGnRiGW1pdm9v8923zzg6nuNtwKgEWRiSTGLSLDrShOh+x6ytZVEgiNdfoVSKSgVGGUSwuHrG3nTCg4dP+Ocvv+T7uz9ydDyntZLWQ5Ay1vcNjtnBIQcHRzx7HFOI2+a3fHBrF6MVSiqGxQAffNR4hcd5H3u6BUExyLF1Szmv8CGgVAxts65B4NFakmcJuzd22b39ESopcEJ2NyqauxedKC/qSHsTjvH3kXBhTbrvBM4OzssN1pcNvL7FzllSX75/mW0+f6BfrsTj0mLqnnjvODp4yl/+8p/58q//wMOH93n27Anzec1gWFDVLSfTGYkE51oAlNbUTYP3gcwFHvz4iOPhgPE45datO5TzCVVjqaoJw0HCFx/skCU1trEgJc55miZ2Vrh1684iXlYoQ54NUekQk20hTAZSI5BIqQnBIUSMJBadwSiFRCpNUBqjEoJvOJrN+P7uj/z93/8jd+/9QGsDaT7iT7/7Gxxw9973FIMMrQSTkxMOD4+YnBxTliVtVVN+/gmfffoRmxtjlJI0TYMw4EKgbT3TWYxYyBJB0zS44MkHGUYatBQE78iMItGSPNEkWlOMxgTZxR2H7tpfwnK9qKV71UVizuJ9JVx4Cen+msO4elzmGrzq9bqa6/y876/WSFgl31Xt96wGfHlc9Bl43nmW5YT7d7/i3vd/5dHD73n89AknswqdZGxsbGKt5fhkwiBLsE2N85EsJycTEDDe3CQgePzwMaNxyngjJ8sSsmRAndRoLRhkhnJakiTxms9mNXtPayb7FanJaFtP2waULshHdzDZmKByQhdREK+fQKJj81zhWVq9nezgLLapqOuS+z/8yH/8//09P/7wE4lJ2L2xwcb2Jv/dv/kbWg+z+oR/8affkxnBt19/ydOh4t69J0wmc/ae7ZMlGuEts51NtFJ4H9CJoW5b5vMK7xzDYoAwCUpJlDQYpUmEip2SkUhvqcspTw6eEVCxzbqQiyCxN4GLtsl5n4n0Mngh6b4/TROvD2+yi8RztvqC/V1iK2GVfPvtXoWGfOEjOHO8yxRl29Y8fvQjDx58x+TkCdPJASeTKT4ohnkeSxI6ByRY66NzaBE4oCB4Ep0glKKaz7EtzKaWo4M5WgWMyWPmWKuop5bSzgFP23rCXKK8oapqPvrwYzZ3PqEYf4hKt/EyJXTNHBdnETxCSKQQIPTpKxbAB2jaim+//4Z//+//33z3/Xdsbw74/W8/ZHMrJysylDgiG+7ywe1bjArBzqYi1zc5OckYZJJ//PMDppMpjx6CFo5qdkwIgTTJGG9ughSdFuupqjlFnlMUOW1doQgoHchzjZZw8Hifn+7foykbPvzkd6RJgevuvzh1H94uXkWfXWu65+B5JPRLIOOrxPOvxYs9yBcPVD/rXLuIpHB6Gfl8R8v5n7/QUYVorZ4c7/Pwh++YHD5GhSZ62pVCS8iLDIRHKoVQCg8EGUs1NnWL1Joiy9BJgtIaEcB7R7CKLB0BnuA9wXkSPWRjIyfYOd42zCYzJn5OVmT86c4f+e//3f/IB598gck38FLhu2gKurhmGUQ3VbnYuUKqeM4rpTm9d+ztPeE//cf/wD/9018ZjYb863/zez7+uAA3Q2qH0If8x//vf+F40vD5x38guIbRsGEw0Ah5i+OThh9+Ol5UDlMq9jJLs9gjrrUWIQVZnoIPXV+3HEJgXk4RRQHkGGNo2gYfPDdu3+aTz39Pmo3OEFWfXXfRu/biTsCvQ4LX2fvsXcKlSfd1CfO87/+aSfhV0nuf/7mruIbL7Vzu+bls+mhcls+nE+5+9yVPHt0n2JLUaLI0Yzx2pHnGcJjT1CVKKdqmZVKVtG2LkoosyxiPBqSJpmljppnRBilU7CzhQErD5uYGRZ7GbsJGY7JtRACd1OghfJrvcPPD33Lz5sdok8VmNj5KB6K3CAPR4hWCIAS+i9MNQiLFSvufYHm295Tvv7/LxtYWf/jiBh/c2aQYtAQvkCrgRUPdHLCxMWYw8CjdxP5qQrO5kbKxkXGjgs8+/ZiP7+ySmOjI09oAksOjIybzOYiA0bEuLwKUkahWobRCaYlUktF4g2peMt7cIRuNkeb17KyXTfQXIc6fdx95VUnr7Vm5r8NZl74Dr0uOL6pQ9L7hdS78xespvOwzz5MJztvORY61J9zrG9Chc+C4puSn+99w//t/4vjgRwQOH2AwHLEtDYGAdxYlJKlJ0EZFh5GtGW6M2N7epm1qnu0dUtcVo9Goa0Ge4pwjeMjyAcPxDsPREK1jB9/hcMxgtInSOcpkoAyehIDGhdjGfTY5JjhLkedoYzotN9adlUIglEYoDQS8EF26cDy32axka3uXWzc3+fzTLUZDizZTfBB4X+G959btEZubO2gDQqUkeYrwEscxu7d2+OPffMbnn33CIDM422CtxTmPc54k09gHj9nbP2A83kJJRVFkDMej2PEieKbljLKSVM7R+EDjIOiMIKPn7wKRgM+7e2ccsadxkXHzPMJ9n6SC1+GsdfTCa+B1Lvwy5OhF2zirg57n+IJVffTFeBGJn/Y2n//d87f5omfleZaPd46njx9w//u/cnL4iLI8YTYvOTqaUNaWwWgDpSXz2ZTgA03dIhAMB2O2NrbJ0oS2bZkcT/DOkWVZdxwhZofphDwv2Nq9wWi8hUpSkmzAcLBJlo/RaY4SCfRWqw/4xtFWcx7d/4a7X/8VvOM3n/+WGx98hEkjOUsEXkhwHpRDSoXUUWKI1mjCH/74t+xsbZMkip2tAUZ7pvNHzOYPmFcHNPMTPvn0Y5IkQ+oUoTTz2uMsbO5+xv/xN3cYDTbBeebTGXiHNhLnKpq2JksMuztblPM5ZVmSpil0lchMknB4cMDJ8UPwoISkrWqGW5pstNFJND+vJPEqsdWXud89zr7Xf75/DqSU760R1uNlk8eadN9Z9Jbp+bUVloP7PC32PFyUmK8ey4eoz44LNG3Nk8cPOD54TF2eMJ3NePrsgCdP9qjbwO6uY2trkzzLAU9dVV3fL4MQira1lGVFnhWMx0PKaoZ1bWy14wNCKTa2tsiGI4I0ZMUGg/EuaTZCyhRk0tVTCBAc2BZXTTl5/BN3/7f/hXZ2zI2bt8hdg2xqhJQI50FIgojEEKQAnSCEig49IdHa8MGdT7hx43bs9CBju/fB5ofUzReU5SFVeUzblihlMCaNTk4PJsmQJsG2jnI2pawnlE2DbVpsU9HWNU1TYbTusvAGHDx4AgSyLCExMmboFTknJyfMqwpFbNfT+IA0sSaDWOkQ8Yp3dOV+vj7OFkR/3/Gyc1iT7juLF5HpqpW8SqYXGbCX135fPHMvy0S+3FKKhOudo5xNODp4Slke07Sxw8PxyZR52bCxuUuR55ycHAGeG7u77O7uUjc1ZVmxt3dAVc7J0oxbN2/gfWA4GGKMjj9JznC0yXhzC50WZMUmxXCbNB2hZIYQOpZs7C2sEAvJzA6ecfLgHjdUIN/e4IMP7zDc2cVJQ3CB4NtY5dcFnLexWEySIaXBK4WUMsoMKiFRBuMDsaC8QCEw6RbFsIXQIvBIoQAZi4gHcLalbudM3SEBiwtzqqbl+GAf35QQPFJAajRFnrO1vcnewTGz2ZT9fY1ta3a3tykGA4rhgNm8YjKfx9KS1nal7UXXJ+168D5JBG8La9J9y3i+tutPhXmtkmXfGr3/3OVwPZbwRZ61EALWWuaTE+5+9zVPHv1AXU5it4fpjOOTKc4LNjc32N7eYDaXeO/IOyfY4dGMprFRuzUJdV3z8NEjBkXO7Vu7CAFFUTDa2GAw3CBJhyT5kLTYIM3GSBkbSsb1QZ8YEM9dSkOW5aRS0djAswcPkSEhGX1ASCQyMQgchw8fIWxDtjlGpBmuaZA6RSUJQUcSFZ37LV4TtXJdJVLE7fSaarS2Y3aYUC0aSZIFbOtpmxopjzEmRQhompKmLvGtQ5oEoyV5njCbTWhti3Uu7kWq2O04TWlaT+sqWmdpqhrnHFJLXtdKPc+hdhHCfZH88Gsh7DXpruDdiaLoifR5YVjXeYwrzQkv+BBc9FnpCW8+m3C4/4j5dJ+mnlPXDVXZIITg9q0dbuxuEIjFu7XRpGlCkhrGoyFNbZE6IUlScmuReAZFjklSlNIoneC9wHqJUBlZvkq4XbiT8JwKfQoBoTSDrRvkf/svOUoSymnN8dGUD2Yz/LxEJoby5Jj/+H/7v7JZ5Hzypz9AUZBs3WCcFBSjjY5Ilw3MTy8q4h/i1DUO3e2N91sqgZYZOTGbrG0qimKGb2twmhBa5lOLw2FCQGpDlhimJ1Nc40l1wjSbYauGto6dkMfjIR4oy5LD/We0TR1jmi92y150N197C+8LrpoX1qS7grdBuOfvs3tAxaqEcN3HFvdzugTk1Qefe+85Ojpgf/8xJ8cHVOWUk5Mp3gU++egOH925g1Tw+Mk+s+mcre1tsiwjz1IG+YCqanjydJ8HP/2ElJLPPv2YO3duU3TEmxUDVFKQ5mMGo210OuwIV53Kegrdsh9C7L8YBEEnyPE227//E1k+oNzfI7SxhGKWZ7THh1HXRTIva3Z2brGxe5tsNAIlCYv7tXLdhOhunV9c5e5KrEZBL/4viM4kY3JMktE0nsnJDBEa8AJjErSMGrILApAQJE1jqasWnCdoj9YarQReCDZGY7Isxzkba+++Qkz1eVglo1+SlXpe482rxJp030mskuxVD+bnE3jv/T/99wu29JwPnJef39fJ9cFTVyXVfEpVlVRlg3eCzY0xt25sk2eC6WwGAnZ2tiP5VTXeeaTSHB9PefL0GUIIPrh1k+2tMUF4ghSYLMfkA9J8TFZskeYjtMlRyqC6UKnT3vJl4RrfW6lCQZqT3vwAhKTZP4DaEmgZb2zzf/o//18YbO+gNsaIPMcnOS7J8DLKCIGVcucd2fa2b//sCmLMb+gSTvr3ZfCIEGMLlFIYk5FmBSbJacoWJRRFMWI2nTKbTXFBUFctAUndWKqyom4tSZqQGM1gkKNUgrUB7wSHR88o5xPywTgWSz91iy47zk5H1rxMNrgIcb0rGWbXbXxdG+m+O0v1dxvnX6cXZYy9rtf5/G1fdqy//OE4vZ8QAs45jg8PefToJw729zjYP2I+nZDmKTvbI8ajjEBs0dPWNWla4J3j6PAI7zwuCMqyRgjJxx9/wvbmCGM02hhkFz3Q2IAOCmVylE5jkXARuwb3qk3MHPOnHvJ+UgghIKQmJBkyH4CeIkSDTFLy3V3M1iYUQxpjcEqB0oiO0OXKufe3NBY6j0WHFoTPMla5N4SFEF16bjwepTRFMeL27Y/QoWXvsaOcnzCvag6OJzx5/BSpNK0VWB/14tYFJtMSbRQhOJqmIcskSZLSNI6jwz1OjvbY3r3dRTDIBeE/X8o6796/OEHiZyNhZaJbt+u5AOm+Knm+K4S7+lC97nbe3DmdtozOEtgyOP2iyQ7PT444b/C+nkPkvGPqCM17qvmccj6jrWuqsqJ1jpvjAbs7GxR5Eq3c4NgYDZFSMJ/OePJsn/3DI5yH0WjM559/zp0PP2SQJ2gjMVksAG6SISYtyAebGBNLMnrvY1pw6MPV6H6WcaFSKhZv+OjAtAiC1JAk+CJHbG/C5iZtMSAkCV4rfBd+JbuIgL5dfCyMs7xOEEkeAr6Tcfvr571jmYq7PMbOI4bSsfX7dF4yOZnirGU6q5mWDWmqaa2nrFucD2R1iwtQ1y1SepxzVFVJlmUkieLkZJ+Dgz0+sRZ1qmvE81c+Fx3y7zMJvmm8lHSvgmieR1hXRYgvwlVt+7qO8UXbPT3oL68xndVn42vPWwLCZZeYFw+oF0gpsUQtNTGKIs+5dfMGSaL54INdNsZpR47w0Z0PQBoaGwhHc7JZw5gYnxsjG7YZDArSVMdleJohVEaQCcYUGJXFmgR1FS1Q2Xnrw7K2lpSqez22ecfHSSF4h3cxA8wHTysFsiggL7AmiS1uhIixuiKWR4w1JE4TbSRzQV9fYvGzIj+cuo8hShPRCu4mCh8nzCzLGY+3KGfzrgpaznhjFx8Ek/IEG2La8nRaMp3NSQykiYpV1rKCJDHdLjzVfIZtW5K0eHmu40uH2cut4/7ZX00GehlBX5WBc9388qrHee2a7osO7F2xht89rFg8i79hNargctfuZVlCr3CIi+M5++XzNWMhBEpKBGCkoCgSaIcMhhmjUUGaGKpyjsTFWgNSUdYVh4dHPNs/AqHZ2hoyyAu895TzkjQZkWYpWTFEJRkmHZCmA4Tols0i7lfKrqOvUIvj8d7jbBstUB/w1uGdw7Uttq1wTQnlHNvUseZB26LqOvY5Uwq6Mo+BSNYgkIKYRAEE76NVG1bb/PRXLay8EMC7jpDjawE68rfgAxJBagzOOuazGilTisJgnWc0EkymFScnJ8zmFQeHx2SpBJEgJTRNjTGKNM2RymC7lu79BPAqLoOfD73nk++r1NV924bSdR/ntZPumlhfjPNv8HnE1fu2/aX0tAsexSt8/nKOkxACrW05Ojri4HCPZ08f01YnaLVBVUKwCuEdRnhsWzJrpvz44zO+/+4hR7OW4XBMkSXMU4WiRbiaLJVoIwkyYWBGaJXEIuNCImS0PEUna/RyqXcO7x3ettR1hXMOhSR4QXAWnI01cWcz3GxKM5mSFgW+qkBqnNKkIiZByO4aeOdwPiCFjJ0elEII8D4SqOyWLH1SwnLxEogt1X2n8cZ3OypHBBA+IIHEKDbGBdZ66soxqUuklAwHQ3a3W5qqpKwqDo8mGCPYCSOy1CCFwFmLVQ2Zidl9zrmVu/jq0kDveD0dT/58vC9c8N460ta4Pvxca3u1kLJXkRRe5XvL5aXAGI2UEucdwVuca6jnJ8g8wShJ05QcHhzw0+MDHjw+xraOGztRUrhz+zZ5ltI0JXU1pSoLNrY2yNKi0z6jzioRxEa9sayj9x4RYseFaN3Gpbt1jr50oyCSrmtqXFlhJzOq4yPa6TTG36Y5wrSU8xk+BJIiw5gkOtKIxOqDp24sSim01kgZrWxCLNwTlqZu/F8IBB9ljP6GCiFASPAebz22aWjKimAdRZbRDh0H7QmuLXEBqralnE4x2lCLhraxTCYVw8Ggi1cOKB9wzuNdwNoG7+2F8xcvc4/fpK77rkQ6vArWpPue4ucD7uUW8+sO0uXXz19OvqyCnBKCIi/Q2hB8wHmHcy2uDZzUcxrbcnhwwuOnhzzZmxBUxp0Pb7O7u83G5pgiLzBKI8SQNMu5efMWW7u3UOkIYXKSJI/L+wDRorM4Z/Hed5EFcbZSQoICrVWMZGgtzrbYpqSZzvGTGdO9Zzy+dx9X1dz69GM28yEmLxDB01QVbduS5zk6MRhtUDqJxXBCwDYtwdlYB1fH5pFBhE7SsIs7Ez8fj5MQiTuIuJoBgZaSoDRaawiQZxl5VjAajZBScHB4jLWBPDNYZ6hKQdM6rBM0jWc+r8mSJN4uH2IUh20IznWOuteP/466/svH1ftKkNeB95Z0fw0haT+3aF98vperDnbZY3n97UghYqJDMUTqziEVAnXrODw64dnBEYfHM8rSkhSbfPTxJ9z+4Cbj0ZA0T8nyIYN8iBAS5wQeTVkJCqPJdBorVHkXnVeLqAWP6moiACglcdYTQtRMm7rGNS3Btvi6xlcV0/09jh4/xc4qlIfyeEZ2PEENBugsRWmBlArb1fBVUpAVA5IkxWiJlGCtpXUeHQJKKaSMsbd0oXNLPdcTuonB9aF7XSiZEoIk0QxHY7zdoZofo7QizVLmsxnlbIZ3BqM1aWKwtmX/4JjpdMpomCPVJolJMVqgpUAGx/Rkn6PDfcbbt7pQt4uHij0fL9/GRR1ovwa8t6R7cQ/+5cn5XSJ0IVY1s7dxTJeP4T317T4+s/u3MQatDWlagB8QhORwUrF/7HCMuPHBh6TFgJs3bnL79i0UnuPDPfafPEXIp53VBlk2YLy1y3BjgFKBti6pqzneRitOaY1UKnackALvLLa1eOcIrmut7h22rnBNiy8r6pMJk71DmpMpgyTjxqe/QUtJ4x2us4BlUSCNQCsJUtO0DU3T4sMU2zYkaYo2JsoLncPKWYcXMjoShULQTQxALzPgo9YsEBAcrpMjJLHpZTEYIbA0TUnbtGilybOsC4nzJKbAJLdQSrJ/cMzRyQkHBxm50QwHGTqP9Rvqas7h4R6364pEqdeOn+0Ng1dNpPk14r0l3YviVbynr4rr2f7FogMuvdUXhNNc7QNyevtlWVLVNXkxIDEghUdngs0bA5Isw6QGETx1NWf/8Q9UkyPqcoaQiiTLSPOMwXhMmg0wRtPUJWJ2AtJ0ERIKYxKSNIlabSA2iiwrnHULx5oQ4F1DW86pjifMDo6ZHZ4QGsswHzJMM9Iki67LpmIyn+GePENoReIdzmYkxYA8zXDBd+2D6ljbIE1Js6xL2BBd+K/H+hCdaoB1Fuk7p1noqpY5j0Lg8di2oW1qgnNIwNk5zrY421LN57i2JU0SjImF1JumJks0rm2wtkVKFWUcBHXTErxHmxSEx2iBMVFrvqg88CJc1XB5mzrtmzS03mjI2JuIy30RXrbfszGFV739y2E5+JYyw4sG5MXI+OyYPm2pXP2AX/UdtU3L06dPefzoMUdHJ3g7J0k0xmRU8wnuaJ/ECDIjY9vw1LBxcxulbyO7yIRFmFaA4Bqq6TFCKIrhJkmaonTMTvPexvCo1uJti/Age4tbSpxtcHVNdXzC4ZNnlCdzimzAaGfMYDDCaB1TZb3Hl3OUd8xnM3j6lC0d2+e0CGQRSLIUITXWStqmwbYtUgh0kkaNWUqU6MPW4vHrYAjWduFmEMtL2lhCUnpU9M5hXcC7lqaeU81ntE1NXZXMZxOCdyTGoLVgNDA0jaW1DYdHh7H1fF1Tt5a8GEb92vu4rSY25uxD6l6P6H4ZFuyb5KQ3FjL2tgn3Ini3ju10Ftnp5+J5A/3tPDwXum4h0FpL27YIEXt3iZAynZywf7BHYgy7u5uMRzmJ0WR5tDLbak5V9tEKFW1bI2Qs/JJmOd5vkecDBHEZ71x00AkZkyF86xBdyUMlBMHH2g9tVdLM55zsHYD13LrzIaPNHbJBEZ1iXbZYcB49HiDzlMO9PaYnJ3g823jS0ZhWxIiAJMtITEJS6MV5WuswadpJHSzrHYSo79o+fM05FAKlDV45nIPguthfFWOWk1B0SXOCNMtRZoIPDnBIJIlSDDYLhNxmf3+f2ZMDynJO3QxpW0dqNIlJkCFQzibUdUWeFK98zyP6MMbXx/PI/12S+q4Kb0xe+KVduKvCiwfVm9ByX0+zhfMcfj9HAKQUJN2S+OSoJE1gY3OD7a0RUnq0BNfMqVsoJ3vYpsI180U5RNu0+BAohhts7dxgsLkFUlO3M/z0kDQbkaYZWqkYm2otwQZkAC1jPG1TV7RVha1KTvYPUFJz85MPKba3MVkBXeEavF8kNkjvGWUJKtH44Dk5PMTj2bkTHV6uEVRlyWg0Jstz0iRB2ZbGOlwbnWRa6yhtSEGw0dEnEAgfCNZiXUOwbYxkEAHVdwFWKUGk6HRIPtykrSvS4oAgFYcHe3jXkGQpeZZSFCkboyECgRTfcDwpaaqGch4nmVhIPacsJzR1QzoIi9N9PVyFM+45W75G383bwi9e030f8HLifT8G0/MQQiA4T1VWVFXFvJxzcnyMpEGpGKsqcRgBwbZI4UkNSOVjDCsSrVKK4QbbN24x3NjC6xwfYlt2oxPSJEdpTXAtTVPGnmeui9oN4KzHtTW2bnBNTTUvGY432N65QTIYQZoSpI4JDd7F7DIV9dgAyMSQbo65KQQ6McznE8rJBJ0aZJITvGd6fERbVxSDAm0SUAIXBMF5GlfjWhut3k62CLbBR7MW0aUfu6bEBRcjLlQa0461QesULSVJMSYfb7F54w7TyQGT42eEYBkUGVmaoIQgH+9gsiH37j7kZDplOp2Tp4ayrKmqhmpeUs6nDLduEEK0vl/fZr0+4r3Q3t8TwoU16V4prq878ErB7Z+Ftb/pyIblfi5zqt57rLXYtsW2LdPplNlkH6MEWapjSBMuljb0Dq0CUkOaZezs3mD3xm1Gm1tIk4I2pNkIlRZIleCto64qqtkRWiroU3ODiHVnncN7S1tVuCZKBsVoyHC8SToYRbJFIKWA4BEqZpvFamQxe8sLgVcSNSzY0rdJjjKatqIp5yRSkaYZrWspZy3ONl0IWYaWmtA5x5xto/WsA0ZLvNRRxrCBxrfxykq6GusiHocxSJ2gVBIrpilQyqCTHJNmJEnGfH5MmirSNCUxGflIkg9usLX9Ec+e7XFwuE/wLaPxBoN8gGtju6Qo5l8FVb55sn2foyHWpPsO4MWEe9aCOG+wvf1Z/kUSgxACrRR5Hq3RpmloraVuW+bzhuPjaO1pFesypEYzGg6588Eddm/dYrSxjTIJKivIBkOSfIxMCjyauqy6dN6G4GrqusVb24WoGSCgpMTZlrZpSVSKSQt0WmCKAUIneJblFqO2GGIPNQJSEhMWAkiTIGQMQ0OAOD6kqUqEkmgV9VcfArZtmE8dPrVkxQCtE2wIeG9x3uKcIPgYp+wJCClI0hTZxcMFfLefJDoGTYpSXecLASiBQEQNOckZNpuE4Lo28LFk43hrhCfBBUFVzzk5KZlOJ2RpRj60NGWJa22Ml2ZJYpepLPY2rdt1Rtoa14Czvc/Os2jfTtzu4l8/G/M/r7fQ//bB09qWLooKrTWDwRBvW2aTE5z3+CBJ8iEff/Ipt27fphiOSPKMfGMzWo7pAG1yhDZ4ZKx3YBLSUFBXFtvOcb6KmqhQSGFxPsY5++DQSUe4OiNJB6gkJXZe8F1kAYuyi3TVx3yXXOFcV61MCLz3mCwjbXOq2RRcQ13NSNIMrTVBBAiWcj6haWuKokAlMXnDe09wnjbUXZKHxTYzgnOkJiXPxzHMTESyl1IjpEJ0CR6BGH0RyVUhlEGZAQQXv+Nihpt3nny0xWhjQnaQMZuDtS0nk2O0GVLNJwTXQshfgzcvlom2qFP8ApJ8n0n0sliT7hXjVSWG3nt7fsjaVWfKXwdeEo4HKCWQInRdDQYMihRnW5TSZFnG7Vu3GY/GbG5ukQ0KsiInLQZkeZQRhM4JMgEkSIGU0Tnn8CgbrULhY/8vhUCgkFrgPWgJxuRonaB0ilDR+g2hjQVylF7E8Ubi9TGEC49HQ1fPwbuYVCGVJMlzCA4fGmxbEdtRZggTPy9CoK1bpq4hyQtMmsXMOCkQMu6jdS1tXcbKZm1Clg2RSoNSaKUR0hBE7BYc+iJD/aUWkoCIkgS9o85DUATfEKQhzQvyPEcKiZIBLTzz6RH7zx5h24pUjOPdC32h8Ve57y8mU3i5HPBrIVxYk+4bw0XJeBla92470C46sfSTiLWOqiyZTqaU8zlaSvJ8RJIaPvnsN4yGscOvUYIkMSgTSSL4GAYmtY5kJBVBiki6QEAjZIJOcsBipcTb2E9M65QgOotYKJQ0nYUoYhxv2xICaJ0ggiX4Lo63s3S9d13ZAkesxRvdTUIKpBAkWYZ3NbaOSQuNtSglEMIjlUJJFev0tg21twTfYEzWxRn7mMyhFHleUAlHcJammaNMgsQQcEgVYoyy6GtKLFc8sTJvF9oWTk/MkWQVw+GInZ1d5pNDytkxRim0FszLCcfHRxSbN+mLp7/CKFj5/WJX3K/Jkn0Z1qR7DXheacPLfD+Sw3J5ftltXBde5Ri8j9JCU5e0bQ1AlqTc/uA2g0GO7FrepEYiQktVHWDnLWk2pBjvkuQDhOwmJBEQQnaFYejKOOou26rvDCGRSoA0SKEQMpZdpJ/Igu2qbrVRw+ykjdCVUQw+ZphJIbpIg7hvKTXex2wyhUQK0InBtdHx5myDayRaprROEGSCVgYkOFvTzlq8qSOR+xYhFSpJSdOU4cYOtqlpm4bW1ggfVwBaR8s6SIMgnqtSMUnE4+lS6yD4RTlISXfcyoDO2NrYobk15emjSOxKCoo8x3uHtS0mSa5ugDwHV0247zOBr0n3GnA15NhbDu+DtPB89EXEjdYgYqHvDz/8gHp+xOTogOkkkKYJJjEUuUEr0CpQFIPYPr0YYbI8OtKUiQXERQxzivaVQxoIstNhjUcIHbviEnVQRUwHjl0c+oQEG51hUhCCJQQZydY5vGsj0SkFynTaqowyewBsgwselEQIj9KS4AR4gW0qVKLwraUJNSQZJjEoPNY2WDtHaoVSEoFGkuBDtMSz4QbGtdTlHGurGLsbHMolKONQwsR6wB1xLrReBAGJC35RZhIERmmCTsiKITdu3EGrlPnJIUFolErJsiwWGuP6SWxt6S6xJt13HmKx/HsHDN1TD85F0qp9n+aqonUagKauOTo8oKomaCMgZEiRUqNQeUaaD8myIWk6QCcZWqddGrCkM3npV8RBKIIEgkHo2E3XC4EVsUOCkBIZix/gg8cHR8ARREyD7Ruj9zUZfLAIbwEX/waEkNESFh4ZFAILeIKLjXe0Uqg0x2tN27Z46zHK0NYVbe0gGJTRCBFiTC4CpUzMVktShM5AJfig0Eajk6h1N3WFbWucawmNA+0QKuk0Z9H1c1N0ti1KSkKXdiwAb0HKhCQboXXCYLhJXc6oG8furQ8ZjcYxEqO7BhdzjF0uVHB1LLwvuO5EizXpvqM4fePfdCzuxfDyyWBV8wudjKBwviXPE6RMsa6lLksEFhlSSt8SfMw8EzJF5xsgFEIo6Lrurm46HoMEqVDEYjnWA9jOUebxYRmK1Zm8xNK60XQVIVrFMWzMdQuMrr+ZsyAVMYQ3RAvXt4jg6YumCynRShG8JnT1IdIkQUmFtU3Ub3GxngMSqQzapMjuR+isK9jTlVoUAZ0mqCTH2+ik820MhfPeoWSKVrorZekJxOsjFs6wEI9JK0RIaQEhY2xvkg0pfODG7Ttk+WAp0yzqb7wYLwoLfBeMgqvAunPEGm8Mr2bFnO+EWRboCTF21TuEBGOiNecbyXA0Xlh/WnpU18HWWtd1WoiJBtJZhHLIEGNQhfCcDV0TUhLQoAJKR2cXwuMseG9jZIESBC87spXdMjwmUeBX3EEdcXnnkCISNgKk1N35xHKKsnPo+U4Kktos6oLLJCFNU2RTRetaBIROYhF2kyBNFglXGRCyaxWvoi4tuiaWUqESgzZ5rIhWlbRNjXctrbdd7zcNMqC7RpixnVMXAdM514SQkaBDjP0t0pxiuAlSIxBXMpW/ScJ9n6zm87Am3TeE1cXbcoCujNSzA+kVBvGqD9nTGU2rmxN0Hvjws4Vk9Np3luuZ13tVORLk6v5kt62fP7h9vOsiy0oIlAQtJGmSYsQGUkdPf1yigwgWKQNJmlGMNknzMTrJurjU0IVkiW5/y1Sq0J+4VNGRpDprUQiEtHinOw+/QymF0kkM9bIt3rl4XsLHqybC8lrK2Mkh3pqwiONFCJwA52PKspAmfk8KpDAxzEyKrq5ubE0kCGiTIHRn4SqDVAaEivUeBDEpoj+pbr9dRV2kVqSFQScW17a4tonZcsEjOj06CNeFjgFdRh7EsLoo88QqZ9lgSNpbuVfGX283Dfh9wpp0V3DtRTMWq+2lp7l7nuPz0T0E3QpzZQxHq0UEf3pb4jQ3h+5z/WJadrGd0eDpygr2kkBPIp3OKhAxQcG5aEF1pBYgarESCOL0IRE76fZ1WXseDAR8l7nsvKNpa2aTY54+/JH9Zw9p6pIsz8iyFGVitoSSAiVAiJh2K5MRKh2jTAFSsqDCzkqlnwAWpChWzsUgXAzHElqBB+9iiccQXDxCrwgIJG0sah78Qm5ACITWyFPWtOr2AUJFRxjeERMZOrlC0HXEiBllQim0SVAhfif+JEhlEFJ1solYHHu3oy5Kox8vIu6DgJQGbQxKZ5Da2HrHh663ZexIIXxYtpcXdBa0AFzMflO6I/+YiScWssLbJcz33Xq9DN4a6b6LVYGu43ica2nLknY2w1UVtLEXV9vUCNs1JOydTasDr0/LBMSZJWPoyDRmP4luP47g3dJh5H1s7e09SkiCdVG3U8vg/P7hFCZ6wevDY1zdYtIUKWNWlBcCoRTS6EUEAV0mVbBRZwy2P/74o4zGmQSRJICgLOdMZlMePbjLT3e/xgWL9xsIKcl0QpJkMQ5XRM+71AJlclD5IlQqnno/G8VZqi/Ustx55yFXKtajDRIZJEGGuLxWitCVU3TCdY4nRWhbnBAoITrLV6Bkl+AA0a7u6jB4AegYA6tV7F1mfdSEhZRRgpAi/jtJo1UtRBfaphCojnCXRLuaggssLFBxigh77SfQ3Ty06bsOx7oWcfIQWB8dikrprnCPRiuFDy7WGg6B1lkSk6zs4cWW6qs60Nb4Od4a6b5rhHtVWKSQOk89nzH56T6zr7/Effcd4dEDmE4RTYUr51A3BOuQ/vSSHhmXk6tm5SrB+K6luEkSQqLRWUrdNNjWknT1DXzTRiOU2NDQ17HpogqRgJSCxsbgf7QiKIlsHdJ5nJQ4ABkNWR/jkAhSRR1QCrzvLe/YDUELhQca5xCJwaUpIi+wScJUaZ4KxY/lEY+OnyETTZKlDDc2CELgQwzml8YsipALZfBBYl1ARR6Lx9qtEugsxIW1210b0S0TpFTgFT502VwqWrLOWWQ/YQQR9VShkU5jbYNQHiliOFbwyxVGcNEpF3ck8YIYKSB0lDE6R5+QiiDlQsYQXRpvb7H2S3zRL2n6dYYQi3OK/606DXtttq8RITvtt3MGChFJWEYpwndtgvqtKym6KIUov9SzCZO9p2zu3ETlxfL44hXsxZtTiei/0Mf1rWAtL7wixCnLQOA754d3DjufMX/8EydffUnzD/+Z8OXXyB9+JD0+IhGeROlYTSuErn7Y8gGJjvMoA0il4jtSxqUrIgbau+jd1701mWW0tsU1LSrNUElKMy/j8jfRpFubMbz06AQ1nYFz6FRhqyaGHfnlWanuOFYnxSBD52vqVNXOEpNaYwZ5fN1ZvIhE7hBYKQlpiiyGhN0b2I0C7yuUgqqtOT4+ZDAeoo1GdjV2dZJGq1fGMCgpVSzirWTnKOu87AHoNF4WS+OevHqHEgQpEK7zqnsXEyWUIsjYIt07F1cI0oHSSGW6TDHwztGGimCbeNYCpFFx1SAEQWqC0iidRBlDqi4CIhKw7F4TQi2y4BakKnoNXHQNM8Pi+ve0u8gwC4FYZU50k0039jqxPCZJdL87fTo62OLEqETUdEXMO4YQcOWcw2ffUj9+wvaHHzLcvYVKUrzopQy5cqEvAvnyj1wh3veY3zXpvg56YhIQvKOdz5g/fMjxt18x/8f/QvjrX0ju/0hycIielySuRWuJTrNFryyBj9YZ0SUlO3JbKA4KQhBdixkbe191nV+j39xHZ4oSqP4n1Qgb00ZDomkThRkMovfeWoyNcajCOZT34EXUf1fmkRXKjamsIi7nkSLGiGqFSTRtU+M6y0pmhnyYU7voEGoTRZVp6pGhLhShkQxUTuo9rqmYT08o8ozgEwRF1zU36qCLuNzFlek1z/6B62hLLCe++MlISFLIhdPLEwg6Wrx4sUgmEN2SHxWzvpyV+K5FulQC5SVNsEgR0DpB6+j8ilEGMSVZyHjMQqooIXSW95Ic+2IvIe4TsXK0S8mkdw8urnnorNhTd2OFBBdORLHUbulkphXt3/mA8wFt6LoRe1zd4A4PmD54SH3/BwYffMD2J59Q3LyFSAv8amjeuVhe/4vgqusuvM+EC2vSfWX03vMQAu28YvrkAbO//iPtX/5C8+U/oe7fJTnaJykbVNsinIsdX53Ce9dZc9Gh5bvlsuycXpHcFB6PkgovBRiFMCo6u4SALMMSl7heCZxJsCFWdsk2h8xUQBuFz1JsUaDGI+QwRQePn84Q87LzatNlJcnoEPIB33lXRKejdm+DEDhAaIFKNHVTR+eMiEvaZu7BQRgNaPKM2XjEdHeL40GCS7ri3dMSCIxGYxSetp7js1j7gM7JBX2H2q6SVu9tpF9m95Pd6Qf/1MPYTQQCeVqJUCCCQAQFKhKR9x7nJCrGniFEXE1gJUmaIjrSjYSrkdJ0EQv9RCAj4ULnyOwSLxxAty8Boav/sDyn/rxWxlR3zaN+71lw+KJs45KMT6mwQiC72F3XtXT33sd6EiK2MDLGoJEEZ2knJ+iDI5RzzB7+RHv3WwaffMr4s89Jb99BZFm0entn3gtJ9vl68EUI8rKW69rS5d10il01+kVe/28fPK6qmD/bY/rd18z+8R8Q//hfkD/8RL6/j65KhG/AES3F0Dn6vUe5SJwClgTCUkMLAeK6UOEkBCURiUFkKcJ52qbBK4koMpxS2NTghzlOa2bBwaCgGipUlmA2N/B5jtcG1TQMU419tEe6LxBtiysrQuiWlM5FmUSEzuIOiyUtdJOB0XgBtipx3i8fdq1RUuF8oKobDvKM+eaI+vY2pXA4a9FZwliPmUwm1E2JUorJJGCMJs3zWEkMg5QGJTUhKivdle8SGRZWrlj8B7D81TvUlndu8RpxmuvlghiREMevkBLXLa97kvZJipYpvcFt24bgW5SQKBGdj7gQtV8RQ9Kca6NOrDV9rTPRZYwhYqH0VbpY2PBC9AJCJ+GGxbt9lMvp73VWdO/q66Qt0cf49tW96JxgdNIXDgG0VYnde4aoKoSz+Kc54ekjqh/vkn32BaNPP8fc/gCRZItr93Lrtr/uv5xEievAa5Pu+zzjPA/nTSL9A4ELNHXJyePHlN98RfNPf8F/+U+Eu9+THhyg6wZp2y6lNIbz+NVtBR9z5INcPI6IFUealKAkXsQfaTRIaL1D5yliNMTWNY0U+M0hbG1gi5SqSLBZwsQ2zKuSsqrQSjPc3UBkKQiBtil2kJCaaFVTN2hizy4fAsK7ZfgTMftKdFEMaNnVPRDYtkF6jyISs7Nt9JjrBIoEm2ccj3KOMknlGqwUuBBQSuNDIE1T5uWc/fIZSElrG3wI3LiVkKYZ+Ba86nTkQF/rNlp4gr6rrpRiIUGsLsWXvCzoaan3RMo+CgK/sOJFR+ZSLx1RUinSbBAJ13vadk5dnUR5SEcj27UeZ32sUkbMYJMqaqpSJzFlV3SEy5Lw43KAzqpe6jkLouwGQ+i/u7B+Pb3+v2S1aM3LziLtpZ7FtpTsFilRGw/ex2LqTQnH+0yePsOVc5qqJkkTNm7fpvjoG6pPPiP5wx/JPv2CYucmqijiCqG7lKdt25/32btMGNpaXngOnmfN/oyc3mOr94Ut2EPAVjXTx484ufst07/+Gf75r5hvv0Ef7JOUJdKHbkluu/DVWDxbhN5mjNtWIXRFTpb2w8KiFEunTZAKpwQiM1jrcTIgbm7SbA2xeUJdpFSpYe4Dc2+xwuMzQ5tCW2haBFZ5FC1KQFYYfFbgkpsoaymqCp3n+HmFaC20FuEjsYVOYghCIBKDTA1t0xCaFhlC1AdlT4bgkXjnqKzlSAkOEsleVdIeB0yWRV26iwoQypAXAwiByWTC4f4ezlmcs2zuVAzHu2SF7+JZDQhQWkeHVZdd1f8sl9yuv1HL0LKwTDZYxsF2JOw7YSd07kHRkZOK1ql3Ieq9XREZERz4BttYdNcOngBJEp1pMStYImUXAdhbwsjlhBpCd5zxmAXdtQ6hkwJiMXXZOd9iskr/Gb+MJV7xH4YgIPjO1bZCg/2NCdExK2TnwOu0edu2SNeSeIdsGphOsfs1ew+fYL7+jtFHHzG4d5fZBx8z+eILtv7uX5Ht3ojdMxZyw2oH31UJYvX5uXp54X3HhUn3MvVTf0kIwePaltmzJ8zufof9y1+ov/or+tuvUY+fksynKO+R3hGExHu6OqzLpoa+K6Yigo/dYDtiDyJ0KaT9Aq7zXUsJRhGUJmhJmySwM6TZHlHtjpjc2mAqPDPvKNsZtW2jRizANm4lpMzghYemRApPaw0mSXDDBPHpbWSWEQ6nyGdHJNMSP68wISCVilW4VCRJYzKqukL4gJaKEKIVHLyPYV4mISBohaAe5JwMM6ZGUjqHq2scMWkgzVJ2dnYIITCfT/HOMRgOqKo6btdbqvkJbWvJyjlplpPlA6TWBC8RSbboFbZIAFg8+D35RmILId4DsbIEXyyThUQoAaj4Oe8WDi9g0Y6HAMG1MeY5xPhj29YIFSMUdNdkEqGik1IIrO8z5zrZoVPtvWujyCvVYqKIZNrd/64mhOR0/HEk2mjlxn5tXQbgQveNUS19KvIpmaV31saeQ3Ey8AASk2S0xEiMePUEWIuwHjuvODg4ZP74MRsffwI/3GX//n2yP/yJwe//QL69HaNmhIorke46rxjtLP/16yHTi+K9caSdu+S/Aqv61JAIfdcA8Lio2R48Y3rvHuU//yPh668QX31J8vgpel4ibBtbaLPUa13ovMdBdK93jQ37/QXoQ4tC6JxWgUUjwrhE7JISBgVt8JR5gvrDJ0xvb7GH5fHBM07ahjTPSfIMoTTzqmI6nWBbSzEcIKRkXpWdhQNGS5So0KWkSjPKLGH+2S7ZzoDBRkZ2/ynJdI5uIgHRNAjnkFrTNC2hrkGAkwKlNVontMFReYckIPMBldHsFQnznW30xoACj0h0tHQ7p2PdlBRFwe6NnRibqzRZNiASQU6aD3A+YBf3oo2JHVqD70KxvOvOq1+eLxVP0Vl/3kcaDqK3DKPlF0QXEyziPRMhVv/ywQK2a2gZC4wLQRfnG4ldCYPJx2TZiEAX2tY5EYNvaNsGTyDRGQGPo11IGc5WCDxSJiBMZwXDIjSui/HtdeZItnRE65FdW/bOIwch1oCIvNtbmX3Jy1jOMnQJGKcIOB5O1+rIIEwCaYLIDNIarK8R3hNsYP7wEeXTpyRfDxh+9RWjL//C9IsvyH/3O8a//QPp7Y8gy2MHj3BaW7/UM3hJK/d9t4zfC9I9S64vlAFeBcv1X4xGqCumT59w/P1XuG++wX/1Fe23X6OePiGdzDDOLksBsvSr9w9BfK2zULyPxNzFSPo+RrMzAvowLQExk8oktARaF1vD1OOM8s42890hj3zNs8MDnh0eoJKE7SSjnlZUdU3btggkHsVkWuHxzMsZSsR02OEgJ0mjhz4gCKnAaajHKTbdISDRTtAezQhNC0qifMALaKczNALRZbs13qNEgkljo0YrJJX1VOOc8MEOYXuMyhNGSoJWSB1bmwsR9VwI0bGWZkgVCacYbpJkQ0xagIjOutDFMge/TNH13iKV7Ii16yEm1Knb2ReC8Z6YANFFRSx1xr4yWtdgsrPWZBcP7T1d9wg6IkyAFsQApTSoHEHMzCMEnC1pq2Ocs6T5sGuzo9FEq9sHiVFFTLoQOn4PEcNGBJ3mKwnIWEehXwmFACJOApFoVJzMO3lBdpZmP35XEyxgyX/9eFvQlIQgZZzYfJxgrFbILEd6CNISXOzlRtNSHhxSHZ9w+NN9tu5/j7z7HXtff4357e8Z/v6PFB98hMwy+qaYa7wY7zzpvk4XhudZwqfVp85x5D1tWTJ/9IiT77+huvc94tsvCV9/h3r0iMFsjnYO6bu+WSHKBn24V1hxYHiiFdU5mLvEo5U9Bk9c2rIg3EDMzApKoooCbRLKVFPd2ubk9g6Pq5Ifjw9xCHQ+RhvNyaxhMptR1TVaK4wxtG1LXddUdUlVlYyKgls3d2OrGwQ6MUgd9UZHoCLgsgT14U0MBvH0iDAt0WUJPmDLEt80scRhiEToQ8A3DdZ7SDNEZvCJZirhWHhKPFVdM69KauswWWzYKKSg6Go7ICAcz0BK8qxgWNbkgzmD0TZJOkSnGdokEPoqYbHHmu/uYOj+H8PvwgrxLjVcKVXk25WpUXQTa383onbqYosfEdA6w7mukAwhhuQ5kCqNYWhSgUgW+/O+oSoniNBSDEbodEzA4ENvGMRDkqrTn0NPsiwjFTrrNcBK650uJbrvAAwE38lPAkQXdiY6PZjAwnG7EHyX0mtH3BC8w3qPw8ffsxLTNNEx2K1sXBdu5ohRLK5rpukPj6inE6ZPnpLdv8/Gj/cpv/ua9De/ZfzFF2QffUQ22IwtlS5hD73PVuur4NpJ9+wFvax1+jrW7PMIl0DMsuret03N/PEjpl/+Ff/dt/jvv0XcvYt++BN6MkdZC77Lvxe+I93lwxtTFPqI27DQ6XxHuLEQdk++3f4XVNsVoVEKtManCXVqmCeG+caI2e2b7Ocp+9MTTDFGCclkOqcsHa1tQCp0UsS23+Wc/YMDDg8OcM5y+/YNxuMNisGQGHjgumW2p2lq0ixdhGWVgwRxZxs7HmCOpuj9I7T1cGKQrUM4i7UhpgF3zigpRDfxQMgz2NmE0QCfGJx1oAzeeqwLmDRBmYQkG3eJHLEQi7UBB8yrCqkNzu+RpHOK4SbFYIzWsZ2PczaSgJSxXQ1qqYd2Om6UBJZWb5Qf/ELawNuO1PySlIOgbRtaW6G1QSDQKsEHD8F2WmXsyoB0GJPGKA1ELLHoWrQx5NkInQ7xaIQPXRRBF7nSWap9+JvsDNJ+rCx12+V4lZ01vCBuluFxvVIsFufeTSKLhJuYui0Rcaz5mGWH93jb0jYV83JOaFsGAprZDF+XCGvx1iNDPH4XXBzn3RgHibOek704xg5//IHdTz5m6953TL7+kPnnXzD8078k/eRzdJYTY2Rcpzmvlg/q7494JcJ930n62kn3XXOs9YYFPuCahsmTh9TffoP99ju49xXi228RPz2kmM4QTRkfCFQ38HyXj+9Z8ZXHKnq915zeYlkuA5c77ghKLC1tsRIl4AVYKWiLnP0i5WCzYGIUT4+nzFuHxROkBJVgEoVrmqh/2pay9hwfTymrlo2NTYyR3Lp9k+Go6FoICJqqpC3nzIUgzXOaJpYHTJOMKskp84wyG5Bkijw3iKMpIng2jEFuDFB1iZ2X+LqGpkE5j/UNtQ/sScWTUUq9OyIZjBmNxyRpzry1uBAYjTZIkoIky7uSh9EJ5fsqZQS8a6mbOd41NNWcJElRKu2cZ6Zbqjuc810R7+iU6h1NwdsYE9ZZgZHoukoCXaVD0csHIpY77DPItE5j3Qeh8J2G6zpZQ8pYp1eLmC3nRUxwcb6F4DHpEJVkBEyn/3b1G5SI1cgW5ubpBIfgwzIiwfeRDR3hyig3IGU3YaxmtvW+gSXJCvrJXSwMi+ijCDHbLgrEBGe7CSrgncXZBiXANi2+buLYDmFRt4OV/QTAIVHOg/XMn+3x8PCAyQ/3uf2bzxk/ecLkhx+Y/e5PDP7m78hvfLCQHVaUndPP43uuz74K3nl54eoRcOWMk8ePmNy7B999Dfe+xX73HTx8gDw6Rtct0oPr42cDOER8GENv2XZWRu+r7iwW6EKG+slGnNp1JFxBfPqVRGjZmcESnee0ecah8pxsjylvbPN4XnE4m9F4z7yu8EBRDCiGI1oLDx8/pZzPSRKDtYGNzS0+++QDilRhXezC4DwEGzg+PkZLiRCKpvUcHx9j24Y7H95hZ8fQCEfdtmhlKXYylPD0FQybakBSV+hZhZrMsbMZvm4ilSQJYjSiUYpWSmSicCKAUWxvbJMkGcqkJGmBUEkMNQOEULFLr4q9zAIBHxqca2LbmyDiklfRySMKGdwixEqpPnqhL1tJF7lgoYsi9r4LG5MSiHqqlvH+iM6pFtN6+xvTL+c9BIlCglCx0aVKlplnHeECCKkJ6E5+6S3Ds8rq0iqPMcLdEAl9DYnQWaY+atC95u87Yup9CCFGyagu7TeqW5HIF5YtnWwWQjc5dNlpzuLahqaumU+n1Ef7iNkM07axc7EU+DZ0WY+RbCXRGOh2tTAu+udCWs/k6T710YTi/o/s/OY3DB8/wf30A9PPfsvoi98zuP0BZAMQMQvzbHW1Xxt+OaS7aj323mqW2l3UbGfMnjxmdvc73Hff4r7/nnDvW8LDB6jjY1RTI7sp3hFjaeOf0RniuwHnV7TiU4VhVv5e+uZk58jpLZJI0i4EVDRgohc5MdRBUGnFbFBwkKcc1g3z1qHzAXVVxiaNSUoQgqf7RxweHtK0FqUSxqMRm1tDjAokiWJQZAgSmrqiaSrKsiIEMCZlXtbs7T9mPp9z54Pb5PmAQMDiEUZQI2itRw0TnGs5bjxbaYHZa8iFYry1TXb7A2TXvsaFAJlh+84N1Ce3cYOE1nvKckpZVSTJkHw4xgWBTkO0XEWXCisFIsiOFLsWPSrBJCGWj6QrwC0cy7TgPhVYdNbhUryUUtM3oDyNZe+wsLAq4/0VXS+1/i4KGQk4OunidyUxsUAQcL7FuRYpNWmRIWVf7rLPmotkHfDYNrZnZ+Xeyy7WOMYBy2Vo2YpDbBHI1U1GCBfD0kIsrBOtxxXSCiwmgdWZfrkCWyaA6ESjE820bTk5PqZwHtNl5fmusFCf0ON7CYSwbKYcwIvYYdl1LG/rlunjp7hZyfTJMwb3f2TrNz8x+fY7jj/6iOHv/sTwk9+gsrS7Bv3TAH2M3Jlae79Y/GJI97zb1dkUNLM580cPmN39Bu7fh7vfEb79FvHgR9TxMbJpuoLfvnOELXWsGI0QorQQVgfxUocTqG4JJhcDPB5Al0bbPVCiIwUhY5PDgCCIrrZCanBZxgFwmGccIZi2LWkxIBkNKZxjMptTVQ0nJxPm85K8KPhgY4Ot8ZAkgTzXaAVGBBKjYuUv2+KVxpuEFJiXNWVZYUzKZ5/d5tatG1jb8OzZM5I0ZWO8RZENaLXHG49DUM3muNYzKhJk7ZgGwaRtCcqgxhuIG1uojQHF5gg/zFBa4usapQEUPnhm0zmNDRSFJ8vpLN5I2j5INCbqvCtLcK11vB8hEJxdhFaFxeXtrFgRnW0hBJSSnQWsFiQog4wTg1hOfH3kQIww6VJoCSBkVyuhq8y10N67ZJYQw7+Cjy3ilUxY5InJ6CKLcbG+s8ZBdRl1sk+WCD2xeZy3nbKvECoghOmiHES0DLvkBy8iifdpFXRRDsL70xQbwsJRFz8ZuoCCzvkoBCoxDLe24MZN5OEUJhNs03ZjvzMKujPvIxr7pqKLrHUfV3lexLBHjyABmnlJ++MDZo8e035/l90//ZH8yaeU9+7S/P4PDP7mX5DevIVI8s7PsZQufi14LdJ9l7LPzlah895RlXPKZ0+Z3/0Wd+8e4t53UUa4dx95dIipa2SnzzroBo9fLA/7siL+zMAI3dpq6cRYZhbF98PiQRALR0hYEIiITyJegDAKrwKWQDnMaT66wXw8oFGCQT7ESsVkMsOGQN1YTiYzqqpBSsVwkHFzd8zWeIiWDrAYo8DHDgKt9TR11G2DC9ja4V1gUAzZ2t4mS1Pmsxmz2QlZljLIcvI0QShBajJA0MoEpQ12XkKSY24oqB1hXgMKtzGm3t2i3hoS8hw6qaAYDClGyyaMWicgYqiXlKqr2BXjlf1CLlArzpXeql1mYjkXW6Wvkm+vYUptOuL1ONel4nY9zYL3MTJaEMOgFpOg7Jb3EKSInYBDJMO+/GIs2elirYXOulRK4FzssgF+UXayt0rj/ReAQikBysSx0EUdhC7KIJZh1J1E0A+wlbW86LRfuupheJTsMtX644ZF5EzcRycxdOeAkCjZ+xpkTF12gcoHrDYMhiNkELi6xjc1zra0jtjCPvQmA91TwbIoUz+26dOuAxYgOHTr8E3gqJxTT0/YePATW59/jjje5+TBj+jPf0f6+e/Jb3+ASbLzpN7zn/FfiBzxWqT7rhAu9JJCJNtmNuPox/vMv/sWnjxGPviB5ttvaO/eIzk+xtRNl9QQyc4JFhrtatztip1K9wR0A3H5e4H+7+44+myhaInJbmnpO+0XdJYTlMBqCVlKMx4y+WCH45s7VEqQpSleGuaTOVVjOTo5YTorEVKyvb3N9taY0cAwLFLyVKNlwNvYleLo8IiqqjHakA/GjEZDvA9U8xLbNpR1hdCaR0+eUJdzPvroDts7W7EzQvAoAdoYkmQAhcQ2Na6sqKuaIydInUCVLa71iPEGbjzGao0QGtX1/hLK4BAIaQhS4oidFqSQXb2JaE1Kqbri23Q6Z3zEYxU2ANVFGfQZWf4UsS6TI1iRFuKSuI/LFTL2KQvOLaICvLcxyUJ0KcBSI4M6NXGGYCORO4eQkRmDa3HWdmPDL9rCR+Lw3UDyXXsysdAxCb5LoLGLMSI6fX2pjXWEtkj3jZ1FhAclZWzwaWNauextdkFMFAl9nYluAugmM4gJKHGiD3E71mKKAVOdMHOe1EepQGizIPEYeRPHfDRGWIx/gehIOEpkhBgtYQnQaei9lWynMw6/+ZbpgweM73zI6PPPsQ9/Yv7Pf2by+R8Y/+GPDD74EJXmiy4ov3Rcqbzwpi3feGuXM3JbVRz/dJ/y668JP94jefKY5u5dyu++h8MD0rpFBdc9LqJbHnUOHPpFJNANX78YWv1roefeLm1z+fpqC2q54kSLOm/cbp/i6YWgIaAGA5xWzLWiurnD4Y1NnriW48bh6oZ543DEsoFKGzY3Ekyacvv2TW7e2GI4SDAqxpkSLNV8ymw6oXWe0cY2H370BRtbOwgpaJqG6ckBTVvhQ6CqK0xaMB4OydIEIQLWOfLBkMFwE5MMMMkQKQwQ8NbS1iVuVsYC6bMKOyuxIWDnJbNJTI/NiiHFaEQ2GKOVWXrUpVwQSnyAPVromKwRIvmIzjPUrwwiqYjF95XSnaMsJkk41wJ6kQ68dKr1348WtOiyuVwv/4gQJQDvcbYmhFi6cdEHrSczoSKZdV1zna1p2zkBR5LkGJMhUDElmhWiXAxQuTh+7zsCCzHmVYiYOhv9dt2E7v2i2ST0ldAkQhm0iJO2ErazsOlGbKf9LrLVujgJEYvgOEKUBhYyQUwvl2mGGY9JxmOoW+azOb4qY2RD8B2J93KaWEQzqC5MsPcE9tUtolMyHsPyOYrfUyEgZiXT7+8ye/KU0acfs/XF54TDCZMfvqP+/R8Z/Olfkm3fRGqJF6JreRqi3i8W5abeSVyW966UdN+45dvNvE055fjRQ8rvv0d+/xXp08eU939gfv8HxN4e6XweyxZCV9jOd7pVH3HQtV855RQLrLpivPerO14hhv6VniZWr0FnfWjVLcc8Xkq80kihKa1DDAuqnRF7Nzb4yTU8KxvMYITUBh0cRkXrIy8KAoHhaMiHH37AeDxiMBxgpIbgaKo5UuVIlXPrw4TtnQ/Iii2CkFjbgGnZzDeRsvNo2walJEaprqlhrDFgkpw0G6F0FqtkEYkoBEiDI7Qtvq7wsynNyTGT6YSynHAyOWY6OaYNjvHWFtu7txmMNsgHI3SaIYIBZaJFJWP0h7VRR5Qy/iwsN0G8U2JJutFJtozrVErhXH/coou77TXTvhZvT2TNMs1Wqq69ewzr0iqJTStdi/VV1N1V35gzWrGyi60NUqCNipMEuuMdG1O9FwVpuoy4lVoQgljEBhG12xjW1q+iPN76RYsdQbRql9llXehYVx5SKYFEYn2/zxgWJ0Xs9yaCjD3yemOgG5Gh07SDIDbdTBKsjuU/8+1N8sEAOz2hnU1pqwpnHdZGLdl5v1IjBFhY1fEsepde72T2opfnQvfMgQGktYjjI6ovZzx79JDxh5+SffEx4dkzjr+/y+R3f2Lw29+T7ewgTNrrMaees3cRl+W997aebp9BdvL0IdNvv0He/R7z+BH1va+o7v+I3ztGVHOk7TKpCNiFh7TL4AF8/3CG07d2mYa5vKinz/H0+a5mOfWIXBFL6pk86xoBCoRJCFmKGiZMRGAyzDjKNK1QZCpBphnpcMRIG0BGvbJbyo5GQ7a3dxgMxiRZhuz6Xik1JMu2UDcEWhu0LnAiLpeNSjEpQHTcQAy3EitL8OgxjDGpUiZd5lVfB6Bb9omA1BkmHUKxAVlO29YcPp1xsLdPWc1obMVkekI5n7KxtcNwYwttUpRJKIohWZaRpHnsaCs0Ua+MSQu9lRotw3ZRRawn3RAkUsneZEPKXseN8buha1vT1yagiwKwbUvjanSaonUa5QpEZAOp0FLHmgze4n0sTOMJeOfpHXsOCMHFAuYiOsN6Rx1E69va3tm3rKHg+xRwEejd/0v9tlv+S4kUS0321OTf3aNezBJCgRYoB7bper4R45ajob4kwHhnI3H1k5DHY52lamqmTUU9n1EdTxBlBU1NqGtc00AAF5Z+iNBvJyyni4UYIDqtFxEt+S6uPcp38ZhaAkEETAixjvP+ASfHE6aPf2TwySfk+08Qj3/i+Nt/pvzjv2T429+TbG3GUMFfmOxwJaR7PYTbK1PLv/oZ204nMV333veExz+SPHhI++23TO7dx+89Qc5LpOvtiD6LjBiv2jX06+EXw2NJo2H178WLq6S6fIBgORkLls4NWF4Xb2O1LV0UyKKA4QCXZ5SDhPk45WBgOAmBRoIpCnSSk2U56OiEGozGGJOgtabIc4pBQWJypDaIToeUKgdc7H7QOXFikRaWThUCatFmPApx/TJaChUTCbxfNCrsz6OvWtYXTokRPhKdDxEmw7qAThJSGchVQZIY0jRBBoetpnhboaxB0eJsRtPWpNmIJCmQOonxod4RvI1OLGL2luo6IcTwMr0YBZE06UKtOqdbiCQpu+V6iCZnvBJJQmhijKrwAWnS2GEhONq2weik67qgOyuXGFXh+qV+n1AhUTpeqxC6sKrYHqKTKETXK23hRqVP0oit0u2Kk40lmXSabJz5/eJ+xevfSyewWDmJWDg+yRTBGWxdx+7Soo1jomu7HhbWcp88EmvpSgRaa5SS2ODxdYWsa0TTEGz0O+Ad3q8QLmERyRDrP6/kx4XQeSzo5CK/iHbon9mo73cSRAAVPL5t8Hv7TKZT5j89YPDhxxSfHeAO9tn74R7p518w+vQzkq3trrX9Uv7rRI2Vp+39wTsXMhYJbNnSW4S4XAneU83nTH+8T/31PyOePSXde0Zz73um336Pe/oEMS8xnRPALaza0HFkv+xZid2le3BWLI/QSQ9x/8ussjNuM/pgekFA+JVZnxWrN3RhRlLirWNeVeQbG/g8o90ac7Rd8JOvOeicLChNkmVxSZ7kmDxjONxgONogS4vuQTFovbSmYuZbH3Dee+aXjqTV9FKlzOJBERAf9pXle3TKrMgoYWXboSe4rqg5Eq1TNja32drZQWqYzI6ZzSZY72idZT6fMxgUpHmKMQaBJRUu3lcZtTqNjwW/pej8Rh5nG5yzKCnQynSWewJBdT+BvthMf0+i9elxbSclCBXDmkQsfpNkw5gGGyL5eqC1Na6tcVYipEFKHTPllCH0FqjsipP36Wz91CpE1O6FJAQLoSt72TmwnOt6rQkVQ8BQ0SHlbGeV92PEd5+TvZoc5Q9iQshqIkG8BfFvT1ebQQl0KgjUuLYltA3KJCsWYlc23cdJxNsYRqgEaCmxWsZ08C4aI1gXz4mAxy5rXSwicjpjRnQqSfcs9Hl3UU6INaOXbVe7yKAg/v/tveuOXUeyJvZF5lp779pVRVKiRLXUarVa6j59zrE9MDwwYA8M/zAMGH6JeSH/8EsZHnjssc9gTp++qlsSJfEikaz7vqyVGf4REZmRa++iKLVIqu1KQayqdcmVl7h8GREZiZGgfEjoiCTW+2qFvFrj/MkzXHz6Gebv/xSHv/wS6cF9nHzyHuYf/QrLn/8c/ZtvIczmMLv73564lfKjE7pCVy43Khib9SUuvvwSl7/7A+IXn2LxzWNsv7yP8z//BenBQ+DyEpQkr0AG5OwwVlRb2VIXgqHkTTBJKYgJLlRJr3vpPG2ng8G8e0M/WWMjZ/MZMgWMRIiHh9jeuYWHYcT9qzWGWY8FIub9HIe37+DOnbfQzw8wXxxgtjjEYr5E3890O2xwSVAkaTY7e6J8XhnVISM7HdaSgNcmUhnraWfF4sDl94rsVVCHDrP5EovFIS4vzzCbzZHzgNXqCs+ePUXOI24dHeHOnWP0fY88Dmqq6DCMCevVGgfLQ/TzpeQ0iBFdjKA4x6gHa5p5IKeEGAO6rgfHHoG6xtst5j8Z73HcaB4FOamibCQgRf9ISOMGhIz5Qg+atPhglvCs4v3XLcM1FlsVsW3Hpa6sejKrQjHPEuu1km9Bck4UPxShZBUj0lNEOCJ0Gm0Bm1BFqiyOQbHhGpKVXY09RNGMmytsVhcIsZMDPi1/L9uEAmkYkQaJyliv1hivVpipkjBQIhacGr4nKS+5VGPUIMBFQQ0YSYWz2HQzAsmmosySGD9bsmBVCJEk3iIwg4Yt8OwJtufnGB9+ie6DD3H80cfgrx/i7E+/R/z1P2Dx0UdY3H4TpGF4f4to90cndAGdzJwxXF3h4tEDnH/yR9Dnf8by68fYPvgKp598gu1XXyCcX4FTHfCyYww1BIwpFwawKAX7BopgliIx5CqQmB3RV+ausroKXI3SRcWCVYgxAUgJNIzoDzR85+gQ28NDPFmd4DwHbFYJvGTcWt7CG3d/gtu330SczdF3M3TdHH2/KLbCytXaRodkrVwXzxgcsrXdWfBtNdOD66u/X0ZZPdsUCLP5HEe3bmG1Psd23GIcB8znklDn4mLA+cUlhmGL2azD5eUVZk9Pceetezi+dQez+YANEsZxi3Xo5Uj32Rzz2Rzz/kBDy2Rks26P3W7XINqg6xf1ZF5tq0RvyQkW45DQd3MQdaKKszjFMmQHHMUeXYySPIdiMZ+IjBNzR04bjMMajCTClez031DyIwBdFYCsqwBmUJAIC84JOQ8i/B2l2a4zUV42xgwT/jHEesyT0qA46MQ5yBYRYrMYI0IXkVeMzdUVwHKMUDeT8D3EDpbU3Y59jzHi6OgY3TYjX17JqcG0QAexPg3bLbbjiJQk8U1grkBGpW+GjPmoTSWIqTwR0Kkgrs68ym/MkDPpYCQtoW6BCHEckL95ivWzC2w++xTLj3+Jo48+An/zEGe//2dc/uofcfSLj7C8cxfoTfj+7ZRXkmXseTZfb7UV5gKG8zNcfHEfV3/5BOHhV1icPAE/fISrTz/F1f37wMkpsF1VBtHJNdsjoBsbSBbSuiAyGN0sS+05MMqWRjFxGBW5TQ/uX19KbaXeSkxZpftms0G+vMJiHNHPZ9hEwrPLNc5XG9x68y6Ojt/A8a03cXh0B/ODI8TYI8auOH4AScxNgCgSVGFbvftQx0d2zbRnatYqABrY3s6TmCvKqOg3fD0m5OU7pGiMgtQ/63vEeIjtNqLrAmKMuLw4x2qzwmbD2GzWOL6V0Z31ABIOl4dA2mKGjPnBIZAZ21UCUsJ8NgepQJQjbDrJNxw7jOOANG7BOSHqOWSSB1f6EGMPHjfYbq4QoxynQyQxvKS5FQhqI9ZwteJcA+uKgNATMPKI7WaDNF4i5aQOP0LfzUCxR98t0fUHCNFOB1bTA2TjQ6Yg4W3jgJxGEbRBzD9CJrZh3XIHD6oUTX1DUjpyKgLfaHIcE4j0hAz9bzabY1hdYXV1iRy3AB+gm5vpqBehzZIEfnZwgHMAq/UG3XZEYCBkCR0chwHjMGqfs6JXqnRFFRET1xMvjBtyJmTdocckNFNySZcWs56Dp8NmVGZgeNwiP3mKi8t/xubLr7D85a+w+Nn7SE+f4eRPf8Dlzz7E8hcf4/Dte8BsrgpazTV7zA8/ls1crz3LmLE+jyPWF+c4/ewzbD75I/rHD3BwdgJ+8g0u/vIXrD/7Eun0BHHYSmZ7EBJymfyU3bLILZFsOega1HqHnba1FpngrR5g395a7JlGgLEFpOkkK1MFIjlDbHWFYXWF9dEM3WyOJQOzfo7DwyMc376D+fxAPeQSRWCbBKQpSc9e83GcsSBby8W6L8pCzARJ39HNpGYvNIoHiunBhKvZhe3U4oLINL8Bs+zIms97pDTDxeUKl5fn2G63ODg4QIwBl1enWK9XwEB4evIU22GL09MnmM/mODhYop8t8Na9d3H7zbfRzRbII+Nqu5aNE/1M7LlBcgDLNc1ty6w5EATFwjYqhB4UGUNaIW0u0fOITqMlYGYIFjoZ84hYUJy+b8IwdIizJWYBSENA2srmkpwT8jAAYwSPW+Q0IHYLxG6uidBtXFE3gnSQjGF6LDrrRhRJli5rMwJVd4alkwSVOWaOoKRhbBQ0ZtZWJ4Kau/kCt964i/l8jvXFOYbNBmPOiLMZuh5iR+9ks8ThG3eQ3nkHV+dXkmFsk5AH2TSSVMNTZQmA3DoxVzoLFOuZeiaYCcWhJm8IoBJhaEl0LNK+rlQ8bwG6L3G9Qn7wAKdPnmL9h9/j4ONfYvHxR8gPv8LZ736Ds/c/wOHf/SMO3n0X4WChqHnX7PBjELjAj8C8MI4j1qfPcPHZZ9j85c+YPXiAw9OvgdMTXHz+Obaff4H89AS03orn3cUBJpa4QBN0VlgRpmlhW44323R3bJkogtKQrgO79dk9gtjPL6OGn1GGIKtAkpKRSNDrfI71OGK1WmO+WGCxOEDfz9H3kl7Q212zBsybsLOdWSGIfRMI7n5rHpD3k7bf+k6IEahBPlR+Nl0iMUcI8nVjRM65RrLkzZmx3W7UTqq7nlLGiBFHR0c4Oj7A0ydPcXZ+jvFqgzSyRAkwMO9nWCzmuDg7wxt3v8Gdu2/j6PgNxG6OIQGb9RqzxULGrZ/prqlOnWXWLhFiVIRPBMUZ5vOAcbhCGgdZumo4HMVe7ZzVdCHyTUwnxWbOYrMN/VK2M3cLhEGSAJGdZkFATlvkMWGIG7GhBnWKUU1YY2Ns2cFSSGAm5GHAdrsC5xFd6FRhSH6OngLA9TQGJrXlsjjkzERUdoCpIAv9HMtb4hS8urrAmEcJv8iSpLzvZ5jPDzD0HcLREvH4CLi4BG1H2QSTsmR3U0Iu9KPHu0NTmZqpSo6gp4b0DLGyrY60DtvsIC3l6qg2pzXV90GVl0JOmK2vgEcbnD89wdXn93H84Yc4/ulPMT5+iPM//gGnP/8Qh3//Dzh6/wP0y8NrzWyvu7wyoVuNCACYMQ4DVk+/wcVnn2Pz2SeYPX6Mo9MT0KOHOL//KVYPH4OfPkPcDuiyGOgZ7Az2SW1ebaCWATHb8WP2JBPKOxjQzAl+sh1mDlopgTRvFIOYEJjKMsgsug3KZEEhFAI6Coh9D5rPMCZBCRIDmbFarbC4dRt9L+aEYMiVAOakMaxZ/5cTc4kC5vODxuEIVATrTQGlhb6TMG90RbjtTJkvur7HbIwvWbjKMi72iJ0kLb+8uMDlxRliDLj39l2EELHerDCmjLfuvo3F7ABn5+e4XF1h3I4IANZ9h2G7wDAMWF1dYHVxgbv3Vrj79ntYLG+BYlfRpzqSmEZkmGCrqFLkggoHEBA6hNkSGDYSEYGErgMkH4FmHbPdVpoxDSwbAex4d0lKFEBhhtB3mHVzCf3KIvgAkhjbrIqeGchJ7tcBLApKJlbeCSEgRT3BY9iiW0iIIEwpqCBjllA+AEheSOWSZqkABgRN0pQDwvwAYdhivNgAPKDr5tKUQAgx4vTZKTaPvsYBEcLt20gUsbkIyLRCHgg8DLrzUvlLJKG4PTKVv4OZAyBhZVT+rkdmRpZtNkFXGgGQ7cxkG5cll1s1X0wNj3orZ3SbFfj+fZw/eoSre2/j1vvv4+i9nwLnJ7i8/yku33sfhx//Cke/+Bj94RE4avw3W7qg3Zj6V1lendBlEZhpGLH++hFO/vBbbD/5BLOTZzi+PAN//RiXn9/H8NWX4LMzxGGUI81BsFT7gUi2NeYkgf0mUFisRCZILA7XArpRBIdBVze3ho6g+8mVkEyziwedy8SblDbHiaFiE97ZbQOVZiT9SkbXR8xvH4G7HstujnnsMCijE0FQkArOnMxUYHGiGeM4gAiYzwUVe4nZZuEXNWPeciv7lldNSFgZpzpeZmawkQLMJEN6XHnAweEhZrMZkCSsb7PdYHG1wO3bt2Qr6nYEYsDx0RJv3rmDzXbAybNTPPjqAQIStrRFHkd0OMLFs2fgYUBkwr33ZugPbwEUNaRKxppTEiGk5oag3nmnYmr7qQP1QBcictItyJZ9zJbDSg91JZP1QEqAoJnPAIiTqwPCDKAsxwTBcnLJ9u+y0klJ6jREzBk8Zj1wU+zggu4yur5HHEeMKSMyI5LuQmMXdUBRl+YWQ6EzYvcLH6CKuthheXgLq/NLfP3lA/Sxw9GtYxweHYFXG/DlGtsHX2P77CkWDCxmcywPltiCMNCVZGYbExhJlK7SKZnghQpYJnSB0BHQW+4OSLxHRzKCHSRELJLtrSNIwh+rL6gCCZpvWvobmFVQswpoN8NpBD18gMsnT4BPP8fx++/j6P33kE6e4uoPfxDh+5/951h+/DHmt++oeeT1o99XInTF9pZw/uwJLn7/L8h/+hO6R1/h7tUVes7A+TnWj7/G8dUKeTYDvfmmolVJwhG6TogtSu7RNAwF/ZVMSMowDGhAdxWrsryvtiV2hFrq0CVQWdrbSQRJIEwGY7QDAjUTua1uGWrjyklS9WW1NeeMzISodcYgziVk4IAJs0AISRTSweIAs/m8IKP2WBn1aMd5iVmtJybUZV5d+tf0iKhdheWgtTCgxuxQ/sk1aiH7cayIw8bVlpiHx7dxuDzGg8sttk/PsF1fYegAPj/HweEhaEy4uDzHOA54886beOP2bbxxfIy33yWcPn0GHhLuHt9GzITx9Bx0eob11RabbUL31k8Q5ocABaCLSDEAMQpa63qE2Vy98cpO2ZLCU1nBEEt6xwhShDogD1mURqjvBjPRKC3RmEA0lv4K2jYBbyOhScd1oFmP6YFLWGMrJeQMzkmSieeEkfXg9MzoU0bOa6RtAro1JAl70HMpLXwMhWZlFSdzxmOq9nyjA9jmjYzuaoXZ2TmuvnqI9Thiffs2+i7i7uk57i6WoMMt4rDVsMQO4XAJHm+B9ey0oPxFLDksbONFCKaKxMbcEUA8gjgjqroiiO25g6S4DGqvCACI1DyTk5zeTEF4PUbQrEc/X6iItBSdat4igFKWHZQpAVlWK7i8Ah5/jXnfYx5WGH77DFef/hmXP/0Zjv/Nf4tbv/o1Qjd7rSgXAOh5xuWU0l/dvjyOOLn/OR7+p38C/fH3uPP4AZbrNbo0IjJAeoZSlyvKEAKVySknwgJAlqUtdODl7GeqEsOEqf8b+qPs2xcUWzqmqfNkaVaZ0Npiu3psaWMVym03PDmDxxF5u5EctlnMAjwyQlJnHxE28xmu7tzGyd07+OOccDGf485P3sVb73+AwzfEkWT9BoC+xFqqEiICEFVZ7KJZwDnDIChiGoPr88RWM0RbRFbk5prfWCLPaJ7ZNGD7+BEe/B//G7Z//hP69RVCIPR9L86jNCKNI8btFsgZxwcHOJ4vEDJEsGXJg0sgSbYCTc0YO1DXy8kMFDDGgG0MGBYz5OUcuZ8hRwn3KstWPcuOlA4YUHMQlJagK6QoWclQ7YrENdYFDIScQeMApLFZMpfQKwCUs6zKwJJbQ49wD5kR9SRoXXM5GpWVjzlcTahJHgXNSKc0RtlWKNV81cxXoXetOlBZrGUSoUcEBE5yzE6G5G8mAsWAeYiSkIaTggiNj2YBD1EFaiUfizLiEgMdQ1TbitBk5iQCMrNuJ1cFmDMwjjAboOStl2s8qIMxBDkMNAZg1ssqxGRAthM1hKaLaYJCOfYpc8ao2dLCIE7E1Qhc3bqL5b/9t3j/f/qfYdvbX2aJMV4LqV8q0iUQzj77DJ/8r/8LDn/3z1iu1wg8Yk0oGjBSRo4kS0Wzz9ly1xifnag0IWiCt1kuTISHEgmlinzYzswCYEduMySBCk9fjgDHDhyq/VB2KFUqJ3YZo5iV+FJJcQeIMyqT2NFmaQTWK4zDEu/+5B1cHh5hdusOFotDxJJ31U4tEKdQPcHAmJGLg8wj2jJ2fiiIi1mxjpVl30LDxB4tT4s3zdjfZcXAwNHyCD8/vI0+RRyvMkLKAIbySlmeIwCbAR0Gt0y+rojasPmyFIOZCAPEcINQTUzNOLjfA7fXbTuzcrQg9syaa9d9m6ELdS7jb/6irKdIBOgWXpiZRt6NROhjhwDCmCRkrJ5modRsggsMI0Tbri3zEZq/c6pqzxuSdF8kmmlTFkJ5X1ZodW6lZ+KQ1j7q2XB6Br2aE3RjidnT7VQO3YJNuW5TNrs763FD4iirIW6yCpAsZqCqcMx5XQACCfRi1XRUNmYY2tHrtvqwlY059dyqNgBYjoz+ywd48r//O+B/+B+Bmd9a/erLSzYvMPpvvsHdP/wOb56dIG224M0aFCWPagzKUkoYsbFLSgnu7xoc48Sr/rFHTMhEpwxK9qAuTxyRZBXwFGziUQU0ZWSzAxUercLHLEyUXQMMFavTJKsczgQMRMizOfj2bXTzHot33kS8u0Q4PNZYUirIgYIIXMNl5piraCcrAq79Kpmq9Jo3PTRj1dhqhTiN4P0ytk28Ys4MQ12mGFm910AcRvDDr0GPH8tJwq5MdUGGCcq8Z+7aZy3SwhAjAeiYJf8ZUSNUdajab/P1LCZIWCvQlYwxu18NGAlYX6gmNWzbq1UlUgccbF7Uxkvt+LLSnqVF9D2v+Li6iptoG1O6BlLKkOuBmESab0EzjLAs8RHqUT+cM5LG4VbHKpc++jYFjXNmGw/JUwoVr2riU54u3fRmLqUvdcaaecL60owlV7ogE7RTxVoUIYkJ0ejewkcJYA7gJOMXh6xzUh3Fr6O8VKHLyOgC4SBKsLcRgk1MIACBETMQyrZKedeWyNFRu5L//m95JGYVsUxG5qQhRdQiIobu7Km7g8ilD2S1fdbvcm1gaRFKhqgqlMzpoI4/Q2ghAjMC5hGMhKOcsek7pE6iFowVpA1VG2cVst5MIAzniZTbcdCSdaktdmrsPFM3fhiCor11CcMI0jJkIkLGLTeRsZx1mBPQcSoiQyU9auunyLSiL/tBqLGc0G9X9MnFskMknnETWcZsvuxDwfvoKKt8KOxugHjn6edQoskGAiJkGWvCxeJRC8+rMJG59DvW7BttR2rolfscpdJQDvVdc7JRcP3RcBsKXFZmTJJW0+bVAEcoY+/7rwhdx4hYQZECjRIynMV8IoJXY40hlTIADgB1ASHkCmS4tp11EgNpfLlFTzjFV/hQJz6rZrUcFbYTro4dgboesKTxf6XQ/Ws2Wrw0oSvdFYGVkEBI0t9FlOWCO2mXSO1bIRRCZ818m8gPkBHiHtwy5SzAIAnCDMjJlDhVZGPCNgYnaBmWSbduGq49smp9cdYG+I0ElfhNwRBSHsDrS+A8on/6DOmtt0FvvC1mlJxL/GpFlEDF+N5xhmIimJoFLGaXjfupxtbuE7j+712BWyMozLxjThXo8zlnDDzqRoENqGOEXFKlFKTmBSWadmgzwU0wfRXuHuXIw8HMOdpFQ+tV0NuclY2yRVROqiq6NDZiT5UQTRl0zzJ+Uh/5PqikUDOmQ5MA56osAipdsVXEXslz24ymWFt3rzFE8AopiN3ZTGqm3EyvkKFQoCLyPawGu8wm0EXgSS4iluRAmUoyf9ZNHiVhGpmZxtm63XeI/J9uk4afXTutg0SIy1BpZAhBeShIP7RfOdK1/fmu5a/ZaPHyd6QFzTuas2ijAJiJecogdSkss114QqVzJapv6XDzHANBzBl1bt2/DCDU7AmMeqxfw1tkjLCnj+6Tnkk9thNTB4BhBK9WiCGgf3aCfHqKdG+NtByA1AGdZdHCHgFp5gM1XeRUUJRHquV7xVbblTE0MwGuEb7VaWNX6oYLBpfYUGbUJCg5I202iOsVaL0C8gBDpo269MNXmJocmqSyQKlSSgKgAHG0yH3raxUsgKIdPykmDCaT1JiIirLVh7huGGnqKmRZ7bs7RQWKDVATQaO06PVNcN8QQUiT5327qUF6ZvusK5Na19REJw7P+gjZZJQhCpq0zeZsn4Dfgw51swQVNEuAplEVJrcwvwyQnSOnFLpnNbVvM4OteD1goAKG9Jumm9jNd9Gmei2jMZa8zvLShG5BFfMZOM7ESWHLCxj9ctVqKmSMxgpNmErGRPH7b7ll2m6hnSWZUX0VBJWgiK4jOOsX6yRPCHvfGHDtk10gzuiYJW/BsEV6dgJ+9hR8sESOHdDPNHdC1PZQaajvfyXWBOZ93ljZsdUiVm0pP09TqyNkOgJE6lvJ6vyBoKYsfcF6hXBxhQVnxKzblHdqbseGmifqhBfZSVCnDqkw5Ko4m+abgKJCR7vzUyz5atev41C2URemrn0uF+wTe+puAWZVzgVUWBRIUz83b5a5KZVWCbvPFGNCiJt6WkHWpIV0369tUAfc5NP7yzUPTACO10eMLLSsCXbIjkua1uzGdMpfpZ9m/y62bzZNKV82hF7qN+hUFd6PpbxcpEsMLJbgw2NJ6ZadhnLLi+xo2wEOLUZApdJdrlPBVJKITBVy5YCyJDE0IyCBAdpno6l21SmamHrzm8KoKIfgUkcqnmYGjwP45BRMHfLiAHl5AFrMARyojStPmN6joKqEJDnLCEncQgVN+Ma1BOua+QJLpCbczMaKLXE3pJ05IZ+fYfv4MbrtUMw3vvZrhgnVqdGiQgWV1gi92mjipo1ekLrKJyh+2irfx4linZYyFdOetALPfp20cLe+b8FchjWqwJ2MaTMGLyBQ/PNlGB0tYdq3a9rM3DSdmuf3vE+EcvIIuPj8jJ+Kb4JohwrK92z2yUw7tpU4OGTLRQ5MGla6H2U74jV9e3Xl5YaMMYH7Hmk2h7GMaEITDhbg77Wx/j9ZLjHDLSudtrNnrO6940mF6JwVaUK3FQlN8cBzy57vsWOQjALARMkwg9OIvAHyeIqYGVgskO/cRrzzJmiZgBx1jCQXq8jKADsNovlSGSt7Nu4IU4suaK4xT56zxVdFYybAzW4r35MTCMyjzJxBKSFuN4jDBnnYYAALmvewZ1KqQsmTMZQE2S26c3Pt6jRks7sstWAu6LjgBXjtGgRmL19LCoYuDZB7MxicUGhH1wf67Vd+KlSKf+HFSl0ZTev3FyyCp16rI0rlm/V5wBKSS/3VoWoAo4mYceNFgDj4WN4r9MyAnZRM5DnO+K/GmvsW2jVRSpP31DxZNy35LhOol7jfwFyA3usoL39HGmnaRWb5GIlnE5rUeNr3gjzL685BVJ7xcEZKaF+b1jqxF8PVybLn25iD0RLQTrQCNe+bt7e2X67nEn7khoIJSFnO4UoZ3YxAaURYXWH99BnGkxPg6JacXMAotk3ZJ7JnWVuWYPYhar5vIWgVeqno37Gn1Y0WVm+rj+QkBEPgSCOGnKTvTMCwBW03iLqbK5f6bcz8OJCbKCc84ThF4VDWuaCS+ESYtr6jzAT3HdMvNMGr+8DrC3igC+UVuqhj2Ix/M55VIRT8OFV6vhONs87Gx1S2G5sXLMW+z9423QrZSuxFW0DXYU37a4il9bs2t5oxrEJqeKd+S06jaGhPR6ZVUlbHbn9KqwxsGwjjgoMBZ56cVkIEPYbq9ZfvJHS/V5iEEaqOhs1Psak1D+9BG2W428k0BqiTuLvws+cLUi6MXVGT18p2saGXHQE/QY3soyjtfS6Tbuin3iNJghMiOEb0AOLqEtsHX4HvvIH+7lvIiyVGcG0zQ3PoojjRauB86Ui1TWbNEhXk9Ngy3sbEytR1g0S9vs8EwWU7q+Y84IycBqSUZGvnsMVwfoHFeoOQuRhldmbTUFF7oZqXyhBbSsM6XbYiCjs7HdTWDVcJ8/M0cFO+FQDbc0XgVjqq6HaCqq75Nrvlr7cWFURtCqQkmHlRXrPK2tXLft5yENQ5O33ioB27qm+nR5fF3oqGbqb9lz6ZaTEVE4HF7BpAYNbjrQpNav2EFpmbOPE7JouytnbKc/7QDNebF573l1G+k9D9XmESQU7DbQpBs0EBpj09KmByJKK/ZJIdMzbuO/GoTvRZcHaR9PWlSX+gE5jLc8UeSd67TMW0IbXa5MvPUGCLfZMdR9arSsmy1bOLGJEwXF1gO6zRdT3yyTOEqwvwnTcA7lWbE+BidJkY09wK01KPi8+VwFl2sVlLDJ2wpelTwS3Hy8jyV/b4Sz2kkRMm0CJ0GTcOiGlAzBm8HoCkO58azVRNCPsUo0+/KX87iWQ4ximV3aJi0BRxmf/9imRPC65pmdRWbzkBQ2Uonl9MGDQIg1R31y3o3n9bzTITaf4dJAWDJ/UoXWKXboq5rgixCYDQS74+8jzgeEby7LZgw49/u9rMO/dF4LdOY3CNhTc0uzMk3v8BTYkKRtRTQSxtAEPTwb7G8vJDxkhy5nqRRKp6Cj3CBk9PIp2iLfulVMI7zzTP6V9V+TmvKldRbC9Z8HjZ2WL7uAvKtqhZRyBEO80oqLBsgZouDBkBYl7IY0YexT7a5QXi5RlW9z8HffgB6O13wGEmSbWdfaKGUmUwj7BTEOr3Q1FghkhyTpDYy6BJggaQphU0R2ENP0I5sTZrfzTnWZUwOUucddZzrfKIMG7Qd3LMfA4BNCa0Muw6aVGF6n7pNUFn++owhecekblWJV7Qmg85MvQzZd+JorD5039qOB6g69X60WrXaPtCkLPCuNKNNK969l1Yt+vX/r66fQKO+EIRmE0kQFkqOIFZEGSl5WatZveD30g0QbFFJ0p9ZYwVJNCU6m381Klmh6ZWRCLztzfUrVld6/xxRedcHwZ0dWRGmWl9sYsNyf0Q5fus/r+30P0uH/P2U6fz9J4+465Oa60arz41FblVLKJoNu+cY08oBQ0ZwnV5aQ3+Ai4aEEVSV8alSsjg8m5txd6RKJocTnDxMGB48kRO+z17hnR1AY5zcDkCRsS/2UolcXhW520VBJ7hLEmOHG1eswlLRqdRTr0NHQwFlxhNToJ2WVvLjk4NLZE4LQIz0uUlNo8fID5+jNk4lO2YTFRyEbfj0aJY75jZO2J+OTt9RDW4Z/MmdpeAkn6z+XadDXIRKpX6MprZN71A9QviGzL6UjMNUdtGqgq+OvBzqcNMFmVsrf7GvqXtJGoFLkToyxBUQVjNZVOkTG6cyPWv6CelNYutrW9V1AwValQmg8o4khw+CV2JFVpU017hNXvL8Q3ZxhYXUWTdN9MLV7VnIKJRtuCaGAsGkNrcFYUSfiCBa+37ruV7C91v/5h10dBUroKLFK3pc/JvuyAljxjYbTsFHJU4hsQEibZNmYAPER5s3OP7ZfUXrnVf8cRA0AQhRhiMtG9X3KQhBNlgILQmTrw0jIgZOBwGXH75JfK990DzJfJcg9ZNd+sRKhbyJiGsbX/NsmAOKMAIvnbAEqK7UVO7WtWAVYl4KF3jRsgQ2skpLv7vf0K4/xUOTp4hDVs9EXaSYrHUwY08kJC368atsCE84i9V6TP+ls6stDGrYCxKRWN0fdrL0jrdZQd5ttgEtTYO7UfkyYmjizWxkQk30v66BpbdhmX7vypqNhPPBCU6Mp/G6xrdlbEgcmzBtaHFuZUV4bKrw0a63blXfzcashSXOrCAoFZkcUTri8X27eyrMu4R5uYKsDlx49KsSLC/kAreMihc0TW5eYAmqCeUVWsIARSp7dxrKi/ZvECg0En2f93OZzpNSl2ywf5VteadCyXUyiaz1Wfl7+pXmkhZe9qIUYUW7zA7le9/aynLOSHmBs1cWyxmkWGH+WUwQgZCBMbVCvn+F+C376F/4y1w7JFjV6M8bKMAAbAjZfRQRhsPOzol6+4tb98F6m62YRwRIxCo02sSUWJZpexY9x0lxtZpTby+2aB/+AjLR4/QjwNCFtSao/RTa3NLWRSbqNRhTA3UOEz3sQLi9ivazJp4xtmpJDVhRTVURMqEboiKoBXarBnFTIjtpQS7bzuxDFmyp1Ot1gRrBaPaBJt9w33U1G8VNLvH6k35zRiGyh/tI42wroGMreNrMv47XTW1U1FlA3C47O2tfYY5sghlWzFLn71Dt86Hn/d2jpu27Kya6jx5lve0Vmgo7IzyaysvOeENQF0EzWcNIZRJRCUFI1yRecYErQauk221T77HJpMdknWFyCGbPeFqTZ1GQPvld/M0lX5YCMzzplY1upkKjH1zBq6uMDt5hvHhQ+C9rxFnPfLsAAihePgZQE6k8eGEcsS83reTgKcC0zs1QggY04CcxL5LsXNWFV3o6dKs1MFcGKoouZQxy3L0UlyvLdPsPl9NszKyMbKxtd9FgNV5m467z+/rN4JU8FLbVl8qWNJXVG/6zaE+zOx5ercx5tcwNkCEeDHfuld2f2+zsE2JUSl4VyADaAfYFOa0TnZg12jyORDS/Sxo3PNZMSfy5C210zbcAMgqqSy7nE7kAlh26bOuzvYXQ/ZO8WiLcknsoUnmdxDtj0HcSnnpQhcxALOuXriu756O4SexXMIu0Uwr2zW6T58tst+WZvuQnP/T6Izqe6XGxotWX64Czmdx8Fqn/Yh0LQPDgNl6Azx9gvX9T2WPxBtvAYslUujKsUUgOSUgUy4HIbLxmF8hNN+pwiyEiMgdkOUoFmRCQCzPCfE7dmeNmTVhy1kyCG3WSOdnWLBkm+IxS75itndtg0LN39CWaUzmRAH74Z3Y8z3ulecmNtgCR3MZD/ifjY1Rl7oN+rO+mkpV5AnDBAVHoZq7/PdRhS+3dmf2r+yFbrX+XZ5RoUVVeVUTgS9UBOfUqr0HrsAZjrRxdiKgmooaJEpoBbxtc7baha+oGV8vsK/j0X3F1UHZRbZAHHJBNHcJX8uWqL6KaHmWX2Al+mrKSxS6qqsDSdgY10MeJnKsIZ5W5+pvZEDLv/ltAthrXgcTHYMYK7Ts7GrgihDKiac73aymEJ58zxiNik1a2m+Oj2IRZFlGxkzAOKA7OcH4299gPH0GfPQR6KcfgA+OgNDJkUWAIlxzgrlE0lBh75yXfjysT4HEbMG2u8iQkRvO0p+ycmAgJeRxCxpW4KffYPv5fdxab+QEYN7qpqNOTZl1O8Oe2XDtosndXe1MNB3+oGjK4Fxl9Gqabh1AzADcPJojtSa7sQ078rFi47XWeOHWADvX5kZus46jExQOWID3r7YK+vf1NYPRzmmgMt3ONmy3fWyCrjGt/04xswrzNhzSNg0F2Kkblt0LqKarWo+LrbYq2GiSCigoQzcBBiWpFFXFRm5TBZEqd3a8yQw7r9A6XTKksQ4VExgBoZ9rdIWuDl5TeclCF2AiJM1G5QVDI+oKg/P09QmAoMlNq5PK5O7oTnJeWwucbxCUPeZCimj3gb1JThReGqESU4ma8M2sOp6LWaF5QL3eRACGAf3FBQ5Oz7B+9A3SxaWknrz3LvjgCBTmIiJFgiCzORaEWKudTbZYSkJnTZ1JAEhOrhLzQYeUt2WbsCT7UTXkBFdRLDkBaQCGFfibx9j85p/RffYpcH4OECGTqTBZ7uYsyblzMIEv42ZRDbvz6sd4V/DujD/pMTxFcLqbPBEqk/6UQykBqFdU50dfL8JS27Fj66htl36Z4aUghFY4W9NUGu32rtKyOWelix7ZtaYr+T0V+e6fb1Ewq4KVgwJ8ffadQEGpRIUnXCyuyz5WDRstt5UTJooZw9OQ639RJk656DyVUzRgNBHaFPcmSxmQqBtUgWuTZvSn4ZZmKmEEcZz8CMpLFLr1aGUpLZl5jEkcICnzWDWh25u+D1wW4d3WWcjEJsUEBhlTaZU6c6oEYXvIa8jK5FnXhYKEdtp0zSiUZc1+I77TzxIDO4zgyyvEYcCCLpE/n2G1XIDAiO/9HBwjMmWHIINELBA0G78K3Jw0f62hQYuBZlBJ5CztTjnJgYPFHFDREhtayFkF7hrh/Azjp39B/pff4uDx15hvNsCY5CRXjcxgRZxsis6PVSMgXLRAg3TbZ3fixWol/kdBU9dtHdmXp0G1kYw/eaQFpYs9szvR/1yuaX+Vvna2lIf6YlVuLm6VKwr99rbbO/5+29a6a8wrnyq8m1hdU5qkf2d9jkiW7Q4xWx1WNxFK9jlAlv2cuakfFp9bYqir4Pfmo+Yn10EWE0G1dKvm1Uca0V7vl2pavn6d5eXbdGVtIZrHbEOFwfSnHzx7dwcxeq1Knsqbe40tuHiwVXI44GIauSGK2qIddVFuoB5i0oIrqs4uI77SbrOYURH0LYmwHmCYEUAY1hvQOCKGAHr6FOPvfoe4WCC+cRdDPwPHDqAgcbvjKB78AFCIoBh1i5xHeX4LcdZxCaiMo7vNKLv3bBkHYT5OwLAFTk8xfPop+Pd/xOGzE/QXl5LKMaeCONiODne5fndEXZnb6UiiaXszB1SX+sV0Q5OnTAiqnr3OEWp4yuZGhE2lt+f6Qnda62nErcfcPJclf+baZecALeYz0lwgpcKpMNKHfQMLcNgzZvpvCWO7plTnJtX+q+YycxgbzJwowDYnhX6TNTSvmIBQYJYf2tpkG7cWRPn+i5lDndUwrTiVAaZA3e+28vguk/oSy8sVupYnIPRg6lTg2ARUR0ZhHtPYaCemCksZwGrPAeCRFMFDI8dxXAbebvHEhly/1TI8WxXk0Io1ujw0bXB7v2xJLsK+fdH6GyBnqtEwomNBDvniEv04InzxAP0v/w758DZS7IR/gXLycOzEbJBhTEKVOYzgLIeCWwIS1PNLGdBYSlZGEdQqzomQBtDVJdIXX4B/81v0n93HbLVCyBk5JVlXMKPu0qqMKBi6DpKXs+YYkV1KdWyKvW46PfpvPWHCj+UeAbWjQut1C5+zXYTshsxiSfVJ7LbEFxcWVT5N7j3eSy7eY1+jeMJ+umyabmPmzQ17EG7Tf4dSyW0G8vU0AER4RpbnPt+H60d5zxRrqwhKX70ymPy6GyZo99r1rNRT6ckEfGMjr7VCYspZN7DIKtoSou+nhx+mvMimsZec2lHmMcTpuUTGoPVZv0XTX5ui2vKU5zF/zTE6+3tuUjKbZ9Xe4TJBDefYpGrTa0znLksUdItqXyyylipyBIwh6ljINd3Fk3PZ7ZQzA5st5iDQkxPg0WPEW28g9r345FMq23IpBxDVxCFiVrGwseBsfAzmodjg7IiTdonXjKqMZNoiX55j+/mnWNz/HIvzM3TDoIqCEXaGhMtQ2YzsAbRlPm3TAhVIBV1K1nG1VHLk5rMFhC7igauC9wi2zpOaNVw/be529ee3MKkqMkJQRx00QZG0swTze6HsGm62TXnW39M2Ka+YoC6oeR8A8NVz/WaNSa9xtyUG11aiDIDdIZVcw8RqWF8V1P5jJrNLlIKBJPOpFPpqY6aL8jEeqw4eB3T0M+S7pH8451sdB+fQYz11RFOSon51z0T+9eVFTBgv8Yw0UnBHCLbnGY4B9+hymVObVFSO1cJ+UpqIgMqo0PvPZRTPi8qsDIZPvFI2MQDVJuydEL7N/mKrNVxfjCihIUSoe+MdkiLFFcVylRlhGEEnJ7j47e8Rj29htlhg6Bd62KayUEraJ/mQuESMPKXtbH1lL3AYttEBJWyqiDn9XxKVh3ELrK7QX10ibgcgyS6lYCYK1w+GHqrCNdKtKXahHMJp1wL8KNvGCp3y+rppw4b5hXnlQMOMXUVi48A7CKzBow0NfXtAffuUp7yC0aYPl/kt42UY5Lq4JhPse5fI1flZhI3aYMWxZ4l1Jo2ACTyZg5yzpnzjumCxLxT7+544dK9InMy05+s2e6sLRS6X0WpleP3p8dWEx0XW2izZrjhxHAuAqquunBmb7WbyhddTXupxPSAgdBFxPivZsoC6g8hhGP23hnEIT3EhRmpvVCKf8BRcjde1bMdEoBTZLFmpiCuUafe2NCMu8SBULe1QLDkG98TI06b7mFFTBKwJZZjLyQz5s/vo3n4b3a1byG/cRQ5AUmQh4Vxcxg3WNlIE75AFdGuk/CdbQ5MmtQlBj+hmTaKSEpAH0PoKw+NHoPMzdGNCGPS03yLIdb4gCV6iepC58kcdd2rDoRgQ4VuOBjeE1JaCtIjcIDoWZ5SlOsUgOSdyzdBG6s0GsdpWVWGV4dkVl+XbuL5UB5Z9R9W1F4JeWGWLJPHRv6YEasRBybfgBbpTCOKojDoelqbTtVyFEsqoGqeZ4rWQRh1WNbOQay+F0I7hdCRkYpE5mxGi+UYTI0z1ZG0i346JmaQo/qkd2lYiQjtkttqiXGzm6rv+e8gJP4aT0l5I6H6fTDpWQgiIXVfyLUhWei/MfAzCdHnXOmCE57hGiLRqFTvIZ39vpGbiuo3SMtvbEwpJqb1chPA0nId0S64t663tXp0Uu7CTrUaQU0eDCXgTVAQA2wEHq0uMf/4Em/kM8Ve/RLx9DHQdElvMJCPnDTqeCTPGDgjmJbeOBAmzUubMnAUVJt3Z1kUJOM/CbEhb8OUZ8qefYfsf/iMOP/8Ccb0B8lj66E05RuQJjAh2dkCz74dG+JoJhBQOcxHI9pyNMVQWO4Y0NFqQq7VAA40sVNGOSyq/ixnHbJbyljM1UMVPLTXqVml8eyFYgiLSVTZVQVaUc640SA4ROtqw1XPpWlEg2iY7jUHftBVLpanrcJ05zXZ70+CYcqozYKuEAk6LsHQmAP3HfAOiIwh2Sozjsh0+Qule5R2ntVDEa+Ex7TVXfm3nC4UvyfXldZcXErrfT+AawRG6rlPEw5OBr4PnCQ2mxe3uRPABQE0IzQ1lle2vZdkkb/lJtvpLWBSZC0oRhAr/nV47Iqm2NxOTVVu0+XW13YZ4y4XJfXBRBF7YBhLm5TQCV1egBw/EdLBdgT78ALN79zDETgTnsEXeXIG7DmF2ADo8RO56SDYqE/OhgkVF0ZSzpGPkBEqSLITHBF5fIZ2fgR89QvenT3H81UPMTk8RtluYbZUMMbOsTIv7hgAKAYEkHBAUJF1gCEAUwc7QEDcTprba0OUuGgENNMtrdidieLTPqtyZxd4NtMK3/Mxy30BhTihJmWDCxFBRPYzzOVJsp4TQIrVpmJaDDqWYEiHv9GGA1LxlcadmkpF3p1uKHcJ0KwZv15e/a3ssD0TbwQmnMmvSJdfiImVljquysXqpTJHV3MIRd9NXae+zKUFTMG27TOnXSnlyv4KalHYPXH0d5aXG6RY276LuThKRFlA1tRe10OueJGUQ/bKE6uwZIdqL4Lr7SwWvX8BRO1dFwALceEGv46kmjM1TkL5ViJl8r6ZIgie/8+SqevtF9shRRxmIOSOtVyAeEcYtVk+fIH1xH0d//2vM33sXY9chnZxi++ABhu2AeLDA8ucfIBzfQu47CQyPfRFmHILE+qYRlBLCeovx4gxhPkOYz5FOz5Du3wc/foT4+BssT8+wWF/BTo8gNhu4MligImhJTRT2HQTIBg8VuGJKiJLzgYLMVaCCeIkCmAKSXQekPpt/UUcyb8rRJhTAWZbJXFNnFmGRGZTkJ+dRhbH0JScSGzkrIlZB0AIOS3v4oiCkOnSNlquphxtFLTSrAtYErpMlRYx688Je+mqbt9c5WhjBJ+yRujwaN79Ks4JzTOTD/mxW7Dqp+ZBZQQ1X/i8rIwMvVPkGzrlpjjd52FZMnl8YNbwIoGaZzKUPZs6Ugym/k958KeUl70iTCY1dV7Som1/UAZ286ZAAFcO4hdJ4ikIzEVZvlef+D/9MkdowB0Qr9ioK9qV8yqntvY6NQkiVo7z2rkzniNl9RRCC3IsEJBIBF5nBw4hxe4ru7Ax8eoLN2Rn4ww+RlgdYPXyM9Ohr8OoK3He4vH8f6fZthMMlMhG6xRLUdYjzBcJioWaFhLReIZ9dYHzyBHx4iMN7b2Hz4BH4kz/j4Owci2FAt90gjKks1WFzYaiMCBQ0UiWKQKWuB4WI0BFCDOAYQLrqQYygbibKIMQqcAMBFOU8K3KKziNihCoUYJEX2ihFs+QUQ0pmm05AShJ3nEZwToAqHbFdxhJBInZMZWguVsPC53B/7y8Mn1/X22arOZqdgPHrvPqLrRDJtj2bnT4bf4m48+aEfXZkHx6mhKgrKwE19lUq4WS+AR6J+u86PpmY57iE43lc65HKZBt3sR8F95lQaKzCJ0yk5sQPBHmP9Ru6cAJ0xe2COF5bealIF5AJiDFKmFZ20idUq5lHAvVdJRKjh7K8o/ax8ge3c/GcUr3U/mIlrmobbAVvI/SdwC09IU9Wk280k6xPOYErVzQHqFMCKmIQwIgA0phAKaEjoMsJ+fMvkU7OMPQd+PQMi20CjVvEQBi/eYJwdITcd8jbAXywQA4RYT4HzxbSxpTB6xX6zYCDYQDPenTv3EP35Cnmz07Qr9eIKYnyK+jWo6MyGAixq8K2nyF0M3GkdgHoZeNG6DpwJFDsga6XtJ8xFoQsDNtpnolq/yy24CK8dKwVhZEKXlazgSFd5oygoXVIIzgNQErgMSHkBB4H8DiKMB7lwFBBwpr8PWWEPJZ5l7nNhTBba3Y7x96fKcJiSulVlJixwKnqsmIyl6dU4VdlAHM9XZfVJOIRJ9zvjRDW/8sjKvdkDNuwPKNO9jTPXHwZ5RGbDzjTCAE+GVF1b+XyQSF3HUsKhr9RlQnXHb6+mEBv5AAV3mzAl7W59Ob1lZePdEEIMdYYTLvHO/NVBKssRVA0sY/dKwCZ6zs7iNTQyOSWEbTZbJsbDKcquUZPlc8429sE3bL7uyoS+pbJpUoYE7RLqNEZBCCSsJI5vDoooBsSKF+CNxuAgVkeBbNkyS0QNwNoMwDEGNOIWT8HdD6o69SnxEAa0eu3MwV06xV4vcZsM4DGVOOTC2OrICQNS1KhiK5DmM3QzRagbgbuenDfgWcdQt8hdBHU9UAXEfpOMtDFCO46oIsAdWJ2CD1yMJNIlHsxqqnC2EaFHgNQZIo0qp1WtyynLZBGhFRP6MjjAOQRaUzgcURIGRgH5GEEkghgHhM4ydHyyAyMg6DkrAjTdt4Z4bCLsnErGSu5ZOHyQs7POTnarPQmYK06vIoJi6tQ8oK1JAcvJOp9JS4CwfwFTEUYA2YnNgFbnWOi3CYIeELHci+XumBC2eztrpXiTPcaictzZsIhJkmmpj4BO4RSHgvNiAlnmr22hW+lMNdZeY0oF3gVR7CDkEMAKAI8wmyvfvfPDsFN3m9sVICboBaJym4sFLQ6kaOmBPc1sSAPEyLNk1zbWCZ1f2OrTfq6b+1+GsVu5j5Ywo7kNgJJPKzkBpcGZUWfPI6ayMR5rxWV01bGvGcG5a3Y04lkgwVn2R+v7aAQEAIB5yPiOGosbC5CxQ6DqI3XnLsxIMSIMJsjzOag2RyYL4B+Buo7UB9Bsx7oOlAvApZmvURX9B1oPgfPZsB8ATo4ApZHiMtb4IMlaHkIXiwkJ3Pfi52YCGSpKFnR+jAAmzWw3gDrS+DqAvniBPnyHHx1Bd6sgfUaYRxB4wAaR+QxIYyWU2LAOIzgYSvCOSVQyhIaRwAnAiWAlLlN+LFNEJlA1DHbM/steGg3yBRA4qCu1FRzHvC0rvKCEF3NC9KiPphtc2JqaH+3Z1CUiu9DE2ap92zpbgJauieJZrh4misMqQLRmRCsnQRYhIuJ1Agg+wxEpU8TaUE1LNPV2IyX2f7RvvmDlheN8vrBhO7zPhiCohRXbJC84GUyj7S7KJW7ufZmCRPe5hCoHu1mqh0hT8myIJQKnYsg9LRLFtPoli3cQOlW+3+nsquWYYLX3A6BAmIQAudsx1g7G3lRRPa+9lJRL8AIOWtaBgLxoJsIKoInoXKw2Y9dw6rt2wZEIg9CVLPBrEdcHKBXezEtDkSI9h3QBdB8Bup7YNYjz2bIBwcIt+8i3n4DePse6O6bwJ27wOEt0EwENndR0DC5+F39fhsBQM4BlsB5AKURYbsGb9fA2Sno5Bnw9BukJ4/B33wDnJ2h225BmxE8bIBhg7jdgrcD8rABhlHyX8QRvDWPvAo3idFzByA44VTUt/5NOoNcx8/ibwslev1OHjEbytR6TCo2fJYq3+ncejpqQrX2CN3SHrZNKD5cjkv3Kn6sDuOChCfCLqOGdbF2oAo6u06ouYorcncsBw7Z2c/J8Zuz8Gr97J3q7JyUpautwH0Z5UWjvH4woXvdB0m9hjkG+HEoQi6Egtykokm9MKFYFZ73tlbE64jEaFkhp2UJreFmrn32FUPHQvGT+/VTRRA5jd9qcT+xz9GpRXt7i93uI+VR9eqGYIf+iQC1DGNlnAo+ljEth6k4BSfe+gQNINPhI0m6M0E4u46+oMg7IHY9KBLCrEeYHyAuFqCDA9DiAHSwAM+X4MUC3Afwcgkc30a49x7iT38KeucnoDfeAR0cIS/myH0vJgRNjNQwOczLbYKI2ia6sRIP+UzYd3lLxuPt9yWueBwRNxvg7BT8zSPg4VfIX34FfP0QuDwD1iuEzRa06VUAb0FhCwqETKzmCLfMJ5mXSgOt7bEgS6q057W9d7bX+ZsU9tf3SDn/HbO7OxTMnCaPSwO9o7h9RzcwqeO61M8mjqvA3f2e+wJLHWbaaHtgNnF7wYCWm3WqYZvCKo0rTeZX7A9uHE0xKtU3pCsgwUDYdRv/XkV5YaH7fTdIMBhdP8OaopjjTOs5EwHDXS8EDEeRhh5UrBRCrHqRpgcHlJq4Hf8Jlds0OqBbCcsYne0FVOUqX61tVwFf3p+aKPYVFbwlrrh+uSDqADu1ASVmMYZQGh0hSXKaxB9cUVTZXOEkk0yDbUSojoysjFLCwPQ5Q15izlWhq3bZ0HWgxRzdYoFueQgcLBCWS/B8gXh4jHDrTeDddxF/8QvE938OuvMWcHgM7udqt51ioHb2YPPsVjs1XGp3SqX77i5Lm7kL4G4OzG8Bt+4ivPsB6O83iBdnwNcPkT77BPnPf0T39WN0F2fAeoO8XiMPAXlLoJCBDQHbLcABxBGZR21Q3UBARm97wINfwTV92JfwoWl/jdSYCvTJF1ATSpnAlyy5wU6rK+575T1ukWvNP9uerAFUXvJf9qxRBbk7A61ZQZrjTQeo5NYIpf5yanCxL0+5yBpZAcLOWLBsAxYWITBCFeKEkg3wdZUXFrrfV+CCIE6bEFToKlPY71nCYMLOsmlXU0mdVrP8HYBCix4BGXGV4IfaKPeL+VJbwRS8Q60sK9tniiND57/aw1CZbg/CkF/3PGAC2NruqRkaAwvNcxA0HAeyxA3MsitNlVqJmwwFX9WgIEOL3kZWxlTQTE2ag+LIlCWxmHCoi0Av/4f5AuFgge5wiXh4BDo4RHf7DvDOu4gf/Qrxl78G/eRd4OgYHGfIEFNTprrxobBXYyIx5qhjNNlqgOuKx1TlmHTDi1onx16OuF8cIrx5D/EXv8bBf/UU+cvPkH/3G9DnfwEePkBckZ4ETIgI6nzUzSFsCkrzPIBdxIITWF5GWI/N5qlCz1YcbsZrh9g8/a2wbVEmFfTZkpUDSwSUNJ8+Hbmz+VauKV9BPX7JoGedBz87INKdkdT2X8feth81aUwsyxyM/clfdiF3EwVAtvqZfsUVUuu6OdG+uwh7KeWlO9IsZAwwIoGOsE0kyp5zE2qsE6gVQF9WnqmaU8jdHjEiJt0ZVf40mYmpzgSsPmNIbv5mxwLyto8pqMhqwi3XFE+olQgKo6CK5fYIb4CIJbcuXIcpowsBgxK5pU4UG7fFP+i4UiXK0gZH+V7flQ0jNiehzoMcYx1BfY8wiwizGcJigbhcIi8OgNt3MPv5LxH/8V8h/N0/gO69A8yXgG6CqEdp7Qk5Y+982mGf546nL07v7XmCy112ypVDB150wHyJcPcnCB//GvzgCwz/6Z+A3/0L8uOvAFyI2GUg2eYLltM5kMn5BNzXbIKNbt0j5fS4soqDklGrWCyWmyapL68bDROMdbVF9Yh0oPm9ocmCpvU6t/esgR4L1EgN119tRakTJqfZgQlUxmzagMr/k/kPzBOESmUDlBRzOTqlVLrCrr2vGebilUQvAHtZwI+52aRgxDgVd6jIoNWtu4zVyugCKAseMEGsDxnJ2zHn3mmg4BPWOJrUb7/72MeaqWwH6tbCTnnwvqd847kg3Kp4tGoidJGQUkUyWYVs8HU5XFO2GQPFweKX48xVENi3LFYWREAM4CgxuaHrBenefhPzX/4K8//63yD+w78C7t4D+rkIWjc2sgN5gpIm6La2mQtKs1wIO3bRa8bWZ/Rty/75KBgAhBR78K230B2/hdnP/x75X98H/cd/j/T//AekL+4jjCPQjyWZDjHprrlQEtEXwUSojjEdTFnOpwmoqLRtqwzfRabq/G1dTVWwm7W19N0jYlTlPs1zwPbLhJtCCCqsNF+d2nTJjsmBByFoeYzc9z2flH7VeIxGTjtZIOZGo52qQAB2Fj+tTQW19/UUhedK7LqCj16n6H0lQpf0cErbyllhXt0JIw+q97QIHKDOZoC3PaHexT4Myk64FidRfcDVY+8Zl9iUELxtU6r1hKSSTe0LZNdR32GzCaAynbxvcYdVA/NEwhcGU5RTWmXdCFJHyAEhZCS22GbXP0e47TJUmZxrPwsGMNkeAgIpYpatZuAIiVSIHWg2Ay0P0X34Cyz/u/8e8V//N6B3fobUz4sQAKcm9A2o9sM6Ur7sl6a856555feV5yHC8gzM5ShjMWXEEQSa9aAPfoFw722Ej3+F9H/9e2z/z3+H8M0DII+aQIUF9Ur4BCyniqeHKnCBcsS4TmbZLmDn1AVZ51S/RSft5OpwNSHemAiAGq3mVZTyEgN11WJFs521W3+Nd0JBKCLkjJKikjwXRVyiiNzGjOr0VGFLbfyJiYDSyImwrWs1Az/m58gogIgBkrRKZUu6vQ2whKqCJNa779HNl7DDNp+ruF9yoefZanPO/G0OtGns39TmBAD5T3/A9re/AY2bJjRLa0CjeyY2qUb76X0u32nb5a9M7zoz1E70QsNwrFeVa3ax9b7SCudrW+WWQ0I0Xon4pZv3bJsa8e0XdV1HsmKgBiO9IGEZqVZWVfTkhLalaaSSNyGgO1iif/9noHd+gjQ7QKJYP+mn0yk/u3Z9A/2M8Atcr9+Y/myfcbZqp4j8JoD2uTovBEbMI8LqCvn+Z+CvH4HHARiTCNycKli1iZk015Cd1QjAObXa13a7bp3SP41G3cvVT9JW1FbF9cfE5ly+YwO60w5ygs7MX0Z3nv5tEqBsVDdfNINC9Tv+7SmHtfRU+afl9AnnUUW6CtaRuxnov/gvsfj4ozKeU+XsZdjzclZcd8/TWAi7af3Ls88TqPx98zn+jZbvG6FxU27KTbkpvtBzllvhuhv/fywvguhvyk25KTflryl/k0J3msjjVZR9u3huyk25KTflu5a/SaG7f+/4X1++iyC9MUPclJtyU75P+ZsUujflptyUm/K3Wv6mhe7Onu8faMlv4TPf9fsvs1ibXlafb8pNuSmvpryQ0P2+jP193vtrlvg/1JLf70d/Xru+7/detI/T8Lt97bopr6/cKLyb8n3KCwndV8nor1qovCjj/JDtetG6bgTsj7vczM9N+T7lJk73ptyUm3JTfuByE6d7U27KTbkpP5LyoxS6P1Qc7nd9d9/z1137Iex5ryPe+KbclJvyestzzQs35abclJtyU37Y8qNEujflptyUm/L/1XIjdG/KTbkpN+UVlhuhe1Nuyk25Ka+w3Ajdm3JTbspNeYXlRujelJtyU27KKyw3Qvem3JSbclNeYfl/AU6yM9pD0ktmAAAAAElFTkSuQmCC\n", "text/plain": [ "Everybody knows that the #SVD is the #bestmatrixdecomposition !!!
— Dr. Daniela Witten (@daniela_witten) July 5, 2020
#UDVt #minimumreconstructionerror #maximalvariance #nonconvexbutstillsolvable #nothanksQR#seeyoulaterEigenDecomp#blessed https://t.co/je7Xetgfhr
\n", " | source | \n", "target | \n", "
---|---|---|
0 | \n", "burr | \n", "hamilton | \n", "
1 | \n", "burr | \n", "weeks | \n", "
2 | \n", "burr | \n", "madison | \n", "
3 | \n", "burr | \n", "jay | \n", "
4 | \n", "burr | \n", "theodosiaDaughter | \n", "
\n", " | character | \n", "PageRank | \n", "
---|---|---|
14 | \n", "hamilton | \n", "0.815778 | \n", "
3 | \n", "burr | \n", "0.381702 | \n", "
17 | \n", "jefferson | \n", "0.238992 | \n", "
4 | \n", "company | \n", "0.206834 | \n", "
43 | \n", "washington | \n", "0.160793 | \n", "