{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# How to fit a Gaussian Process\n", "\n", "In this tutorial we will learn, how to fit a Gaussian process to noisy data points." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import bask\n", "from bask import BayesGPR\n", "plt.style.use('bmh')\n", "colors = plt.cm.get_cmap(\"Set1\").colors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate the dataset\n", "First we start by simulating our 1d toy dataset:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "rand = np.random.RandomState(123)\n", "n_points = 100\n", "noise = 1.\n", "frequency = 3.\n", "X = rand.uniform(-1, 1, size=n_points)[:, None]\n", "y = np.sin(X * frequency).flatten() + rand.randn(n_points) * noise" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1BhZ2VzIDIgMCBSIC9UeXBlIC9DYXRhbG9nID4+CmVuZG9iago4IDAgb2JqCjw8IC9FeHRHU3RhdGUgNCAwIFIgL0ZvbnQgMyAwIFIgL1BhdHRlcm4gNSAwIFIKL1Byb2NTZXQgWyAvUERGIC9UZXh0IC9JbWFnZUIgL0ltYWdlQyAvSW1hZ2VJIF0gL1NoYWRpbmcgNiAwIFIKL1hPYmplY3QgNyAwIFIgPj4KZW5kb2JqCjEwIDAgb2JqCjw8IC9Bbm5vdHMgWyBdIC9Db250ZW50cyA5IDAgUgovR3JvdXAgPDwgL0NTIC9EZXZpY2VSR0IgL1MgL1RyYW5zcGFyZW5jeSAvVHlwZSAvR3JvdXAgPj4KL01lZGlhQm94IFsgMCAwIDUzNC44MzQzNzUgMzA0Ljc3MTg3NSBdIC9QYXJlbnQgMiAwIFIgL1Jlc291cmNlcyA4IDAgUgovVHlwZSAvUGFnZSA+PgplbmRvYmoKOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDExIDAgUiA+PgpzdHJlYW0KeJzVm92PHMUVxd/nr+hHeJh21a3vRxCJJaREgljJQ8iDZT6ChUHgEJL/Pr9z27PTs1u7a48iLGMBu9c91VWnzj333OqeuLw8xOW7JSwv+fe35e/LP/j/10tcnvLvd4dj4NdXh5Ly2lNOrfDrD/tfU8hra7Hz4w+6+uL3fx4O3x6efMJAr5ewjnT6x2/49FbocLCy5m1UC2vaBuHe1tZ6O/zDRXi0tZziu0H2YZ/Kz8vsFiXYaou1xn9/+Wb52/Lj8uQT05yjUFmL4xLXzuLXvgF0CGsdPaRhsTSW8uSzb/79/Ytvvnz66fLi9SH31WqsuV8sZBfdz+zwl8MXy8+nWwaw2W7bd9vhaAHRowOntd+M+yk7+9vhZ/4bFnYmLsnWkWNKxaylZazWerSyvHh1+PTZ8uSPcYlhefbtoTNyH6GaNvvZ14eP4hrCx8uzl4c/PGO4sAaNyJ/TDwzA+l8+/+uvf3n+4+vjq+9//PX18tlPhy/0Z/l/gX4AhodAj6GsyUZPF9jsoteC/ujAD4I+gCmMElvIpbwD6GFt5QMAvdqa+OsYL8HZha+G/fGhHwQ+5raG1ph8r6m+E/LlA6C7xbHmWuO4pOU+fC3ybzH0g8gbNSDm0nuoPfZ3Qt4+AM5bq2u5W6f24auRf3zou8hfYGoVDEIsAvUG+A3bTcQXsP39sKKyrzVY4a/2C9qHr8XqLYZ+BKtkBqFHyznFbrfh2qj4O8NFtagttDQu17QLXw3X40M/BlcbsLANvEaq+TZc5T2wKyPxLfVhl3boHL3aZz028CNQ5VQhYY2hjZLvJGJ7D8wqaHIPLYbLJe3D14L1FkM/BtcgZ1u2PlqzdglXfC+6db5LYs8RiXGrFTmH31HhpwNbpxW6O+6dyqoFom+jhGghlPoWNTV9AAX15i6tsPXWc70E+xy+Fuz9wGewL8adgt3imlsZLfTQH8faPiSsY7S1jU79uwR7F78W7Yuhz3BfjjzFO4ZBvlONYykjv0Vr+kEhXriN5ZJvI36OX434fugd4hcjT5Q3FjSf6zIGE5fZLLEDW5l6n6LLDfgc1/VbSJ3jVyO1H3qH1MXIDyDV8xpKKpZgYT5z8H0hZfyYGlMZt47KzvFrkboY+ozU5cj3I2UW+f9IOKaYxlkf3xtS1dYRLN7C6RS9GqXzsDuMdqM+gFAZawzFSNBa8rlaX4cQHQttX6/WckEM88gxtpobWri201+V5ZdtWXG/qN0nl/0nDxef/PLp/VfevscbXfdTx1pXZCX3XnMCmSRFGrHBIwn88uRPQaJ8uvyoTEwpm/XYWub3bCsMwknHXGz2CXYz1FYjt8YRJcBNMCLXOGaXM5M10vqV2GvtyzFHtmoMfuuhTq6n924thFTGSFiGsSbqU2l5c193p8/9U7BRGJzrj+x1tVDUMrXZdEBhLYNWQQWP6aQgJeZH5nnf+PQVBRArKdh0CokZtNRLml2PtQ46AcOJj8HHI8xpMZMtdUwXkJlAbp0ldCrwEVL3GHOsKfU2Rd9WSMqUWGVdCv41YJdgLUk/QR84Y22jVrrOtKS+1srcI1U9zpdra438KcoSfjf8QRjcYNTpdCDWOjoMsyS+Hek/2L+Cp4ZYs/2NbEBmQih6LnGhC/Ie17AZM35iTFYLKTKfnvISTYdio7IZbT4hKzQ30WpDC2PTBGlpLOQMnaeEOyayLIfaTTvE7At4NWCaAaTjULSkVjxTagsdaiYN6T1Z8eTysDKTiFjSnC5HHSuRl2O0EmdX4wq6DaZCoo9FJ97d1AALrcnlg8Rq8DNwbxbakM4q4qfpVI5QJZBHjJcZjqxMVqFQjmFK/BLX1oViZLFLpkkcISVYPGbbVHRzIGHEDm2qnjVlWNGxOHPVgcYdzSFpRRtY3ZW3SQBMeYzgQSsDlbFYZjY9kpStTYfX/WvIVloyJbkkLkSol8OMNJCq0wHLjjHekTox4LGKwZhTmJ5QHO/ZPUrgbo0eMgPuFEu0A5NMRowi+JCUzBYXMr7Opi/OM5qFlrI0CnauIXdyLEtUZnCCB8AbytOXWtjoAi/J4xmWSExVv4829YXykCACK5kiI30crVPvUe/GUld/tEIq2vRyWMM8lWzQcIHA6PyI6NssmQri0lsKw3RqU5QsCRJwp+m0I4lqOZBOCLYrJVWChdq0TFkiO4akA01bEo0luQtDw5yQFqhLsIOrkVIfvaSkCltstqdskbIYW0ptFSFJ8kphCX1eM9HV0FpP4C5dHbZG6lugkKbZYocuF2X4CJ+OApKhR5qqfKamQd1WxUr6PumCF+ipyFugJoAk2V3HUqN7M4pUmpIRJBhP9QAVYptU/lPBkYZMYZixV8OT2okcCr6tgfKaOpk4u9yk6CQq/1YNn1f61qGFT1kAFkh0h37cP4JNQjThJDBS9WfYUNAoZYn8ROiomzDY8Ab5nuqa15ZjgwlwASFxXZJqhynyOtMmrau3croe3closgnaWaKKZqlRIdlK8/SqQaWSajidT6VYVnELJXOaUZ2MajOnGbRJ8jaBjOPy1fT8iH3OcxHGlmd1VtmGUh2vFTEfuKM8mzy5jcTVJGlscsvcqMehlcxogImuhZ1hbE2dmZG5iP2YTqYjSpSilgZElAFXj0Get3l1oiitQiHLeiZMJsAEfs5lasswKQgiRgjn5uUgUxx6Q4CnngybpIo+iua/uLpLXVOeWgJKE26qp4phI/eQ7TAoPNNSAAwAgkdHQ/vCbRqs5E7TMuZ+gWYu4i/MuahiXF0IptPWsUKXEiQ1Q8eGBLJHKEGcpgYbssKriuiSc9IcMiMl+D/mSiDgosooGTGcvNChWKXw3edVAQLxwPOQe0gmVAZLm8IuK0lh0lmrnCFQ0pcEVLXOc8nEX7YoNGbhEh+riirjzHIJb6IOihJAVagSGj6H5cCMTnNJ1h1jizCa3vXAtQaIHwLqMJMZLIGyDpuBbohu6kf4xHynTA1rl2hJ/49JXYMOoq2XGTTMABMb1QRBSmkqwIA8k593RQ1VQlKTpBFZIDugJJI59/AovERObqaoBQzeI2EmpYEz5NknCqOom5aBLNChoQXQeDb3rG2iHcJeq8FM7g1BN4p097QUQTVDOWWiHaUWWR2sZu4NadcxMCkEbSX9BTYiyaTMLY00HUuSoSIXyLIge2QW7e90tfR86DlNbqCh4WJa5UoL2+aLhVbD+zdM1RIHGVi1cyPcpzSgja2lgnTVKpoW3DyWZk55nAB2ierrvkCuHD2VjZzWVpxjUg1oGPFOgcG3NrZKmlKnUhY1IMmayFGASmsRB/jANKO8tA6H/o1LEeOG3N5M+9zGliLmML5samTLivqu6WSwTKVTnGB6rE7ijingw1NDdqTOrLJUjebQeUaFMCtBCjg9mOhlVR9p6oBot6KahKEOAZc25QEX4N6YF8kkx4jn88Z1lGk3l6lhDE01GBvNUBq0ijo1F0vUm04PiaRVH67eYMl8IOfsAzhVuNO5nIrKfJAI2JfwTtPpHMkq6MB+BczQUrTTlEAdmsw70axjAJwDU+krq0DF+6XtuOZY35bP/UDMzgdih7c85vry9mHj7k08pBGBVG/t543MN1lUWGax56pHTjTAGAZ+dSaidS3osR9yQJFJhTDZmGhZsw4SMRhNegIzYBKWq1SdwDapBe25wljVnrdjRzQClrIVTluQ2wbpOtwx4Q3VcQaV1lFhqK9eFpOkNpxNVnBQHgsqQL1BcBL9GdGRwbSxSaTg2kUlnZjT+pPRiF1Um4P7SBoBf4WbDHloYCSdXt2ax8Ep6u7uylS8k9aiB0Tq2ZPI1PWYMzlQSgUoRUvkWQEjhz9DommgD0UnuW8ku0bUJYrLjKknJE6Rp7kNPg4lmeTmMuJkA8nTt3hRvy0yKa6mTxuhXRE9gUjcrm3gSz0uq0mt3uL0CrF2j4NY9BektBKMI7VXcSqATgbqFu+G6dviOjDGreYtHmUcFHedC5TvbZwE5xzOijjT87S83ZeaVH2cpiMuHOQWr+pItzgC0Qt77MtilTTxilNeARC98Ti+ljLrcb210PWLYGMcuKc4QsackRmHmdoD4AqDmipV9V2hnBcnE/NayXtxXLvY6BfSFvdzAPbUdz0kNtc8PqCGzqycJTmp/1BcW9F0Crxoo4e3+AqT/ShQbk5BpF5nEMRhHuKqMzbtP5vYo78QDKWBscsMq0U3GWHCSc4Xi9H9DA/u9m2WfjZDiVT60eZqGIV1TKxHwQojhGpWs8cBpAwRQCwaFrU+vYasptffq1EWiy3bbdWnq+sfnvSqs841wwxCBVoA1wiKQPDE0vtc1KSs8zcEHJTIU48DGjcwf3an7jT47BuY4dl09ZDlKtssG5gh3CAs2YcRPkZPK8YWq68DJHyxui6F1W3ofGo7+On9zb7ix1l0b4qTwCplvtSBqtIcZ51GsvU6mdaGMACw+puaOqUUpKF5HMioUco2akQjXLTUpHMCjH9RHL1HOFzKklKY/DHFdRqtBSoueceqSHWa3qqp5nzi/kgHmZ02B4938fShEq1FBURx3DPjNJ+ndJNKGNJ2Oq3q6+Ozb4SL8CGTmvTBx8HDSGWVbo2qFZ2iioNbpOAQR2cBOTujEC6fRFdcDxti3uaJ/oulOiFhJ7C2xTWahln8yrY9bQSS5G/O6EEK7YTeDZFVwDvHDU8dKPPhusXlflxN+RS2OEVpNZmNT9hgYG4GlZVuvekc7w383EuP1tsWz9hd2+JDZ2x6S0JxXHL3jMCaMDdK4xbXgYo/EqRgkfNB0uFx406aJvZ2VYdQtjiGcWM4RPczCtvidJdbkSDiJ9uj+fRx69WLQd56CXezxLmMFSuOdtBAMw+HoVGwwvC4LgpZhy2+xIxkKZ50Dh9VvwQ/vYCedygObCmpodShcMeo+kPhrHQlXeLwbaw6SvZxSMuupz3Dtx1Y2AqP68lAN+Ui6Td0cO3rohpQx/vGKvRn+NVklA4mCUpVR/TUynpaRsvWnLE6qus+xQpkVKHsBFe+ua5nnSrgP+LWgig1nFCZ+8AhCZkSiAxO2/UsAydu6m3FrYpXTR6va9LBYfQEZWOLaxRVlGWoXfWEJv+TC0OmEBQ9kDEXAAZx/tFsYgXQDsJQXcbQtvjNi2HSF1reOO6+2SNftj17JbWpgOwHH3jg8e7+fdn5d0C4wfTLJK/u/TIJn3inL6VcXn8e6cE7PPkkbQ+cP7/zJRl/4C0U7n5ZhvJ18wQ6SPP1wtwrt0pw8TIsB6X3aizo6wrnuKLni9UoaWt3QTtd+eKwC49wnv8+LG3DpPVlf7dhp4t3UzsHX+wXcg5L9fFYpK3twzrgOV17c7d9MOzGDftH9DdI7MM3a97d7IzOFOEX+ibRp4fJM/cHn4fffub+Di3GWz6d/wVOoESnGXd1d284gV01ujCkYxcmSFtNtfWgrC3Fzc1M8ceOeh7G2DolQECoil2VQWEEGlfpjxpPN8N0InRI1j6YT7fyAW7Ceucu6ZBpP2rFDurRxsUM+HHQcPoAu9k2meBgddmvq92sa4dB282AKeKuar24Vn1ZodW6GFUHw5j+2zMAJB1j54vZxtm64hyDOMNrN+oZ2d0M9ruwm+15x3brijMM4nkGztxw+vIdInLxUko90737M7bTG7h//un71/9dvn7+r+enl1OkzebKdF2fnM7zw8Z2f58PiZxEXSBdGf11nN8enTp1LPknNfNvv/roP199fPNKzeF/MG6lcAplbmRzdHJlYW0KZW5kb2JqCjExIDAgb2JqCjQyOTQKZW5kb2JqCjE3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNzUgPj4Kc3RyZWFtCnicNY2xEcAwCAN7pmAEywET9smlwvu3CfhopBccyOTmwZ6ydLBN5wf056RN80JRkKow0HRmfXFo5A5WDhdeaEqviujPQe8HmeoXmgplbmRzdHJlYW0KZW5kb2JqCjE4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzA0ID4+CnN0cmVhbQp4nD2SO5LDMAxDe52CF8iM+JPk82Qnlff+7T4yyVaASYkAKC91mbKmPCBpJgn/0eHhYjvld9iezczAtUQvE8spz6ErxNxF+bKZjbqyOsWqwzCdW/SonIuGTZOa5ypLGbcLnsO1ieeWfcQPNzSoB3WNS8IN3dVoWQrNcHX/O71H2Xc1PBebVOrUF48XURXm+SFPoofpSuJ8PCghXHswRhYS5FPRQI6zXK3yXkL2DrcassJBaknnsyc82HV6Ty5uF80QD2S5VPhOUezt0DO+7EoJPRK24VjufTuasekamzjsfu9G1sqMrmghfshXJ+slYNxTJkUSZE62WG6L1Z7uoSimc4ZzGSDq2YqGUuZiV6t/DDtvLC/ZLMiUzAsyRqdNnjh4yH6NmvR5led4/QFs83M7CmVuZHN0cmVhbQplbmRvYmoKMTkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMjcgPj4Kc3RyZWFtCnicNU87sgMhDOs5hS6QGYxtYM+zmVQv92+fZLINEv5I8vRERyZe5sgIrNnxthYZiBn4FlPxrz3tw4TqPbiHCOXiQphhJJw167ibp+PFv13lM9bBuw2+YpYXBLYwk/WVxZnLdsFYGidxTrIbY9dEbGNd6+kU1hFMKAMhne0wJcgcFSl9sqOMOTpO5InnYqrFLr/vYX3BpjGiwhxXBU/QZFCWPe8moB0X9N/Vjd9JNIteAjKRYGGdJObOWU741WtHx1GLIjEnpBnkMhHSnK5iCqEJxTo7CioVBZfqc8rdPv9oXVtNCmVuZHN0cmVhbQplbmRvYmoKMjAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzMgPj4Kc3RyZWFtCnicTY9BEsMwCAPvfoWegLEB8550ekr+fy2QNu4F7YyAkYYwCDxiDOswJbx6++FVpEtwNo75JRlFPAhqC9wXVAVHY4qd+Njdoeyl4ukUTYvrEXPTtKR0N1Eqbb2dyPjAfZ/eH1W2JJ2CHlvqhC7RJPJFAnPYVDDP6sZLS4+n7dneH2Y+M9cKZW5kc3RyZWFtCmVuZG9iagoyMSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0NyA+PgpzdHJlYW0KeJxNUbttRDEM698UXOAA62t5ngtSXfZvQ8kIkMIgoS8ppyUW9sZLDOEHWw++5JFVQ38ePzHsMyw9yeTUP+a5yVQUvhWqm5hQF2Lh/WgEvBZ0LyIrygffj2UMc8734KMQl2AmNGCsb0kmF9W8M2TCiaGOw0GbVBh3TRQsrhXNM8jtVjeyOrMgbHglE+LGAEQE2ReQzWCjjLGVkMVyHqgKkgVaYNfpG1GLgiuU1gl0otbEuszgq+f2djdDL/LgqLp4fQzrS7DC6KV7LHyuQh/M9Ew7d0kjvfCmExFmDwVSmZ2RlTo9Yn23QP+fZSv4+8nP8/0LFShcKgplbmRzdHJlYW0KZW5kb2JqCjIyIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNjggPj4Kc3RyZWFtCnicMzK3UDBQsDQBEoYWJgrmZgYKKYZcQL6piblCLhdIDMTKAbMMgLQlnIKIW0I0QZSCWBClZiZmEEk4AyKXBgDJtBXlCmVuZHN0cmVhbQplbmRvYmoKMjMgMCBvYmoKPDwgL0JCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzcKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnic4zI0MFMwNjVVyOUyNzYCs3LALCNzIyALJItgQWTTAAFfCgoKZW5kc3RyZWFtCmVuZG9iagoyNCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIxNCA+PgpzdHJlYW0KeJw9ULsRQzEI6z0FC+TOfO03z8uly/5tJJykQjZCEpSaTMmUhzrKkqwpTx0+S2KHvIflbmQ2JSpFL5OwJffQCvF9ieYU993VlrNDNJdoOX4LMyqqGx3TSzaacCoTuqDcwzP6DW10A1aHHrFbINCkYNe2IHLHDxgMwZkTiyIMSk0G/61y91Lc7z0cb6KIlHTwrvnl9MvPLbxOPY5Eur35imtxpjoKRHBGavKKdGHFsshDpNUENT0Da7UArt56+TdoR3QZgOwTieM0pRxD/9a4x+sDh4pS9AplbmRzdHJlYW0KZW5kb2JqCjI1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggODAgPj4Kc3RyZWFtCnicRYy7DcAwCER7pmAEfiZmnyiVs38bIErccE+6e7g6EjJT3mGGhwSeDCyGU/EGmaNgNbhGUo2d7KOwbl91geZ6U6v19wcqT3Z2cT3Nyxn0CmVuZHN0cmVhbQplbmRvYmoKMjYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNDcgPj4Kc3RyZWFtCnicPU+5DQMxDOs9BRc4wHosW/NckOqyfxvKRlIIIkDxkWVHxwpcYgKTjjkSL2k/+GkagVgGNUf0hIphWOBukgIPgyxKV54tXgyR2kJdSPjWEN6tTGSiPK8RO3AnF6MHPlQbWR56QDtEFVmuScNY1VZdap2wAhyyzsJ1PcyqBOXRJ2spH1BUQr10/5972vsLAG8v6wplbmRzdHJlYW0KZW5kb2JqCjI3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTQ5ID4+CnN0cmVhbQp4nDWPSw4DIQxD9zmFLzBSfoRwHqqupvffNmFaCQkL2y/BFoORjEtMYOyYY+ElVE+tPiQjj7pJORCpUDcET2hMDDNs0iXwynTfMp5bvJxW6oJOSOTprDYaooxmXsPRU84Km/7L3CRqZUaZAzLrVLcTsrJgBeYFtTz3M+6oXOiEh53KsOhOMaLcZkYafv/b9P4CezIwYwplbmRzdHJlYW0KZW5kb2JqCjI4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNDkgPj4Kc3RyZWFtCnicMza0UDBQMDQwB5JGhkCWkYlCiiEXSADEzOWCCeaAWQZAGqI4B64mhysNAMboDSYKZW5kc3RyZWFtCmVuZG9iagoyOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzMiA+PgpzdHJlYW0KeJwtUjmOJDEMy/0KfmAA6/Lxnh5M1Pv/dElVBQWqbMs85HLDRCV+LJDbUWvi10ZmoMLwr6vMhe9I28g6iGvIRVzJlsJnRCzkMcQ8xILv2/gZHvmszMmzB8Yv2fcZVuypCctCxosztMMqjsMqyLFg6yKqe3hTpMOpJNjji/8+xXMXgha+I2jAL/nnqyN4vqRF2j1m27RbD5ZpR5UUloPtac7L5EvrLFfH4/kg2d4VO0JqV4CiMHfGeS6OMm1lRGthZ4OkxsX25tiPpQRd6MZlpDgC+ZkqwgNKmsxsoiD+yOkhpzIQpq7pSie3URV36slcs7m8nUkyW/dFis0UzuvCmfV3mDKrzTt5lhOlTkX4GXu2BA2d4+rZa5mFRrc5wSslfDZ2enLyvZpZD8mpSEgV07oKTqPIFEvYlviaiprS1Mvw35f3GX//ATPifAEKZW5kc3RyZWFtCmVuZG9iagozMCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDY4ID4+CnN0cmVhbQp4nDMzNlMwULAwAhKmpoYK5kaWCimGXEA+iJXLBRPLAbPMLMyBLCMLkJYcLkMLYzBtYmykYGZiBmRZIDEgutIAcvgSkQplbmRzdHJlYW0KZW5kb2JqCjMxIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTcgPj4Kc3RyZWFtCnicMza0UDCAwxRDLgAalALsCmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzEgPj4Kc3RyZWFtCnicRY/LDQQhDEPvVOES8hk+qYfVntj+r+swmkFC+EEiO/EwCKzz8jbQxfDRosM3/jbVq2OVLB+6elJWD+mQh7zyFVBpMFHEhVlMHUNhzpjKyJYytxvhtk2DrGyVVK2DdjwGD7anZasIfqltYeos8QzCVV64xw0/kEutd71Vvn9CUzCXCmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMzggPj4Kc3RyZWFtCnicNVI5rt1ADOt9Cl0ggHbNnOcFqX7u34aUXwpDtFaKmo4WlWn5ZSFVLZMuv+1JbYkb8vfJCokTklcl2qUMkVD5PIVUv2fLvL7WnBEgS5UKk5OSxyUL/gyX3i4c52NrP48jdz16YFWMhBIByxQTo2tZOrvDmo38PKYBP+IRcq5YtxxjFUgNunHaFe9D83nIGiBmmJaKCl1WiRZ+QfGgR61991hUWCDR7RxJcIyNUJGAdoHaSAw5sxa7qC/6WZSYCXTtiyLuosASScycYl06+g8+dCyovzbjy6+OSvpIK2tM2nejSWnMIpOul0VvN299PbhA8y7Kf17NIEFT1ihpfNCqnWMomhllhXccmgw0xxyHzBM8hzMSlPR9KH5fSya6KJE/Dg2hf18eo4ycBm8Bc9GftooDF/HZYa8cYIXSxZrkfUAqE3pg+v/X+Hn+/AMctoBUCmVuZHN0cmVhbQplbmRvYmoKMzQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNDggPj4Kc3RyZWFtCnicLVE5kgNBCMvnFXpCc9PvscuR9//pCsoBg4ZDIDotcVDGTxCWK97yyFW04e+ZGMF3waHfynUbFjkQFUjSGFRNqF28Hr0HdhxmAvOkNSyDGesDP2MKN3pxeEzG2e11GTUEe9drT2ZQMisXccnEBVN12MiZw0+mjAvtXM8NyLkR1mUYpJuVxoyEI00hUkih6iapM0GQBKOrUaONHMV+6csjnWFVI2oM+1xL29dzE84aNDsWqzw5pUdXnMvJxQsrB/28zcBFVBqrPBAScL/bQ/2c7OQ33tK5s8X0+F5zsrwwFVjx5rUbkE21+Dcv4vg94+v5/AOopVsWCmVuZHN0cmVhbQplbmRvYmoKMzUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4NyA+PgpzdHJlYW0KeJw1TbkRwDAI65mCEcyj2OyTS+Xs3wbsuEE6fSCUG2vkAYLhnW8h+KYvGYR1CE8quyU6bKGGswqSieFXNnhVror2tZKJ7GymMdigZfrRzrdJzwel3huYCmVuZHN0cmVhbQplbmRvYmoKMzYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzggPj4Kc3RyZWFtCnicPY9BDgMxCAPveYU/ECl2Qljes1VP2/9fS5rdXtAIjDEWQkNvqGoOm4INx4ulS6jW8CmKiUoOyJlgDqWk0h1nkXpiOBjcHrQbzuKx6foRu5JWfdDmRrolaIJH7FNp3JZxE8QDNQXqKepco7wQuZ+pV9g0kt20spJrOKbfveep6//TVd5fX98ujAplbmRzdHJlYW0KZW5kb2JqCjM3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjEwID4+CnN0cmVhbQp4nDVQyw1DMQi7ZwoWqBQCgWSeVr11/2tt0DthEf9CWMiUCHmpyc4p6Us+OkwPti6/sSILrXUl7MqaIJ4r76GZsrHR2OJgcBomXoAWN2DoaY0aNXThgqYulUKBxSXwmXx1e+i+Txl4ahlydgQRQ8lgCWq6Fk1YtDyfkE4B4v9+w+4t5KGS88qeG/kbnO3wO7Nu4SdqdiLRchUy1LM0xxgIE0UePHlFpnDis9Z31TQS1GYLTpYBrk4/jA4AYCJeWYDsrkQ5S9KOpZ9vvMf3D0AAU7QKZW5kc3RyZWFtCmVuZG9iagoxNSAwIG9iago8PCAvQmFzZUZvbnQgL0RlamFWdVNhbnMgL0NoYXJQcm9jcyAxNiAwIFIKL0VuY29kaW5nIDw8Ci9EaWZmZXJlbmNlcyBbIDMyIC9zcGFjZSA0MCAvcGFyZW5sZWZ0IC9wYXJlbnJpZ2h0IDQ2IC9wZXJpb2QgNDggL3plcm8gL29uZSAvdHdvIC90aHJlZQo1MyAvZml2ZSA1NSAvc2V2ZW4gNzggL04gOTcgL2EgMTAwIC9kIDEwMiAvZiAxMDUgL2kgMTExIC9vIDExNSAvcyAvdCAxMjAgL3gKL3kgXQovVHlwZSAvRW5jb2RpbmcgPj4KL0ZpcnN0Q2hhciAwIC9Gb250QkJveCBbIC0xMDIxIC00NjMgMTc5NCAxMjMzIF0gL0ZvbnREZXNjcmlwdG9yIDE0IDAgUgovRm9udE1hdHJpeCBbIDAuMDAxIDAgMCAwLjAwMSAwIDAgXSAvTGFzdENoYXIgMjU1IC9OYW1lIC9EZWphVnVTYW5zCi9TdWJ0eXBlIC9UeXBlMyAvVHlwZSAvRm9udCAvV2lkdGhzIDEzIDAgUiA+PgplbmRvYmoKMTQgMCBvYmoKPDwgL0FzY2VudCA5MjkgL0NhcEhlaWdodCAwIC9EZXNjZW50IC0yMzYgL0ZsYWdzIDMyCi9Gb250QkJveCBbIC0xMDIxIC00NjMgMTc5NCAxMjMzIF0gL0ZvbnROYW1lIC9EZWphVnVTYW5zIC9JdGFsaWNBbmdsZSAwCi9NYXhXaWR0aCAxMzQyIC9TdGVtViAwIC9UeXBlIC9Gb250RGVzY3JpcHRvciAvWEhlaWdodCAwID4+CmVuZG9iagoxMyAwIG9iagpbIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwCjYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgMzE4IDQwMSA0NjAgODM4IDYzNgo5NTAgNzgwIDI3NSAzOTAgMzkwIDUwMCA4MzggMzE4IDM2MSAzMTggMzM3IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYKNjM2IDYzNiAzMzcgMzM3IDgzOCA4MzggODM4IDUzMSAxMDAwIDY4NCA2ODYgNjk4IDc3MCA2MzIgNTc1IDc3NSA3NTIgMjk1CjI5NSA2NTYgNTU3IDg2MyA3NDggNzg3IDYwMyA3ODcgNjk1IDYzNSA2MTEgNzMyIDY4NCA5ODkgNjg1IDYxMSA2ODUgMzkwIDMzNwozOTAgODM4IDUwMCA1MDAgNjEzIDYzNSA1NTAgNjM1IDYxNSAzNTIgNjM1IDYzNCAyNzggMjc4IDU3OSAyNzggOTc0IDYzNCA2MTIKNjM1IDYzNSA0MTEgNTIxIDM5MiA2MzQgNTkyIDgxOCA1OTIgNTkyIDUyNSA2MzYgMzM3IDYzNiA4MzggNjAwIDYzNiA2MDAgMzE4CjM1MiA1MTggMTAwMCA1MDAgNTAwIDUwMCAxMzQyIDYzNSA0MDAgMTA3MCA2MDAgNjg1IDYwMCA2MDAgMzE4IDMxOCA1MTggNTE4CjU5MCA1MDAgMTAwMCA1MDAgMTAwMCA1MjEgNDAwIDEwMjMgNjAwIDUyNSA2MTEgMzE4IDQwMSA2MzYgNjM2IDYzNiA2MzYgMzM3CjUwMCA1MDAgMTAwMCA0NzEgNjEyIDgzOCAzNjEgMTAwMCA1MDAgNTAwIDgzOCA0MDEgNDAxIDUwMCA2MzYgNjM2IDMxOCA1MDAKNDAxIDQ3MSA2MTIgOTY5IDk2OSA5NjkgNTMxIDY4NCA2ODQgNjg0IDY4NCA2ODQgNjg0IDk3NCA2OTggNjMyIDYzMiA2MzIgNjMyCjI5NSAyOTUgMjk1IDI5NSA3NzUgNzQ4IDc4NyA3ODcgNzg3IDc4NyA3ODcgODM4IDc4NyA3MzIgNzMyIDczMiA3MzIgNjExIDYwNQo2MzAgNjEzIDYxMyA2MTMgNjEzIDYxMyA2MTMgOTgyIDU1MCA2MTUgNjE1IDYxNSA2MTUgMjc4IDI3OCAyNzggMjc4IDYxMiA2MzQKNjEyIDYxMiA2MTIgNjEyIDYxMiA4MzggNjEyIDYzNCA2MzQgNjM0IDYzNCA1OTIgNjM1IDU5MiBdCmVuZG9iagoxNiAwIG9iago8PCAvTiAxNyAwIFIgL2EgMTggMCBSIC9kIDE5IDAgUiAvZiAyMCAwIFIgL2ZpdmUgMjEgMCBSIC9pIDIyIDAgUgovbyAyNCAwIFIgL29uZSAyNSAwIFIgL3BhcmVubGVmdCAyNiAwIFIgL3BhcmVucmlnaHQgMjcgMCBSIC9wZXJpb2QgMjggMCBSCi9zIDI5IDAgUiAvc2V2ZW4gMzAgMCBSIC9zcGFjZSAzMSAwIFIgL3QgMzIgMCBSIC90aHJlZSAzMyAwIFIgL3R3byAzNCAwIFIKL3ggMzUgMCBSIC95IDM2IDAgUiAvemVybyAzNyAwIFIgPj4KZW5kb2JqCjMgMCBvYmoKPDwgL0YxIDE1IDAgUiA+PgplbmRvYmoKNCAwIG9iago8PCAvQTEgPDwgL0NBIDAgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTIgPDwgL0NBIDEgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTMgPDwgL0NBIDAuOCAvVHlwZSAvRXh0R1N0YXRlIC9jYSAwLjggPj4gPj4KZW5kb2JqCjUgMCBvYmoKPDwgPj4KZW5kb2JqCjYgMCBvYmoKPDwgPj4KZW5kb2JqCjcgMCBvYmoKPDwgL0RlamFWdVNhbnMtbWludXMgMjMgMCBSIC9NMCAxMiAwIFIgPj4KZW5kb2JqCjEyIDAgb2JqCjw8IC9CQm94IFsgLTMuNSAtMy41IDMuNSAzLjUgXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMQovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxtkEEOhCAMRfc9RS/wSUtFZevSa7iZTOL9twNxQEzdNNC+PH5R/pLwTqXA+CQJS06z5HrTkNK6TIwY5tWyKMegUS3WznU4qM/QcGN0i7EUptTW6Hijm+k23pM/+rBZIUY/HA6vhHsWQyZcKTEGh98LL9vD/xGeXtTAH6KNfmNaQ/0KZW5kc3RyZWFtCmVuZG9iagoyIDAgb2JqCjw8IC9Db3VudCAxIC9LaWRzIFsgMTAgMCBSIF0gL1R5cGUgL1BhZ2VzID4+CmVuZG9iagozOCAwIG9iago8PCAvQ3JlYXRpb25EYXRlIChEOjIwMjAwMzA3MjE1MzM3KzAyJzAwJykKL0NyZWF0b3IgKG1hdHBsb3RsaWIgMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZykKL1Byb2R1Y2VyIChtYXRwbG90bGliIHBkZiBiYWNrZW5kIDMuMS4zKSA+PgplbmRvYmoKeHJlZgowIDM5CjAwMDAwMDAwMDAgNjU1MzUgZiAKMDAwMDAwMDAxNiAwMDAwMCBuIAowMDAwMDEyMTczIDAwMDAwIG4gCjAwMDAwMTE2MzggMDAwMDAgbiAKMDAwMDAxMTY3MCAwMDAwMCBuIAowMDAwMDExODEyIDAwMDAwIG4gCjAwMDAwMTE4MzMgMDAwMDAgbiAKMDAwMDAxMTg1NCAwMDAwMCBuIAowMDAwMDAwMDY1IDAwMDAwIG4gCjAwMDAwMDAzOTkgMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDA0NzY4IDAwMDAwIG4gCjAwMDAwMTE5MTEgMDAwMDAgbiAKMDAwMDAxMDMxOSAwMDAwMCBuIAowMDAwMDEwMTE5IDAwMDAwIG4gCjAwMDAwMDk2NzQgMDAwMDAgbiAKMDAwMDAxMTM3MiAwMDAwMCBuIAowMDAwMDA0Nzg5IDAwMDAwIG4gCjAwMDAwMDQ5MzYgMDAwMDAgbiAKMDAwMDAwNTMxMyAwMDAwMCBuIAowMDAwMDA1NjEzIDAwMDAwIG4gCjAwMDAwMDU4MTkgMDAwMDAgbiAKMDAwMDAwNjEzOSAwMDAwMCBuIAowMDAwMDA2Mjc5IDAwMDAwIG4gCjAwMDAwMDY0NDkgMDAwMDAgbiAKMDAwMDAwNjczNiAwMDAwMCBuIAowMDAwMDA2ODg4IDAwMDAwIG4gCjAwMDAwMDcxMDggMDAwMDAgbiAKMDAwMDAwNzMzMCAwMDAwMCBuIAowMDAwMDA3NDUxIDAwMDAwIG4gCjAwMDAwMDc4NTYgMDAwMDAgbiAKMDAwMDAwNzk5NiAwMDAwMCBuIAowMDAwMDA4MDg1IDAwMDAwIG4gCjAwMDAwMDgyODkgMDAwMDAgbiAKMDAwMDAwODcwMCAwMDAwMCBuIAowMDAwMDA5MDIxIDAwMDAwIG4gCjAwMDAwMDkxODAgMDAwMDAgbiAKMDAwMDAwOTM5MSAwMDAwMCBuIAowMDAwMDEyMjMzIDAwMDAwIG4gCnRyYWlsZXIKPDwgL0luZm8gMzggMCBSIC9Sb290IDEgMCBSIC9TaXplIDM5ID4+CnN0YXJ0eHJlZgoxMjM4NwolJUVPRgo=\n", "image/svg+xml": [ "\r\n", "\r\n", "\r\n", "\r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", "\r\n" ], "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(9, 5))\n", "xx = np.linspace(-1, 1, num=100)\n", "yy = np.sin(xx * frequency)\n", "ax.plot(X, y, \"o\", color=colors[1], label=\"Noisy data\")\n", "ax.plot(xx, yy, color=colors[1], label=\"f(x)\")\n", "plt.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting the Gaussian process\n", "In order to fit a Gaussian process, we need to specify:\n", "\n", "1. the (composite) kernel to be used\n", "2. the prior distributions for the kernel hyperparameters\n", "\n", "Here we choose Matérn kernel with initial length scale of 1.0:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from skopt.learning.gaussian_process.kernels import Matern\n", "from scipy.stats import invgamma, halfnorm\n", "kernel = 1.0 ** 2 + Matern(length_scale=1., length_scale_bounds=(0.1, 2.))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The length scale specifies how smooth the target function is. Larger length scales correspond to smooth functions whereas small length scales produce more frequently varying functions.\n", "\n", "The `1.0 ** 2` implicitly defines a `ConstantKernel` for the signal variance, which defines how much the actual target function varies.\n", "The given bounds restrict the length scale which the initial maximum marginal likelihood estimate can produce.\n", "\n", "Don’t worry, all these kernel hyperparameters will be inferred using Markov Chain Monte Carlo (MCMC). These are just the initial values.\n", "You might wonder, where we model the noise of the function. The appropriate `WhiteKernel` will be added by the `BayesGPR` internally and we do not need to add it manually.\n", "\n", "What is left, is the definition of the kernel parameter prior distributions:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "priors = [\n", " # Prior distribution for the signal variance:\n", " lambda x: halfnorm(scale=2.).logpdf(np.sqrt(np.exp(x))) + x / 2.0 - np.log(2.0),\n", " # Prior distribution for the length scale:\n", " lambda x: invgamma(a=9, scale=11).logpdf(np.exp(x)) + x,\n", " # Prior distribution for the noise:\n", " lambda x: halfnorm(scale=2.).logpdf(np.sqrt(np.exp(x))) + x / 2.0 - np.log(2.0)\n", "]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the signal variance and noise, a half-normal distribution is vague enough to not bias the inference too strongly, while still regularizing the parameters towards 0.\n", "Specifying a prior distribution for the length scale is more difficult (due to identifiability issues in both directions). Here we use an inverse gamma distribution, which limits the prior probability weight of small length scales and decays more gradual for large length scales.\n", "\n", "With that we have all necessary ingredients to be able to fit our GP:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 1min 3s\n" ] } ], "source": [ "%%time\n", "gp = BayesGPR(kernel=kernel, normalize_y=True, random_state=rand)\n", "gp.fit(X, y, n_desired_samples=100, n_burnin=100, progress=False, priors=priors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can visualize the Gaussian process by plotting the GP mean process and the standard errors and deviations:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/pdf": "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\n", "image/svg+xml": [ "\r\n", "\r\n", "\r\n", "\r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", "\r\n" ], "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(9, 5))\n", "ax.plot(X, y, \"o\", color=colors[1], zorder=2, label=\"Noisy data\")\n", "xx = np.linspace(-1, 1, num=100)[:, None]\n", "with gp.noise_set_to_zero():\n", " yy, yy_ste = gp.predict(xx, return_std=True)\n", "_, yy_std = gp.predict(xx, return_std=True)\n", "ax.plot(xx, yy, color=colors[6], zorder=3, label=\"GP mean process\")\n", "ax.fill_between(xx.flatten(), yy-yy_ste*1.96, yy+yy_ste * 1.96, alpha=0.3, color=colors[6], zorder=1,\n", " label=\"2xSE\")\n", "ax.fill_between(xx.flatten(), yy-yy_std*1.96, yy+yy_std * 1.96, alpha=0.2, color=colors[6], zorder=0,\n", " label=\"2xSD\")\n", "plt.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To sample GP realizations using the best fit (geometric median) Gaussian process,\n", "we make use of the `sample_y` function:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/pdf": "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\n", "image/svg+xml": [ "\r\n", "\r\n", "\r\n", "\r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", "\r\n" ], "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xx = np.linspace(-1, 1, num=200)[:, None]\n", "YY = gp.sample_y(xx, n_samples=20, sample_mean=True)\n", "\n", "fig, ax = plt.subplots(figsize=(9, 5))\n", "ax.plot(X, y, \"o\", color=colors[1], zorder=2, label=\"Noisy data\", alpha=0.7)\n", "\n", "ax.plot(xx, YY, color=colors[6], zorder=3, label=\"GP realizations\", linewidth=1.);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also simulate function realizations using the complete posterior distribution, by setting `sample_mean=False`:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1BhZ2VzIDIgMCBSIC9UeXBlIC9DYXRhbG9nID4+CmVuZG9iago4IDAgb2JqCjw8IC9FeHRHU3RhdGUgNCAwIFIgL0ZvbnQgMyAwIFIgL1BhdHRlcm4gNSAwIFIKL1Byb2NTZXQgWyAvUERGIC9UZXh0IC9JbWFnZUIgL0ltYWdlQyAvSW1hZ2VJIF0gL1NoYWRpbmcgNiAwIFIKL1hPYmplY3QgNyAwIFIgPj4KZW5kb2JqCjEwIDAgb2JqCjw8IC9Bbm5vdHMgWyBdIC9Db250ZW50cyA5IDAgUgovR3JvdXAgPDwgL0NTIC9EZXZpY2VSR0IgL1MgL1RyYW5zcGFyZW5jeSAvVHlwZSAvR3JvdXAgPj4KL01lZGlhQm94IFsgMCAwIDUzNC44MzQzNzUgMzA0Ljc3MTg3NSBdIC9QYXJlbnQgMiAwIFIgL1Jlc291cmNlcyA4IDAgUgovVHlwZSAvUGFnZSA+PgplbmRvYmoKOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDExIDAgUiA+PgpzdHJlYW0KeJzVfUvPJdtt3bx/RQ2TQR/t92Now4mAABk4FpJBkIHhVyxcObAFx38/a5H760OyqvvqNgKrZUFy37qn69TZtTe5SC4u5uu3n/L1D1e6fov//tv1P6//hf//t1e+fo3//sOnzwn/+LtPvbbXqq3Ojn/8yf5jTe01Z17440/8tPvn//3p099/+tWf4Ua/v9Jr14//ky/8dbj06VPpr6Z3LelV9Sb47jJfI17+yV3e89U/rpub2MvyKP98PX1FT+VVrjIn/vdf/u76H9c/Xb/6s8JnzlyVV5d1ya+FH/9aukCf0mvsleouuU/8lF/9xd/933/8m7/7b7/+8+tvfv+prVcZebTlfoi5ap/s0199+svrnz++MmFt9GuXeR2yWliin71xfa0v9/1zvNl/+/TP+N904c3kq5bXbrnWXsqs136VuXLp19/87tOf/+b61X/OV07Xb/7+08Kd106j8GX/5m8//Yf8Suk/Xr/57af/9BvcLr0S74j/fPwBN8Dv/+1f//d//au//qfff/7dP/7Tv/7++ov/8+kv+Z/r/9eif8IyfGvRc+qvWvaqbm3M1e9d9J+98TcXfWOZ0u55ptb7L1j09Jr9T2DRR3lV/Ouc/eKYy9+97D9/628ufG7zlebEw69Rxy9a+f4nsN1L3q82Rt5+W9rL37vyf8Ctv7nyBT4gt75WGiuvX7Ty5U9gz5c5Xv3up+zl7175n7/1feXdmpaBNUi5c1G/LLyurRrxC2v777dW8OyvkUrHv7I/yF7+3rX6A279M2tVS8GG3rO1mleJy6Vb8d95ueAtxkyzbv+bzOXvXq6fv/XPLdfc2IVzA2vU0eJy9T/C7mow8bOuXTwcel/9bpz1czf+maVqdWATjpzm7u12EOcfYWd12OSVZk7+J9nL37tYf8Ctf265Ns7sbGXtOcv0y5X/KHbr/S0V7xxGYodQ5H35F1r4xxuXhVDoft+bZ+UPhH3bPeWSUh9/gE+tfwIO9cu3zI5XX1YbfrHfl793se2N34vt7vu42DO/2ux7ppXWz691+VNa65zLa+4F/+cX21z/3tV2t34vt7/z43rntHHe4Y1z77v9AaHpn9SKd3xNab3FFX9f/+4Vt7c2K+7u/GB5c4fNx+caACZQ5iwVb0Dd1B/T6OIL8PfwuRVW6n39u1fK3tqslLvzN1ZqtVfqtZeKXdjee/CPtVIFf6wTj7JDqux9/XtXyt36vVL+zl9fqVIy/v+uQEy57rd9/KOt1CivnUoO6/Rx9btX6X1bs0bmrt9Yob5fOfWCAzp6e3vrX7xCVROsWICxRpmtwxi23XKeo03Ywtf8+Ff9+hf9Wdn+KPM3L/s3P7m/+d9+/fVPxu84dl2yjmO8YFbaWqNVrEylRdp5Yh/RwF+/+q+JRvnj4595Emttpaw8Z8M/t/LCDgKSzq2Xp7+Bt5nGHBlfDURUsbgVO6KNvJ8+jid5ZYR+Pa8x1vW5ZbyqvfFPK42HzyP2njOl2veugAz7VeGf+myKvu6Pj++vqeyOm+Pzn/GuR0mdIdN8ehyswqtvhAp0eHicmmiJ8Uc859fuj7iiYxEHjuBkFhJgsNTV69PnAa0TM2BA4nvjr2fsnJkbTsvYjz+g4QHaXPgJCx74Mzb1yrnlUeuaj6tfXtikeCT8ynF14NcEuIRdi0P/sPpYzjzmHgNRZ73qeo2BZ8/w6vn555bXyPhP5ynBPxfgg7TxBXs8Pg421msv7LBSud8+I/7A++vA1NhYT+834wU0PBAseuv5QhQkMW4BzHjanwAmr5JqxvOs2q5cmBTbAy9jPj9Q6QhuchkTtjBPPiBCmpJaw3Z+3HCfK05ZS2MVviE8fcd6TSzT0wIxHQpbMgYwU50XItSGY4jYE7/44ePphSfJMJYITq/PTCvhXO49e376NFDBKhuPgoO+L2a8V2EAzNV6+PjGwZrYnwnfjR86YToHN359fJTP2CoJ5wj3a7gdTmUtA1uo5fS48Xt+zcVVzPixV0OQuFOt2MX76TV1fjmWBHdc2DaDtaaGXbEAcZ6tDrbxgs3BoeW2wa5ePLeVC/C4j2HwsK0KVmVfpeFpVsahnPPx9vz+kVrpsxYecpq4lLH1WnraNNhUCxEw4Rju9xl+YmMf0xns5y2MmJB7fDXBKAnfNhFDNizu41rCdgAk40TszuWDSWl4xR0nfjw9Pvc87lbSrI02CrvzldrCGWs0Kk/LifXAwhdYnnWNjhfdsS9xjp/WEiZmMN6HbVoX3EPFRsAveVwZ2sc9F/w9rPfET31JaQVHsTx+HLsGz8nDhm14YQPDzu8M+/Z0mDqMy5o17cKsTedhqdgE+KbHx844qKUlHCcYbLGU8BL4oeXRTZWK07FpOmDTrorAEmcXOzQ9b8iS4JewO/BpmFK5e6+VHraXp3eKV8RTDFgK38oNiUM+4FjSevaZsKtpzlWx7rSru7wy/FuCI61PP3bz49wy+Cv425kLiVvv+mjlG3watu4c3JWI+2gXxEE/GvmS4BOwkjjdY18jCzaDk6qPmxErgfvRH8AK4TXR/dcORJoaHMPT7uXtcbQrzlCS15rgXuvCSXz6eKFFx0HFfwdv316IWzd/+OMuwFrARC9sP3x/xtpUGE3sSSwjvP7T2sChwZVVnE8YOvhN7OACbNC+4l3ba7Y8sROwF2BIxC7RaqfHlWdOG8d6SCjHz8PuNNjkwqV9OqjcZnXCQ+JVFjleI9FVwhs+Ps+AsxzcW7Bkss3gnQq8zfM2w7apxDYJJw4ffxXWj/Ce27MRBixvjKxa2TzqwFoZ4APoqD09PM42TNyoNI2TaBlftPLmL3naBgDRo+PN4N58dDwZTi6M/X58mAWjBFc068ZGJABnjIFzPp+9E5zSi6vQCD0rQCYWJuHPrT/CMoAUGEQAISA3cQcNzmFNGOBHTAaYRI++O5//EutO61rbIySAawKaWnUAsOHswWynDcfz6AqwDFgQYHTY0HXhayZ2Jb7p0Y0JXkAwl4EviuxFOuMhhuDxsZlWWLQElcHQ5wkTiHcES5AfjwZeyAv7asDo4szR5uBk1Ir9v58tARcu043iRGzZvNgOvQw4vq9hVSwEjAcwD84eTCa2MtayPC47oSQcE3OtRIZYSsQlCVZ1PJ+lwv2LV5QmnkJMfB50qrjP01kCNmEEBRcArzBoaPD3ADkARh/PEqE7gC0MYyHXA6g1YeOnBOvwZGYACXjqADNgN7jdGI/gbzy/qcKAddFo0f5/rowamIguqz8tDZ4AIDYzCMKmpE3FwmDl8fDPUdGEVYJJrTSNMAs4HdiSMJnPGB4WnkaOaKYzBEwSIwFM0gY+rTzeExwjt269NswCIjTYAmzjp2dvfE0IhwCvGWBWwYZY3cxN95WQItFn8EwVbju4WpjVjV/zjA0RrgPA1JT4KhFfAEZUgpRnSEObDkjSsBXxAUIWmD2cLIS/j78WMR/sOYLchIAGH0aoPBDCzucfi221JX4DqLryxgkcfHM7fc3SYLUBa+FBFn0VghageUCa5y0PJAC4BO8ruICoHPaUMPLRtwI5VvqACSC+4GCAWydeFW3KeDRlmTfEYa04o1io+urcA/gLjydKXOuWpT8ohTtuE+092T6Bsb1z5+D+hKkZr6wz7np8GECmvuCcsNPzkE28AArwlx8B2Wf4mRch1URwKPsMHqKUnmgBHxMTq78YRxZGQAi3MoOEzQgBKO1xH+ADQG94LhwmIkZgPglcd3+M5hp8GG4Nb7B1m8HSwFbBTz0bS1hvRHowkQjVt1hvrCWeB5vz6S8AqWLvLHwcHhXPAxOB3VeBnR4f5zNOFbYD3lcCGLo63zRcIJMmz5FoYxoAyAGPsl74FbDiy8OOv7QJvHL9l5O8S69ZJz0EfO038oOWcPFMIvz0V89sxN99lY2Iv/GLWI3+8+87ffMbfnk2lWsTsoBkNPakidSCJatflgxh0EfOLzMJ6BfQsA/hl17YKaVo+Y75dJgSXMbBKjT+pG3izzAvgFyZQXNJKcnljXdUuA+yANjF3MpPn7CFKiLsOgS9dRiyxJzqJKhhdJDzYhjeFldi0eomfg1MHC4nogZcLqwt4+TJZf6mxlsvnAY4DV5FcAt72FkFXFirwQSfXIbfxunC5Q3UW3F4slxesLWw6z99InhOiOGI43FvnCV4b7nembQCptLvZKpNrgPfwMGnlOU6XthccrkACGyG0rwMTw3PJ9cnTQxcjRgDWKZd5Wth2AYu76JGAmu19Dq+azChItcRU8AJ8jo83ML+WV2uI2qHq5Tr5DPAVso64glg6nmZVhxncqr9rfwXrB8xyzBhTOlGcH0CSuQs1xefAVtA3lJLBQeT14kPJ/YOsTewEHBf33Id2xdP36dcxyeariYzrRU/LOsmQMRQ5T6LPq7DQ8p17q895PoitsXGkr1EILLk+u7wSQkbWHYkfOkqwgxmqEOwy/sDSmEdZCcwjoed2tw4XCm4rzzlOgN6hFFbTH8ptcv3FvzlghgJYCFX7GHSC7kOgOP43kwfjtAVO62nseQ68xsw+1gfrDjh4OKmIg5ZOFkwpvDPQK5YT3keJh7g5jbrctgZzHTI9zJhVhFT4HJndmt2LlthwFyYpdDUNs5cl69l3j0TdWgZEC56yM+am8ki+HRcJxIaPPC4jhOBiDfx/kCmhVkYvQ7M0LlnJNlYJ5ZT7r+xHRq+FvfBOc19Y8/IdWbyNnwSrgvCRjCM6xWHArCeCC2PRYi25XXVtHGisGkEN/GHy6rh3DNRDWeI63gyhJB5y3X89k6Aoblk7LDN1a8E/w3mC6sMi8fEhxwu/Aw8Jl4eHnPCb2BZinyt5uCw6HC8ickPbApeZ8yS+Dcu5gQnPLzUcWon0mF8KTVA/FUsrVzHWUf4n7s6cDnoFQu7JzwWfuvCa5ijirEm5C8Il7l1cB2GS7dOxQIuxMk0JCx/bAIwub4lM5e0QAmDAu/K63hippJoGWiylhjan4TNBeOUaQH4vdjyusa74SHlfPAhgfKLHFHcgLEknlR+FNYg6yJvcnBg8Yr+WO5MXsfrfjExJ4VQvJ8Ob809gh/KfFPmnsL2Au4e8r2I4/E82OS4jHgEOFG2TmONATaRJ30wyM8EDLzO7AbivS1bhMikyuXN0KjSl3BT42nEkGCf856ZBx07c6Y+ZIc34kQYam4FHA4EvjSJvI4DvWHNZIPjtw9xScD1kqjmeeBJhU2R3wTzMtucOJM8J0RC8m4Nr4l50Qr8IgSSr13/kRx0B4zCwV9CQMA7wI7AM0p6Fy5E9rPxxNjx2HFcOaxuQvjAhe7kr6WalnfPfEU80lwhvGrsAOYEaKhwIqe4obfHZZABHCxmCtalAw9ju4vRLJKngMdlkRdmERuN2Wmpt/CyMIsHz1XlrbeWoa0jZm8KYgAxItYR8/MTuzP44UpUzBhdrjNYAuie8vGK9U4rOOLKPCuTccER4zp2yJbfZB0xP18Y5Mh12L2++tL7tw4rM4OD5uMv/G/1DrrCUQ4Yf3FwjFsK/OcSh4VTOgSlAFjh1+I4d7meWEHowaGzRg04lMTRM4GGgGfKZak6yupgl6TFHKL4yT2TgiDn52GMsMRivHiYEKsKHiuCnxC3y3UYfATadATY/ZsVQb0Og89ywBC/je+eCndg5mEBei/i57Ehk66OxQVMPLO8KNdhXOA9aC2KpAKXGEGHF+BX65zyFq3/J27EDlR/i4NbBrN8vDzwYFU/Dm+BE1KGfpxhVg9wgeHp6EUcUMEzD9gO7mT6LpwF9av4jTSftCOENfCPChdgG2ngCCoJX9LQt2hhBJYTGz8J/LIwgilqYEHZVEVCatk6BE1NMYfBFtz4DMK0OwoL2/DEVU4hV1h2MqvQsPd4SlzHzTszFgFzYKdhaeQoO8zRWNfIehtY3s2yRpejj9Mpp7bQ38MaLq2+s9YqBhmHHT+1Jm5kGptCloBcx+FbODa0TVjVjWeSp1nMIO81tWqL33ReiYEu3LwsTQTkgr3LFLhetwiFqR0YLvGeCRu5yO7N+CEJP0E2Zk1MdE6CZkU6tKYR0UiMo6tQmdNPI3EjD5qFxn4rh3TgxjY9oDhh1rQZWGMVCI3h0NT5IxaAN1qtizesLE1GZDS4YVNKEQHhiG22eel1WkqYI81MrZ36QUAbPxfHbEqmE3/aRZw/GREZjmXI9c1CuHweb7qQOdHEmzO/JWwpRB/4WZk4kE6+M/EcABNONgKzJDQ0i40mYc9qKWKjyYohdobchxXuIXtHtkWPgAlX9yK9gtcRGs6GW1VBezQVugawIThqeyvaI4Vg6+exgIU1Cbm+MtPqEWBlqRQowAJ66rgnzw+TlLsOsZmV9DGesizX8XZwgCLwYgyR6soReOE6TJG+cwu8YOtg5CU+bqmy7lOnPj9eDhZQrg/uxw6Ezevw7XPVCNSwrgR8Ao3g+WaT9D7NJzZFEUDpABxj6iUHDpAby5AZOMjiY99LXN5osOB0afKxRWaFjxBgB8eHEJygljQHFsFk5zfaGtj/g/0Zu4thcEAQvo4mcEUgOF8SROrnJ21TJmjBdTipKhGxQ4iszCNcuCFErBROliJKgwQ7PU3R20vCf1WeCGyw2bGysjqTIAG28xgARPmy8xuRm7AmxWCs4zkaGyWYCMlyedY8WwCauMyKoaAOuC1GT5VJB8LYlsmX4/XBQ0ZqBmEsk7g5AlPCW8Q/+rXATAySsuJbEm2HXmdNfWQ6Glxn6VzhM+LkUelB5T5J8nZyXXIErL/zeie3RwEu6V9MvMlz5l1kjxDE4jdt+iUeVWxVYa9bPIzrg0FN/cb1HwknCz4ECCNHFFtlwzwzfiw8SU2j9HcOSnIbinxNCqqIKZxilUwKCgdnNWZhHSDGj5asj6C7RIYcTuwQP08m0NTk0TtLxOJ9Yp1WriOCAijaTcAjzPYBlRacNsGd+nk+GUv5in1ZF5fbCwkk56VYFoAOhyWCzcHHwUPIdVgwfMdUKN5Zl8oeVFYBPmpQbfII18koWgoe30ki9ifDBglqskmiKkyIIk4rS9aYJB1N1jC3UwN4JIUOvkYslQWPVcjQWR/TgEdi5SqkcoJHZgNx+6aguJ8gMSSVkoAruT611tPlLQ4WbWT1YcjHXLNWud7IGFRUOV6MX8qS6zW3k5UhSQInr2i+FAfgIC2DNnl/gJYs92F6Eq+dNobP0wRn+6SVpGOTZiQcOl1MWiVFuQaFVh4QRGKazIL5BmRPuj5w0uq44Nbog1k9kl1IMr4HoU04ZeUBhU6Sdi6f4MLtgM+mbCkHQhcruwqQDAglNt0HMDgQCjuI4yD2yya+8FgdD6Mo1KBN1hNgF4aiUAYzLMAJOl0IicW32kQZ/MuGedQ8nIWVJAOuLdkLmxDrUpqRg1Xg6lMl1U8CqEGWWASbtMpD03keJPJnyI+yYJBpstV0H7g0VmYcsySKsCCO/gWuTTM+Nr01BKFLFOHSWzAo8HwKEnFu6070VLgbDPLUpK9FcVLnqkX2sUVxuzC7OBU4GcDGbi/4SHFyFrARKzFKlOcnZAQ6Y4i+aUdyF5tpgRyvA1xLCGCBHK5zh2rGzQA5XG8LGKMHIEeKLKB+KgHI4fmZBW0zAKQlm00BoUNIsBcwX/uGkJgNOElumxEDnEaUKmahsWsVDrsr5sbilxEB0mQAprlai49weZJp0iM+YgjAgqDgINYeF5ec10mvkVWzOAibGut08I7BNbi+BagGpCL2cxwEY5AK3CXzfzMijEX0q1kchzCYWltZUL2DBp15kFRjas1e/5EgQyUNGh5c+jDeRa7KY7U0szaZy29NLe0k3S2Uvui44J5Dxo1meTRNAtiC2CatWHG3xSh4owAAYksA2ck4JJwlwkjifiNKGcD0IT9HblRhQupyiThudaxDipk1uKLEaF0uT1JVF49zxnGDydpayjKVr8r4QuMyV/qCC2E2XzNxpvRVhJ9xL3Hx2KamnzeZNaFlkgJ0hdIXfAE2nSwvwgC8IqVqkatFsoVef5fEsKtw1DVTZsCO0KvGSjugGlIrhkRcofSFX45fuyKqKUI7aYpqbEosM8OdcgA7hYnsqYGEy5TlV4M91wqaBS9kiSH80ooYEVHeehmgZIh7poHDT2H0ICA2JYVGFurg7nj7YjIdpGF+LheFFrauVtnrsSWmDFAnS4NZgChMWcDMyDt0UIRIICtgdVCkk344NI3j622JZTjBIrbeRv6j5o6Yv8Ly0YZUllLuRbh6THkNGKWxqJm6Ah2TQMP1SXJli6BD0kL7VNsMuKDJJBnzAVxMDawdtiBv6BRYPIjIJF5fPpHV2ZgyFPS6hBUM0IQd0QSUSVjRae+ltTObgWqMWzRJgZNR2bYzFIvgbGo+DC9wk7yl7gFmKkmo4EpzjESq7m7sgBdDY1qtSXmKpq1RrmQHDwKMeqvYwX4Dc+htbF6KuQu4PXkck5diJY8gQ69/yUvBY3egRl0cg2gWt2uvB9GYQp4wvLY+5WAStjNPwlpbhl1XJBVqczRvPSAaggn8SWyIS0HhBMCuiUl3qSb6k1n6LaW0JPKWSKSSU8uQf8r94ZmWZiNtqglmhm1lWuMzKSXCXrxH8f04tl0EWrREWfWcuMwRD1hXtO0AEHmcWwMyGC0y9mksWC7FMmy9zCXBBl9yvSu0JP4p7CHb3OAMi3E69TYmc8T74IUeHPUFLy26CmxeAUAmocS8Xe9diswWADGPRYafXO8s2copnDQJfdSIi7gDYS80HYbTQWvPqG4qr1gLlEQfiU0cssMrHdfwOIosKdxWAhqbT6IpT0oPCfBqV4LDCKNYfsJ5kB9rEzhZGLUroivm/rCjYp6my/Es4h1cgZIMoibf+pXLPxS2IpOskt3veEVwBgVOUF6whVx4ZPxFQZoWXDGpgWcoAV0RT5YlR5QcbljfqveWQnDx6EpuUjWv9s4AScsfmeoec1WJu6r4AWxGRoYM6ypzf3KuXWaIHSGIymX/maIo9j9poTPQkFiYowZEBF1FAtuqmSSTASrMqDdNOJoMEC9X1jMDhsJ1luW0HmgwFK/3ofvMZoYQ7TRSvCJY4nXccWjGyJQhqRJYNBlrQRRhKumSmjIy9UYmb9n7coV6I0vGrKNGcMUOW2y0G4rilqnKnHN1xS42VTNbFkWxYN4UjBkQRTr+IUtZsASHwAgngiXCemy9FUlIXNePhzFFSJZ0u8JdC6FIJ8f1rFkeQ1nKSkGKWSFeH0LVDJCLKV0cGoVcTImNnjWASeTexJoltmvlL4w1S1aVPjg8DhXhJDIK1rIidi92zloix4YtNDVDY8qEBDy7n/KhAVFExLsrkmSMuwGiDylhVnW1rk7IW8I+3+qE9G2wWEplYm/OYqZCNhdWQaIBR2XK7Iw7HCGbo+H7qVqRsjAKe4hpKkEKtu7H9MhYspEDlSmTjrIiXhJ8NaRwHqhMMM1NgihXyGO0sboiGlPIW0l6GpSaZIERC3xZyxwuB8ScWJtaVDOAqTIJlU4KyDGfJLszImCCDwHePAU7Q3LqBFhFzpUjOZHqvFa9Aawu8jf1Rn4SFsVWFGsBFs00PL2mhkwtD1hrfmR0DL6ijhrO9oj4aki2UfGYLc0N6Y5ZOeAlNpyTnnCFCtwUOLkj/sFWa8d42XwRriMIb1qpsviHxd5DDWnklSy2uOjtB2DAjABokoOfbhU1Xq/lVOxMhYxoldRveR72PJK2WuQ6fk3SX2uQ0WLqsSn+eTOrFiOSQ9+1QGeRlJc0K28LZ7wOK6JlyHclTPJwPd3ySItsfAQysbK1mFVA7BYrW9yxa6cdABC+iH2Ct4rUYqsQFQq/cf1HgkDsCM5CoPXUap78oSlfk18iaB5tSyRrsA7JP2w7i9Rqau40ZasYCFSIHem9Pdah0kNTZq4hehG94JeIQ7cQCN4OG6AEfjYjPBhH8RGGcs3aQa6aJbC8MFavRpJPWwIY42MsSfbIiPpYtIbcCYiP2dKkVxu827yxxaR9Xu23Y4tJs2A97DKDr/AeWFmNFTmBBGx1uzyNrBALpVljpY4AaPexIp8b0Ay7Q/GVgWmFYa2yTmwKjFkbHLatqa53AY+dYiztxwIeyeiUi5DsT2OWj62fkuvK0pJ6eRYZfgjM8nkcmwMj/OB+vDxdjC1ywucO8I2sA2DsXAJ8yzxQeFtK83ontTKTFkkxja3U4TrelZLgDcuL6YtcNSdCQ0CN0nb0phJT7Jdni2cWCNgBfHmal6DMNhUa2cIbw/h0Ejq28EaHc5gbFkphk8ydlYJgC288O7jZVIhlWOSiPaCkPJfVktDz0NE8ixxvLslmdnmt9aIei9LI3hU5amwM9cEAp3APxEaS7kqrrX4ryQkvpB4uugFwbBhqJ+dnERxrEdguiuAM04v5iKWsbYvUGluIp/J4XHpMOFFNOEgWwVEZYia1cZbpBY/Gzi59HovssnQXKrff1uQGu2baVmTnMmTMEyhUs9BOEh7rUMPeVbkuCXFZfJchg3Hd81CufLUOYGDsG6mdbeP46YLscNSpASR5CBKlP6CXzZxx2fZ8IrXD0xW9bqt+hT2ZU6tpFglWCgnUdCO7s6F0neUxSFACR63nOiQolIWcbkhQ8IqmSwKtHa6iSqTmEB9/IXzEishusRqguNTUAtmWzfRRC8hOiO9Vm3jqEgUVll+lZokjrrVSW/OTRhVlsNiM2madIh08bzNqm7Fa1gyfRYhMhQ5NeHuECHuqlV7H3ZrSNltvyHEwOGqalLIZOKZF19RUmOFuMWO3q3I9XWaOuLcrO9tm5gYTKDUrR+tdmVxSKdVanUm0kdwHtC040BQmpe4Jp7wjLk2kUCnh39YrCXuV2uvqlYApm6XDK6TrBjdaU/qaQaVT7eHqAZXy/CBwqcr4N/k60ua2MpwMXOXW2rXrEph0HV49wJwmFdm3uxvdI6/jvRXJAFsUy1xCbsq1MCgWd8e/3gqGDYolbsIbUxKc4W0xoF0iWOZR7JRaX9Wkos3vkX8wDhh+F0/5cbxguY1Fvbw9FYP0+pufNWWDKn3aol42OLPNc33j+g+Fhic7BRiXuz4GEmHmKbzYRkPu5znE9NhGQ7YHY9NMD3uF611WCkiWUIh9c3zxJplHlIAFjXVVIA/uUkEAptOQTM+pr9HWVfm2qsBvA2+JjXLRktwbx1Ifk054BRwLmzGoLBNrs4lBwb51PcD0rN21m9LCVVxPaaxYgsUNO6VcVkCr9JajtdPc8AWuJrZa1ENbM3CVs0H6UH6XKcCS8IYtpOjQoNhEDvbempx8F2Z5OenJtJgUl2Exhj6LwaT09CtrYshiUl6HN9D6rsGkvP0cSnm0dVy5v+g1+VQjtQnSl9bGdx1X1ibV1QK2xRsRSazIQiPCGHvodZOCzJLYSlkrtl9ykEQY9aTlHAmNqkVTqUeuYou9MopaIleZha+UVs7rRkKjwmW6YeFBJ3CKpBYLT/bKrZQDFia5bhCaRcwLv0Ip8RYxLANdLPNyGJalVvwqRbw22ViJJTXstPSxxvXOuwT6GNEvMKsWhC20xY/a++RELa2MXbd574cmhr5P+so1MSQ1UT1AW7qzDXzRArSlNNzIyiWgXEBrg1pTpJUBVU6F5qb0OymOOxSEmNxkF9HoMkdAsNjtCAO1Dc0mJ2kE2fg/IoSlfsKo2gdpi7xYWIrVtABVaTWZlNMkpOk+IOu6acHPQtXBbAXCNy3+mu4DyoVNhYYGkTK9UM63+maCRimQEpDnJDA/zAnXZMA7iu5IaDKYbISsJTYZ4G8SI8bUJJtHKekhiNGkJpmJBSiKwJNdBjt1BbA21Sgs/TEC7mSFGtCg3zKQmUs5Nbdn8GVmu106sNPgy0zqXj4fN/gSy7cophTxJXniMAo94kuxFnvE5k7pPUBU0QK+hFnagnhC5pMoe2oDrct8wj50jdxcQViBpKIlmxAlLyo94U48iVLHQkEYOEt5vg55YttjrzVFnkx5sOwk1/FasyJJkydl7p1l/RIR6WQpV1nutsOAbcpjK4HJIVIlWeVYKU4UydPshOswEEpsTQo9TSsBcTuQV/PQkx0G7UBD30kg2kU9INJB4TlCjIA8u7Qja8HTIs8u/ZE7x86AXgVrnRLyG2JK5Nh0p1koSTERRkTzG9d/KIiJpdzYVT1ATBY0q3bF2jws383Q9kwvcVH71jdv07NNujZywKNkTm+lzNikbaNmlTIHTMKVzD3YW02h+raD1LQr1rYdULulqKiGSbjq82nF0tacWZ1lV6nHqcohVBtlgCpRd9FS8RunFtlxW/ObtqNhsOx2Kqo2f0qNPjxfbMMtFCZv+ZY+laNZlA1n8qRbYNapfptmW+Yl4ddieZpgo6negOlbaJSB7Ac0m+I01ZBw+1vWkyRzfDqNgDApwYWtLVDJIkNKMg3gpih60XjqhqZaLDJspM6P2SIypKCP2muf3iT4wf2V6Gg4fq2K4kCNfQv4XfCb5SDMN2TEdTzv6T41dWsmmeAotG5tKstNqYhaWH5nPZtYQk0PmrpyUxlc8ae2rtyIHZkav0IydNNWab+nbUIQRasqLyXgSJ4rBYAuuQlff/Ci6YXd1BHVJJ3DkYmEr5Ox9b2wFHAtEUdK+m0rOc+mSKUpQkVjAlNwlqr0HFvkhh2iuNthEJoiN1dY5Kk8g1A0pEU8MKRCt7BEtKPD6nhQIq1XZSQY3CmKfktZJTd9Dw2VXPPsEDGvfcucbmH4ak7P4EgKl82jJuNSocxmtdZywJdTfEPTJJ0vlmOZmyI6mwplBjkrC8WxBQdjjbkjW1D0DPfSDk6LMEW25KRCDV1w8oCyEnVHnjhVee2IMGnngUkVMpqOVZYoqCwcIWalyM/RG7GdrIX8PO34tMnQKeo5GuVY7DlY4F2aHbTYk72OGrX+5KRCyG1gtagG8Iltgt1QdJ0NjZDqGRTUXQFNsutld01qvcEheazMOuUADjsD81OktElJBldrLE34GRTIXGHCKQ5tFCwn4Ik0dUpDjzfdl54tYpvYXkF2Lrb4yW6+0SSlKvLWl2vRZBP1Ys3AGjDJ6sY+zbMGM8LGEmcrjDLYkL6AesjaffpOS9JW48Rq24VhF9JizLVb6NJQDbeTazXYsJH1n7L2BBsU2JaIWOltTP6RtRO2A2gf6Lu63lj76euGDvkLKbQ1IgrknLRWq5bXDe+Q2DZpAdIRDGlPm1bwvnb9R0KBdMmcStV92b2xjtp37N+gLNNMRV6m1UYh6Wxp0GQSjdxY8Mdy6gzFkBtLMYbVUWHRhpnyyyUlG1MPS/GbSUpSNYoxY6i6wyJSMy9AQ/HDSwsw71Rl01EPsRI/tcl5XFGKpZIypdpnrrheSM/pAQSKaEnTHH0Agat1BRY2/UjUgDO+Y1srE7uDZz+gQCbt1ukjtdVySW+kGzoUrLLqkWJ55x/piVhqVA2Vd7VcavTYkCugSWrGA17pMlgRlfSidIOSF71YGvyKspRcVZySSGN3vf7OQGaGVkkrhjYDSa03tp5oa8ib7EhJOvzLHVtGOH6EmaAa8CdZAMB1+vy26t5F5fmU0U15HZ8n3SqSJnn/fogZFn9y9ATszIj9tISQe2ixzDWTMHU4m2bNbMoyk2z2kbJ0/bGJUtFyH98fi+dVNcBQpqeQz1FvMYzHTI9ZRwCmMnhtaWI49qScKrfFpYKLNd1qS/dbKionvengKhDYyl7RRQRKqxoUW7oXjExRpMt3sDBNmk8mzXWw5Neh1bjkKZUWAVyjAAy+HuhKM9QW9JLwvjSj5cDtoj7T3lF0jr6klnFArEmSFiKDpb20nsHJVT9g1Sm9kP6jyjAW3LKVhCm2AFaZPO1VJcJs8nSIOs6MCjDUxEIIuGPjTGcHsioluJzqZsmtH1aAy6lyjsbSZl2TU8W7XO0QQa2iSyMWU0VBl2vt0seTotad9E8uXR1LC2AfZvnokLFYmPJspEBfgThaCB+1MuVysJUorUYWAZtUOStnR+isYrI1sggI8fEzZ2ARiM9aih8C0t7Apu2GtAfJCJr2dEibDThbdSoc0sZpY55Ac7zvXC7z9PVwKSwA3yzLquNwpAPWjtdJpFvWAXYjt5S8RNvHw+pxf+CZMmO6VOHAScZQPKTsiMt5OQ+lfDvSAW3tmOmmGFM5wWgrtcO29wilRGstLstb2Jq4W1SAoYLNJEPqumd5YYxmAPKT3LehIltO6YU4pWojpu1vZo8gTH9M2zLvmbeyYa0uzGb39+HaeiHAxZ2gfc/vrC0FAkvRfkvX90wNzF1vyJyMbHiHG+uV4LqRAnB5fgGllequMwckz+/leKmb0iC98En4WyQ/RANfU29ed4Y2VgMCQzzAdYTmqmYUdGekQUH7ikwDEROSSRVXg/CMDD5X5G+zxfgrmttyQjIir1t09U1AQLPG/uAoGMPS0jxERRcQkLbTtEfYpoWZ/Sz9Q0jGAH+OGJrzxsO113+kgIAWmZOl2o15UJlJjYleUu9YcvBxAmVd6EqlddtkejdN9kgP9Nw5lW1u6blLqEFiIn3/Nyylsv2MRg07Xrt2U9gkMmX5h9bMbbM4+e07y9Y3YYV8mpPcfAAhPTIyU8P1kDMsX/IYPrNc1lKfbbuZkuRhu+c6AAfj9SjnyoYPxLsJ99DrTmqZUkvt1ojOj8xbaplOGq8jh2CD7eBEo4JSTcoZ9hGeZYo5M8EGqap8f7fudKZXAFNbCDbSFmnQHbvTE+mDWA4NQgw5YpHKU27ciCVNQqFnPTGNuc9PtTxeJmzwp6gGmcl2Hx8Ry5cEOD++60OLO7trs7pBR7GgFMERKnEUC27ofdbAUizEtGoTsKNYiCLhIVEb9Uhcx8d6jwEO75OPboqjWOB8zaEsKhvgJGI0Kv5fIcChYQDAUwEgwytm/mu3wzc2gU+mS9o59NaT3sMihsY3Ju5hPaEqu8DFPVLE7Tn2i/Hzre56E60s0gG2YzxEYQMyX/S6Ua0kZemk+yy1g2cAxz7FTjLGedjt5/o7fqJAuijUXT5+omj4GMqVtAn/LAKSSqyylI8iLecqJurULyvFxDXpbOIqagbkdLS4rSimTNo5QN5EXKwJwRGeSsBHCMWeh9xVSdRl/InWcldlcJPCZ3vcoNbv5akggNb4m6dcYaIfHNXJts0Y/fCsnhqfzewL4IGTU0EiQ4omrxCG/SY81FnQXykqcfOXfPQIOeaIGNhbVxtxzW4fGfx3TMQpekdxxCX2hY3wQRxxqpicOlluIgNUAMka0rkuOMpTbmV2WZGBI3FzI6BIT3VVOSXHocZmRJB251BPdpBrPcQVDpbISmifly0c0D6S3H75IIoSifsoP5pYic1DiTZIrjuhJVgOVZV1QRHeG72YUq5NUMTrRWtULvoRc71uQkukmnAEWdQXn9KHoA1mjuGiUVFsvpvSHPuhYmBVNMnCO7GS09HEET1VAF+V4GDApZ83xBeRd1KCoqtWcO7Rqc3aYImCjTtpkcr26pHvUMUi+iCKrCMyKzWIMtUNjssZRz7KBFesVqTZj+jBu7rBQB7+rmh09abc9KnRaaTcsAkePzcr1fsdXXXWzfPRYHxTcbp0x6nGgyuGNA46VSUNG3R1KmOobq2NuXiZy3DF2glwQI8dhZ21ihYVOilGljkg6vIFFSnALMVLtkLClE/Pii1shYT3wdqpOLoJ3Ojx6XJi5MaFIU1OI7c3AbyTMCfTgUPkJmik3YQ7acV61a819JnBBPHJ57iAqwhK0c5BG3DRE+0jGGoCLgmCNf3tAi7O//1g/9iAi1nGdMpNNuBiVbxVpUbZgIsHDHBFJToNEYcS11OVlxwRhzMSDyR3kRjz/4ev6iQ9m7TkT424jCIEHVBSRoqjjJOvijhVCT1GcItZ7aZSK067swnxcjwIccGZa3T/tes/UoQmyhkt+4INFy8VTT0bfg7XaB1Z0nd4Rq8PsN6CUoRoqi4lupjwbCRZf4ldTHgmdrhqmsCEZ53YqGrJ/B2eMWrGiZAkoQm4OqXs82phMg1b5ltJUSe/Sa/ISKEfktlcvCiJot6xFUkZayn8caUZ2v2hfTc2hqJ5IPwSyGuVSBkSNBUXd7wdmofaRmSSE7zB4ej3+lLOHgfzhg5HbKhbFMVpQGtresDpU3AwLVUSrtAQuQVA3OTzaT2ZDlUyuSnxUBL0kFBsIMV9DeNxGiiNngXFjtnRerlAivMGyRORVbAVIXqzeoRXbUVIkHw5XHIjc9EkCa9EIiMtxlQhFaWun6Lafs6niOhUMRqj1jPNx6vwkwJeYnzF+88PVTCrlkGYVk47gImLyJlbHJt6+YIQSXN7aL7DiY41IXCeAMgIabDdAIBTwPBbGINQvlaN7109iEqHWuO24Q9beEfTcRJOGIMi/P30PXoBDPqHdSsHsZdjHrqTJSRh1dbWdIir/BBvDmWPhO5MSjWVW3GGI76zRquBw055WDn9gZReZVTodavD4IUq2yQM/2la47EyGoyPZu03BnujEsJRDbEMdh3R26N2GX0/vJHGmKY4Q/+NKFrjGcswqtK+f3T4HcOowBtqzPgOUAQDtrtqvwgXD9U0M+FJ19n2N60zFgCBzG/i/DR2JwC3HZ7MYZ7t7aTR2BBfDmC0UQsWmNPgI22emHh9MMZtdEJRfc4FvUJ0UvHHWVYs8VAl/5DKXCVnSguj8uNNdCIOZGuC3ZVyGAkj3NRSjotOKBLRY8lmE8jdtfwpsTY5w/fywYlQzE/ezEmACOIuh09vJD0IYbKqTbgaDKvrTdWYXa2FNvNoYTupD44EmzowxdVg4KRKOoonlphPU91VktPVZujeqw6aCIR9ROBbgzcTVnB9+lHDtGGFLLOMT/bFHMakMB0lRBt8W9SzCRIjpLIlGfDrCf7sksQv1yqGiTamHCVN+zqRf6Av7J1+E/lnsFSUfGIjC6HupY+o5R1b8MXBE/RQ4xnMTvZTy3lHEAz1Zj5FDFvjUTbvqdkY7f8h8x4U4ttIgVoinL57hRoP4U1X0aAwHYq1EI04bAjBOufHDAHbFJrY67X6TduNpBkswgixAv7YP1R0nLhbkvFzGpGZmGDKMG7VF7TdosyccChQCBU4H3mNcWsi5VzNqplnGxHwARAPKMXfNpGKUF7esTaDd04qv/ZB2q5QloSb8kdC9yecWe1RJc5e/5GQf6WJZYcysb9T1WUuPQfczgRknSkIvLGqAl/VPT6nugcQgBZVXPkEu0TLy5aDL5cVQ5uCCF4EINaOpHqC2tZv3CkKjZT9UZ4wc6kSFcw03HBzqWiWxYcHRMycoTY5vusEovii48wc6t18i/0Qngzq3WJV+40+T9f7Iapi0LCIHtd0CPHveQBMPawbTZ50G+zo28woGXJw5H2t6r9kze9CuDULb07Z7Vb1P1N0XevKNrnPh2RiWu5v2PNsWKSoZhgNxexyPpOtnGYIs0XaKBUkQ/DoZ2Ck1eRnkhqLreDTa/KfDeZS5otHVgVbXMpcSmPr5MwNvYi5Ma1lO2XbQYOtfShBfZ+zkeOoJ9yQBJ19U9PPLJm0O12dyeiuwp9O0YM16KR1EqfoQR7yyeA5RQ92ksyj+mtAIxEv3oK2BLzBIYlH1MGP2WvuxCKHLlB3WFfR/J1Be1QGxUY5aO+N6liBplW4jVxiWDHXfeQS6Vn19A0amEYy9txHOdcQbuCTejlzdlwSWVia6cagoX3H8Y6wa/LAnOjEUVaStLzsG1zi7fOHBJqDS8wX6n0sB4Uuex0YZTkoUwIhLRFYDsokJ3OdqUVWEGOQPLYDnqGCLYdF3qRncazgT5SNbakpPG5YpxHwCZV5y9H/cgoXg6qa/a6xxrTmmR5opS+YeT15ItdqSEnatuZNzEIkH7UC6cQsKFBw6A5We5ZONGmKJmpWcBlywBXksrDd7DZsaNDsJZURsTlFyValHZFC1/dzk5XohNdVu7Eci4NDCJtqyzsWB3xFepp3ydEEtdxE/O31HwkpNJnkznqVY3GQTq1BkcsSNipgljPVyLC9CQS2CgFZtjc+vWA2ItubMfb0rAwW/RhTy1XD6iYK6NqFY9XRiFJgBYcHEJVJuqnNLVYGjQy605IbxmNO1hM1Mec66mDANTVk82+c1ZPVCjpYIRzRPCIvQQY0jg8awxtwsG945VueTSjNtd0a8zIzCfm0A1rCwhkqqFRqw0xonPOiHUROeAyWpvQzfdtSrKk+cHgJhmDNVHrRBhZHpBbdiq4qtp5IDWtxsoeWH8B0Lrx+bMzL5GqeKc+OCEAR6HXauiwBOnOU2ew3AnSVsZNPkg31o2sszA0iLbBHzCE2eZ35QA50ZGop3kCH0C2OUL0t1G/yglQTzyXCyF7GZrxxoOlBt1JW3fRKfEvZt4491km05OwGBFFOcmuRytXvgRVSOkRqW79n9RF4LLKX+VwcOrMipsk86Osu4s9kzFQ9/VCoB0RXU+oK8oS/Q3WvHO2Ys6LX8duedswWvHyTF6P2w8kGhsmQA6vWb0KzTPD3uR+ST4zFRyyBy7ZuJ5nkWupwCg4KskkmtpjtnW8DIzliO3VNVlmlfSoJ9Y+R2WY6Nnsmkk5CcdkhPA4xqGaHTBaoiaC5thZa+ELEwnLXFbI6HH56ajluOjZ7HagNGOFOJ1vz1D4NfOmUZTy0SQtTqFLaPiRfDUzhRtX2GaeHgC/i5MmbEn4TJo1gR4dSGqVujvpDgCOznpY6ky+hFP44ivdWyGDLCBItUVshA0rHrXajuIpE14cAmIUptMrtYDubLqHKbz3CCoZrSu/ST5OZRSmMj3OOPWmciVo5Be8KBc4uXZQ1YBcp6dVVbiMLOS5G5xg5KCLjkNJN4spe/6EgCpvGKCAUIApf9hkraBvSOLUj6bBNi1w4IStpFtH3qQHPaUO5KXA2aahQlOjb1yoC4XbvU1t46WLFfUsa9aRbUBqgOe1V1QgtSuGMhqxEoDCsGxvpiDnZMiSL400LpW6KN+e8JQW+DtWImFdSnqQtN9L11aMMajrHmHUdp3PJy+GzpWRF5SrKye+snTUOBYlvb6poZRMpjdMesg7r8XL4cEI53+TwWRX5MkHR1Q/xp60gztcPK6WrIrCBqUmIQW+FPBYrKpfkCh1ck/wsHdZlCY60ZLXfBiLiNuSd6M81wgIkCLZ0popbgiNrJGvdhAUyP6Jjp2zmJWmVZkS4kwU911u7VxYBYM1e2NSLqq8pB84O5eZcKIqdRxjUmJTWNrkwrJu8JJ3L4/mK8DqjxjqhSGH0cWCTGeJN03e01J0uK+mie90Ii3Qps6bbpEQCiaREA5vDGTqWN0oUsC8N4CNHqSuZ+r00H+qqiqwl7NQjkbHJgB9dfDtYUSgLR7kqiLuy8K9NXE7cdbZTmHf8xszmsR0VBzrHac91m3JELhfMtFLdTCWPhpMO+gqVPCZBTqPprfmKiD6AJg6pa+3UvGxT1pbRYUots6r9WWaHtUgonKKjoKvjmq8E3OWHih2Oj9KzA89wfAyNcRKuiSzP3G8q/IP9Bpq/dSBrUVrmTJ62JThpj9JI0+WUuLAyh8XnlLZUmFeOIGtzZllTsocTWSU83kPbpkzuaLPvaPcexFQ3f1ZXERibO6JWK5m3itWM2NUmQfhDcMCKoBLqag7Hgq8qYyGViGXBF7U7yxnnaPuXRMB0T835GL1TOsF8kjs2R6Szz+pNdqrx/B+5KJs7YkK0nEYiL4Q6N8C0wCkrhEqIu4s2GHk5qjU1kHAgjhOI4VNj/xJvA8hc9PNvlSpG3PlDCNWUvGBfqHcc6XFy5vdJuJmS16LmjbZBOiFUyv0VtXZO5l8GeSnF1qK+JaUFxf9Ot58deuTwf+P6DwTvNuXoB0ySQ3e7Sn9F8uJSm368qXTEG61xaCm2RffZp62t6bJs7+QTrnJ0oOy0d/lqSyuTfPSN3zazDIcq8Waiwadjp2vQ+C50bcm/6xzUdz/Q3hIIV68nkBCZAD+oIOobFuKQY4ueCtq7TSiRbJ/UnDuVU8FnAStKh8ysOUr1sytlNy2DujmTNP7ljJ+2/UCFumuKA2yDD9137i2KmQIMcZrFfczkEk2fHFpziniHcqCfEQ1gs/luKTLHOPP6zJN3CI9kJDKzI8Kr7K0/8wosFYzgpij7wra8CA+v63RYR+GSuTVHG8BMPKLW+phnmqQbbTR6mrHDhFMVuuCKQL0i0TBpL6ejWAH/Uj35JhLaxTfcoJaAmzVP+ctknEiQZ4EiQC1SEGDI120QJLfOUX4wmShuxHH6Zmx3feYb37fxkIIrVEAjtNFznKmm0YLYKPbvfuijn3qYwrwj7CylJ7tuebYSf2kkMUQtBnEAVLFbnh6AdasZEJVAmIPRLaJSRWvdl5YzxW4AXF6hiiZlqHrU6W2nB2O9orPGXUcHO7NLP2mod9pK5DGzvkGLtMjmGR/STrZFA3Yg8WAF6EQb8yF459TvWX9t+SYqylk8SXMSLj3FfZ/zjdNEhJE1DW06K+TT++Agr3G/KJ867vgLm+Lk+vzYyI1YXWt0Nvk16Qe3DtS2FCVui3zgrBUVpezYTOnWVy5hpc7icrU79iAs5ffbGh22Wj1zuR3OYmNIOdKQBmdVmvojjWRLdFXiqX1LcjE1gN99q7kxu1f3keV0SS4Eg/vMx37jJhEb7WfCtMVH/IFKPnVcniEF/XXj8ggXSWN9B2x0HGuk95NU0w5k9cLviWuv2SmTzGIXOgOt686+X2wID/hFeZEjwh1z+QdCNUxp4AVQmcUnrWCJ4dnlMNqkFWfmZA1FbdKKqWUODbtidopTqMQz2bpao0iMNj9awSQiz9Yk3rTKSElGaAkmeIMTzk3hT60enFROw0wqv2AmCXWyq9pNgb3KwCptg3apLOZwxyHCm4wVZ9OciciOUC+pmjMqx/J7GEuNk5IxmSwOF+w6o97V7ehvvlB8zKBGNn8dD+moP+wzLB+dw26A4+SEgRzgCcWfyn4ittM55BtTnVLuH9OrLSOdShb5NFtbhjn1rlZZsSOXCS6OC1HYYhjmdFxnsK2FLUVmJfeoeEmH0/i2rlvBLQPAxEZaNiHgixQ+2MIaCXXlNN7aDJSY4ANbrOCQtE9OL23OVGTnHKuANkj9oUuKkueV+HvXG6zghsIC3GjhHJOVTu+k60RlKiUp29hmcFg4xilKsfBFKDuPXLYtfFXRWDljqi2Zhy0UHAd8BTIP+1FwPYzVEYW5rnGmBQqdzAu8KU29vOtVHIOdDvXUFqywIjDkPUcxcZlrDcumvZPvwhQNMrxc78HFY6XY2ziiOjg5bDjaPbh4TiMRzBNcuejnwNFFNjPnYLPJK9JwiJf60q4wW8dihogzpaKLlzpc0oPl2MZMcOdZwqTnSWq7cpSsJ2fVjjqPUdCRXOaBHRflwaVBtR6erRGIkf79k3IwZS8KaU+KGwREINO9q47ktRkZ6nIOUi4CUuCiVaWNWZ0Z1v6xUzVP8yYhT1XBG1G5kYQsmeAU8AMLWjDoJcp9DyGIHVqu70vkFtJGQNt/SHHYsoeSh98NhX2LsMSMwIJtknmevkdDHu4yzes0LBrE0flqgW0i+ecMbz4akO8UC1s0lo4bDoLfNbMz/gqcIOm1VsFLJ+nIOjw5jQGKdKbPuk4i/dr1HwqjcBpMomC6l3QU+qhqwVowkmiFlQpphF0aU5IILQW6mMJaornUobIWunBHTM3rOPYPbJAOk/dSjxz30YImCz/NDrN2RanHQewcoAsZmUxFCynItAgyS4N3K52Db/1G0qH40kTC23QOUpNgaqerRTr8lYiKWuwdJLgqR0/PFe1ECK7fENAmrb1oNckiIM57m9onbmt57KtiIVh7+94JF+EPz3JmVb+LcJy210qNTCTWe4/mryvNLTnYWiKzAEhjrnvHH2w/XpiWBA0wGoxf1P04YETW6hg1SqSwUsiB3Sp5Yjr+JMxWEdxQycNm7OkGpJhfG0f7xrb2iUdTL+woTVSGbicJZilNpICPNCKLmkStw39wCikUBD1yho4BRZuTWok4jck0zj+LyinAyLOohq/FYxRsmWf6hakIUt8FfkYV/gxOS+QtV83A28pfIs15ph4rf0TpMJlHAPKddkp0zuuMcTGVP45BmiejaCt8uH8tJySw6ajE+SjYynJ/k45K0ne2d0xH8czU0c5cxw+AyJFPoyiH3+adMuXox0m+GYCYJXVZYjoqS3yip9nUCcm0gyefMRslc4HmaeyzsDFJTka7Ei1shNkqVcuHJk3FqGhNhW8BTSbOINa+QVMPJDKfOvzC1gNJAUc8vW5okiiZFPbL9xNSgJgJZ1liW0BkHil9kMANN1yKtEft8c0NJwWg1iPS+M5qsYub/cE1gFXWFeeop35oOOPSu6bMOVdXBLRAMJFjJyATuK1oqsRxzCnjtVX5wQ3WkVjhoE9bb0zUZdF5CI69xULbh26hrUMS0lDd8gqFSNkMJ4tnWwepJPRBJgsC6rDL+UGoZEk4GUA1HcRWwSA3MzJxxPxpQbT5NLZhNSXkunwaOW8ajgVVx03VlBywNuE1Xn+NsudrS4ozZsdYblxFU+yhDIll3ee6K0Myhd9uM3Qmt2y7pc3k9x3pbZs2o/ruPnQpzxkjahxRjZGVGISwWm40zPZMoKAdarZoSel9bZoJtcmiNjgwychNyMqWcrVJDubNUzGsrUEKIU2z1K4IScEdbPE4VJwttvDT7SaiyAgCy6HX35oeOlNcf6vlzTPQRrR3g87sgzkjYB1EriolGzU3Oh3mh3Cmxc4yjkxTh4Z6xkm1+bCW3EwcWIhWjs6EnX1Df5LGiGro9vqPBJ0pDIP164GTRjWaVeKQGwrakC0kpcg3m6yTV7sVIJk0XmfmJSlRy0BkoD/OyYwQeQk5VL7RYmGObRhKJrMC5+SGNTEWnpCGvattw5ZND9s/zwgGq3Auw327zmh8pwKZgq8669al/DjkBo7gBoQ75zLsHMUy4DuxkOM25YZDy3e7ZfxImT2VwXeZknlDmJzDdHsnAqlnlssZNO5R8+bmbxE10272W/mSl1fS0dg2n8i0JOGICmu884mSljxD12IrIeLbfdNO36JL2iOcZldC0cY1R4yT2vXHAHJHgKMa2458f8Lm2h7ykvy1cLftDqcpUbTi6J4sY4CVlhDgNBze0RfxcBqG5IhG2vwm89C9a2hly7I83NRlCTib1/FxvY/F2dyupybpcDalCrJqagUJdjL7643Bx+bUrDJzjsE32fek4jGOwcfiNxXcLt+ZQKlN1nFvUoSdnTWaNgtShJ0zjKJGR6bAA5WYL59Blfu3fKZJGslBwDeEdS1KDvL5tzKHbP04E1hOHZfhJAQzu8VU4dgCc6apk+otm8QtXgP2nVZgDf5mCLiPlK4B2sxd7nW6JyzxTiI33Qoub8vO/bVuM4NoFOBLtGfTzKSsnCRyYiKf5pXxbbc0L6BkPkMpXB8DMTTHD1whncuCKuUnAzDvFOnHpq4RgFPUcaTTD+Hk1gGKe1MtDiMhyExTXTdddRk9hIeoAYLzl6+l0U8Q48BG0I5ZV3BmJ1BTCQDXJyGpz3mbPUQsmShrffm8Mxn/VADYAZpzgnc7HYIWmi+CFUk8eui8qbZ35pyaNk8m4hALpVif3l1E0LTibNLXWzoKjw67Qdpbx//NWLlm6ITXdEYS2cr1gre+TSRaMmhZ59o5pA1Tww7eB0F00UHQ606ko2It9fGDSAfZhXrdiHSwmLGOUKNt5yicRHqKB7YCTlG2fmgDfqwmcM4qt65WrmzpJWr8LWFJtBHS5jqd88wat5Vxfu3URIGD/oVEAG2+CULsFLvXErUVYmfOb9/HtmNBqImlEYRpI6kkPZy2EBsqNOpSqhS4Qf4saA9V27Xyf4s6qltFO92Ydyk6piPqYerxsPllaUbAhhC8XhX0unI8dc/xCFGHnY9DoKKhwpfWWHIY0hlCZ6v30hoDC7dDZEGWAb1CpDfK8Pqxd6Q3Lg0JlD1pIguyEhC36KK9IwumJFbXTK5lDZCsgCUoMeLgnt5HVNMm/RnCst6q9EnDJiCybaq/5BRDGMkXpdg7mgHMXetKwHI8g8WKZTnjPw2vkg49naKF1QyZUr2ckVfJiP345yAN0uk/o/gf6Q1sCYl0S3v9R4pc2LoIU1pFtt3os3OMJIlql9dn52W2t11eMYR8haQ5LqcNgpVVOWKj9kGsdEphVv+cODGpsqttg0lUVFEMYMILZm+2ZlFs4vxgZU2ies09zjaMUUThVDYcuZvkHqFJUs8dml04fy3dWn5ljFU9hEfXBJPKkR21iXbJ46z79CSKwWV19C4CqDLNsoYAAK6O01P0ssmns8sLsZQ8pOU7irpTO3xHI2XHZpF+pE08EOfsqxolweX61vPpgDiP0m47AvHCOKiqiLUlIGTGC2oW3DR2TuqgIMLlW11ktL36DUdAIC45AzlcC0wlYtYahyMmkLNfVNfIERCo2ZnrXX1kvPIHQc21wAjJO8VRnDwI+wR9rqOFfQP5qJW86ZSJDNeDzX1DC+yTbgTfuCLV3FsDL0XdmyKj0KDSJmP2y2eeSSOiuHUEstQwGOvI7VkgS3Qw1oi4lK48aYwfcOnsU9VsnIgbpxthsUbAh0oEONPGfSNtoXuOsylJs2b3QdSSlhxnzoqMLFORiXZEYZGSiDfYSQy+QmqVvIG+0wNVkW3J4oZtDpVJzlpVWNwCvs3z1jSSsgBus6Izl2bODVDbMk2xjSjGTFdEWR8FcO9c7B7iAkeQR8PlyiJRBGS83j8uv/HYlryf9r9Z3MWn4UiH2L67GUtlrYLZnCsbWqQRSK6/VUbYoVKOCpBFXovtD6rqYYEUpRmGzgZzQIrNjf0AMouYKDf+oa9sxEQ4XSGp/p/jO5LsnD5GTbruXQ6/21EvmdRdqqkFBCS0iqlQ3vEmm0wz0HYTg3Sw8VcpKhbqkE6Reb4z8gyoyQavdpKib54BaxmrjRJVx3C90hp+6/oPBTkYYANObM8zYN2YcVnQHKZlbsqQtIijqVazABEz+oU6q1is0JFLq585R8Xjk0oRCZ1WaEXKyFtdStsysIVTw5KSyOyccOa704zSIywWpzHjQHDKXOSPuYaGNyDzIkout/ksWBIWx1bAOZLU2eoJXAPHIJytt/6NzuRD12ys6d9gXxO2YoQzTDHhXBxlky+wJUt353HwVqmkMQk4d9Q6k88P7SoNiiSTuiyRCMD7AAFqZdwqktBD5ZN3NYAmc75TSzoT02YcmVFj+2sALpl7H6sYGjiwZoVGsgQgIrMjmXK8QisuPQutmwcobG5hnvMGOIooAGg+0DIhaVPrrlFrV+YAncktrod2yBAwTYb52R6AaVnzckbXDA4BRlKTVVYzhNqfXeWhHeQQ9VlND1vIwWzyVmqTo1QOjjs9Hb02NUfBk6aku6CDBveq0qIOinB+adeqmcu1wURgPW7USRavOeq8RYjCaKycvknT5aoDGvSylQwZNLaKSV2Vmj0QcAqaIjPdr4uoYcZMGNPfQCuao7FIJ7FkPm8ZMmbgSJbV4rKbSEi+6YhCaFNRQ7l1vzK/iiVUpOMUz2Duhk7NMDkm+rfyIbxqoAjZhDA1Iwq7ThF4O12xnlJJCsKKOSNhL8DwhO5USoBhBcetayLJtARNl9gcUGLMmdotB8SIQ3KSP8VhfNzuWuM0uSFCjlXOZZMb4iC3Um/V4sRQJd9yQzr5aMXRENJjkfeZ3fcWcJ1s7kOEEEc9sIIPrKFkQq+Phs11ukctpMHewXlecRiffG/pJzlkskA8ZFNVq1y2h6nEorIvLtuTGdBUbSt1WR0croMmDUZhkikdMG+aVhfbzxgdXj4ZsyRJq+7QNa1yDsvUJiVbLhawnZVj7JpZJ333ikxL7lFS+hUZvZMx7F3KnLseEJD0NE19WV+7TmT06f8B25tevQplbmRzdHJlYW0KZW5kb2JqCjExIDAgb2JqCjE5Mzc4CmVuZG9iagoxNyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0NyA+PgpzdHJlYW0KeJxNUbttRDEM698UXOAA62t5ngtSXfZvQ8kIkMIgoS8ppyUW9sZLDOEHWw++5JFVQ38ePzHsMyw9yeTUP+a5yVQUvhWqm5hQF2Lh/WgEvBZ0LyIrygffj2UMc8734KMQl2AmNGCsb0kmF9W8M2TCiaGOw0GbVBh3TRQsrhXNM8jtVjeyOrMgbHglE+LGAEQE2ReQzWCjjLGVkMVyHqgKkgVaYNfpG1GLgiuU1gl0otbEuszgq+f2djdDL/LgqLp4fQzrS7DC6KV7LHyuQh/M9Ew7d0kjvfCmExFmDwVSmZ2RlTo9Yn23QP+fZSv4+8nP8/0LFShcKgplbmRzdHJlYW0KZW5kb2JqCjE4IDAgb2JqCjw8IC9CQm94IFsgLTEwMjEgLTQ2MyAxNzk0IDEyMzMgXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDM3Ci9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nOMyNDBTMDY1VcjlMjc2ArNywCwjcyMgCySLYEFk0wABXwoKCmVuZHN0cmVhbQplbmRvYmoKMTkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MCA+PgpzdHJlYW0KeJxFjLsNwDAIRHumYAR+JmafKJWzfxsgStxwT7p7uDoSMlPeYYaHBJ4MLIZT8QaZo2A1uEZSjZ3so7BuX3WB5npTq/X3BypPdnZxPc3LGfQKZW5kc3RyZWFtCmVuZG9iagoyMCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDQ5ID4+CnN0cmVhbQp4nDM2tFAwUDA0MAeSRoZAlpGJQoohF0gAxMzlggnmgFkGQBqiOAeuJocrDQDG6A0mCmVuZHN0cmVhbQplbmRvYmoKMjEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA2OCA+PgpzdHJlYW0KeJwzMzZTMFCwMAISpqaGCuZGlgophlxAPoiVywUTywGzzCzMgSwjC5CWHC5DC2MwbWJspGBmYgZkWSAxILrSAHL4EpEKZW5kc3RyZWFtCmVuZG9iagoyMiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzOCA+PgpzdHJlYW0KeJw1Ujmu3UAM630KXSCAds2c5wWpfu7fhpRfCkO0VoqajhaVafllIVUtky6/7UltiRvy98kKiROSVyXapQyRUPk8hVS/Z8u8vtacESBLlQqTk5LHJQv+DJfeLhznY2s/jyN3PXpgVYyEEgHLFBOja1k6u8Oajfw8pgE/4hFyrli3HGMVSA26cdoV70PzecgaIGaYlooKXVaJFn5B8aBHrX33WFRYINHtHElwjI1QkYB2gdpIDDmzFruoL/pZlJgJdO2LIu6iwBJJzJxiXTr6Dz50LKi/NuPLr45K+kgra0zad6NJacwik66XRW83b309uEDzLsp/Xs0gQVPWKGl80KqdYyiaGWWFdxyaDDTHHIfMEzyHMxKU9H0ofl9LJrookT8ODaF/Xx6jjJwGbwFz0Z+2igMX8dlhrxxghdLFmuR9QCoTemD6/9f4ef78Axy2gFQKZW5kc3RyZWFtCmVuZG9iagoyMyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0OCA+PgpzdHJlYW0KeJwtUTmSA0EIy+cVekJz0++xy5H3/+kKygGDhkMgOi1xUMZPEJYr3vLIVbTh75kYwXfBod/KdRsWORAVSNIYVE2oXbwevQd2HGYC86Q1LIMZ6wM/Ywo3enF4TMbZ7XUZNQR712tPZlAyKxdxycQFU3XYyJnDT6aMC+1czw3IuRHWZRikm5XGjIQjTSFSSKHqJqkzQZAEo6tRo40cxX7pyyOdYVUjagz7XEvb13MTzho0OxarPDmlR1ecy8nFCysH/bzNwEVUGqs8EBJwv9tD/Zzs5Dfe0rmzxfT4XnOyvDAVWPHmtRuQTbX4Ny/i+D3j6/n8A6ilWxYKZW5kc3RyZWFtCmVuZG9iagoyNCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIxMCA+PgpzdHJlYW0KeJw1UMsNQzEIu2cKFqgUAoFknla9df9rbdA7YRH/QljIlAh5qcnOKelLPjpMD7Yuv7EiC611JezKmiCeK++hmbKx0djiYHAaJl6AFjdg6GmNGjV04YKmLpVCgcUl8Jl8dXvovk8ZeGoZcnYEEUPJYAlquhZNWLQ8n5BOAeL/fsPuLeShkvPKnhv5G5zt8DuzbuEnanYi0XIVMtSzNMcYCBNFHjx5RaZw4rPWd9U0EtRmC06WAa5OP4wOAGAiXlmA7K5EOUvSjqWfb7zH9w9AAFO0CmVuZHN0cmVhbQplbmRvYmoKMTUgMCBvYmoKPDwgL0Jhc2VGb250IC9EZWphVnVTYW5zIC9DaGFyUHJvY3MgMTYgMCBSCi9FbmNvZGluZyA8PAovRGlmZmVyZW5jZXMgWyA0NiAvcGVyaW9kIDQ4IC96ZXJvIC9vbmUgL3R3byAvdGhyZWUgNTMgL2ZpdmUgNTUgL3NldmVuIF0KL1R5cGUgL0VuY29kaW5nID4+Ci9GaXJzdENoYXIgMCAvRm9udEJCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9Gb250RGVzY3JpcHRvciAxNCAwIFIKL0ZvbnRNYXRyaXggWyAwLjAwMSAwIDAgMC4wMDEgMCAwIF0gL0xhc3RDaGFyIDI1NSAvTmFtZSAvRGVqYVZ1U2FucwovU3VidHlwZSAvVHlwZTMgL1R5cGUgL0ZvbnQgL1dpZHRocyAxMyAwIFIgPj4KZW5kb2JqCjE0IDAgb2JqCjw8IC9Bc2NlbnQgOTI5IC9DYXBIZWlnaHQgMCAvRGVzY2VudCAtMjM2IC9GbGFncyAzMgovRm9udEJCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9Gb250TmFtZSAvRGVqYVZ1U2FucyAvSXRhbGljQW5nbGUgMAovTWF4V2lkdGggMTM0MiAvU3RlbVYgMCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL1hIZWlnaHQgMCA+PgplbmRvYmoKMTMgMCBvYmoKWyA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMAo2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDMxOCA0MDEgNDYwIDgzOCA2MzYKOTUwIDc4MCAyNzUgMzkwIDM5MCA1MDAgODM4IDMxOCAzNjEgMzE4IDMzNyA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2CjYzNiA2MzYgMzM3IDMzNyA4MzggODM4IDgzOCA1MzEgMTAwMCA2ODQgNjg2IDY5OCA3NzAgNjMyIDU3NSA3NzUgNzUyIDI5NQoyOTUgNjU2IDU1NyA4NjMgNzQ4IDc4NyA2MDMgNzg3IDY5NSA2MzUgNjExIDczMiA2ODQgOTg5IDY4NSA2MTEgNjg1IDM5MCAzMzcKMzkwIDgzOCA1MDAgNTAwIDYxMyA2MzUgNTUwIDYzNSA2MTUgMzUyIDYzNSA2MzQgMjc4IDI3OCA1NzkgMjc4IDk3NCA2MzQgNjEyCjYzNSA2MzUgNDExIDUyMSAzOTIgNjM0IDU5MiA4MTggNTkyIDU5MiA1MjUgNjM2IDMzNyA2MzYgODM4IDYwMCA2MzYgNjAwIDMxOAozNTIgNTE4IDEwMDAgNTAwIDUwMCA1MDAgMTM0MiA2MzUgNDAwIDEwNzAgNjAwIDY4NSA2MDAgNjAwIDMxOCAzMTggNTE4IDUxOAo1OTAgNTAwIDEwMDAgNTAwIDEwMDAgNTIxIDQwMCAxMDIzIDYwMCA1MjUgNjExIDMxOCA0MDEgNjM2IDYzNiA2MzYgNjM2IDMzNwo1MDAgNTAwIDEwMDAgNDcxIDYxMiA4MzggMzYxIDEwMDAgNTAwIDUwMCA4MzggNDAxIDQwMSA1MDAgNjM2IDYzNiAzMTggNTAwCjQwMSA0NzEgNjEyIDk2OSA5NjkgOTY5IDUzMSA2ODQgNjg0IDY4NCA2ODQgNjg0IDY4NCA5NzQgNjk4IDYzMiA2MzIgNjMyIDYzMgoyOTUgMjk1IDI5NSAyOTUgNzc1IDc0OCA3ODcgNzg3IDc4NyA3ODcgNzg3IDgzOCA3ODcgNzMyIDczMiA3MzIgNzMyIDYxMSA2MDUKNjMwIDYxMyA2MTMgNjEzIDYxMyA2MTMgNjEzIDk4MiA1NTAgNjE1IDYxNSA2MTUgNjE1IDI3OCAyNzggMjc4IDI3OCA2MTIgNjM0CjYxMiA2MTIgNjEyIDYxMiA2MTIgODM4IDYxMiA2MzQgNjM0IDYzNCA2MzQgNTkyIDYzNSA1OTIgXQplbmRvYmoKMTYgMCBvYmoKPDwgL2ZpdmUgMTcgMCBSIC9vbmUgMTkgMCBSIC9wZXJpb2QgMjAgMCBSIC9zZXZlbiAyMSAwIFIgL3RocmVlIDIyIDAgUgovdHdvIDIzIDAgUiAvemVybyAyNCAwIFIgPj4KZW5kb2JqCjMgMCBvYmoKPDwgL0YxIDE1IDAgUiA+PgplbmRvYmoKNCAwIG9iago8PCAvQTEgPDwgL0NBIDAgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTIgPDwgL0NBIDEgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTMgPDwgL0NBIDAuNyAvVHlwZSAvRXh0R1N0YXRlIC9jYSAwLjcgPj4gPj4KZW5kb2JqCjUgMCBvYmoKPDwgPj4KZW5kb2JqCjYgMCBvYmoKPDwgPj4KZW5kb2JqCjcgMCBvYmoKPDwgL0RlamFWdVNhbnMtbWludXMgMTggMCBSIC9NMCAxMiAwIFIgPj4KZW5kb2JqCjEyIDAgb2JqCjw8IC9CQm94IFsgLTMuNSAtMy41IDMuNSAzLjUgXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMQovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxtkEEOhCAMRfc9RS/wSUtFZevSa7iZTOL9twNxQEzdNNC+PH5R/pLwTqXA+CQJS06z5HrTkNK6TIwY5tWyKMegUS3WznU4qM/QcGN0i7EUptTW6Hijm+k23pM/+rBZIUY/HA6vhHsWQyZcKTEGh98LL9vD/xGeXtTAH6KNfmNaQ/0KZW5kc3RyZWFtCmVuZG9iagoyIDAgb2JqCjw8IC9Db3VudCAxIC9LaWRzIFsgMTAgMCBSIF0gL1R5cGUgL1BhZ2VzID4+CmVuZG9iagoyNSAwIG9iago8PCAvQ3JlYXRpb25EYXRlIChEOjIwMjAwMzA3MjE1NDQzKzAyJzAwJykKL0NyZWF0b3IgKG1hdHBsb3RsaWIgMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZykKL1Byb2R1Y2VyIChtYXRwbG90bGliIHBkZiBiYWNrZW5kIDMuMS4zKSA+PgplbmRvYmoKeHJlZgowIDI2CjAwMDAwMDAwMDAgNjU1MzUgZiAKMDAwMDAwMDAxNiAwMDAwMCBuIAowMDAwMDI0MDQ0IDAwMDAwIG4gCjAwMDAwMjM1MDkgMDAwMDAgbiAKMDAwMDAyMzU0MSAwMDAwMCBuIAowMDAwMDIzNjgzIDAwMDAwIG4gCjAwMDAwMjM3MDQgMDAwMDAgbiAKMDAwMDAyMzcyNSAwMDAwMCBuIAowMDAwMDAwMDY1IDAwMDAwIG4gCjAwMDAwMDAzOTkgMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDE5ODUyIDAwMDAwIG4gCjAwMDAwMjM3ODIgMDAwMDAgbiAKMDAwMDAyMjM0MSAwMDAwMCBuIAowMDAwMDIyMTQxIDAwMDAwIG4gCjAwMDAwMjE3OTIgMDAwMDAgbiAKMDAwMDAyMzM5NCAwMDAwMCBuIAowMDAwMDE5ODc0IDAwMDAwIG4gCjAwMDAwMjAxOTQgMDAwMDAgbiAKMDAwMDAyMDM2NCAwMDAwMCBuIAowMDAwMDIwNTE2IDAwMDAwIG4gCjAwMDAwMjA2MzcgMDAwMDAgbiAKMDAwMDAyMDc3NyAwMDAwMCBuIAowMDAwMDIxMTg4IDAwMDAwIG4gCjAwMDAwMjE1MDkgMDAwMDAgbiAKMDAwMDAyNDEwNCAwMDAwMCBuIAp0cmFpbGVyCjw8IC9JbmZvIDI1IDAgUiAvUm9vdCAxIDAgUiAvU2l6ZSAyNiA+PgpzdGFydHhyZWYKMjQyNTgKJSVFT0YK\n", "image/svg+xml": [ "\r\n", "\r\n", "\r\n", "\r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", " \r\n", "\r\n" ], "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xx = np.linspace(-1, 1, num=200)[:, None]\n", "YY = gp.sample_y(xx, n_samples=20, sample_mean=False)\n", "\n", "fig, ax = plt.subplots(figsize=(9, 5))\n", "ax.plot(X, y, \"o\", color=colors[1], zorder=2, label=\"Noisy data\", alpha=0.7)\n", "\n", "ax.plot(xx, YY, color=colors[6], zorder=3, label=\"GP realizations\", linewidth=1.);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As is apparent, the latter realizations are much more chaotic, since the kernel hyperparameters vary for each realization." ] } ], "metadata": { "kernelspec": { "display_name": "Coffee", "language": "python", "name": "coffee" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.2" } }, "nbformat": 4, "nbformat_minor": 4 }