{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Solution of Exercise 3\n", "\n", "http://neuronaldynamics-exercises.readthedocs.io/en/latest/exercises/phase-plane-analysis.html" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fixed_point: (-1.0000000000000002, -4.440892098500626e-16)\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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JsWaKlwcniFVNo6lvDAnYWLB48HM13LLCxc4B1i3LCEqOakLQPDqOXpJYmxW4L15VpWJkkHVpGSSb/c+qNaHRYhkhxRRLdkySXzuX4mDUM0hBrP/7RlVHEJoTgzG0++StxDvakUcQQQQR/CngrSY7BfC6JElVkiR93E8HPi5JUqUkSZUTExNv0m4jiCCCCCJ4s8jO64QQQ5IkZQDHJElqFUKcvdxACPFD4IfgG5G/0R1pQizE3JZC8+Q4yxOSiDOZ5vcLXCJEypv7WJmTSnqS/2n++KiFiVEL67cs92vz+2Ji1EJ61tIKyqvR2ztJWVkH733vnqChBofTw8nSNvZuX7kgdgrUZnjCwoXGPt51aCOSJCGECGg/PmPndG0n7zqwcSF0o2liSVINfPHl0qZeUhNi2TTHR8wTX/7ajE7bOFHTwf3XbVwg0gLtQwhBx9AkFW0DPHLj1oX+B2qjaYKG7hGaekd55OZtIfVLUTVq2gbpHJzk4Vu2LWxHkvyfY6+scLGxn5EpKw/dvAUhfCThUiG9eVjsLs7VdGM06Lll75qg/RJC0DkwyZnKTm7Zt4a8zKSF34m/fs1YnZyr60bVBPcd3LhAXhr8EPazdhfnGnqYsbt49OZtaHN9kiQWHYsQgs7RKU43dbM6O439a/J9n8/FsQ063RX9Gpq1cqq9G4+s8NjuLZc2dBmJadTrUTWNmrERTvR2syUzi+tyfWvUpQXTueuORuvsKCXjHWRGJ3D7sg0LJOcC6SlJzHgnabU10ONo567sh4jWm+fO2dzxCA1ZrsPjOYVAJj7mQ3PX2jBHnOox6IwsEJlXE5uXqUDnP5cwIElvvkblTV9HLknSPwN2IcRX/dn8PqGVTx99kT7r7BWfRRuMxBiNxBqNDNmstM9McXN+IfeuWktxbCpf+v6RBQc1a3cxMWNn38Z87tm/gUNbVy36gbzyXCXf+PJLbNqezwc/cxPrNwd26PZZBxdfq+XG9y4msK7GxKiF7//7iwz1TvL9l78Q0LapcZDHf3yGurp+oqIMPPaB63j44aUJ1dEJK4//+jwnS9vweBWKCjKQgP/3ycOsXbU4plnZ0s8Pnyujtn2IWLOJZRk+8VSM2cgP/vY9i/vSO8q3nztHRdsAJoOe/KzUhe8ObVnJx69SBNpdHn70SjnPn2vA7vayIiP5itUNX3zoINuLrlyh0DE0yf89c4by1n4Meh2rci7Fhw16Hb/464cX9etiaz9fffoMnUOTxJpNVwh1dq9dzufuP7Cozdm6bv73N6cZnLAQHxNFTmoCzP3IP/Ou/Yvi30IIztR08X9PnmZkykpCbBTZqYkLDvzHf/ueRStwhBC8fqGNbz51hslZB0nx0QuCoM3Fy/jiozcs6peiqPzm9Rp+/HwZTrdMRoqPvEWCj9y7h4M7Vi1qMzZt45tPnuV4eRsAq/LS0Ot16HUS3/yrB4i/ahWKqmk8f7qBHzx3HovdTVpSLGmJsSBJrM3P4EsfPLzoOF4pb+U7vzvvI6HjoslKiUc3R3Y+ctNWbtt1SXzm9Hj5wevl/La0HofHy/K0JOKjo3wudu4cf/3Dd5OeEIcmBM/WNPKDkosMzlpJj4slJ2mx6CY/NYm/u/0GvlVZxrOtzUy7XaxJTSPeFHWFnN9HLWpMM4NidjMrO1gZn0Z6VDzzjxFtLlWATmfBZOzFoJ8BJBQ1keLETKJ0hgXycpm+iVx9C8m6URwiAZuWwjyJKSEw6ozkxawAMa/gvERy+ghO7TJVp++7+JgHSIr74KJjDBVvWYxckqRYQCeEsM29Pwb8qxDiNX9t3swY+TzRafd6cSoyP6mvYtbtZndOHnty8shPvJQHQwjBD14oRQAbV2azYWU2SUssQ+zvmcBuc5OTm0xi8ptPeAohsFtdxCUEJztnZhx0dozR1TXOvfdtIzraf44Yp8tLc8cIjW3DHNxTREFeYKJsctZOTdsQHQMTfOy+vUHJUavDTU3HEHXdw3z0jt0B89WAb7TaMTRBRfsgK7NT2LcuP6A9+Ebw9d0jVLYP8MiN2/wuObwcLo9MTecQzX1jfPDWnX5HlVe3qesapmNwkkcPbwvpGntkhfqOYbqHp3j3TVtCauOdazM0buHeQxuD2sMcQdo2iNerLum8l8KUxUF5Qx8bCrNZnp0c1F5RNRq7Rpi2OLhx5+qg9kII2gYm6B2dvsJx+4OsqFT3+BS6WwsCK5KFEHROTNE/beGmNYEJxflReZTewMaMTL92Qgg6beNYZTfbU/2rXT2qmzZbM+sSNmHQLR2gUNQpvEo7MVHBV6W91XgrHflK4Pm5/xqAJ4UQXw7UJkJ2RhBBBBGED3+O/PeOkQshuoHga9EiiCCCCCJ4S/COk+iPO+3MuF1+v+8bm2FgYjbwNsYs1FzsfktzEHvccsi2LqeXl1+oZnLCGtRWCEF98yD1zYMhbdsrK5yq6GBixh6SvaKonG/ooW90JiR7gJ6RaU7WdIZsLysq5xp6aBsYD7mN3enhSFkz4zO2kNtMW508e6qOWbv/++VqjE3b+M3r1dgc7pDb9I/O8KsjFbg9oV1zTRM0dgzz1JHKkO9Bh9PDsdJWSqpCO8+qplHXPsRPXyhH1bSQ+tTQNcwPXigN6TjsLg/Hatp58kxNUFuvonCuo5evHTuH96qMpldjwuHgt80N/LSuOqDdpNvOc711fK3pFKrQljyPsibTZGnk1/2/otvehax5kTUZRVNQhYomNLzKKNP2pxiY+gKyOo6qWVA1G6rmQNOcaJoLTXjQhBchFISffb3VuOaSZn3q2Av0z5GdkiQRs0B0mog2GJE1lSNdbRzMK+CeVWtYH5fBPzz+GkJA9Fw62rruEbYVLeOeveu5eVvRoljvqy/U8LUvv8SqNdk89OheDt683u+KAfApO8tfqeHGh4OTnV6Pwm+/d4LKM618/fnPBbSdnLTx1C/Pc+xoA06nlw9/7BCPPLb0PjwemWeOVPPy8QYGh2fIyUwkNiaKv/zULaxbvZjsHJ208rMXyjlR3o7N6WH1inRAIjrKyA/+cTHZOW118vjLFzha3sas3cXKnFQMet/qg+s3r+QT9+27wl7TBC9faOap4zW0D06QmhBDelLcghLvi+8+yPbiK8lOq8PND1++wJGyZqxODysykzGbDPjyOMMTf/e+Rf0ambLyzWdKOF3TiayoV4hbdq1dzuceun5Rm77RGb7xmzOcr+sBYPXy9IV+feqB/exfQkHZMzTF1351mvLGPvQ6iVV56Qvf/fgf37tkuoH23nH+7xcnqW0bwmjQU5DrI4g3rc7hLz9w0yJ7gAt1vXztFyfpH5khNtrEsswkhBB8+F17ObSraJG9V1Z48kglP/tduU91mp5AQqwZAXz77x5aRHaCTw361Z+fpHNgkugoI8uzkhEIildk8Pcfu3WRfWvfGP/1xEkaukcwGvSszLlEdD9663Zu37N24f9CCI5UtvL1F0qYsDpIjosmM+lKZfS3PnEvGXPisNqBEf7jldPUD41iNhpYmebLRHm5V1qZlsx/P3g7z7Q08vXyUkbsdlKjY8iKWyLXPAKH5ESJcTPutZFoNJMXl7yg6pyHJHmJNfdhMk6ikzRkJY6C+DRMOt2CCjRJN8qaqGrS9cNo6JlW0+fWxcyTnQayzdlzJOe8gnOe9FwaybEPkRb/Eb/fB8M7MvuhJgQuRcYhe3HKMk5Fpmy4nyPdbezJ9pGd2zOXEWs0LeQFebW8lar2QTYVZrNpZTZFy9IXkWNtzUMM9E6Rl59K7vJUYuOCE27hQAiB0+YmJt5/jo55WGaddHaO0dk+yrbt+RQV+1fVudxeWjtGaWgdJicrkZsPrPVrCzBtcVLXPkRd2xD33rCRgmWpAe3tLg91ncNUtQ5ww7ZVbCwMnItGCEHPyDQVrQO4vTIfuG1nQHvwjcYbe0apaBtgW9EydoSghvTICg1dw1xsGeDufevIywxO9nllhYauES429fPgjZtJ91Po4XIoikpj1ygVTX08cPMWUhJigrdRNZo6R6hs6ue9t20j1k+Olav7Vt8+TGv3GI/cuSPgIGIeFruLioY+TEYD14dAkGqaoK13jOrWQd5z67agBPH8tSxt6OWBQ5sW5Ve5GqqmUdczwsDkLPfuDq4a7p+e5VxnHw9u24ApAOkuhKBxYpx+yyx3FgVW8fbZp6mbHuKe5f5JZlmTabO1kB6VQaZ56VS2qmbF7j5LfPQt6KTABP9bjXekI18KwdZBRxBBBBFcq/iTSWMbceIRRBDBnxrecY5c1lTGHP4JL5dHpnM4cEqY8TELF853oGlv3WwlnJmQEIL6mj56ukIj/6ZnHJy70BHy9nuHpmjqHAnZfmh8lurWgZDtXR6Z4xXtKIoa3HgOg+OzlDX2hmwvhKCpe4S6uaRWoUDVNKpaBmjqCv3YFUWlrK6H5q7RkNu4PTJnLnbQ0Rs6eTtrdfLyyQYmQyShhRC09Yzxu+P1Ie9j2uLgxVP1DIRIXM9Ynbxc0kRbX/DjEELQPjTBT1+vwBUCOTowPcsTpTV0jAb+bSqaxsXBQb5RVoYnADGqahpVkwP8X8Mppj1Ov3bj7gleHz3F+clyP8ehYHOXMzDzHzi9TX+0RZivudDKp068QL9tFoNO51N0zr+MRmIMJmKMRp5oqWVtajr3rVzH1sRs/vlnr2My6ImPMZMQE8Xxmg6KlqVxz+713LajeJEo6NWXavi//zhC7vIU7n/3bm6+fWNAIQ5AV30fhZtCK7N1/rV6jj99kX96/KMB7WRZ5bWXa3npuSp6usZ5/0eu57GPLCbvwPfDKa/q4cXX6rhQ0UV8fDRpqXH85WduYe0SZKfbK/PCiQZeLWmirWecFTkpmKMMREcZ+d4/LU6zqSgqL5xt5Mi5Zhq7RsjLTCI+JgpVExzYupKPv2vfojZN3SP86vVqSmq7ACjKS8cr+5z5Fx4+uCgboKppvFjSyHNnGmjpGyMzJZ7k+GiEAL1O4hf/sJjsdHtkfvlaJS+VNDEyZSUvI4losxEJid3rl/PZdy8+Xw6Xl5+9WM5LJU3MWJ3kZSYtEN6ffHA/+zYvJjvtTg+PP1fGkbNNWB1uVmQnLxS1/tE/P7wk2Wmxufjhb87z6tkm3B6FgtxUTEY9G1fn8BcfXprsHBqb5Vs/P835ym40IVg9p9D9wAN7OLh7MdkphOBcVRff+sUZBkdniY81k52RgAR88x+XJjvHp2x881enOVnejhBQtCLdl2o4P4O//fhisnPW5uI7T5fwYomvNmpBju84AN5363Zu23clF9PSP8Z//PYUDT0jmAx6CrOv5F6+/sl7yZhLkTFhc/C/r5XwYk0LAEWZqRj0ei6fVxekp/A/77md2pER/unUSRrGxjAbDBSmLC7RJwEevEhJMp2OCXSSxNqkpYRDGkbTKCbTCJJOQdNM5MakYbpMFBQlOVlvriTH2I1BUrGoKYjLemaQ9GREpXMpE/rVvvTq6IAgLe5BMuM/tER/QsM7LkYuaypOWb5Ediq+9zNuN/9afpKt6dnsyc7jumX55Cck45EVrE43PaPTfPflUjbmZ7OlMIctK3MWVYBvqO2nurKH/IJ08lemsywvJaTUoKFCCIHL4SE6NipoKMhqcdLVMUZn+xj5K9PZuce/8s3jkWnrHKOxdYjZWSef+vChgNu32F3Utw1T2zrI8qxk7r5hY0BizeWRaegcpqplkPiYKN57y9aA50UIwcD4LJUtAzR0jfC591xPYmxggldRNVr7xqhoGUCS4LHbdgTMSwK+h0xTzygXm/pZnpXMLbuLg55XRdVo7h7lYmMfa/IzuW7ryoD2MJeWt2eMiw19rCvMYvfG/JDatHWPU17Xy/b1eWxaE1jluHA8HSOU1/Zyz82byEoPXivS4fJS2dBH39A0j923K+jxCyHoGpiktLabgzuKWJETvG7p4Pgs5+u62bgqh3VBarxqmqBlYIzS5j4evWkb0UFqj47M2jjT2s32gmUUZfpXJAsh6Jia4mxfH49t3rxQQGbJbTqtnBhu5868dSRHLU1Mq0Kl3daJV5PZnLRhaRvNhdV9jmhjIWZj8PvkrcQ7zpH7g6Jp6AMkC4oggggiuFbxlik7/9hgCDJ6iyCCCCJ4p+Ed6fUCKTsBesdnApIWiqJyvqQNVQmueHu7MDVhY3hwOiRbRdUor+jCE6KS0OnyUtXQH3JfPF6FC/W9IRM/Qgja+8YZGp8NeR9ur0xJTVdIqsN5WGwuSudEPqFifNpGaW14bYbHLZRWd4fVpmdgkgs1oe9HVTXqWgZpaA2dvLU53Lx+toVZq39y73IoqkZtyyCVDX2h9UnTqG8f5mx1V2j9cXk4VtUekkLXIyuUtPVysjn4tsfsdn5T30BbkLoGEy47T3fXcXHc/73t1WRqZpp4fvCo3/vZo4wyavsN4/aXg/btD4VrLrTy6dO/Y9xlJ9pgJFrvIzkX3ht8748PdqIJwd35a9mRuIyv/uYM8dFRxMdEER8dRUXHIDpJ4u6da7lz51qykq9Unr3+Wj1f+99XSUqK5Z77tnHHnVtITAos/ih7pYZdt24OqQDzYNc4R35Rwif+5YGgtk11/bz42wpKTjTz6McO8ogfshNgcHiGV16r5/UTjVisLtaszubTH7+BtcWLhTtCCCrq+3j1dBNnL3aQEBdNXnYymhB8+18WKzsBalsHeelME6crOzAa9BTnZ+DyyOxcv5yPPbCY7JyyOHj2ZB3HytvoG5lh25pcJHyx9j9/7/VsW7NY7FPXPsQzJ+soqelCkiTWr8zC41WQFZWf/fNislMIwenKTn53up6Kpn6SE2JYnuXjRLYW5/LZ9y4+X0IIXjvXwnMn6mjoGCYjJY6stAS8ssrHH9zPvi2LyU5NE7xyponnjtbS2j1GRmoc6SnxyIrKD/99abJTUTV+93otz71WS9/QNJlp8SQnxrCuKJsvfvTmJc+xy+3ll89d5OXj9UzPOsnNTibGbOQDD+3h4J6lsxT2D03z3V+coay6B03TKCrIBCH4+r+8m4QlxGwer8JTL1Xy2yNVWGxustITSIgzszo/gy99ejHZqagazx6v5acvlDNjc5GeHEvKHK/0yO3buW3/lWTnjN3Ft58/x0tlzSiaRkFWyhUFrb/xmXsX6gF4FZUnztfw/RPlODxeshLjSY69cvFBQUYy//PwHUw6HPznmRKeb24GYHVaKkbdYo5GRSMly8iF6V5UIVgZn0KMYa4+wWWEpM4wiyFqAJ3egxB6cqMzMekvbU9CZaWpiSJzPUbJi1OLxSsunU+DZCDLnLZou4GQGfcAyxI+EJLtUnjHxMg1IXArPhWnS1VwyV5cqrJAdroUmR81XUQTgr3ZK9iftYKd6bk43V5sLg9Wl4f/ee4MaQmxbFmZw/bCZaxfnnlFTH1szMJPfnSagpUZrFyZQdHqTJJTAiv/ri5gEQiqquF1y5hjTCGQnS56Osfobh9leUE62wOQnV6vQkfnGE0tQ7S0jfDRD15PTnaS333YHR4a2oaobRlketbBZ99/iJiYKL8qP49XoalrhOqWQXqGpvjCo4eIi4kiymTwX0V+wkJVywCVLQPcuLOI7WvyMJsMfklSTRN0DkxQ0dxPS88Yn3/kIHHRUZiMBr9E7DwJWdE8wOSMnU8+uJ8ok2EhhYC/Nu2941xs6MPp9vLBe/dgNOoDKhw1TdDZP0FFfR9er8Kj9+0KuA+YS6faN8HF2l70eh0P3bEt6MNeVTXau8cor+klPy+Vg3uKgt4nbo9MTeMA5bW9vP+B3aQkBa6TKYSgf3iGsupu0lLiuHl/8NS0Y9M2ztf2YNBJ3BMkJa8Qgq7hKc42dLN7zXLW5wcmR6fsTs629BBlNHDHliCKzdlZTnR2sX/FcorT0/3aTbodnBzqJD8+mV0ZS9cU0IRGl72fTnsvt2UdXPI8a8KLxV2OJmRSY24M2Le3Gu8YRx4KHLKXWOPSywXDcbgRRBBBBH9M+JMhOwG/ThwiDjyCCCJ45+EdSXY6ZG/A7yetjqCqzabGQbzewCk1304ossrsdGgqP4DhkVkGQyRHhRC0dIzgcgc+b5ejZ3AqZFINfERcWxjKRvBlHByfDj0traYJalsHcYZxHIqicrG+F68c+rX2eBVKq7rCUqo6XV5KysNTC0/POiirDJ1UFULQ2jFKe/dYyG0mp+2cLmsPmbietjh5vbQlJBJaCEH7wATnG0IjeQemZnmxsjloX2RV5eLAIKe6Ap8bRdOoGB/ghZ6mgHYjrgleHj7NlGd2ye81ITPtukiP5SfvfGWn5KsoWgkMCSHuCmT7+4RW/rrsFabcTsx6I9EGwwLRab7sfYdlkotjA9ydv5bdycv56SuVxEebiDNHEWc20TcxS9vQBHfuWMNdO9ZSkHGlGOLUqWZ+9MPTeLwyd9yxhbvu2kJmZuBCya8/WcqBe7YRHUKmRI/Ly+tPlXL3hw8FtZ2dtvPKs1W8/HQFd79nFw8HIDvdbpmzJW28drSe2rp+Nm7I5c8+czNFq5aOT46OWzh6ppnXz7QwPDbL/h2FCAFf/pt7l7Qfn7Jx9HwLr59vpbN/ght2r8YrK2xZk8ujdy/ObKgoKqcqOjh2oY2yul4KlqWSnZ6AxyPz4XftZdPqxSTsxIydl043cqK8ja7BKfbPCXUUReUbf700Odw9OMnvTtRz6mIHs1Yn+7YU4FVUNhTl8JH7ly7P1do9xnNHazlb0YlXVti+fjleReWxe3eyY+PSCt2m9hGePlJFaZUvV/3mtbnIispX/+4BjMalY/41Df389qUqLtb0YDIaWFuUxerCTD75/oNL2gshOFnSynOv1NDYOkRaShzLl6Xw0D072LdzaX7E4fTwy6cvcOxMCxNTNopWZhAXa+bLX7qPuNjF2RaFEJyv6OLnz16gpWOUpIRoCpanUbginc9/ZOkYcFVTPz94+jyNHcPEmE2szvelC37g8BZu2nNlTFtRNZ4+Xccvj1YyNmMnOzWBzOQ4X/FjCf7j43f66oTOoaSlh/87UkLn6BTx5igKMpKR5mqCSpJEQUYy//zQYWRV5edVtXyvrByL20NWfBypMTEL9UPnXxKQn5fI8fF2Jt1O0syxZMVcyXHpJAlJ5wVzHxgsICA3JhvTVeRpmmGQtdEVxOptyMKES4tf0GsaJAMZZv9CKgn9XARA53uPRHbcXeQlLL2YIBS85TFySZL+AtgBJLyVjtzidS+Qmq45wtN92XuX4uXC2ACnhrrYm7mc3RnLOZixEqEK7C4vdreH58ub6B6bYtvKZWwtWMaNGwuvYNVdLi///V9HiI83s2pVJquLsyguzg4YlnHa3ej1OqKCSPkBZK+C7FVCUnbabS562sfo7hgjNz8tINkpyypd3eM0Nw/R1DzEtq353HrLBr/EotPlpbl9hNqmARpah/nYI9eRm5NEkp/0rLKi0tI9SnXTANXNA7z3ju2sWpFOXEyU3/qdEzN2qpoHqGruJzY6inffuhWzyUhCbNSS/RJC0DM0RUVTP5VNA9xxYB3rV2YRZTKQGL+4vir4RuJdAxNcbOijunmAjz+0n/SUOMxRRr/9EkLQ1T/Jxfo+6luH+PT7DpAQZyY2Jspv7VIhBH1D01ys7aWhdYhPv/8gsTFRxAe4jkII+oemKa/uoa1rjE9/8CDRZhMxAe4TIQRdvRNcqOph1uLgA+/ZhznK6PdhAXNpeZuHKKvqZm1RNru3FRATbQqo1B0Zt1Ba1c3g8Awffu8+9DpdwH5NW5yU1XbT3D3KJx66Dr1OwmjUL7liB6B/bIazdd0Y9DruvW7DQk7waJNxUb8sTjfnWntpH5ngM7fuRYi5Qslz7inmsrS5ozY7Jzq7iDWZuHfdGgQ+8nreXhMCvU7CrSmcHurG6nXzWPG2K86vJgQaAlXT6HMOUzHdyO1Z+0k1Jy06DiFUZtw1zHrqyY1/DCQfSSqAaP3SaYl9flUgUH1/hYZAQycZfq9UuG+pI5ckKRf4OfBl4C/eSkceCqbdTpKiotH5+XF5FQVTAGlvBBFEEMEfI97qNLZfB/4K/JfGkCTp45IkVUqSVDkRZCH/74sUc4xfJw5EnHgEEUTwjsLv7cglSboLGBdCVAWyE0L8UAixQwixIz3A2s83A7KmBiQlnB4vihqYrBkansEdRl3NtwPhkK8ej0xHR+ipVq02F6PjlpDtnS4vgyOh1+2cT7MazgzQ6fbSMzgVsj3A1KyDobHZsNqMjFsYCePYAQaGZ8I6X0IIunrGmZgKnbxVVY3ahv6wSGibzU1tGCpdRdWobRrAYg2tbqmqajS0DTE2Gbx+LPiyRp6p7gyJHPXICudbe5mwBCf1x2x2Xm5qQwtyP405bTzT2YBb9f/b8aheKqZbaLT4J09dyii91mdwKeER9m8X3oyh6X7gHkmS7gDMQIIkSU8IIR59E7a9CP9edZwZjxOzwTBHeBox633vzQYD0XojmhB8r7mM2/KK2ZeSz4tnW4gzm4gzm4g1R6FpGr8ureeOrcXctW0N63KvFASdL+vg2eeraO8Y5dbDG7j7zi3kr/CfkQ3gtV+dZ9fhDaRkBCZF51F7toUt1wcuxQa+H075mVZ+96sytu9bxXs+sjRJBnOZ4dpHefXVek6eaCY9PZ6/+4d7KShY+sHplRXKKrp5/XQTZZXd7NpaQFJCNH/zudv92pfX9nKspIVzlV1sXLOMtKRY1q/O5v7bti7Zpr13nOOlrZwobUNWVPZuKcDlkXnvnTtYtwQJ65UVSqq6OFHWxvmaHtaszCAnIwlFUfm3P186Yme1uzl2roWTF9qpbRlkz5YC4mOjWF2QySN3L5qFAjBjcfDKqSZOl7XT0jnK/h2FRJkMPHD7Vjavy12yzdSMnReP1nG6rJ3uvkn27SjEZNLzj1+4y2/8emzcynNHqikp62BoZJb9u1extiiLx96zNAkL0Nk9zjMvVFFa3onT6WXf7kLuvn0LO7flL2mvaYJjp5t59VgD9Y0DZGUmUliQwd984Xa/peX6Bqf45dMXuFDVjc3u5rpdq8hfnsbHHj2wpP3ohJWfPF3KucouLDY3e7YWYDTouOvGjVy3YzFvU9nSz+MvllPTMURMlJHNRcvmyEv42w8evqJMXv/ELN84co6S5h7cssKe1cvR63TodT6yc0V6En95r+++L+nq5Wunz9M4Ok6COYrf1NSjkyT0Oh0SEnqdhF6S2JCfwcnJLqomhojSG3iyvRa95BNv6edeQtJw6Ydw6kYQkkZGVAqJxlifDRKSpCNGZ2OV+QIpRl8xc4eaBviOwyDpSI9K9ZG46JDQgaRbeC9JOrjsvYSenNibyYsPGHl+Q/i9HbkQ4kvAlwAkSToE/OVb5cQBPrRmJzbZg0dRcKkyblXBpch4VN//LV43Fq+LfvsMJSPdeBWFO/YUk2KMwe7x4nB76RydwiMr9E7MUNbRT2p8LFmXFYjdsD6XqupeAEwmA719k2RnJRIVoE7hxr1FiBCXlmmaRuGm5SGVpZO9CgmJMVx/ywZylgeuqSkEIEmsWJHGnr2FSJJEdnaSf3tNkBBvpmhlJi6XzPriHA7tX1oGDqDT6UhNiqV4ZSYOl5eCvFRuP7ie5ET/6QvSkuNYnZ+Bze6hd2iK+w5vJtpsJDN16dSsRoOe1SsysNh8VerTU+K4+4aNRJn836rxsVFs27AcVRPEmE1s25DH3i0FxAdYQZSUEMN1c847OTGGAztXsWndMtIC1O5MTY7jloPrSEqI4WJtLzfuL2bd6uyASs3MjATuvX0L2ZmJXKzu5a5bNlG8aqn82JdQWJDOww/uYmV+GtW1fTz63r0sC3AddTqJmw6uJTszkQsVXThdXt7zrp0L+dKXworcVD75/oNsWZ9HWVU3jz24h7RU/8eelZ7An73/EDs3reBcZRf3Hd5MdkYi8UusigHYsXY5uRnJnK3torl7lE/e7ysaLoQg4aoc6cvTk/i3h2+htK2P043dvP/QNlLiYnyEpOYjLudxoDCf9VkZnO7soXlsnD+/fi+qJhBCoArhe48gzmTiQ/rtlIz0UjbSzxe3HkAvST6Cc267qvARpMOuSapmmlmftILdqevQ0FCFj6D0EaIqFm8LE66zZMe+C4MuGQ2BDokUU8JlhKaKmCM4hfAVZBZoc0Snz0YvBa/z+kbwpio7L3Pkf1Cy0+p1owrNbw5iu9tDtMkYNM/1nxrCrXf6Ruqjvh37iCCCdyreFmWnEOI0cPrN3OYbQYIp8FruOHPwSuZ/igjXYb4RB/t27COCCP7U8I4dkgYiQYQQeAPU+wNfQimHw/Nmd+v3Qrizp+6u8ZDbaJpgcDg88nJoZDas/sxYnFjt7rD20TcUHtmpqBp9YRKkXlmhdyC8Nm63TG9/4PqSV8Ph8NDXHyZ5O2VnZHQ2ZHtNE7S2jYRFjE9N2+kP45zNzDro7A1t5ZkQgvb+iZAVugMTs7QOBicUZVWlom+QMVtgYlTWVMpHB+iyBD6+Ieck5yYa/H6vCpkxZwWTrrqgfftD4Jpbh/fNprNYvC6i9PMk5xzRednfKL2Rn7RfoDA+jetSV3Kuut9HdEbNvUwmfn6uik152dy1dQ07CnKvEChUVPVwoaKbI0frufH6Ndx1+2bWBhEEvfyLc2y7vpic/NBW5Iz2TpAVou1Q7yS/++V5cgvSuffRxeliL4fN5uLksSZePVLL+LiVb3znA+QFiK339k3y+skmjp9qJjkpls0bc/n0x/xneOsfmuZ4SQvHS1rR63Xs3LyCooIMbr9x6TJZNoebs+UdnChto7Khn/tu2YzQBPcc3kTRnDrwanT2TnCyrI2TpW2oqsb+nYUoispffuzwkvaqqlHTNMCpsnbOXGgnIy2B9auzKVyRzn23bF6yjaKolFZ2c6asnfMVneTnpbKqIIM7btzIuiVqnIJPcHW2rJ0zpe2UV/ZQWJBOwYo0vvDJm/2KrjwemWOnmik530F1bR/r1mRzYP9qHrxvaRIWwGJ18cqrdZwr66C5ZZh9e1bx7gd3sXnj4rS/82hrH+HlV+sou9CFw+nhxkNr+bNP3uS31qzD6eG5F30kbFvHKDu25rN9ywoeeWi33+N45pUaTpe109o1yobVOeQtS+Hm69awa0v+IvuRSSs/f+ki52q7mZixc+POIsxzQqA/f+/1V4i7nB4vPz1eydGadvrGZ9icn012SgI6nY+8zE1N5JO3+8jhgZlZvn66jNMd3dg9Xm4oKsCo1y8Qnj6yU8fuwlzKZvt5tbcdq9fDrsxcYo0mDDqdz1bSoQOs0jgTog8PLpKMcTw3cG5OIapDJ+kwSgqZxipSDE3oJRmvloyKGQkJg85ITnT6FeSm768efNTrFZ9JSOTEHiAvbul6rb8PrjlHfsuyYqyyG7eq4FEV3KpP1elWFSxeN+45ArTLOknjzAjDdgvb85azNj4Th0fG6ZGxezyMWexUq0MLst4dKy+tVMhfkUbfwBSJCdE4nF7qGwdIS40jI0DtxPzibKwzDrJXpIUUDohPjg0p/iuEwDLjoGB1Fpm5wesqTk850Ot1FK7yrcSJjvGvItM0gdXmJjYmivwVaegkiRsCrKQRQuD2yMTGRLFiWQoWm5vr9xSRkRrvv40miIs1k5udzNikldX5GeTnpgasQxkXayInI5E1hZkMjc5ycFdRQLJTp5PISk9g1Yp0Ziy+/C+3HFgbkIQ1GPSsyk9nxuLA41WINhu5/cYNLMtK8tvGaNSzce0yXC7fstTE+GjuvGUTugBcS1SUkd07VqKTJMxmI5kZCezZGbjuY2JCNAevX4M52kR8vJltW1eQH4ToLlqVxZ23QWpKHLX1/dx+y0ZMAc5ZbEwUd9++mYz0BM6Xd7J2dRbX7Vlc3Pny47j/9i3kZidzvqKTrIxEDuxaRVry0ulys9MS+Nj9e1m3MpOz1V3ceWA9mSnxCCEWqUdjokx87JZdbC7I5mR9F4XZqexbs8Kn1tQEpsseknnJSfzz7Tdytmglx9s6ef/uraTFxqBq82Snr01qXAx3RBdzZ/4aXu/v4PYVqylKTkPVfESmJnx/VSGYcM9Sa2knygDvWX4IFQ1tjgjVhIaiPYRd6WXSVUa0YTnxpi2oQkEvSeTFpF5GaGpzROclwlOgXvG9WZ8c8Dq+Ubwj09gKIWi1jLM6IX1JQtOrqFhcbtLj/edsVlQtYG7qawXhkIWaJgJKuq+GqmrodOHVR1VVLaTiG5f3SZLCi5WHexzw9hC3b2ebCN6Z+JNKYytJEmuT/C/xMhn0AZ048I5w4hCeAwzX+YXjkN9om3D79EbbvB3E7dvZJoI/LbwzvNUSCDbTCKY0E0JgC4OY+2OEzeoKj/SasoeVZtVmd+MJY/uqqjE14wjZHnwxdqcrdGUjwMSUDTWIcvdqjIzOhk0mDw4Hrv16NYQQ9IdJqqqqxsBAaOmI52G1upicDE9B2tsXOnGrqhqdPaErHB1OD73DoR23R1Zo7A1NkTxmtdM2FrzfYw471WPDgferypRNtuJU/C9wsMuj9NvPhdS3txvX3Ij8Zx3lWGU3UXoDZp2P2IzS6zHrjUTpDL7P9UbOjHYw6XFwILWQ1vZp4qOiiDEZiY0yEWMycqy5EyHgrs3F7CtagfGyWn21jQM0tg7zyvEGVhdmcufNG9m+eUXAkd6LvzjHuu0FrFq/LKTjaK/qJjU7mdSc4DEzt8vL8ecqiY2P5oZ7llZQzkPTBHXVvbz2Ui0XSzv47s8+RvYy//twubyUnG/n2PEmunomuP/ebTz6iH9C1eX2Unqxi2NnW6htGODd9+5g5Yo0Du1fujyXEIKmthFOnGvlVGkbG9bksGJZKjdfv4aCvKXVsnaHh3MVnZw630ZVfT/vuWcHQgg+7kd1CDA2YeVMaTunzrcxODLDvbdtYfmyFG45tM5vm96BKc6cb+NsaTszFie33bSBG64rpmil/9lcR9cYZ0raKCltx+n0cvMN6/jIB6/3O4MTQtDYNMjZkjbOl3YgSRLve3gvd9y+NAkLPkdZWtbB+XMdXCjvIicnic/+2WHWrl2c9nce09MOjh9vpOxCJw0Ng9x00zo+/7lb/ZKdmiYoOd9Oyfl2Kiq7SUuL5+47t3Df3duWtBdCUFrRxclzrVys7iUmxsSB3au4bk8RW9YvJmHdXpnnT9RTUtVFXfsQW4qXUZiXhk6n40P37SYxLvqKbR+taufIxRYq2wdIT4pjd/FyH3Gp15GVHM9jN20HwOmV+VlZFa83d9I6NsGO5ctYkZqETpJ8RKZOh0Ensa9wBR2uSZ7taKJleoK1KekUJaf5VJ063Zy6U4cTG71yN9PaFHpJYndqsY8IleZJUYlYXSfx+ioM0hSaiEMlDQkdRp2RvJgMdJL+KrJzXt15ieyct8mJ2UFeXOAFC28E15wj35CcjcXrWiA7PZrCrNeFW7XhVRXccwRo0+wItdNDNEwMs8GYy6rEAryKhtXlZmTWRu/EDF3jU0w7nIxa7Dy4c8NCPD0tJY7sjARsdjdDIzOUlHdgNOrZssH/qoHElDgGu8fJLUjD7EcWfTkyV6QTHR88dznA2OA0eoOeBD/E0uWYnXEwOjzrI9ayEpGDFEwYHplletqBaa7GZeHKpVeSzGN6xoHF5sJo0GM2G8nNTiJvmX8S1utVsNhc6HQSyYkxxESbWF+cTZKflLTgK9wgIZEQH01ifDTZmYmkB1AdziMmxkRmegIzFgfFqzLJDpIuITbGREZaAsvzUlFVwaZ1uUFrXaYkx7I8N4Wiwkz6+qfYtmUFgQIfkiSRuyyF1UVZzM46GR+3UlQUWNmp1+tYU5yD1eKbjej1OtLS/BPKAMnJMezYUYAsq8iyRuHKDL8racAXftq+LR9N05AkcLlk1q7x/6CQJImdW/PR63VEm02MjlvYt3OV33NsNhm58/r1JCfEkBQfTXZ6AtdtLUTTNMwm46Jt37y1iLSEGPLSE5myOblnzzofMakJzJeRtjEmIx/au53VGWkca+1kVXoq1xWuQJmz9ZGTgpzEePYnrmBjehZHezuIM5q4Z9VaNE2gzBGZiqahCo1Z70Yard2MK+N8YtVtGHQGVKGiiXn15w045DuZdFfi1SxkxNyKqsnodTpWx2dfRmrOqzsvkZvaFf9XiTUEvvZvFO9IshOgeXaUrOh4UqKW/mF2j0+Tm5J4BSN+OWRZRdW0gDLnawHhkp1CiJDj2JomUFUtYJ7sq+GVFb/5q5eCEAJFCW8f4R7HfBsIL77+RojYN0IQvxHyNtw24dq/lQrdCLnrH39SZCfAuqTAVbtXZgReymc06jESuvP4Y0X4ZGd49jpdeOcoHCcOvv6H48Qh/OO41CY8vJE2b4Qgfjv6Fq79W6nQjTjx8PGOJTuDIZSZSDh1HP8YoWkCVQmd9FMUNSw1q6YJ7GGqX8MlkIUQWG2hpVidh6KoYffL45HDVvK6XN6w29jtblxhkrdTU/awyFshBBPjoaWZncf0tCMsYnzW4sTpDO3YhRAMhJHyeGjSElLdVVlVaRkJTroqmkbV6HBQtXe/Y5IBh3/yVNW8DDqqkLXw7se3A9fciPzZ3hocioeoOQXnPMG58Hfu/Zjbxgv9dRxILWJ8yE2C2Uy0yUiMyUi00Ujv1AxlXf3cuamYQ6tXEn1Z3K65fYT27jEq6/tQFI07btzA3u0rA44MX/xlKQVrstiwoyCkEUVP4wBJGQkkh5j2tvFiNx6Xl+0H1wS1nRy38vrLtZw4Us9Xvv0omYEyIApBe/sox441cupkM3ffs5UPftB/XVAhBJ3d45w83cKJMy3s27OKvTsL2R1A5DIz6+BMaTsnz7XhdHk5fHAt+3etItcP0esrBj3KqXOtnD7fzrZNy8lfnsrD79rldx+yrFJV28vp8+2cK+vgrls3sWHtMq7b61/k4nR5Ka/o4uy5di5UdPPgfdu56dC6gCmLrVYXF8o7KTnXTmVVD+9+cBfvf+y6gCPtyUkbZaUdnD/XTn39AF/44u0cPry0EnYevT0TnD/XTtn5DkZHZvnPrz7MqgCxdUVRuXixmwulHVy40EleXipf/o93Yzb7Dw12d49ztqSN8vIu+vun+dyfH+aWWzb6te8fnOLkmVYuVHTT0T3GIw/tZt+uVawtXqyEFUJwobaX0+UdlNf1YDQYuPXAWvR6HQ/etoX4qzIgtg2M82JpM6VNvQxPWXnkxq0YDXr0OomM5Djedd3Ghe2+3tTBkYY2yrr6SY2L4eDqAgx6HQadbk7dqWPPyjwcOpmnmus4N9hPlF7PrQVFC8rOeVtVyLR5uhiWx7BrTvalFZNsikMvXSJEDdIEBqkcSepDQkOiCEnSYdKZWBGbiSTp0M2RmzrpMjXnnKJTd9nf7JiNLIsJvGDhjeCac+Rp5jh0HgmPpmDxuvDOEZ7zxOc84TnrdXJmrIMzwx0Ui1yuTy/C6ZUZ8HpxemX6pmc50dpF+9gkNf0jfOrQbpJjfAScOcqATicxNe2gd3AKVdWYsTi58+aNflcnKLJCS00/aZmJZAdR4YFP2RkKKQowO2VnsHuc9AAOeR6yrFJb2cPEmBVztBGXM/DIZnraQUP9ABPjVoQQASsrgW9E3do2wtiEFWVutB8X5/84hBB0900yMm7F5fYiKyrJiTFERfm/9VwumZExCw6ndyEGnZ4SmOxzOD1YbO6FmL3ZbCQx0T+hCuD1KCiKhslkINpsJD7OHNDxzcNkMhAfbyYuzkxSEHIUwGw2kpAQTUpqHHHx5oDpdeeRnBxLZmYiWdmJWK0uYgIodMGnVF2+PJWhwWkGB6aJjzcHDZfk5CRTVJTFxLgNq9UdlFDNyU5m04ZcrDY3FquL3JwU4v1ce0mS2LI2F49XwSsrjE3aKF6ZgaoKDPrFA6KiZenctquYKKOe8029bFmVg04noaqC6Mt4KkmSuGFNIXHmKFJio5m0OblpbeEC2aloGqqqkRRtZlt6DolRURQkptA0OcYDxet9JKfQFkhPVdPYJGfT6uhnQp3g+sx1rI7PnrO7RHi6lK1Me2uweBvJiL4LIXQYdTo2JuXNKTrniM15cvMyovPyv2Z9aAO3cPGOJTsHHTNMe5ysS8rGsIS6s29qFqNeR06Sf6n42ISV9NT4NxSjvBYhhMDtlv0uWVvK3un0EusnJ/VSsDs8S1Z2D7QPl0sO6siubuP2yET7Kbzsr43XqwTMOb9UG1lWA0rhr4amCRQlvDaKovqKHYQRX/d6lbD2MR+6CXUfQviI7kArYy5HOEppMVdEOZTf3Z8aifqWFl8OF2+HI48ggggieKfhrS6+/I5EOCrHdwqChWKuRrh1TRVVQ5bVsNqEU7NyHuGqQYGQybt5CCGwvwHyNtw2qqKFfV0cdndY96+qamH1S9ME1hDrfILveoR6TbyywrTVGZLtuNWOwxN8u2N2O9OuwNt0qV7arYFVpVZ5jFnvSEh9ezvxe8fIJUkyA2eBqLntPSOE+Kffd7v+cGy4GbcqY9TpF4hNk96ASXfpfZTOgEGn47ttp1kfn4s8rSM5Ohqz0Ud0xpiM6CSJ750t58biQg6vLSTBfClu2dk7Qe/gFGNTVi7W9XHHofVcv2tVwKn6C0+Ukp2Xwo4DqwNmw5vHUOcoCalxxAcoLXY5pscsTI1ZKdrkX5Q0D0VWKS9p5+gL1fzZl+4iIytwXM5icXLmVAvHX28kJyeZv/n7ewLa2+1uSs63c+JkMwaDnoffs4fNAfqlqhp1DQOcKmnlwsVuPvDIPnZsyycr03+/LFYXJaXtnD7XhtercOvNG7jzlk0B+zU4PMPZc22cKWkjMzOBe+7Yyg4/dS5hLn4/R/iVnG9nVWEmH3jsOpYFUMJqmqC1dZhzJe2cO9fGunXL+H9/dWfAkISiqDTUDXD+XBtl5zu4464tvO/91wU8FofDQ2V5F2Xn2rlY1sU/feVBNm9dEbBNf98k5ec7KC/tZHRklp88+SlMAbgIq9XFxfIuLpZ3UXGxm0ce3cdD7146jS34wmIXyru4WNlNRWUP+/eu4r57trOqcGkR2cDwDGfK27lY20tT+wgfevdeos0mbj+0flEGxFmbi6MVrZQ19lLZOsBtu9ewIisFg15HWmIsh3deUg63jUzwcm0r59p76ZmY4SMHd2Ay6DHodBj0egw6ic3Ls4mPN/PrpnrO9PfSMjnB+zduIc4UhUEnYdD57HSSRLt7gG7XMMPyJKviMtmSsgKDpJsjPHVIuNFEBaroRGMSk64YgxSHSWciP+6SsnPJv1eQnXoyo4vIjg5eqzdcvBlkpwe4UQhhlyTJCJyTJOlVIcSFN2HbiyBrKrNe5wKx6dEUvFe9nyc+a6b6ecZTTbY7nX1pRaQY4nDJ8sLrTEcPJZ29vNbczl/ctJ+1Wb4bUlZUxiatdPSOU1nfx/ikjZauUT74wB6SEpZOjTo+PEt/1zhGo4Gt+1YFPY5wQnWKrFJb2kFiSmhOv66yh5qL3cxMOXDY3BDAkcuyyrmzbdTV9jM2aiEhITBBqKoaFy52U1PbT9/AFBnpCShq4BF238AUNfX9dPdMYLG6cDg9AZd/apqgsWWIjq5xRscsREUZ8XoD78PrVejsHGNoeIaZWQfJSTFoQfLpeDwKg0MzTE07cDq8yLIadFmq16swM+3A4fAgyypaCMsCZVnF5fIie332IYUz52ykuYLFocAcZcQUZURv0CGFEF+OjjaRlBxLbFwURpM+aEw6JtpETnYiqSlxxMZGYTQa0Ov9t8lMj6dwRTpDo7P0DU0TH2v2W14xMc7MtqJcZm0uRqdspCTEkpYYi6JqGK+Kw6/KTOXQmgJkVcWrqBRl+gogq5pAUVVUTaDX6ViekMh9xeuINvoGbpszs0mJjkbW1EvEqKaRGLWKJGMMxfoMYo0mbsyaU5XOK0CFhkfNZNbbiEVuIMZQjFGXTZROz+qE/CVJTSFUNLSFv/PfSWHqG0LFm12zMwY4B3xKCFHuz+7tiJHLmsKJkVZ2pOaTZl7sAK1uNy2jE2zJzSbKsPTzbGTcQrTZ6Nd5v9MghMBicYa0EmPefnraQWoI8vl5OBwedHopLCJyesZBSgjpCS7vl8XiIikp9OsmhMBmcwd9kF3dxm53Ex8g3cBSbRwOD3EhrFyZh6pqeD1KwNzyV8Ph8BATYwpL1et2e4kJcSVVuMS4ompomhayICxUBbCYK7gcCpGqhbAq64+dEH1LyU7JVxKjClgFfEcI8deB7CNkZwQRRBBB+HhLyU4hhCqE2ALkArskSVqkdpAk6eOSJFVKklQ5MRFavb8/NP4QK3r+0AhHCQq+0WK4pLCihEd2zud0CQfhEqpvtE04ash5hHssEP696FvCF14brye8YwmH6BZChEVAWx2hEa+KqjHjCE66KprGqD1wal8hBH32KVTh//oomsyEuz+kvr2deFMFQUKIWUmSTgG3AY1XffdD4IfgG5G/0X1cmOjEoymYdPoFkvPSS49JZ5z7a+DIUC2KqmF2xpMWHYfZaCDaaJgjPQ38pqqBjPhYbl1bRFrcpal7/8g0Q2MWokwGfvFCOQd3FnHTnmISAkyHX3iyjOTUOPbduA5DCLlBxgemiE+OJTrEKbYiq0yNzpKZF1xsBDDQM8Frz1Xy4AcOkJwWOPShaYKG2j6Ov9bA7IyTf/uf9wS0F0LQ3DzEqZPN1NcP8Jf/7w5W+6lzOY+JCSunz7Zx6kwLO3cUcPedW0gLUCJO03zpX0+fbaOyqoePfPAAB68PrGr1eGQuVnRTcq6dgcFpPvvpm1m3LnBaYbvdTfmFLkrOtjE9befv/uFeMgOQsODLMHnhfAfnS9qx29x89VuPBl1/PT5moexcB2Ul7RQWZfKxzwSu2yiEoLtjjAvn2ik/38GHP30jW7YXBGzjcnqpqezhYmkH7S0jfP2HHwpIdqqqRnvrCJXlXVRc6KKgMIMv/PWdfu3nid6Kyh4qKnowGnV84Qu3sdzPPel0eblY08PFml4u1vayb8dKNq5ZxnW7Fy8cUFSN8sZeLjT1caGxj9TEGG7bsxajQU9yQjT7Nl46dovTzbGGDs619VLeOcBtm1dTlJWGQa/DqNdj0OtYm5NOTmoiL7a1cKavl9KBfvbm5bE1K3uB6PT91THsmaLJPsCgdwKXKvPuFTvmUt36XgYkXKIRp9qOS+3BrMsgzlBAlN7Eitj0uZS3PjLzcqLz0vtL36ebl5NpDlzq743gzVi1kg7Ic048GjgM/Nfv3TM/GHROM+Gx4tXUBZLTO094aiqy5iM6ZU1hyDnDuMOOfiqeLYn55EWn4VEU3LKCS5ZpGB5jwu7gp+XVfP7QPu5cX4wkScxYnNS0DGJ3eqhsGqC2dYizlZ188j3XUVywtEy6pW4Aq8XJ9KSdu969K6gzd1qdREWbQnbkTeWdKIoakiMf6pvk5d+U09YwyE13bQnqyCvLuzhxtIGGugFiQ4iRNjYO8tqr9dTV9fuKGEzYWb3av73V6uK11xuprO6lo3OM3GUpC3Uv/aGjc4yz59qoqe1jfMJKfwjFFZqahqiu7qO5ZQhF1picClxhXQhBS/MwjY2DdHaNodfrgi7zE0LQ2TFGV+cY/b2TPtFNkGGJpgn6eycZ7JtiaHCanNzgOehlWWV81ML4qIWxkVk0NfjYx+2Wscw4mJqwYbM4QxqRK7KKw+5hesrOioLAxcAlyVe7U2gCp9NDTExUwPNlMhlIjI/GaNSjqj7F5eSMHXWJYzHodSzPSqZzcJIYsxGjXo9XUXF65EXHkRAdxdplGQxOW+gcnSLObCLKaEBRVRweL4qqYfd4iTEa2Ze3HLvXy6TTQVpMLDnxCb4lsJqKKgQeRSGOWDL1KWSmxNJhG2N90rIFklMRviyosdpmLLIZHUYEOhC5IIwsi1k5R2Sqc3U+VbS5ep3aHNEpa/ICCRqvhjYQCxe/d4xckqRNwM8BPb5QzW+FEP8aqM3bFSM/MdpEWlQ86xOXYVgiS9/xti6KM1LJTUpckuCwOdz0j8xQnB84t/M7CZMTVlLT4kMmfMZGLSSnxIasInS5vNgdHtKDyMGv6NOUjbjY0OTz8xgdnSUzc+nr6g9jY5ago/GrMT5mJSPTvzr4agghsFldJAQoDH01NM2nOg3n+F1OL+ZoY1iqx5lpBylhENfT0w5SUkIjoTVN4HB6QkpPAGB3eogLYVAhhMAtK1fkSvIHr6piWiI9wOVQhYaOwGmGhdCQpD+MBCei7IwggggiuMYRUXZG8JYhXLLzjQwe3kibN6LMfSPH8qdIisOlfCuhIhySW1HUoHV15+EIUfk74wpOiroULxZvYLtZ7ziaCJ8YfytxzWU/bJodQBYqJp0Bo06PSTJgnCM6jXOkp1Gnx6DT0zg7QPVkDxkig5zYJMwGA2bj3MtgoHJgiO6pGW5fu5pliZemx6OTViZnHcRGm3jpTCPpyXHcsncNqQHWV7/wm3Kio00cvGUDUSFMged//OFM/d0OD+YQE065nV7OvFLHvsMbiA+SBRBgasLGyaMNDA/M8Lkv+Se85jEz4+Ds6RZOnmjmfY/tZ9fuwoD2iqJSVdXLmdMtaELwqU/dRGKQ8ML0tJ2SkjbOnmnjuutW8677Fw1EFqGvb5KSM62cO9fOpz59E5u3BFZDCiFobx3h3Nk2LpZ28k9feZCcAMpO8JGErY1DnD/bRnfnGF/52iNBRTuyrFJf3Ut5STup6fG85wOBlZ0AdpuLqgtdXDzXwd0P7WTNhtygx9LfM0FFaSetDYP81b/dHzTkNTvjoPpiN5XlXaSkxPHRP7s5oP3MjIPqql6qKntoaR7i377yELm5Sxdp0TRBV+84lbV9VNT0opMkHrxnO1s35i2ZnKx/ZIbyxl7KG/voHJjks++9HpNRT2JcNJuKLpWhUzWNyq5BStv6KG3rIyHGzH271mOcIzuNBj0F6cnkpiZSPjjImZ4eSvr60ITg0c2bMejmSFGdL4OhTXXTYOtn0DtF9XQ/7y/cS1pULAad3kd26nS41SFmlRYscieKcJIXvR+z3kRebOplROclklO3QHjqFkhQnaQjxZRFWlRodX3DwTXnyKtnehhzWZAvIze9QkGeJz/nCFBVaHg0mZ7ZKTxjseRHZ1AYm4WqCtyKiluWGbc76Jme4etnSvnQ7m18at9uYkxGBkZnOVXRgcPloaZ1kPFpO88cq+XjD+7jlr1rlnS+F8+1M9Q/TUvjIB/45A0kBVFhet0yk0PTLFsVuJLRPEb7JhnuHWfbQf/FhOfhcnh47mcl1JZ1sWr9sqCOfKh/il///Dx1Vb0hrbiZGLfy6yfLqKrsYXBgmpHh2YD2qqpx9LUGTp9pobFhkOXLU5mZdgR05DMzDp57rpKKi910do6RmhbHu4L0a2BgipdfrKGyspv+vikGB2eCOvLenglOHW+iorybwYEp7Lbgy976eiY4f7aNirIOHHYPmqYFrZTU2zVO9YUuqsu72bBledB9CCHobBulobqP2soeDt0SOH85+FbtdLWN0lI/QHvzcFBlK8DEmJWernFaGgZZuzHwgwLA6fAwPmahp3ucmRkHM9MOv45ckkBRNGYtToaGZ0lJjqGheYj1a3KWdORRUQaE8MXHFVVlYHQGWVFJir/Sket1OtLiY4mOMi7wzNN2J7KiomgasqIRZdCTl5ZEQXIynVNTJEdH4/B6QZJwKwp2rxdZ01A0Da+i4PQK8hJT6HdMkxIVQ4IpGlXTkIWKW5XxqoloWhYSVoQYZdKtx6zXsT4p1UdqzpGcmlBRNO/Ce/Wy2p2aUJGQ3hJH/o6OkTfODjDgnGRn6irSohaTaxf7BpE1lW25OUQblx5Fn6/ppjAvjay0wISW2+XFHKLK7Y8ZM1N2klJiQ54pTE741uampYdGXnq9CoOD06wMUuT5ij7NOJBllYyM0EnFsTHLXE7y0EnF0ZFZ4hOiw0rLOz5qIT0zIayZld3mJi7Ewtswl2LXo4Q005uHxy1jijKERXZaZp0khaGgHRmZJSM9Ab0heIRWCMH4hI3MEK/h1KyD5ISYkFLZzjpcJMUGn3XavV7iTIF/o0IIvJpClN7/uVbnHLLuD0B4RsjOCCKIIIJrHBGyM4IIIviDI5yBY6hkpzqX/CoYFE3DowRXr9rkwOE1RZNxqY6Q+vZ24ZqLkfc5xlGFhklnwCDp58hNH8Fp1BnQXzbdcaleftN7nnxDLvnxaZgMPpJznvScdjp5qraBO9aspjD1UpxvyuLA5vAQYzbS1D1Kz/A0t+5dw7J0/2uMX3y6Ap1O4oZbNxIboPTZPOZXO4SS8vbyNuFMlVtr+8lfnUV0CKECRVaputBFT8co7/2w/5qd81BVjfqaPk4da2LjluUcvj1wilmA4eEZzp5qoa62j7/9x/uCJptSFY36+n7Onm7FbDbyiU8HVkOCb/30xQtdnDvTytbt+dxxT/D6iFaLi/Lz7ZSebeODn7ghqDAGfCGoCyXttLcM89m/vjOkEMDY8CzlJW2Yo03cEkK/hBB0t41Sca6d3QeLKSgKzqc4HR7qKnpoqevn/Z++KSjnoaoana0jVF3owmw2cv/79ga172gbobqih5rKHt7z6D52BCC6bXY3tXX9VNX00tw2wqc+egPr1+YsScK63DK1rYNcbOjjYmMfDxzewsrcVOJjzRTmXVlHdWjKwoX2fspa+2gbmuAL9xwgymjAaNBjMujJTk4gMymOYauVsz29lPT0UjE0xF9df4A4kwmDXu8jR3V6hKTRYh2l1zNJ2UQvG5KyOJC1CsMc0WnU6VE0O5NyK5Pedia9XRTHHSTBmExOTDI6dOglwxUKTr10ieDUSXr0c4RnojGFJJP/mrBvFNecIz86UsOIawZF+MhO5TLSUxY+dRWAhIRA0DEzzuxQLEmGOFZEZ2LAgFtR8CgKqhC0jE/wjfNl3LCygL+/6RArkpNo7hnjaGkLDreXkUkr3UNT/OTFCzx8yzY+fO+eK2oIzqOitJOq8i7OHG/io5+9meIg0nCP00vjhQ523BScxAJwOz30Ng+yZkfg1SHgcwCnXqzh6NMX+diX7mbV+sB9cTk9PPWTEs6fbEbTRFBH7vUqPPvrck4ebaS3ZyKkuGp9bT+/frKU+rp+dDodY6OWgI5cUVRe+l01J4430d42ErDw8DycTg/PPFXO+ZI2ujvHyQyShx3AZnXx3K8vcOFcO92d49z/3j1B21hnnbz4dAUXzrYxM2XnM//v9qBk5/SkjVefr+LCmTaK1uWE5MgHeyc58XItpSdbKCjKCurIhRA0VPVy9mgjjTV9PPLxQ0Ed+cSYhYrSDkqON5O/KjhvYbU4aW4corysk+aGQe57yH9BbICpKTud3WNU1/UxPePgdEkrKwvSl3TkHq/MxIyNnsFJ+oam6OqfoG9oiuTE2EWOHMDu9jI26yss0To0jqxoeBUVWVU5sK6AzKQ4oo1GDDod3rmUt1NOJ+MOB7KqIqsaiub7fFy2kpkVjUHSIUkSTsWLovmUnYqm4dW8ODWBS9OjYaLDYiHWoJITk4wsvHg09wKhqc4RndqcP1KFspDKdlXcprfEkb+jY+Q22cWzA6XsSFnFmoTcRerOIYuV09097F+xnBXJSUuOdqtbB9GExobCbMwB1GODfVNkZCeGVSfxjxGWGQeJYRBeM9MOrFYXK/JDuzllWaW1ZZg1a3MwhrBCBnwS/5HhWYrXBM7ncjmmJm3Y7Z6Q+wUwOW7FaDKQGEb626kJGylpcWGRnU6Hh5gw65aGWxvU61UwGvVh9ctqcYalOB0fs6DT6UIiuoUQ9PRNsjwvNaSUsxabCyFESCmkx2ZtpCfEBZ0V2TweTHq937TV87B63SSY/JPRPucsY9SFfg3fLETIzggiiCCCaxwRsjOCCCJ4xyLUAakSAinqUYMTom419HqlbweuuTjApMeChC8FpVHSY9AZMEr+p5CvDVeQrEthVUI2ZoOBKIOvnif4Lv7Pa2rYsWwZ6zMyFrZhd3nwyioxUUacHpnfnqjh1t1rKMjxn7nsxWcrkWWVm2/bGNLUXAiBpmrow0jG5fXImJaIz/vDzISN6LiokNe3Dw9M0d44xKEQiEvwhSJOH2sid3kqew4ESH84B69HoeJCFyWnW/jop28KaUo+Pmbh3Ok2hgan+ewXbwtqL4Sgp2ucc6dbyclN5ubbgh+Lpgnam4coPd3KHe/aTlYQZSeAqqg01w3Q2jjIg+/fH1IIw+tVaKzqRVU0doZwvgDsVhe1F7ooXJtDdt7SwpvLIYRgsGeSppo+Dt+3LWh6XfCF0+oqetBULaRrPzvjoH5OqHTT7ZtYH6Beq6YJenonqK7ppaamj8M3b+DAdauXTEInhGBgZIbKxn4q6/vJyUzk9oPriI2JWqTj8MgKtd3DlLf1c6G1jwf2b6IoJw2TQY/JqCc1PpbEWDMeRaF6cJiSnj7O9fRxw6qV7MxbhlGvx6TXYZpTeA65LXQ4xigd72XG4+JTa/dj0OkwzaW6lRBMeXsY8bQz5G4jPSqX1XGbSI2KWyA69ZL+sveXPruc/IwzxBNrCD1hXKi45hz5k30nGXFN+UgKoaBoKnKAvAdD1ln6ekxESVGkm5KJlsyolz29+y0WbB4Pq1JS+NtDBzlYUMDFpj5+d7YRl0fG7ZVp7Rvn8ZfKuW5TAV985AZyM5IW7ae8tJOLZZ389skyPvyJGzh8+6aAMTuXw8PRJ85z90eCE1LzOPnrUm77wMGQbDsaBvjl117jg395ByuDEK9CCE68XMtvf1KC1y0H/TELIbhQ0s4vf3yWrrYR3v3YvqCOfGLcyk9/cIrzZ9txOjzc++DOoI68uqKbJ35SQlPjICkpcUEduRCC46/W8+IzlbS3DnPPgzuDOnJV1Tj6Qg2vvlBNe/Mw23YXBnXkqqLyynNVHH+5jpGBad71yN6g11CWFV757UVOHKljRWFGSI7cYXPz/C9LOftaAx/83OGQHHlP2yi/+1UZtWVdHLp9E/og5eHcTi/HX6rl9GsNZC1LCnrtZVml7Gwbp441Ul/dx5YdgXOkz846uHixm1NnWujsHEOnk9i6ZcWSZfi8skpr9xgX6/q4UNvD+qJsZixOUpNj+fT7riTgHW4vfeMzNPSO0jo4QWPfKK2D43gVH3l50+ZV3LylCEXTmHa5GLRY6J2ZYcRqpbTXR4jKmjZHeqpMyQ5W5ycx43Hh0RR6bFPImooifClvZU3FrY3hYQpZcjLrHmfY3sxNOYWo84Sm0FDnFJ7qPPF51d/1idvYkRI8PUO4eMfHyJ/sPUG6OYntyUWkRF35VNeE4AcXK1iXkc7O3FxillB3jkxaudDUy/Y1eeRlLE2IAtTV9JGWHk/OsuQ/6pp/wWC3uogLo26l1eLCOuskd0VoeZZVRaO9bYSs7CSSQ0yB6nB4aG8ZZsv2/JDP7eycfLzAT4X3pTAzZUev15EQBtk5O20nMTl0JSy8MRWwIqshP/Dn7fUGXVj9ctjcxIahOJ2ey/ceaurbgcFpzFEG0tODqzsdTg8TM3bylwW/r6asDiRJIiU+8HVzyTJ2j5f0uMD33ZjLRma0/0GGEAKn6iDWEHrK3zcLEbIzgggiiOAaR4TsjCCCCP7kEerANZhSVNHCr9X6VuKai5G7VA86JAxXqTj9oX6mG0XT2JCUj0m/+HBP9/QQazKxPScH3dw01Cv7LpLR4CNRnzxRzZbCHNauyPQ7Va2u6qGtZYTDt24gLYSpoxACVdHCmi6Ho+wEXyxX0wTGENcfe9wyHY2DbAgS95yHIqtUl3cRG2dmfQgZ/QD6eycpOdHM3Q/sCCmEIcsqtZU99HVP8GAQ1eE8HHY3F891EJdgZue+opDaWGYcXCzpYNuelaSGmthpwkpTdR8HbtkQ8nUZH55lZspG8Ub/BOHlEELQ1zFGXGI0aSFWL3K7vLTW9rNx18qQyE5N0+htH8NmcbF5d/B6kpqm0dMxRl1lL1t2FbAyiFDJbndTXz9AbU0fqalxPPjQLr/9cntk6luGqGzoY2LKzicfPUC02bRkvdzhKSvlrf2Ut/WTk5LA3XvWEWXUYzIYiIuOwjx33w9ZrJzr7uN8dx9GvZ7379ziIzsNekx638urKTTbxjg/2kvpWC9f3HSQlKiYOcW4HoMkYVdn6HO10etsx6nYOJx5J3FG8wLJ6furn6v1eeVn8wRolC6KKP2bv/78zajZmQf8AsjEV73wh0KIb/y+2/WHb3c8w7BrEkUoaCE8XWedXmpaQY+RBEMMSaaEuVJOIARMu12M2Gxkxsby4W3b+eCWrRyv7uA3J2uR5yrKD01asLs8rMxO4QsPHWTfhvxF+3npd9WUnGnlp4+f5oEHd/HYhw4QE6BUldPm5sf/9jzv/6u7SA7B8QO8/MPj3P2JwyHZzk7Z+Pl/HeHeD19P/pqcoPadzUP84D+PMD1u4/HXvhjUvr9ngh9+7ShVZZ2865G9QR2516Pw9BOlPPdUOTariy07C1gfxJGPDM3w428d50JJO3Hx5pAceXvzEI9/6zj1Vb3ccf/2kBx5Y00fP/v2CZpq+/nydx4LyZHXVXTzxHdP0t89HnLB7cqSNp76/imWrUgLyZFrmsbx56t54Rfned9nbw7JkVtnHPz6+6e4cLKF777wuaBkpxCCkqONvPCrC6RmxIfkyKsudPHiby9SVdbFX/7LfQEduSyrnDjexInjTTQ1DZGfn8bhWzYuWSJOCEFt8yCvnW7ifGUX8XFm/u9HJ0hPjeMvP37lfe+RFSo7BjhV10lZSx8b8rMYmbbilVU8isLtO9Zw5+61qJpG+/gk1YPDlPb2szw5iWfrmvDOKTu9qoJXUbFpHravyaJ1dpwhh4X6qZEFolPRVDyailfM4JUG0XTDCDSe6j7DTbmFqHNk5uXE5vxLueqz7ck7OZB+KOg5DhdvRs3ObCBbCFEtSVI8UAXcJ4Ro9tfm7YqRCyE4M1HDgHOM7clrKE5Yjl668gf3bHMTDq+X65avoCB5MVGpahq/OFpJcV4GW1blEGNe+ofRUD+Ay+lh7fplQXOI/DEjXNWhw+ZmdtbBshCKQoNvOVpn2wiZ2UkhKyhdLi8dLcNs3Loi5JGvzepiZsrO8hDypszDOusEibDUjTaLk7iE6LBmSuEuIwXf7CqcpaqqoqLTh0d2uhyekPLyzMMy60BTBckhkp2jo7NMTztYF2QVFfhG5i2do2xdH/yBZ3O6GZ+1U5gTWMXrVVX6p2dZlR74Xh1z2ogzRhFr9P8QnPZOkWJ6awopB8LbRnZKkvQC8G0hxDF/NhGyM4IIIoggfLwtZKckSfnAVqB8ie8+LklSpSRJlRMTE2/mbiOIIIII3lSEMsCdT9D3x4A3jeyUJCkOeBb4vBDCevX3QogfAj8E34j8zdpvMEx7LQw6x1ifWLgorALQMzvDgNXC3mV5GPVLT13PN/YQHWVkS+EyvyIfh8PDs89WcPNN64PWfIS5REheFVPUW8s3h0uQjg1Ok+mndNdSGBmcxuX0snJ1aCXr3C4vF891sGVXQcghjNGhGVqbhkIqdwaX0r96vQprA6gOL4emabQ1DJK5LJmUtNCUd6qq0dk8xOoNuSGfY9mrMDVmJSsEcc88XA4PiqwSH8b69rGhGdKyEkMiO8FHEE8Mz5If4nW0W1001faTszyFvPzA4SshBP19U9TX9DEyPMtHP3Wj39+REIKh0VlqGvqpbRzgI49cR2Z6wpLH4ZUV6rtHKG/pZ3TGxp/ffx1mowGT0YDJcEnt7VEUqvuHKe3pp3lknL++5XqijUZMBl8CLdNcSttu6zQlIz2cHelhT+Zyrs8pmKsF7HuBSp+rm3Z7C222Nu5fdh+JpgT0kh7DFWSnHsNl7/VzCnT9XC3Pt0Jn8qZ4EUmSjPic+K+EEM+9Gdv0h/9seZxR99TC/68uYiyEQCfp5phmA04PHK2zo5f0xBqiSTLGY9RdedhNE+Mkmc3cVVTMn+/aS2ltL785Xbvw/azDxei0jYykOB65cSsP37AV41Xxym9983WOH2/k5z8rYeeulXzm0zeTt9x/DM1hdfHPH/4xH/uHeykOUldyHi989yj3fvrWkGxVReXFn5xh2/VrWBEC2Tk7beenX32V5qo+fnT0L4PaO+xunvjeSV56qpz7378vqCMXQnDhTBs/+N/XGBmc4Ru/+BgJGwM7JrfLy69/WsJzT5QRl2AOyZHPTjv4yTePcfLlOu54cEdIjnxyzMKP//c1So418uXvfzAkRz4xMsuP/+dVGip6+MXJvw6J7Bzum+TH/3mEhOQYPv+Vh4LaA7TW9vHjr7zMAx87yN7DwY9fVTVeebKMF35xnm+/+Hn0IQiPulqG+elXXyM2wcyXvvZIUPuhvil+8Z3jlJ5q5Yv/+q6gjvxiWSfP/uYitdW9xMWZeeA9u0j1c477Bqb47YtVnClrx+nyMj5pIzM9gb//wpUFwYUQXGwd4KWyJkrqe0iINfNvvziOW1bwygr37l/Pu67bCEDL6ARHWzt4vaUTVdP4wbmLPgWo6iNGvYqKU5W5aftKyif7KRvrw6TT02udmasF7FN2eoUdVTcMxnEkvY3vt77GjbkrUebJTG2e4FSuIDznSU9VqOxP3cvhrOB59cPFm0F2SsDPgWkhxOdDafNWx8hVoaFovpM55JrgxaFTbE1ey9bkNSSbLq1IEEJQMzrCyx1tXJe3gt3LcoldoqbfS2VNOD0yO4vzKMhKWfKJOjFh5ezZNjZuzKOwMCPkkdAfG8JVHbqcHizTDrJCHMULIejpGCM1PT7kdLlej0xH6wjrNuWFPJpxOjxMT9rIXRF6GluHzY0QIixlq8PmJiYuKqxRluxVQl4SOg9V1cK6p1RVQ6eTwuqXxy2HVRfUYXMjyypJISp0JydtNNT2c8PN64PayrJKRW0vW9bnERNk5Y3LI1PfPcLutYFXTqmaRu3gCFvzLi01XgozHhd2r4e8+CS/NlOeaWINMZj1oSth3wy8ZWSnJEnXASVAAzAfNPpbIcQr/tpEyM4IIogggvDhz5H/3qEVIcQ54NpNLhJBBBFE8AYQLv/0VuKaU3aGCyEEDZY21iYUYtQtnjbKqsqZgV6uy12O2bD0tLJ/YpbBiVl2FvsnRAGOvFrH+nXLyA9hOi+EwOtRwprKvh0Id3rtccvMTtnJDIHgBd9x93aMkZaVSHyIIQyvV6GjaYj1W0PjEsA37Z+esJG3MvR15JYZBzpJCotUtEw7SEiOeUuTZgkhUGQ1rHCMIqvo9FLINWGFENhmnSSEGO4SQjDUN4XJZCAjJymovcvlpaVhkLaWYR54eE/Aakcej0xT6zC1DQNsXLeMndv8K41Hp6xUtAxQ1TbAx+7ZS3ZqwpJE6uCMhbLufsq6+3n39o2sycogaq6+p37uHNm8HspG+ykZ7kETgo+t34VRN6f+1Okx6nRMeSdpsrZQZ2liXUIxmxLXLRCZhivITgMGnf4tJTgvxzXnyP+n9UeMeSYXfa5D8p1Ene+Ezp9Up1vH87XTCAQxhmjiDbFE681z+Yj1ROn0VI0OI0lw44pCPrx5O33d0/z6TO3CtgWCtsEJkmLN3Lq9mI/dtpu0hCtv+K/818tcuNiFzeamaFUmH3zsOvbtXeX3OJx2D5+67as89oVbuen+7SH94F787lHuCZHsBKg520Jmbio5K4NnAFQVlZefKOX4c5V868UvBLXXNI3jv6vhJ//3Grfev4MP/UXwfg30TPDd/3iZmgtdfOPJT1K8ITegvRCCktcb+eH/vAoSPHHsr4LuQ5FVXnzqAk989wQ337uNT3/prqBtvF6F535awq9/cIp/+d4H2BygmPA8PG6ZZ350mld/c5Gfn/6bkMQ6LoeHp759DOu0g8//13uC2gNMj1v5yVdeZO9tm9gfQm51gPoLnfz431/gf575LFF+BGyXwzrj4Gf/+yoOm5svfePRoPZOh4cnv3eKl39dzuf/9V1BHfnQwBSPf/ckZSXtREUZuOXOzX7JTpvdzRO/vcDrJ5qYnnWwPDeFosJM/vGv7l5k2zM8xc9freBUTSduj8zA+CxeWUUTggcPbeJdB33na8Ri41cX6zja1M6wxcasy8eFeBUVj+KzFwju3r+G0ok+zg71sDzel9LWq/lIUR/p6UEYR9CbptAbrTRMjTGUNYKiKXNkprJAaiqXEZ+XL1M8mL6P27L/CMnON4K3IkY+nwtYuewkqkLFq8n8su95VsQsY0vyOlbFrUCHzsdEqxpWj5uvlJ1hR9YyrstbQWHSYjKzvmeEo9Vt7F69nG2rlhEXvVj9pmmCJ54sJTc3hU0bc0lLDbzyQVVUFEX7oxuRh6s69LhlLNOOkEZlMFf4oHeSxOTYkNPFyrJCd+soxRsDO/7L4XZ5mZ60kROi4hR8jlbTRFipXF0OD+YYU9g5cMJRaYLvwRnq6HreXpLCIzu9HiWs5bAuhwevVwmZtJ6dcVBR1snNt28K2i9F1aip7ycpIZqiwsCFtz2yQlljLzvW5C3525yHEIL6oVGyEuLJTPCvRrV5PXRaptia7n+1l0W24lY9ZJpDn/G9GYiksY0ggggiuMYRSWMbQQQRRPAOxZ+EI+93DuJWPX6/rxodxu71+v1eVlXONHXjkQPnIK6t76e9czQkea8QApfDf5/+UHgjM7Rwj8Pp8OAMs83EqCUseyEElmlHWG00TcPjlsNu84eY1b4VCPc4vF4F26wz5G2PDs9y+vVGvN7gubzHxq28fryRF16uCWgnKyo1bYP8+IUyLjT2+u+rolDePcA3jp3nmcoGFHWxvF4IQev0BD9qrOAzp15g2G7F6vXgVi5lWnWrHqqmG/lx99P8sOs3jLknmfLMYpFtOBQXHtWLKtS3/Z645sjOr7d/j4k5slMnSX7yAF+Sydrd8OvaabyaTIzBTKIpjhRTIlH6OWmuTkfb9CSDdivX5+Zz76q1KJMKvz5Xh16SMBl9Mt663hF0ksShjSt573Vb2JSffUW/vvLVI9Q3DjI6ZiEvN4U7b93E/fds88vOOx0ePnbrV7nhnq088pmbiF0i3/LVePH7x7jnk6GlsQUY659Eb9CTlhPaipLa8+08/6NT/MvPPhGSfVvdAN/79xfYtKuQD/+/24PaO+xunvj2CY78upz/+eXHQ4p597SN8L2vvMxw/xRPnPqbkPpVU9bJ9//9RTbvKeTT/3BvSG0unGjmB19+kT//9wfYGkLqWyEEpUcb+NXXj/Ktl/8ipJi3EIJTv6uiq2GAj/3ju0Lql+xVeOHx0ywvymLXzaGlKJgYnuEnX36Bz331kZBWx6iqxpFfnqejvp8v/t/7gtoLITjxQjWP//erfPxLd3HD3VsC2jsdHn714zO8+HQFBoOOzdvzMfnJmKhpgleO1vHLp8oYG7eSkhxLfeMA//A39yyytTs9/OSlco6ca2LG5mJFVjLRUUYE8MANm7jvkI/s9MgKvyyr4fnqJnomZ8hPS+bpigYU7Upn++FbtvPaYDsnBrqQJAmb14tHVeb4NBUNDV3UFLqoaXRGKwYRzYxsXRAfykJdID795WG5IWM3d+XcEPQch4trOkauCe2SPHaBLb5aHqtxcvwsLtXFhsT1FMcVY9bF+Aqqqr58w9+rvUiU3sD1uSvYnZO3kL5SUTW8iorV6eb/XjzL5vxsdq1ezqqs1CXJmteONTIxaWPzxjzWrM4KuMRK9iqMDkyzrCAtLBLrrUa4qkOvV8EybSc9KynkNsP9U8QnRIe8zE9VVHraR1kVQvrTy/s1M24NK2+Mxy2jyGpYZKfH7cUUZQyP7AxTpQnhr1m+OnVFKAi3LqjHLeN1yyFfR4fdzcXzHRwKoRCHpgkam4eYmrZxw/VrA/db1ahs6ScxLpq1+f6JUSEEHWNTOLxeti73T2S6FZnzw30czF2Jwc9v06E4GXCOsiYheP72NxN/0mTnH9PC/QgiiCCCN4o/abIz4sQjiCCCdzL+JBz5jHcGp+KflOmzzjDrdgXcRl3vCE6Pf0IUYGzCSkPzIJoWGtnpsLmD2l0LCHdWN69UDAdyCATZ1VCXILSC4Z1CXL5d0IIUKb4csqzQ3jQUEtkpyyrNzUM8/exF3EEI6IkZO0dLW3j2eF1Au+FZK89XNvGdY2V+r7PN6+FYXyf/dP44teMji8pJCiEYco7z4tAZ/qfl50x5LDgVN7Im/0Hzk19zZOf3u77PlHfqClJzocApuoXcv/PvrW7Bk/VTOFQb8cYYkk2JpJtTiNabMOp9eYYnXA7ODvawL2c5t+evRj8r8WplKyajYUHG2zE6xci0lQNrC7h9WzE3byy6Qgr8X996jYGhGeqbB8lMT+DGA2t48O5tpPsRBjlsbj5619fYuncV7/vUjeTmB5f1D3SMkJKRSGyIebw9Li+nn77Are+/PiT7sYEpnv/hKT75bw+GZD8zYePn//sqaVmJPPr54MpOXw3KKp767kn+6n/fy9oQ0vfaZp384uuvU1PawY9f/38h9WtscJof/cfLpGUn8sm/D43sHOwe50f//gL3ffh6tl5XHFKbvvYRfvk/r/Cl730wZIFPZ8MA9efbuf+Toav7Kk82ERVtYuPe0ApJe90yz373GPd/6maiQkwFUF/aQfWZFj74pcWk4lLoaBzke//yO+54ZA83v2vRTP8KCCE4caSeH33tKC6nl18c+QKmFP+up7FpkG995xgdHWOYTAba2kb5+79d3C9NE7x8tpEf/+4CY1M2UhNjeeF0AwAP3LyZew9tvLT/pi5+cKqc5qFxEmPMnGzuWtjO/Iz9b+8/xLO9TRzpbmPW46Z6fBjBlQ93YbBD9BiSyYKEDotsRxEqslCQtcAPKCEEh7P2cM+ygwHt3giuuRj55WSmhrZAcM6/X/TSVNqsnVTO1FAct5aiuGKyonLRhFjIM3yyv5uq8WGuX5bP9bn55Mcn4VU0vHO5ij2KwuPHKzAa9OwtXsHOwlzir1KQeWWF5rYRXjnewNaNy9m6MY+sDP/FcmWvQnVpJ8Ubc0kKsebh24FwVYeKrGKdcZASYuV5gPHhGaJjo4gP8YGkaRp9HWMUFGcHN76sX9MTVjJCXLEDvmuiyGpYdSu9HhmjyRBW+C5clSa8PWRnuNde9iq4Xd6Qr6Pb5aXiXAfX3bwuaL+EELS3j3LhYhePPrIvIDmsaYK6jiHGp+3cunfNQvul9tE3OUPDwCh3bb2SQL38fMmaStlwPwUJyeQlJC19LKqH6pk2dqeuX7Jgjd++Cg2d9MYDIX/SZGewkxchQyOIIIJrAX/SZGewJ2DEiUcQQQTXMv4kHLmsyVhl/8pAm9fDuNMecBsDU7NYnIHJSU0T1DT2h0SyCSGwWUJTxUUQwTsFvqpCoRHXMzMOzpW00dsTuFi7oqg0dY7w1JFK3B7/xKhXUajsHuQ7r5cxZV/6tyeEoH16ksfrqni+vXlJG5fqoXyqme92PE+btf+PgiB/s2p2/gS4CxgXQoQmP3uD+FXfT5mVp9HNk5zo0V2m6PS9Nyx8ZnULftsywZR3glhDNGlRKaSb04g3xmLQ6TBIOnSSxM9bqtmSns1tK1YTYzdR2tyHyaD3pbs16JmyOylt62NP0XJu2VTELZuKiDNfiqV+6yenGJu0UlXfj9Gg54Z9q7nthvWsLVo6rmu3ufnIPd9gw9YV3PHQTnbsD05ktVX1EB1nZnmIsWK300PJs+Ucfiw0stPj8vL6k6Xc/ZFDIdkrsspLPzuLTq/j3g+HRuC01fbxxDeO8r4/v5U1IeQXV1WNV5+6QMkrdfzXk58KaR9ul5dnvn8SSSfxvs+FlvbXaXfz1DeOsueWjazfGZrIw2F18fS3X+exv747ZIGPZcpG7dlWDr5rZ0j2AMPdY7gcHgo3Bi5lNg8hBKVHath580ZMIWbXnBiapvz1Bu76UGjXcXbKzs//62W2Xb+GA3dtCWrf0TTE9/7rCB1NQzxx/K9ITPbveqam7Pzgeyc4cbwJgJsPb+BLf7c0CdvYMcz//vQkrT1jmIwGXi1pJspk4IHDW7jtwLoFu66xKf77xTOcb+9Dr5M43dwN+M6VUa/HbDLwjw/cxKsDHfysoZpxp4Nl8Qk8XleF4DKyUyejxY6gmmZBp9JomdsO/p25hIRRZ8CoM3BjxnbuyNkT9HyFizclRi5J0vWAHfhFKI7894mR2xUbsib7yE6hoYoriU5t4XPf/2VNYdJt56WhF1ges5L8mNUsj1lJ1Ly6U9MYd9r5Rt15DuQUcH1OAZuSM5EVgaz4pLleReVMcze1fSPsLVrO3tUrKLpK3TljcWKxuvj2T0+xZlUW2zctZ93qHKL8qCQVWeXI0xWs3rCMVWuzMRqDP1PfSCz/jdR6DNfeNuMgKcTK8wBTYxaiok0h18YUQjDYPUFeYfC86pf3a2bCSloYilNVUZG9CuaY0MlORVbRG8IrHPBGruPb0Sbsa6+ouJ1eYsMoEFJ1rp09N6wNqV+9PRMcPdrAzYc3UBjg2gshaOsZ53xNNx+4bzeKooIEZtPih9jorI3X6zu4f9f6hYGYrKq4vQrRJiMGvQ5NCCpHhvCoCgfy8hdtQ9E0HLKb6pkOihOXkRMdeMXZfA1hRajoJB3R+tDvr6vxlpOdkiTlAy+/1Y78jUAVKhKS31i5qmkLVUL8IUKIRhBBBH9o/MHJTkmSPi5JUqUkSZUTE4FjXm825kMufr8PYSlYxIlHEEEEf6x42xy5EOKHQogdQogd6elvb1UNAIdiC/j9mDPw9w6Pl0lb8LSo3QOTyCGoFoUQzM6El2Y1ggiudQghQiYHNU3Q2z1BfW1/UNsZi5Mz5R109y8uA3k5xmbtvFTZQmXXoF8bu9fLiZ4uvldVvmRfhRD0O8Z5buAcx0argx/I24BrTtn50vCvsMoW9JIOnaT3veZUnLr5z9AvfG/1aDzdNs6sMoEOQbo5g0xzFonGBAw6PQadDqNOx3NdjcQaTdy2vJhkTzSNPWMLZKdRr0evk/jl+Rq2Ls/h8MYiDm9YRcZl5aJ+/JvzTEzbae8eY2TCysFdq7hxXzE7Nq5YMu7osLv5+IPfZtXaHG68fRPXH14fMFsiQEtFNzaLk503rQ9phuB2eih/uYqD794X0rkVQlBzqpltN64PyR6g+kwLlik7N9wfGnk3M2Hlme+f5Mb7d1C4PrTSbY3lXRx7upwvfPWRkOyFEJw7Uotl2s5d7z8QUhtN0zj5zEXy1+SwalNopKKvTTk3PLA75Niyqqi0Vnazfk9oKs15vP5ECbc8GtqxAPS1DJG9MiPksn1et0z16Wb23LY5JHtVUXnxp2fJLcxgZwj3y+y0nZ9/7XUunmnl2899luQAnIosqzz763J+86sy7HY3e/YXsWnL0tdkasbBd355hqMlLQCsKcwkOSGGO2/YwA17Vy/Y2VwevvtaGU+dr0XVBPnpyUSbjJhNBqJNRqJNRv7mvkM0Wyb48rnTdM/OkBAVxZHO9oVt6JAwGXR4oydwmEZRJZlMcxK/7T+zZN8Mkg6jzoBBMswVbzZwMGMTN2dtC3q+wsU1FyOf9IzO5TVQUbmM8BQaGj6yUxWaj/REw6PIDDkcVE2XogmJvJhV5JpXkWzKQhUCRVNRNI1v1J8nMyaOgzkr2ZKUTQwmXxpbVUVWVCZsDr5zvIw9q5azv2gFuwrziL9s1crQ2Cx2h4cnX6jwHeOmFezYuJxsP+pOr0fm8W8eo2jdMjZtW0FGdlLQY3fYXESZTWGlGnU7PWGRd2+kNqR91klCSujq1NkpO0ajPmSSTAjBSN8UOSGkMbi8X5YpO8npoStOVVVD9iiYY0KvcK8qKjr9W092uh0ezGEoTt8I3si1dzu9xISQSx9856q6tJMdB1aHdPwjQzMcfbWe5ORY7n0gcBqAnoEpXi9p4dCeIlKTYzEZDSQs0a8Zu4tj9e2szkln0/Js3LKCW5ZxeWUyEuIwGvQIIWicGKd2bITHNm651H9Nw6P6lN4uxUuztY8EcxS7UhendBBCoAoNr6YgCwVFU/FqCtH6KJJModU4XQpvKdkpSdJTwCEgDRgD/kkI8bg/+z9EzU636sKsX9pxCCHwaCpmvf8RcSiE6Py2IvH0CCKI4K2AP0f+poRWhBAPvxnbeSvhz4mDj8gM5MQhNEJ0flsRRBBBBG8n/iSUnQBeLbAq0+oNnlJ20h6cnJyYtuPxBq/7KIRgaiIwwRpBBH/qcLtlervHg9ppmqCzd4KqhsDEqKyq1PUMc7Smza+NEIKOqSl+XlfNqH3p36hL8VI60cove06/c5SdbydOjj2LXbHMKTsvkZs+olM3916/8N7q1fhd9wguxYJNmSYjOocs8zJSTKkYdXr0c+rOi+MDdFomuTWvmGwtgb6RWV9NT70eg16HUa/nhZpm4qJMHF5fxOH1RaxITVro15MvVTI1a2dqxkFJZRf7t6/kxj3F7N2aT9QSwgSnw8Mn3/8DVuSnc+jweq6/aR0JQbLINVV0M9o3yYG7t4ZEYnndXqqON7D3ru0hn9+Omh7ikmLJLghNfDPaN8lI7wRbDwYuxzUPRVY58XQ563auJK8oK6Q2E8MzHP9tOQ9//raQ7AF6mof+f3vnHSfHVeX77+00PT055xw1yjlnybLlbGNjA45gYxweLLDsLrDvbeLtsjyWXdKyZBsw2OCcg2wFK+esyTmnnpnO3VX3/dEzijPd1bIleaz6fj7z6Z7ue6tupdNV53fPObQ3dLPsBu3CUs3BJqJjosgr155lsXpfA6WzCyMKpNnx6n7mXzMzopJ6W5/bzYrbF2pu39XUi713mMr5JZraSylpONpCyYzw0bZjHNhyEovVzLSFpWHbKgGFl3+3gx1vH+NbP74nbMbPPTtqeeqXW6ir6WLO/GL+7w/GF7r9foU/v7af3z2/hxGHh8LcZMqKMli3vJKl885su6pKXtxznB++8gGDTjep8Tae/eAI0VHm02Ln49cvwSn9/NOW99jS3IQA/nz8GEIIooxGokxmrCYTXvMw7cYmPLiJM1l5t+vI6cjOYBRnUNi0GEyYhTH4ajBhMZpYmlrJqoyPPvh90hnyivjZeBUPklFBUyooqMjTAmdQAB0TP20mPwsy4ul0D9PispNpTSbLCpnWeAyY8EsVRVWRSBQpcQS8RMeZWFVZDDIYxeVXVPyKgtloJM4ahdFgwOsPnOMPnzc9n+ERN3uPtlCQk0xmWjyxNgswvqvFYDRQWZVDWWUWeQWpWK3hBbas/BRSsxI1GwBzlJmqCGdH5JRmRiSmZuSnEJOgTbQEMJmNLNk4C4NRuwsqLTuJtZ9aoLk9QOGUbJIzJk4jPB5lswrweyMrYFE2pzDilLRVC8siMuIAM8LUrTyf5KxE4pK1i2pCCIo1pgAYY/aKSryu0MVWxjCajNx831IKyzOJTwqf9nbBkjJKyjJ5+7XDE11CAJjNRj5zywJWL6ngrS0nsFktzJ9VQFzMuUKnwSC4bdE0rplVxntH6nB6/dw4fwoub1DodHn9xEdbSbfE8pubb6duoJ/Xa2u4Z8YsEqxWfEoAT+DMn9vvp9HVjVOMcEf+mVlhUkr8oxHlPjWAf1TkDL4PfCihMxRXRRpbAGdgmGhj7ISBQcM+D/GWidV3KSXegII1TCh9QFExRVhYV0dHR0cLl1TsnAzEmEJPQwtlxGFUENWQD0U34jo6Opebq8bqKDIQUpTwKqG/B3B4vGHX4/H5cbrDP25KKenpmji1ro6OThCnI/x1B+B0edl/pDlsGun+YSdvH6jBHWJSgtPn4/2GBva2jR8BKqWk2dnHs8076fFc+et40t2R7+5/FbfiwIABcVrsDL4Kzv3fIAyM+BReb+lEotDqOkaGNY+s6AJSo7KCUVcGA0ZhoM/j5On6/VyTU0GBIYXBfg9mkwmzwYDZaMBkNLKnqZWGvkHWTynlmqoyytPPZEB88f0jDA67MQjBU6/sYV5VHqsXlLNsdjGx4wTkuFw+nnj4N6RnJLBqbRUr1kwhLUy5tBP7G2mq7mT59bM0ldfyef2c2FnDrFXaIzUbj7USEx9Ner624BuP00tHQ3dE/tUTe+pJyUokIy9FU3uf18/O1w+zMkxtyLMZsTtpPtnOtLOi+8Ix2DNEwBcgLVfbuAC6mnrwefzkV+Zo7nNg01FmrJiCScMT3hi7Xz/Iwo2zNbfvax9guH+E4gjEy8NbTlC5oFRznc/Opl7cDg/F0/I0tT+wrZrNLx/gC9+8ifik0L7i9pZ+nvr5Zk4cbiW3IIV//fE9E7bdfaCRX/5+G7WNPcTHRbNqSTkrFpUxb1bhOe2ONHbyvec2c7SpiyizkUUVBdisFmxRZmKiLNy7bi5Wq5kf7dzJkwcP4ldVipKSSLPZsJrNRJtMWE0mFJOfWllHr9qPQPBS6z6EEJhFsAZwlNEcfDWYsBhG3xuDgueClFKWpGk/J7Uy6Qx5hrUQj+I8LWbKs6I4VakgUQlI32nB0634yYwJ4FW8dHn7UbDgk9GoJCJEHD4lQEBKBn0u+jxOGkb6scVEkZ+STIzJMip2KgQUlYCi4vL56He4aB2wU5icSNToxViYlUx8jIsRpxezyYjBYMDt8TPi8o5ryA0GQWyclczsBGwxFk3FKOITY8gqSMWsUYw0W0xkFWVEtH9TshIxawzrBoiyWcgoiCx3TuEU7UYPwBJlZtri8DMjziYuMYbCKm0pAMZITIsnoCFPzjnrSY5DCUTWJ7skI6LamAD5Ee6zmEQbpggF1ayi9Ij6ZBWm4dXw9DnG7GXlWKLMmiJ6c/JTeOzr1/Hu64fxhhGgF84porQojXe2nKS6rov1K6tIGUfonVGUxS/+1x1sPdbAjpNNPHzdIjyjQqfL48MWZcZmsfB3K1dy7+zZvFZdTWVaGnOys/H4/UGRc0zw9M+l0ztAt9rLHQWLSDDbCEgFrxIUNb2jQqdX9Z8jeKZbIxPgtXLViJ1uxYGUEptp/BwPdq+baJOZqBCBQXaXh4ToqJBBP15fAKPRENZXrqoSIfQAIh0dHe1c9WJntDH0vNXEqPB3CYm28DklJiokcT4Gg27AdXR0PhquGrEzmD5zYveFKiVqmKcTXyC8IArg8mh73BzSa3bq6HxkSCnp7B5iIEx6aEVVOdnSTUvPYMhlNQ4M8k5t3YRt3AEf23tqOTDQdLFD/siYdHfkR+zv4lWcGIThjLgpDAiMQfHzHOHTgMOv8l5HB0ZhoNl5gDhzEtnRpWRE52M2mEdrdhowCsF/Ht/M7JRcSk0ZKC6BxWgKCp0GA0aDgX6niz/tP8L6ylKuqSxlek4mhlHXyNu7TjHk8GA2GXhh81HiY6ysmVfGyrmlJMdfKEy6XT7+4dvP4XL5WLmqkhWrp5Cbmxxy208caKLmSCsrNs4kOYwwOkZPaz9pucmaXTjtdZ1Ex1pJzkzS1B7g6AenmL6sUnP7/s5BjGYjianatkFKSd3hFspmaRfuFEWlq7GHnFJt0aNjHNtezbSlF2azm4i+9gH8Xj9Zxdq1iOM7qqlcWIrRqN1PfmTrCWasqArfcJTBniEcg07yKrI19zm1p47imQWaU996nF4Ge4a0RwG39LPpuT3c/OBKYsOI9W6Xl+ee2sHR/U3Exkfz99+/a8K27Z2D/OqpDzh4pIWBQSe33zSXVcsrmHFemuS+ISc/eukD3j9Yh8PjY/n0IjIS44iJthATZeH25dNJjI3mxRMn+cEH2+kYHiEjNpZnjx4j2mQi2mwm2mzCZBScUpo46W1GQaUgJoWUqFgso9GcFoOJKOPo62hEZ9To57OTC5iXUqRpf0XCpDPkQReJPC1sKjJAYFTwlFI9R/RUpYoz4MerOlGkxK0MMRIYxKP4cQR8JJpzCIxGdgakSpdrmN1KEy5bgBxDCjmWBPyKiscfIKCq9Iw46Bga4URnDykxNjLj48gYzUlus1pwe/34Ayoer5+AotLaY6exvZ+kuOgLDakAIcBoFLjcPnq6h8jKSgwZ6m00GTFbTLhd2qZjAZgspogyMlqslojEToDYxMii1WITYyISCIUQpOVo/2EBMBoNJEUY2QkQo2E20NlYrGZEhG6y2ERbxNpIXJL2NMEQjKCNNO2tLS46olQD1pgoUrK1H5fM/BTmra4iWsO4om1R3H7vEpJSYhm2h35yzclK4q8eXc+mrSd5691jTJ2STXzchW7Q1IQYvv3ZdayfU84be06xdk4ZqfExOD0+XB4fJpMRIQS3Tq1ieWEBb1TXMuB28ekZ00ejOYMRnW6/n0WBAuwBByPmIcrjspidnI9XDeBTgkKnTw3gVUZfRz/3qQHizNpS/kbKVSN2Sinp9TaRFlWAGCe6068qdLqGyY+d+MQcdLmJMpmwjZM75Zx2wy6SxrkLPx+3y0d0BLmvdXR0wqOq8hOrQV31YqcQgnTrxI80ZoMxpBEHSLJpyymixYgDuhHX0bkEfFKNeCiuGrFTC+GeTlSN9QYDGt0GHk/4dLc6Ojra8fsVevvCp4cednqobg2dHtft9/NBYzMO7/iTF6SUNDv6ea/z1EWN9aPkI7kjF0JcC/wXYAR+KaX8t49iueNRP7Idn+o6LWaeLXKKUQFUjEZ3CmHA6VfY2duNEQO93mr80kVOdCUZ1lKijFEYhGFU8BQ833wYgCnWbKIDVmxmCyaDCKa6NQTLef3Xlh3Myc1mfUUp8/JzMI1mvtt+pIFhpxeT0cDeky00dw2yek4pq+aWkZl84dx1j8fPr3+9lb17G1ixooIVKyopLk4L6Ts9eaiFY/saWX7tdDLDCKNjdDT2kFmQqjlDX09rH1ZbFPEpE9dUPJ/6Q02UnBdFFwopJY3HWiOKBu3vtGM0GkjUKPIC1B9upmSmdoEUIt8We28wGjQ1R3s0aMORZgqn5UWUNTHScY0MOnANuyMK1mo63kpueVZEEad1h5oo1Tguj8vHjtcPsujamWHLw0kp2fLmUQ7uqiMqysyj37xxwrZuj49n/7KHvfsaqanrZvHCEj7z6UVUnJeO2B9Q+OOmg7y26yT1HX1MLcxkXkUeMdEWYq0WNiyoJCHGyrGubr63+QP2trSBEGyoKMVmNhNtNmMzB1PZNgS62OWoYTDgJMMax5+b9xM1KnJGGc1n3p8lfFqNZqYmZjM9KbLgLi18aEMuhDACPwHWA23AXiHEy1LKEx922ePhV924lSGkVE8LmvK0wKlc8LnD76du2BtMUevvZ9jfR7PDTqK5k9SoMiSgjNbXqxnqpsHRR7PFTibJTEnMRFUlAXVUEFVV2uxD2N0eAqqK2Whgbl7woDjdPvqGnAQUlb4hJ9UtPcTHWImymLhu0RSs5wmIUkpcLi/9Aw6am/s5ebKD9PR44sYRacbwevwM9o3Q2tBLWhhhdAznsBuP04ctxHLPRvErEUcqeiKI7oPRTJIR9lECAVQ1sgdIn8cfcek9TwRCcnBcasTRoD6PH6nKiJ6HvRqntJ4zLl9kKXmD+yuiLhEdR6vNQtHUXE2zYoQQLFlbRcCv0NtlD9k22mrh059aSGZGIq+/dYSUlLhxj7nZZORz6+cyrSiT13adJMZqYW5FLk63D6fHdzpb7rTMDH50y/W8XVPP+3UNPLxwPopUcfmCQqfL7yfTH8ucpAJkrJdBn4tPF87DqwTwKP7TAqdXGf1TA3gVP141WFv4UvChxU4hxGLgH6SUG0b//zsAKeW/TtTnSoidAL2eeuLMaViN49/VVQ91UxibMmF0p19RaBkcojglKaRx6BoYITXehilMGLbd7iIuzhrRTAEdHZ3Q+HwBLBoC8yZjfd1LKXbmAK1n/d8GaC9lchlJs4aullKREHousNlopCQ1vEtjPFfKeCQmRjbVTUdHJzxajDh8stJjXLZbQSHEw0KIfUKIfb29vZdrtR85Wp5gVFXbU46iqB+Len86Op8knE5v2OtKSklT5wCKOrGrQ0pJy6CdlkH7hG3cAT8fdNfj8Efmkvuo+SjuyNuBs/NY5o5+dg5Syp8DP4ega+WiV+Y6QED1nBY1BWJU5DSeJ3gGX92KwqGBHozCiEcZoNO1nyzbdLKip2I12YK9RFDQPDbYwa7eBqbH5JNmSCDOYsUgxGhkp8AoDDx39DgA68tLWVyQR5QpuAsP1rbh9PgxGgwMDDt55v3DrJlTyurZpRRkXDit0ev1s2NXHU/+fjuLFpawYmk5lRXZIadOVR9tZd/2WpZfM438Ym3RdG313WTmp2ou32bvHcZiNWOL016+rb2uk5xS7XUuATrqu8ku0R4NOdw/gsFoiCj4qL2uK+LIzki3xWF3ogQUEjRGqQJ0NvaQWRha2L5gXPXd5ESwv9wOD26Hh+TMRM19upp6SctLicjV11HfRXaJtn0speTU/kaKp+ZqSpVbd6KDfduqMRgEdz60KuRyN28+xc6ddVTXdGI0Gvj7v7+ZosILhd4dRxt5fvMRDtd2YDAI7lo/h9hoC3G2KJbNCKacHnC6+NG2Xbxf20DH8AjrK0rJTYzHZjZjswRFz0HVwfv2k9S6ehDAuuxKokYFTYvRiNVoxnqW8Dn2viw+LeyT/8XwURjyvUCZEKKIoAG/Cxi/UupHwKC3GbcycJ6oeUbklKP1O8deR/wKm7sDqFISkAHsvg6MopdY0ylSrZUYRBSKVFGkSq/HwQc9dRyUnaQryUxPysEkjGcETyk50tlNff8AbUPD9Dgc3D59KkaDgcbOAboGRgioKg63j+NNXXj9AYYcbu5YNZPs1HOjDAMBlfqGXtraB9m7rxGA6GjLuCffGAO9I1QfbSMmzkpSSqymnORt9d0YDIJsjWHUQ33DRMdGR2TIO+q7IzJ+iqLS3dwbkSEfGXRGbMi7m3rILsmIyGB2NvREtC3OIRc+jz8iQ97d0kd6XkpEqWw7G3siMuSuETcjA86IDHlvWz/JmQkYjdrjG4I/yNoMuRCC+KQYzZGwRRWZdLcN0NIQ+gleCMHy5eUYTQbsQy48Hj9O5/h3yIunFZIUZ+O1HSeoaekhLz2REZeH3kEHgdFU0skxNr6xdjnz83N45Xg1K0oKyU9KCNb29Ptx+fzEqTZuSJpNQrmRLV11fLFiGaqUeEZFzaDwOSpyKgFcip9Bn4vUqI9xzU4hxEbgPwlOP/y1lPI7odpfKbFzxN+JRxkhNap03OjOJkcfRmEgL2ZiP/jxrm4Kk5OIsUx8sg8MuwgoKulhwqqdTi9uj4/UCKb66ejohGZkxBNy9tcYWuvrfpxE0YnEzqsmRF9HR0dnsjORIdfnvV1hdLFTR+ejR0vFLY/Xz4jTE7KNNxCgvrc/ZJsWxyAtjoGIxvdRM+lyrfR7qlGk7yyR0zDqJjlX5Bx771NUqof7MBqMGIGaoRdItVaQbZuN1ZSA8aw0tl4lwM9q32OqLZ+CqAySomwYDeL090aDgaNdXWxvbmF9aQnLiwpPu1hq2npx+/ynI0B/9upOqgoyWDOrlLKc1AsezXz+ANU1Xfzp+b2kp8WxfHEZM6blhXzUqznezs7Np1i6toqSikxNj3utdd1k5CZjsWrLaOgcdmMyGzXXbQQY6BqMKO3txfRxO9wgBNEx2rPHDXbbScpIjHBc9oj8yh6XF1VRI9IUfN5gQFAk+3h4wIHVFqX5OEop6esYJDU7dMzD2Qx2D5GYHh+RGyHS/dXfZSc+ORazhimC9n4HBz6oAWDNzXNCtq2r7Wbb1lPU1nTR2NDLP/zz7VRUXqh1tHXbefbdQxypbae6pZcv3LyInPQE4m1WZlXkYLMGyzv+ad8R3jpZy6G2TqZkprGitIgYS1DstFksKAaF9wZOcWykgzaXnbXZ5WTbErAaTFhNZqzGYLWx6LNET6vRRGFsMvmx2qKyI2HSGfIO125cgb5xBE457mfDfoV3ug2jhSPAFRhAkS1YjftJtJRhNiaMfhcUM7f11LDJWU+yP5mqhBziTNEoUkVVJYqU9DmdbG9uYX97Owc6OvnSogUkRUez+1QL7X1DKKqKokiONXVxoLaN2rZe7lw5k4VTzg0V93oDbNp6ivrGHvYfaqKndwSHw8vyJWUTXkhd7YNsefMoToeH626bR1FZePHr6K46unOSmLtqiqYLtLOxh9gEG5khRNfzOb69muW3L9LcXgkonNpTx5Kb5mvu093ch9FkIK9Ce3jz8R3VLLl5fkSh8Cd21rDs1gWa2/d3DOLz+CnSWIAYggKpyWyK8MdyiFwNx3sMIQQOu4u0HO1Go/5oC9MWl0eU/vb4jmqW36Y9bERV1GBUqwYSkmNITIml+khr2LbFJenY7U6aGnrxev24JojQzc1I5LbVM7BaTAwMu4iNttA36KShvZ+KwnRsVgsmg4FPz51OXlICLx89hcVkpDIzDZfPh8vnp9fhxOXzUWnMYcP0Sl5vPc6qrDIKY1PwKn48agBPwI9nNNJz2OfBo/hxK34UKS+JIb+qfOSqDNDq2EambS5R40R3OvwejtjbmJtcQJRx/Duf+v7gI1Rx8sR3Ooqqcri+g+lFWZjDzEw4VdNJSVG6poLKfn8AcwR5MHR0rkZ6e4ZJTokNO40yeNOlYglzTalSni4gMxGXSxDVxU4dHR2dSY4uduro6Oich5b6ul1DI6fnmI+HVwlQM3Rlo9Un3XP6iK8FSQDBqMB5WtwUBBMxitHUtgKBAb+q0uYewogBozDR7nwbgzCSZVuEzZSOUQTFTMPo6x8at2ElmikxeaRHx49+HhQ6DULgDQT4r507WVlYyOriYhKsQfGtrc+OL6BgFAaMRsGre07i8yusnlnC1PzMCyI2AwGF1o5Bdu6tp73LzvJFZcyZkR/yMa/2VAdb3j7OklWVVE7L0eT7ba7pJCM3GatNm99TSomqyoii+1wj7ojEvovp4/P6EUJoEsku57jkaI76SPzwY1kZI/GRD/U7iLKaNfuvpZT0d9lJSInTvM/8vgA+j5+YeO3bH+n+UlUVn8ev6XxUAgon9jehKiozl5SFbDtkd7F9azUNdd3U13Zz461zWXPNtAvauT1+Xt16jMM1HRyt7WB2ZS7rF1WQEGelND8N62j1r10NLbx85BR7m9pweH08vHw+MZZgbc+YKDNWs4kdg40cGGpjf18rUxIzWJpZdFrctBrNRJsufJ9liycj+qOPG5l0hrxx5EXcgW4k8rSwydnRnKgwJnwiGfJJXuu0Bb+REFA9+KUPAzuJMedjNWYElyAlKiqNjl46+7xYXPEUxaaTFpWAlEGhU5USRVXZ0dLCm7W1LM3P52vLljElLY2Xd5+gpcceXI6q0tA1QEPXAFuPNXDrkmncuWIm5rOK7brcPn7/5110dNk5Xt3JsVMdrFlWyadvmXdBytsxutrtvPinXTTUdnHtzXNYvrYqrF9u22uHscVZueFzSzXNeFACCvs3HWfBhhmafX47Xt7Hus8u19R2bB27Xj3AmruXau7TcqINo9lI0TTtOcx3vLyPtZ9ZFpHvcuerB1gbwbgATu1toGphqeb2g73DDA84KIsgV3rD8TbyyjI0G3IhBCf3NrD4ulma1zE84IjYkEd67Ps77bTXdjFrVfhC0mM1ag/tqAlryOMToiksTuPIwWZOnWjn5tsv8D4AEG01s2JuKQ63j1ON3QgBR+s6GXZ4uP/mOKzJwWtkQWEwX7zRIDje0UNyTDROr58O+zBOnw+n10eU2cQDVfNJj47FbDAwJyUHjxLAHfDjUfwMel24FT/uQDC60634WZJRxMa8KZr3l1auOh95h3MLNlMmCZbycS/w97qOUR6fTa5tfGV5xOtlb3s7i/LysJknNowH6trITkkgMyn0r29NfTcJ8dFkpIUP8R62u7BEmbBGcCeno3O1MTjgQEpITgkdWS2lZNjpISE29A+XLxDAbDSGvCHQIoh+FOhip46Ojs4kRxc7dXR0dM5DUcOnkvYrCg5P6DS1bY4hAiFS4l5qJp2P3Kv0nzVn03COsBkUOg0gRsVPDARUyVDAFZRDhWDYe5wh7zEyYlYQZ84/I3QSFDV39FVTM9TFnIRScmNSMAgwimC0pnFU+PzlwX2k22JYU1xCmi2YzWzQ4UZRVQyj6W5Ptfew5VgDq6eXMLs454KITUVRGRxy0ds/wvNvHmLZ/FIWzCog2jqx26S+tou3XzvCkhXlTJuRj9EU/ne48VQn6TmJxGgUpFRVRVWk5rS3AAF/IKI6jxD0k0eS/e9iRMVI13ExXIw47HX7EEJojtIEsPeNEB0TpVkglVLS12knMVW72Onz+vH7AthirZp1hYvZx5H06W4bwOv2kV8WOsOiElA5tL+Rxvoemht6Wba6koVLyy9oJ6Vk1+EmDp5s43hdJz5/gMc/s4KEuGhyMhJPx320Dw7xyqFT7Gtq42BrJw8tn09BaiIxURZioyzERkVR6+xla28ju7qbcfi9PDRlEdEmE9Emc1D0NJmJNo7+P/pZitVGvEV7dLJWJp0hrx74Ke5A51nCphoUPk+LnjL4SvBzu0/wfGcqUoIEVKkSkB6k3I3FmIbVlAUYUEaXM+J3U9/twDe8m0xrEpnWJECgSnU0AlTSZLfT73ZRsH8vX128lBvKKvjl27tp7BlElRKpShxeH8eau3hx13GunVvB49cvITn2TNrZEaeH7/70LfwBlX1Hmtm8s4Zl80t5+LPLyEpPGHfb21sGeOGZ3ezcVs2662Zw5+eWYA1jDF79ww5UVfKZx9eRlpUYdv+qiuSF/9nEzV9YrdnQvP37D9j4wCpNbSF4Ib/7+21suF97n+p9DZgtRkpmFmru8/bvt3HtfSsjEjur9zVQMjNf8w+TEIJNz+5k7R0LNRun3vZBTh1oZM2nFmj+YTq0rZqE1FhmL6/UPK73/rKHtXcsJFXDcQcY7Bmm6WQ7C6+Zoak9wFtPbWXjg6s1t+9p6aOluoN567Wtw+/1s2fT8bCG3GgykJoezwebT7H5nWPMnFs4bjshBFOKM2jpHGRoxI3RaODdndUMjbh57LMryEgJalXZifEsLy/E7nZT3d2HwSBoGxjC6fPj8PpwerxER1m4Zf5UjEJwpL+T3Jh43KNi56DXjTsQFDrdih9PICh2rs4u4bbi6Zr3l1auOh/5oOco7kAnadGLMI8T3XlgoIGAVJiVVITFMP7F/FpNNZWpqRQnJU9oJOo6+xhwuJldlB0yurO7b5jWjkFmTskNG93Z0z2Ex+0jr+DC3C0T8XFKwamjczkYHnKhBFSSNIid3f0jZIbJJR9QVPyKQrRl4hsbv6pgGn1yv5ToYqeOjo7OJEcXO3V0dHQuEq8/EPp7JcCwL3RK3EvJpPORK6p39PFFnBXdGWp+p4pfVTCIoPypSidtw0+TFrOaWPOFc8l7PUO82r6HxSlTKI7NPB3ReXa795saaB6ys764lJy44GOZLxA80GJUEPUHVH70xnYWlxewoCwXi+ncXS2lxOcL9vnFM9upLMlk0awiYkMEfHR22PnLn3axaGkZM2cXaKoWXneig/SsBOKTtJWYUlUVJaBGFEF5NSOlRAmoEYnDHrcPARFFdg72jmCLiyIqhBh+/rh6OwZJTk/QPDafx4+qqkRFWyJyEVxK953H5UMJKJqClNpb+mms66a1qY/pcwqYNmv8gKuWjgEOHGvlZF0n1Q09fPmB1eRnJ5MYH31atHb7/Lx7vI79Te3sb2qnKjudG2ZNIdZqIc5qISYqCofq5e32GnZ2tbCvp42Hpy4kLzYBm8mCzWTGajJd8D7WbCHK+NFfWx9qiUKIO4B/AKYAC6SUl9xfcqLv27gDrUjkqNCpEpQxx2fQb+KPHemnxU6JQFG9SPZjEjaiTJkYDWdUZCklh9oH+bfBfcSZokmLSsQkjOesYcTrpWV4iH/bsY3Pz5rLY/MW8t3nN1PXFZxRMyaK1nX289SWA8wpyuYbt6xkat4ZwcY+7OZv//1FpITGtn7++Mp+KorSefSeFcybPv4JWHOqk5ef388brxxi0dIyHnp0LVnZiSH313O/3kpPp537v7KB6fOLwu5fJaDyo799hnu+vpG0bG35whuOtRIVbYmopmTDsRaKpuZpNgAn99RhMhspmx1+G8boqO/GbDVHlMp1+2sHqZpfQlK6thqcQgh+9++vcNsj60gI45Mdo7Oxl03P7eXuL2/QHEW59dWDqIrKDfcu0/QjK4Tgj//1NqtvncuMxaGjIsfo6xxky4v7ue2RtZp/ZA5/cIqS6fnEaqgfC0Gxs+FoC4uuD51ffAyXw82WF/Zx6xfXhm1rtpg4caSVN17YT1Jy7ISGPDUpFpPRQFPbAO3ddl7ddBT7sIuvPbSO7NH89dEWM1NzMmjoHcDjC+ALKOxvasPh8eHweHF4fcRGWbhr7Uz6PS5q7X3YTGZG/F563A5cY0JnwH/O+2sLKvhs+WxN2x4JH8pHLoSYAqjA/wBf12rIr6SP3K8M0zbyDKnRy4m1VFxgSHo8dnb0HWdhyhSyosc3ADvbWnD5/SzOzZ8wutPt8/Pa/lMsqywMGd2pqpI3t55gztQ8MsNEd/b2DFNzqpM584qItmm70Dxunx4JqnNV4XR48PsVEjU8hTa29pGXnRyyoIuqSgZdblJiJ/6xUlQVn6oQbdI+pfRiuKRipxBiM5PEkOvo6OhMVq642CmEeFgIsU8Isa+398qmfNTR0dGJBFWVYSNAXf7wKXEvFWGdbUKId4HxZuN/S0r5ktYVSSl/Dvwcgnfkmkd4Cega+TM2Sxlxlhmj9T7PIKXkhbatVCUUUh6Xh0Fc+FvX6Rjh5dqTrCsspSRpYv/rn3YcJjUuhiUVBdhCzEF9Y9sJVFWyZHYRSfETP76pquSpJ7dRXpHFnDmFYYOBAGqOt5GakUByqrbUmaqqEvApEUUdfpKIVLiTUhLwKxGJw57RMmRaUwsDDPQMY4uzanaTSSnpbhsgLStRc6CS1+NDSj5WrrhIjofL6aW9uY/O1gGy8pIpqxq/LKDD6eV4TQen6ro4VdfNykVlrF5aQdRZx1BKyeHmTvY1tHGgqYMhl4evXb+c+OgoYq1RxFmjMBjhndY6dna1sKurhWkpmVxfWEG0yYzNZCHaZCbGbMZmMhM9KnqaIohMjoSwZ5+Uct0lWfNFcqLnMTyB8DX8xhj0m3iq49zfISn9SN5AYCbKlIHJkMCYYCoQHO0YoafPgtlgIi0qEZvp3JBaCZzo6+Ffd21lbUEx/2fZGn762k7qu8+tpN095GDA4SIl1sZXr1/OTXPP1M0cGHLxV//2XHCMwy56BxzE2qL4/O2L+dSG2eP67LZsPsnzf9mL0+mlsDCVLz2+nnnzQot/Lzy1gwO76vjcl9aw8Y4FYUPJA36Vv7v7p9z/tzcwfWFJyLZjHN9Tj8PuYuE12iPWdr99hOmLy7HFaQtXVlWVHa8dZOkNczRf2A3HWnGNeJimUewDeO23WymbVUDF7EJN7YUQfPfxJ7nriWsona6tbmdLXTe/+/4bfOHbN1MQJmJxjDf+tIuedjv3fe1akjUIsUIIfvjNv7Bw3VRu+OxiTca8p22Q333/DT7/zRvJyEvRNK5tL+8nryyTwinaaql2N/fSdKKNhddpE/y8bh9bXtjLhs8uC9tWCSjs2VrDi0/v5At/tWFCQx5lMeFy+Th0vI19h5txuX28+OYh/v4r15MzGgUrhCAjMXjz09Y/hBDwxqFqRjxeHB4fI24vCTYrT9yyhFp73+kJDrX2flwBPy6/L/ga8OMK+HD5g2LnLSVTebBq/BS7H4ar0kfeNvRLrKZcEqOXYjKce6eqSpVnW96jPD6f6QnFmMeJ7uxwDPN6fQ1rCoopTpz4jvyFvcfJSYoPRncaJ76QNu+tJSbawqzK3JBRoKoqee2Vg0yfmUeBxujOrvZB0jLiNd+VjZ0PejTopeNipuupqhpRnpmL7fNJwO3y4vMGSNAgdrZ32jGZDCHTSEspae0fIj81MWQbu9dDkjWyQiaRcknETiHErcCPgDTADhySUm4I1+9KG3IdHR2dychEhvxDzSOXUr4AvPBhlqGjo6PzSSCgqhjPCx68XFyV4Xsjnt2AJDZqHkJcuAv29B8j2hhFVUIxRnGhS0JKye9OHGReZi5TktMmPHB7G9roHXGyrLyA+OiJfcE1zT0cr+9i2exi0pJCB5W8v/kkRqNg7pwiYjSU/Tp1tJWU9HjSMsbPqHg+wZqKAawa56l/0rgYsdPvC2CZoDzfeLidQbEzWmPZNoDeLjtx8TbNx0VKSWfrAOlZiZojOz1uH1KVEY3r44SUkqEBJz2ddmyxVnILU8dtp6qS1o4Bquu6qanvJi7Wyr13LrowpmTIwYGGdg40dnCkuZOvXL+MwrQk4qKjsI0e78O9XezsbGFnZyt2r5u/nrscm9lMjNkSfDUFX61G0yU18JPOkDf0fhFvBGLngN/Ek53niZ2oSOlDYMRkSMZkTDtn9kp1t5fmXgMGYSDJEkeCOY7zD0HLsJ0Rv4/SxBT+9+LVvL79FHXdA+f4mF0+H819dkxGA/csnc2X1i4iJip4IQ4MufjK954HwB9QaGjvh9/AjSum8uidy0keJ1LuvfdP8D+/eJ/e3hFsNgv33buMW2+eiymE//ulp3ez+c2jbPzUPO5/fC1xYSLwAn6VL177Pe54eDXX3b1IU57tfe+foOF4G7c8tFqzQXv9qW3MXFZBTnG6pvaqqvLMf77JrY+s02zMTuytp+FYG9fdu1xzvvDff/8NMvNTWHfHAk0XnhCCr9/xI255cCWrb9YmxLY19vKdx5/iob+7kSXXTNPU5/U/7ubg9loe/uYNVM0p1DSu7zzxe8qn5XDf164lMTl81GlP+yD/9/Gn+OK3b2b2sgtzeY/Hq09uJSE5lmU3zNa0HT2t/TQca2WRxlqiUkoObTnJbA01Pv2+AFvePMozv9jCvU+sm9CQA3T3DrNlRw079tSRkR7P1h01/NPf3kRO1ploZovJyIDDzZHmTuo6+3hl3wmG3V6G3V7cXj9ZSXF8/Y6VSKDH5SCgqnzQ0YxzTOj0B4VO56jQCXBH2TQemDZX07ZHwlWX/VBKid39Jt5AIwnWtVjHybeyqXsPXsXHvOQq0q0XipmqlPzo4E6mp2awODt/wmiuXXUttPTbWVFZRGbCxNP/qpt6OFrXwdJZxWSFSam5ecspjEbBvLlFRGuYJlZ9rJ20zHjN0w+llHg9/oimoH2SUuVezLZEWlzB5w1gNIqI+jhH3BEVfABwObzYYrXfXSsBBWEQk14g9Xn9eNx+4hPDpw3o7R+hq3uI6VW5IdvVd/WTm5JAVIg89W0jQ+TGaXvyvVj0NLY6Ojo6k5wrHtmpo6Oj80nnStwYwyT0kX8U+AMdeP3V2KxLMIgLHz3bXF30eQeZmlCK2TC+22RzWwMJFisz07IwTPC42+dw8kFNEysqikiOmfgxz+P18+oHx1kyo4jstNCPZg2NvTQ09bJgXhHxGupwHj/cSnJKLFm52jIZqqqK2+UjJlZ7XcFPkmsl0rnXUkq8bn9E4rDT4QEJMRqDoQB6OuzEJkRj0yhESilpb+ojIydJc9Spx+VDVWVE7piPG6qqMmJ3I6UkMUQ2SpfbR31DD3UNPbR32nno/hXnRHZCULs62dbD4aZODjd2sLiygPUzy4i1RmEwBM/3XpeT3Z2t7O5oY29XG3+9YDm5cfHEmC2nBc9Lkbb2fCadIW/texh/oPmsTyQgRv8McDpXOYCBAb+J33SljH5/BlV1IsSvMRrisRizMAhLsJcQ1PUGON7lxyAMxJhsJJsTMBoMSBlcvEAw4HHR4RwhLTqGh6fNp/ZUHw09g6eXLwRICSc7exAClpcV8bcbV1KYGjSoA8Muvvz950+3b2zv599/9x4zSrP56mdXUVV0YcTfe1tO8tQfttPU0o/BILhm7VS++PlVJCVOHPjw8rN72Pz2MabNzufRr19HSXnoSMKAX+GBtf/O8munc/9fbSBOg59x97vH2fLyAb7wrZtJydTmI/z991+nfGY+C9ZN09ReUVS+/5Xfcd83btAcdXh4Ry3bXj3Ifd+4QdN2APz8X17CYDDwua9swKbhx0wIwSPXf5/l183kM4+t1TTjo72pj69/9n+486GV3PnQSk0C8Rt/3sPrz+7h/q9sYMPtc8P+2Agh+Kcnfk9MnJVHv30TZVPDR152dwzy1Tt/wueeWM9N9yzR5MN/5sfv4PX6ueux9ZrSOkgp2b/pOHPXTtX847/5z7uYs2Yq8SmhdR4pJTveOc6vvvcGn/r8Cq6/e9GEbZtb+3nlzcO8v/UUZrORQ0db+Mdv3nyO2OlXFJp7Btl8rJ59dW0MOty8vu8UTq8PCWQlxvGtz6ylz+3iWF83DUODvN/SgMvvx+H3nX71qwpjN+p3VEzjgenaUvhGwifCRx7chrG/YH5yOfb/Wd+N5S73B1roH/ktMda1xFiXYTDYUOVYG2hwtLKz/yDzkqYzJb4Ek8F4zrok8JfaYzj8XtbklVAYP/7dbp/DyW8+2M/K8iJmF0wc3enx+fnli7tYMK2A2eU5IaM7a+u72bO3gWVLysjPSwl7MezbWYc12sKU6bmaZm5IKels6Se7YGLF/3x83gBmizGiu/LLEal4MRXeLybt79CAk4RkbYU7xtbhcflC3jGeT0+HnfgkW0Rja2/qI7sg/Dkyht8XwOP2hZ3ZdDYXs48vNZFsh33Ixd4DjaxfPTVku7b+IaSU5IWI7mwespNuiyF6gtTWHwW62Kmjo6MzydHFTh0dHZ1PKFelIZdSxeXehKq6xv3ep/rZN3AIj+KdcBn1Q/3s6mohoKoh1iN57Wg1XUMjYcf03v5amjoHwqreXq+fNzcdo3/AEXaZAEcPtdDa3KdZTVdVlZEht6a2Y1wppf5SoCgTH8/xkFIGxcsIcI54It7HXW2DOIa195FS0lzfgz9M0eCzcTu9Ea1jbD0fR9QQ1yUEx93TM8zO3fU8/addNDaOXyOhf9jJe4fr+M8Xt/HjV7ajnLfcgKpyuLuTnx/cy+dfe55fH95P28gQdo8bv6J8ZNsTjkkndvYMPEEg0AajwuSY0ClOC56c/gxhYNBv4A/dltPy55i7UKrDSH6K0ZCI2ZiD0Zh0ehm1fQr7O0eQvESsyUZqVArRxmAwxtgavEqAA70dJFisbCysQOmSdAxeaLBre/oZcnuoykrnidWLWV1RDMDgiIu//skrp33u7b1D9A85yUtP5PM3LuL6xVMu8G1u2V7NM8/vpba+G59fYfrUXB77wmqmlGdNuL9efHYP294/SVZOEvc/vIpV60OLTH6fwgPX/j9KKrP54t9spLhy4mWPsfu9kzz7s/f4wt9pizoE+MU/v0h8Ugy3Pbxa06wKRVH5u7t/wt1PXMPs5RWa1nFoRy1/+vE7fPHvb6FoSramPv/znZfpaOrjkW/fRK6GqFMhBF+84QcUlWfypW/fRHZ+eCG2ramXL3/mZyxdN5VH/mYjaZmJYfu8/pe9/OXJD7jhzgXc+9haYsPU+hRC8E9feRrniJsvfO1a1t4wK6yvvKt9kMdu/RHrbp7Ng1/XFg369A/fof5EO1/6P7eSFqZ+LAQN6Ku/3sI1n1miuS7o5md3MmfddOI1jKexupMffusvrLh+Frc+sHzCdj29Izzz5z28+fZR3G4fmzaf4J//z21kZ53ZBkVVOdzYyUs7j/PBiUYyk+LYcbIZVQ3+eOWmxvMP926gZrCfra1N7Ghvwa+q7Oxoxenz4fT7LrjRu6tqOvdM+5jV7LxYPoyPPHgXPY6oeVrYDO64sc9VqeBTfUg52l6qqKgMDv8HFnMV0daVGI3FwVkmSKQEV8DDn1peoiKulBmJVSSaE08XXw4WfYbjA9282VzDmrwSFmXmg8qoYHoGKSU/en8nxanJrCwvIiP+zImoqhLf2N2SgKffOUC8zcqymcVkJo+vzgcCCm6Pn1/9bhtzZxUyb3YB0WGqqm9+9zhul49Fy8pJ0iDISSk5uLOeaXMLNIfbjwy5MBoNmmZ5jOEcdmsuPHy6z4gnoil7HpcXg9EQUR6U3k47yWlxEQl4Dac6KSzP0CzEelw+Gmu7qJyhvfh0U203FquZ7DzthaSP7GukvCpH89TIgF+htaGHoorwP95jjAy5iI2P/lhNP1UCCh63jxgN03OdTi9vvn2U9WunEhtrPT2t8Hx6hxw099iZV3YmAjSgqOfUDeh2OvAGAuQnJI67DCklipQfqriELnbq6OjoTHJ0sVNHR0fnE8pVa8j9viOo6tCE39eM1OIKjC+GAniUAFs6GvAqocWkA60dtA7aw47nZHM3Na29msSjXfsb6O4dDtsO4NSJdhrreyISO+0DTk1tz+7zceRinjaVQGQClZQyYuHSMeyOeB93tA4wPDTx+TjeuBpru/F5/Zr7uJxeRiJYx9h6JiuBgEJTUx9bNp9k16668dsoKjVtvfxl2xG++8z7uH0X7s9+t4s362r5p63v8y/bNl92oRM+pNgphPgecCPgA+qBB6SU9o9gXBMybP8mitLBmWjOc//O+OqCr/YA/LlXOeuToGAp5QhSHcFgTMZkzMZozEOM5h6v6fext2sIn+oj1hRLiiWZZEvS6WWPSZ5bOxoxCMGK7CJs9iic7gsPcrt9mJqePkrTkrllRhX3LZyNxWTC7nDzD799Cznq2h8ccXGiuZuMpFiuWziFBzcuIOY8//eOvfW8+MYhGlv66O4dpqgglbtumc+GVVMn9O298uIB3n79CMkpsVx7/UzuumdJyKyJPm+AB2/8ARnZiXz6wRWsvHZ6WP/nrvdO8tv/eItb7lvKhk/N1xR49LN/fgnniJv7v3YdKRpypSuKypdv/SFrb5nDTfcu1eTDPri9ll/866vc9egaVmycqcmP+9/feYXj+5u47682sGj1lLDthRA8fPN/Epdo46GvXct8DUJsS2MvX73vlxSWZfClb2xk5vzQdVcBXn9+H39+ajsz5hby2N9cT2FJaCFWCME/fv1P9HTaufUzi/jcw6uIDlPsubN1gMc+/VMqpuXy+LdumLDm5dn87r/eZtemkzzy7RuZoaHGq5SSX//Li9z4wErSc7X5+z94cS8zlleGjeyEoM/+l995mcrZBVx39+IJ23m9fv787B6ee24vw8NucnOTKSxMJfM84flEczd/ev8g7x2qw2Q0cLi+AwhOmijNSeV/f249e9vbeaH6BO83NZAbn8Cpvl5GfD4UeeYGRwAxFgu3V07ljipt0cyR8GFLvV0DvCelDAghvgsgpfybcP0+jI9cUbpBBg3mOULnBaJnsEVABhj2O0dlUfV0FKjb/QpSerBELcVsnoswWE8Lmk6fl1c7NxEloqiKn0JRbCFi9OFFjrbyKgrfO7iFxZn5rMkpxSbM405FfPVYNQNOF2vKi5mVl31a6FBUlb4hZ3C+jYBdJ5qpae1lxcwSZpVmjxvd6XL7cLl8PPfaAWJjoli+sIz8MBfDO28coaG+h+WrKqmsypnQ4I8hpeTNF/Yze0EJmRrzswz2jTA86KKgLENTe4COpj5SsxKxRGm/l2hr6NE0k2QMx7Ab57CbDI0GA6CppovElNiIoi53bz3F1FkFYWeSjOF2edn2zglWXDNVc6TmyaOtDNvdzFtSqjm3+ua3jlI2JZscDTNpICh27nj/JEvXTNEs9vZ0DBIbb4s4XW4kYnLAH8AUIn3s+aiqitvp0ySMe71+3n3nOKlpccybVzThvh12eth2rJGNCyoRQhBQVFweH/ExZ9Zh97ipGxhgXvaFP4CKquL0+zEIQazl4ou2XHKxc7R+56eklJ8N11YXO3V0dHQi53KInQ8Cb4QYwMNCiH1CiH29veNPvtfR0dHRiZywhlwI8a4Q4tg4fzef1eZbQAD4w0TLkVL+XEo5T0o5Ly0t7aMZ/YdAVTpQlf4Jv+/2dDHiDy0oHuprxxXwhWzTbh+mrrc/rCg0MOLiWFPX6WCDUNQ399LeZQ/bDqC/30FNjbblQtAX3d8XPhL1/D4fRy7maTOSSMixdQwNRiZcDg+5GejTFpk7RntLP/YI1iOlpK66E49Hu9jpHPFEtA74+ArdWnG7fNTWdLF188kJz+Nhp4cdx5v4xau7qG7tueB7RVU53tPDbw4e4K/ffosR78QR4ZeKsI4nKeW6UN8LIe4HbgDWyssgYbuHv4tUujkT2QnnCp6c8344oPBq/8hZn492k15UpQVhSMVozMFgKsYggv6umkEvB3qHGPINEmuOI9mSQqY1C+N5hZoP9rXR5hxiSWYhtqFooqUlKKSOfi+lxOnzs6mmnrzEBNaWF/P5xfPIiItl2OXhe3/ePCp2SgKKytsHakiOs7F8WhEPbJhPQfq5Puq9h5t4c/MJuvuGOXSijbzsJFYtKudzty4gZgIh67VXD/Lkbz8gISGaBQtLuPe+ZWRnT+z79vsDPHzHT0hKiWXF+qnced9SrGGCjna9f5Jf/8dbLFxVyWceWa3JV/yTf3yRrrZB7v7SGqrmFIRtrwQUHr/1h1TNKeSe/7Vekw97/we1/OxfX2XFtdO586GVmvzRP/u31ziwo45rbp3D7fcvxxIm6lQIwSN3/hSjychNn17ArZ9dhDmMP7ejtZ8vP/ArUtLi+PT9y7jh9nlh/d5vvnKIZ57cTnZeMp9/bC3LVleGFG+FEHznm8/R2T7I3EUlPPrVDWF95V2ddh69+79JTY/ngcfXsXbjjLAC8ZM/fJdNrxzizgeXc/1dC8Nuh5SSH3z9j6y5bR6zlmqrC7rnzUNMWVhGXFL4gDZVVXnp11tISotn1c0T18aUUrJtyyl+9tNN9HQPk5wcQ8WUbDLOE957Bh388vXdvLn7FE6Pj00HajEIA/ExUZRkp/DXd63mSHcXvzt8mLfqajEaDNT195+jlxkMQb94nMXC9eUV3FhRqWm7I+HDip3XAv8BrJRSavaXfCixM1AP0nuW0Mk5qWrPMqMA+FU/3d7B09+NiZ2BQC2KdxfGqIUYLfMxGnNO9xz0utnXf4wOdztlsRWUxpUTZ7pQMf9N9V5izBbWZJeSaYpn7Kb39M+JgLreAV4+doo1ZcWsKisiLTZ4MvoVhaauQQwieNENOtw8+c4+VkwvZsX0YtITLzRUQyNuBuxODh5v5VR9NysWlDF/Rj5RISIXjx9v4+k/7GTFigoWLykjPoyRVVWV3/xkEzPmFjJ7QXHIws5jdHcMUnusnQWrKsMavjFOHW4hOS2edA1h3WPs31bD9AVFmiM17QMO6k90MHtJqeaoy6P7GjGajEyZqT3q8uVndjN1VgElFaFzvY8xPOTmz09t59pb5pCjMVJzz45amup72XDjLBI05lZ/5snt5BelsmBpmSaB1OP28fzTO7nulrkkaRR7m+t6MBgEecXan7JH7C7N+eEhGAVsi9Ner1RKicfl05QbPhBQ2PL+SZqb+7jnvuWYzeOf726vn3f217BwSj5pCbGMuL24PD6yUs7U2HX6fGxpbuLa0rJzis0EVBWnz4fD5yPKZCLVpn3bz+eSiJ1CiDogChjzUeySUj4Srt/HQewMV9Xmk1T1RkdH55PBRIb8Q80jl1KWfpj+V5JwRlo34jo6OpOFqzayU0oPUumc8HtXwIndNxByGS2OQUZ8oVOY+hWFE93hIyullBxt6iKgQTi0D7toagsvoEIwOdep6k7NgqSiqPR0TxzxOm6fCKMh4fJEBF6MEOeNQByE4HZEKlwOD7no7RmOaB+0NPcx0K99PVJKqk924HaFFuPPxjHiob9vJKJxXcyx/7gxMuym+mQHwxOk8FVVSVPXAK/vPMGmfTXjtrG73Wyqr+fftmzlRM+FguilZtKlsfU7foZU+86qwCnGeT3zfiTg5317z3ltgsjAMRCJGEz5GEzFCEPQX1ljd3N8wEm7u4lYUzwplnQyrNlEG88VW1qcg2ztrGd+Wj6xzhjSzPGYhSHoax9z3yN58fhJYiwWVpUUcfv0KmbnZDPs8vCzN3YhpURVJaqUbD5aj8cXYMmUAm5cUMWyqedG/B062cZ7O2vw+QO8vOkomWnxLJ5VxJ3Xz6Ege3xf60svH+D3f9iOP6Awe1YBN1w/m/nzJo4kDPgVHr3358TGWZk9v5g771lCVghxFGDPBzX87LuvM21OAXfcv5xCDYFBP/nnl2lr7mflddPZcFv4GpRKQOHR239Mfkk6dzy4nPJpuSHbAxzcVc+P/+Vlps4p5HOPrCZTQ2DQL37wFnu21TJrQRH3PrqG1PT4kO2FEDxx3y9QVZV5i0t54NG1JKeG9i93ddh5/MFfkZgUw9KVFTzwyGriw5Ql2/TWUZ5+cjvJKbFsvGk2d92zJKQ2IoTg3//5ZVqb+ygsTufzj6xm4dKykOvo7Rnmi3f/jLj4aDbcNIt7vrCS6DCZE3/33+/x1osHWLSykgf+13riw/i+pZR898u/p2JWPjfdt1yT736wZwhVUUnJCn0ejnFw6yl8Hj8Lr5kesl1TQy8//H+vc/RwK0ajgaeefewCDcnnD/CHtw/w9Dv7GRxxk5kcx9PvHCA53kZxdgpfunUpXSMj/PfuPbxSfYohj5dtzU0YRm2N0WAgNspCnCWKuKgo1peWsL70o3dkTDpDbrQsQsqxX045zuu5n0WbfUyj5xzDGsRPwFWNwVyIwTwbYa4CETxpk80usqx97B3ooiCmgOKYcjKjc05Hd46xs6cRv6qwJqucXFMiNqM1+DMyWqBZCAiokhPdPczLy2FtaQkzsoKCmNVsYu3MUgwimFZACOjoH6Y4M5lVM0qYWXRh/uycjATWLinH4fLR3DHA8rklrFhQRm6IfNYzZuRRvDOd8vJMVi6vpCyMkTWZjcyaV0TV9FxWrKkKa8gAcgtS2XDrXNZcP5PMHG0X29xl5SxZb2bWwmJNQqTRZOT6Ty9k/vJysjQKhPnF6dx49yLW3Tg7rIEZY9aCYkors1h17XTNUZcr10+lbEoWS1dP0ST2pqbHs2RFBdfeOIv5i7VFahYUprHh+pnceOtcKjTmVp85p4B1107nuhtnkahhxkd6RjzrrpvB9bfNoUpjit0FyysonZLNkjVTNB1HIQR3P7Ge/NIMze7LxLT4iFyds1dU4tHwJFJYnMb/+/G97Pyghk1vHR13H1nMJh64fgGf2zCXLQfrsVnNzC7PpX/YiXv06S0zLo5/XLeWb65ayebGRqZnZJAdH7xu/IqCw+djxOtlxOsjMVp7GuZIuGrT2EqpAIYJTxBVqhhE+KlU4U4wraLp2HHQ2jYSBV/rcnU+vlyM+K4L9tqZLPvqkoidk5mxBFkTEc6IB5cR/sBrPTkiOYkuVVudjy8Xcxz1Y6+dyb6vrlqxE0AqE099l1Ji9/WF7D/i9zDgDZ/2s2lw8IJaf+PR0mvHr0E8klLSqFHsBGhrHyCgUZRSFJXOjsGIBC+/PxCxeHmp28PFRZx63NrFQRit/dg9FNH4nA4PXZ32iPr09Y1ELJA2N/XidGqPMhwZdke8jkgjYT+uOEY8uEMce4/Xz5HaDl7acnTca1mVkprePp4+eJhXTpy6lEMdl0l3Ry5dfwR1cPS/8X5FzxU/nYqPXcPt47aX/mogAKZihKkYDNkIIagfdlFtd9LubsSAgdSobNKtOSSYg5Fxp73sqsKvanYyIzmbFF8iWZYE4szW0eSLQW+8KiXbGptpHx5mVXERa0uKWV9Witvn5/ebD6JKFVUGZ1gcburkRGs3C8vzWTG1mBvmVWIxnTlEx+s62XGogUBA5a3twZDihTMLWbeokkUzC8fdX2+8fZTX3zpCXUMPs2bksWRhKdddM33CQJ9AQOHLX/wtZrORmXMKWbdhGnPmF098QICDuxv4r//7CtNmFbBi/VSWrAoddQjwk399jeb6HmbMK+TWzy4OGw2qKipfuuMn5BaksnRdFWuuD5+W9vDeRn7wjy9RPjWHjZ+ax9xF4dOs/vonm9j+/ikqqrK57bOLmTYrP2yfrz7yJD5vgIqqbD5z/zKmhBFie3qGeeSBXxIba6VqWi73fWEFpWWhg4l27ajjP7//BolJNubMLeLzD6+6IArxfH7yw3c4sL+J7Jwkrt04kzs+vXDCgBeAgX4HD93zP8TEWpk5u4AvPLqW3DB6xNO/2MLrL+yntDKLB59YT0l56O2QUvLdv3qa+OQYPvfEeuI1+O77u+z0tQ9QMTf0eThGV3Mf3a39zFwWOqWwY8TDr3/6Hu+/dRS3y8dvnnuc6JwLdZFtB+v5jz9spr13iDhbFJv315Ecb6MwO5l7Ns7HGwjwm30HeGr/IXqcTnIT4vnFnv0YBMRFRRFvDQqd8VFRLC8qZHlR+EjmSJl0hhxjPhhSOGNOz+Z88RNMwkdGlOm89sH3UjQANoQ5C8zFYAhGpwVinBhwEqCFWHMCedFZ5EYXEm06c9IJBMN+Dzm2RKYnZZMpksiKSsRiNI4KnuK08Fnb109OfByL8/NYkJeH0WDAZDBSkZOGEGAQAqPBwIDDjS3KzIqpxaycWnSOEQdIjIumsigTk8nAkZoOCrKSWLmgjLlT8ybcXXm5SWRnJZKQEM2q5ZUsXlASMlrTaDSQnpFAaXkGq9dNZdrM8IYsOTWO6XMKWbtxBnMWFGt6TC2pyCS3MJXV103XFNJvMBqYu6SUOYuDf1rWkZGdyLylpWy8bR5lVdoEwsLidIxGAxtvnUteYWrY9kIIKqZkk1eQwnU3zSbjrOK9E5GYaKOkJIOVa6u4ZuMMkjQYs/yCFKZU5XDjzbNZuXpKyBkrY5SVZ5KcEstNt8xlSlV22H2WlBxDZVUOG66fydoN07Faw6+jamY+JrORG+9cEHbmDQT315pb5jBjQYnmWqJJ6fEkpoUX3cfILEglWUOO+9g4K0984zqWra7kjRcPkDxBNOvy2SUsmVnE7qPNVLf0cOPyqfQPufCMFu2IMpl4ZNECHlowjx3NrcE+RQUoqorD52PY42XY62XY4yU9NvyxvhiuWrETgnPJhRhfRQ4WSg1gMkx8MgdUFaMQYS8QRVUxalD0tbaLuK2ias5hLaVEUVRNofk6QVRVhs3zfn57IKI+kRzDi+2jqjI442qS+4s/yehi5zhMZMSD3wlMIvQdidZq2FoNrtZ2EbeN4GIWQuhGPEIiMcgX0x4iO4YX2+dixqXz8eCqFjt1dHR0PgnohlxHR0dnkqMbch0dHZ1Jjm7IdXR0dCY5uiHX0dHRmeTohlxHR0dnkqMbch0dHZ1JzhUJCBJC9ALNl33FHw2pQOgkLJ9cruZth6t7+6/mbYePz/YXSCkvKJB6RQz5ZEYIsW+8yKqrgat52+Hq3v6redvh47/9umtFR0dHZ5KjG3IdHR2dSY5uyCPn51d6AFeQq3nb4ere/qt52+Fjvv26j1xHR0dnkqPfkevo6OhMcnRDrqOjozPJ0Q35RSCE+J4Q4pQQ4ogQ4gUhROKVHtPlQghxhxDiuBBCFUJ8bKdjfZQIIa4VQlQLIeqEEH97pcdzORFC/FoI0SOEOHalx3K5EULkCSHeF0KcGD3nv3ylxzQRuiG/ON4BpkkpZwA1wN9d4fFcTo4BtwFbr/RALgdCCCPwE+A6oAq4WwhRdWVHdVn5LXDtlR7EFSIAfE1KWQUsAh77uB573ZBfBFLKt6WUY+XDdwGhq+1+gpBSnpRSVl/pcVxGFgB1UsoGKaUP+BNw8xUe02VDSrkVGLjS47gSSCk7pZQHRt+PACeBnCs7qvHRDfmH50HgjSs9CJ1LRg7Qetb/bXxML2adS4cQohCYDey+wkMZl6u6ZmcohBDvApnjfPUtKeVLo22+RfDx6w+Xc2yXGi3brqNztSCEiAWeA74ipRy+0uMZD92QT4CUcl2o74UQ9wM3AGvlJ2wyfrhtv8poB/LO+j939DOdqwAhhJmgEf+DlPL5Kz2eidBdKxeBEOJa4BvATVJK15Uej84lZS9QJoQoEkJYgLuAl6/wmHQuA0IIAfwKOCml/I8rPZ5Q6Ib84vgxEAe8I4Q4JIT42ZUe0OVCCHGrEKINWAy8JoR460qP6VIyKmo/DrxFUOx6Vkp5/MqO6vIhhPgjsBOoEEK0CSE+f6XHdBlZCtwDrBm9zg8JITZe6UGNhx6ir6OjozPJ0e/IdXR0dCY5uiHX0dHRmeTohlxHR0dnkqMbch0dHZ1Jjm7IdXR0dCY5uiHX0dHRmeTohlxHR0dnkvP/AYJysjawW2w7AAAAAElFTkSuQmCC\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import brian2 as b2\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from neurodynex3.phase_plane_analysis import fitzhugh_nagumo\n", "\n", "fitzhugh_nagumo.plot_flow()\n", "\n", "fixed_point = fitzhugh_nagumo.get_fixed_point()\n", "print(\"fixed_point: {}\".format(fixed_point))\n", "\n", "plt.figure()\n", "trajectory = fitzhugh_nagumo.get_trajectory()\n", "plt.plot(trajectory[0], trajectory[1])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6.1. Exercise: Phase plane analysis\n", "\n", "Plot the nullclines in the 𝑢−𝑤 plane, for voltages in the region 𝑢∈[−2.5,2.5]." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#6.1.1.\n", "\n", "#Equations of the FN-model:\n", "#I_e : amp\n", "# dv/dt = 1/ms * ( v * (1 - (v**2) / (mV**2) ) - w + I_e * Mohm ) : volt\n", "# dw/dt = eps/ms * (v + 0.5 * (a * mV - w)) : volt\n", "\n", "#Set parameters:\n", "I_e = 0.\n", "epsilon = 0.1 #but is meaningless for nullclines right?\n", "\n", "v = np.arange(-2.5, 2.51, .1) # create an array of v values\n", "w_Fe0 = v*(1-v**2)+I_e # calculate nullcline F(v,w) = 0\n", "w_Ge0 = 2*(v+1) # calculate nullcline G(v,w) = 0\n", "plt.plot(v, w_Fe0, color='black',label='F=0 nullcline') # plot F-nullcline as a function of v\n", "plt.plot(v, w_Ge0, color='red',label='G=0 nullcline') # plot G-nullcline as a function of v\n", "plt.xlim(-2.5, 2.5) # constrain the x limits of the plot\n", "plt.xlabel(\"v [mV]\")\n", "plt.ylabel(\"w [mV]\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6.1.2 Get the lists t, u and w by calling t, u, w = fitzhugh_nagumo.get_trajectory(u_0, w_0, I) for 𝑢0=0, 𝑤0=0 and 𝐼=1.3. They are corresponding values of 𝑡, 𝑢(𝑡) and 𝑤(𝑡) during trajectories starting at the given point (𝑢0,𝑤0) for a given constant input current 𝐼. Plot the nullclines for this given current and the trajectories into the 𝑢−𝑤 plane.\n", "\n", "6.1.3 At this point for the same current 𝐼, call the function plot_flow, which adds the flow created by the system Eq. (1) to your plot. This indicates the direction that trajectories will take.\n", "\n", "6.1.4 Finally, change the input current in your python file to other values 𝐼>0 and reload it. You might have to first define 𝐼 as a variable and then use this variable in all following commands if you did not do so already. At which value of 𝐼 do you observe the change in stability of the system?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "length of t,u and w arrays: 5000\n", "For currents between 1.25 and 2.75 (roughly), we observe a change in the stability in the sense that the trajectory converges to a limit cycle instead of a fixed point.\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#6.1.2.-6.1.4.\n", "\n", "%matplotlib inline\n", "import brian2 as b2\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from neurodynex3.phase_plane_analysis import fitzhugh_nagumo\n", "\n", "#Set initial conditions\n", "u_0 = 0.\n", "w_0 = 0.\n", "I = 2.75\n", "\n", "t, u, w = fitzhugh_nagumo.get_trajectory(u_0, w_0, I)\n", "\n", "print(\"length of t,u and w arrays: {}\".format(len(u)))\n", "\n", "fitzhugh_nagumo.plot_flow(I_ext=I)\n", "\n", "\n", "v = np.arange(-2.5, 2.51, .1) # create an array of v values\n", "w_Fe0 = v*(1-v**2)+I # calculate nullcline F(v,w) = 0\n", "w_Ge0 = 2*(v+1) # calculate nullcline G(v,w) = 0\n", "plt.plot(v, w_Fe0, color='black',label='F=0 nullcline') # plot F-nullcline as a function of v\n", "plt.plot(v, w_Ge0, color='red',label='G=0 nullcline') # plot F-nullcline as a function of v\n", "plt.plot(u[0:4000], w[0:4000], color='green',label='trajectory from (0,0)')\n", "plt.xlim(-2.5, 2.5) # constrain the x limits of the plot\n", "plt.ylim(-2.5, 5.5)\n", "plt.xlabel(\"v [mV]\")\n", "plt.ylabel(\"w [mV]\")\n", "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n", "\n", "print(\"For currents between 1.25 and 2.75 (roughly), we observe a change in the stability in the sense that the trajectory converges to a limit cycle instead of a fixed point.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6.2. Exercise: Jacobian & Eigenvalues\n", "\n", "6.2.1 Write a python function get_jacobian(u_0,w_0) that returns the Jacobian evaluated for a given fixed point (𝑢0,𝑣0) as a python list.\n", "\n", "6.2.2 The function u0,w0 = get_fixed_point(I) gives you the numerical coordinates of the fixed point for a given current 𝐼. Use the function you created in the previous exercise to evaluate the Jacobian at this fixed point and store it in a new variable J.\n", "\n", "6.2.3 Calculate the eigenvalues of the Jacobian J, which you computed in the previous exercise, by using the function np.linalg.eigvals(J). Both should be negative for 𝐼=0." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fixed point x0: [-1.0000000000000002, -4.440892098500626e-16]\n", "Jacobian at fixed point J(x0): [[-2.0000000000000013, -1.0], [0.1, -0.05]]\n", "eigenvalues of J(x0): [0.8940763653560053, 0.05592363464399473]\n", "No trajectory from fixed point!\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#6.2.1.-6.2.3.\n", "\n", "%matplotlib inline\n", "import brian2 as b2\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from neurodynex3.phase_plane_analysis import fitzhugh_nagumo\n", "\n", "#Set initial conditions and parameters\n", "u0 = 0.\n", "w0 = 0.\n", "I_0 = .0\n", "epsilon = 0.1\n", "\n", "#Def function that returns Jacobian of Eq. 2\n", "def get_Jac(a,b):\n", " return [[1.-3.*a**2.,-1.],[epsilon,-0.5*epsilon]] # return the matrix\n", "\n", "u0,w0 = fitzhugh_nagumo.get_fixed_point(I_0)\n", "J = get_Jac(u0,w0)\n", "\n", "print(\"fixed point x0: {}\".format([u0, w0]))\n", "print(\"Jacobian at fixed point J(x0): {}\".format(J))\n", "\n", "#6.3.2\n", "u0 = 0.\n", "w0 = 0.\n", "I_0 = 2.0\n", "epsilon = 0.1\n", "u0,w0 = fitzhugh_nagumo.get_fixed_point(I_0)\n", "J = get_Jac(u0,w0)\n", "\n", "#Compute eigenvalues of J\n", "J_EV_1,J_EV_2 = np.linalg.eigvals(J)\n", "print(\"eigenvalues of J(x0): {}\".format([J_EV_1,J_EV_2]))\n", "if J_EV_1 < 0 and J_EV_2 < 0:\n", " print(\"-> both eigenvalues negativ (as expected)\")\n", " \n", "print(\"No trajectory from fixed point!\")\n", "\n", "u_start = 0.\n", "w_start = 0.\n", "t, u, w = fitzhugh_nagumo.get_trajectory(u_start, w_start, I_0)\n", "#print(\"length of t,u and w arrays: {}\".format(len(u)))\n", "\n", "fitzhugh_nagumo.plot_flow(I_0)\n", "\n", "v = np.arange(-2.5, 2.51, .1) # create an array of v values\n", "w_Fe0 = v*(1-v**2)+I_0 # calculate nullcline F(v,w) = 0\n", "w_Ge0 = 2*(v+1) # calculate nullcline G(v,w) = 0\n", "plt.plot(v, w_Fe0, color='black',label='F=0 nullcline') # plot F-nullcline as a function of v\n", "plt.plot(v, w_Ge0, color='red',label='G=0 nullcline') # plot F-nullcline as a function of v\n", "plt.plot(u, w, color='green',label='trajectory from [0, 0]')\n", "plt.xlim(-2.5, 2.5) # constrain the x limits of the plot\n", "plt.ylim(-2.5, 5.5)\n", "plt.xlabel(\"v [mV]\")\n", "plt.ylabel(\"w [mV]\")\n", "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6.3. Exercise: Bifurcation analysis: Wrap the code you wrote so far by a loop, to calculate the eigenvalues for increasing values of 𝐼. Store the changing values of each eigenvalue in seperate lists, and finally plot their real values against 𝐼.\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "In the region around I = [1.3,2.7] (marked blue), the system doesn't converge to a fixed point. Indeed, above, we have seen that there is a limit cycle.\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#7.3.1\n", "\n", "%matplotlib inline\n", "import brian2 as b2\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from neurodynex3.phase_plane_analysis import fitzhugh_nagumo\n", "\n", "#Set initial conditions and parameters\n", "u0 = 0.\n", "w0 = 0.\n", "I = 0.\n", "epsilon = 0.1\n", "\n", "#Def function that returns Jacobian of Eq. 2\n", "def get_Jac(a,b):\n", " return [[1.-3.*a**2.,-1.],[epsilon,-0.5*epsilon]] # return the matrix\n", "\n", "list1 = []\n", "list2 = []\n", "currents = np.arange(0,4,.1) # the I values to use\n", "for I in currents:\n", " u0,w0 = fitzhugh_nagumo.get_fixed_point(I)\n", " J = get_Jac(u0,w0)\n", " J_EV_1,J_EV_2 = np.linalg.eigvals(J)\n", " list1.append(J_EV_1.real) # store each value in a separate list\n", " list2.append(J_EV_2.real)\n", "\n", "ev1 = np.array(list1) #convert lists into arrays\n", "ev2 = np.array(list2)\n", "EV1_pos = np.where(ev1 > 0.) #find positiv eigenvalues\n", "EV2_pos = np.where(ev2 > 0.)\n", "EV_pos = np.intersect1d(EV1_pos,EV2_pos) #both eigenvalues positiv\n", "#print(currents[EV_pos]) \n", "\n", "#plot eigenvalues against I\n", "plt.plot(currents, ev1, color='black',label='EV 1')\n", "plt.plot(currents, ev2, color='red',label='EV 2')\n", "plt.plot(currents, np.zeros(len(currents)), color='grey')\n", "plt.plot(currents[EV_pos], np.zeros(len(EV_pos))-1, color='blue',label='range with both EV with real part > 0')\n", "plt.xlim(min(currents), max(currents)) # constrain the x limits of the plot\n", "#plt.ylim(-2.5, 5.5)\n", "plt.xlabel(\"I\")\n", "plt.ylabel(\"Real part of the eigenvalues of the Jacobian at the fixed point\")\n", "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n", "\n", "print(\"In the region around I = [1.3,2.7] (marked in blue), the system doesn't converge to \\\n", "a fixed point. Indeed, in 6.1.4, we have seen that there is a limit cycle.\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. , 2.1, 2.2, 2.3, 2.4, 2.5,\n", " 2.6, 2.7])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "currents[EV_pos]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }