{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "
\n", "数値計算試験予行演習問題\n", "
\n", "
\n", "
\n", "2020/12/11 実施\n", "
\n", "cc by Shigeto R. Nishitani 2020 \n", "
\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " # 簡単な行列計算:25点 \n", " \n", " 次の行列\n", " $\n", " A = \\left(\\begin{array}{ccc}\n", " 5 & -2 & -2 \\\\\n", " 2 & 1 & -2 \\\\\n", " 6 & -2 & -3\n", " \\end{array}\n", " \\right)\n", " $\n", " の固有値と固有ベクトルを求めよ.\n", " また,対角化行列$P$ を用いて,ドット演算 により$P^{-1}.A.P$が対角化されることを確かめよ.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-1.000 3.000 1.000]\n", "[[-0.408 -0.707 -0.577]\n", " [-0.408 -0.000 -0.577]\n", " [-0.816 -0.707 -0.577]]\n" ] } ], "source": [ "import numpy as np\n", "np.set_printoptions(formatter={'float': '{: 0.3f}'.format}) \n", "\n", "A = np.array([[5, -2, -2], [2,1,-2], [6,-2,-3]])\n", "l, P = np.linalg.eig( A )\n", "print(l)\n", "print(P)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-1. 0. 0.]\n", " [ 0. 3. 0.]\n", " [ 0. -0. 1.]]\n" ] } ], "source": [ "from pprint import pprint\n", "dA = np.dot(np.linalg.inv(P),np.dot(A,P))\n", "np.set_printoptions(precision=3, suppress=True)\n", "print(format(dA))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$P^{-1}.A.P$で固有値(-1,3,1)に対角化されていることが確認できる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# FFTの強度表示:25点\n", "\n", " FFTによって非整合波の重ね合わせを周波数分解したときの様子を観察する.\n", " 1. $\\displaystyle \\cos\\left(\\frac{x}{17}\\right)$と\n", " $\\displaystyle \\cos\\left(\\frac{x}{3}\\right)$を重ね合わせた関数に\n", " FFTをかけて(スペクトル)強度を周波数で表示せよ.\n", " 1. 上記2関数にさらに$\\displaystyle \\frac{1}{4}\\cos(2x)$を\n", " 重ね合わせた関数にFFTをかけて(スペクトル)強度を周波数で表示せよ.\n", " 1. 上で求めた1. 2.のスペクトル強度の違いを述べよ.\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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J38mkA/4K36sf6OQWIoNQ4ecRe/fC3LnKdBBkRaWbDb+gQFVIEIVvfVOHhO8MPSqpEX6E398PUgpXhT86qkInuEGP9KgT/eGyU9bmzWoEdf75mY3j/ZCrwncz6VRUwPDw4TFfkg0SCft6h4nCB57w9+2DadOCe2O4KXz9Nz+FX16uVm8aERK+M5LJ7Anf7YVs/M2rjnRzkW5KChr98VDHli0wcybMnq1MWkFi1Y5X4buNkkOVb4aT8JkofKAJX8qMSSdbws/FRuzWQULCd4Z1g2zwJ3yv+glCKHqIi8ON8DdvhqOOUnMXIyP+8yTDw+pfLv3AzaQTrklxhlM/mCh8oAm/p0eZAHSFH8SkM16Fb23kEBK+G9xMOl5k5FU/elpBCP9wMulIaSZ8yCznd4PXROJ4TDrGtEMouJnOJgIfaMLXY6bohN/a6j+U9fKJDRV+/iBlbgrfq36ChLGwmnT0hUQfZIXf36+ee8aM4ITvJ3xCk07+cMgRvhDiASFEmxBig8txIYS4VQixVQixTgixJB/39YMxZsrUqWqI6reoR2/IxljrOsaj8AcG/LeFO5wwOKhIP1sbvhcRBSF8q0lHCP97HurQn7muLjjh+71YdZOPE/SytF4bmnSccSja8B8EPuZx/FxgnvbvKuDOPN3XE1aFD/52/GRSkX2BQ8kEUfhuhK+nHULBzRWtulq9DNzIxGvSNheTjp7WB9mkY3zJ5Uvhgztx67GoIhHz72E/cMYhp/CllC8CXtr548AvpMJKoFYIMSUf93bErl1E+vrY26zsN/qkLfjb8b0mUPyW7jvFD4HsI2a2tQU776BjbCznS91sxOqFKenrdba9eU7alqWoJ85gu3slWU06+j0/yArf+Mwmwh8ddb3Gz7QJ7n3BrR9kq/C/9z248MJg5zI6qpZov9+GD1L69pMDOWmblz1tA2AasMfwvVn7zaa3hRBXoUYBNDU1EYvFsr7Z4htuYHE8zoyerzM/chxbbl3C7mkfAU7mhRc2Ulzsvqxy27ajiURqiMVetx0r3SN4tP1bxF74nuMQoLPzw/T1tROLbTH9vnv3JGAhzz//OjNmDNiuK+zro/Evf2Fg2jTeqjuFz33uJD772Z1ceunOQM+bSCRcy+mI22+n47TT6Fm0KFBaQVGxYwcL/v3fWXPPPUirlAuAHTsqgGXs3PkOsVhGbu7bN5mbuJfd14+w/oq/t1335pvTgHm8/fbLbN8+SmFPD1OefpqGl19mUnKY3zCTuf/STeI/O0nOns3+c86hc9kyEILijg4+fM9vqS+8l5Ur30qnKeUJ7No1Riz2di5FQUlbG01//jNtZ57J4LRpOaXhhpk/+Qmbnn6a1o95DaC9sXJlPbCIbdvWUFzcR2npaby38l2GppzFGw88wKgDO7/2WgNwLJs2rWZszEyiu3Y1AsfwwgurmDPHvgXc7Jff5duJrcRi55t+b2kpBU5mzZpNNDY67xxvbMsPP7yUrVsrueSSlykvT1GxbRt1b75J21lnMVxfT2FvL1OefJKGV16hYGiIkepqCkZGKEwkSM6eTes559Cl1b0XIokER//4x2z+0pcYMcb6yAOmP/IIJe3tbLv2Wtdn7excTm9vnFhsc17v7QgpZV7+AbOBDS7HngBONXx/Hljql+bSpUtlTtiyRXaecIK85OIxed6UtVJedZUcPfnD8kRWye9/3/vST3xCymOPdTgwOCibpy2Tr7Bcjry6yvHakhIpv/Y1++9//KOUIOWaNS43/cY3pLzqKinPO0/+9rfqXJDyzTe986pjxYoVzgcSCfUwy5ZJuW5dsMSC4mtfk/Kkk6S8666cLl+5Uj3jE0+Yf3/m1k3ydZbJ5DHLHK/73vfUdcP9I1L+8IdSHn+8lHfcIWU8Lru71bGbb5ZSjo2pAr/ySilPOUXK11+X8rjj5LoZ58l/qnnMlOY556giyhk/+5mUn/3sOBNxwOio7JszR8oTT5Ty3XdzTua//1uVy6ZN6vusWVL+5vjvS7l0qVZYdvzyl+qazZvtx558Uh177TWHC1evlu/ULpeby46TMpUyHWprU9fddpt7XvW2nEpJWVamzn/mGe3giSeqcr7tNlvdm6DX/RVXqLpfvdr9hlJK+Yc/SPmxj6nyGBvzPjcbjI2pNJculXLnTtth/VmrqqS8/vr83RZYLV049UB56TQDMwzfpwMTt5PokUeSKi2lvnkdzY0nwN13E3nwAW4u+CqLnvy+p6uO6/Bq7Vo6ZxzPT7iB0f993HZ4eFit8PSy4buONletUuPX5mZ278wM/37/e49nDIKXXoJzzoHLLoOXXx5nYgaMjan1+U88AXfmNh3jZtJZ+PTNfJPv018/Dd55x3ZdIgGzC3dTdM5Zyti/ciV84QtQX2+24QsBS5bAPffAfffBP/8zjI7yx7nXc7Z43pRm0Cibrnj5Zfja19Q9/TY9zgYrV9K3YAF885vw61/nnIx1onpydISTtv4K/vQn+OUvHU0OOZt0fv97HpzyLXZWL4a1a02HsjHp7NihHB1ANWP6+tQmBhdeqEJ+Dg3B66+n694Eve7vvVfV/Q03wA9/6N7vn30WvvENmDwZmpv9MxcUq1crX9jvfAduucXxFCkPQRt+ADwGXKJ565wM9EgpJzQKefuZZ3L07j9nCHj+fD4z6TmKutrh4otd13e7zpivX0/v3MU8wzmIZ5+xHc7Ze0TfwXjSJFiwgOG3N1Jdrb6O25b/3HNw9tlw/PHw1lv+5wfFa6/Bhz6kNuGsq/N3fXKA26RtzZ4NvMZydn/4InjkEdt1VTvW8djY38B//qfqSCUl6WOFheqrrZyPPloRck0NH37v55w0bH75jcuGLyVs3KjuccIJ+S3nxx6j45RTVP05vPyCwjpRvaR8ExuLFqmJrXnzMoF2DMi5Pa9fz1tji1g346+VIDCgrExxcZBJ2w2av195uaZV1qyBWbPg619XFfbtb6sXgB+OPhpeeEFN3n32s87zFq+9BsuX57+fPPII/OM/wpln2l5+OnRvtUOK8IUQvwZeA+YLIZqFEJcLIa4WQlytnfIksB3YCtwLXJOP+3qhf8YMmno2mxR3VV0h9xx9i3r7X3iho5+k03J/ADZsYGjecfRRzWhhmS2Gr9tiE/DpIPqKGIBTTqF2w8vMmpUnwn/pJTjtNLVb9/r140zMgPXr4cQT1eejjw4Wd9oCR4UvJUUj/QxQzp6pH4K3LTb1TZv4p2cv4er6h+HUUx3TdV3zsG4dfPObvFt0PJNH96hFGRr0oGs5YdcuRUQFBbBsmVJ1+cKLL9K1ZImKh7BjR87J9PSoTcRLS9X3BZHNbBybr31Z4Ej4fu7J4KLw9+xhy+AMth5xjhIcBgih+lYQwtffbxddpAZxqd8/Cq+8ooa9s2eb6s8XhYXw05/Cscfa+/2uXerFV1wMixfb29x48O67imt0NzCHEcaBjIUP+fPSuUhKOUVKWSSlnC6lvF9KeZeU8i7tuJRSXiulPEJKeZyUMo+9whn906czNWkm/NpaTe18+cuKBK+7zlYJrsOr9etJLThWnTP1KFtQcbfFJuBD+G+8ASedpD6feioz97zCzJkqbO+4QvYOD2cc3cvLlZTw8MrIClu3wpFHqs8LFiiFmyX0Tm96ue7bB1PVpOf+oumwxzDPv20bXHghNy/5FS1Vc13TdY3I+OabcPzx3F7xNfZXHQmXX56u++pqVTc5OR29/DKccor6vGyZqs98YWiIsdJS9TIpLs7YOLJEd7fZK+mI1Hu82a8R/lFHuSr8ykpn92TX9qy55/T2CQob6xwbfEVFMJPOhg0q9s/xx8OUwe2IXzwEDzyg2t2HP6xUebb42tdUv7/++ky/f/PNTP/Lt8Jvacm4BzY2qiBGFhzISJnwAV5pm6qspHykx5nwQZkDRkbgBz8wXeeo8KWEzk5KpypbYW/DXLWVlgE5K/w33lBEAXDssUzpfS8/Cn/PHqU8dcyf79ixc8LWrcoUADkTvmND37iRyLELAOhJRDIubb29cMEF8POfs6lgIeXl7ivYXAllzx6YMYPubnh94efUSf/5n0CmznLy6Nu4EY47Tn1euHBcphcTurvNiwUWLMhpJOWU1Iz+99gwcpR6MboQvpdd2VXhb9iAPObYjFumg5wPGiL53XfVpkVN5X38hgsZqW+Cs85SB5csyZ2Yv/1t9XA/+Yn6vnMnzJmjPh9xRPDdYfwwOqrelrqHkEs/OSQV/vsV3WPVTCrJBGYxEb4QcMcd8OKL8PTT6XMcCX//fpg8Od3QO2vthJ+zwt+8WZlFgL7BIkRqJD+Ev3OnGvrqOOGE4HFx/dDcDNOnq8/5VPjvvkvhooUUFGjlOW2aUv2XXw5f/SqccAJ9fVBW5k74jiadjg413yAE3d0wNHm2MkmtWAEvvBBo+0pX7N6debEWFqpOno+R1I4dKq63jmOPzRi2s4RV4Td2b2EL89Qm8i42fC/CLytTj2kr5/XrGV1wHKOj2kt0zhybKSqowt+/H6ZPHeP0+y7mp1zHcLlhL8xZs8yjv2wghJrIf/pp9W/Hjkw/KShQo+F8rMIztgtwNX0eyM1P4ANM+KmUYOPYfGYNZ3ziTYQPqoM++KCaCGptdZ8x37ABjj02TQztlfaG7BYhENRovKjIpaG3t6dXw+zeDQOUMaepn6Ym1e5yHMXbCX/ePNtLKieMjSnlrY/1p03LLGnOAomEKhPTvNvGjYiFCzKTqEccAd//vlo5d8EF6ev8CN+mIHfuhCOOYGhIs2xNn60K+5e/hC9/mUkp5T+QUz/ftUvZHnTka1f07dvthJ/jPIyJ8KWkJNVPPxWqjF22GHOLCwWKMx0DqG3YQGK2MnumCd/S5oIq/O5u+LstP2Zs3tG8yikkagzrG2bOVPWXK4qK1G7u3/gGvPdeRuGDGvHkQ+Vv2ZIxe0Ko8Cca/f0RNnMU05PvpX/TCd9ktm9qUrs7X3opg/1jjvFd2LkT5s5Nd4CWMneTjlsncZ1MNJDnrl2wm5kcWbybSZPU4ZxVvpXwp03Lj8uZvsGADiHUbGCW7oiOI6mNG2HBgkzEzJIS+POf4cc/Tp+Sk8LXRiRpXpsxQynEKVPglls49Z5LEIzlpvATCXOlz5iRn3K2Ev6RR+b8wu7pMRB+Rwepuob074Aje/u5CjqGo9i9m576OenjzJ3rqPD9CH9wEOYNrmPRzj8y8K3vMYM9dFUavLpz9AwzYdIkZc5duTKzJR6okWsOAsYGo9kTXE1yoQ0/T0gmI7zHfCb3mAl/dNSBm/7qr2DxYlI/vQ1waOh798K0ael+3ZGyNzgvha+naSOinh7TBc3NsItZTB/LA+Ebh6qgGnI+iMg4Yatj9uysh9iO6x16e6G2lupqSHaPqB3ozzjDNAxIJMjehq8Rftrs1lCSCdZz1lkMHrWIK7k3e8IfHbUHjNFfJuPFtm1mwp86NVh8bweYFP7mzYzOVRO2acI/6ihVrwZ4KXxwac8tLXSVTAbcFX4Qk0532zD3cBUvXXwv9U1FzGQ37WUGwhdC/Quyi4sXzjlHta277878NlH9xMULI1T4eUJ/fyE7mU1d7670b3qjN5l1dPzrv1L0qweZRrP9baup2tJS1b/7EkKZgwy+/F4xXvTfbQ1dm0jUEY8rhV/buzu9ufa4FL7Rhjhutx8NToSfAxnZ1jsYOm91NZy7/kdw3nk2c0MQhW9TkBbCr65G2Wq1E7tu+C5XcxcjO7NUdvv2mdUh5I/wt29XJi0dZWVK+uYA06Tt7t2I2apdpIt2rn3EmpPCHx2ld0Dt01ddjaPCD2LSKfz+9/gdn0QuPIbqapgp9tBSONN8Uj78lru61Mzw/febIy2Og/Db2+GLX4TRjRaTjkt4h9CGnyckkxFamEJFIuOv60n4ZWW0XP8jbuU6O+FrCl8PpdvXh82O2NurCMwtrEwQwu/qgtaimRTt25VW+DlztFVCRyLjCnaWhvVFAjB1KjtXtnDllcrknkv26OpKr5g8pmAjy/b/Cf7935WdS4Mekre83H1S1MukYyL8WbPSaVdMquCr/Jhj77w2O9VonZiD/BF+RwdEo+bfhMi6DgcH1aLUtMJvaaFopnIVTBO+w7yD7pbpBhvhj+clykEAACAASURBVIxAYaHZeWHqVJt5xE/hl+3eTcnLz/MTbqCuTlk7jyzZw245w3zieO34kJkY/8EPlKsmjNuk89RTcNttEH+nxS4GHN6SocLPE/r7C4kTpTSZWSDlSfjA/uPOJkkFc9f/0XJgPzoDp+tszhxFfhpyGgI7EH5X9SzYPU6TztCQ8yrE0tJxzAJraG3N+BbrmDKF39y8j/vug5/9LFgyNhu+rpal5Not1/Nv0Z8pFW7weNHLr7TU34Zv4u3mZpg2zUz4s2en66+yEp7nbJJFtfDYY8EeAOwTtpAfwpcyY7YwoqHB0ZfbC7booC0tlM7xJ3zr1IQVtnAUra0webLZPVkXGYbK8FT4UnLkHXew4bJbGCOSzvOcyG52jE4A4esumf/n/6i8PvXUuBW+PqDpaJeMWenVpZzBeYHbROADS/jJZARJAZGCTGPzI/xkEm7kZo7+9b+Yh8+pVHpn8jThT55sWu3ntvmJjiCE390NyehM2LWL8nJ1TU6E39xsSjcN3c1xPNA6thFyylTKuvelD7tErTDBZtLRCf/xx0lUT+XVEW1tgkHV6mTiZ8OX0vJe0yrHjfD1fDx/9vfh3/7NPRi/FfoqWyNy9FoyobPTHh8mx7StcXRoaaFszmQKCgyEb2nLQeK72MJRaKNg21yW5c1QUaHm0BwHKo89xnBdHTsnn2zK82Ra2TFgbnN5IXxj/d1yC3zrW6qDZ/lSNWLHDogwSv9QBFsAWwfTp/I6c7cM5BsfWMLv71cEHSkuTHfgIITfziS6z71IjctAXVtUlD7HRPgGe0u+FH5RQ026J06alKNJx7jCz4h8TEi1tWWCqmvoq5rKpFQLRx+tyCKIV6LNpNPSotL9l3/huTP/I0Mm9fWqYMiUn58NX08fMKlLExkZOl9ZmfZokSnwD/8At9/u/wCgCMeq8EtKgr8w3LB/P+lJHCNyeGHrpJ4m4NZWxNQp5r2DLcpzYEARsp/C9yL89LWWuSPHFzIogfWv/8r2K6807dAFUBxJ0d5pYcR8EL5RvOiuv3fcMa4kd+6EU+e10cYke5QGB4V/IGPhwwea8FUDKZiSaXB+hK8TSvLy65SfbmenjTzThN/UlB+FbyCMri6tkWseCHV17nn1hBth5IPwR0dNL0CAVjGFqexLh9cJcgtHhb9unSLcqVNJJrWQJwb1GUTh2xa5xePKFIKF8Jua0sMnfb1NMokKu/HQQ7ZYSY5ocbDTgiqf8ZC+wygKcLSJ+8FmI9ZGDzU1BsJubDRtgRXErqy/MNLvU82xoa8vU56AjfBdd7264w646CJG6uvNo5JEgtHSSrsXZr7Ei7GffOlLqu5LS3NefLVjB5x6ZCv7xRS7WHNR+CHh5wHJZCFCQGR65q2qeyp4KXyA8mgZfOUratJQUy46TIRvUfhZE75lCWSa8LXemPPWe9aGrGO8vvhjY47BVfb2VlFNbzpCRJBb2Gz4O3ao4Fhf/nK6HK2ms4y909ukYzzXuCq4t1dZ5kpLsQ2f0v7hZWUq5sp3v+v/EA6jHWBcLpRAXhW+44pmIaipMSj8SMQUUMzP4wxUWx8dNVg+DQq/utow/eCg8MHSF3p74Re/UO4tqG5RUqLV07599NdMtRO+4YWdMwxzc4Cq++uvVxnIwSw3MqKa29G1rfRVTrZnz8WGf6B88OEDTPj9/RGqqkBMnZImjJISVad+hF9RgQpr+tprKhyBE+FbTDpu27rpcJxMBNPEXFeXxv+ay1nOhD9RCr+z0+45ArTuF0gEJy5VDxeU8E2E8tJLKoRCWVma8Ht7cVT4WZl0tAlbPb00GVnc+kwLgi68UC3I8Zt8HRrKhKA0YrxkpIXysCEHhW9q04OD6XDSJsIHE+l77Rusw1RHoPI1daq9H1jmBxwV/s03wzXXpG1r6X4A0NbGcH0Tvb2WuaGgMRq8oIfcMOKSS1QGXMIZe2H3bqWJZpe2MlgzOVT4BxLJZKFqlJa3qi28ggGmoWxBAfy//6dMO06EH42aJneCKHyT7VJzY9MxNqY6YF0d+SF8o3LRYXlJZQ0XU0NrK/RSzYLpfVRU+BP+6KjiyrSy6ehQveWf/xnAlfAzNnxvt0wwlJvh5Wcyu5WWqkxoMBF+QYGawNOCq2WN8fqIt7bmXeFXVmKqPxvhG/IcROHro2UT4RsUfhouCj9d1m1t8Pjj8LnPpc/p7s7Y72lvhwY1itKmchR8ti0MBIMzRhqRiFr/ce+9WSenO+1NLWhhtMGB8KdMCQl/otDfH8ma8JNJVf9pj8bzzrOpPD12uiww+7UHUfhgECUdHSZzQG+veiHkhfDdTDoWW23WcCH8lhZoK5hCbf++QIMI22KTH/9Y5U0rwPEofJM5CNTzai8/r3kW25L/889XsdENrre2h3DzpRtvObuN0HKYxTcpfMN8lGnSFlQ5a/0kG4WfTkMzT9qEj59J5wc/UIHxDPNCJktnWxtisqo/m1nHsvgxK+iur074yEeUidGwBiQIdJfMhtFW5JQp9ne+w0474aRtnpCrwrfaOjn2WHj00fRPVVVKGAwOknYZHBpSc3R+Cl+/B6BI2aDCdfUyoQrf1suzhIfC76mYimjJjvArKrS8PvusyQ3RT+F72fBtkS8NwelshG9geRvhC6FGeN/7nvONDC8SG/Kh8J1MOjksnjPFajEQvk3hT5liK2c/Gz5Y+EsIa7QQ70nb9nYVrfZTnzKlbSX8oqkuhO8SYz4Q0hNmDpg0SUVTDbqKUMOePVpguUQrRdOVwjeZcB1eMIekDV8I8TEhxHtCiK1CiG84HD9DCNEjhHhL+/edfNzXC7oN36hcwF/h2xp5WZmqSW3puSkWeEMDxOO+gdPAhfANCt9E+JoNuKpKmYCyjrbb3+/cisY7DG5pcSX8oVqV5yCEbyKh//ovtS+pgSW8FH5BAZSUuJOeo8J3I3wDGTkuCDr3XBU62KLy+/rgm5e30VfuoMJh/ArfybasI8sYMsmkek8UF+NI+OmkDMIo6KQtaHVkUMvWUMxWbzaTwr/lFuUZY3FCN9nw29sp1AjfZrIfz4vVTRSBqr+aGjXCy8L1s7tblUvB/lbK5zQxPOygrwwhPeAQNOkIISLA7cC5wELgIiHEQodTX5JSHq/9C+ACMT4MDkZU47IojKwUPij3vG9+U22CjIXwtbS9Nj/RYSN8i0LUCd86aWu6Jh/IYXl+Gh4mHX0V6PTpykzpsHtkGnp7rxU9anXj6aebCM5kLjBERtQ7h9d7KyuFbzCROEZxFAJuvNG2AfVf/gIbXtjPhrYJUviplPtKnCyHfbo3lBCYTH01NRYvmxxNOr29mArWZH8H21yJ3g9G2zpV3V90kS1tUxptbRRNbTTlK43xEr6T2UxPt6NDhU+2bJDkhZ4ebW4jmaRuRmX6NiZoIlHHIUf4wEnAVinldinlMPAb4ON5SHdcSBN+cbFJInsRvuPiqUQC/v7v1az9/v1mBampF6/NT3RkpfA1IsppY47BQWfPER319bmHlnWZTGxthUiTIvzGRsVXXpYjvQyOWnE3XHGFekCD94+JTAyK1i++C6jqLikxcKIhJo2jwtcIwzVs7/nnw6uvmkwHa9fCJNrY1OmhEHNV+C6ur2lkGV7B5P4aj6fLQp90TdeTgYiyUfg9PaRHJFI6KHwdWh3qeTnq6Vvh2mttk6a2NNraKJ05AQrfbZ4LMvV3/vlqR7qA90gTPpmkbZcazFBjY2owfiAJv9D/FF9MA4wzm83AhxzOWy6EeBvYB3xFSum4F5wQ4irgKoCmpiZitvXJwdDffzI9PfuIxTaztK+PNVo6PT1z6OqawYoVL9qUYnPz8UQiklgss0RuaSLBmhdfpOmjH6Xsq19l++IbgcW8+OKbVCaTDK9YwYuTo8AJ7NjxNrFYF07Ytq0CWMbKlRsoLu5gzurV9CxaRKeWr9dfnwLMZ9Om1+ip6OS4zZvZffQ7wDE8//wq5sxxjzefSCTS5VTS2sq8ggI2uJTbgrExdj3xBP3WkAABsGjzZjZu2cKIoRWPjgo6Oj5CvGCEvW+/Tcv8jcACnnpqJdOmOUd3XLWqnhKOou6p+3jxH26ldsUKahIJdmh5VqODM1i3biex2E6W9Pfz5vPPs337cUQilabndUJp6YfZuLGdWGwLS3t6WPPyywB0d59GT89eYjFlnpva04N88UVaamro6jqSnp7JxGIv29KbfNZZlH7lK+y89FIAnn32GE6ljZU7ZjDHIR8ileKEHTtYm0PbLerpYYEQrNOutT7rvJERWp9+mr6FToNoO7ZvX0BBQRWx2CoWbNzIzq1bGRgeZu/eScBC/vzn15k5c4CKHTuY8c47bIrFeOedOUQiM3jtNXsf0TE8LICP8Pbb21lT+GemDA2x7pkXGR4+nc7ObcRiGUo4fmyM9U89Raq8nFRKUM6JTH/jN/zlxluRljKKxwcYHYV4XKWxtLmZN7dvAE5l7drNzJyZ8XJpiscp2raNZuP+DAEx7eWXSZWV0epSR0s7Oljzl78w+aMfVXV/2WW+ae7cuZiisWF6hobYvfsNYBkvvPAOqVTm5T+nv5/u556jq7eXeFy57LW2mstrQiGlHNc/4FPAfYbvFwM/s5xTDVRqn88DtgRJe+nSpTJXlJWNyBtu0L4sWyblyIiUUsof/lBKkDKRsF9z/PFS/u3fGn4YG5NyyRL1eWhIyuOOk6te6JMg5RNPSCl/+Uspb75ZPvGESnPlSvf8bNumznnoIe2HK66Qcs2a9PEf/Ugd7+vT7nvCCel0X3vN+1lXrFiR+bJqlZRXXeV+8nXXSfmXv3gn6IYTT5RydNT00/79Ko+/+PZmKT/9afnHP6rvq1e7J/O730l5BffI1mu/q3745S+lvOkm0zlVVVJef7325ZxzpGxrk+edJ+XSpZbndcDcuVL+0z9JVY7HHy+llHJ4WOXru981nPiHP6R/+OY3pSwsVJfYMDgo5XHHpRvNzJlS3sL18nRisrPTJRMnnOCZR1ds2CDlZz6T/mp71m9/W8o//SlwcuefL+XixdqXs8+WsqNDSinl44+r8nj9de1YS4uU554rpZTyi1+UsrbWP+2SEim/9jUp5ZNPSvmtb8m9e1Wad91lOfGTn5Ry8+b01y8V/kw+ccYPHdN85JFXJEh5993aD0uWyGRSpfuDH1hOfuYZKb/xDf+MOuH//l+tE7tA7/d63SeTvkmecIKUl5y9V8q//mvZ2qryfNttlpNuuknKhx+WUkr5+9+rZ73jjtwewQ3AaunCqfkw6TQDxkhd01Eq3vhS6ZVSJrTPTwJFQgiXWanxQ0qDSQdMZgyv8Ao2k4HRBlBcDJdcwoxnH0ifq/vi62kZN4q2IohJp7BQG/Jqssp1s2gveNkmYfzmBottWc9b0RRlatDLt8t5oANAsjfFF7iTgcuuVT8Ywh/oMHmwaWYMvwiOOnTXWZLJ9AWO8ywGk0BFhbL8OUZEKCmBiy+GBx5QexbshsWT29hPE2vWeGQklw06HMrChIaGrOrPZNIx2EpsJh1DH/GLC6UjXUeaSccWqE2H0ZsmleIyeT8rjrzKMc1EQrln1tWpcxGCsjLVJQ7YpC1kwmOUlMBnPgM//7lvkj09MLVYmRCjUZVnW/YMJrmBAdWXDjUb/hvAPCHEHCFEMXAhYIoxK4SYLIRiMSHESdp9AwQryQ2DgyClyDR0QyH7Eb6poVu9Ja66ivo/PkCEUZOXjm4Sd1iEmobjpK2B8PW+mB5CFxZSpS0wyorwLenaMGnS+DxILNBJuXSymhzRJ9u8YgBNeuVRYpxB+XTNFdNgW9bhRPh+ax2M1/b1YZuwBctL2TJpCx6hez//ebj/ft56Q/l9H9O4nzYmuRN+VVVus+0OZWFClq6IJsI3vLBtfvTFxWmf9qATiWkvXy3ProQfjWYmKh97jNVlp9Mx6mToh0SiMJOGtrJb30PXkfBzXUhoWQdjg3Gu5POfh/vu8/ZEQJVFU5F6YRcWqsf2suEPDCj6PaQIX0o5Cvwz8AywEXhESvmOEOJqIcTV2mmfBDZoNvxbgQu1oceEwBY/xNDgbMrGAJuCtHa+6mrk/zmHT/I71bi1dHXCd3PrBewqxTK5apvsamykdkQRc1aE7+XSp6WbkyqyRA3VkXZJrVZvqiAK/9jn/4ufcIPjZKIOJ8L3cp02Iq3wHQjfpPANE5W+hF9drdw0H3kEgDq6GKuqdY8Mmqv6dNr4xIgsR2iOewfj3Q+CTI6DoY6yIfyf/pRfN13vWs4mwjd4sjkSfpajHROCvFj1tGtr4cwzTetxrNAnmycVZNJ13B/eQeEfcn74UsonpZRHSSmPkFL+h/bbXVLKu7TPt0kpj5FSLpZSniylfDUf93WDF+G7KfxUSs2YexI+UPyVL3G9+CnxDplONx5XHci6StsIV5WiweZB0tBA1ZBqGFkRfjYNORu4pGsiUimpq1XvcVeF/8YbdJdPpZkZ6bDETiTnRPidncEJ303hm8rYsPrIl/ABrruO+c/dDkgKI5K6aIG7w9N4ytnvhZ0l4VdWogSGYVMcR8KPRGB0NLDpLB1xUxMZJk8zI/T+t2oVNDbSXTfHtR+YCN9g9nQcMBlGJVnDb8WTtZyvv16tGXHRqf39ikPqMXtC2fqB4SV1qJp03nfIhfAdVxc6qGUxbSq7SuYTfefFNCu57VdhRZrwh4bSQax0GF269DxXDZvd5AJhogjfRXmabOPV1VSM9RGJeBD+HXfw4rHXUlFh8D4MYMNPtXXQ1xesnNPXGgjfFhceVAYs7oKehD9lCvsr5vDR0lcpED4errkqfL/6y9Ut01LGji6/2pqHCVP4N98MN97ouetVX19hOivG+nMVS7kuJnTaUcwI60h45ky1Wcorrzierrev+jEz4QdR+CHhjxO5EL7jalmXzve7KV/klLU/SzeYrAnfId3eXjvhF/XGKSx8nxC+i/I0rUFobETEO6irczHpxOOwfj3rak83iysH520r4Q/vVZ0kK4VvUIiu6lNDIMIH/jT7Or4sboGKCm/Cz2E7QmBiCd+QbiSiyslESJqJK6jCd7Ph25wXolEVaKalBU4+2TPQpa7wa2rMeXYl/Fz2HghiTXbqJ9dfD7fe6nh6WlCM+Jh0DAvnBgdDws8LbIRv6CRuMfEdVxe6dL7905dSnmxTIRekpDMux034thgk0SiiM559PB0/G77XyjMvuJSFSeFrw1XXWzz4IHzucyT7hZnwHRYbmYbDDQ2MtAQn/Opq1QbG2jJlYVrJbIS2z29Qwn+j4EPMYidUVLi/2MBst84GPoS/p62E5u1DgQYPUroTPjgoUC3P2Uza9vaiKqqmhu5uNVdlGbyqOli9Oh3v3nWRG4rwKyq06aIghJ9LOduG0w5wIvxly9QycofYIXpbrRz2UfiGUcUha8N/v8FL4ZeWqn+BFL4LeUaj8Kuqq+HOO6GyksF40lOU6fAjfFMb1F5SWRO+2yydDoMZIyt42PCF0G6p5dmRCMfGVKjpiy8OFCGwoUGV1dAQaZMOBFf4oC3f1/LsSvha2whK+PE4rJr2CWht9Vb4E0D427Ypy0JbG/z+9/5JDQyoqs6W8IOadHQFK6WEggL3Vbbl5Yoo/+7vAO+NzBOJwkwdG4bOeSV8v1EUqAboVLlXXw133237WS/H8v4Ob8LXMTYWmnTyBS/CB2eR67ic3KVhRKPwm9FPqjjetbXIjnh2Ct9iA5LSYdJWy3Pa4yQb5CNWuBUehF9Vpd1SczlzVPh//jMsXw7V1eb5soGBzKayBujv2Y4O1Ggnrgg/qA0fYLQtbiL8ykoHRyNtLUVQwu/ogLapS2DfPiZVD9LZ6fL+zNWk09/vGnb5hRfU32GK2bdjyPEcI0z9ICDhj7XHGRgIZtKZNAlSKUlKi1xiCnpmxJ//rBLUCt/PpJNOw6LwHYXPRBF+fb1zup/6FPzxj6b4QJApx9KkWeH39Tl4c2pvyoGBCEI4Nv8JQ0j4GrIx6USj0NpZjPzE3yO7uynsyZLwLekmk0oAW234OuEHVvhBlXtZmSKWbOBh0kmXmcGkY1P4d9yhdjXCEpXUJV0T4RcVMTakWCUbhS87zITveK1mt85G4U8q7YXFi1m++7eMjuZRefpADzqZLK6na7uH36sGUz9wGK3aomVHowy1qDwHUZ1NTVBOP0NFqvBcFf5995nu7afw3Qg/rwrfy+zplW5JCXz84/A//2P6WS/HwrHhtLu1bZMYHZow0heHeoVOyjcOD8K3hCT1Uvgmwtdsk1ZEo2qeqP/izyO3bKVOdoyL8B1dBnMhfL+d1I1pZxtAzcVLx3RLLc+2zdd37lQPceyxgHtALyNMhA+MaiopqA0fQCYyN3Il/CxMOqOjmq91JA7nnsvSN+4CpLMdPxci8gmc1tqqhOdITZTELv+0s1b4DQ2ManMlQRV+lDj9pSpdW6RM0CLNTVLq3uARNTLiPNdqI3yLScemaXIZSfmtdQDvua6rr4a77jL9pJejcSG6/hw2s442qhwYiBxQ+z0cLoRvMXEEJnxw7IB6W+komsJI3SSWszJ7k46hwekNwqbws7XhBxmq6mnnaRhs2uFIS1dX+OnOeffdqpNoMJl0XOZJrIQ/IosoYjgrhT+WIl33foSvW1G8CF8n9gYRh7lzGZx+BB/mVed3Zy57rvpMJurRqWVdlMG9E0D40SiptuwUfgMd9BVnCN+m8O+8U43sysvTo0qvl6vJhj84mLZ3VFYq08iQ1ZI1USadggL3MOLTpqn9aVetSv/U3Q1FBSkKCjN84bq4TcvzwEDkgNrv4QNM+EJIs23MEGY3kA1fxT5yTF9vK/E4xD90HufzWPaTtoY3hOOy/9JSGB7OboV+UMJ3s0/mkLYp3IE2cqirU+ptcBD13xNPwCc+kb4ma5MO0FPUwIyyuHHtkCvUC0iSMvRXP8KPRFSRexG+npfalMpz/IJruZbbnQnfz8/bCT71pxN+QWOUVHun77YGQQjfZG6IRpHx7Ag/SpzOAlVZNsLv7oY1a+Css0yrmh03MtfQ12dQ+Ibys4UmMeR5Qgjfcn8bvvhFuO229NeeHphR1Y0wFEBI+AcIyaTaFclUXwY542XDTytPt12jMBP+/hnLaKKVJvxjelRWqqHsWHvcUeE7WWO8XNhsiMd5L97gH+cpl04yNOQ4u2RS+NqLxLTW4Xe/U94ZBqY2KXyXzqe/D3WS7Yw0MLc62NC9qgoqSDJUlOlNfoQP/mWtF1mV5mtdeOrJzGEHye0edZ+NR1RAwi+ZUk/1aNx3OUUQwh8cNJhWNFdgCGbSqa+HRhGnXUYZGtLmN4zxyH7xC7jkEkWc2og1nR/s5D02prYmra3VvoyT8Nevdwl/4+e6rKO42GFIoeHUU2HTprTrZk8PzKo0l7GbC7ju3jU4GBJ+XpBMQmmppaYti6+6u819UXdFM63+dOl8RsLvEI28x3xmP3efb770yk25EL5tNF9QQGVZKjjhd3TwxMoo3/ymD8/kYsN3gUnha47ZOrF2dQH33ANXZSIj6r7hfgq/qEjVk074HTQwszwY4VdXK+WZLM6Mohzty2AjoiCEXzGo8lwfFdzHFUx+3KXubRLaBz6ErwdCrZgZJUqcPT4h1E2bxTus7rYpUIMZKgjhFxTAnKoOWkei6bykt1mQUhH+Zz+rvhv6n5vC7+tTQQ9ra7GtRHTd/c2F8FeuhEWLXNxXszF9uvUTIeDyy+EBFT23txdmlHU4Er6Xwg9t+HmAI+FbImaOjCiPQB22SJkBCb99LEoHDdQ++4jv5rN6Q5d9SZPrneOkrZbRaKSbwUHfQH0AjO6P805rlP37ffaVzdako4WpdYJp0laYA6iNrHpTeSRMn54+X0Uy9bfhg3k+ri3VwPTSYIRfUwMNxOkpVBU1MqLahJeXDgQn/NKkcqutr4dfcxGzXnepe8PLJBA8JhMTCZW3yZOhZm52hG8MuW2EjZCESLezIHMlANPL4uwdbEhv+zt7tnYgFoPFizMJWUZSxvzp0JVwXR02s6enwnco4zvuUH/ffdch0/kyfX7mM/DrX0MqRSIBk4vM3j+ek7ahSSd/UIRvMXBaFD6Yh1q21YUeRKS3w3gc9g5GqaWHgr/6qPLL90Ba4UuzfddV4Tc0EJUd6WfyQ8d7cfanVENevdrjxGxNOi7+dlJaTDoa9Oeo/03GFVOHzXTm0fmMhL9vuIEpRcHIs7AQZlfF6ZDmRVeOJGZYPeXlLgiZvBSKUSgqoqwMxkrK2TT9bPjTn+wXZFvOHu6Cukvm5MnQcFQ99XQGJ/zSlKPzgS1EMjCaEoAMTPhTSuLsSkTZtUt9Tyv8Oyx176Dwrc4IpsVxlnbhdg1lZTazSzyeDmrK9u0OmXbxvrPBr/4qK+G00+Dpp0kkoLEgHlzhd3aGhJ8vBDHpgJnws1H4RUWqs8Tj8PaeeiYXdxK59gvKI8EDqnKl8h4xwHVP3GiUurF4+pn80LU1TpyAhJ+NScelLAYGlPg35busjJqifmropmLzWjVhZ4DNg8qjnI2h35sHG2iKBFfLs6o7aRtVb2ZPwjdEXAyi8IuLzdxZXw9Pz3Gp+1wI36UsjIRfd2SURhH3HsVheLkOO09gOBFSf6SaanoD8SFAU0EH23sU4RcUaIO5ffvUv6VLMycaysK0L7QBpuBrLoQfxIHh2WfVO6C+XoXwcUQQ5/cg/eQLX4A77iCZ1Ly3DHkuLnZe1a+PHELCzxOSSSgrmzjCBzV03bQJ3tpQSGVZCubNU6r9vfdcr6mshEoSDJeamb2nR93b1gajUeURQjDCH9jTwWBFA4sXq72XXZEnInLcRUp7SV3Kg2w86bM2U4LN/dUydDfCqPB3JRuIEpzwZ5TF2TcUQOEb4Ef4XV3QUDuKMDhb19fDe6kj1bBi0yb3BwiCgIQvGqI0FcU99xwA9SwFBVCScE7XifB7CqPMroxbqe4J8gAAIABJREFUNzZzRT3KUWDnTuWtWFSEWmh15ZXmEx0I36p8TYRvWY3uSfhCmGyeelmdeqqLwg+KIKbPhQthcJD67u3UywCur5CeRBwcLAht+PlAXhS+z0z+8uXw2muqj5eXajOk11zjqfIrK9Vk4mCZmeBc3a+jURV9j2CEn2qPM/W4KCedpBS+68StS0Pu6oLzz3dQRR4umWApt2iU6qF2LuEXrFl4ie0a24rmkRHcfC310OHxOOwZbKAxC8KfUhxnT39AwtfiwPsRfk8PzKoyE1F6XvaaazKGYx0TpPCprKRG9AUi/IoKVFgKh7bsRPidBVHlbRIQNaOdtA7XsX69Zs4ZHVUzpRdcYD7RMFeiE751Pttmww9i0tEvMHTmtjb1/l2iImAo92Ad/f3BYxkErb+rr+ZTnXer0bil/hwjZhYUIMckw8OHqMIXQnxMCPGeEGKrEOIbDseFEOJW7fg6IcSSfNzXDY42fJ9tDm1mPR+Fv3x5Jk5GSZUWovWv/xpWrHBlDZ3wk6XmdF0XyDY0UDkY3IZflOxmxnG1HHmkIjnjpLQJ5eWOB//wB2WKfuopywEX27Kbwi979TnWcCLtI3a7v229g4evc0ODGpq/8Yby0mkQwQl/UmEnu/oCmHT0A11dgQh/RrmdiPr6ULthvfSSWYLmmfALCrTDQlBQKHyDnnpFygRnwo/LKNPLgue5OJIiRWGG8P/0Jzj7bDupWiZtCwrshO9lw9eVsGNEEEs569vVHnGE+q5PKKsH9J+wjcfh61+Hh58KWH9/93ecOfgUtSNtwRQ+mTVdhxzhCyEiwO3AucBC4CIhxELLaecC87R/VwHexu5xIheFb+O0AISvo2SKZuuLRODCC+FXv3K8Rif8RIk5XS+FXzEYTOGPjUFqVNIwqSAtQLP1vNTnHTdvthzIRuHX1yN+9zt+UXmN6zaS6WtGR22bohuh+3Q/+yx0UUf1aPAHihJne2+U0dEAhK95evgtju3uhmklZrWcXkwXicBFF6mIoDqyNel4TCbqbUQvrsIIdHV6+/j7Eb6+h7KxnexPNahnDIjqalWuqZTmoXPXXaZV1WkYRpVCOMTxQT2+EFIJCMtqdM+V0BbCb2tTbWfuXPXdNGINQPgXXAA/+hHc+3uvcKgZjEWK+L38BJO7NgUm/FSkmGKGDj3CB04Ctkopt0sph4HfAB+3nPNx4BdSYSVQK4SYkod7O8KP8K0LIoaHFXmZ6srHpDNvnjq/tBTKZxga3OWXKxumgz2lshLq6aS30GzScVX40Shl/cEIX29U0ajZi8gThjwODipiBYdpCBd3QZOftw4hoKuLPdHjXfdLTV/js3PMSSepvw89BGUVEYoLfZaWGlCbUhPYHR3KLCSEB+EbAqj5KfzJRWbCMK2Evuwy5Zetl6uLwn/4YfjBDxxuoIUZdoLVi2y0pIKhLu8AeH6EH4mo4jcu4GoZjqpnDIKhIQrLi/n3f1dfF5VqSmHePPu5RUUm11XTBjcauruhomJUFYFlbicSUcsIghC+vl5hzhz13WTHD0D469apvzsTUUb2+5dFfz/cy5XU9O2xdWTHbQ6B4WrlWnugbfgeu7AGxjTA6CDWDHwowDnTANsW0EKIq1CjAJqamojFYtlnaNoJ1Nf3EIttzfw4NsbS5mbWaOkVF5/GunV7icW209lZDHyYzs7NxGL7AFiyezdvrluH9FCgixcvoKurmH1DA7Q/9xw9Ws9ZUF3N3ttvp1cLFqYjlVLKc2vXGGOG59q37yQqK/uIxTaazi9taWHKni0AvPHGu9TWOu96kUgkePp/X2QWJbS1bUSIIeB4XnjhLbq6nMf9i6XknSeeYFRjkVWr6unvX0Rd3TBvv50iFns9fe5R69fTMmMGfZa6WLWqETiGd95ZRTKpyOeYp55CTptGZE+C7dsHiMXeMV2zdu1U4CjWrXuFju4tzEql2OhSx1JCXd2HiceLmT+/l0RfH2tiMRKJhG+7OKJnL53U8+STb/DaazNoaKjllVdWOp47q6+PRCxGW9s0Rkbm8Nxzf6Gw0P7Cbm9fTknRNjbH4+zT7t/TM4+urknEYmrru6Pr6mi59VZ6Fi+msK+PY7Zu5W1DXsfG4MtfPpnh4QJOPtm8tfPSRCLdPnXoz7pjx0IKCiqIxdRsfFmkHNnRSizm7pvZ3LyIVCrCrjffpHtsjC6HMquoWMa77yaJxZTD+o6+ao4pfStQvyvu6GA+MH9+jK98ZQonrv4OG047jQ6Xa43PV1h4oq19bNp0NOXl1cRir7BoyxY2btrEiD55AZSUnMKWLW3EYltM6U7r7CT18su0am159+6Tqa3tZtOmTRQVnc5LLzVzzDGK9RtffJGynh52u+RxdFTQ0XE606YNEN8bpXPzTtf2qaOzs4i9nMIoBay7914SRx2VPtbfP5/29npisddM10wdVFywY0ecWCwLs994IaUc1z/gU8B9hu8XAz+znPMEcKrh+/PAUr+0ly5dKnPFihUr7D+ecEL64+TJUl55pfq8YYMKnPPb3xrOXbLE9x4DA1L290spv/tdKf/wh8yBV16R8h//0fGa7xb+m3zw7x41/dbQIOUXvuBwck+PHDz5IxKkvPtu93ysWLFCrnmsWT7G38jHH5fy7bfV8/zudx6Z/4d/kHLbtvTXW29V11xzjZRCSDk4aDl361ZbEvffr67ZuVP7YWhIyjlzpPzSl+Spp0p55pn2237/++qa/n4p5YsvSnnddR6ZlPLTn1bnf/azUspTTpEymXSuWwt6j1oiQcrnnpPytNOkPP10j5N/9jMp779f3nyzuldXl/Np5eVS/um0H0r561+nf/v616UsKTGc9PrrKtNSSplK2drRX/6iB2mSsrvbcCCZVM9ngf6s55wj5UknZX5fvfgyuUSslamU+2MtXy7l2WdLKa+4QsrVqx3POe00KT/ykcz3M0pelS8vvsY9USPWrZPykksy+V+0SMqREffzly2TcnhYSqke9ayzzIf/9m+lPPLIXvXlxBNtac2YIeWllzqk+/DDUt50k5RSyrExKcvKpLzxRnVo6lQpL7/ccO4dd0h5zz2uWWxuVnVz0UVSwpjsOfIE13N1bNumzu1umqfK2oAbb1Ttxoo9n7pBnk5MPvecb/JZA1gtXTg1HyadZmCG4ft0YF8O5xxQGOPp6GbWIOE1jCgt1eamrEP35cth61bHTawnFXWmFwSB6vqucV6qqoj0q3Gvn0knuVuZMIwmHU/zoyXPHR3K7LF8ucrTVsPgyG0YbPOp/8MflN99d7er7TKRIB2oLMjw+owz1N+FCzF5evihUBu7trUpG64+vHeEVhZeURxHRtTQvX7MbsMfGkq78is71J49av9WB/PMf/935vO2bYYDPmVhNemM1UWpk3HPOYd0CIuAi9uGh2HvUMYV2BdGU99vfwuf/GSm4J1g8Gt3M+lUVmpmn1TKlparyc3QlhMJ5Y/Q1KQO2bxkfEIjt2g2h2XLAATDI/4B8JJJFbtpuH6yChZnsOHU1Kh2k24f+jWl9USJH5I2/DeAeUKIOUKIYuBC4DHLOY8Bl2jeOicDPVJKmzlnwmEI0WokfJ1D0u1geNhhayQPWJd3CwFXXKFs+RZMKojTMZaxTeqePo6mbCGIRFSD81twMtjcQQcNwQnf4prZ0aF+WrBAfTdN3LrMKtsI/667lP91PO7YoSETs0gIAhH+ueeqW59+OsEnQVMpCotUuTU3w9694yf8dETT0QALgq66SsUQcsBzz4E+4g/yUtVhcxuuV6ttvVwz/Wz4YN66tbtbeUNVDwectDWme999qs17wTKP5kT4VVUa4Tt4b1m2tXBMV9dY+oS/LVCix2pmyBC+vmZsZATfAHiJhDLPpGqjKnbQQw+lj7ltgpIoOTg2/HETvpRyFPhn4BlgI/CIlPIdIcTVQgh9uv5JYDuwFbgXuMYxsYmGpcFZFX66T/g0ChuclOc//qNSPZYgOA0izv7RTOfz8yARAooKpa/CH27JKHx9I2lfhW84QZ+j1snINnHr0AFVGGpNra9bpwp10SKIxz0Vfpq4AkQtnD1b1dPJJxOc8Ht6KGyopaBAuXRKGYDwfbY51NtK1XAAwr/gAuWLPjJi211s/34480z1ORvCtyr8gkZFGF6umWnC99iVvLFR3XpsTD1jN7WUjwTc5F7vJ6tXq1VXU3z8MCyLr5y8dCoqRlW5OYwUKir83TJ1wjcqfBvhB1D4c+aoR+uTPvE2UIejxJH1BsLXXhJuETN7C6OHrMJHSvmklPIoKeURUsr/0H67S0p5l/ZZSimv1Y4fJ6X0Wvg/cbC4Zroq/CA74rikm0ZFherZlvg69cRpHc7IeZ1zXT1IKitpqkj4En6qLU6XiKZd7Tw32HbIs869VVWKG/brEX891I1uMhCCTOyUsjIYHHQlfNMG2UGDWOkISvjxOCIapbFRRU0EH8IPsM1hepPqwbjNpAMWwi8rg499DP73f0157u9Xac+erbgxW5OOUeEXT1GE4aXw02GopXRd79DYqDRJV5e2aQ0FFBYE9IbS+8mdd6oQA34wjISdRoBq3+FRV+8tV5OOoYz1dqsrfJuXjE8563PETU0wYwbEx/xX2yaTaiMYEY0qYlm6NL0BsVs8nZ6IGqEdkoR/yMBC+HoldHSo4WJ6rUi2ROS2wOYL9hgrxWKE7v7MytIgPuLTSzv8F17F4wxVRtNm41wJX782TSSm/QjNSBNKTw+8/jr81V+pA0JQXa0sY9Zw4ibTxAQSPtEoy5aRDjCm+2Q7IoBJR28rJaPmTcZdw/Z+4QvKxGUoZ9100tioFgWZFL7PaMf0okTFxK+n01Xh62GoK8q9zRGNjZnb62lFCgNu3BKPK9PnW29lJlu8YBlhDwxkbNv63sA5Eb5hWzhfk46PK3BLi6qG4mIVF6hlxH/xla7wC5q0+tPi6+j3Bzvhd4pDWOEfMnBQ+FK6LLrKxqTjRvjz56sbGAziBRFhIgedWF3bYEMDU0vivoRf0KXZEMmk52vDN5zQ3p555Lo6wyEPUk6/C375S7j44swkpRDUVCmVaG3oJuvCRBG+1qm//nX1taTEx9qgMUkQwrd66brGeJkzR70Y9AZGhvAnTYIjjwxu0kmlFDkayaF8hrdJRw9DXVfY57nPsV7n7e2ZtlhQVuKxTNuS55degs99LtjuXg7xdHSVr5dvVdWoa1kYpuDMMNzbifB7egwDVY9QHqAIf/Jk9Xn6dGjuj/ouvtJt+IWTtDwvWaIy0tzsqvDjRGkgbt2iYMJxeBG+JbyCvg2frX1la9JxCVUAZJQeQCqFiBQ4Er6Xwp9c5E/4xX2aDVFDNgpfSvXIutozKXw/wi+X8OCDcOmlmQM1NTQWqxZubegmpRp05yEdWSr8U0+Fj3wEjj7aJziiRhh+hC8YC074oExcmzal82xU+HPnWuK8+JQzmE06lbO8TTr6NVG8X6p6nZsIvzGgN1R7Ozz9tNrVKgg8CF9/cVVWuhO+58I4zds1Hld1onO6094XXmhpyYiD6dNh72A9wy3BFH7xFEOer7oK7r3X1YbfPhalsaAj610wx4vDi/ANDU5vT/v3O/BOtsoT3G3df/M38PzzSpp0dzNUVmcKAOVrw49GmRTxJ/zSZJzIpNwIv69PdQqjSSeowj8tFVMbXRiHKJoHCTh4Jxht0QMDJvOIL7IkfIBHH1Vb6gaBbv5wm7StoYeCenN8IM+gXueck3ETIqM+GxszZZ0mAo9ytsUfAqpne5t09GeodQjoZYSR8NPx/icHjCGzfbsKSekxgjDB4NxgVb4mwreEVdDhSfjakmerQ5mJcH1CeYCy4euE39iolHhydzDCL5lqyPOnPgWPPkpN+YjpOXV0DpZTKYJuZZc/HLaEr3ujbN7sovCzdcoXwnmX+8JC+PSn1c448TgjVfV0dWVO7epSp7i6Z0WjNBb4E37FUJyiyZmHiPqNRA12G+s6hGxMOp/usG9yQjSqQsXio/CzRTYmHS3PdXXKgcQXVVVUjClmdVP4UcwvVfBR+AUF8NGPqoB6mBW+aRtI8CxnPW2Tl055KeUFQ74Kv3bUm/CNm8Vv3qwmKgsnBST8lha47jr/83R4KHz9OdIK38WG39/v3M30tC07I5rjZrkueFGQ0kz4NTWK8IMo/EZh7n+UlsK551Ib+1/AwbSZFIiDwL6HLeEffbT6SR9xm/pELgrfMQ6qhiuugHvvhY4OZH2UVCqjaLq6VNt2Hdo1qCiRfoQfGRmiZlLGIFhfrzqHKTSsEYbYJlbC1006UuI5n1HR1UzjaIt5owuAaFT5q+Nsw6+qwrZJdSC4BSaxwoUwPNHQQMWAe2TSnh6YXhqnoDELwgel9FatAilpb1fzCVVVDgH8PPJs20NAQ6TQvTj0Z6ge9hYvpaXqGdrbYeNGrV8EifK5datqIAutcRI9EMCk42fDB5c2raVtVfimSVMfU20yqcy8+im1tdBJPal2bxt+MgmNEYc8f/7zRO69i4oKez9IJlGEn80m93nAYUv4kyapCn37bdXYxm3S8eokTU3KaPvqqxRoClFXez6iQ6nlMW+FPzRUQEoKU5Z17vCMma4RrpPCHxrS7J4eneQTrXfywtEOSyqiUapG7CadVEq9hCor8QgR6p9fX+RYf4U9cYqL3QnfGhoZMiMzV8KfM0cxdSxGW5tS98ZAbun68ZhMdFL4AJGIoLvT2YUyvShuyL8smpqUN9OmTdrCuyCEf/vtmZnRoDCsnPI06XjY8MF78ZU1EKHpxerTLqxbjdbWKoU/1u5dFomEttuV9YU9dy6UlnJi+buOwmegsMLFFjhxOLwI32CcFkKpmf/5H/WSNYnUbCdtwb+TXHMNPPooxU2qUej23M5Of8KvSXkTfl+3YIwCqxkd8Om32sYfTgofNDJy6ySDg5yR+BPvLPik/Vh9fTqss/GFY5p8zIWUdfipIhcbsCcMrpluhG8NjQzKHFdW5kH40ahi1Ntvp709YzPXichvExNw2DRGw2BJDSNx51FlmvAH/ct5+XJ48kl1TSCF398Pzzzj4+vqAMML26rw9TZYVTXi6ZYJHoTf0eGq8NOE7zHa0fOi500nfNHpb9IpKrCHggDgmmu4cvRO20isuxuSJbXZxzAfJw4vwjfsXwqqcff1KevG/2/vvMMkq8r8/zlVXZ2rc+7JMz3kMMyQBUGQKBJc0ioqKKgEQZHfohjQ1TXjsigIy4rgioAKoisqaRrEkTAzTGByT+yZzqm6qnN3nd8fp25XuqlCT0933e/z1FNVN597zv3e73nPe95Xm/0IqG0S9ZeyekhOPx2amykoUSEbElH4xWPmMVPGO4fopTSqoRtlFYpCKPGHnsKHUFs0IuannuI510fILdJRpeUqrHMoUvIkogYfkyV8rxe3lctFb69u0nVThOrPKJF5X5/KoqV3zZNJUPRQVqZMZ21tiAP7J0Wxdo8nBxNNYtDoDdoCDOaX4+7Vb3NaGfIGrO/zueeGvVgOPxzrsZInn1RzLhId59IgZVyaw9ZWRdS5uUHDMTRTwg8NCMcq/KhB2yQUfg9luH3WJh2Xy6D3ecEFnDjyd0a6ox/g3l4YzCu2HRsqXcgswo+BZsc/44yYhykZu5oV4QsBRx1F6S41yTiS8E3NzaWlFI72MDwcF6VhEsFOP92URzV0TQ2a9hhD19zZGU7MDjYUvpTIhx/mp6Of0R+ALS/H1dutHpiIZyVKqSYzMB46tsdorETDxISlN4beca0UfpWenZaIJCh6yMpShP6Zz/DB3Y/oK3yLyUBGJp2RgnI8/eaEb5TPNhLnnBP+bWnSkVKNR51zTnIv7NBYV16eInBtZmxLC9TVhbaJCxykoNnwzcIrWCp8k2uOVfjFxTBKDnJ01LRII/5RglkGsbfcbt6Ycy2n7f511OK+PhjOL3EIf8oRMmNAmPAvuCBivQ3XLV3YsXtWV5O39g1cTEyadCwVvtuNWyg7rW5DB2RXgG7Koxq65WAiTCo5TRBrPe4oha9HRqtWMbFgMW3U6HsXhVyEYl1D06LwKyqsCT8Z52YbhF8h9F9SpoSvXc+VV/KB/j9QU6bIIztbEZgdIjIy6YwVlePx66tPrQyefusX65w56lkoLg7FoDFry6tWqQQnwWDSL2y6Ve+vvn7SY5WWlpjJcTp1aGXSCXZ2MzgYrfBzc1Vn3ecjYcLPyVH7B8fNBWBWfw+DOcYv7H8ecQMXt/3PpJCcmFDXM+otcgh/yhEyY4CalHPNNfDRj0ast5TcBrDjMujz4Tr9dK4qeIHOTmU56uuz5j0RiphpZMd39QaSU/ihUImxcVqiFP7YWHzk0AcewP+J2wADd9JQJM5Ywo8irqki/KGhUDS3BBGyAZsRfpmBT7sl4Xs8DI24+JO8mNPbn51cPNkUbUTKhPh7PVFSRu5At26HVLueLH+fLfPWl76kPCyFwJzwf/pTuOWW5Osv4tiRhN/aGlL4Jt5bVoSvZaeK9QWYDK+QoElH23dUZkVl64qFp7+bwXzj47qqK9kmDlMvS8IvlvGiIseGP+WICa/wm99EdCWBqJG1JI9riM5OuP12PicfpLMT9u1TL/0FCyyOna3yXxoSfo8vTuHbIvyKCujsjOtBRyn8WBw4AM3N+A5XSc10CT/EZNOi8JOtv5AN2Mge7/NB8USShF9ejn9PNz/ns5y49ueTi+0SUSCg3mGxZn5ZVkGZ7NKdRapFMhUEbfVYP/Up+Na3Qn+ys5V/Yiyam1WjPeWUtDwnc+aoeWlShhV+ViBg+IIyTWReUUGwPRyYLRKT3rwJKnwI1ZHb/NnOCXQzXGB83JISeGD8ZuTPfgaEx7WCpV5H4U85rJT4VBL+0BAsW0aeZ5ysPU2TuTZNIzkCE8VqGr0R4Xv6+5Mj/JDCjyX8oiLFEb7O0XhXwQcfhM99Lj4WfiRCdutYwo+aVZysDX+qCD9Uf3px2kdGlO93wbi+K2lUXluDYw82d7OP+QS9xZNJUycVvoVXmIFJG6qqqKJDd2Bei3OU1pn7998Pd9yh3iRapvBEEaPwW1pUuxgZUcLL4/MZ1p9pIvPSUmSPYtJUFX7kvS4pgW5RGZ34N/a6BrsYLTQ+bnk5/H38FIK79kJz86THjixzCH/qYUXMaWjIVnj1sM9xbtND7N6t/lsSflkFFRhPvsr299NFRXQ0xRxliTElIgPCFyLUlW2Lsd8HAirc89VX6ycwj4QQcYSv3Z6KCpK/z1NF+CFW0IvTPhk4zaUfZtjUSwegvJyRFlX4A5feonzYiTHpmLz8jMLZu2sqqaRTd77fwACU5o+YBgozRVaMGcPnU9lbLr9c/U/lxRoSXPX16hTr16tVtbXgiZsUE4apScftZmJcjXXFEn5RUah+LKZ59/er1ZEdouJiaJfmhF8w3M1YsXH9qdsk6P7Y7XD//WHPtUqv6XGnAplH+CEzhiGSbchGAeA1jI9PRvDafcyHWd73Ci1bfHg8Nqb+l5kr/NyBPobzy3UDe1kq/K4uXUIpK4Px9hhF9OijKkiax2Ou8AHy86kuHIgKI9HVpR6m4mJSMr1MCeG73RAM6ip8dTppGDa4oMB6cHysVZHc8PvOVVlZ+voSMuno8ZSn3ljhBwIwPy/JlyrEB2P67/9Wdh/NrpQmkw6o2wHWCt+U8AkPrsaadKJMbiYD+rEunaB0QOu4MeFPTEDReHSk2lho76+9y6+Al19m4ICS+K6aIt00qFOJlAhfCFEmhHhJCLEj9K3rbyKE2COE2CiEWCeEmJ7kJxqqq6eG8F0ugyAfIURMBiqvzuKRiU/T8MrPmTfP2sQqKs0JP2/Qx6g3vsFFhAnXh4HCB6U+ZVcEEY2NwWOPTaax0x4gQ8KvqqI+uxMpw+9BjdeEQBlik8nvNlWEH0JRkTIvRMbx9/kgn0HDQG+mQb0AysvVyxMoKnGp6JK//GVCg7Z6Jp2cOUrhG6WSnJebAuFXVYXJaHRUhcC+/vrw+hTGYCJNOhAm/NraEOEbKHwtX4WRt9qoK4dsRuIUfmEhBPzWrtY+nz7hHxgxJvyobFcGmMw50JcFN95IzfMPA5BdlWdv5l0akarCvxt4RUrZALwS+m+Es6WUx0spV6R4ztRQVRWRzkkH2vz3dCOCiKqq4FF5A8u3/ZrD5hsFuwnDbUH4+cN9ugrDkvBDKk6PUIqKILe/PUwYTz+tIn+GNrRU+JWVVAtFGJpQTNZsHwU7hJ/sSbKzKctX9RFJoj6fymgky4xNDWbzJCgvVy9PQoRyww3w2GOUe0fp7495serASOF7K3PJYcSQ8Ouy0kT4zzyj6j7yInSSjNtCjA0fVIZEUISfbaLwXS6TvLbAQK56TvQUPn6/ZVTP2MBroAh/35A54VfTjqyqNjxuZM4Brr+ehat+TTYjeIuDMy6WzqWAlrH3ceCyFI839YhsyHro7Ez+ITFrjRFsd9RRMEQ+vxq9mmtHH9ffPgKemnIq6DI0G+SODeAuiZeAloTvdiODwTi3TFDPRn5/u+oRSQn/9V9w222T6y0Jv6qKShlN+JOiMNEk8ZEoLDSfaZuKwq+oUDFRiLbO9fUpFScq9UnZ1HsEoLwc0a1MOl4v6uZecgmn7HoSKWGizfwlZaTwjZJraPvUudvDyV0TRXW1EkZSKlfMW28Nr0uFpCJs+NXVqne7d68qS0GBucIH80fM71GEr6fw7UxAMzLptIxXMt5mTvhm9zkyqxj5+WxccjnXiV+TlzdhHGV3ipDEKzoK1VLKVgApZasQwogpJfCiEEICD0spHzE6oBDiJuAmgOrqahobG5O6sEAgoLtvlt/PUVu3st7guMft2MF7W7cysX9/wuc8yu1m5/PPMxzl56lQ+dpr5Pn97GtsxO2GhoblPLjjZtZveR+vvbIEaWLXye5upZxu1q9vorEx/roqJyQTwV4aGzdELR8bO5aWFjeNje8DucprAAAgAElEQVQaHntZf4BgUNLRsYvGxubJ5YODh5Hbf4CNHV7kD39IRXU127duVRG2gHXr6oEG1q17g1274n2U630+/F3vAB9i5cr1DAz0snfvicydO8iq5xtZ6nLxXpJ1u2xiwrBdHL1lCzuamhhJIijV4WNj9Da9CXyEV19dzf796g371ls1lNNNx/gIG3XOe+BAHbCUl15aRVlZvDtjwe7djDXvAWDdutfJyQniWbGCIx+9B8HH6W/vZINm14hBIBCgu3uYQKCPxsatUet8viyqyGb925toXBBNSB0dJ5Hv2cXmLuhI4j5Xd3eTtXcvgy0tVJWWsm3btsnM9u7BQY6ZmGBdMvUXDLK8uZk1oX0nJs4C4JhjOmls3MTiri7e2bOHAYNjZ2WdTFOTL+5eAAwOeqhydfLmm41RpvqurvnkD3dzYHiEHSbX3Np6Ijk5AzQ2bp5c1t5eRyeVtG3YSpPOvk1NBRxPN292ttLYuEn3uFJCVtaZrFnTTGPjbh4r+AhfFNdzwP8NelwutvzpT4wlGkgwWUgpTT/Ay8B7Op9Lgb6YbXsNjlEX+q4C1gNnWp1XSsny5ctlsli5cqX+imBQyhNOMN5x2TK1TTK4+WYpV63SX/fQQ1I+/PDk32efVSl6tl12l5S/+Y3pYUfXbJC/5OPy3/9dZ+XEhNzgOV5eeWX8qssvl/Loo80veeSUM2Uh/fJnP4te/vnPS/mY50Yp33pLynPOkXLbtqj1//Ef6vqHhw0O/PTTsv2L35Ug5ZNPqkU1NVJ++tNSynfflfKGG8wvzAT9DQ1STkzorzz1VCkHB5M78Je+JN/90csSpHz11fDi++6T8mp+Iwfu/b7ubo8/ru5FU5PBcffvl1uWfEhmZUU3rZ0X3yYv41k5cNgyw0tauXKlLCuT8pZb4teNjkr5PJfI//xSc9y6ujop/3rMnVK+8orhsU3xl79I+eUvS3n22VJu3Rq9budOKT/ykeSOK6V6xkL47nel/MpXpBwZUf+7Tj5ZytZWw12PPlrKK67QX/f8Sd+Wnyz8bdzyH/1Iyov4Pzl811dNL6u+Pr5ZPvmklEX0ycBJZ+nu849/SLmGZfKvfzU9tKytDbV9KeW110r5v0Wfkxu+8x0pP/pRKTdtMt85QQCrpQGnWpp0pJTnSimP1vk8D7QLIWoBQt+6thIpZUvouwN4Djgp2RdUyhDCukuabN6xmppw2vtYxJgaLrsMXnsNFt1/B/zkJ6bX5KmtoNIoJn53N51U6EYatjTpAKPFauBPz6RTMtZBsHm/6tdqGWNCCARUd9zQ66+qisKBsElHS6OYkktmCOOFhcYeUcPDEdnoE0RNDcVDqv5ibfiVdJJbn4S7IEB5OdmBbrze6KbV/rE7+X98n1GPedYvI5OOxwM97iqC7fHmBr8fysdSMOlUVSl/yZoalZs5EqmOc3k8k0EM774bvvOdcDvy+HymphezSW5dVFCfG+8a7fVCDW0MldSYXpbRoG0/RUiffhTCQH8QibD0P4ic/tPbC8/Mv4t5Tz6p7uNB9NRJ1Yb/R+ATod+fAJ6P3UAIUSCE8Gq/gfNQPYTpg8ulP8I2MWGR/NQCZoQfM2IpBJx5JmTNq1MpAv/yF+PjVlZS7erUJ5S2NlomanXHo+wQ/nBhBZV0xg0KFhcr22TwgQfhG9+I229yYo/Ru7Gqitz+MOH7/cozNR2EP1ZcbDx5LpUkobW1eAOtQPT7xOeD+dmtuOr1M6FbEn5uLq7R4bg6ym6Yz17mm8ZqGRsTjI0Zu4/351QiuqMJX0pFiiWjKQ7avv023HNP/LoUPaGoqjIcBBUTE6bjO2aE3xqspj4r3iGjsBBqaWWwyDiT/cSEOm6scFL/heGA/FhbN92UWxJ+ZcS4b18fDNUsZGDBAvVwzCDC/x7wQSHEDuCDof8IIeqEEC+EtqkG3hBCrAfeBv4spfxriudNDUazbS2iFlqipsbYA6itzVhtfeUr8O1vG6v8rCyyXeO6hDKxv5X9wbqkFf5ggbHCL6Ob0aJyOOaYuP00wjdEVRWurg68XnVbtdtdXs7UEf7YWHKeIxpqasj3KcKPVfjzslpjonuFYUn4QHAiXj16vfAMV5PXutOw7oeG1NiOEeEP5Ffi6YkmjMFBdbjCEZ2kHHaxY4caTDzqqPh1qTg2gHoO9ISRjcFgszkPzeO11IuWuOWFhUrh+wuMFb52zNg60v5PBPUHV4Ot7bRTnbDCLymBfR/7GPzjH+Zeg2lGSoQvpeyWUp4jpWwIffeElrdIKS8K/d4lpTwu9DlKSvmddFx4Sqiu1n+rTlVDhpj4rzFYsACWLYNnn9VfD+ByMeiPlxnDe9poo0ZX4RcWKg40i+7qz6syJPxa2mi9MV7dgyI309y0oQBqVVWq6HGzbFNQiIaEn4pLJkBtLTm9qv5ivXTqXK2G9WeH8AfJoyI/2o3H6wWJwF8yD/7wB/39Bt2T2+phyFuFpy9aLWsvebfLXhwdXXzve8bPQqomHaOesM+nzHUmMMpXALBntI7qYKvuPjW04cszJnytvvVeygBDuaW6PvOiwx7hxyr80lIYrqmBxYsV6R8kZN5MWzB2zUy1q2pm0rFiyHvuge9+19CZ25ddhac3/ppH9irCN1L4YK7y+/JqqaMljlAWbf8Lw+TSVaWfs9RS4btcICVLlyqxGKXwU3yxGhL+gQM2M5YboKYGd0crOTk6fvjSeBKBHcJvd9WxICeajDTb8uYjP6LqXkdBWin8kaJK8vzR7cLvV0HTXO4kzVsvvaTKmpenr7qn6jk5cIARixe2mUln92A1FePxx9UIvyfbmPC1+tYLywDQn1+rQnrGwNWpCN/iPUVFRSjpyaBqupPN/+abVZL7g+SamZmEr/kYx6K1VTXGdB/Xjt9yXZ1Ku/Xkk7qre/PqyOuLb3ATB1ppxdiGD+aE3503h3oORDfYYJAjfv1V1nKCYcasQMDGRFkhWNog2b49Jm/uVJl0UiV8g3g6Ph9kuaXh+I4dwj9APXNdB+L2q6GdA94jVEa0p56K229oSJmojBT+WHkN3sFokvP7oZRegkVmiRYMEAzC17+uTIxGcrqlJeUXq+5z0tLCqIWvvBnhd/uz8YixuOWFhWqmdP+48eC41s5j77P2vyevXoX2jIG7y77ClxL++U+l6SZzvx93nDqJwXOfbmQm4Rsp/OZmmDs3+ePm5ETPydeg9eGs8G//Bj/+MXrxbv2FtRT0xxO+bE1N4Xd46pnD/uiG/vTTTMxbxE4WGxK+pcIHKC3lmPoeBgZg40a1aNKGPxUmnVQJPzTgGxtPZ6BvDDzGYwOWicyBfeN11BFtXxYC5nja6BDV8NWvwg9+EFf3lgq/cg7lQ9FEFAhAFR1MVCbhofP003DyySqin5GA2b8/dcLXU/gtLYzYIPyBgXhBrIXwcGXFhzgpLFCCy6x+jJLMaDmLO7LnhIP3RyC7r52erGrLoSNt+O5vf1Pfk4RfVaUeih/+UPe5Tzcyk/CNbO3796dG+BpiFb2Z/T4SFRXwiU/AfffFrQp4a/H64wek3B1thgpfIwkzwm8XNdTQFm7ow8Pw/e8zdv6HaKfa0PvRFuHPnctRRWoy11/+omK6l5Sgn1QlAZgSvhaRK1nk5FBROBxF+Dm9bQwWGpOnHYW/d6yOmmB8/dW522mVNeqh16l7K8J3V5ZRNBrtiuj3h2Z/VibYixoZUcTz1a+q/0ZhSIxiPdiF0fPX0sKoDZMOxM9qHhpSXmCjRfHBEQsJ4Mdri/D1ilVUBG1ufYWf52unP8/6xXpSyBH98cdVR3HS0zU/Xw2yffzjajb7FCMzCV/LvBCL5ubUCaO4OJ5h7RI+qGxCzz4bpyYGS+ooHoxX+MLvw4/XVOGbNfT+IQ8eMR5WKPffDx/7GPmuIdqpTk3hz5vH4mxF+O+9p/Jeu0aHE08QHwNDwk9VeQLU1LAgt23yRRcMQl5fK8Olxi592dlKCRpGcQzCzuE6KkfjFWItbbRMhAjjllvg97+PshVbDdqWlgkmghCcCIsMvx/msQ8xf55JQXVw330qBZxGupEpqSILk4rrK5grfJuEH9umtXY6Ul4XZ2svDChRlCzhe73KJKen8PP97QyYiAEN8+bB/Pmqc7t4cUxSNrcbPvtZZdKb4nDJmUn48+erAB6xSNUkAPqNOZHjZmcr++nd0XHoRspqKR3RseFPAIikbfh+PwTdHqUy9u9XXfrbbiOvaz/7mWNK+JYib948ygf3Tc6Duuwy0tKLGi0p0Vee6ai/2lrmeVony93dDVXBVmSt+QvbzHskEFCEUTYcr/DzxDA9g6GnPztb2c+//OXJ9VYKv7QUeimlf1/f5DK/H+azF/fi+abXHIU9e5TQuOOO8LL589XySHR0JD+ZS4NR3O4EFH4seWsv6ImqWiWwIpDd3UqHqyYlhb8vqC8SCwfaGS6y15M680z1fWSsH0RdnfJd/sY34K67bB0rWWQm4RuN/IyNJZ8wQkNtbbwSSEThA1x4obL7v/Za+NIqaqkcjSGMoSFGXIpNk7Xh+/3QnR16SG69VXXpc3Jw7d1NW+7C1AZt583D1byPhgbVjb3kElSKvBQJXxql4LPMCG8DNTXUu8MKv61NTdpxzzVW+GAeItnvhxbqKB6Iqb+JCVxuEV0/l16qHv5XXgHsEf5+5uDfGiajQEARfs7SBAj/jjtU3Ue2/wUL4oVROsyeWg9Bx/Q5YjFvwErhy9p4hU9bG7059ghfryfl9ULziM64n5TIiSB5hfZcXzXCj5vaMG+eei4uu0w996++aut4ySAzCR+ipncDqUVwjMSiRUzmLtSQKOGDyor0hS9MskiwqoaKYHv0eFRLC325tbhcUjeagF3C78mrV14CJSVwzjlqxZ499BbN1yX8YNBmOPu5c2HfPi68EK66KjRO29ysGniqMJqBk6q5obaWmmDLZLk1ws9bmDzh9/dDAC85Y/Gmvt6C+uj6EULV/V13weAgg4NuhDAMxU9pKTQzl+Ht4cB3msLPO8wm4f/pT6qxnHVW9HI9hb9/f+pmT9DPEDc6ql7mJrBS+O56HffJ/fvpzau3JHwh9KNyFBWBL+COHynu7qbXXWE7rcM55yiKOeWUmBUa4QM88ICq+2HrsOnJIHMJP9aO32o8sSYhLF4MO3dGL0uG8OfNU3a90NT23KJsshmNHqxqaqKlYAmFheO6PGf0cEQiEIDBvHJ4+GH40Y/CKwYH8ZQU6BK+5kxgi/Cbm/ne91SyeCAtCh9QXiRajkhQrGpk6E4Eixczd3QnfX1KA7S1QT0H8B5mXn9WhA+hOVCRqnbnTnpKFse/kOfOVYlm7r2XoSE3BQXGET80hT+2K5rwK0U3WdU2EpR0dsLXvqa8w2JRq0Oe6RjngvjnxObYgJXC98yvi+9hNzXR7l1i+hxo2Q/1LsHrDR0/Nzfak2b3bvZlLbRN+AsXqtv5oQ/FrIgk/Llz4brrVHytKUDmEn6sHT9dysWI8A2m5Zvixhth82Z44w0KCmCIPAY6Ixh/+3b2ZTeQnx8fnhjU2GhWloXC75ec1v9Xpe40++nQEOTmUlQUn+4PbMTC11BQEO9OkS6Fv3BhdE8qHfZ7gIYG6gd3IKWqtrY2WMp2Sk9qMN3NyqQDIIu1nIYh7NqFr0KH8EG97FevZtGB1aZjJZrCjxQvgf4gLjfWBCol3HSTGjPSmxcRSvsY9ZJK13OyZAk0NYX/25wlbaXwc47Q6WHv2EFXaYOl8DG6z5PPgZZ1XcOePexlQUKJ2yYzvkUikvBBmVZvvtn+QROAQ/gaUvXB17BgQXQ3WErVPUvGM0UIlUv01lspn+hgO0sZ27Q9vH7HDna6Gygo0J+dK4R1PJ2Lmh8mUFAd/bDt3QsLFlgSvi3PPLc7Ohn2VCn8dBFRfT0lA4o8m5sV4RcLP4V15tmS7Cj8iQVL1LRjDTt3MlC9SL9+XC544glu3Pg1lZvWABrhu1vCCt/V1UGvx8bA6qOPKieDOMkZgbKy6JACUyWMtm6Fww+33M1K4Rcu1Ik+2dVFsLTc9DmwIny/H0X4kVaB3bvZGVyYkocqoLgokvCzsvQH5dKAzCX82AGpdHVVs7OjxwZSnZU4fz784Aec/ehH2c5SgpsjEj/s2MH2YAMFBfoKHywIf/16PtzzGL899b7JxCaAItKFC1NX+BCvitKVQjKW8DdvhiOOSP24LheeXDduxtm3D/r39TKUU2Iplu0QPkcdBZsikmTs2sVw/WKGh6PfiZOYM4efzfkaP+m6zjDkhmbSyekME35+51468i3s92vWKDGhZ8qJRKwdP10v7FjC37xZx30lHlYKv6hYRFfGyAjk5FDoFUkrfK83lMJyUcNkEhgA9uxhx1hiCl8XNTW6YRumAplL+LENecMGOPro9By7tDSc12/TJv2Ig4ngvPPoW3Y2J/E2ru0RxNzWxu6hmuQI/8AB+OQnuSnnCYbqlkTbPUOEX1ysH3beMoF5JObNC79YtUGvVEJQa4gl/A0b4NhjUz8u4Fk8n/nspbkZsndto7XEWnnaMel4jo8h/N27mZi7IGqbWKzMOZ/tpSfHuelqyMuDAU8p2f1dk6aXwp699BSaEH5zM3zqU8oF12g0WEOkMAoGjYPzJ4pY54Y0EH5BQShY6mGHhYl51y5YtMg0JIN2PKNiaS7PA0uOUzkCNOzezZZh+zZ8Q7jd6oWumc5efRW++c0UD6qPzCX8hQuTUhi2EKle0nTc9uvvxs04RStDURVDoYB9/cLQpAMGHqg9PXD55cgHfsq7g4fhLRKT0S0B9SK0YdKx1dCPOw7WrlW/t26NS6SSNGInBW3alLb6yzpyKcsKdtDcDMWtW+mrOsxyHzsKP3d5DOGPjJBflhu1TSyGhtz89qh7lY37e9+LWy+EmnzVnRu+H5W9O+gpXax/QL8frrwSHnpIPQNWiHxOdu1SbTsdiG2YNusvJ0fxo55JZ3IuyuGHh3usO3bAkiW2CN9M4QP0zj1WCYsQZFs7zWPWcXRsYe7c8Iv1zTfT95zEIHMJv6RE1fLIiHpStRHOdCCS8NOh8IGSMhdX8Qy57fvUjMiQCu/vx3DQFnQUvs8Hl18O3/gGw8tPZ2Ii1KCPjWjMGzfC4YdPEn6su3RChH/qqSpiFKiGHOeTliTcbsV2IyNKHY2OJp/pKhYNDawo2k5zM1T2bmNoXuqEn5MD2fMiuu4+HxQXW7rODg25KfC6lL39nXfgwQfjtikthW2FK5SZBjiy5w3aF50afzCfT9nr77pL1YsdnHxyuP7WroUTTrC3nx1Eutb29tqK3S+EvogJ3U6FSMJvaoKGhpQIX3uR+GSR2jDU05nw5ICNbFe2cOqpsGqV+v322+q+TwEyl/ABTjxRPUTr1sHxx6fvuMuXh2Ncb9mSFttycTGMkEd/2Xx17K9/HbmkAZ8PCgttEn5zM5x/Ptx+O1x8cfTswuOOU4Q/PKzs7HPnUlQU9rmPREKDtpEP31tvpY/wAU47Dd54Y/KhThuWLuUYz1aammD+8DaCS+0NJg4O6ke59ftDpCEEk6E4X3sNTjrJFuF7vSgx8uSTKnTxvfdGnai0FDZ4lsPq1TA+TtloK675MXb2fftU3d9xB3zkI7ZuA6Duq5YMJd2Ef/zxity6E0vUokfehgp/0yZYutQw6JoGzS1TD9px/X7CpsTXXmPoxPdPXk/KOO009WKVUvWk7PS+kkBKhC+EuFIIsUkIERRCrDDZ7gIhxDYhRJMQQt8YOR14//vVg7dmjSLpdB93dDT1QFMhaOqlq+IIuPNO2LCB4KsrqRw7QH6+sUnH61Wul/z+92qq6333wRVXAGGS8XpRhL9+Pfz97/C+9wERscBjzA0JKXyXS03Fb21VhJHOF+sFF6iobGm03wNw4okcF3iD5i1+ltBE7lJrN1LtXugFPIyaInDkkaoH9eyzcMUVtgh/svnk5MDvfqdOcsklkyac0lJ4O7gCVq9m+K31rA0eHx4Xl1Ltc8kl8J//qXp3iUAINba1aVP6Cf9f/gV++1vV7hIwx+nNuYtS+AsXKqEVCKiX4IoVFBaqW2EUkNKOSae/n/Bz8uKL9Cz/IBCfNCUprFihxKfmLZjqBEIDpKrw3wOuAF432kAI4QZ+BlwIHAlcK4RIk7E8Rbz//fDCC+rhSyfhezyqAq+5RjXqNKCoSLWB15Z/UUUzLCig/85v8Scu4cr1P9QPBjcxwfK+V/hFywVqNuXLLyslEUIU4R95pGpwDz+slCDGhJ/QoC2o7urPf67uS1TUqBRx1lkqBMFDD8EHPpC+4+bk0HzEeTzDVTwlruW8C62nzpuFSI5Sn9ddpxT62rWWCl8RlDuaiNxu+P73lVK/5BL46ldZlHOA7YE6aG5m7Of/w985g8ryoKrvCy6AP/9ZJdlItnd11lnKlGSWpjMZnHGG6q1+85tqoplNWCr8rCz1Yrv6amXCcrsNB3shnAPYlsI/4wx45BF4/XU6Gk6PWp8StAb06KNTZs4BSMloLaXcAiDM30YnAU1Syl2hbZ8CLgU2p3LutKCuTk0AueAC9eZOJ666StlKdZJaJAOXSxHz5vwVylZ9ySV0HX8uJ/MWT9b8WIVXDQRUefLzVXCxPXs4xXUKn+VHrP1lfF7aqPghubnKZHD11epFSJoUPqiwv488At/6VuIFN0N+vvL2uPBC+zZpmzhw0Y2c+4+T2fK1p2zNE4sklFhOnDTpgEp0cvzxqvfncpkS/tAQBINC33vkgx9U9fTUU9z2y+v4ZFsAzqnH0/gi17Cdk/7jfjjvFBUfJ9Xez/nnq5fG5HTpNMHtVmXweBJ6/ixt+ABf/KJS+qEZq2b1ow0DGXnpRCn8qz6gTC4rV+IbyY1anzLuvFP1/m64IU0HjEeaRilNUQ80R/zfDxi+woQQNwE3AVRXV9PY2JjUSQOBgL19r79efUcEKksLcnJw/ehHBLWBmDQgN/cUtm3r4++33UwwN5etr65hnOVsPP4DVH7gFFzDw+R2dOAaHmasuJiRqir+99fzeXfDIl566TU8nujR17ffLgOOZfv2tXg8IVZ/8EGl9IGdO4uBZbz++joGBsIzRDdvXojbPZdVqww7dvEI9RpIsj4jEVW3t96quj5pOG4kilYInvjGH1n2/ndtHXrv3grgaFauXE1zczQbHTiwnPLyURobQ1lgLr4YMT6ObGykr88DnM7atTtYsCA6JEBvr1rX0rKdxsb4SJsAzJvHY+f8gt8+UcXKq59m67o87nngfdz9xTaOPjagPLLScW++8AXlKZTm++y65BKCbvfkce08tyMjx9DTk01j45rJZd3dZ+D3t9DYGPa8y/rVrxhvaYGWFvbs0ernHZqbo0fXfT51n1tbd9DYGB8CORBwA2ewdm0TjY37lahasoR//v094Gi2b19NMGgyImyAuLJWVqqealNT9CzkdEJKafoBXkaZbmI/l0Zs0wisMNj/SuDRiP/XAQ9YnVdKyfLly2WyWLlyZdL7Hqo45hgpL7ss/P+VV6QEKX/yk7WG+9x/v9qmqyt+3TPPqHUbN+rvu26dWv/ss9HLP/95KUtKkihAmnAo1u1LL6l79frr8esaGqS89lr9/YaG1H7f+U78uqYmte7xx83P/ZOfqO16eqR84gn1e/v2xMtwKMBO3f7rv0q5aFH4v9k91PDii2qbN96IX7d7t1r32GP6+05MSCmElF//evTyX/5S7dfUZHnJupiqdgyslgacaqnwpZTnpvhO2Q9EugzMAQzkigMzFBdHh2LRJkUVFpoP2oIyGcRmj4uy4etg0h0tZvKVreQnGQazZDNR9uUYmMU7MovRHgmtXru6wvkzbISlmbEoKwvPa4Rw5AczRx8zG77VfdbMqbHPgVZnabHhHyQcDLfMd4AGIcRCIUQ2cA3wx4Nw3lmH2Jmvmm3dzA/fTkO3IvxYG366AlPOJpilkzS7X2bxjrRlVoSvjTHs2aNIPysrlEpylqKsTAkfLdqENl/QLB2u2XNg5z6XxMS9A+PE54cyUnXLvFwIsR84FfizEOJvoeV1QogXAKSU48CtwN+ALcAzUspNRsd0YIySkmjC135bhVaA5AglarAqAnEDZA4M7/P4uBp8NVOBRoRv9ULWoLls794dDjo5RV59hwQ0Ja+1f03tp6rwze6zXpgRv1+NN6eYsfOgIlUvneeA53SWtwAXRfx/AXghlXM5iDfpaL/NQitYEX52tnGSr+xs5bzjEL41jO6znW6/FeFbKfz6ekU8GuGnIzbdoQyN2Ht6oiOCmCl8s+fAzn02Uvhe78x6uWb2TNsZBk1laKEOOjvVpJusLGm4jxXhW6lHvXg6DuHHw+g+2+n2p2rScbuVWSdTCF/LYqkp+3QpfLP7bKTwZ5L9HhzCn1EoKVF2Sy3UgZ1Iw2a2ZTuTgB3Ct4esLNUbiiWUdCh8OzZibcZ/JhB+pMIHewrfKOgapGbDn0n2e3AIf0ZBI1mt4dl5uM28R+wo/OJih/DtorAwvQrfrkkHogl/NnvoQJjwNe+cnh5lfjSL9GwUdA2svdXAUfgOpgEayWoNr6NDPzNdJNJt0hkbUz0Mh/DjoUfc2r1LRuH7/eB2B20NCi5cqMi+ry89eWAOZegp/LIya1u6GeG73ebBVjWHicjIsWbutocqHMKfQdBc7TTCt6Pwrfy8EyV87bdD+PHQI+5UTTp5eRO2BgUXLFDfpaUqysZshp4N38yco8GI8O0MvhYXK3NqZAjsdOWCOZhwCH8GIdKkEwwqn2srhW/l523Hhh/ZldXMSQ7hx8NM4dsx6cTmHfD7FeHbgZaX5NZbZx4JJQqPR7XbWIVvBTOFb3XPNLEVacd3FL6DKUWkSaenR5G+nQE6PdsyJGfS0cjfIfx4pGLSmZhQqQgiEQhgGvo6EieeCE88YZgJcdYhcrZtqgrfji0+1pyq7TfTXq4O4fY5cVMAAA7JSURBVM8gRJp0OjrUbyuFD6pRJqtsYrNeOYRvDD1C6esL5z0xgtE4i2bSsQMhVORlqxS1swVlZdGDtqkofDveNrEKPxhUx3IUvoMpg9ao29vDMVPsKHw95SmlfcIfHw+rT4fwjaF3n/v61L0yy9tuNmnLLuFnGiIVfnd36grfjrcahNt/Ii6zhxIcwp9ByM1VIfw19ztInvCHhxWRWxF3rCuoQ/jG0LvPvb3WcW2iEmxEIBGFn2nQCH9oSLXlVBW+lVKPVfh2THWHIhzCn2FYtEjlR0/UpBNLJhpxWzVYzae7qyt6P4fw46E3+NrXZ034RjGLHIVvjNJSRfjac3CwFb4d3/1DEQ7hzzAsXqwS7mgKP9mGblehaC8U7XwO4RvD61W23ci8qX19YTdCs/3AUfiJQFP4m0JhGA87zHof7TnQ84ZyFL6DQxKLFqnc1fv2qUbv8VjvY+Y9YkXcmslIU1I+n5qgYue8mQa9eC12TDpmhG/XSyfTsGSJmgT47LPq/zHxGTzjUFiovKFGRsLLpLQ3aJubq2bzxhK+o/AdTCk0f+vXXrOfTzoVk46m8CMJfzbHWk8FesSdiEkncj8tZpKj8PWh5WN/6imYM8e6FwX6caVU3mB7xB0ZnjwRk+qhBIfwZxgWLVLfO3eqPNZ24PWqnNmjo+FldrukZWXKwyTSpOOYc/SRTsLXZnSaJbfJZBxxhLpvAwP21D3o3+dEslaVloYDtbW1qe+aGnvnPlTgEP4Mg6bwAa66yt4+esrGrknH5VIDt5qi0dwMHcQjllDGx5VZxkp96tWP9js3N5jei5wlcLvhpJPUb7uEr7VbvVAhdhR+XR20hJKztrUpM09G2fCFEFcKITYJIYJCiBUm2+0RQmwUQqwTQqxO5ZyZjspKlU92zhw49VR7++hFzLRr0gHVbY006TiEr49YbxvN3mul8LOy1LhIJOGH8xU7Ct8ImlnHLuHrhUdIxNumvl6Nn4Ei/JqamZX8BFJX+O8BVwCv29j2bCnl8VJKwxeDA2sIAddfD1/+svlknkjodWUT8TKorAybdLq67Pk8ZyI0jymt22+X8CF+nEWbRVpYOJa+C5xlOP98NZBqV/jEzimBxEw6msIPBsOEP9OQaorDLQBipr3mZjgeeCCx7Y0I3663TVUVrF2rBhKbm+HKKxM7f6ZA82jS5ixoxGJnQDE2wYZG+F6vo/CNcMYZqieUm2tve6MAaGBf4Y+Nqfpta1OeQjMNKRF+ApDAi0IICTwspXzEaEMhxE3ATQDV1dU0NjYmdcJAIJD0vjMNVmXdsaMIOIE33ljPyIhiki1blpKbW0Fj4yrL44+OLqGlpYbf//4dxsZOZXR0G42NrWm6+sRxqNatlOB2n8maNc00Nu5m9epS4Dh2736Xxkaf6b4ezzJ27pygsXEDAKtWVQNH4Hb3H5JlnSpMZd36/VnA+1i9egcLFijbzFtvVQFHsnnzWwQCQ6b79/ZWAEfz/POraW4+lkWLOmls3JH09UxLO5ZSmn6Al1Gmm9jPpRHbNAIrTI5RF/quAtYDZ1qdV0rJ8uXLZbJYuXJl0vvONFiVdd06KUHK3/0uvOyaa6RsaLB3/G99S+3/8svq+69/Tf5a04FDuW5raqT89KfV72eeUfdr40br/S6+WMply8L/779f7fuHP7wxNRd6iGIq63Z8XN3Te+8NL3voIbWspcV6/3/+U2373HPq+5vfTO16pqqswGppwKmWCl9KeW4aXiotoe8OIcRzwEnYs/s7SAP0Bm37++0Pvmq+xm+/rb4XLkzftc02VFYmZ9IpK4P33gv/1wKDOYO26YPbrZ6FVAZtAd59V33PRBv+lLtlCiEKhBBe7TdwHqqH4OAgQc+G7/PZdynTbNMa4c+bl75rm22oqAgPcCcyaFteHiZ5UDZ8rxfcbmm8k4OEETtW4vcrR4iCAut9Na+cNWvC/2caUnXLvFwIsR84FfizEOJvoeV1QogXQptVA28IIdYDbwN/llL+NZXzOkgMRoO2dglfm9G7ahXU1tofJMtEVFSEFX5vr3K5tBOjvqxM1Y82Oa631/GGmgpEzpYFe+kNNXg86lmYyYSfqpfOc8BzOstbgItCv3cBx6VyHgepISdHdWdjCd+uSWf5ckU+HR1w2mlTc42zBZEurNosWztkopF7b68ild5ee6YgB4mhuDha4SfS0wVl1pnJhO/MtM0AaHltYyde2W3oubnhxNhasmwH+qioUGQ9Pq4S1Wjhpa2g+fBrZh2H8KcGsSadri57OSU0zJ2rvouK7MeyOpTgEH6GIHJijxYhMBFl86lPqW8tlo8DfVRUqPvb26sS1dgd4NYUvkP4U4tYk05Xl/2XMsC3vw2/+AVs26Z6zjMNB8sP38E0I5LwBwfVbMFEQiQcfbQKRWt3VmOmQlOLnZ2K8O3eL43wtVm6DuFPDfQUfiJeZ0cdpT4zFQ7hZwgiCT+RODqRuPzy9F7TbISmFpuaFLHYJRPHpHNwoNnwpVSmzs7OxBT+TIdj0skQFBWFiV6btu8EQUs/NPJ45x31bXfMI9KkMzysPg7hpx8lJap3GwioMAk+n0P4DmYhqqvVICKEY3nX1k7f9cxWxM5ZsKvwi4qUJ1V3d/iF7BB++qHNifD5wuazRAZtZzock06GoLZWRfqTMhzT2yH89KOiQkUxffNN9d8u4QsRztPqEP7UQS+AmqPwHcw61NaqST29vdDaGl7mIL3IyYEPfSjsBZUIaTuEP/WIDJGsTZBzCN/BrING7q2t6lNQMPMSMM8UfOYz6nvhwsQSZGiErw3cOoSffkQqfIfwHcxaxBK+o+6nDuefr1JRJuq+V1mp6mbrVvV/JsZbP9ShzY49cCA8IzqTCN+x4WcIHMI/eHC74Z//VNmYEsExx8Cf/wxvvaWm8DuxdNKPujpVL7t2hXMJay6xmQBH4WcIHMI/uKisTNztdcUKlVXs//4Pjj12aq4r0+F2K1Pbrl3KpFNcnPiLeSbDIfwMgderFI1D+IcuVoSyPY+MOIQ/lVi0KEz4mWTOAYfwMwq1tbBjh5p04hD+oYf6+nBALofwpw6LFsHOnZk3yxYcws8o1NaqZOTabweHFoQIq3yH8KcOixapiVfvvgtz5kz31RxcpJoA5YdCiK1CiA1CiOeEELq5fYQQFwghtgkhmoQQd6dyTgfJo7bW8cE/1PGBDyjVedhh030lsxdaxNeuLvjwh6f3Wg42UlX4LwFHSymPBbYDX47dQAjhBn4GXAgcCVwrhDgyxfM6SAJaLG+A+fOn7zocGOP225V92eOZ7iuZvdAIPzs78wg/1YxXL0b8fRP4F53NTgKaQpmvEEI8BVwKbE7l3A4Sx513wuGHK+JfunS6r8aBHrRE2w6mDlq4i/POs5dveDYhnX74NwBP6yyvB5oj/u8HTk7jeR3YRE1NOJGJAweZCq8Xvvtd+OAHp/tKDj6ElNJ8AyFeBvSyN94jpXw+tM09wArgChlzQCHElcD5UspPh/5fB5wkpbzN4Hw3ATcBVFdXL3/qqacSK1EIgUCAQm1mxSxHJpUVMqu8mVRWyKzyTlVZzz777DVSyhV66ywVvpTyXLP1QohPAB8Czokl+xD2AxHWY+YALSbnewR4BGDFihXyrLPOsrpEXTQ2NpLsvjMNmVRWyKzyZlJZIbPKOx1lTdVL5wLg34APSykHDTZ7B2gQQiwUQmQD1wB/TOW8Dhw4cOAgcaTqpfNTwAu8JIRYJ4T4OYAQok4I8QKAlHIcuBX4G7AFeEZKuSnF8zpw4MCBgwSRqpeObjw/KWULcFHE/xeAF1I5lwMHDhw4SA3OTFsHDhw4yBA4hO/AgQMHGQKH8B04cOAgQ+AQvgMHDhxkCCwnXk0nhBCdwN4kd68AutJ4OYcyMqmskFnlzaSyQmaVd6rKOl9KWam34pAm/FQghFhtNNtstiGTygqZVd5MKitkVnmno6yOSceBAwcOMgQO4Ttw4MBBhmA2E/4j030BBxGZVFbIrPJmUlkhs8p70Ms6a234Dhw4cOAgGrNZ4Ttw4MCBgwg4hO/AgQMHGYJZR/iZkDBdCLFHCLExFKF0dWhZmRDiJSHEjtB36XRfZzIQQvxCCNEhhHgvYplh2YQQXw7V9TYhxPnTc9XJw6C89wohDoTqd50Q4qKIdTO2vEKIuUKIlUKILUKITUKI20PLZ139mpR1eutWSjlrPoAb2AksArKB9cCR031dU1DOPUBFzLIfAHeHft8NfH+6rzPJsp0JnAC8Z1U24MhQHecAC0N1757uMqShvPcCX9LZdkaXF6gFTgj99gLbQ2WadfVrUtZprdvZpvAnE6ZLKUcBLWF6JuBS4PHQ78eBy6bxWpKGlPJ1oCdmsVHZLgWeklKOSCl3A02oNjBjYFBeI8zo8kopW6WUa0O//aj8GPXMwvo1KasRDkpZZxvh6yVMN7vJMxUSeFEIsSaUAxigWkrZCqqxAVXTdnXph1HZZnN93yqE2BAy+WgmjllTXiHEAmAZ8BazvH5jygrTWLezjfCFzrLZ6Hd6upTyBOBC4BYhxJnTfUHThNla3w8Bi4HjgVbgx6Hls6K8QohC4PfAHVLKfrNNdZbNqPLqlHVa63a2EX5CCdNnKqTKKIaUsgN4DtX1axdC1AKEvjum7wrTDqOyzcr6llK2SyknpJRB4L8Jd+1nfHmFEB4UAf5aSvlsaPGsrF+9sk533c42wp/1CdOFEAVCCK/2GzgPeA9Vzk+ENvsE8Pz0XOGUwKhsfwSuEULkCCEWAg3A29NwfWmFRn4hXI6qX5jh5RVCCOB/gC1SyvsiVs26+jUq67TX7XSPZk/B6PhFqBHxncA90309U1C+RajR/PXAJq2MQDnwCrAj9F023deaZPl+g+rqjqFUz6fMygbcE6rrbcCF0339aSrvr4CNwIYQEdTOhvIC70OZKTYA60Kfi2Zj/ZqUdVrr1gmt4MCBAwcZgtlm0nHgwIEDBwZwCN+BAwcOMgQO4Ttw4MBBhsAhfAcOHDjIEDiE78CBAwcZAofwHThw4CBD4BC+AwcOHGQI/j+KJFtHEadmPgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ ":20: DeprecationWarning: Using scipy.fft as a function is deprecated and will be removed in SciPy 1.5.0, use scipy.fft.fft instead.\n", " out = fft(yy)\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from scipy import fft\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "\n", "def func(x):\n", " return np.sin(x/13)+np.sin(x/2)\n", "\n", "\n", "x = np.linspace(0, 256, 256) #0から2πまでの範囲を100分割したnumpy配列\n", "plt.plot(x, func(x), color = 'b')\n", "plt.plot(x, np.cos(x/17), color = 'r', linewidth=0.8)\n", "plt.plot(x, np.cos(x/3), color = 'r', linewidth=0.8)\n", "\n", "plt.grid()\n", "plt.show()\n", "\n", "yy = func(x)\n", "out = fft(yy)\n", "\n", "def spectrum_power(x):\n", " re, im = x.real, x.imag\n", " return np.sqrt(re**2+im**2)\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.show()\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ ":22: DeprecationWarning: Using scipy.fft as a function is deprecated and will be removed in SciPy 1.5.0, use scipy.fft.fft instead.\n", " out = fft(yy)\n" ] }, { "data": { "image/png": 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\n", 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HV1Sxu2uEzfvl4Gwxd7GDOmI8Disj0nM3nbmEextQE/d1NXBgJi+glLpcKXVHS9cgo/4QP/jICdNeGHR6XRF9vgC7OpO/wnPjvl7W7+3j2jNr57RwaSqXLK/AabNw/7p9CX9tYT7xZRmI9dwl3M1mLuG+HmhUStUppRzA1cCTM3kBrfVTWusbRoJw3dl1NJRNf/vcM+ojm3alou5++6vNFLjtXH1azfG/eRby3XY+uaqaRzftp3NoLCnvIcxjYDRAQVy4ux022RXShKY7FfIB4C1gsVKqTSl1ndY6CHwNeB7YBjyktd4ym0bYLRa+cX7jjJ5TU+SmqsDFuj3JDfedHUO8tK2Da8+sPe4Uzbm4bk09gXCY370lvXcxN5P13GVA1XymlVZa62umuP4M8MxcG1FTNPUukMdyen0Rr+3oQmudlHIJwK9faybHbuHa1bVJef2YuhIPf7OsnN+9vY8vn7cwqf+RiOw1Hgzh84cOG1B1O6z0jsgqaLNJ6/YDsZp7cGxkVs8/o76YnhE/TUmqux/oH+WJd/dz9anzKfI4kvIe8W44p55+X4CHN7Yl/b1EdortuVSR75q45nHYGBmXsozZpDXcYzX3/Pz8WT3/jLrk1t1//Nx2LEpx/dl1SXn9I31gQREr5xdw5xt7CIbCKXlPkV1ao+FeU3RoO2oZUDUnQ20cNlM1RS4Wlnp4eFPiFwC93dzDE+8e4MZz66kunP2+7TP15fMaaOn18dAG6b2LmYutdK4pOtRzdzus+OQMVdPJ6HBXSnHt6lr+2trPppa+hL1uIBTm+09sprrQxZfPa0jY607HhUvLOLW2kJ+/uFN+lBYz1trnw2G1UJ6bM3FNBlTNyRA194GBgVm/xsdXVpObY+PutXsT1q5739zLzo5hvn/ZsomNl1JFKcUtlyyle3ic37zRnNL3FpmvrXeUqkLXYQe3u+02/MGwlPpMJqNr7gAep42rVtXw7PvtHByY+xzxps5hfv7iTs5bXMqHls19z/bZWDm/kEtOnMcdrzfLvHcxI619PqoLXYddmziNSUozppLRZZmYa1fXEtaa3729d06vMzIe5Mb7NuKyW/nRx05M2vTK6fjOh5fgD4b56fM70tYGkXlae32HDaYCuJ2y7a8ZZUW41xS5uXBpOb9f1zLrOrXWmu888h7NXcP85zUrDptKlg61JR6uW1PHQxvaeHO3nLMqjm94PEifL0DNERMA5BxVc8qKcAe48byF9I8G+MfHN89qd8XbXmni6ffa+faHl7C6ITH7tc/VTRcuYkGxm1sefV96XeK4JpspA+CyRxbEyRYE5pLxA6oxK+cXctMFi3j0nf08tKH1+E+I0lrzsxd28NMXdnLFKZXceG79nNuSKC5HpDy0r8fHrS/tTHdzhMFNhPsUPXfpIJhLxg+oxvva+Q2saSjh+09sYeuB42+fGwyF+cFTW/nPPzVx9ak1/PxTp6S1zj6Z1QtLuOa0Gn7zRnNCp3uK7DPZAiY4FO6y7a+5ZE1ZBsBqUdx69Snku+x85s63eeLdqQ/AeKeljytuW8s9b+7lujV1/OhjJ2K1GCvYY26+eCkV+S6+/vt3GPAF0t0cYVCtvT48DiuFcfvKABP7FMmBHeaSVeEOUOJ18vsvnsGCYg/ffPBdrr93A8+83872g4Ps6xnhofWtfPX3m/jY7W/SPTzObZ9eyfcuXWq4Hnu8fJedX356BR2DY/zvh/8qJzaJSbX1RWbKHPl3WQZUzSkrtx5sKPPyyJdXc/faPfzshZ28vL3zsMdLvA6uX1PHNy9chHcWu1Gmw4r5hdx88RL+5elt3L12L19Yk5r9bkTmaO0dPaokAxLuZpXWZFNKXQ5c3tCQ+CX+Vovi+rPr+czpC9jdNUxz9wjDY0FW1RbSWOY1dE99KtetqePt5l7+7ZltLJmXa5hZPSL9tNa09vlY3VB81GMuGVA1pawaUJ2My2FleVU+Hzm5kk+fPp9F5bkZGewQ2Zrg51edTH2phxvv25i0rY5F5ukd8ePzh46aKQOHau4jUnM3layruWe7vBw7v732VBw2C1+4Z70cwiCAqWfKQOSnWKfNIj13k5Fwz0A1RW7u+NwqOgbH+Pzdf2FoTGbQmF1b3+QLmGLcsjOk6Ui4Z6iV8wu57dMr2XJgkOvu2SCrD02utTfSc5/q7IHIIdkS7mYi4Z7BLlxWzq1Xn8KGfb186XcbGZNd/0yrtc9Hods+5ewvl8PKaEA6AGYi4Z7hLjupkh9//CT+3NTN5+9ez7Ac8GFKm/b1sWRe3pSPexxWRsblP38zyZq9Zczsk6tq+MWnTuEve3v5zJ3r6PfJIKuZdA2Ns/3gEGsap54aW+Rx0DMynsJWiXTL+qmQZnHliip+/dkPsK19kE/86q2JTaRE9lvbFNkS+uxjhPu8/JyEHGYjMoeUZbLIhcvKuffzp9E5OMaVt61l4z7ZaMwM3tjVTaHbzgmVU3eS5uW56B724w/KUXtmIeGeZc5cWMxjXz0Lb46Na37zNo9uakt3k0QSaa35c1MXqxtKjrnxXUV+5MDsjkHpvZuFhHsWWljq5bGvnMWKmgK+9dBf+d7j7zMelMG0bLSrc5iOwXHOPs5WFPOi4X5Qwt00JNyzVJHHwf3Xn86Xzqnnvrdb+NSv36alR+rw2eaNXZF6+7EGU+FQuLdL3d00JNyzmM1q4ZZLlvKrz66kuWuYS/7jDR7Z2CZbBmeRP+/qoq7EM+XipZiJnvvAaCqaJQxAwt0ELlpewXM3ncOyijz+/g9/5Sv3b6JTfjzPeP5gmHV7elkzjd1Bc502PA4rBwdkOqRZSLibRFWBiwduOIPvXLSYl7d3csHPX+P+dfsIh6UXn6nW7enB5w8dtyQDkR1F5+XncHBQeu5mIYuYTMRqUXzlvAaev+kcllfm893HNvOpX7/Fro6hdDdNzMK9b+6l2OPg3EWl0/r+inyX1NxNRBYxmVBdiYfff/F0fvKJk2iK1uJ/+vwORmTrgozR3DXMS9s6+cwZC8ixW6f1nPI8WchkJlKWMSmlFJ9cVcPL3zqXy06q5JevNHHuT17lvrf3EQjJQheju2vtHhxWC//rjAXTfk5Ffg6dQ+OEpBRnChLuJlfsdfKLq07hsa+spr7Ew/ce38yHf/E6z20+KLNqDKrf5+fhjW1ccUolpbnOaT9vXn4OobCme1gGVc1Awl0AkQO4/+dLZ3Dn51ZhsShuvG8jH7/9TV7b2SUhbzD3r2thLBDmurNndkh6hcx1NxUJdzFBKcWFy8p57ptn86OPnciB/jGuvesvXP7LP/Ps++0ys8YABnwB7l67lzUNJcfc4ncy5Xky191MJNzFUWxWC9ecNp/Xv/NBfvzxExkZD/Hl+zdx4S9e4w8bWmXzqTT6l6e30ufzc/PFS2b8XOm5m4uEu5iSw2bhqlPn89K3zuWXn16B02bl2w+/x+r/+yd+9sIO2qUHmFKv7eziDxvbuPHcepZXzXyGWZHHgcNqkf1lTGLyM7mEiGO1KC47qZJLT6zg9V3d/Pebe/nlK03816u7+dDScj535gLOXFiMUlPvSijmZmgswC2PvEdDmZevn984q9eYWMgkPXdTkHAX06aU4txFpZy7qJTWXh/3rdvHQ+tbeW7LQepKPHxsRRUfXVl13H1OxMyEwpqbH3mf9sExHvny6mnPa5/MvPwcKcuYhJRlxKzUFLm55eKlvHXLBfz0kydTluvkZy/uZM2PX+GaO97mDxta5TzXBNBa809Pbubp99v57iVLWTm/cE6vN08WMpmG9NzFnOTYrXziA9V84gPVtPb6eOyd/TyyqY1vP/we33t8M+ctLuWSEys4f0kZuTn2dDc349z60i7ue7uFG89dyPVn18/59Sryc3huyxhaaymjZbm0hrtS6nLg8oaGhnQ2QyRITZGbb1zQyNfPb2Djvj6e+usBnt18kOe3dOCwWjhnUQkXLa/gg4tLKfZOf/GNGQVCYf716W3c8+ZePrWqmn+4aHFCXndefg7+YJg+X4AijyMhrymMKa3hrrV+Cnhq1apVX0xnO0RiKaVYVVvEqtoi/unyE9jU0sezmw/y7PvtvLStE6Xg5OoCPri4jA8uKWV5ZT6WYxwRZza9I36+ev8m3mru4fo1ddx88ZKE9bIPTYcclXDPclKWEUllsRwK+u9dupTN+wd5ZUcnf9reya0v7+QXL+2kxOvkrIZiVi8s5sz6EmqKXKYsGWiteeb9g/zgqS30jwb42SdP5uMfqE7oe8QWMrX3jx3zQG2R+STcRcoopTixOp8Tq/P5xgWN9AyP8/quLl7Z3sXaph6eePcAENl7/syFxZxeV8TKBYXUl3iyPux3dgzxb89s49UdXZxQmcdvrz2VE6sTH75VhS4A2vrkyMVsJ+Eu0qbY6+SjK6r56IpqtNY0dQ7zVnMPbzb18NK2Dh7e2AZAgdvOyvmFrJxfwIr5hZxQmUeBO/NLClpr3m3t5/ZXd/PC1g48Divfv2wZnztzATZrciaylXqdeBxW9sp5ullPwl0YglKKxvJcGstz+dyZtYTDmt1dw2xq6WPjvj42tfTzp+2dE99fXejihMo8TqjM54TKPBaV51JV4MqI2n1bn48/vtfOo5va2NkxTL7LzjcvaORvV9dSmOQ6uFKK2hIPe7pHkvo+Iv0k3IUhWSyHwv6qU+cDka1u32sbYMuBQbYciHx8fkvHxHNcdisLyzw0luXSUOalttjD/CI3NUUu8l32tJV2uobG2dTSx4a9vby6o4tdncMArJxfwL9cuZwrV1Thdabun2JtiYfN++X0s2wn4S4yRoHbwTmLSjkn7li5obEAOw4OsatzmF0dwzR1DbOuuYfH3tl/2HNzc2zML3JTWeCiLNdJWW4OZXlOyvOclHid5OXYyXPZyc2xYZ9hSWQ8GKJzcJzOoXE6B8foGByjrW802qYhDkQXDdmtitPrirnq1BouWFpOXYln7r8ps1BX7OG5zQcJhMIzvleROSTcRUbLzbFPzMaJNzwepLXXR0uvb+Ljvh4fLT0+Nuztpc8XmPI13Q4rXmck5O1Whc1qwWZR2K0WAqEw48Ew44EQY9GPI/7QUa/htFloKPNyal0RyyvzWbmggBMq8+e0dUCi1JZ4CIU1rb0+6ku96W6OSBIJd5GVvE4bSyvyWFox+Z7n48EQ3cN+OgbH6Bn2MzQWYHA0wOBYkMHRAENjQQLhMMGQJhgOEwhpgtGertNuJcdmwWm3kGOzkueyMy8vh9I8J+XRnwiK3A7D1v/rSiJ7/+ztGZFwz2IS7sKUnDYrVQUuqgpc6W5KytUWR8pBe7plxkw2k4KbECZT5HGQm2Njr8yYyWoS7kKYjFKKuhIPe3sk3LOZhLsQJlRbLHPds52EuxAmVFvi4UD/KOPBo2f6iOwg4S6ECdWVuAlraO2VQdVsJeEuhAnJjJnsJ+EuhAnFVsfKjJnslfB57kopD/BfgB94VWt9f6LfQwgxNwVuBwVuO3tkxkzWmlbPXSl1l1KqUym1+YjrFymldiilmpRSN0cvfwx4WGv9ReAjCW6vECJBaos90nPPYtMty9wDXBR/QSllBW4DLgaWAdcopZYB1UBr9NtkKF4Ig6orkXDPZtMKd63160DvEZdPA5q01s1aaz/wIHAF0EYk4I/5+kqpG5RSG5RSG7q6umbeciHEnNSVeDgwMIbPH0x3U0QSzGVAtYpDPXSIhHoV8CjwcaXU7cBTUz1Za32H1nqV1npVaWnpVN8mhEiShrLIpmHNXdJ7z0ZzGVCdbMs7rbUeAT4/h9cVQqRALNybOodZXiWHZWebufTc24CauK+rgQMzeQGl1OVKqTsGBuRUGCFSrbbYg9Wi2NU5lO6miCSYS7ivBxqVUnVKKQdwNfDkTF5Aa/2U1vqG/HzpNQiRag6bhQXFbpqix/6J7DLdqZAPAG8Bi5VSbUqp67TWQeBrwPPANuAhrfWW5DVVCJFojWXeiTNdRXaZVs1da33NFNefAZ5JaIuEECnTUOblpW2d+INhHDZZsJ5N0vqnKTV3IdKrsSyXUFizT1aqZp20hrvU3IVIr9iMGSnNZB/5OUwIE6svjWwgJoOq2UfCXQgTcztsVBe6pOeehaTmLoTJNZR5pRig3C0AAAsUSURBVOeehaTmLoTJNZZ5ae4aJhTW6W6KSCApywhhcg1lXsaDYdr65FSmbCLhLoTJNZTlAjKomm2k5i6Eycl0yOwkNXchTC7fZac01yk99yyT8DNUhRCZR/aYmTutNaGwJhDSBMJhAsFw5PNQmEAoTDCs8QcPfR4Ka8JaozWEtSYc/ai1Jhw+dE3HPRb//ccj4S6EoKHMy6Ob9qO1RqnJjmrILlprRvwhBkcDDI4FGBwNxn0eYHAsyPB4kFF/CJ8/xFggxGgghM8fZDQQZswfwhcIMuoPMxYIRUI7HGYamZsyEu5CCBrLvAyPB+kYHGdefk66mzMnA6MBWnt97O8fpWtoPPJreHzi8+7o5+PB8DFfJ8duwe2w4bJbcTmskY92KwUuO668HFwOKznRaw6bBYdVYbNasFst2K0q+vHwz21WhSP60WpRWFTsF6jox9g1FfvcwhHfoyZOSqr78dTtl3AXQrBwYlB1KCPCPRAK09w1wvaDg+zsGKK5a4SWXh+tvT4Gxw4/E1YpKHI7KM11UprrpK7EQ2muk2KPg3yXnTyXnbwcO3kuW/SjndwcG3ZrZk8mTGu4K6UuBy5vaGhIZzOEML3GuOmQZzca60xjrTVNncOs39vHhr29bDkwSHP3MIFQpAZitSgWFLmpKXKzcn4hNUUuagrdVBe6KctzUuRxZHxQz0Zaw11r/RTw1KpVq76YznYIYXYl3kgv1giDqlprdncN88r2Ltbt6WXjvl76fAEASrxOTqrO5/ylZSyZl8ui8lzqSz04bdY0t9p4pCwjhEApRWMa95jRWrOtfYgn3t3P81sOsrcnslq2rsTDh5aVs6q2iFNri6gtdptiwDcRJNyFEEBkxsyLWztS+p7D40Ee3tDKA39pZUfHEDaL4qyGEq47u54LlpRRWeBKaXuyiYS7EAKIhPuD61vpHfFT5HEk9b26hsb59Wu7+Z/1rQyNBzm5Op8fXrmcS0+sSPp7m4WEuxACOLQNQVPnMKfVFSXlPQbHAtzxWjN3rd3DeDDMpSdW8PmzalkxvzAp72dmMltGCAHE7zEzlJRwf37LQf7x8c10Do1z+cmV/N2FjdSXehP+PiJCZssIIQCozHfhdlgTPqja7/Pz3cc28/T77SyryOPOa1dxUnVBQt9DHE3KMkIIACwWxcLSxM6Y2dkxxPX3buDgwBjf/vBibjin3pRzztNBwl0IMaGxzMtbzT0Jea0Xt3Zw04Pv4HbaePBLZ7BS6uopJf+FCiEmLCzz0j4wxtBYYE6v8+z77dx430Yayrw89bU1EuxpIOEuhJjQGDdjZrZe2trB1x94hxU1Bfz+i2dkxF412UjCXQgxYcm8PAC2Hxya1fPf3N3NV+7fxLLKPO76/Kl4nFL5TRcJdyHEhOpCF7lOG1sPDM74uZ2DY3zjgXeYX+zmv79wGnk59iS0UEyXhLsQYoLFolhakce29pmFeyisuel/3mV4PMjtn1lJgVtWmaabHJAthDjM0opctrUPEg5P/1ih215p4s3dPfzzFctpLM9NYuvEdMkB2UKIwyyrzGPEH6Kl1zet79+8f4BbX9rJR1dU8ckPVCe5dWK6pCwjhDjMsopIZ2s6pRmtNT/841YK3Q5+cMUJsh2vgUi4CyEO01juxWpRbJ1GuD+/5SDr9vTyrb9ZJAOoBiPhLoQ4TI7dysJSz3FnzIwHQ/zrM9tYMi+Xq1bVpKh1Yrok3IUQR1k2jRkzd6/dS2vvKN+7dBk22S/GcORPRAhxlKUVeRwYGKPf55/08ZHxIL96bTcfXFzKmsaSFLdOTIeEuxDiKMsqIytVp6q7P7i+lX5fgK9f0JjKZokZkHAXQhxlaUU03Cepu/uDYe58o5nT64pkQzADk3AXQhylxOukLNc5ac/9iXf30z4wxpfPW5iGlonpknAXQkxqWWUe77b0o/WhlarhsOZXr+1maUUe5y4qTWPrxPFIuAshJnXZSZU0d4/wwtaOiWvPbG5nd9cIN55bLwuWDE72lhFCTOrKUyqpL/Hwixd3Eg5rBkYD/PNTW1lWkcelJ1aku3niOGRvGSHEpGxWC9+8sJHtB4d4ZnM7P3pmGz0jfv7fJ06See0ZQP6EhBBTuuykShaVe/k/T27lwfWtXH92HcurpDOWCSTchRBTsloUf3fhIrqHx1lQ7OamCxalu0limuQMLCHEMX34hHn8/YcWcf7SMlwOa7qbI6ZJwl0IcUwWi5KVqBlIyjJCCJGFJNyFECILSbgLIUQWknAXQogsJOEuhBBZSMJdCCGykIS7EEJkIQl3IYTIQip+r+a0NUKpIWBHutuRQCVAd7obkWDZdk9yP8aXbfeUjPtZoLWedGN9o6xQ3aG1XpXuRiSKUmpDNt0PZN89yf0YX7bdU6rvR8oyQgiRhSTchRAiCxkl3O9IdwMSLNvuB7LvnuR+jC/b7iml92OIAVUhhBCJZZSeuxBCiASScBdCiCyU1nBXSl2klNqhlGpSSt2czrbMllKqRin1ilJqm1Jqi1Lqm9HrRUqpF5VSu6IfC9Pd1plQSlmVUu8opf4Y/Tpj70cpVaCUelgptT3653RmJt8PgFLq76J/3zYrpR5QSuVk0j0ppe5SSnUqpTbHXZuy/UqpW6I5sUMp9eH0tHpqU9zPT6J/595TSj2mlCqIeyzp95O2cFdKWYHbgIuBZcA1Sqll6WrPHASBv9daLwXOAL4avY+bgZe11o3Ay9GvM8k3gW1xX2fy/fw78JzWeglwMpH7ytj7UUpVAd8AVmmtlwNW4Goy657uAS464tqk7Y/+e7oaOCH6nP+K5oeR3MPR9/MisFxrfRKwE7gFUnc/6ey5nwY0aa2btdZ+4EHgijS2Z1a01u1a603Rz4eIBEcVkXu5N/pt9wJXpqeFM6eUqgYuBe6Mu5yR96OUygPOAX4LoLX2a637ydD7iWMDXEopG+AGDpBB96S1fh3oPeLyVO2/AnhQaz2utd4DNBHJD8OY7H601i9orYPRL98GqqOfp+R+0hnuVUBr3Ndt0WsZSylVC6wA1gHlWut2iPwHAJSlr2UzdivwHSAcdy1T76ce6ALujpaZ7lRKecjc+0FrvR/4KdACtAMDWusXyOB7ipqq/dmQFV8Ano1+npL7SWe4q0muZey8TKWUF3gEuElrPZju9syWUuoyoFNrvTHdbUkQG7ASuF1rvQIYwdjliuOK1qKvAOqASsCjlPpseluVVBmdFUqp7xIp394fuzTJtyX8ftIZ7m1ATdzX1UR+tMw4Sik7kWC/X2v9aPRyh1KqIvp4BdCZrvbN0FnAR5RSe4mUys5XSt1H5t5PG9CmtV4X/fphImGfqfcDcCGwR2vdpbUOAI8Cq8nse4Kp25+xWaGUuha4DPiMPrSoKCX3k85wXw80KqXqlFIOIgMMT6axPbOilFJE6rnbtNY/j3voSeDa6OfXAk+kum2zobW+RWtdrbWuJfJn8iet9WfJ3Ps5CLQqpRZHL10AbCVD7yeqBThDKeWO/v27gMhYTybfE0zd/ieBq5VSTqVUHdAI/CUN7ZsRpdRFwD8AH9Fa++IeSs39aK3T9gu4hMgo8m7gu+lsyxzuYQ2RH6neA96N/roEKCYy4r8r+rEo3W2dxb2dB/wx+nnG3g9wCrAh+mf0OFCYyfcTvacfANuBzcDvAGcm3RPwAJHxggCRnux1x2o/8N1oTuwALk53+6d5P01EauuxXPhVKu9Hth8QQogsJCtUhRAiC0m4CyFEFpJwF0KILCThLoQQWUjCXQghspCEuxBCZCEJdyGEyEL/H8W3dCYD2oVCAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from scipy import fft\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "\n", "def func(x):\n", " return np.sin(x/13)+np.sin(x/2)+1/4*np.cos(2*x)\n", "\n", "\n", "x = np.linspace(0, 256, 256) #0から2πまでの範囲を100分割したnumpy配列\n", "plt.plot(x, func(x), color = 'b')\n", "plt.plot(x, np.cos(x/17), color = 'r', linewidth=0.8)\n", "plt.plot(x, np.cos(x/3), color = 'r', linewidth=0.8)\n", "plt.plot(x, 1/4*np.cos(2*x), color = 'r', linewidth=0.8)\n", "\n", "\n", "plt.grid()\n", "plt.show()\n", "\n", "yy = func(x)\n", "out = fft(yy)\n", "\n", "def spectrum_power(x):\n", " re, im = x.real, x.imag\n", " return np.sqrt(re**2+im**2)\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.show()\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2のスペクトルは1に高周波のノイズが乗った感じ.logでプロットすると周波数90あたりに変な落ち込みがあるね.なんだろう.誤差かな..?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gauss-Seidelの収束性:25点\n", "初期値を$[0,0,0]^{t}$として,\n", " $A(tt)x=b$に\n", " ガウス・ザイデルによる連立一次方程式の反復解法プログラムを適用する.\n", " ただし,\n", " \\begin{equation}\n", " A(tt)=\n", " \\left(\n", " \\begin{array}{ccc}\n", " 5&tt&tt \\\\\n", " tt&5&tt \\\\\n", " tt&tt&5\n", " \\end{array}\n", " \\right)\n", " ,\n", " b=\n", " \\left(\n", " \\begin{array}{c}\n", " 2 \\\\\n", " 2 \\\\\n", " 2 \\\\\n", " \\end{array}\n", " \\right)\n", " \\end{equation}\n", "である.$tt=1,2.5,4.5$に対して有効数字6桁の解を得るための反復回数を求めよ.\n", "(E.クライツィグ著「数値解析」(培風館,2003), p.89, 問題2.3-9改)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tt= 1.0\n", "0 [0.4 0.32 0.256]\n", "1 [0.2848 0.29184 0.284672]\n", "2 [0.2846976 0.28612608 0.285835264]\n", "3 [0.2856077312 0.285711401 0.2857361736]\n", "4 [0.2857104851 0.2857106683 0.2857157693]\n", "5 [0.2857147125 0.2857139036 0.2857142768]\n", "6 [0.2857143639 0.2857142719 0.2857142728]\n", "7 [0.2857142911 0.2857142872 0.2857142843]\n", "8 [0.2857142857 0.285714286 0.2857142857]\n", "9 [0.2857142857 0.2857142857 0.2857142857]\n", "tt= 2.5\n", "0 [0.4 0.2 0.1]\n", "1 [0.25 0.225 0.1625]\n", "2 [0.20625 0.215625 0.1890625]\n", "3 [0.19765625 0.206640625 0.1978515625]\n", "4 [0.1977539062 0.2021972656 0.2000244141]\n", "5 [0.1988891602 0.2005432129 0.2002838135]\n", "6 [0.1995864868 0.2000648499 0.2001743317]\n", "7 [0.1998804092 0.1999726295 0.2000734806]\n", "8 [0.1999769449 0.1999747872 0.2000241339]\n", "9 [0.2000005394 0.1999876633 0.2000058986]\n", "tt= 4.5\n", "0 [0.4 0.04 0.004]\n", "1 [0.3604 0.07204 0.010804]\n", "2 [0.3254404 0.09738004 0.019461604]\n", "3 [0.2948425204 0.117126288 0.0292280724]\n", "4 [0.2682810756 0.1322417668 0.0395294418]\n", "5 [0.2454059122 0.1435581813 0.0499323158]\n", "6 [0.2258585526 0.1517882185 0.0601179061]\n", "7 [0.2092844879 0.1575378454 0.0698599 ]\n", "8 [0.1953420291 0.1613182638 0.0790057364]\n", "9 [0.1837083999 0.1635572774 0.0874608905]\n" ] } ], "source": [ "import numpy as np\n", "np.set_printoptions(precision=10, suppress=True)\n", "\n", "\n", "for tt in [1.0,2.5,4.5]:\n", " print(\"tt= \", tt)\n", " A=np.array([[5,tt,tt],[tt,5,tt],[tt,tt,5]])\n", " b=np.array([2,2,2])\n", " n=3\n", " x0=np.zeros(n)\n", "\n", " for iter in range(0, 10):\n", " for i in range(0, n):\n", " x1 = b[i]\n", " for j in range(0, n):\n", " x1 -= A[i][j]*x0[j]\n", " x1 += A[i][i]*x0[i]\n", " x1 /= A[i][i]\n", " x0[i] = x1\n", " print(iter,x0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "tt=1では6回程度で,tt=2.5では10回程度で収束しているが,tt=4.5では10回でもまだ収束していない.\n", "100回まで繰り返すと収束しており,大体80回程度で収束している.\n", "お互いの差をとってやれば収束判定が可能であろう.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tt= 4.5\n", "0 [0.4 0.04 0.004]\n", "1 [0.3604 0.07204 0.010804]\n", "2 [0.3254404 0.09738004 0.019461604]\n", "3 [0.2948425204 0.117126288 0.0292280724]\n", "4 [0.2682810756 0.1322417668 0.0395294418]\n", "5 [0.2454059122 0.1435581813 0.0499323158]\n", "6 [0.2258585526 0.1517882185 0.0601179061]\n", "7 [0.2092844879 0.1575378454 0.0698599 ]\n", "8 [0.1953420291 0.1613182638 0.0790057364]\n", "9 [0.1837083999 0.1635572774 0.0874608905]\n", "10 [0.1740836489 0.1646099145 0.0951757929]\n", "11 [0.1661928633 0.1647682094 0.1021350345]\n", "12 [0.1597870804 0.1642700965 0.1083485407]\n", "13 [0.1546432265 0.1633074095 0.1138444276]\n", "14 [0.1505633466 0.1620330032 0.1186632852]\n", "15 [0.1473733404 0.1605670369 0.1228536604]\n", "16 [0.1449213724 0.1590024705 0.1264685414]\n", "17 [0.1430760893 0.1574098324 0.1295626705]\n", "18 [0.1417247474 0.1558413239 0.1321905358]\n", "19 [0.1407713263 0.1543343241 0.1344049146]\n", "20 [0.1401346851 0.1529143602 0.1362558592]\n", "21 [0.1397468025 0.1515976045 0.1377900337]\n", "22 [0.1395511256 0.1503929566 0.139050326 ]\n", "23 [0.1395010457 0.1493037655 0.14007567 ]\n", "24 [0.1395585081 0.1483292397 0.1409010269]\n", "25 [0.13969276 0.1474655918 0.1415574834]\n", "26 [0.1398792323 0.1467069558 0.1420724307]\n", "27 [0.1400985522 0.1460461155 0.1424697991]\n", "28 [0.1403356769 0.1454750716 0.1427703264]\n", "29 [0.1405791418 0.1449854786 0.1429918416]\n", "30 [0.1408204118 0.1445689719 0.1431495546]\n", "31 [0.1410533261 0.1442174074 0.1432563399]\n", "32 [0.1412736275 0.1439230294 0.1433230089]\n", "33 [0.1414785656 0.143678583 0.1433585663]\n", "34 [0.1416665657 0.1434773813 0.1433704478]\n", "35 [0.1418369539 0.1433133385 0.1433647368]\n", "36 [0.1419897322 0.1431809779 0.1433463609]\n", "37 [0.1421253951 0.1430754196 0.1433192668]\n", "38 [0.1422447822 0.1429923559 0.1432865757]\n", "39 [0.1423489616 0.1429280164 0.1432507198]\n", "40 [0.1424391374 0.1428791285 0.1432135607]\n", "41 [0.1425165797 0.1428428737 0.143176492 ]\n", "42 [0.1425825709 0.1428168434 0.1431405271]\n", "43 [0.1426383666 0.1427989957 0.143106374 ]\n", "44 [0.1426851673 0.1427876129 0.1430744979]\n", "45 [0.1427241004 0.1427812616 0.1430451742]\n", "46 [0.1427562077 0.1427787562 0.1430185324]\n", "47 [0.1427824402 0.1427791246 0.1429945916]\n", "48 [0.1428036554 0.1427815777 0.1429732903]\n", "49 [0.1428206188 0.1427854818 0.1429545094]\n", "50 [0.1428340079 0.1427903344 0.1429380919]\n", "51 [0.1428444163 0.1427957426 0.142923857 ]\n", "52 [0.1428523604 0.1428014044 0.1429116117]\n", "53 [0.1428582855 0.1428070925 0.1429011598]\n", "54 [0.1428625729 0.1428126405 0.1428923079]\n", "55 [0.1428655464 0.1428179311 0.1428848702]\n", "56 [0.1428674788 0.1428228859 0.1428786718]\n", "57 [0.1428685981 0.1428274571 0.1428735503]\n", "58 [0.1428690933 0.1428316207 0.1428693573]\n", "59 [0.1428691197 0.1428353706 0.1428659587]\n", "60 [0.1428688036 0.1428387139 0.1428632342]\n", "61 [0.1428682467 0.1428416672 0.1428610775]\n", "62 [0.1428675298 0.1428442535 0.1428593951]\n", "63 [0.1428667163 0.1428464997 0.1428581056]\n", "64 [0.1428658552 0.1428484353 0.1428571385]\n", "65 [0.1428649836 0.1428500901 0.1428564337]\n", "66 [0.1428641286 0.142851494 0.1428559397]\n", "67 [0.1428633097 0.1428526755 0.1428556133]\n", "68 [0.14286254 0.142853662 0.1428554182]\n", "69 [0.1428618279 0.1428544786 0.1428553242]\n", "70 [0.1428611775 0.1428551485 0.1428553066]\n", "71 [0.1428605904 0.1428556927 0.1428553452]\n", "72 [0.1428600659 0.14285613 0.1428554237]\n", "73 [0.1428596017 0.1428564772 0.1428555291]\n", "74 [0.1428591944 0.1428567489 0.142855651 ]\n", "75 [0.1428588401 0.142856958 0.1428557817]\n", "76 [0.1428585342 0.1428571156 0.1428559151]\n", "77 [0.1428582723 0.1428572313 0.1428560467]\n", "78 [0.1428580498 0.1428573131 0.1428561734]\n" ] } ], "source": [ "for tt in [4.5]:\n", " print(\"tt= \", tt)\n", " A=np.array([[5,tt,tt],[tt,5,tt],[tt,tt,5]])\n", " b=np.array([2,2,2])\n", " n=3\n", " x0=np.zeros(n)\n", "\n", " for iter in range(0, 100):\n", " for i in range(0, n):\n", " x1 = b[i]\n", " for j in range(0, n):\n", " x1 -= A[i][j]*x0[j]\n", " x1 += A[i][i]*x0[i]\n", " x1 /= A[i][i]\n", " x0[i] = x1\n", " print(iter,x0)\n", " if abs(x0[0]-x0[1])<10**(-6):\n", " break" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "第1項と第2項の差で収束判定をすると,78回目で収束している.\n", "\n", "これらの結果から,Gauss-Seidel法によって解を求める時には,\n", "対角成分と非対角成分が近い値では,収束が遅くなることが確認できた." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 常微分方程式:25点\n", "\n", " スーパーカーの加速性能をEuler法で求める.\n", " 1. 空気抵抗のない場合に,自動車を静止状態から加速度$2 \\times 17.35$ [m/sec$^2$]で\n", " 加速した場合の移動距離と速度の変化をtt=0..5でプロットせよ.\n", " 1. 空気抵抗としてcc=0.5とした場合の移動距離と速度の変化をtt=0..10でプロットせよ.\n", " 1. 上問1. 2.のプロットの違いを,「ゼロよん」と呼ばれる400mを通過するまでの時間や,\n", " その時の時速を用いて,説明せよ.\n", " \n", " 空気抵抗は,テキストにある通り,速度に比例するとして,その係数は規格化された係数とする.\n", " 時間の刻み幅dt=0.1[sec]程度をとれ." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "def euler(x0, v0):\n", " v1 = v0 + g * dt\n", " x1 = x0 + v0 * dt\n", " return x1, v1\n", "import matplotlib.pyplot as plt\n", "\n", "def my_plot(xx, vv, tt):\n", " plt.plot(tt, xx, color = 'b', linestyle='--',label=\"distance\")\n", " plt.plot(tt, vv, color = 'r', label=\"velocity\")\n", " plt.legend()\n", " plt.xlabel('time')\n", " plt.ylabel('distance and velocity')\n", " plt.grid()\n", " plt.show()\n", " \n", "g, dt =2*17.35, 0.1\n", "tt,xx,vv=[0.0],[0.0],[0.0]\n", "t = 0.0\n", "\n", "for i in range(0,50):\n", " t += dt\n", " x, v = euler(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "# print(xx)\n", "# print(vv)\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "408.07199999999995\n", "4.800000000000001\n", "612.108\n" ] } ], "source": [ "print(xx[-2])\n", "print((50-2)*0.1)\n", "print(vv[-2]*60*60/1000)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def my_plot(xx, vv, tt):\n", " plt.plot(tt, xx, color = 'b', linestyle='--',label=\"distance\")\n", " plt.plot(tt, vv, color = 'r', label=\"velocity\")\n", " plt.legend()\n", " plt.xlabel('time')\n", " plt.ylabel('distance and velocity')\n", " plt.grid()\n", " plt.show()\n", "\n", "def euler2(x0, v0):\n", " v1 = v0 + (-cc * v0+ g) * dt\n", " x1 = x0 + v0 * dt\n", " return [x1, v1]\n", "\n", "g, dt, cc =2*17.35, 0.1, 0.5\n", "tt,xx,vv=[0.0],[0.0],[0.0]\n", "t = 0.0\n", "for i in range(0,100):\n", " t += dt\n", " x, v = euler2(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "398.25366550767154\n", "7.6000000000000005\n", "245.02740208619116\n" ] } ], "source": [ "print(xx[-24])\n", "print((100-24)*0.1)\n", "print(vv[-24]*60*60/1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "xx,vvの値をプリントすることで400mを通過する時間が読み取れる.\n", "\n", "空気抵抗がない場合は(50-2)/10秒で4.8秒,\n", "空気抵抗がある場合は(100-24)/10秒で7.6秒である.\n", "\n", "またそれぞれのその時点での時速は,\n", "空気抵抗がない場合は,612km/h, 空気抵抗がある場合は,245km/hである.現実問題として空気抵抗がない状態で,600km/hでは新幹線の最速を抜くが,ジェット機はまだその先にある.自動車にジェットエンジンを積むのは現実的ではないが,空気抵抗は抑えることができそうである.空気抵抗をいかに抑えることができるかが,車の性能に大きく利いていることが実感できる.F1のマシンの空気抵抗はどの程度なのだろう." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }