{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Matplotlib\n", "\n", "Let's start with a simple 2D Plot. We work with vectors and matrices, so we need numpy too." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "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": [ "import numpy as np\n", "\n", "# create 2 numpy arrays with x and y values\n", "nvalues=100\n", "a=-10.0\n", "b=10.0\n", "x=np.linspace(a,b,nvalues)\n", "y=np.sin(x)\n", "\n", "# get the plot lib \n", "import matplotlib.pyplot as plt\n", "plt.plot(x,y)\n", "plt.show\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task\n", "\n", "Extend the plot above with a second function $g(x)=cos(x)$, plotted in a different color and add:\n", " * plot grid\n", " * axis labels\n", " * legends\n", " * a label pointing to the value of $sin(\\pi)$ and saying \"This is $sin(\\pi)$\"\n", " * a title" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# TODO\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Barplots are another useful variant of plots, as a minimalistic example see" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x=np.array([1,2,3,4,5])\n", "h=np.array([1,5,3,7,4])\n", "w=0.4\n", "\n", "fig, ax = plt.subplots()\n", "ax.bar(x,h,w )\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task\n", "\n", "Understand the parameters of bar plots, then make a bar plot of the actual number of Corona cases in \n", "the German states. The data can be found at:\n", "\n", "https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Fallzahlen.html" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "# TODO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting in 3D\n", "\n", "Datas like $z=f(x,y)$ can be plotted with ```surf```" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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hlukgFfWKFatwLQeu8AKhrBfu/LxgMAir1YqsrCyUlpairq4OjY2NKCsrQ0JCAmZmZnD58mW0tLSgs7MTo6OjcDgcop9dtZkTS0tLeuQbx7xnIl+pBjhqxJSL0vZaRvpEipJocEmt3AJHz1BMXveNzz3J/qwUxVPhzdplx/Ql5QhdGDGrFXghUgLMePljkgKL8kM4hcgtXkpVCdKol074EE5x5t4Xi1YJIUhMTERiYiLy8kJl5sFgEMvLy2x0vLS0BEIILzpWM5kZCNkOeuQbv2z4yFepAY5W8ZWzHdxut2jUyxXdaC7LpRDmwqqBmwYmVhCRuWcX7/7AG30AViNSKaQEWanrmhj0dVr/6W3N+8qhVXjVMHFZ3gMWIvycqI1WDQYDUlJSUFhYiKqqKjQ2NmLXrl3Izc2Fz+fD4OAgXC4XLl68iL6+PkxOTsLtdoumRy4vL+uRbxyzoSNfNVkMsYh8g8EghoeHMTExwUYz3D8u+ljipgTYN6VhunOWzXoQouT7aol6pYjEevBM+VgxpFGpUvTLvt4uOxzDy4rbUbjibrQZYc02o/O/LqL6/9gtuQ+xrG2JrNaoV4hY1Eub8Owfa4mqyMJoNMJut8NuD11tnD9/Htu3b2cX9CYmJuDxeJCQkMBGyMnJyVhaWtpwkW+9IYlxMJFdFcnRB8/LDMPcGfMDR8GGFF+lScFcohXf2dlZdHd3Izc3F/jCVwCEUoq404BthVY4r7tF2xFqTTkzpiSzkZs10y656Ka1eEEOGvUC6uwAMa83dXOSKgEWi6o9Uz5Ys+OzjFqIcOAod6goHedE4U6SjlVhBI1wLRYLMjMzkZmZyT7udruxuLiIubk5/OAHP8B//dd/IScnByaTCUeOHEF1dbXoMV966SV8+ctfRiAQwOc//3mcOnWK9/zJkyfx+uuvAwCcTicmJycxPx/6XBqNRuzYsQMAcPny5TMMwxyP5v0tGoL4YVpZNIcQ5c7ZzqyYHzRKNpT40g+Yy+WCzWbTlDqmFmo7eDwe9PT0wOfzoa6uDomJibh+04vUrcmY71yUPUZWdQYWJ+S3EYOu6ishrHTT4vvmf0g+u4D7BeKZ8oUNoBTLgogVl35yDnu+fnT1tVKiv2RWkzFSenyv6P+fXPMg4Zw7ofAKieVEDKniIJvNBpvNhpycHHzzm99EUlISkpKSkJqaiuvXr4uKbyAQwF/+5V/i1VdfRVFRERobG3H8+HHett///vfZn//5n/8Zly6tpinabDa0tbXRu1EJLwDAsLafsXhiw7xLmsUwPT2N0dFR1b0YIhHfyclJtLa2Ii8vD/X19UhMDC2sUOG1FVrZpioGE4FrzANrrgXO62521TwemoQrkblnFwbe6INnSr1PHXAFMde9iLnuRThn+GJTfmc5Aq4g7was+uCJmxIkI9xool/hYpsWtFxBSDWY99z08oSX+uZGmxGem14M3PvhmIqv2gja6XSipqYGDz/8MO68U/yKu6WlBeXl5SgtLYXFYsH999+PF198UfKYv/jFL/DJT34yonNXAzEQGG2GmN/ikfg8Kw7CBjhmszmm2Qtc5ufnMTQ0BJ/Phz179iAnJ4d97u3tobp9mlLEhQqwsCS1qLFYdjoFF7VRb6So6ULGFT8lQabbOmfcrAj3/Opa2HZUgLkR9XpZDGpyfJWKK8RI3JQAS4aZ/cIRLrrO9i/EzHbw+/2aevkqeb5jY2MoLl4NFIqKijA2Nia67fDwMAYHB3HHHXewj7ndbjQ0NGDPnj0ghNyj6sRkIAbAnGiM+S0eiVvxlWqAYzKZYi6+Xq8X7e3t6O3txaZNm5CZmSn7Affc9IY10zGYCC8hn+aQbr59G9upi+b7CkthS+/9kOKCkpaMh4yP3KV621jhnHFLiqpc9sR6QqNeMcuBmy1iSbaJ9j+mfq/zupu3BgCEZ72sR+Qb62yH06dP48SJE7zXHx4eRmtrK/7jP/4DAP6JEBKdYUsIDGZjzG/xSNyJL61Ok0sdowttapATX4ZhMDo6ivPnzyMzMxMNDQ1ISkoS3d6aZoFnIbSiLVduKzXafes9e8IW3Erv/ZBo3irX67Rmhi9u5d5zt+j7UUIY/Z5//Dn254I9OcLNY4baSNcz5cOlf3ttzc4jVgyfHWB/NloNYb44F6PNCGuaBRlP/H1MxDfWUywKCwsxMrI6xHR0dBSFhYWi254+fTrMcqDblpaWAsAbAHYJ99MCIaHsn1jf4pG4XHDjzk4TEquiCYfDga6uLqSlpaG5uZkt61RTXsyFrma7xjyhdKMK6W1Ljtazwhpt6pRpUwn81wclnzdv3wlf+2XF42jxe2N5LGu2md2+/MOhqHKkZe0mGQvJ3F0l+ZxUq8zR88NhjyVlJ2KxZ7W95O4v1cM14wAA9P9uiH18tn8BkTeyXEWr+CrZDo2Njejt7cXg4CAKCwtx+vRpGsXy6O7uxtzcHPbuXfXI5+bmkJiYCKvViunpaQDYD+AfNbydMAghMCXEpSzFnLj7ShCbEszFZDJpinyFx/H5fOjq6kJXVxeqq6uxbds2Xj29mFhTv5d3XDPhCS8QSkEbfeMGb7tYN8WRIpr2jVqjXqlIVuo4mWXS44yo8AJAcVP0i5RqCizkrhyUcqSp5ZC/Mx+ZFemYuhBqGLT7S/XY/SW+aG86yI8gL126hP7+fkxNTcHjiWyRMNbiazKZ8MMf/hBHjx5FVVUV7rvvPtTU1OAb3/gGzpw5w253+vRp3H///by/p66uLjQ0NGDnzp04dOgQADzOMExnJO+LhRA98l1PaE9dMbRGphSGYTAxMYHBwUFs3rwZ27ZtUz2ROKMsDcvTrtBxfNKN1ukUi4BH+/ndCgIHjsHUzq8mo4I507/qV0cTDRfsycH4u5Nhx9fCpX97Dbv+zzuUN1xDxNpwcnseL00usR3amh7ZB79LXEw3HSzETH9IoGtqauBwOOBwODA6Ogqfz4fExES2bDglJUVRWLWIr9vths0m3Qyfcvfdd+Puu/lfSN/61rd49//H//gfYfvt27cPV69e5T70lKoTk4EQwGCKT4821sSl+MoRyUiUQCCA1tZWJCYmoqmpSbZdpFjkS4VXDNeYB/bqUHThuBaKujw3vRi/eRO4bTUn1zMzD2umHYHFJRhTksF4PWHWA7FYZdOmkvIykbynWf7NqmTgud9LRqTWbLNoFNr3mwGRrdWRWZbOE3gA2P5ALdxz/Ei1uKk4zH6IZXWbkl+eskW5+93SdTeWVlLLaH8Hk80qKcBAaM3AYrEgKysLWVmhfH+GYeB0OuFwOHDz5k309YWKXZKTk5Gamoq0tDQkJibyPvNaxJeOx9pIEAOByfr+EN+N9ZvRiN/vR09PD9xuN7Zu3YqamhrFPr1SHjFdbBNChVcMsSbjalFadJMiFpkOUpf/XItAjmgX7+RsimiIZKFSWJTS8YvVq+rs+gzRfO78I/sBAIUHQmtPmWWhRvID936Ytx0hBElJScjPz0dlZSUaGhqwa9cu5Ofnw+/3Y3BwEOfPnw+zK7TMb9twrES+sb7FI3EZ+UY78I9hGExOTqKvrw/FxcXspZ0ahLbD5MlPqdqPRr0U6gcPvD4Iz80eVX1rtSJcdBP6vmoX3bhUHK0Ki0a5lH+4VHRhLNaCeauq27iIRb3cpvNc4c1vzsbixCIyvvszuJ/4kqrjW1OUc76NRiPS0tKQlpbGPub1elm74ubNm2AYBtPT00hLS5O1K7RM4o4fCAym93RMyBKX4qsGqTlrTqcTXV1dsFgsaGhogNVqxcTEBAKBgKpG1WG9HQamVl9zxe8lZvkPtFjTndZ/ehuJmxKi8jKtx+8FJq9HvL8SFUelMwC4iFkDYshFwEqvNfjin1Dy0dsVX0NtdVs0/3ftP20HAJCVhZv85mxej+aER36gKMAZJZF/OXHtCoZhkJaWBpvNxrMrGIZhm+qkpKTAbDZvyCGbIdthw8qSJjbkV4yYNRAIBNDX14fLly+jtLQUO3bsYMe0aElP07KtNS28vaSY8FKc1904+3e/VXXstcKzPfoIPCE9WVE8xYRXLDpOSA+PcDPK8yI/ORGsx++FmSO83KsFWmAhZtd0/XsvLv/kCu+xIk4VI9dySKmtQXqzeFe2gn3bYUmKzSBLGkQI7Yrdu3cjPz8fgUAA58+fx969ezE+Po6vf/3r+O///m/J47300kuorKxEeXk5Hn/88bDnn376aWRnZ6Ourg51dXV48snVns/PPPMMKioqUFFRgWeeeSYm74/otsP6onSpRNPNaCQ7NTWF3t5eFBQUoLm5OWyRQYug0tem2RGUgt15GDs3gcLmfIxfvCG1uyr++JVn8YF/uk900e1WMPDc78MeUxv13grkbI9bRde/9/LuFx/ip6C5593I+O7PJPfPP7IfgfkFFOzbDiB200ykFty4dkVxcTFefPFFfPnLX8a+ffswOCieD66mqQ4AfOITn8APf/hD3mOzs7P45je/idbWVhBCUF9fj4ceeiidYZjwuUuaIHErlrEmLsVXCSqmLpcL3d3dIIRg9+7dSEgQ99S0FmZwsyPsealISJNP16F+b/6+bMz2h1e3AUByyeoxXDe8OPu3/8l7/rbvhrxlpYwHX84mXhQXa7QIX8XRKvS+3KX5NW6V0Fsz7cD+w6q3/+PfhEeIxYfzeXmiAV8QPpcPKfnq+uQSsxmMb1V43U98CQmP/ED1OQlROwV5aWkJWVlZ+MhHPiK5DbepDgC2qY5U60kuL7/8Mg4fPoyMjNBi4uHDh/Gv//qvdwL4hbp3IgEhMJg3pCxpZsPaDsPDw7h06RKKi4tRV1cnKbwAVPeDCAQC6O3thdvtRkVFBWpqanjPFzavRj/cJtv5+7KRvy87gney8rquAN78i5/hzb/gR1K8jIfj9yoeZ/nACenXOHBM8rlYX+ZTCppEJmisUSaDKCqF99IPL+IPd36b91jebVkoPqy+Kb3vri/KPk8zH2Z6xJvWqCUYDKpau1heXkZSUpLsNmqb6vznf/4namtrceLECbYUWWxfAOJ1yRp4P9kOcSm+crbDzMwMpqamEAwGsWfPHjZnUg6DwaAovjMzMzh37hxMJlMo4rXbMfv1z2o+dwrX7+VGvUKEzctf/8JP8cZf/VL165g2lcg+b96+U/RxMWGMhIqjVWsmqFqnFXOr25xH5LNU3vraC3jray+g4z+uhj2Xd9vqZ0oY9VLmT30L/f39mJ6ehte7+ruW8n0BxMT39fv9qiLfWM1vO3bsGIaGhnDlyhUcPnwYn/nMZ6I+piyEwGgxxfwWj8TnWYng8XjQ3d2NQCCAvLw8ZGVlqU4gl7MduMfdtWsXbDYbz+sVIuf3Ci0HGg0vTqyKguuGeL6wECrABhPB/v9HfX7qQkEN0sY7VG+/VmgR94T05DC7I6M8D7N9kXnrUsL7xv3f592n3dYsGWa2SRIVXqmpI3QiCa1WW1hYwMjICHw+H/bLnBO1HjIrowsO1XY1U1NarKapDp2UAQCf//zn8bWvfY3d94033uDtCyC6sB4r6XFxGqnGmrgX32AwiJGREYyOjqKiogI5OTkYGBjQ5OGK9YOgHc2uX7/OHlf4vBjUbrjRLl9AEYkNEfTzX5OWK5/9u99i/2uHcfaOkwCAg6dPaj42xfWzfwUAjLeEymc3H23CYn90HvLmo00YfrlF9bZqXs89t4SM8jzcPPAg8t55VtWxjSnJWNy7Okzh7B0n2ewTYeaJEK4Aq0GsWm1uuRrpf/r31fOxpyEwv/qFnNO0Ha7xyAtvgNiOjVfTVGdiYgL5+SH75cyZM6iqCvn1R48exde//nXMzYXW11555RUAeFn7OxJAAMMGTJGLhLgUX2o7zM/Po6urC1lZWdizZw/7jR9JZzNu4cTi4iI6OzvDOppxt1d7/JIDFZjsGFV9Lly0jE+nwsuFRnK3/aN8D2vz9p3gvlJBUyUrvmtNtK/lgwUjex8AABS/83PJ7W4eeBA9u44BeBa7zv0cl5of4KX9WXMtigIsjHrFGrJkVYh/qRJCJMVOuOg2PDzM9nPQmourtmhCa1OdQCCAhx9+mG2q09DQgOPHj+MHP/gBzpw5A5PJhIyMDDz99NMAgIyMDPzd3/0dGhsbAcopTzUAACAASURBVADf+MY38NnPfnZW05sRgxAY4tQmiDVx+S79fj/a29vhdrtRW1sbtnBgMpnYtpNqMBgM7MDN/v5+zM/Po6qqSrLqjYo1bQ0oh5jwlh8u5xVnqMGSYeZNO+ZOwKBiQMuVhZfPQMjDBF4AABz81d8CAF479g+449df522XkLFaObX5aHi3NiXE8nK1klK2KaJom4owAPTtOML+HLpCWI2OLzU/ADUkFduwPBLq25FYIJ/yx/V75VLMAICYzGD80p/P3NPfxfA9f4n+/n4AYIsjaPFELKrSlpaWQkNfFVBqqvPYY4/hscceE9334YcfxsMPPxzdiQoghIDoke/6YTAYkJOTg+zsbNEPotFohNstPaxQiMlkwszMDLtCu3XrVtkPuJoFOiC6qBdYHTUPhBrw9L8ywAownXoMrPqMdEyR0WzAyOurvnRIePm8duwf2H+pAL/7gf8LQT+DvY8eivicpdBiPWhh6sTHeBOCC1/6NU94gdBsPWF5txjc6Dd1K/9LRM24p5Kj9Zjt6Fdz2pL4XR6YbFZUVoY88UAgwI6A7+/vh8vlgtVqZSPj1NRUxX4kYqixHeKVeM1OiDVxKb5GozHMg+Wipaevy+XC0NAQ/H4/Ghsb2ao3pddf/PrnAGhPji8/XM67z11s4yLWE7fsSClGz6trKC5M+ueK8Rsf40cqrx37B9Y/NpgIzj3xBgBg/N3wvFZbngVLgy5Ungh1he95PlRsQO9f/rdQrwNrrgXbjteE7Q8Ak50zGHn9DTQ/cjDsuT/+zQu8OXj0GD3P9/LGMgGhSSFc6wAAxu7kp8zRxkZCARbupxaphTYAUQsvANjrd2Cpc3XWndFohN1uh92+2jzJ7XbD4XBgbm4OQ0NDCAaDSE5ORkpKCgKBgCrfd3l5OSbZDrccQkAi+LKJ/mXJnQD+FwAjgCcZhnlc8PxDAL6D1UXFHzIM8ySiIC7FF5Dv6avGkw0Gg7h+/TrGx8eRn58Pt9utSniBUORrslnhc0oXO5QcCB9ZQYVXznLIrQ/5ilmV+bxhjQuj80grsqOosVi1AHPhijG9RBY2duciNlfNlhcSrOQSG8YujKKwvoh9joowsCps3WdCWRWNJzfhrVPhE2/PPfEGO/F58+ECDL86HrZN95kOdiaeELHHgNAQU24rTzEyytJEC16suRZeWXhSsQ1MILz/stDvLT9xAFPvKjcp8t31RZh/9xP2vn/fnTC9/RIA8HxfORISEpCQkMAGIMFgEEtLS5ifn4fP50NraytMJhPbWCc1NTXss63G841H1sN2IIQYAfwIwGEAowDOE0LOiDSG/yXDMH8Vq9eNyzxfJZQi3/n5eZw7dw4+nw/Nzc3IyMjQvEAnBk2Uj5SCXcq9YtUgHMApRdHBPBQdjLyAYuxCuKUiFlGe//7vZI9jr07BwtgiAPHpz3JRqlzzeiFCK0EtSpYD9/870vl57LHmxSsg5TAYDEhNTUVubi5SU1PR1NSE7du3Iy0tjV08bmlpQXt7O0ZGRnDlyhUsLi4q2g5KfR2+973vobq6GrW1tfjgBz+I4eHVMUpGo5Ht93D8+PGwfSNmRXxjfVOgCUAfwzADDMN4AZwG8NHYvSlxNqT4SkW+Pp8PnZ2d6O3txY4dO1BRUQGj0RhRdgQXWp8/2dIuuU9GqXxqmZjwSo2sEesRGw25zcqTj2nUu1EQE3EKTfPLKEsLe07YDEks6hVSfuIAW8Dhu/2TClsD7q0N8FTv5T+4d7WbnVzTdTm4fR1oqltpaSl27dqFxsZGbNmyBUajEc888wxaWlrwmc98BidPnsT16+GLm7Svw+9+9zt0dnbiF7/4BTo7+YHerl270NraiitXruDEiRNsji8A2Gw2tLW1oa2tjTduKGoIQMymmN8AZBFCWjm3L3BetRAA93JzFOLVeh8nhFwhhDxPCIn6jzRuxVduQUwY+dImOC0tLUhLS0NDQwPvW1+r+Ar9tPG3+aJry1TXG1gMqeGMQiqP1cE9v7qoGG1jluz6DGTXZ2jeL5qyaWEkKmcTSCHVvlOso1wkVB6rY38WSzETmy4dC7jWhFrkpljQVLeCggJ897vfxebNm/GrX/0Kx44dQ2JiYtj23L4OFouF7evA5dChQ+y+e/bsoYUUa8yaRb7TDMM0cG7/qvHEfg1gC8MwtQBeBRB1G7e4FV85uGLqdDpx4cIFzMzMoLGxEYWFhWHCrVV8udCoNxq23F4GS3KoxJjOBqN+r9zARq4wxIq1EuBoRFqOgt3abBMl60Gsr+7We/aILrRxhVfLYpuxbPUL1tr5DgCAtK6WSsuVIMuhZYSQ0+lEXl4e7rjjDtESfLV9HShPPfUU7rprte2m2+1GQ0MD9uzZgxdeCM+2iRhCAKMx9jd5xgBwI9kiCKr1GIaZYRiGXrI8CUBdFCVD3C64yUFTwfr7+zE5OYlt27YhPV26v4Ba8WUYBjdu3MDo6CgyEapIUrNIUnpXI+ZX+sIKKX/5t/D/z/9b8RhSbL59G4b/1K1pH6PZwPMpzTYzL3LOrs/AbKd271EpgyB/XzYm3taW30wpbM7H2Dnpsm4hedtzRasMk7L4fTSkFt4AYOvdteyIppKj9WwjI26bT26HOXOSDb29vexCl1wzJzkYvw/EpH1FX+v8tlg1U//5z3+O1tZWvPnmm+xjw8PDKCwsxMDAAO644w7s2LEDZWVl0b/Y+mQ7nAdQQQgpQUh07wfAq1EnhOQzDEM/oMcBaG/nJyBuI18522Fubg7Ly8sghKC5uVlWeAF1E49dLhcuXryI6elp7O95FSllm3jPiy22qcnxpUMRuZQcredFvKXHQ/7gwqj42Jut9+wJe0ztopsUSkUFQuQiWzFvNRZwu8jFgvw65aIDKZLyMmH7xv+LzMxMLC8vo7u7m7fItbCwIPkZ8++7E0xDaCoH/TcS1LaTVDO/TU1fBwD4/e9/j29/+9s4c+YML6OCbltaWoqDBw/i0qVLYftGAiG45QtuDMP4AfwVQuXRXQCeZRimgxDyLUIIXU38EiGkgxByGcCXADwU7XvdUJGv1+tFd3c3O3Kb9iFVQk7IGYbB8PAwxsfHUVlZiczMTHjP8luSRprlkPyj/43KwkJMnw7dtyTb4F2SnoQsx9Z79mDw5QsR7StFYoEVznHpxZ+UfP4lvFwUSaHRr9Tl/+b9xRg+y0+lo9aCVPRbsDuP19CI284zVsjNjKOLbbTElvawpdOHFxYWMD4+jqWlJTYzodQAeKr3srYDAN6iWyRoiXwB+c+9mr4Oly5dwhe/+EW89NJLvLz7ubk5JCYmwmq1Ynp6GmfPnuUtxkUHASK4KogWhmF+C+C3gse+wfn5bwH8bSxfM24jXy60Cc758+eRk5OD3bt3x2QktsPh4KWk0Q5OpuyVZikilgOdTAuE7IbSuxolj19UVARCCDL3KIs3jX4pyzdmwrZRu1inhcQCa8wzHdbK/xWStz08ks2pKRLZkk9GSbrkTDUtk0Xo9OGCggJUVVWhsbERtbW1rDgDCM96QGTpZoD6jmZqImRuX4eqqircd999bF8Hmr3w1a9+FUtLS7j33nt5KWVdXV1oaGjAzp07cejQIZw6dUpVA3ZVrI/nuy7EbeRLv7UXFxfR1dWFlJSUsCY4UkM0leD2eKipqYlpMjotsNj24qvsY4Z7/xpZ1h9i+s132cdSthRgcYhfdJBWJD4i3jMzz/MmYxUBcxf0ul9Ud9lYfrgcfa+GWylqoGIpFv3GArHCFyAUsQsnB2dVaYueEwpyoCbj2Gw2h77EMzMR6Jf/PU1OTiItLU118U8gEIDFovxFuby8rKq0WKmvw+9/Hz5uCgD27duHq1fD+yDHDEN8imWsidvINxAIoKenBx0dHaisrERVVRVPeNVOpxAyNTWFc+fOwWazoamp6ZZXAWXvCu9zS4c4Zu5WN16n/MSBqM8jmkwKYQl1LJHyebVmPaiBfqFJoXYyslb8++4EEKpCExZIOBwOSe9Yre2wuLioOMUibiErtkOsb3FI3Ea+09PTSEhIQHNzs2RzHe4QTSUYhkFbWxsYhkF9fX3EK9VKZJRmI+f7/yH6HLUf/DPhloJWyk8cALFYRYdhAuEZDxTu4p1nZnWBb9tHd6mOftVQcqACg2/2Km8oQawX2yIlsLgUuvL46j9FdxxLEozeZd5jlT2vwnfXF8EwDJaXl7GwsICxsTHWO6YDMWn5sFrx3bB9HYBV2+F9QNyKb15enmzbSCq+SjAMg7GxMTidTpSUlKCgIPISX67fGwvErIfce+7GzRfUj5enuahSIkypevBDvDE7YhQ3b8LIOelWj9wqPmo/RJrpQK0HsYhWTniFi21iKWc5NUWymShCy0FusQ1QbzlogZtuRgskkpOT2SwCn8/HTsoYHR2Fz+dDIBAAwzAwmUxITk6W9HU3ckezlW7q630St4S4FV8l1NgOy8vL6OzsRFJSEux2O28hRArmj+LDV412aZHh5vhKRb2MxwNitYLxyF/K+q+Lj/kWPSZn9LxYJVY0l83CTAct0EWvaKNfIWthPXDRstgWDcIIWAzqHdNFYIZhcOXKFRiNRoyOjmJpaQkmk4ntA5yWlsb6wWr6OsQrDCFg4tQmiDVx6/kqIVc4EQwG0d/fjytXrqCiogLV1dUwm80RecTChO/5C6GFhvQ7j4htLonh3r9mfzZlyvdaiLZ5SzQUN29S3miFaL3fWKaMSS22AUBBQ1nY7DQlvzcWcCvdooUQAoPBgPz8fFRXV6OpqQk7duyA3W7H4uIiOjo60NLSgueeew4vvPACnE6n4pWhUmMdj8eDT3ziEygvL0dzczOGhobY5x577DGUl5ejsrISL78c/fQgLozBGPNbPBK34quUxSDV2Wxubg7vvvsuW4BB+6RqKTGONBVIKuqVI+Mjd0k+J5ZuBkDRPogWLQKsFrG0sHg+Nr1qMFdUKk6IjgRP9V7ZaRdiCD1fs9kc1lxn586dCAaDaGtrQ1NTk+QUCjWNdZ566imkp6ejr68PJ0+exCOPPAIA6OzsxOnTp9HR0YGXXnoJf/EXfxFx+X4YZMV2iPUtDolb8VVCKKY+nw8dHR3o6+tDXV0dSktLeZ6Y6hLjKfUlrlpQikIcEuXJFO7i2FqRlKfc/UwrchHpWqIm31ctajqZ3QqUFtwIIdi6dStqa2vx0EMP4eLFi5LFD2oa67z44ovsqPgTJ07gD3/4AxiGwYsvvoj7778fVqsVJSUlKC8vR0tLjKaYrNgOsb7FIxtWfGnkS/sxtLS0wG63o6GhQbSLUzTNdaJlenoa586dY31fNeTec/eaiKFa7JvUNeCRKzKJlIJ920UbGhUe2IWcpugaHWlZbKNXGBcuXEBfXx+mpqbg9coP4RTSa6tDry2U1teRehvvObECDDnUTi5eXl5m5xNKibWaxjrcbWjzdu44Lrl9I4e8b2yHuF1wU7IdjEYjnE4nLl26BJPJhMbGRtkEdK3iK9dQJ/3OI/B18pPMM77z07DtfD4fenp64PF4UF9fD4yvFlmYMjPhn5mBr/0yMj5yF/y94X06kvc0Y+ndc6rPWSvWTPstiajlbIHCA7sw9mbsUtzkEPq+XEQX2/YfBiavo7a2FgsLC1hYWMDIyAj8fj+Sk5PZha6kpCTJz+vmdC+G52JXQaimqGhjZzsgbsUy1sSt+MrBMAzm5uYwNTWFHTt2iLbME6Ikvm63G11dXdipcByxhTZ75RYEAgFezvHk5CR6e3tRUlKC/Pz80B/NvX8N5swPFc81VhCLlZfxYExJ1uQX2zdlYP669DRwe+UWAKHod+B35yW3s2Wmik6CjjaKVUNBQ3inLbWLbebJUNod9Vbp54yO9VlYWMDQ0BCcTicsFgsvL5d+FrgFE9vct+ZLRs0IITWNdeg2RUVF8Pv9WFhYQGZmpuqmPJHAEALGGJ82QayJa9tB7Ft+cXER586dg9/vR15enirhBaTFl2EYjIyM4MKFCygqitwnpH9kXq8XV65cwdjYGBoaGlBQUBDVKHDr8Xsj3jdauFkXSpM6KLH0WtX2UpbKv470XJRS9GjznOLiYmzfvh1NTU3Ytm0bkpKSMDMzg7a2Npw/fx49PT2YnJwM278nbR+bbqZUghwJasSX21jH6/Xi9OnTYeOAjh8/jmeeCfUMf/7553HHHXeAEILjx4/j9OnT8Hg8GBwcRG9vL5qammJ09gRBYoz5LR7ZMJFvIBBAX18f24/B7/djYkL94pjRaAwr2qB5wMnJyWhubobx7efAYKXt3zuvhbpQtf4J/n13wsjtTiWgc899qAgGcePGDfT396OsrAx5edI5qWL5vqaKKtZ68F8fVL3Czs31fT9jr9/BpgHGgkDtXhgmr6tebBMOvQwEAnA4HLh58yYg+PVULryt+XzUtImkqBFfbmOdQCCAhx9+mG2s09DQgOPHj+Nzn/scHnzwQZSXlyMjIwOnT4fa89XU1OC+++5DdXU1TCYTfvSjH8WsdzCIbjvEFdPT07h27RoKCwvR1NQEQggWFxdVj48HQuLrdofG8gSDQQwPD2NiYgJVVVVsP2Dex1tj+7/Ozk5YLBZF75m76BY4cAzGN3+teGzr8XvhOfOcpvOJFhr1Vn7pAfT84OeK2ytZD/lH9mPilbOiz2n1fXOatsvO05Mi4Z5P8P4flSrbosFoNCI9PR3BYBBTntDCW4WrTXTbqakpXpGEGMFgUPUVlNrJxUqNdRISEvDcc+Kfu0cffRSPPvqoqvPRAgOC4PvEdohr8aUDMf1+P3bt2gWbbXVKQSRDMWk00tnZiczMTOzZsyds9dhTvVdVBRKXmZkZlJaWoqREWz6otf1tcL8+lg+cQNKbz/O2MU9ehy8nPO82sLi0puLBRa3lIIW9fkeMziR6xPxe4ZXDzQMPImsuss5tQoLBIKye6/BYQ7/DjtTbYCJBXvS7uLjIlhBLLeSpbScJ8LMdNh4kbm2CWBPX4tvX14ecnBzk5uaGfesrjY8XQgjB9PQ0ZmdnY9pGsmf/J5G30gRFDW1lh7BrVPyyM228A1LvyHr8XuDsqxLPxo6kvEwk72nmPZZeuxVzV64p7hsLv1fK542koX16824sXungPeY88ikkvqJcDEMX26KFmx7WnSD+HuhQgGAwyDbYGR4exvLyMruQZ7PZVEe+altKxiMMIQga4lqWYkZcL7hVV1cjLy9PsquZ2sh3dnYWXV1dbNWbVuG1yvi9O3bsgMlkUhxTRBFG2oEDx9SfyP7D6reNkGgW+JI3xb4TWSwGmApxHvmU5HMjex+I6WupHf0DhD4bKSkpKCoqQk1NDZqamlBVVYWkpCTMzs5icXGRXcibmJiA0+kU9YKFmTcbjffLgltci6/cN72auWx+vx8dHR0YGBhAVVUVEhMTZY/pzt7CsxwCliS29yoAzDSIC6XRaNQsvlLFFssHTqg6zkaEm5UgTDOLdFQT95ha7A0xAR7Z+wDM8LKWQ2+xtiIIMaTsgp60far2t1qtyMnJQVFREbKzs7F7927k5ubC6/Wir68PLS0tuHr1Kq5fv46FhQW4XNrGVM3OzuLw4cOoqKjA4cOHMTc3F7ZNW1sb9u7di5qaGtTW1uKXv/wl+9xDDz2EkpIS1NXVgRDSRgiJcuQ2QdBgjPlN8VUJuZMQ0kMI6SOEnBJ53koI+eXK8+cIIVuie59xLr5yKF2CTU5O4ty5c7Db7aivr0dSUlLUFW5Zw628+5Y//wcAq9OU1bKw/WDE5yAXtYmhlAnB9UDlot702q2aXjeWiEW/anOEU2prAIQW27g4LWm4eeBB3DzwIEb2PiAa8cZiVJVcVZqUDSEGLS02Go2w2+3YvHkzamtr0dTUhLKyMpjNZoyMjODgwYO4ceMGvvrVr+JXv/qVYlDw+OOP44Mf/CB6e3vxwQ9+ULTBTmJiIn7605+yvRy+8pWvYH5+tTjnO9/5Du2VXccwjPiqokoYQhAgppjf5CCEGAH8CMBdAKoBfJIQIpyL9DkAcwzDlAP4PoAnonmfwAYWXyk8Hg/a2towPj6OhoYGFBYWghCypuXFaqJwILSwMj09DSAkwJ7t6qIfIVoFmIvUIt165hNTIo1+14po8rMpVDS3FRhhJJF3BZbq60AIQWJiIvLz87F9+3a88847yMnJwZEjR3Dt2jXFLxBu/4bPfOYzeOGFF8K22bp1KyoqQj06CgoKkJOTg6mpqYjfixLrYDs0AehjGGaAYRgvgNMAPirY5qMAnln5+XkAHyRRfkDiWny1vDfaNL21tRX5+fmoq6vjzcZaT/ENBoMYGBhAe3s7MjMzYfUs8p53Z/KzGdRYD1wRjXbcjZLw0pxjbvRLq9u4mKt3KLbajGVD+lhUyPkgnt7ly9mE4eFh3iW9WmuJi1jk62f497vHlT+XaqdYOJ1OpKSk4MiRI2wXMjlu3ryJ/PyQV5+XlxfKS5ahpaUFXq8XZWWrlYOPPvooamtrQQj5PiEkqqRzZu2KLLIIIa2c2xc4L1sIgDtUcHTlMYhtszJqfgFAVM1XNq4rj5A4B4NBeDwedHZ2wmq1oqmpCWZzeJ6gkkBODfdCy/qwuXrVX5SzHZaWltDe3o6srCw0Nzejt7cXy5mFMDluwGNNCRNitSzuPY6Ud85EtC8X55FPIXF57aKY9SK9eTf7c0ptDXwAnEnqU+acSdkoTUmG3W7H/Pw8OxreaDSyqWBpaWminzUuapvhKKFlfpsw0+FDH/oQbty4Ebbtt7/9bd59QohswDMxMYEHH3wQzzzzDPueHnvsMeTl5cHr9SIhISEDwCMAviV5EEUIAmsjS9MMwzSsxYEjZUOLr8FgwNDQEG7cuIFt27bJTqqI9hJypuEYz/MlH1itfBKrnmMYBoODg7h58yZqamrYvEu1FgUXqVzfaAU4GvtCLWKLYJoj1pVKQ7WvF2mlmxmrHcvGjFuQaphDYmIiEhMT2fFTXq8XDocD8/PzGB4eRjAYREpKCivGwpQwpfxc2vFMCbUZDGIFFlJTiAEgNzcXExMTyM/Px8TEBFuhJ8ThcODDH/4wvv3tb2PPntU5gDRqXrnK/N8A/kbxJGVgAARv/QX5GABuu7uilcfEthklhJgApAGIahjjhrUdlpaWsLS0BJfLhebmZlUjgtYKYeS7tLSElpYWBAIBNDc38xLeDQaDaHoQtR7SxkN5qQsl4lMQhFHqzQMPRnTOkQqvmoU3rVM+KEzD7Zq252aixAqa6WByj4lGrBaLBVlZWSgvL0d9fT3q6+uRn58vmn3gcDjg9/vZ41wcjnx6htrIV2tHM27/hmeeeQYf/ajQ6gx94XzsYx/Dn/3Zn+HECb4lRkv8Vz7T9wDQXnrIgyAIQ8xvCpwHUEEIKSGEWADcD0AY1ZwB8JmVn08AeI3RUvMtwoaLfKl/SksyN2/eHFVdOT1emszVo1SKGYVGswzDsJF4dXW1aOEFtUpiyc0DD8IHC4rfUS4DBpSF15ezKWZFBmIY7WkRTwuJBF8pP9J2WpQLYtSW83KnDAMhEXI6newk4pmZGbhcLqSnp+NIRRpe6S3Bzk2h924iQTBQd0UWje0gx6lTp3DffffhqaeewubNm/Hss88CAFpbW/HjH/8YTz75JJ599ln88Y9/xMzMDJ5++mkAwNNPP426ujp8+tOfxtTUFBXfLAB/rvrFRWAABJhbm5fLMIyfEPJXAF4GYATw/zEM00EI+RaAVoZhzgB4CsDPCCF9AGYREuio2FDiOz8/j66uLuTm5qK5uRmdnZ2aF9EYhmH/qBwOBzo6OlYutdR/iXEtByD0B+jxeNDS0oKMjAw0NzdL+nxUqK2eRXisKbK+b2f5x1Hd95+qz4umS0mJMI2SE73RCZ/YYls8oTbfV2qxzZmUDcbNROTVEkKQlJSEpKQkFBQUsItTLpeLl57lZwwwkSACDFGVBaEl8tVSRJSZmYk//OEPYY83NDTgySefBAA88MADeOAB8eKT1157jXs3BhUqBEHm1l+QMwzzWwC/FTz2Dc7PbgAxTQmKa/GlIun3+9Hb24vFxUXU1tYiKSkJQGQlxgzDgGEY9PX1YW5uDjt27EBycjKmhiObssswDCYnJzE1NYX6+nrFMmMqvraqvfAMRHmFJoEwZ5XrZUYLzcRQU6Irhad6L0xvvyT+5N47Qh3lBDANt4Oo9H3F0LLYBsRuoSwYDMJqtSI5ORnZ2dlokVjbvHr1Kux2O9LS0kTHwqsV341cWgysRL7x7YbGjLgWXyDU0aynpwebNm3Ctm3beJeCWtPHTCYTZmdnce3aNeTn57Md0gAg2Tmt+dyWl5fR3t6OxMREZGVlqervIJcZ0Vn8YVSP/EbzeUSLMyk75hkP6XcewdxLr8T0mGohMZjZFUvxVXOc0tJS1qpYXFyEyWRixTgtLW3NIt+4gyEIBOOzHDjWxLX4+v1+jI+Po76+HgkJCWHPa4l8A4EAnE4n+vr6sHPnTjZ65sItLe5IvU1y8gDDMBgeHsb4+DhqampgNBrR39+v6jwMBkNYZoQUhYEhzdaDGD5YeNGv05IWtfWghnjqZqYE/f9xJmUjsWgrgp2dt1R8uVYFEFrkWlhYwNzcHIaGhrC8vAyDwYCMjAykpaUhISFBctgAPcZGhAHWxXZYD+L6XZrNZtTW1ooKL6A+8p2dncW5c+dgMplQU1MjKrxqcdYfx/nz5+HxeNDc3Iy0tDRN6WN0W+55e6zxH6mYNpXwij+iTVOLVaaC2BBK99bo0zm5awPRwj3Op/Yu4vJ15Sski8WC7OxsNqsiKSkJOTk5cLvduHbtGlpaWtDe3o6RkRE4HA728+d0Oje47UDgZwwxv8Uj8XlWHOT+AEwmk6z4+v1+dHZ2or+/H3V1dUhLSxMVSa7fK2x4spTIH1N0+fJlbN26FZWVlexloNbGOi6XC+fOncNVH38VvtR5FZ3FHw7bp7P8Nch/KwAAIABJREFU44rHjaWvGwncopOYorGpvRAtmQ7cq4FY2Q5StA6E0g9NJPS5UapyYxgGGRkZ2LJlC3bu3ImmpiaUlJTAaDRidHQUra2t+Pu//3u0tLTg2rVrcDjCZ+aJoaaxDhD6jNfV1aGuro43bmhwcBDNzc0oLy/HSuOZqKeFBhlDzG/xSHyelUqMRqOk7TAzM4Nz584hNTWVHScvJ5LdCbt4witlOTQ3N8Nu5+drqo18g8EgxsfHMT09jbq6OtxeqbiLIrfCPgDUfQEIIdnqW0zycnwlBJe7TbSRs1Smw5hxCxYWFjS1goyUd/tDn6MAQxRzgBmGn31BsyoKCgpQXV2NpqYmfOELX0BiYiLa29tx991345VXlD13NY11AMBms6GtrQ1tbW04c2Y1BfaRRx7ByZMn0dfXBwBzCDWgiRiGCf1/xPoWj2x48RVGvj6fD+3t7RgaGkJ9fT2KiorY6FlOrLW8phA1Xc0cDgfOnTsHs9mM3NxcJCYmRnwO8VIOrGQ9TG+Oj2pOtZkOY8YtAIDx8XEsLCygvb0dAwMDmJmZifpzIwUV4FhQWFiIhIQEnDp1Cm+99RaOHFEudlHTWEcKhmHw2muvcQsvnkGo0CIKCPxBQ8xv8Uh8nhUHJduB+0cxNTXF5tru3r07zCtW6xF3pN4mfi4fEB+mKBf5BoNB9Pf3o7OzEzt27EBBQYFohVurQb53bG9qo8JZrx2RRL1qWIsKtWipyLegqqoKKSkp7L+zs7Noa2tDa2srrl27hps3b8LjibyZ0af2RtbPQw1LS0uaRgipbazjdrvR0NCAPXv2sAI9MzMDu93OLXsWa0ijCQZAMEhifotH4jrbQQkqpl6vF93d3QgEAmhoaOB1MxPbXki3uwLJltBwzUjMeakvCG5TnaamJhgMBsnuWDvM7cDK3/OYcQsKA0OazyOWrHWV21ohtgCnhJhfHgwGkZCQgMTERGRnhyJnOgOQNtrhzlyz2+1hzfrlquTMJgKfP6rqVFHEUs1i0VhneHgYhYWFGBgYwB133IEdO3aoHp2liRXb4f3AhhZfk8mE5eVlnD9/HmVlZaKz3risZVtJLjQVbWJiIqzMWBglX/VtDwkvgIFE+UWrPxk+iNuD4dVIa0m0Ue9MwzFktq5OaI5EHJXwVO8NG/Xk3tqAhGv85vdyi21dC5uRl7y6SCWW7UAnEtNp13Tm2vz8PAYHB7G8vAybzcbm59psNlW+sVL2g5YWAsvLy2vSWKewMBTQlpaW4uDBg7h06RI+/vGPY35+Hn6/n0a/Yg1pNMEAcWsTxJq4f5dSYur1etHV1QWXy4XGxkbJWW9ctIqvkhUghtPpRGtrKy8VjQutsqPcXglccNVKHm+9I2AlzNt3rs2Bo8xyALSlnHGFl6L0eaIz14qLi7F9+3Y0NTWhvLwcZrMZ4+PjuHTpEpaWlhR9Y6UIWG2BBRDK8JEbQS9ETWOdubk51maZnp7G2bNnUV1dDUIIDh06hOefZydufwbAi6pfXAQGsbcc4tV2iHvxFcIwDCYmJnD+/HkUFBTAZrOp/rCJia/L5WItBzmyN1contfIyAja2tpQXl6OyspK0ahHyh++6tuOWfdqfubrc7vDtgFC0W8kSK3uU8QWpcTaWIpxK9PMmIbbVXc/ezu4X/x9Cf4vftNTFrZNJHCnSlRVVaG2thZpaWmsb3z58mWcP38e165dw5Ur88oHXEGt+NLSeS2cOnUKr776KioqKvD73/8ep06Fxpe1trbi85//PACgq6sLDQ0N2LlzJw4dOoRTp06hujo0ZeeJJ57A9773PZSXlwOh5uJPaTqBsDcBBIKxv8UjG8p2cLvd6OzshNlsZpumDwwMqN6fK74Mw2B0dBRDzmJR8dUS9brdbrhcLiwuLqKpqUm276ratLStWbOARJCutU+B6DFUVLndikU+/747pfs8SBCwRF4kI0dFftQpqjyCwSBMJhOys7PDfOMvHrmOn7yyCVXVq1dGy8vLokNetUS+gLbe1Woa6+zbtw9Xr4r3SC4tLUVLSwu9G3XjmZDtEJ+RaqyJ+8iXXqaPjY3hwoULKC4uxo4dOxQnCIhBxdflcuHChQtYXIxu1ZlG4RcuXIDFYkF1dbViw+tImqlT6KWxlE0Ry0ILsQibpmJpRaklp9Y+vlp4eVK8LzLllZ5ilOatTRqZWKEG9Y1LSkrCtn/xSh5aWlpw5coV3ugiLZFvrKry1guGAQJBEvNbPBL3ka/L5cKVK1eQkJCA5uZmVd38pTAYDHA4HLh48SK2bduGzMxM/Kkn9BytNFKL1+tF50r9f1NTE1pbW1VVRYmJr8UUhNdvgMXEf/z1ud04lH5R8VwSvQuqetSuBQsFNRgzbkH18K+VN36foTViBYCmpia4XC4sLCxgfHycDRAIIZiZmUFaWprk34Db7ZYsxd9IxLjdddwS9+LrdruxZcsWZGZGNasObrcb3d3d8Hq92LdvX1QiPjk5id7eXpSXlyM3NxfAqqhGIr63bWXwWmfo51l3MjISlhTP4YKrFvW2K5G9AQUi9ZVjTU/aPlQuvK1qW7ksipcn63F7UV/Y47++WgxrbJ0GHkqfh8e/aMQzK10yfX4GZhNhfWPqHQOhXNzJyUnMzs5iaGgIwWCQ7XZmt9vZ1MqlpaWo+pbEAwwD+APxGanGmrgX34yMDNkuYHQyhNSHnFoWw8PDKC0txfj4uGbhpYttPp8P3d3d8Pv9aGxs5C30qbUThNkODMOs+NDiEZLcpf7Lk/U4mnNB3Zu4xcRLdRvlNz1l+HBlP7vY9uurxbznuX5vlNNhWNR8GXd1LvB8XzEIIUhOTmatCm6+8cTEBLxeLzweD9544w1YLBbV9sPs7Cw+8YlPYGhoCFu2bMGzzz7LptFRXn/9dZw8eZK9393djdOnT+Oee+7BQw89hDfffJPN6Ll8+XIdwzBtii8sA4P4XSCLNXHv+Sohlz7mdrtx8eJFLCwsoLm5GVlZWRHn+c7MzKClpQWZmZmoq6sLy7DQIr7Aqugqla1em751s+mcSdmao16aldG5Wd7XlfN9pSoKpehO2KW4zdvB/Zhe5K8L/KanDL++WhwmvEJi5Z1qtR2kMiCEwzO5vnFdXR0aGhqwadMmLC8v49q1a9i5cyebtSCHmr4Ohw4dYns6vPbaa0hMTOSVLX/nO99hn49WeNn3q2c7bAxoiTF3AY5hGIyPj2NoaAiVlZXIygp1JhO2cpRiycv3zTo7O+FyuST7CgPaOpsBoT8o+kdOCOH5vmqtB0D6kjoShAt5N5ZSRfNfI2UtCiyihS62caPUW91Ive3SDOp2Za5EwOG/d6XjGAwGbN68GR/5yEcQCATwL//yL1hYUG649OKLL+KNN94AEOrrcPDgQTzxxBOS2z///PO46667oupLogTDAGvURiPuiPvIV2vhBI125+bm2GiXIjU5mCJscrItIdRqMiUlRbRXBBc1zXVotGs0GnHx4kUMDw9LlhsDK+lmKvjTaLmq7eRQygp4L8L1e2mZus/ng9/vj0nkq0Z8H/+icmSsZYRQSkoKCCFhnffEUNvXgXL69Gl88pP8/iaPPvooamtrcfLkSRBCxOv6NcDEYZ4vISSDEPIqIaR35d90ie0ChJC2lZtw+nEY74nIl0aRExMTGBwc5EW7Wmgo5Ud53e4KVKZPolii5JKLku1AhTcYDKK+vh4ejwdzc3MYHx9Hd3c3EiwWeBObRfe9Np2hKMTU07yVSBWCrCVaLQoAcCzLe7gOt4n1SgOBAIaHh5GQkMCuNRBCYDAYNEfDgUBAVQGQ1WpC26UZWK0m4PZwkdUyQkjYVCcWfR2A0Ij4q1ev4ujRo+xjjz32GPLy8uD1evGFL3wBAB4B8C3FE1XAvwY9L6LkFIA/MAzzOCHk1Mr9R0S2czEMU6f2oBtefI1GI1wuF/r7+2GxWNjiCzX8qQeK1W1qjyUlvgzDIBgMss8ZDAYQQpCQkID8/Hw28nC73Xh3SPl18pIduLEk3rXqNz1lOFI5IrmvcJwQhUa904tmZKWoG3EkRufmY7IpZ62GvWgIviP5PBfaW1lLxkOvrQ4VLu224/E6FwADvF4vOjo6kJKSQiu2EAwGWVGmVzZUjAHICnIk9sWpnwTComEt4ivMdohFXwcAePbZZ/Gxj32M9/dAP7tWqxWf/exn8dOf/rRJ8SQVoJFvnPFRAAdXfn4GwBsQF19NbGjbgWEYOJ1O9PT0sPX1WosvWgdS2akCYqj1ccU8X67w0j9YqfdDLQ2vP/Qreb2Tv9D20iV1fV9f6ZFfTOLy3ODuuLEbol1067UpBxwemRoUmv9dVFSE8vJyGI1GGI1GmM1mWCwW9mY0GkEIYcXY5/PB5/OxVzVc1DZkV7Ieool85VDT14Hyi1/8IsxymJiYABD6nK+0mYzJOO5ggIn5DUAWIaSVc/uChlPKZRhmYuXnGwByJbZLWDn2u4QQxb7GGyLyFaZnAYDH40FnZyc8Hg9KS0vZ8k010IWutj4zqI37br89zHYAoDo7Qhj5MgzDZjIoXdJRzncCjdWr95UyHbJSfOyKfmoSYS+v6Wr+sR3iUXA0vQxou8tYWQ5qMhciQZjpIAZdbBsdHcX4+Dhqa2slF5PEIl26gEu/ZIHVzwtdA1Cb7TAxeAP5JXkh60GAFvEVq5yT4tSpU7jvvvvw1FNPYfPmzXj22WcBhPo6/PjHP2bLi4eGhjAyMoIDBw7w9v/0pz+NqakpMAyDuro6APifql9cAoZRbjQUIdMMw0jmPxJCfg8gT+SpR7l3GIZhCCFSJ7iZYZgxQkgpgNcIIVcZhpH0AjeE+HJhGAY3btzAwMAAtm7dCpfLpWl/KpJSH+a3OlNQVx669C40DyAQsKk+LvcPkUa7WhZu/uZjXrzZE7usf7GUqrUsKogX3g7uV9zGagEGbpjgWAyCSe5FdnY25ufnQQiBzab+dy4UY3rz+XxwOBzIycmB1+tlI+ZIsii0iK+W4Zlq+joAwJYtWzA2Ft4p8rXXXuPd//nPf64uRUcGhlmfCjeGYT4k9Rwh5CYhJJ9hmAlCSD6ASYljjK38O0AIeQPALgCS4hv3tgMXj8eDtrY2TE9Po6mpCdnZ2ZrGxwOr2RFOp1NxW61TiemlaCTCS98bZWepF2OcX3FpsUG19bDWCKNeboTeuflY3BVYSJGaRHBiVz8+8IEPoKioiG3K/84776C9vR2jo6NYXl5WXXRhMBhgMpnYUVbFxcWw2+0wGo2sbyxlU5z+/mbJ42rNdtjYMAgEYn+LkjMItcsEJNpmEkLSabYHISQLwH4AnXIH3RCRLyEEExMT6O/vR0VFBW9hQGuPXoPBgJGRkZW0mgOy26o9Nh1uODExAYPBgPT0dE3e89TUFPr6+kJt/f4IAAbsrxUXfanFto2ClkU3itZFNyyv3lfKdCgqKgIA2O122O12bNmyBQzDYGlpCXNzc+jr64PT6URiYiLbSD05OVnyi3Vqagr9/f2oqalhhZAKJ12840bI3EU8aj3cf3KUJ8ZaIt+NLr6hPN+4W3F7HMCzhJDPARgGcB8AEEIaAPw5wzCfB1AF4CeEkCBCQe3jDMNsfPHt6OiAz+cTzWTQEvm63W44HA6YTCY0NTXhwsv859/q5H9wjUaj4qwuGtHk5eUhISEBc3NzGBoaAhD6g6Z/sGIlzYFAANeuXYPH40F9fT0vLenygLg/0NZrQF1F3H04Y0JH6m2ocby1JscWW2wbvSH+xUoIQUpKClJSUrBp0yZ2YXdubg7Dw8NYXFxEQkIC0tPTYbfbkZqaCkIIBgcHMT8/j927d4ummFHLQUyMGYbBz/6xAF/7l9Dv1u/3ay76eK+Ibwwi1ZjCMMwMgLDST4ZhWgF8fuXntwFoamy9IcSXTgcQQ010ys0BTklJwZYt/397Zx7W1J3v/3cgLIEAISCyugAqYVNQql1QcVpt57Fa7czYTqsdt6q9/oZa67RTW2s7VTutnbG39qq3Y8de24peR6/tiFagUpequCFLAFkFWYUkhLCELN/fH+k5ZM8JBCVwXs/j8+DJSXICOe/zPZ/l/Rln098hdRLQ1GQ57GBcQubq6orAwEC6vlitVkMmk0EikaC6uhoAaCEWCATo6uqCWCxGeHg4YmJi6JXUpsUqfHys77PWtwBhtsuMBw3jLrfTNwWIZF5Q4VCMKyJKPZMQ03PTZD8myTZ7oMa0e3t70yvl7u5uuk67pKQESqUSXl5eiIyMZJxkMyfGjdU19HtSYSy1Wk2LsbW48fAIOww98R0snEJ8PT09LQos1WRhCap2k1rtVlRUQKPR4LOTtk9QS8LOJKnG5XINxFilUkEmk6GtrQ1isRhqtRrBwcHg8XhmE4AKhRp8vvk/z1Bf/R4Wx2FJbLHBttIe65NA9KFqfAcLD3ddvHfF7P5PIObxeODxePDz80NhYSGioqLg7u6O1tZWVFZWwsXFhb7z8fPzYxSGcnFxwf/+ZyR++8cqvPD6XRz8KBTFxcUYM2aMQf5Bv6JCX4ztLTUbiuiqhIbud9uROIX4WsPV1dVi2KG5uZmOpVJxYn1B9fS0r3XZeLVrT1LNzc0NfD4fd+7cQWhoKCIiIiCXy9Ha2oqKigo6VqxzlTJX8eIYlL39r3h4kAm/Mr9HdJZXZmBS42uMpZCDPbS0tKCqqsogvktZjFIXW4lEQk9b8fPzo+98rHW+UQK8cHkxMv5rgoHTmH68WF+MqTi1pcndzoIu7MCKr1NgbnWqUqlQUlICrVZrYv1oaTXb06M7s6kyM8Cw2mEgJWSAriD9zp07iImJofvu9cfLqFQqSKVStLa2wlh8c8/LMDvVUPh+ON+DeameBrW+FB7u1hsKrDHQLjfj5hBzWEu6Ffs+Bi76f/Ld6+zr8LKVbOsvhBBUVVWhvb0dU6dONbuqdXNzMxkfJJPJIJPJUFtbC7VaDV9fX/qCq+8bUl9fj00vtiIhIcGk7M1ceRshBPv27YNCoXCYKdCDRMuGHYYO1oTOOOHW2tqKsrIyREZG0u2P+jCJEadOMtyXSqrpu5AxhfIA5nA4mDZtmsVYs5ubG4KCghAUFIRNkwzjvhMm6YQ3MsIFVXWWhUm/0YIp8k4CX2/bn0d/1VtVp0VkxNA4wUs9k+BqaUn8C8YXonM5dzDlof4FrqkyMh8fHyQlJTH+Lri6uiIgIIAeCqDVaiGXyyGVSulmIR8fHyiVSnA4HCQnJzPynVar1Xj99dfR09ODsrKyAQ0JGAoQQqBWDfyuxBkYGmfQAKCcytRqNcRiMe7cuYOpU6eaFV7AVHzzb7YZPJ5f0Sd6Li4udF0m9X97hFcikeDatWsICgpCfHy83SeGQmG9iuOH8z0OTy6Zoz/lbYfFcTb3GYzuNlu/Dw93IGRMAGaM+glisRiNjY3o6bE9vRrQxVSvX7+O0NBQREdHD8j5jIoJjx8/HsnJyUhOTkZXVxe9sr169SoKCgpQV1eHjo4Os7XGbW1tWLx4MaKiovA///M/jJtDhjJUtcMQq/MdFJz7MvkLarUaeXl5GDNmDEQikdWTwrh8bEqS+fFEhBBwuVy4uroiLy8PXl5eEAqFEAqFZifM6qPValFZWQm5XI6kpCSHzNXKPS/DmHEPJpmSX277Gn27VWjQFGKLwWortsW5nDsIGROAhx56yOzKkwoD8Hg8g79xc3MzqqurER8fb1cXGRMUCgWKiooQFRVFhykIIejs7KRLFxUKBXg8HgQCAZqbm+Hp6Yl169bh3XffxaJFixx6PA8UQqBWj4yVr1OIryWh02g0qKiogFKpxLRp0xiZPLu6uuKjw0LEWqnIo7qPXFxckJCQQNd5SiQSuuiez+fD398fQqHQ4ERVKBQQi8UICgpCcnJyv1dHxiVnlrie34GpU5yvvEjR62nTUa4/5OQ04Ve/Mp+wvJBdATcP3e+UWnlSq0+tVouOjg7IZDLcvn0b3d3d4PP5EAgE6OjoQE9Pj8X47kCgmjKMRZ0aHcTn8xEREQFCCLq7uyGRSLB9+3bcuHEDkyZNglgsxsKFC50+zktBCKBlqx2GNu3t7RCLxQgJCaEHDjKBKukSF7bChetisvJdN68bGo3WIMSgX+dJnQhUBxR1olLZ7o6ODsTHxzus3lK/5Ky2Rk6vfkcHe6G5SdcibU1wBsoP53swOnjwJhcMBjk5TUiZoas6oOK9F7L7pn3sWG1ah+vi4kIPpRw7diwIIZDJZBCLxXScv6SkhF4Ze3t7DyjsQAhBTU0NpFIpI1GnbEiPHz9OT87WaDS4fv36sBFeHYStdhiqaLVaVFVVoa2tDQkJCeDz+WhsbGSc5aXE14Xbt++Nq/cQm6Crx6Vaha2dWMYdUD09PSgsLAQhBB4eHiguLoavry+EQiH8/f37Xf5TfLMecUlh/XquI/jhvG5l2tzUZVOAc8/L6MQghbl6XyZcrhRgRpTMZBtganh/q9YPyWNNZ5+dy7kDAFAp+yo33DzcEDKG2RRshUKBsrIyukxRPwxQVVWFzs5O8Hg8WoypCRJM0Gg0KC4uhoeHB6ZMmcLoe6tUKulBlmfOnKG/U6GhoYze01kgBCMm4eYU4qt/S19UVIRRo0YhJSWF/tJSjRZMvsS6pJflK6u9qwh9Xwb9WXFyuRwSiQT19fVQqVQGrcZMphsAwL63/fCfJ4Hrl+vh6295JLggwHtQV7/3E2veyrbY/Y1jwhhNTU2oqalBQkICbU5uLgzQ1dVFl47ptxxTYmzuu9TT04OCggKEhYUhLIzZhfXevXtYtmwZFixYgA0bNgyzla4hhBBo+znk1tlwCvElhKC6uhpNTU2Ii4sz6eKhGi2YdhHpi++Nq/fon195kvnJa82XQT+eCOjEWCaTQSqVoq6uDhqNBgKBAEKhEAKBwOxxU6JeVjTJYLt+6MEY/dtta7W+thotWjvccD2/w9rHtwt7utsGG3MhBwqtVouKigp0d3dbLQsEDENRlIhSLcd3795FR0cH3N3daTH29fWFXC5HSUkJRCIRoxlrAFBUVITVq1dj27ZtmD9/vn0f1klhww5DCJVKBa1Wi+nTp5u96tvjbKYLOwxsPKpcLjfry2AJFxcXulIC6Cu4l0gkqKmpASHE4CStqqqipyXvy5SB68b8z3T1cjMtwIw/j1Gtb05OEwQBllfaxuSeNz/yHLAuvBfEPngsduAif+OOwCD00N2pu4jqhxwAgOdtueqkt7cXRUVFEAgESExM7Fc8l2o5pkIBPT09tP9DYWEhVCoVwsLCaDczWx4QJ0+exLZt2/DNN98gPj7e7uNxRnR1viNjfLFTiK+HhweioixPX7DH2WzDLtN+fireawsqSdLa2mpwS2ovxgX3arUaUqkUTU1NKCgogLu7O4KDg6FQKLB/awDWbGuHXNpJhx6unq9CSmqkxdc/l3MHM39l2R/WGjk5psMWzcG00eJWlTsmR/az3c6BuHm4Yc+b5u8YqIupfqmXI/D09MTo0aPR3t4OgUCA6OhoyOVytLS0oLy83KClnPL9BXQr8F27duHs2bPIzs7u1zBYZ4UQwlY7OBNMnc2MHcr0/8i/nVoHlcp8CADQ3VIWFxdDIBBg6tSpDo27UbXHnZ2dSElJoa0pqZNUrRpvsvqlKh0scS7nDlRKFR57nNlYeXknwdXL1keHm0N/1VteZpp0u365HpMjTQVNv5nFHOaSbgNFLBabtPM2NjaitrZ2QBdTS/T29qKwsBBCoRCTJk2ip2RQ/g+9vb2QyWS0GY9EIsGJEyfoke6nTp1inB8YNhDmo7ucHacRX3Nz3ChsOZvptwcDhpUOgK7sTBYlM7B+pOKxrq6uZn0ZHIVKpYJYLIa7uzumTZtGr36oVmMASErqxSsfKujV7+iIQNSWN2HMBNsJNqrEypoIn8u5Y/WWfChxrcrX7Ky9G3cE0M02NMXNww1fvhcIudzdoKmCqmyJj493uPCaa5wwxt3d3eDvXFlZidraWnC5XNy+fRurV6+mB1yOFAgh0LBhB+fBkrOZORcyS0yYoItN6hvclJeXQ6lUwt3dHRMnTnS4XZ9EIkFZWRmioqKsju12d3fHP7YIsep9icF2fQEWBHhD1tZp7ukADOtcAdDNBgPBWqyXKQOJ+96q9TPZZineq58EDQsLQ0FBAby9veHp6UknTvWNbgbSqku5ndnTDZefn4+1a9fi448/xrx58wCMnBWgIWTEfO5hIb7mYr7mXMieWVMGABgTY2iqsntT3wlCGdxwuVxIpVJERUWBy+WiubkZ5eXl8PDwgL+/PwICAqyOk7EGVavc3t5ud/uxfuzXEjxvT1qEHAWTWl9jrl/WDV28WGB5LBITqBpfa/x8wXKs+sBf+i5sVHPOxIkT6Zi7foebVCpFaWkpenp67BZjqipHJpMx7oajxq5/8sknOHLkCGJiYujHmJqyDyd0HW6s+A4prIUd9P0amHru1pbWITzatM5S35dhypQptDAGB+tWmFSLJzVOxh7PB+r5RUVFCAwMtLv9+B9bhFi4ugTdekY31sIPbh5uJitACpVSNaDV79XzVRgdMfQTQd981Pc3bmhowN27dzF58mSTjkj9Drdx48aZFWPK+0EoFMLT09Pgb9efxgmtVouPPvoIly9fRnZ2Nl0NM5Jhqx2cDC6Xi66uLkaeu10yuUXhZeLLwOPx6AJ5c54PPj4+tBgbr2gdETs+8YUIC1eXgO/fJ8DivNuIfWhiv16PoruzxyDuK2vrtKvczBhq1QsAZUXNeDTRdhWBcYOFvUk345ADJbxarRa3b9+GSqXC1KlTGa0ojcWYEIKOjg5IJBITMebxeCgvL0dERATjjrOuri6sXbsWwcHBOHnypMM9I5wWQtiVrzNBxXyNPXfnLrmKM4dTAADPrClDl0wOL4HhCb57Ex+EENy9excNDQ2IjY1l7MtgzvOBOkHFYjF6e3vh6+sLgUCAe/fA4+kkAAAgAElEQVTuwcXFxSHmLOYE+GbuLYxPYFbZMFCuntdNZmiua30gq19LSTd9KOFVKpUoLCzEqFGj6IqD/sDhcODr6wtfX18DMa6vr0dZWRnc3d3R1tYGrVYLf39/q3dBDQ0NWLp0KZYtW4a1a9cOyCNCn7KyMixZsoT+f1VVFd5//328+uqr9Lbc3FwsXLgQ48ePBwAsXrwYW7Zsccj7OwKFrOyHc8cfHYwvVesgvOaAcBrxtfQFJYTAzc0Nzc3NIIQgICDAoGZy7pKrFl9z9yY+lEolxGIxeDyeQbVBf49R/wTVarVoaGhAeXk5uFwuuFwuqqqqaM+HgRhfn/hCBAB44U/1tAhXF1YMugBTwmuJ8jIZ5FLTxJ+1uK+1pBuTeK8+Dbfv0BdcmUyGkpISTJo0yeG39BwOB3K5HAqFAo888gg8PDygUCggkUhQXl5Ou6JRMWNKjK9du4b169fj73//O371K5OBuANi0qRJyM/PB6ALg4SFhZm1m0xNTcW///1vh763oyCEPPmgj+F+4TTiaw6qhIzH42H69Ol0zWRFRQW4XC72fRiINW/2XfD0V713K+px757QxJfBkcdWW1uLlpYWpKSkwMvLy6CzjSpro4RY/4LBBLVajdLSUvx5GbD5077nUQI8WEm3ocK1Kl/olz5X3izDV7vC4e+v8wql7mSmTJnicJNxKoyhVquRnJxM/90osyXKFY1yvquoqMBXX32FwsJC3L17F1988QXmzJnj0GMyJicnB1FRURg7tn/NNiyDD8dSEusXhowFPBVWAEyTauaSG0qlEhKJBBKJBBve14mGvvjueFWL3t5eiEQihxeyK5VKFBcXw8fHB1FRURaTL1RZm0QiQXt7O7hcLp3Q8fX1tfi8jo4OeqotFWNcuLoEyq5uep/gyPC+97GQdDNOuBnX+hrHfMV5tw1CHQBMwg6VBVUYFWG+vXnF73VxX3MNFraGmZrDjdv3nKfjG+jfZUdHB7hcLsaPH4/AwECHDpWkGicCAgIwduxYRiEDjUaDDz74ALdu3cKcOXOQl5eH559/Hs8++6zDjsuYFStWIDk5GevXrzfYnpubi2effRbh4eEIDQ3Fzp07ERdne+oIQxwTPxkhOI34ajQaqNVqerVLWUgy+fJTRtS/31CHd15WQCaTgc/nIzw8HAEBAQ6ZNEFBGeLolzIxRalU0gIil8tNytqAvhWdpcaAJ1+4AUBXrhM6UbfqsSS+gKEAWxNfcd5tALjv4pt/s83stBF94V36mO7iSll7BgUFwdfXl77LUKlUDrH4pC569rQhKxQKvPzyy4iKisJf//rX+zJjrbe3F6GhurHzVDcdhVwuh4uLC/h8PjIzM5Geno7y8nJHvTUrvnbgNOKrVqvR29vbr7HtgKEvg0gkglarpVfGvb298PPzo6sU+pMQ02g0dKwvLi7OIatpqqyNWs2p1WrweDxMmjSJkX8slXB84U/1FvextfptqDR8rrH4An0CXFmgiwebE9+GijoEjQ3Byy+FWGwtNifAlsS3RNyOxERdPHjpY11W47tarRbt7e2QSqWQSqVQqVT035upxSfVOGFPG3JdXR2WLl2KNWvWYMWKFQ5LrNnixIkT+Pzzz3HmzBmb+44bNw7Xrl1zVNiNFV87cJqY786dO6HRaJCWloaEhAS7vBUs+TLoJ8aoVVJtbS3tMqbfYmwNqkQtODh4QBl1Y6iyNj6fD7FYjLFjx8LFxQXV1dU2y9oA0Imnbz4KoxOPo8YyN9+uLqyAh5f98dJ7dc0WV7+DQV1dHZqamiw2rOgb2AB9YiyRSFBXVwe1Wm3Rb5nJmHhzXL58Ga+++ip2796NmTNnOuaDMuTQoUN4/vnnzT7W1NSE0aNHg8PhIC8vD1qt1u47NBbH4DQr35qaGpw5cwY5OTkoLi5GTEwM0tLSkJaWZjX21p/aWsplTCKRQCaT0bHYgIAAA5NsQgjq6+tRX19vV4kaUwghuHPnDu7du4e4uDiDxgD9sjZq9U7dWguFQqurOUqIf8iYhnnPXTN4zIVreKExFl9zK18AUEgNS7/0xbehoo7+ef7vp5t9vriwFckpZgx4GKx8k/2vIiYmpt+VKhqNxmBlrNFo4OfnB4FAgMbGRnh7e2PChAmMQ1zffvstvvjiCxw5cgTjxo3r1zH1l87OTowZMwZVVVXw89O1X+/duxcAsHbtWuzevRt79uwBl8sFj8fD3/72NzzyyCOOent25WsHTiO++mi1WhQUFCArKws5OTlobGxESkoK0tLSMHPmTAiFQnqKhIuLC2JiYgYUa9NP3snlcvB4PPj5+UEikdBhAEe3gvb29qK4uBje3t6Ijo62udKnpme0tbXRAkIZtpsra1MqlbR/7bq3dJ4R1EqZihtT2BJgY+EF+sRXX3gBIGhsCB56dIzJ/tbEFzCdMq0vvi8+2unQW3qNRkM7yrm6uoLL5RqsjC2tfjUaDbZu3YrKykocPHjQ4RfjcePGwcfHhz6ma9cML5yEEKSnpyMzMxNeXl44cOAAkpOTHXoMNmDF1w6cUnyNUSqVuHTpErKysnD27FlIJBJ0dXVh8+bN+M1vfuPQUiNCCBobG1FRUQFPT09oNBqbt//2QhnuREdH99tfVr+sTSqVAugrayOEoLy8nFFS8MkXblgU33t3GnDmcArmLrkKnq+pgYzKwigNc6tfcaGuJNBYgJmIL5VwcxRUS3FsbCz8/Pzo3yW1MiaE0DFjahKJXC7HqlWrkJCQgA8++GBQfBlsxWczMzPx2WefITMzE1euXEF6ejquXLni8OOwAiu+djAsxFefPXv24MiRI3jhhRdw8+ZNXLp0CQKBALNnz0ZaWhomT57c71WwviFOXFwcPD09zd7+9zd5R8UXpVIp4uPjHVqFQZW11dTUQKFQgM/nIzAw0GZZmz3oh0kSEhIsHv9/nTbdbo/4lojb6Z8/fsWxZYJU/Nja8avVajpmXFJSgvfeew+9vb145pln8M477zjcdpTClviuWbMGs2fPpuO9kyZNQm5uLkJCQgbleMzAiq8dOE3CjSm//e1vsWbNGpO4bFZWFvbt24f8/HxMmDCBFuPIyEhGwmPJEMdcV1t/knc9PT10UjA5OdnhQxKp34O/vz+mTZtGi3FDQwNKS0vh4eFBXzD649amVqtRXFwMT09Ph5nNU8J7P9BqtSgrK4NGozFonDAHl8ulJ5E0NzfD09MTq1atQktLC1599VUcOHBgUI6Rw+Fg7ty54HA4WLNmDV5++WWDx+vr6xER0efYFx4ejvr6+vspvix2MOzE13hVwOFwEB4ejuXLl2P58uXQarUQi8XIysrCW2+9hdraWiQnJ2P27NmYPXs2Ro0aZSI89iTtjOe1Uck7/c4740YKyjt4MNpggb42W/0whoeHB4KDg03c2qiVsT1ubZRx+Lhx4+jXs8YrT/aYXf1aw1LiTSwWD7h+l2qcCAwMxJgxYxgn1r766iscPHgQ3333nYHoDRYXLlxAWFgYWlpa8MQTTyAmJua+V1KwOI5hJ762oCYXxMfHY8OGDVCpVLSl3/79+9HT04NHHnkEaWlpiI+Px3fffYdHH32034Y4XC4Xo0aNokWPSt7V19ejpKQEGo0GHA4HsbGxDr9d1W9xttVma+zW1tnZSbfGWitroy5M9hiHW+PG1XtmE2+WCA0NpX+fKpXKIMnI5O9FNU5ER0czrnVVq9XYvHkzGhsbkZ2d7fApGJagpiQHBQVh0aJFyMvLMxDfsLAw1NX1JTjv3r3LeDw9y/1nxImvMW5ubkhNTUVqairee+89yOVynDt3Dl9//TV++OEHJCUlob29Hd3d3UhOTh5wh5KHhwdCQkIgEAjoNlUej4e6ujqUlpY6LHmnUqlQXFwMHo9ndxiAw+GAz+eDz+dbdWvr6ekBh8OxOWbdFlS8tz9Q0ymAvpIxym9Zq9Varfhobm5GdXW1XY0TMpkMK1aswPTp0/Hpp586PDxkic7OTmi1Wvj4+KCzsxNnzpwxcSNbsGABdu/ejeeeew5XrlyBn58fG3IYwgy7hJsj6OnpwZIlS7Bz507w+XxkZ2cjOzsbN27cwPjx4+l48YQJE/p18jU3N6Oqqgoikchgteuo5B01jXf8+PEm7aWOoKurC7du3YKHhwc9Bt2ayFmCCj0Yiy+18jWO+VJhB6YJN7VabVClAIAuF5NKpVAoFIiPj2f8e62oqMDy5cuxadMmLFmy5L51rAE6e0jKoUytVuP3v/89Nm/ebFDDSwjB+vXrcfr0aXh5eeGf//wnpk2bdt+OEWzCzS5Y8bUDys2Kqi+urKzE5MmTMXv2bMyZM4fuHLIE1YKsVCoRGxtr86SnOrGo2l1byTvKl7ixsRHx8fEm0xocAVUGFxMTQ3eMGZe1cTgcsyPRjbFXfAGdAFPia2+lg0qlQltbGyoqKqDRaODl5UX/Pv38/Kwm2XJzc/Hmm2/iyy+/dKig1dXVYdmyZWhubgaHw8HLL7+M9PR0k/ceyh68erDiawes+A4AtVqNa9eu0WIsl8vpePFjjz1mUGTf2dmJ4uJiBAcHIyIiol+rJuPOO1dXV4OkWGlpKbhc7qA0fVDeGG1tbUhISLCa3GLq1mZJfCmMp0wDgIdH36raXvHt7u5GQUEBxowZg5CQEPT29tKrYplMBjc3N5PjJIRg//79OHz4MI4cOeLwGGpjYyMaGxuRnJyMjo4OTJ06Ff/3f/+H2NhYep/c3Fzs3LlzyHrw6sGKrx2w4utAFAoFLly4gKysLJw/fx4eHh6YOXMmVCoVOBwONmzY4NAJyFTyrrm5GW1tbfD29kZoaCiEQiG8vb0ddlusHz/uT6jFnFubUCjEyZJJAMyLrznhBfovvhKJBLdv34ZIJKLbbq0dp1QqxV/+8hfaBP9f//qXwzvWzLFw4UKsX78eTzzxBL2NFd/hCSu+gwS1Uly+fDlaWlrg6emJ4OBgOkQRExMz4GQNIYQeChkbGwtXV1c6XtzZ2Qk+n4+AgIABJe+oagBHxo/13drO16cMqvhSoZimpiYkJiYyLkeTSCRYsWIFPaPt1q1buHjx4qCEcihqamowc+ZMFBUVGVykB9mD15Gw4msHrPgOIrW1tTh79iyWLVsGQJewyc7ORk5ODkpLS5GQkECLcWhoqF0rVY1Gg5KSEgCASCQyG/8daPKusbERtbW1iIuLc0gZmTFdXV340+fmRwvdrajHmBjT2tnG6iaMi9EZxdsSX61Wi9LSUhBCIBKJGF/sSktLsXLlSrz99ttYvHjxfUmsKRQKzJo1C5s3b8bixYsNHhtkD15HwoqvHbDi+4DQaDS4efMmHS9ua2vD9OnTkZaWhtTUVPj5+Vk86RUKBYqLi+mVEBNxsCd5R3V7qVQqxMbGDooB+L1791BZWYmvz8ebfXyg4tvb24uCggKMGjWKceMEAGRnZ+Odd97BgQMHkJSUxOg5A0WlUmH+/PmYN28eXnvtNZv7O9iD15Gw4msHrPgOEbq7u3Hx4kVkZWXh3Llz4HA4SE1NRVpaGqZPn07fLtfX16Ourg5xcXEDikFaSt7x+XzU1NQMKDFoDUIIqqurIZVKkZCQAHd3d6z/WGGynznxbaxuAgCMiwnHn37bbrGsjQqVTJgwgbFXrVarxd69e/H999/j8OHDjDr1HAEhBC+99BKEQiF27dpldh9jD97f/OY3uHPnzn0tdWPIkDugoQwrvkMQQggkEgl+/PFH5OTk4PLlywgMDIRKpUJSUhLeffddh84lA3TJptraWty9exdubm7g8/l0iMJRyTu1Wo2ioiJ4eXkZ2GRaEl8ABgJMiS8AbP9/GoOyNqpcrLW1FTU1NUhISGAcn+3t7cVrr70GtVqN//7v/3aooZEtLly4gNTUVIMBAdu3b0dtbS2A++LB60hY8bUDVnydgNraWjzzzDMQiURQqVQQi8UQiUS0mbw9t9XmoJKDEokE8fHxcHd3N0iKUck7Soz7Y9HZ2dmJwsJCi/4P+gJMCS9gWXz/9z8jARiWtTU3N4MQgvDwcAQGBjJya2ttbcVLL72Ep556Cq+//rrDO9ZOnz6N9PR0aDQarFq1Cm+++abB40qlEsuWLcP169cREBCAw4cP33cDdgfCiq8dOFV78ZIlS1BWVgZA1+YpEAiQn59vsp8t02lnw9/fH/v376djkPpm8hs2bEBTUxNSUlIwe/ZszJo1C/7+/ozFmCoj8/LyQlJSEi0+Xl5e8PLyQnh4OD0Gva2tDSUlJXYn76j5ZwMNlZjDzc0NQqEQDQ0NCA0NRUREBGQyGSO3tuLiYqxevRrvv/8+FixY4NDjAnRx/f/4j/9AVlYWwsPDkZKSggULFhjU8O7fvx/+/v6oqKhARkYG3njjDRw+fNjhx8Iy9HDale/GjRvh5+dnttNnCCckBgXKTP7MmTPIzc2FRqOh48UzZsywuFLtbxmZ/gw0iURiMXmnP/8sISHBqkhbWvkCfatfauVLrXoBXcVEYWEh3ThhjP4KXqFQgMfjITc3F3w+H/v378fXX3+NhIQExp/dHi5duoStW7fihx9+AADs2LEDAPDnP/+Z3mfevHnYunUrHn74YajVagQHB+PevXtDMZ7LBKc86AeFU618KQghOHLkCH788ccHfShDAg8PD9oSkxACmUyG3NxcnDx5Em+//Tb8/f3pEMXkyZPh6uoKsViMjo4Ou0xlKPQHUkZFRZnYZrq6usLPzw9SqRQCgQBJSUk2xWT3Jr7Z2C+FfsiBgmp1jouLs9i8YuzWJpPJUFBQgEuXLsHb2xs7d+7E3r17HTrthMKcv67xZAn9fbhcLvz8/NDW1jZiFg4jGacU3/Pnz2P06NGYMGGC2cdtmU4PZ6gE1KJFi7Bo0SK6ySArKwt79uxBfn4+XF1dMWbMGGzbts0hTQPGtpkSiYTuiGtra0NnZyfd7GEreWe86gWA2tI6gxH3hBDU1dWhpaUFycnJjJOPSqUSb775Jvh8Pj2fraCg4L4m2FhYKIac+D7++ONoajJd5Wzbtg0LFy4EYH00NsCaTuvD4XAQERGBFStW4IUXXsDjjz+O1NRUBAQE4K233kJdXR2mTp2KtLQ0zJo1C4GBgQO65aVsGpOSksDn80EIoW/9q6qqrCbvdm/i45k1tt+jpKQEhBC7Jn40Nzdj2bJlePbZZ/HHP/6Rft5g1vIy8del9gkPD6fHE7Gj3EcGThfzVavVCAsLw/Xr1xEeHm5z/61bt4LP5+P111832PbFF1/QK7Xt27fj17/+tclzbWWqnZG6ujqDW+He3l7aTP7HH3+EUqnEo48+irS0NDzyyCOMQxKEEFRWVqKjo8OqTaN+8s5S590za8oMntMl001H9hsdgDeWSRAUFGRXDXJBQQHWrFmDDz/8EE899RSj5zgCtVqNiRMnIicnB2FhYUhJScG3335r0Br8+eefo7CwEHv37kVGRgaOHTuGI0eO3LdjdDBszNcOnE58T58+jR07duCnn34y+7ix6fQTTzyBLVu24Mknn6T3MSfIxmg0GkycONEgU33o0CGDTPVwRC6X46effkJWVhYuXrwIHx8fzJo1C2lpaRbN5FUqFe1HEBkZadfK2Vzybvt+Q+MbSnwB4NB/RTJeGRJC8P333+Ojjz7CN998A5FIxPi4HEVmZiZeffVVaDQarFixAps3b8aWLVswbdo0LFiwAD09PVi6dClu3rwJoVCIjIwMREZG2n7hoQkrvnbgdOL7hz/8ATNmzMDatWvpbQ0NDVi1ahUyMzMtmk7rw0R8mWSqhzuEEHpUTnZ2Nm7evEmbyc+ZMwfR0dEQi8WQy+WIjo5GUFDQgN+TSt6tflsCwFB4j38Zy3glrtVqsXPnTly8eBEZGRmDdiu/adMmfP/993B3d0dUVBT++c9/mh0HNdzKHy3Aiq8dOJ34OoKtW7fiwIED8PX1xbRp0/DJJ5/QxuAUR48exenTp/GPf/wDAHDw4EFcuXIFu3fvfhCHPCSgPB8oP4pbt26BEIKNGzdi/vz5Ns3k7YUQgtu3b0MqlYLP56OjowOenp42k3fd3d145ZVXEBgYiF27dvVr9h5Tzpw5gzlz5oDL5eKNN94AAPz1r3812W+ElD+y4msHQy7h5iisJe7WrVuHd955BxwOB++88w42btyIL7/88gEcpXPh4uICkUgEkUgET09PcDgcvPLKK7h8+TJWrFiBjo4O2kz+0UcfHbD3RFFREfh8PqZPnw4Oh2M1eefv7w8vLy80NjZi6dKlePHFF7Fu3bpBr5edO3cu/fOMGTNw9OjRQX0/luHDiFz56lNTU4P58+ejqKjIYLutsMNIv91sb2+Hj4+PQbWBQqHA+fPnkZWVhQsXLhjUH0+bNo3xCpRqnBg7dqxVgxv95N2lS5ewfft2KJVKrFy5Eunp6RAKhQP+nPbw9NNPY8mSJXjxxRdNHhs/fjzdeTiMyx/Zla8djEjxbWxspLuh/v73v+PKlSvIyMgw2MdWppq93bQOIQQtLS3IyclBdnY2rl27hoiICHr4qCUz+ba2NpSXlyM2Npbx1A9CCI4dO4Zdu3Zhw4YNKC8vR3NzMz1ccqAwKX/ctm0brl27hmPHjpldbdfX1xuUP3722WfDsfyRFV87GJHiu3TpUuTn54PD4WDcuHHYt28fQkJCDBJ3gPlMtTmOHz+Oo0eP4ptvvjF5bKSKrzGEEFRUVNDx4tu3bxuYyY8ePRq5ubnw8/NDYmIi3N2ZjQjSarXYsWMHbty4gUOHDpm9+xhsDhw4gH379iEnJ4dR0wqThK+TwoqvHYxI8XU07O2m/Wg0Gty4cQNZWVnIyspCRUUFxo8fj/Xr1yM1NRW+vr4247WdnZ1Yu3YtIiIisHPnzkExfbfF6dOn8dprr+Gnn36i68aNYVL+OExgxdcOWPG1Anu7eX9YtGgRZs6cibi4OGRnZ+PcuXNwcXHBzJkzkZaWhoceesikhbi+vh5Lly7FypUrsWrVqgdmRBMdHQ2lUkmXss2YMQN79+61u/xxmMCKrx2w4jsABnK7OcJ8Xq3S0dFhUBlBCEFbWxttJn/lyhWMHj2aDlF0dXUhPT0dn332GWbNmvUAj5zFCFZ87YEQYu0fiwVOnTpFRCIRaWlpsbiPQqEgcrmc/vnhhx8mp06dImq1mkRGRpLKykqiVCpJYmIiKS4uNnju559/TtasWUMIIeTQoUPkd7/73eB9mCGOVqsllZWVZN++fWTRokUkODiYVFZWDvr7vvvuuyQ0NJRMnjyZTJ48mZw8edLsfqdOnSITJ04kUVFRZMeOHYN+XEMYW3rC/tP7x4pvP4mKiiLh4eH0iUkJZX19PXnqqacIIYRUVlaSxMREkpiYSGJjY8kHH3xACCHk559/JnPnzqVfa/v27WT79u0Grz937lzy888/E0IIUalUJCAggGi12vvx0YY89+v38O6775KPP/7Y6j5MLqQjiAcuaM70b9g2WQw2FRUVZreHhobS1RKRkZG4deuWyT6sz+vAGEpG43l5eYiOjqb9GJ577jmcOHFi2HuAsAwcxw6sYmEZZuzevRuJiYlYsWIFpFKpyePmLqT19aaexCwsxrDi+wCwx+cVgEWf17q6OqSlpSE2NhZxcXH49NNPTd6Lqp2dMmUKpkyZgvfff38QPpHz8vjjjyM+Pt7k34kTJ7Bu3TpUVlYiPz8fISEh2Lhx44M+XJZhBBt2eACkpKSgvLwc1dXVCAsLQ0ZGBr799luDfRYsWICvvvoKDz/8MI4ePYo5c+aY3G5zuVx88sknSE5ORkdHB6ZOnYonnnjC5JY3NTUV//73vwf9czkj2dnZjPZbvXo15s+fb7KdyYWUhcUc7Mr3AcDlcrF7927MmzcPIpEIv/vd7xAXF4ctW7bgu+++AwCsXLkSbW1tiI6Oxt/+9jd8+OGHJq8TEhKC5ORkAICPjw9EIhF7y+tAGhsb6Z+PHz+O+Ph4k330L6S9vb3IyMgYlEnILMMQGxk5FiehurqaREREkPb2doPtZ8+eJUKhkCQmJpInn3ySFBUVPaAjdD5efPFFEh8fTxISEsjTTz9NGhoaCCGGFS2EEHLy5EkyYcIEEhkZSVe0jFAeeAWBM/1jmyyGAQqFArNmzcLmzZuxePFig8fkcjlcXFzA5/ORmZmJ9PR0lJeXP6AjffAsWbIEZWW6MUUymQwCgQD5+fkm+w1XN7pBZuiUoTgBrPg6OSqVCvPnz8e8efPw2muv2dzfmtGPLcEhhCA9PR2ZmZnw8vLCgQMH6LCHM7Jx40b4+flhy5YtJo+xhkj9ghVfO2ATbk4MIQQrV66ESCSyKLxNTU30hIm8vDxotVqrI3XOnj1rUXBOnTqF8vJylJeX48qVK1i3bp1JfbKzQAjBkSNH8OOPPz7oQ2EZobDi68RcvHgRBw8eREJCAqZMmQJAN4m5trYWALB27VocPXoUe/bsAZfLBY/HQ0ZGRr+bFE6cOIFly5aBw+FgxowZkMlkBt7IzsT58+cxevRoTJgwwezjHA4Hc+fOZd3oWAYNVnydmMceeww2wkZYv3491q9fz+j1bAmOpYaCoSa+TNzoDh06hOeff97ia1y4cMHAjS4mJoZ1o2NxKKz4stAMF8GxVburVqtx7NgxXL9+3eI+VK1uUFAQFi1ahLy8PKf8XbAMXWwl3FhGKBwOZysABSFkp962fQByCSGHfvl/GYDZhJBGo+dOAnBYb1MkgC2EkF16+8wGcAJA9S+bjhFC7kv7HYfDeRLAnwkhZv0oORyONwAXQkjHLz9nAXifEHL6fhwfy8iAXfmyADArOHMBGIvhdwDWczicDADTAbQbCy8AEELKAEz55XVdAdQDOG7mbc8TQkzbxgaf5wAc0t/A4XBCAfyDEPJrAKMBHP8lNs4F8C0rvCyOhhVfFgqzgsPhcNYCACFkL4BMAL8GUAGgC8ByBq/7KwCVhJA7g3LU/VqrlPAAAACpSURBVIAQ8gcz2xqg+2wghFQBmHyfD4tlhMGGHVgGFQ6H8yWAG4SQ3UbbZwP4F4C7ABoAvE4IKb7/R8jC8mBgxZdl0OBwOO7QCWscIaTZ6DFfAFpCiILD4fwawKeEEPN1XywswxDWWIdlMHkKulVvs/EDhBA5IUTxy8+ZANw4HA7bTsYyYmDFl2UweR5GiS0KDocTzPklwMzhcB6C7rvYdh+PjYXlgfL/AZHwAaEEURbcAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib import cm\n", "\n", "fig = plt.figure()\n", "ax = fig.gca(projection='3d')\n", "\n", "# create data vecors\n", "x = np.arange(-8, 8, 0.25)\n", "y = np.arange(-8, 8, 0.25)\n", "# create a meshgrid\n", "X, Y = np.meshgrid(x, y)\n", "# compue function values\n", "R = np.sqrt(X**2 + Y**2)\n", "Z = np.sin(R)\n", "\n", "# plot it\n", "surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,linewidth=0, antialiased=False)\n", "\n", "fig.colorbar(surf, shrink=0.5, aspect=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task\n", "\n", "Extend the plot above with title, axes labels. Then find out what colormaps are available. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# TODO\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parametric curves and surfaces\n", "\n", "Parametric curves are mappings \n", "$$\n", "\\Gamma: \\qquad t \\in [a,b] \\rightarrow R^3\n", "$$\n", "such that we have coordinates $x(t),y(t),z(t)$, for example the screw line\n", "$$\n", "x(t)=r cos(t) \\\\\n", "y(t)=r sin(t) \\\\\n", "z(t)=h t\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "fig = plt.figure()\n", "ax = fig.gca(projection='3d')\n", "\n", "\n", "t = np.linspace(0, 12 * np.pi, 100)\n", "r = 2\n", "h = 1\n", "x = r * np.sin(t)\n", "y = r * np.cos(t)\n", "z = h * t\n", "\n", "ax.plot(x, y, z, label='screw line')\n", "ax.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task \n", "\n", "Visualize torus knots which are curves running around a torus.\n", "A (p,q)-torus knot winds q times around a circle in the interior of the torus, and p times around its center.\n", "\n", "For some pictures see: https://www-user.tu-chemnitz.de/~uro/work/pqcurves/index.html\n", "\n", "For details and parametrization see: https://en.wikipedia.org/wiki/Torus_knot\n", "\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def torus_knot(p,q):\n", " print(\"TODO\")\n", " " ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "TODO\n", "TODO\n", "TODO\n", "TODO\n", "TODO\n" ] } ], "source": [ "torus_knot(1,1)\n", "torus_knot(1,2)\n", "torus_knot(2,1)\n", "torus_knot(4,7)\n", "torus_knot(2,8)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Parametric surfaces \n", "\n", "Parametric surfaces are mappings\n", "$$\n", "\\Sigma: \\qquad (u,v) \\in I \\subset R^2 \\rightarrow R^3\n", "$$\n", "such that we have coordinates $x(u,v),y(u,v),z(u,v)$, for example the sphere with radius r can be parametrized as\n", "$$\n", "x(u,v)=r sin(v) cos(u) \\\\\n", "y(u,v)=r sin(v) sin(u) \\\\\n", "z(u,v)=r cos(v) \\\\\n", "u \\in [0,2\\pi], v \\in [0,\\pi]\n", "$$\n", "\n", "## Task\n", "\n", "Visualize the sphere as parametric surface.\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# TODO\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Task\n", "\n", "Visualize the so called \"Kuensche Fläche\", considered by T. Kühn in 1884 \n", "( Kuen, T. \"Ueber Flächen von constantem Krümmungsmass.\" Sitzungsber. d. königl. Bayer. Akad. Wiss. Math.-phys. Classe, Heft II, 193-206, 1884. )\n", "\n", "The surface is given as:\n", "\n", "$$\n", "x(u,v)=\\frac{2 (cos(u) +u sin(u) ) sin(v) } { 1+u^2 sin^2(v) } \\\\\n", "y(u,v)=\\frac{2 (sin(u) -u cos(u) ) sin(v) } { 1+u^2 sin^2(v) } \\\\\n", "z(u,v)=\\frac{log( tan( \\frac{1}{2} v) ) + 2 cos(v) } { 1+u^2 sin^2(v) } \\\\\n", "$$\n", "\n", "with $u \\in [-4,4] $ and $v \\in [\\epsilon, \\pi-\\epsilon]$ where $\\epsilon$ is a small number like 0.0001 to avoid \n", "trouble with singularities.\n", "\n", "It is a special surface with constant negative Gaussian curvature.\n", "\n", "Further reading: https://mathworld.wolfram.com/KuenSurface.html\n", "\n", "You may use a c-coded notation of the formulas above to avoid typos, which can be easier adopted to python code. \n", "Here is it:\n", "\n", "
\n",
    "void kuen(double u, double v , double *x , double *y , double *z)\n",
    "{\n",
    "   *x=2*(cos(u) +u*sin(u)  ) *sin(v) / ( 1+u*u*sin(v)*sin(v) );\n",
    "   *y=2*(sin(u) -u*cos(u)  ) *sin(v) / ( 1+u*u*sin(v)*sin(v) );\n",
    "   *z=log( tan(v/2.0)  ) + 2*cos(v) /  ( 1+u*u*sin(v)*sin(v) );\n",
    "   return 0;\n",
    "}\n",
    "
\n", "\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# TODO\n" ] }, { "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 }