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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Quarter annulus"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this notebook, we present a set of solutions for 2D using Elementally."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Geoemetry\n",
      "\n",
      "We'll consider a 2D quarter annulus starting at $\\theta=0$ going to $\\theta=\\pi$, with an inner diameter of 2.0 and an outer diameter of 3.0"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Setting up the Python environment\n",
      "Throughout this example we'll use the %pylab magic (populates the environment with e.g. numpy as np and pyplot as plt) and we'll get the modules from elementally."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab\n",
      "%matplotlib inline\n",
      "import elementally.meshers as meshers\n",
      "import elementally.assemblers as assemblers\n",
      "import elementally.boundaries as boundaries\n",
      "# sys.path.insert(0, '../elementally')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using matplotlib backend: Qt4Agg\n",
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/lib/python2.7/dist-packages/pkg_resources.py:1031: UserWarning: /home/tarjei/.python-eggs is writable by group/others and vulnerable to attack when used with get_resource_filename. Consider a more secure location (set with .set_extraction_path or the PYTHON_EGG_CACHE environment variable).\n",
        "  warnings.warn(msg, UserWarning)\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Creating the mesh\n",
      "The mesh itself is created using Andreas Kloeckner terrific (Meshpy)[http://mathema.tician.de/software/meshpy/] package, wrapped in an Elementally front-end."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Creating a mesh on the form of a quarter annulus, centred in origo, with an outer diameter of 4. and an inner of 3.\n",
      "mesh = meshers.quarter_annulus_2d(0.3, 0, 3.14, (0, 0), 3, 4)\n",
      "# Remapping the C++ arrayed points from the Meshpy mesh over to a Numpy array\n",
      "points = np.array(mesh.points)\n",
      "# Creating plotable trianfles on the form of a (n,3) matrix, where n is the number of elements\n",
      "triangles = np.array(mesh.elements)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.triplot(points[:, 0], points[:,1], triangles)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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LOitq+eMPhD9euaJ+jPSILoJcIiYmhmvVqsUXLQo7+Pr68oYNG149dnNz43tW\nvElviiA/cQIf+MOHlV97/bq2YkXMsHuXLw+t0xre3sorA0ZGonZG7dpwqI0cCYeVWmG7ejUcrpaY\nTLDnO1uYSnz1FdaRmIgCVyNGpM689m5WXbpod+7Vq6etMcnRo7jZWLJ+PZyPanuS9uyJyodaWLoU\n35HUyn9IC8iRnQ5t5CaTiTw8PMjFxYWaNm1KlStXTnY8LCyMSpYs+epxiRIl6O7du3paf9INly8T\ntW9PtHw57IpK0Wojnz8fPwcOEBUvbv0cczu5XAoXRp3rkycxdrZsRB07ElWvTjRrFpHSt/vDD9H5\nPiws+fM7dsAO2769svHUMm0aUVQUmmxERBDNnJk683bogOYXu3Ylf/7xYzQU6dZN2/jDhmlr2iDZ\nxy3p1g12/gED1NnLL10ishAfiunfn+izz9DQ48kTbWNlJBz2icmUKROdPXuWnj17Ri1btqSAgADy\ntniX2eJdNRgMVseaPHnyq7+9vb1TjJOeCQ3Fh2vmTHTRUYMWQb54MZyUAQFEZvfVFHh7a2tUXLEi\n0fTpaA5w9CjRmjVE7u5wkvbqRdSpExyV9sienahzZziCpbUwY8wJE+AUdQZPnhBduICmxdLvwEAc\n+/tvombNcHOqVg0/VavKc1IrJVMmdBGaOhWdfqTXu349HufLp238Tp3QZOOff/B6lBIQAOeiNX78\nkah+fTS1GDpU/pgmExSdSpWUr8eSsWOJ7t/H92zPHnyeMhIBAQEUEBCg7CIlKv7UqVN5tkVGh6+v\nL69fv/7V4zfRtPLwIcLl5Ca72OLCBYyjlKVLYVu/ds3xuS9ewE6uZ22Vly9R9a59e9jTu3WD+cae\nnfbYsaQelMywDVepok/iycuXsOX+9hvCKlu1guM5Z05kQA4YgNIF+/fDbBQXB1v5/v14vn9/mJFy\n5GB+912EI379NWLAz5/XJ9MzMRHvtXmFwZo1tRf4kpg2Da9TKfHxjnt2XrsGH5CSMse3b8MspxdG\nI2rMtG3rnEJvaQk5stPuGQ8ePOAn/3k8Xrx4wY0aNeJ9+/YlO8fc2RkUFPTGOTujoyEcvvxS+1jn\nziE9Wgm//QYhpcQB1KiRc2K0mVFk6pdfUNLUxYV5+HBEGljag00mxCcHBuJvLy84V5WQmIjXvXkz\n4vU7d8bNIWtW3BS6dYODbds21PVWepMwGlEUassWxGh36oQ1Z82KyJoePeBY3rkTlRGV+gzWrEEq\nvMmEGP5KDohyAAAgAElEQVQSJfRLzoqMROSR0poogYHyGoFs2oRyD3KrLu7apV/mqUR8PMpNfPJJ\nxk7llyM7Df+daJXz589Tnz59yGQykclkol69etGYMWPI779mhL6+vkRENGTIENq9ezflyJGDVqxY\nQTVq1EgxlsFgSGGCSe/Ex8OeW6wY0bJl2k0CwcFosHv2rLzz161Dw+EDB2DykMuECTDjfPedunXK\n5epVmF7WrCF65x3ERvfoQVSqFI7PmEF06xbMLMOGwdxhzbTEjL6h588nN4tcugT7fdWqSaaQatWI\n3NzQv9JZvHyJRtTSev75B7/j4pLMMnLMM4mJsBkvWUK0fTtMBNOn67fOTz6BKeOrr+Rf8/33+F//\n9JPjc4cPJ7p9m+iPPxx/9ufORRz5ggXy1yKHmBg0m27cOPV8HKmNHNlpV5Cn9mLSEyYTBJPUGFdN\nV3pLTp1C4sXp047P3bgRwm/vXggLJezbh8SYY8fUrVMpzERBQbCJb9yI9fbqhc73DRuiKe/IkRDy\nz56hG7y5wD5/HoLCUkBWqUKUO3fqvAY5PHiQUriHhBAVLJhSwLu5IeFn5UooAVeuwOfg6qrfek6f\nRvPuGzfkfz5btcJn8IMPHJ8bH4/3r1s3vH/2+Owz+FE+/1zeOpTw6BGCC/r3h28goyFLdjpxR5CM\nVJzK6ZhM6NrSuLE+zXUljh+XF0O8ZQvMFmfPqpvn+XPm7NlfT+Gs2FjEA3/4IezpUmGmli1hj86R\nA/+Dvn0RSrl3L+Lh0+vW2Z55pnp1FFOT/gfOoEEDmEHkkJCAom1KzDE3b6K4WFCQ/fMaNkSymbO4\ncwefHyUVJtMLcmSnEOQqmDoVdkS18bS2OHYMtmV7/Pknvjj2usbIoV49Zgt3R6py9SpsppIQ++MP\nPKdXlb20zosX8B2sWJH0PxgwQH0DDFv8/rvt9n6WnDgB279Stm2DELV1AzCZkM2rpISxGi5dStk+\nMSMgR3aKWisKWbSI6Lff5NdPUYKj8MPdu4n69UO8tRU3hCK8vZXHk+vBw4cwCdWti3C/mBiIsY4d\nicqXR2jem0C2bEQ1a8KOzYwY8rx5YTKaMoXo+XN95vngA9im5fhdAgKsx487on17oi5diHr3hsnR\nkgcP8LyLi/KxlVCxInwNffumntkwrfCGfG30YeNGOKP++gtFp/TGZLItyPftwxdl2zai2rW1z9Wk\nCb64qcXLl3CkVayI1xkSQjRuXMaLAVZLvnxEs2fDrv3vv7ChL12Km7sW3noLdun58x2fe+gQPhdq\nmDEDcfqzZ6c8dukSnK7Oyg8wp04dONc//BA+ljeGVNgZMHP6N60UKIDt78CB6FjvDJvt/v1Iobfk\n4EH1af+2kLoR6Wnjt4bRCLtlyZJolPDvv86dL6Nw8iRMIlWqIMZey+ft/n2EIj54YPscyT6upYv9\nnTswbViUY+JFixCbn1o8ecI8aBC+ryNHpt68zkKO7BQauQzi4+EZJ4Jm6eMDjbxLF6JffsGd39qW\nUinWTCtHjmCe//1PXdq/LXLlQtTHiRP6jWnJvn0wHyxciFDJLVuIKlRw3nwZidq1sWP67juUG27R\nQn5YqiWFCsHE8uuvts85exYZwYUKqZuDCNevWEHUvTvMKRKSRq43iYnY2W3YgN1d27YIbS1RAuWZ\niZCJmoGC5WwiBLkM5s5FWFjp0ggXu3ULdUfatcMHpkMHxDN/+CFqXJw7p06wWwryoCCkW69fT9S0\nqU4vxgw1dVfkcP48bna+vviCBQUhTE2gDIMB9ufz5yGIW7WCTV1NKaOhQ3FDTUiwflytfdwSHx+E\nlvbsmfQd0CrIpTyCPXuI5swh6tOHyNMToacdOxJt2oQ8hf79kVMRFYVaPpLSsHWr9teV5kmFnQEz\np1/Tys2bMKtcuMD89tu2t7ihocjU+/RTZldXtGxr3x4hdKdPy8vY27EDmWrM2FoXKoSMOGexYwe6\ny+vF3bvM/fph3T/9hNR3gX48e8Y8bhwiQMaNw2MlNGpku9NO27b6deFJSIBZaNo0PC5eHJm1coiJ\nYf77b1RJHDECkU0FC+I72LQp87BhKElx8iTCaO1RoABeU8mS+tbUT23kyE4hyO1gMqEe97ff4nG+\nfPJtiGFhKPs5cCBqauTNi7Fmz8aH0Fp9iG3b8IU6fRohhnr2jLTG06ewk8fGahsnKgot1PLnR6kC\n8zrWAv25cwf9Vl1cUA5Bbu2XjRsRz21JYiJi+s2bkGglLAy1w7dtQ86CZVip0YiyzX/8gXDezp2T\n4uvd3VHydtYslJIIC1PuI4iNheJlNDL37u2c1n2phRDkGtmyBUJY0iyrVpXfONaSe/egHQwejHFy\n54b2/f33SKaIj8d8ZcrgC6qlnrQSatZU70RNSIAjq0gRfPFu3dJ3bQL7BAejSYebGwSmI2GXkADt\n1DIH4fRpdcXaHLFnT1KM/KFDaPz92WfIlciZE2tp3Rp9ZfUsSMaMnbTUpCUyUl2jl7SCEOQaiIpC\nEaOAgKTnWrXSL9ngwQMUexo2DBpIrlxJH3pfX32rE9pj5MikLbBcTCY0f3Bzw9ZXa3KSQD0mU1Ll\nyMaNHVcknDEDRabM+eEHRHnoRWIimlOMHZv0ma5dG0J8wQIIdbnFttRy7BgKsUn4+SEJLj0mnAlB\nroGRI7F9Nad/f3wgnMHDh0kf+gYNYPKoXh1CfcUKdFZ3Rsjjtm3oKi8X87C4nTvTb+p8RiMhgfnX\nX1Eq9uOPbfcdffAAZj5zM0r79sorT1ry+DFMiT16wDbt7s78zTcQ3kTMkyZpG18pGzci3FXCaMRO\n4NdfU3cdeiBHdoqoFSucPYsCT5bJDcWLq4sYkMPWrYh8KVYMxZMeP0a4WOXKSEBq2RLFl9q0QWeb\nffvgnddKo0bw8NuKZpC4eRNhZR07Iirh7Fmi1q1TJ8lD4JgsWdC558oVRGvUrEn05ZdET58mP69g\nQURCSaGIRiNCXJUmAjEjGmX2bFxbqhTR2rX4PAUH4/MxfTpCAmvVQoXHAwf0ea1yCA/Hd0kiUyY0\nX/nmm+ShkRmGVLihMHP60ciNRmzJrN25/fwQlaE3kg3v9Gnmd96x3WE+PBzmmDFj4LTKkQO1MT79\nlHn5ctSaULN1dHdHHWprPHqE3UmBAnBKOYoUEKQNwsNRu8VaBNHZs8zFisEeHRwME5kcYmPR+GLo\nUOayZWGDHjQIOzNbiWV79mDHt28fdgvOrrci8dVXSUEK5nzxRUrTUlpHjuwUGrkFv/6KWO5+/VIe\nK148ZZ9JPRg5ErGxNWoQvfsutF9rFC2KWPVZs6BFPX6MEqjVqqGcrY8PNC4fH7QR27sXZWEdYS2e\nPDYWrePc3FAP5cIF1DHPkUP76xU4n6JF8Vk+cAA7usqVEW/NjNZ8rq5I0HIUPx4Rgc/YBx9gxzhl\nCsbeuhW1yBcuxM4sWzbr12fNiiS6Zs2IPv0UpYq1lh2QQ0REco1cYsoU7GYPH3b+GlKVVLihMHP6\n0Mjv3YMG888/1o+fPau8g48j9uxBV3BJ023VChUO1RIRgZCuL79E3HCOHLBnDxiA2NyQkJRa+5Yt\nSV3tjUZEEJQuzdyuHc4XpH/27sXOq1497L42b2auX5+5Y0e83xJGI+K4J01CRFO+fCi1u3q1/RR/\nW5w8iXGY4QT19kY3J2fTvLnttnmbNjFXrpx+8hzkyE4hyM3o2RNmC1s8eIAPtl68eMFcrhy2phKD\nB2MrrBfx8SiXOn8+nGBlysDZ1bIlvlB//YUejLlyYftbqxZ+zKN1BBmDxETmlSsRjdWxY5Jz/d9/\ncTPv1w+hr5UqMY8ejc+A1nDAf/6BIiERHg4Ty/792sZ1ROXKthUykykp9Dc9IAS5AvbvR01lezZg\nkwk2bL0aMowbx9ylS/Ln5s6FDdKZ3LuH8MGvvmJu0gSJE9KXet269BmiJZBPTAzsx9J7njMnc4sW\nzPPmyWvgrYSrV6GsmLN3L2z0zrSXO+pXev06/D62onvSEkKQyyQ2Flll27Y5PrdMGWWNjm1x4QJS\njy0bCWzfnpSmnxrEx8OEQoQQR8Gbw9KlSQ0tnBVGGhqKFH1LJk5EMpNezabNiYmBwuXoNU2fjkzq\ntB5CK0d2OnR2hoaGUtOmTalKlSpUtWpV+vnnn1OcExAQQHny5CFPT0/y9PSk6Xp2kE0FZs1CUZ/2\n7R2fq4fD02RCD8OpU+E4MqdcOTQCSA0SE+F8Mpng3HRzS515BWmD/v3hMD9zhmjsWOdUCZScnZZM\nnAin57ff6j9nRAS+V45CY0ePJrp2DTX+0z2OJH1ERAQH/5eXHh0dzRUqVOAQCw/YwYMHuV27dprv\nKq+Dq1exxbp9W975H32E4lha8PNDcoI1E8aLF9AmnKGpmJOYCJt5y5a2wx0FbwYPHyL5bMIE/ceO\njkatFWs4y15++DAcuXI4cCDtF9WSIzsdauRFihQhDw8PIiLKmTMnVapUicLDw63dEPS+xzgdZqLB\ng4m++gphf3IoUUKbRn7vHtH48UiQsNbWLFs2hBA6K/GICJpQv35EkZFEf/wBrUnw5lKgAELyNm9G\nspmeZM2K3Z418VC0KNom9uqF74VeWCYD2aNpU4RfTpmi3/yvA0Vx5Ldu3aLg4GDy8vJK9rzBYKDA\nwEByd3en1q1bU0hIiK6LdBYbN+JNHzFC/jVaszu/+AJCtFo12+c407xiMqFO+O3b6G9oK/5X8GZR\nqBDR/v3Izpw5U79xs2SBwpKYaP34++/DxNOzp37x5bZiyG0xZw5uKOfP6zP/6yCL3BOfP39OnTt3\npnnz5lHOnDmTHatRowaFhoZS9uzZadeuXdSxY0e6cuVKijEmT5786m9vb2/y1qOSvUqePYNQ/d//\n0NdQLsWLI4VeDbt3oyPPsmX2z5ME+XvvqZvHFtIO5N9/iXbtEv0yBckpUgTCvEkTorffxvdDDySt\n3Nb3bNIkoubN0Q1pwgTt84WHp/Q92aNwYexEBg5Eot3rbgAeEBBAAUob6sqx0cTHx3OLFi147ty5\nsmw6pUuX5kePHim286QmQ4fCW6+Uo0eTV1WTS0wMIl7kNIqYPh2hgXpiMjEPGQLbfGpVVhSkT27f\nxmd1wQJ9xitY0HGtc8lefuCA9vl69ECfWCVIpTmWLtU+v97IkZ0O7z3MTP3796fKlSvTCBs2iMjI\nyFc28pMnTxIzU/78+ZXdUVKRU6egiX//vfJr1UatTJ1K5OWFdl2O0Nu0wkw0ahSKY+3ejX6dAoEt\n3n0XmvmsWfDlaEXSyO0h2ct79oTvRgtKbOQSUlGtceOIHj7UNv/rwKFp5dixY7RmzRqqXr06eXp6\nEhHRd999R3fu3CEiIl9fX9q0aRMtWrSIsmTJQtmzZ6cNGzY4d9UaMBqxhZo5E04epRQrhg+atUbJ\ntjh/nmj5cqJ//pF3vp6CnBmhZQEB+HLmyaPPuIKMTZky+Lw0bQqTSN++6sfKls2xICeCvbxfPwjz\n3bvlf78sUSPIiYg8PIg+/hhVI5cvVzf3a8PZ2wKJVJzKLvPnI5tRSxJA4cIpE3lsIdVBVlLH/NEj\npMzrkagwfjxCy+xluQkEtrh8GVmYq1erH6NaNfndeRIS8P2cOlX9fLlyqW83GBWFBCa1XbOcgRzZ\n+UZVPwwPR5jRokXa6mgriVzx84NmMWCA/PHz58c1Wrd4U6civHDfPnW7D4HAzQ1VNMeMgTlSDXJM\nKxJZshCtW4eqikr9fUREz58jQkbtzjNXLqKffiIaNMhxjf60xBslyEeOREZlpUraxpFrJ4+IQAab\nn59yT7hW88qMGUTr12N7XKiQ+nEEAqm5ybBhUAyUYiu70xbFiqm3l0uhh1oUtU6diEqWJJo7V/0Y\nqc0bI8j/+ovo5El0CNGKXEE+YgRuHFWqKJ+jfHn1gnzOHKIVK1CL2sVF3RgCgTnVqxP5+8O/9Oef\nyq5VopFLtGgBu7zS+HK19nFzDAaiBQvg7L19W9tYqcUbIchfvkT89IIF+sROy8nu9PcnOn0aWZxq\nUKuR//QTTEcHDiiLpRUIHFGjBtGOHUjg2b1b/nVynZ2WTJoE88aMGfKvURpDboty5aCIDRumfazU\n4I0Q5DNmEHl6opOJHjjSyGNiiD7/HAJVbeakGkH+yy9E8+ZBiJcooW5egcAetWujO1Dv3vC9yEGN\nRk6UZC//5Rf59nI9NHKJMWOQPJceimpleEF++TIcJz/9pN+YjpydU6YQNWyIcCq1KBXkS5ZgK3jg\nABrhCgTOon59tI3r3j1li0BrKLWRm2NuL79/3/H5egryd96B7Bg2DE7UtEyGFuTM0IwnTIDw1Qt7\nGvnZs0QrVxL9+KO2OZQI8hUrkGK8fz/ifwUCZ9O4MdHvvxN17kx07Jj9c9Vq5BItWhB98gmEuclk\n/1w9BTkRymQ0bowIsLRMhhbka9cSPX0K+7ie2BLkRiMKUs2YgfoNWihWDGuPibF/3urVsMPv2wcH\nqUCQWrz3Hr5jH3yAGkK20CrIiYgmTyaKi3NsL9dbkBMheGDlyrRdVCvDCvInT2DjWrwYtjY9yZMH\n2n5UVPLnFy/GdkxLFpxEpkzQru1p5evXowTv3r2iKYTg9dCiBXaE7dvDuW8Ntc5Oc7Jkwed9wQL7\n5hyllQ/l4OICjXzQIMc7gtdFhhTkUm2RDz8kqlNH//ENhpRaeVgYtAY1MeO2sGde2bQJcfF79iDO\nVyB4XbRpAx9NmzZE586lPK6HRk6UZC/v0cO6vZzZORo5EcKIExKgmadFMqQgHzQIWsL589iKBQQ4\nNlEoxdLhOXw45tWabGSOLUG+bRvRkCEoRVu1qn7zCQRq6dAB2nKrVkQXLiQ/psXZaYk9e3l0NH47\noyjckyewlffvjxDMtEaGFOSSRtylC9Lcv/4aNuuaNYmGDkVI082b2noUmmvkf/4JTWTcOO1rN8ea\nIN+xA9rBzp0o8iMQpBU6dyb64QcI28uXk57XSyOXsGUv11MbN5mQQDhlClHdukRlyya9pgMH9JlD\nT3S2Hr9+YmKINmyA0C5QAIKbCB+k4GCiwECiLVvQeJWZqF49hFPVq4dr5LY9kwT58+fQjpcv179l\nWrlyybPodu9GdbgdO7BWgSCt8fHHMEE0b0508CCRq6s+NnJzpPjyWrWIGjWCpkykXZA/fIgM8F27\n8LtwYSIfHzSIbtgQ5pwdO+CTYtZWBkBvMpwg//13COYWLfBB+vhjPJ81K4R1vXp4zEx05w4Ee1AQ\nhP+lS2jBZi7cbSXWFC+O8ydNQs+/Zs30fy3mGvm+fUjC2LrVOXZ/gUAv+vSBMG/WDGZNvTVyInz/\nVq7E9/vMGQhdpYLcaERvgl278HP5Msr2SsLbMh/j6lUI9MhIyIz69XV9SZrIcILczw/heKVLE/38\ns+3zDAa8UaVKIbGBCNr8qVN4k1avRgx6tmzJBbuHB9pglSiBBJz4+JQ2Qb0oXRp2+H378IHdvDlt\nfXgEAlsMGJAkzAcN0l+QExG1bImbRq9eEMRyBPmDB0la9549iEjx8YGZpmFDfLdtce0aUYUK8Af4\n+aWt76Lhv3q3zp/IYCBnT3X2LFG7drB/Z8qEN+nMGVQyUwMz3rygIPwEBkJD9vTEh+bGDXjq+/bF\nfAZD8h+1z5k/lnYQBw5AWxAI0hPz5qFmSdmyzmkonpiIePZWrWD6ePddRHNJGI2wdUta99WrON/H\nB9cokQ1ffkmULx9uUq6ukDP58un/miyRIzszlCAfNAgNZCdNwuPOnXH37NVLvzmiovDBkNLvO3aE\nwGWGg4Q5+Y+c52yd8+wZtnuVKhGFhOj3GgSC1ESyJWfLBsGXJw9+cudO+tv8x9bzefJY15jDwmAv\nJ0Lp2aZNk7TuvXuhpfv44Kd+fftatz0++AA74y5dsIuvVy91imq9UYL8+XPcXc+fT7Jr//ILkhT0\nbtt06hQ08fv3sVUrWFDf8SW+/BLjr1jhnPEFgtSAGYK2Z08oV1FRUFKs/dg6Jj2fObN1AR8UhGQg\nIjxu1ixJ69argFy1ajC5enjA9j9kCOSNs52eb5Qg//VXeJTNK5WFhEDg3ryp3zwxMSjnOW0a7v6z\nZ8O2pjdXr+KOf/68KEcrSP+cPk3Uti12mGq79zAjHt2W4Je6cMXHo8+onphMRDlzwtGZKxfWUrEi\nlMQGDfSdyxI5stNhHHloaCg1bdqUqlSpQlWrVqWfbXgQhw0bRq6uruTu7k7BwcHqVqwBPz/UOTGn\nUiWiFy+Ibt3Sb54xY4i8vIi6dkVavHm8rJ6MHo25hBAXZARq1oSGPH26+jEMBvQTKFoUQtTLCybO\nzp1h4iRCvSG9S3IQwSeWO3dSspHBgHyOJUv0n0sVjpp6RkREcHBwMDMzR0dHc4UKFTgkJCTZOTt3\n7mQfHx9mZj5+/Dh7eXmpaiCqllOnmN99lzkxMeWxrl2ZV6zQZ54dO5hLl2Z++hSPZ8xgHj1an7HN\n2bOHuVw55thY/ccWCF4XERHMBQowX7m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mnDmDuHQRcigQOJ/oaOZcuZifPEl57Pp1mGbz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\nDMwFORFC+3btgqzRw0+nlq++gs/QvINQutDIHz603pzBYIB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       "text": [
        "<matplotlib.figure.Figure at 0xae7890ac>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Poisson Equation\n",
      "Firstly, let's solve the [Poisson equation](http://en.wikipedia.org/wiki/Poisson%27s_equation) on our established mesh."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Boundary Conditions\n",
      "With the equation written as $\\Delta u = f,$ we'll here solve for $u$ using a simple \"Poisson function\" $f$ of $f=1$. Further, we'll impose two kinds of boundary conditions, Dirichlet and Neuman boundaries. We can sum this up as follows:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Poisson function:\n",
      "def f(x):\n",
      "    return 1.\n",
      "\n",
      "# Dirichlet function:\n",
      "def g(x):\n",
      "    return 0.\n",
      "\n",
      "# Neumann function:\n",
      "def h(x):\n",
      "    return 0."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The boundary conditions themselves are set up in a dictionary called `boundary_dict`, which is a nested dictionary (here) containing two main keys (vis. `dir` and `neu`) where the \"facet markers\" of each facet-zone (set in `quarter_annulus_2d`) is set to a corresponding function handle."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "boundary_dict = {'dir': {2: g, 3: g}, 'neu': {1: h}}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Assembly of the matrices\n",
      "There's a separate module for the assembling of matrices in elementally. We can get the desired matrices through the following lines."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "assembly = assemblers.Poisson_2d(mesh, f)\n",
      "A = assembly.A\n",
      "b = assembly.b\n",
      "points = assembly.points"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Imposing the boundary conditions\n",
      "We impose the boundary conditions on the assembled matrices through the `boundaries` module."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A,b = boundaries.impose_dirichlet(boundary_dict, mesh, b, A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Solving the equations\n",
      "We can now find $u$ using `numpy`'s eminent `linalg` module."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.linalg as la\n",
      "u = la.solve(A, b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plotting the solution\n",
      "Finally, we can visualize the resulting solution through the following matplotlib objects."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "from matplotlib import cm\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "\n",
      "fig1 = plt.figure(1)\n",
      "ax = fig1.gca(projection='3d')\n",
      "\n",
      "ax.plot_trisurf(points[:,0], points[:,1], u,\n",
      "                triangles = mesh.elements,\n",
      "                cmap=cm.jet, linewidth=0.2)\n",
      "\n",
      "plt.show(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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f4S5SsCZf6I2WixiBuIa5XBQul4v6668n9jd/QzYnSVtzM+fo6ESxorubZ1pb\nmdfehnPGNI7ozt32B2DWm6+xa+NG5qxYkXU79XUwmUw4nc68Un4nGurn1O/309LSYnicJUuW0Ktw\nAbW2tpYCaUoIshVLeLvdPq4lTqa0xXwIRSkBy0W2+R5HELuwPiei9oIkSfh8vnR5yGJ0AkilUuzf\n00bPE3ewvOsp5Hicx0Je5KoKHJVOXtg4zNkeiZtX+qixj5VJvW+fT/KSm1h90hcKnsdEQklC4pqF\nQiHsdnv6vimzq7QIaPXll/P4I4/Q8tJLmseImExYAgF98wFq+/p4vK6GG/Z2olcWMT0Rp/1P9+ck\n3UzQcsupA5i5roMyCamYEGP6/X5dFca06i5ce+2148abKEw50hXWhlj6xePxjP3H1MjXApUkieHh\nYUNJB0bUCKJDaiqV0kWIRoJ7ogsEkCbyYvjmwuEw9/z4G1SFNlFfBVvnTqfaOcT5dUHiUpBbnqzj\nr+tlljvG+of9STPvzrqY+V+9mappxV+6TQaUvl8lsrkoZl9/Pf1vvkmVRjry9uZmzjqQDJENH7md\nhBc0sjQxALKMbbqL9e5phM1OQsE4dA9yciCAO0PIwvP8swT+9SbKdNTVEOeT630y6qoBxpSKLKRI\nknp+egNpf/rTn7L+fSJq6Cox5UjXbDaPWea5XC7dLXGMkK4ywwswlOGlN2dcLPVhJJqup8iMHgiy\nFWOLimh6rNtcErBEIkFH+zYe//V13Hj0VlwqgcbWvU7+8lEV57tSLLeMtW63mpsZOPP7LD/jMpLJ\nJKFQSNMiOhjZZUaQ6dpkclHIsszi447jmUsuoUpVuSoByPF4xuLpAOuryrHNns6q8D5ag7uIp2C7\nxc1CS4SF4VH3QqQeNjdVMuyuIixZCA6HmbGvj1XxBGYzHNbTzYb7/sBRf5+75m4hyHQdRAshi8Uy\nxnjK10Whvg/5+nQnG1OOdOPxeDqZwGw2G0r700O6ytoFNpsNt9ud9q8W4zhKshVLfTBWkCXb+IJs\nxQdJJIIU2gFAFG3ftvVpNr5wM3+zomMc4T778XQkKcWSiJmjbaPpsLEkvNF4Lq3X3UZL46jPTW0R\nxeNxzSaLSn3tVIQgkWN+8APeeeklGhQtej5paOAsjZY9MvB6fQ3VDeWcHuyi1j+qavAloY7x/d1c\nZlgtD0PwQMqwE3parHzgriNkLSMclfn4oT/qJt2JiOALN40wALRcFPlK2gqppTuZmHKka7PZqKio\nIBaLGZLdabWaAAAgAElEQVRNgf5CMUo3grIPWiHH0SJbsdQXVnshEGQryzIulyvtcxTzyRfCXx6N\nRtn6/n8z1P5Hzp8ZpMYz2r5GluG+jTNZOWM/O96v43TbaM3ZHaZa9p5yI6su+dtx89CyiJQvoXj5\nRMLGVLSKlZje2Ijjq19F/tGPMDNCrFGTacxLGAPeaJlBU7WNy4OdeAPjFQ0DFhvNFn3tg+rNEvXR\nXqCXx8vqaKwYqalspGreRCKbi0KvpE20lwoGg5ppv4caphzpKr92xZB/ZSLbbPsYOY56qe92uwvu\nNqEcX1igyWRyHNnmC2FdxmKxkZVFcID2j76LV36TGTiZVTUa9OkcNPFGZwsXLW7niRdauNI6QrhJ\nGV6rOZH6L9/GkfMWGTq2eAlFqrPD4dD0EyaTyYMaPc8HJ91wA08/9RQtmzaxo76e0w8UyBkGNs2f\nSatb4mvBbqzBzGMMW53M1Um6ALtkC+/NbuHM8j0EE0mGh4aom4RqbGoIwtQDvZK2VCrF008/zQ03\n3EBlZSU33HADS5cuZeXKlRx55JHjxtWqu/C9732Pp59+Grvdzpw5c7j77rvzTrLQg6ljJqhQqBJB\nyMtEAfHy8nK8Xm9Ri8XE43H8fj+RSASXy0V5ebkmKRolCBE1DwQCBAKBtPXvcDgKVm0IayIQCGAy\nmejpWo+/869orl6LvKuCpbWj9WPf2FXBzuEGLlvSzsMvtnC5pQOTCTrkCl5e9U8c8R+P02SAcHOd\ns1iaOhwOXC4XHo9nTBcPUQ0tFAoRDofTldHEyzmRgne9sNvtNN1wAxGTCb/DwYDFzJuLWkkuq+Vr\n8h5OC3VjzfE4JG2OMbK8bHikfAYDS2q4vGY3VTaJaluK4d6u3Dsy8f3M8oHyORDF0M8//3zeffdd\n6urqmDNnDuvXr+eBBx7Q3P/aa6/l+eefH/O7M844g48++ojNmzczf/58br311gk9hyln6SqXzPmQ\nLoxWFtNTu0BJ1HoDZEpLLFtrH/Ux9EAUEAfSNX+L8WII7amy6Pn7b/+EebU/xVUX5I1HWzhv3qjb\n4OEPm1jWGGR+zV7ueaGFy00dmE3wumcljotvYtWRx+ZVWtIIjETPheSv0PTfYuCoiy7in37x3xyR\n8FF7WDmnxtpGSqjpnEbCZh+JwGXBxyk7W1obOKdiD2XWUX++2wq+3r0kEssmve16sUlcjGcymair\nq8NisXDjjTdm3Uer7sLpp5+e/vfRRx/No48+WrQ5amHKkS6MSnaMBIeEG0H8W68aQe9DonQjiAht\nWVlZ0VQVypq2DoeDRCKBy5Up217/+Fr64849u9j67t9w4hFPYjbDg79r5aqFI8L9YBT+/HEr5x22\nh0pXkj+90sR5sb34TG7eWHItR3z1JsO+9mJDy1ccCoXSfkx1wCaTe2Iiyejcq7+Idd29fNjvZVrP\nMDMMrDllqzUj6coyPFTdwMKmOJc52sf93WQCU9Sfs5uHMpBZLBR7paGcn7KubiH4/e9/zxVXXFHw\nONkwJUkXjFfOEpatyWTKWgYx27G0HkChsxXWp8vlSgfNjD6wWsfQqmlrMpnSwaVCNI5aqcA7P11H\nqOd6Tj/6UwDu/e0srpjXhskEW7udtPnrufqIkf9/cn0DJwQG2O5ZgPWSH3H06lMxmUzpa1Eo8skg\nzDaWIGMlMvmKIXNRnGKQUXldI8fZO0nNgI3Tqnk7Xk112z5OSoZy7psya7+2m3GwY24955V34M7y\neDvkWPqDnU1BooxLFGtVMFEfMr/fX3AQ7eabb8Zut3PllVcWaVba+MySrlbbGqFGKEYATpCtlmLA\naKEWrQdROf9CW6WrXyClikKQbSqV4t3Xf8qsqttZtGQkoeHBPzZzfnMnNis8u206MyrNfHFhOwBr\nP5zGjL0Rtiy8mKVfvxlvecUh6QPMhVwKCi2rGEaki4VU5kp5Kg8cH460D3KkfZCew+w8k2wlsC/C\nBYM9ODPc7oTqOZBl+NP0JpY1hLjY3qG9kxLR0UBotvOPRCJpX7lSxlXMfmaFQBmY8/v9Benc//CH\nP/Dss8+ydu3aYk0vI6Yk6SpvnPpGZiJb5b6Fkm42eZZ6fkaPIZb7elqlG3mI1ckYysw3v2+QTW/f\nwHFLH8Z1QPb81FN1HF82QJkjyX0bZ3Hq3F4aykf2fWd7OXt3VFNxzb+xcs2ZpFIjxamV5yH8qFOx\nXGAuX7HQQStlTEZ9xa7qekISeBRvYL01zrnWNqSZ8GZDHb1BD4ft6WIJ8TH7yopx3zN76Jo7nUu8\n7dh1Lt5Msewpx+L8TaaRhBrx/mTLNFPraSfDV658/gtJjHj++ee54447WLdu3aS0+5mSpAujD4a4\n8GqyzURW+aoR1D7bbPKsfI6hJls9AT69EC1NhIpCGdjbtfNtAntv4PSjPkxvv+71cubGE8jmCA9/\n1MplS9uwH3hSNnc4ee6TpXzjjntxV1SOaeIpXAFapFRohapDAUr3hFCK5BL3Z7IKpzW3sl+y0Wod\n75y1muFEey9Uw44yL08km5E7hjg/NIjZDCmTibgMD9XNZNUMP39lazd2IhF9dR7UH3Utq1hsp2yf\nk6kYzkT6dPWWdRR1F/r7+2lubuY//uM/uPXWW4nH4+mA2po1a7jzzjuLOlclpiTpKhUMgkzi8XhO\ny1Dsk8/ND4fD6SyvXFpYI8cQZAsj5GgkwJfrGMLXLPSsol6uOO6Gt++k0Xszhy8ZLQ249WMnjk43\n/dEI+62NXLZkJIDWMWjiqf0tmNzn8u1f/YhYLEYqlcJut6eTPJQWorKdjVLkXqyl6qECIwoKpVXs\ncrnospTTSvZyjvNsQebZggTnwotSM/2DJvYO+5AXtnC5p0O3dGwMov48dsoMPS4akWQUDocnJHCp\nl3S16i5cd911eR83H0xJ0oWxelIjPk8jhKhMPHA4HLjd7qKpEdSBLLPZbDjAlwlCViZJUro3WzAY\nTM89FAzw/hvfZs3iP+J1j86zuwf2rq/D54uzvNnE/Jou3tzjoaumCddsH4sXX8/C+VeMUX8o3QrZ\nroe6YpqeZAfx4n5WfMXAmHOWXOUgZSddAa8FzrR0sq62kg9rbIRrLezutzDfY1wpYopmybxQoJDr\nrv4YCReUx+MxHLjUM7+pkgIMU5R0o9EoweDIg+PxeAw1jdRrIQqyFT4eo9W5skm0tOrlGu3WoHUe\nwuoX9YSFhlcp4Wpve5/B9us5bdX7KE8nGoUXHmrBmjTzhYW9rO2uYcu0BSy6rJt62z7atv0biw77\nEm63uyglJ/UGsGRZ1iyMU0h1qkJQ6BJ5TAqrpxoU7YpyYXPMhesYJ6t8Di4+fDdbeit5uKOG+T1d\nLPNk7hwxbg45fLoTAaWm1kjgUhC3VjcPNek2NTVN+nnlgylJusKNEAqFDL942UhXkK2wEJWklY8a\nQflQqFUD6hKO+bo9IHerdDH2++/8jlrHD1mzbL9qf7j9tgbmVcpINSnWTZvJsRd34/H46O1x0f7p\nTaw++muaVcoKmbfWWErrSFx7h8ORtTCO3oIoxURRjuEuB53f2o6Ymf3Laji9sYu2gQYAltQNs6Ru\nmO39ZTza0UTj3m5We3QUTorltnQnM3svHxeN2DaRSLBhwwYGBwdZvHjxpM25EExJ0hUtU4wmSIC2\n9jMT2Sr3yVcCpgzAmUymjPVy8zmGSGXOFTyMRiJseP27HL/sQSrKxi9H//471bQeBvWnJjlydV96\n/j3dbnr33Mqxa75yUJf3uawjpWWUKZJ+KCLl1rccDkrw3txmLp4/IgdLyWOLMM2fFmD+tABts108\n2jabms4+TvJmtmZNUf2WbrHuez6uimyBO5EsFI1G+dd//Vc+/vhj7rrrLlauXMnSpUu56aabxikR\ntOouDA4Octlll9HR0cGsWbN46KGHJtxNMSVJVxlIK0T+lWk5nm0fI4jH4+kgmZ50YL0QZBMMBnE4\nHFmDb517trBvx/UsaXmbF94qJ5SqIeUoI+V0g93G2ifbuOGfAxy2qP/AHiPz29ftYXDfTzhq5VWG\n5qVc+k0klNaR0t2RKZIOI/Vchf/8UAjaCa1uNsgyPFo7i2uWt4/skwI5qe1KaK2K0Fq1m+45Dh5r\nn427Y4AzPRqmdCS3eX0o+9HFfRfB4bVr1/LNb36Tq666ikgkwscff6zpcrz22mv51re+xTXXjPaK\nu+222zj99NP5/ve/z+23385tt93GbbfdNqHzn5KkK5Av6QrCEmSbqb2Peh89EEkTMCKdylRVTOsY\nRoJvMFKxLJuu8OHn7mPQdA+e6iR7y5dTe7mJxgOKe0mK8cSv4PJLzRy2aOyStLvLy0D37axckZtw\nJ4NgjSCTVRwOh9MrpENFyia7ckfb7yufxRWr29P+92gC3JZ41n0aKmL81bLd9M+x8mT7bGjzcZ57\nNGDnSgQZGBjA6/VO2nlPdEpxIBBg8eLFNDQ0cP7552vuo1V34cknn2TdunUAfPnLX+akk04qkW42\nGCFDGK1fINwIuchWeRw9xKLU8WZzJRg9htIfLIJv0Wg069xf//g12kL3c8pVglBHScg3kOS9F6po\nqR7gxJP2oay00t1VRl/nbSxdcomueU8FiOskqlIJKP2FuWoxTIiLIoel+yd7M+ev6UxrpAF8Yagv\n01fwfppX4rzFu/HNMfNM2yzCu0Nc5Oij2hTEd6D2bKaglUCxyHIiLGflePkmR/T29lJXVwdAXV3d\nmAaVE4UpSbpG3QtKN4Ldbk8nNxg5XrbjaNW09fv9BT9kwioT2ka9JP7q1rU8seFXXHx1AHXpqs7t\nSfZsn05ZpZ9zlu0aM8e9neUEB37OosPPymuuh5LFqwX1/dAiUz1SNqAo3SxSrswk8aS5nhOP6afS\nNdYHPxR10FSlX6kAUOGSOffwdsJz4S9tLfRvjzJn/16aFZ1zxf1T6qmFzOtgZJvlgprEY7FYwdlk\nk+VumpKkK5CLDNWVuSoqKtJEZhRax8kWgMsnMCa2VwbfQLvweabxX9z8PC8mH+eoFX4c7rEP0Cfr\nIRyro+noMN5N+6mrH70OXXsqCQ/9nKWL/yqtvdUDMVeRLKFWbhwKvlMj0BO0AzS7WSgVFHqQ8mi7\nF15OVrPgmGg67VoJX8zBvGnGSFfAbYcz5nXwP1Ijzaaxz45aQSCapTqdzoyJLUaUIxPhXlCPl8/4\ndXV19PT0UF9fz759+6itnfhmqVOSdHMRmxbZiodJ+PLyOZ5yfGE5Z2qMmS/pKl0UufzB6vGf2/gU\n7896narXeph32dgXdsMLVlwzypl9lMTuBwKce1kXwgru7KgkMvxLliw6X/fchX85FoulXSnCIhTB\nw0JqExxKUBKS2WxGkiQ8Hs84balWo8VshGTyViHJjMkq2xh3U36MnQXTejTnImEnX5m0LMMfulo4\n4rgwi5cfrfvctRJblFbxoVCDIV+cd9553HPPPfzjP/4j99xzDxdccEERZ6aNKUm6MLb2gkAuvarY\nz2iWk9hHrXbI5hM2Srri4Y3H47pTjZV4asNjbJ77FoHNvZx+Yv+Yv732qIOGFS6mtcrseCHIuSeO\nuhX2tFcTD/wPSxZ9Qdc81S4Pu32kO6XFYkn7Q0Xigvib2neqVcc1k5V4KLsslFaxVqNFLSmbkowq\nG2bRn4D6A4H23TELvhXVnNyQubNDEnvGv2VDXIIHemfxpS+388EnK3MmuGS77rl0tVo1GMR+op9Z\noauffCxddd2FH/7wh/zTP/0Tl156KXfddVdaMjbRmLKkC6OBND1kq9zHKATh+v3+gsssqqGsHSHa\nsBsN7j323sN8tPA9TG6Yneqlsn7k97Is89L9Hg47207ZdAgOxZlt7qNuxsjytKOtBil0J4sOOzvj\n2EooOw0LK1xPg9BcvlMtK1EoDaZaGnA2KZt6me72ltFHGfUE8Mdh0/wmLpyTvTRjMo9XNhyFR/wt\nXH1NO1YryDTrPhcjyOaaEYHfYlnFymdC1F3JBa26CwAvvfSSrmMWC1OadGHk4vt8Pl3FbgQEqeS6\nwUoyBwyRrRF/s9PpxO12I0mS4Qf9oXf/yI4lm3BU2fDfv40jrhwJnkWjMuv+r5zll5jTvt2epwN8\n5YpOwET77mnIkV9z+MIzcx5D1HLQan6Zr2Qsm5WoJCeRBjyV3ROgvUx3OBz0OcqR5ACP1c/kmqW5\na+EmU8Ze2aEQPBefxZeuakc8urJpZs79JiLLUH2vc1Um05tlqLfYzaGCKUu6kUgkHWjSW5lLIBdR\naNXk9fl8hqzbTMfIZJXnU/j8/969n72rd2CvsDG4YT+rVw1iNpvo2yux9a1prLo6hdk88rBufzHE\n2Se2YTKZaNtViyn2Gw5bcFrWYyjnmi15pFjQCuaIY+frnjjUkXJVcJ/FxpcUWtxskGT957fPB29Y\nW7jisrFjp3SQLhQvGw30lYnUk2Uo7rUsy+mPmM/nK6iA+WRjypKu1WqloqICn8+X1zJIi+DEMiga\njY6paatUFRj1AyvHVjbELMRFkUqleODtP9B73G7sXhuyLFPTvpfGixO0bZXp3VvHEZckEYGysF+i\nRdpPQ2OEXTvqsCR+w4L5p2Y9hlAkFNudYhRqqZaAHvfEVLCI18lW/va4Pdh0volySt+5tA9a2FLZ\nxCVnj7WeEwkw22YbneakIJtrRrnyEfc6mUzyP//zP3R1deHz+fj000+ZO3eubgPs1ltv5f7778ds\nNrNkyRLuvvtuQ8Wz8sWhmZSuAw6HI/1CFZIKDKOEODw8nK5p6/F40jdPK2inB+LLLcYWJRE9Hk/G\nAJ+eMe967Tf0nrAbm3dkqTb4yC5Wnz3E1jfMBMK1LDxzrI917xN+Tj29k13b67Elf5uRcMVHR/ht\ny8vLcbvdWQk3X/dCoRCWks1mS7tnREt20X5I+KBDoVA6wUTobvOdc7H9y+6jU7wzWK3/+DpaBm/b\nb+OT2hl88ezx7opdHR5aWlflPs4kSLz0Qtxru92evtciULt06VJSqRSffvopZ599NhUVFbz44os5\nx2xvb+e3v/0tGzduZMuWLSSTSR588MG85mcUU9bSFSiEdJVptaITbqavZD7HSSaTDA8Pj2n8WMh5\nyLLM/772K4ZO6sLmGCHcQEeA5S2DfPiqk4rZXuoOG1sMZcfaIGee0MbOT2ZgTv6GeQtPGjeuWpHg\ndDrTMi+90KMhnmhoRdXFfQ6Hw5hMpkPKPRGNRll57D7cbvjzYw1c2NSdc59cjZY397gYnlfDWcdo\nKyCGA41MdzqLpiLQi2I/D4KITz31VPx+P4cddhg33ngjPp9PVwJReXk5NpstnR4eDodpbGws6hwz\n4XNJujAS8RQXPBchGjmOsKiEVlXP2HogSRJ3rvsZ4dP7sSrWoo6399BtNtFyrJvKxrEp0eGgRHNs\nkHCwCjn6C+YvOG7cuIJsYbRvWiwWyyuB5FCEIBWTaaTflyBko+6JiSCmXbvfZ94yH06nCdeXnNx/\nfzNfaurMuk8qlTntfX23h+TiCk5clVlyJpub0x/ZbPUnxO+LiYmynJWBNL0Bterqar7zne8wc+ZM\nXC4XZ555Jqedlj3GUSxMWfdCPtFzYdkmEgkkScLr9RoixWzHEWTr9/uJRqM4HA6sVqvusbOdRyQS\n4Wev/JjImQNYbKPW5/7n9xDu9zHvDCuVGh/pvY/5mdmcxG3+Pa2zVo/5myRJBAIBQqEQTqcz/eXP\nF4LADmVdrRJG3RPCHy+6SRfjPOOJHTidI89x/YwoJ3x9gN91t5KtnEgmed4bXRWYVnhYsyqHtWye\nhcPhSNce8Xg8aTVKMpkkFosRCoXSGWnxeDz9QSrknCfSXZFP14hdu3bxs5/9jPb2drq7uwkGgzzw\nwANFm182fC4sXS1Bv8ViMWSBZntglNaiKOEoSVK62pje8dXnIUkSPp+PuzbeSeqcyBjLY7B9mO6X\nPuVLt9Rgs4//du5cF6a5KkiZ7Q+0th5FMBhMW3fhcLio2XTJZJJAYKRGq3gZhCZzKgSzBLK5J5RW\ncSqVGtfNIh/3hMk81udaWSlx/je7uOu3s7m6bDdODempnBr/TK3trGb6sWaWHrZ//A7q/VXKhUwZ\nZ6K4knh31PUnjEj3iv0hVo+XD+lu2LCBY445hpqaGgAuvPBC3nrrLa66Sn8p03wxZUlXaelmqjSm\ntFZgZPlstVrTefNGj6dFiuFwOF1AR51Flu/DJhIm/AE/D3zyezg3glkIwaMSWx9NsOW1PuZd/1Ue\nfaGb2tiHnHBBFOuBfNJYRGLoHT9nXXA3s2atTM9FuFSKoUhQjgfg9XrTL2YsFstZuetgtdsxCjUR\nC2vQ5XIV7p4wt4/7lcNh4pK/6+Sh++Zwhm8X9arVsiyNdfs8t2c6s0+RWDBnbBaiFlIpSJlacm4n\n5qs0TLQ+Plq+8Wz3ttj3W8u9oBcLFy7kRz/6EZFIBKfTyUsvvcRRRx1V1PllwpQlXQHhf1IilUql\nCRHGFxDPRtSZoCRddeNH0Y5bvX0+44dCIeLxOEk5yQM77yJ1ZiQ9322PhekpX0R/0M/cS5uxLpqB\nb9EMBqNL2P1aG9MH2lm6cAfbHwvzN5f8hlmzVqYVCYlEAovFUhT5l9Kydzqd6bGV1pDJZErLb5Qv\nq1a7ncnwnxYL4hnQk9yRs/aEeby6AMBsNnHBlzt56YnZLN7Tyfxpo0SbkkaL3Ty5p57FZ4SZ3aKv\nu29vn5lptUfoPk91cFS9ChDb5WqlpPSjF+PeqsfJx9JdtmwZ11xzDStXrsRsNrNixQq+8Y1vFDw3\nPZiypJuJQJUFYzLVMMhX8ZBMJscUP8+WLGDU1yyscQDM8Pttv4ZTRwh35wsB9sbnMnDWCkwvbcMm\nx7GefHh6c4vTTvKUBfSwgL3PzuSbxyxlduvKtDJDEIMykJTrXLXmrpWZJiwe9f7Ke5JNCJ+NoJTb\nHUpEnO2e63FPxOPxEV+6e0/W45x2fhdvv9qA74N+VtWHiEtgM42Q7qN7Gjnq3CGaG8K6593ZM4P5\nK3NbukagJ8lBuNmKVSZS/WzmW0v3+9//Pt///vcN71copizpCgiCyLXU19pHL4QgW3QH1mMt6vU1\nKyVrANFElN99+ivMJ8fY83aAzn0t9J1wCkyrIPXaJ+yvmcOyaTFMGsdPDoX5cs1qjl90DH7/iPUj\nFAnhcDhvd4fezDRD/kwdBCWW7IdqTVc9yGQhtrW9z9xlftT1jtVYc9I+PiybxtpXHCwtG6SuLMqD\nHc2cdEEf9bVRQ3NJpmbqXuUUqqtVJjmoXTKZUn+NrHiUfwsGg6U04MmEsJIkScLpdGou9dXQS7rK\ndGCz2YzD4cDtduuaV7ZjCH+oshOE1Wplx+7tPDrwAIPTBtn9UD37jzqG5JqRqvbSx52EzA00dWzF\nfOV4ayUlyxy1XubkFUcQCoV0twnKNndlht5kZKapCcpsNqdXFVov61T1EwPEkztxOPTNdemR/ezw\nlPPQ3TVIZjtXXdnDtOo8akLrTP+dKBhd8WhJ2cSzqbzPyWSyKLLMycLUmakGxFLfZDJRUVGh+4XL\nRbpa6cAigmsUygdEGdgzmca289nXv4/fffIr2iJe+ipOJn7p6AsiDfhJ7JDoW97AAtsnmudZ9+p+\nrj3sfOx2e0YfsxF3hyzLDA8P50wamQxkelmN+IkPNaRoN7T9vIV+fpqYyeHHzOT/3uzmnGWf0jrT\n2MpFT6Gb9PyK6NLJNlamlUC2VkoC/f39hhRChwqmLOmaTKY0wYhsIyP7ahFQtgw1oc80cgwllGUR\n1YG9XXt28p1Hf0HghFVE1iwcs68sy8jP7KLr0otY9Of7MF0xa9yx7B/28fczTqa2tragF0UprRNp\nwEaSRibC95rpmhu1moB0+UxhER9UMja1G9r8Nw8up3bVDOZcZiKVKuPJj2YTf0fGNdTDmpmfcOSi\n3K6GlLm4/tyJRLZ6G8IAevXVV7nxxhuRJImzzjqLZcuWcc4553DSSSflHH94eJivfe1rfPTRR5hM\nJn7/+9+zevXqnPsVA1OWdGGk/oJRMgTt2gtay3018jmOJElEo1HNsogA3fv7ue7x+0h87ypMFss4\nD5983wY6LrwIc9deqheM91PLvQG+nDicwxfMyzmXbIoNpU/c6XQSiUQML9kmShJkZPtMfmLxYRaV\ny5RSp4NiFWdQLmjhdw8vwXbWfCwvDgIjz0DdYjssBpjFu22NrN2QwjnQz+Hl2zhtTWDcGOEwmCyt\nurTTE6GrLcZ1FR9aoZK5+OKLueCCCzj77LP55je/yebNm+nuzp1KDXDDDTdwzjnn8MgjjyBJkqEW\nVYViSpOueMnylX+JYI2exo9GHxohog8GgxmTEBKJBJf+993E//E4bBrLd/mhDXSecRYmu53F763F\nfMXY6lCylOTErU7OOG6Nobmp56lsPeRwONK+bCNQy4sOlcw08YyYTNppwEb9xMUgkFAohNujj3Tv\n+fPhpE5eSGRAouEICTQ6R1S32qhuBWigbX8tP94k4xwI0Mg2/urkfsxm2NFeway5ywzVnpgM90Kh\n44XDYSorK/niF7/IF7/4RV37+3w+Xn/9de655x5gtGLhZGFKky6MPhj53FiRRaUn6GQk+CYi/SaT\nCa/Xq0nkqVSKGx5/m9jcOdjrqsaP89JWepcdQ7K6CsuOnVQsGt+9uGltH3977LU556Q1f2WQ0OFw\nUFlZWVDQTRCXshTmoQT1nPL1Ewt3RSFEsmv3ehYcMb5Tsxp/fGI+0TWLKauzMrRJZs6ZuYO4ZbVW\nyk4HqMHvX82PN8g4ByNEdw3z9ytGa86qZWzq5A5g0ovi5IN8aum2tbUxffp0rr32WjZv3syRRx7J\nz3/+c91B8kIxZWsvCIgHQu+Lnkgk0mTrcDgoLy/P2Y9MHCdX8C0SieDz+YDRLhOZxv3Zi+9xj2sp\ncu34TCLpgzZ85XMIzRppq7JoyxuYl84Ys433g37+fuYphtUEIkjo8/mQZZmKiop0qTy956qEIKFA\nIFaY6sYAACAASURBVJCWBokWPqIzRiGlFIsJPfdYaJqFUkVdj0FYxsp6DGrfcS4kkruw27PP5ZFn\nZuM/chllTSN2kRQwtvIAcJVbmXWKHflwJzvlFRnPVV17QnyItGpP5FMacyIt3XwSIyRJYuPGjfzd\n3/0dGzduxOPxcNtttxVtfrkwpS1dceH1kIRoly58q8lk0pCkKp/gW6Z9nnp/G/+ZmEtT7ybsf7N8\nzN8Se/uJ9zoZOHkxALaPt1G+zDt2Ll1+vm5dQW31NF1zF0gmk+kOGIVWP1OeN4yUyhPthhKJxJgs\nNaUVpfSfTgWJl5aMTZKktBtGuKiUS3YtmdPYQduzHvOpv7TQv+hIyltGVkiR4QQWjw8w3h1hcG+M\nLbvnctaxp+g+VzF/l8ulO/13MktjKkk3nxTgpqYmmpqaWLVqpK7wxRdfXCJdo8hGupnapRutv5BP\n8E1rXpt37+HbHS5CdTOYs/9pzObRzDI5Hif5yj72XTLaBnrJzvcwX9I6ej6xBOfuquCY1cvx+Xy6\nzkF8cGRZxuv15mzil0tjrCwe5PV6CQaDYyxupQ9V3RNLj8RrIrXAxYCYc6boei4/cTbSfW5tE12z\nj6JizqhLamBjgkVnejPukwnRsMS7bzZhO6ySE6bra7muRiZJVy73hPJ+KlvrFAPKZzOfbLT6+nqa\nm5vZvn078+fP56WXXmLRokVFm18uTGnSzWbpqhs/qtulGw32KBMG1EV0sgXflMfoGxzmr98bYm/T\nUXh7diCvGetDSty/kc7LL097+hwffoh7edmYbRa+HuC6476sa87KD47D4SCRSOjqmpoJIuiYSo10\nA7bb7elrkgt6JV7q+g3i5T6U/YoCuv3EqTbN/V98tY62xtVULhj7PKUCGP4QybLMyw9X4716PrXv\n2PDO0k/aRu+nntoT4joYqU6W6/gw4l7IJwj2y1/+kquuuop4PM6cOXO4++67856LUUxp0hVQklum\nxo/Z9jGCQCCALMu6M77EMSRJ4hvPb2VTy0irnJnDW3Esm5XeLvnAu+z94nmYFC/sko5NmFeNWrmV\n6/v43rKLcrpV1Gm7Ho/HcKlJMXehDlGWg8yV9af32maTeIllu/CVp1IpTdfEVCPiYDBIWcX4QuWv\nvlnDJzXHUbNo7EdRllPEIsOAsSDPS/d4cF+1CJPZTGuyPq9557OP1v0Uq0GTSbtzh1HJntq9UF9v\n/PyWLVvGe++9Z3i/YuAzQ7qCGPQ2fjRCuqLQC5AOPOh5OJTbfPfxt3iu+VQxIGbHHqAWAPnpTexb\ncwpy+ahV69qwAeeRo19wS9swf192LFXlo0spLZeHMpNOeQ2MnK9SESICKIUoHIxA+eKK++p2u8dl\nKBnyoRYRhQaFdre/x8IjQiiVC+9uqGSL+yRqlo9viti7MczCM4y9puv+aMd24RIsdivRNj9rGvVJ\nqSYC4lpZrdaMKwB1HQat+5lJtuf3+5k/f/7knlSBmNKkq5QrxePxMR189e6bDcrluShhqEfpoD7G\n/6x9j/+tOBoOEGD97rewXT0SKEu+vZ3hpqVEG8d+rRf3fIT52BFdrhyIclF3PctXLtQ8jtq/XGja\nrrguot+UnvEmWp2Qrw9VWbHsUICU3InNNvr8bNxUxrupU5i2UrsLrdRrwbtSv0to/WMWpFOWYK8Y\nGW96j5sZi41ZghORWaiGEfcEMOaeKueYb4Wxg4kpTbqSJDE8PIzJNJIS7PXq91tlI121hlVYjLFY\nTHP7bMd44cPt/DA8C7l6NPJck9yN2T2XxK59xCLVDK0Ym03mfettHEeNaHdTqRTL3olx+QlnaI4v\ngmRgzL+cCeqeaXqCbgcLuXyoygAPjDSCFCR80JQTiiDa1o9dvBY6jdoTnBk3l0Jh9Co7P3hOJrB0\nGfb6UVdEqzQjyx6TA70knsvdJFxOMFJ34eKLL6aysjLdXXvp0qWUlZVlGn4MkskkK1eupKmpiaee\neiq/E8sTh44JkAdEl129y30ltEhIqbVNpVJpDWs+S3SAT7v28b0uD/7qptE5+/owzY4gBcPIHwTp\nOXZ8VHnR0HbMzSOkO/3Nfr676qJx2wjLLhaLFaXHmWi5EwqFcLlGEjGmUuUmgUz6UyCduCHq2Qr9\nqbIP2ITjQLeI7dvtvNB7GrUnjE96EfB3xaho1Zeeuv2NBAONS7DPGf24x/rDLLTPMqwnnghdbb4Q\nJGy1WscUc6qqquL222/H6XTS3t7OjTfeyIoVK3IPeAA///nPOfzwww/Kh3dKk67JNNLfKZ+gmHIf\n4QsdHh4mmUxSXl6e/npm2icXBn1+/m7DEJ31Y6UoLfvWYztjEalHPmbPF84ct1/5unVY14zob+2f\nDvLtGafgdo1aLqK+rN/vx2w26y5nKc5TDeV4Ih3SiAtlKkCcS7akB2Hhq5tQGkl60DeZDtrbrTy1\n50xmnJbdKgtsSzF7VW7Lbc/WOO3mRTiWVo/5vXeHieULl6YDvmJVFAqF0vGPfJId8kGxnyebzcaa\nNWuQJInf/OY3vPvuu2zfvl3Xvl1dXTz77LN87WtfOyhJO1PPlNFAvqQry3Ja4K8nYUDvcSRJ4utP\nbWRjq4pUUyk8pnb4Y5yOC/5K80FcGGzDMmMO8kCIK/xzWLC09cCu44NkY7pN6DjfsVPJHHQzcq4C\n8Xg8XXdYXNvJ8A3mi1xLWaWPWKmcEMGefNPOQ+E9vLTtDBq/kJtMk8HcapP+jhifdC/AdUbduL+1\nJusz+sKF31TLFy7+XYz7V2xSU88pEomk03f1zvUf/uEfuOOOO9KF/icbU5p0c0mnMkE8dOJhy+YL\nVR8vVypwPB7n+4+9zjMzx1uxFZ0fIjv87Dvpi+Aa78erenkttuNqSckyqz8w84Xjj0+PGQ6HNTPe\njECpMw6Hw0UJugkfWzQaTX+wRN3hUCg0pWReSiJWfnyVyglBwqIugRHlxAcfruXN0PHMvCh34CcR\nlUimhoDM5Bz2x3lv/Uy8lzSP+5sUSXC4rVVjr9EVohJqPbFIddZKdsjnHhbrnmt9CIwESp9++mlq\na2s54ogjePXVV4syJ6OY0qQLxmsvKEsYms1mysvLDasRtCCI7A9vbeGu6mPBMv7SVu15leGLTiI+\nXTt9d0GiE0vtHBpe7ePbq69JKxJMJpPujLdsc4cRayuVSun+0GSCUrsLI0E3IeMShWGcTucYze3B\nknkVCq2ouc1m062cEOf2Ytd+XCsz+3CV2L8hwZIveDL+XZJkXn18Ot6rtUt6mj+McNTCI3WfozIo\nmUwm052AsyWv6PmYToR/WClpNIq33nqLJ598kmeffZZoNIrf7+eaa67h3nvvLdocc2HKky7ol38p\nO/haLJaiFD9Xkvg7u/dyqzQPqXy8JVPx3AMkKpME52pbH9NeeA7L8TNwbO7jhpmnp9N2C2m7I6DU\nGWfqLKFGpmuqdEsIZYfP5yMajabHFEQsXlBBUmLJqlzC5yLig+Fz0wMjygmx7b4FM4jvaKVleW/O\n8VPDJqz2zBbc2vu9I8kPGe5jq1RfsFROr5og2z2cDBh5N2655RZuueUWANatW8dPfvKTSSVc+AyQ\nbi5LV52dJWov5BM8UB5HXdOhs3+QG3fbGJ6haokysI/Zz75CwhfBMXMuwQxjzzf3Yo7VcrGvlaq6\nMl3kKHynmaCUvgmdsd6gmxpqt0RZWVn6OrpcrnTGm5iPUAooLSBluyOxxFVa21pWozjuVLCIM2lP\nZVmmfW8XO1q82FyHM7S3narGzBZvKpUiGhwGtKVkr9zvwH7xEiw2bbdQSpaZLecvFctmnWoRsdhH\ny08s3hnRtaPQe6icmyRJBbeROhjP05QnXRhbF0FcxExaW/U+RqHMfBNZWsFQmK+/0c3u5mPHbFu7\n9knMn1YwFK0nOnMBybiFqufeIXr22LYgdU8/CSfXseZtOGHF8oIbQKZSYyufifGMBt6UKczKmgvK\nurLimiQSibQ6QJCx8keWZc10T+VHQ6lGEX8TZSLVy/dDvQeagCDil/vbSC2qJdY8nQ8enM4pV2T6\n/MLAx1Fmrtb+mL79iAX5jMXYvZn104ktAU5YkH9h+3yQyU8sKs4JqzhTURy9fmJ1CnAhxcdPPPFE\nTjzxxLz3zxefGdKFUR9Ptqi8ch81UWeDCJ4Ia1GMK8syf/v0Rt5pPi29raVzJy1r32dP8HQkUzmz\nap5nyNEIQMXbCaJnj44ryzKz7P20vl/Bt064Jt1uXO95q9OAlY0v1X5go1F3WZbTzT9FqyGxrITR\nokJm80jXDaXVYbVaxxxbWEJqItbKGlOOryZi8Xe9ftRDBZusIWA6JpOJffWLiEffxO7Ufv2inSbm\nnjW+1sKm5yC8cin22ux1GJpDNWmtdT4olh9W6ft1Op3psQv1EwvkW+zmYGPKk65SwSAsWz2pq3of\nKmWKrfBNCrE9wL89/TaPzDjwtZRlGp99BKlzNru5DCzQEHuA9opL0tvv8y/DtukTkstHUnobnnyM\n8gYX/zj3fGw2myHrW8saLYYfWCyJQ6EQTqeTioqK9IsijhmNRtPBMjUpZpqrESIWL6cI5qg/LpmI\nOFPt3oOJ3oF+ttWNpvkGjl/Mu4+s5/jLte+1FByf+bjt9QT9LStw6KgWNjt58LPQBNQEXqifWFkm\nslBL92BhypOuWEoLK89Ice5slp/aavR4POljCfzh9Q/4uWM5WG04d3xI4+s72B0+l5TlQAZUdDex\n+vlgGV0KBpzzmfvEevqWL0SWZRr8e/jmooupq54+JlnDyEchFAoRj8dzVgDTK3kTVb0EeQtfrDh/\nYe0XmkShJmIxfiwWS79ogki1Amx6iFiUUwTS/mi1NWUE+ViBL+zZhnTCKBGarFb2VSxBljeN+yCE\nBxI4qvwopWIdm+LstS/DcXhuqVl0h49VM75AMpnM2+KfbH21UT+xLMv87ne/o6enJ53YY7Rlz8HE\nlM5Ig1FXgtlsxu12G0pdzURCkiQRCAQIh8O4XC7KysrSlqPY/rWPd/IvQ/UknOU0P/oA7hfN7Ipd\nlCZcgFllGxjwrho3/nD/fFI9/TQ/9CfOa17K6nlL0/PRC0GQoltDRUVFXunQ6nOORqNpv20ikUhb\nHIlEIt0x1ev15h2Qy4REIkEwGCSZTOL1evF6vbjdbsrKyigvL09/AMRc1dlUSj+w0gVisVhwOEas\nTKfTmQ7wifPJJxXY6HlvtIxP5R08bhkbn4iP//1miQUn///tfXtYFPX+/2t22QUWELwRcfEG3kgB\nlYtaR1NT85aa1lEz8qTdfpWXOh67nbKnr6lpmWX1dMqjpzpdTdMULTW1VBZSERQVEAUBBRHisizL\n3ub3B+czzM7O7M7szips+3oeHx925/KZ2Zn35/15v1/v17vtGaouMaKwdgD808R1CQm/HowuoZ3R\n0tLCXB/RlXalc7a7cMeAk0lZrVYzJd1ktRkeHo7S0lIcOnQIkZGRiI2NRX5+vtNjlpWVYcyYMbjj\njjswaNAgvPfeey6NzR10eE83MDAQKpUKOp3OLTYCwN8Zl7s0omkal69W4elzZrRcv4pe3+eixPQg\noLDlvHY2HMTV7n/hPe8NTQpit25FVGMBnvzr07xjEnpQ2d4o8dbENtTjm2S4WrkkbqtSqRjjRgyR\nn5+fTVWWHEaXxIUdhSoc0bNIWMJsNjPeHdcj5lLY2MUPJOknFF9kx4hdud4/6uuQ39l+PypEg3JF\nApJhW7pKN9KMx9f4hwknT/dC0Iwo0eeLtUbaxE/tBNQFElnc5b5cE6rcXjN5FmbNmoWmpiZMnDgR\nCxcuRFFREXr27Ol0f5VKhQ0bNiApKQk6nQ7Dhg3D+PHjMXDgQNnG6Awd3uiSl8EVNgLZh0/0m+9B\noSgKTU16PPpTIUwnq0DVjkCJYqT9esFqRqcuzfjDXyC2RlGgsyqwZfNKSQ8kVwGsdTziBFG4oGlb\nrVxu3JZ4ukDrxEaMLVnmEQNHjCH5JyUs0tLSwkhycptjOoMYQ8yWBmRvxxee4Bpi7pKWbMM+nhhD\nvLf4DAyjonj7/lalJKDgSC76j25NelnMVrQYagEEw2y04tfd4QiZ30f0PWmpasLQzm3tn4TukbNE\nFgAmtt7eEpJsI97Y2IjY2FgolUoMGMAve8pFREQEI3oeHByMgQMH4urVqz6jKwXsRJorSyeyTBUj\nfA4Aj6z7EhU1Q3HF8hCjj8tFtOUblIY+yH8AqxU9tZ/isZmD0a1LV7uv+a6DFDcQTiyJpUrtBEGM\nCaGTEZU24u0RGAwGp3FbPgMnxhATz5OUDQcHB8uW6CJGBmgr0CAqcVyPmJ1oY0/azgwx8fzFdrPI\nUTaBomyFaBhEdsUl7QD0RykAoPpUC+6Y3Nrw8sCXIQh+WJoKVuglJfoOinN6jxwlsshzQHoIulvG\nTZJhcoFtdOvq6txKpJWUlCAnJwdpaa71j3MVHd7oEkgxusTLIuRqsfoDT//jU/x+7WEY/GLA67oA\n8NMXoTlyAKDkKbE16tD72HZEhcRh6dKRTq9DqLCDb1sxoGmaqcIjKmpsvi2RilSpVE6NoVhPk22I\n2ROF1Pi72OsTmjDEhCbEGGJyLMI0Icfiy7gbDAbkhVjgCFcH3oGr584hMj4I5moKgakqHPoiAP4P\nDoZCKc1Y9XaRtcA2xGSFExQUZBOaaA9l3NzfobGx0WUBc51Oh9mzZ2Pjxo2SdLjlQIc3umxP11kS\nhF1VpVAomG61YgxuXl4pDu9TwjDEXlyEjR6dcnAp2N7LpRpK0VN7AlcKpmLD91ccPqSksKO5uVkU\n19gZSKzaYrHA398fgYGBzMtEDCEp4+XybaVAyBCT2DCbcka6XLgSmuBCqvfsbNnN/ge0aS+wqxjZ\nKwMAjIFnG+KMCznQj+0hND8DAMwDY5D/bS9ExlfDqNPh+LeBoCcNgkojTRfDpGtBvL/4UIQQ2J4k\nH91OiFEgVLTiCSYEOZ6rPF2TyYRZs2Zh/vz5mDFjhvMdZEaHN7oE5KUQAqF/salQ5G9nsFqtePHF\nIugaezncrrPhZ1TEjLL7PLA6D920VSgpnoXp03/Dvfem8u5PXtimpiZm6e+ON8iN25IkFaFgke+l\n8G2lnp9IPhJ+MzuOLjU0wQcyoZDf1dX7xfb2uCW8xHsm27AVxshnfBN+rtoASsTS+mqPgSg7cRE1\ntUYop6ZC1VVaYYNRb4Tp1xok3zVE0n6ugDAK2GAn7LiGmEzsANyaWMl52PvX19ejc+fOko+xcOFC\nxMfHY+nSpS6PxR14jdEV8vqE4qGO9uHivfeO4+DBRASHnAfMesCPhy1gNaJTVzP+8LftRxVa9hsC\ntWqUVYxHUFAFli/vznsOdnEDoce4es3E2LHlIMnnLS0tjFdL0zRUKhUjACSnwSWC2XzVaq6EJriG\n2FEoQS4Qg65QtGots4s2+DxidmjCbDYjT2NPCeNDc9oA7F36PbrfEQnLr5WgaQ1ABcKKQNCKQFgo\nf5ipAJigholSw0SpYKTUMFBqGBR+aFH5Y2pFgSzX70pehP178k1Y5HkUw5yQAlc83WPHjuGLL75A\nQkIChgxpnaRWr16Ne++916UxuIIOb3SFDKizeCjZx1lIoqjoKjZsCAKggr6pK9B0EQhNsNuuh/U7\nlIb+1eaz2y7uhfF4D1TWtnaPePDBYiQn2wbtuTQ1djJILNgeAJvhQJbZ5BqJYSK8ZsJZJboKXOPm\nSqyO3HcyyYn1nqUYYvJbk/JSd1XY+K7BYDAwinTsa+DziMk+bCO89+wJNI7u6TC0wOx7pBDVluHI\nGfEUEBwimKAVgubqFTzjQEBHKuS4l+zn2N/f327CcoWix/V0zWazZHnSu+66SxQX25Po8EYXsFUa\n46NCCc2kzjxdmqbx0kvnUFWVDACwWrsgUJ+DZo7RVTVfgD5qEKBou53R+d+hLjMNOl2r6lj37hex\nfHlPm2PztTeXwkhgP4DEeBNDQfReiXdBvqcoCsHBwXaGnWvc2Nlroq3qTDfVHQqY0PWxDTFbopK8\nbFzOsjsxYnY4RK1WM8wOMSBGg4zrbIAJlIhQh+VYEarz+0PdJxro5FomfnzNFcSlyEN58mTxhBjm\nBF+3DvLbskMVZJztjdImBl5hdAmsVivq6upEtw13ZnQ3b87Gjz+ye5wFIsCiA1erq0dYHoo1D5JB\noOep/+Jq9mSYjG2UsIcfvoo+fdIY40QUwLjjdIX6Row3CUuw+bbEuDvzPLlGo/VS2gyx0Wi0WUaz\nvWGSKJObAkbADiXwebZyxIhJOMTdZCLQOjnkqJzzp82/X0bNyV6o7DkcXS7+Blitkr1cNDdhZkCb\nVoa7Zc6AvIbMWSKNbYiFunWwmRMAcPr0aeTk5EClUjF0z44ErzC6pLsrTdPo1KmTZO0FPly5Uok1\naygAtss2f8r2peja8hPKut/d+oe5Bb0zv8blkw8AaIvJ9ux5GsuXD2SW/hTF3wnC2ZjYIF4Z0PqS\nk7gtH9/WVc/TmSEmjASgLZ5J/pbK5xS6RuJ1O6KxuRMjpiiKoQ/KFar4JT8HN4bEOKyxN+deQf3x\n23GtV2vVYmNIJFByEejTT9K5hhXlYvLwQUwugCzdPRFDlQp3vGa+cZJSZr1ej99++w15eXkICwvD\ngAEDsGzZMjz88MNOj7tv3z4sXboUFosFixYtwooVK1weo6vwCqNrsVig0Wig0+kkeSh8Bo54hitW\n5KC83F6TVE2zXkizAUFdadT4hwP66+h9/CAun50PgD0GK9LTb8DPLxpNTU2ydIJgG2+KohAQEGAT\npyIUME94nuRYRKeAsB6IgRPyiLnyjc5ArgGAS56nM0NMvCd2iTNZIbibVMyy1ELBSaiyYTpXjsZf\nOqOsz91tn3XriZD879EoxejSNKYpWpjJhFDaSDgIcFzmzKV3eZriJQeUSiVGjhyJpKQkzJ8/Hzt3\n7kReXh5CQkQ0+rRY8Mwzz+DAgQOIiopCSkoK7rvvvptajQZ4idHVaDQuBcfZRpe97P/hh3PYuXMw\n7z5+dNtL3IP6Hlc6zYGq9gIitZdwuXCu3faDBmmxcGFfxlNz9gA68nS5TAyVSoWGhgZGPYuiKBiN\nRlmWyHzgUsDYBp2buWZn+KUYYlL1JRRKcAfs5A77PhHDJEeJs9VqxUkegRsC08VraNqrwZW48bZf\nKP0QYgIaJVxPVGEeHurfh7k29v/s94HPEHNLutmxVjI5ubtakduA81WjaTQaDB8+3MmercjOzkZc\nXBx69eoFAJgzZw527tzpM7qugP3AkQ4FYvcjSzFSMNHSYsbbb1OwWvmrVBSW1nOpm/PRFDUYwVUn\nEZZlRGnJZJ6tW/DYYwYEBQUxIiRix8QGyaaTuC2RmbRYLAgKCrIRpmHTqVz1MvkgJeYpxHl1ZoiJ\nNyY1iSUWjmLD7tDX2Pg1/zSqBvNrLZhLq6HfoUBJP75nBQikpL2OU0z1uO22fnYUNq6wO58hJtfM\nNcQkdsotc3bEKrgVcIUuVlFRgZiYtuKm6OhoZGVlyT00p/AKo0tAaCliQV56vV7PLPv/8Y8TuHhx\nqPBO5tYHLibsHOqvd0GgthvKK/mLHUaNysKCBclM7FUq+JJu7HEDttoRRBVNTAJMrCF2RJ+SAkeG\n2Gg02iRKSAZbrklDroo1R4aYUPOO6K6CCuphd0xzZS2avzbg8oAH7L4jUFD+gt9xEVhZjsdio5kx\nOhOHJ2N1ZojJb0SSUySZ5YhV4IjRIrenS363uro6ySXA7WGyALzE6EotdmBzYwGgU6dOUCgU2L07\nD//9b2+H+9ImBboZ9qCpVg/jyaFoqI/l3c7P7w8891wnyRMBuQZ23JbLtwUcx225CTCul8kuyeWj\nhJF92BQwT3qe7CQWwJ+sc3W5L2fFmpAhJiEXmqaRpzbY7WuubUDzv+tQHG8ffmKDpsVzTsfXXEH8\n4GTBsfJ16XAmhUm+I8L1xGhSFMVwvNkx4pvdCZhtxF3xdKOiolBWVsb8XVZWhujoaFnHKAZeYXQJ\nnBldvmV6XV0dAKCxUYeVK+thMtl7KWyYW6xQXNSivvRpNDcLJ0umTj2Le+9NlSwcTQyuGL6tWCMi\n5GWyX0KDwcC8hOQ8SqXypsSGuQbd3Wo1sg+ZNDxVsUbOYTabodFokFNciMrBkTbbmHV6NH9QgeLB\nCwAn52+hRVKfDM2Y00laUYCzSYO9GmMn5Mi+ZFv28fgMMVldcQt25BDGYb9HrrTqSU5ORlFREUpK\nShAZGYlvvvkGX331lcvjcRV/CqPLXqZzBWTIPq+99jvOnk1ycoZm6Bt+Qc2NtbBahduDcMt9xRhd\nMiGQarFOnTrZ8G0BMEk0ORJMfC8hidtarVYmm6/T6WQpPOCeQ0qyT+py/2ZMGmwqG5k0juorgbC2\n391qMKBlYwmKB//NqcEFAB3Uori6Q4tycd8YeXQWjEYjUw3Jt9Ig/8hvwGU6cMMTKpUKarUaNE0z\n3jRXj4GPOSEWZNv6+np07WovjeoIfn5+2LRpEyZOnAiLxYKFCxfe9CQa4CVGVyi8wF6mK5VKXm4s\nRVE4ePA8tm6NhqBeIwC1+jwiIzMAxKHagcEFWst9hw1LsxmbELgTgkajYdqrkAdS7kovLtiMAa5X\nKESzIi8OCUs4e3nYsWFPTRpkFeDJSYOcA7CnsrW25Wk1ulaTCYb1BSi64zFRBhcAGjrFABfOAvH2\nZeYMaBr3qy1uPwNk8lMqlXbhKWcTnJAUJgmlEUNM/ue2uhIyxNyEnf2l2wqY9+7tOBTIh0mTJmHS\npEnON/QgvMLoErB/WG6XBaEabaPRiJUrr0OvF06edev2E/z8LqCkpBtiYx0L0XTvXoQVK3rxjokL\nvrgtUbBiK6ApFAr4+/tLrjN3BkcUMPb4yUtIkivs+DCbOSGUqHO1tFbKdbAnJnabJTmq1bjn4AtX\nnL18EZdiw0Dhf5PYW2dQGP+4pAozS+cohBYeRb0Do3v7xbN4NEFclwSh6yAMDrZ36whiVhrsqa2b\nbQAAIABJREFU/nJs40u8Xq5HTFo/kWecPbELGWK20XVFYay9wCuMLtvTtVgsaGxsZLiszmJ5b711\nCqdO8bMPACt69Pg3amuN0OlaM6UKRZDAtq1IT7+GXr3aRG34jC4f35bEbZXK1kaKRPuA24wRcK/o\ngMCdslehRA2fISbbq9Vq2ScN9nUoFAqnkwZ7rCQRRGKQbO+da4hJKIHPKyQ4/McVUHd0a42RrjmF\ngv6PA0qJr5dSiSCLAvUONpmsrwXoCDQ2Nkr23om8KV8cXSqE7qvRaLQRVCLJaj6PmM3CAfgNMVmF\nkWdJr9fjk08+QU1NTbthI0iFVxhdAAythSSgxBQiZGUVY+vWGPCHFWrRu/cWXL7cCUCboaVpYaPb\nq1cu/v53/hgRYRBwe7Fx47ZEtEZoCc6lg5FuwEIsBL77JOcyn4BtiMk5rFYr04mXnWDhG6vUMXCp\nbFIMupDBYMcw2WW0NE1DrVY7nMBPKnSwWrvAtO4kLvRdBKhc0wMIVAjvF3j9KhbFRqJTp06SvHdy\nr0jlptwdOwDYnCMoKIg5B5c5Q/4BbYaYPYlxDTF5TtgeellZGTIzM7Ft2zaEh4dj/Pjx+Pjjj0WP\ndfny5di9ezfUajViY2OxZcsWt9r+SIVXGF2r1Yr6+nrmpQ8MdC5zZzab8dJLpWhstA8rBAWdQJcu\nR3D5cldwDbLFIlTkYMWiRfXo3Nl26UdeUpIkU6vVgnxbMfQsPjqYEAuB6w2TLLUnl/nsUEKnTp2c\nThpSOcTcc8h1HexJg+2xkYmBrE74wiiXrpajqGcwzBtO4kLvRwG16zKLSggb3XHVJUi4u5UmJjax\nSCYNpVLJtKCXG2wPmq+llLNCGbLiINfFLcIg1wW0hgrXrl2LBx98EMeOHUNNTQ0qKiokjXfChAlY\nu3YtFAoFXnjhBaxevRpr1qyR41aIglcYXaVSidDQUJskhzO89dZxHDuWaPf5bbdth9lcjrKybrz7\nGY38BPaEhGwsXmyfUSZUHJPJxBgIOXUSnMXbyFKfLNlUKhXD+XWXwsMGWYIrFPai5Wy4qmamVCoZ\nrV5XQiJiwX6G+CQw+cIoGWXnYMgtR2HU30D7Ow4/OT2/kNFtacFfQ4S9ee5zYLVamUmCxOJbWlqY\nyks5EouuetB8hpgcj+sRkzguTdM4ceIEwsPDkZeXh/z8fPj7+6N///7o37+/pHGPH99Wgp2Wlobv\nv/9e0v7uwiuMLgDmpRRDzzpz5go++CAMtsI0ZvTo8RGqqlRoaRFeahgMfJ5uC555hraRmCOxRuJt\nEO+bzbclgi5yL/nICwiAaTNDBNLFJL+kvIDEELLj01LhqJiD3V+NbEu8UTkrnhyVCLPBF8/edeA8\nLiY8DUugY1aLGAhxdZMKczDjbmeURvuVADupSL6XI7HoyLt1FdznwGw2o6mpifnNd+zYgZ9++gnV\n1dVISUnBq6++ildffdWthNq///1vzJ3ruGhFbniN0QXEVaRZrVa8+GIhamraqnkUijLExHyJ0tLu\nsDXEXOig19u/WKNHZ+Phh1OY45O4bWBgIIKCgtDQ0MC0PCfLfLn4tnxgGxBupt1R8kuKcDmXMSAn\nlY2cj/yeJpOJ4X8SgyEURnHFayMGxJXVRn5+GUozmhB+IwMVE2cBanEaG0LQUQGAyQSwJy+axgyV\n2em4HNHZCKRynrn3luQlrFarx+LD7OeXnGPPnj04c+YMtmzZgmHDhiEnJwcnT54UbGs1fvx4VFZW\n2n3+5ptvYtq0aQCAVatWQa1WY968ebJfgyNQtJRyqXYMkkRzRiXZuPEoVqzoB/xvGRcaehhBQadw\n9apzorVSWQ6L5Z8gXEygtdz3++9LMGHCQBu+LRG4YQsxE14i0Oaxueph8oFL2idtUqSAb4nXeu22\nL15LSwsUCgUCAwM9UvLJNiCkhxsXXGNB/ok1xGSCtFqtjK6EVPzjH7/jx8zruBI4E1GaX0HFXEP5\nPdMBjWttvak/roHqfBnWpDZGTcTFfJyIvw2dQ/k9abZ3K1f1ndC9BcB4o86Stq6AzR8ODAxEQ0MD\n/vGPf0ChUODdd9+VjSa2detWfPLJJzh48KBoMSq54JWertCys7XfmQbE4EZFfQGdrk6UwQUAjcaK\nxsYuNp9NmXIGY8YMQX19PZRKJW/clpRa+vn52UkJcpf6bEMsJasvV+cDZ0t9wh9ml3i6ExfkQuwy\nH5Cmmcsu5iB8aHe99KYmPXbtCoK6uxKg/FDRPBYosOL2K79CFX0VV+6ZDARLE2WhwyLQ6eIB1LOM\n7jRTHcI6xfFuTxJ8QpQ5V8G+t+xYOjFQcq82uPxhPz8/HD58GCtXrsRLL72EGTNmyGbc9+3bh3Xr\n1uHIkSM33eACXmh0hWC1WvHCC2dRWZkKQI9evT5GeXkQzGbn4scEGk0wGhvbXvCgoAo8/XSQjUoZ\nqUF3FrflxgXFJJP4FL48RQEjIMciy05CnWKHJtzVoAWkK4E5Gi85N18xB1kRAW0kfjJxSF1tbNmS\nj7KyEejX9SprAApcM9wNFNEILz2KwJgylI4bD4Tyd4HmuQCEKNUMV9e/uhKzOwfa8XJJmMoTusME\n7N9EaHJyxJrgruSEfk8u17q1icAK1NTUICMjA927i7x3IvHss8/CaDQyCbURI0bgww8/lPUcjuA1\nRpddIMH1dM1mMz7++Cj27BkEf//zuP32DJSUdAEcNlSxR0CArYGePv0cUlNTbWrNxfJtuRCTTGJn\nngkDgcRtPUUBc1Yuyt6WO3GILRcmoQR3lcCEQAwxMQjEk+IyPKQkFmmaxo4dCgAUaAvPqoKicN30\nF6CYRni5Fpqo/Si5ezTQNcrpeP1ZDIax1y/hrruTeZXXgLYEstlsdpnzzAd26MXRbyIlRszlk7Np\njKQDSVZWFl588UUsWbIE8+bN80gBRFFRkezHlAKvMboE7GQaeZlLSyuxcaMG3br9Cj+/ApSU8NPB\nnMHPry1O17VrAV5+OY7xbgnkkkMU4jeSh5hUpwGtS3x2AkyO+DDx0sUmTJwVHPAZNiInSLw1TymB\nkYmD60GTuDp3vCT+zk4scsM++/efQ1ZWa9NSq8nBvaEoXDeOAC4NR7fyEwiJ+g0ldw0HHdFLcBcl\n/pdEMxrxQJCSGStFUUyZLJk43OE8C90vZ96tM4gxxMSgA8BXX32F2tpaXLp0CTU1NdixYweiopxP\nTh0VXmN0uaXALS0tTGJh7drLoKhcNDcb0dQkLcZme4420vtDD5WjR4805sHxZF8yAnZJJAlniNFB\nIGEJMS+PnJKIQuXCbKNGwJ045PDYxHprjsYrFPb5/PNG0HTryqelWcRvTVG4YUrBjZIUdC3PQWhU\nFkpHDIEl2r4nmgWtXPCEwhw8MLqVSy7EsHBUdCDVELPvl9w8aGKIyQqNpmmmWCMwMBBarRZlZWW4\ndu0a7rrrLnz77bdISUmR7fztCV5jdIE2CcWmpiaoVCqEhoZi8+ZfkJ19EKWl3cAu53UFFNW6f8+e\np/DkkzHMcp+QuG8GhYZrCIUMG9djAxy/eI48QrmvhYQeSLmou1VqfOeQi87GF/a5dOka9u9vE782\n6KUZpxrzENSUDkFY+Rl0jfoOV1IHwtRrUNvx/idmPlPdGnvW6/Wiyp3FVH/xCdiTEAXh9npCyQ6w\nLzyxWCxYt24dtFot/vWvf6FPnz6wWq0oKipCZGSkk6N1XHiN0TWbzWhoaGDq/Ql/b9u2H2EwSNPd\nFILVGgjAiscea0BUVBxjCElCRq/X2yxD3c3ou5pccuaxsV884gWTBKAnJw4hQ+gons03Xkf315kA\njrugKApbt1agsXEk85mhWQOYdYCfNJpYnWUw6q4MRmjFeXS7fRvKU/uhpU8CGhVB6H7+FNIH9oJO\np3NLoEbIEHMZHiQPQiY+uRkpXErbhQsXsGzZMsycORP79u1jvGqFQiGpwsxisSA5ORnR0dH48ccf\n7b5fvHgx9u7dC41Gg61bt2LIEHl0iN2B1xhdwhklOrQEP/20ESaTCceOncbp01eRn1+D/PwaFBQ0\no6mpExxp6HJhsQQiISELixYNhF6vh1qtZihgjgjmrvBx3W1BzgWfYWPTfsg1kKQZO9nh7ovHLhEW\nYwidGQo+xgShgbFLUj0RH9br9fjhB1tvs6npdlCGc6CDhdTqHKPeMhD15QMRcrUIMRHbUd4vGMMb\n8hA05GGX+cOOQO4tMbqeYqQAbeXIQOtzDADvv/8+9u7di48//thtEfGNGzciPj4ejY32fZQzMjJw\n8eJFFBUVISsrC0899RS0Wq1b55MDXmN0CUWIrz2OSqXC3Xen4O672z6rqanFL7/kID+/Brm5VSgs\nrMfly0pYrcJ6uQYDjaVLW8sSueIhriSS+Cq+PE0BI+Nie9AajcZGbo/LQBCb0efCHSUwLhzdX+JF\nkTGxhWrkSiySeOfWradx6dIom+9oOhwhliw0wjWjS9Bo7YvGq33RLe+fmPXiINnKa7lwFLsVw0IQ\nY4jZzxjxbi9fvozFixdj7NixOHDggNtSn+Xl5cjIyMDLL7+Md955x+77Xbt24ZFHHgHQqrFQV1eH\nqqoq3HbbbW6d1114jdHlUsacoWvXLnjggXF44AEwfdIuXCjG6dNXceFCHfLza3D+fD1u3AhG622y\nokuXTCxY8HfRD4uUxAx52Inn4QkKGOCYnuUoPkxeOrHxYU8LlwNtRp2maSY+LCaxKMUQc68lI8Mf\n9lRDP2iUNOx9LYkw69GjfjPu6BOD6RPvZjR85Zo4pDITXC0ZpiiKEXoiK8HNmzfj66+/xgcffCDb\nEn/ZsmVYt24dGhoaeL/na7leXl7uM7pyg1sN5ghsJSZ/f3+kpg5BSkoSU9xgMBjwyy/ZyM2tQn5+\nNe6++w63Z2e+ZT55qcn3RCdXzmW+o2ScI7ANMdHGdTRxEFqTu5Vxzq5FiGEhNrFI0zRvfJh9T9iJ\nn6CgIGi1xTh6lD/e6K9wzyD6G3Jw2x+n8Mf1JLy2pSsCAwNlmziANu+WTFCu/i6ODDG5v+R5eOON\nN1BdXY3i4mIMGjQIGRkZktumC2H37t0IDw/HkCFDcPjwYcHtuA6YJyZ/qfAaoyvF0yUGiCx9iFHj\n8m1NJhPGjk3F5MkBHvM6CReWvfwWKmV15aWTq9KLDUfxYdJuiExo7sQD+eBKokzqioNk87n84S++\nqIfZfAfvOVQOhZIco3vTdlBXVbhSNQoLFhRg8OBhAByLE4k1xM5Ux+QAmaxIaC84uDWh2KdPH5SU\nlCAmJgb5+fmIjIzEoUOHkJaW5uSIznH8+HHs2rULGRkZMBgMaGhoQHp6Oj777DNmG27L9fLy8nbB\n//Uao0vgyNMlDyBJFpFlL0kgsRMMSqXyllDAyDWQl0iolFXMMp/tqXnyWtgiO3yJRXcnDkDe+DAg\nzJjgxocJc6K6uh67dwuzYJS0C/fWakbPhk9RdTERBkM3hIVdw5Il9rxdQHjiYHuY3GIO7jLfE6sO\noI1DTEIW1dXVeO655xAdHY1t27YxTCISLnEGg8GA0aNHM6uZ6dOnY/Xq1TbbTJgwAR988AH69OkD\nnU6H0NBQG4MLAPfddx82bdqEOXPmQKvVIiws7JaHFgAvM7rEaPJ5umazGXq93iaWSR5a4u2yO8la\nrVY0NTW5XGTAB3e8TmfLfC7/khhpT1V6AY6lBJ1NHGKFfrhG3VPxYTIRms1mm8ITco+3br2M2trR\nwgcwSzNoypZixNQfQEnhKOB/FWizZzegX79kxzuyQCYOriEmRphoTJBQmSucZ0fgipgrlUrs2rUL\n77zzDtasWYOxY8fa/FZixWUCAgJw6NAhaDQamM1m3HXXXTh69Cjuuusum+1Gjx6NXbt24ciRI3j7\n7bcBgGnb88QTT2Dy5MnIyMhAXFwcgoKCsGXLFrevWQ54ldEF7MMLZJlLtDnZVVzkgSA6CXztx515\nl2KpSWwKmFxeJ9dbI2pmRHZRoVAw7dzlzOZLUQJjQ+oyn9DAAM95ao6MOpk4AGDPHscteMxG8Uas\nS/N+BFQ1oKR8bNtnXcqwdKl79CkC4t2SSd2dKjUhcEXM6+rqsHz5cgQEBODAgQN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       "text": [
        "<matplotlib.figure.Figure at 0xad401bac>"
       ]
      }
     ],
     "prompt_number": 9
    }
   ],
   "metadata": {}
  }
 ]
}