{ "metadata": { "name": "special_functions" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import scipy.special\n", "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Special functions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def legendre(z, l, u):\n", " return (-1)**u * scipy.special.gamma(l + u + 1) / \\\n", " scipy.special.gamma(l - u + 1) * ((1 - z) / (1 + z)) ** (u/2.) * \\\n", " scipy.special.hyp2f1(-l, l + 1, u + 1, (1 - z) / 2.)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.pyplot as plt\n", "zz = np.linspace(-1, 1, 1000)\n", "for i in range(1, 5):\n", " plt.plot(zz, legendre(zz, i, 0), label=str(i))\n", "plt.legend()\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:3: RuntimeWarning: divide by zero encountered in divide\n" ] }, { "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD9CAYAAAC7iRw+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4FFX3B/DvJgRSSQLpoaQACZAQQhUQCQjSi4oURVBB\nECnqqy8/CwIiIiBYkaYgIkiVJiVSA6RASCAFQgohCSmk957dPb8/xvBS0nZ3Zmd2cz/Pk0eTzM49\nWZKzZ+/cOVdGRASGYRim2TAQOwCGYRhGu1jiZxiGaWZY4mcYhmlmWOJnGIZpZljiZxiGaWZY4mcY\nhmlmNEr8b731Fuzt7eHt7V3vMYsXL0bnzp3h4+ODmzdvajIcwzAMwwONEv+bb74Jf3//er9/6tQp\n3L17FwkJCdi2bRvmz5+vyXAMwzAMDzRK/IMHD4a1tXW93z9+/DhmzZoFAOjfvz8KCwuRlZWlyZAM\nwzCMhgSd409PT0f79u0fft6uXTukpaUJOSTDMAzTiBZCD/BkRwiZTFbncfV9nWEYhmmYqp13BK34\nnZ2dkZqa+vDztLQ0ODs713t8QFIAiIh9aPixfPly0WPQpw/2fLLnUyofBw8SHBwICz/Kx6x3noXf\nvj/Vys2CJv4JEyZg165dAICrV6/CysoK9vb29R6/LGAZiFjPOIZhmEfl5ABTpwJLlwKHDwNWY76F\nY4vO8Gprq9b5NEr806dPx8CBAxEXF4f27dtjx44d2Lp1K7Zu3QoAGDNmDNzc3NCpUyfMmzcPmzZt\navB8maWZuJB0QZOQGIZh9MqhQ0CPHkCHDsDNm4BHz3zsCP4ZBSZt4eHqqtY5NZrj37t3b6PHbNy4\nscnnW/rccnx+8XMMcx3G5vw14OfnJ3YIeoU9n/xiz2fT5OQACxcCkZFclT9gAPf1VRc24EMagL89\nu+LlBlZVNkRSd+72dZ+Aoqoi/JP4j9ih6DT2h8Uv9nzyiz2fjXuyyq9N+rnludgStgVvFbohztkZ\nnqamap1fRhKZVJfJZDiek4PKrItYF7wOoXNCWdXPMIzG2rRpg4KCArHD0Ji1tTXe2vcWymvKsWb9\nHTgtW4ZiPz8YGhiofG1UUhV/bHk5Xu72MqoV1TgRf0LscBiG0QMFBQWir8bh46OgoAA7bu7A577v\nI76gAJ3NzGCgZnEsucRvIDPAF35fYFnAMihJKXZIDMMwkvGW71twjLiL2CFD4GlurvZ5JJf4AWCi\nx0QYyAxwNPaoyBExDMNIx8fPfgxcuIC43r3hoeb8PiCxxH+nvBxEBJlMhpV+K7E8YDmr+hmGYf5l\nY2oDXLyIuI4d4WFiovZ5JJX4CUBuTQ0AYEznMTAzMsOB2wfEDYphGEYAGzduRJ8+fWBsbIw333yz\naQ/KzwcSEhBjbIxuZmZqjy2pxO9pavpwukcmk+HLoV9i2cVlqFHUiBwZwzAMv5ydnfH555/jrbfe\navqDLl2C/NlnkVhVhS76UvE/mvgBYLjbcLS3bI+dETvFC4phGEYAL774IiZOnIi2bds2/UEXLiBx\n9Gg4t2oFE0NDtceWdOKXyWT4+vmv8cWlL1BRUyFiZAzDMMJQaQ3+uXOI6dcP3TS4sAtIPPEDQD/n\nfujn3A8/X/9ZpKgYhmGEo9KNqrm5iLG3R1d9T/wAsGrYKqwLWofCykIRomIYRp/JZPx8qEulin/4\ncNypqNDowi4gscTvZmyM9OpqVCofX8LZzbYbxnUZh/XB60WKjGEYfUXEz4e6VKr4X3gBMWVl+jXV\nY2RgAFdjY8TXUfWv8FuBzWGbkVmaKUJkDMMw/FIoFKisrIRcLodCoUBVVRUUCkXDjxk+HLHl5Wo3\nZ6slqcQPAN1MTXGnjsTfwbIDZvrMxFdXvhIhKoZhGH59+eWXMDU1xdq1a7F7926YmJjgq68azm8p\nNjawMTKCRQvNds2VVHdOIsKypCQQgC/r2GAgpywHnj974vrb1+Fm7ab9IBmG0Tm1uUXXyWQy/J2b\ni43p6fDv0eOxr+t0d04A8DIzw+2ysjq/Z2tmi8X9FmN5wHItR8UwDCO+OzzM7wMSTPzdzcxwq57E\nDwD/GfAfnE08i+isaC1GxTAMI76Y8nKNl3ICEkz8nU1MkFpVhYp6LnJYtLLAx89+jE8vfKrlyBiG\nYcQVU1am8VJOQIKJv6WBAdxNTOpcz19rfp/5iM6KxuWUy1qMjGEYRlx39LXiB/6d528g8bdq0Qqr\nn1+Nj858xNo2MwzTbJgaGqKNkZHG55Fk4u9uatrgPD8ATPOaBgJh/639WoqKYRhGXHxc2AUkmvgb\nWtlTy0BmgPUj1uPTC5+iUl6ppcgYhmHE052H+X1Aoom/sZU9tYa4DEEP+x7YGLpRC1ExDMOIy1uf\nE7+7iQmyqqtR2sjtywCwdvharA1ai7zyPC1ExjAMIx69TvyGMhk8TE0R04Sq39PGE690ewWrrqzS\nQmQMwzD8qK6uxuzZs+Hi4oLWrVvD19cX/v7+DT7GS58TP8D9gE2Z7gGA5UOW44/IP5CYnyhwVAzD\nMPyQy+Xo0KEDLl++jOLiYqxatQpTpkxBSkpKvY/RtEdPLckm/u5NuMBby97cHu8/8z4+Of+JwFEx\nDMPww9TUFMuXL0eHDh0AAGPHjoWrqytu3Lgh+NiSTfyqVPwA18ohODUYV9OuChgVwzCMMLKyshAf\nH4/u3bsLPpZkE393U9MGb+J6kqmRKb4c+iU+OvORXnTiYxim+aipqcFrr72GN954A126dBF8PMm1\nZa6lJELrwECkDRgAqybOaymUCvTa1gufP/c5JnebLFSoDMPokMbaFsu+0GDfxEfQcvVSqVKpxKuv\nvorS0lIcO3YMhoaGdR5X38+hTltmfq4UCMBAJkO3f+/gfdbSskmPMTQwxHcjv8Ps47Mxrss4GLcw\nFjhKhmGkKicHWLiw8ePUTdh8ICLMnj0bOTk5OHXqVL1Jn2+SneoBgB7m5ogqLVXpMcNch6GnQ098\nG/KtQFExDCN1hw4BPXoA/143laz58+cjNjYWx48fR6tWrbQ2rmSnegBgY3o6okpLsc3DQ6VzJeYn\nov+v/RE1PwpOFk58hskwjITVVvmRkcBvvwEDBkh3B66UlBS4urrC2Nj4sUp/27ZtmD59+lPH8znV\nI+mK38fMDJEqVvwA4N7GHXN6zcGn51nPfoZpLh6t8m/e5JK+lHXs2BFKpRLl5eUoKSl5+FFX0ueb\nZOf4AW6q51ZZGRREMJSpdgHms8GfwWOjB0LTQ9HPuZ9AETIMI7ZHq/zDh6Wf8KVA0hW/ZYsWsG/Z\nEgkVFSo/1qKVBb4a9hXe839Pkm/zGIbRnK5V+VIh6cQPAD7m5mpN9wDArJ6zUKOowZ/Rf/IcFcMw\nYsrJAaZOBZYu5ar8b74BTEzEjkp36HXiN5AZ4IdRP+Dj8x+jrLrpdwEzDCNdrMrXnOQTf08NEj8A\nDOowCM92eBZrg9byGBXDMNrGqnz+SD7x+5iZIUKDxA9wPft/vv4zUgrr73rHMIx0sSqfX5JP/C7G\nxihVKJBbU6P2OTpYdsDifovxnzP/4TEyhmGExqp8YUg+8ctkMo3m+WstGbQEEZkR+OfuPzxFxjCM\nkFiVLxzJJ36Au8Cr6XSPiZEJfhz1IxadXoQqeRVPkTEMwzdW5QtPZxK/phU/AIztMhZdbbtiQ8gG\nHqJiGIZvza3KnzFjBhwdHdG6dWu4ubnhq6++0sq4ku7VU+t6cTHmxMUhsm9fjcdJKkhCn1/64Mbc\nG+ho1VHj8zEMo7m6euzwRaq9egDg9u3bcHd3h7GxMeLi4jBkyBDs3LkTo0aNeupYSfXq8ff3h6en\nJzp37oy1a59eMhkQEABLS0v4+vrC19cXq1apvim6l5kZEioqUKlUahouXK1d8X7/9/HBPx9ofC6G\nYTTX3Kr8R3Xv3h3Gxv9rH9+iRQvY2dkJPzBpQC6Xk7u7OyUlJVF1dTX5+PhQTEzMY8dcvHiRxo8f\n3+i5GgulR2goXSsq0iTchypqKsj9B3c6FX+Kl/MxDKO67GyiKVOIPDyIgoOFG0fDNCe4+fPnk6mp\nKRkaGtLmzZvrPa6+n0Odn0+jij80NBSdOnWCi4sLjIyMMG3aNBw7dqyuFxdNhgEA9LawQHhJicbn\nAQDjFsb4afRPWOy/GJXySl7OyTBM0zXnKv9JmzZtQmlpKc6dO4elS5ciNDRU8DE1Svzp6elo3779\nw8/btWuH9PT0x46RyWQIDg6Gj48PxowZg5iYGLXG6mNhgXAeLvDWGt15NLzsvLA+eD1v52QYpmGS\nXLEjk/HzoVEIMvj5+eGVV17B3r17efrB6qdRW2ZZE37YXr16ITU1Faampjh9+jQmTZqE+Pj4Oo9d\nsWLFw//38/ODn5/fw897W1hg24MHmoT7lO9Gfoc+2/pgRo8ZcLFy4fXcDMM87tAhYNEiYMYMYOdO\nCST8WhK68FtTU4O2bds2eExAQAACAgI0G0jlyaFHhISE0MiRIx9+vnr1alqzZk2Dj3FxcaG8vLyn\nvt5YKOVyORlfukQVCoV6wdbjq8tf0dg9Y0mpVPJ6XoZhONqay6+PhmlOMNnZ2bR3714qLS0luVxO\n/v7+1Lp1awoNDa3z+Pp+DnV+Po2mevr06YOEhAQkJyejuroa+/fvx4QJEx47Jisr6+Ecf2hoKIgI\nbdq0UXksE0NDeJiaqrwHb2M+GvgRkguTcSjmEK/nZRiGzeU3RCaTYcuWLWjXrh3atm2Lzz//HH/8\n8Qf68rBsvTEaTfW0aNECGzduxMiRI6FQKDB79mx07doVW7duBQDMmzcPhw4dwubNm9GiRQuYmppi\n3759ao/X29wc4SUl6Ne6tSZhP6alYUtsHbcVUw5NwQj3EbAytuLt3AzTXLFdsRpnY2Oj+ZSNmnTi\nBq5am9LTEV5Sgu2enryP/86JdyCTybB57Gbez80wzcmjc/krV4o/ly/lG7hUwecNXDqV+EOLizE3\nPh4RffrwPn5hZSG6/dwNf035CwPa62F5Ul0NFBQAJSXcBwAYGwOtWgFt2wKtW2u8MoFp3oS8+1YT\nLPE/TdKbrT+ph7k54svLUaFQwMTQkNdzWxlb4buR32Huibm4MfcGjAyNeD2/1hABcXFAaChw/ToQ\nHQ3cuwdkZQGWloCFBfchkwGVlUBFBZCby33u7Ax07gz4+HAfzzwDPLJcl2HqI9kVO0yddKriB4Ce\nYWHY2qUL+vM4z1+LiDD2z7EY3GEwPhn8Ce/nF4xcDpw9Cxw7Bpw6xX1t4ECgb1+gZ0/AzY1L4C3q\neZ0nAoqLgbQ0IDYWiIriyrbgYO5FYuhQYNQoYPRowMxMez8XI3lSrfIfxSr+Os6la4l/Tlwcepmb\n411nZ0HiSC5MRp9tfXBtzjW4t3EXZAzexMUB27YBe/YArq7A5MnAmDGApyc/0zZKJRATA1y4APz9\nN3DtGjBiBDBlCjBxIjdVxDRbUpvLrw9L/HWcS9cS/5aMDIQWF2OHABd4a60PXo9/Ev/BmRlnmnST\nmtYFBwPr1nH/nTMHmDUL8PAQfty8POD4ceDPP4GICOD114G33wa6dhV+bEYydKHKfxRL/E/TiX78\nj+pvYYFrxcWCjvH+M+8jtzwXu6N2CzqOyqKjuYp+xgzghReA5GRg9WrtJH2Auwj85pvctNLVq1zF\nP2wYNw108aKk7oBkhMHW5esHnav45USwCgxE2oABsKpvzpoHNx7cwOg9oxH5TiQczB0EG6dJ8vKA\n//s/brrls8+Ad94BWrYUN6ZaVVXA7t1c05XWrbkmLOPHsxVCekbXqvxHsYr/aTpX8beQydDL3BzX\nBa76ezn2wmzf2Vh4aqGg4zSIiJu/794dMDcH4uOBxYulk/QBbjno7NnctYBPPuES/6BBwKVLYkfG\n8IRV+fpH5xI/ADzTujWu8dSiuSHLhixDTE4MDt4+KPhYT8nNBSZN4uby//4b+P57bjmmVBkYAC++\nyGWGBQu4KaHRo4Hbt8WOTC1VSiUyqqqQVFGB5MpK3K+sRKlCoReVY1NJspOmnkpISICxsTFef/11\nrYynU+v4az3TujV2ZGYKPo5xC2PsmLgDL+5/EUNdh8LG1EbwMQFw8+UzZwLTpgEHD0qrwm+MoSHw\n2mvAK68AmzcDfn7cxefly7mloRJTLJcjpLgYIcXFiCkrQ2x5OZIqK1GpVKKtkRGMDQxARFAAyK+p\nAQA4tWqFrqam6GZqil4WFnjO0hKOrVqJ+4PwjK3L164FCxagX79+WltMonNz/ACQUVWFHmFhyBk4\nUCtP1IdnPkRmaSb2vLRH2IGIgA0buI+dO4GRI4UdTxuysoCPP+YuCH/zDfdiJvL8f1x5OY7k5uJI\nTg5ul5ejj4UFBrZuDW8zM3iYmsLNxASWhoZ1/m6VKRRIrapCbHk5bpeVIbS4GFeKimBrZIRxbdvi\nJVtbDGjdGgY6eo1Dl+fy6yP1Of59+/bhyJEj6NatG+7evYs//vijzuOa9XLOWh1CQnChZ0900kIp\nUl5TDp8tPtjwwgZM8JjQ+APUUVUFzJvH/cUdO8ZNqOqT4GDg3XcBR0fgl1+Adu20OnyxXI7dWVnY\n9uABcqqrMcnGBi/a2uI5S0u0NNBsxlNJhKiyMhzNzcVfOTkokMsx28EBcxwd0V6H7nXQlXX5qpJy\n4i8uLkbfvn1x8eJFbNu2DYmJiVpJ/Do5xw9w0z1XBb7AW8vUyBTbJ2zHuyffRUFFAf8D5OZyyyJL\nS4HAQP1L+gB3J/H169yFX19fYPt2rSz/TK6sxLvx8eh49SouFhZivbs7UgcMwM9dumC4tbXGSR8A\nDGQy9DQ3xwoXF0T37YvT3t7Ik8vhExaGidHRgi8/1hSbyxfP559/jjlz5sDJyUmr9wzpbMX/bWoq\nkior8VPnzgJG9biFpxaivKYcOybu4O+k6encmvxx44Cvv+Yukuq76GjgjTcAGxtgxw6uRxDPEisq\nsDolBUdzczHPyQmL27WDg5avlZQpFPg9MxNr79+Hh6kplrm44FmJXaDX1yr/UY3lFhlPrZHpkR0D\nmyIiIgIzZszAzZs3YWRkhBUrVmit4pfM1jSqhhJYWEh9wsIEiqZuJVUl5PK9C52MP8nPCRMTiVxd\nib7+mp/z6ZLqaqKVK4ns7IiOHuXttIU1NfTR3bvUNjCQlt27R3nV1bydW11VCgX9kpFBHYKD6aXo\naEosLxc7JNF3xdImCaW5x3z//fdkZmZGDg4O5ODgQObm5mRiYkK9e/eu8/j6fg51fj7JPCOqBl8u\nl5PppUtULpcLFFHdApICyGmDE+WW5Wp2org4Imdnok2b+AlMVwUHE7m4EC1YQKRBQlQqlfRrRgbZ\nBwXR7NhYelBVxWOQ/CiXy2lVcjK1uXKFPk5MpDIt/+7WOniQyMGB6KOPNHrKdYZUE395eTllZWVR\nVlYWZWZm0kcffUSTJ0+m3Ny6cwufiV9n5xVMDA3RzcwM4TxvxdiYIS5DMM1rGuafnK/+BaPkZK7Z\n2cqVwPz5vMancwYM4Nb+5+YC/ftzN4Kp6F5FBYZHRmJLRgZOeXvjVw8PrU/rNIWJoSE+69gR0X37\nIrmyEj5hYbhUWKi18dlcvrSYmJjAzs4OdnZ2sLe3h7m5OUxMTBrdbJ0XKr9UCESdUN5LSKA1KSkC\nRNOwipoK6vZzN9oTtUf1B2dkELm7E/3wA/+B6TKlkujXX4lsbYn272/SQxRKJf2QmkptAwNpXUoK\n1SiVAgfJr2M5OeQcHEzz4+IEr/6bW5X/KAmlOY3U93Oo8/Pp7MVdAPgrJwe/ZWbihLe3QFHVLzwj\nHKP3jMaNeTfQrnUTlybm5wODB3M3OH36qbAB6qqICOCll7i7gNeurXcPgZzqasyKjUWBXI6dnp7w\nMDXVcqD8KJTLsSghAeElJdjfrRu8zc15Pb8+rstXlZSXc6qCLef817OWlgguKoJShH/U3k69sajf\nIrx17K2mPenV1VxCGzWKJf2G9OwJhIVxUz7Dh3M3gD3hUmEhfMPD0cPcHJd79tTZpA8AVi1a4I+u\nXfFxhw4YFhmJzenpvCUp1mOHqY9OJ377li1ha2SEW2Vlooz/yeBPUFRVhM1hjWzQTsT1rbe25nrv\nMA1r0wY4cQJ47jmgTx9uG0lwO6StvX8f02Ji8KuHB9a4ucFIT5a/znRwQJCvL7Y9eIAZd+6gQqFQ\n+1xsLp9pjM7/1Qy2ssKVoiJRxm5h0AK7Ju3CsovLkJCXUP+Bq1dzzcp27+Z62TCNMzTkLn7//DMw\nbhwqDhzA67GxOJiTg+u9e2NUmzZiR8i7LqamCPL1BQEYHBGB1MpKlc/BqnymKXQ/8Vta4rIWV0Y8\nycPGA8uHLMfrR15HjaLm6QOOHgW2buU6bLL9alU3YQIy/vkHQ0pLIY+OxmUfH7TTs4ZojzI1NMSe\nrl0x1dYW/W/cQFATixpW5dfP2toaMplM5z+sra15e070IvFfKSoS9eLNgn4LYG1ijS8uffH4NxIS\ngLlzuTLM0VGc4HRcVGkp+ldWYmK/fti7YQNMZ84EKirEDktQMpkM/+3QAds9PPDirVs4nJPT4PGs\nym9Yfn4+iLtn6eHHsdhjcPneBUWVRU99j5ePKVNAGzc2etyUW7ew88GDJp0zPz+fvydF5XVAAlE3\nFKVSSU5BQXRX5DVqmSWZ5LjekS4mXeS+UFpK5OVFtHmzqHHpsoCCArINDKR9WVncF8rLiaZOJerf\nnygzU9zgtCS8uJicgoJoY1raU99rTnff8imzJJMc1jvQ5eTLwgyQlUVkaUlUUNDgYUqlkuwCAymp\nokKj4dTJnTpf8ctkMlHn+WvZm9tjx8QdeP3I68gry+W2R/T15TpuMio7nJODV27fxt5u3TDVzo77\nookJsHcv19to4EDuHZWe62VhgSu+vvghLQ2f3rv38J0tq/LVQ0SYfXw23uz5JgZ3HCzMIL//zi1H\ntrJq8LC4igoYGxjARYQOrjq5EcuTBlta4kphId5wEHdv3FGdRuGVbq/gzw9fwMKIGsiuXRO997wu\n+iUjA8uTk+Hfowd6Pbl5i0zGXfRt355b9XPsGNCvnziBaombiQmCe/XC2KgopJXUoHJ1F0RFynD4\nMEv4qvrx2o/IKsvCCr8VwgxABGzbBuza1eihlwoL4dfIi4NQdL7iB/43zy8FX3ecgxl7onBg6YuA\nDq8vF8vG9HR8df8+Lvv6Pp30H/X229wf2LhxwKlT2gtQJDZGRliY7IN9weWIGReHsBvEkr6KwjPC\nserKKuyfvB8tDQVq6REQABgbA8880+ihlwoLMYQlfvV5mZkhXy5HelWVuIHU1KDVG2+h+pMlWJCy\nCTE5qvedac6+T0vDt6mpCGjqBjvjxwPHjwNvvcW1d9ZTtSt2vvqsBfx9esDeuxLzku9Argd3o2pL\nSVUJpv01DRtHb4SbtZtwA23bxi3oaOSdPhGxxK8pA5kMflZWOF8gwCYpqli1CrC0hP3Hq7Bm+BpM\nOzQNlXLV12I3RxtSU/FTWhou9uyp2pznM88Aly5xz/2XX2plcxdtenIuf9hAQ5zw9ka+XI7pMTGo\nUSrFDlHyiAjvnHwHQ12GYqrXVOEGyskBTp/mNjdoxN2KCshkMriJtEObXiR+AHhe7MR/7Rq3Xn/n\nTsDAALN9Z8PDxgMfnvlQvJh0xDf372NLRgYCevZER3X+EDw8gKAg4K+/gA8+APQgGTa0Lt/E0BBH\nvbxQqVTitTt3oNCzFzu+7YzYicjMSHw/6nthB9q1C5g4kbtDvxGXioowxNJSq7tuPUp/Er+1Nc4X\nFoqznr+qiptu+P77h+v1ZTIZfhn/C/zv+mP/rf3aj0lHbEpPf5j0Ndqf1tERuHiRa+8wZw4gl/MX\npJY1ZcVOKwMDHOzeHQVyOebExYnSr0oX3Mm5gyXnlmD/5P0wNRLwmptSyRV+c+c26XAxL+wCepT4\nO5uYQAYgXoybe77+GujUiSvRHmFlbIWDrxzEwtMLEZ8Xr/24JG53Vha+vn8f53x84MzH3bjW1sCZ\nM0BqKjBtGveCrENUvfvW2MAAR728kFBRgffu3tWLDpR8qqipwNRDU7F62Gp0t+su7GBnznCLOQYO\nbPRQIsL5ggIM5fFOXFXpTeKXyWRc1a/t6Z7oaK6fzKZNdV7Q6eXYC6uGrsLkA5NRXlOu3dgk7Ghu\nLv6bmIh/evSAK5+9BczNuQZvSiX3tlukBn6qUnddvpmhIU56eyOkuBifJCWx5P+ID/75AN1su2FO\nrznCD/bTT8DixU1avh1TXo5WBgZwF2l+H9CjxA8Aw7Wd+OVyborn668b3DB8bu+58Lb3xqLTi7QX\nm4SdKyjA3Lg4nPD2Rjch+he1agUcOADY2wMjRwISWepbFz567Fi2aIF/evTAybw8fH3/vjCB6phd\nkbtwMfkito3fJvw8+t27wPXrwPTpTTr8bEEBRvzbP0gsepX4h1lZIaCwUHsXu7Zs4SrM2bMbPEwm\nk2HruK0ITg3Gzoid2olNoq4XF+PVmBj81b07eje0Tl9TLVpwO4/06gUMHQpkZws3lpr4vPu2rZER\nzvTogV8fPMBvDx7wF6QOisyMxIdnPsRfU/5C61athR/w55+5ArCJr9hn8/MxQsRpHgC636vnSV2v\nXaOw4mJeztWgrCxum8Dbt5v8kFtZt8hmnQ1FZ0ULGJh03S0vJ8egIDqek6O9QZVKoqVLiTw9uW0v\nJUDIHjuxZWVkHxREp+rZsFvfFVQUUKcfO9HuyN3aGbCkhKhNG6Lk5CYdXqlQkMXly5RbXc1bCOrk\nTr2q+AFob57/44+BmTOBbt2a/JDudt2xfsR6TD4wGSVVJQIGJz25NTUYHRWFZS4uGG9jo72BZTJu\nff+MGcCQIUBamvbGroPQPXY8TE1xpHt3zIqNxfXiYn5PLnFKUuKNo29gpPtIvNbjNe0MumsX93vV\nsWOTDg8pLoaHqSnaGhkJHFgjeHvZ0RBfoRzNyaHnIyJ4OVe9QkKInJyIiorUevjbx9+ml/a/REod\n2xxcXeVyOQ0ID6dPEhPFDWTdOm6j+yZWZ3zSdifNYzk55CiBrrXatObKGur/S3+qkldpZ0Clkqhr\nV6KLF5uMfY52AAAgAElEQVT8kE8TE3n/O1And+plxX+tuBilGmxd1yCFAliwgNtCsbV684c/jf4J\nGSUZ+Drwa56Dkx4FEV67cwduJib4ytVV3GD++19u53E/PyApSWvDitFJc4KNDZa7uGBUVBSyq6uF\nH1BkF5Mu4vtr3+PgKweF68PzpDNnuGtJQ4Y0+SG1F3ZFx+tLjwb4DGV4RAQdFWoeecsWosGDuVd7\nDaQXp5PTBic6GX+Sp8CkR6lU0qL4eBp28yZVKRRih/M/GzcSdehAlJAg6DBS6Jf/2b17NDA8nCqk\n9Pzz7H7hfXJc70hnE89qd+Dnnyf6/fcmH55XXU3mly9TJc//FurkTr2r+AFgdJs2OJWXx/+JS0qA\nFSuAH37QuN2yk4UTDkw+gDePvYm7+Xf5iU9iNmVk4EJhIQ57eaGllDZFX7AA+OwzbrVPXJwgQ0il\nX/5KFxc4t2qFOXFxernGv7ymHJP2T8IHz3yA4W7DtTfwjRvc7860aU1+iH9+PoZaWaGVBP4WxI9A\nAGPatsWpf7db49U33wAjRnAbrPBgUIdB+MLvC0zaN0nvLvZeKizEyuRkHPPygmULCW77MHcu19d/\n2DAghr8uqlLb+9ZAJsNOT0/El5fjKz1b40//bqrS1aYrPhr4kXYH/+Yb4L33gJZNn1Y6mZeHsW3b\nChiUCnh9z6EBPkNRKpXkGhJCUSUlvJ2T0tNVWrbVVEqlkuYcn0Mv739Zby72JldUkENQEJ3Nzxc7\nlMb98QeRoyNRVJTGpzp4kMjBgeijj7hdIqUko7KS2gcH0/7abSz1wJora6jPtj5UXq3lJzspicsF\nKizuqFEqqc2VK5RaWcl7OOrkTr2s+GUy2cOqnzcrVnA3ajVx2VZTyWQybBy9EWnFaVh9ZTWv5xZD\nuUKBF2/dwpL27TFcChexGjNjBvDdd9w7uYgItU4htSq/Lo6tWuG4tzcWJCQgVA+WeZ6MP4kfQ3/E\nkalHYGKk5Sf7u++4RoAqLO64WlyM9sbGaMdHTyo+8P7yoya+QzmZm0vP3bjBz8lu3+Zu1hKwgk0v\nTqf237anQ7cPCTaG0JRKJU27fZtej4nRvXcvhw4R2dsThYer9DApV/l1OZqTQ05BQXRfww2+xXQn\n5w7ZrrOl4PsiXDHPzSWytuZmAFTwf4mJ9Nm9e4KEpE7u1NvEXyaXk/nly1RQU6P5ycaPJ9qwQfPz\nNCI8I5xs1tnQ9fTrgo8lhLUpKdQnLIzK5XKxQ1HP4cNEdnZE1xt//qWwYkdd61JSqOf161Smg/9O\nBRUF1OWnLrT9xnZxAli5kuiNN1R+mFdoKAUXFgoQkEiJ//Tp0+Th4UGdOnWiNWvW1HnMokWLqFOn\nTtSjRw+6UU8VLsSbj9GRkbRP0znNkBCi9u2JBJibq8vhmMPkvMGZUotStTIeX07n5ZFTUJAgc5ha\ndewY9+7u6tV6D9G1Kv9JSqWSZsTE0LTbt3XqnVm1vJqe//15eu/0e+IEUFREZGNDFBur0sOSKyrI\nJjCQ5AI911pP/HK5nNzd3SkpKYmqq6vJx8eHYmJiHjvm5MmTNHr0aCIiunr1KvXv37/uQARI/FvT\n02maCr106vTCC9zafS1ac2UN+W7xpdKqUq2Oq664sjKyDQykQIEqGq07cYJL/k+U8rpc5T+pXC6n\nPmFhtDYlRexQmkSpVNLsY7Np/J/jSa4Q6Z3K6tVEr76q8sM2pqXR60/kRT6pkzs1urgbGhqKTp06\nwcXFBUZGRpg2bRqOHTv22DHHjx/HrFmzAAD9+/dHYWEhsrKyNBm2ySba2OB0fj6q1N2KLziYW6v7\n5pv8BtaIJYOWwMfBBzOOzICSpL2NYLFcjkm3bmGVqysGWVqKHQ4/xo793zZ6QUEApLMuny8mhoY4\n3L07vk9Lgz+fiyAEsjZoLW48uIE/X/4ThgaG2g+gtJS7qLt0qcoPPZKbi0na7E/VBBol/vT0dLRv\n3/7h5+3atUN6enqjx6RpqVGWfcuW8DYzU79p2/Ll3D+0Cmt1+VDbxjmvPA+fnP9Eq2OrQkmEGXfu\nYIiVFeY6OYkdDr9GjQJ274Zy0otYPuyypFfsqKu9sTH2d+uGmXfuIKFcupsEHbh9AJuub8KJV0/A\nvKW5OEFs2sTd89G1q0oPy6upwfXiYoxq00agwNSj0Z01Td1IgJ64kaq+x61YseLh//v5+cHPz0/d\n0B56ycYGh3NzMUbVGyeuXAESE4F/361oW0vDljg89TAGbB8AF0sXzO87X5Q4GrIiORkFcjkOdRd4\nWzuRHCp+AfsVe/Hb1cn49MgBtBrgJ3ZIvBtsZYWVrq6YdOsWrvbqBQuJ3WwXkhqChacW4uzrZ+Fk\nIVJxUVYGfPstcO6cyg89lpuLEW3awNSQv3cpAQEBCAgI0OwkmswthYSE0MiRIx9+vnr16qcu8M6b\nN4/27t378HMPDw/KzMx86lwahlKvpH8vrNSoemFl6FCi7SKtHHjE3by75LjekY7eOSp2KI/5Kzub\nOgQHU2aVljohatFTc/kXLnBz/ufOiR2aIJRKJb0dG0uToqNJIaGLvYn5ieSw3oFOJ5wWN5D164km\nT1broWOjoujPOvIdn9TJnRpl25qaGnJzc6OkpCSqqqpq9OJuSEiIVi/u1vK9fp0CCgqa/oDLl4nc\n3Ih43CxBE9fTr5PNOhtx1i3XIaqkhGwDA7Wz4Y2W1bti59IlLvmfOSNabEKqUihoYHg4rUhKEjsU\nIiLKLs2mLj91oU2hm8QNpKSE+4VQo9V7UU0NWVy+TEV8LClvgNYTPxHRqVOnqEuXLuTu7k6rV68m\nIqItW7bQlkdWwixYsIDc3d2pR48eFF7PDTJCJv4vk5NpUXx80x8wejTRtm2CxaOOU/GnyP4be4rN\nUW0pGd9yq6vJLSSE9ghcxWhbk1bsXLnCJf/TIlegAnlQVUXtgoOF62zbRCVVJdR3W19aemGpqHEQ\nEbduf/p0tR76Z2YmjeWhFUhjREn8fBEy8d8pKyPHoKCmraONiOB6t0hwPfqOGzvI5XsXyigWZwvB\nGqWSno+IoI/u3hVlfKGotC4/KIhL/if1s532taIisg0MpNul4iwlrpJX0YhdI+jt42+Lf49BdjZR\n27ZEav6+v3zrFu3Qwnaf6uROvezV8yRPU1M4tGyJS4WFjR+8di3wwQeAVHpqPOJN3zcx23c2xvw5\nBsVV2u+3siQxEYYA1ri5aX1sIajVY2fgQODvv7klvn//rZU4talf69ZY5+6OSbduoVAu1+rYSlJi\n1tFZMGtphk1jNzV58YhgVq/mfkHc3VV+aLFcjrP5+ZgosWWctZpF4geAV+3t8Wd2dsMH3bvH7aoz\nb552glLDZ4M/w4B2AzBh7wRU1FRobdxdmZn4Oy8P+7p1g6HYf5A80Ghdfv/+wIkTXKOuJ+5b0Qdv\nODhgdJs2eDUmBgot9fAnIrzv/z4ySjKw9+W9aGEg8uqilBTuXo7PP1fr4YdzczHU2hptxN5btx7N\nJvFPs7PDkZychm/mWr+eS/pqbqmoDTKZDBvHbIRza2dMPjgZ1Qrht9W7XlyMDxMTcdTLC9YS/UVu\nKt46afbtC5w6xf2+HD7Me5xiW+/ujnKlEsu0tEXl6iurcSnlEo5NOwbjFsZaGbNBy5cD774LODio\n9fA9WVl41c6O56B4xP+Mk3q0EcqQmzfrv3CVmcl13dORi5bV8mqasHcCvXLgFUFvYX9QVUXtg4Pp\niMgX/PggSI+dGze4rp4HDvB0QunIrqqijiEhdEDgHv4br20k1+9dRbt29ZSoKK5Zn5otSDIqK8nq\nyhWtNStUJ3c2m4ofAKbb2eHP+tpF/PADt42avb12g1KTkaER9k/ej/yKfMw9MVeQ1g7VSiUm376N\ntxwdJXfLuSoE7Zfv6wv88w+weDGwbx9PJ5UG25Ytcbh7d7ybkICo0lJBxth+YzvWBq3F+Znn4Wjh\nKMgYKiHidtZatgxQswXJvuxsTLSxgQmPN23xToAXILVoI5Tc6mqyvHLl6XW1ZWVc1z1VlnxKRElV\nCQ34dQC9d/o93ldBzJXgTT2q0lonzehobjXY7t0CDiKO3ZmZ5BYSQnk839eyO3I3OW1worjcOF7P\nq5HDh4m6dyfSYO1977AwOpOXx2NQDVMndzarxE9E9FJ0NG19chOFrVu5nvs6qqCigHw2+9DSC0t5\nS/6b09Ope2goFQt884lQROmkefs2kZMT0e+/a2lA7fnw7l0aERGh+h3w9Th0+xA5rHegW1m3eDkf\nLyoqiFxdNbpDO6a0lByaunScJ+rkzmY11QMAcxwd8euDB//7AhE3zfPee+IFpSErYyucef0Mjtw5\nguUByzXeZP5yYSGWJyXhqJeX5Hq3NIVonTS7dQPOnwc+/RT47TctDaoda9zcoATw6b17Gp/rZPxJ\nvHvqXZx+7TS620moz9N33wE9ewLPP6/2KX598ABvODhIf+Ub/68/6tFWKHKlktoFB1Nk7UbsZ84Q\neXkR6fB0Rq2s0izy2uRFn1/4XO3KP+XfjdL/0eJbVb5Ipl9+XBxRu3ZEv/wiYhD8y62uJteQEI16\nz5yKP0W262zpWto1HiPjQVoad7NWYqLap6hUKMg2MJDuanl3HnVyZ7Or+A1lMrzh4IDttVV/bbUv\n9VfoJrAzs8P5medxJPYIlgUsU7nyr90o/cP27fGCxNrINkZS/fK7dAEuXgRWrgS2bhUxEH61NTLC\nES8vLL57FzdLSlR+/PG445h1dBaOTz+Ofs79BIhQA++9B8yfD2hwc+LR3Fx4m5nBXRf6dvP/+qMe\nbYZyr7ycbAIDqTI2lrv9Xhf3z2tAdmk2eW3yos/Of9bkyl+pVNKrt2/Tqzq2HZ9kqvy63L1L1LEj\n0c8/ix0Jr/ZnZVHHkBDKVqEz66Hbh8juGztp7id9/DhRp07cHL8Gno+IoL0CL32tizq5s9lV/ADg\namICH3NzHD56FJg7V3921viXrZktLsy8gGNxx/DphU+bVPmvS01FXEUFfvXwEP9W+SaSVJVfF3d3\nrvL/5hvgxx/FjoY3U+zsMN3ODlNjYiBvwu/Wvlv7sODUAvi/5o8+Tn20EKEKSkuBhQuBLVsAY/Vv\nHEusqEBkaSle1JVlz/y//qhH26EcTkmhAZs3c3N7eiq7NJt6be1F7558lxRKRb3H/Z2bq1MbpUu6\nyq9LcjKRuzvX6VGH3k01RK5U0qjISHo/IaHB43ZF7CLH9Y4UlSl8l0q1/Oc/RK+/rvFplty9S/9p\n5LkQijq5s1lW/AAw4eRJZDg54bqFhdihCKa28o/Oisaso7NQo6h56piYsjK8FRuLv7y80E6Cjeme\nJPkqvy4dOwKBgcBff3ENANXdA1pCDGUy/Nm1K07k5WFXZmadx2y+vhmfnP8E52aeg7e9t5YjbILw\ncOCPP4ANGzQ6TZlCge2ZmVjg7MxTYMJrnomfCIabN2OhuTl+eGKPYH1jaWwJ/xn+yCvPw+SDk1Ep\nr3z4vfyaGky4dQvfuLvjGQn3JwIEvvtWGxwcgIAALtm88QZQ8/SLsK6xNjLCUS8vfJiYiLBHLvYS\nEVZeWokNIRtw+c3L6GbbTcQo61FZyW2r+u23gK2tRqf6PTMTgy0t4aZDv5DNM/FfvQpUVmL2oEE4\nmZeHB1VVYkckKFMjUxyddhQmLUwwZs8YlFSVQE6EKTExmGRjg1lqNqLSFp2s8utiZcW1d8jPB156\nCajQXndVoXQ3M8PWLl3w0q1byKquhpKUWOy/GIfvHEbgW4Fws5ZoC+/lywEPD+C11zQ6jZIIP6Sl\n4YN27XgKTDtk/84RiU4mk2l841GTzZrFZZIPP8S78fGwNTLCF66u2hlbRAqlAvNPzsfNzJvoOehX\npMllOOHtLdmbTXJyuOtukZHc/VA6m/CfVFPD9fO/fx84fpx7QdBxy5KScKEgH05J3yKrJA3Hpx2H\npbF6vW4EFxwMvPwyEBWlcbV/Mi8PnyclIbx3b9EWRaiTO5tfxZ+fz/VQnzULAPB+u3bYnJGBUoVC\n5MCEZ2hgiK3jtsKh82z8fj8GK+2NJJv09abKr4uREdfrvWdPwM8PqK9xoA75yMkGdzPDEGI6CKdf\nPS3dpF9Wxv3tb96scdIHgO/+rfZ1ZSVcreaX+HfuBMaPB/5ddtXF1BTDrK2xWc/n+mudKyhAqJE3\nVtjIMe4PPwTeDxQ7pMfo/Fx+UxkYcDcPvvQSt6tXXJzYEaktrTgNQ3Y+h1HyG3Cw64f1GY1seCSm\nRYuAQYOASZM0PtXV4mIklJdjqpT77teH34VF6tNKKEolUefORIGBj305qqSEHIKCtNY/WyxRJSVk\nGxhIlwoKiIjIP8GfbNfZ0oFb0uglr7VOmlKzfTvX0//yZbEjUdmNjBvU7tt2tObKGlIqlfTg3x7+\nu6W4r8WuXdwa4Np2LRoaExlJmySwHFyd3Nm8Ev+FC/X25ZkUHU0/pqYKH4NI0isrqUNwMO154g/y\n5oOb5LzBmb4J+ka0O3Z1bl2+EM6c4e4i37dP7Eia7O+4v8lmnQ0dvH3wsa9Hl5aSbWAgXf63wJCE\nO3e41uuRkbycLqy4mJyDg6lSUf/9MdrCEn9jZswg+v77Or8VVlxM7YKDqUIC/5B8K5HLyff6dVqV\nnFzn91MKU6jnlp4068gsqqjR7LZ1VTXbKr8uUVFE7dsTrVkj+Ru9frz6Izmud6SQ1JA6v/9PXh7Z\nBwVRfFmZliOrQ3k5UY8eXPt1nkyIiqIfJFIoqpM7m8+qnqIi7kaau3cfzu8/aWJ0NAZbWeGj9u2F\ni0PL5ESYdOsW7I2MGmzHUFZdhjePvYn7RfdxeOphOFk4CRqX3q7Y0VR6OjB2LPDMM8DGjYDE2mJX\nyauw2H8xAu8H4sT0E3C1rn813LaMDHyTmoogX1/YtWypxSgfQQTMnAkoFMCePbw0YwwuKsK0mBjE\n9esniV222Kqehuzfz/XZbqCXxlp3d6y9fx/5enBzDcDdSDM/Ph7VSiW2dOnS4MoDs5Zm2D95P8Z1\nGYf+v/bH9fTrgsWl1yt2NOXsDFy+DKSkAKNGAXl5Ykf0UEZJBob+PhQ5ZTm4Ovtqg0kfAOY6OWG6\nnR1GR0WhWC7XUpRP2LABiIkBfv2Vl6RPRFhy7x5WurpKIumrjdf3HBoQPJRnniH6++9GD3snLo4+\nEKnnBt+W3L1L/cLCVN5F6+ido2S7zpZ+j+B3Jyk2l6+Cmhpu/svdneiW+LtUBd0PIucNzrTq0qoG\n+z49SalU0jtxcTT05k3tT6OeOsVth3n/Pm+nPJKTQ96hoVrdYasx6uTO5pH4Y2K4ieQmJMDMqipq\nGxhIiTo+4bw2JYW6XbtGuWrukxqdFU2df+xMc/+ey8u8P5vLV9OuXdxF36NHRRleqVTS5uubyXad\nLZ2IO6HWOeRKJU25dYtejI7mbevGRsXEcM/bEyv4NFGpUFCXq1fpVG4ub+fkA0v89VmyhOi//23y\n4V8lJ9O4qCid6kv/qG3p6eQaEkJpGnbbLKosoikHp1DPLT0pIU+9d0GsyufBtWvcjl5a7u5ZVFlE\n0w9NJ69NXhSfG6/RuSoVChoeEUGzY2OF/7tKTeX2QeB57+NVyck0Pkp6XUZZ4q9LTQ33di8mpskP\nqVQoqOu1a/RXdrYwMQloX1YWOQUFUQJPZbVSqaSfQ38mm3U2Kq/3Z1U+jzIyuOnKCROI8vMFHy48\nI5w6/diJ5v09j8qr+fnHK5HLqV9YGC2Ojxcu+efnE3XvTrRuHa+nvVdeTm0DAylJw81ahMASf11O\nnOD+YFR0qaCAnIODqUjF+XEx7c3KIsegIIouLeX93GHpYeT2gxstOLmg0UTAqnyBVFURvf8+kYsL\n9y5AAEqlkn669hPZrrOlfdH831NQUFNDfYVK/uXlRIMGcT32eTy3UqmkMZGR9HVKCm/n5JM6uVP/\nV/X89hvXEEtFz1lZYXSbNvgoMVGAoPj3Z1YW/nP3Ls74+MDLzIz38/d26o3wueHIq8hDn1/64OaD\nm3Uex1bsCKhlS+C777iVKuPGcbt68bgEOrssGy/ufxE7I3YieHYwpnpN5e3ctaxatMAZHx+EFBfj\n/bt3+VvCXV4OTJjA7Zn7zTe87qG9IzMTGdXV+I+OdeBsEP+vP+oRJJS8PCJLS6LCQrUeXlRTQ24h\nIXQkJ4fnwPi1OzOTHIOC6JYAlX5d9kTtIdt1trT68mqSK7g2F6zK17LERKJevYhefpn7PdfQ4ZjD\n5LDegT459wlV1gi/E1tt5b8oPp4UmlbnpaVEw4ZxO2nx3HYl8d/9ubX1t6UOdXKnfif+rVuJXnlF\no1MEFxaSfVAQpUt0W8IfUlOpXXAw3dbyL2ZKYQr57fSjZ3c8Sxv33GNz+WKorOSmfpydifz91TpF\nQUUBzTwyk9x/cKeg+0E8B9jI2DU1NDA8nGbExFC1uks9S0uJ/PyIZs3iPelXKxQ0MDycvuVxOagQ\n1Mmd+j3Vs2ePxhstDLC0xEJnZ0yJiUGVhLbMIyJ8du8efk5PR6CvL7oJML3TkA6WHbBv9HmUhL6I\n96L7Ycp332HNWoV+dtKUqlatuKmf338H3n4bWLCAazvcRP53/eGzxQdmRmaIeCcCA9sPFDDYp1m1\naIGzPj4olMsx4dYtlKnaGj07m2tr7e4ObN8O8HxD1YeJibA2MsJ7+jTF8y/9TfypqcCtW9zdjxr6\ntEMH2BkZYWFCgvY2i2lAlVKJ2XFxOFtQgEBfX3Q0NtZ6DIcOAT19DDDC/D+IWBSC6Kq/MWD7AERl\nRWk9lmbv+ee5TUWKiwFfXyAoqMHDs0qzMP2v6Xj35Lv4Zfwv2DR2E8xbmmsp2MeZGhriiJcXnFq2\nxLCICGRXVzftgQkJXDvrsWOBX37hPenvysyEf34+dnftCgMd67XfJLy/71AT76GsXUv09tu8na64\npoa8QkNpg8hv+zKrqmhgeDhNio6mEhHaSNc3l69UKumX8F/Idp0tfXb+M96WADIqOnSIyMmJaO7c\np5Z9KpVK+jX8V7JdZ0tLzi6hsmoJNFD7l1KppGX37lHHkBAKLy5u+OBz57h1wr/+Kkgs5/PzyVbi\n8/qPUid36m/i79GD6OJFXk+ZUlFBHUNC6JeMDF7P21ThxcXUITiYlt27p/kFMTU0ZV1+RnEGTT4w\nmVy+d6HDMYd19iY4nVZQQDR/PveP9eefREolRTyIoOd+e476/dKPIh5EiB1hvQ5mZ5NNYGDd/fyV\nSq5zqaMj12JdANeLi8k2MJACpNRSuhEs8deKjuYueAnQGyS+rIycgoLotwcPeD93fRRKJX2Xmko2\ngYF0UISbytRZsXP+3nnq/nN3Gr5rON3Ovi1sgEzdgoOppntXivV2pOffs6ZNoZsersKSsqiSEnK/\nepXeiYujstp3tdnZRBMnEvXrx92ZK4CrRUVkHxRExyS+iu9J6uRO/Zzj//NPYPp0bns7nnU2NcU5\nHx+sSE7G6pQUwef8H1RVYWx0NPZlZ+Nar16YzMM+oapQd13+MNdhuDnvJsZ3GY8hO4fgff/3kVue\nK2ywzEPVimpsoGC0m5GNKL+uOLPPCPM3hcLwQabYoTXK29wc4b17o0yhQK/wcISdPAn4+ABdunCd\nSwW42Oqfn4/x0dHY4eGBCQ108NUb/L/+qIe3UJRKrk/HzZv8nK8e6ZWV1PP6dZoRE6Ny98umkCuV\ntDEtjWwCA+nze/fUX+6mJj7X5WeXZtO7J9+ltmvb0hcBX1BxZSNzuIza5Ao57YrYRW4/uNGYPWPo\nTs4d7htFRUQff0zUpg3Rhx8SafEdq9oyMmjf0qVke+wYvX/xIhUK8HemUCppdXIy2QcFUZCa9/uI\nTZ3cqX8Vf3AwYGrKVQgCcmrVCoG+vjA2MECv8HAEFxXxcl4iwj/5+egXHo592dkI6NkTK11dYSTA\nu5f68H33ra2ZLX4e8zOuzbmG+Lx4dP6pM364+gOq5FX8BMxASUocijkE783e2BK+BdsnbMfJV0/C\n08aTO6B1a+Drr7nVP9XVQLduwPvvAxkZ4gZel6oqbplqjx6YKpfj9nPPocTREV1DQ/Hbgweo4WlZ\ndVJFBcZER+Nkfj7CevfGQEtLXs6rE/h//VEPb6G8+y7RqlX8nKuJDmRlkXNwML16+zbdU/MOphql\nko7m5NDgGzfI89o1OpCVpfULuNq6+zYyM5LG7hlL7b5tR9+FfEelVbqxekKKFEoFHblzhHpt7UW9\ntvaiU/GnmnZBPSOD6IMPiKysiKZP5/7Bxb4QX11NtG0bUYcORGPGEMXGPvbtq0VFNPTmTXINCaGt\n6elqr2rLr66mZffuUdvAQPoqOVnr76b5pk7u1K/EL5cT2dkRibCRSolcTp//+8s0MTqajubkNPqL\nKVcqKaSoiD5OTKR2wcE0IDycdmdmaq9n+SPE6KQZlh5GL+9/mWzX2dLKgJWUXy5810l9UVlTSdtv\nbCfPjZ7UZ1sf+ivmL/VWUBUUEH37LbfhS69eRD/+SFTXihoh5eRwq3U6dCAaPrzRquNKYSGNj4oi\nqytX6K07d+hkbi6VNuFv7WJBAc2PiyPrK1doZkwMpUiw06Y61Mmd+rXnbkAA8MEH3PyESMoUCuzJ\nysKBnBxcKy5GV1NTdDU1hVOrVmhlYIAqpRLZ1dWIr6hARGkpOhobY2LbtnjFzg49zbV/E40U9r6N\nzY3F2qC1OB53HK95v4YFfRfAw8ZD+4HogNzyXGy/sR0/hv4ILzsv/N+g/8NQl6ENbqvZJEolcPYs\nsHs38Pff3J6/L78MjBzJzfnxrbIS8PfntkT19wcmTeJ+EXv3bvIpHlRVYXdWFk7k5SG8tBRdTEzQ\nzcwMji1bwtzQENVKJfLkctwpK0NEaSncTEzwiq0tXre3R3sRbnoUijq5U78S/4IF3J6ln37KT1Aa\nKpHLEV1Whjvl5ciqrkaVUgkjAwPYGxnBzcQEvczNYW1kJFp8hw4BixYBM2YAK1dC9HYLqUWp2BK+\nBV6qnAoAAA4QSURBVL/e+BU97HtgYd+FGNdlHAwNdHhvUx4QEa6mXcWmsE04EX8CEz0m4r3+78HX\n0VeYAcvLgePHuReAM2cAOztg+HCgXz+gb1+gUyfVV8xVVgK3bwNXrgAXLnCrc3x9gSlTgFdeaXAv\n7KYoUyhwu6wMMeXlyK6uRolCgVYGBmjTogU6m5igl4UF2or4tyak5p34FYr/bVTdpQt/gekhKVT5\nDamSV+FgzEFsDN2ItOI0zOgxAzN9ZqKbbTexQ9OqzNJM7Lu1DzsjdqKspgzv9H4Hb/R8A21N22ov\nCIUCuHGDS9bXrwNhYdwG8G5u3EfHjoClJXfx2NQUkMu5i8dlZcCDB9zF44QEICmJ66kzaBAwbBgw\ndCj3gsJorHkn/suXufI1MpK/oPSQ1Kr8xtzKvoVdkbuwO2o3nCycMNNnJl7q+hLatda/xlkAUFJV\nguNxx7E7ejeupl3FRI+JmNFjBoa5DoOBTCKL8AoLgXv3uI/797keQUVF3DuFli25DxMTwNERcHLi\nXiA8PbmmcgzvmnfiX7QIsLcHli7lLyg9IvUqvzEKpQLnk85jd9RunEw4CXdrd7zo+SJe7Pri/5Ys\n6qiMkgwcjzuO43HHEXg/EIM7DsYM7xmY4DEBZi2123WV0T1aTfz5+fmYOnUqUlJS4OLiggMHDsDK\nyuqp41xcXNC6dWsYGhrCyMgIoaGhvAX/kFLJ3c138SLgwS4KPknXqvzG1ChqcCnlEo7EHsHR2KNo\nZdgKw92G43nX5zHMdRhszbR7d7OqSqtLEXg/EBeTL+L8vfNILEjE6E6jMdFjIkZ1GgVL42a0npzR\nmFYT/5IlS2BjY4MlS5Zg7dq1KCgowJo1a546ztXVFeHh4WjTpk3DgWiS+AMDgfnzgeho9R6vp3S9\nym8KIkJMTgzO3TuHc0nncDnlMjpYdkB/5/7o79wf/Zz7obtdd7QwaCFafIkFibiefh1hD8JwNe0q\nIjMj0dupN4a6DMVQl6EY0H4AWhq2FCU+RvdpNfF7enri0qVLsLe3R2ZmJvz8/BAbG/vUca6urggL\nC0Pbtg1fkNIo8b/3HtC2LbBsmXqP10P6VuU3VY2iBpFZkQhND0VoeiiupV9DalEqurTtgq62XdHV\nhvtws3aDc2tn2Jja8DJ3XlJVgvSSdCTkJSAuL477yI1DdHY0WrdqjT5OfdDHsQ/6OffDgPYDYGpk\nysNPyzBaTvzW1tYoKCgAwFU1bdq0efj5o9zc3GBpaQlDQ0PMmzcPb7/9dt2BqJv4lUpunfHZs0DX\nrqo/Xs80hypfVSVVJYjNjUVMTgzu5N7Bndw7SClMQVpxGkqrS+Fk4QQHcwdYGluidavWDz8MZYaQ\nyWSQQQYDmQGqFdUoqS5BaXUpSqtLUVhZiAclD5BRkgECwcnCCZ3adIJHWw/uw8YDXnZesDNjq1cY\n4aiTOxt8/ztixAhkZj7dze+rr756auD6biAJCgqCo6MjcnJyMGLECHh6emLw4MF1HrtixYqH/+/n\n5wc/P79Gwgdw9SpgZcWSPh6v8nfubD5VfmMsWlmgr3Nf9HXu+9T3KmoqkFGSgczSTBRXFaOoqgjF\nVcUoriqGQqkAgUBEUJISbUzaoFPLTrBoaQHzluZo3ao1nCyc4GjhCIuWFprfRMUwTRAQEICAgACN\nzqHRVE9AQAAcHBzw4MEDDB06tM6pnkd98cUXMDc3x4cffvh0IOpW/P/9L5fhVq5U/bF6glX5DNN8\nqZM71Z7cnDBhAn7//XcAwO+//45JkyY9dUx5eTlKSkoAAGVlZThz5gy8vb3VHfJpRMDRo9zt3s0U\n3500GYbRfxot55wyZQru37//2HLOjIwMvP322zh58iTu3buHl156CQAgl8vx2muv4ZNPPqk7EHUq\n/pgYbjP1lBSgmb3NZlU+wzBAc7yBa/Vq7rbwn34SJiiJaq4rdhiGeRrvF3cl79gx4IkLzfrs0Sr/\n8GFW5TMMox6JNP9QQ23zpyFDxI5EK9hcPsMwfNHdiv/4cWD0aEBPW63WYlU+wzB8092Kvxms5mFV\nPsMwQtDNi7vFxVxTtvR0wMJC2MBEwFbsMAzTVFpdxy+q06eBZ5/Vy6TPqnyGYYSmm3P8x44BEyeK\nHQWv2Fw+wzDaonsVf3U1V/GPHy92JLxhVT7DMNqkexV/YCC32bOTk9iRaIxV+QzDiEH3Kv6TJ4Gx\nY8WOQmOsymcYRiy6V/GfOgXs2iV2FGpjVT7DMGLTrYr/3j2goADo3VvsSNTCqnyGYaRAtyr+kye5\nu3UNdOv1ilX5DMNIiW5l0FOngDFjxI5CJazKZxhGanTnzt2yMsDBAUhLAywttReYmtjdtwzDaIN+\n37l74QLQp49OJH1W5TMMI2W6M8d/6pTkl3GyuXyGYXSBblT8RJJfv8+qfIZhdIVuVPy3bgGGhoCn\np9iRPIVV+QzD6BrdqPhrp3kktqE6q/IZhtFFulHxnzoF/N//iR3FQ6zKZxhGl0m/4i8pAW7cAPz8\nxI4EAKvyGYbRfdKv+C9eBPr3B0xNRQ2DVfkMw+gL6Vf8Z84AI0eKGgKr8hmG0SfSr/jPnAEOHhRl\naFblMwyjj6Rd8SclcRure3trfWhW5TMMo6+kXfGfPQuMGKHVbpysymcYRt9Ju+L/5x/ghRe0Nhyr\n8hmGaQ6k251TLgdsbYE7d7iunAJinTQZhtFV+tWd8/p1oGNHwZM+q/IZhmlupDvHf+aMoNM8bC6f\nYZjmSroVv4Dz+6zKZximOZPmHH9hIZeVs7MBY2PexmBz+QzD6Bv9meO/cAEYNIjXpM+qfIZhGI40\n5/h5nN9nc/kMwzCPk2bFf+4cMHy4xqdhVT7DMMzTpFfxp6RwrZi9vNQ+BavyGYZh6ie9iv/iRWDo\nULV322JVPsMwTMOkV/FfuAAMG6byw1iVzzAM0zTSqviJ1Er8rMpnGIZpOmlV/AkJXCdOd/cmHc6q\nfIZhGNVJq+KvrfabML/PqnyGYRj1SKviv3ABGDeuwUNYlc8wDKMZaVX8tSt66sGqfIZhGM1Jq+K3\ntgbat3/qy6zKZxiG4Y+0Kv46VvOwKp9hGIZf0qr4H0n8rMpnGIYRhtoV/8GDB9G9e3cYGhrixo0b\n9R7n7+8PT09PdO7cGWvXrm34pH5+AFiVr6mAgACxQ9Ar7PnkF3s+xad24vf29saRI0fw3HPP1XuM\nQqHAwoUL4e/vj5iYGOzduxd37typ9/gcmR2mTgWWLuWq/G++AUxM1I2w+WJ/WPxizye/2PMpPrUT\nv6enJ7p06dLgMaGhoejUqRNcXFxgZGSEadOm4dixY/Uez6p8hmEY4Qk6x5+eno72j6zSadeuHa5d\nu1bv8Wwun2EYRngNJv4RI0YgMzPzqa+vXr0a48ePb/TkMhU7bA4cqF5HTuZpX3zxhdgh6BX2fPKL\nPZ/iajDxnz17VqOTOzs7IzU19eHnqampaNfu/9u7v1f2/jgO4M+JkiKUHctEbX6N7SxNy8VK2WJb\n1lxxt9ySS/kDRHO/i5VczB0XSLFys1JYK7uckCgbloYSF0u9vnfyYft8jn052+z1uCKv8uy1117p\nnPMedcbaAvnXv4wx9ut9y3P82Za2yWTC2dkZLi8vkU6nsbq6CpfL9R2/kjHGWI5yXvwbGxtobm5G\nOByG0+mE3W4HAFxfX8PpdAIAysvL4fP5MDQ0BJ1Oh7GxMXR1dX1PcsYYY7mhPFhbWyOdTkdlZWV0\ndHSUtS4YDFJHRwdptVryer0yJiwuqVSKrFYrtbW1kc1mo4eHh4x1LS0tpNfryWg0Ul9fn8wpC5uU\nWZueniatVksGg4Gi0ajMCYvLv/oZCoWopqaGjEYjGY1Gmpuby0PK4jAxMUFKpZJ6enqy1nx1NvOy\n+I+Pj+nk5IQGBgayLv7X11fSaDR0cXFB6XSaRFGkWCwmc9LiMDMzQ4uLi0RE5PV6aXZ2NmNda2sr\npVIpOaMVBSmztr29TXa7nYiIwuEwmc3mfEQtClL6GQqFaGRkJE8Ji8ve3h5Fo9Gsiz+X2czLZ/X8\nxBmAUra1tQWPxwMA8Hg82NzczFpLfBP9Eymz9r7HZrMZj4+PSCaT+Yhb8KS+d3kWpbFYLKirq8v6\n81xms7A+pO2dTGcAEolEHhMVrmQyCUEQAACCIGR90RUKBaxWK0wmE5aWluSMWNCkzFqmmng8LlvG\nYiKlnwqFAgcHBxBFEQ6HA7FYTO6Yv0Yus/ljB7jkPgPw22Xr5/z8/B/fKxSKrL3b39+HSqXC3d0d\nbDYbOjs7YbFYfiRvMZE6ax//QuUZzUxKX3p7e3F1dYWqqioEg0G43W6cnp7KkO53+ups/tjil/MM\nQCn4Wz8FQcDt7S0aGxtxc3MDpVKZsU6lUgEAGhoaMDo6ikgkwosf0mbtY008HkdTU5NsGYuJlH5W\nV1e/fW232zE5OYn7+3vU19fLlvO3yGU2836pJ9t1Pj4DIJ3L5UIgEAAABAIBuN3uTzUvLy94enoC\nADw/P2N3dxd6vV7WnIVKyqy5XC6srKwAAMLhMGpra98ur7E/SelnMpl8e+9HIhEQES/9HOU0m99z\n3/lr1tfXSa1WU2VlJQmCQMPDw0RElEgkyOFwvNXt7OxQe3s7aTQaWlhYyEfUopBKpWhwcPDT45zv\n+3l+fk6iKJIoitTd3c39/CDTrPn9fvL7/W81U1NTpNFoyGAw/PUxZPbvfvp8Puru7iZRFKm/v58O\nDw/zGbegjY+Pk0qlooqKClKr1bS8vPy/Z1NBxLfWGWOslOT9Ug9jjDF58eJnjLESw4ufMcZKDC9+\nxhgrMbz4GWOsxPDiZ4yxEvMf7IiLY3Hw5+0AAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": { "name": "Worksheet 1" } } ] }