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Last active March 31, 2017 07:56
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Coursera: Computational Methods for Data Analysis
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{
"metadata": {
"name": "Coursera Data Analysis"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lecture 1"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import scipy as sp\n",
"from numpy.fft import *"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"L = 20\n",
"n = 128\n",
"x = linspace(-L/2., L/2., n, endpoint=False)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"u = exp(-x**2)\n",
"plot(x,u)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 3,
"text": [
"[<matplotlib.lines.Line2D at 0x108498210>]"
]
},
{
"output_type": "display_data",
"png": 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7VEl9GO6kG5EKnwg5G2+qktow3Ek3ogqu3LlLldSG4U66EePKnWjGouHu9/vxwAMP4PDh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\n",
"text": [
"<matplotlib.figure.Figure at 0x108050950>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ut = fft(u)\n",
"plot(ut)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/Library/Python/2.7/site-packages/numpy-1.8.0.dev_3abd869_20121222-py2.7-macosx-10.8-intel.egg/numpy/core/numeric.py:324: ComplexWarning: Casting complex values to real discards the imaginary part\n",
" return array(a, dtype, copy=False, order=order)\n"
]
},
{
"output_type": "pyout",
"prompt_number": 4,
"text": [
"[<matplotlib.lines.Line2D at 0x1084c83d0>]"
]
},
{
"output_type": "display_data",
"png": 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g24eIKAxaQLcPa/554B2TmjmWW/MnIgpD4ElerPnPnDvSwdvnz7IPERUJ7xW8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\nRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10806bad0>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(abs(fftshift(ut)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 5,
"text": [
"[<matplotlib.lines.Line2D at 0x1085d0310>]"
]
},
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD/CAYAAADllv3BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAHFVJREFUeJzt3X1sVOe9J/DvvHo8Hs+Mx47tBGNIYzuYhJemZlMWJXHg\n6mpppL1/sHAvKSuIxP7Bm1K1hKZR2UrbpiRqrQSVEUgNUij5p7tKQGE3V7sLjZPcNvdeYEzubu0U\nMFnjbvAYezwztuftzMzZP6bHy5sNPj4z5znnfD//MQyeH8j+6uH3/J7n2GRZlkFERKZh17sAIiLS\nFoOdiMhkGOxERCbDYCciMhkGOxGRyTDYiYhMxjnXbx49ehSRSAR+vx89PT0AgJMnTyISicDtdqOz\nsxNbtmyB1+utSLFERHR/c67Yu7u78dprr9322qpVq9DT04NDhw4hm83i1KlTZS2QiIjmZ85g7+zs\nRE1NzW2vrVy5Ena7HXa7HatWrUIsFitrgUREND9ztmLu59y5c1i/fv2cv09ERPO3YcMG1X9WdbB/\n8MEH8Hg8WLt27Zzve+qpp9R+BBGRJUUikQX9eVVTMb29vejr68O+ffsW9OFERKS9eQf7pUuX8OGH\nH+LAgQNwu93lqImIiBZgzlbM4cOH0d/fj2QyiV27dmHz5s04ffo08vk8fvrTnwIAOjo6sHPnzooU\nS0RE9zdnsL/88st3vTbXZikREemPJ0+JiEyGwU5EZDIMdiIik2GwExGZDIOdiMhkGOxERCbDYCdD\n+9PNafzPK7yIjuhWC7oEjEhvv/7nr3F1LIV/vSSAGrdD73KIhMAVOxnWwOg0opM5rFnsx38dGNO7\nHCJhMNjJsH77RRSbVjRi6+pmnPrjKHL5ot4lEQmBwU6GdD2ewR+j0/g3HSF8I1SNx0JenL3KXjsR\nwGAng3r/f43i3y5vgMdV6qv/7apG/Jd/GYUsyzpXRqQ/BjsZ0qWvJ/HcN+pmfr2i2Ye0VMDNaUnH\nqojEwGAnw8nmixhPSVjkr5p5zWazobXOg+vxjI6VEYmBwU6G8+dEBo/4q+Cw2257fUmQwU4EMNjJ\ngIYmMmgNeu56fXHQg+sTDHYiBjsZzvV4Bkvq7g72JXUeDHHFTsRgJ+O5Hr/3il1pxXAyhqyOwU6G\nMzRLsAc8pRsy4pl8pUsiEgqDnQxFKhQxMpnDokDVXb9ns9mwJOjBEPvsZHEMdjKU/5vMosnnhttx\n729djjwSMdjJYGbrrytaOfJIxGAnY7k+y6ijgq0YIgY7GczQLKOOCrZiiBjsZDDD8QwWz7Fib/C6\nkM0XkeRkDFkYg50Mo1CU8edEFq33mIhR2Gw2LA56MMxVO1kYg50MY2Qyh7pq18xVvbPhBipZHYOd\nDOPmdA6NPvd939fkc/P6XrK0OR9mffToUUQiEfj9fvT09AAA0uk0jhw5gmg0iqamJuzbtw8ez+w9\nTyKtjE1LeKjGdd/3NdS4MDA6XYGKiMQ054q9u7sbr7322m2vvf/+++jo6MAvf/lLtLe34/333y9r\ngUSKsekcGh4o2N0YT3HFTtY1Z7B3dnaipqbmttcuXLiA5557DkAp+M+fP1++6ohuMZaSHjDYXWzF\nkKXNu8eeSCQQDAYBAIFAAIlEQvOiiO5lbFpCg/f+PfYGrwtjDHaysAVtntpstvu/iUgjY9MPtmKv\nrXJAKhSRlgoVqIpIPPMO9kAggHg8DgCYmJhAIBDQvCiie3nQHrvNZkNDjZurdrKseQd7V1cXent7\nAQCffPIJ1qxZo3VNRHfJF2UkswXUVd8/2AHgoRoXN1DJsuYM9sOHD+PgwYO4ceMGdu3ahY8//hib\nNm3ClStXsH//fly5cgWbNm2qVK1kYbGUhKDHedcDrGdT7+UGKlnXnHPsL7/88j1ff+WVV8pSDNFs\nbj5gG0bxUI0L49O5MlZEJC6ePCVDGH/AjVNFfQ1Pn5J1MdjJEG5OS2iouf+oo+KhGo48knUx2MkQ\nHnTUUdFQ48JYiq0YsiYGOxnCWCqHBu88gt3LcUeyLgY7GcLYPFsxwWonJrMFSIViGasiEhODnQxh\nvq0Yh92GumonYik+SYmsh8FOwivKMmIpaV6tGIB9drIuBjsJL5HJw+t2wO2c37crrxUgq2Kwk/DG\npiXUz3O1DvCWR7IuBjsJ70GfnHSnBs6yk0Ux2El4N6dzqFcd7Oyxk/Uw2El44yo2ToFSj/0mb3gk\nC2Kwk/BiKQkhFcEeqnZigsFOFsRgJ+HFM/kHvof9VsFqF+IZzrGT9TDYSXjxdB7B6jlvmL4nr8uO\nQlFGJs/Tp2QtDHYSXjydR9Az/2C32Wyoq3YhnmY7hqyFwU5Ck2UZ8bSEOhUrdqB0Z8xEmu0YshYG\nOwktLRUBmw0el0PVn6+rdmKCK3ayGAY7CS2eUdeGUQSrXVyxk+Uw2Elo8XRedRsGKK3Y4wx2shgG\nOwltIi2pmohRlIKdrRiyFgY7CS2eySOoYoZdwVYMWRGDnYSmRSuGwU5Ww2AnocXT0oI2T+s8nGMn\n62Gwk9DUnjpVcI6drIjBTkJTe0+MwlflQCZfRI4PtSYLYbCT0CZUXiegsNtsCHg48kjWwmAnocUX\nOO4IcJadrEf1T8zZs2fR29sLSZLQ2dmJHTt2aFgWEVAoypjOFVBbpUGwZ7iBStahasU+NTWFU6dO\n4cc//jEOHTqEGzdu4NKlS1rXRhYXz+RRW+WEw25b0NfhLDtZjaqlkNvtBgCkUikAQDabhc/n064q\nIix8hl3ByRiyGtXBvnPnTuzZswculwsbN25EW1ub1rWRxcUz0oJOnSrqqp0Ym2YrhqxDVSsmmUzi\nnXfewVtvvYVwOIzLly8jEoloXRtZ3EJn2BV1bMWQxagK9qtXr6K9vR3Nzc2ora3F2rVrMTAwoHVt\nZHHatmK4YifrUBXsy5Ytw+DgIKampiBJEvr6+rBy5UqtayOLW+h1Agqu2MlqVP3UeL1ebNq0Cb/4\nxS+Qy+WwevVqPPHEE1rXRhY3kc5jUcCz4K/DOXayGtXLoe7ubnR3d2tYCtHtSlf2LnzF7q9yYiqb\nR6EoL3h0ksgIePKUhBVf4HUCCofdBl+VE4kMV+1kDQx2EtZCn550K97LTlbCYCchybK84Kcn3aqu\n2sVrBcgyGOwkpJRUhNNug8epzbdokBuoZCEMdhKSVqOOiiCv7iULYbCTkEqHk7RpwwB/WbFz85Qs\ngsFOQtJq1FFRWrGzx07WwGAnIS30yUl3Cla7uGIny2Cwk5C0eHLSrbh5SlbCYCchaTnqCHDzlKyF\nwU5CmtDoyl5F6b4YCbIsa/Y1iUTFYCchaXVlr8LjcgA2GzL5omZfk0hUDHYSUjyj7Rw7wHYMWQeD\nnYRUenqSdj12gLPsZB0MdhKOVCgilSugtsqh6dflZAxZBYOdhJPI5BHwOGG3aXt3Og8pkVUw2Ek4\nWj3E+k48pERWwWAn4Wg9w67g5ilZBYOdhKP1dQKKIB+2QRbBYCfhaH2dgKI0FcMeO5kfg52EE89o\ne2Wvoq7axVYMWQKDnYRTts1T9tjJIhjsJBytn56kCHicmMzmUSjyvhgyNwY7CUfrpycpHHYbatwO\nTGa5aidzY7CTcLS+2fFWnGUnK2Cwk1BkWS7NsZehFQPwWgGyBgY7CWU6V4DbYYPbWZ5vzaCHF4GR\n+THYSSgTZbjV8VZcsZMVqP7/biaTwfHjxzE0NARJkrBr1y50dHRoWRtZUOk6gfK0YQBeBEbWoPon\n6Pjx4+js7MSePXtQKBSQzWa1rIssSusnJ92prtqFK2Opsn19IhGoasWkUikMDAxg/fr1AACHwwGv\n16tpYWRNE2WaYVfwYRtkBap+gkZHR+H3+xEOh3Ht2jV0dHTgpZdegtvt1ro+sphEmW52VPD0KVmB\nqhV7oVDA4OAgnn76aRw6dAiSJOHzzz/XujayoHK3YngRGFmBqmCvr6+Hz+dDV1cX3G431q1bh0uX\nLmldG1lQ+VsxvAiMzE9VsAeDQTQ3N+PKlSsoFouIRCJYsWKF1rWRBZXjIda38rrskAoysvli2T6D\nSG+ql0Z79uxBOBxGMplEa2srvvvd72pZF1lUuccdbTYbgtVOJDJ5NPq4J0TmpPon6JFHHsHrr7+u\nZS1EZXt60q2UDVQGO5kVT56SMHKFIrL5ImqrHGX9HG6gktkx2EkYiUweAY8TNputrJ8TrHbx2adk\nagx2EkY5r+u9Fe+LIbNjsJMwyj3DruAhJTI7BjsJo1yPxLtT6WEb7LGTeTHYSRjlnmFXcMVOZsdg\nJ2GUe4ZdwYvAyOwY7CSMyrViuGInc2OwkzDK/fQkRcBTOnkqy3LZP4tIDwx2EkY8U5mpGLfDjiqn\nHVO5Qtk/i0gPDHYSRrxCc+xAaQOVh5TIrBjsJISiLM+cPK0E9tnJzBjsJISpbAEepx1uR2W+Jet4\nXwyZGIOdhFCpUUcFH7hBZsZgJyFUatRREfzLZAyRGTHYSQile2LKP+qoYI+dzIzBTkKoeCuG1wqQ\niTHYSQiVurJXwYdtkJkx2EkIle+xc/OUzIvBTkIotWIq22PnASUyKwY7CSGWkipynYDCV+VANl9E\nLl+s2GcSVQqDnYQQS+XRUFO5FbvdZkOd14lYmn12Mh8GO+lOlmXEUhJCFWzFAECo2oXxFIOdzIfB\nTrpLZgvwuOxwOyv77Vhfw2Anc2Kwk+5iKQkhb2VX6wBQ73UhluIGKpkPg510N56SUK9TsHPFTmbE\nYCfd6RXsIa8LMQY7mRCDnXQ3Pq1fK2Z8msFO5qM62IvFIg4cOIA333xTy3rIgmJpHVsxHHckE1Id\n7B999BFaWlq0rIUsajwlIeSt3OEkBVsxZFaqgn18fBx9fX1Yv3691vWQBY1P67Ni91c5kJGKyPL0\nKZmMqmA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RyTDYiYhMhsFORGQyDHYiIpP5f6KmFHVoRz/MAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x1084b5550>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = (2*pi/L)*r_[linspace(0, n/2-1, n/2), linspace(-n/2,-1,n/2)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(fftshift(k), abs(fftshift(ut)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 7,
"text": [
"[<matplotlib.lines.Line2D at 0x10869e1d0>]"
]
},
{
"output_type": "display_data",
"png": 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Ct7/9bbS0tEy1U3bu3In777+/oGvFHaBERCWAO0CJiEoAw5yIqAQwzImISgDD\nnIioBDDMiYhKAMOciKgE/H9uX7Qmwnl/dwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1085b9750>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Derivatives\n",
"\n",
"Formula for the derivative of a Fourier-transormed function:\n",
"\n",
"$$\\hat{f^{(n)}} = (ik)^n \\hat{f}$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sech = lambda x: 1./(np.cosh(x))\n",
"u = sech(x)\n",
"ut = fft(u)\n",
"# True first derivative\n",
"ud = -sech(x)*tanh(x)\n",
"# True second derivative\n",
"ud2 = sech(x)-2*sech(x)**3"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(x, ud)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 9,
"text": [
"[<matplotlib.lines.Line2D at 0x1086cef10>]"
]
},
{
"output_type": "display_data",
"png": 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3+znkQ6l2yTH/jRs3wuv1jtm+evXqUc9VKtVF33/o0CFYLBZMnToVn376qYQy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\nEMOfiCgL/X/FA0BLYBKJ3AAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1086b1dd0>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Estimated first derivative\n",
"ud_spect = ifft((1j*k)*ut)\n",
"# Estiamted second derivative\n",
"ud2_spect = ifft((1j*k)**2 * ut)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(x, ud)\n",
"plot(x,ud_spect,'r--')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 11,
"text": [
"[<matplotlib.lines.Line2D at 0x1086a9c90>]"
]
},
{
"output_type": "display_data",
"png": 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JiRkZUNZLG/5vfduIm8emQc5lHMgLXp8XplarsWjRom7P6/V6LF68GAAwcuRI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\nAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x1084b1d50>"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(x, ud2)\n",
"plot(x, ud2_spect, 'r--')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 12,
"text": [
"[<matplotlib.lines.Line2D at 0x1087a3b90>]"
]
},
{
"output_type": "display_data",
"png": 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n6tEr0f4+E/76PixHD0vSF5Gchjw5uWzZMthstn7Pz5175nXMgiAMePzu3bth\nMBiQl5eHzz//PIwyieTTm6qHp8MKID/svpIdNgTT08IvikhmQ4b/0qVLB33NYDDAZrPBaDSiq6sL\nBkP/5ewHDx5EbW0t6urq4PP5Tn1JfM8994RfOZFE3DoDvB2dkvSldjoQSDdL0heRnEK+LKG4uBib\nN2/GjTfeiC1btqCkpKRfm7lz5576lLB//36sX7+ewU8x56/fuQvjssdgrAR9absdCGSYJOiJSF4h\nn4ivqKhAfX09KisrUV9fj4qKCgCA1WpFVVWVZAUSye1E8Qy0GzIk6WtEjwOaTM78KfaFPPPXarVY\ntGhRv+dNJhOWLFnS7/nJkydj8uTJoQ5HJJu+/X3CX+UbFEW8UXojKjIY/hT7eAkOJTypVvn2egNY\nM+dOKNXJElRFJC+GPyU8nVqJbglm/t1e7utD8YPhTwlPqpm/g/v6UBxh+FPCyzx+BFeuWRV2P9zX\nh+IJ36mU8HRBHyy1W8Luhzt6UjzhzJ8SnibTjNTugbcnGVY/uz5G0b7tElREJD+GPyW8lCwzRvSG\nv7FbWu1OjD+4V4KKiOTH8KeEp9broAr44e11hdWPoqsLYppRoqqI5MXwp4QnKBRwpujharOG1Y/S\nboOQxq0dKD4w/IkArLpjCRxJA9+J7lwl2W1Qmjjzp/jA8CcCcLDkctiV6rD6UDvtUKVz5k/xgeFP\nBGn299k441tQFBZIVBGRvBj+RAD0EqzyXV98LbSjsiWqiEheDH8iSDPz5wpfiicMfyKEv7+Pxx8E\nAKhV/JGi+MB3KhGAwr1/x4Q/rQn5eKfHjxHc2oHiCD+jEgEwdNuRvG93yMf37evDHyeKH5z5EwFQ\nmU1IdoS+v4//y4P49o53JKyISF4MfyIAyekmaJ2hh7/iwBco2stN3Sh+MPyJAKgzzNCGsbNnwGqD\nT2+QsCIieTH8iQBoM80Y0eMI+XjR2omAMU3CiojkxfAnApCSacKjtzyEQFAM6XjBakXQxPCn+MHw\nJwKgUCqxZ9plIV/rr+yyAWazxFURySfka9NcLhdWrlyJ1tZWZGVlYeHChdBo+u+K6Ha78cILL6Cx\nsRE+nw/z589HYWFhWEUTyUGnVsHhCcCoTRr2sbuLZ2J80QQZqiKSR8jhX11djcLCQixatAhvvfUW\nqqurcdttt/Vr98ILL2DSpElYsGABAoEAPB5PWAUTyUWvUcLpDm3mv3PSJSicZJG4IiL5hHzap7a2\nFjNnzgSjflwyAAAM+klEQVQAlJWVYdeuXf3a9Pb24sCBA5g1axYAQKlUIiUlJdQhiWTVt7lbaPv7\nOD1+6DVc5EXxI+R3q91uh9HYd+MKg8EAu73/ZXJtbW3Q6/V45plncPjwYRQWFmLevHlITk4OvWIi\nmeg1KjhCPOfv8Pih5/YOFEeGDP9ly5bBZrP1e37u3LlnPBYEYcDjA4EADh06hJtvvhk//vGP8dxz\nz2HHjh2nPjEQxZJLt66HVp8KFM4b1nGiKMLpDkDP7R0ojgz5bl26dOmgrxkMBthsNhiNRnR1dcFg\n6L/AxWw2Y8SIESguLgYAlJaWYuvWrQx/iknp9k4Ix48O+zi3PwiFQkAyd/SkOBLyu7W4uBibN28G\nAGzZsgUlJSX92hiNRlgsFtTX1yMYDKKurg5Tp04NuVgiWZlMUNq6hn1YT3Mr/r3mZRkKIpJPyOFf\nUVGB+vp6VFZWor6+HhUVFQAAq9WKqqqqU+0WLFiA1atX495774XVasWll14aftVEMlCkm5A0wGnO\ns/E0HkPp3r/JUBGRfEI+SanVarFo0aJ+z5tMJixZsuTU4+zsbDz++OOhDkMUMUlmM9SO4Ye/t70D\nSh339aH4wpOURCclZ5qhdQ4//P3tVngMRhkqIpIPw5/opKQJBfjf794/7OOCnZ3wcVM3ijMMf6KT\ndCY9/p47afgHWrsQNHLmT/GFFyYTnaQ5eamm2x889ftz8cUFF8OYqgF3rKJ4wpk/0Wn0ahUcw9zf\n54uxk+GdNk2miojkwfAnOo1OrRz2ts4OdwA6bu1AcYbhT3QavUYFh3t4m7v17evDM6gUXxj+RKe5\n+Z3VUG/dMqxjnJ4A9BrO/Cm+MPyJTpNpa4Pyq6+GdYyTM3+KQwx/otME0kyA1Xru7X1+LFyzAqlJ\n/FGi+MJ3LNFpRFMaFF3nHv697Z0o37cFSiV/lCi+8B1LdBrBZIKq69x39nS1tKM7lfv6UPxh+BOd\nRmk2I9l+7vv7uNs60MtN3SgO8VsqotP4L74Ya7q16L9f7cB87Va49dzageIPZ/5Ep9Fa0nEgc+w5\ntw90dMLLHT0pDnHmT3QavVo5rO0djhZeAJfBgjwZayKSA8Of6DQ6tQrd3gCCogiFIJy1/bGsUUjO\nHhOByoikxdM+RKdRKgSkJCnR7Tm3LR4cbj/03NeH4hDDn+hr9Jpz39zN4QlAr+EHaIo/DH+ir7n3\n9Sfh/3TfObV1uP3c0ZPiEsOf6GuybK0IHGs6p7bc14fiFcOf6Gs8hjT4O85ti4fbXl4Bo6dH5oqI\npMfwJ/oavzEN4jlu7nb1jvegS1XLXBGR9EL+vOpyubBy5Uq0trYiKysLCxcuhEaj6ddu48aN2Lx5\nM3w+HyZNmoQ777wznHqJZBc0mSB0dJy1ndvRjRQxiGT9iAhURSStkGf+1dXVKCwsxIoVK1BQUIDq\n6up+bbq7u7Fu3Tr8/Oc/R1VVFU6cOIE9e/aEVTCR3ARLFlRtbWdt52xsRpcxHYKCH6Ap/oT8rq2t\nrcXMmTMBAGVlZdi1a1e/NsnJyQCA3t5eeL1eeDwejBjBWRLFtp5r5+Ctf7nzrO16jzbDkZYhf0FE\nMgj5tI/dbofR2LenicFggN1u79cmOTkZd911FxYsWICkpCTMmTMH48ePD71aogjQ52ThYIP7rO28\nx5ohmDMjUBGR9IYM/2XLlsFm67+97dy5c894LAyyDN7hcOD3v/89fv3rXyM1NRW/+tWvUFdXh6Ki\nojBKJpKXOSUJnb1nX+R1eNwUuL9rxugI1EQktSHDf+nSpYO+ZjAYYLPZYDQa0dXVBYOh/57mDQ0N\nKCgogMViAQDMmDEDBw4cYPhTTNNrVOjxBuANBJE8xB26jhqyoM/KiWBlRNIJ+Zx/cXExNm/eDADY\nsmULSkpK+rWZOHEiDh06hO7ubvh8PnzyySe44IILQi6WKBIUgoA0rQpdZ5n9d/b6YE5JilBVRNIK\nOfwrKipQX1+PyspK1NfXo6KiAgBgtVpRVVUFAEhJSUFFRQWeeOIJPPLIIxg7diymTJkiTeVEMuo7\n9eMbsg3Dn+JZyF/4arVaLFrU/35HJpMJS5YsOfW4rKwMZWVloQ5DFBXzqp+B0jkL+MGNg7Zh+FM8\n4wXKRAPQBX0QD381ZJvOXh/MqQx/ik8Mf6IBBCwWKFpaBn3d1WXH0peXISWJP0IUn/jOJRqAkD0S\nqtbBw995pAlTmg4OepkzUazjXrREA0jKGQlNx+BbPLiONgOmDGgjWBORlBj+RAPQjM7BiM7Bw997\n7DjEdK7upfjF0z5EA0idMhGL76oa9PXgiRPwZWZFsCIiaTH8iQag02nRaMiExx8c8HVFSwsCJ1eu\nE8UjnvYhGoAgCDBpk2Dt9WGkvv/NWjbPvAFT87ijJ8UvzvyJBmFOHXyV7xemXGjHj41sQUQSYvgT\nDWKoLR64upfiHcOfaBCDhb8oiujs8cGkZfhT/GL4Ew3ispp1mPjcb/o93+sLQqkQkJKsjEJVRNJg\n+BMNQqtLQcrRxn7Pd/bwlA/FP4Y/0SBUOSOh7Wjt97xvx078259XRaEiIukw/IkGoR2dgxHW9n7P\nB+oPIbO7KwoVEUmH4U80CN3YXKR1dfR7XjxxAv4Mbu1A8Y3hTzSIlPQ0KIMBuLvsZzyvaGlBkKt7\nKc4x/IkGISgUmP8/f8JR/5kL4VO/OgTV+LwoVUUkDYY/0RDGTxiFumbnqcdeZw/yDn4Ky5xZUayK\nKHwMf6IhFOfqsPu08N9n8+EXj76I1ExzFKsiCh/Dn2gIF1hG4GBHL1y+AACg7ngPskumRrkqovAx\n/ImGoElSojA9BZ+e6AYA1DY5UJyrj3JVROFj+BOdRcnIFDTUfYHOXh86en0oTE+JdklEYQt5P/8d\nO3Zg7dq1aG5uRlVVFcaNGzdgu/379+Oll15CIBBAeXk55syZE3KxRNFwWXczjA/9G/42eROmZeug\nVPCm7RT/Qp75jx49GpWVlZg8efKgbYLBIFatWoUHHngAy5cvx6ZNm9DU1BTqkERRYSmdjhRXN/Z/\n8BGm5+iiXQ6RJEIO/5ycHGRnZw/ZpqGhARaLBZmZmVCpVCgtLUVtbW2oQxJFhUKpxFcXzsBjj96J\nixXd0S6HSBKy3sbRarUiPT391GOTyYSGhoYhj6mrq5OzJKLQPHI/anA/0G1FY5012tUQhW3I8F+2\nbBlsNlu/5+fOnYvi4mLJiykvL5e8TyIi6m/I8F+6dGlYnZtMJnR0/HNjrM7OTphMprD6JCKi8Ml6\nqWd+fj5aWlrQ1tYGv9+P7du3y/KJgYiIhkcQRVEM5cCPP/4YL774IhwOB1JSUpCXl4ef/exnsFqt\n+N3vfoclS5YA6LvUc/Xq1acu9fzWt74l6f8AERENX8jhT0RE8YsrfImIEpCsl3qeq6FWC7/33nvY\ntGkTlEol5s2bh4kTJ0ax0vizdu1a1NTUQK/v24/m1ltvxbRp06JcVXzhKnVpLViwAFqtFgqFAkql\nElVVVdEuKa6sWrUKdXV10Ov1ePLJJwEALpcLK1euRGtrK7KysrBw4UJoNJqhOxJjQFNTk9jc3Cw+\n+uij4qFDh049f+zYMbGyslL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"text": [
"<matplotlib.figure.Figure at 0x1087a3e90>"
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lecture 2"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"T = 30\n",
"n = 512\n",
"\n",
"t = linspace(-T/2., T/2., n, endpoint=False)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = (2*pi/T)*r_[linspace(0, n/2-1, n/2), linspace(-n/2,-1,n/2)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Signal as function of time\n",
"u = sech(t)\n",
"ut = fft(u)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"subplot(211)\n",
"plot(t,u)\n",
"subplot(212)\n",
"plot(fftshift(k), abs(fftshift(ut))/max(abs(fftshift(ut))))\n",
"xlim(-15,15)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 16,
"text": [
"(-15, 15)"
]
},
{
"output_type": "display_data",
"png": 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qciiAGY1GLF68eEyPCa7VIBTyqtrseOXTG3hp4ZSQDnYAWHpXAnJTorD5j9fh6OXOkSQu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\nREQhiOFORBSCGO5ERCGI4U5EFIL+P445nHEkIdSlAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x108845610>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, add noise to every frequency component (white noise)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"noise = 10\n",
"utn = ut + noise*(randn(n) + 1j*randn(n))\n",
"# Transform back to time domain\n",
"un = ifft(utn)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"subplot(211)\n",
"plot(t,abs(un),t,u,'r--')\n",
"subplot(212)\n",
"plot(fftshift(k), abs(fftshift(utn))/max(abs(fftshift(utn))),fftshift(k), abs(fftshift(ut))/max(abs(fftshift(ut))),'r--')\n",
"xlim(-15,15)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 18,
"text": [
"(-15, 15)"
]
},
{
"output_type": "display_data",
"png": 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SU2hUCV/6QZVEJCPEkRSRRaZX0/bSJvsZZdA7CGJLvHGnElh9RPZMzFRzl0UB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HjuueegUChw6NAhbNu2Dc888wyk0pkpBjQVpnN96Zjpph7TIdu1btmyBddffz38fj9ee+01vPrq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\nCPMQYtwJBAJhHkKMO4FAIMxD/j9zv9U3PyFIXwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108ad3f50>"
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Denoising\n",
"\n",
"Can we retrieve the signal from the above?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"filter_ = exp(-k**2)\n",
"\n",
"plot(fftshift(k), abs(fftshift(utn))/max(abs(fftshift(utn))),fftshift(k), fftshift(filter_), 'r--')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 19,
"text": [
"[<matplotlib.lines.Line2D at 0x108afd2d0>,\n",
" <matplotlib.lines.Line2D at 0x108afd510>]"
]
},
{
"output_type": "display_data",
"png": 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nxtxrUYKS72nmTlfCCUujGUvR4FTofJXK0Unbk9GQgBVS3GhGlvUn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\n",
"text": [
"<matplotlib.figure.Figure at 0x10897fdd0>"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Multiply the noisy signal by the filter"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"utnf = filter_ * utn\n",
"\n",
"plot(fftshift(k), abs(fftshift(utn))/max(abs(fftshift(utn))))\n",
"plot(fftshift(k), fftshift(filter_), 'r--')\n",
"plot(fftshift(k), abs(fftshift(utnf))/max(abs(fftshift(utnf))), 'k--')\n",
"xlim(-5,5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 20,
"text": [
"(-5, 5)"
]
},
{
"output_type": "display_data",
"png": 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DZ2AoByskTDYK59NPmPKYHMlF4oXSqRlMiH+KXAQ3w6EqwaYmKAqm2XNRdJxf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\nRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108b04610>"
]
}
],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"unf = ifft(utnf)\n",
"\n",
"plot(t,abs(un),alpha=0.2)\n",
"plot(t,abs(unf),'k--',t,[0.5]*len(t),'r')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 21,
"text": [
"[<matplotlib.lines.Line2D at 0x108b0c7d0>,\n",
" <matplotlib.lines.Line2D at 0x10897fed0>]"
]
},
{
"output_type": "display_data",
"png": 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LHcUGXfITvlbEBOI2haTpk8NmhcfoyUwcSBIkCkb/7NRCsqFqxAnDlRjDcLWU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\nqXgjFRHdPLmBiWLYRpk0qdsTKwyWCF5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a5h8+Szqir8kO6WT1QhbJXWaSxvJeih96LExY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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108b0c310>"
]
}
],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Shift the filter."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"filter_ = exp(-(k+15)**2)\n",
"\n",
"utnf = filter_ * utn\n",
"\n",
"unf = ifft(utnf)\n",
"\n",
"subplot(211)\n",
"plot(t,abs(un),alpha=0.2)\n",
"plot(t,abs(unf),'k--',t,[0.5]*len(t),'r')\n",
"subplot(212)\n",
"plot(fftshift(k), abs(fftshift(utn))/max(abs(fftshift(utn))))\n",
"plot(fftshift(k), fftshift(filter_), 'r--')\n",
"plot(fftshift(k), abs(fftshift(utnf))/max(abs(fftshift(utnf))), 'k--')\n",
"xlim(-20,20)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 22,
"text": [
"(-20, 20)"
]
},
{
"output_type": "display_data",
"png": 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H/d1PcgoJau78kxIyR55ud6IeonJw+69Lzd7nEz9z+7tKCJY2R9Ea05zfOWlT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\nSyihhBI+hSgZ9xJKKKGETyH+P9piWMHzBJKEAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x1087801d0>"
]
}
],
"prompt_number": 22
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lecture 3\n",
"\n",
"Averaging over white noise in signals."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Sample for T seconds\n",
"T = 30\n",
"# Sample with n points\n",
"n = 512"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"t = linspace(-T/2., T/2., n, endpoint=False)\n",
"k = (2*pi/T)*r_[linspace(0, n/2-1, n/2), linspace(-n/2,-1,n/2)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"u = sech(t)\n",
"ut = fft(u)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 25
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"noise = 30\n",
"utn = ut + noise*(randn(n) + 1j*randn(n))\n",
"un = ifft(utn)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 26
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"subplot(211)\n",
"plot(t,abs(un),'k',t,u,'r--')\n",
"subplot(212)\n",
"plot(fftshift(k), abs(fftshift(utn)),fftshift(k), abs(fftshift(ut)),'r--')\n",
"#xlim(-15,15)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 27,
"text": [
"[<matplotlib.lines.Line2D at 0x10886e510>,\n",
" <matplotlib.lines.Line2D at 0x108bc52d0>]"
]
},
{
"output_type": "display_data",
"png": 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Ibt68mV2P2hcPPaKXJEmWghqPWKnMtIlba2srbr75Zpx66qmy71itVjidTni9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Vg+jv7KxVO5zHfZ7FocV8/GDk2OQRkNDR0DFqb6G5aEVwymoEwbCxsxR9/U1IQ9e/Zg7ty5h7xU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\n",
"text": [
"<matplotlib.figure.Figure at 0x108add790>"
]
}
],
"prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sample this data repeatedly, with changing noise for each sample. Then average the samples, which should remove the zero-mean noise."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"realizations = 30\n",
"samples = np.sum([ut + noise*(randn(n) + 1j*randn(n)) for i in range(realizations)], 0)\n",
"avg = abs(fftshift(samples))/realizations\n",
"\n",
"plot(fftshift(k), abs(fftshift(ut)), 'r--')\n",
"plot(fftshift(k), avg, 'k')\n",
"plot(fftshift(k), abs(fftshift(utn)), alpha=0.3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 28,
"text": [
"[<matplotlib.lines.Line2D at 0x108b21c10>]"
]
},
{
"output_type": "display_data",
"png": 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ZNcEBeJ7J8VpBmLRjp/VZbwWZQfDSMqUCJuongsEj+Wt73TBzpBRJ10XoM/Wv\nWq7LdOO6Z6axJ0oTIMqu2pwNke0wunkYCUYvkLbQSJle0+W+AEsoX6hN1O8Tjjpv/mxJJBiyEbud\naCGCgScuhC76ODfNHRnlG9Euu0CasGCOnV95inOxTF3T9xwG81YQ4slTqznLyd++kdZs4tRyAxdE\nXP2swqB+w1K9jXMW90drFrbMub22xG+3103+loiQ4nNmKcM5Y8wo1tUfnZu1SCua72a71HDH9SAw\nUoxeh8ssksas6ZRSx1KthaMnswd5HgjGQrWLpVorc3Xfpf3QNAmjTzRws8st1do4sVRD1ilK1A6r\na8Fu9N6t05iax+yDKM+UPuTudBGi+lBMN6ZMccJ47tB6dYRhpNFH7SsbOUT6+oNIYyu/HfLMAHO5\naIsVAqrhA0js1848czRIFKLYksQivPV2tsome4nxM7vgkmPKPvYihwT13VwT/0Fzd4LRYPSpTMpE\nM8cB01QrzaOZHju/jvWcnj0UdPAcO19NTrzJ9a5Nq+XcZPQkjbg+u9ZAGNIDsN0fqXsGZfnfZ03d\nO4FVo4dVoXfnESeuNoOMvsIRtCNTR0i4qxJlNJNiC1E5KiKE3UbPOdmp2WGFtkPe0zkMtJWVxdj4\nSeTSap8dWWHb4YyoTtNmln2z0TvoS40AFc8oAo0GxvKUR2pwwEx/NBi9AE/9mSBtATRNo/dj1cO2\n0LlUa2PJcaZnGsxO18Uigcb0BKOnNnUXckXDpBoczBlEGj3dQm6OUTPjcA+yNC+ii+tNPH1mDXbW\nhOR+oxn52DebzVTm496dyY3rjjR6a6bGhVammrTWCvD4iWUEIUe1GeL/vuoORcK1v+40pk+4SwnK\n8700j7Q+aFvMTqU5+0MssK/F0GrvJn5TJ8rIRmMkGL1eiUKzTjv4wJ2XyhxtTE1oSa8u1TUtPn9z\n8jjnPANNec/ReSj7aoccYOZOSg5zYKbMWgE4OnhuYnOmS3nVGHzcdEO0k6jOOmrxRjjRnlYPLR6F\n3waA5qpqontlsY4XL1UzzUS0/LQk+iIpd2j0AM8MKaGUxHmyWCyU+SzTT/SaWzMXzFj/9m7PsNXb\nhlH1RnuXW+65CnCbH3lMr/15nlAXeRwbtjJGgtELiKb47zNr6RI445HnpXd8sZi73gwUDwz9jYvr\nzc531abYK63EauVyHm2+KXvMMN1YNfGMxViNh8h8EiawMbpKmmeFqdGL73RrvGJdJqsuG41Io28f\nO6Y8O73qL8p9AAAgAElEQVTSUMJjdKLh6Skb7RDHL1WVe8IOrjd/so6T4s6nC3+RR64DYPJ4BHEt\nfAah2fa2vlia7qHFjXWJejvEiUV5iJCifDE3w6Zp1XvqXx1Ol2XyfdQCxuOXxGfVWgGWLd5N3Plj\n8zFSjJ7iiVOrWG92YZ+MNcYwpZWaRqvHl1pjvnCxhhcuOU69itHVIo+FKr0flXxmX4zVGKjTh9iS\nL43ql4++3nu3odEj0gBtZpq00oR7rdAQbQeVcC4ZfSMMjXwnSp5Rfy56lVmDxfxkvMdjs51D0KeG\nL3bMbjo56ctKU/JXi0dPNHq7t47jJ7Gx67MFimY7RLUpBLP6bR5xdnEeHemAS+Dk2wHtHqfL9TYu\nWdbWBm2XpxgJRq8OruhXK+BYbaTYzOOWevFS1ZiW6V4dOugAymRm2mOqZSvMIDfcWitN4TNmulei\nc+arVE0Gk9ss6Bo9Ny5UcGRr9OJ+IzbdNKpVMw257kSFMIq0GZ7B7Uw+LstL0ehdO2ODkOPKmQoq\nJbeQyKq75JFltx23CEyalT4rCzkMzTdW0lPLpgKnG6OJYXrSE2TtjAVdjI1nIZawzRRPnVlVzHND\nefDIVkaalkshmmmp3k5ivYt3PKZqw7pm59Ig83Sgw6+upG5i6WTDlq3jCuHheyyxzToUS6U8N/Pm\n1qs83baXri1pNms5YnomXUo9aJUihZ7DUyR+UqvVMFYuo1mvK8+y6dLKzWKclnuu0CjSvGFHyDnu\n2D2DyYo6nNshx5VT5Y7OY3U9ZGDQ168CyoVz5LVYa+G5c/IQj6VaC/V2CMYYWfjmZjuS8WabWbjK\nbrbDZLYjwjvYok96tlV3w4bm+ChHgppmTRi0cj8SjN7lbZFmR1UYnDE9ZOosIXnGlXwNxSxna7YC\nrnReha58WUhiHVA0eofGB6T7EOt30+zm/YbLYyUxcSg3TbpU5swV2u30RwymVqth+xVXxIxeZWyK\nRp+jDtIErH4rXj83NcX4fY8wWh0hjwJosXiRWjC1gHOUPJbaXnnaUqwfJL+Tdx0eTNpNl+w7v9bC\naqNtWZdQU9J6TI8TFqUUM/mfLdYUpcq1xcnmYqybc3SzZUcnbm0BjASjF7Aof5Y0WifiOlMAfMdi\nrEAyjYPDRhnDHZeGCAoiNFxwMzCZgC6OcnD4nmn/B3TJlG2fpDZUm1BL69/96Py2PMwNU3ahIJ+T\nbfuONCJcRq1Ww8KOHahPTREalBo07ullib9pwsreV4VmK/oET5rM5VIqdtQyxkxGFisteWIP2Rm2\npN9iubFboCx5ph2Y4lqEdtKVoQkFIcczZ9dxfq0ZOSZw+VokCNPfT4oRprIU5cY1Lq0YsCAYKUYP\naFpX6nOxCMmNhVefLMbSxk7yTem4ndK4IeBCoweePL2quICaZcudsc12iMdPqD7XEaOX0157Hv1H\nGtNOi8Jpu0cFqnPgxkyrdvIktrfbqC8smLRw+WKWRp/FAM3i5Q5RatOO/samG0umIZemB7GpKeGF\nDG41VqczlQPqGjYRfNbX9PTmUyHshL3bZUKkswbl22z5EgFaawVJPYt0DPa6t++XkPwBSD81y5bn\nVsOIMHrZCtYTaSxINFmjYwk/bXcptNFtUv2VpTpaQZh+4LH2jrjKOoLRxuCijqbm5HkMYchRb4Wo\nxlEDbbVBi2tZuBcHT0LsiqfrzaAjj45u4Gw6Hpk3TizW8dML+oKpmyZZV+lp6ufOYcfqKhqNhtFG\neU7kgqU/5IEQYFa+zFVzIoUSQkDrOh5zv5eXpqgMKIJGbRtLn7Fxdkf+ATfNMTYGHt03F0F10F3Z\nQkkTaxzJ2o5WQJInp/d0gSaUHDFONfp6EPybga7j0W9V0Aq18SIbY9en5h6zBASj+SqeM+bIPr3c\nwHjJQ67AR1z/m79LpKWkNvoSGUmGNpNVBiedmgOTFR8eA9aSTWnp7/YKl3BqtEPzkJgMBiR8n13j\nkiMy3WybnERzZUV9AE1AZ3ycKpA1DdfCGZQkSpfi8elT9vpUNXqWmFmQ3OlsPcFKEzfXDhhT6yMt\nL6fM5vZ6NG/x5L7BYLVUyXjk0XXCmON/rM0W5xmCfpcc4+IZLUcXBFkYNKMfCY1e0bwsGi8FtVtb\nTRFaZ5J5STt4wKN472mN10qJkElps3UkI22GJqnPKjiidQbBCKkw0esky+smEnxqhUQLfBvbdZ0M\n1WLP5dpf4zr+IWz7aaRXq1Vsn55OdshGeZkvuJinSHup2pL176BXv+daiBULrLb36MlUTPNGcot3\nS/lZSTT3RGnOy8zaoEcwUrHGZYsYS6/pWLGdXUthi7Qqrr1YELqUHfotxm5iLV/diNRNiITNxEgw\negq1k6RrC2Z8ax4xEmYOEdFBGAMWq208dWbVYJy0tFbKvnOb9tYr49SZue+xJHhbqBg37eXom2Jo\nvnRwMRb9n09L7PybfnqhakyvG7GbnAwoFRHkeRqzyWC+IButXLblWr2Gq+fnsba2hiA0fe91Ae1C\nGHKsNeyzHpvAtTE8OnN0ul5CCgg9iTBXpO4k1QhZqrWs+09o3q6Ik5SmtN/0QcAtJ1s5lDXdRm8t\nmLYPrWdmCkLIR0kGlJRTKw2yXqK+lyeo2VbCaDN6m0YPMaDMODPRoHG/Cy4DmzXpTktL2c3AzjhF\nyYm2RqalLrgeKafwaM980mMD7v4uoa3r2hItW9foGZjFo6c/WKq34q31Mv8nTq3i1HIjaR9x6LLv\nCRolFTYvJnUjM5nO6/yFA9V6A3MzM5gaG0P11ZMJDeJvcu1oMFXYu2vHYIaxHZnSFBjfYuYXhFw5\nppCmEJ4meRpJJFmqt7FSjwQUDe+he93oC8e2zNyB6aIWEGc6R2vG9tGi9m0iFByDi0b61KvNVRXq\n7ERm3GpzY1ZmFdJ2UtQ0A5YKI8Holf5EatRuo+eJm5VkCrJzyAUx8xmga1aqeyXNs51huqE0pu7a\nMz7Aeqnd44lAispwnweaoeiDczPY1kZqM7rGTM1louyKYPQWdwlbPQacJ8KdPrApktXxMUy+/e2Y\nD0NUn3tOpYm8mzqjifO1RTk1CCU/9RaSm/bcDgIh58nMxjjeTvBEhyZrISNRhS+uN/ESCd+hn4Mg\nFQQz37yhCTgXawyq54u+7mVTxGgohCgvreMoypR0QLLF50mLUiqEtaHRkxdcaxUqBsvpR4LRU3Dl\n2qxc0bE0mUDgXtfnGgO1vS7NQe7djDY7eagJlDywmRQEXYmWx+RmnKwOqZiwSF5USDAIc4A+sPoD\nVYOT1x4xu4yVom4rFpmV9A5mKNotTF6wsFYOVD0PE299K+bKZawtLcW3ufLXVY64L3JtEdOL/o3G\ne4h6Hu19Yl9dCO4My0G/QizGIvkd/81paju72kCtHenEplcVU4Rw1slk9JlRV0kjC9u2uTYhr2Wn\nDTlN6Viz0MqUi7GC1ZsEJbNdgxIZqdayVKTSPFg+nonRY/QO5icQEgbs1KJ1zYikSzwckjRqtxSa\nZwizMwjmGJL3xHQxtaMoTNypHwEALqw1EYbSxDRV8RGG5jcLqJqUoFPNVrfH5t140lXn51AWvhOi\nEhoYKrHNxrcwepqPQCLcuSrsbHbmaq2GmZkZzI+NYUUwemtfcH+cqFP7CV/ytx5sjioGXhx9VNDs\nMsGIOPZRwVA0YEZEgAtUuL98uY7lWtsqFHSlxeaSqOdJPs3517Y24ew3hBMbjDZ5VwpXXRdRFBQC\nfVa779pZzI5HDonCqUI5iEgjIBo76Z190IJg9Bg9vXZ0Qi92IdDNMqIfabNCBcJcQG3bNG+HWVIr\nR2qIYqOMU+h0iKVaG412mPTDqYovNXrNdAHIAWunlxsjik6B+w2becHm5lompps6iWfiQhhy4k8u\nTgKws7/qehXT09OYn5jAWuximeRO+kz690c5Z3leKTQKBSQmyvfktyd+7BaC6clU1OQISAbqYnAU\n3PlD5k2VE2E+S9VPdIZPNHPxO9RMgzYhQceLomhZylS9buRmyMQkaw4BqegjaoOSJ9egRBumBW8z\nf2w9jASjT2OuOuiAsnndRB2CGdqA0BA8MnhsCzNykdJNjM4kGOxMzgZuuXbFHPn56+ZQ8ZkyizFA\nNXqiDYm/DBZtjqmDz5afTmse6HUNEI0qlLELK76HhckyAODEYk0JICXzkKUHPGYQ2iC31Um1uo6Z\nmRnMTUxgVTB6rS9E97K/zmWjdwl1Sk5JaPQxq0vMC1q5VKMXCgo97o7eT4M6uXBrvWuNNgCOSmw+\nc8181bz1fiXt56FL4hK6RBl1osC4TCeKUBb3k/qwm3tk3cp7wnSVmN/iZ+utAEGobdyyCQ+dvozn\nG42RYPQUmRtZQBdcxT3ZERnEP/Z8xKCyavSIzQQikJTWGxPTTagG2VJsqB30iNRTlsgmmoDzxH6r\nrwVQEqngoLQpnZpFMyKX96iSX4e928ZshJuqrtlvnypby7DtjQi5XLNIzDfcXI0R0SunpqYwsXs3\n/r9/+zdUa1Wlf3CSp+sbklDZLhu9RTGJ+qWkyGdMnhDF3TNNTjV6zeTI6EUn/Qq2/hTd+8nZdTQD\nnkujp/nRCzqzjejXolc6Ml2stqXwdJlXDUVLJhKL0qa9XX6LqDNRTkgZPQPOrzaxVGsrdW2PhyrL\nVKkYDEaK0adVOCAZqmhY2+HZ0IVA0jmji5LHcP3COEJRmjZYg5DHQdHcdsSzq81kChkVyUga8wu6\n0RZEjsKPmrHIXWy9GWCChLNVSrYwoKRCtFvd+MjnBslaaPRBCGWBWyxg6wzXRlUQxl5Hmgkj0ejj\nv41GAxXfR+XUKZybngYALC0tKfWSNXukjCrUtME0iOBkAr4X72yWncT0qhF5KxydIlZKHAuXgL2+\nbPTqAlysk9hycJpsoNYH5/HGJN1GT/LU8xLC03NIL72tqHB2yjuiBAjoi9EhnVXBdJ12tXFGRJNN\nw0gw+jzeEIBkDsJf2WDmkKaKNBv79qkKwlB0IpXThzwKDUsjBtZbAWwxNkSejGXbUGkZlstUjYLm\nPVXxUfYIo7fscLQoc+SaKYdgGGmVjt2dMFC18ai9EvdKjSZD4JiKXLLBR9hoxUPdJbtWq2EyDMEu\nX8aXv/xl7Ny1C+vrMn66Wkz+bzO1cHeiRKOPYxWpaU2uQfm8odEzej+dXr0vmX1AFRZincRuunFK\nQQAR06TDQbSNDY1Ajb3ZzNpxrv8W9UoEpat/c0jtbMd0JflGkY9rN7CmLmp5bw2VfiQYvUB2XbJ4\nMVZcq28I7Zoh0hwa7VDhG0KSJ4tbcaeh0SEjM0EkRUQjP3l6DefWmg76uDYNtKSgKknac+VLI3gs\nMrPQQa/vdNXLpd8sTAZq3sw4eNwsuXMoNBDNTNqrLe/k0uijehAzOqIkRxTHlVCr1THFGPjEBLZt\n24brXvc6VKs1UgZRKCzlhDzyXEn9MPJbr3PaLvoJYaIdLqw3cYGcQ0wZUKSx0n3A4vvcY8PmAWSV\nCUztF0Kj15OeX2tGszDVhK2mJW1L6bTh9HIDtRYZX6EU0q42oBo6V8qxz2wS7yvy8PULE7hhYYLk\nSwWC+T1pitZWQNdBzcIwxG//9m9j27Zt+OxnP4tarYaDBw/i3Llz2LlzJ+655x6Mj4/3k1Yn8mi2\nAGHQsQYhmFVIuErUMAznVxs4v9rEnu2TSh4Roxf27qjA/z6zFpfNE8ZU46r7njA96IQL4ZJHQ9Sn\nnjztw5n6zX4i3tRcEhJJZ222Q4yXPLk4rQkGesJTEHKsNdqYHjO7UqdKjG2nb8B5dP4tTypLyd/J\nwMh1COpeKjOhDBIA6vUaJgFgMmrz6ekZ1KqqjT7t47IiekZmPXtbc0hhBERrCs1QFiNC+VZboRak\nTpoRDIFMZiydeEnZ7dhQOJvvMey7dhZHXl1BPe4vQMTo660wYcT1dmiYSM1NS2T/AHcIGse3SYoE\n7dqZz6TbuGc2LMmDZkvHL+dcCbnhaSpylulmQ02dOdC1Rv/QQw9h9+7dye9Dhw5h7969uP/++7Fn\nzx4cOnSoLwR2As6By5ZDegXE1D1ZSLVo9O7MSSaIjxvkavNxHnt4eKbm8OpSHWfXmtAh7Oe6B5CV\nfq13q3xeHzrynYCr9miXkiHq49lz65G5KclHfYPOQF6+XMdPztrNG51CfMFqo60sGpcYMzxY9N3N\ngkxD20JkBxbfEQpGQjQ0MaDrtTomOQefiDS5qampaDGWtI0tf1mOvfE4oo1BT55eVd5NDamtS/XE\n9MSha9/6WgPVYJUHOWFlhUz2MaHdCoHz4kXzfF3RV588tYpXluoKXYR6ANlhiimunhuL8od9rHCI\nDZHyv5gip42ezmqdoRgUjV71usnDwvNaZjcKXTH6S5cu4YknnsC73vWu5N6RI0dw9913AwD279+P\nw4cP94fCPIgrsR1wnFs1mWkCRjwYHMxV12Bd9n8/7jV6+4U8OrjEtjP27IqdtigErbsniCdiQCzX\n2zh+saoU7npbaPT6kFfCt1ryaAQJt1A1epiDQddukvw6VumjPy9erOF8LBRDHi9MhqrGJcwUlLd6\n8ejXNWvhH61qpSaDrNVqmIoZPTt1CjMrK6hWq5owt2j3MUSVlX2G26+ZUT6Lc9NVTxXUqlD1hJap\nFaRrw5Q56Zo79aPvNfy1wli1BNRubq0XzaVM34tA9wjY3qf3XjcvrASa0kNMULZNgFE5FuWA5GTc\n1wYwk4MnuTi13MByve3W6O23Nx1dMfq/+Iu/wAc/+EF4ZIQvLy9jfn4eADA3N4fl5WXX6wODB+lT\nTjsunfYB9sYRnUZqgeZArLVCNIMoyFSecRUxgEjy5Jquxu9cXG/i0nrLblIQaalZgmh9slOb71Am\n0Qqk3cBlElApE0gf9GlQtPCkbaLFbbkYy+wvxE/bIceRV1eUdY1o1qTPhqRWJphqrV7D+OtfD0xM\nwH/pJcwd/2nE6Ln5zbb6EwytFXDVvCKYc0qFiDKo8OGEVbHkW/T4SsQTCQyvLNYTQUflWJbpRt8N\nbRLLVCFCnjRJ1DhBmyJctJlGsiBuzDzUdK7fuvKhf4fYEEk5PWORcpbm9MBhKjVqsdGdMH4YhtFM\nvd4KB26ayULHjP7HP/4x5ubmcMMNNzi1hKxTkjYVtOGYmILFDUbMA4Bk5KpGT67Ju4nWQOqg0Q5x\nerlhzAooxkoeJiu+kj+NDpluuklJo93TBZKkm9mSx/nKu81AWrOzGX3/IUgRG4L03Z3CBkzveUxG\nXBTfIoJf0Xatt0KcWWkqC9QAUK83UNmzB/B98PFxzHIkGr3u0eLaxTte9vDmq6Yt3yO0WJoJ1UTV\ncWMzTYh7oZpFMtMTwrDeCs0XHRBZUbqsYQKI6UbPk3NTa7cVSanSZx66GIYjrchbrx+qrHke+Q0k\ni9cekzNDJb+0ceVIp3+f69WsE7E2Cx0vxv70pz/FkSNHcPToUbRaLdRqNXzta1/D3NwclpaWMD8/\nj8XFRczNzW0EvVaktY8ejztMRr2qNT59Zi1ZLEstg0yHAbumFC2c2ePBlH2GbZNlnBCeOpZO4yqd\nbuxQ/qb0UE9jZtTNzF5KhGbsccQsRn0vheJebJGqUhkzRkQbgnwWaet0ZsK18hhh9HqAXavAIu8B\nQBgGKJfjITE5iakwjDV6cfCH+nHNdoiyzxIGHYQcUxUfUxXfuf4TmQ6i68u1FqqtEK9fmIDum617\nQ0XMMJrZlGwcDvLb67GGLU03dm+TWiuQAlXXorW0OmPV67KdLDSbCZJLY9YAhU5x26RVvZOmSEX1\n6CX5hJzjwmoL42UPnkeEmOhAKTBjPNEy3CRaT81KL2rD0TGj/8AHPoAPfOADAIBnn30W3//+93HP\nPffgL//yL/Hoo4/ive99Lx577DHceeedfSe2G9AlGMHg5CF/Upuqxox3asxXF1qUFqI/1FlBcjfm\nKAxAaGle2knFlN61JqDToPsBO8a7Vp7Q6KH8tWv08roZr1om2hYZGLk1+k57t7bImJi0mNDGqEbP\nlLpgLBJAQpulGr2YauvQzVlBEMD3o9kWHx/HdBiiVquBI5r2UyYUAjh6ahW758ewey6yGwckmJxy\neI3GvZJdv4FcT9BnT7ZIlHr7CzpEfxXfLmKoU9u9jfm8cKmG+Th4F+3Htmaja1o2tIIwiSoqypTX\nYrTZM9Bn0TqyTvOKf0R/uFTuOAcabdJnYtOt0Mj1bHUTnWGjJ+lMWuzXeWcLG42++dEfOHAAx48f\nx7333ovjx4/jwIED/co6E2mVSKWyaGihHYlt/LYBZStEDEaar94JPRZ1az1eNqVBMdUge3pnZJPR\n0QCTidH7Lv8Dw6yg0Cwf5T1dqFO7pfJuMmAj7UksyOpviPq/9applHwmNXqiuCV/dQ1NM2eFYQjP\nixn9xARKrRaCIJCzLstopoHLAq4eAiKTypoIdWFGpmfUhJEwdU1FDrna3ylz2j0/homKJxm9pikb\ndBF7vzLr1dYBADErUAUthViQlQqzWRHuBUuWns54Tx1DFEkAuJhasX4QhaqW9a/a4sVMOSUmVJwy\nudLS6W2y1dDT4eC33HILbrnlFgDAxMQE7rvvvr4Q1QkuV1upBzyoEloMjHjQJGoASZNRnrmoqZad\ndBaHecTw6uFmpzGgzSry+txTeqWtPkJev2rpEZFjrtsjzPoSgpnB91Q/dUlN9K/YwCMjPqoDmllY\nj02jLwmNfnYWeMtbEAptIC5QrufQ0uP3c5j+OPnOkMu21BeM6YyT0huFfaDCQjKnHVMVeIzh+IWq\n8l2uQ0s4KUMX8jpKnpqHzXSj02q7tkG30YucdkyXsd4Mk9m28o5GJq1fjzG0468TGn2kONCNflEO\nb7l6GjXH2b660FW1c004pX9ix0pPvzH0O2Mvrrv95gF1oTMyp0hmmwy4HJyeDlCaju4QvXpuLPHZ\npgdlQHtNNZ+o9j7OgRcuVvH8hfX4N09e0KeBaVpEYrLRuFnalmyXVkdpBsyjBRWk8Isg5Di72sjz\nalwOEm1a7BSlaw10YVL3pJIavfx+ndXrwjBcXkb5hePRj+lpBO99b8LoabwY2ndovUcavasDSYaT\naPfk/WS2SNuadkuHCYDOMqFfk+mMldETwUWD1NGJhoDnyAOIHAya2gEdYrFcp9UGXfGhZhhbdSa3\nrN/ElX5A65cu6Is8xkqekp+t/pIziuP7dAMeKdlytXUw9Iw+S1Lq7lK0I5xbbUYaGOlQYgdikr/G\nuPT2Vaaz5MrW0QU9upeNPg2+XGtjsdo2yhR0S+2FapX2emDaX4Nr029xMBHdBJDWydPQDCJvl7yQ\ns5HI88bQ6AlTEHTKc1a5kYeZv5jlxDO81VVUTp1Onvt+KTLdgJhSoLeXpEn4/OtQ24wyV+5kD8JG\nrwtbEcgtCDkurDcN05/aNpJBucZJInQybPSAfc0JiJhlWtz25H2HpMia0Brpma0PRuDccmg8YrdL\nsq6jM3GRRi0nrj99EDmEprwm/TTlnc3E8DP6jAr0NE4vFGTR6a6dH1MGrz6NNMvRmAPRhKi2KeyE\nOgxBAhi/9XLlc7MDCyj2a8u02WD4FtgHKTNozj0wteyizT75e7xHqPZZFORLVoUaOC4K8SvXXZTN\nOJCCwGZSSNZbWi14JWnN9H0PAfFg4fE3UWVbYSah3carfDF5IYTsh+IULDrLsPWeyEYfxWE6tdxQ\nlBTxnfr3uZQOKoDozNQWgE8/4UrkPTPmY2GyRBi9pMMwDzqaXhecduUJyj19sZpeRxsQ9eJ45gEs\nqq5vjhnd681817wWcET13jQMPaPPAv3AxM2M9Flxj57GZgsb/PSZNWWLezLdt3TKpCPa+aZhj9RP\n2DE7txRClCb6TiMItdQaTRmCDDD9s2mZiWJimYEAkathox26M0fEQNLYvL7eIfbjMQZioxeC1hR4\ndCDLKbo6XHU7OEXQaqFUpozeRxgGRlpX9E7bjA9QTUzKHExT9W31muxgZoJh88jkk+TrXkCkX2q3\n0ctwCvo5wTbt3bau88Zd05gs+8nZqkmJTJ7SZKsrnU7FS8n6DZaXXI/EwrFFow84T2b1JrhVaBoK\ngW2MWjg9DQfeyc7kjcDQM/qsRUV9YAsvDoWp6Q3n6ETNgBuMTz2AgzBTZjIiIKpwOcvgVu6QaQIX\nA4fkL3y69ffp0WuCQlf2tDOGXDIBRl7isWak47/PreGpM6smrQQiCJwL+iNBu8fs0Rxtrq26bZZq\nteI9mp7+DVstsHJZlu/7iY2exUZzsdhOXXMp/VmbBWkIgySSJl2HIX3IWHdB1N84F0JT10HN9EBU\nfw0hiAmEsBC0JPct7SS+Xs8biI4VbKmSLKEVkELDyej1D6BZOVR6obWrREewridwc0+NLJ/pWciP\ngG1Nyv4lNDxGpcRw21Uzkk8Mls8PP6PPMgUo7pVMMHU5+Y7u2SW5Dv1wCL18hcE68tDNB2ae8veZ\nlYYiB4h4UP6GPPLHLtl8+0wKnE9sM20GM164bTE2CEGCh7nzS9fo1d+07XxP3TAFpgtZdSYmTBGi\nHby43j0LgYkZrt1GqVJJHpePHkXQaoniVNdBx/zdpSkqvxLmKoMcGJtz4vds2m21FeBitWUxT2iC\nhgi3U8sNPBEHVUvC/nK1D1H6rJ9HbtJyyr4n3StJ0YZG72h8qnyYvNZeoy5zVNozL55lSBdMWb4o\nW1EESH7ifcA169ZnItqoLhh9b8iqQLVBiemGaB7RQFO1cRv0DgJoNnpSjluzM32AXdPWE4t1RQgJ\nWvVgbI02R8X3jHUEQDVJRWU5qNK1IK52aOqtY0QbtNyzwRb+Ng30IHZ6tF5EjwnFJk0bmLxjXQ+J\n77Xm5sD23Jg8n/hfD4E3CaOH0NqlzZWyYpcZhUM1KSkafVInakMlfVUTRiLDsytNhDzKT/csE/C0\nPMGjQ3COnZfRJqlGT02DqYxe+0bfi4L4BSFX0tD1B1kTJlxRWZ2M3EIETauEKab3vWgNR68zayYw\nXU7s3zkAACAASURBVJKTIeAgzG6iipWIDIV0ozH8jD7jue5eqLtfiQHFyABTlD5SQNYpUJTRuBgf\ntZELzclIqzEjvaPpduhWGCqn4ShaiS5UCJ3Q0tls9PqgpkIxuUcFAqVdqy8zDrmZNwX1YPG9+EhA\nQq/xDeQ9UbQe60ffrEbfC6enwa59XfLcGxtDELRlIiH8lG+006B8F9e02uRaavRGF9AELzWfKfSn\nVajQRLWZTuKZBGqCksyPQ7bdZMXDLTunUgqJUPajGZesU+mznhbxk5CZQNGMbX0VwjkgSrlSbyuH\n/7iidUa7pHmy8J2HlogGm2hJARH4c+O+0h8HheFn9BkVqHwg07Ryob3TqVhKa1rPG+0Qk2UPE2UP\nr7si2javTwONaSHhAsJkoG8KEt+k26Vt0J+JAGv64NA1JPqe4UJoYUIAjFOoeMyZTi038N9n14z0\n+uAUESCjxVhxyLksUofhDkfSRY+Yg3HE9AYB/JIMOOePjUmvGzClHTqJZ6Lfp5ukhL3dNfNKNwdw\nRUlxfRd9LQi5PAiECKCAk3DT5P5k2cfseCnTtFn2PdX9leU33dhmiGll6fcv11pYrrfJM9dJUlKj\nzxN4MTHZ2GhJmRDQsq+7YgJ3XDNT2Oh7RaqNnsnGEryIMlJht6UNrzcmzT0I5WCz2Q7pQpptalgu\nMVw5XQFjDFfNVJIpvU9GuckUzD4VhPHhJmLaHcYx8FPqwjadvGXnVBLrhEF1AROzDYO5WPJW+TzR\nmHWNHtHUfrXRxnoj0sDqbbfjmagXDywJapYGUY1UECkMiqnfowvGMAzhe5LR726uoHXqp+RdaaYS\nlOiLmK7NZDK9Gg4hsYdbZKcxW7AwxFArU/9ePWtRJl0fiOiTm73ozMva3pZPLHss9rzhSZktTdI7\nlTKiSOjmQ0dypX5EPQj4nv1dEaZY1+iV77EqCUz564IaiVTNv/C66RFp9aez7kh5p6yTYbzkYb0Z\nSA8TqA2qm27yaMtMLTbBnm2TBiMIyJRZUqWmoQJEaEm+R45ChKbRW2jLs5bBtVGmrA/YBmLyroO5\nxWlfXqzh1aW6NFXFo6wVhHjy1Kr1XUBq9Ig1eqvU074B0HdDq1q+qj2qxhsa1AwAxscraK0tKfkn\nXjeCyRCOknYotm2gi30FLtMXoAoj26cbnkeWa+VIS6HBxy5QlFmKdBxmO+s9UkfZZ1Foa/Le5WoL\nlZK7wWyCSFKgpjESEmGr0+s6GIcxhpLH0GyHznUNlT457gxaUqB3U1cIis3EaDN6oilQRkU72ETZ\nx0TZR7UpN8ZIhqsiUHuTu1yw3BUbhnLRUWxKsS4YxkW2wuhQC3GISpRHNCOZnyil0CYEGbMOHtoZ\nZ8dLCgvMWmhlsM9wRH2dXWliqR4fD8ihHMphUiiRmG4AI1iY+IbxsoeZMZ9+ilVbE2svNvu6uKcz\nevzCL6CtMaOIKdsbSNfkZBKZiLqYJu6VoDNF8Q3MuShKoXttMStnZEp6IGL4wmwk7ntJ588XT4mi\n5Kk2etGf5salu6q+IOna2+Ea0wrz1GaOaWZVGpaiHAe+c9vozQe2pFZlKiUFVdIGgaFn9Gmr2YZe\nrCmFov19UgvjJb1KyCDN8PqgW6WzpL9g6iKqnitPurADRMclljymaJXRqTrAG7ZN4urZsfSCFRrU\n65BHERBvWBg3XOzIsErPRyU9iYEyVpJeQR55Hv3lym+BxHTD5CxAZ4hlj+GNu6ZjOqK7dGAzcuES\nSAkTP3MGpcuXkvvBr/wKAmLKAeTmOpuHhWvCoZpINDNOrI7aBYRJo5GGuwWxbRYj+nAQco2WiDkL\njxX9+9I2mgGS0evdw6cGbv2ZQ6On5iRbeIdkYZrMRmjWen1QU17Z99AIQvV7XNOlDkH7s96ervMp\nNgtDz+hTTfRG+zFlMZZqewKTFT91qpZn+qayovR3A65uDDJ2vWrpI43eU3aB0hPq4eizNhOAGC/i\nWngkqRqiqB9mpQdwj5GQy4W/IJQhhYWm30hCyNq/lWrxerAw3ZsKIIxNsdGT1tAEsGq4AfjFSyiv\nS9fDUqmEdlsGzYvqCIkJR6c5euaYrRBOn7zDJZOSr0ktN0romInFCNSXFeib5QAZZTKImbLK6JEE\nkkvjSbbifI9Zd46rMxR7PtFiv0OVYOYPraqStS6Zr0ogNdNUfIZGO0SFdC6fqQv/vcIm8LPCL2w0\nhp7Rp63P6Yxet0Pb2nSi7KtaqStva3mys1iFhOUd22Ksbl5IBkQ8mCKNXu4UDbjqGWCNBZ5Cr7gW\n/iVg4hBl8SxjAFieixnCaiOAF4cvEMxR+MM39PCwGpHlWB30GIvqyFKOzR5PBYQp1CWS4uKbQRDA\nGx9PnkeMnnhzMKllJnxbodmxtZ6ad6DasSMmZfYNiwJsbVcl/o/8FOycqWDHdNlIL0IV6MHfhHsl\ng2ZmsHQc2zd6zAw6B8g+JmZB9CB528J12tqA7VrsQ0izqlINv+x5CMPIm+jOa2cBAONlH7dcOeX8\nNlvfSRtj3NaeLN3MvNEYekava8ALk2UsTEUdnCX/0I5Bp//qw+uuGMd4yUs6ZxgCJ5fUsLqyA5u0\nUO042ZFJatim7SkHeljmAkI7eOOuKWyfjL6r5EdrAGJc0UViF1OWU3DHQIUc9BGTEcvWKk22zkrX\nC2Rslui0p5cu1TBW8tAOVI2+7LPE95lr7wrodnmfmcPLZo+nDEQXgEyvXPJtQRjCH5emL9/3k+iV\nIl0yI9SkU6MdWjfUiRTUzEa5pwwzoWqUyQlaZNrhinWvm+CAqK7kTFEmWIm9nejJVoA0AYn+06k7\noMsrih5lyTVaZHtpL8XZbJssG4pafEX+jfoNLdqmdAiIxWFfKA8anTbkPvc1Rdp4YAMNbDb0jN5+\nZqv4q3YqnUnrknqinF0daY1uWwdzxieP0/h6x3cMsJmxUtIZS/HHUD/lvJs6TE1DVoJgVAkZsZTJ\nXm8gQifuzXTgjJc8tEIZO6cdckyP+VhvqqYbHb42nfYtzUPrz7PVucYEafuJxWsZiTSEN+Zm9AAA\nrsZMCXnkXfLEqVXUW6HdbAZViOkavS3IFkvek7/HHB4sLq1Xx/SYnxziQX3pBco+Q8X3IqatuUYy\n548IkReYlJy6WTQ6n0GNkyRNS+pA5ODYu2MS26dkOAqleJK/EKLWODwsiq65Y6qStHU51ryMPt2p\nzcYh0KvNANWW5aAUploTNhtDz+gt81t5ydIHgc7oO9sBZ6ai+Qjt3KWFCdjcLTPLYtF7YrCGnB5h\n5yiPZqt9t6AjmXLGXEYcgsxIWldfTXPzK/teZK8XGn3IMV3xkwHh2jmZMHrtN4VnvUeuBaPRGvu6\nK8Zx5XRFuReGIfzxieTdyksvod0iB9uwuE6Y3LPAubYXIINhGHZarppuVGVETStO0br9mhnlvhrf\nxmxcUUWz8Z4JGtufklPxPbxpV3QkY0sLJOSQnaQM2R/VfhX/9UyN3iOJRR9L3E2pMmbprwyCeaoz\npuidKKVYqL9yuoKbYtOM2EGeJ2RH6gdbnnEeRbl9+XLdUAhdAdU2C8PP6C3QNffknskvlXS291yZ\nZyjqUqOnC4OWtJ4n73sMuLDWSlw9AccKfvx/EEbvB1Sjd2jgMtKh+pAyGHFyTqLRU5q1PK+ek5ov\nY5YAYyR9GHKyoUaYbjxi7hHfquZBt+QD9tmRTUN0avTmZyhob98Of0Yy0fGnn1Zt9JCmNLmAzJUQ\nvVaNnmuLttrz0GLUZfF7iXmJIVlAtPWHtPJFm0/Hu6Cjs1Ml/Um6+GVhx9af6/lR+ER4MDIAFM2e\n66YbZjW9qd9h3tSf6ccrJkqJQaWsQyPelIUGHXYBJ68VXUpvI2bfTb1ZGGpGn1Vx8ZEZ5Hf81+Be\n+cV7qgxgZlmvX5iQJgLLAFU7nJk7t9xlDEkkPrEdX99Cb+RDOLdVEDK6+MoU5lTxPUyU47NU47uv\nmx/HwiRZCyH4uSsnsWf7ZPJbuO5Jjw/EB4nI52kQdPme6Xli2HwZrLbXPMK8PTsDf0Jq9GxyMl4s\nDZP1ikTbTBgljK3/li9QNibpn7veDGF4yDDVS4VBhquw9QcdzPJDeJa0Aq6Y/WSy6Hm+KKgq1MPb\naf2rGrQqmGVaKhwU0kl/VdewVA6bl4eKBf6smbZCQ+o9eSXqtFyyrCWh0Oi7hsvIYZv2Rc/ULqIz\nAZpHFkSafdfOYmZcHYARI46uyz5LNvTY4DPJvGx9z7qCD+lHn3gzMIYgCJyLrWnfENEcu55CBnEW\nTG2y4uP1CxPG+3ThleKKiTJmxuQBHtunypodnyv2dpcfvY5oMZYZ9+j3eETzpd8o28ZdO2EYwiOE\n8akplBiTB4TDInh5vNU/RdDSRVVbTP5Xl+pWxqCnq/gefv66OeMbsjX6+C8Drl8Yx46piuInr69Z\nlT2mBMkzyrAU4jNp94clrezjqhAQfX685OH6K8ZhqR4wBtx61bQRXE3kFJ3UJe+n8XDfY/A8y0Hx\nyV+LsHFnp8x42yGpVD0ds8ff2SwMN6PPqDllBybTppGwMQH9woSuGdp2eZp6h6GDJLAF4HJkqAxw\nXUg1Gw3cfvvtWTnF5gvzufC6kUUYxhvlroU8K66NNX+mMQKqUdnMCAITFQ/jZaGFmfn7hlcTS7S2\nqM1Z8sxl1hIIggAL40QoT02hFN9P/Oe5GhBLaPTSrGIWsNYM8LPLteQNDov07gCmRm92InpLatMM\nu2bGMF5ST3/SF73LPkMl3jgoZ4LpBOshBRLGHhOka/ZAJJBvFm6NjCVxl0znAobJio+xEm3X6NK6\nGJtB6/xEyRBk3bYHnakkm9G4WV2uiJqbheFm9M4nDJMVDz+3Y1Jh5nTnKv3ruO3IOeUZYcjWvqZr\nYkxbTNT7HgNWGm3o8AgDEwOo2Wzg/PnzibavwzpeNbMH9Zun19aMQNKYxSm0RmnUE6KogEzr/rdd\nNZMsQtpt9Krwoxp97Hqf0GjOB1S0Tj+PuQnpe84nJ02NXln0i4RUxOi9pBwddLFW7DrV9QPj04zn\nzJ3W8lp6P2WgymcS91+YbjyGMZtUTUFaIDlKj97fpyr22a7abnYIwau7Vwq4+Ore7ZNSGXAVrJWj\nPzPvMSWqrLEWxgrTTdewSUipTTDo4XV1zbrsiD2QS7gr/dXU2KXG7WD6MVT3QHm9Z/skOI/8+I0Z\nCFOvASAMArRaLWdZSlWRwUeFE32sezKkwqJFJo/IM3pwiBIXPmdBHuXcMXTTDYNsV8N7g/4lGQnl\nrl1bR4kcDh7u2gW/XCbHCaqmG3G8YCuQjN4KbrvUGYFo4+ze54qQmZVe0T6VXdWChujvFRNl7JpR\nXRsd+oEVtrRyodyeLrmhaedWxktqKTGLWV7phK+mC0jzbhKfKv6t7Hy1CvLBhkAoZSfZuoh22jFM\nVTys1k3fVQoGppg7br9mRgmaFd3X1I/U/Cz3LNNTqpHY3vGZ/TmN+pfGQMUACoN2pN2Edl9uSo9h\nbtIEh4jDI9wrKWzeIzK6pulZkDAZuOP56ydmuWDbMKUcuKIJVWMB2iIg79g9g9V6AHbhPMKLF5Wg\nZnzXLvhTU5HpBvLAGtpNRARKGpcnFdzcNCXySoOLKRq3beqn8UzWDec0qF50b6zkSTNJHlpSQBlh\n9FdtLyu079KTCRNcO+A4emrVoDW24CkhGfoN2d5RQ+gau+72Ozvmp0by3GgMt0YPoOQBb9w5bTxT\neLahzUWdWfppa9pVSpmicwovFGc60A7typdpcVnkk7QwqlF0TMlAgUijB4B2u22ln4NjYbKMqYov\nDxGPy7l2bswUNsy+EGxjxlLoqPcnKiSypFCHLd+U+NPHv8dKXrI9nUJXmm+/ZibxDRd5inq/ZecU\npsZ8qf0xpjwXSEwuFy4iWFtTo1ciCoOgLsaqwkpolMnkMGN9JxQ2ev0ZSUN/u+COvmgvlz7zmGpG\n0/cr2FBRbNoZ1FFFh6yRRGW7c6GaOKXZlQ5Jek1oMpa+UdFGMnPXQcXihWTEXoKqyOjts2tmTHFQ\n2GwMPaPPWiXfMVXBrulKbO7oYHS4yowb88rpCt72uogZ6QOJkXtZ5fgksc0V1EouI2XGF+LIuyBo\nO8ph2Lsjsk2WNV/Ma+bGpTAkZqLQcDHRNHpNE9eLve2qmUQg2qayAieXGqi3gmSgMGZ3fyt7niIA\ndU3OI/UyO16S4Q8YYRiudmk00GZMMd0AYndsGOfP4sNnyPfGGTvbS2N6wsxgxHTpWNmLGWcON0Fb\ncDNavq8xY2tpjOG2q6eT8CJZlOl9wqbRW73MSB7R37TKjd/R6xLqprle8NbdM3JjHYGvmbvE6VX6\nTHurYLgZPfESefNVIlStqgVUyDTUZo+mkFqVu5GUA6p1qU7yz9vOrtOBXBtJ9Ofib9AWjN6MqHHb\n1dN4wzbpHlm2LBwy7SIq0xGkK4aM4JhjVVaDnnSlERhxhXQsTJZw/RXjzufuemcqc4ZapwwAa9TR\nBgyN3vd9hGEA8KgvRYHYVIGcxmt1xhbyyB1Q1+mzNkTr35WEe3CtKVpookzX5o6Y1XwTZR/jvufu\n24qyoGvZoqzsmYHyZgZRYset/krHGr34q71WdnyvfhYxEGn0wizaxVaEDcWQM3rZMK7VewpXh9Yb\nOa2NbCEKdCai52lbrBW/fc9kQtF7lJmoGlliRyf3hOkmaLeMmctE2Ve8DAzXMthoZA4vAfNmvZUd\nrsnYiaiRoB87ZwNjLHWjy3jJw+5ZIggYEfzxte31+YkSfq6xiAAwNHpquqn4LAmtTGkCmFHnAj7V\nOoAk2mKncPXZWc0cYOvDksFL5kTNDGkheg1SUxTstHFDZxU/f92cszxAda905cvAcEe8zmabHXWy\nISoLIqf58VLyQ3dJ9VjkVqna7rcOujIaXbx4EQ8++CCWl5cxOzuL/fv3Y//+/ajVajh48CDOnTuH\nnTt34p577sH4uFsD6xUu043eGWXnd2jyFm1psuIpoQhygXRmm80vK3qlzU/eWgx5Lt4RcdODIACz\nx4JKULZlrs0QGISNPoUQMsC2TZWxanEFTbLXstFzDTJ3l2bD9xi2WUwL110xHjMzyXVpER5j2FFb\nQZtzg9GXazWEa+vgQORySJQLYdliDHZuFKcRu5gBcS4vNzio6GmuWafRdxjw+m0T2KF9r40Mmysn\nZY5eB8wpLYVYjKf5u9Zv7HQJpq36JtlcFQXdQdgfGz1527wT5zU7XsJbrprGk6fXjENTWNzGtoih\nWwFdafSlUgkf+tCH8OUvfxm/9Vu/hb/6q7/CyZMncejQIezduxf3338/9uzZg0OHDvWbXgW2ODAJ\nLJ2basS2pLTRxEYOijftmsL2FBslzccmaGxwm25sWrf4KzVI0YAiymIQ2BdjlXwYw/UL44r3jW5D\nZSw+vUvLjDIIcfmWq2ewZ/tkqlAwNFLt+5oZ8WJ6gTiQnfYBHe13vAPtUsnU6BcXES5eBoBkE1Hy\nTihjA9my3bN9Ejdum1BOEIuOvbMktli/UjVkiO+xCwRm6YDU64xq9J2YGcT3Wp+l3HPNam2IQmSQ\n8ozxGn27z6IZts1G3+E2gNQxqvAHUZeaRs+gnRa3tfh8d4x+fn4e119/PQBgdnYWN954Iy5fvowj\nR47g7rvvBgDs378fhw8f7huhNljWCpGmg7ptkaYEsGnf02OlVElNBYVNMzOZnbmpJxcUoRVdSBt9\nupupwK6ZMSttytTf5nVjuc4zTba5rtKqbCncrz+jJG2hXn8WvPnNVht9yfcR1urgIEHFEA90TjR6\nC7ZNlTE/UVa0S50pCTOGi04XGJMbnGxQY9iIdyT9qqUsXz5ZyakilSyqakJGzca8GYQcrZDLdTUn\nZfE4c9DYrUZvXdugfVbLn5pVQ+Kq2v2MYmPQs43+7NmzePXVV7F3714sLy9jfn4eADA3N4fl5eWe\nCUwDtdHrSHOZdC6idknHldOVJJ6LyCdvXq7olpREPaYMZS76Yuw4C1IXLN0QA1J+RKjRMVnxU9dC\n0mcutBQzvRIBsk9jxDZzE/ds6xTtdtvqdRPWo/AFdPAmyj2TGqYLVDmg57FSJB5HOXtOmrnIllZh\nVsweSTHPUXcshUZ611ggNXUp58x6suyRMWqVEAk8Cxf2WBR7vxOIfGyHp+iCErDZ6OXpb0D/vH76\nhZ4cO+v1Ov74j/8YH/rQhwxbfFa8iX5gZszHTTu0QEfM3RFd2rjtbifUL0yWsTBZVpiVThP966LJ\npdPaFps8rnY04V4ZBgHGM3z802hUbfTqnOlNu9S67mRR0V71DLPjPubGSzi72khJ1z1ofjumyij5\nHv6f11WsfaHdbtu9bmoxoyeDu+QxNMGlCSWFhuuvGMez59YBxKabLsJb6fl3okzosw5dC2YsWpMa\nT9kk5aZEzQewH85uNUU6stL3qLgEQpQvEJD7kQ9+FNPH5haZhWbbHMOMMeyej8Jy6wKSiqOtvBjb\ntdxpt9t44IEH8Au/8Au48847AURa/NLSEgBgcXERc3P2aWm/kOaFoXbsWA9xaO69avQC1L6d5TUg\n7lOvDIXRZ5iIqCYBIDkgg8ZP7wT6gIw8M/RBxbQOnJ9h6cwmyi/yhZ+qeAh4JLivIZu3eoWez/RY\nCeMlzzoIq9UqSjYbfamEsFZTgn8BKtOPsnNTTTd1hUB6tTk0XoPZsfRZBIXvMczRjWWW9269asYa\n/8Vc6MyeRb9x55Rcc9AUCDW9HVTe2IQo7UtGHbm0/ZxoOpS13XORIjtW8nD9glRqKR0hCRfeR6ef\nvqArRs85x5/8yZ9g9+7d+MVf/MXk/r59+/Doo48CAB577LFEAGw6nB0x/pvGeVOwsrKSKy5L3uyT\nQ681TFSym0U3hdCdsd1AHziMCa3PXSmTZV+JXZ66oMWiA831WYsQivTwjX6Okbx5Xb58Gdu2bTME\nrLewgOCKBQDqomWZzM1znynKRBAuE53q+FkaPc3PYww/R2a+ggGurq1aw1xQ6MHN0sq1rUvJZ+q9\nyYqHacdOUXNXuP6un9Cl++X32nea7fSWELMFvUThssoYg+eNiEb//PPP44c//CF+8pOf4DOf+Qw+\n85nP4Mknn8SBAwdw/Phx3HvvvTh+/DgOHDjQb3pzQ2l+ZmrZalqzO9mSXn/99fjYxz7mLpN0dFv3\n08t/81XT0YaM+LeQIbddpR4VZ9o7WaLRiSyFe2W3jF6ATrvXm0Eq837DtgncoR1r54KILKlzeg9x\nvfNocGQoxxuG1S9/GdtmLWEXdu5E+5prEMUziQjjHJgd9wFG+1a+ckJuj2IobfR22GahvZpHP/ax\nj+HIkSNO2t+6ewY3WM4hyANjJpD8ja5uvWrGaSpyeaIJXD07Jo9FVJ7znupkYaqMyRxKFoWq0YvY\nVWzLbZjqykZ/00034e/+7u+sz+67776eCOoHXHXs3DDVwbTy0KFD+NM//VNnudZ+5sjMFsveBn07\nuW1mIhh8t4xe3yYvNkGlUWgKtJS0JO9k0SxaydRMZ4MZISv/+39j23XXGfd930c7UOs05BzXzI5j\n18wYnj6zJoVVCnZMVzBeYji/1oLVl9KqSBLJqHWsHVOVXIfZ20C73eLikjOdzZSTPmsz74m+24kp\nQy82rczJsp/sdwnDzt0qKfZun+w4Zvzy0hJQngIDEo2+5KVv7BsEttjacO9wMVtlyunoOT976SU8\n/PDDcRIzjW6/NcpgDG/aJUMx0LLz8S97J7NN9j0mpovR714ZvcxXJbRfAQDpgelUUNlMAb1PwDvL\n6+WXX8Z7zp3Dth07jGeTk5NoNNTQDGoYDCjCyoU3bJvAjulKfL5pdM8Wk9+1cK9nf+V0JTU0chq/\nonmFYT53XOV9x7fSujYdCFRFIi1f13muNuj7Wnq1mHQyI/jJMz/BL//yLyfvhWE0Lm+NZ+pbCVuL\nmj7CyuyZymj0tP/xH/+Bv/mbv3HmqXtk2JB1kIL1WVbnsnjdJAcr94nRu1zrXItTdri/gwYco38j\n10TJBDoxg2RSkzOfxcvRhqjShGmmmJ2dRbVaU5pAP4jaYwwLE2XlwHQboh2yADjwlqun8eZd08qz\nvAjDEM1mM3d6HbS/hfqp7lnvwh3uwfYJeijwPFC9dtJF9fxEGftIpNPN1KNXllcALs8qiMrfeto8\nMKKM3mU9UU0EZvp6o456ve7M1OvAOVYxaeRmXvZEhrYnUrJI2w/CEK0evW5caFjczVzI+kbZ/8ng\nZ6r91qbhd4s8kQ8BIIzb/NXTp41ns7OzqFWryj262UjQWyl5eN18+v4FMb0HA8bL8mi8266exp7t\nE0ka+heW3//6r/+K3/zN30z/qDQ6RGa8C0avEfYrv/IrOH/+vEGjQKUkzrmV9w4dOoQvfOELzjI8\nzesmqw3pzGgz10CpSY9GSt2KGDlGT5lGck9n8I7GaDYabkaPDhl9hueADbtmKskByL/3e7+HRtMe\nzTFa2Y9MIY8//l/4gz/4fTzzzDMAumf0rqn+wmR2WNo88BizzKiYKoD7PEh8z769/9ixYwqjbC0u\nAgDe9773GWlnSyXUjz2n3FMC2+UU4l//+tfxw//zf6zHCOpB5xL643TPPPsM/uff/31yf2lpCZcu\nXcou1IGEz/MAYRh2biojyR955BE891xUP7Qe9O5EZyxnz57F2bNnndl2tauUaNSbhaAdSJt+Ynba\ntOI7wsgx+gg2uw31EdcfRXdqtRqqmvZGc+yE0XcC2cGlz/XBgwdxOtYwbTx4vORh7/YJ3HvfvTh3\n7nyiVbVaLaysrHSsqdls8btmKx1tOkk3T5laj+4NRZl+P/CGbZOYnzAF1enTp3Hs2LHkd93zcPdN\nN+FDH/qQkXbW89D8yTOKIBQnF506dQr/4wMfyMVcnnrqKbz00ovKvaeffhrf+c53nO/cdOUU9myf\nxJ/92Z/hU0QwNRqNpJ8uLS3h5MmTmeVTJEy3C40eMNt5bGwsvu+uh0QBYxH9aaYnPUR3nvot4ysy\ndQAAIABJREFUk30Nm4UgDBINKVl/2qIq/Ygyeii90bTJa3fin40MjV5I7zxa80TZw7VkKt9N8wvB\n4vK68cIWwpBjdXUFa2trCW3XX389vvKVrySb1/LB5PR5Qj/nRcTEVUErvFUoE6B/NwrNZlNZYG36\nPsq7d1vTzuzciXXClG66chLXxy6HL774Ii5fuoR3vTOK3JpVpt63nnrqKTzyyCPW9IwxTFV8zI77\nYMwDbZ96vZ4w+g9/+MO49dZbccMNN2g5pK+ihzwEeBj35Q42vhFrmDAXirUrRaO3rCsJNBoNY4E7\nShMlygppbYMekiANt99+e6JE9QJRd5wEhSo0+s2CNpX+5je/iW9961tQzow1XwEQDSDXgGUs6tie\n5xmd9MiRI/j617+u3PMYwzXx4lzuXYyMIQxDfO9734vySGYQ5u5EAAlzb7VaWF+PttiLoGaPP/44\nXv/61+PChQs5CjY1+juvncWOqc62kNNP1E0LyeIxgL/927/Fvn37AKYffSgEQfT3C1/4Aj760Y92\nREMe6Bplo9FItFIds7t2oRq0gbhe5yfKif93uVxODgZMUxD0MgUTrFarRl/SlZDnjx3DyooaM6rZ\nbCb9dDE2O3USV8qL+zLnHIcOHcK//Mu/5H53bryEq2ajulpZWQEgGT6l3BY6WKSp1+vpGr0W/ynP\n0BEzYZr285//PJ5++mkj7YkTJ/DCCy/kyDUd4rtv3j6u8JYnnngC73jHO/Dyyy/3XEa/MHqMPoZo\n8PPnzydMRx9Ex48fj+9Hvxv1Op5//nn86q/+apJm99wYXvrZSwCPBtj09LQxOJ999ln88Ic/7AvN\nr7zyCn79138dgDQRJENG04jX1tYA5slryM4npvM2W6gNuk6X13PgO9/5DlZXV+UHIJr53H777cpg\nnix7mJ8o4dr5MRw7/EO89NJLaNTr+KVf+iXDC0fkc+jQIXz3u9/NRUcnaLVaCmNuNpuoVOxCbXZ+\nHlXfB+L6pSiVSvGhsaFVQ6WgswhR17VaLamj5eVla1t985vfjOqXqxq9EOxZLr82MMbQbrfB21HZ\nr5w4kfvdiu8lMz3R7uK7ds1UsHPGXo8eEJsUOZrNZi7TzbFjx/DTn/40F103XDEer2/JfvuVr3wF\n3/rWt5Lf//Vf/4VXXnkFQCSke0WtVgM4R4lLZcVjDC+88AKOHTummAcHjZFk9FQLEINJ8WtnwJkz\nZ/C2t70tSQ/IDvvii9KWevy5n+B3fud3EIYhPM/D1NSUob2trq5KZpdBTxbd1IXTZSISAmt9fT1h\n/mLgi3fEN5w5cyZHyVGcmW7cwj71qU/hn//5n5Pfzzz7DC5duoS1tTWlnibKPnbNjOGauXGMh9H9\n6vo6zp09m5jEhI1eUDE9bR763g3uv/9+Q4PPq9HPzMxg3fOAlRU89NBDyhpOEMQ2Ws4VRn/27Fl8\n//vfV/JRzBUxz67Vakkd/fVf/zW++tWvGv1ECgeu3BN00P5CN/tkGWNarRaaK5ECdOzYsa5MGUKj\nF3U5P1GWO2ktppvf+H9/A3//9//T0Ogff/xxhXaxGPuOd7wD/+MDH8iko9VqIQxD+B4zTCfVahUL\nCwuoVqt4z3veg9/4jd9QaO4FjXrUNlEbSdORmG2JMbkVMJqMnjR2vV5Hq9lMBtDPXzcHj7FkypvE\nb2dy+k2ZtrjXardQqVQwNjZmaG+rq6tJp3cTlYNeJjXyiLaIaYsx0Go28e0/+3byfG1tTdXuAcPN\nMu8AvmKijDuvNUMA5IGoIwaG3//938cDDzwAwD2YBFON3uOJ+6LuHSUY/YkTJzJNI2n42te+ppiS\nDBt9mkY/O4v1iUlgfAIf/OAH8Y//+I/Ke+AcnHPF5Hf48GFFk6Rl0r5ZrVaTOlLMhiyaJQJQhIMw\nw7kYfdY6AcUN00BQi/rMv/37v+Hd73537ncFRJ9vNBp4/vnnFQVJh1BOTp8+bQjaX/u1X0sUkrGS\npzDrhYUrnGbPtbU1HDt2DP9/e18eHlV1v//OJJkls2SSyTKZLEBCE4IQZBXJF8qWyiIgGmyxWMXW\np1bRFh+qaKUutBVRXCopFQRFFh8QFEVBEWRxCZAQZF8SEkIImUky+5rZ7u+PO+fk3lnCIgWT37z/\nEGbm3nvOuZ/zns/5bGfRokVYtWoVZKI49E5N5P2GzGUyP4g59HqQsCtYvtrtdvOSvci7iRH9dcam\nTZuiJjq5XC64I2yrSZSK0+nEh+vXY+tnn1Ey4ZK23+eD3+WANI49Zi4a0Xem0QNXrtFzJ4DPy9fo\nDQYDvtn1DWV+rkZPBNlsNvO006ampqjPMxgMeOWVV66gZR2IRCahJEzGJ5o5g5Cq281ufZ1OdkKE\njhEh+oEDB+K1114DwGqtpE9tbW1X1OZQR2go0fv37YMkiuNarVbDEgggLiON13ZyH2Jca21txYYN\nG/C3v/0NTqczbOEn5gruromr0XPb5Gn3YMyYMax5i9NOYtIjuwO/388z3RDl5UoQF/CCCQST7ByX\nUVKigGujX79+PZYvX07NFQyAr3Z8RecF6TXpJ1fOXS4XnnzySZw+fRoDsxQ8E6tGnYzURP4ivHfv\nXly4cAHvvfceRowYgdbWVrqQh9bPIeYwMs7EZBMtuu5q4Ha3gwFriuIGSpA5Yo9g7rtZ6BZEf+LE\nCRpHHhrB4XK54IlAOEQ7cjqd+Oijj7B+3Tro9XoA/G22z+eF/fwxZEsZiEQiSKXSMLKLpNE7HA78\n+c9/5rUlEk6fPo1UtZr+n0tIPo5G39TUhGeffRYBJkCF1GazhRF9W1sb0tLSIA1meXbmEKqrq8Py\n5cujNy4EZrMZWVlZYQRLNfpgP8luwuPxwOfzYf369cF+MGhpaaFnF7iD40g1erCRJsnBkEiu6YZo\nR0ePHsXMmTPhdDpRUFBAieWdd96JaOpigmaVaERvNBqxv6ICkihmMrVaDf3Rb5GXxBIql1iJRg+G\nwcqVK/GnP/0J77zzDpxOJyW4pUuXwu/3U5nixohzbfRut5u26XzDeXi9Xpw4cYJD9AwlM9IXp9PJ\n0+i5RE92gdXV1WHjUllZiSNHjiDQ7oLl1H4wPg9yc3Mj9p8LLjnqdDqqhZMdxoYNG/CXv/yF/ub9\n99+nJUXI+uYJjgPpVyAQgNvtxnfffUft5+T+AJCslIedA/z+++/j66+/hjJYhO7UqVNRFS1yH+Kz\nIvPkWoneZrNRK4DX2ASvuZW3UxNyLAMxor+OCARY4gt9cRaLBWvXro3q4ecSPcBAmaTEoUOH6PdE\ncAjB2Gy2Tk03NpuNZ2dsaWmhjkTWRh+Z7RsbG+nfAoGA11a/j0R6xGP79u346qsvAQBmswmtra1B\nZyz/vh9//DESExORlJQEjUaDioqKqIWaHA4HTCYTjEYjtm3bhpSUlIi/IyCF7MiCSNBhugm2OzgR\n2tvbsX//fsyZMwcA8MILL6BPnz6UnOx2OxiGYd9B0JEhE8XRiZ2Y2LENJ5o0aS8xoZhMJgQCATz3\n3HNh7QI6TFncxbm9vR0+nw9+vx+7d+/GZr0eCVHOToiLi4NalQSTgV3cuE48lugDAMPQqJdAIACT\nyUTlZ+HChbBarXRx4eZFOZ1OnkZPfEnnamshFApx8uTJjgWK8wwif50RPcFjjz2GH3/8kffZhx9+\niNWrV9P/P/PMM5c9grKurg7ZnBDUX/3qV7SAocfjobuY6upqdi4Ef0fGnWjpxBFO/iXzNnQOf/DB\nB+jZs2dEQnY4HGhpaaFEeujQoahmEjLPSZQNMWVeKwn/8Y9/xMaNGwEA7taLCHj5oaKCoOkmNTU1\nZrq5XqioqMCdd94Jh8NBBYLU4qg7V4dVq1bB5XJFzDAlpOB0OuGwO3DLLbfwvidaK3lZVqsVCQkJ\nkEgkEZ2xPp+PRyY2mw0Oh4PNPOwkvJKYWQJMAK6QcDuvz4cMhQi9UqQ87fbtf/8bhYWFcDgcvAVE\nIpFAr9fj7NmzUCqV6N+/PwDWMevxePD000/zdh6kb+fOnaMTorPqfWRRam1ltRiyMJB+k+Qbslh5\nPB66eDIMQ2PGye+NrS1g/N5gP1iub25uRnV1NQD++bcikQizZ89GW1sbLBYLdQAbjUaYzWb4/X5K\ndG1tbbStXI2ZjmuQ/Nvb2+kYiDpZ5DIyMlBfXw+A7yCnjlKG4eUstLa2wmq1wu/3w+v10jBKj8fD\n0+i5Nnqi5QoAGIxGDBgwACdOnICXI7uE6Mk1oUQfKVvWZrOFhV5arVYcO3YMw4YNQ1tbG+655x4Y\njUY0NTVFXewJMZIxVqlUKCkpwbhx43g+A5/Ph4qKCnpdmFkvuOC1t7ejZ8+emD9/Pm88CA4ePIiy\nsrKIZOlwOKDT6Xj9cjgcdGcQCWQ+Ew0/mkY/d+5cGAwG3jzhPufw4cP0GW63m4Zbc8+OdblcSE1N\nRX19/eV9dzcIXZroZTIZ7HY7j+gBkn3HagsulwvtVjO0SjHV4oCOF+90OmF32KHN1PLuPWLECDBg\n4AgKuMViiarRk5fJ3T6GOoG4GDVqFC11TDSdp556CtOn38XX6P0dYVtSqZRGMpDftLa28jR68vm2\nbdugVCohl8uRl5eHS5cuYfny5VixYgUv5ItL9ER75jpvV69ejU8//RSvvPIKdDod7VNbWxsOHDhA\nf0f6SAicq3keOXKE/k2+J6Rov3QOPruZJfpgnP2zzz6L8ePH02sIhEIhPv30U9TW1sLhcGD37t2Y\nPHkyjEYj9bf8+OOPmDJlCjZs2IC33nqLNyahGj35zhHsk5hjPgtFRkYG6urqwtrk8XjYhZGjbQMd\nCyEZL2KiYTX6cBt9Y2MjWltbO0jf7cKwYcNw/PhxHlE6HA5eaOjgwYMp0UulUjRwwiTJcm2z2cIS\n56xWKywWC8RiMYRCIVJSUmA0GumcSElJCSNYIuMk3FGn02HFihUoLCzk5XGkpqZi79698AV3o6H3\n8Xq9dNHzeDxUOybjQXDhwgX07ds34vwhGj3pA/nsiy++wNSpU8N+D7AKARehRM8wDL788kts27YN\nVVVVGDlyJADWzNWrVy+kpKSgqakJbW1t+OGHH+g9lEolJkyYQKuACgUCuFwupKWl4fPPPw9zyt8s\ndGmil8vlsNvtYdu+lMQEiLx2ujX2uJ14aNZvkJ6ejvvvvx9ABxk5HA44HQ5otZlh9/9kxRswNLOa\n4eLFixEXFxdVowfY1R5gfQbk/pEE9fjx49R5TCZ3U1MTJBIp30bv83P+7tAkLRZ24n799dcQcjQ6\nolEPHz4cSqUSMpkMSqUSVqsVu3btgkQi4TlnuURPxo9EewBsvZ3Zs2fjlVdeQd++fbFjxw6kpaWh\ntbWVlzdAiISblg8ACxYswPHjxwGwk7itrQ1isZi2gSwqRKMHBPRw+V69evEWPULmhHADgQB69erF\nI6jdu3fj+++/R0tLS1iMNxnXixcv0vvW19ejNphQI5JEL0iWkZSE+qAZLpToATaOnkv0pD2kzS6X\ni2qxQmG4jX7x4sXYunVrMHpDALe7Hf3794der4fBYIDf3SHbVquV1wbiMxgwYEBYzDnDMLDb7RGJ\nHugwhymVSjgcDt54h5qBSP/Onj0Lu90Ou92OjIwMqviQdz9hwgQcOHCAjjcZC7JTdAfHwePxsLX+\nOXLN3RlevHgRffr0iarRE6Lv2bMn/YzITiRt3WQyUd9QJLOKxWLBfffdB6PRiPPnz9OFgZtwuHXr\nVgwdOhRGoxFGoxFut5sqjheDO0hB8PlpwZLXnUUi3Uh0eaInJhKHw4H68+fhcrsQLxTA3+6iGlN7\nezs1G3z5JWvnttlskMlk9NrMzHCif/c/b1Mn78GDB2lESyQbPQDcd999AICRI0fS51itVtTW1ODv\nCxbwriGOJy6xMwzDm2wOh51OEHYSsH/rgk6wY8eOoX+IyYmAaPQKhQImkwlVVVWYMWMGry4K6TfR\nkgFW87Hb7aivr8eIESN499Tr9cjLy0NbWxvPHk6Ig9yDkMTBgwepbfTNN9+E1WpFz549cenSJcTH\nx1MidDgctIyxRqMBwE487liQRYE4l6VSKdRqNY/oSQLc/v376Tvh2ugdDgcGDx5MSWvcuHF4L1gs\nLFocPQBkpKaibv9+AKx5hGTrejweeIx6eKwGHjESciD/cjX6k8ePYcnrS/D666/j0KFDaG9vD4tH\nd7lcSEpKQkFBAXQ6Hez1HdmdZrOZJ39EPiIRvcPh4JmVTCYTDh06BKvVCrFYTPssFAqhUql4SkDo\n4kDGTKfTobGxEbm5uRAIBBCJRFi1ahWOHTsGAPjFL34Bg8FA5ZqYk0jfHA4HJXpC0tz2AuwCqVAo\nkJaWFpXo9Xo9LBYLLf3AXaiI6Y/rTzGZTNQslZeXF5YPQWTR7/ejqakJTqcTDMPw8lD27dsHtVqN\nfv364ejRo7zaWLXnWDkXBk03hOiJ/K9ZswZVVVVhfblR6PJEz9Xo33zhKRzYtR0pKSloa2ujn4fa\nKNeuXQur1QqNRgODwQCJRAx1UAh27NjB+y3XWWqz2SCVSnlC4vP5YDKZsGrVKgAdxE0mytq1azFt\n8kQc2r2dai8JCQkwGo2w2WxU42V8HpiMBt4kXr16NdatWweAr0k2Nzfjt7/9LSZOnIgJw4thO8d3\ntgEdRK9UKtHQ0IDExET07dsXW7Zs4Tmai4uLeRr92bNnMXPmTAwePJhOMq1Wi7lz5wIA8vPz0dra\nypuAhKicnMWCi+TkZLz99tsAWG3KZrMhNTWV5ychCbHcIlsej4dOTkL0RKNPTExESkoK3n77bZqc\nRMaysrKSOnrJNtvlcqGxsRFer5feg4vOMiUzevXC2eC7I9m6hLwDXjfNMCUgCw/X4U9MFS6jHhfP\nncG///1vACyxhDpZ291uyOVypKamhrXFYrGgvb0d27dvR1xcHCW3W265Jaxf5D2bzWbU1NQgPz8f\npaWlsFqtGDBgAC9UdNCgQbxSCNE0epfLRc/XBdgFsrm5mT4rKysLdrudxpiTsSCBCVarjRJ96Jhv\n2bIF33zzDRobG5GTkwOZTAaj0YghQ4ZQhQvo0OhNJhOP6Mncmzp1Kpqbm+H1eqn8GI1GOp75+fm8\nnXZaWhrKy8vp/5uamsAwDNxuN5qbm/HMM8/gxRdfREVFBRQKBW699VYcOHAALpeLavS1NbXB8ius\n6YY8l7yT7du308XkZqBLE71UKoXP54PFYkFdXR1qjlRi5w5Wk66urobLxWr1oUlDixYtgs1mg0aj\nQUtLC2SJiVAls9u+3r17o7a2FgMHDgQAngbsdDqRnJzMmwRnz55FVlYW7rrrLsjlclqylVx34MAB\nWK0WuMytaGhooCQHsFtBEsduramG2WwOixD64osvAHQsILJEGZqbm1FYWIh169ZBKZdBJmYnzKZN\nm6hmlZubi8zMTCiVSpw/fx4pKSnQarU4fPgwtm/fDoA1KxUXF6O+vp6aYt544w18//33AFii0Gq1\n0Gq1dGL36NGDLqIENpsNzc3N1EYcShIZGRn0bzIBUlNT0dLSgvj4+A5nbFAb6tevHwB28pJribZJ\nFhGpVEr9G99++y31MfziF7+gbTpx4gQeffRRAOziSHYDkbbTnRWqS8/IwNmg5kwWk0uXLsHj8aB3\n7960vQSE4MnEttlsCAQC0Ol0aKo7i4bqb2k7gQ4ypBq920XNbqGwWCxwu92QyWSIj4+nhJWRkQG7\n3Y7Kykq8v3wpkqUd35EINAKr1YohQ4ZQUwYA3HXXXdi0aRP9f+g7tFqtbG1+l4v+DSAs0SwrKws2\nmw1uFyuvDQ0NCAQCeOyxx9j72DqIPtQEeubMGZSVlUGv1yM9PZ3uOOrq6nDmzBkA7A7G4XBQnwQh\nepvNBqfTiWnTpuGBBx5AeXk54uPjcfToUTz44IMwm81UhvPz8+FwOFBZWYlt27YBAK+KKJG1jRs3\n4uLFi9BqtcjIyIDFYoFSqcSsWbOwatUqngLZdPEiDSF1uVzUd2Kz2cIWx5uBLk30AoEAcrkcer0e\nDocDOTk59MVVVlYCCNcun3/+eWi1WlitVmRkZKC1tRWJiTLExcVhw4YNSEpKQkpKCiWYUOJVq9W8\n6Ibq6mq6KGg0GuqkJKTHDdmsqanBxIkT0dzcjNTUVF7BJaK9hAp/wwX2Pm63G/feey9GjxkNhmEg\nk7F166dMmYJnn30WAOucy8rKAgA8+eSTmD17NhQKBRoaGpCcnIxJkyZh9OjR8Hg82LJlC8xmMzQa\nDebOnYtvv/02TBCtViuKi4uRmZlJCbpHjx4wm82U6Mmu6rbbbsOSJa+F1V7RarW88s7JyckAWC3K\nYDAgPT0dlZWVeO3V12jk0u9+9zuq8b/00kt4+OGHw0wJUqkUEyZMQEZGBqxWK108S0tLAYDakQkW\nLVpEw0MjJVp1lnlLzElcNDU1wePxYMaMGbjjjjsAgEfMcrmcEv5DDz0EgF38//Wvf1FbPMBGShEZ\nJVE37qBGH0r0EokE69atw8mTJyEWiyGTySghJyUlwe/3Y926ddi4bAlM+ks8jd7r9WLhwoVISEiA\n3W7HrFmzcPfdd9N75+bmwu/3o6ysDLNmzUJTUxPPUWqxWJCZmUl3yNGIPi0tDYFAADa7HXl5+Th9\n+jQKCwvp90aTKWJiIhfHjh1DamoqHSOFQoHW1lasX78ezz77LEQiEbRaLfR6PXr37g25XE41+pSU\nFPz5z3/GihUr4Pf7kZiYiOTkZB7R3nLLLTAajdi0aRPmzZtHnf8EREmbO3cu9u7dy5N/hUKBoqKi\nsN2IyWTEf8r/gyNHjsDlcmHs2LH49NNPoVQqYbPZYDQaqezfDHRpogfYCUVIZ/To0XTrHy0jNC8v\nD3q9nppuampqIJexh/uWlpZS4SKOnVCQCAUAmDdvHp544glMnjwZAEsIBw8eBMDXiFQqFQoLC1FX\nV0dNQQMGDKARKQBLgHFxceEkxLDPtNls6NGzF1LVLKERok9OTqb+haQIseBEo1er1YiLi0NBQQGa\nmprw0EMPYd26dZDJZCgoKADA17wBdiKOHz8ew4YNo4Kem5sLs9kMl8uF5ORkpKSk8Eg1lBR79OhB\nt7fr16+nz+Juoz///HN8//232LtnD1wuF7W/63Q6pKWlUfIm5KLRaPDHP/4RqampKCsrg8fjwaxZ\ns7Bhwwb83//9HwB2gedu9wF28VcoFGFjBETP4uWOCymfm5OTQ4leJBLRhSwvL49eQ3aLACLGqJ8+\nfRqfffYZVCoVT6P/9rtv0dzcTP0rBCtWrMDs2bOpCUQikUAul1NZJM73AwcOoLCwEBs3boTdbodQ\nKITJZILVaqVKDAD06dOHR3BkbKVSKVQqFXbt2oVHHnkE+/bto+Su1WppvDyRNa5vQ6FQICUlhfWd\nmQ1QyNldFlcxio+Ph9lshkAgiFhxUyqVYv/+/VQ+xo8fj5kzZ0Kv12POnDl45513kJiYSMONR44c\niU8//ZT66qRSKXr27AmFQkH9F1KplGe66du3L3Q6HQwGA3Q6HYqLi+nzhUIhr7icXq9Hbm4u5YPQ\nBe6jjz7Cyy+/jN27d2PP7m9QUVEBl8sFhUKBkSNHQqFQwGazwWAwxDT6nwLuZCgqKor6OyKYeXl5\naGxsBMMwEAqF2LNnD44fO4r4kENFoq2+XI3+0KFDePXVV2lIl0ajwdGjR2lWKsF3332HmTNn4ty5\nc1TLKigooEQ/YsQIbNq0CS6XC6+99hr69++PoqIieEx6eCysVtjQ0ACpVAJVsF2E6AGEPS90fAwG\nA+2PXC7H3r176bZdJpPRCUAIbfPmzUhKSoLBYMB9992Hxx57jBJEdnY2zGY2JDI1NZUtEUAmLMMg\nU8N3am/cuJES3YQJEzBhwgQAHURPxi4rKxtnzpyB0+mkWpjX66XZyABbEwUA3nvvPcyaNYv2h4xn\naWkpXWhMJhNN6CG4dOkSWx45AjorcpWeng4AuDsYcldUVIQLFy5Qoidky5VFjUbTaYlou92OpKQk\niEQiajZyu91Y8tpr8Pv8kMvlvISxwYMHo0ePHvT/YrEYcrkcBoMBGzZsQGFhIWQyGc6cOYO///3v\nWLZsGfbs2YPMzEyYzWbYbDZKPpFACIyMPdmRPvfcc8jOzsaxY8eg0WiwefNmzJ8/P6JZ6ciRI1Cp\nVFAoFAi0XYDK3UoDFAhUqg45jLQADh8+HBUVFVQ+Nm7ciIKCArz55psA2Hksk8nobiAuLg4DBw5E\nIBDACy+8QGWFO3aJiYkIBAJUpslOnizE2dnZKCwshEQiQU5ODs9PJBAIkJOTw9PoyfgDrEN/zJgx\nABgwwSqmTqeTtkOhUMBsNsNqtUZVHm8EujzRc+2MkbbYBMTDTwSIYRg89thjmDx5MqTiBBRn8isl\nRtKOAVa71ul0+P3vf4/W1laUlJTwnl9fX8+zvwKs+SI7O5unwWdlZdEt7MiRI1FQUEBJa9KkSZg+\nfTpcunoE2tndyvnz5yGTiHGLlhUWLtGPHz+elz7OBZmQRFDlcjn279+P2bNnA2Bt02RMCKGpVCq6\nMBCBVqvVkMvlUKvVMJlMcDqd9DMCd+tF9ErhhynKZDJeoba8vDx88MEH9FnDhw9Hv379MGnCBJw5\ncxoulwsSiYS2l0v0gwYNwvnz52nVUaBj4pF/O5MBADyi1wQjI1588UVa1TASJBIJVqxYgdumTAEA\n3HnnndiyZQva29shEomoRs4ll549e0YleiKzSqWSpxG3t7fj9GnWFi2TyXjfJSQkICcnBwCrRaan\np0MmkyEQCCArKwsCgYA+f/z48Zg2bRo2bdqEnJwcHtEvW7YsLFMW6Bg/qVSK5ORknDt3DgKBgPok\nTpw4wYuSIfOD65QnRCaXy6HX6SBLlGLp0qW85/iC5B4tymn48OE8mQRANeGFCxfCbrdDJpOF7QbI\neRBEViIpQmKxmEYKqVQqavfPzs5GRUUFqqqq8Nxzz/Hum5mZCbFYTOcDmU9c041arWZoxqW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2NjIwoKCmCxWGhqflJSUsSDursCVq9ejVmzZvGK5nWXvrW0tECpVKK8vBx1dXUoKCjAgw8+eE39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\nnM9Jc/3r34cAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x108b0c910>"
]
}
],
"prompt_number": 28
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can animate this averaging process:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import time, sys\n",
"from IPython.display import clear_output\n",
"f, ax = plt.subplots()\n",
"\n",
"samples = zeros(n)\n",
"for i in range(realizations):\n",
" samples += ut + noise*(randn(n) + 1j*randn(n))\n",
" avg = abs(fftshift(samples))/realizations\n",
" ax.plot(fftshift(k), abs(fftshift(ut)), 'r--', alpha=0.3)\n",
" ax.plot(fftshift(k), avg, 'k')\n",
" time.sleep(0.5)\n",
" clear_output()\n",
" display(f)\n",
" ax.cla() \n",
"plt.close()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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KemlpKRYuXBjzvcPhwJw5c9JWKIJIJzGDok4njFYrRehEr4dmihJZhyTLMIkRusEAk9lM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\n6ARBEBkCCTpBEESGQIJOEASRIfx/Y+k1QBLbkO8AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x108bd6f90>"
]
}
],
"prompt_number": 29
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This will give us an idea about where to filter.\n",
"\n",
"### Moving signals\n",
"\n",
"Moving signals will be lost if we average in the time domain. We need to exploit the frequency domain."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"T = 60\n",
"\n",
"t = linspace(-T/2., T/2., n, endpoint=False)\n",
"k = (2*pi/T)*r_[linspace(0, n/2-1, n/2), linspace(-n/2,-1,n/2)]\n",
"\n",
"timeslice = arange(0, 10.5, 0.5)\n",
"T,S = meshgrid(t, timeslice)\n",
"K,S = meshgrid(k, timeslice)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"U = sech(T - 10*sin(S)) * exp(1j*0*T)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"from matplotlib.collections import PolyCollection\n",
"from matplotlib.colors import colorConverter\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"\n",
"poly = PolyCollection([zip(i,j) for i,j in zip(T,U)])\n",
"poly.set_alpha(0.7)\n",
"ax.add_collection3d(poly, zs=timeslice, zdir='y')\n",
"\n",
"ax.set_ylim3d(0, 10)\n",
"ax.set_xlim3d(T.min()*.6, T.max()*.6)\n",
"ax.set_zlim3d(0, np.real(U).max()*2)\n",
"ax.view_init(20,-120)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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q0eXzeWiaFrXUSdMzOedRHQnGu0uAAoAbUKxU26AcuLBp7xvp7lYImmn2dqqO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\nDoQAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x108ee7290>"
]
}
],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"UT = empty(U.shape)\n",
"for i in range(len(timeslice)):\n",
" UT[i] = abs(fftshift(fft(U[i])))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"\n",
"poly = PolyCollection([zip(i,j) for i,j in zip(fftshift(K),UT)])\n",
"poly.set_alpha(0.7)\n",
"ax.add_collection3d(poly, zs=timeslice, zdir='y')\n",
"\n",
"ax.set_ylim3d(0, 10)\n",
"ax.set_xlim3d(-10, 10)\n",
"ax.set_zlim3d(0, UT.max()*2)\n",
"ax.view_init(20,-120)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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c/K/n53Gl6GxKu+fRIG/gAgzOkMrNIi5JvNvNd/YyBoJ0RSwuLmJ2dhbHjx/f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\n",
"text": [
"<matplotlib.figure.Figure at 0x108bb00d0>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's shift the frequency by 10 and add noise:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"U = sech(T - 10*sin(S)) * exp(1j*10*T)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"\n",
"poly = PolyCollection([zip(i,j) for i,j in zip(T, abs(U))])\n",
"ax.add_collection3d(poly, zs=timeslice, zdir='y')\n",
"\n",
"ax.set_ylim3d(0, 10)\n",
"ax.set_xlim3d(T.min(), T.max())\n",
"ax.set_zlim3d(abs(U).min(), abs(U).max())\n",
"ax.view_init(20,-120)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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EpuMWg1Et6izoi6WbILzLViQMdR+ivK9pUMLQgo8tCNhxHJTLZTfppO10yhr3\nOugkKc9vEK1cYMhIt1ar4cSJE8sydpKlf9JQqqxIo1OzEE13KYBIg8A593nuBWZarnWa5FPEWbrz\nZre84G7XHX8rw5Ulgh8qBmFQT3EjY3+zLks3wz3cZekGfF5LcZTJD8aC5n/fYQx6QfOTboLkCFHr\nQU08AOCzgHMsP4aOdLNqukn1VCC4oSXn3Oe4WG2EGWVJLFVN09rNFLtJTdTUrSQoZK5aderfTZsG\nWmmM+zVNFUa7hmyQVGI4rOuBsJixeaMa35vNkRY/hkyyahGf0bLua/NjEYaS7o8sUXvhxUF2Oqk9\n0GQLOMfyYOhJVyw3etVT5b9VCOtzUAgXCF8Kn0ooDxDanXgAuMtamzBUEujKKsGocwqKXgAE6YZb\num4nXAYnYH6GQ7ss3TRdeGWolm5QcZ20YwSmVsvRCUqxm9GK7tPRTcK7HipZa5irPdCEBRxUBW25\nsBwZboN0HwZhaB5npmnCMAxUKhU89NBDXryeWulf9miqNVSFA0IutpykfuogIuxGnG46sTVoxf5B\n+m/Tpl1aZxi6SFd5uBk2C7TIKQuuqSAgmjXaMfqot33KmhMC6ucM0rhjx4jRdDnnPvmAKGFqI2Xd\nV3THdCgKyrWY1tINgrgPyuUyarWaJ0MYhgHTNEEI8dUezpEdA92CHQBefvllfOc734FlWajX67jj\njjt873PO8alPfQrNZhOjo6Mol8s4fPgwrrrqqi5P7el0sYRZuksWgUU4qsXocyGC8FW4kkCym7yL\nYJT3Ww4NfACI4txhMNvF1MPqSKjTEx0biimbU6rjJ4mCUB056uegvNsakx2KpsNQL0mWbrnof58w\njFf9t22WOr9RCKqCJmvAImSx1/tpORxda+GhMNAt2FutFu677z587GMfw9TUFBqNRtc4mqbhs5/9\nLEZGRnDkyBHcfffd+NznPgcAIISsSSu1Hwi7EZcsVx6oFqPlAYruxAPAJbQgCzMIavSCCsNxuyJ0\nHZsFSxsCFuXthIIw0lVkAZKtT5pq6bYiLF159SRjQYnQCFo9yJasQSgo69yWo2Udhxc6kpDpMKhy\netRHC5tXUqghaIZheKm3/QpBO93uz4Fuwf7444/j8ssv97oGj46OBo4lXhf1dHNEWbrJ5AHGwpMK\nksb6xmUMcwTHEgcVsumeQ3jxbvW4hsNStxkCuuWEpt2Rp+KcrOJ1lXTVtGUAvjKOpsN8TsSRiu6b\nh0lYV+e2TOlyAAAgAElEQVTflaoypvZAk+seDFPpxeXGQLdgP3nyJCil+MIXvgDLsvCWt7wFr3vd\n60LHrNVqq5YcMWgpx2EkYxKWjHQ5D9WFkxaQSUIGVkAclisv+MmJMo6C1rHq7IhODkGWbpKwKvX/\nJSXUrGHTLl0zKBxQpOPqut7VDFRdPXDOfc7NlkN9mYCjZd0XHmYShoIik4huEytBdnI/uaDat8Dq\nhqDl8kIEkpwYSin27t2LW2+9FbZt44tf/CIuu+wy70mrQq69cLojimSSWKpRy/GkCRZJCp4HbUMY\n7yJjo11pzOuhxsI7AatTtwgDi6hXIVursv6/aPqJv+W47Xb0EC6RHbPlchmO43SF6Km6sKVUITMc\nhobV2aZWKvgiOYLkhTRFiJYDWUPQ1gJBLgdWLXohSQv2qakpXHjhhZiYmMDGjRuxY8cO7Nu3L3RM\nXdd9Fufp+IUKRFmZSWoRRPFyUnkhKuxLIMhqZpR3hWcZSm83tZCMjKAHjtwROKwDsBq5okoDVgpt\nWNM0ME3vkigMm3iRAGJMlXSbTngyh01Z1+dOk2W4nBDWb7lcRrVa9ULRTNOEaZpwHGdgs8RWEgPd\ngv3SSy/Fvn37YNs2ms0mDh8+jHPPPTdy3KC6sKcjokg3iWUURS5BUQ1BkEm3WNCCq54FjEUCpA3D\n9lcacygLdPRVlI7DApQjVUggR3edCSuhNCNv31Tm0nKYLxTLcohPPmi1m4eGwQlwMkZt309rMs29\nlDQErd9YC9bzQLdg37JlC6655hrcfffdcBwHb3nLW1CtVldrymsKkaSZIJ81av+kmq7s7a8UC4Hk\nEERiQdu1lJq6DuOBVdCqJT3w9bTGoNo1Akjf7twtgt4tUfgcUYblO09mTEslh3YnhZgrLC+kJbWw\nEDSRNk8IGahszuXGQLdgB4Drr78e119/feIxT4f0xSRP80h5oUdLN2mSQFMirWoI6QbJvkFEbLar\nh8nzC5IvaqVC4PzShow5lHcV3XHbnaccw+kmXcY5dKGBwvFZ9TblMasU3lUDIslDdFAgh6ARQuA4\nDgghXhnKXkPQ1AzUQcRQpQEPO9JciFH3YRJNN4qkZkNSiWXHlNp5olIsBIaBBRa8Ccoqcxg2jxZ9\n2wSSbrFPpMtYV/0HK0EUhHpMdVVgUzd8TTjjVKknSLP1zYt2V1azAsLQ1gKErFOtVrta7wxzCNrQ\nke4gP+FWElHWUpJSh1EkNdNyYuNVCwV/G/RqUQsh3e7xg4jNcKhPXiAh8kKt5A+x8rZPWaCAsu5I\nAzvCeScgr0LCGnsSylApFrwx1WNEkYxDWVfab1xMc7+wnHUSwtqvA8NXBW3oSLdQKIBSuioN6gZJ\nxA8iJIGZph34ukygUSQ13XS6ivyoRYGIUj+hWtQDycEkDKWC5pMUgjikZfubU7YcGui1r5YKgem6\naS3doFRkjnTkHeSwtBRLVXUkOtStIhYGh3XHJ0eR7iBdk0nRSxW0tfB5h4506/U6TNPEyMjIimk7\ng/glR+muxxvxlmoUSS2YBASFyPKODuU+GSPMkda0Kepl3ReeFSQ5qJbuohlct6FWKmDe6JY/ssgL\nQUgjL4RFa8hjBFm65bb2UNDcZp7q++qopsPWBNmkxSBUQVsODIe9LmG1stIGBYJImxESwkzTAaGd\nG1WNVS0UCpEktWgSWDExuBb1F8ypFLWQqASKein+MrQo95bkALAYUpi8Vgy2dNOEegHhERph5yXo\n4R5o6SoREEGWriDdWqk7ztehbhFz/3E4LNtZtjCs5UKaB8UwVUEbOkv3dKi/EGShqllVUR0iFkwC\ni2kYLYeTXRRJLVk0tuiNTbvlBYtYXdu1bLeRZFosmKQrHRZwiSrIwZa2PkFa0k06hqWkLwdauu0K\ncGoKMOBq4OrHdigH1zQvCmC5CpEPCqElqYI2yPrv0JHusHYEll9njMW2BIpyli2YolNw8IWpaVqk\nPJGkahdRgvirpeDoBdfSTU+6ixZFKZB0C4FdJ9KmyoY9dNKQd2A3ZuJ3hAV1lhAlKEfK3ZZu4Fwp\nA0cB1Wq5ywk1yOTTD8ghaIwxz+oFEFouYLUxdKQ76PUXsrYFEj/CSRhlcTDuklIYGjaNTXCIi3CI\n85gz5td0qyEhYy2bYt1IKXKsIDRtis2j3TdVpVgITFMO6vcWhTCHWdTDRvUhBJ1jjo4uHFRvV0Zi\n0mWdMpeyE0puRGmapmcBD4K1CvTfchZjiRC0QcVQku5qWrq99FpL0hE4CRwW3WMMcNu+RGHeiG7m\nGBeQr6byVouFwPTcpsNwlmTpBjmPgtC0KUZSyBJpm1OGOdKSyguc81BrWR5Dre8gY7Ss42RIpIkM\nJyChQizBhfe/WCx6FnDWJIS1pBcPcoJETroZENcNWGC5SDUOTkjigIwoC0vTtK66AyriEixUa7Ok\na4EkJKIXBMKSKAL3SyFLBMXuRiFc000+hloaUkAmSLX0o4zRio79s/Hztmlw2yMBtRC50H6B9DGw\ng2IlB2FQNOc4DCXpiuiFrHVuk5QAFOOL/znnA9NPjQRkU6mIIk3GeKQFBsSnEie1CFsOxYgUvRAm\nQ3TtZ1OMRDgCVSzGfB4VSazUOCyEEKrM52HZfYArL0TFWws4NLzMpQpN01AqlTzvv4iBFZbxSoZg\niXvmdMNQkm6cppuFVIHggtXqmMt9wQqCjzoOZW4pxChEvW9RHtsPLI4YkxbFcShHSSpQWysVEnXd\npRxdoVNRiHuIqAgrlxhHuvJ3E0aoYgzGeaSlWw+pI6HCibB0o64VUYZRxMDKxdfFz2obEFkxqNIC\nMISkW6/X0Ww2sbi46LXxYYzFFqwGokl1LYHy+Fq2ceUD4272qDhgMUZSyKe6GhJn2yuajluWMSji\nIQhhckTS6AW1I4QMQbpqLV0VekGLlA0Eogq6J0FQCFZQ+NmgL98HfX4Cq066SToCA25X4M9//vP4\n0Ic+hMsvv9z3XrPZxHe/+12cOnUKBw8ehG3bOHLkCD7xiU8A6M7xBtY2qcYhqEatirmArC0BkoB0\nTzSiHTwkY7nBWkmPbL+eFYbjdgROSrphckRSecGhPDRWWhC3TaNJNykYj25OmQZqCJYcftZv6Wyt\nkGS/saqkm6QjsNjuu9/9Li688MLAccrlMrZv347LLrsMe/fuxcsvv4yPfvSj3lN7NeowrCaSWJnH\nl8JJM6yYjIxjEfsnnUMQaqVCaLia6TBUdA1WyuI1gJtGTCgHEkanhTkSo5pTitbkuq7DYiz0cwji\nDir9mBXL0ZxSDT+zbXtgw8+AtUPiq6piyx2BdV33OgKr+OEPf4jLL788tBtwqVTC9ddfj4suugib\nN28e6DjdlUCSdjqH581Q6yioqIqKEw078jhZWp4DQK2oh+rNTYdmyl4D2pZugiW4INDZVhjpEq/l\nj5xCLcgJcItytyw7VqJwaPyKIinS1IRIC9nJJv4X+q9lWd75yJEMq0q6QR2B5+fnfdvMzc3h6aef\nTlzIPKj2wul2QSRxYs20SCi52QmKYs+2nEgZIKkjTYXrSAset2WzVLG5vn0dCsbhs1IZY94SmhC3\ndxmlFDYhWAqxUhu2v9arHLEiF2FhvODrCCGjY+lGh3qlQZil2+92PeLhUq1WUavVUCgUYNs2TNP0\nLOE0460Fy7TfWFV5IckJ/853voObbrop8Zcjx+mejl8okCzl9VTLgUWYL1wrzf7zBolc5mftUBuW\nxgu0w8siSLcU0ocNcDVPhzDIodSyI1V2otok3AINi72VoWkaKCLCztrnJqsEE4TlkBfiEBR+tpoV\nwNYKia8q6SbpCHzo0CF85StfAQA0Gg0899xz0HW9q4mlwGpnpA0CksgLTZuGZqUl2d9hPDJWN7ul\nG1ywBuhOiBDFXwTf1EqFSI2UcCTSIR3GQqWBBTOZHBDVodehDJZl9bWLb8bT3TeI8DOZgIcl/Kzf\nWFXSlTsCT05O4oknnsAHP/hB3zZ33XWX9/t9992H17zmNaGECwx+7YWVQFIr07Uouz1LSfcPC+1i\nPF03A8q4R55hmWuAS7pTE51LtmERjJR1Twqol/XQJT3gLuuT3PgkQmtt2DSw0peKqAcXg0tSVsQD\nQn6YJMFqWLpBiAs/E9ZvknjzYcWqkm6SjsBpsVqW7iDleicNuQojzaSNDsNkAIswXxxvsaBFkkKz\nrdWG6aid7fzywpJFMV4pdki3pEfG+CYJpQOCu0YImA6FTTmqxWiyiHpwGY6rC0ed5qTFbgSiNN1+\nZX2lHUsNP1M7QPQba4XEVz1ON0lHYIH3ve99sePl8kJ0DK6MsKV4ksaV7v7B2zmM+zoB10Ja6Ag0\nbYLRDKS7aBGMVTp/j5SjM7iSaqhRhNlyGBzKUC0Ga8uCmKIsXSFdRM1ntKyHFunhHNAAXweJ5Yxe\n6AeCst8AwLKsgQw/W04MXeJzqVSC4yQjnWHFTDPZ5w8jubhiNwINiwZGAjhK0H+1GO4cA1wSGq3E\nRyUYjr9P2oJJMFHt2A31mFoFaVKTo+aQ5JkUpdeK+N2whxthHJO1YmhyhU0ZykqrpEGRF+Igd4AA\n0Nfws7Vi6Q4d6QL+qIVBWvb3A0k+T1Tig4yjC92dHADgZEy2mbf/ouVV7ZdbpbjJFR1CqUc4xwCX\nhMbK8YsuDn/K8KJJMS6R7khJj6ybm5R0oy1dmsiqjBpjyXJby4RZwxZhmKqWQlOt3e4S/ls3a1x0\nGiwHqYnws2q12lP42VrCqssLOfoLk3DMxtTCFXjplAHGAQ3+zKpXFoPJWMWBWQNaQQ/s2SVbtvVy\ndFTBkk2xYzJ9IfNFy2/pjlaiddCkDsIoacChPBHpRjkSRYpxmHxgEYbJWhFHQ74Hm4g+ap3PulYs\n3TAEdQAW4Wdp5YdBN7Jy0h0ymIQlrqj1yqKFJdPBSKkTr2pT4FRINpaKo4s2DMIxWvbfDCZhaNl+\nSzeKDJcskkheUGE4zNcheCQueiGxpRu9XRKLOaoIfMN2OxmHVRizKcf6ehFLdvD7JmGoKI68qIaZ\ng7jkDpuX3AG4VCr5+p/FFV8f1M+qYijlhdMRYnlvUxbYgjwIJxs2TApfiqfFeGSNVxnTDTtQNrCp\n30lXL+k+ElbRsCjGKr0//4uF8HAzAGgkrHMQZxEnId2ocyiK75xqBcs4FmGYqJZCazfYlKGi+29d\nSjuteYYFIvqhUql42W+O48AwjDUtPwylpbsWnnZpoTapFOUq1aWU6bDEgfKUuyUP5fNlkfgC5gIi\nSmGjchlRpUpZnLxgU97lGFoOxLUgEogj1SRREFHOzJbD4BAauqKwKEO1FB4BYZEATbed4qwuyfuJ\n1bQkw4qvA/B1xVgL9/5Qki7gViZbyar0WbtUyEhaXF28pqavapoGi6Yr1r1oEQAV72+TMKRRxIIi\nICzKfBaw2wEh/tzo2vJqk1EFw2VESRRAPCkTGl5LF3Djmw3KsBTycLMIQ9QzyKYMFYV0TcI8UpIT\nEgD3Xhi0Snu9EGRY8XUAa6Kq4FCSbrVahWmaqNfrqz0VH5I2rYzqrSYs3LALq5myVOCSktaatoB4\nEOk2LOojbje1N35eaRMC0iKpbBLniAxrWim+L5Oy9sMsGC2HwSbh9XYtwlCIICSTMIwrcox4UAS1\nJHccB5TSoYuHVbPfDMPwNOBBbb8ODCnpigSJer2+4iFjvbYC6vWGiNJOg3Bw3sQbMd7ZPyVpq8XM\n7YDi3UlTWkfKemwDSZtyN1U4Q7GBBZOAMI5iTA5vHDmHHVtcaxbhkT3ZLOImWIRpthZhiLoMLMJQ\nHfFbukEPW+FwEgQkrN+s3YAHGeJzVCqVgY9eGEpH2nLXXwhKCBCdgIPiVuUnsrBCxN9qecBekaQK\nloxnjzV8nu+oONcg7Dne8BFq02aJM9pUjCawdJcsgjE5K82kvqy0KDRsmijFeTqm7XmsvMDiuw9H\n1dI1CY+8MYOiF8IIHOhYhLJDSsTDOo6TmKT6XSZyuQh/0B8kQ23pZkUWa1Us/Vd7+XZwPlmMrcD+\nWQMLJsX6unspHF9Kt/9LMwYWLYrJqkt8BmGZA/VHYuJsAVfOGKsWPQngVMvG+nopNoVY7GtTjpGI\nbWzKYzPy4qIb4lqii+OEbWIRhkKENW4RhqrSfj5OhxYQDim5HoKoBraWrd9Bt25lnLakm4ZYB6kb\ncBQI43hpphW/oYSWw7BguaTLAexNuf9My0HD7pBunIUXhdGyHpolJ7BoEp+eearlYMNICS/Pxa9s\nGhYBibk5LcqwGFO+MU43T2LpR5XFjNN0LdIdMrZk0VTWY1A1MGH1ygS81rAWMlDX3llNANE9otVq\nect8seyXOwQklQFUCWBQLYGGTRNnk8kQGmbTZjg4l35/OSogrbzR2Y9ifb0US9pLFsF4tWPlzTQd\nbBgpJ2pXTnl84oNNeOxnmI9JHklCulG1GdxstvB5msQNKZPRdGjmmrrC+VatVlGpuJEspmnCNE0Q\nQgJDE3vFWgnvWg4MhKUb1xH4sccew/e//30AwNatW/H2t78d27Zt820zPT2NH/zgB5iensbMzAy+\n/e1v4+KLL/Yqkw1Lm/Wo0LSmzRKnAMs4OG/itdtG0bQpjqWUF4B2rYbNbqRI0lhYFQsmwaumqliM\nkQkWTIrzN/ot3fX1EsakEo9RiCsc7ih1I4IQF3oWVhxeRlTXDcI4oozpoHq+psNgE4aSYgGnJTe5\nGLkceiaiZQb1nllLJL7qlq7oCPw7v/M7+MM//EP813/9F44dO+bbZsOGDfj4xz+Oz372s7jwwgvx\njW98o2ucYrGIjRs34rrrrsP27dvx1re+FR/84Ac9C3WtWKu9II6wwvDjA/MwCceiRTP17Hr88KK3\n396ZVqZY23nDLUgeZyUuWsRX5EYQ0HhFj3QmCUQt64FkXTOmm3ZXs0agQ0hJLN242r5p2x0ZhIWG\nsmWBbP1Wq1XvsxmGkcr5lqMbq066SToCn3vuuajVagCAiy++2NfiR2Bqagq/9Eu/hEsuuQRTU1Ne\ntspKaTziolzNizFpSUYVL50ycMpwMu//5CsNzBoELYfhwJzpszgLCRMe5gwnNpQLcL3+JSVzQAMw\nVi1iIYG0EUeISTpezJsENmWeDipqw4qleJIx4izuJOQvw3BY4toSaVEoFFAquQWJyuUyGGM9l2Jc\nTst00B8Iqy4vBHUEPnDgQOj2P/7xjyPb9QBAvV4/LVv2JHEmBYFxt45C0pKQKpo2xXTTwWStiIZF\nfWnESZf98waB3sNNOFEt4mQCJ6CcKSevegQBJCG7hkVhOgx6SetaRem6jjljPnJ/LcFxSFpL16HL\nWt5RkKTsfJOz3mT/x2oglxdSIM2J+vnPf47HHnsM7373uyO3Ox27R5iU4/FDi5n3PzBr4rHD2fff\nO2NgruVgrKL7SHe8okdmZwksWiQyISAKhHFMVYuJakaYhPkyswR5OI7jFlNJkByyaFEQ7oZeyeOI\nbMG4sLt6WY+da9pOwTblXY605bT4ROhZtVr1UnJV51uOYKw66SbpCAwAR44cwTe/+U18+MMfjk3v\nPR1Jd84geOlUunAvGU2H4Wcnmpn3/z8vzOCVJRvj1aIvG2usWuxKNQ4C49kLcR9bsrFhtJQohbhh\nu2UCRQSLcEoKizXKwSXQtKlHiqq1zDjHscXoFcN4RY+szQBkOxdhOvFyWoByJ4harebrBBFVCazf\nlmlu6aaA3BGYEIInnniiSz6YnZ3Fl770Jfzmb/4mNm3aFDumCBk7nTDddHpqw13WC6k6+KpYVyvi\n4YMLmFC01YlKMZGlC2QvdnNk3kS9pCdyAk43HK8wjPiRkwJaCZ2Rbqput1PWdBhmYgh1vFoMLevY\nC7K2ve8XVOcb0B16lmMANN0kHYHvv/9+NJtNfOtb3/L2+fSnPx065unYhv3n09kfMvVSdA+zJHjN\n1lH8f3tO4lcu3oQFKaRqslZMbIEnte5ExILY/NCClbg05LElCyYhqCiZg+L3EzEpwAImYYEkYjgs\nNqRsvJJMCkmLtBEPadBr6JlaiPx0JuBVJ10gviPwe9/7Xrz3ve9NPF69Xu+SF9bS8iMt5k2C+1+Y\nybz/67dP4NEe9FzAbT5pUQ69oPks7olqMVFUxEgCnVNgsd2QUpCbReLTbgVmWwSnmg62jGqBsafH\nEiaXqFEQniOOschiNwAwUdVxZKH/RsFqW7pBUKueCfIVCUv9SptfS/f3qssLy4FqteqR7lr5InrB\nkUUb0wk7AAfhnHU1HMwY+QAAF2yq4+ftyAH1bCetCDZZLcbqnAKnWg7W1f091ZJKE3OGg+kmgaZp\nnvNMaLsWoYkjOEwlgUJkbZlOfD3i8QROvyyGoGrpDhoRidAzEfcryjH22gV4rWEoSXe1HGmrcYFb\nhOHBF09l3v+cdTUcnO/N6nrDjkk8cnABQFTyajQma0VMN5KT7gaFdJM4wAC3Vu7+WQNNh3tarog6\naNksMfGr+rcgjCT1iJMUdefozjpTj68WMl9OeaGfEDp4qVTyteERVc+yNAMYtAdMFIaSdFczTnel\nntbiOC/PW/iP/dFxoVF46+51+PeXZjPvv2t9DYcXzEyZbDLW1Us4lbC320zTwfqRDulWdC12SS9g\nEYaWw7B/1kChUHBjS9syg+GQxN0llizic6J5GVs9auMChkNRLYbfnk2bYqTsfz9rSc0kWK5oAzn0\nTNTCHXbn21CS7jCHjMkX/nSL4M//83CmcQoa8N8v3oT/fHk+c9RDVdfw9vPX4/t7s5O2wLpaMXFn\nhznDwVStQ7pT9ZJb/yEF/urhwzg0Z4AxjkI7XMymyZ15xxYtX2yu0CuTlliMg0uq4XWCmxbFaNnv\nkglz7q0VCOdbmtCztYiBcKT1G+VyeeijF04ZBF967BgORdTP1TVg81gZ2yerOH9jHWeMVzBa1jFW\n0VErFvAv++aw53h0bK4GYMNICWdOVHD+xjrOmqhitKJjoqJDK2j4o3894EkKYxU9scWpYqxSTFQ7\nAegu+LK+XopsBBmEg/MW/v7pE/i1SzZjfb2EYkFLVZby0IKrQ4psNIGFjPUvVAjSDdPqGzbFqELK\ncdXP1gpU55toQileD3K+cc7XTCnKoSTdtaLtZIFNOQ4uOPjLh49i3ykDpYKGLWNl7Jiq4ryNdWwZ\nK7eJtYjRcgH1ko56SfMcXJxzHG8S/K9npvGvbVmhoAEbR8oesZ45UcFYRcdoWcdoRUetqGG0rKOk\nuwTjMI59Mwb+5N8O+Kqanbu+5tNEq8VCl8MpDJqWXQ/eUE9WT1fFD34xhxMNG7955VZsGaukkgZO\nLNkwCMdI2S8pHe5RHxcIIlX1/cmq//ZV44P73elhNRDUhDKq5dBasPSHknQBdMVgriWhXQVhHE3H\nDceabRFMNx184MozPGKslzTUS9FP+ZZD0XA4liyG50808NozR3H9ORMYqxQxVnHJeayiQw/o1SbC\ne+YNBws2x/5TBg7Om/jAlWdgvFLEWMUl+WpRw53/2qmbsWGkFJso0A+sHynhiaNLibfnnENvk/x0\n08HfP30Cr9s+EUlyKqabNgynIwFwzsG4m07dDzRt2hWhIWPJIjhzouJ77WTD9rpgL8e1vpoZZHF1\nHxhz07vXAtbGLDNgrRIstAL0QsdBwzgHoRTlAke1CIyMF3HGSD2yRCWHhqLeWfYSykDBUS9xbBop\nYfcGt2Jb1Dkiba1TzIVygGsM4xWOa7eP4rodo16BEzHOqZbja1S5aaScWGtN+21R5hIn5em7CC9Z\nDH/1y7tRLmq+h839KaJAWg6DSV1LTFhXDZvieCM6zreia7EVxgCXdHdMViM+A8WY0hF41nDcrhLt\nl9eC1ZcFQS2HOOdwHAfFYnHgS7cOLekO8gUX1IiScw7KGMAZiFIEu1KAT8QUmpaqJ7pjcBTaC3XG\n3FRVvaD5HE/y9kEXKGUcWvuQ4jwWCxo2jJS9/YS14faFK6JQ0GA4zFdRbONoCU+9kswCTfttnWzY\n2DxWxisxdQ6CsH/WwIG5GnZM1VAvaWDQUADw8mw652vTpl62FWMMTYvHasuTtVKiZJEli2K0En57\nNoM0XYOg5RDobf+4sHrFdTAoRNSve1O2fg3DjUYRreYHGYM9uzWKoJKBAHwdhJNceHLJQHkMuRux\nWGKJi08vaAiyG4McD2E1gN0htMBt1Z5xjHMwSuE4FAtKyNfGkXIiB9eEUiQnCY4uWtg2XsEri3Zq\nK/n4koWWw/Czk03smKxiw0gJ9VIB+1NKAw2LemFnAGA0WrGhc1MJozTiohcY931FANzMRIdqKLVl\nCfk6Ed+ZmGtaLIc81+/xhJU7yAYXMMSku9w6bhCxipzypMQq3whBxCr/rmrU8r5iW9V7Kx8/zYWo\nziXKUVHQNBTaHuWG7SctTaqPEIUtY2UcS1nL98iChTfvXIefHFlKbSXPNB1cvm0MZ4x3NNHZlpO6\nv1zDdh8U4pwk6Q+3rl7ySTBhCGrJEweHcljUf92pD1ZCOvHFa8XbP2wYWtItl8uwbdtrtJcF8oWZ\nxGKllHrbytagGCfMYg0j1rA5yZD3E/qWWFZGFZWOItKkBK3OJWligYotY+XUDihX03QdiWn0XMCV\nMhZNijPG3b8Zd/uipe2ccUTpXLyUYB7r6iW8cDJ7Cc04GA7tWpmI/9UHudguJ9+VxdCSrqi/EEe6\nQfoq0CFWNSc8yPITY4jljfxeUotVRtBcgn4P2k+0VVHH6Qexyp9FXcYx5i7Xs2DrWAUPt9OI00DT\nNGybqMS2bQ+CKD8pLPEsXYyfP97wWaQnEljrEwmLrWdFy6axIVSy9StfoytFwMuxAl1L0UlDS7oi\nK21yctInNcialpxNlJRYwyxW8bs8tnCwCL01ypJNIwUEWTJB+4k5UEq9zx4UTpSUnOXPKR5G4py0\nHO4j3clqMXFn4HLCojgqOOfYNl7B3gRtelRMN9xKVwXN1cAXExRaV3FgzsS84WCq5nrRnz/RiN1H\nLpLa7QEAACAASURBVEm5HIhL8AiMdlFWa0HXyFpKPhh0DO1ZlOsviIuKMeZVlrJt2yNFmThFJST1\nR1yIqiQA+PVdARHUXa1WUSqVfPuKOanjhEEdP0ymCNqvWCyiUqmgUql0BZOHzUW28uUOC4JgdV33\nzot4mCyYxGdx7piq9lxIJw7TTQfvevWG1FosADz9SsPn1U9a6EbGnEGwaLoaacPh+MWplc2CdChH\nSRF+GxaNDicMuF7kbeXvXu6sMcgYdMeZiqEl3QMHDuBLX/oSDh8+jH379qHZbHoXkfgRy3GZQIBg\nQgy7kJNe4CLEyrbtwBbWaW+UIIRFTYgxxM1kmiYsywIhxPejEqtIxRQWTtR5mTUcnwV37voaDiQI\nwdKQPRPtmWMNOJRnshyfP9HAvOnWdjVNE88lsFKDMG+6MaJLFk1d/6FXzAaUuDy6YCW+XoDwB7p6\n3faT2JZLCsjlhVXEP/7jP+KKK67AiRMncM8992Dz5s14z3veg9HRUe/JLXK4w574MvqljZbLZd9+\nsqWV1XkVJksEWbGAa4FXKpVIp17QMcMiGsT/ah3apF2At45XEhcOV/HKooUTMckIYZg1COZNgolK\nGS2CzM6tEw0HmqZhznAyPzzCIGJxwySDmZaDDSP+aIhfzBpu4ohkAaeRj4Kcu8I40TQtVH7IkRxD\nSbqXXnoprrjiCmzYsAHFYhHf/e538Xu/93u44YYb8Fu/9VsYHx/3ls1qBovq5U1DiGJ/gbgLXFie\nQZEGYeMkJVbVKRKmPQtLRo54kDXwoLmofxPKMjnCAGDn+hpeOpWtItxIWcepHoq8zDQJdm4YQaNJ\nY5tJhuHRQwt48651iSI33LZIyZfrsy2CdfVSKOlON2ycu74OoPPAOLJgoWlTjEt1GeKIFfAnGqj7\nyfKc/P+gkO9acqIBQyovbN++Hdu2bUOlUoGu6/jVX/1VPPjgg9i9ezd+/dd/HZ///OfRbDah67rX\nflvVdoHosK2sUoB8kcstrIUVIc9DELOqsYoHBoAuKUB22CWRSNR5BAXPx32m6aaDn0q1D8YqeuJo\ngB1TVRzKqP3u2lDDkwkz3oLwzLElMMYw28pupT71yhLmWg6eT9BJeWOKtGgAONWysa4ebhedbDrY\nPOqXF6abNpYs0nXNOI7jyQSFQgHFYhGlUsnrYyayuMI0X/G/+sAVx0iD5STJtaDvDiXpBkHXddx0\n00148MEHcdFFF+E3fuM3cPfdd2NxcTGQfAV60VjF/kmcYOJHOPlEGxmgm1jDdNag40XNJegzyX2s\nhLMxzPEixjnWsH0FtF+zdRR7jiXTSAualtmbv3tDHT8/mb0h5w9emsOsQRK36AmC4TCcatr4SYIe\nc5tG05Jud4cMGVZA9wjGXQefsFwFucpOTyCaXFXE+Qk4557jbTVIL7d0BxyFQgG//Mu/jAceeACX\nXXYZbrnlFtx1111YWFjwkW8Q2ciIIiF1O9VyVS1WzrkXESDaV4vstqAIC/mYKoLmEiZDBEHcrKKS\nvxx7HDQOZRwPv+zvXLFzfR2/SOBEqxYLPXU7qJf0ntrGz5sEsy2na/5pcbLl4GgCXXrLWDkVwbsd\nMsrxGyoQ5TbDHshByLp6C7N+CRmO2r7LgdOOdAUKhQLe+c534oEHHsBrX/tavP/978f/+B//A3Nz\nc9B1HZRSH/kKJLFYw4hVtljFkk5YrKqsII4hwtxkCzxLSFAQklq+Yg62bXtLVMo4COM4umjhX6TO\nEaLyQxLr9ZKto3g2oUWsoqxrcPoQ8Hp4wcJTGecgcCxhcsZkLVlnZAGb8sSt5X3ziXgARFmtWVdv\nYn/xv9B8w6zftWaZ9hunLekKaJqGd7zjHbj//vtxzTXX4EMf+hDuvPNOzM7OBpJvHLGqy7okxBp0\nEwjdrVKp+DRf4fTq5QYRSHSjtR1ylUrFiznmAChjIITi0UMLsKXEhtdsHcWe48lI7IJNI3hxOlvU\nwCVbx/BMD3quwLQijaTFjskqDiQsoJ6FZuL2sQjr6qX206NLcCjL/p2LY6cgaNVPoG6/nDG/a43E\nhzJ6IQs0TcPb3vY2vPWtb8W//du/4bd/+7dx3nnn4R3veAeazSbe9KY3+ZxMglxLpZLvAgxbgkUd\nV0D1MqvbidJ1tm17TrOoMcLmk2ounANKBAdnDCcaNg4v2PjWUyd8Y1x55jj+9olXYo9VKmjgyJ6d\ndeHmEfzdk8ey7dzG1pTL/SC8fvt4qjq8/cbBeRPbJ6u+rLwXp1s4PG9i+0Q5sLWNjOW6doJWgmLV\nJCJ2TlesGdL9+te/jj179mBsbAx33nknAMA0Tfzt3/4tZmZmsHHjRrz//e9HtRpe+DkJNE3Do48+\niu3bt4Nzjn/5l3/Bhg0bcOmll2LTpk2ec0uEeMkWa9SYAr1c2HJIj9DNBBknfdKHLQnV0Dh1ucg5\nx5LNwKF5zpr7X5zxaapnTVRwvGEnItJrz57MrKXWSm7LoF7VhevOmcKDL85k3l8DMFIpJiq4kzUJ\nRNR2CPus+2cNXL5t3Ee6FmE43nCwfaLsfbdJH+5xSBrKqP6IfXVd9+LVRXp6rwScW7rLhGuuuQY3\n3HADvva1r3mvPfDAAzj33HPx4Q9/GP/8z/+MBx98EDfddFPPx/rIRz6C8fFxj1R/9KMf4Xd/93ex\nc+dOfPSjH8W2bds8SUGtZxAU19uztRnwt7iAhbyh1ndIG+cra8YcQKGgo6h3bgbToShoHCPlAhZM\niv/YP4+fHvEv7//bBRvwlcfjrVwNbuTBD38xF7ttEN68s7e28YCrCddLhUQJHGG4fNsYnk4ocaSN\nXBA40bCxeTS89OXJhoPNo93Otr3TLbxmyyhGdM3TVgF0Xa9BSHINBjlV1YzGuGtQJeVBiftdbqwZ\nG3/Xrl2o1+u+15555hlcffXVAICrr74aTz/9dF+ONTk56Svp+KY3vQnf+9738K53vQu33XYbPvGJ\nT+D48eMoFovecj8u2kFGP+J8AX99B7l1iaodqxq0HLOpatC6XoRe0L2uEeKnUiygVtaxf87C3T88\niAdePIV6qYBd62v4b+evx5+89Rw8tH8+UQvzN+9ahx/tz0a4tVIBG0dKqevvqnj7eRt8DsAsuPKs\ncTyZsDfb9skKDkd0bg7DoXkT26fSr95+uH8OB+bcCBIhg7kRMR3LMEmUS9C1I4czyteOiPkNC2dU\noYZSLrf2OyhYM5ZuEJaWljA+7hZFHR8fx9JS746VMGiahuuuuw7XXXcd/vM//xN33HEHtm3bhltv\nvRXbt2/3LE61qEy/Ld8k1oPjuMVbhFUT1NYnzPrVNP8xHcrQsBkKmispTDcd3HLFVoxX3W7Do+3l\n9dd/egzPR6TSlgoatoyXcfkZo9g6XsW/7stGeDe/ZjP+9/PTmfYV2DxaRr1cyFQoR+DGc6fwXynk\nkVdN1fBABinj4JyJS7ZuwGOHwuOAlyyC8YqORclqP75kY99MC7WSjp3ra64/gHFoutuKSRCnsExV\nZ29aq1VGLz6MLNZvLi+sElbypF977bW49tpr8cgjj+CTn/wkNm3ahNtvvx07duzwLAI5aiEOveis\nQKetj9wbSnZccM67Ms2CzhdjHFpBa5c7dMewGfeW4hPVIl4lWV0OZTg0b+FvHjuKZ481oMHtALxj\nqopXbxrBmRNVt1NwuYCRdjv4l2ZNfPb7+2PPyYZ6CdsnK3j15lFsn6xgrFLEeKWI//XsCV/b9zis\nr5dw1mQFF24awVmTFUxWioCmJZqDjHW1Is6adD/XeZvqOLFk499TyCP1so5WihRgAZMw1ErRLXae\nPLqEK84c75Jr/uvlBeyfNfC6syZwwaY61tWK7XC+znUDAIQBpQJQVFKAufuL93caBMV2BxkgYfvJ\n81jODsergTVNumNjY1hYWMDExAQWFhYwNja2ose/+uqrcfXVV+Pxxx/HH/zBH2Bqagp33HEHzj77\nbI98g7TWKMs3jFhVi0Qu1hMWOSGWb0F1Jrq9ywC0tsNHGmdEueEZ55g3CBzm/n90wcSvXryp3Y5d\nl7rr+m+QuZaDhw8t4H8+fMRzCo2UdZw5UcH5G+s4d30dk9Uixqs6xitFjJT945xs2PjGk8fx0IFu\n67JWKuDM8Qp2b6xj14Y6pqpuS/jxahEj5QLGKkUUC64D8MXpFj73/f2BMb4VXcO2iSp2b6jhvI0j\nmKoVMVEtYqw9znhFB+XATw4v4kuPHe3aX6CkazhjvIJd62s4f9MI1tdLoClJKw1enjNx4851XaT7\n3IkmXnvmOL702FFsGi3jpos24opt46iX24k33I231uF+77bdaeHu1QLpk4O4Fw1ZyA5iu6BU9bVE\nyGuadC+55BI88sgjeNvb3oZHHnkEl1566arM46qrrsI//MM/4IknnsCdd96JsbEx3Hbbbdi5c6en\n+QYVE1F/ZGJNUqxGIMg6EMQq0oYBeJYv0L1s0zRAQ4CVweFrCe8Qd9k5VdOxebSM8zb6dXYZlHFM\nNx0sWQRPHFlCrVTAZ258FcbKOkYrBYyUdYxXi6iVui9D8ZnnWg72z5r4m8eOgjDgmh0TuHBTHZvG\nyhhv7z9a1jFa0VErBYdHcc5xfMnGI4cW8Lc/OYZ19RIu3DyCV28ewbbxMkbLLtGPVYsYbT84gnB8\nycIPXprD3z15HIBrRW+frOBC2RqvFr02QvWSe45PLtn41x4cf3OGg3W1YqSFv2SSwK4U33r6OD57\n49k4b2MV45WiL+JG1zToUvKFeE92vAUV7Q/6PQmyjqN+p8IYkWtcryVoPGLGc3PZnB3Lga9+9avY\nu3cvms0mxsbG8K53vQuXX35530PG+oEnn3wS9957L2q1Gt73vvehWCxiy5Yt2Lx5s287TdO8xAc1\ntCYNoiwFGbJTBOj2ZKvjMM49qSEJHOqWFBTWacMiaNoU9ZKOkXL3zave3IAbGmUzoFLSUdIL+MVM\nC5RxjFV0jLTJTE8g2xDGYDgcJV0D58C+mRbKRddaHSm5JC3mKc9FrfjWsAgM4lqE+2ZaKOkaxoUV\nXSpgvFrssuoFmjbBL06ZePDFaSyYLHNxnh1TVZw9VcN/RDgfJ6pF/F/nr8ffP32i6z0NwK9cvAnX\nvmoC6+slVIsFb856QUOlWPB9z+K7B+/U0g3qfhKEpNdiHKIkN3VsIeeppVpXE1NTU6HvrRnS7Sd+\n/OMf4+GHHwYhBDt37sTNN9/c1/EffPBB/OhHP0Kj0UChUMDWrVvxpje9CVdeeaXvKa32VItC3EWY\nFF3E2rZ8w6IpVMjHlG8Ayl0HjUrSYR5xTdMArYCi7u9kYTgUugaU9OQanng4+Mdh0AtAWU8eoEMY\nh65pKLQJiVCGhk1R0rVQ61eF4TA4jKOiazi6aGHeIBir6PjEgy+lKuuo4n1XbMV9P41OBvnvF2/C\nIwcXfHUghGRy3sY6zttYx6bRMjaNlDBS1lHWC6iXCt7nDUPUgxroP7mqUK8hNSNT0zRYloW9e/fi\n7LPPxvr16zPPp1+IIt01LS9kQbPZxD/90z/hzjvvRKlUwl/91V/h+eefx4UXXti3Y1x11VV4/etf\n74We7dmzB/fccw++8pWv4I477sAFF1zQJTsEpVEup5dYRtJeblHRE4X23zTghgiSVlibpMXf4kfn\nFJxxUARbVl1aNOAbR6BWCibbsIcGbychaBp8mVNVjUPX9MDPzqG193Ffp8x9+NRLGoqFAs5ZVwMA\n/OxEsyfCBQDK3dY8UfUmvvfcSXzqhlehqAE1IZlU9EjJJAiyPAXAZ/kzxmDbtu/1JA/HrEkV6rXU\narVw7NgxvPTSS3j66afx1FNPwbIsjI+PY+fOnfjABz4wEKQbhdOOdEW3XMNwYxht2+6K/+0VGzZs\n8P198cUX47777sPPfvYz/Nmf/Rkopbj99ttx0UUXBZJvUsuhH5luYjkt7ydf5HFOPnGDqjdgnNda\ntYjFfiJbKelDQ3M3Dv18SR8asqYtPyjENl0aOwBN/Cu20YCRUkcXFefn0Hy2Iu0yHj24gGteNYEf\n7Q8PU6Mc+LOHDuH3r9+Oc6ZqmKiF396cczC4um7YOQq6hkQPQVmSCXpYR12PUeQqrpX5+XkcOXIE\nL7zwAn76059i3759AICtW7di165d2L17N37lV34Fv//7vz8QkmIanJbywnPPPYe//uu/RrFYxI03\n3oh3v/vdK3r8F198Effccw9M08Ttt9+OSy65xEtqSGr5JkWQZRc1lkiwUK0d2cnXHfmwPFp0lNYq\nf7Z+SS9Rc5LnIkhZ1uI7rZcK0Iu691BpORR/+M8v4fkT2ev+Cvz267bhy48dTZROfNZEBTddvAnn\ntyWF0XLnmmK8HbWgpf/OgGCJSpRyDPqOwgo9OY6D6elpvPzyy3juuefw+OOP49SpUyiVSjj77LOx\na9cunHfeedi1axfOOuusNVWvIdd0JSwtLeFP//RPceutt6Jer+PLX/4y3vKWt+Diiy9e8bn8/Oc/\nx7333otGo4Hbb78dl112WST5JkEap1rQEi4ueiLpfKLIvt+EuFzjRFljQZZ90Dk6MGvi//7ei33p\nn3bexjpeNVXtyqRbXy9hx2QFF20ZxVmTVYxX3KiOsbIbOlcNkVrCPnOQ/KK+J28vP3jklj7iQS0k\ngX379nmSgG3bGB8fx65duzzLddeuXQMvDSRFTroS9uzZg0cffRQf+tCHAAA/+tGPcOrUqb7UbMiK\nffv24d5778X8/Dxuv/12XHHFFYksXyD+hhD/yxaHTKxxVmuctRk1pzRIYrXKVlUQ8WWZk3qOZKs1\nLBtL7BPnYAKAf957Cn/+48NpT0co3nPJZpyzroqy7iariCiK0UoBaJNemgd2Lw8g2QnLOcfc3BwO\nHz6MEydO4OjRo3juuecwPz+ParXqs1rPPffcNScJpEVOuhIMw8Bdd92FT3/60yiXy/jyl7+MG2+8\nERdccMFqTw379+/HPffcg5mZGdx222246qqrInUzgTBrTF4Gy9uK/5fLil7useTtVYs8ap+gn7gH\nUNw5UolaPt+nmjZu/T/7fN16+4H3Xr4Fb961LrDQjXgQCPLVCrovzjrqs8nXRpwksH//fjz33HN4\n4oknPEngnHPO8azW3bt3Y3x8HI8++iiOHTuG97///X09B4OOnHQVPPzww3j44Ydh2zYuvPBCvPOd\n7xwovejAgQP48z//cxw7dgy33XYbXv/618MwDHDOvYIi8g1RLpcDyWc5lvGqtal2U046Tj/mJD6/\n3HBROAXTWK1ZzpE8J3k+cmflx4428f/84OVMY8dhqlbEL796Ay7YNIrNY2WsqxVRlSIUGOMgjIIH\nWOJhDyCZXJvNpicJPPXUU3jmmWe6JAFhua5bt25ZPuNaRk66fYZlWfj2t7+No0ePghCC9773vTjn\nnHP6eoyf/OQneOaZZ/DTn/4U5XIZhBB84AMfwKtf/WoAHQ+7XA0tDfohB4hxBkVr7dVq7WVO6vyO\nLVm444GXMNtDi3iBguaWhjxnXRUXbR7FlrEyxqtuLYrRio7xiptIos4B6IS/BWmtQhI4dOgQXnjh\nBTzxxBM4cOAAADdKQFisu3fvxjnnnDP0kkA/kZNun/G1r30Nu3fvxhve8AYv5KtWq/X1GP/+7/8O\nSik2bdoEzjm++c1v4he/+AU+9rGP4Y1vfKOvAr+aZLGSTixhTfarXqv6epCGGBWilFSDFtumieyI\nglwsaNF08P/+5Bj+6efpOkpUigWc1a5Fsbtd+8ElV91LdQ5LPgkq5yk+l+M4OHnyJE6cOIFjx47h\noYcewvT0NCzLwllnneWzWs8888yBWvWtVeSk20cYhoE/+ZM/wV133bXixz569Ci++MUvYt++ffjY\nxz6G6667zke+cjeLNMTaD5KWb/a4mM2w/VRNOiz7KanWKrRNtdxm3Jyixgw6T0xY2pqGBZPgfz8/\njW8HpOMKrKsVsX3KtVp3TFYxVtUx0bZax9o1JIKOnUQSeOWVV7B371489dRTePbZZ+E4DsbHx73o\ngN27d+OMM87Ac889hyeffBKf/OQnfdXpcvQHOen2EYcPH8Y3v/lNbN26FQcPHsQ555yDm2++2Qvq\nXwm88sor+Iu/+Au88MIL+MhHPoIbbrghkHzDsFzkI1tdsjMnSkuUa/72MicZSeJI++nZB9xstMPz\nFr7+5DE8fHABugacMV7BzvU1vHrzKDaMlNyKZRUd9eL/3965xbRZ/3/8VcqKTEohY2zQMFZOGV5s\nLmYhspnoRoRgRciUzRFlHLIBW3TOxZipmTK26MUMWcQMg2OiXmzRZEZli4ddGHbAURDaAUPn2H+A\nVBijtBjk0P4v+LW2nMahLYd+X3c8hef79Al99/O8P4evhIe9JXhLHS2iyaJ7e2G1WCz09PRw9+5d\nGhsbuX79Onfu3AEgNDR0XJWAj4/PpNc8Fz9bMDVCdJ1Ia2sr77//Pvn5+cTGxvLll1+ybt062w4W\n7qSzs5OTJ0+i0+nYt28fCQkJU0a+rvY1xwqq/Szf+fZax9og9vOOZ/slZLFY6B0YZnDEQv/gCP/X\nO4CfTGoTVz+Z97hBP9a/s4/EAVvyzXo9Vkvg1q1baLVaampq6O3tRSaTjasSUCqVwhJYYAjRdSIG\ng4HCwkJOnDgBjHa3Xbt2jdzc3Hm7Jr1ez0cffURdXR0FBQUkJiZOO/KdKGq1j7geVPs7NpE1UUeS\nvc8606YPVyXp7JNL072eEbMFL7sh7/8Om/83Rc0LH+/x93c6loDJZMJkMlFdXU1TUxONjY0YjUYU\nCoWDsEZHR0/5QRYsLMTAGyeiUCgIDg7m9u3bhIeHo9VqWbdu3bxe06pVqzh69ChdXV2UlJRQUlJC\nfn4+SUlJWCyj2/dMJr5TJcjso9WZeK1jxdFaWiaVSiecNfGgErWZMNX7scd6HyaadzyRdTJitiCR\nOA55l0klLHvov92Zx94v6zmslsCdO3dobGxEo9E4WAJWUY2Li0Mul7N8+XLy8vJm9L4FiwcR6c4C\nvV5PeXk5JpMJpVJJdnb2lN6Zu7l37x4lJSVcu3aNvLw8kpOTbdHmWNsBJo7I3OG1WofCjF1nNuea\nKdYviIki4InqjqcTtQ4ODtosgYaGBjQaDQaDwcESsPqtU1kCg4ODbs0RuIqenh7Ky8sxGo3I5XIe\nf/xx4uPjGRgYWJBzsJ2JsBc8lJ6eHj7++GMuX75MRkYGMTExWCwWNmzY4PB71rpN6wQ2d3mt9rbD\nRJG4uzvgLJb/mhsmEl3rMZPJRHt7Oy0tLdTW1nLjxg2GhoZQKBQOVQKebgkYDAb6+voICwvDZDLx\n3nvvcfDgQa5cuYKfnx+JiYlcvHiRf/75Z17b8F2BsBcWKGazmePHjxMYGMi+ffucfv6//vqLgYEB\nIiIiqK6u5s8//0SlUvHoo4+O7g77v4lZ1qSSvRg9SHCn+xj/oHNYt++2Mtftt8f60lNd40QWivUc\nZrOZjo4ONBoNXV1daLVa7t69i0QicagSeOmll4iIiFhQTzoLBYVCgUKhAMDPz4+1a9fS29tLfX09\nhw4dAkb3GTxx4sSSE92pEKI7j/z888+EhIQwMDDgkvOHh4ezf/9+goKC8Pb2xmAwUFpaSkpKCjk5\nOaSmpuLl5cXQ0NCkLb3TEbHpMB3fdmyFwWTlXdP1gKdrCej1epslUFtba7MEIiMjiYqKoq2tjRUr\nVvDhhx86ffayp/D333/T0dGBSqXCaDTi7+8PgL+/P0bj7LYxWqwI0Z0n7t+/j06nIzk5mZ9++skl\na/j5+eHn52f7WaFQ8MYbb5CXl8cnn3yCWq0mKyuL7du34+XlZatltRdfVyWyJvvbiRJaDzrXVOJq\nPYfRaLRZAhqNhqamJoaGhggICLDZAU8++SS5ubnjHg0tFgttbW1LRnA/++wztFotcrmcI0eOALjU\nZx0YGKCsrIwXXnhh3Dk9sU5YiO48ce7cObZv3+6yKHcq/P39OXToEHv27KGsrAy1Wk1mZibPP/88\nUql0QvEdiysjYKtYWh/77TdHnKjJwnoes9lMT08Pra2t3LhxA41GQ1tbGwBKpdJWfrV7925UKtW0\nLQGJREJYWNiM3tdCJj4+nqeeeory8nLbse+//57IyEgKCgq4ePEilZWVTnnkHxkZobS0lLi4ONtu\n3XK5HIPBgEKhwGAwIJfL57zOYkKI7jzQ0NCAXC5nzZo13Lx5c96uw9/fn4MHD7Jnzx4+/fRT1Go1\nL7/8Munp6Q7i64zNCGcatY71WWH0A9zf3093dzcWi4XW1lbq6+upq6ujr68PHx8fhyqB5ORklEql\nR0ZTUxEdHU13d7fDMVf4rBaLhYqKCkJDQ9m2bZvt+IYNG7h69SpJSUlcvXrVJsaeghDdecDqH+p0\nOoaGhhgYGKC8vHzeZo76+fnx6quvkpubS3l5OWq1moyMDHbu3Im3t7dDY8Nsh9lMxxKwH4oNo5ZA\nW1sbN2/epLa2lqamJkJCQli5ciXd3d2EhYWRkJDA3r17CQgIcOYt8Thc4bPeunWL6upqlEolRUVF\nAKSmpvLMM89w+vRpCgsLbVaGJyFEdx5IS0sjLS0NgJaWFn788ccF8Y/38MMPs3//frKzszlz5gxq\ntZoXX3yRXbt2sWzZsmmJ72RVApMNxTabzdy7d8/BEmhvb0cikaBUKm1Ra1ZWFhEREbb61a6uLurr\n64mLi3PDnZkfWlpaOHfuHGazmS1btrB161a3rOusJ4OoqChOnTo14WsFBQVOWWMxIkRXMI7ly5dT\nUFBAVlYWFRUVPPvss+zYsYOMjAxkMtk48YXJk1kw+iH+999/0ev1/PHHHzZLwGg04uPjQ2RkpC2Z\npVarCQ0NfeAHf+XKlSQkJLj8XswXZrOZiooKDhw4QGBgIMePHyc2NpaQkBCXrOfpPqs7EaI7z1iT\nOwsRX19f9u7dS2ZmJp9//jlpaWkkJSWxfv16LBYLW7ZsAf4b1iKRSOjr66O9vZ3m5mZqa2tpfv1N\nVgAABK5JREFUbm5meHiYwMBAm7AmJCSQl5cnLIEpuH37NsHBwQQFBQGwadMm6uvrXSa6nu6zuhMh\nuouYydosnc3vv/9OU1MTsbGxtLW10d/fz4oVK/Dy8sJgMKDVatHr9XR1dREYGGj7IsnJyUGlUi2J\nllZ309vb61C6FhgYaNvVYa6UlZXR0tJCf38/b775JikpKR7vs7oTIbqLGKlUSnp6ukObpUqlcno0\nFBUVxbvvvotcLrc1FLzzzjv09fURFxdHdnY2RqORyspKtm7dysaNG526/kJBo9Hw7bff0tnZyeHD\nh1mzZo3ttUuXLlFVVYWXlxc7d+4kKipqTmu5suJisol4nuyzuhMhuouYydosnS26vr6+DtsRyWQy\nPvjgg3G/FxsbO+cZCQsZpVJJfn4+X3zxhcPxjo4OLl++zFtvvcX9+/cpLi6msLBwTjNuAwICHGaf\n9PT0CDtmiSAmHy8RrG2Wzt4gc6Ys5ZrY1atXs2rVqnHH6+vr2bRpE1KplKCgIIKDg2ltbZ3TWuHh\n4ej1erq7uxkeHqampmbcoCLB4kREuksA+zZLMXjF/RgMBlQqle3ngIAAent753ROqVRKZmYmp06d\nYmRkhCeeeMJlSTSBexGiu8iZqM1SMHuKi4sxGAzjjqempro90oyJieHtt99265oC1yNEdxEzWZul\nJ/HVV1+h1WpZtmwZ0dHRpKSk2Pzn2SS3Dhw4MONrGOu/jq08EAjsEZ7uIsbaZtnc3ExRURFFRUXo\ndLr5viy38sgjj3DkyBEOHz7M4OAgFy5cAByTW3l5eZw5c2bOs3rtsU8Yrl+/nuvXrzM8PEx3dzd6\nvZ61a9c6bS3B0kLsHCFYMmg0Gn777TdycnK4cOECEomEpKQkAE6ePIlarZ5TorGuro6zZ89iMpnw\n9fUlLCyMV155BRidjVxVVYVUKmXHjh1ER0c75T0JFidi5wjBlMxXj7+zqaqqsnXJuSK5tXHjxklr\nkLdt2+axFo9gZgjR9XBc0eP/zTff0NDQAIzWtqanp9uGqc/GZ51OcquyspKHHnqIxx57bNbXLRC4\nAyG6Ho4revwTExN57rnnAPjuu++4dOkSKSkps24ieFBy68qVK+h0Ol577TXbMZHcEixURCLNw5mo\nx3+uj+HWLVlGRkYYHBy0bTzpiiYCnU7HDz/8QEFBgcMGlyK5JVioiEjXw3FVB9n58+f55ZdfWL16\nNa+//jrgGp/17NmzDA8PU1xcDEBERAS7du0iNDSU+Ph4jh07hlQqZffu3Uu6W06weBCi6+HMtsf/\nQT5ramoqycnJnD9/nq+//pr09HSnXreVo0ePTvqaSG4JFiJCdD0c+x7/gIAAampqJp1CZc90mghk\nMhmbN2/m9OnTgPBZBQIQnq7HY9/jf+zYMTZv3jznHn+9Xg+Merq//vorSqUSED6rQACiOULgAkpL\nS+ns7EQmkxETE8PTTz9t2/5FNBEIPIGpnuCE6AoEAoGTmUp0hb0gEAgEbkSIrkAgELgRIboCgUDg\nRqb0dAUCgUDgXESkKxAIBG5EiK5AIBC4ESG6AoFA4EaE6AoEAoEbEaIrEAgEbkSIrkAgELgRIboC\ngUDgRv4f3J1ScMvD/HQAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x108ee7290>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"UT = empty(U.shape)\n",
"UN = empty(U.shape)\n",
"noise = 10\n",
"for i in range(len(timeslice)):\n",
" UT[i] = fft(U[i]) + noise*(randn(n) + 1j*randn(n))\n",
" UN[i] = ifft(UT[i])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"-c:5: ComplexWarning: Casting complex values to real discards the imaginary part\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"-c:6: ComplexWarning: Casting complex values to real discards the imaginary part\n"
]
}
],
"prompt_number": 36
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I have no idea why there are artifacts in this plot ... !?!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(10,8))\n",
"ax = fig.gca(projection='3d')\n",
"\n",
"poly = PolyCollection([zip(i,j) for i,j in zip(fftshift(K), UT)])\n",
"poly.set_alpha(0.7)\n",
"ax.add_collection3d(poly, zs=timeslice, zdir='y')\n",
"\n",
"ax.set_ylim3d(0, 10)\n",
"ax.set_xlim3d(K.min(), K.max())\n",
"ax.set_zlim3d(UT.min(), UT.max())\n",
"ax.view_init(20,-120)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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rlsVxUYFpJq91qGGi/CwPITxLgH14BGcLJ1Gl/qTzIQ1Ki2FFuO+CPPLrABEBJ1ZG5njO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Hix53T1vu5SOLNWMBdgJWFodZD2IH4cTpDO0Iz01V3ZlUTz6/fD1JGCkOGiSBwgmgzM6pEC8T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L73ve95gPP000/jwIEDuOaaa/DCF74Q1113Ha644optu5ZNU2Ycnm0uy8vL+JM/+RO8613v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\n",
"text": [
"<matplotlib.figure.Figure at 0x108dc79d0>"
]
}
],
"prompt_number": 37
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(10,8))\n",
"ax = fig.gca(projection='3d')\n",
"\n",
"poly = PolyCollection([zip(i,j) for i,j in zip(fftshift(K), abs(UN))])\n",
"poly.set_alpha(0.7)\n",
"ax.add_collection3d(poly, zs=timeslice, zdir='y')\n",
"\n",
"ax.set_ylim3d(0, 10)\n",
"ax.set_xlim3d(K.min(), K.max())\n",
"ax.set_zlim3d(abs(UN).min(), abs(UN).max())\n",
"ax.view_init(20,-120)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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bcF2eObpU/rL28SMzlOhyqEzK/h9qfwinboG6rjbn5HyYcnY0Jm9lseZ4HpoG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\n/yLzuVAlrRjNU67NNPxAcDyIP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WaCi14OYlVgEk8WKOVe0NdMy3P9fQ14/80toAb6A7xc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PVc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IExiphTkfYqG1+54JkqcsZC24L0mHZrpuC+ByK4SpnJ8RxpytRU0FFl8ozoCFfocxsixGJS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\n5xw8/fTT2Lx5M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"text": [
"<matplotlib.figure.Figure at 0x108db0610>"
]
}
],
"prompt_number": 38
}
],
"metadata": {}
}
]
}
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