{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## ThinkDSP\n", "\n", "This notebook contains code examples from Chapter 8: Filtering and Convolution\n", "\n", "Copyright 2015 Allen Downey\n", "\n", "License: [Creative Commons Attribution 4.0 International](http://creativecommons.org/licenses/by/4.0/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Get thinkdsp.py\n", "\n", "import os\n", "\n", "if not os.path.exists('thinkdsp.py'):\n", " !wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/thinkdsp.py" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from thinkdsp import decorate" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# suppress scientific notation for small numbers\n", "np.set_printoptions(precision=3, suppress=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Smoothing\n", "\n", "As the first example, I'll look at [daily closing stock prices for Facebook](https://finance.yahoo.com/quote/FB/history?period1=1337299200&period2=1585353600&interval=1d&filter=history&frequency=1d), from its IPO on 2012-05-18 to 2020-03-27 (note: the dataset includes only trading days )" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "if not os.path.exists('FB_2.csv'):\n", " !wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/FB_2.csv" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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DateOpenHighLowCloseAdj CloseVolume
02012-05-1842.04999945.00000038.00000038.23000038.230000573576400
12012-05-2136.52999936.66000033.00000034.02999934.029999168192700
22012-05-2232.61000133.59000030.94000131.00000031.000000101786600
32012-05-2331.37000132.50000031.36000132.00000032.00000073600000
42012-05-2432.95000133.20999931.77000033.02999933.02999950237200
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" ], "text/plain": [ " Date Open High Low Close Adj Close Volume\n", "0 2012-05-18 42.049999 45.000000 38.000000 38.230000 38.230000 573576400\n", "1 2012-05-21 36.529999 36.660000 33.000000 34.029999 34.029999 168192700\n", "2 2012-05-22 32.610001 33.590000 30.940001 31.000000 31.000000 101786600\n", "3 2012-05-23 31.370001 32.500000 31.360001 32.000000 32.000000 73600000\n", "4 2012-05-24 32.950001 33.209999 31.770000 33.029999 33.029999 50237200" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.read_csv('FB_2.csv', header=0, parse_dates=[0])\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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DateOpenHighLowCloseAdj CloseVolume
19722020-03-23149.660004152.309998142.250000148.100006148.10000629830800
19732020-03-24155.210007161.309998152.570007160.979996160.97999630440400
19742020-03-25158.919998162.990005153.059998156.210007156.21000735184300
19752020-03-26158.250000164.000000157.020004163.339996163.33999626556800
19762020-03-27158.199997160.089996154.750000156.789993156.78999324861900
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" ], "text/plain": [ " Date Open High Low Close Adj Close \\\n", "1972 2020-03-23 149.660004 152.309998 142.250000 148.100006 148.100006 \n", "1973 2020-03-24 155.210007 161.309998 152.570007 160.979996 160.979996 \n", "1974 2020-03-25 158.919998 162.990005 153.059998 156.210007 156.210007 \n", "1975 2020-03-26 158.250000 164.000000 157.020004 163.339996 163.339996 \n", "1976 2020-03-27 158.199997 160.089996 154.750000 156.789993 156.789993 \n", "\n", " Volume \n", "1972 29830800 \n", "1973 30440400 \n", "1974 35184300 \n", "1975 26556800 \n", "1976 24861900 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.tail()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Extract the close prices and days since start of series:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "close = df['Close']\n", "dates = df['Date']\n", "days = (dates - dates[0]) / np.timedelta64(1,'D')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make a window to compute a 30-day moving average and convolve the window with the data. The `valid` flag means the convolution is only computed where the window completely overlaps with the signal." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "M = 30\n", "window = np.ones(M)\n", "window /= sum(window)\n", "smoothed = np.convolve(close, window, mode='valid')\n", "smoothed_days = days[M//2: len(smoothed) + M//2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the original and smoothed signals." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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evJj//u//5vOf/zz/8z//w4wZM7j22msHffaRI0f40pe+xJYtW+jo6Mj8ldXQ0MCSJUsoLS3l5ptv5uc//znXXHMN9fX1bNq0iX//938HYM+ePRiGwfz587PuG4/Hs/YHtNvtLFu2LKtMa2srX/jCF1i/fj1tbW0YhkEkEqGhoQGAQ4cOUVNTQ0VFReaayy67LOseu3bt4ujRo/1aImOxWFY3shBi6pmyrUITkCWSbqnT88qA9J6vSUu6pc5qRDPlpurPRELdFGa325k7dy4Aq1atYuvWrfzbv/0b//7v/05FRQWJRIKenp6sUNba2poVTkbq+PHj3HHHHfzN3/wNX/va1ygqKuKNN97ggQceIJFI4Ha7AfjIRz7CD37wAz7/+c/z2GOP8Rd/8Rdomjbofe+8805mzJjBf/7nf1JVVYVpmixZsiSr6/Lee+/lE5/4BN/73vd44oknWLp0KUuXLgUgFAphsVjYvn07Fosl695erzfz2uVy9avH/fffT2dnJ//2b//GjBkzcDgcrFmzZkTdpqFQiFWrVg04BrG0tHTY9xFCTD69y2yIMRZqwx08jgIsxbMzhxO29B/TrkQHKBM0XUKdOM1iT7eY5erZF8A0TeLxOJAOeTabjZdffpl77rkHSLc4NTQ0ZMbdna22tpZUKsX27du59NJLM9f09PRkymzfvh3TNPmXf/kXdD09ZPNXv/pVv3t94AMf4LOf/SyPPvoo+/fv5/777x+03p2dnRw6dIj//M//zIyPe+ONN/qVu+uuu/joRz/Kc889xxNPPMF9992XObdixQoMw6CtrS1zj+HauHEjP/zhD7ntttuA9ISHjo6OzPkFCxbQ2NhIa2sr5eXlAGzdujXrHitXruSXv/wlZWVl5Ofnj+j5QojJy+/3XxR7jk4EqfYjKGUSdpRjK5sHpFvqIvZSkhYXNiOKN95CyFkloU6cpmkj6gLNlYcffphbb72V6dOnEwwGeeKJJ1i/fj3PP/88AD6fjwceeICHHnqIoqIi8vPz+fjHP86aNWu44oorBrznggULWLduHX/1V3/Fj370I6xWK5/85CdxuVyZMnPnziWZTPK9732PO++8k40bN/LjH/+4370KCwt597vfzWc+8xluvvlmqqurB/0shYWFFBcX8x//8R9UVlbS0NDA5z//+X7lPB4Pd999N1/84hc5cOAA73vf+zLn5s+fz7333st9993Hv/zLv7BixQra29t5+eWXWbZsGbfffvugz583bx4/+9nPWL16NYFAgM985jNZn/mmm25izpw53H///Xzzm98kGAzyhS98ASDT6nfvvffyrW99i7vuuouvfOUrVFdXc+LECX73u9/x2c9+dsjPL4SYvPr+AWq3X9gf5mJobXvTKx2EnRWZHhlN00DTidmLsUVPYkulJ0tM1VAns1+nqLa2Nu677z4WLFjAjTfeyNatW3n++ee56aabMmW+853vcMcdd3DPPfdw7bXXUlFRwe9+97sh7/vYY49RVVXFddddx7vf/W4++tGPUlZWljm/fPly/vVf/5VvfOMbLFmyhJ///Oc88sgjA96rt0v2wx/+8JDP1HWdJ598ku3bt7NkyRI+9alP8a1vfWvAsvfeey+7du3immuuYfr06f3qft999/H3f//3LFiwgLvvvputW7f2K3e2n/zkJ3R3d7Ny5Uo++MEP8olPfCLrM1ssFp566ilCoRCXXnopH/nIRzKzX51OJwBut5vXXnuN6dOn8+53v5uFCxfywAMPEIvFpOVOiCmsb3g4e+iHGF2hUwfS/+usyvxB3fu/KT39b7HVTPdWTdVQpyk1RVfgG4FAIIDP58Pv98sv2HH0s5/9jE996lM0NTVNub9gN27cyNVXX83Ro0eZM2dOrqsjhMiRp59+OvPa5XJlLSMlRo8Kd9Dw2EdQaByofi+33v3nAOzevZsTJ05Q2b2F0sBe2vKX0VJ4KWvWrKGkpGRc6zgeWUO6X8W4i0QiNDc38/Wvf52/+qu/mhKB7ve//z1er5d58+Zx9OhR/u7v/o6rrrpKAp0QIkPaUMbOqe3PARB2VuL0nelJ6W2pMzItdekZsFO1pU66X8W4++Y3v0ltbS0VFRU8/PDDua7OqAgGgzz44IPU1tbyoQ99iEsvvZT//d//zXW1hBA5JAuLj5/W+vQWmBFHKdOmTcscP9P9mh4LbzXS3a+GYYxzDceHtNSJcfflL3+ZL3/5y7muxqi67777smbbCiFES0tLrqtwUVBK4Y6n16eL2QooGmDsYsqSntxmMWPA1G2pk1AnhBBCjIHeljpN06TrdQwdO3oEV6ILgLCjPGtCSt+WuoKCAixm+v1UDXXS/SqEEEKMgd7g4PP5clyTqa3l0DY0TEzNStLixWo9016VCXUWFy63G9sUn/0qoU4IIYQYA7FYuquvt+XoYmqta2pqorOzE8MwxjxAFfr3A+B3zwRNyyx831fKkt4tSDeTWI3IlA110v0qhBBCjDKlFCdOnACm7qD8wUSjUbZv3w6kW8pcLhc33njjmD3PkegEwO+ekXlmr97Xpm5HuSvRevx44q1TNtRJS50QQggxyqLRM5vHRyKRHNZk/PXd61YpRSQSGbtWSqWwJboBiNvS3dx9u7v7BjxVOAtN03DHpm6ok5Y6IYQQYpQFAoHM64utpW6gwGSa5tjsqBHzoxtJDDSWXXEDDpcHt9udOZ1MJjOvrcUz0TQNRyowZX8mEuqEEEKIURYKhTKvp2qAGMxALZNjFuqCLSgUCWsepb5CPB5P1um+LaYWpxdNA4sZn7ItddL9KoQQQoySnp4eYrEYjua3WHriMdzx1swe0BeLHTt29Ds2miHKMAw6OzsxTZOG159AmSYRR9mAEyT6hjpsHtA0LGZCQt1YeOSRR7j00kvJy8ujrKyMu+++m0OHDmWVicViPPjggxQXF+P1ernnnntobW3NKtPQ0MDtt9+O2+2mrKyMz3zmM1l9+kIIIcRYC4VCvP7667z44ot4659Dw6S68w2WL1+e66qNq4FaJkdzTF1dXR1vvvkmf3rmDxgt6Z0k2vOXDBjqso7Z0jNgrdJSNzY2bNjAgw8+yObNm3nxxRdJJpPcfPPNhMPhTJlPfepTPP300/z6179mw4YNNDU18e53vztz3jAMbr/9dhKJBG+++Sb//d//zeOPP86XvvSlXHwkIYQQF6nM7y5lZpYzKXWZuJzpLaoupiVNzjaaIaqxsREAV7wdXRkkLS5itqIBQ93y5cspKCjgiiuuALsbTdOwmHGMKdrwk9Mxdc8991zW+8cff5yysjK2b9/Otddei9/v5yc/+QlPPPEEN9xwAwCPPfYYCxcuZPPmzVxxxRW88MIL7N+/n5deeony8nIuueQSvvrVr/K5z32OL3/5y1Nis3ghhBATX++it/ZUEPN0gNPQ0CIduazWuCsrK6OtrS3r2GiGOq/XSzgcpiBSB0DYUTHo+nT5+flcc8016TfJGJqmoSkT00j2KzsVTKgxdX6/H4CioiIAtm/fTjKZZO3atZkytbW1TJ8+nU2bNgGwadMmli5dSnl5eabMLbfcQiAQYN++fQM+Jx6PEwgEsr6EEEKIC9EbXArCdZjG6RCjgRbz57BW48/lcvU71ncW6oWKx+NYzDhFwYMAdHvnAQwY6rJY7GicXuIkFR+1+kwkEybUmabJJz/5Sa666iqWLFkCpDdDttvtFBQUZJUtLy/PbJTc0tKSFeh6z/eeG8gjjzyCz+fLfNXU1IzypxFCCHGx6e1e9cabMwFP0zS4yELdQK1yvd3RF6qjo4Oenh6ciU40FAmrl6CrJt0C12dNugHpOljSranKSIxKfSaaCRPqHnzwQfbu3cuTTz455s96+OGH8fv9ma/e/nkhhBDifPWGGUeyB1BE7UVoaOjxnlxWa9wNFOoSidEJUb29dK5EFwBRe8mIrtcsp4dkSUvd2PnYxz7GM888w6uvvkp1dXXmeEVFBYlEgp6enqzyra2tVFRUZMqcPRu2931vmbM5HA7y8/OzvoQQQogLEQwGsZhxbEZ6GY2Qsyqr+/VimSgxVqGu7/fPHW8HIGovHtk9bOmFifVE8ILrMxHlNNQppfjYxz7G73//e1555RVmzZqVdX7VqlXYbDZefvnlzLFDhw7R0NDAmjVrAFizZg179uzJGpT54osvkp+fz6JFi8bngwghhLjoHTx4EEcyHeCSFg8xW2G6WzAu3a+jMaaud6kUWypEQewEeXn5hJyVwDDG052mfOnhVvZw8wXXZyLKaah78MEH+Z//+R+eeOIJ8vLyaGlpoaWlJbNYoM/n44EHHuChhx7i1VdfZfv27fzFX/wFa9asSU9PBm6++WYWLVrEBz/4QXbt2sXzzz/PF77wBR588EEcDkcuP54QQoiLTGH4KAAxeyEJa1461AVOgZqa66Kdrauri9aWZiq7t3CF/TCzK9MTH8+eDXs+ekNdSXAfXrebwrmriTjSY+htNtuw7tEb6szuExdcn4kop6HuRz/6EX6/n+uvv57KysrM1y9/+ctMme985zvccccd3HPPPVx77bVUVFTwu9/9LnPeYrHwzDPPYLFYWLNmDR/4wAe47777+MpXvpKLjySEEOIilEwmQSl84fQyGx15iwg7ysHuRUuE8MamZsvQ2bZs2YIvcpzSwF7c3QepPvRfWFNhgsHgBXc/x2IxioIHKQ3spaCwAG3GVZlzww11CS29u4fFjGetiTtV5HSduuH8gJ1OJz/4wQ/4wQ9+MGiZGTNm8Mc//nE0qyaEEEIMW1NTExYzhtWMo9AIOSpB0zGK5kH3AdzxNuLMzHU1x1wqlSI/2gCkZ/4qpZjWvZkTpTdiGEZmLb/zEY1GKQwfxW53YKleDVUrYEcTMPxQl1dUSgTQzSSvvPIKd95553nXZyKaEBMlhBBCiMnMYrHgTPYAkLR6UfrppTPypwHgTnRM6okSDQ0NNDU1nbOcy24lP3oSANPhw2a1kRc9iWamBtw+bCSiPW244+3pYLjwzvQSJacNN9Q53OmJkRYliw8LIYQQYgB2uz0T6mK2gsxxVTAdAHeifdKOqwsGg+zatYvt27efM5gVpFqxmHESFg/O27+Gu6gSXaXwxFvOO9QppQiFQliOr0fDTAdld1FWmeGGOqzpJU10c2puEyahTgghhLhApmnijTVhdziI2Qozx1XeNLC5sBpRfOH6HNbw/K1fvz7zOhgceikQeyjdSld1yVqsNjtaWS26bqEssPu8Q11jYyOvvvoq4YY9ACSnX9OvzHBDnWZN73ahK1l8WAghhBB9BINB1q9fT0vDMfIjJ9A0jaCvNnNes9oxqi8HwHu6W3IyO9e2mvbY6X1ufafXnJ17E5qu4Ym1YsQj5/XMXbt2gTJxJrsBUL7qfmWGvdpF35a6SdwdPhgJdUIIIS4asVjsnK1NI3H06FGCwSDdx3ejoUjZC7nsxndmzmuahiqcCYAz0TFqzx0vZy8aHImcI5jF0qFP957e6cFbimHzprtNA+cek3e23nGInngrukph6HZM55mu19raWgoLC/utczsoa3r2q4ZCUxc2xm8iyunsVyGEEGI8vfjiiwCsXbt2wI3nR6q3hah3h4OEuwKPx5M5r2laZrKEM9ENRiqz/+hksHv37qz3Q032ePvtt/EZ6WVCdPeZLuikowhbtAcVGvladb1dtuX+HQD43bOo7NMqN2/ePObNmzf8G1rsKDQ0FJYp2AUrLXVCCCEuOn7/6OzyoOs6KBNf5DgAcXdF1sbyLpcLHD5MzQIoiE2u3SXO3oZzoN0iADo6OmhpOIrVTO+pas8vzZwzTresacGRt9QZhoFuJvHE0vVo8y2ntLT0HFcNQdMwtXSonoqTJSbPnwtCCCHEKBmt5UUMwyAvdgpXsgtDsxErmA/A9ddfTyqVwuFwEDEM4rYC3Mlu6K4Hz8j2K82ls0PcYKGuqakps5SJu3I+mv1Ma2XcW4OTbVg6DqbHsfUJvcN5vivRiYZJ0uLBml+OxWI5j0/S5566DYuRRFdJUqnUBa2dN9FIS50QQoiLzmDh5Hzu44m1AOD3zKJsRjrU5eXlUVh4pgsy6Do9uL/twKg8d7yc3UU92PctGAziTHQCkPTNzDoX981Jd3lGOiARyhxPJBK0t7cPGbDToTkdFiOO0mHv8TqU3pY6i5mkoaHhgu83kUioE0IIcVHoGx5Gq6XO7BM6wo7yQcfpRe2nW+cinaPy3PFSXZ0903SwUBeLxbCaMQCUIz/rnG53kbR6UKaCcHvm+IYNG9i8eTOnTp3qd79kMkljYyOJWJTiwH4AetyzCIVC/cqOlKmfngGrkhe8IPJEM3XaHIUQQogh1NXVZV6PVqizBhpwJbowNSsB13ScTueA5ZL66bAXH72Zt+NBO6urdLDvm2EYWI10qMPuzTpnsVhIWPPo7m4m0XCIkqLZQDoIQvrncuDAAWbNmsXcuXMB2Lp1K52dnTiSPSxQSUzNit89zBmu52Do6TXtdHPq7SohLXVCCCGmvEQiwf79+zPvRyvU2YPHAfC7Z2JYnAOGOk3TSFkmZ6jr/T71hrt4PD5gOdM0My11miM71Om6Ttyabr2r2/NWv2v9fj+xWIwDB850TXd2pls0Hcn0xJK4zTeisXhDMbR0qLOYMvtVCCGEmHR27tyZ9X60Qp0lll4Qt3cXicHGfKUsLhQKjDikBg5GE1nv+MBAINDvexcMBkkmk5mWOtPmyTqfbqlLh7reBYQHc/a9+4Y6h8PB/Pnzz/9DnFY2M704tD0VnNT78Q5EQp0QQogpq7GxkYaGBtrastdIG62JEr2hLmHLG7KcqdlQ2ulZm/ELHxc2XnpDT15eHpqmkUgk+i1IfOjQIVAKqxlNHxig+zXiSC9GnB9pINg2+OSEs+/tOL2fbtzq46abbmLBggUX8nEAKJmeDnWOVP+AOtlJqBNCCDElxeNxdu7cya5du/r98h6VX+ZGClu8K/0sa/7QMzOzumCH3mprIrJYLJmFlqPRaNY5TdPQVRJNpYOyYXX1uzbsqCRiL0HD5NjWFwZ9Tu84OwCLEcus/5c4a/2/C+JJr3Nnl1AnhBBCTA5DLTB8IS114XCYUCiEcXwjKhElafHgKp3FddddN+R1KYs7/WISjavrO6bOZkuPRevoyN7uTNd1rEY66BmaDU9eQdZ5i8UCmkbUcTpMxQafAdx3zJ4n3opFJYlb81l16wcv+LNkuNL1sxnRoctNQjL7VQghxJQ0FqHONE3eeOMNEokEM9teJD+VpL1wBQsXL8Hr9Q54TW8LU9LiBsysZT0mur6hzp3owIj7OXAAysvLyctLdzk7nU6cp7tJi6fNJr84e3Hl3sWCe8cdOhNdgz6vb6jrHX8XcZThcrtH5wMB2un9X3UzKS11QgghxGQw2ExNOP9Ql0wmM+O+7Kl0N2rMXjysXQnCjnKUAjqPntezc8nVtZ/pDb9lTsszeGLN9PT0ZM4ZhkF+9AT5Ph++uZf16ybtDXWR02v1aV3HCLU1YLfb+z2n77pxrtOLGcfsRaP7YazpbmRdpVDG1NoqTEKdEEKIKWmohWXPXsRWKdVvkP5AksnTa5spE3sq3Y0at+YNK9SF7OU0NTfRenjbOctOFEopHMkefHVPo6HQUJQG9hIInBkXaBgGrkQnuqZBSf+JDL2hLmovJewoR1cpWn77OUqbXyE/ciKrrGmaKKXQVAp3PL3fq+ar7nfPC6HZzoz5szC1Qp10vwohhJiSMgFsAM3NzSilCAaDnDx5knA4TEtLeruva665hoKCggGvS6XSIcBmhNGVgdJ0khbPoIsO95WwekglkyT9HcRjURzOgXefmEiUUpQE9qJZQNPS7UDORCcH6+qoqakhPz8fI5XCkQygafngLet3j8xerZpGe/5SPO2t2IwoxaFD6a+r7uMIszh58iRKKZRSFIaOYjPS4xWTeaMb6nSrDVOzoCsDhy7dr0IIIcSE19zcnHmtqVR6M/mzbNiwgWPHjmUCHcD27dsHvWdv658jmW6pSljzqJk+Y1ibzBu6I70HKopTdQeH/TlyyRpqojh0CDRon3knAHYjjMWIsWfPnvSYtLgfXaXQdB3cxf3u0XdWcNBVTcxWkHXedeKVzCxipdTp7tz0sicdeYvA0r+b9kJ58k936RpTawFiaakTQggxpRWEjlLd9QZxm4/WihsJaOmFcAcbVxeJRAa9V+81heH0uLiIvZTly5cP+fzMGDNNx7A4sRpR9GR4pB8jJ1It6V044r7ZJIpqSVi92FMhnMluurqctLa2YomeDmSuItD7h9u+gVdpFo5W3Ik73kbYWcGsthcBjcqDj5MXCuKNzaJ9XxH50UYAgq5puEdrKZM+lCU9rk4lp9YMWGmpE0IIManFYrFBx895oyeZ3rkBXRm4El3MaXse5+kB+IN1z7pcg3eL9oY6TyzdCtjlnT+i9dN694C1mbFzlJwYVPdxAE7FPFgsFqL29CLCvkg9kB6b6Di9VZrpLh3wHme3Ypq6nZCrGqVZ6chblG7hO/0ttMS6STamW0rDjnJitqLRW5+uD3W69U8zJt/uHkORUCeEEGLSiEQiHDt2LDO2raWlhZdeeoktW7b0K2uxWCg4HT4AElYvNpJU9JwODeGBW8uKi/t3IfYyTROUic1It+a5S2eOqP69CxBbJ0OoMw088fROHN2aD13X6fSmd2MoDB8DpThxvJ68zt0AGJUrBrzNUF3TAfcMuP5hAiUr6fbMpcVSRbJkMY3F11BXfito2piEut4ZsCo5CX4OIyDdr0IIISaN119/nUQiQSgUYvny5ezduxelFJ2dnZimmRm/pZSCRBjf6dmVdWXrSFmcrAi8RH64kZLAXlLRpQM+Y6gQYRgGNiOKhkKhM6t24HsMpjfUqdgk2FXi5FasRjRdZ18Nuq4TdlagNB2LmcBmhDD9XWipGIZuQ1UsG/A25xpvqOWVs9ecCyVzAaisrKS773jIMex+lZY6IYQQIkd6lx3p6OggHo9nbVnVtwtWKUVZYDcWM07S4iHsrCBmK0K50gvgVnVvwb31UXSz/0D5oUKEaZrYjDBWq5WiabMpK68YUf1TltOzZCfDrhIte4D0ZIXlK1ZhsVhQmiUz0cGV6KI0sBelTMKOCixW24C3Ger7WV5e3u9874LAvevYLVy48EI/ST+9oY6UhDohhBAipzRNo6mpKetY73IY4XAYIx7JjPtqKViJ0ixYrFZ6FrwXv3tG+h6xAPNa/oA9mb3zxFALE5umiS0Vwm63k19aPeJWpLjVB0Bn3a4h19GbCFSkC03TidqLcbvdfXaGSM8cndn+EtNUE6ZSdHvmDNoiZ7fbB/w+2Ww2Lr300n7He7//ixYt4vbbb8fn843WR+rz8HS41oyp1f0qoU4IIcSkE4lEMnuR9lJKsXfvXl555RW6X/9P7KkQhm7D754JgNVqZfqi1ZwoXcux8tsxdTuOpJ/ZrX/CakSy7jOYdEtdBDQNTrf6jUTYWQ6AO95Gw/G6EV8/nsxwB0qZJKxeHA5HJrT1fj97deUtxO+Zk7V0SV+aprFu3bp+510uVybs1dbWZo63taXH8em6Pug9L5Q6vVUYMvtVCCGEyC2lFK2trVnHXnjhBY4fP44n1kTi2EYAGouvw9TT3Xg2mw2Hw4HdbifsrGCj4zqSFg92I0xh6MzWXUO11BmGgTvRnt49wVMyrLr2baWKWwswNSu6SmGEB98DNecSEZLRdBex5i7GYrFQU1OD1+tFr1rOidIbSFg8RDw1NOenJ0gMNXbOarX2a63rO8u4rKz/osVjFegAlD29b60eH3x/4MlIJkoIIYSYFM5uQTu7+xXSLWCz2l4Ai0bc5iPgmp4517uVV2+4SFncdOYtpKJnG65kZ6bckN2vRoq8aCN4nFC2aOQfQtNI6Q7sRgo7g+94kWux9jpaW1pIWtw4Pel1/axWK+94xzsAOHlyFjt2zKK0tJRkeztw7hDmcDiy1gB0OByZ1wNdO9DesKNFudOB3BLrHrNn5IK01AkhhJgUzl4UuDi4n9mtf6Sy+y280VPYUkFmtT6HrgxCuo/jpTemu0lP621J6ttiFD29WbwzcabVbKjuVy3mx2Im0XQrFM48r89h9M68TE3crr+mHS8BEHJWDbgFWu/3sO+4wHOFussuu4yioqLM+76hbqBWPo/HM7JKj0DvmnrWWOeAO41MVhLqhBBCTAq968pZjBhlPTuY1rUJb6yZ0sAeZrc9x8JTv8KikkRtRdSV30rcVpjVrRcMnu5O7BvqTg/6dyT9lBemu+SGaqlTkXSLnunwZQXGkTD00yEpMXF3ldDD6W3Two7yAdfz6w1wfRdwPtfSJXl5eVx55ZWZ933D4kDX9rasjgl3EUrTiYYCqMgE7gYfIQl1QgghJoVwOAxKMce/kQr/25njUXsx6vSvM6XpnCpag6GnW4H6tgb1LofSN9SlLG5itgI0FCX+XcA5xtSFOgDQhzmebsB7nB7jpyWjHD9+nPbT3ZcThVKKmD9dp6TVQ01NTb8yvd/D3qDc99hQ+pY5V/frcPbTPV+6xUpzwaU0lFxHS9ckWDNwmGRMnRBCiEkhkUiQH22ghE7yq6bR6E9hLnkPR1pi6GYCb6yZuDWfuP3MrNRoNEpxcTGdnZ3k5eX1v6mm0ZG3mOqujbiTXWCZPWSoS/S04AGsvv4D+wfTbx02W7pb8dTxI7T1eAG44447xmbnhPMQDoczs4HLauYya9asfmUGCmEjrX9h4Zmf00ABbiy/H5qm0ZG/BAB/OE7lmD1pfEmoE0IIMSkopfBF6tF0Ddv8G5i95B4ADjz9NKZuT285dRaLxcLy5cupq6tjxozT69OdFRbipxfTdRhBsAw+pi6RSKAi6ZY6d3H1+X8QezrU9d0qzDCMse1uHIFkIo719PptCy+5LL0361kuJHDdeOONJJPJrO7Xs+93/fXXn/f9h2MsZ9bm0tT8VEIIIaYMpRQ7d+6kdd8b6T1HNaBq4H1Ggaz16/Lz83E4HCxcuBC32w303/M1bkvP7rSnQmjKGLSlrqW5GU8svYyKNX9kO0n0pTvSrXMW88xuBr172U4ETcePoKGw2exojvwBy1xIKHK73f0WFNY0jcrKM+1lXq/3vO8/HBLqhBBCiBzo6emhsbGRQn9626q4bw4U9u8SBFi2bBmLFp1ZamTu3LnnvH9Kd2FoNiwWHVsqNGioO7z1JRypAIZug/LFw67/2V2LmqO3pW7ihTrDMGiqPwhATFlhiAWFR1tFxfkH5ZGaqqFuYrT1CiGEEINIJpPYUmHyoicBCFVfN+jMU4vFwrRp07BYLOTl5Z2zS7OsrIzi4mLKrIvQIm24Ep0kzIHDhSOVHlAftZeA1TFgmYHouo7FYsks/6GcBQB4Yi3Yk34SNl/WLNJcSqVSWI30UisJvf9SJr3GIhT1vedYjy+cqqFuan4qIYQQU0YqlaKy+y10ZRCzFWK4ywctq+s6mqYxbdo08vMH7jrsq7q6mrlz5+KduQpN0yiI1A84pk4phT2VnumZsI68a7DvQrrJ/JmEnJXoKkVR6HD6nqdn5uaaYRg4kz0AOAsGbzkbi1A0lrNdzyahTgghhBhjA3V9dnZ04I2dAqCp6Ip+A/eXLl2aeT3SFp5MgCtfDBq4Eh0D1uHQoUN9Qt0As2jPoW+ocziddHnmA+CNNwMQj8cHvG68NTY2ZlpEq5ZdP2i5s7/PK1euvOBnl5aWkpeXR1VV1QXf61z6hrqhFpuebKT7VQghxIRw5MgRDh48SE1NDZdccknmeFdTPflmHIVO2FHWL1D0DUwjbe3J/EL3lKKhYUuFUUb/rtAjR44wOxUCwFk0bUTPgOzJGx6Ph0ZnurXRFe9Id8HmsKWuoaGB5uZmVq1aRXNzM9MT6Rm+9srBxw2e3dLVd3mS86XrOtddd924LO0iLXVCCCHEBUqlUgNOCkilUhw8mB6g39jYSCCQHr9mmia2rtMD920FKK3/xvB9Q91IA0FmWQ1HHprNgYbCkui/GK3dZsORTB+vnr98RM84u44FBQUkrXkEXDVoKArCdTlrqYvFYuzatYu2tjbq6uqYXlFyZlaup3TQ6/p+n3Vdx+VyjUp9xmutvomyJuBok1AnhBBiXCilePHFF3nuuefo6OjIap1qa2vLKrthwwZisRh/+uOzlPfsACDgng70/4V8IS11JSWnd4bQNDi9ybs90dOvXLE9js0IY2pWyB9592DffWt7A1DYkW6tc6QCOWmp6/159DIMA1s83Urn8JWD1T7YpVktXb3jGCeT8Ry/N54k1AkhhBgXva10Sik2bdrE5s2bAQiFQmzfvr1f+Zajeyjv3IzVjJHSHbT5Lhnwvn1DXd9uznMpLy/PDiOnt/6yJ/39xln5Uults0LOKnTbyFul+q6Np+s6K1asIK98JgUFhdhTwZyEut7ZuL2sViuO9vSyMYm8oRdX7vt9m2yBDiZnnYdDQp0QQohxcfYEBL/fz8mTJ4lGo9kFlaIoeBD7pn+hNLgPSLfSKS3dunJ2V+VIQ11vK1NZWfZWX1pBeo9Tb6ypX10tyfR4uoTNR0FBwTmfcbbehY8h3UpUXV3N4kuvxWa3YU8FxqX79eDBg2zbti0TWM8Oki6Lib1tNwChksEXd4bJPyZtstd/MFPzUwkhhJhwBppVumPHDkLBAM5EJ45kNwAV/u1Ud20kGU9vVRW3+Vhwxycy15w9Jk/XdZYvX86SJUuytp4azA033MDKlSsz24b10k7vUpEXPYWZzA5ZvaGucvbC82rlmT493XVssVjOBAp3MbquYzOiGInoEFdfOKUUR44cobm5mfb2dKvj2d9Ha9tuNDNJ1F5M0jv8lrrJqG+omyhrBI4Gmf0qhBBiXPQLdcrEF6nH/eYzzO9Jb79laDYsKv1Ltsszj6aiNSjdxvySGioqWmhpaRlwyYve0DQcLpeLadP6z2DVvGUYugOLGUeF2sA5M3POmgyRApR95MuZAMyYMQO3253dymdzp78Ab+AIcMt53Xs4+n7ve1vozv552Nv3ooBuzxy85xhzNtlbuvrW/8SJEyxbtiyHtRk9EuqEEEKMi7NDRGXPNkoDe+jd1t7tdlNQWEjTqVN0eedzsujqrJ0jVq5cSSKRGLWZlmfTdJ2orRBvvIVUdwP2kpmZc/rpljrTfn57kmqa1q+7F03DnHkdNNZR3LntfKs9LH1bo3oDTd9xg65EB5ZYAyY6fvds8s7REjeVWuqmkqn5qYQQQkw4fUOdK95OcXA/kJ58sLfmg/irb8A262qSl3+ck8XX9NsKzGKxjFmg6xWzp9dbazv4VuaY3+/HjPSkP4P93LtUjIQx/UoUGrZkEGJ+DMNg7969mS7S0dJ3/Fzvz6Hvz8MdbwOliOfNIGn1nDO0TfZQN9nrPxgJdUIIIcZF3xBR1b0ZXRkEXdXUla3D1O1EKy+HS96Hs3JBzuoYcqa7ZR2tb0O0h1gsxhvrXyIVu7CWusHodjdxWwEKBU07qKuro76+PjMzeLT0bakbKNS5El0oBQlXem26qdqSNdXJT00IIcS46A0RhaHDeOJtmJqFxj4tclZrekTQ2WuIzZ8/f9zqGHBNJ2ovwmbRoesYoVAITzw93i9p8aBZHaP6PF3X6fbMSXeFHn2JYKD/wsejoW9LXW+3aybUKYU31kQylaSuO31uJC2iI1lGRowtCXVCCCHGhWmaoExmhncB0OWtJWU5s9SHw5EOTH1D3dy5c1mwYPxa7jRdJ+yoSNel+wSapmX2Qg24akb9ebqu05G/GIUO8SB6rHvUnwHZLXUnTpwAzoQ6X6QOeypIMJog7KwA0luZDZfP5xvFmooLIaFOCCHEuDBNE2eyG4sZJ7+whKbCy7LOe73prs2+oa436I2XiooKwo7ydHdo4xZUpBv76T1fo/biUR+LpWkaSrMSsRejFNhCJ0f1/r3q6+szr/1+P5zYhP3Q/2JPBcmLnQLSIdvU02v+jSTU9bawityTUCeEEGJc9PT04I6nJwAUzl7BFWuuzDpfXFwMZIe68R7bpes6fvdMUp5KjHiEw6/9BquRXkMuZTn3Gnjn8zyAsKMivetE41vnuOL8BPp06+pmAnY/ib3pLWa0v4wv0gBAyFGRKTOS7tepOulgMpJQJ4QQYlwcPnSIkuB+Eok4FM+jtLSUW2+9leLiYhYuXJgJc7kMdZqmgaYTz5tBLBbFkfJjM9ItdUmLd0xa6gC68mrp6OzEG2vCakTOcdWFsadCGIaJaZq4Ep3pdfnQiTjOLLkyks8poW7ikDZTIYQQY04phdWM4kx2o9Bg5tVAuuvuyiuzW+xy3VIHkHIWoVR6VqjtdEtdwjq6M1/7Pi9hzSNp9WBPhbAnA1ljDUebzQiTNJMYpomh2TBsXpp9KzBOt0T23dJMTC4S6oQQQoy5zs5OHMl0F2DF7EVgHzw49A11Z8+EHWu9rU4pRxEKlZn5aug2DH30x/f1beWKW33YUyEcqSARKoa4auTy8/MJBAJomoY9FcIf9dNKKSdq3oPH6013/Z52zTXXjOje0lI3cUj3qxBCiDHX3t6OPZUOdc6iofcVzeUaab3PTtp9WWElYcnrtxjyaEtY01uQ9X6fBtor90I5nU4cyW5i0ShJqxc0rd9+uXa7fUT3HGl5MXYk1AkhhBhzyWQSRypAXl4+eEqHLNu3dW68W4F6n2dYXKTyzixh0uOZA2RvrTXaErb0bhX2VBCAaDQ6avfurbfPbaMwdBSA4OmFlvtOipg1a9aw77lixQrKy8uZM2fOqNUzV/bu3cvhw4dzXY0LJqFOCCHEmEulUjgT3enlLzwlQ5bt21I33t2vvc82lSI64wYgPb6uPX/JmD87frqlzp3oAKWyukRHS4HyY1FJ4tZ8gqfX3evbUpefP/xt0Kqrq7nsssumxJIm9fX1HDp0KNfVuGAS6oQQQoy9aDd50cZ0S1jx3HMWLygowGazUVhYOA6VO6O3pU4pRTJ/Bocr76Zr4QdB0zPHx0rIWYWpWXEk/TiTXWzZsmXU7t1bb6dKz6yN2woy3cl9Q93Fvj3YWP58x8PF/dMTQggxLmyhJjQUZv408A09pg7g6quv5qabbhr3VqBMS51popQiZi+GPvu9jsUv/UsuuST9TN2eWVbElegc9ecA5FkNABLWM4sL9+1+lVAnoU4IIYQYkh5JLzqs8qqGVV7TtHHveu19LqR/uff+gh/rcX01NWfG7sVs6ZZJZ6JrVJ/R+1msyQBFxcUkLWeCau9OHn3LXawm++eXUCeEEGLMWWMd6Rd55bmtyDmc3VIH2aFurH7pL126FIDw6Za6wkjdmCxCrMe6QZ1Zc2/RokVZW4JJS52EOiGEEGJQsVgMAk0AaHmju/7aaOsNcCdPnszMPh2PUDdz5kwAAu7pxK35WI0oJcH9o3Z/pRQohR7tBlR6ORNgzpw5WZ8vLy9v1J45GU32UDf5p6wIIYSY0NoObMKZ7EFpOlrB9FxXZ0ixWCzz+tixY0B2qBvLLuEVK1bQ0dFBW/gSajpfwxttorGxkZ6eHpYsWXLB3cB5sZNoehBnXhExszCrhe66664jHo9ndcVejMZibcDxJKFOCCHEmEq17MMC9LhnM6NkeGPqcqW4uDgT5nppmsaCBQvo6Oigqmrs6l9dXU11dTU7I13Q+RquZCe7dmxDaVYqKiooLR16fb9z8caawa1hm3EZaxfcnjUJZSRLmUxlk72lTrpfhRBCjCnlT3e9Vi9ZM+G3lCorK+t3TNM05s+fz5VXXjkuuycsWnUVCYsHTZkUhvu3Fp4PpdSZyRe+ahwOR04mokx0EuqEEEKIIfROktDyKnNck3MbKDyNdxC12e105i0CwBeuH7U6OJM96ReT4OeQKxLqhBBCiMEYSWzxnvTrSRomzt4bdaxpmkbImf5euZJd0Gd5lfOlJyPYjDBowASfrJJLEuqEEEKIwbTuS+/OYPGgOSfnuK2+68iNl4SjGIWO1YhiMyIXPIDfFzoCnF4n0OY6R+mLl4Q6IYQQYjCte1Eouj1z0CfpGK6+Oy6Ml8uvvJqYvQCA/OiJCw517kh6XKNRufJCqzZlDNSlLaFOCCGEGEywBaUUEUfZRb+w7UhYLBZ6POk9cksC+y44bNhSAQCU58Jm0E4lA4W6yb6ki/wXJoQQYlQopQgGgyil2LFjB9u2vIkKtoBSxGwFEupGQNM0uk6HOnsqSKCr/fxvphS2ZDD92l0yCrWbmmbOnDnhZ2efi6xTJ4QQYlTs27eP+vp65s2bx8mTJykKHSJhCxO3eEhY8yflEhqzZ8/OyXM1TcOwuEhZXFiNKI0HtjNnwaKsteWGLR5EN5MYaChX4ehXdpI6O8BN9kAH0lInhBBiFCilqK9PL79x5Eh6UH5JYB+JRIJ27yLQtPMLJDlkt9tZvHhxTp7dGzBitgIAHMkegsHg+d0skl5SJmn1gD65fgZjqba2Nuu9hDohhBCCM0Guly0Vxpnsprunh+7T3YiTLdTlsmXx7FDnibec/7i67hOAIm4rmBLBZbTMmjUr11UYdRLqhBBCjMjx48fZsWNHVsgIhUJZZUqC+wAI24owLE4cDocEihHo/V753engURg+hkolzu9m7YcACDqnjUrdpgrpfhVCCHFRU0qxZ88eTp48SUtLCwBtbW2cOnUqU8aWClMS2AuQaaVzu93jX9kLZLPZcvbs3oARdlSgrC50lUI73Y06YqFWFBBxlE6J4CIGl9NQ99prr3HnnXdSVVWFpmk89dRTWec/9KEPoWla1te6deuyynR1dXHvvfeSn59PQUEBDzzwQL+/GIUQQoyOROJMa1EqlQLg7bffTh9QJmX+HcxteRoNRdhRRqd3IQAej2fc63q+evd/nTt3bo5rAmgaSWcRAHs3v8xLL71EIBAY/vVKQTw9Fi9lmXzBejxNhcCb01AXDodZvnw5P/jBDwYts27dOpqbmzNfv/jFL7LO33vvvezbt48XX3yRZ555htdee42PfvSjY111IYS4KIXD4czrXbt2oeIhtEgHuplgZvvLVPS8jc0Ik7K4aC68HE7/opxMLXWrV6/m2muvpaqqKtdVASBhS89YdST9RKNRNmzYMPyLU3Ewk6AgpTunRHAZK1Phe5PTUau33nort95665BlHA4HFRUD71N34MABnnvuObZu3crq1asB+N73vsdtt93Gt7/97QnzH6QQQkwVfXtCLKkw3b/9e2q7Wk8f0VDotBSspCN/CUo7M9Egl12ZI2WxWPD5fDmtg9vtZtasWdhsNrq37cHL6X1gR+p0K52pWzH1yfMzEOdnwo+pW79+PWVlZSxYsIC/+Zu/obOzM3Nu06ZNFBQUZAIdwNq1a9F1nS1btgx6z3g8TiAQyPoSQghxbn1b6oqChwj2CXQFZdUcq7iddt/yrEAHkEwmx7GWU8OSJUtYsGABYUe6Ozgv2ojFiI7oHod2b6Wjo5OkLvu9nstUaKmb0KFu3bp1/PSnP+Xll1/mG9/4Bhs2bODWW2/FMAwAWlpaMmMfelmtVoqKijIDeAfyyCOP4PP5Ml+52KxZCCEmo95wZkuFKQ/sBKClYBUnqm6ne9XHiTjO/JtcWHhmodt4PD6u9ZxKIvay9I4cysAdH/7OEoZh0H7iAOFwiKTuBJBdPaa4Cb1o0Hvf+97M66VLl7Js2TLmzJnD+vXrufHGG8/7vg8//DAPPfRQ5n0gEJBgJ4QQw9D7R/XSch1nwENb3EFb/nKcLhcu75kuy4ULFxIMBunu7gYkTFwQTSNuK8CZ7MFuDH8iYHt7OwXhOgCCrmmnbzX5W6PGSiwWy3UVLtik+q9s9uzZlJSUcPToUQAqKipoa2vLKpNKpejq6hp0HB6kx+nl5+dnfQkhhDi33lDn9B/DarEScM9Mh454nKKioky5/Pz8rCBXUiJ7jl6IhDUPSO8DO1xb39qCN9YEQI87vd2ZhLrBnfeOHRPIpAp1J0+epLOzk8rKSgDWrFlDT08P27dvz5R55ZVXME2Tyy+/PFfVFEKIKcswDFzxdhw9x0CDgCvdy6HrOjabjYqKCux2O4WFhZklQdxuN+Xl5bms9qSXsHqBkYU6qxlDQ6HQMqFQQt3gnE5nrqtwwXLa/RoKhTKtbgD19fXs3LmToqIiioqK+P/+v/+Pe+65h4qKCo4dO8ZnP/tZ5s6dyy233AKkm/fXrVvHX/7lX/LjH/+YZDLJxz72Md773vfKzFchhBgDhmHgixxHs2uEvLOJ6enWuRUrVgDp5UCUUpmQd9ttt6HruoSJC3SmpS407O+lxUyPYzR0O2jpNhz5OQwuV/v8jqacttRt27aNFStWZP4xeOihh1ixYgVf+tKXsFgs7N69m3e+853Mnz+fBx54gFWrVvH666/jcDgy9/j5z39ObW0tN954I7fddhtXX301//Ef/5GrjySEEFNaLBKiIFKPbtGJ+OZnjvf2oGialtXtarFYJEiMgrg1PUzIkezBkgoPax/YyuL0GEdDP/M7U8Y2Ds7lmvwzhHPaUnf99dcP+X/M559//pz3KCoq4oknnhjNagkhhBhAMpmk8ORL2FNBrM5yovmzITj4SgNi9CSs+YQdZXjibRSE6zBNE4vFMuQ11kxL3ZlQJwF7YAUFBbmuwqiQyC6EEGJY4m11FIaOoOk6tssfkMVsx5OmEXKmhxU5kj2ZCStDSqbXtEtZJv9YsbE2Z86cXFdhVEioE0IIMTx7f42GIuGbDWULh9UFKC7ckiVLAIjb0t2pjlQA0zQz55VS7NixI2uMOgCJ9PIn0lI3uBtuuIFVq1Zlhg9MdhLqhBBCnFu0B7Pj9Jpns9LbO+Z6K62LhcfjASBuPR3qkn56enoy51tbWzl58iQHDhzIBG3DMAh1p5f8MnT7+FZ4EvF4PFRVVU2ZsCuhTgghxLkd+iP+gJ+IoxRXUXoh25kzZ7J48WKuv/763NZtiuudHJiwpSdL2IwIOzZvyLTWJRKJTNlIJALAkSNHsBjpMXUpXbpfLxYS6oQQQgwt2AKNWzANg7b8ZZn1vHRdZ/bs2eTl5eW4glNbb6gzdAdRe3oJmdLAXqLR/vvAvvLKKwB0dnZiNdM7JMxesJiCggKWLl06TjUWuTKhtwkTQgiRO+FwmNbWVmZyEk1ByFlJwD1zyB17xOiz2890n7bnL2N6x3q8seZMS91Akya8Xi/ORBcer5eSGbWUlk/+NdjEuUmoE0IIMaBt27YRCASIt/yBucV2gs5qgKy1QsXY67u2XNhRBoAr0YEZ6YK8vIFnwsaDOFIB7PYiKJw1XlUVOSbdr0IIIQYUCARwJrpwx9tpa++g2zsXTdOmzKDyyShp8ZK0pCdOOF//OoTaBuyGtUTSkyRMZxHY3eNaR5E70lInhBBiQC6Xi+LOvQB02ipJWdwgy5jkxLXXXksgECAUCtEUuYwZHa+ilKJ7w484bqyAs4K2HvcDoFxFuaiuyBEJdUIIIfpJpVLYOg9SFDoCQKe3Nsc1urj5fD58Ph+pVIqjR49ywFFKYXwDgfoduCpqiDpKzxQ2TTydewBQrsIc1VjkgoQ6IYQQWerr6zm+7QVmdL4OpANdyJVexmTevHm5rNpFz2q14vP58PuhJ1kEtOJKdmWHuoPP4Ag3EQdU3tRYVFcMj4ypE0IIkdHe3k79theZ0f4SFjOO4S7Dt+aDmfPTp0/PYe0EnJk4EbUWAOltw3r5wsfg2MsopejyzidVdVkOaihyRUKdEEKIjIMH9lPT+RoWM0nYUY7jpv9L+bQZQHrWq8vlynENRSbUaen1Au2p9HZgKMW0+DEAugqWcrL4Giw22U3iYiLdr0IIITI83Qexp0IYuoP6spu5qbwKu93Oddddh9VqlZmvE4DFYgEgpOVTCHhizaBMikMHcUZbQKum1bMQzOzlUMTUJz9tIYQQAIQCPRScSu9IEK9YSVnVdGw2GwD5+fm43bI0xkTQG9S69SJSugOrGccXPUGZfyegCFRfT9hMt9D1BkBxcZCWOiGEELS0tHDk1V8w3Yxj2rwsvOvvwSK/IiaiTFDTdLq98ygN7GVGezqMG3Y3XfmLgQMAsoXbRUZa6oQQQrBz03qmdb0JgGPetRLoJrC+rW9t+cswNStOZ3qsY9hdjdLS56uqqqT79SIjP20hhLjItbe3UxQ6hEUlidqKqLrmvlxXSQyhb1AzLC7yl91GQWEBAG2Fq1GnF4iWQHfxkT/FhBDiIvf26y8wL5DeOaK7aAXYnDmukRjK2ePkYtVX49ZinEgtJG4r4PDhwwBEIpFcVE/k0IhCXU9PD7///e95/fXXOXHiBJFIhNLSUlasWMEtt9zClVdeOVb1FEIIMUZKgvuxqCQReylVq2/LdXXEOZwd6kyri9TyD+LvXo8DSCaTAHR1deWgdiKXhtU229TUxEc+8hEqKyv5p3/6J6LRKJdccgk33ngj1dXVvPrqq9x0000sWrSIX/7yl2NdZyGEEKOgp6eHlp0vUhE9BIAx6zqmz5yd41qJczk71BUXF2dex+Px8a6OmECG1VK3YsUK7r//frZv386iRYsGLBONRnnqqaf47ne/S2NjI5/+9KdHtaJCCCFGj2mabNq0iZmNv8OdSuF3Tadi2VpZh24SOHusnNvtJhQK5ag2YiIZVqjbv39/1l8CA3G5XLzvfe/jfe97H52dnaNSOSGEENlSqRT79++nsrKS0tLSc18wAKUU+/fvxxWsx51oR6FzsvhqqmX3gUlhoLXnJIwLGGb367kC3YWWF0IIMTyHDh3ixIkTbN68+byuT6VSPPPMM9TX11PeswOAzrwFVM2cT2Fh4WhWVYyj3kWixcXtgme/HjhwgM2bN7NixQouueSSUaiSEEKIwbS2tl7Q9Y2NjQDYU8HTrXQaq/78YXDmj0b1RI7Y7dLKKkYY6r7yla/gcrn4zGc+A8Crr77KunXryMvLw+/38/jjj3PvvfeOSUWFEEKM3jIVld1vARB2Vkigm2RSqdSAx61W66DnxMVhRCsT/uY3v8maKPG1r32NT3ziE3R0dPD973+ff/7nfx71CgohxMUklUqxe/fuQccm9y4sC1BXVzfi++u6jsWIkR85AUBr4aXnV1GRM323/urbQ9b3/xsAy5YtG68qiQliWC11P/3pT1FKcfz4cXbu3ElnZydKKTZu3Mg111zDT3/6U0zTpK6ujp/+9KcA3HefrEguhBAjdfToUU6cOMGJEye48847M8dN0+zXSrdv3z5mzx7ZEiTJZBJvvBkNRcxWwKq194xKvcX4KS0tZeXKlbhcLoqKigYtN3369HGslZgIhhXqZsyYAaT77MvLy5kxYwY7d+4kPz+fd7zjHSiliMfjaJrGzJkz+/21IIQQYniCwWDm9eHDh2lqauLKK69k9+7dNDc39yuvlBrRzMdUMklx8GD6Wc5pzM+XrtfJRtM0pk2b1u9439+9N954o8yIvQgNK9Rdd911AKxcuZJnnnmGz33uczz33HPcdtttXHvttQDs2bOHmpqazHshhBAj13dM1KFD6UWBd+/aRfzoBmZFjtPlmYvfMyer/EhmPqpIB95YEwqNeWs/JL/4p5C+oc7lcuWwJiJXRjRR4lvf+hZ33XUXV111FbW1tfzHf/xH5tzjjz/OunXrRr2CQghxMend4glAUwbeWBP2PS9TGjkOgCfWTNRRRsKaHlc14lDnT7f25U2rxTdt3uhVXEwoEtYvTiMKdcuXL+f48eN0dnb2W4vu05/+NPnSjC+EEBckkUgAoJsJZrW9gCeevYSJrgzmxXdx2PUOksnksGc7BoNB9u3bh9Z0GA9gLawe7aqLHJOhT2JEs197DbS4cGVlJR6P54IrJIQQF7NEIgHKZFbb83jirZiahaBzGieLruJg1XtQ6HhCDRTGGgAwDGNY921sbKS9vR1HsgcAR4kMohdiqhlWqHvyySeHfcPGxkY2btx43hUSQoiLlVIKI5Viesd6PPE2DM1GXfmt1Jevw1V7Iwmbj868Wqw2K2Wnd4MYbkudYRhoKoU31gSAo2TmWH0MIUSODCvU/ehHP2LhwoV885vf5MCBA/3O+/1+/vjHP/L+97+flStXyt6vQghxHppOHGVO67MUROoBaCm9Gq1oNkVFRaxcuZKrrroK68LbyM/Lw5nswmLGh91SZxgGedFT2IwISYsHrXThWH4UIUQODGtM3YYNG/jDH/7A9773PR5++GE8Hg/l5eU4nU66u7tpaWmhpKSED33oQ+zdu5fy8vKxrrcQQkwtiQj+F7+dGUNnXfE+Lrv8HnRdzwx6LyoqouiyqyG0Hjo78cRahj2OKh6P40x0YbPZKV36DrBc8C6RQogJZtj/Vb/zne/kne98Jx0dHbzxxhucOHGCaDRKSUkJK1asYMWKFej6eQ3RE0KIi5JpmgQCAXx5HlLbf4Yn3opCp33mO7n0qj8f/MLSWrS6vZT7d6DMdw/rWeFwmNJEB0VFRTjL55z7AiHEpDPiP9VKSkq4++67x6AqQghxcUgkEuzcuZPW1nSr3KzobuZwAoXG8dIbufLm9w99g/m3oN56CleiEz14Cqg690M7j5EXbUQvqIQCmSQhxFQkTWtCCDHODh8+nAl0tlQYd/tO2traaCpag2f2Zdjt9qFv4Mgjkp9ubUvu+i3KHHpcXUdHB4XhI2goqFgKRSPbWkwIMTlIqBNCiHHWuxYdSjGj/WUsKknc5qPTW0s8Hh/WPQKlq1GajtF2kNZ9rw9ZNhgM4om1AKDNvBJkYdopqaysLNdVEDkmoU4IIcZZ7xZORaFDuBPtmJqV4yU3gqZhtQ5vVEzCVUa3J70jRKh+25BlY61HcaQCOBxObGXzL6zyYsJavnw5Xq+X2traXFdF5IhMfxJCiHGmaRpWI0JV92YA2nzLidsLAViyZMmw7qHrOmFHGUWhQ9jCzUOWdTa+BoC95hKwyZ6gU5XT6eQd73hHrqshcui8Q10ikaC+vp45c+YM+y9LIYS42JmmSU93N5XdW9GVQcReyuK7PslSiwWXyzXsPTs1TSPsKEeh4Qo3QU/DwBMglMIROkkSSM68flQ/ixBiYhlx92skEuGBBx7A7XazePFiGhrSW9V8/OMf5+tf//qoV1AIIaaSrVu3Ej65l8LwUQDKrroXb14ebrd7RJuwK6VI2HwE3DOIxWPseOFJ2tvb+xds3oWWjGBqFvDVjNbHEEJMQCMOdQ8//DC7du1i/fr1OJ3OzPG1a9fyy1/+clQrJ4QQU01bW1tmxwhVuYLixdef131CoRAAEUcZKIUl1MTmzZuJRCJnCikFe3+LqUx6PLOx2p2D3E0IMRWMONQ99dRTfP/73+fqq6/O+qty8eLFHDt2bFQrJ4QQE11zczOvv/76sLfrsqeCFIUOA1C07Obzfm4m1NlLAHDHW0GZvPLKK/T09PDss8/SfXw3xAOYWDhVeCUWi+W8nyeEmPhGHOra29sHnDYdDodH1HUghBBTwbZt2+jp6eG5554bVnlfuB5dpbCXzSV/zuUX/PyIo5SU7sRmRCkOHUQpxeuvv45ppGh98VEAAs5pKN0qoU6IKW7EoW716tU8++yzmfe9Qe6//uu/WLNmzejVTAghJrju7u7Ma9M0efvtt9m1a9eg+7EahoE70QZA6fJb4AK2Vpw9O72AsNKstPmWpe/p34096QfAlejClejE1Kyc8q0GkEltQkxxI/4v/J//+Z+59dZb2b9/P6lUin/7t39j//79vPnmm2zYsGEs6iiEEBNSfX191vtTp04B0NDQwNKlS5k5c2bW+XgshifWCpqGpeTC9l9dtGgRLpeLffv24XfPoqJnO3YjTG3Tb2gpWI03ehKANrOAuMULIC11QkxxI/4z8eqrr2bnzp2kUimWLl3KCy+8QFlZGZs2bWLVqlVjUUchhJhwQqFQJsRpKsXMtheY3fon7KkgAHv27MlqyQNIHnkFqxlDtznRCi5sJqqmaRQWpte2S1q91JetI2VJr0FX0bMNbzy9g0S9dmaZEwl1Qkxt59UWP2fOHP7zP/9ztOsihBCTRl1dXeZ1QbiO/GgjALPanud46Y3EbYW0trZmglcsFuPU1qfxAIGKK8Fiu+A69N0jNuys4HDFXVT4t+OOtwMazQWrCVIEpEOgfgHdvUKIiW/Eoe6Pf/wjFouFW265Jev4888/j2ma3HrrraNWOSGEmKh6Z59ajQgVPdszx32WOLNan+dQ1XuyWsaO7XsbTzy9jly3a9ao1MFmyw6GKauHk8XXDljWYrHIZDYhprgR/9n2+c9/fsCp+0opPv/5z49KpYQQYqJLJBJAenKCQ8WJ23wcrrwb5cjHZ1dUd23ENE0g/e9javdv0FBE7CV0xwaeSDFSZ4e6vq666qqs99L1KsTUN+JQd+TIERYtWtTveG1tLUePHh2VSgkhxETy1ltv8fTTTxMIBDLHUqkU9qSfpb4QlZWVNBVeTsxeTGPxtdjsNgrDR7GffBNMg0jLEQrC6e7apqIruPzyC1/KBBi05c3lclFUVMQ111yTOeZ2u0flmUKIiWvEoc7n82WNJel19OhRPB7PqFRKCCEmCqUUra2tAFkz/JVSlPt3gpHAWjILVbIAAM/MlaiiuQB4T7wIf/os9k3fBSBmK2TFO9414FqfF6pvS5zLlZ4w4fV6M8fy8vJG/ZlCiIllxKHurrvu4pOf/GTW7hFHjx7l7//+73nnO985qpUTQoixVFdXx0svvUQ4HB60zGA7RdjiPfgi9WhosPjdrLnyKpYsWcL8+fNJLruXTu8CgtEkpxpP4PcHiDhKOV56I4VFRWPyWfoGxd5Q13ddut5jQoipa8Sh7pvf/CYej4fa2lpmzZrFrFmzWLhwIcXFxXz7298eizoKIcSY2LdvH9FolL179w5aZsBQl4pT0/xHdGWg8qugcCZOp5NZs2ZhtVpx5BVxqvhq9tV8gCOF72C/61KOld+OraBq1CcrzJ49G03TmD9/PrNmzcLpdLJw4cLM+dLSUiwWC9OnTx/iLkKIqWDEs199Ph9vvvkmL774Irt27cLlcrFs2TKuvXbgGVdCCDHRDbVv69nnkokE1rd+hD3pJ2FxkVzxFzjOCmpOpzP9QtMJus+EqbHY0WHx4sXU1tZisVhYsmQJixcvzgqOl112GYZhDDmpQggxNZzXvzCapnHzzTdz883nvxm1EELkUt+tvIaaGer3+7PeH3/lMbyNmzBMaCi7jgpXQb9rHA7HgPdasGDB+VX2HPrW/+yWQF3XZX06IS4Swwp1jz76KB/96EdxOp08+uijQ5b9xCc+MSoVE0KIsdS7JAkM3YJ25MiRzGtnohP7iT+RAJoLLyPkmjZgd6qmaSxbtozdu3dnjpWWllJeXj46lRdCiAEMK9R95zvf4d5778XpdPKd73xn0HKapkmoE0JMCvF4PPO6dz25vpRSbN++Pd1SpxRF4cNUd74BgN81nY68JcDgy4pUVlZy+PBhYrEYIOvECSHG3rBCXd9Nq8/ewFoIISajvi11A42pa2pqorm5GZRiZuIg+Z1vAmBqVloKV8PpMDdYqLPb7axZs4ZXX30VkFAnhBh7IxpokUwmmTNnDgcOHBir+gghxLjo2zqXSqX6nU8kEhSEjrKg6TfUxPZTVFRMzFbAsfLbidsKM+WGms062Ng6IYQYCyOaKGGz2TJdCUIIMZn1bZ0bKNRZEz3UdL6GhiIvr4aws4rD3kWgZf8tPFSo6ztWb6BnCCHEaBrxlKgHH3yQb3zjG/IPlBBiUuvbUtc34HV3d/P29u1Y9/4aDYXpKcNyy9dIrv5ov0AHQ4e6vufk30whxFgb8ZImW7du5eWXX+aFF15g6dKl/bYG+93vfjdqlRNCiOFSSo1oYd++oa7v8iabN2/GEmmnuHk/StMxV34InPnk6YkB7jJ0qOtLQp0QYqyNONQVFBRwzz33jEVdhBBixPx+Pxs3bkTTNK655pqs/U6HMlioS6VS5MfTe72GHJXMXbASSE98GIiEOiHERDHiUPfYY4+NRT2EEOK8vPbaa5nXBw4c4NJLLx3WdQOFut7glRc7BUDMXXlmdwjSW3I1NDSwYsUKtm7dCnDOhX0XLVrEgQMHWLZs2bDqJYQQ52vYoc40Tb71rW/xhz/8gUQiwY033sg//uM/yibRQogJo6WlBb/fj8/nG9F1vaHu8OHDOBOd+CLHAQi7s/dLXbx4MYsWLULTNFatWkVeXt45W+rmzJnDzJkzZUkTIcSYG/ZEia997Wv83//7f/F6vUybNo1/+7d/48EHHxzLugkhxIi99tprHDhwgK6uLiAd2Lq6unj99dczx3qP932tlKL+yAHyYk0ABF3VBCyFnK03xFVVVZGXlzesOkmgE0KMh2G31P30pz/lhz/8IX/1V38FwEsvvcTtt9/Of/3Xf8m+gkKICeXo0aMcPXqU4uJiAoEAyWQSgE2bNnH77bf3K6+UIrjzf1nS+LPMsZCzatzqK4QQo2HYaayhoYHbbrst837t2rVomkZTU9OYVEwIIUbKlgpTGthDaWAPmjLo7OzMBDoYfHKEUgoaNmfdK+isoqSkZOwrLYQQo2TYLXWpVCprwDCkFyPu+w+mEEKMN4/HQzTYTU3HBnzRhszxyu63CDkraSq8nJi9eMh75AcOoYz0jNcu7zyi9hJi9mJ80m0qhJhEhh3qlFJ86EMfytr2JhaL8dd//ddZa9XJOnVCiPHS0tJCOBymPLA3K9D18saamdP6Rw5W/R8MizNrYlfflrqK7q30GBF6PLM5WXwt8+bNI9XWxpIlS8blcwghxGgYdqi7//77+x37wAc+MKqVEUKI4VJKsXXrVnQzQVHoMAAni66iyzsfqxGlNLiP0sAeLGaCgvAxOvMXDzhT1WpEsBmR09dfjc1mo7a2ltra2nH9PEIIcaGGHepkfTohxETS09MDQLl/JzYjjKE76PHMAU0nZfXQXHgZKd1BZc82Knu24XfPJBrVME0TXdczLXWuRCcAMVsBpm5jWkVFrj6SEEJcEJm2KoSYlE6dSi8QnBdtBKC5YDVOr48bbriByspKADryFpOw5lFaVEBxvCE9yzUYzLpPQbgOgKg9PSni7LHDQggxWUioE0JMSrFYDKsRwZnsAWDVHR/mhhtuwOPxsHr1agCUbqUzbyFer4fynrexJ/28vuFViAdRSmE1IhSGjwLQ45kNpHeNEEKIyWjE24QJIcREEAgEKA4eACBqL8aRVzTgmLlO7wLwKEidoDB8FGeiC154FZ9egS9iyVwfdNVgsVgG3eNVCCEmupy21L322mvceeedVFVVoWkaTz31VNZ5pRRf+tKXqKysxOVysXbtWo4cOZJVpquri3vvvZf8/HwKCgp44IEHCIVC4/gphBDjTSlFJBLJdJ0Gyy7tF+jKysoAmD57PsxdS77PR7l/Z2aWrKPrENO63gTA754FgGEY4/URhBBi1OU01IXDYZYvX84PfvCDAc9/85vf5NFHH+XHP/4xW7ZswePxcMsttxCLxTJl7r33Xvbt28eLL77IM888w2uvvcZHP/rR8foIQogcUEqhGXEcqQBuj4eVt7y/X5mVK1eyatUqFi1aBOWL8BamQ56mZf+zl7R46PLOAxj2tl9CCDER5bT79dZbb+XWW28d8JxSiu9+97t84Qtf4K677gLSW5WVl5fz1FNP8d73vpcDBw7w3HPPsXXr1swYmu9973vcdtttfPvb36aqSrb5EWIqMgwDb6wZgJKaBWiu/H5lbDbbmX8DLHmYK+6H41/ABLjpK3S//SqdR7bSkb+UlMUNwOWXXz5On0AIIUbfhJ0oUV9fT0tLC2vXrs0c8/l8XH755WzatAlI7+NYUFCQCXSQ3r5M13W2bNky6L3j8TiBQCDrSwgxeRiGQZl/F6BB2TDXkyuZR33pTRypeCfKkU+8qJbmoitIWs8snt53cWIhhJhsJmyoa2lpAaC8vDzreHl5eeZcS0tLZtxML6vVSlFRUabMQB555BF8Pl/mq6amZpRrL4QYS0YsiDvRjqZraPNuGtY1mqYRdE8nZi+msbExa0cJIYSYCiZsqBtLDz/8MH6/P/PV2NiY6yoJIUbADKT/aDOsXnAVDusaXT/zz92uXbsyr4uKijK7SAghxGQ2YZc0qTi9qntra2tmIdHe95dcckmmTFtbW9Z1qVSKrq6uzPUDcTgcWXvYCiHGl1KKt99+G9M0Wb169YBLkQyl6cgunEBE95yzbK+znxGNRgEoLCzkyiuvHHEdhBBiopmwLXWzZs2ioqKCl19+OXMsEAiwZcsW1qxZA8CaNWvo6elh+/btmTKvvPIKpmnKgGchJrBEIkFTUxMtLS3E4/ERXauUItCUXtoobvUN+7q+LXVwZkcK6B/4hBBiMsppS10oFOLo0aOZ9/X19ezcuZOioiKmT5/OJz/5Sf7pn/6JefPmMWvWLL74xS9SVVXF3XffDcDChQtZt24df/mXf8mPf/xjkskkH/vYx3jve98rM1+FmMD6LkvU0NDA3Llz+4WuwUTCIfIj6bXmYvbhdb3C4MEtEokM+x5CCDGR5TTUbdu2jXe84x2Z9w899BAA999/P48//jif/exnCYfDfPSjH6Wnp4err76a5557Lmtvxp///Od87GMf48Ybb0TXde655x4effTRcf8sQojh6xvqDh06REtLC2vWrMFms53z2lRHHc5kN4ZmI5g3b0TPnTZtWlYLHUBzc/OI7iGEEBOVpmQKGIFAAJ/Ph9/vJz+//3pXQojRdfz4cfbs2ZN1rKioiKuuuuqc1/Zs/RX+LU8QcE1n5p99bUQLBpumybPPPpt1zOl0ctNNw5tBK4QQ52s8ssaEHVMnhJi6+rbU9erq6iIQCBAMBrOOh8NhNm3aRHt7OyTCWBvT61RSsWTEO0AM1AVrmuaI7iGEEBPVhJ39KoSYunpnnp5tw4YNOBwObrrppkwA27JlC+FwmO7ubm5b4ETFA6QsLuJFI1+CREKdEGIqk5Y6IcS4SyQSmdf2pB+rcWayQjwez1oYOBwOA+ldJFT7IeKxOG35S9Hsw1/OpK+SkpKs9xLqhBBThYQ6IcS46w1SnlgzC5p+S+2pX+FMdPU7bxhG5pg1Feb49pcIh0OEnOc/u/3s5Y4WLlx43vcSQoiJREKdEGLc9Ya2yshBNBS6MpjV9gL2pD/rfCgUylxT4X8bXRlE7UXEbEVUV1ef17N1Xeeaa65h2rRpXHnllcyaNesCP40QQkwMEuqEEOPONE0KQkeZ4QoxffoMplVXYzPClAXS23f1dr8GAgEANDOFL1IPQFPhFbjc7n77Qo9EQUEBK1eupLi4WBYeFkJMGRLqhBDjTpkmpYE9aIA253qsV36M6dNn4Is0oJkpTNNEKUVTUxMAlT1bsZhJElYvYUcFHs/5jacTQoipTEKdEGLcFXRsxZXsAosN5t0MJfPRXAVYVZKaztdRpklXVxdtbW3kRRspjRwG4FThGtA0Fi1alONPIIQQE48saSKEGF+mSUHXThSQmr0WemexrvggHPk8BZE6/L9+EGteGVUhG1WJOuxuF80pH0H3dBYvXozPN/w9X4UQ4mIhLXVCiPHVeRTdiJHSHRgzrztzvGQurSVrMDUriVAPkebDlAT3YbXqaHYPx0tuBMDhcOSo4kIIMbFJS50QYlzFd/8WI5Ui4J1FhT07oPUULqPVORtPvA1PrIVy/w50TSdZfQWqJ/3PlYQ6IYQYmIQ6IcT4SUTwn0jv+drqW8nSswKarusozUrIWUXIUYmh25leWYI24zro2QuA3W4f92oLIcRkIKFOCDHmOjs7qaurY0mFHV3TSVi9GPZ8rNbsf4KylhfRNDrylzCjdlVWkNN1GTUihBADkVAnhBhzb775JgCuU8coNQyi9nKWLVvWr9xAga20tDRrEWKLxTJ2FRVCiElM/uQVQowLixHD1bSJWCxK2FGO2+3uV2aghYBtNltWkJOWOiGEGJj86yiEGBfe2CmsZpy4zUdn3sIBJzycHdh6t/DqG/Yk1AkhxMDkX0chxJiz2Wy4El0AhByVKM3Sbzwd9G+pG2hfVul+FUKIgUmoE0KMOavViivRCUDUXgwMHM76tsJdeumlme3A+nbVyl6tQggxMJkoIYQ4J6UU7e3t+Hy+81onzhZtJy92CoVG2FkOMGBLXd+g1zfIWSwWbrnlFjRNk1AnhBCDkJY6IcQ5nTx5ki1btrBx48as4/F4HKXUOa/3BI8BEPLMIG4rpKamZtBJEb3OHjtnt9uzzgshhMgmLXVCiHNqbGwEIBwOZ461t7ezefNm5syZw6JFiwa9VimFJ3wCgHlX383iudcNWnaoUCeEEGJo8q+mEOKcOjs7s94rpdi1axcAx44dG/LaZMM23PF20DRsVcuG7EKVRYaFEOL8SUudEGJIhmFkve/q6uLkyZNEo9FzX6wUxsE/AdBTvJoZnqIhi/cdZyehTgghRkb+1RRCDCmZTGa93/HmKwT3Po/FiA15XTQaxdj/ND0n9mFqVk4555/zWRLqhBDi/ElLnRBiSH1DXXFwP1VdW9AwKfe/zZHKu0lZ3CilsrpUo9Eorz33e+Y3/Q5dpWgqugrD4jzns0zTzLyW9eiEEGJk5E9hIS4SnZ2d/cbGDUcymQRlUhXey7SuTWikg5fNiFLVtQWUor6+HtM06e7uRilFd3c309tfRVcpIo5SurwLWLJkyTmf5fP5Mq9l6RIhhBgZaakTYpJTShGJRHC73YMGoWQyyZtvvgnAunXrhrU0SHNzM3v27GFGqZd5LU/jI4hptdJtLacjfzGz2l6gIFIHHYquJi89PT2cOnWK8vJyZpT7cCfaAWgsvhY0jZKSknM+s6ioiNWrV+P1ekfwHRBCCAES6oSY1EzT5NlnnwVg9uzZLF68eMBywWAw83rLli1cffXVQ963p6eHbdu24Yq3YT/yR3RlgMdH8er3YClegTeRouWNLip6tlEQqcd56L84ZalBL7yctpZTeHb9P7xA2FFO3FYAgMvlGtZnqqysHFY5IYQQ2STUCTGJ9V03rq6ubtBQFwgEMq+7u7tJJBJZy4f01dnZyZtvvommDKq630JXBnGbj54FH6By6U1UkJ4R2zbvJmL+KtTxN7Ekeig2DlEYPoamzEwXbXv+UgBmzpw54A4SQgghRo/8KyvEJGMYBrquo2ka8Xg8c7zveLSz9Q1/AH6/n9LS0gHL9nbTFoUO4Ym3YmoW6ktvotJbniljsVi47PLLiUSW8nKshJJYHdNDO0hF/ACkdCenitYw4/I7mDlz5vl+VCGEECMgoU6ISaSuro79+/dTUVHB6tWrCYVCmXODtbwBJBKJrPd9w2Bffbf8KgjXAdDqW0HC5hvw/larFTSNDtccOp0z8cRbQSlCzkrQdMrLy/tdI4QQYmxIqBNigusNWoFAgH379gHpSQwAe/bsyZTruxzI2fqtNbdjBw6Hg9LSUpRShMNhPB5P5ln5kRPpgAb0eOYCDDi5om+XqtIshJxVrFq1iuPHj1NZWTnscXRCCCEunIQ6ISYwpRR//OMfBwxs9fX1We/7lkkkEhw+fJjCwkIikQj+xv2UR45jajZsRghHKkjDH98kdc0H2LYv3SJXW1vLzFIPZf6dlPfswOV2c1KfTtLqAQZuCdR1ndraWg4ePJg55nA4uPLKK0fl8wshhBg+CXVCTGBtbW3psKYUebGT6CpFwDUdX6Seng2v4SlcQVjPA7JDXV1dHfX19dTX11MS2Mu87q1omBQWFdHd0wVAHhB84RtoVe9CaVZO7Hqd2Y69VPTUARqlNfM4qF8FkXRX7WBdqaWlpVmhbqhuYCGEEGNHQp0QE9hbb72FI9HN9M71uBLpMGZoNiwq3Z1aGDpKS+GltOctztqjNZVKAeALH6Oy+y00FIbuwFK1nB49QCKRpDSwF0cqwNyWp+n2zKPcvxO/10HMVkAgbx4zrv07lkVTnDp1ijlz5gwa1nw+HwsXLqS5uRmfzydrzAkhRI5IqBNiAlJKcfjwYRyJbua0/QmrEcXUrGjKyAQ6AA1FZfdbuONt+BMLMHd3oFcswTRNrKkwNZ2vo6Ho8szjZMm1lKy8jp4dOwgEAoSdFUxvfxVXogtXYgsArfF86irWYXPlgcNLgQMKCgqGrKumacydO5e5c+eO5bdECCHEOUioEyLHlFLE43GcTmfm/eHDhzm1+zXmtL+E1YyTsHo5Vn4Hs2bOoNLSzbZDpwg7yigN7KWyZyu+yHF8keM0tkBV1TSKUnk4u5vRlUHEUcrJ4vRiw1arlfnz57Nt2zaCrhqOl62luutN7Mkg3d65NBdciqnbh7XjhBBCiIlFQp0QObZ//37q6uqorq5mxYoVtLS00LrzeWZ1vIauUiQtLo6W30HK6iFpyyN/yRoKUm8TPnWKdt8yDG8l5c0vYjOiADQ1ncJut+NIJjA0G02FV4CW3ubZarVSWVnJO97xDl599VXCzioOVd6DhoHSzvxzMNgadkIIISYuCXVC5FhDQwMAJ0+eZNbMmZx86cfM8O8CIGorQr/yQVLHm4Azm9zrup65PuGbxWHejT0VImYvpDSwh6LQIbp9i+nIW4hhObOsSO8SJB6PJ3Ns9aWXsm3btsz7OXPmsHDhwjH6tEIIIcaKhDohcqxvQDv4yhNUng50fvdMGoqvY4Ezn9rafBoaGpgzZ06/a3Rdx7A4iVrS3bdtvkto810CwKxZs5gzZw51dXVYrdbMdb3hENJB74YbbuCVV14BoKSkJOu8EEKIyUFCnRA51hu0bKkgZa3rAejIW0xL8RqUUlRUVJCXl8e8efMy11gslszr3m3DTNOkvLyc1tbWzLn58+djt9sH3BN2xowZhEKhTIi7+eabSSaTWa14QgghJg8JdULkWO8uDsWhQ1jMJDFbAS0FK7n5lluIx+MDLhHSt6UuHA5zxx13ZHaFOHDgAMeOHWPFihVDrhm3bNmyrPcOhwOHwzFKn0oIIcR4k1AnxDC0tbUBUFZWNur3Nk0TeypIcTC9gG9rwUpWXLoGm8026CzU8vJyjh49mnmtaVom/NXW1jJr1izZoksIIS4yEuqEOIeGhgZ27UqPc7vtttuyuj5Hg2malAX3YzHjxGwFrFj3QfJ8hUNeU1RUxK233sqpU6eoqKjIOqfrugQ6IYS4CEmoE2IQSilCoVAm0AEkk8lRDXVKKUzTJC96imnV1Vgv/TCcI9D1slqtzJgxY9TqIoQQYnLTz11EiIvTqVOnWL9+fdaxY8eOjeozTNMkL1yPM9mNrlugdMGo3l8IIcTFQ0KdEIPYs2dPv2NNTU2j+gwjlaSqO71Flzb9CrDLzFMhhBDnR0KdEANIpVKkUql+x3Vdz8xWHZXnvP1z7KkQKd2BtuSeUbuvEEKIi4+EOiEGEAwGBzweiUQ4efLk6Dwk0kX8yGsANBVdAdbBlx8RQgghzkVCnRBDcMU7mNPyDPOaf481FQagubn5gu6ZSCTo7OhA7f8D8USckLMK97xrR6O6QgghLmIy+1WIASSTSVAmMzpexp4KATCn7U8crnzXBS0XkkgkeP7553Eke1jpf4l4LEZb+XIumT17tKouhBDiIiUtdUKcJRqNsmXLFip6tmcCHYAj6Sc/cpzjx4+f972ff/55AHyRE4TDIYKuakLOKqxW+ftKCCHEhZFQJ8RZ2tra0JRBaXAvPl8BwZnrsC15J06niwr/DjTVfwLFSDiS3ZQG0mvfBVzTAUZ9QWMhhBAXH2keEOIsFosFR7IHHfCVlFOw7q8gGcGIHiF27AB50ZOkUqkRta6FQiGcTicOh4Pyjp1YzCQReyldnnmZZwohhBAXQkKdEGcxDANXohOny4mWPw00Dewe9OpVaHWHyIs1kUgkhh3qurq62LhxIwCFocMUhOuA9IxXpVtZtGgRDodjzD6PEEKIi4N0vwpxlkBPF2X+Xen16IrOTGDQTu/24Iscp6ulcdj36+joQDNTlPXsYFrXJgDafMuJOMoAmDNnzijWXgghxMVKQp0QfZimSdvhbThSAUJxE+beeOZkaS1xiwerEeXUm78c9j0tFgszOl6lwv82ukoR8c6ixbdyDGovhBDiYiahTog+Tp06hSfRDoDhmwm2PsuXWGy05S8DIC967gWIE4kEO3bsINB6nPxoAwqNEyXX477+70CT//SEEEKMLvnNIkQfyWQST6wFgOK5q/qdt9dcAkAhfgikFyFOpVL09PT02z5s48aN6d0nDj8HQNhZSenyW5gxc+bYfQAhhBAXLQl1QpyWTCape3sDedH0eLmCOf1DXWnNPEKOChLxOG1v/JREIsFbb73F66+/zqlTp7LKhsNhHMkeikJHALDWrmPhwoVj/0GEEEJclCTUCXHawYMHyY+eQEMRdNVgKe6/y4OmaTQXXgpA6Pg2Xnjuj3R2dgJw4sSJTDnDMAAo9e8G0uvRuaZfkjk/d+5cABYsWDAmn0UIIcTFR5Y0EeK05uZmpsVbAXDOuiy9lMlZdF0nai8laXFhM6IUhOvo9s7LnFdKoWkawWCQ/NBRSmJ1+AqLMOeto6amJlOutraWmpoaPB7P2H8wIYQQFwVpqRPitEKXjjveBkDN8usGLKNpGmgand50N2q5/204PZauq6uLZ555hlOnThE/uoEZHeux22zkL7mZWZfdlr62z328Xm/WMSGEEOJCSKgT4rSC7l3oykAvmomjqGbAMoFAAICO/CWYmhV7KoQ70ZZV5uDOzbD39wCkiuZB7R1jW3EhhBACCXVCZDhD6QkSjtqbB+x6BTLdpaZuI+iqBmB6+6voZhKA4uB+Zh9/glioB0N3EJh3Dzi841B7IYQQFzsZUycEQCKCPdpKDEj6ZgxabPr06ezenZ780FR4Be54O3YjzPzm32FqNpzJbgDCjnKaCq9gWXnVeNReCCGEkJY6IQCSh55HmYqYrQDNVThoOU3TuPXWW9PXWD00Fl+Dodmwp0KZQOd3z+RY+e1EHSVYLJZxqb8QQgghLXXiopNKpVBKoZTi4MGDlJWWEtz4O+ypGK0la8g/x+QFq9WKxWLBMAxCrmkcrP5zSgN7cMdaCbpq6MhfnOm+lYkQQgghxouEOnFRMQyD9evXYxgGmqYRj8cJ7f0T01JBlKYTdA08QWIocxcu49Ahx4DnCgsHb/UTQgghRpN0v4qLit/vJxqNkkgkiMfjWFNhqrq3ANDjno2p24bVuta7uDBAZWXlgGWuv/56aakTQggxbiTUiYtKLBY780aZ1HS9gaZMovYSGouvAdILDJ+L1XqmkXugBYSvuOIK8vLyLrzCQgghxDBJqBMXlUyoU4qKnu3kRU8C0FR4GWjD/89hxowZWK1WVq9e3S8E+nw+ioqKRq3OQgghxHDImDpx0VBKsW/fPgCKQocoC6SXJmnzLSfsPNOFOpwu00WLFrFw4cJM2dmzZ1NXV8eVV15JcXHxGNReCCGEGJqEOnHRSCQSAOhmggr/2wC05y+l4PL3429oJBqNAsOfsdq33KJFi5g3bx52u32Uay2EEEIMj3S/iknPMAxOnjyZCW2D6e16LffvxGpEidt8NBesZt78BVkBLZlMjrgOmqZJoBNCCJFTEurEpHfy5El27NjBSy+9hFJq0HLRaBSLEaM4uB+ApsLLqZqW3uqrbyDrO7NVCCGEmCwk1IlJLxQKAekw1vt6IE1NTZT738brchCzFRB0VrNkyRIAysvLx6WuQgghxFiRUCcmPdM0M697x8UNpKO9nfxIA968PEqv+RCrVq/G4UgvGjxnzpxMuaoq2a9VCCHE5CMTJcSkl0qlMq937NjBLbfcMmA5LdaN3QhjtRVTNP9KsJ7pcrVYLNx5551jXlchhBBirEzolrovf/nLaJqW9VVbW5s5H4vFePDBBykuLsbr9XLPPffQ2tqawxqL8dQ7fq7vxIbBJksopSj07wVAK5yRFeiEEEKIqWDCt9QtXryYl156KfO+70r+n/rUp3j22Wf59a9/jc/n42Mf+xjvfve72bhxYy6qKsaJUoo33niDnp4eZsyYQTwe73f+7GVJUvEIxcGDAOhzbxi3ugohhBDjZcKHOqvVSkVFRb/jfr+fn/zkJzzxxBPccEP6l/Rjjz3GwoUL2bx5M1dcccV4V1WMk1gsRk9PDwAnjteTH22kNBWg2zOHlMVNIBDA5/NlXWPWvY6uUiSsXrTK5TmotRBCCDG2JnT3K8CRI0eoqqpi9uzZ3HvvvTQ0NACwfft2kskka9euzZStra1l+vTpbNq0ach7xuNxAoFA1peYPPru3zq9YwMz21+isvstFjT9lqLQIV7bsIGjR4+euSDaQ2T7LwHo8sxHG8berkIIIcRkM6F/u11++eU8/vjjPPfcc/zoRz+ivr6ea665hmAwSEtLC3a7nYKCgqxrysvLaWlpGfK+jzzyCD6fL/NVU1Mzhp9CjLbe7lZfpJ6CSB0ACh2LmaC68w1qm35N/a43zsyKbTtAwN9NwuqlzSetdEIIIaamCd39euutt2ZeL1u2jMsvv5wZM2bwq1/9CpfLdd73ffjhh3nooYcy7wOBgAS7SSQej4MyqepKt8h25C2kvfhyakI7cXfuwZ4KMr1jPc8/62PNlVfja9wCpFvp0Cb03zFCCCHEeZtUv+EKCgqYP38+R48epaKigkQikRlb1au1tXXAMXh9ORwO8vPzs77E5BGPx/HGmrEZUVK6g+bCy1m0bCU1tz3Eoar/Q8riwpnsobrtVWJb/h+hhj2YmpUez2zmzp2b6+oLIYQQY2JShbpQKMSxY8eorKxk1apV2Gw2Xn755cz5Q4cO0dDQwJo1a3JYSzHWWltaqOx5C6fTid89E6VZ8Pl85OfnUzRtNsdL16LQyY82YG/fRyQSoaHkehI2H9XV1bmuvhBCCDEmJnSo+/SnP82GDRs4fvw4b775Ju9617uwWCy8733vw+fz8cADD/DQQw/x6quvsn37dv7iL/6CNWvWyMzXKSwUCpFoPYQr0YVud9HqWwGkFw8GWLlyJRFHGS2Fq1FoGApOeFcQcM8AwOv15qzuQgghxFia0GPqTp48yfve9z46OzspLS3l6quvZvPmzZSWlgLwne98B13Xueeee4jH49xyyy388Ic/zHGtxVgKh8MUh9LrzVmmrSAV8QCgn57RarVacbvdtLOULs88AAyLE4CioqJ+69cJIYQQU8WEDnVPPvnkkOedTic/+MEP+MEPfjBONRK5pjqOUhg+hsVipXDpzZTW9ZBIJLImzuTn5xOJRDJhrte8efPGu7pCCCHEuJnQoU6Is+lNWwFIVVyCVlbLFWX9d5BYuHBhv2VtLrnkEsrKysa1rkIIIcR4mtBj6oTo68S+rYQPvw5AsurSzPGzu1S9Xi933HEHJSUlmWNut3t8KimEEELkiIQ6MWm0vv0sujIIOStxVS0asqymaVx++eWZ9xLqhBBCTHXS/SomhZMnT+KJtwLQ45lDqcNxzmt0XWfNmjX9xtwJIYQQU5GEOjEptJxqpDjeDkDYUZ5ZwuRc+nbBCiGEEFOZdL+KScHV9ja6SpGweIhbfZklTIQQQgiRJr8ZxaRgad8HQLtvGWiarDcnhBBCnEW6X8WEppTi1LF9uCJNAJQuuoYiZxE+ny/HNRNCCCEmFgl1YkI7fPgwqde+jxeIW/OZu/Ry9GGOpxNCCCEuJtL9Kia0pt3r8cZbUGjU3P1FCXRCCCHEICTUiQnLiEeY3rEeAL97Fq4K2eZLCCGEGIyEOjHh9PT0EAwGMU5ux2pESekOThVdketqCSGEEBOajKkTE0osFuP1119HN5PcoG8BoCN/CctWX5njmgkhhBATm7TUjYNdu3axZcsWotForqsy4XV2dgLgiTXTduIQKYuLzrxFVFdX57hmQgghxMQmLXXjoL29nWg0Sjwel+2qzmHHjh0AuBMdAASc1SirM5dVEkIIISYFaakbBzabDYBkMpnjmkxskUgEpRQArkS6xS7qKGHlypW5rJYQQggxKUioGwcS6oYnlUoBYDHjeOItAETtxVRUVOSyWkIIIcSkIKFuHPSGukQikeOaTGymaQJQED5GYZ6LmK2AwlmXyJZgQgghxDDImLpxIC11w9PbUlekhSjwFcD8K/AsXZbbSgkhhBCThIS6cWC32wEJdefS25LpSnaiaTYKZyyB0987IYQQQgxNul/HgbTUDc/OnTuxGDG8KpQ+4KvJbYWEEEKISURC3TiQUDc8hmFQEtwHKMirAqcv11USQgghJg0JdePAak33cvcurNsrGo1y6NAhgsFgLqo1IXljTXi9Xph9PcgECSGEEGLYJNSNA11Pf5sTiQSBQCBz/KWXXuLw4cOsX78+RzUbmN/vz0xaGC9KKTRl4Ep0YrVYoGj2uD5fCCGEmOwk1I0Di8WSed3Rkd4poXeR3V4HDhzgwIED41qvgZw8eZLXXnuNvXv3jvuzvbEmdGWA3QueknF/vhBCCDGZSagbB30DXO+aaw0NDVlljh49ytGjR4lEIuNaN4B4PM6GDRs4ePAgu3fvBqCxsXFc66CUosy/K/26cpl0vQohhBAjJEuajIO+EyR6X584cWLAsqFQCLfbPS716tXU1EQgEMjqGob0xIW+rYxjSaUSuOPt6TezbxiXZwohhBBTibTUjYP8/PzM60gkAjE/hZ1vg1K44u3UdGxgTsszFIYOc+rUqXGv32Czcnt6esatDqrnBBomSYsb3MXj9lwhhBBiqpCWunHg8/mYMWMGJ06cINDdiVr/K/JPHWAZ66morCSgApiagafzdU62zwFWjGv94vE4kN5z1RVvx5EKkLR4SMRXjV8lmnYAEHGUoenyt4YQQggxUhLqxkl1dTUnTpzAH4rQ7psP7EfTdOw2O6WLryXRUU9z/UEs7fvZs2cO5eXllJWVjUvdGuqOUNWzncLQYSwqiW6xYBoGlp0hqPgsjDBkKaVGtl+rkURr2AxAp3dBZrawEEIIIYZPfnuOk77j5Lb0FHKi5B20ll+HduOX4PK/wjJ/LZDezP54fR1btmwZl3oFO5uZ2f4iJcF9WFQSZ2EltoqFKHSidZtp/c2n2fjsE3R3dxOPx/H7/UPeLxKJ8OKLL3Lw4MHhVyLQBGaKlMVFyDntAj+REEIIcXGSlrpx4nA4zrzRdPye2RheL3jS48cs1aswNBuuRCd50ZME3dNH9flKqcwkjG3btlFdVc40s4nEpv/BG2vG1KzUrPs41lnX0HjqFA3x31Pd+TqxtjqqqaPNEuG4VkMikWD58uVMn36mfvF4nHg8Tn5+PsePHycej3PkyBFqa2uHVzn/SQCi9mI0XR9ZK58QQgghAAl142agoNK7fRgArkL8ntkUhQ7hjTePeqhra2vjrbfeSr9RJt7dj1HkU4Q6WklYvYQWvZ9Zc64DIC8vD79nFmFnOdM7NuCNNeE8+gwleQtpKVjNrl27qKmpQdM0TNPkxRdfRCnFDTfcQHd3d+aZ4XAYj8dz7sp11aFIhzohhBBCnB/pfh1HM2bMyHpvGEbW+wVX3YHT5SIvehKH/f9v796jorjP/4G/l4VdlsuywHK/CwoVAcULQRO1kS9qW2pqk5jUeoy5JyatqTG3nsa0Oak2PbWNHmN70lO1qb9oYqKmiZrEC8YLMYGKCJoVBaOEm4Dc0WXZ5/cHZZIR1CRd2HV9v87Zc9jP5zMzzzzOwuPMzmd0Dt32qVOnen8QQXTTIfhdqkVdfT1qTeNgibwdvuFJyliTyYTRo0fDpvVBRegMNPiPBACY204gqfbf8Ov6Eh0X6oCebhw6dKh3Hj4RVJ0oRM+5QnjZOgAAe/bsQVNT09UD67oAVP8HEKDNO4pn6YiIiL4jnqkbQomJiar56S6fj84nJgNewSG4WHUW/i0nAEx32La9vb0BAIEd5QhqtwAAqoJvxgW/EQCAhIQE1fiYmN5LreXl5agOykaHdzgimwrg3d2MYfU70fLmLvhExcB4XuCpD0VAZyW8z55HHACBB1p84lAbOB4HDx5EXl7elQNrOIUeWzfOttjRERwBLYs6IiKi74RF3RC6/FLkuHHj1AO8jbAnTAWq/gn/jjMO227f9+n8LlYjpnE/tJ6eqPEZqRR0wGWXgv8rMTERiYmJaG5uRnGxP3SZ06Cv3IXO8v2w2Ww490UlAgAEdPbGatdoYfPwhq6nA6bOShi7zuG8cRRqvhyDiKjoAWOzN1Wgrq4eTYbeWIZqsmMiIiJ3w6LOSaKjowe81KiJzAAA+HR9Cenphkbbv9j6trq6utDW0oSk5kJER0dDG5mBi6ZbUGspBwAMHz78qsubTCZMnToVACBJI/G+NRFit8O7uwnB7RZ4W5vQpTOjPiAdNq0PxiSGIvL8fpw7dgBhLcVo/2g55OcroPG87JKyzYqWkwXo7raiM6B3+pahmsaFiIjI3bCoG2ITJ05EQ0MDRowYMWC/hykW3VofePV0wn4qH9rk//uft9ne3o6QlmMw2lug9YoBUmcjyTcYkdGxqK6uRnx8/Ddel0ajQXZ2Ng4dOoSLumB8GTQRsbGxMJtMuFBeju8lJSEqLg6a701AVNRYVH2wCrr2Klz64AV4T1kE+PUWbR0X6nFh31/RU3emdyoTQyRSU1O/VSxERET0FRZ1Qyw4OBjBwVe+y1Pr6Yn6gNGIajoEqTkCOKCo++JYAUJaj8HT4AWk3aFMo+Lj44OkpKRrLN1fcHAwUlJSUFFRgYSEBMTFxUGv1/e7EcQz6fu4UFGLgPJ3UFd5HP5NT6E9ZCyqmjoR0noMOls7AKAqaBImTJoKs9n8P+8rERHRjYpFnYvRaDRo840Dmg4BzecA2yXAU3/tBa+gu6MZAeVvQyvd6PaOAKInOCTO4cOHX/OyLQAYYsfgZIcGMY37gJYaoGU3+qYX7tYacC54MrThqQgKCnJIXERERDcqTmnigjSGQFg9/WC1XgJqjw04pra2FocPH1ae29qnoaEBJSUlsNlsAICqd1/677NcDfD+/uJv/civ/1ViYiK6PX1REToTZ81T0OIThy6dGbUBmTgZMRsjJv0YkyZN4qPBiIiI/kc8U+eCoqKicKEuCaaOcvhYtgNRY4HLbqr47LPPAAAffvihasqQgoICAICHhwdGJYTDo7H3Zoiz5u8jKUJ9eXQoeHl5ITo6GlVVVWj2TUKzbxKSk5ORmZAAT09PzktHRETkIDw94oJMJhPOG9PRdbEb3S21QFutqt9qtare//vf/0ZFRYWqreH8efQc3QSgd1LfoOGOuez6XYwePRpjxoyBwWBARkYGRowYAS8vLxZ0REREDsSizgXpdDrYPbzQogtDdXU1zu7/f6r+yws4ACgrK1O9tzVWwFpVAoEG9QGjkZaWNqgxX41Go0F0dDRycnJUz4wlIiIix2FR54L0+t4bIxr9vwcAsFceQFN1pdJfXt57SRUiMFyqR1Db5whvLoRUF8MbVnjZ2hDdVID6+jo0+ybiom8UJ/UlIiJyc/xOnQvS/fe5r22GGHTqzPCxNqDik/cRNOth4GIz/LvOwdxaBh/reWjtX12KvXSwDiMbG2GzdQMA7BpPNBhT+z2OjIiIiNwPizoX1HemDgBaDbHwsTYgpHoX7DsqobHbkFD/1fNj7RpPXNQFwuZhwKXGZuhsNmgA6MzxOKFNRZfODLS1OWEviIiIaCixqHNBGo0GISEhaG1thcRkwdpxEjpbO86dOY3Q0FCIxgOthlhEf/9eHDxWiVFp6SgtLe1dVmzwkB6kj70JHUeOAODzVImIiG4ELOpcVFZWFux2O06ePAlLy08R0HkGdg8vHPOOgsT2/rOlxachLyEdIqIUdaLxRI/GEyEhIcq6xo8f75R9ICIioqHDos5FaTQaaLVaDBs2DJWVlWj2Uz/Oy2QyKVOCaDQa5OXlobS0FFVVVRg9ejT0ej3GjRuHnp4eVYFHRERE7kkjIuLsIJyttbUVAQEBaGlpgdFodHY4AxIRvPfee8r73Nxc1Xfvvj6O878RERG5lqGoNTilyXVCo9EgJSUFABAWFjZgQdc3joiIiG48vPx6HRk+fDjCw8NhMBicHQoRERG5GBZ11xl/f39nh0BEREQuiJdfiYiIiNwAizoiIiIiN8CijoiIiMgNsKgjIiIicgMs6oiIiIjcAIs6IiIiIjfAoo6IiIjIDbCoIyIiInIDLOqIiIiI3ACLOiIiIiI3wKKOiIiIyA2wqCMiIiJyAyzqiIiIiNwAizoiIiIiN8CijoiIiMgNeDo7AFcgIgCA1tZWJ0dCRERE7qivxuirOQYDizoAbW1tAICYmBgnR0JERETurK2tDQEBAYOybo0MZsl4nbDb7aiuroa/vz80Go3D19/a2oqYmBicO3cORqPR4eu/UTGvjsecOh5zOjiYV8djTh3v6zn19/dHW1sbIiMj4eExON9+45k6AB4eHoiOjh707RiNRn5QBgHz6njMqeMxp4ODeXU85tTx+nI6WGfo+vBGCSIiIiI3wKKOiIiIyA2wqBsCer0eS5cuhV6vd3YoboV5dTzm1PGY08HBvDoec+p4Q51T3ihBRERE5AZ4po6IiIjIDbCoIyIiInIDLOqIiIiI3ACLuiGwevVqxMfHw9vbG1lZWfj000+dHZJLeuGFF6DRaFSvlJQUpf/ixYtYuHAhgoOD4efnh5/+9Keoq6tTrePs2bP44Q9/CB8fH4SGhmLJkiWw2WxDvStO9fHHHyMvLw+RkZHQaDTYunWrql9E8PzzzyMiIgIGgwE5OTkoLy9XjWlqasLcuXNhNBphMplw3333ob29XTWmpKQEt9xyC7y9vRETE4OXX355sHfNaa6V03vuuaffsTtjxgzVGOZUbdmyZRg/fjz8/f0RGhqK2267DRaLRTXGUZ/5/Px8ZGZmQq/XIykpCevWrRvs3XOKb5LTqVOn9jtWH374YdUY5lRtzZo1SE9PV+aay87Oxo4dO5R+lzpOhQbVxo0bRafTyT/+8Q8pKyuTBx54QEwmk9TV1Tk7NJezdOlSSU1NlZqaGuV1/vx5pf/hhx+WmJgY2b17txQWFspNN90kEydOVPptNpuMGjVKcnJy5MiRI7J9+3Yxm83y7LPPOmN3nGb79u3y61//Wt555x0BIFu2bFH1L1++XAICAmTr1q1y9OhR+fGPfywJCQnS1dWljJkxY4ZkZGTIJ598Ivv375ekpCS5++67lf6WlhYJCwuTuXPnSmlpqbzxxhtiMBjkb3/721Dt5pC6Vk7nz58vM2bMUB27TU1NqjHMqdr06dNl7dq1UlpaKsXFxfKDH/xAYmNjpb29XRnjiM98RUWF+Pj4yK9+9Ss5fvy4rFq1SrRarezcuXNI93cofJOcTpkyRR544AHVsdrS0qL0M6f9vfvuu/L+++/LyZMnxWKxyHPPPSdeXl5SWloqIq51nLKoG2QTJkyQhQsXKu97enokMjJSli1b5sSoXNPSpUslIyNjwL7m5mbx8vKSt956S2k7ceKEAJCCggIR6f3D6+HhIbW1tcqYNWvWiNFolEuXLg1q7K7q8gLEbrdLeHi4/PGPf1TampubRa/XyxtvvCEiIsePHxcA8tlnnyljduzYIRqNRr788ksREXn11VclMDBQldenn35akpOTB3mPnO9KRd2sWbOuuAxzem319fUCQPbt2ycijvvMP/XUU5Kamqra1pw5c2T69OmDvUtOd3lORXqLul/+8pdXXIY5/WYCAwPl73//u8sdp7z8OoisViuKioqQk5OjtHl4eCAnJwcFBQVOjMx1lZeXIzIyEsOGDcPcuXNx9uxZAEBRURG6u7tVuUxJSUFsbKySy4KCAqSlpSEsLEwZM336dLS2tqKsrGxod8RFVVZWora2VpXHgIAAZGVlqfJoMpkwbtw4ZUxOTg48PDxw+PBhZczkyZOh0+mUMdOnT4fFYsGFCxeGaG9cS35+PkJDQ5GcnIxHHnkEjY2NSh9zem0tLS0AgKCgIACO+8wXFBSo1tE35kb4HXx5Tvts2LABZrMZo0aNwrPPPovOzk6ljzm9up6eHmzcuBEdHR3Izs52ueOUz34dRA0NDejp6VH9QwJAWFgYPv/8cydF5bqysrKwbt06JCcno6amBr/97W9xyy23oLS0FLW1tdDpdDCZTKplwsLCUFtbCwCora0dMNd9ffRVHgbK09fzGBoaqur39PREUFCQakxCQkK/dfT1BQYGDkr8rmrGjBmYPXs2EhIScPr0aTz33HOYOXMmCgoKoNVqmdNrsNvtWLRoESZNmoRRo0YBgMM+81ca09raiq6uLhgMhsHYJacbKKcA8LOf/QxxcXGIjIxESUkJnn76aVgsFrzzzjsAmNMrOXbsGLKzs3Hx4kX4+flhy5YtGDlyJIqLi13qOGVRRy5j5syZys/p6enIyspCXFwc3nzzTbf8JUHu46677lJ+TktLQ3p6OhITE5Gfn49p06Y5MbLrw8KFC1FaWooDBw44OxS3caWcPvjgg8rPaWlpiIiIwLRp03D69GkkJiYOdZjXjeTkZBQXF6OlpQWbN2/G/PnzsW/fPmeH1Q8vvw4is9kMrVbb7y6Yuro6hIeHOymq64fJZMKIESNw6tQphIeHw2q1orm5WTXm67kMDw8fMNd9ffRVHq52TIaHh6O+vl7Vb7PZ0NTUxFx/Q8OGDYPZbMapU6cAMKdX89hjj+G9997D3r17ER0drbQ76jN/pTFGo9Ft/7N4pZwOJCsrCwBUxypz2p9Op0NSUhLGjh2LZcuWISMjA6+88orLHacs6gaRTqfD2LFjsXv3bqXNbrdj9+7dyM7OdmJk14f29nacPn0aERERGDt2LLy8vFS5tFgsOHv2rJLL7OxsHDt2TPXH86OPPoLRaMTIkSOHPH5XlJCQgPDwcFUeW1tbcfjwYVUem5ubUVRUpIzZs2cP7Ha78gcgOzsbH3/8Mbq7u5UxH330EZKTk936MuE3VVVVhcbGRkRERABgTgciInjsscewZcsW7Nmzp9+lZ0d95rOzs1Xr6Bvjjr+Dr5XTgRQXFwOA6lhlTq/Nbrfj0qVLrnecfrf7Puib2rhxo+j1elm3bp0cP35cHnzwQTGZTKq7YKjX4sWLJT8/XyorK+XgwYOSk5MjZrNZ6uvrRaT3tvHY2FjZs2ePFBYWSnZ2tmRnZyvL9902npubK8XFxbJz504JCQm54aY0aWtrkyNHjsiRI0cEgKxYsUKOHDkiX3zxhYj0TmliMplk27ZtUlJSIrNmzRpwSpMxY8bI4cOH5cCBAzJ8+HDV9BvNzc0SFhYm8+bNk9LSUtm4caP4+Pi47fQbV8tpW1ubPPnkk1JQUCCVlZWya9cuyczMlOHDh8vFixeVdTCnao888ogEBARIfn6+anqNzs5OZYwjPvN9U0UsWbJETpw4IatXr3bb6TeuldNTp07J7373OyksLJTKykrZtm2bDBs2TCZPnqysgznt75lnnpF9+/ZJZWWllJSUyDPPPCMajUY+/PBDEXGt45RF3RBYtWqVxMbGik6nkwkTJsgnn3zi7JBc0pw5cyQiIkJ0Op1ERUXJnDlz5NSpU0p/V1eXPProoxIYGCg+Pj7yk5/8RGpqalTrOHPmjMycOVMMBoOYzWZZvHixdHd3D/WuONXevXsFQL/X/PnzRaR3WpPf/OY3EhYWJnq9XqZNmyYWi0W1jsbGRrn77rvFz89PjEajLFiwQNra2lRjjh49KjfffLPo9XqJioqS5cuXD9UuDrmr5bSzs1Nyc3MlJCREvLy8JC4uTh544IF+/3FjTtUGyicAWbt2rTLGUZ/5vXv3yujRo0Wn08mwYcNU23An18rp2bNnZfLkyRIUFCR6vV6SkpJkyZIlqnnqRJjTy917770SFxcnOp1OQkJCZNq0aUpBJ+Jax6lGROTbndsjIiIiIlfD79QRERERuQEWdURERERugEUdERERkRtgUUdERETkBljUEREREbkBFnVEREREboBFHREREZEbYFFHRERE5AZY1BHRdemee+7Bbbfd5rTtz5s3D7///e+vOiY+Ph5/+ctfhiQeq9WK+Ph4FBYWDsn2iMj1eDo7ACKiy2k0mqv2L126FK+88gqc9UCco0ePYvv27VizZo1Ttj8QnU6HJ598Ek8//XS/B4MT0Y2BRR0RuZyamhrl502bNuH555+HxWJR2vz8/ODn5+eM0AAAq1atwh133OHUGAYyd+5cLF68GGVlZUhNTXV2OEQ0xHj5lYhcTnh4uPIKCAiARqNRtfn5+fW7/Dp16lQ8/vjjWLRoEQIDAxEWFobXXnsNHR0dWLBgAfz9/ZGUlIQdO3aotlVaWoqZM2fCz88PYWFhmDdvHhoaGq4YW09PDzZv3oy8vDxVe319PfLy8mAwGJCQkIANGzb0W3bFihVIS0uDr68vYmJi8Oijj6K9vR0A0NHRAaPRiM2bN6uW2bp1K3x9fdHW1gar1YrHHnsMERER8Pb2RlxcHJYtW6aMDQwMxKRJk7Bx48ZvnGsich8s6ojIbaxfvx5msxmffvopHn/8cTzyyCO44447MHHiRPznP/9Bbm4u5s2bh87OTgBAc3Mzbr31VowZMwaFhYXYuXMn6urqcOedd15xGyUlJWhpacG4ceNU7ffccw/OnTuHvXv3YvPmzXj11VdRX1+vGuPh4YGVK1eirKwM69evx549e/DUU08BAHx9fXHXXXdh7dq1qmXWrl2L22+/Hf7+/li5ciXeffddvPnmm7BYLNiwYQPi4+NV4ydMmID9+/d/1xQS0fVMiIhc2Nq1ayUgIKBf+/z582XWrFnK+ylTpsjNN9+svLfZbOLr6yvz5s1T2mpqagSAFBQUiIjIiy++KLm5uar1njt3TgCIxWIZMJ4tW7aIVqsVu92utFksFgEgn376qdJ24sQJASB//vOfr7hvb731lgQHByvvDx8+LFqtVqqrq0VEpK6uTjw9PSU/P19ERB5//HG59dZbVdu+3CuvvCLx8fFX7Cci98UzdUTkNtLT05WftVotgoODkZaWprSFhYUBgHIG7ejRo9i7d6/yHT0/Pz+kpKQAAE6fPj3gNrq6uqDX61U3c5w4cQKenp4YO3as0paSkgKTyaRadteuXZg2bRqioqLg7++PefPmobGxUTlzOGHCBKSmpmL9+vUAgH/961+Ii4vD5MmTAfSeDSwuLkZycjJ+8Ytf4MMPP+wXn8FgUNZHRDcWFnVE5Da8vLxU7zUajaqtrxCz2+0AgPb2duTl5aG4uFj1Ki8vVwqpy5nNZnR2dsJqtX6r2M6cOYMf/ehHSE9Px9tvv42ioiKsXr0aAFTruv/++7Fu3ToAvZdeFyxYoMSdmZmJyspKvPjii+jq6sKdd96J22+/XbWdpqYmhISEfKvYiMg9sKgjohtWZmYmysrKEB8fj6SkJNXL19d3wGVGjx4NADh+/LjSlpKSApvNhqKiIqXNYrGgublZeV9UVAS73Y4//elPuOmmmzBixAhUV1f3W//Pf/5zfPHFF1i5ciWOHz+O+fPnq/qNRiPmzJmD1157DZs2bcLbb7+NpqYmpb+0tBRjxoz5LukgouscizoiumEtXLgQTU1NuPvuu/HZZ5/h9OnT+OCDD7BgwQL09PQMuExISAgyMzNx4MABpS05ORkzZszAQw89hMOHD6OoqAj3338/DAaDMiYpKQnd3d1YtWoVKioq8Prrr+Ovf/1rv/UHBgZi9uzZWLJkCXJzcxEdHa30rVixAm+88QY+//xznDx5Em+99RbCw8NVl3n379+P3NxcB2SHiK43LOqI6IYVGRmJgwcPoqenB7m5uUhLS8OiRYtgMpng4XHlX4/3339/vylL1q5di8jISEyZMgWzZ8/Ggw8+iNDQUKU/IyMDK1aswB/+8AeMGjUKGzZsUE1H8nX33XcfrFYr7r33XlW7v78/Xn75ZYwbNw7jx4/HmTNnsH37diXWgoICtLS09LskS0Q3Bo2Ik6ZkJyK6TnV1dSE5ORmbNm1Cdna2w9f/+uuv44knnkB1dTV0Ot03Xm7OnDnIyMjAc8895/CYiMj18YkSRETfksFgwD//+c+rTlL8XXR2dqKmpgbLly/HQw899K0KOqvVirS0NDzxxBMOjYmIrh88U0dE5CJeeOEFvPTSS5g8eTK2bdvmco8hIyLXxqKOiIiIyA3wRgkiIiIiN8CijoiIiMgNsKgjIiIicgMs6oiIiIjcAIs6IiIiIjfAoo6IiIjIDbCoIyIiInIDLOqIiIiI3ACLOiIiIiI38P8B6endzdbucqwAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(days, close, color='gray', alpha=0.6, label='daily close')\n", "plt.plot(smoothed_days, smoothed, color='C1', alpha=0.6, label='30 day average')\n", "\n", "decorate(xlabel='Time (days)', ylabel='Price ($)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing sound signals\n", "\n", "Generate a 440 Hz sawtooth signal." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from thinkdsp import SawtoothSignal\n", "\n", "signal = SawtoothSignal(freq=440)\n", "wave = signal.make_wave(duration=1.0, framerate=44100)\n", "wave.make_audio()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make a moving average window." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "window = np.ones(11)\n", "window /= sum(window)\n", "plt.plot(window)\n", "decorate(xlabel='Index')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the wave." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "segment = wave.segment(duration=0.01)\n", "segment.plot()\n", "decorate(xlabel='Time (s)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pad the window so it's the same length as the signal, and plot it." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def zero_pad(array, n):\n", " \"\"\"Extends an array with zeros.\n", "\n", " array: NumPy array\n", " n: length of result\n", "\n", " returns: new NumPy array\n", " \"\"\"\n", " res = np.zeros(n)\n", " res[:len(array)] = array\n", " return res" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = len(segment)\n", "padded = zero_pad(window, N)\n", "plt.plot(padded)\n", "decorate(xlabel='Index')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apply the window to the signal (with lag=0)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(-0.9001814882032255)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prod = padded * segment.ys\n", "np.sum(prod)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute a convolution by rolling the window to the right." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "smoothed = np.zeros(N)\n", "rolled = padded.copy()\n", "for i in range(N):\n", " smoothed[i] = sum(rolled * segment.ys)\n", " rolled = np.roll(rolled, 1)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(rolled)\n", "decorate(xlabel='Index')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the result of the convolution and the original." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from thinkdsp import Wave\n", "\n", "segment.plot(color='gray')\n", "smooth = Wave(smoothed, framerate=wave.framerate)\n", "smooth.plot()\n", "decorate(xlabel='Time(s)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the same convolution using `numpy.convolve`." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "segment.plot(color='gray')\n", "ys = np.convolve(segment.ys, window, mode='valid')\n", "smooth2 = Wave(ys, framerate=wave.framerate)\n", "smooth2.plot()\n", "decorate(xlabel='Time(s)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Frequency domain\n", "\n", "Let's see what's happening in the frequency domain." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the smoothed wave using `np.convolve`, which is much faster than my version above." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "convolved = np.convolve(wave.ys, window, mode='same')\n", "smooth = Wave(convolved, framerate=wave.framerate)\n", "smooth.make_audio()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot spectrums of the original and smoothed waves:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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hQa7p37+/HOoAIDo6Gunp6cjJyZFryi6ntKZ0OUREREQNgcbTDVTGYDAAAEJCQpxuDwkJkacZDAYEBwc7TddoNGjatKlTTdu2bcvNo3RakyZNYDAYXC6nIiaTCSaTSb5uNBprsnpEREREbldvR+zqu8mTJyMwMFC+REREeLolIiIiauTqbbALDQ0FAGRmZjrdnpmZKU8LDQ1FVlaW03Sr1Yrs7GynmormUXYZldWUTq/IhAkTkJeXJ1/Onz9f01UkIiIicqt6G+zatm2L0NBQbNu2Tb7NaDQiISEBkZGRAIDIyEjk5uYiKSlJrtm+fTvsdjv69Okj18TFxcFiscg1sbGxaN++PZo0aSLXlF1OaU3pciqi0+mg1+udLkRERESe5NFgV1BQgOTkZCQnJwNwHDCRnJyMc+fOQZIkjB07Fp988gnWr1+PY8eOYeTIkQgPD5ePnO3YsSMGDRqEl156CQcOHMDevXsxZswYDBs2DOHh4QCAZ599FlqtFjExMUhNTcWqVavwxRdfYNy4cXIfb775JjZv3ozp06fjxIkTmDRpEhITEzFmzJi6fkiIiIiIbp7woB07dgg4TqXrdBk1apQQQgi73S4++OADERISInQ6nRgwYIBIT093mse1a9fE8OHDhb+/v9Dr9eKFF14Q+fn5TjVHjhwRffv2FTqdTrRs2VJMmTKlXC+rV68Wd9xxh9BqtaJz585i48aNNVqXvLw8AUDk5eXV7EFws9bjN4jW4zeIhz9d69E+iIiIyD1qkjHqzXnsGjqex46IiIhqgyLOY0dERERENcNgR0RERKQQDHZERERECsFgR0RERKQQDHZERERECsFgp1A81JmIiKjxYbAjIiIiUggGOyIiIiKFYLAjIiIiUggGOyIiIiKFYLAjIiIiUggGOyIiIiKFYLAjIiIiUggGOyIiIiKFYLAjIiIiUggGOyIiIiKFYLBTKMnTDRAREVGdY7AjIiIiUggGOyIiIiKFYLAjIiIiUggGO4USnm6AiIiI6hyDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKQSDHREREZFCMNgRERERKcRNBbvc3FwsWrQIEyZMQHZ2NgDg0KFDuHjxolubIyIiIqLq09T0DkePHkVUVBQCAwNx5swZvPTSS2jatCl++OEHnDt3Dt9++21t9ElEREREVajxiN24cePw/PPP4+TJk/D29pZvf+SRRxAXF+fW5oiIiIio+moc7A4ePIhXXnml3O0tW7aEwWBwS1OlbDYbPvjgA7Rt2xY+Pj647bbb8PHHH0MIIdcIITBx4kSEhYXBx8cHUVFROHnypNN8srOzMWLECOj1egQFBSEmJgYFBQVONUePHkW/fv3g7e2NiIgITJ061a3rQkRERFTbahzsdDodjEZjudt//fVXtGjRwi1Nlfrss88wb948fPnll0hLS8Nnn32GqVOnYs6cOXLN1KlTMXv2bMyfPx8JCQnw8/NDdHQ0SkpK5JoRI0YgNTUVsbGx2LBhA+Li4vDyyy/L041GIwYOHIjWrVsjKSkJ06ZNw6RJk7BgwQK3rg8RERFRbapxsHvsscfw0UcfwWKxAAAkScK5c+cwfvx4PPnkk25tbt++fXj88ccxePBgtGnTBk899RQGDhyIAwcOAHCM1s2aNQvvv/8+Hn/8cdx555349ttvcenSJaxbtw4AkJaWhs2bN2PRokXo06cP+vbtizlz5mDlypW4dOkSAGD58uUwm81YsmQJOnfujGHDhuGNN97AjBkz3Lo+RERERLWpxsFu+vTpKCgoQHBwMIqLi3H//fejXbt2CAgIwKeffurW5u69915s27YNv/76KwDgyJEj2LNnDx5++GEAQEZGBgwGA6KiouT7BAYGok+fPoiPjwcAxMfHIygoCL1795ZroqKioFKpkJCQINf0798fWq1WromOjkZ6ejpycnLcuk5EREREtaXGR8UGBgYiNjYWe/bswdGjR1FQUICePXs6hSt3effdd2E0GtGhQweo1WrYbDZ8+umnGDFiBADI+/SFhIQ43S8kJESeZjAYEBwc7DRdo9GgadOmTjVt27YtN4/SaU2aNCnXm8lkgslkkq9XtHmaiIiIqC7VONiV6tu3L/r27evOXspZvXo1li9fju+++w6dO3dGcnIyxo4di/DwcIwaNapWl12VyZMn41//+pdHeyAiIiIqq1rBbvbs2dWe4RtvvHHTzdzonXfewbvvvothw4YBALp27YqzZ89i8uTJGDVqFEJDQwEAmZmZCAsLk++XmZmJ7t27AwBCQ0ORlZXlNF+r1Yrs7Gz5/qGhocjMzHSqKb1eWnOjCRMmYNy4cfJ1o9GIiIiIP7C2RERERH9MtYLdzJkzna5fuXIFRUVFCAoKAuD4JQpfX18EBwe7NdgVFRVBpXLeDVCtVsNutwMA2rZti9DQUGzbtk0OckajEQkJCXjttdcAAJGRkcjNzUVSUhJ69eoFANi+fTvsdjv69Okj17z33nuwWCzw8vICAMTGxqJ9+/YVboYFHEcH63Q6t60rERER0R9VrYMnMjIy5Munn36K7t27Iy0tDdnZ2cjOzkZaWhp69uyJjz/+2K3NDRkyBJ9++ik2btyIM2fOYO3atZgxYwb+9Kc/AXAckTt27Fh88sknWL9+PY4dO4aRI0ciPDwcQ4cOBQB07NgRgwYNwksvvYQDBw5g7969GDNmDIYNG4bw8HAAwLPPPgutVouYmBikpqZi1apV+OKLL5xG5IiIiIjqPVFDt956qzh06FC52xMTE0WbNm1qOjuXjEajePPNN0WrVq2Et7e3uPXWW8V7770nTCaTXGO328UHH3wgQkJChE6nEwMGDBDp6elO87l27ZoYPny48Pf3F3q9XrzwwgsiPz/fqebIkSOib9++QqfTiZYtW4opU6bUqNe8vDwBQOTl5d38CrtB6/EbROvxG8SgT9d6tA8iIiJyj5pkDEmIMj/jUA2+vr7YtWsX7rrrLqfbDxw4gAceeABFRUVujJ0Nh9FoRGBgIPLy8qDX6z3WR5t3NwIAOugt2PzPoR7rg4iIiNyjJhmjxuexGzBgAF555RUcOnRIvi0pKQmvvfZarZzyhIiIiIiqp8bBbsmSJQgNDUXv3r3lAwjuvvtuhISEYNGiRbXRIxERERFVQ43PY9eiRQts2rQJv/76K06cOAEA6NChA+644w63N0dERERE1XfTJyi+4447GOaIiIiI6pEaB7sXX3zR5fQlS5bcdDNEREREdPNqHOxycnKcrlssFqSkpCA3NxcPPfSQ2xojIiIiopqpcbBbu3Ztudvsdjtee+013HbbbW5pioiIiIhqrsZHxVY4E5UK48aNK/fTY0RERERUd9wS7ADg9OnTsFqt7podEREREdVQjTfF3vj7qUIIXL58GRs3bsSoUaPc1hgRERER1UyNg93hw4edrqtUKrRo0QLTp0+v8ohZIiIiIqo9NQ52O3bsqI0+yN1q9AvAREREpAQ13sfuoYceQm5ubrnbjUYjT3dCRERE5EE1DnY7d+6E2Wwud3tJSQl2797tlqaIiIiIqOaqvSn26NGj8t/Hjx+HwWCQr9tsNmzevBktW7Z0b3dEREREVG3VDnbdu3eHJEmQJKnCTa4+Pj6YM2eOW5ujm8dd7IiIiBqfage7jIwMCCFw66234sCBA2jRooU8TavVIjg4GGq1ulaaJCIiIqKqVTvYtW7dGoDj58OIiIiIqP6pVrBbv349Hn74YXh5eWH9+vUuax977DG3NEa1KykpCWazGZGRkZ5uhYiIiNykWsFu6NChMBgMCA4OxtChQyutkyQJNpvNXb1RLbHb7diwYQMAoEuXLggICPBwR0REROQO1Qp2ZTe/clNswyfE74dWVHTqGiIiImqYanweOyIiIiKqn6o1Yjd79uxqz/CNN9646WaIiIiI6OZVK9jNnDmzWjOTJInBrp6QJE93QERERHWtWsEuIyOjtvsgIiIioj/oD+1jJ4Rw2hGfiIiIiDznpoLd4sWL0aVLF3h7e8Pb2xtdunTBokWL3N0bEREREdVAtX95otTEiRMxY8YMvP766/LJbePj4/HWW2/h3Llz+Oijj9zeJN0EDqQSERE1OjUOdvPmzcPChQsxfPhw+bbHHnsMd955J15//XUGuwZA4pEVREREilTjTbEWiwW9e/cud3uvXr1gtVrd0hQRERER1VyNg91zzz2HefPmlbt9wYIFGDFihFuaoj+OW2KJiIganxpvigUcB09s3boV99xzDwAgISEB586dw8iRIzFu3Di5bsaMGe7pkoiIiIiqVONgl5KSgp49ewIATp8+DQBo3rw5mjdvjpSUFLmO+3HVb5dtAbCBzxEREZGS1DjY7dixozb6oDpkswtsNrcHALxbbEEzD/dDRERE7vGHTlBMDZO9zEmljSU84IWIiEgpajxiV1JSgjlz5mDHjh3IysqC3W53mn7o0CG3NUe1jz8cQkREpBw1DnYxMTHYunUrnnrqKdx9993cl46IiIionqhxsNuwYQM2bdqE++67rzb6ISIiIqKbVON97Fq2bImAgIDa6IWIiIiI/oAaB7vp06dj/PjxOHv2bG30Q0REREQ3qcabYnv37o2SkhLceuut8PX1hZeXl9P07OxstzVHtU/w6AkiIiLFqHGwGz58OC5evIh///vfCAkJ4cETRERERPVEjTfF7tu3D2vWrMH48ePx/PPPY9SoUU4Xd7t48SL+8pe/oFmzZvDx8UHXrl2RmJgoTxdCYOLEiQgLC4OPjw+ioqJw8uRJp3lkZ2djxIgR0Ov1CAoKQkxMDAoKCpxqjh49in79+sHb2xsRERGYOnWq29elvmAUJyIiUqYaB7sOHTqguLi4NnopJycnB/fddx+8vLzw888/4/jx45g+fTqaNGki10ydOhWzZ8/G/PnzkZCQAD8/P0RHR6OkpESuGTFiBFJTUxEbG4sNGzYgLi4OL7/8sjzdaDRi4MCBaN26NZKSkjBt2jRMmjQJCxYsqJP1JCIiInKHGm+KnTJlCt5++218+umn6Nq1a7l97PR6vdua++yzzxAREYGlS5fKt7Vt21b+WwiBWbNm4f3338fjjz8OAPj2228REhKCdevWYdiwYUhLS8PmzZtx8OBB9O7dGwAwZ84cPPLII/j8888RHh6O5cuXw2w2Y8mSJdBqtejcuTOSk5MxY8YMpwBIREREVJ/VeMRu0KBBiI+Px4ABAxAcHIwmTZqgSZMmCAoKchpJc4f169ejd+/e+POf/4zg4GD06NEDCxculKdnZGTAYDAgKipKvi0wMBB9+vRBfHw8ACA+Ph5BQUFyqAOAqKgoqFQqJCQkyDX9+/eHVquVa6Kjo5Geno6cnJwKezOZTDAajU4XIiIiIk+q8Yjdjh07Kp127NixP9TMjX777TfMmzcP48aNwz//+U8cPHgQb7zxBrRaLUaNGgWDwQAACAkJcbpfSEiIPM1gMCA4ONhpukajQdOmTZ1qyo4Elp2nwWCoMLBOnjwZ//rXv9yzokRERERuUONgd//99ztdz8/Px4oVK7Bo0SIkJSVhzJgxbmvObrejd+/e+Pe//w0A6NGjB1JSUjB//vxaOVCjJiZMmIBx48bJ141GIyIiIjzYERERETV2Nd4UWyouLg6jRo1CWFgYPv/8czz00EPYv3+/O3tDWFgYOnXq5HRbx44dce7cOQBAaGgoACAzM9OpJjMzU54WGhqKrKwsp+lWqxXZ2dlONRXNo+wybqTT6aDX650uDRHPYkdERKQcNQp2BoMBU6ZMwe23344///nP0Ov1MJlMWLduHaZMmYK77rrLrc3dd999SE9Pd7rt119/RevWrQE4DqQIDQ3Ftm3b5OlGoxEJCQmIjIwEAERGRiI3NxdJSUlyzfbt22G329GnTx+5Ji4uDhaLRa6JjY1F+/bt3b7fIBEREVFtqXawGzJkCNq3b4+jR49i1qxZuHTpEubMmVObveGtt97C/v378e9//xunTp3Cd999hwULFmD06NEAAEmSMHbsWHzyySdYv349jh07hpEjRyI8PBxDhw4F4BjhGzRoEF566SUcOHAAe/fuxZgxYzBs2DCEh4cDAJ599llotVrExMQgNTUVq1atwhdffOG0qVVJeFJpIiIiZar2PnY///wz3njjDbz22mu4/fbba7Mn2V133YW1a9diwoQJ+Oijj9C2bVvMmjULI0aMkGv+8Y9/oLCwEC+//DJyc3PRt29fbN68Gd7e3nLN8uXLMWbMGAwYMAAqlQpPPvkkZs+eLU8PDAzE1q1bMXr0aPTq1QvNmzfHxIkTeaoTIiIialCqHez27NmDxYsXo1evXujYsSOee+45DBs2rDZ7AwA8+uijePTRRyudLkkSPvroI3z00UeV1jRt2hTfffedy+Xceeed2L179033SURERORp1d4Ue88992DhwoW4fPkyXnnlFaxcuRLh4eGw2+2IjY1Ffn5+bfZJRERERFWo8VGxfn5+ePHFF7Fnzx4cO3YMb7/9NqZMmYLg4GA89thjtdEjEREREVXDTZ/uBADat2+PqVOn4sKFC1ixYoW7eqK6xPOdEBERKcYfCnal1Go1hg4divXr17tjdkRERER0E9wS7IiIiIjI8xjsiIiIiBSCwU6hqrvrnBDcyY6IiEgpGOyIiIiIFILBrhHiKB0REZEyMdgpVXWzG382loiISDEY7Bo7Dt4REREpBoMdERERkUIw2BEREREpBIMdERERkUIw2BEREREpBIMdERERkUIw2BEREREpBINdI8eznRARESkHgx0RERGRQjDYERERESkEgx0RERGRQjDYERERESkEg10jJwQPnyAiIlIKBjsiIiIihWCwIyIiIlIIBjuFqu4GVm6IJSIiUg4GO3KJ++ARERE1HAx2jVB1w1p+fj6mTp2Kn3/+uZY7IiIiIndgsGvkJEmqdFp8fDxKSkpw4MCBOuyIiIiIbhaDHREREZFCMNg1ctyHjoiISDkY7BSq8g2sREREpFQMdo0cB+yIiIiUg8GOiIiISCEY7KhSro6YJSIiovqHwY6IiIhIIRjsiIiIiBSCwa4R4vESREREysRg18hxNzoiIiLlYLBr5Hi6EyIiIuVgsFMo5jUiIqLGp0EFuylTpkCSJIwdO1a+raSkBKNHj0azZs3g7++PJ598EpmZmU73O3fuHAYPHgxfX18EBwfjnXfegdVqdarZuXMnevbsCZ1Oh3bt2mHZsmV1sEZERERE7tNggt3Bgwfx9ddf484773S6/a233sJPP/2ENWvWYNeuXbh06RKeeOIJebrNZsPgwYNhNpuxb98+fPPNN1i2bBkmTpwo12RkZGDw4MF48MEHkZycjLFjx+Kvf/0rtmzZUmfrR0RERPRHNYhgV1BQgBEjRmDhwoVo0qSJfHteXh4WL16MGTNm4KGHHkKvXr2wdOlS7Nu3D/v37wcAbN26FcePH8d///tfdO/eHQ8//DA+/vhjzJ07F2azGQAwf/58tG3bFtOnT0fHjh0xZswYPPXUU5g5c6ZH1peIiIjoZjSIYDd69GgMHjwYUVFRTrcnJSXBYrE43d6hQwe0atUK8fHxAID4+Hh07doVISEhck10dDSMRiNSU1PlmhvnHR0dLc+DiIiIqCHQeLqBqqxcuRKHDh3CwYMHy00zGAzQarUICgpyuj0kJAQGg0GuKRvqSqeXTnNVYzQaUVxcDB8fn3LLNplMMJlM8nWj0Vjzlavn+JNiREREDUu9HrE7f/483nzzTSxfvhze3t6ebsfJ5MmTERgYKF8iIiI83dLN4flOiIiIFKNeB7ukpCRkZWWhZ8+e0Gg00Gg02LVrF2bPng2NRoOQkBCYzWbk5uY63S8zMxOhoaEAgNDQ0HJHyZZer6pGr9dXOFoHABMmTEBeXp58OX/+vDtWuc65inVCCFyyBaBQeNVZP0RERHTz6nWwGzBgAI4dO4bk5GT50rt3b4wYMUL+28vLC9u2bZPvk56ejnPnziEyMhIAEBkZiWPHjiErK0uuiY2NhV6vR6dOneSasvMorSmdR0V0Oh30er3TRWlSrtmxxdweq0u6eboVIiIiqoZ6vY9dQEAAunTp4nSbn58fmjVrJt8eExODcePGoWnTptDr9Xj99dcRGRmJe+65BwAwcOBAdOrUCc899xymTp0Kg8GA999/H6NHj4ZOpwMAvPrqq/jyyy/xj3/8Ay+++CK2b9+O1atXY+PGjXW7wvVMWrbd0y0QERFRDdTrYFcdM2fOhEqlwpNPPgmTyYTo6Gh89dVX8nS1Wo0NGzbgtddeQ2RkJPz8/DBq1Ch89NFHck3btm2xceNGvPXWW/jiiy9wyy23YNGiRYiOjvbEKhERERHdlAYX7Hbu3Ol03dvbG3PnzsXcuXMrvU/r1q2xadMml/N94IEHcPjwYXe0qBg8KpaIiKhhqdf72BERERFR9THYERERESkEg10jJ1ye8ISIiIgaEgY7IiIiIoVgsCMiIiJSCAY7+sOEELh27RoEf56MiIjIoxjsqFLVPdnJzp078eWXX5b79Q4iIiKqWwx29IfFxcUBAPbu3evhToiIiBo3BjsiIiIihWCwIyIiIlIIBrtGzuXxDvxFMSIiogaFwY4qxVxHRETUsDDYERERESkEg10jVN3TzfGsdERERA0Lg10jJ3F7KxERkWIw2BEREREpBIMdVYqDeURERA0Lg10jx593JSIiUg4Gu0ZOMNkREREpBoMdERERkUIw2CmUO8bhuI8dERFRw8JgR0RERKQQDHZERERECsFgR0RERKQQDHZUZ9LS0rBu3TpYLBZPt0JERKRIGk83QI3H6tWrAQBNmzZF//79PdwNERGR8nDEjupcQUGBp1sgIiJSJAY7qpQk8YQnREREDQmDHREREZFCMNgRERERKQSDHREREZFCMNhRnRPCHT94RkRERDdisGvk3JGxsu0+iDW1wzW7zx+fGREREd00nseO/rCfTe1hhgaXTQGY7elmiIiIGjGO2ClVNUfiRHULXTBf///ABvUfnhcRERHdPAY7IiIiIoVgsFOohnx4woULF3Dx4kVPt0FERNTgMNg1QvX5qFSTyYTFixdj0aJFsNlsnm6HiIioQWGwa+Qk1P3PhrkKliUlJfLfVqu1LtohIiJSDAY7haruz7y6GrvjL8USERE1LAx2RERERArBYEf1ilTdoUYiIiIqp14Hu8mTJ+Ouu+5CQEAAgoODMXToUKSnpzvVlJSUYPTo0WjWrBn8/f3x5JNPIjMz06nm3LlzGDx4MHx9fREcHIx33nmn3P5bO3fuRM+ePaHT6dCuXTssW7astlfPY8pufq3PB1LU596IiIjqo3od7Hbt2oXRo0dj//79iI2NhcViwcCBA1FYWCjXvPXWW/jpp5+wZs0a7Nq1C5cuXcITTzwhT7fZbBg8eDDMZjP27duHb775BsuWLcPEiRPlmoyMDAwePBgPPvggkpOTMXbsWPz1r3/Fli1b6nR9PYEDZERERMpRr39SbPPmzU7Xly1bhuDgYCQlJaF///7Iy8vD4sWL8d133+Ghhx4CACxduhQdO3bE/v37cc8992Dr1q04fvw4fvnlF4SEhKB79+74+OOPMX78eEyaNAlarRbz589H27ZtMX36dABAx44dsWfPHsycORPR0dF1vt71BUMfERFRw1KvR+xulJeXBwBo2rQpACApKQkWiwVRUVFyTYcOHdCqVSvEx8cDAOLj49G1a1eEhITINdHR0TAajUhNTZVrys6jtKZ0HlT/WK1W7NixAxcuXPB0K0RERPVGgwl2drsdY8eOxX333YcuXboAAAwGA7RaLYKCgpxqQ0JCYDAY5Jqyoa50euk0VzVGoxHFxcUV9mMymWA0Gp0u9MdV9+CJ/fv3Iy4uDosXL67ljoiIiBqOBhPsRo8ejZSUFKxcudLTrQBwHNgRGBgoXyIiIjzd0k3xxPEJrg6KqO4BE1euXHFXO0RERIrRIILdmDFjsGHDBuzYsQO33HKLfHtoaCjMZjNyc3Od6jMzMxEaGirX3HiUbOn1qmr0ej18fHwq7GnChAnIy8uTL+fPn/9D60jl8ahYIiKimqnXwU4IgTFjxmDt2rXYvn072rZt6zS9V69e8PLywrZt2+Tb0tPTce7cOURGRgIAIiMjcezYMWRlZck1sbGx0Ov16NSpk1xTdh6lNaXzqIhOp4Ner3e60B/H89gRERHdvHp9VOzo0aPx3Xff4ccff0RAQIC8T1xgYCB8fHwQGBiImJgYjBs3Dk2bNoVer8frr7+OyMhI3HPPPQCAgQMHolOnTnjuuecwdepUGAwGvP/++xg9ejR0Oh0A4NVXX8WXX36Jf/zjH3jxxRexfft2rF69Ghs3bvTYuhNDHhERUU3V6xG7efPmIS8vDw888ADCwsLky6pVq+SamTNn4tFHH8WTTz6J/v37IzQ0FD/88IM8Xa1WY8OGDVCr1YiMjMRf/vIXjBw5Eh999JFc07ZtW2zcuBGxsbHo1q0bpk+fjkWLFjXoU50oYSumuzbFcpMuERE1FvV6xK46X8je3t6YO3cu5s6dW2lN69atsWnTJpfzeeCBB3D48OEa90ieUd3RvOPHj2PDhg146qmncOutt9ZyV0RERJ5Vr0fsyLOUsCF0zZo1KC4uxn/+8x9Pt0JERFTrGOyoXuF+dURERDePwY4q5+aQVSi8cMGmV8T+f0RERPVRvd7HjpRldUk3AEDrbDseq0Y9D3ogIiKqGY7YUZ37NdfTHZQXHx+PZcuWwWw2e7oVIiKim8ZgRy7UzoiZO+bq7n3xtm7dirNnzyIxMdGt8yUiIqpLDHaNHDd3OrNYLJ5ugYiI6KYx2FGdY5QkIiKqHQx2VCnJw2ey88RoYlXL3LJlC/bs2VNH3RAREdUMj4pt5DwyeuZiofX5PHZXrlzB/v37AQB9+/b1cDdERETlccSO6lx1w2R9C3nc/46IiOo7Bjuqt+rbgR3VDZp2ux0nTpxAQUFBLXdERETkjMGOGqT6NppXVmJiIlatWoV58+Z5uhUiImpkGOyI3OzXX38FABQVFXm4EyIiamwY7KjO1a8NrM7qcvPvtWvXsG3bNgZAIiJyGx4VS1RN7t78u2DBApjNZly5cgXDhg1z67yJiKhx4ohdI+eR4xOqucz6dvBEdVU3AJb+Lu25c+eqrMvLy/vDfRERkfIx2DVG9Tgw1eeDIsqqy9A5Y8YMzJo1Czk5OXW2TCIiapgY7Bo5T+SoqiKRVahgFQ0j4NUFk8kEAPjtt99c1hUWFvJce0REjRz3saNKeWL0zGKz4z8lPSHBjndcjIo1lJG96nDH6F9RURE+//xzeHl54Z///KcbuiIiooaII3ZUr1wtcOx3JqBCsdlW58t3FbLKhsn69ju2Fy5cAFD1r2PYbDYcO3aMJ08mIlIoBjuqt+rvnoCueWI0sbrLjIuLww8//ICFCxfWckdEROQJDHZUr5TNJ/X4GA+PcMcoYXp6OgDAaDS6rEtNTcX8+fNx7dq1P7xMIiKqOwx2jZyrrFBb406ulqmSfn9JeuRMLNUMT+7cFFsfT+vy/fffIzMzE2vXrnVZl5GRgeTk5LppioiIqsSDJ6heKTtiZ7fbXdQp5+AJd6ju41HTx630iNzKfPvttwCAkJAQhIWFVVp36dIlBAQEICAgoEbLJyKimuGIHdU5V+NT9XH0qlRthSclcHUC5StXrmDhwoWYMWOGy3kIIXDlyhWXgZ6IiFxjsKN6paFEovp2VKynuert/Pnz1ZrHgQMH8NVXX1W5+ddiscBgMNTrx4OIyFMY7KjOufw6boQHT7gjoNTWaGJd9rZnzx4AQEpKisu6b7/9Fl9//XWVdVlZWdUOlURESsFgR5VqhFsU3aK2NsVyhMqh9Jx9hw4dclk3b948LFmyBPn5+ZXWCCGwe/dunDlzxp0tEhF5DIMdVcrTOaI+HxXbWLjjKGFP75voav+/48ePY/v27fjmm29czuPy5ctYtGgRMjIyXNbZ7XaXQZKIqLYx2CmUqGYs8kyQcRECUL1fd7AJ4IS1BXLt3m7tzBVP//IEOXNH6MzJyanWPJYvX46LFy/KRwFX5r///S9mzJiBs2fPuqxLTU3FkSNHqlwuX2dEVFMMdlT3XJ07z2kfu8oL9xokxFtaY62pixsb84z6vI+dOyjhKOHCwsJq1ZWO6CUmJlZaY7PZ8P3332PdunUu55ufn48ZM2bgl19+cbnM4uJiJCYmori4uMr+GBSJlI/Bjuqeiy/6slNcfQWdaYRbu+rzkbh1GU5rusz6tpm47OlczGZzpXV79+5FQUEB9u7d63J+a9aswcaNG7FmzRqXddu3b8esWbOq/J3g48ePy79Q4orZbGZQJKqHGOyoUrU10OL6i7ZsYeXz8PQYkDvCgjspYcROCSN7peoyEJeOEla1/9/u3bthNBrlo48rUlRUhDVr1mDlypWw2WyV1hkMBkyePBnr1q1zuczSXy+papN3fn5+tY5gZpAkqhqDHdVbjeUjXAlfVvV5HerbiJ2ng66rx6PsCKKrE0WXjiIePXrU5bIWLlyIo0ePYuXKlS7rZsyYgSVLlshHPFfEbrdj4cKFWL16tct5lZSUYNOmTVUGRbPZjNOnT7sMsIDj8aqqhqg+YbCjOucqAkjVHIvzzGiickaUqquhBjZP88RvDldXXfZWGoiysrKqVe/qtDOXLl3C5cuXkZaW5nIe27Ztw8GDB7FkyRKXdd999x3++9//YteuXS7rVq1ahWnTpqGkpKTSGiEEfvzxR8THx7ucl9lsxv79+6scwbRardU6CbcQol6/D8gzGOyofqlmdvJ0xKpvX8ieHgVyxzI9MULl6RM717d/JKp75Hd9PlfjtWvXqlVXeuRyVedDTE9Ph8lkchkoz5w5g+TkZGzdutXlvLZt24YtW7Zg/vz5LutWrFiBr7/+usreVq9ejdmzZ8NqtVZaY7fbsXr1auzfv9/lvIqKirB9+3ZkZ2e7rCssLMSvv/5a5U//mc1mHtDjIQx2VCmPDFCJCv8sx9PBrrFQwsiTO3g6ZLlTdQNbfQt2ng6T1d2E7UrpiGRV9b/99hsA4ODBgy7rTpw4gdzcXJf7V6ampiItLQ1btmxxOa/169dj9+7dWLBggcu6efPmYcWKFUhKSnJZN3nyZEydOhUmk6nSmuLiYsyaNQubN292OS+DwYBly5ZVuXn9zJkz2Lx5MywWi8u606dP4+TJky5rhBA4d+4cioqKXI6MCiFgNBpdzquuaTzdAHlWff5vydV/hDX5jC8RGnhLlf9HW1Zdj+6YhBrqKje3ADZIHjny1B08vQm7oYaF+szTwU4IUWkPnu6trpZZ3bqyIbI0oKhU5cd0SkOTyWRCUVERvL29K6wrPUVPWloaWrZsidDQ0ArrSmVkZEClUuH2228v9zgdPHgQRqMRCQkJuPXWWyGEQPv27cvNY/ny5SgoKMCSJUtw77334vbbb0ebNm3K1ZWeaNxoNMJut+Ohhx5CcHCwU43VasV///tfAED//v1x6tQpPPfcc/D2dj4n6qlTp/Ddd9/By8sLTZo0gVarxYsvvlhuHXbv3o0dO3ZgwIAB6Nu3b6WPQ13iiB3VvWp+l7ljxC7ZEoYVJd2RZm1RzXtUT1UfuPl2LezCdZdJlpb4rqQHTluauKzbYr4D/ynpBaPJ9aaPK3Y/GO26RhMW6vOIXX0O4TUJT9VZD5vNVq260pEPV+x2O65du1ZhXdneCgoKkJmZWeE8ytadOXMGV69edblMs9mMpKSkKkddrl69iri4uApH28ou8+jRo5Xut1e27scff6xyU2tWVhYWL16M06dPu6w7cOAAZs+eXeG+e2WXuWTJEsyePbvCg0HK1k2bNg2LFy92ucyMjAwsXLgQGzZscFm3atUqrFixosLfdi67zBUrVmDlypUVjvCVPUXPvn37qvylmLS0NKSnp1dYV3bd4+LicOnSpQr3jSwd0bNYLMjKysKFCxcqHGzYsWMHAMdm9vqCwY7qnFu+jqv5nXfY2hIAsN/S2h1LrZbjeWp8b7oTW823u6w7ag0DAOwz3eLyC++yXQ8AOHjZUukopiHfgg2mjvifqSuEEC73uSkUXhDCcfRgVfvJCCGQl5dX5Rey1WrFlStXKpxW9sPbaDRW+UULOPZ/quqL1mKxIDU11eVO7YBjn6vDhw9XuK5le0tPT8fx48er7G3Xrl04d+6cy5qcnBxs3Lixwi/aso9lWloafvzxR5fPFwBs3ry5Wl8cS5cuRXJyssuakydPYs6cOS6PQC1d5hdffFHhflJlH7eZM2di0aJFVfY2bdq0Kk+PEhcXhy+//NLlCZ4Bx1G08+fPr/C1VLa3b775BnPnznU5L6vVig0bNlS5CXL//v3YsWMHYmNjXS5z7dq12LlzZ4WPb9m65ORk/PTTTy6XCTh+G7l0hKkyp0+fRk5OToWbNMsu88KFC8jLy6swFN/4j8SlS5eq7A0ADh8+XK26qsJpKVebbmuqqKio3G0V/cNU0abbiuoayj/NDHYNjN1ux7T/7UH8ceefLNpx+CRW7/r9J4pKLALT1+xA5rVcp7q9h1NxKev3D8PLWVfw0y9xTl96VqsVJ06cgNX6+382hw4dKvcTSEVFReX27diyZUu5n1PKyclx+gAuKSnBjz/+iNxc594yMzNRXOZL+sSJdKxfv97pPywhhONDqcz7a9OmTdi9e7fTvKxWa7n5//e//y23A3RJSYnTB8np06exePHiciHl9/0sHJtGt2/fjiVLlpT7Qi4pKcG+K449HC7b9Vi0aFG5D28hhNMHiQAwffr0cl9mN46EnM7IwOTJk8t9YdjtdpzN+X0dFi9ejClTppT7gBRCIK3AG6tLuiHO0hafffYZvv76a9yo7DKNRiNmzZqFjRs3lqsra/369fjqq6+Qmprqsm7mzJmYO3dulR+4y5Ytw8yZM13OKysrC99//z1WrVrlsm7jxo1Yv359lfsErVy5EmvWrKmwt7J27tyJpUuXVtlbYmIi/vOf/7is27FjB5KTk5GQkFBuWtnHIyEhAXv27KkyAJ47dw4//vijyxqj0Yjs7OwKe7tx5CkvL6/Kx62wsLDaIaCq06OUiouLc9lbqYr2ubrZkc7q/rpIdc63V9n8anu3hD8SUGq7t6r+sapp3c2q7uNR0eblhhLsuI/dDebOnYtp06bBYDCgW7dumDNnDu6++25PtyWbv+kg5h7Mw9yDeTgz5fdRqBdW/epUd8msw5ykImw9sQ1bPngSALD3yK8YseoMdLAA8AIAfLgrBwISCu0JGDYwEgCw6H9bsCC5CF6SDUAAAGD8/45CDYGfOnWCl5fjvp/NXYzfjBKAtvJy1+xNQ7P4JHw26Z8AHG+E2bNnX5/aGwBQXFKC5OQ0XLp0Ca+99hoAx4flkiVLUCI0ALoDcOy74K+yIDw8HL17O+67fft27NmzB1fNrQA49p0o3cG4X79+ch9LlizB5cuX5WUCjtB2+vRpfPjhhwAcwemzzz5zetxKT8uwevVqjB492vFYXrqEhQsXIqhJU6wzdYKvZIF0fZkpKSno3t3Rb3x8PLZu3YoiUzsAQQCAixcv4uLFixgyZIi8jNWrV+PEiRNybwISCgsLsXHjRnk9bTYbZs+eDT8/PwAtrz9uJlg1Vqxfvx5/+9vfAABXrlzBokWLUBLUBoBe7hdwbCrp0KEDAODIkSOOUZ/cWwEAv9ma4X5klDsNxcaNG/Hbb7/hki0AqdYQRHqdhb/KgqSkJDz66KNyb0uWLCm37wrg+Cmtzp07A3Bsulq5ciWaN29eri47Oxu+vr4AHDt3x8XFVXk03i+//AKDwVDu9rKnyLDZbFi5ciUiIiLK1Z09exZ33XUXAMco3k8//QRvb29YhAoa2OX9NktKSuTeTpw4gcTERFgsFghR+b6dcXFxFY4wlh2xs9lsWL9+fYW9lb1vdnY2tm/fXuEmv7JfeqdPn65w89aN9u/fX2EgLDt/m82G2NhYhIWFuVxmbm4u4uPjkZeXV66u9EtPkiScOXNGPgCgorrSL9fDhw9DrVZXuMzSOqvVin379iEgIMBlXV5eHo4cOVJhMC/b24ULFyoNona7Xf5CT01NLbffVWmNzWaDWq2G1WqtdMSq9Px3arUa+fn5SE9PrzB4la6DWq2GwWCo9H1gsVig0WggSRJOnjwJf3//CpdpNpuh1Wphs9mQlpZW4eNht9tRUlICb29vFBUV4cyZMxUGqtJ+vby8cPXq1Ur/6SkqKoKPjw8kScLZs2eh1+sr7C0/Px8BAQGw2Ww4c+ZMha9Lm82GgoIC+Pv7o6SkpML3fOky1Wo1dDodcnNzKz1gIicnB3q9Xn58fXx8KlzmlStX0Lx5cwghcPny5Qofj5KSEuTn56Np06awWCzV/q3puiaJhhJB68CqVaswcuRIzJ8/H3369MGsWbOwZs0apKenV/glVpbRaERgYCDy8vIqfFG7yyvzfsaWs44X3PNdfbEmNQ9j+7XEp7sqP0/UA6FWXDSaERKgw57M8h+iANAloAQtvExoHuCNDWclFENbYd2iIcGI3Z2A/nd3x+ituahom6gadiwc6IfDh5MxZMij+OuyAzBDA4Pd8cHsCzN8JQsitWcR2b4liouL4evrh61pWfCVzNho6ggAeEyXCgnA3Xe0RG5uLm655RZ5M1O8uRVO2BzPyQs+jpGuxx57DLGxsYiKipJHyZYW/x7sSuvuuusu/Prrr/i///s/fP/995U+bq1bt4ZKpXKMiJ09i2t2H6w3OULL896JkCSgU6dOuHjxIjp06CCPuvxiaofz9iCnZQ4cOBBxcXEYMmSI/NNPpb2pYcNIH8eXQ5cuXXDx4kX07du33Drc7XUOnTVZkCQJISEh0Ov1yMnJwZUrV3DJFoAt5vZOy7zzzjtx+vRp9OrVSx4B+amkI64KP6e6fv364cCBA3jqqaewfPlyp2WGq4yI1jn+abjttttgNBrRs2dP+Qi7fLsWJfBCC5VjdEKn08HPzw9hYWG4fPlypV9SPXv2REpKCh588EGXR+v16tULKSkpGD58OJYtWwbAsSnZYAtAW3UOVJLj46tly5aw2Wzo0KEDdu7cCQDYbW6DAqFFtPZXqCTIX4Tt2rXD6dOnkZ+fj0LhhdUl3RCuykO0zrFPTe/evZGUlITHHntMHv26ZAvATvNtiPQ6i7Yax4d5x44d8dtvv2HkyJFYuHAhAOCyLQBnbUHo7XURGsnxPm3WrBl8fHzQpk0b+VcfLMIRHryu1wQFBaGoqAjdunVDampqpV+gd999Nw4cOICnn37a5Yl6W7VqhczMTIwaNcrlJkY/Pz80b94coaGhFY4alvZ/7do13HfffUhMTKx0U1mPHj1w+PBh/OUvf3HadHhjIG7evDkKCwsxbNgwp5HPG+s0Gg1at26NoKCgSkcNW7RogStXruDBBx/E7t27Kx3R7NChA06cOIEXXnjB5Wirn58f7HY7nnzyySo3f7Zr1w5+fn7ltmSUXc+rV68iOjoaW7durXS0JzQ0FAaDAS+99JL8OqqMVqvFE088UeUJn++44w5otdpKg3/pd9XgwYNdjsZrtVqYzWa8+uqrVZ6iRa1W409/+pPLz1QAaN++PSRJuv7PbXk+Pj4oLi7G448/XuXoMwCMHj26ys3tKpUKQ4YMqXJ+HTt2hMViwalTpyqdj91ux1NPPVXhepYOGtSGmmQMBrsy+vTpg7vuugtffvklAMd/NREREXj99dfx7rvvurxvXQS7GWv3YnZCbq3M21MCpWKYhAa+khnZ1wPHje7SnIcVKvhIFnjBhmRrOAAgTzj+8+qquQxvWNFBcwXFQgOtZINFqHFN+GK7uZ08n2e8j8AbFqgqGHUpEl7It+sQoq78dzRz7N5YZ+pyfV7JMAsNglQl8heSEECu8MYhS0ucszsOiLjX6wz8JTOCVQWwQgUdrCgQOuQJb/xSZh+8W9XX0EF9BT6SBRrJBm9Ycd4eBB2s+NnsGHW7RZULFQTu0Z6DSWjgJ5mhgR2/2ZoCAPZYHCOn93mdQZ7wRi/NRRQILfwlE6xQIdMegMOWcFy7/jjf43UWQVIJQlT5sEOCGgJWqGASaqwxdQMA+Esm9PU6g+aqQjmElBICWFbiCIBP6o4hQDK5PFrZ1YgXABQLDY5awnCH5gqaqCreb04IYGVJN5TAC700F9BKnQu9VOL0nJqEGhrY8W1JLwDAQ9pT0MCOcJVjVKy0B6NdhzO2Jkiy3gIAeESbBgEJoeoClH4qCgAFQocfTZ1gheOfoge1p9BMKkKAyiyvk0WoYIeE70p6AAA6awxoqTIiRJUPjfT7R6wQjnkuL+kBK9T4i/chmKGGn1TBSI4AjlnDEKYyIlhdvc2ErggBWKCGVnL9KwqnrM2ghh2t1bkwQwXvCuqLhQbbTO1wh+bq9XW0l1sHIYAMW1Pss7TGA1rH/lXNVUVOR6iXPh4JllY4ZwvCI7oTyBE+uEVllEN7aR0AbDffBj/JjDu9DCgWGjRTld//zyJUOGINQxt1jvweufG1CwBWISHb7osWqsI6O7WTEMA14YsgqRiq6/uTVPR5VGDX4pw9EHeoryJPeCNIKoFaKv9VfcbWBPl2Le7QXMVVux/CVUandSl93A5bw9FMVQS9VAIrVGihKv+Pg0mokWYNxm3qayiBF/wkE3wrOJtAkfBClt0frVQ5yBc6BEimCteh9D2hk2xVvvfdpexr3CTU0FXyWjfadRAAvCUr8oUOzSt4PIQAztqD0EwqQpHQQi3ZK6wzCTXO2oLQRp2L9/4xTh7tdzcGu5tgNpvh6+uL77//HkOHDpVvHzVqFHJzc8slfZPJ5PSfq9FoRERERK0Fu49W7MKSI65/vJuqxwtWWKCBFlaYoYEadtjK7G6ql5xDhUloYIIGEgQEz6Dnkg4W+NzwZWCBCoVCBwAIkio/YWmuKL+JRC+VwCi84Q0LSq7vPtCYOR4/54/sXOH4IvGGBd4VBMQb60r5wgzt9efKAjUKha7ce6Esf8mEguvPY31TnfemF2zwk0zIFb7wgg0WOG+9UMGOQKn8PxQ5whca2OAvmSFVcuiXDSoYhbfcR+mySjvKFT5Qwy7/c3AjLazwk8zIEbUTCv4oH1hQXMX7zwdmaCQ78it5v/rCDF25zwY1CoQO3rDAx8Vrt5T5+uvUB+YKT2FV2eNX+lwUCJ38uV9ZXaHQ4mbPlNpVcxk/ffLXm7pvVWoS7LiP3XVXr16FzWZDSEiI0+0hISEVDhlPnjwZ//rXv+qqPVwrcN+RQo2d5frLvvTNfeMXmVGU368GAENdNZjgBZOo/AugovDmSulzwVDn4OrxK4EXSlw89jcqghZFwnmXi8pCHYB6G+qA6r03LVDL4fbGUAcAdqgqDQZWqKv12i3to+yyys6jMmZoYBb19+u4qlDnqNHK/3NU9H6t6PVWqqav3WJoUVzJvCpSWOa1W1mou7HuZpSoavb5Vlvq7yupnpswYQLGjRsnXy8dsastLz7UBW1anMGek1flj7DS/x1VkuP/C8f/ir9PLf3r96OABFQ3nKeq9Lpwqr8+vxuGzyX8fl2I6//TXK+VrvdTUW+lY8Jl74sy0+X5Sb/Pwy6u3/f6tNK/cb3OLgBvDaBTAfkWoJlOwCIgf3RahQR/LwGNBNjkBTpO8huoFSi2qaBVCZhsjnlr1UCRVUKA5vdNNpL0+0mBcy0qBHgJWOwSJAioJaDYCvh5CVwzqaBVATa740FRAbBDglYlUGyVICTAXwMUWABfjYDJJsFLJWCxO5adZ5ag1wJGM+B7/R1ph2M+vhqBEpsEmwCKrI75GC1AgBdgtgMaCdCoAG81UGwDSmwSVBBQXe/P3wvwUgEWO6CWHDuZ2wWgkQRK7BKEAPw0AgVWCf4agSKbBJ3qeo9qoIlWINskoYlWINfsWC8ftUCuWUJTnaP/EquArwYwWhx1ZZVuos6zSPBRA1q1+P3FUfqiKfMCyzZJCNIK5JklR++SQJHV8VxI15el1wI5ZglNtQJXTRKsdsc6mu0SfNV2FFolNL+ezY1mQKcGCq3X18sOqCVH31Y7EOAlYLSoYBelfzse20KrBG+1QInV8dqwi98v3hrH4+yrtqPAKiHACyiwSPDX2OHvBeRaJDTxErhicjy+ahVgtgE+aqDYJqG5t4BNOF4v3hoJRgsQ5CVgKJagloBgb4Esk4QWOgGjxfE4FFsdo1L+XuUeMgBAZrGEFt7i9/dTBQ+xTUgwmoGg649baX3p2+OaSYLeC7Bcf9N5qSQUWgG91+/1AHClxNFbnkVCgJeQX3NqlYQrJYC/RqDQqoKPRqCJVuCaSUJTnUCOSUKgViDfAhRZVfD3EnI/3hoJBRbHsrLNEppd79Fidzx/JpuEYJ/f369qCSiyCgR4AVdLJGhUjtfqlRIJIT6O12ygVqDQKkGrcjwGJptAoBaw2CXkW4CmOoFrJY7n40qJo8ffP0t/f/xKbBKKrEATnajoJSvLM0vQqZ2XJdcLx+PbzFvg6vVl5Vsk+GgAi03AKoBAL8Bkdywr6Prj1rxMfY5JQoldQpCXHTlmx2tcur4sP43jdddUK5BZ7OhKo3Ksa4iPHQUWCd4ax+vXYhPw0QCZJSr4qAWKrY73T7CPY5lNtI7XnZ8GMNmAHDPQXOf47CixAXovIMcENLv+uDXXOe4XpHV8rmSbHfcVAMw2AV+NhDwL0KzMZ0PZ74Ls6+91nUo4fedU9r1xzSwh0AvQqITTcyCuv8bzzI7XwtXr76Gr1z9TNCrH50uAF2AVgP36+y/fAgR6OdYl2FtAkn5/Pzle447PHUkCvFQSckyAt1qg2OZ43TXXOZ6jNi380avjfagPGOyua968OdRqdbnz+2RmZiI0NLRcvU6ng05Xd//BdrstHN1uC8dbdbZEIiIiamh4HrvrtFotevXq5XQSULvdjm3btiEyMtKDnRERERFVD0fsyhg3bhxGjRqF3r174+6778asWbNQWFiIF154wdOtEREREVWJwa6MZ555BleuXMHEiRNhMBjQvXt3bN68udwBFURERET1EU934iZ1dYJiIiIialxqkjG4jx0RERGRQjDYERERESkEgx0RERGRQjDYERERESkEgx0RERGRQjDYERERESkEgx0RERGRQjDYERERESkEgx0RERGRQjDYERERESkEgx0RERGRQmg83YBSlP7krtFo9HAnREREpCSl2aI0a7jCYOcm+fn5AICIiAgPd0JERERKlJ+fj8DAQJc1kqhO/KMq2e12XLp0CQEBAZAkqVaWYTQaERERgfPnz0Ov19fKMsj9+Lw1XHzuGi4+dw0Tn7eKCSGQn5+P8PBwqFSu96LjiJ2bqFQq3HLLLXWyLL1ezxd8A8TnreHic9dw8blrmPi8lVfVSF0pHjxBREREpBAMdkREREQKwWDXgOh0Onz44YfQ6XSeboVqgM9bw8XnruHic9cw8Xn743jwBBEREZFCcMSOiIiISCEY7IiIiIgUgsGOiIiISCEY7BqIuXPnok2bNvD29kafPn1w4MABT7fUqEyaNAmSJDldOnToIE8vKSnB6NGj0axZM/j7++PJJ59EZmam0zzOnTuHwYMHw9fXF8HBwXjnnXdgtVqdanbu3ImePXtCp9OhXbt2WLZsWV2snqLExcVhyJAhCA8PhyRJWLdundN0IQQmTpyIsLAw+Pj4ICoqCidPnnSqyc7OxogRI6DX6xEUFISYmBgUFBQ41Rw9ehT9+vWDt7c3IiIiMHXq1HK9rFmzBh06dIC3tze6du2KTZs2uX19laKq5+35558v9x4cNGiQUw2ft7o3efJk3HXXXQgICEBwcDCGDh2K9PR0p5q6/HzkdyUAQfXeypUrhVarFUuWLBGpqanipZdeEkFBQSIzM9PTrTUaH374oejcubO4fPmyfLly5Yo8/dVXXxURERFi27ZtIjExUdxzzz3i3nvvladbrVbRpUsXERUVJQ4fPiw2bdokmjdvLiZMmCDX/Pbbb8LX11eMGzdOHD9+XMyZM0eo1WqxefPmOl3Xhm7Tpk3ivffeEz/88IMAINauXes0fcqUKSIwMFCsW7dOHDlyRDz22GOibdu2ori4WK4ZNGiQ6Natm9i/f7/YvXu3aNeunRg+fLg8PS8vT4SEhIgRI0aIlJQUsWLFCuHj4yO+/vpruWbv3r1CrVaLqVOniuPHj4v3339feHl5iWPHjtX6Y9AQVfW8jRo1SgwaNMjpPZidne1Uw+et7kVHR4ulS5eKlJQUkZycLB555BHRqlUrUVBQINfU1ecjvysdGOwagLvvvluMHj1avm6z2UR4eLiYPHmyB7tqXD788EPRrVu3Cqfl5uYKLy8vsWbNGvm2tLQ0AUDEx8cLIRxfWiqVShgMBrlm3rx5Qq/XC5PJJIQQ4h//+Ifo3Lmz07yfeeYZER0d7ea1aTxuDAh2u12EhoaKadOmybfl5uYKnU4nVqxYIYQQ4vjx4wKAOHjwoFzz888/C0mSxMWLF4UQQnz11VeiSZMm8nMnhBDjx48X7du3l68//fTTYvDgwU799OnTR7zyyituXUclqizYPf7445Xeh89b/ZCVlSUAiF27dgkh6vbzkd+VDtwUW8+ZzWYkJSUhKipKvk2lUiEqKgrx8fEe7KzxOXnyJMLDw3HrrbdixIgROHfuHAAgKSkJFovF6Tnq0KEDWrVqJT9H8fHx6Nq1K0JCQuSa6OhoGI1GpKamyjVl51Faw+fZfTIyMmAwGJwe58DAQPTp08fpuQoKCkLv3r3lmqioKKhUKiQkJMg1/fv3h1arlWuio6ORnp6OnJwcuYbPp3vt3LkTwcHBaN++PV577TVcu3ZNnsbnrX7Iy8sDADRt2hRA3X0+8rvydwx29dzVq1dhs9mcXvAAEBISAoPB4KGuGp8+ffpg2bJl2Lx5M+bNm4eMjAz069cP+fn5MBgM0Gq1CAoKcrpP2efIYDBU+ByWTnNVYzQaUVxcXEtr1riUPtau3k8GgwHBwcFO0zUaDZo2beqW55Pv25szaNAgfPvtt9i2bRs+++wz7Nq1Cw8//DBsNhsAPm/1gd1ux9ixY3HfffehS5cuAFBnn4/8rvydxtMNEDUEDz/8sPz3nXfeiT59+qB169ZYvXo1fHx8PNgZUeMwbNgw+e+uXbvizjvvxG233YadO3diwIABHuyMSo0ePRopKSnYs2ePp1tp1DhiV881b94carW63BFEmZmZCA0N9VBXFBQUhDvuuAOnTp1CaGgozGYzcnNznWrKPkehoaEVPoel01zV6PV6hkc3KX2sXb2fQkNDkZWV5TTdarUiOzvbLc8n37fuceutt6J58+Y4deoUAD5vnjZmzBhs2LABO3bswC233CLfXlefj/yu/B2DXT2n1WrRq1cvbNu2Tb7Nbrdj27ZtiIyM9GBnjVtBQQFOnz6NsLAw9OrVC15eXk7PUXp6Os6dOyc/R5GRkTh27JjTF09sbCz0ej06deok15SdR2kNn2f3adu2LUJDQ50eZ6PRiISEBKfnKjc3F0lJSXLN9u3bYbfb0adPH7kmLi4OFotFromNjUX79u3RpEkTuYbPZ+25cOECrl27hrCwMAB83jxFCIExY8Zg7dq12L59O9q2bes0va4+H/ldWYanj96gqq1cuVLodDqxbNkycfz4cfHyyy+LoKAgpyOIqHa9/fbbYufOnSIjI0Ps3btXREVFiebNm4usrCwhhONw/latWont27eLxMREERkZKSIjI+X7lx7OP3DgQJGcnCw2b94sWrRoUeHh/O+8845IS0sTc+fO5elObkJ+fr44fPiwOHz4sAAgZsyYIQ4fPizOnj0rhHCc7iQoKEj8+OOP4ujRo+Lxxx+v8HQnPXr0EAkJCWLPnj3i9ttvdzptRm5urggJCRHPPfecSElJEStXrhS+vr7lTpuh0WjE559/LtLS0sSHH37I02a44Op5y8/PF3//+99FfHy8yMjIEL/88ovo2bOnuP3220VJSYk8Dz5vde+1114TgYGBYufOnU6noikqKpJr6urzkd+VDgx2DcScOXNEq1athFarFXfffbfYv3+/p1tqVJ555hkRFhYmtFqtaNmypXjmmWfEqVOn5OnFxcXib3/7m2jSpInw9fUVf/rTn8Tly5ed5nHmzBnx8MMPCx8fH9G8eXPx9ttvC4vF4lSzY8cO0b17d6HVasWtt94qli5dWherpyg7duwQAMpdRo0aJYRwnPLkgw8+ECEhIUKn04kBAwaI9PR0p3lcu3ZNDB8+XPj7+wu9Xi9eeOEFkZ+f71Rz5MgR0bdvX6HT6UTLli3FlClTyvWyevVqcccddwitVis6d+4sNm7cWGvr3dC5et6KiorEwIEDRYsWLYSXl5do3bq1eOmll8p9YfN5q3sVPWcAnD676vLzkd+VQkhCCFHXo4RERERE5H7cx46IiIhIIRjsiIiIiBSCwY6IiIhIIRjsiIiIiBSCwY6IiIhIIRjsiIiIiBSCwY6IiIhIIRjsiIiIiBSCwY6ISMHMZjPatWuHffv2uXW+mzdvRvfu3WG32906XyL6YxjsiKjBeP755yFJUrnLqVOnPN1avTV//ny0bdsW9957r3ybJElYt25dudrnn38eQ4cOrdZ8Bw0aBC8vLyxfvtxNnRKROzDYEVGDMmjQIFy+fNnp0rZt23J1ZrPZA93VL0IIfPnll4iJiamV+T///POYPXt2rcybiG4Ogx0RNSg6nQ6hoaFOF7VajQceeABjxozB2LFj0bx5c0RHRwMAUlJS8PDDD8Pf3x8hISF47rnncPXqVXl+hYWFGDlyJPz9/REWFobp06fjgQcewNixY+Waika4goKCsGzZMvn6+fPn8fTTTyMoKAhNmzbF448/jjNnzsjTS0fDPv/8c4SFhaFZs2YYPXo0LBaLXGMymTB+/HhERERAp9OhXbt2WLx4MYQQaNeuHT7//HOnHpKTk12OWCYlJeH06dMYPHhwDR9l4MyZMxWOjj7wwANyzZAhQ5CYmIjTp0/XeP5EVDsY7IhIMb755htotVrs3bsX8+fPR25uLh566CH06NEDiYmJ2Lx5MzIzM/H000/L93nnnXewa9cu/Pjjj9i6dSt27tyJQ4cO1Wi5FosF0dHRCAgIwO7du7F37174+/tj0KBBTiOHO3bswOnTp7Fjxw588803WLZsmVM4HDlyJFasWIHZs2cjLS0NX3/9Nfz9/SFJEl588UUsXbrUablLly5F//790a5duwr72r17N+644w4EBATUaH0AICIiwmlU9PDhw2jWrBn69+8v17Rq1QohISHYvXt3jedPRLVEEBE1EKNGjRJqtVr4+fnJl6eeekoIIcT9998vevTo4VT/8ccfi4EDBzrddv78eQFApKeni/z8fKHVasXq1avl6deuXRM+Pj7izTfflG8DINauXes0n8DAQLF06VIhhBD/+c9/RPv27YXdbpenm0wm4ePjI7Zs2SL33rp1a2G1WuWaP//5z+KZZ54RQgiRnp4uAIjY2NgK1/3ixYtCrVaLhIQEIYQQZrNZNG/eXCxbtqzSx+vNN98UDz30ULnbAQhvb2+nx9HPz09oNBrx+OOPl6svLi4Wffr0EY8++qiw2WxO03r06CEmTZpUaQ9EVLc0no2VREQ18+CDD2LevHnydT8/P/nvXr16OdUeOXIEO3bsgL+/f7n5nD59GsXFxTCbzejTp498e9OmTdG+ffsa9XTkyBGcOnWq3MhYSUmJ02bKzp07Q61Wy9fDwsJw7NgxAI7Nqmq1Gvfff3+FywgPD8fgwYOxZMkS3H333fjpp59gMpnw5z//udK+iouL4e3tXeG0mTNnIioqyum28ePHw2azlat98cUXkZ+fj9jYWKhUzht6fHx8UFRUVGkPRFS3GOyIqEHx8/OrdNNj2ZAHAAUFBRgyZAg+++yzcrVhYWHVPppWkiQIIZxuK7tvXEFBAXr16lXhEaItWrSQ//by8io339LThfj4+FTZx1//+lc899xzmDlzJpYuXYpnnnkGvr6+ldY3b95cDo43Cg0NLfc4BgQEIDc31+m2Tz75BFu2bMGBAwcq3KSbnZ3ttI5E5FkMdkSkWD179sT//vc/tGnTBhpN+Y+72267DV5eXkhISECrVq0AADk5Ofj111+dRs5atGiBy5cvy9dPnjzpNErVs2dPrFq1CsHBwdDr9TfVa9euXWG327Fr165yI2mlHnnkEfj5+WHevHnYvHkz4uLiXM6zR48emDdvHoQQkCSpxj3973//w0cffYSff/4Zt912W7nppSOSPXr0qPG8iah28OAJIlKs0aNHIzs7G8OHD8fBgwdx+vRpbNmyBS+88AJsNhv8/f0RExODd955B9u3b0dKSgqef/75cpsbH3roIXz55Zc4fPgwEhMT8eqrrzqNvo0YMQLNmzfH448/jt27dyMjIwM7d+7EG2+8gQsXLlSr1zZt2mDUqFF48cUXsW7dOnkeq1evlmvUajWef/55TJgwAbfffjsiIyNdzvPBBx9EQUEBUlNTa/CoOaSkpGDkyJEYP348OnfuDIPBAIPBgOzsbLlm//790Ol0VfZBRHWHwY6IFCs8PBx79+6FzWbDwIED0bVrV4wdOxZBQUFyeJs2bRr69euHIUOGICoqCn379i23r9706dMRERGBfv364dlnn8Xf//53p02gvr6+iIuLQ6tWrfDEE0+gY8eOiImJQUlJSY1G8ObNm4ennnoKf/vb39ChQwe89NJLKCwsdKqJiYmB2WzGCy+8UOX8mjVrhj/96U83dRLhxMREFBUV4ZNPPkFYWJh8eeKJJ+SaFStWYMSIES43BxNR3ZLEjTuOEBE1cg888AC6d++OWbNmebqVcnbv3o0BAwbg/PnzCAkJqbL+6NGj+L//+z+cPn26woNIbtbVq1fRvn17JCYmVniCaCLyDI7YERE1ACaTCRcuXMCkSZPw5z//uVqhDgDuvPNOfPbZZ8jIyHBrP2fOnMFXX33FUEdUz/DgCSKiBmDFihWIiYlB9+7d8e2339bovs8//7zb++nduzd69+7t9vkS0R/DTbFERERECsFNsUREREQKwWBHREREpBAMdkREREQKwWBHREREpBAMdkREREQKwWBHREREpBAMdkREREQKwWBHREREpBAMdkREREQK8f8unjmAwszHQwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spectrum = wave.make_spectrum()\n", "spectrum.plot(color='gray')\n", "\n", "spectrum2 = smooth.make_spectrum()\n", "spectrum2.plot()\n", "\n", "decorate(xlabel='Frequency (Hz)', ylabel='Amplitude')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For each harmonic, compute the ratio of the amplitudes before and after smoothing." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "amps = spectrum.amps\n", "amps2 = spectrum2.amps\n", "ratio = amps2 / amps \n", "ratio[amps<280] = 0\n", "\n", "plt.plot(ratio)\n", "decorate(xlabel='Frequency (Hz)', ylabel='Amplitude ratio')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the ratios again, but also plot the FFT of the window." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "padded = zero_pad(window, len(wave))\n", "dft_window = np.fft.rfft(padded)\n", "\n", "plt.plot(np.abs(dft_window), color='gray', label='DFT(window)')\n", "plt.plot(ratio, label='amplitude ratio')\n", "\n", "decorate(xlabel='Frequency (Hz)', ylabel='Amplitude ratio')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gaussian window\n", "\n", "Let's compare boxcar and Gaussian windows." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make the boxcar window." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "boxcar = np.ones(11)\n", "boxcar /= sum(boxcar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make the Gaussian window." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "import scipy\n", "\n", "gaussian = scipy.signal.windows.gaussian(M=11, std=2)\n", "gaussian /= sum(gaussian)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the two windows." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(boxcar, label='boxcar')\n", "plt.plot(gaussian, label='Gaussian')\n", "decorate(xlabel='Index')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convolve the square wave with the Gaussian window." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "ys = np.convolve(wave.ys, gaussian, mode='same')\n", "smooth = Wave(ys, framerate=wave.framerate)\n", "spectrum2 = smooth.make_spectrum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the ratio of the amplitudes." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "amps = spectrum.amps\n", "amps2 = spectrum2.amps\n", "ratio = amps2 / amps \n", "ratio[amps<560] = 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the FFT of the window." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "padded = zero_pad(gaussian, len(wave))\n", "dft_gaussian = np.fft.rfft(padded)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the ratios and the FFT of the window." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(np.abs(dft_gaussian), color='0.7', label='Gaussian filter')\n", "plt.plot(ratio, label='amplitude ratio')\n", "\n", "decorate(xlabel='Frequency (Hz)', ylabel='Amplitude ratio')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Combine the preceding example into one big function so we can interact with it." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "from thinkdsp import SquareSignal\n", "\n", "def plot_filter(M=11, std=2):\n", " signal = SquareSignal(freq=440)\n", " wave = signal.make_wave(duration=1, framerate=44100)\n", " spectrum = wave.make_spectrum()\n", "\n", " gaussian = scipy.signal.windows.gaussian(M=M, std=std)\n", " gaussian /= sum(gaussian)\n", "\n", " ys = np.convolve(wave.ys, gaussian, mode='same')\n", " smooth = Wave(ys, framerate=wave.framerate)\n", " spectrum2 = smooth.make_spectrum()\n", "\n", " # plot the ratio of the original and smoothed spectrum\n", " amps = spectrum.amps\n", " amps2 = spectrum2.amps\n", " ratio = amps2 / amps \n", " ratio[amps<560] = 0\n", "\n", " # plot the same ratio along with the FFT of the window\n", " padded = zero_pad(gaussian, len(wave))\n", " dft_gaussian = np.fft.rfft(padded)\n", "\n", " plt.plot(np.abs(dft_gaussian), color='gray', label='Gaussian filter')\n", " plt.plot(ratio, label='amplitude ratio')\n", "\n", " decorate(xlabel='Frequency (Hz)', ylabel='Amplitude ratio')\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Try out different values of `M` and `std`." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "fac0001fb141419780a12cbb29e6861e", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=11, description='M', min=2), FloatSlider(value=2.0, description='std', m…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ipywidgets import interact, interactive, fixed\n", "import ipywidgets as widgets\n", "\n", "slider = widgets.IntSlider(min=2, max=100, value=11)\n", "slider2 = widgets.FloatSlider(min=0, max=20, value=2)\n", "interact(plot_filter, M=slider, std=slider2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convolution theorem\n", "\n", "Let's use the Convolution theorem to compute convolutions using FFT. \n", "\n", "I'll use the Facebook data again, and smooth it using `np.convolve` and a 30-day Gaussian window.\n", "\n", "I ignore the dates and treat the values as if they are equally spaced in time." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1977, 1948)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "window = scipy.signal.windows.gaussian(M=30, std=6)\n", "window /= window.sum()\n", "smoothed = np.convolve(close, window, mode='valid')\n", "\n", "len(close), len(smoothed)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the original and smoothed data." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(close, color='gray')\n", "plt.plot(smoothed)\n", "decorate(xlabel='Time (days)', ylabel='Price ($)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pad the window and compute its FFT." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = len(close)\n", "padded = zero_pad(window, N)\n", "fft_window = np.fft.fft(padded)\n", "plt.plot(np.abs(fft_window))\n", "decorate(xlabel='Index')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apply the convolution theorem." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "fft_signal = np.fft.fft(close)\n", "smoothed2 = np.fft.ifft(fft_signal * fft_window)\n", "M = len(window)\n", "smoothed2 = smoothed2[M-1:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the two signals (smoothed with numpy and FFT)." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(smoothed)\n", "plt.plot(smoothed2.real)\n", "decorate(xlabel='Time (days)', ylabel='Price ($)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Confirm that the difference is small." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(2.0017365280339838e-13)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff = smoothed - smoothed2\n", "np.max(np.abs(diff))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`scipy.signal` provides `fftconvolve`, which computes convolutions using FFT." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "smoothed3 = scipy.signal.fftconvolve(close, window, mode='valid')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Confirm that it gives the same answer, at least approximately." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(1.4210854715202004e-13)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff = smoothed - smoothed3\n", "np.max(np.abs(diff))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can encapsulate the process in a function:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "def fft_convolve(signal, window):\n", " fft_signal = np.fft.fft(signal)\n", " fft_window = np.fft.fft(window)\n", " return np.fft.ifft(fft_signal * fft_window)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And confirm that it gives the same answer." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1948" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "smoothed4 = fft_convolve(close, padded)[M-1:]\n", "len(smoothed4)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(2.0017365280339838e-13)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff = smoothed - smoothed4\n", "np.max(np.abs(diff))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Autocorrelation\n", "\n", "We can also use the convolution theorem to compute autocorrelation functions.\n", "\n", "Compute autocorrelation using `numpy.correlate`:\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([10515607.461, 10533254.812, 10550927.762, 10570279.165,\n", " 10589752.032, 10609151.979, 10628488.485])" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "corrs = np.correlate(close, close, mode='same')\n", "corrs[:7]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute autocorrelation using my `fft_convolve`. The window is a reversed copy of the signal. We have to pad the window and signal with zeros and then select the middle half from the result." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "def fft_autocorr(signal):\n", " N = len(signal)\n", " signal = zero_pad(signal, 2*N)\n", " window = np.flipud(signal)\n", "\n", " corrs = fft_convolve(signal, window)\n", " corrs = np.roll(corrs, N//2+1)[:N]\n", " return corrs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Test the function." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([10515607.461-0.j, 10533254.812-0.j, 10550927.762+0.j,\n", " 10570279.165-0.j, 10589752.032-0.j, 10609151.979-0.j,\n", " 10628488.485-0.j])" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "corrs2 = fft_autocorr(close)\n", "corrs2[:7]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the results." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1977, 1977)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lags = np.arange(N) - N//2\n", "plt.plot(lags, corrs, color='gray', alpha=0.5, label='np.convolve')\n", "plt.plot(lags, corrs2.real, color='C1', alpha=0.5, label='fft_convolve')\n", "decorate(xlabel='Lag', ylabel='Correlation')\n", "len(corrs), len(corrs2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Confirm that the difference is small." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(2.9802322387695312e-08)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff = corrs - corrs2.real\n", "np.max(np.abs(diff))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.15" } }, "nbformat": 4, "nbformat_minor": 4 }