{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PSF normalization\n", "\n", "Let us assume that we have reduced an observation, for which we have determined the PSF by stacking the flux of point-like sources. The PSF we obtain will not be as high S/N as the instrumental PSF that has been determined by the instrument team. Moreover, it is likely to be fattened due to the some small pointing errors. We need to find out what fraction of a point-like flux the PSF we have determined represent. In order to do this, we use the growth curve of the theoretical PSF that has been determine by the instrument team, and compare it to the growth curve we determine from our PSF.\n", "\n", "We will first look at a theoretical case, then go practical with an example drawn from the PACS observation of the the XMM-LSS.\n", "\n", "## 1) Theoretical example. \n", "\n", "Let us suppose we have a perfect telescope, without any central obscuration and spider to support the secondary. Diffraction theory gives us the shape of a PSF in this case, an Airy function. Let's compute it, and assume the resolution is 10\".\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# import what we will need. \n", "%matplotlib inline\n", "import numpy as np\n", "from astropy.io import fits\n", "from astropy.table import Table\n", "from astropy.io import ascii as asciiread\n", "from matplotlib import pyplot as plt\n", "from scipy import interpolate \n", "from scipy import special\n", "from scipy import signal\n", "from scipy import fftpack" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Let us perform our computation with a 0.1\" resolution on a 5' field of view\n", "resol = 0.1\n", "size = 300.\n", "# wavelength\n", "wavelength = 250e-6\n", "# primary aperture = 3.6 m diameter\n", "aperture = 3.6 / 2." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Ensure we have an odd number of points \n", "nbpix = np.ceil(size/resol) // 2 * 2 + 1\n", "xcen = int((nbpix - 1) / 2)\n", "ycen = int((nbpix - 1) / 2)\n", "x = y = (np.arange(nbpix) - xcen)*resol\n", "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n", "r = np.sqrt(xv**2+yv**2)\n", "# avoid division by 0 problems in the center\n", "r[xcen,ycen] = 1e-6\n", "# coordinates in fourier\n", "q = 2 * np.pi / wavelength * aperture * np.sin(r/3600.*np.pi/180.)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "psf = (2*special.jn(1, q)/q)**2" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put back the correct value at center\n", "psf[xcen, ycen] = 1.\n", "# and normalize the PSF\n", "psf = psf/(np.sum(psf)*resol**2)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "$\\int\\int$ psf dx dy = 1.0000000000000018\n" ] }, { "data": { "image/png": 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BjNOz2dY22sKbfUCyKR290Wc92I/WOD5e7M0I6UykCSK7AKQJHs1sCuekloYudK8II2DyNUZFzUj5s3btCEDL2iZa+jBo6YqVqV3d72KSyjTX6inhVZZjH8Do7IVSXoVFlCBnhkgHmxk6TqIeBKtPB/DeEfb4XZpZjbHsCYOcsxyL0MPVxQDDY/Fw4TwDK9lKW8nEVghEGRahh8mLPoqTJTqORABhgqvS1HpauQQGF8C354g+GYDcwlRUOvoVjtcbUAi2wESmDxNdM3lveScwkZ6QKLewih3ML3ronK7R08VXWo+pgXbhdZNZWEYuwuddDB6INGJgpaUfIm8Nb5r1RXKfpD6yjh0sX3ThH4c4LD0qTbZUHVt7ONMEkV2ZIj3NLs9LxijSvPSwpCbSyIL3iYvNt1KYbg7LzpVd3qQMhllsGd707wZQOmMFSKW5iaKgyFITeWzC/6WN6IMYtpfBtnPl02j6Y1oFZuggXR1znb3UwyKTshprqbwmMVaRg8svDtC7t1KZm+aDQc8KiQlaD4MkMBqEI7RyzL8cIDtfofAIfGRgVAMCtGeB9NcNg2H2vA9+thTAAMCgTIRAt4AKe2+pNBXiAtTiwo5f7vdvClReb0BBu2lN+jpkNkdqJreBifzsKnaQ/eUQve/NlPjqGPlevUQPccLUxnwp1PHjd25qN34NTHaENzkzFDDJ/Vk968G7t8bpWzdbT8l6Lcs2G2kDkTZNRtZFSdNbkpmIUwvx0gE4KjeqWSBwUhg9DvNeVUR2m2O2bexzyBb3ZU2TqB1KcwNh5AgXLwHcXpn61cxrsqhtl+bRBJdqbLMWkxQq8xPYKTZ+jOXGxYtPjxrCPIXNC8UM5Q25FQaRTIUvllHAeSfHdBHgOrYw6G0Q2CmYsS3YVueyPvcIAHqPI/nJCOx7MzCXlLoKbgcVPwKOgdXzHuj9hXjN2m1+e1XjtQYUoP5UlyLlJrUwH3dbU8M6mDQ9Jpvy5g0/76P38VRMmBatQ313efPrIc4qdjB/0UPnZI2+F2+BkXK5toQ3reHSpAuvF+Pk3Yk6jjZg2gckTRCR36MXIMpU82bjoJg4sE838N0U/SDCUW+95Zit6zLbxrfm73uvYYuoKxmfPEc189qwLOosQWa+9pBe+jAOE/h+UqWAG4V721oV1fa/zloYCKjBYXIGm+ZImQmr1EJiP8Yi9PD8YoThoa6J0faQUwuDgFxpKyZlMIcMi8jF9dMhsnsCpJohUFNXAQNg5Oq6rz6eYvnZAPztBTiECFseihYaboMK82LgHjAfd0FOluI7SkctJbwqKHyF47UHFABbGY/5tANvGG2lhm8Dk8XGQzgOMHx3hp6bwDHyspR7Wy9pC3EWGw/h3MPofI6uk8I1s1YWAbSHN2lhIM4tIQQvSuPcyaImBEsgMWs38cuBSFWDZCKMHBj/ogv23RV8N8HxaAn7qFBZiuq79jtJ9fFVDW67skq3OoEDA/lwqdyxi9AD/WkXxe+sEHgJPCtviNWNm56TrXOphNwyHKKEw6a5YiyumSP0EsxL89ewHyKwy2te6hhtYZCaB1JbKQHPPs8xve4hGxjo+9FWCKSfe12sBQDqcZB3Z5hd9MGOKeBXoKJ7VXRQYbxQ72FDgvm0A3KwKj9UfXaXoP5Vx2sPKFIMzAohwi5XPiwvUzUVO1PDDTBZRi7CGx/DswV6blIDg31gIntSzFY+itxQAOCZQihty+DsCm8UKN34GJ4s1ZNPgloztLkNSHQdRi9kXG0cpJc+/Ptr9IIY7o/WrWX4u9LM+vcaO1jIyz7ZGAiMRrkDABQ19lI/Rvl7zdxnUxR+hORHa5UJm30+hH26QddPtuq11HnFftZigoEREbbIUEhlbxIbkxd9RAcbAQa3hEG6tqKs8oTDOFlgtghwk1Ow7gZ+Gb7YVJwhsV8NsdYsmz25AM4WmF31VNipg4qEaj37AwCuScD9GEVBsVz5MPphY459gxgKL0EhlTfj2gMH0Jfu2TtoJuomnnkYnS62mEUbmOh6yTpxMJ0HcNwMB6OlyuIoJrEjxJE3e5KbiHILYWph+qKPzlGI8wea7kLzlwIS0XbAqKW+N2U/lfhFAP98jUEngvvBaqtcYJ8WowPHq6bB+7ZZCzG13wsVGgnnaRNIA7PUg1wDSSdUovbN50O490J0vKS1zKEK5erAIhmLHgqZROg2jpnDf5BhEbm4+PIAo3sL5VVyzDpb2Q6BKgYiWzDM1j7GNz2MBiE6TrJXV5EZIACAC5DTBabjHviQ1JjKbZoK60SYLgIs1h7Qqez73yhRlnMon8dq4yKLTRwcrBupWbYXTJaRK8DkePlSYBLnFpaxg8VnQwRvLTDw4p1sAmhnJcrnsvJRFBRH53N0naQEkqI2wfcBiaT++nal/2Y17sAdxuj6MY7fX7fWCTXDp68KHq+KHu8El5Z6oibI6ACTcwpmEHjMQG5T9J0YSSdU/W+uZwN0y8JOpU9prNIkDLcBi3yfRQWweHaG6SLA2mAYdjcIeBmu8na2KsIPYaWXrxtdjrnpYvrpCMU7IvwGUHpNbgEVADheYjreZipNUNEdtdwi4L0Nbm46WFFXA/JvkA+Fg6i2jfHSwfBotbfQr5WZ3Ph3ZiYpM5VguohcrJ71MHx3qj7rGvneEEdnJUlhYhG5yP98BP8HQgD2rVTpJC8DJCkzaya6ReghXtsYHqxx/vCmVRhubluCyG0A0gSNtpCk9v6XdMqK13aHVM39a4KMBJiCi34kjFMwWgj2ZlB4zEDHTtB3Y0RdUXV+8WIItyME6LaM3D5gobQUWFmlO7ml5T78s2MkP5ii78UojHwvW1EhkFm1vLTeLTB7MkRxf4m+R5RYa9NcHe9eULnsgx/sZyoSVBwjB7MIBsMQs+suDKPK3r3K8XoDCodq29j7/kz1w9RpvBxMM2LJVGw4DjA8ezkwCTMby/LJf/jWDB0nqekl+0KclJmV5rL2kSYWDn80VqKra2Sap6Jet7IrtIkLUzGdxdpDnhkYDUKc9FdborBkIncFER089BBD7of+nmb6l90CNPqxid91gbcypu1y+O5iUfr7pS4j990kAlxyLrwmwh0rrPdhauN62oVpFeh3ovKaGHCNvKzubQ+FlJeFQukrtEwLhz/KMZl1kWQmhp0NGAgcQyvs2xECueX+E8JB35phctEHPwaYSxAgBYA7gQo/WWJ20Qc9FVeJWmUaGy0FhUY1V4uDEPlfDLH+PgNxWy/dVx6vNaAwTrCcBAjKPpqyWK/tqd5M7Yaf91U2Zx+Y6HrEOrMxDz1EobM3PAGqG03e+CmTqWAHkxd9dA5DnB3OVZh0GyvZByTTRQDTLDDsblTV8q6QaR+INAFkV8ZId8/qr7U1rdYt+c0hz/WuptT1tHhLgd4tYdoucBFGMwaGAjalcI0cvpUqd+x87WG6CDAqMzcC7PMtjUUXbs3y/KkwqARw+7DAbOPh4ukBDu8thCZiEhUCNR9ANc3CLIHlnGNy00VRUPAA6JSg0ppWbmgqOFtg8ashyNuLim209lQRneFgidaqi+8tsJwEME+2hfJfZ7zWgFIUFE4vUV4TXbmXow1Msr8covfx9M5gIlnFdBWgyCmOD5camNRFU6Cul6TMVMLrPHKxmgY4OpurTJBkJW1p4DYgkcCkA8nRcKWJwQXsMrx5GRDRGUhT4Gw2zt7lnM0SE3zqgNsMJMhhWgWowdQyFHLJC7VUBSNgBUWeGeChCZJSkFECy8lvdcbWhWRaA80CZOuYa+Cih0Ula7FL7UX2jpWZOx1YtoC6TCc32Yrsa2KSQrUg8OwM11d9JKNQ09sq7URnK2o+6SB6yDFdBJiyAOgCPjLAED1fbwMV/s4cyU9GWH08VY7aJqiYpFCeP9ckYF6MvEe/We0LAIi0Z6NtoxzNquF1YmN+0VMO2F1Ffm1gcrMMwDlp3Ly7wUQPcdapjekyACEcZ2dTdKx0Lytp6iRyWzqQUIPhcLDWJnq+FdYY2n7pQweRNgDRnbNyOYm4dM1uli6QU7iDGK6dwTILuFYCw4tFzH1vm2nsG23MRtYHZWVzqHlqIZ67gMng98T3ytaO+vIhu1Lrt4GLzlpsTuEaguX5ViZcz2sP86VfBxZenm/U9RWU32CC1diKTQtYZwVulgGuki5GvRAdEKWJ7NJVlCjqAMaQYbLo4GYZAL2yPeMtoMI5QddNwL43w/yiB3K+UKwQzSrlEswYL+CaBL0gxnTeue0WfKnxWgOKYbDq5m54TZrNkcJUFPp1TtfKAbvLtKaDiQ4Gh/21AoN9mZycUcSFhaQwsYxdTJ4N0DtdYehHSrzVWQSwm5VIhiPDrTiycTRavTSQ7AKRZppZdvCP5XotiYFgEMGzMwyDCMe9da03a1tIIo7n9kzRviU9miFVMap64Sa5qUyEhlOIvi92ttWy4S4hX2WPrwOLAIFcMRapsay8FIMgan0o1MOgOluRAGsNGGYbD5dPDnB4f46eG4MZBC6yvaCi5ll/jZtlgMmig1EvBGzsBxXZLMklYKcEs6sejHuLMgOUixYHDeOb9Khwi6Dovdq+sq81oFDCd7ch0IxrUWZhtvRFy8fSDm/tTQ1rYc4yAOfAYT+8FUyaYckydhD+9BCj707QK0GsGeLsYiVpYartLCIX8V8cwPl4iqPjmcgG7Qht7gIkOuuRXhW58FT6yx6sx2LdmbPDuTK8ScBuy2I1NZ/bzG670svNjJEu/Oopd7XcSH9ZrVwQeph82oX9rWVtYTVLy5qZhIDJfW04WPcBi0nKbvfHORaRi9k/P0X0/RtRWmHS6lrsYSswcgW6JOAwzwus/u9DsHJuAKjpKlugwlDdjT3get7BdBmA9qUukoPydvMbMwg8ZOAAiiHFbOnDGFQPgDbjm0nFMefWq12N+LUGFEKgPSkbIqy2stp87YFSVm9B0HiiNrM5MswRzCSsPZH0G6opvsaFiTi3MNt4WM19HH88VnqLyuK0hDg6Y5DsZp3amMy6sJ0Mox9eIrBKVnJHIGljIzLFHOdWterc2sHgYI1hEMH53qq1vcJtwu5t6d99Q4KpSfTX6g8HoMGuzBJgrDJE80Mkg6XqGXx1OYDTqVZ/lFpZW5ipn79dwCI1FsfIEf4wxSz08Gw9xOFwhY6dIi9DpV1sRQ+B5E1sfTzGeNxHPjAw9CMwM1MSR02s1dLK6o4cCKYiwx+5/63ZHyIADQBYEOEmDzBfeyDdymsimFRdpDXoN7QfSqsIqy2+lSUmDkbrqq5HU8fFZ+pgss5sTFdCM9HDnH1gIm/UdepgFnrIUhP3TmfolCBg0ip1C2yHODor2WQ2phsPq5sAR6cL9N24Jby5G5Do21VLV25cbGYehscrHPZCeAfzLZ+K/h3A7vTtvrGLqWyP7W21Na42SQU0TZCRrCu3DAzcCIedUK1u8OTFIfyyIfm2eF2xltuARQBBoRb2WsQuLi+G6B6EGPkRmEW22EpbetlFJs4vOIxThutZF3lBMQwiwAZsVKllVaBXng+b5jWmMll0MF0JobazI6UsCwoZLeBbGYpuhJtpByvTreYz4a0iLePfoCwPIfWnZK3bWukU3Vx0yraN6ZYTUnymcsBKn8k8FGu9Hg1Xe8GkmclZZzau5x2YJsPxcIWOnWzpJc0Qpym6rhIH1zddBN0YD+7flNvIaiHHbUCib1N39c4u+giOQwyCCGeDZU1YbmM8+8CjCRZ6uLLvtbuObTCqivbUKxrIWCAoqAakJkXXokhdEwfBRhkZL58cbNVr7QNqHVgoZ6Aw1EPMogXc+znmkYunV0McHazQdRIwVEKrvIH09LLUVYDS4j4Epmsf43kHfAB0rLS88+oZoFZQ6a9xPetiHnogARAgLcGh7qiVbTcAgNkExSDE7MkQ9L52vM10Mr5h1nuyQ4RNmYEwtbB+3kP3/lL0BlVrFOuhUd1OL3WPKHRwfFjW5TSEW52ZbIHJrAvbyTEKNvCtdC+YyDAkLQwFJvPIxezJEIdvT2usxC4BUPaqqIHoDkYSFyY2mY1F5CL8tI/eezM8emdcc/S23US7QETe4BIkmmCxy7z2VZyy8sjahr4fzcpgCS6inwkBKwv0XCNDYKbo2gniTohl7ODZz05vPrc4AAAgAElEQVQRPF6g78WNa7WbsYAAhpEjY0Ytg+OYORZWjvFnB8gezTDwSOk1ycsuau0hkAxDYAO0yzENfVzPusCwqvqVD7ImUzFJ2fMVBKN+iPGkB8MoNRoiwaHZBJvBpKTs70KR319i9bwH62FRLSPbEGlfNQC81oCij6YIu1gGYqmLUgzd7YKl6im+iFysxp2aaa2pIzTDnCi3sE5tXE978IMYIz8qJ2imZZ62wUS/8depg+naB+cEZ4+v0bET+Gaq0o1t4Y3cj4wZrdubbzxEGxsHwzUOv3NRgZPmItZB5K4Asq/v7C4b/j5jW/V7Q9TlVRf7Oui072eTwYjzXGcurpkhNVN07ATD70RYJQ6eXw/g+SkGftRglAJYdBCX+2PR0iAnn/6kEML14wI3qwBRYmPU2aBjJ2A83xkCmWCgZqbEWko4ptTD1U0fbLREB0QxlWb4I4VaxyCAA7CDFa6fD0CONQAxOIC6VlilkzMwl6C4t8ZiGcAy9oi0r3D8fwJQ5E0qdZPlxgU1CnRvzehULQiWZVe0w7dmO01rzTBHD1E63RijYIPAStWN2wYmbSHO1bMhBicrDPwIgQQjjZXsCm9kuldnJNPQRxxbOBqucK+/bGU5bSByG4DoLQPa/CvVOa1SvvI1/acczfTyrtTzlhjMaY1J7QOYNnAxCYPLhUAeWCn6box1auNy2oPrZlvsknEiwgUtvNbDIACKgcpq4fnGw/MvD3Byf9YaAumgAg6VppXsggAYT3rgtf4k2+GP7lPpOgn42QI3XwxhPGQgnthHmwKM8y1QkZmfwiNIUwPLjVuzAuj2/Fc5fi1AIYR8AWAFsZ5kzjn/HiFkBOB/APAWgC8A/F3O+YwQQgD85wD+PQAbAP8R5/ynt31HUzdZxw6iuatW9JMibJvXRILJOhFVw8N3p+jsARP52RoYXA4wOFjXwKApvjb1kriwEJWZoNl1F6cPpujZicrg7GMluk6SFgbiwhJC8MbDZi1CtfP+Ao5ZZpVKoXUXGzFK0XEXgLRlimSYqLeNlM7ZrDCQF6WbtqDIc0NYxgsCzsR3EMpBDNET1TSLqg+twdRC50Z5DpvtHLczNLsBRh5bs5iPQYCEzQplYuvZCZapg+fjAfxOgqFiLLJhUru+ss1Wyi73dobLiyHSo1WZwRFeE2kmk3NDibWGxsQC8fvV5QA4nYvXdoQ/ElSYQYSt/9EM81+NYDye1pjdlkeFsJpIe/2iD8ssduopr2q8Coby+5zzifb3nwD43znn/5AQ8ifl3/8pgH8XwLfKf38bwH9Z/tw75BNSrTc87qB3vK51amsXYauq4+k8QPCWKBKs7NV1nwmAutEstXF9070TmDT1EgUAGwfn51MV4shwZJ9WIoFQgtIydmH9dyO4f3+K43vriiGV4rNBtgsNdTbSVrOzlTlpGN9Uu8jYRvoiADlI4PkpHCuDZTD4tuidqlerNrUSnbkUEqQYFR3XMgvRxga/cWDfE2sSy7aObca12s3OyRa4NFmL1FsMUq36Z1PR1c2/l2EZu8j/6xNc//0peqWWJVkjWtgKCFRzKAl0hHAY51NcTXsoGMXQLzM4LbqK2B+mMkAAgNLxfn3TBTks56EW/ujfbVKxIBlMgDsE2VsLTOcBzAO9K13do2KWFdiic1uG3mGI5bgD+6wqF2CE4NW6UH4zIc8fAvhR+ft/A+DPIADlDwH8t5xzDuD/IoQMCCH3OOcv9m1MD3UWaxfeKNqy1evv1TM6sl7DcTMMvFio/nqXtYZprSbATnvodOOXAhPJJsaLDgyD4fxwXj0FNQDYxUrEzSzY0TJ1cD3rIvATdP7oBUZaqGTSAlZDCAba2YgOInqbSL1Vg+zylkw9dE7W8OwMHSfFQbCBcTjVKqQby6fqGskOw528Ls3rw0YE+VnV8zbOTSwjF+urDpxRpLqvyZ6/eqZGnUcFLs3QTvxtl9fIKj9js0K5Y8M/ShCGPp6MRzgarvYySF1bEZmgSoswDxmuVwEu510c9wk6dmliMwpRhXcLqDBOcD3tgR6UjaQ1UKmb38pF5c0MA48gzw3MVj5or2KmTZHWJHV7fjYysFi7MI3qgcpeMaT8uoDCAfwzIny+/4hz/mMAJxIkOOcvCCHH5XvPATzVPvusfG0noHCUa+iUy3vmqYlRb7lTNwGgRNgoF2nEIjdwMFqWT6FmRWnDAVt6VK5nXSHAlppJ3f26W3xdpQ4uJ330exsMdSBqhCVqX1tYyTp1cBP6SFMTp6Mlek6sBGCb5oqR7AISPfxqgog01CmvynWA3qlYNuJ8FMM5unklhjd91Noc3KXGaDBXzt5F5OLp5RH8o7DmMdGvhzivVAG9zlr0cIhysQ6QvP4SWJaui+tFB2vbwUFQCq23sBXQesrWoMJu//x6gNPDBZhNWsVaAKo/iQKVQNxEMvtDtDmig4pkLS4EQAw7G4ynPSw2HoyAqwxOs3O+rqf0/BjjSQ+ryK2FPq9y/LqA8gPO+UUJGv8bIeSTPe9tSwVszUZCyB8D+GMAcE+6wgiWWih+1sfguzfVesO36Car2EE493B0sqjSwy1gIj8nsyfX845IDbcwk11gIhnF5dMRDs8WGHgRAjPdqZfsYiWLxMX4l4c4fHyDs14JgmamwqSmRtIEEnmDZkrMNbYKGIuCYtQPcdxbwxvNatW1t6WYb2uGtGvsatp0ayjmGUj7C1U0+WQ8gmEwUXinfEd5LZRsshYdWExAOERLkJchVmClmMUevvzrUxx/a4K+E+9nKyWoyHVuKDhowGFQjosvD3D6YApuyy5s2xmgJqhwn2DCKK7nHZABALvqmdKsUgYAxxTna9gPcX3Vh2UUtfBzl57iWRkGgxDRTw+w+a4oWyC3PBBedvxagMI5vyh/jgkh/wTA9wFcyVCGEHIPwLh8+zMAD7SP3wdw0bLNHwP4MQD03j/hcW5itfbgfLSAb+v6B6uBia6bhKmN+YseRudzZXiTbEaOetWwSCvPQg+myVQmQKfZ6nMtYLJIXFx9OcLRgxmGbtQKBPr36swhLiysSlYSRzbuf3BVaS47wpu7AElcWMqnsnjSx/DtGc5GC6UhSf9Mm6C7qx3CVxXwmqSaylckQLcxF6M6Tx0rQd82ceiHykv0q1+eof9I95lksMtlLnYBi66xUMpBOQU1SzMhZXA/yHE57WHjWTgINuiWoGASUmMrzSyQAl5P9Da5fHIA/nBaHXAbUynDH5vn8C2CUUAwYYGYg1q5iV5QKL/LJAUcgyCwUxRHS0yfD2A90FhlQ0+R/hSbFvDtDOlHC3FPWZVe86rGVwYUQkgAgHLOV+XvfwDgPwPwTwH8hwD+Yfnzfyo/8k8B/ANCyD+GEGMXd9FP1rEDxkhrilh/n66bzJc+OidrTYRtTw83MzJZauJ4uKr5TNo0kyaYTH5+hJNvX6PvxAispP7EbAET5XAtLCwTFxfjAYbDNU6OpwjMsrtcS3izD0ja9BfPSzH0I5z81jOVJpVPXB2ktu33rz6dqI/m9pUnAhQgrA4wZf/YzMgEo7MM9O0YR78VYpPZuAl9PIsGrTrIbcCyHQYVcI5zTDcenrw4wNnxvAo5y9RwMwSyStu7W/pNAIA+5Jj8/Aj49nV1kA1QUZpKGXIwi2DUIRjPuphtPJBAfEezSrmW+TEJuEOQnqwxX/qwNCuDieoekX/rqeRoY2MdO7BeF0ABcALgn4hsMEwA/z3n/H8hhPwEwP9ICPkjAF8C+Dvl+/8UImX8KUTa+D++7Qs4J9h83kP/8azqidIS6ui6yTIS5Vd9TYTVXbByKBes9KjMfVGbo8xPRe0GawOTWexh8vkIJ781Rt+JVSZHgkETTCSDiHMLYW5jHnmYjHs4P5uiJz9fFqg1GcM+IJGgOI88TD8dYfDuFI+Op1sZoSaI/DoAsss5u2vc5TsqS3j5twYwZnnsDs2RGRn8krkM3EiUU0QuPv3FfYweTzHwolrmZh+w6GGQLH2waAHPyvH8YoTkeClCWC7s8s0HhQQVqoodE+E1+a0xrn51CPa23vRoG1QoOGyjAOM5YAN8CLy4HMI0ClBPzoGsAocSVIQHpQAzM/S9GONYzH2DVHrKlj+lDH1cM0e/t8Hi0yHc916T4kDO+WcAfrvl9RsA/1bL6xzAf/Iy31EwCvfRSvSS1az1baGObLAUPu+q5UFto711o94caRm7CH96iOOPx+hohif9ht7JTD4f4d5jwUxcoxJ9m2CScar0EhniXK864Bx468E1utI5W07WNlYijrcqjGwCyeTZAKePbvD4bz3bCrm2tZGXqxKW501dlx2O2bahvovT3X1id+yPDjAmqcovzJK5OJwiYzl8M0XXSnD4tzZYpg4+/eU9HN6ftwKL9F4UnGyFQaIFQbXqn/WgwHjZQZRaOOquwUDgGpnaN0vtn7jJbZrXQhP6+BovPj0CfeemOqit8Eea38SNzS2C4+MF5j85Bv3diQKVZuZHhio2xPKko36I8WcHymYvqpfbQx/HyOHbGZJHKyzWr7ap7GvtlOWMoOuJ9KFufgLqKUjZDX42FguXV13gd+kmhvKaTJ4NMPruBF0naW0dUE8NN8IcnZm0pIWbeskmt0WIMxlg2A8x8jYIrEQBUZNBNFlJxgUQxrkAkmnkY/bJCEffvsb77z2vMSSZKr0rE9GXBQXaW0bK13c1sm6OtgpmPbxSupAGNvv2VZTdV8zFKsOQnBmwaQ7XzBBYCfrvxVgkLj7/F+cYfjDFyNsokBXnZg9b0bUVUsAeFJhGPp6ORzg7nKPnEMBMS10FrWKtElQBsHcnuP5Xx7Xwh5pZLaUsbfqqBQEIsu9OMHk2gPmoDGNMXhNp5XmVekpuUfQfLDAbd2GfVXrKVhEhCjAqQCj3KK6W/Z1z4quM1xpQqMF2hjpAlSJOSju+N4gROKlWqt+um8jGRtOlSJvKZUnN2vfU+3UIzcPEMnVw9eVIaSa7PCZtKeF57OH50wOcnM8wcCN0rESFOLexkkS2PihB6cV1H4NBiLd/53lNd2kCyV1BpBlO6RmXZvMjfR1i+X+8Yb3XG1E310vWsxC76o4MkJ3gojMXCgrDEAY2izDYVHQkc40cnd9JMd14+PTiCPeOFlth5S62IrUV8V3lqn+U4emXhzh/cAO4UEylKdbqaWVmZOg7BPzb17j6cgTy6KY8L2wrpJagwsp967kJ8tMVpssA1kAuecFa9RTGRbOkwEmRDMSC77Yh6o9aU8la6NMbbvbegy87XmtAMcquUrtCHbnE5zqxES1cnJ7NhG5gtJjXeBXqyMpfQjiGflTrtKaDSdMCvypTw0cPZoqZtIU5TTBZZ47IBP3NEc7fH2PgRmpiN0McAK2sZJPbCDMb45XoAfrWvRt0reSlgaQNRNo8K81ub5vUwiZ0USws2AcxHEcI5JbBFHhISOHl+eacICvKsonEQnrjwuhn8IMYftnScbvrWnUcCmxuAZd2YCkZi5li4MUYrzpYRC6Ou8JtLOtvmmxFblMsPVG1tDApg/mA4eIXxyjeEw+TjlWmhneAigwmuEPAHsxw+XQE+vCmeihq9ncFKpTBRQbGCYZ+hMvUxDxytbRwo89xaXqzQRBYKYqA4PJiiLUtro8+n9tCn45cZOwVjdcaUFTHNjSZSZnVKa3182kHwyPRXFqfnFt+E17V9qymAc7OpmW5f7vXRL+51qVp7fBsgaEbVdmcPWASFwIIbjYBbqYd3P/gSgOTvDXE0b9bspJ15mAa+bi+GOD8wY3ahmtkLwUkTRBpppnV+j+hh3glurz5TorATjFwI5iDOcz7FbjXXLM7nLJVQSEBO63OqXI/Rx3Mbzpwuwn6QVRbw0jPljXB5WWAxTaEiW0ee/js8xMcnc0x8jZ1hoim30YLgfTj/eAKz66GyEeGWGDLTAVw7AAV0UxJ3LT8jOBy0odxxEGd8tzROqgoj4ohQOWgF+LiYgTH1NPCvLTN63qKqPfxrQzDoxXm0w4cS9OEGlkfygXrkoWLr2q83oACKZA1tZMq1FlFLpwgRcepjE77dJNNZmHyoo+js7kSYdu66etpZWmn7/c2Suhry+Y0wSTMHEw2PsLIwaN7N+jb8RajAKoQp00rWaQuLqZ9dPwY773zAoGVwDeFuU///jYgkWxEisI6iEgdJsxszMrm2AfDNbpOgpG3gX28u6dt0/AmR7OiubkfbQWJeYciHcwqQ2Li4IvZAVwvxTCIVFvMNpFZiaKkzi6awGKUGRGb5gjeSTHZ+Pj8+gBnowX6dtzKVvQQSGiooukRdTmMewwvZj0wDhz64lh3gYrsrsZ4hoEXoWAE40UHdMBLA1sGSjl0j4oECdcQS4genSxwfTGA/SDfq6fYVBYRpoiCFKvIFYWYZeijZ31krY9jvCZZnq9jEFItqwi0GdgsZH/dQ/87k7INo/YkadFNksLEbO2jc1gu8GRuN0iqZXTK8Gi28WAYTNjpS73CJO3uV52ZTCMf642rJu5dwCRhZi1MuvzrY9z7cIyRt1HMxpGp0D1A0mQjku1IgJysA6SJiaPhCvcHCziH9erlu6SYb7Pd69dN3zf9fDFOwUwBojkzcOCGOO2sVE3V5+MD2E6Ow05Yq4tyjBxsD2upA0umQMguFz+fWjm+/Ff3cPrhWIUvjBZwaA6hzlSsUbZYlKACABgCF9M+KIFym+4CFZMwuKbQXJhPkGSmmFPafG1mfqRIyyAMbNFhiNnah9XbradINuKZGbp+jMW/PET4UendamR9AHFvsWYvzl9zvN6AggpR5ZBl9XFuYrHy4X9buGFrtT3YDo/kWsNpYqkV/Wy63W0NkCJsBSabjYPzw3mpz+RbXoQ2ZjKNfKw2Du4fzNG1RFq4Kb4C2Lrp5ecvV10UjOKdj56ja8XwzQwOzfeGNzqQ5MyoMZ0wF31spxd9nD6c4v5gvpUVooRvAZU89wZeHki0C6muBcoHRIFGpqjc94wZ6JoJMptiyEyc+CtschuLxMWTX9zH6GwhyiLahOgdwAJOyxUnBasxicgYeh9leLHoYR07OO2uEFgJmEFUCKTrKmZpta+B6wHH86nIknBvN1OR5jfbyBGA4Kgb4vlkgBlloEF5Lc2sVaQVNUeimvliMsCi1FNkU2s95JRZH1a6aONvz7FY+XCtvDx+Azap+tECqLnAX8V4rQFFH1WmofScxA4IoCqP9awOsB3qhKmN/M9HOPzR+I4irKDfs+uuakFQM0ppoKULsJvcxmQjmMltYKJ/Z1RYKsR5Oh7haLTEsMwEuUZ2J1Yin/JZaelXQvK8B9sST/nzD5Y1DacJUJRwBR5N4HhpIGkMPWylZToTpAKaAlTcEJzCAUHBM+RGaWBzIhx9ECphOs1MnA6W6JbXRdeTLOwPg3RbuzUsMIs9/OryCA+OpyoE8oxsq1+ILtbKcT5a4NnNAIwDJNAeflqYrkBFXiub4GS0xPPnI9hmmY0hbLdIa2QoTIrD4Qrhnx0j/FE5lxqhj2QoMuvTdRNEGwfr2BFZJcJFulu7Fq/aFf1aAwpBfRLm3FCLoS+vOjg8X4jFn/ZmdUSKeLby4f9gqkKdfbqJFGGvng1x+qACEwkITdOans252QQIIwdno0UrmOjiq84i1pkj0sqfH+LRu2MMnEh9trLhbwto+pM9YYbKCM1jD88uhzg4WOPRwbQEprymvUhG1wYgt4HHbb1km2PftinhFciQatsFKBjNxXXnGTwjQ8+KMXQ26lw/uTjA/dNZJXZzsfh5G/hKYAGtPDGyYZJjFPji0xOcvz3BwI0AQOkqengqxVodVM5GC7yY9YTe4kPL/qBmfqNErB3kGhk6NsXpmcj8mA81i8MOPcUxcwQ8RfKDKWYrX6SFtdCnLevjmjkGvQ0mz/vwHoiHYU4NJdD+ug+ItvFaAwo0cNDX4gkTG84wvt3AVmaCwtRCUdCqjwq9XTeZrn0MTkR9SNO4Vv8eqor8FomLm2lHCbBtzKQJJnFhlawmwGTWxTvfukTfjmohjrWD2ei1QUmp26wyB8+nfXT9BO89uFJA0tyWBBJd+W8bTeBo/i1Dl11DgpX83C7W0wQcCTAMRP1tEYaMCvu9a+ToWAkO/BA3mwDjRQfnDRC3ad4aBpmkEOY42ihx+NYlnlwdIB/SMoNDACMDmLhJC3UM26CCIfDkxUGt14jIxlQPOYNw5VHxzRScE8QnK0zXPhxTS1G36Ck2zZEbYg6vQhdhalUPRi3rI8+fMLyJ5UCcYYwwseGauQAhum3Lf1XjNQcUMfTalTg3kXzSx+Cj24RY0d9kk1mYvujj6Hyuiv6aoQ5Q103mkQvOCQZ+ldFpSw9nWpgzjz1c/c0R7n9wpQTYXWGODibrzMHVuoM0N/Hu6TW6Eoj2hDh6eJMw2YvFxcWyB0o4Hh3M1HYswmqgexuI1AVUjSloWoc8fuD2pTR2OWDlvjBOtsCk+ZNyrpiLWbIWh+dwqAnfTNGxEqw8F5erLsa8g7PeEl07hmsYFZCiTu8pYbCAWghECYd5ynCx7CErKE466/IgKlDRPy9BRZ6L+yczPPvkBMb7YyGmmGIdHXUdG+lkxjMM/AiX8x7mkavmcKueUoY+zBJd8K+fD+A+FKs+qszbDoG2F8SY/+wQ8W+nSqBtnvdXNV57QGmmiZcbF/b7S+U52S3EitToYuOhcxSi60jfyL5QxxC6yZMhzh5f10TY1oxOCQrLxMXzpwfKtObWBN/tMEeCwDpzcLXqghCOB4P5rXqJHt5I3WWdOZhsxEpxDw7mSsD1DNk35nYgqbVr1MTStmxRW3OkXeGPDvR6xqittkiJv3x7P2uAo7EWkxTIuQGHCmdsYCVYZS6e3Awx6EQ49EN0rAQeMjDCWgTnSrAFAJhizRtjwHC56uLFsoeT7grMInBLNtIW/sh1dAZuBPb+GM+fHoA+nFTHz1lr5sc2cgRWioNuiItPj2C9U6bFWbEz9LGNAl0nQXQUYrHxYMmevBpANAVa38qweX+55aBl/BvIUCQ4FFxkdpJnHRy9N7lViM0K0RclvPFx/uCm5lFpC3Vk/5Drmy4O394twuphRpwL0fNiMlB2+rppbTvM0RnFi1UXjlngpLMSE9/Itj5bnQdxcyeFiYSZ2OQWZomPJ88PcXY6wwcnY/hmCs/IWhnJbSAiAaTNs6K3x0wKE0lhIE4tRImFZOWALk2wQQZqleFNRkHnFlgvh9NN4DkZXDuDYwgari9C3uYtUSFZA1yarEUHFqtM+bpGjuAkxSQK8K+/OMOj8wmGzga+KYxijpGrdWnEtkrBlmopcsJBexxX6y4ulj3c664AO1bnrhn+WISolDJzCfLzGS4mAxjH5cOrbEC9lfmBsOd3bIrDt6e4vunCPdkd+lBwFfr0vRjPnx7As+tL7+4SaDtuguu/OUT8rQSOmSPnVLSz/GYBSqWdiL6nLvxHWgvI24TYRYDhiXi/bMzUDEFkqJMUJqYbD0E3Rt+taj6aN7bK6BQGwtzG9aqDYT/cAhOdHgN6mCPA5Nm8j8BNcRys0bNikVXYo5dI8TZSYVIXaW7gvYeX6Nmx6BBXS6G21T7tBpFmmjnKLawzG7O1j3hj42C0Vi7Wjp3A9EvD4dnup5xeA6RWLihMTCMfN9MOXD/FsLNRy7k208C3gUsTWGSdkFNWjHceJnix7GGdOAq0lYkN7SGQ0lXAgQ4wDjt4Nu/j/gCAHYvPNMIf3afimwQDl6LoU1yvOjD7mpBP61ofLQVh30xRuBRxV8xB2aS7GfpIF61NRfe14ckSs0UAz8r2CrSWQeFZGfxHS6w0lmISCsa/QYAiSCVRjYyzLwP0P5wIcCB1dG0KsevEBjUK5aA1G6neZqizTm2sbgI8uH9T02aaoY4uws4jD5yjZuPeDyYCDF6sugpMJDPZBSbyeJLSlLZIPDy5GeKgF+K8u1Cfl+GNpQnUTTDRgUTfrmJbmYNp6GOx8HFytEDPTnB0FNa6u7V1jwNQO7fyXAHbVcsSvN4e3NQaQv3y+TH6/Q1GwaZWoyTDPyGkbmekKppfZj24UcveuEaO6yjAp+NDPDqYgTkRCoOoTJCeOatABfDkMQTAGB28WHVBeiV4tmgq+vrCHSsB9wieJX3MI0+tzqCLtPKGZ5rWMfBiPH12gMBJbwl9BGh2nBTrjYN1Yt8i0IpzETgpJp8dInlfVPDray69qvFaAwoglrZIchOrjQP37dVediIBIsoszCZdHJ0stju2Kc9JPaszmXVxdLpAx05UU6L2UKfqtDYZ9/DWg2tR1yPfL7UAUjlgawJsGeZIMAmMtBVMdL0kKixscgvTOMCTLw/x+O0rDJ2NYiVOGcpZjapS/bwUqFhIXm4zLkwsUg/X6wCMUZz0Vng0mME9HG/5VPRMmq7HyLErpNL/1vUZkQouw1Of4lFvpkDt05tDUMpw1AnRtyO4Rl4DXZMWirE0WZhDclAu91eEU7aRw7cy/M3np3j0cIKRG4KZslq4SumK46hAJSgXJ0cAXK27uFp1QXvldxlZaSyrNDJKRCjDOEFgJTjurfHF0yM4Z9rSGIS1hz5cdMw/Ol1gMuvCParmrCmroDWB1uaiPmnQjXB91Ydvy4cKUYJrG0tx315htXFUb2YBWK9uvPaAIpceTaYeBg+nt7IT2aDa68VbnhPdwCbL8JOyu7rtZOi7VTuCpt+kCnVEd/uL8QDnZ9PSWJW3ek2UUa70hlytOyCE46Sz2hvm6HpJVFhY5w4u113EmYkP373AwI5qWolkJbcBiR4y3UQ+xjc9PDyZ4p3htJZqlfvTZDu7DG+to+XBV88a5eq1jBsCeC2KoWPixCvdsamLv/ryPo4PljgoWaBnZLB5vhdYrFK4hdavxCQM1rsFni362GQWTjsrME7UeWzqKjqoyPDnYtnD1boD2uWKvUpHbZtHpWsnOD+b4mI8gHWvALXLNZQapjcZ+iAx6OMAACAASURBVDBDzMEwFr2AbcnMDA7GqybXlJPKm2KnWPdirGLnTiyl4ya4+nKEyE/U+1/leK0BhXMiajoiB52TteiNsoediDWMTaye9XDy7qQmTirhtmlgy2zEf3GA0Q8vVYpYThY5ZKgjtZmb0MdwuFb9Nao+Kttgomdi0txU2Zx9YKKziGXm4ul8AN9J8c5wqj5b+UrqrETetOImlbVBAkiWqYurdUewke4KD96a79VedCZikO2J1wxzdg0Z/hglyFgoUGgFg2aZPnY4QWEId2y3NLAdeWssUxfPF31QynDSWaNnxwpYnFLzsBqNhICKrVRZJg57WOBq08GT2RAPBnO1j83Uclv4c9pd4el8gMkmUAt1SUdtE1SKUhvJHYpouMZN6NfWhGr6UxgRrSA9nmEYRJj+81Osf6i1INBCH6UXlV6TfhDh6leH6DxOVBi3i6W4Zo7OyRrrqGIpr3K83oACIC0M2H/ehfcH47qaXY4t7SR24N1baw7aOjuRn8lLcJiHHpyPq/6rkobuCnUWiYs4snFyPK3aNjYyOqrQrxDaxDz2MJl18e7p9a1gIvctLGwsUxdfzoYY+BGO/VUNTPaxkowbVSe7EpSu1l3kBcW93lKIuEa6xXB0cNIB5K7AsWu0fZ4SwSIMUgGMAkNiwOEEGRWhTtcU1vtl6uLFsodro6NYXl4yDEZIbf91tiIFS/3fmHTxxXSEh8MZmE0QIIVh8J1MxYPwgJz1lvjV5VEl8IODGpl4E7TPEQJGGHwzxciP8GQ8wsJ26z1KGqEPK4RgHFgpwo+nmIceXFPLZmoCrWQptiEaJXn31ljHDlxTOIt3sRTZiCn6P46R/kGEgr1eC339RgcHQZjYKH64xFC6/DSEBursZJNZWL7o4vSt7TSxeG9diA1TG3Fk4+h4poTYpqCqhzrr1MH4l4e4/8FV+WSv6yZySGYgNAoXzz8/xDvfuizNVu2pYT3MCQsb88TDF5MRTgcrHHprdCUQtYQ4OiuRqWnFjCKxNMOj0awWKtkaKEkmIkFkF4DsavUo2UZztLEaffv691BSgMk6E8415iL21TFyBEaKgR1hnnr4/GaEYRDh0AsV0DJlYmsHFhkCydSwSRk+uz7AW4dTwBH7sTv8yYWYaxM8OrnBZ788hfW4UPNR6FjaMep6ipnidLTEs09O4H5YAkQj9AGgWgp4ZePpp+MhQs8WwN8QaOU9IM6NgZ4f4/KLA/hvpTtZCiWiUtk1cyx/uARLbHhW1nqNvup4rQGFcYL1dYDDs4Xq3KbHfG3sxD8O4VtV6LKPnUwXAY5GYtmMXQa2Zqhz+PhGeFQaTtimCJsyA2Hm4Ol4hEfvjks7femA3RPmSDD5xZNTvHV/giNvja5ZlQw008FtrGSVO7iJA3z22Qkev3uJ+6dzBEaqMaMKlPaBSL0xdb06WLfc7zO2yaHrLwXQyoCqp6kAF8lcLC721y4Zi2dk6J3GuIkD/NUvHuKdd65w4IbiPIHsZStN8xchHL94cor3H10qUNkV/jBaAGYKxgkevTvG0/EI9qm2TpQm0up6CoMQXA8f3+Am9KusI9nO+kjDm2+lOBqtMC3Twmo9qgZLoWWo5FsZ/ONQ3ANW1spShAGuZCluislF/5vVsY1zAqubqjy7TPG1ZXbi3ET0WQ+HH05UAZweHtWbJonqY2owBHaqCb1sK9RRbtjUQZqaOOtV1boSrNpE2HXZguBotCwL/TQH7J4wR4LJ44djDJ0NumYVIu0Dk4SZCHNHaS6Bk+J3P/xcMRvJSG4DkirdS2vg0Uw7y/0W720HlHpD6nr9UFPkbe6P2i/CYJR9Xi1eICOGSpt6Rob+hxEuwx5+eXOEB4M5elaMwEwAilamAs5q3enhAeZDVgOVneGPzMiYGZgTIRkZuFx1VV+TNpGWchHG+GaKoUuxWHtYpk69R4kW+sgCQpsWCOwUc8NDmNoVCDVYiqzzSamBrpdg8teHiL8dlw+7esaHgQh3MRUZH6ubIk6tfbfgS4/XGlAYIwj8pDr5+s2kWgwKR+cmsWE/WqvlMyrlv7p5c1n/UpiYLgIcDtaq031TiAWgDGxRbuF61sVpuUayLet6yvdXXotKN1kkLgpGMXQlM8m32h7I41BaR+rii8kIb92fbIFJm/iqhzir3MEs9vH5Tx7g7Y+f4sANEZgpPCOFVa5VbJGiFUiaIKIDiMrA8HraWXfQMk62YnF5kzV7xTZNa3r41hZ6tQEL5eK9JilU9uLGCvDJ//k23v74KXKXomsmtRBInzu0DH88bX/fuj/BF5MR3jm6AbVLUdfIoR+V0jo4ATMJhm6EVeRikYiMjNRTKIHmpOUwIDrGeWaGo/4al9OeYNElsBlakWEl0ObwOMWgE2Ey7yCwRXdBSjhsNRekk7YUdK0M9qM1Noldbr8AINY10oVpkzJYRoHATxBuHLzK8VoDCi8IfKeKCZtaherElptYzAIcHy/aq495dYNIdmKaRclO8lZ2ololFhaWsYvAT8Qqcma2M6sjQ51FKjqtvfPRc3SspGasqwOcoXwmy0wIsKeDlQpzdDBp00tklfEic/Ei7CHNTfwbv/cZhs5GhAY0hUkZDFRP131AIjNDkvHI7cumT7PYw/XTIXqnK3TdpFpnulx1ry0tv8pc4XKOHSwvu2q5Vrl8iAzldKFZHe9OYGHIYMCEACRLMpbfy/B81cc6s3EvWKJvxXDK9LHOVoBKU1Gg4glG/OVsCDrSTHO06hooa39MWsABQcdKcK+/xGc/O4f9Wy/EvKBFa+hT0AKumaHnxFj5DpaxWzVgZ0atgLBiKSItPDeLGksRc0BnT1XGp+fHGI/76LqJYsN631j5XosW8J0U88vu3W/IO4zXGlD+H/beLday5DwP+6pq3fd9n1ufvs30XNjTHFIkaIq0QFigI0GWrQcjDwEswYBgGFAerPfYTwoSOPBLECBAYkCBBScIIsFvESJBtiJDkCFIohiJpEjNrad7+jJ9+lz6nH1f96o81GXVWnvt3WfIHqOJUREbZ7i7dq211671rf///u//f+rwKlKjLQ4ro5gLipJTLDMXTpBbzb3WIzvaFdHWyd5ovqaI1aM0RK8kYt3/c4zuPz0yNVHcFjCxXZ0n5wMc3jlBz91OwmowWRQ+Hk2GGEaxJGC3gIm2IDLuYFF4mGUh7l+MMe6scKM3UZ/Najcos8ASqIAk50zpVGgNRJaFjDCdqCzog/4cPTfFaLjCW+Nj+GqjftLC2OlBpcqdZiHen/XgOQX2VSjYFuppq6oJhvp7uOrG1ZaQtlYCJ8fxqocPnu3h1ugcfS9GV7YHrLlYlIg1UOGhBMFHkyFeGV1UFg1tE75JkrbnJji8c4In5wP4SozW5vroqE/Acow7K6T/5hCLf5Ibd1sL44DKStEK2lFvhdOLnnwAKuvbtlLsiE/o5nCCHMvMRejk4JSCW26VnYnssRKdvc9QGw1pMq8L2YBK6ZqWDubLAINuUgmBWiI7OhKkrRNtcrZZJ5W8Xtb+DP7xOcaqPYcd1Wm6OrqObDdKVA1YyZuwhuulrZmUM6wKF08XPUR+hv1I3rj6SdQGJjZfcp5GePfRFXzu+jF2gyX6blK7IZvujW2R5KqUZspdtZ5n+BdPJSy+tXOyUUDXVMs2Izp25KfNjSoEw6vdc2Od3Z/sICuYxYNIUPRpjhJUunxNi8V2gzRIqP3iswLfe3ANb914Cu6v0HFSeV0avIoGFR8EPaTg0RylIHi66MHp6SgOXyNpGQh8KluBjsMV4lzmKOl+O22uj1TtUnTcDIt/fI75KjQBgaYs37ZSIjeHY1kpHi1qVoqtS/FoiUE3wXQRoOercgVivUSEdhUjP7v8DXmJ8VIDim6wtClUrMnYfO4jHM2rGH8LT6G5k+kixKi3svr9bLZOVrmH1cLH/uHCWBptRGwV1fFw+mSIz712VONN6oW25VM74w6SUsrpk9ypidZ0NKf6TDuYvPPeddy5/Ri7wQJdJzMujgaTplViuzYytOxhXviSCL57FW+8/hR39o6NRqWNyK3EWNtDzKaOrAVia+fBGHLBMPRiHARzLEsPz5IO/uT9N3D7jScY+rGxuDglNVeo6Qapk5HXzVVP7hvCXCMAqr7iuvvDFLEJAKVLcBAtcO9ijPOkYywOxvIaSesQCURcEEROht1ohffvHaJ3K1W80brrownagFH0gwTnFztYRZ7svLDFSvFZgWE3xsU8MlxKswyH5khcZaWczQdI+g4CJwen63J8HUL+bLXRUJ3RNgnZdPW23t5CyoiJlW1JrPIEOgM5d1HkrArDPcc6OV9G2N+dKdHbOhHblNafzLu4duOZyu1ZT0jUx9Ak7DQN8eDhLu68/qQSvJF6NKcNTM6SDj58uocv3Xkgc3pYRb42b/w2IEm5g3ke4DTp4uHZCG8enOIbX/gAHeVqaRDRfn0rkGxwczYNXZipFFQmxenzUnxVzhh6IsHAjXHwhTkmWYi/fHwdN3cvsBcs0HMTZbGsu3LaWgEqMphCgIUC3p0H+MHHh3j9yqkqeoRWUIFQhatZDu5SXB9M8c6HV+HfKsx6bSStQ0t4QtZiuXbjGU7mXfOwsl0ffSxN0HbcDPu7M5wvo0tYKRIkTnO5h0Mnb0kclDk+DpeS/N7eAkulM/FY2S50U/L9FzmeK5MjhPwGIeSEEPJ9670xIeT3CSEfqL8j9T4hhPzPhJC7hJDvEUK+Yn3ml9X8Dwghv3yZkyPmwra4O1wWXVqcdqrszA03sLFOliHGw+XGyI4OE2vuJElc9L0KHGwiVp+HrCInkwUBqDIGW1wdFZVZ5D4ePBvhjVvHleBsgwK2BK2Byf3THbx97Qg7/hI9JzFg4tKyFUwMGJU+JnmIR8sR/uTd1+GzAl+/+RFudi5w4M+w4y4xcGJ0WYqIZfBJgYDm8GkOlxZwaWEiMwziE71ck6wn1/FpLtcmBSKWoctSDJwYO+4SB/4MNzsX+PrNj+CzAn/y7ut4tBxhkodYlj5S7iAXzAASAAN8rnIVQ5ah5yTY8Zd4+9oR7p/u4CzpYFnIz9s6GuP+EFlTJWQ5hl6MN24d48GzERa5OiZnBhjl5+Re8GmJyMlNLdpZGiApXDVfpx1ogJBRLo8W6HspkkS2NclKxxSw0kM/wHSjsvFwiekyRFo6pi2sPTTAuSqzeHHaQVYy0zq2Nte4SS82l+cyutt/C+DnG+/9cwB/IIR4E8AfqP8PAH8fwJvq9SsA/jUgAQjArwH4OoCvAfg1DULbBgFqeTs2GZtzhjhz4fZTKU+2iVsTbaj6+CSFg2ThbdWd6NorSelgsgqxN5qrYkB1MZqR14MY0dvR6QD7vYUsu9jIVJbnokKvgmJVuDhe9LDTX5qITBuYaKsis9ycD5/u4c6VY+z4y4oXsKyJZqRKq2YneYSncQ/fOb6GklN8485d3OxcYM9bYOis0HXaQUTyBXVw0KMEudRLj+Y6GmDWwMVJMXRW2PMWuNm5wDfu3EXJKb5zfA1P4x4meYS4dKub3AIVHdrV4NBxUuz4S9y5cowPn+7hPI2wLHzZalVUN3wbqIz8FXb6SxwvelgVrqzpogpQ6WGOp3J39nsLHJ0OEBcuMnVu3AIKqkh9j8r+QHujOSarEEnpqBu/DpIahLQuJVl4SAqn1nNar2uHhQOngNtPEWeuAUIuSC2E7FCZlvAix3NdHiHEHxFCXm28/Q8BfFP99/8O4A8B/Dfq/f9DCCEA/CkhZEgIOVRzf18IcQ4AhJDfhwSp39x2bELW/XMNEHnJsFgG6HXjGhlbzatCl3nJME98jHYWJuy7kTvhkjuJVx4OBzNVg7atLIGyTkoX53GE4XAp63g0uBZzPlqhW8pKa1nBcK03leSjpZxsA5NF4RnO5Et3HmwEE30c7eKk3EHMJdl6tOpjmXl4a/cEI2+FLksNx+MSy7XRrkPD0rOBwb6hNsnu9WCEGzbIvh5NcII6NheyMpmrCHCfFwhpho6TYuDHeDgbYeqFOIxmMmObZmrtuguke+GAwuzyt68d4bvvvII7tx+DEm6iP02dig4LcxDshUvcvxjjIq0IV8aEeRLrULJnoj4phsMlzuPIPIxklKjaO/pmltXvM5w862PV8VSPpHIDlyLDzqOdBeaJj66boaC0lomsr4MmZ3udBPNFKBuvM7pGzsrv+p/fQmkbB0KIIwBQf/fV+9cAPLLmPVbvbXp/bRBCfoUQ8m1CyLezSdzq7sioCkPxLJBNjDaRsRbXMj/pIvKssPIG7iQrGaZxgJ2RFL0ZOf4W6+Ti3THGkawl6zbmy/OQTyjj6ny8i8P+TBVlqkdQ7O+oXbVZFuLdR1dw5/ZjVQdlO5jkgmHFPSxKH+dZhPcv9uAQjjvjY+z7CwzduGaRyHWKmisDVBaIEbdxByl3kQuGhLtYcQ+pcLDiXutL/1uiPpNyFzl3lLXGahaM7Rrpc6lZLG6MfX+BO+NjOITj/Ys9nGcRFqWPFfdaXaCmpTLyV7hz+zHefXQFs8xyHWpPenkOjpL6d90Uh/0ZHny8a1wfvQf00K6Pq8LW4yjGxbvjrVaKLgIVOjl2RgvZhK5kyvJosVIUgRp5OeYnXXnuloVlzsUiZwO3QPEsQFrWv2N13uv3zI86XjQp26bBFlveX39TiF8H8OsAMHxrX2xyd5LMRXi4MA2128hYzbWscheBarthKn+1AFWmVK7LuwPsfvlJjTsB2q2TSRxi7+1To6HYxONkKlnwbNXB1SsXJgVfA4N9HjaBOs0D3L8Yq9DwQkZgngMmmm85Tbr43vdexZe/dA97wcJYJXZYWbs09ihR3TB6TXt9W6Vr60zsYetU7BC4HYHS/831fE38QoApzkVbLJQKMIfDpzm8XoGO28W3/uJN/MRPfIS9YGHIVrkL2y0VzjLsBgt87vox7l+M4exUmb9rwjcdxWEUfS/B1SsXOFt1ZEMxWoKxfDNB62TYe/sUkzg0yuqmleIQjlJxKT0/xfk7O0h+IjYRH3tUNV0kORuMEqxyF5GbmQhOGznrsRLh4QJJ5iJXrv66JuXlqIdyTAg5FEIcKZfmRL3/GMANa951AE/U+99svP+HzztIE4Vsd2e58jHoxa3FkIDKxcg5wyL20YuSWqjYnlcq3zLjDLPER/9zFzWJvR5t1snZ4yFuf+7jrdZJrhuBZwEmixBvHZygo7iWivepjqNBYV74OFr2Me6ssBssZWjYImDbwCQuXSwLH0exLAb0ta98gLG3QkcRrVUYuO7aaEtBPklV9EUpee0ws85inueyP/J8GmI0XiB0q2I9smqeg4vzLnqDGLtd6Q7qSFbYAEWXlKCCml7F+ryYit5QwsEEN6QrJTKC87WvfIAPzneRcYbDcAbupADTm6cFVFgmH0zBEmnp4GjZN9YqqKyfAlSgoj/bcTLshku8e7yPgZ9UHFxD8MZAjJUy8BO89/41DN+MDQhJ0LXcPlJJ8vufu8As8WWrF7UnzY0PKyrDCvSiBIvYxyBIUHC2IYSsdSY5pvMQgzBpdXuaHsCPOn5YQPltAL8M4F+pv/+39f6vEkJ+C5KAnSrQ+fcA/geLiP05AP/i+YfZ7O7kFz58pT2pldez5hZCVmRLjjrYv70waeNNALKbiF08GeCV106q0gdruhPVj6d0MIlDXHnlmUkWbKtbWwnYPDyZ9XFjZ1LNb3F1tOhrqXJzssLBjd7E8AXPA5N5EeDJcoBl7uHt3acYujKCFKnPtlklpTHJ5To2gCxLWTntyWIALgiudqWrthcscHtwAud6VQLBHiUo+CGppRcsch/vX+yBEoGrXdlAXoe8DcBoQZ5FBgMAtLgMAlT10nFICW+3wL3pLkpOcbUzlXO3gEpIM8AFiojiw4tdXCSRdGtdmSNk8ykuZNazR6XW5MbOBE9mfaWwVlEra9/ZVkrkZLjyyjNM4tCUurCtFK1L0flO/SDFg3v7GL0Ro+AUDqFgVjKsDiE7hCNyc5zdGyPtLWUtGAU++h7ggpl8Hd8pkF/4SIcM0Qa350WO5wIKIeQ3Ia2LXULIY8hozb8C8O8IIf8UwEMA/5Wa/rsA/gGAuwBWAP4JAAghzgkh/z2AP1fz/jtN0G4/NtbcnZJTpLmDYC822pNNylhdXza6tqgRn5vJWBed/aUskNyiijVEr6Cy/MHdMd744mM5t806ge557GCe+6BEoKdKP7oq/GrmNnmTPMD9P7+Bz//UPfQcHbpus67qYHK06mOZe3htcIaxt0JEbWtAPoFtq6QNSJalzFr+eDlAnLu43pvgiztHa5ZFU6PSHGtak4DhZucccenhIgvxzvkBQjfHtc5UqmNZWgMWboGfba2AAxHNKrXu4Az3prs4WvVNJbUmqACW5BwFek6Ka70p/vpPXoP/U/dN5TdGK3ITgDoPKgs9uQlOSBfz3K8s0gZBq60Uj5Xoeynu/tV1jL+4kvONK1kdQ6tnAydHZ38p96DrbCVnfVYguraQe9vNLH6kqZyVOpNgL0aaOyg92irFf5HjMlGeX9zwTz/TMlcA+Gcb1vkNAL/xic7OGtxyS1aJh05YJT+tzbXcnfnKx7AbWxnLzXoqFRk7WwUYdio/tmmdAFDWCcMs8zF8/dwqgr1unZRCVnlfFR4+Ph/glZ0LqVFpieoAdVfn0WSIWz/5SIWVszrvoQGhwZloy2QTmLRZJRpIVqWHZenjLO3gg2d7uDaY4rXeMyMoC2hec5d02BdYjwjZxzDXgtWPN/aWuB5NMM8DHCc9/OD0Ct7cOcWuv6zcM8i6JGvWCi2qCA4AeDCg8kQMcF03LVf/ThVvZitqOSMY+Svc+slHeDQZItjJDZ/SdH101CdyclzpzfHg2QidA2VlCgKK9ar0poj06+eYZT46biotZGZ3C1B5OIQjYAUGUYzJMsTAl+5Js5WpJmddJmvDThYh+hvcHj3fpSWiIMUy9pGFCXwURjX7aYyXWilrD21x5CVD/qSD4K1lRcQ2Q7SWu5M9jRC8NTcAATQybo2E38XqIsTV4cyYs82LXoiqhcbpRQ+v7J9v5k4UqCWlLAHZi1L0FBGr1bD2OWhXJy5dPEukWG8nWNaI26ZoTYeGNWdig0mXpQYEbBdH3+S50mGsuORFzrMO/urkELdG5/ja4QP0naTGuTSBxD7/TZvTmNdE11ShBsgimiEXDAMnxthb4lo0wXHcxx9/fAtf3D/C2FvWXDVY1hWDAGhheBVKRA1UjmLZkhWOVM5qhagNKpwSFCzHTrDEMpeSf1OBz3J95DErFW3PS9CLUkySUHIjW6yUQLXGeHAyxiiI4bEShaDwSP3aSaCQ+WVPLsZIektTXtTMg0CpNCQyCbJA9jRC2pdCzabbo90ph3IEboHJh2Pk/aVyp16wWWKNHwtA0RtTJ/jR/aRR82STu+Mguv4cdweVuzPan9dk081QcSl0qUkPYZih42ZG+bjJOklKF4+fjvC5G8dG9LZ+3pobkmHle/cO8Lfu3Jf1TGzuY4No7TTp4njRxdu7T41lsglMbCthUfiY5BEeL4cAgK8dPsTQXdUEbpUytu4KNDmTtsGsfStv5tJs/BI6YkRNeLjvJNgLFni4GOE07uJ6Z4KhK0V3nBOTIGi7QLrmKxfEgMoPzq5IziKsgK/eX1h+p5BmyB2GK50Z/r93bqF3W7pcDqnanTYJ2sjJsBMt8f6jAwxflYTrJivF4RwdN0MYZljlntEo1d0eDkaoIVxH+3Oschddz4HHnuP2XF8gzh10PVvkZrk9Rmlbgu4nyEpWu5c+jbDxi61Q+ykMHY8vlM4gyR2EUaqK9rTUc1VP7lJQLGNf1lOxCwPX5lFj9cyWgdSp0KJmzdgye82HTOMAoyiWyXMtEns5X+b4zDMfOzuyB49LeC1XR6+rpfVx6eIs7uCN15+qSmvZdt6Ee5jmIb73vVfx5vgMQzeuuTmbwCThLqZFiOO0j//4zm2MghVuD45x4M8wclbosgQRS6WClWhgEgZYLgMmzaE/Z68VEKnIjViKLkswclY48Ge4PTjGKFjhP75zG8dpH9MiNFoWbeXINYUBPJ8WiGiGoRvjzfEZvve9VzHNQ8QtGhWg4lNClqHnpnjj9ac4iztGgauzo/VcbaW4hKPrptjZWWCe+arAVHvIXFcOHEWx1JnwSvdi7y1tdXi0QOTlmC0D5EYy3zxvuR9cJjOFl7FvhIxrUnxFXDuUI4xSJLmDUlAUgpm99KLHSw8ogKXNKBnilY/ALYyp24awhZBFl9hf9qqq4dbTw15Xk6DpQrYVMKK3DWRsWjqYPhjIhC4dPmycg5bYJ4WLp5M+dqKlKSbU5E1soJrlAS6WoXF1zA28gTeZ5QHuTXbw5S/dw9hrSvjXwSThLlalh0ke4eFyhIfzEX728+/ilegc+94cA2eFiKXSwiEVZ/I8EClBW1+bhg0uGlgimiFiKQbOCvveHK9E5/jZz7+Lh/MRHi5HmOQRVqUUyW0DlZDlGHsrfPlL93BvsoNZHtRyf/QeYKQ6h1C5PhfLELN8/cYHKmm+z2T/5J1oiaeTPhJLkm+PCiRKRG6G6YOBEqPRFqFbJV4L3Rzpwq+J7uw1AZj9HDgF2F/2kBaOAYnmOWgFceAWiFc+8g0itxc1fmxcHhmupfC/G8H7u7Pak3std0clDvKvyFwcDRBt7o7O8xnuLEzRaW1x2GRsqdZdZB5Gty5UCvk6KcyV0jEtZY0Rz5VqS21Kt1knuZD9e44XPbwyvkCHZSaq0wwR6++3LHwcrfoYBTH2goUkMk1YuWgHE+5hXgT4aDEGJQI/MX4iXRzLRXJJ0RoGNtcN7cWq257SOdhzXSUJmOomh3JnqAr1+iX8cYGPlmPcW+zg1e45eo5sWh7QvO7+KKI2ohk4I9gLCJa5vEaGg2rwKS4tUYLCg6yo/8r4AseLXqVgBq3VWmEqI9lXClrPLbAsPMN3zXeLIQAAIABJREFU2BJ4fQ2kxL7A6NYFFpmHnpsoYZv6/oqcZYSaOi7DnYXM1/GqAlVNt4eqCA7/yryWAChdtSp8bCJbrIT/3Qj53519tgHFbFzlmmRfXlbNpBv8iZ5fcoo4cxEFKRipV8oHKlNPWz3z2MeoE1drtkn4dd7OrIOr4yk8VmwmY4Usl3C+CrHbXVrgs86bGOskC1CU1GQe66e3va7t6lxksnjxnfGxyQ5+HphM8hD35rsYeDGuRxOVWZzUiNc2ILFBJBdOFW62ws76/AAYi8rWvOi/GrCAOrgYYCECVKiiRrRQv1+Jx6shPpjt4bXeGaDqKm8EFSZDqVc7U7xzfoCLLKysQyFqoWQZFiYmw/ho1scsC0xo3w4jm3CsAond7hLnqxADL4YvKFyQDSFkqTN5cj7AKJBRRJlsWl1jk7BHODp+hgsV7eEKeXRSnx6S5+OIApkAWPrU8FNVl8EqfOyyEtmXl8hLJuv/sopHeZHjpQcUoEr0S3MHflC5JWvz9BNcUKxWPvbHlSWzScyWcYbsgz78r87Xojtt7k5Z0kpO3QAfQ8Zq8HkywLW3ZkoNuu421K2TLg77s1rpx7UiSTofqPBw93wXb+2e1KT4dtU0mzORoegA9+a76LkJrkcTjJR7E5Bio1WieQQdodH8i11XJeaedBm5NOcBaZL7qpdOSLOa3N8mizXx2QQWEBhrBSyR1yCS3//efBdv9k/BHKWcBQyoAFDvqfwdluFm/wLvnu2je5AaIaEmi22CNqfS9Tnsz3C86KLvJZWVgrJ2fq4Kx3bcDPc+PMBhb45A94FqkLPUUsOWJV1ze2xNirZofKdA9kEf2d9aSMuDrovcqCJyA7fAyTxC0V1WFkpL+NihHH6QI80d8KA69ovmUV56QNEXKS8Z0sxBL0o38ic6GTAvGcozH95exXG05e4UQrYudd+oR3eaQ7s7q9zFeLCs5P5kHdi0rmWR+bhy87xqubFmUVUWyiL3wbnMGfFZVcbArNnI0zlLujjszTHy6omCTQWsBoBZEeKjxdhYJpcFEx0NkjoVH4tSRoWO4j4eToZ4a/cEA9W2YkhWte8mxXYeztIR3j3bx83hBIfhTEZtWIqIpdIqQmkARA8JKhQuCv2GHB3g8WqIjxZjvNattCa+rYdRIGMSAgXFYW+Os6RrOKamlaJJYp8V6HsJjngfi9xHh2XgtFiP+GgC1clw5eY5FpmPrpvKm7Th8uiXR0uMB1K4NvBoze0x35tU8nr3jblyexh0H2h7nuFoWInyzEe+I2UHjhKtmXNo8ChzzaM45LNsoajG5jMfo95q7cfVc/TfrGTwrqzWCFY9DH/CKZLMRTfUUaN1MZtW6GbcwWwVYL+/qLk7tfM0nIyLs0UH14cTWc6xhYgtQSvdSRzhoDc33EmbdWIsjTzAO/eu4ht37m7VmmidyaL08UTpMtrAxHar5Gd1dTcHiXCwKANMixBP4gFOVj3cHh7j7cERfnL0oPXY1TqVhfR278i4XH9+9gr2ozmuhlPjcrUBm3aBzNCgEgF353t4EvdlPQ/CQbnSpdjhZGUNdRnFXrjAH7/zBoZvxarDX6MPkJrvKavmoDfHszhC301qrlK154TKwykw8BM8ngwx9JWrark9AEwWssdkBfuTWRc74Qpc5OBCuj1NkZtDObphiiRzUQTrPIo+B5OFfGXVEhKu8yiUCDisRDrzUfSXn20OpeDSPQEncK3ugW38SaGk+VGgq7it8ydar1JyivkixNXdiQpBtxTDRpWQuDrtIBxftHIttrsTFy6y1JG6k5ZQsT5X6Ro5OHnWx41XJxutk5xL0i0uPZwmXbz9+sdysz/H1VkUPs7SLs7iLn5i/AQDJ34umOgyAyvu4SKPcH+5g0IwvNY9w9u9I/RYIosv1SJQ6+AqQVvyK3rdA9fFVX+KiyLCvcUuHFLiVucZRq5W9eZr1krtHJm8Hq92zvG986uInFxeV0cSpptcn76b4O3XP8Zp0pVJmaREDlYjvJtWygdP9nHYmSHnTNaPNaKxipx1iexdnKUO4sJF12Ub3R5dqmB12kE+nKJQnIs9DEgQ2a/4fNLFfndhHmq8sec0aR8FGdLcMcRsk0eB0HM5wKv7idMXDyovNaAIof8S5CWFN0hlzVC0lIW09CdJ5mLQiSsirSW0q/mTMmUyJ6jh7thitoLL3J3+lblqCblB8q/cnWXuYW80V7VX1iX2eoOknGGahbh5cI6OkxldTdM6kToVF/PCx8OzEb5+8yMpeNNiLetG0mAiLYIIf/ze6/jZz7+rXI1kI5hI10ZaJdMiwnHaxzsXB/jq3kPsugv12dxYJRIg6zewPTRBWxG4FDlliKgMDe+6C5zlXfzZ6au4M5IamIGzaj2/OqgkKF2K28MT/L9//Rb+izvvGYLSBcBUTRcQDiooXCoFbGN/iT97+Cp2gqWMuFGrZIHJE5K6jY6T4ebBOaZZqCJ0tOYe2OSsx0rsjeZY5h5GAV1ze+R8XfaxRP/KHHHhoscpSlrnUeR1rGq9lilDph4msmkXzPlqHoUSAc8pMV2GNT1KLftYnS+jHN4gRV5SCMuaeZHjpQYUoCJk85LB84qNhKyeW3CKZOZjr7/YWC/TuDElQ2cYV/JtrNeHkGvK4sDdIFVmtm643RLdKRkuliGuD6fG3WnK7DUZm3EHp4sOXhudV64O6muWOhOaO5ikId48OEXXqROxtYJIVrLg4+UQX//cfYy9ZRVStqIsemgwWXEP50UHD1ZjUAh888oHGDtLRDSthZWZSQrUeSnr19klElRcAJxIS0UDRSByoz3pXklxb7mLu8UeXonO1fH0GvUGVS4KlCCIaIaxt8TXP3cfj5dDdBx5fja4Mghwy0rpOhnePDjFJA1lD2SeoyS0xqVoXYpHCwy8BPcuxtgLF8hFXgsh67na7em6GR5PBtiP5ihYe7RHAoXMwYlzV2lMKAD7O3JVWV9e384wVq7Mek1YPTSPksx8FEO6tqa9tkM5PK+QHArWwexFjJde2Ka5jjR14TmbBW0amUtOAYGq/Qa26E9yB6Gq4mZk2airY3XUaL7yq9q1a8eWlkwpCJLSRRJ78B0VGrRMavtcC1XcmnNqXCM7NGnPzQXDsvDw3t2rMqzcsE6AuquzKj2cZx0AwL4/R48lFt9RBzgbTM7yLr519goGbozP945w4M4wYCv0WIKIpujQVFkpGVxSwCMlPLK5YLX+d5cUCJRYrkNTRDRFjyUYsBUO3Bk+3zvCwI3xrbNXcJZ3VQU2yQHpoV1GzY30WIJ9fw4AOM86WJXempJW//7aShl6Md67exXLQs+ti8b09deuDFc5Xm0iN/0ZV+lBkthDUrpmH6zpclDVep2v/LWasLU+0FCtRb0cSV5FhdYKWGsApRwQUlqhLfXmsTVIeU6BNHWly/PZU8oSw3XksQuX1XmIJiFbcCrFb/20VrS6OUxCYOZK4VuLCwUoN0pHmM5DI3xrB7Sqb/LOSPbxMe5Wi7uTC4p57uOgPze5Rmt8SEMV+8brT2tRHds6secvSx9/dXKIm90L9J2K82haQNJSqsDkPz19HV8af4zXwjPsOnMM2BI9FksQIbkBkbV6sM8ZNsC4pDDr9ViMAVti15njtfAMXxp/jP/09PUaqNiKW1td69McfSfBze4F/urkEMvSr6lhzXFJpaLtOFJi36aeBWDm6lyZg/4c89w3hanXlbPytw2YLONYqVvXwUTzKD4rkJ6HlZXQclPr/eU7hSRmW6rWV+egXKR+ilxzjajuibrQTsBlHHnsSvD5FARuLzmgVFZC8KFf9VzZABJcEGQFg+8VNTfGzLEJWUGxmgWqrEG7/gSouJbuwcKKGrURvdKSWWYeer5MVbfrqehztN2d82WEnlJlNsO2VQ0Ymbz4aDKsJPkN60SubYWV0w5ujc6NCrZyVZpgwpAIB+dFB99+dhN/++AjXPMvjFUS0BweKRHQzABJc1y24r0eGlj0mtraGLAVrvkX+NsHH+Hbz27ivOggUVbKOqhIQJW5OyvcGp3jLO0YkGjWezVWipLYP5oMTZP3thwY3fir56Y4X0aqQj6t5ffItatOhT0/xTLzKstjjXDlxu3oHiwMN6J/u3UZfgmXlVjNgoobEetWhbY8fK9AVmyW1Ru1L+UIPvQ/FTABXnJA0du3FATJ62kt/NoW4RFK+eo5dkZvm4siLRQU1AjUNulPdBg69FTZgRb+BKhcs+kyrDVHb1OechVank4jU/6gzd3RN/2y8OA5JTq6mRcEmpEd2zr54NkeDsKZVM/S9ciRvgYpdzEtIjxYjfG5wQkOvSl6NJFgYlklm4Ak00Qu95BwD0vuY8l98/9z4SBTxaibQ6tmK2slQY8mOPSm+NzgBA9WY0yLCCl31014UhWzjliGg3CGD57t1ayUWvsODSpEXkPPKY3bU+vP03B7AifHdBpJ11Ss3yoM3JCzPiswXYatroSWITBF+oZebsK8ZctNbfrx0BIoaHtfHVQWkiZm85JBWEChz7kZ7k5eT2ttdF/k+DEgZQmKksEJ8q0RHkA1RM8cdPxsY3sAjfQlpwiGibF6gOqHL60fpBCy/09XrdmWjKj95ow7SOY+vP16H581/kTIqNHB3rQmemu6O1oZO8sCHHTnJqzcLONolMTKNbo2mEpXh1RE7yZX5zjtg0LgRmBZJhpINuhLciGzVhMhVbOZqFsGOlnP0yQsyZU7UQcnHY1BQ8B2I7iQhZfSfiv3w5TCU1fG7zsJrg2mmOUBOkqbwwWtRXyM68MKHHTnmGUBRt4KPi1QCgqqCGDD0Snx2sHeFLFKANQhWf2byshP1WcnmfvI9hyzH5rCNZtHWaQeirBOzGo9iiFmKUcwTJR7soWYpRwOKw03A6xL9e1IjxPkKEr2qVgoLz2gCEFQcgLXXX/K2kNf8Cx2wfqiRrKuzYVMNAy83FzoVpJXK2QTDzudVasVUVlIUqsy3FmYroTAOpjootWL3EPfkyUN2qI7trtzsujirZ0TUy6hbsWogklKmfrxcoDXes8Qsax2M1bzK1fnIo/wzsUBvnnlAwxYjIimyp1YBxNtBSXCVblBPqZlhKNsgL84u4H9aI6RJzvnXWQhTlY9fGX3EQ69KQZsZSJFGlzsCvcaVGQEJ8WAOXitc4Y/fPom+k4Mn+aggtc0KjLqI12miGU4COa4N9+RJRyUJVeCmONot8dTupR3n+3jMKoS5ew2nRVXw9H3Uixyr9Ysq/bbCvnXU0l9eclqe6KpR6FEciMn0y6KXsVjrOX1qPmBlyPfQqDquYwIZLFr9lhbpMdcN7dEyYmyZl6sk/LSA4p2JRxWPTk2zSs5RfhuAOewHtfXQ0d4NNfiOs8BKbVmdtQB2z3fDFBKf5KWDiI/qwphN8DEfB9BcbGIsLe3bNWp6JGrnkJZ4ZiEwaa7I7+XBKll6SHOXfTcxFKw1q0THTValAHuL3fw1b2HtdCw10b2Kqsk4S5mPMRRNsQfPL2Nnz64i9eDU3z5lYeGp5HnLS2WeRniOO/jd558AT9z5T0cehP0aayS+oo1UPEgW1fkIsXYWeKrew9xf7mDrpNaQjr1u0LnAsmbv+cmiHMXy9JDnzOUpJ75ywiXldhUuYKscJCWDnKHwUdd2l6RnTIH59HFEDd6k1pSaU2TQqTKOvKzKlenRY8CVKUTsqMOyp2LrZEWSgRcp6y4kZbMY33mDuUI3w1QXtkCPlprw/inFuV5+QFFEJQlhe8WVQi2xZoAJGCs3syqkPEGsNBZxoGbbo/wKPeE7NhRozZORM5NCgcdL9vMyaASyiUrDx4ravOa/AkXsi2qjgRtcnd0vs00C3C9N6kVem5aJ9pCmRYhCsGw6y4MmGheow1MltzHedHFO6tD9JwEv3TjWxg7CxNKtmvM6tBt4rg4cCe4fuMc99M9fGdxE3eiI/U5tICKdD8CmiMXKXbdBe6JXUyL0GRF27yUtlJ0FOd6b4JpFmDXWyAXTJWI3OD29OdISgdadGeL3PSznSnLI1l5KLiSBjSSBfU8SgQCp8Ay87YQo9xEZchOupHA1d+NQhZSSnJ/o3ui9ySjHKs3MwxtbqRZMU/9ZZTLJMHPosvDBUFRMER+DrLhSa7ncUHgBOtFjNrmZZkDFiaGfW+L8AAyth9G2WYwQWX1rDIXwyA2RPBa5EYL6riDnbFu61GpY80xhc6noVjmPnpuaua1uTuaP3myGOCLO0c1Nev696dYlT6exAO81j2TCliaV67OBjA5LXr4veO38XP77+Cqe4GhdmOIBqL6sWRURBKtfZpgyFZ4ko/wO8dfwM8f/ABw0AoqLpGuj8zDSfBa9wxP4gFGSkWLhsJXuycBzTHyYvzVs0NcjyaIWGa+g+32aDVsz02xzH3kQRX1a/IoDpERnJ3xwlRma96ompjVBaFXmWtAgjfyeoAKVMIok5op63dpZh5rTi/LnI0gVc0XcILiufMIkfVmCsvqeZHjpY7yAIpDKelaU+d1Rat0T1yvaHVNKmWgkvKnTo2QbY6qBw+F726P8ABAwRlWy2BNwt9cXxfP7nhZVee2wZ/o71NwhoskVJGgcs3VkecpVahxKZ+MuhGYPsd2d8fHyaqnbtJcEajr65dC1lI5L7r4veO38QsH38dr/gmuOFOM2QJDmqBHcvRojg4p0FOvDinQozl6JMeQJhizBa44U7zmn+AXDr6P3zt+G+dFFwl313ojM8KVXkWSuSNnhZNVDwsVwbFvlspS0ZXXZB2UuPTMdWkObaUETo6LJKyJ1uybSwvpHNWkPC2q8gxtv62WzK+WAQreUj2tEenxXcWNbIj06PUZ5chTx5LKt7sqFAKuVxh9SfPYtWtAOUpLfv8ix0sNKELfXBnbaJ3YiFxyAsb48y0ZEIhzf6slo+fmJVsT1DWH5mbKqVvLWF4/T9XjuHSUC7M5EqX1KqePRrWmY82bXnf4i0sXV7uzSvTWcOV0ZCfhLiZ5hNvDY0tBW8gEv4Z1kgjJmbyzOsTP7b+DG94zDOkKPZqgo4CjQzkiIhARIFCviAAREehQbub1aIIhXeGG9ww/t/8O3lkdYsZDJMKth3ghQJXWRGtUbg+PMckjVYulLnaTgCyM23O1O0NcuqZ9qj1MM3UiJfOnj0at+hJ7uFqMVlY9jdtuWF1OoJy6a6rW5jACs+dEWvT+FOd+qwLWnkeIAGMcJa8eSJv0KIQI8IyZeS9yvNSAAih9ScJaoybNeZzTWrh4c84PgfAqkGjjO+Q8iqKktXYdzaE3WcEpvB3tQm0+V1kekpnC2c0sZPscC87QvzKH3xDI2fyJnrvIfVUIu6rVsnauCnyO4j6GbmxlDa8DlQafo2yInpNIN0eBSUQKRKSET4CAEPWijZd83ydAREpEFqhcdS/QcxIcZUMDEvbQpLBWxA7dGEdxH/kGTYv+vi4p0XVTWV+mocWwwZISAV8l6jVl9fYcI/dnpWo4vn67NMlZbycxxaXbQMW4XZSjKGnrmvIaVOsKj28Bk+p3cygH36CqbZ6rSD6dsPGPBaC4EwaC9RvU/jGEMh2b1smmcDDpbJbc67V1hGnbHHtd3883ggNQEb1J5rZGgvTQhGwhKHpBWkVrWoBCC9rmuW9UtAy6Pmvd3ZEZzg4eToZVa1K1bv34SknMffzB09u45Z9anEmJgHC4BPAIgQsCl9D2F4icQ4CAcASkRERTDNkKt/xT/MHT21hxf02IBmhQ4UYR+3AyRGrzGHoedCSrUsNKuTxbc3moImZ1pnQvSE1Epq2oth3BSSxuxP5Nm/N9P6/92ybAoESYSMu2ORQCpNPOjTR1JoRIDZXYcnxKpN3vTj6LgKKul6B1MNl4g3MKRrdbMoAEH8ctQWprbqjWpvgbg+5t/Iwi9ex2HRvPEQRx6sKhdXJxDfgUmIVuvlagCagTsgVnOFt0WiX5zc+k3MFbuycqqqMTKNdzghLhYlpG+OmDuxg7CwtMynUwAYNLGi+wFlApDaiMnQV++uAupmUk3Z5GDg415RE4Aprjrd0T1d5iS0hUgcrZoiMtDzW3+RkdhQvdvF3Z2vgtHFoiTt0t4djqN3dZaUj1tXmo9qbmMZqjydERIuC45Va+w1jaVIDzzeBk/7e+3J85l0cAKLrtIh099EURAs/lT/RfuoUXsecVxXZ3y3Y7tnEtOmTMBUE6982m3jYy7tSLADVVq5Yqcj4NFXG8uVo9FxQx9zBQOpVNSliuQstH2QAH7syEhl2sWyYUFC5hoI3/6feaoOKCm6zjA3eGo2yg+I4WK8VK7hu4CWLubbQmAGnVOKTEfBpWYNKSqKf/urRExrcHOjWYp3PfEKibjq+5kaa71Zyj/+pIi5y7Baxqa27nUXQNoecBRdEtP0F65+XHcwGFEPIbhJATQsj3rff+W0LIx4SQ76jXP7D+7V8QQu4SQt4jhPw96/2fV+/dJYT88090ls7zrQ4OshGda/O02pFutjjkPLUhW54ircdW7tbzj09AZ86W6FLF/HNBttZ/0fNLQTAaLyritoWQ1XPT0kHIMmOZAO3FkTLh4C/ObphsY6bUmBRy01BCLOAgrS8DNISYzzFFoups4784u4FMSfntUZVolN8/ZJkiRnXhpnViVruwo/FCyd83/3Y6Uc++1pvmUyJAZ5fTbRAiLh2O1XtrI0ho8KPCuKzPG/w5gjWzL5xPA04uZ6H8WwA/3/L+/ySE+LJ6/S4AEEI+D+AfAXhbfeZ/JYQwQggD8L8A+PsAPg/gF9Xc5w4uCMC2R2P0EGI76Njjsje/KC/XslGIy7d25MMcQEXQbRolp5UcfAuocEERuusZy805Wq9SEbHrZKweuWDYj+Zmrkt04SLIgkEgYFaPXEZo7VW9T6r5QG0tl5TYj+a1uif2YDrUquam3NnKOQCSUwndYvscSw5fbnkI2b+n/s22Df17Pi8ca+aVl8v4vcxe1ecrLjGVEgEw8alwKM8Vtgkh/ogQ8uol1/uHAH5LCJECuE8IuQvga+rf7goh7gEAIeS31Ny/vtSqL/57w+4XvQ0EBL/8wfXM57ky1L18laxt1ok9NiVD2qNURO/zQFcXaxp5sarwpm/AH33YlcxcUmDkxbCLIm38HBEoNmhLmuMy10Kfw2XH834z/Zt/kq26bW/Ze/JT6W3+aayJH22P/Coh5HvKJRqp964BeGTNeaze2/T+2iCE/Aoh5NuEkG9n0/hHOL2/GX8z/mb85x4/LKD8awCvA/gygCMA/6N6vw33xJb3198U4teFEF8VQnzVG4RbZv5owzYNt/mchF7+4HrmNlETAPD88pf9stmgxSX4I6ZCoM8zdXVezkUWIhdVM/AXUX1UryFzkBxcZCHa2nCsfU4Q1Sb2+WdxmWuhz+Gy43m/mf7NP8lW3ba37D15GTfmE49Ph0L54XJ5hBDH+r8JIf8bgP9H/d/HAG5YU68DeKL+e9P7WwclAri0r3n5MNhlZMeUCBB2OZLtk5BxdCJ7aRr144aPMMrr0YoN8yjhiHNnY/RBz6EQ8GlhBGKauHRb1nVJiZNVz8zNBUVJCEoIlJoAFQI67b4UG6JLQpjPlEC1lhLZnax6cHfbo3iacNZzfaq1Q1tIalDEufNcIhuQ17+Z0mEP+/fUv9m2cVly3sy7NDd4uT0tj325eShffJMv4Ie0UAghh9b//S8B6AjQbwP4R4QQnxByC8CbAL4F4M8BvEkIuUUI8SCJ29++9AGL7SEzQBFdl/CdtV6Aa4nyFm0BADB2iTUvScbpdXm/2PhddGKaDldq1eWmoYnLi/OuuQHKhkybWdEcnxUq74eCW9Gf5poeKfCV3UeYl5U8XqYYSCuDCwEOjlyU4BCtL/lvXM2Vn9MAkQgX8zLEV3YfwVP1V+xR3fQq3F168Fk1b72TQJWkeXHe3Uo4y89QI1rU13rTfC4IeH+9W0Db+CTkvN5b2zRLAMC57lx4ib24oQiYWVPvi+LTIVGea6EQQn4TwDcB7BJCHgP4NQDfJIR8GdJw+gjAfw0AQogfEEL+HSTZWgD4Z0KIUq3zqwD+PWRdrt8QQvzgMidIADiL9iiAHvoHIQS1Enib5lEiwMvLSZQdp9yqAbCrsuVb1tRtFygR8HupCVduGx4tMM+DamO1qEkhJKD1BjGKFnWofXxKOEKa4Swd1UolurV5AqVSqB56UxznfRy4E/RogoCUyIXasASAkLqUXKAW8QGkZSIBhyOHQCYEcgHkkKK5JfdxnPdx6E1VWYJ2TYxWAk/zADfCCyN2axuSdGboDeKN0TH7WuacoecmW38DHVL2e6kBn03Hl7lf1No/7aUu9F/HqsezNaWktubmecKyUJ4Hfs6CfSq87GWiPL/Y8va/2TL/XwL4ly3v/y6A3/1EZ6e+MeH1m5mLeoUrPSitJ0dtXJYIFDlrkSivbwCZcFUBRXtKuny66WSvtjR3MxcCoZ+vZaSuleyDzPeIc9ds6tp5QT71dU3T3e5SVhXTYdWWYzPl8rx7to+3e0dG7MYJRWnd0IxI8dmArfA7T76A6zfO0adJVfcEJWCBCiXrIcgSAlyIGpgkgiERDCtVW+WPjt/AL934lqniVn2WGMukhMx4fvdsH2+8crqRazH9mzjDbndpavrq712fK8E8zl2M/FWrStkeBWcI/XyrZkn/5nnJWguk2+vqzPg267dZPkMIgiJnW90oOzl2k5XevH/05X7Rbs9LXw+FEoF8KFV9bVmeXGkYiHp6NC2U1tqaREAsHWMitx+Xm5t6a2KWqAoBp+l6QWX9b1wQ4xoFXm5ySNrma2vCIRzzxDc3Vqk+w6yaIFpJ2nNTmWXLGUqmCwHVixFRwuHTAjeHE9Wmgpl1bR5FK1QjmuJnrryH++kehkyWOmBUm/McGlSoEGs3YakArwITasBkUka4n+7hZ668h4im7YpdURWDWnEPN4cT1Ze4frPqolGlApPAqxfeAAAgAElEQVS4dNFTSZJr1omoWqNyQTFPfDg9vtHq0UBRiHq5UH092+anqduQuW++wXWN4m1zOAjE0jH7tvbvqIOEELKhWDOlpLmmAJAPt1cr/GHHSy+9p0SABNvdDj2PUl5j+LclXZGsupk316PgVbm8DYSrzr1wKEf2LKiBxCYXyWelsWY2pc7LjNQSs6c9pI2MWLuRlZ6rs2x1sej2Ku1SIHYYzjDJQ6TctQja+nxdPuDQm2BeBHiSjzDhEeY8wEo4WAmGVACJEOrFGy/5fiqAlWBYCQdzHmDCIzzJR5gXAQ69iSmfYA/tiuk+y5M8xGE4MyK75tDfNxfMZF033Y6ycfOlnGH2tGdq0qyvWf02ecngs03tZ6vfmguK7Flg1M1teiRTCdCUNd3kvlXrkuxyCaoFp5JDuURKCQk+g4BC9NPAKzdyIzZyMypM4ZitwAMBMk7RlsHZnOuycis3AlRd3NggN13e2rI89SbT9TXyLYAnM2059m5cVD1kWm583R4iZDmeLPpVA6sWYlaDxNBd4b3JAeZlYMoHNHNptDy+T2PciY7wH07u4FG2Y0BlKRz54hQrQbASQKJeKwGsBMGSUzNPg8mjbAf/4eQO7kRHsr6scqP0qHKJZPmEeRngvckBhu7KgE8bIat7Ej1Z9Gv1d+1Rmt9GFv/eu3GhVLubb8JcpSv4qlxnW+KnyUwXFGwgXaNt4kbNtehk0m3zuCAg482lSvW8qhBZZUFtAkohCKhXmnkvcrzUgALAKhxTP9W2G5ZRjjxzNla00k8DQgRcv726lR6aQHUpR5q7ivBsbzMJyIzUqJOY2qPVedbXd4hsXbnMPFOLo9kbRn8fh5YYBTGSwm1Nx5fnKbUZMj9HILZacgLrOS8uKdFlKfajOS6KyGqFsb4+IzLTd+ws8PMHP8DvHH8B99J9PC0GOC+7mPAAc+Fizl0JGuolAcTFXLiY8ADnZRdPiwHupfumBOTYWciM59Y8IqYq87u4KCLsR3N0ma71sp6jpK2TuPRAiUDIMnNdmkOTvEnhYhTENQtlvaavzOReZrK1bLNXds1qVFZH1EnWMsn1Oer9UwiGNHfh0iqi1zY01+L6hXFj2vpMAYpkztqrEDb3q+ZvLivp/yTjx4JDcRy77P8Wy4MIFMnl6m96XmFV4KLggoOSem8UQGpB4pUHPm4HErvlQeTlVbsFrBc01laKRws8O+/i1vAZCsHARXtvGJdwdNwU0yxU8+pul03MymplU1xkoWmO3lZQmRKOiKW4Gk5xb7GLXXdhykBq7qRZOLpDATjALxx8H++sDnGc93HLP31+kWoVzTkvurif7mFeBPiFg++bz22qYautk0UZ4N5iF691zxCxtNU9MG1BuIuLLMTV7tToVcx3UKMqPC7rxwy82DRZa6vpWwiGQlA8O+/ilcF5q3Ui41NVe5RoS2sWfW24IIhXHlh/XvtddE8obu3LUhB43uXqJBdJO9diz9NtaXSE6TLh7U8yfiwAxURarJBfk2gFJBhEH3gor29vjFS5MmwjMWv3oxXPfBRXq3aQzfYI+kcMnAJJ4ZgoQnPo0LFDOYIoQ6bKCuphfy9NzAaswPuzHl7tniNnzBCzUDe+rlTmkhIDL8E75we4Hk1MJfy21hMuKTFwYjikxFnerdqVskJWT2upRt+hAHM4/G6Oo2yI/+vR1/DTB3dx4M7QY/HWNhp/dPwGfubKe3i9e2LaaGwCkxLE9P05y7tw1Lm2NSzjgpjvmXIHj+dD3BkfWxX/K/5EE7K6NcnxrIeDg/kaIWsDdikIstJBEGWmVnAbeatBICkcBM7mm1/vyYJTiGc+nMPNlQD1wyO3qvu1Db0nS04RfeCBXWsnje17R1sonwaH8vIDioq06LL/m5oY6fYA8VtJjZht9jExNUWd0lTh2nZsRjm8w6Xxv1vnqYiMzwpM4y6KrgVoli5AR3ocwjHqrmRHOl71o2WN5XXLB88panVSpTVT7znjUtlmM3RzzPMAA0cl3ZH1aI+LEl2W4FbnGf7s9FV0r6QVIFBZMgAtlgpVZGPgZ/ilG1NMywgfJnvPbfT1Sze+tbHRF1DpTTJlaciwcgffPr2Jr+99VLXQaInuaHdnngcI3Vy2a6XtBbft+rueU5jWJM1hnvicIS5cjLorUytYX8P6XBkJWqUe9rsLU42vbejfzztcmk6YmwYXBHnBahGmZp8pPQpOEb+VbF3TAFqjLc2LHC89oOiy/3n+vIK+EnG9MK8aem0CAEhuZNJoeVBfr6r9GQWy6rneaLYWRYeOKeFwWYnJsy6y4QW4UzHqtihJt1vouhlmmY88kjeEA17rDWNcM1pgv7vALA8w9GLkXD6x9NBuj676fq0zxXHSw9hbwleZwk0rBQQISIGRu8Kd0THuLXcR9HT7UaFu9mINVJgKxXqkRIdm6LEEB+4Un4+erLci3X1+K1LAFq85qj2qj2kZ4t5yF3dGxxi5sn3GWndFZZ0k3MWq9HCc9HCtMzVV//U5m/kqrJypdq373UVV/LthJWg3KhcUs8yXHR5piabLY0dNstLB5FkX1wZTK/pWt3z0/kkLB1GQWb2e1q0Ju1xoL0g3gwSqBmBemJs9tmlwQZDndluaF5GhVY2XnpSlRMBhJYrENW7Pmh5FXWyHcHhegaJkGxPETLSFciSToC5aE3VCVVoesrl1Ujgbu63p9ggeLRD0UmRcbka7mlvt+xCO0MlxfDqo9XuplUFUm9enBfpeguNFT0WGKrfHDh9rHqXvJvh4OsCsCJAKHfGpVznTEZ+IZjjwZ+AgeJSMMC0jGfkRrulf3FZFLSA5ApqhR2MM2Qo7qk3GgTvBgTvBFWeKHbbAkK3QozECmq1Fc4A6mEgpfoBpGeFRMgIHwYE/U+5YPbJjNyxLhYNZEeDj6QB9N1nL92l1dxY99D01dwN/ovsnHZ8OEDq5sjrawER2J8g4Q9BL4dHC7Ifm0GU9k8JB6OWq15J9bFLbMyWnSCbBcxvXFZyiKBk8ryKOW2spK3enSFw4z4kw/bDjpQYUvZUZEQg+9GuKUf3X1mIQxY2Y1o2a3GqxPhzKAYcj05GWNs5DWwmsRJxtj/Ro12zQiWU7SqVabS9+zBE4OQaDlYrgVD1um71hXFKi42TICtlq1HZ7qnlVqcQOS/HmzimO4z5WpYec60bm69fApzkGzgqvROd4f7qPo2yAOQ8MqBhgaQNRCNU/p5CAQTN0aCpJWvX/XVLIfj8tT1fT3lQdZ14GmPMAR9kA70/38Up0joGzkn2N16IWijvhjrRO4j7e3DlFh1WCtmaNXO3uLEsPWcHQcbJ1q8eyInJBkRQuBoMVAiffSAjrmr5p6WDQiY1YrX6+9QhPnLnwdNeDlpta7/OMM8DhxpKprYlKncuFaq3LyloJ1IoktxS6giD40K9V1X+R46UGFKByPZLXU2NNbNOjeE6JNHNaCwXrJ5d+KkX9BHnJFI9RzbcLBTuUw6MlFsddk6jXBiba8uh4Geapj0Kx/k3rROtLPFpg3FlhnvvI+HqmcNPtuTGc4FnSMWrYptZFk7M+LbDrL3H/YoxJHhlFbLOfjem4RwrZR3jnIf70+FV8nFqWCncVr+HJsPIGYNn2ao4SpLam1ppMywgfpyP86fGr+OqO7Lfc5uro/kJaQTvJI9y/GGPXX5qeRDVXw5Lkx6WLZ0kHN4aTje6OPkbGHcxzH+POSjapb9GrcCHXLQTFPPVl8zbSTrTqfVNwisVxFx4tTSEoWwRnOBnOkJcMUT8x1mpbyFhbtmnmwNORmw36E2P1vJ5ujQb9KOMlBxSVBUo53DBfE5hVPrtyeSiXupGZX6lbN4CPQzkCL5fcyLZID6TV449jqxF2G+fC4VBJoj676CIpXSv8VwcVefNz9NwUx7OesWiaWhNmgUTfTXD3wytYFn4lXmu4JLaV8sX9IzxcjKTroxSx2v0x8y3XZ9dd4O9c+RDfPb+Ge/EuzooepmXHZBtra0UDy/MqrNlDz88UsFVWSYhp2cFZ0cO9eBffPb+Gv3PlQ9Vvud3VqaI6LmZFgIeLEb64f1SzTmrH1a4Od7AsfNz98Ipxjdbmq7na4jie9ZSMf93lsH/bpHTx7KILnxVK17KekCjD0EokN45l5GZjaFnur7RwEHh5q4VSnYN0o9KZD5dyC6Q0QNVbveQlhRvmRq/yokHlpSdltSvh+zmyorI8WnN0VFQGBMqaoYawakZ6HMIRuAWmqxBZycCdCiS0+2OIWcLRi9KKR2HrYCJrrAoELEcQShI39yh8KyHMJmcdKtthUsqxKjz03AS+dntI9d20GK3jZLj9xhNMslDeELyAy0ro3B7dENwlJSKWYewtcRp3cZL2ELLcWGeSlKXmRtUEZkSBXXeBr+0+wIPVGPM8wGudM4ydJXIhIzS5cnGYkBZeifYi13rYJQgqOb1TkakqmnNvuQsOgq/tPsDYWRowsSMwRgZvWTUnaQ8ApO7GasFqN0Iz1gn3MMlC3H7jiXF3agDRcHdWhQdKpWvalOcbFwJyblo4CMIMAcsNf9IGKpo/6UVpZcmodUtrTQ6CrJSu0SCKTYSpGeHRVmrJZTKojvC0u0cqklY48P281TV7EeMlt1AqwtFlJbLM2VofROfUBP0UWcnWetFW85TAjJVYTsKae7SuwJWWR+jmWCQ+Ct7Oo2iQ8liJUSfGIvekKyMaStiG27PXXWKaBci4s2ZB6NajDpVJfUM/xgfHe1gUXquVYnMpIctxvTPBn71/C+dZp+b6NK0xHTKWlsocb3RO0XEy/OHTN/EwHeOs6GGi3KAV96WFwSurJeGeidJUwjSvskbU3BX3MS8DTMoIZ0UPD9Mx/vDpm+g4Gd7onGLXnbeCifxdSM3VOc86+LP3b+F6Z2Kk9jZ30rROFoWHD473MPRj+LRQupL6TaUtoIw7mGYB9rrLje6ObouScQeL3MOoE8NjZS28rPeT4U84wyLxEbp5uyVjE7KCYjkJFdeyhZAVFFnJEPTTrR0StLuVZU5lHb3gCA/wklsouraDJFs5sqmPcmhFeqz7QiMzI9KVWSNmG36t5kaYX8pG2K784R0dXiVSMcuIbEUaOjkePd1DNphKzoWWLQI3qUfpuBnun+zgIJqjYAycFtKiaoSPfVpi4MX47sPr2AsXCFkOrZqFtTEZOHyao+ekuLl7gfO0g66T1ayUmtANQEQzDN0VvnH7Q7w32Yc/VsWJWFX/w75p9RObCg7mCAQ0R9+JcX+5g3tCqlVHzgo9llgtTPVNuZ4IJ5+gVXavdlPmZYCLIsK9xS4cUuLrex9h5K4Q0ay2rj1y4yo5WJQBJnmE9yb7+MbtDzFUn20TstnWyXnawc3dC/ScFL5qcqaHJrm1OnZZeHh4PMaXbj5WbWDb3B0JEFnJcHrRw639Zxv1J5oTyVRC4pU350YoZytk9XUruLR6mF/WuBb7fJuEbODlFdeyJcKTTX24vZUl5f+suTyK73AoB6hAziXSgmk3oipjoOf6boHJIkTekeFjz8qtqIhZ2RGw142lK2OydKUE357vKI1JtLdEXLjoummrHoWByHaYTg7PL7AqPHTdFIU6N1ky0XJlaImAFdjfmWGWBeg5MuzoitLoRnRDqhIUIcuwFyzwJ+++juGdGCHN1roF2q5P10lRYoFV4eKj5biqEWKVYrFBRWtUGNXcTY6uk2JahHgSD/Cd1XXcHh5j6MaIaKYUr3U3Qw99U1fujYdJHuK9yQH2ozle655h4MToskSRr4Wx3uxhg8mq9DEtQny0HGM3XGDXX6DrpK3nYFsnszzADz68hp9660OELFNcW9mwJIgJK8+yAPs7MwSsUPqT+rwSspCTdo08v0DoqDawDXfH5k/iwkW0t4TbYsnotaVIjknXqBtbXMf6/IJL4n+VeBh24xrX0ozwyLkUoNX99JlUygIVqPj9FEVZWR4gEv3NE0TAhHmzpxGK0WyNFAUsHkURs9NliCJaohCyy51dbMnOv+lHCZaZh4HnIGc5HMuiASrwCZwcu90lpmmAoR+jFHnNoqJEgAmlcWE5dsIVPp4OpDmu1JtUiJqV4pISnBL03AR3XnuC07iLjqPMXCrX01YKgwBoAc4JuizF1XCGe4sdPF4NgUhfhPr1NWUilQhOWysymTDBSIWXJ3mEH0wP8XAyxFu7Jxi4iRGTVUSgVqR6mOYB3j3bx83hBIfhDD+5+wBdliJiWp1btlolFWdSgclFEeHxagguCK6GM5Mw6NKi5urYQLYofZzGXdx57YnkqWjdneKWa5RxB8vSw/G8h2uDKUImtSJt0R3t7kzTALvdpeRaWm76UnEyWelgmXnoR4mKMFVrmpwylbFccIpF7NfC0E0LsIoGUWRPI3i3F7WHlZxDrbkERcngG9foxYMJ8GMAKNqEc1kJ3yuQ5NuJWYeUcFkJtlvxKE1i1p4bOAXO7vaQDmcyU5jWQQKAyb+J3BwPTsbYjZYmDKgBrVpXuj1dL8WD965j762l8vGrQk12uNKhpazfQTlmWYAOy1qtFG11+LTAbrDAd46vYeDL5DbmSNfDBWrqVpeUAAX6ToxXu+f4YLYnz6Gjv5j846KoEbXyn5S1YoWXewpYrv//5L1ZrCRbdp73xRyRc+aZz6nhVt2qO+iSt9lNkwLRfKBkmJD9QvjBhm1QlmjB9IMEQ4AeLBEGbJiWwQebBh8MAbQlQ4Rk0wIkwIRBgCYN8IGEJLbZajbZvH37jnWr6swn5yHm8MOOHbEjMvNUdbtEFtEbKJxTeTIjIiNi/7H+f/1rbXfE+93nBKnJKrWLzJPUrExNaD6OEXPXG/Ho/lUxkatRTboxKtkGJl8s+swil8edKzrmqthW+bkSTGRWZxQ2OJu1+aGD55XMzm3Ria6ntKygEGNVoFRNb8vY5vyLAe+9/Wwj3VHvkTA1GE6a3N8fFnSnPgq6k5hEH7dxf3iWm9820Umt0E+M3SCPetbfqwqyfmTi2LGioXzfRii5E9SKGU8bRa1MvaZH9YM0GgF+ZBLbpfNR1VGkgGvrCfbjaa6jVGmP1FH0TCtqdQwjZRVbhJbowr6N9rhGxOB4wiKy6Vg+ka5j1qp/pTjrGREHrTln0w49e4VnRESasRalSOdsywx5NLjmi2mf5iDXHrZRH8DRY9qmz8P2NZ/OdotIJUUDw8/7yiYFgKjHZ2gS0BKsTEzIwn2quFBVs52csIYmu6FlxU9JbeT260NNDUeZwTxxmcQez5Y9kXlqX9M2/YrnZBvVWSQ2X0z7PBpcC81JrzaaVqOTOPepnE07HHWmxUNgE9hFucdoEdkMjie4xu10J8xrggxD3EMyktlUYRynBkFsYj+eFvrJ+jbLIkM/MmmoWaMtFc5xqhP4Fr3OsnKffF9WG0PO640E+xtNor8wq/hB6jqKoad4OZVJGquNOkqSi6SWkdD2AhaBTc9dbfGY5GleI2LQWTD1Hbq2X9AesX5veYFMTQDVoLHictai7ywF+CjibOmdSbAzYa+/MlqMQ0+E2rqgPeqymTJK8fSQvr1iYnucLrrY7dykZWSCqeUUQIKKq+fLaFrwuHPF5/MBH8/2eKM5JLH0Qg9JNX2jllF2zVfD6VxEpOxJUj1n1e70t4GI3I6aySl1lwafLwakmcbjzhVt0y+OVwUT0QIyzwIlNvPE4XTRpWmLc+Xlwm09OpHAtUosxqGHaaR0bEFLtkUocWrgJybX8yb77bmY+FuyO5LuTH2HQWeBa6ynoaGqtSwCm7YXVKqMN+knSaaz9AU1MrboJ3KbUWJgf6OJ9RdmxdIh34fGNjHkRbX0lOBLS0Fl0vVUb+Eb0UX6Vv96Oy/qKxcgl6PiRzFjxjetwrgmOW39/aae0rJDRp/18aW9fsNE0vNopmmGhJHJPJKUwKi0fFRTyCJKmfFk2Bf28NQsRLdibRjK79c0A44aU0a+x5XfYpE4ZWo4NSupZD0HlYYe0jOXPGzdYOsx3xwecxF0mCQey9TGz9O8m0xwxXkgLWiQLPyTAq76T/3bptYDcqgRiTC8mSxTm0nicRF0+ObwGFuPedi6oWcuXwwmqc0icbjyW4x8j6PGtNSalCe4zADFqV5oJ0+GfQ5as0p0ooKJFGODVFzTMDJpmiGOERfXXR0y4vATk9FnfVp2uEZ31HtNGt/GNy1cM97uP8k/E8Qm+tfbIl1dM6qp+kmcCmoUfGlZNHX616Wh/NkCFCPBy6mMqqPUh6klOGZM8uVZnsHRC36vvl9GHo4R47QCVpGl2OurNnwJPo4R070/YRnZhGmp0ajDynUU14w47E25WTbxE5MgWW/+JI/Bzt2w/eaqtNgrTaTlPuru2Ye9G77xBw8Zhg1WiVX4U9TiwQqoGCKdfK854l57xG/98Ts8WQ64DNtM4gbLHJjqwHLbImISLOr/tg21uE8CyTK18yxOg8uwzZPlgN/643e41x5xrzkS6WFjM5iouskqsRiGDb7xBw952LvZ6IqVVEceg7Tk95srOlY1OpGjqBROTPzE5GbZ5LA3LcRYa5ORLddOlpFN9/5kI90pty1oySqycFqB4rqtUjSguJ/92CT58izvJrehDUNNP/EaZdTzfQsoZSWxuCFcK2a1FNZ62cWs/n7pR2l6AcvArixvUX2f0FEsI6HT9FmGlogMlAmsumblxO96PqOlJ8xoudFtU6Ri6zFtO+DmppU3kNa3RimOHuMZEbvego8/OWQWOawSuxKJyeMuzGt6SNda8f77n/PRcJdxJCKN20BFCqNdc8WBM+UvvvshI7/Bh5MDLoIOo7jBPHFZJg5BYV4zCuHyReCybaggUjheM4sgtVgmDvPcn3IRdPhwcsDIb/AX3/2QA2dKVxFgbwMTmZr+aLjL++9/TtfaTnXkk3uV2MwiYcnf9YSA7ujx1ugkynTmkcPNTYu2HRQZG3UUdCdvlzBaenS9daBS3bGxFHpDi07TFyKrrDKuUSlhoTdYBjZNL7jVfxJnIgpbLR1cS3iRJPh8X/ZDgZLryZRweukSDlTjWqmjgF7QAs+KGX3WJ2gt8HIz2iYbvq3HIoNztstOc4lrRCS6VmRwVJObbSQ0rJBnqx6LyKZhhsSpgWFk6+KsluIaEXcOR9wsm7SsAEcXanxBY5SMj2PEtKyAhw8vOF90sPWk8EGoAq30poCYqHvunDA1+HSyC91rsPNzplPJ/EhNxdFS9DRDN0v6NAyb/N7ZPR70hxx4UzqmX9jZ1Q5oRiaAqR7pbRoqEMpmSCoIyH/LxGYau1ysOnw2GvCD+2cMbDG5i25yuugGty09LNyzDT6d7HLQmrPnzgtwUD0nqhArMlQ254sODx9eiOtjVDuuqfdYlBosY5ubZZM7hyMhxmrpRjE2zqPXRWSzWtk0emNsoxRuSzFWr2R3Rpdt7t+7FkC1he7IWqPlsxa9t64qdKeun6SZsPGnly72YLqeWv4uarJeZvyZABQovSiWkWAdL8oMjl7WNKitDGQzaPtwKWiPvbmFpNyua0Y0+iuWkUXTDCvZHjlMSWWMiL3+jPHKpW2Jp9RGcTYXcnvuistJi5nnVsxSMuOja6KLWqppwpfiLvjoZo8bq5mHyUroq4CKzPpgwpE3JUn1CqikmVb6LlShFsT/s7RoRO3oMZ0Tn+ugye+d3eekO+HAnRXeDRkhqFFCIbxuWc1bRkebgMRPBT2bRS4Xfpvnky6Pd6746slnNI2gAmZrmRxFM5GRiQSTphVy5AndRGZ1NoGJpEc3fpNFYHPcKn0nm7rDxTk1moUus6XD0cG0FFi3iLF+bDFeuez1Z+K9+f2jDjW7s4wsGv1VXj9U875QjWb82MQ+XBbNs6v0rHSTy0yQdbxQop5/PXQH/owBiogmEhpuyNJ3iDx/a/rYzJ/u7UbA3HfoOj6xoWNq5UJZBe3RNGwjodPwmSw92naAa0ZrJjcAS0+wDZ2OHfDxh3fY/UHRL8PS0q1RSsMMORlMOJ+1aVpB0QSorrYL81pM2wy42xvz7X/+AO/HlOY+cuNKWjb/IqRmwHFzwtmyUwEV+XeZ/QEq0Yolz4MhwKlpBOw6C6aRy6ezHVaRxZ32WGRKjLAAKPnUr1MJdRSW9lwALSeyzSj0eDbr4VkRJ80J945HNI2g3L6kKTWKA2wFk5YdFCLsNt2kcgxBg8++dpd3fuyz3JJfM73VI4LY4nzW5mQwoWGGt0YnYWqyii3Gnwx49IPPsI2kiCph3czmJyaTpSeMb9JJu4HuxKnI2Mx9h3ZDdJKrg5r6fuGkdWi4IXZhLfg+BZQsU6KJnNIYubV+9KxL0F7gmdFa+rhKeyJuXkB7Uq2kPedPdvBbC0Iz722hZ2zypHhmxODRkGno0LQCbF3fGqXYWUzbCrjMWswiEaWItLCBkzd2VtPIDhody+fBjzzl+awrAEvPMyV62c5RppLFF8lPWgNOs24BKqkl+H9DDyHNK4MVCmQUVCbFypJC8G0aAT1rxSKxmYQuf3hzJByqrSktKxCZEL00U20zp8WZUfQimUcOp/MOupZx3Jrw7uBC9MFVgWoDkIjtVTuvLVNbpHojr4xMGlPapl8pFtykm4SpySx2eD7r8uBHngrh1lhPE4NMK+siOolc0kwro9JbopMwMZiGDoNHw7Lj2wbvSZTXA/mxxeKyycGjWdGr5Va687zF4K3LW+lOnGeC/CuP3oNlpfObTlbWxL3C8TKLpd8FfgU4RDznfjnLsl/SNG0A/B/AG4gF0//9LMtGmqZpwC8B/w6wBP5qlmVfz7f1V4D/Mt/0f5tl2T98wd4r/5MnzjESrH4gWgQkBrEuVmHbRnvcowXLyKJlB8SZLpbO3GByc4yY/vGEqe/QsgPcLC7olGrFF1FKTM9b8fFHR3TfEk+VTVGKBaR6QsMMOe5MeXLTp3kQlgtHZYLuFJmsnPo0zYDY1ZlHNhfLtgiVrRx4Ukoj2wZQudPMOHkrSqwAACAASURBVFt1+Nb1IY8H1wzsJamhCRpBUugq4iNltKICi8wIdVKDXXvOncaYVWIXwHC27HA9bzKbePQHczwrLorYRLbCZDRs0e6u2G0taFsBLSvgS7una5GOXJRLAok8LqjSJlVzWSQOw7DBR0OhmUiaswlM1AhpldpMI5eLZRvbjOm7S5FWrlEdKRzHuSV/Gds8velxf2dEwwxx9KTokyKHGp0sY5vzJzs8enyGXasJUqOTNLfwT32H/nGeCdpiZpPZnWVk4R4tttIdeQ2iRJjkrH6Qr3y4obXBnzSgADHwt7Is+7qmaW3g9zVN+03grwL/T5Zlv6Bp2t8G/jbwXwD/NvA4//fngb8H/PkcgP4r4N8Asnw7v5Zl2WjbjuuBmQQJy0hoNgKWgUXLMfDyi1Ox4Su0p+UFzJYuXTdX2pWLVUQ/OZ3quAHPvnlI/4dWBUeuVyDrmYadFwHu3hkzCUTUsVFL0UQhmmPEtG2fXmvF9aqJnacQ6wItlJb5thlw1Jzy0c1e6XUgAyO8FVTkjWPrCb/39cf80Jc+Zc/VCk2lQgdUwRaKiCXNdOGK1cREbhghHdMXWRo3n2xdg/RkS0tMLcU4LMsL5GRVJ7tKSW4rMFSpSpCaoj7Hb/GNP3jI++9/zp47X6M5G8EksZnHNtd+k+GiweOdq1upjowgFrHN9apJr7WibYtoRjatLj9T1U4mgcvunbEoFFVczPXKYuminX6nz533z4v3GsoDTx6TFG5nS5d2w99KdyQAhanBMrBoNoKyIPFPG1CyLDsDzvLfZ5qmfQCcAD8F/ET+tn8I/DYCUH4K+JUsyzLgX2ia1tM07Sh/729mWTYEyEHpLwH/+237l0V1Ku2x9EQU9T3tEjZXRUGVrmdQTOaS9jSsiKtRj1XbEhSJKu0BmUGKcc2I5qOJaOlnhdipUOZtLa2kkKW9vuet+OxfndD6crhRSwEJVjGuYbDbWPDHnx/TuheIm0dLQWeN+lgIPaVr+TzoD/nmkxP0uxmGlxWf2Qoq+cJcupfyo1/5iE/HOywih+PmhKYR0jRFwySLBD3TSWsUQ1Ih4SYWUQtQ8cPUf980VJfvxt9r0YgcdUu/FHEXscMisTlddBn5Hj/6lY9Ealhmc24BE2nFv/ZbfOfZAe/ff07XUi3861RHCrfT0OX0vM+fe+O0eHBsmsQyOlnENlff2uPBl58Xtvx6qjjO9OL9s8Ch+WiCa0bYRrw26cvaHYNVZOGPXA66szW6o1ryZZ3P6qxF583rStd+le5s6y30vY7vSkPRNO0N4MvAvwQOcrAhy7IzTdP287edAE+Vjz3LX9v2en0fPwv8LIB30CLdMPEl7TF3fPzIJLIM7KKupvpeU8ujg/05y9CiZRtC79DK2p66ONv1fJ5f9ei6vohSsvUUshql9N8ZMlx6NM1wa5RiIKKDlhVw/+Sas2mnyPhsoj6g6Cn2infunvPBh3ew330ivqPJraBi6HL5jAyzn3K27PDB8IB7nRH9TKdl6EVKtQ4swFrUIsEFKKIXyMHkloec2s1NfaJvAhG5bRVIotQoopJR2BD1S3bIW/0rOpaPp5c1OreCSewwChp88OEd3n37GR17tVE3qVOdeeRwNu1w/+Q6T/uXaxzLUY9OhkuP/jvDrdGJ6oxdxaJ95MneeKMYW9Cd3O26DC3a+/P17J88lhwoosTAj0zMHf9WuvOnljbWNK0F/FPgb2ZZNtW0rQey6Q/ZLa9XX8iyXwZ+GaD79sHa31Xa02r6zBYuHTfAyQzMLFVaBOQCap5qbrsBp2d9Om6Aa8QvEGdDvEbIPLQLQU3wZTZGKQNvycene/Q8HzvXRgwjKtbrgZKCeUT0nSXzwOEqpz4SDNSsj9RT0KFlQuosefftZ3zr+RHvnZyJL7kFVHRN6DDl+RJC6yj0+Pb1PkftGXvevDIhVWCRVEiOesNpmSVTQea2salZtfy8HNuARGoeV6sWZ7M2jwbX9O1VheKs9TbZACY3QZNvPT/i3befMXCWtHLwr+smqvC5iG1xjcyEvrMsa6zqRjOEDuInFrPIYTxu8uj4amt0UtYDWeIea4Q0rPCFYqwfW4xuWhwfjcoUMHVw03IwNJgtXFrSJLeB7gBbl5v5XsdLAYqmaRYCTP5xlmX/LH/5QtO0ozw6OQIu89efAXeVj98BTvPXf6L2+m/ftt8MiFNR8LeJ9nh2xOi8g981BZXRpWpd9khR63XcVsgitMXFq4mzqnPWNWJ6jRXnww4dW1H0M9UyXY1SjvYmXM5axVPJ1GQTHzEKgVZLaZiibufjy10aVpkWFu8pvSkqqDTNAIA3D6/44PyAdw8vyiuogApQMb/Jpk5yFcLWQcC13+J3P3jEe28+Z+AsaJlhBVhkUWJBT2qgUVlR8LsY9cbW9UplCQQSSOax6LT2rU9OePfhKT908Lw4VjNvAlWPSoCNYPLB+QFvHl4xcIQIuw1MVKozChrcTJs82r+mUXmwVAXTKDUK09vlrMXR3uTW6ESu4xPEJlejNoeDaZ752xKd5O9fhDZuKyzrfCqRla4AovCpRFMHrzffSnfi1BD9aF/heJksjwb8feCDLMt+UfnTrwF/BfiF/Of/qbz+NzRN+1WEKDvJQec3gP9O07R+/r6fBP7ObfvO0IovX6c9sgCwtbdgEdi0bOFYrTfflZGBY8R0myuuhm1aTlBM+nqUIvrCxiLL40ZMQ0cY5HItRZywasbHNSM6js9k5TL2PaWBTrpRoE0zTVCfnRHf+ewQ682kABThbi1BBWQLSGFgwwX2KCKVFI3UCAuhVoBvaX5TKZCMVjwjovfOiiu/xb/84g0eH1zRy5/6MktSPPmzKpUwtFRYWl4iMlGH5Opl4+p1j4qsq1nEDuPQ46OLPe7tjvixdz4pDHaq5lEHE1nfJQXYRe41+dbzI948vGLXXRSRTX0VwjqYjEOPjz874K0H5wXV2SbEBqnBMrYY+x4AHccvUv31zI6qnUxDB9eNaNlBIdJvik7CRHhahuMme4NZSdW26DhRaog5sbeoFA5Wr0fZU+VVjpeJUL4K/GXgDzVN+0b+2s8hgOSfaJr214AvgH8v/9uvI1LGHyPSxj8DkGXZUNO0nwe+lr/vv5EC7baRZSIkMxV6VfY8ESDRdEIunvfpeUJ93yTOyr4nnhVhWgmrSIizW6MUTcM1xLo5zy97NI4ixXcg/C4ySjFB0CQzZL8959PPDmg+DDemkeXxO0aejnZW3L93zbNJF7ufFE8yXcsgq5ne8khFgop+lPEHH9zn3befsevOSdGKJzdQc9QKCqRnWeEzcXRRDb3jLhgHHr/7R4959OY5O+6CpiHS2vIpXpnAWQks8vvcNurCbX3iy05pQSJE0xu/ycefHPL2o1O+fOcZbTOopJnrQKJuM5J1K6nM5rQKzURGJnURVoKJ6oadRw7PJl3u37um6+Sir/ECITZyeP50h4cPLmhILU2K3YrvRGZ2FpHN5XWHk/2xiE62aSd5dLKKLExL3MNln5TNYmwQm8yuWhycjCpay8asUfxqrWgvk+X5HbbLbv/mhvdnwF/fsq1/APyDlz24LBONdVNd2OAl7ZE3g7DMx1jtoASJTeKsGqW0VoznHk07LOzQG7UUQ2gpjVbA1HeFlqKnGEZU86WkWJqgPk0rZO94zPWyUfUI6JQFWVoKmY6txySGxsAVHpmLZUuhU+SZhGqkUgEV4N23n/Htp4e8deeC1F2ABTZxxVErv7+MVgyNKg3KnbmD95ZMI5cPrg6wzYSD1kxoLPlkUn0a0simPvU2LU4uh5ywaiQQ5x3SVoklfCHzNmFscLc35sfe+1i0BdBjHD2q0Bv5faAKVjK6kGsXX/tNvvPs4FYwKY4VYXaTYHKxbOFaMQNX9C+RWR01OokVnWcZ21wvG+wdj0VmsOZRUX0nUmuZ+i6NViDot3GbdpK3NJh7dFurW6MTKcauIgurHQhqVG9roGR3klzofZXjtXbKym5XVpaIzEmd9mjCjNZu+kzmLi2nFGc3OWdtI6FphwwnTZY5AJl6emuU0m+siP/XAxZ/LSifOop7VoKRjDoG3pLPrnYYWvLJsIX6IAxvqRlx2JrxZNTnUmsXTxKdrKA/6g1hkaAb5dov799/zmejgejl0tBpmwGpoZHqWqkRqBQIcmBJiRAU0UkjPCOkbfnsuXMWsc00dPn2zT5hbHLQmdG2RDmCrcdFJ3jpldhGf9R1kdJMJ8if5n4sxMuLqTCX7bfmPOjdFFkyOfHNPFOlakPFtmuRjrTTz2KHi2Wb4aLB+/ef07FXhQArQXAto5OLsLPI4XLZZhnY3O+PaJjRZgNbjeoMVw3mS5cHezfC9Kakfje5YheRjfWPBng/c/ES0YnJMrKIY4OmHRZLmG52xgoxdjJ3aTf9sl3CBrpTtFYIbF7leL0BJRYI6hh6KbjWxFlDT2naEaObtuglIUM8I6s4Z0UXtRjHMBh0F4xmDRpWVIDEtiilZQdc/fSQxaIhIiBDZEJE6J+uUZ+WFXA8mPDFHx3hvR+VDXX0WNTN1PQUEBf4bm/M58NBhe96sBFUdCX7Y2kp5k7C2aLDJ6NdTtoT+s6S2IgKCpRm2ppgCxSZnUTTcTIxkdNMo2369O0lR41p0f9jkdvmr5726RzOaLsBnpXb72vZhqJGJW8QtYosZr7D9LzN3t0RfXdF115xcDArqJUaPajURh5zcU8owmuCXlAcKaI+n3WxzZjHO1fCZ6JQN3He18FklVjMYofrVYvx0uONwZCWWZYX1MEkyie6n9vxzz7Y594PnNGygi1UR89bV+j4icVw0cD+6SG9XDu5LTpZxRajWYNBd1F8F7N2PPJch3l0EvsWzf5sq9Vebbq0uGrwKsdrDSiakbEMbFwzFktRZNVQ1dRT7Ew0U+r2F0yXruCYRrKWQpZRimvERZSykGnhDVGKFE9dI6Lj+jy5HDB1XaHcm9kGgbakPl3b5/DdS84mHax+2R7QMLJKKtnMHbGeIVo03uuP+PRqR6yZIvS9CqiI/VTpT6Ep6Skjv8Ef//OHPPiRp+y4CyLTKDrSJ+TekToNggoVSjMNMxeB00wjMkVflcjVudM0iAYXRWm+rIuJU30tWyBF4Lbl03eWmO0U8+C5AEDlqb+JRt0GJKpWUoivsdBePvvaXR78yFP67rJwwKouXSidoXUwuVq1OB+3ebh3U1A9WatUHEMxeUVEM48cziYdDt+9pGv7W6mOFGL92GIauCyWDrv7w4Jy19srqNHJIrSL6MRVWitsShUHicl06dLtC1v+xjV9lPqqZWBjdcLtE/B7GK81oOh6xmLp0HaDvFK4zPhIxJVP+oYTMvu4x+rd8qmkppBBRClprqUMuotCS5Fl5XX3rKkn2Gh4pmhXcDVp0bRCYcevCbR16tN1fOa+w8j3ckdsVmSFNom0AKmt8cbukA+fHGLeK28ECSpqf1aZUi6fQuI7OD/2GU/HolfLYXNKbOl4RoRNTKpVaZDcf1nTJMRbi6SgEw5xRf8of19vQlUfRhFRZcWTUqUd6vfZJvJWnLk1IXeV+z7OFx0Wgc07P/YZHcvfqpdUBFgFTEZBg8+f7fL2/XM6tn+rCKvqJiPfw9BTunlWZxvVUS32V5MWe/1ZEe2aerVSvp7ZGc+9Ijox88xkcTxKqlhGJ+GTFv33LiuRVQFWSnQSJQaLpUOzEWy8dt/reK0BRdMyopldWOZj3cAkLUTXujjrPZwyWzk07ZAwNcXfSCtaivSZNO2Q8bTBIrQFAG3I+KBR9D/p2AFz2yluorpAu4n6HLZnfHK+lzsVyyeX0GAU+3mmY+oJTUJw4O3753z45JA37lwXkYqDhq3HlexPPVoxLNGCwN2JuPGb/P4HDyqZG8+IiPSkkrmhdtPVwUVuv8jSyDoUqqLrplERbRXwgJqDdkOmaBuQSCBQM0IPH15w3JqIqGSDgCyPUYKJzCrJyESCSc9Z0TTCQvRcozqpUaaIA4+rYYc3D69upTpSiJUAZNsxHTsoohO1ZmeT7yRN9CI6UTM78jvJSCZKDWYrB+/hdKsYC0JMTvJWk9HMxu3NN16773W81oCia5nwmfg2TTvE0FPivGsaVFPIlp7QcgPOP99hmRdO2bp4KleqkKVj1YwYdBdcDdu4+3EZRajZpPymkua1neaSLz44xH0nLkxLGPFG6pPqCU0r4O7+kM8/PsB4fC4urhkWomxdpDWMfGLloPL59YAs00g9jTbiSWJqyZr5DUQtkJ5lxTmx9YT22wHXqyZ/OD7i/mBULNGh6gq3UY1qGYMoYpStE+QxwItredau65ZUcx1EZDSkppalR+TJsE+/ueJLb39RtFNQKY48P1D1mRSNkiKhmZyP2xUwkZHJJt0kyM1rk9DjySf7vPHoIm9dsZ3qBIkQoeehw/XHO9x797w0va35aORaOybLyOZq2GZvMMtp+WaHroxOlpHF8rLJ4Rs3lbYS6mfifNXNIDFZ+MKn4prxxmvxvY7XGlA0MppOyOr/3sf/SUFltqWQRWvGiM7RjOnSxTXjXBGP1jI+0pfStENmXshk5SrpOAPDKE+yEFSTQqDdf3zN+bCDs6/UgeRZHzl0TUQKqaHRtX1OHlzz5GIH81BO3M0iLZle0B8ceLh3wxejvugr25iRWKKjW11TUSMVSYEsXaSEG2ZIz11xMW8Xa850bL+YPOrTXJ2ImyKIbUCgb2iQ/DJDrSNRF6xX+85KbWCRiMzT2bSDaaQ82BnemtYu9rHBtDbPsznjpSc0E+V8bAOTQoQNXZ5c7HDy4Jqu7eMa8dp6P3K/Ub6e8SK2OR922H98XZrY8houdcR5F/5VbDFZubheKDI7Nd+J+r0k0E6XLp2jmUg01Gp36qliPzaxfqeD95OXleVlXsV4zQEFbCNh8tUZaS7OWkY1hbwpSjn7eA+/4W/N+KhRSq+5YvQ7hyx+PBTeET0lSo1awR3YekJqRHQdn6UnCsCKDEdOl1RbPuiFntJzV8R9ndNpB6OnNBTOe75uoz+6naEPMp6OeySZxkFjTmrppIZOKp/Gt0QrppYU/puWFTANXS7mLc7SDgftmZhIRU1LSqQnaxqHrmUkbI42XmRqk2NTAZpKoeoaTZwaxSSWKeyLWRtdTwtA9IyoyA7VwVBuF0rxNaj5TJaBzRuDEpS20pys1FvmkcPptMNuf0bPXVV0k21ZnWVsM1x6uF4otBZDRCd1qiOXSxEmOZvgawP6P35+a3QiMzV+bLI6a3H06GprdFI0XEpMFoFN/NUZXSMp6sde1Xi9AUXLcMyYlhdw/axH815Yza1viFJcM6Z9Z8pk4RVRyiZfisgQxbSskNWP3jBaeMJJmwNQsgZaVerz5GynaCpUz/qoeorM4NCAKNE5n7XRO+JilxmcW+gPcL8/4nze5tPRgDvdCT17RWpoOGiF0Co+W41WUjR0I8PKU+aeEdGxfdG1fdXgo9N97h0M6dp+4Z+Q4KJmYOS26zrId/tsU/UX+buMHtRIQLRbFJ3ivrgYsL8z5aQ7KaiNPEazBoDqfjYZ6Mahx7NJF9eKud8fFanh2yITFUzOZ8I3s9tYFMeySTeRWZ1lbDMNXEajFvePbjZSHVCFWCHcjhYe7o/e0MoLBrdFJ/K7TRYe7TtTJSpfj07i1BAVyLHJ/KLF7p1x8QB9leO1BhQQXgnPinAGK+a+I7wP2fYoxTFi2m7A89MBC0/W7FSjFLUS2THFshjP5n0mvls2kNaqXd1U6tO2A473xzw/HWDdVVKLip6ybs3XiuVGL+ZtaImL3STcGqmoHdjNdsLQb/LBJ8c8enBB31mSomHrWpE+rkcrQhMSVcwmegEsTSOkY/kcNadMQo9PRwPSVF8zsBWTNj+3haBac8nKfaqjLtTK6EP+HmdG3u29jEZUw5uup+y1Fnzp3jNcIy6iiBcBCZSUSTpnF7Go6fn4swPu37tm4C5omFHpM7kFTBaJLaKaeZss0zhsz26x1iu6SWIyCx2enw44OR6KJTc2UB21GZKfWEx8lzCw2O/Miwm/zeMTxCKtvJq6DI6Ht9vs833MfQdnsCo8RC8bZb7seO0BRU76diNg9OGA1btlYd+mKEX2ke3vzhjPvIImSa1DppFlBsjWYzxTZ7c/4/y0j3unfCJAvdcIBefsOD7B/pTLaQu7p7gXcz2lbHMgRFrySOWgPeN02uFy0SoWLd8GKjoUNnpZCe08iHly02fZsdjzxJMyNXThm1GiFfGZzcCS6mIh8yg1aFkBe968mMxPxn0mkwYHexM6dpCnN/PucoX4WN7gampYHfWUcrGeTD5Rpfi4ii2mocPFVZdud8mgueTRznXFlVvvXbsNSNSoRO1je7VqcjNt8taDc7qO6MSnbrdy3BvA5HLRIogNjjuin65cPkMVYYv9S90kcricttjdn4piwVuoTpg7iOehw9V5l8PjUVFGojpd1Zqdogn2zKO/OxPR9RabvYxOVpGF/1mb/tvDEqy2COff63itAUW4SIRA6Jgx1j1RWfyiKMXSdVpOyHTWYB7YRV2NWolcF2hbdkh7Z8F45RYrsUlvSj3rI2z5olvbKhTWa62YvCmkVPwFpp4IWcWISC2No/aMZ+MulwhQ2UZ/QGR1ZJpZFg5a+wkX8zafjQalyGqG2LpGqunFE1x8z6z6U1IhGdHpOlEWiajFXglw6VmsYot5ZPN01MNf2uwM5jRtQYtkf41NTZ3VofYXkevrBol4qt4MW7iNkH5rSccOOLj/fC0ykpNWBRL1u6j72Ka9nE072GbCo/3rNcpUn0ybaM7losXCt7nTm1TApO4fKfdtMI+c/J6AnrcqUsSbsjqqI3a8cmnvLGhtEWLl5wpjXWCTJgYtJ3yhdhLmFcjWPWF6kwWW267d9zpea0BBTuA86mg3fG4+2mH1Vrg1SpHuWc+M6HcXXJ91adzNXY+p8GuYKJEAwmIfZzqDxoqnF30m+QprhTipPMUK6oNGMwvZa895ejkovCl6nsHZBiquEYPtc6cHZ7N2hf54RGvZH1B1lUgIylqK3YkZBQ2+88Uhx4cjdr0FDVN4TRw0cXORYWRqm8ByQoqFw8idsSJqERMqom2KZt5RanC3PS6eiEGcZxRCBz+0WAUWwcxBn5qkvQjdysPySEcfW6SdGKcd4DkRrh3hGIKSdto+97tDTD0tnKJywr0MiEAVSFQ9YZVYolhv1eT0vM/9k2v6zjKvy4k36iVie6WGU4i38zZBbHCnN6GdZ3RuBxOh/Yx9j9Gkyd39oQD63MBWz+oUfV9jm4nvspi53D0QFcKy8Zb63tKdLKKN0UWH3aOy94oaWW+KTpZPOuw8vlGimc1Nl/7/jNccUMifpCmxJsxrzp05c98pqUyql0guzWh6gmUIQ9BqZynSwkWIF+XhuNLeAGFeSy2NvZ0Zl5/uYD9KXkB9RH+SFI3j3TFPv9jFvJu/3wT0uJL5STKteiPaPlon42LW5nTa4bA9E0teGMLDUuf2dV1FdN5PaL4Rcr1s8u2Lfe7ujGlbfkUfqAOLPKe3gQvICVst7lMXkpf9NOTE3nbt5HVRMyGq9qC6aIEXgoj8qQKJpDfLWNTWPL3p0Wut+HNvnFbE0216SemAzbuo5QJslmkKzYkLnwuwltFRweTieZ+7966L9Z1s2TZyA9URXdscrj8bsP/whoYVKhGNONaKIzYXrScrl+bOkqYd5t3bqtFJpZ1BYgrt5M4c15TLkb56MIE/I4Cia6KZUpLFdBo+wz/YY/l+WdUpHK611QA1sRpgt7Hi9IsdPFuZYIZqN69Sn7YTEN0fcTNrVlrn1Q1vFReto3Fy94bTD/fR37lAdwWo1Ot9oIxaiqKtTsbFvMXTcY/jzpTU1sAU9RWWnlTbSOa6iq5nIlWdRytuns4+nXa41Foctme088yNpaWlWEd1/Zw1OiTBBQqAgXpWprro/DbbvRx1jaX8LutZo/rvcmwDkiAxifLU7Cx0OZ+1STON+zujIqIozW6bKY4KJnI7p9MOthlz2J5tpTkqyEpBeex7nH64z8nbl4VusskNqxrYFpHNzaxJ//6Itmz8tZXqiDTxLHCYXzU5vndTLNZeoYGUWaAoN72FH3YYfOlK1PgUzu3vQ0CB8kYX3dFinHcmTBfCvGboaVHjo1YiyzqchhUxOJownDRxTaW4qtKEqaQ+KRo9T2MV2IyXXjXNpycVUClWgjNDcCF564pnF32MI8Vxmmd+KrqIoqkA6O2M62WTT873uH9wI55G+QJmwmuyjQKVS4XIlPYscnhy06fdCNjJ05tuuj6xdG09alF/yt/TTEMnKQot69FItTJpfdQXAHtRdkiOTSCiahxBKjIp88jhZtlktnQ4GUxoW0ElBb6txUJ9W8vYEg7Yix12+zN2G4JCbtNM6k7YSejy7KLPwVtX9NxVngmq9rstwCRvY7CKLcZLD03L6Hl+IYCveU7yaMNPLJaRzXDSZHA0KUxsanRSryhexRbThYvzzkRE9UWU9urBBF57QCkbLQstRSu7tF32Wcn1RvJq4W0CbdOOmBspM9+prO9qIquQS+pj6zGpqTFoLXn+xQ6uHRWCq9h4UttPKdJ2HZ94YHA26kBf+RoKqFToTw4qupZBQ2S0Pv3okPtvXpI6K1JTeE3EusRaJSNRRCvoGHLdXF20o2wehIx9j+88PWBnZ14CS95lX040NWqRRZfl9jfTjjLjkF+bl3SjvOgGVoGqHhnJFLOsWVGB5OamxZ3DEUcH0yKd6+jrlFEd6vak52UcCDv9yYNreu6qqM9RwWRTelj6Zc5GHXYG88K8tmkp0QJMpEcldBhftDm5d7OW1VGpjoyCgsRk5jsYhmjZcbsQm2tKkUUwcundHVUWEatfx1c1XmtAyaC40QUAJMS6jmdFdA7mjKcN7DrqbhNo20sWv73P4ifKBba2Up9M2OwP7ow4P+1jpTI9/wAAIABJREFUnAzLMLS26qClpUVqt2UF0IA0g9NhF31HmUS1mh+gaHwtaYGppViPEp5eDggGBv38xk4MDUdX2xVUo5WCBuWiplgDKKL3xopZ6PDkZoBtxey2FjStsJh4qs+kXhFcBxixr9upycuOTR4VYK2Sue5TWcY2i8jmet4kjEwOe1OO3hCLlquRxCZ6I/azWS8Z+aLQ741HF8JOn2tQZm07m8BkFjmcDru0Gn4B3IK2iOMo9q0U/knd5Py0z8GdkbDjbzCwyc+pnpP4dwf0f+LyhUKsdNCOpw06B3M8K8qj+fXG3K9yvNaAog55EuSSoS03YLF0mPlO2Yh3i0DrmCIjE3x1yPWojb2bFP06qt4UYUTDgDSLaTsB4d6Mi2EHc7fKOdVQVmZ+ABpmyG5DuHKfD7ucDCbll9hAf+Q+vTyDo2sp9mHC+azNbOVy1J3StvwKBTKKaustNCgTi7S7RkTDDOnaPovcAv7pJwcc3hvSdYTGYhuJkkbNqk/2rDzvEmTUa/HdDvXmVU1u4mc52aVfJUxNUfgW20wCl/MvBgyOJ+y35zTNcKMBbxu9UQFKUpxZ5HI26WDoKW8eXtGU4qvSRa2+nTqYPB926TR9Bt6yoDmbzGt1EfZi2KG/N6PtiH2qa/IUx6xQnVVscT1q0/7qUKTvzZgXCbEz3yEDWm6gRCd1D8+f4kJff9IjQ1u7iU0tIdU1XDOm214y/+YOix9Sq4U3CbR5P1nPJ4hMRkuvkuatUp+qntJvrEhSnatZU4CQjITS9cwPeoKbH7uWH++zmx7HOaikeQsCS9MqYbR01Oo5/TF10YluErh8+s0Tjt69LG/YrAzpVcFWfFeVBglgcXTR5V4Ay4qj9ox56PBs3CMMTPb6M1qWuEFdhTqpBjZVVJRAo16TF40qnVGbVZcZI9Xw5icWQWwyj2yuRm1sR0RX7739rDCIqZP+tlaU9ahERjrDVYOzD/ZFcyTHLyILWRuk0lNgzdE7CV1OczDZKfSWuAJs8ntGipFvEdlczZo0GgH9xup23SQrDWyjpYftRHQ9v+KILT5TE2IXoU3wrR7d92+KdgbVZlHlguqvcrzegJIJvmvXlumUKcCmHRG8O2W2fJFAK6hPYsT0W0tOn4qsT7UFwXY9pd9YcT5uM1p66E1xDK4Zbcz8qKCSeRppRlVTyVPK0qeSZFq1oLBYgkO0ILB/4IzTYZdVZLLbWNK0AlIzIs70vE/q5mhFAguaKF40tRQn03HzQsGes2IVWywim2fjLv7KZqc/p+0EuaCZFA7ZOrCU+kp1Asuncj3zU4BInmpWgUROtFD2dQ0cbkYtXC+k31zxYF/oCzKbUfesbDoOuU+5L6m9LGOLReRwvRQ9YO/9wFlBcdQo7WXA5GzUodUoI5NtYCIzOn5siRKApUeS6Oy1Fy/WTRKzoDrz6ybHd2+Ka6NG4puE2NnSxXp3qmgt69FJnHe+e5Xj9QaUnD/qGBVXpppGbns+Fxc95o5dWuy1qCKcqtQnRWP3aMLVRRfrOMkF13SrnuISgQ37XY3nVz0MPUP3ygls6/GtoKI1hRX/ydkOdw5G9NxVBVT0HEyKxcPyVozyxjT1BGcvZrhq8J1Pjzi5e1NkERJDU2pbNgMLgJPfqFYeIaWZ6OLWsgz6rs5+YyaigtzFerro4s8cejtzGk5YZAekEU1Xbs7KeVaGTCvLG11qI9KcFaWC4y8Dm/FNC7cd0G2uaDsBuyd5t3kjWQOR76YxtgQCPze7jX2P50932Dse82DvpoxKahSn0iBJoV9yG88u+uwM5i+MTCSYFRmdlcdk2uBkbyzWfTKiW3UTIT7bXF102c2zOpuojjzPUridBzbBwubgYLwxTVy4l/PeKK9yvN6AkpEvo1EVCaVAa+k6DSuiN5gzumrjHKu1D0phVaV4UKPlBASDBTfTJlZPQW7FRVvoKTqFSHu4O+H0ix20E3khg43pZBVUigyOkfDs2wekb1+SuhoNszSw1cVauW89L4iTi5q1HwRczlpMVi777XlZyJfFtwKL3KYatajgEhs6rSwQN5mrE7cmhHtmxSq/DC2WC5dkYmHv+DhOhGUkWEZaZMFkXCLF9CzTiJLcch9YhDcuRjei0fRp2BFu3vH+pDspRElJuTYZ4OT32DS2CbmyRuly1gLg4YOLNWG6PqFV8TVSsjLSZ3Lw1lWFJm2NTIou90L4vT7tcnzvpiLC1nUTCbh+YuHHFjfTJu3BQqzosKH4r/CnpGbhORldtenvid4oaiaoPFd5pPj9toxGkiOooafoekaaVZ+Ktp6vwueE+F2fycLD0DJxg2/J+oCgMT3P5yIQNEZEERku0VaRFiC1NQ7vDjl/soN+Lyt0Ehe2ggqI7I+ppxhvX/L86Q7xyYieq4vCvkxbE2u3RSt2bh2fBi6fn+3Q6y0YNFalQPmSwAKsgUuSCYCr05JYcWnGfYP0jriB06xcxkKChzrK2qasKGMwD9Mi6ioyd2uRxxbdZsu4DUikED0eNznam9CRQvQtUYncphQ2ZW2OdMCevH0peqEY0QvBxJdp5cDl6mmfw/s3wj2rRF+3ibCjpUeWaaVHRckEyX2lFeCymSw8vK5f1Peo/YzFfsrF16WD9lWO1xpQ0iTvLiWpTG01vbqD9uK0x8KKS69JnvXZpKd4ZsSgs+D8yQ7miRrObxNpE9IsJrMDsntDrr+1h/YDl1Veeguo6FomVvy7d83pdY+kq5N5Gk1LtHZM9ARLk1FYyeE3Rit6QvM4ZLhq8Nm/OmHvvatq1mYDsMjzpY5N4LKtSlh9XdVEoKQ39aEK43J/1cbVGVUQ5aVBRO63DiRqVujqW3v03xny6Piq0GE2RSWbKI4EhEVe6DeaNLl777oAJTWS2hiZyHYEgcv1t/Y4eO8q7yWbU5AtIqws/Jvmy44c3r9ZSxGruoma1VkENquxy8FxleqU+ymFWEk5p6Pvp2U09IzZyhFPdy1F1wzM2ho1JoLGxJZOf3/G+IsezkMlRVYzvKl6SguN3TtjZr+/i/Ujl+VF3iDSkoGttIbkvSsuPtlFf3QFQGpEGyMVSaX0LMv7yWYY+ylXsxbPgi77nTltW7g7U6kXiC2KQ9kQrcj1lx0zpvflFeOVx4ffOeHw/k3RcsA1I8y0pj9siVqgCi4AppZPXPkEVUBDFV1flHZU96WmUtUJdRt4qGNTbZHMoPixVbRCOH+yw+6dMQ++/FycizyaUM+FPJ4k27w9YcMXLQg0De7uD8voIndP130mamQiweTik132c8BXMzrbRNhVbDELHBZf32X3h69pbUkRi/NRNbBNnnbp3xuL/kEqPVK1E7lca2QxWzlYXvRS5/5lx2sNKIae4j9ps3xU7WlSpz5yBcGWExKdzBhOmpj9tLIGrqqnFNTH0Oi4PulXrrm87GIcpgWN0c0oT49WMz8ooJI+GHL28R7pm9d0HTHJ7FybKKIihPktVfQfnQyzmzJeeXz+dI+T4yGxowtQySmQnt0SrehZEc66RiRaWT4WwPLxH96h9+aQnufny2LGqEar74ZSVARe5fUCbKAAnBeNlwUNdbwoxSz7iCwim/HKZfzJgMGjIY8en60ByaaIqF7oKCmO7LT2/HTA7v6UnlfSyvo6Ourx1SOki0922X0wrIDJxqI/xLIZUoS9vOzS/8o1HbdcEkZtvSF1k8LCH1kMJ02aJzNaTrWr4Taqswwt/CdtBm/durz4dz1eCCiapt0FfgU4RDw2fznLsl/SNO2/Bv5T4Cp/689lWfbr+Wf+DvDXEF0C//Msy34jf/0vAb+EUCX+lyzLfuH2fWc0HkyZTBs4lhp1lNRHzfpkWUTiaVz5oslvdUFprTLJRVpWgkpA3DO4GrXR+oBd0ikdtR9tDVRc0B/ecPVH+2TvXZE5GhTd6as3nqz90bMUzNyIpic4xzGnlz1W/Xmhh0i/ikG2NVpJM30NWJpmyOAHl0xDhyeXAzwvpN9Y5RWsoiRefboW4CJLHF6CbsjxvQDEi8amwkMVRGS5v5x8y0ikYVcrm73+jEc/+KyYuC8CknoFdV13GY1anBwPy+ZIRlmyUAeT0mciBFhJc+qRSR1M5OfDJC8nCB2uRm3avSUdNyjAZJPfRGR1xOJhk5XIKXaKeqD1rE6d6kymDRoPpnjWn3yEEgN/K8uyr2ua1gZ+X9O038z/9j9mWfbfq2/WNO3PAf8B8B5wDPyWpmlv5X/+n4B/C3gGfE3TtF/LsuyPt+1Y1zJaboC/spmt3IpwJ6mPfJ9JQmpoNIjodZZcPe1jn8RKHU68UU9xESe031gRJzrDeQO9regiRr5A2DZQAUF/vhiQ3h0BkGaCcqjmNyj3KxffNnNznXWUcLNo8ORywOFgSiunQLaerGkr8AJgMSOaVkDfXbGMbCYrl2cf7tN/MKLjBgUfV7uwrQmiNYApr8erAZE6TdoEICqFUL0qq9hi6juMPuvTvT9hp7mk0RuvpZlfBCT1SGcZ28IOP+zgeiH3j0oBdZNeIo+7TrlGvsfV0z4HLwEmEoSKor95A8uOC8NbJa1c002k4W0W2MwvWuzdHYmsjrE5qyMNb4LquOi6mFvOn/QyGlmWnQFn+e8zTdM+AE5u+chPAb+aZVkAfKZp2sfAj+Z/+zjLsk8BNE371fy9WwEFEE2nWytWX99h+RVBfYx0c9ZHrgzYtEOioynDqw7GweQFeooQaVMzot9ccTluMVw0lOgnTydLjWELqGj3bzh/OiA71uh5K6DUXCpZDEWsla0CdFuY2Ca2y7NvH7D76Ia+qxdaiNRWVBoEW4AFLddYRNTSsgN231swD21Oh12SRGfQXdC0Q0Xsq3pMthnYDKriax1wto26aKsKvuLnemapCOlzEFmEosrWMFIGnQVvvndaPMG/WyDZBgTXH++w//i6AgQyotskvqoR0yK2Ga9EaljVsupgIoe6lOsyshkuGsSxzn5vnovHVRG2OJeKbrIIbYZXHXpHU9EXZYOBTaU6YWqwDC2Sb3Zpf+Wm6I3yKsd3paFomvYG8GXgXwJfBf6Gpmn/MfD/IqKYEQJs/oXysWeUAPS09vqfv31/IjXcsCPC9yeMx01sM9lKfaSdPTU02m5A1DMYTURfE50M3VzXU6RI6wLYkPXgatRmqHtKWjha86jUQUXTMvR7N5xfd0lSjbSh0cwnkqlpG8XaNL/JCru7keC+G3OzaDCZe+x150rIrVdokK6lxcSsA4tppIWTNk5jYlMXawy7K8GfI4vLaYvlVZPO4YyWG4i2EEZp0VZvZlV3gbqgejuoVGz3WyKRMltRmq38WKQ0p+dtGnsLOg2f+/uiEbN8ctc9K8BGIBHHUaU3MjKYBi5Xkxa2HXPv3fPCcLYpJSy/gxo5+YlwG4+WwrR2fE9GNvFGMKl7TRaRoFhFGUT+2bU6HUU3CWJxDUeTJs3eirYbKA7a9eI/SXVWkcV43KTx/oSGXYLWqxwvDSiaprWAfwr8zSzLppqm/T3g5xHS5c8D/wPwn0DtcSSGMHdsfr2+n58FfhbAO2hhGQkeQhsJQ4Pp0i0BIac6sJ5KzjLRXOkm1hnNGxht4RuRDtZ1kVYIqi0rhP6Mi5uu+CJ5I2kVVOR+JKjoZlRwVmMv43LSIohM9toLUlu0NhAfSqo6jhqtKL4Mx4hFtmLYYdZwGDSXNK0Q19DXaNAmYAGw89DaylPBSabh5q0uu7bOjrck6k1YxRarSBiogqFH62COl5vOZO/RouapljVQwWSbUxbUAsCy3kSCSJKJSlo/NlmFFvOLFs5gRbsR0PV8Dh/PsHL9og4i9WhEnoM6kNTpTTGRFw0WS4e9/qwSUWyKSuR3qqeF56HD1axJkugVB6zU3zbRnAqYLBosFy4HOxOxbIZRRoybwMTPM0GjeQPDTOgW9UDbUsQl1ZkuXUxbuMu9gh79KQCKpmkWAkz+cZZl/wwgy7IL5e//M/B/5f99BtxVPn4HOM1/3/Z6MbIs+2XglwF67+xnulY2Vuq2fK5Pu8zyKEXTMjBYr/VR9JS0veTypsPYdNcngxIxyMyPPCPpYMrldQfpdAUFVGqaikgp58DmZOi9jNHS4/l1j4PBlJYtMjh2TkdkY6YXRSsNK2LquwR//4j5Tw/puOuZG0PTlZui6umoRC0aFXBJM1EP1M5v1LilE+3kmZPEYB7YXE5ahGdNtJ0ArxHiWBGWUQKMrNhWz70clQZJaWnaihKdILJYLW2yGwf7aEHDDfHsiGYr5LgzrTTBfikqlv9fpTZAEZHUM0JT38X6RwPsnx6yuz+sZIS2RSVARXyVmsvFsEOjEbDXXhQO2JcFk/HSYz5z2d+dFgWamzI6qQpieTPrwLfY35mu6SbqdYgzcS1l5fFq6LF7rDRaqoHxqxgvk+XRgL8PfJBl2S8qrx/l+grAvwv8Uf77rwH/m6Zpv4gQZR8Dv4d4Fj/WNO0B8Bwh3P5HL9q/vDC2Ltbn6ezPmV43cY7isgVBrdYHSj2lYUUMeguGHw+w3hS1OzLLUhFpoQIqLTSynRkX5z1xIC8AFVFkmE8sW6S8R3rK8+cDDo9HYo3iLKroKrdFK8LAJmjI/GciZkuP4WiH/d0pHTuoVAcnchLUNBaoRi0quKRZ7pDVFfphlS7Y2DOI2zrJzkhMzFQnSoWNfhlaIrpIdOLYIEl0skQjS8XE0/QMzcgwjBTTTMRPPcU0Ulwrpu2EGJ0Z5lFaVH3LCaFGny8qSNwWjWyiJUEsmmtfXndotAK8n7mgt8G1ui0qUfWSwu9y2qe/N1sTUVX6dRuYjG9aHByOC6+JBBN136UIaxQi7OLzLoNHQ8Vav66byFqdKBV2/Ol1k86+6Iti1+jUqxwvE6F8FfjLwB9qmvaN/LWfA/5DTdN+CEFbPgf+M4Asy76lado/QYitMfDXsyxLADRN+xvAbyDSxv8gy7JvvWjnqv09RaOVayPjmVcCyi16CkDLCUgejhg96aO/MVJOfjXzI5eXkA2oATgcc3UjepVK+mNnsQAPSpt+cTJ1ATq6lqE3M2wz4fzpAP9gRq+xommFpPnTMNWytSxQEa1kaRE52XpCwwpZNkSIfDVq53w7LCzZ8iZRxdt1OgQquIAURkvLPcZmjUO8tyzyU4v/1J/ldau5ZHNDXT1K3KbRbAIQ9XtsAxLZT0VGJKvYYh6KNgiuG3GyP66k0bdlcMSZqm6vAgYXbQ7uiD6wqi1+k51epoZlhDRcNJjPXA4Ox5XPq+eqntERRX8Ooyd9eg9HRW3Pi3STZSTW7vF6fpHVsYyqwe9VjpfJ8vwOm3WRX7/lM38X+LsbXv/12z63bYjCNi2nPhqdhs/1qL0xlSzer/hTdAqvSXJnyvVpF+1EDQ3X08kSbOTZ0XYzroYdMiBraDSs3MRmJBXzm2o8k5PF0FLMeynDeYPzcYed9qKgQPJptGY0y4/DMGL01Cicsa4R07BC5qHDeOlxedMpWg4UwGLoytNWVybn5om5CWBMDSTIiHdU7fjyfeXvW6z3qsai1aOmdWt+/X3qe+W+t0UjRcPoxFBSqqIVgtcIi3R8XSxV6WfxfWpRSZzqBcW5mTXRtIyTvMjvNvFVBZMiNbz0WC5ymqM8EIp7YQuYzAKH69MunTtTxaOyzW9STRGniUGns/zXSnXkeK2dsuqQT+s0E9Sn21kw+qKPcSJOqNRT6qACaaFvdD2NbB+ub9rouxk4+c2cshapqPRHJ0PfmXA1anOd6gyagh6kWX4zKTb9TWKtXP1wvHI5/XiP3QdDkjwtnGZaJVqR37Vw2eqiZ4pY/LwElpYdsGwKn8nwgx06bwmfiWtGRZagqj/olSf/iwBGnMPy7yXQyJFn1LaASbmNzWH1thv6NgCR+9uWYvbzhtFT32H6nT7NRxNO9tYjkjqdKr6jopXUo5yJ73L92YD+/VGlWK+ul8hjVe300oQ3XDQIA7MQYOs0Z71Gp+wRc33Tpr0/p+vl/Vu2mtfKBtgz32F51qJ/b1QsParqM+p5fVXjtQYU0bFNmaiZKPbLMtFcKTqZMnvWwbxfbemoa9XMj0kCBmRZROpqJIkuPA39/OSaVJaP2Ep/+jOuxi2u0yaDlgZ2/voWUFF1FfnPephyddPGb5v0PJ+WHQgKZCSkSd7JraatSBokgUVSOtsQVMh/f8XUd3jy6T7N/QXdxkr0zlBs22sTKVPbQaSV6AOqdTdibLPnf2/Xtr79OoDAdhApC+mUxdUji8nSY3HZpH884c7758XEq9ORbfRG6i5qVDEPHcYrsQjX/sObjRRHnIftYDIPHYZz4TNRO+RtozmF1yRPDw8nTbxmUBoTt4iwqrV+EVrMnnVo3RFNlmwFTOop7Fc5Xm9AycSFll+5rqe03YD0eM543MQYVE/umkibZ36ahGRNGKZNrict6M7zD+TNkmAr/dG0DK0Ho4XH5ahN1ocspz+pjAiUY803W6FAlp7gHsQMlx5Pn+2wdzih6/p4mbhJ0zwTtIkGqfqKqYkUcmzoBRXqP1oJzrzwOB0N6O/PaNiRUiy2OXNCpm+gHy8OiddBZ/PYtHbPbV3dxN6rnhU1EpHVtavIYhlajC7bNPorOg2fg0ezF3acq+x3Q7SjRiVX513aOwvuHoxoWOHG7arHrx6nXM71atTGsmP2e3ORCVJADtbBRK7SOI9srictDDOl1xT626aMjpoFkoa38bhJ43guPCpbdBOZjn6V4/UGFPmFdYp+mBJU0lxPST2fONbXRFpBY6onXgJGixDacDMVi2jTyXe4AVRU+qMjMjimnjJaepyd99nfn5AilveQGSBVrK1TIDPNxVMjoemEXI/aLHybfn7DlO5KrUglbwMWlQq5+blqWiZdx8dvL1hGFtfTJsFcdF9rOuLJ+FIGNgVkxHnfBB4vXyW8/tr3ZngLYlGmP75p4bQCOk2f+/eu16KRTZmi6pFvbkUp22KOFh5hYHF4PBJZGMVQt43ilJ3WrIKqXF52afeW9BurNToqr+c2MLmZCr1m0F7QysFERjVrGZ2aCGs5wm9SdNurgYk8p1H6fdRgSXZs07WMVMmmCF1CQySRIGutuB63mCy88sY34rXMD5SA0SCCzoLrSYurcQt6ZaQiJ9p6SpmiC5vWzDCNhPHX9om+ck3HFc2SitThFgokoxXpR3H3YqGD/M4hix8Z0vX82pPwxcACYjKqUUvDDGnZpnDH9oRxbLTwCD/qYD2a0fKCinlNagGVVptK1LKxDUENKFTvxKZRpzNqNFL2RC0ph2p6m68coo/b2I+ntL2A+3eui4Xbt9E69ZiK/W4BkjA1itqn4GsD3B+9Yb8zX6t9qmef6hRMNkea+qIFQT+/N+plDus+E72gOfPI5mos2ibsdueF12QTmMh9F7Rv4ZGmOoPOvKC9ci2e+rlP8uU5XuV4rQElzURJuaZl6EZWXZazJtL2O0uuz7oYhridt2V+IK/Lyf0gg86C4YZIpS7Uyv2pk0v3MvQfvub6WY/4UPgR0tyRquoqYv/yglajFZkWnv94xHjh8fSyz95gJmptcvu8KZtvbwEWQGSFtLqAK8DFSw1iW6fr+IQ/PMePTfzQYjhukQQGzd4Kz46K0NjWk2pKfkvKl+IbbaY+t7llZepZ/j/JvRZRIibVKrRYjD0MJ6HdWtFtrnB/eCaqiGvGtxeVB8hj2abByFqhq2FbNMf+8fONRrNNFKeul/h5p7XpeZvdHy5bENQL/eQxbQITEZmIe7Oh0NXNYKI4YVcuq5EnFlC/RYQt1vpJTFbR9xGgJInOMrKKmhqRpl0XaSEmszWSgymj5130I0VPMdczP+WqfbFoVdDNuJmWmoqgMCICqoOKWqWsaxm6l2HeTxhOm5z/f+2da4wk13Xff7ceXdXv7tnZ9y7JpSiSFgFKZijCgAxHdgI/FAPKhwAmDBhCYsBArCAv5IMMA4kC5IsdBAnygAUFNmAZQWRZThAjgJDIjh9xEoumZYoWrRe5Ii3ucnd2d/r9rqqbD/fe6lvV1T0zq9mdSdgHGFR1TXfVqVv3/uuc/zn33LnHmcYI6Yu0BMHygW6yVvQ8Hi9iVFaT4LpumVZtYk3iOxywFFktiROrzuvpzltStWPP1YZpZux0oSyYcT+EyCFsTQlLC3xP6eYKuQIymRUV14gpD5kHj1gKFrHLInKZzn2m3RC8hEpDXbdZmXC2PkzB7ahzjNLrHwJIusMySewsgXwlr6TYKrHrudpgIKXgwqP3Ulcps4hXAZjYxPLdXg0hZGqZ2NxXEZjMIi+N6Axv1Whf7ql1e1wbCC29tfWXWjT96tEG5QFyqgEFoD8KMx1ZNZKSlKR10AWWBPJSn9kf7zD44D5OeX04OQMqAI0R+4Mqdzp1dpojSEttrgcVU13fQeK3EhUWvrnD2fM93TGdFRfI6K3vQFkr7tINCtyIsr9gNC9xt1uj68W062MralPsCqmzbQYXgMRxSGSU6dCJdFRx6sQhbumtzoydRy7TRcB87rGYecj9AFlKENUIz49xXDXzWwiJ0AaJlCgQSQRJ7BAtXOTIQ8wdxM4MP4golZQ1FJYW1MMZbquPqcxnk8ZFAAKruSy2FHEy+eU6xgufzqBCFLlrZ18fZJXYLs5orqrT13dGaVjZjuQcBCaDWaAij17CTn10KDCx0+oXL7dpfXB/WWApl2RnrmuvONAfhXBIYv2wcqoBxXUTZv2AgZc194pIWlNImhCS5zv0r7cQ7+mQzgY8AFQcJNShOyqzd7dBckat6pa4gpLMdbJcBMjx1NvbdRICL+bOzRaT3ZFaJMxzCuZoLK0Vu/SA5yR4SZwWUa6W5qqjdup4XkyrNqHsLzZ2/I3ggsDV7WYGmyn0bVsQRS5Jamlcyn2Wy0zavJh2tgtW25bNOpfKBhDzjNeVjzSyjtjNl0GYLHy6w3IGSAKd27MOSGC9VWKKSQ/vVtm92KMWrPIlts55new8k3IN6KVEAAAb7klEQVR1Rqs6SQnYg8Akzbm53qL2fIe65mqKIjo2CTuNPAaTkFk/YOd8f83ouz851YDiCEljd0T0UpvhC7rL+GZw5EhaWFanDwXyWo/OzSZc6h0IKoa8rTFHVBWQ3bnRQl5SHcRupXwHsXkVY0GVrkZ0hhVu3m2x2x5QlXMd3l1GCezwct4NUoWX4nRZTAMsnUGFOwuXnZYaCKGVk5B3h2LEWnAx959Yg7QogQyWAzWfYp+J0qzJZbA7dJ57cfK65dyKgwDE1i2fPZuGbq2BN5qX2O9W8fyYpnYl1wGJrYcdDjZWhb2G0d1OnVKw4NLVeyu5P3mrBFgBuKHOgK2fG9IIZ2loeD0BmwWTzs0m9Wu9jWCSzrjWJQyG0wD5cpPGCx3K/kMusHSSIoRal7X3fI/+vSruWeshucv6JOitg8B1Esr+Agkk5xw6txuIC/b6wkXZtMvoTxVVSFqcg3tvtkke7SADQeItUlxyhCx0gSBaukCNhN4kZPR755h9aF/lzPgiDW0Wh5dhhV/RCWwGWCaayb97p077zHBtnomD3AguK/um4+ZM4IMKUt9PpmxhxKhApyLZVJV/bZ7KvRphbc7ZnUHaViVr0BbxJEXnTmvGLkoMpgHR/9qh/qH9dHnQwItWeB6jsx3FMuTtYFai81abxpU+Te0mHRZMBrMSndsNqudGCkz0YuhFllUknZTsHs99+veqVJ/vnUzFtpMUgVq+ohbOiBsO3U4V98zSjMbJgoonYkNTUPGBikpG299rwDnLtNsAKraJ7j6S0H1jh8VjPVplZeIHnlgJK2d4FSkzLtDowxGdQYXBKGSnOaIezIh0XZN08MvlZD4bWEpCuSOOUBm7oRtR9hZUS3OmdeU73/iLM4TtKfXKNH1D5s1lT9hFsje7Dyufre/mweZ+5SDQsCVfbT/PY2TyMCyycTAOmXZC6ueGXLrYSQtI2ZPpDgskeffEVI5rf3gvtXTs8x4UyZnoEgSjN5u0Hl9OmSjKgF0HJvt7DWq7Ixrl6XLWsZNfv3iZrGcAttupEjZm1EKVYGemexyXnG5AEYpsBUgqiuTr9CuIpllkKzoYVADZFocGFZOmDyDKEveJffa7VaLIpV0bZyJAxsUBOy9kCQ6GGCu5MaO5z50bLSZnR+ptZN6U0mLjDwAWm2Mpewtq/pydisqOHU4C7l7foXJ5mKnAZpvA6s3pFJr2h3ExjgIE9yNFS3Xk0+8zRLIFIqbC2/hGjfDiiHplyvnmYAVg17k25lr56xjSdLJQxaCHd6rsXOxRLS1S4nWdVQKk5SDsSE5nWGE29dl5Yn85a/iIYFJtT44EJuOFT6dfwQ8j6pVl/zuxim0nIULnfkgZI/0F1KDTq9IblnHqpnNHKzkqay2VW03k+f5GTgXUMRN5cYTEOxPTGVTY22/Q1kRe4qlJfea3B1krgRcRPhLRG6v1ddvn+9SC+Wqn3AAsNseSSEHkKMK34s9phlNm9VFKOs5vVahcWa5NbFdfywOMOnvxIFuXXn9UcDlsspvaigx3YwNIvsrbeFZi/HaN0oUx9cqMnSf3VD6NNcjykaL8Pa7LzjXWxNC4F2fGXHrkXjqID7JK7JR4Ewnq9Kq4XpwWR8rPGj6QM7l9OMskm2vi0xuWEUCzpuZ52TVrj1NONaCAGqyuk+ATE0pBoz6mc69O3w3TJUQhm6MCy8Q3sCyVMyJD1EopCvNUlKjSB+nxhqQ3LnPndpP4bD/lVVQVtmIXaBm1SNKQqO8klEsLOr0qw3FAq74kCDN+fS7MnAeWBIHjSjyZkDiq4wZ6Tk8jnDJrjJgsVGhw9Kd1kucGVMIZoa/fhk6STmVfXQB9CTIRqzyI4WWOKivV7guIXzvKFFlkYqTX4Z0uPMbTAOfLdeLvHVAtz2g9eScHIsnKQF8HJOa65lqGJ0nnxAzKJLHL7sVeIRGeJ5fzoJSxLO40qLYm6eTN5VKh68FkFnnpSoKdm02q51bBpChxbR67y/DwOGQx8WmfGahUfDfOVNs7Tjn1gALLyIrRVu4M6dxu6HWIFWCk7kdh4tvSUnEuJPTeaCMf71IP1Ro6iStWO6FQVfWBtFO6VTUHZ/9Gi/n5oeW6CBK5NKkhm8GaWisa5EyuyXCmcheGjanKBPUiAtfNAIsj5MrMYLXVA0KQukP2W7HsLaiVHHYqE2YfHqop7XOfvUGF+G5A6cKYSjin5CnS1ySPpesQWx3Vniavtq61f7BkI0I2eCzXprHXSzZ5MPPYZR65jKcl5rcquLszKpUZzeqE0oeHK1bXUUEkP4dmbrlPvVGZST+kvTtILck8N7UpimMTw71JyPB2jdbF/ko0xg4LG71sTsgkrfWvt9JoTh5M8olrdqW2gc6ebZ9Xs45t4M3002OSUw8o6dtY6Hohns6+PDeg93YTLtodO1oBFUedBFCgIgBxrcfsj3dInu+QhIIyC5XgpicUwmpY2ZC1rpPgX43p9ivsTX12miMi31EWBktuxbZWbG7Fkwq8jBtUKS0YTANuv7FL+eKQhiZX546bfRMay2eD1VIELokUlD31ho8Dh6g2UrVjY5fZQg2caT8ACUFjRlCK1MoCOjvW0+SynUNi2sferpN8mNnOmo0T48IIIg0es7nHrB+AgLAxIywtaNUmlJ4apoMwXzayCERMGy31KOZijBWRlkoch0zeqVG/0mfn0n6awr7OvQHWApNZ0Q/g7NVOxhIt4kuAFTAySWtpnskh3RyTazJ+p0briqpyH1gFluyxdZxyqgFFInT5ApnWjPOdGLQLk1zu079Vh3NAZaJ/lQUVyHIqjq8e4uCD+3RvNkguiLRrJM4yWU5ti3kVz0nw3Zj+JGTv+hmaV3tUg7ku7yiy1oXp6GvcIN+JCbyI2hMzhtOAW2+eoXJuRL08y4Q48zVX0xsiO3Dy4JIgKJkSj5YpbQZULB2iVjYzdha5DMYB84lP+esh4/fO8cIIvxSl9WEVuK4CjBEbQOJERchMHdrF3COaelS+VWLy9JRSeZFmzlbqc/zmMGMxGdciDyDqbg8GEaOPbQnZmaZmnd/xXpXGxQEXn7izdlkRc03IAokBk0XsMlqUGM1K9L7TpHp5kHFRNrk4pkJcCm6TkOGtGq0P7qeWjQ2m9n3mwcTUhmlc7lMN5ikQ2X3SLu95XHK6AUXqjmnVJwFwhXq7yxC4AOOvtxg8nSzJ1g2gkna+EMTlHp3bDeK2Q1JVfi2A54hCXsUu3OSgFi73H4np7NWZtabEVUHFXygXyuqIRu8iN8gTIgWW0IuoPDZnOA24+7VdSo8qi8UUFvbdGC8pMrmLrBZ1xYxJLtTWk8ZEzmbFmsEmLU4hvuDQktYcnESQaMtiHjnqGSVqa4sQ4DhJunWFpORFuCWJW50obuzycn6QJ5I0XG+b8tn2X1oG60BE3VexW2O7EvNkubTE/K0a5cf7XHjMIlxzVkSRe2NbOXY0pTcqM+mGtB/pFrpLtv42yK+co1OmfbmXOYcBVvteVyyTacDsmw0aT3fTXBPXaksbTN6V9VAypQREjlMJQT7dZfZaC57pHggqCU4aFnaExL3Yo9OvcC+qEtcnJCVV22RtBKjABSpdiumPw7QKuukAicWtrHODEmlmB8dE0sXXlfqnz0wZz9TC2V64oFnTfE0ugmEPwES6Gd4gm6mqU/wt68UATFo/1l12cFh2VrVvH1egY2Sd2Wy7BSIPDBkLY9UizFsDmwDE6Gp0MzrZ1ojhFWaRiXqERFOfZntE+5m9tG7IJiAx5y0CqDQadKdOuTnl/KVuoYWZ50vy1lJKBCdOSgTnw//2PReCyWstys900/SBlG8pAJN3Xz0U6ayUZywCFZ7pMvl6i+TJfur+JDJejf5YafrCgEIroTssc2+/RtwaUS05qlykRdaq3666QJ42QUtuzLC0oLtfY1KdU69Mlz6zjgQVuUHrgEVFbNTEudFcDYC7gyb1s6pQUuhFGaslDQObAWgRuea+1wKMblsDMrAEGtWOq6Tqus95WY0QrWbnQnHWrq17XorcGbOfz1OZ62jHaFZicKeGX59Rr06ptgeFAH0QkBSBwGAcMhuV0hdKWsgqF0Gz2ywPSKO5WtnPDyJ2GsNMrsg6MLGjOb1xmdk3G5SfUQGHTWBiCPB3Xz2UyAOPZUbfBlART3dTTiUpT9NwsZrtyyqoOGBIVFGXDLyQzlttoiv9lKw1U/89kQUVEwUy1oorFK8S+BGDSUjvlV2m1oPN++O2G1QMLCrPxddJbPVgzrShBsWt7+zgN9SgMGFgu05I0UQ723oxbZAfqHbl+wz7b2HGd+tzbyJxi4Bjed3VKvtFExptEDFh5sEoZNEPqJ0dcf7yMmvWdZIVTqMISMw1i5ZLNRaB/z19zp/vrnWZbN3zVpMhXwdvN1TZxpUck1UwMTk5djRntFdN3ZyDwMRYa+O5f/SHuEFONaDEscPI3PAhQYULMLjRgIvqcOjpym65jFoDKoZoVcckzpWEwY0G8cUhcVlzIjJecYHsbT4RzncSRs8u6A0qTMYBrcY4nSVc5AZBMbCA6kiJ4+h6KWreTqM8ZTL3GQzLdO6FlC8OqQTKHQpyHSnz1rUmCeYBxrSJvS2S7Ho+h5dN58zLUfJVbILZDJJZ5DGe+UzeqeGdmVKrTim3humcqHxyn9JvPZAUuTeThU+3X0ECzWfvZUKyRcRr5ly5yJKJxtSu9FdeQLZLaNrGzoC1ozmNy/0jgclo7tMflo/0HA+SUw0oAINhGaeuPxwCVEQIzpUe3b06SVsgK1P942JQsYs0KUtDEa29fpX53CWuK7JWSpG6QPk3mjpXnHZQY62EfqQI1htNgvaURtWeb+Nk8xCKgAU1mTCRCZ4UJI76HCUOFX9BI5wxaw2Zzn16gzKLTkB4drKSwJbPkE31llmuIpGb80uyLtP9p2yvA6OMa1Uwy9m2QtIIVS7hbXqnjN+eUa3MaLznLoGrLLd1bo2596Lr5oHEEKb9UcisE9I4P8wMYNsqUW20GsXJn8skzrUf6azkiRwEJoZUnnTKtK700prBhwGTyUK9kHg3RXlcNyGOHHrDEGr64AGg4vjqIYrzfbr7NeLYIalNkP6SbHUyLozKVckszuUk+G5Cfxxy550mjV09o1O7QOuiQEq9JbdiOln56kIVVn51l/FT6i2yjNxsBpb0PoVccYci16EiBYvSnGZ5yqylcktGk4DuGzs456aUK0tw8S2AKYqmmPuxgcboAqSAkx7f4L7Yss5NWlci0mzz0ScDIIt46c5MxgHJXoh/Sa2R3Lo2zoCIiSAVvgQOCSQmIjScBsy/0SB4ukfraqeQ4ziKi9O/W6XcmtLQFmzebbXFWGI2GPWGZZUBe76fzjq3w+ybwKQ3DIkjh2ZzfKhneFg51YDiCEmzOabbrR4aVBwp05op4syA/qDCfq+KbIzV4lyoFQhx8hGGLFnr6AiO78X092osdtxMCHedtZLlVpRbUdIh4en75wqkvrlL5dFlfoANLMbKMcl8kI10JMJ0fG21yCy4xCWHeXnKojFalnbsVQm+UmH+gRFBuCD0Izw3xneSlQzZFffIisDYzwXgqEmWxRmzy2xZ25WxM2YXiUOk72U29Sm9UmX2/jHlyox2c0Rpp79SC/eoIAIUkrmThc9oVmL8VoPgypCd99/JcDB5q8e+vyJeJ7Uq9ss0zg1XXJRNkRwbEDr9CgJonxlkLJui0HARmERzj1ZrRKW0ONpDPEBONaAIgbrh1ohup0pPluEA9wdIM2oB3OaI3rDMvXs1Wu2R6jwWWVsUAbL5EFdISpdiesOQvbuN9CGss1bsbUmoUo2R42qrR1ks0/fOGIxD7l7fJbw2yMwOdp0ET+Y66QarBbLgkjgOAdHyrR46LCoTFj/YV2+3hcdgHKhs1ERQas4olSJKXoTvKoBZVz+26B7z+7YUA8hqxmya46K3i9hhHnnM5x7zXgCOTLN4W40x/g8O8HV7rrO28gN8kzViWxCxxU0MpwHTb9fxHxlx5r330kmWefcp3wbrrJKxjuJ4pYjdS72VNIAiF8cGk/QcnSp+GNGsTTI6HQpMBmWiuUurPUqzZ49TTjegIFUCGyBbY3rdyqEsFViCiiMk1GDghHTu1InPjJAosnZdWNnwKrYL5Lmxmhfx5TPMn+0Rl0UKAomznltRasbpLGGTlFdyY2ZPzRiMA27/xQ6188twcOBGRI6z+vazPId8FMYGl0QKPG3JmBC0GbRJqMzmqDHS7oN6ew71BLLwjYDpe2Z44QLfj/EMyDiqHYz1JtgMKnkwkWZrJcjFiUMUOywWLtF0eW2/vCAIFtQqU/z6OA3N+3qpj0yN4YLoW1Eb5d2rTUAympUY3q4R7ExoP7VP4EWpO7FcenS9e7OOOI1fbVJ5tpeul2NcHNPPDgoLD6cB/Xuqnompf2O7doezTFyarXG6yoEn7p8LK5IDAUUIEQJ/gCrb7AGfl1L+EyHENeCzwA7wZeCnpJRzIUQAfAb4S8A94CeklG/qc/0c8NOoBIe/K6X8bxuvjVryItQoKtry0O6PbeKmLoybEL3Upvd8j6Q81REg7SoV8ComCW7pFkjGz0UMhmUm4xLNxjj1XY214ki5krdi3KBEqhnCkXRwhaosV/YXTCozhpOAye+fo//9faqhTpXOkIk5H/1Q4CLwWM7rUYlrDom3TGwylkJUVYMquSDSuTVxopOmFh5R5Co+au4ipy5+10U6ENVi8CS4lk4SiAVEAm/oIhJYtGJEGOOUYpW+76lt4EdUggVec4R7Yelqmje2MNZHbtBlCfGjgUg+7GqWoRhNS/h/2CD60IDdK93UglhLalvnBtI1hfIWRa9fwXEk9efupf0lz+/YYkeubECSLzfTSmvGVTZtZe79QDenPaJcWhBqMHGdhwwowAz4ISnlUAjhA38ohPgC8A+Bfyml/KwQ4lMooPglve1IKZ8QQrwI/ALwE0KI9wEvAs8Al4DfFkI8KaVcXzJKqMFMAqEXqe7RGtHrVegNyiQWqJiHbkAlQaQd0ZjrrpMwfCGhf7dK1HBoVKcpWes6yVpeJS2ahExzTYbTgN7rbWaPDojKTsZlsfNW1HlW+RVPOCmfY96A8x+ekMxK3L3ZxK/PqVZmVIJ5mmdiD7RMCvcacDGRIhtg0AADkDjZjNiibFj7uJRZVwGWNEqeeDXXFNbn9FiOqynKos2DR9E2f79QDCKQHexmDaB57DKelRiNAxaDErWzI8o/vEfTjQtdkXVAss7SGUwCpm/VqVxbhnMPY5XY50mjSv2AxgudtNLacgEvK0pnZcCapLWRTi+IIyd11wMLTA5LrB9WDgQUKaUE9LJ6+PpPAj8E/KQ+/qvAJ1GA8lG9D/B54N8KIYQ+/lkp5Qz4thDideAF4P9sur4jJGhQwfh7zTH9QYXeoIKsqcW1jC+YBxXjX6cJbCF452N6g4pa6KqhZwt7EYlcrk+crVW7tFbMG9N3EsInI3rDkNv9Jo32OPOwbTcovQ/IAEsiReoK+U5MnDiU/QW1cMZ07jMaB3Rv1ameHafAsuwMbnFnz4HLJoCBJcgs91cJU1glMPP7Bz7D3H5Wr2LgyO/nf5fXzehkWyL2AI30IEuB5E4Fv6GAO2wN0wFvA3cRkGSvk3Vv5rGrXJNOBb+8YOfJ/bWWTvZ8WatJWRaeWjdHSHbO9yn7q3lGpk3y6fRp/VgdGm42xw8cTOCQHIoQwgX+BHgC+HfAG0BXSmkYnbeBy3r/MvAdACllJIToAWf08T+yTmv/xr7WzwA/oz/OvvCX/81Xj3JDD0F2gbsnrYQlW302y2nTB06fTk8d14kOBSjaLfmAEKIF/Gfge4q+prdFry254Xj+Wp8GPg0ghHhZSvn8YXR8WHLadNrqs1lOmz5w+nQSQrx8XOc6Uv60lLIL/B7wfUBLCGEA6QpwU++/DVwF0P9vAvv28YLfbGUrW/n/QA4EFCHEWW2ZIIQoA38V+Brwu8Df0F/7GPBf9P5v6c/o//8PzcP8FvCiECLQEaL3Ai8d141sZStbOXk5jMtzEfhVzaM4wOeklP9VCPHnwGeFEP8M+FPgl/X3fxn4NU267qMiO0gpXxNCfA74cyACPr4xwqPk00e+owcvp02nrT6b5bTpA6dPp2PTR8h8qa2tbGUrW7lPOd76b1vZylbe1bIFlK1sZSvHJqcWUIQQPyqE+IYQ4nUhxCce4nXfFEL8mRDiFRNOE0LsCCG+KIT4lt629XEhhPjXWsdXhRDPHZMOvyKE2BNCfNU6dmQdhBAf09//lhDiY0XX+i70+aQQ4oZup1eEEB+x/vdzWp9vCCF+xDp+LM9UCHFVCPG7QoivCSFeE0L8PX38RNpogz4n0kZCiFAI8ZIQ4itan3+qj18TQnxJ3+uvCyFK+nigP7+u///YQXquFSnlqftDlZF+A3gcKAFfAd73kK79JrCbO/aLwCf0/ieAX9D7HwG+gMqx+T7gS8ekww8AzwFfvV8dUHOsruttW++3j1GfTwL/qOC779PPKwCu6efoHuczRQUKntP7deCb+ron0kYb9DmRNtL3WdP7PvAlfd+fA17Uxz8F/G29/7PAp/T+i8Cvb9Jz07VPq4XyAvC6lPK6lHKOmoT40RPU56Oo6QXo7V+3jn9GKvkjVG7Oxe/2YlLKP0BFyL4bHX4E+KKUcl9K2QG+CPzoMeqzTtIpFlLKbwNmisWxPVMp5TtSyi/r/QEqjeEyJ9RGG/RZJw+0jfR9rpsu83l9PN8+pt0+D/wVIbLTZXJ6rpXTCihp+r6WwjT9ByQS+O9CiD8RahoAwHkp5TugOg9qabGHredRdXgYuv0d7UL8inEvHrY+2jz/XtRb+MTbKKcPnFAbCSFcIcQrwB4KKA89XQawp8scSZ/TCiiHStN/QPIhKeVzwI8BHxdC/MCG756kngfp8KB1+yXgPcAHgHeAf/Gw9RFC1IDfBP6+lLK/6asPQ6cCfU6sjaSUsZTyA6iM9Bd4gNNlbDmtgHJiafpSypt6u4eat/QCcNu4Mnq7dwJ6HlWHB6qblPK27rQJ8O9ZmsIPRR+hSmn8JvAfpJT/SR8+sTYq0uek20jr8HCny9wPKfag/1AZvNdRRJAhp555CNetAnVr/3+jfOp/Tpbs+0W9/9fIkn0vHaMuj5ElQY+kA4po/DaKbGzr/Z1j1Oeitf8PUL42qHo3NpF3HUU2Htsz1ff6GeBf5Y6fSBtt0OdE2gg4C7T0fhn4n8CPA79BlpT9Wb3/cbKk7Oc26bnx2g9qcB7DgPoIii1/A/j5h3TNx3UDfgV4zVwX5U/+DvAtvd2xOpIp5/BnwPPHpMd/RJnIC9Rb4qfvRwfgb6GItNeBv3nM+vyavt6rqHla9uD5ea3PN4AfO+5nCnw/yvR+FXhF/33kpNpogz4n0kbAs6jpMK8CXwX+sdW/X9L3+htAoI+H+vPr+v+PH6Tnur9t6v1WtrKVY5PTyqFsZStb+X9QtoCyla1s5dhkCyhb2cpWjk22gLKVrWzl2GQLKFvZylaOTbaAspWtbOXYZAsoW9nKVo5N/i8Y+dfQSqsaLgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.imshow(np.log10(psf))\n", "print(r'$\\int\\int$ psf dx dy = {}'.format(np.sum(psf)*resol**2))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Without obscuration')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now suppose that we observe a point source, and our image reconstruction has a ...This will shows a a blurring of the image, with a gaussian of 10\" FWHM. Let's generate this blurring" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fwhm = 10.\n", "sigma = fwhm / 2. / np.sqrt(2. * np.log(fwhm))\n", "sigmasq = sigma**2\n", "kernel_blur = 1./ 2./ np.pi / sigmasq * np.exp(-(r**2/2./sigmasq))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9999999999999996" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Check our kernel is properly normalized\n", "np.sum(kernel_blur*resol**2)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# apply the blur\n", "psfblur = signal.convolve(psf, kernel_blur, mode='same')*resol**2" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Original')\n", "plt.plot(y[ycen-500:ycen+500], psfblur[ycen-500:ycen+500, xcen], label='With blurring')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see the effect of blurring, the, observed PSF is wider, and we have lost some flux in the central core. Suppose now that we observed this psf with sources of unknown fluxes, so that we re unsure of its scaling, and that a background remain in our observation" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "psfobs = psfblur * 2. + 1e-4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The question is now how to recover the PSF that serve for our observation. For this, we will use the PSFs curve of growth. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0 212.10000000000002\n", "10.0 212.10000000000002\n", "20.0 212.10000000000002\n", "30.0 212.10000000000002\n", "40.0 212.10000000000002\n", "50.0 212.10000000000002\n", "60.0 212.10000000000002\n", "70.0 212.10000000000002\n", "80.0 212.10000000000002\n", "90.0 212.10000000000002\n", "100.0 212.10000000000002\n", "110.0 212.10000000000002\n", "120.0 212.10000000000002\n", "130.0 212.10000000000002\n", "140.0 212.10000000000002\n", "150.0 212.10000000000002\n", "160.0 212.10000000000002\n", "170.0 212.10000000000002\n", "180.0 212.10000000000002\n", "190.0 212.10000000000002\n", "200.0 212.10000000000002\n", "210.0 212.10000000000002\n" ] } ], "source": [ "radii = np.arange(0, np.max(r), resol)\n", "growth_psf = np.zeros(radii.shape)\n", "growth_psfobs = np.zeros(radii.shape)\n", "nbpix_psfobs = np.zeros(radii.shape)\n", "for i, radius in enumerate(radii):\n", " if ((i % 100) == 0):\n", " print(radius, np.max(radii))\n", " if i == 0:\n", " idj, idi = np.where(r <= radius)\n", " growth_psf[i] = np.sum(psf[idj, idi])*resol**2\n", " growth_psfobs[i] = np.sum(psfobs[idj, idi])*resol**2\n", " nbpix_psfobs[i] =len(idi)\n", " else:\n", " idj, idi = np.where((r > radii[i-1]) & (r <= radius))\n", " growth_psf[i] = growth_psf[i-1]+np.sum(psf[idj, idi])*resol**2\n", " growth_psfobs[i] = growth_psfobs[i-1]+np.sum(psfobs[idj, idi])*resol**2\n", " nbpix_psfobs[i] = nbpix_psfobs[i-1]+len(idi)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radii, growth_psf, label='PSF')\n", "plt.plot(radii, growth_psfobs, label='Observed PSF')\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This strongly rising shape of the observed PSF is a sure sign of an non zero background. Let's determine it. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Encircled flux')" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(nbpix_psfobs, growth_psfobs)\n", "plt.xlabel('Number of pixels')\n", "plt.ylabel('Encircled flux')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When plotted as a function of the intergated area, there is a clear linear relation, that we will fit:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "idx, = np.where(radii > 50)\n", "p = np.polyfit(nbpix_psfobs[idx], growth_psfobs[idx], 1)\n", "bkg = p[0]/resol**2" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Correct PSF and curve of growth\n", "psfcor = psfobs-bkg\n", "growth_psfcor = growth_psfobs - bkg*nbpix_psfobs*resol**2" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Uwvi3HouiL6qr1OUoEckqHSWM29z9HDP7gbvf1GMR9RW1VTBicqajEBHpMR0ljFFmdhZwsZktJHhwr427L09rZL2Ze9DCGKQWhohkjw5bGMDNBIMC/jsHJwwHPprGuHq3/fsg2ggD1YchItkjacJw90eAR8zsn9z9Oz0YU+9XFz6Gok5vEckinY5Wq2SRQO2O4F2d3iKSRVIZ3lzaq60M3tXCEJEsooTxQbReklIfhohkkY4e3Bve0Y7unnQ2vX6vtjIcFqQk05GIiPSYju6SWsaBeTDGA7vC5aHAJoJ5MbJTXSUUjdCwICKSVZJeknL3Se5+FPAM8Al3L3H3EcBFBPNYZK/aKl2OEpGsk0ofxkx3f6p1xd2fBs5KX0h9gB7aE5EslErC2Glm3zKziWY2wcxuBao73as/q92hFoaIZJ1UEsaVQCnwePgqDcs6ZWYLzKzSzFYm2W5m9h9mts7M3gynf23ddo2ZrQ1f16TyeT3CPbgkpVtqRSTLpDIfRg1wg5kNcvfawzz+fcB/Ag8k2X4BMDl8nQL8DDglvEPrdqCcoON9mZktcvddh/n53a+pFqINemhPRLJOpy0MM/uwma0GVofr083sp6kc3N3/DHR0++0lwAMeeAUYamajgPOBxe5eEyaJxcCcVD4z7fTQnohkqVSmaP0RwQl8EYC7v2FmH+mmzx8DbI5brwjLkpVnnsaRkjSIxZzmWIxoi9PcEqM5fI+2BOWxmNPiTkvMicU4sNxW5u3KoCUWIxoLylpiTjSsF18W8wP1Yx5sj3lw/Fjrsdxxp20fD8tiHsTdEu7TeqzWZfcg1tay+P28tW6stS54OF9bsBzU8bh1DloP9mlfn3bbE80A11rvoLJE/1ESFLYvSvVYCaq1/Xs7rZd0GrsDhg/M58nrz+i8YhelkjBw981mB41u3tJNn28JyryD8kMPYDYPmAcwfvz4bgqrA60tDHV69wktMae+KUpDcwuNTTHqm6M0NLUEr+bg1RJzoi3hSdTDE2pLcLKNhevNUWd/tIWmaIz90Rj7oy3Be3Ow3NTSuhyLOzHHiDnBe4wDJ22PP4kHyaEllsJZoYflGERyDDMLls3IyTEiOUaOtb44sJ4DOWZEzDCjrU7bcg4H7de6jEFODhg5tJ5mgmKLWzesrfzg9bBG3LYD+7YuHyK1Itqd9xLWS1DlAx8reWwJ9o0rGjQgpVN5l6XyKZvN7MOAm1k+8DVgTTd9fgUwLm59LLA1LJ/drvyFRAdw9/nAfIDy8vL0/1/XOvCgWhhdFm2J0dQSY19jlN31zeyub2JXfTN7GpqC9YZmdtc3s7exmZaWA79eIfwVHHOaosExmqKxtuW2ZNAUnMi7S26OMSA3hwF5EQbk5pCfmxOs50bC8hyKC3KJ5OSQ23pizTFywxNqbk7rCRdyc3KCsoiRFzHyIjnhy8jNySEvN4e8nKA8NxLs33pijoTHaFtudyKPhJ8ZiXu1xRA5sE9rfK0n+fYn/EQnOMluqSSMLwE/JrgkVAH8EfhqN33+IuC6cIKmU4A97r7NzJ4Bvmdmw8J65wG3dNNndk1dFWBQlN3DgtTuj1Kxq54tuxrYsruBil0N1NQ1Ubc/Sl1TCw1NUfZHD5zI98ed2Ft/qXf2ozovYgwpzGdwYS55OTltJ7EDv04hLxKctIsLcsmPBCfxovwIhXkRCvNzKcyLUJQfoSA/QlG75cKwXm4kJziBRg49ubeeePMiOURydAKV7JbKXVI7gas+yMHN7NcELYUSM6sguPMpLzzuPcBTwMeBdUA98PlwW42ZfQdYEh7qzl4zdlVtJRQNh0jPNAHTxd2prmtiT0MztY1R6vZHD77U0vpqDtb3NjZTUdPA5l31bKqpZ3d980HHy8/NoWRgPgMH5FI0IJfCvByGD8xvO4nnx/0Sz8/NOah8cEEeQ4vyGFqYx5CiPIYW5TO0MI+i/Ih+5Yr0Ih0NPvgTkvQbALj71zo7uLt3+LyGBz1GCVsr7r4AWNDZZ/S4ur45LEjFrnqWvFfDaxtreGPzHt6vrqOuKfWuqPxIDmOGFTJ2WCEXThvF2GFFjB1W2FZWMnAAOfoFLtKvdfQzeWmPRdGX1PaNYUEq9zby0vpq/rZuJy+tr2bL7gYAigtyKRs3lFmThjNhRBHDB+YzaEAuRfm5FOSFrYC8A9fmD1ynz9GvfZEs19EUrff3ZCB9Rl0ljJ3Z4x8bizkbq+vYVF3P7oYm9jVGaWxuoaEpFtwBFHby7tjXyJpte9mxdz8AQwrzOO2oEfyfMycxa9IIphxZrGvxIvKBdHoh3swWA5e7++5wfRiw0N3PT3dwvVJtZY9dknJ3Xni3iseWb+FPb1dSuz+asF5+bk7QyZsXYWhRHh8+uoQTRg3m1KNGcMLowUoQItItUum5LW1NFgDuvsvM+t5F/O6wvxaa63vkktRL63fyz0+9zVtb9jCsKI9PTB/Fh8YP4+iRgxhamEdxQdApXJAXUUIQkR6RSsJoMbPx7r4JwMwm0EFneL9Wl/6H9ur2R/nnp9fwy1c2MW54If9y2UlcevIY8iKaTVdEMiuVhHEr8FczezFc/wjhk9VZp25n8J6mgQdf21jDjQ+/weZd9Vx7xiT+8fwpFORpVj8R6R06TBgW3BazCvgQcCrBQ+t/Hz6bkX3aEkb3PrRX3xTlX595h/teeo9xw4p4aN5pzJrU4ZTqIiI9rsOE4e5uZr919xnA73oopt6rvnsThruzePUOvvP71WyuaeCzp03gpjnHMbCHxoURETkcqZyZXjGzme6+pPOq/VxrC+MwhwVxdxqaW6ipa2JXXTO76ptYW1nLY8srWLV1L0eVDOQ3X1SrQkR6t1QSxtnAF83sfaCO4LKUu/tJaY2sN6qvhrwiyC/qtOqW3Q0s+OtG/rK2ik019TQ2HzoI3nFHFvMvl53Ep04eQ646tUWkl0slYVyQ9ij6irqdKbUuFq/ewQ0LXyfa4nz4mBF8ZHIpJcUDGFaUx7CifIYPzOeIwQWMG9554hER6S06GktqsLvvBfb1YDy9W/1OGDiiwyqvbazhS79cxoljhnD3353M2GFKCiLSP3TUwvgVcBGwjEMnNXLgqDTG1TvV7ezwltp9jc3csPB1xg4r5JfXzqK4IK8HgxMRSa+OxpK6KHyf1HPh9HL11TDy+KSb//vPG9i2p5HHvvJhJQsR6Xc67Wk1s0vNbEjc+lAz+2R6w+ql6nZCUeJLUrvqmvj5Xzdy4bRgCA8Rkf4mlVtzbnf3Pa0r4bhSt6cvpF6qqQ6iDUmfwXh0eQX1TS1cf84xPRyYiEjPSCVhJKqT0pNlZjbHzN4xs3VmdnOC7T8ysxXh610z2x23rSVu26JUPi+t6qqC9wR3Sbk7C5ds5uTxQznuyME9HJiISM9I5cS/1Mx+CNxN0Nl9PUFHeIfMLBLucy7BXOBLzGyRu69urePufx9X/3rg5LhDNLh7WUr/ip5QVx28J2hhvL55N+sqa/nBp6f1cFAiIj0nlRbG9UAT8BDwMNBIkmlV25kFrHP3De7eBCwELumg/pXAr1M4bmbUJ3/K+5mV28mLGB+fNqqHgxIR6TmdtjDcvQ445HJSCsYAm+PWK4BTElUMh0yfBDwfV1xgZkuBKPB9d//tB4ih+7QNPHhop/fiNTs49agRujNKRPq1VGbcOxa4EZgYX9/dP9rZrgnKks2jcQXwiLu3xJWNd/etZnYU8LyZveXu6xPEN49wuPXx48d3ElIXJGlhbKiqZUNVHZ89dUL6PltEpBdIpQ/jYeAe4OdASyd141UA4+LWxwJbk9S9gnaXudx9a/i+wcxeIOjfOCRhuPt8YD5AeXl5+iZ2qtsJkXwYUHxQ8fNvB5MqnXP8EWn7aBGR3iCVhBF19599gGMvASab2SRgC0FS+Lv2lcxsCjAMeDmubBhQ7+77zawEOB34lw8QQ/eprw5aF3Zww+nVjTVMGFGkcaFEpN9LpdP7STP7ipmNMrPhra/OdnL3KHAd8AywBviNu68yszvN7OK4qlcCC909vnVwPMHdWW8AfyLow1hNJtUdOo5ULOYsfa+GmRM1LLmI9H+ptDCuCd//Ma4spbGk3P0p4Kl2Zbe1W78jwX4vAb3rHtX6Q0eqXVdVy676Zs1jISJZIZW7pDSWFAQtjOEH58jXNtYAMEstDBHJAkkvSZnZ/41bvrzdtu+lM6heqbUPI85rG2sYWTyACSPUfyEi/V9HfRhXxC3f0m7bnDTE0ns1N0JT7SF9GMve38XMicMxS3QHsYhI/9JRwrAky4nW+7cEz2BU1+5ny+4Gpo8bkmQnEZH+paOE4UmWE633b21PeR9IGKu27gVg6mglDBHJDh11ek83s70ErYnCcJlwvSDtkfUmCVoYBxKGRqcVkezQ0Yx7kZ4MpFdLMFLtyq17GDO0kKFF+RkKSkSkZ6Xy4J60zoURN5/36q17OXGMWhcikj2UMFJRVwU5eVAQ9Ffsa2xm48469V+ISFZRwkhF3c6gdRHePrtm2z4AtTBEJKsoYaSirqrdHVLBFOdqYYhINlHCSEVd1UH9Fyu37KVk0ABGFg/IYFAiIj1LCSMVdVUwaGTb6tvb93L8qGI94S0iWUUJozPuB12SisWc9VW1TB5Z3MmOIiL9ixJGZ5pqIdrYdklqy+4GGptjHD1yYIYDExHpWUoYnWn3DMb6qloAjikdlKmIREQyQgmjM23jSAUJY11lmDBGKmGISHZJa8Iwszlm9o6ZrTOzmxNs/5yZVZnZivD1hbht15jZ2vB1Tft9e0xtZfAe9mGsr6pjaFEewwdqSBARyS6pTNH6gZhZBLgbOBeoAJaY2aIEc3M/5O7Xtdt3OHA7UE4wMu6ycN9d6Yo3qbZLUsFdUusrazmmdJDukBKRrJPOFsYsYJ27b3D3JmAhcEmK+54PLHb3mjBJLCZTkza1G9p8fVUtR6v/QkSyUDoTxhhgc9x6RVjW3qfN7E0ze8TMxh3mvpjZPDNbamZLq6qquiPug9VVwYAhkDuAXXVNVNc1qf9CRLJSOhNGoms27SdeehKY6O4nAc8C9x/GvkGh+3x3L3f38tLS0kRVuibuGYzWO6R0S62IZKN0JowKYFzc+lhga3wFd6929/3h6n8DM1Ldt8fEDQvSdodUqR7aE5Hsk86EsQSYbGaTzCwfuAJYFF/BzEbFrV4MrAmXnwHOM7NhZjYMOC8s63l1VTDowDMY+bk5jBlWmJFQREQyKW13Sbl71MyuIzjRR4AF7r7KzO4Elrr7IuBrZnYxEAVqgM+F+9aY2XcIkg7Ane5ek65YO1RXBRM+DAQtjKNKBhLJ0R1SIpJ90pYwANz9KeCpdmW3xS3fAtySZN8FwIJ0xteplijU1xy4JFVVy/SxQzMakohIpuhJ74401AAOA0tpbG6hYleDbqkVkaylhNGRtof2SthQVYe7hgQRkeylhNGRtmFBSg/cUqsWhohkKSWMjrQ95T2SdZW1mMFRpXoGQ0SykxJGR+IuSa2vqmXssEIK8iKZjUlEJEOUMDpSVwU5uVAwlHXhoIMiItlKCaMjdVVQVEILxsaddeq/EJGspoTRkdodMKiULbsa2B+N6Q4pEclqShgd2bcdikfHDTqohCEi2UsJoyP7tkPxEZrHW0QEJYzkWqJBH0bxKNZX1TJ8YD7DNC2riGQxJYxk6ioBh0FHsL6yjqP1/IWIZDkljGT2bQvewxaG7pASkWynhJHMvu0A7M0robquSQlDRLKeEkYyYcLY2BgkCk3LKiLZTgkjmX3bAeOd2gJAgw6KiKQ1YZjZHDN7x8zWmdnNCbb/g5mtNrM3zew5M5sQt63FzFaEr0Xt90272u0waCTrqveTn5vD2GFFPR6CiEhvkrYZ98wsAtwNnAtUAEvMbJG7r46r9jpQ7u71ZvZl4F+AueG2BncvS1d8ndq3PbxDStOyiqSiubmZiooKGhsbMx2KJFBQUMDYsWPJy8v7wMdI5xSts4B17r4BwMwWApcAbQnD3f8UV/8V4DNpjOfw7NsWPOW9tZapo4dkOhqRXq+iooLi4mImTpyImX5g9SbuTnV1NRUVFUyaNOkDHyedl6TGAJvj1ivCsmSuBZ6OWy8ws6Vm9oqZfTIdAXZo3w5aBh1324wKAAARPklEQVTBppp6PYMhkoLGxkZGjBihZNELmRkjRozocusvnS2MRH81nrCi2WeAcuCsuOLx7r7VzI4Cnjezt9x9fYJ95wHzAMaPH9/1qKHtKe/dOcOJucaQEkmVkkXv1R3/bdLZwqgAxsWtjwW2tq9kZh8DbgUudvf9reXuvjV83wC8AJyc6EPcfb67l7t7eWlpafdEXrsdcLbFhgK6Q0qkr4hEIpSVlXHiiSdy+eWXU19fD8Bdd93F1KlTOemkkygrK+PVV18FYPbs2UyZMoWysjLKysp45JFHMhl+r5fOFsYSYLKZTQK2AFcAfxdfwcxOBv4LmOPulXHlw4B6d99vZiXA6QQd4j1j9yYANjSPAGBSiS5JifQFhYWFrFixAoCrrrqKe+65h9NOO43f/e53LF++nAEDBrBz506ampra9nnwwQcpLy/PVMh9StoShrtHzew64BkgAixw91Vmdiew1N0XAf8KDAIeDptLm9z9YuB44L/MLEbQCvp+u7ur0mt30PWysm4wo4cUMHBAOvOqiKTDmWeeyZtvvsnEiRMpKSlhwIABAJSUlGQ4sr4rrWdCd38KeKpd2W1xyx9Lst9LwLR0xtahsIXxSs1AphxZnLEwRPqqbz+5itVb93brMU8YPZjbPzE1pbrRaJSnn36aOXPmcN5553HnnXdy7LHH8rGPfYy5c+dy1lkHukuvuuoqCgsLAXjuuecYMWJEt8bdn+hJ70T2bMIHlrJmZzPHjRqc6WhEJEUNDQ2UlZVRXl7O+PHjufbaaxk0aBDLli1j/vz5lJaWMnfuXO677762fR588EFWrFjBihUrlCw6oWstiezeTGPRaJqrnePUwhA5bKm2BLpbfB9GvEgkwuzZs5k9ezbTpk3j/vvv53Of+1zPB9jHqYWRyO5N1OQdCcDxamGI9GnvvPMOa9eubVtfsWIFEyZM6GAPSUYtjPZiMdhTweYBp5IfydEdUiJ9XG1tLddffz27d+8mNzeXY445hvnz52c6rD5JCaO9ukpo2c+7jcM4ZuQg8iJqhIn0FbW1tYeUzZgxg5deeilh/RdeeCHNEfUvOhu2F95Su2JfMceNUv+FiEgrJYz2dr8PwKq6IRx/pPovRERaKWG0V70ex3jfj2D6uKGZjkZEpNdQwmhv5zvsHXAkzTkFTBujYc1FRFopYbRX9S4bbSzHHVlMYX4k09GIiPQaShjxYjG8ei1vNIzk5PG6HCUiEk8JI96eTVi0kTXRUZw8blimoxGRw1RRUcEll1zC5MmTOfroo7nhhhvaRqa97777uO666zIc4aEGDUo8fUJvHKpdCSPe9pUAvBsbqxaGSB/j7nzqU5/ik5/8JGvXruXdd9+ltraWW2+9NW2fGY1G03bs1mFOVq5cSX5+Pvfccw8vv/xy21Dtb775Js8++yzjxh2Ydih+XKzLLrus22NSwoi3ZSlRIuwafJye8BbpY55//nkKCgr4/Oc/DwS/0H/0ox+xYMGCtl/nmzdvZs6cOUyZMoVvf/vbANTV1XHhhRcyffp0TjzxRB566CEAli1bxllnncWMGTM4//zz2bZtGxD8kv/mN7/JWWedxV133cXEiROJxWIA1NfXM27cOJqbm1m/fj1z5sxhxowZnHnmmbz99tsAbNy4kdNOO42ZM2fyT//0Tyn9284880zWrVvHtm3bDhmqffTo0d30DXZOT3rHiW1eyts+gQ8fN1ZTTYp0xdM3w/a3uveYR06DC76fdPOqVauYMWPGQWWDBw9m/PjxrFu3DoDXXnuNlStXUlRUxMyZM7nwwgt5//33GT16NL///e8B2LNnD83NzVx//fU88cQTlJaW8tBDD3HrrbeyYMECAHbv3s2LL74IwPLly3nxxRc5++yzefLJJzn//PPJy8tj3rx53HPPPUyePJlXX32Vr3zlKzz//PPccMMNfPnLX+azn/0sd999d6f/7N40VLtaGK1iLfiW5SxvOZrZU0ZmOhoROUzunvCHXnz5ueeey4gRIygsLORTn/oUf/3rX5k2bRrPPvssN910E3/5y18YMmQI77zzDitXruTcc8+lrKyM7373u1RUVLQdc+7cuQctt7ZKFi5cyNy5c6mtreWll17i8ssvp6ysjC9+8YttLZS//e1vXHnllQBcffXVSf89vXGo9rS2MMxsDvBjghn3fu7u32+3fQDwADADqAbmuvt74bZbgGuBFuBr7v5MOmOlcg2RaB2rc47lsmM0Jr5Il3TQEkiXqVOn8uijjx5UtnfvXjZv3szRRx/NsmXLDkkoZsaxxx7LsmXLeOqpp7jllls477zzuPTSS5k6dSovv/xyws8aOPDAJeuLL76YW265hZqaGpYtW8ZHP/pR6urqGDp0aMKh1ls/tzO9caj2tLUwzCwC3A1cAJwAXGlmJ7Srdi2wy92PAX4E/CDc9wSCOcCnAnOAn4bHS5uGlU8CMGTqORTl60qdSF9zzjnnUF9fzwMPPABAS0sL3/jGN/jc5z5HUVERAIsXL6ampoaGhgZ++9vfcvrpp7N161aKior4zGc+w4033sjy5cuZMmUKVVVVbQmjubmZVatWJfzcQYMGMWvWLG644QYuuugiIpEIgwcPZtKkSTz88MNA0Mp54403ADj99NNZuHAhELQIDkemh2pP5yWpWcA6d9/g7k3AQuCSdnUuAe4Plx8BzrEg9V4CLHT3/e6+EVgXHi89WprZ/+r/8HLsBD51Vvo+RkTSx8x4/PHHefjhh5k8eTLHHnssBQUFfO9732urc8YZZ3D11VdTVlbGpz/9acrLy3nrrbeYNWsWZWVl3HXXXXzrW98iPz+fRx55hJtuuonp06dTVlaWdMRbCC5L/fKXvzzoUtWDDz7Ivffey/Tp05k6dSpPPPEEAD/+8Y+5++67mTlzJnv27Dmsf2NtbS3XXHMNJ5xwAieddBKrV6/mjjvuOLwvqgvM3dNzYLPLgDnu/oVw/WrgFHe/Lq7OyrBORbi+HjgFuAN4xd1/GZbfCzzt7h3eWFxeXu5Lly49rDgba3ex6f+dx7HRd/nFUf/G1Z/9P4e1v4gE1qxZw/HHH5/pMKQDif4bmdkydy9PZf90XntJdJGufXZKVieVfYMDmM0D5gGMHz/+cOIDoGDQMPYWTeCF0Vdy5eXXHvb+IiLZIp0JowIYF7c+FtiapE6FmeUCQ4CaFPcFwN3nA/MhaGF8kEDL/6H7n4gUEelv0tmHsQSYbGaTzCyfoBN7Ubs6i4BrwuXLgOc9uEa2CLjCzAaY2SRgMvBaGmMVEZFOpK2F4e5RM7sOeIbgttoF7r7KzO4Elrr7IuBe4Bdmto6gZXFFuO8qM/sNsBqIAl9195Z0xSoi3SPZsxCSed3RX522Tu9M+CCd3iLSPTZu3EhxcTEjRoxQ0uhl3J3q6mr27dvHpEmTDtrWWzq9RSSLjB07loqKCqqqqjIdiiRQUFDA2LFju3QMJQwR6RZ5eXmH/HqV/kVjSYmISEqUMEREJCVKGCIikpJ+dZeUmVUB73/A3UuAnd0YTn+j7yc5fTcd0/fTsUx/PxPcvTSViv0qYXSFmS1N9daybKTvJzl9Nx3T99OxvvT96JKUiIikRAlDRERSooRxwPxMB9DL6ftJTt9Nx/T9dKzPfD/qwxARkZSohSEiIinJ+oRhZnPM7B0zW2dmN2c6nt7AzN4zs7fMbIWZLQ3LhpvZYjNbG74Py3ScPcXMFphZZThDZGtZwu/DAv8R/j29aWYfylzkPSPJ93OHmW0J/4ZWmNnH47bdEn4/75jZ+ZmJumeY2Tgz+5OZrTGzVWZ2Q1jeJ/9+sjphmFkEuBu4ADgBuNLMTshsVL3G2e5eFne7383Ac+4+GXguXM8W9wFz2pUl+z4uIJi/ZTLBTJA/66EYM+k+Dv1+AH4U/g2VuftTAOH/X1cAU8N9fhr+f9hfRYFvuPvxwKnAV8PvoE/+/WR1wgBmAevcfYO7NwELgUsyHFNvdQlwf7h8P/DJDMbSo9z9zwTztcRL9n1cAjzggVeAoWY2qmcizYwk308ylwAL3X2/u28E1hH8f9gvufs2d18eLu8D1gBj6KN/P9meMMYAm+PWK8KybOfAH81sWThnOsAR7r4Ngv8JgJEZi653SPZ96G/qgOvCyyoL4i5hZu33Y2YTgZOBV+mjfz/ZnjASzfKi28bgdHf/EEHz+Ktm9pFMB9SH6G8q8DPgaKAM2Ab8e1ield+PmQ0CHgW+7u57O6qaoKzXfD/ZnjAqgHFx62OBrRmKpddw963heyXwOMElgx2tTePwvTJzEfYKyb4P/U0B7r7D3VvcPQb8NwcuO2Xd92NmeQTJ4kF3fyws7pN/P9meMJYAk81skpnlE3TGLcpwTBllZgPNrLh1GTgPWEnwvVwTVrsGeCIzEfYayb6PRcBnw7tdTgX2tF56yCbtrrtfSvA3BMH3c4WZDTCzSQSdu6/1dHw9xYK5au8F1rj7D+M29cm/n6yecc/do2Z2HfAMEAEWuPuqDIeVaUcAj4dzMucCv3L3P5jZEuA3ZnYtsAm4PIMx9igz+zUwGygxswrgduD7JP4+ngI+TtCZWw98vscD7mFJvp/ZZlZGcDnlPeCLAO6+ysx+A6wmuIPoq+7ekom4e8jpwNXAW2a2Iiz7Jn3070dPeouISEqy/ZKUiIikSAlDRERSooQhIiIpUcIQEZGUKGGIiEhKlDBERCQlShjSr5hZSzic9koze9LMhh7m/neY2Y3h8p1m9rEuxjPRzBri7sHPODObGw6f/btMxyJ9ixKG9DcN4XDaJxKMoPrVD3ogd7/N3Z/thpjWu3vZ4eyQziG/3f0h4AvpOr70X0oY0p+9TDjSp5kNMrPnzGy5BZNDtQ1jb2a3hpP5PAtMiSu/z8wuC5ffM7OScLnczF4Il8+KmyTo9dZhVTpiZr8NRwJeFTcaMGZWG7ZqXgVOM7OZZvaSmb1hZq+ZWbGZTQ2XV4QjwU4O9/1MXPl/tSYcCyYIWx4e47muf6WSzbJ6aBDpv8IT5jkE4/gANAKXuvve8MT/ipktAj5EMIbYyQT/PywHlh3GR91IMLzF38IRSRtT2Od/u3uNmRUCS8zsUXevBgYCK939tnBss7eBue6+xMwGAw3Al4Afu/uDYZ2ImR0PzCUYZbjZzH4KXGVmTxMM/PcRd99oZsMP498lcgglDOlvCsP+gokEJ/7FYbkB3wuHao8RtDyOAM4EHnf3eoAwiRyOvwE/NLMHgcfcvSKFfb5mZpeGy+MIBuCrBloIRjWFoKWzzd2XALQOiW1mLwO3mtnY8PPWmtk5wAyC5ANQSDD66anAn8OJinD3VCc5EklIl6Skv2kI+wsmAPkc6MO4CigFZoTbdwAF4bZUBlSLcuD/l9b9cPfvE/QHFBK0Wo7r6CBmNhv4GHCau08HXo87XmPcQHyWKC53/xVwMUFr4xkz+2hY9/646VCnuPsdyY4h8kEpYUi/5O57gK8BN4bzEQwBKsNLNmcTJBSAPwOXmllh2P/wiSSHfI/gVzzAp1sLzexod3/L3X8ALAU6TBhhHLvcvT5MLqcmqfc2MNrMZoafU2xmuWZ2FLDB3f+DYCjskwjmhL7MzEaGdYeb2QSCPpyzwmHE0SUp6SpdkpJ+y91fN7M3CPooHgSeNLOlwAqCEzLuvtzMHgrL3gf+kuRw3wbuNbNvEkyx2errYQJqIRiy++lOwvoD8CUzexN4B3glSexNZjYX+EnY19FA0DKZC3zGzJqB7cCdYX/Itwim1c0Bmgn6VV4JO9UfC8srgXM7iU8kKQ1vLpJGFszj/LvwNt9eI7w0dqO7X5TpWKTv0CUpkfRqAYb0tgf3gJ8CuzIdi/QtamGIiEhK1MIQEZGUKGGIiEhKlDBERCQlShgiIpISJQwREUnJ/wcVYKni140+lQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radii, growth_psf, label='PSF')\n", "plt.plot(radii, growth_psfcor, label='Observed PSF')\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Let's have a look at the ratio of the two:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Ratio of encircled flux')" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radii[1:], growth_psfcor[1:]/growth_psf[1:])\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Ratio of encircled flux')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Due to the different resolution, the ratio is not constant. Let's note the calibration $C(r)$. Let us assume that our observed PSF encirled energy is of the form:\n", "\n", "$E(r) = \\alpha C(r \\times \\beta)$\n", "\n", "Where $\\beta$ is the fattening of the PSF. If we differentiate as a function of $r$:\n", "\n", "$E'(r) = \\alpha \\beta C'(r \\times \\beta)$\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# compute the derivatives\n", "deriv_growth_psf = (growth_psf[2:]-growth_psf[0:-2])/(radii[2:]-radii[0:-2])\n", "deriv_growth_psfcor = (growth_psfcor[2:]-growth_psfcor[0:-2])/(radii[2:]-radii[0:-2])" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 60)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radii[1:-1], deriv_growth_psf)\n", "plt.plot(radii[1:-1], deriv_growth_psfcor)\n", "plt.xlim([0,60])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compared with the growth curve plot, the derivative show clear maxima and minima that are out of phase. Findind the positions of the these will tell us if our assumption of homothetical variation is correct." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 6.18050404 17.4854638 23.79928199 32.07353691 38.40607579\n", " 46.76238796] [ 0. 6.5206172 18.75895207 24.07489413 32.78746844 38.5386345\n", " 47.21468159]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Find the local minima and maxima of the two curves.\n", "# To find a local extremum, we will fit the portion of curve with a degree 3 polynomial, \n", "# extract the roots of its derivative and only retain the one that are between the bounds.\n", "# This is what the following function does.\n", "def local_max(xvalues, yvalues, lower_bound, upper_bound, check_plot=False):\n", " idx,=np.where((xvalues > lower_bound) & (xvalues < upper_bound))\n", " p = np.polyfit(xvalues[idx], yvalues[idx], 3)\n", " delta = (2.*p[1])**2 - 4.*3.*p[0]*p[2]\n", " r1 = (-2*p[1]+np.sqrt(delta))/(2*3*p[0])\n", " r2 = (-2*p[1]-np.sqrt(delta))/(2*3*p[0])\n", " result = r1 if ((r1 > lower_bound) and (r1 < upper_bound)) else r2\n", " if check_plot:\n", " plt.plot(xvalues[idx], yvalues[idx])\n", " plt.plot(xvalues[idx], p[0]*xvalues[idx]**3+p[1]*xvalues[idx]**2+\n", " p[2]*xvalues[idx]+p[3], '--')\n", " plt.plot(np.array([result, result]), np.array([np.min(yvalues), np.max(yvalues)]), '-')\n", " return result\n", " \n", " \n", "max_dpsf_1 = local_max(radii[1:-1], deriv_growth_psf, 3, 10, check_plot=True)\n", "max_dpsfcor_1 = local_max(radii[1:-1], deriv_growth_psfcor, 3, 10, check_plot=True)\n", "\n", "max_dpsf_2 = local_max(radii[1:-1], deriv_growth_psf, 14, 21, check_plot=True)\n", "max_dpsfcor_2 = local_max(radii[1:-1], deriv_growth_psfcor, 14, 21, check_plot=True)\n", "\n", "max_dpsf_3 = local_max(radii[1:-1], deriv_growth_psf, 21, 28, check_plot=True)\n", "max_dpsfcor_3 = local_max(radii[1:-1], deriv_growth_psfcor, 21, 28, check_plot=True)\n", "\n", "max_dpsf_4 = local_max(radii[1:-1], deriv_growth_psf, 28, 35, check_plot=True)\n", "max_dpsfcor_4 = local_max(radii[1:-1], deriv_growth_psfcor, 28, 35, check_plot=True)\n", "\n", "max_dpsf_5 = local_max(radii[1:-1], deriv_growth_psf, 35, 45, check_plot=True)\n", "max_dpsfcor_5 = local_max(radii[1:-1], deriv_growth_psfcor, 35, 45, check_plot=True)\n", "\n", "max_dpsf_6 = local_max(radii[1:-1], deriv_growth_psf, 40, 50, check_plot=True)\n", "max_dpsfcor_6 = local_max(radii[1:-1], deriv_growth_psfcor, 40, 50, check_plot=True)\n", "\n", "plt.xlabel('Radius [arcsec]')\n", "\n", "# Lets pack all of them, adding the r=0 point. \n", "max_dpsf = np.array([0, max_dpsf_1, max_dpsf_2, max_dpsf_3, max_dpsf_4, max_dpsf_5, max_dpsf_6])\n", "max_dpsfcor = np.array([0, max_dpsfcor_1, max_dpsfcor_2, max_dpsfcor_3, max_dpsfcor_4, \n", " max_dpsfcor_5, max_dpsfcor_6])\n", "\n", "print(max_dpsf,max_dpsfcor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the plot, we can deduce that our homothetical assumption is not perfect: the spacing increases for the first three (don't forget the point at 0, 0, not shown), is very small for the 4th and 6th, and gets narrower for the 5th and 7th...\n", "Let's plot the situation" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.07402639 -0.04610159]\n", "1.0550300032613567\n", "1.072831254463463\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(max_dpsf, max_dpsfcor, 'o-')\n", "p = np.polyfit(max_dpsf[0:3], max_dpsfcor[0:3], 1)\n", "plt.plot(max_dpsf, p[0]*max_dpsf+p[1])\n", "plt.xlabel('extremum position of theoretical psf [arcsec]')\n", "plt.ylabel('extremum position of observed blurred psf [arcsec]')\n", "\n", "\n", "print(p)\n", "print((max_dpsfcor[1]-max_dpsfcor[0])/(max_dpsf[1]-max_dpsf[0]))\n", "print((max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0]))\n", "\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Encircled flux')" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Lets use the data before 20\", corresponding to the central core\n", "beta = (max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0])\n", "\n", "# lets interpolate at the scaled radius\n", "tckpsfcor = interpolate.splrep(radii, growth_psfcor, s=0)\n", "interp_growth_psfcor = interpolate.splev(radii*beta, tckpsfcor, der=0)\n", "\n", "# check interpolation\n", "plt.plot(radii*beta, growth_psf)\n", "plt.plot(radii, growth_psfcor)\n", "plt.plot(radii*beta, interp_growth_psfcor)\n", "plt.xlim([0,60])\n", "plt.xlabel('radius [arcsec]')\n", "plt.ylabel('Encircled flux')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check the ratio, using the psf with a corrected radius" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "alpha = 2.005\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radii[1:]*beta, interp_growth_psfcor[1:]/growth_psf[1:])\n", "plt.xlabel('radius [arcsec]')\n", "plt.ylabel('Ratio of encircled flux')\n", "plt.xlim([0,60])\n", "idx, = np.where(((radii*p[0]) > 0) & ((radii*p[0]) < 60))\n", "scale_factor = np.median(interp_growth_psfcor[idx]/growth_psf[idx])\n", "print(\"alpha = {:.3f}\".format(scale_factor))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now have a much better looking ratio [compared with the cell where we computed the direct ratio](#the_ratio), and we have a decent determination of the psf scaling. The normalized PSF to use for our observations is then:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "psf_obs_norm = psfcor / scale_factor" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\int \\int psf_obs_norm dx dy = 0.966450534666256\n" ] } ], "source": [ "print('\\int \\int psf_obs_norm dx dy = {}'.format(np.sum(psf_obs_norm)*resol**2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed, let's look at the encircled energy in the core of our psf:\n", "In this example, we have used the derivative of the scale factor" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "central core for observation: 0.8526531289184243\n", "central core for theoretical: 0.8526789463354869\n" ] } ], "source": [ "idj, idi = np.where(r" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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yWrGR6+dYO9B6fUr2EY1k38c4nFtfto9kI1HBmd03v4IwsyInCDMrcoIwsyInCDMrcoIwsyInCDMrcoIwsyInCDMrcoIws6LurKRMUl9vLq4/Wa14NFeVx7HkdOcFrfs+xt59uW0uPz0Xl1QfyvVo7B/NVSD213P9Env2HknF1Q7k4rKiN/dUj8xzal7u+ZR9fpLsXRnJatBcxWWysrRVQGFwziclPV91k3pU0tWFn71S0jOStkm6MbVHZtY12h2cA/D5aiDO2oi4Z+KdkurAF4CrgPOB6ySd38nOmtn0amtwTtKFwLaI2B4Rx4FvAte2sR4zmyGdXKS8oZrNuUnS4ib3rwaeG3d7R7XMzGaJdhPEF4HXAWuBF4DPNolpdtWqeGVE0kZJWyRtOT46uReozKw9bSWIiNgVEaMR0QC+TPOBODuANeNunwnsfJl1jhucM0P9G8zsJO0Ozlk57ua7aD4Q5yHgXEnnSOoDNgB3tbM9M5sZLd8crgbnXAKcLmkHcBNwiaS1jJ0yPAt8sIpdBXwlIq6OiBFJNwD3AnVgU0Q8OSVHYWZTYsoG51S37wFOeQvUzGaH7qykHB6hsefFlmEayA35bSSrFWuJykd4BRWXI4mKtjlzcutK9qSk+RzlU9QOJisaj+cmmetIrro05iSrCxu53pUoV8HJ3lz/Ula1rljV0VwVahzPxWVp/kAqrt7f+jmlPblffX8Ww8yKnCDMrMgJwsyKnCDMrMgJwsyKnCDMrMgJwsyKnCDMrKg7C6XqtVQRVGPoYG51a1al4mLv/lRctrgpUyiTLfbiUPITrsnCoZiTG8qrw7misNFFuSKz2oHk4NvM4GNIt//LPmY6lBh8e/BQbl3JwqZ0UVgt+dhm1pfsXudXEGZW5ARhZkVOEGZW5ARhZkVOEGZW5ARhZkWZjlKbgGuA3RHxxmrZHcB5VcgiYF9ErG3ys88CB4BRYCQi1k3SfpvZNMjUQdwK3Ax87cSCiPjDE99L+izwcgUEl0ZE6+4vZtZ1Mi3nHpB0drP7JAn4A+Ctk7tbZtYNOq2k/F1gV0RsLdwfwH2SAviniLiltCJJG4GNAP09C9BpC1puvN6ba18W+3PtxuJIsg3bvMlry9/Y81Jum0sWpeIiOQhW2YrLeu4yVe1wcqBxsjUdc5MDl7OVlCO51nnsT1TnZisaky3nss9P9SWrXzPPz2Snvk4TxHXA7S9z//qI2ClpObBZ0tPVKL9TVMnjFoCFc85IFoKa2VRq+10MST3Au4E7SjFVl2siYjdwJ80H7JhZl+rkbc63AU9HxI5md0oakLTgxPfAFTQfsGNmXaplgqgG5/wIOE/SDknvr+7awITTC0mrJJ2Yg7ECeFDSY8BPgbsj4vuTt+tmNtXaHZxDRPxJk2W/GpwTEduBCzrcPzObQa6kNLMiJwgzK3KCMLMiJwgzK+rOnpQRMJyofEtW26knd5jZSrVs9Z4SlZ5K9oakkasdi8O5atBsnFYuz8Ule1dSy/1NirnJoca5ucwwmhikTO4xa6xcmlpXbSjXfzOzzbHAZPljtmo0wa8gzKzICcLMipwgzKzICcLMipwgzKzICcLMipwgzKzICcLMipwgzKyoOyspGw3iUKIKLXJTkdWfq7jMVqo1DiSnii9f1nqTySrP7ATo2rJclR+RrMwczJUqRnJ9WnhaKo6RXOUjq8/Ixe3cnYur11vHbPtlbl2JvqoAsSA5BTz5WKSqbpOVuZmGMWsk/UDSU5KelPSRavkSSZslba2+Li78/PVVzFZJ16f2ysy6QuYUYwT4WET8BvAW4MOSzgduBO6PiHOB+6vbJ5G0BLgJuIixfpQ3lRKJmXWflgkiIl6IiEeq7w8ATwGrgWuB26qw24B3NvnxtwObI2IwIvYCm4ErJ2PHzWzqvaKLlNUAnTcBPwFWRMQLMJZEgGYf+1sNPDfu9o5qmZnNAukEIWk+8C3goxGRm/TRfDxH06sjkjZK2iJpy/FIfnTYzKZUKkFI6mUsOXw9Ir5dLd4laWV1/0qg2WXiHcCacbfPBHY220ZE3BIR6yJiXZ+S7zqY2ZTKvIsh4KvAUxHxuXF33QWceFfieuC7TX78XuAKSYuri5NXVMvMbBbIvIJYD7wPeKukR6t/VwOfAS6XtBW4vLqNpHWSvgIQEYPAp4GHqn+fqpaZ2SyQmYvxIOVRn5c1id8CfGDc7U3ApnZ30MxmTndWUkqQqTAcTk5PHh7ObXZubmp3ZPplAo3Bva23OW9eal3qSVT4vQIxdCAXmO3nme2rmK24TPa4jGT1q+bnqhVTj1myF2r6/+5grndl1HLPAfUmTgySE8r9WQwzK3KCMLMiJwgzK3KCMLMiJwgzK3KCMLMiJwgzK3KCMLMiJwgzK1K2l+B0krQH+MWExacDL87A7kwmH0P3eDUcRyfHcFZEtGya2pUJohlJWyJi3UzvRyd8DN3j1XAc03EMPsUwsyInCDMrmk0J4paZ3oFJ4GPoHq+G45jyY5g11yDMbPrNplcQZjbNuj5BSLpS0jOStkk6ZTjPbCHpWUmPVy37tsz0/mRI2iRpt6Qnxi1LTVTrJoXj+KSk5ye0UexanU64a1dXJwhJdeALwFXA+cB11VSv2erSiFg7i95eu5VTBx21nKjWhW6l+cCmz1ePx9qIuGea9+mVanvCXSe6OkEwNq5vW0Rsj4jjwDcZm+hl0yAiHgAmNhnOTFTrKoXjmFU6nHDXtm5PEK+myVwB3CfpYUkbZ3pnOpCZqDZb3CDpZ9UpSNefKp3QxoS7tnV7gkhP5poF1kfEmxk7XfqwpN+b6R36NfdF4HXAWuAF4LMzuzs5bU64a1u3J4j0ZK5uFxE7q6+7gTsZO32ajTIT1bpeROyKiNGIaABfZhY8Hh1MuGtbtyeIh4BzJZ0jqQ/YwNhEr1lF0oCkBSe+Z2zC2BMv/1NdKzNRreud+KWqvIsufzw6nHDX/na7vVCqevvp74E6sCki/maGd+kVk/Raxl41wNgskm/MhuOQdDtwCWOfGtwF3AR8B/gX4DXAL4H3dvu0tMJxXMLY6UUAzwIfPHEu340k/Q7wQ+BxoFEt/jhj1yGm7PHo+gRhZjOn208xzGwGOUGYWZEThJkVOUGYWZEThJkVOUGYWZEThJkVOUGYWdH/AXMNO4rugmo5AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "stackhd_im = fits.open('../dmu18_HELP-PACS-maps/data/GAMA-09_PACS160_v0.9.fits')\n", "stackhd = fits.open('./data/output_data/GAMA09-160um-psffromstack.fits')\n", "psf = stackhd[0].data\n", "hd = stackhd[0].header\n", "plt.imshow(psf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the resolution of the psf. Because the map is in units of Jy/pixel, this turns out to be:\n", "* =1 if psf at same resolution of map\n", "* otherwise, should be in factor of map pixel size" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [], "source": [ "resol= np.abs(stackhd[0].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "resol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's build the growthcurve for our PSF." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# find the brightest pixel, it will be our center.\n", "jmax, imax = np.unravel_index(np.argmax(psf), psf.shape)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# build the array of coordinates\n", "x = np.arange(hd['NAXIS1'])\n", "y = np.arange(hd['NAXIS2'])\n", "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n", "xp = (xv-imax)*np.abs(hd['CDELT1'])*3600.\n", "yp = (yv-jmax)*np.abs(hd['CDELT2'])*3600.\n", "r = np.sqrt(xp**2 + yp**2)\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# build the growth curve\n", "radii = np.unique(r)\n", "encircled_flux = np.zeros(radii.shape)\n", "nbpix = np.zeros(radii.shape)\n", "for i, radius in enumerate(radii):\n", " idj, idi = np.where(r <= radius)\n", " nbpix[i] =len(idi)\n", " encircled_flux[i] = np.sum(psf[idj, idi])*resol**2\n", " #multiply by ((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10 as map is in units of MJy/sr\n", " #encircled_flux[i] = np.sum(psf[idj, idi])*((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-3.0000000726000002" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hd['CDELT1']*3600." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Encircled flux')" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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y9wVxrUxEDolVm8q55vH5rN5cyS1TR/LNk4Zofg05KI0ecQC3Av2AX7NncDgwJY51icgh8PbHJVzz+Hw6pKXwxJWTOHZo97BLklZgn7eGuvuz7n4W8Et3n+Lup9R77Dc0zOwRMys2s6X12m43s/Vmtih4nF3vuR+aWZ6ZrTSzM+u1Tw3a8szs1oP4WUWSzmPvrqVjeiqvXH+iQkMOmf2OKeDudx7ge/8ZmNpA+2/cfWzwmA2fTk97EdHxr6YC95tZipmlAL8HzgIOJzqk++emshWRhrk7PTul06tTu7BLkVYkbgPtu/vbZjYoxs2nAU+7exWw2szygGOC5/LcPR8g6GuZBiw/xOWKiEiMwhjF7DozWxKcyuoatGUDBfW2KQza9tX+OWZ2tZnlmlluSYlGRBFZtamchQVb6dSubdilSCuzz+Aws26NPQ7w+z0ADAXGAhuIdrrDXldsBbyR9s83us9w9xx3z8nKyjrA8kRah7ziCqb/8X1S2hh3TBsTdjnSyjR2qmo+n314DwDKguUuwDqi83I0ibtv2r1sZn8EXg5WC4H+9TbtBxQFy/tqF5EG5JdU8NU/vgfAU1dNZFhP3bMhh1ZjV1UNdvchwGvAOe7ew927A18Enj+Qb2Zmfeqtng/svuJqFnCRmaWb2WBgOPAB0fnOh5vZYDNLI9qBPutAvrdIMohEnMv/PI+6iAehkbn/F4k0USyd4xPc/ZrdK+7+dzPb75VWZvYUMBnoYWaFwG3AZDMbS/RIZg3BhFDuvszMZhLt9K4FrnX3uuB9riMaXinAI+6+LPYfTyS5LCwoY82WHdz9laMY3kuhIfERS3BsNrMfA48T/cC/BNiyvxe5+/QGmh9uZPv/Bf63gfbZwOwY6hRJeq8s2UhaahtOP7xX2KVIKxbLVVXTgSzgb8EjK2gTkRZkV00dr3xYxMmHZZGpK6kkjmKZj6MUuMHMOrp7RTPUJCIH4Lf/WMWm7VVceuzAsEuRVm6/RxxmdpyZLSe46c7MjjKz++NemYjEZP7aMr7xpw948J+f8JWcfpw4XJejS3zF0sfxG+BMgquZ3H2xmZ0U16pEpFHuznv5pdz3xir+88kWumWkcfOZI7jihCZfJS/SZDENOeLuBXsNw1wXn3JEpDHuzj8/LuF3b+SRu7aMnpnp/PgLo/jqxAF0SIvbCEIie4jlN63AzI4DPLiX4npgRXzLEpGG/ODZJTwzv5C+ndtx57TRXJDTn3ZtNQWsNK9YguMa4B6iY0QVAq8D18azKBH5vM0VVTy/cD0X5vTnzvPGkJYaxlBzIrFdVbUZuLgZahGRRsz+cAN1EefyEwYrNCRU+wwOM7uPfQwoCODu18elIhFp0IuLihjZO5MRvXVHuISrsSOO3GarQkQaVVC6g/lry7j5zBFhlyKy7+Bw90ebsxAR2bdZi6ODQk8b2zfkSkRiuwFwjpl1qbfe1cxei29ZIrJb8fZdPLegkAmDutKva4ewyxGJ6aqqLHffunvF3cvMrGccaxJJett21PD3pRuYtbiI9/K3EHG44dThYZclAsQWHHVmNsDd1wGY2UAa6TQXkQNXUxfhjpeW8/S8ddTUOYO6d+C6U4Zx7ti+mltDWoxYguO/gX+b2T+D9ZOAq+NXkkhy2lFdy7VPLODNlSV8deIALprQnyOyO7PXqA0ioWs0OCz6G7sMOBqYRHTq2O8G93aIyCFSVlnN5Y/OY3HBVn52/hF8deKAsEsS2adGg8Pd3cxecPfxfDY/uIgcQqWV1XzlD++yrnQH9188nqljeoddkkijYrn99D0zmxD3SkSS1CtLisgrruCRyyYoNCQhxNLHcQrwTTNbC1QSPV3l7n5kXCsTSRLLN2yna4e2HD+se9iliMQkluA4K+5ViCSx5UXbObxvJ3WCS8LY56kqM+sULJbv4yEiB6m2LsJHG8sZ1bvT/jcWaSEaO+J4EvgiMJ/ofRv1/xxyYEgc6xJJCmu2VFJVG+HwvgoOSRyNjVX1xeCr5qIUiZNlRdsBFBySUGIZq+p8M+tcb72LmZ0X37JEWreq2jqenV/IPXNXkZ7ahqFZHcMuSSRmsXSO3+buf9u94u5bzew24IX4lSXSOu2srmPG2/n85b01bK6o5rBeHblv+jjapmhiJkkcsQRHQ7/RsbxOROopKa/iysdyWVywlSkje3L58YM5flh3XU0lCSeWAMg1s7uB3xPtFP8O0Q5zEYnRx5vK+caf5rGlsoo/fG08Z47WjX6SuGI5Pv4OUA38FXgG2AVcG8+iRFqTf60q4b/u/w/VdRFmfvNYhYYkvP0ecbh7JXBrU9/YzB4hejlvsbuPCdq6EQ2gQcAa4CvB/B4G3AOcDewAvu7uC4LXXAb8OHjbn2pmQkkUH23czr1zVzH7w42M7J3Jw1+fQHaX9mGXJXLQ9hscZnYYcBPRD/tPt3f3Kft56Z+B3wGP1Wu7FZjr7neZ2a3B+i1E704fHjwmAg8AE4OguQ3IIXqabL6ZzXL3slh+OJEwLC+KBsaryzbSMT2V604ZxjWTh9IxXV2D0jrE8pv8DPAg8BBQF+sbu/vbZjZor+ZpwORg+VHgLaLBMQ14zN2d6KCKXcysT7DtHHcvheg0tsBU4KlY6xBpLkvXb+OeuauYs3wTmempXD9lGJefMJguHdLCLk3kkIolOGrd/YFD9P16ufsGAHffUG8K2mygoN52hUHbvto/x8yuJphgasAAzWUgzev3b+bxf6+tpFO7VG48bTjfOH4wndu3DbsskbiIJTheMrNvA38DqnY37j4KOEQauh5x72FO6rd/vtF9BjADICcnR1PbSrPZUV3Lg//8hMkjsrh3+jg6tVNgSOsWS3BcFny9uV7bgY5VtcnM+gRHG32A4qC9EOhfb7t+QFHQPnmv9rcO4PuKxM2Li4oo31XLdacMU2hIUtjv5bjuPriBx4EOcDiLz4LoMuDFeu2XWtQkYFtwSus14Awz62pmXYEzgjaRFqG2LsKj/1nDyN6ZjB/YNexyRJpFY8Oq/6De8gV7Pfez/b2xmT0FvAuMMLNCM7sCuAs43cxWAacH6wCzgXwgD/gj8G349HTYncC84HHHIT5FJnJQfvrKCj7aWM63Jg/VHeCSNCx6IVMDT5gtcPej915uaL2lycnJ8dzc3LDLkFbu8ffW8uMXlnL58YP5yTmHh12OyEEzs/nunrO/7Ro7VWX7WG5oXSSpvJO3mdtmLeOUEVn89xdGhV2OSLNqLDh8H8sNrYsklRlv59MrM517p48jpY3+jpLk0thVVUeZ2XaiRxftg2WC9XZxr0ykBauujdC3S3sydRWVJKHGZgBMac5CRBLFth01LCrYyrSxfcMuRSQUmj1GpIlm5haws6aOrx07MOxSREKhUddEYhSJOEvWb+PRd9cwYVBXRvftvN/XiLRGCg6RRpRWVvP2xyW8tbKYt1dtprSympQ2xk/PGxN2aSKhUXCINGBRwVZ+9dpK3vlkM+7QLSONkw/LYvKILE4cnkW3DI14K8lLwSFSz9otlfzytZW8smQD3TPS+M6U4UwZ2ZMjsjvrsluRgIJDBNhSUcV9b+TxxPtrSW3ThuunDOOqk4bocluRBig4JOnNnFfAnS8vp7K6lgsnDOC7pw2nZyfdqiSyLwoOSWol5VX8vxeXcmS/zvz8S0cwrGdm2CWJtHgKDklqj7yzmpq6CL/88lEM7pERdjkiCUE3AErS2rajhsffXctZR/RRaIg0gYJDktLCdWWcd/87VFbX8q2Th4ZdjkhC0akqSSo1dRHunbuK37+ZR+9O7Xj8yomMydYd4CJNoeCQpLFqUznfnbmIpeu386Wjs7n93NGaI1zkACg4JCls2LaT837/DultU3jwkqOZOqZP2CWJJCwFhySFB9/6hKraCK9cfyKD1BEuclDUOS6t3qbtu3hqXgFfHt9PoSFyCCg4pFX7pKSCm55ZTCTiXHvKsLDLEWkVdKpKWqW84grue2MVLy0uIj01hR+ePYr+3TqEXZZIq6DgkFZn7opNfOuJBaS2Ma46aQhXnTiEHh3Twy5LpNVQcEir8sqSDdzw9EJG9+3Ew1+foMAQiQMFh7Qaz80v5OZnFzN+YFce+foEDYkuEicKDkloJeVVzF2xiTnLNzH3o2JOGNaDGZeOp0OafrVF4kX/uyThrN+6k1mLipizfCMLC7biDtld2nP1SUP43umH0a5tStglirRqCg5JGDur63jgrTwefDuf6toIY7I7ceOph3H64b0Y1ScTM03tKtIcQgkOM1sDlAN1QK2755hZN+CvwCBgDfAVdy+z6KfBPcDZwA7g6+6+IIy6JRzuzstLNvDz2Sso2raLaWP7ctMZI3R5rUhIwjziOMXdN9dbvxWY6+53mdmtwfotwFnA8OAxEXgg+CpJYHnRdm5/aRkfrC5ldN9O3DN9HBMGdQu7LJGk1pJOVU0DJgfLjwJvEQ2OacBj7u7Ae2bWxcz6uPuGUKqUZvPWymIu//M8Ordvy8/OP4ILJ/QnpY1OR4mELazgcOB1M3PgD+4+A+i1OwzcfYOZ9Qy2zQYK6r22MGjbIzjM7GrgaoABAwbEuXyJt101dfzkxWUMyerIc9ccR+cOurRWpKUIKziOd/eiIBzmmNlHjWzb0J+Y/rmGaPjMAMjJyfnc85JYHvpXPutKd/D4FRMVGiItTCiDHLp7UfC1GPgbcAywycz6AARfi4PNC4H+9V7eDyhqvmqluRWX7+J3b+Zx1pjenDC8R9jliMhemj04zCzDzDJ3LwNnAEuBWcBlwWaXAS8Gy7OASy1qErBN/RutW15xBbtqIlwyaWDYpYhIA8I4VdUL+FtwzX0q8KS7v2pm84CZZnYFsA64INh+NtFLcfOIXo77jeYvWeLN3VmxoZzXlm1k9ofRvwvatdWo/yItUbMHh7vnA0c10L4FOLWBdgeubYbSpJnVRZwF68p4belGXl++iXWlOzCDCQO7cfs5h3NUvy5hlygiDWhJl+NKEqiqreM/n2zh9WUbmbN8E5srqklLacNxw7rz7clDOe3wXhrRVqSFU3BIs6iti3Dv3FX86Z01lFfVkpGWwuSRPTlzdG9OGZGlkWxFEoiCQ+KusGwHNzy9iPlryzj7iN58eXw/jhvaQ4MRiiQoBYfE1d8/3MAtzy0h4nDPRWOZNjY77JJE5CApOCQudlbXcecry3ny/XUc1a8z904fx8DuGWGXJSKHgIJDDrklhVu58elF5G+u5JsnDeH7Z4wgLVWX1oq0FgoOOaReXbqB655cSFZmOk9eOZHjhunOb5HWRsEhh0xB6Q5ufmYJo7M789g3jtEYUyKtlM4fyCFRUxfh+qcXAvC76eMUGiKtmI445KAUl+9iccE2Zi0uYuG6rdw3fZxm5hNp5RQcErOd1XUsLdrGonVbWVQQfazfuhOA1DbGVScO5pyj+oZcpYjEm4JDGlVVW8ec5ZuYmVvIf/I2UxuJTnWS3aU9Ywd04RvHD2Js/y6Mye6sG/pEkoSCQxq0vGg7M3MLeGHRerbuqKFv53ZcceJgcgZ2Y2z/LmRlajwpkWSl4JBPbdtRw4uL1zMzt4Cl67eTltKGM0b34is5/Tl+WA/N9y0igIJDgK07qrl91jJmL91IdW2EUX06cfs5h3PeuGy6dEgLuzwRaWEUHEmuoqqWy/40jxVF25l+TH8uyOnPmOzOYZclIi2YgiOJ7aqp48pH57F0/TYeuPhozhjdO+ySRCQB6AbAJFVVW8e1Tyzg/dWl/OqCIxUaIhIzHXEkmZq6CM8vKOTeuXms37qTn543hvPH9Qu7LBFJIAqOVm5ndR1rtlSyenMl+SUVzMwtZF3pDo7q15mff+kITjosK+wSRSTBKDhagZq6CAWlO1i9ufJzjw3bdu2x7ZH9OnPbOTlMGdkTM11eKyJNp+BIYK8s2cCv56xk7ZYd1AV3dAN0bt+WwT0yOHZIdwb1yGBw8BjUI4OO6fonF5GDo0+RBFRVW8fPXlnBo++uZXTfTnzr5KGfBsSQHhl0zdC9FyISPwqOBFNQuoPrnlzA4sJtXH78YG49a6Rm1xORZqXgSAB1EWd92U7mrSnljpeXE4k4D15yNFPH9Am7NBFJQgqOFqSiqpb8kgrySyr5pKRck4G0AAAIzUlEQVQi+iiuZPWWSqprIwCM7tuJ+y8+moHdM0KuVkSSlYIjBO7O6s2VzF9bxofrt30aEBu3f3YFVBuDgd0zGJqVwckjshialcGQrI4c1a+LTk2JSKgUHM1gZ3UdSwq3Mn9dGQvWljF/bRllO2oA6JieytCeHTluWHeGZnVkaFYGQ7M6MqB7B9JTNb+FiLQ8CRMcZjYVuAdIAR5y97tCLgmIHj1s21lDSXkVxeVVwdddn66v2VzJsqLtn06ANCQrg9NG9WL8wK6MH9iVoVkdaaPhykUkgSREcJhZCvB74HSgEJhnZrPcfXm8vmdNXYTNFVUUb6/aZyiUBI/qusjnXt+ubRt6ZrYju0t7rj5pCOMHdmXcgK5006WyIpLgEiI4gGOAPHfPBzCzp4FpwCENjpLyKi556H1KKqooraxucJtuGWlkdUynZ6d0hvTIIKtTerDe7tP2rMx0MtNTdWe2iLRKiRIc2UBBvfVCYGL9DczsauBqgAEDBhzQN8lsl8rA7h3IGdSVnpntyMpMp2dmNAh6dkqne0a6OqZFJOklSnA09Ke777HiPgOYAZCTk+MNbL9f7dqmMOPSnAN5qYhI0kiUP58Lgf711vsBRSHVIiKS1BIlOOYBw81ssJmlARcBs0KuSUQkKSXEqSp3rzWz64DXiF6O+4i7Lwu5LBGRpJQQwQHg7rOB2WHXISKS7BLlVJWIiLQQCg4REWkSBYeIiDSJgkNERJrE3A/oXrkWzcxKgLUH8RY9gM2HqJxEpX2gfQDaB7sly34Y6O5Z+9uoVQbHwTKzXHdP6lvItQ+0D0D7YDfthz3pVJWIiDSJgkNERJpEwdGwGWEX0AJoH2gfgPbBbtoP9aiPQ0REmkRHHCIi0iQKjnrMbKqZrTSzPDO7Nex6mouZPWJmxWa2tF5bNzObY2argq9dw6wx3sysv5m9aWYrzGyZmd0QtCfNfjCzdmb2gZktDvbB/wTtg83s/WAf/DUYobpVM7MUM1toZi8H60m3Dxqj4AjUm9f8LOBwYLqZHR5uVc3mz8DUvdpuBea6+3BgbrDemtUC33f3UcAk4Nrg3z+Z9kMVMMXdjwLGAlPNbBLwC+A3wT4oA64IscbmcgOwot56Mu6DfVJwfObTec3dvRrYPa95q+fubwOlezVPAx4Nlh8FzmvWopqZu29w9wXBcjnRD41skmg/eFRFsNo2eDgwBXg2aG/V+wDAzPoBXwAeCtaNJNsH+6Pg+ExD85pnh1RLS9DL3TdA9EMV6BlyPc3GzAYB44D3SbL9EJyiWQQUA3OAT4Ct7l4bbJIM/y9+C/wAiATr3Um+fdAoBcdn9juvubR+ZtYReA640d23h11Pc3P3OncfS3R65mOAUQ1t1rxVNR8z+yJQ7O7z6zc3sGmr3QexSJiJnJqB5jXf0yYz6+PuG8ysD9G/QFs1M2tLNDSecPfng+ak2w8A7r7VzN4i2t/TxcxSg7+4W/v/i+OBc83sbKAd0InoEUgy7YP90hHHZzSv+Z5mAZcFy5cBL4ZYS9wF57EfBla4+931nkqa/WBmWWbWJVhuD5xGtK/nTeDLwWateh+4+w/dvZ+7DyL6GfCGu19MEu2DWOgGwHqCvzJ+y2fzmv9vyCU1CzN7CphMdATQTcBtwAvATGAAsA64wN337kBvNczsBOBfwId8dm77R0T7OZJiP5jZkUQ7flOI/lE5093vMLMhRC8W6QYsBC5x96rwKm0eZjYZuMndv5is+2BfFBwiItIkOlUlIiJNouAQEZEmUXCIiEiTKDhERKRJFBwiItIkCg4REWkSBYe0WmZWZ2aLzGypmb20++a2Jrz+djO7KVi+w8xOO8h6BpnZzmAsqBbBzC4MphF4OexaJHEoOKQ12+nuY919DNHRf6890Ddy95+4+z8OQU2fBGNBxSwY8j8u3P2vwJXxen9pnRQckizeJRjR1Mw6mtlcM1tgZh+a2afD55vZfweTef0DGFGv/c9m9uVgeY2Z9QiWc4IxnTCzk4MjnEXBJECZ+yvKzF4ws/nBxElX12uvCI5y3geONbMJZvafYJKlD8ws08xGB8uLzGyJmQ0PXntJvfY/7A4ei05UtiB4j7kHv0slWWmQQ2n1gg/OU4mORQWwCzjf3bcHAfCemc0CjiY6PtE4ov83FgDzG3jLfbkJuNbd3wlG2d0Vw2sud/fSYGyoeWb2nLtvATKApe7+k2DstI+AC919npl1AnYC1wD3uPsTwTYpZjYKuBA43t1rzOx+4GIz+zvwR+Akd19tZt2a8HOJ7EHBIa1Z+6A/YRDRAJgTtBvwMzM7iei4VNlAL+BE4G/uvgMgCJOmeAe428yeAJ5398IYXnO9mZ0fLPcHhgNbgDqiI/VC9Mhng7vPA9g93LuZvQv8dzDx0PPuvsrMTgXGEw0hgPZER/SdBLzt7quD92iV421J89CpKmnNdgb9CQOBND7r47gYyALGB89vIjqENsQ2z0Itn/3f2f063P0uov0F7YkexYxs7E2CQfROA44NpmtdWO/9drl73e5NG6rL3Z8EziV69PGamU0Jtn006NsZ6+4j3P32fb2HyIFQcEir5+7bgOuBm4I5NzoTnaynxsxOIRosAG8D55tZ+6B/4px9vOUaon/VA/zX7kYzG+ruH7r7L4BcoNHgCOooc/cdQchM2sd2HwF9zWxC8H0yzSw1GLE1393vJTr8+5FE50X/spn1DLbtZmYDifbxnGxmg3e376c2kX3SqSpJCu6+0MwWE+3DeAJ4ycxygUVEP5hx9wVm9tegbS3RYdYb8j/Aw2a2e9j13W4MgqgOWA78fT9lvQpcY2ZLgJXAe/uovdrMLgTuC/pCdhI9UrkQuMTMaoCNwB1Bf8mPgdfNrA1QQ7Tf5b2g8/35oL0YOH0/9Yk0SMOqizQTi85l/nJweXCLUX/eibBrkcSgU1UizacO6NzSbgAE7gfKwq5FEoeOOEREpEl0xCEiIk2i4BARkSZRcIiISJMoOEREpEkUHCIi0iT/H/+mg+nTxcxtAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radii, encircled_flux)\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the shape of the encircled flux, it looks like the background level of our PSF is not zero. Let's check" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.48406457901001\n" ] } ], "source": [ "# This is clearly. \n", "print(np.median(psf[0:5,:]))" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Encircled flux')" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(nbpix, encircled_flux)\n", "plt.xlabel('Number of pixels')\n", "plt.ylabel('Encircled flux')" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "75" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(nbpix)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "#Lets do a linear fit to the outer part of the curve to determine the backgound\n", "p = np.polyfit(nbpix[50:], encircled_flux[50:], 1)\n", "bkg = p[0]/resol**2" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "341.0" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nbpix[50]" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.480343407733379\n" ] } ], "source": [ "print(bkg)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 6.44883084 31.78281617 56.60859179 80.69713688 128.11493206\n", " 151.16510081 174.17855859 219.76287389 264.73189759 287.13694954\n", " 331.81850958 354.03734136 398.39469719 442.65056992 464.82115364\n", " 509.07785797 553.37123299 575.48174238 619.68949056 641.77236962\n", " 685.92164421 730.11336994 774.17670846 818.20583344 840.25722766\n", " 884.39455175 906.42334032 950.46656775 994.49746156 1038.43340898\n", " 1082.52384114 1104.54224372 1192.67568874 1236.76498318 1258.74957561\n", " 1302.64569211 1346.52512431 1390.45622635 1412.43930101 1456.36975145\n", " 1500.30450153 1544.31053925 1588.12131476 1632.08811331 1676.0206871\n", " 1697.95399356 1741.9168396 1763.87961888 1807.84880829 1851.77648878\n", " 1895.70031166 1939.57587337 1983.36384392 2027.17270112 2071.08432937\n", " 2082.00283718 2104.03272343 2169.80037951 2191.83217716 2257.51126051\n", " 2301.26257777 2323.18073273 2367.17460775 2389.02238536 2432.81204295\n", " 2454.71559501 2476.60768104 2520.50798011 2542.47740865 2586.2664907\n", " 2608.19034672 2630.1025362 2652.00147462 2673.89712071 2679.3143363 ]\n" ] } ], "source": [ "print(encircled_flux)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Lets correct the psf and encircled flux\n", "psf = psf - bkg\n", "encircled_flux = encircled_flux - bkg * nbpix*resol**2" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Encircled flux')" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radii, encircled_flux)\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our PSF does now behaves correctly.\n", "\n", "Now let us compare our growth curve with the encircled energy curve provided by the instrument team. We use the standard growth curve for 160 µm PACS, taken with 20\"/s scan speed. " ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": true }, "outputs": [], "source": [ "f = open('./data/EEF_red_20.txt', 'r')\n", "lines = f.readlines()\n", "f.close()\n", "radiuseff = np.zeros(len(lines)-3)\n", "valeff = np.zeros(len(lines)-3)\n", "i = 0\n", "for line in lines:\n", " if line[0] != '#':\n", " bits = line.split()\n", " radiuseff[i] = float(bits[0])\n", " valeff[i] = float(bits[1])\n", " i = i+1" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radiuseff, valeff, label='Calibration')\n", "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n", "plt.xlim([0, 100])\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will work below 30\" where our PSF is well behaved" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radiuseff, valeff, label='Calibration')\n", "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n", "plt.xlim([0, 30])\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that while the calibration curve still rises beyond 30\", our PSF has reached a plateau. Let's note the calibration $C(r)$. Our PSF encirled energy is of the form:\n", "\n", "$E(r) = \\alpha C(r \\times \\beta)$\n", "\n", "Where $\\beta$ is the fattening of the PSF.\n", "\n", "We could take the derivative, but this too noisy. Instead we do a brute force approach" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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w3333ER4eTlBQEO+++26DdyEt3r6VMOs2aNMbbp4Pbfyox1g/UOl0kVtcTm5ROTmF5eQUlZNTWEZuUTmHC8vJLSojp9DaXvXL3+mqv8bUERxAbFgIMWHBxIQH0zk+nP7JwcSEBRMbHmJPreWaiSDKEYQj2Ie/5z5Iu/tWbvPY3/nrp+Dr/4Pfr9GGbs2ktMJJdn4p2fllHCwotS78hWX2xd+62B8uspLA0eKKOo8RIBAfEUJ8RAgJEaHER4YQFx58zMU/1r7oV13wY8KC9SLvJdrdt/I9R/fBDy9ZFc+aHE5ZhdPFoYIyDuSXctBOADUTQXZ+KQfySskvrTzuvSIQH25f8CND6NUuuno+ISKEhMhQ4iNCSIwMIT4ilJiwYAIDvF+RqjxHE4RqPqX5sG8F7F9rNXDbv87qIiMgCEY+5u3oWrzyShfZ+aVkHi0h80gJWUdLyMor4UDeLwngcOHxrfeDAoQ2UaG0iXaQmhjBWV0TaBPtoG20g7bRobSJcpAYGUJseIhe8NUx/CZBuPNIqWq8RhVFOishaw3s+Ap2LIGMlWDsSsj4rtYQnmfeAt0uhMS0pg3YxxhjyC+pJPOodeGva3qwoOy4xlAJESG0i3HQPsbBgE6xtI0OPebC3y7GQXx4CAF64VeN4BcJwuFwkJOTQ0JCgiYJDzDGkJOTU90Yzy3rPoTPHoSyPECgw0AYfg90Pd9q4OaI8Vi8LZExhtyicjKOlNiv4upp1R1BUfmxT/CEBAbQIdZBh9gwzk1LomNsGB1jw+gQG0bHuDDaxzi0PF95lF8kiOTkZDIyMjh06JC3Q/FbDoeD5ORk93betxLm3GUlgmF3QOr5EB7v2QC9zBhDTnUCKK41tRJA7Uc4ox1BJMeF0yUhgrO7JVoJIM5KAB1iHSRGhOovf+VVfpEggoODSU1N9XYYyuWEFf+Gr56E6A4w8X2/SQzGGA4Xllf/4q+dADKOFB/XnUJMWDDJcWF0S4rg/O5JJMeFkRwXTnKclQiiHcFeOhul3OMXCUK1AAc2WCO6Za2BtEtgzLM+lxwKSivYk1PM7pwi9uUeXwxUOwHEhlsJ4LSkSEbUTADxVlFQlCYA5eM0QahT9/0L8OUT4IiFCW9CnytbbF9J+aUV7DlczK6cIvYcLmK3nRD25BQd9wRQXHgwyXHhdG8bxYU921T/+k+OC6djXBiRofrfR/k3/YarU7NvJSyeCj3HwLiXWsRdgzGGzKMlbM8uZGt2AduzC9l1uJDdOcXkFh2bBNpFO0hJDOeiXm3pkhBBaqJVJ9ApPlwTgGr19H+AaryyAvjsPqszvSv+DaGRzR5CaYWTLQcK2JCZx8asPDbvL2B7dsExTwS1iQqla1IEl/SxkkBKQgQpieF0iY8gLESfAlKqPpog1Mk7nA4/vmoN9VleAFe/0yzJweUybD9YyKo9uazZc5SNWXlsP1hY3e9PTFgwvdpHMWFwMt3bRdG9bRTd20QRE651AUo1hiYIdXLWz7Q61pMA6HMFnHkbJA8+8fsaobzSxdp9R1m2I4fVe4/w094jFNhdRCREhNA/OYaLe7elT4cY+nSIJjkuTNvBKNWENEEo96183Wr81uVs+PV0iGzTpIc3xrA1u4Cl2w/zffphVuzKpbjciQj0aBvF2AEdGNw5jiEpcXSOD9dkoJSHeTRBiMgo4AUgEHjdGPNUre2dgbeBWHufh4wx8z0Zk2qE/P1WkdLSZ6H7KCs5BIc1yaErnC5W7Mxl8aYDLN6UTVaeNZhS16QIJgxO5uxuiZzVNUGLiZTyAo8lCBEJBF4GLgYygJUiMtcYs6nGbv8DfGiM+ZeI9AbmAymeikm5yRg4uBm2fgZb5lttGwAGTLSeVAo8tYt1eaWLb7cdYt66LL7acpCC0kocwQGcm5bEvRd155y0RDrENk0CUko1nifvIM4E0o0xOwFE5H1gPFAzQRgg2p6PAbI8GI9yR8EBq8Hb9kXWcschcOH/Qs/LIKlno9s3GGNYs/cIs37K5LN1+zlSXEFceDCj+rTj4t5tOTctSZ8oUqqF8WSC6Ajsq7GcAQyttc/jwCIR+T0QAVxU14FEZDIwGaBz585NHqiybZ4Hc6dARTFcNA0GXAtR7U7pkLlF5cxcvY8ZK/ayO6cYR3AAF/dux+UDO3Be9ySCdfhHpVosTyaIun5q1u4zeiIw3RjzDxE5C3hHRPoaY47p08AY8yrwKlgjynkk2tasNN8aD3rtf6H9QLjyNUjq3ujDGWNYtecI7y7fw/z1Byh3ujgzJZ67L0xjVN922gBNKR/hyf+pGUCnGsvJHF+E9DtgFIAxZpmIOIBE4KAH41I1HdkNb4+DvH1w7oNw/p8gKKRRh6p0upi/4QCvfbuT9Zl5RDmCuG5oZ64b2pnubaOaNm6llMd5MkGsBNJEJBXIBK4Frqu1z15gJDBdRHoBDkD77G5Oi6dC0WG4+XPoPKxRhygqq+T9lft4c+kuMo+W0DUpgr9e0Y/LT+9AeIjeLSjlqzz2v9cYUykidwMLsR5hfdMYs1FEngBWGWPmAg8Ar4nIfVjFT5NMo4YuU42SsQo2zYERDzcqORSUVvCfZXt4/budHCmu4MzUeKaN68OFPdvoOAZK+QGP/ryz2zTMr7Vuao35TcBwT8agGvDF4xCRBGfddVJvyy+tYPr3u3lj6S7ySiq4oEcSvx+ZxqDOcZ6JUynlFXr/35rtXQ5Db4NQ9+oHyitdvLtiDy9+uZ0jxRWM7NmGKSPTGNAp1sOBKqW8QRNEa1Scaz3S6qqEwBNXSBtj+HzDAZ5esIXdOcWc1TWBh0f3pH+yJgal/JkmiNairBC2fg4bZkL6l+CqgPhukHZxg29btTuXv8zfzE97j9KjbRRv3XwGI7onaT9ISrUCmiD8WWUZbF8MGz62kkNlCUR3hGG3Q9+rrDYP9Vzodx4q5G8LtrBwYzZtokL521X9mDC4E4Fa+axUq6EJwh+5XLDkz/Dj61CWB+EJMPA66DcBOg2DgPpbL+eXVvDCF9t5+4fdhAYF8MDF3fnduan6uKpSrZD+r/c3Lpc1ytvq6dB7PJx+I3Q9/4Qd7Llchk9+yuSpz7eQU1TGtWd05oFfdScxMrR54lZKtTiaIPyJywWf3gNr/gPnPmB1sudGXcGGzDymztnAmr1HOb1zLG9NOoN+yTHNELBSqiXTBOEvXC6YNwV+egfO+wNc8OgJk8ORonL+vmgrM37cS0JECM9M6M9Vg5K1kZtSCtAE4R+MsYqVfnoHzvsjXPBIg8nB5TJ8uGofTy3YQkFpJTefncq9F6cR7dBBeZRSv9AE4Q+W/MWqczjn/hMmh23ZBTzyyXpW7TnCmanxPDm+Lz3aaUd6SqnjaYLwdWvegW+fgUE3wsip9SaH0gonL321nX9/s5MoRxDPTOjPhMHJ2p5BKVUvTRC+zBj4/nlr1LfLnqs3OXyz7RD/O3sDe3OLmTA4mUdG9yI+onFdeiulWg9NEL7s4CbISYfLnoXA4/8pc4vKmTZvI3PWZtE1MYIZtw7l7G6JXghUKeWLNEH4so2zQQKg17jjNi3YcID/mb2evJIK7r0ojTtGdCM0SMd8Vkq5TxOErzIGNs2GLsMhMql69ZGich6bu5G5P2fRt2M0/71lKD3bRXsxUKWUr9IE4asObYHD26zuum2LNh7gkVkbOFpczv0Xd+eOEd0IDqy/Ww2llGqIJghfZAysfRcQ6DmWwrJK/nf2Bmb9lEnv9tH857dn0ruD3jUopU6NJghfk7kaFj8Gu7+DHpexpSiMO/+9lN05RUwZmcbdF5xGSJDeNSilTp0mCF+RuxO+fAI2zoLwRBj9dz6Wi3j05e+JcgQz49ZhDOua4O0olVJ+RBNES1d4CL59Gla9aY3+dv6fKD3jTh5bsJcPVm3irK4JvDBxIG2iHN6OVCnlZ06YIESktzFmU611I4wxX3ssKmXZ8RV8cCNUFFstpUc8xJ7yKG5/Yw2b9+dz1wXduO+i7gRpRbRSygPcuYP4UETeAZ4GHPZ0CHCWJwNr9fb/DB/8BmK7wK+nQ1J31uw9wi1v/4DLGN6adAYX9Gzj7SiVUn7MnZ+eQ4FOwA/ASiALGO7JoFq9I3vg3V+DIxZu+BiSurNo4wGue205UY4gZt05XJODUsrj3LmDqABKgDCsO4hdxhiXR6NqzYpz4b9XQWUp/HYuRLfno1X7+NPH6+jXMYY3Jp2ho7wppZqFO3cQK7ESxBnAOcBEEZnp0ahaq4oSmHENHN0LE9+HNj15Z/ke/jBzHcNPS+S9ycM0OSilmo07dxC/M8assucPAONF5DcejKl1cjnh41sgY6VV59DlbN76fhfT5m1iZM82vHz9IBzB2peSUqr5uJMgDopI51rrvvFEMK2WMfD5H2HLpzDqb9Dncj5Zk8G0eZu4pE9bXpo4SBu/KaWanTsJ4jPAAIJVB5EKbAX6eDCu1mXpc7DydTj79zDsdpZsPcgfZ67j7G4JvDjxdE0OSimvOGGCMMb0q7ksIoOA2+rZXZ2s9TPhy2nQdwJc9AQbMvO4879r6NEuin//ZrB20a2U8pqT/mlqjFmDVWGtmsLS56Bdf7j8FQ4WlXPrf1YRFx7MWzefQZQj2NvRKaVaMXdaUt9fYzEAGAQc8lhErUl5kTUq3LkPUkYQt7+znKPFFXx0+1nadYZSyuvcuYOIqvEKxaqTGO/OwUVklIhsFZF0EXmonn2uFpFNIrJRRGa4G7hf2P8zGBd0HMyTn25izd6j/OPqAfTtGOPtyJRSyq06iGmNObCIBAIvAxcDGcBKEZlbs18nEUkDHgaGG2OOiEjrah6cuQaAL/I78t/le5l8XldG92vv5aCUUspSb4IQkXlYTy/VyRhz/EDIxzoTSDfG7LSP9z7WnUfNjv9uBV42xhyxj3nQzbj9Q+ZqKqOSue/TLAZ2iuXBX/XwdkRKKVWtoTuIv5/isTsC+2osZ2D161RTdwAR+R4IBB43xiw4xc/1GSZzNT+Wp4LAS/o4q1KqhWkoQUw1xowUkb8ZY/7UiGNLHetq35EEAWnACCAZ+E5E+hpjjh5zIJHJwGSAzp1rt9nzUUWHkaN7WFIxnMeu7EOn+HBvR6SUUsdo6CdrexE5HxgnIqeLyKCaLzeOnYHVC2yVZKyeYGvvM8cYU2GM2YXVAC+t9oGMMa8aY4YYY4YkJSW58dEt3+GtywAwHQZx1aCOXo5GKaWO1+AdBPAQ1oX9Hxx7R2CAC09w7JVAmoikApnAtcB1tfaZDUwEpotIIlaR0063o/dRxhiWfrOQsUaYdNXliNR1s6WUUt5Vb4IwxswEZorI/xpjnjzZAxtjKkXkbmAhVv3Cm8aYjSLyBLDKGDPX3vYrEdkEOIE/GGNyGnUmPmThxgNE564nL7obye38445IKeV/3HnM9aSTQ433zgfm11o3tca8Ae63X61CcXklT8zdyPygnUSnnehBMKWU8h59bKaZvfRVOgEF+4g1+QQkD/Z2OEopVS9NEM0o40gxb3y3i8ldj1grOmqCUEq1XA01lItv6I3GmNymD8e/PbtoGyIwIXoj5MRAm97eDkkpperVUB3Ean4ZB6IzcMSejwX2Yo0Lody0KSufWWszuXN4B8LXLYC+V0Kg9taqlGq56i1iMsakGmO6Yj1pNNYYk2iMSQDGAJ80V4D+4pmFW4h2BHNX++1QXgj9rvZ2SEop1SB36iDOsJ9GAsAY8zlwvudC8j/rM/JYsvUQk8/rSvjWTyCqA3QZ7u2wlFKqQe4kiMMi8j8ikiIiXUTkUcDv2yo0pZeXpBPtCOLGgVGQvhj6XQUB+nyAUqplc+cqNRFIAmbZryR7nXLDtuwCFmw8wKThqUTt+AxclVq8pJTyCe40lMsF7hGRSGNMYTPE5FdeXpJOeEggN5+dAh/cA4k9oF2/E75PKaW87YR3ECJytt0VxiZ7eYCIvOLxyPzA7sNFzPs5i98M60JcWSbs/QH6/xq07yWllA9wp4jpOeAS7HoHY8zPwHmeDMpf/OvrHQQHBjC5Vym8PQ6Cw6H/Nd4OSyml3OJWTakxZl+tVU4PxOJXMo+W8PGaDKb2yCDhvbHgLIeb50Osn4xnoZTyeyesgwD2icjZgBGREGAKsNmzYfmzjhCeAAAWg0lEQVS+t77byY0BC7hu5zvQti9MfB9idNwHpZTvcCdB3A68gDWEaAawCLjLk0H5upKSUtJWP841QYugxxi44t8QGuntsJRS6qS48xTTYeD6ZojFP5QcJe+Na7mGZWT1mUyHq/6mbR6UUj6poc76XuL4MaSrGWOmeCQiX5a7CzPjGhIPp/OPsCncP+EJfWJJKeWzGrqDWNVsUfiDPcvg/etwulzcUP4wl426WocSVUr5tIaGHH27OQPxaWvfg3lTILYzT8dOY/32IF4/XSuklVK+zZ2GcotFJLbGcpyILPRsWD5k/zqYfTt0GsqRifOZvjWQKwclExnqTv2/Ukq1XO7UniYZY45WLRhjjgBtPBeSj9m/1pqOe5EPNhZSXuniN2d18W5MSinVBNxJEE4RqW7dJSJdaKDyutXJSYeAYFzRnZmxYi9npsbTvW2Ut6NSSqlT5k45yKPAUhH5xl4+D5jsuZB8TM4OiO/K8j1H2ZtbzP0Xd/d2REop1SQaTBBiPYazERgEDMMacvQ+u22EAusOIjGNj1ZlEOUIYlTfdt6OSCmlmkSDRUzGGAPMNsYcNsZ8aoyZp8mhBpcTcndSFpPK/PX7GTegA47gQG9HpZRSTcKdOojlInKGxyPxRXn7wFnOT0UJlFW6uHpIJ29HpJRSTcadOogLgNtEZA9QhFXMZIwx/T0amS/ISQdgzr5werSNon9yjJcDUkqppuNOgrjU41H4qsNWglicHcUdYzppy2mllF9pqC+maGNMPlDQjPH4lpx0SgMjyAuM4fKBHbwdjVJKNamG7iBmAGOA1VjtHmr+PDZAVw/G5RNcOemkO9tzUa92JESGejscpZRqUg31xTTGnqY2Xzi+pTx7G9udKVyu/S4ppfyQO30xXSEiMTWWY0Xkcs+G5QMqSggpyiIroCMjeiR5OxqllGpy7jzm+pgxJq9qwe6X6TF3Di4io0Rkq4iki8hDDew3QUSMiAxx57gtQfmhdAIwRCf3IjRI2z4opfyPOwmirn1O+PSTiAQCL2M9BdUbmCgivevYLwprnOsVbsTSYmze8BMAvfqe7uVIlFLKM9xJEKtE5FkR6SYiXUXkOayK6xM5E0g3xuw0xpQD7wPj69jvSeBpoNTtqFuAvdvXATBgwCAvR6KUUp7hToL4PVAOfAB8hHUhv8uN93UE9tVYzrDXVROR04FOxphP3Yq2hSgpd1J5cBv5QQkEh2vjOKWUfzphUZExpgiot/6gAXW1GqvuJlxEAoDngEknPJDIZOweZDt37nyCvT1vydaDdDL7MQmneTsUpZTyGHeeYuouIq+KyCIR+arq5caxM4CanRMlA1k1lqOAvsDXIrIbq7fYuXVVVBtjXjXGDDHGDElK8v4TQ/N+zqJbwAGiOvbydihKKeUx7nS18RHw/4DXAedJHHslkCYiqUAmcC1wXdVG+8moxKplEfkaeNAYs+okPqPZFZZVsnrLTuKC8iFR7yCUUv7LnQRRaYz518ke2BhTKSJ3AwuBQOBNY8xGEXkCWGWMmXuyx2wJvtiUTQdnlvWX0yImpZQfcydBzBORO4FZQFnVSmNM7oneaIyZD8yvtW5qPfuOcCMWr5v3cxaDIg5DJZoglFJ+zZ0EcZM9/UONda2yL6a84gq+3X6I6V3yYX8gxHbxdkhKKeUx7jzFpH0x2RZvzqbCaegTegjiukBQiLdDUkopj6n3KSYR+WON+V/X2vZXTwbVUi3ceIAOMQ5iivdAQpq3w1FKKY9q6DHXa2vMP1xr2ygPxNKiFZVV8u22Q1zSuw2Su1PrH5RSfq+hBCH1zNe17Pe+2XaIskoXY7sCFcWQ0M3bISmllEc1lCBMPfN1Lfu9BRsOkBARwsDM960VnYZ6NyCllPKwhiqpB4hIPtbdQpg9j73s8HhkLUhZpZMlWw7y27RiAlb8CwbdBO36ejsspZTyqIZGlNNBDmw/7MihsKycm4++BI4YuOhxb4eklFIe5047iFZv4YYDXBf6A7GHV8O4f0J4vLdDUkopj9MEcQJOl2HFxnTmBb0LHYbBwOu9HZJSSjULd8aDaNVW7c7llvL/Eu4qhMv+AQH6J1NKtQ56tTuB9T9+ycTAr3CecZtWTCulWhVNEA0wzgrO3fp/5AXFEzzyEW+Ho5RSzUoTRAP2f/EyPcxONg94BEKjvB2OUko1K00Q9Sk4QMKPT/Otqx89L/yNt6NRSqlmpwmiPov+B3GW8XHbe4mPDPV2NEop1ew0QdRl5zew/iP+VTmOAQMGezsapZTyCk0QtVWWw2cPkO9I5pXKcVzcu623I1JKKa/QBFHbDy9CznZeckymW/tEOsWHezsipZTyCk0QNR3ZDd8+Q1naZbyefRqX9Gnn7YiUUsprNEHU9PlDIIEsSL4XY+BXfbR4SSnVemmCqJK7E7Z9Dufcy+yd0Ck+jJ7ttO2DUqr10gRRZfM8AIp6XsX36Tlc0rsdIq1u4DyllKqmCaLK5nnQfgBLssMod7r4ldY/KKVaOU0QAPlZkLESeo1l0cZsEiJCGNwlzttRKaWUV2mCANj8KQDl3cewZMtBLurVlsAALV5SSrVumiAANs+FxB4sy0+koKxSG8cppRSaIKAoB/Z8D73GsmDDAcJDAjknLdHbUSmllNdpgtj6GRgXzp5jWbzpABf0bIMjONDbUSmllNdpgtg8D2I7s7qsE4cLyxmlTy8ppRTQ2hNEaR7sWAK9xrFgYzYhgQFc0LONt6NSSqkWwaMJQkRGichWEUkXkYfq2H6/iGwSkXUi8qWIdPFkPMfZtghcFZheY1m48QDnpiUSGRrUrCEopVRL5bEEISKBwMvApUBvYKKI9K6120/AEGNMf2Am8LSn4qnT5rkQ2Y4N0oPMoyVc0leLl5RSqoon7yDOBNKNMTuNMeXA+8D4mjsYY5YYY4rtxeVAsgfjOVZ5MaR/Ab3GsGBTNoEBwsW99PFWpZSq4skE0RHYV2M5w15Xn98Bn3swnmPt+BIqiqsfbx3WNZ64iJBm+3illGrpPJkg6mqKbOrcUeQGYAjwTD3bJ4vIKhFZdejQoaaJbvM8CIsjPXwAOw4V6dNLSilViycTRAbQqcZyMpBVeycRuQh4FBhnjCmr60DGmFeNMUOMMUOSkpJOPbLKcti6AHpcxoJNhwG0cz6llKrFkwliJZAmIqkiEgJcC8ytuYOInA78Gys5HPRgLMfa9S2U5UHvcSzYeIBBnWNpG+1oto9XSilf4LEEYYypBO4GFgKbgQ+NMRtF5AkRGWfv9gwQCXwkImtFZG49h2tam+dASBR7Y85gQ2Y+o/TpJaWUOo5HH/o3xswH5tdaN7XG/EWe/Pw6uZyw5TPo/is+3ZwLwOh+7Zs9DKWUaulaX0vqvcugOAd6jeOzdfsZ2CmW5Lhwb0ellFItTutLEJvmQpCD3XFnszErnzH99e5BKaXq0roSRFkhbJoN3Uby2dZ8AC7V4iWllKpT60oQX06DwoNw9u/5dN1+BnWOpWNsmLejUkqpFqn1JIjdS+HHV2HobewI78fm/flc1r+Dt6NSSqkWq3UkiPJimHM3xKXAyKnMX7cfgNH99PFWpZSqT+vo2/qrJ+HILrjpUwiJ4NN1+zkjJY72MVq8pJRS9fH/O4i9y2H5v+CMWyD1XLZlF7A1u0DbPiil1An4d4KoKIE5d0FMJ7hoGgAfr8kgKEAYO0DrH5RSqiH+XcS05C+Qkw43zoHQSJwuw+yfMhnRI4nEyFBvR6eUUi2a/95B7FsJy16GwZOg6wgAvk8/THZ+GVcOar5xiZRSylf5Z4KoKIU5d0JUB7j4yerVH6/JICYsmJG92ngxOKWU8g3+mSC+eQoOb4NxL4AjGoCC0goWbjzA2AHtCQ0K9HKASinV8vlfgshcA9+/CKffAKf90lns7LVZlFa4mDC4UwNvVkopVcW/EkRlmfXUUmQb+NVfqlcbY5ixYi+920czIDnGiwEqpZTv8K8E8e0zcHATjH0BwmKrV/+ckcfm/flcN7QzInUNla2UUqo2/0kQ+3+G756FAROh+yXHbJqxYg/hIYGMH6htH5RSyl3+kSAqy2H2XRCRCJf89ZhN+aUVzPt5P+MGdCDKEeylAJVSyvf4R0O5pc9B9nq4dgaExx+zadaaTEoqnFw3tLOXglNKKd/k+3cQBzbAt09D3wnQ87JjNrlchre+38WATrH0T46t5wBKKaXq4tsJwllhNYgLi4NLnz5u85dbDrI7p5hbzkn1QnBKKeXbfLuI6fsXrMrpq/8DEQnHbX5j6U46xoZxaV8d90EppU6W795BHNwM3/wNel8Ovccft3nV7lyW78xl0tkpBAX67mkqpZS3+OaV01kJs++E0CgY/fc6d3nui20kRoZw/TCtnFZKqcbwzQSx7J+QtQZGPwORScdtXrEzh+/Tc7j9/G6Eh/h2KZpSSnmL7yWIylJY8lfoOQb6XHncZmMMf1+0laSoUK4f2sULASqllH/wvQRxdC+EhMNlz0Id3WZ8tn4/K3cf4Z6RaYSFaK+tSinVWL5X/lJeBJe+DlFtj9tUUu7k/+ZvoVf7aCaeqXUPSil1KnzvDsIRA/1+Xeem577YRubREh4b25vAAO2UTymlToXvJYj41DqLln7ae4TXv9vJxDM7M6zr8W0ilFJKnRzfSxAcnxxyi8q5e8ZPtI8J45HRPb0Qk1JK+R/fq4OopdLpYsp7P3GosIyZt5+lPbYqpVQT8egdhIiMEpGtIpIuIg/VsT1URD6wt68QkZST/QwDpLWN5M/j+2qHfEop1YQ8dgchIoHAy8DFQAawUkTmGmM21djtd8ARY8xpInIt8DfgmpP5nODAAB4b26epwlZKKWXz5B3EmUC6MWanMaYceB+o3WnSeOBte34mMFJ0TFCllGoRPJkgOgL7aixn2Ovq3McYUwnkAcc9giQik0VklYisOnTokIfCVUopVZMnE0RddwKmEftgjHnVGDPEGDMkKen4vpeUUko1PU8miAygU43lZCCrvn1EJAiIAXI9GJNSSik3eTJBrATSRCRVREKAa4G5tfaZC9xkz08AvjLGHHcHoZRSqvl57CkmY0yliNwNLAQCgTeNMRtF5AlglTFmLvAG8I6IpGPdOVzrqXiUUkqdHI82lDPGzAfm11o3tcZ8KVB3x0pKKaW8yge72lBKKdUcxNeK/EWkANjq7Tg8KBE47O0gPMifz8+fzw30/HxdD2NM1Mm8wRf7YtpqjBni7SA8RURW6fn5Jn8+N9Dz83Uisupk36NFTEoppeqkCUIppVSdfDFBvOrtADxMz893+fO5gZ6frzvp8/O5SmqllFLNwxfvIJRSSjUDn0oQJxqAyNeIyJsiclBENtRYFy8ii0Vkuz2N82aMjSUinURkiYhsFpGNInKPvd5fzs8hIj+KyM/2+U2z16fag19ttwfDCvF2rI0lIoEi8pOIfGov+825AYjIbhFZLyJrq57w8aPvZ6yIzBSRLfb/wbMac24+kyBqDEB0KdAbmCgivb0b1SmbDoyqte4h4EtjTBrwpb3siyqBB4wxvYBhwF32v5e/nF8ZcKExZgAwEBglIsOwBr16zj6/I1iDYvmqe4DNNZb96dyqXGCMGVjj8VZ/+X6+ACwwxvQEBmD9O578uRljfOIFnAUsrLH8MPCwt+NqgvNKATbUWN4KtLfn22O1+/B6nE1wnnOwRhf0u/MDwoE1wFCshlZB9vpjvrO+9MLqfflL4ELgU6yu+f3i3Gqc424gsdY6n/9+AtHALuw65lM5N5+5g8C9AYj8QVtjzH4Ae9rGy/GcMnus8dOBFfjR+dlFMGuBg8BiYAdw1FiDX4Fvf0efB/4IuOzlBPzn3KoYYJGIrBaRyfY6f/h+dgUOAW/ZRYSvi0gEjTg3X0oQbg0upFoWEYkEPgbuNcbkezuepmSMcRpjBmL92j4T6FXXbs0b1akTkTHAQWPM6pqr69jV586tluHGmEFYxdZ3ich53g6oiQQBg4B/GWNOB4poZFGZLyUIdwYg8gfZItIewJ4e9HI8jSYiwVjJ4V1jzCf2ar85vyrGmKPA11h1LbH24Ffgu9/R4cA4EdmNNZb8hVh3FP5wbtWMMVn29CAwCyvJ+8P3MwPIMMassJdnYiWMkz43X0oQ7gxA5A9qDqJ0E1bZvc8REcEa72OzMebZGpv85fySRCTWng8DLsKqCFyCNfgV+Oj5GWMeNsYkG2NSsP6ffWWMuR4/OLcqIhIhIlFV88CvgA34wffTGHMA2CciPexVI4FNNObcvF2hcpKVL6OBbVhlvY96O54mOJ/3gP1ABVbW/x1WWe+XwHZ7Gu/tOBt5budgFUGsA9bar9F+dH79gZ/s89sATLXXdwV+BNKBj4BQb8d6iuc5AvjU387NPpef7dfGquuJH30/BwKr7O/nbCCuMeemLamVUkrVyZeKmJRSSjUjTRBKKaXqpAlCKaVUnTRBKKWUqpMmCKWUUnXSBKGUUqpOmiCUTxIRp91N8wYRmVfVaO0k3v+4iDxozz8hIhedYjwpIlJi983UIojINXbX+J96OxblmzRBKF9VYqxumvsCucBdjT2QMWaqMeaLJohph7H6ZnKb3Y29RxhjPgBu8dTxlf/TBKH8wTLsnkVFJFJEvhSRNfZgMOOrdhKRR+0Bp74AetRYP11EJtjzu0Uk0Z4fIiJf2/Pn23csa+0eMqNOFJSIzLZ7Ct1Yo7dQRKTQvmtZAZwlImeIyA/24EM/ikiUiPSx59eKyDoRSbPfe0ON9f+uSjBiDaa1xj7Gl6f+J1XK6vVPKZ9lXyBHYvX7BFAKXGGMybcv9MtFZC5WZ2XXYnU7HoQ1fsPqOg5ZnweBu4wx39s91Ja68Z7fGmNy7b6aVorIx8aYHCACawyQqXa/YluAa4wxK0UkGigBbgdeMMa8a+8TKCK9gGuweiGtEJFXgOtF5HPgNeA8Y8wuEYk/ifNSql6aIJSvCrPL+1OwLvSL7fUC/NXuutmFdWfRFjgXmGWMKQawk8bJ+B54VkTeBT4xxmS48Z4pInKFPd8JSANyACdWL7dg3cnsN8asBDB2l+gisgx4VESS7c/bLiIjgcFYyQYgDKtHzmHAt8aYXfYxck/y3JSqkxYxKV9VYpf3dwFC+KUO4nogCRhsb88GHPY2dzoeq+SX/xdV78MY8xRWeX4Y1l1Jz4YOIiIjsHp4PctYw5L+VON4pcYYZ9WudcVljJkBjMO6m1goIhfa+75t170MNMb0MMY8Xt8xlDpVmiCUTzPG5AFTgAft8SdisAa7qRCRC7ASCMC3wBUiEmbXH4yt55C7sX6lA1xVtVJEuhlj1htj/obVS2aDCcKO44gxpthOJsPq2W8L0EFEzrA/J0pEgkSkK7DTGPMiVjfN/bF64JwgIm3sfeNFpAtWHcz5IpJatf4EsSnlFi1iUj7PGPOTiPyMVcfwLjBPRFZhdTG+xd5njYh8YK/bA3xXz+GmAW+IyCNYQ6RWuddOOE6svvU/P0FYC4DbRWQd1ljAy+uJvVxErgFesusqSrDuPK4BbhCRCuAA8IRdn/E/WMNkBmB1E3+XMWa5XQn+ib3+INb430qdEu3uW6kmINa425/aj922GHZR14PGmDHejkX5Hi1iUqppOIGYltZQDngFOOLtWJRv0jsIpZRSddI7CKWUUnXSBKGUUqpOmiCUUkrVSROEUkqpOmmCUEopVaf/Dy8CoACelb48AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radiuseff, valeff, label='Calibration')\n", "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n", "plt.xlim([0, 60])\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "rfactor = np.arange(1.,2., 1e-3)\n", "ffactor = np.arange(1.,2., 1e-3)\n", "# work with the data points between 3 and 10\"\n", "idx, = np.where((radii > 2) & (radii < 10))\n", "xv = radii[idx]\n", "yv = encircled_flux[idx]/np.max(encircled_flux)\n", "resid = np.zeros((len(rfactor), len(ffactor)))\n", "for i, rf in enumerate(rfactor):\n", " #print(i, rf)\n", " tck = interpolate.splrep(radiuseff*rf, valeff, s=0)\n", " yfit = interpolate.splev(xv, tck, der=0)\n", " for j, ff in enumerate(ffactor):\n", " resid[i, j] = np.sum((yv-yfit*ff)**2)\n" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.imshow(np.log(resid))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This shows a minimum, with some degeneracy. " ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rf = 1.000, ff = 1.005, residual = 0.007\n" ] } ], "source": [ "imin = np.argmin(resid)\n", "rmin, fmin = np.unravel_index(imin, resid.shape)\n", "print(\"rf = {:.3f}, ff = {:.3f}, residual = {:.3f}\".format(rfactor[rmin], ffactor[fmin], resid[rmin, fmin]))" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(radiuseff*rfactor[rmin], valeff, label='Calibration')\n", "plt.plot(radii, encircled_flux/np.max(encircled_flux)/ffactor[fmin], label='Our PSF')\n", "plt.xlim([0, 80])\n", "plt.xlabel('Radius [arcsec]')\n", "plt.ylabel('Encircled flux')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9851686764850778" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# The two curve overlap\n", "psfok = psf/np.max(encircled_flux)/ffactor[fmin]\n", "np.sum(psfok)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "psfok is the PSF that a source of flux 1 Jy has in our data, and is to be used for source extraction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Validation\n", "To check PSF is reasonable, lets look at a 160 micron source, e.g. `----`. We can see from `GAMA-09_PACS160_v0.9.fits` that it has a flux of -- Jy. Maximum value in our normalised PSF gives ---" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from astropy.table import Table" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "ename": "FileNotFoundError", "evalue": "[Errno 2] No such file or directory: './data/GAMA09_PACSxID24_v1.fits'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mFileNotFoundError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./data/GAMA09_PACSxID24_v1.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/table/table.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[1;32m 2532\u001b[0m \u001b[0mpassed\u001b[0m \u001b[0mthrough\u001b[0m \u001b[0mto\u001b[0m \u001b[0mthe\u001b[0m \u001b[0munderlying\u001b[0m \u001b[0mdata\u001b[0m \u001b[0mreader\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m~\u001b[0m\u001b[0mastropy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mascii\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2533\u001b[0m \"\"\"\n\u001b[0;32m-> 2534\u001b[0;31m \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio_registry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2535\u001b[0m \u001b[0;31m# For some readers (e.g., ascii.ecsv), the returned `out` class is not\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2536\u001b[0m \u001b[0;31m# guaranteed to be the same as the desired output `cls`. If so,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/io/registry.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, format, *args, **kwargs)\u001b[0m\n\u001b[1;32m 500\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 501\u001b[0m \u001b[0mctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_readable_fileobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'binary'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 502\u001b[0;31m \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mctx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 503\u001b[0m \u001b[0;32mexcept\u001b[0m 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\u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"generator didn't yield\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/utils/data.py\u001b[0m in \u001b[0;36mget_readable_fileobj\u001b[0;34m(name_or_obj, encoding, cache, show_progress, remote_timeout)\u001b[0m\n\u001b[1;32m 191\u001b[0m \u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshow_progress\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mshow_progress\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 192\u001b[0m timeout=remote_timeout)\n\u001b[0;32m--> 193\u001b[0;31m \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFileIO\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 194\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mis_url\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 195\u001b[0m \u001b[0mdelete_fds\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfileobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: './data/GAMA09_PACSxID24_v1.fits'" ] } ], "source": [ "PACScat=Table.read('./data/GAMA09_PACSxID24_v1.fits')" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'PACScat' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined" ] } ], "source": [ "PACScat['HELP_ID']" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'PACScat' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'GAMA09-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined" ] } ], "source": [ "PACScat[PACScat['HELP_ID']=='GAMA09-PACSxID24-1-69605']" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Max PSF = 0.0005 Jy/pix, off pixel Max PSF = 0.0001 Jy/pix\n" ] } ], "source": [ "cpix=np.int((hd['NAXIS1']+1)/2.0)\n", "\n", "print(\"Max PSF = {:.4f} Jy/pix, off pixel Max PSF = {:.4f} Jy/pix\".format(psfok[cpix-1,cpix-1]*0.0185,psfok[cpix-3,cpix-3]*0.0185))" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/mc741/anaconda3/lib/python3.6/site-packages/mpl_toolkits/axes_grid/__init__.py:12: MatplotlibDeprecationWarning: \n", "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist provies the same functionality instead.\n", " obj_type='module')\n", "WARNING: hdu=0 does not contain any data, using hdu=1 instead [aplpy.core]\n", "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n", "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import aplpy\n", "import seaborn as sns\n", "sns.set_style(\"white\")\n", "cmap=sns.cubehelix_palette(8, start=.5, rot=-.75,as_cmap=True)\n", "fig=aplpy.FITSFigure('./data/input_data/GAMA-09_PACS160_v0.9.fits')\n", "fig.recenter(PACScat[PACScat['HELP_ID']=='GAMA09-PACSxID24-1-69605']['RA'],PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']['Dec'], radius=0.005)\n", "fig.show_colorscale(vmin=-0.001,vmax=0.002,cmap=cmap)\n", "fig.add_colorbar()\n", "fig.colorbar.set_location('top')" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rad=20\n", "plt.imshow(psfok[cpix-1-rad:cpix+rad:5,cpix-1-rad:cpix+rad:5]*0.0185,vmin=0,vmax=2,cmap=cmap)\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In summary, the PSF is within 10% of this source, and given noise and shape of source will add additional uncertianty, as well as non-zero background, this seems reasonable.\n" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "stackhd[0].data=psfok\n", "stackhd.writeto('dmu18_PACS_160_PSF_GAMA09_20190131.fits',output_verify='fix+warn', overwrite=True)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.hist(psfok.flatten(),bins=np.arange(-0.01,0.05,0.0005));\n", "plt.yscale('log')" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.035564297362154086" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.max(psfok)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(~np.isnan(psf))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python (herschelhelp_internal)", "language": "python", "name": "helpint" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }