{
 "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": "iVBORw0KGgoAAAANSUhEUgAAARQAAAD8CAYAAAC2EFsiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAIABJREFUeJzsvUuMJEl6JvaZ+ds93vmszHr0o6YfGm5zOJyeBTEDaAhBhKQLT7tYCQtIAgFetHfxrNNeBR2EnYMECYKw0mWhPVDSCgIoYAkJHGp2OdhZ9nB6uru6qrIyIyPj7eFvMx3MzdzcwyMyq6emVVKXAYXMjIrw8If559///d//G+Gc4814M96MN+NVDPr/9g68GW/Gm/H/n/EGUN6MN+PNeGXjDaC8GW/Gm/HKxhtAeTPejDfjlY03gPJmvBlvxisbbwDlzXgz3oxXNr52QCGE/DuEkF8QQj4lhPzJ1/39b8ab8Wb85gb5On0ohBADwN8A+LcBPAPwEwD/Puf8X39tO/FmvBlvxm9sfN0M5fsAPuWcf8Y5TwH8YwB/+DXvw5vxZrwZv6Fhfs3fdw7gqfb3MwB/W38DIeSPAfwxABiu9bvBoyHAAQ6Ag4BzgHGCohBYaBgMlHAQAhBUP/UhP/dVP9/cDiC2wTlBwSg4I6AGg0FZ63ZI+en6qH8L50Qdo9w2YwS8IKCm3EdtPwEQwrWtlXtIdp779mOq7Vb7njbPgfbH3QbRf939oept2nF9pePZfW45F38zTsByCmJwUCrOLSV877lt7q18pTm/CkbBCgpCeTknxLbl8dw2v76WeV4dGJa/GE8450cvc553ja8bUNqmR+2scM5/DODHAND/4IT/3j/6eygYRc4pktzEJrWwWPgwTIZuJ0JgZ3DMHAZhMKk4aRQcrPwqxglyRpEUJtLCwDp2sJwEcHoJekEM38rgGDkMWn4eHJQwtT+MU7DyJs8KAykzEOcm1rGDzec9uI9W6HoJXDOvbcckhZpEVJucTE7mcrs5o8iYgSQX+xcmNtbXAaxuisBP4DspbKOATYvaPpq0UNvWt08bk4xpp5xxsuNndYz6/3FOaq9z7f/k+3hj22o/iA6m9f2UN5i8VvoNp78ur0PzPL7M8cr9ypmhznfBKFJmIC0MbBIb4cZBtrLROQoRlOfbMXNYtKjNiea51s9Vzg217aQwEecmVpGD+EkX/ttLdFwxR2xawDKKrWPUr4O+nU1mYRm6SJYOeochOm4i9s/I1XyX50Feq5xRFOX9EqYWVmsPRU7R72/gl/eLScQDkBKO//nf/C+e4BWNrxtQngF4oP19H8DFzneXaJ9zijg3EaUW5vMApp2j34nhWZm68PpElJNKnzxRZmEdO+B/2UfwvQW6XqxAQF4YkxS1r2dcfDfjBFm5jU15gRgj6D+ewbczeFZWm3z6zV5tqwKSnNPaRY8yC+vIgf3nXRQ/XOLwbCG2aRRquyZhtUm966baBSBt4JEzqkBDnivGCQpOkBcGCla+XlDkuYGioGCpAR4bsOYGOAXyTgGYHDB4hR4cQEGAnMBcGyAMyAYFiFuA2gUMg8E0y5+UwaAcplHAKI9LB05CeO1BoYMMJeJa7wQYUgchxglMQsAohcULOAaFa+bougmiroUwthH9s2MsfrBCx0vU/JIPq33XwCY5KAwwKm5UyxDXbfM4x2LpI45sdDuRmC/I1Jw1Ae2YmNAgKDRGKs7HymTI/2KIxfcW6LiJOM28esgwEHHsBOJ8ca7ubtoFFmsX83kADEJwAK6ZAwwArQDtVYyvG1B+AuBbhJC3ATwH8PcA/Ae73swBBSabxMZi7sN0bgcTeQNlzEBWGNhkFlYbF/HSQe/7M/W0sGgB2yjuzEpWkYviZ304H20DUnOyVduqM5K0MFBwiiizkOQmVhsHydRD52QN7w/GGO5gOi8DIrUnMzfU3wUT+5AV4mmaM4qsoMgKA0liIYssuL9yEL+bwHQzWFYB02BwrBy+k9XoO0GDKZAGU+D1feKoh4kFEz+TzESWGcjj6rstL4PjlIBago5Z3qQUXD1Z9YeAOj8aUdoFLowzmJyA0ZJZGBSemSGwU8R/EIMlNibPBnBGEbp+AsfM4VkZcsLEfOG8FVhMWoBxAkpLYCRinx0rxypyEf30AOlHCxQeUWwFBkBLMJBz0CQFGCioUWdt6+8zLG8CFD0K5hNwK4MF7eFFoEAFACxaVHd4pwSVWQA+2ADQQOUVjq8VUDjnOSHkHwD4XwEYAP4rzvnPd74fRDzBU0uAiV28FJgkuaCei7WHLDYxPFq1MopdtFNuI8osLNYu8tTE4Ls3W9vQb/pqO9t0WN+n1cZF9mUA9+0VBg+nO0Mmfbt3ARF9/wXbEICRsRI4MhNJaiJZOgAjsPsJbDtHx49hdTcwThkMUr9pJVMAdoQdDTBpnoPm+RBzoR5OFYyiOBU/s4IizU2sNy7ShQNQDqeXwLFzOFZeMjdxsxrEEMDSFprcAi6ME1DOYRKCnBowKINj5HDNHMHDFOvYwewXI1gPQ3R98QApuAyFCExUjFa/VoxzUM5AtX0zCMfmuznm8wBpaqh5zEDUPAKnNbYCTgWAaSBuHDHMZwEYI0AHcDkBzBI85LHtAxXuYTH3QYaljmLmrdfuq46vm6GAc/6nAP70bu8FNjLMeUlmIuPH5coHB3BwsK59dheYyHAk07SS5bgDbxRh1FvCszIVB9/GStri6uXGRfKsA//REv0PJ63bM2lDO2gBkiaIyNBMhnhZITSCODMRbRw4f+Uj/U4Ix83Q9RMMuxtYJT0XE77+xJXf2dQxmr+/zGgHGKqOSz+mQoaFA4qMUeTlscyXPux/GSD57Q08P4Fr5bANcf6kziSYC2sFF4rq2HRgMcGQEyrCoVKj8KwM0YcJwsTGzS8P4Nxfo+dXzDSnVIF/7XpJxoJCsRUKLvbRLLDcuJhc9NE7XpdsmYDx8uFUO+cCVOR8gCW2bRxwzJY+ZosAva5gG3cGlUb486rH1w4oLzMYJ1gs/DtpJroYJbWO+bQDy8vQ70RKfJWC2C69RIY4UWZhuXERzV30jtfousmdWElTJ0kKwXDCxEbySR/2+0scvbcNJCatb+9lQESGdknJQDaxjewiAD2O4fkJhv0Q9u8vVVwvwaP5VAfuJnyq1+8ILApIGpK8OK6i9p667rPNtvIORfb7KwWWs0UANnZhnYXw3RSOlcMpAUbpFDu0jwo0xRyyjUKFQyZhsLgAKc/KEL0nGMv0r47gfLBA4KRiPho5GCWt31FnKxwGq8K3lVlgOQmQDQz0fDG3ORch0D5dRVwvDtLnWKw9zG664KO1OG8WlN5zl/BnsfCB/uZO1/Cu47UGlKKgMEx2ZzBRzCSxMR934Q0jdbGaWoccbSFOmFpYLANQo8DRvUUNjNpYSTO8SQujznCuOnCGMQYfTba29bJAoodPEkTi1BKZipkD9yhC4CVwPwhhawCyS+dp+95dQKGft5cZtAkkJStphiGME3UDSLBhnADGDlHbpciDDdKRAJdN7GD2rA9rmCDwE7h2VgOXrQfBHtZCCd8CFtfMsfkoxTJ0cTUeoney3tLj2sIgYJutmJTBuZdjvvIwmXXR74UIbBECsTKkatNVYECJtbTLsTRczK564McrAIBThjB3ApWVh+XK/0rXdNd4rQEFALqd6M5gIm/g1fMegnvrncKpHDqYqFRf7GD9vAe//LxfshLbKG5lJSkz6qC08kEAHJ6LrI1nZncGkirdSbcYT1oYiFIL69BFfuPCu7dGvxvBGa7qIV3JxPY9mfXxMoAhQeGuQ9/2ru+RwMM4rd3gEmh0kNEBlnGC3KbIvBhJNxT2gsTC4mkf5kGMThDDs7NaulUPL2Wm6FZgKT/vmjkiP8F86SPcOOh3NwjsrNRXKGxa1ELFNrYiszcGZVhFLmZfDpGdL9EtQyAgb9VVTKC0owrgIIHw0Sye9cHOl+Au1F19G6iwDrD4JgGKYTDlM7krmCwvuwpM/FqIsg0mul6yySysIhebiw6695cvFeLorERuJ/vrHvxvz8sJooNadbMD7UDSBCldg1E+lV6CbieCO1wpn0obg6rrIToL2Q0e+8Ci6Te562Dc2NqH5qhpB7XX6yDDUAGMyZk4V1ScL8/MkBUGOo6BNIgQZyZWoYvZZU/5THQB3OZF6/lqAxbKqAhdSkHYNnPxAPrZAZIPl2rOMU5qbKVNW4FRbdcgHMY5w+pZD+xsDebF5Tlr11V0UFHn8x6wvOwCpwBeAlR4J3qp63jbeK0BhRJ+ZzBZxQ6iTwYI3lui70e3poWbGsd87SFLTAwfzRDY22xC7o/4fJ1+J4WJJDexTmzMpx04QYr+dyYI7BSOkW+xG/0mB7aBpJkVClMLq9BFtnLQPVrj9MG0ZpLSn7Y6UN0GIE3gqImmLX6W5u9tf7ddw11/N3WaXaBDGw+DGsCUDEZnLzml8KQmZhnouQnivgDjq+dDWN0E3SCuPazaMmtNYJH+DpMQkcYu51f4nRyrjYurqwEGozU6ToqC53CMdm0FqHwrui5iPiownwfIcwpeMnMgB+i2rmICKq3sl2ItjoHNJwPwD+Z3BpWv+oDYNV5rQCEE9ezDHjBJfj6A18IIdoGJ0B9MhKmN2dIHpQwHo/VOEKg+X2clEpCWGxfRwsXwaIWOk+4Mb24DEl1/2SQ2FrMAppsJHakR0sj9k8cJ6E/D/QCidB9Np9GPT76/qePI3/kO8NGHfqxtblj5nmZ4AF7Xdhg3tsCxDWDkvpgGU6GsTXM43IBnZujYKQZerGwAs5su+sMQfsla2kJbHVgo4WCEqHSz1EKkvrJ2bMyuu4j7MXp+jNyi1VzCtrPZpMV2CDTiQleZdzDsbcBtAsfIW8VaPa0MAPAjrD5gSH4+AL59O6gYhCnN5VWN1xtQUHdJ7gpzok/uBiYy3s4KA1FuYZ3YmF314A0j9IMqE9QW4ugWbglIahvjLrxBjNOz2dY22sKbfUCyKR290Wc92I/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": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
       "<matplotlib.legend.Legend at 0x7fd0841abf98>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
       "<matplotlib.legend.Legend at 0x7fd08292c908>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAD8CAYAAABpcuN4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAIABJREFUeJzs3Xt8XHWd+P/Xey6ZSZtbc2uSJm3SNr2k91LKVUEQKIIUWRDYnywqytcVXHZlVVhdVFz8iruI6wruoijoFy0IXiqLIHIRubW0BUrvTdK0TZO2adqmuc5kZt6/P85JSdNJMm2TTC7v5+Mxj8z5zOd85n3aZN5zzudzPh9RVYwxxpjeeJIdgDHGmOHNEoUxxpg+WaIwxhjTJ0sUxhhj+mSJwhhjTJ8sURhjjOmTJQpjjDF9skRhjDGmT5YojDHG9MmX7AAGQm5urpaWliY7DGOMGVHWrl17QFXz+quXUKIQkWXAfwJe4Ceq+p0erweAnwOnAY3Atapa4752J3ATEAX+QVWf67afF1gD7FHVy92yMmAFkA2sA25Q1XBf8ZWWlrJmzZpEDsUYY4xLRHYmUq/fS0/uh/kDwKVABXC9iFT0qHYTcEhVpwP3A/e6+1YA1wFzgGXAg257XW4DNvdo617gflUtBw65bRtjjEmSRPoolgKVqlrtfrNfASzvUWc58Kj7/EngQhERt3yFqoZUdQdQ6baHiBQDlwE/6WrE3ecCtw3cNq88mQMzxhgzMBJJFJOA3d22a92yuHVUNQI0ATn97Pt94MtArNvrOcBht43e3ssYY8wQSqSPQuKU9ZybvLc6cctF5HJgv6quFZHzT/C9nIoiNwM3A0yePDleFWNMEnR2dlJbW0tHR0eyQzGuYDBIcXExfr//pPZPJFHUAiXdtouBul7q1IqID8gEDvax7xXAFSLyESAIZIjI/wNuALJExOeeVcR7LwBU9SHgIYAlS5bYohrGDBO1tbWkp6dTWlqKczXZJJOq0tjYSG1tLWVlZSfVRiKXnt4CykWkTERScDqnV/aosxK40X1+NfCiOisirQSuE5GAO5qpHFitqneqarGqlrrtvaiqn3D3ecltA7fN35/UkRljkqKjo4OcnBxLEsOEiJCTk3NKZ3j9Jgr3m/2twHM4I5SeUNWNInK3iFzhVnsYyBGRSuCLwB3uvhuBJ4BNwLPALaoa7ectvwJ80W0rx23bGDOCWJIYXk71/yOh+yhU9RngmR5ld3V73gFc08u+9wD39NH2y8DL3barcUdGGTNSqSovb21gY10TFUUZfGhmvn14mhHLpvAwZoB1dEb57M/X8qlH3uI//rSNTz+yhs88uoaOzv5Ops1Aqq2tZfny5ZSXlzNt2jRuu+02wuHj792tq6vj6quvjtPCsT7ykY9w+PDhk4rlG9/4Bv/xH/9xUvsOB5YojBlAqsqXnlzPnzfv42uXzWbDNy/hrssreGHLfv751+/idMOZwaaqXHXVVVx55ZVs376dbdu20dLSwle/+tVj6kUiEYqKinjyySd7ael9zzzzDFlZWYMV8rBmicKYAfTMe3v5w7t1fOmSmXzmA1NJC/j49LllfOmSmTy9vp4/rK9PdohjwosvvkgwGORTn/oUAF6vl/vvv5+f/vSnPPjgg1xzzTV89KMf5eKLL6ampoa5c+cC0NbWxsc//nHmz5/PtddeyxlnnHF0eqDS0lIOHDhATU0Ns2fP5rOf/Sxz5szh4osvpr29HYAf//jHnH766SxYsIC/+Zu/oa2tLTn/AANsVEwKaMxwEIpE+bf/3cTcSRn8nw9OPea1z503jWc37OXeP27hkjkTCfi8vbQyunzzDxvZVHdkQNusKMrg6x+d02edjRs3ctpppx1TlpGRweTJk4lEIrzxxhusX7+e7OxsampqjtZ58MEHmTBhAuvXr2fDhg0sXLgwbvvbt2/nV7/6FT/+8Y/5+Mc/zlNPPcUnPvEJrrrqKj772c8C8LWvfY2HH36YL3zhC6d2wMOAnVEYM0CeXFtLfVMHdyybjc977J+W1yN8edlM9hxu5/G3dvfSghkoqhp38EBX+UUXXUR2dvZxr7/66qtcd911AMydO5f58+fHbb+srOxoEjnttNOOJpsNGzbwgQ98gHnz5vHYY4+xcePGATqi5LIzCmMGQCym/PiVahaWZHHO9Jy4dc6dnsuCkiwefb2GG86cMiZGQfX3zX+wzJkzh6eeeuqYsiNHjrB79268Xi/jx4+Pu1+ifUiBQODoc6/Xe/TS0yc/+Ul+97vfsWDBAh555BFefvnlkzuAYcbOKIwZAKt2HKSmsY0bz+49AYgIN5w5haqGVt6obhziCMeWCy+8kLa2Nn7+858DEI1Guf322/nkJz/JuHHjet3v3HPP5YknngBg06ZNvPfeeyf0vs3NzRQWFtLZ2cljjz128gcwzFiiMGYAPP7WLtKDPi6dW9hnvcvnF5KZ6uexVbuGKLKxSUT47W9/y69//WvKy8uZMWMGwWCQb3/7233u9/nPf56Ghgbmz5/Pvffey/z588nMzEz4fb/1rW9xxhlncNFFFzFr1qxTPYxhQ0bDcL0lS5aoLVxkkqUlFOG0bz3PNUuK+bcr5/Vb/19/t4Ffr93Nun+9iHEpo+/q7+bNm5k9e3aywzgp0WiUzs5OgsEgVVVVXHjhhWzbto2UlJRkh3bK4v2/iMhaVV3S376j77fUmCH20pb9hCIxli9MbEb8y+YX8os3d/Lilv1cPr9okKMzJ6KtrY0PfehDdHZ2oqr86Ec/GhVJ4lRZojDmFD27cS+5aSksnjwhofqnl2aTmxbgf9fXW6IYZtLT021Z5Tisj8KYU9DRGeWlLfu5qKIAryexUUxej3Dp3AJe2rrfpvUwI4IlCmNOwRtVjbSFo1wyZ+IJ7XfB7Hw6OmOs3nFwkCIzZuBYojDmFPx1+wFSfB7OnBr/3onenFmWQ4rPw1+2NQxSZMYMHEsUxpyCVysbWFqaTdB/YlNypKZ4OXNqDi9v3T9IkRkzcCxRGHOS9h/pYNu+Fs6ZnntS+583I4+qhlZqD42OieOGi3/6p3/i+9///tHtSy65hM985jNHt2+//Xa+973vHTO9+DvvvMMzz7y/5E6i04KnpaXFLf/kJz+Z0Iy0fUl0+vOhYInCmJP0auUBAD5QfnKJomuqjzerrZ9iIJ199tm8/vrrAMRiMQ4cOHDMnEuvv/4655xzzjHTi/dMFEMtEokct53o9OdDIaFEISLLRGSriFSKyB1xXg+IyOPu66tEpLTba3e65VtF5BK3LCgiq0XkXRHZKCLf7Fb/ERHZISLvuI/40zcak2Svbj9A9vgUKgozTmr/GfnpZI3zs3qHTecxkM4555yjiWLjxo3MnTuX9PR0Dh06RCgUYvPmzSxatOjo9OLhcJi77rqLxx9/nIULF/L4448DzhQe559/PlOnTuUHP/hBr+93++23s3jxYi688EIaGo7vc+qanhxgzZo1nH/++YBz1nLzzTdz8cUX83d/93c88sgjvU5//sgjj3DVVVexbNkyysvL+fKXv3y0/YcffpgZM2Zw/vnn89nPfpZbb711QP4du+v3PgoR8QIPABcBtcBbIrJSVTd1q3YTcEhVp4vIdcC9wLUiUgFcB8wBioA/i8gMIARcoKotIuIHXhWRP6rqm257X1LV4ZFKjenFqh0HOXNqNp4Eh8X25PEIp5dms2o0j3z64x2w98TmS+pXwTy49Du9vlxUVITP52PXrl28/vrrnHXWWezZs4c33niDzMxM5s+ff8xNdCkpKdx9992sWbOGH/7wh4DzIb5lyxZeeuklmpubmTlzJn//93+P3+8/5r1aW1tZvHgx9913H3fffTff/OY3j7aRiLVr1/Lqq6+SmprKI4880uv05+Cc9bz99tsEAgFmzpzJF77wBbxeL9/61rdYt24d6enpXHDBBSxYsCDh909UImcUS4FKVa1W1TCwAljeo85y4FH3+ZPAheLMjLYcWKGqIVXdAVQCS9XR4tb3u4+RP5eIGTPqm9rZc7idJVOOn6r6RJxRls3Oxjb2NnUMUGQG3j+r6EoUZ5111tHts88+O6E2LrvsMgKBALm5ueTn57Nv377j6ng8Hq699loAPvGJT/Dqq6+eUJxXXHEFqampR7d7m/4cnIkOMzMzCQaDVFRUsHPnTlavXs15551HdnY2fr+fa6655oTeP1GJ3Jk9Ceg+gX4tcEZvdVQ1IiJNQI5b/maPfSfB0TOVtcB04AFVXdWt3j0ichfwAnCHqoZ6BiUiNwM3A0yePDmBwzBm4Kzb6aydfNqUxO7G7s0ZZU4/xaodjQlPATKi9PHNfzB19VO89957zJ07l5KSEu677z4yMjL49Kc/nVAbPacS79mPEE+8mYN9Ph+xWAyAjo5jvxD0nO68t+nPe4tnqObqS+SMIt55dc/oeqvT676qGlXVhUAxsFRE5rqv3wnMAk4HsoGvxAtKVR9S1SWquiQvL6//ozBmAK3ZeZCg30NF0cn1T3SpKMogLeAb3ZefkuCcc87h6aefJjs7G6/XS3Z2NocPH+aNN97grLPOOq5+eno6zc3NJ/w+sVjsaIfzL3/5S84999zj6pSWlrJ27VqA49bIOFVLly7lL3/5C4cOHSISiQx4+10SSRS1QEm37WKgrrc6IuIDMoGDieyrqoeBl4Fl7na9e2kqBPwM59KXMcPKup2HWFCchd/bx59Q6wGoeQ2a9/ZaxesRFk3OYt3OQ4MQ5dg1b948Dhw4wJlnnnlMWWZmJrm5x49S+9CHPsSmTZuO6cxOxPjx448uu/riiy9y1113HVfn61//Orfddhsf+MAH8HoHdgncSZMm8S//8i+cccYZfPjDH6aiouKEpkVPmKr2+cC5PFUNlAEpwLvAnB51bgH+231+HfCE+3yOWz/g7l8NeIE8IMutkwr8Fbjc3S50fwrwfeA7/cV42mmnqTFDpS0U0Wl3/q/e+8fN8SuE21Sfvl31G1mqX89wfj79RdXOjrjV73tui5bd8bS2hjoHMeqhs2nTpmSHMKY0NzerqmpnZ6defvnl+pvf/CZuvXj/L8Aa7efzVVX776NQp8/hVuA590P+p6q6UUTudt9kJfAw8AsRqcQ5k7jO3XejiDwBbAIiwC2qGhWRQuBRt5/C4yaWp923fExE8txE8Q7wuRPIe8YMundrDxOJafz+iUgYHr8BKp+H0z8DMy6F7c/B6ofgYDX87RPgPXbkzIKSLGIKG/YcYWnZqXWOm7HnG9/4Bn/+85/p6Ojg4osv5sorrxzw90homnFVfQZ4pkfZXd2edwBxu9tV9R7gnh5l64FFvdS/IJGYjEmWte5lorjTir90j5MkPvqfcNonnbLyD8PEufCHf4AX7oaLv3XMLgtKsgB4Z/chSxTmhCVyB/mpsjuzjTlB7+w+TFnueCaM77GgzZ518JqbILqSRJfTbnTKXv8vqHv7mJdy0wIUT0jl3d1Ngxn2kNJRsHLmaHKq/x+WKIw5QRv2NDFvUo8OQ1V4/i4YlwMXfSv+jhfdDePznJvQevzhLijJ4p3dhwcp4qEVDAZpbGy0ZDFMqCqNjY0Eg8GTbsNWuDPmBBxoCVHf1HF8oqh+CWr+Cpd+F4K9DJkNZsJ5X4Zn/hl2vAJTzzv60sLiLP53fT0NzSHy0gPx9x8hiouLqa2tjTudhUmOYDBIcXHxSe9vicKYE/DeHufy0LziHonitR9AeiGc9qm+G1h0A7zy7/DX+45NFJOdfop3dx/mwxUntgjScOP3+ykrK0t2GGYA2aUnY07AhlonUczpfqPd/i3OGcXpN4EvpZc9Xf4gnPl52PEX2Pf+jKZzizLxeoR3a0fH5SczuliiMOYEvLeniam540kPdhvi+tZPwBvo/2yiy6IbwJsC635xtCg1xcu0vPFsqjsywBEbc+osURhzAjbsaWJu9/6JSBg2PAmzL4fxCa5LMT4HZl0O61dA5/tz/1QUZrCp3hKFGX4sURiToMaWEHU9O7KrXoD2QzD/2hNrbPHfOftte/ZoUUVRBvVNHRxsDQ9QxMYMDEsUxiSoqyP7mDOK9U84Q2KnneB9omUfdIbKbvrd0aI5RU67dvnJDDeWKIxJ0Eb3A3zOJLcjO9QMW/8Icz523LQc/fJ4YfZHYdufIOysmT3bXSlvU/3oufHOjA6WKIxJ0Ja9zRRPSCWjqyO78s8QaYc5V51cgxXLobPVaQfIHp9CYWbQzijMsGOJwpgEbd17hFkF6d0KnoXUCVDScx2vBE0517ls1e3yU0VhxtEzF2OGC0sUxiQgFIlS1dDKrAL3slMsCtv/BOUXg/ck71v1+mDmpc4ZRdRZPW1OUQZVDS10dEYHKHJjTp0lCmMSULW/lWhMmdl1RrF7NbQfhBnLTq3h6RdBRxPsWQM4I59iClv3nvhqa8YMFksUxiRgy17nctDRS0/bngWPD6ZfeGoNTz0fxAvbnwe6d2jb5SczfFiiMCYBW/c2k+L1UJY73imofAEmn+VM9HcqUrOgZKmzhgVQMmEcqX4v2/bZGYUZPhJKFCKyTES2ikiliNwR5/WAiDzuvr5KREq7vXanW75VRC5xy4IislpE3hWRjSLyzW71y9w2trtt9jN5jjGDb8veZqbnp+HzeqC1Efa9B2Xn9b9jIqZ/GOrfhZb9eDzCjIlplijMsNJvonCXK30AuBSoAK4XkYoe1W4CDqnqdOB+4F533wqcZVHnAMuAB932QsAFqroAWAgsE5GuVdDvBe5X1XLgkNu2MUm1Ze8RZhW6l51qXnF+Th3ARAFQ9RIAMyams21fy8C0bcwASOSMYilQqarVqhoGVgDLe9RZDjzqPn8SuFBExC1foaohVd0BVAJL3XW9u/4S/O5D3X0ucNvAbXPgF4A15gQcag2z70jo/f6J6r9ASjoULR6YNyiY51zC2vkq4CSKhuaQTeVhho1EEsUkYHe37Vq3LG4dVY0ATUBOX/uKiFdE3gH2A8+r6ip3n8NuG729lzFDaos7Auno0Ngdr0DpOSc/LLYnjxemnAM1bqJwE5JdfjLDRSKJQuKU9VzjsLc6ve6rqlFVXQgUA0tFZG6C7+W8ocjNIrJGRNbYSlpmMG3tPuKpqRYOVjlzNQ2kKefAwWo4UsfMiZYozPCSSKKoBUq6bRcDdb3VEREfkAkcTGRfVT0MvIzTh3EAyHLb6O29uvZ7SFWXqOqSvLy8BA7DmJOzZW8z2eNTnCVKd7j9EwPVkd2l9FznZ81rTMwIkBH02b0UZthIJFG8BZS7o5FScDqnV/aosxK40X1+NfCiOiurrwSuc0dFlQHlwGoRyRORLAARSQU+DGxx93nJbQO3zd+f/OEZc+q27G1m5sR0RARqXoPUbMjvOZ7jFBXMg0Am1PwVEWFmQbqdUZhho99E4fYX3Ao8B2wGnlDVjSJyt4hc4VZ7GMgRkUrgi8Ad7r4bgSeATcCzwC2qGgUKgZdEZD1OInpeVZ922/oK8EW3rRy3bWOSQlXZvq+52x3ZbzpzO3kG+BYkjxemnAU7XwPeH/nkfHcyJrkS6o1T1WeAZ3qU3dXteQdwTS/73gPc06NsPbCol/rVOCOtjEm6+qYOWsNRpuWnOfdPNFbCok8MzpuVnuvc8d28lxkT02lq38X+5hATM4KD837GJMjuzDamD5X7nVHc5flpsHuVU1hyZh97nIKudnevYobboW39FGY4sERhTB+6EsX0/DTnspPHD0ULB+fNCueDNwVq32LGxDTARj6Z4cEShTF9qGxoIWucn5zxKc6MsUULwZ86OG/mC0DhQtj9FjlpAXLTAnZGYYYFSxTG9KFyXwvT89KQaBj2rDv5RYoSVbIU6t6GSNjmfDLDhiUKY/pQ2dDiXHaqXw/R0OAniuLTnffZ+x7l+WlUNbTayCeTdJYojOnFwdYwB1vD7/dPwNCcUQDUvsW0/DRaQhH2HQkN7nsa0w9LFMb04tiO7NUwoRTSJw7um2YUQUYx1K5mep7ToV3VYDPJmuSyRGFML7bvd/oHpuenOf0Gk04bmjcuOR12O2cU8H7CMiZZLFEY04vK/S2k+r0U+VqgaTcUxb1HdOAVnw5Nu8jnEOkBn51RmKSzRGFMLyr3Ox3Znvp3nIKBWn+iP8VOP4XsWcvU/DQ7ozBJZ4nCmF50JQrq1gHi3BA3FArmgnih/h2m56XZGYVJOksUxsTREopQ39Txfv9E3kwIpA/Nm/tTndlp695men4a+46EONLROTTvbUwcliiMiaPKvdwzLXe8c6PdUPVPdClaAHVvMy13HADVDa1D+/7GdGOJwpg4uvoFZo5vhtb9Q9c/0aVoEbQ1Miu16Zh4jEkGSxTGxLF9fwt+r1DSvsUpGPIzCuf9JrVvxe8V66cwSWWJwpg4Kve3UJozHt/ed8DjczqYh1L+HPD48O59h9Kc8XZGYZIqoUQhIstEZKuIVIrIHXFeD4jI4+7rq0SktNtrd7rlW0XkEresREReEpHNIrJRRG7rVv8bIrJHRN5xHx859cM05sRUdc3xtGcd5M8evBlje+MPHu3QnmYjn0yS9ZsoRMQLPABcClQA14tIzwWDbwIOqep04H7gXnffCpw1tucAy4AH3fYiwO2qOhs4E7ilR5v3q+pC93HMynrGDLZQJMrOxlam5413RjwNdf9El6KF7hDZ8exsbCMciSUnDjPmJXJGsRSoVNVqVQ0DK4DlPeosBx51nz8JXCgi4pavUNWQqu4AKoGlqlqvqusAVLUZZy3uSad+OMacuh0HWokpzE87BB2Hh75/okvRImg/xLy0w0Rjyq6DNvLJJEciiWISsLvbdi3Hf6gfraOqEaAJyElkX/cy1SJgVbfiW0VkvYj8VEQmJBCjMQOmar/zgTwzWukUTErWGYWToGbFqgAb+WSSJ5FEIXHKek6Q31udPvcVkTTgKeAfVfWIW/wjYBqwEKgH7osblMjNIrJGRNY0NDT0fQTGnIBqtz+gsH2bs/Rp3uzkBJJfAR4/hW3OyKsqu5fCJEkiiaIWKOm2XQzU9VZHRHxAJnCwr31FxI+TJB5T1d90VVDVfaoaVdUY8GOcS1/HUdWHVHWJqi7Jy8tL4DCMSUz1gVaKMoP492+EvFngS0lOIL4ATKwgZd+7FGUG7YzCJE0iieItoFxEykQkBadzemWPOiuBG93nVwMvqrMs10rgOndUVBlQDqx2+y8eBjar6ve6NyQihd02PwZsONGDMuZUVDW0MDUvDfZtgIJ5yQ2mYD7s28C0PBsia5Kn30Th9jncCjyH0+n8hKpuFJG7ReQKt9rDQI6IVAJfBO5w990IPAFsAp4FblHVKHAOcANwQZxhsN8VkfdEZD3wIeCfBupgjemPqlLd0Mr8rA5o2Zf8RFG4ANoaWZjVQXVDiy2LapLCl0gld4jqMz3K7ur2vAO4ppd97wHu6VH2KvH7L1DVGxKJyZjBsL85REsowqKUWqdgqG+068lNVItSdtEazmHfkRAFmcHkxmTGHLsz25huum5smx6rcQomJjlRTJwDwPRoNWDLoprksERhTDdds7RObN8OmSUwLju5AQXSIXsq+W3bAUsUJjksURjTTVWDs/xpauOm5J9NdCmYR+DARmdZVOvQNklgicKYbqobWpmZ40Matye/I7tLwTzk0A7m5HrsXgqTFJYojOmmqqGFczIaQGPDKFEsAOCc9Hq79GSSwhKFMa6Ozih7Drez0L/LKRg2icKJY4FvN/VNHbSEIkkOyIw1liiMcdU0tqIK07UGUtIha0qyQ3KkF8C4XKZGnDmfdtjlJzPELFEY4+qaDDC/dZtz/4RnmPx5iEDBPHJbtgE28skMvWHyl2BM8lU3tCDEGHdo8/C57NSlYB6BQ1sJeKKWKMyQs0RhjKuqoYUlGUeQcOvwGRrbpWA+Eg1zTuZBSxRmyFmiMMZVfaCVc9PqnY3hdkZROB+As8fXHb0p0JihYonCGN6fDHChfxeI11knezjJmQ6+VOb5dlF9oJVozCYHNEPHEoUxvD8Z4NToDsgtB39qskM6lscLEyso7awmHImx51B7siMyY4glCmN4fyRRXtswuiO7p4J55DRvAdT6KcyQskRhDM4yo1k0E2yrH9aJwhduoohGSxRmSFmiMAZnaOxCv7sGxXAb8dSlwOnQXjquzhKFGVKWKIzBmQzwnPRhOuKpS34FIJw5bs/RmwONGQoJJQoRWSYiW0WkUkTuiPN6QEQed19fJSKl3V670y3fKiKXuGUlIvKSiGwWkY0iclu3+tki8ryIbHd/Tjj1wzSmb1UNLcz37Ya0AkjLT3Y48QXSIHsqcz277IzCDKl+E4WIeIEHgEuBCuB6EanoUe0m4JCqTgfuB+51960ArgPmAMuAB932IsDtqjobOBO4pVubdwAvqGo58IK7bcyg6ZoMcGqkOvlLn/anYB6Tw1U0toY51BpOdjRmjEjkjGIpUKmq1aoaBlYAy3vUWQ486j5/ErhQRMQtX6GqIVXdAVQCS1W1XlXXAahqM7AZmBSnrUeBK0/u0IxJTE1jKz6NkNNeM3wvO3UpmEdGRy1ptFF9wM4qzNBIJFFMAnZ3267l/Q/14+qoagRoAnIS2de9TLUIWOUWTVTVereteiDudQARuVlE1ojImoaGhgQOw5j4qva3Ui61eLRzBCQKp0N7luyyfgozZBJJFBKnrOdtob3V6XNfEUkDngL+UVWPJBDL+42oPqSqS1R1SV5e3onsaswxqhtaqPDsdDYmDvdE4cQ332f9FGboJJIoaoGSbtvFQF1vdUTEB2QCB/vaV0T8OEniMVX9Tbc6+0Sk0K1TCOxP9GCMORlVDS0sCe4BXyrkTEt2OH1LL4BxOZwe3GOJwgyZRBLFW0C5iJSJSApO5/TKHnVWAje6z68GXlRVdcuvc0dFlQHlwGq3/+JhYLOqfq+Ptm4Efn+iB2XMiag+0OqMeJo4x5kqYzhz16ao8Oy0yQHNkOk3Ubh9DrcCz+F0Oj+hqhtF5G4RucKt9jCQIyKVwBdxRyqp6kbgCWAT8Cxwi6pGgXOAG4ALROQd9/ERt63vABeJyHbgInfbmEHhTAbYQtlIGPHUpWAek8I11B5sJhyJJTsaMwb4Eqmkqs9IpN1gAAAe50lEQVQAz/Qou6vb8w7gml72vQe4p0fZq8Tvv0BVG4ELE4nLmFO1vzlERmgfqdI8/DuyuxTMx6dhpmgduw62Mj0/PdkRmVHO7sw2Y1pV945sd0TRsOdOMVIhNVTayCczBCxRmDGtqqGVCtmJIu4UGSNAbjnqDVDh2Wkd2mZIWKIwY1p1Qwtzfbsge6ozRcZI4PUj+bNZ5N9ticIMCUsUZkyrbmhlnncXMlI6srsUzGOm7KRqvyUKM/gsUZgxbe/+fRTG9o6c/okuBfPIjDXR3LAbZyS6MYPHEoUZszo6o2Qe2eZsjMBEATC5s4qG5lCSgzGjnSUKM2btONDKbOka8TRChsZ2mTgHgArZSaX1U5hBZonCjFnV7oinSDDbmRpjJAlmEsmc4o58siGyZnBZojBj1vb9zVR4apCCec7UGCOMt2g+czy7rEPbDDpLFGbMqt53mBmePXiLRlj/hEsmzmOK7KV2n02zbwaXJQozZoX2biVA58jryO5SMA8PiqdhU7IjMaOcJQozJkWiMdIPb3Y2RlpHdhc37vzWbbSHo0kOxoxmlijMmLT7UDsztIaoJwVyypMdzsnJLCbsz2S27LJlUc2gskRhxqTK/S1USA0d2bPAm9AkysOPCJ15FTbyyQw6SxRmTNq+7wgVnp34J43Q/glXoHgBs2QX1fuakh2KGcUsUZgxqaFuB9nSQsqkhckO5ZT4ihaQKmGa67YmOxQziiWUKERkmYhsFZFKEbkjzusBEXncfX2ViJR2e+1Ot3yriFzSrfynIrJfRDb0aOsbIrInzsp3xgwY2ef+2o3Ujuwubvz+hg39VDTm5PWbKETECzwAXApUANeLSM+J+28CDqnqdOB+4F533wqcNbbnAMuAB932AB5xy+K5X1UXuo9neqljzElRVTK7Rjy5U2GMWLkziYqPCc3biMVsckAzOBI5o1gKVKpqtaqGgRXA8h51lgOPus+fBC4UEXHLV6hqSFV3AJVue6jqK8DBATgGY05IXVMH07WGI+MmQ2CELyPqS+FI2jRmag17DrcnOxozSiWSKCYBu7tt17plceuoagRoAnIS3DeeW0VkvXt5akIC9Y1JmDPiaSedeSP8bMIVyZ9rq92ZQZVIoog3CU7Pc9ze6iSyb08/AqYBC4F64L64QYncLCJrRGRNQ4NNYWASV7NnL2WefaSWjOyO7C7jJi8kXw5TV7sz2aGYUSqRRFELlHTbLgbqeqsjIj4gE+eyUiL7HkNV96lqVFVjwI9xL1XFqfeQqi5R1SV5eXkJHIYxjvbadwEYN3lRkiMZGOMmOwkv5B6XMQMtkUTxFlAuImUikoLTOb2yR52VwI3u86uBF9VZdmslcJ07KqoMKAdW9/VmIlLYbfNjgA3nMAPKt3+j82TiCFv+tBfSNfLpgM35ZAZHv7ekqmpERG4FngO8wE9VdaOI3A2sUdWVwMPAL0SkEudM4jp3340i8gSwCYgAt6hqFEBEfgWcD+SKSC3wdVV9GPiuiCzEuURVA/yfgTxgM7apKrnNm2nxZZGWUZTscAZG6gQO+SeS07wFVUVG4JTpZnhLaO4Cd4jqMz3K7ur2vAO4ppd97wHuiVN+fS/1b0gkJmNOxoGWMDNjlRzOnEPaKPpAbc6azfR922loCZGfHkx2OGaUsTuzzZhSXXeActlDrGBBskMZUFI4j6lSx/ZaG9hhBp4lCjOmNFavxScx0qeenuxQBlRW6SK8ojRUv5PsUMwoZInCjCmR2nUAZE0bXYkivXQxANHat5MciRmNLFGYMWV84waaPJlIZnGyQxlYE0pp9qSTftAGCZqBZ4nCjBmqSkn7VvaPnw2jqCMbABH2pc2mpGOLzflkBpwlCjNm7Gk4yFRqCeWP8BljexHKW0A5u6ltaEx2KGaUsURhxoy6rWvwSYzglCXJDmVQpJYuwScx6re+lexQzChjicKMGe071wJQOPusJEcyOCbOco4rtHNNkiMxo40lCjNmpOxfzyEyGJ87OdmhDIrxuZNpZAKB/TbnkxlYlijMmDGxZRO1qTNHX0d2FxFqU2dS0Lol2ZGYUcYShRkTQu0tTI7upiV7dEwE2JvmnHmURGsJtzYlOxQziliiMGNC3Za38EkMb/HiZIcyqLwlp+ERZe+WN5MdihlFLFGYMaG56g0AcmaeneRIBlfujDMBOFLd52z+xpwQSxRmTPDVrWWP5jJ5ytRkhzKoppRMoVZz8dbbnE9m4FiiMGNCftN7VKbMwu8d3b/yKT4PNSkzyD6yMdmhmFFkdP/VGAPQvJfc6D4OTRhdU4v3pmnCPCZG6tFWu0PbDAxLFGbUO7z9dQC8k0fXjLG98ZQ4d553HbcxpyqhRCEiy0Rkq4hUisgdcV4PiMjj7uurRKS022t3uuVbReSSbuU/FZH9IrKhR1vZIvK8iGx3f044+cMzBpq2v0lYveTPWJrsUIZE3syziaiHpm2vJjsUM0r0myhExAs8AFwKVADXi0hFj2o3AYdUdTpwP3Cvu28FzvrZc4BlwINuewCPuGU93QG8oKrlwAvutjEnzVu3hk06hdmT85MdypCYOXkim3QKvj0255MZGImcUSwFKlW1WlXDwApgeY86y4FH3edPAheKs8L7cmCFqoZUdQdQ6baHqr4CHIzzft3behS48gSOx5hjRSPkHtlIVcpsMoL+ZEczJNKDfranVJB3ZCNEI8kOx4wCiSSKScDubtu1blncOqoaAZqAnAT37Wmiqta7bdUDcb8GisjNIrJGRNY0NNg6waYXDZsJagdHchcmO5Ih1ZS7mIB2wD5byMicukQSRbyJcXqujNJbnUT2PSmq+pCqLlHVJXl5eQPRpBmF2qpXAeCfMjY6srt4p5wBQHv1G0mOxIwGiSSKWqCk23YxUNdbHRHxAZk4l5US2benfSJS6LZVCOxPIEZj4mqpfJ1GTWfy1DnJDmVITSmbQb1m01r5WrJDMaNAIoniLaBcRMpEJAWnc3pljzorgRvd51cDL6qquuXXuaOiyoByoL+5Bbq3dSPw+wRiNCauQP1q1sRmMmdSZrJDGVJzJmWxNlZOYK+tTWFOXb+Jwu1zuBV4DtgMPKGqG0XkbhG5wq32MJAjIpXAF3FHKqnqRuAJYBPwLHCLqkYBRORXwBvATBGpFZGb3La+A1wkItuBi9xtY07ckXoy23ezJWUeOWmBZEczpPLSA2xPqSC9ox6O9HcSb0zffIlUUtVngGd6lN3V7XkHcE0v+94D3BOn/Ppe6jcCFyYSlzF92uXccHZk4tjqn+jSNnEJ1P0Mdq+GOTZ40Jw8uzPbjFrh6ldp0SCZZaN7avHeZE87jQ71E6q2O7TNqbFEYUatzupXWRubwcIpuckOJSnmT8ljXayczqpXkh2KGeEsUZjRqe0g4w9vY3VsFgtKspIdTVLML87kTa1g/OEt0Bbv3lZjEmOJwoxOu5wV3mozFpKZOjbuyO4pPehnV8YSBIWdNkzWnDxLFGZU0p2vEcJPcIzdaNdTcMrptJOC7rDLT+bkWaIwo1Jn1V95JzaNuaUTkx1KUs2dksea6Aw6q/6a7FDMCGaJwow+bQfx71/P69E5LBqj/RNdFpZk8UasgpTGzdB6INnhmBHKEoUZfXa8gqCskvnMLEhPdjRJNasgnXWeuc5Gja1PYU6OJQoz+lS/RJukEis6bdSvkd0fn9cDRYtolyDU2OUnc3LG9l+RGZViVS/xerSCJVNtVmGAxWX5vBmdRazqpWSHYkYoSxRmdDm4A8/hnbwSncvSsuxkRzMsLC3L5uXoAjwHq+BgdbLDMSOQJQozulQ735pf17mcNsWWWwc4bcoEXoktcDa2/zm5wZgRyRKFGV0qX+CAN4/Ugtmkj5GlT/uTHvSTVjSTvd5CqLREYU6cJQozenR2oFUv8qfOhSydmpPsaIaVpWXZPN8537nxrrMj2eGYEcYShRk9av6KdLbxp8gi65/oYWlZNi9G5iOR9qPTrxuTKEsUZvTY+kc6Pam8Eavg9FJLFN2dXprNG7EKIpIC255LdjhmhEkoUYjIMhHZKiKVInJHnNcDIvK4+/oqESnt9tqdbvlWEbmkvzZF5BER2SEi77iPhad2iGZMUIVtz/FOyiJKJ+aQPT4l2RENK9njUygtyOXdwGLY/LTz72VMgvpNFCLiBR4ALgUqgOtFpKJHtZuAQ6o6HbgfuNfdtwJnje05wDLgQRHxJtDml1R1oft455SO0IwNe9+DI7X8pmUeH5wxNtef6M8HZ+TxRMtCOFILdW8nOxwzgiRyRrEUqFTValUNAyuA5T3qLAcedZ8/CVwoIuKWr1DVkKruACrd9hJp05jEbXkaRXg+spAPlNuNdvF8sDyPZyOLiYkXNq9MdjhmBEkkUUwCdnfbrnXL4tZR1QjQBOT0sW9/bd4jIutF5H4RCSQQoxnLVGHDb6hJX0yzb4J1ZPdiSekEQv4MdqQtgk0r7fKTSVgiiULilPX8DeutzomWA9wJzAJOB7KBr8QNSuRmEVkjImsaGhriVTFjxd73oHE7v+s8g6Vl2QT93mRHNCwF/V7OnJrDyvASOFgF+zcnOyQzQiSSKGqBkm7bxUBdb3VExAdkAgf72LfXNlW1Xh0h4Gc4l6mOo6oPqeoSVV2Sl2eXGsa0DU+hHh8/PzyfD9plpz59sDyPXzbNR8UDG55MdjhmhEgkUbwFlItImYik4HRO97zAuRK40X1+NfCiqqpbfp07KqoMKAdW99WmiBS6PwW4EthwKgdoRjn3stOe7DM5RAYXzs5PdkTD2nkz82ggi7qcs+DdxyEWS3ZIZgToN1G4fQ63As8Bm4EnVHWjiNwtIle41R4GckSkEvgicIe770bgCWAT8Cxwi6pGe2vTbesxEXkPeA/IBf5tYA7VjEq7V0PTLp6Onsn0/DSm5qUlO6JhbWrueKbmjud3+kFn9JNNPW4S4Eukkqo+AzzTo+yubs87gGt62fce4J5E2nTLL0gkJmMAWPdz1D+eB/bN4YYPju1lTxMhIlwyt4AHX5nF59PSkXdXwNTzkh2WGebszmwzcnU0wcbfUFN0Kc2xABfPKUh2RCPCsjkFtMb81BRcDJt+D6GWZIdkhjlLFGbkeu/X0NnGLzs/xMSMAPMnZSY7ohFhfnEmRZlBVkTOg85WWP94skMyw5wlCjMyqcKanxHNn8MjOyfw0flFeDzxRl2bnkSEZXML+dmuPCIFC2DV/9g9FaZPlijMyFT9EuzbwKr8a+mMwpWLet4DavrysUWTCEeU1fnXwIGtUP1yskMyw5glCjMyvf5fkDaRH+xfQHl+GnOKMpId0Ygyd1IGMyam8f36eTA+D954INkhmWHMEoUZeerXQ9WLHJr7ad7c1crHFk/Cue3GJEpE+JvFxaze3UrjvJug8nnYszbZYZlhyhKFGXle/DcIZvKTjvPxeZwPPHPiPrZoEl6P8LPOiyB1Arx8b7JDMsOUJQozsux8HbY/R/jM2/j5O01cOq+QiRnBZEc1IuVnBFk2t4BH1zYSXvp52P4c7FqV7LDMMGSJwowcsRj86V8hvZCn/JfR3BHhk2dPSXZUI9qnzymjuSPCr72XQ3oR/PFLEIsmOywzzFiiMCPHmodhzxqiF9zF/7xez7xJmSyePCHZUY1op02ZwMKSLB5atY/oh78J9e/Cukf739GMKZYozMjQtAf+/E2Y+iF+G/0ANY1tfOGC6daJPQA+d940dja28VToTCj9ADz/dThUk+ywzDBiicIMf9FOePJToDFCy/6DH7xYyZyiDC6qsLmdBsIlcyayoCSL+1/YTuiy/3IKf3MzRCPJDcwMG5YozPCmCs99FXavguX/xY83KLsOtnHHpbPsbGKAiAhfWTaT+qYOHt4Yhcvuc/69//hlu2PbAJYozHD3l+/C6v+BM2+hpmAZP3ypkkvnFti62APs7Gm5XDJnIv/55+1UF34EzrnN6RP6633JDs0MA5YozPAUi8KfvgYvfxsW/C2dH76b21a8TYrXw10frUh2dKPSt5bPJcXn4fZfv0v4/Ltg3sfhxW85Z3S2wNGYltB6FMZ0F4pE2dXYRnMoQlsoSiQWY1yKj/EBL0WZqWSN85/aZaHGKvjDbc6iOktuQi/9Lnf9fjPv1jbxwN8upjAzdeAOxhyVnxHkO1fN55ZfruMbT2/mnit/hKRmwRs/hLp3YPkPIbvspNtXVQ62hjnQEuZga5jOaAyPCCk+DzlpKeSlB0gP+OyS4jCUUKIQkWXAfwJe4Ceq+p0erweAnwOnAY3Atapa4752J3ATEAX+QVWf66tNd8nUFUA2sA64QVXDp3aY5mQ1HOlg+65a9uzczuG6atoaa2lvOUwq7aTTjocYUbxE8BDCz2FNp82fRWrmRAonTWZq2TQWzZpGTno/H+6xGOx9F9b8DN79FfiCcMV/oYtu4N5nt/Kr1bv4/PnTuGx+4dAc+Bh12fxC3tszjf/+SxUZQT9fWXYvUrgAnr0Tfng6LPxbWHwjTFoM/XygN7WFeWvbLjZv20bj3l10HKpjfLiRDGkjQCcBwniJEcJPOyl0aIA2Xya+rCLSc4vJLZxC2ZRSKiZlkTUuZYj+BUw8ov10VomIF9gGXATU4qx3fb2qbupW5/PAfFX9nIhcB3xMVa8VkQrgV8BSoAj4MzDD3S1umyLyBPAbVV0hIv8NvKuqP+orxiVLluiaNWtO9NhNl0iYzoM17NuxiYO1Wwntr8LXVENGxx4m6gHSpOO4XRQh6hsHXj8Si0IsgicaQjj+EkVEPTR5JxAZl09wQhEZuZOQcdkQi0BnmzMUc+970NoAvlRYcC2c/y80ebP52u838Id367h+6WS+/bG59m1zCKgq//r7Dfy/N3dx2fxCvv2xeWSG98Or34N1P4doGMblQsE8mFAKwQxQJdbZzqGDB2ht2IW3dS9ZkQOMl1Dc94h6A6g3BRUfEg3jjbTH/d0Jq5d6zeGAL5+OcZPwTCghLb+MiSXTySuejmQWg9/uzD9ZIrJWVZf0Wy+BRHEW8A1VvcTdvhNAVf9vtzrPuXXeEBEfsBfI4/21s/9v93rubse1CXwHaAAKVDXS8717c7KJIhzuBBSvx4PHI4h4+v2WdIxYzPmjiYYg2kkk3EEo1EG426Mz3E5nOEQk1EGkM0Sks4NoZ5hoZwexzhCxSBjt7CAW7SQShXAMInjweLx4fT68Xr/z05eCPyUFv9+PPyVAICXg/AykEEwJEgymEAgESPEHEK8fvH7ngzjcBuEWCLcSaT9C68E9dByqI9q0Fz1ST7C9nqzO/Xi7/ZG2aoC9viLaxhUjWSWMzyslr3gaafllkFEIgQzwjwOP5/h/j47D0NYIrQ10HtnH3j017N2zkyMNtXjb9pPPYSZ6DpNJK+r14/EHkQmlePJmQtkH0ZmXsqs9wNPr6/nZazs41NbJFy+awefPn2ZJYgipKv/zSjXffXYLWeNSuOncMi6bV8iUcWFk2x+h5jV073qiTXVIqImoCu3qp1lT2acTCKUWEMguJq9wCkUlpfgyCyGtANInQjDr+L8zVYiEoO0ANO+F5npaDuzmUP0OQgd24m2uJa1jLzmxg3jk2M+sFl82obRJeLNK8GZPJpg7Bf+EyRBIB38q+ALOFxCvz/kd1SjEokSiEdrDnYRCHYRCYUIdIULhDsLhEOFwmM5wmHA45P7dhol0holGwsQinfiJ4hV1/s68fvCmIN4UPL4UvP4AXr/7MyWI3x/AlxLEH0jFn5JCSiDVfQRJCaYSDAZJSQkiHu+J/R/FYnRGIni9XrzeE9u3S6KJIpFLT5OA3d22a4EzeqvjfsA3ATlu+Zs99u1aOCBemznAYVWNxKk/4N7+n89yRuNvjyuPqaACMTyAoIDicX86v+B+OvH1+Abkcx/jByvgU+QDMgGfBtinE2ggiyb/DNozP4zkTCVz0gyKyioonVzKNN9J/OJ5PDAu23nkluMHSuZBiftyY0uIV7Y38JNtB3it6gD7jjjfNr1HhIkHA/irPBz47Wpaw84UEh+ckceXL5nJXFu5bsiJCJ87bxrnTs/l3me38O/PbeXfn9tKetBH1rgCItGr2N98GdGY86GdMz6F82bm8aGZ+XywPI/Mcf4TfUPnzCCz2HkAae6ju/b2dnZUb6du53aa9lYRbtyJv3kPExsbKDr4NpN2PI9fOhN6Sx+Q7j6Gg0710ik+FA9y9JNG3efuw/1i7yGGV5QU4L3zH2be+VcPamyJJIp4X+N6nob0Vqe38nijrfqqf3xQIjcDNwNMnjw5XpV+jZt3OW/WFKCxGKqKqvszFnW39ZjXcF/3iBDzpoDHj3pTjn6bwBfA0/VNwhfAm+J8k/D5A/hTgs4jEHS+SQSCBNxvFYFg0Nlf9ei3nfd/xohGOgmFQrSHOujo6KAjFKIjFCYUCrmPDsKdzrefznCYzs4QkXAnHVGI+MYhgTQkkIY3mE5aThG52TnkZwSYlzuecSlDN54hJy3AxxYV87FFxagqVQ2trK89zI4DrdQd7qAzGiN7fApT88Zz3ow8puQM15Q7dsydlMkvbjqDnY2tvFbZyOb6I7SEInhEKMgMMDU3jYWTsyjLGT8kKwympqZSMWc+FXPmHy2LxpSdja1UNbTyVnMHbYf3Ejm0G+lsQzo7INqBNxoi4Im5Z+levF4fKX4/KX4fKSkB55u+e6YeCAQIBgIEgkGCKQGCqUFS/O7fuNcPHp/zUzzOzaCxTudnNExnOEQ41EEo1E5nKERnZwedoQ4i4a6Hc1Uh1hki2hkmFulAIyE0EkYjIYiEiUajRBRAEBHE40FE8IgHca98OGVexOujpGTWoP+7J/IpUcv7XwoBioG6XurUupeeMoGD/ewbr/wAkCUiPvesIt57AaCqDwEPgXPpKYHjOI6ThQc3Ew8ELzDOfYwWIsL0/DSm5/f8zmiGoyk544dt4vZ6hKl5aUzN6/pdmsLxFz0GiS9wzKbffQzPf6mTl8h9FG8B5SJSJiIpwHXAyh51VgI3us+vBl5Up/NjJXCdiATc0UzlwOre2nT3eYn3P71vBH5/8odnjDHmVPV7RuH2OdwKPIfz5fanqrpRRO4G1qjqSuBh4BciUolzJnGdu+9GdxTTJiAC3KKqUYB4bbpv+RVghYj8G/C227Yxxpgk6XfU00hgw2ONMebEJTrqyabwMMYY0ydLFMYYY/pkicIYY0yfLFEYY4zpkyUKY4wxfRoVo55EpAHYmew4TkIuzk2GY4kd8+g31o4XRu4xT1HVflcBGxWJYqQSkTWJDE0bTeyYR7+xdrww+o/ZLj0ZY4zpkyUKY4wxfbJEkVwPJTuAJLBjHv3G2vHCKD9m66MwxhjTJzujMMYY0ydLFEkiIv8sIioiue62iMgPRKRSRNaLyOJkxzhQROTfRWSLe1y/FZGsbq/d6R7zVhHpc8nbkUZElrnHVSkidyQ7nsEgIiUi8pKIbBaRjSJym1ueLSLPi8h29+eEZMc60ETEKyJvi8jT7naZiKxyj/lxdwmFUcESRRKISAlwEbCrW/GlOOt1lOOs3PejJIQ2WJ4H5qrqfGAbcCeAiFTgTEk/B1gGPCgiJ7f47zDjHscDOP+vFcD17vGONhHgdlWdDZwJ3OIe5x3AC6paDrzgbo82twGbu23fC9zvHvMh4KakRDUILFEkx/3Alzl2mdflwM/V8SbOSn+FSYlugKnqn7qtg/4mzsqF4BzzClUNqeoOoBJYmowYB8FSoFJVq1U1DKzAOd5RRVXrVXWd+7wZ54NzEs6xPupWexS4MjkRDg4RKQYuA37ibgtwAfCkW2VUHbMliiEmIlcAe1T13R4vTQJ2d9uudctGm08Df3Sfj+ZjHs3HFpeIlAKLgFXARFWtByeZAPnJi2xQfB/ny17M3c4BDnf7QjSq/r8TWTPbnCAR+TNQEOelrwL/Alwcb7c4ZSNmSFpfx6yqv3frfBXnUsVjXbvFqT9ijrkfo/nYjiMiacBTwD+q6hHnC/boJCKXA/tVda2InN9VHKfqqPn/tkQxCFT1w/HKRWQeUAa86/4hFQPrRGQpzjeQkm7Vi4G6QQ51wPR2zF1E5EbgcuBCfX9M9og+5n6M5mM7hoj4cZLEY6r6G7d4n4gUqmq9ewl1f/IiHHDnAFeIyEeAIJCBc4aRJSI+96xiVP1/26WnIaSq76lqvqqWqmopzofJYlXdC6wE/s4d/XQm0NR16j7SicgynLXQr1DVtm4vrQSuE5GAiJThdOSvTkaMg+AtoNwdCZOC02m/MskxDTj32vzDwGZV/V63l1YCN7rPbwR+P9SxDRZVvVNVi92/4euAF1X1/wNeAq52q42qY7YziuHjGeAjOB26bcCnkhvOgPohEACed8+k3lTVz6nqRhF5AtiEc0nqFlWNJjHOAaOqERG5FXgO+P/bt2MTBIIgDKP/YFnWYWhkEcLFBlZhLDbjgVw9a3DGk+mBvBduNNkHy8wuyW2MsWw81jfskxyTvKpq/rxNSa5JHlV1yrrdd9hovl86J7lX1SXJM2tA/4LLbABavp4AaAkFAC2hAKAlFAC0hAKAllAA0BIKAFpCAUDrDcaR1kKuhCtEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
       "<matplotlib.legend.Legend at 0x7fd0828a2e10>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
       "<matplotlib.legend.Legend at 0x7fd0827ea278>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
    "<a id='direct_ratio'></a> 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": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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<max_dpsfcor_2)\n",
    "print('central core for observation: {}'.format(np.sum(psf_obs_norm[idj, idi])*resol**2))\n",
    "idj, idi = np.where(r<max_dpsf_2)\n",
    "print('central core for theoretical: {}'.format(np.sum(psf[idj, idi])*resol**2))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two agree extremely well. \n",
    "\n",
    "Unfortunately, with real data, it is not always possible as we will see to use the derivative of the curve of growth to derive the factor beta of PSF fattening. For real observation, one can use a brute force approach to try all the reasonable couples alpha, beta and try to match the theoretical psf to the observed one. This is how we will proceed next on real data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Real data: PACS observations\n",
    "\n",
    "We will look at a real stack of point sources in the PACS ELAIS-N1 observations, and try to find its normalization factor. \n",
    "\n",
    "Let's load the stacked PSF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f92e7caf1d0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQgAAAD8CAYAAACLgjpEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAF0BJREFUeJzt3X+M5HV9x/Hna3bvbvfu9vaA45dwItUrSk05zIkSWoOlIBAi2mh7pLG01Zw1kmhik1KbiNGY2DRq02K1qBewUdRW0Us8gQu1QVpFDgSBAr0rRTnvuN/cr727ZXfe/WO/Z5a9+TBvZmZ3vwuvR3LZ+fGe74+d2ffN9zvveb8VEZiZtdKY7Q0ws/pygjCzIicIMytygjCzIicIMytygjCzIicIMytygjCzIicIMyvqn+0NaGV+YyAGG4vbB0q5Bfb15eLGxnNxydX2dGHZfc1qJJfXTFba9np50czFZWVfAxnN5LYp+/9v8neS/d0lnorDYwcYbR5uG1nLBDHYWMyFi69uHzh/Xm6BS5fk4nbtycVlX2yZP+rksjQvua/J0vkYXJBb7+GjufUumJ+LOzqaCoujyfVmZV8DiedMB0dyyxrI/Y6z/zHFkdzvRH3tE9N/7fpWalldHWJIulzSE5I2S7q+xf0LJH2zuv9eSa/qZn1mNrM6ThCS+oDPA1cA5wLXSDp3Sth7gb0R8Rrgc8Dfdro+M5t53byDuADYHBFPRsQo8A1g6nHB1cAt1eV/Ay6Ren0wbWbTpZsEcQbw9KTrW6rbWsZExBiwDzip1cIkrZG0UdLG0eaRLjbLzHqlmwTR6p3A1DNkmZiJGyNuiohVEbFqfmOgi80ys17pJkFsAZZPun4msLUUI6kfGAaSHxWY2WzrJkHcB6yQdLak+cBqYN2UmHXAtdXldwH/Hm5hZTZndFwHERFjkq4D7gD6gLUR8aikTwAbI2Id8BXgXyRtZuKdw+pebLSZzYyuCqUiYj2wfsptH5t0+Qjw7he9YAnmtd80DQ7mlpetkFycqN4E4kjuJKoG2p9Lae7bn1vWSbnzMtkCqObCXGFT33iyanD0uVRYHDiYitOJS3PL608WrSWL6jKFYTG0KLfOpFiyMBWnI8lzc8+NtY9p5A4e/F0MMytygjCzIicIMytygjCzIicIMytygjCzIicIMytygjCzIicIMyuqZcs5+vrghOG2YZFsLdFcmqt8a2z6ZSou2yYunmtfXdhYnKzKy7YbS1aNNp7ZlYprJlu/NZYMpeI0lKxWTbaw06HDueWloiBGcstLSVZc6nCuDZ8OHErFpVrTZV8nqSgze1lygjCzIicIMytygjCzIicIMyvqpu39ckk/lPSYpEclfahFzMWS9kl6sPr3sVbLMrN66uZjzjHgIxHxgKQh4H5JGyLiv6fE/SgirupiPWY2Szp+BxER2yLigeryAeAxjm97b2ZzWE/OQVQj9c4H7m1x94WSHpL0A0m/1Yv1mdnM6LqSUtJi4NvAhyNiaoPFB4CzIuKgpCuB7wIrCstZA6wBGOgbSlUENnfvTW1jI9HfEkBDuWrATL9MgEgMUY39uR6NaYeTlYDJ6dlakBxA2598KSWrXzWSHJ6UbZK+L9kLc2Gij+j2nbllJQcGZ/e1ebB3lZSRnFDe7fDeeUwkh69FxHeO24iI/RFxsLq8HpgnaVmrZT1vcE5fromnmU2vbj7FEBNt7R+LiM8WYk47NotT0gXV+nZ3uk4zm1ndHGJcBLwHeFjSg9VtHwVeCRARX2RiWM4HJI0Bh4HVHpxjNnd0MzjnHlrP3pwccyNwY6frMLPZ5UpKMytygjCzIicIMytygjCzIicIMyuqZ09K5aY2N5a271sJpKvoIjmhOlcLCOxvX9WY7YHYOPmk3DobyYnn2U+bk1Ogs7LTx3kmV63YfOXpqbjGoWS1YmIKeCPZzzHGk1PlExW3ADrztFRc42D715Seyf3p+x2EmRU5QZhZkROEmRU5QZhZkROEmRU5QZhZkROEmRU5QZhZkROEmRXVs5ISpSr44sCB3OKS07iz/RKz6830uFRyKnba0dyk6Gxfzebi9j0aARr7R1Jx0Zf7HTeGc/0csxWSSlbJkunVmKwuzU4ez1a1RrIHa6oyc3wGelICSHpK0sPVYJyNLe6XpH+QtFnSzyW9odt1mtnM6NU7iLdGxK7CfVcw0cl6BfAm4AvVTzOruZk4B3E18NWY8BNgqaTcN2zMbFb1IkEEcKek+6vZFlOdATw96foWPIHLbE7oxSHGRRGxVdIpwAZJj0fE3ZPub3VW6rizMs8bnNOfO0FlZtOr63cQEbG1+rkDuA24YErIFmD5pOtnAltbLMeDc8xqptvJWouqyd5IWgRcBjwyJWwd8CfVpxlvBvZFxLZu1mtmM6PbQ4xTgduq4Vn9wNcj4nZJfwG/Hp6zHrgS2AyMAH/W5TrNbIaojoOuhvtPjguXXN02Lj1sN1uIcjA54DW53lR7teQQVR1uP5AVIBbnDs9iQbLl2MHkEN3kfmRaCQKMnZIcfDuWW2//rmRR3eH2+zt+Wq79X9+eqbOsC5LFbdm/1fHtO9rG3Bt3sT/2tK1ac6m1mRU5QZhZkROEmRU5QZhZkROEmRU5QZhZkROEmRU5QZhZkROEmRXVs+VcXyNXrdhItogbyLVNU2JwKwDJgbtKtHXLVhZmKyRJDoxt7M61iMsujwXzU2HN4dx+9D+b+x3HvGQ7wUSFJACJ10DfvkOpRTV37UnFNbJtB7ODnlee2zZGj/9nblmpKDN7WXKCMLMiJwgzK3KCMLMiJwgzK3KCMLOijhOEpHOqYTnH/u2X9OEpMRdL2jcp5mPdb7KZzZSO6yAi4glgJYCkPuBXTDStnepHEXFVp+sxs9nTq0OMS4D/jYhf9Gh5ZlYDvaqkXA3cWrjvQkkPMdHq/i8j4tFWQc+bizFvCbFkUfu1PjeW27psNWDWYK4yMxKVlDqS7DW5aDAVlx4Ym6x8PHTOyam4o0uTFaHJ/5IW7sw9twNP78stcCDRHxSITDVtcohu4+Rc78rs0OhcFIwPJCp4k1XIvRjeOx94O/CvLe5+ADgrIs4D/hH4bmk5nothVj+9OMS4AnggIrZPvSMi9kfEweryemCepGU9WKeZzYBeJIhrKBxeSDpN1dAMSRdU69vdg3Wa2Qzo6hyEpIXApcD7J902eWjOu4APSBoDDgOro46DOMyspa4SRESMACdNue2Lky7fCNzYzTrMbPa4ktLMipwgzKzICcLMipwgzKyonj0pAcbaVz8qEQOkKyljJNm3cGmyh2DGeHK6997kpOhkxeDIilw5yvY35vp0jq7IVXA2x3L/Jw3/LLcfp+/IbV/Mz73UNdK+slULcttGskq2eSjXH7SxdDgV17+j/Wsl+7fjdxBmVuQEYWZFThBmVuQEYWZFThBmVuQEYWZFThBmVuQEYWZFThBmVlTPSspmoKOjbcNiz7OpxWlocS6ul30LgeZgYlJ0uq9mLpcfeu0pqbid5+f24by3PZ6K+9SZ61Jx/7TrLam42w68MRW3dHOidymw8Klc78pUhWGyn2eWktW09OVeA81ndrQPSr7uUmuUtFbSDkmPTLrtREkbJG2qfp5QeOy1VcwmSdemtsrMaiF7iHEzcPmU264H7oqIFcBd1fXnkXQicAPwJuAC4IZSIjGz+kkliIi4G9gz5eargVuqy7cA72jx0LcBGyJiT0TsBTZwfKIxs5rq5iTlqRGxDaD62erg9wzg6UnXt1S3mdkcMN0nKVtN52jZtPZ5g3P6evh1ajPrWDfvILZLOh2g+tnq1OkWYPmk62cyMWHrOB6cY1Y/3SSIdcCxTyWuBb7XIuYO4DJJJ1QnJy+rbjOzOSD7MeetwI+BcyRtkfRe4NPApZI2MTEb49NV7CpJXwaIiD3AJ4H7qn+fqG4zszkgdQ4iIq4p3HVJi9iNwPsmXV8LrO1o68xsVtW0knKcOHCwbViMtq+2BOBIstdkdspyf26SdebtWQwmqzeT29Y3mqvKGzn7uVTcO5b9LBX36nm5atVLh1sOdz/Od/pXpeLGFuaOkrM9KTPVr3qut9Pis8f56YncJyxtHzTau9ewmb1MOUGYWZEThJkVOUGYWZEThJkVOUGYWZEThJkVOUGYWZEThJkV1bOSstFACxPf6Ez21dPAQCouU70JEMlKSh1KTLyOlt9+Pz5sONd7MXLFdjQO5vbhnv2/mYobZ3Mq7j+efW0qbsHO3EuzfyRXETq+MNeDs3E08ZpKtpBsZCeyZ19PI8nK4VTVbe5153cQZlbkBGFmRU4QZlbkBGFmRU4QZlbUNkEUhub8naTHJf1c0m2SWn4BXdJTkh6W9KCkjb3ccDObfpl3EDdz/CyLDcDrI+K3gf8B/voFHv/WiFgZEbkOIGZWG20TRKuhORFxZ0Qc+8D4J0x0qzazl5henIP4c+AHhfsCuFPS/dXcCzObQ7qqpJT0N8AY8LVCyEURsVXSKcAGSY9X70haLWvS4JzFMNa+ok0nJnrvQbpakVOXpcJ0JFnRllhvPJerBFRyonT053L+ks25uNub5+fiTn9dKq65M1fVuuz/cs/Zgj1HU3EaS5Y/JjQOHErFxaLBVFxmkj1AJP4mAGIkUcGbnCje8TuIalL3VcAfR7T+S4iIrdXPHcBtTAzwbel5g3MauV+smU2vjhKEpMuBvwLeHhEjhZhFkoaOXWZiaM4jrWLNrJ4yH3O2GppzIzDExGHDg5K+WMW+QtL66qGnAvdIegj4KfD9iLh9WvbCzKZF23MQhaE5XynEbgWurC4/CZzX1daZ2axyJaWZFTlBmFmRE4SZFTlBmFmRE4SZFdWzJ6UE/e03Lebn+gzGwtwE7cbuZA/BZq4KLVP5psR+AjCWmyg970CuMnP4ydxqF2/L/R9yZDhX3Da4N7cfC3blqgv79ucmt2emdgM0En0fYyD3emLPvlRYss4XzcvtA4OJJR5NTgrPrdHMXo6cIMysyAnCzIqcIMysyAnCzIqcIMysyAnCzIqcIMysyAnCzIrqWUnZDOJI+16DSvZzZM+zudUezPUa1NBQbr3N9lWDsWRxbp3JHoLztuX2lRhOhTWeyfVBXDyeq5BM94bcuj0XtyBZJTuUm46uZqYKMdmTNNtHdCAZNy/356pnDySCelRJWRic83FJv6q6ST0o6crCYy+X9ISkzZKuT22RmdVGp4NzAD5XDcRZGRHrp94pqQ/4PHAFcC5wjaRzu9lYM5tZHQ3OSboA2BwRT0bEKPAN4OoOlmNms6Sbk5TXVbM510o6ocX9ZwBPT7q+pbrNzOaIThPEF4BXAyuBbcBnWsS0OgtSPAMkaY2kjZI2jjYTgz/MbNp1lCAiYntEjEdEE/gSrQfibAGWT7p+JrD1BZbpwTlmNdPp4JzTJ119J60H4twHrJB0tqT5wGpgXSfrM7PZ0faD1WpwzsXAMklbgBuAiyWtZOKQ4Sng/VXsK4AvR8SVETEm6TrgDqAPWBsRj07LXpjZtJi2wTnV9fXAcR+BmtncUMtKyhgbY3x3+09WG8negBrMTZRunHZKKo5G7sgsDrUcW/o8Gkn2VFyWq3yM5LZlKy5jMPk7Ppybsp1dXla6T2OyEjUjhnPVrzGvLxWnkeSE8oO5k/eR6ZmabITp72KYWZEThJkVOUGYWZEThJkVOUGYWZEThJkVOUGYWZEThJkV1bJQShKNxGBeDSXbtS1amFtxJKtHku3VItPCbmFu2zSaa/2mZCuxLO3PteGLZBs2JQcfM7wkt95EMRoAh3PPrQYTXxRMtohLv576cwVVZFvOJYZGt/yudQt+B2FmRU4QZlbkBGFmRU4QZlbkBGFmRU4QZlaU6Si1FrgK2BERr69u+yZwThWyFHg2Ila2eOxTwAFgHBiLiFU92m4zmwGZD1ZvBm4Evnrshoj4o2OXJX0G2PcCj39rROzqdAPNbPZkWs7dLelVre7TRFXOHwK/19vNMrM66LaS8neB7RGxqXB/AHdKCuCfI+Km0oIkrQHWAAxoEWRaiSUrGps7d6fiGotzA16z1XtKVEk29+5NLYv9+1NhjSW5CkSSw2yzv2MiWSE5mhu4nGqbxotoOZetauxrf1ou+nKVj409iSG6QBzJtR2MbNu8/sSfdbbIMxdWdA1w6wvcf1FEbJV0CrBB0uPVKL/jVMnjJoDhvmXJzTez6dTxpxiS+oE/AL5Ziqm6XBMRO4DbaD1gx8xqqpuPOX8feDwitrS6U9IiSUPHLgOX0XrAjpnVVNsEUQ3O+TFwjqQtkt5b3bWaKYcXkl4h6dgcjFOBeyQ9BPwU+H5E3N67TTez6dbp4Bwi4k9b3PbrwTkR8SRwXpfbZ2azyJWUZlbkBGFmRU4QZlbkBGFmRbXsSRnRJA63H1SqTMXYi1txKqw5kqukbCR6CGarN1Eylx/NDYJtHshV+aV6NAIaHkrFZQcfcyDZC3Npsi/pkeRw4UQf0di6PbesRbnfHWeclgrT7tzA5VQVciPXlNLvIMysyAnCzIqcIMysyAnCzIqcIMysyAnCzIqcIMysyAnCzIqcIMysqJaVlFIDzU9OUM4sL1lxGSPtqzcBGiedmFtxov9i83CuH2FjcCAVF8keko2Tl6XiSPaGjOR+pCetDycrJA/lnrP09PHEVPHs/6oayD1nJPdh7JlcBWffOa9pH5SsaM00jFku6YeSHpP0qKQPVbefKGmDpE3VzxMKj7+2itkk6drUVplZLWTSyBjwkYh4HfBm4IOSzgWuB+6KiBXAXdX155F0InAD8CYm+lHeUEokZlY/bRNERGyLiAeqyweAx4AzgKuBW6qwW4B3tHj424ANEbEnIvYCG4DLe7HhZjb9XtRJymqAzvnAvcCpEbENJpIIcEqLh5wBPD3p+pbqNjObA9IJQtJi4NvAhyMiN8UFWn2ntOV3qiWtkbRR0sbRyJ3wMrPplUoQkuYxkRy+FhHfqW7eLun06v7TgR0tHroFWD7p+pnA1lbriIibImJVRKyar+TZXzObVplPMQR8BXgsIj476a51wLFPJa4Fvtfi4XcAl0k6oTo5eVl1m5nNAZl3EBcB7wF+T9KD1b8rgU8Dl0raBFxaXUfSKklfBoiIPcAngfuqf5+objOzOSAzF+MeWp9LALikRfxG4H2Trq8F1na6gWY2e2pZSQmA2vfM08CC3LLmJydAJ6c2Z6d7Z/o+akFyH5Lblus0CDGaqywk22vymZ25uGxPymQPSZbkKi7Hd+feuPb3t/89ZyskYzD33OpI7rnoP2t5+yAgEvuQ5e9imFmRE4SZFTlBmFmRE4SZFTlBmFmRE4SZFTlBmFmRE4SZFTlBmFmRIjnReiZJ2gn8YsrNy4Bds7A5veR9qI+Xwn50sw9nRcTJ7YJqmSBakbQxIlbN9nZ0w/tQHy+F/ZiJffAhhpkVOUGYWdFcShA3zfYG9ID3oT5eCvsx7fswZ85BmNnMm0vvIMxshtU+QUi6XNITkjZLOm44z1wh6SlJD1ct+zbO9vZkSForaYekRybdlpqoVieF/fi4pF9NaaNYW91OuOtUrROEpD7g88AVwLnANdVUr7nqrRGxcg59vHYzxw86ajtRrYZupvXAps9Vz8fKiFg/w9v0YnU84a4btU4QTIzr2xwRT0bEKPANJiZ62QyIiLuBqb3aMhPVaqWwH3NKlxPuOlb3BPFSmswVwJ2S7pe0ZrY3pguZiWpzxXWSfl4dgtT+UOmYDibcdazuCSI9mWsOuCgi3sDE4dIHJb1ltjfoZe4LwKuBlcA24DOzuzk5HU6461jdE0R6MlfdRcTW6ucO4DYmDp/mosxEtdqLiO0RMR4RTeBLzIHno4sJdx2re4K4D1gh6WxJ84HVTEz0mlMkLZI0dOwyExPGHnnhR9VWZqJa7R37o6q8k5o/H11OuOt8vXUvlKo+fvp7oA9YGxGfmuVNetEk/QYT7xpgYhbJ1+fCfki6FbiYiW8NbgduAL4LfAt4JfBL4N11n5ZW2I+LmTi8COAp4P3HjuXrSNLvAD8CHgaa1c0fZeI8xLQ9H7VPEGY2e+p+iGFms8gJwsyKnCDMrMgJwsyKnCDMrMgJwsyKnCDMrMgJwsyK/h+p8ixe6PiD9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd_im = fits.open('../dmu18_HELP-PACS-maps/data/AKARI-SEP_PACS160_v0.9.fits')\n",
    "stackhd = fits.open('./data/output_data/160um/Akari-SEP-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": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[0].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 4,
     "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": 5,
   "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": 6,
   "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": 7,
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.0000000726000002"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9474514126777649\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "75\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "193.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(len(nbpix))\n",
    "nbpix[30]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[30:], encircled_flux[30:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9939626048556277e-10\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.47331039e-10 1.66601319e-09 2.90436590e-09 4.01576728e-09\n",
      " 6.13610517e-09 7.08523366e-09 8.00598341e-09 9.81309303e-09\n",
      " 1.15281366e-08 1.23574932e-08 1.40183192e-08 1.48477344e-08\n",
      " 1.64903024e-08 1.81311453e-08 1.89550360e-08 2.05965772e-08\n",
      " 2.22337909e-08 2.30460999e-08 2.46908101e-08 2.55067022e-08\n",
      " 2.71537141e-08 2.87716928e-08 3.04024811e-08 3.20170676e-08\n",
      " 3.28287784e-08 3.44550824e-08 3.52608117e-08 3.68713841e-08\n",
      " 3.84800144e-08 4.00910632e-08 4.17172064e-08 4.25196664e-08\n",
      " 4.56940201e-08 4.72752340e-08 4.80761609e-08 4.96756967e-08\n",
      " 5.12844838e-08 5.28743596e-08 5.36710584e-08 5.52674341e-08\n",
      " 5.68726293e-08 5.84786126e-08 6.00677687e-08 6.16727874e-08\n",
      " 6.32708779e-08 6.40703448e-08 6.56575142e-08 6.64431309e-08\n",
      " 6.80237564e-08 6.96319492e-08 7.12192781e-08 7.28461388e-08\n",
      " 7.44348464e-08 7.60383922e-08 7.76222048e-08 7.80217532e-08\n",
      " 7.88245254e-08 8.11977847e-08 8.20054626e-08 8.44027938e-08\n",
      " 8.59845259e-08 8.67878681e-08 8.83760053e-08 8.91619449e-08\n",
      " 9.07618476e-08 9.15537585e-08 9.23497060e-08 9.39430315e-08\n",
      " 9.47396382e-08 9.63521877e-08 9.71390445e-08 9.79506225e-08\n",
      " 9.87482852e-08 9.95322002e-08 9.97265849e-08]\n"
     ]
    }
   ],
   "source": [
    "print(encircled_flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 18,
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f92e7b0a400>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f92e7a6edd8>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f92e7a5d7f0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 22,
   "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 > 1) & (radii < 7))\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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f92e79c46a0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.000, ff = 1.305, residual = 0.008\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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f92e71fcb38>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "110737532657.26154"
      ]
     },
     "execution_count": 26,
     "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": [
    "### As units of map in MJy/sr, divide by 1E6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[215.84697348, 218.05317806, 226.76892547, 216.05091024,\n",
       "        217.91174471, 218.03111019, 219.53049845, 222.69296538,\n",
       "        221.92267855, 226.85777858, 221.87917354, 226.01545059,\n",
       "        221.81530358, 218.40201707, 218.44559917, 226.93140353,\n",
       "        227.1432522 , 220.74724427, 224.98457517, 222.89381166,\n",
       "        219.21184244, 220.40787993],\n",
       "       [217.58085993, 223.24864943, 224.2280098 , 222.74881129,\n",
       "        218.22508874, 222.70530628, 215.1606903 , 224.83837646,\n",
       "        229.15596178, 235.14694139, 225.10428404, 222.70263627,\n",
       "        215.35668711, 224.35961808, 226.68975027, 229.88279966,\n",
       "        225.50389525, 227.89622953, 227.69576167, 233.1004047 ,\n",
       "        228.99316837, 226.08222181],\n",
       "       [226.38749975, 227.38273301, 236.49975952, 216.07041322,\n",
       "        217.55640938, 219.92988541, 221.02027888, 220.40188818,\n",
       "        222.41316815, 216.87302746, 213.65118264, 220.29541723,\n",
       "        221.80918568, 228.39661428, 222.58133661, 226.8372034 ,\n",
       "        219.99253599, 219.80865583, 226.31628552, 227.67449271,\n",
       "        221.35686108, 216.85722466],\n",
       "       [224.30952564, 214.49945333, 230.1237311 , 223.10985105,\n",
       "        225.9242148 , 227.32074116, 219.93888355, 219.37977264,\n",
       "        217.8326466 , 216.36280363, 217.23038808, 222.61353789,\n",
       "        223.08490995, 222.82990666, 221.78173576, 218.79582575,\n",
       "        223.64438527, 213.00293831, 228.69144344, 223.18048363,\n",
       "        214.86890256, 211.31203128],\n",
       "       [226.75877804, 223.1936865 , 221.73783129, 218.98390364,\n",
       "        223.02979286, 217.97050592, 213.75581752, 223.85286315,\n",
       "        225.29473761, 224.69784714, 226.13764726, 225.91723493,\n",
       "        230.96427207, 217.41754093, 234.12414608, 227.93497618,\n",
       "        231.45067607, 221.64443007, 226.8497195 , 224.50210961,\n",
       "        229.43617948, 223.38118274],\n",
       "       [228.15605425, 216.52556901, 217.78993348, 218.20749892,\n",
       "        216.43251117, 223.22304959, 225.80357388, 225.886225  ,\n",
       "        221.74183981, 224.65391464, 231.94603616, 224.79612586,\n",
       "        232.01779701, 225.89409486, 227.81928284, 224.80655361,\n",
       "        226.27730059, 223.02640104, 220.77969783, 220.62269295,\n",
       "        214.66404776, 215.95558885],\n",
       "       [215.92627482, 223.31272962, 222.62700006, 216.04113423,\n",
       "        223.11706218, 227.87789687, 226.37292333, 221.55798768,\n",
       "        228.52956806, 232.17203377, 226.18137652, 224.25670713,\n",
       "        226.31646071, 239.2507789 , 237.18576239, 225.62569948,\n",
       "        221.40056232, 234.442725  , 223.82606496, 220.06988213,\n",
       "        219.61010814, 208.24151495],\n",
       "       [223.43694457, 224.09350727, 228.72740796, 225.85712822,\n",
       "        220.30393182, 225.8207222 , 227.91754754, 228.71811549,\n",
       "        226.5717233 , 221.98847568, 220.61450072, 223.78226561,\n",
       "        235.18437757, 229.80058303, 233.02476148, 220.83085547,\n",
       "        223.7873113 , 226.00457433, 214.12806991, 221.2006551 ,\n",
       "        215.65408116, 233.26356953],\n",
       "       [230.70392176, 228.01171263, 226.33495455, 225.58777275,\n",
       "        224.92241514, 228.44940475, 223.62085276, 230.36892334,\n",
       "        222.23837022, 225.95177685, 248.38545829, 258.26947792,\n",
       "        260.1109706 , 245.96596842, 229.29824308, 225.53601945,\n",
       "        228.81604382, 218.08270232, 224.37673836, 225.2012663 ,\n",
       "        220.8172111 , 237.42918864],\n",
       "       [228.55911335, 225.81430297, 223.53711542, 219.15755928,\n",
       "        227.02474168, 228.76508941, 222.68577528, 221.19822336,\n",
       "        225.47625611, 246.61614693, 284.78651279, 311.94188282,\n",
       "        308.83127432, 272.97759251, 233.29746672, 232.59634782,\n",
       "        227.60193997, 221.82059454, 220.65856636, 214.70312379,\n",
       "        222.83683046, 225.79284479],\n",
       "       [224.46231878, 215.31686825, 222.1031739 , 222.84074087,\n",
       "        230.9791148 , 235.70007457, 226.20429234, 223.52609901,\n",
       "        248.34304651, 281.86468297, 339.16287479, 375.79450306,\n",
       "        347.29707902, 299.37667049, 249.06061294, 229.74192694,\n",
       "        225.3890779 , 225.987412  , 225.99552013, 218.93805799,\n",
       "        224.5524263 , 213.49465429],\n",
       "       [217.64773627, 212.68049804, 217.73424874, 218.15625018,\n",
       "        224.92961225, 230.5684241 , 230.88677877, 231.21362   ,\n",
       "        244.96735736, 306.00050509, 361.69589315, 385.68033072,\n",
       "        365.89806544, 301.92183995, 255.2015475 , 233.72117108,\n",
       "        234.65655691, 231.92257372, 232.10581617, 225.81215154,\n",
       "        226.8778562 , 221.56570337],\n",
       "       [223.25047148, 215.27424623, 221.99556767, 215.44652833,\n",
       "        227.5929979 , 224.7462787 , 223.86759375, 232.01614314,\n",
       "        245.6189795 , 297.28356633, 345.34702003, 360.89117653,\n",
       "        343.27394444, 287.12944841, 248.7311858 , 239.20500332,\n",
       "        235.23675458, 231.6170365 , 221.91497687, 223.74788488,\n",
       "        220.51743436, 220.93378043],\n",
       "       [221.08618113, 224.81063921, 223.54541277, 227.04071968,\n",
       "        222.89292165, 222.31999818, 219.66810548, 227.8375314 ,\n",
       "        247.73439679, 270.80438812, 296.13658411, 314.24848951,\n",
       "        299.03853954, 263.52492286, 237.58074138, 235.35586077,\n",
       "        235.23539505, 223.90411189, 228.01632383, 224.15527486,\n",
       "        218.07803506, 213.39739171],\n",
       "       [223.43822701, 228.04373171, 233.20151462, 222.95603476,\n",
       "        221.72099833, 219.92491681, 221.86807303, 226.11987523,\n",
       "        239.55623904, 248.18229941, 253.92566205, 263.97260122,\n",
       "        252.45913381, 240.21491111, 229.89914207, 235.12729125,\n",
       "        229.61995453, 228.86483979, 218.84571495, 218.73842407,\n",
       "        220.7415048 , 217.59171516],\n",
       "       [218.97897008, 220.24467306, 218.04746662, 212.63254301,\n",
       "        218.88511334, 217.37987349, 227.64791877, 225.93736161,\n",
       "        225.58269904, 239.0853365 , 233.98759724, 232.20993948,\n",
       "        229.92448962, 216.06379776, 219.67933914, 226.51087374,\n",
       "        226.0984521 , 221.6691329 , 222.7639974 , 226.56743447,\n",
       "        229.58160032, 220.93913446],\n",
       "       [210.11623907, 213.22410748, 217.63353127, 224.25829793,\n",
       "        226.14752839, 219.60798475, 221.58206681, 232.75275703,\n",
       "        234.54778737, 225.10497081, 229.73750496, 225.05751335,\n",
       "        229.85298106, 216.26163065, 222.11680426, 225.45816874,\n",
       "        225.3353834 , 230.33287472, 233.08467198, 227.46502672,\n",
       "        223.42362256, 219.66148302],\n",
       "       [212.412411  , 219.68758743, 226.18812513, 225.05381318,\n",
       "        223.52068891, 213.89144132, 219.20953684, 229.38991335,\n",
       "        230.0230837 , 225.08187279, 222.66341308, 218.68880117,\n",
       "        224.18266872, 224.18222722, 217.94908278, 217.44089824,\n",
       "        222.13603392, 229.21737897, 232.14164053, 229.59513256,\n",
       "        226.26252795, 221.40342855],\n",
       "       [214.90593929, 218.62363475, 214.78334316, 220.87567797,\n",
       "        215.28718981, 218.72102347, 210.88943417, 212.07233887,\n",
       "        218.84502117, 225.92818827, 221.1758962 , 218.38023653,\n",
       "        221.10607654, 219.60520962, 220.79710545, 220.59009923,\n",
       "        224.14423742, 231.21651426, 222.57036926, 218.63565329,\n",
       "        216.92033777, 219.07123603],\n",
       "       [210.48052348, 216.56655118, 214.90531558, 220.12239229,\n",
       "        210.63288914, 217.25241389, 215.91844701, 216.83336278,\n",
       "        215.68518921, 212.60276646, 216.95073101, 224.47867521,\n",
       "        226.06786964, 218.94573163, 228.35966865, 224.14938122,\n",
       "        217.2810061 , 211.35566945, 215.87304986, 230.44200167,\n",
       "        220.24383211, 223.01761313],\n",
       "       [213.36549177, 216.86891383, 217.12211609, 215.36659627,\n",
       "        219.33274966, 216.77253425, 212.19643468, 216.15269291,\n",
       "        213.98560641, 223.44724617, 221.83845066, 219.75583732,\n",
       "        226.16630254, 226.5877924 , 222.155628  , 219.13558253,\n",
       "        226.08446434, 217.26775417, 221.43016367, 224.2322636 ,\n",
       "        208.85043097, 228.85467134],\n",
       "       [214.42613673, 221.00924845, 223.88266773, 225.65532886,\n",
       "        219.69149083, 210.68261717, 214.04921708, 217.62866779,\n",
       "        215.89173291, 219.51466761, 228.2646486 , 215.40886089,\n",
       "        221.39943405, 216.9191254 , 223.67084008, 209.70475648,\n",
       "        221.23543528, 221.5169985 , 226.66810288, 222.34660015,\n",
       "        223.52592381, 230.84528502]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psfok=psfok/1.0E6\n",
    "psfok"
   ]
  },
  {
   "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 `AKARI-SEP_PACS160_v0.9.fits` that it has a flux of -- mJy. Maximum value in our normalised PSF gives a peak ---."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: './data/AKARI-SEP_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<ipython-input-29-c9817b5c7410>\u001b[0m in \u001b[0;36m<module>\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/AKARI-SEP_PACSxID24_v1.fits'\u001b[0m\u001b[0;34m)\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   2548\u001b[0m         \u001b[0;31m# RST table and inserts at the end of the docstring.  DO NOT REMOVE.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2549\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2550\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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2551\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[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2552\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[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[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[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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    503\u001b[0m                     \u001b[0;32mexcept\u001b[0m \u001b[0mOSError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    504\u001b[0m                         \u001b[0;32mraise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/contextlib.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     79\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgen\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     82\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m             \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[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[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[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[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[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: './data/AKARI-SEP_PACSxID24_v1.fits'"
     ]
    }
   ],
   "source": [
    "PACScat=Table.read('./data/AKARI-SEP_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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<ipython-input-30-c5b280bad8ff>\u001b[0m in \u001b[0;36m<module>\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[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": 31,
   "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<ipython-input-31-929c5207480a>\u001b[0m in \u001b[0;36m<module>\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'AKARI-SEP-PACSxID24-1-11000'\u001b[0m\u001b[0;34m]\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']=='AKARI-SEP-PACSxID24-1-11000']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 1.3567 Jy/sr, off pixel Max PSF = 0.8890 Jy/sr\n"
     ]
    }
   ],
   "source": [
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "\n",
    "print(\"Max PSF = {:.4f} Jy/sr, off pixel Max PSF = {:.4f} Jy/sr\".format(psfok[cpix-1,cpix-1]*0.004,psfok[cpix-3,cpix-3]*0.004))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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, which provide 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"
     ]
    },
    {
     "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<ipython-input-33-f738872bb7f0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcubehelix_palette\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrot\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m.75\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mas_cmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maplpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFITSFigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'../dmu18_HELP-PACS-maps/data/AKARI-SEP_PACS160_v0.9.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecenter\u001b[0m\u001b[0;34m(\u001b[0m\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'AKARI-SEP-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'RA'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\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'AKARI-SEP-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Dec'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mradius\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.005\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      7\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow_colorscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvmin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.001\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvmax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.002\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_colorbar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x648 with 1 Axes>"
      ]
     },
     "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('../dmu18_HELP-PACS-maps/data/AKARI-SEP_PACS160_v0.9.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='AKARI-SEP-PACSxID24-1-69605']['RA'],PACScat[PACScat['HELP_ID']=='AKARI-SEP-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": "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": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "stackhd[0].data=psfok\n",
    "stackhd.writeto('dmu18_PACS_160_PSF_AKARI-SEP_20190128sr.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAADmRJREFUeJzt3X9M1HUcx/HXiTDLH5g2fowxms1WK6x/DHVL1hlQQwQR/mitNparf5KM5gKaNpjRjxUu+6PhmFtb/mnqxq00IYWtlLV0ZOnSNRc6ObcksZogx6c/HEzkDgEP7ntvn49/HN/uuPfXz/Xs/Erfj8855wQAMGtWrAcAAEwvQg8AxhF6ADCO0AOAcYQeAIwj9ABgHKEHAOMIPQAYR+gBwLjZsR5AknJycpSRkRHrMQAgrly8eFHHjx+/4+M8EfqMjAx9/fXXsR4DAOJKaWnphB7HpRsAMI7QA4BxhB4AjCP0AGAcoQcA4wg9ABhH6AHAOEIPAMYResSt6zdCo34FEB6hR9wZDvucxAQ9VB3QnMSEGE8EeBuhR9wZDjyAiSH0AGAcoUfc4Fo8MDWEHnGDSzbA1BB6ADCO0AOAcYQecY+fpwfGR+gR9/h5emB8hB4AjCP08DwuyQB3h9DD8/ixSuDuEHoAMI7QA4BxhB4AjCP0AGAcoQcA4wg9ABhH6AHAOEIPAMYRegAwjtDDs7j1ARAdhB6exa0PgOgg9ABgHKEHAOMIPQAYR+gBwDhCDzPYOxYIj9DDDPaOBcIj9ABgHKEHAOMIPQAYR+gBwDhCDwDGEXoAMI7QA4BxhB4AjCP0AGAcoQcA4wg9PId71QDRRejhOewsBUQXoQcA4wg9ABhH6AHAOEIPAMYRegAwjtADgHGEHgCMI/QAYByhBwDjCD0AGEfoAcA4Qg8AxhF6ADCO0AOAcYQeAIwj9ABgHKEHAOMIPQAYR+gBwDhCD3OGNxdnk3HgJkIPc4Y3F5+TmBDrUQBPIPQAYByhh1lcwgFuIvQwi0s4wE2EHgCMI/TwDC6xANOD0MMzhi+1AIguQg8AxhF6ADCO0AOAcYQeAIwj9ABgHKEHAOMIPQAYR+gBwDhCDwDGEXoAMI7QA4BxhB4AjCP0AGAcoYd57DSFe13UQ9/d3a3a2lpVVlZG+1sDU8JOU7jXTSj0NTU1WrlypdauXTvqeHt7uwoKCpSXl6ddu3ZJkjIzM9XQ0BD9SQEAUzKh0JeWlqq5uXnUsVAopPr6ejU3NysQCKilpUXnzp2bliEBAFM3odAvX75cycnJo451dXUpKytLmZmZSkpKUmFhoVpbW6dlSADA1E35Gn0wGFRaWtrI16mpqQoGg+rt7dW2bdv022+/qampKSpDAgCmbvZUn+icG3PM5/PpgQceUH19/V0NBQCInil/ok9LS1NPT8/I18FgUCkpKVEZCgAQPVMOfXZ2ts6fP6/u7m4NDAwoEAjI7/dHczYAQBRM6NJNVVWVOjs71dvbq9WrV2vTpk0qLy/Xtm3btHHjRoVCIW3YsEFLly6d7nkBAJM0odA3NjaGPZ6bm6vc3NyoDgQAiC5ugQAAxhF6ADCO0AOAcYQeAIwj9ABgHKEHAOMIPQAYR+gBwDhCDwDGEXoAMI7QA4BxhB4xd/1GKNYjAKYResTcnMQEPVQdiPUYgFmEHgCMI/QAYByhBwDjCD0AGEfoAcA4Qg8AxhF6ADCO0AOAcYQeAIwj9ABgHKEHAOMIPQAYR+gBwDhCDwDGEXogguH75HO/fMQ7Qg9EMHyf/DmJCbEeBbgrhB4AjCP0AGAcoQcA4wg9ABhH6AHAOEIPAMYRegAwjtADgHGEHgCMI/S4Z9x+SwNubYB7BaHHPePWWxpwawPcSwg9ABhH6AHAOEIPAMYRegAwjtADgHGEHgCMI/QAYByhBwDjCD0AGEfoAcA4Qg8AxhF6ADCO0CNmvHb3SO5qCasIPWJm+C6SXsFdLWEVoQcA4wg9ABhH6AHAOEIPAMYRegAwjtADgHGEHgCMI/QAYByhBwDjCD0AGEfoAcA4Qg8AxhF6ADCO0AOAcYQeAIwj9ABgHKEHAOMIPXCbSFsJ3nr8TtsNemVbwnBzxHqmWPDKesQKoQduE2mLw+HjE9lu0CvbEt46x0Rnt8gr6xErhB4AjCP0AGAcoQcA4wg9ABhH6AHAOEIPAMYRegAwjtADgHGEHgCMI/QAYByhBwDjCD0AGEfoAcA4Qg8AxhF6ADCO0AOAcYQeAIwj9ABgHKEHAOMIPQAYR+gBwDhCDwDGEXoAMI7QA4BxhB4AjCP0AGAcoQcA4wg9ABg3O9rf8L///lNdXZ0SExP19NNPa926ddF+CQDAJEzoE31NTY1WrlyptWvXjjre3t6ugoIC5eXladeuXZKkQ4cOqaCgQNu3b1dbW1v0JwYATMqEQl9aWqrm5uZRx0KhkOrr69Xc3KxAIKCWlhadO3dOwWBQ6enpkqSEhIToTwwAmJQJhX758uVKTk4edayrq0tZWVnKzMxUUlKSCgsL1draqtTUVPX09EiShoaGoj8xAGBSpvyXscFgUGlpaSNfp6amKhgMKj8/X4cOHdJ7772nZ599NipDAtPh+o3QqF/v5rmT/V4Tfd6dXicas0/2tabymlOZK9zrRWuGiX6faD8uVqYceufcmGM+n0/333+/PvjgA9XV1fEXsfC0OYkJeqg6oDmJk7/EePtzb/36oerApJ4/3gx3ep1ozD7eTJFeezrc6Vzv9rzHe62ZelysTDn0aWlpI5dopJuf8FNSUqIyFAAgeqYc+uzsbJ0/f17d3d0aGBhQIBCQ3++P5mwAgCiY0M/RV1VVqbOzU729vVq9erU2bdqk8vJybdu2TRs3blQoFNKGDRu0dOnS6Z4XADBJEwp9Y2Nj2OO5ubnKzc2N6kAAgOjiFggAYByhBwDjCD0AGEfoAcA4nwv3fz7NsJycHGVkZMR6DACIKxcvXtTx48fv+DhPhB4AMH24dAMAxhF6ADCO0AOAcYQeAIwj9ABgnOdDH26/2r///lsVFRXKz89XRUWFrl69KunmPfK3b9+uvLw8FRUV6ddff43V2GGFO5fPP/9czzzzjIqLi1VcXKyjR4+O/LOmpibl5eWpoKBAHR0dsRg5okuXLunll1/WCy+8oMLCQn355ZeS4nNtIp1LPK5Nf3+/ysrKtG7dOhUWFmrnzp2SpO7ubpWXlys/P1+bN2/WwMCAJGlgYECbN29WXl6eysvLdeHChViOP0qkc6murpbf7x9Zl9OnT0vy9ntsWCgUUklJiV5//XVJM7guzuM6OzvdqVOnXGFh4cixjz76yDU1NTnnnGtqanIff/yxc865I0eOuFdffdUNDQ25EydOuLKyspjMHEm4c9m5c6drbm4e89izZ8+6oqIi19/f7/7880+3Zs0aNzg4OJPjjisYDLpTp04555y7du2ay8/Pd2fPno3LtYl0LvG4NkNDQ+6ff/5xzjk3MDDgysrK3IkTJ1xlZaVraWlxzjm3detWt2fPHuecc1999ZXbunWrc865lpYW9+abb8Zm8DAincs777zjvvnmmzGP9/J7bNju3btdVVWVe+2115xzbsbWxfOf6MPtV9va2qqSkhJJUklJiQ4fPjzquM/n01NPPaW+vj5dvnx5xmeOJNy5RNLa2qrCwkIlJSUpMzNTWVlZ6urqmuYJJy4lJUWPP/64JGnevHlasmSJgsFgXK5NpHOJxMtr4/P5NHfuXEnS4OCgBgcH5fP5dOzYMRUUFEiS1q9fr9bWVklSW1ub1q9fL0kqKCjQjz/+GHb3uFiIdC6RePk9Jkk9PT06cuSIysrKJN38E8hMrYvnQx/OX3/9NbKbVUpKiq5cuSJp7D62aWlp4/4L6xV79uxRUVGRampqRi51RNqT14suXLig06dP68knn4z7tbn1XKT4XJtQKKTi4mKtWrVKq1atUmZmphYsWKDZs2/elfzW3/tgMKj09HRJ0uzZszV//nz19vbGbPbb3X4uw+uyY8cOFRUVqaGhYeRyh9ffYw0NDdqyZYtmzbqZ3d7e3hlbl7gMfSTh/os33icAL3jxxRf13Xff6cCBA0pJSdGHH34oKX7O5d9//1VlZaVqa2s1b968iI+Lh/O5/VzidW0SEhJ04MABHT16VF1dXfrjjz/GPGZ43ng7l99//11VVVX69ttvtXfvXl29elW7du2S5O1z+f7777Vo0SI98cQT4z5uutYlLkO/ePHikT+SXb58WYsWLZI0dh/bnp4ez+9j++CDDyohIUGzZs1SeXm5fvnlF0nxsSfvjRs3VFlZqaKiIuXn50uK37UJdy7xvDaStGDBAuXk5OjkyZPq6+vT4OCgpNG/92lpabp06ZKkm5dHrl27poULF8Zs5kiGz6Wjo0MpKSny+XxKSkpSaWlpxHXx0nvs559/Vltbm/x+v6qqqnTs2DG9//77M7YucRl6v9+v/fv3S5L279+vNWvWjDrunNPJkyc1f/58zyx0JLdeQzx8+PDIdox+v1+BQEADAwPq7u7W+fPntWzZsliNOYZzTu+++66WLFmiioqKkePxuDaRziUe1+bKlSvq6+uTJF2/fl0//PCDHn74YeXk5OjgwYOSpH379o3s7+z3+7Vv3z5J0sGDB7VixQrPfAoOdy5LliwZWRfn3Jh18ep77O2331Z7e7va2trU2NioFStW6NNPP52xdfH8Tc1u3a928eLF2rRpk5577jlt3rxZly5dUnp6uj777DMtXLhQzjnV19ero6ND9913nxoaGpSdnR3rUxgR7lw6Ozt15swZSVJGRobq6+tH3pxffPGF9u7dq4SEBNXW1npq28affvpJL730kh555JGRa45VVVVatmxZ3K1NpHNpaWmJu7U5c+aMqqurFQqF5JzT888/rzfeeEPd3d166623dPXqVT322GP65JNPlJSUpP7+fm3ZskWnT59WcnKyduzYoczMzFifhqTI5/LKK6+ot7dXzjk9+uijqqur09y5cz39HrvV8ePHtXv3bjU1Nc3Yung+9ACAuxOXl24AABNH6AHAOEIPAMYRegAwjtADgHGEHgCMI/QAYByhBwDj/gfj+ge+3RU7KAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(psfok.flatten(),bins=np.arange(100,400,2));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "385.68033072125303"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
